LMFDB - Embedded newform 525.2.bc.d.418.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.6
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.d.157.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.698503 + 2.60685i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-4.57570 + 2.64178i) q^{4} +2.69881i q^{6} +(-2.58926 + 0.543835i) q^{7} +(-6.26618 - 6.26618i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.698503 + 2.60685i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-4.57570 + 2.64178i) q^{4} +2.69881i q^{6} +(-2.58926 + 0.543835i) q^{7} +(-6.26618 - 6.26618i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.69545 + 2.93661i) q^{11} +(-5.10353 + 1.36749i) q^{12} +(-4.01246 + 4.01246i) q^{13} +(-3.22630 - 6.36993i) q^{14} +(6.67447 - 11.5605i) q^{16} +(1.00749 - 3.76002i) q^{17} +(-0.698503 + 2.60685i) q^{18} +(0.721181 - 1.24912i) q^{19} +(-2.64178 - 0.144844i) q^{21} +(-6.47102 + 6.47102i) q^{22} +(-0.739216 + 0.198072i) q^{23} +(-4.43086 - 7.67447i) q^{24} +(-13.2626 - 7.65716i) q^{26} +(0.707107 + 0.707107i) q^{27} +(10.4110 - 9.32868i) q^{28} +5.95804i q^{29} +(3.17447 - 1.83278i) q^{31} +(17.6792 + 4.73712i) q^{32} +(0.877631 + 3.27536i) q^{33} +10.5055 q^{34} -5.28357 q^{36} +(0.325192 + 1.21363i) q^{37} +(3.76002 + 1.00749i) q^{38} +(-4.91424 + 2.83724i) q^{39} -1.05498i q^{41} +(-1.46771 - 6.98790i) q^{42} +(6.74494 + 6.74494i) q^{43} +(-15.5158 - 8.95804i) q^{44} +(-1.03269 - 1.78867i) q^{46} +(-6.55073 + 1.75526i) q^{47} +(9.43913 - 9.43913i) q^{48} +(6.40849 - 2.81626i) q^{49} +(1.94633 - 3.37114i) q^{51} +(7.75977 - 28.9599i) q^{52} +(-2.94397 + 10.9870i) q^{53} +(-1.34940 + 2.33724i) q^{54} +(19.6325 + 12.8170i) q^{56} +(1.01990 - 1.01990i) q^{57} +(-15.5317 + 4.16171i) q^{58} +(3.22630 + 5.58811i) q^{59} +(10.9254 + 6.30775i) q^{61} +(6.99517 + 6.99517i) q^{62} +(-2.51428 - 0.823652i) q^{63} +22.6979i q^{64} +(-7.92535 + 4.57570i) q^{66} +(0.544617 + 0.145930i) q^{67} +(5.32317 + 19.8663i) q^{68} -0.765293 q^{69} -6.73985 q^{71} +(-2.29358 - 8.55976i) q^{72} +(4.78910 + 1.28324i) q^{73} +(-2.93661 + 1.69545i) q^{74} +7.62082i q^{76} +(-5.98699 - 6.68159i) q^{77} +(-10.8289 - 10.8289i) q^{78} +(-6.79587 - 3.92360i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.75018 - 0.736908i) q^{82} +(1.49011 - 1.49011i) q^{83} +(12.4707 - 6.31626i) q^{84} +(-12.8717 + 22.2944i) q^{86} +(-1.54205 + 5.75503i) q^{87} +(7.77732 - 29.0254i) q^{88} +(1.78394 - 3.08987i) q^{89} +(8.20716 - 12.5714i) q^{91} +(2.85917 - 2.85917i) q^{92} +(3.54066 - 0.948718i) q^{93} +(-9.15141 - 15.8507i) q^{94} +(15.8507 + 9.15141i) q^{96} +(-1.36798 - 1.36798i) q^{97} +(11.8179 + 14.7388i) q^{98} +3.39091i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 24 q^{11} + 48 q^{16} - 24 q^{21} - 144 q^{26} - 36 q^{31} - 48 q^{36} + 48 q^{46} + 24 q^{51} + 168 q^{56} + 144 q^{61} - 72 q^{66} + 96 q^{71} + 12 q^{81} - 168 q^{86} + 12 q^{91} + 144 q^{96}+O(q^{100}) $ 24 * q + 24 * q^11 + 48 * q^16 - 24 * q^21 - 144 * q^26 - 36 * q^31 - 48 * q^36 + 48 * q^46 + 24 * q^51 + 168 * q^56 + 144 * q^61 - 72 * q^66 + 96 * q^71 + 12 * q^81 - 168 * q^86 + 12 * q^91 + 144 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.698503	+	2.60685i	0.493916	+	1.84332i	0.536017	+	0.844207i	$0.319928\pi$
$2$	0.698503	+	2.60685i	0.493916	+	1.84332i	−0.0421009	+	0.999113i	$0.513405\pi$
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−4.57570	+	2.64178i	−2.28785	+	1.32089i
$5$		0			0
$5$		0			0
$6$			2.69881i			1.10178i
$7$	−2.58926	+	0.543835i	−0.978647	+	0.205550i
$7$	−2.58926	+	0.543835i	−0.978647	+	0.205550i
$8$	−6.26618	−	6.26618i	−2.21543	−	2.21543i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	1.69545	+	2.93661i	0.511198	+	0.885422i	0.999916	+	0.0129794i	$0.00413158\pi$
$11$	1.69545	+	2.93661i	0.511198	+	0.885422i	−0.488717	+	0.872442i	$0.662535\pi$
$12$	−5.10353	+	1.36749i	−1.47326	+	0.394760i
$13$	−4.01246	+	4.01246i	−1.11286	+	1.11286i	−0.120093	+	0.992763i	$0.538319\pi$
$13$	−4.01246	+	4.01246i	−1.11286	+	1.11286i	−0.992763	+	0.120093i	$0.961681\pi$
$14$	−3.22630	−	6.36993i	−0.862265	−	1.70243i
$15$		0			0
$16$	6.67447	−	11.5605i	1.66862	−	2.89013i
$17$	1.00749	−	3.76002i	0.244353	−	0.911939i	−0.729354	−	0.684137i	$-0.760179\pi$
$17$	1.00749	−	3.76002i	0.244353	−	0.911939i	0.973707	−	0.227803i	$-0.0731541\pi$
$18$	−0.698503	+	2.60685i	−0.164639	+	0.614440i
$19$	0.721181	−	1.24912i	0.165450	−	0.286568i	−0.771365	−	0.636393i	$-0.780426\pi$
$19$	0.721181	−	1.24912i	0.165450	−	0.286568i	0.936815	+	0.349825i	$0.113759\pi$
$20$		0			0
$21$	−2.64178	−	0.144844i	−0.576484	−	0.0316076i
$22$	−6.47102	+	6.47102i	−1.37963	+	1.37963i
$23$	−0.739216	+	0.198072i	−0.154137	+	0.0413010i	−0.335063	−	0.942196i	$-0.608757\pi$
$23$	−0.739216	+	0.198072i	−0.154137	+	0.0413010i	0.180925	+	0.983497i	$0.442091\pi$
$24$	−4.43086	−	7.67447i	−0.904445	−	1.56655i
$25$		0			0
$26$	−13.2626	−	7.65716i	−2.60101	−	1.50169i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	10.4110	−	9.32868i	1.96749	−	1.76296i
$29$			5.95804i			1.10638i	0.833055	+	0.553190i	$0.186590\pi$
$29$			5.95804i			1.10638i	−0.833055	+	0.553190i	$0.813410\pi$
$30$		0			0
$31$	3.17447	−	1.83278i	0.570152	−	0.329178i	−0.187058	−	0.982349i	$-0.559895\pi$
$31$	3.17447	−	1.83278i	0.570152	−	0.329178i	0.757210	+	0.653171i	$0.226562\pi$
$32$	17.6792	+	4.73712i	3.12526	+	0.837412i
$33$	0.877631	+	3.27536i	0.152776	+	0.570168i
$34$	10.5055			1.80169
$35$		0			0
$36$	−5.28357			−0.880595
$37$	0.325192	+	1.21363i	0.0534612	+	0.199520i	0.987491	−	0.157675i	$-0.0503998\pi$
$37$	0.325192	+	1.21363i	0.0534612	+	0.199520i	−0.934030	+	0.357195i	$0.883733\pi$
$38$	3.76002	+	1.00749i	0.609956	+	0.163437i
$39$	−4.91424	+	2.83724i	−0.786908	+	0.454321i
$40$		0			0
$41$		−	1.05498i		−	0.164760i	−0.996601	−	0.0823802i	$-0.973748\pi$
$41$		−	1.05498i		−	0.164760i	0.996601	−	0.0823802i	$-0.0262522\pi$
$42$	−1.46771	−	6.98790i	−0.226472	−	1.07826i
$43$	6.74494	+	6.74494i	1.02859	+	1.02859i	0.999579	+	0.0290150i	$0.00923706\pi$
$43$	6.74494	+	6.74494i	1.02859	+	1.02859i	0.0290150	+	0.999579i	$0.490763\pi$
$44$	−15.5158	−	8.95804i	−2.33909	−	1.35048i
$45$		0			0
$46$	−1.03269	−	1.78867i	−0.152262	−	0.263725i
$47$	−6.55073	+	1.75526i	−0.955522	+	0.256031i	−0.702704	−	0.711483i	$-0.748024\pi$
$47$	−6.55073	+	1.75526i	−0.955522	+	0.256031i	−0.252818	+	0.967514i	$0.581357\pi$
$48$	9.43913	−	9.43913i	1.36242	−	1.36242i
$49$	6.40849	−	2.81626i	0.915498	−	0.402322i
$50$		0			0
$51$	1.94633	−	3.37114i	0.272541	−	0.472054i
$52$	7.75977	−	28.9599i	1.07609	−	4.01601i
$53$	−2.94397	+	10.9870i	−0.404385	+	1.50918i	0.400803	+	0.916164i	$0.368731\pi$
$53$	−2.94397	+	10.9870i	−0.404385	+	1.50918i	−0.805188	+	0.593020i	$0.797935\pi$
$54$	−1.34940	+	2.33724i	−0.183631	+	0.318058i
$55$		0			0
$56$	19.6325	+	12.8170i	2.62351	+	1.71274i
$57$	1.01990	−	1.01990i	0.135090	−	0.135090i
$58$	−15.5317	+	4.16171i	−2.03941	+	0.546459i
$59$	3.22630	+	5.58811i	0.420028	+	0.727510i	0.995942	−	0.0900003i	$-0.0286868\pi$
$59$	3.22630	+	5.58811i	0.420028	+	0.727510i	−0.575913	+	0.817511i	$0.695353\pi$
$60$		0			0
$61$	10.9254	+	6.30775i	1.39885	+	0.807625i	0.994272	−	0.106879i	$-0.0340858\pi$
$61$	10.9254	+	6.30775i	1.39885	+	0.807625i	0.404576	+	0.914504i	$0.367419\pi$
$62$	6.99517	+	6.99517i	0.888387	+	0.888387i
$63$	−2.51428	−	0.823652i	−0.316769	−	0.103770i
$64$			22.6979i			2.83724i
$65$		0			0
$66$	−7.92535	+	4.57570i	−0.975543	+	0.563230i
$67$	0.544617	+	0.145930i	0.0665355	+	0.0178281i	0.291933	−	0.956439i	$-0.405701\pi$
$67$	0.544617	+	0.145930i	0.0665355	+	0.0178281i	−0.225398	+	0.974267i	$0.572368\pi$
$68$	5.32317	+	19.8663i	0.645529	+	2.40915i
$69$	−0.765293			−0.0921305
$70$		0			0
$71$	−6.73985			−0.799873			−0.399937	−	0.916543i	$-0.630968\pi$
$71$	−6.73985			−0.799873			−0.399937	+	0.916543i	$0.630968\pi$
$72$	−2.29358	−	8.55976i	−0.270301	−	1.00878i
$73$	4.78910	+	1.28324i	0.560522	+	0.150191i	0.527946	−	0.849278i	$-0.322962\pi$
$73$	4.78910	+	1.28324i	0.560522	+	0.150191i	0.0325757	+	0.999469i	$0.489629\pi$
$74$	−2.93661	+	1.69545i	−0.341374	+	0.197092i
$75$		0			0
$76$			7.62082i			0.874168i
$77$	−5.98699	−	6.68159i	−0.682281	−	0.761438i
$78$	−10.8289	−	10.8289i	−1.22613	−	1.22613i
$79$	−6.79587	−	3.92360i	−0.764595	−	0.441439i	0.0663482	−	0.997797i	$-0.478865\pi$
$79$	−6.79587	−	3.92360i	−0.764595	−	0.441439i	−0.830943	+	0.556357i	$0.812199\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.75018	−	0.736908i	0.303706	−	0.0813778i
$83$	1.49011	−	1.49011i	0.163561	−	0.163561i	−0.620581	−	0.784142i	$-0.713103\pi$
$83$	1.49011	−	1.49011i	0.163561	−	0.163561i	0.784142	+	0.620581i	$0.213103\pi$
$84$	12.4707	−	6.31626i	1.36066	−	0.689160i
$85$		0			0
$86$	−12.8717	+	22.2944i	−1.38799	+	2.40407i
$87$	−1.54205	+	5.75503i	−0.165326	+	0.617003i
$88$	7.77732	−	29.0254i	0.829065	−	3.09411i
$89$	1.78394	−	3.08987i	0.189097	−	0.327525i	−0.755853	−	0.654742i	$-0.772777\pi$
$89$	1.78394	−	3.08987i	0.189097	−	0.327525i	0.944949	+	0.327217i	$0.106111\pi$
$90$		0			0
$91$	8.20716	−	12.5714i	0.860344	−	1.31784i
$92$	2.85917	−	2.85917i	0.298089	−	0.298089i
$93$	3.54066	−	0.948718i	0.367150	−	0.0983775i
$94$	−9.15141	−	15.8507i	−0.943896	−	1.63487i
$95$		0			0
$96$	15.8507	+	9.15141i	1.61776	+	0.934012i
$97$	−1.36798	−	1.36798i	−0.138898	−	0.138898i	0.634239	−	0.773137i	$-0.281313\pi$
$97$	−1.36798	−	1.36798i	−0.138898	−	0.138898i	−0.773137	+	0.634239i	$0.781313\pi$
$98$	11.8179	+	14.7388i	1.19379	+	1.48884i
$99$			3.39091i			0.340799i
$100$		0			0
$101$	17.1133	−	9.88036i	1.70284	−	0.983133i	0.759971	−	0.649957i	$-0.225213\pi$
$101$	17.1133	−	9.88036i	1.70284	−	0.983133i	0.942865	−	0.333176i	$-0.108120\pi$
$102$	10.1476	+	2.71904i	1.00476	+	0.269225i
$103$	−2.46530	−	9.20061i	−0.242913	−	0.906563i	−0.974421	−	0.224730i	$-0.927850\pi$
$103$	−2.46530	−	9.20061i	−0.242913	−	0.906563i	0.731508	−	0.681833i	$-0.238817\pi$
$104$	50.2856			4.93091
$105$		0			0
$106$	−30.6979			−2.98164
$107$	0.698503	+	2.60685i	0.0675268	+	0.252014i	0.991435	−	0.130601i	$-0.0416905\pi$
$107$	0.698503	+	2.60685i	0.0675268	+	0.252014i	−0.923908	+	0.382614i	$0.875024\pi$
$108$	−5.10353	−	1.36749i	−0.491088	−	0.131587i
$109$	6.49671	−	3.75088i	0.622272	−	0.359269i	−0.155481	−	0.987839i	$-0.549693\pi$
$109$	6.49671	−	3.75088i	0.622272	−	0.359269i	0.777753	+	0.628570i	$0.216359\pi$
$110$		0			0
$111$			1.25645i			0.119257i
$112$	−10.9949	+	33.5630i	−1.03892	+	3.17140i
$113$	−2.03981	−	2.03981i	−0.191889	−	0.191889i	0.604623	−	0.796512i	$-0.293324\pi$
$113$	−2.03981	−	2.03981i	−0.191889	−	0.191889i	−0.796512	+	0.604623i	$0.793324\pi$
$114$	3.37114	+	1.94633i	0.315736	+	0.182291i
$115$		0			0
$116$	−15.7399	−	27.2622i	−1.46141	−	2.53123i
$117$	−5.48112	+	1.46866i	−0.506730	+	0.135778i
$118$	−12.3138	+	12.3138i	−1.13358	+	1.13358i
$119$	−0.563829	+	10.2836i	−0.0516861	+	0.942693i
$120$		0			0
$121$	−0.249123	+	0.431493i	−0.0226475	+	0.0392267i
$122$	−8.81197	+	32.8867i	−0.797798	+	2.97742i
$123$	0.273049	−	1.01903i	0.0246200	−	0.0918832i
$124$	−9.68363	+	16.7725i	−0.869616	+	1.50622i
$125$		0			0
$126$	0.390906	−	7.12967i	0.0348247	−	0.635161i
$127$	5.58258	−	5.58258i	0.495374	−	0.495374i	−0.414621	−	0.909994i	$-0.636086\pi$
$127$	5.58258	−	5.58258i	0.495374	−	0.495374i	0.909994	+	0.414621i	$0.136086\pi$
$128$	−23.8117	+	6.38031i	−2.10467	+	0.563945i
$129$	4.76939	+	8.26083i	0.419922	+	0.727326i
$130$		0			0
$131$	−11.1762	−	6.45260i	−0.976472	−	0.563766i	−0.0752685	−	0.997163i	$-0.523981\pi$
$131$	−11.1762	−	6.45260i	−0.976472	−	0.563766i	−0.901203	+	0.433397i	$0.857315\pi$
$132$	−12.6686	−	12.6686i	−1.10266	−	1.10266i
$133$	−1.18801	+	3.62650i	−0.103013	+	0.314458i
$134$			1.52167i			0.131452i
$135$		0			0
$136$	−29.8741	+	17.2478i	−2.56168	+	1.47899i
$137$	2.04721	+	0.548549i	0.174905	+	0.0468657i	0.345209	−	0.938526i	$-0.387808\pi$
$137$	2.04721	+	0.548549i	0.174905	+	0.0468657i	−0.170303	+	0.985392i	$0.554475\pi$
$138$	−0.534560	−	1.99500i	−0.0455047	−	0.169826i
$139$	1.07053			0.0908011			0.0454005	−	0.998969i	$-0.485544\pi$
$139$	1.07053			0.0908011			0.0454005	+	0.998969i	$0.485544\pi$
$140$		0			0
$141$	−6.78181			−0.571132
$142$	−4.70781	−	17.5698i	−0.395070	−	1.47442i
$143$	−18.5860	−	4.98009i	−1.55424	−	0.416456i
$144$	11.5605	−	6.67447i	0.963377	−	0.556206i
$145$		0			0
$146$			13.3808i			1.10740i
$147$	6.91902	−	1.06166i	0.570671	−	0.0875640i
$148$	−4.69414	−	4.69414i	−0.385856	−	0.385856i
$149$	−7.41936	−	4.28357i	−0.607817	−	0.350923i	0.164293	−	0.986412i	$-0.447466\pi$
$149$	−7.41936	−	4.28357i	−0.607817	−	0.350923i	−0.772111	+	0.635488i	$0.780799\pi$
$150$		0			0
$151$	7.70716	+	13.3492i	0.627200	+	1.08634i	0.988111	+	0.153742i	$0.0491325\pi$
$151$	7.70716	+	13.3492i	0.627200	+	1.08634i	−0.360911	+	0.932600i	$0.617534\pi$
$152$	−12.3463	+	3.30818i	−1.00142	+	0.268329i
$153$	2.75253	−	2.75253i	0.222529	−	0.222529i
$154$	13.2360	−	20.2743i	1.06658	−	1.63375i
$155$		0			0
$156$	14.9907	−	25.9647i	1.20022	−	2.07884i
$157$	−4.60318	+	17.1793i	−0.367374	+	1.37106i	0.496800	+	0.867865i	$0.334508\pi$
$157$	−4.60318	+	17.1793i	−0.367374	+	1.37106i	−0.864174	+	0.503193i	$0.832159\pi$
$158$	5.48129	−	20.4564i	0.436068	−	1.62743i
$159$	−5.68730	+	9.85070i	−0.451033	+	0.781211i
$160$		0			0
$161$	1.80630	−	0.914872i	0.142356	−	0.0721020i
$162$	−1.90835	+	1.90835i	−0.149934	+	0.149934i
$163$	−2.22680	+	0.596668i	−0.174416	+	0.0467347i	−0.344970	−	0.938614i	$-0.612111\pi$
$163$	−2.22680	+	0.596668i	−0.174416	+	0.0467347i	0.170554	+	0.985348i	$0.445444\pi$
$164$	2.78703	+	4.82728i	0.217631	+	0.376947i
$165$		0			0
$166$	4.92535	+	2.84365i	0.382281	+	0.220710i
$167$	−2.75253	−	2.75253i	−0.212997	−	0.212997i	0.592542	−	0.805539i	$-0.298124\pi$
$167$	−2.75253	−	2.75253i	−0.212997	−	0.212997i	−0.805539	+	0.592542i	$0.798124\pi$
$168$	15.6463	+	17.4615i	1.20714	+	1.34719i
$169$		−	19.1996i		−	1.47690i
$170$		0			0
$171$	1.24912	−	0.721181i	0.0955228	−	0.0551501i
$172$	−48.6815	−	13.0442i	−3.71193	−	0.994609i
$173$	−3.28646	−	12.2652i	−0.249865	−	0.932508i	−0.970876	−	0.239584i	$-0.922989\pi$
$173$	−3.28646	−	12.2652i	−0.249865	−	0.932508i	0.721011	−	0.692924i	$-0.243678\pi$
$174$	−16.0796			−1.21899
$175$		0			0
$176$	45.2650			3.41198
$177$	1.67006	+	6.23273i	0.125529	+	0.468481i
$178$	9.30090	+	2.49217i	0.697132	+	0.186796i
$179$	−21.3890	+	12.3489i	−1.59869	+	0.923004i	−0.606949	+	0.794741i	$0.707607\pi$
$179$	−21.3890	+	12.3489i	−1.59869	+	0.923004i	−0.991740	+	0.128263i	$0.959060\pi$
$180$		0			0
$181$			21.0993i			1.56830i	0.620571	+	0.784150i	$0.286901\pi$
$181$			21.0993i			1.56830i	−0.620571	+	0.784150i	$0.713099\pi$
$182$	38.5045	+	12.6137i	2.85414	+	0.934988i
$183$	8.92051	+	8.92051i	0.659423	+	0.659423i
$184$	5.87322	+	3.39091i	0.432980	+	0.249981i
$185$		0			0
$186$	4.94633	+	8.56730i	0.362683	+	0.628185i
$187$	12.7499	−	3.41632i	0.932364	−	0.249826i
$188$	25.3372	−	25.3372i	1.84790	−	1.84790i
$189$	−2.21543	−	1.44633i	−0.161149	−	0.105205i
$190$		0			0
$191$	−0.892661	+	1.54613i	−0.0645907	+	0.111874i	−0.896512	−	0.443019i	$-0.853908\pi$
$191$	−0.892661	+	1.54613i	−0.0645907	+	0.111874i	0.831922	+	0.554893i	$0.187241\pi$
$192$	−5.87465	+	21.9245i	−0.423966	+	1.58226i
$193$	4.01578	−	14.9871i	0.289062	−	1.07879i	−0.656757	−	0.754102i	$-0.728072\pi$
$193$	4.01578	−	14.9871i	0.289062	−	1.07879i	0.945820	−	0.324693i	$-0.105261\pi$
$194$	2.61058	−	4.52167i	0.187429	−	0.324637i
$195$		0			0
$196$	−21.8834	+	29.8162i	−1.56310	+	2.12973i
$197$	11.7063	−	11.7063i	0.834040	−	0.834040i	−0.154027	−	0.988067i	$-0.549224\pi$
$197$	11.7063	−	11.7063i	0.834040	−	0.834040i	0.988067	+	0.154027i	$0.0492243\pi$
$198$	−8.83958	+	2.36856i	−0.628202	+	0.168326i
$199$	4.86539	+	8.42711i	0.344898	+	0.597382i	0.985335	−	0.170629i	$-0.0545800\pi$
$199$	4.86539	+	8.42711i	0.344898	+	0.597382i	−0.640437	+	0.768011i	$0.721247\pi$
$200$		0			0
$201$	0.488290	+	0.281914i	0.0344413	+	0.0198847i
$202$	37.7103	+	37.7103i	2.65329	+	2.65329i
$203$	−3.24019	−	15.4269i	−0.227417	−	1.08276i
$204$			20.5671i			1.43999i
$205$		0			0
$206$	22.2626	−	12.8533i	1.55111	−	0.895533i
$207$	−0.739216	−	0.198072i	−0.0513791	−	0.0137670i
$208$	19.6051	+	73.1672i	1.35937	+	5.07323i
$209$	4.89092			0.338312
$210$		0			0
$211$	3.49825			0.240829			0.120415	−	0.992724i	$-0.461578\pi$
$211$	3.49825			0.240829			0.120415	+	0.992724i	$0.461578\pi$
$212$	−15.5546	−	58.0507i	−1.06830	−	3.98694i
$213$	−6.51020	−	1.74440i	−0.446071	−	0.119524i
$214$	−6.30775	+	3.64178i	−0.431189	+	0.248947i
$215$		0			0
$216$		−	8.86172i		−	0.602964i
$217$	−7.22279	+	6.47193i	−0.490315	+	0.439344i
$218$	14.3159	+	14.3159i	0.969598	+	0.969598i
$219$	4.29379	+	2.47902i	0.290147	+	0.167517i
$220$		0			0
$221$	11.0444	+	19.1295i	0.742927	+	1.28679i
$222$	−3.27536	+	0.877631i	−0.219828	+	0.0589027i
$223$	16.1092	−	16.1092i	1.07875	−	1.07875i	0.0821283	−	0.996622i	$-0.473828\pi$
$223$	16.1092	−	16.1092i	1.07875	−	1.07875i	0.996622	−	0.0821283i	$-0.0261717\pi$
$224$	−48.3521	−	2.65105i	−3.23066	−	0.177131i
$225$		0			0
$226$	3.89266	−	6.74229i	0.258936	−	0.448490i
$227$	2.50303	−	9.34143i	0.166132	−	0.620013i	−0.831761	−	0.555134i	$-0.812667\pi$
$227$	2.50303	−	9.34143i	0.166132	−	0.620013i	0.997893	−	0.0648792i	$-0.0206662\pi$
$228$	−1.97241	+	7.36115i	−0.130626	+	0.487504i
$229$	11.4598	−	19.8489i	0.757285	−	1.31166i	−0.186946	−	0.982370i	$-0.559859\pi$
$229$	11.4598	−	19.8489i	0.757285	−	1.31166i	0.944231	−	0.329285i	$-0.106808\pi$
$230$		0			0
$231$	−4.05367	−	8.00347i	−0.266712	−	0.526589i
$232$	37.3342	−	37.3342i	2.45111	−	2.45111i
$233$	−2.95687	+	0.792290i	−0.193711	+	0.0519046i	−0.354370	−	0.935105i	$-0.615305\pi$
$233$	−2.95687	+	0.792290i	−0.193711	+	0.0519046i	0.160659	+	0.987010i	$0.448638\pi$
$234$	−7.65716	−	13.2626i	−0.500564	−	0.867002i
$235$		0			0
$236$	−29.5252	−	17.0464i	−1.92193	−	1.10962i
$237$	−5.54880	−	5.54880i	−0.360433	−	0.360433i
$238$	−27.2015	+	5.71329i	−1.76321	+	0.370337i
$239$		−	5.77830i		−	0.373767i	−0.982382	−	0.186884i	$-0.940161\pi$
$239$		−	5.77830i		−	0.373767i	0.982382	−	0.186884i	$-0.0598388\pi$
$240$		0			0
$241$	19.7725	−	11.4157i	1.27366	−	0.735349i	0.297986	−	0.954570i	$-0.403685\pi$
$241$	19.7725	−	11.4157i	1.27366	−	0.735349i	0.975675	+	0.219221i	$0.0703517\pi$
$242$	−1.29885	−	0.348026i	−0.0834933	−	0.0223720i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−66.6549			−4.26714
$245$		0			0
$246$	2.84719			0.181530
$247$	2.11834	+	7.90576i	0.134787	+	0.503032i
$248$	−31.3764	−	8.40727i	−1.99240	−	0.533862i
$249$	1.82501	−	1.05367i	0.115655	−	0.0667736i
$250$		0			0
$251$		−	12.8325i		−	0.809981i	−0.914321	−	0.404991i	$-0.867275\pi$
$251$		−	12.8325i		−	0.809981i	0.914321	−	0.404991i	$-0.132725\pi$
$252$	13.6805	−	2.87339i	0.861791	−	0.181007i
$253$	−1.83497	−	1.83497i	−0.115363	−	0.115363i
$254$	18.4524	+	10.6535i	1.15781	+	0.668460i
$255$		0			0
$256$	−10.5671	−	18.3028i	−0.660446	−	1.14393i
$257$	23.4122	−	6.27328i	1.46041	−	0.391317i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	23.4122	−	6.27328i	1.46041	−	0.391317i	0.899633	+	0.436648i	$0.143834\pi$
$258$	−18.2033	+	18.2033i	−1.13329	+	1.13329i
$259$	−1.50202	−	2.96556i	−0.0933311	−	0.184271i
$260$		0			0
$261$	−2.97902	+	5.15981i	−0.184397	+	0.319384i
$262$	9.01432	−	33.6419i	0.556906	−	2.07840i
$263$	2.53977	−	9.47856i	0.156609	−	0.584473i	−0.842353	−	0.538926i	$-0.818830\pi$
$263$	2.53977	−	9.47856i	0.156609	−	0.584473i	0.998962	−	0.0455471i	$-0.0145031\pi$
$264$	15.0246	−	26.0234i	0.924702	−	1.60163i
$265$		0			0
$266$	−10.2836	−	0.563829i	−0.630526	−	0.0345706i
$267$	2.52287	−	2.52287i	0.154397	−	0.154397i
$268$	−2.87752	+	0.771029i	−0.175772	+	0.0470981i
$269$	10.9812	+	19.0199i	0.669533	+	1.15966i	0.978035	+	0.208441i	$0.0668389\pi$
$269$	10.9812	+	19.0199i	0.669533	+	1.15966i	−0.308502	+	0.951224i	$0.599828\pi$
$270$		0			0
$271$	−21.9488	−	12.6721i	−1.33329	−	0.769777i	−0.347490	−	0.937684i	$-0.612966\pi$
$271$	−21.9488	−	12.6721i	−1.33329	−	0.769777i	−0.985803	+	0.167907i	$0.946299\pi$
$272$	−36.7433	−	36.7433i	−2.22789	−	2.22789i
$273$	11.1812	−	10.0189i	0.676719	−	0.606369i
$274$			5.71994i			0.345554i
$275$		0			0
$276$	3.50175	−	2.02174i	0.210781	−	0.121694i
$277$	−13.5087	−	3.61963i	−0.811657	−	0.217483i	−0.170961	−	0.985278i	$-0.554687\pi$
$277$	−13.5087	−	3.61963i	−0.811657	−	0.217483i	−0.640696	+	0.767795i	$0.721354\pi$
$278$	0.747768	+	2.79071i	0.0448481	+	0.167375i
$279$	3.66557			0.219452
$280$		0			0
$281$	−17.9161			−1.06878			−0.534392	−	0.845237i	$-0.679459\pi$
$281$	−17.9161			−1.06878			−0.534392	+	0.845237i	$0.679459\pi$
$282$	−4.73712	−	17.6792i	−0.282091	−	1.05278i
$283$	18.2310	+	4.88498i	1.08372	+	0.290382i	0.756119	−	0.654434i	$-0.227093\pi$
$283$	18.2310	+	4.88498i	1.08372	+	0.290382i	0.327601	+	0.944816i	$0.393760\pi$
$284$	30.8396	−	17.8052i	1.82999	−	1.05655i
$285$		0			0
$286$		−	51.9294i		−	3.07065i
$287$	0.573736	+	2.73162i	0.0338666	+	0.161242i
$288$	12.9420	+	12.9420i	0.762617	+	0.762617i
$289$	1.59972	+	0.923596i	0.0941009	+	0.0543292i
$290$		0			0
$291$	−0.967310	−	1.67543i	−0.0567047	−	0.0982155i
$292$	−25.3035	+	6.78006i	−1.48078	+	0.396773i
$293$	−12.6686	+	12.6686i	−0.740106	+	0.740106i	−0.972598	−	0.232492i	$-0.925312\pi$
$293$	−12.6686	+	12.6686i	−0.740106	+	0.740106i	0.232492	+	0.972598i	$0.425312\pi$
$294$	7.60054	+	17.2953i	0.443272	+	1.00868i
$295$		0			0
$296$	5.56713	−	9.64256i	0.323583	−	0.560462i
$297$	−0.877631	+	3.27536i	−0.0509253	+	0.190056i
$298$	5.98417	−	22.3332i	0.346654	−	1.29373i
$299$	2.17132	−	3.76083i	0.125571	−	0.217495i
$300$		0			0
$301$	−21.1325	−	13.7962i	−1.21806	−	0.795202i
$302$	−29.4159	+	29.4159i	−1.69269	+	1.69269i
$303$	19.0874	−	5.11445i	1.09654	−	0.293818i
$304$	−9.62701	−	16.6745i	−0.552147	−	0.956347i
$305$		0			0
$306$	9.09807	+	5.25277i	0.520102	+	0.300281i
$307$	8.19576	+	8.19576i	0.467757	+	0.467757i	0.901187	−	0.433430i	$-0.142697\pi$
$307$	8.19576	+	8.19576i	0.467757	+	0.467757i	−0.433430	+	0.901187i	$0.642697\pi$
$308$	45.0460	+	14.7566i	2.56674	+	0.840837i
$309$		−	9.52517i		−	0.541868i
$310$		0			0
$311$	−15.0899	+	8.71214i	−0.855668	+	0.494020i	−0.862559	−	0.505956i	$-0.831140\pi$
$311$	−15.0899	+	8.71214i	−0.855668	+	0.494020i	0.00689127	+	0.999976i	$0.497806\pi$
$312$	48.5721	+	13.0149i	2.74986	+	0.736822i
$313$	−1.08089	−	4.03393i	−0.0610954	−	0.228011i	0.928627	−	0.371015i	$-0.120990\pi$
$313$	−1.08089	−	4.03393i	−0.0610954	−	0.228011i	−0.989722	+	0.143004i	$0.954324\pi$
$314$	−47.9992			−2.70875
$315$		0			0
$316$	41.4612			2.33237
$317$	6.03229	+	22.5128i	0.338807	+	1.26445i	0.899682	+	0.436545i	$0.143798\pi$
$317$	6.03229	+	22.5128i	0.338807	+	1.26445i	−0.560875	+	0.827900i	$0.689535\pi$
$318$	−29.6519	−	7.94520i	−1.66280	−	0.445545i
$319$	−17.4964	+	10.1016i	−0.979613	+	0.565580i
$320$		0			0
$321$			2.69881i			0.150633i
$322$	3.64664	+	4.06971i	0.203219	+	0.226796i
$323$	−3.97014	−	3.97014i	−0.220905	−	0.220905i
$324$	−4.57570	−	2.64178i	−0.254206	−	0.146766i
$325$		0			0
$326$	−3.11085	−	5.38815i	−0.172294	−	0.298422i
$327$	7.24614	−	1.94160i	0.400712	−	0.107371i
$328$	−6.61070	+	6.61070i	−0.365015	+	0.365015i
$329$	16.0069	−	8.10734i	0.882491	−	0.446972i
$330$		0			0
$331$	−3.06713	+	5.31243i	−0.168585	+	0.291998i	−0.937923	−	0.346845i	$-0.887253\pi$
$331$	−3.06713	+	5.31243i	−0.168585	+	0.291998i	0.769338	+	0.638842i	$0.220586\pi$
$332$	−2.88176	+	10.7549i	−0.158157	+	0.590251i
$333$	−0.325192	+	1.21363i	−0.0178204	+	0.0665067i
$334$	5.25277	−	9.09807i	0.287419	−	0.497824i
$335$		0			0
$336$	−19.3070	+	29.5737i	−1.05328	+	1.61337i
$337$	10.4816	−	10.4816i	0.570967	−	0.570967i	−0.361432	−	0.932399i	$-0.617712\pi$
$337$	10.4816	−	10.4816i	0.570967	−	0.570967i	0.932399	+	0.361432i	$0.117712\pi$
$338$	50.0506	−	13.4110i	2.72239	−	0.729463i
$339$	−1.44236	−	2.49825i	−0.0783384	−	0.135686i
$340$		0			0
$341$	10.7643	+	6.21480i	0.582922	+	0.336550i
$342$	2.75253	+	2.75253i	0.148840	+	0.148840i
$343$	−15.0616	+	10.7772i	−0.813251	+	0.581912i
$344$		−	84.5301i		−	4.55756i
$345$		0			0
$346$	29.6780	−	17.1346i	1.59550	−	0.921161i
$347$	11.3462	+	3.04020i	0.609096	+	0.163207i	0.550166	−	0.835055i	$-0.314565\pi$
$347$	11.3462	+	3.04020i	0.609096	+	0.163207i	0.0589298	+	0.998262i	$0.481231\pi$
$348$	−8.14755	−	30.4071i	−0.436754	−	1.62999i
$349$	12.3258			0.659786			0.329893	−	0.944018i	$-0.392987\pi$
$349$	12.3258			0.659786			0.329893	+	0.944018i	$0.392987\pi$
$350$		0			0
$351$	−5.67447			−0.302881
$352$	16.0631	+	59.9484i	0.856167	+	3.19526i
$353$	6.32074	+	1.69364i	0.336419	+	0.0901432i	0.423074	−	0.906095i	$-0.360951\pi$
$353$	6.32074	+	1.69364i	0.336419	+	0.0901432i	−0.0866548	+	0.996238i	$0.527618\pi$
$354$	−15.0812	+	8.70716i	−0.801559	+	0.462781i
$355$		0			0
$356$			18.8511i			0.999106i
$357$	−3.20620	+	9.78723i	−0.169690	+	0.517995i
$358$	−47.1321	−	47.1321i	−2.49101	−	2.49101i
$359$	−15.5521	−	8.97902i	−0.820809	−	0.473895i	0.0298861	−	0.999553i	$-0.490486\pi$
$359$	−15.5521	−	8.97902i	−0.820809	−	0.473895i	−0.850696	+	0.525659i	$0.823819\pi$
$360$		0			0
$361$	8.45979	+	14.6528i	0.445252	+	0.771200i
$362$	−55.0027	+	14.7379i	−2.89088	+	0.774609i
$363$	−0.352313	+	0.352313i	−0.0184916	+	0.0184916i
$364$	−4.34264	+	79.2045i	−0.227616	+	4.15145i
$365$		0			0
$366$	−17.0234	+	29.4854i	−0.889828	+	1.54123i
$367$	1.67283	−	6.24307i	0.0873208	−	0.325886i	−0.908423	−	0.418053i	$-0.862713\pi$
$367$	1.67283	−	6.24307i	0.0873208	−	0.325886i	0.995744	+	0.0921671i	$0.0293794\pi$
$368$	−2.64406	+	9.86776i	−0.137831	+	0.514393i
$369$	0.527491	−	0.913641i	0.0274601	−	0.0475622i
$370$		0			0
$371$	1.64754	−	30.0493i	0.0855362	−	1.56008i
$372$	−13.6947	+	13.6947i	−0.710038	+	0.710038i
$373$	−21.3994	+	5.73395i	−1.10802	+	0.296893i	−0.766026	−	0.642810i	$-0.777769\pi$
$373$	−21.3994	+	5.73395i	−1.10802	+	0.296893i	−0.341993	+	0.939702i	$0.611102\pi$
$374$	17.8117	+	30.8507i	0.921019	+	1.59525i
$375$		0			0
$376$	52.0468	+	30.0493i	2.68411	+	1.54967i
$377$	−23.9064	−	23.9064i	−1.23124	−	1.23124i
$378$	2.22288	−	6.78556i	0.114333	−	0.349011i
$379$			4.30211i			0.220984i	0.993877	+	0.110492i	$0.0352427\pi$
$379$			4.30211i			0.220984i	−0.993877	+	0.110492i	$0.964757\pi$
$380$		0			0
$381$	6.83724	−	3.94748i	0.350282	−	0.202236i
$382$	−4.65406	−	1.24705i	−0.238123	−	0.0638048i
$383$	6.59463	+	24.6115i	0.336970	+	1.25759i	0.901718	+	0.432326i	$0.142307\pi$
$383$	6.59463	+	24.6115i	0.336970	+	1.25759i	−0.564748	+	0.825264i	$0.691026\pi$
$384$	−24.6516			−1.25800
$385$		0			0
$386$	41.8741			2.13134
$387$	2.46882	+	9.21376i	0.125497	+	0.468362i
$388$	9.87340	+	2.64557i	0.501246	+	0.134308i
$389$	14.8024	−	8.54615i	0.750510	−	0.433307i	−0.0753681	−	0.997156i	$-0.524013\pi$
$389$	14.8024	−	8.54615i	0.750510	−	0.433307i	0.825878	+	0.563849i	$0.190680\pi$
$390$		0			0
$391$			2.97903i			0.150656i
$392$	−57.8039	−	22.5096i	−2.91954	−	1.13690i
$393$	−9.12535	−	9.12535i	−0.460313	−	0.460313i
$394$	38.6935	+	22.3397i	1.94935	+	1.12546i
$395$		0			0
$396$	−8.95804	−	15.5158i	−0.450158	−	0.779697i
$397$	13.0643	−	3.50057i	0.655679	−	0.175689i	0.0843839	−	0.996433i	$-0.473108\pi$
$397$	13.0643	−	3.50057i	0.655679	−	0.175689i	0.571295	+	0.820745i	$0.306441\pi$
$398$	−18.5697	+	18.5697i	−0.930815	+	0.930815i
$399$	−2.08613	+	3.19545i	−0.104437	+	0.159973i
$400$		0			0
$401$	−13.5217	+	23.4202i	−0.675240	+	1.16955i	0.301159	+	0.953574i	$0.402627\pi$
$401$	−13.5217	+	23.4202i	−0.675240	+	1.16955i	−0.976399	+	0.215976i	$0.930707\pi$
$402$	−0.393836	+	1.46982i	−0.0196428	+	0.0733078i
$403$	−5.38348	+	20.0914i	−0.268170	+	1.00082i
$404$	−52.2036	+	90.4192i	−2.59722	+	4.49852i
$405$		0			0
$406$	37.9523	−	19.2224i	1.88354	−	0.953993i
$407$	−3.01262	+	3.01262i	−0.149330	+	0.149330i
$408$	−33.3203	+	8.92813i	−1.64960	+	0.442009i
$409$	1.25341	+	2.17096i	0.0619770	+	0.107347i	0.895349	−	0.445365i	$-0.146926\pi$
$409$	1.25341	+	2.17096i	0.0619770	+	0.107347i	−0.833372	+	0.552712i	$0.813593\pi$
$410$		0			0
$411$	1.83548	+	1.05972i	0.0905377	+	0.0522719i
$412$	35.5865	+	35.5865i	1.75322	+	1.75322i
$413$	−11.3927	−	12.7145i	−0.560599	−	0.625639i
$414$		−	2.06538i		−	0.101508i
$415$		0			0
$416$	−89.9444	+	51.9294i	−4.40989	+	2.54605i
$417$	1.03405	+	0.277073i	0.0506377	+	0.0135683i
$418$	3.41632	+	12.7499i	0.167098	+	0.623617i
$419$	−21.0422			−1.02798			−0.513989	−	0.857797i	$-0.671833\pi$
$419$	−21.0422			−1.02798			−0.513989	+	0.857797i	$0.671833\pi$
$420$		0			0
$421$	−18.0619			−0.880282			−0.440141	−	0.897929i	$-0.645071\pi$
$421$	−18.0619			−0.880282			−0.440141	+	0.897929i	$0.645071\pi$
$422$	2.44354	+	9.11940i	0.118949	+	0.443925i
$423$	−6.55073	−	1.75526i	−0.318507	−	0.0853438i
$424$	87.2941	−	50.3993i	4.23938	−	2.44761i
$425$		0			0
$426$		−	18.1896i		−	0.881288i
$427$	−31.7189	−	10.3908i	−1.53499	−	0.502846i
$428$	−10.0829	−	10.0829i	−0.487374	−	0.487374i
$429$	−16.6637	−	9.62080i	−0.804532	−	0.464497i
$430$		0			0
$431$	6.45979	+	11.1887i	0.311157	+	0.538940i	0.978613	−	0.205709i	$-0.0659500\pi$
$431$	6.45979	+	11.1887i	0.311157	+	0.538940i	−0.667456	+	0.744649i	$0.732617\pi$
$432$	12.8941	−	3.45496i	0.620367	−	0.166227i
$433$	22.1861	−	22.1861i	1.06620	−	1.06620i	0.0685478	−	0.997648i	$-0.478163\pi$
$433$	22.1861	−	22.1861i	1.06620	−	1.06620i	0.997648	−	0.0685478i	$-0.0218366\pi$
$434$	−21.9165	−	14.3081i	−1.05203	−	0.686809i
$435$		0			0
$436$	−19.8180	+	34.3258i	−0.949111	+	1.64391i
$437$	−0.285692	+	1.06622i	−0.0136665	+	0.0510041i
$438$	−3.46321	+	12.9249i	−0.165478	+	0.617574i
$439$	−4.57570	+	7.92535i	−0.218386	+	0.378256i	−0.954315	−	0.298803i	$-0.903413\pi$
$439$	−4.57570	+	7.92535i	−0.218386	+	0.378256i	0.735928	+	0.677059i	$0.236746\pi$
$440$		0			0
$441$	6.95804	+	0.765293i	0.331335	+	0.0364425i
$442$	−42.1531	+	42.1531i	−2.00502	+	2.00502i
$443$	−26.7986	+	7.18065i	−1.27324	+	0.341163i	−0.831271	−	0.555868i	$-0.812386\pi$
$443$	−26.7986	+	7.18065i	−1.27324	+	0.341163i	−0.441967	+	0.897031i	$0.645719\pi$
$444$	−3.31926	−	5.74912i	−0.157525	−	0.272841i
$445$		0			0
$446$	53.2465	+	30.7419i	2.52129	+	1.45567i
$447$	−6.05788	−	6.05788i	−0.286528	−	0.286528i
$448$	−12.3439	−	58.7706i	−0.583195	−	2.77665i
$449$		−	28.3525i		−	1.33804i	−0.743247	−	0.669018i	$-0.766715\pi$
$449$		−	28.3525i		−	1.33804i	0.743247	−	0.669018i	$-0.233285\pi$
$450$		0			0
$451$	3.09807	−	1.78867i	0.145882	−	0.0842252i
$452$	14.7223	+	3.94483i	0.692478	+	0.185549i
$453$	3.98952	+	14.8891i	0.187444	+	0.699551i
$454$	26.1001			1.22494
$455$		0			0
$456$	−12.7818			−0.598563
$457$	−2.40189	−	8.96398i	−0.112356	−	0.419317i	0.886720	−	0.462307i	$-0.152978\pi$
$457$	−2.40189	−	8.96398i	−0.112356	−	0.419317i	−0.999076	+	0.0429900i	$0.986312\pi$
$458$	59.7479	+	16.0094i	2.79184	+	0.748070i
$459$	3.37114	−	1.94633i	0.157351	−	0.0908469i
$460$		0			0
$461$		−	13.5762i		−	0.632306i	−0.948708	−	0.316153i	$-0.897609\pi$
$461$		−	13.5762i		−	0.632306i	0.948708	−	0.316153i	$-0.102391\pi$
$462$	18.0323	−	16.1577i	0.838940	−	0.751727i
$463$	20.5644	+	20.5644i	0.955710	+	0.955710i	0.999060	−	0.0433497i	$-0.0138030\pi$
$463$	20.5644	+	20.5644i	0.955710	+	0.955710i	−0.0433497	+	0.999060i	$0.513803\pi$
$464$	68.8781	+	39.7668i	3.19758	+	1.84613i
$465$		0			0
$466$	−4.13076	−	7.15469i	−0.191354	−	0.331434i
$467$	−36.3357	+	9.73612i	−1.68142	+	0.450534i	−0.968152	−	0.250362i	$-0.919450\pi$
$467$	−36.3357	+	9.73612i	−1.68142	+	0.450534i	−0.713263	+	0.700896i	$0.752784\pi$
$468$	21.2001	−	21.2001i	0.979975	−	0.979975i
$469$	−1.48951	−	0.0816672i	−0.0687793	−	0.00377104i
$470$		0			0
$471$	−8.89266	+	15.4025i	−0.409752	+	0.709712i
$472$	14.7996	−	55.2327i	0.681205	−	2.54229i
$473$	−8.37154	+	31.2430i	−0.384924	+	1.43655i
$474$	10.5890	−	18.3407i	0.486370	−	0.842418i
$475$		0			0
$476$	−24.5870	−	48.5441i	−1.12695	−	2.22501i
$477$	−8.04306	+	8.04306i	−0.368267	+	0.368267i
$478$	15.0632	−	4.03616i	0.688973	−	0.184610i
$479$	−11.3591	−	19.6745i	−0.519009	−	0.898950i	−0.999756	−	0.0220904i	$-0.992968\pi$
$479$	−11.3591	−	19.6745i	−0.519009	−	0.898950i	0.480747	−	0.876859i	$-0.340365\pi$
$480$		0			0
$481$	−6.17447	−	3.56483i	−0.281532	−	0.162542i
$482$	43.5701	+	43.5701i	1.98457	+	1.98457i
$483$	1.98154	−	0.416193i	0.0901632	−	0.0189375i
$484$		−	2.63251i		−	0.119660i
$485$		0			0
$486$	−2.33724	+	1.34940i	−0.106019	+	0.0612102i
$487$	29.7704	+	7.97697i	1.34903	+	0.361471i	0.859776	−	0.510672i	$-0.170603\pi$
$487$	29.7704	+	7.97697i	1.34903	+	0.361471i	0.489252	+	0.872143i	$0.337270\pi$
$488$	−28.9347	−	107.986i	−1.30981	−	4.88829i
$489$	−2.30535			−0.104252
$490$		0			0
$491$	−33.4867			−1.51123			−0.755617	−	0.655013i	$-0.772663\pi$
$491$	−33.4867			−1.51123			−0.755617	+	0.655013i	$0.772663\pi$
$492$	1.44267	+	5.38413i	0.0650408	+	0.242735i
$493$	22.4024	+	6.00269i	1.00895	+	0.270348i
$494$	−19.1295	+	11.0444i	−0.860675	+	0.496911i
$495$		0			0
$496$		−	48.9314i		−	2.19709i
$497$	17.4512	−	3.66537i	0.782793	−	0.164414i
$498$	4.02153	+	4.02153i	0.180209	+	0.180209i
$499$	−1.61577	−	0.932866i	−0.0723318	−	0.0417608i	0.463398	−	0.886150i	$-0.346630\pi$
$499$	−1.61577	−	0.932866i	−0.0723318	−	0.0417608i	−0.535730	+	0.844390i	$0.679963\pi$
$500$		0			0
$501$	−1.94633	−	3.37114i	−0.0869556	−	0.150612i
$502$	33.4524	−	8.96355i	1.49306	−	0.400063i
$503$	6.45394	−	6.45394i	0.287767	−	0.287767i	−0.548430	−	0.836197i	$-0.684774\pi$
$503$	6.45394	−	6.45394i	0.287767	−	0.287767i	0.836197	+	0.548430i	$0.184774\pi$
$504$	10.5938	+	20.9161i	0.471884	+	0.931676i
$505$		0			0
$506$	3.50175	−	6.06522i	0.155672	−	0.269632i
$507$	4.96923	−	18.5454i	0.220691	−	0.823632i
$508$	−10.7963	+	40.2922i	−0.479007	+	1.78768i
$509$	11.2864	−	19.5486i	0.500260	−	0.866476i	−0.499740	−	0.866176i	$-0.666571\pi$
$509$	11.2864	−	19.5486i	0.500260	−	0.866476i	1.00000		0.000300571i	$-9.56748e-5\pi$
$510$		0			0
$511$	−13.0981	−	0.718143i	−0.579424	−	0.0317688i
$512$	5.46881	−	5.46881i	0.241689	−	0.241689i
$513$	1.39322	−	0.373311i	0.0615120	−	0.0164821i
$514$	32.7070	+	56.6502i	1.44264	+	2.49873i
$515$		0			0
$516$	−43.6467	−	25.1994i	−1.92144	−	1.10934i
$517$	−16.2610	−	16.2610i	−0.715157	−	0.715157i
$518$	6.68159	−	5.98699i	0.293572	−	0.263053i
$519$		−	12.6979i		−	0.557376i
$520$		0			0
$521$	−9.15281	+	5.28438i	−0.400992	+	0.231513i	−0.686912	−	0.726741i	$-0.741034\pi$
$521$	−9.15281	+	5.28438i	−0.400992	+	0.231513i	0.285920	+	0.958253i	$0.407701\pi$
$522$	−15.5317	−	4.16171i	−0.679804	−	0.182153i
$523$	−3.42627	−	12.7870i	−0.149820	−	0.559137i	−0.999493	−	0.0318274i	$-0.989867\pi$
$523$	−3.42627	−	12.7870i	−0.149820	−	0.559137i	0.849673	−	0.527310i	$-0.176799\pi$
$524$	68.1855			2.97870
$525$		0			0
$526$	26.4832			1.15472
$527$	−3.69304	−	13.7826i	−0.160871	−	0.600380i
$528$	43.7227	+	11.7155i	1.90278	+	0.509850i
$529$	−19.4114	+	11.2072i	−0.843973	+	0.487268i
$530$		0			0
$531$			6.45260i			0.280019i
$532$	−4.14447	−	19.7322i	−0.179686	−	0.855502i
$533$	4.23307	+	4.23307i	0.183355	+	0.183355i
$534$	8.33896	+	4.81450i	0.360862	+	0.208344i
$535$		0			0
$536$	−2.49825	−	4.32709i	−0.107908	−	0.186902i
$537$	−23.8563	+	6.39229i	−1.02948	+	0.275847i
$538$	−41.9117	+	41.9117i	−1.80694	+	1.80694i
$539$	19.1355	+	14.0444i	0.824226	+	0.604935i
$540$		0			0
$541$	−1.67623	+	2.90331i	−0.0720667	+	0.124823i	−0.899807	−	0.436288i	$-0.856293\pi$
$541$	−1.67623	+	2.90331i	−0.0720667	+	0.124823i	0.827740	+	0.561111i	$0.189626\pi$
$542$	17.7030	−	66.0686i	0.760411	−	2.83789i
$543$	−5.46090	+	20.3804i	−0.234350	+	0.874606i
$544$	35.6233	−	61.7014i	1.52734	−	2.64543i
$545$		0			0
$546$	33.9278	+	22.1496i	1.45198	+	0.947914i
$547$	−25.3496	+	25.3496i	−1.08387	+	1.08387i	−0.0877278	+	0.996144i	$0.527961\pi$
$547$	−25.3496	+	25.3496i	−1.08387	+	1.08387i	−0.996144	+	0.0877278i	$0.972039\pi$
$548$	−10.8166	+	2.89830i	−0.462062	+	0.123809i
$549$	6.30775	+	10.9254i	0.269208	+	0.466283i
$550$		0			0
$551$	7.44232	+	4.29683i	0.317054	+	0.183051i
$552$	4.79547	+	4.79547i	0.204109	+	0.204109i
$553$	19.7300	+	6.46336i	0.839006	+	0.274850i
$554$		−	37.7434i		−	1.60356i
$555$		0			0
$556$	−4.89842	+	2.82811i	−0.207739	+	0.119938i
$557$	18.2388	+	4.88707i	0.772803	+	0.207072i	0.623609	−	0.781736i	$-0.285666\pi$
$557$	18.2388	+	4.88707i	0.772803	+	0.207072i	0.149193	+	0.988808i	$0.452332\pi$
$558$	2.56041	+	9.55558i	0.108391	+	0.404520i
$559$	−54.1276			−2.28935
$560$		0			0
$561$	13.1996			0.557290
$562$	−12.5144	−	46.7045i	−0.527890	−	1.97011i
$563$	−33.9371	−	9.09342i	−1.43028	−	0.383242i	−0.541160	−	0.840920i	$-0.682015\pi$
$563$	−33.9371	−	9.09342i	−1.43028	−	0.383242i	−0.889118	+	0.457678i	$0.848681\pi$
$564$	31.0316	−	17.9161i	1.30666	−	0.754403i
$565$		0			0
$566$			50.9376i			2.14107i
$567$	−1.76560	−	1.97044i	−0.0741484	−	0.0827508i
$568$	42.2331	+	42.2331i	1.77206	+	1.77206i
$569$	31.8176	+	18.3699i	1.33387	+	0.770107i	0.985890	−	0.167396i	$-0.0535359\pi$
$569$	31.8176	+	18.3699i	1.33387	+	0.770107i	0.347975	+	0.937504i	$0.386869\pi$
$570$		0			0
$571$	−10.5362	−	18.2492i	−0.440926	−	0.763707i	0.556832	−	0.830625i	$-0.312017\pi$
$571$	−10.5362	−	18.2492i	−0.440926	−	0.763707i	−0.997758	+	0.0669184i	$0.978683\pi$
$572$	98.2002	−	26.3127i	4.10596	−	1.10019i
$573$	−1.26241	+	1.26241i	−0.0527381	+	0.0527381i
$574$	−6.72015	+	3.40368i	−0.280494	+	0.142067i
$575$		0			0
$576$	−11.3489	+	19.6570i	−0.472873	+	0.819040i
$577$	−5.18335	+	19.3445i	−0.215786	+	0.805323i	0.770103	+	0.637920i	$0.220205\pi$
$577$	−5.18335	+	19.3445i	−0.215786	+	0.805323i	−0.985888	+	0.167403i	$0.946462\pi$
$578$	−1.29027	+	4.81535i	−0.0536681	+	0.200292i
$579$	7.75789	−	13.4371i	0.322407	−	0.558425i
$580$		0			0
$581$	−3.04791	+	4.66866i	−0.126449	+	0.193689i
$582$	3.69192	−	3.69192i	0.153035	−	0.153035i
$583$	−37.2560	+	9.98271i	−1.54299	+	0.413442i
$584$	−21.9684	−	38.0503i	−0.909058	−	1.57453i
$585$		0			0
$586$	−41.8741	−	24.1760i	−1.72980	−	0.998703i
$587$	−29.8075	−	29.8075i	−1.23029	−	1.23029i	−0.963853	−	0.266434i	$-0.914154\pi$
$587$	−29.8075	−	29.8075i	−1.23029	−	1.23029i	−0.266434	−	0.963853i	$-0.585846\pi$
$588$	−28.8547	+	23.1364i	−1.18995	+	0.954129i
$589$		−	5.28708i		−	0.217850i
$590$		0			0
$591$	14.3372	−	8.27761i	0.589755	−	0.340495i
$592$	16.2007	+	4.34097i	0.665846	+	0.178413i
$593$	7.84014	+	29.2598i	0.321956	+	1.20156i	0.917337	+	0.398112i	$0.130334\pi$
$593$	7.84014	+	29.2598i	0.321956	+	1.20156i	−0.595381	+	0.803443i	$0.702999\pi$
$594$	−9.15141			−0.375487
$595$		0			0
$596$	45.2650			1.85413
$597$	2.51851	+	9.39921i	0.103076	+	0.384684i
$598$	11.3206	+	3.03334i	0.462934	+	0.124043i
$599$	−15.5885	+	9.00000i	−0.636927	+	0.367730i	−0.783430	−	0.621480i	$-0.786532\pi$
$599$	−15.5885	+	9.00000i	−0.636927	+	0.367730i	0.146503	+	0.989210i	$0.453198\pi$
$600$		0			0
$601$		−	5.48584i		−	0.223772i	−0.993721	−	0.111886i	$-0.964311\pi$
$601$		−	5.48584i		−	0.223772i	0.993721	−	0.111886i	$-0.0356892\pi$
$602$	21.2036	−	64.7260i	0.864194	−	2.63803i
$603$	0.398687	+	0.398687i	0.0162358	+	0.0162358i
$604$	−70.5314	−	40.7213i	−2.86988	−	1.65693i
$605$		0			0
$606$	26.6652	+	46.1855i	1.08320	+	1.87616i
$607$	9.88585	−	2.64891i	0.401254	−	0.107516i	−0.0525474	−	0.998618i	$-0.516734\pi$
$607$	9.88585	−	2.64891i	0.401254	−	0.107516i	0.453802	+	0.891103i	$0.350067\pi$
$608$	18.6671	−	18.6671i	0.757052	−	0.757052i
$609$	0.862987	−	15.7399i	0.0349700	−	0.637811i
$610$		0			0
$611$	19.2416	−	33.3274i	0.778432	−	1.34828i
$612$	−5.32317	+	19.8663i	−0.215176	+	0.803049i
$613$	−4.80405	+	17.9289i	−0.194034	+	0.724143i	0.798481	+	0.602020i	$0.205637\pi$
$613$	−4.80405	+	17.9289i	−0.194034	+	0.724143i	−0.992515	+	0.122124i	$0.961030\pi$
$614$	−15.6403	+	27.0899i	−0.631193	+	1.09326i
$615$		0			0
$616$	−4.35246	+	79.3836i	−0.175365	+	3.19846i
$617$	20.7002	−	20.7002i	0.833358	−	0.833358i	−0.154616	−	0.987975i	$-0.549414\pi$
$617$	20.7002	−	20.7002i	0.833358	−	0.833358i	0.987975	+	0.154616i	$0.0494141\pi$
$618$	24.8307	−	6.65336i	0.998837	−	0.267638i
$619$	19.4680	+	33.7196i	0.782485	+	1.35530i	0.930490	+	0.366317i	$0.119381\pi$
$619$	19.4680	+	33.7196i	0.782485	+	1.35530i	−0.148005	+	0.988987i	$0.547285\pi$
$620$		0			0
$621$	−0.662763	−	0.382647i	−0.0265958	−	0.0153551i
$622$	−33.2515	−	33.2515i	−1.33327	−	1.33327i
$623$	−2.93869	+	8.97063i	−0.117736	+	0.359401i
$624$			75.7482i			3.03236i
$625$		0			0
$626$	9.76083	−	5.63542i	0.390121	−	0.225237i
$627$	4.72426	+	1.26586i	0.188669	+	0.0505537i
$628$	−24.3212	−	90.7680i	−0.970522	−	3.62204i
$629$	4.89092			0.195014
$630$		0			0
$631$	−32.0468			−1.27576			−0.637882	−	0.770134i	$-0.720189\pi$
$631$	−32.0468			−1.27576			−0.637882	+	0.770134i	$0.720189\pi$
$632$	17.9982	+	67.1701i	0.715929	+	2.67188i
$633$	3.37905	+	0.905413i	0.134305	+	0.0359869i
$634$	−54.4739	+	31.4505i	−2.16344	+	1.24906i
$635$		0			0
$636$		−	60.0985i		−	2.38306i
$637$	−14.4137	+	37.0139i	−0.571090	+	1.46654i
$638$	−38.5546	−	38.5546i	−1.52639	−	1.52639i
$639$	−5.83688	−	3.36993i	−0.230904	−	0.133312i
$640$		0			0
$641$	20.5881	+	35.6597i	0.813182	+	1.40847i	0.910626	+	0.413231i	$0.135600\pi$
$641$	20.5881	+	35.6597i	0.813182	+	1.40847i	−0.0974447	+	0.995241i	$0.531067\pi$
$642$	−7.03539	+	1.88513i	−0.277665	+	0.0744000i
$643$	−6.68412	+	6.68412i	−0.263596	+	0.263596i	−0.826513	−	0.562917i	$-0.809679\pi$
$643$	−6.68412	+	6.68412i	−0.263596	+	0.263596i	0.562917	+	0.826513i	$0.309679\pi$
$644$	−5.84820	+	8.95804i	−0.230452	+	0.352996i
$645$		0			0
$646$	7.57640	−	13.1227i	0.298090	−	0.516306i
$647$	−7.19743	+	26.8612i	−0.282960	+	1.05602i	0.667357	+	0.744738i	$0.267426\pi$
$647$	−7.19743	+	26.8612i	−0.282960	+	1.05602i	−0.950317	+	0.311284i	$0.899241\pi$
$648$	2.29358	−	8.55976i	0.0901004	−	0.336259i
$649$	−10.9401	+	18.9488i	−0.429436	+	0.743804i
$650$		0			0
$651$	−8.65174	+	4.38201i	−0.339088	+	0.171745i
$652$	8.61289	−	8.61289i	0.337307	−	0.337307i
$653$	42.0596	−	11.2698i	1.64592	−	0.441023i	0.687453	−	0.726229i	$-0.258729\pi$
$653$	42.0596	−	11.2698i	1.64592	−	0.441023i	0.958466	+	0.285206i	$0.0920621\pi$
$654$	10.1229	+	17.5334i	0.395837	+	0.685609i
$655$		0			0
$656$	−12.1961	−	7.04144i	−0.476179	−	0.274922i
$657$	3.50586	+	3.50586i	0.136777	+	0.136777i
$658$	32.3155	+	36.0647i	1.25979	+	1.40595i
$659$			36.8357i			1.43491i	0.696603	+	0.717457i	$0.254694\pi$
$659$			36.8357i			1.43491i	−0.696603	+	0.717457i	$0.745306\pi$
$660$		0			0
$661$	6.22921	−	3.59644i	0.242288	−	0.139885i	−0.373940	−	0.927453i	$-0.621993\pi$
$661$	6.22921	−	3.59644i	0.242288	−	0.139885i	0.616228	+	0.787568i	$0.288660\pi$
$662$	−15.9911	−	4.28480i	−0.621512	−	0.166534i
$663$	5.71700	+	21.3361i	0.222030	+	0.828627i
$664$	−18.6746			−0.724717
$665$		0			0
$666$	−3.39091			−0.131395
$667$	−1.18012	−	4.40428i	−0.0456946	−	0.170534i
$668$	19.8663	+	5.32317i	0.768651	+	0.205959i
$669$	19.7296	−	11.3909i	0.762792	−	0.440398i
$670$		0			0
$671$			42.7780i			1.65143i
$672$	−46.0184	−	15.0752i	−1.77520	−	0.581537i
$673$	14.1515	+	14.1515i	0.545500	+	0.545500i	0.925136	−	0.379636i	$-0.123951\pi$
$673$	14.1515	+	14.1515i	0.545500	+	0.545500i	−0.379636	+	0.925136i	$0.623951\pi$
$674$	34.6452	+	20.0024i	1.33448	+	0.770465i
$675$		0			0
$676$	50.7213	+	87.8519i	1.95082	+	3.37892i
$677$	14.7290	−	3.94663i	0.566083	−	0.151681i	0.0355835	−	0.999367i	$-0.488671\pi$
$677$	14.7290	−	3.94663i	0.566083	−	0.151681i	0.530500	+	0.847685i	$0.322004\pi$
$678$	5.50505	−	5.50505i	0.211420	−	0.211420i
$679$	4.28602	+	2.79810i	0.164482	+	0.107381i
$680$		0			0
$681$	4.83548	−	8.37530i	0.185296	−	0.320942i
$682$	−8.68211	+	32.4021i	−0.332455	+	1.24074i
$683$	8.77573	−	32.7515i	0.335794	−	1.25320i	−0.567212	−	0.823572i	$-0.691978\pi$
$683$	8.77573	−	32.7515i	0.335794	−	1.25320i	0.903006	−	0.429628i	$-0.141355\pi$
$684$	−3.81041	+	6.59982i	−0.145695	+	0.252351i
$685$		0			0
$686$	−38.6150	−	31.7355i	−1.47433	−	1.21167i
$687$	16.2066	−	16.2066i	0.618320	−	0.618320i
$688$	122.994	−	32.9561i	4.68910	−	1.25644i
$689$	−32.2725	−	55.8975i	−1.22948	−	2.12953i
$690$		0			0
$691$	−24.7032	−	14.2624i	−0.939752	−	0.542566i	−0.0498697	−	0.998756i	$-0.515881\pi$
$691$	−24.7032	−	14.2624i	−0.939752	−	0.542566i	−0.889883	+	0.456189i	$0.849214\pi$
$692$	47.4399	+	47.4399i	1.80339	+	1.80339i
$693$	−1.84409	−	8.77992i	−0.0700514	−	0.333522i
$694$			31.7014i			1.20337i
$695$		0			0
$696$	45.7248	−	26.3992i	1.73319	−	1.00066i
$697$	−3.96675	−	1.06289i	−0.150251	−	0.0402598i
$698$	8.60962	+	32.1315i	0.325879	+	1.21620i
$699$	−3.06117			−0.115784
$700$		0			0
$701$	−2.52517			−0.0953745			−0.0476873	−	0.998862i	$-0.515185\pi$
$701$	−2.52517			−0.0953745			−0.0476873	+	0.998862i	$0.515185\pi$
$702$	−3.96364	−	14.7925i	−0.149598	−	0.558307i
$703$	1.75050	+	0.469045i	0.0660213	+	0.0176904i
$704$	−66.6549	+	38.4832i	−2.51215	+	1.45039i
$705$		0			0
$706$			17.6602i			0.664652i
$707$	−38.9374	+	34.8896i	−1.46439	+	1.31216i
$708$	−24.1072	−	24.1072i	−0.906004	−	0.906004i
$709$	−8.83619	−	5.10158i	−0.331850	−	0.191594i	0.324812	−	0.945779i	$-0.394699\pi$
$709$	−8.83619	−	5.10158i	−0.331850	−	0.191594i	−0.656662	+	0.754185i	$0.728032\pi$
$710$		0			0
$711$	−3.92360	−	6.79587i	−0.147146	−	0.254865i
$712$	−30.5401	+	8.18321i	−1.14454	+	0.306679i
$713$	−1.98360	+	1.98360i	−0.0742864	+	0.0742864i
$714$	−27.7534	−	1.52167i	−1.03864	−	0.0569469i
$715$		0			0
$716$	65.2465	−	113.010i	2.43838	−	4.22339i
$717$	1.49554	−	5.58141i	0.0558518	−	0.208442i
$718$	12.5437	−	46.8139i	0.468128	−	1.74708i
$719$	15.2105	−	26.3454i	0.567258	−	0.982519i	−0.429578	−	0.903030i	$-0.641338\pi$
$719$	15.2105	−	26.3454i	0.567258	−	0.982519i	0.996836	−	0.0794893i	$-0.0253290\pi$
$720$		0			0
$721$	11.3869	+	22.4820i	0.424070	+	0.837274i
$722$	−32.2884	+	32.2884i	−1.20165	+	1.20165i
$723$	22.0534	−	5.90919i	0.820175	−	0.219765i
$724$	−55.7398	−	96.5442i	−2.07155	−	3.58804i
$725$		0			0
$726$	−1.16452	−	0.672335i	−0.0432193	−	0.0249527i
$727$	−15.0688	−	15.0688i	−0.558871	−	0.558871i	0.370115	−	0.928986i	$-0.379318\pi$
$727$	−15.0688	−	15.0688i	−0.558871	−	0.558871i	−0.928986	+	0.370115i	$0.879318\pi$
$728$	−130.202	+	27.3471i	−4.82562	+	1.01355i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	32.1566	−	18.5656i	1.18936	−	0.686675i
$732$	−64.3837	−	17.2516i	−2.37969	−	0.637636i
$733$	−11.7423	−	43.8230i	−0.433713	−	1.61864i	−0.744128	−	0.668037i	$-0.767135\pi$
$733$	−11.7423	−	43.8230i	−0.433713	−	1.61864i	0.310416	−	0.950601i	$-0.399532\pi$
$734$	17.4432			0.643841
$735$		0			0
$736$	−14.0070			−0.516306
$737$	0.494834	+	1.84674i	0.0182274	+	0.0680257i
$738$	2.75018	+	0.736908i	0.101235	+	0.0271259i
$739$	31.7277	−	18.3180i	1.16712	−	0.673839i	0.214123	−	0.976807i	$-0.431311\pi$
$739$	31.7277	−	18.3180i	1.16712	−	0.673839i	0.953001	+	0.302968i	$0.0979775\pi$
$740$		0			0
$741$			8.18465i			0.300671i
$742$	79.4847	−	16.6946i	2.91797	−	0.612878i
$743$	−4.92766	−	4.92766i	−0.180778	−	0.180778i	0.610917	−	0.791695i	$-0.290801\pi$
$743$	−4.92766	−	4.92766i	−0.180778	−	0.180778i	−0.791695	+	0.610917i	$0.790801\pi$
$744$	−28.1313	−	16.2416i	−1.03134	−	0.595446i
$745$		0			0
$746$	−29.8951	−	51.7798i	−1.09454	−	1.89579i
$747$	2.03553	−	0.545420i	0.0744763	−	0.0199559i
$748$	−49.3145	+	49.3145i	−1.80312	+	1.80312i
$749$	−3.22630	−	6.36993i	−0.117886	−	0.232752i
$750$		0			0
$751$	−19.1745	+	33.2112i	−0.699686	+	1.21189i	0.268889	+	0.963171i	$0.413344\pi$
$751$	−19.1745	+	33.2112i	−0.699686	+	1.21189i	−0.968575	+	0.248721i	$0.919990\pi$
$752$	−23.4309	+	87.4453i	−0.854437	+	3.18880i
$753$	3.32130	−	12.3953i	0.121035	−	0.451708i
$754$	45.6217	−	79.0190i	1.66144	−	2.87770i
$755$		0			0
$756$	13.9580	+	0.765293i	0.507649	+	0.0278334i
$757$	3.24686	−	3.24686i	0.118009	−	0.118009i	−0.645636	−	0.763645i	$-0.723408\pi$
$757$	3.24686	−	3.24686i	0.118009	−	0.118009i	0.763645	+	0.645636i	$0.223408\pi$
$758$	−11.2149	+	3.00503i	−0.407345	+	0.109148i
$759$	−1.29752	−	2.24737i	−0.0470969	−	0.0815743i
$760$		0			0
$761$	−17.0864	−	9.86481i	−0.619380	−	0.357599i	0.157248	−	0.987559i	$-0.449738\pi$
$761$	−17.0864	−	9.86481i	−0.619380	−	0.357599i	−0.776628	+	0.629960i	$0.783071\pi$
$762$	15.0663	+	15.0663i	0.545795	+	0.545795i
$763$	−14.7818	+	13.2451i	−0.535136	+	0.479506i
$764$		−	9.43287i		−	0.341269i
$765$		0			0
$766$	−59.5521	+	34.3824i	−2.15170	+	1.24229i
$767$	−35.3675	−	9.47668i	−1.27705	−	0.342183i
$768$	−5.46995	−	20.4141i	−0.197380	−	0.736632i
$769$	39.4021			1.42088			0.710439	−	0.703759i	$-0.248497\pi$
$769$	39.4021			1.42088			0.710439	+	0.703759i	$0.248497\pi$
$770$		0			0
$771$	24.2381			0.872914
$772$	21.2176	+	79.1853i	0.763640	+	2.84994i
$773$	8.04523	+	2.15571i	0.289367	+	0.0775356i	0.400583	−	0.916261i	$-0.368808\pi$
$773$	8.04523	+	2.15571i	0.289367	+	0.0775356i	−0.111216	+	0.993796i	$0.535474\pi$
$774$	−22.2944	+	12.8717i	−0.801356	+	0.462663i
$775$		0			0
$776$			17.1441i			0.615436i
$777$	−0.683300	−	3.25326i	−0.0245132	−	0.116710i
$778$	32.6180	+	32.6180i	1.16941	+	1.16941i
$779$	−1.31780	−	0.760833i	−0.0472151	−	0.0272597i
$780$		0			0
$781$	−11.4271	−	19.7923i	−0.408894	−	0.708225i
$782$	−7.76587	+	2.08086i	−0.277707	+	0.0744114i
$783$	−4.21297	+	4.21297i	−0.150559	+	0.150559i
$784$	10.2159	−	92.8825i	0.364852	−	3.31723i
$785$		0			0
$786$	17.4143	−	30.1625i	0.621148	−	1.07586i
$787$	2.81226	−	10.4955i	0.100246	−	0.374124i	−0.897516	−	0.440981i	$-0.854631\pi$
$787$	2.81226	−	10.4955i	0.100246	−	0.374124i	0.997763	+	0.0668573i	$0.0212972\pi$
$788$	−22.6391	+	84.4901i	−0.806483	+	3.00984i
$789$	4.90646	−	8.49825i	0.174675	−	0.302546i
$790$		0			0
$791$	6.39091	+	4.17227i	0.227234	+	0.148349i
$792$	21.2480	−	21.2480i	0.755016	−	0.755016i
$793$	−69.1471	+	18.5279i	−2.45549	+	0.657946i
$794$	18.2509	+	31.6115i	0.647701	+	1.12185i
$795$		0			0
$796$	−44.5252	−	25.7066i	−1.57815	−	0.911147i
$797$	17.6324	+	17.6324i	0.624572	+	0.624572i	0.946697	−	0.322125i	$-0.104397\pi$
$797$	17.6324	+	17.6324i	0.624572	+	0.624572i	−0.322125	+	0.946697i	$0.604397\pi$
$798$	−9.78723	−	3.20620i	−0.346464	−	0.113498i
$799$			26.3993i			0.933940i
$800$		0			0
$801$	3.08987	−	1.78394i	0.109175	−	0.0630323i
$802$	−70.4979	−	18.8898i	−2.48937	−	0.667024i
$803$	4.35133	+	16.2394i	0.153555	+	0.573076i
$804$	−2.97903			−0.105062
$805$		0			0
$806$	−56.1356			−1.97729
$807$	5.68426	+	21.2140i	0.200095	+	0.746767i
$808$	−169.147	−	45.3228i	−5.95057	−	1.59445i
$809$	−11.2614	+	6.50175i	−0.395929	+	0.228590i	−0.684726	−	0.728801i	$-0.740078\pi$
$809$	−11.2614	+	6.50175i	−0.395929	+	0.228590i	0.288797	+	0.957390i	$0.406745\pi$
$810$		0			0
$811$		−	25.6972i		−	0.902349i	−0.892436	−	0.451175i	$-0.851005\pi$
$811$		−	25.6972i		−	0.902349i	0.892436	−	0.451175i	$-0.148995\pi$
$812$	55.5807	+	62.0290i	1.95050	+	2.17679i
$813$	−17.9211	−	17.9211i	−0.628520	−	0.628520i
$814$	−9.95777	−	5.74912i	−0.349020	−	0.201507i
$815$		0			0
$816$	−25.9815	−	45.0012i	−0.909533	−	1.57536i
$817$	13.2896	−	3.56093i	0.464944	−	0.124581i
$818$	−4.78387	+	4.78387i	−0.167264	+	0.167264i
$819$	13.3933	−	6.78357i	0.468000	−	0.237037i
$820$		0			0
$821$	18.2860	−	31.6723i	0.638186	−	1.10537i	−0.347644	−	0.937626i	$-0.613018\pi$
$821$	18.2860	−	31.6723i	0.638186	−	1.10537i	0.985831	−	0.167744i	$-0.0536483\pi$
$822$	−1.48043	+	5.52504i	−0.0516359	+	0.192708i
$823$	11.3424	−	42.3303i	0.395370	−	1.47554i	−0.425779	−	0.904827i	$-0.640000\pi$
$823$	11.3424	−	42.3303i	0.395370	−	1.47554i	0.821149	−	0.570713i	$-0.193333\pi$
$824$	−42.2047	+	73.1007i	−1.47027	+	2.54658i
$825$		0			0
$826$	25.1869	−	38.5802i	0.876363	−	1.34238i
$827$	17.7382	−	17.7382i	0.616819	−	0.616819i	−0.327895	−	0.944714i	$-0.606339\pi$
$827$	17.7382	−	17.7382i	0.616819	−	0.616819i	0.944714	+	0.327895i	$0.106339\pi$
$828$	3.90570	−	1.04653i	0.135732	−	0.0363694i
$829$	14.9866	+	25.9575i	0.520506	+	0.901543i	0.999716	+	0.0238423i	$0.00758997\pi$
$829$	14.9866	+	25.9575i	0.520506	+	0.901543i	−0.479210	+	0.877700i	$0.659077\pi$
$830$		0			0
$831$	−12.1115	−	6.99260i	−0.420144	−	0.242571i
$832$	−91.0744	−	91.0744i	−3.15744	−	3.15744i
$833$	−4.13267	−	26.9334i	−0.143189	−	0.933187i
$834$			2.88915i			0.100043i
$835$		0			0
$836$	−22.3794	+	12.9207i	−0.774007	+	0.446873i
$837$	3.54066	+	0.948718i	0.122383	+	0.0327925i
$838$	−14.6980	−	54.8538i	−0.507735	−	1.89489i
$839$	14.5585			0.502615			0.251308	−	0.967907i	$-0.419139\pi$
$839$	14.5585			0.502615			0.251308	+	0.967907i	$0.419139\pi$
$840$		0			0
$841$	−6.49825			−0.224077
$842$	−12.6163	−	47.0846i	−0.434785	−	1.62264i
$843$	−17.3056	−	4.63702i	−0.596037	−	0.159708i
$844$	−16.0069	+	9.24161i	−0.550981	+	0.318109i
$845$		0			0
$846$		−	18.3028i		−	0.629264i
$847$	0.410381	−	1.25273i	0.0141009	−	0.0430442i
$848$	107.366	+	107.366i	3.68698	+	3.68698i
$849$	16.3455	+	9.43706i	0.560975	+	0.323879i
$850$		0			0
$851$	−0.480775	−	0.832726i	−0.0164807	−	0.0285455i
$852$	34.3971	−	9.21667i	1.17842	−	0.315758i
$853$	26.8710	−	26.8710i	0.920046	−	0.920046i	−0.0769857	−	0.997032i	$-0.524530\pi$
$853$	26.8710	−	26.8710i	0.920046	−	0.920046i	0.997032	+	0.0769857i	$0.0245296\pi$
$854$	4.93148	−	89.9444i	0.168752	−	3.07783i
$855$		0			0
$856$	11.9580	−	20.7119i	0.408717	−	0.707919i
$857$	4.93665	−	18.4238i	0.168633	−	0.629347i	−0.828916	−	0.559373i	$-0.811042\pi$
$857$	4.93665	−	18.4238i	0.168633	−	0.629347i	0.997549	−	0.0699734i	$-0.0222914\pi$
$858$	13.4403	−	50.1600i	0.458845	−	1.71243i
$859$	−27.1174	+	46.9687i	−0.925233	+	1.60255i	−0.134047	+	0.990975i	$0.542797\pi$
$859$	−27.1174	+	46.9687i	−0.925233	+	1.60255i	−0.791186	+	0.611576i	$0.790536\pi$
$860$		0			0
$861$	−0.152808	+	2.78703i	−0.00520767	+	0.0949818i
$862$	−24.6550	+	24.6550i	−0.839754	+	0.839754i
$863$	30.5038	−	8.17346i	1.03836	−	0.278228i	0.300927	−	0.953647i	$-0.402704\pi$
$863$	30.5038	−	8.17346i	1.03836	−	0.278228i	0.737434	+	0.675419i	$0.236037\pi$
$864$	9.15141	+	15.8507i	0.311337	+	0.539252i
$865$		0			0
$866$	73.3328	+	42.3387i	2.49195	+	1.43873i
$867$	1.30616	+	1.30616i	0.0443596	+	0.0443596i
$868$	15.9519	−	48.6947i	0.541443	−	1.65281i
$869$		−	26.6091i		−	0.902652i
$870$		0			0
$871$	−2.77079	+	1.59972i	−0.0938846	+	0.0542043i
$872$	−64.2132	−	17.2059i	−2.17453	−	0.582665i
$873$	−0.500717	−	1.86870i	−0.0169467	−	0.0632459i
$874$	−2.97903			−0.100767
$875$		0			0
$876$	−26.1961			−0.885086
$877$	−8.62823	−	32.2010i	−0.291355	−	1.08735i	−0.944070	−	0.329746i	$-0.893037\pi$
$877$	−8.62823	−	32.2010i	−0.291355	−	1.08735i	0.652715	−	0.757604i	$-0.273630\pi$
$878$	−23.8563	−	6.39229i	−0.805112	−	0.215729i
$879$	−15.5158	+	8.95804i	−0.523334	+	0.302147i
$880$		0			0
$881$		−	41.6003i		−	1.40155i	−0.713382	−	0.700775i	$-0.752838\pi$
$881$		−	41.6003i		−	1.40155i	0.713382	−	0.700775i	$-0.247162\pi$
$882$	2.86521	+	18.6731i	0.0964766	+	0.628757i
$883$	15.0375	+	15.0375i	0.506053	+	0.506053i	0.913313	−	0.407259i	$-0.133515\pi$
$883$	15.0375	+	15.0375i	0.506053	+	0.506053i	−0.407259	+	0.913313i	$0.633515\pi$
$884$	−101.072	−	58.3538i	−3.39941	−	1.96265i
$885$		0			0
$886$	−37.4377	−	64.8441i	−1.25775	−	2.17848i
$887$	−12.7904	+	3.42718i	−0.429460	+	0.115073i	−0.467073	−	0.884219i	$-0.654691\pi$
$887$	−12.7904	+	3.42718i	−0.429460	+	0.115073i	0.0376127	+	0.999292i	$0.488025\pi$
$888$	7.87312	−	7.87312i	0.264204	−	0.264204i
$889$	−11.4187	+	17.4907i	−0.382972	+	0.586620i
$890$		0			0
$891$	−1.69545	+	2.93661i	−0.0567998	+	0.0983802i
$892$	−31.1539	+	116.268i	−1.04311	+	3.89293i
$893$	−2.53172	+	9.44853i	−0.0847209	+	0.316183i
$894$	11.5605	−	20.0234i	0.386642	−	0.669683i
$895$		0			0
$896$	58.1846	−	29.4699i	1.94381	−	0.984520i
$897$	3.07071	−	3.07071i	0.102528	−	0.102528i
$898$	73.9106	−	19.8043i	2.46643	−	0.660877i
$899$	10.9198	+	18.9136i	0.364196	+	0.630805i
$900$		0			0
$901$	38.3454	+	22.1387i	1.27747	+	0.737549i
$902$	6.82681	+	6.82681i	0.227308	+	0.227308i
$903$	−16.8417	−	18.7956i	−0.560457	−	0.625480i
$904$			25.5636i			0.850234i
$905$		0			0
$906$	−36.0269	+	20.8002i	−1.19691	+	0.691039i
$907$	47.5472	+	12.7402i	1.57878	+	0.423033i	0.938548	−	0.345149i	$-0.112171\pi$
$907$	47.5472	+	12.7402i	1.57878	+	0.423033i	0.640232	+	0.768181i	$0.278838\pi$
$908$	13.2249	+	49.3561i	0.438885	+	1.63794i
$909$	19.7607			0.655422
$910$		0			0
$911$	55.6594			1.84408			0.922040	−	0.387095i	$-0.126521\pi$
$911$	55.6594			1.84408			0.922040	+	0.387095i	$0.126521\pi$
$912$	−4.98331	−	18.5980i	−0.165014	−	0.615840i
$913$	6.90230	+	1.84947i	0.228433	+	0.0612084i
$914$	21.6900	−	12.5227i	0.717442	−	0.414215i
$915$		0			0
$916$			121.097i			4.00116i
$917$	32.4473	+	10.6294i	1.07150	+	0.351014i
$918$	7.42854	+	7.42854i	0.245178	+	0.245178i
$919$	−12.5459	−	7.24336i	−0.413850	−	0.238936i	0.278593	−	0.960409i	$-0.410132\pi$
$919$	−12.5459	−	7.24336i	−0.413850	−	0.238936i	−0.692443	+	0.721473i	$0.743465\pi$
$920$		0			0
$921$	5.79528	+	10.0377i	0.190961	+	0.330754i
$922$	35.3911	−	9.48301i	1.16554	−	0.312306i
$923$	27.0434	−	27.0434i	0.890144	−	0.890144i
$924$	39.6918	+	25.9126i	1.30576	+	0.852461i
$925$		0			0
$926$	−39.2440	+	67.9727i	−1.28964	+	2.23372i
$927$	2.46530	−	9.20061i	0.0809710	−	0.302188i
$928$	−28.2239	+	105.333i	−0.926496	+	3.45773i
$929$	−22.1906	+	38.4353i	−0.728051	+	1.26102i	0.229655	+	0.973272i	$0.426240\pi$
$929$	−22.1906	+	38.4353i	−0.728051	+	1.26102i	−0.957706	+	0.287749i	$0.907093\pi$
$930$		0			0
$931$	1.10383	−	10.0360i	0.0361766	−	0.328917i
$932$	11.4367	−	11.4367i	0.374621	−	0.374621i
$933$	−16.8306	+	4.50974i	−0.551008	+	0.147642i
$934$	−50.7612	−	87.9210i	−1.66096	−	2.87686i
$935$		0			0
$936$	43.5486	+	25.1428i	1.42343	+	0.821818i
$937$	13.2536	+	13.2536i	0.432975	+	0.432975i	0.889639	−	0.456664i	$-0.150956\pi$
$937$	13.2536	+	13.2536i	0.432975	+	0.432975i	−0.456664	+	0.889639i	$0.650956\pi$
$938$	−0.827535	−	3.93998i	−0.0270200	−	0.128645i
$939$		−	4.17623i		−	0.136286i
$940$		0			0
$941$	−47.9804	+	27.7015i	−1.56412	+	0.903043i	−0.567283	+	0.823523i	$0.692005\pi$
$941$	−47.9804	+	27.7015i	−1.56412	+	0.903043i	−0.996833	+	0.0795198i	$0.974661\pi$
$942$	−46.3636	−	12.4231i	−1.51061	−	0.404766i
$943$	0.208963	+	0.779859i	0.00680476	+	0.0253957i
$944$	86.1354			2.80347
$945$		0			0
$946$	−87.2933			−2.83815
$947$	13.6548	+	50.9602i	0.443720	+	1.65598i	0.719294	+	0.694705i	$0.244465\pi$
$947$	13.6548	+	50.9602i	0.443720	+	1.65598i	−0.275575	+	0.961280i	$0.588868\pi$
$948$	40.0484	+	10.7309i	1.30071	+	0.348525i
$949$	−24.3650	+	14.0671i	−0.790921	+	0.456638i
$950$		0			0
$951$			23.3070i			0.755780i
$952$	67.9717	−	60.9056i	2.20298	−	1.97396i
$953$	8.29260	+	8.29260i	0.268624	+	0.268624i	0.828545	−	0.559922i	$-0.189169\pi$
$953$	8.29260	+	8.29260i	0.268624	+	0.268624i	−0.559922	+	0.828545i	$0.689169\pi$
$954$	−26.5852	−	15.3489i	−0.860726	−	0.496940i
$955$		0			0
$956$	15.2650	+	26.4398i	0.493706	+	0.855124i
$957$	−19.5148	+	5.22896i	−0.630822	+	0.169028i
$958$	43.3540	−	43.3540i	1.40071	−	1.40071i
$959$	−5.59908	−	0.306987i	−0.180804	−	0.00991313i
$960$		0			0
$961$	−8.78181	+	15.2105i	−0.283284	+	0.490663i
$962$	4.98009	−	18.5860i	0.160565	−	0.599236i
$963$	−0.698503	+	2.60685i	−0.0225089	+	0.0840045i
$964$	−60.3155	+	104.470i	−1.94263	+	3.36474i
$965$		0			0
$966$	2.46906	+	4.87486i	0.0794409	+	0.156846i
$967$	35.6264	−	35.6264i	1.14567	−	1.14567i	0.158271	−	0.987396i	$-0.449408\pi$
$967$	35.6264	−	35.6264i	1.14567	−	1.14567i	0.987396	−	0.158271i	$-0.0505919\pi$
$968$	4.26486	−	1.14277i	0.137078	−	0.0367299i
$969$	−2.80731	−	4.86241i	−0.0901839	−	0.156203i
$970$		0			0
$971$	4.01991	+	2.32090i	0.129005	+	0.0744811i	0.563114	−	0.826379i	$-0.309603\pi$
$971$	4.01991	+	2.32090i	0.129005	+	0.0744811i	−0.434109	+	0.900861i	$0.642937\pi$
$972$	−3.73605	−	3.73605i	−0.119834	−	0.119834i
$973$	−2.77187	+	0.582191i	−0.0888621	+	0.0186642i
$974$			83.1790i			2.66523i
$975$		0			0
$976$	145.842	−	84.2019i	4.66829	−	2.69524i
$977$	−36.2863	−	9.72288i	−1.16090	−	0.311062i	−0.373575	−	0.927600i	$-0.621868\pi$
$977$	−36.2863	−	9.72288i	−1.16090	−	0.311062i	−0.787325	+	0.616538i	$0.788535\pi$
$978$	−1.61029	−	6.00970i	−0.0514915	−	0.192169i
$979$	12.0983			0.386664
$980$		0			0
$981$	7.50175			0.239513
$982$	−23.3906	−	87.2948i	−0.746423	−	2.78569i
$983$	−42.6564	−	11.4298i	−1.36053	−	0.364553i	−0.496518	−	0.868026i	$-0.665389\pi$
$983$	−42.6564	−	11.4298i	−1.36053	−	0.364553i	−0.864011	+	0.503473i	$0.832055\pi$
$984$	−8.09643	+	4.67447i	−0.258105	+	0.149017i
$985$		0			0
$986$			62.5925i			1.99335i
$987$	17.5598	−	3.68819i	0.558936	−	0.117396i
$988$	−30.5782	−	30.5782i	−0.972823	−	0.972823i
$989$	−6.32196	−	3.64998i	−0.201027	−	0.116063i
$990$		0			0
$991$	−12.8781	−	22.3056i	−0.409087	−	0.708560i	0.585701	−	0.810528i	$-0.300819\pi$
$991$	−12.8781	−	22.3056i	−0.409087	−	0.708560i	−0.994788	+	0.101968i	$0.967486\pi$
$992$	64.8041	−	17.3642i	2.05753	−	0.551314i
$993$	−4.33758	+	4.33758i	−0.137649	+	0.137649i
$994$	21.7448	+	42.9324i	0.689703	+	1.36173i
$995$		0			0
$996$	−5.56713	+	9.64256i	−0.176401	+	0.305536i
$997$	−10.8943	+	40.6580i	−0.345026	+	1.28765i	0.547557	+	0.836769i	$0.315558\pi$
$997$	−10.8943	+	40.6580i	−0.345026	+	1.28765i	−0.892582	+	0.450885i	$0.851109\pi$
$998$	1.30322	−	4.86368i	0.0412527	−	0.153957i
$999$	−0.628223	+	1.08811i	−0.0198761	+	0.0344264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.d.418.6	yes	24
5.2	odd	4	inner	525.2.bc.d.82.1	✓	24
5.3	odd	4	inner	525.2.bc.d.82.6	yes	24
5.4	even	2	inner	525.2.bc.d.418.1	yes	24
7.3	odd	6	inner	525.2.bc.d.493.1	yes	24
35.3	even	12	inner	525.2.bc.d.157.1	yes	24
35.17	even	12	inner	525.2.bc.d.157.6	yes	24
35.24	odd	6	inner	525.2.bc.d.493.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.d.82.1	✓	24	5.2	odd	4	inner
525.2.bc.d.82.6	yes	24	5.3	odd	4	inner
525.2.bc.d.157.1	yes	24	35.3	even	12	inner
525.2.bc.d.157.6	yes	24	35.17	even	12	inner
525.2.bc.d.418.1	yes	24	5.4	even	2	inner
525.2.bc.d.418.6	yes	24	1.1	even	1	trivial
525.2.bc.d.493.1	yes	24	7.3	odd	6	inner
525.2.bc.d.493.6	yes	24	35.24	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.698503 + 2.60685i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-4.57570 + 2.64178i) q^{4} +2.69881i q^{6} +(-2.58926 + 0.543835i) q^{7} +(-6.26618 - 6.26618i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.698503 + 2.60685i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-4.57570 + 2.64178i) q^{4} +2.69881i q^{6} +(-2.58926 + 0.543835i) q^{7} +(-6.26618 - 6.26618i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.69545 + 2.93661i) q^{11} +(-5.10353 + 1.36749i) q^{12} +(-4.01246 + 4.01246i) q^{13} +(-3.22630 - 6.36993i) q^{14} +(6.67447 - 11.5605i) q^{16} +(1.00749 - 3.76002i) q^{17} +(-0.698503 + 2.60685i) q^{18} +(0.721181 - 1.24912i) q^{19} +(-2.64178 - 0.144844i) q^{21} +(-6.47102 + 6.47102i) q^{22} +(-0.739216 + 0.198072i) q^{23} +(-4.43086 - 7.67447i) q^{24} +(-13.2626 - 7.65716i) q^{26} +(0.707107 + 0.707107i) q^{27} +(10.4110 - 9.32868i) q^{28} +5.95804i q^{29} +(3.17447 - 1.83278i) q^{31} +(17.6792 + 4.73712i) q^{32} +(0.877631 + 3.27536i) q^{33} +10.5055 q^{34} -5.28357 q^{36} +(0.325192 + 1.21363i) q^{37} +(3.76002 + 1.00749i) q^{38} +(-4.91424 + 2.83724i) q^{39} -1.05498i q^{41} +(-1.46771 - 6.98790i) q^{42} +(6.74494 + 6.74494i) q^{43} +(-15.5158 - 8.95804i) q^{44} +(-1.03269 - 1.78867i) q^{46} +(-6.55073 + 1.75526i) q^{47} +(9.43913 - 9.43913i) q^{48} +(6.40849 - 2.81626i) q^{49} +(1.94633 - 3.37114i) q^{51} +(7.75977 - 28.9599i) q^{52} +(-2.94397 + 10.9870i) q^{53} +(-1.34940 + 2.33724i) q^{54} +(19.6325 + 12.8170i) q^{56} +(1.01990 - 1.01990i) q^{57} +(-15.5317 + 4.16171i) q^{58} +(3.22630 + 5.58811i) q^{59} +(10.9254 + 6.30775i) q^{61} +(6.99517 + 6.99517i) q^{62} +(-2.51428 - 0.823652i) q^{63} +22.6979i q^{64} +(-7.92535 + 4.57570i) q^{66} +(0.544617 + 0.145930i) q^{67} +(5.32317 + 19.8663i) q^{68} -0.765293 q^{69} -6.73985 q^{71} +(-2.29358 - 8.55976i) q^{72} +(4.78910 + 1.28324i) q^{73} +(-2.93661 + 1.69545i) q^{74} +7.62082i q^{76} +(-5.98699 - 6.68159i) q^{77} +(-10.8289 - 10.8289i) q^{78} +(-6.79587 - 3.92360i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.75018 - 0.736908i) q^{82} +(1.49011 - 1.49011i) q^{83} +(12.4707 - 6.31626i) q^{84} +(-12.8717 + 22.2944i) q^{86} +(-1.54205 + 5.75503i) q^{87} +(7.77732 - 29.0254i) q^{88} +(1.78394 - 3.08987i) q^{89} +(8.20716 - 12.5714i) q^{91} +(2.85917 - 2.85917i) q^{92} +(3.54066 - 0.948718i) q^{93} +(-9.15141 - 15.8507i) q^{94} +(15.8507 + 9.15141i) q^{96} +(-1.36798 - 1.36798i) q^{97} +(11.8179 + 14.7388i) q^{98} +3.39091i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 24 q^{11} + 48 q^{16} - 24 q^{21} - 144 q^{26} - 36 q^{31} - 48 q^{36} + 48 q^{46} + 24 q^{51} + 168 q^{56} + 144 q^{61} - 72 q^{66} + 96 q^{71} + 12 q^{81} - 168 q^{86} + 12 q^{91} + 144 q^{96}+O(q^{100}) \) 24 * q + 24 * q^11 + 48 * q^16 - 24 * q^21 - 144 * q^26 - 36 * q^31 - 48 * q^36 + 48 * q^46 + 24 * q^51 + 168 * q^56 + 144 * q^61 - 72 * q^66 + 96 * q^71 + 12 * q^81 - 168 * q^86 + 12 * q^91 + 144 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more