LMFDB - Embedded newform 350.2.o.d.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.478584585616890104119296.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 $ x^16 - 31x^12 + 336x^8 - 19375*x^4 + 390625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.2
Root			$-1.04705 + 1.97578i$ of defining polynomial
Character	$\chi$	$=$	350.143
Dual form			350.2.o.d.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.339939 + 1.26867i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.31342i q^{6} +(-0.884806 - 2.49342i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.10411 - 0.637459i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.339939 + 1.26867i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.31342i q^{6} +(-0.884806 - 2.49342i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.10411 - 0.637459i) q^{9} +(2.63746 - 4.56821i) q^{11} +(-0.339939 + 1.26867i) q^{12} +(-0.296014 + 0.296014i) q^{13} +(0.209313 + 2.63746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.34607 - 0.896575i) q^{17} +(-1.23148 + 0.329973i) q^{18} +(2.83616 + 4.91238i) q^{19} +(2.86254 - 1.97014i) q^{21} +(-3.72993 + 3.72993i) q^{22} +(-0.776457 + 2.89778i) q^{23} +(0.656712 - 1.13746i) q^{24} +(0.362541 - 0.209313i) q^{26} +(3.97025 + 3.97025i) q^{27} +(0.480443 - 2.60176i) q^{28} -2.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(6.69213 + 1.79315i) q^{33} -3.46410 q^{34} +1.27492 q^{36} +(5.09518 + 1.36525i) q^{37} +(-1.46811 - 5.47904i) q^{38} +(-0.476171 - 0.274917i) q^{39} +5.19615i q^{41} +(-3.27491 + 1.16213i) q^{42} +(-5.85125 - 5.85125i) q^{43} +(4.56821 - 2.63746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(3.26126 - 12.1712i) q^{47} +(-0.928731 + 0.928731i) q^{48} +(-5.43424 + 4.41238i) q^{49} +(2.27492 + 3.94027i) q^{51} +(-0.404362 + 0.108349i) q^{52} +(9.48998 - 2.54283i) q^{53} +(-2.80739 - 4.86254i) q^{54} +(-1.13746 + 2.38876i) q^{56} +(-5.26806 + 5.26806i) q^{57} +(-0.588792 + 2.19740i) q^{58} +(5.19615 - 9.00000i) q^{59} +(-12.4124 + 7.16629i) q^{61} +(2.44949 + 2.44949i) q^{62} +(-2.56637 - 2.18898i) q^{63} +1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(-0.964122 - 3.59815i) q^{67} +(3.34607 + 0.896575i) q^{68} -3.94027 q^{69} -6.00000 q^{71} +(-1.23148 - 0.329973i) q^{72} +(2.47303 + 9.22947i) q^{73} +(-4.56821 - 2.63746i) q^{74} +5.67232i q^{76} +(-13.7241 - 2.53430i) q^{77} +(0.388792 + 0.388792i) q^{78} +(-8.66025 + 5.00000i) q^{79} +(-1.77492 + 3.07425i) q^{81} +(1.34486 - 5.01910i) q^{82} +(-10.1347 + 10.1347i) q^{83} +(3.46410 - 0.274917i) q^{84} +(4.13746 + 7.16629i) q^{86} +(2.88612 - 0.773333i) q^{87} +(-5.09518 + 1.36525i) q^{88} +(-1.97014 - 3.41238i) q^{89} +(1.00000 + 0.476171i) q^{91} +(-2.12132 + 2.12132i) q^{92} +(1.17758 - 4.39480i) q^{93} +(-6.30026 + 10.9124i) q^{94} +(1.13746 - 0.656712i) q^{96} +(13.5129 + 13.5129i) q^{97} +(6.39108 - 2.85554i) q^{98} -6.72508i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 12 q^{11} + 8 q^{16} + 76 q^{21} + 36 q^{26} - 48 q^{31} - 40 q^{36} + 24 q^{46} - 24 q^{51} + 12 q^{56} - 108 q^{61} - 96 q^{66} - 96 q^{71} + 32 q^{81} + 36 q^{86} + 16 q^{91} - 12 q^{96}+O(q^{100}) $ 16 * q + 12 * q^11 + 8 * q^16 + 76 * q^21 + 36 * q^26 - 48 * q^31 - 40 * q^36 + 24 * q^46 - 24 * q^51 + 12 * q^56 - 108 * q^61 - 96 * q^66 - 96 * q^71 + 32 * q^81 + 36 * q^86 + 16 * q^91 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.339939	+	1.26867i	0.196264	+	0.732467i	0.991936	+	0.126739i	$0.0404512\pi$
$3$	0.339939	+	1.26867i	0.196264	+	0.732467i	−0.795672	+	0.605728i	$0.792882\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.31342i		−	0.536203i
$7$	−0.884806	−	2.49342i	−0.334425	−	0.942422i
$7$	−0.884806	−	2.49342i	−0.334425	−	0.942422i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.10411	−	0.637459i	0.368037	−	0.212486i
$10$		0			0
$11$	2.63746	−	4.56821i	0.795224	−	1.37737i	−0.127473	−	0.991842i	$-0.540687\pi$
$11$	2.63746	−	4.56821i	0.795224	−	1.37737i	0.922697	−	0.385526i	$-0.125980\pi$
$12$	−0.339939	+	1.26867i	−0.0981320	+	0.366234i
$13$	−0.296014	+	0.296014i	−0.0820995	+	0.0820995i	−0.746964	−	0.664865i	$-0.768489\pi$
$13$	−0.296014	+	0.296014i	−0.0820995	+	0.0820995i	0.664865	+	0.746964i	$0.268489\pi$
$14$	0.209313	+	2.63746i	0.0559414	+	0.704890i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.34607	−	0.896575i	0.811540	−	0.217451i	0.170896	−	0.985289i	$-0.445334\pi$
$17$	3.34607	−	0.896575i	0.811540	−	0.217451i	0.640644	+	0.767838i	$0.278667\pi$
$18$	−1.23148	+	0.329973i	−0.290262	+	0.0777753i
$19$	2.83616	+	4.91238i	0.650660	+	1.12698i	0.982963	+	0.183804i	$0.0588410\pi$
$19$	2.83616	+	4.91238i	0.650660	+	1.12698i	−0.332303	+	0.943173i	$0.607826\pi$
$20$		0			0
$21$	2.86254	−	1.97014i	0.624658	−	0.429919i
$22$	−3.72993	+	3.72993i	−0.795224	+	0.795224i
$23$	−0.776457	+	2.89778i	−0.161903	+	0.604228i	0.836512	+	0.547948i	$0.184591\pi$
$23$	−0.776457	+	2.89778i	−0.161903	+	0.604228i	−0.998415	+	0.0562805i	$0.982076\pi$
$24$	0.656712	−	1.13746i	0.134051	−	0.232183i
$25$		0			0
$26$	0.362541	−	0.209313i	0.0711002	−	0.0410497i
$27$	3.97025	+	3.97025i	0.764075	+	0.764075i
$28$	0.480443	−	2.60176i	0.0907953	−	0.491687i
$29$		−	2.27492i		−	0.422442i	−0.977438	−	0.211221i	$-0.932256\pi$
$29$		−	2.27492i		−	0.422442i	0.977438	−	0.211221i	$-0.0677439\pi$
$30$		0			0
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	6.69213	+	1.79315i	1.16495	+	0.312148i
$34$	−3.46410			−0.594089
$35$		0			0
$36$	1.27492			0.212486
$37$	5.09518	+	1.36525i	0.837642	+	0.224446i	0.652045	−	0.758180i	$-0.273911\pi$
$37$	5.09518	+	1.36525i	0.837642	+	0.224446i	0.185597	+	0.982626i	$0.440578\pi$
$38$	−1.46811	−	5.47904i	−0.238158	−	0.888818i
$39$	−0.476171	−	0.274917i	−0.0762483	−	0.0440220i
$40$		0			0
$41$			5.19615i			0.811503i	0.913984	+	0.405751i	$0.132990\pi$
$41$			5.19615i			0.811503i	−0.913984	+	0.405751i	$0.867010\pi$
$42$	−3.27491	+	1.16213i	−0.505330	+	0.179320i
$43$	−5.85125	−	5.85125i	−0.892307	−	0.892307i	0.102433	−	0.994740i	$-0.467337\pi$
$43$	−5.85125	−	5.85125i	−0.892307	−	0.892307i	−0.994740	+	0.102433i	$0.967337\pi$
$44$	4.56821	−	2.63746i	0.688684	−	0.397612i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	3.26126	−	12.1712i	0.475703	−	1.77535i	−0.142999	−	0.989723i	$-0.545675\pi$
$47$	3.26126	−	12.1712i	0.475703	−	1.77535i	0.618702	−	0.785625i	$-0.287659\pi$
$48$	−0.928731	+	0.928731i	−0.134051	+	0.134051i
$49$	−5.43424	+	4.41238i	−0.776320	+	0.630339i
$50$		0			0
$51$	2.27492	+	3.94027i	0.318552	+	0.551748i
$52$	−0.404362	+	0.108349i	−0.0560750	+	0.0150252i
$53$	9.48998	−	2.54283i	1.30355	−	0.349285i	0.460758	−	0.887526i	$-0.347578\pi$
$53$	9.48998	−	2.54283i	1.30355	−	0.349285i	0.842791	+	0.538241i	$0.180911\pi$
$54$	−2.80739	−	4.86254i	−0.382037	−	0.661708i
$55$		0			0
$56$	−1.13746	+	2.38876i	−0.151999	+	0.319212i
$57$	−5.26806	+	5.26806i	−0.697772	+	0.697772i
$58$	−0.588792	+	2.19740i	−0.0773122	+	0.288533i
$59$	5.19615	−	9.00000i	0.676481	−	1.17170i	−0.299552	−	0.954080i	$-0.596837\pi$
$59$	5.19615	−	9.00000i	0.676481	−	1.17170i	0.976034	−	0.217620i	$-0.0698294\pi$
$60$		0			0
$61$	−12.4124	+	7.16629i	−1.58924	+	0.917549i	−0.595810	+	0.803126i	$0.703169\pi$
$61$	−12.4124	+	7.16629i	−1.58924	+	0.917549i	−0.993432	+	0.114424i	$0.963498\pi$
$62$	2.44949	+	2.44949i	0.311086	+	0.311086i
$63$	−2.56637	−	2.18898i	−0.323333	−	0.275785i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−6.00000	−	3.46410i	−0.738549	−	0.426401i
$67$	−0.964122	−	3.59815i	−0.117786	−	0.439584i	0.881694	−	0.471822i	$-0.156403\pi$
$67$	−0.964122	−	3.59815i	−0.117786	−	0.439584i	−0.999480	+	0.0322373i	$0.989737\pi$
$68$	3.34607	+	0.896575i	0.405770	+	0.108726i
$69$	−3.94027			−0.474353
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.23148	−	0.329973i	−0.145131	−	0.0388877i
$73$	2.47303	+	9.22947i	0.289446	+	1.08023i	0.945529	+	0.325539i	$0.105546\pi$
$73$	2.47303	+	9.22947i	0.289446	+	1.08023i	−0.656083	+	0.754689i	$0.727788\pi$
$74$	−4.56821	−	2.63746i	−0.531044	−	0.306598i
$75$		0			0
$76$			5.67232i			0.650660i
$77$	−13.7241	−	2.53430i	−1.56400	−	0.288810i
$78$	0.388792	+	0.388792i	0.0440220	+	0.0440220i
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.900561	−	0.434730i	$-0.856844\pi$
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.0737937	+	0.997274i	$0.523511\pi$
$80$		0			0
$81$	−1.77492	+	3.07425i	−0.197213	+	0.341583i
$82$	1.34486	−	5.01910i	0.148515	−	0.554267i
$83$	−10.1347	+	10.1347i	−1.11242	+	1.11242i	−0.119602	+	0.992822i	$0.538162\pi$
$83$	−10.1347	+	10.1347i	−1.11242	+	1.11242i	−0.992822	+	0.119602i	$0.961838\pi$
$84$	3.46410	−	0.274917i	0.377964	−	0.0299959i
$85$		0			0
$86$	4.13746	+	7.16629i	0.446154	+	0.772761i
$87$	2.88612	−	0.773333i	0.309425	−	0.0829100i
$88$	−5.09518	+	1.36525i	−0.543148	+	0.145536i
$89$	−1.97014	−	3.41238i	−0.208834	−	0.361711i	0.742513	−	0.669831i	$-0.233634\pi$
$89$	−1.97014	−	3.41238i	−0.208834	−	0.361711i	−0.951348	+	0.308120i	$0.900300\pi$
$90$		0			0
$91$	1.00000	+	0.476171i	0.104828	+	0.0499162i
$92$	−2.12132	+	2.12132i	−0.221163	+	0.221163i
$93$	1.17758	−	4.39480i	0.122110	−	0.455720i
$94$	−6.30026	+	10.9124i	−0.649823	+	1.12553i
$95$		0			0
$96$	1.13746	−	0.656712i	0.116091	−	0.0670254i
$97$	13.5129	+	13.5129i	1.37203	+	1.37203i	0.857438	+	0.514588i	$0.172055\pi$
$97$	13.5129	+	13.5129i	1.37203	+	1.37203i	0.514588	+	0.857438i	$0.327945\pi$
$98$	6.39108	−	2.85554i	0.645596	−	0.288453i
$99$		−	6.72508i		−	0.675896i
$100$		0			0
$101$	3.41238	+	1.97014i	0.339544	+	0.196036i	0.660070	−	0.751204i	$-0.270526\pi$
$101$	3.41238	+	1.97014i	0.339544	+	0.196036i	−0.320526	+	0.947240i	$0.603860\pi$
$102$	−1.17758	−	4.39480i	−0.116598	−	0.435150i
$103$	−4.61474	−	1.23651i	−0.454703	−	0.121837i	0.0241959	−	0.999707i	$-0.492297\pi$
$103$	−4.61474	−	1.23651i	−0.454703	−	0.121837i	−0.478899	+	0.877870i	$0.658964\pi$
$104$	0.418627			0.0410497
$105$		0			0
$106$	−9.82475			−0.954264
$107$	−6.59220	−	1.76638i	−0.637292	−	0.170762i	−0.0743157	−	0.997235i	$-0.523677\pi$
$107$	−6.59220	−	1.76638i	−0.637292	−	0.170762i	−0.562977	+	0.826473i	$0.690344\pi$
$108$	1.45321	+	5.42346i	0.139835	+	0.521873i
$109$	7.64246	+	4.41238i	0.732015	+	0.422629i	0.819159	−	0.573567i	$-0.194441\pi$
$109$	7.64246	+	4.41238i	0.732015	+	0.422629i	−0.0871440	+	0.996196i	$0.527774\pi$
$110$		0			0
$111$			6.92820i			0.657596i
$112$	1.71696	−	2.01297i	0.162237	−	0.190208i
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	0.478806	−	0.877920i	$-0.341070\pi$
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	−0.877920	+	0.478806i	$0.841070\pi$
$114$	6.45203	−	3.72508i	0.604288	−	0.348886i
$115$		0			0
$116$	1.13746	−	1.97014i	0.105610	−	0.182923i
$117$	−0.138135	+	0.515529i	−0.0127706	+	0.0476606i
$118$	−7.34847	+	7.34847i	−0.676481	+	0.676481i
$119$	−5.19615	−	7.54983i	−0.476331	−	0.692092i
$120$		0			0
$121$	−8.41238	−	14.5707i	−0.764761	−	1.32461i
$122$	13.8442	−	3.70954i	1.25340	−	0.335846i
$123$	−6.59220	+	1.76638i	−0.594399	+	0.159269i
$124$	−1.73205	−	3.00000i	−0.155543	−	0.269408i
$125$		0			0
$126$	1.91238	+	2.77862i	0.170368	+	0.247539i
$127$	−12.2152	+	12.2152i	−1.08392	+	1.08392i	−0.0877853	+	0.996139i	$0.527979\pi$
$127$	−12.2152	+	12.2152i	−1.08392	+	1.08392i	−0.996139	+	0.0877853i	$0.972021\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	5.43424	−	9.41238i	0.478458	−	0.828713i
$130$		0			0
$131$	7.91238	−	4.56821i	0.691307	−	0.399127i	−0.112794	−	0.993618i	$-0.535980\pi$
$131$	7.91238	−	4.56821i	0.691307	−	0.399127i	0.804102	+	0.594492i	$0.202647\pi$
$132$	4.89898	+	4.89898i	0.426401	+	0.426401i
$133$	9.73914	−	11.4182i	0.844491	−	0.990086i
$134$			3.72508i			0.321798i
$135$		0			0
$136$	−3.00000	−	1.73205i	−0.257248	−	0.148522i
$137$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$137$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$138$	3.80601	+	1.01982i	0.323989	+	0.0868126i
$139$	4.41644			0.374598			0.187299	−	0.982303i	$-0.440027\pi$
$139$	4.41644			0.374598			0.187299	+	0.982303i	$0.440027\pi$
$140$		0			0
$141$	16.5498			1.39375
$142$	5.79555	+	1.55291i	0.486352	+	0.130318i
$143$	0.571530	+	2.13298i	0.0477937	+	0.178369i
$144$	1.10411	+	0.637459i	0.0920092	+	0.0531216i
$145$		0			0
$146$		−	9.55505i		−	0.790782i
$147$	−7.44516	−	5.39432i	−0.614066	−	0.444916i
$148$	3.72993	+	3.72993i	0.306598	+	0.306598i
$149$	−11.1066	+	6.41238i	−0.909885	+	0.525322i	−0.880394	−	0.474243i	$-0.842722\pi$
$149$	−11.1066	+	6.41238i	−0.909885	+	0.525322i	−0.0294908	+	0.999565i	$0.509389\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	1.46811	−	5.47904i	0.119079	−	0.444409i
$153$	3.12290	−	3.12290i	0.252471	−	0.252471i
$154$	12.6005	+	6.00000i	1.01538	+	0.483494i
$155$		0			0
$156$	−0.274917	−	0.476171i	−0.0220110	−	0.0381242i
$157$	−9.63383	+	2.58138i	−0.768864	+	0.206016i	−0.621869	−	0.783121i	$-0.713627\pi$
$157$	−9.63383	+	2.58138i	−0.768864	+	0.206016i	−0.146994	+	0.989137i	$0.546960\pi$
$158$	9.65926	−	2.58819i	0.768449	−	0.205905i
$159$	6.45203	+	11.1752i	0.511679	+	0.886255i
$160$		0			0
$161$	7.91238	−	0.627940i	0.623583	−	0.0494886i
$162$	2.51011	−	2.51011i	0.197213	−	0.197213i
$163$	3.10583	−	11.5911i	0.243267	−	0.907886i	−0.730979	−	0.682400i	$-0.760936\pi$
$163$	3.10583	−	11.5911i	0.243267	−	0.907886i	0.974246	−	0.225486i	$-0.0723970\pi$
$164$	−2.59808	+	4.50000i	−0.202876	+	0.351391i
$165$		0			0
$166$	12.4124	−	7.16629i	0.963387	−	0.556212i
$167$	1.22474	+	1.22474i	0.0947736	+	0.0947736i	0.752904	−	0.658130i	$-0.228652\pi$
$167$	1.22474	+	1.22474i	0.0947736	+	0.0947736i	−0.658130	+	0.752904i	$0.728652\pi$
$168$	−3.41722	−	0.631026i	−0.263644	−	0.0486847i
$169$			12.8248i			0.986519i
$170$		0			0
$171$	6.26287	+	3.61587i	0.478934	+	0.276513i
$172$	−2.14171	−	7.99296i	−0.163304	−	0.609457i
$173$	4.55915	+	1.22162i	0.346626	+	0.0928781i	0.427932	−	0.903811i	$-0.359242\pi$
$173$	4.55915	+	1.22162i	0.346626	+	0.0928781i	−0.0813058	+	0.996689i	$0.525909\pi$
$174$	−2.98793			−0.226514
$175$		0			0
$176$	5.27492			0.397612
$177$	13.1844	+	3.53275i	0.991001	+	0.265538i
$178$	1.01982	+	3.80601i	0.0764386	+	0.285273i
$179$	8.50848	+	4.91238i	0.635954	+	0.367168i	0.783054	−	0.621953i	$-0.213661\pi$
$179$	8.50848	+	4.91238i	0.635954	+	0.367168i	−0.147100	+	0.989122i	$0.546994\pi$
$180$		0			0
$181$		−	21.2608i		−	1.58030i	−0.612913	−	0.790151i	$-0.710002\pi$
$181$		−	21.2608i		−	1.58030i	0.612913	−	0.790151i	$-0.289998\pi$
$182$	−0.842684	−	0.718765i	−0.0624639	−	0.0532784i
$183$	−13.3111	−	13.3111i	−0.983986	−	0.983986i
$184$	2.59808	−	1.50000i	0.191533	−	0.110581i
$185$		0			0
$186$	−2.27492	+	3.94027i	−0.166805	+	0.288915i
$187$	4.72936	−	17.6502i	0.345845	−	1.29071i
$188$	8.90992	−	8.90992i	0.649823	−	0.649823i
$189$	6.38658	−	13.4124i	0.464555	−	0.975607i
$190$		0			0
$191$	−4.54983	−	7.88054i	−0.329214	−	0.570216i	0.653142	−	0.757236i	$-0.273451\pi$
$191$	−4.54983	−	7.88054i	−0.329214	−	0.570216i	−0.982356	+	0.187019i	$0.940117\pi$
$192$	−1.26867	+	0.339939i	−0.0915584	+	0.0245330i
$193$	10.1904	−	2.73050i	0.733518	−	0.196546i	0.127323	−	0.991861i	$-0.459362\pi$
$193$	10.1904	−	2.73050i	0.733518	−	0.196546i	0.606195	+	0.795316i	$0.292695\pi$
$194$	−9.55505	−	16.5498i	−0.686013	−	1.18821i
$195$		0			0
$196$	−6.91238	+	1.10411i	−0.493741	+	0.0788650i
$197$	−11.1898	+	11.1898i	−0.797239	+	0.797239i	−0.982659	−	0.185420i	$-0.940635\pi$
$197$	−11.1898	+	11.1898i	−0.797239	+	0.797239i	0.185420	+	0.982659i	$0.440635\pi$
$198$	−1.74058	+	6.49593i	−0.123698	+	0.461646i
$199$	−9.13642	+	15.8248i	−0.647664	+	1.12179i	0.336015	+	0.941857i	$0.390921\pi$
$199$	−9.13642	+	15.8248i	−0.647664	+	1.12179i	−0.983679	+	0.179930i	$0.942413\pi$
$200$		0			0
$201$	4.23713	−	2.44631i	0.298864	−	0.172549i
$202$	−2.78619	−	2.78619i	−0.196036	−	0.196036i
$203$	−5.67231	+	2.01286i	−0.398118	+	0.141275i
$204$			4.54983i			0.318552i
$205$		0			0
$206$	4.13746	+	2.38876i	0.288270	+	0.166433i
$207$	0.989919	+	3.69443i	0.0688041	+	0.256780i
$208$	−0.404362	−	0.108349i	−0.0280375	−	0.00751262i
$209$	29.9210			2.06968
$210$		0			0
$211$	−5.82475			−0.400992			−0.200496	−	0.979694i	$-0.564255\pi$
$211$	−5.82475			−0.400992			−0.200496	+	0.979694i	$0.564255\pi$
$212$	9.48998	+	2.54283i	0.651775	+	0.174642i
$213$	−2.03963	−	7.61202i	−0.139753	−	0.521567i
$214$	5.91041	+	3.41238i	0.404027	+	0.233265i
$215$		0			0
$216$		−	5.61478i		−	0.382037i
$217$	−1.66430	+	9.01277i	−0.112980	+	0.611827i
$218$	−6.24004	−	6.24004i	−0.422629	−	0.422629i
$219$	−10.8685	+	6.27492i	−0.734424	+	0.424020i
$220$		0			0
$221$	−0.725083	+	1.25588i	−0.0487743	+	0.0844796i
$222$	1.79315	−	6.69213i	0.120348	−	0.449146i
$223$	−6.16441	+	6.16441i	−0.412800	+	0.412800i	−0.882713	−	0.469913i	$-0.844285\pi$
$223$	−6.16441	+	6.16441i	−0.412800	+	0.412800i	0.469913	+	0.882713i	$0.344285\pi$
$224$	−2.17945	+	1.50000i	−0.145621	+	0.100223i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	3.34607	−	0.896575i	0.222086	−	0.0595078i	−0.146060	−	0.989276i	$-0.546659\pi$
$227$	3.34607	−	0.896575i	0.222086	−	0.0595078i	0.368146	+	0.929768i	$0.379993\pi$
$228$	−7.19631	+	1.92824i	−0.476587	+	0.127701i
$229$	6.92820	+	12.0000i	0.457829	+	0.792982i	0.998846	−	0.0480291i	$-0.0152940\pi$
$229$	6.92820	+	12.0000i	0.457829	+	0.792982i	−0.541017	+	0.841011i	$0.681961\pi$
$230$		0			0
$231$	−1.45017	−	18.2728i	−0.0954139	−	1.20227i
$232$	−1.60861	+	1.60861i	−0.105610	+	0.105610i
$233$	−6.63858	+	24.7755i	−0.434908	+	1.62310i	0.306379	+	0.951910i	$0.400883\pi$
$233$	−6.63858	+	24.7755i	−0.434908	+	1.62310i	−0.741287	+	0.671188i	$0.765784\pi$
$234$	0.266857	−	0.462210i	0.0174450	−	0.0302156i
$235$		0			0
$236$	9.00000	−	5.19615i	0.585850	−	0.338241i
$237$	−9.28731	−	9.28731i	−0.603276	−	0.603276i
$238$	3.06506	+	8.63744i	0.198678	+	0.559882i
$239$		−	4.54983i		−	0.294304i	−0.989114	−	0.147152i	$-0.952989\pi$
$239$		−	4.54983i		−	0.294304i	0.989114	−	0.147152i	$-0.0470107\pi$
$240$		0			0
$241$	7.91238	+	4.56821i	0.509681	+	0.294264i	0.732702	−	0.680549i	$-0.238259\pi$
$241$	7.91238	+	4.56821i	0.509681	+	0.294264i	−0.223022	+	0.974814i	$0.571592\pi$
$242$	4.35457	+	16.2515i	0.279922	+	1.04468i
$243$	11.7668	+	3.15291i	0.754841	+	0.202259i
$244$	−14.3326			−0.917549
$245$		0			0
$246$	6.82475			0.435130
$247$	−2.29367	−	0.614588i	−0.145943	−	0.0391053i
$248$	0.896575	+	3.34607i	0.0569326	+	0.212475i
$249$	−16.3027	−	9.41238i	−1.03314	−	0.596485i
$250$		0			0
$251$			19.5287i			1.23264i	0.787495	+	0.616321i	$0.211378\pi$
$251$			19.5287i			1.23264i	−0.787495	+	0.616321i	$0.788622\pi$
$252$	−1.12805	−	3.17890i	−0.0710607	−	0.200252i
$253$	11.1898	+	11.1898i	0.703496	+	0.703496i
$254$	14.9605	−	8.63746i	0.938706	−	0.541962i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.72936	+	17.6502i	−0.295009	+	1.10099i	0.646200	+	0.763168i	$0.276357\pi$
$257$	−4.72936	+	17.6502i	−0.295009	+	1.10099i	−0.941210	+	0.337823i	$0.890310\pi$
$258$	−7.68517	+	7.68517i	−0.478458	+	0.478458i
$259$	−1.10411	−	13.9124i	−0.0686061	−	0.864473i
$260$		0			0
$261$	−1.45017	−	2.51176i	−0.0897630	−	0.155474i
$262$	−8.82511	+	2.36468i	−0.545217	+	0.146090i
$263$	−18.1833	+	4.87220i	−1.12123	+	0.300433i	−0.771382	−	0.636373i	$-0.780434\pi$
$263$	−18.1833	+	4.87220i	−1.12123	+	0.300433i	−0.349850	+	0.936806i	$0.613767\pi$
$264$	−3.46410	−	6.00000i	−0.213201	−	0.369274i
$265$		0			0
$266$	−12.3625	+	8.50848i	−0.757996	+	0.521689i
$267$	3.65945	−	3.65945i	0.223955	−	0.223955i
$268$	0.964122	−	3.59815i	0.0588931	−	0.219792i
$269$	3.22602	−	5.58762i	0.196694	−	0.340683i	−0.750761	−	0.660574i	$-0.770313\pi$
$269$	3.22602	−	5.58762i	0.196694	−	0.340683i	0.947454	+	0.319891i	$0.103646\pi$
$270$		0			0
$271$	−6.82475	+	3.94027i	−0.414574	+	0.239354i	−0.692753	−	0.721175i	$-0.743602\pi$
$271$	−6.82475	+	3.94027i	−0.414574	+	0.239354i	0.278179	+	0.960529i	$0.410269\pi$
$272$	2.44949	+	2.44949i	0.148522	+	0.148522i
$273$	−0.264164	+	1.43054i	−0.0159879	+	0.0865802i
$274$		0			0
$275$		0			0
$276$	−3.41238	−	1.97014i	−0.205401	−	0.118588i
$277$	−3.90808	−	14.5852i	−0.234814	−	0.876337i	−0.978233	−	0.207511i	$-0.933464\pi$
$277$	−3.90808	−	14.5852i	−0.234814	−	0.876337i	0.743419	−	0.668826i	$-0.233203\pi$
$278$	−4.26596	−	1.14306i	−0.255855	−	0.0685562i
$279$	−4.41644			−0.264406
$280$		0			0
$281$	−8.37459			−0.499586			−0.249793	−	0.968299i	$-0.580363\pi$
$281$	−8.37459			−0.499586			−0.249793	+	0.968299i	$0.580363\pi$
$282$	−15.9859	−	4.28341i	−0.951947	−	0.255073i
$283$	−1.82294	−	6.80330i	−0.108362	−	0.404414i	0.890343	−	0.455291i	$-0.150465\pi$
$283$	−1.82294	−	6.80330i	−0.108362	−	0.404414i	−0.998705	+	0.0508774i	$0.983798\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$		−	2.20822i		−	0.130575i
$287$	12.9562	−	4.59759i	0.764778	−	0.271387i
$288$	−0.901503	−	0.901503i	−0.0531216	−	0.0531216i
$289$	−4.33013	+	2.50000i	−0.254713	+	0.147059i
$290$		0			0
$291$	−12.5498	+	21.7370i	−0.735684	+	1.27424i
$292$	−2.47303	+	9.22947i	−0.144723	+	0.540114i
$293$	3.33753	−	3.33753i	0.194981	−	0.194981i	−0.602864	−	0.797844i	$-0.705974\pi$
$293$	3.33753	−	3.33753i	0.194981	−	0.194981i	0.797844	+	0.602864i	$0.205974\pi$
$294$	5.79532	+	7.13746i	0.337990	+	0.416265i
$295$		0			0
$296$	−2.63746	−	4.56821i	−0.153299	−	0.265522i
$297$	28.6083	−	7.66557i	1.66002	−	0.444802i
$298$	12.3878	−	3.31929i	0.717604	−	0.192281i
$299$	−0.627940	−	1.08762i	−0.0363147	−	0.0628989i
$300$		0			0
$301$	−9.41238	+	19.7668i	−0.542520	+	1.13934i
$302$	1.41421	−	1.41421i	0.0813788	−	0.0813788i
$303$	−1.33945	+	4.99891i	−0.0769496	+	0.287180i
$304$	−2.83616	+	4.91238i	−0.162665	+	0.281744i
$305$		0			0
$306$	−3.82475	+	2.20822i	−0.218646	+	0.126236i
$307$	2.19417	+	2.19417i	0.125228	+	0.125228i	0.766943	−	0.641715i	$-0.221777\pi$
$307$	2.19417	+	2.19417i	0.125228	+	0.125228i	−0.641715	+	0.766943i	$0.721777\pi$
$308$	−10.6183	−	9.05681i	−0.605031	−	0.516060i
$309$		−	6.27492i		−	0.356968i
$310$		0			0
$311$	22.6495	+	13.0767i	1.28434	+	0.741511i	0.977638	−	0.210296i	$-0.0674426\pi$
$311$	22.6495	+	13.0767i	1.28434	+	0.741511i	0.306698	+	0.951807i	$0.400776\pi$
$312$	0.142308	+	0.531099i	0.00805658	+	0.0300676i
$313$	−19.2677	−	5.16276i	−1.08907	−	0.291816i	−0.330765	−	0.943713i	$-0.607307\pi$
$313$	−19.2677	−	5.16276i	−1.08907	−	0.291816i	−0.758308	+	0.651897i	$0.773974\pi$
$314$	9.97368			0.562847
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−17.3867	−	4.65874i	−0.976532	−	0.261661i	−0.264949	−	0.964262i	$-0.585355\pi$
$317$	−17.3867	−	4.65874i	−0.976532	−	0.261661i	−0.711584	+	0.702601i	$0.752022\pi$
$318$	−3.33982	−	12.4644i	−0.187288	−	0.698967i
$319$	−10.3923	−	6.00000i	−0.581857	−	0.335936i
$320$		0			0
$321$		−	8.96379i		−	0.500310i
$322$	−7.80529	−	1.44133i	−0.434972	−	0.0803222i
$323$	13.8943	+	13.8943i	0.773099	+	0.773099i
$324$	−3.07425	+	1.77492i	−0.170791	+	0.0986065i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−2.99988	+	11.1957i	−0.165894	+	0.619124i
$328$	3.67423	−	3.67423i	0.202876	−	0.202876i
$329$	−33.2334	+	2.63746i	−1.83221	+	0.145408i
$330$		0			0
$331$	−3.08762	−	5.34792i	−0.169711	−	0.293948i	0.768607	−	0.639721i	$-0.220950\pi$
$331$	−3.08762	−	5.34792i	−0.169711	−	0.293948i	−0.938318	+	0.345773i	$0.887617\pi$
$332$	−13.8442	+	3.70954i	−0.759800	+	0.203588i
$333$	6.49593	−	1.74058i	0.355975	−	0.0953832i
$334$	−0.866025	−	1.50000i	−0.0473868	−	0.0820763i
$335$		0			0
$336$	3.13746	+	1.49397i	0.171162	+	0.0815025i
$337$	25.5968	−	25.5968i	1.39435	−	1.39435i	0.579065	−	0.815281i	$-0.303418\pi$
$337$	25.5968	−	25.5968i	1.39435	−	1.39435i	0.815281	−	0.579065i	$-0.196582\pi$
$338$	3.31929	−	12.3878i	0.180546	−	0.673805i
$339$	3.94027	−	6.82475i	0.214006	−	0.370670i
$340$		0			0
$341$	−15.8248	+	9.13642i	−0.856958	+	0.494765i
$342$	−5.11361	−	5.11361i	−0.276513	−	0.276513i
$343$	15.8101	+	9.64572i	0.853667	+	0.520820i
$344$			8.27492i			0.446154i
$345$		0			0
$346$	−4.08762	−	2.35999i	−0.219752	−	0.126874i
$347$	1.33945	+	4.99891i	0.0719056	+	0.268355i	0.992514	−	0.122132i	$-0.0389732\pi$
$347$	1.33945	+	4.99891i	0.0719056	+	0.268355i	−0.920608	+	0.390487i	$0.872306\pi$
$348$	2.88612	+	0.773333i	0.154712	+	0.0414550i
$349$	−3.94027			−0.210918			−0.105459	−	0.994424i	$-0.533631\pi$
$349$	−3.94027			−0.210918			−0.105459	+	0.994424i	$0.533631\pi$
$350$		0			0
$351$	−2.35050			−0.125460
$352$	−5.09518	−	1.36525i	−0.271574	−	0.0727680i
$353$	0.246484	+	0.919891i	0.0131190	+	0.0489609i	0.972175	−	0.234255i	$-0.0752652\pi$
$353$	0.246484	+	0.919891i	0.0131190	+	0.0489609i	−0.959056	+	0.283216i	$0.908599\pi$
$354$	−11.8208	−	6.82475i	−0.628269	−	0.362731i
$355$		0			0
$356$		−	3.94027i		−	0.208834i
$357$	7.81187	−	9.15869i	0.413448	−	0.484729i
$358$	−6.94715	−	6.94715i	−0.367168	−	0.367168i
$359$	11.8208	−	6.82475i	0.623879	−	0.360197i	−0.154499	−	0.987993i	$-0.549376\pi$
$359$	11.8208	−	6.82475i	0.623879	−	0.360197i	0.778378	+	0.627796i	$0.216043\pi$
$360$		0			0
$361$	−6.58762	+	11.4101i	−0.346717	+	0.600532i
$362$	−5.50269	+	20.5363i	−0.289215	+	1.07937i
$363$	15.6257	−	15.6257i	0.820135	−	0.820135i
$364$	0.627940	+	0.912376i	0.0329130	+	0.0478215i
$365$		0			0
$366$	9.41238	+	16.3027i	0.491993	+	0.852156i
$367$	−5.82782	+	1.56156i	−0.304210	+	0.0815128i	−0.407695	−	0.913118i	$-0.633667\pi$
$367$	−5.82782	+	1.56156i	−0.304210	+	0.0815128i	0.103485	+	0.994631i	$0.467001\pi$
$368$	−2.89778	+	0.776457i	−0.151057	+	0.0404756i
$369$	3.31233	+	5.73713i	0.172433	+	0.298663i
$370$		0			0
$371$	−14.7371	−	21.4125i	−0.765114	−	1.11168i
$372$	3.21722	−	3.21722i	0.166805	−	0.166805i
$373$	5.83633	−	21.7815i	0.302194	−	1.12780i	−0.633141	−	0.774037i	$-0.718235\pi$
$373$	5.83633	−	21.7815i	0.302194	−	1.12780i	0.935334	−	0.353765i	$-0.115099\pi$
$374$	−9.13642	+	15.8248i	−0.472433	+	0.818278i
$375$		0			0
$376$	−10.9124	+	6.30026i	−0.562763	+	0.324911i
$377$	0.673407	+	0.673407i	0.0346822	+	0.0346822i
$378$	−9.64034	+	11.3024i	−0.495846	+	0.581332i
$379$		−	25.8248i		−	1.32653i	−0.748385	−	0.663264i	$-0.769171\pi$
$379$		−	25.8248i		−	1.32653i	0.748385	−	0.663264i	$-0.230829\pi$
$380$		0			0
$381$	−19.6495	−	11.3446i	−1.00667	−	0.581204i
$382$	2.35517	+	8.78961i	0.120501	+	0.449715i
$383$	20.2431	+	5.42413i	1.03438	+	0.277160i	0.735781	−	0.677220i	$-0.236815\pi$
$383$	20.2431	+	5.42413i	1.03438	+	0.277160i	0.298595	+	0.954380i	$0.403482\pi$
$384$	1.31342			0.0670254
$385$		0			0
$386$	−10.5498			−0.536972
$387$	−10.1904	−	2.73050i	−0.518005	−	0.138799i
$388$	4.94606	+	18.4589i	0.251098	+	0.937111i
$389$	−2.68439	−	1.54983i	−0.136104	−	0.0785797i	0.430402	−	0.902637i	$-0.358372\pi$
$389$	−2.68439	−	1.54983i	−0.136104	−	0.0785797i	−0.566506	+	0.824058i	$0.691705\pi$
$390$		0			0
$391$			10.3923i			0.525561i
$392$	6.96261	+	0.722565i	0.351665	+	0.0364951i
$393$	8.48528	+	8.48528i	0.428026	+	0.428026i
$394$	13.7046	−	7.91238i	0.690430	−	0.398620i
$395$		0			0
$396$	3.36254	−	5.82409i	0.168974	−	0.292672i
$397$	0.433394	−	1.61745i	0.0217514	−	0.0811775i	−0.954197	−	0.299179i	$-0.903287\pi$
$397$	0.433394	−	1.61745i	0.0217514	−	0.0811775i	0.975948	+	0.218002i	$0.0699538\pi$
$398$	12.9209	−	12.9209i	0.647664	−	0.647664i
$399$	17.7967	+	8.47425i	0.890948	+	0.424243i
$400$		0			0
$401$	9.04983	+	15.6748i	0.451927	+	0.782761i	0.998506	−	0.0546470i	$-0.0174034\pi$
$401$	9.04983	+	15.6748i	0.451927	+	0.782761i	−0.546579	+	0.837408i	$0.684070\pi$
$402$	−4.72590	+	1.26630i	−0.235707	+	0.0631574i
$403$	1.40075	−	0.375330i	0.0697764	−	0.0186965i
$404$	1.97014	+	3.41238i	0.0980179	+	0.169772i
$405$		0			0
$406$	6.00000	−	0.476171i	0.297775	−	0.0236319i
$407$	19.6751	−	19.6751i	0.975257	−	0.975257i
$408$	1.17758	−	4.39480i	0.0582991	−	0.217575i
$409$	8.89834	−	15.4124i	0.439995	−	0.762093i	−0.557694	−	0.830047i	$-0.688314\pi$
$409$	8.89834	−	15.4124i	0.439995	−	0.762093i	0.997688	+	0.0679538i	$0.0216470\pi$
$410$		0			0
$411$		0			0
$412$	−3.37822	−	3.37822i	−0.166433	−	0.166433i
$413$	−27.0383	−	4.99291i	−1.33047	−	0.245685i
$414$		−	3.82475i		−	0.187976i
$415$		0			0
$416$	0.362541	+	0.209313i	0.0177751	+	0.0102624i
$417$	1.50132	+	5.60301i	0.0735200	+	0.274381i
$418$	−28.9015	−	7.74413i	−1.41362	−	0.378778i
$419$	−27.4093			−1.33903			−0.669515	−	0.742798i	$-0.733498\pi$
$419$	−27.4093			−1.33903			−0.669515	+	0.742798i	$0.733498\pi$
$420$		0			0
$421$	34.8248			1.69725			0.848627	−	0.528991i	$-0.177430\pi$
$421$	34.8248			1.69725			0.848627	+	0.528991i	$0.177430\pi$
$422$	5.62628	+	1.50756i	0.273883	+	0.0733867i
$423$	−4.15783	−	15.5172i	−0.202161	−	0.754474i
$424$	−8.50848	−	4.91238i	−0.413209	−	0.238566i
$425$		0			0
$426$			7.88054i			0.381814i
$427$	28.8511	+	24.6084i	1.39620	+	1.19089i
$428$	−4.82583	−	4.82583i	−0.233265	−	0.233265i
$429$	−2.51176	+	1.45017i	−0.121269	+	0.0700147i
$430$		0			0
$431$	17.2749	−	29.9210i	0.832103	−	1.44125i	−0.0642636	−	0.997933i	$-0.520470\pi$
$431$	17.2749	−	29.9210i	0.832103	−	1.44125i	0.896367	−	0.443313i	$-0.146197\pi$
$432$	−1.45321	+	5.42346i	−0.0699177	+	0.260936i
$433$	−7.94050	+	7.94050i	−0.381596	+	0.381596i	−0.871677	−	0.490081i	$-0.836967\pi$
$433$	−7.94050	+	7.94050i	−0.381596	+	0.381596i	0.490081	+	0.871677i	$0.336967\pi$
$434$	3.94027	−	8.27492i	0.189139	−	0.397209i
$435$		0			0
$436$	4.41238	+	7.64246i	0.211314	+	0.366007i
$437$	−16.4371	+	4.40432i	−0.786295	+	0.210687i
$438$	12.1222	−	3.24814i	0.579222	−	0.155202i
$439$	10.3923	+	18.0000i	0.495998	+	0.859093i	0.999989	−	0.00461537i	$-0.00146912\pi$
$439$	10.3923	+	18.0000i	0.495998	+	0.859093i	−0.503992	+	0.863708i	$0.668136\pi$
$440$		0			0
$441$	−3.18729	+	8.33585i	−0.151776	+	0.396945i
$442$	1.02542	−	1.02542i	0.0487743	−	0.0487743i
$443$	−2.89237	+	10.7945i	−0.137421	+	0.512860i	0.862556	+	0.505962i	$0.168862\pi$
$443$	−2.89237	+	10.7945i	−0.137421	+	0.512860i	−0.999976	+	0.00689820i	$0.997804\pi$
$444$	−3.46410	+	6.00000i	−0.164399	+	0.284747i
$445$		0			0
$446$	7.54983	−	4.35890i	0.357495	−	0.206400i
$447$	−11.9107	−	11.9107i	−0.563359	−	0.563359i
$448$	2.49342	−	0.884806i	0.117803	−	0.0418031i
$449$			22.4502i			1.05949i	0.848157	+	0.529744i	$0.177712\pi$
$449$			22.4502i			1.05949i	−0.848157	+	0.529744i	$0.822288\pi$
$450$		0			0
$451$	23.7371	+	13.7046i	1.11774	+	0.645326i
$452$	−1.55291	−	5.79555i	−0.0730429	−	0.272600i
$453$	−2.53734	−	0.679878i	−0.119215	−	0.0319435i
$454$	−3.46410			−0.162578
$455$		0			0
$456$	7.45017			0.348886
$457$	33.3726	+	8.94216i	1.56110	+	0.418296i	0.933013	−	0.359844i	$-0.117170\pi$
$457$	33.3726	+	8.94216i	1.56110	+	0.418296i	0.628091	+	0.778140i	$0.283837\pi$
$458$	−3.58630	−	13.3843i	−0.167577	−	0.625405i
$459$	16.8443	+	9.72508i	0.786226	+	0.453928i
$460$		0			0
$461$		−	15.7611i		−	0.734067i	−0.930208	−	0.367034i	$-0.880373\pi$
$461$		−	15.7611i		−	0.734067i	0.930208	−	0.367034i	$-0.119627\pi$
$462$	−3.32861	+	18.0255i	−0.154861	+	0.838624i
$463$	22.3091	+	22.3091i	1.03679	+	1.03679i	0.999297	+	0.0374951i	$0.0119379\pi$
$463$	22.3091	+	22.3091i	1.03679	+	1.03679i	0.0374951	+	0.999297i	$0.488062\pi$
$464$	1.97014	−	1.13746i	0.0914613	−	0.0528052i
$465$		0			0
$466$	12.8248	−	22.2131i	0.594095	−	1.02900i
$467$	−3.46306	+	12.9243i	−0.160251	+	0.598066i	0.838347	+	0.545137i	$0.183522\pi$
$467$	−3.46306	+	12.9243i	−0.160251	+	0.598066i	−0.998598	+	0.0529290i	$0.983144\pi$
$468$	−0.377393	+	0.377393i	−0.0174450	+	0.0174450i
$469$	−8.11863	+	5.58762i	−0.374883	+	0.258013i
$470$		0			0
$471$	−6.54983	−	11.3446i	−0.301800	−	0.522734i
$472$	−10.0382	+	2.68973i	−0.462045	+	0.123805i
$473$	−42.1622	+	11.2973i	−1.93862	+	0.519451i
$474$	6.56712	+	11.3746i	0.301638	+	0.522452i
$475$		0			0
$476$	−0.725083	−	9.13642i	−0.0332341	−	0.418767i
$477$	8.85704	−	8.85704i	0.405536	−	0.405536i
$478$	−1.17758	+	4.39480i	−0.0538614	+	0.201014i
$479$	3.94027	−	6.82475i	0.180036	−	0.311831i	−0.761857	−	0.647745i	$-0.775712\pi$
$479$	3.94027	−	6.82475i	0.180036	−	0.311831i	0.941892	+	0.335915i	$0.109045\pi$
$480$		0			0
$481$	−1.91238	+	1.10411i	−0.0871968	+	0.0503431i
$482$	−6.46043	−	6.46043i	−0.294264	−	0.294264i
$483$	3.48638	+	9.82473i	0.158636	+	0.447041i
$484$		−	16.8248i		−	0.764761i
$485$		0			0
$486$	−10.5498	−	6.09095i	−0.478550	−	0.276291i
$487$	2.35517	+	8.78961i	0.106723	+	0.398295i	0.998535	−	0.0541110i	$-0.0172325\pi$
$487$	2.35517	+	8.78961i	0.106723	+	0.398295i	−0.891812	+	0.452406i	$0.850566\pi$
$488$	13.8442	+	3.70954i	0.626698	+	0.167923i
$489$	15.7611			0.712741
$490$		0			0
$491$	−19.4502			−0.877774			−0.438887	−	0.898542i	$-0.644627\pi$
$491$	−19.4502			−0.877774			−0.438887	+	0.898542i	$0.644627\pi$
$492$	−6.59220	−	1.76638i	−0.297200	−	0.0796344i
$493$	−2.03963	−	7.61202i	−0.0918605	−	0.342828i
$494$	2.05645	+	1.18729i	0.0925241	+	0.0534188i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	5.30883	+	14.9605i	0.238134	+	0.671070i
$498$	13.3111	+	13.3111i	0.596485	+	0.596485i
$499$	3.46410	−	2.00000i	0.155074	−	0.0895323i	−0.420455	−	0.907314i	$-0.638129\pi$
$499$	3.46410	−	2.00000i	0.155074	−	0.0895323i	0.575529	+	0.817781i	$0.304796\pi$
$500$		0			0
$501$	−1.13746	+	1.97014i	−0.0508179	+	0.0880192i
$502$	5.05441	−	18.8633i	0.225589	−	0.841910i
$503$	15.0336	−	15.0336i	0.670317	−	0.670317i	−0.287472	−	0.957789i	$-0.592815\pi$
$503$	15.0336	−	15.0336i	0.670317	−	0.670317i	0.957789	+	0.287472i	$0.0928148\pi$
$504$	0.266857	+	3.36254i	0.0118868	+	0.149779i
$505$		0			0
$506$	−7.91238	−	13.7046i	−0.351748	−	0.609245i
$507$	−16.2704	+	4.35964i	−0.722593	+	0.193618i
$508$	−16.6863	+	4.47108i	−0.740334	+	0.198372i
$509$	0.714256	+	1.23713i	0.0316588	+	0.0548347i	0.881421	−	0.472332i	$-0.156588\pi$
$509$	0.714256	+	1.23713i	0.0316588	+	0.0548347i	−0.849762	+	0.527167i	$0.823254\pi$
$510$		0			0
$511$	20.8248	−	14.3326i	0.921233	−	0.634036i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−8.24309	+	30.7636i	−0.363941	+	1.35825i
$514$	9.13642	−	15.8248i	0.402990	−	0.698000i
$515$		0			0
$516$	9.41238	−	5.43424i	0.414357	−	0.239229i
$517$	−46.9991	−	46.9991i	−2.06702	−	2.06702i
$518$	−2.53430	+	13.7241i	−0.111351	+	0.603002i
$519$			6.19934i			0.272121i
$520$		0			0
$521$	−23.7371	−	13.7046i	−1.03994	−	0.600411i	−0.120125	−	0.992759i	$-0.538330\pi$
$521$	−23.7371	−	13.7046i	−1.03994	−	0.600411i	−0.919817	+	0.392348i	$0.871663\pi$
$522$	0.750661	+	2.80150i	0.0328555	+	0.122619i
$523$	−30.9233	−	8.28588i	−1.35218	−	0.362316i	−0.491242	−	0.871023i	$-0.663457\pi$
$523$	−30.9233	−	8.28588i	−1.35218	−	0.362316i	−0.860940	+	0.508707i	$0.830124\pi$
$524$	9.13642			0.399127
$525$		0			0
$526$	18.8248			0.820798
$527$	−11.5911	−	3.10583i	−0.504917	−	0.135292i
$528$	1.79315	+	6.69213i	0.0780369	+	0.291238i
$529$	12.1244	+	7.00000i	0.527146	+	0.304348i
$530$		0			0
$531$		−	13.2493i		−	0.574972i
$532$	14.1435	−	5.01890i	0.613197	−	0.217597i
$533$	−1.53813	−	1.53813i	−0.0666239	−	0.0666239i
$534$	−4.48190	+	2.58762i	−0.193951	+	0.111977i
$535$		0			0
$536$	−1.86254	+	3.22602i	−0.0804495	+	0.139343i
$537$	−3.33982	+	12.4644i	−0.144124	+	0.537877i
$538$	−4.56228	+	4.56228i	−0.196694	+	0.196694i
$539$	5.82409	+	36.4622i	0.250861	+	1.57054i
$540$		0			0
$541$	4.58762	+	7.94600i	0.197237	+	0.341625i	0.947632	−	0.319365i	$-0.103470\pi$
$541$	4.58762	+	7.94600i	0.197237	+	0.341625i	−0.750394	+	0.660990i	$0.770136\pi$
$542$	7.61202	−	2.03963i	0.326964	−	0.0876098i
$543$	26.9729	−	7.22737i	1.15752	−	0.310156i
$544$	−1.73205	−	3.00000i	−0.0742611	−	0.128624i
$545$		0			0
$546$	0.625414	−	1.31342i	0.0267652	−	0.0562094i
$547$	−9.06847	+	9.06847i	−0.387740	+	0.387740i	−0.873881	−	0.486141i	$-0.838404\pi$
$547$	−9.06847	+	9.06847i	−0.387740	+	0.387740i	0.486141	+	0.873881i	$0.338404\pi$
$548$		0			0
$549$	−9.13642	+	15.8248i	−0.389933	+	0.675384i
$550$		0			0
$551$	11.1752	−	6.45203i	0.476082	−	0.274866i
$552$	2.78619	+	2.78619i	0.118588	+	0.118588i
$553$	20.1297	+	17.1696i	0.856003	+	0.730125i
$554$			15.0997i			0.641523i
$555$		0			0
$556$	3.82475	+	2.20822i	0.162206	+	0.0936494i
$557$	−5.22174	−	19.4878i	−0.221252	−	0.825724i	−0.983871	−	0.178877i	$-0.942754\pi$
$557$	−5.22174	−	19.4878i	−0.221252	−	0.825724i	0.762619	−	0.646848i	$-0.223913\pi$
$558$	4.26596	+	1.14306i	0.180592	+	0.0483896i
$559$	3.46410			0.146516
$560$		0			0
$561$	24.0000			1.01328
$562$	8.08923	+	2.16750i	0.341224	+	0.0914306i
$563$	1.66991	+	6.23218i	0.0703783	+	0.262655i	0.992146	−	0.125088i	$-0.0399213\pi$
$563$	1.66991	+	6.23218i	0.0703783	+	0.262655i	−0.921767	+	0.387743i	$0.873255\pi$
$564$	14.3326	+	8.27492i	0.603510	+	0.348437i
$565$		0			0
$566$			7.04329i			0.296052i
$567$	9.23583	+	1.70549i	0.387868	+	0.0716240i
$568$	4.24264	+	4.24264i	0.178017	+	0.178017i
$569$	8.50848	−	4.91238i	0.356694	−	0.205938i	−0.310935	−	0.950431i	$-0.600642\pi$
$569$	8.50848	−	4.91238i	0.356694	−	0.205938i	0.667630	+	0.744494i	$0.267309\pi$
$570$		0			0
$571$	14.8248	−	25.6772i	0.620397	−	1.07456i	−0.369015	−	0.929423i	$-0.620305\pi$
$571$	14.8248	−	25.6772i	0.620397	−	1.07456i	0.989412	−	0.145135i	$-0.0463617\pi$
$572$	−0.571530	+	2.13298i	−0.0238969	+	0.0891843i
$573$	8.45115	−	8.45115i	0.353052	−	0.353052i
$574$	−13.7046	+	1.08762i	−0.572020	+	0.0453966i
$575$		0			0
$576$	0.637459	+	1.10411i	0.0265608	+	0.0460046i
$577$	−21.6938	+	5.81285i	−0.903126	+	0.241992i	−0.680358	−	0.732880i	$-0.738176\pi$
$577$	−21.6938	+	5.81285i	−0.903126	+	0.241992i	−0.222768	+	0.974871i	$0.571509\pi$
$578$	4.82963	−	1.29410i	0.200886	−	0.0538273i
$579$	6.92820	+	12.0000i	0.287926	+	0.498703i
$580$		0			0
$581$	34.2371	+	16.3027i	1.42040	+	0.676351i
$582$	17.7481	−	17.7481i	0.735684	−	0.735684i
$583$	13.4132	−	50.0589i	0.555519	−	2.07323i
$584$	4.77753	−	8.27492i	0.197695	−	0.342419i
$585$		0			0
$586$	−4.08762	+	2.35999i	−0.168858	+	0.0974903i
$587$	−7.34847	−	7.34847i	−0.303304	−	0.303304i	0.539001	−	0.842305i	$-0.318802\pi$
$587$	−7.34847	−	7.34847i	−0.303304	−	0.303304i	−0.842305	+	0.539001i	$0.818802\pi$
$588$	−3.75054	−	8.39419i	−0.154670	−	0.346171i
$589$		−	19.6495i		−	0.809644i
$590$		0			0
$591$	−18.0000	−	10.3923i	−0.740421	−	0.427482i
$592$	1.36525	+	5.09518i	0.0561114	+	0.209411i
$593$	−31.9544	−	8.56215i	−1.31221	−	0.351605i	−0.466155	−	0.884703i	$-0.654361\pi$
$593$	−31.9544	−	8.56215i	−1.31221	−	0.351605i	−0.846054	+	0.533098i	$0.821028\pi$
$594$	−29.6175			−1.21522
$595$		0			0
$596$	−12.8248			−0.525322
$597$	−23.1822	−	6.21166i	−0.948785	−	0.254226i
$598$	0.325046	+	1.21309i	0.0132921	+	0.0496068i
$599$	−2.51176	−	1.45017i	−0.102628	−	0.0592522i	0.447808	−	0.894130i	$-0.352205\pi$
$599$	−2.51176	−	1.45017i	−0.102628	−	0.0592522i	−0.550435	+	0.834878i	$0.685538\pi$
$600$		0			0
$601$		−	6.92820i		−	0.282607i	−0.989966	−	0.141304i	$-0.954871\pi$
$601$		−	6.92820i		−	0.282607i	0.989966	−	0.141304i	$-0.0451294\pi$
$602$	14.2077	−	16.6572i	0.579062	−	0.678896i
$603$	−3.35817	−	3.35817i	−0.136755	−	0.136755i
$604$	−1.73205	+	1.00000i	−0.0704761	+	0.0406894i
$605$		0			0
$606$	2.58762	−	4.48190i	0.105115	−	0.182065i
$607$	−5.64083	+	21.0519i	−0.228954	+	0.854469i	0.751827	+	0.659360i	$0.229173\pi$
$607$	−5.64083	+	21.0519i	−0.228954	+	0.854469i	−0.980782	+	0.195109i	$0.937494\pi$
$608$	4.01094	−	4.01094i	0.162665	−	0.162665i
$609$	−4.48190	−	6.51204i	−0.181616	−	0.263881i
$610$		0			0
$611$	2.63746	+	4.56821i	0.106700	+	0.184810i
$612$	4.26596	−	1.14306i	0.172441	−	0.0462054i
$613$	−13.6922	+	3.66882i	−0.553024	+	0.148182i	−0.524500	−	0.851411i	$-0.675748\pi$
$613$	−13.6922	+	3.66882i	−0.553024	+	0.148182i	−0.0285247	+	0.999593i	$0.509081\pi$
$614$	−1.55151	−	2.68729i	−0.0626138	−	0.108450i
$615$		0			0
$616$	7.91238	+	11.4964i	0.318799	+	0.463204i
$617$	22.3796	−	22.3796i	0.900968	−	0.900968i	−0.0945520	−	0.995520i	$-0.530142\pi$
$617$	22.3796	−	22.3796i	0.900968	−	0.900968i	0.995520	+	0.0945520i	$0.0301419\pi$
$618$	−1.62407	+	6.06110i	−0.0653296	+	0.243813i
$619$	1.10411	−	1.91238i	0.0443780	−	0.0768649i	−0.842983	−	0.537940i	$-0.819203\pi$
$619$	1.10411	−	1.91238i	0.0443780	−	0.0768649i	0.887361	+	0.461075i	$0.152536\pi$
$620$		0			0
$621$	−14.5876	+	8.42217i	−0.585381	+	0.337970i
$622$	−18.4932	−	18.4932i	−0.741511	−	0.741511i
$623$	−6.76528	+	7.93166i	−0.271045	+	0.317775i
$624$		−	0.549834i		−	0.0220110i
$625$		0			0
$626$	17.2749	+	9.97368i	0.690445	+	0.398628i
$627$	10.1713	+	37.9599i	0.406204	+	1.51597i
$628$	−9.63383	−	2.58138i	−0.384432	−	0.103008i
$629$	18.2728			0.728586
$630$		0			0
$631$	−35.6495			−1.41918			−0.709592	−	0.704613i	$-0.751121\pi$
$631$	−35.6495			−1.41918			−0.709592	+	0.704613i	$0.751121\pi$
$632$	9.65926	+	2.58819i	0.384225	+	0.102953i
$633$	−1.98006	−	7.38969i	−0.0787004	−	0.293714i
$634$	15.5885	+	9.00000i	0.619097	+	0.357436i
$635$		0			0
$636$			12.9041i			0.511679i
$637$	0.302485	−	2.91473i	0.0119849	−	0.115486i
$638$	8.48528	+	8.48528i	0.335936	+	0.335936i
$639$	−6.62466	+	3.82475i	−0.262068	+	0.151305i
$640$		0			0
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$	−2.32000	+	8.65836i	−0.0915631	+	0.341718i
$643$	4.98036	−	4.98036i	0.196406	−	0.196406i	−0.602051	−	0.798457i	$-0.705650\pi$
$643$	4.98036	−	4.98036i	0.196406	−	0.196406i	0.798457	+	0.602051i	$0.205650\pi$
$644$	7.16629	+	3.41238i	0.282391	+	0.134466i
$645$		0			0
$646$	−9.82475	−	17.0170i	−0.386550	−	0.669524i
$647$	5.01910	−	1.34486i	0.197321	−	0.0528720i	−0.158805	−	0.987310i	$-0.550764\pi$
$647$	5.01910	−	1.34486i	0.197321	−	0.0528720i	0.356126	+	0.934438i	$0.384097\pi$
$648$	3.42888	−	0.918765i	0.134699	−	0.0360925i
$649$	−27.4093	−	47.4743i	−1.07591	−	1.86353i
$650$		0			0
$651$	−12.0000	+	0.952341i	−0.470317	+	0.0373252i
$652$	8.48528	−	8.48528i	0.332309	−	0.332309i
$653$	7.62850	−	28.4699i	0.298526	−	1.11412i	−0.639850	−	0.768500i	$-0.721004\pi$
$653$	7.62850	−	28.4699i	0.298526	−	1.11412i	0.938376	−	0.345615i	$-0.112330\pi$
$654$	5.79532	−	10.0378i	0.226615	−	0.392509i
$655$		0			0
$656$	−4.50000	+	2.59808i	−0.175695	+	0.101438i
$657$	8.61390	+	8.61390i	0.336060	+	0.336060i
$658$	32.7836	+	6.05384i	1.27804	+	0.236003i
$659$			16.5498i			0.644690i	0.946622	+	0.322345i	$0.104471\pi$
$659$			16.5498i			0.644690i	−0.946622	+	0.322345i	$0.895529\pi$
$660$		0			0
$661$	−8.58762	−	4.95807i	−0.334020	−	0.192846i	0.323605	−	0.946192i	$-0.395105\pi$
$661$	−8.58762	−	4.95807i	−0.334020	−	0.192846i	−0.657624	+	0.753346i	$0.728439\pi$
$662$	1.59827	+	5.96483i	0.0621186	+	0.231830i
$663$	−1.83978	−	0.492968i	−0.0714512	−	0.0191453i
$664$	14.3326			0.556212
$665$		0			0
$666$	−6.72508			−0.260592
$667$	6.59220	+	1.76638i	0.255251	+	0.0683943i
$668$	0.448288	+	1.67303i	0.0173448	+	0.0647316i
$669$	−9.91613	−	5.72508i	−0.383380	−	0.221344i
$670$		0			0
$671$			75.6032i			2.91863i
$672$	−2.64389	−	2.25509i	−0.101990	−	0.0869921i
$673$	−12.8689	−	12.8689i	−0.496059	−	0.496059i	0.414150	−	0.910209i	$-0.364079\pi$
$673$	−12.8689	−	12.8689i	−0.496059	−	0.496059i	−0.910209	+	0.414150i	$0.864079\pi$
$674$	−31.3495	+	18.0997i	−1.20754	+	0.697173i
$675$		0			0
$676$	−6.41238	+	11.1066i	−0.246630	+	0.427175i
$677$	−7.99062	+	29.8214i	−0.307104	+	1.14613i	0.624014	+	0.781413i	$0.285501\pi$
$677$	−7.99062	+	29.8214i	−0.307104	+	1.14613i	−0.931119	+	0.364716i	$0.881166\pi$
$678$	−5.57239	+	5.57239i	−0.214006	+	0.214006i
$679$	21.7370	−	45.6495i	0.834188	−	1.75187i
$680$		0			0
$681$	2.27492	+	3.94027i	0.0871750	+	0.150992i
$682$	17.6502	−	4.72936i	0.675862	−	0.181097i
$683$	29.7744	−	7.97803i	1.13929	−	0.305271i	0.360622	−	0.932712i	$-0.382564\pi$
$683$	29.7744	−	7.97803i	1.13929	−	0.305271i	0.778664	+	0.627441i	$0.215898\pi$
$684$	3.61587	+	6.26287i	0.138256	+	0.239467i
$685$		0			0
$686$	−12.7749	−	13.4090i	−0.487749	−	0.511958i
$687$	−12.8689	+	12.8689i	−0.490978	+	0.490978i
$688$	2.14171	−	7.99296i	0.0816518	−	0.304729i
$689$	−2.05645	+	3.56188i	−0.0783446	+	0.135697i
$690$		0			0
$691$	35.4743	−	20.4811i	1.34950	−	0.779137i	0.361325	−	0.932440i	$-0.382324\pi$
$691$	35.4743	−	20.4811i	1.34950	−	0.779137i	0.988179	+	0.153303i	$0.0489911\pi$
$692$	3.33753	+	3.33753i	0.126874	+	0.126874i
$693$	−16.7684	+	5.95039i	−0.636980	+	0.226037i
$694$		−	5.17525i		−	0.196450i
$695$		0			0
$696$	−2.58762	−	1.49397i	−0.0980836	−	0.0566286i
$697$	4.65874	+	17.3867i	0.176462	+	0.658567i
$698$	3.80601	+	1.01982i	0.144060	+	0.0386007i
$699$	−33.6887			−1.27422
$700$		0			0
$701$	−8.27492			−0.312539			−0.156270	−	0.987714i	$-0.549947\pi$
$701$	−8.27492			−0.312539			−0.156270	+	0.987714i	$0.549947\pi$
$702$	2.27041	+	0.608353i	0.0856909	+	0.0229608i
$703$	7.74413	+	28.9015i	0.292076	+	1.09004i
$704$	4.56821	+	2.63746i	0.172171	+	0.0994030i
$705$		0			0
$706$		−	0.952341i		−	0.0358418i
$707$	1.89308	−	10.2517i	0.0711965	−	0.385553i
$708$	9.65166	+	9.65166i	0.362731	+	0.362731i
$709$	11.4101	−	6.58762i	0.428515	−	0.247403i	−0.270199	−	0.962805i	$-0.587089\pi$
$709$	11.4101	−	6.58762i	0.428515	−	0.247403i	0.698714	+	0.715401i	$0.253756\pi$
$710$		0			0
$711$	−6.37459	+	11.0411i	−0.239066	+	0.414074i
$712$	−1.01982	+	3.80601i	−0.0382193	+	0.142636i
$713$	7.34847	−	7.34847i	0.275202	−	0.275202i
$714$	−9.91613	+	6.82475i	−0.371102	+	0.255410i
$715$		0			0
$716$	4.91238	+	8.50848i	0.183584	+	0.317977i
$717$	5.77224	−	1.54667i	0.215568	−	0.0577613i
$718$	−13.1844	+	3.53275i	−0.492038	+	0.131841i
$719$	−19.5287	−	33.8248i	−0.728299	−	1.26145i	−0.957602	−	0.288095i	$-0.906978\pi$
$719$	−19.5287	−	33.8248i	−0.728299	−	1.26145i	0.229303	−	0.973355i	$-0.426355\pi$
$720$		0			0
$721$	1.00000	+	12.6005i	0.0372419	+	0.469268i
$722$	9.31631	−	9.31631i	0.346717	−	0.346717i
$723$	−3.10583	+	11.5911i	−0.115507	+	0.431078i
$724$	10.6304	−	18.4124i	0.395075	−	0.684291i
$725$		0			0
$726$	−19.1375	+	11.0490i	−0.710258	+	0.410067i
$727$	1.30612	+	1.30612i	0.0484415	+	0.0484415i	0.730913	−	0.682471i	$-0.239095\pi$
$727$	1.30612	+	1.30612i	0.0484415	+	0.0484415i	−0.682471	+	0.730913i	$0.739095\pi$
$728$	−0.370403	−	1.04381i	−0.0137281	−	0.0386862i
$729$			26.6495i			0.987019i
$730$		0			0
$731$	−24.8248	−	14.3326i	−0.918177	−	0.530110i
$732$	−4.87220	−	18.1833i	−0.180082	−	0.672075i
$733$	−30.5189	−	8.17753i	−1.12724	−	0.302044i	−0.353432	−	0.935460i	$-0.614985\pi$
$733$	−30.5189	−	8.17753i	−1.12724	−	0.302044i	−0.773811	+	0.633416i	$0.781652\pi$
$734$	6.03341			0.222697
$735$		0			0
$736$	3.00000			0.110581
$737$	−18.9800	−	5.08567i	−0.699136	−	0.187333i
$738$	−1.71459	−	6.39893i	−0.0631149	−	0.235548i
$739$	3.61587	+	2.08762i	0.133012	+	0.0767945i	0.565029	−	0.825071i	$-0.308865\pi$
$739$	3.61587	+	2.08762i	0.133012	+	0.0767945i	−0.432017	+	0.901865i	$0.642198\pi$
$740$		0			0
$741$		−	3.11884i		−	0.114573i
$742$	8.69300	+	24.4972i	0.319130	+	0.899320i
$743$	10.6066	+	10.6066i	0.389118	+	0.389118i	0.874373	−	0.485254i	$-0.161273\pi$
$743$	10.6066	+	10.6066i	0.389118	+	0.389118i	−0.485254	+	0.874373i	$0.661273\pi$
$744$	−3.94027	+	2.27492i	−0.144457	+	0.0834025i
$745$		0			0
$746$	−11.2749	+	19.5287i	−0.412804	+	0.714998i
$747$	−4.72936	+	17.6502i	−0.173038	+	0.645788i
$748$	12.9209	−	12.9209i	0.472433	−	0.472433i
$749$	1.42851	+	18.0000i	0.0521967	+	0.657706i
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	12.1712	−	3.26126i	0.443837	−	0.118926i
$753$	−24.7755	+	6.63858i	−0.902870	+	0.241923i
$754$	−0.476171	−	0.824752i	−0.0173411	−	0.0300357i
$755$		0			0
$756$	12.2371	−	8.42217i	0.445060	−	0.306311i
$757$	−4.24264	+	4.24264i	−0.154201	+	0.154201i	−0.779992	−	0.625790i	$-0.784777\pi$
$757$	−4.24264	+	4.24264i	−0.154201	+	0.154201i	0.625790	+	0.779992i	$0.284777\pi$
$758$	−6.68394	+	24.9448i	−0.242772	+	0.906036i
$759$	−10.3923	+	18.0000i	−0.377217	+	0.653359i
$760$		0			0
$761$	−43.9124	+	25.3528i	−1.59182	+	0.919039i	−0.598828	+	0.800878i	$0.704367\pi$
$761$	−43.9124	+	25.3528i	−1.59182	+	0.919039i	−0.992994	+	0.118161i	$0.962300\pi$
$762$	16.0438	+	16.0438i	0.581204	+	0.581204i
$763$	4.23979	−	22.9599i	0.153491	−	0.831205i
$764$		−	9.09967i		−	0.329214i
$765$		0			0
$766$	−18.1495	−	10.4786i	−0.655768	−	0.378608i
$767$	1.12599	+	4.20226i	0.0406572	+	0.151735i
$768$	−1.26867	−	0.339939i	−0.0457792	−	0.0122665i
$769$	−17.9693			−0.647990			−0.323995	−	0.946059i	$-0.605026\pi$
$769$	−17.9693			−0.647990			−0.323995	+	0.946059i	$0.605026\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	10.1904	+	2.73050i	0.366759	+	0.0982728i
$773$	−8.64071	−	32.2476i	−0.310785	−	1.15986i	−0.927850	−	0.372953i	$-0.878345\pi$
$773$	−8.64071	−	32.2476i	−0.310785	−	1.15986i	0.617066	−	0.786912i	$-0.288321\pi$
$774$	9.13642	+	5.27492i	0.328402	+	0.189603i
$775$		0			0
$776$		−	19.1101i		−	0.686013i
$777$	17.2749	−	6.13011i	0.619733	−	0.219917i
$778$	2.19180	+	2.19180i	0.0785797	+	0.0785797i
$779$	−25.5255	+	14.7371i	−0.914544	+	0.528012i
$780$		0			0
$781$	−15.8248	+	27.4093i	−0.566254	+	0.980781i
$782$	2.68973	−	10.0382i	0.0961844	−	0.358965i
$783$	9.03199	−	9.03199i	0.322777	−	0.322777i
$784$	−6.53835	−	2.50000i	−0.233512	−	0.0892857i
$785$		0			0
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	−30.6857	+	8.22221i	−1.09383	+	0.293090i	−0.760249	−	0.649632i	$-0.774923\pi$
$787$	−30.6857	+	8.22221i	−1.09383	+	0.293090i	−0.333578	+	0.942722i	$0.608256\pi$
$788$	−15.2855	+	4.09575i	−0.544525	+	0.145905i
$789$	−12.3624	−	21.4124i	−0.440115	−	0.762301i
$790$		0			0
$791$	−6.82475	+	14.3326i	−0.242660	+	0.509608i
$792$	−4.75535	+	4.75535i	−0.168974	+	0.168974i
$793$	1.55291	−	5.79555i	0.0551456	−	0.205806i
$794$	−0.837253	+	1.45017i	−0.0297130	+	0.0514645i
$795$		0			0
$796$	−15.8248	+	9.13642i	−0.560893	+	0.323832i
$797$	−9.79796	−	9.79796i	−0.347062	−	0.347062i	0.511952	−	0.859014i	$-0.328922\pi$
$797$	−9.79796	−	9.79796i	−0.347062	−	0.347062i	−0.859014	+	0.511952i	$0.828922\pi$
$798$	−14.9970	−	12.7916i	−0.530887	−	0.452818i
$799$		−	43.6495i		−	1.54421i
$800$		0			0
$801$	−4.35050	−	2.51176i	−0.153717	−	0.0887487i
$802$	−4.68454	−	17.4829i	−0.165417	−	0.617344i
$803$	48.6847	+	13.0450i	1.71805	+	0.460349i
$804$	4.89261			0.172549
$805$		0			0
$806$	−1.45017			−0.0510799
$807$	8.18550	+	2.19330i	0.288143	+	0.0772078i
$808$	−1.01982	−	3.80601i	−0.0358771	−	0.133895i
$809$	5.28247	+	3.04983i	0.185722	+	0.107226i	0.589978	−	0.807419i	$-0.299136\pi$
$809$	5.28247	+	3.04983i	0.185722	+	0.107226i	−0.404256	+	0.914646i	$0.632470\pi$
$810$		0			0
$811$			17.0170i			0.597547i	0.954324	+	0.298773i	$0.0965774\pi$
$811$			17.0170i			0.597547i	−0.954324	+	0.298773i	$0.903423\pi$
$812$	−5.91880	−	1.09297i	−0.207709	−	0.0383557i
$813$	−7.31891	−	7.31891i	−0.256685	−	0.256685i
$814$	−24.0969	+	13.9124i	−0.844597	+	0.487629i
$815$		0			0
$816$	−2.27492	+	3.94027i	−0.0796380	+	0.137937i
$817$	12.1484	−	45.3386i	0.425020	−	1.58620i
$818$	−12.5842	+	12.5842i	−0.439995	+	0.439995i
$819$	1.40765	−	0.111714i	0.0491873	−	0.00390359i
$820$		0			0
$821$	−24.0997	−	41.7419i	−0.841084	−	1.45680i	−0.888979	−	0.457948i	$-0.848584\pi$
$821$	−24.0997	−	41.7419i	−0.841084	−	1.45680i	0.0478946	−	0.998852i	$-0.484749\pi$
$822$		0			0
$823$	−18.1833	+	4.87220i	−0.633830	+	0.169834i	−0.561407	−	0.827540i	$-0.689740\pi$
$823$	−18.1833	+	4.87220i	−0.633830	+	0.169834i	−0.0724232	+	0.997374i	$0.523073\pi$
$824$	2.38876	+	4.13746i	0.0832165	+	0.144135i
$825$		0			0
$826$	24.8248	+	11.8208i	0.863764	+	0.411299i
$827$	18.7201	−	18.7201i	0.650963	−	0.650963i	−0.302262	−	0.953225i	$-0.597742\pi$
$827$	18.7201	−	18.7201i	0.650963	−	0.650963i	0.953225	+	0.302262i	$0.0977418\pi$
$828$	−0.989919	+	3.69443i	−0.0344020	+	0.128390i
$829$	5.67232	−	9.82475i	0.197008	−	0.341228i	−0.750549	−	0.660815i	$-0.770211\pi$
$829$	5.67232	−	9.82475i	0.197008	−	0.341228i	0.947557	+	0.319587i	$0.103544\pi$
$830$		0			0
$831$	17.1752	−	9.91613i	0.595803	−	0.343987i
$832$	−0.296014	−	0.296014i	−0.0102624	−	0.0102624i
$833$	−14.2273	+	19.6363i	−0.492946	+	0.680358i
$834$		−	5.80066i		−	0.200861i
$835$		0			0
$836$	25.9124	+	14.9605i	0.896198	+	0.517420i
$837$	−5.03407	−	18.7874i	−0.174003	−	0.649388i
$838$	26.4753	+	7.09404i	0.914575	+	0.245060i
$839$	−2.51176			−0.0867156			−0.0433578	−	0.999060i	$-0.513806\pi$
$839$	−2.51176			−0.0867156			−0.0433578	+	0.999060i	$0.513806\pi$
$840$		0			0
$841$	23.8248			0.821543
$842$	−33.6381	−	9.01331i	−1.15925	−	0.310619i
$843$	−2.84685	−	10.6246i	−0.0980507	−	0.365930i
$844$	−5.04438	−	2.91238i	−0.173635	−	0.100248i
$845$		0			0
$846$			16.0646i			0.552313i
$847$	−28.8874	+	33.8678i	−0.992583	+	1.16371i
$848$	6.94715	+	6.94715i	0.238566	+	0.238566i
$849$	8.01145	−	4.62541i	0.274952	−	0.158744i
$850$		0			0
$851$	−7.91238	+	13.7046i	−0.271233	+	0.469789i
$852$	2.03963	−	7.61202i	0.0698767	−	0.260784i
$853$	−24.3616	+	24.3616i	−0.834127	+	0.834127i	−0.988078	−	0.153952i	$-0.950800\pi$
$853$	−24.3616	+	24.3616i	−0.834127	+	0.834127i	0.153952	+	0.988078i	$0.450800\pi$
$854$	−21.4989	−	31.2371i	−0.735676	−	1.06891i
$855$		0			0
$856$	3.41238	+	5.91041i	0.116633	+	0.202014i
$857$	−15.2240	+	4.07927i	−0.520043	+	0.139345i	−0.509287	−	0.860597i	$-0.670091\pi$
$857$	−15.2240	+	4.07927i	−0.520043	+	0.139345i	−0.0107567	+	0.999942i	$0.503424\pi$
$858$	2.80150	−	0.750661i	0.0956418	−	0.0256271i
$859$	1.25588	+	2.17525i	0.0428501	+	0.0742185i	0.886655	−	0.462431i	$-0.153023\pi$
$859$	1.25588	+	2.17525i	0.0428501	+	0.0742185i	−0.843805	+	0.536650i	$0.819690\pi$
$860$		0			0
$861$	10.2371	+	14.8742i	0.348880	+	0.506911i
$862$	−24.4304	+	24.4304i	−0.832103	+	0.832103i
$863$	−10.0939	+	37.6711i	−0.343602	+	1.28234i	0.550635	+	0.834746i	$0.314385\pi$
$863$	−10.0939	+	37.6711i	−0.343602	+	1.28234i	−0.894237	+	0.447593i	$0.852281\pi$
$864$	2.80739	−	4.86254i	0.0955093	−	0.165427i
$865$		0			0
$866$	9.72508	−	5.61478i	0.330472	−	0.190798i
$867$	−4.64366	−	4.64366i	−0.157707	−	0.157707i
$868$	−5.94772	+	6.97314i	−0.201879	+	0.236684i
$869$			52.7492i			1.78939i
$870$		0			0
$871$	1.35050	+	0.779710i	0.0457598	+	0.0264195i
$872$	−2.28401	−	8.52406i	−0.0773465	−	0.288661i
$873$	23.5336	+	6.30582i	0.796492	+	0.213420i
$874$	17.0170			0.575608
$875$		0			0
$876$	−12.5498			−0.424020
$877$	13.6922	+	3.66882i	0.462354	+	0.123887i	0.482474	−	0.875910i	$-0.339738\pi$
$877$	13.6922	+	3.66882i	0.462354	+	0.123887i	−0.0201202	+	0.999798i	$0.506405\pi$
$878$	−5.37945	−	20.0764i	−0.181548	−	0.677545i
$879$	5.36878	+	3.09967i	0.181085	+	0.104549i
$880$		0			0
$881$		−	31.3495i		−	1.05619i	−0.849184	−	0.528097i	$-0.822906\pi$
$881$		−	31.3495i		−	1.05619i	0.849184	−	0.528097i	$-0.177094\pi$
$882$	5.23617	−	7.22688i	0.176311	−	0.243342i
$883$	6.43444	+	6.43444i	0.216536	+	0.216536i	0.807037	−	0.590501i	$-0.201070\pi$
$883$	6.43444	+	6.43444i	0.216536	+	0.216536i	−0.590501	+	0.807037i	$0.701070\pi$
$884$	−1.25588	+	0.725083i	−0.0422398	+	0.0243872i
$885$		0			0
$886$	5.58762	−	9.67805i	0.187720	−	0.325140i
$887$	5.74918	−	21.4562i	0.193039	−	0.720430i	−0.799727	−	0.600363i	$-0.795023\pi$
$887$	5.74918	−	21.4562i	0.193039	−	0.720430i	0.992766	−	0.120066i	$-0.0383107\pi$
$888$	4.89898	−	4.89898i	0.164399	−	0.164399i
$889$	41.2657	+	19.6495i	1.38401	+	0.659023i
$890$		0			0
$891$	9.36254	+	16.2164i	0.313657	+	0.543270i
$892$	−8.42075	+	2.25633i	−0.281947	+	0.0755476i
$893$	69.0388	−	18.4989i	2.31030	−	0.619042i
$894$	8.42217	+	14.5876i	0.281679	+	0.487883i
$895$		0			0
$896$	−2.63746	+	0.209313i	−0.0881113	+	0.00699267i
$897$	1.16637	−	1.16637i	0.0389441	−	0.0389441i
$898$	5.81053	−	21.6852i	0.193900	−	0.723644i
$899$	−3.94027	+	6.82475i	−0.131415	+	0.227618i
$900$		0			0
$901$	29.4743	−	17.0170i	0.981930	−	0.566917i
$902$	−19.3813	−	19.3813i	−0.645326	−	0.645326i
$903$	−28.2772	−	5.22169i	−0.941006	−	0.173767i
$904$			6.00000i			0.199557i
$905$		0			0
$906$	2.27492	+	1.31342i	0.0755791	+	0.0436356i
$907$	−7.22737	−	26.9729i	−0.239981	−	0.895621i	−0.975840	−	0.218486i	$-0.929888\pi$
$907$	−7.22737	−	26.9729i	−0.239981	−	0.895621i	0.735859	−	0.677135i	$-0.236779\pi$
$908$	3.34607	+	0.896575i	0.111043	+	0.0297539i
$909$	5.02352			0.166620
$910$		0			0
$911$	−19.6495			−0.651017			−0.325509	−	0.945539i	$-0.605535\pi$
$911$	−19.6495			−0.651017			−0.325509	+	0.945539i	$0.605535\pi$
$912$	−7.19631	−	1.92824i	−0.238294	−	0.0638506i
$913$	19.5675	+	73.0270i	0.647591	+	2.41684i
$914$	−29.9210	−	17.2749i	−0.989700	−	0.571403i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	−18.3914	−	15.6869i	−0.607336	−	0.518026i
$918$	−13.7533	−	13.7533i	−0.453928	−	0.453928i
$919$	29.1413	−	16.8248i	0.961284	−	0.554997i	0.0647157	−	0.997904i	$-0.479386\pi$
$919$	29.1413	−	16.8248i	0.961284	−	0.554997i	0.896568	+	0.442906i	$0.146053\pi$
$920$		0			0
$921$	−2.03779	+	3.52956i	−0.0671475	+	0.116303i
$922$	−4.07927	+	15.2240i	−0.134344	+	0.501377i
$923$	1.77608	−	1.77608i	0.0584605	−	0.0584605i
$924$	7.88054	−	16.5498i	0.259251	−	0.544450i
$925$		0			0
$926$	−15.7749	−	27.3230i	−0.518396	−	0.897888i
$927$	−5.88341	+	1.57645i	−0.193236	+	0.0517775i
$928$	−2.19740	+	0.588792i	−0.0721332	+	0.0193280i
$929$	−6.53835	−	11.3248i	−0.214516	−	0.371553i	0.738607	−	0.674137i	$-0.235484\pi$
$929$	−6.53835	−	11.3248i	−0.214516	−	0.371553i	−0.953123	+	0.302584i	$0.902151\pi$
$930$		0			0
$931$	−37.0876	−	14.1808i	−1.21550	−	0.464757i
$932$	−18.1369	+	18.1369i	−0.594095	+	0.594095i
$933$	−8.89056	+	33.1800i	−0.291064	+	1.08627i
$934$	6.69012	−	11.5876i	0.218907	−	0.379159i
$935$		0			0
$936$	0.462210	−	0.266857i	0.0151078	−	0.00872250i
$937$	37.5785	+	37.5785i	1.22764	+	1.22764i	0.964856	+	0.262781i	$0.0846397\pi$
$937$	37.5785	+	37.5785i	1.22764	+	1.22764i	0.262781	+	0.964856i	$0.415360\pi$
$938$	9.28818	−	3.29597i	0.303270	−	0.107617i
$939$		−	26.1993i		−	0.854983i
$940$		0			0
$941$	−4.35050	−	2.51176i	−0.141822	−	0.0818811i	0.427410	−	0.904058i	$-0.359426\pi$
$941$	−4.35050	−	2.51176i	−0.141822	−	0.0818811i	−0.569232	+	0.822177i	$0.692759\pi$
$942$	3.39044	+	12.6533i	0.110467	+	0.412267i
$943$	−15.0573	−	4.03459i	−0.490333	−	0.131384i
$944$	10.3923			0.338241
$945$		0			0
$946$	43.6495			1.41917
$947$	18.1833	+	4.87220i	0.590878	+	0.158325i	0.541855	−	0.840472i	$-0.317722\pi$
$947$	18.1833	+	4.87220i	0.590878	+	0.158325i	0.0490237	+	0.998798i	$0.484389\pi$
$948$	−3.39939	−	12.6867i	−0.110407	−	0.412045i
$949$	−3.46410	−	2.00000i	−0.112449	−	0.0649227i
$950$		0			0
$951$		−	23.6416i		−	0.766632i
$952$	−1.66430	+	9.01277i	−0.0539404	+	0.292106i
$953$	−27.7886	−	27.7886i	−0.900161	−	0.900161i	0.0952888	−	0.995450i	$-0.469623\pi$
$953$	−27.7886	−	27.7886i	−0.900161	−	0.900161i	−0.995450	+	0.0952888i	$0.969623\pi$
$954$	−10.8476	+	6.26287i	−0.351204	+	0.202768i
$955$		0			0
$956$	2.27492	−	3.94027i	0.0735761	−	0.127438i
$957$	4.07927	−	15.2240i	0.131864	−	0.492123i
$958$	−5.57239	+	5.57239i	−0.180036	+	0.180036i
$959$		0			0
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	2.13298	−	0.571530i	0.0687700	−	0.0184269i
$963$	−8.40451	+	2.25198i	−0.270832	+	0.0725691i
$964$	4.56821	+	7.91238i	0.147132	+	0.254840i
$965$		0			0
$966$	−0.824752	−	10.3923i	−0.0265359	−	0.334367i
$967$	19.7455	−	19.7455i	0.634974	−	0.634974i	−0.314337	−	0.949311i	$-0.601782\pi$
$967$	19.7455	−	19.7455i	0.634974	−	0.634974i	0.949311	+	0.314337i	$0.101782\pi$
$968$	−4.35457	+	16.2515i	−0.139961	+	0.522342i
$969$	−12.9041	+	22.3505i	−0.414538	+	0.718001i
$970$		0			0
$971$	41.7371	−	24.0969i	1.33941	−	0.773308i	0.352689	−	0.935741i	$-0.385267\pi$
$971$	41.7371	−	24.0969i	1.33941	−	0.773308i	0.986720	+	0.162433i	$0.0519342\pi$
$972$	8.61390	+	8.61390i	0.276291	+	0.276291i
$973$	−3.90769	−	11.0120i	−0.125275	−	0.353029i
$974$		−	9.09967i		−	0.291572i
$975$		0			0
$976$	−12.4124	−	7.16629i	−0.397310	−	0.229387i
$977$	5.08567	+	18.9800i	0.162705	+	0.607223i	0.998322	+	0.0579102i	$0.0184437\pi$
$977$	5.08567	+	18.9800i	0.162705	+	0.607223i	−0.835617	+	0.549313i	$0.814890\pi$
$978$	−15.2240	−	4.07927i	−0.486811	−	0.130441i
$979$	−20.7846			−0.664279
$980$		0			0
$981$	11.2508			0.359211
$982$	18.7874	+	5.03407i	0.599531	+	0.160644i
$983$	−9.01044	−	33.6274i	−0.287388	−	1.07255i	−0.947076	−	0.321008i	$-0.895978\pi$
$983$	−9.01044	−	33.6274i	−0.287388	−	1.07255i	0.659688	−	0.751539i	$-0.270688\pi$
$984$	5.91041	+	3.41238i	0.188417	+	0.108783i
$985$		0			0
$986$			7.88054i			0.250968i
$987$	−14.6434	−	41.2656i	−0.466104	−	1.31350i
$988$	−1.67909	−	1.67909i	−0.0534188	−	0.0534188i
$989$	21.4989	−	12.4124i	0.683624	−	0.394691i
$990$		0			0
$991$	10.8248	−	18.7490i	0.343860	−	0.595582i	−0.641286	−	0.767302i	$-0.721599\pi$
$991$	10.8248	−	18.7490i	0.343860	−	0.595582i	0.985146	+	0.171719i	$0.0549322\pi$
$992$	−0.896575	+	3.34607i	−0.0284663	+	0.106238i
$993$	5.73514	−	5.73514i	0.181999	−	0.181999i
$994$	−1.25588	−	15.8248i	−0.0398341	−	0.501931i
$995$		0			0
$996$	−9.41238	−	16.3027i	−0.298243	−	0.516571i
$997$	29.3059	−	7.85248i	0.928126	−	0.248691i	0.237071	−	0.971492i	$-0.423813\pi$
$997$	29.3059	−	7.85248i	0.928126	−	0.248691i	0.691055	+	0.722802i	$0.257146\pi$
$998$	−3.86370	+	1.03528i	−0.122303	+	0.0327711i
$999$	14.8087	+	25.6495i	0.468528	+	0.811514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.d.143.2	✓	16
5.2	odd	4	inner	350.2.o.d.157.4	yes	16
5.3	odd	4	inner	350.2.o.d.157.1	yes	16
5.4	even	2	inner	350.2.o.d.143.3	yes	16
7.5	odd	6	inner	350.2.o.d.243.4	yes	16
35.12	even	12	inner	350.2.o.d.257.2	yes	16
35.19	odd	6	inner	350.2.o.d.243.1	yes	16
35.33	even	12	inner	350.2.o.d.257.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.d.143.2	✓	16	1.1	even	1	trivial
350.2.o.d.143.3	yes	16	5.4	even	2	inner
350.2.o.d.157.1	yes	16	5.3	odd	4	inner
350.2.o.d.157.4	yes	16	5.2	odd	4	inner
350.2.o.d.243.1	yes	16	35.19	odd	6	inner
350.2.o.d.243.4	yes	16	7.5	odd	6	inner
350.2.o.d.257.2	yes	16	35.12	even	12	inner
350.2.o.d.257.3	yes	16	35.33	even	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.339939 + 1.26867i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.31342i q^{6} +(-0.884806 - 2.49342i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.10411 - 0.637459i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.339939 + 1.26867i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.31342i q^{6} +(-0.884806 - 2.49342i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.10411 - 0.637459i) q^{9} +(2.63746 - 4.56821i) q^{11} +(-0.339939 + 1.26867i) q^{12} +(-0.296014 + 0.296014i) q^{13} +(0.209313 + 2.63746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.34607 - 0.896575i) q^{17} +(-1.23148 + 0.329973i) q^{18} +(2.83616 + 4.91238i) q^{19} +(2.86254 - 1.97014i) q^{21} +(-3.72993 + 3.72993i) q^{22} +(-0.776457 + 2.89778i) q^{23} +(0.656712 - 1.13746i) q^{24} +(0.362541 - 0.209313i) q^{26} +(3.97025 + 3.97025i) q^{27} +(0.480443 - 2.60176i) q^{28} -2.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(6.69213 + 1.79315i) q^{33} -3.46410 q^{34} +1.27492 q^{36} +(5.09518 + 1.36525i) q^{37} +(-1.46811 - 5.47904i) q^{38} +(-0.476171 - 0.274917i) q^{39} +5.19615i q^{41} +(-3.27491 + 1.16213i) q^{42} +(-5.85125 - 5.85125i) q^{43} +(4.56821 - 2.63746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(3.26126 - 12.1712i) q^{47} +(-0.928731 + 0.928731i) q^{48} +(-5.43424 + 4.41238i) q^{49} +(2.27492 + 3.94027i) q^{51} +(-0.404362 + 0.108349i) q^{52} +(9.48998 - 2.54283i) q^{53} +(-2.80739 - 4.86254i) q^{54} +(-1.13746 + 2.38876i) q^{56} +(-5.26806 + 5.26806i) q^{57} +(-0.588792 + 2.19740i) q^{58} +(5.19615 - 9.00000i) q^{59} +(-12.4124 + 7.16629i) q^{61} +(2.44949 + 2.44949i) q^{62} +(-2.56637 - 2.18898i) q^{63} +1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(-0.964122 - 3.59815i) q^{67} +(3.34607 + 0.896575i) q^{68} -3.94027 q^{69} -6.00000 q^{71} +(-1.23148 - 0.329973i) q^{72} +(2.47303 + 9.22947i) q^{73} +(-4.56821 - 2.63746i) q^{74} +5.67232i q^{76} +(-13.7241 - 2.53430i) q^{77} +(0.388792 + 0.388792i) q^{78} +(-8.66025 + 5.00000i) q^{79} +(-1.77492 + 3.07425i) q^{81} +(1.34486 - 5.01910i) q^{82} +(-10.1347 + 10.1347i) q^{83} +(3.46410 - 0.274917i) q^{84} +(4.13746 + 7.16629i) q^{86} +(2.88612 - 0.773333i) q^{87} +(-5.09518 + 1.36525i) q^{88} +(-1.97014 - 3.41238i) q^{89} +(1.00000 + 0.476171i) q^{91} +(-2.12132 + 2.12132i) q^{92} +(1.17758 - 4.39480i) q^{93} +(-6.30026 + 10.9124i) q^{94} +(1.13746 - 0.656712i) q^{96} +(13.5129 + 13.5129i) q^{97} +(6.39108 - 2.85554i) q^{98} -6.72508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 12 q^{11} + 8 q^{16} + 76 q^{21} + 36 q^{26} - 48 q^{31} - 40 q^{36} + 24 q^{46} - 24 q^{51} + 12 q^{56} - 108 q^{61} - 96 q^{66} - 96 q^{71} + 32 q^{81} + 36 q^{86} + 16 q^{91} - 12 q^{96}+O(q^{100}) \) 16 * q + 12 * q^11 + 8 * q^16 + 76 * q^21 + 36 * q^26 - 48 * q^31 - 40 * q^36 + 24 * q^46 - 24 * q^51 + 12 * q^56 - 108 * q^61 - 96 * q^66 - 96 * q^71 + 32 * q^81 + 36 * q^86 + 16 * q^91 - 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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