LMFDB - Embedded newform 770.2.bv.a.537.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			537.1
Character	$\chi$	$=$	770.537
Dual form			770.2.bv.a.423.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0523360 + 0.998630i) q^{2} +(-1.17662 - 3.06520i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-2.19152 + 0.444112i) q^{5} +(3.12258 - 1.01459i) q^{6} +(0.953749 - 2.46787i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-5.78157 + 5.20575i) q^{9} +O(q^{10})$	\(q+(-0.0523360 + 0.998630i) q^{2} +(-1.17662 - 3.06520i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-2.19152 + 0.444112i) q^{5} +(3.12258 - 1.01459i) q^{6} +(0.953749 - 2.46787i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-5.78157 + 5.20575i) q^{9} +(-0.328808 - 2.21176i) q^{10} +(-1.83123 + 2.76525i) q^{11} +(0.849773 + 3.17140i) q^{12} +(-2.05701 + 1.04810i) q^{13} +(2.41457 + 1.08160i) q^{14} +(3.93988 + 6.19489i) q^{15} +(0.978148 + 0.207912i) q^{16} +(-0.330692 - 6.30998i) q^{17} +(-4.89603 - 6.04609i) q^{18} +(-0.0151576 - 0.144215i) q^{19} +(2.22594 - 0.212603i) q^{20} +(-8.68670 - 0.0196925i) q^{21} +(-2.66562 - 1.97344i) q^{22} +(1.07978 + 4.02980i) q^{23} +(-3.21152 + 0.682630i) q^{24} +(4.60553 - 1.94656i) q^{25} +(-0.939008 - 2.10905i) q^{26} +(13.9831 + 7.12475i) q^{27} +(-1.20649 + 2.35465i) q^{28} +(-0.567730 + 0.781413i) q^{29} +(-6.39260 + 3.61026i) q^{30} +(1.15242 + 5.42170i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(10.6307 + 2.35943i) q^{33} +6.31864 q^{34} +(-0.994152 + 5.83195i) q^{35} +(6.29405 - 4.57289i) q^{36} +(2.91489 + 1.11892i) q^{37} +(0.144810 - 0.00758918i) q^{38} +(5.63295 + 5.07193i) q^{39} +(0.0958152 + 2.23401i) q^{40} +(5.43209 + 7.47663i) q^{41} +(0.474292 - 8.67376i) q^{42} +(0.476294 - 0.476294i) q^{43} +(2.11024 - 2.55869i) q^{44} +(10.3585 - 13.9762i) q^{45} +(-4.08079 + 0.867398i) q^{46} +(-2.28510 - 1.85044i) q^{47} +(-0.513617 - 3.24285i) q^{48} +(-5.18072 - 4.70745i) q^{49} +(1.70286 + 4.70109i) q^{50} +(-18.9522 + 8.43808i) q^{51} +(2.15530 - 0.827342i) q^{52} +(-6.57816 + 10.1295i) q^{53} +(-7.84680 + 13.5911i) q^{54} +(2.78509 - 6.87337i) q^{55} +(-2.28828 - 1.32807i) q^{56} +(-0.424211 + 0.216147i) q^{57} +(-0.750629 - 0.607848i) q^{58} +(-0.401111 + 3.81632i) q^{59} +(-3.27075 - 6.57279i) q^{60} +(1.66129 - 7.81574i) q^{61} +(-5.47458 + 0.867089i) q^{62} +(7.33292 + 19.2331i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(4.04251 - 3.21048i) q^{65} +(-2.91256 + 10.4926i) q^{66} +(-2.42073 + 9.03428i) q^{67} +(-0.330692 + 6.30998i) q^{68} +(11.0816 - 8.05128i) q^{69} +(-5.77193 - 1.29801i) q^{70} +(-1.19263 - 3.67053i) q^{71} +(4.23722 + 6.52475i) q^{72} +(8.13116 - 6.58448i) q^{73} +(-1.26994 + 2.85233i) q^{74} +(-11.3856 - 11.8265i) q^{75} +0.145009i q^{76} +(5.07773 + 7.15658i) q^{77} +(-5.35979 + 5.35979i) q^{78} +(-0.745834 + 0.671552i) q^{79} +(-2.23597 - 0.0212353i) q^{80} +(2.94632 - 28.0323i) q^{81} +(-7.75067 + 5.03335i) q^{82} +(-7.30756 + 14.3419i) q^{83} +(8.63705 + 0.927592i) q^{84} +(3.52706 + 13.6816i) q^{85} +(0.450714 + 0.500569i) q^{86} +(3.06319 + 0.820779i) q^{87} +(2.44474 + 2.24126i) q^{88} +(-8.79491 + 15.2332i) q^{89} +(13.4149 + 11.0758i) q^{90} +(0.624696 + 6.07606i) q^{91} +(-0.652638 - 4.12059i) q^{92} +(15.2626 - 9.91167i) q^{93} +(1.96749 - 2.18512i) q^{94} +(0.0972656 + 0.309318i) q^{95} +(3.26528 - 0.343195i) q^{96} +(-7.19756 - 14.1260i) q^{97} +(4.97214 - 4.92725i) q^{98} +(-3.80783 - 25.5204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.0523360	+	0.998630i	−0.0370071	+	0.706138i
$2$	−0.0523360	+	0.998630i	−0.0370071	+	0.706138i
$3$	−1.17662	−	3.06520i	−0.679321	−	1.76969i	−0.637351	−	0.770574i	$-0.719970\pi$
$3$	−1.17662	−	3.06520i	−0.679321	−	1.76969i	−0.0419706	−	0.999119i	$-0.513364\pi$
$4$	−0.994522	−	0.104528i	−0.497261	−	0.0522642i
$5$	−2.19152	+	0.444112i	−0.980078	+	0.198613i
$5$	−2.19152	+	0.444112i	−0.980078	+	0.198613i
$6$	3.12258	−	1.01459i	1.27479	−	0.414203i
$7$	0.953749	−	2.46787i	0.360483	−	0.932766i
$7$	0.953749	−	2.46787i	0.360483	−	0.932766i
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−5.78157	+	5.20575i	−1.92719	+	1.73525i
$10$	−0.328808	−	2.21176i	−0.103978	−	0.699420i
$11$	−1.83123	+	2.76525i	−0.552136	+	0.833754i
$11$	−1.83123	+	2.76525i	−0.552136	+	0.833754i
$12$	0.849773	+	3.17140i	0.245308	+	0.915503i
$13$	−2.05701	+	1.04810i	−0.570513	+	0.290691i	−0.715352	−	0.698765i	$-0.753734\pi$
$13$	−2.05701	+	1.04810i	−0.570513	+	0.290691i	0.144839	+	0.989455i	$0.453734\pi$
$14$	2.41457	+	1.08160i	0.645321	+	0.289070i
$15$	3.93988	+	6.19489i	1.01727	+	1.59951i
$16$	0.978148	+	0.207912i	0.244537	+	0.0519779i
$17$	−0.330692	−	6.30998i	−0.0802046	−	1.53040i	−0.681767	−	0.731569i	$-0.738788\pi$
$17$	−0.330692	−	6.30998i	−0.0802046	−	1.53040i	0.601562	−	0.798826i	$-0.294545\pi$
$18$	−4.89603	−	6.04609i	−1.15401	−	1.42508i
$19$	−0.0151576	−	0.144215i	−0.00347738	−	0.0330851i	0.992646	−	0.121057i	$-0.0386282\pi$
$19$	−0.0151576	−	0.144215i	−0.00347738	−	0.0330851i	−0.996123	+	0.0879715i	$0.971962\pi$
$20$	2.22594	−	0.212603i	0.497735	−	0.0475395i
$21$	−8.68670	−	0.0196925i	−1.89559	−	0.00429726i
$22$	−2.66562	−	1.97344i	−0.568312	−	0.420739i
$23$	1.07978	+	4.02980i	0.225150	+	0.840271i	0.982344	+	0.187082i	$0.0599029\pi$
$23$	1.07978	+	4.02980i	0.225150	+	0.840271i	−0.757194	+	0.653190i	$0.773430\pi$
$24$	−3.21152	+	0.682630i	−0.655550	+	0.139341i
$25$	4.60553	−	1.94656i	0.921106	−	0.389313i
$26$	−0.939008	−	2.10905i	−0.184155	−	0.413618i
$27$	13.9831	+	7.12475i	2.69105	+	1.37116i
$28$	−1.20649	+	2.35465i	−0.228005	+	0.444988i
$29$	−0.567730	+	0.781413i	−0.105425	+	0.145105i	−0.858470	−	0.512864i	$-0.828584\pi$
$29$	−0.567730	+	0.781413i	−0.105425	+	0.145105i	0.753045	+	0.657969i	$0.228584\pi$
$30$	−6.39260	+	3.61026i	−1.16712	+	0.659141i
$31$	1.15242	+	5.42170i	0.206980	+	0.973766i	0.951852	+	0.306558i	$0.0991774\pi$
$31$	1.15242	+	5.42170i	0.206980	+	0.973766i	−0.744871	+	0.667208i	$0.767489\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	10.6307	+	2.35943i	1.85057	+	0.410724i
$34$	6.31864			1.08364
$35$	−0.994152	+	5.83195i	−0.168042	+	0.985780i
$36$	6.29405	−	4.57289i	1.04901	−	0.762149i
$37$	2.91489	+	1.11892i	0.479204	+	0.183949i	0.585966	−	0.810335i	$-0.300715\pi$
$37$	2.91489	+	1.11892i	0.479204	+	0.183949i	−0.106762	+	0.994285i	$0.534048\pi$
$38$	0.144810	−	0.00758918i	0.0234913	−	0.00123113i
$39$	5.63295	+	5.07193i	0.901994	+	0.812159i
$40$	0.0958152	+	2.23401i	0.0151497	+	0.353229i
$41$	5.43209	+	7.47663i	0.848349	+	1.16765i	0.984224	+	0.176927i	$0.0566155\pi$
$41$	5.43209	+	7.47663i	0.848349	+	1.16765i	−0.135875	+	0.990726i	$0.543384\pi$
$42$	0.474292	−	8.67376i	0.0731849	−	1.33839i
$43$	0.476294	−	0.476294i	0.0726342	−	0.0726342i	−0.669856	−	0.742491i	$-0.733644\pi$
$43$	0.476294	−	0.476294i	0.0726342	−	0.0726342i	0.742491	+	0.669856i	$0.233644\pi$
$44$	2.11024	−	2.55869i	0.318131	−	0.385736i
$45$	10.3585	−	13.9762i	1.54415	−	2.08344i
$46$	−4.08079	+	0.867398i	−0.601679	+	0.127891i
$47$	−2.28510	−	1.85044i	−0.333316	−	0.269914i	0.448021	−	0.894023i	$-0.352129\pi$
$47$	−2.28510	−	1.85044i	−0.333316	−	0.269914i	−0.781337	+	0.624109i	$0.785462\pi$
$48$	−0.513617	−	3.24285i	−0.0741342	−	0.468065i
$49$	−5.18072	−	4.70745i	−0.740103	−	0.672493i
$50$	1.70286	+	4.70109i	0.240821	+	0.664835i
$51$	−18.9522	+	8.43808i	−2.65384	+	1.18157i
$52$	2.15530	−	0.827342i	0.298886	−	0.114732i
$53$	−6.57816	+	10.1295i	−0.903580	+	1.39139i	0.0165861	+	0.999862i	$0.494720\pi$
$53$	−6.57816	+	10.1295i	−0.903580	+	1.39139i	−0.920166	+	0.391529i	$0.871946\pi$
$54$	−7.84680	+	13.5911i	−1.06781	+	1.84951i
$55$	2.78509	−	6.87337i	0.375542	−	0.926806i
$56$	−2.28828	−	1.32807i	−0.305785	−	0.177470i
$57$	−0.424211	+	0.216147i	−0.0561882	+	0.0286293i
$58$	−0.750629	−	0.607848i	−0.0985625	−	0.0798143i
$59$	−0.401111	+	3.81632i	−0.0522203	+	0.496843i	0.936886	+	0.349636i	$0.113695\pi$
$59$	−0.401111	+	3.81632i	−0.0522203	+	0.496843i	−0.989106	+	0.147206i	$0.952972\pi$
$60$	−3.27075	−	6.57279i	−0.422252	−	0.848543i
$61$	1.66129	−	7.81574i	0.212706	−	1.00070i	−0.734136	−	0.679003i	$-0.762412\pi$
$61$	1.66129	−	7.81574i	0.212706	−	1.00070i	0.946842	−	0.321700i	$-0.104254\pi$
$62$	−5.47458	+	0.867089i	−0.695273	+	0.110120i
$63$	7.33292	+	19.2331i	0.923861	+	2.42314i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	4.04251	−	3.21048i	0.501412	−	0.398211i
$66$	−2.91256	+	10.4926i	−0.358512	+	1.29155i
$67$	−2.42073	+	9.03428i	−0.295739	+	1.10371i	0.644890	+	0.764276i	$0.276903\pi$
$67$	−2.42073	+	9.03428i	−0.295739	+	1.10371i	−0.940629	+	0.339437i	$0.889763\pi$
$68$	−0.330692	+	6.30998i	−0.0401023	+	0.765198i
$69$	11.0816	−	8.05128i	1.33407	−	0.969261i
$70$	−5.77193	−	1.29801i	−0.689878	−	0.155142i
$71$	−1.19263	−	3.67053i	−0.141539	−	0.435612i	0.855011	−	0.518610i	$-0.173550\pi$
$71$	−1.19263	−	3.67053i	−0.141539	−	0.435612i	−0.996550	+	0.0829981i	$0.973550\pi$
$72$	4.23722	+	6.52475i	0.499361	+	0.768949i
$73$	8.13116	−	6.58448i	0.951680	−	0.770656i	−0.0217205	−	0.999764i	$-0.506914\pi$
$73$	8.13116	−	6.58448i	0.951680	−	0.770656i	0.973401	+	0.229109i	$0.0735811\pi$
$74$	−1.26994	+	2.85233i	−0.147628	+	0.331577i
$75$	−11.3856	−	11.8265i	−1.31469	−	1.36561i
$76$			0.145009i			0.0166337i
$77$	5.07773	+	7.15658i	0.578661	+	0.815568i
$78$	−5.35979	+	5.35979i	−0.606877	+	0.606877i
$79$	−0.745834	+	0.671552i	−0.0839129	+	0.0755555i	−0.710020	−	0.704182i	$-0.751314\pi$
$79$	−0.745834	+	0.671552i	−0.0839129	+	0.0755555i	0.626107	+	0.779737i	$0.284647\pi$
$80$	−2.23597	−	0.0212353i	−0.249989	−	0.00237418i
$81$	2.94632	−	28.0323i	0.327369	−	3.11470i
$82$	−7.75067	+	5.03335i	−0.855919	+	0.555840i
$83$	−7.30756	+	14.3419i	−0.802109	+	1.57423i	0.0164918	+	0.999864i	$0.494750\pi$
$83$	−7.30756	+	14.3419i	−0.802109	+	1.57423i	−0.818601	+	0.574363i	$0.805250\pi$
$84$	8.63705	+	0.927592i	0.942380	+	0.101209i
$85$	3.52706	+	13.6816i	0.382563	+	1.48398i
$86$	0.450714	+	0.500569i	0.0486018	+	0.0539778i
$87$	3.06319	+	0.820779i	0.328408	+	0.0879967i
$88$	2.44474	+	2.24126i	0.260610	+	0.238919i
$89$	−8.79491	+	15.2332i	−0.932259	+	1.61472i	−0.152809	+	0.988256i	$0.548832\pi$
$89$	−8.79491	+	15.2332i	−0.932259	+	1.61472i	−0.779450	+	0.626464i	$0.784501\pi$
$90$	13.4149	+	11.0758i	1.41405	+	1.16749i
$91$	0.624696	+	6.07606i	0.0654859	+	0.636944i
$92$	−0.652638	−	4.12059i	−0.0680422	−	0.429601i
$93$	15.2626	−	9.91167i	1.58266	−	1.02779i
$94$	1.96749	−	2.18512i	0.202932	−	0.225378i
$95$	0.0972656	+	0.309318i	0.00997924	+	0.0317353i
$96$	3.26528	−	0.343195i	0.333262	−	0.0350272i
$97$	−7.19756	−	14.1260i	−0.730801	−	1.43428i	−0.894177	−	0.447714i	$-0.852238\pi$
$97$	−7.19756	−	14.1260i	−0.730801	−	1.43428i	0.163376	−	0.986564i	$-0.447762\pi$
$98$	4.97214	−	4.92725i	0.502262	−	0.497728i
$99$	−3.80783	−	25.5204i	−0.382701	−	2.56490i
$100$	−4.78377	+	1.45449i	−0.478377	+	0.145449i
$101$	−1.39100	−	6.54413i	−0.138409	−	0.651165i	−0.991576	−	0.129526i	$-0.958654\pi$
$101$	−1.39100	−	6.54413i	−0.138409	−	0.651165i	0.853167	−	0.521639i	$-0.174679\pi$
$102$	−7.43463	−	19.3679i	−0.736138	−	1.91771i
$103$	0.675547	+	0.259318i	0.0665637	+	0.0255514i	0.391422	−	0.920211i	$-0.371983\pi$
$103$	0.675547	+	0.259318i	0.0665637	+	0.0255514i	−0.324858	+	0.945763i	$0.605317\pi$
$104$	0.713409	+	2.19565i	0.0699555	+	0.215301i
$105$	19.0458	−	3.81471i	1.85868	−	0.372278i
$106$	−9.77132	−	7.09928i	−0.949075	−	0.689543i
$107$	−1.95155	+	2.40996i	−0.188663	+	0.232980i	−0.862697	−	0.505720i	$-0.831227\pi$
$107$	−1.95155	+	2.40996i	−0.188663	+	0.232980i	0.674034	+	0.738700i	$0.264560\pi$
$108$	−13.1618	−	8.54735i	−1.26649	−	0.822469i
$109$	−13.2339	+	7.64058i	−1.26757	+	0.731835i	−0.974529	−	0.224264i	$-0.928002\pi$
$109$	−13.2339	+	7.64058i	−1.26757	+	0.731835i	−0.293046	+	0.956098i	$0.594669\pi$
$110$	6.71819	+	3.14100i	0.640555	+	0.299482i
$111$		−	10.2512i		−	0.973005i
$112$	1.44601	−	2.21564i	0.136635	−	0.209358i
$113$	0.546638	−	3.45133i	0.0514233	−	0.324674i	−0.948544	−	0.316644i	$-0.897444\pi$
$113$	0.546638	−	3.45133i	0.0514233	−	0.324674i	0.999968	−	0.00803006i	$-0.00255608\pi$
$114$	−0.193649	−	0.434942i	−0.0181369	−	0.0407361i
$115$	−4.15605	−	8.35185i	−0.387553	−	0.778814i
$116$	0.646300	−	0.717788i	0.0600074	−	0.0666450i
$117$	6.43661	−	16.7680i	0.595065	−	1.55020i
$118$	−3.79010	−	0.600292i	−0.348907	−	0.0552614i
$119$	−15.8876	−	5.20204i	−1.45641	−	0.476870i
$120$	6.73496	−	2.92228i	0.614815	−	0.266766i
$121$	−4.29321	−	10.1276i	−0.390292	−	0.920691i
$122$	7.71808	+	2.06805i	0.698762	+	0.187233i
$123$	16.5258	−	25.4476i	1.49008	−	2.29453i
$124$	−0.579383	−	5.51246i	−0.0520301	−	0.495034i
$125$	−9.22862	+	6.31131i	−0.825433	+	0.564500i
$126$	−19.5905	+	6.31629i	−1.74526	+	0.562700i
$127$	−4.90766	+	9.63182i	−0.435484	+	0.854685i	0.564096	+	0.825709i	$0.309225\pi$
$127$	−4.90766	+	9.63182i	−0.435484	+	0.854685i	−0.999580	+	0.0289763i	$0.990775\pi$
$128$	0.358368	−	0.933580i	0.0316756	−	0.0825176i
$129$	−2.02035	−	0.899520i	−0.177882	−	0.0791983i
$130$	2.99451	+	4.20499i	0.262636	+	0.368802i
$131$	10.0188	+	5.78437i	0.875348	+	0.505383i	0.869122	−	0.494598i	$-0.164685\pi$
$131$	10.0188	+	5.78437i	0.875348	+	0.505383i	0.00622648	+	0.999981i	$0.498018\pi$
$132$	−10.3258	−	3.45771i	−0.898748	−	0.300955i
$133$	−0.370359	−	0.100138i	−0.0321142	−	0.00868304i
$134$	−8.89521	−	2.89023i	−0.768429	−	0.249678i
$135$	−33.8085	−	9.40396i	−2.90977	−	0.809364i
$136$	−6.28403	−	0.660478i	−0.538851	−	0.0566355i
$137$	0.992011	−	0.0519891i	0.0847532	−	0.00444173i	−0.00991220	−	0.999951i	$-0.503155\pi$
$137$	0.992011	−	0.0519891i	0.0847532	−	0.00444173i	0.0946654	+	0.995509i	$0.469822\pi$
$138$	7.46028	+	11.4878i	0.635061	+	0.977909i
$139$	−6.53136	−	4.74531i	−0.553983	−	0.402492i	0.275269	−	0.961367i	$-0.411233\pi$
$139$	−6.53136	−	4.74531i	−0.553983	−	0.402492i	−0.829252	+	0.558875i	$0.811233\pi$
$140$	1.59831	−	5.69609i	0.135082	−	0.481407i
$141$	−2.98326	+	9.18154i	−0.251236	+	0.773225i
$142$	3.72792	−	0.998893i	0.312840	−	0.0838253i
$143$	0.868598	−	7.60746i	0.0726358	−	0.636168i
$144$	−6.73756	+	3.88993i	−0.561464	+	0.324161i
$145$	0.897157	−	1.96462i	0.0745048	−	0.163153i
$146$	6.14991	+	8.46462i	0.508970	+	0.700537i
$147$	−8.33353	+	21.4188i	−0.687338	+	1.76659i
$148$	−2.78196	−	1.41748i	−0.228676	−	0.116516i
$149$	0.146957	−	0.691377i	0.0120392	−	0.0566398i	−0.971718	−	0.236144i	$-0.924116\pi$
$149$	0.146957	−	0.691377i	0.0120392	−	0.0566398i	0.983757	+	0.179505i	$0.0574495\pi$
$150$	12.4062	−	10.7510i	1.01296	−	0.877815i
$151$	−5.67202	−	2.52535i	−0.461583	−	0.205510i	0.162752	−	0.986667i	$-0.447963\pi$
$151$	−5.67202	−	2.52535i	−0.461583	−	0.205510i	−0.624334	+	0.781157i	$0.714630\pi$
$152$	−0.144810	−	0.00758918i	−0.0117457	−	0.000615564i
$153$	34.7601	+	34.7601i	2.81019	+	2.81019i
$154$	−7.41252	+	4.69623i	−0.597318	+	0.378433i
$155$	−4.93339	−	11.3700i	−0.396260	−	0.913258i
$156$	−5.07193	−	5.63295i	−0.406080	−	0.450997i
$157$	−7.37187	+	2.82980i	−0.588339	+	0.225842i	−0.634282	−	0.773102i	$-0.718704\pi$
$157$	−7.37187	+	2.82980i	−0.588339	+	0.225842i	0.0459426	+	0.998944i	$0.485371\pi$
$158$	−0.631598	−	0.779958i	−0.0502472	−	0.0620501i
$159$	38.7888	+	8.24482i	3.07616	+	0.653857i
$160$	0.138228	−	2.23179i	0.0109279	−	0.176439i
$161$	10.9748	+	1.17866i	0.864939	+	0.0928917i
$162$	27.8397	+	4.40938i	2.18730	+	0.346434i
$163$	15.8958	+	0.833061i	1.24505	+	0.0652504i	0.663448	−	0.748222i	$-0.269092\pi$
$163$	15.8958	+	0.833061i	1.24505	+	0.0652504i	0.581603	+	0.813473i	$0.302426\pi$
$164$	−4.62081	−	8.00348i	−0.360825	−	0.624966i
$165$	−24.3452	−	0.449511i	−1.89527	−	0.0349944i
$166$	−13.9398	−	8.04814i	−1.08194	−	0.624657i
$167$	−4.71303	−	9.24984i	−0.364705	−	0.715774i	0.633619	−	0.773645i	$-0.281569\pi$
$167$	−4.71303	−	9.24984i	−0.364705	−	0.715774i	−0.998324	+	0.0578713i	$0.981569\pi$
$168$	−1.37835	+	8.57667i	−0.106342	+	0.661704i
$169$	−4.50842	+	6.20531i	−0.346802	+	0.477332i
$170$	−13.8474	+	2.80619i	−1.06205	+	0.215225i
$171$	0.838379	+	0.754880i	0.0641125	+	0.0577271i
$172$	−0.523472	+	0.423899i	−0.0399143	+	0.0323220i
$173$	−15.9898	+	19.7458i	−1.21568	+	1.50124i	−0.406537	+	0.913634i	$0.633264\pi$
$173$	−15.9898	+	19.7458i	−1.21568	+	1.50124i	−0.809146	+	0.587608i	$0.800070\pi$
$174$	−0.979969	+	3.01603i	−0.0742912	+	0.228645i
$175$	−0.411337	−	13.2224i	−0.0310941	−	0.999516i
$176$	−2.36614	+	2.32409i	−0.178354	+	0.175185i
$177$	12.1697	−	3.26087i	0.914733	−	0.245102i
$178$	−14.7521	−	9.58011i	−1.10571	−	0.718059i
$179$	4.87585	−	10.9513i	0.364438	−	0.818542i	−0.634520	−	0.772907i	$-0.718802\pi$
$179$	4.87585	−	10.9513i	0.364438	−	0.818542i	0.998958	−	0.0456352i	$-0.0145312\pi$
$180$	−11.7627	+	12.8169i	−0.876737	+	0.955312i
$181$	−0.0133488	+	0.00433727i	−0.000992205	+	0.000322387i	−0.309513	−	0.950895i	$-0.600166\pi$
$181$	−0.0133488	+	0.00433727i	−0.000992205	+	0.000322387i	0.308521	+	0.951218i	$0.400166\pi$
$182$	−6.10042	+	0.305844i	−0.452193	+	0.0226706i
$183$	−25.9115	+	4.10398i	−1.91543	+	0.303375i
$184$	4.14910	−	0.436088i	0.305876	−	0.0321488i
$185$	−6.88496	−	1.15760i	−0.506192	−	0.0851084i
$186$	9.09930	+	15.7604i	0.667193	+	1.15561i
$187$	18.0542	+	10.6406i	1.32026	+	0.778115i
$188$	2.07916	+	2.07916i	0.151638	+	0.151638i
$189$	30.9193	−	27.7132i	2.24905	−	2.01584i
$190$	−0.313984	+	0.0809438i	−0.0227788	+	0.00587228i
$191$	−6.93812	+	3.08905i	−0.502025	+	0.223516i	−0.642094	−	0.766626i	$-0.721934\pi$
$191$	−6.93812	+	3.08905i	−0.502025	+	0.223516i	0.140069	+	0.990142i	$0.455267\pi$
$192$	0.171833	+	3.27877i	0.0124010	+	0.236625i
$193$	−0.602377	−	11.4940i	−0.0433600	−	0.827359i	−0.930597	−	0.366045i	$-0.880712\pi$
$193$	−0.602377	−	11.4940i	−0.0433600	−	0.827359i	0.887237	−	0.461314i	$-0.152622\pi$
$194$	14.4833	−	6.44840i	1.03984	−	0.462968i
$195$	−14.5972	−	8.61359i	−1.04533	−	0.616832i
$196$	4.66028	+	5.22320i	0.332877	+	0.373085i
$197$	1.71251	+	1.71251i	0.122011	+	0.122011i	0.765476	−	0.643465i	$-0.222504\pi$
$197$	1.71251	+	1.71251i	0.122011	+	0.122011i	−0.643465	+	0.765476i	$0.722504\pi$
$198$	25.6847	−	2.46698i	1.82533	−	0.175320i
$199$	9.14209	+	15.8346i	0.648066	+	1.12248i	0.983584	+	0.180449i	$0.0577551\pi$
$199$	9.14209	+	15.8346i	0.648066	+	1.12248i	−0.335519	+	0.942034i	$0.608912\pi$
$200$	−1.20213	−	4.85334i	−0.0850037	−	0.343183i
$201$	30.5401	−	3.20990i	2.15414	−	0.226409i
$202$	6.60796	−	1.04660i	0.464934	−	0.0736383i
$203$	1.38695	+	2.14635i	0.0973448	+	0.150644i
$204$	19.7304	−	6.41081i	1.38141	−	0.448846i
$205$	−15.2250	−	13.9727i	−1.06336	−	0.975897i
$206$	−0.294318	+	0.661050i	−0.0205061	+	0.0460575i
$207$	−27.2210	−	17.6775i	−1.89199	−	1.22867i
$208$	−2.22997	+	0.597520i	−0.154621	+	0.0414305i
$209$	0.426546	+	0.222175i	0.0295048	+	0.0153682i
$210$	2.81270	+	19.2194i	0.194095	+	1.32626i
$211$	−2.06936	+	6.36882i	−0.142460	+	0.438448i	−0.996676	−	0.0814715i	$-0.974038\pi$
$211$	−2.06936	+	6.36882i	−0.142460	+	0.438448i	0.854215	+	0.519919i	$0.174038\pi$
$212$	7.60094	−	9.38638i	0.522035	−	0.644659i
$213$	−9.84764	+	7.97446i	−0.674749	+	0.546401i
$214$	−2.30452	−	2.07500i	−0.157534	−	0.141844i
$215$	−0.832281	+	1.25534i	−0.0567611	+	0.0856133i
$216$	9.22447	−	12.6964i	0.627646	−	0.863880i
$217$	14.4791	+	2.32693i	0.982909	+	0.157962i
$218$	−6.93750	−	13.6156i	−0.469867	−	0.922166i
$219$	−29.7500	−	17.1762i	−2.01032	−	1.16066i
$220$	−3.48830	+	6.54460i	−0.235181	+	0.441237i
$221$	7.29373	+	12.6331i	0.490629	+	0.849795i
$222$	10.2372	+	0.536509i	0.687076	+	0.0360081i
$223$	−16.3022	−	2.58202i	−1.09168	−	0.172905i	−0.415463	−	0.909610i	$-0.636381\pi$
$223$	−16.3022	−	2.58202i	−1.09168	−	0.172905i	−0.676214	+	0.736705i	$0.736381\pi$
$224$	2.13693	+	1.55998i	0.142779	+	0.104231i
$225$	−16.4939	+	35.2294i	−1.09959	+	2.34863i
$226$	3.41799	+	0.726517i	0.227362	+	0.0483272i
$227$	4.09821	+	5.06087i	0.272008	+	0.335902i	0.894785	−	0.446498i	$-0.147329\pi$
$227$	4.09821	+	5.06087i	0.272008	+	0.335902i	−0.622777	+	0.782400i	$0.713996\pi$
$228$	0.444481	−	0.170620i	0.0294365	−	0.0112996i
$229$	10.0973	+	11.2142i	0.667247	+	0.741052i	0.977808	−	0.209501i	$-0.0671839\pi$
$229$	10.0973	+	11.2142i	0.667247	+	0.741052i	−0.310562	+	0.950553i	$0.600517\pi$
$230$	8.55791	−	3.71325i	0.564292	−	0.244844i
$231$	15.9618	−	23.9848i	1.05021	−	1.57809i
$232$	0.682980	+	0.682980i	0.0448398	+	0.0448398i
$233$	−11.4329	−	0.599171i	−0.748992	−	0.0392530i	−0.325980	−	0.945377i	$-0.605694\pi$
$233$	−11.4329	−	0.599171i	−0.748992	−	0.0392530i	−0.423013	+	0.906124i	$0.639027\pi$
$234$	16.4081	+	7.30536i	1.07263	+	0.477566i
$235$	5.82965	+	3.04043i	0.380284	+	0.198336i
$236$	0.797828	−	3.75349i	0.0519342	−	0.244331i
$237$	2.93600	+	1.49597i	0.190714	+	0.0971735i
$238$	6.02640	−	15.5936i	0.390634	−	1.01078i
$239$	−11.9122	−	16.3957i	−0.770535	−	1.06055i	−0.996264	−	0.0863598i	$-0.972477\pi$
$239$	−11.9122	−	16.3957i	−0.770535	−	1.06055i	0.225729	−	0.974190i	$-0.427523\pi$
$240$	2.56579	+	6.87867i	0.165621	+	0.444016i
$241$	1.32034	−	0.762301i	0.0850508	−	0.0491041i	−0.456871	−	0.889533i	$-0.651030\pi$
$241$	1.32034	−	0.762301i	0.0850508	−	0.0491041i	0.541922	+	0.840429i	$0.317697\pi$
$242$	10.3384	−	3.75729i	0.664578	−	0.241528i
$243$	−43.9148	+	11.7669i	−2.81713	+	0.754849i
$244$	−2.46915	+	7.59927i	−0.158071	+	0.486494i
$245$	13.4443	+	8.01566i	0.858925	+	0.512101i
$246$	24.5478	+	17.8350i	1.56511	+	1.13712i
$247$	0.182331	+	0.280764i	0.0116014	+	0.0178646i
$248$	5.53523	−	0.290089i	0.351487	−	0.0184207i
$249$	52.5589	+	5.52417i	3.33079	+	0.350080i
$250$	−5.81967	−	9.54628i	−0.368068	−	0.603760i
$251$	−17.5420	−	5.69975i	−1.10724	−	0.359765i	−0.302357	−	0.953195i	$-0.597773\pi$
$251$	−17.5420	−	5.69975i	−1.10724	−	0.359765i	−0.804886	+	0.593430i	$0.797773\pi$
$252$	−5.28234	−	19.8943i	−0.332756	−	1.25322i
$253$	−13.1207	−	4.39361i	−0.824893	−	0.276224i
$254$	−9.36177	−	5.40502i	−0.587410	−	0.339141i
$255$	37.7868	−	26.9092i	2.36630	−	1.68512i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	2.67757	−	6.97531i	0.167022	−	0.435108i	−0.824367	−	0.566056i	$-0.808469\pi$
$257$	2.67757	−	6.97531i	0.167022	−	0.435108i	0.991389	+	0.130948i	$0.0418020\pi$
$258$	1.00402	−	1.97051i	0.0625078	−	0.122678i
$259$	5.54142	−	6.12638i	0.344327	−	0.380675i
$260$	−4.35595	+	2.77033i	−0.270145	+	0.171809i
$261$	−0.785470	−	7.47325i	−0.0486194	−	0.462583i
$262$	−6.30079	+	9.70236i	−0.389264	+	0.599414i
$263$	27.5760	+	7.38896i	1.70041	+	0.455623i	0.973042	−	0.230628i	$-0.0740781\pi$
$263$	27.5760	+	7.38896i	1.70041	+	0.455623i	0.727365	+	0.686251i	$0.240745\pi$
$264$	3.99339	−	10.1307i	0.245776	−	0.623503i
$265$	9.91755	−	25.1204i	0.609230	−	1.54313i
$266$	0.119384	−	0.364610i	0.00731988	−	0.0223557i
$267$	57.0412	+	9.03443i	3.49086	+	0.552898i
$268$	3.35181	−	8.73176i	0.204744	−	0.533377i
$269$	8.20151	−	9.10869i	0.500055	−	0.555367i	−0.439288	−	0.898346i	$-0.644769\pi$
$269$	8.20151	−	9.10869i	0.500055	−	0.555367i	0.939343	+	0.342979i	$0.111436\pi$
$270$	11.1605	−	33.2700i	0.679205	−	2.02474i
$271$	4.61126	+	10.3571i	0.280114	+	0.629147i	0.997734	−	0.0672885i	$-0.0214348\pi$
$271$	4.61126	+	10.3571i	0.280114	+	0.629147i	−0.717619	+	0.696436i	$0.754768\pi$
$272$	0.988453	−	6.24085i	0.0599338	−	0.378407i
$273$	17.8893	−	9.06402i	1.08271	−	0.548579i
$274$			0.993372i			0.0600118i
$275$	−3.05103	+	16.3000i	−0.183984	+	0.982929i
$276$	−11.8625	+	6.84883i	−0.714040	+	0.412251i
$277$	9.09657	+	5.90738i	0.546560	+	0.354940i	0.788194	−	0.615427i	$-0.211017\pi$
$277$	9.09657	+	5.90738i	0.546560	+	0.354940i	−0.241634	+	0.970368i	$0.577683\pi$
$278$	5.08063	−	6.27406i	0.304716	−	0.376293i
$279$	−34.8868	−	25.3467i	−2.08862	−	1.51747i
$280$	5.60463	+	1.89423i	0.334941	+	0.113202i
$281$	6.05091	+	18.6228i	0.360967	+	1.11094i	0.952468	+	0.304639i	$0.0985357\pi$
$281$	6.05091	+	18.6228i	0.360967	+	1.11094i	−0.591501	+	0.806304i	$0.701464\pi$
$282$	−9.01283	−	3.45970i	−0.536706	−	0.206022i
$283$	5.14385	+	13.4002i	0.305770	+	0.796558i	0.997246	+	0.0741590i	$0.0236272\pi$
$283$	5.14385	+	13.4002i	0.305770	+	0.796558i	−0.691476	+	0.722399i	$0.743039\pi$
$284$	0.802420	+	3.77509i	0.0476149	+	0.224010i
$285$	0.833675	−	0.662087i	0.0493826	−	0.0392187i
$286$	7.55158	+	1.26555i	0.446534	+	0.0748336i
$287$	23.6322	−	6.27483i	1.39496	−	0.370392i
$288$	−3.53199	−	6.93191i	−0.208124	−	0.408467i
$289$	−22.7996	+	2.39634i	−1.34116	+	0.140961i
$290$	1.91497	+	0.998747i	0.112451	+	0.0586485i
$291$	−34.8302	+	38.6829i	−2.04178	+	2.26763i
$292$	−8.77488	+	5.69848i	−0.513511	+	0.333478i
$293$	0.757476	+	4.78252i	0.0442522	+	0.279398i	0.999885	−	0.0151630i	$-0.00482671\pi$
$293$	0.757476	+	4.78252i	0.0442522	+	0.279398i	−0.955633	+	0.294561i	$0.904827\pi$
$294$	−20.9533	−	9.44308i	−1.22202	−	0.550732i
$295$	−0.815831	−	8.54168i	−0.0474995	−	0.497316i
$296$	1.56113	−	2.70396i	0.0907390	−	0.157165i
$297$	−45.3079	+	25.6197i	−2.62903	+	1.48661i
$298$	0.682739	+	0.182939i	0.0395500	+	0.0105974i
$299$	−6.44476	−	7.15763i	−0.372710	−	0.413936i
$300$	10.0870	+	12.9518i	0.582372	+	0.747774i
$301$	−0.721165	−	1.62970i	−0.0415673	−	0.0939341i
$302$	2.81874	−	5.53208i	0.162200	−	0.318336i
$303$	−18.4224	+	11.9636i	−1.05834	+	0.687292i
$304$	0.0151576	−	0.144215i	0.000869346	−	0.00827127i
$305$	−0.169678	+	17.8662i	−0.00971572	+	1.02301i
$306$	−36.5317	+	32.8933i	−2.08838	+	1.88038i
$307$	3.68045	−	3.68045i	0.210054	−	0.210054i	−0.594236	−	0.804291i	$-0.702546\pi$
$307$	3.68045	−	3.68045i	0.210054	−	0.210054i	0.804291	+	0.594236i	$0.202546\pi$
$308$	−4.30185	−	7.64814i	−0.245121	−	0.435793i
$309$		−	2.37581i		−	0.135155i
$310$	11.6126	−	4.33157i	0.659550	−	0.246017i
$311$	−13.9764	+	31.3916i	−0.792531	+	1.78005i	−0.190309	+	0.981724i	$0.560949\pi$
$311$	−13.9764	+	31.3916i	−0.792531	+	1.78005i	−0.602222	+	0.798329i	$0.705718\pi$
$312$	5.89068	−	4.77018i	0.333494	−	0.270058i
$313$	−13.0633	−	20.1157i	−0.738380	−	1.13701i	−0.985772	−	0.168090i	$-0.946240\pi$
$313$	−13.0633	−	20.1157i	−0.738380	−	1.13701i	0.247391	−	0.968916i	$-0.420427\pi$
$314$	−2.44010	−	7.50987i	−0.137703	−	0.423806i
$315$	−24.6119	−	38.8931i	−1.38672	−	2.19138i
$316$	0.811945	−	0.589912i	0.0456754	−	0.0331852i
$317$	−0.861406	+	16.4366i	−0.0483814	+	0.923172i	0.861360	+	0.507996i	$0.169613\pi$
$317$	−0.861406	+	16.4366i	−0.0483814	+	0.923172i	−0.909741	+	0.415176i	$0.863720\pi$
$318$	−10.2636	+	38.3042i	−0.575553	+	2.14799i
$319$	−1.12116	−	3.00086i	−0.0627729	−	0.168016i
$320$	2.22150	+	0.254841i	0.124186	+	0.0142461i
$321$	9.68323	+	3.14627i	0.540465	+	0.175608i
$322$	−1.75143	+	10.8981i	−0.0976032	+	0.607328i
$323$	−0.904979	+	0.143335i	−0.0503544	+	0.00797535i
$324$	−5.86035	+	27.5708i	−0.325575	+	1.53171i
$325$	−7.43343	+	8.83116i	−0.412333	+	0.489865i
$326$	−1.66384	+	15.8304i	−0.0921515	+	0.876763i
$327$	38.9911	+	31.5744i	2.15621	+	1.74607i
$328$	8.23434	−	4.19561i	0.454665	−	0.231664i
$329$	−6.74604	+	3.87447i	−0.371921	+	0.213606i
$330$	1.72303	−	24.2884i	0.0948495	−	1.33703i
$331$	−5.82900	+	10.0961i	−0.320391	+	0.554933i	−0.980569	−	0.196176i	$-0.937147\pi$
$331$	−5.82900	+	10.0961i	−0.320391	+	0.554933i	0.660178	+	0.751109i	$0.270481\pi$
$332$	8.76666	−	13.4995i	0.481133	−	0.740880i
$333$	−22.6774	+	8.70505i	−1.24272	+	0.477034i
$334$	9.48382	−	4.22247i	0.518932	−	0.231043i
$335$	1.29284	−	20.8739i	0.0706354	−	1.14046i
$336$	−8.49278	−	1.82533i	−0.463319	−	0.0995798i
$337$	−0.351977	−	2.22230i	−0.0191734	−	0.121056i	0.976245	−	0.216669i	$-0.0695191\pi$
$337$	−0.351977	−	2.22230i	−0.0191734	−	0.121056i	−0.995419	+	0.0956123i	$0.969519\pi$
$338$	−5.96085	−	4.82701i	−0.324228	−	0.262554i
$339$	−11.2222	+	2.38535i	−0.609506	+	0.129555i
$340$	−2.07762	−	13.9753i	−0.112675	−	0.757918i
$341$	−17.1027	−	6.74164i	−0.926163	−	0.365080i
$342$	−0.797723	+	0.797723i	−0.0431359	+	0.0431359i
$343$	−16.5585	+	8.29560i	−0.894073	+	0.447920i
$344$	−0.395922	−	0.544939i	−0.0213467	−	0.0293812i
$345$	−20.7100	+	22.5661i	−1.11499	+	1.21492i
$346$	−18.8819	−	17.0013i	−1.01510	−	0.913996i
$347$	9.83007	−	0.515172i	0.527706	−	0.0276559i	0.213377	−	0.976970i	$-0.431554\pi$
$347$	9.83007	−	0.515172i	0.527706	−	0.0276559i	0.314329	+	0.949314i	$0.398220\pi$
$348$	−2.96061	−	1.13647i	−0.158705	−	0.0609213i
$349$	7.06484	−	5.13291i	0.378172	−	0.274758i	−0.382419	−	0.923989i	$-0.624909\pi$
$349$	7.06484	−	5.13291i	0.378172	−	0.274758i	0.760592	+	0.649231i	$0.224909\pi$
$350$	13.2258	+	0.281232i	0.706947	+	0.0150325i
$351$	−36.2309			−1.93386
$352$	−2.19707	−	2.48453i	−0.117104	−	0.132426i
$353$	8.41141	−	31.3918i	0.447694	−	1.67082i	−0.261030	−	0.965331i	$-0.584062\pi$
$353$	8.41141	−	31.3918i	0.447694	−	1.67082i	0.708724	−	0.705486i	$-0.249271\pi$
$354$	2.61949	+	12.3237i	0.139224	+	0.654998i
$355$	4.24380	+	7.51439i	0.225238	+	0.398822i
$356$	10.3390	−	14.2305i	0.547968	−	0.754213i
$357$	2.74836	+	54.8194i	0.145459	+	2.90135i
$358$	10.6812	+	5.44232i	0.564516	+	0.287635i
$359$	2.56944	+	5.77106i	0.135610	+	0.304585i	0.968567	−	0.248753i	$-0.0800206\pi$
$359$	2.56944	+	5.77106i	0.135610	+	0.304585i	−0.832957	+	0.553338i	$0.813354\pi$
$360$	−12.1837	−	12.4173i	−0.642136	−	0.654450i
$361$	18.5642	−	3.94595i	0.977065	−	0.207682i
$362$	−0.00363271	−	0.0135575i	−0.000190931	−	0.000712564i
$363$	−25.9916	+	25.0759i	−1.36421	+	1.31614i
$364$	0.0138468	−	6.10807i	0.000725771	−	0.320150i
$365$	−14.8954	+	18.0412i	−0.779659	+	0.944319i
$366$	−2.74225	−	26.0908i	−0.143340	−	1.36379i
$367$	−10.4212	−	12.8691i	−0.543980	−	0.671760i	0.428824	−	0.903388i	$-0.358928\pi$
$367$	−10.4212	−	12.8691i	−0.543980	−	0.671760i	−0.972804	+	0.231628i	$0.925595\pi$
$368$	0.218343	+	4.16624i	0.0113819	+	0.217180i
$369$	−70.3274	−	14.9486i	−3.66110	−	0.778191i
$370$	1.51634	−	6.81494i	0.0788310	−	0.354292i
$371$	18.7243	+	25.8950i	0.972116	+	1.34440i
$372$	−16.2151	+	8.26199i	−0.840712	+	0.428364i
$373$	−4.85971	−	18.1367i	−0.251626	−	0.939082i	−0.969936	−	0.243359i	$-0.921751\pi$
$373$	−4.85971	−	18.1367i	−0.251626	−	0.939082i	0.718310	−	0.695723i	$-0.244916\pi$
$374$	−11.5709	+	17.4726i	−0.598315	+	0.903488i
$375$	30.2040	+	20.8615i	1.55973	+	1.07729i
$376$	−2.18512	+	1.96749i	−0.112689	+	0.101466i
$377$	0.348828	−	2.20241i	0.0179656	−	0.113430i
$378$	26.0570	+	32.3273i	1.34023	+	1.66274i
$379$	−13.2082	+	4.29161i	−0.678460	+	0.220445i	−0.627921	−	0.778277i	$-0.716094\pi$
$379$	−13.2082	+	4.29161i	−0.678460	+	0.220445i	−0.0505390	+	0.998722i	$0.516094\pi$
$380$	−0.0644003	−	0.317790i	−0.00330366	−	0.0163023i
$381$	35.2979	+	3.70995i	1.80836	+	0.190067i
$382$	−2.72170	−	7.09028i	−0.139254	−	0.362770i
$383$	−1.88069	+	35.8857i	−0.0960988	+	1.83367i	0.347767	+	0.937581i	$0.386940\pi$
$383$	−1.88069	+	35.8857i	−0.0960988	+	1.83367i	−0.443866	+	0.896093i	$0.646393\pi$
$384$	−3.28327			−0.167549
$385$	−14.3063	−	13.4287i	−0.729116	−	0.684390i
$386$	11.5098			0.585834
$387$	−0.274260	+	5.23320i	−0.0139414	+	0.266018i
$388$	5.68156	+	14.8010i	0.288437	+	0.751405i
$389$	−5.64936	−	0.593772i	−0.286434	−	0.0301054i	−0.0397780	−	0.999209i	$-0.512665\pi$
$389$	−5.64936	−	0.593772i	−0.286434	−	0.0301054i	−0.246656	+	0.969103i	$0.579332\pi$
$390$	9.36574	−	14.1264i	0.474253	−	0.715320i
$391$	25.0709	−	8.14603i	1.26789	−	0.411962i
$392$	−5.45994	+	4.38053i	−0.275769	+	0.221250i
$393$	5.94190	−	37.5157i	0.299729	−	1.89241i
$394$	−1.79979	+	1.62054i	−0.0906722	+	0.0816416i
$395$	1.33627	−	1.80295i	0.0672349	−	0.0907165i
$396$	1.11936	+	25.7786i	0.0562500	+	1.29542i
$397$	−6.52734	−	24.3604i	−0.327598	−	1.22261i	−0.911674	−	0.410913i	$-0.865210\pi$
$397$	−6.52734	−	24.3604i	−0.327598	−	1.22261i	0.584076	−	0.811699i	$-0.301457\pi$
$398$	−16.2913	+	8.30085i	−0.816610	+	0.416084i
$399$	0.128829	+	1.25305i	0.00644953	+	0.0627308i
$400$	4.90960	−	0.946483i	0.245480	−	0.0473242i
$401$	15.3931	+	3.27190i	0.768694	+	0.163391i	0.575536	−	0.817777i	$-0.304794\pi$
$401$	15.3931	+	3.27190i	0.768694	+	0.163391i	0.193158	+	0.981168i	$0.438127\pi$
$402$	1.60715	+	30.6663i	0.0801574	+	1.52949i
$403$	−8.05302	−	9.94466i	−0.401150	−	0.495379i
$404$	0.699330	+	6.65368i	0.0347929	+	0.331033i
$405$	5.99259	+	62.7420i	0.297774	+	3.11767i
$406$	−2.21600	+	1.27272i	−0.109978	+	0.0631640i
$407$	−8.43191	+	6.01139i	−0.417954	+	0.297974i
$408$	5.36941	+	20.0389i	0.265825	+	0.992074i
$409$	−6.01253	+	1.27800i	−0.297300	+	0.0631931i	−0.354147	−	0.935190i	$-0.615229\pi$
$409$	−6.01253	+	1.27800i	−0.297300	+	0.0631931i	0.0568466	+	0.998383i	$0.481895\pi$
$410$	14.7504	−	14.4729i	0.728470	−	0.714763i
$411$	−1.32658	−	2.97954i	−0.0654352	−	0.146970i
$412$	−0.644741	−	0.328512i	−0.0317641	−	0.0161846i
$413$	9.03561	+	4.62970i	0.444613	+	0.227813i
$414$	19.0779	−	26.2585i	0.937628	−	1.29053i
$415$	9.64526	−	34.6759i	0.473467	−	1.70217i
$416$	−0.479993	−	2.25819i	−0.0235336	−	0.110717i
$417$	−6.86039	+	25.6033i	−0.335955	+	1.25380i
$418$	−0.244194	+	0.414334i	−0.0119439	+	0.0202657i
$419$	−36.6058			−1.78831			−0.894155	−	0.447758i	$-0.852223\pi$
$419$	−36.6058			−1.78831			−0.894155	+	0.447758i	$0.852223\pi$
$420$	−19.3402	+	1.80299i	−0.943707	+	0.0879767i
$421$	−4.14478	+	3.01136i	−0.202004	+	0.146765i	−0.684189	−	0.729305i	$-0.739844\pi$
$421$	−4.14478	+	3.01136i	−0.202004	+	0.146765i	0.482184	+	0.876070i	$0.339844\pi$
$422$	−6.25179	−	2.39984i	−0.304333	−	0.116822i
$423$	22.8444	−	1.19722i	1.11073	−	0.0582110i
$424$	8.97572	+	8.08177i	0.435899	+	0.392486i
$425$	−13.8058	−	28.4171i	−0.669679	−	1.37843i
$426$	−7.44815	−	10.2515i	−0.360864	−	0.496687i
$427$	−17.7037	−	11.5541i	−0.856744	−	0.559142i
$428$	2.19277	−	2.19277i	0.105991	−	0.105991i
$429$	−24.3404	+	6.28866i	−1.17516	+	0.303619i
$430$	−1.21006	−	0.896840i	−0.0583542	−	0.0432495i
$431$	10.5464	−	2.24171i	0.508003	−	0.107979i	0.0532222	−	0.998583i	$-0.483051\pi$
$431$	10.5464	−	2.24171i	0.508003	−	0.107979i	0.454781	+	0.890603i	$0.349718\pi$
$432$	12.1962	+	9.87630i	0.586791	+	0.475174i
$433$	−1.65466	−	10.4471i	−0.0795180	−	0.502057i	−0.995014	−	0.0997309i	$-0.968202\pi$
$433$	−1.65466	−	10.4471i	−0.0795180	−	0.502057i	0.915496	−	0.402326i	$-0.131798\pi$
$434$	−3.08152	+	14.3375i	−0.147918	+	0.688223i
$435$	−7.07756	−	0.438354i	−0.339343	−	0.0210175i
$436$	13.9600	−	6.21541i	0.668564	−	0.297664i
$437$	0.564789	−	0.216802i	0.0270175	−	0.0103711i
$438$	18.7096	−	28.8103i	0.893981	−	1.37661i
$439$	−7.74274	+	13.4108i	−0.369541	+	0.640064i	−0.989494	−	0.144575i	$-0.953818\pi$
$439$	−7.74274	+	13.4108i	−0.369541	+	0.640064i	0.619953	+	0.784639i	$0.287152\pi$
$440$	−6.35307	−	3.82603i	−0.302871	−	0.182399i
$441$	54.4585	+	0.246913i	2.59326	+	0.0117578i
$442$	−12.9975	+	6.62257i	−0.618229	+	0.315003i
$443$	−12.2690	−	9.93523i	−0.582917	−	0.472037i	0.291928	−	0.956440i	$-0.405703\pi$
$443$	−12.2690	−	9.93523i	−0.582917	−	0.472037i	−0.874845	+	0.484403i	$0.839037\pi$
$444$	−1.07155	+	10.1951i	−0.0508534	+	0.483837i
$445$	12.5090	−	37.2899i	0.592982	−	1.76771i
$446$	3.43167	−	16.1447i	0.162494	−	0.764476i
$447$	−2.29212	+	0.363036i	−0.108414	+	0.0171710i
$448$	−1.66968	+	2.05236i	−0.0788851	+	0.0969647i
$449$	3.26633	+	1.06130i	0.154148	+	0.0500857i	0.385074	−	0.922885i	$-0.374176\pi$
$449$	3.26633	+	1.06130i	0.154148	+	0.0500857i	−0.230927	+	0.972971i	$0.574176\pi$
$450$	−34.3179	−	18.3150i	−1.61776	−	0.863378i
$451$	−30.6221	+	1.32968i	−1.44194	+	0.0626120i
$452$	−0.904406	+	3.37529i	−0.0425397	+	0.158760i
$453$	−1.06688	+	20.3572i	−0.0501263	+	0.956467i
$454$	−5.26842	+	3.82773i	−0.247259	+	0.179644i
$455$	−4.06749	−	13.0384i	−0.190687	−	0.611248i
$456$	0.147124	+	0.452801i	0.00688972	+	0.0212044i
$457$	13.4486	+	20.7090i	0.629098	+	0.968726i	0.999210	+	0.0397392i	$0.0126527\pi$
$457$	13.4486	+	20.7090i	0.629098	+	0.968726i	−0.370112	+	0.928987i	$0.620681\pi$
$458$	−11.7272	+	9.49653i	−0.547978	+	0.443744i
$459$	40.3329	−	90.5892i	1.88258	−	4.22834i
$460$	3.26028	+	8.74052i	0.152011	+	0.407529i
$461$		−	36.3578i		−	1.69335i	−0.532108	−	0.846676i	$-0.678600\pi$
$461$		−	36.3578i		−	1.69335i	0.532108	−	0.846676i	$-0.321400\pi$
$462$	23.1166	+	17.1952i	1.07548	+	0.799991i
$463$	4.19661	−	4.19661i	0.195033	−	0.195033i	−0.602834	−	0.797867i	$-0.705962\pi$
$463$	4.19661	−	4.19661i	0.195033	−	0.195033i	0.797867	+	0.602834i	$0.205962\pi$
$464$	−0.717788	+	0.646300i	−0.0333225	+	0.0300037i
$465$	−29.0465	+	28.4999i	−1.34700	+	1.32165i
$466$	1.19670	−	11.3858i	0.0554361	−	0.527439i
$467$	16.6221	−	10.7945i	0.769179	−	0.499511i	−0.0994082	−	0.995047i	$-0.531695\pi$
$467$	16.6221	−	10.7945i	0.769179	−	0.499511i	0.868587	+	0.495536i	$0.165028\pi$
$468$	−8.15408	+	16.0033i	−0.376923	+	0.739752i
$469$	19.9866	+	14.5905i	0.922897	+	0.673726i
$470$	−3.34136	+	5.66253i	−0.154126	+	0.261193i
$471$	17.3478	+	19.2667i	0.799343	+	0.887760i
$472$	3.70659	+	0.993177i	0.170609	+	0.0457147i
$473$	0.444870	+	2.18928i	0.0204551	+	0.100663i
$474$	−1.64758	+	2.85369i	−0.0756757	+	0.131074i
$475$	−0.350531	−	0.634679i	−0.0160835	−	0.0291211i
$476$	15.2568	+	6.83425i	0.699294	+	0.313247i
$477$	−14.6994	−	92.8085i	−0.673041	−	4.24941i
$478$	16.9967	−	11.0378i	0.777409	−	0.504856i
$479$	−4.69174	+	5.21070i	−0.214371	+	0.238083i	−0.840734	−	0.541448i	$-0.817876\pi$
$479$	−4.69174	+	5.21070i	−0.214371	+	0.238083i	0.626363	+	0.779532i	$0.284543\pi$
$480$	−7.00352	+	2.20227i	−0.319666	+	0.100520i
$481$	−7.16870	+	0.753460i	−0.326864	+	0.0343548i
$482$	0.692155	+	1.35843i	0.0315268	+	0.0618748i
$483$	−9.30038	−	35.0269i	−0.423182	−	1.59378i
$484$	3.21107	+	10.5209i	0.145958	+	0.478222i
$485$	22.0471	+	27.7609i	1.00111	+	1.26056i
$486$	−9.45248	−	44.4704i	−0.428773	−	2.01722i
$487$	9.29336	+	24.2100i	0.421122	+	1.09706i	0.965999	+	0.258545i	$0.0832431\pi$
$487$	9.29336	+	24.2100i	0.421122	+	1.09706i	−0.544877	+	0.838516i	$0.683424\pi$
$488$	−7.45963	−	2.86348i	−0.337682	−	0.129624i
$489$	−16.1497	−	49.7038i	−0.730317	−	2.24768i
$490$	−8.70829	+	13.0064i	−0.393400	+	0.587568i
$491$	−20.7352	−	15.0650i	−0.935768	−	0.679875i	0.0116300	−	0.999932i	$-0.496298\pi$
$491$	−20.7352	−	15.0650i	−0.935768	−	0.679875i	−0.947398	+	0.320057i	$0.896298\pi$
$492$	−19.0953	+	23.5807i	−0.860883	+	1.06310i
$493$	5.11845	+	3.32396i	0.230523	+	0.149704i
$494$	−0.289922	+	0.167387i	−0.0130442	+	0.00753108i
$495$	19.6789	+	54.2374i	0.884499	+	2.43779i
$496$			5.54283i			0.248880i
$497$	−10.1959	−	0.557522i	−0.457346	−	0.0250083i
$498$	−8.26732	+	52.1978i	−0.370467	+	2.33904i
$499$	9.25202	+	20.7804i	0.414177	+	0.930257i	0.993359	+	0.115059i	$0.0367056\pi$
$499$	9.25202	+	20.7804i	0.414177	+	0.930257i	−0.579181	+	0.815199i	$0.696628\pi$
$500$	9.83777	−	5.31208i	0.439959	−	0.237563i
$501$	−22.8071	+	25.3299i	−1.01895	+	1.13166i
$502$	6.61001	−	17.2197i	0.295019	−	0.768552i
$503$	21.5171	+	3.40797i	0.959400	+	0.151954i	0.616445	−	0.787398i	$-0.288572\pi$
$503$	21.5171	+	3.40797i	0.959400	+	0.151954i	0.342955	+	0.939352i	$0.388572\pi$
$504$	20.1434	−	4.23392i	0.897260	−	0.188594i
$505$	5.95473	+	13.7238i	0.264982	+	0.610702i
$506$	5.07428	−	12.8728i	0.225579	−	0.572266i
$507$	24.3252	+	6.51792i	1.08032	+	0.289471i
$508$	5.88757	−	9.06606i	0.261219	−	0.402241i
$509$	1.64534	+	15.6543i	0.0729283	+	0.693867i	0.968511	+	0.248971i	$0.0800925\pi$
$509$	1.64534	+	15.6543i	0.0729283	+	0.693867i	−0.895583	+	0.444895i	$0.853241\pi$
$510$	24.8947	+	39.1433i	1.10235	+	1.73329i
$511$	−8.49453	−	26.3466i	−0.375776	−	1.16550i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	0.815542	−	2.12456i	0.0360071	−	0.0938016i
$514$	6.82562	+	3.03896i	0.301065	+	0.134043i
$515$	−1.59564	−	0.268283i	−0.0703124	−	0.0118219i
$516$	1.91526	+	1.10578i	0.0843147	+	0.0486791i
$517$	9.30146	−	2.93030i	0.409078	−	0.128874i
$518$	5.82797	+	5.85445i	0.256066	+	0.257230i
$519$	79.3386	+	25.7787i	3.48258	+	1.13156i
$520$	−2.53856	−	4.49497i	−0.111323	−	0.197117i
$521$	−2.17899	−	0.229021i	−0.0954633	−	0.0100336i	0.0566764	−	0.998393i	$-0.481950\pi$
$521$	−2.17899	−	0.229021i	−0.0954633	−	0.0100336i	−0.152140	+	0.988359i	$0.548616\pi$
$522$	7.50412	−	0.393274i	0.328446	−	0.0172131i
$523$	−23.6805	−	36.4648i	−1.03548	−	1.59449i	−0.778055	−	0.628196i	$-0.783794\pi$
$523$	−23.6805	−	36.4648i	−1.03548	−	1.59449i	−0.257422	−	0.966299i	$-0.582873\pi$
$524$	−9.35930	−	6.79993i	−0.408863	−	0.297056i
$525$	−40.0452	+	16.8185i	−1.74771	+	0.734020i
$526$	−8.82205	+	27.1515i	−0.384659	+	1.18386i
$527$	33.8297	−	9.06465i	1.47365	−	0.394862i
$528$	9.90784	+	4.51811i	0.431183	+	0.196626i
$529$	4.84523	−	2.79739i	0.210662	−	0.121626i
$530$	24.5669	+	11.2187i	1.06712	+	0.487307i
$531$	−17.5477	−	24.1524i	−0.761507	−	1.04812i
$532$	0.357863	+	0.138302i	0.0155153	+	0.00599616i
$533$	−19.0101	−	9.68614i	−0.823420	−	0.419553i
$534$	−12.0074	+	56.4902i	−0.519609	+	2.44457i
$535$	3.20656	−	6.14819i	0.138632	−	0.265809i
$536$	8.54437	+	3.80420i	0.369061	+	0.164316i
$537$	−39.3050	−	2.05989i	−1.69614	−	0.0888908i
$538$	8.66698	+	8.66698i	0.373660	+	0.373660i
$539$	22.5044	−	5.70558i	0.969332	−	0.245757i
$540$	32.6403	+	12.8864i	1.40461	+	0.554542i
$541$	19.0447	+	21.1513i	0.818796	+	0.909365i	0.997214	−	0.0745897i	$-0.0237647\pi$
$541$	19.0447	+	21.1513i	0.818796	+	0.909365i	−0.178418	+	0.983955i	$0.557098\pi$
$542$	−10.5842	+	4.06290i	−0.454631	+	0.174516i
$543$	0.0290010	+	0.0358133i	0.00124455	+	0.00153689i
$544$	6.18056	+	1.31372i	0.264989	+	0.0563253i
$545$	25.6090	−	22.6218i	1.09697	−	0.969012i
$546$	8.11534	+	18.3391i	0.347305	+	0.784843i
$547$	−39.5050	−	6.25698i	−1.68911	−	0.267529i	−0.763447	−	0.645870i	$-0.776495\pi$
$547$	−39.5050	−	6.25698i	−1.68911	−	0.267529i	−0.925666	+	0.378341i	$0.876495\pi$
$548$	−0.992011	−	0.0519891i	−0.0423766	−	0.00222086i
$549$	31.0819	+	53.8355i	1.32654	+	2.29764i
$550$	−16.1180	−	3.89993i	−0.687275	−	0.166294i
$551$	0.121297	+	0.0700306i	0.00516741	+	0.00298340i
$552$	−6.21861	−	12.2047i	−0.264682	−	0.519467i
$553$	0.945961	+	2.48111i	0.0402264	+	0.105508i
$554$	−6.37536	+	8.77493i	−0.270863	+	0.372811i
$555$	4.55270	+	22.4658i	0.193252	+	0.953621i
$556$	5.99956	+	5.40203i	0.254438	+	0.229097i
$557$	−13.0902	+	10.6002i	−0.554650	+	0.449147i	−0.865212	−	0.501406i	$-0.832816\pi$
$557$	−13.0902	+	10.6002i	−0.554650	+	0.449147i	0.310562	+	0.950553i	$0.399483\pi$
$558$	27.1378	−	33.5124i	1.14884	−	1.41869i
$559$	−0.480539	+	1.47895i	−0.0203246	+	0.0625528i
$560$	−2.18496	+	5.49781i	−0.0923313	+	0.232325i
$561$	11.3725	−	67.8597i	0.480146	−	2.86504i
$562$	−18.9140	+	5.06798i	−0.797837	+	0.213780i
$563$	23.1183	+	15.0132i	0.974318	+	0.632730i	0.930493	−	0.366310i	$-0.119379\pi$
$563$	23.1183	+	15.0132i	0.974318	+	0.632730i	0.0438251	+	0.999039i	$0.486046\pi$
$564$	3.92665	−	8.81941i	0.165342	−	0.371364i
$565$	0.334812	+	7.80644i	0.0140857	+	0.328419i
$566$	−13.6510	+	4.43549i	−0.573795	+	0.186437i
$567$	−66.3700	−	34.0069i	−2.78728	−	1.42816i
$568$	−3.81191	+	0.603747i	−0.159944	+	0.0253327i
$569$	26.5547	−	2.79101i	1.11323	−	0.117005i	0.469992	−	0.882670i	$-0.344257\pi$
$569$	26.5547	−	2.79101i	1.11323	−	0.117005i	0.643239	+	0.765665i	$0.277590\pi$
$570$	0.617549	+	0.867183i	0.0258663	+	0.0363223i
$571$	−3.78937	−	6.56338i	−0.158580	−	0.274669i	0.775777	−	0.631008i	$-0.217358\pi$
$571$	−3.78937	−	6.56338i	−0.158580	−	0.274669i	−0.934357	+	0.356339i	$0.884025\pi$
$572$	−1.65904	+	7.47499i	−0.0693678	+	0.312545i
$573$	17.6321	+	17.6321i	0.736590	+	0.736590i
$574$	5.02942	+	23.9282i	0.209924	+	0.998743i
$575$	12.8172	+	16.4575i	0.534515	+	0.686325i
$576$	7.10726	−	3.16436i	0.296136	−	0.131848i
$577$	−1.89026	−	36.0683i	−0.0786926	−	1.50154i	−0.697831	−	0.716262i	$-0.745851\pi$
$577$	−1.89026	−	36.0683i	−0.0786926	−	1.50154i	0.619138	−	0.785282i	$-0.287482\pi$
$578$	−1.19981	−	22.8938i	−0.0499057	−	0.952257i
$579$	−34.5227	+	15.3705i	−1.43471	+	0.638776i
$580$	−1.09760	+	1.86008i	−0.0455754	+	0.0772355i
$581$	28.4243	+	31.7126i	1.17924	+	1.31566i
$582$	−36.8070	−	36.8070i	−1.52570	−	1.52570i
$583$	−15.9644	−	36.7396i	−0.661179	−	1.52160i
$584$	−5.23142	−	9.06109i	−0.216478	−	0.374951i
$585$	−6.65912	+	39.6059i	−0.275321	+	1.63750i
$586$	−4.81561	+	0.506141i	−0.198931	+	0.0209085i
$587$	−6.09349	+	0.965115i	−0.251505	+	0.0398345i	−0.280914	−	0.959733i	$-0.590638\pi$
$587$	−6.09349	+	0.965115i	−0.251505	+	0.0398345i	0.0294087	+	0.999567i	$0.490638\pi$
$588$	10.5268	−	20.4304i	0.434116	−	0.842535i
$589$	0.764420	−	0.248375i	0.0314974	−	0.0102341i
$590$	8.57267	−	0.367676i	0.352931	−	0.0151370i
$591$	3.23421	−	7.26416i	0.133038	−	0.298808i
$592$	2.61855	+	1.70051i	0.107622	+	0.0698904i
$593$	3.46382	−	0.928126i	0.142242	−	0.0381136i	−0.186996	−	0.982361i	$-0.559875\pi$
$593$	3.46382	−	0.928126i	0.142242	−	0.0381136i	0.329237	+	0.944247i	$0.393208\pi$
$594$	−23.2134	−	46.5867i	−0.952457	−	1.91147i
$595$	37.1283	+	4.34450i	1.52211	+	0.178107i
$596$	−0.218420	+	0.672229i	−0.00894684	+	0.0275356i
$597$	37.7793	−	46.6536i	1.54620	−	1.90940i
$598$	7.48511	−	6.06132i	0.306089	−	0.247866i
$599$	10.9239	+	9.83596i	0.446340	+	0.401886i	0.861416	−	0.507900i	$-0.169578\pi$
$599$	10.9239	+	9.83596i	0.446340	+	0.401886i	−0.415076	+	0.909787i	$0.636245\pi$
$600$	−13.4620	+	9.39531i	−0.549583	+	0.383562i
$601$	−22.9365	+	31.5694i	−0.935601	+	1.28774i	0.0220334	+	0.999757i	$0.492986\pi$
$601$	−22.9365	+	31.5694i	−0.935601	+	1.28774i	−0.957634	+	0.287987i	$0.907014\pi$
$602$	1.66521	−	0.634885i	0.0678687	−	0.0258760i
$603$	−33.0346	−	64.8340i	−1.34527	−	2.64025i
$604$	5.37698	+	3.10440i	0.218786	+	0.126316i
$605$	13.9065	+	20.2882i	0.565378	+	0.824832i
$606$	−10.9831	−	19.0232i	−0.446157	−	0.772767i
$607$	35.2758	+	1.84872i	1.43180	+	0.0750374i	0.752388	−	0.658720i	$-0.228902\pi$
$607$	35.2758	+	1.84872i	1.43180	+	0.0750374i	0.679411	+	0.733758i	$0.262235\pi$
$608$	0.143224	+	0.0226844i	0.00580848	+	0.000919974i
$609$	4.94708	−	6.77672i	0.200466	−	0.274606i
$610$	−17.8328	−	1.10449i	−0.722028	−	0.0447194i
$611$	6.63992	+	1.41136i	0.268623	+	0.0570975i
$612$	−30.9363	−	38.2031i	−1.25052	−	1.54427i
$613$	−6.09754	+	2.34062i	−0.246277	+	0.0945369i	−0.478376	−	0.878155i	$-0.658774\pi$
$613$	−6.09754	+	2.34062i	−0.246277	+	0.0945369i	0.232098	+	0.972692i	$0.425441\pi$
$614$	3.48279	+	3.86803i	0.140554	+	0.156101i
$615$	−24.9151	+	63.1082i	−1.00468	+	2.54477i
$616$	7.86280	−	3.89568i	0.316801	−	0.156962i
$617$	2.61329	+	2.61329i	0.105207	+	0.105207i	0.757751	−	0.652544i	$-0.226298\pi$
$617$	2.61329	+	2.61329i	0.105207	+	0.105207i	−0.652544	+	0.757751i	$0.726298\pi$
$618$	2.37255	+	0.124340i	0.0954379	+	0.00500169i
$619$	9.78367	+	4.35597i	0.393239	+	0.175081i	0.593824	−	0.804595i	$-0.297618\pi$
$619$	9.78367	+	4.35597i	0.393239	+	0.175081i	−0.200585	+	0.979676i	$0.564284\pi$
$620$	3.71788	+	11.8234i	0.149314	+	0.474838i
$621$	−13.6126	+	64.0423i	−0.546255	+	2.56993i
$622$	−30.6171	−	15.6002i	−1.22763	−	0.625510i
$623$	29.2054	+	36.2334i	1.17009	+	1.45166i
$624$	4.45535	+	6.13226i	0.178357	+	0.245487i
$625$	17.4218	−	17.9299i	0.696871	−	0.717196i
$626$	20.7718	−	11.9926i	0.830208	−	0.479321i
$627$	0.179128	−	1.56886i	0.00715370	−	0.0626544i
$628$	7.62728	−	2.04372i	0.304362	−	0.0815535i
$629$	6.09643	−	18.7629i	0.243081	−	0.748126i
$630$	40.1279	−	22.5427i	1.59873	−	0.898122i
$631$	26.8430	+	19.5026i	1.06860	+	0.776387i	0.975661	−	0.219285i	$-0.0703724\pi$
$631$	26.8430	+	19.5026i	1.06860	+	0.776387i	0.0929436	+	0.995671i	$0.470372\pi$
$632$	0.546610	+	0.841705i	0.0217430	+	0.0334812i
$633$	21.9565	−	1.15069i	0.872694	−	0.0457360i
$634$	−16.3690	−	1.72045i	−0.650096	−	0.0683278i
$635$	6.47762	−	23.2879i	0.257057	−	0.924151i
$636$	−37.7145	−	12.2542i	−1.49548	−	0.485910i
$637$	15.5907	+	4.25337i	0.617726	+	0.168525i
$638$	3.05542	−	0.962571i	0.120965	−	0.0381085i
$639$	26.0031	+	15.0129i	1.02867	+	0.593902i
$640$	−0.370756	+	2.20512i	−0.0146554	+	0.0871649i
$641$	2.20961	+	0.983783i	0.0872744	+	0.0388571i	0.449910	−	0.893074i	$-0.351456\pi$
$641$	2.20961	+	0.983783i	0.0872744	+	0.0388571i	−0.362635	+	0.931931i	$0.618123\pi$
$642$	−3.64874	+	9.50530i	−0.144004	+	0.375144i
$643$	−3.09265	+	6.06966i	−0.121962	+	0.239364i	−0.943913	−	0.330194i	$-0.892886\pi$
$643$	−3.09265	+	6.06966i	−0.121962	+	0.239364i	0.821951	+	0.569558i	$0.192886\pi$
$644$	−10.7915	−	2.31939i	−0.425246	−	0.0913968i
$645$	4.82714	+	1.07405i	0.190068	+	0.0422907i
$646$	−0.0957752	−	0.911240i	−0.00376822	−	0.0358523i
$647$	9.41009	−	14.4903i	0.369949	−	0.569671i	−0.603845	−	0.797101i	$-0.706366\pi$
$647$	9.41009	−	14.4903i	0.369949	−	0.569671i	0.973794	+	0.227430i	$0.0730323\pi$
$648$	−27.2263	−	7.29527i	−1.06955	−	0.286585i
$649$	−9.81855	−	8.09772i	−0.385412	−	0.317863i
$650$	−8.43002	−	7.88543i	−0.330653	−	0.309292i
$651$	−9.90394	−	47.1194i	−0.388166	−	1.84675i
$652$	−15.7216	−	2.49006i	−0.615705	−	0.0975181i
$653$	10.9332	−	28.4819i	0.427848	−	1.11458i	−0.535075	−	0.844805i	$-0.679717\pi$
$653$	10.9332	−	28.4819i	0.427848	−	1.11458i	0.962923	−	0.269777i	$-0.0869501\pi$
$654$	−33.5717	+	37.2852i	−1.31276	+	1.45797i
$655$	−24.5254	−	8.22708i	−0.958285	−	0.321459i
$656$	3.75890	+	8.44264i	0.146761	+	0.329630i
$657$	−12.7337	+	80.3974i	−0.496789	+	3.13660i
$658$	−3.51610	−	6.93957i	−0.137072	−	0.270533i
$659$		−	38.7077i		−	1.50784i	−0.656967	−	0.753919i	$-0.728161\pi$
$659$		−	38.7077i		−	1.50784i	0.656967	−	0.753919i	$-0.271839\pi$
$660$	24.1649	+	2.99182i	0.940617	+	0.116456i
$661$	−11.7200	+	6.76652i	−0.455853	+	0.263187i	−0.710299	−	0.703900i	$-0.751440\pi$
$661$	−11.7200	+	6.76652i	−0.455853	+	0.263187i	0.254446	+	0.967087i	$0.418107\pi$
$662$	−9.77722	−	6.34940i	−0.380002	−	0.246776i
$663$	30.1410	−	37.2211i	1.17058	−	1.44555i
$664$	13.0222	+	9.46116i	0.505358	+	0.367164i
$665$	0.856121	+	0.0549730i	0.0331990	+	0.00213176i
$666$	−7.50627	−	23.1019i	−0.290862	−	0.895182i
$667$	−3.76196	−	1.44408i	−0.145664	−	0.0559151i
$668$	3.72034	+	9.69181i	0.143944	+	0.374987i
$669$	11.2671	+	53.0076i	0.435612	+	2.04939i
$670$	20.7776	+	2.38352i	0.802710	+	0.0920836i
$671$	18.5703	+	18.9063i	0.716898	+	0.729868i
$672$	2.26730	−	8.38561i	0.0874631	−	0.323482i
$673$	−0.144864	−	0.284312i	−0.00558410	−	0.0109594i	0.888198	−	0.459462i	$-0.151958\pi$
$673$	−0.144864	−	0.284312i	−0.00558410	−	0.0109594i	−0.893782	+	0.448502i	$0.851958\pi$
$674$	2.23767	−	0.235189i	0.0861920	−	0.00905914i
$675$	78.2684	+	5.59423i	3.01255	+	0.215322i
$676$	5.13236	−	5.70006i	0.197398	−	0.219233i
$677$	−1.56565	+	1.01674i	−0.0601727	+	0.0390766i	−0.574375	−	0.818592i	$-0.694755\pi$
$677$	−1.56565	+	1.01674i	−0.0601727	+	0.0390766i	0.514202	+	0.857669i	$0.328088\pi$
$678$	−1.79476	−	11.3317i	−0.0689273	−	0.435190i
$679$	−41.7257	+	4.28994i	−1.60129	+	0.164633i
$680$	14.0649	−	1.34336i	0.539364	−	0.0515156i
$681$	10.6905	−	18.5165i	0.409662	−	0.709556i
$682$	7.62749	−	16.7264i	0.292072	−	0.640488i
$683$	−22.2445	−	5.96039i	−0.851162	−	0.228068i	−0.193237	−	0.981152i	$-0.561899\pi$
$683$	−22.2445	−	5.96039i	−0.851162	−	0.228068i	−0.657924	+	0.753084i	$0.728565\pi$
$684$	−0.754880	−	0.838379i	−0.0288636	−	0.0320562i
$685$	−2.15092	+	0.554500i	−0.0821826	+	0.0211863i
$686$	−7.41763	−	16.9699i	−0.283206	−	0.647915i
$687$	22.4930	−	44.1449i	0.858160	−	1.68423i
$688$	0.564914	−	0.366859i	0.0215371	−	0.0139864i
$689$	2.91465	−	27.7310i	0.111039	−	1.05647i
$690$	−21.4512	−	21.8626i	−0.816635	−	0.832295i
$691$	−17.4669	+	15.7273i	−0.664473	+	0.598294i	−0.930774	−	0.365596i	$-0.880865\pi$
$691$	−17.4669	+	15.7273i	−0.664473	+	0.598294i	0.266301	+	0.963890i	$0.414199\pi$
$692$	17.9662	−	17.9662i	0.682973	−	0.682973i
$693$	−66.6126	−	14.9429i	−2.53040	−	0.567632i
$694$			9.84356i			0.373656i
$695$	16.4211	+	7.49879i	0.622886	+	0.284445i
$696$	1.28986	−	2.89708i	0.0488921	−	0.109813i
$697$	45.3810	−	36.7488i	1.71893	−	1.39196i
$698$	4.75613	+	7.32380i	0.180022	+	0.277210i
$699$	11.6156	+	35.7490i	0.439341	+	1.35215i
$700$	−0.973030	+	13.1929i	−0.0367771	+	0.498646i
$701$	0.785995	−	0.571059i	0.0296866	−	0.0215686i	−0.572843	−	0.819665i	$-0.694160\pi$
$701$	0.785995	−	0.571059i	0.0296866	−	0.0215686i	0.602530	+	0.798097i	$0.294160\pi$
$702$	1.89618	−	36.1812i	0.0715666	−	1.36557i
$703$	0.117182	−	0.437329i	0.00441960	−	0.0164942i
$704$	2.59611	−	2.06403i	0.0978446	−	0.0777910i
$705$	2.46025	−	21.4464i	0.0926583	−	0.807720i
$706$	30.9086	+	10.0428i	1.16326	+	0.377966i
$707$	−17.4767	−	2.80866i	−0.657279	−	0.105631i
$708$	−12.4439	+	1.97092i	−0.467671	+	0.0740718i
$709$	−5.43242	+	25.5575i	−0.204019	+	0.959833i	0.750313	+	0.661083i	$0.229903\pi$
$709$	−5.43242	+	25.5575i	−0.204019	+	0.959833i	−0.954332	+	0.298750i	$0.903430\pi$
$710$	−7.72619	+	3.84471i	−0.289959	+	0.144289i
$711$	0.816160	−	7.76525i	0.0306084	−	0.291220i
$712$	13.6699	+	11.0696i	0.512300	+	0.414852i
$713$	−20.6040	+	10.4983i	−0.771626	+	0.393163i
$714$	−54.8881	−	0.124430i	−2.05414	−	0.00465667i
$715$	1.47502	+	17.0577i	0.0551625	+	0.637921i
$716$	−5.99387	+	10.3817i	−0.224001	+	0.387982i
$717$	−36.2400	+	55.8047i	−1.35341	+	2.08406i
$718$	−5.89763	+	2.26389i	−0.220097	+	0.0844875i
$719$	−11.8890	+	5.29334i	−0.443386	+	0.197408i	−0.616272	−	0.787534i	$-0.711358\pi$
$719$	−11.8890	+	5.29334i	−0.443386	+	0.197408i	0.172885	+	0.984942i	$0.444691\pi$
$720$	13.0379	−	11.5171i	0.485895	−	0.429217i
$721$	1.28427	−	1.41984i	0.0478286	−	0.0528774i
$722$	2.96897	+	18.7453i	0.110493	+	0.697628i
$723$	−3.89014	−	3.15018i	−0.144676	−	0.117156i
$724$	0.0137290	−	0.00291819i	0.000510234	−	0.000108454i
$725$	−1.09363	+	4.70394i	−0.0406162	+	0.174700i
$726$	−23.6812	−	27.2684i	−0.878892	−	1.01202i
$727$	18.3060	−	18.3060i	0.678932	−	0.678932i	−0.280826	−	0.959759i	$-0.590609\pi$
$727$	18.3060	−	18.3060i	0.678932	−	0.678932i	0.959759	+	0.280826i	$0.0906085\pi$
$728$	6.09897	+	0.333499i	0.226043	+	0.0123603i
$729$	38.0357	+	52.3516i	1.40873	+	1.93895i
$730$	−17.2369	−	15.8191i	−0.637966	−	0.585493i
$731$	−3.16292	−	2.84790i	−0.116985	−	0.105333i
$732$	26.1985	−	1.37301i	0.968325	−	0.0507478i
$733$	−3.89653	−	1.49574i	−0.143922	−	0.0552464i	0.285341	−	0.958426i	$-0.407893\pi$
$733$	−3.89653	−	1.49574i	−0.143922	−	0.0552464i	−0.429263	+	0.903180i	$0.641227\pi$
$734$	13.3968	−	9.73337i	0.494486	−	0.359265i
$735$	8.75074	−	50.6408i	0.322776	−	1.86791i
$736$	−4.17196			−0.153780
$737$	−20.5491	−	23.2377i	−0.756937	−	0.855973i
$738$	18.6087	−	69.4487i	0.684996	−	2.55644i
$739$	2.06605	+	9.72002i	0.0760011	+	0.357557i	0.999671	−	0.0256310i	$-0.00815950\pi$
$739$	2.06605	+	9.72002i	0.0760011	+	0.357557i	−0.923670	+	0.383188i	$0.874826\pi$
$740$	6.72624	+	1.87093i	0.247262	+	0.0687768i
$741$	0.646065	−	0.889232i	0.0237338	−	0.0326668i
$742$	−26.8395	+	17.3434i	−0.985308	+	0.636695i
$743$	5.43174	+	2.76761i	0.199271	+	0.101534i	0.550779	−	0.834651i	$-0.314331\pi$
$743$	5.43174	+	2.76761i	0.199271	+	0.101534i	−0.351508	+	0.936185i	$0.614331\pi$
$744$	−7.40204	−	16.6252i	−0.271372	−	0.609511i
$745$	−0.0150096	+	1.58043i	−0.000549910	+	0.0579026i
$746$	18.3662	−	3.90385i	0.672433	−	0.142930i
$747$	−32.4111	−	120.960i	−1.18586	−	4.42569i
$748$	−16.8431	−	12.4695i	−0.615845	−	0.455929i
$749$	4.08617	+	7.11466i	0.149305	+	0.259964i
$750$	−22.4137	+	29.0708i	−0.818433	+	1.06151i
$751$	2.66999	+	25.4033i	0.0974294	+	0.926979i	0.928630	+	0.371007i	$0.120987\pi$
$751$	2.66999	+	25.4033i	0.0974294	+	0.926979i	−0.831201	+	0.555972i	$0.812346\pi$
$752$	−1.85044	−	2.28510i	−0.0674785	−	0.0833290i
$753$	3.16942	+	60.4762i	0.115500	+	2.20387i
$754$	2.18114	+	0.463615i	0.0794324	+	0.0168839i
$755$	13.5519	+	3.01534i	0.493204	+	0.109739i
$756$	−33.6467	+	24.3294i	−1.22372	+	0.884853i
$757$	−3.02263	+	1.54011i	−0.109859	+	0.0559761i	−0.508057	−	0.861324i	$-0.669636\pi$
$757$	−3.02263	+	1.54011i	−0.109859	+	0.0559761i	0.398197	+	0.917300i	$0.369636\pi$
$758$	−3.59446	−	13.4147i	−0.130557	−	0.487244i
$759$	1.97081	+	45.3872i	0.0715358	+	1.64745i
$760$	0.320725	−	0.0476802i	0.0116339	−	0.00172954i
$761$	−3.86706	+	3.48192i	−0.140181	+	0.126220i	−0.736238	−	0.676722i	$-0.763400\pi$
$761$	−3.86706	+	3.48192i	−0.140181	+	0.126220i	0.596057	+	0.802942i	$0.296733\pi$
$762$	−5.55222	+	35.0553i	−0.201136	+	1.26992i
$763$	6.23413	+	39.9466i	0.225691	+	1.44616i
$764$	7.22301	−	2.34690i	0.261319	−	0.0849078i
$765$	−91.6149	−	60.7401i	−3.31234	−	2.19606i
$766$	−35.7381	−	3.75623i	−1.29127	−	0.135718i
$767$	−3.17479	−	8.27062i	−0.114635	−	0.298635i
$768$	0.171833	−	3.27877i	0.00620049	−	0.118312i
$769$	21.6333			0.780116			0.390058	−	0.920790i	$-0.372455\pi$
$769$	21.6333			0.780116			0.390058	+	0.920790i	$0.372455\pi$
$770$	14.1590	−	13.5839i	0.510256	−	0.489529i
$771$	−24.5312			−0.883469
$772$	−0.602377	+	11.4940i	−0.0216800	+	0.413679i
$773$	−10.6139	−	27.6502i	−0.381756	−	0.994507i	−0.981011	−	0.193950i	$-0.937870\pi$
$773$	−10.6139	−	27.6502i	−0.381756	−	0.994507i	0.599256	−	0.800558i	$-0.295463\pi$
$774$	−5.21167	−	0.547769i	−0.187330	−	0.0196891i
$775$	15.8612	+	22.7265i	0.569750	+	0.816362i
$776$	−15.0780	+	4.89915i	−0.541270	+	0.175869i
$777$	−25.2987	−	9.77712i	−0.907586	−	0.350752i
$778$	0.888622	−	5.61054i	0.0318587	−	0.201148i
$779$	0.995901	−	0.896713i	0.0356819	−	0.0321281i
$780$	13.6169	+	10.0922i	0.487564	+	0.361360i
$781$	12.3339	+	3.42366i	0.441342	+	0.122508i
$782$	6.82275	+	25.4629i	0.243981	+	0.910550i
$783$	−13.5060	+	6.88165i	−0.482665	+	0.245930i
$784$	−4.08878	−	5.68172i	−0.146028	−	0.202918i
$785$	14.8989	−	9.47550i	0.531763	−	0.338195i
$786$	37.1533	+	7.89717i	1.32521	+	0.281683i
$787$	1.00099	+	19.1000i	0.0356815	+	0.680843i	0.956656	+	0.291220i	$0.0940613\pi$
$787$	1.00099	+	19.1000i	0.0356815	+	0.680843i	−0.920975	+	0.389623i	$0.872605\pi$
$788$	−1.52412	−	1.88214i	−0.0542947	−	0.0670484i
$789$	−9.79779	−	93.2198i	−0.348811	−	3.31871i
$790$	1.73055	+	1.42879i	0.0615702	+	0.0508342i
$791$	−7.99607	−	4.64074i	−0.284308	−	0.165006i
$792$	−25.8019	−	0.231321i	−0.916829	−	0.00821965i
$793$	4.77439	+	17.8183i	0.169544	+	0.632745i
$794$	24.6686	−	5.24347i	0.875456	−	0.186084i
$795$	−88.6682	−	0.842096i	−3.14474	−	0.0298661i
$796$	−7.43685	−	16.7034i	−0.263592	−	0.592038i
$797$	−35.0712	−	17.8697i	−1.24229	−	0.632977i	−0.295655	−	0.955295i	$-0.595538\pi$
$797$	−35.0712	−	17.8697i	−1.24229	−	0.632977i	−0.946631	+	0.322318i	$0.895538\pi$
$798$	−1.25807	+	0.0630732i	−0.0445353	+	0.00223277i
$799$	−10.9206	+	15.0309i	−0.386342	+	0.531754i
$800$	0.688237	+	4.95241i	0.0243329	+	0.175094i
$801$	−28.4520	−	133.856i	−1.00530	−	4.72957i
$802$	−4.07303	+	15.2007i	−0.143824	+	0.536757i
$803$	3.31774	+	34.5424i	0.117081	+	1.21897i
$804$	−30.7084			−1.08300
$805$	−24.5751	+	2.29100i	−0.866157	+	0.0807471i
$806$	10.3525	−	7.52152i	0.364651	−	0.264934i
$807$	−37.5700	−	14.4218i	−1.32253	−	0.507670i
$808$	−6.68116	+	0.350145i	−0.235042	+	0.0123180i
$809$	−2.23683	−	2.01405i	−0.0786426	−	0.0708101i	0.628872	−	0.777509i	$-0.283517\pi$
$809$	−2.23683	−	2.01405i	−0.0786426	−	0.0708101i	−0.707515	+	0.706699i	$0.750184\pi$
$810$	−62.9696	+	2.70072i	−2.21253	+	0.0948936i
$811$	−15.3678	−	21.1520i	−0.539637	−	0.742747i	0.448923	−	0.893570i	$-0.351808\pi$
$811$	−15.3678	−	21.1520i	−0.539637	−	0.742747i	−0.988561	+	0.150823i	$0.951808\pi$
$812$	−1.15500	−	2.27957i	−0.0405325	−	0.0799973i
$813$	26.3208	−	26.3208i	0.923109	−	0.923109i
$814$	−5.56186	−	8.73497i	−0.194943	−	0.306160i
$815$	−35.2058	+	5.23383i	−1.23321	+	0.183333i
$816$	−20.2925	+	4.31330i	−0.710378	+	0.150996i
$817$	−0.0759081	−	0.0614691i	−0.00265569	−	0.00215053i
$818$	−0.961579	−	6.07117i	−0.0336208	−	0.212274i
$819$	−35.2421	−	31.8771i	−1.23146	−	1.11388i
$820$	13.6810	+	15.4876i	0.477763	+	0.540851i
$821$	−46.5193	+	20.7117i	−1.62354	+	0.722845i	−0.998338	−	0.0576220i	$-0.981648\pi$
$821$	−46.5193	+	20.7117i	−1.62354	+	0.722845i	−0.625197	+	0.780467i	$0.714982\pi$
$822$	3.04488	−	1.16882i	0.106202	−	0.0407673i
$823$	−3.53084	+	5.43701i	−0.123077	+	0.189522i	−0.894838	−	0.446390i	$-0.852709\pi$
$823$	−3.53084	+	5.43701i	−0.123077	+	0.189522i	0.771761	+	0.635912i	$0.219376\pi$
$824$	0.361805	−	0.626664i	0.0126041	−	0.0218309i
$825$	53.5527	−	9.82691i	1.86447	−	0.342129i
$826$	−5.09624	+	8.78092i	−0.177321	+	0.305527i
$827$	18.8121	−	9.58522i	0.654160	−	0.333311i	−0.0952155	−	0.995457i	$-0.530354\pi$
$827$	18.8121	−	9.58522i	0.654160	−	0.333311i	0.749375	+	0.662146i	$0.230354\pi$
$828$	25.2240	+	20.4260i	0.876596	+	0.709853i
$829$	3.25571	−	30.9760i	0.113075	−	1.07584i	−0.779952	−	0.625839i	$-0.784757\pi$
$829$	3.25571	−	30.9760i	0.113075	−	1.07584i	0.893028	−	0.450002i	$-0.148577\pi$
$830$	34.1236	+	11.4468i	1.18445	+	0.397325i
$831$	7.40409	−	34.8335i	0.256845	−	1.20836i
$832$	2.28022	−	0.361151i	0.0790523	−	0.0125206i
$833$	−27.9907	+	34.2470i	−0.969821	+	1.18659i
$834$	−25.2092	−	8.19096i	−0.872923	−	0.283630i
$835$	14.4367	+	18.1781i	0.499601	+	0.629079i
$836$	−0.400986	−	0.265544i	−0.0138684	−	0.00918404i
$837$	−22.5139	+	84.0229i	−0.778193	+	2.90426i
$838$	1.91580	−	36.5556i	0.0661802	−	1.26279i
$839$	20.7318	−	15.0625i	0.715741	−	0.520016i	−0.169280	−	0.985568i	$-0.554144\pi$
$839$	20.7318	−	15.0625i	0.715741	−	0.520016i	0.885021	+	0.465552i	$0.154144\pi$
$840$	−0.788324	−	19.4081i	−0.0271998	−	0.669643i
$841$	8.67320	+	26.6934i	0.299076	+	0.920461i
$842$	−2.79031	−	4.29670i	−0.0961604	−	0.148074i
$843$	49.9629	−	40.4592i	1.72081	−	1.39349i
$844$	2.72374	−	6.11763i	0.0937551	−	0.210577i
$845$	7.12445	−	15.6013i	0.245088	−	0.536702i
$846$			22.8757i			0.786484i
$847$	−29.0882	+	0.935881i	−0.999483	+	0.0321572i
$848$	−8.54045	+	8.54045i	−0.293280	+	0.293280i
$849$	35.0219	−	31.5338i	1.20195	−	1.08224i
$850$	29.1007	−	12.2996i	0.998145	−	0.421874i
$851$	−1.36158	+	12.9546i	−0.0466745	+	0.444078i
$852$	10.6273	−	6.90142i	0.364084	−	0.236439i
$853$	7.49617	−	14.7121i	0.256664	−	0.503731i	−0.726335	−	0.687340i	$-0.758778\pi$
$853$	7.49617	−	14.7121i	0.256664	−	0.503731i	0.982999	+	0.183609i	$0.0587781\pi$
$854$	12.4648	−	17.0748i	0.426537	−	0.584287i
$855$	−2.17258	−	1.28200i	−0.0743006	−	0.0438435i
$856$	2.07500	+	2.30452i	0.0709221	+	0.0787669i
$857$	−48.3517	−	12.9558i	−1.65166	−	0.442562i	−0.691585	−	0.722295i	$-0.743087\pi$
$857$	−48.3517	−	12.9558i	−1.65166	−	0.442562i	−0.960078	+	0.279733i	$0.909754\pi$
$858$	−5.00616	−	24.6361i	−0.170908	−	0.841064i
$859$	1.19147	−	2.06368i	0.0406523	−	0.0704118i	−0.844983	−	0.534793i	$-0.820390\pi$
$859$	1.19147	−	2.06368i	0.0406523	−	0.0704118i	0.885636	+	0.464381i	$0.153723\pi$
$860$	0.958940	−	1.16146i	0.0326996	−	0.0396056i
$861$	−47.0396	−	65.0541i	−1.60311	−	2.21704i
$862$	1.68668	+	10.6493i	0.0574486	+	0.362716i
$863$	−45.6202	+	29.6261i	−1.55293	+	1.00848i	−0.570623	+	0.821212i	$0.693298\pi$
$863$	−45.6202	+	29.6261i	−1.55293	+	1.00848i	−0.982308	+	0.187272i	$0.940035\pi$
$864$	−10.5011	+	11.6626i	−0.357254	+	0.396770i
$865$	26.2727	−	50.3745i	0.893297	−	1.71279i
$866$	10.5194	−	1.10563i	0.357464	−	0.0375710i
$867$	34.1717	+	67.0658i	1.16053	+	2.27767i
$868$	−14.1566	−	3.82767i	−0.480506	−	0.129919i
$869$	−0.491217	−	3.29218i	−0.0166634	−	0.111680i
$870$	0.808164	−	7.04492i	0.0273993	−	0.238845i
$871$	−4.48936	−	21.1208i	−0.152116	−	0.715651i
$872$	5.47628	+	14.2662i	0.185450	+	0.483114i
$873$	115.150	+	44.2018i	3.89722	+	1.49600i
$874$	0.186946	+	0.575361i	0.00632355	+	0.0194619i
$875$	6.77367	+	28.7944i	0.228992	+	0.973428i
$876$	27.7916	+	20.1918i	0.938993	+	0.682218i
$877$	7.44633	−	9.19545i	0.251445	−	0.310508i	−0.635758	−	0.771889i	$-0.719312\pi$
$877$	7.44633	−	9.19545i	0.251445	−	0.310508i	0.887202	+	0.461380i	$0.152646\pi$
$878$	−12.9872	−	8.43400i	−0.438298	−	0.284634i
$879$	13.7681	−	7.94902i	0.464386	−	0.268114i
$880$	4.15328	−	6.14412i	0.140007	−	0.207118i
$881$		−	50.8218i		−	1.71223i	−0.516784	−	0.856116i	$-0.672871\pi$
$881$		−	50.8218i		−	1.71223i	0.516784	−	0.856116i	$-0.327129\pi$
$882$	−3.09671	+	54.3710i	−0.104272	+	1.83077i
$883$	−0.721447	+	4.55504i	−0.0242786	+	0.153289i	−0.996849	−	0.0793181i	$-0.974726\pi$
$883$	−0.721447	+	4.55504i	−0.0242786	+	0.153289i	0.972571	+	0.232607i	$0.0747257\pi$
$884$	−5.93325	−	13.3263i	−0.199557	−	0.448212i
$885$	−25.2220	+	12.5510i	−0.847829	+	0.421897i
$886$	10.5637	−	11.7322i	0.354895	−	0.394151i
$887$	−8.70835	+	22.6860i	−0.292398	+	0.761722i	0.706161	+	0.708051i	$0.250425\pi$
$887$	−8.70835	+	22.6860i	−0.292398	+	0.761722i	−0.998559	+	0.0536708i	$0.982908\pi$
$888$	−10.1250	−	1.60365i	−0.339774	−	0.0538149i
$889$	19.0894	+	21.2978i	0.640236	+	0.714304i
$890$	36.5841	+	14.4434i	1.22630	+	0.484145i
$891$	72.1210	+	59.4809i	2.41615	+	1.99268i
$892$	15.9430	+	4.27192i	0.533812	+	0.143034i
$893$	−0.232223	+	0.357593i	−0.00777106	+	0.0119664i
$894$	−0.242578	−	2.30798i	−0.00811303	−	0.0771903i
$895$	−5.82190	+	26.1655i	−0.194605	+	0.874617i
$896$	−1.96216	−	1.77481i	−0.0655511	−	0.0592921i
$897$	−14.3565	+	28.1763i	−0.479350	+	0.940778i
$898$	−1.23079	+	3.20631i	−0.0410719	+	0.106996i
$899$	−4.89085	−	2.17755i	−0.163119	−	0.0726253i
$900$	20.0860	−	33.3123i	0.669533	−	1.11041i
$901$	66.0922	+	38.1583i	2.20185	+	1.27124i
$902$	0.274784	−	30.6497i	0.00914931	−	1.02052i
$903$	−4.14681	+	4.12805i	−0.137997	+	0.137373i
$904$	−3.32333	−	1.07982i	−0.110532	−	0.0359141i
$905$	0.0273278	−	0.0154336i	0.000908408	−	0.000513029i
$906$	−20.2735	−	2.13083i	−0.673542	−	0.0707921i
$907$	−16.7422	+	0.877423i	−0.555916	+	0.0291343i	−0.328226	−	0.944599i	$-0.606451\pi$
$907$	−16.7422	+	0.877423i	−0.555916	+	0.0291343i	−0.227690	+	0.973734i	$0.573117\pi$
$908$	−3.54676	−	5.46153i	−0.117703	−	0.181247i
$909$	42.1092	+	30.5941i	1.39667	+	1.01474i
$910$	13.2334	−	3.37954i	0.438682	−	0.112031i
$911$	−13.8844	+	42.7319i	−0.460012	+	1.41577i	0.405138	+	0.914256i	$0.367224\pi$
$911$	−13.8844	+	42.7319i	−0.460012	+	1.41577i	−0.865149	+	0.501515i	$0.832776\pi$
$912$	−0.459881	+	0.123225i	−0.0152282	+	0.00408038i
$913$	−26.2771	−	46.4705i	−0.869646	−	1.53795i
$914$	−21.3845	+	12.3463i	−0.707335	+	0.408380i
$915$	54.9629	−	20.5016i	1.81702	−	0.677761i
$916$	−8.86976	−	12.2082i	−0.293065	−	0.403370i
$917$	23.8305	−	19.2083i	0.786952	−	0.634313i
$918$	88.3542	+	45.0187i	2.91612	+	1.48584i
$919$	−0.868341	+	4.08523i	−0.0286439	+	0.134759i	−0.990146	−	0.140038i	$-0.955277\pi$
$919$	−0.868341	+	4.08523i	−0.0286439	+	0.134759i	0.961502	+	0.274797i	$0.0886108\pi$
$920$	−8.89917	+	2.79836i	−0.293397	+	0.0922593i
$921$	−15.6118	−	6.95082i	−0.514426	−	0.229037i
$922$	36.3080	+	1.90282i	1.19574	+	0.0626661i
$923$	6.30034	+	6.30034i	0.207378	+	0.207378i
$924$	−18.3814	+	22.1850i	−0.604705	+	0.729832i
$925$	15.6026	−	0.520793i	0.513012	−	0.0171236i
$926$	3.97123	+	4.41050i	0.130503	+	0.144938i
$927$	−5.25567	+	2.01746i	−0.172619	+	0.0662622i
$928$	−0.607848	−	0.750629i	−0.0199536	−	0.0246406i
$929$	−31.3104	−	6.65523i	−1.02726	−	0.218351i	−0.336690	−	0.941616i	$-0.609307\pi$
$929$	−31.3104	−	6.65523i	−1.02726	−	0.218351i	−0.690571	+	0.723265i	$0.742641\pi$
$930$	−26.9407	−	30.4982i	−0.883421	−	1.00008i
$931$	−0.600356	+	0.818489i	−0.0196759	+	0.0268249i
$932$	11.3076	+	1.79095i	0.370393	+	0.0586645i
$933$	112.666	+	5.90459i	3.68853	+	0.193308i
$934$	9.90979	+	17.1643i	0.324258	+	0.561632i
$935$	−44.2919	−	15.3009i	−1.44850	−	0.500393i
$936$	−15.5546	−	8.98045i	−0.508418	−	0.293535i
$937$	−7.28115	−	14.2901i	−0.237865	−	0.466836i	0.740956	−	0.671553i	$-0.234373\pi$
$937$	−7.28115	−	14.2901i	−0.237865	−	0.466836i	−0.978821	+	0.204717i	$0.934373\pi$
$938$	−15.6165	+	19.1956i	−0.509897	+	0.626760i
$939$	−46.2880	+	63.7100i	−1.51055	+	2.07910i
$940$	−5.47990	−	3.63314i	−0.178735	−	0.118500i
$941$	30.8173	+	27.7481i	1.00462	+	0.904561i	0.995439	−	0.0953969i	$-0.0304120\pi$
$941$	30.8173	+	27.7481i	1.00462	+	0.904561i	0.00917745	+	0.999958i	$0.497079\pi$
$942$	−20.1482	+	16.3157i	−0.656463	+	0.531593i
$943$	−24.2638	+	29.9633i	−0.790139	+	0.975741i
$944$	−1.18580	+	3.64953i	−0.0385946	+	0.118782i
$945$	−55.4525	+	74.4657i	−1.80387	+	2.42237i
$946$	−2.20956	+	0.329682i	−0.0718390	+	0.0107189i
$947$	−16.7288	+	4.48246i	−0.543612	+	0.145661i	−0.520167	−	0.854065i	$-0.674130\pi$
$947$	−16.7288	+	4.48246i	−0.543612	+	0.145661i	−0.0234455	+	0.999725i	$0.507464\pi$
$948$	−2.76355	−	1.79467i	−0.0897558	−	0.0582881i
$949$	−9.82470	+	22.0666i	−0.318923	+	0.716313i
$950$	0.652155	−	0.316834i	0.0211587	−	0.0102795i
$951$	51.3950	−	16.6992i	1.66660	−	0.541510i
$952$	−7.62336	+	14.8782i	−0.247074	+	0.482205i
$953$	8.54543	−	1.35346i	0.276814	−	0.0438430i	−0.0164841	−	0.999864i	$-0.505247\pi$
$953$	8.54543	−	1.35346i	0.276814	−	0.0438430i	0.293298	+	0.956021i	$0.405247\pi$
$954$	93.4506	−	9.82206i	3.02558	−	0.318001i
$955$	13.8332	−	9.85102i	0.447630	−	0.318772i
$956$	10.1331	+	17.5510i	0.327728	+	0.567641i
$957$	−7.87905	+	6.96745i	−0.254693	+	0.225226i
$958$	−4.95802	−	4.95802i	−0.160186	−	0.160186i
$959$	0.817828	−	2.49773i	0.0264090	−	0.0806561i
$960$	−1.83272	−	7.10918i	−0.0591507	−	0.229448i
$961$	0.253134	−	0.112703i	0.00816562	−	0.00363557i
$962$	−0.377247	−	7.19830i	−0.0121629	−	0.232083i
$963$	−1.26264	−	24.0926i	−0.0406880	−	0.776374i
$964$	−1.39279	+	0.620111i	−0.0448588	+	0.0199724i
$965$	6.42476	+	24.9219i	0.206820	+	0.802264i
$966$	35.4657	−	7.45447i	1.14109	−	0.239843i
$967$	5.48070	+	5.48070i	0.176247	+	0.176247i	0.789718	−	0.613470i	$-0.210227\pi$
$967$	5.48070	+	5.48070i	0.176247	+	0.176247i	−0.613470	+	0.789718i	$0.710227\pi$
$968$	−10.6745	+	2.65605i	−0.343092	+	0.0853687i
$969$	1.50416	+	2.60529i	0.0483207	+	0.0836939i
$970$	−28.8767	+	20.5640i	−0.927175	+	0.660271i
$971$	−28.8923	+	3.03670i	−0.927196	+	0.0974523i	−0.556075	−	0.831132i	$-0.687693\pi$
$971$	−28.8923	+	3.03670i	−0.927196	+	0.0974523i	−0.371121	+	0.928584i	$0.621027\pi$
$972$	44.9042	−	7.11212i	1.44030	−	0.228122i
$973$	−17.9401	+	11.5927i	−0.575132	+	0.371644i
$974$	−24.6632	+	8.01357i	−0.790261	+	0.256771i
$975$	35.8156	+	12.3940i	1.14702	+	0.396927i
$976$	3.24997	−	7.29955i	0.104029	−	0.233653i
$977$	−25.9063	−	16.8237i	−0.828816	−	0.538239i	0.0590964	−	0.998252i	$-0.481178\pi$
$977$	−25.9063	−	16.8237i	−0.828816	−	0.538239i	−0.887912	+	0.460013i	$0.847845\pi$
$978$	50.4809	−	13.5263i	1.61420	−	0.432524i
$979$	−26.0182	−	52.2157i	−0.831546	−	1.66882i
$980$	−12.5328	−	9.37706i	−0.400345	−	0.299539i
$981$	36.7376	−	113.067i	1.17294	−	3.60994i
$982$	16.1296	−	19.9184i	0.514716	−	0.635621i
$983$	12.4427	−	10.0759i	0.396859	−	0.321370i	−0.410031	−	0.912071i	$-0.634482\pi$
$983$	12.4427	−	10.0759i	0.396859	−	0.321370i	0.806890	+	0.590701i	$0.201149\pi$
$984$	−22.5490	−	20.3033i	−0.718837	−	0.647244i
$985$	−4.51355	−	2.99246i	−0.143814	−	0.0953477i
$986$	−3.58728	+	4.93747i	−0.114242	+	0.157241i
$987$	19.8135	+	16.1192i	0.630672	+	0.513079i
$988$	−0.151984	−	0.298285i	−0.00483525	−	0.00948971i
$989$	2.43367	+	1.40508i	0.0773861	+	0.0446789i
$990$	−55.1929	+	16.8133i	−1.75415	+	0.534362i
$991$	−11.7750	−	20.3950i	−0.374046	−	0.647867i	0.616137	−	0.787639i	$-0.288697\pi$
$991$	−11.7750	−	20.3950i	−0.374046	−	0.647867i	−0.990184	+	0.139771i	$0.955363\pi$
$992$	−5.53523	−	0.290089i	−0.175744	−	0.00921034i
$993$	37.8051	+	5.98774i	1.19971	+	0.190015i
$994$	1.09037	−	10.1527i	0.0345844	−	0.322024i
$995$	−27.0674	−	30.6417i	−0.858095	−	0.971406i
$996$	−51.6936	−	10.9878i	−1.63797	−	0.348162i
$997$	−18.8151	−	23.2347i	−0.595881	−	0.735851i	0.386594	−	0.922250i	$-0.373652\pi$
$997$	−18.8151	−	23.2347i	−0.595881	−	0.735851i	−0.982474	+	0.186399i	$0.940318\pi$
$998$	−21.2361	+	8.15178i	−0.672217	+	0.258040i
$999$	32.7871	+	36.4138i	1.03734	+	1.15208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.537.1	yes	768
5.3	odd	4	inner	770.2.bv.a.383.48	yes	768
7.3	odd	6	inner	770.2.bv.a.647.24	yes	768
11.5	even	5	inner	770.2.bv.a.467.24	yes	768
35.3	even	12	inner	770.2.bv.a.493.24	yes	768
55.38	odd	20	inner	770.2.bv.a.313.24	✓	768
77.38	odd	30	inner	770.2.bv.a.577.48	yes	768
385.38	even	60	inner	770.2.bv.a.423.1	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.24	✓	768	55.38	odd	20	inner
770.2.bv.a.383.48	yes	768	5.3	odd	4	inner
770.2.bv.a.423.1	yes	768	385.38	even	60	inner
770.2.bv.a.467.24	yes	768	11.5	even	5	inner
770.2.bv.a.493.24	yes	768	35.3	even	12	inner
770.2.bv.a.537.1	yes	768	1.1	even	1	trivial
770.2.bv.a.577.48	yes	768	77.38	odd	30	inner
770.2.bv.a.647.24	yes	768	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0523360 + 0.998630i) q^{2} +(-1.17662 - 3.06520i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-2.19152 + 0.444112i) q^{5} +(3.12258 - 1.01459i) q^{6} +(0.953749 - 2.46787i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-5.78157 + 5.20575i) q^{9} +O(q^{10})\)	\(q+(-0.0523360 + 0.998630i) q^{2} +(-1.17662 - 3.06520i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-2.19152 + 0.444112i) q^{5} +(3.12258 - 1.01459i) q^{6} +(0.953749 - 2.46787i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-5.78157 + 5.20575i) q^{9} +(-0.328808 - 2.21176i) q^{10} +(-1.83123 + 2.76525i) q^{11} +(0.849773 + 3.17140i) q^{12} +(-2.05701 + 1.04810i) q^{13} +(2.41457 + 1.08160i) q^{14} +(3.93988 + 6.19489i) q^{15} +(0.978148 + 0.207912i) q^{16} +(-0.330692 - 6.30998i) q^{17} +(-4.89603 - 6.04609i) q^{18} +(-0.0151576 - 0.144215i) q^{19} +(2.22594 - 0.212603i) q^{20} +(-8.68670 - 0.0196925i) q^{21} +(-2.66562 - 1.97344i) q^{22} +(1.07978 + 4.02980i) q^{23} +(-3.21152 + 0.682630i) q^{24} +(4.60553 - 1.94656i) q^{25} +(-0.939008 - 2.10905i) q^{26} +(13.9831 + 7.12475i) q^{27} +(-1.20649 + 2.35465i) q^{28} +(-0.567730 + 0.781413i) q^{29} +(-6.39260 + 3.61026i) q^{30} +(1.15242 + 5.42170i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(10.6307 + 2.35943i) q^{33} +6.31864 q^{34} +(-0.994152 + 5.83195i) q^{35} +(6.29405 - 4.57289i) q^{36} +(2.91489 + 1.11892i) q^{37} +(0.144810 - 0.00758918i) q^{38} +(5.63295 + 5.07193i) q^{39} +(0.0958152 + 2.23401i) q^{40} +(5.43209 + 7.47663i) q^{41} +(0.474292 - 8.67376i) q^{42} +(0.476294 - 0.476294i) q^{43} +(2.11024 - 2.55869i) q^{44} +(10.3585 - 13.9762i) q^{45} +(-4.08079 + 0.867398i) q^{46} +(-2.28510 - 1.85044i) q^{47} +(-0.513617 - 3.24285i) q^{48} +(-5.18072 - 4.70745i) q^{49} +(1.70286 + 4.70109i) q^{50} +(-18.9522 + 8.43808i) q^{51} +(2.15530 - 0.827342i) q^{52} +(-6.57816 + 10.1295i) q^{53} +(-7.84680 + 13.5911i) q^{54} +(2.78509 - 6.87337i) q^{55} +(-2.28828 - 1.32807i) q^{56} +(-0.424211 + 0.216147i) q^{57} +(-0.750629 - 0.607848i) q^{58} +(-0.401111 + 3.81632i) q^{59} +(-3.27075 - 6.57279i) q^{60} +(1.66129 - 7.81574i) q^{61} +(-5.47458 + 0.867089i) q^{62} +(7.33292 + 19.2331i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(4.04251 - 3.21048i) q^{65} +(-2.91256 + 10.4926i) q^{66} +(-2.42073 + 9.03428i) q^{67} +(-0.330692 + 6.30998i) q^{68} +(11.0816 - 8.05128i) q^{69} +(-5.77193 - 1.29801i) q^{70} +(-1.19263 - 3.67053i) q^{71} +(4.23722 + 6.52475i) q^{72} +(8.13116 - 6.58448i) q^{73} +(-1.26994 + 2.85233i) q^{74} +(-11.3856 - 11.8265i) q^{75} +0.145009i q^{76} +(5.07773 + 7.15658i) q^{77} +(-5.35979 + 5.35979i) q^{78} +(-0.745834 + 0.671552i) q^{79} +(-2.23597 - 0.0212353i) q^{80} +(2.94632 - 28.0323i) q^{81} +(-7.75067 + 5.03335i) q^{82} +(-7.30756 + 14.3419i) q^{83} +(8.63705 + 0.927592i) q^{84} +(3.52706 + 13.6816i) q^{85} +(0.450714 + 0.500569i) q^{86} +(3.06319 + 0.820779i) q^{87} +(2.44474 + 2.24126i) q^{88} +(-8.79491 + 15.2332i) q^{89} +(13.4149 + 11.0758i) q^{90} +(0.624696 + 6.07606i) q^{91} +(-0.652638 - 4.12059i) q^{92} +(15.2626 - 9.91167i) q^{93} +(1.96749 - 2.18512i) q^{94} +(0.0972656 + 0.309318i) q^{95} +(3.26528 - 0.343195i) q^{96} +(-7.19756 - 14.1260i) q^{97} +(4.97214 - 4.92725i) q^{98} +(-3.80783 - 25.5204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

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