LMFDB - Embedded newform 350.2.o.d.243.1

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			243.1
Root			$1.97578 - 1.04705i$ of defining polynomial
Character	$\chi$	$=$	350.243
Dual form			350.2.o.d.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.26867 - 0.339939i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.31342i q^{6} +(-2.49342 - 0.884806i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.10411 - 0.637459i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.26867 - 0.339939i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.31342i q^{6} +(-2.49342 - 0.884806i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.10411 - 0.637459i) q^{9} +(2.63746 + 4.56821i) q^{11} +(1.26867 - 0.339939i) q^{12} +(-0.296014 + 0.296014i) q^{13} +(-0.209313 + 2.63746i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.896575 + 3.34607i) q^{17} +(-0.329973 + 1.23148i) q^{18} +(-2.83616 + 4.91238i) q^{19} +(2.86254 + 1.97014i) q^{21} +(3.72993 - 3.72993i) q^{22} +(-2.89778 + 0.776457i) q^{23} +(-0.656712 - 1.13746i) q^{24} +(0.362541 + 0.209313i) q^{26} +(3.97025 + 3.97025i) q^{27} +(2.60176 - 0.480443i) q^{28} -2.27492i q^{29} +(-3.00000 + 1.73205i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.79315 - 6.69213i) q^{33} +3.46410 q^{34} +1.27492 q^{36} +(1.36525 + 5.09518i) q^{37} +(5.47904 + 1.46811i) q^{38} +(0.476171 - 0.274917i) q^{39} -5.19615i q^{41} +(1.16213 - 3.27491i) q^{42} +(5.85125 + 5.85125i) q^{43} +(-4.56821 - 2.63746i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-12.1712 + 3.26126i) q^{47} +(-0.928731 + 0.928731i) q^{48} +(5.43424 + 4.41238i) q^{49} +(2.27492 - 3.94027i) q^{51} +(0.108349 - 0.404362i) q^{52} +(2.54283 - 9.48998i) q^{53} +(2.80739 - 4.86254i) q^{54} +(-1.13746 - 2.38876i) q^{56} +(5.26806 - 5.26806i) q^{57} +(-2.19740 + 0.588792i) q^{58} +(-5.19615 - 9.00000i) q^{59} +(-12.4124 - 7.16629i) q^{61} +(2.44949 + 2.44949i) q^{62} +(2.18898 + 2.56637i) q^{63} +1.00000i q^{64} +(-6.00000 + 3.46410i) q^{66} +(-3.59815 - 0.964122i) q^{67} +(-0.896575 - 3.34607i) q^{68} +3.94027 q^{69} -6.00000 q^{71} +(-0.329973 - 1.23148i) q^{72} +(-9.22947 - 2.47303i) q^{73} +(4.56821 - 2.63746i) q^{74} -5.67232i q^{76} +(-2.53430 - 13.7241i) q^{77} +(-0.388792 - 0.388792i) q^{78} +(8.66025 + 5.00000i) q^{79} +(-1.77492 - 3.07425i) q^{81} +(-5.01910 + 1.34486i) q^{82} +(-10.1347 + 10.1347i) q^{83} +(-3.46410 - 0.274917i) q^{84} +(4.13746 - 7.16629i) q^{86} +(-0.773333 + 2.88612i) q^{87} +(-1.36525 + 5.09518i) q^{88} +(1.97014 - 3.41238i) q^{89} +(1.00000 - 0.476171i) q^{91} +(2.12132 - 2.12132i) q^{92} +(4.39480 - 1.17758i) q^{93} +(6.30026 + 10.9124i) q^{94} +(1.13746 + 0.656712i) q^{96} +(13.5129 + 13.5129i) q^{97} +(2.85554 - 6.39108i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.26867	−	0.339939i	−0.732467	−	0.196264i	−0.126739	−	0.991936i	$-0.540451\pi$
$3$	−1.26867	−	0.339939i	−0.732467	−	0.196264i	−0.605728	+	0.795672i	$0.707118\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.31342i			0.536203i
$7$	−2.49342	−	0.884806i	−0.942422	−	0.334425i
$7$	−2.49342	−	0.884806i	−0.942422	−	0.334425i
$8$	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	0.922697	+	0.385526i	$0.125980\pi$
$11$	2.63746	+	4.56821i	0.795224	+	1.37737i	−0.127473	+	0.991842i	$0.540687\pi$
$12$	1.26867	−	0.339939i	0.366234	−	0.0981320i
$13$	−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
$17$	−0.896575	+	3.34607i	−0.217451	+	0.811540i	0.767838	+	0.640644i	$0.221333\pi$
$17$	−0.896575	+	3.34607i	−0.217451	+	0.811540i	−0.985289	+	0.170896i	$0.945334\pi$
$18$	−0.329973	+	1.23148i	−0.0777753	+	0.290262i
$19$	−2.83616	+	4.91238i	−0.650660	+	1.12698i	0.332303	+	0.943173i	$0.392174\pi$
$19$	−2.83616	+	4.91238i	−0.650660	+	1.12698i	−0.982963	+	0.183804i	$0.941159\pi$
$20$		0			0
$21$	2.86254	+	1.97014i	0.624658	+	0.429919i
$22$	3.72993	−	3.72993i	0.795224	−	0.795224i
$23$	−2.89778	+	0.776457i	−0.604228	+	0.161903i	−0.547948	−	0.836512i	$-0.684591\pi$
$23$	−2.89778	+	0.776457i	−0.604228	+	0.161903i	−0.0562805	+	0.998415i	$0.517924\pi$
$24$	−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
$28$	2.60176	−	0.480443i	0.491687	−	0.0907953i
$29$		−	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	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−1.79315	−	6.69213i	−0.312148	−	1.16495i
$34$	3.46410			0.594089
$35$		0			0
$36$	1.27492			0.212486
$37$	1.36525	+	5.09518i	0.224446	+	0.837642i	0.982626	+	0.185597i	$0.0594220\pi$
$37$	1.36525	+	5.09518i	0.224446	+	0.837642i	−0.758180	+	0.652045i	$0.773911\pi$
$38$	5.47904	+	1.46811i	0.888818	+	0.238158i
$39$	0.476171	−	0.274917i	0.0762483	−	0.0440220i
$40$		0			0
$41$		−	5.19615i		−	0.811503i	−0.913984	−	0.405751i	$-0.867010\pi$
$41$		−	5.19615i		−	0.811503i	0.913984	−	0.405751i	$-0.132990\pi$
$42$	1.16213	−	3.27491i	0.179320	−	0.505330i
$43$	5.85125	+	5.85125i	0.892307	+	0.892307i	0.994740	−	0.102433i	$-0.0326626\pi$
$43$	5.85125	+	5.85125i	0.892307	+	0.892307i	−0.102433	+	0.994740i	$0.532663\pi$
$44$	−4.56821	−	2.63746i	−0.688684	−	0.397612i
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	−12.1712	+	3.26126i	−1.77535	+	0.475703i	−0.989723	−	0.142999i	$-0.954325\pi$
$47$	−12.1712	+	3.26126i	−1.77535	+	0.475703i	−0.785625	+	0.618702i	$0.787659\pi$
$48$	−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
$52$	0.108349	−	0.404362i	0.0150252	−	0.0560750i
$53$	2.54283	−	9.48998i	0.349285	−	1.30355i	−0.538241	−	0.842791i	$-0.680911\pi$
$53$	2.54283	−	9.48998i	0.349285	−	1.30355i	0.887526	−	0.460758i	$-0.152422\pi$
$54$	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
$58$	−2.19740	+	0.588792i	−0.288533	+	0.0773122i
$59$	−5.19615	−	9.00000i	−0.676481	−	1.17170i	−0.976034	−	0.217620i	$-0.930171\pi$
$59$	−5.19615	−	9.00000i	−0.676481	−	1.17170i	0.299552	−	0.954080i	$-0.403163\pi$
$60$		0			0
$61$	−12.4124	−	7.16629i	−1.58924	−	0.917549i	−0.993432	−	0.114424i	$-0.963498\pi$
$61$	−12.4124	−	7.16629i	−1.58924	−	0.917549i	−0.595810	−	0.803126i	$-0.703169\pi$
$62$	2.44949	+	2.44949i	0.311086	+	0.311086i
$63$	2.18898	+	2.56637i	0.275785	+	0.323333i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−6.00000	+	3.46410i	−0.738549	+	0.426401i
$67$	−3.59815	−	0.964122i	−0.439584	−	0.117786i	0.0322373	−	0.999480i	$-0.489737\pi$
$67$	−3.59815	−	0.964122i	−0.439584	−	0.117786i	−0.471822	+	0.881694i	$0.656403\pi$
$68$	−0.896575	−	3.34607i	−0.108726	−	0.405770i
$69$	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	$0.615871\pi$
$72$	−0.329973	−	1.23148i	−0.0388877	−	0.145131i
$73$	−9.22947	−	2.47303i	−1.08023	−	0.289446i	−0.325539	−	0.945529i	$-0.605546\pi$
$73$	−9.22947	−	2.47303i	−1.08023	−	0.289446i	−0.754689	+	0.656083i	$0.772212\pi$
$74$	4.56821	−	2.63746i	0.531044	−	0.306598i
$75$		0			0
$76$		−	5.67232i		−	0.650660i
$77$	−2.53430	−	13.7241i	−0.288810	−	1.56400i
$78$	−0.388792	−	0.388792i	−0.0440220	−	0.0440220i
$79$	8.66025	+	5.00000i	0.974355	+	0.562544i	0.900561	−	0.434730i	$-0.143156\pi$
$79$	8.66025	+	5.00000i	0.974355	+	0.562544i	0.0737937	+	0.997274i	$0.476489\pi$
$80$		0			0
$81$	−1.77492	−	3.07425i	−0.197213	−	0.341583i
$82$	−5.01910	+	1.34486i	−0.554267	+	0.148515i
$83$	−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
$87$	−0.773333	+	2.88612i	−0.0829100	+	0.309425i
$88$	−1.36525	+	5.09518i	−0.145536	+	0.543148i
$89$	1.97014	−	3.41238i	0.208834	−	0.361711i	−0.742513	−	0.669831i	$-0.766366\pi$
$89$	1.97014	−	3.41238i	0.208834	−	0.361711i	0.951348	+	0.308120i	$0.0996998\pi$
$90$		0			0
$91$	1.00000	−	0.476171i	0.104828	−	0.0499162i
$92$	2.12132	−	2.12132i	0.221163	−	0.221163i
$93$	4.39480	−	1.17758i	0.455720	−	0.122110i
$94$	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	$0.327945\pi$
$98$	2.85554	−	6.39108i	0.288453	−	0.645596i
$99$		−	6.72508i		−	0.675896i
$100$		0			0
$101$	3.41238	−	1.97014i	0.339544	−	0.196036i	−0.320526	−	0.947240i	$-0.603860\pi$
$101$	3.41238	−	1.97014i	0.339544	−	0.196036i	0.660070	+	0.751204i	$0.270526\pi$
$102$	−4.39480	−	1.17758i	−0.435150	−	0.116598i
$103$	1.23651	+	4.61474i	0.121837	+	0.454703i	0.999707	−	0.0241959i	$-0.00770256\pi$
$103$	1.23651	+	4.61474i	0.121837	+	0.454703i	−0.877870	+	0.478899i	$0.841036\pi$
$104$	−0.418627			−0.0410497
$105$		0			0
$106$	−9.82475			−0.954264
$107$	−1.76638	−	6.59220i	−0.170762	−	0.637292i	−0.997235	−	0.0743157i	$-0.976323\pi$
$107$	−1.76638	−	6.59220i	−0.170762	−	0.637292i	0.826473	−	0.562977i	$-0.190344\pi$
$108$	−5.42346	−	1.45321i	−0.521873	−	0.139835i
$109$	−7.64246	+	4.41238i	−0.732015	+	0.422629i	−0.819159	−	0.573567i	$-0.805559\pi$
$109$	−7.64246	+	4.41238i	−0.732015	+	0.422629i	0.0871440	+	0.996196i	$0.472226\pi$
$110$		0			0
$111$		−	6.92820i		−	0.657596i
$112$	−2.01297	+	1.71696i	−0.190208	+	0.162237i
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$	−6.45203	−	3.72508i	−0.604288	−	0.348886i
$115$		0			0
$116$	1.13746	+	1.97014i	0.105610	+	0.182923i
$117$	0.515529	−	0.138135i	0.0476606	−	0.0127706i
$118$	−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
$122$	−3.70954	+	13.8442i	−0.335846	+	1.25340i
$123$	−1.76638	+	6.59220i	−0.159269	+	0.594399i
$124$	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	$-0.472021\pi$
$127$	12.2152	−	12.2152i	1.08392	−	1.08392i	0.996139	−	0.0877853i	$-0.0279789\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−5.43424	−	9.41238i	−0.478458	−	0.828713i
$130$		0			0
$131$	7.91238	+	4.56821i	0.691307	+	0.399127i	0.804102	−	0.594492i	$-0.202647\pi$
$131$	7.91238	+	4.56821i	0.691307	+	0.399127i	−0.112794	+	0.993618i	$0.535980\pi$
$132$	4.89898	+	4.89898i	0.426401	+	0.426401i
$133$	11.4182	−	9.73914i	0.990086	−	0.844491i
$134$			3.72508i			0.321798i
$135$		0			0
$136$	−3.00000	+	1.73205i	−0.257248	+	0.148522i
$137$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$137$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$138$	−1.01982	−	3.80601i	−0.0868126	−	0.323989i
$139$	−4.41644			−0.374598			−0.187299	−	0.982303i	$-0.559973\pi$
$139$	−4.41644			−0.374598			−0.187299	+	0.982303i	$0.559973\pi$
$140$		0			0
$141$	16.5498			1.39375
$142$	1.55291	+	5.79555i	0.130318	+	0.486352i
$143$	−2.13298	−	0.571530i	−0.178369	−	0.0477937i
$144$	−1.10411	+	0.637459i	−0.0920092	+	0.0531216i
$145$		0			0
$146$			9.55505i			0.790782i
$147$	−5.39432	−	7.44516i	−0.444916	−	0.614066i
$148$	−3.72993	−	3.72993i	−0.306598	−	0.306598i
$149$	11.1066	+	6.41238i	0.909885	+	0.525322i	0.880394	−	0.474243i	$-0.157278\pi$
$149$	11.1066	+	6.41238i	0.909885	+	0.525322i	0.0294908	+	0.999565i	$0.490611\pi$
$150$		0			0
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$	−5.47904	+	1.46811i	−0.444409	+	0.119079i
$153$	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
$157$	2.58138	−	9.63383i	0.206016	−	0.768864i	−0.783121	−	0.621869i	$-0.786373\pi$
$157$	2.58138	−	9.63383i	0.206016	−	0.768864i	0.989137	−	0.146994i	$-0.0469599\pi$
$158$	2.58819	−	9.65926i	0.205905	−	0.768449i
$159$	−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
$163$	11.5911	−	3.10583i	0.907886	−	0.243267i	0.225486	−	0.974246i	$-0.427603\pi$
$163$	11.5911	−	3.10583i	0.907886	−	0.243267i	0.682400	+	0.730979i	$0.260936\pi$
$164$	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	$0.728652\pi$
$168$	0.631026	+	3.41722i	0.0486847	+	0.263644i
$169$			12.8248i			0.986519i
$170$		0			0
$171$	6.26287	−	3.61587i	0.478934	−	0.276513i
$172$	−7.99296	−	2.14171i	−0.609457	−	0.163304i
$173$	−1.22162	−	4.55915i	−0.0928781	−	0.346626i	0.903811	−	0.427932i	$-0.140758\pi$
$173$	−1.22162	−	4.55915i	−0.0928781	−	0.346626i	−0.996689	+	0.0813058i	$0.974091\pi$
$174$	2.98793			0.226514
$175$		0			0
$176$	5.27492			0.397612
$177$	3.53275	+	13.1844i	0.265538	+	0.991001i
$178$	−3.80601	−	1.01982i	−0.285273	−	0.0764386i
$179$	−8.50848	+	4.91238i	−0.635954	+	0.367168i	−0.783054	−	0.621953i	$-0.786339\pi$
$179$	−8.50848	+	4.91238i	−0.635954	+	0.367168i	0.147100	+	0.989122i	$0.453006\pi$
$180$		0			0
$181$			21.2608i			1.58030i	0.612913	+	0.790151i	$0.289998\pi$
$181$			21.2608i			1.58030i	−0.612913	+	0.790151i	$0.710002\pi$
$182$	−0.718765	−	0.842684i	−0.0532784	−	0.0624639i
$183$	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
$187$	−17.6502	+	4.72936i	−1.29071	+	0.345845i
$188$	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	−0.982356	−	0.187019i	$-0.940117\pi$
$191$	−4.54983	+	7.88054i	−0.329214	+	0.570216i	0.653142	+	0.757236i	$0.273451\pi$
$192$	0.339939	−	1.26867i	0.0245330	−	0.0915584i
$193$	2.73050	−	10.1904i	0.196546	−	0.733518i	−0.795316	−	0.606195i	$-0.792695\pi$
$193$	2.73050	−	10.1904i	0.196546	−	0.733518i	0.991861	−	0.127323i	$-0.0406384\pi$
$194$	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	−0.185420	−	0.982659i	$-0.559365\pi$
$197$	11.1898	−	11.1898i	0.797239	−	0.797239i	0.982659	+	0.185420i	$0.0593645\pi$
$198$	−6.49593	+	1.74058i	−0.461646	+	0.123698i
$199$	9.13642	+	15.8248i	0.647664	+	1.12179i	0.983679	+	0.179930i	$0.0575873\pi$
$199$	9.13642	+	15.8248i	0.647664	+	1.12179i	−0.336015	+	0.941857i	$0.609079\pi$
$200$		0			0
$201$	4.23713	+	2.44631i	0.298864	+	0.172549i
$202$	−2.78619	−	2.78619i	−0.196036	−	0.196036i
$203$	−2.01286	+	5.67231i	−0.141275	+	0.398118i
$204$			4.54983i			0.318552i
$205$		0			0
$206$	4.13746	−	2.38876i	0.288270	−	0.166433i
$207$	3.69443	+	0.989919i	0.256780	+	0.0688041i
$208$	0.108349	+	0.404362i	0.00751262	+	0.0280375i
$209$	−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	$0.564255\pi$
$212$	2.54283	+	9.48998i	0.174642	+	0.651775i
$213$	7.61202	+	2.03963i	0.521567	+	0.139753i
$214$	−5.91041	+	3.41238i	−0.404027	+	0.233265i
$215$		0			0
$216$			5.61478i			0.382037i
$217$	9.01277	−	1.66430i	0.611827	−	0.112980i
$218$	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
$222$	−6.69213	+	1.79315i	−0.449146	+	0.120348i
$223$	−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
$227$	−0.896575	+	3.34607i	−0.0595078	+	0.222086i	−0.989276	−	0.146060i	$-0.953341\pi$
$227$	−0.896575	+	3.34607i	−0.0595078	+	0.222086i	0.929768	+	0.368146i	$0.120007\pi$
$228$	−1.92824	+	7.19631i	−0.127701	+	0.476587i
$229$	−6.92820	+	12.0000i	−0.457829	+	0.792982i	−0.998846	−	0.0480291i	$-0.984706\pi$
$229$	−6.92820	+	12.0000i	−0.457829	+	0.792982i	0.541017	+	0.841011i	$0.318039\pi$
$230$		0			0
$231$	−1.45017	+	18.2728i	−0.0954139	+	1.20227i
$232$	1.60861	−	1.60861i	0.105610	−	0.105610i
$233$	−24.7755	+	6.63858i	−1.62310	+	0.434908i	−0.951910	−	0.306379i	$-0.900883\pi$
$233$	−24.7755	+	6.63858i	−1.62310	+	0.434908i	−0.671188	+	0.741287i	$0.734216\pi$
$234$	−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
$238$	−8.63744	−	3.06506i	−0.559882	−	0.198678i
$239$		−	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	−0.223022	−	0.974814i	$-0.571592\pi$
$241$	7.91238	−	4.56821i	0.509681	−	0.294264i	0.732702	+	0.680549i	$0.238259\pi$
$242$	16.2515	+	4.35457i	1.04468	+	0.279922i
$243$	−3.15291	−	11.7668i	−0.202259	−	0.754841i
$244$	14.3326			0.917549
$245$		0			0
$246$	6.82475			0.435130
$247$	−0.614588	−	2.29367i	−0.0391053	−	0.145943i
$248$	−3.34607	−	0.896575i	−0.212475	−	0.0569326i
$249$	16.3027	−	9.41238i	1.03314	−	0.596485i
$250$		0			0
$251$		−	19.5287i		−	1.23264i	−0.787495	−	0.616321i	$-0.788622\pi$
$251$		−	19.5287i		−	1.23264i	0.787495	−	0.616321i	$-0.211378\pi$
$252$	−3.17890	−	1.12805i	−0.200252	−	0.0710607i
$253$	−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
$257$	17.6502	−	4.72936i	1.10099	−	0.295009i	0.337823	−	0.941210i	$-0.390310\pi$
$257$	17.6502	−	4.72936i	1.10099	−	0.295009i	0.763168	+	0.646200i	$0.223643\pi$
$258$	−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
$262$	2.36468	−	8.82511i	0.146090	−	0.545217i
$263$	−4.87220	+	18.1833i	−0.300433	+	1.12123i	0.636373	+	0.771382i	$0.280434\pi$
$263$	−4.87220	+	18.1833i	−0.300433	+	1.12123i	−0.936806	+	0.349850i	$0.886233\pi$
$264$	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
$268$	3.59815	−	0.964122i	0.219792	−	0.0588931i
$269$	−3.22602	−	5.58762i	−0.196694	−	0.340683i	0.750761	−	0.660574i	$-0.229687\pi$
$269$	−3.22602	−	5.58762i	−0.196694	−	0.340683i	−0.947454	+	0.319891i	$0.896354\pi$
$270$		0			0
$271$	−6.82475	−	3.94027i	−0.414574	−	0.239354i	0.278179	−	0.960529i	$-0.410269\pi$
$271$	−6.82475	−	3.94027i	−0.414574	−	0.239354i	−0.692753	+	0.721175i	$0.743602\pi$
$272$	2.44949	+	2.44949i	0.148522	+	0.148522i
$273$	−1.43054	+	0.264164i	−0.0865802	+	0.0159879i
$274$		0			0
$275$		0			0
$276$	−3.41238	+	1.97014i	−0.205401	+	0.118588i
$277$	−14.5852	−	3.90808i	−0.876337	−	0.234814i	−0.207511	−	0.978233i	$-0.566536\pi$
$277$	−14.5852	−	3.90808i	−0.876337	−	0.234814i	−0.668826	+	0.743419i	$0.733203\pi$
$278$	1.14306	+	4.26596i	0.0685562	+	0.255855i
$279$	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	$0.580363\pi$
$282$	−4.28341	−	15.9859i	−0.255073	−	0.951947i
$283$	6.80330	+	1.82294i	0.404414	+	0.108362i	0.455291	−	0.890343i	$-0.349535\pi$
$283$	6.80330	+	1.82294i	0.404414	+	0.108362i	−0.0508774	+	0.998705i	$0.516202\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$			2.20822i			0.130575i
$287$	−4.59759	+	12.9562i	−0.271387	+	0.764778i
$288$	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
$292$	9.22947	−	2.47303i	0.540114	−	0.144723i
$293$	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
$297$	−7.66557	+	28.6083i	−0.444802	+	1.66002i
$298$	3.31929	−	12.3878i	0.192281	−	0.717604i
$299$	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
$303$	−4.99891	+	1.33945i	−0.287180	+	0.0769496i
$304$	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	$0.721777\pi$
$308$	9.05681	+	10.6183i	0.516060	+	0.605031i
$309$		−	6.27492i		−	0.356968i
$310$		0			0
$311$	22.6495	−	13.0767i	1.28434	−	0.741511i	0.306698	−	0.951807i	$-0.400776\pi$
$311$	22.6495	−	13.0767i	1.28434	−	0.741511i	0.977638	+	0.210296i	$0.0674426\pi$
$312$	0.531099	+	0.142308i	0.0300676	+	0.00805658i
$313$	5.16276	+	19.2677i	0.291816	+	1.08907i	0.943713	+	0.330765i	$0.107307\pi$
$313$	5.16276	+	19.2677i	0.291816	+	1.08907i	−0.651897	+	0.758308i	$0.726026\pi$
$314$	−9.97368			−0.562847
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−4.65874	−	17.3867i	−0.261661	−	0.976532i	−0.964262	−	0.264949i	$-0.914645\pi$
$317$	−4.65874	−	17.3867i	−0.261661	−	0.976532i	0.702601	−	0.711584i	$-0.252022\pi$
$318$	12.4644	+	3.33982i	0.698967	+	0.187288i
$319$	10.3923	−	6.00000i	0.581857	−	0.335936i
$320$		0			0
$321$			8.96379i			0.500310i
$322$	−1.44133	−	7.80529i	−0.0803222	−	0.434972i
$323$	−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
$327$	11.1957	−	2.99988i	0.619124	−	0.165894i
$328$	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	−0.938318	−	0.345773i	$-0.887617\pi$
$331$	−3.08762	+	5.34792i	−0.169711	+	0.293948i	0.768607	+	0.639721i	$0.220950\pi$
$332$	3.70954	−	13.8442i	0.203588	−	0.759800i
$333$	1.74058	−	6.49593i	0.0953832	−	0.355975i
$334$	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	$0.696582\pi$
$337$	−25.5968	+	25.5968i	−1.39435	+	1.39435i	−0.815281	+	0.579065i	$0.803418\pi$
$338$	12.3878	−	3.31929i	0.673805	−	0.180546i
$339$	−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
$343$	−9.64572	−	15.8101i	−0.520820	−	0.853667i
$344$			8.27492i			0.446154i
$345$		0			0
$346$	−4.08762	+	2.35999i	−0.219752	+	0.126874i
$347$	4.99891	+	1.33945i	0.268355	+	0.0719056i	0.390487	−	0.920608i	$-0.372306\pi$
$347$	4.99891	+	1.33945i	0.268355	+	0.0719056i	−0.122132	+	0.992514i	$0.538973\pi$
$348$	−0.773333	−	2.88612i	−0.0414550	−	0.154712i
$349$	3.94027			0.210918			0.105459	−	0.994424i	$-0.466369\pi$
$349$	3.94027			0.210918			0.105459	+	0.994424i	$0.466369\pi$
$350$		0			0
$351$	−2.35050			−0.125460
$352$	−1.36525	−	5.09518i	−0.0727680	−	0.271574i
$353$	−0.919891	−	0.246484i	−0.0489609	−	0.0131190i	0.234255	−	0.972175i	$-0.424735\pi$
$353$	−0.919891	−	0.246484i	−0.0489609	−	0.0131190i	−0.283216	+	0.959056i	$0.591401\pi$
$354$	11.8208	−	6.82475i	0.628269	−	0.362731i
$355$		0			0
$356$			3.94027i			0.208834i
$357$	−9.15869	+	7.81187i	−0.484729	+	0.413448i
$358$	6.94715	+	6.94715i	0.367168	+	0.367168i
$359$	−11.8208	−	6.82475i	−0.623879	−	0.360197i	0.154499	−	0.987993i	$-0.450624\pi$
$359$	−11.8208	−	6.82475i	−0.623879	−	0.360197i	−0.778378	+	0.627796i	$0.783957\pi$
$360$		0			0
$361$	−6.58762	−	11.4101i	−0.346717	−	0.600532i
$362$	20.5363	−	5.50269i	1.07937	−	0.289215i
$363$	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
$367$	1.56156	−	5.82782i	0.0815128	−	0.304210i	−0.913118	−	0.407695i	$-0.866333\pi$
$367$	1.56156	−	5.82782i	0.0815128	−	0.304210i	0.994631	+	0.103485i	$0.0329994\pi$
$368$	−0.776457	+	2.89778i	−0.0404756	+	0.151057i
$369$	−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
$373$	21.7815	−	5.83633i	1.12780	−	0.302194i	0.353765	−	0.935334i	$-0.384901\pi$
$373$	21.7815	−	5.83633i	1.12780	−	0.302194i	0.774037	+	0.633141i	$0.218235\pi$
$374$	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
$378$	−11.3024	+	9.64034i	−0.581332	+	0.495846i
$379$		−	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
$382$	8.78961	+	2.35517i	0.449715	+	0.120501i
$383$	−5.42413	−	20.2431i	−0.277160	−	1.03438i	−0.954380	−	0.298595i	$-0.903482\pi$
$383$	−5.42413	−	20.2431i	−0.277160	−	1.03438i	0.677220	−	0.735781i	$-0.263185\pi$
$384$	−1.31342			−0.0670254
$385$		0			0
$386$	−10.5498			−0.536972
$387$	−2.73050	−	10.1904i	−0.138799	−	0.518005i
$388$	−18.4589	−	4.94606i	−0.937111	−	0.251098i
$389$	2.68439	−	1.54983i	0.136104	−	0.0785797i	−0.430402	−	0.902637i	$-0.641628\pi$
$389$	2.68439	−	1.54983i	0.136104	−	0.0785797i	0.566506	+	0.824058i	$0.308295\pi$
$390$		0			0
$391$		−	10.3923i		−	0.525561i
$392$	0.722565	+	6.96261i	0.0364951	+	0.351665i
$393$	−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
$397$	−1.61745	+	0.433394i	−0.0811775	+	0.0217514i	−0.299179	−	0.954197i	$-0.596713\pi$
$397$	−1.61745	+	0.433394i	−0.0811775	+	0.0217514i	0.218002	+	0.975948i	$0.430046\pi$
$398$	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	−0.546579	−	0.837408i	$-0.684070\pi$
$401$	9.04983	−	15.6748i	0.451927	−	0.782761i	0.998506	+	0.0546470i	$0.0174034\pi$
$402$	1.26630	−	4.72590i	0.0631574	−	0.235707i
$403$	0.375330	−	1.40075i	0.0186965	−	0.0697764i
$404$	−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
$408$	4.39480	−	1.17758i	0.217575	−	0.0582991i
$409$	−8.89834	−	15.4124i	−0.439995	−	0.762093i	0.557694	−	0.830047i	$-0.311686\pi$
$409$	−8.89834	−	15.4124i	−0.439995	−	0.762093i	−0.997688	+	0.0679538i	$0.978353\pi$
$410$		0			0
$411$		0			0
$412$	−3.37822	−	3.37822i	−0.166433	−	0.166433i
$413$	4.99291	+	27.0383i	0.245685	+	1.33047i
$414$		−	3.82475i		−	0.187976i
$415$		0			0
$416$	0.362541	−	0.209313i	0.0177751	−	0.0102624i
$417$	5.60301	+	1.50132i	0.274381	+	0.0735200i
$418$	7.74413	+	28.9015i	0.378778	+	1.41362i
$419$	27.4093			1.33903			0.669515	−	0.742798i	$-0.266502\pi$
$419$	27.4093			1.33903			0.669515	+	0.742798i	$0.266502\pi$
$420$		0			0
$421$	34.8248			1.69725			0.848627	−	0.528991i	$-0.177430\pi$
$421$	34.8248			1.69725			0.848627	+	0.528991i	$0.177430\pi$
$422$	1.50756	+	5.62628i	0.0733867	+	0.273883i
$423$	15.5172	+	4.15783i	0.754474	+	0.202161i
$424$	8.50848	−	4.91238i	0.413209	−	0.238566i
$425$		0			0
$426$		−	7.88054i		−	0.381814i
$427$	24.6084	+	28.8511i	1.19089	+	1.39620i
$428$	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	0.896367	+	0.443313i	$0.146197\pi$
$431$	17.2749	+	29.9210i	0.832103	+	1.44125i	−0.0642636	+	0.997933i	$0.520470\pi$
$432$	5.42346	−	1.45321i	0.260936	−	0.0699177i
$433$	−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
$437$	4.40432	−	16.4371i	0.210687	−	0.786295i
$438$	3.24814	−	12.1222i	0.155202	−	0.579222i
$439$	−10.3923	+	18.0000i	−0.495998	+	0.859093i	−0.999989	−	0.00461537i	$-0.998531\pi$
$439$	−10.3923	+	18.0000i	−0.495998	+	0.859093i	0.503992	+	0.863708i	$0.331864\pi$
$440$		0			0
$441$	−3.18729	−	8.33585i	−0.151776	−	0.396945i
$442$	−1.02542	+	1.02542i	−0.0487743	+	0.0487743i
$443$	−10.7945	+	2.89237i	−0.512860	+	0.137421i	−0.505962	−	0.862556i	$-0.668862\pi$
$443$	−10.7945	+	2.89237i	−0.512860	+	0.137421i	−0.00689820	+	0.999976i	$0.502196\pi$
$444$	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
$448$	0.884806	−	2.49342i	0.0418031	−	0.117803i
$449$			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
$452$	−5.79555	−	1.55291i	−0.272600	−	0.0730429i
$453$	0.679878	+	2.53734i	0.0319435	+	0.119215i
$454$	3.46410			0.162578
$455$		0			0
$456$	7.45017			0.348886
$457$	8.94216	+	33.3726i	0.418296	+	1.56110i	0.778140	+	0.628091i	$0.216163\pi$
$457$	8.94216	+	33.3726i	0.418296	+	1.56110i	−0.359844	+	0.933013i	$0.617170\pi$
$458$	13.3843	+	3.58630i	0.625405	+	0.167577i
$459$	−16.8443	+	9.72508i	−0.786226	+	0.453928i
$460$		0			0
$461$			15.7611i			0.734067i	0.930208	+	0.367034i	$0.119627\pi$
$461$			15.7611i			0.734067i	−0.930208	+	0.367034i	$0.880373\pi$
$462$	18.0255	−	3.32861i	0.838624	−	0.154861i
$463$	−22.3091	−	22.3091i	−1.03679	−	1.03679i	−0.999297	−	0.0374951i	$-0.988062\pi$
$463$	−22.3091	−	22.3091i	−1.03679	−	1.03679i	−0.0374951	−	0.999297i	$-0.511938\pi$
$464$	−1.97014	−	1.13746i	−0.0914613	−	0.0528052i
$465$		0			0
$466$	12.8248	+	22.2131i	0.594095	+	1.02900i
$467$	12.9243	−	3.46306i	0.598066	−	0.160251i	0.0529290	−	0.998598i	$-0.483144\pi$
$467$	12.9243	−	3.46306i	0.598066	−	0.160251i	0.545137	+	0.838347i	$0.316478\pi$
$468$	−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
$472$	2.68973	−	10.0382i	0.123805	−	0.462045i
$473$	−11.2973	+	42.1622i	−0.519451	+	1.93862i
$474$	−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
$478$	−4.39480	+	1.17758i	−0.201014	+	0.0538614i
$479$	−3.94027	−	6.82475i	−0.180036	−	0.311831i	0.761857	−	0.647745i	$-0.224288\pi$
$479$	−3.94027	−	6.82475i	−0.180036	−	0.311831i	−0.941892	+	0.335915i	$0.890955\pi$
$480$		0			0
$481$	−1.91238	−	1.10411i	−0.0871968	−	0.0503431i
$482$	−6.46043	−	6.46043i	−0.294264	−	0.294264i
$483$	−9.82473	−	3.48638i	−0.447041	−	0.158636i
$484$		−	16.8248i		−	0.764761i
$485$		0			0
$486$	−10.5498	+	6.09095i	−0.478550	+	0.276291i
$487$	8.78961	+	2.35517i	0.398295	+	0.106723i	0.452406	−	0.891812i	$-0.350566\pi$
$487$	8.78961	+	2.35517i	0.398295	+	0.106723i	−0.0541110	+	0.998535i	$0.517232\pi$
$488$	−3.70954	−	13.8442i	−0.167923	−	0.626698i
$489$	−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	$0.644627\pi$
$492$	−1.76638	−	6.59220i	−0.0796344	−	0.297200i
$493$	7.61202	+	2.03963i	0.342828	+	0.0918605i
$494$	−2.05645	+	1.18729i	−0.0925241	+	0.0534188i
$495$		0			0
$496$			3.46410i			0.155543i
$497$	14.9605	+	5.30883i	0.671070	+	0.238134i
$498$	−13.3111	−	13.3111i	−0.596485	−	0.596485i
$499$	−3.46410	−	2.00000i	−0.155074	−	0.0895323i	0.420455	−	0.907314i	$-0.361871\pi$
$499$	−3.46410	−	2.00000i	−0.155074	−	0.0895323i	−0.575529	+	0.817781i	$0.695204\pi$
$500$		0			0
$501$	−1.13746	−	1.97014i	−0.0508179	−	0.0880192i
$502$	−18.8633	+	5.05441i	−0.841910	+	0.225589i
$503$	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
$507$	4.35964	−	16.2704i	0.193618	−	0.722593i
$508$	−4.47108	+	16.6863i	−0.198372	+	0.740334i
$509$	−0.714256	+	1.23713i	−0.0316588	+	0.0548347i	−0.881421	−	0.472332i	$-0.843412\pi$
$509$	−0.714256	+	1.23713i	−0.0316588	+	0.0548347i	0.849762	+	0.527167i	$0.176746\pi$
$510$		0			0
$511$	20.8248	+	14.3326i	0.921233	+	0.634036i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−30.7636	+	8.24309i	−1.35825	+	0.363941i
$514$	−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
$518$	−13.7241	+	2.53430i	−0.603002	+	0.111351i
$519$			6.19934i			0.272121i
$520$		0			0
$521$	−23.7371	+	13.7046i	−1.03994	+	0.600411i	−0.919817	−	0.392348i	$-0.871663\pi$
$521$	−23.7371	+	13.7046i	−1.03994	+	0.600411i	−0.120125	+	0.992759i	$0.538330\pi$
$522$	2.80150	+	0.750661i	0.122619	+	0.0328555i
$523$	8.28588	+	30.9233i	0.362316	+	1.35218i	0.871023	+	0.491242i	$0.163457\pi$
$523$	8.28588	+	30.9233i	0.362316	+	1.35218i	−0.508707	+	0.860940i	$0.669876\pi$
$524$	−9.13642			−0.399127
$525$		0			0
$526$	18.8248			0.820798
$527$	−3.10583	−	11.5911i	−0.135292	−	0.504917i
$528$	−6.69213	−	1.79315i	−0.291238	−	0.0780369i
$529$	−12.1244	+	7.00000i	−0.527146	+	0.304348i
$530$		0			0
$531$			13.2493i			0.574972i
$532$	−5.01890	+	14.1435i	−0.217597	+	0.613197i
$533$	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
$537$	12.4644	−	3.33982i	0.537877	−	0.144124i
$538$	−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	−0.750394	−	0.660990i	$-0.770136\pi$
$541$	4.58762	−	7.94600i	0.197237	−	0.341625i	0.947632	+	0.319365i	$0.103470\pi$
$542$	−2.03963	+	7.61202i	−0.0876098	+	0.326964i
$543$	7.22737	−	26.9729i	0.310156	−	1.15752i
$544$	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	−0.486141	−	0.873881i	$-0.661596\pi$
$547$	9.06847	−	9.06847i	0.387740	−	0.387740i	0.873881	+	0.486141i	$0.161596\pi$
$548$		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
$553$	−17.1696	−	20.1297i	−0.730125	−	0.856003i
$554$			15.0997i			0.641523i
$555$		0			0
$556$	3.82475	−	2.20822i	0.162206	−	0.0936494i
$557$	−19.4878	−	5.22174i	−0.825724	−	0.221252i	−0.178877	−	0.983871i	$-0.557246\pi$
$557$	−19.4878	−	5.22174i	−0.825724	−	0.221252i	−0.646848	+	0.762619i	$0.723913\pi$
$558$	−1.14306	−	4.26596i	−0.0483896	−	0.180592i
$559$	−3.46410			−0.146516
$560$		0			0
$561$	24.0000			1.01328
$562$	2.16750	+	8.08923i	0.0914306	+	0.341224i
$563$	−6.23218	−	1.66991i	−0.262655	−	0.0703783i	0.125088	−	0.992146i	$-0.460079\pi$
$563$	−6.23218	−	1.66991i	−0.262655	−	0.0703783i	−0.387743	+	0.921767i	$0.626745\pi$
$564$	−14.3326	+	8.27492i	−0.603510	+	0.348437i
$565$		0			0
$566$		−	7.04329i		−	0.296052i
$567$	1.70549	+	9.23583i	0.0716240	+	0.387868i
$568$	−4.24264	−	4.24264i	−0.178017	−	0.178017i
$569$	−8.50848	−	4.91238i	−0.356694	−	0.205938i	0.310935	−	0.950431i	$-0.399358\pi$
$569$	−8.50848	−	4.91238i	−0.356694	−	0.205938i	−0.667630	+	0.744494i	$0.732691\pi$
$570$		0			0
$571$	14.8248	+	25.6772i	0.620397	+	1.07456i	0.989412	+	0.145135i	$0.0463617\pi$
$571$	14.8248	+	25.6772i	0.620397	+	1.07456i	−0.369015	+	0.929423i	$0.620305\pi$
$572$	2.13298	−	0.571530i	0.0891843	−	0.0238969i
$573$	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
$577$	5.81285	−	21.6938i	0.241992	−	0.903126i	−0.732880	−	0.680358i	$-0.761824\pi$
$577$	5.81285	−	21.6938i	0.241992	−	0.903126i	0.974871	−	0.222768i	$-0.0715092\pi$
$578$	1.29410	−	4.82963i	0.0538273	−	0.200886i
$579$	−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
$583$	50.0589	−	13.4132i	2.07323	−	0.555519i
$584$	−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	$0.818802\pi$
$588$	8.39419	+	3.75054i	0.346171	+	0.154670i
$589$		−	19.6495i		−	0.809644i
$590$		0			0
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$	5.09518	+	1.36525i	0.209411	+	0.0561114i
$593$	8.56215	+	31.9544i	0.351605	+	1.31221i	0.884703	+	0.466155i	$0.154361\pi$
$593$	8.56215	+	31.9544i	0.351605	+	1.31221i	−0.533098	+	0.846054i	$0.678972\pi$
$594$	29.6175			1.21522
$595$		0			0
$596$	−12.8248			−0.525322
$597$	−6.21166	−	23.1822i	−0.254226	−	0.948785i
$598$	−1.21309	−	0.325046i	−0.0496068	−	0.0132921i
$599$	2.51176	−	1.45017i	0.102628	−	0.0592522i	−0.447808	−	0.894130i	$-0.647795\pi$
$599$	2.51176	−	1.45017i	0.102628	−	0.0592522i	0.550435	+	0.834878i	$0.314462\pi$
$600$		0			0
$601$			6.92820i			0.282607i	0.989966	+	0.141304i	$0.0451294\pi$
$601$			6.92820i			0.282607i	−0.989966	+	0.141304i	$0.954871\pi$
$602$	−16.6572	+	14.2077i	−0.678896	+	0.579062i
$603$	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
$607$	21.0519	−	5.64083i	0.854469	−	0.228954i	0.195109	−	0.980782i	$-0.437494\pi$
$607$	21.0519	−	5.64083i	0.854469	−	0.228954i	0.659360	+	0.751827i	$0.270827\pi$
$608$	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
$612$	−1.14306	+	4.26596i	−0.0462054	+	0.172441i
$613$	−3.66882	+	13.6922i	−0.148182	+	0.553024i	0.851411	+	0.524500i	$0.175748\pi$
$613$	−3.66882	+	13.6922i	−0.148182	+	0.553024i	−0.999593	+	0.0285247i	$0.990919\pi$
$614$	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	−0.995520	−	0.0945520i	$-0.969858\pi$
$617$	−22.3796	+	22.3796i	−0.900968	+	0.900968i	0.0945520	+	0.995520i	$0.469858\pi$
$618$	−6.06110	+	1.62407i	−0.243813	+	0.0653296i
$619$	−1.10411	−	1.91238i	−0.0443780	−	0.0768649i	0.842983	−	0.537940i	$-0.180797\pi$
$619$	−1.10411	−	1.91238i	−0.0443780	−	0.0768649i	−0.887361	+	0.461075i	$0.847464\pi$
$620$		0			0
$621$	−14.5876	−	8.42217i	−0.585381	−	0.337970i
$622$	−18.4932	−	18.4932i	−0.741511	−	0.741511i
$623$	−7.93166	+	6.76528i	−0.317775	+	0.271045i
$624$		−	0.549834i		−	0.0220110i
$625$		0			0
$626$	17.2749	−	9.97368i	0.690445	−	0.398628i
$627$	37.9599	+	10.1713i	1.51597	+	0.406204i
$628$	2.58138	+	9.63383i	0.103008	+	0.384432i
$629$	−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	$0.751121\pi$
$632$	2.58819	+	9.65926i	0.102953	+	0.384225i
$633$	7.38969	+	1.98006i	0.293714	+	0.0787004i
$634$	−15.5885	+	9.00000i	−0.619097	+	0.357436i
$635$		0			0
$636$		−	12.9041i		−	0.511679i
$637$	−2.91473	+	0.302485i	−0.115486	+	0.0119849i
$638$	−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	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$	8.65836	−	2.32000i	0.341718	−	0.0915631i
$643$	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
$647$	−1.34486	+	5.01910i	−0.0528720	+	0.197321i	−0.987310	−	0.158805i	$-0.949236\pi$
$647$	−1.34486	+	5.01910i	−0.0528720	+	0.197321i	0.934438	+	0.356126i	$0.115903\pi$
$648$	0.918765	−	3.42888i	0.0360925	−	0.134699i
$649$	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
$653$	28.4699	−	7.62850i	1.11412	−	0.298526i	0.345615	−	0.938376i	$-0.387670\pi$
$653$	28.4699	−	7.62850i	1.11412	−	0.298526i	0.768500	+	0.639850i	$0.221004\pi$
$654$	−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
$658$	−6.05384	−	32.7836i	−0.236003	−	1.27804i
$659$			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	−0.657624	−	0.753346i	$-0.728439\pi$
$661$	−8.58762	+	4.95807i	−0.334020	+	0.192846i	0.323605	+	0.946192i	$0.395105\pi$
$662$	5.96483	+	1.59827i	0.231830	+	0.0621186i
$663$	0.492968	+	1.83978i	0.0191453	+	0.0714512i
$664$	−14.3326			−0.556212
$665$		0			0
$666$	−6.72508			−0.260592
$667$	1.76638	+	6.59220i	0.0683943	+	0.255251i
$668$	−1.67303	−	0.448288i	−0.0647316	−	0.0173448i
$669$	9.91613	−	5.72508i	0.383380	−	0.221344i
$670$		0			0
$671$		−	75.6032i		−	2.91863i
$672$	−2.25509	−	2.64389i	−0.0869921	−	0.101990i
$673$	12.8689	+	12.8689i	0.496059	+	0.496059i	0.910209	−	0.414150i	$-0.135921\pi$
$673$	12.8689	+	12.8689i	0.496059	+	0.496059i	−0.414150	+	0.910209i	$0.635921\pi$
$674$	31.3495	+	18.0997i	1.20754	+	0.697173i
$675$		0			0
$676$	−6.41238	−	11.1066i	−0.246630	−	0.427175i
$677$	29.8214	−	7.99062i	1.14613	−	0.307104i	0.364716	−	0.931119i	$-0.381166\pi$
$677$	29.8214	−	7.99062i	1.14613	−	0.307104i	0.781413	+	0.624014i	$0.214499\pi$
$678$	−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
$682$	−4.72936	+	17.6502i	−0.181097	+	0.675862i
$683$	7.97803	−	29.7744i	0.305271	−	1.13929i	−0.627441	−	0.778664i	$-0.715898\pi$
$683$	7.97803	−	29.7744i	0.305271	−	1.13929i	0.932712	−	0.360622i	$-0.117436\pi$
$684$	−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
$688$	7.99296	−	2.14171i	0.304729	−	0.0816518i
$689$	2.05645	+	3.56188i	0.0783446	+	0.135697i
$690$		0			0
$691$	35.4743	+	20.4811i	1.34950	+	0.779137i	0.988179	−	0.153303i	$-0.0489911\pi$
$691$	35.4743	+	20.4811i	1.34950	+	0.779137i	0.361325	+	0.932440i	$0.382324\pi$
$692$	3.33753	+	3.33753i	0.126874	+	0.126874i
$693$	−5.95039	+	16.7684i	−0.226037	+	0.636980i
$694$		−	5.17525i		−	0.196450i
$695$		0			0
$696$	−2.58762	+	1.49397i	−0.0980836	+	0.0566286i
$697$	17.3867	+	4.65874i	0.658567	+	0.176462i
$698$	−1.01982	−	3.80601i	−0.0386007	−	0.144060i
$699$	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	$0.549947\pi$
$702$	0.608353	+	2.27041i	0.0229608	+	0.0856909i
$703$	−28.9015	−	7.74413i	−1.09004	−	0.292076i
$704$	−4.56821	+	2.63746i	−0.172171	+	0.0994030i
$705$		0			0
$706$			0.952341i			0.0358418i
$707$	−10.2517	+	1.89308i	−0.385553	+	0.0711965i
$708$	−9.65166	−	9.65166i	−0.362731	−	0.362731i
$709$	−11.4101	−	6.58762i	−0.428515	−	0.247403i	0.270199	−	0.962805i	$-0.412911\pi$
$709$	−11.4101	−	6.58762i	−0.428515	−	0.247403i	−0.698714	+	0.715401i	$0.746244\pi$
$710$		0			0
$711$	−6.37459	−	11.0411i	−0.239066	−	0.414074i
$712$	3.80601	−	1.01982i	0.142636	−	0.0382193i
$713$	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
$717$	−1.54667	+	5.77224i	−0.0577613	+	0.215568i
$718$	−3.53275	+	13.1844i	−0.131841	+	0.492038i
$719$	19.5287	−	33.8248i	0.728299	−	1.26145i	−0.229303	−	0.973355i	$-0.573645\pi$
$719$	19.5287	−	33.8248i	0.728299	−	1.26145i	0.957602	−	0.288095i	$-0.0930220\pi$
$720$		0			0
$721$	1.00000	−	12.6005i	0.0372419	−	0.469268i
$722$	−9.31631	+	9.31631i	−0.346717	+	0.346717i
$723$	−11.5911	+	3.10583i	−0.431078	+	0.115507i
$724$	−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	$0.739095\pi$
$728$	1.04381	+	0.370403i	0.0386862	+	0.0137281i
$729$			26.6495i			0.987019i
$730$		0			0
$731$	−24.8248	+	14.3326i	−0.918177	+	0.530110i
$732$	−18.1833	−	4.87220i	−0.672075	−	0.180082i
$733$	8.17753	+	30.5189i	0.302044	+	1.12724i	0.935460	+	0.353432i	$0.114985\pi$
$733$	8.17753	+	30.5189i	0.302044	+	1.12724i	−0.633416	+	0.773811i	$0.718348\pi$
$734$	−6.03341			−0.222697
$735$		0			0
$736$	3.00000			0.110581
$737$	−5.08567	−	18.9800i	−0.187333	−	0.699136i
$738$	6.39893	+	1.71459i	0.235548	+	0.0631149i
$739$	−3.61587	+	2.08762i	−0.133012	+	0.0767945i	−0.565029	−	0.825071i	$-0.691135\pi$
$739$	−3.61587	+	2.08762i	−0.133012	+	0.0767945i	0.432017	+	0.901865i	$0.357802\pi$
$740$		0			0
$741$			3.11884i			0.114573i
$742$	24.4972	+	8.69300i	0.899320	+	0.319130i
$743$	−10.6066	−	10.6066i	−0.389118	−	0.389118i	0.485254	−	0.874373i	$-0.338727\pi$
$743$	−10.6066	−	10.6066i	−0.389118	−	0.389118i	−0.874373	+	0.485254i	$0.838727\pi$
$744$	3.94027	+	2.27492i	0.144457	+	0.0834025i
$745$		0			0
$746$	−11.2749	−	19.5287i	−0.412804	−	0.714998i
$747$	17.6502	−	4.72936i	0.645788	−	0.173038i
$748$	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	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−3.26126	+	12.1712i	−0.118926	+	0.443837i
$753$	−6.63858	+	24.7755i	−0.241923	+	0.902870i
$754$	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	−0.625790	−	0.779992i	$-0.715223\pi$
$757$	4.24264	−	4.24264i	0.154201	−	0.154201i	0.779992	+	0.625790i	$0.215223\pi$
$758$	−24.9448	+	6.68394i	−0.906036	+	0.242772i
$759$	10.3923	+	18.0000i	0.377217	+	0.653359i
$760$		0			0
$761$	−43.9124	−	25.3528i	−1.59182	−	0.919039i	−0.992994	−	0.118161i	$-0.962300\pi$
$761$	−43.9124	−	25.3528i	−1.59182	−	0.919039i	−0.598828	−	0.800878i	$-0.704367\pi$
$762$	16.0438	+	16.0438i	0.581204	+	0.581204i
$763$	22.9599	−	4.23979i	0.831205	−	0.153491i
$764$		−	9.09967i		−	0.329214i
$765$		0			0
$766$	−18.1495	+	10.4786i	−0.655768	+	0.378608i
$767$	4.20226	+	1.12599i	0.151735	+	0.0406572i
$768$	0.339939	+	1.26867i	0.0122665	+	0.0457792i
$769$	17.9693			0.647990			0.323995	−	0.946059i	$-0.394974\pi$
$769$	17.9693			0.647990			0.323995	+	0.946059i	$0.394974\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	2.73050	+	10.1904i	0.0982728	+	0.366759i
$773$	32.2476	+	8.64071i	1.15986	+	0.310785i	0.786912	−	0.617066i	$-0.211679\pi$
$773$	32.2476	+	8.64071i	1.15986	+	0.310785i	0.372953	+	0.927850i	$0.378345\pi$
$774$	−9.13642	+	5.27492i	−0.328402	+	0.189603i
$775$		0			0
$776$			19.1101i			0.686013i
$777$	−6.13011	+	17.2749i	−0.219917	+	0.619733i
$778$	−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
$782$	−10.0382	+	2.68973i	−0.358965	+	0.0961844i
$783$	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
$787$	8.22221	−	30.6857i	0.293090	−	1.09383i	−0.649632	−	0.760249i	$-0.725077\pi$
$787$	8.22221	−	30.6857i	0.293090	−	1.09383i	0.942722	−	0.333578i	$-0.108256\pi$
$788$	−4.09575	+	15.2855i	−0.145905	+	0.544525i
$789$	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
$793$	5.79555	−	1.55291i	0.205806	−	0.0551456i
$794$	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	$0.828922\pi$
$798$	12.7916	+	14.9970i	0.452818	+	0.530887i
$799$		−	43.6495i		−	1.54421i
$800$		0			0
$801$	−4.35050	+	2.51176i	−0.153717	+	0.0887487i
$802$	−17.4829	−	4.68454i	−0.617344	−	0.165417i
$803$	−13.0450	−	48.6847i	−0.460349	−	1.71805i
$804$	−4.89261			−0.172549
$805$		0			0
$806$	−1.45017			−0.0510799
$807$	2.19330	+	8.18550i	0.0772078	+	0.288143i
$808$	3.80601	+	1.01982i	0.133895	+	0.0358771i
$809$	−5.28247	+	3.04983i	−0.185722	+	0.107226i	−0.589978	−	0.807419i	$-0.700864\pi$
$809$	−5.28247	+	3.04983i	−0.185722	+	0.107226i	0.404256	+	0.914646i	$0.367530\pi$
$810$		0			0
$811$		−	17.0170i		−	0.597547i	−0.954324	−	0.298773i	$-0.903423\pi$
$811$		−	17.0170i		−	0.597547i	0.954324	−	0.298773i	$-0.0965774\pi$
$812$	−1.09297	−	5.91880i	−0.0383557	−	0.207709i
$813$	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
$817$	−45.3386	+	12.1484i	−1.58620	+	0.425020i
$818$	−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	0.0478946	+	0.998852i	$0.484749\pi$
$821$	−24.0997	+	41.7419i	−0.841084	+	1.45680i	−0.888979	+	0.457948i	$0.848584\pi$
$822$		0			0
$823$	−4.87220	+	18.1833i	−0.169834	+	0.633830i	0.827540	+	0.561407i	$0.189740\pi$
$823$	−4.87220	+	18.1833i	−0.169834	+	0.633830i	−0.997374	+	0.0724232i	$0.976927\pi$
$824$	−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	−0.953225	−	0.302262i	$-0.902258\pi$
$827$	−18.7201	+	18.7201i	−0.650963	+	0.650963i	0.302262	+	0.953225i	$0.402258\pi$
$828$	−3.69443	+	0.989919i	−0.128390	+	0.0344020i
$829$	−5.67232	−	9.82475i	−0.197008	−	0.341228i	0.750549	−	0.660815i	$-0.229789\pi$
$829$	−5.67232	−	9.82475i	−0.197008	−	0.341228i	−0.947557	+	0.319587i	$0.896456\pi$
$830$		0			0
$831$	17.1752	+	9.91613i	0.595803	+	0.343987i
$832$	−0.296014	−	0.296014i	−0.0102624	−	0.0102624i
$833$	−19.6363	+	14.2273i	−0.680358	+	0.492946i
$834$		−	5.80066i		−	0.200861i
$835$		0			0
$836$	25.9124	−	14.9605i	0.896198	−	0.517420i
$837$	−18.7874	−	5.03407i	−0.649388	−	0.174003i
$838$	−7.09404	−	26.4753i	−0.245060	−	0.914575i
$839$	2.51176			0.0867156			0.0433578	−	0.999060i	$-0.486194\pi$
$839$	2.51176			0.0867156			0.0433578	+	0.999060i	$0.486194\pi$
$840$		0			0
$841$	23.8248			0.821543
$842$	−9.01331	−	33.6381i	−0.310619	−	1.15925i
$843$	10.6246	+	2.84685i	0.365930	+	0.0980507i
$844$	5.04438	−	2.91238i	0.173635	−	0.100248i
$845$		0			0
$846$		−	16.0646i		−	0.552313i
$847$	33.8678	−	28.8874i	1.16371	−	0.992583i
$848$	−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
$852$	−7.61202	+	2.03963i	−0.260784	+	0.0698767i
$853$	−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
$857$	4.07927	−	15.2240i	0.139345	−	0.520043i	−0.860597	−	0.509287i	$-0.829909\pi$
$857$	4.07927	−	15.2240i	0.139345	−	0.520043i	0.999942	−	0.0107567i	$-0.00342404\pi$
$858$	0.750661	−	2.80150i	0.0256271	−	0.0956418i
$859$	−1.25588	+	2.17525i	−0.0428501	+	0.0742185i	−0.886655	−	0.462431i	$-0.846977\pi$
$859$	−1.25588	+	2.17525i	−0.0428501	+	0.0742185i	0.843805	+	0.536650i	$0.180310\pi$
$860$		0			0
$861$	10.2371	−	14.8742i	0.348880	−	0.506911i
$862$	24.4304	−	24.4304i	0.832103	−	0.832103i
$863$	−37.6711	+	10.0939i	−1.28234	+	0.343602i	−0.834746	−	0.550635i	$-0.814385\pi$
$863$	−37.6711	+	10.0939i	−1.28234	+	0.343602i	−0.447593	+	0.894237i	$0.647719\pi$
$864$	−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
$868$	−6.97314	+	5.94772i	−0.236684	+	0.201879i
$869$			52.7492i			1.78939i
$870$		0			0
$871$	1.35050	−	0.779710i	0.0457598	−	0.0264195i
$872$	−8.52406	−	2.28401i	−0.288661	−	0.0773465i
$873$	−6.30582	−	23.5336i	−0.213420	−	0.796492i
$874$	−17.0170			−0.575608
$875$		0			0
$876$	−12.5498			−0.424020
$877$	3.66882	+	13.6922i	0.123887	+	0.462354i	0.999798	−	0.0201202i	$-0.00640488\pi$
$877$	3.66882	+	13.6922i	0.123887	+	0.462354i	−0.875910	+	0.482474i	$0.839738\pi$
$878$	20.0764	+	5.37945i	0.677545	+	0.181548i
$879$	−5.36878	+	3.09967i	−0.181085	+	0.104549i
$880$		0			0
$881$			31.3495i			1.05619i	0.849184	+	0.528097i	$0.177094\pi$
$881$			31.3495i			1.05619i	−0.849184	+	0.528097i	$0.822906\pi$
$882$	−7.22688	+	5.23617i	−0.243342	+	0.176311i
$883$	−6.43444	−	6.43444i	−0.216536	−	0.216536i	0.590501	−	0.807037i	$-0.298930\pi$
$883$	−6.43444	−	6.43444i	−0.216536	−	0.216536i	−0.807037	+	0.590501i	$0.798930\pi$
$884$	1.25588	+	0.725083i	0.0422398	+	0.0243872i
$885$		0			0
$886$	5.58762	+	9.67805i	0.187720	+	0.325140i
$887$	−21.4562	+	5.74918i	−0.720430	+	0.193039i	−0.600363	−	0.799727i	$-0.704977\pi$
$887$	−21.4562	+	5.74918i	−0.720430	+	0.193039i	−0.120066	+	0.992766i	$0.538311\pi$
$888$	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
$892$	2.25633	−	8.42075i	0.0755476	−	0.281947i
$893$	18.4989	−	69.0388i	0.619042	−	2.31030i
$894$	−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
$898$	21.6852	−	5.81053i	0.723644	−	0.193900i
$899$	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
$903$	5.22169	+	28.2772i	0.173767	+	0.941006i
$904$			6.00000i			0.199557i
$905$		0			0
$906$	2.27492	−	1.31342i	0.0755791	−	0.0436356i
$907$	−26.9729	−	7.22737i	−0.895621	−	0.239981i	−0.218486	−	0.975840i	$-0.570112\pi$
$907$	−26.9729	−	7.22737i	−0.895621	−	0.239981i	−0.677135	+	0.735859i	$0.736779\pi$
$908$	−0.896575	−	3.34607i	−0.0297539	−	0.111043i
$909$	−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	$0.605535\pi$
$912$	−1.92824	−	7.19631i	−0.0638506	−	0.238294i
$913$	−73.0270	−	19.5675i	−2.41684	−	0.647591i
$914$	29.9210	−	17.2749i	0.989700	−	0.571403i
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$	−15.6869	−	18.3914i	−0.518026	−	0.607336i
$918$	13.7533	+	13.7533i	0.453928	+	0.453928i
$919$	−29.1413	−	16.8248i	−0.961284	−	0.554997i	−0.0647157	−	0.997904i	$-0.520614\pi$
$919$	−29.1413	−	16.8248i	−0.961284	−	0.554997i	−0.896568	+	0.442906i	$0.853947\pi$
$920$		0			0
$921$	−2.03779	−	3.52956i	−0.0671475	−	0.116303i
$922$	15.2240	−	4.07927i	0.501377	−	0.134344i
$923$	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
$927$	1.57645	−	5.88341i	0.0517775	−	0.193236i
$928$	−0.588792	+	2.19740i	−0.0193280	+	0.0721332i
$929$	6.53835	−	11.3248i	0.214516	−	0.371553i	−0.738607	−	0.674137i	$-0.764516\pi$
$929$	6.53835	−	11.3248i	0.214516	−	0.371553i	0.953123	+	0.302584i	$0.0978492\pi$
$930$		0			0
$931$	−37.0876	+	14.1808i	−1.21550	+	0.464757i
$932$	18.1369	−	18.1369i	0.594095	−	0.594095i
$933$	−33.1800	+	8.89056i	−1.08627	+	0.291064i
$934$	−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	$0.415360\pi$
$938$	3.29597	−	9.28818i	0.107617	−	0.303270i
$939$		−	26.1993i		−	0.854983i
$940$		0			0
$941$	−4.35050	+	2.51176i	−0.141822	+	0.0818811i	−0.569232	−	0.822177i	$-0.692759\pi$
$941$	−4.35050	+	2.51176i	−0.141822	+	0.0818811i	0.427410	+	0.904058i	$0.359426\pi$
$942$	12.6533	+	3.39044i	0.412267	+	0.110467i
$943$	4.03459	+	15.0573i	0.131384	+	0.490333i
$944$	−10.3923			−0.338241
$945$		0			0
$946$	43.6495			1.41917
$947$	4.87220	+	18.1833i	0.158325	+	0.590878i	0.998798	+	0.0490237i	$0.0156110\pi$
$947$	4.87220	+	18.1833i	0.158325	+	0.590878i	−0.840472	+	0.541855i	$0.817722\pi$
$948$	12.6867	+	3.39939i	0.412045	+	0.110407i
$949$	3.46410	−	2.00000i	0.112449	−	0.0649227i
$950$		0			0
$951$			23.6416i			0.766632i
$952$	9.01277	−	1.66430i	0.292106	−	0.0539404i
$953$	27.7886	+	27.7886i	0.900161	+	0.900161i	0.995450	−	0.0952888i	$-0.0303775\pi$
$953$	27.7886	+	27.7886i	0.900161	+	0.900161i	−0.0952888	+	0.995450i	$0.530377\pi$
$954$	10.8476	+	6.26287i	0.351204	+	0.202768i
$955$		0			0
$956$	2.27492	+	3.94027i	0.0735761	+	0.127438i
$957$	−15.2240	+	4.07927i	−0.492123	+	0.131864i
$958$	−5.57239	+	5.57239i	−0.180036	+	0.180036i
$959$		0			0
$960$		0			0
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−0.571530	+	2.13298i	−0.0184269	+	0.0687700i
$963$	−2.25198	+	8.40451i	−0.0725691	+	0.270832i
$964$	−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	−0.949311	−	0.314337i	$-0.898218\pi$
$967$	−19.7455	+	19.7455i	−0.634974	+	0.634974i	0.314337	+	0.949311i	$0.398218\pi$
$968$	−16.2515	+	4.35457i	−0.522342	+	0.139961i
$969$	12.9041	+	22.3505i	0.414538	+	0.718001i
$970$		0			0
$971$	41.7371	+	24.0969i	1.33941	+	0.773308i	0.986720	−	0.162433i	$-0.0519342\pi$
$971$	41.7371	+	24.0969i	1.33941	+	0.773308i	0.352689	+	0.935741i	$0.385267\pi$
$972$	8.61390	+	8.61390i	0.276291	+	0.276291i
$973$	11.0120	+	3.90769i	0.353029	+	0.125275i
$974$		−	9.09967i		−	0.291572i
$975$		0			0
$976$	−12.4124	+	7.16629i	−0.397310	+	0.229387i
$977$	18.9800	+	5.08567i	0.607223	+	0.162705i	0.549313	−	0.835617i	$-0.314890\pi$
$977$	18.9800	+	5.08567i	0.607223	+	0.162705i	0.0579102	+	0.998322i	$0.481556\pi$
$978$	4.07927	+	15.2240i	0.130441	+	0.486811i
$979$	20.7846			0.664279
$980$		0			0
$981$	11.2508			0.359211
$982$	5.03407	+	18.7874i	0.160644	+	0.599531i
$983$	33.6274	+	9.01044i	1.07255	+	0.287388i	0.751539	−	0.659688i	$-0.229312\pi$
$983$	33.6274	+	9.01044i	1.07255	+	0.287388i	0.321008	+	0.947076i	$0.395978\pi$
$984$	−5.91041	+	3.41238i	−0.188417	+	0.108783i
$985$		0			0
$986$		−	7.88054i		−	0.250968i
$987$	−41.2656	−	14.6434i	−1.31350	−	0.466104i
$988$	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	0.985146	−	0.171719i	$-0.0549322\pi$
$991$	10.8248	+	18.7490i	0.343860	+	0.595582i	−0.641286	+	0.767302i	$0.721599\pi$
$992$	3.34607	−	0.896575i	0.106238	−	0.0284663i
$993$	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
$997$	−7.85248	+	29.3059i	−0.248691	+	0.928126i	0.722802	+	0.691055i	$0.242854\pi$
$997$	−7.85248	+	29.3059i	−0.248691	+	0.928126i	−0.971492	+	0.237071i	$0.923813\pi$
$998$	−1.03528	+	3.86370i	−0.0327711	+	0.122303i
$999$	−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.243.1	yes	16
5.2	odd	4	inner	350.2.o.d.257.3	yes	16
5.3	odd	4	inner	350.2.o.d.257.2	yes	16
5.4	even	2	inner	350.2.o.d.243.4	yes	16
7.3	odd	6	inner	350.2.o.d.143.3	yes	16
35.3	even	12	inner	350.2.o.d.157.4	yes	16
35.17	even	12	inner	350.2.o.d.157.1	yes	16
35.24	odd	6	inner	350.2.o.d.143.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.d.143.2	✓	16	35.24	odd	6	inner
350.2.o.d.143.3	yes	16	7.3	odd	6	inner
350.2.o.d.157.1	yes	16	35.17	even	12	inner
350.2.o.d.157.4	yes	16	35.3	even	12	inner
350.2.o.d.243.1	yes	16	1.1	even	1	trivial
350.2.o.d.243.4	yes	16	5.4	even	2	inner
350.2.o.d.257.2	yes	16	5.3	odd	4	inner
350.2.o.d.257.3	yes	16	5.2	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

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

Groups

Database

Properties

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