LMFDB - Embedded newform 429.2.m.a.109.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.7
Character	$\chi$	$=$	429.109
Dual form			429.2.m.a.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156364 - 0.156364i) q^{2} -1.00000 q^{3} -1.95110i q^{4} +(2.94387 - 2.94387i) q^{5} +(0.156364 + 0.156364i) q^{6} +(3.04129 - 3.04129i) q^{7} +(-0.617812 + 0.617812i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.156364 - 0.156364i) q^{2} -1.00000 q^{3} -1.95110i q^{4} +(2.94387 - 2.94387i) q^{5} +(0.156364 + 0.156364i) q^{6} +(3.04129 - 3.04129i) q^{7} +(-0.617812 + 0.617812i) q^{8} +1.00000 q^{9} -0.920633 q^{10} +(-2.62591 + 2.02598i) q^{11} +1.95110i q^{12} +(-3.43792 + 1.08659i) q^{13} -0.951100 q^{14} +(-2.94387 + 2.94387i) q^{15} -3.70899 q^{16} +3.38264 q^{17} +(-0.156364 - 0.156364i) q^{18} +(4.02944 + 4.02944i) q^{19} +(-5.74379 - 5.74379i) q^{20} +(-3.04129 + 3.04129i) q^{21} +(0.727390 + 0.0938077i) q^{22} +4.41253i q^{23} +(0.617812 - 0.617812i) q^{24} -12.3327i q^{25} +(0.707473 + 0.367664i) q^{26} -1.00000 q^{27} +(-5.93387 - 5.93387i) q^{28} +2.78109i q^{29} +0.920633 q^{30} +(1.86873 - 1.86873i) q^{31} +(1.81558 + 1.81558i) q^{32} +(2.62591 - 2.02598i) q^{33} +(-0.528924 - 0.528924i) q^{34} -17.9064i q^{35} -1.95110i q^{36} +(-0.509007 - 0.509007i) q^{37} -1.26012i q^{38} +(3.43792 - 1.08659i) q^{39} +3.63751i q^{40} +(0.774176 + 0.774176i) q^{41} +0.951100 q^{42} -9.21047 q^{43} +(3.95289 + 5.12341i) q^{44} +(2.94387 - 2.94387i) q^{45} +(0.689963 - 0.689963i) q^{46} +(6.01114 + 6.01114i) q^{47} +3.70899 q^{48} -11.4989i q^{49} +(-1.92840 + 1.92840i) q^{50} -3.38264 q^{51} +(2.12005 + 6.70773i) q^{52} +0.0464865 q^{53} +(0.156364 + 0.156364i) q^{54} +(-1.76612 + 13.6946i) q^{55} +3.75789i q^{56} +(-4.02944 - 4.02944i) q^{57} +(0.434864 - 0.434864i) q^{58} +(4.66009 + 4.66009i) q^{59} +(5.74379 + 5.74379i) q^{60} -9.48278i q^{61} -0.584407 q^{62} +(3.04129 - 3.04129i) q^{63} +6.85020i q^{64} +(-6.92201 + 13.3196i) q^{65} +(-0.727390 - 0.0938077i) q^{66} +(5.39129 - 5.39129i) q^{67} -6.59986i q^{68} -4.41253i q^{69} +(-2.79992 + 2.79992i) q^{70} +(-6.85463 + 6.85463i) q^{71} +(-0.617812 + 0.617812i) q^{72} +(0.740734 - 0.740734i) q^{73} +0.159181i q^{74} +12.3327i q^{75} +(7.86184 - 7.86184i) q^{76} +(-1.82456 + 14.1478i) q^{77} +(-0.707473 - 0.367664i) q^{78} -0.631817i q^{79} +(-10.9188 + 10.9188i) q^{80} +1.00000 q^{81} -0.242107i q^{82} +(0.524316 + 0.524316i) q^{83} +(5.93387 + 5.93387i) q^{84} +(9.95804 - 9.95804i) q^{85} +(1.44019 + 1.44019i) q^{86} -2.78109i q^{87} +(0.370644 - 2.87399i) q^{88} +(0.786034 + 0.786034i) q^{89} -0.920633 q^{90} +(-7.15109 + 13.7604i) q^{91} +8.60930 q^{92} +(-1.86873 + 1.86873i) q^{93} -1.87986i q^{94} +23.7243 q^{95} +(-1.81558 - 1.81558i) q^{96} +(-2.33658 + 2.33658i) q^{97} +(-1.79802 + 1.79802i) q^{98} +(-2.62591 + 2.02598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.156364	−	0.156364i	−0.110566	−	0.110566i	0.649659	−	0.760226i	$-0.274912\pi$
$2$	−0.156364	−	0.156364i	−0.110566	−	0.110566i	−0.760226	+	0.649659i	$0.774912\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		−	1.95110i		−	0.975550i
$5$	2.94387	−	2.94387i	1.31654	−	1.31654i	0.400042	−	0.916497i	$-0.368995\pi$
$5$	2.94387	−	2.94387i	1.31654	−	1.31654i	0.916497	−	0.400042i	$-0.131005\pi$
$6$	0.156364	+	0.156364i	0.0638355	+	0.0638355i
$7$	3.04129	−	3.04129i	1.14950	−	1.14950i	0.162850	−	0.986651i	$-0.447931\pi$
$7$	3.04129	−	3.04129i	1.14950	−	1.14950i	0.986651	−	0.162850i	$-0.0520687\pi$
$8$	−0.617812	+	0.617812i	−0.218429	+	0.218429i
$9$	1.00000			0.333333
$10$	−0.920633			−0.291130
$11$	−2.62591	+	2.02598i	−0.791742	+	0.610856i
$11$	−2.62591	+	2.02598i	−0.791742	+	0.610856i
$12$			1.95110i			0.563234i
$13$	−3.43792	+	1.08659i	−0.953508	+	0.301367i
$13$	−3.43792	+	1.08659i	−0.953508	+	0.301367i
$14$	−0.951100			−0.254192
$15$	−2.94387	+	2.94387i	−0.760104	+	0.760104i
$16$	−3.70899			−0.927248
$17$	3.38264			0.820410			0.410205	−	0.911993i	$-0.365457\pi$
$17$	3.38264			0.820410			0.410205	+	0.911993i	$0.365457\pi$
$18$	−0.156364	−	0.156364i	−0.0368554	−	0.0368554i
$19$	4.02944	+	4.02944i	0.924416	+	0.924416i	0.997338	−	0.0729214i	$-0.0232322\pi$
$19$	4.02944	+	4.02944i	0.924416	+	0.924416i	−0.0729214	+	0.997338i	$0.523232\pi$
$20$	−5.74379	−	5.74379i	−1.28435	−	1.28435i
$21$	−3.04129	+	3.04129i	−0.663665	+	0.663665i
$22$	0.727390	+	0.0938077i	0.155080	+	0.0199999i
$23$			4.41253i			0.920077i	0.887899	+	0.460038i	$0.152164\pi$
$23$			4.41253i			0.920077i	−0.887899	+	0.460038i	$0.847836\pi$
$24$	0.617812	−	0.617812i	0.126110	−	0.126110i
$25$		−	12.3327i		−	2.46655i
$26$	0.707473	+	0.367664i	0.138747	+	0.0721049i
$27$	−1.00000			−0.192450
$28$	−5.93387	−	5.93387i	−1.12140	−	1.12140i
$29$			2.78109i			0.516435i	0.966087	+	0.258218i	$0.0831352\pi$
$29$			2.78109i			0.516435i	−0.966087	+	0.258218i	$0.916865\pi$
$30$	0.920633			0.168084
$31$	1.86873	−	1.86873i	0.335634	−	0.335634i	−0.519087	−	0.854721i	$-0.673728\pi$
$31$	1.86873	−	1.86873i	0.335634	−	0.335634i	0.854721	+	0.519087i	$0.173728\pi$
$32$	1.81558	+	1.81558i	0.320952	+	0.320952i
$33$	2.62591	−	2.02598i	0.457112	−	0.352678i
$34$	−0.528924	−	0.528924i	−0.0907097	−	0.0907097i
$35$		−	17.9064i		−	3.02673i
$36$		−	1.95110i		−	0.325183i
$37$	−0.509007	−	0.509007i	−0.0836802	−	0.0836802i	0.664028	−	0.747708i	$-0.268846\pi$
$37$	−0.509007	−	0.509007i	−0.0836802	−	0.0836802i	−0.747708	+	0.664028i	$0.768846\pi$
$38$		−	1.26012i		−	0.204419i
$39$	3.43792	−	1.08659i	0.550508	−	0.173994i
$40$			3.63751i			0.575142i
$41$	0.774176	+	0.774176i	0.120906	+	0.120906i	0.764971	−	0.644065i	$-0.222753\pi$
$41$	0.774176	+	0.774176i	0.120906	+	0.120906i	−0.644065	+	0.764971i	$0.722753\pi$
$42$	0.951100			0.146758
$43$	−9.21047			−1.40458			−0.702292	−	0.711889i	$-0.747840\pi$
$43$	−9.21047			−1.40458			−0.702292	+	0.711889i	$0.747840\pi$
$44$	3.95289	+	5.12341i	0.595921	+	0.772384i
$45$	2.94387	−	2.94387i	0.438846	−	0.438846i
$46$	0.689963	−	0.689963i	0.101730	−	0.101730i
$47$	6.01114	+	6.01114i	0.876815	+	0.876815i	0.993204	−	0.116389i	$-0.0371320\pi$
$47$	6.01114	+	6.01114i	0.876815	+	0.876815i	−0.116389	+	0.993204i	$0.537132\pi$
$48$	3.70899			0.535347
$49$		−	11.4989i		−	1.64271i
$50$	−1.92840	+	1.92840i	−0.272717	+	0.272717i
$51$	−3.38264			−0.473664
$52$	2.12005	+	6.70773i	0.293998	+	0.930195i
$53$	0.0464865			0.00638541			0.00319271	−	0.999995i	$-0.498984\pi$
$53$	0.0464865			0.00638541			0.00319271	+	0.999995i	$0.498984\pi$
$54$	0.156364	+	0.156364i	0.0212785	+	0.0212785i
$55$	−1.76612	+	13.6946i	−0.238143	+	1.84657i
$56$			3.75789i			0.502170i
$57$	−4.02944	−	4.02944i	−0.533712	−	0.533712i
$58$	0.434864	−	0.434864i	0.0571004	−	0.0571004i
$59$	4.66009	+	4.66009i	0.606692	+	0.606692i	0.942080	−	0.335388i	$-0.108867\pi$
$59$	4.66009	+	4.66009i	0.606692	+	0.606692i	−0.335388	+	0.942080i	$0.608867\pi$
$60$	5.74379	+	5.74379i	0.741520	+	0.741520i
$61$		−	9.48278i		−	1.21415i	−0.794646	−	0.607073i	$-0.792344\pi$
$61$		−	9.48278i		−	1.21415i	0.794646	−	0.607073i	$-0.207656\pi$
$62$	−0.584407			−0.0742197
$63$	3.04129	−	3.04129i	0.383167	−	0.383167i
$64$			6.85020i			0.856275i
$65$	−6.92201	+	13.3196i	−0.858570	+	1.65209i
$66$	−0.727390	−	0.0938077i	−0.0895355	−	0.0115469i
$67$	5.39129	−	5.39129i	0.658651	−	0.658651i	−0.296410	−	0.955061i	$-0.595789\pi$
$67$	5.39129	−	5.39129i	0.658651	−	0.658651i	0.955061	+	0.296410i	$0.0957894\pi$
$68$		−	6.59986i		−	0.800351i
$69$		−	4.41253i		−	0.531207i
$70$	−2.79992	+	2.79992i	−0.334654	+	0.334654i
$71$	−6.85463	+	6.85463i	−0.813495	+	0.813495i	−0.985156	−	0.171661i	$-0.945086\pi$
$71$	−6.85463	+	6.85463i	−0.813495	+	0.813495i	0.171661	+	0.985156i	$0.445086\pi$
$72$	−0.617812	+	0.617812i	−0.0728098	+	0.0728098i
$73$	0.740734	−	0.740734i	0.0866963	−	0.0866963i	−0.662429	−	0.749125i	$-0.730474\pi$
$73$	0.740734	−	0.740734i	0.0866963	−	0.0866963i	0.749125	+	0.662429i	$0.230474\pi$
$74$			0.159181i			0.0185044i
$75$			12.3327i			1.42406i
$76$	7.86184	−	7.86184i	0.901814	−	0.901814i
$77$	−1.82456	+	14.1478i	−0.207928	+	1.61229i
$78$	−0.707473	−	0.367664i	−0.0801056	−	0.0416298i
$79$		−	0.631817i		−	0.0710850i	−0.999368	−	0.0355425i	$-0.988684\pi$
$79$		−	0.631817i		−	0.0710850i	0.999368	−	0.0355425i	$-0.0113159\pi$
$80$	−10.9188	+	10.9188i	−1.22076	+	1.22076i
$81$	1.00000			0.111111
$82$		−	0.242107i		−	0.0267363i
$83$	0.524316	+	0.524316i	0.0575511	+	0.0575511i	0.735297	−	0.677745i	$-0.237043\pi$
$83$	0.524316	+	0.524316i	0.0575511	+	0.0575511i	−0.677745	+	0.735297i	$0.737043\pi$
$84$	5.93387	+	5.93387i	0.647438	+	0.647438i
$85$	9.95804	−	9.95804i	1.08010	−	1.08010i
$86$	1.44019	+	1.44019i	0.155300	+	0.155300i
$87$		−	2.78109i		−	0.298164i
$88$	0.370644	−	2.87399i	0.0395108	−	0.306369i
$89$	0.786034	+	0.786034i	0.0833194	+	0.0833194i	0.747538	−	0.664219i	$-0.231236\pi$
$89$	0.786034	+	0.786034i	0.0833194	+	0.0833194i	−0.664219	+	0.747538i	$0.731236\pi$
$90$	−0.920633			−0.0970433
$91$	−7.15109	+	13.7604i	−0.749638	+	1.44248i
$92$	8.60930			0.897581
$93$	−1.86873	+	1.86873i	−0.193779	+	0.193779i
$94$		−	1.87986i		−	0.193892i
$95$	23.7243			2.43406
$96$	−1.81558	−	1.81558i	−0.185302	−	0.185302i
$97$	−2.33658	+	2.33658i	−0.237244	+	0.237244i	−0.815708	−	0.578464i	$-0.803652\pi$
$97$	−2.33658	+	2.33658i	−0.237244	+	0.237244i	0.578464	+	0.815708i	$0.303652\pi$
$98$	−1.79802	+	1.79802i	−0.181628	+	0.181628i
$99$	−2.62591	+	2.02598i	−0.263914	+	0.203619i
$100$	−24.0624			−2.40624
$101$	−13.9422			−1.38730			−0.693652	−	0.720310i	$-0.743999\pi$
$101$	−13.9422			−1.38730			−0.693652	+	0.720310i	$0.743999\pi$
$102$	0.528924	+	0.528924i	0.0523713	+	0.0523713i
$103$		−	0.957068i		−	0.0943027i	−0.998888	−	0.0471514i	$-0.984986\pi$
$103$		−	0.957068i		−	0.0943027i	0.998888	−	0.0471514i	$-0.0150143\pi$
$104$	1.45268	−	2.79530i	0.142447	−	0.274102i
$105$			17.9064i			1.74748i
$106$	−0.00726884	−	0.00726884i	−0.000706012	−	0.000706012i
$107$		−	4.31790i		−	0.417427i	−0.977977	−	0.208713i	$-0.933072\pi$
$107$		−	4.31790i		−	0.417427i	0.977977	−	0.208713i	$-0.0669276\pi$
$108$			1.95110i			0.187745i
$109$	−10.3834	−	10.3834i	−0.994551	−	0.994551i	0.00543429	−	0.999985i	$-0.498270\pi$
$109$	−10.3834	−	10.3834i	−0.994551	−	0.994551i	−0.999985	+	0.00543429i	$0.998270\pi$
$110$	2.41750	−	1.86518i	0.230500	−	0.177838i
$111$	0.509007	+	0.509007i	0.0483128	+	0.0483128i
$112$	−11.2801	+	11.2801i	−1.06587	+	1.06587i
$113$	17.5712			1.65296			0.826482	−	0.562964i	$-0.190339\pi$
$113$	17.5712			1.65296			0.826482	+	0.562964i	$0.190339\pi$
$114$			1.26012i			0.118021i
$115$	12.9899	+	12.9899i	1.21132	+	1.21132i
$116$	5.42619			0.503809
$117$	−3.43792	+	1.08659i	−0.317836	+	0.100456i
$118$		−	1.45735i		−	0.134160i
$119$	10.2876	−	10.2876i	0.943062	−	0.943062i
$120$		−	3.63751i		−	0.332058i
$121$	2.79081	−	10.6401i	0.253710	−	0.967280i
$122$	−1.48277	+	1.48277i	−0.134244	+	0.134244i
$123$	−0.774176	−	0.774176i	−0.0698051	−	0.0698051i
$124$	−3.64609	−	3.64609i	−0.327428	−	0.327428i
$125$	−21.5867	−	21.5867i	−1.93077	−	1.93077i
$126$	−0.951100			−0.0847308
$127$	14.5438			1.29055			0.645276	−	0.763950i	$-0.276742\pi$
$127$	14.5438			1.29055			0.645276	+	0.763950i	$0.276742\pi$
$128$	4.70228	−	4.70228i	0.415627	−	0.415627i
$129$	9.21047			0.810937
$130$	3.16507	−	1.00035i	0.277595	−	0.0877368i
$131$		−	0.432457i		−	0.0377839i	−0.999822	−	0.0188920i	$-0.993986\pi$
$131$		−	0.432457i		−	0.0377839i	0.999822	−	0.0188920i	$-0.00601385\pi$
$132$	−3.95289	−	5.12341i	−0.344055	−	0.445936i
$133$	24.5094			2.12523
$134$	−1.68601			−0.145649
$135$	−2.94387	+	2.94387i	−0.253368	+	0.253368i
$136$	−2.08983	+	2.08983i	−0.179202	+	0.179202i
$137$	3.89871	+	3.89871i	0.333089	+	0.333089i	0.853758	−	0.520669i	$-0.174318\pi$
$137$	3.89871	+	3.89871i	0.333089	+	0.333089i	−0.520669	+	0.853758i	$0.674318\pi$
$138$	−0.689963	+	0.689963i	−0.0587336	+	0.0587336i
$139$			14.5809i			1.23674i	0.785887	+	0.618370i	$0.212207\pi$
$139$			14.5809i			1.23674i	−0.785887	+	0.618370i	$0.787793\pi$
$140$	−34.9371			−2.95272
$141$	−6.01114	−	6.01114i	−0.506229	−	0.506229i
$142$	2.14364			0.179890
$143$	6.82626	−	9.81846i	0.570841	−	0.821061i
$144$	−3.70899			−0.309083
$145$	8.18717	+	8.18717i	0.679907	+	0.679907i
$146$	−0.231649			−0.0191714
$147$			11.4989i			0.948416i
$148$	−0.993124	+	0.993124i	−0.0816343	+	0.0816343i
$149$	−5.46697	−	5.46697i	−0.447871	−	0.447871i	0.446775	−	0.894646i	$-0.352572\pi$
$149$	−5.46697	−	5.46697i	−0.447871	−	0.447871i	−0.894646	+	0.446775i	$0.852572\pi$
$150$	1.92840	−	1.92840i	0.157453	−	0.157453i
$151$	−11.7849	+	11.7849i	−0.959039	+	0.959039i	−0.999193	−	0.0401547i	$-0.987215\pi$
$151$	−11.7849	+	11.7849i	−0.959039	+	0.959039i	0.0401547	+	0.999193i	$0.487215\pi$
$152$	−4.97887			−0.403839
$153$	3.38264			0.273470
$154$	2.49750	−	1.92691i	0.201255	−	0.155275i
$155$		−	11.0026i		−	0.883751i
$156$	−2.12005	−	6.70773i	−0.169740	−	0.537048i
$157$	13.2651			1.05867			0.529337	−	0.848412i	$-0.322441\pi$
$157$	13.2651			1.05867			0.529337	+	0.848412i	$0.322441\pi$
$158$	−0.0987937	+	0.0987937i	−0.00785960	+	0.00785960i
$159$	−0.0464865			−0.00368662
$160$	10.6897			0.845091
$161$	13.4198	+	13.4198i	1.05763	+	1.05763i
$162$	−0.156364	−	0.156364i	−0.0122851	−	0.0122851i
$163$	−0.896297	−	0.896297i	−0.0702034	−	0.0702034i	0.671133	−	0.741337i	$-0.265808\pi$
$163$	−0.896297	−	0.896297i	−0.0702034	−	0.0702034i	−0.741337	+	0.671133i	$0.765808\pi$
$164$	1.51050	−	1.51050i	0.117950	−	0.117950i
$165$	1.76612	−	13.6946i	0.137492	−	1.06612i
$166$		−	0.163969i		−	0.0127264i
$167$	4.49045	−	4.49045i	0.347481	−	0.347481i	−0.511689	−	0.859171i	$-0.670980\pi$
$167$	4.49045	−	4.49045i	0.347481	−	0.347481i	0.859171	+	0.511689i	$0.170980\pi$
$168$		−	3.75789i		−	0.289928i
$169$	10.6386	−	7.47125i	0.818356	−	0.574711i
$170$	−3.11417			−0.238846
$171$	4.02944	+	4.02944i	0.308139	+	0.308139i
$172$			17.9706i			1.37024i
$173$	13.3509			1.01505			0.507524	−	0.861637i	$-0.330561\pi$
$173$	13.3509			1.01505			0.507524	+	0.861637i	$0.330561\pi$
$174$	−0.434864	+	0.434864i	−0.0329669	+	0.0329669i
$175$	−37.5075	−	37.5075i	−2.83530	−	2.83530i
$176$	9.73948	−	7.51435i	0.734141	−	0.566415i
$177$	−4.66009	−	4.66009i	−0.350274	−	0.350274i
$178$		−	0.245815i		−	0.0184246i
$179$			17.1595i			1.28256i	0.767305	+	0.641282i	$0.221597\pi$
$179$			17.1595i			1.28256i	−0.767305	+	0.641282i	$0.778403\pi$
$180$	−5.74379	−	5.74379i	−0.428117	−	0.428117i
$181$			10.1184i			0.752097i	0.926600	+	0.376048i	$0.122717\pi$
$181$			10.1184i			0.752097i	−0.926600	+	0.376048i	$0.877283\pi$
$182$	3.26981	−	1.03346i	0.242374	−	0.0766051i
$183$			9.48278i			0.700987i
$184$	−2.72611	−	2.72611i	−0.200972	−	0.200972i
$185$	−2.99690			−0.220337
$186$	0.584407			0.0428508
$187$	−8.88250	+	6.85315i	−0.649553	+	0.501152i
$188$	11.7283	−	11.7283i	0.855377	−	0.855377i
$189$	−3.04129	+	3.04129i	−0.221222	+	0.221222i
$190$	−3.70963	−	3.70963i	−0.269125	−	0.269125i
$191$	−18.2190			−1.31828			−0.659142	−	0.752019i	$-0.729080\pi$
$191$	−18.2190			−1.31828			−0.659142	+	0.752019i	$0.729080\pi$
$192$		−	6.85020i		−	0.494371i
$193$	−0.653446	+	0.653446i	−0.0470361	+	0.0470361i	−0.730234	−	0.683198i	$-0.760589\pi$
$193$	−0.653446	+	0.653446i	−0.0470361	+	0.0470361i	0.683198	+	0.730234i	$0.260589\pi$
$194$	0.730718			0.0524625
$195$	6.92201	−	13.3196i	0.495696	−	0.953836i
$196$	−22.4356			−1.60254
$197$	−12.6244	−	12.6244i	−0.899448	−	0.899448i	0.0959388	−	0.995387i	$-0.469415\pi$
$197$	−12.6244	−	12.6244i	−0.899448	−	0.899448i	−0.995387	+	0.0959388i	$0.969415\pi$
$198$	0.727390	+	0.0938077i	0.0516934	+	0.00666663i
$199$			2.07669i			0.147212i	0.997287	+	0.0736062i	$0.0234508\pi$
$199$			2.07669i			0.147212i	−0.997287	+	0.0736062i	$0.976549\pi$
$200$	7.61931	+	7.61931i	0.538767	+	0.538767i
$201$	−5.39129	+	5.39129i	−0.380272	+	0.380272i
$202$	2.18007	+	2.18007i	0.153389	+	0.153389i
$203$	8.45811	+	8.45811i	0.593643	+	0.593643i
$204$			6.59986i			0.462083i
$205$	4.55815			0.318355
$206$	−0.149651	+	0.149651i	−0.0104267	+	0.0104267i
$207$			4.41253i			0.306692i
$208$	12.7512	−	4.03017i	0.884139	−	0.279442i
$209$	−18.7445	−	2.41738i	−1.29658	−	0.167214i
$210$	2.79992	−	2.79992i	0.193213	−	0.193213i
$211$			24.7944i			1.70691i	0.521163	+	0.853457i	$0.325498\pi$
$211$			24.7944i			1.70691i	−0.521163	+	0.853457i	$0.674502\pi$
$212$		−	0.0906999i		−	0.00622929i
$213$	6.85463	−	6.85463i	0.469671	−	0.469671i
$214$	−0.675166	+	0.675166i	−0.0461534	+	0.0461534i
$215$	−27.1144	+	27.1144i	−1.84919	+	1.84919i
$216$	0.617812	−	0.617812i	0.0420368	−	0.0420368i
$217$		−	11.3667i		−	0.771624i
$218$			3.24719i			0.219928i
$219$	−0.740734	+	0.740734i	−0.0500542	+	0.0500542i
$220$	26.7195	+	3.44587i	1.80143	+	0.232321i
$221$	−11.6292	+	3.67555i	−0.782267	+	0.247244i
$222$		−	0.159181i		−	0.0106835i
$223$	1.02524	−	1.02524i	0.0686554	−	0.0686554i	−0.671945	−	0.740601i	$-0.734541\pi$
$223$	1.02524	−	1.02524i	0.0686554	−	0.0686554i	0.740601	+	0.671945i	$0.234541\pi$
$224$	11.0434			0.737869
$225$		−	12.3327i		−	0.822183i
$226$	−2.74752	−	2.74752i	−0.182762	−	0.182762i
$227$	−7.22237	−	7.22237i	−0.479366	−	0.479366i	0.425563	−	0.904929i	$-0.360076\pi$
$227$	−7.22237	−	7.22237i	−0.479366	−	0.479366i	−0.904929	+	0.425563i	$0.860076\pi$
$228$	−7.86184	+	7.86184i	−0.520663	+	0.520663i
$229$	2.07405	+	2.07405i	0.137057	+	0.137057i	0.772307	−	0.635250i	$-0.219103\pi$
$229$	2.07405	+	2.07405i	0.137057	+	0.137057i	−0.635250	+	0.772307i	$0.719103\pi$
$230$		−	4.06233i		−	0.267862i
$231$	1.82456	−	14.1478i	0.120047	−	0.930855i
$232$	−1.71819	−	1.71819i	−0.112805	−	0.112805i
$233$	4.60901			0.301947			0.150973	−	0.988538i	$-0.451759\pi$
$233$	4.60901			0.301947			0.150973	+	0.988538i	$0.451759\pi$
$234$	0.707473	+	0.367664i	0.0462490	+	0.0240350i
$235$	35.3920			2.30872
$236$	9.09231	−	9.09231i	0.591859	−	0.591859i
$237$			0.631817i			0.0410409i
$238$	−3.21723			−0.208542
$239$	−10.9705	−	10.9705i	−0.709625	−	0.709625i	0.256831	−	0.966456i	$-0.417321\pi$
$239$	−10.9705	−	10.9705i	−0.709625	−	0.709625i	−0.966456	+	0.256831i	$0.917321\pi$
$240$	10.9188	−	10.9188i	0.704805	−	0.704805i
$241$	−3.17657	+	3.17657i	−0.204621	+	0.204621i	−0.801977	−	0.597355i	$-0.796218\pi$
$241$	−3.17657	+	3.17657i	−0.204621	+	0.204621i	0.597355	+	0.801977i	$0.296218\pi$
$242$	−2.10011	+	1.22735i	−0.135000	+	0.0788969i
$243$	−1.00000			−0.0641500
$244$	−18.5018			−1.18446
$245$	−33.8514	−	33.8514i	−2.16269	−	2.16269i
$246$			0.242107i			0.0154362i
$247$	−18.2313	−	9.47454i	−1.16003	−	0.602850i
$248$			2.30905i			0.146625i
$249$	−0.524316	−	0.524316i	−0.0332272	−	0.0332272i
$250$			6.75077i			0.426956i
$251$		−	16.2519i		−	1.02581i	−0.858445	−	0.512905i	$-0.828569\pi$
$251$		−	16.2519i		−	1.02581i	0.858445	−	0.512905i	$-0.171431\pi$
$252$	−5.93387	−	5.93387i	−0.373799	−	0.373799i
$253$	−8.93971	−	11.5869i	−0.562034	−	0.728463i
$254$	−2.27413	−	2.27413i	−0.142692	−	0.142692i
$255$	−9.95804	+	9.95804i	−0.623597	+	0.623597i
$256$	12.2299			0.764367
$257$			7.39687i			0.461404i	0.973024	+	0.230702i	$0.0741023\pi$
$257$			7.39687i			0.461404i	−0.973024	+	0.230702i	$0.925898\pi$
$258$	−1.44019	−	1.44019i	−0.0896623	−	0.0896623i
$259$	−3.09608			−0.192381
$260$	25.9879	+	13.5055i	1.61170	+	0.837578i
$261$			2.78109i			0.172145i
$262$	−0.0676208	+	0.0676208i	−0.00417763	+	0.00417763i
$263$			1.48046i			0.0912893i	0.998958	+	0.0456447i	$0.0145342\pi$
$263$			1.48046i			0.0912893i	−0.998958	+	0.0456447i	$0.985466\pi$
$264$	−0.370644	+	2.87399i	−0.0228115	+	0.176882i
$265$	0.136850	−	0.136850i	0.00840665	−	0.00840665i
$266$	−3.83240	−	3.83240i	−0.234979	−	0.234979i
$267$	−0.786034	−	0.786034i	−0.0481045	−	0.0481045i
$268$	−10.5189	−	10.5189i	−0.642547	−	0.642547i
$269$	−15.4547			−0.942291			−0.471146	−	0.882056i	$-0.656159\pi$
$269$	−15.4547			−0.942291			−0.471146	+	0.882056i	$0.656159\pi$
$270$	0.920633			0.0560280
$271$	16.8671	−	16.8671i	1.02461	−	1.02461i	0.0249163	−	0.999690i	$-0.492068\pi$
$271$	16.8671	−	16.8671i	1.02461	−	1.02461i	0.999690	−	0.0249163i	$-0.00793193\pi$
$272$	−12.5462			−0.760723
$273$	7.15109	−	13.7604i	0.432803	−	0.832816i
$274$		−	1.21924i		−	0.0736569i
$275$	24.9859	+	32.3847i	1.50671	+	1.95287i
$276$	−8.60930			−0.518219
$277$	11.3480			0.681833			0.340916	−	0.940094i	$-0.389263\pi$
$277$	11.3480			0.681833			0.340916	+	0.940094i	$0.389263\pi$
$278$	2.27994	−	2.27994i	0.136742	−	0.136742i
$279$	1.86873	−	1.86873i	0.111878	−	0.111878i
$280$	11.0628	+	11.0628i	0.661126	+	0.661126i
$281$	7.57143	−	7.57143i	0.451674	−	0.451674i	−0.444236	−	0.895910i	$-0.646525\pi$
$281$	7.57143	−	7.57143i	0.451674	−	0.451674i	0.895910	+	0.444236i	$0.146525\pi$
$282$			1.87986i			0.111944i
$283$	17.2873			1.02762			0.513810	−	0.857904i	$-0.328234\pi$
$283$	17.2873			1.02762			0.513810	+	0.857904i	$0.328234\pi$
$284$	13.3741	+	13.3741i	0.793605	+	0.793605i
$285$	−23.7243			−1.40531
$286$	−2.60264	+	0.467873i	−0.153897	+	0.0276659i
$287$	4.70899			0.277963
$288$	1.81558	+	1.81558i	0.106984	+	0.106984i
$289$	−5.55778			−0.326928
$290$		−	2.56036i		−	0.150350i
$291$	2.33658	−	2.33658i	0.136973	−	0.136973i
$292$	−1.44525	−	1.44525i	−0.0845766	−	0.0845766i
$293$	−8.81427	+	8.81427i	−0.514935	+	0.514935i	−0.916035	−	0.401099i	$-0.868628\pi$
$293$	−8.81427	+	8.81427i	−0.514935	+	0.514935i	0.401099	+	0.916035i	$0.368628\pi$
$294$	1.79802	−	1.79802i	0.104863	−	0.104863i
$295$	27.4374			1.59747
$296$	0.628941			0.0365564
$297$	2.62591	−	2.02598i	0.152371	−	0.117559i
$298$			1.70968i			0.0990390i
$299$	−4.79463	−	15.1700i	−0.277280	−	0.877301i
$300$	24.0624			1.38925
$301$	−28.0118	+	28.0118i	−1.61457	+	1.61457i
$302$	3.68547			0.212075
$303$	13.9422			0.800960
$304$	−14.9452	−	14.9452i	−0.857163	−	0.857163i
$305$	−27.9161	−	27.9161i	−1.59847	−	1.59847i
$306$	−0.528924	−	0.528924i	−0.0302366	−	0.0302366i
$307$	7.12552	−	7.12552i	0.406675	−	0.406675i	−0.473903	−	0.880577i	$-0.657155\pi$
$307$	7.12552	−	7.12552i	0.406675	−	0.406675i	0.880577	+	0.473903i	$0.157155\pi$
$308$	27.6037	+	3.55991i	1.57287	+	0.202845i
$309$			0.957068i			0.0544457i
$310$	−1.72042	+	1.72042i	−0.0977132	+	0.0977132i
$311$		−	19.6146i		−	1.11224i	−0.831101	−	0.556122i	$-0.812289\pi$
$311$		−	19.6146i		−	1.11224i	0.831101	−	0.556122i	$-0.187711\pi$
$312$	−1.45268	+	2.79530i	−0.0822418	+	0.158253i
$313$	−25.2002			−1.42440			−0.712200	−	0.701977i	$-0.752301\pi$
$313$	−25.2002			−1.42440			−0.712200	+	0.701977i	$0.752301\pi$
$314$	−2.07420	−	2.07420i	−0.117054	−	0.117054i
$315$		−	17.9064i		−	1.00891i
$316$	−1.23274			−0.0693469
$317$	−7.09610	+	7.09610i	−0.398557	+	0.398557i	−0.877724	−	0.479167i	$-0.840939\pi$
$317$	−7.09610	+	7.09610i	−0.398557	+	0.398557i	0.479167	+	0.877724i	$0.340939\pi$
$318$	0.00726884	+	0.00726884i	0.000407616	+	0.000407616i
$319$	−5.63443	−	7.30289i	−0.315468	−	0.408884i
$320$	20.1661	+	20.1661i	1.12732	+	1.12732i
$321$			4.31790i			0.241002i
$322$		−	4.19676i		−	0.233876i
$323$	13.6301	+	13.6301i	0.758400	+	0.758400i
$324$		−	1.95110i		−	0.108394i
$325$	13.4007	+	42.3990i	0.743336	+	2.35188i
$326$			0.280298i			0.0155243i
$327$	10.3834	+	10.3834i	0.574204	+	0.574204i
$328$	−0.956590			−0.0528188
$329$	36.5633			2.01580
$330$	−2.41750	+	1.86518i	−0.133079	+	0.102675i
$331$	−22.8731	+	22.8731i	−1.25722	+	1.25722i	−0.304807	+	0.952414i	$0.598592\pi$
$331$	−22.8731	+	22.8731i	−1.25722	+	1.25722i	−0.952414	+	0.304807i	$0.901408\pi$
$332$	1.02299	−	1.02299i	0.0561440	−	0.0561440i
$333$	−0.509007	−	0.509007i	−0.0278934	−	0.0278934i
$334$	−1.40429			−0.0768395
$335$		−	31.7425i		−	1.73428i
$336$	11.2801	−	11.2801i	0.615382	−	0.615382i
$337$	32.5240			1.77169			0.885847	−	0.463977i	$-0.153578\pi$
$337$	32.5240			1.77169			0.885847	+	0.463977i	$0.153578\pi$
$338$	−2.83174	−	0.495267i	−0.154026	−	0.0269390i
$339$	−17.5712			−0.954339
$340$	−19.4291	−	19.4291i	−1.05369	−	1.05369i
$341$	−1.12111	+	8.69314i	−0.0607115	+	0.470760i
$342$		−	1.26012i		−	0.0681396i
$343$	−13.6826	−	13.6826i	−0.738790	−	0.738790i
$344$	5.69034	−	5.69034i	0.306802	−	0.306802i
$345$	−12.9899	−	12.9899i	−0.699354	−	0.699354i
$346$	−2.08760	−	2.08760i	−0.112230	−	0.112230i
$347$			19.8977i			1.06816i	0.845433	+	0.534082i	$0.179343\pi$
$347$			19.8977i			1.06816i	−0.845433	+	0.534082i	$0.820657\pi$
$348$	−5.42619			−0.290874
$349$	−9.56410	+	9.56410i	−0.511955	+	0.511955i	−0.915125	−	0.403170i	$-0.867908\pi$
$349$	−9.56410	+	9.56410i	−0.511955	+	0.511955i	0.403170	+	0.915125i	$0.367908\pi$
$350$			11.7297i			0.626978i
$351$	3.43792	−	1.08659i	0.183503	−	0.0579980i
$352$	−8.44587	−	1.08922i	−0.450166	−	0.0580556i
$353$	−4.97676	+	4.97676i	−0.264886	+	0.264886i	−0.827036	−	0.562149i	$-0.809975\pi$
$353$	−4.97676	+	4.97676i	−0.264886	+	0.264886i	0.562149	+	0.827036i	$0.309975\pi$
$354$			1.45735i			0.0774571i
$355$			40.3583i			2.14199i
$356$	1.53363	−	1.53363i	0.0812823	−	0.0812823i
$357$	−10.2876	+	10.2876i	−0.544477	+	0.544477i
$358$	2.68314	−	2.68314i	0.141808	−	0.141808i
$359$	−22.0132	+	22.0132i	−1.16181	+	1.16181i	−0.177734	+	0.984079i	$0.556877\pi$
$359$	−22.0132	+	22.0132i	−1.16181	+	1.16181i	−0.984079	+	0.177734i	$0.943123\pi$
$360$			3.63751i			0.191714i
$361$			13.4727i			0.709091i
$362$	1.58216	−	1.58216i	0.0831566	−	0.0831566i
$363$	−2.79081	+	10.6401i	−0.146480	+	0.558460i
$364$	26.8479	+	13.9525i	1.40721	+	0.731309i
$365$		−	4.36125i		−	0.228278i
$366$	1.48277	−	1.48277i	0.0775056	−	0.0775056i
$367$	−12.5690			−0.656095			−0.328047	−	0.944661i	$-0.606391\pi$
$367$	−12.5690			−0.656095			−0.328047	+	0.944661i	$0.606391\pi$
$368$		−	16.3661i		−	0.853140i
$369$	0.774176	+	0.774176i	0.0403020	+	0.0403020i
$370$	0.468609	+	0.468609i	0.0243618	+	0.0243618i
$371$	0.141379	−	0.141379i	0.00734004	−	0.00734004i
$372$	3.64609	+	3.64609i	0.189041	+	0.189041i
$373$			20.4228i			1.05745i	0.848792	+	0.528727i	$0.177330\pi$
$373$			20.4228i			1.05745i	−0.848792	+	0.528727i	$0.822670\pi$
$374$	2.46050	+	0.317317i	0.127229	+	0.0164081i
$375$	21.5867	+	21.5867i	1.11473	+	1.11473i
$376$	−7.42750			−0.383044
$377$	−3.02191	−	9.56117i	−0.155636	−	0.492426i
$378$	0.951100			0.0489193
$379$	23.4987	−	23.4987i	1.20705	−	1.20705i	0.235071	−	0.971978i	$-0.424468\pi$
$379$	23.4987	−	23.4987i	1.20705	−	1.20705i	0.971978	−	0.235071i	$-0.0755324\pi$
$380$		−	46.2885i		−	2.37455i
$381$	−14.5438			−0.745100
$382$	2.84881	+	2.84881i	0.145758	+	0.145758i
$383$	−15.5889	+	15.5889i	−0.796554	+	0.796554i	−0.982550	−	0.185996i	$-0.940449\pi$
$383$	−15.5889	+	15.5889i	−0.796554	+	0.796554i	0.185996	+	0.982550i	$0.440449\pi$
$384$	−4.70228	+	4.70228i	−0.239962	+	0.239962i
$385$	36.2779	+	47.0205i	1.84889	+	2.39639i
$386$	0.204352			0.0104012
$387$	−9.21047			−0.468195
$388$	4.55891	+	4.55891i	0.231444	+	0.231444i
$389$		−	26.7102i		−	1.35426i	−0.735862	−	0.677131i	$-0.763223\pi$
$389$		−	26.7102i		−	1.35426i	0.735862	−	0.677131i	$-0.236777\pi$
$390$	−3.16507	+	1.00035i	−0.160269	+	0.0506549i
$391$			14.9260i			0.754840i
$392$	7.10417	+	7.10417i	0.358815	+	0.358815i
$393$			0.432457i			0.0218145i
$394$			3.94800i			0.198897i
$395$	−1.85999	−	1.85999i	−0.0935861	−	0.0935861i
$396$	3.95289	+	5.12341i	0.198640	+	0.257461i
$397$	−10.6764	−	10.6764i	−0.535833	−	0.535833i	0.386469	−	0.922302i	$-0.373694\pi$
$397$	−10.6764	−	10.6764i	−0.535833	−	0.535833i	−0.922302	+	0.386469i	$0.873694\pi$
$398$	0.324720	−	0.324720i	0.0162767	−	0.0162767i
$399$	−24.5094			−1.22700
$400$			45.7421i			2.28710i
$401$	19.2039	+	19.2039i	0.958995	+	0.958995i	0.999192	−	0.0401969i	$-0.0127985\pi$
$401$	19.2039	+	19.2039i	0.958995	+	0.958995i	−0.0401969	+	0.999192i	$0.512799\pi$
$402$	1.68601			0.0840906
$403$	−4.39401	+	8.45511i	−0.218881	+	0.421179i
$404$			27.2027i			1.35338i
$405$	2.94387	−	2.94387i	0.146282	−	0.146282i
$406$		−	2.64510i		−	0.131274i
$407$	2.36784	+	0.305369i	0.117370	+	0.0151366i
$408$	2.08983	−	2.08983i	0.103462	−	0.103462i
$409$	−16.6828	−	16.6828i	−0.824913	−	0.824913i	0.161895	−	0.986808i	$-0.448239\pi$
$409$	−16.6828	−	16.6828i	−0.824913	−	0.824913i	−0.986808	+	0.161895i	$0.948239\pi$
$410$	−0.712732	−	0.712732i	−0.0351993	−	0.0351993i
$411$	−3.89871	−	3.89871i	−0.192309	−	0.192309i
$412$	−1.86734			−0.0919970
$413$	28.3454			1.39479
$414$	0.689963	−	0.689963i	0.0339098	−	0.0339098i
$415$	3.08704			0.151537
$416$	−8.21461	−	4.26902i	−0.402754	−	0.209306i
$417$		−	14.5809i		−	0.714032i
$418$	2.55298	+	3.30897i	0.124870	+	0.161847i
$419$	−38.7041			−1.89082			−0.945409	−	0.325887i	$-0.894337\pi$
$419$	−38.7041			−1.89082			−0.945409	+	0.325887i	$0.894337\pi$
$420$	34.9371			1.70476
$421$	−2.28588	+	2.28588i	−0.111407	+	0.111407i	−0.760613	−	0.649206i	$-0.775101\pi$
$421$	−2.28588	+	2.28588i	−0.111407	+	0.111407i	0.649206	+	0.760613i	$0.275101\pi$
$422$	3.87696	−	3.87696i	0.188727	−	0.188727i
$423$	6.01114	+	6.01114i	0.292272	+	0.292272i
$424$	−0.0287199	+	0.0287199i	−0.00139476	+	0.00139476i
$425$		−	41.7172i		−	2.02358i
$426$	−2.14364			−0.103860
$427$	−28.8399	−	28.8399i	−1.39566	−	1.39566i
$428$	−8.42465			−0.407221
$429$	−6.82626	+	9.81846i	−0.329575	+	0.474040i
$430$	8.47947			0.408916
$431$	−14.9203	−	14.9203i	−0.718685	−	0.718685i	0.249651	−	0.968336i	$-0.419684\pi$
$431$	−14.9203	−	14.9203i	−0.718685	−	0.718685i	−0.968336	+	0.249651i	$0.919684\pi$
$432$	3.70899			0.178449
$433$		−	9.35014i		−	0.449339i	−0.974435	−	0.224669i	$-0.927870\pi$
$433$		−	9.35014i		−	0.449339i	0.974435	−	0.224669i	$-0.0721302\pi$
$434$	−1.77735	+	1.77735i	−0.0853156	+	0.0853156i
$435$	−8.18717	−	8.18717i	−0.392545	−	0.392545i
$436$	−20.2591	+	20.2591i	−0.970234	+	0.970234i
$437$	−17.7800	+	17.7800i	−0.850534	+	0.850534i
$438$	0.231649			0.0110686
$439$	11.9656			0.571085			0.285543	−	0.958366i	$-0.407826\pi$
$439$	11.9656			0.571085			0.285543	+	0.958366i	$0.407826\pi$
$440$	−7.36953	−	9.55179i	−0.351329	−	0.455364i
$441$		−	11.4989i		−	0.547568i
$442$	2.39312	+	1.24367i	0.113829	+	0.0591556i
$443$	32.7364			1.55535			0.777676	−	0.628665i	$-0.216399\pi$
$443$	32.7364			1.55535			0.777676	+	0.628665i	$0.216399\pi$
$444$	0.993124	−	0.993124i	0.0471316	−	0.0471316i
$445$	4.62796			0.219386
$446$	−0.320623			−0.0151820
$447$	5.46697	+	5.46697i	0.258579	+	0.258579i
$448$	20.8335	+	20.8335i	0.984289	+	0.984289i
$449$	23.0512	+	23.0512i	1.08785	+	1.08785i	0.995749	+	0.0921039i	$0.0293592\pi$
$449$	23.0512	+	23.0512i	1.08785	+	1.08785i	0.0921039	+	0.995749i	$0.470641\pi$
$450$	−1.92840	+	1.92840i	−0.0909058	+	0.0909058i
$451$	−3.60138	−	0.464452i	−0.169582	−	0.0218702i
$452$		−	34.2833i		−	1.61255i
$453$	11.7849	−	11.7849i	0.553701	−	0.553701i
$454$			2.25864i			0.106003i
$455$	19.4569	+	61.5607i	0.912154	+	2.88601i
$456$	4.97887			0.233157
$457$	−6.69653	−	6.69653i	−0.313250	−	0.313250i	0.532917	−	0.846167i	$-0.321096\pi$
$457$	−6.69653	−	6.69653i	−0.313250	−	0.313250i	−0.846167	+	0.532917i	$0.821096\pi$
$458$		−	0.648615i		−	0.0303078i
$459$	−3.38264			−0.157888
$460$	25.3447	−	25.3447i	1.18170	−	1.18170i
$461$	15.6183	+	15.6183i	0.727415	+	0.727415i	0.970104	−	0.242689i	$-0.0780295\pi$
$461$	15.6183	+	15.6183i	0.727415	+	0.727415i	−0.242689	+	0.970104i	$0.578029\pi$
$462$	−2.49750	+	1.92691i	−0.116194	+	0.0896480i
$463$	4.68321	+	4.68321i	0.217647	+	0.217647i	0.807506	−	0.589859i	$-0.200817\pi$
$463$	4.68321	+	4.68321i	0.217647	+	0.217647i	−0.589859	+	0.807506i	$0.700817\pi$
$464$		−	10.3150i		−	0.478864i
$465$			11.0026i			0.510234i
$466$	−0.720686	−	0.720686i	−0.0333851	−	0.0333851i
$467$			20.4185i			0.944857i	0.881369	+	0.472429i	$0.156623\pi$
$467$			20.4185i			0.944857i	−0.881369	+	0.472429i	$0.843377\pi$
$468$	2.12005	+	6.70773i	0.0979994	+	0.310065i
$469$		−	32.7930i		−	1.51424i
$470$	−5.53405	−	5.53405i	−0.255267	−	0.255267i
$471$	−13.2651			−0.611226
$472$	−5.75812			−0.265039
$473$	24.1859	−	18.6602i	1.11207	−	0.857999i
$474$	0.0987937	−	0.0987937i	0.00453774	−	0.00453774i
$475$	49.6940	−	49.6940i	2.28012	−	2.28012i
$476$	−20.0721	−	20.0721i	−0.920004	−	0.920004i
$477$	0.0464865			0.00212847
$478$			3.43080i			0.156921i
$479$	9.45090	−	9.45090i	0.431823	−	0.431823i	−0.457425	−	0.889248i	$-0.651228\pi$
$479$	9.45090	−	9.45090i	0.431823	−	0.431823i	0.889248	+	0.457425i	$0.151228\pi$
$480$	−10.6897			−0.487914
$481$	2.30301	+	1.19684i	0.105008	+	0.0545714i
$482$	0.993406			0.0452484
$483$	−13.4198	−	13.4198i	−0.610623	−	0.610623i
$484$	−20.7599	−	5.44515i	−0.943630	−	0.247507i
$485$			13.7572i			0.624683i
$486$	0.156364	+	0.156364i	0.00709283	+	0.00709283i
$487$	14.5181	−	14.5181i	0.657877	−	0.657877i	−0.297001	−	0.954877i	$-0.595986\pi$
$487$	14.5181	−	14.5181i	0.657877	−	0.657877i	0.954877	+	0.297001i	$0.0959864\pi$
$488$	5.85857	+	5.85857i	0.265205	+	0.265205i
$489$	0.896297	+	0.896297i	0.0405319	+	0.0405319i
$490$			10.5863i			0.478240i
$491$	25.0721			1.13149			0.565743	−	0.824582i	$-0.308589\pi$
$491$	25.0721			1.13149			0.565743	+	0.824582i	$0.308589\pi$
$492$	−1.51050	+	1.51050i	−0.0680984	+	0.0680984i
$493$			9.40741i			0.423689i
$494$	1.36924	+	4.33220i	0.0616050	+	0.194915i
$495$	−1.76612	+	13.6946i	−0.0793811	+	0.615525i
$496$	−6.93112	+	6.93112i	−0.311216	+	0.311216i
$497$			41.6939i			1.87023i
$498$			0.163969i			0.00734761i
$499$	6.13907	−	6.13907i	0.274823	−	0.274823i	−0.556215	−	0.831038i	$-0.687747\pi$
$499$	6.13907	−	6.13907i	0.274823	−	0.274823i	0.831038	+	0.556215i	$0.187747\pi$
$500$	−42.1177	+	42.1177i	−1.88356	+	1.88356i
$501$	−4.49045	+	4.49045i	−0.200618	+	0.200618i
$502$	−2.54122	+	2.54122i	−0.113420	+	0.113420i
$503$		−	33.4413i		−	1.49107i	−0.666465	−	0.745536i	$-0.732194\pi$
$503$		−	33.4413i		−	1.49107i	0.666465	−	0.745536i	$-0.267806\pi$
$504$			3.75789i			0.167390i
$505$	−41.0441	+	41.0441i	−1.82644	+	1.82644i
$506$	−0.413930	+	3.20963i	−0.0184014	+	0.142686i
$507$	−10.6386	+	7.47125i	−0.472478	+	0.331810i
$508$		−	28.3764i		−	1.25900i
$509$	−22.6437	+	22.6437i	−1.00366	+	1.00366i	−0.00366912	+	0.999993i	$0.501168\pi$
$509$	−22.6437	+	22.6437i	−1.00366	+	1.00366i	−0.999993	+	0.00366912i	$0.998832\pi$
$510$	3.11417			0.137898
$511$		−	4.50558i		−	0.199315i
$512$	−11.3169	−	11.3169i	−0.500140	−	0.500140i
$513$	−4.02944	−	4.02944i	−0.177904	−	0.177904i
$514$	1.15661	−	1.15661i	0.0510158	−	0.0510158i
$515$	−2.81748	−	2.81748i	−0.124153	−	0.124153i
$516$		−	17.9706i		−	0.791110i
$517$	−27.9632	−	3.60626i	−1.22982	−	0.158603i
$518$	0.484117	+	0.484117i	0.0212709	+	0.0212709i
$519$	−13.3509			−0.586039
$520$	−3.95250	−	12.5055i	−0.173328	−	0.548402i
$521$	−10.1239			−0.443535			−0.221767	−	0.975100i	$-0.571183\pi$
$521$	−10.1239			−0.443535			−0.221767	+	0.975100i	$0.571183\pi$
$522$	0.434864	−	0.434864i	0.0190335	−	0.0190335i
$523$			23.7902i			1.04027i	0.854084	+	0.520135i	$0.174119\pi$
$523$			23.7902i			1.04027i	−0.854084	+	0.520135i	$0.825881\pi$
$524$	−0.843766			−0.0368601
$525$	37.5075	+	37.5075i	1.63696	+	1.63696i
$526$	0.231492	−	0.231492i	0.0100935	−	0.0100935i
$527$	6.32124	−	6.32124i	0.275358	−	0.275358i
$528$	−9.73948	+	7.51435i	−0.423857	+	0.327020i
$529$	3.52955			0.153459
$530$	−0.0427970			−0.00185898
$531$	4.66009	+	4.66009i	0.202231	+	0.202231i
$532$		−	47.8203i		−	2.07327i
$533$	−3.50277	−	1.82034i	−0.151722	−	0.0788478i
$534$			0.245815i			0.0106375i
$535$	−12.7113	−	12.7113i	−0.549559	−	0.549559i
$536$			6.66160i			0.287737i
$537$		−	17.1595i		−	0.740489i
$538$	2.41657	+	2.41657i	0.104186	+	0.104186i
$539$	23.2966	+	30.1952i	1.00346	+	1.30060i
$540$	5.74379	+	5.74379i	0.247173	+	0.247173i
$541$	0.483642	−	0.483642i	0.0207934	−	0.0207934i	−0.696634	−	0.717427i	$-0.745320\pi$
$541$	0.483642	−	0.483642i	0.0207934	−	0.0207934i	0.717427	+	0.696634i	$0.245320\pi$
$542$	−5.27484			−0.226574
$543$		−	10.1184i		−	0.434223i
$544$	6.14144	+	6.14144i	0.263312	+	0.263312i
$545$	−61.1349			−2.61873
$546$	−3.26981	+	1.03346i	−0.139935	+	0.0442280i
$547$		−	18.5426i		−	0.792823i	−0.918073	−	0.396411i	$-0.870255\pi$
$547$		−	18.5426i		−	0.792823i	0.918073	−	0.396411i	$-0.129745\pi$
$548$	7.60677	−	7.60677i	0.324945	−	0.324945i
$549$		−	9.48278i		−	0.404715i
$550$	1.15691	−	8.97072i	0.0493307	−	0.382513i
$551$	−11.2062	+	11.2062i	−0.477401	+	0.477401i
$552$	2.72611	+	2.72611i	0.116031	+	0.116031i
$553$	−1.92154	−	1.92154i	−0.0817122	−	0.0817122i
$554$	−1.77442	−	1.77442i	−0.0753877	−	0.0753877i
$555$	2.99690			0.127211
$556$	28.4489			1.20650
$557$	6.23332	−	6.23332i	0.264114	−	0.264114i	−0.562609	−	0.826723i	$-0.690202\pi$
$557$	6.23332	−	6.23332i	0.264114	−	0.264114i	0.826723	+	0.562609i	$0.190202\pi$
$558$	−0.584407			−0.0247399
$559$	31.6649	−	10.0080i	1.33928	−	0.423295i
$560$			66.4145i			2.80653i
$561$	8.88250	−	6.85315i	0.375019	−	0.289340i
$562$	−2.36781			−0.0998798
$563$	−41.6206			−1.75410			−0.877049	−	0.480400i	$-0.840491\pi$
$563$	−41.6206			−1.75410			−0.877049	+	0.480400i	$0.840491\pi$
$564$	−11.7283	+	11.7283i	−0.493852	+	0.493852i
$565$	51.7275	−	51.7275i	2.17619	−	2.17619i
$566$	−2.70311	−	2.70311i	−0.113620	−	0.113620i
$567$	3.04129	−	3.04129i	0.127722	−	0.127722i
$568$		−	8.46974i		−	0.355382i
$569$	−3.23860			−0.135769			−0.0678846	−	0.997693i	$-0.521625\pi$
$569$	−3.23860			−0.135769			−0.0678846	+	0.997693i	$0.521625\pi$
$570$	3.70963	+	3.70963i	0.155379	+	0.155379i
$571$	−2.37379			−0.0993402			−0.0496701	−	0.998766i	$-0.515817\pi$
$571$	−2.37379			−0.0993402			−0.0496701	+	0.998766i	$0.515817\pi$
$572$	−19.1568	−	13.3187i	−0.800986	−	0.556884i
$573$	18.2190			0.761111
$574$	−0.736319	−	0.736319i	−0.0307334	−	0.0307334i
$575$	54.4187			2.26942
$576$			6.85020i			0.285425i
$577$	−27.9863	+	27.9863i	−1.16508	+	1.16508i	−0.181738	+	0.983347i	$0.558172\pi$
$577$	−27.9863	+	27.9863i	−1.16508	+	1.16508i	−0.983347	+	0.181738i	$0.941828\pi$
$578$	0.869039	+	0.869039i	0.0361472	+	0.0361472i
$579$	0.653446	−	0.653446i	0.0271563	−	0.0271563i
$580$	15.9740	−	15.9740i	0.663284	−	0.663284i
$581$	3.18920			0.132310
$582$	−0.730718			−0.0302892
$583$	−0.122069	+	0.0941808i	−0.00505560	+	0.00390057i
$584$			0.915268i			0.0378741i
$585$	−6.92201	+	13.3196i	−0.286190	+	0.550697i
$586$	2.75648			0.113869
$587$	−18.0813	+	18.0813i	−0.746295	+	0.746295i	−0.973781	−	0.227486i	$-0.926949\pi$
$587$	−18.0813	+	18.0813i	−0.746295	+	0.746295i	0.227486	+	0.973781i	$0.426949\pi$
$588$	22.4356			0.925228
$589$	15.0599			0.620532
$590$	−4.29024	−	4.29024i	−0.176626	−	0.176626i
$591$	12.6244	+	12.6244i	0.519297	+	0.519297i
$592$	1.88790	+	1.88790i	0.0775924	+	0.0775924i
$593$	6.01480	−	6.01480i	0.246998	−	0.246998i	−0.572739	−	0.819738i	$-0.694119\pi$
$593$	6.01480	−	6.01480i	0.246998	−	0.246998i	0.819738	+	0.572739i	$0.194119\pi$
$594$	−0.727390	−	0.0938077i	−0.0298452	−	0.00384898i
$595$		−	60.5707i		−	2.48315i
$596$	−10.6666	+	10.6666i	−0.436921	+	0.436921i
$597$		−	2.07669i		−	0.0849931i
$598$	−1.62233	+	3.12175i	−0.0663421	+	0.127658i
$599$	−11.0811			−0.452761			−0.226380	−	0.974039i	$-0.572689\pi$
$599$	−11.0811			−0.452761			−0.226380	+	0.974039i	$0.572689\pi$
$600$	−7.61931	−	7.61931i	−0.311057	−	0.311057i
$601$		−	15.6238i		−	0.637308i	−0.947871	−	0.318654i	$-0.896769\pi$
$601$		−	15.6238i		−	0.637308i	0.947871	−	0.318654i	$-0.103231\pi$
$602$	8.76009			0.357034
$603$	5.39129	−	5.39129i	0.219550	−	0.219550i
$604$	22.9935	+	22.9935i	0.935590	+	0.935590i
$605$	−23.1072	−	39.5388i	−0.939443	−	1.60748i
$606$	−2.18007	−	2.18007i	−0.0885593	−	0.0885593i
$607$		−	6.55756i		−	0.266163i	−0.991105	−	0.133082i	$-0.957513\pi$
$607$		−	6.55756i		−	0.266163i	0.991105	−	0.133082i	$-0.0424872\pi$
$608$			14.6315i			0.593386i
$609$	−8.45811	−	8.45811i	−0.342740	−	0.342740i
$610$			8.73016i			0.353474i
$611$	−27.1975	−	14.1342i	−1.10029	−	0.571807i
$612$		−	6.59986i		−	0.266784i
$613$	5.90315	+	5.90315i	0.238426	+	0.238426i	0.816198	−	0.577772i	$-0.196078\pi$
$613$	5.90315	+	5.90315i	0.238426	+	0.238426i	−0.577772	+	0.816198i	$0.696078\pi$
$614$	−2.22835			−0.0899291
$615$	−4.55815			−0.183802
$616$	−7.61342	−	9.86789i	−0.306753	−	0.397589i
$617$	22.7330	−	22.7330i	0.915197	−	0.915197i	−0.0814778	−	0.996675i	$-0.525964\pi$
$617$	22.7330	−	22.7330i	0.915197	−	0.915197i	0.996675	+	0.0814778i	$0.0259640\pi$
$618$	0.149651	−	0.149651i	0.00601986	−	0.00601986i
$619$	−26.4159	−	26.4159i	−1.06175	−	1.06175i	−0.997964	−	0.0637823i	$-0.979684\pi$
$619$	−26.4159	−	26.4159i	−1.06175	−	1.06175i	−0.0637823	−	0.997964i	$-0.520316\pi$
$620$	−21.4672			−0.862144
$621$		−	4.41253i		−	0.177069i
$622$	−3.06703	+	3.06703i	−0.122977	+	0.122977i
$623$	4.78112			0.191551
$624$	−12.7512	+	4.03017i	−0.510458	+	0.161336i
$625$	−65.4329			−2.61732
$626$	3.94042	+	3.94042i	0.157491	+	0.157491i
$627$	18.7445	+	2.41738i	0.748583	+	0.0965409i
$628$		−	25.8816i		−	1.03279i
$629$	−1.72179	−	1.72179i	−0.0686521	−	0.0686521i
$630$	−2.79992	+	2.79992i	−0.111551	+	0.111551i
$631$	−25.2247	−	25.2247i	−1.00418	−	1.00418i	−0.999991	−	0.00419009i	$-0.998666\pi$
$631$	−25.2247	−	25.2247i	−1.00418	−	1.00418i	−0.00419009	−	0.999991i	$-0.501334\pi$
$632$	0.390344	+	0.390344i	0.0155270	+	0.0155270i
$633$		−	24.7944i		−	0.985488i
$634$	2.21915			0.0881339
$635$	42.8150	−	42.8150i	1.69906	−	1.69906i
$636$			0.0906999i			0.00359648i
$637$	12.4947	+	39.5325i	0.495056	+	1.56633i
$638$	−0.260888	+	2.02294i	−0.0103286	+	0.0800889i
$639$	−6.85463	+	6.85463i	−0.271165	+	0.271165i
$640$		−	27.6858i		−	1.09438i
$641$			7.55802i			0.298524i	0.988798	+	0.149262i	$0.0476898\pi$
$641$			7.55802i			0.298524i	−0.988798	+	0.149262i	$0.952310\pi$
$642$	0.675166	−	0.675166i	0.0266467	−	0.0266467i
$643$	4.06815	−	4.06815i	0.160432	−	0.160432i	−0.622326	−	0.782758i	$-0.713812\pi$
$643$	4.06815	−	4.06815i	0.160432	−	0.160432i	0.782758	+	0.622326i	$0.213812\pi$
$644$	26.1834	−	26.1834i	1.03177	−	1.03177i
$645$	27.1144	−	27.1144i	1.06763	−	1.06763i
$646$		−	4.26253i		−	0.167707i
$647$			1.40243i			0.0551352i	0.999620	+	0.0275676i	$0.00877616\pi$
$647$			1.40243i			0.0551352i	−0.999620	+	0.0275676i	$0.991224\pi$
$648$	−0.617812	+	0.617812i	−0.0242699	+	0.0242699i
$649$	−21.6782	−	2.79573i	−0.850946	−	0.109742i
$650$	4.53431	−	8.72509i	0.177850	−	0.342226i
$651$			11.3667i			0.445497i
$652$	−1.74877	+	1.74877i	−0.0684869	+	0.0684869i
$653$	9.23368			0.361342			0.180671	−	0.983544i	$-0.442173\pi$
$653$	9.23368			0.361342			0.180671	+	0.983544i	$0.442173\pi$
$654$		−	3.24719i		−	0.126975i
$655$	−1.27310	−	1.27310i	−0.0497440	−	0.0497440i
$656$	−2.87141	−	2.87141i	−0.112110	−	0.112110i
$657$	0.740734	−	0.740734i	0.0288988	−	0.0288988i
$658$	−5.71720	−	5.71720i	−0.222879	−	0.222879i
$659$			28.5473i			1.11204i	0.831167	+	0.556022i	$0.187673\pi$
$659$			28.5473i			1.11204i	−0.831167	+	0.556022i	$0.812327\pi$
$660$	−26.7195	−	3.44587i	−1.04005	−	0.134130i
$661$	−22.8908	−	22.8908i	−0.890348	−	0.890348i	0.104208	−	0.994556i	$-0.466769\pi$
$661$	−22.8908	−	22.8908i	−0.890348	−	0.890348i	−0.994556	+	0.104208i	$0.966769\pi$
$662$	7.15309			0.278013
$663$	11.6292	−	3.67555i	0.451642	−	0.142746i
$664$	−0.647857			−0.0251417
$665$	72.1525	−	72.1525i	2.79795	−	2.79795i
$666$			0.159181i			0.00616815i
$667$	−12.2717			−0.475160
$668$	−8.76131	−	8.76131i	−0.338985	−	0.338985i
$669$	−1.02524	+	1.02524i	−0.0396382	+	0.0396382i
$670$	−4.96340	+	4.96340i	−0.191753	+	0.191753i
$671$	19.2119	+	24.9009i	0.741668	+	0.961289i
$672$	−11.0434			−0.426009
$673$	−20.4851			−0.789643			−0.394822	−	0.918758i	$-0.629194\pi$
$673$	−20.4851			−0.789643			−0.394822	+	0.918758i	$0.629194\pi$
$674$	−5.08560	−	5.08560i	−0.195890	−	0.195890i
$675$			12.3327i			0.474688i
$676$	−14.5771	−	20.7570i	−0.560660	−	0.798348i
$677$		−	17.7018i		−	0.680337i	−0.940364	−	0.340169i	$-0.889516\pi$
$677$		−	17.7018i		−	0.680337i	0.940364	−	0.340169i	$-0.110484\pi$
$678$	2.74752	+	2.74752i	0.105518	+	0.105518i
$679$			14.2125i			0.545425i
$680$			12.3044i			0.471852i
$681$	7.22237	+	7.22237i	0.276762	+	0.276762i
$682$	1.53460	−	1.18400i	0.0587629	−	0.0453376i
$683$	3.77484	+	3.77484i	0.144440	+	0.144440i	0.775629	−	0.631189i	$-0.217433\pi$
$683$	3.77484	+	3.77484i	0.144440	+	0.144440i	−0.631189	+	0.775629i	$0.717433\pi$
$684$	7.86184	−	7.86184i	0.300605	−	0.300605i
$685$	22.9546			0.877050
$686$			4.27894i			0.163371i
$687$	−2.07405	−	2.07405i	−0.0791300	−	0.0791300i
$688$	34.1616			1.30240
$689$	−0.159817	+	0.0505119i	−0.00608855	+	0.00192435i
$690$			4.06233i			0.154650i
$691$	−20.0936	+	20.0936i	−0.764397	+	0.764397i	−0.977114	−	0.212717i	$-0.931769\pi$
$691$	−20.0936	+	20.0936i	−0.764397	+	0.764397i	0.212717	+	0.977114i	$0.431769\pi$
$692$		−	26.0489i		−	0.990231i
$693$	−1.82456	+	14.1478i	−0.0693095	+	0.537429i
$694$	3.11129	−	3.11129i	0.118103	−	0.118103i
$695$	42.9244	+	42.9244i	1.62822	+	1.62822i
$696$	1.71819	+	1.71819i	0.0651278	+	0.0651278i
$697$	2.61876	+	2.61876i	0.0991924	+	0.0991924i
$698$	2.99097			0.113210
$699$	−4.60901			−0.174329
$700$	−73.1809	+	73.1809i	−2.76598	+	2.76598i
$701$	−26.9112			−1.01642			−0.508211	−	0.861233i	$-0.669693\pi$
$701$	−26.9112			−1.01642			−0.508211	+	0.861233i	$0.669693\pi$
$702$	−0.707473	−	0.367664i	−0.0267019	−	0.0138766i
$703$		−	4.10202i		−	0.154711i
$704$	−13.8784	−	17.9880i	−0.523061	−	0.677949i
$705$	−35.3920			−1.33294
$706$	1.55638			0.0585750
$707$	−42.4024	+	42.4024i	−1.59471	+	1.59471i
$708$	−9.09231	+	9.09231i	−0.341710	+	0.341710i
$709$	14.9363	+	14.9363i	0.560943	+	0.560943i	0.929575	−	0.368633i	$-0.120174\pi$
$709$	14.9363	+	14.9363i	0.560943	+	0.560943i	−0.368633	+	0.929575i	$0.620174\pi$
$710$	6.31060	−	6.31060i	0.236833	−	0.236833i
$711$		−	0.631817i		−	0.0236950i
$712$	−0.971241			−0.0363988
$713$	8.24585	+	8.24585i	0.308809	+	0.308809i
$714$	3.21723			0.120402
$715$	−8.80864	−	48.9999i	−0.329424	−	1.83249i
$716$	33.4800			1.25121
$717$	10.9705	+	10.9705i	0.409702	+	0.409702i
$718$	6.88416			0.256915
$719$		−	11.2940i		−	0.421194i	−0.977573	−	0.210597i	$-0.932459\pi$
$719$		−	11.2940i		−	0.421194i	0.977573	−	0.210597i	$-0.0675408\pi$
$720$	−10.9188	+	10.9188i	−0.406919	+	0.406919i
$721$	−2.91073	−	2.91073i	−0.108401	−	0.108401i
$722$	2.10666	−	2.10666i	0.0784016	−	0.0784016i
$723$	3.17657	−	3.17657i	0.118138	−	0.118138i
$724$	19.7421			0.733708
$725$	34.2985			1.27381
$726$	2.10011	−	1.22735i	0.0779425	−	0.0455511i
$727$			32.3168i			1.19856i	0.800538	+	0.599282i	$0.204547\pi$
$727$			32.3168i			1.19856i	−0.800538	+	0.599282i	$0.795453\pi$
$728$	−4.08330	−	12.9193i	−0.151337	−	0.478823i
$729$	1.00000			0.0370370
$730$	−0.681944	+	0.681944i	−0.0252399	+	0.0252399i
$731$	−31.1557			−1.15233
$732$	18.5018			0.683848
$733$	−6.13700	−	6.13700i	−0.226675	−	0.226675i	0.584627	−	0.811302i	$-0.301241\pi$
$733$	−6.13700	−	6.13700i	−0.226675	−	0.226675i	−0.811302	+	0.584627i	$0.801241\pi$
$734$	1.96534	+	1.96534i	0.0725420	+	0.0725420i
$735$	33.8514	+	33.8514i	1.24863	+	1.24863i
$736$	−8.01130	+	8.01130i	−0.295300	+	0.295300i
$737$	−3.23440	+	25.0797i	−0.119141	+	0.923822i
$738$		−	0.242107i		−	0.00891209i
$739$	−12.2687	+	12.2687i	−0.451311	+	0.451311i	−0.895790	−	0.444478i	$-0.853389\pi$
$739$	−12.2687	+	12.2687i	−0.451311	+	0.451311i	0.444478	+	0.895790i	$0.353389\pi$
$740$			5.84726i			0.214949i
$741$	18.2313	+	9.47454i	0.669742	+	0.348056i
$742$	−0.0442133			−0.00162312
$743$	−34.4152	−	34.4152i	−1.26257	−	1.26257i	−0.949843	−	0.312727i	$-0.898758\pi$
$743$	−34.4152	−	34.4152i	−1.26257	−	1.26257i	−0.312727	−	0.949843i	$-0.601242\pi$
$744$		−	2.30905i		−	0.0846539i
$745$	−32.1881			−1.17928
$746$	3.19340	−	3.19340i	0.116919	−	0.116919i
$747$	0.524316	+	0.524316i	0.0191837	+	0.0191837i
$748$	13.3712	+	17.3306i	0.488899	+	0.633671i
$749$	−13.1320	−	13.1320i	−0.479833	−	0.479833i
$750$		−	6.75077i		−	0.246503i
$751$			12.5623i			0.458406i	0.973379	+	0.229203i	$0.0736119\pi$
$751$			12.5623i			0.458406i	−0.973379	+	0.229203i	$0.926388\pi$
$752$	−22.2953	−	22.2953i	−0.813025	−	0.813025i
$753$			16.2519i			0.592252i
$754$	−1.02251	+	1.96755i	−0.0372375	+	0.0716538i
$755$			69.3862i			2.52522i
$756$	5.93387	+	5.93387i	0.215813	+	0.215813i
$757$	23.6184			0.858425			0.429213	−	0.903204i	$-0.358791\pi$
$757$	23.6184			0.858425			0.429213	+	0.903204i	$0.358791\pi$
$758$	−7.34874			−0.266918
$759$	8.93971	+	11.5869i	0.324491	+	0.420578i
$760$	−14.6571	+	14.6571i	−0.531670	+	0.531670i
$761$	−21.9135	+	21.9135i	−0.794364	+	0.794364i	−0.982200	−	0.187836i	$-0.939853\pi$
$761$	−21.9135	+	21.9135i	−0.794364	+	0.794364i	0.187836	+	0.982200i	$0.439853\pi$
$762$	2.27413	+	2.27413i	0.0823830	+	0.0823830i
$763$	−63.1580			−2.28647
$764$			35.5472i			1.28605i
$765$	9.95804	−	9.95804i	0.360034	−	0.360034i
$766$	4.87509			0.176144
$767$	−21.0847	−	10.9574i	−0.761323	−	0.395649i
$768$	−12.2299			−0.441307
$769$	22.1198	+	22.1198i	0.797660	+	0.797660i	0.982726	−	0.185066i	$-0.0592498\pi$
$769$	22.1198	+	22.1198i	0.797660	+	0.797660i	−0.185066	+	0.982726i	$0.559250\pi$
$770$	1.67975	−	13.0249i	0.0605341	−	0.469385i
$771$		−	7.39687i		−	0.266392i
$772$	1.27494	+	1.27494i	0.0458861	+	0.0458861i
$773$	22.0151	−	22.0151i	0.791827	−	0.791827i	−0.189964	−	0.981791i	$-0.560837\pi$
$773$	22.0151	−	22.0151i	0.791827	−	0.791827i	0.981791	+	0.189964i	$0.0608371\pi$
$774$	1.44019	+	1.44019i	0.0517666	+	0.0517666i
$775$	−23.0466	−	23.0466i	−0.827859	−	0.827859i
$776$		−	2.88714i		−	0.103642i
$777$	3.09608			0.111071
$778$	−4.17653	+	4.17653i	−0.149736	+	0.149736i
$779$			6.23899i			0.223535i
$780$	−25.9879	−	13.5055i	−0.930515	−	0.483576i
$781$	4.11230	−	31.8870i	0.147150	−	1.14101i
$782$	2.33389	−	2.33389i	0.0834599	−	0.0834599i
$783$		−	2.78109i		−	0.0993881i
$784$			42.6495i			1.52320i
$785$	39.0509	−	39.0509i	1.39379	−	1.39379i
$786$	0.0676208	−	0.0676208i	0.00241195	−	0.00241195i
$787$	−17.9098	+	17.9098i	−0.638414	+	0.638414i	−0.950164	−	0.311750i	$-0.899085\pi$
$787$	−17.9098	+	17.9098i	−0.638414	+	0.638414i	0.311750	+	0.950164i	$0.399085\pi$
$788$	−24.6314	+	24.6314i	−0.877457	+	0.877457i
$789$		−	1.48046i		−	0.0527059i
$790$			0.581672i			0.0206949i
$791$	53.4393	−	53.4393i	1.90008	−	1.90008i
$792$	0.370644	−	2.87399i	0.0131703	−	0.102123i
$793$	10.3039	+	32.6011i	0.365903	+	1.15770i
$794$			3.33882i			0.118490i
$795$	−0.136850	+	0.136850i	−0.00485358	+	0.00485358i
$796$	4.05182			0.143613
$797$			22.2190i			0.787039i	0.919316	+	0.393519i	$0.128743\pi$
$797$			22.2190i			0.787039i	−0.919316	+	0.393519i	$0.871257\pi$
$798$	3.83240	+	3.83240i	0.135665	+	0.135665i
$799$	20.3335	+	20.3335i	0.719347	+	0.719347i
$800$	22.3911	−	22.3911i	0.791644	−	0.791644i
$801$	0.786034	+	0.786034i	0.0277731	+	0.0277731i
$802$		−	6.00560i		−	0.212065i
$803$	−0.444389	+	3.44581i	−0.0156821	+	0.121600i
$804$	10.5189	+	10.5189i	0.370975	+	0.370975i
$805$	79.0124			2.78482
$806$	2.00915	−	0.635012i	0.0707691	−	0.0223673i
$807$	15.4547			0.544032
$808$	8.61367	−	8.61367i	0.303028	−	0.303028i
$809$		−	0.284714i		−	0.0100100i	−0.999987	−	0.00500500i	$-0.998407\pi$
$809$		−	0.284714i		−	0.0100100i	0.999987	−	0.00500500i	$-0.00159315\pi$
$810$	−0.920633			−0.0323478
$811$	8.06572	+	8.06572i	0.283226	+	0.283226i	0.834394	−	0.551168i	$-0.185818\pi$
$811$	8.06572	+	8.06572i	0.283226	+	0.283226i	−0.551168	+	0.834394i	$0.685818\pi$
$812$	16.5026	−	16.5026i	0.579129	−	0.579129i
$813$	−16.8671	+	16.8671i	−0.591556	+	0.591556i
$814$	−0.322498	−	0.417996i	−0.0113035	−	0.0146507i
$815$	−5.27716			−0.184851
$816$	12.5462			0.439204
$817$	−37.1130	−	37.1130i	−1.29842	−	1.29842i
$818$			5.21720i			0.182415i
$819$	−7.15109	+	13.7604i	−0.249879	+	0.480827i
$820$		−	8.89340i		−	0.310571i
$821$	−26.3780	−	26.3780i	−0.920597	−	0.920597i	0.0764743	−	0.997072i	$-0.475634\pi$
$821$	−26.3780	−	26.3780i	−0.920597	−	0.920597i	−0.997072	+	0.0764743i	$0.975634\pi$
$822$			1.21924i			0.0425258i
$823$		−	15.9646i		−	0.556490i	−0.960510	−	0.278245i	$-0.910247\pi$
$823$		−	15.9646i		−	0.556490i	0.960510	−	0.278245i	$-0.0897527\pi$
$824$	0.591288	+	0.591288i	0.0205985	+	0.0205985i
$825$	−24.9859	−	32.3847i	−0.869897	−	1.12749i
$826$	−4.43222	−	4.43222i	−0.154217	−	0.154217i
$827$	3.33184	−	3.33184i	0.115859	−	0.115859i	−0.646800	−	0.762660i	$-0.723893\pi$
$827$	3.33184	−	3.33184i	0.115859	−	0.115859i	0.762660	+	0.646800i	$0.223893\pi$
$828$	8.60930			0.299194
$829$			44.0585i			1.53022i	0.643902	+	0.765108i	$0.277315\pi$
$829$			44.0585i			1.53022i	−0.643902	+	0.765108i	$0.722685\pi$
$830$	−0.482703	−	0.482703i	−0.0167549	−	0.0167549i
$831$	−11.3480			−0.393656
$832$	−7.44338	−	23.5505i	−0.258053	−	0.816466i
$833$		−	38.8967i		−	1.34769i
$834$	−2.27994	+	2.27994i	−0.0789479	+	0.0789479i
$835$		−	26.4386i		−	0.914945i
$836$	−4.71655	+	36.5724i	−0.163125	+	1.26488i
$837$	−1.86873	+	1.86873i	−0.0645929	+	0.0645929i
$838$	6.05194	+	6.05194i	0.209061	+	0.209061i
$839$	4.66476	+	4.66476i	0.161045	+	0.161045i	0.783030	−	0.621984i	$-0.213673\pi$
$839$	4.66476	+	4.66476i	0.161045	+	0.161045i	−0.621984	+	0.783030i	$0.713673\pi$
$840$	−11.0628	−	11.0628i	−0.381701	−	0.381701i
$841$	21.2655			0.733294
$842$	0.714861			0.0246357
$843$	−7.57143	+	7.57143i	−0.260774	+	0.260774i
$844$	48.3763			1.66518
$845$	9.32438	−	53.3131i	0.320768	−	1.83403i
$846$		−	1.87986i		−	0.0646308i
$847$	−23.8719	−	40.8473i	−0.820250	−	1.40353i
$848$	−0.172418			−0.00592086
$849$	−17.2873			−0.593297
$850$	−6.52308	+	6.52308i	−0.223740	+	0.223740i
$851$	2.24601	−	2.24601i	0.0769923	−	0.0769923i
$852$	−13.3741	−	13.3741i	−0.458188	−	0.458188i
$853$	1.28087	−	1.28087i	0.0438561	−	0.0438561i	−0.684839	−	0.728695i	$-0.740127\pi$
$853$	1.28087	−	1.28087i	0.0438561	−	0.0438561i	0.728695	+	0.684839i	$0.240127\pi$
$854$			9.01907i			0.308626i
$855$	23.7243			0.811353
$856$	2.66765	+	2.66765i	0.0911783	+	0.0911783i
$857$	47.3193			1.61640			0.808199	−	0.588909i	$-0.200443\pi$
$857$	47.3193			1.61640			0.808199	+	0.588909i	$0.200443\pi$
$858$	2.60264	−	0.467873i	0.0888527	−	0.0159729i
$859$	9.94848			0.339438			0.169719	−	0.985493i	$-0.445714\pi$
$859$	9.94848			0.339438			0.169719	+	0.985493i	$0.445714\pi$
$860$	52.9030	+	52.9030i	1.80398	+	1.80398i
$861$	−4.70899			−0.160482
$862$			4.66600i			0.158925i
$863$	1.86206	−	1.86206i	0.0633852	−	0.0633852i	−0.674704	−	0.738089i	$-0.735729\pi$
$863$	1.86206	−	1.86206i	0.0633852	−	0.0633852i	0.738089	+	0.674704i	$0.235729\pi$
$864$	−1.81558	−	1.81558i	−0.0617672	−	0.0617672i
$865$	39.3033	−	39.3033i	1.33635	−	1.33635i
$866$	−1.46203	+	1.46203i	−0.0496818	+	0.0496818i
$867$	5.55778			0.188752
$868$	−22.1776			−0.752758
$869$	1.28005	+	1.65909i	0.0434227	+	0.0562809i
$870$			2.56036i			0.0868045i
$871$	−12.6767	+	24.3930i	−0.429534	+	0.826525i
$872$	12.8300			0.434478
$873$	−2.33658	+	2.33658i	−0.0790814	+	0.0790814i
$874$	5.56033			0.188081
$875$	−131.303			−4.43884
$876$	1.44525	+	1.44525i	0.0488303	+	0.0488303i
$877$	−35.6396	−	35.6396i	−1.20346	−	1.20346i	−0.973106	−	0.230357i	$-0.926011\pi$
$877$	−35.6396	−	35.6396i	−1.20346	−	1.20346i	−0.230357	−	0.973106i	$-0.573989\pi$
$878$	−1.87099	−	1.87099i	−0.0631428	−	0.0631428i
$879$	8.81427	−	8.81427i	0.297298	−	0.297298i
$880$	6.55052	−	50.7930i	0.220818	−	1.71223i
$881$			6.08417i			0.204981i	0.994734	+	0.102491i	$0.0326811\pi$
$881$			6.08417i			0.204981i	−0.994734	+	0.102491i	$0.967319\pi$
$882$	−1.79802	+	1.79802i	−0.0605426	+	0.0605426i
$883$		−	34.3709i		−	1.15667i	−0.815798	−	0.578337i	$-0.803702\pi$
$883$		−	34.3709i		−	1.15667i	0.815798	−	0.578337i	$-0.196298\pi$
$884$	7.17136	+	22.6898i	0.241199	+	0.763141i
$885$	−27.4374			−0.922299
$886$	−5.11880	−	5.11880i	−0.171970	−	0.171970i
$887$			47.7862i			1.60450i	0.596987	+	0.802251i	$0.296365\pi$
$887$			47.7862i			1.60450i	−0.596987	+	0.802251i	$0.703635\pi$
$888$	−0.628941			−0.0211059
$889$	44.2319	−	44.2319i	1.48349	−	1.48349i
$890$	−0.723649	−	0.723649i	−0.0242568	−	0.0242568i
$891$	−2.62591	+	2.02598i	−0.0879713	+	0.0678729i
$892$	−2.00035	−	2.00035i	−0.0669768	−	0.0669768i
$893$			48.4430i			1.62108i
$894$		−	1.70968i		−	0.0571802i
$895$	50.5155	+	50.5155i	1.68855	+	1.68855i
$896$		−	28.6021i		−	0.955527i
$897$	4.79463	+	15.1700i	0.160088	+	0.506510i
$898$		−	7.20878i		−	0.240560i
$899$	5.19711	+	5.19711i	0.173333	+	0.173333i
$900$	−24.0624			−0.802081
$901$	0.157247			0.00523866
$902$	0.490504	+	0.635752i	0.0163320	+	0.0211682i
$903$	28.0118	−	28.0118i	0.932173	−	0.932173i
$904$	−10.8557	+	10.8557i	−0.361056	+	0.361056i
$905$	29.7873	+	29.7873i	0.990165	+	0.990165i
$906$	−3.68547			−0.122441
$907$		−	2.33612i		−	0.0775697i	−0.999248	−	0.0387848i	$-0.987651\pi$
$907$		−	2.33612i		−	0.0775697i	0.999248	−	0.0387848i	$-0.0123487\pi$
$908$	−14.0916	+	14.0916i	−0.467645	+	0.467645i
$909$	−13.9422			−0.462435
$910$	6.58353	−	12.6683i	0.218242	−	0.419949i
$911$	−12.2892			−0.407159			−0.203579	−	0.979058i	$-0.565257\pi$
$911$	−12.2892			−0.407159			−0.203579	+	0.979058i	$0.565257\pi$
$912$	14.9452	+	14.9452i	0.494884	+	0.494884i
$913$	−2.43906	−	0.314553i	−0.0807211	−	0.0104102i
$914$			2.09420i			0.0692699i
$915$	27.9161	+	27.9161i	0.922877	+	0.922877i
$916$	4.04668	−	4.04668i	0.133706	−	0.133706i
$917$	−1.31523	−	1.31523i	−0.0434326	−	0.0434326i
$918$	0.528924	+	0.528924i	0.0174571	+	0.0174571i
$919$			49.2612i			1.62498i	0.582977	+	0.812489i	$0.301888\pi$
$919$			49.2612i			1.62498i	−0.582977	+	0.812489i	$0.698112\pi$
$920$	−16.0507			−0.529174
$921$	−7.12552	+	7.12552i	−0.234794	+	0.234794i
$922$		−	4.88428i		−	0.160855i
$923$	16.1175	−	31.0139i	0.530514	−	1.02083i
$924$	−27.6037	−	3.55991i	−0.908095	−	0.117112i
$925$	−6.27746	+	6.27746i	−0.206401	+	0.206401i
$926$		−	1.46457i		−	0.0481289i
$927$		−	0.957068i		−	0.0314342i
$928$	−5.04929	+	5.04929i	−0.165751	+	0.165751i
$929$	−33.0466	+	33.0466i	−1.08422	+	1.08422i	−0.0881136	+	0.996110i	$0.528084\pi$
$929$	−33.0466	+	33.0466i	−1.08422	+	1.08422i	−0.996110	+	0.0881136i	$0.971916\pi$
$930$	1.72042	−	1.72042i	0.0564147	−	0.0564147i
$931$	46.3342	−	46.3342i	1.51854	−	1.51854i
$932$		−	8.99265i		−	0.294564i
$933$			19.6146i			0.642154i
$934$	3.19273	−	3.19273i	0.104469	−	0.104469i
$935$	−5.97413	+	46.3237i	−0.195375	+	1.51495i
$936$	1.45268	−	2.79530i	0.0474823	−	0.0913672i
$937$			10.1174i			0.330522i	0.986250	+	0.165261i	$0.0528467\pi$
$937$			10.1174i			0.330522i	−0.986250	+	0.165261i	$0.947153\pi$
$938$	−5.12766	+	5.12766i	−0.167424	+	0.167424i
$939$	25.2002			0.822378
$940$		−	69.0534i		−	2.25227i
$941$	41.1294	+	41.1294i	1.34078	+	1.34078i	0.895284	+	0.445495i	$0.146972\pi$
$941$	41.1294	+	41.1294i	1.34078	+	1.34078i	0.445495	+	0.895284i	$0.353028\pi$
$942$	2.07420	+	2.07420i	0.0675810	+	0.0675810i
$943$	−3.41608	+	3.41608i	−0.111243	+	0.111243i
$944$	−17.2843	−	17.2843i	−0.562555	−	0.562555i
$945$			17.9064i			0.582494i
$946$	−6.69961	−	0.864014i	−0.217823	−	0.0280915i
$947$	20.3526	+	20.3526i	0.661370	+	0.661370i	0.955703	−	0.294333i	$-0.0950976\pi$
$947$	20.3526	+	20.3526i	0.661370	+	0.661370i	−0.294333	+	0.955703i	$0.595098\pi$
$948$	1.23274			0.0400375
$949$	−1.74171	+	3.35146i	−0.0565383	+	0.108793i
$950$	−15.5408			−0.504209
$951$	7.09610	−	7.09610i	0.230107	−	0.230107i
$952$			12.7116i			0.411985i
$953$	32.0810			1.03920			0.519602	−	0.854408i	$-0.326080\pi$
$953$	32.0810			1.03920			0.519602	+	0.854408i	$0.326080\pi$
$954$	−0.00726884	−	0.00726884i	−0.000235337	−	0.000235337i
$955$	−53.6345	+	53.6345i	−1.73557	+	1.73557i
$956$	−21.4046	+	21.4046i	−0.692275	+	0.692275i
$957$	5.63443	+	7.30289i	0.182135	+	0.236069i
$958$	−2.95557			−0.0954901
$959$	23.7142			0.765773
$960$	−20.1661	−	20.1661i	−0.650858	−	0.650858i
$961$			24.0157i			0.774699i
$962$	−0.172965	−	0.547253i	−0.00557662	−	0.0176441i
$963$		−	4.31790i		−	0.139142i
$964$	6.19781	+	6.19781i	0.199618	+	0.199618i
$965$			3.84732i			0.123850i
$966$			4.19676i			0.135029i
$967$	−26.0663	−	26.0663i	−0.838235	−	0.838235i	0.150392	−	0.988627i	$-0.451947\pi$
$967$	−26.0663	−	26.0663i	−0.838235	−	0.838235i	−0.988627	+	0.150392i	$0.951947\pi$
$968$	4.84937	+	8.29776i	0.155865	+	0.266700i
$969$	−13.6301	−	13.6301i	−0.437862	−	0.437862i
$970$	2.15114	−	2.15114i	0.0690689	−	0.0690689i
$971$	−12.3190			−0.395336			−0.197668	−	0.980269i	$-0.563337\pi$
$971$	−12.3190			−0.395336			−0.197668	+	0.980269i	$0.563337\pi$
$972$			1.95110i			0.0625816i
$973$	44.3449	+	44.3449i	1.42163	+	1.42163i
$974$	−4.54022			−0.145478
$975$	−13.4007	−	42.3990i	−0.429165	−	1.35786i
$976$			35.1716i			1.12581i
$977$	−43.7907	+	43.7907i	−1.40099	+	1.40099i	−0.604015	+	0.796973i	$0.706433\pi$
$977$	−43.7907	+	43.7907i	−1.40099	+	1.40099i	−0.796973	+	0.604015i	$0.793567\pi$
$978$		−	0.280298i		−	0.00896294i
$979$	−3.65654	−	0.471565i	−0.116864	−	0.0150713i
$980$	−66.0474	+	66.0474i	−2.10981	+	2.10981i
$981$	−10.3834	−	10.3834i	−0.331517	−	0.331517i
$982$	−3.92038	−	3.92038i	−0.125104	−	0.125104i
$983$	−19.9163	−	19.9163i	−0.635232	−	0.635232i	0.314144	−	0.949376i	$-0.398283\pi$
$983$	−19.9163	−	19.9163i	−0.635232	−	0.635232i	−0.949376	+	0.314144i	$0.898283\pi$
$984$	0.956590			0.0304950
$985$	−74.3290			−2.36832
$986$	1.47098	−	1.47098i	0.0468457	−	0.0468457i
$987$	−36.5633			−1.16382
$988$	−18.4858	+	35.5710i	−0.588111	+	1.13166i
$989$		−	40.6415i		−	1.29233i
$990$	2.41750	−	1.86518i	0.0768332	−	0.0592795i
$991$	54.4699			1.73029			0.865146	−	0.501520i	$-0.167225\pi$
$991$	54.4699			1.73029			0.865146	+	0.501520i	$0.167225\pi$
$992$	6.78566			0.215445
$993$	22.8731	−	22.8731i	0.725857	−	0.725857i
$994$	6.51944	−	6.51944i	0.206784	−	0.206784i
$995$	6.11350	+	6.11350i	0.193811	+	0.193811i
$996$	−1.02299	+	1.02299i	−0.0324148	+	0.0324148i
$997$			19.4934i			0.617361i	0.951166	+	0.308681i	$0.0998874\pi$
$997$			19.4934i			0.617361i	−0.951166	+	0.308681i	$0.900113\pi$
$998$	−1.91987			−0.0607723
$999$	0.509007	+	0.509007i	0.0161043	+	0.0161043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.a.109.7	✓	28
11.10	odd	2	inner	429.2.m.a.109.8	yes	28
13.8	odd	4	inner	429.2.m.a.307.8	yes	28
143.21	even	4	inner	429.2.m.a.307.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.a.109.7	✓	28	1.1	even	1	trivial
429.2.m.a.109.8	yes	28	11.10	odd	2	inner
429.2.m.a.307.7	yes	28	143.21	even	4	inner
429.2.m.a.307.8	yes	28	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.156364 - 0.156364i) q^{2} -1.00000 q^{3} -1.95110i q^{4} +(2.94387 - 2.94387i) q^{5} +(0.156364 + 0.156364i) q^{6} +(3.04129 - 3.04129i) q^{7} +(-0.617812 + 0.617812i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.156364 - 0.156364i) q^{2} -1.00000 q^{3} -1.95110i q^{4} +(2.94387 - 2.94387i) q^{5} +(0.156364 + 0.156364i) q^{6} +(3.04129 - 3.04129i) q^{7} +(-0.617812 + 0.617812i) q^{8} +1.00000 q^{9} -0.920633 q^{10} +(-2.62591 + 2.02598i) q^{11} +1.95110i q^{12} +(-3.43792 + 1.08659i) q^{13} -0.951100 q^{14} +(-2.94387 + 2.94387i) q^{15} -3.70899 q^{16} +3.38264 q^{17} +(-0.156364 - 0.156364i) q^{18} +(4.02944 + 4.02944i) q^{19} +(-5.74379 - 5.74379i) q^{20} +(-3.04129 + 3.04129i) q^{21} +(0.727390 + 0.0938077i) q^{22} +4.41253i q^{23} +(0.617812 - 0.617812i) q^{24} -12.3327i q^{25} +(0.707473 + 0.367664i) q^{26} -1.00000 q^{27} +(-5.93387 - 5.93387i) q^{28} +2.78109i q^{29} +0.920633 q^{30} +(1.86873 - 1.86873i) q^{31} +(1.81558 + 1.81558i) q^{32} +(2.62591 - 2.02598i) q^{33} +(-0.528924 - 0.528924i) q^{34} -17.9064i q^{35} -1.95110i q^{36} +(-0.509007 - 0.509007i) q^{37} -1.26012i q^{38} +(3.43792 - 1.08659i) q^{39} +3.63751i q^{40} +(0.774176 + 0.774176i) q^{41} +0.951100 q^{42} -9.21047 q^{43} +(3.95289 + 5.12341i) q^{44} +(2.94387 - 2.94387i) q^{45} +(0.689963 - 0.689963i) q^{46} +(6.01114 + 6.01114i) q^{47} +3.70899 q^{48} -11.4989i q^{49} +(-1.92840 + 1.92840i) q^{50} -3.38264 q^{51} +(2.12005 + 6.70773i) q^{52} +0.0464865 q^{53} +(0.156364 + 0.156364i) q^{54} +(-1.76612 + 13.6946i) q^{55} +3.75789i q^{56} +(-4.02944 - 4.02944i) q^{57} +(0.434864 - 0.434864i) q^{58} +(4.66009 + 4.66009i) q^{59} +(5.74379 + 5.74379i) q^{60} -9.48278i q^{61} -0.584407 q^{62} +(3.04129 - 3.04129i) q^{63} +6.85020i q^{64} +(-6.92201 + 13.3196i) q^{65} +(-0.727390 - 0.0938077i) q^{66} +(5.39129 - 5.39129i) q^{67} -6.59986i q^{68} -4.41253i q^{69} +(-2.79992 + 2.79992i) q^{70} +(-6.85463 + 6.85463i) q^{71} +(-0.617812 + 0.617812i) q^{72} +(0.740734 - 0.740734i) q^{73} +0.159181i q^{74} +12.3327i q^{75} +(7.86184 - 7.86184i) q^{76} +(-1.82456 + 14.1478i) q^{77} +(-0.707473 - 0.367664i) q^{78} -0.631817i q^{79} +(-10.9188 + 10.9188i) q^{80} +1.00000 q^{81} -0.242107i q^{82} +(0.524316 + 0.524316i) q^{83} +(5.93387 + 5.93387i) q^{84} +(9.95804 - 9.95804i) q^{85} +(1.44019 + 1.44019i) q^{86} -2.78109i q^{87} +(0.370644 - 2.87399i) q^{88} +(0.786034 + 0.786034i) q^{89} -0.920633 q^{90} +(-7.15109 + 13.7604i) q^{91} +8.60930 q^{92} +(-1.86873 + 1.86873i) q^{93} -1.87986i q^{94} +23.7243 q^{95} +(-1.81558 - 1.81558i) q^{96} +(-2.33658 + 2.33658i) q^{97} +(-1.79802 + 1.79802i) q^{98} +(-2.62591 + 2.02598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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