LMFDB - Embedded newform 71.2.g.a.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	71.10
Dual form			71.2.g.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.931498 - 0.257077i) q^{2} +(1.04905 - 2.45439i) q^{3} +(-0.915297 + 0.546865i) q^{4} +(-1.09157 + 3.35950i) q^{5} +(0.346226 - 2.55594i) q^{6} +(-0.0991455 - 2.20765i) q^{7} +(-2.04759 + 2.14161i) q^{8} +(-2.85031 - 2.98119i) q^{9} +O(q^{10})$	\(q+(0.931498 - 0.257077i) q^{2} +(1.04905 - 2.45439i) q^{3} +(-0.915297 + 0.546865i) q^{4} +(-1.09157 + 3.35950i) q^{5} +(0.346226 - 2.55594i) q^{6} +(-0.0991455 - 2.20765i) q^{7} +(-2.04759 + 2.14161i) q^{8} +(-2.85031 - 2.98119i) q^{9} +(-0.153143 + 3.40999i) q^{10} +(3.81476 + 0.692276i) q^{11} +(0.382020 + 2.82018i) q^{12} +(-3.34249 + 0.606572i) q^{13} +(-0.659889 - 2.03093i) q^{14} +(7.10040 + 6.20343i) q^{15} +(-0.346268 + 0.643474i) q^{16} +(1.77538 - 1.28989i) q^{17} +(-3.42145 - 2.04422i) q^{18} +(-1.31638 + 1.15008i) q^{19} +(-0.838084 - 3.67188i) q^{20} +(-5.52242 - 2.07260i) q^{21} +(3.73141 - 0.335833i) q^{22} +(-4.87533 - 6.11347i) q^{23} +(3.10830 + 7.27224i) q^{24} +(-6.04965 - 4.39533i) q^{25} +(-2.95759 + 1.42430i) q^{26} +(-2.81017 + 1.05467i) q^{27} +(1.29803 + 1.96643i) q^{28} +(3.21498 + 0.289353i) q^{29} +(8.20877 + 3.95314i) q^{30} +(1.95119 + 3.62592i) q^{31} +(1.16151 - 5.08893i) q^{32} +(5.70100 - 8.63664i) q^{33} +(1.32216 - 1.65794i) q^{34} +(7.52482 + 2.07672i) q^{35} +(4.23918 + 1.16994i) q^{36} +(-4.09361 + 5.13323i) q^{37} +(-0.930542 + 1.40971i) q^{38} +(-2.01769 + 8.84008i) q^{39} +(-4.95966 - 9.21660i) q^{40} +(6.24873 + 3.00923i) q^{41} +(-5.67695 - 0.510934i) q^{42} +(-6.12786 - 9.28331i) q^{43} +(-3.87022 + 1.45252i) q^{44} +(13.1266 - 6.32144i) q^{45} +(-6.11300 - 4.44135i) q^{46} +(-0.119877 - 0.280467i) q^{47} +(1.21608 + 1.52491i) q^{48} +(2.10795 - 0.189719i) q^{49} +(-6.76518 - 2.53901i) q^{50} +(-1.30341 - 5.71062i) q^{51} +(2.72766 - 2.38308i) q^{52} +(5.79359 + 3.46151i) q^{53} +(-2.34653 + 1.70486i) q^{54} +(-6.48977 + 12.0600i) q^{55} +(4.93093 + 4.30802i) q^{56} +(1.44180 + 4.43740i) q^{57} +(3.06913 - 0.556966i) q^{58} +(0.957622 + 7.06945i) q^{59} +(-9.89141 - 1.79503i) q^{60} +(-0.0768731 + 1.71171i) q^{61} +(2.74967 + 2.87593i) q^{62} +(-6.29881 + 6.58804i) q^{63} +(-0.291866 - 6.49891i) q^{64} +(1.61077 - 11.8912i) q^{65} +(3.09019 - 9.51062i) q^{66} +(6.12464 - 3.65930i) q^{67} +(-0.919603 + 2.15152i) q^{68} +(-20.1193 + 5.55258i) q^{69} +7.54323 q^{70} +(-0.559666 + 8.40754i) q^{71} +12.2208 q^{72} +(-5.71692 + 1.57777i) q^{73} +(-2.49356 + 5.83397i) q^{74} +(-17.1342 + 10.2372i) q^{75} +(0.575936 - 1.77255i) q^{76} +(1.15008 - 8.49026i) q^{77} +(0.393108 + 8.75322i) q^{78} +(2.62400 - 2.74449i) q^{79} +(-1.78378 - 1.86568i) q^{80} +(0.195694 - 4.35748i) q^{81} +(6.59428 + 1.19669i) q^{82} +(1.26208 + 9.31702i) q^{83} +(6.18809 - 1.12297i) q^{84} +(2.39543 + 7.37238i) q^{85} +(-8.09462 - 7.07206i) q^{86} +(4.08288 - 7.58725i) q^{87} +(-9.29364 + 6.75222i) q^{88} +(-12.1461 - 7.25693i) q^{89} +(10.6023 - 9.26296i) q^{90} +(1.67049 + 7.31889i) q^{91} +(7.80562 + 2.92950i) q^{92} +(10.9463 - 0.985186i) q^{93} +(-0.183767 - 0.230437i) q^{94} +(-2.42679 - 5.67777i) q^{95} +(-11.2717 - 8.18937i) q^{96} +(-10.9118 + 5.25486i) q^{97} +(1.91478 - 0.718628i) q^{98} +(-8.80941 - 13.3457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{17}{35}\right)$

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 $

$2$	0.931498	−	0.257077i	0.658669	−	0.181781i	0.0793053	−	0.996850i	$-0.474730\pi$
$2$	0.931498	−	0.257077i	0.658669	−	0.181781i	0.579363	+	0.815069i	$0.303301\pi$
$3$	1.04905	−	2.45439i	0.605672	−	1.41704i	−0.283279	−	0.959038i	$-0.591422\pi$
$3$	1.04905	−	2.45439i	0.605672	−	1.41704i	0.888951	−	0.458003i	$-0.151435\pi$
$4$	−0.915297	+	0.546865i	−0.457649	+	0.273432i
$5$	−1.09157	+	3.35950i	−0.488164	+	1.50242i	0.339181	+	0.940721i	$0.389850\pi$
$5$	−1.09157	+	3.35950i	−0.488164	+	1.50242i	−0.827345	+	0.561694i	$0.810150\pi$
$6$	0.346226	−	2.55594i	0.141346	−	1.04346i
$7$	−0.0991455	−	2.20765i	−0.0374735	−	0.834412i	−0.926441	−	0.376441i	$-0.877148\pi$
$7$	−0.0991455	−	2.20765i	−0.0374735	−	0.834412i	0.888967	−	0.457971i	$-0.151424\pi$
$8$	−2.04759	+	2.14161i	−0.723932	+	0.757174i
$9$	−2.85031	−	2.98119i	−0.950102	−	0.993729i
$10$	−0.153143	+	3.40999i	−0.0484280	+	1.07833i
$11$	3.81476	+	0.692276i	1.15019	+	0.208729i	0.719977	−	0.693998i	$-0.244152\pi$
$11$	3.81476	+	0.692276i	1.15019	+	0.208729i	0.430215	+	0.902727i	$0.358438\pi$
$12$	0.382020	+	2.82018i	0.110280	+	0.814117i
$13$	−3.34249	+	0.606572i	−0.927039	+	0.168233i	−0.621022	−	0.783793i	$-0.713282\pi$
$13$	−3.34249	+	0.606572i	−0.927039	+	0.168233i	−0.306017	+	0.952026i	$0.598997\pi$
$14$	−0.659889	−	2.03093i	−0.176363	−	0.542789i
$15$	7.10040	+	6.20343i	1.83332	+	1.60172i
$16$	−0.346268	+	0.643474i	−0.0865670	+	0.160868i
$17$	1.77538	−	1.28989i	0.430592	−	0.312843i	−0.351294	−	0.936265i	$-0.614258\pi$
$17$	1.77538	−	1.28989i	0.430592	−	0.312843i	0.781886	+	0.623422i	$0.214258\pi$
$18$	−3.42145	−	2.04422i	−0.806443	−	0.481827i
$19$	−1.31638	+	1.15008i	−0.301997	+	0.263847i	−0.795576	−	0.605854i	$-0.792832\pi$
$19$	−1.31638	+	1.15008i	−0.301997	+	0.263847i	0.493578	+	0.869701i	$0.335689\pi$
$20$	−0.838084	−	3.67188i	−0.187401	−	0.821058i
$21$	−5.52242	−	2.07260i	−1.20509	−	0.452278i
$22$	3.73141	−	0.335833i	0.795538	−	0.0715998i
$23$	−4.87533	−	6.11347i	−1.01658	−	1.27475i	−0.961075	−	0.276289i	$-0.910895\pi$
$23$	−4.87533	−	6.11347i	−1.01658	−	1.27475i	−0.0555028	−	0.998459i	$-0.517676\pi$
$24$	3.10830	+	7.27224i	0.634480	+	1.48444i
$25$	−6.04965	−	4.39533i	−1.20993	−	0.879066i
$26$	−2.95759	+	1.42430i	−0.580030	+	0.279328i
$27$	−2.81017	+	1.05467i	−0.540817	+	0.202972i
$28$	1.29803	+	1.96643i	0.245305	+	0.371621i
$29$	3.21498	+	0.289353i	0.597007	+	0.0537316i	0.384022	−	0.923324i	$-0.374539\pi$
$29$	3.21498	+	0.289353i	0.597007	+	0.0537316i	0.212985	+	0.977056i	$0.431682\pi$
$30$	8.20877	+	3.95314i	1.49871	+	0.721741i
$31$	1.95119	+	3.62592i	0.350444	+	0.651235i	0.993404	−	0.114665i	$-0.0365795\pi$
$31$	1.95119	+	3.62592i	0.350444	+	0.651235i	−0.642960	+	0.765900i	$0.722294\pi$
$32$	1.16151	−	5.08893i	0.205329	−	0.899604i
$33$	5.70100	−	8.63664i	0.992417	−	1.50345i
$34$	1.32216	−	1.65794i	0.226748	−	0.284334i
$35$	7.52482	+	2.07672i	1.27193	+	0.351029i
$36$	4.23918	+	1.16994i	0.706530	+	0.194990i
$37$	−4.09361	+	5.13323i	−0.672986	+	0.843898i	−0.994687	−	0.102944i	$-0.967174\pi$
$37$	−4.09361	+	5.13323i	−0.672986	+	0.843898i	0.321701	+	0.946841i	$0.395745\pi$
$38$	−0.930542	+	1.40971i	−0.150954	+	0.228685i
$39$	−2.01769	+	8.84008i	−0.323089	+	1.41555i
$40$	−4.95966	−	9.21660i	−0.784191	−	1.45727i
$41$	6.24873	+	3.00923i	0.975887	+	0.469963i	0.852689	−	0.522419i	$-0.174970\pi$
$41$	6.24873	+	3.00923i	0.975887	+	0.469963i	0.123199	+	0.992382i	$0.460685\pi$
$42$	−5.67695	−	0.510934i	−0.875972	−	0.0788389i
$43$	−6.12786	−	9.28331i	−0.934490	−	1.41569i	−0.909361	−	0.416007i	$-0.863429\pi$
$43$	−6.12786	−	9.28331i	−0.934490	−	1.41569i	−0.0251287	−	0.999684i	$-0.508000\pi$
$44$	−3.87022	+	1.45252i	−0.583457	+	0.218975i
$45$	13.1266	−	6.32144i	1.95680	−	0.942345i
$46$	−6.11300	−	4.44135i	−0.901313	−	0.654842i
$47$	−0.119877	−	0.280467i	−0.0174859	−	0.0409104i	0.910557	−	0.413383i	$-0.135653\pi$
$47$	−0.119877	−	0.280467i	−0.0174859	−	0.0409104i	−0.928043	+	0.372473i	$0.878510\pi$
$48$	1.21608	+	1.52491i	0.175526	+	0.220102i
$49$	2.10795	−	0.189719i	0.301136	−	0.0271027i
$50$	−6.76518	−	2.53901i	−0.956741	−	0.359071i
$51$	−1.30341	−	5.71062i	−0.182514	−	0.799646i
$52$	2.72766	−	2.38308i	0.378258	−	0.330474i
$53$	5.79359	+	3.46151i	0.795810	+	0.475474i	0.852379	−	0.522924i	$-0.175159\pi$
$53$	5.79359	+	3.46151i	0.795810	+	0.475474i	−0.0565690	+	0.998399i	$0.518016\pi$
$54$	−2.34653	+	1.70486i	−0.319323	+	0.232001i
$55$	−6.48977	+	12.0600i	−0.875080	+	1.62617i
$56$	4.93093	+	4.30802i	0.658923	+	0.575684i
$57$	1.44180	+	4.43740i	0.190971	+	0.587748i
$58$	3.06913	−	0.556966i	0.402997	−	0.0731332i
$59$	0.957622	+	7.06945i	0.124672	+	0.920364i	0.939954	+	0.341301i	$0.110867\pi$
$59$	0.957622	+	7.06945i	0.124672	+	0.920364i	−0.815282	+	0.579064i	$0.803418\pi$
$60$	−9.89141	−	1.79503i	−1.27698	−	0.231737i
$61$	−0.0768731	+	1.71171i	−0.00984259	+	0.219162i	0.988044	+	0.154175i	$0.0492720\pi$
$61$	−0.0768731	+	1.71171i	−0.00984259	+	0.219162i	−0.997886	+	0.0649870i	$0.979299\pi$
$62$	2.74967	+	2.87593i	0.349209	+	0.365244i
$63$	−6.29881	+	6.58804i	−0.793575	+	0.830015i
$64$	−0.291866	−	6.49891i	−0.0364833	−	0.812363i
$65$	1.61077	−	11.8912i	0.199792	−	1.47492i
$66$	3.09019	−	9.51062i	0.380376	−	1.17068i
$67$	6.12464	−	3.65930i	0.748244	−	0.447055i	−0.0875068	−	0.996164i	$-0.527890\pi$
$67$	6.12464	−	3.65930i	0.748244	−	0.447055i	0.835751	+	0.549109i	$0.185033\pi$
$68$	−0.919603	+	2.15152i	−0.111518	+	0.260910i
$69$	−20.1193	+	5.55258i	−2.42208	+	0.668452i
$70$	7.54323			0.901589
$71$	−0.559666	+	8.40754i	−0.0664201	+	0.997792i
$71$	−0.559666	+	8.40754i	−0.0664201	+	0.997792i
$72$	12.2208			1.44023
$73$	−5.71692	+	1.57777i	−0.669115	+	0.184664i	−0.584058	−	0.811712i	$-0.698536\pi$
$73$	−5.71692	+	1.57777i	−0.669115	+	0.184664i	−0.0850573	+	0.996376i	$0.527107\pi$
$74$	−2.49356	+	5.83397i	−0.289870	+	0.678185i
$75$	−17.1342	+	10.2372i	−1.97849	+	1.18209i
$76$	0.575936	−	1.77255i	0.0660644	−	0.203325i
$77$	1.15008	−	8.49026i	0.131064	−	0.967555i
$78$	0.393108	+	8.75322i	0.0445107	+	0.991107i
$79$	2.62400	−	2.74449i	0.295223	−	0.308779i	−0.558502	−	0.829503i	$-0.688624\pi$
$79$	2.62400	−	2.74449i	0.295223	−	0.308779i	0.853725	+	0.520724i	$0.174338\pi$
$80$	−1.78378	−	1.86568i	−0.199432	−	0.208590i
$81$	0.195694	−	4.35748i	0.0217438	−	0.484164i
$82$	6.59428	+	1.19669i	0.728217	+	0.132152i
$83$	1.26208	+	9.31702i	0.138531	+	1.02268i	0.918097	+	0.396356i	$0.129725\pi$
$83$	1.26208	+	9.31702i	0.138531	+	1.02268i	−0.779566	+	0.626320i	$0.784560\pi$
$84$	6.18809	−	1.12297i	0.675176	−	0.122526i
$85$	2.39543	+	7.37238i	0.259821	+	0.799647i
$86$	−8.09462	−	7.07206i	−0.872865	−	0.762599i
$87$	4.08288	−	7.58725i	0.437730	−	0.813439i
$88$	−9.29364	+	6.75222i	−0.990705	+	0.719789i
$89$	−12.1461	−	7.25693i	−1.28748	−	0.769233i	−0.304423	−	0.952537i	$-0.598464\pi$
$89$	−12.1461	−	7.25693i	−1.28748	−	0.769233i	−0.983056	+	0.183304i	$0.941321\pi$
$90$	10.6023	−	9.26296i	1.11758	−	0.976402i
$91$	1.67049	+	7.31889i	0.175115	+	0.767228i
$92$	7.80562	+	2.92950i	0.813792	+	0.305421i
$93$	10.9463	−	0.985186i	1.13508	−	0.102159i
$94$	−0.183767	−	0.230437i	−0.0189542	−	0.0237678i
$95$	−2.42679	−	5.67777i	−0.248984	−	0.582526i
$96$	−11.2717	−	8.18937i	−1.15041	−	0.835824i
$97$	−10.9118	+	5.25486i	−1.10793	+	0.533550i	−0.896143	−	0.443766i	$-0.853642\pi$
$97$	−10.9118	+	5.25486i	−1.10793	+	0.533550i	−0.211786	+	0.977316i	$0.567928\pi$
$98$	1.91478	−	0.718628i	0.193422	−	0.0725924i
$99$	−8.80941	−	13.3457i	−0.885379	−	1.34129i
$100$	7.94088	+	0.714692i	0.794088	+	0.0714692i
$101$	2.51076	+	1.20912i	0.249830	+	0.120312i	0.554608	−	0.832112i	$-0.312868\pi$
$101$	2.51076	+	1.20912i	0.249830	+	0.120312i	−0.304778	+	0.952423i	$0.598582\pi$
$102$	−2.68220	−	4.98435i	−0.265577	−	0.493525i
$103$	−1.25365	+	5.49258i	−0.123525	+	0.541200i	0.874859	+	0.484378i	$0.160954\pi$
$103$	−1.25365	+	5.49258i	−0.123525	+	0.541200i	−0.998384	+	0.0568222i	$0.981903\pi$
$104$	5.54500	−	8.40031i	0.543732	−	0.823719i
$105$	12.9910	−	16.2902i	1.26779	−	1.58976i
$106$	6.28659	+	1.73499i	0.610608	+	0.168517i
$107$	−0.0596932	−	0.0164743i	−0.00577076	−	0.00159263i	0.263150	−	0.964755i	$-0.415238\pi$
$107$	−0.0596932	−	0.0164743i	−0.00577076	−	0.00159263i	−0.268921	+	0.963162i	$0.586667\pi$
$108$	1.99537	−	2.50212i	0.192005	−	0.240767i
$109$	4.21194	−	6.38082i	0.403431	−	0.611172i	−0.574899	−	0.818225i	$-0.694959\pi$
$109$	4.21194	−	6.38082i	0.403431	−	0.611172i	0.978330	+	0.207053i	$0.0663872\pi$
$110$	−2.94486	+	12.9023i	−0.280781	+	1.23018i
$111$	8.30450	+	15.4323i	0.788228	+	1.46477i
$112$	1.45489	+	0.700640i	0.137474	+	0.0662042i
$113$	2.13556	+	0.192204i	0.200896	+	0.0180810i	0.189630	−	0.981856i	$-0.439271\pi$
$113$	2.13556	+	0.192204i	0.200896	+	0.0180810i	0.0112659	+	0.999937i	$0.496414\pi$
$114$	2.48379	+	3.76277i	0.232628	+	0.352416i
$115$	25.8600	−	9.70542i	2.41146	−	0.905035i
$116$	−3.10090	+	1.49331i	−0.287911	+	0.138651i
$117$	11.3354	+	8.23566i	1.04796	+	0.761387i
$118$	2.70942	+	6.33900i	0.249422	+	0.583552i
$119$	−3.02363	−	3.79151i	−0.277176	−	0.347568i
$120$	−27.8240	+	2.50421i	−2.53998	+	0.228602i
$121$	3.77453	+	1.41660i	0.343139	+	0.128782i
$122$	0.368435	+	1.61422i	0.0333565	+	0.146145i
$123$	13.9411	−	12.1799i	1.25702	−	1.09823i
$124$	−3.76881	−	2.25176i	−0.338449	−	0.202214i
$125$	7.08091	−	5.14458i	0.633336	−	0.460146i
$126$	−4.17369	+	7.75602i	−0.371822	+	0.690962i
$127$	−1.82530	−	1.59471i	−0.161969	−	0.141508i	0.573139	−	0.819458i	$-0.305726\pi$
$127$	−1.82530	−	1.59471i	−0.161969	−	0.141508i	−0.735108	+	0.677950i	$0.762868\pi$
$128$	1.28342	+	3.94996i	0.113439	+	0.349130i
$129$	−29.2133	+	5.30143i	−2.57209	+	0.466765i
$130$	−1.55653	−	11.4907i	−0.136516	−	1.00780i
$131$	4.61037	+	0.836659i	0.402810	+	0.0730992i	0.376181	−	0.926546i	$-0.377237\pi$
$131$	4.61037	+	0.836659i	0.402810	+	0.0730992i	0.0266288	+	0.999645i	$0.491523\pi$
$132$	−0.495033	+	11.0228i	−0.0430871	+	0.959409i
$133$	2.66949	+	2.79207i	0.231474	+	0.242103i
$134$	4.76437	−	4.98314i	0.411579	−	0.430478i
$135$	−0.475688	−	10.5920i	−0.0409407	−	0.911615i
$136$	−0.872807	+	6.44332i	−0.0748426	+	0.552510i
$137$	−0.395582	+	1.21747i	−0.0337968	+	0.104016i	−0.966532	−	0.256547i	$-0.917415\pi$
$137$	−0.395582	+	1.21747i	−0.0337968	+	0.104016i	0.932735	+	0.360563i	$0.117415\pi$
$138$	−17.3137	+	10.3444i	−1.47384	+	0.880577i
$139$	0.372152	−	0.870692i	0.0315655	−	0.0738512i	−0.903003	−	0.429634i	$-0.858643\pi$
$139$	0.372152	−	0.870692i	0.0315655	−	0.0738512i	0.934569	+	0.355782i	$0.115786\pi$
$140$	−8.02313	+	2.21424i	−0.678078	+	0.187138i
$141$	−0.814133			−0.0685624
$142$	1.64006	+	7.97549i	0.137631	+	0.669288i
$143$	−13.1707			−1.10139
$144$	2.90528	−	0.801807i	0.242107	−	0.0668173i
$145$	−4.48146	+	10.4849i	−0.372165	+	0.870722i
$146$	−4.91970	+	2.93938i	−0.407157	+	0.243265i
$147$	1.74571	−	5.37274i	0.143984	−	0.443137i
$148$	0.939692	−	6.93708i	0.0772422	−	0.570225i
$149$	−0.350073	−	7.79499i	−0.0286791	−	0.638590i	−0.960932	−	0.276784i	$-0.910731\pi$
$149$	−0.350073	−	7.79499i	−0.0286791	−	0.638590i	0.932253	−	0.361807i	$-0.117840\pi$
$150$	−13.3288	+	13.9408i	−1.08829	+	1.13826i
$151$	−9.70229	−	10.1478i	−0.789561	−	0.825816i	0.198464	−	0.980108i	$-0.436405\pi$
$151$	−9.70229	−	10.1478i	−0.789561	−	0.825816i	−0.988025	+	0.154292i	$0.950690\pi$
$152$	0.232367	−	5.17406i	0.0188475	−	0.419672i
$153$	−8.90575	−	1.61616i	−0.719987	−	0.130658i
$154$	−1.11135	−	8.20433i	−0.0895553	−	0.661124i
$155$	−14.3112	+	2.59709i	−1.14950	+	0.208603i
$156$	−2.98754	−	9.19470i	−0.239195	−	0.736165i
$157$	−8.41699	−	7.35370i	−0.671749	−	0.586889i	0.253000	−	0.967466i	$-0.418583\pi$
$157$	−8.41699	−	7.35370i	−0.671749	−	0.586889i	−0.924749	+	0.380577i	$0.875725\pi$
$158$	1.73871	−	3.23106i	0.138324	−	0.257049i
$159$	14.5737	−	10.5884i	1.15577	−	0.839713i
$160$	15.8284	+	9.45702i	1.25134	+	0.747643i
$161$	−13.0130	+	11.3691i	−1.02557	+	0.896013i
$162$	−0.937918	−	4.10929i	−0.0736898	−	0.322856i
$163$	16.8307	+	6.31668i	1.31829	+	0.494761i	0.908677	−	0.417500i	$-0.137094\pi$
$163$	16.8307	+	6.31668i	1.31829	+	0.494761i	0.409609	+	0.912261i	$0.365665\pi$
$164$	−7.36508	+	0.662870i	−0.575116	+	0.0517614i
$165$	22.7918	+	28.5800i	1.77434	+	2.22495i
$166$	3.57081	+	8.35434i	0.277149	+	0.648422i
$167$	−8.54704	−	6.20979i	−0.661390	−	0.480528i	0.205742	−	0.978606i	$-0.434039\pi$
$167$	−8.54704	−	6.20979i	−0.661390	−	0.480528i	−0.867132	+	0.498078i	$0.834039\pi$
$168$	15.7464	−	7.58305i	1.21486	−	0.585045i
$169$	−1.36676	+	0.512955i	−0.105136	+	0.0394581i
$170$	4.12661	+	6.25155i	0.316497	+	0.479472i
$171$	7.18069	+	0.646274i	0.549121	+	0.0494218i
$172$	10.6855	+	5.14588i	0.814764	+	0.392370i
$173$	7.46295	+	13.8685i	0.567397	+	1.05440i	0.989041	+	0.147639i	$0.0471675\pi$
$173$	7.46295	+	13.8685i	0.567397	+	1.05440i	−0.421644	+	0.906761i	$0.638547\pi$
$174$	1.85268	−	8.11713i	0.140451	−	0.615358i
$175$	−9.10354	+	13.7913i	−0.688163	+	1.04252i
$176$	−1.76639	+	2.21498i	−0.133147	+	0.166961i
$177$	18.3558	+	5.06587i	1.37970	+	0.380774i
$178$	−13.1796	−	3.63734i	−0.987854	−	0.272631i
$179$	6.73968	−	8.45129i	0.503747	−	0.631679i	−0.463323	−	0.886190i	$-0.653343\pi$
$179$	6.73968	−	8.45129i	0.503747	−	0.631679i	0.967070	+	0.254511i	$0.0819143\pi$
$180$	−8.55777	+	12.9645i	−0.637859	+	0.966315i
$181$	3.25541	−	14.2629i	0.241973	−	1.06015i	−0.697246	−	0.716832i	$-0.745591\pi$
$181$	3.25541	−	14.2629i	0.241973	−	1.06015i	0.939219	−	0.343320i	$-0.111552\pi$
$182$	3.43758	+	6.38809i	0.254810	+	0.473517i
$183$	4.12056	+	1.98436i	0.304600	+	0.146688i
$184$	23.0754	+	2.07682i	1.70114	+	0.153105i
$185$	−12.7766	−	19.3558i	−0.939357	−	1.42307i
$186$	9.94321	−	3.73175i	0.729071	−	0.273625i
$187$	7.66558	−	3.69155i	0.560563	−	0.269953i
$188$	0.263101	+	0.191154i	0.0191886	+	0.0139414i
$189$	2.60696	+	6.09929i	0.189628	+	0.443658i
$190$	−3.72018	−	4.66496i	−0.269890	−	0.338431i
$191$	−13.2100	+	1.18892i	−0.955844	+	0.0860275i	−0.556567	−	0.830803i	$-0.687882\pi$
$191$	−13.2100	+	1.18892i	−0.955844	+	0.0860275i	−0.399277	+	0.916830i	$0.630739\pi$
$192$	−16.2570	−	6.10136i	−1.17325	−	0.440327i
$193$	−3.11184	−	13.6339i	−0.223995	−	0.981388i	−0.954437	−	0.298413i	$-0.903543\pi$
$193$	−3.11184	−	13.6339i	−0.223995	−	0.981388i	0.730442	−	0.682975i	$-0.239314\pi$
$194$	−8.81344	+	7.70007i	−0.632768	+	0.552833i
$195$	−27.4958	−	16.4280i	−1.96902	−	1.17643i
$196$	−1.82565	+	1.32641i	−0.130404	+	0.0947437i
$197$	5.47794	−	10.1797i	0.390287	−	0.725275i	−0.607317	−	0.794460i	$-0.707754\pi$
$197$	5.47794	−	10.1797i	0.390287	−	0.725275i	0.997604	+	0.0691848i	$0.0220398\pi$
$198$	−11.6368	−	10.1668i	−0.826993	−	0.722522i
$199$	−1.99096	−	6.12754i	−0.141135	−	0.434370i	0.855358	−	0.518037i	$-0.173337\pi$
$199$	−1.99096	−	6.12754i	−0.141135	−	0.434370i	−0.996494	+	0.0836668i	$0.973337\pi$
$200$	21.8003	−	3.95617i	1.54151	−	0.279743i
$201$	−2.55626	−	18.8710i	−0.180304	−	1.33106i
$202$	2.64961	+	0.480833i	0.186426	+	0.0338313i
$203$	0.320039	−	7.12623i	0.0224623	−	0.500163i
$204$	4.31594	+	4.51412i	0.302177	+	0.316052i
$205$	−16.9304	+	17.7078i	−1.18247	+	1.23677i
$206$	0.244248	+	5.43861i	0.0170176	+	0.378926i
$207$	−4.32921	+	31.9595i	−0.300901	+	2.22134i
$208$	0.767083	−	2.36084i	0.0531876	−	0.163695i
$209$	−5.81783	+	3.47599i	−0.402428	+	0.240439i
$210$	7.91326	−	18.5140i	0.546067	−	1.27759i
$211$	−5.62143	+	1.55142i	−0.386995	+	0.106804i	−0.454120	−	0.890941i	$-0.650046\pi$
$211$	−5.62143	+	1.55142i	−0.386995	+	0.106804i	0.0671243	+	0.997745i	$0.478618\pi$
$212$	−7.19583			−0.494211
$213$	20.0482	+	10.1936i	1.37368	+	0.698455i
$214$	−0.0598392			−0.00409053
$215$	37.8763	−	10.4532i	2.58314	−	0.712902i
$216$	3.49537	−	8.17782i	0.237830	−	0.556430i
$217$	7.81130	−	4.66703i	0.530266	−	0.316819i
$218$	2.28305	−	7.02652i	0.154628	−	0.475896i
$219$	−2.12491	+	15.6867i	−0.143588	+	1.06001i
$220$	−0.655126	−	14.5875i	−0.0441686	−	0.983491i
$221$	−5.15176	+	5.38832i	−0.346545	+	0.362458i
$222$	11.7029	+	12.2403i	0.785449	+	0.821516i
$223$	0.973686	−	21.6808i	0.0652028	−	1.45185i	−0.653706	−	0.756749i	$-0.726787\pi$
$223$	0.973686	−	21.6808i	0.0652028	−	1.45185i	0.718908	−	0.695105i	$-0.244642\pi$
$224$	−11.3497	−	2.05967i	−0.758334	−	0.137617i
$225$	4.14006	+	30.5632i	0.276004	+	2.03754i
$226$	2.03868	−	0.369966i	0.135611	−	0.0246097i
$227$	−1.15259	−	3.54729i	−0.0764998	−	0.235442i	0.905493	−	0.424362i	$-0.139501\pi$
$227$	−1.15259	−	3.54729i	−0.0764998	−	0.235442i	−0.981993	+	0.188920i	$0.939501\pi$
$228$	−3.74633	−	3.27307i	−0.248107	−	0.216764i
$229$	−12.4591	+	23.1529i	−0.823319	+	1.52998i	0.0245005	+	0.999700i	$0.492200\pi$
$229$	−12.4591	+	23.1529i	−0.823319	+	1.52998i	−0.847820	+	0.530284i	$0.822085\pi$
$230$	21.5935	−	15.6886i	1.42383	−	1.03448i
$231$	−19.6319	−	11.7295i	−1.29168	−	0.771745i
$232$	−7.20264	+	6.29276i	−0.472877	+	0.413140i
$233$	4.59869	+	20.1482i	0.301270	+	1.31995i	0.868212	+	0.496193i	$0.165269\pi$
$233$	4.59869	+	20.1482i	0.301270	+	1.31995i	−0.566942	+	0.823758i	$0.691874\pi$
$234$	12.6761	+	4.75743i	0.828664	+	0.311003i
$235$	1.07309	−	0.0965794i	0.0700004	−	0.00630015i
$236$	−4.74254	−	5.94696i	−0.308713	−	0.387114i
$237$	−3.98332	−	9.31943i	−0.258744	−	0.605362i
$238$	−3.79122	−	2.75448i	−0.245748	−	0.178547i
$239$	4.56961	−	2.20061i	0.295583	−	0.142345i	−0.280215	−	0.959937i	$-0.590406\pi$
$239$	4.56961	−	2.20061i	0.295583	−	0.142345i	0.575798	+	0.817592i	$0.304691\pi$
$240$	−6.45039	+	2.42087i	−0.416371	+	0.156267i
$241$	1.72738	+	2.61686i	0.111270	+	0.168567i	0.885941	−	0.463797i	$-0.153513\pi$
$241$	1.72738	+	2.61686i	0.111270	+	0.168567i	−0.774671	+	0.632364i	$0.782085\pi$
$242$	3.88014	+	0.349219i	0.249425	+	0.0224486i
$243$	−18.6026	−	8.95853i	−1.19336	−	0.574690i
$244$	−0.865713	−	1.60876i	−0.0554216	−	0.102991i
$245$	−1.66361	+	7.28875i	−0.106284	+	0.465661i
$246$	9.85489	−	14.9295i	0.628325	−	0.951872i
$247$	3.70236	−	4.64262i	0.235576	−	0.295403i
$248$	−11.7606	−	3.24571i	−0.746796	−	0.206103i
$249$	24.1915	+	6.67644i	1.53308	+	0.423102i
$250$	5.27330	−	6.61251i	0.333513	−	0.418212i
$251$	−5.86648	+	8.88734i	−0.370289	+	0.560964i	−0.971174	−	0.238371i	$-0.923386\pi$
$251$	−5.86648	+	8.88734i	−0.370289	+	0.560964i	0.600885	+	0.799336i	$0.294815\pi$
$252$	2.16252	−	9.47461i	0.136226	−	0.596844i
$253$	−14.3660	−	26.6965i	−0.903182	−	1.67839i
$254$	−2.11023	−	1.01623i	−0.132407	−	0.0637640i
$255$	20.6076	+	1.85472i	1.29050	+	0.116147i
$256$	9.37862	+	14.2080i	0.586164	+	0.888000i
$257$	−17.0343	+	6.39307i	−1.06257	+	0.398789i	−0.820605	−	0.571496i	$-0.806363\pi$
$257$	−17.0343	+	6.39307i	−1.06257	+	0.398789i	−0.241964	+	0.970285i	$0.577792\pi$
$258$	−25.8493	+	12.4483i	−1.60930	+	0.775000i
$259$	11.7382	+	8.52831i	0.729377	+	0.529924i
$260$	5.02855	+	11.7649i	0.311857	+	0.729626i
$261$	−8.30106	−	10.4092i	−0.513823	−	0.644313i
$262$	4.50964	−	0.405875i	0.278606	−	0.0250750i
$263$	16.1440	+	6.05896i	0.995484	+	0.373611i	0.795346	−	0.606156i	$-0.207289\pi$
$263$	16.1440	+	6.05896i	0.995484	+	0.373611i	0.200138	+	0.979768i	$0.435861\pi$
$264$	6.82302	+	29.8936i	0.419928	+	1.83983i
$265$	−17.9530	+	15.6851i	−1.10285	+	0.963528i
$266$	3.20440	+	1.91454i	0.196475	+	0.117388i
$267$	−30.5532	+	22.1982i	−1.86982	+	1.35851i
$268$	−3.60472	+	6.69870i	−0.220194	+	0.409188i
$269$	4.63589	+	4.05026i	0.282655	+	0.246948i	0.787576	−	0.616217i	$-0.211336\pi$
$269$	4.63589	+	4.05026i	0.282655	+	0.246948i	−0.504921	+	0.863165i	$0.668478\pi$
$270$	−3.16607	−	9.74415i	−0.192681	−	0.593010i
$271$	29.5284	−	5.35861i	1.79372	−	0.325512i	0.823423	−	0.567428i	$-0.192062\pi$
$271$	29.5284	−	5.35861i	1.79372	−	0.325512i	0.970297	+	0.241916i	$0.0777758\pi$
$272$	0.215252	+	1.58905i	0.0130516	+	0.0963505i
$273$	19.7158	+	3.57789i	1.19326	+	0.216544i
$274$	−0.0554985	+	1.23577i	−0.00335279	+	0.0746556i
$275$	−20.0352	−	20.9551i	−1.20817	−	1.26364i
$276$	15.3786	−	16.0848i	0.925686	−	0.968191i
$277$	−1.35369	−	30.1422i	−0.0813353	−	1.81107i	−0.462560	−	0.886588i	$-0.653069\pi$
$277$	−1.35369	−	30.1422i	−0.0813353	−	1.81107i	0.381225	−	0.924482i	$-0.375502\pi$
$278$	0.122824	−	0.906720i	0.00736647	−	0.0543815i
$279$	5.24805	−	16.1518i	0.314193	−	0.966986i
$280$	−19.8553	+	11.8630i	−1.18658	+	0.708948i
$281$	4.04963	−	9.47459i	0.241581	−	0.565207i	−0.754233	−	0.656606i	$-0.771991\pi$
$281$	4.04963	−	9.47459i	0.241581	−	0.565207i	0.995814	+	0.0913998i	$0.0291341\pi$
$282$	−0.758363	+	0.209295i	−0.0451599	+	0.0124633i
$283$	−7.78026			−0.462489			−0.231244	−	0.972896i	$-0.574280\pi$
$283$	−7.78026			−0.462489			−0.231244	+	0.972896i	$0.574280\pi$
$284$	−4.08553	−	8.00146i	−0.242431	−	0.474799i
$285$	−16.4813			−0.976266
$286$	−12.2685	+	3.38588i	−0.725450	+	0.200211i
$287$	6.02378	−	14.0933i	0.355572	−	0.831903i
$288$	−18.4817	+	11.0423i	−1.08905	+	0.650674i
$289$	−3.76514	+	11.5879i	−0.221479	+	0.681641i
$290$	−1.47904	+	10.9187i	−0.0868524	+	0.641170i
$291$	1.45035	+	32.2945i	0.0850208	+	1.89314i
$292$	4.36986	−	4.57051i	0.255727	−	0.267469i
$293$	20.3091	+	21.2416i	1.18647	+	1.24095i	0.963969	+	0.266016i	$0.0857073\pi$
$293$	20.3091	+	21.2416i	1.18647	+	1.24095i	0.222500	+	0.974933i	$0.428578\pi$
$294$	0.244916	−	5.45349i	0.0142838	−	0.318054i
$295$	−24.7951	−	4.49966i	−1.44363	−	0.261980i
$296$	−2.61134	−	19.2777i	−0.151781	−	1.12049i
$297$	−11.4502	+	2.07791i	−0.664409	+	0.120572i
$298$	−2.33001	−	7.17102i	−0.134974	−	0.415406i
$299$	20.0040	+	17.4770i	1.15686	+	1.01072i
$300$	10.0845	−	18.7402i	0.582232	−	1.08197i
$301$	−19.8867	+	14.4485i	−1.14625	+	0.832800i
$302$	−11.6464	−	6.95842i	−0.670177	−	0.400412i
$303$	5.60157	−	4.89394i	0.321802	−	0.281150i
$304$	−0.284229	−	1.24529i	−0.0163017	−	0.0714223i
$305$	−5.66659	−	2.12671i	−0.324468	−	0.121775i
$306$	−8.71117	+	0.784020i	−0.497984	+	0.0448194i
$307$	19.2211	+	24.1025i	1.09701	+	1.37560i	0.920242	+	0.391349i	$0.127992\pi$
$307$	19.2211	+	24.1025i	1.09701	+	1.37560i	0.176764	+	0.984253i	$0.443437\pi$
$308$	3.59036	+	8.40006i	0.204580	+	0.478638i
$309$	12.1658	+	8.83895i	0.692086	+	0.502830i
$310$	−12.6632	+	6.09826i	−0.719219	+	0.346358i
$311$	−4.54003	+	1.70390i	−0.257441	+	0.0966194i	−0.476759	−	0.879034i	$-0.658188\pi$
$311$	−4.54003	+	1.70390i	−0.257441	+	0.0966194i	0.219317	+	0.975654i	$0.429617\pi$
$312$	−14.8006	−	22.4220i	−0.837919	−	1.26939i
$313$	−14.3026	−	1.28726i	−0.808431	−	0.0727601i	−0.322291	−	0.946641i	$-0.604453\pi$
$313$	−14.3026	−	1.28726i	−0.808431	−	0.0727601i	−0.486140	+	0.873881i	$0.661596\pi$
$314$	−9.73088	−	4.68614i	−0.549145	−	0.264454i
$315$	−15.2569	−	28.3522i	−0.859631	−	1.59746i
$316$	−0.900877	+	3.94700i	−0.0506783	+	0.222036i
$317$	7.86672	−	11.9176i	0.441839	−	0.669357i	−0.543608	−	0.839339i	$-0.682942\pi$
$317$	7.86672	−	11.9176i	0.441839	−	0.669357i	0.985447	+	0.169982i	$0.0543709\pi$
$318$	10.8533	−	13.6096i	0.608623	−	0.763189i
$319$	12.0640	+	3.32947i	0.675457	+	0.186414i
$320$	22.1517	+	6.11348i	1.23832	+	0.341754i
$321$	−0.103056	+	0.129228i	−0.00575200	+	0.00721278i
$322$	−9.19886	+	13.9357i	−0.512633	+	0.776605i
$323$	−0.853586	+	3.73981i	−0.0474948	+	0.208088i
$324$	2.20383	+	4.09540i	0.122435	+	0.227522i
$325$	22.8870	+	11.0218i	1.26954	+	0.611378i
$326$	17.3017	+	1.55718i	0.958252	+	0.0862442i
$327$	−11.2424	−	17.0316i	−0.621708	−	0.941848i
$328$	−19.2394	+	7.22068i	−1.06232	+	0.398695i
$329$	−0.607287	+	0.292454i	−0.0334808	+	0.0161235i
$330$	28.5778	+	20.7630i	1.57316	+	1.14296i
$331$	−5.68346	−	13.2971i	−0.312391	−	0.730876i	−0.999989	−	0.00478342i	$-0.998477\pi$
$331$	−5.68346	−	13.2971i	−0.312391	−	0.730876i	0.687597	−	0.726092i	$-0.258665\pi$
$332$	−6.25032	−	7.83766i	−0.343031	−	0.430147i
$333$	26.9712	−	2.42745i	1.47801	−	0.133023i
$334$	−9.55795	−	3.58716i	−0.522988	−	0.196281i
$335$	5.60797	+	24.5701i	0.306396	+	1.34241i
$336$	3.24590	−	2.83586i	0.177078	−	0.154709i
$337$	19.6752	+	11.7554i	1.07178	+	0.640356i	0.936577	−	0.350462i	$-0.113975\pi$
$337$	19.6752	+	11.7554i	1.07178	+	0.640356i	0.135199	+	0.990818i	$0.456833\pi$
$338$	−1.14127	+	0.829180i	−0.0620768	+	0.0451015i
$339$	2.71206	−	5.03985i	0.147299	−	0.273727i
$340$	−6.22422	−	5.43794i	−0.337556	−	0.294914i
$341$	4.93318	+	15.1828i	0.267147	+	0.822193i
$342$	6.85494	−	1.24399i	0.370673	−	0.0672672i
$343$	−2.70429	−	19.9639i	−0.146018	−	1.07795i
$344$	32.4286	+	5.88492i	1.74843	+	0.317294i
$345$	3.30771	−	73.6519i	0.178081	−	3.96529i
$346$	10.5170	+	10.9999i	0.565397	+	0.591359i
$347$	−21.9903	+	23.0001i	−1.18050	+	1.23471i	−0.214344	+	0.976758i	$0.568762\pi$
$347$	−21.9903	+	23.0001i	−1.18050	+	1.23471i	−0.966158	+	0.257951i	$0.916953\pi$
$348$	0.412156	+	9.17737i	0.0220939	+	0.491959i
$349$	−1.41787	+	10.4671i	−0.0758967	+	0.560292i	0.912578	+	0.408903i	$0.134089\pi$
$349$	−1.41787	+	10.4671i	−0.0758967	+	0.560292i	−0.988474	+	0.151388i	$0.951626\pi$
$350$	−4.93451	+	15.1869i	−0.263761	+	0.811771i
$351$	8.75321	−	5.22980i	0.467212	−	0.279146i
$352$	7.95384	−	18.6089i	0.423941	−	0.991859i
$353$	13.0087	−	3.59018i	0.692384	−	0.191086i	0.0979036	−	0.995196i	$-0.468786\pi$
$353$	13.0087	−	3.59018i	0.692384	−	0.191086i	0.594481	+	0.804110i	$0.297358\pi$
$354$	18.4007			0.977985
$355$	−27.6342	−	11.0576i	−1.46667	−	0.586877i
$356$	15.0858			0.799546
$357$	−12.4778	+	3.44365i	−0.660395	+	0.182257i
$358$	4.10537	−	9.60498i	0.216975	−	0.507639i
$359$	1.49824	−	0.895159i	0.0790743	−	0.0472447i	−0.472818	−	0.881160i	$-0.656763\pi$
$359$	1.49824	−	0.895159i	0.0790743	−	0.0472447i	0.551892	+	0.833916i	$0.313906\pi$
$360$	−13.3398	+	41.0558i	−0.703071	+	2.16383i
$361$	−2.14028	+	15.8002i	−0.112646	+	0.831587i
$362$	−0.634253	−	14.1227i	−0.0333356	−	0.742275i
$363$	7.43658	−	7.77805i	0.390319	−	0.408242i
$364$	−5.53144	−	5.78543i	−0.289926	−	0.303239i
$365$	0.939889	−	20.9283i	0.0491961	−	1.09544i
$366$	4.34842	+	0.789123i	0.227296	+	0.0412481i
$367$	−1.96399	−	14.4988i	−0.102520	−	0.756830i	−0.967111	−	0.254355i	$-0.918137\pi$
$367$	−1.96399	−	14.4988i	−0.102520	−	0.756830i	0.864591	−	0.502476i	$-0.167577\pi$
$368$	5.62203	−	1.02025i	0.293069	−	0.0531841i
$369$	−8.83971	−	27.2058i	−0.460177	−	1.41628i
$370$	−16.8773	−	14.7453i	−0.877411	−	0.766571i
$371$	7.06737	−	13.1334i	0.366920	−	0.681851i
$372$	−9.48037	+	6.88789i	−0.491534	+	0.357121i
$373$	13.5146	+	8.07460i	0.699760	+	0.418087i	0.818246	−	0.574869i	$-0.194947\pi$
$373$	13.5146	+	8.07460i	0.699760	+	0.418087i	−0.118486	+	0.992956i	$0.537804\pi$
$374$	6.19146	−	5.40932i	0.320153	−	0.279709i
$375$	−5.19853	−	22.7762i	−0.268451	−	1.17616i
$376$	0.846111	+	0.317551i	0.0436349	+	0.0163764i
$377$	−10.9215	+	0.982957i	−0.562488	+	0.0506248i
$378$	3.99637	+	5.01128i	0.205551	+	0.257753i
$379$	−3.76451	−	8.80752i	−0.193370	−	0.452412i	0.794585	−	0.607153i	$-0.207688\pi$
$379$	−3.76451	−	8.80752i	−0.193370	−	0.452412i	−0.987955	+	0.154741i	$0.950546\pi$
$380$	5.32621	+	3.86972i	0.273229	+	0.198512i
$381$	−5.82888	+	2.80704i	−0.298623	+	0.143809i
$382$	−11.9995	+	4.50348i	−0.613946	+	0.230418i
$383$	10.5554	+	15.9907i	0.539353	+	0.817086i	0.997417	−	0.0718341i	$-0.0228852\pi$
$383$	10.5554	+	15.9907i	0.539353	+	0.817086i	−0.458063	+	0.888920i	$0.651457\pi$
$384$	11.0411	+	0.993717i	0.563439	+	0.0507104i
$385$	27.2677	+	13.1314i	1.38969	+	0.669239i
$386$	−6.40363	−	11.8999i	−0.325936	−	0.605691i
$387$	−10.2090	+	44.7286i	−0.518953	+	2.27368i
$388$	7.11387	−	10.7771i	0.361152	−	0.547122i
$389$	−8.75673	+	10.9806i	−0.443984	+	0.556738i	−0.952588	−	0.304262i	$-0.901590\pi$
$389$	−8.75673	+	10.9806i	−0.443984	+	0.556738i	0.508604	+	0.861000i	$0.330162\pi$
$390$	−29.8356	−	8.23410i	−1.51078	−	0.416950i
$391$	−16.5412	−	4.56509i	−0.836526	−	0.230867i
$392$	−3.90991	+	4.90287i	−0.197480	+	0.247632i
$393$	6.89001	−	10.4379i	0.347555	−	0.526524i
$394$	2.48572	−	10.8906i	0.125229	−	0.548663i
$395$	6.35585	+	11.8111i	0.319797	+	0.594283i
$396$	15.3615	+	7.39772i	0.771945	+	0.371749i
$397$	−19.9469	−	1.79525i	−1.00110	−	0.0901010i	−0.423056	−	0.906104i	$-0.639043\pi$
$397$	−19.9469	−	1.79525i	−1.00110	−	0.0901010i	−0.578048	+	0.816003i	$0.696185\pi$
$398$	−3.42983	−	5.19596i	−0.171922	−	0.260450i
$399$	9.65325	−	3.62293i	0.483267	−	0.181373i
$400$	4.92308	−	2.37083i	0.246154	−	0.118542i
$401$	−9.23101	−	6.70672i	−0.460975	−	0.334918i	0.332939	−	0.942948i	$-0.391960\pi$
$401$	−9.23101	−	6.70672i	−0.460975	−	0.334918i	−0.793913	+	0.608031i	$0.791960\pi$
$402$	−7.23246	−	16.9212i	−0.360722	−	0.843952i
$403$	−8.72122	−	10.9361i	−0.434435	−	0.544764i
$404$	−2.95932	+	0.266343i	−0.147231	+	0.0132511i
$405$	14.4253	+	5.41392i	0.716801	+	0.269020i
$406$	−1.53387	−	6.72034i	−0.0761249	−	0.333525i
$407$	−19.1697	+	16.7481i	−0.950209	+	0.830173i
$408$	14.8988	+	8.90160i	0.737599	+	0.440695i
$409$	8.61375	−	6.25826i	0.425923	−	0.309451i	−0.354094	−	0.935210i	$-0.615211\pi$
$409$	8.61375	−	6.25826i	0.425923	−	0.309451i	0.780016	+	0.625759i	$0.215211\pi$
$410$	−11.2184	+	20.8472i	−0.554036	+	1.02957i
$411$	2.57317	+	2.24811i	0.126925	+	0.110891i
$412$	−1.85624	−	5.71292i	−0.0914503	−	0.281455i
$413$	15.5119	−	2.81500i	0.763291	−	0.138517i
$414$	4.18341	+	30.8832i	0.205604	+	1.51783i
$415$	−32.6782	−	5.93022i	−1.60411	−	0.291103i
$416$	−0.795546	+	17.7142i	−0.0390049	+	0.868511i
$417$	−1.74661	−	1.82681i	−0.0855317	−	0.0894592i
$418$	−4.52570	+	4.73351i	−0.221359	+	0.231524i
$419$	0.450070	+	10.0216i	0.0219873	+	0.489586i	0.979530	+	0.201296i	$0.0645153\pi$
$419$	0.450070	+	10.0216i	0.0219873	+	0.489586i	−0.957543	+	0.288290i	$0.906913\pi$
$420$	−2.98210	+	22.0147i	−0.145511	+	1.07421i
$421$	−7.02272	+	21.6137i	−0.342267	+	1.05339i	0.620764	+	0.783997i	$0.286822\pi$
$421$	−7.02272	+	21.6137i	−0.342267	+	1.05339i	−0.963031	+	0.269391i	$0.913178\pi$
$422$	−4.83752	+	2.89028i	−0.235487	+	0.140697i
$423$	−0.494438	+	1.15679i	−0.0240404	+	0.0562453i
$424$	−19.2761	+	5.31986i	−0.936129	+	0.258355i
$425$	−16.4099			−0.795996
$426$	21.2954	+	4.34139i	1.03177	+	0.210341i
$427$	3.78648			0.183240
$428$	0.0636462	−	0.0175652i	0.00307645	−	0.000849048i
$429$	−13.8168	+	32.3259i	−0.667080	+	1.56071i
$430$	32.5944	−	19.4743i	1.57184	−	0.939132i
$431$	1.38381	−	4.25893i	0.0666559	−	0.205146i	−0.912181	−	0.409787i	$-0.865603\pi$
$431$	1.38381	−	4.25893i	0.0666559	−	0.205146i	0.978837	+	0.204642i	$0.0656029\pi$
$432$	0.294416	−	2.17347i	0.0141651	−	0.104571i
$433$	−0.786663	−	17.5164i	−0.0378046	−	0.841785i	−0.924903	−	0.380204i	$-0.875854\pi$
$433$	−0.786663	−	17.5164i	−0.0378046	−	0.841785i	0.887098	−	0.461581i	$-0.152718\pi$
$434$	6.07642	−	6.35544i	0.291678	−	0.305071i
$435$	21.0327	+	21.9984i	1.00844	+	1.05474i
$436$	−0.365734	+	8.14371i	−0.0175155	+	0.390013i
$437$	13.4488	+	2.44059i	0.643342	+	0.116749i
$438$	2.05334	+	15.1584i	0.0981126	+	0.724296i
$439$	26.8997	−	4.88158i	1.28385	−	0.232985i	0.506605	−	0.862178i	$-0.330900\pi$
$439$	26.8997	−	4.88158i	1.28385	−	0.232985i	0.777249	+	0.629193i	$0.216614\pi$
$440$	−12.5395	−	38.5925i	−0.597796	−	1.83983i
$441$	−6.57388	−	5.74343i	−0.313042	−	0.273497i
$442$	−3.41364	+	6.34361i	−0.162370	+	0.301735i
$443$	18.1804	−	13.2088i	0.863777	−	0.627571i	−0.0651328	−	0.997877i	$-0.520747\pi$
$443$	18.1804	−	13.2088i	0.863777	−	0.627571i	0.928910	+	0.370306i	$0.120747\pi$
$444$	−16.0405	−	9.58375i	−0.761248	−	0.454824i
$445$	37.6379	−	32.8833i	1.78421	−	1.55882i
$446$	−4.66665	−	20.4459i	−0.220972	−	0.968143i
$447$	−19.4992	−	7.31815i	−0.922278	−	0.346137i
$448$	−14.3183	+	1.28867i	−0.676478	+	0.0608841i
$449$	−23.0711	−	28.9303i	−1.08879	−	1.36530i	−0.925509	−	0.378725i	$-0.876363\pi$
$449$	−23.0711	−	28.9303i	−1.08879	−	1.36530i	−0.163284	−	0.986579i	$-0.552209\pi$
$450$	11.7136	+	27.4052i	0.552182	+	1.29189i
$451$	21.7541	+	15.8053i	1.02436	+	0.744243i
$452$	−2.05978	+	0.991937i	−0.0968838	+	0.0466568i
$453$	−35.0848	+	13.1676i	−1.64843	+	0.618666i
$454$	−1.98556	−	3.00799i	−0.0931869	−	0.141172i
$455$	−26.4113	−	2.37706i	−1.23818	−	0.111438i
$456$	−12.4554	−	5.99820i	−0.583277	−	0.280891i
$457$	19.6645	+	36.5428i	0.919867	+	1.70940i	0.671917	+	0.740627i	$0.265471\pi$
$457$	19.6645	+	36.5428i	0.919867	+	1.70940i	0.247950	+	0.968773i	$0.420243\pi$
$458$	−5.65354	+	24.7698i	−0.264173	+	1.15742i
$459$	−3.62869	+	5.49723i	−0.169373	+	0.256589i
$460$	−18.3620	+	23.0253i	−0.856134	+	1.07356i
$461$	−2.49754	−	0.689279i	−0.116322	−	0.0321029i	0.207391	−	0.978258i	$-0.433503\pi$
$461$	−2.49754	−	0.689279i	−0.116322	−	0.0321029i	−0.323713	+	0.946155i	$0.604931\pi$
$462$	−21.3025	−	5.87910i	−0.991080	−	0.273521i
$463$	1.02058	−	1.27977i	0.0474304	−	0.0594759i	−0.757551	−	0.652777i	$-0.773604\pi$
$463$	1.02058	−	1.27977i	0.0474304	−	0.0594759i	0.804981	+	0.593301i	$0.202175\pi$
$464$	−1.29944	+	1.96856i	−0.0603248	+	0.0913882i
$465$	−8.63892	+	37.8496i	−0.400620	+	1.75523i
$466$	9.46331	+	17.5858i	0.438379	+	0.814645i
$467$	15.2464	+	7.34230i	0.705521	+	0.339761i	0.752004	−	0.659158i	$-0.229087\pi$
$467$	15.2464	+	7.34230i	0.705521	+	0.339761i	−0.0464836	+	0.998919i	$0.514802\pi$
$468$	−14.8791	−	1.33914i	−0.687785	−	0.0619018i
$469$	−8.68568	−	13.1582i	−0.401067	−	0.607591i
$470$	0.974749	−	0.365829i	0.0449618	−	0.0168744i
$471$	−26.8787	+	12.9441i	−1.23851	+	0.596433i
$472$	−17.1008	−	12.4245i	−0.787129	−	0.571883i
$473$	−16.9497	−	39.6557i	−0.779347	−	1.82337i
$474$	−6.10627	−	7.65702i	−0.280470	−	0.351698i
$475$	13.0186	−	1.17170i	0.597335	−	0.0537611i
$476$	4.84097	+	1.81685i	0.221885	+	0.0832750i
$477$	−6.19410	−	27.1381i	−0.283608	−	1.24257i
$478$	3.69086	−	3.22460i	0.168816	−	0.147490i
$479$	−24.8214	−	14.8301i	−1.13412	−	0.677604i	−0.181989	−	0.983300i	$-0.558254\pi$
$479$	−24.8214	−	14.8301i	−1.13412	−	0.677604i	−0.952129	+	0.305696i	$0.901111\pi$
$480$	39.8160	−	28.9280i	1.81735	−	1.32038i
$481$	10.5692	−	19.6408i	0.481913	−	0.895544i
$482$	2.28178	+	1.99353i	0.103932	+	0.0908030i
$483$	14.2529	+	43.8658i	0.648528	+	1.99596i
$484$	−4.22950	+	0.767542i	−0.192250	+	0.0348883i
$485$	−5.74271	−	42.3944i	−0.260763	−	1.92503i
$486$	−19.6313	−	3.56255i	−0.890494	−	0.161601i
$487$	−1.00948	+	22.4779i	−0.0457440	+	1.01857i	0.836556	+	0.547882i	$0.184566\pi$
$487$	−1.00948	+	22.4779i	−0.0457440	+	1.01857i	−0.882300	+	0.470688i	$0.844006\pi$
$488$	−3.50841	−	3.66951i	−0.158818	−	0.166111i
$489$	33.1599	−	34.6826i	1.49954	−	1.56840i
$490$	0.324122	+	7.21714i	0.0146423	+	0.326037i
$491$	2.98860	−	22.0628i	0.134874	−	0.995679i	−0.789381	−	0.613903i	$-0.789598\pi$
$491$	2.98860	−	22.0628i	0.134874	−	0.995679i	0.924255	−	0.381775i	$-0.124687\pi$
$492$	−6.09944	+	18.7721i	−0.274984	+	0.846314i
$493$	6.08103	−	3.63325i	0.273876	−	0.163633i
$494$	2.25523	−	5.27638i	0.101468	−	0.237396i
$495$	54.4510	−	15.0275i	2.44739	−	0.675436i
$496$	−3.00882			−0.135100
$497$	18.6164	+	0.401974i	0.835058	+	0.0180310i
$498$	24.2507			1.08670
$499$	18.8030	−	5.18929i	0.841737	−	0.232305i	0.181527	−	0.983386i	$-0.441896\pi$
$499$	18.8030	−	5.18929i	0.841737	−	0.232305i	0.660210	+	0.751081i	$0.270467\pi$
$500$	−3.66775	+	8.58112i	−0.164027	+	0.383759i
$501$	−24.2075	+	14.4633i	−1.08151	+	0.646174i
$502$	−3.17989	+	9.78668i	−0.141925	+	0.436801i
$503$	−2.85206	+	21.0547i	−0.127167	+	0.938784i	0.809144	+	0.587611i	$0.199931\pi$
$503$	−2.85206	+	21.0547i	−0.127167	+	0.938784i	−0.936311	+	0.351173i	$0.885783\pi$
$504$	−1.21164	−	26.9792i	−0.0539706	−	1.20175i
$505$	−6.80270	+	7.11507i	−0.302716	+	0.316616i
$506$	−20.2450	−	21.1746i	−0.899998	−	0.941324i
$507$	−0.174821	+	3.89268i	−0.00776405	+	0.172880i
$508$	2.54278	+	0.461447i	0.112818	+	0.0204734i
$509$	−1.87299	−	13.8270i	−0.0830188	−	0.612869i	−0.983889	−	0.178781i	$-0.942785\pi$
$509$	−1.87299	−	13.8270i	−0.0830188	−	0.612869i	0.900870	−	0.434089i	$-0.142930\pi$
$510$	19.6728	−	3.57008i	0.871124	−	0.158086i
$511$	4.04997	+	12.4645i	0.179160	+	0.551398i
$512$	6.13336	+	5.35855i	0.271059	+	0.236817i
$513$	2.48627	−	4.62027i	0.109772	−	0.203990i
$514$	−14.2239	+	10.3343i	−0.627389	+	0.455825i
$515$	−17.0839	−	10.2072i	−0.752806	−	0.449781i
$516$	23.8397	−	20.8281i	1.04948	−	0.916906i
$517$	−0.263142	−	1.15290i	−0.0115730	−	0.0507046i
$518$	13.1266	+	4.92648i	0.576748	+	0.216457i
$519$	41.8676	−	3.76816i	1.83779	−	0.165404i
$520$	22.1681	+	27.7980i	0.972137	+	1.21902i
$521$	7.08425	+	16.5744i	0.310367	+	0.726139i	0.999998	+	0.00197854i	$0.000629789\pi$
$521$	7.08425	+	16.5744i	0.310367	+	0.726139i	−0.689631	+	0.724161i	$0.742227\pi$
$522$	−10.4084	−	7.56214i	−0.455563	−	0.330986i
$523$	28.4871	−	13.7186i	1.24565	−	0.599874i	0.309309	−	0.950961i	$-0.399902\pi$
$523$	28.4871	−	13.7186i	1.24565	−	0.599874i	0.936343	+	0.351087i	$0.114188\pi$
$524$	−4.67740	+	1.75546i	−0.204333	+	0.0766875i
$525$	24.2990	+	36.8114i	1.06049	+	1.60658i
$526$	16.5958	+	1.49365i	0.723610	+	0.0651260i
$527$	8.14112	+	3.92056i	0.354633	+	0.170782i
$528$	3.58338	+	6.65904i	0.155947	+	0.289797i
$529$	−8.48772	+	37.1871i	−0.369031	+	1.61683i
$530$	−12.6909	+	19.2260i	−0.551259	+	0.835122i
$531$	18.3458	−	23.0049i	0.796141	−	0.998329i
$532$	−3.97026	−	1.09572i	−0.172133	−	0.0475056i
$533$	−22.7116	−	6.26800i	−0.983749	−	0.271497i
$534$	−22.7536	+	28.5321i	−0.984644	+	1.23470i
$535$	0.120505	−	0.182557i	0.00520987	−	0.00789261i
$536$	−4.70395	+	20.6093i	−0.203180	+	0.890188i
$537$	−13.6724	−	25.4076i	−0.590009	−	1.09642i
$538$	5.35955	+	2.58102i	0.231067	+	0.111276i
$539$	8.17265	+	0.735551i	0.352021	+	0.0316824i
$540$	6.22779	+	9.43470i	0.268001	+	0.406005i
$541$	31.8145	−	11.9402i	1.36781	−	0.513348i	0.443942	−	0.896055i	$-0.353580\pi$
$541$	31.8145	−	11.9402i	1.36781	−	0.513348i	0.923870	+	0.382707i	$0.125008\pi$
$542$	26.1280	−	12.5826i	1.12230	−	0.540469i
$543$	−31.5915	−	22.9526i	−1.35572	−	0.984990i
$544$	−4.50201	−	10.5330i	−0.193022	−	0.451598i
$545$	16.8388	+	21.1151i	0.721293	+	0.904473i
$546$	19.2850	−	1.73568i	0.825324	−	0.0742805i
$547$	−14.7478	−	5.53496i	−0.630572	−	0.236658i	0.0155653	−	0.999879i	$-0.495045\pi$
$547$	−14.7478	−	5.53496i	−0.630572	−	0.236658i	−0.646137	+	0.763221i	$0.723617\pi$
$548$	−0.303719	−	1.33068i	−0.0129742	−	0.0568439i
$549$	5.32204	−	4.64973i	0.227139	−	0.198446i
$550$	−24.0498	−	14.3691i	−1.02549	−	0.612700i
$551$	−4.56491	+	3.31660i	−0.194471	+	0.141292i
$552$	29.3046	−	54.4571i	1.24729	−	2.31785i
$553$	−6.31902	−	5.52076i	−0.268712	−	0.234767i
$554$	−9.00984	−	27.7294i	−0.382791	−	1.17811i
$555$	−60.9099	+	11.0535i	−2.58548	+	0.469196i
$556$	0.135521	+	1.00046i	0.00574739	+	0.0424289i
$557$	−26.0025	−	4.71875i	−1.10176	−	0.199940i	−0.402932	−	0.915230i	$-0.632009\pi$
$557$	−26.0025	−	4.71875i	−1.10176	−	0.199940i	−0.698828	+	0.715290i	$0.746295\pi$
$558$	0.736281	−	16.3946i	0.0311693	−	0.694038i
$559$	26.1133	+	27.3124i	1.10447	+	1.15519i
$560$	−3.94192	+	4.12292i	−0.166576	+	0.174225i
$561$	−1.01887	−	22.6869i	−0.0430168	−	0.957843i
$562$	1.33653	−	9.86663i	0.0563780	−	0.416199i
$563$	5.56904	−	17.1398i	0.234707	−	0.722354i	−0.762453	−	0.647044i	$-0.776005\pi$
$563$	5.56904	−	17.1398i	0.234707	−	0.722354i	0.997160	−	0.0753108i	$-0.0239949\pi$
$564$	0.745174	−	0.445221i	0.0313775	−	0.0187472i
$565$	−2.97681	+	6.96460i	−0.125236	+	0.293003i
$566$	−7.24730	+	2.00013i	−0.304627	+	0.0840717i
$567$	−9.63917			−0.404807
$568$	−16.8597	−	18.4138i	−0.707418	−	0.772625i
$569$	−0.728626			−0.0305456			−0.0152728	−	0.999883i	$-0.504862\pi$
$569$	−0.728626			−0.0305456			−0.0152728	+	0.999883i	$0.504862\pi$
$570$	−15.3523	+	4.23696i	−0.643036	+	0.177467i
$571$	3.43127	−	8.02786i	0.143594	−	0.335955i	−0.832258	−	0.554389i	$-0.812952\pi$
$571$	3.43127	−	8.02786i	0.143594	−	0.335955i	0.975852	+	0.218434i	$0.0700948\pi$
$572$	12.0551	−	7.20258i	0.504049	−	0.301155i
$573$	−10.9400	+	33.6698i	−0.457024	+	1.40657i
$574$	1.98807	−	14.6765i	0.0829803	−	0.612585i
$575$	2.62333	+	58.4131i	0.109401	+	2.43599i
$576$	−18.5425	+	19.3940i	−0.772606	+	0.808082i
$577$	−14.6944	−	15.3691i	−0.611734	−	0.639824i	0.342275	−	0.939600i	$-0.388802\pi$
$577$	−14.6944	−	15.3691i	−0.611734	−	0.639824i	−0.954010	+	0.299776i	$0.903088\pi$
$578$	−0.528234	+	11.7620i	−0.0219716	+	0.489236i
$579$	−36.7273	−	6.66502i	−1.52633	−	0.276989i
$580$	−1.63195	−	12.0475i	−0.0677630	−	0.500247i
$581$	20.4436	−	3.70996i	0.848141	−	0.153915i
$582$	9.65317	+	29.7094i	0.400137	+	1.23149i
$583$	19.7048	+	17.2156i	0.816089	+	0.712996i
$584$	8.32694	−	15.4740i	0.344571	−	0.640321i
$585$	−40.0411	+	29.0916i	−1.65550	+	1.20279i
$586$	24.3786	+	14.5655i	1.00707	+	0.601697i
$587$	−11.6117	+	10.1448i	−0.479264	+	0.418721i	−0.863372	−	0.504568i	$-0.831652\pi$
$587$	−11.6117	+	10.1448i	−0.479264	+	0.418721i	0.384108	+	0.923288i	$0.374509\pi$
$588$	1.34032	+	5.87233i	0.0552739	+	0.242171i
$589$	−6.73862	−	2.52904i	−0.277660	−	0.104207i
$590$	−24.2534	+	2.18285i	−0.998497	+	0.0898663i
$591$	−19.2383	−	24.1241i	−0.791358	−	0.992331i
$592$	−1.88561	−	4.41161i	−0.0774981	−	0.181316i
$593$	7.42111	+	5.39176i	0.304749	+	0.221413i	0.729640	−	0.683832i	$-0.239688\pi$
$593$	7.42111	+	5.39176i	0.304749	+	0.221413i	−0.424891	+	0.905244i	$0.639688\pi$
$594$	−10.1317	+	4.87916i	−0.415708	+	0.200194i
$595$	16.0381	−	6.01920i	0.657498	−	0.246763i
$596$	4.58322	+	6.94329i	0.187736	+	0.284408i
$597$	−17.1280	−	1.54155i	−0.701001	−	0.0630912i
$598$	23.1266	+	11.1372i	0.945718	+	0.455434i
$599$	−11.7639	−	21.8610i	−0.480661	−	0.893218i	−0.999270	−	0.0382061i	$-0.987836\pi$
$599$	−11.7639	−	21.8610i	−0.480661	−	0.893218i	0.518609	−	0.855012i	$-0.326450\pi$
$600$	13.1597	−	57.6565i	0.537244	−	2.35382i
$601$	7.81715	−	11.8425i	0.318868	−	0.483065i	−0.639424	−	0.768854i	$-0.720827\pi$
$601$	7.81715	−	11.8425i	0.318868	−	0.483065i	0.958292	+	0.285789i	$0.0922558\pi$
$602$	−14.8100	+	18.5712i	−0.603613	+	0.756906i
$603$	−28.3662	−	7.82856i	−1.15516	−	0.318804i
$604$	14.4300	+	3.98241i	0.587146	+	0.162042i
$605$	−8.87924	+	11.1342i	−0.360992	+	0.452670i
$606$	3.95973	−	5.99873i	0.160853	−	0.243682i
$607$	6.05847	−	26.5439i	0.245906	−	1.07738i	−0.689633	−	0.724159i	$-0.742228\pi$
$607$	6.05847	−	26.5439i	0.245906	−	1.07738i	0.935539	−	0.353225i	$-0.114915\pi$
$608$	4.32370	+	8.03478i	0.175349	+	0.325853i
$609$	−17.1548	−	8.26130i	−0.695146	−	0.334765i
$610$	−5.82514	−	0.524272i	−0.235853	−	0.0212272i
$611$	0.570813	+	0.864744i	0.0230926	+	0.0349838i
$612$	9.03523	−	3.39098i	0.365227	−	0.137072i
$613$	−32.6026	+	15.7006i	−1.31681	+	0.634140i	−0.954581	−	0.297951i	$-0.903697\pi$
$613$	−32.6026	+	15.7006i	−1.31681	+	0.634140i	−0.362224	+	0.932091i	$0.617982\pi$
$614$	24.1006	+	17.5101i	0.972622	+	0.706651i
$615$	25.7009	+	60.1303i	1.03636	+	2.42469i
$616$	15.8279	+	19.8476i	0.637726	+	0.799683i
$617$	32.7055	−	2.94355i	1.31667	−	0.118503i	0.591073	−	0.806618i	$-0.298705\pi$
$617$	32.7055	−	2.94355i	1.31667	−	0.118503i	0.725601	+	0.688115i	$0.241562\pi$
$618$	13.6047	+	5.10592i	0.547261	+	0.205390i
$619$	−4.63927	−	20.3260i	−0.186468	−	0.816969i	−0.978460	−	0.206438i	$-0.933813\pi$
$619$	−4.63927	−	20.3260i	−0.186468	−	0.816969i	0.791992	−	0.610532i	$-0.209044\pi$
$620$	11.6787	−	10.2034i	0.469028	−	0.409777i
$621$	20.1482	+	12.0380i	0.808520	+	0.483068i
$622$	−3.79100	+	2.75432i	−0.152005	+	0.110438i
$623$	−14.8165	+	27.5337i	−0.593611	+	1.10311i
$624$	−4.98970	−	4.35937i	−0.199748	−	0.174514i
$625$	−1.99987	−	6.15495i	−0.0799946	−	0.246198i
$626$	−13.6538	+	2.47779i	−0.545715	+	0.0990326i
$627$	2.42820	+	17.9257i	0.0969730	+	0.715884i
$628$	11.7255	+	2.12787i	0.467899	+	0.0849112i
$629$	−0.646422	+	14.3937i	−0.0257745	+	0.573915i
$630$	−21.5005	−	22.4878i	−0.856601	−	0.895934i
$631$	−12.9443	+	13.5386i	−0.515303	+	0.538964i	−0.928331	−	0.371754i	$-0.878757\pi$
$631$	−12.9443	+	13.5386i	−0.515303	+	0.538964i	0.413029	+	0.910718i	$0.364471\pi$
$632$	0.504752	+	11.2392i	0.0200780	+	0.447071i
$633$	−2.08942	+	15.4247i	−0.0830468	+	0.613076i
$634$	4.26410	−	13.1235i	0.169349	−	0.521203i
$635$	7.34989	−	4.39135i	0.291671	−	0.174266i
$636$	−7.54882	+	17.6613i	−0.299330	+	0.700318i
$637$	−6.93071	+	1.91276i	−0.274605	+	0.0757861i
$638$	12.0936			0.478789
$639$	26.6597	−	22.2956i	1.05464	−	0.882000i
$640$	−14.6708			−0.579916
$641$	−24.5820	+	6.78421i	−0.970932	+	0.267960i	−0.715303	−	0.698815i	$-0.753711\pi$
$641$	−24.5820	+	6.78421i	−0.970932	+	0.267960i	−0.255629	+	0.966775i	$0.582283\pi$
$642$	−0.0627747	+	0.146869i	−0.00247752	+	0.00579644i
$643$	−0.745034	+	0.445137i	−0.0293813	+	0.0175545i	−0.527515	−	0.849546i	$-0.676876\pi$
$643$	−0.745034	+	0.445137i	−0.0293813	+	0.0175545i	0.498134	+	0.867100i	$0.334019\pi$
$644$	5.69340	−	17.5225i	0.224352	−	0.690483i
$645$	14.0781	−	103.929i	0.554326	−	4.09220i
$646$	0.166305	+	3.70306i	0.00654317	+	0.145695i
$647$	14.4162	−	15.0782i	0.566760	−	0.592785i	−0.375850	−	0.926681i	$-0.622649\pi$
$647$	14.4162	−	15.0782i	0.566760	−	0.592785i	0.942610	+	0.333896i	$0.108363\pi$
$648$	8.93131	+	9.34142i	0.350855	+	0.366966i
$649$	−1.24092	+	27.6312i	−0.0487102	+	1.08462i
$650$	24.1526	+	4.38305i	0.947344	+	0.171918i
$651$	−3.26022	−	24.0679i	−0.127778	−	0.943296i
$652$	−18.8595	+	3.42250i	−0.738595	+	0.134035i
$653$	14.9402	+	45.9813i	0.584656	+	1.79939i	0.600647	+	0.799514i	$0.294910\pi$
$653$	14.9402	+	45.9813i	0.584656	+	1.79939i	−0.0159911	+	0.999872i	$0.505090\pi$
$654$	−14.8507	−	12.9747i	−0.580710	−	0.507351i
$655$	−7.84329	+	14.5753i	−0.306463	+	0.569503i
$656$	−4.10009	+	2.97889i	−0.160082	+	0.116306i
$657$	20.9986	+	12.5461i	0.819234	+	0.489469i
$658$	−0.490504	+	0.428540i	−0.0191218	+	0.0167062i
$659$	3.84127	+	16.8297i	0.149635	+	0.655593i	0.992986	+	0.118230i	$0.0377221\pi$
$659$	3.84127	+	16.8297i	0.149635	+	0.655593i	−0.843351	+	0.537362i	$0.819421\pi$
$660$	−36.4907	−	13.6952i	−1.42040	−	0.533084i
$661$	21.6053	−	1.94451i	0.840347	−	0.0756326i	0.338902	−	0.940822i	$-0.389945\pi$
$661$	21.6053	−	1.94451i	0.840347	−	0.0756326i	0.501446	+	0.865189i	$0.332802\pi$
$662$	−8.71252	−	10.9252i	−0.338622	−	0.424618i
$663$	7.82054	+	18.2971i	0.303724	+	0.710599i
$664$	−22.5376	−	16.3746i	−0.874630	−	0.635456i
$665$	−12.2939	+	5.92043i	−0.476737	+	0.229584i
$666$	24.4995	−	9.19483i	0.949338	−	0.356293i
$667$	−13.9051	−	21.0654i	−0.538409	−	0.815655i
$668$	11.2190	+	1.00973i	0.434076	+	0.0390675i
$669$	−52.1916	−	25.1341i	−2.01784	−	0.971742i
$670$	11.5402	+	21.4454i	0.445838	+	0.828506i
$671$	−1.47823	+	6.47654i	−0.0570664	+	0.250024i
$672$	−16.9617	+	25.6959i	−0.654311	+	0.991239i
$673$	13.5220	−	16.9560i	0.521234	−	0.653607i	−0.449636	−	0.893212i	$-0.648446\pi$
$673$	13.5220	−	16.9560i	0.521234	−	0.653607i	0.970871	+	0.239605i	$0.0770178\pi$
$674$	21.3495	+	5.89207i	0.822350	+	0.226954i
$675$	21.6362	+	5.97120i	0.832776	+	0.229832i
$676$	0.970478	−	1.21694i	0.0373261	−	0.0468054i
$677$	−5.60881	+	8.49699i	−0.215564	+	0.326566i	−0.926226	−	0.376968i	$-0.876967\pi$
$677$	−5.60881	+	8.49699i	−0.215564	+	0.326566i	0.710662	+	0.703533i	$0.248395\pi$
$678$	1.23065	−	5.39182i	0.0472627	−	0.207071i
$679$	12.6827	+	23.5685i	0.486718	+	0.904474i
$680$	−20.6936	−	9.96552i	−0.793564	−	0.382160i
$681$	−9.91555	−	0.892416i	−0.379965	−	0.0341974i
$682$	8.49839	+	12.8745i	0.325420	+	0.492991i
$683$	−16.9259	+	6.35240i	−0.647652	+	0.243068i	−0.653513	−	0.756915i	$-0.726706\pi$
$683$	−16.9259	+	6.35240i	−0.647652	+	0.243068i	0.00586157	+	0.999983i	$0.498134\pi$
$684$	−6.92589	+	3.33533i	−0.264818	+	0.127530i
$685$	−3.65831	−	2.65791i	−0.139777	−	0.101554i
$686$	−7.65131	−	17.9011i	−0.292128	−	0.683468i
$687$	43.7558	+	54.8680i	1.66939	+	2.09335i
$688$	8.09545	−	0.728604i	0.308636	−	0.0277777i
$689$	−21.4646	−	8.05581i	−0.817738	−	0.306902i
$690$	−15.8531	−	69.4570i	−0.603517	−	2.64418i
$691$	−17.8782	+	15.6197i	−0.680118	+	0.594201i	−0.927098	−	0.374820i	$-0.877705\pi$
$691$	−17.8782	+	15.6197i	−0.680118	+	0.594201i	0.246980	+	0.969021i	$0.420562\pi$
$692$	−14.4150	−	8.61256i	−0.547976	−	0.327400i
$693$	−28.5891	+	20.7712i	−1.08601	+	0.789034i
$694$	−14.5712	+	27.0777i	−0.553114	+	1.02786i
$695$	2.51886	+	2.20067i	0.0955460	+	0.0834760i
$696$	7.88889	+	24.2795i	0.299028	+	0.920312i
$697$	14.9754	−	2.71763i	0.567234	−	0.102938i
$698$	1.37012	+	10.1146i	0.0518596	+	0.382843i
$699$	54.2757	+	9.84958i	2.05289	+	0.372545i
$700$	0.790485	−	17.6015i	0.0298775	−	0.665275i
$701$	3.37333	+	3.52823i	0.127409	+	0.133259i	0.783422	−	0.621490i	$-0.213473\pi$
$701$	3.37333	+	3.52823i	0.127409	+	0.133259i	−0.656013	+	0.754750i	$0.727758\pi$
$702$	6.80914	−	7.12180i	0.256994	−	0.268795i
$703$	−0.514905	−	11.4653i	−0.0194200	−	0.432420i
$704$	3.38564	−	24.9938i	0.127601	−	0.941989i
$705$	0.888682	−	2.73508i	0.0334697	−	0.103009i
$706$	11.1946	−	6.68849i	0.421316	−	0.251725i
$707$	2.42037	−	5.66275i	0.0910276	−	0.212970i
$708$	−19.5713	+	5.40134i	−0.735535	+	0.202995i
$709$	10.9723			0.412075			0.206037	−	0.978544i	$-0.433943\pi$
$709$	10.9723			0.412075			0.206037	+	0.978544i	$0.433943\pi$
$710$	−28.5839	−	3.19601i	−1.07274	−	0.119944i
$711$	−15.6610			−0.587335
$712$	40.4117	−	11.1529i	1.51449	−	0.417973i
$713$	12.6543	−	29.6061i	0.473906	−	1.10876i
$714$	−10.7378	+	6.41551i	−0.401851	+	0.240095i
$715$	14.3767	−	44.2470i	0.537658	−	1.65474i
$716$	−1.54710	+	11.4211i	−0.0578178	+	0.426828i
$717$	−0.607370	−	13.5241i	−0.0226826	−	0.505068i
$718$	1.16549	−	1.21900i	0.0434956	−	0.0454928i
$719$	20.8989	+	21.8585i	0.779397	+	0.815185i	0.986608	−	0.163111i	$-0.0521530\pi$
$719$	20.8989	+	21.8585i	0.779397	+	0.815185i	−0.207211	+	0.978296i	$0.566439\pi$
$720$	−0.477643	+	10.6355i	−0.0178007	+	0.396363i
$721$	12.2500	+	2.22304i	0.456213	+	0.0827904i
$722$	2.06820	+	15.2680i	0.0769703	+	0.568218i
$723$	8.23490	−	1.49441i	0.306259	−	0.0555779i
$724$	4.82020	+	14.8351i	0.179141	+	0.551340i
$725$	−18.1777	−	15.8814i	−0.675103	−	0.589820i
$726$	4.92760	−	9.15701i	0.182880	−	0.339849i
$727$	−0.876392	+	0.636736i	−0.0325036	+	0.0236152i	−0.603918	−	0.797046i	$-0.706395\pi$
$727$	−0.876392	+	0.636736i	−0.0325036	+	0.0236152i	0.571415	+	0.820661i	$0.306395\pi$
$728$	−19.0947	−	11.4085i	−0.707696	−	0.422829i
$729$	−31.6484	+	27.6504i	−1.17216	+	1.02409i
$730$	−4.50467	−	19.7363i	−0.166725	−	0.730472i
$731$	−22.8537	−	8.57712i	−0.845273	−	0.317236i
$732$	−4.85671	+	0.437112i	−0.179509	+	0.0161561i
$733$	−29.4433	−	36.9207i	−1.08751	−	1.36370i	−0.926304	−	0.376777i	$-0.877032\pi$
$733$	−29.4433	−	36.9207i	−1.08751	−	1.36370i	−0.161209	−	0.986920i	$-0.551539\pi$
$734$	−5.55676	−	13.0007i	−0.205104	−	0.479864i
$735$	16.1442	+	11.7294i	0.595487	+	0.432647i
$736$	−36.7738	+	17.7093i	−1.35550	+	0.652775i
$737$	25.8973	−	9.71940i	0.953938	−	0.358019i
$738$	−15.2282	−	23.0697i	−0.560557	−	0.849208i
$739$	8.96673	+	0.807020i	0.329846	+	0.0296867i	0.253325	−	0.967381i	$-0.418476\pi$
$739$	8.96673	+	0.807020i	0.329846	+	0.0296867i	0.0765214	+	0.997068i	$0.475619\pi$
$740$	22.2794	+	10.7292i	0.819007	+	0.394413i
$741$	−7.51079	−	13.9574i	−0.275916	−	0.512737i
$742$	3.20695	−	14.0506i	0.117731	−	0.515813i
$743$	18.7614	−	28.4223i	0.688289	−	1.04271i	−0.307545	−	0.951534i	$-0.599507\pi$
$743$	18.7614	−	28.4223i	0.688289	−	1.04271i	0.995834	−	0.0911804i	$-0.0290640\pi$
$744$	−20.3037	+	25.4600i	−0.744369	+	0.933409i
$745$	26.5694	+	7.33269i	0.973428	+	0.268649i
$746$	14.6646	+	4.04718i	0.536910	+	0.148178i
$747$	24.1785	−	30.3188i	0.884644	−	1.10931i
$748$	−4.99751	+	7.57090i	−0.182727	+	0.276820i
$749$	−0.0304510	+	0.133415i	−0.00111266	+	0.00487487i
$750$	−10.6977	−	19.8796i	−0.390624	−	0.725901i
$751$	−37.3837	−	18.0030i	−1.36415	−	0.656940i	−0.398592	−	0.917128i	$-0.630501\pi$
$751$	−37.3837	−	18.0030i	−1.36415	−	0.656940i	−0.965558	+	0.260188i	$0.916215\pi$
$752$	0.221983	+	0.0199788i	0.00809489	+	0.000728553i
$753$	15.6587	+	23.7219i	0.570635	+	0.864475i
$754$	−9.92070	+	3.72330i	−0.361291	+	0.135595i
$755$	44.6823	−	21.5178i	1.62615	−	0.783115i
$756$	−5.72163	−	4.15701i	−0.208094	−	0.151189i
$757$	13.6885	+	32.0257i	0.497515	+	1.16399i	0.960664	+	0.277714i	$0.0895768\pi$
$757$	13.6885	+	32.0257i	0.497515	+	1.16399i	−0.463148	+	0.886281i	$0.653280\pi$
$758$	−5.77085	−	7.23642i	−0.209607	−	0.262839i
$759$	−80.5942	+	7.25361i	−2.92538	+	0.263289i
$760$	17.1286	+	6.42849i	0.621321	+	0.233186i
$761$	9.80101	+	42.9410i	0.355286	+	1.55661i	0.764776	+	0.644296i	$0.222850\pi$
$761$	9.80101	+	42.9410i	0.355286	+	1.55661i	−0.409490	+	0.912315i	$0.634293\pi$
$762$	−4.70797	+	4.11323i	−0.170552	+	0.149007i
$763$	−14.5042	−	8.66585i	−0.525087	−	0.313725i
$764$	11.4409	−	8.31232i	0.413918	−	0.300729i
$765$	15.1507	−	28.1548i	0.547775	−	1.01794i
$766$	13.9431	+	12.1818i	0.503786	+	0.440145i
$767$	−7.48897	−	23.0487i	−0.270411	−	0.832240i
$768$	44.7106	−	8.11378i	1.61335	−	0.292781i
$769$	3.20439	+	23.6558i	0.115553	+	0.853050i	0.952236	+	0.305362i	$0.0987775\pi$
$769$	3.20439	+	23.6558i	0.115553	+	0.853050i	−0.836683	+	0.547688i	$0.815508\pi$
$770$	28.7756	+	5.22200i	1.03700	+	0.188188i
$771$	−2.17883	+	48.5154i	−0.0784686	+	1.74724i
$772$	10.3041	+	10.7773i	0.370854	+	0.387883i
$773$	33.9688	−	35.5286i	1.22177	−	1.27787i	0.272963	−	0.962025i	$-0.411996\pi$
$773$	33.9688	−	35.5286i	1.22177	−	1.27787i	0.948809	−	0.315849i	$-0.102289\pi$
$774$	1.98902	+	44.2891i	0.0714940	+	1.59194i
$775$	4.13309	−	30.5117i	0.148465	−	1.09601i
$776$	11.0891	−	34.1287i	0.398075	−	1.22515i
$777$	33.2458	−	19.8634i	1.19269	−	0.712597i
$778$	−5.33402	+	12.4796i	−0.191234	+	0.447414i
$779$	−11.6865	+	3.22528i	−0.418714	+	0.115558i
$780$	34.1507			1.22279
$781$	−7.95533	+	31.6853i	−0.284664	+	1.13379i
$782$	−16.5817			−0.592961
$783$	−9.33980	+	2.57762i	−0.333777	+	0.0921167i
$784$	−0.607836	+	1.42210i	−0.0217084	+	0.0507894i
$785$	33.8925	−	20.2498i	1.20968	−	0.722747i
$786$	3.73468	−	11.4942i	0.133212	−	0.409984i
$787$	−2.77147	+	20.4598i	−0.0987921	+	0.729313i	0.872020	+	0.489471i	$0.162810\pi$
$787$	−2.77147	+	20.4598i	−0.0987921	+	0.729313i	−0.970812	+	0.239842i	$0.922904\pi$
$788$	0.552985	+	12.3132i	0.0196993	+	0.438638i
$789$	31.8070	−	33.2675i	1.13236	−	1.18435i
$790$	8.95684	+	9.36812i	0.318670	+	0.333303i
$791$	0.212587	−	4.73361i	0.00755871	−	0.168308i
$792$	46.6193	+	8.46016i	1.65655	+	0.300619i
$793$	−0.781329	−	5.76800i	−0.0277458	−	0.204828i
$794$	−19.0420	+	3.45561i	−0.675775	+	0.122635i
$795$	19.6636	+	60.5182i	0.697394	+	2.14636i
$796$	5.17325	+	4.51974i	0.183361	+	0.160198i
$797$	−6.14245	+	11.4146i	−0.217577	+	0.404325i	−0.965864	−	0.259049i	$-0.916591\pi$
$797$	−6.14245	+	11.4146i	−0.217577	+	0.404325i	0.748287	+	0.663375i	$0.230876\pi$
$798$	8.06062	−	5.85638i	0.285343	−	0.207314i
$799$	−0.574598	−	0.343307i	−0.0203278	−	0.0121453i
$800$	−29.3943	+	25.6810i	−1.03924	+	0.907960i
$801$	12.9857	+	56.8941i	0.458828	+	2.01025i
$802$	−10.3228	−	3.87422i	−0.364511	−	0.136803i
$803$	−22.9009	+	2.06112i	−0.808156	+	0.0727353i
$804$	12.6596	+	15.8747i	0.446471	+	0.559857i
$805$	−23.9900	−	56.1275i	−0.845538	−	1.97823i
$806$	−10.9352	−	7.94489i	−0.385176	−	0.279847i
$807$	14.8042	−	7.12932i	0.521132	−	0.250964i
$808$	−7.73047	+	2.90129i	−0.271957	+	0.102067i
$809$	16.7146	+	25.3216i	0.587655	+	0.890259i	0.999782	−	0.0208672i	$-0.00664271\pi$
$809$	16.7146	+	25.3216i	0.587655	+	0.890259i	−0.412127	+	0.911126i	$0.635214\pi$
$810$	14.8290	+	1.33463i	0.521037	+	0.0468942i
$811$	−16.9674	−	8.17106i	−0.595805	−	0.286925i	0.111577	−	0.993756i	$-0.464410\pi$
$811$	−16.9674	−	8.17106i	−0.595805	−	0.286925i	−0.707382	+	0.706831i	$0.750124\pi$
$812$	3.60415	+	6.69763i	0.126481	+	0.235041i
$813$	17.8248	−	78.0955i	0.625142	−	2.73893i
$814$	−13.5510	+	20.5289i	−0.474963	+	0.719539i
$815$	−39.5928	+	49.6478i	−1.38688	+	1.73909i
$816$	4.12596	+	1.13869i	0.144438	+	0.0398622i
$817$	18.7432	+	5.17278i	0.655740	+	0.180973i
$818$	6.41484	−	8.04396i	0.224290	−	0.281250i
$819$	17.0576	−	25.8411i	0.596040	−	0.902961i
$820$	5.81258	−	25.4666i	0.202984	−	0.889332i
$821$	−16.2781	−	30.2498i	−0.568110	−	1.05573i	−0.988902	−	0.148568i	$-0.952534\pi$
$821$	−16.2781	−	30.2498i	−0.568110	−	1.05573i	0.420792	−	0.907157i	$-0.361752\pi$
$822$	2.97484	+	1.43261i	0.103759	+	0.0499679i
$823$	−50.6703	−	4.56041i	−1.76626	−	0.158966i	−0.841683	−	0.539972i	$-0.818435\pi$
$823$	−50.6703	−	4.56041i	−1.76626	−	0.158966i	−0.924573	+	0.381006i	$0.875578\pi$
$824$	−9.19601	−	13.9314i	−0.320358	−	0.485322i
$825$	−72.4500	+	27.1909i	−2.52238	+	0.946666i
$826$	13.7256	−	6.60992i	0.477576	−	0.229989i
$827$	−21.9240	−	15.9287i	−0.762373	−	0.553896i	0.137265	−	0.990534i	$-0.456169\pi$
$827$	−21.9240	−	15.9287i	−0.762373	−	0.553896i	−0.899637	+	0.436638i	$0.856169\pi$
$828$	−13.5150	−	31.6200i	−0.469680	−	1.09887i
$829$	18.9653	+	23.7817i	0.658692	+	0.825974i	0.993200	−	0.116419i	$-0.0371415\pi$
$829$	18.9653	+	23.7817i	0.658692	+	0.825974i	−0.334508	+	0.942393i	$0.608570\pi$
$830$	−31.9642	+	2.87683i	−1.10949	+	0.0998562i
$831$	−75.4007	−	28.2984i	−2.61562	−	0.981659i
$832$	4.91761	+	21.5455i	0.170488	+	0.746955i
$833$	3.49769	−	3.05584i	0.121188	−	0.105878i
$834$	−2.09659	−	1.25266i	−0.0725991	−	0.0433759i
$835$	30.1915	−	21.9354i	1.04482	−	0.759106i
$836$	3.42415	−	6.36313i	0.118427	−	0.220073i
$837$	−9.30733	−	8.13157i	−0.321709	−	0.281068i
$838$	2.99556	+	9.21938i	0.103480	+	0.318478i
$839$	−25.2790	+	4.58747i	−0.872729	+	0.158377i	−0.596401	−	0.802686i	$-0.703403\pi$
$839$	−25.2790	+	4.58747i	−0.872729	+	0.158377i	−0.276328	+	0.961063i	$0.589118\pi$
$840$	8.28703	+	61.1773i	0.285930	+	2.11082i
$841$	−18.2816	−	3.31762i	−0.630400	−	0.114401i
$842$	−0.985260	+	21.9385i	−0.0339543	+	0.756051i
$843$	−19.0060	−	19.8787i	−0.654602	−	0.684660i
$844$	4.29687	−	4.49417i	0.147904	−	0.154696i
$845$	−0.231357	−	5.15157i	−0.00795893	−	0.177219i
$846$	−0.163182	+	1.20466i	−0.00561033	+	0.0414171i
$847$	2.75313	−	8.47327i	0.0945987	−	0.291145i
$848$	−4.23352	+	2.52941i	−0.145380	+	0.0868603i
$849$	−8.16192	+	19.0958i	−0.280116	+	0.655365i
$850$	−15.2858	+	4.21861i	−0.524298	+	0.144697i
$851$	51.3396			1.75990
$852$	−23.9246	+	1.63349i	−0.819644	+	0.0559624i
$853$	−29.9662			−1.02602			−0.513012	−	0.858382i	$-0.671470\pi$
$853$	−29.9662			−1.02602			−0.513012	+	0.858382i	$0.671470\pi$
$854$	3.52710	−	0.973416i	0.120695	−	0.0333096i
$855$	−10.0094	+	23.4181i	−0.342313	+	0.800882i
$856$	0.157509	−	0.0941070i	0.00538353	−	0.00321651i
$857$	8.13206	−	25.0279i	0.277786	−	0.854937i	−0.710683	−	0.703512i	$-0.751614\pi$
$857$	8.13206	−	25.0279i	0.277786	−	0.854937i	0.988469	−	0.151425i	$-0.0483861\pi$
$858$	−4.56004	+	33.6635i	−0.155677	+	1.14925i
$859$	−1.71670	−	38.2252i	−0.0585729	−	1.30423i	−0.786079	−	0.618126i	$-0.787892\pi$
$859$	−1.71670	−	38.2252i	−0.0585729	−	1.30423i	0.727506	−	0.686101i	$-0.240679\pi$
$860$	−28.9516	+	30.2810i	−0.987241	+	1.03257i
$861$	−28.2712	−	29.5694i	−0.963480	−	1.00772i
$862$	0.194143	−	4.32294i	0.00661255	−	0.147240i
$863$	−36.7692	−	6.67263i	−1.25164	−	0.227139i	−0.488035	−	0.872824i	$-0.662286\pi$
$863$	−36.7692	−	6.67263i	−1.25164	−	0.227139i	−0.763604	+	0.645685i	$0.776572\pi$
$864$	2.10311	+	15.5257i	0.0715491	+	0.528197i
$865$	−54.7375	+	9.93339i	−1.86113	+	0.337745i
$866$	−5.23585	−	16.1143i	−0.177921	−	0.547586i
$867$	24.4913	+	21.3974i	0.831769	+	0.726695i
$868$	−4.59742	+	8.54345i	−0.156047	+	0.289983i
$869$	11.9099	−	8.65303i	0.404015	−	0.293534i
$870$	25.2472	+	15.0845i	0.855960	+	0.511412i
$871$	−18.2519	+	15.9462i	−0.618442	+	0.540317i
$872$	5.04090	+	22.0856i	0.170707	+	0.747914i
$873$	46.7677	+	17.5522i	1.58285	+	0.594053i
$874$	13.1549	−	1.18397i	0.444972	−	0.0400482i
$875$	−12.0595	−	15.1221i	−0.407684	−	0.511220i
$876$	−6.63358	−	15.5200i	−0.224128	−	0.524373i
$877$	−3.96721	−	2.88235i	−0.133963	−	0.0973299i	0.518786	−	0.854904i	$-0.326384\pi$
$877$	−3.96721	−	2.88235i	−0.133963	−	0.0973299i	−0.652749	+	0.757574i	$0.726384\pi$
$878$	23.8021	−	11.4625i	0.803283	−	0.386841i
$879$	73.4404	−	27.5627i	2.47708	−	0.929665i
$880$	−5.51310	−	8.35199i	−0.185847	−	0.281546i
$881$	−41.5564	−	3.74015i	−1.40007	−	0.126009i	−0.636273	−	0.771464i	$-0.719525\pi$
$881$	−41.5564	−	3.74015i	−1.40007	−	0.126009i	−0.763798	+	0.645455i	$0.776668\pi$
$882$	−7.60007	−	3.66000i	−0.255908	−	0.123239i
$883$	13.1742	+	24.4817i	0.443346	+	0.823876i	0.999976	−	0.00688498i	$-0.00219158\pi$
$883$	13.1742	+	24.4817i	0.443346	+	0.823876i	−0.556630	+	0.830761i	$0.687906\pi$
$884$	1.76871	−	7.74923i	0.0594882	−	0.260635i
$885$	−37.0554	+	56.1365i	−1.24560	+	1.88701i
$886$	13.5393	−	16.9778i	0.454863	−	0.570380i
$887$	28.6594	+	7.90948i	0.962287	+	0.265574i	0.711672	−	0.702512i	$-0.247938\pi$
$887$	28.6594	+	7.90948i	0.962287	+	0.265574i	0.250616	+	0.968087i	$0.419367\pi$
$888$	−50.0543	−	13.8141i	−1.67971	−	0.463571i
$889$	−3.33960	+	4.18772i	−0.112006	+	0.140452i
$890$	26.6061	−	40.3066i	0.891840	−	1.35108i
$891$	3.76310	−	16.4872i	0.126069	−	0.552343i
$892$	10.9653	+	20.3769i	0.367144	+	0.682267i
$893$	0.480365	+	0.231331i	0.0160748	+	0.00774121i
$894$	−20.0448	−	1.80406i	−0.670397	−	0.0603368i
$895$	21.0353	+	31.8671i	0.703133	+	1.06520i
$896$	8.59287	−	3.22496i	0.287068	−	0.107738i
$897$	63.8805	−	30.7632i	2.13291	−	1.02715i
$898$	−28.9280	−	21.0174i	−0.965340	−	0.701361i
$899$	5.22387	+	12.2219i	0.174226	+	0.407622i
$900$	−20.5033	−	25.7103i	−0.683443	−	0.857011i
$901$	14.7507	−	1.32759i	0.491418	−	0.0442285i
$902$	24.3271	+	9.13013i	0.810005	+	0.304000i
$903$	14.6000	+	63.9670i	0.485859	+	2.12869i
$904$	−4.78437	+	4.17998i	−0.159126	+	0.139024i
$905$	44.3627	+	26.5055i	1.47467	+	0.881072i
$906$	−29.2964	+	21.2851i	−0.973308	+	0.707149i
$907$	−21.9576	+	40.8041i	−0.729090	+	1.35488i	0.198061	+	0.980190i	$0.436535\pi$
$907$	−21.9576	+	40.8041i	−0.729090	+	1.35488i	−0.927151	+	0.374687i	$0.877750\pi$
$908$	2.99485	+	2.61652i	0.0993875	+	0.0868322i
$909$	−3.55183	−	10.9314i	−0.117807	−	0.362572i
$910$	−25.2132	+	4.57551i	−0.835808	+	0.151677i
$911$	−2.62894	−	19.4076i	−0.0871007	−	0.643003i	−0.980897	−	0.194529i	$-0.937682\pi$
$911$	−2.62894	−	19.4076i	−0.0871007	−	0.643003i	0.893796	−	0.448474i	$-0.148032\pi$
$912$	−3.35460	−	0.608769i	−0.111082	−	0.0201584i
$913$	−1.63544	+	36.4158i	−0.0541251	+	1.20519i
$914$	27.7118	+	28.9842i	0.916624	+	0.958714i
$915$	−11.1643	+	11.6770i	−0.369081	+	0.386028i
$916$	−1.25771	−	28.0052i	−0.0415560	−	0.925317i
$917$	1.38995	−	10.2610i	0.0459002	−	0.338849i
$918$	−1.96691	+	6.05352i	−0.0649176	+	0.199796i
$919$	−21.7931	+	13.0207i	−0.718887	+	0.429515i	−0.825217	−	0.564816i	$-0.808947\pi$
$919$	−21.7931	+	13.0207i	−0.718887	+	0.429515i	0.106330	+	0.994331i	$0.466090\pi$
$920$	−32.1654	+	75.2547i	−1.06046	+	2.48108i
$921$	79.3208	−	21.8912i	2.61371	−	0.721338i
$922$	−2.50366			−0.0824535
$923$	−3.22910	−	28.4416i	−0.106287	−	0.936166i
$924$	24.3835			0.802157
$925$	47.3272	−	13.0615i	1.55611	−	0.429458i
$926$	0.621670	−	1.45447i	0.0204293	−	0.0477968i
$927$	19.9477	−	11.9182i	0.655168	−	0.391444i
$928$	5.20674	−	16.0247i	0.170920	−	0.526037i
$929$	6.14057	−	45.3315i	0.201466	−	1.48728i	−0.554235	−	0.832361i	$-0.686989\pi$
$929$	6.14057	−	45.3315i	0.201466	−	1.48728i	0.755700	−	0.654918i	$-0.227297\pi$
$930$	1.68313	+	37.4777i	0.0551918	+	1.22894i
$931$	−2.55666	+	2.67406i	−0.0837912	+	0.0876387i
$932$	−15.2275	−	15.9267i	−0.498793	−	0.521697i
$933$	−0.580708	+	12.9305i	−0.0190115	+	0.423325i
$934$	16.0896	+	2.91983i	0.526467	+	0.0955396i
$935$	4.03426	+	29.7821i	0.131934	+	0.973979i
$936$	−40.8478	+	7.41279i	−1.33515	+	0.242295i
$937$	−15.0872	−	46.4336i	−0.492877	−	1.51692i	−0.820240	−	0.572020i	$-0.806160\pi$
$937$	−15.0872	−	46.4336i	−0.492877	−	1.51692i	0.327363	−	0.944899i	$-0.393840\pi$
$938$	−11.4734	−	10.0240i	−0.374619	−	0.327295i
$939$	−18.1636	+	33.7537i	−0.592748	+	1.10151i
$940$	−0.929376	+	0.675231i	−0.0303129	+	0.0220236i
$941$	3.75202	+	2.24173i	0.122312	+	0.0730783i	0.572752	−	0.819728i	$-0.305876\pi$
$941$	3.75202	+	2.24173i	0.122312	+	0.0730783i	−0.450440	+	0.892807i	$0.648733\pi$
$942$	−21.7098	+	18.9673i	−0.707345	+	0.617988i
$943$	−12.0678	−	52.8724i	−0.392981	−	1.72176i
$944$	−4.88060	−	1.83172i	−0.158850	−	0.0596174i
$945$	−23.3362	+	2.10030i	−0.759128	+	0.0683228i
$946$	−25.9832	−	32.5819i	−0.844786	−	1.05933i
$947$	6.39435	+	14.9603i	0.207788	+	0.486145i	0.990713	−	0.135972i	$-0.0434157\pi$
$947$	6.39435	+	14.9603i	0.207788	+	0.486145i	−0.782924	+	0.622117i	$0.786273\pi$
$948$	8.74239	+	6.35172i	0.283940	+	0.206294i
$949$	18.1517	−	8.74140i	0.589229	−	0.283758i
$950$	11.8256	−	4.43822i	0.383673	−	0.143995i
$951$	−20.9977	−	31.8101i	−0.680897	−	1.03151i
$952$	14.3111	+	1.28802i	0.463826	+	0.0417451i
$953$	44.9476	+	21.6456i	1.45600	+	0.701171i	0.983625	−	0.180228i	$-0.0576836\pi$
$953$	44.9476	+	21.6456i	1.45600	+	0.701171i	0.472372	+	0.881399i	$0.343398\pi$
$954$	−12.7464	−	23.6867i	−0.412679	−	0.766886i
$955$	10.4255	−	45.6769i	0.337360	−	1.47807i
$956$	−2.97912	+	4.51317i	−0.0963515	+	0.145966i
$957$	20.8276	−	26.1170i	0.673262	−	0.844244i
$958$	−26.9336	−	7.43319i	−0.870184	−	0.240156i
$959$	2.72697	+	0.752597i	0.0880586	+	0.0243026i
$960$	38.2432	−	47.9554i	1.23429	−	1.54775i
$961$	7.73765	−	11.7220i	0.249602	−	0.378130i
$962$	4.79596	−	21.0125i	0.154628	−	0.677470i
$963$	0.121031	+	0.224913i	0.00390017	+	0.00724772i
$964$	−3.01213	−	1.45057i	−0.0970142	−	0.0467196i
$965$	49.1998	+	4.42806i	1.58380	+	0.142544i
$966$	24.5534	+	37.1968i	0.789993	+	1.19679i
$967$	−7.90158	+	2.96551i	−0.254098	+	0.0953644i	−0.475173	−	0.879892i	$-0.657615\pi$
$967$	−7.90158	+	2.96551i	−0.254098	+	0.0953644i	0.221076	+	0.975257i	$0.429043\pi$
$968$	−10.7625	+	5.18294i	−0.345920	+	0.166586i
$969$	8.28347	+	6.01829i	0.266103	+	0.193335i
$970$	−16.2479	−	38.0139i	−0.521690	−	1.22055i
$971$	−23.1277	−	29.0012i	−0.742203	−	0.930693i	0.257161	−	0.966369i	$-0.417213\pi$
$971$	−23.1277	−	29.0012i	−0.742203	−	0.930693i	−0.999363	+	0.0356761i	$0.988642\pi$
$972$	21.9260	−	1.97337i	0.703276	−	0.0632960i
$973$	−1.95908	−	0.735254i	−0.0628052	−	0.0235712i
$974$	4.83822	+	21.1976i	0.155027	+	0.679216i
$975$	51.0614	−	44.6110i	1.63527	−	1.42870i
$976$	−1.07482	−	0.642177i	−0.0344042	−	0.0205556i
$977$	−19.7552	+	14.3530i	−0.632024	+	0.459192i	−0.857101	−	0.515149i	$-0.827737\pi$
$977$	−19.7552	+	14.3530i	−0.632024	+	0.459192i	0.225077	+	0.974341i	$0.427737\pi$
$978$	21.9723	−	40.8314i	0.702598	−	1.30565i
$979$	−41.3104	−	36.0918i	−1.32029	−	1.15350i
$980$	−2.46326	−	7.58114i	−0.0786860	−	0.242171i
$981$	−31.0277	+	5.63070i	−0.990639	+	0.179775i
$982$	−2.88795	−	21.3197i	−0.0921583	−	0.680340i
$983$	−59.5442	−	10.8057i	−1.89917	−	0.344648i	−0.902817	−	0.430024i	$-0.858505\pi$
$983$	−59.5442	−	10.8057i	−1.89917	−	0.344648i	−0.996349	+	0.0853764i	$0.972791\pi$
$984$	−2.46088	+	54.7958i	−0.0784501	+	1.74683i
$985$	28.2192	+	29.5150i	0.899140	+	0.940427i
$986$	4.73044	−	4.94766i	0.150648	−	0.157566i
$987$	0.0807176	+	1.79732i	0.00256927	+	0.0572092i
$988$	−0.849880	+	6.27407i	−0.0270383	+	0.199605i
$989$	−26.8779	+	82.7218i	−0.854668	+	2.63040i
$990$	46.8577	−	27.9962i	1.48924	−	0.889778i
$991$	7.49636	−	17.5386i	0.238130	−	0.557132i	−0.757253	−	0.653122i	$-0.773459\pi$
$991$	7.49636	−	17.5386i	0.238130	−	0.557132i	0.995382	+	0.0959899i	$0.0306016\pi$
$992$	20.7184	−	5.71791i	0.657810	−	0.181544i
$993$	−38.5985			−1.22489
$994$	17.4445	−	4.41141i	0.553304	−	0.139921i
$995$	22.7588			0.721501
$996$	−25.7936	+	7.11857i	−0.817300	+	0.225561i
$997$	−10.2430	+	23.9646i	−0.324398	+	0.758967i	0.675371	+	0.737478i	$0.263983\pi$
$997$	−10.2430	+	23.9646i	−0.324398	+	0.758967i	−0.999769	+	0.0214887i	$0.993159\pi$
$998$	16.1809	−	9.66764i	0.512197	−	0.306024i
$999$	6.08986	−	18.7427i	0.192675	−	0.592991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.10.4	✓	120
3.2	odd	2		639.2.v.a.10.2		120
71.8	even	35		5041.2.a.s.1.22		60
71.63	odd	70		5041.2.a.t.1.22		60
71.64	even	35	inner	71.2.g.a.64.4	yes	120
213.206	odd	70		639.2.v.a.64.2		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.10.4	✓	120	1.1	even	1	trivial
71.2.g.a.64.4	yes	120	71.64	even	35	inner
639.2.v.a.10.2		120	3.2	odd	2
639.2.v.a.64.2		120	213.206	odd	70
5041.2.a.s.1.22		60	71.8	even	35
5041.2.a.t.1.22		60	71.63	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.931498 - 0.257077i) q^{2} +(1.04905 - 2.45439i) q^{3} +(-0.915297 + 0.546865i) q^{4} +(-1.09157 + 3.35950i) q^{5} +(0.346226 - 2.55594i) q^{6} +(-0.0991455 - 2.20765i) q^{7} +(-2.04759 + 2.14161i) q^{8} +(-2.85031 - 2.98119i) q^{9} +O(q^{10})\)	\(q+(0.931498 - 0.257077i) q^{2} +(1.04905 - 2.45439i) q^{3} +(-0.915297 + 0.546865i) q^{4} +(-1.09157 + 3.35950i) q^{5} +(0.346226 - 2.55594i) q^{6} +(-0.0991455 - 2.20765i) q^{7} +(-2.04759 + 2.14161i) q^{8} +(-2.85031 - 2.98119i) q^{9} +(-0.153143 + 3.40999i) q^{10} +(3.81476 + 0.692276i) q^{11} +(0.382020 + 2.82018i) q^{12} +(-3.34249 + 0.606572i) q^{13} +(-0.659889 - 2.03093i) q^{14} +(7.10040 + 6.20343i) q^{15} +(-0.346268 + 0.643474i) q^{16} +(1.77538 - 1.28989i) q^{17} +(-3.42145 - 2.04422i) q^{18} +(-1.31638 + 1.15008i) q^{19} +(-0.838084 - 3.67188i) q^{20} +(-5.52242 - 2.07260i) q^{21} +(3.73141 - 0.335833i) q^{22} +(-4.87533 - 6.11347i) q^{23} +(3.10830 + 7.27224i) q^{24} +(-6.04965 - 4.39533i) q^{25} +(-2.95759 + 1.42430i) q^{26} +(-2.81017 + 1.05467i) q^{27} +(1.29803 + 1.96643i) q^{28} +(3.21498 + 0.289353i) q^{29} +(8.20877 + 3.95314i) q^{30} +(1.95119 + 3.62592i) q^{31} +(1.16151 - 5.08893i) q^{32} +(5.70100 - 8.63664i) q^{33} +(1.32216 - 1.65794i) q^{34} +(7.52482 + 2.07672i) q^{35} +(4.23918 + 1.16994i) q^{36} +(-4.09361 + 5.13323i) q^{37} +(-0.930542 + 1.40971i) q^{38} +(-2.01769 + 8.84008i) q^{39} +(-4.95966 - 9.21660i) q^{40} +(6.24873 + 3.00923i) q^{41} +(-5.67695 - 0.510934i) q^{42} +(-6.12786 - 9.28331i) q^{43} +(-3.87022 + 1.45252i) q^{44} +(13.1266 - 6.32144i) q^{45} +(-6.11300 - 4.44135i) q^{46} +(-0.119877 - 0.280467i) q^{47} +(1.21608 + 1.52491i) q^{48} +(2.10795 - 0.189719i) q^{49} +(-6.76518 - 2.53901i) q^{50} +(-1.30341 - 5.71062i) q^{51} +(2.72766 - 2.38308i) q^{52} +(5.79359 + 3.46151i) q^{53} +(-2.34653 + 1.70486i) q^{54} +(-6.48977 + 12.0600i) q^{55} +(4.93093 + 4.30802i) q^{56} +(1.44180 + 4.43740i) q^{57} +(3.06913 - 0.556966i) q^{58} +(0.957622 + 7.06945i) q^{59} +(-9.89141 - 1.79503i) q^{60} +(-0.0768731 + 1.71171i) q^{61} +(2.74967 + 2.87593i) q^{62} +(-6.29881 + 6.58804i) q^{63} +(-0.291866 - 6.49891i) q^{64} +(1.61077 - 11.8912i) q^{65} +(3.09019 - 9.51062i) q^{66} +(6.12464 - 3.65930i) q^{67} +(-0.919603 + 2.15152i) q^{68} +(-20.1193 + 5.55258i) q^{69} +7.54323 q^{70} +(-0.559666 + 8.40754i) q^{71} +12.2208 q^{72} +(-5.71692 + 1.57777i) q^{73} +(-2.49356 + 5.83397i) q^{74} +(-17.1342 + 10.2372i) q^{75} +(0.575936 - 1.77255i) q^{76} +(1.15008 - 8.49026i) q^{77} +(0.393108 + 8.75322i) q^{78} +(2.62400 - 2.74449i) q^{79} +(-1.78378 - 1.86568i) q^{80} +(0.195694 - 4.35748i) q^{81} +(6.59428 + 1.19669i) q^{82} +(1.26208 + 9.31702i) q^{83} +(6.18809 - 1.12297i) q^{84} +(2.39543 + 7.37238i) q^{85} +(-8.09462 - 7.07206i) q^{86} +(4.08288 - 7.58725i) q^{87} +(-9.29364 + 6.75222i) q^{88} +(-12.1461 - 7.25693i) q^{89} +(10.6023 - 9.26296i) q^{90} +(1.67049 + 7.31889i) q^{91} +(7.80562 + 2.92950i) q^{92} +(10.9463 - 0.985186i) q^{93} +(-0.183767 - 0.230437i) q^{94} +(-2.42679 - 5.67777i) q^{95} +(-11.2717 - 8.18937i) q^{96} +(-10.9118 + 5.25486i) q^{97} +(1.91478 - 0.718628i) q^{98} +(-8.80941 - 13.3457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more