LMFDB - Embedded newform 7.11.d.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,11,Mod(3,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, 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:	$4.44750076872$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 4910 x^{10} - 54096 x^{9} + 18202260 x^{8} - 174741840 x^{7} + 27563858336 x^{6} + \cdots + 11\!\cdots\!56 $ x^12 + 4910x^10 - 54096x^9 + 18202260x^8 - 174741840x^7 + 27563858336x^6 - 252071930880x^5 + 30697152907840x^4 - 189098231540736x^3 + 8152925099420160x^2 + 45404497829053440x + 1172250515460473856
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.6
Root			$-30.0701 - 52.0830i$ of defining polynomial
Character	$\chi$	$=$	7.3
Dual form			7.11.d.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(29.0701 + 50.3510i) q^{2} +(-331.655 - 191.481i) q^{3} +(-1178.15 + 2040.61i) q^{4} +(-1040.60 + 600.792i) q^{5} -22265.5i q^{6} +(7773.05 + 14901.5i) q^{7} -77459.9 q^{8} +(43805.3 + 75873.0i) q^{9} +O(q^{10})$	\(q+(29.0701 + 50.3510i) q^{2} +(-331.655 - 191.481i) q^{3} +(-1178.15 + 2040.61i) q^{4} +(-1040.60 + 600.792i) q^{5} -22265.5i q^{6} +(7773.05 + 14901.5i) q^{7} -77459.9 q^{8} +(43805.3 + 75873.0i) q^{9} +(-60500.9 - 34930.2i) q^{10} +(-47487.4 + 82250.6i) q^{11} +(781475. - 451185. i) q^{12} +820.540i q^{13} +(-524341. + 824570. i) q^{14} +460160. q^{15} +(-1.04535e6 - 1.81059e6i) q^{16} +(696204. + 401954. i) q^{17} +(-2.54685e6 + 4.41128e6i) q^{18} +(624477. - 360542. i) q^{19} -2.83128e6i q^{20} +(275384. - 6.43054e6i) q^{21} -5.52186e6 q^{22} +(-2.16879e6 - 3.75645e6i) q^{23} +(2.56899e7 + 1.48321e7i) q^{24} +(-4.16091e6 + 7.20691e6i) q^{25} +(-41315.0 + 23853.2i) q^{26} -1.09380e7i q^{27} +(-3.95659e7 - 1.69439e6i) q^{28} +3.73632e7 q^{29} +(1.33769e7 + 2.31695e7i) q^{30} +(-3.85492e7 - 2.22564e7i) q^{31} +(2.11173e7 - 3.65763e7i) q^{32} +(3.14988e7 - 1.81859e7i) q^{33} +4.67394e7i q^{34} +(-1.70414e7 - 1.08365e7i) q^{35} -2.06436e8 q^{36} +(3.83411e7 + 6.64088e7i) q^{37} +(3.63073e7 + 2.09620e7i) q^{38} +(157118. - 272136. i) q^{39} +(8.06049e7 - 4.65372e7i) q^{40} +1.39791e8i q^{41} +(3.31789e8 - 1.73071e8i) q^{42} +6.08906e7 q^{43} +(-1.11894e8 - 1.93806e8i) q^{44} +(-9.11678e7 - 5.26357e7i) q^{45} +(1.26094e8 - 2.18401e8i) q^{46} +(-1.33727e8 + 7.72073e7i) q^{47} +8.00656e8i q^{48} +(-1.61635e8 + 2.31660e8i) q^{49} -4.83833e8 q^{50} +(-1.53933e8 - 2.66620e8i) q^{51} +(-1.67440e6 - 966717. i) q^{52} +(1.86521e8 - 3.23065e8i) q^{53} +(5.50739e8 - 3.17969e8i) q^{54} -1.14120e8i q^{55} +(-6.02100e8 - 1.15427e9i) q^{56} -2.76147e8 q^{57} +(1.08615e9 + 1.88127e9i) q^{58} +(2.87503e8 + 1.65990e8i) q^{59} +(-5.42136e8 + 9.39008e8i) q^{60} +(5.01844e8 - 2.89740e8i) q^{61} -2.58799e9i q^{62} +(-7.90121e8 + 1.24253e9i) q^{63} +3.14665e8 q^{64} +(-492974. - 853856. i) q^{65} +(1.83135e9 + 1.05733e9i) q^{66} +(3.53271e8 - 6.11884e8i) q^{67} +(-1.64046e9 + 9.47121e8i) q^{68} +1.66113e9i q^{69} +(5.02360e7 - 1.17307e9i) q^{70} +1.88600e9 q^{71} +(-3.39315e9 - 5.87711e9i) q^{72} +(-1.00370e9 - 5.79487e8i) q^{73} +(-2.22917e9 + 3.86103e9i) q^{74} +(2.75997e9 - 1.59347e9i) q^{75} +1.69908e9i q^{76} +(-1.59478e9 - 6.82956e7i) q^{77} +1.82697e7 q^{78} +(5.30307e8 + 9.18518e8i) q^{79} +(2.17558e9 + 1.25607e9i) q^{80} +(4.92242e8 - 8.52587e8i) q^{81} +(-7.03863e9 + 4.06375e9i) q^{82} -5.63344e9i q^{83} +(1.27978e10 + 8.13807e9i) q^{84} -9.65962e8 q^{85} +(1.77010e9 + 3.06590e9i) q^{86} +(-1.23917e10 - 7.15434e9i) q^{87} +(3.67837e9 - 6.37112e9i) q^{88} +(6.92112e9 - 3.99591e9i) q^{89} -6.12051e9i q^{90} +(-1.22273e7 + 6.37810e6i) q^{91} +1.02206e10 q^{92} +(8.52335e9 + 1.47629e10i) q^{93} +(-7.77493e9 - 4.48886e9i) q^{94} +(-4.33221e8 + 7.50361e8i) q^{95} +(-1.40073e10 + 8.08713e9i) q^{96} +1.31942e10i q^{97} +(-1.63631e10 - 1.40405e9i) q^{98} -8.32080e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 246 q^{3} - 3700 q^{4} + 3330 q^{5} - 12572 q^{7} - 93504 q^{8} + 182964 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 246 * q^3 - 3700 * q^4 + 3330 * q^5 - 12572 * q^7 - 93504 * q^8 + 182964 * q^9	\( 12 q - 12 q^{2} - 246 q^{3} - 3700 q^{4} + 3330 q^{5} - 12572 q^{7} - 93504 q^{8} + 182964 q^{9} - 445740 q^{10} + 82566 q^{11} + 1581468 q^{12} - 934752 q^{14} - 729900 q^{15} - 230152 q^{16} + 389178 q^{17} + 378144 q^{18} - 5517150 q^{19} + 11878986 q^{21} - 19846048 q^{22} - 8131674 q^{23} + 31899384 q^{24} + 6794220 q^{25} + 37885176 q^{26} - 64544228 q^{28} - 86390616 q^{29} + 69082560 q^{30} - 44673798 q^{31} + 82297536 q^{32} + 293090418 q^{33} - 192479070 q^{35} - 895531584 q^{36} + 83071214 q^{37} + 528863040 q^{38} + 45216696 q^{39} + 840782640 q^{40} - 267874488 q^{42} - 975196744 q^{43} - 123891084 q^{44} + 960213420 q^{45} + 348447776 q^{46} + 782650314 q^{47} - 531271524 q^{49} - 3793600080 q^{50} + 90752418 q^{51} + 1019252472 q^{52} + 417566766 q^{53} + 4229214768 q^{54} - 2911004880 q^{56} - 3616618428 q^{57} + 2420166368 q^{58} + 456895242 q^{59} + 1019560500 q^{60} + 1469956122 q^{61} + 962168676 q^{63} - 1697861600 q^{64} - 480821880 q^{65} - 875442996 q^{66} + 1667792862 q^{67} - 3587950548 q^{68} + 4620799680 q^{70} + 9772297272 q^{71} - 5075622576 q^{72} - 3308125038 q^{73} - 8441358900 q^{74} - 13137007020 q^{75} + 1048649574 q^{77} + 25651166688 q^{78} - 2397038922 q^{79} + 1013632920 q^{80} + 394526610 q^{81} - 22926766968 q^{82} + 16162834044 q^{84} + 20859080820 q^{85} - 840264960 q^{86} - 31859197092 q^{87} - 3607027256 q^{88} - 2675986686 q^{89} + 17848798800 q^{91} + 58847183592 q^{92} + 8231670714 q^{93} - 26955870432 q^{94} - 13809374190 q^{95} - 30016813680 q^{96} - 50762451012 q^{98} + 20038367016 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 246 * q^3 - 3700 * q^4 + 3330 * q^5 - 12572 * q^7 - 93504 * q^8 + 182964 * q^9 - 445740 * q^10 + 82566 * q^11 + 1581468 * q^12 - 934752 * q^14 - 729900 * q^15 - 230152 * q^16 + 389178 * q^17 + 378144 * q^18 - 5517150 * q^19 + 11878986 * q^21 - 19846048 * q^22 - 8131674 * q^23 + 31899384 * q^24 + 6794220 * q^25 + 37885176 * q^26 - 64544228 * q^28 - 86390616 * q^29 + 69082560 * q^30 - 44673798 * q^31 + 82297536 * q^32 + 293090418 * q^33 - 192479070 * q^35 - 895531584 * q^36 + 83071214 * q^37 + 528863040 * q^38 + 45216696 * q^39 + 840782640 * q^40 - 267874488 * q^42 - 975196744 * q^43 - 123891084 * q^44 + 960213420 * q^45 + 348447776 * q^46 + 782650314 * q^47 - 531271524 * q^49 - 3793600080 * q^50 + 90752418 * q^51 + 1019252472 * q^52 + 417566766 * q^53 + 4229214768 * q^54 - 2911004880 * q^56 - 3616618428 * q^57 + 2420166368 * q^58 + 456895242 * q^59 + 1019560500 * q^60 + 1469956122 * q^61 + 962168676 * q^63 - 1697861600 * q^64 - 480821880 * q^65 - 875442996 * q^66 + 1667792862 * q^67 - 3587950548 * q^68 + 4620799680 * q^70 + 9772297272 * q^71 - 5075622576 * q^72 - 3308125038 * q^73 - 8441358900 * q^74 - 13137007020 * q^75 + 1048649574 * q^77 + 25651166688 * q^78 - 2397038922 * q^79 + 1013632920 * q^80 + 394526610 * q^81 - 22926766968 * q^82 + 16162834044 * q^84 + 20859080820 * q^85 - 840264960 * q^86 - 31859197092 * q^87 - 3607027256 * q^88 - 2675986686 * q^89 + 17848798800 * q^91 + 58847183592 * q^92 + 8231670714 * q^93 - 26955870432 * q^94 - 13809374190 * q^95 - 30016813680 * q^96 - 50762451012 * q^98 + 20038367016 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	29.0701	+	50.3510i	0.908442	+	1.57347i	0.816229	+	0.577728i	$0.196061\pi$
$2$	29.0701	+	50.3510i	0.908442	+	1.57347i	0.0922127	+	0.995739i	$0.470606\pi$
$3$	−331.655	−	191.481i	−1.36483	−	0.787987i	−0.374571	−	0.927198i	$-0.622210\pi$
$3$	−331.655	−	191.481i	−1.36483	−	0.787987i	−0.990263	+	0.139211i	$0.955543\pi$
$4$	−1178.15	+	2040.61i	−1.15053	+	1.99278i
$5$	−1040.60	+	600.792i	−0.332993	+	0.192253i	−0.657169	−	0.753743i	$-0.728246\pi$
$5$	−1040.60	+	600.792i	−0.332993	+	0.192253i	0.324176	+	0.945997i	$0.394913\pi$
$6$		−	22265.5i		−	2.86336i
$7$	7773.05	+	14901.5i	0.462489	+	0.886625i
$7$	7773.05	+	14901.5i	0.462489	+	0.886625i
$8$	−77459.9			−2.36389
$9$	43805.3	+	75873.0i	0.741847	+	1.28492i
$10$	−60500.9	−	34930.2i	−0.605009	−	0.349302i
$11$	−47487.4	+	82250.6i	−0.294859	+	0.510712i	−0.974952	−	0.222415i	$-0.928606\pi$
$11$	−47487.4	+	82250.6i	−0.294859	+	0.510712i	0.680093	+	0.733126i	$0.261939\pi$
$12$	781475.	−	451185.i	3.14057	−	1.81321i
$13$			820.540i			0.00220995i	0.999999	+	0.00110498i	$0.000351725\pi$
$13$			820.540i			0.00220995i	−0.999999	+	0.00110498i	$0.999648\pi$
$14$	−524341.	+	824570.i	−0.974931	+	1.53316i
$15$	460160.			0.605973
$16$	−1.04535e6	−	1.81059e6i	−0.996921	−	1.72672i
$17$	696204.	+	401954.i	0.490334	+	0.283095i	0.724713	−	0.689051i	$-0.241972\pi$
$17$	696204.	+	401954.i	0.490334	+	0.283095i	−0.234379	+	0.972145i	$0.575306\pi$
$18$	−2.54685e6	+	4.41128e6i	−1.34785	+	2.33454i
$19$	624477.	−	360542.i	0.252202	−	0.145609i	−0.368570	−	0.929600i	$-0.620153\pi$
$19$	624477.	−	360542.i	0.252202	−	0.145609i	0.620772	+	0.783991i	$0.286819\pi$
$20$		−	2.83128e6i		−	0.884776i
$21$	275384.	−	6.43054e6i	0.0674284	−	1.57453i
$22$	−5.52186e6			−1.07145
$23$	−2.16879e6	−	3.75645e6i	−0.336960	−	0.583632i	0.646899	−	0.762575i	$-0.276065\pi$
$23$	−2.16879e6	−	3.75645e6i	−0.336960	−	0.583632i	−0.983859	+	0.178944i	$0.942732\pi$
$24$	2.56899e7	+	1.48321e7i	3.22631	+	1.86271i
$25$	−4.16091e6	+	7.20691e6i	−0.426077	+	0.737988i
$26$	−41315.0	+	23853.2i	−0.00347729	+	0.00200761i
$27$		−	1.09380e7i		−	0.762288i
$28$	−3.95659e7	−	1.69439e6i	−2.29896	−	0.0984516i
$29$	3.73632e7			1.82161			0.910803	−	0.412842i	$-0.135464\pi$
$29$	3.73632e7			1.82161			0.910803	+	0.412842i	$0.135464\pi$
$30$	1.33769e7	+	2.31695e7i	0.550491	+	0.953478i
$31$	−3.85492e7	−	2.22564e7i	−1.34650	−	0.777404i	−0.358751	−	0.933433i	$-0.616797\pi$
$31$	−3.85492e7	−	2.22564e7i	−1.34650	−	0.777404i	−0.987752	+	0.156029i	$0.950131\pi$
$32$	2.11173e7	−	3.65763e7i	0.629346	−	1.09006i
$33$	3.14988e7	−	1.81859e7i	0.804868	−	0.464691i
$34$			4.67394e7i			1.02870i
$35$	−1.70414e7	−	1.08365e7i	−0.324462	−	0.206324i
$36$	−2.06436e8			−3.41408
$37$	3.83411e7	+	6.64088e7i	0.552913	+	0.957673i	0.998063	+	0.0622168i	$0.0198170\pi$
$37$	3.83411e7	+	6.64088e7i	0.552913	+	0.957673i	−0.445150	+	0.895456i	$0.646850\pi$
$38$	3.63073e7	+	2.09620e7i	0.458221	+	0.264554i
$39$	157118.	−	272136.i	0.00174141	−	0.00301622i
$40$	8.06049e7	−	4.65372e7i	0.787157	−	0.454465i
$41$			1.39791e8i			1.20659i	0.797517	+	0.603296i	$0.206146\pi$
$41$			1.39791e8i			1.20659i	−0.797517	+	0.603296i	$0.793854\pi$
$42$	3.31789e8	−	1.73071e8i	2.53873	−	1.32427i
$43$	6.08906e7			0.414198			0.207099	−	0.978320i	$-0.433598\pi$
$43$	6.08906e7			0.414198			0.207099	+	0.978320i	$0.433598\pi$
$44$	−1.11894e8	−	1.93806e8i	−0.678491	−	1.17518i
$45$	−9.11678e7	−	5.26357e7i	−0.494059	−	0.285245i
$46$	1.26094e8	−	2.18401e8i	0.612217	−	1.06039i
$47$	−1.33727e8	+	7.72073e7i	−0.583082	+	0.336643i	−0.762357	−	0.647156i	$-0.775958\pi$
$47$	−1.33727e8	+	7.72073e7i	−0.583082	+	0.336643i	0.179275	+	0.983799i	$0.442625\pi$
$48$			8.00656e8i			3.14224i
$49$	−1.61635e8	+	2.31660e8i	−0.572208	+	0.820109i
$50$	−4.83833e8			−1.54827
$51$	−1.53933e8	−	2.66620e8i	−0.446150	−	0.772754i
$52$	−1.67440e6	−	966717.i	−0.00440396	−	0.00254263i
$53$	1.86521e8	−	3.23065e8i	0.446015	−	0.772520i	−0.552107	−	0.833773i	$-0.686176\pi$
$53$	1.86521e8	−	3.23065e8i	0.446015	−	0.772520i	0.998122	+	0.0612526i	$0.0195095\pi$
$54$	5.50739e8	−	3.17969e8i	1.19944	−	0.692495i
$55$		−	1.14120e8i		−	0.226751i
$56$	−6.02100e8	−	1.15427e9i	−1.09327	−	2.09588i
$57$	−2.76147e8			−0.458951
$58$	1.08615e9	+	1.88127e9i	1.65482	+	2.86624i
$59$	2.87503e8	+	1.65990e8i	0.402145	+	0.232179i	0.687409	−	0.726270i	$-0.258748\pi$
$59$	2.87503e8	+	1.65990e8i	0.402145	+	0.232179i	−0.285264	+	0.958449i	$0.592081\pi$
$60$	−5.42136e8	+	9.39008e8i	−0.697192	+	1.20757i
$61$	5.01844e8	−	2.89740e8i	0.594183	−	0.343051i	−0.172567	−	0.984998i	$-0.555206\pi$
$61$	5.01844e8	−	2.89740e8i	0.594183	−	0.343051i	0.766750	+	0.641946i	$0.221873\pi$
$62$		−	2.58799e9i		−	2.82491i
$63$	−7.90121e8	+	1.24253e9i	−0.796143	+	1.25200i
$64$	3.14665e8			0.293055
$65$	−492974.	−	853856.i	−0.000424871	−	0.000735898i
$66$	1.83135e9	+	1.05733e9i	1.46235	+	0.844289i
$67$	3.53271e8	−	6.11884e8i	0.261658	−	0.453205i	−0.705024	−	0.709183i	$-0.749064\pi$
$67$	3.53271e8	−	6.11884e8i	0.261658	−	0.453205i	0.966683	+	0.255978i	$0.0823973\pi$
$68$	−1.64046e9	+	9.47121e8i	−1.12829	+	0.651420i
$69$			1.66113e9i			1.06208i
$70$	5.02360e7	−	1.17307e9i	0.0298899	−	0.697964i
$71$	1.88600e9			1.04532			0.522662	−	0.852540i	$-0.324939\pi$
$71$	1.88600e9			1.04532			0.522662	+	0.852540i	$0.324939\pi$
$72$	−3.39315e9	−	5.87711e9i	−1.75364	−	3.03740i
$73$	−1.00370e9	−	5.79487e8i	−0.484161	−	0.279531i	0.237988	−	0.971268i	$-0.423512\pi$
$73$	−1.00370e9	−	5.79487e8i	−0.484161	−	0.279531i	−0.722149	+	0.691738i	$0.756846\pi$
$74$	−2.22917e9	+	3.86103e9i	−1.00458	+	1.73998i
$75$	2.75997e9	−	1.59347e9i	1.16305	−	0.671487i
$76$			1.69908e9i			0.670111i
$77$	−1.59478e9	−	6.82956e7i	−0.589179	−	0.0252313i
$78$	1.82697e7			0.00632790
$79$	5.30307e8	+	9.18518e8i	0.172342	+	0.298505i	0.939238	−	0.343266i	$-0.111533\pi$
$79$	5.30307e8	+	9.18518e8i	0.172342	+	0.298505i	−0.766896	+	0.641771i	$0.778200\pi$
$80$	2.17558e9	+	1.25607e9i	0.663935	+	0.383323i
$81$	4.92242e8	−	8.52587e8i	0.141173	−	0.244520i
$82$	−7.03863e9	+	4.06375e9i	−1.89853	+	1.09612i
$83$		−	5.63344e9i		−	1.43016i	−0.699045	−	0.715078i	$-0.746391\pi$
$83$		−	5.63344e9i		−	1.43016i	0.699045	−	0.715078i	$-0.253609\pi$
$84$	1.27978e10	+	8.13807e9i	3.06012	+	1.94592i
$85$	−9.65962e8			−0.217704
$86$	1.77010e9	+	3.06590e9i	0.376275	+	0.651727i
$87$	−1.23917e10	−	7.15434e9i	−2.48619	−	1.43540i
$88$	3.67837e9	−	6.37112e9i	0.697015	−	1.20726i
$89$	6.92112e9	−	3.99591e9i	1.23944	−	0.715592i	0.270462	−	0.962731i	$-0.412823\pi$
$89$	6.92112e9	−	3.99591e9i	1.23944	−	0.715592i	0.968980	+	0.247138i	$0.0794902\pi$
$90$		−	6.12051e9i		−	1.03651i
$91$	−1.22273e7	+	6.37810e6i	−0.00195940	+	0.00102208i
$92$	1.02206e10			1.55073
$93$	8.52335e9	+	1.47629e10i	1.22517	+	2.12205i
$94$	−7.77493e9	−	4.48886e9i	−1.05939	−	0.611641i
$95$	−4.33221e8	+	7.50361e8i	−0.0559876	+	0.0969733i
$96$	−1.40073e10	+	8.08713e9i	−1.71790	+	0.991832i
$97$			1.31942e10i			1.53647i	0.640166	+	0.768237i	$0.278866\pi$
$97$			1.31942e10i			1.53647i	−0.640166	+	0.768237i	$0.721134\pi$
$98$	−1.63631e10	−	1.40405e9i	−1.81023	−	0.155329i
$99$	−8.32080e9			−0.874962
$100$	−9.80432e9	−	1.69816e10i	−0.980432	−	1.69816i
$101$	5.06568e9	+	2.92467e9i	0.481982	+	0.278272i	0.721242	−	0.692683i	$-0.243572\pi$
$101$	5.06568e9	+	2.92467e9i	0.481982	+	0.278272i	−0.239260	+	0.970956i	$0.576905\pi$
$102$	8.94970e9	−	1.55013e10i	0.810602	−	1.40400i
$103$	−7.87997e9	+	4.54950e9i	−0.679733	+	0.392444i	−0.799754	−	0.600327i	$-0.795037\pi$
$103$	−7.87997e9	+	4.54950e9i	−0.679733	+	0.392444i	0.120022	+	0.992771i	$0.461704\pi$
$104$		−	6.35589e7i		−	0.00522408i
$105$	3.57685e9	+	6.85708e9i	0.280256	+	0.537270i
$106$	2.16888e10			1.62071
$107$	2.47778e8	+	4.29164e8i	0.0176662	+	0.0305988i	0.874723	−	0.484623i	$-0.161043\pi$
$107$	2.47778e8	+	4.29164e8i	0.0176662	+	0.0305988i	−0.857057	+	0.515221i	$0.827710\pi$
$108$	2.23202e10	+	1.28866e10i	1.51907	+	0.877038i
$109$	−3.89801e9	+	6.75155e9i	−0.253344	+	0.438805i	−0.964444	−	0.264286i	$-0.914864\pi$
$109$	−3.89801e9	+	6.75155e9i	−0.253344	+	0.438805i	0.711100	+	0.703090i	$0.248197\pi$
$110$	5.74606e9	−	3.31749e9i	0.356785	−	0.205990i
$111$		−	2.93664e10i		−	1.74275i
$112$	1.88550e10	−	2.96511e10i	1.06989	−	1.68248i
$113$	−4.46902e9			−0.242561			−0.121280	−	0.992618i	$-0.538700\pi$
$113$	−4.46902e9			−0.242561			−0.121280	+	0.992618i	$0.538700\pi$
$114$	−8.02764e9	−	1.39043e10i	−0.416931	−	0.722145i
$115$	4.51369e9	+	2.60598e9i	0.224410	+	0.129563i
$116$	−4.40193e10	+	7.62437e10i	−2.09582	+	3.63006i
$117$	−6.22569e7	+	3.59440e7i	−0.00283961	+	0.00163945i
$118$			1.93014e10i			0.843683i
$119$	−5.78083e8	+	1.34989e10i	−0.0242245	+	0.565671i
$120$	−3.56440e10			−1.43245
$121$	8.45860e9	+	1.46507e10i	0.326116	+	0.564849i
$122$	2.91774e10	+	1.68456e10i	1.07956	+	0.623285i
$123$	2.67673e10	−	4.63624e10i	0.950779	−	1.64680i
$124$	9.08333e10	−	5.24426e10i	3.09839	−	1.78886i
$125$		−	2.17336e10i		−	0.712166i
$126$	−8.55315e10	−	3.66284e9i	−2.69323	−	0.115336i
$127$	−5.83688e10			−1.76670			−0.883349	−	0.468716i	$-0.844717\pi$
$127$	−5.83688e10			−1.76670			−0.883349	+	0.468716i	$0.844717\pi$
$128$	−1.24768e10	−	2.16105e10i	−0.363123	−	0.628947i
$129$	−2.01946e10	−	1.16594e10i	−0.565311	−	0.326383i
$130$	2.86616e7	−	4.96434e7i	0.000771941	−	0.00133704i
$131$	2.87805e10	−	1.66164e10i	0.746005	−	0.430706i	−0.0782436	−	0.996934i	$-0.524931\pi$
$131$	2.87805e10	−	1.66164e10i	0.746005	−	0.430706i	0.824249	+	0.566228i	$0.191598\pi$
$132$			8.57024e10i			2.13857i
$133$	1.02267e10	+	6.50313e9i	0.245741	+	0.156266i
$134$	4.10786e10			0.950805
$135$	6.57146e9	+	1.13821e10i	0.146553	+	0.253836i
$136$	−5.39279e10	−	3.11353e10i	−1.15909	−	0.669204i
$137$	−1.08035e9	+	1.87122e9i	−0.0223852	+	0.0387724i	−0.877001	−	0.480489i	$-0.840459\pi$
$137$	−1.08035e9	+	1.87122e9i	−0.0223852	+	0.0387724i	0.854616	+	0.519261i	$0.173793\pi$
$138$	−8.36393e10	+	4.82892e10i	−1.67115	+	0.964838i
$139$			4.22809e10i			0.814836i	0.913242	+	0.407418i	$0.133571\pi$
$139$			4.22809e10i			0.814836i	−0.913242	+	0.407418i	$0.866429\pi$
$140$	4.21904e10	−	2.20077e10i	0.784464	−	0.409199i
$141$	5.91349e10			1.06108
$142$	5.48264e10	+	9.49621e10i	0.949616	+	1.64478i
$143$	−6.74899e7	−	3.89653e7i	−0.00112865	−	0.000651626i
$144$	9.15835e10	−	1.58627e11i	1.47913	−	2.56192i
$145$	−3.88802e10	+	2.24475e10i	−0.606581	+	0.350210i
$146$		−	6.73831e10i		−	1.01575i
$147$	9.79653e10	−	4.58813e10i	1.42720	−	0.668420i
$148$	−1.80686e11			−2.54458
$149$	−1.57088e10	−	2.72085e10i	−0.213901	−	0.370487i	0.739031	−	0.673671i	$-0.235284\pi$
$149$	−1.57088e10	−	2.72085e10i	−0.213901	−	0.370487i	−0.952932	+	0.303184i	$0.901950\pi$
$150$	1.60465e11	+	9.26448e10i	2.11312	+	1.22001i
$151$	−4.62392e9	+	8.00886e9i	−0.0589014	+	0.102020i	−0.893973	−	0.448122i	$-0.852093\pi$
$151$	−4.62392e9	+	8.00886e9i	−0.0589014	+	0.102020i	0.835071	+	0.550142i	$0.185426\pi$
$152$	−4.83719e10	+	2.79275e10i	−0.596177	+	0.344203i
$153$			7.04309e10i			0.840051i
$154$	−4.29217e10	−	8.22841e10i	−0.495534	−	0.949975i
$155$	5.34859e10			0.597834
$156$	3.70215e8	+	6.41232e8i	0.00400711	+	0.00694052i
$157$	−1.09413e11	−	6.31697e10i	−1.14702	−	0.662232i	−0.198861	−	0.980028i	$-0.563724\pi$
$157$	−1.09413e11	−	6.31697e10i	−1.14702	−	0.662232i	−0.948159	+	0.317796i	$0.897057\pi$
$158$	−3.08322e10	+	5.34029e10i	−0.313126	+	0.542350i
$159$	−1.23721e11	+	7.14305e10i	−1.21747	+	0.702908i
$160$			5.07485e10i			0.483975i
$161$	3.91187e10	−	6.15173e10i	0.361622	−	0.568680i
$162$	5.72381e10			0.512992
$163$	−4.62552e10	−	8.01163e10i	−0.401996	−	0.696278i	0.591970	−	0.805960i	$-0.298350\pi$
$163$	−4.62552e10	−	8.01163e10i	−0.401996	−	0.696278i	−0.993967	+	0.109681i	$0.965017\pi$
$164$	−2.85259e11	−	1.64695e11i	−2.40448	−	1.38823i
$165$	−2.18518e10	+	3.78485e10i	−0.178677	+	0.309477i
$166$	2.83649e11	−	1.63765e11i	2.25030	−	1.29921i
$167$			2.04363e11i			1.57333i	0.617382	+	0.786663i	$0.288193\pi$
$167$			2.04363e11i			1.57333i	−0.617382	+	0.786663i	$0.711807\pi$
$168$	−2.13312e10	+	4.98109e11i	−0.159393	+	3.72201i
$169$	1.37858e11			0.999995
$170$	−2.80807e10	−	4.86371e10i	−0.197771	−	0.342549i
$171$	5.47108e10	+	3.15873e10i	0.374190	+	0.216039i
$172$	−7.17380e10	+	1.24254e11i	−0.476549	+	0.825406i
$173$	−3.93998e10	+	2.27475e10i	−0.254252	+	0.146792i	−0.621710	−	0.783248i	$-0.713562\pi$
$173$	−3.93998e10	+	2.27475e10i	−0.254252	+	0.146792i	0.367458	+	0.930040i	$0.380228\pi$
$174$		−	8.31911e11i		−	5.21591i
$175$	−1.39737e11	−	5.98415e9i	−0.851374	−	0.0364596i
$176$	1.98563e11			1.17581
$177$	−6.35679e10	−	1.10103e11i	−0.365908	−	0.633770i
$178$	4.02396e11	+	2.32323e11i	2.25192	+	1.30015i
$179$	1.02392e11	−	1.77348e11i	0.557187	−	0.965076i	−0.440543	−	0.897731i	$-0.645214\pi$
$179$	1.02392e11	−	1.77348e11i	0.557187	−	0.965076i	0.997730	−	0.0673442i	$-0.0214526\pi$
$180$	2.14818e11	−	1.24025e11i	1.13686	−	0.656368i
$181$			1.96209e11i			1.01001i	0.863116	+	0.505006i	$0.168510\pi$
$181$			1.96209e11i			1.01001i	−0.863116	+	0.505006i	$0.831490\pi$
$182$	−6.76593e8	−	4.30243e8i	−0.00338821	−	0.00215455i
$183$	−2.21919e11			−1.08128
$184$	1.67994e11	+	2.90974e11i	0.796535	+	1.37964i
$185$	−7.97957e10	−	4.60701e10i	−0.368232	−	0.212599i
$186$	−4.95550e11	+	8.58318e11i	−2.22599	+	3.85553i
$187$	−6.61219e10	+	3.81755e10i	−0.289159	+	0.166946i
$188$		−	3.63846e11i		−	1.54927i
$189$	1.62993e11	−	8.50217e10i	0.675864	−	0.352550i
$190$	−5.03752e10			−0.203446
$191$	−3.30797e10	−	5.72957e10i	−0.130135	−	0.225401i	0.793593	−	0.608448i	$-0.208208\pi$
$191$	−3.30797e10	−	5.72957e10i	−0.130135	−	0.225401i	−0.923729	+	0.383048i	$0.874874\pi$
$192$	−1.04360e11	−	6.02523e10i	−0.399971	−	0.230923i
$193$	1.23498e11	−	2.13905e11i	0.461183	−	0.798792i	−0.537837	−	0.843049i	$-0.680759\pi$
$193$	1.23498e11	−	2.13905e11i	0.461183	−	0.798792i	0.999020	+	0.0442564i	$0.0140919\pi$
$194$	−6.64342e11	+	3.83558e11i	−2.41759	+	1.39580i
$195$			3.77580e8i			0.00133917i
$196$	−2.82299e11	−	6.02763e11i	−0.975954	−	2.08385i
$197$	2.53527e11			0.854462			0.427231	−	0.904143i	$-0.359489\pi$
$197$	2.53527e11			0.854462			0.427231	+	0.904143i	$0.359489\pi$
$198$	−2.41887e11	−	4.18960e11i	−0.794852	−	1.37672i
$199$	4.85554e11	+	2.80335e11i	1.55586	+	0.898279i	0.997645	+	0.0685858i	$0.0218487\pi$
$199$	4.85554e11	+	2.80335e11i	1.55586	+	0.898279i	0.558220	+	0.829693i	$0.311485\pi$
$200$	3.22304e11	−	5.58246e11i	1.00720	−	1.74452i
$201$	−2.34328e11	+	1.35289e11i	−0.714240	+	0.412367i
$202$			3.40082e11i			1.01118i
$203$	2.90426e11	+	5.56768e11i	0.842472	+	1.61508i
$204$	7.25422e11			2.05324
$205$	−8.39854e10	−	1.45467e11i	−0.231972	−	0.401787i
$206$	−4.58143e11	−	2.64509e11i	−1.23500	−	0.713025i
$207$	1.90009e11	−	3.29105e11i	0.499945	−	0.865930i
$208$	1.48567e9	−	8.57750e8i	0.00381597	−	0.00220315i
$209$			6.84848e10i			0.171737i
$210$	−2.41281e11	+	3.79434e11i	−0.590782	+	0.929052i
$211$	−1.86314e11			−0.445485			−0.222742	−	0.974877i	$-0.571501\pi$
$211$	−1.86314e11			−0.445485			−0.222742	+	0.974877i	$0.571501\pi$
$212$	4.39499e11	+	7.61234e11i	1.02631	+	1.77762i
$213$	−6.25502e11	−	3.61133e11i	−1.42669	−	0.823701i
$214$	−1.44059e10	+	2.49517e10i	−0.0320975	+	0.0555945i
$215$	−6.33629e10	+	3.65826e10i	−0.137925	+	0.0796310i
$216$			8.47256e11i			1.80196i
$217$	3.20088e10	−	7.47442e11i	0.0665228	−	1.55338i
$218$	−4.53263e11			−0.920593
$219$	2.21921e11	+	3.84379e11i	0.440533	+	0.763025i
$220$	2.32875e11	+	1.34450e11i	0.451865	+	0.260884i
$221$	−3.29819e8	+	5.71264e8i	−0.000625626	+	0.00108362i
$222$	1.47863e12	−	8.53685e11i	2.74216	−	1.58319i
$223$		−	1.28609e11i		−	0.233210i	−0.993178	−	0.116605i	$-0.962799\pi$
$223$		−	1.28609e11i		−	0.233210i	0.993178	−	0.116605i	$-0.0372012\pi$
$224$	7.09188e11	+	3.03706e10i	1.25754	+	0.0538534i
$225$	−7.29080e11			−1.26434
$226$	−1.29915e11	−	2.25020e11i	−0.220352	−	0.381661i
$227$	−1.55587e11	−	8.98282e10i	−0.258133	−	0.149033i	0.365349	−	0.930870i	$-0.380950\pi$
$227$	−1.55587e11	−	8.98282e10i	−0.258133	−	0.149033i	−0.623483	+	0.781837i	$0.714283\pi$
$228$	3.25342e11	−	5.63509e11i	0.528039	−	0.914590i
$229$	6.27407e11	−	3.62233e11i	0.996258	−	0.575190i	0.0891188	−	0.996021i	$-0.471595\pi$
$229$	6.27407e11	−	3.62233e11i	0.996258	−	0.575190i	0.907139	+	0.420831i	$0.138262\pi$
$230$			3.03025e11i			0.470803i
$231$	5.15839e11	+	3.28020e11i	0.784249	+	0.498702i
$232$	−2.89415e12			−4.30607
$233$	2.18791e11	+	3.78958e11i	0.318604	+	0.551838i	0.980197	−	0.198025i	$-0.0634528\pi$
$233$	2.18791e11	+	3.78958e11i	0.318604	+	0.551838i	−0.661593	+	0.749863i	$0.730119\pi$
$234$	−3.61963e9	−	2.08980e9i	−0.00515923	−	0.00297869i
$235$	9.27711e10	−	1.60684e11i	0.129441	−	0.224199i
$236$	−6.77442e11	+	3.91121e11i	−0.925363	+	0.534259i
$237$		−	4.06174e11i		−	0.543213i
$238$	−6.96488e11	+	3.63308e11i	−0.912071	+	0.475762i
$239$	7.04423e11			0.903325			0.451662	−	0.892189i	$-0.350831\pi$
$239$	7.04423e11			0.903325			0.451662	+	0.892189i	$0.350831\pi$
$240$	−4.81027e11	−	8.33164e11i	−0.604107	−	1.04634i
$241$	−1.13679e12	−	6.56324e11i	−1.39828	−	0.807297i	−0.404067	−	0.914729i	$-0.632404\pi$
$241$	−1.13679e12	−	6.56324e11i	−1.39828	−	0.807297i	−0.994212	+	0.107433i	$0.965737\pi$
$242$	−4.91786e11	+	8.51798e11i	−0.592515	+	1.02627i
$243$	−8.85855e11	+	5.11449e11i	−1.04552	+	0.603630i
$244$			1.36542e12i			1.57877i
$245$	2.90175e10	−	3.38175e11i	0.0328723	−	0.383099i
$246$	3.11252e12			3.45491
$247$	2.95839e8	+	5.12408e8i	0.000321789	+	0.000557354i
$248$	2.98602e12	+	1.72398e12i	3.18298	+	1.83770i
$249$	−1.07870e12	+	1.86836e12i	−1.12694	+	1.95192i
$250$	1.09431e12	−	6.31798e11i	1.12057	−	0.646961i
$251$			2.37286e11i			0.238179i	0.992884	+	0.119089i	$0.0379975\pi$
$251$			2.37286e11i			0.238179i	−0.992884	+	0.119089i	$0.962003\pi$
$252$	−1.60464e12	−	3.07621e12i	−1.57897	−	3.02701i
$253$	4.11961e11			0.397423
$254$	−1.69679e12	−	2.93893e12i	−1.60494	−	2.77984i
$255$	3.20366e11	+	1.84963e11i	0.297129	+	0.171548i
$256$	8.86513e11	−	1.53549e12i	0.806279	−	1.39652i
$257$	1.03919e12	−	5.99977e11i	0.926893	−	0.535142i	0.0410652	−	0.999156i	$-0.486925\pi$
$257$	1.03919e12	−	5.99977e11i	0.926893	−	0.535142i	0.885827	+	0.464015i	$0.153592\pi$
$258$		−	1.35576e12i		−	1.18600i
$259$	−6.91564e11	+	1.08754e12i	−0.593381	+	0.933139i
$260$	2.32318e9			0.00195531
$261$	1.63671e12	+	2.83486e12i	1.35135	+	2.34061i
$262$	1.67331e12	+	9.66084e11i	1.35540	+	0.782543i
$263$	3.24035e11	−	5.61246e11i	0.257522	−	0.446040i	−0.708056	−	0.706156i	$-0.750428\pi$
$263$	3.24035e11	−	5.61246e11i	0.257522	−	0.446040i	0.965577	+	0.260116i	$0.0837608\pi$
$264$	−2.43989e12	+	1.40867e12i	−1.90262	+	1.09848i
$265$			4.48242e11i			0.342991i
$266$	−3.01472e10	+	7.03971e11i	−0.0226380	+	0.528624i
$267$	−3.06056e12			−2.25551
$268$	8.32411e11	+	1.44178e12i	0.602093	+	1.04286i
$269$	3.64460e11	+	2.10421e11i	0.258755	+	0.149392i	0.623767	−	0.781611i	$-0.285602\pi$
$269$	3.64460e11	+	2.10421e11i	0.258755	+	0.149392i	−0.365011	+	0.931003i	$0.618935\pi$
$270$	−3.82067e11	+	6.61759e11i	−0.266269	+	0.461191i
$271$	1.52741e12	−	8.81849e11i	1.04498	−	0.603320i	0.123741	−	0.992315i	$-0.460511\pi$
$271$	1.52741e12	−	8.81849e11i	1.04498	−	0.603320i	0.921240	+	0.388995i	$0.127178\pi$
$272$		−	1.68073e12i		−	1.12889i
$273$	5.27652e9	+	2.25964e8i	0.00347964	+	0.000149014i
$274$	−1.25624e11			−0.0813427
$275$	−3.95182e11	−	6.84475e11i	−0.251266	−	0.435205i
$276$	−3.38971e12	−	1.95705e12i	−2.11649	−	1.22196i
$277$	1.41961e11	−	2.45883e11i	0.0870500	−	0.150775i	−0.819213	−	0.573490i	$-0.805589\pi$
$277$	1.41961e11	−	2.45883e11i	0.0870500	−	0.150775i	0.906263	+	0.422714i	$0.138923\pi$
$278$	−2.12888e12	+	1.22911e12i	−1.28212	+	0.740231i
$279$		−	3.89980e12i		−	2.30686i
$280$	1.32002e12	+	8.39398e11i	0.766992	+	0.487728i
$281$	1.19851e12			0.684086			0.342043	−	0.939684i	$-0.388881\pi$
$281$	1.19851e12			0.684086			0.342043	+	0.939684i	$0.388881\pi$
$282$	1.71906e12	+	2.97750e12i	0.963930	+	1.66958i
$283$	−1.27481e12	−	7.36013e11i	−0.702286	−	0.405465i	0.105913	−	0.994375i	$-0.466224\pi$
$283$	−1.27481e12	−	7.36013e11i	−0.702286	−	0.405465i	−0.808198	+	0.588911i	$0.799557\pi$
$284$	−2.22199e12	+	3.84860e12i	−1.20268	+	2.08310i
$285$	2.87359e11	−	1.65907e11i	0.152827	−	0.0882349i
$286$		−	4.53091e9i		−	0.00236786i
$287$	−2.08310e12	+	1.08661e12i	−1.06980	+	0.558036i
$288$	3.70021e12			1.86751
$289$	−6.84863e11	−	1.18622e12i	−0.339715	−	0.588403i
$290$	−2.26051e12	−	1.30510e12i	−1.10209	−	0.636290i
$291$	2.52644e12	−	4.37592e12i	1.21072	−	2.09703i
$292$	2.36501e12	−	1.36544e12i	1.11409	−	0.643219i
$293$			6.66874e11i			0.308820i	0.988007	+	0.154410i	$0.0493477\pi$
$293$			6.66874e11i			0.308820i	−0.988007	+	0.154410i	$0.950652\pi$
$294$	5.15803e12	+	3.59887e12i	2.34827	+	1.63844i
$295$	−3.98902e11			−0.178549
$296$	−2.96990e12	−	5.14402e12i	−1.30702	−	2.26383i
$297$	8.99658e11	+	5.19418e11i	0.389309	+	0.224768i
$298$	9.13316e11	−	1.58191e12i	0.388633	−	0.673132i
$299$	3.08232e9	−	1.77958e9i	0.00128980	−	0.000744666i
$300$			7.50936e12i			3.09027i
$301$	4.73306e11	+	9.07362e11i	0.191562	+	0.367238i
$302$	−5.37672e11			−0.214034
$303$	−1.12004e12	−	1.93996e12i	−0.438550	−	0.759591i
$304$	−1.30559e12	−	7.53783e11i	−0.502851	−	0.290321i
$305$	−3.48147e11	+	6.03008e11i	−0.131906	+	0.228467i
$306$	−3.54626e12	+	2.04743e12i	−1.32179	+	0.763138i
$307$			4.33078e12i			1.58809i	0.607860	+	0.794044i	$0.292028\pi$
$307$			4.33078e12i			1.58809i	−0.607860	+	0.794044i	$0.707972\pi$
$308$	2.01825e12	−	3.17386e12i	0.728150	−	1.14508i
$309$	3.48457e12			1.23696
$310$	1.55484e12	+	2.69307e12i	0.543098	+	0.940673i
$311$	3.40521e12	+	1.96600e12i	1.17042	+	0.675743i	0.953779	−	0.300508i	$-0.0971563\pi$
$311$	3.40521e12	+	1.96600e12i	1.17042	+	0.675743i	0.216642	+	0.976251i	$0.430490\pi$
$312$	−1.21703e10	+	2.10796e10i	−0.00411651	+	0.00713000i
$313$	−3.37555e12	+	1.94887e12i	−1.12363	+	0.648727i	−0.942325	−	0.334700i	$-0.891365\pi$
$313$	−3.37555e12	+	1.94887e12i	−1.12363	+	0.648727i	−0.181304	+	0.983427i	$0.558032\pi$
$314$		−	7.34540e12i		−	2.40640i
$315$	7.56998e10	−	1.76768e12i	0.0244085	−	0.569968i
$316$	−2.49911e12			−0.793142
$317$	−2.87580e11	−	4.98104e11i	−0.0898386	−	0.155605i	0.817604	−	0.575781i	$-0.195302\pi$
$317$	−2.87580e11	−	4.98104e11i	−0.0898386	−	0.155605i	−0.907443	+	0.420176i	$0.861968\pi$
$318$	−7.19319e12	−	4.15299e12i	−2.21200	−	1.27710i
$319$	−1.77428e12	+	3.07315e12i	−0.537117	+	0.930315i
$320$	−3.27441e11	+	1.89048e11i	−0.0975850	+	0.0563407i
$321$		−	1.89779e11i		−	0.0556830i
$322$	4.23464e12	+	1.81346e11i	1.22331	+	0.0523877i
$323$	5.79685e11			0.164884
$324$	1.15987e12	+	2.00895e12i	0.324850	+	0.562656i
$325$	−5.91356e9	−	3.41420e9i	−0.00163092	−	0.000941611i
$326$	2.68929e12	−	4.65798e12i	0.730381	−	1.26506i
$327$	2.58559e12	−	1.49279e12i	0.691545	−	0.399264i
$328$		−	1.08282e13i		−	2.85225i
$329$	−2.18997e12	−	1.39260e12i	−0.568145	−	0.361282i
$330$	−2.54094e12			−0.649270
$331$	−4.33735e11	−	7.51252e11i	−0.109165	−	0.189080i	0.806267	−	0.591552i	$-0.201484\pi$
$331$	−4.33735e11	−	7.51252e11i	−0.109165	−	0.189080i	−0.915432	+	0.402472i	$0.868151\pi$
$332$	1.14957e13	+	6.63702e12i	2.84999	+	1.64544i
$333$	−3.35909e12	+	5.81812e12i	−0.820353	+	1.42089i
$334$	−1.02899e13	+	5.94085e12i	−2.47558	+	1.42928i
$335$			8.48970e11i			0.201219i
$336$	−1.19310e13	+	6.22354e12i	−2.78599	+	1.45325i
$337$	2.19605e12			0.505233			0.252617	−	0.967566i	$-0.418709\pi$
$337$	2.19605e12			0.505233			0.252617	+	0.967566i	$0.418709\pi$
$338$	4.00755e12	+	6.94127e12i	0.908437	+	1.57346i
$339$	1.48217e12	+	8.55732e11i	0.331055	+	0.191135i
$340$	1.13804e12	−	1.97115e12i	0.250475	−	0.433836i
$341$	3.66121e12	−	2.11380e12i	0.794058	−	0.458450i
$342$			3.67299e12i			0.785035i
$343$	−4.70848e12	−	6.07889e11i	−0.991769	−	0.128042i
$344$	−4.71658e12			−0.979117
$345$	−9.97991e11	−	1.72857e12i	−0.204188	−	0.353665i
$346$	−2.29072e12	−	1.32255e12i	−0.461946	−	0.266704i
$347$	−5.46745e11	+	9.46991e11i	−0.108677	+	0.188234i	−0.915235	−	0.402921i	$-0.867995\pi$
$347$	−5.46745e11	+	9.46991e11i	−0.108677	+	0.188234i	0.806558	+	0.591156i	$0.201328\pi$
$348$	2.91984e13	−	1.68577e13i	5.72088	−	3.30295i
$349$		−	1.44565e12i		−	0.279214i	−0.990207	−	0.139607i	$-0.955416\pi$
$349$		−	1.44565e12i		−	0.279214i	0.990207	−	0.139607i	$-0.0445839\pi$
$350$	−3.76086e12	−	7.20984e12i	−0.716056	−	1.37273i
$351$	8.97508e9			0.00168462
$352$	2.00562e12	+	3.47383e12i	0.371137	+	0.642828i
$353$	−5.15921e12	−	2.97867e12i	−0.941261	−	0.543437i	−0.0509056	−	0.998703i	$-0.516211\pi$
$353$	−5.15921e12	−	2.97867e12i	−0.941261	−	0.543437i	−0.890355	+	0.455266i	$0.849544\pi$
$354$	3.69585e12	−	6.40141e12i	0.664812	−	1.15149i
$355$	−1.96258e12	+	1.13310e12i	−0.348085	+	0.200967i
$356$			1.88311e13i			3.29325i
$357$	2.77651e12	−	4.36628e12i	0.478804	−	0.752958i
$358$	1.19062e13			2.02469
$359$	−1.14116e12	−	1.97654e12i	−0.191370	−	0.331462i	0.754335	−	0.656490i	$-0.227960\pi$
$359$	−1.14116e12	−	1.97654e12i	−0.191370	−	0.331462i	−0.945704	+	0.325028i	$0.894626\pi$
$360$	7.06184e12	+	4.07716e12i	1.16790	+	0.674287i
$361$	−2.80555e12	+	4.85936e12i	−0.457596	+	0.792580i
$362$	−9.87932e12	+	5.70383e12i	−1.58922	+	0.917537i
$363$		−	6.47864e12i		−	1.02790i
$364$	1.39031e9	−	3.24655e10i	0.000217574	−	0.00508060i
$365$	1.39260e12			0.214963
$366$	−6.45120e12	−	1.11738e13i	−0.982280	−	1.70136i
$367$	4.40851e12	+	2.54525e12i	0.662158	+	0.382297i	0.793099	−	0.609093i	$-0.208467\pi$
$367$	4.40851e12	+	2.54525e12i	0.662158	+	0.382297i	−0.130941	+	0.991390i	$0.541800\pi$
$368$	−4.53428e12	+	7.85360e12i	−0.671845	+	1.16367i
$369$	−1.06064e13	+	6.12360e12i	−1.55037	+	0.895107i
$370$		−	5.35706e12i		−	0.772534i
$371$	6.26399e12	+	2.68252e11i	0.891213	+	0.0381657i
$372$	−4.01670e13			−5.63839
$373$	−2.85466e12	−	4.94441e12i	−0.395376	−	0.684811i	0.597773	−	0.801665i	$-0.296052\pi$
$373$	−2.85466e12	−	4.94441e12i	−0.395376	−	0.684811i	−0.993149	+	0.116854i	$0.962719\pi$
$374$	−3.84435e12	−	2.21953e12i	−0.525369	−	0.303322i
$375$	−4.16156e12	+	7.20804e12i	−0.561177	+	0.971988i
$376$	1.03585e13	−	5.98047e12i	1.37834	−	0.795785i
$377$			3.06580e10i			0.00402566i
$378$	9.01915e12	+	5.73525e12i	1.16871	+	0.743179i
$379$	4.68574e12			0.599214			0.299607	−	0.954063i	$-0.403144\pi$
$379$	4.68574e12			0.599214			0.299607	+	0.954063i	$0.403144\pi$
$380$	−1.02080e12	−	1.76807e12i	−0.128831	−	0.223142i
$381$	1.93583e13	+	1.11765e13i	2.41125	+	1.39213i
$382$	1.92326e12	−	3.33119e12i	0.236440	−	0.409527i
$383$	−3.30138e12	+	1.90605e12i	−0.400591	+	0.231281i	−0.686739	−	0.726904i	$-0.740958\pi$
$383$	−3.30138e12	+	1.90605e12i	−0.400591	+	0.231281i	0.286148	+	0.958185i	$0.407625\pi$
$384$			9.55627e12i			1.14454i
$385$	1.70056e12	−	8.87062e11i	0.201043	−	0.104870i
$386$	1.43604e13			1.67583
$387$	2.66733e12	+	4.61995e12i	0.307271	+	0.532210i
$388$	−2.69242e13	−	1.55447e13i	−3.06186	−	1.76776i
$389$	7.42342e12	−	1.28577e13i	0.833405	−	1.44350i	−0.0619169	−	0.998081i	$-0.519721\pi$
$389$	7.42342e12	−	1.28577e13i	0.833405	−	1.44350i	0.895322	−	0.445419i	$-0.146945\pi$
$390$	−1.90115e10	+	1.09763e10i	−0.00210714	+	0.00121656i
$391$		−	3.48701e12i		−	0.381566i
$392$	1.25202e13	−	1.79444e13i	1.35263	−	1.93864i
$393$	−1.27269e13			−1.35756
$394$	7.37006e12	+	1.27653e13i	0.776229	+	1.34447i
$395$	−1.10368e12	−	6.37208e11i	−0.114777	−	0.0662667i
$396$	9.80312e12	−	1.69795e13i	1.00667	−	1.74361i
$397$	8.82475e12	−	5.09497e12i	0.894849	−	0.516642i	0.0193238	−	0.999813i	$-0.493849\pi$
$397$	8.82475e12	−	5.09497e12i	0.894849	−	0.516642i	0.875526	+	0.483172i	$0.160515\pi$
$398$			3.25975e13i			3.26414i
$399$	−2.14651e12	−	4.11501e12i	−0.212260	−	0.406918i
$400$	1.73984e13			1.69906
$401$	−4.67707e12	−	8.10092e12i	−0.451078	−	0.781290i	0.547375	−	0.836887i	$-0.315627\pi$
$401$	−4.67707e12	−	8.10092e12i	−0.451078	−	0.781290i	−0.998453	+	0.0555971i	$0.982294\pi$
$402$	−1.36239e13	−	7.86576e12i	−1.29769	−	0.749222i
$403$	1.82623e10	−	3.16312e10i	0.00171803	−	0.00297571i
$404$	−1.19362e13	+	6.89138e12i	−1.10907	+	0.640324i
$405$			1.18294e12i			0.108564i
$406$	−1.95911e13	+	3.08086e13i	−1.77594	+	2.79281i
$407$	−7.28289e12			−0.652126
$408$	1.19236e13	+	2.06523e13i	1.05465	+	1.82670i
$409$	6.94378e12	+	4.00899e12i	0.606707	+	0.350283i	0.771676	−	0.636016i	$-0.219419\pi$
$409$	6.94378e12	+	4.00899e12i	0.606707	+	0.350283i	−0.164968	+	0.986299i	$0.552752\pi$
$410$	4.88294e12	−	8.45750e12i	0.421465	−	0.729999i
$411$	7.16606e11	−	4.13733e11i	0.0611042	−	0.0352785i
$412$		−	2.14399e13i		−	1.80608i
$413$	−2.38724e11	+	5.57449e12i	−0.0198676	+	0.463932i
$414$	2.20944e13			1.81668
$415$	3.38453e12	+	5.86217e12i	0.274952	+	0.476231i
$416$	3.00123e10	+	1.73276e10i	0.00240898	+	0.00139083i
$417$	8.09598e12	−	1.40227e13i	0.642080	−	1.11212i
$418$	−3.44827e12	+	1.99086e12i	−0.270222	+	0.156013i
$419$		−	2.16475e12i		−	0.167625i	−0.996482	−	0.0838123i	$-0.973290\pi$
$419$		−	2.16475e12i		−	0.167625i	0.996482	−	0.0838123i	$-0.0267096\pi$
$420$	−1.82067e13	−	7.79691e11i	−1.39311	−	0.0596590i
$421$	−2.55524e12			−0.193207			−0.0966033	−	0.995323i	$-0.530798\pi$
$421$	−2.55524e12			−0.193207			−0.0966033	+	0.995323i	$0.530798\pi$
$422$	−5.41617e12	−	9.38108e12i	−0.404697	−	0.700955i
$423$	−1.17159e13	−	6.76418e12i	−0.865115	−	0.499475i
$424$	−1.44479e13	+	2.50245e13i	−1.05433	+	1.82615i
$425$	−5.79369e12	+	3.34499e12i	−0.417841	+	0.241240i
$426$		−	4.19928e13i		−	2.99314i
$427$	8.21843e12	+	5.22607e12i	0.578961	+	0.368160i
$428$	−1.16767e12			−0.0813023
$429$	1.49222e10	+	2.58461e10i	0.00102695	+	0.00177872i
$430$	−3.68394e12	−	2.12692e12i	−0.250593	−	0.144680i
$431$	−1.18094e13	+	2.04545e13i	−0.794041	+	1.37532i	0.129406	+	0.991592i	$0.458693\pi$
$431$	−1.18094e13	+	2.04545e13i	−0.794041	+	1.37532i	−0.923447	+	0.383727i	$0.874640\pi$
$432$	−1.98043e13	+	1.14340e13i	−1.31626	+	0.759941i
$433$		−	2.23575e13i		−	1.46887i	−0.678678	−	0.734436i	$-0.737447\pi$
$433$		−	2.23575e13i		−	1.46887i	0.678678	−	0.734436i	$-0.262553\pi$
$434$	3.85649e13	−	2.01166e13i	2.50463	−	1.30649i
$435$	1.71931e13			1.10384
$436$	−9.18486e12	−	1.59086e13i	−0.582962	−	1.00972i
$437$	−2.70872e12	−	1.56388e12i	−0.169964	−	0.0981286i
$438$	−1.29026e13	+	2.23479e13i	−0.800397	+	1.38633i
$439$	6.93245e12	−	4.00245e12i	0.425171	−	0.245473i	−0.272116	−	0.962264i	$-0.587723\pi$
$439$	6.93245e12	−	4.00245e12i	0.425171	−	0.245473i	0.697287	+	0.716792i	$0.254390\pi$
$440$			8.83973e12i			0.536014i
$441$	−2.46572e13	−	2.11574e12i	−1.47826	−	0.126844i
$442$	−3.83516e10			−0.00227338
$443$	1.24631e13	+	2.15867e13i	0.730477	+	1.26522i	0.956679	+	0.291144i	$0.0940357\pi$
$443$	1.24631e13	+	2.15867e13i	0.730477	+	1.26522i	−0.226202	+	0.974080i	$0.572631\pi$
$444$	5.99253e13	+	3.45979e13i	3.47292	+	2.00509i
$445$	−4.80142e12	+	8.31630e12i	−0.275150	+	0.476574i
$446$	6.47559e12	−	3.73868e12i	0.366948	−	0.211858i
$447$			1.20318e13i			0.674204i
$448$	2.44591e12	+	4.68898e12i	0.135535	+	0.259829i
$449$	−2.83564e13			−1.55388			−0.776942	−	0.629572i	$-0.783230\pi$
$449$	−2.83564e13			−1.55388			−0.776942	+	0.629572i	$0.783230\pi$
$450$	−2.11945e13	−	3.67099e13i	−1.14858	−	1.98939i
$451$	−1.14979e13	−	6.63833e12i	−0.616221	−	0.355775i
$452$	5.26516e12	−	9.11953e12i	0.279074	−	0.483370i
$453$	3.06709e12	−	1.77078e12i	0.160781	−	0.0928270i
$454$		−	1.04453e13i		−	0.541553i
$455$	8.89183e9	−	1.39831e10i	0.000455968	−	0.000717046i
$456$	2.13903e13			1.08491
$457$	−5.74814e12	−	9.95607e12i	−0.288368	−	0.499467i	0.685053	−	0.728494i	$-0.259779\pi$
$457$	−5.74814e12	−	9.95607e12i	−0.288368	−	0.499467i	−0.973420	+	0.229026i	$0.926446\pi$
$458$	3.64776e13	+	2.10604e13i	1.81008	+	1.04505i
$459$	4.39657e12	−	7.61509e12i	0.215800	−	0.373776i
$460$	−1.06356e13	+	6.14045e12i	−0.516383	+	0.298134i
$461$			2.29717e13i			1.10329i	0.834079	+	0.551645i	$0.185999\pi$
$461$			2.29717e13i			1.10329i	−0.834079	+	0.551645i	$0.814001\pi$
$462$	−1.52063e12	+	3.55086e13i	−0.0722462	+	1.68703i
$463$	2.25844e13			1.06146			0.530731	−	0.847541i	$-0.321918\pi$
$463$	2.25844e13			1.06146			0.530731	+	0.847541i	$0.321918\pi$
$464$	−3.90575e13	−	6.76496e13i	−1.81600	−	3.14540i
$465$	−1.77388e13	−	1.02415e13i	−0.815944	−	0.471086i
$466$	−1.27206e13	+	2.20327e13i	−0.578866	+	1.00263i
$467$	2.82742e13	−	1.63241e13i	1.27293	−	0.734929i	0.297395	−	0.954754i	$-0.403882\pi$
$467$	2.82742e13	−	1.63241e13i	1.27293	−	0.734929i	0.975539	+	0.219825i	$0.0705487\pi$
$468$		−	1.69389e11i		−	0.00754496i
$469$	1.18640e13	+	5.08069e11i	0.522837	+	0.0223902i
$470$	1.07875e13			0.470360
$471$	2.41916e13	+	4.19010e13i	1.04366	+	1.80767i
$472$	−2.22700e13	−	1.28576e13i	−0.950626	−	0.548844i
$473$	−2.89154e12	+	5.00829e12i	−0.122130	+	0.211536i
$474$	2.04513e13	−	1.18075e13i	0.854729	−	0.493478i
$475$			6.00073e12i			0.248162i
$476$	−2.68649e13	−	1.70833e13i	−1.09939	−	0.699097i
$477$	3.26825e13			1.32350
$478$	2.04777e13	+	3.54684e13i	0.820618	+	1.42135i
$479$	−3.87135e13	−	2.23512e13i	−1.53527	−	0.886388i	−0.999106	−	0.0422729i	$-0.986540\pi$
$479$	−3.87135e13	−	2.23512e13i	−1.53527	−	0.886388i	−0.536162	−	0.844115i	$-0.680127\pi$
$480$	9.71736e12	−	1.68310e13i	0.381366	−	0.660546i
$481$	−5.44911e10	+	3.14605e10i	−0.00211641	+	0.00122191i
$482$		−	7.63178e13i		−	2.93353i
$483$	−2.47533e13	+	1.29120e13i	−0.941667	+	0.491200i
$484$	−3.98619e13			−1.50083
$485$	−7.92698e12	−	1.37299e13i	−0.295392	−	0.511634i
$486$	−5.15039e13	−	2.97358e13i	−1.89958	−	1.09673i
$487$	−3.02786e10	+	5.24441e10i	−0.00110533	+	0.00191448i	−0.866578	−	0.499042i	$-0.833685\pi$
$487$	−3.02786e10	+	5.24441e10i	−0.00110533	+	0.00191448i	0.865472	+	0.500957i	$0.167019\pi$
$488$	−3.88728e13	+	2.24432e13i	−1.40458	+	0.810935i
$489$			3.54279e13i			1.26707i
$490$	1.78710e13	−	8.36973e12i	0.632656	−	0.296300i
$491$	−2.42214e13			−0.848775			−0.424387	−	0.905481i	$-0.639511\pi$
$491$	−2.42214e13			−0.848775			−0.424387	+	0.905481i	$0.639511\pi$
$492$	6.30717e13	+	1.09243e14i	2.18781	+	3.78939i
$493$	2.60124e13	+	1.50183e13i	0.893195	+	0.515687i
$494$	−1.72002e10	+	2.97916e10i	−0.000584653	+	0.00101265i
$495$	8.65864e12	−	4.99907e12i	0.291356	−	0.168214i
$496$			9.30627e13i			3.10004i
$497$	1.46600e13	+	2.81043e13i	0.483451	+	0.926810i
$498$	−1.25431e14			−4.09505
$499$	−1.23473e13	−	2.13862e13i	−0.399090	−	0.691244i	0.594524	−	0.804078i	$-0.297340\pi$
$499$	−1.23473e13	−	2.13862e13i	−0.399090	−	0.691244i	−0.993614	+	0.112834i	$0.964007\pi$
$500$	4.43497e13	+	2.56053e13i	1.41919	+	0.819371i
$501$	3.91315e13	−	6.77778e13i	1.23976	−	2.14733i
$502$	−1.19476e13	+	6.89793e12i	−0.374766	+	0.216371i
$503$		−	2.43755e13i		−	0.757031i	−0.925595	−	0.378515i	$-0.876435\pi$
$503$		−	2.43755e13i		−	0.757031i	0.925595	−	0.378515i	$-0.123565\pi$
$504$	6.12027e13	−	9.62462e13i	1.88199	−	2.95959i
$505$	−7.02847e12			−0.213995
$506$	1.19758e13	+	2.07426e13i	0.361036	+	0.625333i
$507$	−4.57212e13	−	2.63971e13i	−1.36483	−	0.787983i
$508$	6.87670e13	−	1.19108e14i	2.03264	−	3.52064i
$509$	−2.74525e13	+	1.58497e13i	−0.803513	+	0.463909i	−0.844698	−	0.535243i	$-0.820220\pi$
$509$	−2.74525e13	+	1.58497e13i	−0.803513	+	0.463909i	0.0411849	+	0.999152i	$0.486887\pi$
$510$			2.15076e13i			0.623364i
$511$	8.33408e11	−	1.94610e13i	0.0239196	−	0.558549i
$512$	7.75318e13			2.20359
$513$	−3.94361e12	−	6.83053e12i	−0.110996	−	0.192251i
$514$	6.04188e13	+	3.48828e13i	1.68406	+	0.972290i
$515$	5.46661e12	−	9.46844e12i	0.150897	−	0.261362i
$516$	4.75845e13	−	2.74729e13i	1.30082	−	0.751028i
$517$		−	1.46655e13i		−	0.397049i
$518$	−7.48625e13	−	3.20595e12i	−2.00732	−	0.0859622i
$519$	1.74228e13			0.462682
$520$	3.81857e10	+	6.61396e10i	0.00100435	+	0.00173958i
$521$	2.19243e13	+	1.26580e13i	0.571134	+	0.329744i	0.757602	−	0.652717i	$-0.226371\pi$
$521$	2.19243e13	+	1.26580e13i	0.571134	+	0.329744i	−0.186468	+	0.982461i	$0.559704\pi$
$522$	−9.51586e13	+	1.64820e14i	−2.45525	+	4.25262i
$523$	2.43323e13	−	1.40483e13i	0.621836	−	0.359017i	−0.155748	−	0.987797i	$-0.549779\pi$
$523$	2.43323e13	−	1.40483e13i	0.621836	−	0.359017i	0.777583	+	0.628780i	$0.216445\pi$
$524$			7.83063e13i			1.98217i
$525$	4.51985e13	+	2.87416e13i	1.13325	+	0.720633i
$526$	3.76790e13			0.935773
$527$	−1.78921e13	−	3.09900e13i	−0.440158	−	0.762376i
$528$	−6.58544e13	−	3.80211e13i	−1.60478	−	0.926520i
$529$	1.13060e13	−	1.95825e13i	0.272916	−	0.472705i
$530$	−2.25694e13	+	1.30305e13i	−0.539686	+	0.311588i
$531$			2.90850e13i			0.688964i
$532$	−2.53189e13	+	1.32071e13i	−0.594137	+	0.309919i
$533$	−1.14704e11			−0.00266651
$534$	−8.89709e13	−	1.54102e14i	−2.04900	−	3.54897i
$535$	−5.15676e11	−	2.97726e11i	−0.0117654	−	0.00679278i
$536$	−2.73644e13	+	4.73965e13i	−0.618531	+	1.07133i
$537$	−6.79175e13	+	3.92122e13i	−1.52093	+	0.878112i
$538$			2.44679e13i			0.542857i
$539$	−1.13786e13	−	2.42955e13i	−0.250118	−	0.534050i
$540$	−3.09686e13			−0.674454
$541$	1.88948e13	+	3.27267e13i	0.407714	+	0.706181i	0.994633	−	0.103465i	$-0.0329929\pi$
$541$	1.88948e13	+	3.27267e13i	0.407714	+	0.706181i	−0.586920	+	0.809645i	$0.699660\pi$
$542$	8.88039e13	+	5.12709e13i	1.89861	+	1.09616i
$543$	3.75703e13	−	6.50737e13i	0.795876	−	1.37850i
$544$	2.94040e13	−	1.69764e13i	0.617180	−	0.356329i
$545$		−	9.36757e12i		−	0.194825i
$546$	1.42012e11	+	2.72247e11i	0.00292658	+	0.00561047i
$547$	−9.46225e13			−1.93223			−0.966113	−	0.258119i	$-0.916897\pi$
$547$	−9.46225e13			−1.93223			−0.966113	+	0.258119i	$0.916897\pi$
$548$	−2.54562e12	−	4.40914e12i	−0.0515099	−	0.0892178i
$549$	4.39669e13	+	2.53843e13i	0.881585	+	0.508983i
$550$	2.29760e13	−	3.97956e13i	0.456521	−	0.790717i
$551$	2.33325e13	−	1.34710e13i	0.459412	−	0.265242i
$552$		−	1.28671e14i		−	2.51064i
$553$	−9.56520e12	+	1.50421e13i	−0.184956	+	0.290858i
$554$	1.65073e13			0.316320
$555$	1.76431e13	+	3.05587e13i	0.335050	+	0.580323i
$556$	−8.62788e13	−	4.98131e13i	−1.62379	−	0.937496i
$557$	−4.52952e13	+	7.84536e13i	−0.844844	+	1.46331i	0.0409135	+	0.999163i	$0.486973\pi$
$557$	−4.52952e13	+	7.84536e13i	−0.844844	+	1.46331i	−0.885757	+	0.464149i	$0.846360\pi$
$558$	1.96359e14	−	1.13368e14i	3.62977	−	2.09565i
$559$			4.99632e10i			0.000915358i
$560$	−1.80646e12	+	4.21829e13i	−0.0328011	+	0.765944i
$561$	2.92395e13			0.526206
$562$	3.48409e13	+	6.03463e13i	0.621453	+	1.07639i
$563$	7.94700e12	+	4.58820e12i	0.140495	+	0.0811149i	0.568600	−	0.822614i	$-0.307485\pi$
$563$	7.94700e12	+	4.58820e12i	0.140495	+	0.0811149i	−0.428105	+	0.903729i	$0.640819\pi$
$564$	−6.96695e13	+	1.20671e14i	−1.22081	+	2.11450i
$565$	4.65047e12	−	2.68495e12i	0.0807709	−	0.0466331i
$566$		−	8.55840e13i		−	1.47336i
$567$	1.65311e13	+	7.07933e11i	0.282088	+	0.0120803i
$568$	−1.46090e14			−2.47103
$569$	2.56522e13	+	4.44309e13i	0.430094	+	0.744944i	0.996881	−	0.0789199i	$-0.0251471\pi$
$569$	2.56522e13	+	4.44309e13i	0.430094	+	0.744944i	−0.566787	+	0.823864i	$0.691814\pi$
$570$	1.67072e13	+	9.64588e12i	0.277670	+	0.160313i
$571$	−5.52268e13	+	9.56557e13i	−0.909850	+	1.57591i	−0.0955777	+	0.995422i	$0.530470\pi$
$571$	−5.52268e13	+	9.56557e13i	−0.909850	+	1.57591i	−0.814272	+	0.580484i	$0.802864\pi$
$572$	1.59026e11	−	9.18137e10i	0.00259710	−	0.00149943i
$573$			2.53365e13i			0.410179i
$574$	−1.15268e14	−	7.32984e13i	−1.84990	−	1.17635i
$575$	3.60966e13			0.574284
$576$	1.37840e13	+	2.38746e13i	0.217402	+	0.376551i
$577$	5.82340e11	+	3.36214e11i	0.00910537	+	0.00525699i	0.504546	−	0.863385i	$-0.331660\pi$
$577$	5.82340e11	+	3.36214e11i	0.00910537	+	0.00525699i	−0.495440	+	0.868642i	$0.664993\pi$
$578$	3.98181e13	−	6.89670e13i	0.617223	−	1.06906i
$579$	−8.19173e13	+	4.72950e13i	−1.25888	+	0.726812i
$580$		−	1.05786e14i		−	1.61171i
$581$	8.39468e13	−	4.37890e13i	1.26801	−	0.661431i
$582$	2.93776e14			4.39948
$583$	1.77148e13	+	3.06830e13i	0.263023	+	0.455570i
$584$	7.77465e13	+	4.48870e13i	1.14450	+	0.660779i
$585$	4.31898e10	−	7.48068e10i	0.000630378	−	0.00109185i
$586$	−3.35777e13	+	1.93861e13i	−0.485918	+	0.280545i
$587$		−	5.09965e13i		−	0.731729i	−0.930668	−	0.365864i	$-0.880773\pi$
$587$		−	5.09965e13i		−	0.731729i	0.930668	−	0.365864i	$-0.119227\pi$
$588$	−2.17917e13	+	2.53964e14i	−0.310030	+	3.61314i
$589$	−3.20975e13			−0.452787
$590$	−1.15961e13	−	2.00851e13i	−0.162201	−	0.280940i
$591$	−8.40833e13	−	4.85455e13i	−1.16620	−	0.673305i
$592$	8.01596e13	−	1.38841e14i	1.10242	−	1.90945i
$593$	−5.94955e13	+	3.43498e13i	−0.811355	+	0.468436i	−0.847426	−	0.530913i	$-0.821849\pi$
$593$	−5.94955e13	+	3.43498e13i	−0.811355	+	0.468436i	0.0360713	+	0.999349i	$0.488516\pi$
$594$			6.03982e13i			0.816754i
$595$	−7.50848e12	−	1.43943e13i	−0.100686	−	0.193021i
$596$	7.40292e13			0.984400
$597$	−1.07357e14	−	1.85948e14i	−1.41566	−	2.45200i
$598$	1.79207e11	+	1.03465e11i	0.00234341	+	0.00135297i
$599$	4.30536e13	−	7.45711e13i	0.558311	−	0.967022i	−0.439327	−	0.898327i	$-0.644783\pi$
$599$	4.30536e13	−	7.45711e13i	0.558311	−	0.967022i	0.997638	−	0.0686951i	$-0.0218836\pi$
$600$	−2.13787e14	+	1.23430e14i	−2.74932	+	1.58732i
$601$			5.86721e13i			0.748272i	0.927374	+	0.374136i	$0.122061\pi$
$601$			5.86721e13i			0.748272i	−0.927374	+	0.374136i	$0.877939\pi$
$602$	−3.19275e13	+	5.02085e13i	−0.403815	+	0.635031i
$603$	6.19007e13			0.776441
$604$	−1.08953e13	−	1.88712e13i	−0.135536	−	0.234755i
$605$	−1.76041e13	−	1.01637e13i	−0.217188	−	0.125394i
$606$	6.51193e13	−	1.12790e14i	0.796795	−	1.38009i
$607$	4.98389e13	−	2.87745e13i	0.604819	−	0.349192i	−0.166116	−	0.986106i	$-0.553123\pi$
$607$	4.98389e13	−	2.87745e13i	0.604819	−	0.349192i	0.770935	+	0.636914i	$0.219789\pi$
$608$		−	3.04547e13i		−	0.366553i
$609$	1.02892e13	−	2.40266e14i	0.122828	−	2.86817i
$610$	−4.04827e13			−0.479314
$611$	−6.33517e10	−	1.09728e11i	−0.000743965	−	0.00128858i
$612$	−1.43722e14	−	8.29778e13i	−1.67404	−	0.966507i
$613$	−4.48421e13	+	7.76688e13i	−0.518064	+	0.897313i	0.481716	+	0.876328i	$0.340014\pi$
$613$	−4.48421e13	+	7.76688e13i	−0.518064	+	0.897313i	−0.999780	+	0.0209857i	$0.993320\pi$
$614$	−2.18059e14	+	1.25896e14i	−2.49880	+	1.44269i
$615$			6.43264e13i			0.731162i
$616$	1.23531e14	+	5.29016e12i	1.39275	+	0.0596438i
$617$	−1.20483e13			−0.134741			−0.0673705	−	0.997728i	$-0.521461\pi$
$617$	−1.20483e13			−0.134741			−0.0673705	+	0.997728i	$0.521461\pi$
$618$	1.01297e14	+	1.75451e14i	1.12371	+	1.94632i
$619$	1.17772e14	+	6.79956e13i	1.29595	+	0.748217i	0.979702	−	0.200459i	$-0.0642435\pi$
$619$	1.17772e14	+	6.79956e13i	1.29595	+	0.748217i	0.316248	+	0.948677i	$0.397577\pi$
$620$	−6.30142e13	+	1.09144e14i	−0.687828	+	1.19135i
$621$	−4.10881e13	+	2.37222e13i	−0.444896	+	0.256861i
$622$			2.28608e14i			2.45549i
$623$	1.13343e14	+	7.20747e13i	1.20769	+	0.767967i
$624$	−6.56970e11			−0.00694421
$625$	−2.75765e13	−	4.77640e13i	−0.289161	−	0.500842i
$626$	−1.96255e14	−	1.13308e14i	−2.04150	−	1.17866i
$627$	1.31135e13	−	2.27133e13i	0.135326	−	0.234392i
$628$	2.57809e14	−	1.48846e14i	2.63937	−	1.52384i
$629$			6.16455e13i			0.626106i
$630$	9.12049e13	−	4.75751e13i	0.919000	−	0.479377i
$631$	−7.48919e13			−0.748666			−0.374333	−	0.927294i	$-0.622128\pi$
$631$	−7.48919e13			−0.748666			−0.374333	+	0.927294i	$0.622128\pi$
$632$	−4.10775e13	−	7.11483e13i	−0.407397	−	0.705633i
$633$	6.17918e13	+	3.56755e13i	0.608012	+	0.351036i
$634$	1.67200e13	−	2.89599e13i	0.163226	−	0.282716i
$635$	6.07387e13	−	3.50675e13i	0.588297	−	0.339654i
$636$		−	3.36622e14i		−	3.23487i
$637$	−1.90087e11	−	1.32628e11i	−0.00181240	−	0.00126455i
$638$	−2.06315e14			−1.95176
$639$	8.26170e13	+	1.43097e14i	0.775470	+	1.34315i
$640$	2.59668e13	+	1.49919e13i	0.241834	+	0.139623i
$641$	3.37283e13	−	5.84191e13i	0.311676	−	0.539839i	−0.667049	−	0.745014i	$-0.732443\pi$
$641$	3.37283e13	−	5.84191e13i	0.311676	−	0.539839i	0.978725	+	0.205174i	$0.0657762\pi$
$642$	9.55555e12	−	5.51690e12i	0.0876154	−	0.0505848i
$643$		−	1.42366e14i		−	1.29525i	−0.761961	−	0.647623i	$-0.775763\pi$
$643$		−	1.42366e14i		−	1.29525i	0.761961	−	0.647623i	$-0.224237\pi$
$644$	7.94453e13	+	1.52302e14i	0.717198	+	1.37492i
$645$	2.80194e13			0.250993
$646$	1.68515e13	+	2.91877e13i	0.149788	+	0.259440i
$647$	−6.18013e13	−	3.56810e13i	−0.545100	−	0.314713i	0.202044	−	0.979377i	$-0.435242\pi$
$647$	−6.18013e13	−	3.56810e13i	−0.545100	−	0.314713i	−0.747143	+	0.664663i	$0.768575\pi$
$648$	−3.81290e13	+	6.60413e13i	−0.333718	+	0.578017i
$649$	−2.73056e13	+	1.57649e13i	−0.237153	+	0.136920i
$650$		−	3.97005e11i		−	0.00342160i
$651$	−1.53737e14	+	2.41763e14i	−1.31484	+	2.06769i
$652$	2.17981e14			1.85004
$653$	−9.09144e12	−	1.57468e13i	−0.0765714	−	0.132626i	0.825197	−	0.564845i	$-0.191064\pi$
$653$	−9.09144e12	−	1.57468e13i	−0.0765714	−	0.132626i	−0.901769	+	0.432219i	$0.857731\pi$
$654$	1.50327e14	+	8.67912e13i	1.25646	+	0.725415i
$655$	−1.99660e13	+	3.45822e13i	−0.165609	+	0.286844i
$656$	2.53105e14	−	1.46130e14i	2.08345	−	1.20288i
$657$		−	1.01538e14i		−	0.829475i
$658$	6.45579e12	−	1.50750e14i	0.0523384	−	1.22216i
$659$	9.61020e13			0.773224			0.386612	−	0.922242i	$-0.373645\pi$
$659$	9.61020e13			0.773224			0.386612	+	0.922242i	$0.373645\pi$
$660$	−5.14893e13	−	8.91821e13i	−0.411147	−	0.712128i
$661$	4.23112e13	+	2.44284e13i	0.335311	+	0.193592i	0.658197	−	0.752846i	$-0.271320\pi$
$661$	4.23112e13	+	2.44284e13i	0.335311	+	0.193592i	−0.322885	+	0.946438i	$0.604653\pi$
$662$	2.52175e13	−	4.36780e13i	0.198341	−	0.343536i
$663$	2.18772e11	−	1.26308e11i	0.00170775	−	0.000985970i
$664$			4.36366e14i			3.38073i
$665$	−1.45490e13	−	6.23051e11i	−0.111873	−	0.00479088i
$666$	−3.90597e14			−2.98097
$667$	−8.10329e13	−	1.40353e14i	−0.613808	−	1.06315i
$668$	−4.17024e14	−	2.40769e14i	−3.13530	−	1.81017i
$669$	−2.46262e13	+	4.26538e13i	−0.183766	+	0.318293i
$670$	−4.27465e13	+	2.46797e13i	−0.316611	+	0.182796i
$671$			5.50360e13i			0.404608i
$672$	−2.29390e14	−	1.45868e14i	−1.67390	−	1.06443i
$673$	1.61280e14			1.16816			0.584082	−	0.811694i	$-0.301455\pi$
$673$	1.61280e14			1.16816			0.584082	+	0.811694i	$0.301455\pi$
$674$	6.38394e13	+	1.10573e14i	0.458975	+	0.794968i
$675$	7.88292e13	+	4.55121e13i	0.562559	+	0.324794i
$676$	−1.62417e14	+	2.81314e14i	−1.15053	+	1.99277i
$677$	1.47948e14	−	8.54179e13i	1.04032	−	0.600628i	0.120394	−	0.992726i	$-0.461584\pi$
$677$	1.47948e14	−	8.54179e13i	1.04032	−	0.600628i	0.919923	+	0.392099i	$0.128251\pi$
$678$			9.95050e13i			0.694539i
$679$	−1.96614e14	+	1.02559e14i	−1.36228	+	0.710602i
$680$	7.48233e13			0.514627
$681$	3.44008e13	+	5.95839e13i	0.234873	+	0.406811i
$682$	2.12864e14	+	1.22897e14i	1.44271	+	0.832950i
$683$	1.22088e14	−	2.11462e14i	0.821426	−	1.42275i	−0.0831935	−	0.996533i	$-0.526512\pi$
$683$	1.22088e14	−	2.11462e14i	0.821426	−	1.42275i	0.904620	−	0.426219i	$-0.140155\pi$
$684$	−1.28915e14	+	7.44289e13i	−0.861037	+	0.497120i
$685$		−	2.59626e12i		−	0.0172145i
$686$	−1.06268e14	−	2.54748e14i	−0.699494	−	1.67683i
$687$	−2.77443e14			−1.81297
$688$	−6.36518e13	−	1.10248e14i	−0.412923	−	0.715203i
$689$	2.65087e11	+	1.53048e11i	0.00170723	+	0.000985672i
$690$	5.80235e13	−	1.00500e14i	0.370987	−	0.642568i
$691$	8.82145e13	−	5.09307e13i	0.559951	−	0.323288i	−0.193175	−	0.981164i	$-0.561879\pi$
$691$	8.82145e13	−	5.09307e13i	0.559951	−	0.323288i	0.753126	+	0.657877i	$0.228545\pi$
$692$		−	1.07200e14i		−	0.675558i
$693$	−6.46780e13	−	1.23992e14i	−0.404660	−	0.775763i
$694$	−6.35759e13			−0.394907
$695$	−2.54020e13	−	4.39976e13i	−0.156655	−	0.271334i
$696$	9.59858e14	+	5.54174e14i	5.87707	+	3.39313i
$697$	−5.61896e13	+	9.73233e13i	−0.341580	+	0.591634i
$698$	7.27901e13	−	4.20254e13i	0.439334	−	0.253650i
$699$		−	1.67577e14i		−	1.00422i
$700$	1.76842e14	−	2.78098e14i	1.05219	−	1.65466i
$701$	−3.70885e13			−0.219103			−0.109552	−	0.993981i	$-0.534942\pi$
$701$	−3.70885e13			−0.219103			−0.109552	+	0.993981i	$0.534942\pi$
$702$	2.60907e11	+	4.51904e11i	0.00153038	+	0.00265070i
$703$	4.78863e13	+	2.76472e13i	0.278891	+	0.161018i
$704$	−1.49426e13	+	2.58814e13i	−0.0864099	+	0.149666i
$705$	−6.15359e13	+	3.55278e13i	−0.353332	+	0.203996i
$706$		−	3.46362e14i		−	1.97472i
$707$	−4.20621e12	+	9.82199e13i	−0.0238119	+	0.556035i
$708$	2.99569e14			1.68396
$709$	−1.39173e14	−	2.41054e14i	−0.776824	−	1.34550i	−0.933763	−	0.357891i	$-0.883496\pi$
$709$	−1.39173e14	−	2.41054e14i	−0.776824	−	1.34550i	0.156939	−	0.987608i	$-0.449837\pi$
$710$	−1.14105e14	−	6.58785e13i	−0.632430	−	0.365134i
$711$	−4.64605e13	+	8.04719e13i	−0.255703	+	0.442891i
$712$	−5.36109e14	+	3.09523e14i	−2.92990	+	1.69158i
$713$			1.93078e14i			1.04782i
$714$	3.00560e14	+	1.28713e13i	1.61972	+	0.0693636i
$715$	9.36402e10			0.000501109
$716$	2.41265e14	+	4.17884e14i	1.28212	+	2.22070i
$717$	−2.33625e14	−	1.34883e14i	−1.23289	−	0.711808i
$718$	6.63471e13	−	1.14917e14i	0.347696	−	0.602227i
$719$	−6.87174e13	+	3.96740e13i	−0.357620	+	0.206472i	−0.668036	−	0.744129i	$-0.732865\pi$
$719$	−6.87174e13	+	3.96740e13i	−0.357620	+	0.206472i	0.310416	+	0.950601i	$0.399532\pi$
$720$			2.20091e14i			1.13747i
$721$	−1.29046e14	−	8.20599e13i	−0.662320	−	0.421167i
$722$	−3.26231e14			−1.66280
$723$	2.51347e14	+	4.35346e14i	1.27228	+	2.20365i
$724$	−4.00386e14	−	2.31163e14i	−2.01273	−	1.16205i
$725$	−1.55465e14	+	2.69273e14i	−0.776145	+	1.34432i
$726$	3.26206e14	−	1.88335e14i	1.61737	−	0.933787i
$727$			1.72327e13i			0.0848559i	0.999100	+	0.0424280i	$0.0135093\pi$
$727$			1.72327e13i			0.0848559i	−0.999100	+	0.0424280i	$0.986491\pi$
$728$	9.47124e11	−	4.94047e11i	0.00463180	−	0.00241608i
$729$	3.33598e14			1.62026
$730$	4.04832e13	+	7.01189e13i	0.195281	+	0.338237i
$731$	4.23923e13	+	2.44752e13i	0.203095	+	0.117257i
$732$	2.61453e14	−	4.52849e14i	1.24405	−	2.15476i
$733$	7.98024e13	−	4.60739e13i	0.377134	−	0.217739i	−0.299436	−	0.954116i	$-0.596799\pi$
$733$	7.98024e13	−	4.60739e13i	0.377134	−	0.217739i	0.676571	+	0.736378i	$0.263465\pi$
$734$			2.95964e14i			1.38918i
$735$	−7.43778e13	+	1.06601e14i	−0.346742	+	0.496963i
$736$	−1.83196e14			−0.848257
$737$	3.35519e13	+	5.81136e13i	0.154305	+	0.267264i
$738$	−6.16658e14	−	3.56028e14i	−2.81684	−	1.62631i
$739$	−3.80482e13	+	6.59014e13i	−0.172628	+	0.299001i	−0.939338	−	0.342993i	$-0.888559\pi$
$739$	−3.80482e13	+	6.59014e13i	−0.172628	+	0.299001i	0.766710	+	0.641994i	$0.221893\pi$
$740$	1.88022e14	−	1.08555e14i	0.847326	−	0.489204i
$741$		−	2.26590e11i		−	0.00101426i
$742$	1.68588e14	+	3.23196e14i	0.749563	+	1.43697i
$743$	1.20938e14			0.534094			0.267047	−	0.963684i	$-0.413952\pi$
$743$	1.20938e14			0.534094			0.267047	+	0.963684i	$0.413952\pi$
$744$	−6.60218e14	−	1.14353e15i	−2.89616	−	5.01630i
$745$	3.26933e13	+	1.88755e13i	0.142455	+	0.0822463i
$746$	1.65971e14	−	2.87470e14i	0.718352	−	1.24422i
$747$	4.27426e14	−	2.46775e14i	1.83763	−	1.06096i
$748$		−	1.79905e14i		−	0.768309i
$749$	−4.46920e12	+	7.02818e12i	−0.0189592	+	0.0298149i
$750$	−4.83909e14			−2.03919
$751$	1.17583e14	+	2.03659e14i	0.492203	+	0.852520i	0.999960	−	0.00898037i	$-0.00285858\pi$
$751$	1.17583e14	+	2.03659e14i	0.492203	+	0.852520i	−0.507757	+	0.861500i	$0.669525\pi$
$752$	2.79582e14	+	1.61417e14i	1.16257	+	0.671212i
$753$	4.54357e13	−	7.86969e13i	0.187682	−	0.325074i
$754$	−1.54366e12	+	8.91233e11i	−0.00633425	+	0.00365708i
$755$		−	1.11120e13i		−	0.0452959i
$756$	−1.85332e13	+	4.32772e14i	−0.0750485	+	1.75247i
$757$	5.89605e13			0.237182			0.118591	−	0.992943i	$-0.462162\pi$
$757$	5.89605e13			0.237182			0.118591	+	0.992943i	$0.462162\pi$
$758$	1.36215e14	+	2.35931e14i	0.544351	+	0.942844i
$759$	−1.36629e14	−	7.88826e13i	−0.542416	−	0.313164i
$760$	3.35572e13	−	5.81229e13i	0.132348	−	0.229234i
$761$	−2.51979e14	+	1.45480e14i	−0.987280	+	0.570006i	−0.904460	−	0.426558i	$-0.859726\pi$
$761$	−2.51979e14	+	1.45480e14i	−0.987280	+	0.570006i	−0.0828199	+	0.996565i	$0.526393\pi$
$762$			1.29961e15i			5.05869i
$763$	−1.30908e14	−	5.60605e12i	−0.506224	−	0.0216788i
$764$	1.55891e14			0.598899
$765$	−4.23143e13	−	7.32905e13i	−0.161503	−	0.279731i
$766$	−1.91943e14	−	1.10818e14i	−0.727828	−	0.420211i
$767$	−1.36202e11	+	2.35908e11i	−0.000513104	+	0.000888723i
$768$	−5.88032e14	+	3.39501e14i	−2.20087	+	1.27067i
$769$		−	4.69785e14i		−	1.74690i	−0.486917	−	0.873449i	$-0.661878\pi$
$769$		−	4.69785e14i		−	1.74690i	0.486917	−	0.873449i	$-0.338122\pi$
$770$	9.41000e13	+	5.98379e13i	0.347645	+	0.221067i
$771$	−4.59536e14			−1.68674
$772$	2.90997e14	+	5.04022e14i	1.06121	+	1.83807i
$773$	−2.54864e14	−	1.47146e14i	−0.923446	−	0.533152i	−0.0387131	−	0.999250i	$-0.512326\pi$
$773$	−2.54864e14	−	1.47146e14i	−0.923446	−	0.533152i	−0.884733	+	0.466099i	$0.845659\pi$
$774$	−1.55079e14	+	2.68605e14i	−0.558277	+	0.966963i
$775$	3.20800e14	−	1.85214e14i	1.14743	−	0.662468i
$776$		−	1.02202e15i		−	3.63205i
$777$	4.37603e14	−	2.28266e14i	1.54517	−	0.806004i
$778$	8.63200e14			3.02840
$779$	5.04006e13	+	8.72964e13i	0.175691	+	0.304305i
$780$	−7.70494e11	−	4.44845e11i	−0.00266868	−	0.00154076i
$781$	−8.95614e13	+	1.55125e14i	−0.308224	+	0.533859i
$782$	1.75574e14	−	1.01368e14i	0.600382	−	0.346631i
$783$		−	4.08679e14i		−	1.38859i
$784$	5.88407e14	+	5.04890e13i	1.98654	+	0.170458i
$785$	1.51807e14			0.509266
$786$	−3.69973e14	−	6.40812e14i	−1.23327	−	2.13608i
$787$	7.08016e13	+	4.08773e13i	0.234514	+	0.135397i	0.612653	−	0.790352i	$-0.290102\pi$
$787$	7.08016e13	+	4.08773e13i	0.234514	+	0.135397i	−0.378138	+	0.925749i	$0.623436\pi$
$788$	−2.98692e14	+	5.17349e14i	−0.983087	+	1.70276i
$789$	−2.14936e14	+	1.24093e14i	−0.702948	+	0.405847i
$790$		−	7.40949e13i		−	0.240798i
$791$	−3.47379e13	−	6.65952e13i	−0.112182	−	0.215060i
$792$	6.44528e14			2.06831
$793$	2.37743e11	+	4.11784e11i	0.000758128	+	0.00131312i
$794$	5.13074e14	+	2.96223e14i	1.62584	+	0.938678i
$795$	8.58298e13	−	1.48661e14i	0.270273	−	0.468126i
$796$	−1.14411e15	+	6.60550e14i	−3.58015	+	2.06700i
$797$			2.56041e14i			0.796193i	0.917344	+	0.398097i	$0.130329\pi$
$797$			2.56041e14i			0.796193i	−0.917344	+	0.398097i	$0.869671\pi$
$798$	1.44795e14	−	2.27703e14i	0.447446	−	0.703645i
$799$	−1.24135e14			−0.381207
$800$	1.75735e14	+	3.04381e14i	0.536300	+	0.928899i
$801$	6.06364e14	+	3.50084e14i	1.83895	+	1.06172i
$802$	2.71926e14	−	4.70990e14i	0.819557	−	1.41951i
$803$	9.53263e13	−	5.50367e13i	0.285519	−	0.164844i
$804$		−	6.37563e14i		−	1.89777i
$805$	−3.74788e12	+	8.75173e13i	−0.0110868	+	0.258889i
$806$	2.12355e12			0.00624291
$807$	−8.05833e13	−	1.39574e14i	−0.235438	−	0.407791i
$808$	−3.92387e14	−	2.26545e14i	−1.13935	−	0.657805i
$809$	7.59643e13	−	1.31574e14i	0.219213	−	0.379689i	−0.735354	−	0.677683i	$-0.762984\pi$
$809$	7.59643e13	−	1.31574e14i	0.219213	−	0.379689i	0.954568	+	0.297994i	$0.0963176\pi$
$810$	−5.95621e13	+	3.43882e13i	−0.170822	+	0.0986244i
$811$		−	1.20484e14i		−	0.343420i	−0.985148	−	0.171710i	$-0.945071\pi$
$811$		−	1.20484e14i		−	0.343420i	0.985148	−	0.171710i	$-0.0549292\pi$
$812$	−1.47831e15	−	6.33078e13i	−4.18780	−	0.179340i
$813$	−6.75429e14			−1.90163
$814$	−2.11715e14	−	3.66700e14i	−0.592419	−	1.02610i
$815$	9.62664e13	+	5.55794e13i	0.267724	+	0.154570i
$816$	−3.21827e14	+	5.57420e14i	−0.889552	+	1.54075i
$817$	3.80248e13	−	2.19536e13i	0.104461	−	0.0603109i
$818$			4.66168e14i			1.27285i
$819$	−1.01955e12	−	6.48326e11i	−0.00276686	−	0.00175944i
$820$	3.95789e14			1.06756
$821$	−1.69712e14	−	2.93949e14i	−0.454984	−	0.788055i	0.543704	−	0.839277i	$-0.317022\pi$
$821$	−1.69712e14	−	2.93949e14i	−0.454984	−	0.788055i	−0.998687	+	0.0512224i	$0.983688\pi$
$822$	4.16637e13	+	2.40545e13i	0.111019	+	0.0640970i
$823$	1.56874e13	−	2.71713e13i	0.0415481	−	0.0719634i	−0.844504	−	0.535550i	$-0.820104\pi$
$823$	1.56874e13	−	2.71713e13i	0.0415481	−	0.0719634i	0.886052	+	0.463587i	$0.153438\pi$
$824$	6.10381e14	−	3.52404e14i	1.60681	−	0.927693i
$825$			3.02679e14i			0.791977i
$826$	−2.87620e14	+	1.50031e14i	−0.748031	+	0.390194i
$827$	−3.57925e14			−0.925262			−0.462631	−	0.886551i	$-0.653094\pi$
$827$	−3.57925e14			−0.925262			−0.462631	+	0.886551i	$0.653094\pi$
$828$	4.47717e14	+	7.75468e14i	1.15041	+	1.99256i
$829$	3.54589e14	+	2.04722e14i	0.905633	+	0.522868i	0.879024	−	0.476778i	$-0.158196\pi$
$829$	3.54589e14	+	2.04722e14i	0.905633	+	0.522868i	0.0266098	+	0.999646i	$0.491529\pi$
$830$	−1.96777e14	+	3.40828e14i	−0.499556	+	0.865257i
$831$	−9.41637e13	+	5.43655e13i	−0.237618	+	0.137189i
$832$			2.58195e11i			0.000647637i
$833$	−2.05647e14	+	9.63134e13i	−0.512741	+	0.240138i
$834$	9.41405e14			2.33317
$835$	−1.22779e14	−	2.12660e14i	−0.302477	−	0.523906i
$836$	−1.39751e14	−	8.06851e13i	−0.342233	−	0.197589i
$837$	−2.43441e14	+	4.21652e14i	−0.592606	+	1.02642i
$838$	1.08997e14	−	6.29296e13i	0.263752	−	0.152277i
$839$		−	3.77168e14i		−	0.907247i	−0.891194	−	0.453623i	$-0.850131\pi$
$839$		−	3.77168e14i		−	0.907247i	0.891194	−	0.453623i	$-0.149869\pi$
$840$	−2.77062e14	−	5.31149e14i	−0.662493	−	1.27005i
$841$	9.75302e14			2.31825
$842$	−7.42813e13	−	1.28659e14i	−0.175517	−	0.304004i
$843$	−3.97492e14	−	2.29492e14i	−0.933664	−	0.539051i
$844$	2.19505e14	−	3.80194e14i	0.512545	−	0.887754i
$845$	−1.43455e14	+	8.28238e13i	−0.332991	+	0.192252i
$846$		−	7.86543e14i		−	1.81497i
$847$	−1.52569e14	+	2.39927e14i	−0.349984	+	0.550379i
$848$	−7.79918e14			−1.77857
$849$	2.81865e14	+	4.88204e14i	0.639002	+	1.10678i
$850$	−3.36847e14	−	1.94479e14i	−0.759168	−	0.438306i
$851$	1.66308e14	−	2.88053e14i	0.372619	−	0.645395i
$852$	1.47386e15	−	8.50936e14i	3.28291	−	1.89539i
$853$			1.84401e14i			0.408336i	0.978936	+	0.204168i	$0.0654489\pi$
$853$			1.84401e14i			0.408336i	−0.978936	+	0.204168i	$0.934551\pi$
$854$	−2.42270e13	+	5.65728e14i	−0.0533347	+	1.24543i
$855$	−7.59095e13			−0.166137
$856$	−1.91928e13	−	3.32430e13i	−0.0417610	−	0.0723321i
$857$	5.28702e14	+	3.05246e14i	1.14369	+	0.660308i	0.947341	−	0.320227i	$-0.103759\pi$
$857$	5.28702e14	+	3.05246e14i	1.14369	+	0.660308i	0.196345	+	0.980535i	$0.437093\pi$
$858$	−8.67583e11	+	1.50270e12i	−0.00186584	+	0.00323173i
$859$	−6.35156e14	+	3.66707e14i	−1.35805	+	0.784068i	−0.989360	−	0.145486i	$-0.953525\pi$
$859$	−6.35156e14	+	3.66707e14i	−1.35805	+	0.784068i	−0.368686	+	0.929554i	$0.620192\pi$
$860$		−	1.72398e14i		−	0.366472i
$861$	8.98934e14	+	3.84963e13i	1.89982	+	0.0813586i
$862$	−1.37321e15			−2.88536
$863$	−5.40540e13	−	9.36243e13i	−0.112921	−	0.195585i	0.804026	−	0.594594i	$-0.202687\pi$
$863$	−5.40540e13	−	9.36243e13i	−0.112921	−	0.195585i	−0.916947	+	0.399010i	$0.869354\pi$
$864$	−4.00072e14	−	2.30982e14i	−0.830939	−	0.479743i
$865$	2.73330e13	−	4.73422e13i	0.0564426	−	0.0977615i
$866$	1.12572e15	−	6.49936e14i	2.31122	−	1.33439i
$867$			5.24553e14i			1.07076i
$868$	1.48753e15	+	9.45914e14i	3.01902	+	1.91979i
$869$	−1.00732e14			−0.203267
$870$	4.99805e14	+	8.65688e14i	1.00278	+	1.73686i
$871$	5.02076e11	+	2.89873e11i	0.00100156	+	0.000578253i
$872$	3.01939e14	−	5.22974e14i	0.598877	−	1.03728i
$873$	−1.00109e15	+	5.77977e14i	−1.97424	+	1.13983i
$874$		−	1.81849e14i		−	0.356577i
$875$	3.23863e14	−	1.68936e14i	0.631424	−	0.329369i
$876$	−1.04582e15			−2.02739
$877$	−4.64313e14	−	8.04214e14i	−0.894979	−	1.55015i	−0.833831	−	0.552020i	$-0.813857\pi$
$877$	−4.64313e14	−	8.04214e14i	−0.894979	−	1.55015i	−0.0611482	−	0.998129i	$-0.519476\pi$
$878$	4.03054e14	+	2.32704e14i	0.772487	+	0.445996i
$879$	1.27694e14	−	2.21172e14i	0.243346	−	0.421488i
$880$	−2.06625e14	+	1.19295e14i	−0.391535	+	0.226053i
$881$			5.85489e14i			1.10316i	0.834122	+	0.551581i	$0.185975\pi$
$881$			5.85489e14i			1.10316i	−0.834122	+	0.551581i	$0.814025\pi$
$882$	−6.10259e14	−	1.30302e15i	−1.14333	−	2.44123i
$883$	2.07633e14			0.386806			0.193403	−	0.981119i	$-0.438048\pi$
$883$	2.07633e14			0.386806			0.193403	+	0.981119i	$0.438048\pi$
$884$	−7.77151e11	−	1.34606e12i	−0.00143961	−	0.00249347i
$885$	1.32298e14	+	7.63821e13i	0.243689	+	0.140694i
$886$	−7.24607e14	+	1.25506e15i	−1.32719	+	2.29876i
$887$	3.23567e14	−	1.86811e14i	0.589313	−	0.340240i	−0.175513	−	0.984477i	$-0.556158\pi$
$887$	3.23567e14	−	1.86811e14i	0.589313	−	0.340240i	0.764826	+	0.644237i	$0.222825\pi$
$888$			2.27472e15i			4.11967i
$889$	−4.53704e14	−	8.69783e14i	−0.817078	−	1.56640i
$890$	−5.58312e14			−0.999832
$891$	4.67506e13	+	8.09743e13i	0.0832527	+	0.144198i
$892$	2.62441e14	+	1.51520e14i	0.464737	+	0.268316i
$893$	−5.56729e13	+	9.64283e13i	−0.0980363	+	0.169804i
$894$	−6.05811e14	+	3.49765e14i	−1.06084	+	0.612475i
$895$			2.46065e14i			0.428484i
$896$	2.25045e14	−	3.53902e14i	0.389700	−	0.612835i
$897$	−1.36302e12			−0.00234715
$898$	−8.24323e14	−	1.42777e15i	−1.41161	−	2.44499i
$899$	−1.44032e15	−	8.31571e14i	−2.45280	−	1.41612i
$900$	8.58963e14	−	1.48777e15i	1.45466	−	2.51955i
$901$	2.59714e14	−	1.49946e14i	0.437393	−	0.252529i
$902$		−	7.71908e14i		−	1.29280i
$903$	1.67683e13	−	3.91560e14i	0.0279287	−	0.652167i
$904$	3.46170e14			0.573386
$905$	−1.17881e14	−	2.04176e14i	−0.194178	−	0.336327i
$906$	1.78321e14	+	1.02954e14i	0.292121	+	0.168656i
$907$	−4.55596e14	+	7.89115e14i	−0.742238	+	1.28559i	0.209236	+	0.977865i	$0.432902\pi$
$907$	−4.55596e14	+	7.89115e14i	−0.742238	+	1.28559i	−0.951474	+	0.307729i	$0.900431\pi$
$908$	3.66609e14	−	2.11662e14i	0.593982	−	0.342936i
$909$			5.12465e14i			0.825742i
$910$	9.62550e11	+	4.12207e10i	0.00154247	+	6.60554e-5i
$911$	1.07850e15			1.71881			0.859404	−	0.511296i	$-0.170835\pi$
$911$	1.07850e15			1.71881			0.859404	+	0.511296i	$0.170835\pi$
$912$	2.88670e14	+	4.99991e14i	0.457538	+	0.792479i
$913$	4.63354e14	+	2.67518e14i	0.730397	+	0.421695i
$914$	3.34199e14	−	5.78849e14i	0.523930	−	0.907474i
$915$	2.30929e14	−	1.33327e14i	0.360058	−	0.207880i
$916$			1.70706e15i			2.64710i
$917$	4.71322e14	+	2.99712e14i	0.726894	+	0.462230i
$918$	5.11236e14			0.784166
$919$	4.91641e14	+	8.51547e14i	0.750016	+	1.29907i	0.947814	+	0.318823i	$0.103288\pi$
$919$	4.91641e14	+	8.51547e14i	0.750016	+	1.29907i	−0.197798	+	0.980243i	$0.563379\pi$
$920$	−3.49630e14	−	2.01859e14i	−0.530481	−	0.306273i
$921$	8.29262e14	−	1.43632e15i	1.25139	−	2.16748i
$922$	−1.15665e15	+	6.67792e14i	−1.73599	+	1.00227i
$923$			1.54754e12i			0.00231012i
$924$	−1.27709e15	+	6.66169e14i	−1.89611	+	0.989065i
$925$	−6.38136e14			−0.942334
$926$	6.56532e14	+	1.13715e15i	0.964276	+	1.67017i
$927$	−6.90369e14	−	3.98585e14i	−1.00852	−	0.582266i
$928$	7.89012e14	−	1.36661e15i	1.14642	−	1.98566i
$929$	−6.58542e14	+	3.80209e14i	−0.951710	+	0.549470i	−0.893612	−	0.448841i	$-0.851837\pi$
$929$	−6.58542e14	+	3.80209e14i	−0.951710	+	0.549470i	−0.0580983	+	0.998311i	$0.518504\pi$
$930$		−	1.19089e15i		−	1.71182i
$931$	−1.74137e13	+	2.02943e14i	−0.0248968	+	0.290151i
$932$	−1.03107e15			−1.46626
$933$	−7.52902e14	−	1.30407e15i	−1.06495	−	1.84455i
$934$	1.64387e15	+	9.49089e14i	2.31277	+	1.33528i
$935$	4.58710e13	−	7.94510e13i	0.0641920	−	0.111184i
$936$	4.82241e12	−	2.78422e12i	0.00671251	−	0.00387547i
$937$		−	7.31340e14i		−	1.01256i	−0.862369	−	0.506280i	$-0.831020\pi$
$937$		−	7.31340e14i		−	1.01256i	0.862369	−	0.506280i	$-0.168980\pi$
$938$	3.19306e14	+	6.12133e14i	0.439737	+	0.843008i
$939$	1.49269e15			2.04475
$940$	2.18596e14	+	3.78619e14i	0.297853	+	0.515897i
$941$	−6.80540e14	−	3.92910e14i	−0.922371	−	0.532531i	−0.0379801	−	0.999278i	$-0.512092\pi$
$941$	−6.80540e14	−	3.92910e14i	−0.922371	−	0.532531i	−0.884391	+	0.466748i	$0.845426\pi$
$942$	−1.40650e15	+	2.43614e15i	−1.89621	+	3.28433i
$943$	5.25119e14	−	3.03178e14i	0.704206	−	0.406573i
$944$		−	6.94070e14i		−	0.925855i
$945$	−1.18530e14	+	1.86398e14i	−0.157279	+	0.247334i
$946$	−3.36230e14			−0.443793
$947$	1.82203e14	+	3.15585e14i	0.239224	+	0.414349i	0.960492	−	0.278308i	$-0.0897735\pi$
$947$	1.82203e14	+	3.15585e14i	0.239224	+	0.414349i	−0.721268	+	0.692657i	$0.756440\pi$
$948$	8.28843e14	+	4.78533e14i	1.08251	+	0.624985i
$949$	4.75492e11	−	8.23577e11i	0.000617750	−	0.00106997i
$950$	−3.02142e14	+	1.74442e14i	−0.390475	+	0.225441i
$951$			2.20264e14i			0.283166i
$952$	4.47782e13	−	1.04562e15i	0.0572641	−	1.33718i
$953$	−8.26066e14			−1.05087			−0.525437	−	0.850833i	$-0.676098\pi$
$953$	−8.26066e14			−1.05087			−0.525437	+	0.850833i	$0.676098\pi$
$954$	9.50085e14	+	1.64560e15i	1.20232	+	2.08248i
$955$	6.88456e13	+	3.97480e13i	0.0866681	+	0.0500378i
$956$	−8.29913e14	+	1.43745e15i	−1.03931	+	1.80013i
$957$	1.17690e15	−	6.79482e14i	1.46615	−	0.846483i
$958$		−	2.59901e15i		−	3.22093i
$959$	−3.62816e13	−	1.55374e12i	−0.0447295	−	0.00191551i
$960$	1.44796e14			0.177583
$961$	5.80882e14	+	1.00612e15i	0.708714	+	1.22753i
$962$	−3.16813e12	−	1.82912e12i	−0.00384528	−	0.00222007i
$963$	−2.17080e13	+	3.75993e13i	−0.0262113	+	0.0453992i
$964$	2.67860e15	−	1.54649e15i	3.21753	−	1.85764i
$965$			2.96786e14i			0.354656i
$966$	−1.36971e15	−	8.70997e14i	−1.62834	−	1.03545i
$967$	2.97414e14			0.351746			0.175873	−	0.984413i	$-0.443725\pi$
$967$	2.97414e14			0.351746			0.175873	+	0.984413i	$0.443725\pi$
$968$	−6.55202e14	−	1.13484e15i	−0.770901	−	1.33524i
$969$	−1.92255e14	−	1.10998e14i	−0.225040	−	0.129927i
$970$	4.60877e14	−	7.98262e14i	0.536693	−	0.929580i
$971$	−4.16968e14	+	2.40737e14i	−0.483066	+	0.278899i	−0.721694	−	0.692213i	$-0.756636\pi$
$971$	−4.16968e14	+	2.40737e14i	−0.483066	+	0.278899i	0.238627	+	0.971111i	$0.423303\pi$
$972$		−	2.41025e15i		−	2.77799i
$973$	−6.30049e14	+	3.28652e14i	−0.722454	+	0.376853i
$974$	−3.52081e12			−0.00401650
$975$	1.30751e12	+	2.26467e12i	0.00148395	+	0.00257028i
$976$	−1.04920e15	−	6.05758e14i	−1.18471	−	0.683990i
$977$	5.98387e14	−	1.03644e15i	0.672216	−	1.16431i	−0.305058	−	0.952334i	$-0.598676\pi$
$977$	5.98387e14	−	1.03644e15i	0.672216	−	1.16431i	0.977274	−	0.211979i	$-0.0679908\pi$
$978$	−1.78383e15	+	1.02989e15i	−1.99370	+	1.15106i
$979$			7.59022e14i			0.843997i
$980$	6.55896e14	+	4.57633e14i	0.725612	+	0.506276i
$981$	−6.83014e14			−0.751770
$982$	−7.04121e14	−	1.21957e15i	−0.771063	−	1.33552i
$983$	1.22977e15	+	7.10006e14i	1.33985	+	0.773561i	0.986784	−	0.162039i	$-0.0518070\pi$
$983$	1.22977e15	+	7.10006e14i	1.33985	+	0.773561i	0.353062	+	0.935600i	$0.385140\pi$
$984$	−2.07339e15	+	3.59123e15i	−2.24754	+	3.89285i
$985$	−2.63820e14	+	1.52317e14i	−0.284529	+	0.164273i
$986$			1.74633e15i			1.87389i
$987$	4.59659e14	+	8.81199e14i	0.490738	+	0.940780i
$988$	−1.39417e12			−0.00148091
$989$	−1.32059e14	−	2.28733e14i	−0.139568	−	0.241739i
$990$	5.03416e14	+	2.90647e14i	0.529360	+	0.305626i
$991$	−6.32282e14	+	1.09514e15i	−0.661519	+	1.14578i	0.318698	+	0.947856i	$0.396755\pi$
$991$	−6.32282e14	+	1.09514e15i	−0.661519	+	1.14578i	−0.980217	+	0.197928i	$0.936579\pi$
$992$	−1.62812e15	+	9.39993e14i	−1.69483	+	0.978512i
$993$			3.32208e14i			0.344084i
$994$	−9.88910e14	+	1.55514e15i	−1.01912	+	1.60265i
$995$	−6.73691e14			−0.690789
$996$	−2.54172e15	−	4.40239e15i	−2.59317	−	4.49151i
$997$	9.75561e14	+	5.63240e14i	0.990327	+	0.571765i	0.905372	−	0.424619i	$-0.139592\pi$
$997$	9.75561e14	+	5.63240e14i	0.990327	+	0.571765i	0.0849547	+	0.996385i	$0.472925\pi$
$998$	7.17878e14	−	1.24340e15i	0.725100	−	1.25591i
$999$	7.26380e14	−	4.19376e14i	0.730023	−	0.421479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.11.d.a.3.6	✓	12
3.2	odd	2		63.11.m.c.10.1		12
4.3	odd	2		112.11.s.b.17.6		12
7.2	even	3		49.11.d.c.19.6		12
7.3	odd	6		49.11.b.a.48.1		12
7.4	even	3		49.11.b.a.48.2		12
7.5	odd	6	inner	7.11.d.a.5.6	yes	12
7.6	odd	2		49.11.d.c.31.6		12
21.5	even	6		63.11.m.c.19.1		12
28.19	even	6		112.11.s.b.33.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.11.d.a.3.6	✓	12	1.1	even	1	trivial
7.11.d.a.5.6	yes	12	7.5	odd	6	inner
49.11.b.a.48.1		12	7.3	odd	6
49.11.b.a.48.2		12	7.4	even	3
49.11.d.c.19.6		12	7.2	even	3
49.11.d.c.31.6		12	7.6	odd	2
63.11.m.c.10.1		12	3.2	odd	2
63.11.m.c.19.1		12	21.5	even	6
112.11.s.b.17.6		12	4.3	odd	2
112.11.s.b.33.6		12	28.19	even	6

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(29.0701 + 50.3510i) q^{2} +(-331.655 - 191.481i) q^{3} +(-1178.15 + 2040.61i) q^{4} +(-1040.60 + 600.792i) q^{5} -22265.5i q^{6} +(7773.05 + 14901.5i) q^{7} -77459.9 q^{8} +(43805.3 + 75873.0i) q^{9} +O(q^{10})\)	\(q+(29.0701 + 50.3510i) q^{2} +(-331.655 - 191.481i) q^{3} +(-1178.15 + 2040.61i) q^{4} +(-1040.60 + 600.792i) q^{5} -22265.5i q^{6} +(7773.05 + 14901.5i) q^{7} -77459.9 q^{8} +(43805.3 + 75873.0i) q^{9} +(-60500.9 - 34930.2i) q^{10} +(-47487.4 + 82250.6i) q^{11} +(781475. - 451185. i) q^{12} +820.540i q^{13} +(-524341. + 824570. i) q^{14} +460160. q^{15} +(-1.04535e6 - 1.81059e6i) q^{16} +(696204. + 401954. i) q^{17} +(-2.54685e6 + 4.41128e6i) q^{18} +(624477. - 360542. i) q^{19} -2.83128e6i q^{20} +(275384. - 6.43054e6i) q^{21} -5.52186e6 q^{22} +(-2.16879e6 - 3.75645e6i) q^{23} +(2.56899e7 + 1.48321e7i) q^{24} +(-4.16091e6 + 7.20691e6i) q^{25} +(-41315.0 + 23853.2i) q^{26} -1.09380e7i q^{27} +(-3.95659e7 - 1.69439e6i) q^{28} +3.73632e7 q^{29} +(1.33769e7 + 2.31695e7i) q^{30} +(-3.85492e7 - 2.22564e7i) q^{31} +(2.11173e7 - 3.65763e7i) q^{32} +(3.14988e7 - 1.81859e7i) q^{33} +4.67394e7i q^{34} +(-1.70414e7 - 1.08365e7i) q^{35} -2.06436e8 q^{36} +(3.83411e7 + 6.64088e7i) q^{37} +(3.63073e7 + 2.09620e7i) q^{38} +(157118. - 272136. i) q^{39} +(8.06049e7 - 4.65372e7i) q^{40} +1.39791e8i q^{41} +(3.31789e8 - 1.73071e8i) q^{42} +6.08906e7 q^{43} +(-1.11894e8 - 1.93806e8i) q^{44} +(-9.11678e7 - 5.26357e7i) q^{45} +(1.26094e8 - 2.18401e8i) q^{46} +(-1.33727e8 + 7.72073e7i) q^{47} +8.00656e8i q^{48} +(-1.61635e8 + 2.31660e8i) q^{49} -4.83833e8 q^{50} +(-1.53933e8 - 2.66620e8i) q^{51} +(-1.67440e6 - 966717. i) q^{52} +(1.86521e8 - 3.23065e8i) q^{53} +(5.50739e8 - 3.17969e8i) q^{54} -1.14120e8i q^{55} +(-6.02100e8 - 1.15427e9i) q^{56} -2.76147e8 q^{57} +(1.08615e9 + 1.88127e9i) q^{58} +(2.87503e8 + 1.65990e8i) q^{59} +(-5.42136e8 + 9.39008e8i) q^{60} +(5.01844e8 - 2.89740e8i) q^{61} -2.58799e9i q^{62} +(-7.90121e8 + 1.24253e9i) q^{63} +3.14665e8 q^{64} +(-492974. - 853856. i) q^{65} +(1.83135e9 + 1.05733e9i) q^{66} +(3.53271e8 - 6.11884e8i) q^{67} +(-1.64046e9 + 9.47121e8i) q^{68} +1.66113e9i q^{69} +(5.02360e7 - 1.17307e9i) q^{70} +1.88600e9 q^{71} +(-3.39315e9 - 5.87711e9i) q^{72} +(-1.00370e9 - 5.79487e8i) q^{73} +(-2.22917e9 + 3.86103e9i) q^{74} +(2.75997e9 - 1.59347e9i) q^{75} +1.69908e9i q^{76} +(-1.59478e9 - 6.82956e7i) q^{77} +1.82697e7 q^{78} +(5.30307e8 + 9.18518e8i) q^{79} +(2.17558e9 + 1.25607e9i) q^{80} +(4.92242e8 - 8.52587e8i) q^{81} +(-7.03863e9 + 4.06375e9i) q^{82} -5.63344e9i q^{83} +(1.27978e10 + 8.13807e9i) q^{84} -9.65962e8 q^{85} +(1.77010e9 + 3.06590e9i) q^{86} +(-1.23917e10 - 7.15434e9i) q^{87} +(3.67837e9 - 6.37112e9i) q^{88} +(6.92112e9 - 3.99591e9i) q^{89} -6.12051e9i q^{90} +(-1.22273e7 + 6.37810e6i) q^{91} +1.02206e10 q^{92} +(8.52335e9 + 1.47629e10i) q^{93} +(-7.77493e9 - 4.48886e9i) q^{94} +(-4.33221e8 + 7.50361e8i) q^{95} +(-1.40073e10 + 8.08713e9i) q^{96} +1.31942e10i q^{97} +(-1.63631e10 - 1.40405e9i) q^{98} -8.32080e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 246 q^{3} - 3700 q^{4} + 3330 q^{5} - 12572 q^{7} - 93504 q^{8} + 182964 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 246 * q^3 - 3700 * q^4 + 3330 * q^5 - 12572 * q^7 - 93504 * q^8 + 182964 * q^9	\( 12 q - 12 q^{2} - 246 q^{3} - 3700 q^{4} + 3330 q^{5} - 12572 q^{7} - 93504 q^{8} + 182964 q^{9} - 445740 q^{10} + 82566 q^{11} + 1581468 q^{12} - 934752 q^{14} - 729900 q^{15} - 230152 q^{16} + 389178 q^{17} + 378144 q^{18} - 5517150 q^{19} + 11878986 q^{21} - 19846048 q^{22} - 8131674 q^{23} + 31899384 q^{24} + 6794220 q^{25} + 37885176 q^{26} - 64544228 q^{28} - 86390616 q^{29} + 69082560 q^{30} - 44673798 q^{31} + 82297536 q^{32} + 293090418 q^{33} - 192479070 q^{35} - 895531584 q^{36} + 83071214 q^{37} + 528863040 q^{38} + 45216696 q^{39} + 840782640 q^{40} - 267874488 q^{42} - 975196744 q^{43} - 123891084 q^{44} + 960213420 q^{45} + 348447776 q^{46} + 782650314 q^{47} - 531271524 q^{49} - 3793600080 q^{50} + 90752418 q^{51} + 1019252472 q^{52} + 417566766 q^{53} + 4229214768 q^{54} - 2911004880 q^{56} - 3616618428 q^{57} + 2420166368 q^{58} + 456895242 q^{59} + 1019560500 q^{60} + 1469956122 q^{61} + 962168676 q^{63} - 1697861600 q^{64} - 480821880 q^{65} - 875442996 q^{66} + 1667792862 q^{67} - 3587950548 q^{68} + 4620799680 q^{70} + 9772297272 q^{71} - 5075622576 q^{72} - 3308125038 q^{73} - 8441358900 q^{74} - 13137007020 q^{75} + 1048649574 q^{77} + 25651166688 q^{78} - 2397038922 q^{79} + 1013632920 q^{80} + 394526610 q^{81} - 22926766968 q^{82} + 16162834044 q^{84} + 20859080820 q^{85} - 840264960 q^{86} - 31859197092 q^{87} - 3607027256 q^{88} - 2675986686 q^{89} + 17848798800 q^{91} + 58847183592 q^{92} + 8231670714 q^{93} - 26955870432 q^{94} - 13809374190 q^{95} - 30016813680 q^{96} - 50762451012 q^{98} + 20038367016 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 246 * q^3 - 3700 * q^4 + 3330 * q^5 - 12572 * q^7 - 93504 * q^8 + 182964 * q^9 - 445740 * q^10 + 82566 * q^11 + 1581468 * q^12 - 934752 * q^14 - 729900 * q^15 - 230152 * q^16 + 389178 * q^17 + 378144 * q^18 - 5517150 * q^19 + 11878986 * q^21 - 19846048 * q^22 - 8131674 * q^23 + 31899384 * q^24 + 6794220 * q^25 + 37885176 * q^26 - 64544228 * q^28 - 86390616 * q^29 + 69082560 * q^30 - 44673798 * q^31 + 82297536 * q^32 + 293090418 * q^33 - 192479070 * q^35 - 895531584 * q^36 + 83071214 * q^37 + 528863040 * q^38 + 45216696 * q^39 + 840782640 * q^40 - 267874488 * q^42 - 975196744 * q^43 - 123891084 * q^44 + 960213420 * q^45 + 348447776 * q^46 + 782650314 * q^47 - 531271524 * q^49 - 3793600080 * q^50 + 90752418 * q^51 + 1019252472 * q^52 + 417566766 * q^53 + 4229214768 * q^54 - 2911004880 * q^56 - 3616618428 * q^57 + 2420166368 * q^58 + 456895242 * q^59 + 1019560500 * q^60 + 1469956122 * q^61 + 962168676 * q^63 - 1697861600 * q^64 - 480821880 * q^65 - 875442996 * q^66 + 1667792862 * q^67 - 3587950548 * q^68 + 4620799680 * q^70 + 9772297272 * q^71 - 5075622576 * q^72 - 3308125038 * q^73 - 8441358900 * q^74 - 13137007020 * q^75 + 1048649574 * q^77 + 25651166688 * q^78 - 2397038922 * q^79 + 1013632920 * q^80 + 394526610 * q^81 - 22926766968 * q^82 + 16162834044 * q^84 + 20859080820 * q^85 - 840264960 * q^86 - 31859197092 * q^87 - 3607027256 * q^88 - 2675986686 * q^89 + 17848798800 * q^91 + 58847183592 * q^92 + 8231670714 * q^93 - 26955870432 * q^94 - 13809374190 * q^95 - 30016813680 * q^96 - 50762451012 * q^98 + 20038367016 * q^99

Introduction

L-functions

Modular forms

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