LMFDB - Embedded newform 350.2.o.d.157.3

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			157.3
Root			$2.23460 + 0.0811201i$ of defining polynomial
Character	$\chi$	$=$	350.157
Dual form			350.2.o.d.243.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-2.94170 + 0.788227i) q^{3} +(-0.866025 - 0.500000i) q^{4} +3.04547i q^{6} +(-1.71696 - 2.01297i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(5.43424 - 3.13746i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-2.94170 + 0.788227i) q^{3} +(-0.866025 - 0.500000i) q^{4} +3.04547i q^{6} +(-1.71696 - 2.01297i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(5.43424 - 3.13746i) q^{9} +(-1.13746 + 1.97014i) q^{11} +(2.94170 + 0.788227i) q^{12} +(3.37822 + 3.37822i) q^{13} +(-2.38876 + 1.13746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.896575 + 3.34607i) q^{17} +(-1.62407 - 6.06110i) q^{18} +(3.70219 + 6.41238i) q^{19} +(6.63746 + 4.56821i) q^{21} +(1.60861 + 1.60861i) q^{22} +(2.89778 + 0.776457i) q^{23} +(1.52274 - 2.63746i) q^{24} +(4.13746 - 2.38876i) q^{26} +(-7.05246 + 7.05246i) q^{27} +(0.480443 + 2.60176i) q^{28} -5.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(0.965926 - 0.258819i) q^{32} +(1.79315 - 6.69213i) q^{33} +3.46410 q^{34} -6.27492 q^{36} +(0.588792 - 2.19740i) q^{37} +(7.15208 - 1.91639i) q^{38} +(-12.6005 - 7.27492i) q^{39} +5.19615i q^{41} +(6.13045 - 5.22895i) q^{42} +(-0.512711 + 0.512711i) q^{43} +(1.97014 - 1.13746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-0.459945 - 0.123242i) q^{47} +(-2.15348 - 2.15348i) q^{48} +(-1.10411 + 6.91238i) q^{49} +(-5.27492 - 9.13642i) q^{51} +(-1.23651 - 4.61474i) q^{52} +(3.31929 + 12.3878i) q^{53} +(4.98684 + 8.63746i) q^{54} +(2.63746 + 0.209313i) q^{56} +(-15.9451 - 15.9451i) q^{57} +(-5.09518 - 1.36525i) q^{58} +(-5.19615 + 9.00000i) q^{59} +(-1.08762 + 0.627940i) q^{61} +(-2.44949 + 2.44949i) q^{62} +(-15.6460 - 5.55208i) q^{63} -1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(10.8907 - 2.91816i) q^{67} +(0.896575 - 3.34607i) q^{68} -9.13642 q^{69} -6.00000 q^{71} +(-1.62407 + 6.06110i) q^{72} +(0.808725 - 0.216697i) q^{73} +(-1.97014 - 1.13746i) q^{74} -7.40437i q^{76} +(5.91880 - 1.09297i) q^{77} +(-10.2883 + 10.2883i) q^{78} +(8.66025 - 5.00000i) q^{79} +(5.77492 - 10.0025i) q^{81} +(5.01910 + 1.34486i) q^{82} +(0.888041 + 0.888041i) q^{83} +(-3.46410 - 7.27492i) q^{84} +(0.362541 + 0.627940i) q^{86} +(4.15783 + 15.5172i) q^{87} +(-0.588792 - 2.19740i) q^{88} +(-4.56821 - 7.91238i) q^{89} +(1.00000 - 12.6005i) q^{91} +(-2.12132 - 2.12132i) q^{92} +(10.1904 + 2.73050i) q^{93} +(-0.238085 + 0.412376i) q^{94} +(-2.63746 + 1.52274i) q^{96} +(-1.18406 + 1.18406i) q^{97} +(6.39108 + 2.85554i) q^{98} +14.2749i 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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
$3$	−2.94170	+	0.788227i	−1.69839	+	0.455083i	−0.972534	−	0.232761i	$-0.925224\pi$
$3$	−2.94170	+	0.788227i	−1.69839	+	0.455083i	−0.725859	+	0.687844i	$0.758557\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			3.04547i			1.24331i
$7$	−1.71696	−	2.01297i	−0.648949	−	0.760832i
$7$	−1.71696	−	2.01297i	−0.648949	−	0.760832i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	5.43424	−	3.13746i	1.81141	−	1.04582i
$10$		0			0
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	−0.984980	−	0.172666i	$-0.944762\pi$
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	0.642024	+	0.766685i	$0.278095\pi$
$12$	2.94170	+	0.788227i	0.849196	+	0.227542i
$13$	3.37822	+	3.37822i	0.936950	+	0.936950i	0.998127	−	0.0611771i	$-0.0194854\pi$
$13$	3.37822	+	3.37822i	0.936950	+	0.936950i	−0.0611771	+	0.998127i	$0.519485\pi$
$14$	−2.38876	+	1.13746i	−0.638424	+	0.303999i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.896575	+	3.34607i	0.217451	+	0.811540i	0.985289	+	0.170896i	$0.0546661\pi$
$17$	0.896575	+	3.34607i	0.217451	+	0.811540i	−0.767838	+	0.640644i	$0.778667\pi$
$18$	−1.62407	−	6.06110i	−0.382797	−	1.42862i
$19$	3.70219	+	6.41238i	0.849340	+	1.47110i	0.881798	+	0.471627i	$0.156333\pi$
$19$	3.70219	+	6.41238i	0.849340	+	1.47110i	−0.0324583	+	0.999473i	$0.510334\pi$
$20$		0			0
$21$	6.63746	+	4.56821i	1.44841	+	0.996866i
$22$	1.60861	+	1.60861i	0.342957	+	0.342957i
$23$	2.89778	+	0.776457i	0.604228	+	0.161903i	0.547948	−	0.836512i	$-0.315409\pi$
$23$	2.89778	+	0.776457i	0.604228	+	0.161903i	0.0562805	+	0.998415i	$0.482076\pi$
$24$	1.52274	−	2.63746i	0.310827	−	0.538369i
$25$		0			0
$26$	4.13746	−	2.38876i	0.811422	−	0.468475i
$27$	−7.05246	+	7.05246i	−1.35725	+	1.35725i
$28$	0.480443	+	2.60176i	0.0907953	+	0.491687i
$29$		−	5.27492i		−	0.979528i	−0.871855	−	0.489764i	$-0.837083\pi$
$29$		−	5.27492i		−	0.979528i	0.871855	−	0.489764i	$-0.162917\pi$
$30$		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	$0.767359\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	1.79315	−	6.69213i	0.312148	−	1.16495i
$34$	3.46410			0.594089
$35$		0			0
$36$	−6.27492			−1.04582
$37$	0.588792	−	2.19740i	0.0967968	−	0.361251i	−0.900489	−	0.434879i	$-0.856791\pi$
$37$	0.588792	−	2.19740i	0.0967968	−	0.361251i	0.997286	+	0.0736283i	$0.0234579\pi$
$38$	7.15208	−	1.91639i	1.16022	−	0.310880i
$39$	−12.6005	−	7.27492i	−2.01770	−	1.16492i
$40$		0			0
$41$			5.19615i			0.811503i	0.913984	+	0.405751i	$0.132990\pi$
$41$			5.19615i			0.811503i	−0.913984	+	0.405751i	$0.867010\pi$
$42$	6.13045	−	5.22895i	0.945950	−	0.806845i
$43$	−0.512711	+	0.512711i	−0.0781877	+	0.0781877i	−0.745119	−	0.666931i	$-0.767607\pi$
$43$	−0.512711	+	0.512711i	−0.0781877	+	0.0781877i	0.666931	+	0.745119i	$0.267607\pi$
$44$	1.97014	−	1.13746i	0.297009	−	0.171478i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−0.459945	−	0.123242i	−0.0670899	−	0.0179767i	0.225118	−	0.974332i	$-0.427723\pi$
$47$	−0.459945	−	0.123242i	−0.0670899	−	0.0179767i	−0.292208	+	0.956355i	$0.594390\pi$
$48$	−2.15348	−	2.15348i	−0.310827	−	0.310827i
$49$	−1.10411	+	6.91238i	−0.157730	+	0.987482i
$50$		0			0
$51$	−5.27492	−	9.13642i	−0.738636	−	1.27936i
$52$	−1.23651	−	4.61474i	−0.171474	−	0.639949i
$53$	3.31929	+	12.3878i	0.455940	+	1.70159i	0.685311	+	0.728251i	$0.259666\pi$
$53$	3.31929	+	12.3878i	0.455940	+	1.70159i	−0.229371	+	0.973339i	$0.573667\pi$
$54$	4.98684	+	8.63746i	0.678623	+	1.17541i
$55$		0			0
$56$	2.63746	+	0.209313i	0.352445	+	0.0279707i
$57$	−15.9451	−	15.9451i	−2.11199	−	2.11199i
$58$	−5.09518	−	1.36525i	−0.669030	−	0.179266i
$59$	−5.19615	+	9.00000i	−0.676481	+	1.17170i	0.299552	+	0.954080i	$0.403163\pi$
$59$	−5.19615	+	9.00000i	−0.676481	+	1.17170i	−0.976034	+	0.217620i	$0.930171\pi$
$60$		0			0
$61$	−1.08762	+	0.627940i	−0.139256	+	0.0803995i	−0.568009	−	0.823022i	$-0.692286\pi$
$61$	−1.08762	+	0.627940i	−0.139256	+	0.0803995i	0.428753	+	0.903422i	$0.358953\pi$
$62$	−2.44949	+	2.44949i	−0.311086	+	0.311086i
$63$	−15.6460	−	5.55208i	−1.97121	−	0.699497i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−6.00000	−	3.46410i	−0.738549	−	0.426401i
$67$	10.8907	−	2.91816i	1.33051	−	0.356510i	0.477608	−	0.878573i	$-0.341504\pi$
$67$	10.8907	−	2.91816i	1.33051	−	0.356510i	0.852907	+	0.522063i	$0.174837\pi$
$68$	0.896575	−	3.34607i	0.108726	−	0.405770i
$69$	−9.13642			−1.09990
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.62407	+	6.06110i	−0.191398	+	0.714308i
$73$	0.808725	−	0.216697i	0.0946541	−	0.0253625i	−0.211181	−	0.977447i	$-0.567731\pi$
$73$	0.808725	−	0.216697i	0.0946541	−	0.0253625i	0.305835	+	0.952084i	$0.401064\pi$
$74$	−1.97014	−	1.13746i	−0.229024	−	0.132227i
$75$		0			0
$76$		−	7.40437i		−	0.849340i
$77$	5.91880	−	1.09297i	0.674510	−	0.124555i
$78$	−10.2883	+	10.2883i	−1.16492	+	1.16492i
$79$	8.66025	−	5.00000i	0.974355	−	0.562544i	0.0737937	−	0.997274i	$-0.476489\pi$
$79$	8.66025	−	5.00000i	0.974355	−	0.562544i	0.900561	+	0.434730i	$0.143156\pi$
$80$		0			0
$81$	5.77492	−	10.0025i	0.641657	−	1.11138i
$82$	5.01910	+	1.34486i	0.554267	+	0.148515i
$83$	0.888041	+	0.888041i	0.0974752	+	0.0974752i	0.754163	−	0.656688i	$-0.228043\pi$
$83$	0.888041	+	0.888041i	0.0974752	+	0.0974752i	−0.656688	+	0.754163i	$0.728043\pi$
$84$	−3.46410	−	7.27492i	−0.377964	−	0.793759i
$85$		0			0
$86$	0.362541	+	0.627940i	0.0390938	+	0.0677125i
$87$	4.15783	+	15.5172i	0.445766	+	1.66362i
$88$	−0.588792	−	2.19740i	−0.0627654	−	0.234244i
$89$	−4.56821	−	7.91238i	−0.484230	−	0.838710i	0.515606	−	0.856826i	$-0.327567\pi$
$89$	−4.56821	−	7.91238i	−0.484230	−	0.838710i	−0.999836	+	0.0181154i	$0.994233\pi$
$90$		0			0
$91$	1.00000	−	12.6005i	0.104828	−	1.32089i
$92$	−2.12132	−	2.12132i	−0.221163	−	0.221163i
$93$	10.1904	+	2.73050i	1.05669	+	0.283139i
$94$	−0.238085	+	0.412376i	−0.0245566	+	0.0425333i
$95$		0			0
$96$	−2.63746	+	1.52274i	−0.269184	+	0.155414i
$97$	−1.18406	+	1.18406i	−0.120223	+	0.120223i	−0.764658	−	0.644436i	$-0.777092\pi$
$97$	−1.18406	+	1.18406i	−0.120223	+	0.120223i	0.644436	+	0.764658i	$0.277092\pi$
$98$	6.39108	+	2.85554i	0.645596	+	0.288453i
$99$			14.2749i			1.43468i
$100$		0			0
$101$	−7.91238	−	4.56821i	−0.787311	−	0.454554i	0.0517042	−	0.998662i	$-0.483535\pi$
$101$	−7.91238	−	4.56821i	−0.787311	−	0.454554i	−0.839015	+	0.544108i	$0.816868\pi$
$102$	−10.1904	+	2.73050i	−1.00900	+	0.270360i
$103$	−0.108349	+	0.404362i	−0.0106759	+	0.0398430i	−0.971058	−	0.238842i	$-0.923232\pi$
$103$	−0.108349	+	0.404362i	−0.0106759	+	0.0398430i	0.960382	+	0.278685i	$0.0898987\pi$
$104$	−4.77753			−0.468475
$105$		0			0
$106$	12.8248			1.24565
$107$	−4.09575	+	15.2855i	−0.395951	+	1.47771i	0.424204	+	0.905567i	$0.360554\pi$
$107$	−4.09575	+	15.2855i	−0.395951	+	1.47771i	−0.820155	+	0.572142i	$0.806113\pi$
$108$	9.63383	−	2.58138i	0.927016	−	0.248393i
$109$	11.9726	+	6.91238i	1.14677	+	0.662086i	0.948097	−	0.317981i	$-0.103005\pi$
$109$	11.9726	+	6.91238i	1.14677	+	0.662086i	0.198669	+	0.980067i	$0.436338\pi$
$110$		0			0
$111$			6.92820i			0.657596i
$112$	0.884806	−	2.49342i	0.0836063	−	0.235606i
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	−0.877920	−	0.478806i	$-0.841070\pi$
$113$	−4.24264	+	4.24264i	−0.399114	+	0.399114i	0.478806	+	0.877920i	$0.341070\pi$
$114$	−19.5287	+	11.2749i	−1.82903	+	1.05599i
$115$		0			0
$116$	−2.63746	+	4.56821i	−0.244882	+	0.424148i
$117$	28.9571	+	7.75903i	2.67708	+	0.717322i
$118$	7.34847	+	7.34847i	0.676481	+	0.676481i
$119$	5.19615	−	7.54983i	0.476331	−	0.692092i
$120$		0			0
$121$	2.91238	+	5.04438i	0.264761	+	0.458580i
$122$	0.325046	+	1.21309i	0.0294283	+	0.109828i
$123$	−4.09575	−	15.2855i	−0.369301	−	1.37825i
$124$	1.73205	+	3.00000i	0.155543	+	0.269408i
$125$		0			0
$126$	−9.41238	+	13.6759i	−0.838521	+	1.21834i
$127$	−6.87667	−	6.87667i	−0.610206	−	0.610206i	0.332794	−	0.943000i	$-0.392009\pi$
$127$	−6.87667	−	6.87667i	−0.610206	−	0.610206i	−0.943000	+	0.332794i	$0.892009\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	1.10411	−	1.91238i	0.0972115	−	0.168375i
$130$		0			0
$131$	−3.41238	+	1.97014i	−0.298141	+	0.172132i	−0.641607	−	0.767033i	$-0.721732\pi$
$131$	−3.41238	+	1.97014i	−0.298141	+	0.172132i	0.343467	+	0.939165i	$0.388399\pi$
$132$	−4.89898	+	4.89898i	−0.426401	+	0.426401i
$133$	6.55143	−	18.4622i	0.568081	−	1.60087i
$134$		−	11.2749i		−	0.974004i
$135$		0			0
$136$	−3.00000	−	1.73205i	−0.257248	−	0.148522i
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$	−2.36468	+	8.82511i	−0.201295	+	0.751243i
$139$	21.7370			1.84370			0.921852	−	0.387542i	$-0.126676\pi$
$139$	21.7370			1.84370			0.921852	+	0.387542i	$0.126676\pi$
$140$		0			0
$141$	1.45017			0.122126
$142$	−1.55291	+	5.79555i	−0.130318	+	0.486352i
$143$	−10.4981	+	2.81297i	−0.877899	+	0.235232i
$144$	5.43424	+	3.13746i	0.452853	+	0.261455i
$145$		0			0
$146$		−	0.837253i		−	0.0692916i
$147$	−2.20055	−	21.2044i	−0.181499	−	1.74891i
$148$	−1.60861	+	1.60861i	−0.132227	+	0.132227i
$149$	−8.50848	+	4.91238i	−0.697042	+	0.402438i	−0.806245	−	0.591582i	$-0.798504\pi$
$149$	−8.50848	+	4.91238i	−0.697042	+	0.402438i	0.109203	+	0.994020i	$0.465170\pi$
$150$		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	$0.192599\pi$
$152$	−7.15208	−	1.91639i	−0.580110	−	0.155440i
$153$	15.3703	+	15.3703i	1.24262	+	1.24262i
$154$	0.476171	−	6.00000i	0.0383709	−	0.483494i
$155$		0			0
$156$	7.27492	+	12.6005i	0.582460	+	1.00885i
$157$	−1.45321	−	5.42346i	−0.115979	−	0.432839i	0.883379	−	0.468659i	$-0.155263\pi$
$157$	−1.45321	−	5.42346i	−0.115979	−	0.432839i	−0.999358	+	0.0358194i	$0.988596\pi$
$158$	−2.58819	−	9.65926i	−0.205905	−	0.768449i
$159$	−19.5287	−	33.8248i	−1.54873	−	2.68248i
$160$		0			0
$161$	−3.41238	−	7.16629i	−0.268933	−	0.564783i
$162$	−8.16697	−	8.16697i	−0.641657	−	0.641657i
$163$	−11.5911	−	3.10583i	−0.907886	−	0.243267i	−0.225486	−	0.974246i	$-0.572397\pi$
$163$	−11.5911	−	3.10583i	−0.907886	−	0.243267i	−0.682400	+	0.730979i	$0.739064\pi$
$164$	2.59808	−	4.50000i	0.202876	−	0.351391i
$165$		0			0
$166$	1.08762	−	0.627940i	0.0844160	−	0.0487376i
$167$	−1.22474	+	1.22474i	−0.0947736	+	0.0947736i	−0.752904	−	0.658130i	$-0.771348\pi$
$167$	−1.22474	+	1.22474i	−0.0947736	+	0.0947736i	0.658130	+	0.752904i	$0.271348\pi$
$168$	−7.92361	+	1.46318i	−0.611319	+	0.112887i
$169$			9.82475i			0.755750i
$170$		0			0
$171$	40.2371	+	23.2309i	3.07701	+	1.77651i
$172$	0.700376	−	0.187665i	0.0534032	−	0.0143093i
$173$	4.60612	−	17.1903i	0.350197	−	1.30695i	−0.536226	−	0.844075i	$-0.680150\pi$
$173$	4.60612	−	17.1903i	0.350197	−	1.30695i	0.886422	−	0.462877i	$-0.153183\pi$
$174$	16.0646			1.21786
$175$		0			0
$176$	−2.27492			−0.171478
$177$	8.19149	−	30.5711i	0.615710	−	2.29786i
$178$	−8.82511	+	2.36468i	−0.661470	+	0.177240i
$179$	11.1066	+	6.41238i	0.830143	+	0.479283i	0.853902	−	0.520434i	$-0.174230\pi$
$179$	11.1066	+	6.41238i	0.830143	+	0.479283i	−0.0237584	+	0.999718i	$0.507563\pi$
$180$		0			0
$181$		−	8.18408i		−	0.608318i	−0.952621	−	0.304159i	$-0.901625\pi$
$181$		−	8.18408i		−	0.608318i	0.952621	−	0.304159i	$-0.0983754\pi$
$182$	−11.9124	−	4.22718i	−0.883002	−	0.313340i
$183$	2.70451	−	2.70451i	0.199923	−	0.199923i
$184$	−2.59808	+	1.50000i	−0.191533	+	0.110581i
$185$		0			0
$186$	5.27492	−	9.13642i	0.386776	−	0.669915i
$187$	−7.61202	−	2.03963i	−0.556646	−	0.149153i
$188$	0.336703	+	0.336703i	0.0245566	+	0.0245566i
$189$	26.3052	+	2.08762i	1.91342	+	0.151852i
$190$		0			0
$191$	10.5498	+	18.2728i	0.763359	+	1.32218i	0.941110	+	0.338101i	$0.109785\pi$
$191$	10.5498	+	18.2728i	0.763359	+	1.32218i	−0.177750	+	0.984076i	$0.556882\pi$
$192$	0.788227	+	2.94170i	0.0568854	+	0.212299i
$193$	1.17758	+	4.39480i	0.0847643	+	0.316345i	0.995269	−	0.0971530i	$-0.0309736\pi$
$193$	1.17758	+	4.39480i	0.0847643	+	0.316345i	−0.910505	+	0.413498i	$0.864307\pi$
$194$	0.837253	+	1.45017i	0.0601113	+	0.104116i
$195$		0			0
$196$	4.41238	−	5.43424i	0.315170	−	0.388160i
$197$	4.82583	+	4.82583i	0.343826	+	0.343826i	0.857804	−	0.513978i	$-0.171829\pi$
$197$	4.82583	+	4.82583i	0.343826	+	0.343826i	−0.513978	+	0.857804i	$0.671829\pi$
$198$	13.7885	+	3.69462i	0.979907	+	0.262565i
$199$	−3.94027	+	6.82475i	−0.279318	+	0.483794i	−0.971216	−	0.238202i	$-0.923442\pi$
$199$	−3.94027	+	6.82475i	−0.279318	+	0.483794i	0.691897	+	0.721996i	$0.256775\pi$
$200$		0			0
$201$	−29.7371	+	17.1687i	−2.09750	+	1.21099i
$202$	−6.46043	+	6.46043i	−0.454554	+	0.454554i
$203$	−10.6183	+	9.05681i	−0.745256	+	0.635664i
$204$			10.5498i			0.738636i
$205$		0			0
$206$	0.362541	+	0.209313i	0.0252595	+	0.0145836i
$207$	18.1833	−	4.87220i	1.26383	−	0.338642i
$208$	−1.23651	+	4.61474i	−0.0857369	+	0.319974i
$209$	−16.8443			−1.16515
$210$		0			0
$211$	16.8248			1.15826			0.579132	−	0.815234i	$-0.303392\pi$
$211$	16.8248			1.15826			0.579132	+	0.815234i	$0.303392\pi$
$212$	3.31929	−	12.3878i	0.227970	−	0.850795i
$213$	17.6502	−	4.72936i	1.20937	−	0.324051i
$214$	13.7046	+	7.91238i	0.936830	+	0.540879i
$215$		0			0
$216$		−	9.97368i		−	0.678623i
$217$	1.66430	+	9.01277i	0.112980	+	0.611827i
$218$	9.77558	−	9.77558i	0.662086	−	0.662086i
$219$	−2.20822	+	1.27492i	−0.149218	+	0.0861509i
$220$		0			0
$221$	−8.27492	+	14.3326i	−0.556631	+	0.964113i
$222$	6.69213	+	1.79315i	0.449146	+	0.120348i
$223$	−6.16441	−	6.16441i	−0.412800	−	0.412800i	0.469913	−	0.882713i	$-0.344285\pi$
$223$	−6.16441	−	6.16441i	−0.412800	−	0.412800i	−0.882713	+	0.469913i	$0.844285\pi$
$224$	−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	$-0.0466593\pi$
$227$	0.896575	+	3.34607i	0.0595078	+	0.222086i	−0.929768	+	0.368146i	$0.879993\pi$
$228$	5.83633	+	21.7815i	0.386520	+	1.44251i
$229$	−6.92820	−	12.0000i	−0.457829	−	0.792982i	0.541017	−	0.841011i	$-0.318039\pi$
$229$	−6.92820	−	12.0000i	−0.457829	−	0.792982i	−0.998846	+	0.0480291i	$0.984706\pi$
$230$		0			0
$231$	−16.5498	+	7.88054i	−1.08890	+	0.518502i
$232$	3.72993	+	3.72993i	0.244882	+	0.244882i
$233$	−18.9800	−	5.08567i	−1.24342	−	0.333173i	−0.423628	−	0.905836i	$-0.639244\pi$
$233$	−18.9800	−	5.08567i	−1.24342	−	0.333173i	−0.819791	+	0.572663i	$0.805910\pi$
$234$	14.9893	−	25.9622i	0.979880	−	1.69720i
$235$		0			0
$236$	9.00000	−	5.19615i	0.585850	−	0.338241i
$237$	−21.5348	+	21.5348i	−1.39883	+	1.39883i
$238$	−5.94772	−	6.97314i	−0.385533	−	0.452001i
$239$		−	10.5498i		−	0.682412i	−0.939989	−	0.341206i	$-0.889165\pi$
$239$		−	10.5498i		−	0.682412i	0.939989	−	0.341206i	$-0.110835\pi$
$240$		0			0
$241$	−3.41238	−	1.97014i	−0.219810	−	0.126908i	0.386052	−	0.922477i	$-0.373839\pi$
$241$	−3.41238	−	1.97014i	−0.219810	−	0.126908i	−0.605862	+	0.795569i	$0.707172\pi$
$242$	5.62628	−	1.50756i	0.361671	−	0.0969094i
$243$	−1.35976	+	5.07468i	−0.0872284	+	0.325541i
$244$	1.25588			0.0803995
$245$		0			0
$246$	−15.8248			−1.00895
$247$	−9.15562	+	34.1692i	−0.582558	+	2.17414i
$248$	3.34607	−	0.896575i	0.212475	−	0.0569326i
$249$	−3.31233	−	1.91238i	−0.209911	−	0.121192i
$250$		0			0
$251$			6.45203i			0.407249i	0.979049	+	0.203624i	$0.0652721\pi$
$251$			6.45203i			0.407249i	−0.979049	+	0.203624i	$0.934728\pi$
$252$	10.7738	+	12.6312i	0.678684	+	0.795693i
$253$	−4.82583	+	4.82583i	−0.303397	+	0.303397i
$254$	−8.42217	+	4.86254i	−0.528454	+	0.305103i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.61202	+	2.03963i	0.474825	+	0.127229i	0.488292	−	0.872680i	$-0.337620\pi$
$257$	7.61202	+	2.03963i	0.474825	+	0.127229i	−0.0134670	+	0.999909i	$0.504287\pi$
$258$	−1.56145	−	1.56145i	−0.0972115	−	0.0972115i
$259$	−5.43424	+	2.58762i	−0.337667	+	0.160787i
$260$		0			0
$261$	−16.5498	−	28.6652i	−1.02441	−	1.77433i
$262$	1.01982	+	3.80601i	0.0630045	+	0.235136i
$263$	−0.989919	−	3.69443i	−0.0610410	−	0.227808i	0.928666	−	0.370917i	$-0.120957\pi$
$263$	−0.989919	−	3.69443i	−0.0610410	−	0.227808i	−0.989707	+	0.143109i	$0.954290\pi$
$264$	3.46410	+	6.00000i	0.213201	+	0.369274i
$265$		0			0
$266$	−16.1375	−	11.1066i	−0.989451	−	0.680987i
$267$	19.6751	+	19.6751i	1.20409	+	1.20409i
$268$	−10.8907	−	2.91816i	−0.665257	−	0.178255i
$269$	−9.76436	+	16.9124i	−0.595344	+	1.03117i	0.398154	+	0.917318i	$0.369651\pi$
$269$	−9.76436	+	16.9124i	−0.595344	+	1.03117i	−0.993498	+	0.113847i	$0.963683\pi$
$270$		0			0
$271$	15.8248	−	9.13642i	0.961285	−	0.554998i	0.0647169	−	0.997904i	$-0.479386\pi$
$271$	15.8248	−	9.13642i	0.961285	−	0.554998i	0.896568	+	0.442905i	$0.146052\pi$
$272$	−2.44949	+	2.44949i	−0.148522	+	0.148522i
$273$	6.99037	+	37.8552i	0.423076	+	2.29110i
$274$		0			0
$275$		0			0
$276$	7.91238	+	4.56821i	0.476269	+	0.274974i
$277$	−14.5852	+	3.90808i	−0.876337	+	0.234814i	−0.668826	−	0.743419i	$-0.733203\pi$
$277$	−14.5852	+	3.90808i	−0.876337	+	0.234814i	−0.207511	+	0.978233i	$0.566536\pi$
$278$	5.62594	−	20.9963i	0.337421	−	1.25927i
$279$	−21.7370			−1.30136
$280$		0			0
$281$	29.3746			1.75234			0.876170	−	0.482001i	$-0.160090\pi$
$281$	29.3746			1.75234			0.876170	+	0.482001i	$0.160090\pi$
$282$	0.375330	−	1.40075i	0.0223506	−	0.0834136i
$283$	26.8797	−	7.20239i	1.59783	−	0.428138i	0.653445	−	0.756974i	$-0.273323\pi$
$283$	26.8797	−	7.20239i	1.59783	−	0.428138i	0.944387	+	0.328837i	$0.106657\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$		0			0
$286$			10.8685i			0.642666i
$287$	10.4597	−	8.92158i	0.617417	−	0.526624i
$288$	4.43704	−	4.43704i	0.261455	−	0.261455i
$289$	4.33013	−	2.50000i	0.254713	−	0.147059i
$290$		0			0
$291$	2.54983	−	4.41644i	0.149474	−	0.258896i
$292$	−0.808725	−	0.216697i	−0.0473270	−	0.0126812i
$293$	−12.5842	−	12.5842i	−0.735174	−	0.735174i	0.236466	−	0.971640i	$-0.424011\pi$
$293$	−12.5842	−	12.5842i	−0.735174	−	0.735174i	−0.971640	+	0.236466i	$0.924011\pi$
$294$	−21.0515	−	3.36254i	−1.22775	−	0.196107i
$295$		0			0
$296$	1.13746	+	1.97014i	0.0661134	+	0.114512i
$297$	−5.87242	−	21.9162i	−0.340752	−	1.27171i
$298$	2.54283	+	9.48998i	0.147302	+	0.549740i
$299$	7.16629	+	12.4124i	0.414437	+	0.717826i
$300$		0			0
$301$	1.91238	+	0.151770i	0.110228	+	0.00874785i
$302$	1.41421	+	1.41421i	0.0813788	+	0.0813788i
$303$	26.8766	+	7.20158i	1.54402	+	0.413720i
$304$	−3.70219	+	6.41238i	−0.212335	+	0.367775i
$305$		0			0
$306$	18.8248	−	10.8685i	1.07614	−	0.621309i
$307$	13.2169	−	13.2169i	0.754327	−	0.754327i	−0.220957	−	0.975284i	$-0.570918\pi$
$307$	13.2169	−	13.2169i	0.754327	−	0.754327i	0.975284	+	0.220957i	$0.0709180\pi$
$308$	−5.67231	−	2.01286i	−0.323210	−	0.114693i
$309$		−	1.27492i		−	0.0725275i
$310$		0			0
$311$	−22.6495	−	13.0767i	−1.28434	−	0.741511i	−0.306698	−	0.951807i	$-0.599224\pi$
$311$	−22.6495	−	13.0767i	−1.28434	−	0.741511i	−0.977638	+	0.210296i	$0.932557\pi$
$312$	14.0541	−	3.76577i	0.795655	−	0.213195i
$313$	−2.90642	+	10.8469i	−0.164281	+	0.613104i	0.833850	+	0.551991i	$0.186132\pi$
$313$	−2.90642	+	10.8469i	−0.164281	+	0.613104i	−0.998131	+	0.0611132i	$0.980535\pi$
$314$	−5.61478			−0.316860
$315$		0			0
$316$	−10.0000			−0.562544
$317$	4.65874	−	17.3867i	0.261661	−	0.976532i	−0.702601	−	0.711584i	$-0.747978\pi$
$317$	4.65874	−	17.3867i	0.261661	−	0.976532i	0.964262	−	0.264949i	$-0.0853551\pi$
$318$	−37.7266	+	10.1088i	−2.11560	+	0.566874i
$319$	10.3923	+	6.00000i	0.581857	+	0.335936i
$320$		0			0
$321$		−	48.1939i		−	2.68992i
$322$	−7.80529	+	1.44133i	−0.434972	+	0.0803222i
$323$	−18.1369	+	18.1369i	−1.00917	+	1.00917i
$324$	−10.0025	+	5.77492i	−0.555692	+	0.320829i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−40.6683	−	10.8970i	−2.24896	−	0.602608i
$328$	−3.67423	−	3.67423i	−0.202876	−	0.202876i
$329$	0.541624	+	1.13746i	0.0298607	+	0.0627101i
$330$		0			0
$331$	−14.4124	−	24.9630i	−0.792176	−	1.37209i	−0.924617	−	0.380898i	$-0.875615\pi$
$331$	−14.4124	−	24.9630i	−0.792176	−	1.37209i	0.132441	−	0.991191i	$-0.457718\pi$
$332$	−0.325046	−	1.21309i	−0.0178392	−	0.0665768i
$333$	−3.69462	−	13.7885i	−0.202464	−	0.755606i
$334$	0.866025	+	1.50000i	0.0473868	+	0.0820763i
$335$		0			0
$336$	−0.637459	+	8.03231i	−0.0347762	+	0.438199i
$337$	−17.1115	−	17.1115i	−0.932124	−	0.932124i	0.0657148	−	0.997838i	$-0.479067\pi$
$337$	−17.1115	−	17.1115i	−0.932124	−	0.932124i	−0.997838	+	0.0657148i	$0.979067\pi$
$338$	9.48998	+	2.54283i	0.516187	+	0.138312i
$339$	9.13642	−	15.8248i	0.496222	−	0.859483i
$340$		0			0
$341$	6.82475	−	3.94027i	0.369581	−	0.213378i
$342$	32.8535	−	32.8535i	1.77651	−	1.77651i
$343$	15.8101	−	9.64572i	0.853667	−	0.520820i
$344$		−	0.725083i		−	0.0390938i
$345$		0			0
$346$	−15.4124	−	8.89834i	−0.828574	−	0.478378i
$347$	−26.8766	+	7.20158i	−1.44281	+	0.386601i	−0.893518	−	0.449027i	$-0.851771\pi$
$347$	−26.8766	+	7.20158i	−1.44281	+	0.386601i	−0.549296	+	0.835628i	$0.685104\pi$
$348$	4.15783	−	15.5172i	0.222883	−	0.831811i
$349$	−9.13642			−0.489062			−0.244531	−	0.969642i	$-0.578634\pi$
$349$	−9.13642			−0.489062			−0.244531	+	0.969642i	$0.578634\pi$
$350$		0			0
$351$	−47.6495			−2.54334
$352$	−0.588792	+	2.19740i	−0.0313827	+	0.117122i
$353$	−24.3423	+	6.52251i	−1.29561	+	0.347158i	−0.839789	−	0.542912i	$-0.817322\pi$
$353$	−24.3423	+	6.52251i	−1.29561	+	0.347158i	−0.455823	+	0.890070i	$0.650655\pi$
$354$	−27.4093	−	15.8248i	−1.45679	−	0.841076i
$355$		0			0
$356$			9.13642i			0.484230i
$357$	−9.33455	+	26.3051i	−0.494037	+	1.39221i
$358$	9.06847	−	9.06847i	0.479283	−	0.479283i
$359$	27.4093	−	15.8248i	1.44661	−	0.835198i	0.448329	−	0.893869i	$-0.352019\pi$
$359$	27.4093	−	15.8248i	1.44661	−	0.835198i	0.998277	+	0.0586703i	$0.0186861\pi$
$360$		0			0
$361$	−17.9124	+	31.0251i	−0.942757	+	1.63290i
$362$	−7.90522	−	2.11820i	−0.415489	−	0.111330i
$363$	−12.5435	−	12.5435i	−0.658361	−	0.658361i
$364$	−7.16629	+	10.4124i	−0.375616	+	0.545757i
$365$		0			0
$366$	−1.91238	−	3.31233i	−0.0999615	−	0.173138i
$367$	−3.81789	−	14.2486i	−0.199292	−	0.743769i	−0.991114	−	0.133017i	$-0.957534\pi$
$367$	−3.81789	−	14.2486i	−0.199292	−	0.743769i	0.791821	−	0.610753i	$-0.209133\pi$
$368$	0.776457	+	2.89778i	0.0404756	+	0.151057i
$369$	16.3027	+	28.2371i	0.848685	+	1.46997i
$370$		0			0
$371$	19.2371	−	27.9509i	0.998742	−	1.45114i
$372$	−7.45986	−	7.45986i	−0.386776	−	0.386776i
$373$	−7.19631	−	1.92824i	−0.372611	−	0.0998407i	0.0676538	−	0.997709i	$-0.478449\pi$
$373$	−7.19631	−	1.92824i	−0.372611	−	0.0998407i	−0.440264	+	0.897868i	$0.645115\pi$
$374$	−3.94027	+	6.82475i	−0.203747	+	0.352900i
$375$		0			0
$376$	0.412376	−	0.238085i	0.0212667	−	0.0122783i
$377$	17.8198	−	17.8198i	0.917768	−	0.917768i
$378$	8.82477	−	24.8685i	0.453897	−	1.27910i
$379$			3.17525i			0.163102i	0.996669	+	0.0815508i	$0.0259873\pi$
$379$			3.17525i			0.163102i	−0.996669	+	0.0815508i	$0.974013\pi$
$380$		0			0
$381$	25.6495	+	14.8087i	1.31406	+	0.758675i
$382$	20.3807	−	5.46100i	1.04277	−	0.279409i
$383$	−8.11386	+	30.2813i	−0.414599	+	1.54730i	0.371039	+	0.928617i	$0.379002\pi$
$383$	−8.11386	+	30.2813i	−0.414599	+	1.54730i	−0.785638	+	0.618687i	$0.787665\pi$
$384$	3.04547			0.155414
$385$		0			0
$386$	4.54983			0.231580
$387$	−1.17758	+	4.39480i	−0.0598599	+	0.223400i
$388$	1.61745	−	0.433394i	0.0821136	−	0.0220023i
$389$	−23.4690	−	13.5498i	−1.18993	−	0.687004i	−0.231636	−	0.972803i	$-0.574408\pi$
$389$	−23.4690	−	13.5498i	−1.18993	−	0.687004i	−0.958290	+	0.285799i	$0.907741\pi$
$390$		0			0
$391$			10.3923i			0.525561i
$392$	−4.10706	−	5.66851i	−0.207438	−	0.286303i
$393$	8.48528	−	8.48528i	0.428026	−	0.428026i
$394$	5.91041	−	3.41238i	0.297762	−	0.171913i
$395$		0			0
$396$	7.13746	−	12.3624i	0.358671	−	0.621236i
$397$	18.4589	+	4.94606i	0.926428	+	0.248236i	0.690331	−	0.723494i	$-0.257465\pi$
$397$	18.4589	+	4.94606i	0.926428	+	0.248236i	0.236097	+	0.971729i	$0.424132\pi$
$398$	5.57239	+	5.57239i	0.279318	+	0.279318i
$399$	−4.71998	+	59.4743i	−0.236295	+	2.97744i
$400$		0			0
$401$	−6.04983	−	10.4786i	−0.302114	−	0.523277i	0.674500	−	0.738275i	$-0.264359\pi$
$401$	−6.04983	−	10.4786i	−0.302114	−	0.523277i	−0.976615	+	0.214997i	$0.931026\pi$
$402$	8.88719	+	33.1675i	0.443253	+	1.65424i
$403$	−4.28341	−	15.9859i	−0.213372	−	0.796315i
$404$	4.56821	+	7.91238i	0.227277	+	0.393655i
$405$		0			0
$406$	6.00000	+	12.6005i	0.297775	+	0.625354i
$407$	3.65945	+	3.65945i	0.181392	+	0.181392i
$408$	10.1904	+	2.73050i	0.504498	+	0.135180i
$409$	−2.35999	+	4.08762i	−0.116694	+	0.202120i	−0.918456	−	0.395524i	$-0.870563\pi$
$409$	−2.35999	+	4.08762i	−0.116694	+	0.202120i	0.801762	+	0.597644i	$0.203896\pi$
$410$		0			0
$411$		0			0
$412$	0.296014	−	0.296014i	0.0145836	−	0.0145836i
$413$	27.0383	−	4.99291i	1.33047	−	0.245685i
$414$		−	18.8248i		−	0.925186i
$415$		0			0
$416$	4.13746	+	2.38876i	0.202856	+	0.117119i
$417$	−63.9437	+	17.1336i	−3.13133	+	0.839038i
$418$	−4.35964	+	16.2704i	−0.213237	+	0.795810i
$419$	−11.8208			−0.577485			−0.288742	−	0.957407i	$-0.593237\pi$
$419$	−11.8208			−0.577485			−0.288742	+	0.957407i	$0.593237\pi$
$420$		0			0
$421$	12.1752			0.593385			0.296693	−	0.954973i	$-0.404116\pi$
$421$	12.1752			0.593385			0.296693	+	0.954973i	$0.404116\pi$
$422$	4.35457	−	16.2515i	0.211977	−	0.791109i
$423$	−2.88612	+	0.773333i	−0.140328	+	0.0376008i
$424$	−11.1066	−	6.41238i	−0.539382	−	0.311412i
$425$		0			0
$426$		−	18.2728i		−	0.885322i
$427$	3.13143	+	1.11121i	0.151541	+	0.0537752i
$428$	11.1898	−	11.1898i	0.540879	−	0.540879i
$429$	28.6652	−	16.5498i	1.38397	−	0.799034i
$430$		0			0
$431$	9.72508	−	16.8443i	0.468441	−	0.811363i	−0.530909	−	0.847429i	$-0.678149\pi$
$431$	9.72508	−	16.8443i	0.468441	−	0.811363i	0.999349	+	0.0360659i	$0.0114826\pi$
$432$	−9.63383	−	2.58138i	−0.463508	−	0.124197i
$433$	14.1049	+	14.1049i	0.677839	+	0.677839i	0.959511	−	0.281672i	$-0.0908890\pi$
$433$	14.1049	+	14.1049i	0.677839	+	0.677839i	−0.281672	+	0.959511i	$0.590889\pi$
$434$	9.13642	+	0.725083i	0.438562	+	0.0348051i
$435$		0			0
$436$	−6.91238	−	11.9726i	−0.331043	−	0.573383i
$437$	5.74918	+	21.4562i	0.275021	+	1.02639i
$438$	0.659946	+	2.46295i	0.0315334	+	0.117684i
$439$	−10.3923	−	18.0000i	−0.495998	−	0.859093i	0.503992	−	0.863708i	$-0.331864\pi$
$439$	−10.3923	−	18.0000i	−0.495998	−	0.859093i	−0.999989	+	0.00461537i	$0.998531\pi$
$440$		0			0
$441$	15.6873	+	41.0276i	0.747014	+	1.95370i
$442$	11.7025	+	11.7025i	0.556631	+	0.556631i
$443$	32.6722	+	8.75449i	1.55230	+	0.415938i	0.930217	−	0.367010i	$-0.119619\pi$
$443$	32.6722	+	8.75449i	1.55230	+	0.415938i	0.622086	+	0.782949i	$0.286285\pi$
$444$	3.46410	−	6.00000i	0.164399	−	0.284747i
$445$		0			0
$446$	−7.54983	+	4.35890i	−0.357495	+	0.206400i
$447$	21.1574	−	21.1574i	1.00071	−	1.00071i
$448$	−2.01297	+	1.71696i	−0.0951040	+	0.0811186i
$449$		−	37.5498i		−	1.77209i	−0.463603	−	0.886043i	$-0.653444\pi$
$449$		−	37.5498i		−	1.77209i	0.463603	−	0.886043i	$-0.346556\pi$
$450$		0			0
$451$	−10.2371	−	5.91041i	−0.482048	−	0.278310i
$452$	5.79555	−	1.55291i	0.272600	−	0.0730429i
$453$	1.57645	−	5.88341i	0.0740683	−	0.276427i
$454$	3.46410			0.162578
$455$		0			0
$456$	22.5498			1.05599
$457$	−5.03407	+	18.7874i	−0.235484	+	0.878838i	0.742446	+	0.669906i	$0.233666\pi$
$457$	−5.03407	+	18.7874i	−0.235484	+	0.878838i	−0.977930	+	0.208932i	$0.933001\pi$
$458$	−13.3843	+	3.58630i	−0.625405	+	0.167577i
$459$	−29.9210	−	17.2749i	−1.39659	−	0.806324i
$460$		0			0
$461$			36.5457i			1.70210i	0.525082	+	0.851051i	$0.324035\pi$
$461$			36.5457i			1.70210i	−0.525082	+	0.851051i	$0.675965\pi$
$462$	3.32861	+	18.0255i	0.154861	+	0.838624i
$463$	11.6320	−	11.6320i	0.540586	−	0.540586i	−0.383115	−	0.923701i	$-0.625149\pi$
$463$	11.6320	−	11.6320i	0.540586	−	0.540586i	0.923701	+	0.383115i	$0.125149\pi$
$464$	4.56821	−	2.63746i	0.212074	−	0.122441i
$465$		0			0
$466$	−9.82475	+	17.0170i	−0.455123	+	0.788296i
$467$	−25.5554	−	6.84756i	−1.18256	−	0.316867i	−0.386621	−	0.922239i	$-0.626358\pi$
$467$	−25.5554	−	6.84756i	−1.18256	−	0.316867i	−0.795943	+	0.605371i	$0.793025\pi$
$468$	−21.1981	−	21.1981i	−0.979880	−	0.979880i
$469$	−24.5731	−	16.9124i	−1.13468	−	0.780941i
$470$		0			0
$471$	8.54983	+	14.8087i	0.393956	+	0.682351i
$472$	−2.68973	−	10.0382i	−0.123805	−	0.462045i
$473$	−0.426923	−	1.59330i	−0.0196299	−	0.0732599i
$474$	15.2274	+	26.3746i	0.699416	+	1.21142i
$475$		0			0
$476$	−8.27492	+	3.94027i	−0.379280	+	0.180602i
$477$	56.9039	+	56.9039i	2.60545	+	2.60545i
$478$	−10.1904	−	2.73050i	−0.466096	−	0.124890i
$479$	9.13642	−	15.8248i	0.417454	−	0.723051i	−0.578229	−	0.815875i	$-0.696256\pi$
$479$	9.13642	−	15.8248i	0.417454	−	0.723051i	0.995683	+	0.0928234i	$0.0295892\pi$
$480$		0			0
$481$	9.41238	−	5.43424i	0.429167	−	0.247780i
$482$	−2.78619	+	2.78619i	−0.126908	+	0.126908i
$483$	15.6869	+	18.3914i	0.713777	+	0.836836i
$484$		−	5.82475i		−	0.264761i
$485$		0			0
$486$	4.54983	+	2.62685i	0.206385	+	0.119156i
$487$	20.3807	−	5.46100i	0.923538	−	0.247461i	0.234441	−	0.972130i	$-0.424674\pi$
$487$	20.3807	−	5.46100i	0.923538	−	0.247461i	0.689097	+	0.724669i	$0.258007\pi$
$488$	0.325046	−	1.21309i	0.0147141	−	0.0549139i
$489$	36.5457			1.65265
$490$		0			0
$491$	−34.5498			−1.55921			−0.779606	−	0.626270i	$-0.784581\pi$
$491$	−34.5498			−1.55921			−0.779606	+	0.626270i	$0.784581\pi$
$492$	−4.09575	+	15.2855i	−0.184651	+	0.689125i
$493$	17.6502	−	4.72936i	0.794926	−	0.213000i
$494$	30.6353	+	17.6873i	1.37835	+	0.795789i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	10.3017	+	12.0778i	0.462097	+	0.541765i
$498$	−2.70451	+	2.70451i	−0.121192	+	0.121192i
$499$	−3.46410	+	2.00000i	−0.155074	+	0.0895323i	−0.575529	−	0.817781i	$-0.695204\pi$
$499$	−3.46410	+	2.00000i	−0.155074	+	0.0895323i	0.420455	+	0.907314i	$0.361871\pi$
$500$		0			0
$501$	2.63746	−	4.56821i	0.117833	−	0.204093i
$502$	6.23218	+	1.66991i	0.278156	+	0.0745317i
$503$	−5.78702	−	5.78702i	−0.258031	−	0.258031i	0.566222	−	0.824253i	$-0.308404\pi$
$503$	−5.78702	−	5.78702i	−0.258031	−	0.258031i	−0.824253	+	0.566222i	$0.808404\pi$
$504$	14.9893	−	7.13746i	0.667676	−	0.317928i
$505$		0			0
$506$	3.41238	+	5.91041i	0.151699	+	0.262750i
$507$	−7.74413	−	28.9015i	−0.343929	−	1.28356i
$508$	2.51704	+	9.39371i	0.111675	+	0.416778i
$509$	18.9008	+	32.7371i	0.837763	+	1.45105i	0.891761	+	0.452507i	$0.149470\pi$
$509$	18.9008	+	32.7371i	0.837763	+	1.45105i	−0.0539983	+	0.998541i	$0.517197\pi$
$510$		0			0
$511$	−1.82475	−	1.25588i	−0.0807223	−	0.0555569i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−71.3325	−	19.1135i	−3.14941	−	0.843881i
$514$	3.94027	−	6.82475i	0.173798	−	0.301027i
$515$		0			0
$516$	−1.91238	+	1.10411i	−0.0841877	+	0.0486058i
$517$	0.765972	−	0.765972i	0.0336874	−	0.0336874i
$518$	1.09297	+	5.91880i	0.0480223	+	0.260057i
$519$			54.1993i			2.37909i
$520$		0			0
$521$	10.2371	+	5.91041i	0.448497	+	0.258940i	0.707195	−	0.707018i	$-0.249960\pi$
$521$	10.2371	+	5.91041i	0.448497	+	0.258940i	−0.258698	+	0.965958i	$0.583294\pi$
$522$	−31.9718	+	8.56682i	−1.39937	+	0.374960i
$523$	−10.5422	+	39.3441i	−0.460979	+	1.72040i	0.208911	+	0.977935i	$0.433008\pi$
$523$	−10.5422	+	39.3441i	−0.460979	+	1.72040i	−0.669889	+	0.742461i	$0.733659\pi$
$524$	3.94027			0.172132
$525$		0			0
$526$	−3.82475			−0.166767
$527$	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
$531$			65.2109i			2.82991i
$532$	−14.9048	+	12.7130i	−0.646205	+	0.551178i
$533$	−17.5538	+	17.5538i	−0.760337	+	0.760337i
$534$	24.0969	−	13.9124i	1.04278	−	0.602047i
$535$		0			0
$536$	−5.63746	+	9.76436i	−0.243501	+	0.421756i
$537$	−37.7266	−	10.1088i	−1.62802	−	0.436228i
$538$	13.8089	+	13.8089i	0.595344	+	0.595344i
$539$	−12.3624	−	10.0378i	−0.532488	−	0.432358i
$540$		0			0
$541$	15.9124	+	27.5610i	0.684126	+	1.18494i	0.973710	+	0.227789i	$0.0731497\pi$
$541$	15.9124	+	27.5610i	0.684126	+	1.18494i	−0.289584	+	0.957153i	$0.593517\pi$
$542$	−4.72936	−	17.6502i	−0.203143	−	0.758142i
$543$	6.45091	+	24.0751i	0.276835	+	1.03316i
$544$	1.73205	+	3.00000i	0.0742611	+	0.128624i
$545$		0			0
$546$	38.3746	+	3.04547i	1.64228	+	0.130334i
$547$	6.94715	+	6.94715i	0.297039	+	0.297039i	0.839853	−	0.542814i	$-0.182641\pi$
$547$	6.94715	+	6.94715i	0.297039	+	0.297039i	−0.542814	+	0.839853i	$0.682641\pi$
$548$		0			0
$549$	−3.94027	+	6.82475i	−0.168167	+	0.291273i
$550$		0			0
$551$	33.8248	−	19.5287i	1.44098	−	0.831952i
$552$	6.46043	−	6.46043i	0.274974	−	0.274974i
$553$	−24.9342	−	8.84806i	−1.06031	−	0.376258i
$554$			15.0997i			0.641523i
$555$		0			0
$556$	−18.8248	−	10.8685i	−0.798347	−	0.460926i
$557$	41.3655	−	11.0839i	1.75271	−	0.469638i	0.767512	−	0.641035i	$-0.221495\pi$
$557$	41.3655	−	11.0839i	1.75271	−	0.469638i	0.985202	+	0.171397i	$0.0548279\pi$
$558$	−5.62594	+	20.9963i	−0.238165	+	0.888844i
$559$	−3.46410			−0.146516
$560$		0			0
$561$	24.0000			1.01328
$562$	7.60270	−	28.3737i	0.320701	−	1.19687i
$563$	18.8633	−	5.05441i	0.794993	−	0.213018i	0.161609	−	0.986855i	$-0.448332\pi$
$563$	18.8633	−	5.05441i	0.794993	−	0.213018i	0.633385	+	0.773837i	$0.281665\pi$
$564$	−1.25588	−	0.725083i	−0.0528821	−	0.0305315i
$565$		0			0
$566$		−	27.8279i		−	1.16969i
$567$	−30.0499	+	5.54904i	−1.26198	+	0.233038i
$568$	4.24264	−	4.24264i	0.178017	−	0.178017i
$569$	11.1066	−	6.41238i	0.465611	−	0.268821i	−0.248789	−	0.968558i	$-0.580033\pi$
$569$	11.1066	−	6.41238i	0.465611	−	0.268821i	0.714401	+	0.699737i	$0.246699\pi$
$570$		0			0
$571$	−7.82475	+	13.5529i	−0.327456	+	0.567170i	−0.982006	−	0.188848i	$-0.939525\pi$
$571$	−7.82475	+	13.5529i	−0.327456	+	0.567170i	0.654551	+	0.756018i	$0.272858\pi$
$572$	10.4981	+	2.81297i	0.438949	+	0.117616i
$573$	−45.4376	−	45.4376i	−1.89818	−	1.89818i
$574$	−5.91041	−	12.4124i	−0.246696	−	0.518083i
$575$		0			0
$576$	−3.13746	−	5.43424i	−0.130727	−	0.226427i
$577$	−10.3255	−	38.5353i	−0.429857	−	1.60425i	−0.753083	−	0.657925i	$-0.771434\pi$
$577$	−10.3255	−	38.5353i	−0.429857	−	1.60425i	0.323227	−	0.946322i	$-0.395232\pi$
$578$	−1.29410	−	4.82963i	−0.0538273	−	0.200886i
$579$	−6.92820	−	12.0000i	−0.287926	−	0.498703i
$580$		0			0
$581$	0.262873	−	3.31233i	0.0109058	−	0.137419i
$582$	−3.60601	−	3.60601i	−0.149474	−	0.149474i
$583$	−28.1811	−	7.55111i	−1.16714	−	0.312735i
$584$	−0.418627	+	0.725083i	−0.0173229	+	0.0300041i
$585$		0			0
$586$	−15.4124	+	8.89834i	−0.636679	+	0.367587i
$587$	7.34847	−	7.34847i	0.303304	−	0.303304i	−0.539001	−	0.842305i	$-0.681198\pi$
$587$	7.34847	−	7.34847i	0.303304	−	0.303304i	0.842305	+	0.539001i	$0.181198\pi$
$588$	−8.69649	+	19.4639i	−0.358637	+	0.802676i
$589$		−	25.6495i		−	1.05687i
$590$		0			0
$591$	−18.0000	−	10.3923i	−0.740421	−	0.427482i
$592$	2.19740	−	0.588792i	0.0903126	−	0.0241992i
$593$	4.97585	−	18.5701i	0.204333	−	0.762583i	−0.785318	−	0.619092i	$-0.787501\pi$
$593$	4.97585	−	18.5701i	0.204333	−	0.762583i	0.989652	−	0.143491i	$-0.0458327\pi$
$594$	−22.6893			−0.930953
$595$		0			0
$596$	9.82475			0.402438
$597$	6.21166	−	23.1822i	0.254226	−	0.948785i
$598$	13.8442	−	3.70954i	0.566132	−	0.151695i
$599$	28.6652	+	16.5498i	1.17123	+	0.676208i	0.953969	−	0.299906i	$-0.0969554\pi$
$599$	28.6652	+	16.5498i	1.17123	+	0.676208i	0.217258	+	0.976114i	$0.430289\pi$
$600$		0			0
$601$		−	6.92820i		−	0.282607i	−0.989966	−	0.141304i	$-0.954871\pi$
$601$		−	6.92820i		−	0.282607i	0.989966	−	0.141304i	$-0.0451294\pi$
$602$	0.641557	−	1.80793i	0.0261479	−	0.0736858i
$603$	50.0272	−	50.0272i	2.03727	−	2.03727i
$604$	1.73205	−	1.00000i	0.0704761	−	0.0406894i
$605$		0			0
$606$	13.9124	−	24.0969i	0.565152	−	0.978871i
$607$	21.0519	+	5.64083i	0.854469	+	0.228954i	0.659360	−	0.751827i	$-0.270827\pi$
$607$	21.0519	+	5.64083i	0.854469	+	0.228954i	0.195109	+	0.980782i	$0.437494\pi$
$608$	5.23568	+	5.23568i	0.212335	+	0.212335i
$609$	24.0969	−	35.0120i	0.976457	−	1.41876i
$610$		0			0
$611$	−1.13746	−	1.97014i	−0.0460166	−	0.0797032i
$612$	−5.62594	−	20.9963i	−0.227415	−	0.848724i
$613$	9.53095	+	35.5700i	0.384951	+	1.43666i	0.838244	+	0.545296i	$0.183583\pi$
$613$	9.53095	+	35.5700i	0.384951	+	1.43666i	−0.453292	+	0.891362i	$0.649751\pi$
$614$	−9.34574	−	16.1873i	−0.377163	−	0.653266i
$615$		0			0
$616$	−3.41238	+	4.95807i	−0.137489	+	0.199766i
$617$	−9.65166	−	9.65166i	−0.388561	−	0.388561i	0.485613	−	0.874174i	$-0.338596\pi$
$617$	−9.65166	−	9.65166i	−0.388561	−	0.388561i	−0.874174	+	0.485613i	$0.838596\pi$
$618$	−1.23148	−	0.329973i	−0.0495372	−	0.0132735i
$619$	5.43424	−	9.41238i	0.218420	−	0.378315i	−0.735905	−	0.677085i	$-0.763243\pi$
$619$	5.43424	−	9.41238i	0.218420	−	0.378315i	0.954325	+	0.298770i	$0.0965762\pi$
$620$		0			0
$621$	−25.9124	+	14.9605i	−1.03983	+	0.600345i
$622$	−18.4932	+	18.4932i	−0.741511	+	0.741511i
$623$	−8.08396	+	22.7809i	−0.323877	+	0.912697i
$624$		−	14.5498i		−	0.582460i
$625$		0			0
$626$	9.72508	+	5.61478i	0.388692	+	0.224412i
$627$	49.5510	−	13.2772i	1.97888	−	0.530239i
$628$	−1.45321	+	5.42346i	−0.0579895	+	0.216420i
$629$	7.88054			0.314218
$630$		0			0
$631$	9.64950			0.384141			0.192070	−	0.981381i	$-0.438480\pi$
$631$	9.64950			0.384141			0.192070	+	0.981381i	$0.438480\pi$
$632$	−2.58819	+	9.65926i	−0.102953	+	0.384225i
$633$	−49.4934	+	13.2617i	−1.96719	+	0.527106i
$634$	−15.5885	−	9.00000i	−0.619097	−	0.357436i
$635$		0			0
$636$			39.0575i			1.54873i
$637$	−27.0815	+	19.6216i	−1.07301	+	0.777436i
$638$	8.48528	−	8.48528i	0.335936	−	0.335936i
$639$	−32.6054	+	18.8248i	−1.28985	+	0.744696i
$640$		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	$-0.0123508\pi$
$642$	−46.5517	−	12.4735i	−1.83725	−	0.492290i
$643$	19.6773	+	19.6773i	0.775997	+	0.775997i	0.979147	−	0.203151i	$-0.0651181\pi$
$643$	19.6773	+	19.6773i	0.775997	+	0.775997i	−0.203151	+	0.979147i	$0.565118\pi$
$644$	−0.627940	+	7.91238i	−0.0247443	+	0.311791i
$645$		0			0
$646$	12.8248	+	22.2131i	0.504583	+	0.873964i
$647$	1.34486	+	5.01910i	0.0528720	+	0.197321i	0.987310	−	0.158805i	$-0.0507641\pi$
$647$	1.34486	+	5.01910i	0.0528720	+	0.197321i	−0.934438	+	0.356126i	$0.884097\pi$
$648$	2.98932	+	11.1563i	0.117431	+	0.438260i
$649$	−11.8208	−	20.4743i	−0.464008	−	0.803685i
$650$		0			0
$651$	−12.0000	−	25.2011i	−0.470317	−	0.987707i
$652$	8.48528	+	8.48528i	0.332309	+	0.332309i
$653$	37.1633	+	9.95787i	1.45431	+	0.389682i	0.897521	−	0.440972i	$-0.145366\pi$
$653$	37.1633	+	9.95787i	1.45431	+	0.389682i	0.556790	+	0.830653i	$0.312033\pi$
$654$	−21.0515	+	36.4622i	−0.823177	+	1.42579i
$655$		0			0
$656$	−4.50000	+	2.59808i	−0.175695	+	0.101438i
$657$	3.71492	−	3.71492i	0.144933	−	0.144933i
$658$	1.23888	−	0.228773i	0.0482967	−	0.00891850i
$659$		−	1.45017i		−	0.0564904i	−0.999601	−	0.0282452i	$-0.991008\pi$
$659$		−	1.45017i		−	0.0564904i	0.999601	−	0.0282452i	$-0.00899193\pi$
$660$		0			0
$661$	−19.9124	−	11.4964i	−0.774502	−	0.447159i	0.0599765	−	0.998200i	$-0.480897\pi$
$661$	−19.9124	−	11.4964i	−0.774502	−	0.447159i	−0.834478	+	0.551041i	$0.814231\pi$
$662$	−27.8426	+	7.46039i	−1.08213	+	0.289956i
$663$	13.0450	−	48.6847i	0.506627	−	1.89076i
$664$	−1.25588			−0.0487376
$665$		0			0
$666$	−14.2749			−0.553142
$667$	4.09575	−	15.2855i	0.158588	−	0.591858i
$668$	1.67303	−	0.448288i	0.0647316	−	0.0173448i
$669$	22.9928	+	13.2749i	0.888954	+	0.513238i
$670$		0			0
$671$		−	2.85702i		−	0.110294i
$672$	7.59363	+	2.69465i	0.292931	+	0.103949i
$673$	29.8394	−	29.8394i	1.15023	−	1.15023i	0.163719	−	0.986507i	$-0.447651\pi$
$673$	29.8394	−	29.8394i	1.15023	−	1.15023i	0.986507	−	0.163719i	$-0.0523490\pi$
$674$	−20.9572	+	12.0997i	−0.807243	+	0.466062i
$675$		0			0
$676$	4.91238	−	8.50848i	0.188938	−	0.327249i
$677$	8.07197	+	2.16288i	0.310231	+	0.0831261i	0.410575	−	0.911827i	$-0.365328\pi$
$677$	8.07197	+	2.16288i	0.310231	+	0.0831261i	−0.100345	+	0.994953i	$0.531995\pi$
$678$	−12.9209	−	12.9209i	−0.496222	−	0.496222i
$679$	4.41644	+	0.350497i	0.169488	+	0.0134508i
$680$		0			0
$681$	−5.27492	−	9.13642i	−0.202135	−	0.350109i
$682$	−2.03963	−	7.61202i	−0.0781017	−	0.291479i
$683$	−2.11591	−	7.89668i	−0.0809630	−	0.302158i	0.913556	−	0.406713i	$-0.133325\pi$
$683$	−2.11591	−	7.89668i	−0.0809630	−	0.302158i	−0.994519	+	0.104555i	$0.966658\pi$
$684$	−23.2309	−	40.2371i	−0.888256	−	1.53851i
$685$		0			0
$686$	−5.22508	−	17.7679i	−0.199495	−	0.678382i
$687$	29.8394	+	29.8394i	1.13845	+	1.13845i
$688$	−0.700376	−	0.187665i	−0.0267016	−	0.00715467i
$689$	−30.6353	+	53.0619i	−1.16711	+	2.02150i
$690$		0			0
$691$	−32.4743	+	18.7490i	−1.23538	+	0.713246i	−0.968146	−	0.250386i	$-0.919443\pi$
$691$	−32.4743	+	18.7490i	−1.23538	+	0.713246i	−0.267233	+	0.963632i	$0.586109\pi$
$692$	−12.5842	+	12.5842i	−0.478378	+	0.478378i
$693$	28.7350	−	24.5094i	1.09155	−	0.931036i
$694$			27.8248i			1.05621i
$695$		0			0
$696$	−13.9124	−	8.03231i	−0.527347	−	0.304464i
$697$	−17.3867	+	4.65874i	−0.658567	+	0.176462i
$698$	−2.36468	+	8.82511i	−0.0895045	+	0.334035i
$699$	59.8421			2.26343
$700$		0			0
$701$	−0.725083			−0.0273860			−0.0136930	−	0.999906i	$-0.504359\pi$
$701$	−0.725083			−0.0273860			−0.0136930	+	0.999906i	$0.504359\pi$
$702$	−12.3326	+	46.0259i	−0.465464	+	1.73714i
$703$	16.2704	−	4.35964i	0.613649	−	0.164427i
$704$	1.97014	+	1.13746i	0.0742523	+	0.0428696i
$705$		0			0
$706$			25.2011i			0.948454i
$707$	4.38953	+	23.7708i	0.165085	+	0.893994i
$708$	−22.3796	+	22.3796i	−0.841076	+	0.841076i
$709$	−31.0251	+	17.9124i	−1.16517	+	0.672713i	−0.952538	−	0.304418i	$-0.901538\pi$
$709$	−31.0251	+	17.9124i	−1.16517	+	0.672713i	−0.212635	+	0.977132i	$0.568205\pi$
$710$		0			0
$711$	31.3746	−	54.3424i	1.17664	−	2.03800i
$712$	8.82511	+	2.36468i	0.330735	+	0.0886202i
$713$	−7.34847	−	7.34847i	−0.275202	−	0.275202i
$714$	22.9928	+	15.8248i	0.860485	+	0.592226i
$715$		0			0
$716$	−6.41238	−	11.1066i	−0.239642	−	0.415072i
$717$	8.31566	+	31.0345i	0.310554	+	1.15900i
$718$	−8.19149	−	30.5711i	−0.305704	−	1.14090i
$719$	6.45203	+	11.1752i	0.240620	+	0.416766i	0.960891	−	0.276926i	$-0.0893158\pi$
$719$	6.45203	+	11.1752i	0.240620	+	0.416766i	−0.720271	+	0.693693i	$0.755983\pi$
$720$		0			0
$721$	1.00000	−	0.476171i	0.0372419	−	0.0177335i
$722$	25.3319	+	25.3319i	0.942757	+	0.942757i
$723$	11.5911	+	3.10583i	0.431078	+	0.115507i
$724$	−4.09204	+	7.08762i	−0.152080	+	0.263409i
$725$		0			0
$726$	−15.3625	+	8.86957i	−0.570157	+	0.329181i
$727$	23.3515	−	23.3515i	0.866060	−	0.866060i	−0.125973	−	0.992034i	$-0.540205\pi$
$727$	23.3515	−	23.3515i	0.866060	−	0.866060i	0.992034	+	0.125973i	$0.0402054\pi$
$728$	8.20281	+	9.61702i	0.304016	+	0.356431i
$729$			18.6495i			0.690722i
$730$		0			0
$731$	−2.17525	−	1.25588i	−0.0804545	−	0.0464504i
$732$	−3.69443	+	0.989919i	−0.136550	+	0.0365884i
$733$	−9.30569	+	34.7293i	−0.343714	+	1.28276i	0.550394	+	0.834905i	$0.314477\pi$
$733$	−9.30569	+	34.7293i	−0.343714	+	1.28276i	−0.894108	+	0.447852i	$0.852189\pi$
$734$	−14.7512			−0.544477
$735$		0			0
$736$	3.00000			0.110581
$737$	−6.63858	+	24.7755i	−0.244535	+	0.912618i
$738$	31.4944	−	8.43891i	1.15933	−	0.310640i
$739$	−23.2309	−	13.4124i	−0.854563	−	0.493382i	0.00762477	−	0.999971i	$-0.497573\pi$
$739$	−23.2309	−	13.4124i	−0.854563	−	0.493382i	−0.862188	+	0.506589i	$0.830906\pi$
$740$		0			0
$741$		−	107.732i		−	3.95765i
$742$	−22.0196	−	25.8159i	−0.808363	−	0.947730i
$743$	10.6066	−	10.6066i	0.389118	−	0.389118i	−0.485254	−	0.874373i	$-0.661273\pi$
$743$	10.6066	−	10.6066i	0.389118	−	0.389118i	0.874373	+	0.485254i	$0.161273\pi$
$744$	−9.13642	+	5.27492i	−0.334958	+	0.193388i
$745$		0			0
$746$	−3.72508	+	6.45203i	−0.136385	+	0.236226i
$747$	7.61202	+	2.03963i	0.278509	+	0.0746263i
$748$	5.57239	+	5.57239i	0.203747	+	0.203747i
$749$	37.8016	−	18.0000i	1.38124	−	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	$0.572942\pi$
$752$	−0.123242	−	0.459945i	−0.00449417	−	0.0167725i
$753$	−5.08567	−	18.9800i	−0.185332	−	0.691668i
$754$	−12.6005	−	21.8248i	−0.458884	−	0.794811i
$755$		0			0
$756$	−21.7371	−	14.9605i	−0.790572	−	0.544109i
$757$	−4.24264	−	4.24264i	−0.154201	−	0.154201i	0.625790	−	0.779992i	$-0.284777\pi$
$757$	−4.24264	−	4.24264i	−0.154201	−	0.154201i	−0.779992	+	0.625790i	$0.784777\pi$
$758$	3.06705	+	0.821815i	0.111400	+	0.0298497i
$759$	10.3923	−	18.0000i	0.377217	−	0.653359i
$760$		0			0
$761$	−32.5876	+	18.8145i	−1.18130	+	0.682024i	−0.956315	−	0.292338i	$-0.905567\pi$
$761$	−32.5876	+	18.8145i	−1.18130	+	0.682024i	−0.224985	+	0.974362i	$0.572233\pi$
$762$	20.9427	−	20.9427i	0.758675	−	0.758675i
$763$	−6.64201	−	35.9687i	−0.240457	−	1.30216i
$764$		−	21.0997i		−	0.763359i
$765$		0			0
$766$	27.1495	+	15.6748i	0.980951	+	0.566353i
$767$	−47.9577	+	12.8502i	−1.73165	+	0.463995i
$768$	0.788227	−	2.94170i	0.0284427	−	0.106150i
$769$	−47.4142			−1.70980			−0.854899	−	0.518794i	$-0.826381\pi$
$769$	−47.4142			−1.70980			−0.854899	+	0.518794i	$0.826381\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	1.17758	−	4.39480i	0.0423822	−	0.158172i
$773$	−19.6164	+	5.25621i	−0.705555	+	0.189053i	−0.593717	−	0.804674i	$-0.702340\pi$
$773$	−19.6164	+	5.25621i	−0.705555	+	0.189053i	−0.111837	+	0.993727i	$0.535674\pi$
$774$	3.94027	+	2.27492i	0.141630	+	0.0817702i
$775$		0			0
$776$		−	1.67451i		−	0.0601113i
$777$	13.9463	−	11.8954i	0.500320	−	0.426746i
$778$	−19.1624	+	19.1624i	−0.687004	+	0.687004i
$779$	−33.3197	+	19.2371i	−1.19380	+	0.689242i
$780$		0			0
$781$	6.82475	−	11.8208i	0.244209	−	0.422982i
$782$	10.0382	+	2.68973i	0.358965	+	0.0961844i
$783$	37.2011	+	37.2011i	1.32946	+	1.32946i
$784$	−6.53835	+	2.50000i	−0.233512	+	0.0892857i
$785$		0			0
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	4.18762	+	15.6284i	0.149272	+	0.557092i	0.999528	+	0.0307222i	$0.00978073\pi$
$787$	4.18762	+	15.6284i	0.149272	+	0.557092i	−0.850255	+	0.526370i	$0.823553\pi$
$788$	−1.76638	−	6.59220i	−0.0629245	−	0.234838i
$789$	5.82409	+	10.0876i	0.207343	+	0.359129i
$790$		0			0
$791$	15.8248	+	1.25588i	0.562663	+	0.0446540i
$792$	−10.0939	−	10.0939i	−0.358671	−	0.358671i
$793$	−5.79555	−	1.55291i	−0.205806	−	0.0551456i
$794$	9.55505	−	16.5498i	0.339096	−	0.587332i
$795$		0			0
$796$	6.82475	−	3.94027i	0.241897	−	0.139659i
$797$	9.79796	−	9.79796i	0.347062	−	0.347062i	−0.511952	−	0.859014i	$-0.671078\pi$
$797$	9.79796	−	9.79796i	0.347062	−	0.347062i	0.859014	+	0.511952i	$0.171078\pi$
$798$	56.2261	+	19.9522i	1.99038	+	0.706301i
$799$		−	1.64950i		−	0.0583552i
$800$		0			0
$801$	−49.6495	−	28.6652i	−1.75428	−	1.01283i
$802$	−11.6874	+	3.13162i	−0.412696	+	0.110582i
$803$	−0.492968	+	1.83978i	−0.0173965	+	0.0649245i
$804$	34.3375			1.21099
$805$		0			0
$806$	−16.5498			−0.582943
$807$	15.3931	−	57.4477i	0.541862	−	2.02226i
$808$	8.82511	−	2.36468i	0.310466	−	0.0831892i
$809$	20.8709	+	12.0498i	0.733783	+	0.423650i	0.819804	−	0.572644i	$-0.194082\pi$
$809$	20.8709	+	12.0498i	0.733783	+	0.423650i	−0.0860217	+	0.996293i	$0.527415\pi$
$810$		0			0
$811$		−	22.2131i		−	0.780008i	−0.920813	−	0.390004i	$-0.872474\pi$
$811$		−	22.2131i		−	0.780008i	0.920813	−	0.390004i	$-0.127526\pi$
$812$	13.7241	−	2.53430i	0.481621	−	0.0889365i
$813$	−39.3501	+	39.3501i	−1.38007	+	1.38007i
$814$	4.48190	−	2.58762i	0.157090	−	0.0906962i
$815$		0			0
$816$	5.27492	−	9.13642i	0.184659	−	0.319839i
$817$	−5.18585	−	1.38954i	−0.181430	−	0.0486140i
$818$	3.33753	+	3.33753i	0.116694	+	0.116694i
$819$	−34.0994	−	71.6117i	−1.19153	−	2.50232i
$820$		0			0
$821$	6.09967	+	10.5649i	0.212880	+	0.368719i	0.952615	−	0.304180i	$-0.0983824\pi$
$821$	6.09967	+	10.5649i	0.212880	+	0.368719i	−0.739735	+	0.672899i	$0.765049\pi$
$822$		0			0
$823$	−0.989919	−	3.69443i	−0.0345064	−	0.128780i	0.946524	−	0.322633i	$-0.104568\pi$
$823$	−0.989919	−	3.69443i	−0.0345064	−	0.128780i	−0.981030	+	0.193854i	$0.937901\pi$
$824$	−0.209313	−	0.362541i	−0.00729178	−	0.0126297i
$825$		0			0
$826$	2.17525	−	27.4093i	0.0756866	−	0.953691i
$827$	−29.3267	−	29.3267i	−1.01979	−	1.01979i	−0.999800	−	0.0199900i	$-0.993637\pi$
$827$	−29.3267	−	29.3267i	−1.01979	−	1.01979i	−0.0199900	−	0.999800i	$-0.506363\pi$
$828$	−18.1833	−	4.87220i	−0.631914	−	0.169321i
$829$	7.40437	−	12.8248i	0.257165	−	0.445422i	−0.708317	−	0.705895i	$-0.750545\pi$
$829$	7.40437	−	12.8248i	0.257165	−	0.445422i	0.965481	+	0.260473i	$0.0838784\pi$
$830$		0			0
$831$	39.8248	−	22.9928i	1.38151	−	0.797612i
$832$	3.37822	−	3.37822i	0.117119	−	0.117119i
$833$	−24.1192	+	2.50304i	−0.835680	+	0.0867252i
$834$			66.1993i			2.29230i
$835$		0			0
$836$	14.5876	+	8.42217i	0.504524	+	0.291287i
$837$	33.3726	−	8.94216i	1.15353	−	0.309086i
$838$	−3.05945	+	11.4180i	−0.105687	+	0.394429i
$839$	28.6652			0.989631			0.494816	−	0.868998i	$-0.335236\pi$
$839$	28.6652			0.989631			0.494816	+	0.868998i	$0.335236\pi$
$840$		0			0
$841$	1.17525			0.0405258
$842$	3.15119	−	11.7604i	0.108597	−	0.405290i
$843$	−86.4113	+	23.1538i	−2.97616	+	0.797461i
$844$	−14.5707	−	8.41238i	−0.501543	−	0.289566i
$845$		0			0
$846$			2.98793i			0.102727i
$847$	5.15377	−	14.5235i	0.177086	−	0.499034i
$848$	−9.06847	+	9.06847i	−0.311412	+	0.311412i
$849$	−73.3949	+	42.3746i	−2.51891	+	1.45429i
$850$		0			0
$851$	3.41238	−	5.91041i	0.116975	−	0.202606i
$852$	−17.6502	−	4.72936i	−0.604686	−	0.162025i
$853$	−28.0359	−	28.0359i	−0.959930	−	0.959930i	0.0392974	−	0.999228i	$-0.487488\pi$
$853$	−28.0359	−	28.0359i	−0.959930	−	0.959930i	−0.999228	+	0.0392974i	$0.987488\pi$
$854$	1.88382	−	2.73713i	0.0644630	−	0.0936626i
$855$		0			0
$856$	−7.91238	−	13.7046i	−0.270439	−	0.468415i
$857$	9.45872	+	35.3004i	0.323104	+	1.20584i	0.916204	+	0.400711i	$0.131237\pi$
$857$	9.45872	+	35.3004i	0.323104	+	1.20584i	−0.593101	+	0.805128i	$0.702096\pi$
$858$	−8.56682	−	31.9718i	−0.292467	−	1.09150i
$859$	−14.3326	−	24.8248i	−0.489021	−	0.847010i	0.510899	−	0.859641i	$-0.329313\pi$
$859$	−14.3326	−	24.8248i	−0.489021	−	0.847010i	−0.999920	+	0.0126311i	$0.995979\pi$
$860$		0			0
$861$	−23.7371	+	34.4892i	−0.808959	+	1.17539i
$862$	−13.7533	−	13.7533i	−0.468441	−	0.468441i
$863$	37.6711	+	10.0939i	1.28234	+	0.343602i	0.834746	−	0.550635i	$-0.185615\pi$
$863$	37.6711	+	10.0939i	1.28234	+	0.343602i	0.447593	+	0.894237i	$0.352281\pi$
$864$	−4.98684	+	8.63746i	−0.169656	+	0.293852i
$865$		0			0
$866$	17.2749	−	9.97368i	0.587026	−	0.338919i
$867$	−10.7674	+	10.7674i	−0.365679	+	0.365679i
$868$	3.06506	−	8.63744i	0.104035	−	0.293174i
$869$			22.7492i			0.771713i
$870$		0			0
$871$	46.6495	+	26.9331i	1.58066	+	0.912593i
$872$	−13.3537	+	3.57811i	−0.452213	+	0.121170i
$873$	−2.71951	+	10.1494i	−0.0920416	+	0.343504i
$874$	22.2131			0.751370
$875$		0			0
$876$	2.54983			0.0861509
$877$	−9.53095	+	35.5700i	−0.321837	+	1.20111i	0.595616	+	0.803269i	$0.296908\pi$
$877$	−9.53095	+	35.5700i	−0.321837	+	1.20111i	−0.917453	+	0.397844i	$0.869759\pi$
$878$	−20.0764	+	5.37945i	−0.677545	+	0.181548i
$879$	46.9380	+	27.0997i	1.58318	+	0.914049i
$880$		0			0
$881$			20.9572i			0.706067i	0.935611	+	0.353034i	$0.114850\pi$
$881$			20.9572i			0.706067i	−0.935611	+	0.353034i	$0.885150\pi$
$882$	43.6898	−	4.53404i	1.47111	−	0.152669i
$883$	−14.9197	+	14.9197i	−0.502089	+	0.502089i	−0.912086	−	0.409998i	$-0.865529\pi$
$883$	−14.9197	+	14.9197i	−0.502089	+	0.502089i	0.409998	+	0.912086i	$0.365529\pi$
$884$	14.3326	−	8.27492i	0.482057	−	0.278316i
$885$		0			0
$886$	16.9124	−	29.2931i	0.568182	−	0.984121i
$887$	−16.4371	−	4.40432i	−0.551905	−	0.147882i	−0.0279202	−	0.999610i	$-0.508888\pi$
$887$	−16.4371	−	4.40432i	−0.551905	−	0.147882i	−0.523985	+	0.851728i	$0.675555\pi$
$888$	−4.89898	−	4.89898i	−0.164399	−	0.164399i
$889$	−2.03559	+	25.6495i	−0.0682715	+	0.860257i
$890$		0			0
$891$	13.1375	+	22.7547i	0.440121	+	0.762313i
$892$	2.25633	+	8.42075i	0.0755476	+	0.281947i
$893$	−0.912530	−	3.40561i	−0.0305367	−	0.113964i
$894$	−14.9605	−	25.9124i	−0.500355	−	0.866639i
$895$		0			0
$896$	1.13746	+	2.38876i	0.0379998	+	0.0798030i
$897$	−30.8649	−	30.8649i	−1.03055	−	1.03055i
$898$	−36.2704	−	9.71861i	−1.21036	−	0.324314i
$899$	−9.13642	+	15.8248i	−0.304717	+	0.527785i
$900$		0			0
$901$	−38.4743	+	22.2131i	−1.28176	+	0.740026i
$902$	−8.35858	+	8.35858i	−0.278310	+	0.278310i
$903$	−5.74527	+	1.06093i	−0.191191	+	0.0353054i
$904$		−	6.00000i		−	0.199557i
$905$		0			0
$906$	−5.27492	−	3.04547i	−0.175247	−	0.101179i
$907$	−24.0751	+	6.45091i	−0.799402	+	0.214199i	−0.635321	−	0.772248i	$-0.719132\pi$
$907$	−24.0751	+	6.45091i	−0.799402	+	0.214199i	−0.164081	+	0.986447i	$0.552466\pi$
$908$	0.896575	−	3.34607i	0.0297539	−	0.111043i
$909$	−57.3303			−1.90153
$910$		0			0
$911$	25.6495			0.849806			0.424903	−	0.905239i	$-0.360308\pi$
$911$	25.6495			0.849806			0.424903	+	0.905239i	$0.360308\pi$
$912$	5.83633	−	21.7815i	0.193260	−	0.721256i
$913$	−2.75967	+	0.739452i	−0.0913318	+	0.0244723i
$914$	16.8443	+	9.72508i	0.557161	+	0.321677i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	9.82473	+	3.48638i	0.324441	+	0.115130i
$918$	−24.4304	+	24.4304i	−0.806324	+	0.806324i
$919$	10.0888	−	5.82475i	0.332798	−	0.192141i	−0.324285	−	0.945959i	$-0.605124\pi$
$919$	10.0888	−	5.82475i	0.332798	−	0.192141i	0.657083	+	0.753819i	$0.271790\pi$
$920$		0			0
$921$	−28.4622	+	49.2980i	−0.937862	+	1.62442i
$922$	35.3004	+	9.45872i	1.16256	+	0.311506i
$923$	−20.2693	−	20.2693i	−0.667173	−	0.667173i
$924$	18.2728	+	1.45017i	0.601133	+	0.0477069i
$925$		0			0
$926$	−8.22508	−	14.2463i	−0.270293	−	0.468161i
$927$	0.679878	+	2.53734i	0.0223301	+	0.0833372i
$928$	−1.36525	−	5.09518i	−0.0448165	−	0.167257i
$929$	−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
$931$	−48.4124	+	18.5109i	−1.58665	+	0.606671i
$932$	13.8943	+	13.8943i	0.455123	+	0.455123i
$933$	76.9355	+	20.6148i	2.51876	+	0.674899i
$934$	−13.2285	+	22.9124i	−0.432849	+	0.749716i
$935$		0			0
$936$	−25.9622	+	14.9893i	−0.848601	+	0.489940i
$937$	30.2300	−	30.2300i	0.987572	−	0.987572i	−0.0123513	−	0.999924i	$-0.503932\pi$
$937$	30.2300	−	30.2300i	0.987572	−	0.987572i	0.999924	+	0.0123513i	$0.00393164\pi$
$938$	−22.6961	+	19.3586i	−0.741054	+	0.632079i
$939$		−	34.1993i		−	1.11605i
$940$		0			0
$941$	−49.6495	−	28.6652i	−1.61853	−	0.934457i	−0.987301	−	0.158859i	$-0.949219\pi$
$941$	−49.6495	−	28.6652i	−1.61853	−	0.934457i	−0.631226	−	0.775599i	$-0.717448\pi$
$942$	16.5170	−	4.42572i	0.538153	−	0.144198i
$943$	−4.03459	+	15.0573i	−0.131384	+	0.490333i
$944$	−10.3923			−0.338241
$945$		0			0
$946$	−1.64950			−0.0536300
$947$	0.989919	−	3.69443i	0.0321680	−	0.120053i	−0.947975	−	0.318345i	$-0.896873\pi$
$947$	0.989919	−	3.69443i	0.0321680	−	0.120053i	0.980143	+	0.198292i	$0.0635396\pi$
$948$	29.4170	−	7.88227i	0.955421	−	0.256004i
$949$	3.46410	+	2.00000i	0.112449	+	0.0649227i
$950$		0			0
$951$			54.8185i			1.77761i
$952$	1.66430	+	9.01277i	0.0539404	+	0.292106i
$953$	36.2739	−	36.2739i	1.17503	−	1.17503i	0.194031	−	0.980995i	$-0.437844\pi$
$953$	36.2739	−	36.2739i	1.17503	−	1.17503i	0.980995	−	0.194031i	$-0.0621561\pi$
$954$	69.6927	−	40.2371i	2.25639	−	1.30273i
$955$		0			0
$956$	−5.27492	+	9.13642i	−0.170603	+	0.295493i
$957$	−35.3004	−	9.45872i	−1.14110	−	0.305757i
$958$	−12.9209	−	12.9209i	−0.417454	−	0.417454i
$959$		0			0
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	−2.81297	−	10.4981i	−0.0906937	−	0.338474i
$963$	25.7005	+	95.9155i	0.828186	+	3.09083i
$964$	1.97014	+	3.41238i	0.0634538	+	0.109905i
$965$		0			0
$966$	21.8248	−	10.3923i	0.702200	−	0.334367i
$967$	−17.6242	−	17.6242i	−0.566757	−	0.566757i	0.364462	−	0.931218i	$-0.381253\pi$
$967$	−17.6242	−	17.6242i	−0.566757	−	0.566757i	−0.931218	+	0.364462i	$0.881253\pi$
$968$	−5.62628	−	1.50756i	−0.180835	−	0.0484547i
$969$	39.0575	−	67.6495i	1.25471	−	2.17322i
$970$		0			0
$971$	7.76287	−	4.48190i	0.249122	−	0.143831i	−0.370240	−	0.928936i	$-0.620725\pi$
$971$	7.76287	−	4.48190i	0.249122	−	0.143831i	0.619362	+	0.785105i	$0.287391\pi$
$972$	3.71492	−	3.71492i	0.119156	−	0.119156i
$973$	−37.3214	−	43.7559i	−1.19647	−	1.40275i
$974$		−	21.0997i		−	0.676077i
$975$		0			0
$976$	−1.08762	−	0.627940i	−0.0348140	−	0.0200999i
$977$	24.7755	−	6.63858i	0.792639	−	0.212387i	0.160289	−	0.987070i	$-0.448757\pi$
$977$	24.7755	−	6.63858i	0.792639	−	0.212387i	0.632350	+	0.774683i	$0.282091\pi$
$978$	9.45872	−	35.3004i	0.302457	−	1.12878i
$979$	20.7846			0.664279
$980$		0			0
$981$	86.7492			2.76969
$982$	−8.94216	+	33.3726i	−0.285356	+	1.06496i
$983$	16.8971	−	4.52756i	0.538933	−	0.144407i	0.0209228	−	0.999781i	$-0.493340\pi$
$983$	16.8971	−	4.52756i	0.538933	−	0.144407i	0.518010	+	0.855374i	$0.326673\pi$
$984$	13.7046	+	7.91238i	0.436888	+	0.252237i
$985$		0			0
$986$		−	18.2728i		−	0.581926i
$987$	−2.48987	−	2.91914i	−0.0792535	−	0.0929173i
$988$	25.0136	−	25.0136i	0.795789	−	0.795789i
$989$	−1.88382	+	1.08762i	−0.0599020	+	0.0345844i
$990$		0			0
$991$	−11.8248	+	20.4811i	−0.375626	+	0.650603i	−0.990420	−	0.138084i	$-0.955905\pi$
$991$	−11.8248	+	20.4811i	−0.375626	+	0.650603i	0.614795	+	0.788687i	$0.289239\pi$
$992$	−3.34607	−	0.896575i	−0.106238	−	0.0284663i
$993$	62.0734	+	62.0734i	1.96984	+	1.96984i
$994$	14.3326	−	6.82475i	0.454602	−	0.216468i
$995$		0			0
$996$	1.91238	+	3.31233i	0.0605959	+	0.104955i
$997$	5.59615	+	20.8851i	0.177232	+	0.661438i	0.996161	+	0.0875432i	$0.0279016\pi$
$997$	5.59615	+	20.8851i	0.177232	+	0.661438i	−0.818929	+	0.573895i	$0.805432\pi$
$998$	1.03528	+	3.86370i	0.0327711	+	0.122303i
$999$	11.3446	+	19.6495i	0.358929	+	0.621683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.d.157.3	yes	16
5.2	odd	4	inner	350.2.o.d.143.4	yes	16
5.3	odd	4	inner	350.2.o.d.143.1	✓	16
5.4	even	2	inner	350.2.o.d.157.2	yes	16
7.5	odd	6	inner	350.2.o.d.257.1	yes	16
35.12	even	12	inner	350.2.o.d.243.2	yes	16
35.19	odd	6	inner	350.2.o.d.257.4	yes	16
35.33	even	12	inner	350.2.o.d.243.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.d.143.1	✓	16	5.3	odd	4	inner
350.2.o.d.143.4	yes	16	5.2	odd	4	inner
350.2.o.d.157.2	yes	16	5.4	even	2	inner
350.2.o.d.157.3	yes	16	1.1	even	1	trivial
350.2.o.d.243.2	yes	16	35.12	even	12	inner
350.2.o.d.243.3	yes	16	35.33	even	12	inner
350.2.o.d.257.1	yes	16	7.5	odd	6	inner
350.2.o.d.257.4	yes	16	35.19	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-2.94170 + 0.788227i) q^{3} +(-0.866025 - 0.500000i) q^{4} +3.04547i q^{6} +(-1.71696 - 2.01297i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(5.43424 - 3.13746i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-2.94170 + 0.788227i) q^{3} +(-0.866025 - 0.500000i) q^{4} +3.04547i q^{6} +(-1.71696 - 2.01297i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(5.43424 - 3.13746i) q^{9} +(-1.13746 + 1.97014i) q^{11} +(2.94170 + 0.788227i) q^{12} +(3.37822 + 3.37822i) q^{13} +(-2.38876 + 1.13746i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.896575 + 3.34607i) q^{17} +(-1.62407 - 6.06110i) q^{18} +(3.70219 + 6.41238i) q^{19} +(6.63746 + 4.56821i) q^{21} +(1.60861 + 1.60861i) q^{22} +(2.89778 + 0.776457i) q^{23} +(1.52274 - 2.63746i) q^{24} +(4.13746 - 2.38876i) q^{26} +(-7.05246 + 7.05246i) q^{27} +(0.480443 + 2.60176i) q^{28} -5.27492i q^{29} +(-3.00000 - 1.73205i) q^{31} +(0.965926 - 0.258819i) q^{32} +(1.79315 - 6.69213i) q^{33} +3.46410 q^{34} -6.27492 q^{36} +(0.588792 - 2.19740i) q^{37} +(7.15208 - 1.91639i) q^{38} +(-12.6005 - 7.27492i) q^{39} +5.19615i q^{41} +(6.13045 - 5.22895i) q^{42} +(-0.512711 + 0.512711i) q^{43} +(1.97014 - 1.13746i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-0.459945 - 0.123242i) q^{47} +(-2.15348 - 2.15348i) q^{48} +(-1.10411 + 6.91238i) q^{49} +(-5.27492 - 9.13642i) q^{51} +(-1.23651 - 4.61474i) q^{52} +(3.31929 + 12.3878i) q^{53} +(4.98684 + 8.63746i) q^{54} +(2.63746 + 0.209313i) q^{56} +(-15.9451 - 15.9451i) q^{57} +(-5.09518 - 1.36525i) q^{58} +(-5.19615 + 9.00000i) q^{59} +(-1.08762 + 0.627940i) q^{61} +(-2.44949 + 2.44949i) q^{62} +(-15.6460 - 5.55208i) q^{63} -1.00000i q^{64} +(-6.00000 - 3.46410i) q^{66} +(10.8907 - 2.91816i) q^{67} +(0.896575 - 3.34607i) q^{68} -9.13642 q^{69} -6.00000 q^{71} +(-1.62407 + 6.06110i) q^{72} +(0.808725 - 0.216697i) q^{73} +(-1.97014 - 1.13746i) q^{74} -7.40437i q^{76} +(5.91880 - 1.09297i) q^{77} +(-10.2883 + 10.2883i) q^{78} +(8.66025 - 5.00000i) q^{79} +(5.77492 - 10.0025i) q^{81} +(5.01910 + 1.34486i) q^{82} +(0.888041 + 0.888041i) q^{83} +(-3.46410 - 7.27492i) q^{84} +(0.362541 + 0.627940i) q^{86} +(4.15783 + 15.5172i) q^{87} +(-0.588792 - 2.19740i) q^{88} +(-4.56821 - 7.91238i) q^{89} +(1.00000 - 12.6005i) q^{91} +(-2.12132 - 2.12132i) q^{92} +(10.1904 + 2.73050i) q^{93} +(-0.238085 + 0.412376i) q^{94} +(-2.63746 + 1.52274i) q^{96} +(-1.18406 + 1.18406i) q^{97} +(6.39108 + 2.85554i) q^{98} +14.2749i 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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