LMFDB - Embedded newform 740.2.u.a.191.32

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			191.32
Character	$\chi$	$=$	740.191
Dual form			740.2.u.a.31.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.282160 + 1.38578i) q^{2} -3.03129 q^{3} +(-1.84077 - 0.782022i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.855307 - 4.20069i) q^{6} -4.17536i q^{7} +(1.60310 - 2.33025i) 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} +(5.78613 + 1.17812i) q^{14} +(2.14344 + 2.14344i) q^{15} +(2.77688 + 2.87905i) q^{16} +(-2.87103 - 2.87103i) q^{17} +(-1.74620 + 8.57617i) q^{18} +(-3.33871 + 3.33871i) q^{19} +(0.748649 + 1.85460i) q^{20} +12.6567i q^{21} +(0.723924 - 3.55543i) q^{22} +(5.11336 - 5.11336i) q^{23} +(-4.85946 + 7.06365i) 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} +(-4.77325 + 3.03580i) 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} +(-17.5394 - 3.57121i) 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} +(-1.38578 - 0.282160i) q^{50} +(8.70292 + 8.70292i) q^{51} +(-1.45407 - 3.60210i) q^{52} +0.614883 q^{53} +(2.72731 - 13.3947i) q^{54} +(1.81419 + 1.81419i) q^{55} +(-9.72963 - 6.69353i) q^{56} +(10.1206 - 10.1206i) q^{57} +(-0.303364 - 0.458485i) q^{58} +(-6.70004 + 6.70004i) q^{59} +(-2.26937 - 5.62181i) 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} +(-2.19442 + 10.7775i) q^{66} -14.4644 q^{67} +(3.03970 + 7.53013i) q^{68} +(-15.5001 + 15.5001i) q^{69} +(-3.25836 - 4.92447i) q^{70} +7.59870i q^{71} +(9.92111 - 14.4212i) q^{72} +9.40041i q^{73} +(8.45023 - 1.61046i) q^{74} -3.03129i q^{75} +(8.75675 - 3.53486i) q^{76} +10.7125i q^{77} +(6.94382 - 4.59450i) q^{78} +(-1.43429 + 1.43429i) q^{79} +(0.0722433 - 3.99935i) q^{80} +10.7338 q^{81} +(-11.5659 - 2.35495i) 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} +(-4.11300 + 5.97861i) q^{88} +(3.33838 - 3.33838i) q^{89} +(7.29901 - 4.82952i) q^{90} +(5.73436 - 5.73436i) q^{91} +(-13.4113 + 5.41377i) q^{92} +(12.1408 + 12.1408i) q^{93} +(-10.4188 - 2.12138i) q^{94} +4.72165 q^{95} +(14.4691 - 9.20236i) q^{96} +(-7.76820 - 7.76820i) q^{97} +(2.94395 - 14.4587i) 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 $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.282160	+	1.38578i	−0.199517	+	0.979894i
$2$	−0.282160	+	1.38578i	−0.199517	+	0.979894i
$3$	−3.03129			−1.75011			−0.875057	−	0.484020i	$-0.839176\pi$
$3$	−3.03129			−1.75011			−0.875057	+	0.484020i	$0.839176\pi$
$4$	−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
$6$	0.855307	−	4.20069i	0.349177	−	1.71493i
$7$		−	4.17536i		−	1.57814i	−0.614305	−	0.789069i	$-0.710563\pi$
$7$		−	4.17536i		−	1.57814i	0.614305	−	0.789069i	$-0.289437\pi$
$8$	1.60310	−	2.33025i	0.566782	−	0.823868i
$9$	6.18869			2.06290
$10$	1.17941	−	0.780377i	0.372963	−	0.246777i
$11$	−2.56565			−0.773574			−0.386787	−	0.922169i	$-0.626415\pi$
$11$	−2.56565			−0.773574			−0.386787	+	0.922169i	$0.626415\pi$
$12$	5.57991	+	2.37053i	1.61078	+	0.684314i
$13$	1.37338	+	1.37338i	0.380908	+	0.380908i	0.871429	−	0.490521i	$-0.163194\pi$
$13$	1.37338	+	1.37338i	0.380908	+	0.380908i	−0.490521	+	0.871429i	$0.663194\pi$
$14$	5.78613	+	1.17812i	1.54641	+	0.314865i
$15$	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	0.267289	−	0.963616i	$-0.413872\pi$
$17$	−2.87103	−	2.87103i	−0.696328	−	0.696328i	−0.963616	+	0.267289i	$0.913872\pi$
$18$	−1.74620	+	8.57617i	−0.411583	+	2.02142i
$19$	−3.33871	+	3.33871i	−0.765953	+	0.765953i	−0.977391	−	0.211438i	$-0.932185\pi$
$19$	−3.33871	+	3.33871i	−0.765953	+	0.765953i	0.211438	+	0.977391i	$0.432185\pi$
$20$	0.748649	+	1.85460i	0.167403	+	0.414700i
$21$			12.6567i			2.76192i
$22$	0.723924	−	3.55543i	0.154341	−	0.758020i
$23$	5.11336	−	5.11336i	1.06621	−	1.06621i	0.0685622	−	0.997647i	$-0.478159\pi$
$23$	5.11336	−	5.11336i	1.06621	−	1.06621i	0.997647	−	0.0685622i	$-0.0218411\pi$
$24$	−4.85946	+	7.06365i	−0.991933	+	1.44186i
$25$			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	−0.732168	−	0.681124i	$-0.761491\pi$
$29$	−0.274881	+	0.274881i	−0.0510441	+	0.0510441i	0.681124	+	0.732168i	$0.261491\pi$
$30$	−3.57513	+	2.36555i	−0.652727	+	0.431888i
$31$	−4.00516	−	4.00516i	−0.719347	−	0.719347i	0.249124	−	0.968472i	$-0.419857\pi$
$31$	−4.00516	−	4.00516i	−0.719347	−	0.719347i	−0.968472	+	0.249124i	$0.919857\pi$
$32$	−4.77325	+	3.03580i	−0.843800	+	0.536658i
$33$	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	$0.225954\pi$
$41$			8.34615i			1.30345i	−0.758455	+	0.651725i	$0.774046\pi$
$42$	−17.5394	−	3.57121i	−2.70639	−	0.551050i
$43$	3.95530	−	3.95530i	0.603177	−	0.603177i	−0.337977	−	0.941154i	$-0.609743\pi$
$43$	3.95530	−	3.95530i	0.603177	−	0.603177i	0.941154	+	0.337977i	$0.109743\pi$
$44$	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
$50$	−1.38578	−	0.282160i	−0.195979	−	0.0399034i
$51$	8.70292	+	8.70292i	1.21865	+	1.21865i
$52$	−1.45407	−	3.60210i	−0.201643	−	0.499521i
$53$	0.614883			0.0844607			0.0422304	−	0.999108i	$-0.486554\pi$
$53$	0.614883			0.0844607			0.0422304	+	0.999108i	$0.486554\pi$
$54$	2.72731	−	13.3947i	0.371140	−	1.82279i
$55$	1.81419	+	1.81419i	0.244625	+	0.244625i
$56$	−9.72963	−	6.69353i	−1.30018	−	0.894461i
$57$	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	$-0.961567\pi$
$59$	−6.70004	+	6.70004i	−0.872271	+	0.872271i	0.120448	+	0.992720i	$0.461567\pi$
$60$	−2.26937	−	5.62181i	−0.292974	−	0.725772i
$61$	2.54053	−	2.54053i	0.325281	−	0.325281i	−0.525508	−	0.850789i	$-0.676125\pi$
$61$	2.54053	−	2.54053i	0.325281	−	0.325281i	0.850789	+	0.525508i	$0.176125\pi$
$62$	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
$66$	−2.19442	+	10.7775i	−0.270114	+	1.32662i
$67$	−14.4644			−1.76710			−0.883552	−	0.468332i	$-0.844855\pi$
$67$	−14.4644			−1.76710			−0.883552	+	0.468332i	$0.844855\pi$
$68$	3.03970	+	7.53013i	0.368618	+	0.913162i
$69$	−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	$0.851103\pi$
$72$	9.92111	−	14.4212i	1.16921	−	1.69955i
$73$			9.40041i			1.10023i	0.835087	+	0.550117i	$0.185417\pi$
$73$			9.40041i			1.10023i	−0.835087	+	0.550117i	$0.814583\pi$
$74$	8.45023	−	1.61046i	0.982319	−	0.187212i
$75$		−	3.03129i		−	0.350023i
$76$	8.75675	−	3.53486i	1.00447	−	0.405476i
$77$			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	$-0.786400\pi$
$79$	−1.43429	+	1.43429i	−0.161371	+	0.161371i	0.621803	+	0.783174i	$0.286400\pi$
$80$	0.0722433	−	3.99935i	0.00807704	−	0.447141i
$81$	10.7338			1.19265
$82$	−11.5659	−	2.35495i	−1.27724	−	0.260060i
$83$			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
$88$	−4.11300	+	5.97861i	−0.438448	+	0.637322i
$89$	3.33838	−	3.33838i	0.353867	−	0.353867i	−0.507679	−	0.861546i	$-0.669496\pi$
$89$	3.33838	−	3.33838i	0.353867	−	0.353867i	0.861546	+	0.507679i	$0.169496\pi$
$90$	7.29901	−	4.82952i	0.769384	−	0.509076i
$91$	5.73436	−	5.73436i	0.601125	−	0.601125i
$92$	−13.4113	+	5.41377i	−1.39822	+	0.564424i
$93$	12.1408	+	12.1408i	1.25894	+	1.25894i
$94$	−10.4188	−	2.12138i	−1.07462	−	0.218804i
$95$	4.72165			0.484431
$96$	14.4691	−	9.20236i	1.47675	−	0.939212i
$97$	−7.76820	−	7.76820i	−0.788742	−	0.788742i	0.192546	−	0.981288i	$-0.438325\pi$
$97$	−7.76820	−	7.76820i	−0.788742	−	0.788742i	−0.981288	+	0.192546i	$0.938325\pi$
$98$	2.94395	−	14.4587i	0.297384	−	1.46055i
$99$	−15.8780			−1.59580
$100$	0.782022	−	1.84077i	0.0782022	−	0.184077i
$101$			0.530975i			0.0528340i	0.999651	+	0.0264170i	$0.00840977\pi$
$101$			0.530975i			0.0528340i	−0.999651	+	0.0264170i	$0.991590\pi$
$102$	−14.5159	+	9.60472i	−1.43729	+	0.951009i
$103$	7.76263	+	7.76263i	0.764874	+	0.764874i	0.977199	−	0.212325i	$-0.0681035\pi$
$103$	7.76263	+	7.76263i	0.764874	+	0.764874i	−0.212325	+	0.977199i	$0.568103\pi$
$104$	5.40199	−	0.998651i	0.529709	−	0.0979257i
$105$	8.94965	−	8.94965i	0.873396	−	0.873396i
$106$	−0.173495	+	0.852093i	−0.0168514	+	0.0827626i
$107$			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	0.929384	−	0.369115i	$-0.120339\pi$
$109$	5.84938	+	5.84938i	0.560269	+	0.560269i	−0.369115	+	0.929384i	$0.620339\pi$
$110$	−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	−0.805373	−	0.592769i	$-0.798035\pi$
$113$	−2.26001	+	2.26001i	−0.212604	+	0.212604i	0.592769	+	0.805373i	$0.298035\pi$
$114$	11.1693	+	16.8805i	1.04610	+	1.58101i
$115$	−7.23138			−0.674330
$116$	0.720956	−	0.291030i	0.0669391	−	0.0270215i
$117$	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
$124$	4.24046	+	10.5047i	0.380804	+	0.943350i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	35.8086	+	7.29101i	3.19008	+	0.649535i
$127$		−	15.6722i		−	1.39068i	−0.718680	−	0.695341i	$-0.755253\pi$
$127$		−	15.6722i		−	1.39068i	0.718680	−	0.695341i	$-0.244747\pi$
$128$	11.1605	−	1.85542i	0.986461	−	0.163997i
$129$	−11.9896	+	11.9896i	−1.05563	+	1.05563i
$130$	2.69154	+	0.548026i	0.236064	+	0.0480651i
$131$	9.01346	+	9.01346i	0.787509	+	0.787509i	0.981085	−	0.193576i	$-0.0620086\pi$
$131$	9.01346	+	9.01346i	0.787509	+	0.787509i	−0.193576	+	0.981085i	$0.562009\pi$
$132$	−14.3161	−	6.08197i	−1.24606	−	0.529367i
$133$	13.9403	+	13.9403i	1.20878	+	1.20878i
$134$	4.08126	−	20.0444i	0.352567	−	1.73158i
$135$	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	$-0.171252\pi$
$139$	20.2486			1.71746			0.858732	+	0.512424i	$0.171252\pi$
$140$	7.74360	−	3.12588i	0.654454	−	0.264185i
$141$		−	22.7903i		−	1.91929i
$142$	−10.5301	−	2.14405i	−0.883669	−	0.179924i
$143$	−3.52362	−	3.52362i	−0.294660	−	0.294660i
$144$	17.1853	+	17.8176i	1.43211	+	1.48480i
$145$	0.388740			0.0322831
$146$	−13.0269	−	2.65242i	−1.07811	−	0.219515i
$147$	31.6273			2.60858
$148$	−0.152571	+	12.1646i	−0.0125413	+	0.999921i
$149$	1.76340			0.144463			0.0722315	−	0.997388i	$-0.476988\pi$
$149$	1.76340			0.144463			0.0722315	+	0.997388i	$0.476988\pi$
$150$	4.20069	+	0.855307i	0.342985	+	0.0698355i
$151$	−0.802374			−0.0652962			−0.0326481	−	0.999467i	$-0.510394\pi$
$151$	−0.802374			−0.0652962			−0.0326481	+	0.999467i	$0.510394\pi$
$152$	2.42773	+	13.1323i	0.196915	+	1.06517i
$153$	−17.7679	−	17.7679i	−1.43645	−	1.43645i
$154$	−14.8452	−	3.02264i	−1.19626	−	0.243572i
$155$			5.66415i			0.454955i
$156$	4.40769	+	10.9190i	0.352898	+	0.874219i
$157$	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
$162$	−3.02866	+	14.8747i	−0.237954	+	1.16867i
$163$	−12.2305	−	12.2305i	−0.957969	−	0.957969i	0.0411825	−	0.999152i	$-0.486888\pi$
$163$	−12.2305	−	12.2305i	−0.957969	−	0.957969i	−0.999152	+	0.0411825i	$0.986888\pi$
$164$	6.52688	−	15.3634i	0.509664	−	1.19968i
$165$	−5.49933	−	5.49933i	−0.428122	−	0.428122i
$166$	−23.5144	−	4.78779i	−1.82507	−	0.371604i
$167$	5.90631	−	5.90631i	0.457044	−	0.457044i	−0.440640	−	0.897684i	$-0.645248\pi$
$167$	5.90631	−	5.90631i	0.457044	−	0.457044i	0.897684	+	0.440640i	$0.145248\pi$
$168$	29.4933	+	20.2900i	2.27546	+	1.56541i
$169$		−	9.22764i		−	0.709819i
$170$	−5.62662	−	1.14564i	−0.431542	−	0.0878666i
$171$	−20.6623	+	20.6623i	−1.58008	+	1.58008i
$172$	−10.3739	+	4.18767i	−0.791004	+	0.319307i
$173$		−	3.96533i		−	0.301478i	−0.988574	−	0.150739i	$-0.951835\pi$
$173$		−	3.96533i		−	0.301478i	0.988574	−	0.150739i	$-0.0481653\pi$
$174$	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	0.989479	+	0.144676i	$0.0462139\pi$
$179$	15.1740	+	15.1740i	1.13415	+	1.13415i	0.144676	+	0.989479i	$0.453786\pi$
$180$	4.63316	+	11.4775i	0.345335	+	0.855484i
$181$	−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
$190$	−1.33226	+	6.54317i	−0.0966523	+	0.474691i
$191$	14.1936	−	14.1936i	1.02701	−	1.02701i	0.0273890	−	0.999625i	$-0.491281\pi$
$191$	14.1936	−	14.1936i	1.02701	−	1.02701i	0.999625	−	0.0273890i	$-0.00871929\pi$
$192$	8.66986	+	22.6475i	0.625693	+	1.63444i
$193$	−4.72356	−	4.72356i	−0.340010	−	0.340010i	0.516361	−	0.856371i	$-0.327286\pi$
$193$	−4.72356	−	4.72356i	−0.340010	−	0.340010i	−0.856371	+	0.516361i	$0.827286\pi$
$194$	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	$0.591698\pi$
$198$	4.48014	−	22.0035i	0.318390	−	1.56372i
$199$	13.5444	+	13.5444i	0.960140	+	0.960140i	0.999235	−	0.0390952i	$-0.0124476\pi$
$199$	13.5444	+	13.5444i	0.960140	+	0.960140i	−0.0390952	+	0.999235i	$0.512448\pi$
$200$	2.33025	+	1.60310i	0.164774	+	0.113356i
$201$	43.8457			3.09263
$202$	−0.735815	−	0.149820i	−0.0517717	−	0.0105413i
$203$	1.14773	+	1.14773i	0.0805546	+	0.0805546i
$204$	−9.21421	−	22.8260i	−0.645124	−	1.59814i
$205$	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
$208$	−0.140315	+	7.76775i	−0.00972908	+	0.538597i
$209$	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
$214$	−10.4080	−	2.11918i	−0.711476	−	0.144864i
$215$	−5.59363			−0.381483
$216$	−15.4953	+	22.5238i	−1.05432	+	1.53255i
$217$	−16.7230	+	16.7230i	−1.13523	+	1.13523i
$218$	−9.75641	+	6.45549i	−0.660787	+	0.437221i
$219$		−	28.4953i		−	1.92554i
$220$	−1.92077	−	4.75825i	−0.129499	−	0.320801i
$221$		−	7.88605i		−	0.530473i
$222$	−25.6151	+	4.88177i	−1.71917	+	0.327643i
$223$			20.0574i			1.34314i	0.740940	+	0.671572i	$0.234380\pi$
$223$			20.0574i			1.34314i	−0.740940	+	0.671572i	$0.765620\pi$
$224$	12.6755	+	19.9301i	0.846920	+	1.33163i
$225$			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	$-0.891646\pi$
$227$	−9.17178	+	9.17178i	−0.608753	+	0.608753i	0.333867	+	0.942620i	$0.391646\pi$
$228$	−26.5442	+	10.7152i	−1.75793	+	0.709629i
$229$	−29.0497			−1.91966			−0.959830	−	0.280582i	$-0.909473\pi$
$229$	−29.0497			−1.91966			−0.959830	+	0.280582i	$0.909473\pi$
$230$	2.04040	−	10.0211i	0.134540	−	0.660772i
$231$		−	32.4727i		−	2.13655i
$232$	0.199879	+	1.08120i	0.0131227	+	0.0709845i
$233$			27.9431i			1.83061i	0.402758	+	0.915306i	$0.368052\pi$
$233$			27.9431i			1.83061i	−0.402758	+	0.915306i	$0.631948\pi$
$234$	−14.1766	+	9.38015i	−0.926750	+	0.613200i
$235$	5.31629	−	5.31629i	0.346797	−	0.346797i
$236$	17.5728	−	7.09367i	1.14389	−	0.461758i
$237$	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	$-0.868724\pi$
$239$	−7.96684	+	7.96684i	−0.515332	+	0.515332i	0.400824	+	0.916155i	$0.368724\pi$
$240$	−0.218990	+	12.1232i	−0.0141357	+	0.782547i
$241$	−0.00750678	−	0.00750678i	−0.000483554	−	0.000483554i	0.706865	−	0.707349i	$-0.250109\pi$
$241$	−0.00750678	−	0.00750678i	−0.000483554	−	0.000483554i	−0.707349	+	0.706865i	$0.750109\pi$
$242$	1.24642	−	6.12158i	0.0801228	−	0.393510i
$243$	−3.53982			−0.227080
$244$	−6.66328	+	2.68978i	−0.426573	+	0.172196i
$245$	7.37769	+	7.37769i	0.471344	+	0.471344i
$246$	35.0596	+	7.13852i	2.23532	+	0.455135i
$247$	−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	$-0.417541\pi$
$251$	−11.2559	−	11.2559i	−0.710468	−	0.710468i	−0.966633	+	0.256165i	$0.917541\pi$
$252$	−20.2075	+	47.5656i	−1.27295	+	2.99635i
$253$	−13.1191	+	13.1191i	−0.824791	+	0.824791i
$254$	21.7182	+	4.42206i	1.36272	+	0.277465i
$255$		−	12.3078i		−	0.770744i
$256$	−0.577852	+	15.9896i	−0.0361157	+	0.999348i
$257$	3.28455	+	3.28455i	0.204885	+	0.204885i	0.802089	−	0.597204i	$-0.203722\pi$
$257$	3.28455	+	3.28455i	0.204885	+	0.204885i	−0.597204	+	0.802089i	$0.703722\pi$
$258$	−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	$-0.612944\pi$
$263$	−11.2686			−0.694851			−0.347426	+	0.937708i	$0.612944\pi$
$264$	12.4677	−	18.1229i	0.767333	−	1.11539i
$265$	−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	$-0.161310\pi$
$272$	0.293326	−	16.2384i	0.0177855	−	0.984596i
$273$	−17.3825	+	17.3825i	−1.05204	+	1.05204i
$274$	5.03796	−	24.7431i	0.304355	−	1.49479i
$275$		−	2.56565i		−	0.154715i
$276$	40.6534	−	16.4107i	2.44705	−	0.987806i
$277$	8.89156	−	8.89156i	0.534242	−	0.534242i	−0.387590	−	0.921832i	$-0.626692\pi$
$277$	8.89156	−	8.89156i	0.534242	−	0.534242i	0.921832	+	0.387590i	$0.126692\pi$
$278$	−5.71334	+	28.0601i	−0.342663	+	1.68293i
$279$	−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	0.938187	+	0.346129i	$0.112504\pi$
$281$	21.5291	+	21.5291i	1.28432	+	1.28432i	0.346129	+	0.938187i	$0.387496\pi$
$282$	31.5824	+	6.43051i	1.88070	+	0.382931i
$283$	−18.4422	−	18.4422i	−1.09628	−	1.09628i	−0.994842	−	0.101436i	$-0.967656\pi$
$283$	−18.4422	−	18.4422i	−1.09628	−	1.09628i	−0.101436	−	0.994842i	$-0.532344\pi$
$284$	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
$288$	−29.5402	+	18.7876i	−1.74067	+	1.10707i
$289$		−	0.514341i		−	0.0302553i
$290$	−0.109687	+	0.538709i	−0.00644103	+	0.0316341i
$291$	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	$0.414291\pi$
$294$	−8.92396	+	43.8285i	−0.520456	+	2.55613i
$295$	9.47529			0.551673
$296$	−16.8144	−	3.64378i	−0.977315	−	0.211790i
$297$	24.7992			1.43900
$298$	−0.497559	+	2.44368i	−0.0288228	+	0.141559i
$299$	14.0452			0.812254
$300$	−2.37053	+	5.57991i	−0.136863	+	0.322156i
$301$	−16.5148	−	16.5148i	−0.951896	−	0.951896i
$302$	0.226397	−	1.11191i	0.0130277	−	0.0639834i
$303$		−	1.60954i		−	0.0924655i
$304$	−18.8835	−	0.341107i	−1.08304	−	0.0195639i
$305$	−3.59285			−0.205726
$306$	29.6359	−	19.6091i	1.69417	−	1.12098i
$307$	0.962294			0.0549210			0.0274605	−	0.999623i	$-0.491258\pi$
$307$	0.962294			0.0549210			0.0274605	+	0.999623i	$0.491258\pi$
$308$	8.37744	−	19.7193i	0.477349	−	1.12361i
$309$	−23.5307	−	23.5307i	−1.33862	−	1.33862i
$310$	−7.84926	−	1.59819i	−0.445808	−	0.0907713i
$311$	−16.0417	−	16.0417i	−0.909641	−	0.909641i	0.0866024	−	0.996243i	$-0.472399\pi$
$311$	−16.0417	−	16.0417i	−0.909641	−	0.909641i	−0.996243	+	0.0866024i	$0.972399\pi$
$312$	−16.3750	+	3.02720i	−0.927051	+	0.171381i
$313$	−1.37531	−	1.37531i	−0.0777374	−	0.0777374i	0.667169	−	0.744906i	$-0.267506\pi$
$313$	−1.37531	−	1.37531i	−0.0777374	−	0.0777374i	−0.744906	+	0.667169i	$0.767506\pi$
$314$	−0.747357	+	3.67052i	−0.0421758	+	0.207139i
$315$	−18.2717	+	18.2717i	−1.02949	+	1.02949i
$316$	3.76186	−	1.51856i	0.211621	−	0.0854256i
$317$		−	7.10068i		−	0.398814i	−0.979917	−	0.199407i	$-0.936098\pi$
$317$		−	7.10068i		−	0.398814i	0.979917	−	0.199407i	$-0.0639015\pi$
$318$	0.525914	−	2.58294i	0.0294918	−	0.144844i
$319$	0.705249	−	0.705249i	0.0394864	−	0.0394864i
$320$	−3.26056	+	7.30539i	−0.182271	+	0.408384i
$321$		−	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
$328$	19.4486	+	13.3797i	1.07387	+	0.738772i
$329$	31.3919			1.73069
$330$	9.17255	−	6.06917i	0.504932	−	0.334097i
$331$	−23.2588	+	23.2588i	−1.27842	+	1.27842i	−0.336869	+	0.941552i	$0.609368\pi$
$331$	−23.2588	+	23.2588i	−1.27842	+	1.27842i	−0.941552	+	0.336869i	$0.890632\pi$
$332$	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	$-0.908483\pi$
$337$		−	10.4111i		−	0.567131i	0.958953	−	0.283565i	$-0.0915173\pi$
$338$	12.7875	+	2.60367i	0.695547	+	0.141621i
$339$	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
$346$	5.49507	+	1.11885i	0.295417	+	0.0601500i
$347$	−3.15558	−	3.15558i	−0.169400	−	0.169400i	0.617315	−	0.786716i	$-0.288220\pi$
$347$	−3.15558	−	3.15558i	−0.169400	−	0.169400i	−0.786716	+	0.617315i	$0.788220\pi$
$348$	−2.18542	+	0.882195i	−0.117151	+	0.0472906i
$349$	−24.4846			−1.31063			−0.655314	−	0.755356i	$-0.727464\pi$
$349$	−24.4846			−1.31063			−0.655314	+	0.755356i	$0.727464\pi$
$350$	−1.17812	+	5.78613i	−0.0629731	+	0.309282i
$351$	−13.2749	−	13.2749i	−0.708561	−	0.708561i
$352$	12.2465	−	7.78880i	0.652741	−	0.415144i
$353$	−6.23059	+	6.23059i	−0.331621	+	0.331621i	−0.853202	−	0.521581i	$-0.825342\pi$
$353$	−6.23059	+	6.23059i	−0.331621	+	0.331621i	0.521581	+	0.853202i	$0.325342\pi$
$354$	22.4142	+	33.8754i	1.19130	+	1.80046i
$355$	5.37309	−	5.37309i	0.285174	−	0.285174i
$356$	−8.75588	+	3.53451i	−0.464061	+	0.187328i
$357$	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
$362$	0.0903235	−	0.443609i	0.00474730	−	0.0233156i
$363$	13.3905			0.702818
$364$	−15.0401	+	6.07126i	−0.788313	+	0.318220i
$365$	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	$0.739696\pi$
$368$	28.9208	+	0.522418i	1.50760	+	0.0272329i
$369$			51.6518i			2.68888i
$370$	−7.11398	−	4.83645i	−0.369838	−	0.251435i
$371$		−	2.56736i		−	0.133291i
$372$	−12.8540	−	31.8428i	−0.666451	−	1.65097i
$373$		−	29.0888i		−	1.50616i	−0.657928	−	0.753081i	$-0.728567\pi$
$373$		−	29.0888i		−	1.50616i	0.657928	−	0.753081i	$-0.271433\pi$
$374$	−12.2862	+	8.12935i	−0.635303	+	0.420359i
$375$	−2.14344	+	2.14344i	−0.110687	+	0.110687i
$376$	17.5197	+	12.0527i	0.903509	+	0.621572i
$377$	−0.755033			−0.0388862
$378$	−55.9278	−	11.3875i	−2.87662	−	0.585710i
$379$		−	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	$-0.783975\pi$
$383$	−2.94850	+	2.94850i	−0.150662	+	0.150662i	0.627752	+	0.778413i	$0.283975\pi$
$384$	−33.8308	+	5.62430i	−1.72642	+	0.287014i
$385$	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
$388$	8.22458	+	20.3744i	0.417540	+	1.03435i
$389$	−17.8576	−	17.8576i	−0.905416	−	0.905416i	0.0904818	−	0.995898i	$-0.471159\pi$
$389$	−17.8576	−	17.8576i	−0.905416	−	0.905416i	−0.995898	+	0.0904818i	$0.971159\pi$
$390$	−8.15882	−	1.66122i	−0.413138	−	0.0841193i
$391$	−29.3612			−1.48486
$392$	−16.7262	+	24.3130i	−0.844800	+	1.22799i
$393$	−27.3224	−	27.3224i	−1.37823	−	1.37823i
$394$	2.25031	−	11.0520i	0.113369	−	0.556793i
$395$	2.02840			0.102060
$396$	29.2278	+	12.4170i	1.46875	+	0.623977i
$397$		−	3.19025i		−	0.160114i	−0.996790	−	0.0800571i	$-0.974490\pi$
$397$		−	3.19025i		−	0.160114i	0.996790	−	0.0800571i	$-0.0255103\pi$
$398$	−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	−0.957571	−	0.288197i	$-0.906944\pi$
$401$	−13.4042	+	13.4042i	−0.669374	+	0.669374i	0.288197	+	0.957571i	$0.406944\pi$
$402$	−12.3715	+	60.7604i	−0.617033	+	3.03046i
$403$		−	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	−0.522108	−	0.852879i	$-0.674854\pi$
$409$	6.68943	−	6.68943i	0.330771	−	0.330771i	0.852879	+	0.522108i	$0.174854\pi$
$410$	6.51315	+	9.84355i	0.321661	+	0.486138i
$411$	54.1236			2.66972
$412$	−8.21868	−	20.3598i	−0.404905	−	1.00305i
$413$	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	$-0.293870\pi$
$420$	−23.4731	+	9.47543i	−1.14537	+	0.462354i
$421$	−17.0681	+	17.0681i	−0.831850	+	0.831850i	−0.987770	−	0.155919i	$-0.950166\pi$
$421$	−17.0681	+	17.0681i	−0.831850	+	0.831850i	0.155919	+	0.987770i	$0.450166\pi$
$422$	−10.9310	−	2.22566i	−0.532112	−	0.108344i
$423$			46.5289i			2.26231i
$424$	0.985721	−	1.43283i	0.0478708	−	0.0695845i
$425$	2.87103	−	2.87103i	0.139266	−	0.139266i
$426$	31.9198	+	6.49922i	1.54652	+	0.314888i
$427$	−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
$430$	1.57830	−	7.75154i	0.0761123	−	0.373813i
$431$	12.4968	+	12.4968i	0.601949	+	0.601949i	0.940829	−	0.338881i	$-0.110048\pi$
$431$	12.4968	+	12.4968i	0.601949	+	0.601949i	−0.338881	+	0.940829i	$0.610048\pi$
$432$	−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
$436$	−6.19303	−	15.3417i	−0.296592	−	0.734735i
$437$			34.1441i			1.63333i
$438$	39.4882	+	8.04023i	1.88682	+	0.384177i
$439$	6.37945	+	6.37945i	0.304474	+	0.304474i	0.842761	−	0.538287i	$-0.180928\pi$
$439$	6.37945	+	6.37945i	0.304474	+	0.304474i	−0.538287	+	0.842761i	$0.680928\pi$
$440$	7.13585	−	1.31918i	0.340188	−	0.0628896i
$441$	−64.5706			−3.07479
$442$	10.9283	+	2.22512i	0.519808	+	0.105838i
$443$	−10.7845			−0.512388			−0.256194	−	0.966625i	$-0.582469\pi$
$443$	−10.7845			−0.512388			−0.256194	+	0.966625i	$0.582469\pi$
$444$	0.462486	−	36.8743i	0.0219486	−	1.74998i
$445$	−4.72118			−0.223805
$446$	−27.7952	−	5.65939i	−1.31614	−	0.267980i
$447$	−5.34536			−0.252827
$448$	−31.1952	+	11.9421i	−1.47383	+	0.564209i
$449$	5.06489	+	5.06489i	0.239027	+	0.239027i	0.816447	−	0.577420i	$-0.195941\pi$
$449$	5.06489	+	5.06489i	0.239027	+	0.239027i	−0.577420	+	0.816447i	$0.695941\pi$
$450$	−8.57617	−	1.74620i	−0.404284	−	0.0823166i
$451$		−	21.4133i		−	1.00831i
$452$	5.92755	−	2.39279i	0.278808	−	0.112547i
$453$	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	0.651960	−	0.758254i	$-0.273947\pi$
$457$	−2.27230	−	2.27230i	−0.106294	−	0.106294i	−0.758254	+	0.651960i	$0.773947\pi$
$458$	8.19666	−	40.2565i	0.383005	−	1.88106i
$459$	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	0.117549	−	0.993067i	$-0.462496\pi$
$461$	−18.7982	−	18.7982i	−0.875519	−	0.875519i	−0.993067	+	0.117549i	$0.962496\pi$
$462$	45.0001	+	9.16249i	2.09359	+	0.426278i
$463$	−7.71828	+	7.71828i	−0.358699	+	0.358699i	−0.863333	−	0.504634i	$-0.831627\pi$
$463$	−7.71828	+	7.71828i	−0.358699	+	0.358699i	0.504634	+	0.863333i	$0.331627\pi$
$464$	−1.55471	−	0.0280839i	−0.0721755	−	0.00130376i
$465$		−	17.1696i		−	0.796223i
$466$	−38.7230	−	7.88441i	−1.79381	−	0.365238i
$467$	−14.7105	+	14.7105i	−0.680719	+	0.680719i	−0.960162	−	0.279443i	$-0.909850\pi$
$467$	−14.7105	+	14.7105i	−0.680719	+	0.680719i	0.279443	+	0.960162i	$0.409850\pi$
$468$	−8.99878	−	22.2923i	−0.415969	−	1.03046i
$469$			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
$476$	31.4410	−	12.6919i	1.44110	−	0.581731i
$477$	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	$-0.948740\pi$
$479$	−18.0936	+	18.0936i	−0.826718	+	0.826718i	0.160343	+	0.987061i	$0.448740\pi$
$480$	−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
$486$	0.998795	−	4.90542i	0.0453063	−	0.222514i
$487$	2.92917	−	2.92917i	0.132734	−	0.132734i	−0.637619	−	0.770352i	$-0.720080\pi$
$487$	2.92917	−	2.92917i	0.132734	−	0.132734i	0.770352	+	0.637619i	$0.220080\pi$
$488$	−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
$494$	2.58759	−	12.7085i	0.116421	−	0.571783i
$495$	11.2275	+	11.2275i	0.504637	+	0.504637i
$496$	0.409196	−	22.6529i	0.0183735	−	1.01714i
$497$	31.7273			1.42316
$498$	71.2789	+	14.5132i	3.19409	+	0.650350i
$499$	−9.73793	−	9.73793i	−0.435930	−	0.435930i	0.454710	−	0.890640i	$-0.349743\pi$
$499$	−9.73793	−	9.73793i	−0.435930	−	0.435930i	−0.890640	+	0.454710i	$0.849743\pi$
$500$	−1.85460	+	0.748649i	−0.0829400	+	0.0334806i
$501$	−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	$-0.926041\pi$
$503$	−16.6607	+	16.6607i	−0.742865	+	0.742865i	0.230263	+	0.973128i	$0.426041\pi$
$504$	−60.2137	−	41.4242i	−2.68213	−	1.84518i
$505$	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	$0.198516\pi$
$509$			26.3516i			1.16801i	−0.811748	+	0.584007i	$0.801484\pi$
$510$	17.0559	+	3.47276i	0.755247	+	0.153776i
$511$	39.2501			1.73632
$512$	−21.9950	−	5.31238i	−0.972049	−	0.234776i
$513$	32.2715	−	32.2715i	1.42482	−	1.42482i
$514$	−5.47843	+	3.62490i	−0.241643	+	0.159887i
$515$		−	10.9780i		−	0.483749i
$516$	31.4463	−	12.6940i	1.38435	−	0.558823i
$517$		−	19.2895i		−	0.848353i
$518$	−6.72425	−	35.2828i	−0.295447	−	1.55024i
$519$			12.0200i			0.527621i
$520$	−4.52594	−	3.11363i	−0.198476	−	0.136542i
$521$		−	10.5363i		−	0.461603i	−0.973001	−	0.230801i	$-0.925865\pi$
$521$		−	10.5363i		−	0.461603i	0.973001	−	0.230801i	$-0.0741348\pi$
$522$	−1.87743	−	2.83742i	−0.0821728	−	0.124191i
$523$	−16.8809	+	16.8809i	−0.738151	+	0.738151i	−0.972220	−	0.234069i	$-0.924796\pi$
$523$	−16.8809	+	16.8809i	−0.738151	+	0.738151i	0.234069	+	0.972220i	$0.424796\pi$
$524$	−9.54299	−	23.6404i	−0.416888	−	1.03274i
$525$	−12.6567			−0.552384
$526$	3.17954	−	15.6158i	0.138635	−	0.680881i
$527$			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
$532$	−14.7593	−	36.5626i	−0.639897	−	1.58519i
$533$	−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
$536$	−23.1879	+	33.7056i	−1.00156	+	1.45586i
$537$	−45.9966	−	45.9966i	−1.98490	−	1.98490i
$538$	−2.30201	+	11.3059i	−0.0992468	+	0.487434i
$539$	26.7691			1.15303
$540$	−7.23632	−	17.9262i	−0.311402	−	0.771422i
$541$	27.1744	+	27.1744i	1.16832	+	1.16832i	0.982603	+	0.185717i	$0.0594609\pi$
$541$	27.1744	+	27.1744i	1.16832	+	1.16832i	0.185717	+	0.982603i	$0.440539\pi$
$542$	22.1446	+	4.50888i	0.951193	+	0.193673i
$543$	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	$-0.149974\pi$
$547$	10.2236	+	10.2236i	0.437128	+	0.437128i	−0.453917	+	0.891044i	$0.649974\pi$
$548$	32.8670	+	13.9630i	1.40401	+	0.596471i
$549$	15.7226	−	15.7226i	0.671022	−	0.671022i
$550$	3.55543	+	0.723924i	0.151604	+	0.0308682i
$551$		−	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	−0.862178	−	0.506605i	$-0.830900\pi$
$557$	−8.39184	+	8.39184i	−0.355574	+	0.355574i	0.506605	+	0.862178i	$0.330900\pi$
$558$	41.3427	−	27.3551i	1.75018	−	1.15803i
$559$	10.8643			0.459509
$560$	−16.6987	−	0.301642i	−0.705650	−	0.0127467i
$561$	−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	0.0638020	−	0.997963i	$-0.479677\pi$
$563$	25.1931	−	25.1931i	1.06176	−	1.06176i	0.997963	−	0.0638020i	$-0.0203226\pi$
$564$	−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
$568$	17.7069	+	12.1815i	0.742964	+	0.511124i
$569$	−12.9804	+	12.9804i	−0.544165	+	0.544165i	−0.924747	−	0.380582i	$-0.875724\pi$
$569$	−12.9804	+	12.9804i	−0.544165	+	0.544165i	0.380582	+	0.924747i	$0.375724\pi$
$570$	4.03846	−	19.8342i	0.169152	−	0.830764i
$571$		−	23.7574i		−	0.994215i	−0.867689	−	0.497107i	$-0.834396\pi$
$571$		−	23.7574i		−	0.994215i	0.867689	−	0.497107i	$-0.165604\pi$
$572$	3.73063	+	9.24173i	0.155986	+	0.386416i
$573$	−43.0249	+	43.0249i	−1.79739	+	1.79739i
$574$	−9.83275	+	48.2919i	−0.410411	+	2.01567i
$575$	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	0.995903	+	0.0904262i	$0.0288229\pi$
$577$	26.0945	+	26.0945i	1.08633	+	1.08633i	0.0904262	+	0.995903i	$0.471177\pi$
$578$	0.712763	+	0.145126i	0.0296470	+	0.00603646i
$579$	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
$584$	21.9053	+	15.0698i	0.906447	+	0.623593i
$585$		−	12.0200i		−	0.496967i
$586$	−2.56966	+	12.6204i	−0.106152	+	0.521346i
$587$	−18.0329	−	18.0329i	−0.744297	−	0.744297i	0.229105	−	0.973402i	$-0.426420\pi$
$587$	−18.0329	−	18.0329i	−0.744297	−	0.744297i	−0.973402	+	0.229105i	$0.926420\pi$
$588$	−58.2187	−	24.7333i	−2.40090	−	1.01998i
$589$	26.7441			1.10197
$590$	−2.67355	+	13.1307i	−0.110068	+	0.540581i
$591$	24.1754			0.994445
$592$	9.79381	−	22.2729i	0.402523	−	0.915410i
$593$	11.2720			0.462886			0.231443	−	0.972848i	$-0.425655\pi$
$593$	11.2720			0.462886			0.231443	+	0.972848i	$0.425655\pi$
$594$	−6.99733	+	34.3662i	−0.287104	+	1.41006i
$595$	16.9530			0.695006
$596$	−3.24601	−	1.37902i	−0.132962	−	0.0564867i
$597$	−41.0571	−	41.0571i	−1.68035	−	1.68035i
$598$	−3.96299	+	19.4635i	−0.162059	+	0.795923i
$599$		−	0.201520i		−	0.00823388i	−0.999992	−	0.00411694i	$-0.998690\pi$
$599$		−	0.201520i		−	0.00823388i	0.999992	−	0.00411694i	$-0.00131047\pi$
$600$	−7.06365	−	4.85946i	−0.288372	−	0.198387i
$601$	−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
$606$	2.23046	+	0.454146i	0.0906064	+	0.0184484i
$607$	−5.05524	−	5.05524i	−0.205186	−	0.205186i	0.597032	−	0.802218i	$-0.296347\pi$
$607$	−5.05524	−	5.05524i	−0.205186	−	0.205186i	−0.802218	+	0.597032i	$0.796347\pi$
$608$	5.80087	−	26.0722i	0.235256	−	1.05737i
$609$	−3.47909	−	3.47909i	−0.140980	−	0.140980i
$610$	1.01376	−	4.97890i	0.0410458	−	0.201590i
$611$	−10.3256	+	10.3256i	−0.417729	+	0.417729i
$612$	18.8118	+	46.6017i	0.760422	+	1.88376i
$613$		−	38.0315i		−	1.53608i	−0.640403	−	0.768039i	$-0.721233\pi$
$613$		−	38.0315i		−	1.53608i	0.640403	−	0.768039i	$-0.278767\pi$
$614$	−0.271521	+	1.33353i	−0.0109577	+	0.0538168i
$615$	−17.8895	+	17.8895i	−0.721374	+	0.721374i
$616$	24.9629	+	17.1733i	1.00578	+	0.691931i
$617$		−	25.5694i		−	1.02939i	−0.857374	−	0.514693i	$-0.827906\pi$
$617$		−	25.5694i		−	1.02939i	0.857374	−	0.514693i	$-0.172094\pi$
$618$	39.2478	−	25.9690i	1.57878	−	1.04463i
$619$	−35.8211			−1.43977			−0.719886	−	0.694092i	$-0.755806\pi$
$619$	−35.8211			−1.43977			−0.719886	+	0.694092i	$0.755806\pi$
$620$	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
$624$	0.425334	−	23.5463i	0.0170270	−	0.942606i
$625$	−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	$-0.133117\pi$
$631$	12.7535	+	12.7535i	0.507707	+	0.507707i	−0.406115	+	0.913822i	$0.633117\pi$
$632$	1.04294	+	5.64159i	0.0414861	+	0.224410i
$633$		−	23.9107i		−	0.950364i
$634$	9.83997	+	2.00352i	0.390795	+	0.0795701i
$635$	−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	$0.301287\pi$
$642$	31.5496	+	6.42384i	1.24516	+	0.253529i
$643$	−17.7201	−	17.7201i	−0.698812	−	0.698812i	0.265342	−	0.964154i	$-0.414515\pi$
$643$	−17.7201	−	17.7201i	−0.698812	−	0.698812i	−0.964154	+	0.265342i	$0.914515\pi$
$644$	22.6044	+	55.9970i	0.890739	+	2.20659i
$645$	16.9559			0.667638
$646$	−5.40931	+	26.5669i	−0.212827	+	1.04526i
$647$	−1.52190	−	1.52190i	−0.0598319	−	0.0598319i	0.676558	−	0.736390i	$-0.263471\pi$
$647$	−1.52190	−	1.52190i	−0.0598319	−	0.0598319i	−0.736390	+	0.676558i	$0.763471\pi$
$648$	17.2074	−	25.0125i	0.675972	−	0.982585i
$649$	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
$652$	12.9491	+	32.0782i	0.507125	+	1.25628i
$653$	−27.6146	+	27.6146i	−1.08064	+	1.08064i	−0.0841929	+	0.996449i	$0.526831\pi$
$653$	−27.6146	+	27.6146i	−1.08064	+	1.08064i	−0.996449	+	0.0841929i	$0.973169\pi$
$654$	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
$658$	−8.85753	+	43.5023i	−0.345303	+	1.69590i
$659$	15.0789			0.587390			0.293695	−	0.955899i	$-0.405115\pi$
$659$	15.0789			0.587390			0.293695	+	0.955899i	$0.405115\pi$
$660$	5.82241	+	14.4236i	0.226637	+	0.561438i
$661$	−5.51201	+	5.51201i	−0.214392	+	0.214392i	−0.806130	−	0.591738i	$-0.798442\pi$
$661$	−5.51201	+	5.51201i	−0.214392	+	0.214392i	0.591738	+	0.806130i	$0.298442\pi$
$662$	−25.6689	−	38.7943i	−0.997650	−	1.50778i
$663$			23.9049i			0.928388i
$664$	39.5405	+	27.2020i	1.53447	+	1.05564i
$665$		−	19.7146i		−	0.764499i
$666$	52.2959	−	9.96664i	2.02642	−	0.386200i
$667$			2.81113i			0.108847i
$668$	−15.4910	+	6.25330i	−0.599366	+	0.241948i
$669$		−	60.7997i		−	2.35065i
$670$	−17.0595	+	11.2877i	−0.659064	+	0.436081i
$671$	−6.51811	+	6.51811i	−0.251629	+	0.251629i
$672$	−38.4232	−	60.4137i	−1.48221	−	2.33051i
$673$	−1.07819			−0.0415612			−0.0207806	−	0.999784i	$-0.506615\pi$
$673$	−1.07819			−0.0415612			−0.0207806	+	0.999784i	$0.506615\pi$
$674$	14.4275	+	2.93760i	0.555728	+	0.113152i
$675$		−	9.66584i		−	0.372038i
$676$	−7.21622	+	16.9860i	−0.277547	+	0.653307i
$677$		−	28.4175i		−	1.09217i	−0.837729	−	0.546086i	$-0.816117\pi$
$677$		−	28.4175i		−	1.09217i	0.837729	−	0.546086i	$-0.183883\pi$
$678$	7.56062	+	11.4266i	0.290364	+	0.438837i
$679$	−32.4351	+	32.4351i	−1.24474	+	1.24474i
$680$	9.46140	+	6.50900i	0.362828	+	0.249609i
$681$	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	0.0609308	−	0.998142i	$-0.480593\pi$
$683$	27.6781	−	27.6781i	1.05907	−	1.05907i	0.998142	−	0.0609308i	$-0.0194069\pi$
$684$	54.1929	−	21.8762i	2.07212	−	0.836456i
$685$	12.6254	+	12.6254i	0.482392	+	0.482392i
$686$	−19.8675	−	4.04523i	−0.758543	−	0.154448i
$687$	88.0580			3.35962
$688$	22.3709	+	0.404102i	0.852882	+	0.0154063i
$689$	0.844470	+	0.844470i	0.0321717	+	0.0321717i
$690$	−6.18505	+	30.3768i	−0.235461	+	1.15643i
$691$	−4.06655			−0.154699			−0.0773494	−	0.997004i	$-0.524646\pi$
$691$	−4.06655			−0.154699			−0.0773494	+	0.997004i	$0.524646\pi$
$692$	−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
$698$	6.90856	−	33.9302i	0.261493	−	1.28428i
$699$		−	84.7035i		−	3.20378i
$700$	−7.68589	−	3.26523i	−0.290499	−	0.123414i
$701$	0.252080	+	0.252080i	0.00952092	+	0.00952092i	0.711851	−	0.702330i	$-0.247857\pi$
$701$	0.252080	+	0.252080i	0.00952092	+	0.00952092i	−0.702330	+	0.711851i	$0.747857\pi$
$702$	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
$708$	−53.2683	+	21.5029i	−2.00194	+	0.808130i
$709$	30.0226	+	30.0226i	1.12752	+	1.12752i	0.990579	+	0.136944i	$0.0437282\pi$
$709$	30.0226	+	30.0226i	1.12752	+	1.12752i	0.136944	+	0.990579i	$0.456272\pi$
$710$	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
$716$	−16.0654	−	39.7982i	−0.600393	−	1.48733i
$717$	24.1498	−	24.1498i	0.901889	−	0.901889i
$718$	47.3943	+	9.65000i	1.76874	+	0.360135i
$719$			10.5873i			0.394840i	0.980319	+	0.197420i	$0.0632563\pi$
$719$			10.5873i			0.394840i	−0.980319	+	0.197420i	$0.936744\pi$
$720$	0.447091	−	24.7507i	0.0166621	−	0.922405i
$721$	32.4118	−	32.4118i	1.20708	−	1.20708i
$722$	4.56475	+	0.929433i	0.169883	+	0.0345899i
$723$	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
$726$	−3.77825	+	18.5562i	−0.140224	+	0.688687i
$727$	−13.2560	−	13.2560i	−0.491639	−	0.491639i	0.417184	−	0.908822i	$-0.363017\pi$
$727$	−13.2560	−	13.2560i	−0.491639	−	0.491639i	−0.908822	+	0.417184i	$0.863017\pi$
$728$	−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
$732$	20.1983	−	8.15350i	0.746551	−	0.301362i
$733$		−	11.3778i		−	0.420250i	−0.977675	−	0.210125i	$-0.932613\pi$
$733$		−	11.3778i		−	0.420250i	0.977675	−	0.210125i	$-0.0673870\pi$
$734$	−38.7396	−	7.88779i	−1.42990	−	0.291144i
$735$	−22.3639	−	22.3639i	−0.824905	−	0.824905i
$736$	−8.88424	+	39.9305i	−0.327478	+	1.47186i
$737$	37.1106			1.36699
$738$	−71.5780	−	14.5740i	−2.63482	−	0.536478i
$739$	49.3563			1.81560			0.907800	−	0.419404i	$-0.137761\pi$
$739$	49.3563			1.81560			0.907800	+	0.419404i	$0.137761\pi$
$740$	8.70953	−	8.49376i	0.320169	−	0.312237i
$741$	27.7989			1.02122
$742$	3.55780	+	0.724405i	0.130611	+	0.0265938i
$743$	−26.9933			−0.990288			−0.495144	−	0.868811i	$-0.664885\pi$
$743$	−26.9933			−0.990288			−0.495144	+	0.868811i	$0.664885\pi$
$744$	47.7539	−	8.82813i	1.75074	−	0.323655i
$745$	−1.24691	−	1.24691i	−0.0456832	−	0.0456832i
$746$	40.3107	+	8.20769i	1.47588	+	0.300505i
$747$			105.012i			3.84219i
$748$	−7.79883	−	19.3197i	−0.285153	−	0.706398i
$749$	31.3593			1.14585
$750$	−2.36555	−	3.57513i	−0.0863776	−	0.130545i
$751$	−36.7133			−1.33969			−0.669843	−	0.742503i	$-0.733639\pi$
$751$	−36.7133			−1.33969			−0.669843	+	0.742503i	$0.733639\pi$
$752$	−21.6458	+	20.8776i	−0.789340	+	0.761329i
$753$	34.1199	+	34.1199i	1.24340	+	1.24340i
$754$	0.213040	−	1.04631i	0.00775845	−	0.0381043i
$755$	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	0.986403	−	0.164346i	$-0.0525515\pi$
$757$	22.6178	+	22.6178i	0.822056	+	0.822056i	−0.164346	+	0.986403i	$0.552551\pi$
$758$	17.1910	+	3.50026i	0.624403	+	0.127135i
$759$	39.7678	−	39.7678i	1.44348	−	1.44348i
$760$	7.56929	−	11.0026i	0.274567	−	0.399107i
$761$			8.69822i			0.315310i	0.987494	+	0.157655i	$0.0503934\pi$
$761$			8.69822i			0.315310i	−0.987494	+	0.157655i	$0.949607\pi$
$762$	−65.8341	−	13.4045i	−2.38492	−	0.485595i
$763$	24.4233	−	24.4233i	0.884181	−	0.884181i
$764$	−37.2269	+	15.0275i	−1.34682	+	0.543675i
$765$			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	−0.866308	−	0.499510i	$-0.833513\pi$
$769$	−10.1716	+	10.1716i	−0.366797	+	0.366797i	0.499510	+	0.866308i	$0.333513\pi$
$770$	8.35981	+	12.6345i	0.301267	+	0.455315i
$771$	−9.95641	−	9.95641i	−0.358571	−	0.358571i
$772$	5.00107	+	12.3889i	0.179993	+	0.445888i
$773$	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
$782$	8.28456	−	40.6882i	0.296255	−	1.45501i
$783$	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
$790$	−0.572332	+	2.81091i	−0.0203627	+	0.100008i
$791$	9.43636	+	9.43636i	0.335518	+	0.335518i
$792$	−25.4541	+	36.9998i	−0.904473	+	1.31473i
$793$	6.97823			0.247804
$794$	4.42099	+	0.900161i	0.156895	+	0.0319455i
$795$	1.31797	+	1.31797i	0.0467435	+	0.0467435i
$796$	−14.3402	−	35.5243i	−0.508274	−	1.25913i
$797$	−22.8746	+	22.8746i	−0.810261	+	0.810261i	−0.984673	−	0.174412i	$-0.944198\pi$
$797$	−22.8746	+	22.8746i	−0.810261	+	0.810261i	0.174412	+	0.984673i	$0.444198\pi$
$798$	70.4823	−	46.6358i	2.49505	−	1.65089i
$799$	21.5855	−	21.5855i	0.763640	−	0.763640i
$800$	−3.03580	−	4.77325i	−0.107332	−	0.168760i
$801$	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
$806$	15.2453	+	3.10410i	0.536992	+	0.109337i
$807$	−24.7309			−0.870568
$808$	1.23730	+	0.851207i	0.0435282	+	0.0299454i
$809$	8.18910	−	8.18910i	0.287914	−	0.287914i	−0.548341	−	0.836255i	$-0.684740\pi$
$809$	8.18910	−	8.18910i	0.287914	−	0.287914i	0.836255	+	0.548341i	$0.184740\pi$
$810$	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	$-0.0355603\pi$
$812$	−1.21516	−	3.01025i	−0.0426436	−	0.105639i
$813$			48.4396i			1.69885i
$814$	−21.6804	+	4.13188i	−0.759896	+	0.144822i
$815$			17.2966i			0.605873i
$816$	−0.889155	+	49.2231i	−0.0311266	+	1.72315i
$817$			26.4112i			0.924010i
$818$	7.38260	+	11.1576i	0.258126	+	0.390115i
$819$	35.4882	−	35.4882i	1.24006	−	1.24006i
$820$	−15.4787	+	6.24834i	−0.540541	+	0.218201i
$821$	−8.05259			−0.281037			−0.140519	−	0.990078i	$-0.544877\pi$
$821$	−8.05259			−0.281037			−0.140519	+	0.990078i	$0.544877\pi$
$822$	−15.2715	+	75.0034i	−0.532655	+	2.61605i
$823$			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	$-0.875015\pi$
$827$	−15.5652	+	15.5652i	−0.541257	+	0.541257i	0.382641	+	0.923897i	$0.375015\pi$
$828$	−82.9983	+	33.5041i	−2.88439	+	1.16435i
$829$	−7.55467	+	7.55467i	−0.262385	+	0.262385i	−0.826022	−	0.563638i	$-0.809401\pi$
$829$	−7.55467	+	7.55467i	−0.262385	+	0.262385i	0.563638	+	0.826022i	$0.309401\pi$
$830$	13.2417	+	20.0127i	0.459627	+	0.694650i
$831$	−26.9529	+	26.9529i	−0.934985	+	0.934985i
$832$	6.33284	−	14.1889i	0.219552	−	0.491913i
$833$	29.9553	+	29.9553i	1.03789	+	1.03789i
$834$	17.3188	−	85.0582i	0.599700	−	2.94533i
$835$	−8.35278			−0.289060
$836$	−22.4668	+	9.06922i	−0.777030	+	0.313666i
$837$	38.7132	+	38.7132i	1.33812	+	1.33812i
$838$	45.2468	+	9.21273i	1.56302	+	0.318249i
$839$	−21.9712			−0.758530			−0.379265	−	0.925288i	$-0.623823\pi$
$839$	−21.9712			−0.758530			−0.379265	+	0.925288i	$0.623823\pi$
$840$	−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
$846$	−64.4788	−	13.1286i	−2.21683	−	0.451370i
$847$			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	−0.714659	−	0.699473i	$-0.753418\pi$
$853$	−0.443551	+	0.443551i	−0.0151869	+	0.0151869i	0.699473	+	0.714659i	$0.253418\pi$
$854$	17.6929	−	11.7068i	0.605438	−	0.400598i
$855$	29.2209			0.999332
$856$	17.5015	+	12.0402i	0.598189	+	0.411526i
$857$	−2.98933	−	2.98933i	−0.102114	−	0.102114i	0.654204	−	0.756318i	$-0.273004\pi$
$857$	−2.98933	−	2.98933i	−0.102114	−	0.102114i	−0.756318	+	0.654204i	$0.773004\pi$
$858$	−17.8154	+	11.7879i	−0.608209	+	0.402432i
$859$	−19.3397	+	19.3397i	−0.659861	+	0.659861i	−0.955347	−	0.295486i	$-0.904518\pi$
$859$	−19.3397	+	19.3397i	−0.659861	+	0.659861i	0.295486	+	0.955347i	$0.404518\pi$
$860$	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	$-0.268423\pi$
$864$	46.1375	−	29.3435i	1.56963	−	0.998287i
$865$	−2.80391	+	2.80391i	−0.0953358	+	0.0953358i
$866$	−3.92724	+	19.2880i	−0.133453	+	0.655432i
$867$			1.55911i			0.0529503i
$868$	43.8609	−	17.7054i	1.48874	−	0.600962i
$869$	3.67990	−	3.67990i	0.124832	−	0.124832i
$870$	0.332492	−	1.63298i	0.0112725	−	0.0553632i
$871$	−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
$874$	−47.3162	−	9.63408i	−1.60049	−	0.325878i
$875$	−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
$880$	−0.185351	+	10.2609i	−0.00624819	+	0.345896i
$881$		−	36.6929i		−	1.23621i	−0.786094	−	0.618107i	$-0.787900\pi$
$881$		−	36.6929i		−	1.23621i	0.786094	−	0.618107i	$-0.212100\pi$
$882$	18.2192	−	89.4806i	0.613473	−	3.01297i
$883$	9.25331	+	9.25331i	0.311399	+	0.311399i	0.845451	−	0.534053i	$-0.179332\pi$
$883$	9.25331	+	9.25331i	0.311399	+	0.311399i	−0.534053	+	0.845451i	$0.679332\pi$
$884$	−6.16707	+	14.5164i	−0.207421	+	0.488240i
$885$	−28.7223			−0.965490
$886$	3.04296	−	14.9450i	0.102230	−	0.502086i
$887$	−6.08915			−0.204454			−0.102227	−	0.994761i	$-0.532597\pi$
$887$	−6.08915			−0.204454			−0.102227	+	0.994761i	$0.532597\pi$
$888$	50.9691	+	11.0453i	1.71041	+	0.370657i
$889$	−65.4370			−2.19469
$890$	1.33213	−	6.54252i	0.0446530	−	0.219306i
$891$	−27.5393			−0.922602
$892$	15.6853	−	36.9211i	0.525184	−	1.23621i
$893$	−25.1017	−	25.1017i	−0.839996	−	0.839996i
$894$	1.50824	−	7.40749i	0.0504432	−	0.247743i
$895$		−	21.4592i		−	0.717303i
$896$	−7.74703	−	46.5992i	−0.258810	−	1.55677i
$897$	−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
$902$	29.6742	+	6.04198i	0.988042	+	0.201176i
$903$	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
$906$	−0.686276	+	3.37053i	−0.0228000	+	0.111978i
$907$	6.34639	−	6.34639i	0.210728	−	0.210728i	−0.593848	−	0.804577i	$-0.702392\pi$
$907$	6.34639	−	6.34639i	0.210728	−	0.210728i	0.804577	+	0.593848i	$0.202392\pi$
$908$	24.0557	−	9.71062i	0.798316	−	0.322258i
$909$			3.28604i			0.108991i
$910$	2.28821	−	11.2381i	0.0758533	−	0.372541i
$911$	6.06994	−	6.06994i	0.201106	−	0.201106i	−0.599368	−	0.800474i	$-0.704581\pi$
$911$	6.06994	−	6.06994i	0.201106	−	0.201106i	0.800474	+	0.599368i	$0.204581\pi$
$912$	57.2414	+	1.03399i	1.89545	+	0.0342390i
$913$		−	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	$-0.210822\pi$
$919$	5.26338	+	5.26338i	0.173623	+	0.173623i	−0.614946	+	0.788569i	$0.710822\pi$
$920$	−11.5926	+	16.8509i	−0.382198	+	0.555558i
$921$	−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	$0.0606163\pi$
$929$			11.5385i			0.378566i	−0.981923	+	0.189283i	$0.939384\pi$
$930$	23.7934	+	4.84458i	0.780215	+	0.158860i
$931$	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	$0.753389\pi$
$938$	−83.6928	−	17.0407i	−2.73267	−	0.556400i
$939$	4.16897	+	4.16897i	0.136049	+	0.136049i
$940$	−13.9435	+	5.62862i	−0.454788	+	0.183585i
$941$	−42.8376			−1.39647			−0.698234	−	0.715870i	$-0.746030\pi$
$941$	−42.8376			−1.39647			−0.698234	+	0.715870i	$0.746030\pi$
$942$	2.26545	−	11.1264i	0.0738124	−	0.362517i
$943$	42.6769	+	42.6769i	1.38975	+	1.38975i
$944$	−37.8950	−	0.684526i	−1.23338	−	0.0222794i
$945$	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	$-0.632895\pi$
$947$	15.6521	−	15.6521i	0.508626	−	0.508626i	0.914104	+	0.405479i	$0.132895\pi$
$948$	−11.4033	+	4.60319i	−0.370361	+	0.149505i
$949$	−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	$0.349311\pi$
$953$			54.9512i			1.78004i	−0.455917	+	0.890022i	$0.650689\pi$
$954$	−1.07371	+	5.27334i	−0.0347626	+	0.170731i
$955$	−20.0728			−0.649541
$956$	20.8954	−	8.43488i	0.675805	−	0.272804i
$957$	−2.13781	+	2.13781i	−0.0691056	+	0.0691056i
$958$	−19.9685	−	30.1791i	−0.645152	−	0.975041i
$959$			74.5511i			2.40738i
$960$	9.88370	−	22.1447i	0.318995	−	0.714718i
$961$			1.08256i			0.0349214i
$962$	13.8172	+	9.39362i	0.445484	+	0.302862i
$963$			46.4806i			1.49782i
$964$	0.00794780	+	0.0196887i	0.000255981	+	0.000634131i
$965$			6.68013i			0.215041i
$966$	−107.946	+	71.4244i	−3.47311	+	2.29804i
$967$	36.1626	−	36.1626i	1.16291	−	1.16291i	0.179074	−	0.983836i	$-0.442690\pi$
$967$	36.1626	−	36.1626i	1.16291	−	1.16291i	0.983836	−	0.179074i	$-0.0573101\pi$
$968$	−7.08158	+	10.2937i	−0.227611	+	0.330852i
$969$	−58.1131			−1.86686
$970$	−15.2240	−	3.09978i	−0.488814	−	0.0995279i
$971$		−	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
$976$	14.3691	+	0.259559i	0.459942	+	0.00830829i
$977$	10.9626	−	10.9626i	0.350723	−	0.350723i	−0.509655	−	0.860379i	$-0.670227\pi$
$977$	10.9626	−	10.9626i	0.350723	−	0.350723i	0.860379	+	0.509655i	$0.170227\pi$
$978$	−61.8376	+	40.9159i	−1.97735	+	1.30835i
$979$	−8.56512	+	8.56512i	−0.273742	+	0.273742i
$980$	−7.81113	−	19.3502i	−0.249517	−	0.618119i
$981$	36.2000	+	36.2000i	1.15578	+	1.15578i
$982$	3.08655	+	0.628455i	0.0984958	+	0.0200548i
$983$	−13.4505			−0.429003			−0.214502	−	0.976724i	$-0.568813\pi$
$983$	−13.4505			−0.429003			−0.214502	+	0.976724i	$0.568813\pi$
$984$	−58.9543	−	40.5578i	−1.87939	−	1.29294i
$985$	5.63940	+	5.63940i	0.179686	+	0.179686i
$986$	−0.445356	+	2.18729i	−0.0141830	+	0.0696576i
$987$	−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	$-0.106805\pi$
$991$	19.3589	+	19.3589i	0.614955	+	0.614955i	−0.329278	+	0.944233i	$0.606805\pi$
$992$	31.2765	+	6.95879i	0.993029	+	0.220942i
$993$	70.5041	−	70.5041i	2.23738	−	2.23738i
$994$	−8.95217	+	43.9671i	−0.283946	+	1.39455i
$995$		−	19.1547i		−	0.607246i
$996$	−40.2241	+	94.6819i	−1.27455	+	3.00011i
$997$	−31.4511	−	31.4511i	−0.996066	−	0.996066i	0.00392580	−	0.999992i	$-0.498750\pi$
$997$	−31.4511	−	31.4511i	−0.996066	−	0.996066i	−0.999992	+	0.00392580i	$0.998750\pi$
$998$	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.191.32	yes	152
4.3	odd	2	inner	740.2.u.a.191.7	yes	152
37.31	odd	4	inner	740.2.u.a.31.7	✓	152
148.31	even	4	inner	740.2.u.a.31.32	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.7	✓	152	37.31	odd	4	inner
740.2.u.a.31.32	yes	152	148.31	even	4	inner
740.2.u.a.191.7	yes	152	4.3	odd	2	inner
740.2.u.a.191.32	yes	152	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 $\F_{q}$
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+(-0.282160 + 1.38578i) q^{2} -3.03129 q^{3} +(-1.84077 - 0.782022i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.855307 - 4.20069i) q^{6} -4.17536i q^{7} +(1.60310 - 2.33025i) 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} +(5.78613 + 1.17812i) q^{14} +(2.14344 + 2.14344i) q^{15} +(2.77688 + 2.87905i) q^{16} +(-2.87103 - 2.87103i) q^{17} +(-1.74620 + 8.57617i) q^{18} +(-3.33871 + 3.33871i) q^{19} +(0.748649 + 1.85460i) q^{20} +12.6567i q^{21} +(0.723924 - 3.55543i) q^{22} +(5.11336 - 5.11336i) q^{23} +(-4.85946 + 7.06365i) 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} +(-4.77325 + 3.03580i) 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} +(-17.5394 - 3.57121i) 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} +(-1.38578 - 0.282160i) q^{50} +(8.70292 + 8.70292i) q^{51} +(-1.45407 - 3.60210i) q^{52} +0.614883 q^{53} +(2.72731 - 13.3947i) q^{54} +(1.81419 + 1.81419i) q^{55} +(-9.72963 - 6.69353i) q^{56} +(10.1206 - 10.1206i) q^{57} +(-0.303364 - 0.458485i) q^{58} +(-6.70004 + 6.70004i) q^{59} +(-2.26937 - 5.62181i) 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} +(-2.19442 + 10.7775i) q^{66} -14.4644 q^{67} +(3.03970 + 7.53013i) q^{68} +(-15.5001 + 15.5001i) q^{69} +(-3.25836 - 4.92447i) q^{70} +7.59870i q^{71} +(9.92111 - 14.4212i) q^{72} +9.40041i q^{73} +(8.45023 - 1.61046i) q^{74} -3.03129i q^{75} +(8.75675 - 3.53486i) q^{76} +10.7125i q^{77} +(6.94382 - 4.59450i) q^{78} +(-1.43429 + 1.43429i) q^{79} +(0.0722433 - 3.99935i) q^{80} +10.7338 q^{81} +(-11.5659 - 2.35495i) 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} +(-4.11300 + 5.97861i) q^{88} +(3.33838 - 3.33838i) q^{89} +(7.29901 - 4.82952i) q^{90} +(5.73436 - 5.73436i) q^{91} +(-13.4113 + 5.41377i) q^{92} +(12.1408 + 12.1408i) q^{93} +(-10.4188 - 2.12138i) q^{94} +4.72165 q^{95} +(14.4691 - 9.20236i) q^{96} +(-7.76820 - 7.76820i) q^{97} +(2.94395 - 14.4587i) 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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