LMFDB - Embedded newform 294.2.j.a.251.11

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			251.11
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(-1.69264 - 0.367384i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.13620 + 1.02874i) q^{5} +(-1.09430 - 1.34258i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.73006 + 1.24370i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(-1.69264 - 0.367384i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.13620 + 1.02874i) q^{5} +(-1.09430 - 1.34258i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.73006 + 1.24370i) q^{9} +(1.02874 + 2.13620i) q^{10} +(-2.95567 - 2.35707i) q^{11} +(-0.0184746 - 1.73195i) q^{12} +(3.59671 + 2.86828i) q^{13} +(-2.54479 + 0.723897i) q^{14} +(-3.23788 - 2.52610i) 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} +(3.39455 - 3.07848i) q^{21} +(-0.841228 - 3.68566i) q^{22} +(5.35612 - 1.22250i) q^{23} +(1.06541 - 1.36561i) q^{24} +(0.387609 + 0.486046i) q^{25} +(1.02368 + 4.48502i) q^{26} +(-4.16409 - 3.10811i) 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} +(4.13693 + 5.07553i) q^{33} +(-2.19224 + 1.74826i) q^{34} +(-5.50052 + 3.01596i) q^{35} +(-0.605021 + 2.93836i) q^{36} +(2.03185 - 8.90210i) q^{37} +(-4.98766 + 6.25432i) q^{38} +(-5.03417 - 6.17634i) q^{39} +(-1.85373 + 1.47830i) q^{40} +(-3.26974 - 1.57462i) q^{41} +(4.57337 - 0.290380i) q^{42} +(6.98003 - 3.36141i) q^{43} +(1.64027 - 3.40606i) q^{44} +(4.55252 + 5.46532i) 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} +(2.06043 - 4.39791i) q^{51} +(-1.99602 + 4.14478i) q^{52} +(-4.76629 + 1.08788i) q^{53} +(-1.31774 - 5.02629i) q^{54} +(-3.88910 - 8.07580i) q^{55} +(-1.27202 - 2.31991i) q^{56} +(2.93892 - 13.5404i) q^{57} +(-0.214952 - 0.269541i) q^{58} +(9.34907 - 4.50227i) q^{59} +(1.74227 - 3.71881i) q^{60} +(-7.60031 - 1.73472i) q^{61} +(2.74634 - 3.44381i) q^{62} +(-6.87674 + 3.96364i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(4.73258 + 9.82731i) q^{65} +(0.0698422 + 6.54755i) q^{66} +6.99996 q^{67} -2.80399 q^{68} +(-9.51510 + 0.101497i) q^{69} +(-6.18090 - 1.07154i) q^{70} +(-11.0631 + 2.52507i) q^{71} +(-2.30506 + 1.92008i) q^{72} +(7.61996 - 6.07671i) q^{73} +(7.13893 - 5.69310i) q^{74} +(-0.477517 - 0.965103i) q^{75} +(-7.79901 + 1.78007i) q^{76} +(9.62044 - 2.73665i) q^{77} +(-0.0849899 - 7.96761i) q^{78} +4.27717 q^{79} -2.37101 q^{80} +(5.90643 + 6.79074i) q^{81} +(-1.57462 - 3.26974i) q^{82} +(6.09768 + 7.64625i) q^{83} +(3.75665 + 2.62442i) q^{84} +(-4.14513 + 5.19783i) q^{85} +(7.55301 + 1.72393i) q^{86} +(0.540733 + 0.253334i) q^{87} +(3.40606 - 1.64027i) q^{88} +(-1.65793 - 2.07898i) q^{89} +(0.151731 + 7.11140i) q^{90} +(-11.7070 + 3.33019i) q^{91} +(2.38370 + 4.94980i) q^{92} +(-1.61825 + 7.45573i) q^{93} +(3.32612 - 0.759165i) q^{94} +(-8.22950 + 17.0887i) q^{95} +(1.56845 + 0.734821i) 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
$3$	−1.69264	−	0.367384i	−0.977246	−	0.212109i
$3$	−1.69264	−	0.367384i	−0.977246	−	0.212109i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	2.13620	+	1.02874i	0.955339	+	0.460067i	0.845555	−	0.533888i	$-0.179270\pi$
$5$	2.13620	+	1.02874i	0.955339	+	0.460067i	0.109784	+	0.993955i	$0.464984\pi$
$6$	−1.09430	−	1.34258i	−0.446746	−	0.548104i
$7$	−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
$9$	2.73006	+	1.24370i	0.910019	+	0.414566i
$10$	1.02874	+	2.13620i	0.325317	+	0.675527i
$11$	−2.95567	−	2.35707i	−0.891168	−	0.710683i	0.0667365	−	0.997771i	$-0.478741\pi$
$11$	−2.95567	−	2.35707i	−0.891168	−	0.710683i	−0.957904	+	0.287088i	$0.907313\pi$
$12$	−0.0184746	−	1.73195i	−0.00533316	−	0.499972i
$13$	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
$15$	−3.23788	−	2.52610i	−0.836017	−	0.652235i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.623946	+	2.73368i	−0.151329	+	0.663016i	0.841171	+	0.540770i	$0.181867\pi$
$17$	−0.623946	+	2.73368i	−0.151329	+	0.663016i	−0.992500	+	0.122246i	$0.960990\pi$
$18$	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
$21$	3.39455	−	3.07848i	0.740752	−	0.671778i
$22$	−0.841228	−	3.68566i	−0.179350	−	0.785785i
$23$	5.35612	−	1.22250i	1.11683	−	0.254909i	0.376010	−	0.926615i	$-0.377296\pi$
$23$	5.35612	−	1.22250i	1.11683	−	0.254909i	0.740817	+	0.671707i	$0.234439\pi$
$24$	1.06541	−	1.36561i	0.217476	−	0.278755i
$25$	0.387609	+	0.486046i	0.0775218	+	0.0972092i
$26$	1.02368	+	4.48502i	0.200760	+	0.879585i
$27$	−4.16409	−	3.10811i	−0.801379	−	0.598157i
$28$	−2.44094	−	1.02069i	−0.461295	−	0.192892i
$29$	−0.336112	−	0.0767154i	−0.0624145	−	0.0142457i	0.191200	−	0.981551i	$-0.438762\pi$
$29$	−0.336112	−	0.0767154i	−0.0624145	−	0.0142457i	−0.253614	+	0.967305i	$0.581619\pi$
$30$	−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
$33$	4.13693	+	5.07553i	0.720148	+	0.883537i
$34$	−2.19224	+	1.74826i	−0.375967	+	0.299824i
$35$	−5.50052	+	3.01596i	−0.929757	+	0.509791i
$36$	−0.605021	+	2.93836i	−0.100837	+	0.489726i
$37$	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
$39$	−5.03417	−	6.17634i	−0.806112	−	0.989005i
$40$	−1.85373	+	1.47830i	−0.293100	+	0.233740i
$41$	−3.26974	−	1.57462i	−0.510647	−	0.245915i	0.160773	−	0.986991i	$-0.448601\pi$
$41$	−3.26974	−	1.57462i	−0.510647	−	0.245915i	−0.671420	+	0.741077i	$0.734316\pi$
$42$	4.57337	−	0.290380i	0.705686	−	0.0448066i
$43$	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
$45$	4.55252	+	5.46532i	0.678649	+	0.814721i
$46$	4.94980	+	2.38370i	0.729808	+	0.351457i
$47$	2.12713	−	2.66734i	0.310274	−	0.389072i	−0.602105	−	0.798417i	$-0.705671\pi$
$47$	2.12713	−	2.66734i	0.310274	−	0.389072i	0.912380	+	0.409345i	$0.134243\pi$
$48$	1.68442	−	0.403407i	0.243125	−	0.0582268i
$49$	−2.26753	−	6.62256i	−0.323933	−	0.946080i
$50$			0.621676i			0.0879183i
$51$	2.06043	−	4.39791i	0.288518	−	0.615831i
$52$	−1.99602	+	4.14478i	−0.276799	+	0.574778i
$53$	−4.76629	+	1.08788i	−0.654701	+	0.149431i	−0.536953	−	0.843612i	$-0.680425\pi$
$53$	−4.76629	+	1.08788i	−0.654701	+	0.149431i	−0.117748	+	0.993044i	$0.537567\pi$
$54$	−1.31774	−	5.02629i	−0.179322	−	0.683991i
$55$	−3.88910	−	8.07580i	−0.524406	−	1.08894i
$56$	−1.27202	−	2.31991i	−0.169980	−	0.310011i
$57$	2.93892	−	13.5404i	0.389269	−	1.79347i
$58$	−0.214952	−	0.269541i	−0.0282246	−	0.0353925i
$59$	9.34907	−	4.50227i	1.21714	−	0.586146i	0.288630	−	0.957441i	$-0.406800\pi$
$59$	9.34907	−	4.50227i	1.21714	−	0.586146i	0.928515	+	0.371295i	$0.121086\pi$
$60$	1.74227	−	3.71881i	0.224926	−	0.480096i
$61$	−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
$63$	−6.87674	+	3.96364i	−0.866388	+	0.499372i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	4.73258	+	9.82731i	0.587005	+	1.21893i
$66$	0.0698422	+	6.54755i	0.00859698	+	0.805947i
$67$	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
$69$	−9.51510	+	0.101497i	−1.14548	+	0.0122188i
$70$	−6.18090	−	1.07154i	−0.738759	−	0.128074i
$71$	−11.0631	+	2.52507i	−1.31294	+	0.299671i	−0.820986	−	0.570948i	$-0.806576\pi$
$71$	−11.0631	+	2.52507i	−1.31294	+	0.299671i	−0.491958	+	0.870619i	$0.663719\pi$
$72$	−2.30506	+	1.92008i	−0.271654	+	0.226283i
$73$	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
$75$	−0.477517	−	0.965103i	−0.0551389	−	0.111440i
$76$	−7.79901	+	1.78007i	−0.894608	+	0.204188i
$77$	9.62044	−	2.73665i	1.09635	−	0.311870i
$78$	−0.0849899	−	7.96761i	−0.00962321	−	0.902154i
$79$	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
$81$	5.90643	+	6.79074i	0.656270	+	0.754526i
$82$	−1.57462	−	3.26974i	−0.173888	−	0.361082i
$83$	6.09768	+	7.64625i	0.669307	+	0.839285i	0.994321	−	0.106425i	$-0.0339403\pi$
$83$	6.09768	+	7.64625i	0.669307	+	0.839285i	−0.325014	+	0.945709i	$0.605369\pi$
$84$	3.75665	+	2.62442i	0.409884	+	0.286348i
$85$	−4.14513	+	5.19783i	−0.449602	+	0.563784i
$86$	7.55301	+	1.72393i	0.814462	+	0.185896i
$87$	0.540733	+	0.253334i	0.0579727	+	0.0271603i
$88$	3.40606	−	1.64027i	0.363087	−	0.174854i
$89$	−1.65793	−	2.07898i	−0.175740	−	0.220371i	0.686158	−	0.727452i	$-0.259296\pi$
$89$	−1.65793	−	2.07898i	−0.175740	−	0.220371i	−0.861898	+	0.507081i	$0.830724\pi$
$90$	0.151731	+	7.11140i	0.0159938	+	0.749608i
$91$	−11.7070	+	3.33019i	−1.22722	+	0.349099i
$92$	2.38370	+	4.94980i	0.248517	+	0.516052i
$93$	−1.61825	+	7.45573i	−0.167805	+	0.773123i
$94$	3.32612	−	0.759165i	0.343063	−	0.0783019i
$95$	−8.22950	+	17.0887i	−0.844329	+	1.75327i
$96$	1.56845	+	0.734821i	0.160079	+	0.0749973i
$97$			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	0.815193	−	0.579189i	$-0.196631\pi$
$101$	8.74971	+	4.21364i	0.870629	+	0.419273i	0.0554361	+	0.998462i	$0.482345\pi$
$102$	4.35296	−	2.15377i	0.431007	−	0.213255i
$103$	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
$105$	10.4184	−	3.08413i	1.01673	−	0.300981i
$106$	−4.40472	−	2.12120i	−0.427824	−	0.206029i
$107$	−10.7422	+	8.56659i	−1.03848	+	0.828163i	−0.985371	−	0.170425i	$-0.945486\pi$
$107$	−10.7422	+	8.56659i	−1.03848	+	0.828163i	−0.0531135	+	0.998588i	$0.516915\pi$
$108$	2.10359	−	4.75131i	0.202418	−	0.457195i
$109$	−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
$111$	−6.70967	+	14.3216i	−0.636854	+	1.35934i
$112$	0.451936	−	2.60687i	0.0427039	−	0.246326i
$113$	4.98621	−	3.97637i	0.469063	−	0.374065i	−0.360244	−	0.932858i	$-0.617307\pi$
$113$	4.98621	−	3.97637i	0.469063	−	0.374065i	0.829307	+	0.558793i	$0.188735\pi$
$114$	10.7400	−	8.75393i	1.00590	−	0.819880i
$115$	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
$120$	3.68080	−	1.82120i	0.336009	−	0.166252i
$121$	0.732482	+	3.20921i	0.0665893	+	0.291747i
$122$	−4.86058	−	6.09498i	−0.440056	−	0.551813i
$123$	4.95600	+	3.86652i	0.446867	+	0.348632i
$124$	4.29436	−	0.980159i	0.385644	−	0.0880208i
$125$	−2.31000	−	10.1208i	−0.206613	−	0.905229i
$126$	−7.84774	−	1.18867i	−0.699132	−	0.105896i
$127$	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	−0.884294	−	0.466930i	$-0.845360\pi$
$131$	−12.2534	+	5.90091i	−1.07058	+	0.515565i	−0.186288	+	0.982495i	$0.559646\pi$
$132$	−4.02772	+	5.16262i	−0.350568	+	0.449349i
$133$	−17.2200	−	12.3054i	−1.49317	−	1.06701i
$134$	5.47279	+	4.36440i	0.472777	+	0.377027i
$135$	−5.69790	−	10.9233i	−0.490397	−	0.940131i
$136$	−2.19224	−	1.74826i	−0.187983	−	0.149912i
$137$	−6.31457	−	13.1123i	−0.539491	−	1.12026i	−0.975434	−	0.220290i	$-0.929300\pi$
$137$	−6.31457	−	13.1123i	−0.539491	−	1.12026i	0.435944	−	0.899974i	$-0.356415\pi$
$138$	−7.50249	−	5.85321i	−0.638654	−	0.498259i
$139$	−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
$141$	−4.58041	+	3.73337i	−0.385740	+	0.314407i
$142$	−10.2238	−	4.92353i	−0.857963	−	0.413173i
$143$	−3.86995	−	16.9554i	−0.323622	−	1.41788i
$144$	−2.99932	+	0.0639943i	−0.249943	+	0.00533286i
$145$	−0.639084	−	0.509653i	−0.0530730	−	0.0423243i
$146$	9.74629			0.806609
$147$	1.40509	+	12.0427i	0.115890	+	0.993262i
$148$	9.13103			0.750566
$149$	1.87558	+	1.49573i	0.153654	+	0.122535i	0.697299	−	0.716780i	$-0.254385\pi$
$149$	1.87558	+	1.49573i	0.153654	+	0.122535i	−0.543645	+	0.839315i	$0.682956\pi$
$150$	0.228394	−	1.05227i	0.0186483	−	0.0859178i
$151$	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
$153$	−5.10329	+	6.68712i	−0.412576	+	0.540621i
$154$	9.22784	+	3.85865i	0.743601	+	0.310939i
$155$	4.53139	−	9.40954i	0.363970	−	0.755792i
$156$	4.90128	−	6.28232i	0.392416	−	0.502988i
$157$	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
$159$	8.46728	−	0.0903199i	0.671499	−	0.00716283i
$160$	−1.85373	−	1.47830i	−0.146550	−	0.116870i
$161$	−5.60751	+	13.4102i	−0.441934	+	1.05687i
$162$	0.383878	+	8.99181i	0.0301603	+	0.706463i
$163$	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	$-0.618471\pi$
$167$	4.75773	−	20.8450i	0.368164	−	1.61303i	0.731820	−	0.681498i	$-0.238671\pi$
$168$	1.30077	+	4.39409i	0.100357	+	0.339011i
$169$	1.81651	+	7.95867i	0.139732	+	0.612205i
$170$	−6.48159	+	1.47938i	−0.497115	+	0.113463i
$171$	−9.94906	+	21.8393i	−0.760824	+	1.67009i
$172$	4.83033	+	6.05705i	0.368309	+	0.461845i
$173$	4.24603	+	18.6031i	0.322820	+	1.41436i	0.832511	+	0.554008i	$0.186902\pi$
$173$	4.24603	+	18.6031i	0.322820	+	1.41436i	−0.509692	+	0.860357i	$0.670241\pi$
$174$	0.264811	+	0.535206i	0.0200753	+	0.0405739i
$175$	−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	0.146228	−	0.989251i	$-0.453287\pi$
$179$	−2.02351	−	0.461853i	−0.151244	−	0.0345205i	−0.297473	+	0.954730i	$0.596144\pi$
$180$	−4.31526	+	5.65452i	−0.321640	+	0.421463i
$181$	−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
$183$	12.2273	+	5.72849i	0.903866	+	0.423462i
$184$	−1.22250	+	5.35612i	−0.0901238	+	0.394858i
$185$	13.4984	−	16.9265i	0.992422	−	1.24446i
$186$	−5.91377	+	4.82016i	−0.433619	+	0.353431i
$187$	8.28765	−	6.60918i	0.606053	−	0.483311i
$188$	3.07380	+	1.48026i	0.224180	+	0.107959i
$189$	13.0960	−	4.18262i	0.952595	−	0.304241i
$190$	−17.0887	+	8.22950i	−1.23975	+	0.597031i
$191$	3.16653	−	6.57538i	0.229122	−	0.475778i	−0.754435	−	0.656375i	$-0.772089\pi$
$191$	3.16653	−	6.57538i	0.229122	−	0.475778i	0.983557	+	0.180598i	$0.0578032\pi$
$192$	0.768111	+	1.55242i	0.0554336	+	0.112036i
$193$	−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	$0.331797\pi$
$197$			24.2425i			1.72720i	−0.504175	+	0.863602i	$0.668203\pi$
$198$	2.28725	−	11.1083i	0.162548	−	0.789432i
$199$	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
$201$	−11.8484	−	2.57168i	−0.835723	−	0.181392i
$202$	4.21364	+	8.74971i	0.296471	+	0.615628i
$203$	0.682166	−	0.605513i	0.0478787	−	0.0424987i
$204$	4.74614	+	1.03014i	0.332296	+	0.0721242i
$205$	−5.36495	−	6.72743i	−0.374704	−	0.469864i
$206$	0.229356	−	0.110452i	0.0159800	−	0.00769555i
$207$	16.1429	+	3.32390i	1.12201	+	0.231027i
$208$	−4.48502	−	1.02368i	−0.310980	−	0.0709792i
$209$	18.8555	−	23.6441i	1.30427	−	1.63550i
$210$	10.0684	+	4.08450i	0.694783	+	0.281857i
$211$	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
$213$	19.6535	−	0.209642i	1.34663	−	0.0143644i
$214$	−13.7397			−0.939229
$215$	18.3688			1.25274
$216$	4.60704	−	2.40315i	0.313470	−	0.163514i
$217$	9.48184	+	6.77570i	0.643669	+	0.459965i
$218$	−1.59543	+	0.364146i	−0.108056	+	0.0246631i
$219$	−15.1303	+	7.48623i	−1.02241	+	0.505873i
$220$	7.00791	−	5.58862i	0.472473	−	0.376785i
$221$	−10.0851	+	8.04261i	−0.678399	+	0.541005i
$222$	−14.1752	+	7.01364i	−0.951376	+	0.470725i
$223$	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
$225$	0.453700	+	1.80900i	0.0302467	+	0.120600i
$226$	6.37760			0.424232
$227$	−14.1568			−0.939622			−0.469811	−	0.882767i	$-0.655678\pi$
$227$	−14.1568			−0.939622			−0.469811	+	0.882767i	$0.655678\pi$
$228$	13.8549	−	0.147789i	0.917562	−	0.00978757i
$229$	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
$231$	−17.2893	+	1.09776i	−1.13756	+	0.0722276i
$232$	0.214952	−	0.269541i	0.0141123	−	0.0176962i
$233$	14.3975	+	3.28613i	0.943209	+	0.215281i	0.666358	−	0.745632i	$-0.267852\pi$
$233$	14.3975	+	3.28613i	0.943209	+	0.215281i	0.276851	+	0.960913i	$0.410709\pi$
$234$	−2.78332	+	13.5175i	−0.181951	+	0.883668i
$235$	7.28799	−	3.50971i	0.475416	−	0.228948i
$236$	6.46975	+	8.11282i	0.421145	+	0.528099i
$237$	−7.23970	−	1.57136i	−0.470269	−	0.102071i
$238$	−0.391093	−	7.40833i	−0.0253508	−	0.480211i
$239$	−2.71183	−	5.63116i	−0.175413	−	0.364250i	0.794663	−	0.607051i	$-0.207648\pi$
$239$	−2.71183	−	5.63116i	−0.175413	−	0.364250i	−0.970076	+	0.242802i	$0.921934\pi$
$240$	4.01326	+	0.871071i	0.259055	+	0.0562274i
$241$	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
$243$	−7.50265	−	13.6642i	−0.481295	−	0.876559i
$244$		−	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
$249$	−7.51206	−	15.1825i	−0.476058	−	0.962154i
$250$	4.50416	−	9.35299i	0.284868	−	0.591535i
$251$	−17.6266	+	8.48852i	−1.11258	+	0.535791i	−0.897593	−	0.440826i	$-0.854686\pi$
$251$	−17.6266	+	8.48852i	−1.11258	+	0.535791i	−0.214988	+	0.976617i	$0.568971\pi$
$252$	−5.39449	−	5.82233i	−0.339821	−	0.366772i
$253$	−18.7124	−	9.01142i	−1.17644	−	0.566543i
$254$	14.9443	−	11.9177i	0.937688	−	0.747782i
$255$	8.92581	−	7.27519i	0.558956	−	0.455590i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	2.92870	−	12.8315i	0.182687	−	0.800404i	−0.797657	−	0.603111i	$-0.793928\pi$
$257$	2.92870	−	12.8315i	0.182687	−	0.800404i	0.980344	−	0.197294i	$-0.0632152\pi$
$258$	−12.1512	−	5.69284i	−0.756500	−	0.354421i
$259$	16.0373	+	18.0675i	0.996510	+	1.12266i
$260$	−8.52782	+	6.80071i	−0.528873	+	0.421762i
$261$	−0.822195	−	0.627460i	−0.0508926	−	0.0388388i
$262$	−13.2592	−	3.02633i	−0.819158	−	0.186967i
$263$			18.5946i			1.14659i	0.819348	+	0.573297i	$0.194336\pi$
$263$			18.5946i			1.14659i	−0.819348	+	0.573297i	$0.805664\pi$
$264$	−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
$267$	2.04249	+	4.12806i	0.124999	+	0.252633i
$268$	1.55764	+	6.82446i	0.0951479	+	0.416870i
$269$	−6.39776	−	8.02253i	−0.390078	−	0.489143i	0.547555	−	0.836770i	$-0.315559\pi$
$269$	−6.39776	−	8.02253i	−0.390078	−	0.489143i	−0.937633	+	0.347627i	$0.886987\pi$
$270$	2.35579	−	12.0928i	0.143369	−	0.735944i
$271$	−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
$273$	21.0391	−	1.33585i	1.27335	−	0.0808495i
$274$	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
$279$	5.47823	−	12.0253i	0.327973	−	0.719938i
$280$	−0.330703	−	6.26437i	−0.0197633	−	0.374368i
$281$	−6.25145	−	4.98537i	−0.372930	−	0.297402i	0.419033	−	0.907971i	$-0.362369\pi$
$281$	−6.25145	−	4.98537i	−0.372930	−	0.297402i	−0.791963	+	0.610569i	$0.790941\pi$
$282$	−5.90883	+	0.0630290i	−0.351866	+	0.00375332i
$283$	−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
$285$	20.2077	−	25.9017i	1.19700	−	1.53428i
$286$	7.54585	−	15.6691i	0.446195	−	0.926534i
$287$	8.41926	−	4.61632i	0.496973	−	0.272493i
$288$	−2.38486	−	1.82001i	−0.140529	−	0.107245i
$289$	8.23275	+	3.96468i	0.484279	+	0.233217i
$290$	−0.181893	−	0.796925i	−0.0106811	−	0.0467970i
$291$	3.66698	−	16.8948i	0.214962	−	0.990390i
$292$	7.61996	+	6.07671i	0.445924	+	0.355613i
$293$	−15.8995			−0.928859			−0.464429	−	0.885610i	$-0.653741\pi$
$293$	−15.8995			−0.928859			−0.464429	+	0.885610i	$0.653741\pi$
$294$	−6.40994	+	10.2914i	−0.373835	+	0.600206i
$295$	24.6032			1.43245
$296$	7.13893	+	5.69310i	0.414942	+	0.330905i
$297$	4.98164	+	19.0016i	0.289064	+	1.10258i
$298$	0.533819	+	2.33881i	0.0309233	+	0.135484i
$299$	22.7709	+	10.9659i	1.31687	+	0.634172i
$300$	0.834648	−	0.680300i	0.0481884	−	0.0392771i
$301$	−3.50126	+	20.1961i	−0.201809	+	1.16408i
$302$	−6.93642	+	14.4036i	−0.399146	+	0.828835i
$303$	−13.2621	−	10.3467i	−0.761887	−	0.594401i
$304$	−3.47089	−	7.20737i	−0.199069	−	0.413371i
$305$	−14.4512	−	11.5245i	−0.827475	−	0.659890i
$306$	−8.15926	+	2.04635i	−0.466434	+	0.116982i
$307$	−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
$309$	−0.271217	+	0.347638i	−0.0154290	+	0.0197764i
$310$	9.40954	−	4.53139i	0.534426	−	0.257366i
$311$	4.59661	−	20.1391i	0.260650	−	1.14198i	−0.659899	−	0.751355i	$-0.729401\pi$
$311$	4.59661	−	20.1391i	0.260650	−	1.14198i	0.920549	−	0.390628i	$-0.127742\pi$
$312$	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
$315$	−18.7677	+	1.39277i	−1.05744	+	0.0784735i
$316$	0.951759	+	4.16993i	0.0535406	+	0.234577i
$317$	1.10675	−	0.252609i	0.0621615	−	0.0141880i	−0.191327	−	0.981526i	$-0.561279\pi$
$317$	1.10675	−	0.252609i	0.0621615	−	0.0141880i	0.253489	+	0.967338i	$0.418422\pi$
$318$	6.67630	+	5.20865i	0.374388	+	0.292087i
$319$	0.812613	+	1.01898i	0.0454976	+	0.0570522i
$320$	−0.527599	−	2.31156i	−0.0294937	−	0.129220i
$321$	21.3298	−	10.5536i	1.19052	−	0.589047i
$322$	−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
$327$	2.19707	−	1.79077i	0.121498	−	0.0990300i
$328$	2.83737	−	2.26273i	0.156668	−	0.124938i
$329$	2.46969	+	8.68196i	0.136158	+	0.478652i
$330$	−6.58654	+	14.0587i	−0.362577	+	0.773908i
$331$	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
$333$	16.6186	−	21.7762i	0.910692	−	1.19333i
$334$	16.7164	−	13.3309i	0.914679	−	0.729432i
$335$	14.9533	+	7.20115i	0.816989	+	0.393441i
$336$	−1.72269	+	4.24645i	−0.0939802	+	0.231663i
$337$	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
$339$	−9.90071	+	4.89871i	−0.537733	+	0.266061i
$340$	−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
$345$	−20.4306	−	9.57176i	−1.09995	−	0.515326i
$346$	−8.27914	+	17.1918i	−0.445089	+	0.924238i
$347$	23.5226	−	5.36887i	1.26276	−	0.288216i	0.461825	−	0.886971i	$-0.347195\pi$
$347$	23.5226	−	5.36887i	1.26276	−	0.288216i	0.800932	+	0.598755i	$0.204338\pi$
$348$	−0.126658	+	0.583548i	−0.00678958	+	0.0312814i
$349$	−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
$351$	−6.06208	−	23.1227i	−0.323570	−	1.23420i
$352$	2.35707	+	2.95567i	0.125632	+	0.157538i
$353$	−13.1768	+	6.34562i	−0.701331	+	0.337743i	−0.750337	−	0.661055i	$-0.770109\pi$
$353$	−13.1768	+	6.34562i	−0.701331	+	0.337743i	0.0490061	+	0.998798i	$0.484395\pi$
$354$	−16.2753	−	7.62500i	−0.865023	−	0.405264i
$355$	−26.2306	−	5.98697i	−1.39218	−	0.317755i
$356$	1.65793	−	2.07898i	0.0878701	−	0.110186i
$357$	6.29756	+	11.2004i	0.333302	+	0.592790i
$358$	−1.29408	−	1.62273i	−0.0683945	−	0.0857640i
$359$	−3.73278	−	7.75120i	−0.197009	−	0.409093i	0.778938	−	0.627101i	$-0.215758\pi$
$359$	−3.73278	−	7.75120i	−0.197009	−	0.409093i	−0.975947	+	0.218008i	$0.930044\pi$
$360$	−6.89934	+	1.73036i	−0.363627	+	0.0911981i
$361$	−44.9933			−2.36807
$362$	−1.64588			−0.0865057
$363$	−0.0608137	−	5.70115i	−0.00319189	−	0.299233i
$364$	−5.85174	−	10.6724i	−0.306715	−	0.559387i
$365$	22.5291	−	5.14213i	1.17923	−	0.269151i
$366$	5.98801	+	12.1023i	0.312999	+	0.632597i
$367$	−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
$369$	−6.96822	−	8.36538i	−0.362751	−	0.435484i
$370$	21.1069	−	4.81752i	1.09730	−	0.250451i
$371$	4.99000	−	11.9334i	0.259068	−	0.619553i
$372$	−7.62889	+	0.0813768i	−0.395540	+	0.00421919i
$373$	−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
$375$	0.191786	+	17.9795i	0.00990376	+	0.928455i
$376$	1.48026	+	3.07380i	0.0763387	+	0.158519i
$377$	−0.988857	−	1.23999i	−0.0509287	−	0.0638626i
$378$	12.8467	+	4.89513i	0.660763	+	0.251779i
$379$	−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
$381$	−14.0457	+	29.9801i	−0.719584	+	1.53593i
$382$	6.57538	−	3.16653i	0.336426	−	0.162014i
$383$	13.1384	+	16.4750i	0.671339	+	0.841832i	0.994525	−	0.104503i	$-0.0333253\pi$
$383$	13.1384	+	16.4750i	0.671339	+	0.841832i	−0.323186	+	0.946336i	$0.604754\pi$
$384$	−0.367384	+	1.69264i	−0.0187480	+	0.0863772i
$385$	23.3665	+	4.05091i	1.19087	+	0.206453i
$386$	−5.65564	−	11.7441i	−0.287865	−	0.597757i
$387$	23.2365	−	0.495780i	1.18118	−	0.0252019i
$388$	−9.73108	+	2.22105i	−0.494021	+	0.112757i
$389$	1.90521	−	3.95621i	0.0965981	−	0.200588i	−0.847070	−	0.531481i	$-0.821636\pi$
$389$	1.90521	−	3.95621i	0.0965981	−	0.200588i	0.943668	+	0.330893i	$0.107350\pi$
$390$	8.01506	−	17.1079i	0.405858	−	0.866291i
$391$			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
$396$	8.71415	−	7.25874i	0.437903	−	0.364765i
$397$	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
$399$	24.6265	+	27.1550i	1.23287	+	1.35945i
$400$	−0.560111	−	0.269735i	−0.0280056	−	0.0134868i
$401$	1.24286	−	0.991149i	0.0620656	−	0.0494956i	−0.591966	−	0.805963i	$-0.701648\pi$
$401$	1.24286	−	0.991149i	0.0620656	−	0.0494956i	0.654031	+	0.756468i	$0.273076\pi$
$402$	−7.66005	−	9.39798i	−0.382048	−	0.468729i
$403$	12.6342	−	15.8428i	0.629353	−	0.789184i
$404$	−2.16100	+	9.46796i	−0.107514	+	0.471049i
$405$	5.63143	+	20.5826i	0.279828	+	1.02276i
$406$	0.910870	−	0.0480858i	0.0452057	−	0.00238646i
$407$	−26.9883	+	21.5225i	−1.33776	+	1.06683i
$408$	3.06840	+	3.76456i	0.151908	+	0.186374i
$409$	−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
$414$	10.5486	+	12.6637i	0.518437	+	0.622386i
$415$	5.15987	+	22.6069i	0.253288	+	1.10973i
$416$	−2.86828	−	3.59671i	−0.140629	−	0.176343i
$417$	11.3323	−	14.5254i	0.554944	−	0.711312i
$418$	29.4837	−	6.72947i	1.44210	−	0.329149i
$419$	6.76718	+	29.6489i	0.330598	+	1.44845i	0.817975	+	0.575254i	$0.195097\pi$
$419$	6.76718	+	29.6489i	0.330598	+	1.44845i	−0.487377	+	0.873192i	$0.662046\pi$
$420$	5.32512	+	9.47092i	0.259839	+	0.462133i
$421$	−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
$426$	15.4964	+	12.0898i	0.750803	+	0.585754i
$427$	15.4254	−	13.6921i	0.746489	−	0.662608i
$428$	−10.7422	−	8.56659i	−0.519242	−	0.414082i
$429$	0.321299	+	30.1211i	0.0155125	+	1.45426i
$430$	14.3613	+	11.4528i	0.692563	+	0.552301i
$431$	−8.92867	−	18.5406i	−0.430079	−	0.893068i	−0.997569	−	0.0696879i	$-0.977800\pi$
$431$	−8.92867	−	18.5406i	−0.430079	−	0.893068i	0.567490	−	0.823380i	$-0.307915\pi$
$432$	5.10027	+	0.993583i	0.245387	+	0.0478038i
$433$	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
$435$	0.894501	+	1.09745i	0.0428880	+	0.0526186i
$436$	−1.47440	−	0.710032i	−0.0706108	−	0.0340044i
$437$	9.77947	+	42.8467i	0.467816	+	2.04963i
$438$	−16.4970	−	3.58063i	−0.788255	−	0.171089i
$439$	−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
$441$	2.04598	−	20.9001i	0.0974275	−	0.995243i
$442$	−12.8994			−0.613560
$443$	5.48403	+	4.37337i	0.260554	+	0.207785i	0.745050	−	0.667009i	$-0.232426\pi$
$443$	5.48403	+	4.37337i	0.260554	+	0.207785i	−0.484496	+	0.874793i	$0.660997\pi$
$444$	−15.4555	−	3.35460i	−0.733488	−	0.159202i
$445$	−1.40294	−	6.14670i	−0.0665059	−	0.291382i
$446$	5.14899	+	2.47962i	0.243812	+	0.117414i
$447$	−2.62518	−	3.22078i	−0.124167	−	0.152338i
$448$	2.64207	−	0.139478i	0.124826	−	0.00658970i
$449$	−0.844819	+	1.75428i	−0.0398695	+	0.0827898i	−0.919952	−	0.392031i	$-0.871773\pi$
$449$	−0.844819	+	1.75428i	−0.0398695	+	0.0827898i	0.880083	+	0.474820i	$0.157487\pi$
$450$	−0.773178	+	1.69721i	−0.0364480	+	0.0800074i
$451$	5.95277	+	12.3611i	0.280305	+	0.582059i
$452$	4.98621	+	3.97637i	0.234532	+	0.187033i
$453$	−0.295350	−	27.6884i	−0.0138768	−	1.30091i
$454$	−11.0683	−	8.82664i	−0.519459	−	0.414255i
$455$	−28.4344	−	4.92949i	−1.33302	−	0.231098i
$456$	10.9243	+	8.52284i	0.511579	+	0.399118i
$457$	−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	$-0.810243\pi$
$461$	3.47089	−	15.2070i	0.161656	−	0.708260i	0.989165	−	0.146808i	$-0.0468999\pi$
$462$	−14.2018	−	9.92147i	−0.660728	−	0.461588i
$463$	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
$465$	−11.1269	+	14.2622i	−0.515999	+	0.661393i
$466$	9.20752	+	11.5459i	0.426530	+	0.534852i
$467$	3.35797	+	14.7122i	0.155389	+	0.680802i	0.991265	+	0.131884i	$0.0421027\pi$
$467$	3.35797	+	14.7122i	0.155389	+	0.680802i	−0.835877	+	0.548917i	$0.815040\pi$
$468$	−10.6041	+	8.83305i	−0.490175	+	0.408308i
$469$	−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
$474$	−4.68050	−	5.74242i	−0.214982	−	0.263758i
$475$	−3.88816	+	3.10071i	−0.178401	+	0.142270i
$476$	4.31325	−	6.03591i	0.197698	−	0.276656i
$477$	−14.3652	−	2.95787i	−0.657739	−	0.135431i
$478$	1.39078	−	6.09342i	0.0636129	−	0.278706i
$479$	19.6833	−	24.6821i	0.899353	−	1.12775i	−0.0918983	−	0.995768i	$-0.529293\pi$
$479$	19.6833	−	24.6821i	0.899353	−	1.12775i	0.991252	−	0.131985i	$-0.0421351\pi$
$480$	2.59459	+	3.18326i	0.118426	+	0.145295i
$481$	32.8417	−	26.1903i	1.49745	−	1.19418i
$482$	8.88337	+	4.27801i	0.404627	+	0.194858i
$483$	14.4182	−	20.6385i	0.656050	−	0.939085i
$484$	−2.96576	+	1.42823i	−0.134807	+	0.0649198i
$485$	−10.2682	+	21.3222i	−0.466255	+	0.968189i
$486$	2.65368	−	15.3609i	0.120373	−	0.696786i
$487$	−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	$0.107300\pi$
$491$			14.6576i			0.661489i	−0.943720	+	0.330744i	$0.892700\pi$
$492$	−2.66676	+	5.69212i	−0.120227	+	0.256621i
$493$	0.419432	−	0.870959i	0.0188902	−	0.0392260i
$494$	−35.8783	+	8.18898i	−1.61424	+	0.368440i
$495$	−0.573610	−	26.8843i	−0.0257818	−	1.20836i
$496$	1.91117	+	3.96858i	0.0858140	+	0.178195i
$497$	11.5823	−	27.6988i	0.519538	−	1.24246i
$498$	3.59299	−	16.5539i	0.161006	−	0.741797i
$499$	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
$501$	−15.7112	+	33.5351i	−0.701926	+	1.49824i
$502$	−19.0735	−	4.35341i	−0.851294	−	0.194302i
$503$	−11.7410	+	14.7228i	−0.523506	+	0.656455i	−0.971349	−	0.237657i	$-0.923621\pi$
$503$	−11.7410	+	14.7228i	−0.523506	+	0.656455i	0.447844	+	0.894112i	$0.352192\pi$
$504$	−0.587415	−	7.91549i	−0.0261656	−	0.352584i
$505$	14.3564	+	18.0024i	0.638853	+	0.801096i
$506$	−9.01142	−	18.7124i	−0.400607	−	0.831868i
$507$	−0.150814	−	14.1385i	−0.00669791	−	0.627913i
$508$	19.1145			0.848068
$509$	−18.8085			−0.833672			−0.416836	−	0.908982i	$-0.636861\pi$
$509$	−18.8085			−0.833672			−0.416836	+	0.908982i	$0.636861\pi$
$510$	11.5145	−	0.122824i	0.509870	−	0.00543875i
$511$	1.35939	+	25.7504i	0.0601359	+	1.13913i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	24.8636	−	33.3110i	1.09775	−	1.47071i
$514$	10.2900	−	8.20603i	0.453874	−	0.361952i
$515$	0.471895	−	0.376324i	0.0207942	−	0.0165828i
$516$	−5.95075	−	12.0270i	−0.261967	−	0.529458i
$517$	−12.5742	+	2.86998i	−0.553013	+	0.126222i
$518$	1.27357	+	24.1248i	0.0559577	+	1.05998i
$519$	−0.352523	−	33.0482i	−0.0154740	−	1.45066i
$520$	−10.9075			−0.478325
$521$	−14.9668			−0.655709			−0.327854	−	0.944728i	$-0.606326\pi$
$521$	−14.9668			−0.655709			−0.327854	+	0.944728i	$0.606326\pi$
$522$	−0.251603	−	1.00320i	−0.0110124	−	0.0439088i
$523$	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
$525$	2.81204	+	0.456665i	0.122728	+	0.0199305i
$526$	−11.5936	+	14.5379i	−0.505503	+	0.633881i
$527$	12.0413	+	2.74835i	0.524528	+	0.119720i
$528$	−5.92944	−	2.77795i	−0.258046	−	0.120895i
$529$	6.47119	−	3.11636i	0.281356	−	0.135494i
$530$	−7.22721	−	9.06263i	−0.313930	−	0.393656i
$531$	31.1230	−	0.664048i	1.35062	−	0.0288172i
$532$	8.16507	−	19.5265i	0.354001	−	0.846581i
$533$	−7.24384	−	15.0420i	−0.313765	−	0.651540i
$534$	−0.976916	+	4.50092i	−0.0422753	+	0.194774i
$535$	−31.7603	+	7.24907i	−1.37312	+	0.313405i
$536$	−3.03717	+	6.30675i	−0.131186	+	0.272410i
$537$	3.25540	+	1.52516i	0.140481	+	0.0658154i
$538$		−	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
$543$	2.55510	−	1.26422i	0.109650	−	0.0542529i
$544$	1.21660	−	2.52630i	0.0521615	−	0.108314i
$545$	−3.49581	+	1.68349i	−0.149744	+	0.0721129i
$546$	17.2820	+	12.0733i	0.739599	+	0.516689i
$547$	−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
$549$	−18.5918	−	14.1884i	−0.793480	−	0.605545i
$550$	1.46533	−	1.83747i	0.0624820	−	0.0783500i
$551$	0.613691	−	2.68876i	0.0261441	−	0.114545i
$552$	4.03700	−	8.61685i	0.171826	−	0.366757i
$553$	−6.57938	+	9.20710i	−0.279784	+	0.391526i
$554$	7.67564	−	6.12112i	0.326107	−	0.260061i
$555$	−29.0664	+	23.6913i	−1.23380	+	1.00564i
$556$	−10.3699	−	2.36685i	−0.439780	−	0.100377i
$557$			33.7943i			1.43191i	0.698145	+	0.715956i	$0.254009\pi$
$557$			33.7943i			1.43191i	−0.698145	+	0.715956i	$0.745991\pi$
$558$	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
$561$	−16.4561	+	8.14221i	−0.694778	+	0.343764i
$562$	−1.77926	−	7.79543i	−0.0750534	−	0.328830i
$563$	−20.9196	−	26.2323i	−0.881656	−	1.10556i	−0.993724	−	0.111861i	$-0.964319\pi$
$563$	−20.9196	−	26.2323i	−0.881656	−	1.10556i	0.112068	−	0.993701i	$-0.464253\pi$
$564$	−4.65900	−	3.63482i	−0.196179	−	0.153053i
$565$	14.7422	−	3.36482i	0.620210	−	0.141559i
$566$	−4.77807	−	20.9341i	−0.200837	−	0.879925i
$567$	−23.7035	+	2.26839i	−0.995452	+	0.0952635i
$568$	2.52507	−	11.0631i	0.105950	−	0.464196i
$569$		−	8.41221i		−	0.352658i	−0.984331	−	0.176329i	$-0.943578\pi$
$569$		−	8.41221i		−	0.352658i	0.984331	−	0.176329i	$-0.0564223\pi$
$570$	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
$573$	−7.77549	+	9.96641i	−0.324826	+	0.416353i
$574$	9.46067	+	1.64014i	0.394881	+	0.0684579i
$575$	2.67027	+	2.12947i	0.111358	+	0.0888050i
$576$	−0.729801	−	2.90988i	−0.0304084	−	0.121245i
$577$	−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
$579$	17.8007	+	13.8875i	0.739771	+	0.577147i
$580$	0.354665	−	0.736469i	0.0147267	−	0.0305802i
$581$	−25.8393	+	1.36408i	−1.07199	+	0.0565916i
$582$	13.4007	−	10.9226i	0.555477	−	0.452754i
$583$	16.6518	+	8.01907i	0.689646	+	0.332116i
$584$	2.16875	+	9.50193i	0.0897437	+	0.393193i
$585$	0.698017	+	32.7150i	0.0288595	+	1.35260i
$586$	−12.4307	−	9.91318i	−0.513509	−	0.409510i
$587$	27.3667			1.12954			0.564772	−	0.825247i	$-0.308964\pi$
$587$	27.3667			1.12954			0.564772	+	0.825247i	$0.308964\pi$
$588$	−11.4281	+	4.04960i	−0.471286	+	0.167003i
$589$	35.2365			1.45189
$590$	19.2355	+	15.3398i	0.791915	+	0.631531i
$591$	8.90630	−	41.0337i	0.366356	−	1.68790i
$592$	2.03185	+	8.90210i	0.0835083	+	0.365874i
$593$	−6.01851	−	2.89836i	−0.247151	−	0.119021i	0.306208	−	0.951965i	$-0.400940\pi$
$593$	−6.01851	−	2.89836i	−0.247151	−	0.119021i	−0.553358	+	0.832943i	$0.686654\pi$
$594$	−7.95250	+	17.9620i	−0.326295	+	0.736991i
$595$	−4.81266	−	16.9185i	−0.197300	−	0.693590i
$596$	−1.04087	+	2.16139i	−0.0426357	+	0.0885339i
$597$	−7.26242	+	9.30876i	−0.297231	+	0.380982i
$598$	10.9659	+	22.7709i	0.448428	+	0.931170i
$599$	12.2325	+	9.75512i	0.499808	+	0.398583i	0.840685	−	0.541524i	$-0.182153\pi$
$599$	12.2325	+	9.75512i	0.499808	+	0.398583i	−0.340877	+	0.940108i	$0.610724\pi$
$600$	1.07671	−	0.0114852i	0.0439567	−	0.000468882i
$601$	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
$603$	19.1103	+	8.70584i	0.778232	+	0.354529i
$604$	−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
$609$	−1.37712	+	0.774299i	−0.0558036	+	0.0313762i
$610$	−4.11304	−	18.0204i	−0.166532	−	0.729625i
$611$	15.3014	−	3.49243i	0.619027	−	0.141289i
$612$	−7.65504	−	3.48731i	−0.309437	−	0.140966i
$613$	−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
$615$	6.60937	+	13.3581i	0.266515	+	0.538651i
$616$	−1.70852	+	9.85511i	−0.0688381	+	0.397074i
$617$	33.1966	+	7.57691i	1.33645	+	0.305035i	0.830254	−	0.557386i	$-0.188195\pi$
$617$	33.1966	+	7.57691i	1.33645	+	0.305035i	0.506192	+	0.862421i	$0.331053\pi$
$618$	−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
$621$	−26.1030	−	11.5568i	−1.04748	−	0.463759i
$622$	16.1503	−	12.8794i	0.647568	−	0.516418i
$623$	7.02557	−	0.370887i	0.281473	−	0.0148593i
$624$	7.21544	+	3.38044i	0.288849	+	0.135326i
$625$	6.16870	−	27.0269i	0.246748	−	1.08107i
$626$	7.33609	−	9.19917i	0.293209	−	0.367673i
$627$	−40.6021	+	33.0937i	−1.62149	+	1.32164i
$628$	−4.88627	+	3.89667i	−0.194983	+	0.155494i
$629$	23.0678	+	11.1088i	0.919772	+	0.442939i
$630$	−15.5415	−	10.6125i	−0.619190	−	0.422814i
$631$	−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
$633$	−3.52792	−	7.13023i	−0.140222	−	0.283401i
$634$	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
$639$	−33.3432	−	6.86552i	−1.31904	−	0.271596i
$640$	1.02874	−	2.13620i	0.0406646	−	0.0844409i
$641$	−26.1068	+	5.95870i	−1.03116	+	0.235355i	−0.704437	−	0.709767i	$-0.748800\pi$
$641$	−26.1068	+	5.95870i	−1.03116	+	0.235355i	−0.326719	+	0.945121i	$0.605943\pi$
$642$	23.2564	+	5.04776i	0.917858	+	0.199219i
$643$	−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
$645$	−31.0917	−	6.74840i	−1.22424	−	0.265718i
$646$	−13.9853	−	17.5370i	−0.550245	−	0.689985i
$647$	−26.9374	+	12.9724i	−1.05902	+	0.509997i	−0.880552	−	0.473949i	$-0.842828\pi$
$647$	−26.9374	+	12.9724i	−1.05902	+	0.509997i	−0.178467	+	0.983946i	$0.557114\pi$
$648$	−8.68095	+	2.37512i	−0.341020	+	0.0933035i
$649$	−38.2449	−	8.72915i	−1.50124	−	0.342649i
$650$	−1.78314	+	2.23599i	−0.0699406	+	0.0877027i
$651$	−13.5600	−	14.9523i	−0.531460	−	0.586027i
$652$	7.15750	+	8.97522i	0.280309	+	0.351497i
$653$	19.2941	+	40.0645i	0.755035	+	1.56785i	0.821600	+	0.570065i	$0.193082\pi$
$653$	19.2941	+	40.0645i	0.755035	+	1.56785i	−0.0665645	+	0.997782i	$0.521204\pi$
$654$	2.83427	−	0.0302329i	0.110829	−	0.00118220i
$655$	−32.2462			−1.25996
$656$	3.62914			0.141694
$657$	28.3605	−	7.11285i	1.10645	−	0.277499i
$658$	−3.48223	+	8.32766i	−0.135752	+	0.324646i
$659$	38.4079	−	8.76635i	1.49616	−	0.341488i	0.605384	−	0.795934i	$-0.293020\pi$
$659$	38.4079	−	8.76635i	1.49616	−	0.341488i	0.890775	+	0.454445i	$0.150163\pi$
$660$	−13.9150	+	6.88493i	−0.541642	+	0.267996i
$661$	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
$663$	20.0252	−	9.90813i	0.777714	−	0.384800i
$664$	−9.53472	+	2.17624i	−0.370019	+	0.0844544i
$665$	−24.1264	−	44.0018i	−0.935583	−	1.70632i
$666$	26.5702	−	6.66383i	1.02957	−	0.258218i
$667$	−1.89404			−0.0733376
$668$	21.3810			0.827257
$669$	−9.89801	+	0.105581i	−0.382679	+	0.00408201i
$670$	7.20115	+	14.9533i	0.278205	+	0.577698i
$671$	18.3752	+	23.0417i	0.709365	+	0.889515i
$672$	−3.99447	+	2.24593i	−0.154090	+	0.0866387i
$673$	−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
$675$	−0.103351	−	3.22867i	−0.00397800	−	0.124272i
$676$	−7.35491	+	3.54194i	−0.282881	+	0.136228i
$677$	−4.58183	−	5.74544i	−0.176094	−	0.220815i	0.685949	−	0.727649i	$-0.259387\pi$
$677$	−4.58183	−	5.74544i	−0.176094	−	0.220815i	−0.862044	+	0.506834i	$0.830816\pi$
$678$	−10.7950	−	2.34303i	−0.414579	−	0.0899835i
$679$	−21.4860	−	15.3538i	−0.824557	−	0.589227i
$680$	−2.88458	−	5.98989i	−0.110618	−	0.229702i
$681$	23.9624	+	5.20100i	0.918242	+	0.199303i
$682$	−16.2346	+	3.70543i	−0.621654	+	0.141888i
$683$	20.2037	−	41.9533i	0.773071	−	1.60530i	−0.0227301	−	0.999742i	$-0.507236\pi$
$683$	20.2037	−	41.9533i	0.773071	−	1.60530i	0.795801	−	0.605558i	$-0.207050\pi$
$684$	−23.5056	−	4.83991i	−0.898760	−	0.185059i
$685$		−	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
$690$	−10.0054	−	20.2218i	−0.380899	−	0.769830i
$691$	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
$693$	29.6679	+	4.49371i	1.12699	+	0.170702i
$694$	21.7381	+	10.4685i	0.825167	+	0.397380i
$695$	−19.7172	+	15.7240i	−0.747918	+	0.596444i
$696$	−0.462861	+	0.377266i	−0.0175447	+	0.0143002i
$697$	6.34466	−	7.95595i	0.240321	−	0.301353i
$698$	1.89181	−	8.28855i	0.0716060	−	0.313726i
$699$	−23.1624	−	10.8516i	−0.876084	−	0.410446i
$700$	−0.450030	−	1.58204i	−0.0170095	−	0.0597954i
$701$	6.44118	−	5.13667i	0.243280	−	0.194009i	−0.494257	−	0.869316i	$-0.664560\pi$
$701$	6.44118	−	5.13667i	0.243280	−	0.194009i	0.737537	+	0.675306i	$0.235989\pi$
$702$	9.67727	−	21.8577i	0.365245	−	0.824967i
$703$	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
$708$	−7.97044	−	16.1090i	−0.299548	−	0.605412i
$709$	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
$711$	11.6769	+	5.31950i	0.437918	+	0.199497i
$712$	2.59244	−	0.591708i	0.0971559	−	0.0221752i
$713$	−5.38485	−	23.5926i	−0.201664	−	0.883549i
$714$	−2.05972	+	12.6833i	−0.0770833	+	0.474661i
$715$	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	−0.350852	−	0.936431i	$-0.614108\pi$
$719$	4.35804	−	2.09872i	0.162527	−	0.0782690i	0.513379	+	0.858162i	$0.328394\pi$
$720$	−6.47299	−	2.94882i	−0.241234	−	0.109896i
$721$	0.323812	+	0.590569i	0.0120594	+	0.0219939i
$722$	−35.1771	−	28.0528i	−1.30916	−	1.04402i
$723$	−17.0767	+	0.182156i	−0.635090	+	0.00677445i
$724$	−1.28680	−	1.02619i	−0.0478237	−	0.0381381i
$725$	−0.0929929	−	0.193102i	−0.00345367	−	0.00717162i
$726$	3.50706	−	4.49525i	0.130159	−	0.166834i
$727$	−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
$729$	7.67927	+	25.8849i	0.284417	+	0.958701i
$730$	20.8201	+	10.0264i	0.770585	+	0.371094i
$731$	4.83386	+	21.1785i	0.178787	+	0.783317i
$732$	−2.86404	+	13.1954i	−0.105858	+	0.487717i
$733$	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
$735$	−9.38724	+	27.1711i	−0.346253	+	1.00222i
$736$	−5.49386			−0.202506
$737$	−20.6896	−	16.4994i	−0.762110	−	0.607763i
$738$	−0.232244	−	10.8849i	−0.00854901	−	0.400680i
$739$	−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
$741$	49.4081	−	40.2712i	1.81505	−	1.47940i
$742$	11.3417	−	6.21872i	0.416368	−	0.228296i
$743$	−15.5203	+	32.2283i	−0.569386	+	1.18234i	0.395205	+	0.918593i	$0.370674\pi$
$743$	−15.5203	+	32.2283i	−0.569386	+	1.18234i	−0.964591	+	0.263750i	$0.915041\pi$
$744$	−6.01524	−	4.69291i	−0.220530	−	0.172051i
$745$	2.46791	+	5.12467i	0.0904172	+	0.187753i
$746$	−7.56178	−	6.03032i	−0.276857	−	0.220786i
$747$	7.13739	+	28.4584i	0.261143	+	1.04124i
$748$	8.28765	+	6.60918i	0.303027	+	0.241656i
$749$	−1.91639	−	36.3014i	−0.0700233	−	1.32642i
$750$	−11.0601	+	14.1765i	−0.403857	+	0.517652i
$751$	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
$756$	6.99189	+	11.8370i	0.254292	+	0.430506i
$757$	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
$759$	28.3627	+	22.1277i	1.02950	+	0.803186i
$760$	−11.8258	−	14.8290i	−0.428966	−	0.537906i
$761$	−7.74729	−	33.9431i	−0.280839	−	1.23044i	−0.896720	−	0.442598i	$-0.854057\pi$
$761$	−7.74729	−	33.9431i	−0.280839	−	1.23044i	0.615881	−	0.787839i	$-0.288800\pi$
$762$	−29.6737	+	14.6820i	−1.07496	+	0.531874i
$763$	−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
$768$	−1.34258	+	1.09430i	−0.0484460	+	0.0394871i
$769$	−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
$771$	−9.67130	+	20.6431i	−0.348303	+	0.743442i
$772$	2.90054	−	12.7081i	0.104393	−	0.457375i
$773$	13.5986	−	17.0521i	0.489106	−	0.613320i	−0.474627	−	0.880187i	$-0.657417\pi$
$773$	13.5986	−	17.0521i	0.489106	−	0.613320i	0.963733	+	0.266867i	$0.0859885\pi$
$774$	18.4761	+	14.1001i	0.664110	+	0.506817i
$775$	2.14093	−	1.70734i	0.0769046	−	0.0613294i
$776$	−8.99287	−	4.33074i	−0.322825	−	0.155464i
$777$	−20.5077	−	36.4736i	−0.735709	−	1.30848i
$778$	3.95621	−	1.90521i	0.141837	−	0.0683052i
$779$	12.5963	−	26.1565i	0.451310	−	0.937155i
$780$	16.9330	−	8.37817i	0.606299	−	0.299986i
$781$	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
$786$	21.3313	+	9.99372i	0.760861	+	0.356464i
$787$	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
$789$	6.83137	−	31.4740i	0.243203	−	1.12050i
$790$	4.40010	+	9.13690i	0.156548	+	0.325076i
$791$	0.889533	+	16.8501i	0.0316281	+	0.599120i
$792$	11.3387	−	0.241927i	0.402905	−	0.00859649i
$793$	−22.3604	−	28.0391i	−0.794043	−	0.995698i
$794$	3.11311	−	1.49920i	0.110480	−	0.0532045i
$795$	18.1808	+	8.51771i	0.644805	+	0.302092i
$796$	6.64564	+	1.51682i	0.235548	+	0.0537624i
$797$	12.0499	−	15.1101i	0.426829	−	0.535227i	−0.521190	−	0.853441i	$-0.674512\pi$
$797$	12.0499	−	15.1101i	0.426829	−	0.535227i	0.948019	+	0.318214i	$0.103083\pi$
$798$	2.32292	+	36.5850i	0.0822304	+	1.29510i
$799$	5.96445	+	7.47919i	0.211007	+	0.264595i
$800$	−0.269735	−	0.560111i	−0.00953658	−	0.0198029i
$801$	−1.94062	−	7.73769i	−0.0685685	−	0.273398i
$802$	1.58968			0.0561335
$803$	−36.8453			−1.30024
$804$	−0.129322	−	12.1236i	−0.00456082	−	0.427566i
$805$	−25.7744	+	22.8782i	−0.908428	+	0.806351i
$806$	19.7556	−	4.50909i	0.695861	−	0.158826i
$807$	7.88175	+	15.9297i	0.277451	+	0.560752i
$808$	−7.59272	+	6.05499i	−0.267111	+	0.213014i
$809$	13.6824	−	10.9113i	0.481048	−	0.383623i	−0.352728	−	0.935726i	$-0.614746\pi$
$809$	13.6824	−	10.9113i	0.481048	−	0.383623i	0.833776	+	0.552103i	$0.186175\pi$
$810$	−8.43021	+	19.6033i	−0.296207	+	0.688788i
$811$	−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
$813$	28.8606	−	0.307853i	1.01218	−	0.0107969i
$814$	−34.5193			−1.20990
$815$	27.2185			0.953424
$816$	0.0518025	+	4.85637i	0.00181345	+	0.170007i
$817$	26.8898	+	55.8373i	0.940756	+	1.95350i
$818$	−24.4468	−	30.6553i	−0.854763	−	1.07184i
$819$	−36.1025	−	5.46833i	−1.26152	−	0.191079i
$820$	5.36495	−	6.72743i	0.187352	−	0.234932i
$821$	−20.9249	−	4.77598i	−0.730285	−	0.166683i	−0.158818	−	0.987308i	$-0.550768\pi$
$821$	−20.9249	−	4.77598i	−0.730285	−	0.166683i	−0.571467	+	0.820625i	$0.693626\pi$
$822$	−10.6943	+	22.8266i	−0.373006	+	0.796170i
$823$	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
$825$	−0.863431	+	3.97806i	−0.0300608	+	0.138498i
$826$	−20.5323	+	18.2251i	−0.714409	+	0.634133i
$827$	−13.6909	−	28.4294i	−0.476078	−	0.988587i	−0.991311	−	0.131537i	$-0.958009\pi$
$827$	−13.6909	−	28.4294i	−0.476078	−	0.988587i	0.515233	−	0.857050i	$-0.327705\pi$
$828$	0.351575	+	16.4778i	0.0122181	+	0.572644i
$829$	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
$831$	−7.21411	+	15.3983i	−0.250255	+	0.534161i
$832$		−	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
$837$	−13.6906	+	18.3419i	−0.473216	+	0.633990i
$838$	−13.1950	+	27.3997i	−0.455814	+	0.946508i
$839$	−11.0489	+	5.32089i	−0.381452	+	0.183697i	−0.614776	−	0.788701i	$-0.710754\pi$
$839$	−11.0489	+	5.32089i	−0.381452	+	0.183697i	0.233325	+	0.972399i	$0.425039\pi$
$840$	−1.74167	+	10.7248i	−0.0600934	+	0.370041i
$841$	−26.0210	−	12.5311i	−0.897276	−	0.432105i
$842$	−17.0283	+	13.5796i	−0.586835	+	0.467985i
$843$	8.74991	+	10.7351i	0.301363	+	0.369737i
$844$	−2.86368	+	3.59094i	−0.0985718	+	0.123605i
$845$	−4.30697	+	18.8701i	−0.148164	+	0.649150i
$846$	10.0247	+	2.06412i	0.344655	+	0.0709661i
$847$	−8.03496	−	3.35984i	−0.276085	−	0.115446i
$848$	3.82227	−	3.04816i	0.131257	−	0.104674i
$849$	23.4973	+	28.8284i	0.806424	+	0.989388i
$850$	−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
$855$	−43.7202	+	36.4182i	−1.49520	+	1.24548i
$856$	−3.05738	−	13.3953i	−0.104499	−	0.457841i
$857$	30.9361	+	38.7927i	1.05676	+	1.32513i	0.943429	+	0.331575i	$0.107580\pi$
$857$	30.9361	+	38.7927i	1.05676	+	1.32513i	0.113329	+	0.993557i	$0.463849\pi$
$858$	−18.5290	+	23.7499i	−0.632569	+	0.810810i
$859$	−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
$861$	−15.9467	+	4.72067i	−0.543463	+	0.160880i
$862$	4.57915	−	20.0625i	0.155966	−	0.683333i
$863$		−	50.7998i		−	1.72925i	−0.502421	−	0.864623i	$-0.667557\pi$
$863$		−	50.7998i		−	1.72925i	0.502421	−	0.864623i	$-0.332443\pi$
$864$	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
$867$	−12.4785	−	9.73536i	−0.423793	−	0.330630i
$868$	−4.49592	+	10.7518i	−0.152601	+	0.364941i
$869$	−12.6419	−	10.0816i	−0.428847	−	0.341994i
$870$	0.0151015	+	1.41573i	0.000511989	+	0.0479978i
$871$	25.1768	+	20.0778i	0.853084	+	0.680312i
$872$	−0.710032	−	1.47440i	−0.0240447	−	0.0499294i
$873$	−12.4138	+	27.2496i	−0.420142	+	0.922259i
$874$	−19.0686	+	39.5963i	−0.645004	+	1.33936i
$875$	25.3395	+	10.5958i	0.856632	+	0.358203i
$876$	−10.6654	−	13.0851i	−0.360349	−	0.442106i
$877$	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
$879$	26.9121	+	5.84123i	0.907724	+	0.197020i
$880$	7.00791	+	5.58862i	0.236237	+	0.188392i
$881$	0.787268			0.0265237			0.0132619	−	0.999912i	$-0.495778\pi$
$881$	0.787268			0.0265237			0.0132619	+	0.999912i	$0.495778\pi$
$882$	14.6306	−	15.0647i	0.492638	−	0.507255i
$883$	−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
$885$	−41.6443	−	9.03882i	−1.39986	−	0.303837i
$886$	1.56084	+	6.83847i	0.0524373	+	0.229743i
$887$	−43.4895	−	20.9434i	−1.46023	−	0.703211i	−0.475895	−	0.879502i	$-0.657876\pi$
$887$	−43.4895	−	20.9434i	−1.46023	−	0.703211i	−0.984338	+	0.176291i	$0.943590\pi$
$888$	−9.99207	−	12.2591i	−0.335312	−	0.411389i
$889$	33.5718	+	37.8217i	1.12596	+	1.26850i
$890$	2.73554	−	5.68041i	0.0916955	−	0.190408i
$891$	−1.45123	−	33.9930i	−0.0486180	−	1.13881i
$892$	2.47962	+	5.14899i	0.0830239	+	0.172401i
$893$	21.3376	+	17.0162i	0.714036	+	0.569424i
$894$	−0.0443198	−	4.15488i	−0.00148228	−	0.138960i
$895$	−3.84751	−	3.06828i	−0.128608	−	0.102561i
$896$	2.15262	+	1.53826i	0.0719139	+	0.0513896i
$897$	−34.5142	−	26.9269i	−1.15239	−	0.899063i
$898$	−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
$903$	13.3461	−	32.8983i	0.444130	−	1.09479i
$904$	1.41915	+	6.21770i	0.0472002	+	0.206798i
$905$	−3.80456	+	0.868366i	−0.126468	+	0.0288655i
$906$	17.0325	−	21.8318i	0.565868	−	0.725313i
$907$	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
$909$	18.6467	+	22.3855i	0.618473	+	0.742480i
$910$	−19.1574	−	21.5826i	−0.635062	−	0.715455i
$911$	−33.3967	−	7.62258i	−1.10648	−	0.252547i	−0.370019	−	0.929024i	$-0.620649\pi$
$911$	−33.3967	−	7.62258i	−1.10648	−	0.252547i	−0.736464	+	0.676477i	$0.763506\pi$
$912$	3.22709	+	13.4746i	0.106860	+	0.446190i
$913$		−	36.9724i		−	1.22361i
$914$	−3.75648	−	0.857392i	−0.124253	−	0.0283600i
$915$	20.2268	+	24.8159i	0.668678	+	0.820390i
$916$	−4.88057	+	3.89213i	−0.161259	+	0.128600i
$917$	6.14642	−	35.4540i	0.202973	−	1.17079i
$918$	14.5625	−	0.466152i	0.480633	−	0.0153853i
$919$	−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
$921$	1.09397	+	1.34217i	0.0360475	+	0.0442261i
$922$	12.1951	−	9.72523i	0.401623	−	0.320283i
$923$	−47.0332	−	22.6500i	−1.54812	−	0.745534i
$924$	−4.91748	−	16.6116i	−0.161773	−	0.546481i
$925$	5.11439	−	2.46296i	0.168160	−	0.0809817i
$926$	−13.8379	+	28.7347i	−0.454741	+	0.944280i
$927$	0.586789	−	0.488785i	0.0192727	−	0.0160538i
$928$	0.310614	+	0.149584i	0.0101964	+	0.00491034i
$929$	−15.9819	+	20.0407i	−0.524351	+	0.657515i	−0.971526	−	0.236931i	$-0.923858\pi$
$929$	−15.9819	+	20.0407i	−0.524351	+	0.657515i	0.447176	+	0.894446i	$0.352430\pi$
$930$	−17.5917	+	4.21310i	−0.576855	+	0.138153i
$931$	52.9777	−	18.1393i	1.73627	−	0.594491i
$932$			14.7677i			0.483733i
$933$	−15.1792	+	32.3995i	−0.496945	+	1.06071i
$934$	−6.54757	+	13.5962i	−0.214243	+	0.444880i
$935$	24.5033	−	5.59271i	0.801342	−	0.182901i
$936$	−13.7979	+	0.294397i	−0.451000	+	0.00962266i
$937$	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
$939$	−4.32271	+	19.9159i	−0.141066	+	0.649931i
$940$	5.04345	+	6.32428i	0.164499	+	0.206275i
$941$	−43.9891	+	21.1840i	−1.43400	+	0.690579i	−0.979737	−	0.200287i	$-0.935813\pi$
$941$	−43.9891	+	21.1840i	−1.43400	+	0.690579i	−0.454266	+	0.890866i	$0.650098\pi$
$942$	4.59246	−	9.80246i	0.149631	−	0.319381i
$943$	−19.4381	−	4.43661i	−0.632991	−	0.144476i
$944$	−6.46975	+	8.11282i	−0.210573	+	0.264050i
$945$	32.2786	+	4.53750i	1.05002	+	0.147605i
$946$	−18.2608	−	22.8983i	−0.593710	−	0.744488i
$947$	−1.56074	−	3.24091i	−0.0507172	−	0.105315i	0.874070	−	0.485800i	$-0.161472\pi$
$947$	−1.56074	−	3.24091i	−0.0507172	−	0.105315i	−0.924787	+	0.380484i	$0.875757\pi$
$948$	−0.0790189	−	7.40785i	−0.00256642	−	0.240596i
$949$	44.8365			1.45545
$950$	−4.97315			−0.161350
$951$	−1.96614	+	0.0209727i	−0.0637565	+	0.000680086i
$952$	7.13556	−	2.02980i	0.231265	−	0.0657861i
$953$	15.1378	−	3.45509i	0.490360	−	0.111921i	0.0298106	−	0.999556i	$-0.490510\pi$
$953$	15.1378	−	3.45509i	0.490360	−	0.111921i	0.460549	+	0.887634i	$0.347652\pi$
$954$	−9.38700	−	11.2691i	−0.303915	−	0.364852i
$955$	13.5287	−	10.7888i	0.437779	−	0.349117i
$956$	4.88654	−	3.89689i	0.158042	−	0.126034i
$957$	−1.00110	−	2.02332i	−0.0323610	−	0.0654045i
$958$	30.7781	−	7.02489i	0.994394	−	0.226964i
$959$	37.9393	+	6.57730i	1.22512	+	0.212392i
$960$	0.0438034	+	4.10647i	0.00141375	+	0.132536i
$961$	11.5978			0.374123
$962$	42.0061			1.35433
$963$	−39.9810	+	10.0273i	−1.28837	+	0.323124i
$964$	4.27801	+	8.88337i	0.137785	+	0.286114i
$965$	−19.2695	−	24.1632i	−0.620308	−	0.777841i
$966$	24.1405	−	7.14624i	0.776708	−	0.229927i
$967$	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
$969$	35.1815	+	16.4826i	1.13019	+	0.529496i
$970$	−21.3222	+	10.2682i	−0.684613	+	0.329692i
$971$	−1.65568	−	2.07616i	−0.0531333	−	0.0666271i	0.754555	−	0.656237i	$-0.227853\pi$
$971$	−1.65568	−	2.07616i	−0.0531333	−	0.0666271i	−0.807688	+	0.589610i	$0.799281\pi$
$972$	11.6521	−	10.3551i	0.373742	−	0.332140i
$973$	−13.5299	−	24.6758i	−0.433747	−	0.791069i
$974$	−3.82673	−	7.94629i	−0.122616	−	0.254615i
$975$	1.05070	−	4.84084i	0.0336492	−	0.155031i
$976$	7.60031	−	1.73472i	0.243280	−	0.0555271i
$977$	18.3077	−	38.0163i	0.585715	−	1.21625i	−0.371920	−	0.928265i	$-0.621301\pi$
$977$	18.3077	−	38.0163i	0.585715	−	1.21625i	0.957635	−	0.287984i	$-0.0929851\pi$
$978$	−18.0054	−	8.43555i	−0.575749	−	0.269739i
$979$			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	0.730845	−	0.682544i	$-0.239126\pi$
$983$	20.4698	+	9.85773i	0.652885	+	0.314413i	−0.0779600	+	0.996956i	$0.524841\pi$
$984$	−5.63394	+	2.78758i	−0.179603	+	0.0888648i
$985$	−24.9392	+	51.7868i	−0.794630	+	1.65007i
$986$	0.870959	−	0.419432i	0.0277370	−	0.0133574i
$987$	−0.990676	−	15.6028i	−0.0315336	−	0.496641i
$988$	−33.1565	−	15.9673i	−1.05485	−	0.507989i
$989$	33.2765	−	26.5372i	1.05813	−	0.843833i
$990$	16.3136	−	21.3766i	0.518480	−	0.679393i
$991$	−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
$993$	−17.2969	+	36.9197i	−0.548901	+	1.17161i
$994$	26.3253	−	14.4343i	0.834988	−	0.457828i
$995$	12.6360	−	10.0769i	0.400589	−	0.319459i
$996$	13.1303	−	10.7022i	0.416049	−	0.339111i
$997$	−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.251.11	yes	120
3.2	odd	2	inner	294.2.j.a.251.8	yes	120
49.41	odd	14	inner	294.2.j.a.41.8	✓	120
147.41	even	14	inner	294.2.j.a.41.11	yes	120

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

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)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.69264 - 0.367384i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.13620 + 1.02874i) q^{5} +(-1.09430 - 1.34258i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.73006 + 1.24370i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.69264 - 0.367384i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.13620 + 1.02874i) q^{5} +(-1.09430 - 1.34258i) q^{6} +(-1.53826 + 2.15262i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.73006 + 1.24370i) q^{9} +(1.02874 + 2.13620i) q^{10} +(-2.95567 - 2.35707i) q^{11} +(-0.0184746 - 1.73195i) q^{12} +(3.59671 + 2.86828i) q^{13} +(-2.54479 + 0.723897i) q^{14} +(-3.23788 - 2.52610i) 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} +(3.39455 - 3.07848i) q^{21} +(-0.841228 - 3.68566i) q^{22} +(5.35612 - 1.22250i) q^{23} +(1.06541 - 1.36561i) q^{24} +(0.387609 + 0.486046i) q^{25} +(1.02368 + 4.48502i) q^{26} +(-4.16409 - 3.10811i) 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} +(4.13693 + 5.07553i) q^{33} +(-2.19224 + 1.74826i) q^{34} +(-5.50052 + 3.01596i) q^{35} +(-0.605021 + 2.93836i) q^{36} +(2.03185 - 8.90210i) q^{37} +(-4.98766 + 6.25432i) q^{38} +(-5.03417 - 6.17634i) q^{39} +(-1.85373 + 1.47830i) q^{40} +(-3.26974 - 1.57462i) q^{41} +(4.57337 - 0.290380i) q^{42} +(6.98003 - 3.36141i) q^{43} +(1.64027 - 3.40606i) q^{44} +(4.55252 + 5.46532i) 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} +(2.06043 - 4.39791i) q^{51} +(-1.99602 + 4.14478i) q^{52} +(-4.76629 + 1.08788i) q^{53} +(-1.31774 - 5.02629i) q^{54} +(-3.88910 - 8.07580i) q^{55} +(-1.27202 - 2.31991i) q^{56} +(2.93892 - 13.5404i) q^{57} +(-0.214952 - 0.269541i) q^{58} +(9.34907 - 4.50227i) q^{59} +(1.74227 - 3.71881i) q^{60} +(-7.60031 - 1.73472i) q^{61} +(2.74634 - 3.44381i) q^{62} +(-6.87674 + 3.96364i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(4.73258 + 9.82731i) q^{65} +(0.0698422 + 6.54755i) q^{66} +6.99996 q^{67} -2.80399 q^{68} +(-9.51510 + 0.101497i) q^{69} +(-6.18090 - 1.07154i) q^{70} +(-11.0631 + 2.52507i) q^{71} +(-2.30506 + 1.92008i) q^{72} +(7.61996 - 6.07671i) q^{73} +(7.13893 - 5.69310i) q^{74} +(-0.477517 - 0.965103i) q^{75} +(-7.79901 + 1.78007i) q^{76} +(9.62044 - 2.73665i) q^{77} +(-0.0849899 - 7.96761i) q^{78} +4.27717 q^{79} -2.37101 q^{80} +(5.90643 + 6.79074i) q^{81} +(-1.57462 - 3.26974i) q^{82} +(6.09768 + 7.64625i) q^{83} +(3.75665 + 2.62442i) q^{84} +(-4.14513 + 5.19783i) q^{85} +(7.55301 + 1.72393i) q^{86} +(0.540733 + 0.253334i) q^{87} +(3.40606 - 1.64027i) q^{88} +(-1.65793 - 2.07898i) q^{89} +(0.151731 + 7.11140i) q^{90} +(-11.7070 + 3.33019i) q^{91} +(2.38370 + 4.94980i) q^{92} +(-1.61825 + 7.45573i) q^{93} +(3.32612 - 0.759165i) q^{94} +(-8.22950 + 17.0887i) q^{95} +(1.56845 + 0.734821i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more