LMFDB - Embedded newform 429.2.bd.b.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.3
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.b.175.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77380 - 0.475288i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18842 + 0.686133i) q^{4} +(-0.611710 - 0.611710i) q^{5} +(-0.475288 - 1.77380i) q^{6} +(-4.35587 + 1.16715i) q^{7} +(0.815121 + 0.815121i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.77380 - 0.475288i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18842 + 0.686133i) q^{4} +(-0.611710 - 0.611710i) q^{5} +(-0.475288 - 1.77380i) q^{6} +(-4.35587 + 1.16715i) q^{7} +(0.815121 + 0.815121i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.794312 + 1.37579i) q^{10} +(2.94755 - 1.52051i) q^{11} +1.37227i q^{12} +(-0.148240 - 3.60250i) q^{13} +8.28118 q^{14} +(0.223901 - 0.835611i) q^{15} +(-2.43071 - 4.21011i) q^{16} +(2.18190 - 3.77917i) q^{17} +(1.29851 - 1.29851i) q^{18} +(1.77556 + 6.62647i) q^{19} +(-0.307252 - 1.14668i) q^{20} +(-3.18872 - 3.18872i) q^{21} +(-5.95104 + 1.29614i) q^{22} +(2.38186 - 1.37517i) q^{23} +(-0.298355 + 1.11348i) q^{24} -4.25162i q^{25} +(-1.44928 + 6.46058i) q^{26} -1.00000 q^{27} +(-5.97741 - 1.60164i) q^{28} +(6.92026 - 3.99541i) q^{29} +(-0.794312 + 1.37579i) q^{30} +(2.01631 + 2.01631i) q^{31} +(1.71387 + 6.39623i) q^{32} +(2.79057 + 1.79240i) q^{33} +(-5.66645 + 5.66645i) q^{34} +(3.37849 + 1.95057i) q^{35} +(-1.18842 + 0.686133i) q^{36} +(-6.19975 - 1.66122i) q^{37} -12.5979i q^{38} +(3.04574 - 1.92963i) q^{39} -0.997234i q^{40} +(0.830482 + 0.222527i) q^{41} +(4.14059 + 7.17171i) q^{42} +(4.50727 - 7.80683i) q^{43} +(4.54619 + 0.215412i) q^{44} +(0.835611 - 0.223901i) q^{45} +(-4.87855 + 1.30720i) q^{46} +(6.11641 - 6.11641i) q^{47} +(2.43071 - 4.21011i) q^{48} +(11.5492 - 6.66793i) q^{49} +(-2.02075 + 7.54153i) q^{50} +4.36381 q^{51} +(2.29562 - 4.38299i) q^{52} -4.70395 q^{53} +(1.77380 + 0.475288i) q^{54} +(-2.73315 - 0.872935i) q^{55} +(-4.50193 - 2.59919i) q^{56} +(-4.85091 + 4.85091i) q^{57} +(-14.1741 + 3.79795i) q^{58} +(-1.18181 - 4.41058i) q^{59} +(0.839428 - 0.839428i) q^{60} +(4.66597 + 2.69390i) q^{61} +(-2.61820 - 4.53486i) q^{62} +(1.16715 - 4.35587i) q^{63} -2.43738i q^{64} +(-2.11301 + 2.29437i) q^{65} +(-4.09802 - 4.50568i) q^{66} +(3.16876 - 11.8260i) q^{67} +(5.18602 - 2.99415i) q^{68} +(2.38186 + 1.37517i) q^{69} +(-5.06568 - 5.06568i) q^{70} +(-10.2153 + 2.73719i) q^{71} +(-1.11348 + 0.298355i) q^{72} +(-3.48467 - 3.48467i) q^{73} +(10.2076 + 5.89334i) q^{74} +(3.68201 - 2.12581i) q^{75} +(-2.43654 + 9.09327i) q^{76} +(-11.0645 + 10.0634i) q^{77} +(-6.31966 + 1.97518i) q^{78} +11.7040i q^{79} +(-1.08848 + 4.06225i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.36734 - 0.789437i) q^{82} +(4.72727 - 4.72727i) q^{83} +(-1.60164 - 5.97741i) q^{84} +(-3.64644 + 0.977062i) q^{85} +(-11.7055 + 11.7055i) q^{86} +(6.92026 + 3.99541i) q^{87} +(3.64201 + 1.16321i) q^{88} +(12.9642 + 3.47376i) q^{89} -1.58862 q^{90} +(4.85038 + 15.5190i) q^{91} +3.77419 q^{92} +(-0.738021 + 2.75433i) q^{93} +(-13.7563 + 7.94223i) q^{94} +(2.96735 - 5.13960i) q^{95} +(-4.68237 + 4.68237i) q^{96} +(2.37304 - 0.635853i) q^{97} +(-23.6552 + 6.33838i) q^{98} +(-0.156975 + 3.31291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	−1.77380	−	0.475288i	−1.25427	−	0.336080i	−0.430283	−	0.902694i	$-0.641586\pi$
$2$	−1.77380	−	0.475288i	−1.25427	−	0.336080i	−0.823983	+	0.566614i	$0.808253\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.18842	+	0.686133i	0.594208	+	0.343066i
$5$	−0.611710	−	0.611710i	−0.273565	−	0.273565i	0.556969	−	0.830534i	$-0.311964\pi$
$5$	−0.611710	−	0.611710i	−0.273565	−	0.273565i	−0.830534	+	0.556969i	$0.811964\pi$
$6$	−0.475288	−	1.77380i	−0.194036	−	0.724151i
$7$	−4.35587	+	1.16715i	−1.64637	+	0.441142i	−0.958592	−	0.284784i	$-0.908078\pi$
$7$	−4.35587	+	1.16715i	−1.64637	+	0.441142i	−0.687773	+	0.725926i	$0.741412\pi$
$8$	0.815121	+	0.815121i	0.288189	+	0.288189i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.794312	+	1.37579i	0.251184	+	0.435063i
$11$	2.94755	−	1.52051i	0.888720	−	0.458451i
$11$	2.94755	−	1.52051i	0.888720	−	0.458451i
$12$			1.37227i			0.396139i
$13$	−0.148240	−	3.60250i	−0.0411143	−	0.999154i
$13$	−0.148240	−	3.60250i	−0.0411143	−	0.999154i
$14$	8.28118			2.21324
$15$	0.223901	−	0.835611i	0.0578111	−	0.215754i
$16$	−2.43071	−	4.21011i	−0.607677	−	1.05253i
$17$	2.18190	−	3.77917i	0.529189	−	0.916583i	−0.470231	−	0.882543i	$-0.655829\pi$
$17$	2.18190	−	3.77917i	0.529189	−	0.916583i	0.999420	−	0.0340395i	$-0.0108372\pi$
$18$	1.29851	−	1.29851i	0.306062	−	0.306062i
$19$	1.77556	+	6.62647i	0.407341	+	1.52022i	0.799698	+	0.600403i	$0.204993\pi$
$19$	1.77556	+	6.62647i	0.407341	+	1.52022i	−0.392357	+	0.919813i	$0.628340\pi$
$20$	−0.307252	−	1.14668i	−0.0687036	−	0.256405i
$21$	−3.18872	−	3.18872i	−0.695836	−	0.695836i
$22$	−5.95104	+	1.29614i	−1.26877	+	0.276339i
$23$	2.38186	−	1.37517i	0.496652	−	0.286742i	−0.230678	−	0.973030i	$-0.574094\pi$
$23$	2.38186	−	1.37517i	0.496652	−	0.286742i	0.727330	+	0.686288i	$0.240761\pi$
$24$	−0.298355	+	1.11348i	−0.0609014	+	0.227287i
$25$		−	4.25162i		−	0.850325i
$26$	−1.44928	+	6.46058i	−0.284227	+	1.26702i
$27$	−1.00000			−0.192450
$28$	−5.97741	−	1.60164i	−1.12962	−	0.302682i
$29$	6.92026	−	3.99541i	1.28506	−	0.741929i	0.307291	−	0.951616i	$-0.400578\pi$
$29$	6.92026	−	3.99541i	1.28506	−	0.741929i	0.977769	+	0.209686i	$0.0672443\pi$
$30$	−0.794312	+	1.37579i	−0.145021	+	0.251184i
$31$	2.01631	+	2.01631i	0.362140	+	0.362140i	0.864600	−	0.502460i	$-0.167572\pi$
$31$	2.01631	+	2.01631i	0.362140	+	0.362140i	−0.502460	+	0.864600i	$0.667572\pi$
$32$	1.71387	+	6.39623i	0.302971	+	1.13070i
$33$	2.79057	+	1.79240i	0.485777	+	0.312017i
$34$	−5.66645	+	5.66645i	−0.971789	+	0.971789i
$35$	3.37849	+	1.95057i	0.571069	+	0.329707i
$36$	−1.18842	+	0.686133i	−0.198069	+	0.114355i
$37$	−6.19975	−	1.66122i	−1.01923	−	0.273103i	−0.289751	−	0.957102i	$-0.593572\pi$
$37$	−6.19975	−	1.66122i	−1.01923	−	0.273103i	−0.729483	+	0.683999i	$0.760239\pi$
$38$		−	12.5979i		−	2.04365i
$39$	3.04574	−	1.92963i	0.487709	−	0.308988i
$40$		−	0.997234i		−	0.157677i
$41$	0.830482	+	0.222527i	0.129700	+	0.0347529i	0.323085	−	0.946370i	$-0.395280\pi$
$41$	0.830482	+	0.222527i	0.129700	+	0.0347529i	−0.193385	+	0.981123i	$0.561947\pi$
$42$	4.14059	+	7.17171i	0.638907	+	1.10662i
$43$	4.50727	−	7.80683i	0.687353	−	1.19053i	−0.285338	−	0.958427i	$-0.592106\pi$
$43$	4.50727	−	7.80683i	0.687353	−	1.19053i	0.972691	−	0.232103i	$-0.0745607\pi$
$44$	4.54619	+	0.215412i	0.685364	+	0.0324746i
$45$	0.835611	−	0.223901i	0.124566	−	0.0333772i
$46$	−4.87855	+	1.30720i	−0.719302	+	0.192736i
$47$	6.11641	−	6.11641i	0.892170	−	0.892170i	−0.102557	−	0.994727i	$-0.532703\pi$
$47$	6.11641	−	6.11641i	0.892170	−	0.892170i	0.994727	+	0.102557i	$0.0327025\pi$
$48$	2.43071	−	4.21011i	0.350843	−	0.607677i
$49$	11.5492	−	6.66793i	1.64989	−	0.952562i
$50$	−2.02075	+	7.54153i	−0.285777	+	1.06653i
$51$	4.36381			0.611055
$52$	2.29562	−	4.38299i	0.318346	−	0.607811i
$53$	−4.70395			−0.646138			−0.323069	−	0.946375i	$-0.604715\pi$
$53$	−4.70395			−0.646138			−0.323069	+	0.946375i	$0.604715\pi$
$54$	1.77380	+	0.475288i	0.241384	+	0.0646785i
$55$	−2.73315	−	0.872935i	−0.368538	−	0.117706i
$56$	−4.50193	−	2.59919i	−0.601596	−	0.347332i
$57$	−4.85091	+	4.85091i	−0.642519	+	0.642519i
$58$	−14.1741	+	3.79795i	−1.86115	+	0.498695i
$59$	−1.18181	−	4.41058i	−0.153859	−	0.574208i	−0.999200	−	0.0399823i	$-0.987270\pi$
$59$	−1.18181	−	4.41058i	−0.153859	−	0.574208i	0.845342	−	0.534226i	$-0.179397\pi$
$60$	0.839428	−	0.839428i	0.108370	−	0.108370i
$61$	4.66597	+	2.69390i	0.597416	+	0.344918i	0.768024	−	0.640421i	$-0.221240\pi$
$61$	4.66597	+	2.69390i	0.597416	+	0.344918i	−0.170608	+	0.985339i	$0.554573\pi$
$62$	−2.61820	−	4.53486i	−0.332512	−	0.575928i
$63$	1.16715	−	4.35587i	0.147047	−	0.548788i
$64$		−	2.43738i		−	0.304673i
$65$	−2.11301	+	2.29437i	−0.262086	+	0.284581i
$66$	−4.09802	−	4.50568i	−0.504431	−	0.554611i
$67$	3.16876	−	11.8260i	0.387126	−	1.44477i	−0.447663	−	0.894202i	$-0.647743\pi$
$67$	3.16876	−	11.8260i	0.387126	−	1.44477i	0.834789	−	0.550571i	$-0.185590\pi$
$68$	5.18602	−	2.99415i	0.628897	−	0.363094i
$69$	2.38186	+	1.37517i	0.286742	+	0.165551i
$70$	−5.06568	−	5.06568i	−0.605464	−	0.605464i
$71$	−10.2153	+	2.73719i	−1.21234	+	0.324844i	−0.807678	−	0.589624i	$-0.799276\pi$
$71$	−10.2153	+	2.73719i	−1.21234	+	0.324844i	−0.404658	+	0.914468i	$0.632609\pi$
$72$	−1.11348	+	0.298355i	−0.131224	+	0.0351615i
$73$	−3.48467	−	3.48467i	−0.407849	−	0.407849i	0.473139	−	0.880988i	$-0.343121\pi$
$73$	−3.48467	−	3.48467i	−0.407849	−	0.407849i	−0.880988	+	0.473139i	$0.843121\pi$
$74$	10.2076	+	5.89334i	1.18661	+	0.685087i
$75$	3.68201	−	2.12581i	0.425162	−	0.245468i
$76$	−2.43654	+	9.09327i	−0.279490	+	1.04307i
$77$	−11.0645	+	10.0634i	−1.26092	+	1.14683i
$78$	−6.31966	+	1.97518i	−0.715561	+	0.223645i
$79$			11.7040i			1.31680i	0.752667	+	0.658401i	$0.228767\pi$
$79$			11.7040i			1.31680i	−0.752667	+	0.658401i	$0.771233\pi$
$80$	−1.08848	+	4.06225i	−0.121695	+	0.454174i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.36734	−	0.789437i	−0.150998	−	0.0871787i
$83$	4.72727	−	4.72727i	0.518885	−	0.518885i	−0.398349	−	0.917234i	$-0.630417\pi$
$83$	4.72727	−	4.72727i	0.518885	−	0.518885i	0.917234	+	0.398349i	$0.130417\pi$
$84$	−1.60164	−	5.97741i	−0.174754	−	0.652189i
$85$	−3.64644	+	0.977062i	−0.395512	+	0.105977i
$86$	−11.7055	+	11.7055i	−1.26224	+	1.26224i
$87$	6.92026	+	3.99541i	0.741929	+	0.428353i
$88$	3.64201	+	1.16321i	0.388239	+	0.123999i
$89$	12.9642	+	3.47376i	1.37421	+	0.368218i	0.869013	−	0.494789i	$-0.164755\pi$
$89$	12.9642	+	3.47376i	1.37421	+	0.368218i	0.505193	+	0.863006i	$0.331421\pi$
$90$	−1.58862			−0.167456
$91$	4.85038	+	15.5190i	0.508458	+	1.62684i
$92$	3.77419			0.393487
$93$	−0.738021	+	2.75433i	−0.0765293	+	0.285611i
$94$	−13.7563	+	7.94223i	−1.41886	+	0.819178i
$95$	2.96735	−	5.13960i	0.304444	−	0.527312i
$96$	−4.68237	+	4.68237i	−0.477892	+	0.477892i
$97$	2.37304	−	0.635853i	0.240945	−	0.0645611i	−0.136325	−	0.990664i	$-0.543529\pi$
$97$	2.37304	−	0.635853i	0.240945	−	0.0645611i	0.377271	+	0.926103i	$0.376863\pi$
$98$	−23.6552	+	6.33838i	−2.38953	+	0.640273i
$99$	−0.156975	+	3.31291i	−0.0157766	+	0.332960i
$100$	2.91718	−	5.05270i	0.291718	−	0.505270i
$101$	−3.94907	−	6.83999i	−0.392947	−	0.680605i	0.599889	−	0.800083i	$-0.295211\pi$
$101$	−3.94907	−	6.83999i	−0.392947	−	0.680605i	−0.992837	+	0.119478i	$0.961878\pi$
$102$	−7.74052	−	2.07407i	−0.766426	−	0.205363i
$103$			13.7601i			1.35583i	0.735142	+	0.677913i	$0.237116\pi$
$103$			13.7601i			1.35583i	−0.735142	+	0.677913i	$0.762884\pi$
$104$	2.81564	−	3.05731i	0.276096	−	0.299794i
$105$			3.90114i			0.380712i
$106$	8.34387	+	2.23573i	0.810429	+	0.217154i
$107$	−2.80093	+	1.61712i	−0.270776	+	0.156333i	−0.629240	−	0.777211i	$-0.716634\pi$
$107$	−2.80093	+	1.61712i	−0.270776	+	0.156333i	0.358464	+	0.933543i	$0.383300\pi$
$108$	−1.18842	−	0.686133i	−0.114355	−	0.0660232i
$109$	−10.0254	+	10.0254i	−0.960256	+	0.960256i	−0.999240	−	0.0389838i	$-0.987588\pi$
$109$	−10.0254	+	10.0254i	−0.960256	+	0.960256i	0.0389838	+	0.999240i	$0.487588\pi$
$110$	4.43317	+	2.84745i	0.422687	+	0.271493i
$111$	−1.66122	−	6.19975i	−0.157676	−	0.588455i
$112$	15.5017	+	15.5017i	1.46477	+	1.46477i
$113$	−5.19308	+	8.99468i	−0.488524	+	0.846149i	−0.999913	−	0.0132008i	$-0.995798\pi$
$113$	−5.19308	+	8.99468i	−0.488524	+	0.846149i	0.511389	+	0.859350i	$0.329131\pi$
$114$	10.9101	−	6.29897i	1.02183	−	0.589952i
$115$	−2.29821	−	0.615804i	−0.214309	−	0.0574240i
$116$	10.9655			1.01812
$117$	3.19398	+	1.67287i	0.295283	+	0.154657i
$118$			8.38518i			0.771919i
$119$	−5.09323	+	19.0082i	−0.466895	+	1.74248i
$120$	0.863630	−	0.498617i	0.0788383	−	0.0455173i
$121$	6.37610	−	8.96355i	0.579646	−	0.814869i
$122$	−6.99611	−	6.99611i	−0.633398	−	0.633398i
$123$	0.222527	+	0.830482i	0.0200646	+	0.0748821i
$124$	1.01276	+	3.77968i	0.0909487	+	0.339425i
$125$	−5.65931	+	5.65931i	−0.506184	+	0.506184i
$126$	−4.14059	+	7.17171i	−0.368873	+	0.638907i
$127$	−2.88867	−	5.00332i	−0.256328	−	0.443973i	0.708928	−	0.705281i	$-0.249179\pi$
$127$	−2.88867	−	5.00332i	−0.256328	−	0.443973i	−0.965255	+	0.261309i	$0.915846\pi$
$128$	2.26927	−	8.46904i	0.200577	−	0.748564i
$129$	9.01455			0.793687
$130$	4.83853	−	3.06546i	0.424368	−	0.268858i
$131$			4.51702i			0.394654i	0.980338	+	0.197327i	$0.0632261\pi$
$131$			4.51702i			0.394654i	−0.980338	+	0.197327i	$0.936774\pi$
$132$	2.08654	+	4.04482i	0.181610	+	0.352057i
$133$	−15.4682	−	26.7917i	−1.34126	−	2.32314i
$134$	−11.2415	+	19.4708i	−0.971117	+	1.68202i
$135$	0.611710	+	0.611710i	0.0526476	+	0.0526476i
$136$	4.85899	−	1.30196i	0.416655	−	0.111642i
$137$	0.130905	+	0.488545i	0.0111840	+	0.0417393i	0.971292	−	0.237889i	$-0.0764554\pi$
$137$	0.130905	+	0.488545i	0.0111840	+	0.0417393i	−0.960108	+	0.279628i	$0.909789\pi$
$138$	−3.57134	−	3.57134i	−0.304013	−	0.304013i
$139$	−2.09384	−	1.20888i	−0.177597	−	0.102536i	0.408566	−	0.912729i	$-0.366029\pi$
$139$	−2.09384	−	1.20888i	−0.177597	−	0.102536i	−0.586163	+	0.810193i	$0.699362\pi$
$140$	2.67670	+	4.63618i	0.226222	+	0.391829i
$141$	8.35517	+	2.23876i	0.703632	+	0.188538i
$142$	19.4209			1.62977
$143$	−5.91458	−	10.3932i	−0.494602	−	0.869119i
$144$	4.86142			0.405118
$145$	−6.67722	−	1.78916i	−0.554513	−	0.148581i
$146$	4.52488	+	7.83732i	0.374482	+	0.648621i
$147$	11.5492	+	6.66793i	0.952562	+	0.549962i
$148$	−6.22807	−	6.22807i	−0.511945	−	0.511945i
$149$	−4.85563	−	18.1215i	−0.397789	−	1.48457i	−0.816978	−	0.576668i	$-0.804352\pi$
$149$	−4.85563	−	18.1215i	−0.397789	−	1.48457i	0.419190	−	0.907899i	$-0.362314\pi$
$150$	−7.54153	+	2.02075i	−0.615763	+	0.164993i
$151$	−7.78600	−	7.78600i	−0.633616	−	0.633616i	0.315357	−	0.948973i	$-0.397876\pi$
$151$	−7.78600	−	7.78600i	−0.633616	−	0.633616i	−0.948973	+	0.315357i	$0.897876\pi$
$152$	−3.95408	+	6.84866i	−0.320718	+	0.555500i
$153$	2.18190	+	3.77917i	0.176396	+	0.305528i
$154$	24.4092	−	12.5916i	1.96695	−	1.01466i
$155$		−	2.46679i		−	0.198138i
$156$	4.94359	−	0.203424i	0.395804	−	0.0162870i
$157$	−10.6901			−0.853163			−0.426581	−	0.904449i	$-0.640282\pi$
$157$	−10.6901			−0.853163			−0.426581	+	0.904449i	$0.640282\pi$
$158$	5.56277	−	20.7605i	0.442550	−	1.65162i
$159$	−2.35198	−	4.07374i	−0.186524	−	0.323069i
$160$	2.86425	−	4.96102i	0.226439	−	0.392203i
$161$	−8.77005	+	8.77005i	−0.691177	+	0.691177i
$162$	0.475288	+	1.77380i	0.0373422	+	0.139363i
$163$	5.61110	+	20.9409i	0.439495	+	1.64022i	0.730075	+	0.683367i	$0.239485\pi$
$163$	5.61110	+	20.9409i	0.439495	+	1.64022i	−0.290580	+	0.956851i	$0.593848\pi$
$164$	0.834276	+	0.834276i	0.0651460	+	0.0651460i
$165$	−0.610594	−	2.80345i	−0.0475347	−	0.218248i
$166$	−10.6320	+	6.13841i	−0.825207	+	0.476433i
$167$	3.67613	−	13.7195i	0.284468	−	1.06165i	−0.664760	−	0.747057i	$-0.731466\pi$
$167$	3.67613	−	13.7195i	0.284468	−	1.06165i	0.949227	−	0.314591i	$-0.101867\pi$
$168$		−	5.19838i		−	0.401064i
$169$	−12.9560	+	1.06807i	−0.996619	+	0.0821592i
$170$	6.93245			0.531695
$171$	−6.62647	−	1.77556i	−0.506739	−	0.135780i
$172$	10.7130	−	6.18518i	0.816862	−	0.471615i
$173$	−5.91483	+	10.2448i	−0.449696	+	0.778896i	−0.998366	−	0.0571429i	$-0.981801\pi$
$173$	−5.91483	+	10.2448i	−0.449696	+	0.778896i	0.548670	+	0.836039i	$0.315134\pi$
$174$	−10.3762	−	10.3762i	−0.786616	−	0.786616i
$175$	4.96229	+	18.5195i	0.375114	+	1.39994i
$176$	−13.5662	−	8.71360i	−1.02259	−	0.656812i
$177$	3.22877	−	3.22877i	0.242689	−	0.242689i
$178$	−21.3449	−	12.3235i	−1.59987	−	0.923686i
$179$	13.8641	−	8.00442i	1.03625	−	0.598279i	0.117481	−	0.993075i	$-0.462518\pi$
$179$	13.8641	−	8.00442i	1.03625	−	0.598279i	0.918769	+	0.394796i	$0.129185\pi$
$180$	1.14668	+	0.307252i	0.0854685	+	0.0229012i
$181$		−	20.6818i		−	1.53727i	−0.639688	−	0.768635i	$-0.720936\pi$
$181$		−	20.6818i		−	1.53727i	0.639688	−	0.768635i	$-0.279064\pi$
$182$	−1.22760	−	29.8330i	−0.0909959	−	2.21137i
$183$			5.38779i			0.398277i
$184$	3.06243	+	0.820576i	0.225765	+	0.0604937i
$185$	2.77626	+	4.80863i	0.204115	+	0.353538i
$186$	2.61820	−	4.53486i	0.191976	−	0.332512i
$187$	0.685011	−	14.4569i	0.0500929	−	1.05719i
$188$	11.4655	−	3.07217i	0.836208	−	0.224061i
$189$	4.35587	−	1.16715i	0.316843	−	0.0848979i
$190$	−7.70627	+	7.70627i	−0.559072	+	0.559072i
$191$	0.797305	−	1.38097i	0.0576909	−	0.0999236i	−0.835738	−	0.549129i	$-0.814960\pi$
$191$	0.797305	−	1.38097i	0.0576909	−	0.0999236i	0.893428	+	0.449205i	$0.148293\pi$
$192$	2.11083	−	1.21869i	0.152336	−	0.0879514i
$193$	−1.62938	+	6.08094i	−0.117286	+	0.437716i	−0.999448	−	0.0332300i	$-0.989421\pi$
$193$	−1.62938	+	6.08094i	−0.117286	+	0.437716i	0.882162	+	0.470946i	$0.156087\pi$
$194$	−4.51150			−0.323907
$195$	−3.04348	−	0.682734i	−0.217948	−	0.0488916i
$196$	18.3004			1.30717
$197$	20.9183	+	5.60503i	1.49036	+	0.399342i	0.909860	−	0.414915i	$-0.136189\pi$
$197$	20.9183	+	5.60503i	1.49036	+	0.399342i	0.580504	+	0.814257i	$0.302855\pi$
$198$	1.85303	−	5.80183i	0.131689	−	0.412318i
$199$	14.1494	+	8.16916i	1.00302	+	0.579096i	0.909142	−	0.416487i	$-0.136739\pi$
$199$	14.1494	+	8.16916i	1.00302	+	0.579096i	0.0938823	+	0.995583i	$0.470072\pi$
$200$	3.46559	−	3.46559i	0.245054	−	0.245054i
$201$	11.8260	−	3.16876i	0.834140	−	0.223507i
$202$	3.75390	+	14.0097i	0.264123	+	0.985721i
$203$	−25.4805	+	25.4805i	−1.78838	+	1.78838i
$204$	5.18602	+	2.99415i	0.363094	+	0.209632i
$205$	−0.371892	−	0.644136i	−0.0259741	−	0.0449884i
$206$	6.54003	−	24.4077i	0.455666	−	1.70057i
$207$			2.75034i			0.191162i
$208$	−14.8066	+	9.38074i	−1.02665	+	0.650437i
$209$	15.3091	+	16.8321i	1.05896	+	1.16430i
$210$	1.85417	−	6.91984i	0.127950	−	0.477515i
$211$	6.28906	−	3.63099i	0.432957	−	0.249968i	−0.267649	−	0.963517i	$-0.586247\pi$
$211$	6.28906	−	3.63099i	0.432957	−	0.249968i	0.700606	+	0.713549i	$0.252913\pi$
$212$	−5.59026	−	3.22754i	−0.383940	−	0.221668i
$213$	−7.47814	−	7.47814i	−0.512394	−	0.512394i
$214$	5.73688	−	1.53719i	0.392165	−	0.105080i
$215$	−7.53265	+	2.01837i	−0.513723	+	0.137652i
$216$	−0.815121	−	0.815121i	−0.0554619	−	0.0554619i
$217$	−11.1361	−	6.42945i	−0.755971	−	0.436460i
$218$	22.5479	−	13.0181i	1.52714	−	0.881694i
$219$	1.27548	−	4.76014i	0.0861887	−	0.321661i
$220$	−2.64918	−	2.91272i	−0.178608	−	0.196375i
$221$	−13.9379	−	7.30009i	−0.937565	−	0.491057i
$222$			11.7867i			0.791070i
$223$	1.35113	−	5.04250i	0.0904787	−	0.337671i	−0.905817	−	0.423670i	$-0.860742\pi$
$223$	1.35113	−	5.04250i	0.0904787	−	0.337671i	0.996295	+	0.0859992i	$0.0274082\pi$
$224$	−14.9308	−	25.8608i	−0.997603	−	1.72790i
$225$	3.68201	+	2.12581i	0.245468	+	0.141721i
$226$	13.4866	−	13.4866i	0.897113	−	0.897113i
$227$	−3.50211	−	13.0701i	−0.232443	−	0.867491i	−0.979285	−	0.202488i	$-0.935097\pi$
$227$	−3.50211	−	13.0701i	−0.232443	−	0.867491i	0.746841	−	0.665002i	$-0.231569\pi$
$228$	−9.09327	+	2.43654i	−0.602217	+	0.161363i
$229$	14.1123	−	14.1123i	0.932569	−	0.932569i	−0.0652969	−	0.997866i	$-0.520799\pi$
$229$	14.1123	−	14.1123i	0.932569	−	0.932569i	0.997866	+	0.0652969i	$0.0207994\pi$
$230$	3.78388	+	2.18462i	0.249502	+	0.144050i
$231$	−14.2474	−	4.55043i	−0.937409	−	0.299397i
$232$	8.89759	+	2.38410i	0.584155	+	0.156524i
$233$	17.4137			1.14081			0.570406	−	0.821363i	$-0.306786\pi$
$233$	17.4137			1.14081			0.570406	+	0.821363i	$0.306786\pi$
$234$	−4.87038	−	4.48540i	−0.318387	−	0.293220i
$235$	−7.48293			−0.488133
$236$	1.62176	−	6.05248i	0.105567	−	0.393983i
$237$	−10.1360	+	5.85200i	−0.658401	+	0.380128i
$238$	18.0687	−	31.2960i	1.17122	−	2.02862i
$239$	7.62946	−	7.62946i	0.493509	−	0.493509i	−0.415901	−	0.909410i	$-0.636534\pi$
$239$	7.62946	−	7.62946i	0.493509	−	0.493509i	0.909410	+	0.415901i	$0.136534\pi$
$240$	−4.06225	+	1.08848i	−0.262217	+	0.0702609i
$241$	−7.70799	+	2.06535i	−0.496515	+	0.133041i	−0.498382	−	0.866957i	$-0.666072\pi$
$241$	−7.70799	+	2.06535i	−0.496515	+	0.133041i	0.00186692	+	0.999998i	$0.499406\pi$
$242$	−15.5702	+	12.8691i	−1.00089	+	0.827255i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.69674	+	6.40295i	0.236660	+	0.409907i
$245$	−11.1436	−	2.98592i	−0.711938	−	0.190763i
$246$		−	1.57887i		−	0.100665i
$247$	23.6087	−	7.37875i	1.50218	−	0.469499i
$248$			3.28708i			0.208729i
$249$	6.45757	+	1.73030i	0.409232	+	0.109653i
$250$	12.7283	−	7.34868i	0.805007	−	0.464771i
$251$	11.0718	+	6.39233i	0.698848	+	0.403480i	0.806918	−	0.590663i	$-0.201134\pi$
$251$	11.0718	+	6.39233i	0.698848	+	0.403480i	−0.108070	+	0.994143i	$0.534467\pi$
$252$	4.37577	−	4.37577i	0.275648	−	0.275648i
$253$	4.92970	−	7.67502i	0.309927	−	0.482524i
$254$	2.74590	+	10.2478i	0.172293	+	0.643006i
$255$	−2.66938	−	2.66938i	−0.167163	−	0.167163i
$256$	−10.4879	+	18.1655i	−0.655491	+	1.13534i
$257$	5.46980	−	3.15799i	0.341196	−	0.196990i	−0.319605	−	0.947551i	$-0.603550\pi$
$257$	5.46980	−	3.15799i	0.341196	−	0.196990i	0.660801	+	0.750561i	$0.270217\pi$
$258$	−15.9900	−	4.28451i	−0.995494	−	0.266742i
$259$	28.9442			1.79851
$260$	−4.08537	+	1.27686i	−0.253364	+	0.0791875i
$261$			7.99082i			0.494620i
$262$	2.14689	−	8.01229i	0.132635	−	0.495001i
$263$	−23.5667	+	13.6062i	−1.45318	+	0.838996i	−0.998661	−	0.0517384i	$-0.983524\pi$
$263$	−23.5667	+	13.6062i	−1.45318	+	0.838996i	−0.454524	+	0.890735i	$0.650190\pi$
$264$	0.813634	+	3.73568i	0.0500757	+	0.229915i
$265$	2.87745	+	2.87745i	0.176761	+	0.176761i
$266$	14.7037	+	54.8750i	0.901542	+	3.36460i
$267$	3.47376	+	12.9642i	0.212590	+	0.793399i
$268$	11.8800	−	11.8800i	0.725686	−	0.725686i
$269$	6.62972	−	11.4830i	0.404221	−	0.700131i	−0.590010	−	0.807396i	$-0.700876\pi$
$269$	6.62972	−	11.4830i	0.404221	−	0.700131i	0.994230	+	0.107265i	$0.0342094\pi$
$270$	−0.794312	−	1.37579i	−0.0483403	−	0.0837278i
$271$	−2.38686	+	8.90790i	−0.144992	+	0.541116i	0.854764	+	0.519017i	$0.173702\pi$
$271$	−2.38686	+	8.90790i	−0.144992	+	0.541116i	−0.999756	+	0.0220995i	$0.992965\pi$
$272$	−21.2143			−1.28631
$273$	−11.0147	+	11.9601i	−0.666639	+	0.723856i
$274$		−	0.928800i		−	0.0561108i
$275$	−6.46463	−	12.5319i	−0.389832	−	0.755700i
$276$	1.88710	+	3.26855i	0.113590	+	0.196743i
$277$	−2.05394	+	3.55753i	−0.123409	+	0.213751i	−0.921110	−	0.389302i	$-0.872716\pi$
$277$	−2.05394	+	3.55753i	−0.123409	+	0.213751i	0.797701	+	0.603053i	$0.206049\pi$
$278$	3.13949	+	3.13949i	0.188294	+	0.188294i
$279$	−2.75433	+	0.738021i	−0.164898	+	0.0441842i
$280$	1.16392	+	4.34382i	0.0695578	+	0.259593i
$281$	3.25314	+	3.25314i	0.194066	+	0.194066i	0.797450	−	0.603385i	$-0.206182\pi$
$281$	3.25314	+	3.25314i	0.194066	+	0.194066i	−0.603385	+	0.797450i	$0.706182\pi$
$282$	−13.7563	−	7.94223i	−0.819178	−	0.472953i
$283$	−9.24288	−	16.0091i	−0.549432	−	0.951645i	−0.998313	−	0.0580532i	$-0.981511\pi$
$283$	−9.24288	−	16.0091i	−0.549432	−	0.951645i	0.448881	−	0.893591i	$-0.351823\pi$
$284$	−14.0181	−	3.75615i	−0.831824	−	0.222886i
$285$	5.93470			0.351541
$286$	5.55154	+	21.2465i	0.328270	+	1.25633i
$287$	−3.87720			−0.228864
$288$	−6.39623	−	1.71387i	−0.376902	−	0.100990i
$289$	−1.02140	−	1.76913i	−0.0600826	−	0.104066i
$290$	10.9937	+	6.34721i	0.645572	+	0.372721i
$291$	1.73718	+	1.73718i	0.101835	+	0.101835i
$292$	−1.75029	−	6.53218i	−0.102428	−	0.382267i
$293$	−17.5846	+	4.71179i	−1.02731	+	0.275266i	−0.732844	−	0.680397i	$-0.761807\pi$
$293$	−17.5846	+	4.71179i	−1.02731	+	0.275266i	−0.294462	+	0.955663i	$0.595141\pi$
$294$	−17.3168	−	17.3168i	−1.00994	−	1.00994i
$295$	−1.97507	+	3.42092i	−0.114993	+	0.199173i
$296$	−3.69945	−	6.40764i	−0.215026	−	0.372437i
$297$	−2.94755	+	1.52051i	−0.171034	+	0.0882289i
$298$			34.4517i			1.99573i
$299$	−5.30713	−	8.37680i	−0.306919	−	0.484443i
$300$	5.83436			0.336847
$301$	−10.5214	+	39.2662i	−0.606441	+	2.26327i
$302$	10.1102	+	17.5114i	0.581778	+	1.00767i
$303$	3.94907	−	6.83999i	0.226868	−	0.392947i
$304$	23.5823	−	23.5823i	1.35254	−	1.35254i
$305$	−1.20633	−	4.50210i	−0.0690745	−	0.257789i
$306$	−2.07407	−	7.74052i	−0.118566	−	0.442496i
$307$	−3.42743	−	3.42743i	−0.195614	−	0.195614i	0.602503	−	0.798117i	$-0.294170\pi$
$307$	−3.42743	−	3.42743i	−0.195614	−	0.195614i	−0.798117	+	0.602503i	$0.794170\pi$
$308$	−20.0540	+	4.36779i	−1.14268	+	0.248878i
$309$	−11.9166	+	6.88007i	−0.677913	+	0.391393i
$310$	−1.17244	+	4.37560i	−0.0665900	+	0.248517i
$311$		−	26.4854i		−	1.50185i	−0.660387	−	0.750926i	$-0.729608\pi$
$311$		−	26.4854i		−	1.50185i	0.660387	−	0.750926i	$-0.270392\pi$
$312$	4.05553	+	0.909763i	0.229599	+	0.0515052i
$313$	21.3410			1.20627			0.603133	−	0.797641i	$-0.293919\pi$
$313$	21.3410			1.20627			0.603133	+	0.797641i	$0.293919\pi$
$314$	18.9621	+	5.08088i	1.07009	+	0.286731i
$315$	−3.37849	+	1.95057i	−0.190356	+	0.109902i
$316$	−8.03049	+	13.9092i	−0.451751	+	0.782455i
$317$	−11.7501	−	11.7501i	−0.659954	−	0.659954i	0.295415	−	0.955369i	$-0.404542\pi$
$317$	−11.7501	−	11.7501i	−0.659954	−	0.659954i	−0.955369	+	0.295415i	$0.904542\pi$
$318$	2.23573	+	8.34387i	0.125374	+	0.467901i
$319$	14.3227	−	22.2990i	0.801920	−	1.24850i
$320$	−1.49097	+	1.49097i	−0.0833478	+	0.0833478i
$321$	−2.80093	−	1.61712i	−0.156333	−	0.0902586i
$322$	19.7246	−	11.3880i	1.09921	−	0.634629i
$323$	28.9166	+	7.74819i	1.60896	+	0.431121i
$324$		−	1.37227i		−	0.0762370i
$325$	−15.3165	+	0.630260i	−0.849606	+	0.0349605i
$326$		−	39.8119i		−	2.20497i
$327$	−13.6949	−	3.66954i	−0.757330	−	0.202926i
$328$	0.495557	+	0.858330i	0.0273625	+	0.0473933i
$329$	−19.5035	+	33.7811i	−1.07526	+	1.86241i
$330$	−0.249375	+	5.26297i	−0.0137276	+	0.289717i
$331$	−11.6730	+	3.12778i	−0.641608	+	0.171918i	−0.564932	−	0.825138i	$-0.691097\pi$
$331$	−11.6730	+	3.12778i	−0.641608	+	0.171918i	−0.0766761	+	0.997056i	$0.524431\pi$
$332$	8.86150	−	2.37443i	0.486338	−	0.130314i
$333$	4.53853	−	4.53853i	0.248710	−	0.248710i
$334$	−13.0415	+	22.5885i	−0.713596	+	1.23599i
$335$	−9.17243	+	5.29570i	−0.501143	+	0.289335i
$336$	−5.67402	+	21.1757i	−0.309543	+	1.15523i
$337$	−30.3439			−1.65294			−0.826468	−	0.562984i	$-0.809653\pi$
$337$	−30.3439			−1.65294			−0.826468	+	0.562984i	$0.809653\pi$
$338$	23.4891	+	4.26332i	1.27764	+	0.231894i
$339$	−10.3862			−0.564099
$340$	−5.00389	−	1.34079i	−0.271374	−	0.0727144i
$341$	9.00900	+	2.87736i	0.487865	+	0.155818i
$342$	10.9101	+	6.29897i	0.589952	+	0.340609i
$343$	−20.2033	+	20.2033i	−1.09088	+	1.09088i
$344$	10.0375	−	2.68953i	0.541184	−	0.145010i
$345$	−0.615804	−	2.29821i	−0.0331537	−	0.123731i
$346$	15.3609	−	15.3609i	0.825809	−	0.825809i
$347$	20.5718	+	11.8771i	1.10435	+	0.637597i	0.937360	−	0.348361i	$-0.113262\pi$
$347$	20.5718	+	11.8771i	1.10435	+	0.637597i	0.166991	+	0.985958i	$0.446595\pi$
$348$	5.48277	+	9.49643i	0.293907	+	0.509062i
$349$	−0.759969	+	2.83624i	−0.0406802	+	0.151821i	−0.983278	−	0.182108i	$-0.941708\pi$
$349$	−0.759969	+	2.83624i	−0.0406802	+	0.151821i	0.942598	+	0.333929i	$0.108375\pi$
$350$		−	35.2085i		−	1.88197i
$351$	0.148240	+	3.60250i	0.00791246	+	0.192287i
$352$	14.7772	+	16.2473i	0.787629	+	0.865982i
$353$	1.19341	−	4.45386i	0.0635187	−	0.237055i	−0.926867	−	0.375391i	$-0.877509\pi$
$353$	1.19341	−	4.45386i	0.0635187	−	0.237055i	0.990385	+	0.138336i	$0.0441752\pi$
$354$	−7.26178	+	4.19259i	−0.385959	+	0.222834i
$355$	7.92318	+	4.57445i	0.420519	+	0.242787i
$356$	13.0235	+	13.0235i	0.690242	+	0.690242i
$357$	−19.0082	+	5.09323i	−1.00602	+	0.269562i
$358$	−28.3965	+	7.60882i	−1.50080	+	0.402139i
$359$	18.3147	+	18.3147i	0.966611	+	0.966611i	0.999460	−	0.0328491i	$-0.0104581\pi$
$359$	18.3147	+	18.3147i	0.966611	+	0.966611i	−0.0328491	+	0.999460i	$0.510458\pi$
$360$	0.863630	+	0.498617i	0.0455173	+	0.0262794i
$361$	−24.3030	+	14.0313i	−1.27910	+	0.738492i
$362$	−9.82984	+	36.6855i	−0.516645	+	1.92814i
$363$	10.9507	+	1.04009i	0.574764	+	0.0545906i
$364$	−4.88383	+	21.7711i	−0.255982	+	1.14111i
$365$			4.26321i			0.223146i
$366$	2.56076	−	9.55687i	0.133853	−	0.499546i
$367$	−0.553416	−	0.958544i	−0.0288881	−	0.0500356i	0.851220	−	0.524809i	$-0.175863\pi$
$367$	−0.553416	−	0.958544i	−0.0288881	−	0.0500356i	−0.880108	+	0.474774i	$0.842530\pi$
$368$	−11.5792	−	6.68527i	−0.603609	−	0.348494i
$369$	−0.607955	+	0.607955i	−0.0316489	+	0.0316489i
$370$	−2.63905	−	9.84908i	−0.137198	−	0.512029i
$371$	20.4898	−	5.49023i	1.06378	−	0.285039i
$372$	−2.76692	+	2.76692i	−0.143458	+	0.143458i
$373$	5.61043	+	3.23918i	0.290497	+	0.167718i	0.638166	−	0.769899i	$-0.279693\pi$
$373$	5.61043	+	3.23918i	0.290497	+	0.167718i	−0.347669	+	0.937617i	$0.613027\pi$
$374$	−8.08626	+	25.3181i	−0.418131	+	1.30917i
$375$	−7.73076	−	2.07145i	−0.399215	−	0.106969i
$376$	9.97122			0.514226
$377$	−15.4193	−	24.3380i	−0.794136	−	1.25347i
$378$	−8.28118			−0.425938
$379$	−2.79550	+	10.4329i	−0.143595	+	0.535904i	0.856219	+	0.516613i	$0.172807\pi$
$379$	−2.79550	+	10.4329i	−0.143595	+	0.535904i	−0.999814	+	0.0192907i	$0.993859\pi$
$380$	7.05289	−	4.07199i	0.361806	−	0.208889i
$381$	2.88867	−	5.00332i	0.147991	−	0.256328i
$382$	−2.07062	+	2.07062i	−0.105942	+	0.105942i
$383$	−5.31705	+	1.42470i	−0.271688	+	0.0727987i	−0.392091	−	0.919926i	$-0.628248\pi$
$383$	−5.31705	+	1.42470i	−0.271688	+	0.0727987i	0.120402	+	0.992725i	$0.461581\pi$
$384$	8.46904	−	2.26927i	0.432184	−	0.115803i
$385$	12.9241	+	0.612383i	0.658674	+	0.0312099i
$386$	5.78040	−	10.0120i	0.294215	−	0.509595i
$387$	4.50727	+	7.80683i	0.229118	+	0.396843i
$388$	3.25643	+	0.872559i	0.165320	+	0.0442975i
$389$		−	0.597925i		−	0.0303160i	−0.999885	−	0.0151580i	$-0.995175\pi$
$389$		−	0.597925i		−	0.0303160i	0.999885	−	0.0151580i	$-0.00482513\pi$
$390$	5.07403	+	2.65756i	0.256934	+	0.134571i
$391$		−	12.0019i		−	0.606964i
$392$	14.8492	+	3.97882i	0.749996	+	0.200961i
$393$	−3.91186	+	2.25851i	−0.197327	+	0.113927i
$394$	−34.4408	−	19.8844i	−1.73510	−	1.00176i
$395$	7.15944	−	7.15944i	0.360231	−	0.360231i
$396$	−2.45965	+	3.82941i	−0.123602	+	0.192435i
$397$	4.74300	+	17.7011i	0.238045	+	0.888394i	0.976753	+	0.214369i	$0.0687695\pi$
$397$	4.74300	+	17.7011i	0.238045	+	0.888394i	−0.738708	+	0.674025i	$0.764564\pi$
$398$	−21.2155	−	21.2155i	−1.06344	−	1.06344i
$399$	15.4682	−	26.7917i	0.774378	−	1.34126i
$400$	−17.8998	+	10.3345i	−0.894990	+	0.516723i
$401$	−1.77384	−	0.475299i	−0.0885814	−	0.0237353i	0.214256	−	0.976778i	$-0.431267\pi$
$401$	−1.77384	−	0.475299i	−0.0885814	−	0.0237353i	−0.302838	+	0.953042i	$0.597934\pi$
$402$	−22.4830			−1.12135
$403$	6.96487	−	7.56267i	0.346945	−	0.376723i
$404$		−	10.8384i		−	0.539228i
$405$	−0.223901	+	0.835611i	−0.0111257	+	0.0415218i
$406$	57.3079	−	33.0867i	2.84414	−	1.64207i
$407$	−20.8000	+	4.53026i	−1.03102	+	0.224556i
$408$	3.55703	+	3.55703i	0.176099	+	0.176099i
$409$	−1.98643	−	7.41345i	−0.0982225	−	0.366571i	0.899266	−	0.437403i	$-0.144102\pi$
$409$	−1.98643	−	7.41345i	−0.0982225	−	0.366571i	−0.997488	+	0.0708312i	$0.977435\pi$
$410$	0.353512	+	1.31932i	0.0174587	+	0.0651568i
$411$	−0.357640	+	0.357640i	−0.0176411	+	0.0176411i
$412$	−9.44128	+	16.3528i	−0.465139	+	0.805644i
$413$	10.2956	+	17.8326i	0.506615	+	0.877483i
$414$	1.30720	−	4.87855i	0.0642455	−	0.239767i
$415$	−5.78343			−0.283897
$416$	22.7884	−	7.12238i	1.11729	−	0.349204i
$417$		−	2.41776i		−	0.118398i
$418$	−19.1553	−	37.1330i	−0.936915	−	1.81624i
$419$	4.32582	+	7.49255i	0.211330	+	0.366035i	0.952131	−	0.305690i	$-0.0988871\pi$
$419$	4.32582	+	7.49255i	0.211330	+	0.366035i	−0.740801	+	0.671725i	$0.765554\pi$
$420$	−2.67670	+	4.63618i	−0.130610	+	0.226222i
$421$	−16.8436	−	16.8436i	−0.820906	−	0.820906i	0.165332	−	0.986238i	$-0.447130\pi$
$421$	−16.8436	−	16.8436i	−0.820906	−	0.820906i	−0.986238	+	0.165332i	$0.947130\pi$
$422$	−12.8813	+	3.45154i	−0.627052	+	0.168018i
$423$	2.23876	+	8.35517i	0.108852	+	0.406242i
$424$	−3.83429	−	3.83429i	−0.186210	−	0.186210i
$425$	−16.0676	−	9.27663i	−0.779393	−	0.449983i
$426$	9.71045	+	16.8190i	0.470473	+	0.814883i
$427$	−23.4685	−	6.28838i	−1.13572	−	0.304316i
$428$	−4.43823			−0.214530
$429$	6.04345	−	10.3188i	0.291780	−	0.498194i
$430$	14.3207			0.690607
$431$	1.38629	+	0.371455i	0.0667751	+	0.0178923i	0.292052	−	0.956402i	$-0.405662\pi$
$431$	1.38629	+	0.371455i	0.0667751	+	0.0178923i	−0.225277	+	0.974295i	$0.572329\pi$
$432$	2.43071	+	4.21011i	0.116948	+	0.202559i
$433$	−16.9202	−	9.76890i	−0.813135	−	0.469464i	0.0349085	−	0.999391i	$-0.488886\pi$
$433$	−16.9202	−	9.76890i	−0.813135	−	0.469464i	−0.848043	+	0.529927i	$0.822219\pi$
$434$	16.6974	+	16.6974i	0.801503	+	0.801503i
$435$	−1.78916	−	6.67722i	−0.0857834	−	0.320148i
$436$	−18.7930	+	5.03558i	−0.900024	+	0.241161i
$437$	13.3416	+	13.3416i	0.638217	+	0.638217i
$438$	−4.52488	+	7.83732i	−0.216207	+	0.374482i
$439$	3.24292	+	5.61690i	0.154776	+	0.268080i	0.932977	−	0.359935i	$-0.117201\pi$
$439$	3.24292	+	5.61690i	0.154776	+	0.268080i	−0.778201	+	0.628015i	$0.783868\pi$
$440$	−1.51630	−	2.93940i	−0.0722869	−	0.140130i
$441$			13.3359i			0.635041i
$442$	21.2534	+	19.5734i	1.01092	+	0.931013i
$443$	10.9002			0.517884			0.258942	−	0.965893i	$-0.416626\pi$
$443$	10.9002			0.517884			0.258942	+	0.965893i	$0.416626\pi$
$444$	2.27963	−	8.50771i	0.108187	−	0.403758i
$445$	−5.80542	−	10.0553i	−0.275203	−	0.476666i
$446$	−4.79329	+	8.30221i	−0.226969	+	0.393121i
$447$	13.2658	−	13.2658i	0.627452	−	0.627452i
$448$	2.84480	+	10.6169i	0.134404	+	0.501603i
$449$	−2.98208	−	11.1293i	−0.140733	−	0.525223i	−0.999908	−	0.0135416i	$-0.995689\pi$
$449$	−2.98208	−	11.1293i	−0.140733	−	0.525223i	0.859175	−	0.511682i	$-0.170977\pi$
$450$	−5.52078	−	5.52078i	−0.260252	−	0.260252i
$451$	2.78624	−	0.606846i	0.131199	−	0.0285753i
$452$	−12.3431	+	7.12629i	−0.580570	+	0.335192i
$453$	2.84988	−	10.6359i	0.133899	−	0.499717i
$454$			24.8482i			1.16618i
$455$	6.52611	−	12.4602i	0.305949	−	0.584141i
$456$	−7.90816			−0.370333
$457$	−7.84774	−	2.10279i	−0.367102	−	0.0983646i	0.0705523	−	0.997508i	$-0.477524\pi$
$457$	−7.84774	−	2.10279i	−0.367102	−	0.0983646i	−0.437654	+	0.899143i	$0.644191\pi$
$458$	−31.7399	+	18.3250i	−1.48311	+	0.856272i
$459$	−2.18190	+	3.77917i	−0.101843	+	0.176396i
$460$	−2.30871	−	2.30871i	−0.107644	−	0.107644i
$461$	0.0268065	+	0.100043i	0.00124850	+	0.00465948i	0.966547	−	0.256489i	$-0.0825656\pi$
$461$	0.0268065	+	0.100043i	0.00124850	+	0.00465948i	−0.965299	+	0.261148i	$0.915899\pi$
$462$	23.1093	+	14.8432i	1.07514	+	0.690567i
$463$	3.84198	−	3.84198i	0.178552	−	0.178552i	−0.612172	−	0.790724i	$-0.709704\pi$
$463$	3.84198	−	3.84198i	0.178552	−	0.178552i	0.790724	+	0.612172i	$0.209704\pi$
$464$	−33.6423	−	19.4234i	−1.56180	−	0.901707i
$465$	2.13631	−	1.23340i	0.0990689	−	0.0571974i
$466$	−30.8885	−	8.27655i	−1.43088	−	0.383404i
$467$			8.79002i			0.406754i	0.979101	+	0.203377i	$0.0651917\pi$
$467$			8.79002i			0.406754i	−0.979101	+	0.203377i	$0.934808\pi$
$468$	2.64797	+	4.17956i	0.122402	+	0.193200i
$469$			55.2109i			2.54940i
$470$	13.2732	+	3.55655i	0.612248	+	0.164051i
$471$	−5.34505	−	9.25790i	−0.246287	−	0.426581i
$472$	2.63183	−	4.55847i	0.121140	−	0.209821i
$473$	1.41506	−	29.8644i	0.0650646	−	1.37316i
$474$	20.7605	−	5.56277i	0.953563	−	0.255507i
$475$	28.1732	−	7.54900i	1.29268	−	0.346372i
$476$	−19.0950	+	19.0950i	−0.875219	+	0.875219i
$477$	2.35198	−	4.07374i	0.107690	−	0.186524i
$478$	−17.1593	+	9.90694i	−0.784849	+	0.453133i
$479$	5.43926	−	20.2996i	0.248526	−	0.927513i	−0.723052	−	0.690794i	$-0.757261\pi$
$479$	5.43926	−	20.2996i	0.248526	−	0.927513i	0.971578	−	0.236719i	$-0.0760720\pi$
$480$	5.72850			0.261469
$481$	−5.06549	+	22.5809i	−0.230967	+	1.02960i
$482$	14.6541			0.667475
$483$	−11.9801	−	3.21006i	−0.545114	−	0.146063i
$484$	13.7277	−	6.27758i	0.623984	−	0.285345i
$485$	−1.84057	−	1.06265i	−0.0835758	−	0.0482525i
$486$	−1.29851	+	1.29851i	−0.0589017	+	0.0589017i
$487$	0.720995	−	0.193190i	0.0326714	−	0.00875428i	−0.242446	−	0.970165i	$-0.577950\pi$
$487$	0.720995	−	0.193190i	0.0326714	−	0.00875428i	0.275118	+	0.961411i	$0.411283\pi$
$488$	1.60747	+	5.99918i	0.0727670	+	0.271570i
$489$	−15.3298	+	15.3298i	−0.693238	+	0.693238i
$490$	18.3473	+	10.5928i	0.828848	+	0.478536i
$491$	12.1422	+	21.0310i	0.547971	+	0.949114i	0.998413	+	0.0563085i	$0.0179330\pi$
$491$	12.1422	+	21.0310i	0.547971	+	0.949114i	−0.450442	+	0.892806i	$0.648734\pi$
$492$	−0.305366	+	1.13964i	−0.0137670	+	0.0513790i
$493$		−	34.8704i		−	1.57048i
$494$	−45.3841	+	1.86752i	−2.04193	+	0.0840235i
$495$	2.12256	−	1.93051i	0.0954020	−	0.0867702i
$496$	3.58783	−	13.3900i	0.161098	−	0.601227i
$497$	41.3019	−	23.8457i	1.85265	−	1.06963i
$498$	−10.6320	−	6.13841i	−0.476433	−	0.275069i
$499$	−8.53075	−	8.53075i	−0.381889	−	0.381889i	0.489893	−	0.871782i	$-0.337036\pi$
$499$	−8.53075	−	8.53075i	−0.381889	−	0.381889i	−0.871782	+	0.489893i	$0.837036\pi$
$500$	−10.6086	+	2.84258i	−0.474433	+	0.127124i
$501$	13.7195	−	3.67613i	0.612943	−	0.164238i
$502$	−16.6010	−	16.6010i	−0.740940	−	0.740940i
$503$	−1.97778	−	1.14187i	−0.0881848	−	0.0509135i	0.455259	−	0.890359i	$-0.349547\pi$
$503$	−1.97778	−	1.14187i	−0.0881848	−	0.0509135i	−0.543444	+	0.839445i	$0.682880\pi$
$504$	4.50193	−	2.59919i	0.200532	−	0.115777i
$505$	−1.76840	+	6.59977i	−0.0786930	+	0.293686i
$506$	−12.3921	+	11.2709i	−0.550898	+	0.501053i
$507$	−7.40300	−	10.6862i	−0.328779	−	0.474592i
$508$		−	7.92803i		−	0.351750i
$509$	−8.21497	+	30.6587i	−0.364122	+	1.35892i	0.504484	+	0.863421i	$0.331683\pi$
$509$	−8.21497	+	30.6587i	−0.364122	+	1.35892i	−0.868607	+	0.495502i	$0.834984\pi$
$510$	3.46622	+	6.00368i	0.153487	+	0.265847i
$511$	19.2459	+	11.1116i	0.851388	+	0.491549i
$512$	14.8377	−	14.8377i	0.655738	−	0.655738i
$513$	−1.77556	−	6.62647i	−0.0783927	−	0.292566i
$514$	−11.2033	+	3.00191i	−0.494155	+	0.132409i
$515$	8.41721	−	8.41721i	0.370906	−	0.370906i
$516$	10.7130	+	6.18518i	0.471615	+	0.272287i
$517$	8.72836	−	27.3285i	0.383873	−	1.20190i
$518$	−51.3413	−	13.7569i	−2.25581	−	0.604441i
$519$	−11.8297			−0.519264
$520$	−3.59254	+	0.147830i	−0.157543	+	0.00648277i
$521$	11.2662			0.493581			0.246791	−	0.969069i	$-0.420624\pi$
$521$	11.2662			0.493581			0.246791	+	0.969069i	$0.420624\pi$
$522$	3.79795	−	14.1741i	0.166232	−	0.620385i
$523$	2.87482	−	1.65978i	0.125707	−	0.0725769i	−0.435828	−	0.900030i	$-0.643544\pi$
$523$	2.87482	−	1.65978i	0.125707	−	0.0725769i	0.561535	+	0.827453i	$0.310211\pi$
$524$	−3.09928	+	5.36810i	−0.135393	+	0.234507i
$525$	−13.5572	+	13.5572i	−0.591686	+	0.591686i
$526$	48.2695	−	12.9338i	2.10465	−	0.563939i
$527$	12.0194	−	3.22058i	0.523572	−	0.140291i
$528$	0.763123	−	16.1054i	0.0332107	−	0.700899i
$529$	−7.71783	+	13.3677i	−0.335558	+	0.581203i
$530$	−3.73641	−	6.47165i	−0.162299	−	0.281110i
$531$	4.41058	+	1.18181i	0.191403	+	0.0512862i
$532$		−	42.4529i		−	1.84057i
$533$	0.678544	−	3.02480i	0.0293910	−	0.131019i
$534$		−	24.6470i		−	1.06658i
$535$	2.70256	+	0.724149i	0.116842	+	0.0313077i
$536$	12.2225	−	7.05668i	0.527932	−	0.304802i
$537$	13.8641	+	8.00442i	0.598279	+	0.345416i
$538$	−17.2175	+	17.2175i	−0.742300	+	0.742300i
$539$	23.9032	−	37.2147i	1.02958	−	1.60295i
$540$	0.307252	+	1.14668i	0.0132220	+	0.0493452i
$541$	−17.2696	−	17.2696i	−0.742476	−	0.742476i	0.230578	−	0.973054i	$-0.425938\pi$
$541$	−17.2696	−	17.2696i	−0.742476	−	0.742476i	−0.973054	+	0.230578i	$0.925938\pi$
$542$	8.46764	−	14.6664i	0.363716	−	0.629975i
$543$	17.9110	−	10.3409i	0.768635	−	0.443771i
$544$	27.9119	+	7.47898i	1.19671	+	0.320659i
$545$	12.2652			0.525385
$546$	25.2223	−	15.9796i	1.07942	−	0.683865i
$547$			26.7889i			1.14541i	0.819761	+	0.572705i	$0.194106\pi$
$547$			26.7889i			1.14541i	−0.819761	+	0.572705i	$0.805894\pi$
$548$	−0.179637	+	0.670414i	−0.00767371	+	0.0286387i
$549$	−4.66597	+	2.69390i	−0.199139	+	0.114973i
$550$	5.51071	+	25.3016i	0.234978	+	1.07886i
$551$	38.7628	+	38.7628i	1.65135	+	1.65135i
$552$	0.820576	+	3.06243i	0.0349260	+	0.130346i
$553$	−13.6603	−	50.9811i	−0.580897	−	2.16794i
$554$	5.33413	−	5.33413i	0.226625	−	0.226625i
$555$	−2.77626	+	4.80863i	−0.117846	+	0.204115i
$556$	−1.65890	−	2.87331i	−0.0703532	−	0.121855i
$557$	1.38970	−	5.18642i	0.0588833	−	0.219756i	−0.930214	−	0.367017i	$-0.880379\pi$
$557$	1.38970	−	5.18642i	0.0588833	−	0.219756i	0.989098	+	0.147261i	$0.0470458\pi$
$558$	5.23641			0.221675
$559$	−28.7923	−	15.0802i	−1.21778	−	0.637824i
$560$		−	18.9651i		−	0.801421i
$561$	12.8625	−	6.63521i	0.543057	−	0.280139i
$562$	−4.22424	−	7.31659i	−0.178189	−	0.308632i
$563$	−21.5903	+	37.3954i	−0.909921	+	1.57603i	−0.0957492	+	0.995405i	$0.530525\pi$
$563$	−21.5903	+	37.3954i	−0.909921	+	1.57603i	−0.814172	+	0.580624i	$0.802809\pi$
$564$	8.39334	+	8.39334i	0.353423	+	0.353423i
$565$	8.67879	−	2.32548i	0.365120	−	0.0978335i
$566$	8.78607	+	32.7900i	0.369306	+	1.37827i
$567$	3.18872	+	3.18872i	0.133914	+	0.133914i
$568$	−10.5579	−	6.09558i	−0.442998	−	0.255765i
$569$	6.92785	+	11.9994i	0.290431	+	0.503041i	0.973912	−	0.226928i	$-0.0728681\pi$
$569$	6.92785	+	11.9994i	0.290431	+	0.503041i	−0.683481	+	0.729968i	$0.739535\pi$
$570$	−10.5270	−	2.82069i	−0.440926	−	0.118146i
$571$	45.2672			1.89437			0.947186	−	0.320683i	$-0.103912\pi$
$571$	45.2672			1.89437			0.947186	+	0.320683i	$0.103912\pi$
$572$	0.102096	−	16.4096i	0.00426884	−	0.686119i
$573$	1.59461			0.0666158
$574$	6.87737	+	1.84279i	0.287056	+	0.0769164i
$575$	−5.84669	−	10.1268i	−0.243824	−	0.422316i
$576$	2.11083	+	1.21869i	0.0879514	+	0.0507788i
$577$	15.3212	+	15.3212i	0.637829	+	0.637829i	0.950020	−	0.312190i	$-0.101063\pi$
$577$	15.3212	+	15.3212i	0.637829	+	0.637829i	−0.312190	+	0.950020i	$0.601063\pi$
$578$	0.970924	+	3.62354i	0.0403851	+	0.150719i
$579$	−6.08094	+	1.62938i	−0.252715	+	0.0677149i
$580$	−6.70772	−	6.70772i	−0.278523	−	0.278523i
$581$	−15.0739	+	26.1088i	−0.625372	+	1.08318i
$582$	−2.25575	−	3.90708i	−0.0935039	−	0.161954i
$583$	−13.8651	+	7.15241i	−0.574235	+	0.296222i
$584$		−	5.68084i		−	0.235075i
$585$	−0.930476	−	2.97710i	−0.0384704	−	0.123088i
$586$	33.4311			1.38103
$587$	−4.58348	+	17.1058i	−0.189180	+	0.706031i	0.804517	+	0.593930i	$0.202424\pi$
$587$	−4.58348	+	17.1058i	−0.189180	+	0.706031i	−0.993697	+	0.112100i	$0.964242\pi$
$588$	9.15018	+	15.8486i	0.377347	+	0.653584i
$589$	−9.78095	+	16.9411i	−0.403017	+	0.698046i
$590$	5.12930	−	5.12930i	0.211170	−	0.211170i
$591$	5.60503	+	20.9183i	0.230560	+	0.860462i
$592$	8.07588	+	30.1396i	0.331917	+	1.23873i
$593$	−12.1717	−	12.1717i	−0.499832	−	0.499832i	0.411554	−	0.911385i	$-0.364986\pi$
$593$	−12.1717	−	12.1717i	−0.499832	−	0.499832i	−0.911385	+	0.411554i	$0.864986\pi$
$594$	5.95104	−	1.29614i	0.244174	−	0.0531814i
$595$	14.7431	−	8.51191i	0.604407	−	0.348954i
$596$	6.66321	−	24.8674i	0.272936	−	1.01861i
$597$			16.3383i			0.668683i
$598$	5.43239	+	17.3812i	0.222147	+	0.710770i
$599$	9.53492			0.389586			0.194793	−	0.980844i	$-0.437596\pi$
$599$	9.53492			0.389586			0.194793	+	0.980844i	$0.437596\pi$
$600$	4.73408	+	1.26849i	0.193268	+	0.0517860i
$601$	9.34705	−	5.39652i	0.381274	−	0.220129i	−0.297098	−	0.954847i	$-0.596019\pi$
$601$	9.34705	−	5.39652i	0.381274	−	0.220129i	0.678372	+	0.734718i	$0.262686\pi$
$602$	37.3255	−	64.6497i	1.52128	−	2.63493i
$603$	8.65722	+	8.65722i	0.352549	+	0.352549i
$604$	−3.91079	−	14.5953i	−0.159128	−	0.593872i
$605$	−9.38342	+	1.58277i	−0.381490	+	0.0643487i
$606$	−10.2558	+	10.2558i	−0.416615	+	0.416615i
$607$	−2.62300	−	1.51439i	−0.106464	−	0.0614671i	0.445822	−	0.895121i	$-0.352911\pi$
$607$	−2.62300	−	1.51439i	−0.106464	−	0.0614671i	−0.552287	+	0.833654i	$0.686245\pi$
$608$	−39.3414	+	22.7137i	−1.59550	+	0.921164i
$609$	−34.8070	−	9.32651i	−1.41045	−	0.377929i
$610$			8.55918i			0.346551i
$611$	−22.9411	−	21.1277i	−0.928096	−	0.854734i
$612$			5.98830i			0.242063i
$613$	18.0217	+	4.82890i	0.727889	+	0.195037i	0.603689	−	0.797220i	$-0.293697\pi$
$613$	18.0217	+	4.82890i	0.727889	+	0.195037i	0.124200	+	0.992257i	$0.460364\pi$
$614$	4.45056	+	7.70860i	0.179610	+	0.311094i
$615$	0.371892	−	0.644136i	0.0149961	−	0.0259741i
$616$	−17.2218	−	0.816018i	−0.693885	−	0.0328783i
$617$	−21.4845	+	5.75675i	−0.864933	+	0.231758i	−0.663895	−	0.747825i	$-0.731098\pi$
$617$	−21.4845	+	5.75675i	−0.864933	+	0.231758i	−0.201038	+	0.979584i	$0.564431\pi$
$618$	24.4077	−	6.54003i	0.981823	−	0.263079i
$619$	−14.1396	+	14.1396i	−0.568320	+	0.568320i	−0.931658	−	0.363338i	$-0.881637\pi$
$619$	−14.1396	+	14.1396i	−0.568320	+	0.568320i	0.363338	+	0.931658i	$0.381637\pi$
$620$	1.69255	−	2.93158i	0.0679744	−	0.117735i
$621$	−2.38186	+	1.37517i	−0.0955808	+	0.0551836i
$622$	−12.5882	+	46.9799i	−0.504742	+	1.88372i
$623$	−60.5250			−2.42488
$624$	−15.5273	−	8.13253i	−0.621588	−	0.325562i
$625$	−14.3344			−0.573376
$626$	−37.8547	−	10.1431i	−1.51298	−	0.405401i
$627$	−6.92245	+	21.6742i	−0.276456	+	0.865583i
$628$	−12.7043	−	7.33483i	−0.506956	−	0.292691i
$629$	−19.8053	+	19.8053i	−0.789689	+	0.789689i
$630$	6.91984	−	1.85417i	0.275693	−	0.0738718i
$631$	11.3870	+	42.4969i	0.453309	+	1.69177i	0.693011	+	0.720927i	$0.256284\pi$
$631$	11.3870	+	42.4969i	0.453309	+	1.69177i	−0.239702	+	0.970847i	$0.577050\pi$
$632$	−9.54017	+	9.54017i	−0.379487	+	0.379487i
$633$	6.28906	+	3.63099i	0.249968	+	0.144319i
$634$	15.2577	+	26.4271i	0.605960	+	1.04955i
$635$	−1.29355	+	4.82760i	−0.0513330	+	0.191578i
$636$		−	6.45507i		−	0.255960i
$637$	−25.7333	−	40.6176i	−1.01959	−	1.60933i
$638$	−36.0041	+	32.7465i	−1.42542	+	1.29645i
$639$	2.73719	−	10.2153i	0.108281	−	0.404112i
$640$	−6.56873	+	3.79246i	−0.259652	+	0.149910i
$641$	−35.3809	−	20.4272i	−1.39746	−	0.806825i	−0.403336	−	0.915052i	$-0.632149\pi$
$641$	−35.3809	−	20.4272i	−1.39746	−	0.806825i	−0.994126	+	0.108227i	$0.965483\pi$
$642$	4.19969	+	4.19969i	0.165748	+	0.165748i
$643$	−8.72737	+	2.33849i	−0.344174	+	0.0922211i	−0.426765	−	0.904362i	$-0.640347\pi$
$643$	−8.72737	+	2.33849i	−0.344174	+	0.0922211i	0.0825915	+	0.996583i	$0.473680\pi$
$644$	−16.4399	+	4.40506i	−0.647823	+	0.173584i
$645$	−5.51428	−	5.51428i	−0.217125	−	0.217125i
$646$	−47.6097	−	27.4875i	−1.87318	−	1.08148i
$647$	25.6898	−	14.8320i	1.00997	−	0.583106i	0.0987865	−	0.995109i	$-0.468504\pi$
$647$	25.6898	−	14.8320i	1.00997	−	0.583106i	0.911183	+	0.412003i	$0.135171\pi$
$648$	0.298355	−	1.11348i	0.0117205	−	0.0437414i
$649$	−10.1898	−	11.2034i	−0.399983	−	0.439774i
$650$	27.4679	+	6.16179i	1.07738	+	0.241685i
$651$		−	12.8589i		−	0.503980i
$652$	−7.69992	+	28.7365i	−0.301552	+	1.12541i
$653$	13.7869	+	23.8796i	0.539523	+	0.934480i	0.998930	+	0.0462547i	$0.0147286\pi$
$653$	13.7869	+	23.8796i	0.539523	+	0.934480i	−0.459407	+	0.888226i	$0.651938\pi$
$654$	22.5479	+	13.0181i	0.881694	+	0.509046i
$655$	2.76311	−	2.76311i	0.107963	−	0.107963i
$656$	−1.08180	−	4.03732i	−0.0422371	−	0.157631i
$657$	4.76014	−	1.27548i	0.185711	−	0.0497611i
$658$	50.6511	−	50.6511i	1.97458	−	1.97458i
$659$	16.0828	+	9.28542i	0.626498	+	0.361709i	0.779394	−	0.626534i	$-0.215527\pi$
$659$	16.0828	+	9.28542i	0.626498	+	0.361709i	−0.152897	+	0.988242i	$0.548860\pi$
$660$	1.19790	−	3.75061i	0.0466281	−	0.145992i
$661$	27.2415	+	7.29935i	1.05957	+	0.283912i	0.746202	−	0.665719i	$-0.231875\pi$
$661$	27.2415	+	7.29935i	1.05957	+	0.283912i	0.313370	+	0.949631i	$0.398542\pi$
$662$	22.1922			0.862525
$663$	−0.646890	−	15.7206i	−0.0251231	−	0.610538i
$664$	7.70659			0.299074
$665$	−6.92670	+	25.8508i	−0.268606	+	1.00245i
$666$	−10.2076	+	5.89334i	−0.395535	+	0.228362i
$667$	10.9887	−	19.0330i	0.425485	−	0.736962i
$668$	13.7822	−	13.7822i	0.533249	−	0.533249i
$669$	5.04250	−	1.35113i	0.194954	−	0.0522379i
$670$	18.7870	−	5.03397i	0.725806	−	0.194479i
$671$	17.8493	+	0.845751i	0.689063	+	0.0326499i
$672$	14.9308	−	25.8608i	0.575967	−	0.997603i
$673$	−6.02132	−	10.4292i	−0.232105	−	0.402017i	0.726322	−	0.687354i	$-0.241228\pi$
$673$	−6.02132	−	10.4292i	−0.232105	−	0.402017i	−0.958427	+	0.285337i	$0.907895\pi$
$674$	53.8239	+	14.4221i	2.07322	+	0.555518i
$675$			4.25162i			0.163645i
$676$	−16.1300	−	7.62026i	−0.620386	−	0.293087i
$677$			16.7879i			0.645213i	0.946533	+	0.322606i	$0.104559\pi$
$677$			16.7879i			0.645213i	−0.946533	+	0.322606i	$0.895441\pi$
$678$	18.4230	+	4.93642i	0.707530	+	0.189582i
$679$	−9.59450	+	5.53939i	−0.368203	+	0.212582i
$680$	−3.76871	−	2.17587i	−0.144524	−	0.0834408i
$681$	9.56795	−	9.56795i	0.366645	−	0.366645i
$682$	−14.6126	−	9.38573i	−0.559545	−	0.359398i
$683$	8.93756	+	33.3554i	0.341986	+	1.27631i	0.896094	+	0.443865i	$0.146393\pi$
$683$	8.93756	+	33.3554i	0.341986	+	1.27631i	−0.554107	+	0.832445i	$0.686940\pi$
$684$	−6.65674	−	6.65674i	−0.254527	−	0.254527i
$685$	0.218772	−	0.378924i	0.00835884	−	0.0144779i
$686$	45.4390	−	26.2342i	1.73487	−	1.00163i
$687$	19.2778	+	5.16547i	0.735494	+	0.197075i
$688$	−43.8235			−1.67075
$689$	0.697314	+	16.9460i	0.0265655	+	0.645591i
$690$			4.36925i			0.166334i
$691$	−9.90767	+	36.9759i	−0.376906	+	1.40663i	0.473635	+	0.880721i	$0.342942\pi$
$691$	−9.90767	+	36.9759i	−0.376906	+	1.40663i	−0.850540	+	0.525910i	$0.823725\pi$
$692$	−14.0586	+	8.11671i	−0.534426	+	0.308551i
$693$	−3.18290	−	14.6138i	−0.120909	−	0.555133i
$694$	−30.8452	−	30.8452i	−1.17087	−	1.17087i
$695$	0.541339	+	2.02031i	0.0205342	+	0.0766346i
$696$	2.38410	+	8.89759i	0.0903691	+	0.337262i
$697$	2.65300	−	2.65300i	0.100490	−	0.100490i
$698$	2.69606	−	4.66972i	0.102048	−	0.176752i
$699$	8.70687	+	15.0807i	0.329324	+	0.570406i
$700$	−6.80958	+	25.4137i	−0.257378	+	0.960548i
$701$	1.57204			0.0593752			0.0296876	−	0.999559i	$-0.490549\pi$
$701$	1.57204			0.0593752			0.0296876	+	0.999559i	$0.490549\pi$
$702$	1.44928	−	6.46058i	0.0546995	−	0.243839i
$703$		−	44.0321i		−	1.66070i
$704$	−3.70606	−	7.18431i	−0.139677	−	0.270769i
$705$	−3.74146	−	6.48041i	−0.140912	−	0.244066i
$706$	−4.23374	+	7.33305i	−0.159339	+	0.275983i
$707$	25.1850	+	25.1850i	0.947178	+	0.947178i
$708$	6.05248	−	1.62176i	0.227466	−	0.0609494i
$709$	5.60050	+	20.9014i	0.210331	+	0.784967i	0.987758	+	0.155993i	$0.0498579\pi$
$709$	5.60050	+	20.9014i	0.210331	+	0.784967i	−0.777427	+	0.628973i	$0.783475\pi$
$710$	−11.8799	−	11.8799i	−0.445847	−	0.445847i
$711$	−10.1360	−	5.85200i	−0.380128	−	0.219467i
$712$	7.73589	+	13.3989i	0.289915	+	0.502147i
$713$	7.57534	+	2.02981i	0.283699	+	0.0760169i
$714$	36.1375			1.35241
$715$	−2.73959	+	9.97560i	−0.102455	+	0.373066i
$716$	21.9684			0.820997
$717$	10.4220	+	2.79258i	0.389218	+	0.104291i
$718$	−23.7818	−	41.1913i	−0.887529	−	1.53725i
$719$	−10.7682	−	6.21701i	−0.401585	−	0.231855i	0.285583	−	0.958354i	$-0.407813\pi$
$719$	−10.7682	−	6.21701i	−0.401585	−	0.231855i	−0.687168	+	0.726499i	$0.741146\pi$
$720$	−2.97378	−	2.97378i	−0.110826	−	0.110826i
$721$	−16.0602	−	59.9374i	−0.598112	−	2.23219i
$722$	49.7776	−	13.3379i	1.85253	−	0.496384i
$723$	−5.64264	−	5.64264i	−0.209852	−	0.209852i
$724$	14.1905	−	24.5786i	0.527385	−	0.913458i
$725$	−16.9870	−	29.4223i	−0.630881	−	1.09272i
$726$	−18.9300	−	7.04966i	−0.702560	−	0.261637i
$727$			2.33553i			0.0866198i	0.999062	+	0.0433099i	$0.0137903\pi$
$727$			2.33553i			0.0866198i	−0.999062	+	0.0433099i	$0.986210\pi$
$728$	−8.69623	+	16.6035i	−0.322304	+	0.615368i
$729$	1.00000			0.0370370
$730$	2.02625	−	7.56208i	0.0749949	−	0.279885i
$731$	−19.6689	−	34.0675i	−0.727479	−	1.26003i
$732$	−3.69674	+	6.40295i	−0.136636	+	0.236660i
$733$	3.65997	−	3.65997i	0.135184	−	0.135184i	−0.636277	−	0.771461i	$-0.719526\pi$
$733$	3.65997	−	3.65997i	0.135184	−	0.135184i	0.771461	+	0.636277i	$0.219526\pi$
$734$	0.526064	+	1.96330i	0.0194174	+	0.0724667i
$735$	−2.98592	−	11.1436i	−0.110137	−	0.411038i
$736$	12.8781	+	12.8781i	0.474692	+	0.474692i
$737$	−8.64143	−	39.6758i	−0.318311	−	1.46148i
$738$	1.36734	−	0.789437i	0.0503327	−	0.0290596i
$739$	1.80976	−	6.75412i	0.0665731	−	0.248454i	−0.924618	−	0.380897i	$-0.875615\pi$
$739$	1.80976	−	6.75412i	0.0665731	−	0.248454i	0.991191	+	0.132442i	$0.0422820\pi$
$740$			7.61955i			0.280100i
$741$	18.1945	+	16.7563i	0.668392	+	0.615559i
$742$	−38.9543			−1.43006
$743$	39.3572	+	10.5457i	1.44387	+	0.386885i	0.893888	−	0.448289i	$-0.147967\pi$
$743$	39.3572	+	10.5457i	1.44387	+	0.386885i	0.549985	+	0.835174i	$0.314633\pi$
$744$	−2.84669	+	1.64354i	−0.104365	+	0.0602550i
$745$	−8.11483	+	14.0553i	−0.297304	+	0.514946i
$746$	−8.41223	−	8.41223i	−0.307994	−	0.307994i
$747$	1.73030	+	6.45757i	0.0633084	+	0.236270i
$748$	10.7334	−	16.7108i	0.392453	−	0.611007i
$749$	10.3131	−	10.3131i	0.376831	−	0.376831i
$750$	12.7283	+	7.34868i	0.464771	+	0.268336i
$751$	−34.3192	+	19.8142i	−1.25233	+	0.723031i	−0.971571	−	0.236748i	$-0.923918\pi$
$751$	−34.3192	+	19.8142i	−1.25233	+	0.723031i	−0.280756	+	0.959779i	$0.590585\pi$
$752$	−40.6180	−	10.8836i	−1.48118	−	0.396882i
$753$			12.7847i			0.465899i
$754$	15.7833	+	50.4993i	0.574793	+	1.83908i
$755$			9.52555i			0.346670i
$756$	5.97741	+	1.60164i	0.217396	+	0.0582512i
$757$	17.6011	+	30.4861i	0.639724	+	1.10804i	0.985493	+	0.169715i	$0.0542848\pi$
$757$	17.6011	+	30.4861i	0.639724	+	1.10804i	−0.345769	+	0.938320i	$0.612382\pi$
$758$	9.91730	−	17.1773i	0.360213	−	0.623907i
$759$	9.11161	+	0.431735i	0.330730	+	0.0156710i
$760$	6.60814	−	1.77065i	0.239702	−	0.0642281i
$761$	2.96615	−	0.794778i	0.107523	−	0.0288107i	−0.204656	−	0.978834i	$-0.565608\pi$
$761$	2.96615	−	0.794778i	0.107523	−	0.0288107i	0.312179	+	0.950023i	$0.398941\pi$
$762$	−7.50193	+	7.50193i	−0.271766	+	0.271766i
$763$	31.9681	−	55.3704i	1.15732	−	2.00454i
$764$	1.89506	−	1.09411i	0.0685609	−	0.0395836i
$765$	0.977062	−	3.64644i	0.0353257	−	0.131837i
$766$	10.1085			0.365236
$767$	−15.7139	+	4.91130i	−0.567397	+	0.177337i
$768$	−20.9757			−0.756895
$769$	−17.4055	−	4.66378i	−0.627658	−	0.168180i	−0.0690511	−	0.997613i	$-0.521997\pi$
$769$	−17.4055	−	4.66378i	−0.627658	−	0.168180i	−0.558607	+	0.829433i	$0.688664\pi$
$770$	−22.6337	−	7.22893i	−0.815664	−	0.260513i
$771$	5.46980	+	3.15799i	0.196990	+	0.113732i
$772$	−6.10872	+	6.10872i	−0.219858	+	0.219858i
$773$	42.3388	−	11.3447i	1.52282	−	0.408039i	0.602153	−	0.798381i	$-0.294310\pi$
$773$	42.3388	−	11.3447i	1.52282	−	0.408039i	0.920670	+	0.390342i	$0.127643\pi$
$774$	−4.28451	−	15.9900i	−0.154003	−	0.574749i
$775$	8.57260	−	8.57260i	0.307937	−	0.307937i
$776$	2.45261	+	1.41601i	0.0880435	+	0.0508319i
$777$	14.4721	+	25.0664i	0.519184	+	0.899253i
$778$	−0.284187	+	1.06060i	−0.0101886	+	0.0380243i
$779$			5.89827i			0.211328i
$780$	−3.14848	−	2.89960i	−0.112734	−	0.103822i
$781$	−25.9483	+	23.6005i	−0.928502	+	0.844492i
$782$	−5.70438	+	21.2890i	−0.203988	+	0.761294i
$783$	−6.92026	+	3.99541i	−0.247310	+	0.142784i
$784$	−56.1455	−	32.4156i	−2.00520	−	1.15770i
$785$	6.53924	+	6.53924i	0.233395	+	0.233395i
$786$	8.01229	−	2.14689i	0.285789	−	0.0765769i
$787$	28.1097	−	7.53197i	1.00200	−	0.268486i	0.279719	−	0.960082i	$-0.409759\pi$
$787$	28.1097	−	7.53197i	1.00200	−	0.268486i	0.722284	+	0.691596i	$0.243092\pi$
$788$	21.0138	+	21.0138i	0.748586	+	0.748586i
$789$	−23.5667	−	13.6062i	−0.838996	−	0.484395i
$790$	−16.1022	+	9.29662i	−0.572891	+	0.330759i
$791$	12.1222	−	45.2408i	0.431017	−	1.60858i
$792$	−2.82837	+	2.57247i	−0.100502	+	0.0914086i
$793$	9.01309	−	17.2085i	0.320064	−	0.611092i
$794$		−	33.6526i		−	1.19428i
$795$	−1.05322	+	3.93067i	−0.0373539	+	0.139407i
$796$	11.2103	+	19.4167i	0.397337	+	0.688207i
$797$	2.56824	+	1.48277i	0.0909718	+	0.0525226i	0.544796	−	0.838569i	$-0.316607\pi$
$797$	2.56824	+	1.48277i	0.0909718	+	0.0525226i	−0.453824	+	0.891091i	$0.649941\pi$
$798$	−40.1713	+	40.1713i	−1.42205	+	1.42205i
$799$	−9.76952	−	36.4603i	−0.345621	−	1.28987i
$800$	27.1944	−	7.28671i	0.961466	−	0.257624i
$801$	−9.49048	+	9.49048i	−0.335330	+	0.335330i
$802$	2.92053	+	1.68617i	0.103128	+	0.0595408i
$803$	−15.5697	−	4.97276i	−0.549442	−	0.175485i
$804$	16.2284	+	4.34838i	0.572331	+	0.153356i
$805$	10.7294			0.378163
$806$	−15.9487	+	10.1043i	−0.561770	+	0.355910i
$807$	13.2594			0.466754
$808$	2.35645	−	8.79439i	0.0828996	−	0.309386i
$809$	−1.39487	+	0.805329i	−0.0490411	+	0.0283139i	−0.524320	−	0.851521i	$-0.675680\pi$
$809$	−1.39487	+	0.805329i	−0.0490411	+	0.0283139i	0.475279	+	0.879835i	$0.342347\pi$
$810$	0.794312	−	1.37579i	0.0279093	−	0.0483403i
$811$	14.8196	−	14.8196i	0.520386	−	0.520386i	−0.397302	−	0.917688i	$-0.630053\pi$
$811$	14.8196	−	14.8196i	0.520386	−	0.520386i	0.917688	+	0.397302i	$0.130053\pi$
$812$	−47.7645	+	12.7984i	−1.67620	+	0.449137i
$813$	−8.90790	+	2.38686i	−0.312414	+	0.0837110i
$814$	39.0482	+	1.85022i	1.36864	+	0.0648502i
$815$	9.37739	−	16.2421i	0.328476	−	0.568936i
$816$	−10.6071	−	18.3721i	−0.371324	−	0.643153i
$817$	59.7346	+	16.0058i	2.08985	+	0.559973i
$818$			14.0941i			0.492789i
$819$	−15.8651	−	3.55896i	−0.554370	−	0.124360i
$820$		−	1.02067i		−	0.0356433i
$821$	−19.0262	−	5.09807i	−0.664021	−	0.177924i	−0.0889608	−	0.996035i	$-0.528355\pi$
$821$	−19.0262	−	5.09807i	−0.664021	−	0.177924i	−0.575060	+	0.818111i	$0.695021\pi$
$822$	0.804364	−	0.464400i	0.0280554	−	0.0161978i
$823$	−24.5655	−	14.1829i	−0.856299	−	0.494384i	0.00647246	−	0.999979i	$-0.497940\pi$
$823$	−24.5655	−	14.1829i	−0.856299	−	0.494384i	−0.862771	+	0.505595i	$0.831273\pi$
$824$	−11.2162	+	11.2162i	−0.390734	+	0.390734i
$825$	7.62060	−	11.8645i	0.265315	−	0.413068i
$826$	−9.78679	−	36.5248i	−0.340526	−	1.27086i
$827$	−10.7083	−	10.7083i	−0.372363	−	0.372363i	0.495974	−	0.868337i	$-0.334811\pi$
$827$	−10.7083	−	10.7083i	−0.372363	−	0.372363i	−0.868337	+	0.495974i	$0.834811\pi$
$828$	−1.88710	+	3.26855i	−0.0655811	+	0.113590i
$829$	−25.4617	+	14.7003i	−0.884322	+	0.510564i	−0.872081	−	0.489362i	$-0.837230\pi$
$829$	−25.4617	+	14.7003i	−0.884322	+	0.510564i	−0.0122410	+	0.999925i	$0.503897\pi$
$830$	10.2586	+	2.74880i	0.356083	+	0.0954121i
$831$	−4.10788			−0.142501
$832$	−8.78068	+	0.361317i	−0.304415	+	0.0125264i
$833$		−	58.1952i		−	2.01634i
$834$	−1.14913	+	4.28862i	−0.0397912	+	0.148503i
$835$	−10.6411	+	6.14363i	−0.368250	+	0.212609i
$836$	6.64460	+	30.5077i	0.229808	+	1.05513i
$837$	−2.01631	−	2.01631i	−0.0696939	−	0.0696939i
$838$	−4.11203	−	15.3463i	−0.142048	−	0.530129i
$839$	−12.4447	−	46.4441i	−0.429638	−	1.60343i	−0.753582	−	0.657353i	$-0.771676\pi$
$839$	−12.4447	−	46.4441i	−0.429638	−	1.60343i	0.323945	−	0.946076i	$-0.394991\pi$
$840$	−3.17990	+	3.17990i	−0.109717	+	0.109717i
$841$	17.4266	−	30.1838i	0.600919	−	1.04082i
$842$	21.8716	+	37.8827i	0.753745	+	1.30552i
$843$	−1.19073	+	4.44387i	−0.0410109	+	0.153055i
$844$	9.96537			0.343022
$845$	8.57869	+	7.27199i	0.295116	+	0.250164i
$846$		−	15.8845i		−	0.546119i
$847$	−17.3117	+	46.4860i	−0.594836	+	1.59728i
$848$	11.4339	+	19.8042i	0.392643	+	0.680078i
$849$	9.24288	−	16.0091i	0.317215	−	0.549432i
$850$	24.0916	+	24.0916i	0.826336	+	0.826336i
$851$	−17.0514	+	4.56891i	−0.584515	+	0.156620i
$852$	−3.75615	−	14.0181i	−0.128684	−	0.480254i
$853$	19.9542	+	19.9542i	0.683218	+	0.683218i	0.960724	−	0.277506i	$-0.0895079\pi$
$853$	19.9542	+	19.9542i	0.683218	+	0.683218i	−0.277506	+	0.960724i	$0.589508\pi$
$854$	38.6397	+	22.3086i	1.32222	+	0.763386i
$855$	2.96735	+	5.13960i	0.101481	+	0.175771i
$856$	−3.60124	−	0.964949i	−0.123088	−	0.0329813i
$857$	34.9849			1.19506			0.597531	−	0.801846i	$-0.296148\pi$
$857$	34.9849			1.19506			0.597531	+	0.801846i	$0.296148\pi$
$858$	−15.6242	+	15.4310i	−0.533403	+	0.526807i
$859$	−32.7995			−1.11911			−0.559553	−	0.828795i	$-0.689027\pi$
$859$	−32.7995			−1.11911			−0.559553	+	0.828795i	$0.689027\pi$
$860$	−10.3368	−	2.76974i	−0.352482	−	0.0944473i
$861$	−1.93860	−	3.35775i	−0.0660673	−	0.114432i
$862$	−2.28245	−	1.31777i	−0.0777405	−	0.0448835i
$863$	−29.2415	−	29.2415i	−0.995392	−	0.995392i	0.00459714	−	0.999989i	$-0.498537\pi$
$863$	−29.2415	−	29.2415i	−0.995392	−	0.995392i	−0.999989	+	0.00459714i	$0.998537\pi$
$864$	−1.71387	−	6.39623i	−0.0583069	−	0.217604i
$865$	9.88498	−	2.64867i	0.336100	−	0.0900576i
$866$	25.3701	+	25.3701i	0.862110	+	0.862110i
$867$	1.02140	−	1.76913i	0.0346887	−	0.0600826i
$868$	−8.82292	−	15.2817i	−0.299469	−	0.518696i
$869$	17.7960	+	34.4981i	0.603689	+	1.17027i
$870$			12.6944i			0.430381i
$871$	−43.0729	−	9.66239i	−1.45947	−	0.327398i
$872$	−16.3438			−0.553470
$873$	−0.635853	+	2.37304i	−0.0215204	+	0.0803151i
$874$	−17.3243	−	30.0065i	−0.586002	−	1.01499i
$875$	18.0459	−	31.2565i	0.610064	−	1.05666i
$876$	4.78189	−	4.78189i	0.161565	−	0.161565i
$877$	14.6081	+	54.5181i	0.493279	+	1.84094i	0.539461	+	0.842011i	$0.318628\pi$
$877$	14.6081	+	54.5181i	0.493279	+	1.84094i	−0.0461813	+	0.998933i	$0.514705\pi$
$878$	−3.08264	−	11.5046i	−0.104034	−	0.388261i
$879$	−12.8729	−	12.8729i	−0.434191	−	0.434191i
$880$	2.96835	+	13.6287i	0.100063	+	0.459425i
$881$	−8.90672	+	5.14230i	−0.300075	+	0.173248i	−0.642477	−	0.766305i	$-0.722093\pi$
$881$	−8.90672	+	5.14230i	−0.300075	+	0.173248i	0.342402	+	0.939554i	$0.388760\pi$
$882$	6.33838	−	23.6552i	0.213424	−	0.796511i
$883$			36.8662i			1.24065i	0.784346	+	0.620324i	$0.212999\pi$
$883$			36.8662i			1.24065i	−0.784346	+	0.620324i	$0.787001\pi$
$884$	−11.5552	−	18.2388i	−0.388644	−	0.613437i
$885$	−3.95013			−0.132782
$886$	−19.3348	−	5.18073i	−0.649564	−	0.174050i
$887$	−51.1951	+	29.5575i	−1.71896	+	0.992444i	−0.798134	+	0.602480i	$0.794179\pi$
$887$	−51.1951	+	29.5575i	−1.71896	+	0.992444i	−0.920830	+	0.389964i	$0.872487\pi$
$888$	3.69945	−	6.40764i	0.124146	−	0.215026i
$889$	18.4223	+	18.4223i	0.617864	+	0.617864i
$890$	5.51849	+	20.5953i	0.184980	+	0.690356i
$891$	−2.79057	−	1.79240i	−0.0934878	−	0.0600476i
$892$	5.06554	−	5.06554i	0.169607	−	0.169607i
$893$	51.3902	+	29.6701i	1.71971	+	0.992874i
$894$	−29.8360	+	17.2258i	−0.997865	+	0.576118i
$895$	−13.3772	−	3.58440i	−0.447149	−	0.119813i
$896$			39.5386i			1.32089i
$897$	4.60096	−	8.78451i	0.153622	−	0.293306i
$898$			21.1585i			0.706067i
$899$	22.0094	+	5.89740i	0.734054	+	0.196689i
$900$	2.91718	+	5.05270i	0.0972393	+	0.168423i
$901$	−10.2636	+	17.7770i	−0.341929	+	0.592239i
$902$	−5.23066	−	0.247844i	−0.174162	−	0.00825232i
$903$	−39.2662	+	10.5214i	−1.30670	+	0.350129i
$904$	−11.5647	+	3.09876i	−0.384638	+	0.103063i
$905$	−12.6513	+	12.6513i	−0.420543	+	0.420543i
$906$	−10.1102	+	17.5114i	−0.335890	+	0.581778i
$907$	−23.7145	+	13.6916i	−0.787428	+	0.454622i	−0.839056	−	0.544045i	$-0.816892\pi$
$907$	−23.7145	+	13.6916i	−0.787428	+	0.454622i	0.0516284	+	0.998666i	$0.483559\pi$
$908$	4.80583	−	17.9356i	0.159487	−	0.595214i
$909$	7.89814			0.261965
$910$	−17.4982	+	19.0001i	−0.580059	+	0.629846i
$911$	−37.3009			−1.23583			−0.617917	−	0.786243i	$-0.712023\pi$
$911$	−37.3009			−1.23583			−0.617917	+	0.786243i	$0.712023\pi$
$912$	32.2140	+	8.63172i	1.06671	+	0.285825i
$913$	6.74600	−	21.1217i	0.223260	−	0.699027i
$914$	12.9209	+	7.45988i	0.427385	+	0.246751i
$915$	3.29577	−	3.29577i	0.108955	−	0.108955i
$916$	26.4543	−	7.08840i	0.874073	−	0.234207i
$917$	−5.27205	−	19.6756i	−0.174099	−	0.649745i
$918$	5.66645	−	5.66645i	0.187021	−	0.187021i
$919$	−8.62654	−	4.98053i	−0.284563	−	0.164293i	0.350924	−	0.936404i	$-0.385867\pi$
$919$	−8.62654	−	4.98053i	−0.284563	−	0.164293i	−0.635487	+	0.772111i	$0.719201\pi$
$920$	−1.37136	−	2.37527i	−0.0452125	−	0.0783104i
$921$	1.25453	−	4.68196i	0.0413381	−	0.154276i
$922$		−	0.190198i		−	0.00626383i
$923$	11.3750	+	36.3950i	0.374414	+	1.19796i
$924$	−13.8096	−	15.1834i	−0.454304	−	0.499498i
$925$	−7.06288	+	26.3590i	−0.232226	+	0.866679i
$926$	−8.64095	+	4.98885i	−0.283959	+	0.163944i
$927$	−11.9166	−	6.88007i	−0.391393	−	0.225971i
$928$	37.4160	+	37.4160i	1.22824	+	1.22824i
$929$	49.3431	−	13.2215i	1.61890	−	0.433782i	0.668219	−	0.743965i	$-0.267057\pi$
$929$	49.3431	−	13.2215i	1.61890	−	0.433782i	0.950677	+	0.310183i	$0.100390\pi$
$930$	−4.37560	+	1.17244i	−0.143482	+	0.0384458i
$931$	64.6911	+	64.6911i	2.12017	+	2.12017i
$932$	20.6948	+	11.9481i	0.677880	+	0.391374i
$933$	22.9371	−	13.2427i	0.750926	−	0.433547i
$934$	4.17780	−	15.5917i	0.136702	−	0.510178i
$935$	−9.26245	+	8.42439i	−0.302914	+	0.275507i
$936$	1.23989	+	3.96707i	0.0405269	+	0.129668i
$937$		−	22.6941i		−	0.741383i	−0.928756	−	0.370691i	$-0.879121\pi$
$937$		−	22.6941i		−	0.741383i	0.928756	−	0.370691i	$-0.120879\pi$
$938$	26.2411	−	97.9331i	0.856802	−	3.19763i
$939$	10.6705	+	18.4819i	0.348219	+	0.603133i
$940$	−8.89284	−	5.13428i	−0.290052	−	0.167462i
$941$	15.8557	−	15.8557i	0.516879	−	0.516879i	−0.399746	−	0.916626i	$-0.630902\pi$
$941$	15.8557	−	15.8557i	0.516879	−	0.516879i	0.916626	+	0.399746i	$0.130902\pi$
$942$	5.08088	+	18.9621i	0.165544	+	0.617819i
$943$	2.28410	−	0.612024i	0.0743807	−	0.0199302i
$944$	−15.6964	+	15.6964i	−0.510874	+	0.510874i
$945$	−3.37849	−	1.95057i	−0.109902	−	0.0634521i
$946$	−16.7042	+	52.3008i	−0.543101	+	1.70045i
$947$	−37.7997	−	10.1284i	−1.22832	−	0.329128i	−0.414397	−	0.910096i	$-0.636008\pi$
$947$	−37.7997	−	10.1284i	−1.22832	−	0.329128i	−0.813927	+	0.580968i	$0.802674\pi$
$948$	−16.0610			−0.521637
$949$	−12.0369	+	13.0701i	−0.390736	+	0.424273i
$950$	−53.5616			−1.73777
$951$	4.30085	−	16.0510i	0.139465	−	0.520489i
$952$	−19.6456	+	11.3424i	−0.636716	+	0.367608i
$953$	−14.7677	+	25.5783i	−0.478371	+	0.828564i	−0.999693	−	0.0247969i	$-0.992106\pi$
$953$	−14.7677	+	25.5783i	−0.478371	+	0.828564i	0.521321	+	0.853361i	$0.325439\pi$
$954$	−6.10814	+	6.10814i	−0.197758	+	0.197758i
$955$	−1.33247	+	0.357035i	−0.0431178	+	0.0115534i
$956$	14.3018	−	3.83216i	0.462553	−	0.123941i
$957$	26.4729	+	1.25436i	0.855746	+	0.0405478i
$958$	−19.2963	+	33.4222i	−0.623436	+	1.07982i
$959$	−1.14041	−	1.97526i	−0.0368259	−	0.0637843i
$960$	−2.03670	−	0.545733i	−0.0657343	−	0.0176135i
$961$		−	22.8690i		−	0.737709i
$962$	19.7176	−	37.6464i	0.635721	−	1.21377i
$963$		−	3.23423i		−	0.104222i
$964$	−10.5774	−	2.83421i	−0.340675	−	0.0912837i
$965$	4.71648	−	2.72306i	0.151829	−	0.0876585i
$966$	19.7246	+	11.3880i	0.634629	+	0.366403i
$967$	−26.3986	+	26.3986i	−0.848921	+	0.848921i	−0.989999	−	0.141078i	$-0.954943\pi$
$967$	−26.3986	+	26.3986i	−0.848921	+	0.848921i	0.141078	+	0.989999i	$0.454943\pi$
$968$	12.5037	−	2.10908i	0.401883	−	0.0677885i
$969$	7.74819	+	28.9166i	0.248908	+	0.928936i
$970$	2.75973	+	2.75973i	0.0886096	+	0.0886096i
$971$	−1.81079	+	3.13637i	−0.0581109	+	0.100651i	−0.893617	−	0.448830i	$-0.851841\pi$
$971$	−1.81079	+	3.13637i	−0.0581109	+	0.100651i	0.835506	+	0.549481i	$0.185174\pi$
$972$	1.18842	−	0.686133i	0.0381185	−	0.0220077i
$973$	10.5315	+	2.82189i	0.337623	+	0.0904658i
$974$	−1.37072			−0.0439208
$975$	−8.20406	−	12.9493i	−0.262740	−	0.414711i
$976$		−	26.1923i		−	0.838396i
$977$	4.65067	−	17.3565i	0.148788	−	0.555285i	−0.850769	−	0.525539i	$-0.823864\pi$
$977$	4.65067	−	17.3565i	0.148788	−	0.555285i	0.999557	−	0.0297458i	$-0.00946977\pi$
$978$	34.4781	−	19.9059i	1.10249	−	0.636521i
$979$	43.4946	−	9.47317i	1.39009	−	0.302764i
$980$	−11.1945	−	11.1945i	−0.357595	−	0.357595i
$981$	−3.66954	−	13.6949i	−0.117159	−	0.437245i
$982$	−11.5421	−	43.0758i	−0.368324	−	1.37460i
$983$	−0.883070	+	0.883070i	−0.0281656	+	0.0281656i	−0.721049	−	0.692884i	$-0.756340\pi$
$983$	−0.883070	+	0.883070i	−0.0281656	+	0.0281656i	0.692884	+	0.721049i	$0.256340\pi$
$984$	−0.495557	+	0.858330i	−0.0157978	+	0.0273625i
$985$	−9.36725	−	16.2246i	−0.298465	−	0.516957i
$986$	−16.5735	+	61.8531i	−0.527808	+	1.96981i
$987$	−39.0070			−1.24161
$988$	33.1197	+	7.42964i	1.05368	+	0.236368i
$989$		−	24.7930i		−	0.788372i
$990$	−4.68255	+	2.41552i	−0.148821	+	0.0767702i
$991$	−8.93617	−	15.4779i	−0.283867	−	0.491672i	0.688467	−	0.725268i	$-0.258284\pi$
$991$	−8.93617	−	15.4779i	−0.283867	−	0.491672i	−0.972334	+	0.233596i	$0.924951\pi$
$992$	−9.44111	+	16.3525i	−0.299756	+	0.519192i
$993$	−8.54525	−	8.54525i	−0.271175	−	0.271175i
$994$	−84.5950	+	22.6672i	−2.68319	+	0.718958i
$995$	−3.65817	−	13.6525i	−0.115972	−	0.432812i
$996$	6.48707	+	6.48707i	0.205551	+	0.205551i
$997$	24.1586	+	13.9479i	0.765109	+	0.441736i	0.831127	−	0.556083i	$-0.187696\pi$
$997$	24.1586	+	13.9479i	0.765109	+	0.441736i	−0.0660180	+	0.997818i	$0.521029\pi$
$998$	11.0773	+	19.1864i	0.350645	+	0.607335i
$999$	6.19975	+	1.66122i	0.196152	+	0.0525586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.b.76.3	✓	56
11.10	odd	2	inner	429.2.bd.b.76.12	yes	56
13.6	odd	12	inner	429.2.bd.b.175.12	yes	56
143.32	even	12	inner	429.2.bd.b.175.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.b.76.3	✓	56	1.1	even	1	trivial
429.2.bd.b.76.12	yes	56	11.10	odd	2	inner
429.2.bd.b.175.3	yes	56	143.32	even	12	inner
429.2.bd.b.175.12	yes	56	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77380 - 0.475288i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18842 + 0.686133i) q^{4} +(-0.611710 - 0.611710i) q^{5} +(-0.475288 - 1.77380i) q^{6} +(-4.35587 + 1.16715i) q^{7} +(0.815121 + 0.815121i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.77380 - 0.475288i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.18842 + 0.686133i) q^{4} +(-0.611710 - 0.611710i) q^{5} +(-0.475288 - 1.77380i) q^{6} +(-4.35587 + 1.16715i) q^{7} +(0.815121 + 0.815121i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.794312 + 1.37579i) q^{10} +(2.94755 - 1.52051i) q^{11} +1.37227i q^{12} +(-0.148240 - 3.60250i) q^{13} +8.28118 q^{14} +(0.223901 - 0.835611i) q^{15} +(-2.43071 - 4.21011i) q^{16} +(2.18190 - 3.77917i) q^{17} +(1.29851 - 1.29851i) q^{18} +(1.77556 + 6.62647i) q^{19} +(-0.307252 - 1.14668i) q^{20} +(-3.18872 - 3.18872i) q^{21} +(-5.95104 + 1.29614i) q^{22} +(2.38186 - 1.37517i) q^{23} +(-0.298355 + 1.11348i) q^{24} -4.25162i q^{25} +(-1.44928 + 6.46058i) q^{26} -1.00000 q^{27} +(-5.97741 - 1.60164i) q^{28} +(6.92026 - 3.99541i) q^{29} +(-0.794312 + 1.37579i) q^{30} +(2.01631 + 2.01631i) q^{31} +(1.71387 + 6.39623i) q^{32} +(2.79057 + 1.79240i) q^{33} +(-5.66645 + 5.66645i) q^{34} +(3.37849 + 1.95057i) q^{35} +(-1.18842 + 0.686133i) q^{36} +(-6.19975 - 1.66122i) q^{37} -12.5979i q^{38} +(3.04574 - 1.92963i) q^{39} -0.997234i q^{40} +(0.830482 + 0.222527i) q^{41} +(4.14059 + 7.17171i) q^{42} +(4.50727 - 7.80683i) q^{43} +(4.54619 + 0.215412i) q^{44} +(0.835611 - 0.223901i) q^{45} +(-4.87855 + 1.30720i) q^{46} +(6.11641 - 6.11641i) q^{47} +(2.43071 - 4.21011i) q^{48} +(11.5492 - 6.66793i) q^{49} +(-2.02075 + 7.54153i) q^{50} +4.36381 q^{51} +(2.29562 - 4.38299i) q^{52} -4.70395 q^{53} +(1.77380 + 0.475288i) q^{54} +(-2.73315 - 0.872935i) q^{55} +(-4.50193 - 2.59919i) q^{56} +(-4.85091 + 4.85091i) q^{57} +(-14.1741 + 3.79795i) q^{58} +(-1.18181 - 4.41058i) q^{59} +(0.839428 - 0.839428i) q^{60} +(4.66597 + 2.69390i) q^{61} +(-2.61820 - 4.53486i) q^{62} +(1.16715 - 4.35587i) q^{63} -2.43738i q^{64} +(-2.11301 + 2.29437i) q^{65} +(-4.09802 - 4.50568i) q^{66} +(3.16876 - 11.8260i) q^{67} +(5.18602 - 2.99415i) q^{68} +(2.38186 + 1.37517i) q^{69} +(-5.06568 - 5.06568i) q^{70} +(-10.2153 + 2.73719i) q^{71} +(-1.11348 + 0.298355i) q^{72} +(-3.48467 - 3.48467i) q^{73} +(10.2076 + 5.89334i) q^{74} +(3.68201 - 2.12581i) q^{75} +(-2.43654 + 9.09327i) q^{76} +(-11.0645 + 10.0634i) q^{77} +(-6.31966 + 1.97518i) q^{78} +11.7040i q^{79} +(-1.08848 + 4.06225i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.36734 - 0.789437i) q^{82} +(4.72727 - 4.72727i) q^{83} +(-1.60164 - 5.97741i) q^{84} +(-3.64644 + 0.977062i) q^{85} +(-11.7055 + 11.7055i) q^{86} +(6.92026 + 3.99541i) q^{87} +(3.64201 + 1.16321i) q^{88} +(12.9642 + 3.47376i) q^{89} -1.58862 q^{90} +(4.85038 + 15.5190i) q^{91} +3.77419 q^{92} +(-0.738021 + 2.75433i) q^{93} +(-13.7563 + 7.94223i) q^{94} +(2.96735 - 5.13960i) q^{95} +(-4.68237 + 4.68237i) q^{96} +(2.37304 - 0.635853i) q^{97} +(-23.6552 + 6.33838i) q^{98} +(-0.156975 + 3.31291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

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