LMFDB - Embedded newform 294.2.j.a.251.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(41,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("294.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, degree $6$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.8
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781831 - 0.623490i) q^{2} +(1.34258 + 1.09430i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-2.13620 - 1.02874i) q^{5} +(-0.367384 - 1.69264i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.605021 + 2.93836i) q^{9} +O(q^{10})$	\(q+(-0.781831 - 0.623490i) q^{2} +(1.34258 + 1.09430i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-2.13620 - 1.02874i) q^{5} +(-0.367384 - 1.69264i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.605021 + 2.93836i) q^{9} +(1.02874 + 2.13620i) q^{10} +(2.95567 + 2.35707i) q^{11} +(-0.768111 + 1.55242i) q^{12} +(3.59671 + 2.86828i) q^{13} +(2.54479 - 0.723897i) q^{14} +(-1.74227 - 3.71881i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.623946 - 2.73368i) q^{17} +(1.35901 - 2.67453i) q^{18} +7.99958i q^{19} +(0.527599 - 2.31156i) q^{20} +(-4.42083 + 1.20674i) q^{21} +(-0.841228 - 3.68566i) q^{22} +(-5.35612 + 1.22250i) q^{23} +(1.56845 - 0.734821i) q^{24} +(0.387609 + 0.486046i) q^{25} +(-1.02368 - 4.48502i) q^{26} +(-2.40315 + 4.60704i) q^{27} +(-2.44094 - 1.02069i) q^{28} +(0.336112 + 0.0767154i) q^{29} +(-0.956481 + 3.99377i) q^{30} -4.40479i q^{31} +(0.974928 + 0.222521i) q^{32} +(1.38887 + 6.39893i) q^{33} +(-2.19224 + 1.74826i) q^{34} +(5.50052 - 3.01596i) q^{35} +(-2.73006 + 1.24370i) q^{36} +(2.03185 - 8.90210i) q^{37} +(4.98766 - 6.25432i) q^{38} +(1.69010 + 7.78676i) q^{39} +(-1.85373 + 1.47830i) q^{40} +(3.26974 + 1.57462i) q^{41} +(4.20874 + 1.81288i) q^{42} +(6.98003 - 3.36141i) q^{43} +(-1.64027 + 3.40606i) q^{44} +(1.73036 - 6.89934i) q^{45} +(4.94980 + 2.38370i) q^{46} +(-2.12713 + 2.66734i) q^{47} +(-1.68442 - 0.403407i) q^{48} +(-2.26753 - 6.62256i) q^{49} -0.621676i q^{50} +(3.82916 - 2.98740i) q^{51} +(-1.99602 + 4.14478i) q^{52} +(4.76629 - 1.08788i) q^{53} +(4.75131 - 2.10359i) q^{54} +(-3.88910 - 8.07580i) q^{55} +(1.27202 + 2.31991i) q^{56} +(-8.75393 + 10.7400i) q^{57} +(-0.214952 - 0.269541i) q^{58} +(-9.34907 + 4.50227i) q^{59} +(3.23788 - 2.52610i) q^{60} +(-7.60031 - 1.73472i) q^{61} +(-2.74634 + 3.44381i) q^{62} +(-7.25584 - 3.21757i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-4.73258 - 9.82731i) q^{65} +(2.90380 - 5.86883i) q^{66} +6.99996 q^{67} +2.80399 q^{68} +(-8.52877 - 4.21989i) q^{69} +(-6.18090 - 1.07154i) q^{70} +(11.0631 - 2.52507i) q^{71} +(2.90988 + 0.729801i) q^{72} +(7.61996 - 6.07671i) q^{73} +(-7.13893 + 5.69310i) q^{74} +(-0.0114852 + 1.07671i) q^{75} +(-7.79901 + 1.78007i) q^{76} +(-9.62044 + 2.73665i) q^{77} +(3.53359 - 7.14169i) q^{78} +4.27717 q^{79} +2.37101 q^{80} +(-8.26790 + 3.55554i) q^{81} +(-1.57462 - 3.26974i) q^{82} +(-6.09768 - 7.64625i) q^{83} +(-2.16021 - 4.04147i) q^{84} +(-4.14513 + 5.19783i) q^{85} +(-7.55301 - 1.72393i) q^{86} +(0.367307 + 0.470804i) q^{87} +(3.40606 - 1.64027i) q^{88} +(1.65793 + 2.07898i) q^{89} +(-5.65452 + 4.31526i) q^{90} +(-11.7070 + 3.33019i) q^{91} +(-2.38370 - 4.94980i) q^{92} +(4.82016 - 5.91377i) q^{93} +(3.32612 - 0.759165i) q^{94} +(8.22950 - 17.0887i) q^{95} +(1.06541 + 1.36561i) q^{96} +9.98133i q^{97} +(-2.35627 + 6.59151i) q^{98} +(-5.13767 + 10.1109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$3$	1.34258	+	1.09430i	0.775137	+	0.631794i
$3$	1.34258	+	1.09430i	0.775137	+	0.631794i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−2.13620	−	1.02874i	−0.955339	−	0.460067i	−0.109784	−	0.993955i	$-0.535016\pi$
$5$	−2.13620	−	1.02874i	−0.955339	−	0.460067i	−0.845555	+	0.533888i	$0.820730\pi$
$6$	−0.367384	−	1.69264i	−0.149984	−	0.691017i
$7$	−1.53826	+	2.15262i	−0.581407	+	0.813613i
$7$	−1.53826	+	2.15262i	−0.581407	+	0.813613i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$	0.605021	+	2.93836i	0.201674	+	0.979453i
$10$	1.02874	+	2.13620i	0.325317	+	0.675527i
$11$	2.95567	+	2.35707i	0.891168	+	0.710683i	0.957904	−	0.287088i	$-0.0926872\pi$
$11$	2.95567	+	2.35707i	0.891168	+	0.710683i	−0.0667365	+	0.997771i	$0.521259\pi$
$12$	−0.768111	+	1.55242i	−0.221735	+	0.448145i
$13$	3.59671	+	2.86828i	0.997547	+	0.795518i	0.978907	−	0.204309i	$-0.0654946\pi$
$13$	3.59671	+	2.86828i	0.997547	+	0.795518i	0.0186410	+	0.999826i	$0.494066\pi$
$14$	2.54479	−	0.723897i	0.680125	−	0.193470i
$15$	−1.74227	−	3.71881i	−0.449851	−	0.960192i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.623946	−	2.73368i	0.151329	−	0.663016i	−0.841171	−	0.540770i	$-0.818133\pi$
$17$	0.623946	−	2.73368i	0.151329	−	0.663016i	0.992500	−	0.122246i	$-0.0390098\pi$
$18$	1.35901	−	2.67453i	0.320322	−	0.630392i
$19$			7.99958i			1.83523i	0.397471	+	0.917615i	$0.369888\pi$
$19$			7.99958i			1.83523i	−0.397471	+	0.917615i	$0.630112\pi$
$20$	0.527599	−	2.31156i	0.117975	−	0.516881i
$21$	−4.42083	+	1.20674i	−0.964705	+	0.263332i
$22$	−0.841228	−	3.68566i	−0.179350	−	0.785785i
$23$	−5.35612	+	1.22250i	−1.11683	+	0.254909i	−0.740817	−	0.671707i	$-0.765561\pi$
$23$	−5.35612	+	1.22250i	−1.11683	+	0.254909i	−0.376010	+	0.926615i	$0.622704\pi$
$24$	1.56845	−	0.734821i	0.320159	−	0.149995i
$25$	0.387609	+	0.486046i	0.0775218	+	0.0972092i
$26$	−1.02368	−	4.48502i	−0.200760	−	0.879585i
$27$	−2.40315	+	4.60704i	−0.462487	+	0.886626i
$28$	−2.44094	−	1.02069i	−0.461295	−	0.192892i
$29$	0.336112	+	0.0767154i	0.0624145	+	0.0142457i	0.253614	−	0.967305i	$-0.418381\pi$
$29$	0.336112	+	0.0767154i	0.0624145	+	0.0142457i	−0.191200	+	0.981551i	$0.561238\pi$
$30$	−0.956481	+	3.99377i	−0.174629	+	0.729159i
$31$		−	4.40479i		−	0.791124i	−0.918439	−	0.395562i	$-0.870550\pi$
$31$		−	4.40479i		−	0.791124i	0.918439	−	0.395562i	$-0.129450\pi$
$32$	0.974928	+	0.222521i	0.172345	+	0.0393365i
$33$	1.38887	+	6.39893i	0.241772	+	1.11391i
$34$	−2.19224	+	1.74826i	−0.375967	+	0.299824i
$35$	5.50052	−	3.01596i	0.929757	−	0.509791i
$36$	−2.73006	+	1.24370i	−0.455010	+	0.207283i
$37$	2.03185	−	8.90210i	0.334033	−	1.46350i	−0.477211	−	0.878789i	$-0.658352\pi$
$37$	2.03185	−	8.90210i	0.334033	−	1.46350i	0.811245	−	0.584707i	$-0.198791\pi$
$38$	4.98766	−	6.25432i	0.809105	−	1.01459i
$39$	1.69010	+	7.78676i	0.270633	+	1.24688i
$40$	−1.85373	+	1.47830i	−0.293100	+	0.233740i
$41$	3.26974	+	1.57462i	0.510647	+	0.245915i	0.671420	−	0.741077i	$-0.265684\pi$
$41$	3.26974	+	1.57462i	0.510647	+	0.245915i	−0.160773	+	0.986991i	$0.551399\pi$
$42$	4.20874	+	1.81288i	0.649422	+	0.279733i
$43$	6.98003	−	3.36141i	1.06445	−	0.512610i	0.182133	−	0.983274i	$-0.441700\pi$
$43$	6.98003	−	3.36141i	1.06445	−	0.512610i	0.882312	+	0.470664i	$0.155986\pi$
$44$	−1.64027	+	3.40606i	−0.247280	+	0.513483i
$45$	1.73036	−	6.89934i	0.257947	−	1.02849i
$46$	4.94980	+	2.38370i	0.729808	+	0.351457i
$47$	−2.12713	+	2.66734i	−0.310274	+	0.389072i	−0.912380	−	0.409345i	$-0.865757\pi$
$47$	−2.12713	+	2.66734i	−0.310274	+	0.389072i	0.602105	+	0.798417i	$0.294329\pi$
$48$	−1.68442	−	0.403407i	−0.243125	−	0.0582268i
$49$	−2.26753	−	6.62256i	−0.323933	−	0.946080i
$50$		−	0.621676i		−	0.0879183i
$51$	3.82916	−	2.98740i	0.536190	−	0.418319i
$52$	−1.99602	+	4.14478i	−0.276799	+	0.574778i
$53$	4.76629	−	1.08788i	0.654701	−	0.149431i	0.117748	−	0.993044i	$-0.462433\pi$
$53$	4.76629	−	1.08788i	0.654701	−	0.149431i	0.536953	+	0.843612i	$0.319575\pi$
$54$	4.75131	−	2.10359i	0.646571	−	0.286262i
$55$	−3.88910	−	8.07580i	−0.524406	−	1.08894i
$56$	1.27202	+	2.31991i	0.169980	+	0.310011i
$57$	−8.75393	+	10.7400i	−1.15949	+	1.42255i
$58$	−0.214952	−	0.269541i	−0.0282246	−	0.0353925i
$59$	−9.34907	+	4.50227i	−1.21714	+	0.586146i	−0.928515	−	0.371295i	$-0.878914\pi$
$59$	−9.34907	+	4.50227i	−1.21714	+	0.586146i	−0.288630	+	0.957441i	$0.593200\pi$
$60$	3.23788	−	2.52610i	0.418009	−	0.326118i
$61$	−7.60031	−	1.73472i	−0.973120	−	0.222108i	−0.293732	−	0.955888i	$-0.594897\pi$
$61$	−7.60031	−	1.73472i	−0.973120	−	0.222108i	−0.679388	+	0.733779i	$0.737755\pi$
$62$	−2.74634	+	3.44381i	−0.348786	+	0.437364i
$63$	−7.25584	−	3.21757i	−0.914150	−	0.405376i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−4.73258	−	9.82731i	−0.587005	−	1.21893i
$66$	2.90380	−	5.86883i	0.357433	−	0.722403i
$67$	6.99996			0.855181			0.427591	−	0.903972i	$-0.359362\pi$
$67$	6.99996			0.855181			0.427591	+	0.903972i	$0.359362\pi$
$68$	2.80399			0.340033
$69$	−8.52877	−	4.21989i	−1.02674	−	0.508015i
$70$	−6.18090	−	1.07154i	−0.738759	−	0.128074i
$71$	11.0631	−	2.52507i	1.31294	−	0.299671i	0.491958	−	0.870619i	$-0.336281\pi$
$71$	11.0631	−	2.52507i	1.31294	−	0.299671i	0.820986	+	0.570948i	$0.193424\pi$
$72$	2.90988	+	0.729801i	0.342932	+	0.0860078i
$73$	7.61996	−	6.07671i	0.891848	−	0.711225i	−0.0662078	−	0.997806i	$-0.521090\pi$
$73$	7.61996	−	6.07671i	0.891848	−	0.711225i	0.958056	+	0.286580i	$0.0925186\pi$
$74$	−7.13893	+	5.69310i	−0.829883	+	0.661810i
$75$	−0.0114852	+	1.07671i	−0.00132620	+	0.124328i
$76$	−7.79901	+	1.78007i	−0.894608	+	0.204188i
$77$	−9.62044	+	2.73665i	−1.09635	+	0.311870i
$78$	3.53359	−	7.14169i	0.400100	−	0.808637i
$79$	4.27717			0.481219			0.240609	−	0.970622i	$-0.422653\pi$
$79$	4.27717			0.481219			0.240609	+	0.970622i	$0.422653\pi$
$80$	2.37101			0.265087
$81$	−8.26790	+	3.55554i	−0.918655	+	0.395060i
$82$	−1.57462	−	3.26974i	−0.173888	−	0.361082i
$83$	−6.09768	−	7.64625i	−0.669307	−	0.839285i	0.325014	−	0.945709i	$-0.394631\pi$
$83$	−6.09768	−	7.64625i	−0.669307	−	0.839285i	−0.994321	+	0.106425i	$0.966060\pi$
$84$	−2.16021	−	4.04147i	−0.235699	−	0.440960i
$85$	−4.14513	+	5.19783i	−0.449602	+	0.563784i
$86$	−7.55301	−	1.72393i	−0.814462	−	0.185896i
$87$	0.367307	+	0.470804i	0.0393794	+	0.0504754i
$88$	3.40606	−	1.64027i	0.363087	−	0.174854i
$89$	1.65793	+	2.07898i	0.175740	+	0.220371i	0.861898	−	0.507081i	$-0.169276\pi$
$89$	1.65793	+	2.07898i	0.175740	+	0.220371i	−0.686158	+	0.727452i	$0.740704\pi$
$90$	−5.65452	+	4.31526i	−0.596039	+	0.454868i
$91$	−11.7070	+	3.33019i	−1.22722	+	0.349099i
$92$	−2.38370	−	4.94980i	−0.248517	−	0.516052i
$93$	4.82016	−	5.91377i	0.499827	−	0.613229i
$94$	3.32612	−	0.759165i	0.343063	−	0.0783019i
$95$	8.22950	−	17.0887i	0.844329	−	1.75327i
$96$	1.06541	+	1.36561i	0.108738	+	0.139377i
$97$			9.98133i			1.01345i	0.862108	+	0.506725i	$0.169144\pi$
$97$			9.98133i			1.01345i	−0.862108	+	0.506725i	$0.830856\pi$
$98$	−2.35627	+	6.59151i	−0.238019	+	0.665843i
$99$	−5.13767	+	10.1109i	−0.516355	+	1.01618i
$100$	−0.387609	+	0.486046i	−0.0387609	+	0.0486046i
$101$	−8.74971	−	4.21364i	−0.870629	−	0.419273i	−0.0554361	−	0.998462i	$-0.517655\pi$
$101$	−8.74971	−	4.21364i	−0.870629	−	0.419273i	−0.815193	+	0.579189i	$0.803369\pi$
$102$	−4.85637	−	0.0518025i	−0.480852	−	0.00512922i
$103$	0.110452	−	0.229356i	0.0108831	−	0.0225991i	−0.895456	−	0.445149i	$-0.853151\pi$
$103$	0.110452	−	0.229356i	0.0108831	−	0.0225991i	0.906340	+	0.422550i	$0.138865\pi$
$104$	4.14478	−	1.99602i	0.406429	−	0.195726i
$105$	10.6852	+	1.97005i	1.04277	+	0.192257i
$106$	−4.40472	−	2.12120i	−0.427824	−	0.206029i
$107$	10.7422	−	8.56659i	1.03848	−	0.828163i	0.0531135	−	0.998588i	$-0.483085\pi$
$107$	10.7422	−	8.56659i	1.03848	−	0.828163i	0.985371	+	0.170425i	$0.0545141\pi$
$108$	−5.02629	−	1.31774i	−0.483655	−	0.126799i
$109$	−1.02031	+	1.27943i	−0.0977284	+	0.122548i	−0.828291	−	0.560298i	$-0.810687\pi$
$109$	−1.02031	+	1.27943i	−0.0977284	+	0.122548i	0.730562	+	0.682846i	$0.239258\pi$
$110$	−1.99456	+	8.73872i	−0.190174	+	0.833205i
$111$	12.4695	−	9.72830i	1.18355	−	0.923369i
$112$	0.451936	−	2.60687i	0.0427039	−	0.246326i
$113$	−4.98621	+	3.97637i	−0.469063	+	0.374065i	−0.829307	−	0.558793i	$-0.811265\pi$
$113$	−4.98621	+	3.97637i	−0.469063	+	0.374065i	0.360244	+	0.932858i	$0.382693\pi$
$114$	13.5404	−	2.93892i	1.26817	−	0.275255i
$115$	12.6994	+	2.89855i	1.18422	+	0.270291i
$116$			0.344756i			0.0320098i
$117$	−6.25195	+	12.3038i	−0.577993	+	1.13749i
$118$	10.1165	+	2.30903i	0.931301	+	0.212563i
$119$	4.92479	+	5.54823i	0.451455	+	0.508605i
$120$	−4.10647	−	0.0438034i	−0.374868	−	0.00399869i
$121$	0.732482	+	3.20921i	0.0665893	+	0.291747i
$122$	4.86058	+	6.09498i	0.440056	+	0.551813i
$123$	2.66676	+	5.69212i	0.240454	+	0.513241i
$124$	4.29436	−	0.980159i	0.385644	−	0.0880208i
$125$	2.31000	+	10.1208i	0.206613	+	0.905229i
$126$	3.66672	+	7.03954i	0.326658	+	0.627132i
$127$	4.25337	−	18.6352i	0.377426	−	1.65361i	−0.327890	−	0.944716i	$-0.606338\pi$
$127$	4.25337	−	18.6352i	0.377426	−	1.65361i	0.705316	−	0.708893i	$-0.250805\pi$
$128$			1.00000i			0.0883883i
$129$	13.0496	+	3.12530i	1.14895	+	0.275167i
$130$	−2.42715	+	10.6340i	−0.212875	+	0.932665i
$131$	12.2534	−	5.90091i	1.07058	−	0.515565i	0.186288	−	0.982495i	$-0.440354\pi$
$131$	12.2534	−	5.90091i	1.07058	−	0.515565i	0.884294	+	0.466930i	$0.154640\pi$
$132$	−5.92944	+	2.77795i	−0.516091	+	0.241789i
$133$	−17.2200	−	12.3054i	−1.49317	−	1.06701i
$134$	−5.47279	−	4.36440i	−0.472777	−	0.377027i
$135$	9.87309	−	7.36936i	0.849740	−	0.634253i
$136$	−2.19224	−	1.74826i	−0.187983	−	0.149912i
$137$	6.31457	+	13.1123i	0.539491	+	1.12026i	0.975434	+	0.220290i	$0.0707003\pi$
$137$	6.31457	+	13.1123i	0.539491	+	1.12026i	−0.435944	+	0.899974i	$0.643585\pi$
$138$	4.03700	+	8.61685i	0.343652	+	0.733515i
$139$	−4.61502	+	9.58319i	−0.391441	+	0.812835i	0.608375	+	0.793650i	$0.291822\pi$
$139$	−4.61502	+	9.58319i	−0.391441	+	0.812835i	−0.999816	+	0.0191856i	$0.993893\pi$
$140$	4.16433	+	4.69149i	0.351950	+	0.396504i
$141$	−5.77471	+	1.25339i	−0.486318	+	0.105554i
$142$	−10.2238	−	4.92353i	−0.857963	−	0.413173i
$143$	3.86995	+	16.9554i	0.323622	+	1.41788i
$144$	−1.82001	−	2.38486i	−0.151668	−	0.198738i
$145$	−0.639084	−	0.509653i	−0.0530730	−	0.0423243i
$146$	−9.74629			−0.806609
$147$	4.20273	−	11.3726i	0.346635	−	0.938000i
$148$	9.13103			0.750566
$149$	−1.87558	−	1.49573i	−0.153654	−	0.122535i	0.543645	−	0.839315i	$-0.317044\pi$
$149$	−1.87558	−	1.49573i	−0.153654	−	0.122535i	−0.697299	+	0.716780i	$0.745615\pi$
$150$	0.680300	−	0.834648i	0.0555462	−	0.0681487i
$151$	3.55740	+	15.5860i	0.289497	+	1.26837i	0.885217	+	0.465178i	$0.154010\pi$
$151$	3.55740	+	15.5860i	0.289497	+	1.26837i	−0.595720	+	0.803192i	$0.703133\pi$
$152$	7.20737	+	3.47089i	0.584595	+	0.281526i
$153$	8.41004	+	0.179439i	0.679912	+	0.0145068i
$154$	9.22784	+	3.85865i	0.743601	+	0.310939i
$155$	−4.53139	+	9.40954i	−0.363970	+	0.755792i
$156$	−7.21544	+	3.38044i	−0.577698	+	0.270652i
$157$	2.71167	+	5.63085i	0.216415	+	0.449391i	0.980708	−	0.195479i	$-0.0626260\pi$
$157$	2.71167	+	5.63085i	0.216415	+	0.449391i	−0.764293	+	0.644869i	$0.776912\pi$
$158$	−3.34402	−	2.66677i	−0.266036	−	0.212157i
$159$	7.58957	+	3.75519i	0.601892	+	0.297806i
$160$	−1.85373	−	1.47830i	−0.146550	−	0.116870i
$161$	5.60751	−	13.4102i	0.441934	−	1.05687i
$162$	8.68095	+	2.37512i	0.682039	+	0.186607i
$163$	10.3429	−	4.98087i	0.810117	−	0.390132i	0.0174966	−	0.999847i	$-0.494430\pi$
$163$	10.3429	−	4.98087i	0.810117	−	0.390132i	0.792621	+	0.609715i	$0.208716\pi$
$164$	−0.807559	+	3.53815i	−0.0630597	+	0.276283i
$165$	3.61592	−	15.0982i	0.281499	−	1.17539i
$166$			9.77992i			0.759069i
$167$	−4.75773	+	20.8450i	−0.368164	+	1.61303i	0.363656	+	0.931533i	$0.381529\pi$
$167$	−4.75773	+	20.8450i	−0.368164	+	1.61303i	−0.731820	+	0.681498i	$0.761329\pi$
$168$	−0.830892	+	4.50662i	−0.0641047	+	0.347693i
$169$	1.81651	+	7.95867i	0.139732	+	0.612205i
$170$	6.48159	−	1.47938i	0.497115	−	0.113463i
$171$	−23.5056	+	4.83991i	−1.79752	+	0.370117i
$172$	4.83033	+	6.05705i	0.368309	+	0.461845i
$173$	−4.24603	−	18.6031i	−0.322820	−	1.41436i	−0.832511	−	0.554008i	$-0.813098\pi$
$173$	−4.24603	−	18.6031i	−0.322820	−	1.41436i	0.509692	−	0.860357i	$-0.329759\pi$
$174$	0.00636923	−	0.597101i	0.000482850	−	0.0452661i
$175$	−1.64251	+	0.0867100i	−0.124162	+	0.00655466i
$176$	−3.68566	−	0.841228i	−0.277817	−	0.0634099i
$177$	−17.4787	−	4.18603i	−1.31378	−	0.314641i
$178$		−	2.65911i		−	0.199309i
$179$	2.02351	+	0.461853i	0.151244	+	0.0345205i	0.297473	−	0.954730i	$-0.403856\pi$
$179$	2.02351	+	0.461853i	0.151244	+	0.0345205i	−0.146228	+	0.989251i	$0.546713\pi$
$180$	7.11140	+	0.151731i	0.530053	+	0.0113094i
$181$	−1.28680	+	1.02619i	−0.0956474	+	0.0762762i	−0.670146	−	0.742229i	$-0.733769\pi$
$181$	−1.28680	+	1.02619i	−0.0956474	+	0.0762762i	0.574499	+	0.818506i	$0.305197\pi$
$182$	11.2292	+	4.69553i	0.832365	+	0.348056i
$183$	−8.30569	−	10.6460i	−0.613975	−	0.786975i
$184$	−1.22250	+	5.35612i	−0.0901238	+	0.394858i
$185$	−13.4984	+	16.9265i	−0.992422	+	1.24446i
$186$	−7.45573	+	1.61825i	−0.546680	+	0.118656i
$187$	8.28765	−	6.60918i	0.606053	−	0.483311i
$188$	−3.07380	−	1.48026i	−0.224180	−	0.107959i
$189$	−6.22054	−	12.2599i	−0.452477	−	0.891776i
$190$	−17.0887	+	8.22950i	−1.23975	+	0.597031i
$191$	−3.16653	+	6.57538i	−0.229122	+	0.475778i	−0.983557	−	0.180598i	$-0.942197\pi$
$191$	−3.16653	+	6.57538i	−0.229122	+	0.475778i	0.754435	+	0.656375i	$0.227911\pi$
$192$	0.0184746	−	1.73195i	0.00133329	−	0.124993i
$193$	−11.7441	−	5.65564i	−0.845356	−	0.407102i	−0.0395044	−	0.999219i	$-0.512578\pi$
$193$	−11.7441	−	5.65564i	−0.845356	−	0.407102i	−0.805852	+	0.592117i	$0.798292\pi$
$194$	6.22326	−	7.80372i	0.446804	−	0.560274i
$195$	4.40016	−	18.3728i	0.315102	−	1.31570i
$196$	5.95195	−	3.68434i	0.425139	−	0.263167i
$197$		−	24.2425i		−	1.72720i	−0.504175	−	0.863602i	$-0.668203\pi$
$197$		−	24.2425i		−	1.72720i	0.504175	−	0.863602i	$-0.331797\pi$
$198$	10.3208	−	4.70173i	0.733469	−	0.334137i
$199$	2.95759	−	6.14149i	0.209658	−	0.435359i	−0.769448	−	0.638709i	$-0.779469\pi$
$199$	2.95759	−	6.14149i	0.209658	−	0.435359i	0.979106	+	0.203350i	$0.0651830\pi$
$200$	0.606090	−	0.138336i	0.0428570	−	0.00978183i
$201$	9.39798	+	7.66005i	0.662882	+	0.540298i
$202$	4.21364	+	8.74971i	0.296471	+	0.615628i
$203$	−0.682166	+	0.605513i	−0.0478787	+	0.0424987i
$204$	3.76456	+	3.06840i	0.263572	+	0.214831i
$205$	−5.36495	−	6.72743i	−0.374704	−	0.469864i
$206$	−0.229356	+	0.110452i	−0.0159800	+	0.00769555i
$207$	−6.83270	−	14.9986i	−0.474906	−	1.04247i
$208$	−4.48502	−	1.02368i	−0.310980	−	0.0709792i
$209$	−18.8555	+	23.6441i	−1.30427	+	1.63550i
$210$	−7.12574	−	8.20238i	−0.491723	−	0.566018i
$211$	2.86368	+	3.59094i	0.197144	+	0.247210i	0.870571	−	0.492043i	$-0.163750\pi$
$211$	2.86368	+	3.59094i	0.197144	+	0.247210i	−0.673427	+	0.739254i	$0.735178\pi$
$212$	2.12120	+	4.40472i	0.145685	+	0.302517i
$213$	17.6162	+	8.71619i	1.20704	+	0.597224i
$214$	−13.7397			−0.939229
$215$	−18.3688			−1.25274
$216$	3.10811	+	4.16409i	0.211480	+	0.283330i
$217$	9.48184	+	6.77570i	0.643669	+	0.459965i
$218$	1.59543	−	0.364146i	0.108056	−	0.0246631i
$219$	16.8801	+	0.180059i	1.14065	+	0.0121673i
$220$	7.00791	−	5.58862i	0.472473	−	0.376785i
$221$	10.0851	−	8.04261i	0.678399	−	0.541005i
$222$	−15.8145	−	0.168692i	−1.06140	−	0.0113219i
$223$	5.57166	−	1.27170i	0.373106	−	0.0851590i	−0.0318561	−	0.999492i	$-0.510142\pi$
$223$	5.57166	−	1.27170i	0.373106	−	0.0851590i	0.404962	+	0.914333i	$0.367285\pi$
$224$	−1.97869	+	1.75635i	−0.132207	+	0.117351i
$225$	−1.19367	+	1.43300i	−0.0795778	+	0.0955335i
$226$	6.37760			0.424232
$227$	14.1568			0.939622			0.469811	−	0.882767i	$-0.344322\pi$
$227$	14.1568			0.939622			0.469811	+	0.882767i	$0.344322\pi$
$228$	−12.4187	−	6.14456i	−0.822448	−	0.406934i
$229$	2.70851	+	5.62429i	0.178984	+	0.371663i	0.971088	−	0.238723i	$-0.0767287\pi$
$229$	2.70851	+	5.62429i	0.178984	+	0.371663i	−0.792104	+	0.610386i	$0.791014\pi$
$230$	−8.12157	−	10.1841i	−0.535520	−	0.671521i
$231$	−15.9109	−	6.85348i	−1.04686	−	0.450926i
$232$	0.214952	−	0.269541i	0.0141123	−	0.0176962i
$233$	−14.3975	−	3.28613i	−0.943209	−	0.215281i	−0.276851	−	0.960913i	$-0.589291\pi$
$233$	−14.3975	−	3.28613i	−0.943209	−	0.215281i	−0.666358	+	0.745632i	$0.732148\pi$
$234$	12.5593	−	5.72146i	0.821024	−	0.374024i
$235$	7.28799	−	3.50971i	0.475416	−	0.228948i
$236$	−6.46975	−	8.11282i	−0.421145	−	0.528099i
$237$	5.74242	+	4.68050i	0.373010	+	0.304031i
$238$	−0.391093	−	7.40833i	−0.0253508	−	0.480211i
$239$	2.71183	+	5.63116i	0.175413	+	0.364250i	0.970076	−	0.242802i	$-0.0780665\pi$
$239$	2.71183	+	5.63116i	0.175413	+	0.364250i	−0.794663	+	0.607051i	$0.792352\pi$
$240$	3.18326	+	2.59459i	0.205478	+	0.167480i
$241$	9.61260	−	2.19401i	0.619202	−	0.141329i	0.0985982	−	0.995127i	$-0.468564\pi$
$241$	9.61260	−	2.19401i	0.619202	−	0.141329i	0.520604	+	0.853799i	$0.325707\pi$
$242$	1.42823	−	2.96576i	0.0918104	−	0.190646i
$243$	−14.9911	−	4.27397i	−0.961680	−	0.274175i
$244$		−	7.79577i		−	0.499073i
$245$	−1.96900	+	16.4798i	−0.125795	+	1.05286i
$246$	1.46402	−	6.11298i	0.0933424	−	0.389749i
$247$	−22.9450	+	28.7722i	−1.45996	+	1.83073i
$248$	−3.96858	−	1.91117i	−0.252005	−	0.121359i
$249$	0.180680	−	16.9384i	0.0114501	−	1.07342i
$250$	4.50416	−	9.35299i	0.284868	−	0.591535i
$251$	17.6266	−	8.48852i	1.11258	−	0.535791i	0.214988	−	0.976617i	$-0.431029\pi$
$251$	17.6266	−	8.48852i	1.11258	−	0.535791i	0.897593	+	0.440826i	$0.145314\pi$
$252$	1.52232	−	7.78990i	0.0958974	−	0.490718i
$253$	−18.7124	−	9.01142i	−1.17644	−	0.566543i
$254$	−14.9443	+	11.9177i	−0.937688	+	0.747782i
$255$	−11.2531	+	2.44247i	−0.704698	+	0.152953i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−2.92870	+	12.8315i	−0.182687	+	0.800404i	0.797657	+	0.603111i	$0.206072\pi$
$257$	−2.92870	+	12.8315i	−0.182687	+	0.800404i	−0.980344	+	0.197294i	$0.936785\pi$
$258$	−8.25400	−	10.5798i	−0.513872	−	0.658667i
$259$	16.0373	+	18.0675i	0.996510	+	1.12266i
$260$	8.52782	−	6.80071i	0.528873	−	0.421762i
$261$	−0.0220624	+	1.03403i	−0.00136563	+	0.0640050i
$262$	−13.2592	−	3.02633i	−0.819158	−	0.186967i
$263$		−	18.5946i		−	1.14659i	−0.819348	−	0.573297i	$-0.805664\pi$
$263$		−	18.5946i		−	1.14659i	0.819348	−	0.573297i	$-0.194336\pi$
$264$	6.36784	+	1.52506i	0.391914	+	0.0938608i
$265$	−11.3009	−	2.57936i	−0.694210	−	0.158449i
$266$	5.79087	+	20.3573i	0.355061	+	1.24818i
$267$	−0.0491261	+	4.60546i	−0.00300647	+	0.281849i
$268$	1.55764	+	6.82446i	0.0951479	+	0.416870i
$269$	6.39776	+	8.02253i	0.390078	+	0.489143i	0.937633	−	0.347627i	$-0.113013\pi$
$269$	6.39776	+	8.02253i	0.390078	+	0.489143i	−0.547555	+	0.836770i	$0.684441\pi$
$270$	−12.3138	−	0.394171i	−0.749395	−	0.0239885i
$271$	−16.2458	+	3.70800i	−0.986862	+	0.225245i	−0.685347	−	0.728216i	$-0.740350\pi$
$271$	−16.2458	+	3.70800i	−0.986862	+	0.225245i	−0.301515	+	0.953461i	$0.597492\pi$
$272$	0.623946	+	2.73368i	0.0378323	+	0.165754i
$273$	−19.3617	−	8.33989i	−1.17182	−	0.504753i
$274$	3.23848	−	14.1887i	0.195644	−	0.857172i
$275$			2.35021i			0.141723i
$276$	2.21626	−	9.25395i	0.133403	−	0.557022i
$277$	2.18460	−	9.57137i	0.131260	−	0.575088i	−0.865929	−	0.500166i	$-0.833272\pi$
$277$	2.18460	−	9.57137i	0.131260	−	0.575088i	0.997189	−	0.0749216i	$-0.0238706\pi$
$278$	9.58319	−	4.61502i	0.574761	−	0.276790i
$279$	12.9429	−	2.66499i	0.774869	−	0.159549i
$280$	−0.330703	−	6.26437i	−0.0197633	−	0.374368i
$281$	6.25145	+	4.98537i	0.372930	+	0.297402i	0.791963	−	0.610569i	$-0.209059\pi$
$281$	6.25145	+	4.98537i	0.372930	+	0.297402i	−0.419033	+	0.907971i	$0.637631\pi$
$282$	5.29632	+	2.62053i	0.315391	+	0.156050i
$283$	−16.7878	−	13.3878i	−0.997933	−	0.795825i	−0.0189611	−	0.999820i	$-0.506036\pi$
$283$	−16.7878	−	13.3878i	−0.997933	−	0.795825i	−0.978972	+	0.203995i	$0.934607\pi$
$284$	4.92353	+	10.2238i	0.292158	+	0.606671i
$285$	29.7489	−	13.9374i	1.76217	−	0.825580i
$286$	7.54585	−	15.6691i	0.446195	−	0.926534i
$287$	−8.41926	+	4.61632i	−0.496973	+	0.272493i
$288$	−0.0639943	+	2.99932i	−0.00377090	+	0.176736i
$289$	8.23275	+	3.96468i	0.484279	+	0.233217i
$290$	0.181893	+	0.796925i	0.0106811	+	0.0467970i
$291$	−10.9226	+	13.4007i	−0.640291	+	0.785563i
$292$	7.61996	+	6.07671i	0.445924	+	0.355613i
$293$	15.8995			0.928859			0.464429	−	0.885610i	$-0.346259\pi$
$293$	15.8995			0.928859			0.464429	+	0.885610i	$0.346259\pi$
$294$	−10.3766	+	6.27114i	−0.605173	+	0.365740i
$295$	24.6032			1.43245
$296$	−7.13893	−	5.69310i	−0.414942	−	0.330905i
$297$	−17.9620	+	7.95250i	−1.04226	+	0.461451i
$298$	0.533819	+	2.33881i	0.0309233	+	0.135484i
$299$	−22.7709	−	10.9659i	−1.31687	−	0.634172i
$300$	−1.05227	+	0.228394i	−0.0607531	+	0.0131863i
$301$	−3.50126	+	20.1961i	−0.201809	+	1.16408i
$302$	6.93642	−	14.4036i	0.399146	−	0.828835i
$303$	−7.13618	−	15.2319i	−0.409963	−	0.875052i
$304$	−3.47089	−	7.20737i	−0.199069	−	0.413371i
$305$	14.4512	+	11.5245i	0.827475	+	0.659890i
$306$	−6.46336	−	5.38387i	−0.369486	−	0.307775i
$307$	−0.781596	−	0.623302i	−0.0446080	−	0.0355737i	0.600932	−	0.799300i	$-0.294796\pi$
$307$	−0.781596	−	0.623302i	−0.0446080	−	0.0355737i	−0.645540	+	0.763726i	$0.723368\pi$
$308$	−4.80879	−	8.77028i	−0.274006	−	0.499733i
$309$	0.399274	−	0.187060i	0.0227139	−	0.0106415i
$310$	9.40954	−	4.53139i	0.534426	−	0.257366i
$311$	−4.59661	+	20.1391i	−0.260650	+	1.14198i	0.659899	+	0.751355i	$0.270599\pi$
$311$	−4.59661	+	20.1391i	−0.260650	+	1.14198i	−0.920549	+	0.390628i	$0.872258\pi$
$312$	7.74893	+	1.85582i	0.438697	+	0.105065i
$313$		−	11.7662i		−	0.665063i	−0.943092	−	0.332532i	$-0.892097\pi$
$313$		−	11.7662i		−	0.665063i	0.943092	−	0.332532i	$-0.107903\pi$
$314$	1.39071	−	6.09308i	0.0784820	−	0.343852i
$315$	12.1899	+	14.3378i	0.686824	+	0.807842i
$316$	0.951759	+	4.16993i	0.0535406	+	0.234577i
$317$	−1.10675	+	0.252609i	−0.0621615	+	0.0141880i	−0.253489	−	0.967338i	$-0.581578\pi$
$317$	−1.10675	+	0.252609i	−0.0621615	+	0.0141880i	0.191327	+	0.981526i	$0.438721\pi$
$318$	−3.59244	−	7.66795i	−0.201454	−	0.429997i
$319$	0.812613	+	1.01898i	0.0454976	+	0.0570522i
$320$	0.527599	+	2.31156i	0.0294937	+	0.129220i
$321$	23.7966	+	0.253836i	1.32820	+	0.0141678i
$322$	−12.7452	+	6.98828i	−0.710265	+	0.389442i
$323$	21.8683	+	4.99130i	1.21679	+	0.277723i
$324$	−5.30617	−	7.26942i	−0.294787	−	0.403857i
$325$			2.85994i			0.158641i
$326$	−11.1919	−	2.55448i	−0.619863	−	0.141480i
$327$	−2.76993	+	0.601209i	−0.153178	+	0.0332469i
$328$	2.83737	−	2.26273i	0.156668	−	0.124938i
$329$	−2.46969	−	8.68196i	−0.136158	−	0.478652i
$330$	−12.2406	+	9.54976i	−0.673824	+	0.525697i
$331$	5.23791	−	22.9488i	0.287901	−	1.26138i	−0.599498	−	0.800376i	$-0.704633\pi$
$331$	5.23791	−	22.9488i	0.287901	−	1.26138i	0.887399	−	0.461002i	$-0.152510\pi$
$332$	6.09768	−	7.64625i	0.334654	−	0.419642i
$333$	27.3869	+	0.584334i	1.50079	+	0.0320213i
$334$	16.7164	−	13.3309i	0.914679	−	0.729432i
$335$	−14.9533	−	7.20115i	−0.816989	−	0.393441i
$336$	3.45945	−	3.00536i	0.188728	−	0.163956i
$337$	23.8151	−	11.4687i	1.29729	−	0.624742i	0.347515	−	0.937675i	$-0.387026\pi$
$337$	23.8151	−	11.4687i	1.29729	−	0.624742i	0.949775	+	0.312933i	$0.101311\pi$
$338$	3.54194	−	7.35491i	0.192656	−	0.400055i
$339$	−11.0457	−	0.117824i	−0.599920	−	0.00639930i
$340$	−5.98989	−	2.88458i	−0.324847	−	0.156438i
$341$	10.3824	−	13.0191i	0.562238	−	0.705024i
$342$	21.3951	+	10.8715i	1.15691	+	0.587865i
$343$	17.7439	+	5.30607i	0.958080	+	0.286501i
$344$		−	7.74725i		−	0.417704i
$345$	13.8780	+	17.7885i	0.747167	+	0.957698i
$346$	−8.27914	+	17.1918i	−0.445089	+	0.924238i
$347$	−23.5226	+	5.36887i	−1.26276	+	0.288216i	−0.800932	−	0.598755i	$-0.795662\pi$
$347$	−23.5226	+	5.36887i	−1.26276	+	0.288216i	−0.461825	+	0.886971i	$0.652805\pi$
$348$	−0.377266	+	0.462861i	−0.0202236	+	0.0248120i
$349$	−3.68875	−	7.65977i	−0.197454	−	0.410018i	0.778607	−	0.627511i	$-0.215926\pi$
$349$	−3.68875	−	7.65977i	−0.197454	−	0.410018i	−0.976062	+	0.217493i	$0.930212\pi$
$350$	1.33823	+	0.956298i	0.0715315	+	0.0511163i
$351$	−21.8577	+	9.67727i	−1.16668	+	0.516535i
$352$	2.35707	+	2.95567i	0.125632	+	0.157538i
$353$	13.1768	−	6.34562i	0.701331	−	0.337743i	−0.0490061	−	0.998798i	$-0.515605\pi$
$353$	13.1768	−	6.34562i	0.701331	−	0.337743i	0.750337	+	0.661055i	$0.229891\pi$
$354$	11.0554	+	14.1705i	0.587589	+	0.753155i
$355$	−26.2306	−	5.98697i	−1.39218	−	0.317755i
$356$	−1.65793	+	2.07898i	−0.0878701	+	0.110186i
$357$	0.540489	+	12.8381i	0.0286057	+	0.679465i
$358$	−1.29408	−	1.62273i	−0.0683945	−	0.0857640i
$359$	3.73278	+	7.75120i	0.197009	+	0.409093i	0.975947	−	0.218008i	$-0.0699558\pi$
$359$	3.73278	+	7.75120i	0.197009	+	0.409093i	−0.778938	+	0.627101i	$0.784242\pi$
$360$	−5.46532	−	4.55252i	−0.288047	−	0.239939i
$361$	−44.9933			−2.36807
$362$	1.64588			0.0865057
$363$	−2.52843	+	5.11017i	−0.132708	+	0.268214i
$364$	−5.85174	−	10.6724i	−0.306715	−	0.559387i
$365$	−22.5291	+	5.14213i	−1.17923	+	0.269151i
$366$	−0.144024	+	13.5019i	−0.00752824	+	0.705756i
$367$	−1.55842	+	1.24280i	−0.0813488	+	0.0648735i	−0.663320	−	0.748336i	$-0.730853\pi$
$367$	−1.55842	+	1.24280i	−0.0813488	+	0.0648735i	0.581971	+	0.813209i	$0.302282\pi$
$368$	4.29527	−	3.42536i	0.223907	−	0.178559i
$369$	−2.64855	+	10.5603i	−0.137878	+	0.549749i
$370$	21.1069	−	4.81752i	1.09730	−	0.250451i
$371$	−4.99000	+	11.9334i	−0.259068	+	0.619553i
$372$	6.83808	+	3.38337i	0.354538	+	0.175420i
$373$	−9.67188			−0.500791			−0.250396	−	0.968144i	$-0.580561\pi$
$373$	−9.67188			−0.500791			−0.250396	+	0.968144i	$0.580561\pi$
$374$	−10.6003			−0.548129
$375$	−7.97379	+	16.1157i	−0.411765	+	0.832212i
$376$	1.48026	+	3.07380i	0.0763387	+	0.158519i
$377$	0.988857	+	1.23999i	0.0509287	+	0.0638626i
$378$	−2.78051	+	13.4636i	−0.143014	+	0.692493i
$379$	−16.5361	+	20.7356i	−0.849403	+	1.06512i	0.147698	+	0.989032i	$0.452814\pi$
$379$	−16.5361	+	20.7356i	−0.849403	+	1.06512i	−0.997101	+	0.0760852i	$0.975758\pi$
$380$	18.4915	+	4.22057i	0.948595	+	0.216511i
$381$	26.1030	−	20.3648i	1.33730	−	1.04332i
$382$	6.57538	−	3.16653i	0.336426	−	0.162014i
$383$	−13.1384	−	16.4750i	−0.671339	−	0.841832i	0.323186	−	0.946336i	$-0.395246\pi$
$383$	−13.1384	−	16.4750i	−0.671339	−	0.841832i	−0.994525	+	0.104503i	$0.966675\pi$
$384$	−1.09430	+	1.34258i	−0.0558432	+	0.0685130i
$385$	23.3665	+	4.05091i	1.19087	+	0.206453i
$386$	5.65564	+	11.7441i	0.287865	+	0.597757i
$387$	14.1001	+	18.4761i	0.716748	+	0.939194i
$388$	−9.73108	+	2.22105i	−0.494021	+	0.112757i
$389$	−1.90521	+	3.95621i	−0.0965981	+	0.200588i	−0.943668	−	0.330893i	$-0.892650\pi$
$389$	−1.90521	+	3.95621i	−0.0965981	+	0.200588i	0.847070	+	0.531481i	$0.178364\pi$
$390$	−14.8954	+	11.6210i	−0.754259	+	0.588450i
$391$			15.4047i			0.779049i
$392$	−6.95057	−	0.830447i	−0.351057	−	0.0419439i
$393$	22.9084	+	5.48642i	1.15558	+	0.276753i
$394$	−15.1149	+	18.9535i	−0.761479	+	0.954864i
$395$	−9.13690	−	4.40010i	−0.459727	−	0.221393i
$396$	−11.0006	−	2.75897i	−0.552802	−	0.138643i
$397$	1.49920	−	3.11311i	0.0752425	−	0.156243i	−0.859954	−	0.510371i	$-0.829508\pi$
$397$	1.49920	−	3.11311i	0.0752425	−	0.156243i	0.935197	+	0.354128i	$0.115222\pi$
$398$	−6.14149	+	2.95759i	−0.307845	+	0.148250i
$399$	−9.65342	−	35.3648i	−0.483275	−	1.77045i
$400$	−0.560111	−	0.269735i	−0.0280056	−	0.0134868i
$401$	−1.24286	+	0.991149i	−0.0620656	+	0.0494956i	−0.654031	−	0.756468i	$-0.726924\pi$
$401$	−1.24286	+	0.991149i	−0.0620656	+	0.0494956i	0.591966	+	0.805963i	$0.298352\pi$
$402$	−2.57168	−	11.8484i	−0.128264	−	0.590945i
$403$	12.6342	−	15.8428i	0.629353	−	0.789184i
$404$	2.16100	−	9.46796i	0.107514	−	0.471049i
$405$	21.3196	+	0.910178i	1.05938	+	0.0452271i
$406$	0.910870	−	0.0480858i	0.0452057	−	0.00238646i
$407$	26.9883	−	21.5225i	1.33776	−	1.06683i
$408$	−1.03014	−	4.74614i	−0.0509995	−	0.234969i
$409$	−38.2266	−	8.72497i	−1.89018	−	0.431422i	−0.890462	−	0.455057i	$-0.849619\pi$
$409$	−38.2266	−	8.72497i	−1.89018	−	0.431422i	−0.999721	+	0.0236347i	$0.992476\pi$
$410$			8.60471i			0.424956i
$411$	−5.87103	+	24.5144i	−0.289597	+	1.20920i
$412$	0.248183	+	0.0566462i	0.0122271	+	0.00279076i
$413$	4.68959	−	27.0506i	0.230760	−	1.33107i
$414$	−4.00942	+	15.9865i	−0.197052	+	0.785692i
$415$	5.15987	+	22.6069i	0.253288	+	1.10973i
$416$	2.86828	+	3.59671i	0.140629	+	0.176343i
$417$	−16.6829	+	7.81595i	−0.816964	+	0.382749i
$418$	29.4837	−	6.72947i	1.44210	−	0.329149i
$419$	−6.76718	−	29.6489i	−0.330598	−	1.44845i	−0.817975	−	0.575254i	$-0.804903\pi$
$419$	−6.76718	−	29.6489i	−0.330598	−	1.44845i	0.487377	−	0.873192i	$-0.337954\pi$
$420$	0.457029	+	10.8557i	0.0223007	+	0.529704i
$421$	−4.84652	+	21.2340i	−0.236205	+	1.03488i	0.708178	+	0.706034i	$0.249517\pi$
$421$	−4.84652	+	21.2340i	−0.236205	+	1.03488i	−0.944383	+	0.328847i	$0.893340\pi$
$422$		−	4.59298i		−	0.223583i
$423$	−9.12456	−	4.63648i	−0.443651	−	0.225433i
$424$	1.08788	−	4.76629i	0.0528319	−	0.231472i
$425$	1.57054	−	0.756334i	0.0761826	−	0.0366876i
$426$	−8.33843	−	17.7981i	−0.403998	−	0.862321i
$427$	15.4254	−	13.6921i	0.746489	−	0.662608i
$428$	10.7422	+	8.56659i	0.519242	+	0.414082i
$429$	−13.3585	+	26.9988i	−0.644956	+	1.30351i
$430$	14.3613	+	11.4528i	0.692563	+	0.552301i
$431$	8.92867	+	18.5406i	0.430079	+	0.893068i	0.997569	+	0.0696879i	$0.0222003\pi$
$431$	8.92867	+	18.5406i	0.430079	+	0.893068i	−0.567490	+	0.823380i	$0.692085\pi$
$432$	0.166246	−	5.19349i	0.00799853	−	0.249872i
$433$	7.22900	−	15.0112i	0.347403	−	0.721390i	−0.651916	−	0.758292i	$-0.726034\pi$
$433$	7.22900	−	15.0112i	0.347403	−	0.721390i	0.999319	+	0.0369011i	$0.0117486\pi$
$434$	−3.18862	−	11.2093i	−0.153058	−	0.538063i
$435$	−0.300307	−	1.38360i	−0.0143986	−	0.0663384i
$436$	−1.47440	−	0.710032i	−0.0706108	−	0.0340044i
$437$	−9.77947	−	42.8467i	−0.467816	−	2.04963i
$438$	−13.0851	−	10.6654i	−0.625232	−	0.509610i
$439$	−26.6150	−	21.2248i	−1.27027	−	1.01300i	−0.998720	−	0.0505778i	$-0.983894\pi$
$439$	−26.6150	−	21.2248i	−1.27027	−	1.01300i	−0.271546	−	0.962426i	$-0.587535\pi$
$440$	−8.96346			−0.427316
$441$	18.0876	−	10.6696i	0.861312	−	0.508076i
$442$	−12.8994			−0.613560
$443$	−5.48403	−	4.37337i	−0.260554	−	0.207785i	0.484496	−	0.874793i	$-0.339003\pi$
$443$	−5.48403	−	4.37337i	−0.260554	−	0.207785i	−0.745050	+	0.667009i	$0.767574\pi$
$444$	12.2591	+	9.99207i	0.581791	+	0.474203i
$445$	−1.40294	−	6.14670i	−0.0665059	−	0.291382i
$446$	−5.14899	−	2.47962i	−0.243812	−	0.117414i
$447$	−0.881340	−	4.06057i	−0.0416859	−	0.192059i
$448$	2.64207	−	0.139478i	0.124826	−	0.00658970i
$449$	0.844819	−	1.75428i	0.0398695	−	0.0827898i	−0.880083	−	0.474820i	$-0.842513\pi$
$449$	0.844819	−	1.75428i	0.0398695	−	0.0827898i	0.919952	+	0.392031i	$0.128227\pi$
$450$	1.82671	−	0.376127i	0.0861119	−	0.0177308i
$451$	5.95277	+	12.3611i	0.280305	+	0.582059i
$452$	−4.98621	−	3.97637i	−0.234532	−	0.187033i
$453$	−12.2796	+	24.8182i	−0.576948	+	1.16606i
$454$	−11.0683	−	8.82664i	−0.519459	−	0.414255i
$455$	28.4344	+	4.92949i	1.33302	+	0.231098i
$456$	5.87826	+	12.5469i	0.275275	+	0.587565i
$457$	−3.47151	+	1.67179i	−0.162390	+	0.0782031i	−0.513313	−	0.858201i	$-0.671582\pi$
$457$	−3.47151	+	1.67179i	−0.162390	+	0.0782031i	0.350923	+	0.936404i	$0.385868\pi$
$458$	1.38908	−	6.08598i	0.0649076	−	0.284379i
$459$	11.0948	+	9.44401i	0.517859	+	0.440809i
$460$			13.0260i			0.607339i
$461$	−3.47089	+	15.2070i	−0.161656	+	0.708260i	0.827509	+	0.561452i	$0.189757\pi$
$461$	−3.47089	+	15.2070i	−0.161656	+	0.708260i	−0.989165	+	0.146808i	$0.953100\pi$
$462$	8.16656	+	15.2785i	0.379943	+	0.710822i
$463$	7.09688	+	31.0935i	0.329820	+	1.44504i	0.819473	+	0.573118i	$0.194267\pi$
$463$	7.09688	+	31.0935i	0.329820	+	1.44504i	−0.489652	+	0.871918i	$0.662876\pi$
$464$	−0.336112	+	0.0767154i	−0.0156036	+	0.00356143i
$465$	−16.3806	+	7.67432i	−0.759631	+	0.355888i
$466$	9.20752	+	11.5459i	0.426530	+	0.534852i
$467$	−3.35797	−	14.7122i	−0.155389	−	0.680802i	−0.991265	−	0.131884i	$-0.957897\pi$
$467$	−3.35797	−	14.7122i	−0.155389	−	0.680802i	0.835877	−	0.548917i	$-0.184960\pi$
$468$	−13.3865	−	3.35735i	−0.618791	−	0.155193i
$469$	−10.7677	+	15.0682i	−0.497208	+	0.695787i
$470$	−7.88625	−	1.79999i	−0.363766	−	0.0830272i
$471$	−2.52120	+	10.5272i	−0.116171	+	0.485069i
$472$			10.3767i			0.477625i
$473$	28.5537	+	6.51720i	1.31290	+	0.299661i
$474$	−1.57136	−	7.23970i	−0.0721751	−	0.332530i
$475$	−3.88816	+	3.10071i	−0.178401	+	0.142270i
$476$	−4.31325	+	6.03591i	−0.197698	+	0.276656i
$477$	6.08027	+	13.3469i	0.278397	+	0.611112i
$478$	1.39078	−	6.09342i	0.0636129	−	0.278706i
$479$	−19.6833	+	24.6821i	−0.899353	+	1.12775i	0.0918983	+	0.995768i	$0.470707\pi$
$479$	−19.6833	+	24.6821i	−0.899353	+	1.12775i	−0.991252	+	0.131985i	$0.957865\pi$
$480$	−0.871071	−	4.01326i	−0.0397588	−	0.183179i
$481$	32.8417	−	26.1903i	1.49745	−	1.19418i
$482$	−8.88337	−	4.27801i	−0.404627	−	0.194858i
$483$	22.2033	−	11.8679i	1.01028	−	0.540009i
$484$	−2.96576	+	1.42823i	−0.134807	+	0.0649198i
$485$	10.2682	−	21.3222i	0.466255	−	0.968189i
$486$	9.05574	+	12.6883i	0.410777	+	0.575554i
$487$	−7.94629	−	3.82673i	−0.360081	−	0.173406i	0.245092	−	0.969500i	$-0.421182\pi$
$487$	−7.94629	−	3.82673i	−0.360081	−	0.173406i	−0.605173	+	0.796094i	$0.706896\pi$
$488$	−4.86058	+	6.09498i	−0.220028	+	0.275907i
$489$	19.3367	+	4.63101i	0.874435	+	0.209421i
$490$	11.8144	−	11.6568i	0.533722	−	0.526601i
$491$		−	14.6576i		−	0.661489i	−0.943720	−	0.330744i	$-0.892700\pi$
$491$		−	14.6576i		−	0.661489i	0.943720	−	0.330744i	$-0.107300\pi$
$492$	−4.95600	+	3.86652i	−0.223434	+	0.174316i
$493$	0.419432	−	0.870959i	0.0188902	−	0.0392260i
$494$	35.8783	−	8.18898i	1.61424	−	0.368440i
$495$	21.3766	−	16.3136i	0.960807	−	0.733241i
$496$	1.91117	+	3.96858i	0.0858140	+	0.178195i
$497$	−11.5823	+	27.6988i	−0.519538	+	1.24246i
$498$	−10.7022	+	13.1303i	−0.479575	+	0.588382i
$499$	3.35579	+	4.20803i	0.150226	+	0.188377i	0.851250	−	0.524760i	$-0.175845\pi$
$499$	3.35579	+	4.20803i	0.150226	+	0.188377i	−0.701024	+	0.713137i	$0.747274\pi$
$500$	−9.35299	+	4.50416i	−0.418279	+	0.201432i
$501$	−29.1982	+	22.7796i	−1.30448	+	1.01772i
$502$	−19.0735	−	4.35341i	−0.851294	−	0.194302i
$503$	11.7410	−	14.7228i	0.523506	−	0.656455i	−0.447844	−	0.894112i	$-0.647808\pi$
$503$	11.7410	−	14.7228i	0.523506	−	0.656455i	0.971349	+	0.237657i	$0.0763793\pi$
$504$	−6.04712	+	5.14124i	−0.269360	+	0.229009i
$505$	14.3564	+	18.0024i	0.638853	+	0.801096i
$506$	9.01142	+	18.7124i	0.400607	+	0.831868i
$507$	−6.27035	+	12.6729i	−0.278476	+	0.562824i
$508$	19.1145			0.848068
$509$	18.8085			0.833672			0.416836	−	0.908982i	$-0.363139\pi$
$509$	18.8085			0.833672			0.416836	+	0.908982i	$0.363139\pi$
$510$	10.3209	+	5.10661i	0.457017	+	0.226125i
$511$	1.35939	+	25.7504i	0.0601359	+	1.13913i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$	−36.8544	−	19.2242i	−1.62716	−	0.848770i
$514$	10.2900	−	8.20603i	0.453874	−	0.361952i
$515$	−0.471895	+	0.376324i	−0.0207942	+	0.0165828i
$516$	−0.143127	+	13.4179i	−0.00630083	+	0.590689i
$517$	−12.5742	+	2.86998i	−0.553013	+	0.126222i
$518$	−1.27357	−	24.1248i	−0.0559577	−	1.05998i
$519$	14.6567	−	29.6225i	0.643357	−	1.30028i
$520$	−10.9075			−0.478325
$521$	14.9668			0.655709			0.327854	−	0.944728i	$-0.393674\pi$
$521$	14.9668			0.655709			0.327854	+	0.944728i	$0.393674\pi$
$522$	0.661958	−	0.794684i	0.0289731	−	0.0347824i
$523$	17.5704	+	36.4853i	0.768300	+	1.59539i	0.802989	+	0.595993i	$0.203242\pi$
$523$	17.5704	+	36.4853i	0.768300	+	1.59539i	−0.0346894	+	0.999398i	$0.511044\pi$
$524$	8.47960	+	10.6331i	0.370433	+	0.464508i
$525$	−2.30009	−	1.68099i	−0.100384	−	0.0733643i
$526$	−11.5936	+	14.5379i	−0.505503	+	0.633881i
$527$	−12.0413	−	2.74835i	−0.524528	−	0.119720i
$528$	−4.02772	−	5.16262i	−0.175284	−	0.224674i
$529$	6.47119	−	3.11636i	0.281356	−	0.135494i
$530$	7.22721	+	9.06263i	0.313930	+	0.393656i
$531$	−18.8857	−	24.7469i	−0.819568	−	1.07393i
$532$	8.16507	−	19.5265i	0.354001	−	0.846581i
$533$	7.24384	+	15.0420i	0.313765	+	0.651540i
$534$	2.90986	−	3.57006i	0.125922	−	0.154492i
$535$	−31.7603	+	7.24907i	−1.37312	+	0.313405i
$536$	3.03717	−	6.30675i	0.131186	−	0.272410i
$537$	2.21131	+	2.83440i	0.0954252	+	0.122313i
$538$		−	10.2612i		−	0.442392i
$539$	8.90775	−	24.9188i	0.383684	−	1.07333i
$540$	9.38156	+	7.98571i	0.403718	+	0.343650i
$541$	1.37849	−	1.72857i	0.0592660	−	0.0743172i	−0.751315	−	0.659944i	$-0.770580\pi$
$541$	1.37849	−	1.72857i	0.0592660	−	0.0743172i	0.810581	+	0.585627i	$0.199151\pi$
$542$	15.0134	+	7.23006i	0.644880	+	0.310558i
$543$	−2.85059	−	0.0304071i	−0.122331	−	0.00130489i
$544$	1.21660	−	2.52630i	0.0521615	−	0.108314i
$545$	3.49581	−	1.68349i	0.149744	−	0.0721129i
$546$	9.93777	+	18.5922i	0.425297	+	0.795674i
$547$	−27.3337	−	13.1632i	−1.16870	−	0.562818i	−0.254103	−	0.967177i	$-0.581780\pi$
$547$	−27.3337	−	13.1632i	−1.16870	−	0.562818i	−0.914600	+	0.404359i	$0.867494\pi$
$548$	−11.3785	+	9.07403i	−0.486064	+	0.387623i
$549$	0.498884	−	23.3820i	0.0212919	−	0.997919i
$550$	1.46533	−	1.83747i	0.0624820	−	0.0783500i
$551$	−0.613691	+	2.68876i	−0.0261441	+	0.114545i
$552$	−7.50249	+	5.85321i	−0.319327	+	0.249129i
$553$	−6.57938	+	9.20710i	−0.279784	+	0.391526i
$554$	−7.67564	+	6.12112i	−0.326107	+	0.260061i
$555$	−36.6452	+	7.95377i	−1.55550	+	0.337619i
$556$	−10.3699	−	2.36685i	−0.439780	−	0.100377i
$557$		−	33.7943i		−	1.43191i	−0.698145	−	0.715956i	$-0.745991\pi$
$557$		−	33.7943i		−	1.43191i	0.698145	−	0.715956i	$-0.254009\pi$
$558$	−11.7807	−	5.98617i	−0.498718	−	0.253415i
$559$	34.7466	+	7.93068i	1.46962	+	0.335432i
$560$	−3.64722	+	5.10387i	−0.154123	+	0.215678i
$561$	18.3592	+	0.195837i	0.775127	+	0.00826822i
$562$	−1.77926	−	7.79543i	−0.0750534	−	0.328830i
$563$	20.9196	+	26.2323i	0.881656	+	1.10556i	0.993724	+	0.111861i	$0.0356812\pi$
$563$	20.9196	+	26.2323i	0.881656	+	1.10556i	−0.112068	+	0.993701i	$0.535747\pi$
$564$	−2.50696	−	5.35102i	−0.105562	−	0.225318i
$565$	14.7422	−	3.36482i	0.620210	−	0.141559i
$566$	4.77807	+	20.9341i	0.200837	+	0.879925i
$567$	5.06444	−	23.2670i	0.212686	−	0.977120i
$568$	2.52507	−	11.0631i	0.105950	−	0.464196i
$569$			8.41221i			0.352658i	0.984331	+	0.176329i	$0.0564223\pi$
$569$			8.41221i			0.352658i	−0.984331	+	0.176329i	$0.943578\pi$
$570$	−31.9485	−	7.65145i	−1.33817	−	0.320484i
$571$	8.29114	−	36.3258i	0.346973	−	1.52019i	−0.437038	−	0.899443i	$-0.643973\pi$
$571$	8.29114	−	36.3258i	0.346973	−	1.52019i	0.784011	−	0.620746i	$-0.213170\pi$
$572$	−15.6691	+	7.54585i	−0.655159	+	0.315508i
$573$	−11.4467	+	5.36281i	−0.478194	+	0.224035i
$574$	9.46067	+	1.64014i	0.394881	+	0.0684579i
$575$	−2.67027	−	2.12947i	−0.111358	−	0.0888050i
$576$	1.92008	−	2.30506i	0.0800032	−	0.0960442i
$577$	−24.9075	−	19.8630i	−1.03691	−	0.826909i	−0.0517709	−	0.998659i	$-0.516487\pi$
$577$	−24.9075	−	19.8630i	−1.03691	−	0.826909i	−0.985141	+	0.171750i	$0.945058\pi$
$578$	−3.96468	−	8.23275i	−0.164909	−	0.342437i
$579$	−9.57834	−	20.4446i	−0.398062	−	0.849650i
$580$	0.354665	−	0.736469i	0.0147267	−	0.0305802i
$581$	25.8393	−	1.36408i	1.07199	−	0.0565916i
$582$	16.8948	−	3.66698i	0.700312	−	0.152001i
$583$	16.6518	+	8.01907i	0.689646	+	0.332116i
$584$	−2.16875	−	9.50193i	−0.0897437	−	0.393193i
$585$	26.0129	−	19.8518i	1.07550	−	0.820769i
$586$	−12.4307	−	9.91318i	−0.513509	−	0.409510i
$587$	−27.3667			−1.12954			−0.564772	−	0.825247i	$-0.691036\pi$
$587$	−27.3667			−1.12954			−0.564772	+	0.825247i	$0.691036\pi$
$588$	12.0227	+	1.56670i	0.495808	+	0.0646098i
$589$	35.2365			1.45189
$590$	−19.2355	−	15.3398i	−0.791915	−	0.631531i
$591$	26.5285	−	32.5473i	1.09124	−	1.33882i
$592$	2.03185	+	8.90210i	0.0835083	+	0.365874i
$593$	6.01851	+	2.89836i	0.247151	+	0.119021i	0.553358	−	0.832943i	$-0.313346\pi$
$593$	6.01851	+	2.89836i	0.247151	+	0.119021i	−0.306208	+	0.951965i	$0.599060\pi$
$594$	19.0016	+	4.98164i	0.779645	+	0.204399i
$595$	−4.81266	−	16.9185i	−0.197300	−	0.693590i
$596$	1.04087	−	2.16139i	0.0426357	−	0.0885339i
$597$	10.6914	−	5.00894i	0.437570	−	0.205002i
$598$	10.9659	+	22.7709i	0.448428	+	0.931170i
$599$	−12.2325	−	9.75512i	−0.499808	−	0.398583i	0.340877	−	0.940108i	$-0.389276\pi$
$599$	−12.2325	−	9.75512i	−0.499808	−	0.398583i	−0.840685	+	0.541524i	$0.817847\pi$
$600$	0.965103	+	0.477517i	0.0394001	+	0.0194945i
$601$	7.52339	+	5.99970i	0.306885	+	0.244733i	0.764807	−	0.644260i	$-0.222834\pi$
$601$	7.52339	+	5.99970i	0.306885	+	0.244733i	−0.457921	+	0.888993i	$0.651406\pi$
$602$	15.3294	−	13.6069i	0.624781	−	0.554576i
$603$	4.23512	+	20.5684i	0.172468	+	0.837610i
$604$	−14.4036	+	6.93642i	−0.586075	+	0.282239i
$605$	1.73672	−	7.60907i	0.0706078	−	0.309353i
$606$	−3.91767	+	16.3581i	−0.159144	+	0.664504i
$607$			19.5501i			0.793515i	0.917923	+	0.396758i	$0.129865\pi$
$607$			19.5501i			0.793515i	−0.917923	+	0.396758i	$0.870135\pi$
$608$	−1.78007	+	7.79901i	−0.0721915	+	0.316292i
$609$	−1.57847	+	0.0664543i	−0.0639629	+	0.00269286i
$610$	−4.11304	−	18.0204i	−0.166532	−	0.729625i
$611$	−15.3014	+	3.49243i	−0.619027	+	0.141289i
$612$	1.69647	+	8.23912i	0.0685758	+	0.333046i
$613$	−20.4225	−	25.6090i	−0.824855	−	1.03434i	−0.998770	−	0.0495753i	$-0.984213\pi$
$613$	−20.4225	−	25.6090i	−0.824855	−	1.03434i	0.173915	−	0.984761i	$-0.444358\pi$
$614$	0.222454	+	0.974634i	0.00897751	+	0.0393330i
$615$	0.158969	−	14.9029i	0.00641023	−	0.600945i
$616$	−1.70852	+	9.85511i	−0.0688381	+	0.397074i
$617$	−33.1966	−	7.57691i	−1.33645	−	0.305035i	−0.506192	−	0.862421i	$-0.668947\pi$
$617$	−33.1966	−	7.57691i	−1.33645	−	0.305035i	−0.830254	+	0.557386i	$0.811805\pi$
$618$	−0.428795	−	0.102694i	−0.0172487	−	0.00413094i
$619$			15.1725i			0.609835i	0.952379	+	0.304917i	$0.0986288\pi$
$619$			15.1725i			0.609835i	−0.952379	+	0.304917i	$0.901371\pi$
$620$	−10.1819	−	2.32396i	−0.408917	−	0.0933326i
$621$	7.23947	−	27.6137i	0.290510	−	1.10810i
$622$	16.1503	−	12.8794i	0.647568	−	0.516418i
$623$	−7.02557	+	0.370887i	−0.281473	+	0.0148593i
$624$	−4.90128	−	6.28232i	−0.196208	−	0.251494i
$625$	6.16870	−	27.0269i	0.246748	−	1.08107i
$626$	−7.33609	+	9.19917i	−0.293209	+	0.367673i
$627$	−51.1887	+	11.1104i	−2.04428	+	0.443707i
$628$	−4.88627	+	3.89667i	−0.194983	+	0.155494i
$629$	−23.0678	−	11.1088i	−0.919772	−	0.442939i
$630$	−0.590998	−	18.8100i	−0.0235459	−	0.749409i
$631$	−20.4660	+	9.85593i	−0.814740	+	0.392358i	−0.794370	−	0.607434i	$-0.792199\pi$
$631$	−20.4660	+	9.85593i	−0.814740	+	0.392358i	−0.0203703	+	0.999793i	$0.506485\pi$
$632$	1.85579	−	3.85359i	0.0738195	−	0.153288i
$633$	−0.0848535	+	7.95483i	−0.00337263	+	0.316176i
$634$	1.02279	+	0.492552i	0.0406204	+	0.0195617i
$635$	−28.2569	+	35.4330i	−1.12134	+	1.40612i
$636$	−1.97220	+	8.23489i	−0.0782029	+	0.326535i
$637$	10.8397	−	30.3233i	0.429485	−	1.20145i
$638$		−	1.30333i		−	0.0515993i
$639$	14.1130	+	30.9795i	0.558300	+	1.22553i
$640$	1.02874	−	2.13620i	0.0406646	−	0.0844409i
$641$	26.1068	−	5.95870i	1.03116	−	0.235355i	0.326719	−	0.945121i	$-0.394057\pi$
$641$	26.1068	−	5.95870i	1.03116	−	0.235355i	0.704437	+	0.709767i	$0.251200\pi$
$642$	−18.4466	−	15.0354i	−0.728031	−	0.593399i
$643$	−2.40047	−	4.98462i	−0.0946651	−	0.196574i	0.848259	−	0.529581i	$-0.177651\pi$
$643$	−2.40047	−	4.98462i	−0.0946651	−	0.196574i	−0.942924	+	0.333007i	$0.891937\pi$
$644$	14.3218	+	2.48287i	0.564356	+	0.0978388i
$645$	−24.6615	−	20.1009i	−0.971046	−	0.791474i
$646$	−13.9853	−	17.5370i	−0.550245	−	0.689985i
$647$	26.9374	−	12.9724i	1.05902	−	0.509997i	0.178467	−	0.983946i	$-0.442886\pi$
$647$	26.9374	−	12.9724i	1.05902	−	0.509997i	0.880552	+	0.473949i	$0.157172\pi$
$648$	−0.383878	+	8.99181i	−0.0150802	+	0.353232i
$649$	−38.2449	−	8.72915i	−1.50124	−	0.342649i
$650$	1.78314	−	2.23599i	0.0699406	−	0.0877027i
$651$	5.31544	+	19.4729i	0.208329	+	0.763201i
$652$	7.15750	+	8.97522i	0.280309	+	0.351497i
$653$	−19.2941	−	40.0645i	−0.755035	−	1.56785i	−0.821600	−	0.570065i	$-0.806918\pi$
$653$	−19.2941	−	40.0645i	−0.755035	−	1.56785i	0.0665645	−	0.997782i	$-0.478796\pi$
$654$	2.54047	+	1.25698i	0.0993402	+	0.0491519i
$655$	−32.2462			−1.25996
$656$	−3.62914			−0.141694
$657$	22.4658	+	18.7136i	0.876474	+	0.730088i
$658$	−3.48223	+	8.32766i	−0.135752	+	0.324646i
$659$	−38.4079	+	8.76635i	−1.49616	+	0.341488i	−0.890775	−	0.454445i	$-0.849837\pi$
$659$	−38.4079	+	8.76635i	−1.49616	+	0.341488i	−0.605384	+	0.795934i	$0.706980\pi$
$660$	15.5243	+	0.165596i	0.604282	+	0.00644583i
$661$	3.48217	−	2.77694i	0.135441	−	0.108010i	−0.553426	−	0.832898i	$-0.686680\pi$
$661$	3.48217	−	2.77694i	0.135441	−	0.108010i	0.688867	+	0.724888i	$0.258108\pi$
$662$	−18.4035	+	14.6763i	−0.715272	+	0.570410i
$663$	22.3411	+	0.238310i	0.867655	+	0.00925521i
$664$	−9.53472	+	2.17624i	−0.370019	+	0.0844544i
$665$	24.1264	+	44.0018i	0.935583	+	1.70632i
$666$	−21.0476	−	17.5323i	−0.815577	−	0.679362i
$667$	−1.89404			−0.0733376
$668$	−21.3810			−0.827257
$669$	8.87199	+	4.38971i	0.343011	+	0.169716i
$670$	7.20115	+	14.9533i	0.278205	+	0.577698i
$671$	−18.3752	−	23.0417i	−0.709365	−	0.889515i
$672$	−4.57852	+	0.192757i	−0.176620	+	0.00743578i
$673$	−14.0125	+	17.5711i	−0.540141	+	0.677316i	−0.974749	−	0.223304i	$-0.928316\pi$
$673$	−14.0125	+	17.5711i	−0.540141	+	0.677316i	0.434608	+	0.900620i	$0.356887\pi$
$674$	−25.7700	−	5.88184i	−0.992624	−	0.226560i
$675$	−3.17072	+	0.617687i	−0.122041	+	0.0237748i
$676$	−7.35491	+	3.54194i	−0.282881	+	0.136228i
$677$	4.58183	+	5.74544i	0.176094	+	0.220815i	0.862044	−	0.506834i	$-0.169184\pi$
$677$	4.58183	+	5.74544i	0.176094	+	0.220815i	−0.685949	+	0.727649i	$0.740613\pi$
$678$	8.56242	+	6.97900i	0.328838	+	0.268027i
$679$	−21.4860	−	15.3538i	−0.824557	−	0.589227i
$680$	2.88458	+	5.98989i	0.110618	+	0.229702i
$681$	19.0066	+	15.4918i	0.728335	+	0.593647i
$682$	−16.2346	+	3.70543i	−0.621654	+	0.141888i
$683$	−20.2037	+	41.9533i	−0.773071	+	1.60530i	0.0227301	+	0.999742i	$0.492764\pi$
$683$	−20.2037	+	41.9533i	−0.773071	+	1.60530i	−0.795801	+	0.605558i	$0.792950\pi$
$684$	−9.94906	−	21.8393i	−0.380412	−	0.835047i
$685$		−	34.5067i		−	1.31843i
$686$	−10.5644	−	15.2116i	−0.403352	−	0.580781i
$687$	−2.51826	+	10.5150i	−0.0960777	+	0.401171i
$688$	−4.83033	+	6.05705i	−0.184155	+	0.230923i
$689$	20.2633	+	9.75829i	0.771970	+	0.371761i
$690$	0.240650	−	22.5604i	0.00916138	−	0.858859i
$691$	6.30042	−	13.0830i	0.239679	−	0.497699i	−0.746081	−	0.665855i	$-0.768067\pi$
$691$	6.30042	−	13.0830i	0.239679	−	0.497699i	0.985760	+	0.168156i	$0.0537812\pi$
$692$	17.1918	−	8.27914i	0.653535	−	0.314726i
$693$	−13.8618	−	26.6126i	−0.526568	−	1.01093i
$694$	21.7381	+	10.4685i	0.825167	+	0.397380i
$695$	19.7172	−	15.7240i	0.747918	−	0.596444i
$696$	0.583548	−	0.126658i	0.0221193	−	0.00480096i
$697$	6.34466	−	7.95595i	0.240321	−	0.301353i
$698$	−1.89181	+	8.28855i	−0.0716060	+	0.313726i
$699$	−15.7337	−	20.1670i	−0.595103	−	0.762786i
$700$	−0.450030	−	1.58204i	−0.0170095	−	0.0597954i
$701$	−6.44118	+	5.13667i	−0.243280	+	0.194009i	−0.737537	−	0.675306i	$-0.764011\pi$
$701$	−6.44118	+	5.13667i	−0.243280	+	0.194009i	0.494257	+	0.869316i	$0.335440\pi$
$702$	23.1227	+	6.06208i	0.872712	+	0.228798i
$703$	71.2130	+	16.2539i	2.68585	+	0.613028i
$704$		−	3.78044i		−	0.142481i
$705$	13.6254	+	3.26319i	0.513161	+	0.122899i
$706$	−14.2585	−	3.25440i	−0.536625	−	0.122481i
$707$	22.5297	−	12.3531i	0.847315	−	0.464587i
$708$	0.191705	−	17.9719i	0.00720472	−	0.675426i
$709$	5.80498	+	25.4333i	0.218011	+	0.955166i	0.958946	+	0.283590i	$0.0915254\pi$
$709$	5.80498	+	25.4333i	0.218011	+	0.955166i	−0.740935	+	0.671577i	$0.765617\pi$
$710$	16.7751	+	21.0353i	0.629558	+	0.789441i
$711$	2.58778	+	12.5678i	0.0970492	+	0.471331i
$712$	2.59244	−	0.591708i	0.0971559	−	0.0221752i
$713$	5.38485	+	23.5926i	0.201664	+	0.883549i
$714$	7.58186	−	10.3742i	0.283744	−	0.388246i
$715$	9.17569	−	40.2013i	0.343151	−	1.50344i
$716$			2.07555i			0.0775669i
$717$	−2.52134	+	10.5278i	−0.0941613	+	0.393168i
$718$	1.91439	−	8.38749i	0.0714444	−	0.313018i
$719$	−4.35804	+	2.09872i	−0.162527	+	0.0782690i	−0.513379	−	0.858162i	$-0.671606\pi$
$719$	−4.35804	+	2.09872i	−0.162527	+	0.0782690i	0.350852	+	0.936431i	$0.385892\pi$
$720$	1.43451	+	6.96687i	0.0534610	+	0.259640i
$721$	0.323812	+	0.590569i	0.0120594	+	0.0219939i
$722$	35.1771	+	28.0528i	1.30916	+	1.04402i
$723$	15.3065	+	7.57342i	0.569257	+	0.281659i
$724$	−1.28680	−	1.02619i	−0.0478237	−	0.0381381i
$725$	0.0929929	+	0.193102i	0.00345367	+	0.00717162i
$726$	5.16294	−	2.41884i	0.191615	−	0.0897717i
$727$	−10.6709	+	22.1584i	−0.395762	+	0.821809i	0.603931	+	0.797037i	$0.293600\pi$
$727$	−10.6709	+	22.1584i	−0.395762	+	0.821809i	−0.999693	+	0.0247722i	$0.992114\pi$
$728$	−2.07907	+	11.9925i	−0.0770554	+	0.444473i
$729$	−15.4497	−	22.1429i	−0.572211	−	0.820106i
$730$	20.8201	+	10.0264i	0.770585	+	0.371094i
$731$	−4.83386	−	21.1785i	−0.178787	−	0.783317i
$732$	8.53090	−	10.4664i	0.315311	−	0.386850i
$733$	0.138668	+	0.110584i	0.00512180	+	0.00408450i	0.626047	−	0.779785i	$-0.284672\pi$
$733$	0.138668	+	0.110584i	0.00512180	+	0.00408450i	−0.620926	+	0.783870i	$0.713243\pi$
$734$	1.99329			0.0735737
$735$	−20.6774	+	19.9708i	−0.762697	+	0.736633i
$736$	−5.49386			−0.202506
$737$	20.6896	+	16.4994i	0.762110	+	0.607763i
$738$	8.65498	−	6.60507i	0.318594	−	0.243136i
$739$	−4.37128	−	19.1518i	−0.160800	−	0.704512i	−0.989466	−	0.144768i	$-0.953757\pi$
$739$	−4.37128	−	19.1518i	−0.160800	−	0.704512i	0.828665	−	0.559744i	$-0.189101\pi$
$740$	−19.5057	−	9.39347i	−0.717045	−	0.345311i
$741$	−62.2908	+	13.5201i	−2.28831	+	0.496673i
$742$	11.3417	−	6.21872i	0.416368	−	0.228296i
$743$	15.5203	−	32.2283i	0.569386	−	1.18234i	−0.395205	−	0.918593i	$-0.629326\pi$
$743$	15.5203	−	32.2283i	0.569386	−	1.18234i	0.964591	−	0.263750i	$-0.0849592\pi$
$744$	−3.23673	−	6.90870i	−0.118664	−	0.253285i
$745$	2.46791	+	5.12467i	0.0904172	+	0.187753i
$746$	7.56178	+	6.03032i	0.276857	+	0.220786i
$747$	18.7782	−	22.5433i	0.687058	−	0.824816i
$748$	8.28765	+	6.60918i	0.303027	+	0.241656i
$749$	1.91639	+	36.3014i	0.0700233	+	1.32642i
$750$	16.2821	−	7.62820i	0.594540	−	0.278543i
$751$	20.8149	−	10.0239i	0.759548	−	0.365779i	−0.0136805	−	0.999906i	$-0.504355\pi$
$751$	20.8149	−	10.0239i	0.759548	−	0.365779i	0.773229	+	0.634127i	$0.218641\pi$
$752$	0.759165	−	3.32612i	0.0276839	−	0.121291i
$753$	32.9540	+	7.89228i	1.20091	+	0.287611i
$754$		−	1.58600i		−	0.0577588i
$755$	8.43463	−	36.9545i	0.306967	−	1.34491i
$756$	10.5683	−	8.79266i	0.384366	−	0.319786i
$757$	10.3573	+	45.3783i	0.376442	+	1.64930i	0.708256	+	0.705956i	$0.249482\pi$
$757$	10.3573	+	45.3783i	0.376442	+	1.64930i	−0.331814	+	0.943345i	$0.607661\pi$
$758$	25.8569	−	5.90167i	0.939165	−	0.214358i
$759$	−15.2617	−	32.5755i	−0.553963	−	1.18242i
$760$	−11.8258	−	14.8290i	−0.428966	−	0.537906i
$761$	7.74729	+	33.9431i	0.280839	+	1.23044i	0.896720	+	0.442598i	$0.145943\pi$
$761$	7.74729	+	33.9431i	0.280839	+	1.23044i	−0.615881	+	0.787839i	$0.711200\pi$
$762$	−33.1054	−	0.353132i	−1.19928	−	0.0127926i
$763$	−1.18463	−	4.16445i	−0.0428864	−	0.150763i
$764$	−7.11514	−	1.62398i	−0.257417	−	0.0587537i
$765$	−17.7810	−	9.03508i	−0.642872	−	0.326664i
$766$			21.0723i			0.761373i
$767$	−46.5396	−	10.6224i	−1.68045	−	0.383552i
$768$	1.69264	−	0.367384i	0.0610779	−	0.0132568i
$769$	−8.53359	+	6.80531i	−0.307729	+	0.245406i	−0.765161	−	0.643839i	$-0.777341\pi$
$769$	−8.53359	+	6.80531i	−0.307729	+	0.245406i	0.457432	+	0.889245i	$0.348769\pi$
$770$	−15.7430	−	17.7359i	−0.567338	−	0.639158i
$771$	−17.9734	+	14.0223i	−0.647298	+	0.505002i
$772$	2.90054	−	12.7081i	0.104393	−	0.457375i
$773$	−13.5986	+	17.0521i	−0.489106	+	0.613320i	−0.963733	−	0.266867i	$-0.914012\pi$
$773$	−13.5986	+	17.0521i	−0.489106	+	0.613320i	0.474627	+	0.880187i	$0.342583\pi$
$774$	0.495780	−	23.2365i	0.0178204	−	0.835218i
$775$	2.14093	−	1.70734i	0.0769046	−	0.0613294i
$776$	8.99287	+	4.33074i	0.322825	+	0.155464i
$777$	1.76007	+	41.8066i	0.0631423	+	1.49980i
$778$	3.95621	−	1.90521i	0.141837	−	0.0683052i
$779$	−12.5963	+	26.1565i	−0.451310	+	0.937155i
$780$	18.8913	+	0.201512i	0.676416	+	0.00721528i
$781$	38.6505	+	18.6131i	1.38302	+	0.666029i
$782$	9.60467	−	12.0439i	0.343462	−	0.430688i
$783$	−1.16116	+	1.36412i	−0.0414965	+	0.0487498i
$784$	4.91640	+	4.98288i	0.175586	+	0.177960i
$785$		−	14.8183i		−	0.528886i
$786$	−14.4898	−	18.5726i	−0.516835	−	0.662464i
$787$	9.24299	−	19.1933i	0.329477	−	0.684166i	−0.668763	−	0.743476i	$-0.733176\pi$
$787$	9.24299	−	19.1933i	0.329477	−	0.684166i	0.998240	+	0.0593101i	$0.0188901\pi$
$788$	23.6346	−	5.39445i	0.841949	−	0.192169i
$789$	20.3481	−	24.9647i	0.724411	−	0.888767i
$790$	4.40010	+	9.13690i	0.156548	+	0.325076i
$791$	−0.889533	−	16.8501i	−0.0316281	−	0.599120i
$792$	6.88045	+	9.01583i	0.244486	+	0.320364i
$793$	−22.3604	−	28.0391i	−0.794043	−	0.995698i
$794$	−3.11311	+	1.49920i	−0.110480	+	0.0532045i
$795$	−12.3497	−	15.8296i	−0.438000	−	0.561417i
$796$	6.64564	+	1.51682i	0.235548	+	0.0537624i
$797$	−12.0499	+	15.1101i	−0.426829	+	0.535227i	−0.948019	−	0.318214i	$-0.896917\pi$
$797$	−12.0499	+	15.1101i	−0.426829	+	0.535227i	0.521190	+	0.853441i	$0.325488\pi$
$798$	−14.5023	+	33.6681i	−0.513374	+	1.19184i
$799$	5.96445	+	7.47919i	0.211007	+	0.264595i
$800$	0.269735	+	0.560111i	0.00953658	+	0.0198029i
$801$	−5.10570	+	6.12942i	−0.180401	+	0.216572i
$802$	1.58968			0.0561335
$803$	36.8453			1.30024
$804$	−5.37675	+	10.8669i	−0.189623	+	0.383245i
$805$	−25.7744	+	22.8782i	−0.908428	+	0.806351i
$806$	−19.7556	+	4.50909i	−0.695861	+	0.158826i
$807$	−0.189572	+	17.7719i	−0.00667324	+	0.625601i
$808$	−7.59272	+	6.05499i	−0.267111	+	0.213014i
$809$	−13.6824	+	10.9113i	−0.481048	+	0.383623i	−0.833776	−	0.552103i	$-0.813825\pi$
$809$	−13.6824	+	10.9113i	−0.481048	+	0.383623i	0.352728	+	0.935726i	$0.385254\pi$
$810$	−16.1009	−	14.0042i	−0.565727	−	0.492057i
$811$	−2.29787	+	0.524474i	−0.0806891	+	0.0184168i	−0.262675	−	0.964884i	$-0.584605\pi$
$811$	−2.29787	+	0.524474i	−0.0806891	+	0.0184168i	0.181986	+	0.983301i	$0.441748\pi$
$812$	−0.742128	−	0.530323i	−0.0260436	−	0.0186107i
$813$	−25.8689	−	12.7995i	−0.907261	−	0.448898i
$814$	−34.5193			−1.20990
$815$	−27.2185			−0.953424
$816$	−2.15377	+	4.35296i	−0.0753971	+	0.152384i
$817$	26.8898	+	55.8373i	0.940756	+	1.95350i
$818$	24.4468	+	30.6553i	0.854763	+	1.07184i
$819$	−16.8683	−	32.3844i	−0.589425	−	1.13160i
$820$	5.36495	−	6.72743i	0.187352	−	0.234932i
$821$	20.9249	+	4.77598i	0.730285	+	0.166683i	0.571467	−	0.820625i	$-0.306374\pi$
$821$	20.9249	+	4.77598i	0.730285	+	0.166683i	0.158818	+	0.987308i	$0.449232\pi$
$822$	19.8746	−	15.5056i	0.693207	−	0.540819i
$823$	2.17924	−	1.04947i	0.0759635	−	0.0365821i	−0.395516	−	0.918459i	$-0.629434\pi$
$823$	2.17924	−	1.04947i	0.0759635	−	0.0365821i	0.471480	+	0.881877i	$0.343720\pi$
$824$	−0.158719	−	0.199027i	−0.00552924	−	0.00693345i
$825$	−2.57183	+	3.15534i	−0.0895398	+	0.109855i
$826$	−20.5323	+	18.2251i	−0.714409	+	0.634133i
$827$	13.6909	+	28.4294i	0.476078	+	0.988587i	0.991311	+	0.131537i	$0.0419911\pi$
$827$	13.6909	+	28.4294i	0.476078	+	0.988587i	−0.515233	+	0.857050i	$0.672295\pi$
$828$	13.1021	−	9.99888i	0.455329	−	0.347485i
$829$	2.27608	−	0.519501i	0.0790517	−	0.0180430i	−0.182812	−	0.983148i	$-0.558520\pi$
$829$	2.27608	−	0.519501i	0.0790517	−	0.0180430i	0.261864	+	0.965105i	$0.415663\pi$
$830$	10.0610	−	20.8919i	0.349223	−	0.725168i
$831$	13.4069	−	10.4597i	0.465081	−	0.362842i
$832$		−	4.60036i		−	0.159489i
$833$	−19.5188	+	2.06659i	−0.676286	+	0.0716032i
$834$	17.9164	+	4.29085i	0.620393	+	0.148580i
$835$	31.6076	−	39.6346i	1.09382	−	1.37161i
$836$	−27.2471	−	13.1215i	−0.942359	−	0.453816i
$837$	20.2931	+	10.5854i	0.701431	+	0.365885i
$838$	−13.1950	+	27.3997i	−0.455814	+	0.946508i
$839$	11.0489	−	5.32089i	0.381452	−	0.183697i	−0.233325	−	0.972399i	$-0.574961\pi$
$839$	11.0489	−	5.32089i	0.381452	−	0.183697i	0.614776	+	0.788701i	$0.289246\pi$
$840$	6.41110	−	8.77228i	0.221204	−	0.302673i
$841$	−26.0210	−	12.5311i	−0.897276	−	0.432105i
$842$	17.0283	−	13.5796i	0.586835	−	0.467985i
$843$	2.93757	+	13.5342i	0.101175	+	0.466142i
$844$	−2.86368	+	3.59094i	−0.0985718	+	0.123605i
$845$	4.30697	−	18.8701i	0.148164	−	0.649150i
$846$	4.24307	+	9.31402i	0.145880	+	0.320223i
$847$	−8.03496	−	3.35984i	−0.276085	−	0.115446i
$848$	−3.82227	+	3.04816i	−0.131257	+	0.104674i
$849$	−7.88864	−	36.3451i	−0.270737	−	1.24736i
$850$	−1.69947	−	0.387892i	−0.0582912	−	0.0133046i
$851$			50.1646i			1.71962i
$852$	−4.57769	+	19.1140i	−0.156829	+	0.654837i
$853$	−36.7162	−	8.38023i	−1.25714	−	0.286934i	−0.458473	−	0.888708i	$-0.651603\pi$
$853$	−36.7162	−	8.38023i	−1.25714	−	0.286934i	−0.798666	+	0.601775i	$0.794461\pi$
$854$	−20.5970	+	1.08734i	−0.704814	+	0.0372079i
$855$	55.1918	+	13.8422i	1.88752	+	0.473392i
$856$	−3.05738	−	13.3953i	−0.104499	−	0.457841i
$857$	−30.9361	−	38.7927i	−1.05676	−	1.32513i	−0.943429	−	0.331575i	$-0.892420\pi$
$857$	−30.9361	−	38.7927i	−1.05676	−	1.32513i	−0.113329	−	0.993557i	$-0.536151\pi$
$858$	27.2776	−	12.7796i	0.931241	−	0.436287i
$859$	−21.1936	+	4.83730i	−0.723116	+	0.165047i	−0.568211	−	0.822883i	$-0.692364\pi$
$859$	−21.1936	+	4.83730i	−0.723116	+	0.165047i	−0.154905	+	0.987929i	$0.549507\pi$
$860$	−4.08744	−	17.9082i	−0.139381	−	0.610666i
$861$	−16.3551	−	3.01542i	−0.557381	−	0.102765i
$862$	4.57915	−	20.0625i	0.155966	−	0.683333i
$863$			50.7998i			1.72925i	0.502421	+	0.864623i	$0.332443\pi$
$863$			50.7998i			1.72925i	−0.502421	+	0.864623i	$0.667557\pi$
$864$	−3.36807	+	3.95678i	−0.114584	+	0.134612i
$865$	−10.0674	+	44.1080i	−0.342301	+	1.49972i
$866$	−15.0112	+	7.22900i	−0.510100	+	0.245651i
$867$	6.71455	+	14.3320i	0.228038	+	0.486739i
$868$	−4.49592	+	10.7518i	−0.152601	+	0.364941i
$869$	12.6419	+	10.0816i	0.428847	+	0.341994i
$870$	−0.627869	+	1.26898i	−0.0212867	+	0.0430224i
$871$	25.1768	+	20.0778i	0.853084	+	0.680312i
$872$	0.710032	+	1.47440i	0.0240447	+	0.0499294i
$873$	−29.3287	+	6.03891i	−0.992627	+	0.204386i
$874$	−19.0686	+	39.5963i	−0.645004	+	1.33936i
$875$	−25.3395	−	10.5958i	−0.856632	−	0.358203i
$876$	3.58063	+	16.4970i	0.120978	+	0.557380i
$877$	13.3458	+	6.42700i	0.450656	+	0.217024i	0.645423	−	0.763825i	$-0.276681\pi$
$877$	13.3458	+	6.42700i	0.450656	+	0.217024i	−0.194768	+	0.980849i	$0.562395\pi$
$878$	7.57504	+	33.1884i	0.255645	+	1.12005i
$879$	21.3463	+	17.3988i	0.719993	+	0.586847i
$880$	7.00791	+	5.58862i	0.236237	+	0.188392i
$881$	−0.787268			−0.0265237			−0.0132619	−	0.999912i	$-0.504222\pi$
$881$	−0.787268			−0.0265237			−0.0132619	+	0.999912i	$0.504222\pi$
$882$	−20.7938	−	2.93557i	−0.700164	−	0.0988458i
$883$	−20.9635			−0.705478			−0.352739	−	0.935722i	$-0.614750\pi$
$883$	−20.9635			−0.705478			−0.352739	+	0.935722i	$0.614750\pi$
$884$	10.0851	+	8.04261i	0.339199	+	0.270502i
$885$	33.0317	+	26.9232i	1.11035	+	0.905015i
$886$	1.56084	+	6.83847i	0.0524373	+	0.229743i
$887$	43.4895	+	20.9434i	1.46023	+	0.703211i	0.984338	−	0.176291i	$-0.0564099\pi$
$887$	43.4895	+	20.9434i	1.46023	+	0.703211i	0.475895	+	0.879502i	$0.342124\pi$
$888$	−3.35460	−	15.4555i	−0.112573	−	0.518654i
$889$	33.5718	+	37.8217i	1.12596	+	1.26850i
$890$	−2.73554	+	5.68041i	−0.0916955	+	0.190408i
$891$	−32.8178	−	8.97900i	−1.09944	−	0.300808i
$892$	2.47962	+	5.14899i	0.0830239	+	0.172401i
$893$	−21.3376	−	17.0162i	−0.714036	−	0.569424i
$894$	−1.84267	+	3.72419i	−0.0616280	+	0.124556i
$895$	−3.84751	−	3.06828i	−0.128608	−	0.102561i
$896$	−2.15262	−	1.53826i	−0.0719139	−	0.0513896i
$897$	−18.5717	−	39.6406i	−0.620090	−	1.32356i
$898$	−1.75428	+	0.844819i	−0.0585412	+	0.0281920i
$899$	0.337916	−	1.48051i	0.0112701	−	0.0493776i
$900$	−1.66269	−	0.844866i	−0.0554230	−	0.0281622i
$901$		−	13.7083i		−	0.456690i
$902$	3.05293	−	13.3758i	0.101651	−	0.445364i
$903$	−26.8012	+	23.2833i	−0.891889	+	0.774820i
$904$	1.41915	+	6.21770i	0.0472002	+	0.206798i
$905$	3.80456	−	0.868366i	0.126468	−	0.0288655i
$906$	25.0745	−	11.7474i	0.833046	−	0.390283i
$907$	7.86265	+	9.85946i	0.261075	+	0.327378i	0.895042	−	0.445983i	$-0.147146\pi$
$907$	7.86265	+	9.85946i	0.261075	+	0.327378i	−0.633966	+	0.773361i	$0.718574\pi$
$908$	3.15019	+	13.8019i	0.104543	+	0.458032i
$909$	7.08742	−	28.2591i	0.235075	−	0.937296i
$910$	−19.1574	−	21.5826i	−0.635062	−	0.715455i
$911$	33.3967	+	7.62258i	1.10648	+	0.252547i	0.736464	−	0.676477i	$-0.236494\pi$
$911$	33.3967	+	7.62258i	1.10648	+	0.252547i	0.370019	+	0.929024i	$0.379351\pi$
$912$	3.22709	−	13.4746i	0.106860	−	0.446190i
$913$		−	36.9724i		−	1.22361i
$914$	3.75648	+	0.857392i	0.124253	+	0.0283600i
$915$	6.79067	+	31.2865i	0.224492	+	1.03430i
$916$	−4.88057	+	3.89213i	−0.161259	+	0.128600i
$917$	−6.14642	+	35.4540i	−0.202973	+	1.17079i
$918$	−2.78599	−	14.3011i	−0.0919514	−	0.472006i
$919$	−0.403405	+	1.76743i	−0.0133071	+	0.0583023i	−0.981146	−	0.193270i	$-0.938091\pi$
$919$	−0.403405	+	1.76743i	−0.0133071	+	0.0583023i	0.967838	+	0.251573i	$0.0809477\pi$
$920$	8.12157	−	10.1841i	0.267760	−	0.335761i
$921$	−0.367274	−	1.69213i	−0.0121021	−	0.0557576i
$922$	12.1951	−	9.72523i	0.401623	−	0.320283i
$923$	47.0332	+	22.6500i	1.54812	+	0.745534i
$924$	3.14114	−	17.0370i	0.103336	−	0.560477i
$925$	5.11439	−	2.46296i	0.168160	−	0.0809817i
$926$	13.8379	−	28.7347i	0.454741	−	0.944280i
$927$	0.740755	+	0.185782i	0.0243296	+	0.00610189i
$928$	0.310614	+	0.149584i	0.0101964	+	0.00491034i
$929$	15.9819	−	20.0407i	0.524351	−	0.657515i	−0.447176	−	0.894446i	$-0.647570\pi$
$929$	15.9819	−	20.0407i	0.524351	−	0.657515i	0.971526	+	0.236931i	$0.0761416\pi$
$930$	17.5917	+	4.21310i	0.576855	+	0.138153i
$931$	52.9777	−	18.1393i	1.73627	−	0.594491i
$932$		−	14.7677i		−	0.483733i
$933$	−28.2095	+	22.0082i	−0.923537	+	0.720516i
$934$	−6.54757	+	13.5962i	−0.214243	+	0.444880i
$935$	−24.5033	+	5.59271i	−0.801342	+	0.182901i
$936$	8.37271	+	10.9712i	0.273671	+	0.358606i
$937$	3.83235	+	7.95796i	0.125197	+	0.259975i	0.954141	−	0.299357i	$-0.0967720\pi$
$937$	3.83235	+	7.95796i	0.125197	+	0.259975i	−0.828944	+	0.559332i	$0.811058\pi$
$938$	17.8135	−	5.06725i	0.581630	−	0.165452i
$939$	12.8757	−	15.7970i	0.420183	−	0.515515i
$940$	5.04345	+	6.32428i	0.164499	+	0.206275i
$941$	43.9891	−	21.1840i	1.43400	−	0.690579i	0.454266	−	0.890866i	$-0.349902\pi$
$941$	43.9891	−	21.1840i	1.43400	−	0.690579i	0.979737	+	0.200287i	$0.0641875\pi$
$942$	8.53477	−	6.65857i	0.278078	−	0.216948i
$943$	−19.4381	−	4.43661i	−0.632991	−	0.144476i
$944$	6.46975	−	8.11282i	0.210573	−	0.264050i
$945$	0.676073	+	32.5890i	0.0219926	+	1.06012i
$946$	−18.2608	−	22.8983i	−0.593710	−	0.744488i
$947$	1.56074	+	3.24091i	0.0507172	+	0.105315i	0.924787	−	0.380484i	$-0.124243\pi$
$947$	1.56074	+	3.24091i	0.0507172	+	0.105315i	−0.874070	+	0.485800i	$0.838528\pi$
$948$	−3.28534	+	6.63995i	−0.106703	+	0.215656i
$949$	44.8365			1.45545
$950$	4.97315			0.161350
$951$	−1.76233	−	0.871972i	−0.0571475	−	0.0282756i
$952$	7.13556	−	2.02980i	0.231265	−	0.0657861i
$953$	−15.1378	+	3.45509i	−0.490360	+	0.111921i	−0.460549	−	0.887634i	$-0.652348\pi$
$953$	−15.1378	+	3.45509i	−0.490360	+	0.111921i	−0.0298106	+	0.999556i	$0.509490\pi$
$954$	3.56790	−	14.2260i	0.115515	−	0.460584i
$955$	13.5287	−	10.7888i	0.437779	−	0.349117i
$956$	−4.88654	+	3.89689i	−0.158042	+	0.126034i
$957$	−0.0240785	+	2.25731i	−0.000778348	+	0.0729683i
$958$	30.7781	−	7.02489i	0.994394	−	0.226964i
$959$	−37.9393	−	6.57730i	−1.22512	−	0.212392i
$960$	−1.82120	+	3.68080i	−0.0587789	+	0.118797i
$961$	11.5978			0.374123
$962$	−42.0061			−1.35433
$963$	31.6709	+	26.3814i	1.02058	+	0.850127i
$964$	4.27801	+	8.88337i	0.137785	+	0.286114i
$965$	19.2695	+	24.1632i	0.620308	+	0.777841i
$966$	−24.7587	−	4.56480i	−0.796599	−	0.146870i
$967$	25.3544	−	31.7934i	0.815343	−	1.02241i	−0.183878	−	0.982949i	$-0.558865\pi$
$967$	25.3544	−	31.7934i	0.815343	−	1.02241i	0.999221	−	0.0394584i	$-0.0125633\pi$
$968$	3.20921	+	0.732482i	0.103148	+	0.0235429i
$969$	23.8979	+	30.6317i	0.767711	+	0.984031i
$970$	−21.3222	+	10.2682i	−0.684613	+	0.329692i
$971$	1.65568	+	2.07616i	0.0531333	+	0.0666271i	0.807688	−	0.589610i	$-0.200719\pi$
$971$	1.65568	+	2.07616i	0.0531333	+	0.0666271i	−0.754555	+	0.656237i	$0.772147\pi$
$972$	0.830979	−	15.5663i	0.0266537	−	0.499289i
$973$	−13.5299	−	24.6758i	−0.433747	−	0.791069i
$974$	3.82673	+	7.94629i	0.122616	+	0.254615i
$975$	−3.12963	+	3.83968i	−0.100228	+	0.122968i
$976$	7.60031	−	1.73472i	0.243280	−	0.0555271i
$977$	−18.3077	+	38.0163i	−0.585715	+	1.21625i	0.371920	+	0.928265i	$0.378699\pi$
$977$	−18.3077	+	38.0163i	−0.585715	+	1.21625i	−0.957635	+	0.287984i	$0.907015\pi$
$978$	−12.2306	−	15.6769i	−0.391093	−	0.501292i
$979$			10.0526i			0.321283i
$980$	−16.5048	+	1.74748i	−0.527227	+	0.0558212i
$981$	−4.37675	−	2.22397i	−0.139739	−	0.0710058i
$982$	−9.13887	+	11.4598i	−0.291633	+	0.365696i
$983$	−20.4698	−	9.85773i	−0.652885	−	0.314413i	0.0779600	−	0.996956i	$-0.475159\pi$
$983$	−20.4698	−	9.85773i	−0.652885	−	0.314413i	−0.730845	+	0.682544i	$0.760874\pi$
$984$	6.28549	+	0.0670468i	0.200374	+	0.00213738i
$985$	−24.9392	+	51.7868i	−0.794630	+	1.65007i
$986$	−0.870959	+	0.419432i	−0.0277370	+	0.0133574i
$987$	6.18491	−	14.3588i	0.196868	−	0.457045i
$988$	−33.1565	−	15.9673i	−1.05485	−	0.507989i
$989$	−33.2765	+	26.5372i	−1.05813	+	0.843833i
$990$	−26.8843	−	0.573610i	−0.854438	−	0.0182305i
$991$	−27.7052	+	34.7413i	−0.880086	+	1.10359i	0.113836	+	0.993500i	$0.463686\pi$
$991$	−27.7052	+	34.7413i	−0.880086	+	1.10359i	−0.993921	+	0.110093i	$0.964885\pi$
$992$	0.980159	−	4.29436i	0.0311201	−	0.136346i
$993$	32.1451	−	25.0786i	1.02009	−	0.795846i
$994$	26.3253	−	14.4343i	0.834988	−	0.457828i
$995$	−12.6360	+	10.0769i	−0.400589	+	0.319459i
$996$	16.5539	−	3.59299i	0.524530	−	0.113848i
$997$	−49.7021	−	11.3442i	−1.57408	−	0.359274i	−0.655716	−	0.755008i	$-0.727633\pi$
$997$	−49.7021	−	11.3442i	−1.57408	−	0.359274i	−0.918365	+	0.395734i	$0.870490\pi$
$998$		−	5.38228i		−	0.170373i
$999$	36.1295	+	30.7539i	1.14309	+	0.973011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.8	yes	120
3.2	odd	2	inner	294.2.j.a.251.11	yes	120
49.41	odd	14	inner	294.2.j.a.41.11	yes	120
147.41	even	14	inner	294.2.j.a.41.8	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.8	✓	120	147.41	even	14	inner
294.2.j.a.41.11	yes	120	49.41	odd	14	inner
294.2.j.a.251.8	yes	120	1.1	even	1	trivial
294.2.j.a.251.11	yes	120	3.2	odd	2	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 - 0.623490i) q^{2} +(1.34258 + 1.09430i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-2.13620 - 1.02874i) q^{5} +(-0.367384 - 1.69264i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.605021 + 2.93836i) q^{9} +O(q^{10})\)	\(q+(-0.781831 - 0.623490i) q^{2} +(1.34258 + 1.09430i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-2.13620 - 1.02874i) q^{5} +(-0.367384 - 1.69264i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.605021 + 2.93836i) q^{9} +(1.02874 + 2.13620i) q^{10} +(2.95567 + 2.35707i) q^{11} +(-0.768111 + 1.55242i) q^{12} +(3.59671 + 2.86828i) q^{13} +(2.54479 - 0.723897i) q^{14} +(-1.74227 - 3.71881i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.623946 - 2.73368i) q^{17} +(1.35901 - 2.67453i) q^{18} +7.99958i q^{19} +(0.527599 - 2.31156i) q^{20} +(-4.42083 + 1.20674i) q^{21} +(-0.841228 - 3.68566i) q^{22} +(-5.35612 + 1.22250i) q^{23} +(1.56845 - 0.734821i) q^{24} +(0.387609 + 0.486046i) q^{25} +(-1.02368 - 4.48502i) q^{26} +(-2.40315 + 4.60704i) q^{27} +(-2.44094 - 1.02069i) q^{28} +(0.336112 + 0.0767154i) q^{29} +(-0.956481 + 3.99377i) q^{30} -4.40479i q^{31} +(0.974928 + 0.222521i) q^{32} +(1.38887 + 6.39893i) q^{33} +(-2.19224 + 1.74826i) q^{34} +(5.50052 - 3.01596i) q^{35} +(-2.73006 + 1.24370i) q^{36} +(2.03185 - 8.90210i) q^{37} +(4.98766 - 6.25432i) q^{38} +(1.69010 + 7.78676i) q^{39} +(-1.85373 + 1.47830i) q^{40} +(3.26974 + 1.57462i) q^{41} +(4.20874 + 1.81288i) q^{42} +(6.98003 - 3.36141i) q^{43} +(-1.64027 + 3.40606i) q^{44} +(1.73036 - 6.89934i) q^{45} +(4.94980 + 2.38370i) q^{46} +(-2.12713 + 2.66734i) q^{47} +(-1.68442 - 0.403407i) q^{48} +(-2.26753 - 6.62256i) q^{49} -0.621676i q^{50} +(3.82916 - 2.98740i) q^{51} +(-1.99602 + 4.14478i) q^{52} +(4.76629 - 1.08788i) q^{53} +(4.75131 - 2.10359i) q^{54} +(-3.88910 - 8.07580i) q^{55} +(1.27202 + 2.31991i) q^{56} +(-8.75393 + 10.7400i) q^{57} +(-0.214952 - 0.269541i) q^{58} +(-9.34907 + 4.50227i) q^{59} +(3.23788 - 2.52610i) q^{60} +(-7.60031 - 1.73472i) q^{61} +(-2.74634 + 3.44381i) q^{62} +(-7.25584 - 3.21757i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-4.73258 - 9.82731i) q^{65} +(2.90380 - 5.86883i) q^{66} +6.99996 q^{67} +2.80399 q^{68} +(-8.52877 - 4.21989i) q^{69} +(-6.18090 - 1.07154i) q^{70} +(11.0631 - 2.52507i) q^{71} +(2.90988 + 0.729801i) q^{72} +(7.61996 - 6.07671i) q^{73} +(-7.13893 + 5.69310i) q^{74} +(-0.0114852 + 1.07671i) q^{75} +(-7.79901 + 1.78007i) q^{76} +(-9.62044 + 2.73665i) q^{77} +(3.53359 - 7.14169i) q^{78} +4.27717 q^{79} +2.37101 q^{80} +(-8.26790 + 3.55554i) q^{81} +(-1.57462 - 3.26974i) q^{82} +(-6.09768 - 7.64625i) q^{83} +(-2.16021 - 4.04147i) q^{84} +(-4.14513 + 5.19783i) q^{85} +(-7.55301 - 1.72393i) q^{86} +(0.367307 + 0.470804i) q^{87} +(3.40606 - 1.64027i) q^{88} +(1.65793 + 2.07898i) q^{89} +(-5.65452 + 4.31526i) q^{90} +(-11.7070 + 3.33019i) q^{91} +(-2.38370 - 4.94980i) q^{92} +(4.82016 - 5.91377i) q^{93} +(3.32612 - 0.759165i) q^{94} +(8.22950 - 17.0887i) q^{95} +(1.06541 + 1.36561i) q^{96} +9.98133i q^{97} +(-2.35627 + 6.59151i) q^{98} +(-5.13767 + 10.1109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

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