LMFDB - Embedded newform 16.12.e.a.13.14

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			13.14
Character	$\chi$	$=$	16.13
Dual form			16.12.e.a.5.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(25.1148 + 37.6464i) q^{2} +(367.824 + 367.824i) q^{3} +(-786.499 + 1890.96i) q^{4} +(-502.344 + 502.344i) q^{5} +(-4609.43 + 23085.1i) q^{6} +33063.2i q^{7} +(-90940.4 + 17882.1i) q^{8} +93442.1i q^{9} +O(q^{10})$	\(q+(25.1148 + 37.6464i) q^{2} +(367.824 + 367.824i) q^{3} +(-786.499 + 1890.96i) q^{4} +(-502.344 + 502.344i) q^{5} +(-4609.43 + 23085.1i) q^{6} +33063.2i q^{7} +(-90940.4 + 17882.1i) q^{8} +93442.1i q^{9} +(-31527.7 - 6295.18i) q^{10} +(335681. - 335681. i) q^{11} +(-984833. + 406247. i) q^{12} +(568061. + 568061. i) q^{13} +(-1.24471e6 + 830373. i) q^{14} -369548. q^{15} +(-2.95714e6 - 2.97447e6i) q^{16} -6.78457e6 q^{17} +(-3.51776e6 + 2.34678e6i) q^{18} +(1.33879e6 + 1.33879e6i) q^{19} +(-554819. - 1.34500e6i) q^{20} +(-1.21614e7 + 1.21614e7i) q^{21} +(2.10677e7 + 4.20662e6i) q^{22} -1.07133e6i q^{23} +(-4.00276e7 - 2.68726e7i) q^{24} +4.83234e7i q^{25} +(-7.11873e6 + 3.56522e7i) q^{26} +(3.07887e7 - 3.07887e7i) q^{27} +(-6.25211e7 - 2.60041e7i) q^{28} +(5.01359e7 + 5.01359e7i) q^{29} +(-9.28112e6 - 1.39122e7i) q^{30} +2.95969e8 q^{31} +(3.77101e7 - 1.86029e8i) q^{32} +2.46943e8 q^{33} +(-1.70393e8 - 2.55414e8i) q^{34} +(-1.66091e7 - 1.66091e7i) q^{35} +(-1.76695e8 - 7.34921e7i) q^{36} +(5.11883e8 - 5.11883e8i) q^{37} +(-1.67772e7 + 8.40240e7i) q^{38} +4.17893e8i q^{39} +(3.67004e7 - 5.46664e7i) q^{40} +9.31803e8i q^{41} +(-7.63265e8 - 1.52402e8i) q^{42} +(-1.27362e9 + 1.27362e9i) q^{43} +(3.70746e8 + 8.98771e8i) q^{44} +(-4.69401e7 - 4.69401e7i) q^{45} +(4.03318e7 - 2.69063e7i) q^{46} -1.80739e7 q^{47} +(6.37366e6 - 2.18179e9i) q^{48} +8.84154e8 q^{49} +(-1.81920e9 + 1.21363e9i) q^{50} +(-2.49553e9 - 2.49553e9i) q^{51} +(-1.52096e9 + 6.27401e8i) q^{52} +(2.29607e9 - 2.29607e9i) q^{53} +(1.93233e9 + 3.85832e8i) q^{54} +3.37255e8i q^{55} +(-5.91240e8 - 3.00678e9i) q^{56} +9.84878e8i q^{57} +(-6.28284e8 + 3.14658e9i) q^{58} +(-4.81453e8 + 4.81453e8i) q^{59} +(2.90649e8 - 6.98801e8i) q^{60} +(1.30887e9 + 1.30887e9i) q^{61} +(7.43318e9 + 1.11422e10i) q^{62} -3.08949e9 q^{63} +(7.95039e9 - 3.25242e9i) q^{64} -5.70724e8 q^{65} +(6.20191e9 + 9.29651e9i) q^{66} +(-9.42251e9 - 9.42251e9i) q^{67} +(5.33606e9 - 1.28293e10i) q^{68} +(3.94062e8 - 3.94062e8i) q^{69} +(2.08139e8 - 1.04240e9i) q^{70} -1.74203e10i q^{71} +(-1.67094e9 - 8.49767e9i) q^{72} -8.91310e9i q^{73} +(3.21263e10 + 6.41472e9i) q^{74} +(-1.77745e10 + 1.77745e10i) q^{75} +(-3.58455e9 + 1.47864e9i) q^{76} +(1.10987e10 + 1.10987e10i) q^{77} +(-1.57322e10 + 1.04953e10i) q^{78} -4.07466e10 q^{79} +(2.97971e9 + 8.70463e6i) q^{80} +3.92026e10 q^{81} +(-3.50790e10 + 2.34020e10i) q^{82} +(1.16461e10 + 1.16461e10i) q^{83} +(-1.34318e10 - 3.25617e10i) q^{84} +(3.40819e9 - 3.40819e9i) q^{85} +(-7.99336e10 - 1.59605e10i) q^{86} +3.68824e10i q^{87} +(-2.45243e10 + 3.65297e10i) q^{88} -7.96706e10i q^{89} +(5.88235e8 - 2.94601e9i) q^{90} +(-1.87819e10 + 1.87819e10i) q^{91} +(2.02585e9 + 8.42602e8i) q^{92} +(1.08864e11 + 1.08864e11i) q^{93} +(-4.53922e8 - 6.80417e8i) q^{94} -1.34507e9 q^{95} +(8.22966e10 - 5.45552e10i) q^{96} -1.03397e10 q^{97} +(2.22053e10 + 3.32852e10i) q^{98} +(3.13667e10 + 3.13667e10i) 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 $

$2$	25.1148	+	37.6464i	0.554963	+	0.831875i
$2$	25.1148	+	37.6464i	0.554963	+	0.831875i
$3$	367.824	+	367.824i	0.873923	+	0.873923i	0.992897	−	0.118974i	$-0.0379606\pi$
$3$	367.824	+	367.824i	0.873923	+	0.873923i	−0.118974	+	0.992897i	$0.537961\pi$
$4$	−786.499	+	1890.96i	−0.384032	+	0.923320i
$5$	−502.344	+	502.344i	−0.0718896	+	0.0718896i	−0.742137	−	0.670248i	$-0.766188\pi$
$5$	−502.344	+	502.344i	−0.0718896	+	0.0718896i	0.670248	+	0.742137i	$0.266188\pi$
$6$	−4609.43	+	23085.1i	−0.242000	+	1.21199i
$7$			33063.2i			0.743542i	0.928325	+	0.371771i	$0.121249\pi$
$7$			33063.2i			0.743542i	−0.928325	+	0.371771i	$0.878751\pi$
$8$	−90940.4	+	17882.1i	−0.981210	+	0.192941i
$9$			93442.1i			0.527483i
$10$	−31527.7	−	6295.18i	−0.0996993	−	0.0199071i
$11$	335681.	−	335681.i	0.628444	−	0.628444i	−0.319232	−	0.947677i	$-0.603425\pi$
$11$	335681.	−	335681.i	0.628444	−	0.628444i	0.947677	+	0.319232i	$0.103425\pi$
$12$	−984833.	+	406247.i	−1.14253	+	0.471295i
$13$	568061.	+	568061.i	0.424333	+	0.424333i	0.886692	−	0.462360i	$-0.152997\pi$
$13$	568061.	+	568061.i	0.424333	+	0.424333i	−0.462360	+	0.886692i	$0.652997\pi$
$14$	−1.24471e6	+	830373.i	−0.618534	+	0.412638i
$15$	−369548.			−0.125652
$16$	−2.95714e6	−	2.97447e6i	−0.705038	−	0.709169i
$17$	−6.78457e6			−1.15892			−0.579460	−	0.815001i	$-0.696736\pi$
$17$	−6.78457e6			−1.15892			−0.579460	+	0.815001i	$0.696736\pi$
$18$	−3.51776e6	+	2.34678e6i	−0.438800	+	0.292734i
$19$	1.33879e6	+	1.33879e6i	0.124042	+	0.124042i	0.766402	−	0.642361i	$-0.222045\pi$
$19$	1.33879e6	+	1.33879e6i	0.124042	+	0.124042i	−0.642361	+	0.766402i	$0.722045\pi$
$20$	−554819.	−	1.34500e6i	−0.0387691	−	0.0939850i
$21$	−1.21614e7	+	1.21614e7i	−0.649798	+	0.649798i
$22$	2.10677e7	+	4.20662e6i	0.871550	+	0.174024i
$23$		−	1.07133e6i		−	0.0347074i	−0.999849	−	0.0173537i	$-0.994476\pi$
$23$		−	1.07133e6i		−	0.0347074i	0.999849	−	0.0173537i	$-0.00552412\pi$
$24$	−4.00276e7	−	2.68726e7i	−1.02612	−	0.688887i
$25$			4.83234e7i			0.989664i
$26$	−7.11873e6	+	3.56522e7i	−0.117503	+	0.588481i
$27$	3.07887e7	−	3.07887e7i	0.412943	−	0.412943i
$28$	−6.25211e7	−	2.60041e7i	−0.686526	−	0.285544i
$29$	5.01359e7	+	5.01359e7i	0.453899	+	0.453899i	0.896647	−	0.442747i	$-0.145996\pi$
$29$	5.01359e7	+	5.01359e7i	0.453899	+	0.453899i	−0.442747	+	0.896647i	$0.645996\pi$
$30$	−9.28112e6	−	1.39122e7i	−0.0697322	−	0.104527i
$31$	2.95969e8			1.85676			0.928382	−	0.371628i	$-0.121200\pi$
$31$	2.95969e8			1.85676			0.928382	+	0.371628i	$0.121200\pi$
$32$	3.77101e7	−	1.86029e8i	0.198670	−	0.980066i
$33$	2.46943e8			1.09842
$34$	−1.70393e8	−	2.55414e8i	−0.643157	−	0.964076i
$35$	−1.66091e7	−	1.66091e7i	−0.0534529	−	0.0534529i
$36$	−1.76695e8	−	7.34921e7i	−0.487036	−	0.202571i
$37$	5.11883e8	−	5.11883e8i	1.21356	−	1.21356i	0.243711	−	0.969848i	$-0.421635\pi$
$37$	5.11883e8	−	5.11883e8i	1.21356	−	1.21356i	0.969848	−	0.243711i	$-0.0783649\pi$
$38$	−1.67772e7	+	8.40240e7i	−0.0343487	+	0.172026i
$39$			4.17893e8i			0.741669i
$40$	3.67004e7	−	5.46664e7i	0.0566684	−	0.0844093i
$41$			9.31803e8i			1.25607i	0.778186	+	0.628034i	$0.216140\pi$
$41$			9.31803e8i			1.25607i	−0.778186	+	0.628034i	$0.783860\pi$
$42$	−7.63265e8	−	1.52402e8i	−0.901165	−	0.179937i
$43$	−1.27362e9	+	1.27362e9i	−1.32118	+	1.32118i	−0.408358	+	0.912822i	$0.633899\pi$
$43$	−1.27362e9	+	1.27362e9i	−1.32118	+	1.32118i	−0.912822	+	0.408358i	$0.866101\pi$
$44$	3.70746e8	+	8.98771e8i	0.338912	+	0.821598i
$45$	−4.69401e7	−	4.69401e7i	−0.0379206	−	0.0379206i
$46$	4.03318e7	−	2.69063e7i	0.0288722	−	0.0192613i
$47$	−1.80739e7			−0.0114951			−0.00574756	−	0.999983i	$-0.501830\pi$
$47$	−1.80739e7			−0.0114951			−0.00574756	+	0.999983i	$0.501830\pi$
$48$	6.37366e6	−	2.18179e9i	0.00361046	−	1.23591i
$49$	8.84154e8			0.447146
$50$	−1.81920e9	+	1.21363e9i	−0.823277	+	0.549227i
$51$	−2.49553e9	−	2.49553e9i	−1.01281	−	1.01281i
$52$	−1.52096e9	+	6.27401e8i	−0.554752	+	0.228837i
$53$	2.29607e9	−	2.29607e9i	0.754168	−	0.754168i	−0.221086	−	0.975254i	$-0.570960\pi$
$53$	2.29607e9	−	2.29607e9i	0.754168	−	0.754168i	0.975254	+	0.221086i	$0.0709602\pi$
$54$	1.93233e9	+	3.85832e8i	0.572685	+	0.114349i
$55$			3.37255e8i			0.0903572i
$56$	−5.91240e8	−	3.00678e9i	−0.143460	−	0.729571i
$57$			9.84878e8i			0.216806i
$58$	−6.28284e8	+	3.14658e9i	−0.125690	+	0.629485i
$59$	−4.81453e8	+	4.81453e8i	−0.0876734	+	0.0876734i	−0.749583	−	0.661910i	$-0.769746\pi$
$59$	−4.81453e8	+	4.81453e8i	−0.0876734	+	0.0876734i	0.661910	+	0.749583i	$0.269746\pi$
$60$	2.90649e8	−	6.98801e8i	0.0482545	−	0.116017i
$61$	1.30887e9	+	1.30887e9i	0.198419	+	0.198419i	0.799322	−	0.600903i	$-0.205192\pi$
$61$	1.30887e9	+	1.30887e9i	0.198419	+	0.198419i	−0.600903	+	0.799322i	$0.705192\pi$
$62$	7.43318e9	+	1.11422e10i	1.03043	+	1.54460i
$63$	−3.08949e9			−0.392206
$64$	7.95039e9	−	3.25242e9i	0.925548	−	0.378631i
$65$	−5.70724e8			−0.0610103
$66$	6.20191e9	+	9.29651e9i	0.609585	+	0.913752i
$67$	−9.42251e9	−	9.42251e9i	−0.852619	−	0.852619i	0.137836	−	0.990455i	$-0.455985\pi$
$67$	−9.42251e9	−	9.42251e9i	−0.852619	−	0.852619i	−0.990455	+	0.137836i	$0.955985\pi$
$68$	5.33606e9	−	1.28293e10i	0.445063	−	1.07005i
$69$	3.94062e8	−	3.94062e8i	0.0303316	−	0.0303316i
$70$	2.08139e8	−	1.04240e9i	0.0148018	−	0.0741305i
$71$		−	1.74203e10i		−	1.14587i	−0.819601	−	0.572934i	$-0.805805\pi$
$71$		−	1.74203e10i		−	1.14587i	0.819601	−	0.572934i	$-0.194195\pi$
$72$	−1.67094e9	−	8.49767e9i	−0.101773	−	0.517572i
$73$		−	8.91310e9i		−	0.503215i	−0.967829	−	0.251607i	$-0.919041\pi$
$73$		−	8.91310e9i		−	0.503215i	0.967829	−	0.251607i	$-0.0809591\pi$
$74$	3.21263e10	+	6.41472e9i	1.68301	+	0.336049i
$75$	−1.77745e10	+	1.77745e10i	−0.864890	+	0.864890i
$76$	−3.58455e9	+	1.47864e9i	−0.162166	+	0.0668941i
$77$	1.10987e10	+	1.10987e10i	0.467274	+	0.467274i
$78$	−1.57322e10	+	1.04953e10i	−0.616976	+	0.411599i
$79$	−4.07466e10			−1.48985			−0.744924	−	0.667149i	$-0.767514\pi$
$79$	−4.07466e10			−1.48985			−0.744924	+	0.667149i	$0.767514\pi$
$80$	2.97971e9	+	8.70463e6i	0.101667	+	0.000296999i
$81$	3.92026e10			1.24924
$82$	−3.50790e10	+	2.34020e10i	−1.04489	+	0.697071i
$83$	1.16461e10	+	1.16461e10i	0.324527	+	0.324527i	0.850501	−	0.525974i	$-0.176299\pi$
$83$	1.16461e10	+	1.16461e10i	0.324527	+	0.324527i	−0.525974	+	0.850501i	$0.676299\pi$
$84$	−1.34318e10	−	3.25617e10i	−0.350428	−	0.849515i
$85$	3.40819e9	−	3.40819e9i	0.0833143	−	0.0833143i
$86$	−7.99336e10	−	1.59605e10i	−1.83226	−	0.365851i
$87$			3.68824e10i			0.793346i
$88$	−2.45243e10	+	3.65297e10i	−0.495383	+	0.737889i
$89$		−	7.96706e10i		−	1.51235i	−0.654368	−	0.756176i	$-0.727065\pi$
$89$		−	7.96706e10i		−	1.51235i	0.654368	−	0.756176i	$-0.272935\pi$
$90$	5.88235e8	−	2.94601e9i	0.0105007	−	0.0525897i
$91$	−1.87819e10	+	1.87819e10i	−0.315509	+	0.315509i
$92$	2.02585e9	+	8.42602e8i	0.0320460	+	0.0133288i
$93$	1.08864e11	+	1.08864e11i	1.62267	+	1.62267i
$94$	−4.53922e8	−	6.80417e8i	−0.00637937	−	0.00956251i
$95$	−1.34507e9			−0.0178346
$96$	8.22966e10	−	5.45552e10i	1.03013	−	0.682880i
$97$	−1.03397e10			−0.122254			−0.0611269	−	0.998130i	$-0.519469\pi$
$97$	−1.03397e10			−0.122254			−0.0611269	+	0.998130i	$0.519469\pi$
$98$	2.22053e10	+	3.32852e10i	0.248149	+	0.371970i
$99$	3.13667e10	+	3.13667e10i	0.331494	+	0.331494i
$100$	−9.13776e10	−	3.80063e10i	−0.913776	−	0.380063i
$101$	−3.36018e10	+	3.36018e10i	−0.318123	+	0.318123i	−0.848046	−	0.529923i	$-0.822221\pi$
$101$	−3.36018e10	+	3.36018e10i	−0.318123	+	0.318123i	0.529923	+	0.848046i	$0.322221\pi$
$102$	3.12730e10	−	1.56622e11i	0.280459	−	1.40460i
$103$		−	9.27041e10i		−	0.787942i	−0.919123	−	0.393971i	$-0.871101\pi$
$103$		−	9.27041e10i		−	0.787942i	0.919123	−	0.393971i	$-0.128899\pi$
$104$	−6.18179e10	−	4.15016e10i	−0.498231	−	0.334489i
$105$		−	1.22184e10i		−	0.0934275i
$106$	1.44104e11	+	2.87735e10i	1.04591	+	0.208838i
$107$	2.88146e10	−	2.88146e10i	0.198610	−	0.198610i	−0.600794	−	0.799404i	$-0.705149\pi$
$107$	2.88146e10	−	2.88146e10i	0.198610	−	0.198610i	0.799404	+	0.600794i	$0.205149\pi$
$108$	3.40049e10	+	8.24354e10i	0.222695	+	0.539862i
$109$	−2.21468e10	−	2.21468e10i	−0.137868	−	0.137868i	0.634804	−	0.772673i	$-0.281081\pi$
$109$	−2.21468e10	−	2.21468e10i	−0.137868	−	0.137868i	−0.772673	+	0.634804i	$0.781081\pi$
$110$	−1.26964e10	+	8.47006e9i	−0.0751659	+	0.0501449i
$111$	3.76565e11			2.12111
$112$	9.83455e10	−	9.77725e10i	0.527297	−	0.524225i
$113$	−1.71538e11			−0.875849			−0.437924	−	0.899012i	$-0.644286\pi$
$113$	−1.71538e11			−0.875849			−0.437924	+	0.899012i	$0.644286\pi$
$114$	−3.70771e10	+	2.47350e10i	−0.180355	+	0.120319i
$115$	5.38178e8	+	5.38178e8i	0.00249510	+	0.00249510i
$116$	−1.34237e11	+	5.53731e10i	−0.593406	+	0.244782i
$117$	−5.30808e10	+	5.30808e10i	−0.223829	+	0.223829i
$118$	−3.02165e10	−	6.03339e9i	−0.121589	−	0.0242778i
$119$		−	2.24319e11i		−	0.861705i
$120$	3.36069e10	−	6.60832e9i	0.123291	−	0.0242434i
$121$			5.99484e10i			0.210116i
$122$	−1.64023e10	+	8.21462e10i	−0.0549446	+	0.275175i
$123$	−3.42740e11	+	3.42740e11i	−1.09771	+	1.09771i
$124$	−2.32779e11	+	5.59665e11i	−0.713057	+	1.71439i
$125$	−4.88035e10	−	4.88035e10i	−0.143036	−	0.143036i
$126$	−7.75918e10	−	1.16308e11i	−0.217660	−	0.326266i
$127$	5.54635e11			1.48966			0.744830	−	0.667254i	$-0.232531\pi$
$127$	5.54635e11			1.48966			0.744830	+	0.667254i	$0.232531\pi$
$128$	3.22114e11	+	2.17620e11i	0.828619	+	0.559814i
$129$	−9.36933e11			−2.30922
$130$	−1.43336e10	−	2.14857e10i	−0.0338584	−	0.0507529i
$131$	−4.50085e11	−	4.50085e11i	−1.01930	−	1.01930i	−0.999810	−	0.0194915i	$-0.993795\pi$
$131$	−4.50085e11	−	4.50085e11i	−1.01930	−	1.01930i	−0.0194915	−	0.999810i	$-0.506205\pi$
$132$	−1.94220e11	+	4.66959e11i	−0.421830	+	1.01420i
$133$	−4.42646e10	+	4.42646e10i	−0.0922301	+	0.0922301i
$134$	1.18079e11	−	5.91367e11i	0.236101	−	1.18244i
$135$			3.09330e10i			0.0593727i
$136$	6.16992e11	−	1.21323e11i	1.13714	−	0.223603i
$137$		−	7.75745e11i		−	1.37327i	−0.727002	−	0.686635i	$-0.759087\pi$
$137$		−	7.75745e11i		−	1.37327i	0.727002	−	0.686635i	$-0.240913\pi$
$138$	2.47318e10	+	4.93824e9i	0.0420650	+	0.00839918i
$139$	−3.80649e11	+	3.80649e11i	−0.622219	+	0.622219i	−0.946098	−	0.323880i	$-0.895013\pi$
$139$	−3.80649e11	+	3.80649e11i	−0.622219	+	0.622219i	0.323880	+	0.946098i	$0.395013\pi$
$140$	4.44701e10	−	1.83441e10i	0.0698818	−	0.0288265i
$141$	−6.64802e9	−	6.64802e9i	−0.0100459	−	0.0100459i
$142$	6.55811e11	−	4.37507e11i	0.953220	−	0.635915i
$143$	3.81374e11			0.533339
$144$	2.77941e11	−	2.76322e11i	0.374075	−	0.371896i
$145$	−5.03709e10			−0.0652613
$146$	3.35546e11	−	2.23850e11i	0.418612	−	0.279265i
$147$	3.25213e11	+	3.25213e11i	0.390771	+	0.390771i
$148$	5.65354e11	+	1.37054e12i	0.654457	+	1.58655i
$149$	−1.21482e11	+	1.21482e11i	−0.135515	+	0.135515i	−0.771610	−	0.636095i	$-0.780549\pi$
$149$	−1.21482e11	+	1.21482e11i	−0.135515	+	0.135515i	0.636095	+	0.771610i	$0.280549\pi$
$150$	−1.11555e12	−	2.22744e11i	−1.19946	−	0.239499i
$151$		−	4.18981e11i		−	0.434331i	−0.976135	−	0.217166i	$-0.930319\pi$
$151$		−	4.18981e11i		−	0.434331i	0.976135	−	0.217166i	$-0.0696812\pi$
$152$	−1.45691e11	−	9.78097e10i	−0.145644	−	0.0977783i
$153$		−	6.33965e11i		−	0.611311i
$154$	−1.39084e11	+	6.96565e11i	−0.129394	+	0.648034i
$155$	−1.48678e11	+	1.48678e11i	−0.133482	+	0.133482i
$156$	−7.90219e11	−	3.28672e11i	−0.684797	−	0.284825i
$157$	1.64950e12	+	1.64950e12i	1.38008	+	1.38008i	0.844456	+	0.535626i	$0.179924\pi$
$157$	1.64950e12	+	1.64950e12i	1.38008	+	1.38008i	0.535626	+	0.844456i	$0.320076\pi$
$158$	−1.02334e12	−	1.53396e12i	−0.826810	−	1.23937i
$159$	1.68910e12			1.31817
$160$	7.45070e10	+	1.12394e11i	0.0561743	+	0.0847389i
$161$	3.54217e10			0.0258064
$162$	9.84564e11	+	1.47584e12i	0.693284	+	1.03922i
$163$	1.07698e12	+	1.07698e12i	0.733121	+	0.733121i	0.971237	−	0.238116i	$-0.0765299\pi$
$163$	1.07698e12	+	1.07698e12i	0.733121	+	0.733121i	−0.238116	+	0.971237i	$0.576530\pi$
$164$	−1.76200e12	−	7.32862e11i	−1.15975	−	0.482371i
$165$	−1.24050e11	+	1.24050e11i	−0.0789653	+	0.0789653i
$166$	−1.45944e11	+	7.30922e11i	−0.0898655	+	0.450066i
$167$		−	1.59845e12i		−	0.952268i	−0.879373	−	0.476134i	$-0.842038\pi$
$167$		−	1.59845e12i		−	0.952268i	0.879373	−	0.476134i	$-0.157962\pi$
$168$	8.88493e11	−	1.32344e12i	0.512216	−	0.762961i
$169$		−	1.14677e12i		−	0.639883i
$170$	2.13902e11	+	4.27101e10i	0.115543	+	0.0230708i
$171$	−1.25099e11	+	1.25099e11i	−0.0654299	+	0.0654299i
$172$	−1.40666e12	−	3.41005e12i	−0.712495	−	1.72725i
$173$	1.45486e12	+	1.45486e12i	0.713785	+	0.713785i	0.967325	−	0.253540i	$-0.0815949\pi$
$173$	1.45486e12	+	1.45486e12i	0.713785	+	0.713785i	−0.253540	+	0.967325i	$0.581595\pi$
$174$	−1.38849e12	+	9.26291e11i	−0.659965	+	0.440278i
$175$	−1.59773e12			−0.735856
$176$	−1.99113e12	−	5.81668e9i	−0.888751	−	0.00259631i
$177$	−3.54180e11			−0.153240
$178$	2.99931e12	−	2.00091e12i	1.25809	−	0.839299i
$179$	−1.30891e12	−	1.30891e12i	−0.532376	−	0.532376i	0.388903	−	0.921279i	$-0.372854\pi$
$179$	−1.30891e12	−	1.30891e12i	−0.532376	−	0.532376i	−0.921279	+	0.388903i	$0.872854\pi$
$180$	1.25680e11	−	5.18434e10i	0.0495756	−	0.0204501i
$181$	−2.38152e12	+	2.38152e12i	−0.911219	+	0.911219i	−0.996368	−	0.0851488i	$-0.972863\pi$
$181$	−2.38152e12	+	2.38152e12i	−0.911219	+	0.911219i	0.0851488	+	0.996368i	$0.472863\pi$
$182$	−1.17877e12	−	2.35368e11i	−0.437560	−	0.0873683i
$183$			9.62869e11i			0.346806i
$184$	1.91577e10	+	9.74275e10i	0.00669647	+	0.0340552i
$185$			5.14282e11i			0.174485i
$186$	−1.36425e12	+	6.83245e12i	−0.449337	+	2.25038i
$187$	−2.27745e12	+	2.27745e12i	−0.728316	+	0.728316i
$188$	1.42151e10	−	3.41770e10i	0.00441450	−	0.0106137i
$189$	1.01797e12	+	1.01797e12i	0.307040	+	0.307040i
$190$	−3.37810e10	−	5.06369e10i	−0.00989755	−	0.0148362i
$191$	−3.52280e12			−1.00278			−0.501388	−	0.865223i	$-0.667177\pi$
$191$	−3.52280e12			−1.00278			−0.501388	+	0.865223i	$0.667177\pi$
$192$	4.12066e12	+	1.72803e12i	1.13975	+	0.477963i
$193$	4.01739e12			1.07989			0.539944	−	0.841701i	$-0.318445\pi$
$193$	4.01739e12			1.07989			0.539944	+	0.841701i	$0.318445\pi$
$194$	−2.59678e11	−	3.89251e11i	−0.0678463	−	0.101700i
$195$	−2.09926e11	−	2.09926e11i	−0.0533183	−	0.0533183i
$196$	−6.95386e11	+	1.67190e12i	−0.171719	+	0.412859i
$197$	3.98851e12	−	3.98851e12i	0.957737	−	0.957737i	−0.0414057	−	0.999142i	$-0.513184\pi$
$197$	3.98851e12	−	3.98851e12i	0.957737	−	0.957737i	0.999142	+	0.0414057i	$0.0131836\pi$
$198$	−3.93076e11	+	1.96861e12i	−0.0917947	+	0.459728i
$199$		−	1.41250e11i		−	0.0320846i	−0.999871	−	0.0160423i	$-0.994893\pi$
$199$		−	1.41250e11i		−	0.0320846i	0.999871	−	0.0160423i	$-0.00510665\pi$
$200$	−8.64126e11	−	4.39455e12i	−0.190947	−	0.971068i
$201$		−	6.93165e12i		−	1.49025i
$202$	−2.10889e12	−	4.21086e11i	−0.441186	−	0.0880923i
$203$	−1.65765e12	+	1.65765e12i	−0.337493	+	0.337493i
$204$	6.68167e12	−	2.75621e12i	1.32409	−	0.546194i
$205$	−4.68086e11	−	4.68086e11i	−0.0902982	−	0.0902982i
$206$	3.48997e12	−	2.32824e12i	0.655469	−	0.437278i
$207$	1.00108e11			0.0183076
$208$	9.84338e9	−	3.36952e12i	0.00175306	−	0.600095i
$209$	8.98812e11			0.155907
$210$	4.59980e11	−	3.06863e11i	0.0777200	−	0.0518488i
$211$	−3.64182e12	−	3.64182e12i	−0.599466	−	0.599466i	0.340704	−	0.940170i	$-0.389334\pi$
$211$	−3.64182e12	−	3.64182e12i	−0.599466	−	0.599466i	−0.940170	+	0.340704i	$0.889334\pi$
$212$	2.53592e12	+	6.14763e12i	0.406713	+	0.985963i
$213$	6.40761e12	−	6.40761e12i	1.00140	−	1.00140i
$214$	1.80843e12	+	3.61093e11i	0.275440	+	0.0549976i
$215$		−	1.27959e12i		−	0.189958i
$216$	−2.24937e12	+	3.35050e12i	−0.325510	+	0.484858i
$217$			9.78567e12i			1.38058i
$218$	2.77535e11	−	1.38996e12i	0.0381775	−	0.191201i
$219$	3.27845e12	−	3.27845e12i	0.439771	−	0.439771i
$220$	−6.37734e11	−	2.65250e11i	−0.0834286	−	0.0347001i
$221$	−3.85405e12	−	3.85405e12i	−0.491768	−	0.491768i
$222$	9.45735e12	+	1.41763e13i	1.17714	+	1.76450i
$223$	−5.31451e12			−0.645337			−0.322668	−	0.946512i	$-0.604580\pi$
$223$	−5.31451e12			−0.645337			−0.322668	+	0.946512i	$0.604580\pi$
$224$	6.15070e12	+	1.24682e12i	0.728720	+	0.147720i
$225$	−4.51544e12			−0.522031
$226$	−4.30814e12	−	6.45779e12i	−0.486064	−	0.728597i
$227$	−4.88964e12	−	4.88964e12i	−0.538437	−	0.538437i	0.384633	−	0.923070i	$-0.374328\pi$
$227$	−4.88964e12	−	4.88964e12i	−0.538437	−	0.538437i	−0.923070	+	0.384633i	$0.874328\pi$
$228$	−1.86236e12	−	7.74605e11i	−0.200181	−	0.0832605i
$229$	−7.07133e12	+	7.07133e12i	−0.742003	+	0.742003i	−0.972963	−	0.230960i	$-0.925813\pi$
$229$	−7.07133e12	+	7.07133e12i	−0.742003	+	0.742003i	0.230960	+	0.972963i	$0.425813\pi$
$230$	−6.74424e9	+	3.37766e10i	−0.000690924	+	0.00346030i
$231$			8.16472e12i			0.816724i
$232$	−5.45592e12	−	3.66284e12i	−0.532947	−	0.357795i
$233$			1.54810e13i			1.47687i	0.674324	+	0.738435i	$0.264435\pi$
$233$			1.54810e13i			1.47687i	−0.674324	+	0.738435i	$0.735565\pi$
$234$	−3.33141e12	−	6.65189e11i	−0.310414	−	0.0619809i
$235$	9.07932e9	−	9.07932e9i	0.000826380	−	0.000826380i
$236$	−5.31746e11	−	1.28907e12i	−0.0472811	−	0.114620i
$237$	−1.49876e13	−	1.49876e13i	−1.30201	−	1.30201i
$238$	8.44481e12	−	5.63373e12i	0.716831	−	0.478214i
$239$	1.47869e13			1.22656			0.613280	−	0.789866i	$-0.289850\pi$
$239$	1.47869e13			1.22656			0.613280	+	0.789866i	$0.289850\pi$
$240$	1.09281e12	+	1.09921e12i	0.0885895	+	0.0891086i
$241$	−3.70990e12			−0.293946			−0.146973	−	0.989140i	$-0.546953\pi$
$241$	−3.70990e12			−0.293946			−0.146973	+	0.989140i	$0.546953\pi$
$242$	−2.25684e12	+	1.50559e12i	−0.174790	+	0.116606i
$243$	8.96555e12	+	8.96555e12i	0.678801	+	0.678801i
$244$	−3.50445e12	+	1.44560e12i	−0.259403	+	0.107005i
$245$	−4.44149e11	+	4.44149e11i	−0.0321452	+	0.0321452i
$246$	−2.15107e13	−	4.29508e12i	−1.52234	−	0.303968i
$247$			1.52103e12i			0.105270i
$248$	−2.69155e13	+	5.29255e12i	−1.82188	+	0.358246i
$249$			8.56743e12i			0.567223i
$250$	6.11587e11	−	3.06296e12i	0.0396085	−	0.198368i
$251$	1.64619e13	−	1.64619e13i	1.04297	−	1.04297i	0.0439391	−	0.999034i	$-0.486009\pi$
$251$	1.64619e13	−	1.64619e13i	1.04297	−	1.04297i	0.999034	−	0.0439391i	$-0.0139908\pi$
$252$	2.42988e12	−	5.84210e12i	0.150620	−	0.362131i
$253$	−3.59626e11	−	3.59626e11i	−0.0218116	−	0.0218116i
$254$	1.39295e13	+	2.08800e13i	0.826706	+	1.23921i
$255$	2.50723e12			0.145621
$256$	−1.02783e11	+	1.75919e13i	−0.00584255	+	0.999983i
$257$	2.20187e13			1.22506			0.612532	−	0.790446i	$-0.290151\pi$
$257$	2.20187e13			1.22506			0.612532	+	0.790446i	$0.290151\pi$
$258$	−2.35308e13	−	3.52721e13i	−1.28153	−	1.92098i
$259$	1.69245e13	+	1.69245e13i	0.902331	+	0.902331i
$260$	4.48874e11	−	1.07922e12i	0.0234299	−	0.0563320i
$261$	−4.68480e12	+	4.68480e12i	−0.239424	+	0.239424i
$262$	5.64030e12	−	2.82479e13i	0.282257	−	1.41361i
$263$			4.64085e12i			0.227426i	0.993514	+	0.113713i	$0.0362745\pi$
$263$			4.64085e12i			0.227426i	−0.993514	+	0.113713i	$0.963726\pi$
$264$	−2.24571e13	+	4.41587e12i	−1.07779	+	0.211931i
$265$			2.30684e12i			0.108434i
$266$	−2.77810e12	−	5.54708e11i	−0.127908	−	0.0255397i
$267$	2.93047e13	−	2.93047e13i	1.32168	−	1.32168i
$268$	2.52284e13	−	1.04068e13i	1.11467	−	0.459807i
$269$	−3.23177e12	−	3.23177e12i	−0.139895	−	0.139895i	0.633691	−	0.773586i	$-0.281539\pi$
$269$	−3.23177e12	−	3.23177e12i	−0.139895	−	0.139895i	−0.773586	+	0.633691i	$0.781539\pi$
$270$	−1.16452e12	+	7.76875e11i	−0.0493906	+	0.0329496i
$271$	−3.04462e13			−1.26533			−0.632663	−	0.774427i	$-0.718038\pi$
$271$	−3.04462e13			−1.26533			−0.632663	+	0.774427i	$0.718038\pi$
$272$	2.00630e13	+	2.01805e13i	0.817083	+	0.821870i
$273$	−1.38169e13			−0.551461
$274$	2.92040e13	−	1.94826e13i	1.14239	−	0.762114i
$275$	1.62212e13	+	1.62212e13i	0.621949	+	0.621949i
$276$	4.35226e11	+	1.05508e12i	0.0163574	+	0.0396540i
$277$	1.12987e13	−	1.12987e13i	0.416282	−	0.416282i	−0.467638	−	0.883920i	$-0.654895\pi$
$277$	1.12987e13	−	1.12987e13i	0.416282	−	0.416282i	0.883920	+	0.467638i	$0.154895\pi$
$278$	−2.38899e13	−	4.77014e12i	−0.862916	−	0.172300i
$279$			2.76559e13i			0.979412i
$280$	1.80744e12	+	1.21343e12i	0.0627618	+	0.0421353i
$281$		−	2.01696e13i		−	0.686772i	−0.939194	−	0.343386i	$-0.888426\pi$
$281$		−	2.01696e13i		−	0.686772i	0.939194	−	0.343386i	$-0.111574\pi$
$282$	8.33104e10	−	4.17237e11i	0.00278182	−	0.0139320i
$283$	−2.67176e12	+	2.67176e12i	−0.0874929	+	0.0874929i	−0.749499	−	0.662006i	$-0.769705\pi$
$283$	−2.67176e12	+	2.67176e12i	−0.0874929	+	0.0874929i	0.662006	+	0.749499i	$0.269705\pi$
$284$	3.29411e13	+	1.37010e13i	1.05800	+	0.440051i
$285$	−4.94748e11	−	4.94748e11i	−0.0155861	−	0.0155861i
$286$	9.57813e12	+	1.43574e13i	0.295983	+	0.443672i
$287$	−3.08084e13			−0.933938
$288$	1.73829e13	+	3.52371e12i	0.516969	+	0.104795i
$289$	1.17585e13			0.343095
$290$	−1.26505e12	−	1.89628e12i	−0.0362176	−	0.0542893i
$291$	−3.80318e12	−	3.80318e12i	−0.106840	−	0.106840i
$292$	1.68543e13	+	7.01014e12i	0.464628	+	0.193251i
$293$	−3.85320e13	+	3.85320e13i	−1.04244	+	1.04244i	−0.0433791	+	0.999059i	$0.513812\pi$
$293$	−3.85320e13	+	3.85320e13i	−1.04244	+	1.04244i	−0.999059	+	0.0433791i	$0.986188\pi$
$294$	−4.07545e12	+	2.04107e13i	−0.108209	+	0.541936i
$295$		−	4.83710e11i		−	0.0126056i
$296$	−3.73973e13	+	5.57044e13i	−0.956611	+	1.42490i
$297$		−	2.06703e13i		−	0.519024i
$298$	−7.62436e12	−	1.52237e12i	−0.187938	−	0.0375258i
$299$	6.08583e11	−	6.08583e11i	0.0147275	−	0.0147275i
$300$	−1.96312e13	−	4.75905e13i	−0.466424	−	1.13072i
$301$	−4.21098e13	−	4.21098e13i	−0.982352	−	0.982352i
$302$	1.57731e13	−	1.05226e13i	0.361309	−	0.241038i
$303$	−2.47191e13			−0.556031
$304$	2.31986e10	−	7.94119e12i	0.000512456	−	0.175421i
$305$	−1.31501e12			−0.0285285
$306$	2.38665e13	−	1.59219e13i	0.508534	−	0.339255i
$307$	−3.24055e13	−	3.24055e13i	−0.678199	−	0.678199i	0.281393	−	0.959593i	$-0.409203\pi$
$307$	−3.24055e13	−	3.24055e13i	−0.678199	−	0.678199i	−0.959593	+	0.281393i	$0.909203\pi$
$308$	−2.97162e13	+	1.22580e13i	−0.610892	+	0.251995i
$309$	3.40988e13	−	3.40988e13i	0.688601	−	0.688601i
$310$	−9.33121e12	−	1.86318e12i	−0.185118	−	0.0369628i
$311$		−	5.32038e13i		−	1.03696i	−0.855091	−	0.518478i	$-0.826499\pi$
$311$		−	5.32038e13i		−	1.03696i	0.855091	−	0.518478i	$-0.173501\pi$
$312$	−7.47282e12	−	3.80034e13i	−0.143098	−	0.727733i
$313$			7.41435e13i			1.39502i	0.716577	+	0.697508i	$0.245708\pi$
$313$			7.41435e13i			1.39502i	−0.716577	+	0.697508i	$0.754292\pi$
$314$	−2.06709e13	+	1.03525e14i	−0.382161	+	1.91395i
$315$	1.55199e12	−	1.55199e12i	0.0281955	−	0.0281955i
$316$	3.20471e13	−	7.70501e13i	0.572150	−	1.37561i
$317$	6.45432e12	+	6.45432e12i	0.113246	+	0.113246i	0.761459	−	0.648213i	$-0.224483\pi$
$317$	6.45432e12	+	6.45432e12i	0.113246	+	0.113246i	−0.648213	+	0.761459i	$0.724483\pi$
$318$	4.24214e13	+	6.35885e13i	0.731535	+	1.09655i
$319$	3.36593e13			0.570501
$320$	−2.36000e12	+	5.62767e12i	−0.0393176	+	0.0937569i
$321$	2.11974e13			0.347140
$322$	8.89607e11	+	1.33350e12i	0.0143216	+	0.0214677i
$323$	−9.08312e12	−	9.08312e12i	−0.143754	−	0.143754i
$324$	−3.08328e13	+	7.41305e13i	−0.479751	+	1.15345i
$325$	−2.74507e13	+	2.74507e13i	−0.419947	+	0.419947i
$326$	−1.34963e13	+	6.75924e13i	−0.203010	+	1.01672i
$327$		−	1.62922e13i		−	0.240973i
$328$	−1.66626e13	−	8.47386e13i	−0.242347	−	1.23247i
$329$		−	5.97580e11i		−	0.00854710i
$330$	−7.78554e12	−	1.55455e12i	−0.109512	−	0.0218665i
$331$	−5.80148e13	+	5.80148e13i	−0.802574	+	0.802574i	−0.983497	−	0.180923i	$-0.942091\pi$
$331$	−5.80148e13	+	5.80148e13i	−0.802574	+	0.802574i	0.180923	+	0.983497i	$0.442091\pi$
$332$	−3.11819e13	+	1.28626e13i	−0.424271	+	0.175013i
$333$	4.78314e13	+	4.78314e13i	0.640132	+	0.640132i
$334$	6.01759e13	−	4.01447e13i	0.792168	−	0.528473i
$335$	9.46668e12			0.122589
$336$	7.21369e13	+	2.10733e11i	0.918949	+	0.00268453i
$337$	−7.30225e13			−0.915150			−0.457575	−	0.889171i	$-0.651282\pi$
$337$	−7.30225e13			−0.915150			−0.457575	+	0.889171i	$0.651282\pi$
$338$	4.31719e13	−	2.88009e13i	0.532303	−	0.355111i
$339$	−6.30958e13	−	6.30958e13i	−0.765425	−	0.765425i
$340$	3.76421e12	+	9.12528e12i	0.0449303	+	0.108921i
$341$	9.93510e13	−	9.93510e13i	1.16687	−	1.16687i
$342$	−7.85138e12	−	1.56770e12i	−0.0907407	−	0.0181184i
$343$			9.46096e13i			1.07601i
$344$	9.30482e13	−	1.38598e14i	1.04145	−	1.55127i
$345$			3.95910e11i			0.00436105i
$346$	−1.82317e13	+	9.13086e13i	−0.197656	+	0.989904i
$347$	−4.07174e13	+	4.07174e13i	−0.434478	+	0.434478i	−0.890149	−	0.455670i	$-0.849400\pi$
$347$	−4.07174e13	+	4.07174e13i	−0.434478	+	0.434478i	0.455670	+	0.890149i	$0.349400\pi$
$348$	−6.97430e13	−	2.90079e13i	−0.732512	−	0.304671i
$349$	7.50423e13	+	7.50423e13i	0.775829	+	0.775829i	0.979119	−	0.203290i	$-0.0651633\pi$
$349$	7.50423e13	+	7.50423e13i	0.775829	+	0.775829i	−0.203290	+	0.979119i	$0.565163\pi$
$350$	−4.01265e13	−	6.01486e13i	−0.408373	−	0.612140i
$351$	3.49797e13			0.350451
$352$	−4.97878e13	−	7.51049e13i	−0.491064	−	0.740770i
$353$	1.92000e14			1.86441			0.932205	−	0.361931i	$-0.117882\pi$
$353$	1.92000e14			1.86441			0.932205	+	0.361931i	$0.117882\pi$
$354$	−8.89514e12	−	1.33336e13i	−0.0850423	−	0.127476i
$355$	8.75099e12	+	8.75099e12i	0.0823761	+	0.0823761i
$356$	1.50654e14	+	6.26608e13i	1.39638	+	0.580792i
$357$	8.25101e13	−	8.25101e13i	0.753064	−	0.753064i
$358$	1.64028e13	−	8.21487e13i	0.147421	−	0.738319i
$359$		−	6.04811e13i		−	0.535304i	−0.963516	−	0.267652i	$-0.913752\pi$
$359$		−	6.04811e13i		−	0.535304i	0.963516	−	0.267652i	$-0.0862477\pi$
$360$	5.10814e12	+	3.42936e12i	0.0445245	+	0.0298916i
$361$		−	1.12906e14i		−	0.969227i
$362$	−1.49467e14	−	2.98444e13i	−1.26371	−	0.252328i
$363$	−2.20505e13	+	2.20505e13i	−0.183625	+	0.183625i
$364$	−2.07439e13	−	5.02877e13i	−0.170150	−	0.412481i
$365$	4.47744e12	+	4.47744e12i	0.0361759	+	0.0361759i
$366$	−3.62485e13	+	2.41822e13i	−0.288499	+	0.192464i
$367$	7.73489e13			0.606444			0.303222	−	0.952920i	$-0.401938\pi$
$367$	7.73489e13			0.606444			0.303222	+	0.952920i	$0.401938\pi$
$368$	−3.18665e12	+	3.16809e12i	−0.0246134	+	0.0244700i
$369$	−8.70696e13			−0.662555
$370$	−1.93609e13	+	1.29161e13i	−0.145149	+	0.0968325i
$371$	7.59154e13	+	7.59154e13i	0.560755	+	0.560755i
$372$	−2.91480e14	+	1.20236e14i	−2.12140	+	0.875084i
$373$	−7.33207e13	+	7.33207e13i	−0.525809	+	0.525809i	−0.919320	−	0.393511i	$-0.871260\pi$
$373$	−7.33207e13	+	7.33207e13i	−0.525809	+	0.525809i	0.393511	+	0.919320i	$0.371260\pi$
$374$	−1.42935e14	−	2.85401e13i	−1.01006	−	0.201680i
$375$		−	3.59022e13i		−	0.250005i
$376$	1.64365e12	−	3.23200e11i	0.0112791	−	0.00221788i
$377$			5.69605e13i			0.385209i
$378$	−1.27568e13	+	6.38890e13i	−0.0850233	+	0.425815i
$379$	−1.92106e14	+	1.92106e14i	−1.26190	+	1.26190i	−0.311734	+	0.950169i	$0.600910\pi$
$379$	−1.92106e14	+	1.92106e14i	−1.26190	+	1.26190i	−0.950169	+	0.311734i	$0.899090\pi$
$380$	1.05789e12	−	2.54346e12i	0.00684907	−	0.0164671i
$381$	2.04008e14	+	2.04008e14i	1.30185	+	1.30185i
$382$	−8.84741e13	−	1.32620e14i	−0.556503	−	0.834184i
$383$	1.28679e14			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$383$	1.28679e14			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$384$	3.84355e13	+	1.98527e14i	0.234915	+	1.21338i
$385$	−1.11507e13			−0.0671844
$386$	1.00896e14	+	1.51240e14i	0.599298	+	0.898333i
$387$	−1.19009e14	−	1.19009e14i	−0.696900	−	0.696900i
$388$	8.13214e12	−	1.95519e13i	0.0469494	−	0.112879i
$389$	−2.00352e14	+	2.00352e14i	−1.14044	+	1.14044i	−0.152068	+	0.988370i	$0.548593\pi$
$389$	−2.00352e14	+	2.00352e14i	−1.14044	+	1.14044i	−0.988370	+	0.152068i	$0.951407\pi$
$390$	2.63071e12	−	1.31752e13i	0.0147645	−	0.0739438i
$391$			7.26854e12i			0.0402230i
$392$	−8.04053e13	+	1.58106e13i	−0.438744	+	0.0862728i
$393$		−	3.31104e14i		−	1.78158i
$394$	2.50323e14	+	4.99825e13i	1.32823	+	0.265209i
$395$	2.04688e13	−	2.04688e13i	0.107105	−	0.107105i
$396$	−8.39830e13	+	3.46433e13i	−0.433379	+	0.178770i
$397$	−1.54966e14	−	1.54966e14i	−0.788657	−	0.788657i	0.192617	−	0.981274i	$-0.438303\pi$
$397$	−1.54966e14	−	1.54966e14i	−0.788657	−	0.788657i	−0.981274	+	0.192617i	$0.938303\pi$
$398$	5.31756e12	−	3.54746e12i	0.0266904	−	0.0178058i
$399$	−3.25632e13			−0.161204
$400$	1.43737e14	−	1.42899e14i	0.701839	−	0.697751i
$401$	−3.58680e14			−1.72748			−0.863740	−	0.503938i	$-0.831884\pi$
$401$	−3.58680e14			−1.72748			−0.863740	+	0.503938i	$0.831884\pi$
$402$	2.60951e14	−	1.74087e14i	1.23970	−	0.827032i
$403$	1.68128e14	+	1.68128e14i	0.787886	+	0.787886i
$404$	−3.71119e13	−	8.99675e13i	−0.171560	−	0.415899i
$405$	−1.96932e13	+	1.96932e13i	−0.0898077	+	0.0898077i
$406$	−1.04036e14	−	2.07730e13i	−0.468048	−	0.0934560i
$407$		−	3.43658e14i		−	1.52531i
$408$	2.71570e14	+	1.82319e14i	1.18919	+	0.798365i
$409$			4.56728e13i			0.197324i	0.995121	+	0.0986618i	$0.0314562\pi$
$409$			4.56728e13i			0.197324i	−0.995121	+	0.0986618i	$0.968544\pi$
$410$	5.86587e12	−	2.93776e13i	0.0250047	−	0.125229i
$411$	2.85338e14	−	2.85338e14i	1.20013	−	1.20013i
$412$	1.75300e14	+	7.29116e13i	0.727522	+	0.302595i
$413$	−1.59184e13	−	1.59184e13i	−0.0651888	−	0.0651888i
$414$	2.51418e12	+	3.76869e12i	0.0101600	+	0.0152296i
$415$	−1.17007e13			−0.0466602
$416$	1.27097e14	−	8.42541e13i	0.500177	−	0.331572i
$417$	−2.80024e14			−1.08754
$418$	2.25734e13	+	3.38370e13i	0.0865224	+	0.129695i
$419$	2.11630e13	+	2.11630e13i	0.0800572	+	0.0800572i	0.746001	−	0.665944i	$-0.231971\pi$
$419$	2.11630e13	+	2.11630e13i	0.0800572	+	0.0800572i	−0.665944	+	0.746001i	$0.731971\pi$
$420$	2.31046e13	+	9.60979e12i	0.0862634	+	0.0358792i
$421$	−1.92706e14	+	1.92706e14i	−0.710138	+	0.710138i	−0.966564	−	0.256426i	$-0.917455\pi$
$421$	−1.92706e14	+	1.92706e14i	−0.710138	+	0.710138i	0.256426	+	0.966564i	$0.417455\pi$
$422$	4.56379e13	−	2.28565e14i	0.166000	−	0.831362i
$423$		−	1.68886e12i		−	0.00606349i
$424$	−1.67747e14	+	2.49864e14i	−0.594488	+	0.885508i
$425$		−	3.27854e14i		−	1.14694i
$426$	4.02149e14	+	8.02977e13i	1.38878	+	0.277300i
$427$	−4.32754e13	+	4.32754e13i	−0.147533	+	0.147533i
$428$	3.18245e13	+	7.71498e13i	0.107108	+	0.259653i
$429$	1.40279e14	+	1.40279e14i	0.466097	+	0.466097i
$430$	4.81718e13	−	3.21365e13i	0.158022	−	0.105420i
$431$	3.15533e14			1.02193			0.510964	−	0.859602i	$-0.329289\pi$
$431$	3.15533e14			1.02193			0.510964	+	0.859602i	$0.329289\pi$
$432$	−1.82627e14	−	5.33507e11i	−0.583987	−	0.00170600i
$433$	9.43423e13			0.297867			0.148934	−	0.988847i	$-0.452416\pi$
$433$	9.43423e13			0.297867			0.148934	+	0.988847i	$0.452416\pi$
$434$	−3.68395e14	+	2.45765e14i	−1.14847	+	0.766171i
$435$	−1.85276e13	−	1.85276e13i	−0.0570334	−	0.0570334i
$436$	5.92970e13	−	2.44602e13i	0.180243	−	0.0743507i
$437$	1.43429e12	−	1.43429e12i	0.00430516	−	0.00430516i
$438$	2.05759e14	+	4.10843e13i	0.609891	+	0.121778i
$439$		−	4.26118e12i		−	0.0124731i	−0.999981	−	0.00623655i	$-0.998015\pi$
$439$		−	4.26118e12i		−	0.0124731i	0.999981	−	0.00623655i	$-0.00198517\pi$
$440$	−6.03083e12	−	3.06701e13i	−0.0174336	−	0.0886595i
$441$			8.26172e13i			0.235862i
$442$	4.82975e13	−	2.41885e14i	0.136177	−	0.682002i
$443$	1.07675e13	−	1.07675e13i	0.0299843	−	0.0299843i	−0.691956	−	0.721940i	$-0.743251\pi$
$443$	1.07675e13	−	1.07675e13i	0.0299843	−	0.0299843i	0.721940	+	0.691956i	$0.243251\pi$
$444$	−2.96168e14	+	7.12070e14i	−0.814577	+	1.95847i
$445$	4.00220e13	+	4.00220e13i	0.108722	+	0.108722i
$446$	−1.33473e14	−	2.00072e14i	−0.358138	−	0.536840i
$447$	−8.93681e13			−0.236860
$448$	1.07535e14	+	2.62865e14i	0.281528	+	0.688183i
$449$	1.49573e14			0.386811			0.193405	−	0.981119i	$-0.438047\pi$
$449$	1.49573e14			0.386811			0.193405	+	0.981119i	$0.438047\pi$
$450$	−1.13404e14	−	1.69990e14i	−0.289708	−	0.434265i
$451$	3.12788e14	+	3.12788e14i	0.789368	+	0.789368i
$452$	1.34914e14	−	3.24371e14i	0.336354	−	0.808688i
$453$	1.54111e14	−	1.54111e14i	0.379572	−	0.379572i
$454$	6.12752e13	−	3.06880e14i	0.149100	−	0.746725i
$455$		−	1.88700e13i		−	0.0453637i
$456$	−1.76117e13	−	8.95653e13i	−0.0418307	−	0.212732i
$457$		−	5.73073e13i		−	0.134484i	−0.997737	−	0.0672420i	$-0.978580\pi$
$457$		−	5.73073e13i		−	0.134484i	0.997737	−	0.0672420i	$-0.0214200\pi$
$458$	−4.43804e14	−	8.86152e13i	−1.02904	−	0.205470i
$459$	−2.08888e14	+	2.08888e14i	−0.478568	+	0.478568i
$460$	−1.44095e12	+	5.94396e11i	−0.00326197	+	0.00134557i
$461$	−5.04689e14	−	5.04689e14i	−1.12893	−	1.12893i	−0.990351	−	0.138583i	$-0.955745\pi$
$461$	−5.04689e14	−	5.04689e14i	−1.12893	−	1.12893i	−0.138583	−	0.990351i	$-0.544255\pi$
$462$	−3.07372e14	+	2.05055e14i	−0.679412	+	0.453251i
$463$	−1.04606e14			−0.228487			−0.114243	−	0.993453i	$-0.536444\pi$
$463$	−1.04606e14			−0.228487			−0.114243	+	0.993453i	$0.536444\pi$
$464$	8.68755e11	−	2.97387e14i	0.00187520	−	0.641908i
$465$	−1.09375e14			−0.233306
$466$	−5.82805e14	+	3.88802e14i	−1.22857	+	0.819608i
$467$	−5.83143e14	−	5.83143e14i	−1.21488	−	1.21488i	−0.969404	−	0.245472i	$-0.921057\pi$
$467$	−5.83143e14	−	5.83143e14i	−1.21488	−	1.21488i	−0.245472	−	0.969404i	$-0.578943\pi$
$468$	−5.86256e13	−	1.42122e14i	−0.120708	−	0.292623i
$469$	3.11538e14	−	3.11538e14i	0.633958	−	0.633958i
$470$	5.69828e11	+	1.13779e11i	0.00114606	+	0.000228835i
$471$			1.21345e15i			2.41217i
$472$	3.51741e13	−	5.23930e13i	0.0691103	−	0.102942i
$473$			8.55057e14i			1.66058i
$474$	1.87819e14	−	9.40637e14i	0.360543	−	1.80568i
$475$	−6.46949e13	+	6.46949e13i	−0.122760	+	0.122760i
$476$	4.24179e14	+	1.76427e14i	0.795629	+	0.330923i
$477$	2.14550e14	+	2.14550e14i	0.397811	+	0.397811i
$478$	3.71369e14	+	5.56673e14i	0.680695	+	1.02034i
$479$	−9.29337e12			−0.0168394			−0.00841972	−	0.999965i	$-0.502680\pi$
$479$	−9.29337e12			−0.0168394			−0.00841972	+	0.999965i	$0.502680\pi$
$480$	−1.39357e13	+	6.87467e13i	−0.0249633	+	0.123147i
$481$	5.81561e14			1.02991
$482$	−9.31731e13	−	1.39664e14i	−0.163129	−	0.244527i
$483$	1.30289e13	+	1.30289e13i	0.0225528	+	0.0225528i
$484$	−1.13360e14	−	4.71494e13i	−0.194004	−	0.0806912i
$485$	5.19407e12	−	5.19407e12i	0.00878878	−	0.00878878i
$486$	−1.12353e14	+	5.62688e14i	−0.187968	+	0.941386i
$487$		−	2.67485e14i		−	0.442477i	−0.975220	−	0.221238i	$-0.928990\pi$
$487$		−	2.67485e14i		−	0.442477i	0.975220	−	0.221238i	$-0.0710099\pi$
$488$	−1.42435e14	−	9.56239e13i	−0.232974	−	0.156407i
$489$			7.92278e14i			1.28138i
$490$	−2.78753e13	−	5.56591e12i	−0.0445801	−	0.00890139i
$491$	3.39834e13	−	3.39834e13i	0.0537425	−	0.0537425i	−0.679725	−	0.733467i	$-0.737901\pi$
$491$	3.39834e13	−	3.39834e13i	0.0537425	−	0.0537425i	0.733467	+	0.679725i	$0.237901\pi$
$492$	−3.78542e14	−	9.17670e14i	−0.591979	−	1.43509i
$493$	−3.40150e14	−	3.40150e14i	−0.526033	−	0.526033i
$494$	−5.72612e13	+	3.82003e13i	−0.0875714	+	0.0584209i
$495$	−3.15138e13			−0.0476619
$496$	−8.75222e14	−	8.80351e14i	−1.30909	−	1.31676i
$497$	5.75970e14			0.852001
$498$	−3.22533e14	+	2.15169e14i	−0.471859	+	0.314788i
$499$	1.03300e14	+	1.03300e14i	0.149468	+	0.149468i	0.777880	−	0.628412i	$-0.216295\pi$
$499$	1.03300e14	+	1.03300e14i	0.149468	+	0.149468i	−0.628412	+	0.777880i	$0.716295\pi$
$500$	1.30669e14	−	5.39015e13i	0.186999	−	0.0771376i
$501$	5.87949e14	−	5.87949e14i	0.832209	−	0.832209i
$502$	1.03316e15	+	2.06294e14i	1.44644	+	0.288812i
$503$		−	1.03966e15i		−	1.43969i	−0.694136	−	0.719843i	$-0.744214\pi$
$503$		−	1.03966e15i		−	1.43969i	0.694136	−	0.719843i	$-0.255786\pi$
$504$	2.80960e14	−	5.52467e13i	0.384836	−	0.0756726i
$505$		−	3.37594e13i		−	0.0457395i
$506$	4.50670e12	−	2.25705e13i	0.00603991	−	0.0302492i
$507$	4.21811e14	−	4.21811e14i	0.559209	−	0.559209i
$508$	−4.36220e14	+	1.04879e15i	−0.572078	+	1.37543i
$509$	5.30191e14	+	5.30191e14i	0.687835	+	0.687835i	0.961753	−	0.273918i	$-0.0883196\pi$
$509$	5.30191e14	+	5.30191e14i	0.687835	+	0.687835i	−0.273918	+	0.961753i	$0.588320\pi$
$510$	6.29684e13	+	9.43880e13i	0.0808140	+	0.121138i
$511$	2.94695e14			0.374161
$512$	−6.64852e14	+	4.37946e14i	−0.835103	+	0.550093i
$513$	8.24391e13			0.102444
$514$	5.52993e14	+	8.28923e14i	0.679865	+	1.01910i
$515$	4.65693e13	+	4.65693e13i	0.0566448	+	0.0566448i
$516$	7.36897e14	−	1.77170e15i	0.886815	−	2.13215i
$517$	−6.06706e12	+	6.06706e12i	−0.00722405	+	0.00722405i
$518$	−2.12091e14	+	1.06220e15i	−0.249867	+	1.25139i
$519$			1.07026e15i			1.24759i
$520$	5.19019e13	−	1.02058e13i	0.0598639	−	0.0117714i
$521$			7.25048e14i			0.827484i	0.910394	+	0.413742i	$0.135778\pi$
$521$			7.25048e14i			0.827484i	−0.910394	+	0.413742i	$0.864222\pi$
$522$	−2.94023e14	−	5.87081e13i	−0.332043	−	0.0662996i
$523$	6.35477e14	−	6.35477e14i	0.710134	−	0.710134i	−0.256429	−	0.966563i	$-0.582546\pi$
$523$	6.35477e14	−	6.35477e14i	0.710134	−	0.710134i	0.966563	+	0.256429i	$0.0825459\pi$
$524$	1.20508e15	−	4.97101e14i	1.33259	−	0.549696i
$525$	−5.87682e14	−	5.87682e14i	−0.643082	−	0.643082i
$526$	−1.74711e14	+	1.16554e14i	−0.189190	+	0.126213i
$527$	−2.00802e15			−2.15184
$528$	−7.30246e14	−	7.34525e14i	−0.774431	−	0.778969i
$529$	9.51662e14			0.998795
$530$	−8.68440e13	+	5.79356e13i	−0.0902033	+	0.0601767i
$531$	−4.49880e13	−	4.49880e13i	−0.0462463	−	0.0462463i
$532$	−4.88885e13	−	1.18517e14i	−0.0497385	−	0.120577i
$533$	−5.29321e14	+	5.29321e14i	−0.532991	+	0.532991i
$534$	1.83920e15	+	3.67236e14i	1.83295	+	0.365989i
$535$			2.89497e13i			0.0285560i
$536$	1.02538e15	+	6.88392e14i	1.00110	+	0.672094i
$537$		−	9.62898e14i		−	0.930511i
$538$	4.04993e13	−	2.02830e14i	0.0387387	−	0.194012i
$539$	2.96793e14	−	2.96793e14i	0.281006	−	0.281006i
$540$	−5.84931e13	−	2.43288e13i	−0.0548199	−	0.0228010i
$541$	−1.14149e15	−	1.14149e15i	−1.05898	−	1.05898i	−0.998148	−	0.0608311i	$-0.980625\pi$
$541$	−1.14149e15	−	1.14149e15i	−1.05898	−	1.05898i	−0.0608311	−	0.998148i	$-0.519375\pi$
$542$	−7.64650e14	−	1.14619e15i	−0.702209	−	1.05259i
$543$	−1.75196e15			−1.59267
$544$	−2.55847e14	+	1.26213e15i	−0.230243	+	1.13582i
$545$	2.22506e13			0.0198226
$546$	−3.47007e14	−	5.20155e14i	−0.306041	−	0.458747i
$547$	−7.92097e14	−	7.92097e14i	−0.691589	−	0.691589i	0.270993	−	0.962581i	$-0.412648\pi$
$547$	−7.92097e14	−	7.92097e14i	−0.691589	−	0.691589i	−0.962581	+	0.270993i	$0.912648\pi$
$548$	1.46690e15	+	6.10122e14i	1.26797	+	0.527380i
$549$	−1.22304e14	+	1.22304e14i	−0.104663	+	0.104663i
$550$	−2.03279e14	+	1.01806e15i	−0.172225	+	0.862542i
$551$			1.34243e14i			0.112605i
$552$	−2.87895e13	+	4.28829e13i	−0.0239094	+	0.0356138i
$553$		−	1.34721e15i		−	1.10776i
$554$	7.09116e14	+	1.41590e14i	0.577316	+	0.115274i
$555$	−1.89165e14	+	1.89165e14i	−0.152486	+	0.152486i
$556$	−4.20411e14	−	1.01917e15i	−0.335554	−	0.813459i
$557$	1.32985e15	+	1.32985e15i	1.05099	+	1.05099i	0.998628	+	0.0523642i	$0.0166757\pi$
$557$	1.32985e15	+	1.32985e15i	1.05099	+	1.05099i	0.0523642	+	0.998628i	$0.483324\pi$
$558$	−1.04115e15	+	6.94572e14i	−0.814748	+	0.543537i
$559$	−1.44698e15			−1.12124
$560$	−2.87803e11	+	9.85187e13i	−0.000220831	+	0.0755935i
$561$	−1.67540e15			−1.27299
$562$	7.59312e14	−	5.06555e14i	0.571309	−	0.381133i
$563$	6.09588e14	+	6.09588e14i	0.454193	+	0.454193i	0.896743	−	0.442551i	$-0.145926\pi$
$563$	6.09588e14	+	6.09588e14i	0.454193	+	0.454193i	−0.442551	+	0.896743i	$0.645926\pi$
$564$	1.77998e13	−	7.34247e12i	0.0131335	−	0.00541760i
$565$	8.61711e13	−	8.61711e13i	0.0629644	−	0.0629644i
$566$	−1.67683e14	−	3.34815e13i	−0.121338	−	0.0242279i
$567$			1.29616e15i			0.928865i
$568$	3.11512e14	+	1.58421e15i	0.221085	+	1.12434i
$569$			1.37610e15i			0.967234i	0.875280	+	0.483617i	$0.160677\pi$
$569$			1.37610e15i			0.967234i	−0.875280	+	0.483617i	$0.839323\pi$
$570$	6.19999e12	−	3.10509e13i	0.00431598	−	0.0216154i
$571$	−4.57011e14	+	4.57011e14i	−0.315085	+	0.315085i	−0.846876	−	0.531790i	$-0.821519\pi$
$571$	−4.57011e14	+	4.57011e14i	−0.315085	+	0.315085i	0.531790	+	0.846876i	$0.321519\pi$
$572$	−2.99950e14	+	7.21163e14i	−0.204820	+	0.492442i
$573$	−1.29577e15	−	1.29577e15i	−0.876349	−	0.876349i
$574$	−7.73744e14	−	1.15982e15i	−0.518301	−	0.776920i
$575$	5.17705e13			0.0343486
$576$	3.03913e14	+	7.42901e14i	0.199722	+	0.488211i
$577$	1.10753e15			0.720921			0.360460	−	0.932775i	$-0.382620\pi$
$577$	1.10753e15			0.720921			0.360460	+	0.932775i	$0.382620\pi$
$578$	2.95312e14	+	4.42665e14i	0.190405	+	0.285412i
$579$	1.47769e15	+	1.47769e15i	0.943740	+	0.943740i
$580$	3.96166e13	−	9.52493e13i	0.0250625	−	0.0602570i
$581$	−3.85057e14	+	3.85057e14i	−0.241299	+	0.241299i
$582$	4.76600e13	−	2.38692e14i	0.0295854	−	0.148170i
$583$		−	1.54149e15i		−	0.947905i
$584$	1.59385e14	+	8.10561e14i	0.0970907	+	0.493759i
$585$		−	5.33297e13i		−	0.0321819i
$586$	−2.41831e15	−	4.82869e14i	−1.44569	−	0.288664i
$587$	7.20142e14	−	7.20142e14i	0.426490	−	0.426490i	−0.460941	−	0.887431i	$-0.652488\pi$
$587$	7.20142e14	−	7.20142e14i	0.426490	−	0.426490i	0.887431	+	0.460941i	$0.152488\pi$
$588$	−8.70744e14	+	3.59185e14i	−0.510876	+	0.210738i
$589$	3.96240e14	+	3.96240e14i	0.230316	+	0.230316i
$590$	1.82099e13	−	1.21483e13i	0.0104863	−	0.00699565i
$591$	2.93414e15			1.67398
$592$	−3.03629e15	−	8.86991e12i	−1.71622	−	0.00501360i
$593$	1.05889e15			0.592996			0.296498	−	0.955034i	$-0.404181\pi$
$593$	1.05889e15			0.592996			0.296498	+	0.955034i	$0.404181\pi$
$594$	7.78163e14	−	5.19130e14i	0.431763	−	0.288039i
$595$	1.12686e14	+	1.12686e14i	0.0619476	+	0.0619476i
$596$	−1.34172e14	−	3.25263e14i	−0.0730816	−	0.177166i
$597$	5.19552e13	−	5.19552e13i	0.0280395	−	0.0280395i
$598$	3.81953e13	+	7.62653e12i	0.0204246	+	0.00407822i
$599$		−	8.03403e14i		−	0.425682i	−0.977087	−	0.212841i	$-0.931728\pi$
$599$		−	8.03403e14i		−	0.425682i	0.977087	−	0.212841i	$-0.0682717\pi$
$600$	1.29858e15	−	1.93427e15i	0.681766	−	1.01551i
$601$		−	1.38624e15i		−	0.721155i	−0.932729	−	0.360578i	$-0.882580\pi$
$601$		−	1.38624e15i		−	0.721155i	0.932729	−	0.360578i	$-0.117420\pi$
$602$	5.27704e14	−	2.64286e15i	0.272025	−	1.36236i
$603$	8.80459e14	−	8.80459e14i	0.449742	−	0.449742i
$604$	7.92276e14	+	3.29528e14i	0.401027	+	0.166797i
$605$	−3.01147e13	−	3.01147e13i	−0.0151051	−	0.0151051i
$606$	−6.20815e14	−	9.30586e14i	−0.308576	−	0.462548i
$607$	3.18636e15			1.56948			0.784742	−	0.619823i	$-0.212796\pi$
$607$	3.18636e15			1.56948			0.784742	+	0.619823i	$0.212796\pi$
$608$	2.99540e14	−	1.98568e14i	0.146213	−	0.0969257i
$609$	−1.21945e15			−0.589886
$610$	−3.30261e13	−	4.95053e13i	−0.0158323	−	0.0237322i
$611$	−1.02671e13	−	1.02671e13i	−0.00487776	−	0.00487776i
$612$	1.19880e15	+	4.98612e14i	0.564435	+	0.234763i
$613$	1.13972e15	−	1.13972e15i	0.531820	−	0.531820i	−0.389294	−	0.921114i	$-0.627281\pi$
$613$	1.13972e15	−	1.13972e15i	0.531820	−	0.531820i	0.921114	+	0.389294i	$0.127281\pi$
$614$	4.06093e14	−	2.03380e15i	0.187802	−	0.940552i
$615$		−	3.44346e14i		−	0.157827i
$616$	−1.20779e15	−	8.10850e14i	−0.548651	−	0.368338i
$617$			4.02609e15i			1.81265i	0.422578	+	0.906326i	$0.361125\pi$
$617$			4.02609e15i			1.81265i	−0.422578	+	0.906326i	$0.638875\pi$
$618$	2.14008e15	+	4.27313e14i	0.954977	+	0.190682i
$619$	1.12455e14	−	1.12455e14i	0.0497370	−	0.0497370i	−0.681801	−	0.731538i	$-0.738803\pi$
$619$	1.12455e14	−	1.12455e14i	0.0497370	−	0.0497370i	0.731538	+	0.681801i	$0.238803\pi$
$620$	−1.64209e14	−	3.98079e14i	−0.0719851	−	0.174508i
$621$	−3.29849e13	−	3.29849e13i	−0.0143322	−	0.0143322i
$622$	2.00293e15	−	1.33620e15i	0.862618	−	0.575472i
$623$	2.63416e15			1.12450
$624$	1.24301e15	−	1.23577e15i	0.525969	−	0.522905i
$625$	−2.31051e15			−0.969098
$626$	−2.79124e15	+	1.86210e15i	−1.16048	+	0.774182i
$627$	3.30605e14	+	3.30605e14i	0.136250	+	0.136250i
$628$	−4.41647e15	+	1.82181e15i	−1.80425	+	0.744260i
$629$	−3.47290e15	+	3.47290e15i	−1.40642	+	1.40642i
$630$	9.74045e13	+	1.94489e13i	0.0391026	+	0.00780769i
$631$			3.54561e15i			1.41101i	0.708706	+	0.705504i	$0.249279\pi$
$631$			3.54561e15i			1.41101i	−0.708706	+	0.705504i	$0.750721\pi$
$632$	3.70551e15	−	7.28636e14i	1.46185	−	0.287453i
$633$		−	2.67910e15i		−	1.04777i
$634$	−8.08830e13	+	4.05080e14i	−0.0313593	+	0.157054i
$635$	−2.78618e14	+	2.78618e14i	−0.107091	+	0.107091i
$636$	−1.32848e15	+	3.19402e15i	−0.506220	+	1.21709i
$637$	5.02253e14	+	5.02253e14i	0.189739	+	0.189739i
$638$	8.45345e14	+	1.26715e15i	0.316607	+	0.474586i
$639$	1.62779e15			0.604427
$640$	−2.71132e14	+	5.24920e13i	−0.0998139	+	0.0193243i
$641$	−3.99466e15			−1.45801			−0.729005	−	0.684509i	$-0.760017\pi$
$641$	−3.99466e15			−1.45801			−0.729005	+	0.684509i	$0.760017\pi$
$642$	5.32367e14	+	7.98005e14i	0.192650	+	0.288777i
$643$	−7.20860e14	−	7.20860e14i	−0.258637	−	0.258637i	0.565863	−	0.824500i	$-0.308543\pi$
$643$	−7.20860e14	−	7.20860e14i	−0.258637	−	0.258637i	−0.824500	+	0.565863i	$0.808543\pi$
$644$	−2.78591e13	+	6.69809e13i	−0.00991048	+	0.0238275i
$645$	4.70663e14	−	4.70663e14i	0.166009	−	0.166009i
$646$	1.13826e14	−	5.70067e14i	0.0398073	−	0.199364i
$647$		−	2.38050e15i		−	0.825458i	−0.910854	−	0.412729i	$-0.864576\pi$
$647$		−	2.38050e15i		−	0.825458i	0.910854	−	0.412729i	$-0.135424\pi$
$648$	−3.56510e15	+	7.01027e14i	−1.22577	+	0.241030i
$649$			3.23229e14i			0.110196i
$650$	−1.72283e15	−	3.44001e14i	−0.582398	−	0.116288i
$651$	−3.59940e15	+	3.59940e15i	−1.20652	+	1.20652i
$652$	−2.88356e15	+	1.18948e15i	−0.958447	+	0.395362i
$653$	3.05366e15	+	3.05366e15i	1.00646	+	1.00646i	0.999979	+	0.00648374i	$0.00206385\pi$
$653$	3.05366e15	+	3.05366e15i	1.00646	+	1.00646i	0.00648374	+	0.999979i	$0.497936\pi$
$654$	6.13343e14	−	4.09175e14i	0.200459	−	0.133731i
$655$	4.52195e14			0.146554
$656$	2.77162e15	−	2.75548e15i	0.890764	−	0.885575i
$657$	8.32859e14			0.265437
$658$	2.24967e13	−	1.50081e13i	0.00711012	−	0.00474332i
$659$	−3.38786e15	−	3.38786e15i	−1.06183	−	1.06183i	−0.997958	−	0.0638750i	$-0.979654\pi$
$659$	−3.38786e15	−	3.38786e15i	−1.06183	−	1.06183i	−0.0638750	−	0.997958i	$-0.520346\pi$
$660$	−1.37009e14	−	3.32139e14i	−0.0425850	−	0.103235i
$661$	2.17225e15	−	2.17225e15i	0.669580	−	0.669580i	−0.288039	−	0.957619i	$-0.593003\pi$
$661$	2.17225e15	−	2.17225e15i	0.669580	−	0.669580i	0.957619	+	0.288039i	$0.0930032\pi$
$662$	−3.64108e15	−	7.27020e14i	−1.11304	−	0.222243i
$663$		−	2.83523e15i		−	0.859534i
$664$	−1.26736e15	−	8.50844e14i	−0.381044	−	0.255815i
$665$		−	4.44722e13i		−	0.0132608i
$666$	−5.99405e14	+	3.00195e15i	−0.177260	+	0.887760i
$667$	5.37122e13	−	5.37122e13i	0.0157536	−	0.0157536i
$668$	3.02261e15	+	1.25718e15i	0.879248	+	0.365702i
$669$	−1.95480e15	−	1.95480e15i	−0.563975	−	0.563975i
$670$	2.37753e14	+	3.56386e14i	0.0680323	+	0.101979i
$671$	8.78726e14			0.249390
$672$	1.80377e15	+	2.72099e15i	0.507750	+	0.765941i
$673$	−2.38223e14			−0.0665121			−0.0332561	−	0.999447i	$-0.510588\pi$
$673$	−2.38223e14			−0.0665121			−0.0332561	+	0.999447i	$0.510588\pi$
$674$	−1.83394e15	−	2.74903e15i	−0.507874	−	0.761291i
$675$	1.48781e15	+	1.48781e15i	0.408675	+	0.408675i
$676$	2.16850e15	+	9.01936e14i	0.590817	+	0.245736i
$677$	1.90659e15	−	1.90659e15i	0.515252	−	0.515252i	−0.400879	−	0.916131i	$-0.631295\pi$
$677$	1.90659e15	−	1.90659e15i	0.515252	−	0.515252i	0.916131	+	0.400879i	$0.131295\pi$
$678$	7.90693e14	−	3.95997e15i	0.211955	−	1.06152i
$679$		−	3.41862e14i		−	0.0909007i
$680$	−2.48996e14	+	3.70888e14i	−0.0656741	+	0.0978236i
$681$		−	3.59706e15i		−	0.941106i
$682$	6.23538e15	+	1.24503e15i	1.61826	+	0.323121i
$683$	−2.55329e15	+	2.55329e15i	−0.657334	+	0.657334i	−0.954748	−	0.297415i	$-0.903876\pi$
$683$	−2.55329e15	+	2.55329e15i	−0.657334	+	0.657334i	0.297415	+	0.954748i	$0.403876\pi$
$684$	−1.38167e14	−	3.34948e14i	−0.0352855	−	0.0855400i
$685$	3.89691e14	+	3.89691e14i	0.0987239	+	0.0987239i
$686$	−3.56171e15	+	2.37610e15i	−0.895109	+	0.597147i
$687$	−5.20201e15			−1.29691
$688$	7.55460e15	+	2.20692e13i	1.86842	+	0.00545822i
$689$	2.60862e15			0.640037
$690$	−1.49046e13	+	9.94317e12i	−0.00362785	+	0.00242022i
$691$	−4.73213e14	−	4.73213e14i	−0.114269	−	0.114269i	0.647660	−	0.761929i	$-0.275748\pi$
$691$	−4.73213e14	−	4.73213e14i	−0.114269	−	0.114269i	−0.761929	+	0.647660i	$0.775748\pi$
$692$	−3.89532e15	+	1.60683e15i	−0.933168	+	0.384935i
$693$	−1.03708e15	+	1.03708e15i	−0.246479	+	0.246479i
$694$	−2.55547e15	−	5.10255e14i	−0.602551	−	0.120312i
$695$		−	3.82433e14i		−	0.0894621i
$696$	−6.59535e14	−	3.35410e15i	−0.153069	−	0.778440i
$697$		−	6.32188e15i		−	1.45568i
$698$	−9.40401e14	+	4.70974e15i	−0.214837	+	1.07595i
$699$	−5.69430e15	+	5.69430e15i	−1.29067	+	1.29067i
$700$	1.25661e15	−	3.02123e15i	0.282593	−	0.679430i
$701$	4.29380e14	+	4.29380e14i	0.0958061	+	0.0958061i	0.753385	−	0.657579i	$-0.228420\pi$
$701$	4.29380e14	+	4.29380e14i	0.0958061	+	0.0958061i	−0.657579	+	0.753385i	$0.728420\pi$
$702$	8.78507e14	+	1.31686e15i	0.194487	+	0.291531i
$703$	1.37061e15			0.301064
$704$	1.57702e15	−	3.76057e15i	0.343706	−	0.819604i
$705$	6.67918e12			0.00144439
$706$	4.82204e15	+	7.22812e15i	1.03468	+	1.55096i
$707$	−1.11098e15	−	1.11098e15i	−0.236538	−	0.236538i
$708$	2.78562e14	−	6.69740e14i	0.0588490	−	0.141489i
$709$	−1.83229e14	+	1.83229e14i	−0.0384097	+	0.0384097i	−0.726051	−	0.687641i	$-0.758646\pi$
$709$	−1.83229e14	+	1.83229e14i	−0.0384097	+	0.0384097i	0.687641	+	0.726051i	$0.258646\pi$
$710$	−1.09664e14	+	5.49222e14i	−0.0228109	+	0.114242i
$711$		−	3.80744e15i		−	0.785870i
$712$	1.42468e15	+	7.24528e15i	0.291795	+	1.48394i
$713$		−	3.17081e14i		−	0.0644433i
$714$	5.17843e15	+	1.03398e15i	1.04438	+	0.208533i
$715$	−1.91581e14	+	1.91581e14i	−0.0383415	+	0.0383415i
$716$	3.50455e15	−	1.44564e15i	0.696003	−	0.287104i
$717$	5.43898e15	+	5.43898e15i	1.07192	+	1.07192i
$718$	2.27689e15	−	1.51897e15i	0.445306	−	0.297074i
$719$	−4.63852e15			−0.900265			−0.450133	−	0.892962i	$-0.648623\pi$
$719$	−4.63852e15			−0.900265			−0.450133	+	0.892962i	$0.648623\pi$
$720$	−8.13379e11	+	2.78431e14i	−0.000156662	+	0.0536276i
$721$	3.06509e15			0.585867
$722$	4.25048e15	−	2.83559e15i	0.806276	−	0.537885i
$723$	−1.36459e15	−	1.36459e15i	−0.256887	−	0.256887i
$724$	−2.63030e15	−	6.37643e15i	−0.491409	−	1.19128i
$725$	−2.42274e15	+	2.42274e15i	−0.449208	+	0.449208i
$726$	−1.38391e15	−	2.76328e14i	−0.254658	−	0.0508480i
$727$			3.43021e15i			0.626442i	0.949680	+	0.313221i	$0.101408\pi$
$727$			3.43021e15i			0.626442i	−0.949680	+	0.313221i	$0.898592\pi$
$728$	1.37217e15	−	2.04389e15i	0.248706	−	0.370455i
$729$		−	3.49140e14i		−	0.0628055i
$730$	−5.61096e13	+	2.81009e14i	−0.0100176	+	0.0501701i
$731$	8.64094e15	−	8.64094e15i	1.53114	−	1.53114i
$732$	−1.82074e15	−	7.57295e14i	−0.320212	−	0.133185i
$733$	4.05712e15	+	4.05712e15i	0.708184	+	0.708184i	0.966153	−	0.257969i	$-0.0830534\pi$
$733$	4.05712e15	+	4.05712e15i	0.708184	+	0.708184i	−0.257969	+	0.966153i	$0.583053\pi$
$734$	1.94260e15	+	2.91191e15i	0.336554	+	0.504486i
$735$	−3.26738e14			−0.0561848
$736$	−1.99299e14	−	4.04001e13i	−0.0340155	−	0.00689533i
$737$	−6.32591e15			−1.07165
$738$	−2.18673e15	−	3.27786e15i	−0.367693	−	0.551163i
$739$	1.67030e15	+	1.67030e15i	0.278772	+	0.278772i	0.832619	−	0.553846i	$-0.186841\pi$
$739$	1.67030e15	+	1.67030e15i	0.278772	+	0.278772i	−0.553846	+	0.832619i	$0.686841\pi$
$740$	−9.72487e14	−	4.04482e14i	−0.161105	−	0.0670078i
$741$	−5.59471e14	+	5.59471e14i	−0.0919978	+	0.0919978i
$742$	−9.51343e14	+	4.76454e15i	−0.155280	+	0.777677i
$743$		−	4.61265e15i		−	0.747330i	−0.927564	−	0.373665i	$-0.878101\pi$
$743$		−	4.61265e15i		−	0.747330i	0.927564	−	0.373665i	$-0.121899\pi$
$744$	−1.18469e16	−	7.95345e15i	−1.90526	−	1.27910i
$745$		−	1.22052e14i		−	0.0194843i
$746$	−4.60169e15	−	9.18827e14i	−0.729212	−	0.145603i
$747$	−1.08824e15	+	1.08824e15i	−0.171183	+	0.171183i
$748$	−2.51535e15	−	6.09778e15i	−0.392772	−	0.952166i
$749$	9.52701e14	+	9.52701e14i	0.147675	+	0.147675i
$750$	1.35159e15	−	9.01675e14i	0.207973	−	0.138744i
$751$	−6.38439e14			−0.0975214			−0.0487607	−	0.998810i	$-0.515527\pi$
$751$	−6.38439e14			−0.0975214			−0.0487607	+	0.998810i	$0.515527\pi$
$752$	5.34471e13	+	5.37603e13i	0.00810450	+	0.00815199i
$753$	1.21101e16			1.82296
$754$	−2.14436e15	+	1.43055e15i	−0.320446	+	0.213777i
$755$	2.10473e14	+	2.10473e14i	0.0312239	+	0.0312239i
$756$	−2.72557e15	+	1.12431e15i	−0.401410	+	0.165583i
$757$	−3.03835e15	+	3.03835e15i	−0.444232	+	0.444232i	−0.893432	−	0.449199i	$-0.851709\pi$
$757$	−3.03835e15	+	3.03835e15i	−0.444232	+	0.444232i	0.449199	+	0.893432i	$0.351709\pi$
$758$	−1.20568e16	−	2.40740e15i	−1.75006	−	0.349437i
$759$		−	2.64558e14i		−	0.0381234i
$760$	1.22321e14	−	2.40527e13i	0.0174995	−	0.00344103i
$761$		−	2.97530e15i		−	0.422586i	−0.977423	−	0.211293i	$-0.932233\pi$
$761$		−	2.97530e15i		−	0.422586i	0.977423	−	0.211293i	$-0.0677674\pi$
$762$	−2.55655e15	+	1.28038e16i	−0.360498	+	1.80545i
$763$	7.32242e14	−	7.32242e14i	0.102511	−	0.102511i
$764$	2.77067e15	−	6.66146e15i	0.385099	−	0.925883i
$765$	3.18468e14	+	3.18468e14i	0.0439469	+	0.0439469i
$766$	3.23174e15	+	4.84429e15i	0.442769	+	0.663700i
$767$	−5.46989e14			−0.0744054
$768$	−6.50853e15	+	6.43291e15i	−0.879014	+	0.868802i
$769$	−4.50036e15			−0.603465			−0.301733	−	0.953393i	$-0.597565\pi$
$769$	−4.50036e15			−0.603465			−0.301733	+	0.953393i	$0.597565\pi$
$770$	−2.80047e14	−	4.19783e14i	−0.0372848	−	0.0558890i
$771$	8.09899e15	+	8.09899e15i	1.07061	+	1.07061i
$772$	−3.15967e15	+	7.59672e15i	−0.414712	+	0.997083i
$773$	6.33340e15	−	6.33340e15i	0.825372	−	0.825372i	−0.161500	−	0.986873i	$-0.551633\pi$
$773$	6.33340e15	−	6.33340e15i	0.825372	−	0.825372i	0.986873	+	0.161500i	$0.0516333\pi$
$774$	1.49138e15	−	7.46916e15i	0.192980	−	0.966488i
$775$			1.43022e16i			1.83757i
$776$	9.40294e14	−	1.84895e14i	0.119957	−	0.0235878i
$777$			1.24504e16i			1.57714i
$778$	−1.25743e16	−	2.51074e15i	−1.58160	−	0.315801i
$779$	−1.24749e15	+	1.24749e15i	−0.155805	+	0.155805i
$780$	5.62068e14	−	2.31855e14i	0.0697058	−	0.0287539i
$781$	−5.84766e15	−	5.84766e15i	−0.720115	−	0.720115i
$782$	−2.73634e14	+	1.82548e14i	−0.0334605	+	0.0223223i
$783$	3.08723e15			0.374869
$784$	−2.61457e15	−	2.62989e15i	−0.315255	−	0.317102i
$785$	−1.65723e15			−0.198427
$786$	1.24649e16	−	8.31560e15i	1.48205	−	0.988712i
$787$	−3.25291e15	−	3.25291e15i	−0.384071	−	0.384071i	0.488496	−	0.872566i	$-0.337546\pi$
$787$	−3.25291e15	−	3.25291e15i	−0.384071	−	0.384071i	−0.872566	+	0.488496i	$0.837546\pi$
$788$	4.40515e15	+	1.06791e16i	0.516495	+	1.25210i
$789$	−1.70702e15	+	1.70702e15i	−0.198753	+	0.198753i
$790$	1.28464e15	+	2.56507e14i	0.148537	+	0.0296586i
$791$		−	5.67159e15i		−	0.651230i
$792$	−3.41341e15	−	2.29160e15i	−0.389224	−	0.261306i
$793$			1.48704e15i			0.168391i
$794$	1.94197e15	−	9.72583e15i	0.218389	−	1.09374i
$795$	−8.48510e14	+	8.48510e14i	−0.0947628	+	0.0947628i
$796$	2.67098e14	+	1.11093e14i	0.0296244	+	0.0123215i
$797$	−2.11952e15	−	2.11952e15i	−0.233462	−	0.233462i	0.580674	−	0.814136i	$-0.302789\pi$
$797$	−2.11952e15	−	2.11952e15i	−0.233462	−	0.233462i	−0.814136	+	0.580674i	$0.802789\pi$
$798$	−8.17817e14	−	1.22589e15i	−0.0894623	−	0.134102i
$799$	1.22624e14			0.0133219
$800$	8.98955e15	+	1.82228e15i	0.969936	+	0.196617i
$801$	7.44458e15			0.797740
$802$	−9.00816e15	−	1.35030e16i	−0.958687	−	1.43705i
$803$	−2.99196e15	−	2.99196e15i	−0.316242	−	0.316242i
$804$	1.31075e16	+	5.45173e15i	1.37597	+	0.572303i
$805$	−1.77939e13	+	1.77939e13i	−0.00185521	+	0.00185521i
$806$	−2.10692e15	+	1.05519e16i	−0.218175	+	1.09267i
$807$		−	2.37745e15i		−	0.244515i
$808$	2.45489e15	−	3.65664e15i	0.250767	−	0.373525i
$809$			6.90043e15i			0.700098i	0.936731	+	0.350049i	$0.113835\pi$
$809$			6.90043e15i			0.700098i	−0.936731	+	0.350049i	$0.886165\pi$
$810$	−1.23597e15	−	2.46788e14i	−0.124549	−	0.0248689i
$811$	−1.16275e15	+	1.16275e15i	−0.116378	+	0.116378i	−0.762898	−	0.646519i	$-0.776224\pi$
$811$	−1.16275e15	+	1.16275e15i	−0.116378	+	0.116378i	0.646519	+	0.762898i	$0.276224\pi$
$812$	−1.83081e15	−	4.43829e15i	−0.182006	−	0.441222i
$813$	−1.11989e16	−	1.11989e16i	−1.10580	−	1.10580i
$814$	1.29375e16	−	8.63089e15i	1.26887	−	0.846489i
$815$	−1.08203e15			−0.105408
$816$	−4.32426e13	+	1.48025e16i	−0.00418423	+	1.43232i
$817$	−3.41021e15			−0.327763
$818$	−1.71941e15	+	1.14706e15i	−0.164149	+	0.109507i
$819$	−1.75502e15	−	1.75502e15i	−0.166426	−	0.166426i
$820$	1.25328e15	−	5.16982e14i	0.118052	−	0.0486966i
$821$	8.05348e15	−	8.05348e15i	0.753523	−	0.753523i	−0.221612	−	0.975135i	$-0.571132\pi$
$821$	8.05348e15	−	8.05348e15i	0.753523	−	0.753523i	0.975135	+	0.221612i	$0.0711319\pi$
$822$	1.79081e16	+	3.57574e15i	1.66439	+	0.332331i
$823$			1.72899e16i			1.59622i	0.602510	+	0.798111i	$0.294167\pi$
$823$			1.72899e16i			1.59622i	−0.602510	+	0.798111i	$0.705833\pi$
$824$	1.65775e15	+	8.43055e15i	0.152026	+	0.773137i
$825$			1.19331e16i			1.08707i
$826$	1.99483e14	−	9.99054e14i	0.0180516	−	0.0904063i
$827$	1.23292e16	−	1.23292e16i	1.10829	−	1.10829i	0.114913	−	0.993376i	$-0.463341\pi$
$827$	1.23292e16	−	1.23292e16i	1.10829	−	1.10829i	0.993376	−	0.114913i	$-0.0366590\pi$
$828$	−7.87345e13	+	1.89299e14i	−0.00703070	+	0.0169037i
$829$	−1.23351e16	−	1.23351e16i	−1.09419	−	1.09419i	−0.995076	−	0.0991110i	$-0.968400\pi$
$829$	−1.23351e16	−	1.23351e16i	−1.09419	−	1.09419i	−0.0991110	−	0.995076i	$-0.531600\pi$
$830$	−2.93860e14	−	4.40489e14i	−0.0258947	−	0.0388155i
$831$	8.31183e15			0.727598
$832$	6.36388e15	+	2.66874e15i	0.553406	+	0.232074i
$833$	−5.99860e15			−0.518206
$834$	−7.03272e15	−	1.05419e16i	−0.603546	−	0.904699i
$835$	8.02973e14	+	8.02973e14i	0.0684582	+	0.0684582i
$836$	−7.06915e14	+	1.69962e15i	−0.0598732	+	0.143952i
$837$	9.11249e15	−	9.11249e15i	0.766738	−	0.766738i
$838$	−2.65207e14	+	1.32821e15i	−0.0221688	+	0.111026i
$839$		−	5.85813e15i		−	0.486484i	−0.969966	−	0.243242i	$-0.921789\pi$
$839$		−	5.85813e15i		−	0.486484i	0.969966	−	0.243242i	$-0.0782109\pi$
$840$	2.18492e14	+	1.11115e15i	0.0180260	+	0.0916720i
$841$		−	7.17330e15i		−	0.587951i
$842$	−1.20944e16	−	2.41491e15i	−0.984846	−	0.196646i
$843$	7.41886e15	−	7.41886e15i	0.600186	−	0.600186i
$844$	9.75081e15	−	4.02224e15i	0.783713	−	0.323284i
$845$	5.76075e14	+	5.76075e14i	0.0460010	+	0.0460010i
$846$	6.35796e13	−	4.24154e13i	0.00504406	−	0.00336501i
$847$	−1.98209e15			−0.156230
$848$	−1.36194e16	−	3.97864e13i	−1.06655	−	0.00311571i
$849$	−1.96548e15			−0.152924
$850$	1.23425e16	−	8.23396e15i	0.954112	−	0.636510i
$851$	−5.48397e14	−	5.48397e14i	−0.0421194	−	0.0421194i
$852$	7.07695e15	+	1.71561e16i	0.540043	+	1.30918i
$853$	−1.14683e16	+	1.14683e16i	−0.869522	+	0.869522i	−0.992419	−	0.122898i	$-0.960781\pi$
$853$	−1.14683e16	+	1.14683e16i	−0.869522	+	0.869522i	0.122898	+	0.992419i	$0.460781\pi$
$854$	−2.71601e15	−	5.42311e14i	−0.204604	−	0.0408536i
$855$		−	1.25686e14i		−	0.00940747i
$856$	−2.10514e15	+	3.13568e15i	−0.156558	+	0.233198i
$857$			3.71190e15i			0.274285i	0.990551	+	0.137142i	$0.0437918\pi$
$857$			3.71190e15i			0.274285i	−0.990551	+	0.137142i	$0.956208\pi$
$858$	−1.75792e15	+	8.80405e15i	−0.129068	+	0.646402i
$859$	1.20180e15	−	1.20180e15i	0.0876735	−	0.0876735i	−0.661910	−	0.749583i	$-0.730254\pi$
$859$	1.20180e15	−	1.20180e15i	0.0876735	−	0.0876735i	0.749583	+	0.661910i	$0.230254\pi$
$860$	2.41965e15	+	1.00639e15i	0.175392	+	0.0729501i
$861$	−1.13321e16	−	1.13321e16i	−0.816190	−	0.816190i
$862$	7.92454e15	+	1.18787e16i	0.567132	+	0.850116i
$863$	4.89836e15			0.348331			0.174165	−	0.984716i	$-0.444277\pi$
$863$	4.89836e15			0.348331			0.174165	+	0.984716i	$0.444277\pi$
$864$	−4.56654e15	−	6.88863e15i	−0.322672	−	0.486751i
$865$	−1.46168e15			−0.102627
$866$	2.36938e15	+	3.55164e15i	0.165305	+	0.247788i
$867$	4.32506e15	+	4.32506e15i	0.299839	+	0.299839i
$868$	−1.85043e16	−	7.69641e15i	−1.27472	−	0.530188i
$869$	−1.36778e16	+	1.36778e16i	−0.936287	+	0.936287i
$870$	2.32181e14	−	1.16282e15i	0.0157932	−	0.0790960i
$871$		−	1.07051e16i		−	0.723589i
$872$	2.41007e15	+	1.61801e15i	0.161878	+	0.108677i
$873$		−	9.66161e14i		−	0.0644868i
$874$	9.00177e13	+	1.79740e13i	0.00597056	+	0.00119215i
$875$	1.61360e15	−	1.61360e15i	0.106353	−	0.106353i
$876$	3.62092e15	+	8.77792e15i	0.237163	+	0.574935i
$877$	3.94432e15	+	3.94432e15i	0.256729	+	0.256729i	0.823722	−	0.566993i	$-0.191894\pi$
$877$	3.94432e15	+	3.94432e15i	0.256729	+	0.256729i	−0.566993	+	0.823722i	$0.691894\pi$
$878$	1.60418e14	−	1.07018e14i	0.0103761	−	0.00692211i
$879$	−2.83460e16			−1.82202
$880$	1.00315e15	−	9.97310e14i	0.0640786	−	0.0637053i
$881$	−8.41637e15			−0.534266			−0.267133	−	0.963660i	$-0.586076\pi$
$881$	−8.41637e15			−0.534266			−0.267133	+	0.963660i	$0.586076\pi$
$882$	−3.11024e15	+	2.07491e15i	−0.196208	+	0.130895i
$883$	−4.32184e15	−	4.32184e15i	−0.270947	−	0.270947i	0.558534	−	0.829482i	$-0.311364\pi$
$883$	−4.32184e15	−	4.32184e15i	−0.270947	−	0.270947i	−0.829482	+	0.558534i	$0.811364\pi$
$884$	1.03191e16	−	4.25665e15i	0.642913	−	0.265204i
$885$	1.77920e14	−	1.77920e14i	0.0110163	−	0.0110163i
$886$	6.75779e14	+	1.34934e14i	0.0415833	+	0.00830301i
$887$			2.87494e16i			1.75812i	0.476707	+	0.879062i	$0.341830\pi$
$887$			2.87494e16i			1.75812i	−0.476707	+	0.879062i	$0.658170\pi$
$888$	−3.42450e16	+	6.73380e15i	−2.08126	+	0.409250i
$889$			1.83380e16i			1.10762i
$890$	−5.01541e14	+	2.51183e15i	−0.0301066	+	0.150780i
$891$	1.31596e16	−	1.31596e16i	0.785081	−	0.785081i
$892$	4.17985e15	−	1.00495e16i	0.247830	−	0.595852i
$893$	−2.41972e13	−	2.41972e13i	−0.00142587	−	0.00142587i
$894$	−2.24446e15	−	3.36439e15i	−0.131448	−	0.197038i
$895$	1.31505e15			0.0765446
$896$	−7.19520e15	+	1.06501e16i	−0.416245	+	0.616112i
$897$	4.47703e14			0.0257414
$898$	3.75649e15	+	5.63088e15i	0.214666	+	0.321778i
$899$	1.48387e16	+	1.48387e16i	0.842784	+	0.842784i
$900$	3.55139e15	−	8.53851e15i	0.200477	−	0.482002i
$901$	−1.55779e16	+	1.55779e16i	−0.874020	+	0.874020i
$902$	−3.91974e15	+	1.96309e16i	−0.218586	+	1.09473i
$903$		−	3.09780e16i		−	1.71700i
$904$	1.55997e16	−	3.06747e15i	0.859392	−	0.168987i
$905$		−	2.39269e15i		−	0.131014i
$906$	9.67220e15	+	1.93126e15i	0.526405	+	0.105108i
$907$	−5.17663e15	+	5.17663e15i	−0.280031	+	0.280031i	−0.833121	−	0.553090i	$-0.813449\pi$
$907$	−5.17663e15	+	5.17663e15i	−0.280031	+	0.280031i	0.553090	+	0.833121i	$0.313449\pi$
$908$	1.30918e16	−	5.40042e15i	0.703927	−	0.290372i
$909$	−3.13983e15	−	3.13983e15i	−0.167805	−	0.167805i
$910$	7.10385e14	−	4.73914e14i	0.0377369	−	0.0251751i
$911$	−2.22340e16			−1.17400			−0.586998	−	0.809588i	$-0.699690\pi$
$911$	−2.22340e16			−1.17400			−0.586998	+	0.809588i	$0.699690\pi$
$912$	2.92949e15	−	2.91243e15i	0.153752	−	0.152856i
$913$	7.81874e15			0.407894
$914$	2.15741e15	−	1.43926e15i	0.111874	−	0.0746337i
$915$	−4.83691e14	−	4.83691e14i	−0.0249317	−	0.0249317i
$916$	−7.81000e15	−	1.89332e16i	−0.400153	−	0.970059i
$917$	1.48812e16	−	1.48812e16i	0.757893	−	0.757893i
$918$	−1.31100e16	−	2.61770e15i	−0.663696	−	0.132521i
$919$			1.58068e16i			0.795444i	0.917506	+	0.397722i	$0.130199\pi$
$919$			1.58068e16i			0.795444i	−0.917506	+	0.397722i	$0.869801\pi$
$920$	−5.85659e13	−	3.93184e13i	−0.00292962	−	0.00196681i
$921$		−	2.38390e16i		−	1.18539i
$922$	6.32457e15	−	3.16748e16i	0.312616	−	1.56565i
$923$	9.89580e15	−	9.89580e15i	0.486230	−	0.486230i
$924$	−1.54391e16	−	6.42154e15i	−0.754097	−	0.313648i
$925$	2.47359e16	+	2.47359e16i	1.20102	+	1.20102i
$926$	−2.62715e15	−	3.93804e15i	−0.126802	−	0.190073i
$927$	8.66246e15			0.415626
$928$	1.12174e16	−	7.43609e15i	0.535028	−	0.354675i
$929$	3.46893e16			1.64479			0.822393	−	0.568920i	$-0.192639\pi$
$929$	3.46893e16			1.64479			0.822393	+	0.568920i	$0.192639\pi$
$930$	−2.74692e15	−	4.11756e15i	−0.129476	−	0.194082i
$931$	1.18370e15	+	1.18370e15i	0.0554647	+	0.0554647i
$932$	−2.92740e16	−	1.21758e16i	−1.36362	−	0.567166i
$933$	1.95696e16	−	1.95696e16i	0.906220	−	0.906220i
$934$	7.30772e15	−	3.65987e16i	0.336414	−	1.68484i
$935$		−	2.28813e15i		−	0.104717i
$936$	3.87800e15	−	5.77639e15i	0.176437	−	0.262809i
$937$		−	2.05502e16i		−	0.929496i	−0.885443	−	0.464748i	$-0.846145\pi$
$937$		−	2.05502e16i		−	0.929496i	0.885443	−	0.464748i	$-0.153855\pi$
$938$	1.95525e16	+	3.90408e15i	0.879197	+	0.175551i
$939$	−2.72718e16	+	2.72718e16i	−1.21914	+	1.21914i
$940$	1.00277e13	+	2.43095e13i	0.000445656	+	0.00108037i
$941$	1.82034e16	+	1.82034e16i	0.804286	+	0.804286i	0.983762	−	0.179476i	$-0.0574402\pi$
$941$	1.82034e16	+	1.82034e16i	0.804286	+	0.804286i	−0.179476	+	0.983762i	$0.557440\pi$
$942$	−4.56821e16	+	3.04756e16i	−2.00662	+	1.33866i
$943$	9.98271e14			0.0435948
$944$	2.85579e15	+	8.34263e12i	0.123988	+	0.000362207i
$945$	−1.02274e15			−0.0441460
$946$	−3.21898e16	+	2.14745e16i	−1.38139	+	0.921558i
$947$	2.56323e15	+	2.56323e15i	0.109361	+	0.109361i	0.759670	−	0.650309i	$-0.225360\pi$
$947$	2.56323e15	+	2.56323e15i	0.109361	+	0.109361i	−0.650309	+	0.759670i	$0.725360\pi$
$948$	4.01286e16	−	1.65532e16i	1.70219	−	0.702159i
$949$	5.06319e15	−	5.06319e15i	0.213530	−	0.213530i
$950$	−4.06033e15	−	8.10732e14i	−0.170248	−	0.0339936i
$951$			4.74811e15i			0.197937i
$952$	4.01131e15	+	2.03997e16i	0.166258	+	0.845514i
$953$			7.68907e15i			0.316857i	0.987370	+	0.158428i	$0.0506427\pi$
$953$			7.68907e15i			0.316857i	−0.987370	+	0.158428i	$0.949357\pi$
$954$	−2.68866e15	+	1.34654e16i	−0.110159	+	0.551700i
$955$	1.76966e15	−	1.76966e15i	0.0720892	−	0.0720892i
$956$	−1.16299e16	+	2.79614e16i	−0.471039	+	1.13251i
$957$	1.23807e16	+	1.23807e16i	0.498574	+	0.498574i
$958$	−2.33401e14	−	3.49862e14i	−0.00934527	−	0.0140083i
$959$	2.56486e16			1.02108
$960$	−2.93806e15	+	1.20193e15i	−0.116297	+	0.0475758i
$961$	6.21890e16			2.44757
$962$	1.46058e16	+	2.18937e16i	0.571559	+	0.856753i
$963$	2.69249e15	+	2.69249e15i	0.104764	+	0.104764i
$964$	2.91783e15	−	7.01526e15i	0.112885	−	0.271406i
$965$	−2.01811e15	+	2.01811e15i	−0.0776328	+	0.0776328i
$966$	−1.63274e14	+	8.17711e14i	−0.00624514	+	0.0312770i
$967$			2.35131e16i			0.894260i	0.894469	+	0.447130i	$0.147554\pi$
$967$			2.35131e16i			0.894260i	−0.894469	+	0.447130i	$0.852446\pi$
$968$	−1.07201e15	−	5.45174e15i	−0.0405399	−	0.206168i
$969$		−	6.68198e15i		−	0.251261i
$970$	3.25986e14	+	6.50901e13i	0.0121886	+	0.00243372i
$971$	−2.96572e16	+	2.96572e16i	−1.10262	+	1.10262i	−0.108522	+	0.994094i	$0.534612\pi$
$971$	−2.96572e16	+	2.96572e16i	−1.10262	+	1.10262i	−0.994094	+	0.108522i	$0.965388\pi$
$972$	−2.40049e16	+	9.90209e15i	−0.887431	+	0.366068i
$973$	−1.25855e16	−	1.25855e16i	−0.462645	−	0.462645i
$974$	1.00699e16	−	6.71783e15i	0.368086	−	0.245558i
$975$	−2.01940e16			−0.734003
$976$	2.26801e13	−	7.76372e15i	0.000819732	−	0.280605i
$977$	−3.19671e16			−1.14890			−0.574450	−	0.818539i	$-0.694784\pi$
$977$	−3.19671e16			−1.14890			−0.574450	+	0.818539i	$0.694784\pi$
$978$	−2.98264e16	+	1.98979e16i	−1.06595	+	0.711119i
$979$	−2.67439e16	−	2.67439e16i	−0.950429	−	0.950429i
$980$	−4.90545e14	−	1.18919e15i	−0.0173355	−	0.0420250i
$981$	2.06944e15	−	2.06944e15i	0.0727233	−	0.0727233i
$982$	2.13283e15	+	4.25867e14i	0.0745322	+	0.0148820i
$983$		−	3.59807e16i		−	1.25033i	−0.780492	−	0.625166i	$-0.785031\pi$
$983$		−	3.59807e16i		−	1.25033i	0.780492	−	0.625166i	$-0.214969\pi$
$984$	2.50400e16	−	3.72978e16i	0.865288	−	1.28887i
$985$			4.00721e15i			0.137703i
$986$	4.26264e15	−	2.13482e16i	0.145665	−	0.729522i
$987$	2.19804e14	−	2.19804e14i	0.00746951	−	0.00746951i
$988$	−2.87620e15	−	1.19629e15i	−0.0971978	−	0.0404271i
$989$	1.36447e15	+	1.36447e15i	0.0458547	+	0.0458547i
$990$	−7.91460e14	−	1.18638e15i	−0.0264506	−	0.0396488i
$991$	−2.28338e16			−0.758881			−0.379441	−	0.925216i	$-0.623884\pi$
$991$	−2.28338e16			−0.758881			−0.379441	+	0.925216i	$0.623884\pi$
$992$	1.11610e16	−	5.50587e16i	0.368884	−	1.81975i
$993$	−4.26785e16			−1.40278
$994$	1.44654e16	+	2.16832e16i	0.472829	+	0.708758i
$995$	7.09562e13	+	7.09562e13i	0.00230655	+	0.00230655i
$996$	−1.62006e16	−	6.73827e15i	−0.523728	−	0.217832i
$997$	−2.26548e16	+	2.26548e16i	−0.728346	+	0.728346i	−0.970290	−	0.241945i	$-0.922215\pi$
$997$	−2.26548e16	+	2.26548e16i	−0.728346	+	0.728346i	0.241945	+	0.970290i	$0.422215\pi$
$998$	−1.29452e15	+	6.48324e15i	−0.0413895	+	0.207288i
$999$		−	3.15204e16i		−	1.00226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.12.e.a.13.14	yes	42
4.3	odd	2		64.12.e.a.17.5		42
8.3	odd	2		128.12.e.a.33.17		42
8.5	even	2		128.12.e.b.33.5		42
16.3	odd	4		128.12.e.a.97.17		42
16.5	even	4	inner	16.12.e.a.5.14	✓	42
16.11	odd	4		64.12.e.a.49.5		42
16.13	even	4		128.12.e.b.97.5		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.14	✓	42	16.5	even	4	inner
16.12.e.a.13.14	yes	42	1.1	even	1	trivial
64.12.e.a.17.5		42	4.3	odd	2
64.12.e.a.49.5		42	16.11	odd	4
128.12.e.a.33.17		42	8.3	odd	2
128.12.e.a.97.17		42	16.3	odd	4
128.12.e.b.33.5		42	8.5	even	2
128.12.e.b.97.5		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)

\(f(q)\)	\(=\)	\(q+(25.1148 + 37.6464i) q^{2} +(367.824 + 367.824i) q^{3} +(-786.499 + 1890.96i) q^{4} +(-502.344 + 502.344i) q^{5} +(-4609.43 + 23085.1i) q^{6} +33063.2i q^{7} +(-90940.4 + 17882.1i) q^{8} +93442.1i q^{9} +O(q^{10})\)	\(q+(25.1148 + 37.6464i) q^{2} +(367.824 + 367.824i) q^{3} +(-786.499 + 1890.96i) q^{4} +(-502.344 + 502.344i) q^{5} +(-4609.43 + 23085.1i) q^{6} +33063.2i q^{7} +(-90940.4 + 17882.1i) q^{8} +93442.1i q^{9} +(-31527.7 - 6295.18i) q^{10} +(335681. - 335681. i) q^{11} +(-984833. + 406247. i) q^{12} +(568061. + 568061. i) q^{13} +(-1.24471e6 + 830373. i) q^{14} -369548. q^{15} +(-2.95714e6 - 2.97447e6i) q^{16} -6.78457e6 q^{17} +(-3.51776e6 + 2.34678e6i) q^{18} +(1.33879e6 + 1.33879e6i) q^{19} +(-554819. - 1.34500e6i) q^{20} +(-1.21614e7 + 1.21614e7i) q^{21} +(2.10677e7 + 4.20662e6i) q^{22} -1.07133e6i q^{23} +(-4.00276e7 - 2.68726e7i) q^{24} +4.83234e7i q^{25} +(-7.11873e6 + 3.56522e7i) q^{26} +(3.07887e7 - 3.07887e7i) q^{27} +(-6.25211e7 - 2.60041e7i) q^{28} +(5.01359e7 + 5.01359e7i) q^{29} +(-9.28112e6 - 1.39122e7i) q^{30} +2.95969e8 q^{31} +(3.77101e7 - 1.86029e8i) q^{32} +2.46943e8 q^{33} +(-1.70393e8 - 2.55414e8i) q^{34} +(-1.66091e7 - 1.66091e7i) q^{35} +(-1.76695e8 - 7.34921e7i) q^{36} +(5.11883e8 - 5.11883e8i) q^{37} +(-1.67772e7 + 8.40240e7i) q^{38} +4.17893e8i q^{39} +(3.67004e7 - 5.46664e7i) q^{40} +9.31803e8i q^{41} +(-7.63265e8 - 1.52402e8i) q^{42} +(-1.27362e9 + 1.27362e9i) q^{43} +(3.70746e8 + 8.98771e8i) q^{44} +(-4.69401e7 - 4.69401e7i) q^{45} +(4.03318e7 - 2.69063e7i) q^{46} -1.80739e7 q^{47} +(6.37366e6 - 2.18179e9i) q^{48} +8.84154e8 q^{49} +(-1.81920e9 + 1.21363e9i) q^{50} +(-2.49553e9 - 2.49553e9i) q^{51} +(-1.52096e9 + 6.27401e8i) q^{52} +(2.29607e9 - 2.29607e9i) q^{53} +(1.93233e9 + 3.85832e8i) q^{54} +3.37255e8i q^{55} +(-5.91240e8 - 3.00678e9i) q^{56} +9.84878e8i q^{57} +(-6.28284e8 + 3.14658e9i) q^{58} +(-4.81453e8 + 4.81453e8i) q^{59} +(2.90649e8 - 6.98801e8i) q^{60} +(1.30887e9 + 1.30887e9i) q^{61} +(7.43318e9 + 1.11422e10i) q^{62} -3.08949e9 q^{63} +(7.95039e9 - 3.25242e9i) q^{64} -5.70724e8 q^{65} +(6.20191e9 + 9.29651e9i) q^{66} +(-9.42251e9 - 9.42251e9i) q^{67} +(5.33606e9 - 1.28293e10i) q^{68} +(3.94062e8 - 3.94062e8i) q^{69} +(2.08139e8 - 1.04240e9i) q^{70} -1.74203e10i q^{71} +(-1.67094e9 - 8.49767e9i) q^{72} -8.91310e9i q^{73} +(3.21263e10 + 6.41472e9i) q^{74} +(-1.77745e10 + 1.77745e10i) q^{75} +(-3.58455e9 + 1.47864e9i) q^{76} +(1.10987e10 + 1.10987e10i) q^{77} +(-1.57322e10 + 1.04953e10i) q^{78} -4.07466e10 q^{79} +(2.97971e9 + 8.70463e6i) q^{80} +3.92026e10 q^{81} +(-3.50790e10 + 2.34020e10i) q^{82} +(1.16461e10 + 1.16461e10i) q^{83} +(-1.34318e10 - 3.25617e10i) q^{84} +(3.40819e9 - 3.40819e9i) q^{85} +(-7.99336e10 - 1.59605e10i) q^{86} +3.68824e10i q^{87} +(-2.45243e10 + 3.65297e10i) q^{88} -7.96706e10i q^{89} +(5.88235e8 - 2.94601e9i) q^{90} +(-1.87819e10 + 1.87819e10i) q^{91} +(2.02585e9 + 8.42602e8i) q^{92} +(1.08864e11 + 1.08864e11i) q^{93} +(-4.53922e8 - 6.80417e8i) q^{94} -1.34507e9 q^{95} +(8.22966e10 - 5.45552e10i) q^{96} -1.03397e10 q^{97} +(2.22053e10 + 3.32852e10i) q^{98} +(3.13667e10 + 3.13667e10i) 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

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