LMFDB - Embedded newform 476.2.bh.a.457.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(9,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

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

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

chi := DirichletCharacter("476.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bh (of order $24$, degree $8$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.7
Character	$\chi$	$=$	476.457
Dual form			476.2.bh.a.25.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.175573 - 0.228811i) q^{3} +(-0.294259 + 2.23512i) q^{5} +(2.11926 - 1.58390i) q^{7} +(0.754929 + 2.81743i) q^{9} +O(q^{10})$	\(q+(0.175573 - 0.228811i) q^{3} +(-0.294259 + 2.23512i) q^{5} +(2.11926 - 1.58390i) q^{7} +(0.754929 + 2.81743i) q^{9} +(-1.46989 + 0.193514i) q^{11} +2.89472i q^{13} +(0.459756 + 0.459756i) q^{15} +(-4.12101 + 0.131452i) q^{17} +(5.92405 - 1.58735i) q^{19} +(0.00967227 - 0.762999i) q^{21} +(2.99330 + 3.90095i) q^{23} +(-0.0795433 - 0.0213136i) q^{25} +(1.57657 + 0.653037i) q^{27} +(-1.59262 + 0.659683i) q^{29} +(-3.20839 + 4.18125i) q^{31} +(-0.213794 + 0.370302i) q^{33} +(2.91658 + 5.20288i) q^{35} +(9.23084 + 1.21526i) q^{37} +(0.662342 + 0.508233i) q^{39} +(-0.589848 - 0.244323i) q^{41} +(0.605036 - 0.605036i) q^{43} +(-6.51944 + 0.858301i) q^{45} +(-5.56044 - 3.21032i) q^{47} +(1.98255 - 6.71338i) q^{49} +(-0.693460 + 0.966011i) q^{51} +(2.28753 - 8.53719i) q^{53} -3.34231i q^{55} +(0.676901 - 1.63418i) q^{57} +(3.99942 + 1.07164i) q^{59} +(-0.0229858 + 0.0176376i) q^{61} +(6.06241 + 4.77515i) q^{63} +(-6.47004 - 0.851796i) q^{65} +(2.73527 + 4.73763i) q^{67} +1.41812 q^{69} +(-4.93065 - 11.9036i) q^{71} +(-9.54095 - 7.32103i) q^{73} +(-0.0188424 + 0.0144583i) q^{75} +(-2.80857 + 2.73825i) q^{77} +(0.0620999 + 0.0809302i) q^{79} +(-7.15189 + 4.12915i) q^{81} +(2.69365 + 2.69365i) q^{83} +(0.918834 - 9.24963i) q^{85} +(-0.128677 + 0.480230i) q^{87} +(-13.6961 - 7.90745i) q^{89} +(4.58493 + 6.13466i) q^{91} +(0.393411 + 1.46823i) q^{93} +(1.80470 + 13.7081i) q^{95} +(-7.55146 + 3.12792i) q^{97} +(-1.65487 - 3.99521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{5}+O(q^{10}) $ 96 * q + 4 * q^5	$ 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) $ 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	0.175573	−	0.228811i	0.101367	−	0.132104i	−0.739915	−	0.672700i	$-0.765135\pi$
$3$	0.175573	−	0.228811i	0.101367	−	0.132104i	0.841282	+	0.540596i	$0.181801\pi$
$4$		0			0
$5$	−0.294259	+	2.23512i	−0.131597	+	0.999576i	0.790458	+	0.612516i	$0.209843\pi$
$5$	−0.294259	+	2.23512i	−0.131597	+	0.999576i	−0.922055	+	0.387060i	$0.873491\pi$
$6$		0			0
$7$	2.11926	−	1.58390i	0.801006	−	0.598656i
$7$	2.11926	−	1.58390i	0.801006	−	0.598656i
$8$		0			0
$9$	0.754929	+	2.81743i	0.251643	+	0.939144i
$10$		0			0
$11$	−1.46989	+	0.193514i	−0.443187	+	0.0583467i	−0.348818	−	0.937191i	$-0.613417\pi$
$11$	−1.46989	+	0.193514i	−0.443187	+	0.0583467i	−0.0943694	+	0.995537i	$0.530083\pi$
$12$		0			0
$13$			2.89472i			0.802850i	0.915892	+	0.401425i	$0.131485\pi$
$13$			2.89472i			0.802850i	−0.915892	+	0.401425i	$0.868515\pi$
$14$		0			0
$15$	0.459756	+	0.459756i	0.118708	+	0.118708i
$16$		0			0
$17$	−4.12101	+	0.131452i	−0.999492	+	0.0318818i
$17$	−4.12101	+	0.131452i	−0.999492	+	0.0318818i
$18$		0			0
$19$	5.92405	−	1.58735i	1.35907	−	0.364162i	0.495596	−	0.868553i	$-0.334950\pi$
$19$	5.92405	−	1.58735i	1.35907	−	0.364162i	0.863475	+	0.504391i	$0.168283\pi$
$20$		0			0
$21$	0.00967227	−	0.762999i	0.00211066	−	0.166500i
$22$		0			0
$23$	2.99330	+	3.90095i	0.624147	+	0.813404i	0.993251	−	0.115984i	$-0.0370020\pi$
$23$	2.99330	+	3.90095i	0.624147	+	0.813404i	−0.369104	+	0.929388i	$0.620335\pi$
$24$		0			0
$25$	−0.0795433	−	0.0213136i	−0.0159087	−	0.00426271i
$26$		0			0
$27$	1.57657	+	0.653037i	0.303411	+	0.125677i
$28$		0			0
$29$	−1.59262	+	0.659683i	−0.295741	+	0.122500i	−0.525621	−	0.850719i	$-0.676167\pi$
$29$	−1.59262	+	0.659683i	−0.295741	+	0.122500i	0.229879	+	0.973219i	$0.426167\pi$
$30$		0			0
$31$	−3.20839	+	4.18125i	−0.576243	+	0.750975i	−0.986991	−	0.160774i	$-0.948601\pi$
$31$	−3.20839	+	4.18125i	−0.576243	+	0.750975i	0.410748	+	0.911749i	$0.365268\pi$
$32$		0			0
$33$	−0.213794	+	0.370302i	−0.0372167	+	0.0644613i
$34$		0			0
$35$	2.91658	+	5.20288i	0.492993	+	0.879448i
$36$		0			0
$37$	9.23084	+	1.21526i	1.51754	+	0.199788i	0.842784	−	0.538252i	$-0.180915\pi$
$37$	9.23084	+	1.21526i	1.51754	+	0.199788i	0.674757	+	0.738040i	$0.264248\pi$
$38$		0			0
$39$	0.662342	+	0.508233i	0.106060	+	0.0813825i
$40$		0			0
$41$	−0.589848	−	0.244323i	−0.0921187	−	0.0381568i	0.336148	−	0.941809i	$-0.390876\pi$
$41$	−0.589848	−	0.244323i	−0.0921187	−	0.0381568i	−0.428267	+	0.903652i	$0.640876\pi$
$42$		0			0
$43$	0.605036	−	0.605036i	0.0922671	−	0.0922671i	−0.659467	−	0.751734i	$-0.729218\pi$
$43$	0.605036	−	0.605036i	0.0922671	−	0.0922671i	0.751734	+	0.659467i	$0.229218\pi$
$44$		0			0
$45$	−6.51944	+	0.858301i	−0.971861	+	0.127948i
$46$		0			0
$47$	−5.56044	−	3.21032i	−0.811074	−	0.468274i	0.0362550	−	0.999343i	$-0.488457\pi$
$47$	−5.56044	−	3.21032i	−0.811074	−	0.468274i	−0.847329	+	0.531069i	$0.821790\pi$
$48$		0			0
$49$	1.98255	−	6.71338i	0.283221	−	0.959055i
$50$		0			0
$51$	−0.693460	+	0.966011i	−0.0971038	+	0.135269i
$52$		0			0
$53$	2.28753	−	8.53719i	0.314217	−	1.17267i	−0.610499	−	0.792017i	$-0.709031\pi$
$53$	2.28753	−	8.53719i	0.314217	−	1.17267i	0.924716	−	0.380657i	$-0.124302\pi$
$54$		0			0
$55$		−	3.34231i		−	0.450678i
$56$		0			0
$57$	0.676901	−	1.63418i	0.0896577	−	0.216453i
$58$		0			0
$59$	3.99942	+	1.07164i	0.520680	+	0.139516i	0.509581	−	0.860423i	$-0.329800\pi$
$59$	3.99942	+	1.07164i	0.520680	+	0.139516i	0.0110986	+	0.999938i	$0.496467\pi$
$60$		0			0
$61$	−0.0229858	+	0.0176376i	−0.00294303	+	0.00225827i	−0.610232	−	0.792223i	$-0.708924\pi$
$61$	−0.0229858	+	0.0176376i	−0.00294303	+	0.00225827i	0.607289	+	0.794481i	$0.292257\pi$
$62$		0			0
$63$	6.06241	+	4.77515i	0.763792	+	0.601612i
$64$		0			0
$65$	−6.47004	−	0.851796i	−0.802509	−	0.105652i
$66$		0			0
$67$	2.73527	+	4.73763i	0.334167	+	0.578794i	0.983324	−	0.181860i	$-0.0582117\pi$
$67$	2.73527	+	4.73763i	0.334167	+	0.578794i	−0.649157	+	0.760654i	$0.724878\pi$
$68$		0			0
$69$	1.41812			0.170722
$70$		0			0
$71$	−4.93065	−	11.9036i	−0.585160	−	1.41270i	−0.888081	−	0.459686i	$-0.847962\pi$
$71$	−4.93065	−	11.9036i	−0.585160	−	1.41270i	0.302921	−	0.953016i	$-0.402038\pi$
$72$		0			0
$73$	−9.54095	−	7.32103i	−1.11668	−	0.856862i	−0.125864	−	0.992048i	$-0.540170\pi$
$73$	−9.54095	−	7.32103i	−1.11668	−	0.856862i	−0.990820	+	0.135186i	$0.956837\pi$
$74$		0			0
$75$	−0.0188424	+	0.0144583i	−0.00217574	+	0.00166950i
$76$		0			0
$77$	−2.80857	+	2.73825i	−0.320066	+	0.312053i
$78$		0			0
$79$	0.0620999	+	0.0809302i	0.00698679	+	0.00910536i	0.796834	−	0.604199i	$-0.206507\pi$
$79$	0.0620999	+	0.0809302i	0.00698679	+	0.00910536i	−0.789847	+	0.613304i	$0.789840\pi$
$80$		0			0
$81$	−7.15189	+	4.12915i	−0.794655	+	0.458794i
$82$		0			0
$83$	2.69365	+	2.69365i	0.295667	+	0.295667i	0.839314	−	0.543647i	$-0.182957\pi$
$83$	2.69365	+	2.69365i	0.295667	+	0.295667i	−0.543647	+	0.839314i	$0.682957\pi$
$84$		0			0
$85$	0.918834	−	9.24963i	0.0996615	−	1.00326i
$86$		0			0
$87$	−0.128677	+	0.480230i	−0.0137957	+	0.0514861i
$88$		0			0
$89$	−13.6961	−	7.90745i	−1.45178	−	0.838188i	−0.453201	−	0.891408i	$-0.649718\pi$
$89$	−13.6961	−	7.90745i	−1.45178	−	0.838188i	−0.998583	+	0.0532206i	$0.983051\pi$
$90$		0			0
$91$	4.58493	+	6.13466i	0.480631	+	0.643087i
$92$		0			0
$93$	0.393411	+	1.46823i	0.0407948	+	0.152248i
$94$		0			0
$95$	1.80470	+	13.7081i	0.185158	+	1.40642i
$96$		0			0
$97$	−7.55146	+	3.12792i	−0.766734	+	0.317592i	−0.731549	−	0.681789i	$-0.761202\pi$
$97$	−7.55146	+	3.12792i	−0.766734	+	0.317592i	−0.0351855	+	0.999381i	$0.511202\pi$
$98$		0			0
$99$	−1.65487	−	3.99521i	−0.166321	−	0.401534i
$100$		0			0
$101$	2.74664	+	4.75732i	0.273301	+	0.473371i	0.969705	−	0.244279i	$-0.0785511\pi$
$101$	2.74664	+	4.75732i	0.273301	+	0.473371i	−0.696404	+	0.717650i	$0.745218\pi$
$102$		0			0
$103$	1.84329	−	3.19267i	0.181625	−	0.314584i	−0.760809	−	0.648976i	$-0.775198\pi$
$103$	1.84329	−	3.19267i	0.181625	−	0.314584i	0.942434	+	0.334392i	$0.108531\pi$
$104$		0			0
$105$	1.70255	+	0.246138i	0.166152	+	0.0240206i
$106$		0			0
$107$	1.05374	−	8.00399i	0.101869	−	0.773775i	−0.861908	−	0.507065i	$-0.830730\pi$
$107$	1.05374	−	8.00399i	0.101869	−	0.773775i	0.963777	−	0.266709i	$-0.0859364\pi$
$108$		0			0
$109$	−1.46649	−	11.1391i	−0.140464	−	1.06693i	−0.905922	−	0.423445i	$-0.860821\pi$
$109$	−1.46649	−	11.1391i	−0.140464	−	1.06693i	0.765458	−	0.643486i	$-0.222513\pi$
$110$		0			0
$111$	1.89875	−	1.89875i	0.180221	−	0.180221i
$112$		0			0
$113$	3.96624	−	9.57536i	0.373113	−	0.900774i	−0.620106	−	0.784518i	$-0.712911\pi$
$113$	3.96624	−	9.57536i	0.373113	−	0.900774i	0.993219	−	0.116256i	$-0.0370894\pi$
$114$		0			0
$115$	−9.59990	+	5.54250i	−0.895195	+	0.516841i
$116$		0			0
$117$	−8.15566	+	2.18530i	−0.753991	+	0.202031i
$118$		0			0
$119$	−8.52530	+	6.80583i	−0.781513	+	0.623889i
$120$		0			0
$121$	−8.50207	+	2.27812i	−0.772915	+	0.207102i
$122$		0			0
$123$	−0.159465	+	0.0920672i	−0.0143785	+	0.00830142i
$124$		0			0
$125$	−4.24258	+	10.2425i	−0.379468	+	0.916116i
$126$		0			0
$127$	15.3171	−	15.3171i	1.35918	−	1.35918i	0.484241	−	0.874935i	$-0.339096\pi$
$127$	15.3171	−	15.3171i	1.35918	−	1.35918i	0.874935	−	0.484241i	$-0.160904\pi$
$128$		0			0
$129$	−0.0322110	−	0.244667i	−0.00283602	−	0.0215417i
$130$		0			0
$131$	0.912592	−	6.93182i	0.0797335	−	0.605636i	−0.904201	−	0.427107i	$-0.859533\pi$
$131$	0.912592	−	6.93182i	0.0797335	−	0.605636i	0.983935	−	0.178529i	$-0.0571339\pi$
$132$		0			0
$133$	10.0404	−	12.7471i	0.870616	−	1.10531i
$134$		0			0
$135$	−1.92354	+	3.33166i	−0.165552	+	0.286744i
$136$		0			0
$137$	2.58653	+	4.48001i	0.220982	+	0.382753i	0.955107	−	0.296263i	$-0.0957403\pi$
$137$	2.58653	+	4.48001i	0.220982	+	0.382753i	−0.734124	+	0.679015i	$0.762407\pi$
$138$		0			0
$139$	−5.32366	−	12.8524i	−0.451547	−	1.09013i	−0.971734	−	0.236078i	$-0.924138\pi$
$139$	−5.32366	−	12.8524i	−0.451547	−	1.09013i	0.520187	−	0.854052i	$-0.325862\pi$
$140$		0			0
$141$	−1.71082	+	0.708644i	−0.144077	+	0.0596786i
$142$		0			0
$143$	−0.560168	−	4.25490i	−0.0468436	−	0.355813i
$144$		0			0
$145$	−1.00583	−	3.75380i	−0.0835295	−	0.311737i
$146$		0			0
$147$	−1.18801	−	1.63232i	−0.0979857	−	0.134631i
$148$		0			0
$149$	8.57410	+	4.95026i	0.702418	+	0.405541i	0.808247	−	0.588843i	$-0.200416\pi$
$149$	8.57410	+	4.95026i	0.702418	+	0.405541i	−0.105829	+	0.994384i	$0.533750\pi$
$150$		0			0
$151$	2.01966	−	7.53748i	0.164358	−	0.613391i	−0.833764	−	0.552122i	$-0.813818\pi$
$151$	2.01966	−	7.53748i	0.164358	−	0.613391i	0.998121	−	0.0612696i	$-0.0195149\pi$
$152$		0			0
$153$	−3.48142	−	11.5114i	−0.281457	−	0.930644i
$154$		0			0
$155$	−8.40150	−	8.40150i	−0.674825	−	0.674825i
$156$		0			0
$157$	8.81564	−	5.08971i	0.703565	−	0.406203i	−0.105109	−	0.994461i	$-0.533519\pi$
$157$	8.81564	−	5.08971i	0.703565	−	0.406203i	0.808674	+	0.588257i	$0.200186\pi$
$158$		0			0
$159$	−1.55177	−	2.02231i	−0.123064	−	0.160380i
$160$		0			0
$161$	12.5223	+	3.52606i	0.986895	+	0.277892i
$162$		0			0
$163$	3.26506	−	2.50537i	0.255740	−	0.196236i	−0.472932	−	0.881099i	$-0.656805\pi$
$163$	3.26506	−	2.50537i	0.255740	−	0.196236i	0.728672	+	0.684863i	$0.240138\pi$
$164$		0			0
$165$	−0.764758	−	0.586820i	−0.0595363	−	0.0456838i
$166$		0			0
$167$	6.74056	+	16.2731i	0.521600	+	1.25925i	0.936909	+	0.349573i	$0.113673\pi$
$167$	6.74056	+	16.2731i	0.521600	+	1.25925i	−0.415309	+	0.909680i	$0.636327\pi$
$168$		0			0
$169$	4.62062			0.355433
$170$		0			0
$171$	8.94448	+	15.4923i	0.684001	+	1.18472i
$172$		0			0
$173$	−1.87215	−	0.246473i	−0.142337	−	0.0187390i	0.0590210	−	0.998257i	$-0.481202\pi$
$173$	−1.87215	−	0.246473i	−0.142337	−	0.0187390i	−0.201358	+	0.979518i	$0.564535\pi$
$174$		0			0
$175$	−0.202332	+	0.0808193i	−0.0152948	+	0.00610936i
$176$		0			0
$177$	0.947391	−	0.726959i	0.0712103	−	0.0546416i
$178$		0			0
$179$	−11.2959	−	3.02673i	−0.844295	−	0.226228i	−0.189355	−	0.981909i	$-0.560640\pi$
$179$	−11.2959	−	3.02673i	−0.844295	−	0.226228i	−0.654940	+	0.755681i	$0.727306\pi$
$180$		0			0
$181$	−6.15514	+	14.8598i	−0.457508	+	1.10452i	0.511895	+	0.859048i	$0.328943\pi$
$181$	−6.15514	+	14.8598i	−0.457508	+	1.10452i	−0.969403	+	0.245474i	$0.921057\pi$
$182$		0			0
$183$			0.00835610i			0.000617701i
$184$		0			0
$185$	−5.43252	+	20.2744i	−0.399407	+	1.49061i
$186$		0			0
$187$	6.03198	−	0.990693i	0.441102	−	0.0724467i
$188$		0			0
$189$	4.37551	−	1.11317i	0.318272	−	0.0809710i
$190$		0			0
$191$	20.9351	+	12.0869i	1.51481	+	0.874576i	0.999849	+	0.0173619i	$0.00552675\pi$
$191$	20.9351	+	12.0869i	1.51481	+	0.874576i	0.514960	+	0.857214i	$0.327807\pi$
$192$		0			0
$193$	−23.4169	+	3.08290i	−1.68559	+	0.221912i	−0.911539	−	0.411214i	$-0.865105\pi$
$193$	−23.4169	+	3.08290i	−1.68559	+	0.221912i	−0.774049	+	0.633126i	$0.781772\pi$
$194$		0			0
$195$	−1.33086	+	1.33086i	−0.0953050	+	0.0953050i
$196$		0			0
$197$	17.9852	+	7.44973i	1.28140	+	0.530771i	0.916410	−	0.400242i	$-0.131074\pi$
$197$	17.9852	+	7.44973i	1.28140	+	0.530771i	0.364986	+	0.931013i	$0.381074\pi$
$198$		0			0
$199$	−14.1358	−	10.8467i	−1.00206	−	0.768905i	−0.0290257	−	0.999579i	$-0.509240\pi$
$199$	−14.1358	−	10.8467i	−1.00206	−	0.768905i	−0.973031	+	0.230673i	$0.925907\pi$
$200$		0			0
$201$	1.56426	+	0.205939i	0.110335	+	0.0145258i
$202$		0			0
$203$	−2.33030	+	3.92058i	−0.163555	+	0.275171i
$204$		0			0
$205$	0.719659	−	1.24649i	0.0502632	−	0.0870584i
$206$		0			0
$207$	−8.73093	+	11.3784i	−0.606842	+	0.790851i
$208$		0			0
$209$	−8.40051	+	3.47961i	−0.581076	+	0.240689i
$210$		0			0
$211$	−6.28578	−	2.60365i	−0.432731	−	0.179243i	0.155676	−	0.987808i	$-0.450245\pi$
$211$	−6.28578	−	2.60365i	−0.432731	−	0.179243i	−0.588407	+	0.808565i	$0.700245\pi$
$212$		0			0
$213$	−3.58937	−	0.961769i	−0.245940	−	0.0658993i
$214$		0			0
$215$	1.17429	+	1.53037i	0.0800860	+	0.104370i
$216$		0			0
$217$	−0.176749	+	13.9429i	−0.0119985	+	0.946507i
$218$		0			0
$219$	−3.35026	+	0.897700i	−0.226390	+	0.0606610i
$220$		0			0
$221$	−0.380516	−	11.9291i	−0.0255963	−	0.802441i
$222$		0			0
$223$	12.8133	+	12.8133i	0.858041	+	0.858041i	0.991107	−	0.133066i	$-0.0424823\pi$
$223$	12.8133	+	12.8133i	0.858041	+	0.858041i	−0.133066	+	0.991107i	$0.542482\pi$
$224$		0			0
$225$		−	0.240198i		−	0.0160132i
$226$		0			0
$227$	−7.91595	+	1.04216i	−0.525400	+	0.0691703i	−0.388561	−	0.921423i	$-0.627028\pi$
$227$	−7.91595	+	1.04216i	−0.525400	+	0.0691703i	−0.136839	+	0.990593i	$0.543694\pi$
$228$		0			0
$229$	5.70770	+	21.3014i	0.377175	+	1.40764i	0.850141	+	0.526556i	$0.176517\pi$
$229$	5.70770	+	21.3014i	0.377175	+	1.40764i	−0.472965	+	0.881081i	$0.656816\pi$
$230$		0			0
$231$	0.133434	+	1.12339i	0.00877932	+	0.0739139i
$232$		0			0
$233$	0.613104	−	4.65699i	0.0401658	−	0.305090i	−0.959556	−	0.281517i	$-0.909163\pi$
$233$	0.613104	−	4.65699i	0.0401658	−	0.305090i	0.999722	−	0.0235728i	$-0.00750416\pi$
$234$		0			0
$235$	8.81166	−	11.4836i	0.574810	−	0.749106i
$236$		0			0
$237$	0.0294208			0.00191108
$238$		0			0
$239$	7.99588			0.517211			0.258605	−	0.965983i	$-0.416737\pi$
$239$	7.99588			0.517211			0.258605	+	0.965983i	$0.416737\pi$
$240$		0			0
$241$	6.25853	−	8.15627i	0.403147	−	0.525392i	−0.547025	−	0.837116i	$-0.684240\pi$
$241$	6.25853	−	8.15627i	0.403147	−	0.525392i	0.950173	+	0.311724i	$0.100907\pi$
$242$		0			0
$243$	−0.979101	+	7.43701i	−0.0628093	+	0.477084i
$244$		0			0
$245$	14.4218	+	6.40671i	0.921377	+	0.409310i
$246$		0			0
$247$	4.59491	+	17.1485i	0.292367	+	1.09113i
$248$		0			0
$249$	1.08927	−	0.143405i	0.0690297	−	0.00908793i
$250$		0			0
$251$			15.6504i			0.987846i	0.869506	+	0.493923i	$0.164438\pi$
$251$			15.6504i			0.987846i	−0.869506	+	0.493923i	$0.835562\pi$
$252$		0			0
$253$	−5.15471	−	5.15471i	−0.324074	−	0.324074i
$254$		0			0
$255$	−1.95509	−	1.83422i	−0.122433	−	0.114863i
$256$		0			0
$257$	−16.6291	+	4.45575i	−1.03729	+	0.277942i	−0.736992	−	0.675902i	$-0.763754\pi$
$257$	−16.6291	+	4.45575i	−1.03729	+	0.277942i	−0.300303	+	0.953844i	$0.597088\pi$
$258$		0			0
$259$	21.4874	−	12.0452i	1.33516	−	0.748454i
$260$		0			0
$261$	−3.06092	−	3.98907i	−0.189466	−	0.246917i
$262$		0			0
$263$	20.7041	+	5.54766i	1.27667	+	0.342083i	0.832584	−	0.553900i	$-0.186861\pi$
$263$	20.7041	+	5.54766i	1.27667	+	0.342083i	0.444089	+	0.895983i	$0.353527\pi$
$264$		0			0
$265$	18.4085	+	7.62506i	1.13083	+	0.468404i
$266$		0			0
$267$	−4.21397	+	1.74548i	−0.257891	+	0.106822i
$268$		0			0
$269$	5.68229	−	7.40531i	0.346456	−	0.451510i	−0.587327	−	0.809349i	$-0.699820\pi$
$269$	5.68229	−	7.40531i	0.346456	−	0.451510i	0.933783	+	0.357840i	$0.116487\pi$
$270$		0			0
$271$	13.9229	−	24.1152i	0.845756	−	1.46489i	−0.0392074	−	0.999231i	$-0.512483\pi$
$271$	13.9229	−	24.1152i	0.845756	−	1.46489i	0.884963	−	0.465661i	$-0.154183\pi$
$272$		0			0
$273$	2.20867	+	0.0279985i	0.133675	+	0.00169454i
$274$		0			0
$275$	0.121044	+	0.0159358i	0.00729923	+	0.000960962i
$276$		0			0
$277$	2.60193	+	1.99653i	0.156335	+	0.119960i	0.683967	−	0.729513i	$-0.260253\pi$
$277$	2.60193	+	1.99653i	0.156335	+	0.119960i	−0.527632	+	0.849473i	$0.676920\pi$
$278$		0			0
$279$	−14.2025	−	5.88287i	−0.850281	−	0.352198i
$280$		0			0
$281$	8.11633	−	8.11633i	0.484179	−	0.484179i	−0.422284	−	0.906464i	$-0.638772\pi$
$281$	8.11633	−	8.11633i	0.484179	−	0.484179i	0.906464	+	0.422284i	$0.138772\pi$
$282$		0			0
$283$	−6.89071	+	0.907179i	−0.409610	+	0.0539262i	−0.332516	−	0.943098i	$-0.607898\pi$
$283$	−6.89071	+	0.907179i	−0.409610	+	0.0539262i	−0.0770941	+	0.997024i	$0.524564\pi$
$284$		0			0
$285$	3.45341	+	1.99383i	0.204562	+	0.118104i
$286$		0			0
$287$	−1.63702	+	0.416473i	−0.0966305	+	0.0245836i
$288$		0			0
$289$	16.9654	−	1.08343i	0.997967	−	0.0637312i
$290$		0			0
$291$	−0.610129	+	2.27703i	−0.0357664	+	0.133482i
$292$		0			0
$293$		−	22.2615i		−	1.30053i	−0.759706	−	0.650267i	$-0.774657\pi$
$293$		−	22.2615i		−	1.30053i	0.759706	−	0.650267i	$-0.225343\pi$
$294$		0			0
$295$	−3.57211	+	8.62383i	−0.207976	+	0.502099i
$296$		0			0
$297$	−2.44375	−	0.654802i	−0.141801	−	0.0379954i
$298$		0			0
$299$	−11.2921	+	8.66476i	−0.653041	+	0.501096i
$300$		0			0
$301$	0.323916	−	2.24054i	0.0186702	−	0.129143i
$302$		0			0
$303$	1.57076	+	0.206795i	0.0902380	+	0.0118801i
$304$		0			0
$305$	−0.0326585	−	0.0565661i	−0.00187002	−	0.00323897i
$306$		0			0
$307$	24.3839			1.39166			0.695831	−	0.718205i	$-0.255036\pi$
$307$	24.3839			1.39166			0.695831	+	0.718205i	$0.255036\pi$
$308$		0			0
$309$	−0.406887	−	0.982312i	−0.0231470	−	0.0558818i
$310$		0			0
$311$	−23.7672	−	18.2372i	−1.34771	−	1.03414i	−0.995152	−	0.0983460i	$-0.968645\pi$
$311$	−23.7672	−	18.2372i	−1.34771	−	1.03414i	−0.352559	−	0.935789i	$-0.614689\pi$
$312$		0			0
$313$	−7.41728	+	5.69148i	−0.419249	+	0.321701i	−0.796751	−	0.604308i	$-0.793450\pi$
$313$	−7.41728	+	5.69148i	−0.419249	+	0.321701i	0.377502	+	0.926009i	$0.376783\pi$
$314$		0			0
$315$	−12.4570	+	12.1451i	−0.701870	+	0.684298i
$316$		0			0
$317$	20.4592	+	26.6629i	1.14910	+	1.49754i	0.836760	+	0.547569i	$0.184447\pi$
$317$	20.4592	+	26.6629i	1.14910	+	1.49754i	0.312342	+	0.949970i	$0.398887\pi$
$318$		0			0
$319$	2.21331	−	1.27785i	0.123921	−	0.0715460i
$320$		0			0
$321$	−1.64639	−	1.64639i	−0.0918926	−	0.0918926i
$322$		0			0
$323$	−24.2044	+	7.32020i	−1.34677	+	0.407307i
$324$		0			0
$325$	0.0616967	−	0.230255i	0.00342232	−	0.0127723i
$326$		0			0
$327$	−2.80622	−	1.62017i	−0.155184	−	0.0895957i
$328$		0			0
$329$	−16.8688	+	2.00364i	−0.930010	+	0.110464i
$330$		0			0
$331$	−8.61799	−	32.1628i	−0.473688	−	1.76783i	−0.626344	−	0.779547i	$-0.715449\pi$
$331$	−8.61799	−	32.1628i	−0.473688	−	1.76783i	0.152656	−	0.988279i	$-0.451217\pi$
$332$		0			0
$333$	3.54470	+	26.9247i	0.194249	+	1.47546i
$334$		0			0
$335$	−11.3941	+	4.71957i	−0.622524	+	0.257858i
$336$		0			0
$337$	11.0964	+	26.7891i	0.604460	+	1.45930i	0.868946	+	0.494907i	$0.164798\pi$
$337$	11.0964	+	26.7891i	0.604460	+	1.45930i	−0.264486	+	0.964390i	$0.585202\pi$
$338$		0			0
$339$	−1.49458	−	2.58869i	−0.0811746	−	0.140598i
$340$		0			0
$341$	3.90683	−	6.76683i	0.211567	−	0.366445i
$342$		0			0
$343$	−6.43175	−	17.3676i	−0.347282	−	0.937761i
$344$		0			0
$345$	−0.417296	+	3.16967i	−0.0224664	+	0.170650i
$346$		0			0
$347$	3.41624	+	25.9489i	0.183393	+	1.39301i	0.797277	+	0.603613i	$0.206273\pi$
$347$	3.41624	+	25.9489i	0.183393	+	1.39301i	−0.613884	+	0.789396i	$0.710394\pi$
$348$		0			0
$349$	5.97297	−	5.97297i	0.319726	−	0.319726i	−0.528936	−	0.848662i	$-0.677409\pi$
$349$	5.97297	−	5.97297i	0.319726	−	0.319726i	0.848662	+	0.528936i	$0.177409\pi$
$350$		0			0
$351$	−1.89036	+	4.56373i	−0.100900	+	0.243594i
$352$		0			0
$353$	−23.9365	+	13.8197i	−1.27401	+	0.735549i	−0.975740	−	0.218933i	$-0.929743\pi$
$353$	−23.9365	+	13.8197i	−1.27401	+	0.735549i	−0.298269	+	0.954482i	$0.596409\pi$
$354$		0			0
$355$	28.0569	−	7.51784i	1.48911	−	0.399005i
$356$		0			0
$357$	0.0604383	+	3.14560i	0.00319873	+	0.166483i
$358$		0			0
$359$	−14.2628	+	3.82171i	−0.752763	+	0.201702i	−0.614744	−	0.788727i	$-0.710740\pi$
$359$	−14.2628	+	3.82171i	−0.752763	+	0.201702i	−0.138020	+	0.990429i	$0.544074\pi$
$360$		0			0
$361$	16.1203	−	9.30705i	0.848436	−	0.489845i
$362$		0			0
$363$	−0.971472	+	2.34534i	−0.0509891	+	0.123099i
$364$		0			0
$365$	19.1709	−	19.1709i	1.00345	−	1.00345i
$366$		0			0
$367$	2.78086	+	21.1227i	0.145160	+	1.10260i	0.896614	+	0.442812i	$0.146019\pi$
$367$	2.78086	+	21.1227i	0.145160	+	1.10260i	−0.751455	+	0.659785i	$0.770648\pi$
$368$		0			0
$369$	0.243070	−	1.84630i	0.0126537	−	0.0961146i
$370$		0			0
$371$	−8.67414	−	21.7158i	−0.450339	−	1.12743i
$372$		0			0
$373$	1.89760	−	3.28674i	0.0982541	−	0.170181i	−0.812708	−	0.582671i	$-0.802008\pi$
$373$	1.89760	−	3.28674i	0.0982541	−	0.170181i	0.910962	+	0.412490i	$0.135341\pi$
$374$		0			0
$375$	1.59871	+	2.76905i	0.0825571	+	0.142993i
$376$		0			0
$377$	−1.90959	−	4.61017i	−0.0983491	−	0.237436i
$378$		0			0
$379$	−15.7510	+	6.52426i	−0.809072	+	0.335129i	−0.748584	−	0.663040i	$-0.769266\pi$
$379$	−15.7510	+	6.52426i	−0.809072	+	0.335129i	−0.0604883	+	0.998169i	$0.519266\pi$
$380$		0			0
$381$	−0.815455	−	6.19400i	−0.0417770	−	0.317328i
$382$		0			0
$383$	−1.41805	−	5.29224i	−0.0724590	−	0.270421i	0.920186	−	0.391481i	$-0.128037\pi$
$383$	−1.41805	−	5.29224i	−0.0724590	−	0.270421i	−0.992645	+	0.121060i	$0.961371\pi$
$384$		0			0
$385$	−5.29388	−	7.08324i	−0.269801	−	0.360996i
$386$		0			0
$387$	2.16141	+	1.24789i	0.109870	+	0.0634337i
$388$		0			0
$389$	5.79325	−	21.6207i	0.293729	−	1.09621i	−0.648492	−	0.761222i	$-0.724600\pi$
$389$	5.79325	−	21.6207i	0.293729	−	1.09621i	0.942221	−	0.334991i	$-0.108733\pi$
$390$		0			0
$391$	−12.8482	−	15.6824i	−0.649763	−	0.793092i
$392$		0			0
$393$	−1.42585	−	1.42585i	−0.0719246	−	0.0719246i
$394$		0			0
$395$	−0.199162	+	0.114986i	−0.0100209	+	0.00578559i
$396$		0			0
$397$	−10.1955	−	13.2870i	−0.511698	−	0.666857i	0.464036	−	0.885816i	$-0.346401\pi$
$397$	−10.1955	−	13.2870i	−0.511698	−	0.666857i	−0.975734	+	0.218959i	$0.929734\pi$
$398$		0			0
$399$	−1.15384	−	4.53540i	−0.0577645	−	0.227054i
$400$		0			0
$401$	−6.33729	+	4.86277i	−0.316469	+	0.242835i	−0.754765	−	0.655996i	$-0.772249\pi$
$401$	−6.33729	+	4.86277i	−0.316469	+	0.242835i	0.438296	+	0.898831i	$0.355582\pi$
$402$		0			0
$403$	−12.1035	−	9.28737i	−0.602920	−	0.462637i
$404$		0			0
$405$	−7.12463	−	17.2004i	−0.354026	−	0.854694i
$406$		0			0
$407$	−13.8035			−0.684212
$408$		0			0
$409$	7.77812	+	13.4721i	0.384603	+	0.666153i	0.991714	−	0.128465i	$-0.0410049\pi$
$409$	7.77812	+	13.4721i	0.384603	+	0.666153i	−0.607111	+	0.794617i	$0.707672\pi$
$410$		0			0
$411$	1.47920	+	0.194740i	0.0729635	+	0.00960583i
$412$		0			0
$413$	10.1732	−	4.06357i	0.500589	−	0.199955i
$414$		0			0
$415$	−6.81327	+	5.22801i	−0.334450	+	0.256633i
$416$		0			0
$417$	−3.87547	−	1.03843i	−0.189783	−	0.0508521i
$418$		0			0
$419$	12.6278	−	30.4861i	0.616906	−	1.48934i	−0.238372	−	0.971174i	$-0.576614\pi$
$419$	12.6278	−	30.4861i	0.616906	−	1.48934i	0.855278	−	0.518169i	$-0.173386\pi$
$420$		0			0
$421$			3.81127i			0.185750i	0.995678	+	0.0928749i	$0.0296057\pi$
$421$			3.81127i			0.185750i	−0.995678	+	0.0928749i	$0.970394\pi$
$422$		0			0
$423$	4.84713	−	18.0897i	0.235675	−	0.879552i
$424$		0			0
$425$	0.330601	+	0.0773773i	0.0160365	+	0.00375335i
$426$		0			0
$427$	−0.0207768	+	0.0737860i	−0.00100546	+	0.00357075i
$428$		0			0
$429$	−1.07192	−	0.618872i	−0.0517527	−	0.0298794i
$430$		0			0
$431$	−9.44116	+	1.24295i	−0.454765	+	0.0598709i	−0.354430	−	0.935083i	$-0.615325\pi$
$431$	−9.44116	+	1.24295i	−0.454765	+	0.0598709i	−0.100335	+	0.994954i	$0.531992\pi$
$432$		0			0
$433$	−8.29977	+	8.29977i	−0.398861	+	0.398861i	−0.877831	−	0.478970i	$-0.841010\pi$
$433$	−8.29977	+	8.29977i	−0.398861	+	0.398861i	0.478970	+	0.877831i	$0.341010\pi$
$434$		0			0
$435$	−1.03551	−	0.428921i	−0.0496488	−	0.0205652i
$436$		0			0
$437$	23.9247	+	18.3580i	1.14447	+	0.878184i
$438$		0			0
$439$	−19.7915	−	2.60560i	−0.944597	−	0.124359i	−0.357534	−	0.933900i	$-0.616383\pi$
$439$	−19.7915	−	2.60560i	−0.944597	−	0.124359i	−0.587063	+	0.809541i	$0.699716\pi$
$440$		0			0
$441$	20.4112	+	0.517573i	0.971961	+	0.0246464i
$442$		0			0
$443$	−9.20848	+	15.9496i	−0.437508	+	0.757787i	−0.997497	−	0.0707139i	$-0.977472\pi$
$443$	−9.20848	+	15.9496i	−0.437508	+	0.757787i	0.559988	+	0.828500i	$0.310806\pi$
$444$		0			0
$445$	21.7043	−	28.2856i	1.02888	−	1.34087i
$446$		0			0
$447$	2.63805	−	1.09272i	0.124776	−	0.0516837i
$448$		0			0
$449$	−22.0697	−	9.14156i	−1.04153	−	0.431417i	−0.204671	−	0.978831i	$-0.565612\pi$
$449$	−22.0697	−	9.14156i	−1.04153	−	0.431417i	−0.836862	+	0.547414i	$0.815612\pi$
$450$		0			0
$451$	0.914289	+	0.244983i	0.0430522	+	0.0115358i
$452$		0			0
$453$	−1.37006	−	1.78550i	−0.0643710	−	0.0838899i
$454$		0			0
$455$	−15.0609	+	8.44268i	−0.706064	+	0.395799i
$456$		0			0
$457$	−31.5638	+	8.45749i	−1.47649	+	0.395625i	−0.905152	−	0.425089i	$-0.860243\pi$
$457$	−31.5638	+	8.45749i	−1.47649	+	0.395625i	−0.571340	+	0.820714i	$0.693576\pi$
$458$		0			0
$459$	−6.58291	−	2.48393i	−0.307264	−	0.115940i
$460$		0			0
$461$	−4.09443	−	4.09443i	−0.190697	−	0.190697i	0.605300	−	0.795997i	$-0.293053\pi$
$461$	−4.09443	−	4.09443i	−0.190697	−	0.190697i	−0.795997	+	0.605300i	$0.793053\pi$
$462$		0			0
$463$		−	15.8674i		−	0.737419i	−0.929545	−	0.368709i	$-0.879800\pi$
$463$		−	15.8674i		−	0.737419i	0.929545	−	0.368709i	$-0.120200\pi$
$464$		0			0
$465$	−3.39743	+	0.447280i	−0.157552	+	0.0207421i
$466$		0			0
$467$	−1.73755	−	6.48461i	−0.0804041	−	0.300072i	0.914000	−	0.405714i	$-0.132977\pi$
$467$	−1.73755	−	6.48461i	−0.0804041	−	0.300072i	−0.994404	+	0.105642i	$0.966310\pi$
$468$		0			0
$469$	13.3007	+	5.70790i	0.614168	+	0.263566i
$470$		0			0
$471$	0.383205	−	2.91073i	0.0176571	−	0.134119i
$472$		0			0
$473$	−0.772251	+	1.00642i	−0.0355081	+	0.0462751i
$474$		0			0
$475$	−0.505051			−0.0231733
$476$		0			0
$477$	25.7799			1.18038
$478$		0			0
$479$	18.5540	−	24.1801i	0.847756	−	1.10482i	−0.145556	−	0.989350i	$-0.546497\pi$
$479$	18.5540	−	24.1801i	0.847756	−	1.10482i	0.993311	−	0.115467i	$-0.0368363\pi$
$480$		0			0
$481$	−3.51784	+	26.7207i	−0.160400	+	1.21836i
$482$		0			0
$483$	3.00538	−	2.24616i	0.136749	−	0.102204i
$484$		0			0
$485$	−4.76918	−	17.7988i	−0.216557	−	0.808203i
$486$		0			0
$487$	−21.5862	+	2.84187i	−0.978162	+	0.128777i	−0.602620	−	0.798028i	$-0.705877\pi$
$487$	−21.5862	+	2.84187i	−0.978162	+	0.128777i	−0.375542	+	0.926806i	$0.622543\pi$
$488$		0			0
$489$		−	1.18696i		−	0.0536761i
$490$		0			0
$491$	13.1952	+	13.1952i	0.595490	+	0.595490i	0.939109	−	0.343619i	$-0.111653\pi$
$491$	13.1952	+	13.1952i	0.595490	+	0.595490i	−0.343619	+	0.939109i	$0.611653\pi$
$492$		0			0
$493$	6.47647	−	2.92791i	0.291685	−	0.131867i
$494$		0			0
$495$	9.41674	−	2.52321i	0.423251	−	0.113410i
$496$		0			0
$497$	−29.3035	−	17.4173i	−1.31444	−	0.781273i
$498$		0			0
$499$	−20.3578	−	26.5308i	−0.911340	−	1.18768i	−0.981753	−	0.190163i	$-0.939098\pi$
$499$	−20.3578	−	26.5308i	−0.911340	−	1.18768i	0.0704128	−	0.997518i	$-0.477568\pi$
$500$		0			0
$501$	4.90693	+	1.31481i	0.219226	+	0.0587413i
$502$		0			0
$503$	−2.21775	−	0.918622i	−0.0988846	−	0.0409593i	0.332693	−	0.943035i	$-0.392043\pi$
$503$	−2.21775	−	0.918622i	−0.0988846	−	0.0409593i	−0.431577	+	0.902076i	$0.642043\pi$
$504$		0			0
$505$	−11.4414	+	4.73919i	−0.509136	+	0.210891i
$506$		0			0
$507$	0.811256	−	1.05725i	0.0360291	−	0.0469541i
$508$		0			0
$509$	−5.66378	+	9.80995i	−0.251043	+	0.434819i	−0.963813	−	0.266579i	$-0.914107\pi$
$509$	−5.66378	+	9.80995i	−0.251043	+	0.434819i	0.712771	+	0.701397i	$0.247440\pi$
$510$		0			0
$511$	−31.8155	−	0.403314i	−1.40744	−	0.0178416i
$512$		0			0
$513$	10.3763	+	1.36607i	0.458125	+	0.0603132i
$514$		0			0
$515$	6.59361	+	5.05945i	0.290549	+	0.222946i
$516$		0			0
$517$	8.79446	+	3.64278i	0.386780	+	0.160209i
$518$		0			0
$519$	−0.385094	+	0.385094i	−0.0169038	+	0.0169038i
$520$		0			0
$521$	17.6906	−	2.32902i	0.775041	−	0.102036i	0.267378	−	0.963592i	$-0.413843\pi$
$521$	17.6906	−	2.32902i	0.775041	−	0.102036i	0.507663	+	0.861556i	$0.330509\pi$
$522$		0			0
$523$	6.79637	+	3.92389i	0.297185	+	0.171580i	0.641177	−	0.767393i	$-0.278446\pi$
$523$	6.79637	+	3.92389i	0.297185	+	0.171580i	−0.343993	+	0.938972i	$0.611780\pi$
$524$		0			0
$525$	−0.0170316	+	0.0604854i	−0.000743320	+	0.00263980i
$526$		0			0
$527$	12.6722	−	17.6527i	0.552008	−	0.768965i
$528$		0			0
$529$	−0.304705	+	1.13717i	−0.0132480	+	0.0494423i
$530$		0			0
$531$			12.0771i			0.524101i
$532$		0			0
$533$	0.707245	−	1.70744i	0.0306342	−	0.0739575i
$534$		0			0
$535$	17.5798	+	4.71049i	0.760041	+	0.203652i
$536$		0			0
$537$	−2.67580	+	2.05321i	−0.115469	+	0.0886027i
$538$		0			0
$539$	−1.61499	+	10.2516i	−0.0695624	+	0.441566i
$540$		0			0
$541$	−29.7163	−	3.91222i	−1.27760	−	0.168200i	−0.538980	−	0.842318i	$-0.681190\pi$
$541$	−29.7163	−	3.91222i	−1.27760	−	0.168200i	−0.738623	+	0.674119i	$0.764524\pi$
$542$		0			0
$543$	2.31941	+	4.01734i	0.0995356	+	0.172401i
$544$		0			0
$545$	25.3287			1.08496
$546$		0			0
$547$	1.49867	+	3.61812i	0.0640787	+	0.154700i	0.952675	−	0.303990i	$-0.0983190\pi$
$547$	1.49867	+	3.61812i	0.0640787	+	0.154700i	−0.888597	+	0.458690i	$0.848319\pi$
$548$		0			0
$549$	−0.0670455	−	0.0514458i	−0.00286143	−	0.00219565i
$550$		0			0
$551$	−8.38760	+	6.43603i	−0.357324	+	0.274184i
$552$		0			0
$553$	0.259791	+	0.0731526i	0.0110474	+	0.00311076i
$554$		0			0
$555$	3.68521	+	4.80266i	0.156428	+	0.203862i
$556$		0			0
$557$	−21.5522	+	12.4432i	−0.913196	+	0.527234i	−0.881458	−	0.472262i	$-0.843438\pi$
$557$	−21.5522	+	12.4432i	−0.913196	+	0.527234i	−0.0317380	+	0.999496i	$0.510104\pi$
$558$		0			0
$559$	1.75141	+	1.75141i	0.0740766	+	0.0740766i
$560$		0			0
$561$	0.832370	−	1.55412i	0.0351427	−	0.0656150i
$562$		0			0
$563$	10.6821	−	39.8661i	0.450197	−	1.68016i	−0.251642	−	0.967820i	$-0.580970\pi$
$563$	10.6821	−	39.8661i	0.450197	−	1.68016i	0.701838	−	0.712336i	$-0.252363\pi$
$564$		0			0
$565$	20.2350	+	11.6827i	0.851292	+	0.491494i
$566$		0			0
$567$	−8.61660	+	20.0786i	−0.361863	+	0.843222i
$568$		0			0
$569$	−6.12953	−	22.8757i	−0.256963	−	0.958999i	−0.966988	−	0.254823i	$-0.917983\pi$
$569$	−6.12953	−	22.8757i	−0.256963	−	0.958999i	0.710025	−	0.704177i	$-0.248684\pi$
$570$		0			0
$571$	3.74841	+	28.4720i	0.156866	+	1.19152i	0.870920	+	0.491425i	$0.163524\pi$
$571$	3.74841	+	28.4720i	0.156866	+	1.19152i	−0.714054	+	0.700091i	$0.753143\pi$
$572$		0			0
$573$	6.44124	−	2.66805i	0.269087	−	0.111459i
$574$		0			0
$575$	−0.154954	−	0.374093i	−0.00646204	−	0.0156007i
$576$		0			0
$577$	19.0640	+	33.0199i	0.793647	+	1.37464i	0.923695	+	0.383129i	$0.125153\pi$
$577$	19.0640	+	33.0199i	0.793647	+	1.37464i	−0.130048	+	0.991508i	$0.541513\pi$
$578$		0			0
$579$	−3.40598	+	5.89932i	−0.141548	+	0.245168i
$580$		0			0
$581$	9.97503	+	1.44209i	0.413834	+	0.0598281i
$582$		0			0
$583$	−1.71035	+	12.9914i	−0.0708353	+	0.538048i
$584$		0			0
$585$	−2.48454	−	18.8719i	−0.102723	−	0.780258i
$586$		0			0
$587$	−6.01955	+	6.01955i	−0.248453	+	0.248453i	−0.820336	−	0.571882i	$-0.806213\pi$
$587$	−6.01955	+	6.01955i	−0.248453	+	0.248453i	0.571882	+	0.820336i	$0.306213\pi$
$588$		0			0
$589$	−12.3696	+	29.8628i	−0.509679	+	1.23047i
$590$		0			0
$591$	4.86230	−	2.80725i	0.200008	−	0.115475i
$592$		0			0
$593$	6.29175	−	1.68587i	0.258371	−	0.0692304i	−0.127308	−	0.991863i	$-0.540634\pi$
$593$	6.29175	−	1.68587i	0.258371	−	0.0692304i	0.385679	+	0.922633i	$0.373967\pi$
$594$		0			0
$595$	−12.7032	−	21.0577i	−0.520780	−	0.863283i
$596$		0			0
$597$	−4.96371	+	1.33002i	−0.203151	+	0.0544341i
$598$		0			0
$599$	15.8300	−	9.13945i	0.646796	−	0.373428i	−0.140431	−	0.990090i	$-0.544849\pi$
$599$	15.8300	−	9.13945i	0.646796	−	0.373428i	0.787228	+	0.616662i	$0.211516\pi$
$600$		0			0
$601$	−10.2746	+	24.8050i	−0.419108	+	1.01182i	0.563498	+	0.826117i	$0.309455\pi$
$601$	−10.2746	+	24.8050i	−0.419108	+	1.01182i	−0.982607	+	0.185700i	$0.940545\pi$
$602$		0			0
$603$	−11.2830	+	11.2830i	−0.459480	+	0.459480i
$604$		0			0
$605$	−2.59006	−	19.6735i	−0.105301	−	0.799841i
$606$		0			0
$607$	2.22477	−	16.8988i	0.0903008	−	0.685902i	−0.885090	−	0.465420i	$-0.845903\pi$
$607$	2.22477	−	16.8988i	0.0903008	−	0.685902i	0.975391	−	0.220483i	$-0.0707633\pi$
$608$		0			0
$609$	0.487934	+	1.22155i	0.0197721	+	0.0494995i
$610$		0			0
$611$	9.29297	−	16.0959i	0.375953	−	0.651170i
$612$		0			0
$613$	−22.0843	−	38.2511i	−0.891975	−	1.54495i	−0.837504	−	0.546431i	$-0.815986\pi$
$613$	−22.0843	−	38.2511i	−0.891975	−	1.54495i	−0.0544709	−	0.998515i	$-0.517347\pi$
$614$		0			0
$615$	−0.158857	−	0.383515i	−0.00640574	−	0.0154648i
$616$		0			0
$617$	4.30382	−	1.78270i	0.173265	−	0.0717688i	−0.294365	−	0.955693i	$-0.595108\pi$
$617$	4.30382	−	1.78270i	0.173265	−	0.0717688i	0.467630	+	0.883924i	$0.345108\pi$
$618$		0			0
$619$	−4.15518	−	31.5618i	−0.167011	−	1.26857i	−0.845505	−	0.533968i	$-0.820700\pi$
$619$	−4.15518	−	31.5618i	−0.167011	−	1.26857i	0.678494	−	0.734606i	$-0.262633\pi$
$620$		0			0
$621$	2.17169	+	8.10487i	0.0871470	+	0.325237i
$622$		0			0
$623$	−41.5502	+	4.93524i	−1.66467	+	0.197726i
$624$		0			0
$625$	−22.0013	−	12.7025i	−0.880054	−	0.508099i
$626$		0			0
$627$	−0.678730	+	2.53305i	−0.0271058	+	0.101160i
$628$		0			0
$629$	−38.2001	−	3.79470i	−1.52314	−	0.151305i
$630$		0			0
$631$	−0.736500	−	0.736500i	−0.0293196	−	0.0293196i	0.692295	−	0.721615i	$-0.256600\pi$
$631$	−0.736500	−	0.736500i	−0.0293196	−	0.0293196i	−0.721615	+	0.692295i	$0.756600\pi$
$632$		0			0
$633$	−1.69936	+	0.981124i	−0.0675434	+	0.0389962i
$634$		0			0
$635$	29.7284	+	38.7428i	1.17974	+	1.53746i
$636$		0			0
$637$	19.4333	+	5.73892i	0.769977	+	0.227384i
$638$		0			0
$639$	29.8154	−	22.8782i	1.17948	−	0.905046i
$640$		0			0
$641$	−7.06284	−	5.41951i	−0.278965	−	0.214058i	0.459796	−	0.888024i	$-0.347922\pi$
$641$	−7.06284	−	5.41951i	−0.278965	−	0.214058i	−0.738762	+	0.673967i	$0.764589\pi$
$642$		0			0
$643$	5.37608	+	12.9790i	0.212012	+	0.511842i	0.993732	−	0.111787i	$-0.0356575\pi$
$643$	5.37608	+	12.9790i	0.212012	+	0.511842i	−0.781720	+	0.623629i	$0.785657\pi$
$644$		0			0
$645$	0.556338			0.0219058
$646$		0			0
$647$	17.2245	+	29.8337i	0.677165	+	1.17288i	0.975831	+	0.218526i	$0.0701250\pi$
$647$	17.2245	+	29.8337i	0.677165	+	1.17288i	−0.298666	+	0.954358i	$0.596542\pi$
$648$		0			0
$649$	−6.08606	−	0.801245i	−0.238899	−	0.0314516i
$650$		0			0
$651$	3.15926	+	2.48844i	0.123821	+	0.0975297i
$652$		0			0
$653$	5.52237	−	4.23747i	0.216107	−	0.165825i	−0.495035	−	0.868873i	$-0.664845\pi$
$653$	5.52237	−	4.23747i	0.216107	−	0.165825i	0.711142	+	0.703048i	$0.248178\pi$
$654$		0			0
$655$	15.2249	+	4.07950i	0.594887	+	0.159399i
$656$		0			0
$657$	13.4238	−	32.4078i	0.523711	−	1.26435i
$658$		0			0
$659$			39.5733i			1.54156i	0.637103	+	0.770778i	$0.280132\pi$
$659$			39.5733i			1.54156i	−0.637103	+	0.770778i	$0.719868\pi$
$660$		0			0
$661$	−9.78063	+	36.5018i	−0.380422	+	1.41976i	0.464835	+	0.885397i	$0.346114\pi$
$661$	−9.78063	+	36.5018i	−0.380422	+	1.41976i	−0.845258	+	0.534359i	$0.820553\pi$
$662$		0			0
$663$	−2.79633	−	2.00737i	−0.108600	−	0.0779597i
$664$		0			0
$665$	25.5368	+	26.1925i	0.990274	+	1.01570i
$666$		0			0
$667$	−7.34057	−	4.23808i	−0.284228	−	0.164099i
$668$		0			0
$669$	5.18148	−	0.682155i	0.200328	−	0.0263736i
$670$		0			0
$671$	0.0303734	−	0.0303734i	0.00117255	−	0.00117255i
$672$		0			0
$673$	26.7281	+	11.0711i	1.03029	+	0.426761i	0.832818	−	0.553547i	$-0.186726\pi$
$673$	26.7281	+	11.0711i	1.03029	+	0.426761i	0.197474	+	0.980308i	$0.436726\pi$
$674$		0			0
$675$	−0.111487	−	0.0855471i	−0.00429114	−	0.00329271i
$676$		0			0
$677$	33.3292	+	4.38787i	1.28095	+	0.168640i	0.740109	−	0.672487i	$-0.234774\pi$
$677$	33.3292	+	4.38787i	1.28095	+	0.168640i	0.540837	+	0.841127i	$0.318107\pi$
$678$		0			0
$679$	−11.0492	+	18.5896i	−0.424031	+	0.713403i
$680$		0			0
$681$	−1.15137	+	1.99423i	−0.0441206	+	0.0764191i
$682$		0			0
$683$	0.428658	−	0.558638i	0.0164021	−	0.0213757i	−0.785080	−	0.619394i	$-0.787378\pi$
$683$	0.428658	−	0.558638i	0.0164021	−	0.0213757i	0.801482	+	0.598018i	$0.204045\pi$
$684$		0			0
$685$	−10.7745	+	4.46293i	−0.411671	+	0.170520i
$686$		0			0
$687$	5.87611	+	2.43396i	0.224188	+	0.0928616i
$688$		0			0
$689$	24.7127	+	6.62176i	0.941481	+	0.252269i
$690$		0			0
$691$	0.251707	+	0.328031i	0.00957539	+	0.0124789i	0.798117	−	0.602503i	$-0.205830\pi$
$691$	0.251707	+	0.328031i	0.00957539	+	0.0124789i	−0.788541	+	0.614982i	$0.789163\pi$
$692$		0			0
$693$	−9.83511	−	5.84576i	−0.373605	−	0.222062i
$694$		0			0
$695$	30.2933	−	8.11706i	1.14909	−	0.307898i
$696$		0			0
$697$	2.46289	+	0.929321i	0.0932884	+	0.0352005i
$698$		0			0
$699$	−0.957926	−	0.957926i	−0.0362321	−	0.0362321i
$700$		0			0
$701$			40.9518i			1.54673i	0.633963	+	0.773363i	$0.281427\pi$
$701$			40.9518i			1.54673i	−0.633963	+	0.773363i	$0.718573\pi$
$702$		0			0
$703$	56.6131	−	7.45325i	2.13520	−	0.281105i
$704$		0			0
$705$	−1.08048	−	4.03241i	−0.0406933	−	0.151869i
$706$		0			0
$707$	13.3560	+	5.73163i	0.502303	+	0.215560i
$708$		0			0
$709$	−4.67812	+	35.5339i	−0.175691	+	1.33450i	0.645462	+	0.763793i	$0.276665\pi$
$709$	−4.67812	+	35.5339i	−0.175691	+	1.33450i	−0.821152	+	0.570709i	$0.806668\pi$
$710$		0			0
$711$	−0.181134	+	0.236059i	−0.00679307	+	0.00885290i
$712$		0			0
$713$	−25.9145			−0.970507
$714$		0			0
$715$	9.67505			0.361826
$716$		0			0
$717$	1.40386	−	1.82954i	0.0524281	−	0.0683256i
$718$		0			0
$719$	2.78566	−	21.1592i	0.103888	−	0.789106i	−0.857612	−	0.514298i	$-0.828053\pi$
$719$	2.78566	−	21.1592i	0.103888	−	0.789106i	0.961499	−	0.274808i	$-0.0886141\pi$
$720$		0			0
$721$	−1.15044	−	9.68570i	−0.0428448	−	0.360714i
$722$		0			0
$723$	−0.767417	−	2.86404i	−0.0285405	−	0.106515i
$724$		0			0
$725$	0.140742	−	0.0185291i	0.00522703	−	0.000688152i
$726$		0			0
$727$			14.1525i			0.524889i	0.964947	+	0.262444i	$0.0845286\pi$
$727$			14.1525i			0.524889i	−0.964947	+	0.262444i	$0.915471\pi$
$728$		0			0
$729$	−15.9887	−	15.9887i	−0.592175	−	0.592175i
$730$		0			0
$731$	−2.41383	+	2.57289i	−0.0892786	+	0.0951619i
$732$		0			0
$733$	31.5423	−	8.45172i	1.16504	−	0.312171i	0.376063	−	0.926594i	$-0.377278\pi$
$733$	31.5423	−	8.45172i	1.16504	−	0.312171i	0.788977	+	0.614423i	$0.210611\pi$
$734$		0			0
$735$	3.99801	−	2.17503i	0.147469	−	0.0802271i
$736$		0			0
$737$	−4.93734	−	6.43447i	−0.181869	−	0.237017i
$738$		0			0
$739$	23.4772	+	6.29069i	0.863621	+	0.231407i	0.663328	−	0.748329i	$-0.269144\pi$
$739$	23.4772	+	6.29069i	0.863621	+	0.231407i	0.200294	+	0.979736i	$0.435810\pi$
$740$		0			0
$741$	4.73050	+	1.95944i	0.173779	+	0.0719817i
$742$		0			0
$743$	−12.8841	+	5.33677i	−0.472672	+	0.195787i	−0.606287	−	0.795246i	$-0.707342\pi$
$743$	−12.8841	+	5.33677i	−0.472672	+	0.195787i	0.133615	+	0.991033i	$0.457342\pi$
$744$		0			0
$745$	−13.5874	+	17.7075i	−0.497805	+	0.648752i
$746$		0			0
$747$	−5.55567	+	9.62270i	−0.203271	+	0.352076i
$748$		0			0
$749$	−10.4443	−	18.6316i	−0.381627	−	0.680783i
$750$		0			0
$751$	−36.7480	−	4.83797i	−1.34095	−	0.176540i	−0.574323	−	0.818629i	$-0.694735\pi$
$751$	−36.7480	−	4.83797i	−1.34095	−	0.176540i	−0.766630	+	0.642089i	$0.778068\pi$
$752$		0			0
$753$	3.58099	+	2.74779i	0.130498	+	0.100135i
$754$		0			0
$755$	16.2529	+	6.73216i	0.591502	+	0.245008i
$756$		0			0
$757$	−27.5305	+	27.5305i	−1.00061	+	1.00061i	−0.000611611		1.00000i	$0.500195\pi$
$757$	−27.5305	+	27.5305i	−1.00061	+	1.00061i	−1.00000		0.000611611i	$0.999805\pi$
$758$		0			0
$759$	−2.08448	+	0.274427i	−0.0756618	+	0.00996107i
$760$		0			0
$761$	−6.67974	−	3.85655i	−0.242140	−	0.139800i	0.374020	−	0.927421i	$-0.377979\pi$
$761$	−6.67974	−	3.85655i	−0.242140	−	0.139800i	−0.616160	+	0.787621i	$0.711313\pi$
$762$		0			0
$763$	−20.7510	−	21.2839i	−0.751238	−	0.770529i
$764$		0			0
$765$	26.7539	−	4.39406i	0.967288	−	0.158868i
$766$		0			0
$767$	−3.10209	+	11.5772i	−0.112010	+	0.418027i
$768$		0			0
$769$		−	12.2151i		−	0.440488i	−0.975445	−	0.220244i	$-0.929315\pi$
$769$		−	12.2151i		−	0.440488i	0.975445	−	0.220244i	$-0.0706853\pi$
$770$		0			0
$771$	−1.90009	+	4.58723i	−0.0684301	+	0.165205i
$772$		0			0
$773$	26.9541	+	7.22233i	0.969471	+	0.259769i	0.708604	−	0.705606i	$-0.249325\pi$
$773$	26.9541	+	7.22233i	0.969471	+	0.259769i	0.260867	+	0.965375i	$0.415992\pi$
$774$		0			0
$775$	0.344323	−	0.264209i	0.0123685	−	0.00949065i
$776$		0			0
$777$	1.01653	−	7.03137i	0.0364678	−	0.252249i
$778$		0			0
$779$	−3.88212	−	0.511090i	−0.139091	−	0.0183117i
$780$		0			0
$781$	9.55101	+	16.5428i	0.341762	+	0.591949i
$782$		0			0
$783$	−2.94167			−0.105127
$784$		0			0
$785$	8.78204	+	21.2017i	0.313444	+	0.756721i
$786$		0			0
$787$	−23.4256	−	17.9751i	−0.835033	−	0.640743i	0.100125	−	0.994975i	$-0.468076\pi$
$787$	−23.4256	−	17.9751i	−0.835033	−	0.640743i	−0.935158	+	0.354232i	$0.884742\pi$
$788$		0			0
$789$	4.90445	−	3.76332i	0.174603	−	0.133978i
$790$		0			0
$791$	−6.76086	−	26.5748i	−0.240388	−	0.944892i
$792$		0			0
$793$	−0.0510560	−	0.0665374i	−0.00181305	−	0.00236281i
$794$		0			0
$795$	4.97673	−	2.87332i	0.176507	−	0.101906i
$796$		0			0
$797$	18.7519	+	18.7519i	0.664226	+	0.664226i	0.956373	−	0.292147i	$-0.0943697\pi$
$797$	18.7519	+	18.7519i	0.664226	+	0.664226i	−0.292147	+	0.956373i	$0.594370\pi$
$798$		0			0
$799$	23.3366	+	12.4988i	0.825591	+	0.442177i
$800$		0			0
$801$	11.9391	−	44.5574i	0.421848	−	1.57436i
$802$		0			0
$803$	15.4408	+	8.91477i	0.544895	+	0.314595i
$804$		0			0
$805$	−11.5660	+	26.9513i	−0.407647	+	0.949907i
$806$		0			0
$807$	−0.696759	−	2.60034i	−0.0245271	−	0.0915363i
$808$		0			0
$809$	−6.50358	−	49.3996i	−0.228654	−	1.73680i	−0.592705	−	0.805420i	$-0.701940\pi$
$809$	−6.50358	−	49.3996i	−0.228654	−	1.73680i	0.364051	−	0.931379i	$-0.381393\pi$
$810$		0			0
$811$	5.93937	−	2.46017i	0.208560	−	0.0863882i	−0.275958	−	0.961170i	$-0.588995\pi$
$811$	5.93937	−	2.46017i	0.208560	−	0.0863882i	0.484518	+	0.874781i	$0.338995\pi$
$812$		0			0
$813$	−3.07333	−	7.41968i	−0.107786	−	0.260219i
$814$		0			0
$815$	4.63903	+	8.03504i	0.162498	+	0.281455i
$816$		0			0
$817$	2.62387	−	4.54467i	0.0917974	−	0.158998i
$818$		0			0
$819$	−13.8227	+	17.5489i	−0.483004	+	0.613210i
$820$		0			0
$821$	2.73432	−	20.7692i	0.0954285	−	0.724851i	−0.875113	−	0.483918i	$-0.839213\pi$
$821$	2.73432	−	20.7692i	0.0954285	−	0.724851i	0.970542	−	0.240933i	$-0.0774535\pi$
$822$		0			0
$823$	5.99166	+	45.5112i	0.208856	+	1.58642i	0.699223	+	0.714904i	$0.253530\pi$
$823$	5.99166	+	45.5112i	0.208856	+	1.58642i	−0.490366	+	0.871516i	$0.663137\pi$
$824$		0			0
$825$	0.0248983	−	0.0248983i	0.000866848	−	0.000866848i
$826$		0			0
$827$	−5.89521	+	14.2323i	−0.204997	+	0.494906i	−0.992622	−	0.121249i	$-0.961310\pi$
$827$	−5.89521	+	14.2323i	−0.204997	+	0.494906i	0.787626	+	0.616154i	$0.211310\pi$
$828$		0			0
$829$	4.38124	−	2.52951i	0.152167	−	0.0878536i	−0.421983	−	0.906604i	$-0.638666\pi$
$829$	4.38124	−	2.52951i	0.152167	−	0.0878536i	0.574150	+	0.818750i	$0.305333\pi$
$830$		0			0
$831$	0.913657	−	0.244814i	0.0316944	−	0.00849249i
$832$		0			0
$833$	−7.28762	+	27.9265i	−0.252501	+	0.967597i
$834$		0			0
$835$	−38.3559	+	10.2774i	−1.32736	+	0.355665i
$836$		0			0
$837$	−7.78877	+	4.49685i	−0.269219	+	0.155434i
$838$		0			0
$839$	4.59155	−	11.0850i	0.158518	−	0.382696i	−0.824588	−	0.565734i	$-0.808593\pi$
$839$	4.59155	−	11.0850i	0.158518	−	0.382696i	0.983106	+	0.183038i	$0.0585930\pi$
$840$		0			0
$841$	−18.4049	+	18.4049i	−0.634650	+	0.634650i
$842$		0			0
$843$	−0.432098	−	3.28211i	−0.0148822	−	0.113042i
$844$		0			0
$845$	−1.35966	+	10.3276i	−0.0467737	+	0.355282i
$846$		0			0
$847$	−14.4098	+	18.2943i	−0.495127	+	0.628600i
$848$		0			0
$849$	−1.00225	+	1.73595i	−0.0343971	+	0.0595775i
$850$		0			0
$851$	22.8900	+	39.6467i	0.784661	+	1.35907i
$852$		0			0
$853$	−4.32204	−	10.4343i	−0.147984	−	0.357265i	0.832454	−	0.554094i	$-0.186935\pi$
$853$	−4.32204	−	10.4343i	−0.147984	−	0.357265i	−0.980438	+	0.196830i	$0.936935\pi$
$854$		0			0
$855$	−37.2591	+	15.4332i	−1.27423	+	0.527805i
$856$		0			0
$857$	−6.36539	−	48.3499i	−0.217438	−	1.65160i	−0.657367	−	0.753570i	$-0.728330\pi$
$857$	−6.36539	−	48.3499i	−0.217438	−	1.65160i	0.439930	−	0.898032i	$-0.355003\pi$
$858$		0			0
$859$	−7.40634	−	27.6408i	−0.252701	−	0.943093i	−0.969355	−	0.245664i	$-0.920994\pi$
$859$	−7.40634	−	27.6408i	−0.252701	−	0.943093i	0.716654	−	0.697429i	$-0.245673\pi$
$860$		0			0
$861$	−0.192123	+	0.447690i	−0.00654755	+	0.0152572i
$862$		0			0
$863$	25.6225	+	14.7932i	0.872201	+	0.503565i	0.868079	−	0.496426i	$-0.165355\pi$
$863$	25.6225	+	14.7932i	0.872201	+	0.503565i	0.00412197	+	0.999992i	$0.498688\pi$
$864$		0			0
$865$	1.10179	−	4.11195i	0.0374621	−	0.139811i
$866$		0			0
$867$	2.73077	−	4.07210i	0.0927418	−	0.138296i
$868$		0			0
$869$	−0.106941	−	0.106941i	−0.00362772	−	0.00362772i
$870$		0			0
$871$	−13.7141	+	7.91784i	−0.464685	+	0.268286i
$872$		0			0
$873$	−14.5135	−	18.9144i	−0.491208	−	0.640154i
$874$		0			0
$875$	7.23189	+	28.4263i	0.244483	+	0.960985i
$876$		0			0
$877$	−24.9363	+	19.1343i	−0.842040	+	0.646120i	−0.936988	−	0.349362i	$-0.886398\pi$
$877$	−24.9363	+	19.1343i	−0.842040	+	0.646120i	0.0949478	+	0.995482i	$0.469732\pi$
$878$		0			0
$879$	−5.09368	−	3.90852i	−0.171806	−	0.131831i
$880$		0			0
$881$	−3.58062	−	8.64438i	−0.120634	−	0.291237i	0.852014	−	0.523518i	$-0.175381\pi$
$881$	−3.58062	−	8.64438i	−0.120634	−	0.291237i	−0.972649	+	0.232282i	$0.925381\pi$
$882$		0			0
$883$	16.2354			0.546366			0.273183	−	0.961962i	$-0.411924\pi$
$883$	16.2354			0.546366			0.273183	+	0.961962i	$0.411924\pi$
$884$		0			0
$885$	1.34606	+	2.33145i	0.0452474	+	0.0783708i
$886$		0			0
$887$	19.0611	+	2.50944i	0.640008	+	0.0842586i	0.443544	−	0.896252i	$-0.353721\pi$
$887$	19.0611	+	2.50944i	0.640008	+	0.0842586i	0.196464	+	0.980511i	$0.437054\pi$
$888$		0			0
$889$	8.20029	−	56.7218i	0.275029	−	1.90239i
$890$		0			0
$891$	9.71342	−	7.45337i	0.325412	−	0.249697i
$892$		0			0
$893$	−38.0362	−	10.1918i	−1.27283	−	0.341055i
$894$		0			0
$895$	10.0890	−	24.3570i	0.337239	−	0.814166i
$896$		0			0
$897$			4.10506i			0.137064i
$898$		0			0
$899$	2.35143	−	8.77565i	0.0784245	−	0.292684i
$900$		0			0
$901$	−8.30472	+	35.4826i	−0.276670	+	1.18210i
$902$		0			0
$903$	−0.455790	−	0.467494i	−0.0151677	−	0.0155572i
$904$		0			0
$905$	−31.4023	−	18.1301i	−1.04385	−	0.602665i
$906$		0			0
$907$	27.6487	−	3.64001i	0.918059	−	0.120865i	0.343336	−	0.939213i	$-0.388443\pi$
$907$	27.6487	−	3.64001i	0.918059	−	0.120865i	0.574723	+	0.818348i	$0.305110\pi$
$908$		0			0
$909$	−11.3299	+	11.3299i	−0.375790	+	0.375790i
$910$		0			0
$911$	−32.1337	−	13.3102i	−1.06464	−	0.440987i	−0.219542	−	0.975603i	$-0.570456\pi$
$911$	−32.1337	−	13.3102i	−1.06464	−	0.440987i	−0.845095	+	0.534616i	$0.820456\pi$
$912$		0			0
$913$	−4.48062	−	3.43810i	−0.148287	−	0.113785i
$914$		0			0
$915$	−0.0186769	−	0.00245886i	−0.000617439	−	8.12874e-5i
$916$		0			0
$917$	−9.04526	−	16.1358i	−0.298701	−	0.532851i
$918$		0			0
$919$	−15.5713	+	26.9702i	−0.513649	+	0.889666i	0.486226	+	0.873833i	$0.338373\pi$
$919$	−15.5713	+	26.9702i	−0.513649	+	0.889666i	−0.999875	+	0.0158325i	$0.994960\pi$
$920$		0			0
$921$	4.28115	−	5.57930i	0.141069	−	0.183844i
$922$		0			0
$923$	34.4576	−	14.2728i	1.13419	−	0.469796i
$924$		0			0
$925$	−0.708350	−	0.293408i	−0.0232904	−	0.00964721i
$926$		0			0
$927$	10.3867	+	2.78311i	0.341144	+	0.0914092i
$928$		0			0
$929$	−6.44384	−	8.39777i	−0.211415	−	0.275522i	0.675593	−	0.737274i	$-0.263888\pi$
$929$	−6.44384	−	8.39777i	−0.211415	−	0.275522i	−0.887009	+	0.461752i	$0.847221\pi$
$930$		0			0
$931$	1.08827	−	42.9174i	0.0356667	−	1.40656i
$932$		0			0
$933$	−8.34573	+	2.23623i	−0.273227	+	0.0732109i
$934$		0			0
$935$	0.439354	+	13.7737i	0.0143684	+	0.450449i
$936$		0			0
$937$	21.4868	+	21.4868i	0.701943	+	0.701943i	0.964827	−	0.262884i	$-0.0846738\pi$
$937$	21.4868	+	21.4868i	0.701943	+	0.701943i	−0.262884	+	0.964827i	$0.584674\pi$
$938$		0			0
$939$			2.69642i			0.0879944i
$940$		0			0
$941$	30.4516	−	4.00903i	0.992694	−	0.130691i	0.383356	−	0.923601i	$-0.374768\pi$
$941$	30.4516	−	4.00903i	0.992694	−	0.130691i	0.609339	+	0.792910i	$0.291435\pi$
$942$		0			0
$943$	−0.812502	−	3.03230i	−0.0264587	−	0.0987453i
$944$		0			0
$945$	1.20053	+	10.1074i	0.0390532	+	0.328792i
$946$		0			0
$947$	5.16083	−	39.2004i	0.167705	−	1.27384i	−0.675946	−	0.736951i	$-0.736265\pi$
$947$	5.16083	−	39.2004i	0.167705	−	1.27384i	0.843651	−	0.536892i	$-0.180402\pi$
$948$		0			0
$949$	21.1923	−	27.6183i	0.687931	−	0.896529i
$950$		0			0
$951$	9.69284			0.314312
$952$		0			0
$953$	−4.97044			−0.161008			−0.0805041	−	0.996754i	$-0.525653\pi$
$953$	−4.97044			−0.161008			−0.0805041	+	0.996754i	$0.525653\pi$
$954$		0			0
$955$	−33.1760	+	43.2358i	−1.07355	+	1.39908i
$956$		0			0
$957$	0.0962096	−	0.730785i	0.00311002	−	0.0236229i
$958$		0			0
$959$	12.5774	+	5.39751i	0.406145	+	0.174295i
$960$		0			0
$961$	0.834272	+	3.11355i	0.0269120	+	0.100437i
$962$		0			0
$963$	23.3462	−	3.07358i	0.752320	−	0.0990448i
$964$		0			0
$965$		−	53.2468i		−	1.71408i
$966$		0			0
$967$	8.14025	+	8.14025i	0.261773	+	0.261773i	0.825774	−	0.564001i	$-0.190739\pi$
$967$	8.14025	+	8.14025i	0.261773	+	0.261773i	−0.564001	+	0.825774i	$0.690739\pi$
$968$		0			0
$969$	−2.57470	+	6.82346i	−0.0827112	+	0.219201i
$970$		0			0
$971$	−25.7914	+	6.91079i	−0.827686	+	0.221778i	−0.647704	−	0.761892i	$-0.724271\pi$
$971$	−25.7914	+	6.91079i	−0.827686	+	0.221778i	−0.179982	+	0.983670i	$0.557604\pi$
$972$		0			0
$973$	−31.6392	−	18.8056i	−1.01431	−	0.602880i
$974$		0			0
$975$	−0.0418527	−	0.0545434i	−0.00134036	−	0.00174679i
$976$		0			0
$977$	3.93636	+	1.05474i	0.125935	+	0.0337443i	0.321236	−	0.946999i	$-0.395902\pi$
$977$	3.93636	+	1.05474i	0.125935	+	0.0337443i	−0.195301	+	0.980743i	$0.562568\pi$
$978$		0			0
$979$	21.6619	+	8.97266i	0.692318	+	0.286767i
$980$		0			0
$981$	30.2765	−	12.5409i	0.966655	−	0.400402i
$982$		0			0
$983$	10.6585	−	13.8904i	0.339954	−	0.443036i	−0.591823	−	0.806068i	$-0.701592\pi$
$983$	10.6585	−	13.8904i	0.339954	−	0.443036i	0.931777	+	0.363032i	$0.118258\pi$
$984$		0			0
$985$	−21.9434	+	38.0070i	−0.699174	+	1.21100i
$986$		0			0
$987$	−2.50326	+	4.21156i	−0.0796795	+	0.134055i
$988$		0			0
$989$	4.17127	+	0.549158i	0.132639	+	0.0174622i
$990$		0			0
$991$	−9.15714	−	7.02652i	−0.290886	−	0.223205i	0.453001	−	0.891510i	$-0.350353\pi$
$991$	−9.15714	−	7.02652i	−0.290886	−	0.223205i	−0.743887	+	0.668305i	$0.767020\pi$
$992$		0			0
$993$	−8.87228	−	3.67502i	−0.281553	−	0.116623i
$994$		0			0
$995$	28.4033	−	28.4033i	0.900447	−	0.900447i
$996$		0			0
$997$	−45.4245	+	5.98025i	−1.43861	+	0.189396i	−0.809133	−	0.587625i	$-0.800063\pi$
$997$	−45.4245	+	5.98025i	−1.43861	+	0.189396i	−0.629474	+	0.777021i	$0.716730\pi$
$998$		0			0
$999$	13.7595	+	7.94404i	0.435331	+	0.251338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bh.a.457.7	yes	96
7.4	even	3	inner	476.2.bh.a.389.6	yes	96
17.8	even	8	inner	476.2.bh.a.93.6	yes	96
119.25	even	24	inner	476.2.bh.a.25.7	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bh.a.25.7	✓	96	119.25	even	24	inner
476.2.bh.a.93.6	yes	96	17.8	even	8	inner
476.2.bh.a.389.6	yes	96	7.4	even	3	inner
476.2.bh.a.457.7	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.175573 - 0.228811i) q^{3} +(-0.294259 + 2.23512i) q^{5} +(2.11926 - 1.58390i) q^{7} +(0.754929 + 2.81743i) q^{9} +O(q^{10})\)	\(q+(0.175573 - 0.228811i) q^{3} +(-0.294259 + 2.23512i) q^{5} +(2.11926 - 1.58390i) q^{7} +(0.754929 + 2.81743i) q^{9} +(-1.46989 + 0.193514i) q^{11} +2.89472i q^{13} +(0.459756 + 0.459756i) q^{15} +(-4.12101 + 0.131452i) q^{17} +(5.92405 - 1.58735i) q^{19} +(0.00967227 - 0.762999i) q^{21} +(2.99330 + 3.90095i) q^{23} +(-0.0795433 - 0.0213136i) q^{25} +(1.57657 + 0.653037i) q^{27} +(-1.59262 + 0.659683i) q^{29} +(-3.20839 + 4.18125i) q^{31} +(-0.213794 + 0.370302i) q^{33} +(2.91658 + 5.20288i) q^{35} +(9.23084 + 1.21526i) q^{37} +(0.662342 + 0.508233i) q^{39} +(-0.589848 - 0.244323i) q^{41} +(0.605036 - 0.605036i) q^{43} +(-6.51944 + 0.858301i) q^{45} +(-5.56044 - 3.21032i) q^{47} +(1.98255 - 6.71338i) q^{49} +(-0.693460 + 0.966011i) q^{51} +(2.28753 - 8.53719i) q^{53} -3.34231i q^{55} +(0.676901 - 1.63418i) q^{57} +(3.99942 + 1.07164i) q^{59} +(-0.0229858 + 0.0176376i) q^{61} +(6.06241 + 4.77515i) q^{63} +(-6.47004 - 0.851796i) q^{65} +(2.73527 + 4.73763i) q^{67} +1.41812 q^{69} +(-4.93065 - 11.9036i) q^{71} +(-9.54095 - 7.32103i) q^{73} +(-0.0188424 + 0.0144583i) q^{75} +(-2.80857 + 2.73825i) q^{77} +(0.0620999 + 0.0809302i) q^{79} +(-7.15189 + 4.12915i) q^{81} +(2.69365 + 2.69365i) q^{83} +(0.918834 - 9.24963i) q^{85} +(-0.128677 + 0.480230i) q^{87} +(-13.6961 - 7.90745i) q^{89} +(4.58493 + 6.13466i) q^{91} +(0.393411 + 1.46823i) q^{93} +(1.80470 + 13.7081i) q^{95} +(-7.55146 + 3.12792i) q^{97} +(-1.65487 - 3.99521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{5}+O(q^{10}) \) 96 * q + 4 * q^5	\( 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) \) 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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