LMFDB - Embedded newform 740.2.u.a.31.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(31,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.u (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38578 - 0.282160i) q^{2} +3.03129 q^{3} +(1.84077 + 0.782022i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-4.20069 - 0.855307i) q^{6} -4.17536i q^{7} +(-2.33025 - 1.60310i) q^{8} +6.18869 q^{9} +(1.17941 - 0.780377i) q^{10} +2.56565 q^{11} +(5.57991 + 2.37053i) q^{12} +(1.37338 - 1.37338i) q^{13} +(-1.17812 + 5.78613i) q^{14} +(-2.14344 + 2.14344i) q^{15} +(2.77688 + 2.87905i) q^{16} +(-2.87103 + 2.87103i) q^{17} +(-8.57617 - 1.74620i) q^{18} +(3.33871 + 3.33871i) q^{19} +(-1.85460 + 0.748649i) q^{20} -12.6567i q^{21} +(-3.55543 - 0.723924i) q^{22} +(-5.11336 - 5.11336i) q^{23} +(-7.06365 - 4.85946i) q^{24} -1.00000i q^{25} +(-2.29072 + 1.51569i) q^{26} +9.66584 q^{27} +(3.26523 - 7.68589i) q^{28} +(-0.274881 - 0.274881i) q^{29} +(3.57513 - 2.36555i) q^{30} +(4.00516 - 4.00516i) q^{31} +(-3.03580 - 4.77325i) q^{32} +7.77723 q^{33} +(4.78871 - 3.16853i) q^{34} +(2.95243 + 2.95243i) q^{35} +(11.3920 + 4.83970i) q^{36} +(-2.30803 + 5.62788i) q^{37} +(-3.68467 - 5.56877i) q^{38} +(4.16311 - 4.16311i) q^{39} +(2.78130 - 0.514171i) q^{40} -8.34615i q^{41} +(-3.57121 + 17.5394i) q^{42} +(-3.95530 - 3.95530i) q^{43} +(4.72278 + 2.00640i) q^{44} +(-4.37607 + 4.37607i) q^{45} +(5.64321 + 8.52877i) q^{46} +7.51837i q^{47} +(8.41752 + 8.72722i) q^{48} -10.4336 q^{49} +(-0.282160 + 1.38578i) q^{50} +(-8.70292 + 8.70292i) q^{51} +(3.60210 - 1.45407i) q^{52} +0.614883 q^{53} +(-13.3947 - 2.72731i) q^{54} +(-1.81419 + 1.81419i) q^{55} +(-6.69353 + 9.72963i) q^{56} +(10.1206 + 10.1206i) q^{57} +(0.303364 + 0.458485i) q^{58} +(6.70004 + 6.70004i) q^{59} +(-5.62181 + 2.26937i) q^{60} +(2.54053 + 2.54053i) q^{61} +(-6.68036 + 4.42017i) q^{62} -25.8400i q^{63} +(2.86013 + 7.47126i) q^{64} +1.94226i q^{65} +(-10.7775 - 2.19442i) q^{66} +14.4644 q^{67} +(-7.53013 + 3.03970i) q^{68} +(-15.5001 - 15.5001i) q^{69} +(-3.25836 - 4.92447i) q^{70} +7.59870i q^{71} +(-14.4212 - 9.92111i) q^{72} -9.40041i q^{73} +(4.78638 - 7.14777i) q^{74} -3.03129i q^{75} +(3.53486 + 8.75675i) q^{76} -10.7125i q^{77} +(-6.94382 + 4.59450i) q^{78} +(1.43429 + 1.43429i) q^{79} +(-3.99935 - 0.0722433i) q^{80} +10.7338 q^{81} +(-2.35495 + 11.5659i) q^{82} +16.9684i q^{83} +(9.89783 - 23.2981i) q^{84} -4.06025i q^{85} +(4.36514 + 6.59719i) q^{86} +(-0.833243 - 0.833243i) q^{87} +(-5.97861 - 4.11300i) q^{88} +(3.33838 + 3.33838i) q^{89} +(7.29901 - 4.82952i) q^{90} +(-5.73436 - 5.73436i) q^{91} +(-5.41377 - 13.4113i) q^{92} +(12.1408 - 12.1408i) q^{93} +(2.12138 - 10.4188i) q^{94} -4.72165 q^{95} +(-9.20236 - 14.4691i) q^{96} +(-7.76820 + 7.76820i) q^{97} +(14.4587 + 2.94395i) q^{98} +15.8780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) $ 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−1.38578	−	0.282160i	−0.979894	−	0.199517i
$2$	−1.38578	−	0.282160i	−0.979894	−	0.199517i
$3$	3.03129			1.75011			0.875057	−	0.484020i	$-0.160824\pi$
$3$	3.03129			1.75011			0.875057	+	0.484020i	$0.160824\pi$
$4$	1.84077	+	0.782022i	0.920386	+	0.391011i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−4.20069	−	0.855307i	−1.71493	−	0.349177i
$7$		−	4.17536i		−	1.57814i	−0.614305	−	0.789069i	$-0.710563\pi$
$7$		−	4.17536i		−	1.57814i	0.614305	−	0.789069i	$-0.289437\pi$
$8$	−2.33025	−	1.60310i	−0.823868	−	0.566782i
$9$	6.18869			2.06290
$10$	1.17941	−	0.780377i	0.372963	−	0.246777i
$11$	2.56565			0.773574			0.386787	−	0.922169i	$-0.373585\pi$
$11$	2.56565			0.773574			0.386787	+	0.922169i	$0.373585\pi$
$12$	5.57991	+	2.37053i	1.61078	+	0.684314i
$13$	1.37338	−	1.37338i	0.380908	−	0.380908i	−0.490521	−	0.871429i	$-0.663194\pi$
$13$	1.37338	−	1.37338i	0.380908	−	0.380908i	0.871429	+	0.490521i	$0.163194\pi$
$14$	−1.17812	+	5.78613i	−0.314865	+	1.54641i
$15$	−2.14344	+	2.14344i	−0.553435	+	0.553435i
$16$	2.77688	+	2.87905i	0.694221	+	0.719762i
$17$	−2.87103	+	2.87103i	−0.696328	+	0.696328i	−0.963616	−	0.267289i	$-0.913872\pi$
$17$	−2.87103	+	2.87103i	−0.696328	+	0.696328i	0.267289	+	0.963616i	$0.413872\pi$
$18$	−8.57617	−	1.74620i	−2.02142	−	0.411583i
$19$	3.33871	+	3.33871i	0.765953	+	0.765953i	0.977391	−	0.211438i	$-0.0678147\pi$
$19$	3.33871	+	3.33871i	0.765953	+	0.765953i	−0.211438	+	0.977391i	$0.567815\pi$
$20$	−1.85460	+	0.748649i	−0.414700	+	0.167403i
$21$		−	12.6567i		−	2.76192i
$22$	−3.55543	−	0.723924i	−0.758020	−	0.154341i
$23$	−5.11336	−	5.11336i	−1.06621	−	1.06621i	−0.997647	−	0.0685622i	$-0.978159\pi$
$23$	−5.11336	−	5.11336i	−1.06621	−	1.06621i	−0.0685622	−	0.997647i	$-0.521841\pi$
$24$	−7.06365	−	4.85946i	−1.44186	−	0.991933i
$25$		−	1.00000i		−	0.200000i
$26$	−2.29072	+	1.51569i	−0.449247	+	0.297252i
$27$	9.66584			1.86019
$28$	3.26523	−	7.68589i	0.617070	−	1.45250i
$29$	−0.274881	−	0.274881i	−0.0510441	−	0.0510441i	0.681124	−	0.732168i	$-0.261491\pi$
$29$	−0.274881	−	0.274881i	−0.0510441	−	0.0510441i	−0.732168	+	0.681124i	$0.761491\pi$
$30$	3.57513	−	2.36555i	0.652727	−	0.431888i
$31$	4.00516	−	4.00516i	0.719347	−	0.719347i	−0.249124	−	0.968472i	$-0.580143\pi$
$31$	4.00516	−	4.00516i	0.719347	−	0.719347i	0.968472	+	0.249124i	$0.0801427\pi$
$32$	−3.03580	−	4.77325i	−0.536658	−	0.843800i
$33$	7.77723			1.35384
$34$	4.78871	−	3.16853i	0.821257	−	0.543398i
$35$	2.95243	+	2.95243i	0.499051	+	0.499051i
$36$	11.3920	+	4.83970i	1.89866	+	0.806616i
$37$	−2.30803	+	5.62788i	−0.379438	+	0.925217i
$37$	−2.30803	+	5.62788i	−0.379438	+	0.925217i
$38$	−3.68467	−	5.56877i	−0.597732	−	0.903374i
$39$	4.16311	−	4.16311i	0.666632	−	0.666632i
$40$	2.78130	−	0.514171i	0.439762	−	0.0812975i
$41$		−	8.34615i		−	1.30345i	−0.758455	−	0.651725i	$-0.774046\pi$
$41$		−	8.34615i		−	1.30345i	0.758455	−	0.651725i	$-0.225954\pi$
$42$	−3.57121	+	17.5394i	−0.551050	+	2.70639i
$43$	−3.95530	−	3.95530i	−0.603177	−	0.603177i	0.337977	−	0.941154i	$-0.390257\pi$
$43$	−3.95530	−	3.95530i	−0.603177	−	0.603177i	−0.941154	+	0.337977i	$0.890257\pi$
$44$	4.72278	+	2.00640i	0.711986	+	0.302476i
$45$	−4.37607	+	4.37607i	−0.652346	+	0.652346i
$46$	5.64321	+	8.52877i	0.832045	+	1.25750i
$47$			7.51837i			1.09667i	0.836260	+	0.548334i	$0.184738\pi$
$47$			7.51837i			1.09667i	−0.836260	+	0.548334i	$0.815262\pi$
$48$	8.41752	+	8.72722i	1.21496	+	1.25967i
$49$	−10.4336			−1.49052
$50$	−0.282160	+	1.38578i	−0.0399034	+	0.195979i
$51$	−8.70292	+	8.70292i	−1.21865	+	1.21865i
$52$	3.60210	−	1.45407i	0.499521	−	0.201643i
$53$	0.614883			0.0844607			0.0422304	−	0.999108i	$-0.486554\pi$
$53$	0.614883			0.0844607			0.0422304	+	0.999108i	$0.486554\pi$
$54$	−13.3947	−	2.72731i	−1.82279	−	0.371140i
$55$	−1.81419	+	1.81419i	−0.244625	+	0.244625i
$56$	−6.69353	+	9.72963i	−0.894461	+	1.30018i
$57$	10.1206	+	10.1206i	1.34050	+	1.34050i
$58$	0.303364	+	0.458485i	0.0398337	+	0.0602020i
$59$	6.70004	+	6.70004i	0.872271	+	0.872271i	0.992720	−	0.120448i	$-0.0384332\pi$
$59$	6.70004	+	6.70004i	0.872271	+	0.872271i	−0.120448	+	0.992720i	$0.538433\pi$
$60$	−5.62181	+	2.26937i	−0.725772	+	0.292974i
$61$	2.54053	+	2.54053i	0.325281	+	0.325281i	0.850789	−	0.525508i	$-0.176125\pi$
$61$	2.54053	+	2.54053i	0.325281	+	0.325281i	−0.525508	+	0.850789i	$0.676125\pi$
$62$	−6.68036	+	4.42017i	−0.848407	+	0.561362i
$63$		−	25.8400i		−	3.25554i
$64$	2.86013	+	7.47126i	0.357516	+	0.933907i
$65$			1.94226i			0.240907i
$66$	−10.7775	−	2.19442i	−1.32662	−	0.270114i
$67$	14.4644			1.76710			0.883552	−	0.468332i	$-0.155145\pi$
$67$	14.4644			1.76710			0.883552	+	0.468332i	$0.155145\pi$
$68$	−7.53013	+	3.03970i	−0.913162	+	0.368618i
$69$	−15.5001	−	15.5001i	−1.86599	−	1.86599i
$70$	−3.25836	−	4.92447i	−0.389448	−	0.588586i
$71$			7.59870i			0.901800i	0.892574	+	0.450900i	$0.148897\pi$
$71$			7.59870i			0.901800i	−0.892574	+	0.450900i	$0.851103\pi$
$72$	−14.4212	−	9.92111i	−1.69955	−	1.16921i
$73$		−	9.40041i		−	1.10023i	−0.835087	−	0.550117i	$-0.814583\pi$
$73$		−	9.40041i		−	1.10023i	0.835087	−	0.550117i	$-0.185417\pi$
$74$	4.78638	−	7.14777i	0.556405	−	0.830911i
$75$		−	3.03129i		−	0.350023i
$76$	3.53486	+	8.75675i	0.405476	+	1.00447i
$77$		−	10.7125i		−	1.22081i
$78$	−6.94382	+	4.59450i	−0.786233	+	0.520224i
$79$	1.43429	+	1.43429i	0.161371	+	0.161371i	0.783174	−	0.621803i	$-0.213600\pi$
$79$	1.43429	+	1.43429i	0.161371	+	0.161371i	−0.621803	+	0.783174i	$0.713600\pi$
$80$	−3.99935	−	0.0722433i	−0.447141	−	0.00807704i
$81$	10.7338			1.19265
$82$	−2.35495	+	11.5659i	−0.260060	+	1.27724i
$83$			16.9684i			1.86252i	0.364355	+	0.931260i	$0.381289\pi$
$83$			16.9684i			1.86252i	−0.364355	+	0.931260i	$0.618711\pi$
$84$	9.89783	−	23.2981i	1.07994	−	2.54203i
$85$		−	4.06025i		−	0.440396i
$86$	4.36514	+	6.59719i	0.470706	+	0.711394i
$87$	−0.833243	−	0.833243i	−0.0893330	−	0.0893330i
$88$	−5.97861	−	4.11300i	−0.637322	−	0.438448i
$89$	3.33838	+	3.33838i	0.353867	+	0.353867i	0.861546	−	0.507679i	$-0.169496\pi$
$89$	3.33838	+	3.33838i	0.353867	+	0.353867i	−0.507679	+	0.861546i	$0.669496\pi$
$90$	7.29901	−	4.82952i	0.769384	−	0.509076i
$91$	−5.73436	−	5.73436i	−0.601125	−	0.601125i
$92$	−5.41377	−	13.4113i	−0.564424	−	1.39822i
$93$	12.1408	−	12.1408i	1.25894	−	1.25894i
$94$	2.12138	−	10.4188i	0.218804	−	1.07462i
$95$	−4.72165			−0.484431
$96$	−9.20236	−	14.4691i	−0.939212	−	1.47675i
$97$	−7.76820	+	7.76820i	−0.788742	+	0.788742i	−0.981288	−	0.192546i	$-0.938325\pi$
$97$	−7.76820	+	7.76820i	−0.788742	+	0.788742i	0.192546	+	0.981288i	$0.438325\pi$
$98$	14.4587	+	2.94395i	1.46055	+	0.297384i
$99$	15.8780			1.59580
$100$	0.782022	−	1.84077i	0.0782022	−	0.184077i
$101$		−	0.530975i		−	0.0528340i	−0.999651	−	0.0264170i	$-0.991590\pi$
$101$		−	0.530975i		−	0.0528340i	0.999651	−	0.0264170i	$-0.00840977\pi$
$102$	14.5159	−	9.60472i	1.43729	−	0.951009i
$103$	−7.76263	+	7.76263i	−0.764874	+	0.764874i	−0.977199	−	0.212325i	$-0.931897\pi$
$103$	−7.76263	+	7.76263i	−0.764874	+	0.764874i	0.212325	+	0.977199i	$0.431897\pi$
$104$	−5.40199	+	0.998651i	−0.529709	+	0.0979257i
$105$	8.94965	+	8.94965i	0.873396	+	0.873396i
$106$	−0.852093	−	0.173495i	−0.0827626	−	0.0168514i
$107$			7.51057i			0.726074i	0.931775	+	0.363037i	$0.118260\pi$
$107$			7.51057i			0.726074i	−0.931775	+	0.363037i	$0.881740\pi$
$108$	17.7926	+	7.55890i	1.71209	+	0.727356i
$109$	5.84938	−	5.84938i	0.560269	−	0.560269i	−0.369115	−	0.929384i	$-0.620339\pi$
$109$	5.84938	−	5.84938i	0.560269	−	0.560269i	0.929384	+	0.369115i	$0.120339\pi$
$110$	3.02596	−	2.00218i	0.288514	−	0.190900i
$111$	−6.99630	+	17.0597i	−0.664059	+	1.61924i
$112$	12.0211	−	11.5945i	1.13588	−	1.09558i
$113$	−2.26001	−	2.26001i	−0.212604	−	0.212604i	0.592769	−	0.805373i	$-0.298035\pi$
$113$	−2.26001	−	2.26001i	−0.212604	−	0.212604i	−0.805373	+	0.592769i	$0.798035\pi$
$114$	−11.1693	−	16.8805i	−1.04610	−	1.58101i
$115$	7.23138			0.674330
$116$	−0.291030	−	0.720956i	−0.0270215	−	0.0669391i
$117$	8.49944	−	8.49944i	0.785773	−	0.785773i
$118$	−7.39430	−	11.1753i	−0.680701	−	1.02877i
$119$	11.9876	+	11.9876i	1.09890	+	1.09890i
$120$	8.43091	−	1.55860i	0.769634	−	0.142280i
$121$	−4.41742			−0.401584
$122$	−2.80378	−	4.23745i	−0.253842	−	0.383640i
$123$		−	25.2996i		−	2.28119i
$124$	10.5047	−	4.24046i	0.943350	−	0.380804i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−7.29101	+	35.8086i	−0.649535	+	3.19008i
$127$		−	15.6722i		−	1.39068i	−0.718680	−	0.695341i	$-0.755253\pi$
$127$		−	15.6722i		−	1.39068i	0.718680	−	0.695341i	$-0.244747\pi$
$128$	−1.85542	−	11.1605i	−0.163997	−	0.986461i
$129$	−11.9896	−	11.9896i	−1.05563	−	1.05563i
$130$	0.548026	−	2.69154i	0.0480651	−	0.236064i
$131$	−9.01346	+	9.01346i	−0.787509	+	0.787509i	−0.981085	−	0.193576i	$-0.937991\pi$
$131$	−9.01346	+	9.01346i	−0.787509	+	0.787509i	0.193576	+	0.981085i	$0.437991\pi$
$132$	14.3161	+	6.08197i	1.24606	+	0.529367i
$133$	13.9403	−	13.9403i	1.20878	−	1.20878i
$134$	−20.0444	−	4.08126i	−1.73158	−	0.352567i
$135$	−6.83478	+	6.83478i	−0.588244	+	0.588244i
$136$	11.2928	−	2.08766i	0.968348	−	0.179016i
$137$	−17.8550			−1.52546			−0.762728	−	0.646719i	$-0.776141\pi$
$137$	−17.8550			−1.52546			−0.762728	+	0.646719i	$0.776141\pi$
$138$	17.1062	+	25.8531i	1.45617	+	2.20077i
$139$	−20.2486			−1.71746			−0.858732	−	0.512424i	$-0.828748\pi$
$139$	−20.2486			−1.71746			−0.858732	+	0.512424i	$0.828748\pi$
$140$	3.12588	+	7.74360i	0.264185	+	0.654454i
$141$			22.7903i			1.91929i
$142$	2.14405	−	10.5301i	0.179924	−	0.883669i
$143$	3.52362	−	3.52362i	0.294660	−	0.294660i
$144$	17.1853	+	17.8176i	1.43211	+	1.48480i
$145$	0.388740			0.0322831
$146$	−2.65242	+	13.0269i	−0.219515	+	1.07811i
$147$	−31.6273			−2.60858
$148$	−8.64968	+	8.55471i	−0.710999	+	0.703193i
$149$	1.76340			0.144463			0.0722315	−	0.997388i	$-0.476988\pi$
$149$	1.76340			0.144463			0.0722315	+	0.997388i	$0.476988\pi$
$150$	−0.855307	+	4.20069i	−0.0698355	+	0.342985i
$151$	0.802374			0.0652962			0.0326481	−	0.999467i	$-0.489606\pi$
$151$	0.802374			0.0652962			0.0326481	+	0.999467i	$0.489606\pi$
$152$	−2.42773	−	13.1323i	−0.196915	−	1.06517i
$153$	−17.7679	+	17.7679i	−1.43645	+	1.43645i
$154$	−3.02264	+	14.8452i	−0.243572	+	1.19626i
$155$			5.66415i			0.454955i
$156$	10.9190	−	4.40769i	0.874219	−	0.352898i
$157$	2.64870			0.211390			0.105695	−	0.994399i	$-0.466293\pi$
$157$	2.64870			0.211390			0.105695	+	0.994399i	$0.466293\pi$
$158$	−1.58292	−	2.39232i	−0.125930	−	0.190322i
$159$	1.86389			0.147816
$160$	5.52183	+	1.22857i	0.436539	+	0.0971268i
$161$	−21.3501	+	21.3501i	−1.68262	+	1.68262i
$162$	−14.8747	−	3.02866i	−1.16867	−	0.237954i
$163$	12.2305	−	12.2305i	0.957969	−	0.957969i	−0.0411825	−	0.999152i	$-0.513112\pi$
$163$	12.2305	−	12.2305i	0.957969	−	0.957969i	0.999152	+	0.0411825i	$0.0131125\pi$
$164$	6.52688	−	15.3634i	0.509664	−	1.19968i
$165$	−5.49933	+	5.49933i	−0.428122	+	0.428122i
$166$	4.78779	−	23.5144i	0.371604	−	1.82507i
$167$	−5.90631	−	5.90631i	−0.457044	−	0.457044i	0.440640	−	0.897684i	$-0.354752\pi$
$167$	−5.90631	−	5.90631i	−0.457044	−	0.457044i	−0.897684	+	0.440640i	$0.854752\pi$
$168$	−20.2900	+	29.4933i	−1.56541	+	2.27546i
$169$			9.22764i			0.709819i
$170$	−1.14564	+	5.62662i	−0.0878666	+	0.431542i
$171$	20.6623	+	20.6623i	1.58008	+	1.58008i
$172$	−4.18767	−	10.3739i	−0.319307	−	0.791004i
$173$			3.96533i			0.301478i	0.988574	+	0.150739i	$0.0481653\pi$
$173$			3.96533i			0.301478i	−0.988574	+	0.150739i	$0.951835\pi$
$174$	0.919583	+	1.38980i	0.0697134	+	0.105360i
$175$	−4.17536			−0.315628
$176$	7.12452	+	7.38664i	0.537031	+	0.556789i
$177$	20.3097	+	20.3097i	1.52657	+	1.52657i
$178$	−3.68430	−	5.56821i	−0.276150	−	0.417355i
$179$	−15.1740	+	15.1740i	−1.13415	+	1.13415i	−0.144676	+	0.989479i	$0.546214\pi$
$179$	−15.1740	+	15.1740i	−1.13415	+	1.13415i	−0.989479	+	0.144676i	$0.953786\pi$
$180$	−11.4775	+	4.63316i	−0.855484	+	0.345335i
$181$	−0.320115			−0.0237940			−0.0118970	−	0.999929i	$-0.503787\pi$
$181$	−0.320115			−0.0237940			−0.0118970	+	0.999929i	$0.503787\pi$
$182$	6.32856	+	9.56457i	0.469104	+	0.708973i
$183$	7.70107	+	7.70107i	0.569279	+	0.569279i
$184$	3.71816	+	20.1126i	0.274107	+	1.48272i
$185$	−2.34749	−	5.61153i	−0.172591	−	0.412568i
$186$	−20.2501	+	13.3988i	−1.48481	+	0.982448i
$187$	−7.36607	+	7.36607i	−0.538661	+	0.538661i
$188$	−5.87953	+	13.8396i	−0.428809	+	1.00936i
$189$		−	40.3584i		−	2.93564i
$190$	6.54317	+	1.33226i	0.474691	+	0.0966523i
$191$	−14.1936	−	14.1936i	−1.02701	−	1.02701i	−0.999625	−	0.0273890i	$-0.991281\pi$
$191$	−14.1936	−	14.1936i	−1.02701	−	1.02701i	−0.0273890	−	0.999625i	$-0.508719\pi$
$192$	8.66986	+	22.6475i	0.625693	+	1.63444i
$193$	−4.72356	+	4.72356i	−0.340010	+	0.340010i	−0.856371	−	0.516361i	$-0.827286\pi$
$193$	−4.72356	+	4.72356i	−0.340010	+	0.340010i	0.516361	+	0.856371i	$0.327286\pi$
$194$	12.9569	−	8.57315i	0.930251	−	0.615516i
$195$			5.88753i			0.421615i
$196$	−19.2059	−	8.15934i	−1.37185	−	0.582810i
$197$	−7.97531			−0.568217			−0.284109	−	0.958792i	$-0.591698\pi$
$197$	−7.97531			−0.568217			−0.284109	+	0.958792i	$0.591698\pi$
$198$	−22.0035	−	4.48014i	−1.56372	−	0.318390i
$199$	−13.5444	+	13.5444i	−0.960140	+	0.960140i	−0.999235	−	0.0390952i	$-0.987552\pi$
$199$	−13.5444	+	13.5444i	−0.960140	+	0.960140i	0.0390952	+	0.999235i	$0.487552\pi$
$200$	−1.60310	+	2.33025i	−0.113356	+	0.164774i
$201$	43.8457			3.09263
$202$	−0.149820	+	0.735815i	−0.0105413	+	0.0517717i
$203$	−1.14773	+	1.14773i	−0.0805546	+	0.0805546i
$204$	−22.8260	+	9.21421i	−1.59814	+	0.645124i
$205$	5.90162	+	5.90162i	0.412187	+	0.412187i
$206$	12.9476	−	8.56699i	0.902101	−	0.596891i
$207$	−31.6450	−	31.6450i	−2.19948	−	2.19948i
$208$	7.76775	+	0.140315i	0.538597	+	0.00972908i
$209$	8.56598	+	8.56598i	0.592521	+	0.592521i
$210$	−9.87701	−	14.9275i	−0.681578	−	1.03009i
$211$			7.88796i			0.543030i	0.962434	+	0.271515i	$0.0875246\pi$
$211$			7.88796i			0.543030i	−0.962434	+	0.271515i	$0.912475\pi$
$212$	1.13186	+	0.480853i	0.0777365	+	0.0330251i
$213$			23.0338i			1.57825i
$214$	2.11918	−	10.4080i	0.144864	−	0.711476i
$215$	5.59363			0.381483
$216$	−22.5238	−	15.4953i	−1.53255	−	1.05432i
$217$	−16.7230	−	16.7230i	−1.13523	−	1.13523i
$218$	−9.75641	+	6.45549i	−0.660787	+	0.437221i
$219$		−	28.4953i		−	1.92554i
$220$	−4.75825	+	1.92077i	−0.320801	+	0.129499i
$221$			7.88605i			0.530473i
$222$	14.5089	−	21.6669i	0.973773	−	1.45419i
$223$			20.0574i			1.34314i	0.740940	+	0.671572i	$0.234380\pi$
$223$			20.0574i			1.34314i	−0.740940	+	0.671572i	$0.765620\pi$
$224$	−19.9301	+	12.6755i	−1.33163	+	0.846920i
$225$		−	6.18869i		−	0.412580i
$226$	2.49419	+	3.76956i	0.165911	+	0.250748i
$227$	9.17178	+	9.17178i	0.608753	+	0.608753i	0.942620	−	0.333867i	$-0.108354\pi$
$227$	9.17178	+	9.17178i	0.608753	+	0.608753i	−0.333867	+	0.942620i	$0.608354\pi$
$228$	10.7152	+	26.5442i	0.709629	+	1.75793i
$229$	−29.0497			−1.91966			−0.959830	−	0.280582i	$-0.909473\pi$
$229$	−29.0497			−1.91966			−0.959830	+	0.280582i	$0.909473\pi$
$230$	−10.0211	−	2.04040i	−0.660772	−	0.134540i
$231$		−	32.4727i		−	2.13655i
$232$	0.199879	+	1.08120i	0.0131227	+	0.0709845i
$233$		−	27.9431i		−	1.83061i	−0.402758	−	0.915306i	$-0.631948\pi$
$233$		−	27.9431i		−	1.83061i	0.402758	−	0.915306i	$-0.368052\pi$
$234$	−14.1766	+	9.38015i	−0.926750	+	0.613200i
$235$	−5.31629	−	5.31629i	−0.346797	−	0.346797i
$236$	7.09367	+	17.5728i	0.461758	+	1.14389i
$237$	4.34776	+	4.34776i	0.282417	+	0.282417i
$238$	−13.2298	−	19.9946i	−0.857558	−	1.29606i
$239$	7.96684	+	7.96684i	0.515332	+	0.515332i	0.916155	−	0.400824i	$-0.131276\pi$
$239$	7.96684	+	7.96684i	0.515332	+	0.515332i	−0.400824	+	0.916155i	$0.631276\pi$
$240$	−12.1232	−	0.218990i	−0.782547	−	0.0141357i
$241$	−0.00750678	+	0.00750678i	−0.000483554	+	0.000483554i	−0.707349	−	0.706865i	$-0.750109\pi$
$241$	−0.00750678	+	0.00750678i	−0.000483554	+	0.000483554i	0.706865	+	0.707349i	$0.250109\pi$
$242$	6.12158	+	1.24642i	0.393510	+	0.0801228i
$243$	3.53982			0.227080
$244$	2.68978	+	6.66328i	0.172196	+	0.426573i
$245$	7.37769	−	7.37769i	0.471344	−	0.471344i
$246$	−7.13852	+	35.0596i	−0.455135	+	2.23532i
$247$	9.17065			0.583515
$248$	−15.7537	+	2.91234i	−1.00036	+	0.184934i
$249$			51.4360i			3.25962i
$250$	−0.780377	−	1.17941i	−0.0493554	−	0.0745925i
$251$	11.2559	−	11.2559i	0.710468	−	0.710468i	−0.256165	−	0.966633i	$-0.582459\pi$
$251$	11.2559	−	11.2559i	0.710468	−	0.710468i	0.966633	+	0.256165i	$0.0824591\pi$
$252$	20.2075	−	47.5656i	1.27295	−	2.99635i
$253$	−13.1191	−	13.1191i	−0.824791	−	0.824791i
$254$	−4.42206	+	21.7182i	−0.277465	+	1.36272i
$255$		−	12.3078i		−	0.770744i
$256$	−0.577852	+	15.9896i	−0.0361157	+	0.999348i
$257$	3.28455	−	3.28455i	0.204885	−	0.204885i	−0.597204	−	0.802089i	$-0.703722\pi$
$257$	3.28455	−	3.28455i	0.204885	−	0.204885i	0.802089	+	0.597204i	$0.203722\pi$
$258$	13.2320	+	19.9980i	0.823788	+	1.24502i
$259$	23.4984	+	9.63685i	1.46012	+	0.598805i
$260$	−1.51889	+	3.57525i	−0.0941974	+	0.221728i
$261$	−1.70115	−	1.70115i	−0.105299	−	0.105299i
$262$	15.0339	−	9.94743i	0.928797	−	0.614554i
$263$	11.2686			0.694851			0.347426	−	0.937708i	$-0.387056\pi$
$263$	11.2686			0.694851			0.347426	+	0.937708i	$0.387056\pi$
$264$	−18.1229	−	12.4677i	−1.11539	−	0.767333i
$265$	−0.434788	+	0.434788i	−0.0267088	+	0.0267088i
$266$	−23.2516	+	15.3848i	−1.42565	+	0.943304i
$267$	10.1196	+	10.1196i	0.619308	+	0.619308i
$268$	26.6256	+	11.3115i	1.62642	+	0.690958i
$269$	8.15854			0.497435			0.248718	−	0.968576i	$-0.419991\pi$
$269$	8.15854			0.497435			0.248718	+	0.968576i	$0.419991\pi$
$270$	11.4000	−	7.54300i	0.693782	−	0.459053i
$271$		−	15.9799i		−	0.970710i	−0.874317	−	0.485355i	$-0.838690\pi$
$271$		−	15.9799i		−	0.970710i	0.874317	−	0.485355i	$-0.161310\pi$
$272$	−16.2384	−	0.293326i	−0.984596	−	0.0177855i
$273$	−17.3825	−	17.3825i	−1.05204	−	1.05204i
$274$	24.7431	+	5.03796i	1.49479	+	0.304355i
$275$		−	2.56565i		−	0.154715i
$276$	−16.4107	−	40.6534i	−0.987806	−	2.44705i
$277$	8.89156	+	8.89156i	0.534242	+	0.534242i	0.921832	−	0.387590i	$-0.126692\pi$
$277$	8.89156	+	8.89156i	0.534242	+	0.534242i	−0.387590	+	0.921832i	$0.626692\pi$
$278$	28.0601	+	5.71334i	1.68293	+	0.342663i
$279$	24.7867	−	24.7867i	1.48394	−	1.48394i
$280$	−2.14685	−	11.6129i	−0.128299	−	0.694005i
$281$	21.5291	−	21.5291i	1.28432	−	1.28432i	0.346129	−	0.938187i	$-0.387496\pi$
$281$	21.5291	−	21.5291i	1.28432	−	1.28432i	0.938187	−	0.346129i	$-0.112504\pi$
$282$	6.43051	−	31.5824i	0.382931	−	1.88070i
$283$	18.4422	−	18.4422i	1.09628	−	1.09628i	0.101436	−	0.994842i	$-0.467656\pi$
$283$	18.4422	−	18.4422i	1.09628	−	1.09628i	0.994842	−	0.101436i	$-0.0323436\pi$
$284$	−5.94235	+	13.9875i	−0.352614	+	0.830004i
$285$	−14.3127			−0.847810
$286$	−5.87719	+	3.88874i	−0.347525	+	0.229946i
$287$	−34.8482			−2.05702
$288$	−18.7876	−	29.5402i	−1.10707	−	1.74067i
$289$			0.514341i			0.0302553i
$290$	−0.538709	−	0.109687i	−0.0316341	−	0.00644103i
$291$	−23.5476	+	23.5476i	−1.38039	+	1.38039i
$292$	7.35133	−	17.3040i	0.430204	−	1.01264i
$293$	9.10710			0.532043			0.266021	−	0.963967i	$-0.414291\pi$
$293$	9.10710			0.532043			0.266021	+	0.963967i	$0.414291\pi$
$294$	43.8285	+	8.92396i	2.55613	+	0.520456i
$295$	−9.47529			−0.551673
$296$	14.4003	−	9.41435i	0.837003	−	0.547198i
$297$	24.7992			1.43900
$298$	−2.44368	−	0.497559i	−0.141559	−	0.0288228i
$299$	−14.0452			−0.812254
$300$	2.37053	−	5.57991i	0.136863	−	0.322156i
$301$	−16.5148	+	16.5148i	−0.951896	+	0.951896i
$302$	−1.11191	−	0.226397i	−0.0639834	−	0.0130277i
$303$		−	1.60954i		−	0.0924655i
$304$	−0.341107	+	18.8835i	−0.0195639	+	1.08304i
$305$	−3.59285			−0.205726
$306$	29.6359	−	19.6091i	1.69417	−	1.12098i
$307$	−0.962294			−0.0549210			−0.0274605	−	0.999623i	$-0.508742\pi$
$307$	−0.962294			−0.0549210			−0.0274605	+	0.999623i	$0.508742\pi$
$308$	8.37744	−	19.7193i	0.477349	−	1.12361i
$309$	−23.5307	+	23.5307i	−1.33862	+	1.33862i
$310$	1.59819	−	7.84926i	0.0907713	−	0.445808i
$311$	16.0417	−	16.0417i	0.909641	−	0.909641i	−0.0866024	−	0.996243i	$-0.527601\pi$
$311$	16.0417	−	16.0417i	0.909641	−	0.909641i	0.996243	+	0.0866024i	$0.0276010\pi$
$312$	−16.3750	+	3.02720i	−0.927051	+	0.171381i
$313$	−1.37531	+	1.37531i	−0.0777374	+	0.0777374i	−0.744906	−	0.667169i	$-0.767506\pi$
$313$	−1.37531	+	1.37531i	−0.0777374	+	0.0777374i	0.667169	+	0.744906i	$0.267506\pi$
$314$	−3.67052	−	0.747357i	−0.207139	−	0.0421758i
$315$	18.2717	+	18.2717i	1.02949	+	1.02949i
$316$	1.51856	+	3.76186i	0.0854256	+	0.211621i
$317$			7.10068i			0.398814i	0.979917	+	0.199407i	$0.0639015\pi$
$317$			7.10068i			0.398814i	−0.979917	+	0.199407i	$0.936098\pi$
$318$	−2.58294	−	0.525914i	−0.144844	−	0.0294918i
$319$	−0.705249	−	0.705249i	−0.0394864	−	0.0394864i
$320$	−7.30539	−	3.26056i	−0.408384	−	0.182271i
$321$			22.7667i			1.27071i
$322$	35.6107	−	23.5624i	1.98451	−	1.31308i
$323$	−19.1711			−1.06671
$324$	19.7586	+	8.39410i	1.09770	+	0.466339i
$325$	−1.37338	−	1.37338i	−0.0761815	−	0.0761815i
$326$	−20.3998	+	13.4979i	−1.12984	+	0.747577i
$327$	17.7311	−	17.7311i	0.980534	−	0.980534i
$328$	−13.3797	+	19.4486i	−0.738772	+	1.07387i
$329$	31.3919			1.73069
$330$	9.17255	−	6.06917i	0.504932	−	0.334097i
$331$	23.2588	+	23.2588i	1.27842	+	1.27842i	0.941552	+	0.336869i	$0.109368\pi$
$331$	23.2588	+	23.2588i	1.27842	+	1.27842i	0.336869	+	0.941552i	$0.390632\pi$
$332$	−13.2696	+	31.2349i	−0.728266	+	1.71424i
$333$	−14.2837	+	34.8292i	−0.782741	+	1.90863i
$334$	6.51832	+	9.85137i	0.356667	+	0.539043i
$335$	−10.2279	+	10.2279i	−0.558808	+	0.558808i
$336$	36.4393	−	35.1462i	1.98793	−	1.91738i
$337$			10.4111i			0.567131i	0.958953	+	0.283565i	$0.0915173\pi$
$337$			10.4111i			0.567131i	−0.958953	+	0.283565i	$0.908483\pi$
$338$	2.60367	−	12.7875i	0.141621	−	0.695547i
$339$	−6.85074	−	6.85074i	−0.372081	−	0.372081i
$340$	3.17521	−	7.47400i	0.172200	−	0.405335i
$341$	10.2758	−	10.2758i	0.556468	−	0.556468i
$342$	−22.8033	−	34.4634i	−1.23306	−	1.86357i
$343$			14.3367i			0.774107i
$344$	2.87608	+	15.5576i	0.155068	+	0.838808i
$345$	21.9204			1.18015
$346$	1.11885	−	5.49507i	0.0601500	−	0.295417i
$347$	3.15558	−	3.15558i	0.169400	−	0.169400i	−0.617315	−	0.786716i	$-0.711780\pi$
$347$	3.15558	−	3.15558i	0.169400	−	0.169400i	0.786716	+	0.617315i	$0.211780\pi$
$348$	−0.882195	−	2.18542i	−0.0472906	−	0.117151i
$349$	−24.4846			−1.31063			−0.655314	−	0.755356i	$-0.727464\pi$
$349$	−24.4846			−1.31063			−0.655314	+	0.755356i	$0.727464\pi$
$350$	5.78613	+	1.17812i	0.309282	+	0.0629731i
$351$	13.2749	−	13.2749i	0.708561	−	0.708561i
$352$	−7.78880	−	12.2465i	−0.415144	−	0.652741i
$353$	−6.23059	−	6.23059i	−0.331621	−	0.331621i	0.521581	−	0.853202i	$-0.325342\pi$
$353$	−6.23059	−	6.23059i	−0.331621	−	0.331621i	−0.853202	+	0.521581i	$0.825342\pi$
$354$	−22.4142	−	33.8754i	−1.19130	−	1.80046i
$355$	−5.37309	−	5.37309i	−0.285174	−	0.285174i
$356$	3.53451	+	8.75588i	0.187328	+	0.464061i
$357$	36.3378	+	36.3378i	1.92320	+	1.92320i
$358$	25.3092	−	16.7463i	1.33764	−	0.885069i
$359$		−	34.2005i		−	1.80503i	−0.430656	−	0.902516i	$-0.641718\pi$
$359$		−	34.2005i		−	1.80503i	0.430656	−	0.902516i	$-0.358282\pi$
$360$	17.2126	−	3.18204i	0.907184	−	0.167708i
$361$			3.29400i			0.173368i
$362$	0.443609	+	0.0903235i	0.0233156	+	0.00474730i
$363$	−13.3905			−0.702818
$364$	−6.07126	−	15.0401i	−0.318220	−	0.788313i
$365$	6.64709	+	6.64709i	0.347925	+	0.347925i
$366$	−8.49905	−	12.8449i	−0.444253	−	0.671414i
$367$			27.9551i			1.45924i	0.683851	+	0.729621i	$0.260304\pi$
$367$			27.9551i			1.45924i	−0.683851	+	0.729621i	$0.739696\pi$
$368$	0.522418	−	28.9208i	0.0272329	−	1.50760i
$369$		−	51.6518i		−	2.68888i
$370$	1.66975	+	8.43872i	0.0868063	+	0.438708i
$371$		−	2.56736i		−	0.133291i
$372$	31.8428	−	12.8540i	1.65097	−	0.666451i
$373$			29.0888i			1.50616i	0.657928	+	0.753081i	$0.271433\pi$
$373$			29.0888i			1.50616i	−0.657928	+	0.753081i	$0.728567\pi$
$374$	12.2862	−	8.12935i	0.635303	−	0.420359i
$375$	2.14344	+	2.14344i	0.110687	+	0.110687i
$376$	12.0527	−	17.5197i	0.621572	−	0.903509i
$377$	−0.755033			−0.0388862
$378$	−11.3875	+	55.9278i	−0.585710	+	2.87662i
$379$		−	12.4053i		−	0.637215i	−0.947887	−	0.318608i	$-0.896785\pi$
$379$		−	12.4053i		−	0.637215i	0.947887	−	0.318608i	$-0.103215\pi$
$380$	−8.69148	−	3.69244i	−0.445864	−	0.189418i
$381$		−	47.5069i		−	2.43385i
$382$	15.6644	+	23.6741i	0.801458	+	1.21127i
$383$	2.94850	+	2.94850i	0.150662	+	0.150662i	0.778413	−	0.627752i	$-0.216025\pi$
$383$	2.94850	+	2.94850i	0.150662	+	0.150662i	−0.627752	+	0.778413i	$0.716025\pi$
$384$	−5.62430	−	33.8308i	−0.287014	−	1.72642i
$385$	7.57490	+	7.57490i	0.386053	+	0.386053i
$386$	7.87862	−	5.21302i	0.401011	−	0.265336i
$387$	−24.4781	−	24.4781i	−1.24429	−	1.24429i
$388$	−20.3744	+	8.22458i	−1.03435	+	0.417540i
$389$	−17.8576	+	17.8576i	−0.905416	+	0.905416i	−0.995898	−	0.0904818i	$-0.971159\pi$
$389$	−17.8576	+	17.8576i	−0.905416	+	0.905416i	0.0904818	+	0.995898i	$0.471159\pi$
$390$	1.66122	−	8.15882i	0.0841193	−	0.413138i
$391$	29.3612			1.48486
$392$	24.3130	+	16.7262i	1.22799	+	0.844800i
$393$	−27.3224	+	27.3224i	−1.37823	+	1.37823i
$394$	11.0520	+	2.25031i	0.556793	+	0.113369i
$395$	−2.02840			−0.102060
$396$	29.2278	+	12.4170i	1.46875	+	0.623977i
$397$			3.19025i			0.160114i	0.996790	+	0.0800571i	$0.0255103\pi$
$397$			3.19025i			0.160114i	−0.996790	+	0.0800571i	$0.974490\pi$
$398$	22.5913	−	14.9479i	1.13240	−	0.749272i
$399$	42.2571	−	42.2571i	2.11550	−	2.11550i
$400$	2.87905	−	2.77688i	0.143952	−	0.138844i
$401$	−13.4042	−	13.4042i	−0.669374	−	0.669374i	0.288197	−	0.957571i	$-0.406944\pi$
$401$	−13.4042	−	13.4042i	−0.669374	−	0.669374i	−0.957571	+	0.288197i	$0.906944\pi$
$402$	−60.7604	−	12.3715i	−3.03046	−	0.617033i
$403$		−	11.0012i		−	0.548010i
$404$	0.415234	−	0.977404i	0.0206587	−	0.0486277i
$405$	−7.58997	+	7.58997i	−0.377149	+	0.377149i
$406$	1.91434	−	1.26665i	0.0950071	−	0.0628630i
$407$	−5.92160	+	14.4392i	−0.293523	+	0.715724i
$408$	34.2316	−	6.32830i	1.69472	−	0.313298i
$409$	6.68943	+	6.68943i	0.330771	+	0.330771i	0.852879	−	0.522108i	$-0.174854\pi$
$409$	6.68943	+	6.68943i	0.330771	+	0.330771i	−0.522108	+	0.852879i	$0.674854\pi$
$410$	−6.51315	−	9.84355i	−0.321661	−	0.486138i
$411$	−54.1236			−2.66972
$412$	−20.3598	+	8.21868i	−1.00305	+	0.404905i
$413$	27.9751	−	27.9751i	1.37656	−	1.37656i
$414$	34.9241	+	52.7820i	1.71642	+	2.59409i
$415$	−11.9984	−	11.9984i	−0.588981	−	0.588981i
$416$	−10.7248	−	2.38619i	−0.525827	−	0.116993i
$417$	−61.3793			−3.00576
$418$	−9.45359	−	14.2875i	−0.462390	−	0.698826i
$419$		−	32.6508i		−	1.59510i	−0.603256	−	0.797548i	$-0.706130\pi$
$419$		−	32.6508i		−	1.59510i	0.603256	−	0.797548i	$-0.293870\pi$
$420$	9.47543	+	23.4731i	0.462354	+	1.14537i
$421$	−17.0681	−	17.0681i	−0.831850	−	0.831850i	0.155919	−	0.987770i	$-0.450166\pi$
$421$	−17.0681	−	17.0681i	−0.831850	−	0.831850i	−0.987770	+	0.155919i	$0.950166\pi$
$422$	2.22566	−	10.9310i	0.108344	−	0.532112i
$423$			46.5289i			2.26231i
$424$	−1.43283	−	0.985721i	−0.0695845	−	0.0478708i
$425$	2.87103	+	2.87103i	0.139266	+	0.139266i
$426$	6.49922	−	31.9198i	0.314888	−	1.54652i
$427$	10.6076	−	10.6076i	0.513339	−	0.513339i
$428$	−5.87343	+	13.8252i	−0.283903	+	0.668268i
$429$	10.6811	−	10.6811i	0.515689	−	0.515689i
$430$	−7.75154	−	1.57830i	−0.373813	−	0.0761123i
$431$	−12.4968	+	12.4968i	−0.601949	+	0.601949i	−0.940829	−	0.338881i	$-0.889952\pi$
$431$	−12.4968	+	12.4968i	−0.601949	+	0.601949i	0.338881	+	0.940829i	$0.389952\pi$
$432$	26.8409	+	27.8284i	1.29138	+	1.33890i
$433$	13.9185			0.668880			0.334440	−	0.942417i	$-0.391453\pi$
$433$	13.9185			0.668880			0.334440	+	0.942417i	$0.391453\pi$
$434$	18.4558	+	27.8929i	0.885907	+	1.33890i
$435$	1.17838			0.0564991
$436$	15.3417	−	6.19303i	0.734735	−	0.296592i
$437$		−	34.1441i		−	1.63333i
$438$	−8.04023	+	39.4882i	−0.384177	+	1.88682i
$439$	−6.37945	+	6.37945i	−0.304474	+	0.304474i	−0.842761	−	0.538287i	$-0.819072\pi$
$439$	−6.37945	+	6.37945i	−0.304474	+	0.304474i	0.538287	+	0.842761i	$0.319072\pi$
$440$	7.13585	−	1.31918i	0.340188	−	0.0628896i
$441$	−64.5706			−3.07479
$442$	2.22512	−	10.9283i	0.105838	−	0.519808i
$443$	10.7845			0.512388			0.256194	−	0.966625i	$-0.417531\pi$
$443$	10.7845			0.512388			0.256194	+	0.966625i	$0.417531\pi$
$444$	−26.2197	+	25.9318i	−1.24433	+	1.23067i
$445$	−4.72118			−0.223805
$446$	5.65939	−	27.7952i	0.267980	−	1.31614i
$447$	5.34536			0.252827
$448$	31.1952	−	11.9421i	1.47383	−	0.564209i
$449$	5.06489	−	5.06489i	0.239027	−	0.239027i	−0.577420	−	0.816447i	$-0.695941\pi$
$449$	5.06489	−	5.06489i	0.239027	−	0.239027i	0.816447	+	0.577420i	$0.195941\pi$
$450$	−1.74620	+	8.57617i	−0.0823166	+	0.404284i
$451$		−	21.4133i		−	1.00831i
$452$	−2.39279	−	5.92755i	−0.112547	−	0.278808i
$453$	2.43222			0.114276
$454$	−10.1222	−	15.2980i	−0.475057	−	0.717970i
$455$	8.10962			0.380185
$456$	−7.35916	−	39.8078i	−0.344624	−	1.86417i
$457$	−2.27230	+	2.27230i	−0.106294	+	0.106294i	−0.758254	−	0.651960i	$-0.773947\pi$
$457$	−2.27230	+	2.27230i	−0.106294	+	0.106294i	0.651960	+	0.758254i	$0.273947\pi$
$458$	40.2565	+	8.19666i	1.88106	+	0.383005i
$459$	−27.7509	+	27.7509i	−1.29530	+	1.29530i
$460$	13.3113	+	5.65510i	0.620644	+	0.263670i
$461$	−18.7982	+	18.7982i	−0.875519	+	0.875519i	−0.993067	−	0.117549i	$-0.962496\pi$
$461$	−18.7982	+	18.7982i	−0.875519	+	0.875519i	0.117549	+	0.993067i	$0.462496\pi$
$462$	−9.16249	+	45.0001i	−0.426278	+	2.09359i
$463$	7.71828	+	7.71828i	0.358699	+	0.358699i	0.863333	−	0.504634i	$-0.168373\pi$
$463$	7.71828	+	7.71828i	0.358699	+	0.358699i	−0.504634	+	0.863333i	$0.668373\pi$
$464$	0.0280839	−	1.55471i	0.00130376	−	0.0721755i
$465$			17.1696i			0.796223i
$466$	−7.88441	+	38.7230i	−0.365238	+	1.79381i
$467$	14.7105	+	14.7105i	0.680719	+	0.680719i	0.960162	−	0.279443i	$-0.0901499\pi$
$467$	14.7105	+	14.7105i	0.680719	+	0.680719i	−0.279443	+	0.960162i	$0.590150\pi$
$468$	22.2923	−	8.99878i	1.03046	−	0.415969i
$469$		−	60.3940i		−	2.78874i
$470$	5.86717	+	8.86725i	0.270632	+	0.409016i
$471$	8.02898			0.369956
$472$	−4.87192	−	26.3536i	−0.224248	−	1.21302i
$473$	−10.1479	−	10.1479i	−0.466602	−	0.466602i
$474$	−4.79827	−	7.25180i	−0.220392	−	0.333086i
$475$	3.33871	−	3.33871i	0.153191	−	0.153191i
$476$	12.6919	+	31.4410i	0.581731	+	1.44110i
$477$	3.80532			0.174234
$478$	−8.79236	−	13.2882i	−0.402153	−	0.607788i
$479$	18.0936	+	18.0936i	0.826718	+	0.826718i	0.987061	−	0.160343i	$-0.0512600\pi$
$479$	18.0936	+	18.0936i	0.826718	+	0.826718i	−0.160343	+	0.987061i	$0.551260\pi$
$480$	16.7382	+	3.72414i	0.763993	+	0.169983i
$481$	4.55942	+	10.8990i	0.207892	+	0.496953i
$482$	0.0125209	−	0.00828463i	0.000570309	−	0.000377355i
$483$	−64.7183	+	64.7183i	−2.94478	+	2.94478i
$484$	−8.13147	−	3.45452i	−0.369612	−	0.157024i
$485$		−	10.9859i		−	0.498844i
$486$	−4.90542	−	0.998795i	−0.222514	−	0.0453063i
$487$	−2.92917	−	2.92917i	−0.132734	−	0.132734i	0.637619	−	0.770352i	$-0.279920\pi$
$487$	−2.92917	−	2.92917i	−0.132734	−	0.132734i	−0.770352	+	0.637619i	$0.779920\pi$
$488$	−1.84734	−	9.99279i	−0.0836251	−	0.452352i
$489$	37.0742	−	37.0742i	1.67655	−	1.67655i
$490$	−12.3055	+	8.14217i	−0.555908	+	0.367826i
$491$		−	2.22730i		−	0.100517i	−0.998736	−	0.0502584i	$-0.983996\pi$
$491$		−	2.22730i		−	0.100517i	0.998736	−	0.0502584i	$-0.0160045\pi$
$492$	19.7848	−	46.5707i	0.891969	−	2.09957i
$493$	1.57838			0.0710869
$494$	−12.7085	−	2.58759i	−0.571783	−	0.116421i
$495$	−11.2275	+	11.2275i	−0.504637	+	0.504637i
$496$	22.6529	+	0.409196i	1.01714	+	0.0183735i
$497$	31.7273			1.42316
$498$	14.5132	−	71.2789i	0.650350	−	3.19409i
$499$	9.73793	−	9.73793i	0.435930	−	0.435930i	−0.454710	−	0.890640i	$-0.650257\pi$
$499$	9.73793	−	9.73793i	0.435930	−	0.435930i	0.890640	+	0.454710i	$0.150257\pi$
$500$	0.748649	+	1.85460i	0.0334806	+	0.0829400i
$501$	−17.9037	−	17.9037i	−0.799879	−	0.799879i
$502$	−18.7742	+	12.4223i	−0.837934	+	0.554433i
$503$	16.6607	+	16.6607i	0.742865	+	0.742865i	0.973128	−	0.230263i	$-0.0739586\pi$
$503$	16.6607	+	16.6607i	0.742865	+	0.742865i	−0.230263	+	0.973128i	$0.573959\pi$
$504$	−41.4242	+	60.2137i	−1.84518	+	2.68213i
$505$	0.375456	+	0.375456i	0.0167076	+	0.0167076i
$506$	14.4785	+	21.8819i	0.643648	+	0.972768i
$507$			27.9716i			1.24226i
$508$	12.2560	−	28.8489i	0.543772	−	1.27996i
$509$		−	26.3516i		−	1.16801i	−0.811748	−	0.584007i	$-0.801484\pi$
$509$		−	26.3516i		−	1.16801i	0.811748	−	0.584007i	$-0.198516\pi$
$510$	−3.47276	+	17.0559i	−0.153776	+	0.755247i
$511$	−39.2501			−1.73632
$512$	5.31238	−	21.9950i	0.234776	−	0.972049i
$513$	32.2715	+	32.2715i	1.42482	+	1.42482i
$514$	−5.47843	+	3.62490i	−0.241643	+	0.159887i
$515$		−	10.9780i		−	0.483749i
$516$	−12.6940	−	31.4463i	−0.558823	−	1.38435i
$517$			19.2895i			0.848353i
$518$	−29.8445	−	19.9849i	−1.31129	−	0.878084i
$519$			12.0200i			0.527621i
$520$	3.11363	−	4.52594i	0.136542	−	0.198476i
$521$			10.5363i			0.461603i	0.973001	+	0.230801i	$0.0741348\pi$
$521$			10.5363i			0.461603i	−0.973001	+	0.230801i	$0.925865\pi$
$522$	1.87743	+	2.83742i	0.0821728	+	0.124191i
$523$	16.8809	+	16.8809i	0.738151	+	0.738151i	0.972220	−	0.234069i	$-0.0752043\pi$
$523$	16.8809	+	16.8809i	0.738151	+	0.738151i	−0.234069	+	0.972220i	$0.575204\pi$
$524$	−23.6404	+	9.54299i	−1.03274	+	0.416888i
$525$	−12.6567			−0.552384
$526$	−15.6158	−	3.17954i	−0.680881	−	0.138635i
$527$			22.9979i			1.00180i
$528$	21.5964	+	22.3910i	0.939865	+	0.974444i
$529$			29.2929i			1.27360i
$530$	0.725200	−	0.479841i	0.0315007	−	0.0208430i
$531$	41.4645	+	41.4645i	1.79941	+	1.79941i
$532$	36.5626	−	14.7593i	1.58519	−	0.639897i
$533$	−11.4625	−	11.4625i	−0.496494	−	0.496494i
$534$	−11.1682	−	16.8788i	−0.483294	−	0.730419i
$535$	−5.31077	−	5.31077i	−0.229605	−	0.229605i
$536$	−33.7056	−	23.1879i	−1.45586	−	1.00156i
$537$	−45.9966	+	45.9966i	−1.98490	+	1.98490i
$538$	−11.3059	−	2.30201i	−0.487434	−	0.0992468i
$539$	−26.7691			−1.15303
$540$	−17.9262	+	7.23632i	−0.771422	+	0.311402i
$541$	27.1744	−	27.1744i	1.16832	−	1.16832i	0.185717	−	0.982603i	$-0.440539\pi$
$541$	27.1744	−	27.1744i	1.16832	−	1.16832i	0.982603	−	0.185717i	$-0.0594609\pi$
$542$	−4.50888	+	22.1446i	−0.193673	+	0.951193i
$543$	−0.970360			−0.0416421
$544$	22.4200	+	4.98830i	0.961251	+	0.213871i
$545$			8.27227i			0.354345i
$546$	19.1837	+	28.9930i	0.820985	+	1.24078i
$547$	−10.2236	+	10.2236i	−0.437128	+	0.437128i	−0.891044	−	0.453917i	$-0.850026\pi$
$547$	−10.2236	+	10.2236i	−0.437128	+	0.437128i	0.453917	+	0.891044i	$0.350026\pi$
$548$	−32.8670	−	13.9630i	−1.40401	−	0.596471i
$549$	15.7226	+	15.7226i	0.671022	+	0.671022i
$550$	−0.723924	+	3.55543i	−0.0308682	+	0.151604i
$551$		−	1.83550i		−	0.0781948i
$552$	11.2708	+	60.9672i	0.479718	+	2.59493i
$553$	5.98870	−	5.98870i	0.254665	−	0.254665i
$554$	−9.81291	−	14.8306i	−0.416911	−	0.630091i
$555$	−7.11590	−	17.0102i	−0.302053	−	0.722041i
$556$	−37.2731	−	15.8349i	−1.58073	−	0.671548i
$557$	−8.39184	−	8.39184i	−0.355574	−	0.355574i	0.506605	−	0.862178i	$-0.330900\pi$
$557$	−8.39184	−	8.39184i	−0.355574	−	0.355574i	−0.862178	+	0.506605i	$0.830900\pi$
$558$	−41.3427	+	27.3551i	−1.75018	+	1.15803i
$559$	−10.8643			−0.459509
$560$	−0.301642	+	16.6987i	−0.0127467	+	0.705650i
$561$	−22.3287	+	22.3287i	−0.942717	+	0.942717i
$562$	−35.9092	+	23.7599i	−1.51474	+	1.00225i
$563$	−25.1931	−	25.1931i	−1.06176	−	1.06176i	−0.997963	−	0.0638020i	$-0.979677\pi$
$563$	−25.1931	−	25.1931i	−1.06176	−	1.06176i	−0.0638020	−	0.997963i	$-0.520323\pi$
$564$	−17.8225	+	41.9518i	−0.750465	+	1.76649i
$565$	3.19614			0.134463
$566$	−30.7606	+	20.3532i	−1.29296	+	0.855510i
$567$		−	44.8177i		−	1.88216i
$568$	12.1815	−	17.7069i	0.511124	−	0.742964i
$569$	−12.9804	−	12.9804i	−0.544165	−	0.544165i	0.380582	−	0.924747i	$-0.375724\pi$
$569$	−12.9804	−	12.9804i	−0.544165	−	0.544165i	−0.924747	+	0.380582i	$0.875724\pi$
$570$	19.8342	+	4.03846i	0.830764	+	0.169152i
$571$		−	23.7574i		−	0.994215i	−0.867689	−	0.497107i	$-0.834396\pi$
$571$		−	23.7574i		−	0.994215i	0.867689	−	0.497107i	$-0.165604\pi$
$572$	9.24173	−	3.73063i	0.386416	−	0.155986i
$573$	−43.0249	−	43.0249i	−1.79739	−	1.79739i
$574$	48.2919	+	9.83275i	2.01567	+	0.410411i
$575$	−5.11336	+	5.11336i	−0.213242	+	0.213242i
$576$	17.7004	+	46.2373i	0.737518	+	1.92655i
$577$	26.0945	−	26.0945i	1.08633	−	1.08633i	0.0904262	−	0.995903i	$-0.471177\pi$
$577$	26.0945	−	26.0945i	1.08633	−	1.08633i	0.995903	−	0.0904262i	$-0.0288229\pi$
$578$	0.145126	−	0.712763i	0.00603646	−	0.0296470i
$579$	−14.3185	+	14.3185i	−0.595056	+	0.595056i
$580$	0.715582	+	0.304004i	0.0297129	+	0.0126231i
$581$	70.8490			2.93931
$582$	39.2760	−	25.9877i	1.62804	−	1.07722i
$583$	1.57758			0.0653366
$584$	−15.0698	+	21.9053i	−0.623593	+	0.906447i
$585$			12.0200i			0.496967i
$586$	−12.6204	−	2.56966i	−0.521346	−	0.106152i
$587$	18.0329	−	18.0329i	0.744297	−	0.744297i	−0.229105	−	0.973402i	$-0.573580\pi$
$587$	18.0329	−	18.0329i	0.744297	−	0.744297i	0.973402	+	0.229105i	$0.0735798\pi$
$588$	−58.2187	−	24.7333i	−2.40090	−	1.01998i
$589$	26.7441			1.10197
$590$	13.1307	+	2.67355i	0.540581	+	0.110068i
$591$	−24.1754			−0.994445
$592$	−22.6121	+	8.98302i	−0.929350	+	0.369200i
$593$	11.2720			0.462886			0.231443	−	0.972848i	$-0.425655\pi$
$593$	11.2720			0.462886			0.231443	+	0.972848i	$0.425655\pi$
$594$	−34.3662	−	6.99733i	−1.41006	−	0.287104i
$595$	−16.9530			−0.695006
$596$	3.24601	+	1.37902i	0.132962	+	0.0564867i
$597$	−41.0571	+	41.0571i	−1.68035	+	1.68035i
$598$	19.4635	+	3.96299i	0.795923	+	0.162059i
$599$		−	0.201520i		−	0.00823388i	−0.999992	−	0.00411694i	$-0.998690\pi$
$599$		−	0.201520i		−	0.00823388i	0.999992	−	0.00411694i	$-0.00131047\pi$
$600$	−4.85946	+	7.06365i	−0.198387	+	0.288372i
$601$	−8.33263			−0.339895			−0.169948	−	0.985453i	$-0.554360\pi$
$601$	−8.33263			−0.339895			−0.169948	+	0.985453i	$0.554360\pi$
$602$	27.5457	−	18.2261i	1.12268	−	0.742838i
$603$	89.5156			3.64536
$604$	1.47699	+	0.627474i	0.0600977	+	0.0255316i
$605$	3.12359	−	3.12359i	0.126992	−	0.126992i
$606$	−0.454146	+	2.23046i	−0.0184484	+	0.0906064i
$607$	5.05524	−	5.05524i	0.205186	−	0.205186i	−0.597032	−	0.802218i	$-0.703653\pi$
$607$	5.05524	−	5.05524i	0.205186	−	0.205186i	0.802218	+	0.597032i	$0.203653\pi$
$608$	5.80087	−	26.0722i	0.235256	−	1.05737i
$609$	−3.47909	+	3.47909i	−0.140980	+	0.140980i
$610$	4.97890	+	1.01376i	0.201590	+	0.0410458i
$611$	10.3256	+	10.3256i	0.417729	+	0.417729i
$612$	−46.6017	+	18.8118i	−1.88376	+	0.760422i
$613$			38.0315i			1.53608i	0.640403	+	0.768039i	$0.278767\pi$
$613$			38.0315i			1.53608i	−0.640403	+	0.768039i	$0.721233\pi$
$614$	1.33353	+	0.271521i	0.0538168	+	0.0109577i
$615$	17.8895	+	17.8895i	0.721374	+	0.721374i
$616$	−17.1733	+	24.9629i	−0.691931	+	1.00578i
$617$			25.5694i			1.02939i	0.857374	+	0.514693i	$0.172094\pi$
$617$			25.5694i			1.02939i	−0.857374	+	0.514693i	$0.827906\pi$
$618$	39.2478	−	25.9690i	1.57878	−	1.04463i
$619$	35.8211			1.43977			0.719886	−	0.694092i	$-0.244194\pi$
$619$	35.8211			1.43977			0.719886	+	0.694092i	$0.244194\pi$
$620$	−4.42949	+	10.4264i	−0.177893	+	0.418734i
$621$	−49.4249	−	49.4249i	−1.98335	−	1.98335i
$622$	−26.7566	+	17.7039i	−1.07284	+	0.709863i
$623$	13.9389	−	13.9389i	0.558452	−	0.558452i
$624$	23.5463	+	0.425334i	0.942606	+	0.0170270i
$625$	−1.00000			−0.0400000
$626$	2.29394	−	1.51782i	0.0916843	−	0.0606645i
$627$	25.9659	+	25.9659i	1.03698	+	1.03698i
$628$	4.87566	+	2.07135i	0.194560	+	0.0826557i
$629$	−9.53139	−	22.7842i	−0.380042	−	0.908467i
$630$	−20.1650	−	30.4760i	−0.803392	−	1.21419i
$631$	−12.7535	+	12.7535i	−0.507707	+	0.507707i	−0.913822	−	0.406115i	$-0.866883\pi$
$631$	−12.7535	+	12.7535i	−0.507707	+	0.507707i	0.406115	+	0.913822i	$0.366883\pi$
$632$	−1.04294	−	5.64159i	−0.0414861	−	0.224410i
$633$			23.9107i			0.950364i
$634$	2.00352	−	9.83997i	0.0795701	−	0.390795i
$635$	11.0819	+	11.0819i	0.439772	+	0.439772i
$636$	3.43099	+	1.45760i	0.136048	+	0.0577977i
$637$	−14.3294	+	14.3294i	−0.567750	+	0.567750i
$638$	0.778327	+	1.17631i	0.0308143	+	0.0465707i
$639$			47.0260i			1.86032i
$640$	9.20366	+	6.57971i	0.363807	+	0.260086i
$641$	29.5972			1.16902			0.584509	−	0.811387i	$-0.301287\pi$
$641$	29.5972			1.16902			0.584509	+	0.811387i	$0.301287\pi$
$642$	6.42384	−	31.5496i	0.253529	−	1.24516i
$643$	17.7201	−	17.7201i	0.698812	−	0.698812i	−0.265342	−	0.964154i	$-0.585485\pi$
$643$	17.7201	−	17.7201i	0.698812	−	0.698812i	0.964154	+	0.265342i	$0.0854849\pi$
$644$	−55.9970	+	22.6044i	−2.20659	+	0.890739i
$645$	16.9559			0.667638
$646$	26.5669	+	5.40931i	1.04526	+	0.212827i
$647$	1.52190	−	1.52190i	0.0598319	−	0.0598319i	−0.676558	−	0.736390i	$-0.736529\pi$
$647$	1.52190	−	1.52190i	0.0598319	−	0.0598319i	0.736390	+	0.676558i	$0.236529\pi$
$648$	−25.0125	−	17.2074i	−0.982585	−	0.675972i
$649$	17.1900	+	17.1900i	0.674766	+	0.674766i
$650$	1.51569	+	2.29072i	0.0594503	+	0.0898493i
$651$	−50.6921	−	50.6921i	−1.98678	−	1.98678i
$652$	32.0782	−	12.9491i	1.25628	−	0.507125i
$653$	−27.6146	−	27.6146i	−1.08064	−	1.08064i	−0.996449	−	0.0841929i	$-0.973169\pi$
$653$	−27.6146	−	27.6146i	−1.08064	−	1.08064i	−0.0841929	−	0.996449i	$-0.526831\pi$
$654$	−29.5745	+	19.5684i	−1.15645	+	0.765187i
$655$		−	12.7470i		−	0.498065i
$656$	24.0290	−	23.1763i	0.938174	−	0.904882i
$657$		−	58.1762i		−	2.26967i
$658$	−43.5023	−	8.85753i	−1.69590	−	0.345303i
$659$	−15.0789			−0.587390			−0.293695	−	0.955899i	$-0.594885\pi$
$659$	−15.0789			−0.587390			−0.293695	+	0.955899i	$0.594885\pi$
$660$	−14.4236	+	5.82241i	−0.561438	+	0.226637i
$661$	−5.51201	−	5.51201i	−0.214392	−	0.214392i	0.591738	−	0.806130i	$-0.298442\pi$
$661$	−5.51201	−	5.51201i	−0.214392	−	0.214392i	−0.806130	+	0.591738i	$0.798442\pi$
$662$	−25.6689	−	38.7943i	−0.997650	−	1.50778i
$663$			23.9049i			0.928388i
$664$	27.2020	−	39.5405i	1.05564	−	1.53447i
$665$			19.7146i			0.764499i
$666$	29.6214	−	44.2353i	1.14781	−	1.71408i
$667$			2.81113i			0.108847i
$668$	−6.25330	−	15.4910i	−0.241948	−	0.599366i
$669$			60.7997i			2.35065i
$670$	17.0595	−	11.2877i	0.659064	−	0.436081i
$671$	6.51811	+	6.51811i	0.251629	+	0.251629i
$672$	−60.4137	+	38.4232i	−2.33051	+	1.48221i
$673$	−1.07819			−0.0415612			−0.0207806	−	0.999784i	$-0.506615\pi$
$673$	−1.07819			−0.0415612			−0.0207806	+	0.999784i	$0.506615\pi$
$674$	2.93760	−	14.4275i	0.113152	−	0.555728i
$675$		−	9.66584i		−	0.372038i
$676$	−7.21622	+	16.9860i	−0.277547	+	0.653307i
$677$			28.4175i			1.09217i	0.837729	+	0.546086i	$0.183883\pi$
$677$			28.4175i			1.09217i	−0.837729	+	0.546086i	$0.816117\pi$
$678$	7.56062	+	11.4266i	0.290364	+	0.438837i
$679$	32.4351	+	32.4351i	1.24474	+	1.24474i
$680$	−6.50900	+	9.46140i	−0.249609	+	0.362828i
$681$	27.8023	+	27.8023i	1.06539	+	1.06539i
$682$	−17.1395	+	11.3406i	−0.656305	+	0.434255i
$683$	−27.6781	−	27.6781i	−1.05907	−	1.05907i	−0.998142	−	0.0609308i	$-0.980593\pi$
$683$	−27.6781	−	27.6781i	−1.05907	−	1.05907i	−0.0609308	−	0.998142i	$-0.519407\pi$
$684$	21.8762	+	54.1929i	0.836456	+	2.07212i
$685$	12.6254	−	12.6254i	0.482392	−	0.482392i
$686$	4.04523	−	19.8675i	0.154448	−	0.758543i
$687$	−88.0580			−3.35962
$688$	0.404102	−	22.3709i	0.0154063	−	0.852882i
$689$	0.844470	−	0.844470i	0.0321717	−	0.0321717i
$690$	−30.3768	−	6.18505i	−1.15643	−	0.235461i
$691$	4.06655			0.154699			0.0773494	−	0.997004i	$-0.475354\pi$
$691$	4.06655			0.154699			0.0773494	+	0.997004i	$0.475354\pi$
$692$	−3.10097	+	7.29926i	−0.117881	+	0.277476i
$693$		−	66.2965i		−	2.51840i
$694$	−5.26332	+	3.48256i	−0.199793	+	0.132196i
$695$	14.3179	−	14.3179i	0.543110	−	0.543110i
$696$	0.605890	+	3.27744i	0.0229662	+	0.124231i
$697$	23.9621	+	23.9621i	0.907628	+	0.907628i
$698$	33.9302	+	6.90856i	1.28428	+	0.261493i
$699$		−	84.7035i		−	3.20378i
$700$	−7.68589	−	3.26523i	−0.290499	−	0.123414i
$701$	0.252080	−	0.252080i	0.00952092	−	0.00952092i	−0.702330	−	0.711851i	$-0.747857\pi$
$701$	0.252080	−	0.252080i	0.00952092	−	0.00952092i	0.711851	+	0.702330i	$0.247857\pi$
$702$	−22.1417	+	14.6504i	−0.835685	+	0.552945i
$703$	−26.4957	+	11.0840i	−0.999304	+	0.418042i
$704$	7.33809	+	19.1687i	0.276565	+	0.722446i
$705$	−16.1152	−	16.1152i	−0.606934	−	0.606934i
$706$	6.87620	+	10.3922i	0.258789	+	0.391117i
$707$	−2.21701			−0.0833793
$708$	21.5029	+	53.2683i	0.808130	+	2.00194i
$709$	30.0226	−	30.0226i	1.12752	−	1.12752i	0.136944	−	0.990579i	$-0.456272\pi$
$709$	30.0226	−	30.0226i	1.12752	−	1.12752i	0.990579	−	0.136944i	$-0.0437282\pi$
$710$	5.92985	+	8.96199i	0.222543	+	0.336338i
$711$	8.87641	+	8.87641i	0.332891	+	0.332891i
$712$	−2.42749	−	13.1310i	−0.0909741	−	0.492106i
$713$	−40.9596			−1.53395
$714$	−40.1032	−	60.6093i	−1.50082	−	2.26825i
$715$			4.98315i			0.186359i
$716$	−39.7982	+	16.0654i	−1.48733	+	0.600393i
$717$	24.1498	+	24.1498i	0.901889	+	0.901889i
$718$	−9.65000	+	47.3943i	−0.360135	+	1.76874i
$719$			10.5873i			0.394840i	0.980319	+	0.197420i	$0.0632563\pi$
$719$			10.5873i			0.394840i	−0.980319	+	0.197420i	$0.936744\pi$
$720$	−24.7507	−	0.447091i	−0.922405	−	0.0166621i
$721$	32.4118	+	32.4118i	1.20708	+	1.20708i
$722$	0.929433	−	4.56475i	0.0345899	−	0.169883i
$723$	−0.0227552	+	0.0227552i	−0.000846275	+	0.000846275i
$724$	−0.589259	−	0.250337i	−0.0218996	−	0.00930370i
$725$	−0.274881	+	0.274881i	−0.0102088	+	0.0102088i
$726$	18.5562	+	3.77825i	0.688687	+	0.140224i
$727$	13.2560	−	13.2560i	0.491639	−	0.491639i	−0.417184	−	0.908822i	$-0.636983\pi$
$727$	13.2560	−	13.2560i	0.491639	−	0.491639i	0.908822	+	0.417184i	$0.136983\pi$
$728$	4.16973	+	22.5553i	0.154540	+	0.835954i
$729$	−21.4713			−0.795234
$730$	−7.33586	−	11.0869i	−0.271513	−	0.410346i
$731$	22.7116			0.840018
$732$	8.15350	+	20.1983i	0.301362	+	0.746551i
$733$			11.3778i			0.420250i	0.977675	+	0.210125i	$0.0673870\pi$
$733$			11.3778i			0.420250i	−0.977675	+	0.210125i	$0.932613\pi$
$734$	7.88779	−	38.7396i	0.291144	−	1.42990i
$735$	22.3639	−	22.3639i	0.824905	−	0.824905i
$736$	−8.88424	+	39.9305i	−0.327478	+	1.47186i
$737$	37.1106			1.36699
$738$	−14.5740	+	71.5780i	−0.536478	+	2.63482i
$739$	−49.3563			−1.81560			−0.907800	−	0.419404i	$-0.862239\pi$
$739$	−49.3563			−1.81560			−0.907800	+	0.419404i	$0.862239\pi$
$740$	0.0671560	−	12.1653i	0.00246870	−	0.447207i
$741$	27.7989			1.02122
$742$	−0.724405	+	3.55780i	−0.0265938	+	0.130611i
$743$	26.9933			0.990288			0.495144	−	0.868811i	$-0.335115\pi$
$743$	26.9933			0.990288			0.495144	+	0.868811i	$0.335115\pi$
$744$	−47.7539	+	8.82813i	−1.75074	+	0.323655i
$745$	−1.24691	+	1.24691i	−0.0456832	+	0.0456832i
$746$	8.20769	−	40.3107i	0.300505	−	1.47588i
$747$			105.012i			3.84219i
$748$	−19.3197	+	7.79883i	−0.706398	+	0.285153i
$749$	31.3593			1.14585
$750$	−2.36555	−	3.57513i	−0.0863776	−	0.130545i
$751$	36.7133			1.33969			0.669843	−	0.742503i	$-0.266361\pi$
$751$	36.7133			1.33969			0.669843	+	0.742503i	$0.266361\pi$
$752$	−21.6458	+	20.8776i	−0.789340	+	0.761329i
$753$	34.1199	−	34.1199i	1.24340	−	1.24340i
$754$	1.04631	+	0.213040i	0.0381043	+	0.00775845i
$755$	−0.567364	+	0.567364i	−0.0206485	+	0.0206485i
$756$	31.5611	−	74.2905i	1.14787	−	2.70192i
$757$	22.6178	−	22.6178i	0.822056	−	0.822056i	−0.164346	−	0.986403i	$-0.552551\pi$
$757$	22.6178	−	22.6178i	0.822056	−	0.822056i	0.986403	+	0.164346i	$0.0525515\pi$
$758$	−3.50026	+	17.1910i	−0.127135	+	0.624403i
$759$	−39.7678	−	39.7678i	−1.44348	−	1.44348i
$760$	11.0026	+	7.56929i	0.399107	+	0.274567i
$761$		−	8.69822i		−	0.315310i	−0.987494	−	0.157655i	$-0.949607\pi$
$761$		−	8.69822i		−	0.315310i	0.987494	−	0.157655i	$-0.0503934\pi$
$762$	−13.4045	+	65.8341i	−0.485595	+	2.38492i
$763$	−24.4233	−	24.4233i	−0.884181	−	0.884181i
$764$	−15.0275	−	37.2269i	−0.543675	−	1.34682i
$765$		−	25.1277i		−	0.908493i
$766$	−3.25403	−	4.91793i	−0.117573	−	0.177692i
$767$	18.4034			0.664510
$768$	−1.75163	+	48.4689i	−0.0632066	+	1.74897i
$769$	−10.1716	−	10.1716i	−0.366797	−	0.366797i	0.499510	−	0.866308i	$-0.333513\pi$
$769$	−10.1716	−	10.1716i	−0.366797	−	0.366797i	−0.866308	+	0.499510i	$0.833513\pi$
$770$	−8.35981	−	12.6345i	−0.301267	−	0.455315i
$771$	9.95641	−	9.95641i	0.358571	−	0.358571i
$772$	−12.3889	+	5.00107i	−0.445888	+	0.179993i
$773$	17.9842			0.646846			0.323423	−	0.946255i	$-0.395166\pi$
$773$	17.9842			0.646846			0.323423	+	0.946255i	$0.395166\pi$
$774$	27.0145	+	40.8280i	0.971017	+	1.46753i
$775$	−4.00516	−	4.00516i	−0.143869	−	0.143869i
$776$	30.5551	−	5.64863i	1.09686	−	0.202774i
$777$	71.2304	+	29.2121i	2.55538	+	1.04798i
$778$	29.7854	−	19.7080i	1.06786	−	0.706566i
$779$	27.8654	−	27.8654i	0.998382	−	0.998382i
$780$	−4.60418	+	10.8376i	−0.164856	+	0.388048i
$781$			19.4956i			0.697609i
$782$	−40.6882	−	8.28456i	−1.45501	−	0.296255i
$783$	−2.65695	−	2.65695i	−0.0949518	−	0.0949518i
$784$	−28.9730	−	30.0390i	−1.03475	−	1.07282i
$785$	−1.87292	+	1.87292i	−0.0668472	+	0.0668472i
$786$	45.5720	−	30.1535i	1.62550	−	1.07554i
$787$		−	21.8710i		−	0.779618i	−0.920896	−	0.389809i	$-0.872541\pi$
$787$		−	21.8710i		−	0.779618i	0.920896	−	0.389809i	$-0.127459\pi$
$788$	−14.6807	−	6.23687i	−0.522979	−	0.222179i
$789$	34.1583			1.21607
$790$	2.81091	+	0.572332i	0.100008	+	0.0203627i
$791$	−9.43636	+	9.43636i	−0.335518	+	0.335518i
$792$	−36.9998	−	25.4541i	−1.31473	−	0.904473i
$793$	6.97823			0.247804
$794$	0.900161	−	4.42099i	0.0319455	−	0.156895i
$795$	−1.31797	+	1.31797i	−0.0467435	+	0.0467435i
$796$	−35.5243	+	14.3402i	−1.25913	+	0.508274i
$797$	−22.8746	−	22.8746i	−0.810261	−	0.810261i	0.174412	−	0.984673i	$-0.444198\pi$
$797$	−22.8746	−	22.8746i	−0.810261	−	0.810261i	−0.984673	+	0.174412i	$0.944198\pi$
$798$	−70.4823	+	46.6358i	−2.49505	+	1.65089i
$799$	−21.5855	−	21.5855i	−0.763640	−	0.763640i
$800$	−4.77325	+	3.03580i	−0.168760	+	0.107332i
$801$	20.6602	+	20.6602i	0.729992	+	0.729992i
$802$	14.7932	+	22.3574i	0.522365	+	0.789468i
$803$		−	24.1182i		−	0.851112i
$804$	80.7099	+	34.2883i	2.84642	+	1.20925i
$805$		−	30.1936i		−	1.06419i
$806$	−3.10410	+	15.2453i	−0.109337	+	0.536992i
$807$	24.7309			0.870568
$808$	−0.851207	+	1.23730i	−0.0299454	+	0.0435282i
$809$	8.18910	+	8.18910i	0.287914	+	0.287914i	0.836255	−	0.548341i	$-0.184740\pi$
$809$	8.18910	+	8.18910i	0.287914	+	0.287914i	−0.548341	+	0.836255i	$0.684740\pi$
$810$	12.6596	−	8.37645i	0.444814	−	0.294318i
$811$		−	6.34968i		−	0.222968i	−0.993766	−	0.111484i	$-0.964440\pi$
$811$		−	6.34968i		−	0.222968i	0.993766	−	0.111484i	$-0.0355603\pi$
$812$	−3.01025	+	1.21516i	−0.105639	+	0.0426436i
$813$		−	48.4396i		−	1.69885i
$814$	12.2802	−	18.3387i	0.430420	−	0.642771i
$815$			17.2966i			0.605873i
$816$	−49.2231	−	0.889155i	−1.72315	−	0.0311266i
$817$		−	26.4112i		−	0.924010i
$818$	−7.38260	−	11.1576i	−0.258126	−	0.390115i
$819$	−35.4882	−	35.4882i	−1.24006	−	1.24006i
$820$	6.24834	+	15.4787i	0.218201	+	0.540541i
$821$	−8.05259			−0.281037			−0.140519	−	0.990078i	$-0.544877\pi$
$821$	−8.05259			−0.281037			−0.140519	+	0.990078i	$0.544877\pi$
$822$	75.0034	+	15.2715i	2.61605	+	0.532655i
$823$			35.7076i			1.24469i	0.782744	+	0.622344i	$0.213819\pi$
$823$			35.7076i			1.24469i	−0.782744	+	0.622344i	$0.786181\pi$
$824$	30.5331	−	5.64457i	1.06367	−	0.196638i
$825$		−	7.77723i		−	0.270768i
$826$	−46.6608	+	30.8739i	−1.62354	+	1.07424i
$827$	15.5652	+	15.5652i	0.541257	+	0.541257i	0.923897	−	0.382641i	$-0.124985\pi$
$827$	15.5652	+	15.5652i	0.541257	+	0.541257i	−0.382641	+	0.923897i	$0.624985\pi$
$828$	−33.5041	−	82.9983i	−1.16435	−	2.88439i
$829$	−7.55467	−	7.55467i	−0.262385	−	0.262385i	0.563638	−	0.826022i	$-0.309401\pi$
$829$	−7.55467	−	7.55467i	−0.262385	−	0.262385i	−0.826022	+	0.563638i	$0.809401\pi$
$830$	13.2417	+	20.0127i	0.459627	+	0.694650i
$831$	26.9529	+	26.9529i	0.934985	+	0.934985i
$832$	14.1889	+	6.33284i	0.491913	+	0.219552i
$833$	29.9553	−	29.9553i	1.03789	−	1.03789i
$834$	85.0582	+	17.3188i	2.94533	+	0.599700i
$835$	8.35278			0.289060
$836$	9.06922	+	22.4668i	0.313666	+	0.777030i
$837$	38.7132	−	38.7132i	1.33812	−	1.33812i
$838$	−9.21273	+	45.2468i	−0.318249	+	1.56302i
$839$	21.9712			0.758530			0.379265	−	0.925288i	$-0.376177\pi$
$839$	21.9712			0.758530			0.379265	+	0.925288i	$0.376177\pi$
$840$	−6.50771	−	35.2021i	−0.224537	−	1.21459i
$841$		−	28.8489i		−	0.994789i
$842$	18.8367	+	28.4686i	0.649157	+	0.981094i
$843$	65.2607	−	65.2607i	2.24770	−	2.24770i
$844$	−6.16856	+	14.5199i	−0.212331	+	0.499797i
$845$	−6.52493	−	6.52493i	−0.224464	−	0.224464i
$846$	13.1286	−	64.4788i	0.451370	−	2.21683i
$847$			18.4443i			0.633755i
$848$	1.70746	+	1.77028i	0.0586344	+	0.0607917i
$849$	55.9037	−	55.9037i	1.91861	−	1.91861i
$850$	−3.16853	−	4.78871i	−0.108680	−	0.164251i
$851$	40.5791	−	16.9756i	1.39103	−	0.581915i
$852$	−18.0130	+	42.4000i	−0.617114	+	1.45260i
$853$	−0.443551	−	0.443551i	−0.0151869	−	0.0151869i	0.699473	−	0.714659i	$-0.253418\pi$
$853$	−0.443551	−	0.443551i	−0.0151869	−	0.0151869i	−0.714659	+	0.699473i	$0.753418\pi$
$854$	−17.6929	+	11.7068i	−0.605438	+	0.400598i
$855$	−29.2209			−0.999332
$856$	12.0402	−	17.5015i	0.411526	−	0.598189i
$857$	−2.98933	+	2.98933i	−0.102114	+	0.102114i	−0.756318	−	0.654204i	$-0.773004\pi$
$857$	−2.98933	+	2.98933i	−0.102114	+	0.102114i	0.654204	+	0.756318i	$0.273004\pi$
$858$	−17.8154	+	11.7879i	−0.608209	+	0.402432i
$859$	19.3397	+	19.3397i	0.659861	+	0.659861i	0.955347	−	0.295486i	$-0.0954817\pi$
$859$	19.3397	+	19.3397i	0.659861	+	0.659861i	−0.295486	+	0.955347i	$0.595482\pi$
$860$	10.2966	+	4.37435i	0.351111	+	0.149164i
$861$	−105.635			−3.60003
$862$	20.8439	−	13.7917i	0.709945	−	0.469747i
$863$		−	43.8788i		−	1.49365i	−0.665020	−	0.746825i	$-0.731577\pi$
$863$		−	43.8788i		−	1.49365i	0.665020	−	0.746825i	$-0.268423\pi$
$864$	−29.3435	−	46.1375i	−0.998287	−	1.56963i
$865$	−2.80391	−	2.80391i	−0.0953358	−	0.0953358i
$866$	−19.2880	−	3.92724i	−0.655432	−	0.133453i
$867$			1.55911i			0.0529503i
$868$	−17.7054	−	43.8609i	−0.600962	−	1.48874i
$869$	3.67990	+	3.67990i	0.124832	+	0.124832i
$870$	−1.63298	−	0.332492i	−0.0553632	−	0.0112725i
$871$	19.8651	−	19.8651i	0.673104	−	0.673104i
$872$	−23.0077	+	4.25336i	−0.779138	+	0.144037i
$873$	−48.0750	+	48.0750i	−1.62709	+	1.62709i
$874$	−9.63408	+	47.3162i	−0.325878	+	1.60049i
$875$	2.95243	−	2.95243i	0.0998102	−	0.0998102i
$876$	22.2840	−	52.4534i	0.752906	−	1.77224i
$877$	−25.0522			−0.845952			−0.422976	−	0.906141i	$-0.639015\pi$
$877$	−25.0522			−0.845952			−0.422976	+	0.906141i	$0.639015\pi$
$878$	10.6405	−	7.04049i	0.359100	−	0.237605i
$879$	27.6062			0.931135
$880$	−10.2609	−	0.185351i	−0.345896	−	0.00624819i
$881$			36.6929i			1.23621i	0.786094	+	0.618107i	$0.212100\pi$
$881$			36.6929i			1.23621i	−0.786094	+	0.618107i	$0.787900\pi$
$882$	89.4806	+	18.2192i	3.01297	+	0.613473i
$883$	−9.25331	+	9.25331i	−0.311399	+	0.311399i	−0.845451	−	0.534053i	$-0.820668\pi$
$883$	−9.25331	+	9.25331i	−0.311399	+	0.311399i	0.534053	+	0.845451i	$0.320668\pi$
$884$	−6.16707	+	14.5164i	−0.207421	+	0.488240i
$885$	−28.7223			−0.965490
$886$	−14.9450	−	3.04296i	−0.502086	−	0.102230i
$887$	6.08915			0.204454			0.102227	−	0.994761i	$-0.467403\pi$
$887$	6.08915			0.204454			0.102227	+	0.994761i	$0.467403\pi$
$888$	43.6516	−	28.5376i	1.46485	−	0.957659i
$889$	−65.4370			−2.19469
$890$	6.54252	+	1.33213i	0.219306	+	0.0446530i
$891$	27.5393			0.922602
$892$	−15.6853	+	36.9211i	−0.525184	+	1.23621i
$893$	−25.1017	+	25.1017i	−0.839996	+	0.839996i
$894$	−7.40749	−	1.50824i	−0.247743	−	0.0504432i
$895$		−	21.4592i		−	0.717303i
$896$	−46.5992	+	7.74703i	−1.55677	+	0.258810i
$897$	−42.5750			−1.42154
$898$	−8.44793	+	5.58971i	−0.281911	+	0.186531i
$899$	−2.20188			−0.0734369
$900$	4.83970	−	11.3920i	0.161323	−	0.379732i
$901$	−1.76535	+	1.76535i	−0.0588124	+	0.0588124i
$902$	−6.04198	+	29.6742i	−0.201176	+	0.988042i
$903$	−50.0610	+	50.0610i	−1.66593	+	1.66593i
$904$	1.64336	+	8.88942i	0.0546574	+	0.295658i
$905$	0.226355	−	0.226355i	0.00752431	−	0.00752431i
$906$	−3.37053	−	0.686276i	−0.111978	−	0.0228000i
$907$	−6.34639	−	6.34639i	−0.210728	−	0.210728i	0.593848	−	0.804577i	$-0.297608\pi$
$907$	−6.34639	−	6.34639i	−0.210728	−	0.210728i	−0.804577	+	0.593848i	$0.797608\pi$
$908$	9.71062	+	24.0557i	0.322258	+	0.798316i
$909$		−	3.28604i		−	0.108991i
$910$	−11.2381	−	2.28821i	−0.372541	−	0.0758533i
$911$	−6.06994	−	6.06994i	−0.201106	−	0.201106i	0.599368	−	0.800474i	$-0.295419\pi$
$911$	−6.06994	−	6.06994i	−0.201106	−	0.201106i	−0.800474	+	0.599368i	$0.795419\pi$
$912$	−1.03399	+	57.2414i	−0.0342390	+	1.89545i
$913$			43.5349i			1.44080i
$914$	3.79006	−	2.50776i	0.125364	−	0.0829493i
$915$	−10.8910			−0.360044
$916$	−53.4739	−	22.7175i	−1.76683	−	0.750609i
$917$	37.6344	+	37.6344i	1.24280	+	1.24280i
$918$	46.2869	−	30.6265i	1.52770	−	1.01083i
$919$	−5.26338	+	5.26338i	−0.173623	+	0.173623i	−0.788569	−	0.614946i	$-0.789178\pi$
$919$	−5.26338	+	5.26338i	−0.173623	+	0.173623i	0.614946	+	0.788569i	$0.289178\pi$
$920$	−16.8509	−	11.5926i	−0.555558	−	0.382198i
$921$	−2.91699			−0.0961180
$922$	31.3542	−	20.7461i	1.03260	−	0.683235i
$923$	10.4359	+	10.4359i	0.343502	+	0.343502i
$924$	25.3944	−	59.7749i	0.835414	−	1.96645i
$925$	5.62788	+	2.30803i	0.185043	+	0.0758875i
$926$	−8.51806	−	12.8736i	−0.279921	−	0.423054i
$927$	−48.0405	+	48.0405i	−1.57786	+	1.57786i
$928$	−0.477594	+	2.14656i	−0.0156778	+	0.0704642i
$929$		−	11.5385i		−	0.378566i	−0.981923	−	0.189283i	$-0.939384\pi$
$929$		−	11.5385i		−	0.378566i	0.981923	−	0.189283i	$-0.0606163\pi$
$930$	4.84458	−	23.7934i	0.158860	−	0.780215i
$931$	−34.8349	−	34.8349i	−1.14167	−	1.14167i
$932$	21.8521	−	51.4369i	0.715790	−	1.68487i
$933$	48.6269	−	48.6269i	1.59197	−	1.59197i
$934$	−16.2348	−	24.5362i	−0.531218	−	0.802848i
$935$		−	10.4172i		−	0.340679i
$936$	−33.4313	+	6.18034i	−1.09274	+	0.202011i
$937$	−43.7482			−1.42919			−0.714596	−	0.699538i	$-0.753389\pi$
$937$	−43.7482			−1.42919			−0.714596	+	0.699538i	$0.753389\pi$
$938$	−17.0407	+	83.6928i	−0.556400	+	2.73267i
$939$	−4.16897	+	4.16897i	−0.136049	+	0.136049i
$940$	−5.62862	−	13.9435i	−0.183585	−	0.454788i
$941$	−42.8376			−1.39647			−0.698234	−	0.715870i	$-0.746030\pi$
$941$	−42.8376			−1.39647			−0.698234	+	0.715870i	$0.746030\pi$
$942$	−11.1264	−	2.26545i	−0.362517	−	0.0738124i
$943$	−42.6769	+	42.6769i	−1.38975	+	1.38975i
$944$	−0.684526	+	37.8950i	−0.0222794	+	1.23338i
$945$	28.5377	+	28.5377i	0.928331	+	0.928331i
$946$	11.1994	+	16.9261i	0.364125	+	0.550315i
$947$	−15.6521	−	15.6521i	−0.508626	−	0.508626i	0.405479	−	0.914104i	$-0.367105\pi$
$947$	−15.6521	−	15.6521i	−0.508626	−	0.508626i	−0.914104	+	0.405479i	$0.867105\pi$
$948$	4.60319	+	11.4033i	0.149505	+	0.370361i
$949$	−12.9103	−	12.9103i	−0.419088	−	0.419088i
$950$	−5.56877	+	3.68467i	−0.180675	+	0.119546i
$951$			21.5242i			0.697969i
$952$	−8.71675	−	47.1514i	−0.282511	−	1.52819i
$953$		−	54.9512i		−	1.78004i	−0.455917	−	0.890022i	$-0.650689\pi$
$953$		−	54.9512i		−	1.78004i	0.455917	−	0.890022i	$-0.349311\pi$
$954$	−5.27334	−	1.07371i	−0.170731	−	0.0347626i
$955$	20.0728			0.649541
$956$	8.43488	+	20.8954i	0.272804	+	0.675805i
$957$	−2.13781	−	2.13781i	−0.0691056	−	0.0691056i
$958$	−19.9685	−	30.1791i	−0.645152	−	0.975041i
$959$			74.5511i			2.40738i
$960$	−22.1447	−	9.88370i	−0.714718	−	0.318995i
$961$		−	1.08256i		−	0.0349214i
$962$	−3.24309	−	16.3901i	−0.104561	−	0.528439i
$963$			46.4806i			1.49782i
$964$	−0.0196887	+	0.00794780i	−0.000634131	+	0.000255981i
$965$		−	6.68013i		−	0.215041i
$966$	107.946	−	71.4244i	3.47311	−	2.29804i
$967$	−36.1626	−	36.1626i	−1.16291	−	1.16291i	−0.983836	−	0.179074i	$-0.942690\pi$
$967$	−36.1626	−	36.1626i	−1.16291	−	1.16291i	−0.179074	−	0.983836i	$-0.557310\pi$
$968$	10.2937	+	7.08158i	0.330852	+	0.227611i
$969$	−58.1131			−1.86686
$970$	−3.09978	+	15.2240i	−0.0995279	+	0.488814i
$971$		−	44.3938i		−	1.42467i	−0.701842	−	0.712333i	$-0.747639\pi$
$971$		−	44.3938i		−	1.42467i	0.701842	−	0.712333i	$-0.252361\pi$
$972$	6.51601	+	2.76822i	0.209001	+	0.0887907i
$973$			84.5453i			2.71040i
$974$	3.23270	+	4.88569i	0.103582	+	0.156547i
$975$	−4.16311	−	4.16311i	−0.133326	−	0.133326i
$976$	−0.259559	+	14.3691i	−0.00830829	+	0.459942i
$977$	10.9626	+	10.9626i	0.350723	+	0.350723i	0.860379	−	0.509655i	$-0.170227\pi$
$977$	10.9626	+	10.9626i	0.350723	+	0.350723i	−0.509655	+	0.860379i	$0.670227\pi$
$978$	−61.8376	+	40.9159i	−1.97735	+	1.30835i
$979$	8.56512	+	8.56512i	0.273742	+	0.273742i
$980$	19.3502	−	7.81113i	0.618119	−	0.249517i
$981$	36.2000	−	36.2000i	1.15578	−	1.15578i
$982$	−0.628455	+	3.08655i	−0.0200548	+	0.0984958i
$983$	13.4505			0.429003			0.214502	−	0.976724i	$-0.431187\pi$
$983$	13.4505			0.429003			0.214502	+	0.976724i	$0.431187\pi$
$984$	−40.5578	+	58.9543i	−1.29294	+	1.87939i
$985$	5.63940	−	5.63940i	0.179686	−	0.179686i
$986$	−2.18729	−	0.445356i	−0.0696576	−	0.0141830i
$987$	95.1579			3.02891
$988$	16.8811	+	7.17166i	0.537059	+	0.228161i
$989$			40.4497i			1.28623i
$990$	18.7267	−	12.3909i	0.595175	−	0.393807i
$991$	−19.3589	+	19.3589i	−0.614955	+	0.614955i	−0.944233	−	0.329278i	$-0.893195\pi$
$991$	−19.3589	+	19.3589i	−0.614955	+	0.614955i	0.329278	+	0.944233i	$0.393195\pi$
$992$	−31.2765	−	6.95879i	−0.993029	−	0.220942i
$993$	70.5041	+	70.5041i	2.23738	+	2.23738i
$994$	−43.9671	−	8.95217i	−1.39455	−	0.283946i
$995$		−	19.1547i		−	0.607246i
$996$	−40.2241	+	94.6819i	−1.27455	+	3.00011i
$997$	−31.4511	+	31.4511i	−0.996066	+	0.996066i	−0.999992	−	0.00392580i	$-0.998750\pi$
$997$	−31.4511	+	31.4511i	−0.996066	+	0.996066i	0.00392580	+	0.999992i	$0.498750\pi$
$998$	−16.2423	+	10.7470i	−0.514140	+	0.340190i
$999$	−22.3090	+	54.3982i	−0.705827	+	1.72108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.u.a.31.7	✓	152
4.3	odd	2	inner	740.2.u.a.31.32	yes	152
37.6	odd	4	inner	740.2.u.a.191.32	yes	152
148.43	even	4	inner	740.2.u.a.191.7	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.7	✓	152	1.1	even	1	trivial
740.2.u.a.31.32	yes	152	4.3	odd	2	inner
740.2.u.a.191.7	yes	152	148.43	even	4	inner
740.2.u.a.191.32	yes	152	37.6	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38578 - 0.282160i) q^{2} +3.03129 q^{3} +(1.84077 + 0.782022i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-4.20069 - 0.855307i) q^{6} -4.17536i q^{7} +(-2.33025 - 1.60310i) q^{8} +6.18869 q^{9} +(1.17941 - 0.780377i) q^{10} +2.56565 q^{11} +(5.57991 + 2.37053i) q^{12} +(1.37338 - 1.37338i) q^{13} +(-1.17812 + 5.78613i) q^{14} +(-2.14344 + 2.14344i) q^{15} +(2.77688 + 2.87905i) q^{16} +(-2.87103 + 2.87103i) q^{17} +(-8.57617 - 1.74620i) q^{18} +(3.33871 + 3.33871i) q^{19} +(-1.85460 + 0.748649i) q^{20} -12.6567i q^{21} +(-3.55543 - 0.723924i) q^{22} +(-5.11336 - 5.11336i) q^{23} +(-7.06365 - 4.85946i) q^{24} -1.00000i q^{25} +(-2.29072 + 1.51569i) q^{26} +9.66584 q^{27} +(3.26523 - 7.68589i) q^{28} +(-0.274881 - 0.274881i) q^{29} +(3.57513 - 2.36555i) q^{30} +(4.00516 - 4.00516i) q^{31} +(-3.03580 - 4.77325i) q^{32} +7.77723 q^{33} +(4.78871 - 3.16853i) q^{34} +(2.95243 + 2.95243i) q^{35} +(11.3920 + 4.83970i) q^{36} +(-2.30803 + 5.62788i) q^{37} +(-3.68467 - 5.56877i) q^{38} +(4.16311 - 4.16311i) q^{39} +(2.78130 - 0.514171i) q^{40} -8.34615i q^{41} +(-3.57121 + 17.5394i) q^{42} +(-3.95530 - 3.95530i) q^{43} +(4.72278 + 2.00640i) q^{44} +(-4.37607 + 4.37607i) q^{45} +(5.64321 + 8.52877i) q^{46} +7.51837i q^{47} +(8.41752 + 8.72722i) q^{48} -10.4336 q^{49} +(-0.282160 + 1.38578i) q^{50} +(-8.70292 + 8.70292i) q^{51} +(3.60210 - 1.45407i) q^{52} +0.614883 q^{53} +(-13.3947 - 2.72731i) q^{54} +(-1.81419 + 1.81419i) q^{55} +(-6.69353 + 9.72963i) q^{56} +(10.1206 + 10.1206i) q^{57} +(0.303364 + 0.458485i) q^{58} +(6.70004 + 6.70004i) q^{59} +(-5.62181 + 2.26937i) q^{60} +(2.54053 + 2.54053i) q^{61} +(-6.68036 + 4.42017i) q^{62} -25.8400i q^{63} +(2.86013 + 7.47126i) q^{64} +1.94226i q^{65} +(-10.7775 - 2.19442i) q^{66} +14.4644 q^{67} +(-7.53013 + 3.03970i) q^{68} +(-15.5001 - 15.5001i) q^{69} +(-3.25836 - 4.92447i) q^{70} +7.59870i q^{71} +(-14.4212 - 9.92111i) q^{72} -9.40041i q^{73} +(4.78638 - 7.14777i) q^{74} -3.03129i q^{75} +(3.53486 + 8.75675i) q^{76} -10.7125i q^{77} +(-6.94382 + 4.59450i) q^{78} +(1.43429 + 1.43429i) q^{79} +(-3.99935 - 0.0722433i) q^{80} +10.7338 q^{81} +(-2.35495 + 11.5659i) q^{82} +16.9684i q^{83} +(9.89783 - 23.2981i) q^{84} -4.06025i q^{85} +(4.36514 + 6.59719i) q^{86} +(-0.833243 - 0.833243i) q^{87} +(-5.97861 - 4.11300i) q^{88} +(3.33838 + 3.33838i) q^{89} +(7.29901 - 4.82952i) q^{90} +(-5.73436 - 5.73436i) q^{91} +(-5.41377 - 13.4113i) q^{92} +(12.1408 - 12.1408i) q^{93} +(2.12138 - 10.4188i) q^{94} -4.72165 q^{95} +(-9.20236 - 14.4691i) q^{96} +(-7.76820 + 7.76820i) q^{97} +(14.4587 + 2.94395i) q^{98} +15.8780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) \) 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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