LMFDB - Embedded newform 435.2.q.c.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	435.41
Dual form			435.2.q.c.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48187 + 1.48187i) q^{2} +(1.72513 + 0.154682i) q^{3} -2.39186i q^{4} -1.00000 q^{5} +(-2.78563 + 2.32719i) q^{6} +2.93783 q^{7} +(0.580678 + 0.580678i) q^{8} +(2.95215 + 0.533693i) q^{9} +O(q^{10})$	\(q+(-1.48187 + 1.48187i) q^{2} +(1.72513 + 0.154682i) q^{3} -2.39186i q^{4} -1.00000 q^{5} +(-2.78563 + 2.32719i) q^{6} +2.93783 q^{7} +(0.580678 + 0.580678i) q^{8} +(2.95215 + 0.533693i) q^{9} +(1.48187 - 1.48187i) q^{10} +(3.37899 - 3.37899i) q^{11} +(0.369977 - 4.12626i) q^{12} -2.99160i q^{13} +(-4.35347 + 4.35347i) q^{14} +(-1.72513 - 0.154682i) q^{15} +3.06274 q^{16} +(-2.15342 + 2.15342i) q^{17} +(-5.16555 + 3.58383i) q^{18} +(0.118585 + 0.118585i) q^{19} +2.39186i q^{20} +(5.06814 + 0.454429i) q^{21} +10.0144i q^{22} -1.66622i q^{23} +(0.911925 + 1.09157i) q^{24} +1.00000 q^{25} +(4.43316 + 4.43316i) q^{26} +(5.01028 + 1.37733i) q^{27} -7.02687i q^{28} +(4.21312 + 3.35405i) q^{29} +(2.78563 - 2.32719i) q^{30} +(-1.53396 - 1.53396i) q^{31} +(-5.69992 + 5.69992i) q^{32} +(6.35186 - 5.30653i) q^{33} -6.38215i q^{34} -2.93783 q^{35} +(1.27652 - 7.06111i) q^{36} +(-3.65691 + 3.65691i) q^{37} -0.351454 q^{38} +(0.462747 - 5.16090i) q^{39} +(-0.580678 - 0.580678i) q^{40} +(1.26361 + 1.26361i) q^{41} +(-8.18371 + 6.83690i) q^{42} +(-2.21073 - 2.21073i) q^{43} +(-8.08206 - 8.08206i) q^{44} +(-2.95215 - 0.533693i) q^{45} +(2.46912 + 2.46912i) q^{46} +(3.31975 + 3.31975i) q^{47} +(5.28362 + 0.473750i) q^{48} +1.63085 q^{49} +(-1.48187 + 1.48187i) q^{50} +(-4.04802 + 3.38183i) q^{51} -7.15548 q^{52} +13.5559i q^{53} +(-9.46560 + 5.38355i) q^{54} +(-3.37899 + 3.37899i) q^{55} +(1.70593 + 1.70593i) q^{56} +(0.186231 + 0.222917i) q^{57} +(-11.2135 + 1.27303i) q^{58} -9.91104i q^{59} +(-0.369977 + 4.12626i) q^{60} +(-0.353285 - 0.353285i) q^{61} +4.54625 q^{62} +(8.67291 + 1.56790i) q^{63} -10.7676i q^{64} +2.99160i q^{65} +(-1.54905 + 17.2762i) q^{66} +12.6338i q^{67} +(5.15066 + 5.15066i) q^{68} +(0.257735 - 2.87445i) q^{69} +(4.35347 - 4.35347i) q^{70} -4.70345 q^{71} +(1.40434 + 2.02415i) q^{72} +(-10.2297 + 10.2297i) q^{73} -10.8381i q^{74} +(1.72513 + 0.154682i) q^{75} +(0.283638 - 0.283638i) q^{76} +(9.92690 - 9.92690i) q^{77} +(6.96204 + 8.33350i) q^{78} +(-9.13962 - 9.13962i) q^{79} -3.06274 q^{80} +(8.43034 + 3.15108i) q^{81} -3.74501 q^{82} -13.0304i q^{83} +(1.08693 - 12.1223i) q^{84} +(2.15342 - 2.15342i) q^{85} +6.55201 q^{86} +(6.74937 + 6.43786i) q^{87} +3.92421 q^{88} +(7.82234 - 7.82234i) q^{89} +(5.16555 - 3.58383i) q^{90} -8.78882i q^{91} -3.98537 q^{92} +(-2.40900 - 2.88356i) q^{93} -9.83884 q^{94} +(-0.118585 - 0.118585i) q^{95} +(-10.7148 + 8.95143i) q^{96} +(10.9110 - 10.9110i) q^{97} +(-2.41670 + 2.41670i) q^{98} +(11.7786 - 8.17193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.48187	+	1.48187i	−1.04784	+	1.04784i	−0.0490410	+	0.998797i	$0.515617\pi$
$2$	−1.48187	+	1.48187i	−1.04784	+	1.04784i	−0.998797	+	0.0490410i	$0.984383\pi$
$3$	1.72513	+	0.154682i	0.996004	+	0.0893056i
$3$	1.72513	+	0.154682i	0.996004	+	0.0893056i
$4$		−	2.39186i		−	1.19593i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−2.78563	+	2.32719i	−1.13723	+	0.950073i
$7$	2.93783			1.11040			0.555198	−	0.831718i	$-0.312643\pi$
$7$	2.93783			1.11040			0.555198	+	0.831718i	$0.312643\pi$
$8$	0.580678	+	0.580678i	0.205301	+	0.205301i
$9$	2.95215	+	0.533693i	0.984049	+	0.177898i
$10$	1.48187	−	1.48187i	0.468607	−	0.468607i
$11$	3.37899	−	3.37899i	1.01880	−	1.01880i	0.0189839	−	0.999820i	$-0.493957\pi$
$11$	3.37899	−	3.37899i	1.01880	−	1.01880i	0.999820	−	0.0189839i	$-0.00604314\pi$
$12$	0.369977	−	4.12626i	0.106803	−	1.19115i
$13$		−	2.99160i		−	0.829721i	−0.909885	−	0.414861i	$-0.863830\pi$
$13$		−	2.99160i		−	0.829721i	0.909885	−	0.414861i	$-0.136170\pi$
$14$	−4.35347	+	4.35347i	−1.16351	+	1.16351i
$15$	−1.72513	−	0.154682i	−0.445427	−	0.0399387i
$16$	3.06274			0.765684
$17$	−2.15342	+	2.15342i	−0.522280	+	0.522280i	−0.918259	−	0.395979i	$-0.870405\pi$
$17$	−2.15342	+	2.15342i	−0.522280	+	0.522280i	0.395979	+	0.918259i	$0.370405\pi$
$18$	−5.16555	+	3.58383i	−1.21753	+	0.844716i
$19$	0.118585	+	0.118585i	0.0272052	+	0.0272052i	0.720579	−	0.693373i	$-0.243876\pi$
$19$	0.118585	+	0.118585i	0.0272052	+	0.0272052i	−0.693373	+	0.720579i	$0.743876\pi$
$20$			2.39186i			0.534835i
$21$	5.06814	+	0.454429i	1.10596	+	0.0991646i
$22$			10.0144i			2.13508i
$23$		−	1.66622i		−	0.347432i	−0.984796	−	0.173716i	$-0.944423\pi$
$23$		−	1.66622i		−	0.347432i	0.984796	−	0.173716i	$-0.0555774\pi$
$24$	0.911925	+	1.09157i	0.186146	+	0.222815i
$25$	1.00000			0.200000
$26$	4.43316	+	4.43316i	0.869413	+	0.869413i
$27$	5.01028	+	1.37733i	0.964230	+	0.265068i
$28$		−	7.02687i		−	1.32795i
$29$	4.21312	+	3.35405i	0.782356	+	0.622831i
$29$	4.21312	+	3.35405i	0.782356	+	0.622831i
$30$	2.78563	−	2.32719i	0.508584	−	0.424886i
$31$	−1.53396	−	1.53396i	−0.275507	−	0.275507i	0.555805	−	0.831313i	$-0.312410\pi$
$31$	−1.53396	−	1.53396i	−0.275507	−	0.275507i	−0.831313	+	0.555805i	$0.812410\pi$
$32$	−5.69992	+	5.69992i	−1.00761	+	1.00761i
$33$	6.35186	−	5.30653i	1.10572	−	0.923748i
$34$		−	6.38215i		−	1.09453i
$35$	−2.93783			−0.496584
$36$	1.27652	−	7.06111i	0.212753	−	1.17685i
$37$	−3.65691	+	3.65691i	−0.601192	+	0.601192i	−0.940629	−	0.339436i	$-0.889764\pi$
$37$	−3.65691	+	3.65691i	−0.601192	+	0.601192i	0.339436	+	0.940629i	$0.389764\pi$
$38$	−0.351454			−0.0570133
$39$	0.462747	−	5.16090i	0.0740988	−	0.826406i
$40$	−0.580678	−	0.580678i	−0.0918133	−	0.0918133i
$41$	1.26361	+	1.26361i	0.197343	+	0.197343i	0.798860	−	0.601517i	$-0.205437\pi$
$41$	1.26361	+	1.26361i	0.197343	+	0.197343i	−0.601517	+	0.798860i	$0.705437\pi$
$42$	−8.18371	+	6.83690i	−1.26277	+	1.05496i
$43$	−2.21073	−	2.21073i	−0.337133	−	0.337133i	0.518154	−	0.855287i	$-0.326619\pi$
$43$	−2.21073	−	2.21073i	−0.337133	−	0.337133i	−0.855287	+	0.518154i	$0.826619\pi$
$44$	−8.08206	−	8.08206i	−1.21842	−	1.21842i
$45$	−2.95215	−	0.533693i	−0.440080	−	0.0795582i
$46$	2.46912	+	2.46912i	0.364052	+	0.364052i
$47$	3.31975	+	3.31975i	0.484235	+	0.484235i	0.906481	−	0.422246i	$-0.138758\pi$
$47$	3.31975	+	3.31975i	0.484235	+	0.484235i	−0.422246	+	0.906481i	$0.638758\pi$
$48$	5.28362	+	0.473750i	0.762625	+	0.0683799i
$49$	1.63085			0.232979
$50$	−1.48187	+	1.48187i	−0.209568	+	0.209568i
$51$	−4.04802	+	3.38183i	−0.566836	+	0.473551i
$52$	−7.15548			−0.992287
$53$			13.5559i			1.86205i	0.364960	+	0.931023i	$0.381083\pi$
$53$			13.5559i			1.86205i	−0.364960	+	0.931023i	$0.618917\pi$
$54$	−9.46560	+	5.38355i	−1.28810	+	0.732608i
$55$	−3.37899	+	3.37899i	−0.455623	+	0.455623i
$56$	1.70593	+	1.70593i	0.227965	+	0.227965i
$57$	0.186231	+	0.222917i	0.0246669	+	0.0295261i
$58$	−11.2135	+	1.27303i	−1.47241	+	0.167157i
$59$		−	9.91104i		−	1.29031i	−0.764053	−	0.645154i	$-0.776793\pi$
$59$		−	9.91104i		−	1.29031i	0.764053	−	0.645154i	$-0.223207\pi$
$60$	−0.369977	+	4.12626i	−0.0477638	+	0.532698i
$61$	−0.353285	−	0.353285i	−0.0452335	−	0.0452335i	0.684128	−	0.729362i	$-0.260183\pi$
$61$	−0.353285	−	0.353285i	−0.0452335	−	0.0452335i	−0.729362	+	0.684128i	$0.760183\pi$
$62$	4.54625			0.577374
$63$	8.67291	+	1.56790i	1.09268	+	0.197537i
$64$		−	10.7676i		−	1.34595i
$65$			2.99160i			0.371063i
$66$	−1.54905	+	17.2762i	−0.190675	+	2.12655i
$67$			12.6338i			1.54347i	0.635945	+	0.771734i	$0.280610\pi$
$67$			12.6338i			1.54347i	−0.635945	+	0.771734i	$0.719390\pi$
$68$	5.15066	+	5.15066i	0.624609	+	0.624609i
$69$	0.257735	−	2.87445i	0.0310276	−	0.346044i
$70$	4.35347	−	4.35347i	0.520340	−	0.520340i
$71$	−4.70345			−0.558197			−0.279099	−	0.960262i	$-0.590036\pi$
$71$	−4.70345			−0.558197			−0.279099	+	0.960262i	$0.590036\pi$
$72$	1.40434	+	2.02415i	0.165504	+	0.238549i
$73$	−10.2297	+	10.2297i	−1.19730	+	1.19730i	−0.222327	+	0.974972i	$0.571365\pi$
$73$	−10.2297	+	10.2297i	−1.19730	+	1.19730i	−0.974972	+	0.222327i	$0.928635\pi$
$74$		−	10.8381i		−	1.25990i
$75$	1.72513	+	0.154682i	0.199201	+	0.0178611i
$76$	0.283638	−	0.283638i	0.0325355	−	0.0325355i
$77$	9.92690	−	9.92690i	1.13128	−	1.13128i
$78$	6.96204	+	8.33350i	0.788296	+	0.943583i
$79$	−9.13962	−	9.13962i	−1.02829	−	1.02829i	−0.999588	−	0.0286990i	$-0.990864\pi$
$79$	−9.13962	−	9.13962i	−1.02829	−	1.02829i	−0.0286990	−	0.999588i	$-0.509136\pi$
$80$	−3.06274			−0.342424
$81$	8.43034	+	3.15108i	0.936705	+	0.350120i
$82$	−3.74501			−0.413567
$83$		−	13.0304i		−	1.43028i	−0.698983	−	0.715139i	$-0.746364\pi$
$83$		−	13.0304i		−	1.43028i	0.698983	−	0.715139i	$-0.253636\pi$
$84$	1.08693	−	12.1223i	0.118594	−	1.32265i
$85$	2.15342	−	2.15342i	0.233571	−	0.233571i
$86$	6.55201			0.706522
$87$	6.74937	+	6.43786i	0.723608	+	0.690211i
$88$	3.92421			0.418322
$89$	7.82234	−	7.82234i	0.829167	−	0.829167i	−0.158235	−	0.987402i	$-0.550580\pi$
$89$	7.82234	−	7.82234i	0.829167	−	0.829167i	0.987402	+	0.158235i	$0.0505802\pi$
$90$	5.16555	−	3.58383i	0.544497	−	0.377768i
$91$		−	8.78882i		−	0.921319i
$92$	−3.98537			−0.415503
$93$	−2.40900	−	2.88356i	−0.249802	−	0.299011i
$94$	−9.83884			−1.01480
$95$	−0.118585	−	0.118585i	−0.0121665	−	0.0121665i
$96$	−10.7148	+	8.95143i	−1.09357	+	0.913602i
$97$	10.9110	−	10.9110i	1.10784	−	1.10784i	0.114409	−	0.993434i	$-0.463502\pi$
$97$	10.9110	−	10.9110i	1.10784	−	1.10784i	0.993434	−	0.114409i	$-0.0364976\pi$
$98$	−2.41670	+	2.41670i	−0.244124	+	0.244124i
$99$	11.7786	−	8.17193i	1.18380	−	0.821310i
$100$		−	2.39186i		−	0.239186i
$101$	−8.10218	+	8.10218i	−0.806197	+	0.806197i	−0.984056	−	0.177859i	$-0.943083\pi$
$101$	−8.10218	+	8.10218i	−0.806197	+	0.806197i	0.177859	+	0.984056i	$0.443083\pi$
$102$	0.987203	−	11.0100i	0.0977476	−	1.09016i
$103$	2.34418			0.230979			0.115489	−	0.993309i	$-0.463156\pi$
$103$	2.34418			0.230979			0.115489	+	0.993309i	$0.463156\pi$
$104$	1.73716	−	1.73716i	0.170342	−	0.170342i
$105$	−5.06814	−	0.454429i	−0.494600	−	0.0443477i
$106$	−20.0880	−	20.0880i	−1.95112	−	1.95112i
$107$		−	1.48303i		−	0.143370i	−0.997427	−	0.0716851i	$-0.977162\pi$
$107$		−	1.48303i		−	0.143370i	0.997427	−	0.0716851i	$-0.0228377\pi$
$108$	3.29438	−	11.9839i	0.317002	−	1.15315i
$109$		−	1.08155i		−	0.103593i	−0.998658	−	0.0517966i	$-0.983505\pi$
$109$		−	1.08155i		−	0.103593i	0.998658	−	0.0517966i	$-0.0164948\pi$
$110$		−	10.0144i		−	0.954838i
$111$	−6.87430	+	5.74299i	−0.652480	+	0.545100i
$112$	8.99780			0.850212
$113$	−8.61038	−	8.61038i	−0.809996	−	0.809996i	0.174636	−	0.984633i	$-0.444125\pi$
$113$	−8.61038	−	8.61038i	−0.809996	−	0.809996i	−0.984633	+	0.174636i	$0.944125\pi$
$114$	−0.606303	−	0.0543635i	−0.0567855	−	0.00509161i
$115$			1.66622i			0.155376i
$116$	8.02240	−	10.0772i	0.744861	−	0.935642i
$117$	1.59660	−	8.83165i	0.147605	−	0.816486i
$118$	14.6868	+	14.6868i	1.35203	+	1.35203i
$119$	−6.32637	+	6.32637i	−0.579938	+	0.579938i
$120$	−0.911925	−	1.09157i	−0.0832470	−	0.0996459i
$121$		−	11.8351i		−	1.07592i
$122$	1.04704			0.0947947
$123$	1.98444	+	2.37536i	0.178931	+	0.214179i
$124$	−3.66901	+	3.66901i	−0.329487	+	0.329487i
$125$	−1.00000			−0.0894427
$126$	−15.1755	+	10.5287i	−1.35194	+	0.937969i
$127$	−4.41841	−	4.41841i	−0.392071	−	0.392071i	0.483354	−	0.875425i	$-0.339418\pi$
$127$	−4.41841	−	4.41841i	−0.392071	−	0.392071i	−0.875425	+	0.483354i	$0.839418\pi$
$128$	4.55626	+	4.55626i	0.402721	+	0.402721i
$129$	−3.47184	−	4.15576i	−0.305678	−	0.365894i
$130$	−4.43316	−	4.43316i	−0.388813	−	0.388813i
$131$	10.4377	+	10.4377i	0.911949	+	0.911949i	0.996425	−	0.0844762i	$-0.0269217\pi$
$131$	10.4377	+	10.4377i	0.911949	+	0.911949i	−0.0844762	+	0.996425i	$0.526922\pi$
$132$	−12.6925	−	15.1927i	−1.10474	−	1.32236i
$133$	0.348382	+	0.348382i	0.0302086	+	0.0302086i
$134$	−18.7217	−	18.7217i	−1.61730	−	1.61730i
$135$	−5.01028	−	1.37733i	−0.431217	−	0.118542i
$136$	−2.50088			−0.214449
$137$	0.890323	−	0.890323i	0.0760654	−	0.0760654i	−0.668051	−	0.744116i	$-0.732871\pi$
$137$	0.890323	−	0.890323i	0.0760654	−	0.0760654i	0.744116	+	0.668051i	$0.232871\pi$
$138$	3.87763	+	4.64148i	0.330086	+	0.395109i
$139$	18.4952			1.56874			0.784370	−	0.620294i	$-0.212987\pi$
$139$	18.4952			1.56874			0.784370	+	0.620294i	$0.212987\pi$
$140$			7.02687i			0.593879i
$141$	5.21349	+	6.24050i	0.439055	+	0.525545i
$142$	6.96989	−	6.96989i	0.584900	−	0.584900i
$143$	−10.1086	−	10.1086i	−0.845323	−	0.845323i
$144$	9.04165	+	1.63456i	0.753471	+	0.136213i
$145$	−4.21312	−	3.35405i	−0.349880	−	0.278538i
$146$		−	30.3182i		−	2.50915i
$147$	2.81343	+	0.252263i	0.232048	+	0.0208063i
$148$	8.74681	+	8.74681i	0.718983	+	0.718983i
$149$	3.58220			0.293466			0.146733	−	0.989176i	$-0.453124\pi$
$149$	3.58220			0.293466			0.146733	+	0.989176i	$0.453124\pi$
$150$	−2.78563	+	2.32719i	−0.227446	+	0.190015i
$151$		−	16.7679i		−	1.36455i	−0.731093	−	0.682277i	$-0.760990\pi$
$151$		−	16.7679i		−	1.36455i	0.731093	−	0.682277i	$-0.239010\pi$
$152$			0.137719i			0.0111705i
$153$	−7.50646	+	5.20794i	−0.606862	+	0.421037i
$154$			29.4207i			2.37079i
$155$	1.53396	+	1.53396i	0.123211	+	0.123211i
$156$	−12.3441	−	1.10682i	−0.988322	−	0.0886168i
$157$	−10.3205	+	10.3205i	−0.823665	+	0.823665i	−0.986632	−	0.162967i	$-0.947894\pi$
$157$	−10.3205	+	10.3205i	−0.823665	+	0.823665i	0.162967	+	0.986632i	$0.447894\pi$
$158$	27.0874			2.15496
$159$	−2.09685	+	23.3857i	−0.166291	+	1.85461i
$160$	5.69992	−	5.69992i	0.450619	−	0.450619i
$161$		−	4.89509i		−	0.385787i
$162$	−17.1621	+	7.82317i	−1.34838	+	0.614646i
$163$	−12.2779	+	12.2779i	−0.961683	+	0.961683i	−0.999293	−	0.0376093i	$-0.988026\pi$
$163$	−12.2779	+	12.2779i	−0.961683	+	0.961683i	0.0376093	+	0.999293i	$0.488026\pi$
$164$	3.02238	−	3.02238i	0.236008	−	0.236008i
$165$	−6.35186	+	5.30653i	−0.494492	+	0.413113i
$166$	19.3094	+	19.3094i	1.49870	+	1.49870i
$167$	−7.89385			−0.610845			−0.305422	−	0.952217i	$-0.598798\pi$
$167$	−7.89385			−0.610845			−0.305422	+	0.952217i	$0.598798\pi$
$168$	2.67908	+	3.20684i	0.206696	+	0.247413i
$169$	4.05031			0.311563
$170$			6.38215i			0.489489i
$171$	0.286792	+	0.413368i	0.0219315	+	0.0316110i
$172$	−5.28775	+	5.28775i	−0.403187	+	0.403187i
$173$	−9.85503			−0.749264			−0.374632	−	0.927174i	$-0.622231\pi$
$173$	−9.85503			−0.749264			−0.374632	+	0.927174i	$0.622231\pi$
$174$	−19.5417	+	0.461609i	−1.48145	+	0.0349945i
$175$	2.93783			0.222079
$176$	10.3490	−	10.3490i	0.780082	−	0.780082i
$177$	1.53306	−	17.0978i	0.115232	−	1.28515i
$178$			23.1833i			1.73766i
$179$	−21.2369			−1.58732			−0.793659	−	0.608363i	$-0.791827\pi$
$179$	−21.2369			−1.58732			−0.793659	+	0.608363i	$0.791827\pi$
$180$	−1.27652	+	7.06111i	−0.0951459	+	0.526304i
$181$	−2.49590			−0.185519			−0.0927596	−	0.995689i	$-0.529569\pi$
$181$	−2.49590			−0.185519			−0.0927596	+	0.995689i	$0.529569\pi$
$182$	13.0239	+	13.0239i	0.965393	+	0.965393i
$183$	−0.554815	−	0.664109i	−0.0410131	−	0.0490923i
$184$	0.967540	−	0.967540i	0.0713280	−	0.0713280i
$185$	3.65691	−	3.65691i	0.268861	−	0.268861i
$186$	7.84287	+	0.703222i	0.575067	+	0.0515627i
$187$			14.5527i			1.06420i
$188$	7.94036	−	7.94036i	0.579110	−	0.579110i
$189$	14.7194	+	4.04637i	1.07068	+	0.294330i
$190$	0.351454			0.0254971
$191$	−16.8734	+	16.8734i	−1.22092	+	1.22092i	−0.253611	+	0.967306i	$0.581618\pi$
$191$	−16.8734	+	16.8734i	−1.22092	+	1.22092i	−0.967306	+	0.253611i	$0.918382\pi$
$192$	1.66555	−	18.5755i	0.120201	−	1.34057i
$193$	−8.37214	−	8.37214i	−0.602640	−	0.602640i	0.338373	−	0.941012i	$-0.390124\pi$
$193$	−8.37214	−	8.37214i	−0.602640	−	0.602640i	−0.941012	+	0.338373i	$0.890124\pi$
$194$			32.3373i			2.32168i
$195$	−0.462747	+	5.16090i	−0.0331380	+	0.369580i
$196$		−	3.90076i		−	0.278626i
$197$			18.1453i			1.29280i	0.763000	+	0.646398i	$0.223725\pi$
$197$			18.1453i			1.29280i	−0.763000	+	0.646398i	$0.776275\pi$
$198$	−5.34462	+	29.5640i	−0.379826	+	2.10103i
$199$	21.7350			1.54075			0.770377	−	0.637589i	$-0.220068\pi$
$199$	21.7350			1.54075			0.770377	+	0.637589i	$0.220068\pi$
$200$	0.580678	+	0.580678i	0.0410602	+	0.0410602i
$201$	−1.95422	+	21.7950i	−0.137840	+	1.53730i
$202$		−	24.0127i		−	1.68953i
$203$	12.3774	+	9.85362i	0.868725	+	0.691589i
$204$	8.08885	+	9.68227i	0.566332	+	0.677895i
$205$	−1.26361	−	1.26361i	−0.0882546	−	0.0882546i
$206$	−3.47376	+	3.47376i	−0.242028	+	0.242028i
$207$	0.889252	−	4.91894i	0.0618073	−	0.341890i
$208$		−	9.16249i		−	0.635304i
$209$	0.801394			0.0554336
$210$	8.18371	−	6.83690i	0.564730	−	0.471791i
$211$	−0.0633356	+	0.0633356i	−0.00436020	+	0.00436020i	−0.709284	−	0.704923i	$-0.750981\pi$
$211$	−0.0633356	+	0.0633356i	−0.00436020	+	0.00436020i	0.704923	+	0.709284i	$0.250981\pi$
$212$	32.4238			2.22687
$213$	−8.11407	−	0.727539i	−0.555967	−	0.0498501i
$214$	2.19766	+	2.19766i	0.150229	+	0.150229i
$215$	2.21073	+	2.21073i	0.150770	+	0.150770i
$216$	2.10958	+	3.70915i	0.143539	+	0.252376i
$217$	−4.50651	−	4.50651i	−0.305922	−	0.305922i
$218$	1.60271	+	1.60271i	0.108549	+	0.108549i
$219$	−19.2300	+	16.0653i	−1.29944	+	1.08559i
$220$	8.08206	+	8.08206i	0.544892	+	0.544892i
$221$	6.44216	+	6.44216i	0.433347	+	0.433347i
$222$	1.67646	−	18.6971i	0.112517	−	1.25487i
$223$	22.9240			1.53510			0.767551	−	0.640988i	$-0.221475\pi$
$223$	22.9240			1.53510			0.767551	+	0.640988i	$0.221475\pi$
$224$	−16.7454	+	16.7454i	−1.11885	+	1.11885i
$225$	2.95215	+	0.533693i	0.196810	+	0.0355795i
$226$	25.5189			1.69749
$227$		−	14.0588i		−	0.933113i	−0.884491	−	0.466557i	$-0.845494\pi$
$227$		−	14.0588i		−	0.933113i	0.884491	−	0.466557i	$-0.154506\pi$
$228$	0.533186	−	0.445439i	0.0353111	−	0.0294999i
$229$	−13.3218	+	13.3218i	−0.880328	+	0.880328i	−0.993568	−	0.113239i	$-0.963877\pi$
$229$	−13.3218	+	13.3218i	−0.880328	+	0.880328i	0.113239	+	0.993568i	$0.463877\pi$
$230$	−2.46912	−	2.46912i	−0.162809	−	0.162809i
$231$	18.6607	−	15.5897i	1.22778	−	1.02573i
$232$	0.498844	+	4.39409i	0.0327507	+	0.288486i
$233$		−	22.4266i		−	1.46922i	−0.678491	−	0.734608i	$-0.737366\pi$
$233$		−	22.4266i		−	1.46922i	0.678491	−	0.734608i	$-0.262634\pi$
$234$	10.7214	+	15.4533i	0.700879	+	1.01021i
$235$	−3.31975	−	3.31975i	−0.216556	−	0.216556i
$236$	−23.7058			−1.54311
$237$	−14.3533	−	17.1808i	−0.932347	−	1.11601i
$238$		−	18.7497i		−	1.21536i
$239$		−	6.95344i		−	0.449780i	−0.974384	−	0.224890i	$-0.927798\pi$
$239$		−	6.95344i		−	0.449780i	0.974384	−	0.224890i	$-0.0722023\pi$
$240$	−5.28362	−	0.473750i	−0.341056	−	0.0305804i
$241$			13.5512i			0.872908i	0.899727	+	0.436454i	$0.143766\pi$
$241$			13.5512i			0.872908i	−0.899727	+	0.436454i	$0.856234\pi$
$242$	17.5381	+	17.5381i	1.12739	+	1.12739i
$243$	14.0560	+	6.74004i	0.901694	+	0.432374i
$244$	−0.845006	+	0.845006i	−0.0540960	+	0.0540960i
$245$	−1.63085			−0.104191
$246$	−6.46063	−	0.579285i	−0.411915	−	0.0369339i
$247$	0.354759	−	0.354759i	0.0225728	−	0.0225728i
$248$		−	1.78147i		−	0.113124i
$249$	2.01557	−	22.4792i	0.127732	−	1.42456i
$250$	1.48187	−	1.48187i	0.0937215	−	0.0937215i
$251$	−6.29434	+	6.29434i	−0.397295	+	0.397295i	−0.877278	−	0.479983i	$-0.840643\pi$
$251$	−6.29434	+	6.29434i	−0.397295	+	0.397295i	0.479983	+	0.877278i	$0.340643\pi$
$252$	3.75019	−	20.7443i	0.236240	−	1.30677i
$253$	−5.63016	−	5.63016i	−0.353965	−	0.353965i
$254$	13.0950			0.821653
$255$	4.04802	−	3.38183i	0.253497	−	0.211778i
$256$	8.03161			0.501975
$257$			17.5726i			1.09615i	0.836429	+	0.548075i	$0.184639\pi$
$257$			17.5726i			1.09615i	−0.836429	+	0.548075i	$0.815361\pi$
$258$	11.3031	+	1.01348i	0.703698	+	0.0630963i
$259$	−10.7434	+	10.7434i	−0.667562	+	0.667562i
$260$	7.15548			0.443764
$261$	10.6477	+	12.1502i	0.659077	+	0.752076i
$262$	−30.9347			−1.91115
$263$	−19.1585	+	19.1585i	−1.18136	+	1.18136i	−0.201971	+	0.979391i	$0.564735\pi$
$263$	−19.1585	+	19.1585i	−1.18136	+	1.18136i	−0.979391	+	0.201971i	$0.935265\pi$
$264$	6.76978	+	0.607004i	0.416651	+	0.0373585i
$265$		−	13.5559i		−	0.832733i
$266$	−1.03251			−0.0633074
$267$	14.7045	−	12.2846i	0.899903	−	0.751805i
$268$	30.2183			1.84588
$269$	−18.2741	−	18.2741i	−1.11419	−	1.11419i	−0.992578	−	0.121612i	$-0.961194\pi$
$269$	−18.2741	−	18.2741i	−1.11419	−	1.11419i	−0.121612	−	0.992578i	$-0.538806\pi$
$270$	9.46560	−	5.38355i	0.576058	−	0.327632i
$271$	−15.4985	+	15.4985i	−0.941466	+	0.941466i	−0.998379	−	0.0569136i	$-0.981874\pi$
$271$	−15.4985	+	15.4985i	−0.941466	+	0.941466i	0.0569136	+	0.998379i	$0.481874\pi$
$272$	−6.59535	+	6.59535i	−0.399902	+	0.399902i
$273$	1.35947	−	15.1619i	0.0822789	−	0.917638i
$274$			2.63868i			0.159408i
$275$	3.37899	−	3.37899i	0.203761	−	0.203761i
$276$	−6.87528	−	0.616464i	−0.413843	−	0.0371068i
$277$	−24.5084			−1.47257			−0.736284	−	0.676673i	$-0.763421\pi$
$277$	−24.5084			−1.47257			−0.736284	+	0.676673i	$0.763421\pi$
$278$	−27.4074	+	27.4074i	−1.64378	+	1.64378i
$279$	−3.70981	−	5.34714i	−0.222101	−	0.320125i
$280$	−1.70593	−	1.70593i	−0.101949	−	0.101949i
$281$		−	0.198216i		−	0.0118246i	−0.999983	−	0.00591230i	$-0.998118\pi$
$281$		−	0.198216i		−	0.0118246i	0.999983	−	0.00591230i	$-0.00188195\pi$
$282$	−16.9733	−	1.52189i	−1.01074	−	0.0906272i
$283$			17.8836i			1.06307i	0.847036	+	0.531535i	$0.178385\pi$
$283$			17.8836i			1.06307i	−0.847036	+	0.531535i	$0.821615\pi$
$284$			11.2500i			0.667564i
$285$	−0.186231	−	0.222917i	−0.0110314	−	0.0132045i
$286$	29.9592			1.77152
$287$	3.71228	+	3.71228i	0.219129	+	0.219129i
$288$	−19.8690	+	13.7850i	−1.17079	+	0.812289i
$289$			7.72560i			0.454447i
$290$	11.2135	−	1.27303i	0.658481	−	0.0747548i
$291$	20.5106	−	17.1351i	1.20235	−	1.00448i
$292$	24.4680	+	24.4680i	1.43188	+	1.43188i
$293$	13.3739	−	13.3739i	0.781312	−	0.781312i	−0.198740	−	0.980052i	$-0.563685\pi$
$293$	13.3739	−	13.3739i	0.781312	−	0.781312i	0.980052	+	0.198740i	$0.0636849\pi$
$294$	−4.54295	+	3.79531i	−0.264950	+	0.221347i
$295$			9.91104i			0.577043i
$296$	−4.24698			−0.246851
$297$	21.5837	−	12.2757i	1.25241	−	0.712309i
$298$	−5.30835	+	5.30835i	−0.307504	+	0.307504i
$299$	−4.98468			−0.288272
$300$	0.369977	−	4.12626i	0.0213606	−	0.238230i
$301$	−6.49475	−	6.49475i	−0.374351	−	0.374351i
$302$	24.8478	+	24.8478i	1.42983	+	1.42983i
$303$	−15.2306	+	12.7241i	−0.874974	+	0.730978i
$304$	0.363194	+	0.363194i	0.0208306	+	0.0208306i
$305$	0.353285	+	0.353285i	0.0202290	+	0.0202290i
$306$	3.40611	−	18.8410i	0.194714	−	1.07707i
$307$	−6.17304	−	6.17304i	−0.352314	−	0.352314i	0.508656	−	0.860970i	$-0.330142\pi$
$307$	−6.17304	−	6.17304i	−0.352314	−	0.352314i	−0.860970	+	0.508656i	$0.830142\pi$
$308$	−23.7437	−	23.7437i	−1.35292	−	1.35292i
$309$	4.04401	+	0.362602i	0.230056	+	0.0206277i
$310$	−4.54625			−0.258209
$311$	−2.72924	+	2.72924i	−0.154761	+	0.154761i	−0.780241	−	0.625479i	$-0.784903\pi$
$311$	−2.72924	+	2.72924i	−0.154761	+	0.154761i	0.625479	+	0.780241i	$0.284903\pi$
$312$	3.26553	−	2.72812i	0.184874	−	0.154449i
$313$	−4.74050			−0.267949			−0.133974	−	0.990985i	$-0.542774\pi$
$313$	−4.74050			−0.267949			−0.133974	+	0.990985i	$0.542774\pi$
$314$		−	30.5872i		−	1.72613i
$315$	−8.67291	−	1.56790i	−0.488663	−	0.0883411i
$316$	−21.8606	+	21.8606i	−1.22976	+	1.22976i
$317$	−19.9095	−	19.9095i	−1.11823	−	1.11823i	−0.992002	−	0.126226i	$-0.959714\pi$
$317$	−19.9095	−	19.9095i	−1.11823	−	1.11823i	−0.126226	−	0.992002i	$-0.540286\pi$
$318$	−31.5472	−	37.7617i	−1.76908	−	2.11757i
$319$	25.5694	−	2.90279i	1.43161	−	0.162525i
$320$			10.7676i			0.601926i
$321$	0.229398	−	2.55842i	0.0128038	−	0.142797i
$322$	7.25386	+	7.25386i	0.404242	+	0.404242i
$323$	−0.510725			−0.0284175
$324$	7.53693	−	20.1642i	0.418718	−	1.12023i
$325$		−	2.99160i		−	0.165944i
$326$		−	36.3886i		−	2.01538i
$327$	0.167296	−	1.86581i	0.00925146	−	0.103179i
$328$			1.46751i			0.0810294i
$329$	9.75285	+	9.75285i	0.537692	+	0.537692i
$330$	1.54905	−	17.2762i	0.0852724	−	0.951022i
$331$	4.48279	−	4.48279i	0.246396	−	0.246396i	−0.573094	−	0.819490i	$-0.694257\pi$
$331$	4.48279	−	4.48279i	0.246396	−	0.246396i	0.819490	+	0.573094i	$0.194257\pi$
$332$	−31.1670			−1.71051
$333$	−12.7474	+	8.84407i	−0.698554	+	0.484652i
$334$	11.6976	−	11.6976i	0.640066	−	0.640066i
$335$		−	12.6338i		−	0.690260i
$336$	15.5224	+	1.39180i	0.846815	+	0.0759287i
$337$	3.25834	−	3.25834i	0.177493	−	0.177493i	−0.612769	−	0.790262i	$-0.709944\pi$
$337$	3.25834	−	3.25834i	0.177493	−	0.177493i	0.790262	+	0.612769i	$0.209944\pi$
$338$	−6.00203	+	6.00203i	−0.326467	+	0.326467i
$339$	−13.5222	−	16.1859i	−0.734423	−	0.879097i
$340$	−5.15066	−	5.15066i	−0.279334	−	0.279334i
$341$	−10.3665			−0.561376
$342$	−1.03754	−	0.187568i	−0.0561039	−	0.0101425i
$343$	−15.7737			−0.851697
$344$		−	2.56745i		−	0.138427i
$345$	−0.257735	+	2.87445i	−0.0138760	+	0.154755i
$346$	14.6038	−	14.6038i	0.785107	−	0.785107i
$347$	−1.88155			−0.101007			−0.0505034	−	0.998724i	$-0.516083\pi$
$347$	−1.88155			−0.101007			−0.0505034	+	0.998724i	$0.516083\pi$
$348$	15.3984	−	16.1435i	0.825443	−	0.865383i
$349$	−23.5825			−1.26234			−0.631171	−	0.775644i	$-0.717425\pi$
$349$	−23.5825			−1.26234			−0.631171	+	0.775644i	$0.717425\pi$
$350$	−4.35347	+	4.35347i	−0.232703	+	0.232703i
$351$	4.12043	−	14.9888i	0.219932	−	0.800042i
$352$			38.5200i			2.05312i
$353$	16.1391			0.858997			0.429498	−	0.903068i	$-0.358690\pi$
$353$	16.1391			0.858997			0.429498	+	0.903068i	$0.358690\pi$
$354$	23.0649	+	27.6085i	1.22589	+	1.46737i
$355$	4.70345			0.249633
$356$	−18.7099	−	18.7099i	−0.991624	−	0.991624i
$357$	−11.8924	+	9.93524i	−0.629412	+	0.525829i
$358$	31.4702	−	31.4702i	1.66325	−	1.66325i
$359$	7.41198	−	7.41198i	0.391189	−	0.391189i	−0.483922	−	0.875111i	$-0.660788\pi$
$359$	7.41198	−	7.41198i	0.391189	−	0.391189i	0.875111	+	0.483922i	$0.160788\pi$
$360$	−1.40434	−	2.02415i	−0.0740154	−	0.106682i
$361$		−	18.9719i		−	0.998520i
$362$	3.69860	−	3.69860i	0.194394	−	0.194394i
$363$	1.83068	−	20.4172i	0.0960859	−	1.07162i
$364$	−21.0216			−1.10183
$365$	10.2297	−	10.2297i	0.535448	−	0.535448i
$366$	1.80628	+	0.161958i	0.0944159	+	0.00846570i
$367$	22.5850	+	22.5850i	1.17893	+	1.17893i	0.980018	+	0.198907i	$0.0637393\pi$
$367$	22.5850	+	22.5850i	1.17893	+	1.17893i	0.198907	+	0.980018i	$0.436261\pi$
$368$		−	5.10321i		−	0.266023i
$369$	3.05599	+	4.40475i	0.159089	+	0.229302i
$370$			10.8381i			0.563446i
$371$			39.8250i			2.06761i
$372$	−6.89705	+	5.76199i	−0.357595	+	0.298745i
$373$	−22.5466			−1.16742			−0.583710	−	0.811962i	$-0.698400\pi$
$373$	−22.5466			−1.16742			−0.583710	+	0.811962i	$0.698400\pi$
$374$	−21.5652	−	21.5652i	−1.11511	−	1.11511i
$375$	−1.72513	−	0.154682i	−0.0890853	−	0.00798774i
$376$			3.85541i			0.198828i
$377$	10.0340	−	12.6040i	0.516776	−	0.649138i
$378$	−27.8083	+	15.8160i	−1.43031	+	0.813485i
$379$	24.0656	+	24.0656i	1.23617	+	1.23617i	0.961556	+	0.274610i	$0.0885488\pi$
$379$	24.0656	+	24.0656i	1.23617	+	1.23617i	0.274610	+	0.961556i	$0.411451\pi$
$380$	−0.283638	+	0.283638i	−0.0145503	+	0.0145503i
$381$	−6.93889	−	8.30579i	−0.355490	−	0.425518i
$382$		−	50.0083i		−	2.55865i
$383$	37.8367			1.93337			0.966683	−	0.255975i	$-0.0823964\pi$
$383$	37.8367			1.93337			0.966683	+	0.255975i	$0.0823964\pi$
$384$	7.15537	+	8.56492i	0.365146	+	0.437077i
$385$	−9.92690	+	9.92690i	−0.505922	+	0.505922i
$386$	24.8128			1.26294
$387$	−5.34655	−	7.70625i	−0.271780	−	0.391731i
$388$	−26.0975	−	26.0975i	−1.32490	−	1.32490i
$389$	8.09893	+	8.09893i	0.410632	+	0.410632i	0.881959	−	0.471327i	$-0.156225\pi$
$389$	8.09893	+	8.09893i	0.410632	+	0.410632i	−0.471327	+	0.881959i	$0.656225\pi$
$390$	−6.96204	−	8.33350i	−0.352537	−	0.421983i
$391$	3.58807	+	3.58807i	0.181457	+	0.181457i
$392$	0.946999	+	0.946999i	0.0478307	+	0.0478307i
$393$	16.3919	+	19.6210i	0.826863	+	0.989748i
$394$	−26.8889	−	26.8889i	−1.35464	−	1.35464i
$395$	9.13962	+	9.13962i	0.459864	+	0.459864i
$396$	−19.5461	−	28.1728i	−0.982228	−	1.41573i
$397$	14.8915			0.747382			0.373691	−	0.927553i	$-0.378092\pi$
$397$	14.8915			0.747382			0.373691	+	0.927553i	$0.378092\pi$
$398$	−32.2084	+	32.2084i	−1.61446	+	1.61446i
$399$	0.547116	+	0.654893i	0.0273901	+	0.0327857i
$400$	3.06274			0.153137
$401$		−	12.9978i		−	0.649081i	−0.945872	−	0.324541i	$-0.894790\pi$
$401$		−	12.9978i		−	0.649081i	0.945872	−	0.324541i	$-0.105210\pi$
$402$	−29.4014	−	35.1932i	−1.46641	−	1.75528i
$403$	−4.58900	+	4.58900i	−0.228594	+	0.228594i
$404$	19.3793	+	19.3793i	0.964154	+	0.964154i
$405$	−8.43034	−	3.15108i	−0.418907	−	0.156578i
$406$	−32.9435	+	3.73994i	−1.63496	+	0.185610i
$407$			24.7133i			1.22499i
$408$	−4.31435	−	0.386841i	−0.213592	−	0.0191515i
$409$	14.8397	+	14.8397i	0.733776	+	0.733776i	0.971366	−	0.237589i	$-0.0763573\pi$
$409$	14.8397	+	14.8397i	0.733776	+	0.733776i	−0.237589	+	0.971366i	$0.576357\pi$
$410$	3.74501			0.184953
$411$	1.67364	−	1.39821i	0.0825545	−	0.0689684i
$412$		−	5.60694i		−	0.276234i
$413$		−	29.1170i		−	1.43275i
$414$	5.97146	+	8.60696i	0.293481	+	0.423009i
$415$			13.0304i			0.639640i
$416$	17.0519	+	17.0519i	0.836038	+	0.836038i
$417$	31.9066	+	2.86087i	1.56247	+	0.140097i
$418$	−1.18756	+	1.18756i	−0.0580854	+	0.0580854i
$419$	12.6943			0.620155			0.310077	−	0.950711i	$-0.399645\pi$
$419$	12.6943			0.620155			0.310077	+	0.950711i	$0.399645\pi$
$420$	−1.08693	+	12.1223i	−0.0530367	+	0.591506i
$421$	−9.72150	+	9.72150i	−0.473797	+	0.473797i	−0.903141	−	0.429344i	$-0.858745\pi$
$421$	−9.72150	+	9.72150i	−0.473797	+	0.473797i	0.429344	+	0.903141i	$0.358745\pi$
$422$		−	0.187710i		−	0.00913757i
$423$	8.02866	+	11.5721i	0.390367	+	0.562655i
$424$	−7.87162	+	7.87162i	−0.382280	+	0.382280i
$425$	−2.15342	+	2.15342i	−0.104456	+	0.104456i
$426$	13.1021	−	10.9459i	0.634798	−	0.530328i
$427$	−1.03789	−	1.03789i	−0.0502270	−	0.0502270i
$428$	−3.54720			−0.171460
$429$	−15.8750	−	19.0023i	−0.766453	−	0.917438i
$430$	−6.55201			−0.315966
$431$			4.31482i			0.207837i	0.994586	+	0.103919i	$0.0331382\pi$
$431$			4.31482i			0.207837i	−0.994586	+	0.103919i	$0.966862\pi$
$432$	15.3452	+	4.21841i	0.738295	+	0.202958i
$433$	−0.0462764	+	0.0462764i	−0.00222390	+	0.00222390i	−0.708218	−	0.705994i	$-0.750501\pi$
$433$	−0.0462764	+	0.0462764i	−0.00222390	+	0.00222390i	0.705994	+	0.708218i	$0.250501\pi$
$434$	13.3561			0.641114
$435$	−6.74937	−	6.43786i	−0.323607	−	0.308672i
$436$	−2.58690			−0.123890
$437$	0.197589	−	0.197589i	0.00945196	−	0.00945196i
$438$	4.68967	−	52.3028i	0.224081	−	2.49912i
$439$		−	27.8714i		−	1.33023i	−0.746741	−	0.665115i	$-0.768382\pi$
$439$		−	27.8714i		−	1.33023i	0.746741	−	0.665115i	$-0.231618\pi$
$440$	−3.92421			−0.187079
$441$	4.81451	+	0.870373i	0.229262	+	0.0414463i
$442$	−19.0929			−0.908154
$443$	22.5157	+	22.5157i	1.06975	+	1.06975i	0.997377	+	0.0723761i	$0.0230582\pi$
$443$	22.5157	+	22.5157i	1.06975	+	1.06975i	0.0723761	+	0.997377i	$0.476942\pi$
$444$	13.7364	+	16.4423i	0.651901	+	0.780319i
$445$	−7.82234	+	7.82234i	−0.370815	+	0.370815i
$446$	−33.9702	+	33.9702i	−1.60854	+	1.60854i
$447$	6.17977	+	0.554102i	0.292293	+	0.0262081i
$448$		−	31.6333i		−	1.49453i
$449$	4.64320	−	4.64320i	0.219126	−	0.219126i	−0.589004	−	0.808130i	$-0.700480\pi$
$449$	4.64320	−	4.64320i	0.219126	−	0.219126i	0.808130	+	0.589004i	$0.200480\pi$
$450$	−5.16555	+	3.58383i	−0.243506	+	0.168943i
$451$	8.53947			0.402108
$452$	−20.5948	+	20.5948i	−0.968698	+	0.968698i
$453$	2.59369	−	28.9269i	0.121862	−	1.35910i
$454$	20.8332	+	20.8332i	0.977751	+	0.977751i
$455$			8.78882i			0.412026i
$456$	−0.0213027	+	0.237584i	−0.000997589	+	0.0111259i
$457$		−	22.4554i		−	1.05042i	−0.850973	−	0.525210i	$-0.823987\pi$
$457$		−	22.4554i		−	1.05042i	0.850973	−	0.525210i	$-0.176013\pi$
$458$		−	39.4822i		−	1.84488i
$459$	−13.7552	+	7.82326i	−0.642038	+	0.365158i
$460$	3.98537			0.185819
$461$	3.28785	+	3.28785i	0.153130	+	0.153130i	0.779514	−	0.626384i	$-0.215466\pi$
$461$	3.28785	+	3.28785i	0.153130	+	0.153130i	−0.626384	+	0.779514i	$0.715466\pi$
$462$	−4.55085	+	50.7545i	−0.211724	+	2.36131i
$463$		−	7.60616i		−	0.353488i	−0.984257	−	0.176744i	$-0.943444\pi$
$463$		−	7.60616i		−	0.353488i	0.984257	−	0.176744i	$-0.0565565\pi$
$464$	12.9037	+	10.2726i	0.599038	+	0.476892i
$465$	2.40900	+	2.88356i	0.111715	+	0.133722i
$466$	33.2333	+	33.2333i	1.53950	+	1.53950i
$467$	2.63900	−	2.63900i	0.122118	−	0.122118i	−0.643406	−	0.765525i	$-0.722479\pi$
$467$	2.63900	−	2.63900i	0.122118	−	0.122118i	0.765525	+	0.643406i	$0.222479\pi$
$468$	−21.1240	−	3.81883i	−0.976459	−	0.176525i
$469$			37.1161i			1.71386i
$470$	9.83884			0.453832
$471$	−19.4006	+	16.2078i	−0.893932	+	0.746816i
$472$	5.75513	−	5.75513i	0.264901	−	0.264901i
$473$	−14.9401			−0.686945
$474$	46.7293	+	4.18993i	2.14635	+	0.192450i
$475$	0.118585	+	0.118585i	0.00544105	+	0.00544105i
$476$	15.1318	+	15.1318i	0.693564	+	0.693564i
$477$	−7.23469	+	40.0190i	−0.331254	+	1.83235i
$478$	10.3041	+	10.3041i	0.471297	+	0.471297i
$479$	8.67211	+	8.67211i	0.396239	+	0.396239i	0.876904	−	0.480665i	$-0.159605\pi$
$479$	8.67211	+	8.67211i	0.396239	+	0.396239i	−0.480665	+	0.876904i	$0.659605\pi$
$480$	10.7148	−	8.95143i	0.489061	−	0.408575i
$481$	10.9400	+	10.9400i	0.498822	+	0.498822i
$482$	−20.0810	−	20.0810i	−0.914666	−	0.914666i
$483$	0.757181	−	8.44466i	0.0344529	−	0.384245i
$484$	−28.3080			−1.28673
$485$	−10.9110	+	10.9110i	−0.495443	+	0.495443i
$486$	−30.8170	+	10.8413i	−1.39789	+	0.491772i
$487$	2.35949			0.106919			0.0534594	−	0.998570i	$-0.482975\pi$
$487$	2.35949			0.106919			0.0534594	+	0.998570i	$0.482975\pi$
$488$		−	0.410290i		−	0.0185729i
$489$	−23.0802	+	19.2819i	−1.04372	+	0.871957i
$490$	2.41670	−	2.41670i	0.109175	−	0.109175i
$491$	2.05519	+	2.05519i	0.0927493	+	0.0927493i	0.751959	−	0.659210i	$-0.229109\pi$
$491$	2.05519	+	2.05519i	0.0927493	+	0.0927493i	−0.659210	+	0.751959i	$0.729109\pi$
$492$	5.68151	−	4.74649i	0.256142	−	0.213988i
$493$	−16.2953	+	1.84994i	−0.733901	+	0.0833169i
$494$			1.05141i			0.0473052i
$495$	−11.7786	+	8.17193i	−0.529409	+	0.367301i
$496$	−4.69811	−	4.69811i	−0.210952	−	0.210952i
$497$	−13.8180			−0.619820
$498$	30.3244	+	36.2980i	1.35887	+	1.62655i
$499$			6.71513i			0.300610i	0.988640	+	0.150305i	$0.0480256\pi$
$499$			6.71513i			0.300610i	−0.988640	+	0.150305i	$0.951974\pi$
$500$			2.39186i			0.106967i
$501$	−13.6179	−	1.22104i	−0.608404	−	0.0545518i
$502$		−	18.6548i		−	0.832602i
$503$	−12.8392	−	12.8392i	−0.572473	−	0.572473i	0.360346	−	0.932819i	$-0.382659\pi$
$503$	−12.8392	−	12.8392i	−0.572473	−	0.572473i	−0.932819	+	0.360346i	$0.882659\pi$
$504$	4.12573	+	5.94662i	0.183774	+	0.264883i
$505$	8.10218	−	8.10218i	0.360542	−	0.360542i
$506$	16.6863			0.741795
$507$	6.98732	+	0.626510i	0.310318	+	0.0278243i
$508$	−10.5682	+	10.5682i	−0.468888	+	0.468888i
$509$		−	2.97068i		−	0.131673i	−0.997830	−	0.0658366i	$-0.979028\pi$
$509$		−	2.97068i		−	0.131673i	0.997830	−	0.0658366i	$-0.0209716\pi$
$510$	−0.987203	+	11.0100i	−0.0437141	+	0.487533i
$511$	−30.0532	+	30.0532i	−1.32948	+	1.32948i
$512$	−21.0143	+	21.0143i	−0.928709	+	0.928709i
$513$	0.430813	+	0.757475i	0.0190209	+	0.0334433i
$514$	−26.0403	−	26.0403i	−1.14859	−	1.14859i
$515$	−2.34418			−0.103297
$516$	−9.93997	+	8.30413i	−0.437583	+	0.365569i
$517$	22.4348			0.986681
$518$		−	31.8405i		−	1.39899i
$519$	−17.0012	−	1.52439i	−0.746270	−	0.0669135i
$520$	−1.73716	+	1.73716i	−0.0761795	+	0.0761795i
$521$	−13.9466			−0.611014			−0.305507	−	0.952190i	$-0.598826\pi$
$521$	−13.9466			−0.611014			−0.305507	+	0.952190i	$0.598826\pi$
$522$	−33.7834	−	2.22641i	−1.47866	−	0.0974474i
$523$	−30.1510			−1.31841			−0.659206	−	0.751963i	$-0.729107\pi$
$523$	−30.1510			−1.31841			−0.659206	+	0.751963i	$0.729107\pi$
$524$	24.9656	−	24.9656i	1.09063	−	1.09063i
$525$	5.06814	+	0.454429i	0.221192	+	0.0198329i
$526$		−	56.7806i		−	2.47575i
$527$	6.60651			0.287784
$528$	19.4541	−	16.2525i	0.846631	−	0.707299i
$529$	20.2237			0.879291
$530$	20.0880	+	20.0880i	0.872569	+	0.872569i
$531$	5.28945	−	29.2588i	0.229543	−	1.26973i
$532$	0.833280	−	0.833280i	0.0361273	−	0.0361273i
$533$	3.78023	−	3.78023i	0.163740	−	0.163740i
$534$	−3.58604	+	39.9943i	−0.155183	+	1.73072i
$535$			1.48303i			0.0641171i
$536$	−7.33619	+	7.33619i	−0.316875	+	0.316875i
$537$	−36.6364	−	3.28496i	−1.58098	−	0.141756i
$538$	54.1594			2.33498
$539$	5.51063	−	5.51063i	0.237359	−	0.237359i
$540$	−3.29438	+	11.9839i	−0.141768	+	0.515704i
$541$	−14.5727	−	14.5727i	−0.626529	−	0.626529i	0.320664	−	0.947193i	$-0.396094\pi$
$541$	−14.5727	−	14.5727i	−0.626529	−	0.626529i	−0.947193	+	0.320664i	$0.896094\pi$
$542$		−	45.9333i		−	1.97301i
$543$	−4.30576	−	0.386071i	−0.184778	−	0.0165679i
$544$		−	24.5486i		−	1.05251i
$545$			1.08155i			0.0463283i
$546$	20.4533	+	24.4824i	0.875320	+	1.04775i
$547$	34.1064			1.45828			0.729142	−	0.684363i	$-0.239920\pi$
$547$	34.1064			1.45828			0.729142	+	0.684363i	$0.239920\pi$
$548$	−2.12952	−	2.12952i	−0.0909688	−	0.0909688i
$549$	−0.854403	−	1.23149i	−0.0364650	−	0.0525589i
$550$			10.0144i			0.427016i
$551$	0.101873	+	0.897351i	0.00433992	+	0.0382284i
$552$	1.81879	−	1.51947i	0.0774130	−	0.0646730i
$553$	−26.8506	−	26.8506i	−1.14181	−	1.14181i
$554$	36.3182	−	36.3182i	1.54301	−	1.54301i
$555$	6.87430	−	5.74299i	0.291798	−	0.243776i
$556$		−	44.2378i		−	1.87610i
$557$	26.8844			1.13913			0.569563	−	0.821948i	$-0.307112\pi$
$557$	26.8844			1.13913			0.569563	+	0.821948i	$0.307112\pi$
$558$	13.4212	+	2.42630i	0.568164	+	0.102713i
$559$	−6.61362	+	6.61362i	−0.279726	+	0.279726i
$560$	−8.99780			−0.380227
$561$	−2.25104	+	25.1054i	−0.0950392	+	1.05995i
$562$	0.293730	+	0.293730i	0.0123903	+	0.0123903i
$563$	−13.7161	−	13.7161i	−0.578065	−	0.578065i	0.356305	−	0.934370i	$-0.384036\pi$
$563$	−13.7161	−	13.7161i	−0.578065	−	0.578065i	−0.934370	+	0.356305i	$0.884036\pi$
$564$	14.9264	−	12.4699i	0.628514	−	0.525078i
$565$	8.61038	+	8.61038i	0.362241	+	0.362241i
$566$	−26.5011	−	26.5011i	−1.11393	−	1.11393i
$567$	24.7669	+	9.25733i	1.04011	+	0.388771i
$568$	−2.73119	−	2.73119i	−0.114598	−	0.114598i
$569$	3.42433	+	3.42433i	0.143556	+	0.143556i	0.775232	−	0.631677i	$-0.217633\pi$
$569$	3.42433	+	3.42433i	0.143556	+	0.143556i	−0.631677	+	0.775232i	$0.717633\pi$
$570$	0.606303	+	0.0543635i	0.0253953	+	0.00227704i
$571$	−33.5328			−1.40330			−0.701652	−	0.712520i	$-0.747554\pi$
$571$	−33.5328			−1.40330			−0.701652	+	0.712520i	$0.747554\pi$
$572$	−24.1783	+	24.1783i	−1.01095	+	1.01095i
$573$	−31.7188	+	26.4988i	−1.32507	+	1.10700i
$574$	−11.0022			−0.459223
$575$		−	1.66622i		−	0.0694864i
$576$	5.74658	−	31.7875i	0.239441	−	1.32448i
$577$	15.9032	−	15.9032i	0.662060	−	0.662060i	−0.293805	−	0.955865i	$-0.594922\pi$
$577$	15.9032	−	15.9032i	0.662060	−	0.662060i	0.955865	+	0.293805i	$0.0949217\pi$
$578$	−11.4483	−	11.4483i	−0.476187	−	0.476187i
$579$	−13.1480	−	15.7380i	−0.546413	−	0.654051i
$580$	−8.02240	+	10.0772i	−0.333112	+	0.418432i
$581$		−	38.2813i		−	1.58817i
$582$	−5.00199	+	55.7860i	−0.207339	+	2.31240i
$583$	45.8053	+	45.8053i	1.89706	+	1.89706i
$584$	−11.8804			−0.491613
$585$	−1.59660	+	8.83165i	−0.0660111	+	0.365144i
$586$			39.6367i			1.63738i
$587$		−	33.6458i		−	1.38871i	−0.719633	−	0.694355i	$-0.755690\pi$
$587$		−	33.6458i		−	1.38871i	0.719633	−	0.694355i	$-0.244310\pi$
$588$	0.603377	−	6.72932i	0.0248828	−	0.277512i
$589$		−	0.363809i		−	0.0149905i
$590$	−14.6868	−	14.6868i	−0.604647	−	0.604647i
$591$	−2.80674	+	31.3029i	−0.115454	+	1.28763i
$592$	−11.2002	+	11.2002i	−0.460324	+	0.460324i
$593$	−8.65130			−0.355266			−0.177633	−	0.984097i	$-0.556844\pi$
$593$	−8.65130			−0.355266			−0.177633	+	0.984097i	$0.556844\pi$
$594$	−13.7932	+	50.1751i	−0.565941	+	2.05871i
$595$	6.32637	−	6.32637i	0.259356	−	0.259356i
$596$		−	8.56812i		−	0.350964i
$597$	37.4957	+	3.36201i	1.53460	+	0.137598i
$598$	7.38663	−	7.38663i	0.302062	−	0.302062i
$599$	−20.2183	+	20.2183i	−0.826099	+	0.826099i	−0.986975	−	0.160875i	$-0.948568\pi$
$599$	−20.2183	+	20.2183i	−0.826099	+	0.826099i	0.160875	+	0.986975i	$0.448568\pi$
$600$	0.911925	+	1.09157i	0.0372292	+	0.0445630i
$601$	−1.59255	−	1.59255i	−0.0649614	−	0.0649614i	0.673880	−	0.738841i	$-0.264627\pi$
$601$	−1.59255	−	1.59255i	−0.0649614	−	0.0649614i	−0.738841	+	0.673880i	$0.764627\pi$
$602$	19.2487			0.784518
$603$	−6.74258	+	37.2969i	−0.274579	+	1.51885i
$604$	−40.1065			−1.63191
$605$			11.8351i			0.481167i
$606$	3.71433	−	41.4250i	0.150884	−	1.68278i
$607$	−23.2231	+	23.2231i	−0.942598	+	0.942598i	−0.998440	−	0.0558415i	$-0.982216\pi$
$607$	−23.2231	+	23.2231i	−0.942598	+	0.942598i	0.0558415	+	0.998440i	$0.482216\pi$
$608$	−1.35185			−0.0548247
$609$	19.8285	+	18.9133i	0.803491	+	0.766408i
$610$	−1.04704			−0.0423935
$611$	9.93136	−	9.93136i	0.401780	−	0.401780i
$612$	12.4566	+	17.9544i	0.503530	+	0.725763i
$613$		−	45.7208i		−	1.84665i	−0.384024	−	0.923323i	$-0.625462\pi$
$613$		−	45.7208i		−	1.84665i	0.384024	−	0.923323i	$-0.374538\pi$
$614$	18.2952			0.738335
$615$	−1.98444	−	2.37536i	−0.0800203	−	0.0957836i
$616$	11.5287			0.464503
$617$	−25.4766	−	25.4766i	−1.02565	−	1.02565i	−0.999662	−	0.0259877i	$-0.991727\pi$
$617$	−25.4766	−	25.4766i	−1.02565	−	1.02565i	−0.0259877	−	0.999662i	$-0.508273\pi$
$618$	−6.53002	+	5.45536i	−0.262676	+	0.219447i
$619$	12.9980	−	12.9980i	0.522433	−	0.522433i	−0.395872	−	0.918306i	$-0.629558\pi$
$619$	12.9980	−	12.9980i	0.522433	−	0.522433i	0.918306	+	0.395872i	$0.129558\pi$
$620$	3.66901	−	3.66901i	0.147351	−	0.147351i
$621$	2.29495	−	8.34826i	0.0920930	−	0.335004i
$622$		−	8.08874i		−	0.324329i
$623$	22.9807	−	22.9807i	0.920703	−	0.920703i
$624$	1.41727	−	15.8065i	0.0567362	−	0.632766i
$625$	1.00000			0.0400000
$626$	7.02478	−	7.02478i	0.280767	−	0.280767i
$627$	1.38251	+	0.123961i	0.0552121	+	0.00495053i
$628$	24.6851	+	24.6851i	0.985044	+	0.985044i
$629$		−	15.7497i		−	0.627982i
$630$	15.1755	−	10.5287i	0.604607	−	0.419472i
$631$		−	3.25970i		−	0.129767i	−0.997893	−	0.0648833i	$-0.979332\pi$
$631$		−	3.25970i		−	0.129767i	0.997893	−	0.0648833i	$-0.0206675\pi$
$632$		−	10.6144i		−	0.422216i
$633$	−0.119059	+	0.0994653i	−0.00473217	+	0.00395339i
$634$	59.0063			2.34344
$635$	4.41841	+	4.41841i	0.175339	+	0.175339i
$636$	55.9352	+	5.01537i	2.21798	+	0.198872i
$637$		−	4.87886i		−	0.193307i
$638$	−33.5889	+	42.1919i	−1.32980	+	1.67040i
$639$	−13.8853	−	2.51020i	−0.549294	−	0.0993019i
$640$	−4.55626	−	4.55626i	−0.180102	−	0.180102i
$641$	−21.8489	+	21.8489i	−0.862979	+	0.862979i	−0.991683	−	0.128704i	$-0.958918\pi$
$641$	−21.8489	+	21.8489i	−0.862979	+	0.862979i	0.128704	+	0.991683i	$0.458918\pi$
$642$	3.45130	+	4.13118i	0.136212	+	0.163045i
$643$		−	1.06078i		−	0.0418330i	−0.999781	−	0.0209165i	$-0.993342\pi$
$643$		−	1.06078i		−	0.0418330i	0.999781	−	0.0209165i	$-0.00665841\pi$
$644$	−11.7083			−0.461373
$645$	3.47184	+	4.15576i	0.136703	+	0.163633i
$646$	0.756826	−	0.756826i	0.0297769	−	0.0297769i
$647$	21.7981			0.856971			0.428485	−	0.903549i	$-0.359047\pi$
$647$	21.7981			0.856971			0.428485	+	0.903549i	$0.359047\pi$
$648$	3.06556	+	6.72508i	0.120426	+	0.264186i
$649$	−33.4893	−	33.4893i	−1.31457	−	1.31457i
$650$	4.43316	+	4.43316i	0.173883	+	0.173883i
$651$	−7.07725	−	8.47140i	−0.277379	−	0.332020i
$652$	29.3671	+	29.3671i	1.15010	+	1.15010i
$653$	22.1144	+	22.1144i	0.865404	+	0.865404i	0.991959	−	0.126556i	$-0.0403923\pi$
$653$	22.1144	+	22.1144i	0.865404	+	0.865404i	−0.126556	+	0.991959i	$0.540392\pi$
$654$	2.51697	+	3.01279i	0.0984212	+	0.117809i
$655$	−10.4377	−	10.4377i	−0.407836	−	0.407836i
$656$	3.87011	+	3.87011i	0.151103	+	0.151103i
$657$	−35.6592	+	24.7401i	−1.39120	+	0.965204i
$658$	−28.9049			−1.12683
$659$	0.0995621	−	0.0995621i	0.00387839	−	0.00387839i	−0.705165	−	0.709043i	$-0.749127\pi$
$659$	0.0995621	−	0.0995621i	0.00387839	−	0.00387839i	0.709043	+	0.705165i	$0.249127\pi$
$660$	12.6925	+	15.1927i	0.494053	+	0.591377i
$661$	−17.6381			−0.686044			−0.343022	−	0.939327i	$-0.611450\pi$
$661$	−17.6381			−0.686044			−0.343022	+	0.939327i	$0.611450\pi$
$662$			13.2858i			0.516366i
$663$	10.1171	+	12.1101i	0.392915	+	0.470316i
$664$	7.56650	−	7.56650i	0.293637	−	0.293637i
$665$	−0.348382	−	0.348382i	−0.0135097	−	0.0135097i
$666$	5.78422	−	31.9957i	0.224134	−	1.23981i
$667$	5.58860	−	7.02000i	0.216391	−	0.271815i
$668$			18.8810i			0.730526i
$669$	39.5468	+	3.54592i	1.52897	+	0.137093i
$670$	18.7217	+	18.7217i	0.723281	+	0.723281i
$671$	−2.38749			−0.0921681
$672$	−31.4782	+	26.2978i	−1.21430	+	1.01446i
$673$		−	26.7233i		−	1.03011i	−0.857157	−	0.515055i	$-0.827772\pi$
$673$		−	26.7233i		−	1.03011i	0.857157	−	0.515055i	$-0.172228\pi$
$674$			9.65684i			0.371968i
$675$	5.01028	+	1.37733i	0.192846	+	0.0530136i
$676$		−	9.68777i		−	0.372607i
$677$	2.05317	+	2.05317i	0.0789098	+	0.0789098i	0.745460	−	0.666550i	$-0.232230\pi$
$677$	2.05317	+	2.05317i	0.0789098	+	0.0789098i	−0.666550	+	0.745460i	$0.732230\pi$
$678$	44.0234	+	3.94731i	1.69071	+	0.151595i
$679$	32.0546	−	32.0546i	1.23014	−	1.23014i
$680$	2.50088			0.0959045
$681$	2.17464	−	24.2532i	0.0833322	−	0.929385i
$682$	15.3617	−	15.3617i	0.588231	−	0.588231i
$683$			1.81829i			0.0695749i	0.999395	+	0.0347874i	$0.0110754\pi$
$683$			1.81829i			0.0695749i	−0.999395	+	0.0347874i	$0.988925\pi$
$684$	0.988716	−	0.685965i	0.0378045	−	0.0262285i
$685$	−0.890323	+	0.890323i	−0.0340175	+	0.0340175i
$686$	23.3744	−	23.3744i	0.892441	−	0.892441i
$687$	−25.0424	+	20.9212i	−0.955429	+	0.798192i
$688$	−6.77088	−	6.77088i	−0.258137	−	0.258137i
$689$	40.5539			1.54498
$690$	−3.87763	−	4.64148i	−0.147619	−	0.176698i
$691$	45.1774			1.71863			0.859314	−	0.511448i	$-0.170891\pi$
$691$	45.1774			1.71863			0.859314	+	0.511448i	$0.170891\pi$
$692$			23.5718i			0.896066i
$693$	34.6036	−	24.0078i	1.31448	−	0.911979i
$694$	2.78820	−	2.78820i	0.105839	−	0.105839i
$695$	−18.4952			−0.701562
$696$	0.180884	+	7.65754i	0.00685640	+	0.290258i
$697$	−5.44217			−0.206137
$698$	34.9461	−	34.9461i	1.32273	−	1.32273i
$699$	3.46899	−	38.6888i	0.131209	−	1.46335i
$700$		−	7.02687i		−	0.265591i
$701$	−20.3945			−0.770288			−0.385144	−	0.922857i	$-0.625848\pi$
$701$	−20.3945			−0.770288			−0.385144	+	0.922857i	$0.625848\pi$
$702$	16.1054	+	28.3173i	0.607861	+	1.06877i
$703$	−0.867308			−0.0327112
$704$	−36.3835	−	36.3835i	−1.37126	−	1.37126i
$705$	−5.21349	−	6.24050i	−0.196351	−	0.235031i
$706$	−23.9160	+	23.9160i	−0.900089	+	0.900089i
$707$	−23.8028	+	23.8028i	−0.895198	+	0.895198i
$708$	−40.8956	−	3.66685i	−1.53695	−	0.137809i
$709$			25.3501i			0.952043i	0.879434	+	0.476022i	$0.157922\pi$
$709$			25.3501i			0.952043i	−0.879434	+	0.476022i	$0.842078\pi$
$710$	−6.96989	+	6.96989i	−0.261575	+	0.261575i
$711$	−22.1037	−	31.8592i	−0.828955	−	1.19481i
$712$	9.08453			0.340457
$713$	−2.55592	+	2.55592i	−0.0957200	+	0.0957200i
$714$	2.90023	−	32.3456i	0.108539	−	1.21050i
$715$	10.1086	+	10.1086i	0.378040	+	0.378040i
$716$			50.7955i			1.89832i
$717$	1.07557	−	11.9956i	0.0401679	−	0.447983i
$718$			21.9671i			0.819806i
$719$		−	0.589669i		−	0.0219910i	−0.999940	−	0.0109955i	$-0.996500\pi$
$719$		−	0.589669i		−	0.0219910i	0.999940	−	0.0109955i	$-0.00350004\pi$
$720$	−9.04165	−	1.63456i	−0.336962	−	0.0609164i
$721$	6.88680			0.256478
$722$	28.1138	+	28.1138i	1.04629	+	1.04629i
$723$	−2.09612	+	23.3775i	−0.0779556	+	0.869420i
$724$			5.96984i			0.221868i
$725$	4.21312	+	3.35405i	0.156471	+	0.124566i
$726$	27.5427	+	32.9683i	1.02220	+	1.22357i
$727$	0.593767	+	0.593767i	0.0220216	+	0.0220216i	0.718032	−	0.696010i	$-0.245043\pi$
$727$	0.593767	+	0.593767i	0.0220216	+	0.0220216i	−0.696010	+	0.718032i	$0.745043\pi$
$728$	5.10348	−	5.10348i	0.189148	−	0.189148i
$729$	23.2059	+	13.8017i	0.859478	+	0.511173i
$730$			30.3182i			1.12213i
$731$	9.52124			0.352156
$732$	−1.58845	+	1.32704i	−0.0587109	+	0.0490487i
$733$	34.9532	−	34.9532i	1.29102	−	1.29102i	0.356871	−	0.934154i	$-0.383844\pi$
$733$	34.9532	−	34.9532i	1.29102	−	1.29102i	0.934154	−	0.356871i	$-0.116156\pi$
$734$	−66.9358			−2.47065
$735$	−2.81343	−	0.252263i	−0.103775	−	0.00930486i
$736$	9.49735	+	9.49735i	0.350077	+	0.350077i
$737$	42.6896	+	42.6896i	1.57249	+	1.57249i
$738$	−11.0558	−	1.99869i	−0.406971	−	0.0735726i
$739$	−31.2706	−	31.2706i	−1.15031	−	1.15031i	−0.986491	−	0.163816i	$-0.947620\pi$
$739$	−31.2706	−	31.2706i	−1.15031	−	1.15031i	−0.163816	−	0.986491i	$-0.552380\pi$
$740$	−8.74681	−	8.74681i	−0.321539	−	0.321539i
$741$	0.666880	−	0.557130i	0.0244984	−	0.0204667i
$742$	−59.0153	−	59.0153i	−2.16652	−	2.16652i
$743$	−2.88563	−	2.88563i	−0.105864	−	0.105864i	0.652191	−	0.758055i	$-0.273850\pi$
$743$	−2.88563	−	2.88563i	−0.105864	−	0.105864i	−0.758055	+	0.652191i	$0.773850\pi$
$744$	0.275562	−	3.07328i	0.0101026	−	0.112672i
$745$	−3.58220			−0.131242
$746$	33.4111	−	33.4111i	1.22327	−	1.22327i
$747$	6.95425	−	38.4678i	0.254443	−	1.40746i
$748$	34.8081			1.27271
$749$		−	4.35690i		−	0.159198i
$750$	2.78563	−	2.32719i	0.101717	−	0.0849771i
$751$	−6.33764	+	6.33764i	−0.231264	+	0.231264i	−0.813220	−	0.581956i	$-0.802287\pi$
$751$	−6.33764	+	6.33764i	−0.231264	+	0.231264i	0.581956	+	0.813220i	$0.302287\pi$
$752$	10.1675	+	10.1675i	0.370771	+	0.370771i
$753$	−11.8322	+	9.88494i	−0.431189	+	0.360227i
$754$	3.80839	+	33.5464i	0.138693	+	1.22169i
$755$			16.7679i			0.610247i
$756$	9.67834	−	35.2066i	0.351998	−	1.28045i
$757$	0.520064	+	0.520064i	0.0189020	+	0.0189020i	0.716495	−	0.697593i	$-0.245745\pi$
$757$	0.520064	+	0.520064i	0.0189020	+	0.0189020i	−0.697593	+	0.716495i	$0.745745\pi$
$758$	−71.3239			−2.59060
$759$	−8.84187	−	10.5836i	−0.320939	−	0.384162i
$760$		−	0.137719i		−	0.00499560i
$761$			12.5827i			0.456123i	0.973647	+	0.228061i	$0.0732387\pi$
$761$			12.5827i			0.456123i	−0.973647	+	0.228061i	$0.926761\pi$
$762$	22.5906	+	2.02556i	0.818370	+	0.0733782i
$763$		−	3.17740i		−	0.115030i
$764$	40.3588	+	40.3588i	1.46013	+	1.46013i
$765$	7.50646	−	5.20794i	0.271397	−	0.188293i
$766$	−56.0690	+	56.0690i	−2.02585	+	2.02585i
$767$	−29.6499			−1.07060
$768$	13.8556	+	1.24234i	0.499970	+	0.0448292i
$769$	18.3024	−	18.3024i	0.660002	−	0.660002i	−0.295378	−	0.955380i	$-0.595446\pi$
$769$	18.3024	−	18.3024i	0.660002	−	0.660002i	0.955380	+	0.295378i	$0.0954457\pi$
$770$		−	29.4207i		−	1.06025i
$771$	−2.71816	+	30.3150i	−0.0978923	+	1.09177i
$772$	−20.0249	+	20.0249i	−0.720714	+	0.720714i
$773$	20.4866	−	20.4866i	0.736853	−	0.736853i	−0.235114	−	0.971968i	$-0.575546\pi$
$773$	20.4866	−	20.4866i	0.736853	−	0.736853i	0.971968	+	0.235114i	$0.0755465\pi$
$774$	19.3425	+	3.49676i	0.695252	+	0.125688i
$775$	−1.53396	−	1.53396i	−0.0551015	−	0.0551015i
$776$	12.6716			0.454882
$777$	−20.1955	+	16.8719i	−0.724511	+	0.605277i
$778$	−24.0031			−0.860552
$779$			0.299691i			0.0107375i
$780$	12.3441	+	1.10682i	0.441991	+	0.0396306i
$781$	−15.8929	+	15.8929i	−0.568694	+	0.568694i
$782$	−10.6341			−0.380274
$783$	16.4893	+	22.6076i	0.589279	+	0.807930i
$784$	4.99486			0.178388
$785$	10.3205	−	10.3205i	0.368354	−	0.368354i
$786$	−53.3663	−	4.78503i	−1.90351	−	0.170676i
$787$		−	18.8003i		−	0.670158i	−0.942190	−	0.335079i	$-0.891237\pi$
$787$		−	18.8003i		−	0.670158i	0.942190	−	0.335079i	$-0.108763\pi$
$788$	43.4009			1.54609
$789$	−36.0143	+	30.0874i	−1.28214	+	1.07114i
$790$	−27.0874			−0.963726
$791$	−25.2958	−	25.2958i	−0.899417	−	0.899417i
$792$	11.5849	+	2.09432i	0.411650	+	0.0744185i
$793$	−1.05689	+	1.05689i	−0.0375312	+	0.0375312i
$794$	−22.0672	+	22.0672i	−0.783135	+	0.783135i
$795$	2.09685	−	23.3857i	0.0743677	−	0.829405i
$796$		−	51.9870i		−	1.84263i
$797$	4.40744	−	4.40744i	0.156120	−	0.156120i	−0.624725	−	0.780845i	$-0.714789\pi$
$797$	4.40744	−	4.40744i	0.156120	−	0.156120i	0.780845	+	0.624725i	$0.214789\pi$
$798$	−1.78122	−	0.159711i	−0.0630544	−	0.00565370i
$799$	−14.2976			−0.505812
$800$	−5.69992	+	5.69992i	−0.201523	+	0.201523i
$801$	27.2674	−	18.9180i	0.963448	−	0.668434i
$802$	19.2611	+	19.2611i	0.680132	+	0.680132i
$803$			69.1323i			2.43963i
$804$	52.1305	+	4.67422i	1.83850	+	0.164847i
$805$			4.89509i			0.172529i
$806$		−	13.6006i		−	0.479059i
$807$	−28.6985	−	34.3518i	−1.01023	−	1.20924i
$808$	−9.40953			−0.331026
$809$	19.8447	+	19.8447i	0.697703	+	0.697703i	0.963915	−	0.266212i	$-0.0857721\pi$
$809$	19.8447	+	19.8447i	0.697703	+	0.697703i	−0.266212	+	0.963915i	$0.585772\pi$
$810$	17.1621	−	7.82317i	0.603015	−	0.274878i
$811$			14.2755i			0.501282i	0.968080	+	0.250641i	$0.0806413\pi$
$811$			14.2755i			0.501282i	−0.968080	+	0.250641i	$0.919359\pi$
$812$	23.5685	−	29.6050i	0.827091	−	1.03893i
$813$	−29.1342	+	24.3396i	−1.02178	+	0.853626i
$814$	−36.6219	−	36.6219i	−1.28360	−	1.28360i
$815$	12.2779	−	12.2779i	0.430078	−	0.430078i
$816$	−12.3980	+	10.3576i	−0.434017	+	0.362590i
$817$		−	0.524318i		−	0.0183436i
$818$	−43.9809			−1.53776
$819$	4.69053	−	25.9459i	0.163900	−	0.906623i
$820$	−3.02238	+	3.02238i	−0.105546	+	0.105546i
$821$	14.1770			0.494782			0.247391	−	0.968916i	$-0.420427\pi$
$821$	14.1770			0.494782			0.247391	+	0.968916i	$0.420427\pi$
$822$	−0.408156	+	4.55206i	−0.0142361	+	0.158771i
$823$	16.6929	+	16.6929i	0.581879	+	0.581879i	0.935419	−	0.353541i	$-0.115022\pi$
$823$	16.6929	+	16.6929i	0.581879	+	0.581879i	−0.353541	+	0.935419i	$0.615022\pi$
$824$	1.36121	+	1.36121i	0.0474201	+	0.0474201i
$825$	6.35186	−	5.30653i	0.221144	−	0.184750i
$826$	43.1474	+	43.1474i	1.50129	+	1.50129i
$827$	−24.0323	−	24.0323i	−0.835686	−	0.835686i	0.152602	−	0.988288i	$-0.451235\pi$
$827$	−24.0323	−	24.0323i	−0.835686	−	0.835686i	−0.988288	+	0.152602i	$0.951235\pi$
$828$	−11.7654	−	2.12696i	−0.408876	−	0.0739170i
$829$	−2.15475	−	2.15475i	−0.0748374	−	0.0748374i	0.668697	−	0.743535i	$-0.266852\pi$
$829$	−2.15475	−	2.15475i	−0.0748374	−	0.0748374i	−0.743535	+	0.668697i	$0.766852\pi$
$830$	−19.3094	−	19.3094i	−0.670238	−	0.670238i
$831$	−42.2802	−	3.79101i	−1.46668	−	0.131509i
$832$	−32.2123			−1.11676
$833$	−3.51190	+	3.51190i	−0.121680	+	0.121680i
$834$	−51.5207	+	43.0418i	−1.78402	+	1.49042i
$835$	7.89385			0.273178
$836$		−	1.91682i		−	0.0662946i
$837$	−5.57280	−	9.79835i	−0.192624	−	0.338680i
$838$	−18.8112	+	18.8112i	−0.649822	+	0.649822i
$839$	4.05251	+	4.05251i	0.139908	+	0.139908i	0.773592	−	0.633684i	$-0.218458\pi$
$839$	4.05251	+	4.05251i	0.139908	+	0.139908i	−0.633684	+	0.773592i	$0.718458\pi$
$840$	−2.67908	−	3.20684i	−0.0924371	−	0.110646i
$841$	6.50073	+	28.2620i	0.224163	+	0.974552i
$842$		−	28.8119i		−	0.992925i
$843$	0.0306605	−	0.341949i	0.00105600	−	0.0117773i
$844$	0.151490	+	0.151490i	0.00521449	+	0.00521449i
$845$	−4.05031			−0.139335
$846$	−29.0457	−	5.25092i	−0.998612	−	0.180530i
$847$		−	34.7696i		−	1.19470i
$848$			41.5182i			1.42574i
$849$	−2.76627	+	30.8516i	−0.0949382	+	1.05882i
$850$		−	6.38215i		−	0.218906i
$851$	6.09323	+	6.09323i	0.208873	+	0.208873i
$852$	−1.74017	+	19.4077i	−0.0596172	+	0.664896i
$853$	−13.0725	+	13.0725i	−0.447594	+	0.447594i	−0.894554	−	0.446960i	$-0.852507\pi$
$853$	−13.0725	+	13.0725i	−0.447594	+	0.447594i	0.446960	+	0.894554i	$0.352507\pi$
$854$	3.07603			0.105260
$855$	−0.286792	−	0.413368i	−0.00980808	−	0.0141369i
$856$	0.861165	−	0.861165i	0.0294340	−	0.0294340i
$857$		−	4.24092i		−	0.144867i	−0.997373	−	0.0724336i	$-0.976923\pi$
$857$		−	4.24092i		−	0.144867i	0.997373	−	0.0724336i	$-0.0230765\pi$
$858$	51.6835	+	4.63414i	1.76444	+	0.158207i
$859$	−36.2139	+	36.2139i	−1.23560	+	1.23560i	−0.273821	+	0.961781i	$0.588287\pi$
$859$	−36.2139	+	36.2139i	−1.23560	+	1.23560i	−0.961781	+	0.273821i	$0.911713\pi$
$860$	5.28775	−	5.28775i	0.180311	−	0.180311i
$861$	5.82995	+	6.97839i	0.198684	+	0.237823i
$862$	−6.39398	−	6.39398i	−0.217780	−	0.217780i
$863$	20.4997			0.697819			0.348910	−	0.937156i	$-0.386552\pi$
$863$	20.4997			0.697819			0.348910	+	0.937156i	$0.386552\pi$
$864$	−36.4089	+	20.7075i	−1.23866	+	0.704485i
$865$	9.85503			0.335081
$866$		−	0.137151i		−	0.00466058i
$867$	−1.19501	+	13.3277i	−0.0405847	+	0.452631i
$868$	−10.7789	+	10.7789i	−0.365861	+	0.365861i
$869$	−61.7653			−2.09525
$870$	19.5417	−	0.461609i	0.662526	−	0.0156500i
$871$	37.7954			1.28065
$872$	0.628030	−	0.628030i	0.0212678	−	0.0212678i
$873$	38.0340	−	26.3877i	1.28725	−	0.893089i
$874$			0.585601i			0.0198082i
$875$	−2.93783			−0.0993168
$876$	38.4258	+	45.9953i	1.29829	+	1.55404i
$877$	4.46979			0.150934			0.0754670	−	0.997148i	$-0.475955\pi$
$877$	4.46979			0.150934			0.0754670	+	0.997148i	$0.475955\pi$
$878$	41.3017	+	41.3017i	1.39387	+	1.39387i
$879$	25.1404	−	21.0030i	0.847966	−	0.708415i
$880$	−10.3490	+	10.3490i	−0.348863	+	0.348863i
$881$	38.3277	−	38.3277i	1.29129	−	1.29129i	0.357303	−	0.933989i	$-0.383696\pi$
$881$	38.3277	−	38.3277i	1.29129	−	1.29129i	0.933989	−	0.357303i	$-0.116304\pi$
$882$	−8.42424	+	5.84468i	−0.283659	+	0.196801i
$883$			22.6962i			0.763788i	0.924206	+	0.381894i	$0.124728\pi$
$883$			22.6962i			0.763788i	−0.924206	+	0.381894i	$0.875272\pi$
$884$	15.4087	−	15.4087i	0.518252	−	0.518252i
$885$	−1.53306	+	17.0978i	−0.0515332	+	0.574737i
$886$	−66.7305			−2.24186
$887$	5.13174	−	5.13174i	0.172307	−	0.172307i	−0.615685	−	0.787992i	$-0.711121\pi$
$887$	5.13174	−	5.13174i	0.172307	−	0.172307i	0.787992	+	0.615685i	$0.211121\pi$
$888$	−7.32659	−	0.656930i	−0.245864	−	0.0220451i
$889$	−12.9806	−	12.9806i	−0.435354	−	0.435354i
$890$		−	23.1833i		−	0.777107i
$891$	39.1335	−	17.8386i	1.31102	−	0.597615i
$892$		−	54.8308i		−	1.83587i
$893$			0.787343i			0.0263474i
$894$	−9.97870	+	8.33649i	−0.333738	+	0.278814i
$895$	21.2369			0.709870
$896$	13.3855	+	13.3855i	0.447179	+	0.447179i
$897$	−8.59922	−	0.771040i	−0.287120	−	0.0257443i
$898$			13.7612i			0.459217i
$899$	−1.31778	−	11.6077i	−0.0439504	−	0.387139i
$900$	1.27652	−	7.06111i	0.0425505	−	0.235370i
$901$	−29.1915	−	29.1915i	−0.972510	−	0.972510i
$902$	−12.6544	+	12.6544i	−0.421344	+	0.421344i
$903$	−10.1997	−	12.2089i	−0.339424	−	0.406287i
$904$		−	9.99972i		−	0.332586i
$905$	2.49590			0.0829667
$906$	39.0222	+	46.7093i	1.29643	+	1.55181i
$907$	26.5065	−	26.5065i	0.880134	−	0.880134i	−0.113414	−	0.993548i	$-0.536179\pi$
$907$	26.5065	−	26.5065i	0.880134	−	0.880134i	0.993548	+	0.113414i	$0.0361787\pi$
$908$	−33.6265			−1.11594
$909$	−28.2429	+	19.5948i	−0.936758	+	0.649917i
$910$	−13.0239	−	13.0239i	−0.431737	−	0.431737i
$911$	−0.284529	−	0.284529i	−0.00942686	−	0.00942686i	0.702378	−	0.711804i	$-0.252122\pi$
$911$	−0.284529	−	0.284529i	−0.00942686	−	0.00942686i	−0.711804	+	0.702378i	$0.752122\pi$
$912$	0.570378	+	0.682737i	0.0188871	+	0.0226077i
$913$	−44.0297	−	44.0297i	−1.45717	−	1.45717i
$914$	33.2759	+	33.2759i	1.10067	+	1.10067i
$915$	0.554815	+	0.664109i	0.0183416	+	0.0219548i
$916$	31.8638	+	31.8638i	1.05281	+	1.05281i
$917$	30.6643	+	30.6643i	1.01262	+	1.01262i
$918$	8.79034	−	31.9764i	0.290125	−	1.05538i
$919$	2.05188			0.0676853			0.0338426	−	0.999427i	$-0.489225\pi$
$919$	2.05188			0.0676853			0.0338426	+	0.999427i	$0.489225\pi$
$920$	−0.967540	+	0.967540i	−0.0318989	+	0.0318989i
$921$	−9.69443	−	11.6041i	−0.319442	−	0.382370i
$922$	−9.74430			−0.320911
$923$			14.0709i			0.463148i
$924$	−37.2883	−	44.6337i	−1.22669	−	1.46834i
$925$	−3.65691	+	3.65691i	−0.120238	+	0.120238i
$926$	11.2713	+	11.2713i	0.370398	+	0.370398i
$927$	6.92036	+	1.25107i	0.227295	+	0.0410906i
$928$	−43.1323	+	4.89664i	−1.41589	+	0.160740i
$929$			32.7193i			1.07349i	0.843746	+	0.536743i	$0.180345\pi$
$929$			32.7193i			1.07349i	−0.843746	+	0.536743i	$0.819655\pi$
$930$	−7.84287	−	0.703222i	−0.257178	−	0.0230596i
$931$	0.193394	+	0.193394i	0.00633824	+	0.00633824i
$932$	−53.6413			−1.75708
$933$	−5.13046	+	4.28613i	−0.167964	+	0.140322i
$934$			7.82130i			0.255921i
$935$		−	14.5527i		−	0.475925i
$936$	6.05546	−	4.20124i	0.197929	−	0.137322i
$937$		−	9.99090i		−	0.326389i	−0.986594	−	0.163194i	$-0.947820\pi$
$937$		−	9.99090i		−	0.326389i	0.986594	−	0.163194i	$-0.0521797\pi$
$938$	−55.0011	−	55.0011i	−1.79585	−	1.79585i
$939$	−8.17797	−	0.733269i	−0.266878	−	0.0239293i
$940$	−7.94036	+	7.94036i	−0.258986	+	0.258986i
$941$	−22.0400			−0.718482			−0.359241	−	0.933245i	$-0.616964\pi$
$941$	−22.0400			−0.718482			−0.359241	+	0.933245i	$0.616964\pi$
$942$	4.73128	−	52.7669i	0.154153	−	1.71924i
$943$	2.10546	−	2.10546i	0.0685633	−	0.0685633i
$944$		−	30.3549i		−	0.987968i
$945$	−14.7194	−	4.04637i	−0.478821	−	0.131628i
$946$	22.1392	−	22.1392i	0.719807	−	0.719807i
$947$	21.3891	−	21.3891i	0.695051	−	0.695051i	−0.268288	−	0.963339i	$-0.586458\pi$
$947$	21.3891	−	21.3891i	0.695051	−	0.695051i	0.963339	+	0.268288i	$0.0864579\pi$
$948$	−41.0939	+	34.3310i	−1.33467	+	1.11502i
$949$	30.6033	+	30.6033i	0.993424	+	0.993424i
$950$	−0.351454			−0.0114027
$951$	−31.2668	−	37.4261i	−1.01390	−	1.21362i
$952$	−7.34717			−0.238123
$953$			50.5628i			1.63789i	0.573873	+	0.818944i	$0.305440\pi$
$953$			50.5628i			1.63789i	−0.573873	+	0.818944i	$0.694560\pi$
$954$	−48.5820	−	70.0237i	−1.57290	−	2.26710i
$955$	16.8734	−	16.8734i	0.546011	−	0.546011i
$956$	−16.6316			−0.537905
$957$	44.5595	−	1.05257i	1.44040	−	0.0340248i
$958$	−25.7018			−0.830388
$959$	2.61562	−	2.61562i	0.0844627	−	0.0844627i
$960$	−1.66555	+	18.5755i	−0.0537553	+	0.599521i
$961$		−	26.2939i		−	0.848191i
$962$	−32.4233			−1.04537
$963$	0.791483	−	4.37813i	0.0255052	−	0.141083i
$964$	32.4125			1.04394
$965$	8.37214	+	8.37214i	0.269509	+	0.269509i
$966$	11.3918	+	13.6359i	0.366526	+	0.438728i
$967$	−19.1659	+	19.1659i	−0.616335	+	0.616335i	−0.944589	−	0.328254i	$-0.893540\pi$
$967$	−19.1659	+	19.1659i	−0.616335	+	0.616335i	0.328254	+	0.944589i	$0.393540\pi$
$968$	6.87241	−	6.87241i	0.220888	−	0.220888i
$969$	−0.881067	−	0.0789999i	−0.0283039	−	0.00253784i
$970$		−	32.3373i		−	1.03829i
$971$	27.0629	−	27.0629i	0.868489	−	0.868489i	−0.123817	−	0.992305i	$-0.539513\pi$
$971$	27.0629	−	27.0629i	0.868489	−	0.868489i	0.992305	+	0.123817i	$0.0395134\pi$
$972$	16.1212	−	33.6200i	0.517088	−	1.07836i
$973$	54.3357			1.74192
$974$	−3.49645	+	3.49645i	−0.112034	+	0.112034i
$975$	0.462747	−	5.16090i	0.0148198	−	0.165281i
$976$	−1.08202	−	1.08202i	−0.0346346	−	0.0346346i
$977$			8.13996i			0.260420i	0.991486	+	0.130210i	$0.0415652\pi$
$977$			8.13996i			0.260420i	−0.991486	+	0.130210i	$0.958435\pi$
$978$	5.62865	−	62.7750i	0.179984	−	2.00732i
$979$		−	52.8632i		−	1.68952i
$980$			3.90076i			0.124605i
$981$	0.577213	−	3.19288i	0.0184290	−	0.101941i
$982$	−6.09103			−0.194372
$983$	29.0425	+	29.0425i	0.926313	+	0.926313i	0.997465	−	0.0711522i	$-0.0226676\pi$
$983$	29.0425	+	29.0425i	0.926313	+	0.926313i	−0.0711522	+	0.997465i	$0.522668\pi$
$984$	−0.226996	+	2.53164i	−0.00723638	+	0.0807057i
$985$		−	18.1453i		−	0.578156i
$986$	21.4060	−	26.8887i	0.681707	−	0.856312i
$987$	15.3164	+	18.3335i	0.487525	+	0.583563i
$988$	−0.848532	−	0.848532i	−0.0269954	−	0.0269954i
$989$	−3.68357	+	3.68357i	−0.117131	+	0.117131i
$990$	5.34462	−	29.5640i	0.169863	−	0.939607i
$991$		−	18.0003i		−	0.571799i	−0.958260	−	0.285900i	$-0.907708\pi$
$991$		−	18.0003i		−	0.571799i	0.958260	−	0.285900i	$-0.0922924\pi$
$992$	17.4869			0.555210
$993$	8.42679	−	7.03998i	0.267416	−	0.223407i
$994$	20.4764	−	20.4764i	0.649471	−	0.649471i
$995$	−21.7350			−0.689046
$996$	−53.7671	−	4.82096i	−1.70367	−	0.152758i
$997$	0.815506	+	0.815506i	0.0258273	+	0.0258273i	0.719903	−	0.694075i	$-0.244186\pi$
$997$	0.815506	+	0.815506i	0.0258273	+	0.0258273i	−0.694075	+	0.719903i	$0.744186\pi$
$998$	−9.95092	−	9.95092i	−0.314991	−	0.314991i
$999$	−23.3589	+	13.2854i	−0.739044	+	0.420331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.c.41.4	✓	36
3.2	odd	2		435.2.q.d.41.15	yes	36
29.17	odd	4		435.2.q.d.191.15	yes	36
87.17	even	4	inner	435.2.q.c.191.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.4	✓	36	1.1	even	1	trivial
435.2.q.c.191.4	yes	36	87.17	even	4	inner
435.2.q.d.41.15	yes	36	3.2	odd	2
435.2.q.d.191.15	yes	36	29.17	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48187 + 1.48187i) q^{2} +(1.72513 + 0.154682i) q^{3} -2.39186i q^{4} -1.00000 q^{5} +(-2.78563 + 2.32719i) q^{6} +2.93783 q^{7} +(0.580678 + 0.580678i) q^{8} +(2.95215 + 0.533693i) q^{9} +O(q^{10})\)	\(q+(-1.48187 + 1.48187i) q^{2} +(1.72513 + 0.154682i) q^{3} -2.39186i q^{4} -1.00000 q^{5} +(-2.78563 + 2.32719i) q^{6} +2.93783 q^{7} +(0.580678 + 0.580678i) q^{8} +(2.95215 + 0.533693i) q^{9} +(1.48187 - 1.48187i) q^{10} +(3.37899 - 3.37899i) q^{11} +(0.369977 - 4.12626i) q^{12} -2.99160i q^{13} +(-4.35347 + 4.35347i) q^{14} +(-1.72513 - 0.154682i) q^{15} +3.06274 q^{16} +(-2.15342 + 2.15342i) q^{17} +(-5.16555 + 3.58383i) q^{18} +(0.118585 + 0.118585i) q^{19} +2.39186i q^{20} +(5.06814 + 0.454429i) q^{21} +10.0144i q^{22} -1.66622i q^{23} +(0.911925 + 1.09157i) q^{24} +1.00000 q^{25} +(4.43316 + 4.43316i) q^{26} +(5.01028 + 1.37733i) q^{27} -7.02687i q^{28} +(4.21312 + 3.35405i) q^{29} +(2.78563 - 2.32719i) q^{30} +(-1.53396 - 1.53396i) q^{31} +(-5.69992 + 5.69992i) q^{32} +(6.35186 - 5.30653i) q^{33} -6.38215i q^{34} -2.93783 q^{35} +(1.27652 - 7.06111i) q^{36} +(-3.65691 + 3.65691i) q^{37} -0.351454 q^{38} +(0.462747 - 5.16090i) q^{39} +(-0.580678 - 0.580678i) q^{40} +(1.26361 + 1.26361i) q^{41} +(-8.18371 + 6.83690i) q^{42} +(-2.21073 - 2.21073i) q^{43} +(-8.08206 - 8.08206i) q^{44} +(-2.95215 - 0.533693i) q^{45} +(2.46912 + 2.46912i) q^{46} +(3.31975 + 3.31975i) q^{47} +(5.28362 + 0.473750i) q^{48} +1.63085 q^{49} +(-1.48187 + 1.48187i) q^{50} +(-4.04802 + 3.38183i) q^{51} -7.15548 q^{52} +13.5559i q^{53} +(-9.46560 + 5.38355i) q^{54} +(-3.37899 + 3.37899i) q^{55} +(1.70593 + 1.70593i) q^{56} +(0.186231 + 0.222917i) q^{57} +(-11.2135 + 1.27303i) q^{58} -9.91104i q^{59} +(-0.369977 + 4.12626i) q^{60} +(-0.353285 - 0.353285i) q^{61} +4.54625 q^{62} +(8.67291 + 1.56790i) q^{63} -10.7676i q^{64} +2.99160i q^{65} +(-1.54905 + 17.2762i) q^{66} +12.6338i q^{67} +(5.15066 + 5.15066i) q^{68} +(0.257735 - 2.87445i) q^{69} +(4.35347 - 4.35347i) q^{70} -4.70345 q^{71} +(1.40434 + 2.02415i) q^{72} +(-10.2297 + 10.2297i) q^{73} -10.8381i q^{74} +(1.72513 + 0.154682i) q^{75} +(0.283638 - 0.283638i) q^{76} +(9.92690 - 9.92690i) q^{77} +(6.96204 + 8.33350i) q^{78} +(-9.13962 - 9.13962i) q^{79} -3.06274 q^{80} +(8.43034 + 3.15108i) q^{81} -3.74501 q^{82} -13.0304i q^{83} +(1.08693 - 12.1223i) q^{84} +(2.15342 - 2.15342i) q^{85} +6.55201 q^{86} +(6.74937 + 6.43786i) q^{87} +3.92421 q^{88} +(7.82234 - 7.82234i) q^{89} +(5.16555 - 3.58383i) q^{90} -8.78882i q^{91} -3.98537 q^{92} +(-2.40900 - 2.88356i) q^{93} -9.83884 q^{94} +(-0.118585 - 0.118585i) q^{95} +(-10.7148 + 8.95143i) q^{96} +(10.9110 - 10.9110i) q^{97} +(-2.41670 + 2.41670i) q^{98} +(11.7786 - 8.17193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

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