LMFDB - Embedded newform 3150.2.m.j.1457.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.4
Root			$-3.16053i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.j.2843.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +5.26561i q^{11} +(3.16053 - 3.16053i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-3.05545 + 3.05545i) q^{17} +(3.72335 + 3.72335i) q^{22} +(-4.32106 - 4.32106i) q^{23} -4.46967i q^{26} +(0.707107 - 0.707107i) q^{28} +9.96230 q^{29} +1.26561 q^{31} +(-0.707107 + 0.707107i) q^{32} +4.32106i q^{34} +(2.93351 + 2.93351i) q^{37} +10.6798i q^{41} +(-0.597714 + 0.597714i) q^{43} +5.26561 q^{44} -6.11091 q^{46} +(3.42614 - 3.42614i) q^{47} +1.00000i q^{49} +(-3.16053 - 3.16053i) q^{52} +(9.88388 + 9.88388i) q^{53} -1.00000i q^{56} +(7.04441 - 7.04441i) q^{58} +3.12563 q^{59} +3.05545 q^{61} +(0.894921 - 0.894921i) q^{62} +1.00000i q^{64} +(-4.59771 - 4.59771i) q^{67} +(3.05545 + 3.05545i) q^{68} +9.23654i q^{71} +(-10.2160 + 10.2160i) q^{73} +4.14860 q^{74} +(-3.72335 + 3.72335i) q^{77} +3.57969i q^{79} +(7.55178 + 7.55178i) q^{82} +(6.21016 + 6.21016i) q^{83} +0.845296i q^{86} +(3.72335 - 3.72335i) q^{88} -3.61916 q^{89} +4.46967 q^{91} +(-4.32106 + 4.32106i) q^{92} -4.84530i q^{94} +(4.63630 + 4.63630i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{22} + 8 q^{23} + 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} + 24 q^{44} - 12 q^{47} - 4 q^{52} + 32 q^{53} - 12 q^{58} + 16 q^{59} + 4 q^{62} - 20 q^{67} - 36 q^{73} + 40 q^{74} - 4 q^{77} + 12 q^{82} + 56 q^{83} + 4 q^{88} + 72 q^{89} + 8 q^{92} + 4 q^{97}+O(q^{100}) $ 8 * q + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^22 + 8 * q^23 + 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 + 24 * q^44 - 12 * q^47 - 4 * q^52 + 32 * q^53 - 12 * q^58 + 16 * q^59 + 4 * q^62 - 20 * q^67 - 36 * q^73 + 40 * q^74 - 4 * q^77 + 12 * q^82 + 56 * q^83 + 4 * q^88 + 72 * q^89 + 8 * q^92 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			5.26561i			1.58764i	0.608152	+	0.793821i	$0.291911\pi$
$11$			5.26561i			1.58764i	−0.608152	+	0.793821i	$0.708089\pi$
$12$		0			0
$13$	3.16053	−	3.16053i	0.876574	−	0.876574i	−0.116605	−	0.993178i	$-0.537201\pi$
$13$	3.16053	−	3.16053i	0.876574	−	0.876574i	0.993178	+	0.116605i	$0.0372011\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.05545	+	3.05545i	−0.741056	+	0.741056i	−0.972781	−	0.231725i	$-0.925563\pi$
$17$	−3.05545	+	3.05545i	−0.741056	+	0.741056i	0.231725	+	0.972781i	$0.425563\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$	3.72335	+	3.72335i	0.793821	+	0.793821i
$23$	−4.32106	−	4.32106i	−0.901004	−	0.901004i	0.0945192	−	0.995523i	$-0.469869\pi$
$23$	−4.32106	−	4.32106i	−0.901004	−	0.901004i	−0.995523	+	0.0945192i	$0.969869\pi$
$24$		0			0
$25$		0			0
$26$		−	4.46967i		−	0.876574i
$27$		0			0
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	9.96230			1.84995			0.924977	−	0.380024i	$-0.124084\pi$
$29$	9.96230			1.84995			0.924977	+	0.380024i	$0.124084\pi$
$30$		0			0
$31$	1.26561			0.227310			0.113655	−	0.993520i	$-0.463744\pi$
$31$	1.26561			0.227310			0.113655	+	0.993520i	$0.463744\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			4.32106i			0.741056i
$35$		0			0
$36$		0			0
$37$	2.93351	+	2.93351i	0.482265	+	0.482265i	0.905854	−	0.423589i	$-0.139230\pi$
$37$	2.93351	+	2.93351i	0.482265	+	0.482265i	−0.423589	+	0.905854i	$0.639230\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			10.6798i			1.66791i	0.551834	+	0.833954i	$0.313928\pi$
$41$			10.6798i			1.66791i	−0.551834	+	0.833954i	$0.686072\pi$
$42$		0			0
$43$	−0.597714	+	0.597714i	−0.0911506	+	0.0911506i	−0.751212	−	0.660061i	$-0.770530\pi$
$43$	−0.597714	+	0.597714i	−0.0911506	+	0.0911506i	0.660061	+	0.751212i	$0.270530\pi$
$44$	5.26561			0.793821
$45$		0			0
$46$	−6.11091			−0.901004
$47$	3.42614	−	3.42614i	0.499754	−	0.499754i	−0.411607	−	0.911361i	$-0.635032\pi$
$47$	3.42614	−	3.42614i	0.499754	−	0.499754i	0.911361	+	0.411607i	$0.135032\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	−3.16053	−	3.16053i	−0.438287	−	0.438287i
$53$	9.88388	+	9.88388i	1.35766	+	1.35766i	0.876800	+	0.480855i	$0.159674\pi$
$53$	9.88388	+	9.88388i	1.35766	+	1.35766i	0.480855	+	0.876800i	$0.340326\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	7.04441	−	7.04441i	0.924977	−	0.924977i
$59$	3.12563			0.406923			0.203461	−	0.979083i	$-0.434781\pi$
$59$	3.12563			0.406923			0.203461	+	0.979083i	$0.434781\pi$
$60$		0			0
$61$	3.05545			0.391211			0.195605	−	0.980683i	$-0.437333\pi$
$61$	3.05545			0.391211			0.195605	+	0.980683i	$0.437333\pi$
$62$	0.894921	−	0.894921i	0.113655	−	0.113655i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−4.59771	−	4.59771i	−0.561700	−	0.561700i	0.368090	−	0.929790i	$-0.380012\pi$
$67$	−4.59771	−	4.59771i	−0.561700	−	0.561700i	−0.929790	+	0.368090i	$0.880012\pi$
$68$	3.05545	+	3.05545i	0.370528	+	0.370528i
$69$		0			0
$70$		0			0
$71$			9.23654i			1.09618i	0.836421	+	0.548088i	$0.184644\pi$
$71$			9.23654i			1.09618i	−0.836421	+	0.548088i	$0.815356\pi$
$72$		0			0
$73$	−10.2160	+	10.2160i	−1.19569	+	1.19569i	−0.220246	+	0.975444i	$0.570686\pi$
$73$	−10.2160	+	10.2160i	−1.19569	+	1.19569i	−0.975444	+	0.220246i	$0.929314\pi$
$74$	4.14860			0.482265
$75$		0			0
$76$		0			0
$77$	−3.72335	+	3.72335i	−0.424315	+	0.424315i
$78$		0			0
$79$			3.57969i			0.402746i	0.979515	+	0.201373i	$0.0645403\pi$
$79$			3.57969i			0.402746i	−0.979515	+	0.201373i	$0.935460\pi$
$80$		0			0
$81$		0			0
$82$	7.55178	+	7.55178i	0.833954	+	0.833954i
$83$	6.21016	+	6.21016i	0.681653	+	0.681653i	0.960373	−	0.278719i	$-0.0899099\pi$
$83$	6.21016	+	6.21016i	0.681653	+	0.681653i	−0.278719	+	0.960373i	$0.589910\pi$
$84$		0			0
$85$		0			0
$86$			0.845296i			0.0911506i
$87$		0			0
$88$	3.72335	−	3.72335i	0.396910	−	0.396910i
$89$	−3.61916			−0.383630			−0.191815	−	0.981431i	$-0.561437\pi$
$89$	−3.61916			−0.383630			−0.191815	+	0.981431i	$0.561437\pi$
$90$		0			0
$91$	4.46967			0.468548
$92$	−4.32106	+	4.32106i	−0.450502	+	0.450502i
$93$		0			0
$94$		−	4.84530i		−	0.499754i
$95$		0			0
$96$		0			0
$97$	4.63630	+	4.63630i	0.470745	+	0.470745i	0.902156	−	0.431411i	$-0.141984\pi$
$97$	4.63630	+	4.63630i	0.470745	+	0.470745i	−0.431411	+	0.902156i	$0.641984\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	2.12652i		−	0.211597i	−0.994388	−	0.105798i	$-0.966260\pi$
$101$		−	2.12652i		−	0.211597i	0.994388	−	0.105798i	$-0.0337398\pi$
$102$		0			0
$103$	10.9225	−	10.9225i	1.07622	−	1.07622i	0.0793778	−	0.996845i	$-0.474707\pi$
$103$	10.9225	−	10.9225i	1.07622	−	1.07622i	0.996845	−	0.0793778i	$-0.0252933\pi$
$104$	−4.46967			−0.438287
$105$		0			0
$106$	13.9779			1.35766
$107$	6.40811	−	6.40811i	0.619496	−	0.619496i	−0.325906	−	0.945402i	$-0.605669\pi$
$107$	6.40811	−	6.40811i	0.619496	−	0.619496i	0.945402	+	0.325906i	$0.105669\pi$
$108$		0			0
$109$		−	9.55760i		−	0.915452i	−0.889093	−	0.457726i	$-0.848664\pi$
$109$		−	9.55760i		−	0.915452i	0.889093	−	0.457726i	$-0.151336\pi$
$110$		0			0
$111$		0			0
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−3.29809	−	3.29809i	−0.310259	−	0.310259i	0.534751	−	0.845010i	$-0.320405\pi$
$113$	−3.29809	−	3.29809i	−0.310259	−	0.310259i	−0.845010	+	0.534751i	$0.820405\pi$
$114$		0			0
$115$		0			0
$116$		−	9.96230i		−	0.924977i
$117$		0			0
$118$	2.21016	−	2.21016i	0.203461	−	0.203461i
$119$	−4.32106			−0.396111
$120$		0			0
$121$	−16.7266			−1.52060
$122$	2.16053	−	2.16053i	0.195605	−	0.195605i
$123$		0			0
$124$		−	1.26561i		−	0.113655i
$125$		0			0
$126$		0			0
$127$	8.32106	+	8.32106i	0.738375	+	0.738375i	0.972263	−	0.233889i	$-0.0751451\pi$
$127$	8.32106	+	8.32106i	0.738375	+	0.738375i	−0.233889	+	0.972263i	$0.575145\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	17.4246i		−	1.52240i	−0.648520	−	0.761198i	$-0.724612\pi$
$131$		−	17.4246i		−	1.52240i	0.648520	−	0.761198i	$-0.275388\pi$
$132$		0			0
$133$		0			0
$134$	−6.50215			−0.561700
$135$		0			0
$136$	4.32106			0.370528
$137$	−2.35876	+	2.35876i	−0.201523	+	0.201523i	−0.800652	−	0.599130i	$-0.795513\pi$
$137$	−2.35876	+	2.35876i	−0.201523	+	0.201523i	0.599130	+	0.800652i	$0.295513\pi$
$138$		0			0
$139$		−	21.8449i		−	1.85286i	−0.376464	−	0.926431i	$-0.622860\pi$
$139$		−	21.8449i		−	1.85286i	0.376464	−	0.926431i	$-0.377140\pi$
$140$		0			0
$141$		0			0
$142$	6.53122	+	6.53122i	0.548088	+	0.548088i
$143$	16.6421	+	16.6421i	1.39168	+	1.39168i
$144$		0			0
$145$		0			0
$146$			14.4476i			1.19569i
$147$		0			0
$148$	2.93351	−	2.93351i	0.241133	−	0.241133i
$149$	6.08541			0.498536			0.249268	−	0.968435i	$-0.419810\pi$
$149$	6.08541			0.498536			0.249268	+	0.968435i	$0.419810\pi$
$150$		0			0
$151$	22.7530			1.85162			0.925808	−	0.377995i	$-0.123386\pi$
$151$	22.7530			1.85162			0.925808	+	0.377995i	$0.123386\pi$
$152$		0			0
$153$		0			0
$154$			5.26561i			0.424315i
$155$		0			0
$156$		0			0
$157$	10.7181	+	10.7181i	0.855400	+	0.855400i	0.990792	−	0.135392i	$-0.0432293\pi$
$157$	10.7181	+	10.7181i	0.855400	+	0.855400i	−0.135392	+	0.990792i	$0.543229\pi$
$158$	2.53122	+	2.53122i	0.201373	+	0.201373i
$159$		0			0
$160$		0			0
$161$		−	6.11091i		−	0.481607i
$162$		0			0
$163$	4.04441	−	4.04441i	0.316783	−	0.316783i	−0.530747	−	0.847530i	$-0.678089\pi$
$163$	4.04441	−	4.04441i	0.316783	−	0.316783i	0.847530	+	0.530747i	$0.178089\pi$
$164$	10.6798			0.833954
$165$		0			0
$166$	8.78249			0.681653
$167$	−5.76929	+	5.76929i	−0.446441	+	0.446441i	−0.894169	−	0.447729i	$-0.852233\pi$
$167$	−5.76929	+	5.76929i	−0.446441	+	0.446441i	0.447729	+	0.894169i	$0.352233\pi$
$168$		0			0
$169$		−	6.97792i		−	0.536763i
$170$		0			0
$171$		0			0
$172$	0.597714	+	0.597714i	0.0455753	+	0.0455753i
$173$	6.14492	+	6.14492i	0.467189	+	0.467189i	0.901003	−	0.433813i	$-0.142832\pi$
$173$	6.14492	+	6.14492i	0.467189	+	0.467189i	−0.433813	+	0.901003i	$0.642832\pi$
$174$		0			0
$175$		0			0
$176$		−	5.26561i		−	0.396910i
$177$		0			0
$178$	−2.55913	+	2.55913i	−0.191815	+	0.191815i
$179$	0.391244			0.0292430			0.0146215	−	0.999893i	$-0.495346\pi$
$179$	0.391244			0.0292430			0.0146215	+	0.999893i	$0.495346\pi$
$180$		0			0
$181$	−15.0113			−1.11578			−0.557890	−	0.829915i	$-0.688389\pi$
$181$	−15.0113			−1.11578			−0.557890	+	0.829915i	$0.688389\pi$
$182$	3.16053	−	3.16053i	0.234274	−	0.234274i
$183$		0			0
$184$			6.11091i			0.450502i
$185$		0			0
$186$		0			0
$187$	−16.0888	−	16.0888i	−1.17653	−	1.17653i
$188$	−3.42614	−	3.42614i	−0.249877	−	0.249877i
$189$		0			0
$190$		0			0
$191$			23.3474i			1.68936i	0.535270	+	0.844681i	$0.320210\pi$
$191$			23.3474i			1.68936i	−0.535270	+	0.844681i	$0.679790\pi$
$192$		0			0
$193$	−6.69059	+	6.69059i	−0.481599	+	0.481599i	−0.905642	−	0.424043i	$-0.860611\pi$
$193$	−6.69059	+	6.69059i	−0.481599	+	0.481599i	0.424043	+	0.905642i	$0.360611\pi$
$194$	6.55672			0.470745
$195$		0			0
$196$	1.00000			0.0714286
$197$	0.375629	−	0.375629i	0.0267625	−	0.0267625i	−0.693599	−	0.720361i	$-0.743976\pi$
$197$	0.375629	−	0.375629i	0.0267625	−	0.0267625i	0.720361	+	0.693599i	$0.243976\pi$
$198$		0			0
$199$		−	18.0481i		−	1.27940i	−0.768626	−	0.639698i	$-0.779059\pi$
$199$		−	18.0481i		−	1.27940i	0.768626	−	0.639698i	$-0.220941\pi$
$200$		0			0
$201$		0			0
$202$	−1.50368	−	1.50368i	−0.105798	−	0.105798i
$203$	7.04441	+	7.04441i	0.494421	+	0.494421i
$204$		0			0
$205$		0			0
$206$		−	15.4467i		−	1.07622i
$207$		0			0
$208$	−3.16053	+	3.16053i	−0.219143	+	0.219143i
$209$		0			0
$210$		0			0
$211$	−8.22181			−0.566013			−0.283006	−	0.959118i	$-0.591332\pi$
$211$	−8.22181			−0.566013			−0.283006	+	0.959118i	$0.591332\pi$
$212$	9.88388	−	9.88388i	0.678828	−	0.678828i
$213$		0			0
$214$		−	9.06244i		−	0.619496i
$215$		0			0
$216$		0			0
$217$	0.894921	+	0.894921i	0.0607512	+	0.0607512i
$218$	−6.75825	−	6.75825i	−0.457726	−	0.457726i
$219$		0			0
$220$		0			0
$221$			19.3137i			1.29918i
$222$		0			0
$223$	13.2365	−	13.2365i	0.886384	−	0.886384i	−0.107789	−	0.994174i	$-0.534377\pi$
$223$	13.2365	−	13.2365i	0.886384	−	0.886384i	0.994174	+	0.107789i	$0.0343772\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−4.66421			−0.310259
$227$	−5.46878	+	5.46878i	−0.362976	+	0.362976i	−0.864907	−	0.501932i	$-0.832623\pi$
$227$	−5.46878	+	5.46878i	−0.362976	+	0.362976i	0.501932	+	0.864907i	$0.332623\pi$
$228$		0			0
$229$		−	13.0966i		−	0.865445i	−0.901527	−	0.432723i	$-0.857553\pi$
$229$		−	13.0966i		−	0.865445i	0.901527	−	0.432723i	$-0.142447\pi$
$230$		0			0
$231$		0			0
$232$	−7.04441	−	7.04441i	−0.462488	−	0.462488i
$233$	−0.642125	−	0.642125i	−0.0420670	−	0.0420670i	0.685760	−	0.727827i	$-0.259470\pi$
$233$	−0.642125	−	0.642125i	−0.0420670	−	0.0420670i	−0.727827	+	0.685760i	$0.759470\pi$
$234$		0			0
$235$		0			0
$236$		−	3.12563i		−	0.203461i
$237$		0			0
$238$	−3.05545	+	3.05545i	−0.198056	+	0.198056i
$239$	−25.4246			−1.64458			−0.822291	−	0.569068i	$-0.807304\pi$
$239$	−25.4246			−1.64458			−0.822291	+	0.569068i	$0.807304\pi$
$240$		0			0
$241$	−7.46878			−0.481106			−0.240553	−	0.970636i	$-0.577329\pi$
$241$	−7.46878			−0.481106			−0.240553	+	0.970636i	$0.577329\pi$
$242$	−11.8275	+	11.8275i	−0.760302	+	0.760302i
$243$		0			0
$244$		−	3.05545i		−	0.195605i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.894921	−	0.894921i	−0.0568276	−	0.0568276i
$249$		0			0
$250$		0			0
$251$			1.23654i			0.0780497i	0.999238	+	0.0390249i	$0.0124252\pi$
$251$			1.23654i			0.0780497i	−0.999238	+	0.0390249i	$0.987575\pi$
$252$		0			0
$253$	22.7530	−	22.7530i	1.43047	−	1.43047i
$254$	11.7678			0.738375
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.8076	+	10.8076i	−0.674159	+	0.674159i	−0.958672	−	0.284513i	$-0.908168\pi$
$257$	−10.8076	+	10.8076i	−0.674159	+	0.674159i	0.284513	+	0.958672i	$0.408168\pi$
$258$		0			0
$259$			4.14860i			0.257782i
$260$		0			0
$261$		0			0
$262$	−12.3211	−	12.3211i	−0.761198	−	0.761198i
$263$	6.99265	+	6.99265i	0.431185	+	0.431185i	0.889031	−	0.457846i	$-0.151379\pi$
$263$	6.99265	+	6.99265i	0.431185	+	0.431185i	−0.457846	+	0.889031i	$0.651379\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−4.59771	+	4.59771i	−0.280850	+	0.280850i
$269$	21.7374			1.32535			0.662677	−	0.748905i	$-0.269420\pi$
$269$	21.7374			1.32535			0.662677	+	0.748905i	$0.269420\pi$
$270$		0			0
$271$	−4.98566			−0.302857			−0.151429	−	0.988468i	$-0.548387\pi$
$271$	−4.98566			−0.302857			−0.151429	+	0.988468i	$0.548387\pi$
$272$	3.05545	−	3.05545i	0.185264	−	0.185264i
$273$		0			0
$274$			3.33579i			0.201523i
$275$		0			0
$276$		0			0
$277$	−1.80787	−	1.80787i	−0.108624	−	0.108624i	0.650706	−	0.759330i	$-0.274473\pi$
$277$	−1.80787	−	1.80787i	−0.108624	−	0.108624i	−0.759330	+	0.650706i	$0.774473\pi$
$278$	−15.4467	−	15.4467i	−0.926431	−	0.926431i
$279$		0			0
$280$		0			0
$281$			8.66296i			0.516789i	0.966040	+	0.258394i	$0.0831934\pi$
$281$			8.66296i			0.516789i	−0.966040	+	0.258394i	$0.916807\pi$
$282$		0			0
$283$	1.55760	−	1.55760i	0.0925899	−	0.0925899i	−0.659295	−	0.751885i	$-0.729145\pi$
$283$	1.55760	−	1.55760i	0.0925899	−	0.0925899i	0.751885	+	0.659295i	$0.229145\pi$
$284$	9.23654			0.548088
$285$		0			0
$286$	23.5355			1.39168
$287$	−7.55178	+	7.55178i	−0.445767	+	0.445767i
$288$		0			0
$289$		−	1.67158i		−	0.0983284i
$290$		0			0
$291$		0			0
$292$	10.2160	+	10.2160i	0.597845	+	0.597845i
$293$	−5.39366	−	5.39366i	−0.315101	−	0.315101i	0.531781	−	0.846882i	$-0.321523\pi$
$293$	−5.39366	−	5.39366i	−0.315101	−	0.315101i	−0.846882	+	0.531781i	$0.821523\pi$
$294$		0			0
$295$		0			0
$296$		−	4.14860i		−	0.241133i
$297$		0			0
$298$	4.30303	−	4.30303i	0.249268	−	0.249268i
$299$	−27.3137			−1.57959
$300$		0			0
$301$	−0.845296			−0.0487220
$302$	16.0888	−	16.0888i	0.925808	−	0.925808i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.46878	+	1.46878i	0.0838277	+	0.0838277i	0.747777	−	0.663950i	$-0.231121\pi$
$307$	1.46878	+	1.46878i	0.0838277	+	0.0838277i	−0.663950	+	0.747777i	$0.731121\pi$
$308$	3.72335	+	3.72335i	0.212157	+	0.212157i
$309$		0			0
$310$		0			0
$311$		−	30.9822i		−	1.75684i	−0.477889	−	0.878420i	$-0.658598\pi$
$311$		−	30.9822i		−	1.75684i	0.477889	−	0.878420i	$-0.341402\pi$
$312$		0			0
$313$	−6.74720	+	6.74720i	−0.381375	+	0.381375i	−0.871597	−	0.490223i	$-0.836915\pi$
$313$	−6.74720	+	6.74720i	−0.381375	+	0.381375i	0.490223	+	0.871597i	$0.336915\pi$
$314$	15.1577			0.855400
$315$		0			0
$316$	3.57969			0.201373
$317$	−20.4151	+	20.4151i	−1.14663	+	1.14663i	−0.159415	+	0.987212i	$0.550961\pi$
$317$	−20.4151	+	20.4151i	−1.14663	+	1.14663i	−0.987212	+	0.159415i	$0.949039\pi$
$318$		0			0
$319$			52.4576i			2.93706i
$320$		0			0
$321$		0			0
$322$	−4.32106	−	4.32106i	−0.240803	−	0.240803i
$323$		0			0
$324$		0			0
$325$		0			0
$326$		−	5.71966i		−	0.316783i
$327$		0			0
$328$	7.55178	−	7.55178i	0.416977	−	0.416977i
$329$	4.84530			0.267130
$330$		0			0
$331$	−18.2513			−1.00318			−0.501590	−	0.865105i	$-0.667251\pi$
$331$	−18.2513			−1.00318			−0.501590	+	0.865105i	$0.667251\pi$
$332$	6.21016	−	6.21016i	0.340827	−	0.340827i
$333$		0			0
$334$			8.15900i			0.446441i
$335$		0			0
$336$		0			0
$337$	7.21016	+	7.21016i	0.392762	+	0.392762i	0.875671	−	0.482909i	$-0.160420\pi$
$337$	7.21016	+	7.21016i	0.392762	+	0.392762i	−0.482909	+	0.875671i	$0.660420\pi$
$338$	−4.93413	−	4.93413i	−0.268381	−	0.268381i
$339$		0			0
$340$		0			0
$341$			6.66421i			0.360887i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	0.845296			0.0455753
$345$		0			0
$346$	8.69022			0.467189
$347$	−10.8284	+	10.8284i	−0.581300	+	0.581300i	−0.935261	−	0.353960i	$-0.884835\pi$
$347$	−10.8284	+	10.8284i	−0.581300	+	0.581300i	0.353960	+	0.935261i	$0.384835\pi$
$348$		0			0
$349$			16.0598i			0.859659i	0.902910	+	0.429829i	$0.141426\pi$
$349$			16.0598i			0.859659i	−0.902910	+	0.429829i	$0.858574\pi$
$350$		0			0
$351$		0			0
$352$	−3.72335	−	3.72335i	−0.198455	−	0.198455i
$353$	−9.26561	−	9.26561i	−0.493159	−	0.493159i	0.416141	−	0.909300i	$-0.363382\pi$
$353$	−9.26561	−	9.26561i	−0.493159	−	0.493159i	−0.909300	+	0.416141i	$0.863382\pi$
$354$		0			0
$355$		0			0
$356$			3.61916i			0.191815i
$357$		0			0
$358$	0.276651	−	0.276651i	0.0146215	−	0.0146215i
$359$	−7.35787			−0.388334			−0.194167	−	0.980969i	$-0.562200\pi$
$359$	−7.35787			−0.388334			−0.194167	+	0.980969i	$0.562200\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	−10.6146	+	10.6146i	−0.557890	+	0.557890i
$363$		0			0
$364$		−	4.46967i		−	0.234274i
$365$		0			0
$366$		0			0
$367$	−23.1443	−	23.1443i	−1.20812	−	1.20812i	−0.971635	−	0.236487i	$-0.924004\pi$
$367$	−23.1443	−	23.1443i	−1.20812	−	1.20812i	−0.236487	−	0.971635i	$-0.575996\pi$
$368$	4.32106	+	4.32106i	0.225251	+	0.225251i
$369$		0			0
$370$		0			0
$371$			13.9779i			0.725697i
$372$		0			0
$373$	−0.0812231	+	0.0812231i	−0.00420557	+	0.00420557i	−0.709206	−	0.705001i	$-0.750947\pi$
$373$	−0.0812231	+	0.0812231i	−0.00420557	+	0.00420557i	0.705001	+	0.709206i	$0.250947\pi$
$374$	−22.7530			−1.17653
$375$		0			0
$376$	−4.84530			−0.249877
$377$	31.4862	−	31.4862i	1.62162	−	1.62162i
$378$		0			0
$379$			12.3548i			0.634623i	0.948321	+	0.317312i	$0.102780\pi$
$379$			12.3548i			0.634623i	−0.948321	+	0.317312i	$0.897220\pi$
$380$		0			0
$381$		0			0
$382$	16.5091	+	16.5091i	0.844681	+	0.844681i
$383$	−11.7546	−	11.7546i	−0.600631	−	0.600631i	0.339849	−	0.940480i	$-0.389624\pi$
$383$	−11.7546	−	11.7546i	−0.600631	−	0.600631i	−0.940480	+	0.339849i	$0.889624\pi$
$384$		0			0
$385$		0			0
$386$			9.46192i			0.481599i
$387$		0			0
$388$	4.63630	−	4.63630i	0.235372	−	0.235372i
$389$	−11.4960			−0.582873			−0.291436	−	0.956590i	$-0.594133\pi$
$389$	−11.4960			−0.582873			−0.291436	+	0.956590i	$0.594133\pi$
$390$		0			0
$391$	26.4056			1.33539
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	0.531220i		−	0.0267625i
$395$		0			0
$396$		0			0
$397$	11.2424	+	11.2424i	0.564238	+	0.564238i	0.930509	−	0.366270i	$-0.119365\pi$
$397$	11.2424	+	11.2424i	0.564238	+	0.564238i	−0.366270	+	0.930509i	$0.619365\pi$
$398$	−12.7619	−	12.7619i	−0.639698	−	0.639698i
$399$		0			0
$400$		0			0
$401$			29.5269i			1.47450i	0.675619	+	0.737251i	$0.263877\pi$
$401$			29.5269i			1.47450i	−0.675619	+	0.737251i	$0.736123\pi$
$402$		0			0
$403$	4.00000	−	4.00000i	0.199254	−	0.199254i
$404$	−2.12652			−0.105798
$405$		0			0
$406$	9.96230			0.494421
$407$	−15.4467	+	15.4467i	−0.765664	+	0.765664i
$408$		0			0
$409$		−	26.2916i		−	1.30004i	−0.759919	−	0.650018i	$-0.774761\pi$
$409$		−	26.2916i		−	1.30004i	0.759919	−	0.650018i	$-0.225239\pi$
$410$		0			0
$411$		0			0
$412$	−10.9225	−	10.9225i	−0.538111	−	0.538111i
$413$	2.21016	+	2.21016i	0.108755	+	0.108755i
$414$		0			0
$415$		0			0
$416$			4.46967i			0.219143i
$417$		0			0
$418$		0			0
$419$	20.5980			1.00628			0.503138	−	0.864206i	$-0.332179\pi$
$419$	20.5980			1.00628			0.503138	+	0.864206i	$0.332179\pi$
$420$		0			0
$421$	−1.73402			−0.0845111			−0.0422556	−	0.999107i	$-0.513454\pi$
$421$	−1.73402			−0.0845111			−0.0422556	+	0.999107i	$0.513454\pi$
$422$	−5.81370	+	5.81370i	−0.283006	+	0.283006i
$423$		0			0
$424$		−	13.9779i		−	0.678828i
$425$		0			0
$426$		0			0
$427$	2.16053	+	2.16053i	0.104555	+	0.104555i
$428$	−6.40811	−	6.40811i	−0.309748	−	0.309748i
$429$		0			0
$430$		0			0
$431$		−	1.70102i		−	0.0819353i	−0.999160	−	0.0409676i	$-0.986956\pi$
$431$		−	1.70102i		−	0.0819353i	0.999160	−	0.0409676i	$-0.0130441\pi$
$432$		0			0
$433$	−2.88757	+	2.88757i	−0.138768	+	0.138768i	−0.773078	−	0.634311i	$-0.781284\pi$
$433$	−2.88757	+	2.88757i	−0.138768	+	0.138768i	0.634311	+	0.773078i	$0.281284\pi$
$434$	1.26561			0.0607512
$435$		0			0
$436$	−9.55760			−0.457726
$437$		0			0
$438$		0			0
$439$		−	32.8011i		−	1.56551i	−0.622328	−	0.782756i	$-0.713813\pi$
$439$		−	32.8011i		−	1.56551i	0.622328	−	0.782756i	$-0.286187\pi$
$440$		0			0
$441$		0			0
$442$	13.6569	+	13.6569i	0.649590	+	0.649590i
$443$	−20.0650	−	20.0650i	−0.953315	−	0.953315i	0.0456425	−	0.998958i	$-0.485466\pi$
$443$	−20.0650	−	20.0650i	−0.953315	−	0.953315i	−0.998958	+	0.0456425i	$0.985466\pi$
$444$		0			0
$445$		0			0
$446$		−	18.7193i		−	0.886384i
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−11.9767			−0.565214			−0.282607	−	0.959236i	$-0.591199\pi$
$449$	−11.9767			−0.565214			−0.282607	+	0.959236i	$0.591199\pi$
$450$		0			0
$451$	−56.2358			−2.64804
$452$	−3.29809	+	3.29809i	−0.155129	+	0.155129i
$453$		0			0
$454$			7.73402i			0.362976i
$455$		0			0
$456$		0			0
$457$	−6.46878	−	6.46878i	−0.302597	−	0.302597i	0.539432	−	0.842029i	$-0.318639\pi$
$457$	−6.46878	−	6.46878i	−0.302597	−	0.302597i	−0.842029	+	0.539432i	$0.818639\pi$
$458$	−9.26067	−	9.26067i	−0.432723	−	0.432723i
$459$		0			0
$460$		0			0
$461$		−	37.0915i		−	1.72752i	−0.503901	−	0.863761i	$-0.668102\pi$
$461$		−	37.0915i		−	1.72752i	0.503901	−	0.863761i	$-0.331898\pi$
$462$		0			0
$463$	0.232240	−	0.232240i	0.0107931	−	0.0107931i	−0.701690	−	0.712483i	$-0.747571\pi$
$463$	0.232240	−	0.232240i	0.0107931	−	0.0107931i	0.712483	+	0.701690i	$0.247571\pi$
$464$	−9.96230			−0.462488
$465$		0			0
$466$	−0.908103			−0.0420670
$467$	22.1997	−	22.1997i	1.02728	−	1.02728i	0.0276636	−	0.999617i	$-0.491193\pi$
$467$	22.1997	−	22.1997i	1.02728	−	1.02728i	0.999617	−	0.0276636i	$-0.00880672\pi$
$468$		0			0
$469$		−	6.50215i		−	0.300241i
$470$		0			0
$471$		0			0
$472$	−2.21016	−	2.21016i	−0.101731	−	0.101731i
$473$	−3.14733	−	3.14733i	−0.144714	−	0.144714i
$474$		0			0
$475$		0			0
$476$			4.32106i			0.198056i
$477$		0			0
$478$	−17.9779	+	17.9779i	−0.822291	+	0.822291i
$479$	−20.7751			−0.949239			−0.474620	−	0.880191i	$-0.657414\pi$
$479$	−20.7751			−0.949239			−0.474620	+	0.880191i	$0.657414\pi$
$480$		0			0
$481$	18.5429			0.845482
$482$	−5.28123	+	5.28123i	−0.240553	+	0.240553i
$483$		0			0
$484$			16.7266i			0.760302i
$485$		0			0
$486$		0			0
$487$	1.00735	+	1.00735i	0.0456476	+	0.0456476i	0.729562	−	0.683915i	$-0.239724\pi$
$487$	1.00735	+	1.00735i	0.0456476	+	0.0456476i	−0.683915	+	0.729562i	$0.739724\pi$
$488$	−2.16053	−	2.16053i	−0.0978027	−	0.0978027i
$489$		0			0
$490$		0			0
$491$		−	6.95620i		−	0.313929i	−0.987604	−	0.156964i	$-0.949829\pi$
$491$		−	6.95620i		−	0.313929i	0.987604	−	0.156964i	$-0.0501708\pi$
$492$		0			0
$493$	−30.4393	+	30.4393i	−1.37092	+	1.37092i
$494$		0			0
$495$		0			0
$496$	−1.26561			−0.0568276
$497$	−6.53122	+	6.53122i	−0.292965	+	0.292965i
$498$		0			0
$499$		−	20.9969i		−	0.939951i	−0.882679	−	0.469976i	$-0.844263\pi$
$499$		−	20.9969i		−	0.939951i	0.882679	−	0.469976i	$-0.155737\pi$
$500$		0			0
$501$		0			0
$502$	0.874366	+	0.874366i	0.0390249	+	0.0390249i
$503$	7.29315	+	7.29315i	0.325186	+	0.325186i	0.850752	−	0.525567i	$-0.176147\pi$
$503$	7.29315	+	7.29315i	0.325186	+	0.325186i	−0.525567	+	0.850752i	$0.676147\pi$
$504$		0			0
$505$		0			0
$506$		−	32.1776i		−	1.43047i
$507$		0			0
$508$	8.32106	−	8.32106i	0.369187	−	0.369187i
$509$	−0.545062			−0.0241595			−0.0120797	−	0.999927i	$-0.503845\pi$
$509$	−0.545062			−0.0241595			−0.0120797	+	0.999927i	$0.503845\pi$
$510$		0			0
$511$	−14.4476			−0.639123
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			15.2843i			0.674159i
$515$		0			0
$516$		0			0
$517$	18.0407	+	18.0407i	0.793430	+	0.793430i
$518$	2.93351	+	2.93351i	0.128891	+	0.128891i
$519$		0			0
$520$		0			0
$521$		−	21.6963i		−	0.950533i	−0.879842	−	0.475267i	$-0.842352\pi$
$521$		−	21.6963i		−	0.950533i	0.879842	−	0.475267i	$-0.157648\pi$
$522$		0			0
$523$	−26.9822	+	26.9822i	−1.17985	+	1.17985i	−0.200068	+	0.979782i	$0.564116\pi$
$523$	−26.9822	+	26.9822i	−1.17985	+	1.17985i	−0.979782	+	0.200068i	$0.935884\pi$
$524$	−17.4246			−0.761198
$525$		0			0
$526$	9.88909			0.431185
$527$	−3.86701	+	3.86701i	−0.168450	+	0.168450i
$528$		0			0
$529$			14.3432i			0.623616i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	33.7539	+	33.7539i	1.46204	+	1.46204i
$534$		0			0
$535$		0			0
$536$			6.50215i			0.280850i
$537$		0			0
$538$	15.3707	−	15.3707i	0.662677	−	0.662677i
$539$	−5.26561			−0.226806
$540$		0			0
$541$	−15.2249			−0.654569			−0.327284	−	0.944926i	$-0.606134\pi$
$541$	−15.2249			−0.654569			−0.327284	+	0.944926i	$0.606134\pi$
$542$	−3.52539	+	3.52539i	−0.151429	+	0.151429i
$543$		0			0
$544$		−	4.32106i		−	0.185264i
$545$		0			0
$546$		0			0
$547$	−6.84898	−	6.84898i	−0.292841	−	0.292841i	0.545360	−	0.838202i	$-0.316393\pi$
$547$	−6.84898	−	6.84898i	−0.292841	−	0.292841i	−0.838202	+	0.545360i	$0.816393\pi$
$548$	2.35876	+	2.35876i	0.100761	+	0.100761i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−2.53122	+	2.53122i	−0.107638	+	0.107638i
$554$	−2.55672			−0.108624
$555$		0			0
$556$	−21.8449			−0.926431
$557$	25.8839	−	25.8839i	1.09674	−	1.09674i	0.101945	−	0.994790i	$-0.467493\pi$
$557$	25.8839	−	25.8839i	1.09674	−	1.09674i	0.994790	−	0.101945i	$-0.0325066\pi$
$558$		0			0
$559$			3.77819i			0.159800i
$560$		0			0
$561$		0			0
$562$	6.12563	+	6.12563i	0.258394	+	0.258394i
$563$	−14.9926	−	14.9926i	−0.631865	−	0.631865i	0.316671	−	0.948535i	$-0.397435\pi$
$563$	−14.9926	−	14.9926i	−0.631865	−	0.631865i	−0.948535	+	0.316671i	$0.897435\pi$
$564$		0			0
$565$		0			0
$566$		−	2.20278i		−	0.0925899i
$567$		0			0
$568$	6.53122	−	6.53122i	0.274044	−	0.274044i
$569$	4.97742			0.208664			0.104332	−	0.994543i	$-0.466730\pi$
$569$	4.97742			0.208664			0.104332	+	0.994543i	$0.466730\pi$
$570$		0			0
$571$	34.6949			1.45194			0.725968	−	0.687728i	$-0.241392\pi$
$571$	34.6949			1.45194			0.725968	+	0.687728i	$0.241392\pi$
$572$	16.6421	−	16.6421i	0.695842	−	0.695842i
$573$		0			0
$574$			10.6798i			0.445767i
$575$		0			0
$576$		0			0
$577$	−32.5782	−	32.5782i	−1.35625	−	1.35625i	−0.878495	−	0.477751i	$-0.841452\pi$
$577$	−32.5782	−	32.5782i	−1.35625	−	1.35625i	−0.477751	−	0.878495i	$-0.658548\pi$
$578$	−1.18199	−	1.18199i	−0.0491642	−	0.0491642i
$579$		0			0
$580$		0			0
$581$			8.78249i			0.364359i
$582$		0			0
$583$	−52.0447	+	52.0447i	−2.15547	+	2.15547i
$584$	14.4476			0.597845
$585$		0			0
$586$	−7.62778			−0.315101
$587$	−18.4320	+	18.4320i	−0.760769	+	0.760769i	−0.976461	−	0.215693i	$-0.930799\pi$
$587$	−18.4320	+	18.4320i	−0.760769	+	0.760769i	0.215693	+	0.976461i	$0.430799\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−2.93351	−	2.93351i	−0.120566	−	0.120566i
$593$	−22.1213	−	22.1213i	−0.908413	−	0.908413i	0.0877310	−	0.996144i	$-0.472038\pi$
$593$	−22.1213	−	22.1213i	−0.908413	−	0.908413i	−0.996144	+	0.0877310i	$0.972038\pi$
$594$		0			0
$595$		0			0
$596$		−	6.08541i		−	0.249268i
$597$		0			0
$598$	−19.3137	+	19.3137i	−0.789796	+	0.789796i
$599$	−17.6906			−0.722818			−0.361409	−	0.932407i	$-0.617704\pi$
$599$	−17.6906			−0.722818			−0.361409	+	0.932407i	$0.617704\pi$
$600$		0			0
$601$	18.6979			0.762705			0.381353	−	0.924430i	$-0.375458\pi$
$601$	18.6979			0.762705			0.381353	+	0.924430i	$0.375458\pi$
$602$	−0.597714	+	0.597714i	−0.0243610	+	0.0243610i
$603$		0			0
$604$		−	22.7530i		−	0.925808i
$605$		0			0
$606$		0			0
$607$	−5.23654	−	5.23654i	−0.212545	−	0.212545i	0.592803	−	0.805348i	$-0.298021\pi$
$607$	−5.23654	−	5.23654i	−0.212545	−	0.212545i	−0.805348	+	0.592803i	$0.798021\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	21.6569i		−	0.876143i
$612$		0			0
$613$	−21.4426	+	21.4426i	−0.866060	+	0.866060i	−0.992034	−	0.125973i	$-0.959795\pi$
$613$	−21.4426	+	21.4426i	−0.866060	+	0.866060i	0.125973	+	0.992034i	$0.459795\pi$
$614$	2.07717			0.0838277
$615$		0			0
$616$	5.26561			0.212157
$617$	−2.18109	+	2.18109i	−0.0878073	+	0.0878073i	−0.749646	−	0.661839i	$-0.769776\pi$
$617$	−2.18109	+	2.18109i	−0.0878073	+	0.0878073i	0.661839	+	0.749646i	$0.269776\pi$
$618$		0			0
$619$			19.7573i			0.794114i	0.917794	+	0.397057i	$0.129969\pi$
$619$			19.7573i			0.794114i	−0.917794	+	0.397057i	$0.870031\pi$
$620$		0			0
$621$		0			0
$622$	−21.9077	−	21.9077i	−0.878420	−	0.878420i
$623$	−2.55913	−	2.55913i	−0.102529	−	0.102529i
$624$		0			0
$625$		0			0
$626$			9.54199i			0.381375i
$627$		0			0
$628$	10.7181	−	10.7181i	0.427700	−	0.427700i
$629$	−17.9264			−0.714771
$630$		0			0
$631$	2.15507			0.0857920			0.0428960	−	0.999080i	$-0.486342\pi$
$631$	2.15507			0.0857920			0.0428960	+	0.999080i	$0.486342\pi$
$632$	2.53122	−	2.53122i	0.100687	−	0.100687i
$633$		0			0
$634$			28.8713i			1.14663i
$635$		0			0
$636$		0			0
$637$	3.16053	+	3.16053i	0.125225	+	0.125225i
$638$	37.0931	+	37.0931i	1.46853	+	1.46853i
$639$		0			0
$640$		0			0
$641$			39.5147i			1.56074i	0.625320	+	0.780368i	$0.284968\pi$
$641$			39.5147i			1.56074i	−0.625320	+	0.780368i	$0.715032\pi$
$642$		0			0
$643$	−9.61574	+	9.61574i	−0.379208	+	0.379208i	−0.870816	−	0.491608i	$-0.836409\pi$
$643$	−9.61574	+	9.61574i	−0.379208	+	0.379208i	0.491608	+	0.870816i	$0.336409\pi$
$644$	−6.11091			−0.240803
$645$		0			0
$646$		0			0
$647$	14.6510	−	14.6510i	0.575991	−	0.575991i	−0.357805	−	0.933796i	$-0.616475\pi$
$647$	14.6510	−	14.6510i	0.575991	−	0.575991i	0.933796	+	0.357805i	$0.116475\pi$
$648$		0			0
$649$			16.4584i			0.646048i
$650$		0			0
$651$		0			0
$652$	−4.04441	−	4.04441i	−0.158391	−	0.158391i
$653$	32.0836	+	32.0836i	1.25553	+	1.25553i	0.953206	+	0.302323i	$0.0977621\pi$
$653$	32.0836	+	32.0836i	1.25553	+	1.25553i	0.302323	+	0.953206i	$0.402238\pi$
$654$		0			0
$655$		0			0
$656$		−	10.6798i		−	0.416977i
$657$		0			0
$658$	3.42614	−	3.42614i	0.133565	−	0.133565i
$659$	−38.5499			−1.50169			−0.750845	−	0.660479i	$-0.770353\pi$
$659$	−38.5499			−1.50169			−0.750845	+	0.660479i	$0.770353\pi$
$660$		0			0
$661$	−39.4176			−1.53317			−0.766584	−	0.642144i	$-0.778045\pi$
$661$	−39.4176			−1.53317			−0.766584	+	0.642144i	$0.778045\pi$
$662$	−12.9056	+	12.9056i	−0.501590	+	0.501590i
$663$		0			0
$664$		−	8.78249i		−	0.340827i
$665$		0			0
$666$		0			0
$667$	−43.0477	−	43.0477i	−1.66681	−	1.66681i
$668$	5.76929	+	5.76929i	0.223220	+	0.223220i
$669$		0			0
$670$		0			0
$671$			16.0888i			0.621102i
$672$		0			0
$673$	13.3431	−	13.3431i	0.514340	−	0.514340i	−0.401513	−	0.915853i	$-0.631516\pi$
$673$	13.3431	−	13.3431i	0.514340	−	0.514340i	0.915853	+	0.401513i	$0.131516\pi$
$674$	10.1967			0.392762
$675$		0			0
$676$	−6.97792			−0.268381
$677$	18.1024	−	18.1024i	0.695731	−	0.695731i	−0.267755	−	0.963487i	$-0.586282\pi$
$677$	18.1024	−	18.1024i	0.695731	−	0.695731i	0.963487	+	0.267755i	$0.0862819\pi$
$678$		0			0
$679$			6.55672i			0.251624i
$680$		0			0
$681$		0			0
$682$	4.71231	+	4.71231i	0.180444	+	0.180444i
$683$	27.4077	+	27.4077i	1.04873	+	1.04873i	0.998750	+	0.0499779i	$0.0159151\pi$
$683$	27.4077	+	27.4077i	1.04873	+	1.04873i	0.0499779	+	0.998750i	$0.484085\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	0.597714	−	0.597714i	0.0227876	−	0.0227876i
$689$	62.4766			2.38017
$690$		0			0
$691$	−12.9221			−0.491579			−0.245789	−	0.969323i	$-0.579047\pi$
$691$	−12.9221			−0.491579			−0.245789	+	0.969323i	$0.579047\pi$
$692$	6.14492	−	6.14492i	0.233595	−	0.233595i
$693$		0			0
$694$			15.3137i			0.581300i
$695$		0			0
$696$		0			0
$697$	−32.6317	−	32.6317i	−1.23601	−	1.23601i
$698$	11.3560	+	11.3560i	0.429829	+	0.429829i
$699$		0			0
$700$		0			0
$701$			13.5732i			0.512653i	0.966590	+	0.256327i	$0.0825123\pi$
$701$			13.5732i			0.512653i	−0.966590	+	0.256327i	$0.917488\pi$
$702$		0			0
$703$		0			0
$704$	−5.26561			−0.198455
$705$		0			0
$706$	−13.1036			−0.493159
$707$	1.50368	−	1.50368i	0.0565516	−	0.0565516i
$708$		0			0
$709$			40.4429i			1.51886i	0.650586	+	0.759432i	$0.274523\pi$
$709$			40.4429i			1.51886i	−0.650586	+	0.759432i	$0.725477\pi$
$710$		0			0
$711$		0			0
$712$	2.55913	+	2.55913i	0.0959074	+	0.0959074i
$713$	−5.46878	−	5.46878i	−0.204807	−	0.204807i
$714$		0			0
$715$		0			0
$716$		−	0.391244i		−	0.0146215i
$717$		0			0
$718$	−5.20280	+	5.20280i	−0.194167	+	0.194167i
$719$	−16.9706			−0.632895			−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$		0			0
$721$	15.4467			0.575265
$722$	13.4350	−	13.4350i	0.500000	−	0.500000i
$723$		0			0
$724$			15.0113i			0.557890i
$725$		0			0
$726$		0			0
$727$	29.8787	+	29.8787i	1.10814	+	1.10814i	0.993395	+	0.114743i	$0.0366045\pi$
$727$	29.8787	+	29.8787i	1.10814	+	1.10814i	0.114743	+	0.993395i	$0.463395\pi$
$728$	−3.16053	−	3.16053i	−0.117137	−	0.117137i
$729$		0			0
$730$		0			0
$731$		−	3.65258i		−	0.135095i
$732$		0			0
$733$	8.55913	−	8.55913i	0.316139	−	0.316139i	−0.531143	−	0.847282i	$-0.678237\pi$
$733$	8.55913	−	8.55913i	0.316139	−	0.316139i	0.847282	+	0.531143i	$0.178237\pi$
$734$	−32.7309			−1.20812
$735$		0			0
$736$	6.11091			0.225251
$737$	24.2098	−	24.2098i	0.891778	−	0.891778i
$738$		0			0
$739$		−	35.3584i		−	1.30068i	−0.759644	−	0.650339i	$-0.774627\pi$
$739$		−	35.3584i		−	1.30068i	0.759644	−	0.650339i	$-0.225373\pi$
$740$		0			0
$741$		0			0
$742$	9.88388	+	9.88388i	0.362849	+	0.362849i
$743$	−35.1733	−	35.1733i	−1.29038	−	1.29038i	−0.934548	−	0.355837i	$-0.884196\pi$
$743$	−35.1733	−	35.1733i	−1.29038	−	1.29038i	−0.355837	−	0.934548i	$-0.615804\pi$
$744$		0			0
$745$		0			0
$746$			0.114867i			0.00420557i
$747$		0			0
$748$	−16.0888	+	16.0888i	−0.588266	+	0.588266i
$749$	9.06244			0.331134
$750$		0			0
$751$	16.2358			0.592452			0.296226	−	0.955118i	$-0.404272\pi$
$751$	16.2358			0.592452			0.296226	+	0.955118i	$0.404272\pi$
$752$	−3.42614	+	3.42614i	−0.124939	+	0.124939i
$753$		0			0
$754$		−	44.5282i		−	1.62162i
$755$		0			0
$756$		0			0
$757$	1.76016	+	1.76016i	0.0639741	+	0.0639741i	0.738370	−	0.674396i	$-0.235596\pi$
$757$	1.76016	+	1.76016i	0.0639741	+	0.0639741i	−0.674396	+	0.738370i	$0.735596\pi$
$758$	8.73616	+	8.73616i	0.317312	+	0.317312i
$759$		0			0
$760$		0			0
$761$			29.0125i			1.05170i	0.850576	+	0.525852i	$0.176253\pi$
$761$			29.0125i			1.05170i	−0.850576	+	0.525852i	$0.823747\pi$
$762$		0			0
$763$	6.75825	−	6.75825i	0.244665	−	0.244665i
$764$	23.3474			0.844681
$765$		0			0
$766$	−16.6235			−0.600631
$767$	9.87867	−	9.87867i	0.356698	−	0.356698i
$768$		0			0
$769$			29.2439i			1.05456i	0.849691	+	0.527281i	$0.176789\pi$
$769$			29.2439i			1.05456i	−0.849691	+	0.527281i	$0.823211\pi$
$770$		0			0
$771$		0			0
$772$	6.69059	+	6.69059i	0.240800	+	0.240800i
$773$	−8.95467	−	8.95467i	−0.322077	−	0.322077i	0.527486	−	0.849564i	$-0.323135\pi$
$773$	−8.95467	−	8.95467i	−0.322077	−	0.322077i	−0.849564	+	0.527486i	$0.823135\pi$
$774$		0			0
$775$		0			0
$776$		−	6.55672i		−	0.235372i
$777$		0			0
$778$	−8.12893	+	8.12893i	−0.291436	+	0.291436i
$779$		0			0
$780$		0			0
$781$	−48.6360			−1.74033
$782$	18.6716	−	18.6716i	0.667694	−	0.667694i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	29.9264	+	29.9264i	1.06676	+	1.06676i	0.997606	+	0.0691541i	$0.0220300\pi$
$787$	29.9264	+	29.9264i	1.06676	+	1.06676i	0.0691541	+	0.997606i	$0.477970\pi$
$788$	−0.375629	−	0.375629i	−0.0133812	−	0.0133812i
$789$		0			0
$790$		0			0
$791$		−	4.66421i		−	0.165840i
$792$		0			0
$793$	9.65685	−	9.65685i	0.342925	−	0.342925i
$794$	15.8991			0.564238
$795$		0			0
$796$	−18.0481			−0.639698
$797$	7.21473	−	7.21473i	0.255559	−	0.255559i	−0.567686	−	0.823245i	$-0.692161\pi$
$797$	7.21473	−	7.21473i	0.255559	−	0.255559i	0.823245	+	0.567686i	$0.192161\pi$
$798$		0			0
$799$			20.9368i			0.740692i
$800$		0			0
$801$		0			0
$802$	20.8787	+	20.8787i	0.737251	+	0.737251i
$803$	−53.7934	−	53.7934i	−1.89833	−	1.89833i
$804$		0			0
$805$		0			0
$806$		−	5.65685i		−	0.199254i
$807$		0			0
$808$	−1.50368	+	1.50368i	−0.0528992	+	0.0528992i
$809$	33.5606			1.17993			0.589964	−	0.807429i	$-0.299142\pi$
$809$	33.5606			1.17993			0.589964	+	0.807429i	$0.299142\pi$
$810$		0			0
$811$	44.7236			1.57046			0.785229	−	0.619206i	$-0.212545\pi$
$811$	44.7236			1.57046			0.785229	+	0.619206i	$0.212545\pi$
$812$	7.04441	−	7.04441i	0.247210	−	0.247210i
$813$		0			0
$814$			21.8449i			0.765664i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−18.5910	−	18.5910i	−0.650018	−	0.650018i
$819$		0			0
$820$		0			0
$821$		−	47.8955i		−	1.67156i	−0.549061	−	0.835782i	$-0.685015\pi$
$821$		−	47.8955i		−	1.67156i	0.549061	−	0.835782i	$-0.314985\pi$
$822$		0			0
$823$	37.8926	−	37.8926i	1.32085	−	1.32085i	0.407769	−	0.913085i	$-0.366307\pi$
$823$	37.8926	−	37.8926i	1.32085	−	1.32085i	0.913085	−	0.407769i	$-0.133693\pi$
$824$	−15.4467			−0.538111
$825$		0			0
$826$	3.12563			0.108755
$827$	−13.7405	+	13.7405i	−0.477803	+	0.477803i	−0.904428	−	0.426626i	$-0.859702\pi$
$827$	−13.7405	+	13.7405i	−0.477803	+	0.477803i	0.426626	+	0.904428i	$0.359702\pi$
$828$		0			0
$829$		−	12.9445i		−	0.449583i	−0.974407	−	0.224791i	$-0.927830\pi$
$829$		−	12.9445i		−	0.449583i	0.974407	−	0.224791i	$-0.0721701\pi$
$830$		0			0
$831$		0			0
$832$	3.16053	+	3.16053i	0.109572	+	0.109572i
$833$	−3.05545	−	3.05545i	−0.105865	−	0.105865i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	14.5650	−	14.5650i	0.503138	−	0.503138i
$839$	6.27763			0.216728			0.108364	−	0.994111i	$-0.465439\pi$
$839$	6.27763			0.216728			0.108364	+	0.994111i	$0.465439\pi$
$840$		0			0
$841$	70.2475			2.42233
$842$	−1.22614	+	1.22614i	−0.0422556	+	0.0422556i
$843$		0			0
$844$			8.22181i			0.283006i
$845$		0			0
$846$		0			0
$847$	−11.8275	−	11.8275i	−0.406399	−	0.406399i
$848$	−9.88388	−	9.88388i	−0.339414	−	0.339414i
$849$		0			0
$850$		0			0
$851$		−	25.3517i		−	0.869046i
$852$		0			0
$853$	−16.2350	+	16.2350i	−0.555876	+	0.555876i	−0.928131	−	0.372254i	$-0.878585\pi$
$853$	−16.2350	+	16.2350i	−0.555876	+	0.555876i	0.372254	+	0.928131i	$0.378585\pi$
$854$	3.05545			0.104555
$855$		0			0
$856$	−9.06244			−0.309748
$857$	33.9488	−	33.9488i	1.15967	−	1.15967i	0.175124	−	0.984546i	$-0.443967\pi$
$857$	33.9488	−	33.9488i	1.15967	−	1.15967i	0.984546	−	0.175124i	$-0.0560327\pi$
$858$		0			0
$859$			50.2444i			1.71432i	0.515053	+	0.857158i	$0.327772\pi$
$859$			50.2444i			1.71432i	−0.515053	+	0.857158i	$0.672228\pi$
$860$		0			0
$861$		0			0
$862$	−1.20280	−	1.20280i	−0.0409676	−	0.0409676i
$863$	−7.09190	−	7.09190i	−0.241411	−	0.241411i	0.576023	−	0.817434i	$-0.304604\pi$
$863$	−7.09190	−	7.09190i	−0.241411	−	0.241411i	−0.817434	+	0.576023i	$0.804604\pi$
$864$		0			0
$865$		0			0
$866$			4.08364i			0.138768i
$867$		0			0
$868$	0.894921	−	0.894921i	0.0303756	−	0.0303756i
$869$	−18.8492			−0.639416
$870$		0			0
$871$	−29.0624			−0.984743
$872$	−6.75825	+	6.75825i	−0.228863	+	0.228863i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−29.0150	−	29.0150i	−0.979765	−	0.979765i	0.0200339	−	0.999799i	$-0.493623\pi$
$877$	−29.0150	−	29.0150i	−0.979765	−	0.979765i	−0.999799	+	0.0200339i	$0.993623\pi$
$878$	−23.1939	−	23.1939i	−0.782756	−	0.782756i
$879$		0			0
$880$		0			0
$881$		−	15.5887i		−	0.525197i	−0.964905	−	0.262598i	$-0.915421\pi$
$881$		−	15.5887i		−	0.525197i	0.964905	−	0.262598i	$-0.0845794\pi$
$882$		0			0
$883$	−22.8048	+	22.8048i	−0.767443	+	0.767443i	−0.977656	−	0.210213i	$-0.932584\pi$
$883$	−22.8048	+	22.8048i	−0.767443	+	0.767443i	0.210213	+	0.977656i	$0.432584\pi$
$884$	19.3137			0.649590
$885$		0			0
$886$	−28.3761			−0.953315
$887$	−16.2013	+	16.2013i	−0.543985	+	0.543985i	−0.924695	−	0.380710i	$-0.875680\pi$
$887$	−16.2013	+	16.2013i	−0.543985	+	0.543985i	0.380710	+	0.924695i	$0.375680\pi$
$888$		0			0
$889$			11.7678i			0.394678i
$890$		0			0
$891$		0			0
$892$	−13.2365	−	13.2365i	−0.443192	−	0.443192i
$893$		0			0
$894$		0			0
$895$		0			0
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	−8.46878	+	8.46878i	−0.282607	+	0.282607i
$899$	12.6084			0.420513
$900$		0			0
$901$	−60.3995			−2.01220
$902$	−39.7647	+	39.7647i	−1.32402	+	1.32402i
$903$		0			0
$904$			4.66421i			0.155129i
$905$		0			0
$906$		0			0
$907$	19.9114	+	19.9114i	0.661148	+	0.661148i	0.955651	−	0.294503i	$-0.0951540\pi$
$907$	19.9114	+	19.9114i	0.661148	+	0.661148i	−0.294503	+	0.955651i	$0.595154\pi$
$908$	5.46878	+	5.46878i	0.181488	+	0.181488i
$909$		0			0
$910$		0			0
$911$			28.4723i			0.943331i	0.881778	+	0.471665i	$0.156347\pi$
$911$			28.4723i			0.943331i	−0.881778	+	0.471665i	$0.843653\pi$
$912$		0			0
$913$	−32.7003	+	32.7003i	−1.08222	+	1.08222i
$914$	−9.14824			−0.302597
$915$		0			0
$916$	−13.0966			−0.432723
$917$	12.3211	−	12.3211i	0.406877	−	0.406877i
$918$		0			0
$919$		−	57.2261i		−	1.88772i	−0.330353	−	0.943858i	$-0.607168\pi$
$919$		−	57.2261i		−	1.88772i	0.330353	−	0.943858i	$-0.392832\pi$
$920$		0			0
$921$		0			0
$922$	−26.2276	−	26.2276i	−0.863761	−	0.863761i
$923$	29.1924	+	29.1924i	0.960879	+	0.960879i
$924$		0			0
$925$		0			0
$926$		−	0.328437i		−	0.0107931i
$927$		0			0
$928$	−7.04441	+	7.04441i	−0.231244	+	0.231244i
$929$	28.6166			0.938881			0.469441	−	0.882964i	$-0.344456\pi$
$929$	28.6166			0.938881			0.469441	+	0.882964i	$0.344456\pi$
$930$		0			0
$931$		0			0
$932$	−0.642125	+	0.642125i	−0.0210335	+	0.0210335i
$933$		0			0
$934$		−	31.3952i		−	1.02728i
$935$		0			0
$936$		0			0
$937$	4.09342	+	4.09342i	0.133726	+	0.133726i	0.770802	−	0.637075i	$-0.219856\pi$
$937$	4.09342	+	4.09342i	0.133726	+	0.133726i	−0.637075	+	0.770802i	$0.719856\pi$
$938$	−4.59771	−	4.59771i	−0.150121	−	0.150121i
$939$		0			0
$940$		0			0
$941$			18.7890i			0.612502i	0.951951	+	0.306251i	$0.0990748\pi$
$941$			18.7890i			0.612502i	−0.951951	+	0.306251i	$0.900925\pi$
$942$		0			0
$943$	46.1482	−	46.1482i	1.50279	−	1.50279i
$944$	−3.12563			−0.101731
$945$		0			0
$946$	−4.45100			−0.144714
$947$	−22.6009	+	22.6009i	−0.734429	+	0.734429i	−0.971494	−	0.237065i	$-0.923815\pi$
$947$	−22.6009	+	22.6009i	−0.734429	+	0.734429i	0.237065	+	0.971494i	$0.423815\pi$
$948$		0			0
$949$			64.5759i			2.09622i
$950$		0			0
$951$		0			0
$952$	3.05545	+	3.05545i	0.0990278	+	0.0990278i
$953$	−29.8241	−	29.8241i	−0.966097	−	0.966097i	0.0333465	−	0.999444i	$-0.489384\pi$
$953$	−29.8241	−	29.8241i	−0.966097	−	0.966097i	−0.999444	+	0.0333465i	$0.989384\pi$
$954$		0			0
$955$		0			0
$956$			25.4246i			0.822291i
$957$		0			0
$958$	−14.6902	+	14.6902i	−0.474620	+	0.474620i
$959$	−3.33579			−0.107718
$960$		0			0
$961$	−29.3982			−0.948330
$962$	13.1118	−	13.1118i	0.422741	−	0.422741i
$963$		0			0
$964$			7.46878i			0.240553i
$965$		0			0
$966$		0			0
$967$	−10.4975	−	10.4975i	−0.337576	−	0.337576i	0.517878	−	0.855454i	$-0.326722\pi$
$967$	−10.4975	−	10.4975i	−0.337576	−	0.337576i	−0.855454	+	0.517878i	$0.826722\pi$
$968$	11.8275	+	11.8275i	0.380151	+	0.380151i
$969$		0			0
$970$		0			0
$971$		−	15.3579i		−	0.492858i	−0.969161	−	0.246429i	$-0.920743\pi$
$971$		−	15.3579i		−	0.492858i	0.969161	−	0.246429i	$-0.0792572\pi$
$972$		0			0
$973$	15.4467	−	15.4467i	0.495198	−	0.495198i
$974$	1.42461			0.0456476
$975$		0			0
$976$	−3.05545			−0.0978027
$977$	15.5459	−	15.5459i	0.497359	−	0.497359i	−0.413256	−	0.910615i	$-0.635609\pi$
$977$	15.5459	−	15.5459i	0.497359	−	0.497359i	0.910615	+	0.413256i	$0.135609\pi$
$978$		0			0
$979$		−	19.0571i		−	0.609066i
$980$		0			0
$981$		0			0
$982$	−4.91878	−	4.91878i	−0.156964	−	0.156964i
$983$	−42.6546	−	42.6546i	−1.36047	−	1.36047i	−0.873317	−	0.487153i	$-0.838035\pi$
$983$	−42.6546	−	42.6546i	−1.36047	−	1.36047i	−0.487153	−	0.873317i	$-0.661965\pi$
$984$		0			0
$985$		0			0
$986$			43.0477i			1.37092i
$987$		0			0
$988$		0			0
$989$	5.16552			0.164254
$990$		0			0
$991$	8.98099			0.285291			0.142645	−	0.989774i	$-0.454439\pi$
$991$	8.98099			0.285291			0.142645	+	0.989774i	$0.454439\pi$
$992$	−0.894921	+	0.894921i	−0.0284138	+	0.0284138i
$993$		0			0
$994$			9.23654i			0.292965i
$995$		0			0
$996$		0			0
$997$	25.7038	+	25.7038i	0.814047	+	0.814047i	0.985238	−	0.171191i	$-0.0547614\pi$
$997$	25.7038	+	25.7038i	0.814047	+	0.814047i	−0.171191	+	0.985238i	$0.554761\pi$
$998$	−14.8471	−	14.8471i	−0.469976	−	0.469976i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.j.1457.4		8
3.2	odd	2		3150.2.m.i.1457.1		8
5.2	odd	4		630.2.m.c.323.3	yes	8
5.3	odd	4		3150.2.m.i.2843.2		8
5.4	even	2		630.2.m.d.197.2	yes	8
15.2	even	4		630.2.m.d.323.2	yes	8
15.8	even	4	inner	3150.2.m.j.2843.3		8
15.14	odd	2		630.2.m.c.197.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.c.197.3	✓	8	15.14	odd	2
630.2.m.c.323.3	yes	8	5.2	odd	4
630.2.m.d.197.2	yes	8	5.4	even	2
630.2.m.d.323.2	yes	8	15.2	even	4
3150.2.m.i.1457.1		8	3.2	odd	2
3150.2.m.i.2843.2		8	5.3	odd	4
3150.2.m.j.1457.4		8	1.1	even	1	trivial
3150.2.m.j.2843.3		8	15.8	even	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +5.26561i q^{11} +(3.16053 - 3.16053i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-3.05545 + 3.05545i) q^{17} +(3.72335 + 3.72335i) q^{22} +(-4.32106 - 4.32106i) q^{23} -4.46967i q^{26} +(0.707107 - 0.707107i) q^{28} +9.96230 q^{29} +1.26561 q^{31} +(-0.707107 + 0.707107i) q^{32} +4.32106i q^{34} +(2.93351 + 2.93351i) q^{37} +10.6798i q^{41} +(-0.597714 + 0.597714i) q^{43} +5.26561 q^{44} -6.11091 q^{46} +(3.42614 - 3.42614i) q^{47} +1.00000i q^{49} +(-3.16053 - 3.16053i) q^{52} +(9.88388 + 9.88388i) q^{53} -1.00000i q^{56} +(7.04441 - 7.04441i) q^{58} +3.12563 q^{59} +3.05545 q^{61} +(0.894921 - 0.894921i) q^{62} +1.00000i q^{64} +(-4.59771 - 4.59771i) q^{67} +(3.05545 + 3.05545i) q^{68} +9.23654i q^{71} +(-10.2160 + 10.2160i) q^{73} +4.14860 q^{74} +(-3.72335 + 3.72335i) q^{77} +3.57969i q^{79} +(7.55178 + 7.55178i) q^{82} +(6.21016 + 6.21016i) q^{83} +0.845296i q^{86} +(3.72335 - 3.72335i) q^{88} -3.61916 q^{89} +4.46967 q^{91} +(-4.32106 + 4.32106i) q^{92} -4.84530i q^{94} +(4.63630 + 4.63630i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{22} + 8 q^{23} + 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} + 24 q^{44} - 12 q^{47} - 4 q^{52} + 32 q^{53} - 12 q^{58} + 16 q^{59} + 4 q^{62} - 20 q^{67} - 36 q^{73} + 40 q^{74} - 4 q^{77} + 12 q^{82} + 56 q^{83} + 4 q^{88} + 72 q^{89} + 8 q^{92} + 4 q^{97}+O(q^{100}) \) 8 * q + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^22 + 8 * q^23 + 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 + 24 * q^44 - 12 * q^47 - 4 * q^52 + 32 * q^53 - 12 * q^58 + 16 * q^59 + 4 * q^62 - 20 * q^67 - 36 * q^73 + 40 * q^74 - 4 * q^77 + 12 * q^82 + 56 * q^83 + 4 * q^88 + 72 * q^89 + 8 * q^92 + 4 * q^97

Introduction

L-functions

Modular forms

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Database

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