LMFDB - Embedded newform 16.12.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,12,Mod(5,16)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2934908890$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	16.13
Dual form			16.12.e.a.5.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.0143 + 4.65973i) q^{2} +(13.6026 + 13.6026i) q^{3} +(2004.57 - 419.509i) q^{4} +(-3501.81 + 3501.81i) q^{5} +(-675.697 - 548.928i) q^{6} -37649.1i q^{7} +(-88279.7 + 28224.7i) q^{8} -176777. i q^{9} +O(q^{10})$	\(q+(-45.0143 + 4.65973i) q^{2} +(13.6026 + 13.6026i) q^{3} +(2004.57 - 419.509i) q^{4} +(-3501.81 + 3501.81i) q^{5} +(-675.697 - 548.928i) q^{6} -37649.1i q^{7} +(-88279.7 + 28224.7i) q^{8} -176777. i q^{9} +(141314. - 173949. i) q^{10} +(-283274. + 283274. i) q^{11} +(32973.9 + 21561.0i) q^{12} +(1.70921e6 + 1.70921e6i) q^{13} +(175435. + 1.69475e6i) q^{14} -95267.6 q^{15} +(3.84233e6 - 1.68187e6i) q^{16} +1.57559e6 q^{17} +(823733. + 7.95749e6i) q^{18} +(1.25182e7 + 1.25182e7i) q^{19} +(-5.55059e6 + 8.48867e6i) q^{20} +(512127. - 512127. i) q^{21} +(1.14314e7 - 1.40714e7i) q^{22} -6.83457e6i q^{23} +(-1.58477e6 - 816906. i) q^{24} +2.43028e7i q^{25} +(-8.49036e7 - 6.89746e7i) q^{26} +(4.81430e6 - 4.81430e6i) q^{27} +(-1.57942e7 - 7.54705e7i) q^{28} +(5.00021e7 + 5.00021e7i) q^{29} +(4.28840e6 - 443921. i) q^{30} +7.19392e7 q^{31} +(-1.65123e8 + 9.36126e7i) q^{32} -7.70654e6 q^{33} +(-7.09241e7 + 7.34183e6i) q^{34} +(1.31840e8 + 1.31840e8i) q^{35} +(-7.41595e7 - 3.54362e8i) q^{36} +(9.81694e7 - 9.81694e7i) q^{37} +(-6.21828e8 - 5.05165e8i) q^{38} +4.64996e7i q^{39} +(2.10301e8 - 4.07976e8i) q^{40} +7.24665e8i q^{41} +(-2.06667e7 + 2.54394e7i) q^{42} +(1.93444e8 - 1.93444e8i) q^{43} +(-4.49008e8 + 6.86679e8i) q^{44} +(6.19039e8 + 6.19039e8i) q^{45} +(3.18473e7 + 3.07653e8i) q^{46} +1.39935e9 q^{47} +(7.51437e7 + 2.93879e7i) q^{48} +5.59869e8 q^{49} +(-1.13245e8 - 1.09397e9i) q^{50} +(2.14322e7 + 2.14322e7i) q^{51} +(4.14328e9 + 2.70922e9i) q^{52} +(-3.32394e9 + 3.32394e9i) q^{53} +(-1.94279e8 + 2.39145e8i) q^{54} -1.98394e9i q^{55} +(1.06263e9 + 3.32365e9i) q^{56} +3.40560e8i q^{57} +(-2.48380e9 - 2.01781e9i) q^{58} +(5.46840e9 - 5.46840e9i) q^{59} +(-1.90971e8 + 3.99656e7i) q^{60} +(-4.88510e9 - 4.88510e9i) q^{61} +(-3.23829e9 + 3.35217e8i) q^{62} -6.65550e9 q^{63} +(6.99667e9 - 4.98333e9i) q^{64} -1.19707e10 q^{65} +(3.46904e8 - 3.59104e7i) q^{66} +(-7.47892e9 - 7.47892e9i) q^{67} +(3.15839e9 - 6.60975e8i) q^{68} +(9.29681e7 - 9.29681e7i) q^{69} +(-6.54903e9 - 5.32035e9i) q^{70} -2.58697e10i q^{71} +(4.98947e9 + 1.56058e10i) q^{72} +1.88841e10i q^{73} +(-3.96158e9 + 4.87647e9i) q^{74} +(-3.30582e8 + 3.30582e8i) q^{75} +(3.03451e10 + 1.98421e10i) q^{76} +(1.06650e10 + 1.06650e10i) q^{77} +(-2.16676e8 - 2.09315e9i) q^{78} +3.09391e10 q^{79} +(-7.56550e9 + 1.93447e10i) q^{80} -3.11845e10 q^{81} +(-3.37675e9 - 3.26203e10i) q^{82} +(2.96846e10 + 2.96846e10i) q^{83} +(8.11755e8 - 1.24144e9i) q^{84} +(-5.51742e9 + 5.51742e9i) q^{85} +(-7.80635e9 + 9.60915e9i) q^{86} +1.36032e9i q^{87} +(1.70120e10 - 3.30026e10i) q^{88} +6.42083e10i q^{89} +(-3.07502e10 - 2.49810e10i) q^{90} +(6.43504e10 - 6.43504e10i) q^{91} +(-2.86716e9 - 1.37004e10i) q^{92} +(9.78562e8 + 9.78562e8i) q^{93} +(-6.29908e10 + 6.52060e9i) q^{94} -8.76724e10 q^{95} +(-3.51948e9 - 9.72725e8i) q^{96} +8.87261e10 q^{97} +(-2.52021e10 + 2.60884e9i) q^{98} +(5.00763e10 + 5.00763e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8}+O(q^{10}) $ 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8	\( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8} - 988948 q^{10} - 540846 q^{11} + 2300260 q^{12} - 2 q^{13} - 1829956 q^{14} - 6075004 q^{15} - 3721448 q^{16} - 4 q^{17} - 32219106 q^{18} - 11291290 q^{19} + 68655164 q^{20} + 354292 q^{21} - 85011388 q^{22} - 66180944 q^{24} + 305685384 q^{26} - 66463304 q^{27} - 322075880 q^{28} + 77673206 q^{29} + 290643636 q^{30} + 343549808 q^{31} + 404698568 q^{32} - 4 q^{33} - 882461836 q^{34} - 434731684 q^{35} + 1854387628 q^{36} - 522762058 q^{37} - 1276252832 q^{38} - 483241016 q^{40} + 2372079160 q^{42} + 3824193658 q^{43} - 2657283740 q^{44} + 97301954 q^{45} - 1032658964 q^{46} - 4586900144 q^{47} - 1058870552 q^{48} - 8474257474 q^{49} + 6515930886 q^{50} + 7074245796 q^{51} - 13915491564 q^{52} - 2100608058 q^{53} + 4385621536 q^{54} + 12910845976 q^{56} - 21491153128 q^{58} + 955824746 q^{59} + 25615752768 q^{60} + 2150827022 q^{61} - 15814519760 q^{62} + 27758037828 q^{63} + 9674332160 q^{64} - 1884965292 q^{65} + 10932459412 q^{66} - 3186519018 q^{67} + 13817664656 q^{68} - 16193060732 q^{69} - 27206453120 q^{70} - 20773133628 q^{72} + 14141420908 q^{74} + 28890034486 q^{75} - 11786004940 q^{76} - 22711870540 q^{77} + 37031200508 q^{78} + 48011833792 q^{79} - 8952586328 q^{80} - 90656394430 q^{81} - 81555388352 q^{82} + 55713221118 q^{83} + 61178517160 q^{84} - 84575506252 q^{85} + 10047297860 q^{86} - 162855622152 q^{88} + 160133627736 q^{90} - 147369662716 q^{91} - 169766721928 q^{92} - 69689773328 q^{93} + 160320530128 q^{94} + 375702304500 q^{95} + 230764310192 q^{96} - 4 q^{97} - 108887063494 q^{98} - 286271331106 q^{99}+O(q^{100}) \) 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8 - 988948 * q^10 - 540846 * q^11 + 2300260 * q^12 - 2 * q^13 - 1829956 * q^14 - 6075004 * q^15 - 3721448 * q^16 - 4 * q^17 - 32219106 * q^18 - 11291290 * q^19 + 68655164 * q^20 + 354292 * q^21 - 85011388 * q^22 - 66180944 * q^24 + 305685384 * q^26 - 66463304 * q^27 - 322075880 * q^28 + 77673206 * q^29 + 290643636 * q^30 + 343549808 * q^31 + 404698568 * q^32 - 4 * q^33 - 882461836 * q^34 - 434731684 * q^35 + 1854387628 * q^36 - 522762058 * q^37 - 1276252832 * q^38 - 483241016 * q^40 + 2372079160 * q^42 + 3824193658 * q^43 - 2657283740 * q^44 + 97301954 * q^45 - 1032658964 * q^46 - 4586900144 * q^47 - 1058870552 * q^48 - 8474257474 * q^49 + 6515930886 * q^50 + 7074245796 * q^51 - 13915491564 * q^52 - 2100608058 * q^53 + 4385621536 * q^54 + 12910845976 * q^56 - 21491153128 * q^58 + 955824746 * q^59 + 25615752768 * q^60 + 2150827022 * q^61 - 15814519760 * q^62 + 27758037828 * q^63 + 9674332160 * q^64 - 1884965292 * q^65 + 10932459412 * q^66 - 3186519018 * q^67 + 13817664656 * q^68 - 16193060732 * q^69 - 27206453120 * q^70 - 20773133628 * q^72 + 14141420908 * q^74 + 28890034486 * q^75 - 11786004940 * q^76 - 22711870540 * q^77 + 37031200508 * q^78 + 48011833792 * q^79 - 8952586328 * q^80 - 90656394430 * q^81 - 81555388352 * q^82 + 55713221118 * q^83 + 61178517160 * q^84 - 84575506252 * q^85 + 10047297860 * q^86 - 162855622152 * q^88 + 160133627736 * q^90 - 147369662716 * q^91 - 169766721928 * q^92 - 69689773328 * q^93 + 160320530128 * q^94 + 375702304500 * q^95 + 230764310192 * q^96 - 4 * q^97 - 108887063494 * q^98 - 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−45.0143	+	4.65973i	−0.994685	+	0.102966i
$2$	−45.0143	+	4.65973i	−0.994685	+	0.102966i
$3$	13.6026	+	13.6026i	0.0323189	+	0.0323189i	0.723082	−	0.690763i	$-0.242725\pi$
$3$	13.6026	+	13.6026i	0.0323189	+	0.0323189i	−0.690763	+	0.723082i	$0.742725\pi$
$4$	2004.57	−	419.509i	0.978796	−	0.204838i
$5$	−3501.81	+	3501.81i	−0.501138	+	0.501138i	−0.911791	−	0.410653i	$-0.865301\pi$
$5$	−3501.81	+	3501.81i	−0.501138	+	0.501138i	0.410653	+	0.911791i	$0.365301\pi$
$6$	−675.697	−	548.928i	−0.0354748	−	0.0288193i
$7$		−	37649.1i		−	0.846673i	−0.905972	−	0.423337i	$-0.860859\pi$
$7$		−	37649.1i		−	0.846673i	0.905972	−	0.423337i	$-0.139141\pi$
$8$	−88279.7	+	28224.7i	−0.952502	+	0.304533i
$9$		−	176777.i		−	0.997911i
$10$	141314.	−	173949.i	0.446874	−	0.550075i
$11$	−283274.	+	283274.i	−0.530331	+	0.530331i	−0.920671	−	0.390340i	$-0.872357\pi$
$11$	−283274.	+	283274.i	−0.530331	+	0.530331i	0.390340	+	0.920671i	$0.372357\pi$
$12$	32973.9	+	21561.0i	0.0382537	+	0.0250134i
$13$	1.70921e6	+	1.70921e6i	1.27676	+	1.27676i	0.942472	+	0.334284i	$0.108494\pi$
$13$	1.70921e6	+	1.70921e6i	1.27676	+	1.27676i	0.334284	+	0.942472i	$0.391506\pi$
$14$	175435.	+	1.69475e6i	0.0871790	+	0.842173i
$15$	−95267.6			−0.0323924
$16$	3.84233e6	−	1.68187e6i	0.916082	−	0.400990i
$17$	1.57559e6			0.269138			0.134569	−	0.990904i	$-0.457035\pi$
$17$	1.57559e6			0.269138			0.134569	+	0.990904i	$0.457035\pi$
$18$	823733.	+	7.95749e6i	0.102751	+	0.992607i
$19$	1.25182e7	+	1.25182e7i	1.15983	+	1.15983i	0.984511	+	0.175323i	$0.0560971\pi$
$19$	1.25182e7	+	1.25182e7i	1.15983	+	1.15983i	0.175323	+	0.984511i	$0.443903\pi$
$20$	−5.55059e6	+	8.48867e6i	−0.387859	+	0.593164i
$21$	512127.	−	512127.i	0.0273635	−	0.0273635i
$22$	1.14314e7	−	1.40714e7i	0.472906	−	0.582118i
$23$		−	6.83457e6i		−	0.221416i	−0.993853	−	0.110708i	$-0.964688\pi$
$23$		−	6.83457e6i		−	0.221416i	0.993853	−	0.110708i	$-0.0353118\pi$
$24$	−1.58477e6	−	816906.i	−0.0406259	−	0.0209416i
$25$			2.43028e7i			0.497721i
$26$	−8.49036e7	−	6.89746e7i	−1.40143	−	1.13851i
$27$	4.81430e6	−	4.81430e6i	0.0645702	−	0.0645702i
$28$	−1.57942e7	−	7.54705e7i	−0.173431	−	0.828720i
$29$	5.00021e7	+	5.00021e7i	0.452688	+	0.452688i	0.896246	−	0.443558i	$-0.146284\pi$
$29$	5.00021e7	+	5.00021e7i	0.452688	+	0.452688i	−0.443558	+	0.896246i	$0.646284\pi$
$30$	4.28840e6	−	443921.i	0.0322202	−	0.00333533i
$31$	7.19392e7			0.451311			0.225656	−	0.974207i	$-0.427548\pi$
$31$	7.19392e7			0.451311			0.225656	+	0.974207i	$0.427548\pi$
$32$	−1.65123e8	+	9.36126e7i	−0.869925	+	0.493184i
$33$	−7.70654e6			−0.0342794
$34$	−7.09241e7	+	7.34183e6i	−0.267707	+	0.0277122i
$35$	1.31840e8	+	1.31840e8i	0.424300	+	0.424300i
$36$	−7.41595e7	−	3.54362e8i	−0.204411	−	0.976751i
$37$	9.81694e7	−	9.81694e7i	0.232738	−	0.232738i	−0.581097	−	0.813834i	$-0.697376\pi$
$37$	9.81694e7	−	9.81694e7i	0.232738	−	0.232738i	0.813834	+	0.581097i	$0.197376\pi$
$38$	−6.21828e8	−	5.05165e8i	−1.27309	−	1.03425i
$39$			4.64996e7i			0.0825266i
$40$	2.10301e8	−	4.07976e8i	0.324722	−	0.629948i
$41$			7.24665e8i			0.976846i	0.872607	+	0.488423i	$0.162428\pi$
$41$			7.24665e8i			0.976846i	−0.872607	+	0.488423i	$0.837572\pi$
$42$	−2.06667e7	+	2.54394e7i	−0.0244005	+	0.0300356i
$43$	1.93444e8	−	1.93444e8i	0.200668	−	0.200668i	−0.599618	−	0.800286i	$-0.704681\pi$
$43$	1.93444e8	−	1.93444e8i	0.200668	−	0.200668i	0.800286	+	0.599618i	$0.204681\pi$
$44$	−4.49008e8	+	6.86679e8i	−0.410453	+	0.627718i
$45$	6.19039e8	+	6.19039e8i	0.500091	+	0.500091i
$46$	3.18473e7	+	3.07653e8i	0.0227984	+	0.220239i
$47$	1.39935e9			0.889997			0.444999	−	0.895531i	$-0.353204\pi$
$47$	1.39935e9			0.889997			0.444999	+	0.895531i	$0.353204\pi$
$48$	7.51437e7	+	2.93879e7i	0.0425663	+	0.0166472i
$49$	5.59869e8			0.283144
$50$	−1.13245e8	−	1.09397e9i	−0.0512486	−	0.495076i
$51$	2.14322e7	+	2.14322e7i	0.00869822	+	0.00869822i
$52$	4.14328e9	+	2.70922e9i	1.51121	+	0.988155i
$53$	−3.32394e9	+	3.32394e9i	−1.09178	+	1.09178i	−0.0964437	+	0.995338i	$0.530747\pi$
$53$	−3.32394e9	+	3.32394e9i	−1.09178	+	1.09178i	−0.995338	+	0.0964437i	$0.969253\pi$
$54$	−1.94279e8	+	2.39145e8i	−0.0575784	+	0.0708756i
$55$		−	1.98394e9i		−	0.531538i
$56$	1.06263e9	+	3.32365e9i	0.257840	+	0.806458i
$57$			3.40560e8i			0.0749690i
$58$	−2.48380e9	−	2.01781e9i	−0.496894	−	0.403670i
$59$	5.46840e9	−	5.46840e9i	0.995805	−	0.995805i	−0.00418651	−	0.999991i	$-0.501333\pi$
$59$	5.46840e9	−	5.46840e9i	0.995805	−	0.995805i	0.999991	+	0.00418651i	$0.00133261\pi$
$60$	−1.90971e8	+	3.99656e7i	−0.0317056	+	0.00663521i
$61$	−4.88510e9	−	4.88510e9i	−0.740558	−	0.740558i	0.232127	−	0.972685i	$-0.425431\pi$
$61$	−4.88510e9	−	4.88510e9i	−0.740558	−	0.740558i	−0.972685	+	0.232127i	$0.925431\pi$
$62$	−3.23829e9	+	3.35217e8i	−0.448912	+	0.0464699i
$63$	−6.65550e9			−0.844905
$64$	6.99667e9	−	4.98333e9i	0.814520	−	0.580136i
$65$	−1.19707e10			−1.27966
$66$	3.46904e8	−	3.59104e7i	0.0340972	−	0.00352963i
$67$	−7.47892e9	−	7.47892e9i	−0.676749	−	0.676749i	0.282514	−	0.959263i	$-0.408832\pi$
$67$	−7.47892e9	−	7.47892e9i	−0.676749	−	0.676749i	−0.959263	+	0.282514i	$0.908832\pi$
$68$	3.15839e9	−	6.60975e8i	0.263431	−	0.0551297i
$69$	9.29681e7	−	9.29681e7i	0.00715590	−	0.00715590i
$70$	−6.54903e9	−	5.32035e9i	−0.465734	−	0.378356i
$71$		−	2.58697e10i		−	1.70165i	−0.525446	−	0.850827i	$-0.676102\pi$
$71$		−	2.58697e10i		−	1.70165i	0.525446	−	0.850827i	$-0.323898\pi$
$72$	4.98947e9	+	1.56058e10i	0.303897	+	0.950512i
$73$			1.88841e10i			1.06615i	0.846067	+	0.533077i	$0.178964\pi$
$73$			1.88841e10i			1.06615i	−0.846067	+	0.533077i	$0.821036\pi$
$74$	−3.96158e9	+	4.87647e9i	−0.207536	+	0.255465i
$75$	−3.30582e8	+	3.30582e8i	−0.0160858	+	0.0160858i
$76$	3.03451e10	+	1.98421e10i	1.37282	+	0.897662i
$77$	1.06650e10	+	1.06650e10i	0.449017	+	0.449017i
$78$	−2.16676e8	−	2.09315e9i	−0.00849748	−	0.0820880i
$79$	3.09391e10			1.13125			0.565626	−	0.824662i	$-0.308635\pi$
$79$	3.09391e10			1.13125			0.565626	+	0.824662i	$0.308635\pi$
$80$	−7.56550e9	+	1.93447e10i	−0.258132	+	0.660035i
$81$	−3.11845e10			−0.993737
$82$	−3.37675e9	−	3.26203e10i	−0.100582	−	0.971654i
$83$	2.96846e10	+	2.96846e10i	0.827183	+	0.827183i	0.987126	−	0.159943i	$-0.0511312\pi$
$83$	2.96846e10	+	2.96846e10i	0.827183	+	0.827183i	−0.159943	+	0.987126i	$0.551131\pi$
$84$	8.11755e8	−	1.24144e9i	0.0211782	−	0.0323884i
$85$	−5.51742e9	+	5.51742e9i	−0.134875	+	0.134875i
$86$	−7.80635e9	+	9.60915e9i	−0.178940	+	0.220264i
$87$			1.36032e9i			0.0292607i
$88$	1.70120e10	−	3.30026e10i	0.343638	−	0.666644i
$89$			6.42083e10i			1.21884i	0.792848	+	0.609419i	$0.208597\pi$
$89$			6.42083e10i			1.21884i	−0.792848	+	0.609419i	$0.791403\pi$
$90$	−3.07502e10	−	2.49810e10i	−0.548926	−	0.445940i
$91$	6.43504e10	−	6.43504e10i	1.08100	−	1.08100i
$92$	−2.86716e9	−	1.37004e10i	−0.0453544	−	0.216721i
$93$	9.78562e8	+	9.78562e8i	0.0145859	+	0.0145859i
$94$	−6.29908e10	+	6.52060e9i	−0.885267	+	0.0916399i
$95$	−8.76724e10			−1.16247
$96$	−3.51948e9	−	9.72725e8i	−0.0440541	−	0.0121758i
$97$	8.87261e10			1.04908			0.524538	−	0.851387i	$-0.324238\pi$
$97$	8.87261e10			1.04908			0.524538	+	0.851387i	$0.324238\pi$
$98$	−2.52021e10	+	2.60884e9i	−0.281640	+	0.0291544i
$99$	5.00763e10	+	5.00763e10i	0.529223	+	0.529223i
$100$	1.01952e10	+	4.87168e10i	0.101952	+	0.487168i
$101$	2.42328e10	−	2.42328e10i	0.229422	−	0.229422i	−0.583029	−	0.812451i	$-0.698133\pi$
$101$	2.42328e10	−	2.42328e10i	0.229422	−	0.229422i	0.812451	+	0.583029i	$0.198133\pi$
$102$	−1.06462e9	−	8.64886e8i	−0.00954761	−	0.00775636i
$103$			2.02400e9i			0.0172031i	0.999963	+	0.00860155i	$0.00273799\pi$
$103$			2.02400e9i			0.0172031i	−0.999963	+	0.00860155i	$0.997262\pi$
$104$	−1.99131e11	−	1.02647e11i	−1.60493	−	0.827299i
$105$			3.58674e9i			0.0274258i
$106$	1.34136e11	−	1.65114e11i	0.973562	−	1.19840i
$107$	−8.81978e10	+	8.81978e10i	−0.607921	+	0.607921i	−0.942402	−	0.334482i	$-0.891439\pi$
$107$	−8.81978e10	+	8.81978e10i	−0.607921	+	0.607921i	0.334482	+	0.942402i	$0.391439\pi$
$108$	7.63097e9	−	1.16703e10i	0.0499746	−	0.0764275i
$109$	−1.43460e10	−	1.43460e10i	−0.0893067	−	0.0893067i	0.661042	−	0.750349i	$-0.270114\pi$
$109$	−1.43460e10	−	1.43460e10i	−0.0893067	−	0.0893067i	−0.750349	+	0.661042i	$0.770114\pi$
$110$	9.24464e9	+	8.93058e10i	0.0547306	+	0.528713i
$111$	2.67072e9			0.0150436
$112$	−6.33211e10	−	1.44660e11i	−0.339507	−	0.775622i
$113$	−2.02263e11			−1.03273			−0.516363	−	0.856370i	$-0.672715\pi$
$113$	−2.02263e11			−1.03273			−0.516363	+	0.856370i	$0.672715\pi$
$114$	−1.58692e9	−	1.53301e10i	−0.00771930	−	0.0745705i
$115$	2.39334e10	+	2.39334e10i	0.110960	+	0.110960i
$116$	1.21209e11	+	7.92565e10i	0.535817	+	0.350361i
$117$	3.02150e11	−	3.02150e11i	1.27409	−	1.27409i
$118$	−2.20675e11	+	2.71637e11i	−0.887977	+	1.09305i
$119$		−	5.93196e10i		−	0.227872i
$120$	8.41019e9	−	2.68890e9i	0.0308538	−	0.00986455i
$121$			1.24823e11i			0.437499i
$122$	2.42662e11	+	1.97136e11i	0.812875	+	0.660369i
$123$	−9.85735e9	+	9.85735e9i	−0.0315706	+	0.0315706i
$124$	1.44207e11	−	3.01791e10i	0.441741	−	0.0924459i
$125$	−2.56090e11	−	2.56090e11i	−0.750565	−	0.750565i
$126$	2.99593e11	−	3.10128e10i	0.840414	−	0.0869969i
$127$	−7.32920e11			−1.96850			−0.984251	−	0.176774i	$-0.943434\pi$
$127$	−7.32920e11			−1.96850			−0.984251	+	0.176774i	$0.943434\pi$
$128$	−2.91729e11	+	2.56924e11i	−0.750456	+	0.660921i
$129$	5.26270e9			0.0129707
$130$	5.38852e11	−	5.57802e10i	1.27286	−	0.131762i
$131$	5.27271e11	+	5.27271e11i	1.19410	+	1.19410i	0.975905	+	0.218198i	$0.0700178\pi$
$131$	5.27271e11	+	5.27271e11i	1.19410	+	1.19410i	0.218198	+	0.975905i	$0.429982\pi$
$132$	−1.54483e10	+	3.23296e9i	−0.0335525	+	0.00702173i
$133$	4.71298e11	−	4.71298e11i	0.982001	−	0.982001i
$134$	3.71508e11	+	3.01809e11i	0.742834	+	0.603470i
$135$			3.37175e10i			0.0647172i
$136$	−1.39093e11	+	4.44706e10i	−0.256354	+	0.0819612i
$137$			2.26117e11i			0.400286i	0.979767	+	0.200143i	$0.0641406\pi$
$137$			2.26117e11i			0.400286i	−0.979767	+	0.200143i	$0.935859\pi$
$138$	−3.75169e9	+	4.61810e9i	−0.00638104	+	0.00785468i
$139$	−1.23904e11	+	1.23904e11i	−0.202537	+	0.202537i	−0.801086	−	0.598549i	$-0.795744\pi$
$139$	−1.23904e11	+	1.23904e11i	−0.202537	+	0.202537i	0.598549	+	0.801086i	$0.295744\pi$
$140$	3.19591e11	+	2.08975e11i	0.502216	+	0.328390i
$141$	1.90349e10	+	1.90349e10i	0.0287637	+	0.0287637i
$142$	1.20546e11	+	1.16451e12i	0.175213	+	1.69261i
$143$	−9.68352e11			−1.35421
$144$	−2.97316e11	−	6.79235e11i	−0.400152	−	0.914169i
$145$	−3.50195e11			−0.453718
$146$	−8.79947e10	−	8.50054e11i	−0.109778	−	1.06049i
$147$	7.61569e9	+	7.61569e9i	0.00915090	+	0.00915090i
$148$	1.55605e11	−	2.37971e11i	0.180129	−	0.275476i
$149$	6.94464e11	−	6.94464e11i	0.774686	−	0.774686i	−0.204236	−	0.978922i	$-0.565471\pi$
$149$	6.94464e11	−	6.94464e11i	0.774686	−	0.774686i	0.978922	+	0.204236i	$0.0654710\pi$
$150$	1.33405e10	−	1.64213e10i	0.0143440	−	0.0176566i
$151$		−	9.65622e11i		−	1.00100i	−0.865737	−	0.500500i	$-0.833150\pi$
$151$		−	9.65622e11i		−	1.00100i	0.865737	−	0.500500i	$-0.166850\pi$
$152$	−1.45842e12	−	7.51778e11i	−1.45795	−	0.751537i
$153$		−	2.78528e11i		−	0.268575i
$154$	−5.29774e11	−	4.30382e11i	−0.492864	−	0.400397i
$155$	−2.51917e11	+	2.51917e11i	−0.226169	+	0.226169i
$156$	1.95070e10	+	9.32119e10i	0.0169046	+	0.0807767i
$157$	−4.89896e11	−	4.89896e11i	−0.409879	−	0.409879i	0.471817	−	0.881696i	$-0.343598\pi$
$157$	−4.89896e11	−	4.89896e11i	−0.409879	−	0.409879i	−0.881696	+	0.471817i	$0.843598\pi$
$158$	−1.39270e12	+	1.44168e11i	−1.12524	+	0.116481i
$159$	−9.04287e10			−0.0705703
$160$	2.50414e11	−	9.06041e11i	0.188799	−	0.683106i
$161$	−2.57316e11			−0.187467
$162$	1.40375e12	−	1.45312e11i	0.988455	−	0.102322i
$163$	1.72041e12	+	1.72041e12i	1.17112	+	1.17112i	0.981944	+	0.189174i	$0.0605809\pi$
$163$	1.72041e12	+	1.72041e12i	1.17112	+	1.17112i	0.189174	+	0.981944i	$0.439419\pi$
$164$	3.04004e11	+	1.45264e12i	0.200096	+	0.956133i
$165$	2.69868e10	−	2.69868e10i	0.0171787	−	0.0171787i
$166$	−1.47455e12	−	1.19791e12i	−0.907958	−	0.737614i
$167$			9.34742e11i			0.556867i	0.960456	+	0.278433i	$0.0898151\pi$
$167$			9.34742e11i			0.556867i	−0.960456	+	0.278433i	$0.910185\pi$
$168$	−3.07558e10	+	5.96651e10i	−0.0177307	+	0.0343969i
$169$			4.05067e12i			2.26021i
$170$	2.22653e11	−	2.74072e11i	0.120271	−	0.148046i
$171$	2.21292e12	−	2.21292e12i	1.15741	−	1.15741i
$172$	3.06622e11	−	4.68925e11i	0.155309	−	0.237518i
$173$	1.11086e12	+	1.11086e12i	0.545011	+	0.545011i	0.924994	−	0.379982i	$-0.124070\pi$
$173$	1.11086e12	+	1.11086e12i	0.545011	+	0.545011i	−0.379982	+	0.924994i	$0.624070\pi$
$174$	−6.33872e9	−	6.12338e10i	−0.00301287	−	0.0291052i
$175$	9.14979e11			0.421407
$176$	−6.12000e11	+	1.56486e12i	−0.273169	+	0.698484i
$177$	1.48769e11			0.0643665
$178$	−2.99193e11	−	2.89029e12i	−0.125499	−	1.21236i
$179$	−3.71029e11	−	3.71029e11i	−0.150909	−	0.150909i	0.627615	−	0.778524i	$-0.284031\pi$
$179$	−3.71029e11	−	3.71029e11i	−0.150909	−	0.150909i	−0.778524	+	0.627615i	$0.784031\pi$
$180$	1.50060e12	+	9.81217e11i	0.591925	+	0.387049i
$181$	5.02297e11	−	5.02297e11i	0.192189	−	0.192189i	−0.604452	−	0.796641i	$-0.706608\pi$
$181$	5.02297e11	−	5.02297e11i	0.192189	−	0.192189i	0.796641	+	0.604452i	$0.206608\pi$
$182$	−2.59683e12	+	3.19655e12i	−0.963943	+	1.18656i
$183$		−	1.32900e11i		−	0.0478680i
$184$	1.92904e11	+	6.03354e11i	0.0674283	+	0.210899i
$185$			6.87541e11i			0.233267i
$186$	−4.86091e10	−	3.94894e10i	−0.0160102	−	0.0130065i
$187$	−4.46324e11	+	4.46324e11i	−0.142732	+	0.142732i
$188$	2.80510e12	−	5.87041e11i	0.871126	−	0.182306i
$189$	−1.81254e11	−	1.81254e11i	−0.0546699	−	0.0546699i
$190$	3.94651e12	−	4.08530e11i	1.15630	−	0.119696i
$191$	−4.16083e11			−0.118439			−0.0592197	−	0.998245i	$-0.518861\pi$
$191$	−4.16083e11			−0.118439			−0.0592197	+	0.998245i	$0.518861\pi$
$192$	1.62960e11	+	2.73867e10i	0.0450737	+	0.00757500i
$193$	−1.46842e12			−0.394716			−0.197358	−	0.980331i	$-0.563236\pi$
$193$	−1.46842e12			−0.394716			−0.197358	+	0.980331i	$0.563236\pi$
$194$	−3.99394e12	+	4.13440e11i	−1.04350	+	0.108020i
$195$	−1.62833e11	−	1.62833e11i	−0.0413572	−	0.0413572i
$196$	1.12230e12	−	2.34870e11i	0.277141	−	0.0579989i
$197$	−2.84431e12	+	2.84431e12i	−0.682987	+	0.682987i	−0.960672	−	0.277685i	$-0.910433\pi$
$197$	−2.84431e12	+	2.84431e12i	−0.682987	+	0.682987i	0.277685	+	0.960672i	$0.410433\pi$
$198$	−2.48749e12	−	2.02081e12i	−0.580902	−	0.471918i
$199$		−	8.06275e12i		−	1.83143i	−0.401823	−	0.915717i	$-0.631623\pi$
$199$		−	8.06275e12i		−	1.83143i	0.401823	−	0.915717i	$-0.368377\pi$
$200$	−6.85939e11	−	2.14544e12i	−0.151572	−	0.474080i
$201$		−	2.03466e11i		−	0.0437435i
$202$	−9.77903e11	+	1.20374e12i	−0.204580	+	0.251826i
$203$	1.88254e12	−	1.88254e12i	0.383279	−	0.383279i
$204$	5.19534e10	+	3.39714e10i	0.0102955	+	0.00673205i
$205$	−2.53764e12	−	2.53764e12i	−0.489535	−	0.489535i
$206$	−9.43131e9	−	9.11091e10i	−0.00177134	−	0.0171117i
$207$	−1.20819e12			−0.220953
$208$	9.44204e12	+	3.69268e12i	1.68158	+	0.657648i
$209$	−7.09214e12			−1.23019
$210$	−1.67133e10	−	1.61455e11i	−0.00282394	−	0.0272800i
$211$	−4.42900e11	−	4.42900e11i	−0.0729041	−	0.0729041i	0.669715	−	0.742619i	$-0.266416\pi$
$211$	−4.42900e11	−	4.42900e11i	−0.0729041	−	0.0729041i	−0.742619	+	0.669715i	$0.766416\pi$
$212$	−5.26866e12	+	8.05751e12i	−0.844993	+	1.29227i
$213$	3.51896e11	−	3.51896e11i	0.0549955	−	0.0549955i
$214$	3.55918e12	−	4.38114e12i	0.542094	−	0.667285i
$215$			1.35481e12i			0.201125i
$216$	−2.89123e11	+	5.60886e11i	−0.0418395	+	0.0811670i
$217$		−	2.70845e12i		−	0.382113i
$218$	7.12622e11	+	5.78925e11i	0.0980276	+	0.0796364i
$219$	−2.56873e11	+	2.56873e11i	−0.0344569	+	0.0344569i
$220$	−8.32282e11	−	3.97696e12i	−0.108879	−	0.520267i
$221$	2.69302e12	+	2.69302e12i	0.343623	+	0.343623i
$222$	−1.20221e11	+	1.24449e10i	−0.0149637	+	0.00154899i
$223$	−1.29842e12			−0.157666			−0.0788328	−	0.996888i	$-0.525119\pi$
$223$	−1.29842e12			−0.157666			−0.0788328	+	0.996888i	$0.525119\pi$
$224$	3.52443e12	+	6.21672e12i	0.417566	+	0.736542i
$225$	4.29617e12			0.496682
$226$	9.10473e12	−	9.42492e11i	1.02724	−	0.106336i
$227$	−7.45606e12	−	7.45606e12i	−0.821045	−	0.821045i	0.165213	−	0.986258i	$-0.447169\pi$
$227$	−7.45606e12	−	7.45606e12i	−0.821045	−	0.821045i	−0.986258	+	0.165213i	$0.947169\pi$
$228$	1.42868e11	+	6.82678e11i	0.0153565	+	0.0733794i
$229$	−5.34297e12	+	5.34297e12i	−0.560644	+	0.560644i	−0.929490	−	0.368846i	$-0.879753\pi$
$229$	−5.34297e12	+	5.34297e12i	−0.560644	+	0.560644i	0.368846	+	0.929490i	$0.379753\pi$
$230$	−1.18887e12	−	9.65820e11i	−0.121795	−	0.0989449i
$231$			2.90145e11i			0.0290234i
$232$	−5.82546e12	−	3.00287e12i	−0.569045	−	0.293328i
$233$		−	1.06344e13i		−	1.01450i	−0.861798	−	0.507252i	$-0.830661\pi$
$233$		−	1.06344e13i		−	1.01450i	0.861798	−	0.507252i	$-0.169339\pi$
$234$	−1.21931e13	+	1.50090e13i	−1.13613	+	1.39851i
$235$	−4.90026e12	+	4.90026e12i	−0.446012	+	0.446012i
$236$	8.66777e12	−	1.32559e13i	0.770710	−	1.17867i
$237$	4.20854e11	+	4.20854e11i	0.0365608	+	0.0365608i
$238$	2.76414e11	+	2.67023e12i	0.0234631	+	0.226660i
$239$	2.22235e13			1.84342			0.921711	−	0.387876i	$-0.126791\pi$
$239$	2.22235e13			1.84342			0.921711	+	0.387876i	$0.126791\pi$
$240$	−3.66049e11	+	1.60228e11i	−0.0296741	+	0.0129890i
$241$	1.82051e13			1.44245			0.721223	−	0.692703i	$-0.243580\pi$
$241$	1.82051e13			1.44245			0.721223	+	0.692703i	$0.243580\pi$
$242$	−5.81644e11	−	5.61884e12i	−0.0450477	−	0.435173i
$243$	−1.27703e12	−	1.27703e12i	−0.0966866	−	0.0966866i
$244$	−1.18419e13	−	7.74320e12i	−0.876550	−	0.573160i
$245$	−1.96055e12	+	1.96055e12i	−0.141894	+	0.141894i
$246$	3.97789e11	−	4.89654e11i	0.0281520	−	0.0346535i
$247$			4.27925e13i			2.96165i
$248$	−6.35077e12	+	2.03046e12i	−0.429875	+	0.137439i
$249$			8.07577e11i			0.0534672i
$250$	1.27210e13	+	1.03344e13i	0.823859	+	0.669293i
$251$	−7.53196e12	+	7.53196e12i	−0.477202	+	0.477202i	−0.904236	−	0.427034i	$-0.859559\pi$
$251$	−7.53196e12	+	7.53196e12i	−0.477202	+	0.477202i	0.427034	+	0.904236i	$0.359559\pi$
$252$	−1.33414e13	+	2.79204e12i	−0.826989	+	0.173069i
$253$	1.93606e12	+	1.93606e12i	0.117423	+	0.117423i
$254$	3.29919e13	−	3.41521e12i	1.95804	−	0.202690i
$255$	−1.50103e11			−0.00871802
$256$	1.19348e13	−	1.29246e13i	0.678414	−	0.734680i
$257$	1.74570e13			0.971265			0.485632	−	0.874163i	$-0.338589\pi$
$257$	1.74570e13			0.971265			0.485632	+	0.874163i	$0.338589\pi$
$258$	−2.36897e11	+	2.45228e10i	−0.0129018	+	0.00133555i
$259$	−3.69599e12	−	3.69599e12i	−0.197053	−	0.197053i
$260$	−2.39961e13	+	5.02181e12i	−1.25253	+	0.262124i
$261$	8.83921e12	−	8.83921e12i	0.451742	−	0.451742i
$262$	−2.61917e13	−	2.12778e13i	−1.31071	−	1.06480i
$263$		−	1.00586e13i		−	0.492927i	−0.969152	−	0.246463i	$-0.920731\pi$
$263$		−	1.00586e13i		−	0.492927i	0.969152	−	0.246463i	$-0.0792685\pi$
$264$	6.80331e11	−	2.17515e11i	0.0326512	−	0.0104392i
$265$		−	2.32796e13i		−	1.09427i
$266$	−1.90190e13	+	2.34113e13i	−0.875668	+	1.07789i
$267$	−8.73401e11	+	8.73401e11i	−0.0393914	+	0.0393914i
$268$	−1.81295e13	−	1.18546e13i	−0.801023	−	0.523775i
$269$	1.01600e13	+	1.01600e13i	0.439801	+	0.439801i	0.891945	−	0.452144i	$-0.149341\pi$
$269$	1.01600e13	+	1.01600e13i	0.439801	+	0.439801i	−0.452144	+	0.891945i	$0.649341\pi$
$270$	−1.57114e11	−	1.51777e12i	−0.00666370	−	0.0643732i
$271$	−8.09279e12			−0.336331			−0.168166	−	0.985759i	$-0.553784\pi$
$271$	−8.09279e12			−0.336331			−0.168166	+	0.985759i	$0.553784\pi$
$272$	6.05394e12	−	2.64994e12i	0.246552	−	0.107921i
$273$	1.75067e12			0.0698731
$274$	−1.05364e12	−	1.01785e13i	−0.0412160	−	0.398158i
$275$	−6.88435e12	−	6.88435e12i	−0.263957	−	0.263957i
$276$	1.47361e11	−	2.25362e11i	0.00553836	−	0.00846997i
$277$	−2.98040e13	+	2.98040e13i	−1.09809	+	1.09809i	−0.103451	+	0.994635i	$0.532988\pi$
$277$	−2.98040e13	+	2.98040e13i	−1.09809	+	1.09809i	−0.994635	+	0.103451i	$0.967012\pi$
$278$	5.00009e12	−	6.15481e12i	0.180606	−	0.222315i
$279$		−	1.27172e13i		−	0.450368i
$280$	−1.53599e13	−	7.91766e12i	−0.533360	−	0.274933i
$281$		−	4.65745e13i		−	1.58585i	−0.609316	−	0.792927i	$-0.708556\pi$
$281$		−	4.65745e13i		−	1.58585i	0.609316	−	0.792927i	$-0.291444\pi$
$282$	−9.45538e11	−	7.68144e11i	−0.0315725	−	0.0256491i
$283$	−2.43231e13	+	2.43231e13i	−0.796514	+	0.796514i	−0.982544	−	0.186030i	$-0.940438\pi$
$283$	−2.43231e13	+	2.43231e13i	−0.796514	+	0.796514i	0.186030	+	0.982544i	$0.440438\pi$
$284$	−1.08526e13	−	5.18578e13i	−0.348564	−	1.66557i
$285$	−1.19258e12	−	1.19258e12i	−0.0375698	−	0.0375698i
$286$	4.35897e13	−	4.51226e12i	1.34701	−	0.139438i
$287$	2.72830e13			0.827070
$288$	1.65485e13	+	2.91899e13i	0.492154	+	0.868107i
$289$	−3.17894e13			−0.927565
$290$	1.57638e13	−	1.63182e12i	0.451307	−	0.0467178i
$291$	1.20691e12	+	1.20691e12i	0.0339049	+	0.0339049i
$292$	7.92204e12	+	3.78545e13i	0.218389	+	1.04355i
$293$	1.69439e13	−	1.69439e13i	0.458395	−	0.458395i	−0.439733	−	0.898129i	$-0.644927\pi$
$293$	1.69439e13	−	1.69439e13i	0.458395	−	0.458395i	0.898129	+	0.439733i	$0.144927\pi$
$294$	−3.78302e11	−	3.07328e11i	−0.0100445	−	0.00816003i
$295$			3.82986e13i			0.998071i
$296$	−5.89556e12	+	1.14372e13i	−0.150807	+	0.292559i
$297$			2.72753e12i			0.0684871i
$298$	−2.80248e13	+	3.44968e13i	−0.690801	+	0.850335i
$299$	1.16817e13	−	1.16817e13i	0.282694	−	0.282694i
$300$	−5.23994e11	+	8.01358e11i	−0.0124497	+	0.0190397i
$301$	−7.28301e12	−	7.28301e12i	−0.169901	−	0.169901i
$302$	4.49954e12	+	4.34668e13i	0.103069	+	0.995679i
$303$	6.59259e11			0.0148293
$304$	6.91529e13	+	2.70449e13i	1.52759	+	0.597422i
$305$	3.42133e13			0.742244
$306$	1.29787e12	+	1.25377e13i	0.0276543	+	0.267148i
$307$	−4.62265e13	−	4.62265e13i	−0.967453	−	0.967453i	0.0320342	−	0.999487i	$-0.489801\pi$
$307$	−4.62265e13	−	4.62265e13i	−0.967453	−	0.967453i	−0.999487	+	0.0320342i	$0.989801\pi$
$308$	2.58529e13	+	1.69047e13i	0.531472	+	0.347520i
$309$	−2.75318e10	+	2.75318e10i	−0.000555984	+	0.000555984i
$310$	1.01660e13	−	1.25137e13i	0.201679	−	0.248255i
$311$		−	4.23251e13i		−	0.824927i	−0.910974	−	0.412464i	$-0.864668\pi$
$311$		−	4.23251e13i		−	0.824927i	0.910974	−	0.412464i	$-0.135332\pi$
$312$	−1.31244e12	−	4.10497e12i	−0.0251321	−	0.0786067i
$313$			9.67939e13i			1.82119i	0.413305	+	0.910593i	$0.364374\pi$
$313$			9.67939e13i			1.82119i	−0.413305	+	0.910593i	$0.635626\pi$
$314$	2.43351e13	+	1.97695e13i	0.449904	+	0.365497i
$315$	2.33063e13	−	2.33063e13i	0.423414	−	0.423414i
$316$	6.20198e13	−	1.29792e13i	1.10726	−	0.231724i
$317$	−1.40318e13	−	1.40318e13i	−0.246199	−	0.246199i	0.573210	−	0.819409i	$-0.305698\pi$
$317$	−1.40318e13	−	1.40318e13i	−0.246199	−	0.246199i	−0.819409	+	0.573210i	$0.805698\pi$
$318$	4.07058e12	−	4.21373e11i	0.0701952	−	0.00726638i
$319$	−2.83286e13			−0.480149
$320$	−7.05032e12	+	4.19517e13i	−0.117458	+	0.698915i
$321$	−2.39944e12			−0.0392946
$322$	1.15829e13	−	1.19902e12i	0.186470	−	0.0193028i
$323$	1.97235e13	+	1.97235e13i	0.312155	+	0.312155i
$324$	−6.25117e13	+	1.30822e13i	−0.972666	+	0.203556i
$325$	−4.15387e13	+	4.15387e13i	−0.635469	+	0.635469i
$326$	−8.54598e13	−	6.94264e13i	−1.28548	−	1.04431i
$327$		−	3.90286e11i		−	0.00577258i
$328$	−2.04534e13	−	6.39732e13i	−0.297482	−	0.930448i
$329$		−	5.26844e13i		−	0.753537i
$330$	−1.08904e12	+	1.34054e12i	−0.0153186	+	0.0188562i
$331$	1.57682e13	−	1.57682e13i	0.218136	−	0.218136i	−0.589577	−	0.807712i	$-0.700705\pi$
$331$	1.57682e13	−	1.57682e13i	0.218136	−	0.218136i	0.807712	+	0.589577i	$0.200705\pi$
$332$	7.19579e13	+	4.70520e13i	0.979082	+	0.640204i
$333$	−1.73541e13	−	1.73541e13i	−0.232252	−	0.232252i
$334$	−4.35565e12	−	4.20768e13i	−0.0573386	−	0.553907i
$335$	5.23795e13			0.678289
$336$	1.10643e12	−	2.82909e12i	0.0140947	−	0.0360397i
$337$	−1.08071e14			−1.35440			−0.677199	−	0.735800i	$-0.736806\pi$
$337$	−1.08071e14			−1.35440			−0.677199	+	0.735800i	$0.736806\pi$
$338$	−1.88750e13	−	1.82338e14i	−0.232726	−	2.24820i
$339$	−2.75131e12	−	2.75131e12i	−0.0333765	−	0.0333765i
$340$	−8.74546e12	+	1.33747e13i	−0.104388	+	0.159643i
$341$	−2.03785e13	+	2.03785e13i	−0.239344	+	0.239344i
$342$	−8.93015e13	+	1.09925e14i	−1.03208	+	1.27043i
$343$		−	9.55232e13i		−	1.08640i
$344$	−1.16173e13	+	2.25371e13i	−0.130027	+	0.252247i
$345$			6.51113e11i			0.00717218i
$346$	−5.51809e13	−	4.48282e13i	−0.598232	−	0.485997i
$347$	5.48946e13	−	5.48946e13i	0.585757	−	0.585757i	−0.350722	−	0.936479i	$-0.614064\pi$
$347$	5.48946e13	−	5.48946e13i	0.585757	−	0.585757i	0.936479	+	0.350722i	$0.114064\pi$
$348$	5.70666e11	+	2.72686e12i	0.00599372	+	0.0286403i
$349$	9.06961e13	+	9.06961e13i	0.937667	+	0.937667i	0.998168	−	0.0605011i	$-0.0192699\pi$
$349$	9.06961e13	+	9.06961e13i	0.937667	+	0.937667i	−0.0605011	+	0.998168i	$0.519270\pi$
$350$	−4.11872e13	+	4.26356e12i	−0.419167	+	0.0433908i
$351$	1.64573e13			0.164881
$352$	2.02569e13	−	7.32929e13i	0.199797	−	0.722899i
$353$	−1.21957e12			−0.0118426			−0.00592130	−	0.999982i	$-0.501885\pi$
$353$	−1.21957e12			−0.0118426			−0.00592130	+	0.999982i	$0.501885\pi$
$354$	−6.69674e12	+	6.93225e11i	−0.0640244	+	0.00662760i
$355$	9.05909e13	+	9.05909e13i	0.852763	+	0.852763i
$356$	2.69359e13	+	1.28710e14i	0.249665	+	1.19299i
$357$	8.06903e11	−	8.06903e11i	0.00736455	−	0.00736455i
$358$	1.84305e13	+	1.49727e13i	0.165646	+	0.134569i
$359$			4.50417e12i			0.0398653i	0.999801	+	0.0199327i	$0.00634518\pi$
$359$			4.50417e12i			0.0398653i	−0.999801	+	0.0199327i	$0.993655\pi$
$360$	−7.21207e13	−	3.71764e13i	−0.628632	−	0.324044i
$361$			1.96919e14i			1.69043i
$362$	−2.02700e13	+	2.49511e13i	−0.171378	+	0.210956i
$363$	−1.69793e12	+	1.69793e12i	−0.0141395	+	0.0141395i
$364$	1.02000e14	−	1.55991e14i	0.836644	−	1.27950i
$365$	−6.61284e13	−	6.61284e13i	−0.534291	−	0.534291i
$366$	6.19280e11	+	5.98241e12i	0.00492880	+	0.0476135i
$367$	−1.64509e14			−1.28981			−0.644905	−	0.764263i	$-0.723103\pi$
$367$	−1.64509e14			−1.28981			−0.644905	+	0.764263i	$0.723103\pi$
$368$	−1.14949e13	−	2.62607e13i	−0.0887854	−	0.202835i
$369$	1.28104e14			0.974806
$370$	−3.20376e12	−	3.09492e13i	−0.0240187	−	0.232028i
$371$	1.25144e14	+	1.25144e14i	0.924383	+	0.924383i
$372$	2.37211e12	+	1.55108e12i	0.0172643	+	0.0112888i
$373$	1.52240e14	−	1.52240e14i	1.09177	−	1.09177i	0.0964284	−	0.995340i	$-0.469258\pi$
$373$	1.52240e14	−	1.52240e14i	1.09177	−	1.09177i	0.995340	−	0.0964284i	$-0.0307419\pi$
$374$	1.80112e13	−	2.21707e13i	0.127277	−	0.156670i
$375$		−	6.96701e12i		−	0.0485148i
$376$	−1.23534e14	+	3.94963e13i	−0.847724	+	0.271033i
$377$			1.70929e14i			1.15594i
$378$	9.00362e12	+	7.31443e12i	0.0600084	+	0.0487501i
$379$	4.13623e13	−	4.13623e13i	0.271700	−	0.271700i	−0.558085	−	0.829784i	$-0.688464\pi$
$379$	4.13623e13	−	4.13623e13i	0.271700	−	0.271700i	0.829784	+	0.558085i	$0.188464\pi$
$380$	−1.75746e14	+	3.67794e13i	−1.13782	+	0.238119i
$381$	−9.96964e12	−	9.96964e12i	−0.0636198	−	0.0636198i
$382$	1.87297e13	−	1.93883e12i	0.117810	−	0.0121953i
$383$	−6.41682e13			−0.397857			−0.198928	−	0.980014i	$-0.563746\pi$
$383$	−6.41682e13			−0.397857			−0.198928	+	0.980014i	$0.563746\pi$
$384$	−7.46312e12	−	4.73445e11i	−0.0456141	−	0.00289366i
$385$	−7.46937e13			−0.450039
$386$	6.60999e13	−	6.84244e12i	0.392618	−	0.0406426i
$387$	−3.41965e13	−	3.41965e13i	−0.200249	−	0.200249i
$388$	1.77858e14	−	3.72214e13i	1.02683	−	0.214891i
$389$	1.21900e14	−	1.21900e14i	0.693877	−	0.693877i	−0.269206	−	0.963083i	$-0.586761\pi$
$389$	1.21900e14	−	1.21900e14i	0.693877	−	0.693877i	0.963083	+	0.269206i	$0.0867612\pi$
$390$	8.08856e12	+	6.57104e12i	0.0453958	+	0.0368790i
$391$		−	1.07685e13i		−	0.0595913i
$392$	−4.94251e13	+	1.58021e13i	−0.269696	+	0.0862268i
$393$			1.43445e13i			0.0771840i
$394$	1.14781e14	−	1.41288e14i	0.609032	−	0.749681i
$395$	−1.08343e14	+	1.08343e14i	−0.566913	+	0.566913i
$396$	1.21389e14	+	7.93742e13i	0.626406	+	0.409596i
$397$	5.19861e13	+	5.19861e13i	0.264570	+	0.264570i	0.826908	−	0.562338i	$-0.190098\pi$
$397$	5.19861e13	+	5.19861e13i	0.264570	+	0.264570i	−0.562338	+	0.826908i	$0.690098\pi$
$398$	3.75703e13	+	3.62939e14i	0.188576	+	1.82170i
$399$	1.28218e13			0.0634743
$400$	4.08742e13	+	9.33793e13i	0.199581	+	0.455954i
$401$	−2.94281e14			−1.41732			−0.708661	−	0.705549i	$-0.750700\pi$
$401$	−2.94281e14			−1.41732			−0.708661	+	0.705549i	$0.750700\pi$
$402$	9.48097e11	+	9.15888e12i	0.00450412	+	0.0435110i
$403$	1.22959e14	+	1.22959e14i	0.576214	+	0.576214i
$404$	3.84105e13	−	5.87422e13i	0.177563	−	0.271552i
$405$	1.09202e14	−	1.09202e14i	0.498000	−	0.498000i
$406$	−7.59689e13	+	9.35131e13i	−0.341777	+	0.420707i
$407$			5.56177e13i			0.246856i
$408$	−2.49694e12	−	1.28711e12i	−0.0109340	−	0.00563618i
$409$		−	3.29100e14i		−	1.42184i	−0.703274	−	0.710919i	$-0.748279\pi$
$409$		−	3.29100e14i		−	1.42184i	0.703274	−	0.710919i	$-0.251721\pi$
$410$	1.26055e14	+	1.02405e14i	0.537339	+	0.436527i
$411$	−3.07578e12	+	3.07578e12i	−0.0129368	+	0.0129368i
$412$	8.49088e11	+	4.05726e12i	0.00352385	+	0.0168383i
$413$	−2.05881e14	−	2.05881e14i	−0.843121	−	0.843121i
$414$	5.43860e13	−	5.62986e12i	0.219779	−	0.0227508i
$415$	−2.07899e14			−0.829065
$416$	−4.42234e14	−	1.22226e14i	−1.74036	−	0.481006i
$417$	−3.37084e12			−0.0130915
$418$	3.19248e14	−	3.30475e13i	1.22365	−	0.126669i
$419$	−7.64006e13	−	7.64006e13i	−0.289015	−	0.289015i	0.547676	−	0.836691i	$-0.315513\pi$
$419$	−7.64006e13	−	7.64006e13i	−0.289015	−	0.289015i	−0.836691	+	0.547676i	$0.815513\pi$
$420$	1.50467e12	+	7.18989e12i	0.00561786	+	0.0268442i
$421$	1.13866e13	−	1.13866e13i	0.0419608	−	0.0419608i	−0.685815	−	0.727776i	$-0.740554\pi$
$421$	1.13866e13	−	1.13866e13i	0.0419608	−	0.0419608i	0.727776	+	0.685815i	$0.240554\pi$
$422$	2.20006e13	+	1.78730e13i	0.0800233	+	0.0650099i
$423$		−	2.47373e14i		−	0.888138i
$424$	1.99619e14	−	3.87254e14i	0.707441	−	1.37241i
$425$			3.82913e13i			0.133956i
$426$	−1.42006e13	+	1.74801e13i	−0.0490405	+	0.0603659i
$427$	−1.83920e14	+	1.83920e14i	−0.627011	+	0.627011i
$428$	−1.39799e14	+	2.13799e14i	−0.470505	+	0.719556i
$429$	−1.31721e13	−	1.31721e13i	−0.0437664	−	0.0437664i
$430$	−6.31305e12	−	6.09858e13i	−0.0207092	−	0.200056i
$431$	−4.52834e14			−1.46661			−0.733304	−	0.679901i	$-0.762023\pi$
$431$	−4.52834e14			−1.46661			−0.733304	+	0.679901i	$0.762023\pi$
$432$	1.04011e13	−	2.65951e13i	0.0332596	−	0.0850436i
$433$	3.07829e14			0.971910			0.485955	−	0.873984i	$-0.338472\pi$
$433$	3.07829e14			0.971910			0.485955	+	0.873984i	$0.338472\pi$
$434$	1.26206e13	+	1.21919e14i	0.0393448	+	0.380082i
$435$	−4.76358e12	−	4.76358e12i	−0.0146637	−	0.0146637i
$436$	−3.47758e13	−	2.27393e13i	−0.105706	−	0.0691196i
$437$	8.55563e13	−	8.55563e13i	0.256805	−	0.256805i
$438$	1.03660e13	−	1.27599e13i	0.0307258	−	0.0378216i
$439$			2.23842e14i			0.655218i	0.944813	+	0.327609i	$0.106243\pi$
$439$			2.23842e14i			0.655218i	−0.944813	+	0.327609i	$0.893757\pi$
$440$	5.59961e13	+	1.75142e14i	0.161871	+	0.506291i
$441$		−	9.89719e13i		−	0.282553i
$442$	−1.33773e14	−	1.08676e14i	−0.377178	−	0.306415i
$443$	1.88897e14	−	1.88897e14i	0.526022	−	0.526022i	−0.393362	−	0.919384i	$-0.628688\pi$
$443$	1.88897e14	−	1.88897e14i	0.526022	−	0.526022i	0.919384	+	0.393362i	$0.128688\pi$
$444$	5.35366e12	−	1.12039e12i	0.0147246	−	0.00308151i
$445$	−2.24845e14	−	2.24845e14i	−0.610806	−	0.610806i
$446$	5.84473e13	−	6.05027e12i	0.156828	−	0.0162343i
$447$	1.88931e13			0.0500739
$448$	−1.87618e14	−	2.63419e14i	−0.491186	−	0.689632i
$449$	1.84294e14			0.476603			0.238301	−	0.971191i	$-0.423409\pi$
$449$	1.84294e14			0.476603			0.238301	+	0.971191i	$0.423409\pi$
$450$	−1.93389e14	+	2.00190e13i	−0.494042	+	0.0511416i
$451$	−2.05279e14	−	2.05279e14i	−0.518052	−	0.518052i
$452$	−4.05451e14	+	8.48512e13i	−1.01083	+	0.211542i
$453$	1.31350e13	−	1.31350e13i	0.0323512	−	0.0323512i
$454$	3.70373e14	+	3.00886e14i	0.901222	+	0.732141i
$455$			4.50686e14i			1.08346i
$456$	−9.61220e12	−	3.00645e13i	−0.0228305	−	0.0714081i
$457$			3.30279e13i			0.0775073i	0.999249	+	0.0387536i	$0.0123388\pi$
$457$			3.30279e13i			0.0775073i	−0.999249	+	0.0387536i	$0.987661\pi$
$458$	2.15613e14	−	2.65407e14i	0.499937	−	0.615392i
$459$	7.58536e12	−	7.58536e12i	0.0173783	−	0.0173783i
$460$	5.80164e13	+	3.79359e13i	0.131336	+	0.0858781i
$461$	2.66530e14	+	2.66530e14i	0.596198	+	0.596198i	0.939299	−	0.343101i	$-0.111477\pi$
$461$	2.66530e14	+	2.66530e14i	0.596198	+	0.596198i	−0.343101	+	0.939299i	$0.611477\pi$
$462$	−1.35200e12	−	1.30607e13i	−0.00298844	−	0.0288692i
$463$	4.98919e14			1.08977			0.544885	−	0.838511i	$-0.316573\pi$
$463$	4.98919e14			1.08977			0.544885	+	0.838511i	$0.316573\pi$
$464$	2.76222e14	+	1.08027e14i	0.596223	+	0.233176i
$465$	−6.85347e12			−0.0146191
$466$	4.95533e13	+	4.78698e14i	0.104460	+	1.00911i
$467$	4.27807e14	+	4.27807e14i	0.891262	+	0.891262i	0.994642	−	0.103380i	$-0.0329658\pi$
$467$	4.27807e14	+	4.27807e14i	0.891262	+	0.891262i	−0.103380	+	0.994642i	$0.532966\pi$
$468$	4.78927e14	−	7.32436e14i	0.986091	−	1.50806i
$469$	−2.81575e14	+	2.81575e14i	−0.572985	+	0.572985i
$470$	1.97748e14	−	2.43416e14i	0.397717	−	0.489565i
$471$		−	1.33278e13i		−	0.0264937i
$472$	−3.28405e14	+	6.37092e14i	−0.645251	+	1.25176i
$473$			1.09595e14i			0.212841i
$474$	−2.09055e13	−	1.69834e13i	−0.0401310	−	0.0326019i
$475$	−3.04226e14	+	3.04226e14i	−0.577274	+	0.577274i
$476$	−2.48851e13	−	1.18911e14i	−0.0466769	−	0.223040i
$477$	5.87596e14	+	5.87596e14i	1.08950	+	1.08950i
$478$	−1.00038e15	+	1.03556e14i	−1.83362	+	0.189811i
$479$	1.01796e15			1.84453			0.922264	−	0.386561i	$-0.126337\pi$
$479$	1.01796e15			1.84453			0.922264	+	0.386561i	$0.126337\pi$
$480$	1.57308e13	−	8.91825e12i	0.0281790	−	0.0159754i
$481$	3.35585e14			0.594299
$482$	−8.19490e14	+	8.48309e13i	−1.43478	+	0.148524i
$483$	−3.50017e12	−	3.50017e12i	−0.00605871	−	0.00605871i
$484$	5.23646e13	+	2.50218e14i	0.0896165	+	0.428222i
$485$	−3.10702e14	+	3.10702e14i	−0.525732	+	0.525732i
$486$	6.34352e13	+	5.15340e13i	0.106128	+	0.0862173i
$487$		−	3.80487e14i		−	0.629405i	−0.949190	−	0.314702i	$-0.898095\pi$
$487$		−	3.80487e14i		−	0.629405i	0.949190	−	0.314702i	$-0.101905\pi$
$488$	5.69135e14	+	2.93375e14i	0.930907	+	0.479859i
$489$			4.68042e13i			0.0756983i
$490$	7.91173e13	−	9.73886e13i	0.126530	−	0.155751i
$491$	4.01164e14	−	4.01164e14i	0.634416	−	0.634416i	−0.314757	−	0.949172i	$-0.601923\pi$
$491$	4.01164e14	−	4.01164e14i	0.634416	−	0.634416i	0.949172	+	0.314757i	$0.101923\pi$
$492$	−1.56245e13	+	2.38950e13i	−0.0244343	+	0.0373680i
$493$	7.87828e13	+	7.87828e13i	0.121835	+	0.121835i
$494$	−1.99401e14	−	1.92627e15i	−0.304951	−	2.94591i
$495$	−3.50715e14			−0.530427
$496$	2.76414e14	−	1.20993e14i	0.413438	−	0.180971i
$497$	−9.73973e14			−1.44074
$498$	−3.76309e12	−	3.63525e13i	−0.00550533	−	0.0531830i
$499$	−7.67694e14	−	7.67694e14i	−1.11080	−	1.11080i	−0.993043	−	0.117755i	$-0.962430\pi$
$499$	−7.67694e14	−	7.67694e14i	−1.11080	−	1.11080i	−0.117755	−	0.993043i	$-0.537570\pi$
$500$	−6.20785e14	−	4.05920e14i	−0.888395	−	0.580905i
$501$	−1.27150e13	+	1.27150e13i	−0.0179973	+	0.0179973i
$502$	3.03949e14	−	3.74143e14i	0.425530	−	0.523801i
$503$		−	1.56404e14i		−	0.216583i	−0.994119	−	0.108291i	$-0.965462\pi$
$503$		−	1.56404e14i		−	0.216583i	0.994119	−	0.108291i	$-0.0345379\pi$
$504$	5.87545e14	−	1.87849e14i	0.804773	−	0.257301i
$505$			1.69717e14i			0.229944i
$506$	−9.61717e13	−	7.81287e13i	−0.128890	−	0.104709i
$507$	−5.50997e13	+	5.50997e13i	−0.0730475	+	0.0730475i
$508$	−1.46919e15	+	3.07467e14i	−1.92676	+	0.403225i
$509$	−5.43363e14	−	5.43363e14i	−0.704924	−	0.704924i	0.260539	−	0.965463i	$-0.416100\pi$
$509$	−5.43363e14	−	5.43363e14i	−0.704924	−	0.704924i	−0.965463	+	0.260539i	$0.916100\pi$
$510$	6.75677e12	−	6.99439e11i	0.00867168	−	0.000897664i
$511$	7.10969e14			0.902684
$512$	−4.77011e14	+	6.37406e14i	−0.599161	+	0.800629i
$513$	1.20532e14			0.149781
$514$	−7.85815e14	+	8.13450e13i	−0.966102	+	0.100008i
$515$	−7.08767e12	−	7.08767e12i	−0.00862112	−	0.00862112i
$516$	1.05495e13	−	2.20775e12i	0.0126957	−	0.00265691i
$517$	−3.96400e14	+	3.96400e14i	−0.471993	+	0.471993i
$518$	1.83595e14	+	1.49150e14i	0.216295	+	0.175716i
$519$			3.02212e13i			0.0352283i
$520$	1.05677e15	−	3.37869e14i	1.21888	−	0.389699i
$521$		−	9.64380e14i		−	1.10063i	−0.834958	−	0.550314i	$-0.814508\pi$
$521$		−	9.64380e14i		−	1.10063i	0.834958	−	0.550314i	$-0.185492\pi$
$522$	−3.56703e14	+	4.39079e14i	−0.402827	+	0.495856i
$523$	2.60723e14	−	2.60723e14i	0.291353	−	0.291353i	−0.546261	−	0.837615i	$-0.683949\pi$
$523$	2.60723e14	−	2.60723e14i	0.291353	−	0.291353i	0.837615	+	0.546261i	$0.183949\pi$
$524$	1.27815e15	+	8.35758e14i	1.41338	+	0.924184i
$525$	1.24461e13	+	1.24461e13i	0.0136194	+	0.0136194i
$526$	4.68705e13	+	4.52782e14i	0.0507549	+	0.490307i
$527$	1.13347e14			0.121465
$528$	−2.96111e13	+	1.29614e13i	−0.0314027	+	0.0137457i
$529$	9.06098e14			0.950975
$530$	1.08477e14	+	1.04792e15i	0.112673	+	1.08845i
$531$	−9.66687e14	−	9.66687e14i	−0.993724	−	0.993724i
$532$	7.47038e14	−	1.14247e15i	0.760027	−	1.16233i
$533$	−1.23861e15	+	1.23861e15i	−1.24719	+	1.24719i
$534$	3.52457e13	−	4.33853e13i	0.0351261	−	0.0432381i
$535$		−	6.17703e14i		−	0.609304i
$536$	8.71327e14	+	4.49147e14i	0.850697	+	0.438512i
$537$		−	1.00939e13i		−	0.00975444i
$538$	−5.04688e14	−	4.10002e14i	−0.482748	−	0.392178i
$539$	−1.58596e14	+	1.58596e14i	−0.150160	+	0.150160i
$540$	1.41448e13	+	6.75892e13i	0.0132566	+	0.0633449i
$541$	7.80888e14	+	7.80888e14i	0.724442	+	0.724442i	0.969507	−	0.245064i	$-0.0788091\pi$
$541$	7.80888e14	+	7.80888e14i	0.724442	+	0.724442i	−0.245064	+	0.969507i	$0.578809\pi$
$542$	3.64291e14	−	3.77102e13i	0.334544	−	0.0346309i
$543$	1.36651e13			0.0124226
$544$	−2.60166e14	+	1.47495e14i	−0.234129	+	0.132734i
$545$	1.00474e14			0.0895099
$546$	−7.88052e13	+	8.15765e12i	−0.0695017	+	0.00719458i
$547$	−4.05263e13	−	4.05263e13i	−0.0353839	−	0.0353839i	0.689193	−	0.724577i	$-0.257965\pi$
$547$	−4.05263e13	−	4.05263e13i	−0.0353839	−	0.0353839i	−0.724577	+	0.689193i	$0.757965\pi$
$548$	9.48581e13	+	4.53268e14i	0.0819939	+	0.391798i
$549$	−8.63573e14	+	8.63573e14i	−0.739011	+	0.739011i
$550$	3.41973e14	+	2.77815e14i	0.289733	+	0.235375i
$551$			1.25187e15i			1.05009i
$552$	−5.58320e12	+	1.08312e13i	−0.00463680	+	0.00899521i
$553$		−	1.16483e15i		−	0.957801i
$554$	1.20273e15	−	1.48049e15i	0.979183	−	1.20531i
$555$	−9.35237e12	+	9.35237e12i	−0.00753894	+	0.00753894i
$556$	−1.96396e14	+	3.00354e14i	−0.156755	+	0.239729i
$557$	−9.73064e14	−	9.73064e14i	−0.769021	−	0.769021i	0.208913	−	0.977934i	$-0.433007\pi$
$557$	−9.73064e14	−	9.73064e14i	−0.769021	−	0.769021i	−0.977934	+	0.208913i	$0.933007\pi$
$558$	5.92587e13	+	5.72455e14i	0.0463729	+	0.447975i
$559$	6.61275e14			0.512409
$560$	7.28311e14	+	2.84834e14i	0.558834	+	0.218554i
$561$	−1.21424e13			−0.00922587
$562$	2.17025e14	+	2.09652e15i	0.163290	+	1.57743i
$563$	−4.90526e14	−	4.90526e14i	−0.365482	−	0.365482i	0.500345	−	0.865826i	$-0.333207\pi$
$563$	−4.90526e14	−	4.90526e14i	−0.365482	−	0.365482i	−0.865826	+	0.500345i	$0.833207\pi$
$564$	4.61421e13	+	3.01715e13i	0.0340457	+	0.0222619i
$565$	7.08287e14	−	7.08287e14i	0.517539	−	0.517539i
$566$	9.81548e14	−	1.20823e15i	0.710266	−	0.874295i
$567$			1.17407e15i			0.841371i
$568$	7.30165e14	+	2.28377e15i	0.518209	+	1.62083i
$569$		−	6.24602e14i		−	0.439022i	−0.975610	−	0.219511i	$-0.929554\pi$
$569$		−	6.24602e14i		−	0.439022i	0.975610	−	0.219511i	$-0.0704461\pi$
$570$	5.92400e13	+	4.81259e13i	0.0412386	+	0.0335017i
$571$	7.95287e14	−	7.95287e14i	0.548309	−	0.548309i	−0.377642	−	0.925952i	$-0.623265\pi$
$571$	7.95287e14	−	7.95287e14i	0.548309	−	0.548309i	0.925952	+	0.377642i	$0.123265\pi$
$572$	−1.94113e15	+	4.06232e14i	−1.32549	+	0.277394i
$573$	−5.65982e12	−	5.65982e12i	−0.00382783	−	0.00382783i
$574$	−1.22813e15	+	1.27132e14i	−0.822674	+	0.0851605i
$575$	1.66099e14			0.110203
$576$	−8.80938e14	−	1.23685e15i	−0.578924	−	0.812818i
$577$	−1.00625e15			−0.654999			−0.327499	−	0.944851i	$-0.606206\pi$
$577$	−1.00625e15			−0.654999			−0.327499	+	0.944851i	$0.606206\pi$
$578$	1.43098e15	−	1.48130e14i	0.922635	−	0.0955081i
$579$	−1.99744e13	−	1.99744e13i	−0.0127568	−	0.0127568i
$580$	−7.01993e14	+	1.46910e14i	−0.444098	+	0.0929390i
$581$	1.11760e15	−	1.11760e15i	0.700353	−	0.700353i
$582$	−5.99520e13	−	4.87043e13i	−0.0372158	−	0.0302337i
$583$		−	1.88317e15i		−	1.15801i
$584$	−5.32997e14	−	1.66708e15i	−0.324679	−	1.01551i
$585$			2.11614e15i			1.27699i
$586$	−6.83762e14	+	8.41669e14i	−0.408760	+	0.503158i
$587$	−1.53564e15	+	1.53564e15i	−0.909453	+	0.909453i	−0.996228	−	0.0867748i	$-0.972344\pi$
$587$	−1.53564e15	+	1.53564e15i	−0.909453	+	0.909453i	0.0867748	+	0.996228i	$0.472344\pi$
$588$	1.84611e13	+	1.20714e13i	0.0108313	+	0.00708241i
$589$	9.00546e14	+	9.00546e14i	0.523446	+	0.523446i
$590$	−1.78461e14	−	1.72398e15i	−0.102768	−	0.992766i
$591$	−7.73801e13			−0.0441467
$592$	2.12091e14	−	5.42308e14i	0.119881	−	0.306532i
$593$	1.63157e15			0.913704			0.456852	−	0.889543i	$-0.348977\pi$
$593$	1.63157e15			0.913704			0.456852	+	0.889543i	$0.348977\pi$
$594$	−1.27096e13	−	1.22778e14i	−0.00705188	−	0.0681231i
$595$	2.07726e14	+	2.07726e14i	0.114195	+	0.114195i
$596$	1.10077e15	−	1.68344e15i	0.599574	−	0.916944i
$597$	1.09675e14	−	1.09675e14i	0.0591899	−	0.0591899i
$598$	−4.71412e14	+	5.80279e14i	−0.252083	+	0.310299i
$599$			1.76391e15i			0.934608i	0.884097	+	0.467304i	$0.154775\pi$
$599$			1.76391e15i			0.934608i	−0.884097	+	0.467304i	$0.845225\pi$
$600$	1.98531e13	−	3.85142e13i	0.0104231	−	0.0202204i
$601$		−	5.73310e14i		−	0.298250i	−0.988818	−	0.149125i	$-0.952354\pi$
$601$		−	5.73310e14i		−	0.298250i	0.988818	−	0.149125i	$-0.0476457\pi$
$602$	3.61776e14	+	2.93903e14i	0.186492	+	0.151503i
$603$	−1.32210e15	+	1.32210e15i	−0.675335	+	0.675335i
$604$	−4.05087e14	−	1.93566e15i	−0.205043	−	0.979775i
$605$	−4.37108e14	−	4.37108e14i	−0.219247	−	0.219247i
$606$	−2.96761e13	+	3.07197e12i	−0.0147505	+	0.00152692i
$607$	−2.36189e15			−1.16338			−0.581690	−	0.813411i	$-0.697608\pi$
$607$	−2.36189e15			−1.16338			−0.581690	+	0.813411i	$0.697608\pi$
$608$	−3.23889e15	−	8.95175e14i	−1.58098	−	0.436956i
$609$	5.12149e13			0.0247743
$610$	−1.54009e15	+	1.59425e14i	−0.738298	+	0.0764262i
$611$	2.39179e15	+	2.39179e15i	1.13631	+	1.13631i
$612$	−1.16845e14	−	5.58330e14i	−0.0550146	−	0.262880i
$613$	2.34434e15	−	2.34434e15i	1.09392	−	1.09392i	0.0988186	−	0.995105i	$-0.468494\pi$
$613$	2.34434e15	−	2.34434e15i	1.09392	−	1.09392i	0.995105	−	0.0988186i	$-0.0315064\pi$
$614$	2.29626e15	+	1.86545e15i	1.06193	+	0.862695i
$615$		−	6.90371e13i		−	0.0316424i
$616$	−1.24252e15	−	6.40488e14i	−0.564430	−	0.290949i
$617$		−	1.75185e15i		−	0.788728i	−0.918954	−	0.394364i	$-0.870965\pi$
$617$		−	1.75185e15i		−	0.788728i	0.918954	−	0.394364i	$-0.129035\pi$
$618$	1.11103e12	−	1.36761e12i	0.000495781	−	0.000610277i
$619$	−8.88285e14	+	8.88285e14i	−0.392874	+	0.392874i	−0.875711	−	0.482836i	$-0.839607\pi$
$619$	−8.88285e14	+	8.88285e14i	−0.392874	+	0.392874i	0.482836	+	0.875711i	$0.339607\pi$
$620$	−3.99305e14	+	6.10668e14i	−0.175045	+	0.267702i
$621$	−3.29036e13	−	3.29036e13i	−0.0142968	−	0.0142968i
$622$	1.97223e14	+	1.90523e15i	0.0849399	+	0.820543i
$623$	2.41739e15			1.03196
$624$	7.82065e13	+	1.78667e14i	0.0330923	+	0.0756012i
$625$	6.06900e14			0.254552
$626$	−4.51034e14	−	4.35711e15i	−0.187521	−	1.81151i
$627$	−9.64718e13	−	9.64718e13i	−0.0397584	−	0.0397584i
$628$	−1.18755e15	−	7.76517e14i	−0.485147	−	0.317229i
$629$	1.54675e14	−	1.54675e14i	0.0626385	−	0.0626385i
$630$	−9.40515e14	+	1.15772e15i	−0.377566	+	0.464761i
$631$			7.19169e14i			0.286200i	0.989708	+	0.143100i	$0.0457071\pi$
$631$			7.19169e14i			0.286200i	−0.989708	+	0.143100i	$0.954293\pi$
$632$	−2.73130e15	+	8.73247e14i	−1.07752	+	0.344503i
$633$		−	1.20492e13i		−	0.00471235i
$634$	6.97014e14	+	5.66245e14i	0.270240	+	0.219540i
$635$	2.56655e15	−	2.56655e15i	0.986492	−	0.986492i
$636$	−1.81271e14	+	3.79356e13i	−0.0690739	+	0.0144555i
$637$	9.56936e14	+	9.56936e14i	0.361507	+	0.361507i
$638$	1.27519e15	−	1.32004e14i	0.477597	−	0.0494392i
$639$	−4.57317e15			−1.69810
$640$	1.21882e14	−	1.92128e15i	0.0448693	−	0.707294i
$641$	−2.50058e15			−0.912686			−0.456343	−	0.889804i	$-0.650841\pi$
$641$	−2.50058e15			−0.912686			−0.456343	+	0.889804i	$0.650841\pi$
$642$	1.08009e14	−	1.11808e13i	0.0390857	−	0.00404603i
$643$	9.02176e14	+	9.02176e14i	0.323691	+	0.323691i	0.850181	−	0.526490i	$-0.176492\pi$
$643$	9.02176e14	+	9.02176e14i	0.323691	+	0.323691i	−0.526490	+	0.850181i	$0.676492\pi$
$644$	−5.15808e14	+	1.07946e14i	−0.183492	+	0.0384004i
$645$	−1.84290e13	+	1.84290e13i	−0.00650014	+	0.00650014i
$646$	−9.79746e14	−	7.95934e14i	−0.342637	−	0.278354i
$647$		−	9.34714e14i		−	0.324120i	−0.986781	−	0.162060i	$-0.948186\pi$
$647$		−	9.34714e14i		−	0.324120i	0.986781	−	0.162060i	$-0.0518138\pi$
$648$	2.75296e15	−	8.80173e14i	0.946537	−	0.302626i
$649$			3.09811e15i			1.05621i
$650$	1.67628e15	−	2.06339e15i	0.566659	−	0.697523i
$651$	3.68420e13	−	3.68420e13i	0.0123495	−	0.0123495i
$652$	4.17042e15	+	2.72696e15i	1.38617	+	0.906395i
$653$	−1.81794e15	−	1.81794e15i	−0.599179	−	0.599179i	0.340915	−	0.940094i	$-0.389263\pi$
$653$	−1.81794e15	−	1.81794e15i	−0.599179	−	0.599179i	−0.940094	+	0.340915i	$0.889263\pi$
$654$	1.81863e12	+	1.75684e13i	0.000594382	+	0.00574190i
$655$	−3.69280e15			−1.19682
$656$	1.21880e15	+	2.78440e15i	0.391706	+	0.894872i
$657$	3.33827e15			1.06393
$658$	2.45495e14	+	2.37155e15i	0.0775891	+	0.749532i
$659$	3.21447e15	+	3.21447e15i	1.00749	+	1.00749i	0.999972	+	0.00751594i	$0.00239242\pi$
$659$	3.21447e15	+	3.21447e15i	1.00749	+	1.00749i	0.00751594	+	0.999972i	$0.497608\pi$
$660$	4.27759e13	−	6.54183e13i	0.0132956	−	0.0203333i
$661$	1.30629e15	−	1.30629e15i	0.402653	−	0.402653i	−0.476514	−	0.879167i	$-0.658100\pi$
$661$	1.30629e15	−	1.30629e15i	0.402653	−	0.402653i	0.879167	+	0.476514i	$0.158100\pi$
$662$	−6.36317e14	+	7.83268e14i	−0.194516	+	0.239437i
$663$			7.32644e13i			0.0222110i
$664$	−3.45838e15	−	1.78271e15i	−1.03980	−	0.535989i
$665$			3.30079e15i			0.984236i
$666$	8.62048e14	+	7.00317e14i	0.254931	+	0.207103i
$667$	3.41743e14	−	3.41743e14i	0.100232	−	0.100232i
$668$	3.92133e14	+	1.87376e15i	0.114068	+	0.545059i
$669$	−1.76619e13	−	1.76619e13i	−0.00509557	−	0.00509557i
$670$	−2.35783e15	+	2.44074e14i	−0.674684	+	0.0698411i
$671$	2.76764e15			0.785481
$672$	−3.66222e13	+	1.32505e14i	−0.0103089	+	0.0372994i
$673$	6.94406e14			0.193879			0.0969395	−	0.995290i	$-0.469095\pi$
$673$	6.94406e14			0.193879			0.0969395	+	0.995290i	$0.469095\pi$
$674$	4.86476e15	−	5.03583e14i	1.34720	−	0.139458i
$675$	1.17001e14	+	1.17001e14i	0.0321380	+	0.0321380i
$676$	1.69929e15	+	8.11986e15i	0.462979	+	2.21229i
$677$	−3.20116e14	+	3.20116e14i	−0.0865107	+	0.0865107i	−0.749038	−	0.662527i	$-0.769484\pi$
$677$	−3.20116e14	+	3.20116e14i	−0.0865107	+	0.0865107i	0.662527	+	0.749038i	$0.269484\pi$
$678$	1.36669e14	+	1.11028e14i	0.0366358	+	0.0297625i
$679$		−	3.34046e15i		−	0.888225i
$680$	3.31349e14	−	6.42803e14i	0.0873949	−	0.169543i
$681$		−	2.02844e14i		−	0.0530705i
$682$	8.22365e14	−	1.01228e15i	0.213428	−	0.262716i
$683$	−4.63633e13	+	4.63633e13i	−0.0119360	+	0.0119360i	−0.713050	−	0.701114i	$-0.752687\pi$
$683$	−4.63633e13	+	4.63633e13i	−0.0119360	+	0.0119360i	0.701114	+	0.713050i	$0.252687\pi$
$684$	3.50763e15	−	5.36431e15i	0.895787	−	1.36995i
$685$	−7.91818e14	−	7.91818e14i	−0.200598	−	0.200598i
$686$	4.45113e14	+	4.29991e15i	0.111863	+	1.08063i
$687$	−1.45357e14			−0.0362388
$688$	4.17927e14	−	1.06862e15i	0.103363	−	0.264295i
$689$	−1.13627e16			−2.78788
$690$	−3.03401e12	−	2.93094e13i	−0.000738495	−	0.00713406i
$691$	−4.46516e15	−	4.46516e15i	−1.07822	−	1.07822i	−0.996669	−	0.0815506i	$-0.974013\pi$
$691$	−4.46516e15	−	4.46516e15i	−1.07822	−	1.07822i	−0.0815506	−	0.996669i	$-0.525987\pi$
$692$	2.69281e15	+	1.76078e15i	0.645094	+	0.421815i
$693$	1.88533e15	−	1.88533e15i	0.448079	−	0.448079i
$694$	−2.21525e15	+	2.72684e15i	−0.522330	+	0.642957i
$695$		−	8.67776e14i		−	0.202998i
$696$	−3.83946e13	−	1.20089e14i	−0.00891085	−	0.0278709i
$697$			1.14178e15i			0.262906i
$698$	−4.50524e15	−	3.66000e15i	−1.02923	−	0.836135i
$699$	1.44655e14	−	1.44655e14i	0.0327876	−	0.0327876i
$700$	1.83414e15	−	3.83842e14i	0.412472	−	0.0863204i
$701$	−2.39258e15	−	2.39258e15i	−0.533847	−	0.533847i	0.387868	−	0.921715i	$-0.373212\pi$
$701$	−2.39258e15	−	2.39258e15i	−0.533847	−	0.533847i	−0.921715	+	0.387868i	$0.873212\pi$
$702$	−7.40815e14	+	7.66867e13i	−0.164004	+	0.0169772i
$703$	2.45780e15			0.539874
$704$	−5.70326e14	+	3.39362e15i	−0.124301	+	0.739629i
$705$	−1.33313e14			−0.0288292
$706$	5.48982e13	−	5.68288e12i	0.0117797	−	0.00121939i
$707$	−9.12343e14	−	9.12343e14i	−0.194246	−	0.194246i
$708$	2.98219e14	−	6.24100e13i	0.0630017	−	0.0131847i
$709$	−9.78586e14	+	9.78586e14i	−0.205137	+	0.205137i	−0.802197	−	0.597060i	$-0.796336\pi$
$709$	−9.78586e14	+	9.78586e14i	−0.205137	+	0.205137i	0.597060	+	0.802197i	$0.296336\pi$
$710$	−4.50001e15	−	3.65576e15i	−0.936037	−	0.760425i
$711$		−	5.46933e15i		−	1.12889i
$712$	−1.81226e15	−	5.66828e15i	−0.371176	−	1.16095i
$713$		−	4.91673e14i		−	0.0999273i
$714$	−3.25622e13	+	4.00821e13i	−0.00656710	+	0.00808371i
$715$	3.39098e15	−	3.39098e15i	0.678644	−	0.678644i
$716$	−8.99406e14	−	5.88105e14i	−0.178622	−	0.116797i
$717$	3.02299e14	+	3.02299e14i	0.0595773	+	0.0595773i
$718$	−2.09882e13	−	2.02752e14i	−0.00410479	−	0.0396534i
$719$	−8.22741e15			−1.59681			−0.798406	−	0.602119i	$-0.794323\pi$
$719$	−8.22741e15			−1.59681			−0.798406	+	0.602119i	$0.794323\pi$
$720$	3.41970e15	+	1.33741e15i	0.658656	+	0.257593i
$721$	7.62020e13			0.0145654
$722$	−9.17588e14	−	8.86416e15i	−0.174058	−	1.68145i
$723$	2.47637e14	+	2.47637e14i	0.0466182	+	0.0466182i
$724$	7.96173e14	−	1.21761e15i	0.148746	−	0.227481i
$725$	−1.21519e15	+	1.21519e15i	−0.225313	+	0.225313i
$726$	6.85191e13	−	8.43429e13i	0.0126084	−	0.0155202i
$727$		−	4.13322e14i		−	0.0754831i	−0.999288	−	0.0377415i	$-0.987984\pi$
$727$		−	4.13322e14i		−	0.0754831i	0.999288	−	0.0377415i	$-0.0120164\pi$
$728$	−3.86457e15	+	7.49711e15i	−0.700452	+	1.35885i
$729$			5.48950e15i			0.987488i
$730$	3.28487e15	+	2.66858e15i	0.586465	+	0.476437i
$731$	3.04789e14	−	3.04789e14i	0.0540074	−	0.0540074i
$732$	−5.57529e13	−	2.66409e14i	−0.00980520	−	0.0468530i
$733$	5.11410e14	+	5.11410e14i	0.0892683	+	0.0892683i	0.750331	−	0.661063i	$-0.229894\pi$
$733$	5.11410e14	+	5.11410e14i	0.0892683	+	0.0892683i	−0.661063	+	0.750331i	$0.729894\pi$
$734$	7.40525e15	−	7.66567e14i	1.28295	−	0.132807i
$735$	−5.33374e13			−0.00917173
$736$	6.39802e14	+	1.12854e15i	0.109199	+	0.192615i
$737$	4.23717e15			0.717802
$738$	−5.76652e15	+	5.96931e14i	−0.969624	+	0.100372i
$739$	6.68018e15	+	6.68018e15i	1.11492	+	1.11492i	0.992475	+	0.122445i	$0.0390736\pi$
$739$	6.68018e15	+	6.68018e15i	1.11492	+	1.11492i	0.122445	+	0.992475i	$0.460926\pi$
$740$	2.88430e14	+	1.37823e15i	0.0477821	+	0.228321i
$741$	−5.82090e14	+	5.82090e14i	−0.0957172	+	0.0957172i
$742$	−6.21638e15	−	5.05011e15i	−1.01465	−	0.824289i
$743$			1.04581e15i			0.169440i	0.996405	+	0.0847200i	$0.0269996\pi$
$743$			1.04581e15i			0.169440i	−0.996405	+	0.0847200i	$0.973000\pi$
$744$	−1.14007e14	−	5.87675e13i	−0.0183349	−	0.00945118i
$745$			4.86376e15i			0.776449i
$746$	−6.14358e15	+	7.56238e15i	−0.973550	+	1.19838i
$747$	5.24755e15	−	5.24755e15i	0.825455	−	0.825455i
$748$	−7.07452e14	+	1.08193e15i	−0.110468	+	0.168942i
$749$	3.32057e15	+	3.32057e15i	0.514710	+	0.514710i
$750$	3.24644e13	+	3.13615e14i	0.00499540	+	0.0482569i
$751$	−1.46013e15			−0.223034			−0.111517	−	0.993763i	$-0.535571\pi$
$751$	−1.46013e15			−0.223034			−0.111517	+	0.993763i	$0.535571\pi$
$752$	5.37677e15	−	2.35353e15i	0.815311	−	0.356880i
$753$	−2.04909e14			−0.0308452
$754$	−7.96481e14	−	7.69423e15i	−0.119024	−	1.14980i
$755$	3.38142e15	+	3.38142e15i	0.501639	+	0.501639i
$756$	−4.39375e14	−	2.87299e14i	−0.0647091	−	0.0423121i
$757$	−1.31824e15	+	1.31824e15i	−0.192737	+	0.192737i	−0.796878	−	0.604140i	$-0.793517\pi$
$757$	−1.31824e15	+	1.31824e15i	−0.192737	+	0.192737i	0.604140	+	0.796878i	$0.293517\pi$
$758$	−1.66916e15	+	2.05463e15i	−0.242279	+	0.298231i
$759$			5.26709e13i			0.00758999i
$760$	7.73970e15	−	2.47453e15i	1.10726	−	0.354012i
$761$		−	1.34562e15i		−	0.191121i	−0.995424	−	0.0955603i	$-0.969536\pi$
$761$		−	1.34562e15i		−	0.191121i	0.995424	−	0.0955603i	$-0.0304643\pi$
$762$	4.95232e14	+	4.02320e14i	0.0698323	+	0.0567309i
$763$	−5.40113e14	+	5.40113e14i	−0.0756136	+	0.0756136i
$764$	−8.34069e14	+	1.74551e14i	−0.115928	+	0.0242610i
$765$	9.75352e14	+	9.75352e14i	0.134593	+	0.134593i
$766$	2.88849e15	−	2.99007e14i	0.395742	−	0.0409659i
$767$	1.86933e16			2.54280
$768$	3.38153e14	−	1.34644e13i	0.0456696	−	0.00181844i
$769$	−4.50197e15			−0.603682			−0.301841	−	0.953358i	$-0.597601\pi$
$769$	−4.50197e15			−0.603682			−0.301841	+	0.953358i	$0.597601\pi$
$770$	3.36228e15	−	3.48053e14i	0.447647	−	0.0463389i
$771$	2.37461e14	+	2.37461e14i	0.0313902	+	0.0313902i
$772$	−2.94356e15	+	6.16015e14i	−0.386347	+	0.0808531i
$773$	−9.86354e14	+	9.86354e14i	−0.128542	+	0.128542i	−0.768451	−	0.639909i	$-0.778972\pi$
$773$	−9.86354e14	+	9.86354e14i	−0.128542	+	0.128542i	0.639909	+	0.768451i	$0.278972\pi$
$774$	1.69868e15	+	1.37998e15i	0.219804	+	0.178566i
$775$			1.74832e15i			0.224627i
$776$	−7.83271e15	+	2.50427e15i	−0.999247	+	0.319478i
$777$		−	1.00550e14i		−	0.0127370i
$778$	−4.91924e15	+	6.05528e15i	−0.618743	+	0.761635i
$779$	−9.07148e15	+	9.07148e15i	−1.13298	+	1.13298i
$780$	−3.94720e14	−	2.58100e14i	−0.0489518	−	0.0320087i
$781$	7.32822e15	+	7.32822e15i	0.902439	+	0.902439i
$782$	5.01783e13	+	4.84736e14i	0.00613590	+	0.0592745i
$783$	4.81450e14			0.0584603
$784$	2.15120e15	−	9.41629e14i	0.259384	−	0.113538i
$785$	3.43104e15			0.410812
$786$	−6.68417e13	−	6.45709e14i	−0.00794737	−	0.0767738i
$787$	−4.85920e15	−	4.85920e15i	−0.573726	−	0.573726i	0.359442	−	0.933167i	$-0.382967\pi$
$787$	−4.85920e15	−	4.85920e15i	−0.573726	−	0.573726i	−0.933167	+	0.359442i	$0.882967\pi$
$788$	−4.50841e15	+	6.89484e15i	−0.528603	+	0.808407i
$789$	1.36824e14	−	1.36824e14i	0.0159308	−	0.0159308i
$790$	4.37213e15	−	5.38183e15i	0.505527	−	0.622273i
$791$			7.61503e15i			0.874382i
$792$	−5.83411e15	−	3.00733e15i	−0.665252	−	0.342920i
$793$		−	1.66994e16i		−	1.89102i
$794$	−2.58236e15	−	2.09788e15i	−0.290405	−	0.235922i
$795$	3.16664e14	−	3.16664e14i	0.0353655	−	0.0353655i
$796$	−3.38240e15	−	1.61624e16i	−0.375148	−	1.79260i
$797$	−5.66561e15	−	5.66561e15i	−0.624059	−	0.624059i	0.322508	−	0.946567i	$-0.395474\pi$
$797$	−5.66561e15	−	5.66561e15i	−0.624059	−	0.624059i	−0.946567	+	0.322508i	$0.895474\pi$
$798$	−5.77164e14	+	5.97461e13i	−0.0631369	+	0.00653572i
$799$	2.20481e15			0.239532
$800$	−2.27505e15	−	4.01294e15i	−0.245468	−	0.432980i
$801$	1.13505e16			1.21629
$802$	1.32469e16	−	1.37127e15i	1.40979	−	0.145937i
$803$	−5.34937e15	−	5.34937e15i	−0.565414	−	0.565414i
$804$	−8.53558e13	−	4.07863e14i	−0.00896035	−	0.0428160i
$805$	9.01070e14	−	9.01070e14i	0.0939467	−	0.0939467i
$806$	−6.10789e15	−	4.96197e15i	−0.632483	−	0.513821i
$807$			2.76405e14i			0.0284277i
$808$	−1.45530e15	+	2.82322e15i	−0.148658	+	0.288392i
$809$		−	2.05127e15i		−	0.208117i	−0.994571	−	0.104058i	$-0.966817\pi$
$809$		−	2.05127e15i		−	0.208117i	0.994571	−	0.104058i	$-0.0331829\pi$
$810$	−4.40681e15	+	5.42452e15i	−0.444075	+	0.546630i
$811$	−1.24615e16	+	1.24615e16i	−1.24726	+	1.24726i	−0.290330	+	0.956926i	$0.593765\pi$
$811$	−1.24615e16	+	1.24615e16i	−1.24726	+	1.24726i	−0.956926	+	0.290330i	$0.906235\pi$
$812$	2.98394e15	−	4.56342e15i	0.296642	−	0.453662i
$813$	−1.10083e14	−	1.10083e14i	−0.0108698	−	0.0108698i
$814$	−2.59163e14	−	2.50359e15i	−0.0254179	−	0.245544i
$815$	−1.20491e16			−1.17378
$816$	1.18396e14	+	4.63032e13i	0.0114562	+	0.00448039i
$817$	4.84313e15			0.465484
$818$	1.53352e15	+	1.48142e16i	0.146402	+	1.41428i
$819$	−1.13757e16	−	1.13757e16i	−1.07874	−	1.07874i
$820$	−6.15145e15	−	4.02232e15i	−0.579430	−	0.378879i
$821$	−3.95265e15	+	3.95265e15i	−0.369829	+	0.369829i	−0.867415	−	0.497586i	$-0.834220\pi$
$821$	−3.95265e15	+	3.95265e15i	−0.369829	+	0.369829i	0.497586	+	0.867415i	$0.334220\pi$
$822$	1.24122e14	−	1.52787e14i	0.0115360	−	0.0142001i
$823$			2.80796e15i			0.259234i	0.991564	+	0.129617i	$0.0413747\pi$
$823$			2.80796e15i			0.259234i	−0.991564	+	0.129617i	$0.958625\pi$
$824$	−5.71269e13	−	1.78678e14i	−0.00523891	−	0.0163860i
$825$		−	1.87291e14i		−	0.0170616i
$826$	1.02269e16	+	8.30822e15i	0.925453	+	0.751827i
$827$	1.38092e16	−	1.38092e16i	1.24133	−	1.24133i	0.281886	−	0.959448i	$-0.409040\pi$
$827$	1.38092e16	−	1.38092e16i	1.24133	−	1.24133i	0.959448	−	0.281886i	$-0.0909599\pi$
$828$	−2.42192e15	+	5.06849e14i	−0.216268	+	0.0452597i
$829$	−1.20417e15	−	1.20417e15i	−0.106816	−	0.106816i	0.651679	−	0.758495i	$-0.274065\pi$
$829$	−1.20417e15	−	1.20417e15i	−0.106816	−	0.106816i	−0.758495	+	0.651679i	$0.774065\pi$
$830$	9.35845e15	−	9.68756e14i	0.824659	−	0.0853660i
$831$	−8.10826e14			−0.0709777
$832$	2.04764e16	+	3.44123e15i	1.78064	+	0.299250i
$833$	8.82125e14			0.0762048
$834$	1.51736e14	−	1.57072e13i	0.0130219	−	0.00134799i
$835$	−3.27329e15	−	3.27329e15i	−0.279067	−	0.279067i
$836$	−1.42167e16	+	2.97522e15i	−1.20411	+	0.251990i
$837$	3.46336e14	−	3.46336e14i	0.0291412	−	0.0291412i
$838$	3.79513e15	+	3.08311e15i	0.317237	+	0.257720i
$839$			1.42124e16i			1.18026i	0.807308	+	0.590130i	$0.200924\pi$
$839$			1.42124e16i			1.18026i	−0.807308	+	0.590130i	$0.799076\pi$
$840$	−1.01235e14	−	3.16637e14i	−0.00835205	−	0.0261231i
$841$		−	7.20009e15i		−	0.590147i
$842$	−4.59503e14	+	5.65620e14i	−0.0374172	+	0.0460584i
$843$	6.33536e14	−	6.33536e14i	0.0512530	−	0.0512530i
$844$	−1.07363e15	−	7.02025e14i	−0.0862918	−	0.0564247i
$845$	−1.41847e16	−	1.41847e16i	−1.13268	−	1.13268i
$846$	1.15269e15	+	1.11353e16i	0.0914485	+	0.883418i
$847$	4.69949e15			0.370418
$848$	−7.18122e15	+	1.83621e16i	−0.562369	+	1.43796i
$849$	−6.61716e14			−0.0514848
$850$	−1.78427e14	−	1.72365e15i	−0.0137929	−	0.133244i
$851$	−6.70946e14	−	6.70946e14i	−0.0515318	−	0.0515318i
$852$	5.57779e14	−	8.53026e14i	0.0425642	−	0.0650945i
$853$	−5.62449e14	+	5.62449e14i	−0.0426446	+	0.0426446i	−0.728108	−	0.685463i	$-0.759600\pi$
$853$	−5.62449e14	+	5.62449e14i	−0.0426446	+	0.0426446i	0.685463	+	0.728108i	$0.259600\pi$
$854$	7.42200e15	−	9.13603e15i	0.559117	−	0.688239i
$855$			1.54985e16i			1.16005i
$856$	5.29672e15	−	1.02754e16i	0.393914	−	0.764177i
$857$		−	2.59619e16i		−	1.91841i	−0.282706	−	0.959207i	$-0.591232\pi$
$857$		−	2.59619e16i		−	1.91841i	0.282706	−	0.959207i	$-0.408768\pi$
$858$	6.54313e14	+	5.31555e14i	0.0480402	+	0.0390273i
$859$	−1.35069e16	+	1.35069e16i	−0.985358	+	0.985358i	−0.999894	−	0.0145364i	$-0.995373\pi$
$859$	−1.35069e16	+	1.35069e16i	−0.985358	+	0.985358i	0.0145364	+	0.999894i	$0.495373\pi$
$860$	5.68355e14	+	2.71581e15i	0.0411982	+	0.196860i
$861$	3.71121e14	+	3.71121e14i	0.0267299	+	0.0267299i
$862$	2.03840e16	−	2.11008e15i	1.45881	−	0.151011i
$863$	1.03296e16			0.734552			0.367276	−	0.930112i	$-0.380290\pi$
$863$	1.03296e16			0.734552			0.367276	+	0.930112i	$0.380290\pi$
$864$	−3.44271e14	+	1.24563e15i	−0.0243262	+	0.0880162i
$865$	−7.78003e15			−0.546252
$866$	−1.38567e16	+	1.43440e15i	−0.966744	+	0.100074i
$867$	−4.32420e14	−	4.32420e14i	−0.0299778	−	0.0299778i
$868$	−1.13622e15	−	5.42928e15i	−0.0782714	−	0.374011i
$869$	−8.76425e15	+	8.76425e15i	−0.599938	+	0.599938i
$870$	2.36626e14	+	1.92232e14i	0.0160956	+	0.0130759i
$871$		−	2.55662e16i		−	1.72809i
$872$	1.67137e15	+	8.61547e14i	0.112262	+	0.0578680i
$873$		−	1.56847e16i		−	1.04688i
$874$	−3.45259e15	+	4.24993e15i	−0.228998	+	0.281883i
$875$	−9.64159e15	+	9.64159e15i	−0.635483	+	0.635483i
$876$	−4.07161e14	+	6.22682e14i	−0.0266682	+	0.0407843i
$877$	1.24365e16	+	1.24365e16i	0.809471	+	0.809471i	0.984554	−	0.175083i	$-0.0560194\pi$
$877$	1.24365e16	+	1.24365e16i	0.809471	+	0.809471i	−0.175083	+	0.984554i	$0.556019\pi$
$878$	−1.04304e15	−	1.00761e16i	−0.0674655	−	0.651735i
$879$	4.60962e14			0.0296296
$880$	−3.33674e15	−	7.62296e15i	−0.213141	−	0.486933i
$881$	1.72927e16			1.09773			0.548864	−	0.835912i	$-0.315061\pi$
$881$	1.72927e16			1.09773			0.548864	+	0.835912i	$0.315061\pi$
$882$	4.61183e14	+	4.45515e15i	0.0290935	+	0.281051i
$883$	7.01748e14	+	7.01748e14i	0.0439944	+	0.0439944i	0.728762	−	0.684767i	$-0.240096\pi$
$883$	7.01748e14	+	7.01748e14i	0.0439944	+	0.0439944i	−0.684767	+	0.728762i	$0.740096\pi$
$884$	6.52811e15	+	4.26861e15i	0.406724	+	0.265950i
$885$	−5.20961e14	+	5.20961e14i	−0.0322565	+	0.0322565i
$886$	−7.62284e15	+	9.38326e15i	−0.469063	+	0.577389i
$887$		−	4.10664e15i		−	0.251135i	−0.992085	−	0.125567i	$-0.959925\pi$
$887$		−	4.10664e15i		−	0.251135i	0.992085	−	0.125567i	$-0.0400751\pi$
$888$	−2.35771e14	+	7.53803e13i	−0.0143291	+	0.00458128i
$889$			2.75938e16i			1.66668i
$890$	1.11690e16	+	9.07352e15i	0.670452	+	0.544667i
$891$	8.83376e15	−	8.83376e15i	0.527009	−	0.527009i
$892$	−2.60277e15	+	5.44697e14i	−0.154322	+	0.0322960i
$893$	1.75173e16	+	1.75173e16i	1.03225	+	1.03225i
$894$	−8.50459e14	+	8.80367e13i	−0.0498078	+	0.00515593i
$895$	2.59855e15			0.151253
$896$	9.67296e15	+	1.09834e16i	0.559584	+	0.635391i
$897$	3.17805e14			0.0182727
$898$	−8.29587e15	+	8.58761e14i	−0.474069	+	0.0490741i
$899$	3.59711e15	+	3.59711e15i	0.204303	+	0.204303i
$900$	8.61200e15	−	1.80228e15i	0.486150	−	0.101739i
$901$	−5.23717e15	+	5.23717e15i	−0.293840	+	0.293840i
$902$	1.01970e16	+	8.28394e15i	0.568640	+	0.461956i
$903$		−	1.98136e14i		−	0.0109820i
$904$	1.78557e16	−	5.70881e15i	0.983674	−	0.314499i
$905$			3.51789e15i			0.192626i
$906$	−5.30057e14	+	6.52468e14i	−0.0288481	+	0.0355103i
$907$	−2.26950e16	+	2.26950e16i	−1.22770	+	1.22770i	−0.262863	+	0.964833i	$0.584667\pi$
$907$	−2.26950e16	+	2.26950e16i	−1.22770	+	1.22770i	−0.964833	+	0.262863i	$0.915333\pi$
$908$	−1.80741e16	−	1.18183e16i	−0.971817	−	0.635454i
$909$	−4.28379e15	−	4.28379e15i	−0.228943	−	0.228943i
$910$	−2.10007e15	−	2.02873e16i	−0.111560	−	1.07770i
$911$	1.61026e15			0.0850248			0.0425124	−	0.999096i	$-0.486464\pi$
$911$	1.61026e15			0.0850248			0.0425124	+	0.999096i	$0.486464\pi$
$912$	5.72779e14	+	1.30854e15i	0.0300618	+	0.0686778i
$913$	−1.68177e16			−0.877361
$914$	−1.53901e14	−	1.48673e15i	−0.00798065	−	0.0770953i
$915$	4.65391e14	+	4.65391e14i	0.0239885	+	0.0239885i
$916$	−8.46895e15	+	1.29518e16i	−0.433915	+	0.663598i
$917$	1.98513e16	−	1.98513e16i	1.01101	−	1.01101i
$918$	−3.06104e14	+	3.76795e14i	−0.0154965	+	0.0190753i
$919$			1.59993e16i			0.805128i	0.915392	+	0.402564i	$0.131881\pi$
$919$			1.59993e16i			0.805128i	−0.915392	+	0.402564i	$0.868119\pi$
$920$	−2.78834e15	−	1.43732e15i	−0.139480	−	0.0718985i
$921$		−	1.25760e15i		−	0.0625339i
$922$	−1.32396e16	−	1.07557e16i	−0.654417	−	0.531640i
$923$	4.42169e16	−	4.42169e16i	2.17260	−	2.17260i
$924$	1.21718e14	+	5.81616e14i	0.00594511	+	0.0284080i
$925$	2.38579e15	+	2.38579e15i	0.115839	+	0.115839i
$926$	−2.24585e16	+	2.32483e15i	−1.08398	+	0.112210i
$927$	3.57797e14			0.0171672
$928$	−1.29373e16	−	3.57565e15i	−0.617063	−	0.170546i
$929$	6.95072e15			0.329567			0.164783	−	0.986330i	$-0.447308\pi$
$929$	6.95072e15			0.329567			0.164783	+	0.986330i	$0.447308\pi$
$930$	3.08504e14	−	3.19353e13i	0.0145414	−	0.00150527i
$931$	7.00853e15	+	7.00853e15i	0.328401	+	0.328401i
$932$	−4.46121e15	−	2.13174e16i	−0.207809	−	0.992993i
$933$	5.75732e14	−	5.75732e14i	0.0266607	−	0.0266607i
$934$	−2.12509e16	−	1.72640e16i	−0.978295	−	0.794755i
$935$		−	3.12588e15i		−	0.143057i
$936$	−1.81456e16	+	3.52018e16i	−0.825570	+	1.60157i
$937$			1.30193e16i			0.588873i	0.955671	+	0.294436i	$0.0951319\pi$
$937$			1.30193e16i			0.588873i	−0.955671	+	0.294436i	$0.904868\pi$
$938$	1.13628e16	−	1.39870e16i	0.510941	−	0.628938i
$939$	−1.31665e15	+	1.31665e15i	−0.0588586	+	0.0588586i
$940$	−7.76723e15	+	1.18786e16i	−0.345194	+	0.527915i
$941$	−1.61753e16	−	1.61753e16i	−0.714678	−	0.714678i	0.252832	−	0.967510i	$-0.418638\pi$
$941$	−1.61753e16	−	1.61753e16i	−0.714678	−	0.714678i	−0.967510	+	0.252832i	$0.918638\pi$
$942$	6.21037e13	+	5.99939e14i	0.00272796	+	0.0263528i
$943$	4.95278e15			0.216289
$944$	1.18142e16	−	3.02085e16i	0.512932	−	1.31155i
$945$	1.26943e15			0.0547943
$946$	−5.10685e14	−	4.93336e15i	−0.0219155	−	0.211710i
$947$	−1.32938e16	−	1.32938e16i	−0.567186	−	0.567186i	0.364153	−	0.931339i	$-0.381358\pi$
$947$	−1.32938e16	−	1.32938e16i	−0.567186	−	0.567186i	−0.931339	+	0.364153i	$0.881358\pi$
$948$	1.02018e15	+	6.67080e14i	0.0432746	+	0.0282965i
$949$	−3.22769e16	+	3.22769e16i	−1.36122	+	1.36122i
$950$	1.22769e16	−	1.51122e16i	0.514766	−	0.633646i
$951$		−	3.81737e14i		−	0.0159137i
$952$	1.67428e15	+	5.23672e15i	0.0693944	+	0.217048i
$953$			3.67846e16i			1.51585i	0.652343	+	0.757924i	$0.273786\pi$
$953$			3.67846e16i			1.51585i	−0.652343	+	0.757924i	$0.726214\pi$
$954$	−2.91883e16	−	2.37122e16i	−1.19589	−	0.971528i
$955$	1.45704e15	−	1.45704e15i	0.0593545	−	0.0593545i
$956$	4.45487e16	−	9.32298e15i	1.80433	−	0.377604i
$957$	−3.85343e14	−	3.85343e14i	−0.0155179	−	0.0155179i
$958$	−4.58227e16	+	4.74342e15i	−1.83472	+	0.189925i
$959$	8.51311e15			0.338911
$960$	−6.66556e14	+	4.74750e14i	−0.0263843	+	0.0187920i
$961$	−2.02332e16			−0.796318
$962$	−1.51061e16	+	1.56374e15i	−0.591140	+	0.0611929i
$963$	1.55913e16	+	1.55913e16i	0.606651	+	0.606651i
$964$	3.64935e16	−	7.63720e15i	1.41186	−	0.295468i
$965$	5.14213e15	−	5.14213e15i	0.197807	−	0.197807i
$966$	1.73868e14	+	1.41248e14i	0.00665035	+	0.00540266i
$967$		−	2.80260e16i		−	1.06590i	−0.846147	−	0.532949i	$-0.821084\pi$
$967$		−	2.80260e16i		−	1.06590i	0.846147	−	0.532949i	$-0.178916\pi$
$968$	−3.52310e15	−	1.10194e16i	−0.133233	−	0.416718i
$969$			5.36583e14i			0.0201770i
$970$	1.25382e16	−	1.54338e16i	0.468805	−	0.577070i
$971$	1.02066e16	−	1.02066e16i	0.379469	−	0.379469i	−0.491441	−	0.870911i	$-0.663530\pi$
$971$	1.02066e16	−	1.02066e16i	0.379469	−	0.379469i	0.870911	+	0.491441i	$0.163530\pi$
$972$	−3.09563e15	−	2.02417e15i	−0.114442	−	0.0748313i
$973$	4.66488e15	+	4.66488e15i	0.171482	+	0.171482i
$974$	1.77297e15	+	1.71273e16i	0.0648076	+	0.626060i
$975$	−1.13007e15			−0.0410753
$976$	−2.69863e16	−	1.05540e16i	−0.975369	−	0.381456i
$977$	3.07634e15			0.110564			0.0552820	−	0.998471i	$-0.482394\pi$
$977$	3.07634e15			0.110564			0.0552820	+	0.998471i	$0.482394\pi$
$978$	−2.18095e14	−	2.10686e15i	−0.00779439	−	0.0752960i
$979$	−1.81885e16	−	1.81885e16i	−0.646387	−	0.646387i
$980$	−3.10761e15	+	4.75255e15i	−0.109820	+	0.167951i
$981$	−2.53604e15	+	2.53604e15i	−0.0891201	+	0.0891201i
$982$	−1.61888e16	+	1.99274e16i	−0.565720	+	0.696367i
$983$		−	1.45877e16i		−	0.506924i	−0.967345	−	0.253462i	$-0.918431\pi$
$983$		−	1.45877e16i		−	0.506924i	0.967345	−	0.253462i	$-0.0815693\pi$
$984$	5.91983e14	−	1.14842e15i	0.0204567	−	0.0396853i
$985$		−	1.99204e16i		−	0.684541i
$986$	−3.91346e15	−	3.17925e15i	−0.133733	−	0.108643i
$987$	7.16646e14	−	7.16646e14i	0.0243534	−	0.0243534i
$988$	1.79518e16	+	8.57806e16i	0.606660	+	2.89885i
$989$	−1.32211e15	−	1.32211e15i	−0.0444311	−	0.0444311i
$990$	1.57872e16	−	1.63424e15i	0.527608	−	0.0546163i
$991$	2.09474e16			0.696184			0.348092	−	0.937460i	$-0.386830\pi$
$991$	2.09474e16			0.696184			0.348092	+	0.937460i	$0.386830\pi$
$992$	−1.18788e16	+	6.73441e15i	−0.392607	+	0.222580i
$993$	4.28977e14			0.0140998
$994$	4.38427e16	−	4.53845e15i	1.43309	−	0.148348i
$995$	2.82342e16	+	2.82342e16i	0.917801	+	0.917801i
$996$	3.38786e14	+	1.61885e15i	0.0109521	+	0.0523335i
$997$	1.98050e16	−	1.98050e16i	0.636723	−	0.636723i	−0.313022	−	0.949746i	$-0.601341\pi$
$997$	1.98050e16	−	1.98050e16i	0.636723	−	0.636723i	0.949746	+	0.313022i	$0.101341\pi$
$998$	3.81344e16	+	3.09799e16i	1.21927	+	0.990519i
$999$		−	9.45233e14i		−	0.0300558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.12.e.a.13.1	yes	42
4.3	odd	2		64.12.e.a.17.10		42
8.3	odd	2		128.12.e.a.33.12		42
8.5	even	2		128.12.e.b.33.10		42
16.3	odd	4		128.12.e.a.97.12		42
16.5	even	4	inner	16.12.e.a.5.1	✓	42
16.11	odd	4		64.12.e.a.49.10		42
16.13	even	4		128.12.e.b.97.10		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.1	✓	42	16.5	even	4	inner
16.12.e.a.13.1	yes	42	1.1	even	1	trivial
64.12.e.a.17.10		42	4.3	odd	2
64.12.e.a.49.10		42	16.11	odd	4
128.12.e.a.33.12		42	8.3	odd	2
128.12.e.a.97.12		42	16.3	odd	4
128.12.e.b.33.10		42	8.5	even	2
128.12.e.b.97.10		42	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-45.0143 + 4.65973i) q^{2} +(13.6026 + 13.6026i) q^{3} +(2004.57 - 419.509i) q^{4} +(-3501.81 + 3501.81i) q^{5} +(-675.697 - 548.928i) q^{6} -37649.1i q^{7} +(-88279.7 + 28224.7i) q^{8} -176777. i q^{9} +O(q^{10})\)	\(q+(-45.0143 + 4.65973i) q^{2} +(13.6026 + 13.6026i) q^{3} +(2004.57 - 419.509i) q^{4} +(-3501.81 + 3501.81i) q^{5} +(-675.697 - 548.928i) q^{6} -37649.1i q^{7} +(-88279.7 + 28224.7i) q^{8} -176777. i q^{9} +(141314. - 173949. i) q^{10} +(-283274. + 283274. i) q^{11} +(32973.9 + 21561.0i) q^{12} +(1.70921e6 + 1.70921e6i) q^{13} +(175435. + 1.69475e6i) q^{14} -95267.6 q^{15} +(3.84233e6 - 1.68187e6i) q^{16} +1.57559e6 q^{17} +(823733. + 7.95749e6i) q^{18} +(1.25182e7 + 1.25182e7i) q^{19} +(-5.55059e6 + 8.48867e6i) q^{20} +(512127. - 512127. i) q^{21} +(1.14314e7 - 1.40714e7i) q^{22} -6.83457e6i q^{23} +(-1.58477e6 - 816906. i) q^{24} +2.43028e7i q^{25} +(-8.49036e7 - 6.89746e7i) q^{26} +(4.81430e6 - 4.81430e6i) q^{27} +(-1.57942e7 - 7.54705e7i) q^{28} +(5.00021e7 + 5.00021e7i) q^{29} +(4.28840e6 - 443921. i) q^{30} +7.19392e7 q^{31} +(-1.65123e8 + 9.36126e7i) q^{32} -7.70654e6 q^{33} +(-7.09241e7 + 7.34183e6i) q^{34} +(1.31840e8 + 1.31840e8i) q^{35} +(-7.41595e7 - 3.54362e8i) q^{36} +(9.81694e7 - 9.81694e7i) q^{37} +(-6.21828e8 - 5.05165e8i) q^{38} +4.64996e7i q^{39} +(2.10301e8 - 4.07976e8i) q^{40} +7.24665e8i q^{41} +(-2.06667e7 + 2.54394e7i) q^{42} +(1.93444e8 - 1.93444e8i) q^{43} +(-4.49008e8 + 6.86679e8i) q^{44} +(6.19039e8 + 6.19039e8i) q^{45} +(3.18473e7 + 3.07653e8i) q^{46} +1.39935e9 q^{47} +(7.51437e7 + 2.93879e7i) q^{48} +5.59869e8 q^{49} +(-1.13245e8 - 1.09397e9i) q^{50} +(2.14322e7 + 2.14322e7i) q^{51} +(4.14328e9 + 2.70922e9i) q^{52} +(-3.32394e9 + 3.32394e9i) q^{53} +(-1.94279e8 + 2.39145e8i) q^{54} -1.98394e9i q^{55} +(1.06263e9 + 3.32365e9i) q^{56} +3.40560e8i q^{57} +(-2.48380e9 - 2.01781e9i) q^{58} +(5.46840e9 - 5.46840e9i) q^{59} +(-1.90971e8 + 3.99656e7i) q^{60} +(-4.88510e9 - 4.88510e9i) q^{61} +(-3.23829e9 + 3.35217e8i) q^{62} -6.65550e9 q^{63} +(6.99667e9 - 4.98333e9i) q^{64} -1.19707e10 q^{65} +(3.46904e8 - 3.59104e7i) q^{66} +(-7.47892e9 - 7.47892e9i) q^{67} +(3.15839e9 - 6.60975e8i) q^{68} +(9.29681e7 - 9.29681e7i) q^{69} +(-6.54903e9 - 5.32035e9i) q^{70} -2.58697e10i q^{71} +(4.98947e9 + 1.56058e10i) q^{72} +1.88841e10i q^{73} +(-3.96158e9 + 4.87647e9i) q^{74} +(-3.30582e8 + 3.30582e8i) q^{75} +(3.03451e10 + 1.98421e10i) q^{76} +(1.06650e10 + 1.06650e10i) q^{77} +(-2.16676e8 - 2.09315e9i) q^{78} +3.09391e10 q^{79} +(-7.56550e9 + 1.93447e10i) q^{80} -3.11845e10 q^{81} +(-3.37675e9 - 3.26203e10i) q^{82} +(2.96846e10 + 2.96846e10i) q^{83} +(8.11755e8 - 1.24144e9i) q^{84} +(-5.51742e9 + 5.51742e9i) q^{85} +(-7.80635e9 + 9.60915e9i) q^{86} +1.36032e9i q^{87} +(1.70120e10 - 3.30026e10i) q^{88} +6.42083e10i q^{89} +(-3.07502e10 - 2.49810e10i) q^{90} +(6.43504e10 - 6.43504e10i) q^{91} +(-2.86716e9 - 1.37004e10i) q^{92} +(9.78562e8 + 9.78562e8i) q^{93} +(-6.29908e10 + 6.52060e9i) q^{94} -8.76724e10 q^{95} +(-3.51948e9 - 9.72725e8i) q^{96} +8.87261e10 q^{97} +(-2.52021e10 + 2.60884e9i) q^{98} +(5.00763e10 + 5.00763e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8}+O(q^{10}) \) 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8	\( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8} - 988948 q^{10} - 540846 q^{11} + 2300260 q^{12} - 2 q^{13} - 1829956 q^{14} - 6075004 q^{15} - 3721448 q^{16} - 4 q^{17} - 32219106 q^{18} - 11291290 q^{19} + 68655164 q^{20} + 354292 q^{21} - 85011388 q^{22} - 66180944 q^{24} + 305685384 q^{26} - 66463304 q^{27} - 322075880 q^{28} + 77673206 q^{29} + 290643636 q^{30} + 343549808 q^{31} + 404698568 q^{32} - 4 q^{33} - 882461836 q^{34} - 434731684 q^{35} + 1854387628 q^{36} - 522762058 q^{37} - 1276252832 q^{38} - 483241016 q^{40} + 2372079160 q^{42} + 3824193658 q^{43} - 2657283740 q^{44} + 97301954 q^{45} - 1032658964 q^{46} - 4586900144 q^{47} - 1058870552 q^{48} - 8474257474 q^{49} + 6515930886 q^{50} + 7074245796 q^{51} - 13915491564 q^{52} - 2100608058 q^{53} + 4385621536 q^{54} + 12910845976 q^{56} - 21491153128 q^{58} + 955824746 q^{59} + 25615752768 q^{60} + 2150827022 q^{61} - 15814519760 q^{62} + 27758037828 q^{63} + 9674332160 q^{64} - 1884965292 q^{65} + 10932459412 q^{66} - 3186519018 q^{67} + 13817664656 q^{68} - 16193060732 q^{69} - 27206453120 q^{70} - 20773133628 q^{72} + 14141420908 q^{74} + 28890034486 q^{75} - 11786004940 q^{76} - 22711870540 q^{77} + 37031200508 q^{78} + 48011833792 q^{79} - 8952586328 q^{80} - 90656394430 q^{81} - 81555388352 q^{82} + 55713221118 q^{83} + 61178517160 q^{84} - 84575506252 q^{85} + 10047297860 q^{86} - 162855622152 q^{88} + 160133627736 q^{90} - 147369662716 q^{91} - 169766721928 q^{92} - 69689773328 q^{93} + 160320530128 q^{94} + 375702304500 q^{95} + 230764310192 q^{96} - 4 q^{97} - 108887063494 q^{98} - 286271331106 q^{99}+O(q^{100}) \) 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8 - 988948 * q^10 - 540846 * q^11 + 2300260 * q^12 - 2 * q^13 - 1829956 * q^14 - 6075004 * q^15 - 3721448 * q^16 - 4 * q^17 - 32219106 * q^18 - 11291290 * q^19 + 68655164 * q^20 + 354292 * q^21 - 85011388 * q^22 - 66180944 * q^24 + 305685384 * q^26 - 66463304 * q^27 - 322075880 * q^28 + 77673206 * q^29 + 290643636 * q^30 + 343549808 * q^31 + 404698568 * q^32 - 4 * q^33 - 882461836 * q^34 - 434731684 * q^35 + 1854387628 * q^36 - 522762058 * q^37 - 1276252832 * q^38 - 483241016 * q^40 + 2372079160 * q^42 + 3824193658 * q^43 - 2657283740 * q^44 + 97301954 * q^45 - 1032658964 * q^46 - 4586900144 * q^47 - 1058870552 * q^48 - 8474257474 * q^49 + 6515930886 * q^50 + 7074245796 * q^51 - 13915491564 * q^52 - 2100608058 * q^53 + 4385621536 * q^54 + 12910845976 * q^56 - 21491153128 * q^58 + 955824746 * q^59 + 25615752768 * q^60 + 2150827022 * q^61 - 15814519760 * q^62 + 27758037828 * q^63 + 9674332160 * q^64 - 1884965292 * q^65 + 10932459412 * q^66 - 3186519018 * q^67 + 13817664656 * q^68 - 16193060732 * q^69 - 27206453120 * q^70 - 20773133628 * q^72 + 14141420908 * q^74 + 28890034486 * q^75 - 11786004940 * q^76 - 22711870540 * q^77 + 37031200508 * q^78 + 48011833792 * q^79 - 8952586328 * q^80 - 90656394430 * q^81 - 81555388352 * q^82 + 55713221118 * q^83 + 61178517160 * q^84 - 84575506252 * q^85 + 10047297860 * q^86 - 162855622152 * q^88 + 160133627736 * q^90 - 147369662716 * q^91 - 169766721928 * q^92 - 69689773328 * q^93 + 160320530128 * q^94 + 375702304500 * q^95 + 230764310192 * q^96 - 4 * q^97 - 108887063494 * q^98 - 286271331106 * q^99

Introduction

L-functions

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