LMFDB - Embedded newform 476.2.bl.a.465.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, 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:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			465.1
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58952 - 0.879025i) q^{3} +(0.0752031 - 1.14738i) q^{5} +(2.14067 + 1.55484i) q^{7} +(3.55289 + 2.72623i) q^{9} +O(q^{10})$	\(q+(-2.58952 - 0.879025i) q^{3} +(0.0752031 - 1.14738i) q^{5} +(2.14067 + 1.55484i) q^{7} +(3.55289 + 2.72623i) q^{9} +(3.21317 + 2.81787i) q^{11} +(-4.37784 - 4.37784i) q^{13} +(-1.20331 + 2.90506i) q^{15} +(2.49493 - 3.28258i) q^{17} +(0.0295505 - 0.00389040i) q^{19} +(-4.17659 - 5.90799i) q^{21} +(-1.61481 - 4.75708i) q^{23} +(3.64640 + 0.480058i) q^{25} +(-2.24599 - 3.36137i) q^{27} +(-4.74410 - 3.16991i) q^{29} +(2.56833 - 7.56606i) q^{31} +(-5.84359 - 10.1214i) q^{33} +(1.94497 - 2.33923i) q^{35} +(-6.86319 - 7.82597i) q^{37} +(7.48830 + 15.1848i) q^{39} +(1.42931 - 0.955031i) q^{41} +(6.87109 - 2.84610i) q^{43} +(3.39520 - 3.87148i) q^{45} +(-1.56957 + 5.85772i) q^{47} +(2.16497 + 6.65679i) q^{49} +(-9.34614 + 6.30722i) q^{51} +(3.17906 - 2.43938i) q^{53} +(3.47480 - 3.47480i) q^{55} +(-0.0799415 - 0.0159014i) q^{57} +(-1.15874 + 8.80152i) q^{59} +(2.90016 - 5.88094i) q^{61} +(3.36674 + 11.3601i) q^{63} +(-5.35227 + 4.69381i) q^{65} +(0.368382 + 0.212686i) q^{67} +13.7380i q^{69} +(2.59138 - 0.515457i) q^{71} +(13.2423 - 6.53037i) q^{73} +(-9.02047 - 4.44840i) q^{75} +(2.49701 + 11.0281i) q^{77} +(-10.5629 + 3.58563i) q^{79} +(-0.615892 - 2.29854i) q^{81} +(-9.53271 - 3.94858i) q^{83} +(-3.57873 - 3.10948i) q^{85} +(9.49854 + 12.3787i) q^{87} +(1.43148 + 0.383563i) q^{89} +(-2.56470 - 16.1784i) q^{91} +(-13.3015 + 17.3349i) q^{93} +(-0.00224147 - 0.0341982i) q^{95} +(-0.667402 + 0.998837i) q^{97} +(3.73387 + 18.7714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	−2.58952	−	0.879025i	−1.49506	−	0.507505i	−0.550217	−	0.835022i	$-0.685455\pi$
$3$	−2.58952	−	0.879025i	−1.49506	−	0.507505i	−0.944845	+	0.327517i	$0.893788\pi$
$4$		0			0
$5$	0.0752031	−	1.14738i	0.0336318	−	0.513123i	−0.947497	−	0.319766i	$-0.896396\pi$
$5$	0.0752031	−	1.14738i	0.0336318	−	0.513123i	0.981128	−	0.193357i	$-0.0619376\pi$
$6$		0			0
$7$	2.14067	+	1.55484i	0.809099	+	0.587673i
$7$	2.14067	+	1.55484i	0.809099	+	0.587673i
$8$		0			0
$9$	3.55289	+	2.72623i	1.18430	+	0.908742i
$10$		0			0
$11$	3.21317	+	2.81787i	0.968806	+	0.849620i	0.988658	−	0.150182i	$-0.0479861\pi$
$11$	3.21317	+	2.81787i	0.968806	+	0.849620i	−0.0198519	+	0.999803i	$0.506319\pi$
$12$		0			0
$13$	−4.37784	−	4.37784i	−1.21420	−	1.21420i	−0.969634	−	0.244562i	$-0.921356\pi$
$13$	−4.37784	−	4.37784i	−1.21420	−	1.21420i	−0.244562	−	0.969634i	$-0.578644\pi$
$14$		0			0
$15$	−1.20331	+	2.90506i	−0.310694	+	0.750082i
$16$		0			0
$17$	2.49493	−	3.28258i	0.605108	−	0.796143i
$17$	2.49493	−	3.28258i	0.605108	−	0.796143i
$18$		0			0
$19$	0.0295505	−	0.00389040i	0.00677935	−	0.000892519i	−0.127136	−	0.991885i	$-0.540578\pi$
$19$	0.0295505	−	0.00389040i	0.00677935	−	0.000892519i	0.133915	+	0.990993i	$0.457245\pi$
$20$		0			0
$21$	−4.17659	−	5.90799i	−0.911406	−	1.28923i
$22$		0			0
$23$	−1.61481	−	4.75708i	−0.336711	−	0.991920i	−0.975016	−	0.222136i	$-0.928697\pi$
$23$	−1.61481	−	4.75708i	−0.336711	−	0.991920i	0.638304	−	0.769784i	$-0.279636\pi$
$24$		0			0
$25$	3.64640	+	0.480058i	0.729281	+	0.0960117i
$26$		0			0
$27$	−2.24599	−	3.36137i	−0.432242	−	0.646896i
$28$		0			0
$29$	−4.74410	−	3.16991i	−0.880958	−	0.588637i	0.0307267	−	0.999528i	$-0.490218\pi$
$29$	−4.74410	−	3.16991i	−0.880958	−	0.588637i	−0.911685	+	0.410890i	$0.865218\pi$
$30$		0			0
$31$	2.56833	−	7.56606i	0.461286	−	1.35890i	−0.428919	−	0.903343i	$-0.641105\pi$
$31$	2.56833	−	7.56606i	0.461286	−	1.35890i	0.890205	−	0.455561i	$-0.150561\pi$
$32$		0			0
$33$	−5.84359	−	10.1214i	−1.01724	−	1.76191i
$34$		0			0
$35$	1.94497	−	2.33923i	0.328760	−	0.395402i
$36$		0			0
$37$	−6.86319	−	7.82597i	−1.12830	−	1.28658i	−0.953304	−	0.302012i	$-0.902342\pi$
$37$	−6.86319	−	7.82597i	−1.12830	−	1.28658i	−0.174997	−	0.984569i	$-0.555992\pi$
$38$		0			0
$39$	7.48830	+	15.1848i	1.19909	+	2.43151i
$40$		0			0
$41$	1.42931	−	0.955031i	0.223220	−	0.149151i	−0.438932	−	0.898520i	$-0.644643\pi$
$41$	1.42931	−	0.955031i	0.223220	−	0.149151i	0.662152	+	0.749369i	$0.269643\pi$
$42$		0			0
$43$	6.87109	−	2.84610i	1.04783	−	0.434026i	0.208715	−	0.977977i	$-0.433072\pi$
$43$	6.87109	−	2.84610i	1.04783	−	0.434026i	0.839117	+	0.543950i	$0.183072\pi$
$44$		0			0
$45$	3.39520	−	3.87148i	0.506127	−	0.577127i
$46$		0			0
$47$	−1.56957	+	5.85772i	−0.228946	+	0.854436i	0.751840	+	0.659346i	$0.229167\pi$
$47$	−1.56957	+	5.85772i	−0.228946	+	0.854436i	−0.980785	+	0.195090i	$0.937500\pi$
$48$		0			0
$49$	2.16497	+	6.65679i	0.309281	+	0.950971i
$50$		0			0
$51$	−9.34614	+	6.30722i	−1.30872	+	0.883188i
$52$		0			0
$53$	3.17906	−	2.43938i	0.436677	−	0.335074i	−0.366915	−	0.930255i	$-0.619586\pi$
$53$	3.17906	−	2.43938i	0.436677	−	0.335074i	0.803592	+	0.595180i	$0.202919\pi$
$54$		0			0
$55$	3.47480	−	3.47480i	0.468542	−	0.468542i
$56$		0			0
$57$	−0.0799415	−	0.0159014i	−0.0105885	−	0.00210619i
$58$		0			0
$59$	−1.15874	+	8.80152i	−0.150855	+	1.14586i	0.733716	+	0.679456i	$0.237784\pi$
$59$	−1.15874	+	8.80152i	−0.150855	+	1.14586i	−0.884572	+	0.466405i	$0.845549\pi$
$60$		0			0
$61$	2.90016	−	5.88094i	0.371327	−	0.752977i	−0.628362	−	0.777921i	$-0.716274\pi$
$61$	2.90016	−	5.88094i	0.371327	−	0.752977i	0.999689	+	0.0249444i	$0.00794087\pi$
$62$		0			0
$63$	3.36674	+	11.3601i	0.424169	+	1.43124i
$64$		0			0
$65$	−5.35227	+	4.69381i	−0.663867	+	0.582196i
$66$		0			0
$67$	0.368382	+	0.212686i	0.0450051	+	0.0259837i	0.522334	−	0.852741i	$-0.325062\pi$
$67$	0.368382	+	0.212686i	0.0450051	+	0.0259837i	−0.477329	+	0.878725i	$0.658395\pi$
$68$		0			0
$69$			13.7380i			1.65386i
$70$		0			0
$71$	2.59138	−	0.515457i	0.307540	−	0.0611735i	−0.0389078	−	0.999243i	$-0.512388\pi$
$71$	2.59138	−	0.515457i	0.307540	−	0.0611735i	0.346448	+	0.938069i	$0.387388\pi$
$72$		0			0
$73$	13.2423	−	6.53037i	1.54989	−	0.764322i	0.552298	−	0.833647i	$-0.313751\pi$
$73$	13.2423	−	6.53037i	1.54989	−	0.764322i	0.997594	+	0.0693247i	$0.0220845\pi$
$74$		0			0
$75$	−9.02047	−	4.44840i	−1.04159	−	0.513657i
$76$		0			0
$77$	2.49701	+	11.0281i	0.284561	+	1.25677i
$78$		0			0
$79$	−10.5629	+	3.58563i	−1.18842	+	0.403414i	−0.844485	−	0.535579i	$-0.820093\pi$
$79$	−10.5629	+	3.58563i	−1.18842	+	0.403414i	−0.343935	+	0.938993i	$0.611760\pi$
$80$		0			0
$81$	−0.615892	−	2.29854i	−0.0684324	−	0.255393i
$82$		0			0
$83$	−9.53271	−	3.94858i	−1.04635	−	0.433413i	−0.207763	−	0.978179i	$-0.566618\pi$
$83$	−9.53271	−	3.94858i	−1.04635	−	0.433413i	−0.838588	+	0.544767i	$0.816618\pi$
$84$		0			0
$85$	−3.57873	−	3.10948i	−0.388168	−	0.337271i
$86$		0			0
$87$	9.49854	+	12.3787i	1.01835	+	1.32714i
$88$		0			0
$89$	1.43148	+	0.383563i	0.151736	+	0.0406576i	0.333888	−	0.942613i	$-0.391639\pi$
$89$	1.43148	+	0.383563i	0.151736	+	0.0406576i	−0.182151	+	0.983271i	$0.558306\pi$
$90$		0			0
$91$	−2.56470	−	16.1784i	−0.268854	−	1.69595i
$92$		0			0
$93$	−13.3015	+	17.3349i	−1.37930	+	1.79754i
$94$		0			0
$95$	−0.00224147	−	0.0341982i	−0.000229970	−	0.00350866i
$96$		0			0
$97$	−0.667402	+	0.998837i	−0.0677644	+	0.101417i	−0.863804	−	0.503828i	$-0.831925\pi$
$97$	−0.667402	+	0.998837i	−0.0677644	+	0.101417i	0.796040	+	0.605244i	$0.206925\pi$
$98$		0			0
$99$	3.73387	+	18.7714i	0.375268	+	1.88660i
$100$		0			0
$101$	−7.61824	+	13.1952i	−0.758043	+	1.31297i	0.185804	+	0.982587i	$0.440511\pi$
$101$	−7.61824	+	13.1952i	−0.758043	+	1.31297i	−0.943847	+	0.330382i	$0.892822\pi$
$102$		0			0
$103$	7.44198	−	4.29663i	0.733280	−	0.423359i	−0.0863410	−	0.996266i	$-0.527517\pi$
$103$	7.44198	−	4.29663i	0.733280	−	0.423359i	0.819621	+	0.572906i	$0.194184\pi$
$104$		0			0
$105$	−7.09279	+	4.34782i	−0.692185	+	0.424304i
$106$		0			0
$107$	9.19635	+	0.602760i	0.889044	+	0.0582710i	0.503077	−	0.864241i	$-0.332201\pi$
$107$	9.19635	+	0.602760i	0.889044	+	0.0582710i	0.385967	+	0.922513i	$0.373868\pi$
$108$		0			0
$109$	17.5579	−	1.15081i	1.68174	−	0.110227i	0.805657	−	0.592383i	$-0.201813\pi$
$109$	17.5579	−	1.15081i	1.68174	−	0.110227i	0.876086	+	0.482156i	$0.160146\pi$
$110$		0			0
$111$	10.8932	+	26.2984i	1.03393	+	2.49614i
$112$		0			0
$113$	−0.982493	+	4.93933i	−0.0924252	+	0.464653i	0.906659	+	0.421864i	$0.138624\pi$
$113$	−0.982493	+	4.93933i	−0.0924252	+	0.464653i	−0.999084	+	0.0427884i	$0.986376\pi$
$114$		0			0
$115$	−5.57961	+	1.49505i	−0.520301	+	0.139414i
$116$		0			0
$117$	−3.61899	−	27.4890i	−0.334576	−	2.54136i
$118$		0			0
$119$	10.4447	−	3.14773i	0.957464	−	0.288552i
$120$		0			0
$121$	0.948253	+	7.20270i	0.0862048	+	0.654791i
$122$		0			0
$123$	−4.54072	+	1.21668i	−0.409423	+	0.109704i
$124$		0			0
$125$	1.94664	−	9.78643i	0.174113	−	0.875325i
$126$		0			0
$127$	−0.689130	−	1.66371i	−0.0611504	−	0.147630i	0.890351	−	0.455275i	$-0.150459\pi$
$127$	−0.689130	−	1.66371i	−0.0611504	−	0.147630i	−0.951501	+	0.307645i	$0.900459\pi$
$128$		0			0
$129$	−20.2947	+	1.33018i	−1.78684	+	0.117116i
$130$		0			0
$131$	−8.90019	−	0.583349i	−0.777613	−	0.0509675i	−0.328573	−	0.944479i	$-0.606568\pi$
$131$	−8.90019	−	0.583349i	−0.777613	−	0.0509675i	−0.449041	+	0.893511i	$0.648234\pi$
$132$		0			0
$133$	0.0693069	+	0.0376181i	0.00600967	+	0.00326191i
$134$		0			0
$135$	−4.02566	+	2.32422i	−0.346474	+	0.200037i
$136$		0			0
$137$	−4.51203	+	7.81506i	−0.385488	+	0.667686i	−0.991837	−	0.127514i	$-0.959300\pi$
$137$	−4.51203	+	7.81506i	−0.385488	+	0.667686i	0.606348	+	0.795199i	$0.292634\pi$
$138$		0			0
$139$	−1.85683	−	9.33493i	−0.157495	−	0.791779i	−0.976083	−	0.217398i	$-0.930243\pi$
$139$	−1.85683	−	9.33493i	−0.157495	−	0.791779i	0.818588	−	0.574381i	$-0.194757\pi$
$140$		0			0
$141$	9.21353	−	13.7890i	0.775919	−	1.16124i
$142$		0			0
$143$	−1.73054	−	26.4030i	−0.144715	−	2.20793i
$144$		0			0
$145$	−3.99385	+	5.20489i	−0.331671	+	0.432243i
$146$		0			0
$147$	0.245254	−	19.1410i	0.0202282	−	1.57872i
$148$		0			0
$149$	18.6494	+	4.99709i	1.52782	+	0.409378i	0.922307	−	0.386459i	$-0.126302\pi$
$149$	18.6494	+	4.99709i	1.52782	+	0.409378i	0.605512	+	0.795836i	$0.292968\pi$
$150$		0			0
$151$	4.61923	+	6.01990i	0.375908	+	0.489892i	0.942547	−	0.334074i	$-0.108423\pi$
$151$	4.61923	+	6.01990i	0.375908	+	0.489892i	−0.566639	+	0.823966i	$0.691757\pi$
$152$		0			0
$153$	17.8133	−	4.86091i	1.44012	−	0.392981i
$154$		0			0
$155$	−8.48798	−	3.51583i	−0.681771	−	0.282399i
$156$		0			0
$157$	2.31501	+	8.63973i	0.184758	+	0.689526i	0.994682	+	0.102991i	$0.0328414\pi$
$157$	2.31501	+	8.63973i	0.184758	+	0.689526i	−0.809924	+	0.586534i	$0.800492\pi$
$158$		0			0
$159$	−10.3765	+	3.52236i	−0.822912	+	0.279341i
$160$		0			0
$161$	3.93970	−	12.6941i	0.310492	−	1.00044i
$162$		0			0
$163$	−4.06899	−	2.00660i	−0.318708	−	0.157169i	0.275897	−	0.961187i	$-0.411025\pi$
$163$	−4.06899	−	2.00660i	−0.318708	−	0.157169i	−0.594605	+	0.804018i	$0.702692\pi$
$164$		0			0
$165$	−12.0525	+	5.94365i	−0.938288	+	0.462712i
$166$		0			0
$167$	−19.5460	+	3.88794i	−1.51251	+	0.300858i	−0.880480	−	0.474083i	$-0.842780\pi$
$167$	−19.5460	+	3.88794i	−1.51251	+	0.300858i	−0.632034	+	0.774941i	$0.717780\pi$
$168$		0			0
$169$			25.3310i			1.94854i
$170$		0			0
$171$	0.115596	+	0.0667393i	0.00883983	+	0.00510368i
$172$		0			0
$173$	9.75442	−	8.55440i	0.741615	−	0.650379i	−0.202768	−	0.979227i	$-0.564994\pi$
$173$	9.75442	−	8.55440i	0.741615	−	0.650379i	0.944383	+	0.328848i	$0.106660\pi$
$174$		0			0
$175$	7.05935	+	6.69721i	0.533637	+	0.506262i
$176$		0			0
$177$	10.7373	−	21.7732i	0.807069	−	1.63657i
$178$		0			0
$179$	0.102909	−	0.781672i	0.00769179	−	0.0584249i	−0.987169	−	0.159682i	$-0.948953\pi$
$179$	0.102909	−	0.781672i	0.00769179	−	0.0584249i	0.994860	+	0.101257i	$0.0322865\pi$
$180$		0			0
$181$	−2.10283	−	0.418278i	−0.156302	−	0.0310904i	0.116319	−	0.993212i	$-0.462890\pi$
$181$	−2.10283	−	0.418278i	−0.156302	−	0.0310904i	−0.272621	+	0.962122i	$0.587890\pi$
$182$		0			0
$183$	−12.6795	+	12.6795i	−0.937297	+	0.937297i
$184$		0			0
$185$	−9.49547	+	7.28613i	−0.698121	+	0.535687i
$186$		0			0
$187$	17.2665	−	3.51710i	1.26265	−	0.257196i
$188$		0			0
$189$	0.418437	−	10.6877i	0.0304368	−	0.777419i
$190$		0			0
$191$	0.709983	−	2.64969i	0.0513726	−	0.191725i	−0.935471	−	0.353404i	$-0.885024\pi$
$191$	0.709983	−	2.64969i	0.0513726	−	0.191725i	0.986843	+	0.161679i	$0.0516908\pi$
$192$		0			0
$193$	3.13768	−	3.57783i	0.225855	−	0.257538i	−0.627803	−	0.778372i	$-0.716046\pi$
$193$	3.13768	−	3.57783i	0.225855	−	0.257538i	0.853658	+	0.520834i	$0.174379\pi$
$194$		0			0
$195$	17.9858	−	7.44996i	1.28799	−	0.533503i
$196$		0			0
$197$	−7.49484	+	5.00789i	−0.533985	+	0.356798i	−0.793141	−	0.609038i	$-0.791556\pi$
$197$	−7.49484	+	5.00789i	−0.533985	+	0.356798i	0.259156	+	0.965836i	$0.416556\pi$
$198$		0			0
$199$	2.98324	+	6.04941i	0.211476	+	0.428832i	0.976604	−	0.215047i	$-0.0689906\pi$
$199$	2.98324	+	6.04941i	0.211476	+	0.428832i	−0.765127	+	0.643879i	$0.777324\pi$
$200$		0			0
$201$	−0.766979	−	0.874572i	−0.0540985	−	0.0616875i
$202$		0			0
$203$	−5.22689	−	14.1620i	−0.366856	−	0.993981i
$204$		0			0
$205$	−0.988293	−	1.71177i	−0.0690254	−	0.119555i
$206$		0			0
$207$	7.23164	−	21.3037i	0.502634	−	1.48071i
$208$		0			0
$209$	0.105913	+	0.0707691i	0.00732618	+	0.00489520i
$210$		0			0
$211$	0.770798	+	1.15358i	0.0530640	+	0.0794158i	0.857053	−	0.515228i	$-0.172293\pi$
$211$	0.770798	+	1.15358i	0.0530640	+	0.0794158i	−0.803989	+	0.594644i	$0.797293\pi$
$212$		0			0
$213$	−7.16353	−	0.943097i	−0.490837	−	0.0646199i
$214$		0			0
$215$	−2.74882	−	8.09777i	−0.187468	−	0.552264i
$216$		0			0
$217$	17.2619	−	12.2031i	1.17182	−	0.828402i
$218$		0			0
$219$	−40.0316	+	5.27026i	−2.70508	+	0.356131i
$220$		0			0
$221$	−25.2930	+	3.44823i	−1.70139	+	0.231953i
$222$		0			0
$223$	−4.17662	+	10.0832i	−0.279687	+	0.675224i	−0.999827	−	0.0186049i	$-0.994078\pi$
$223$	−4.17662	+	10.0832i	−0.279687	+	0.675224i	0.720140	+	0.693829i	$0.244078\pi$
$224$		0			0
$225$	11.6465	+	11.6465i	0.776435	+	0.776435i
$226$		0			0
$227$	14.1084	+	12.3727i	0.936408	+	0.821208i	0.984093	−	0.177655i	$-0.0568510\pi$
$227$	14.1084	+	12.3727i	0.936408	+	0.821208i	−0.0476848	+	0.998862i	$0.515184\pi$
$228$		0			0
$229$	3.61362	+	2.77283i	0.238795	+	0.183234i	0.721225	−	0.692701i	$-0.243579\pi$
$229$	3.61362	+	2.77283i	0.238795	+	0.183234i	−0.482431	+	0.875934i	$0.660246\pi$
$230$		0			0
$231$	3.22790	−	30.7524i	0.212380	−	2.02336i
$232$		0			0
$233$	−1.13373	+	17.2974i	−0.0742731	+	1.13319i	0.784261	+	0.620431i	$0.213042\pi$
$233$	−1.13373	+	17.2974i	−0.0742731	+	1.13319i	−0.858534	+	0.512757i	$0.828624\pi$
$234$		0			0
$235$	6.60298	+	2.24141i	0.430731	+	0.146213i
$236$		0			0
$237$	30.5048			1.98150
$238$		0			0
$239$	−23.2282			−1.50251			−0.751254	−	0.660013i	$-0.770551\pi$
$239$	−23.2282			−1.50251			−0.751254	+	0.660013i	$0.770551\pi$
$240$		0			0
$241$	−16.7112	−	5.67270i	−1.07646	−	0.365411i	−0.273767	−	0.961796i	$-0.588270\pi$
$241$	−16.7112	−	5.67270i	−1.07646	−	0.365411i	−0.802698	+	0.596386i	$0.796603\pi$
$242$		0			0
$243$	−1.21882	+	18.5956i	−0.0781873	+	1.19291i
$244$		0			0
$245$	7.80067	−	1.98342i	0.498366	−	0.126716i
$246$		0			0
$247$	−0.146399	−	0.112336i	−0.00931515	−	0.00714777i
$248$		0			0
$249$	21.2143	+	18.6044i	1.34440	+	1.17901i
$250$		0			0
$251$	8.42316	+	8.42316i	0.531665	+	0.531665i	0.921068	−	0.389403i	$-0.127319\pi$
$251$	8.42316	+	8.42316i	0.531665	+	0.531665i	−0.389403	+	0.921068i	$0.627319\pi$
$252$		0			0
$253$	8.21619	−	19.8356i	0.516547	−	1.24706i
$254$		0			0
$255$	6.53391	+	11.1979i	0.409169	+	0.701238i
$256$		0			0
$257$	−19.4588	+	2.56180i	−1.21381	+	0.159801i	−0.710117	−	0.704083i	$-0.751358\pi$
$257$	−19.4588	+	2.56180i	−1.21381	+	0.159801i	−0.503691	+	0.863884i	$0.668025\pi$
$258$		0			0
$259$	−2.52375	−	27.4240i	−0.156818	−	1.70404i
$260$		0			0
$261$	−8.21338	−	24.1958i	−0.508396	−	1.49768i
$262$		0			0
$263$	9.11528	+	1.20005i	0.562072	+	0.0739982i	0.406209	−	0.913780i	$-0.366851\pi$
$263$	9.11528	+	1.20005i	0.562072	+	0.0739982i	0.155864	+	0.987779i	$0.450184\pi$
$264$		0			0
$265$	−2.55981	−	3.83103i	−0.157248	−	0.235338i
$266$		0			0
$267$	−3.36968	−	2.25155i	−0.206221	−	0.137793i
$268$		0			0
$269$	−6.12084	+	18.0314i	−0.373194	+	1.09939i	0.584447	+	0.811432i	$0.301311\pi$
$269$	−6.12084	+	18.0314i	−0.373194	+	1.09939i	−0.957641	+	0.287963i	$0.907022\pi$
$270$		0			0
$271$	2.56078	+	4.43541i	0.155557	+	0.269432i	0.933262	−	0.359198i	$-0.116950\pi$
$271$	2.56078	+	4.43541i	0.155557	+	0.269432i	−0.777705	+	0.628629i	$0.783616\pi$
$272$		0			0
$273$	−7.57983	+	44.1487i	−0.458752	+	2.67200i
$274$		0			0
$275$	10.3638	+	11.8176i	0.624959	+	0.712629i
$276$		0			0
$277$	−14.1507	−	28.6948i	−0.850235	−	1.72411i	−0.672595	−	0.740011i	$-0.734820\pi$
$277$	−14.1507	−	28.6948i	−0.850235	−	1.72411i	−0.177640	−	0.984096i	$-0.556846\pi$
$278$		0			0
$279$	29.7518	−	19.8795i	1.78119	−	1.19015i
$280$		0			0
$281$	23.9497	−	9.92030i	1.42872	−	0.591796i	0.471685	−	0.881767i	$-0.343646\pi$
$281$	23.9497	−	9.92030i	1.42872	−	0.591796i	0.957035	+	0.289971i	$0.0936458\pi$
$282$		0			0
$283$	−0.288818	+	0.329334i	−0.0171685	+	0.0195769i	−0.760360	−	0.649501i	$-0.774978\pi$
$283$	−0.288818	+	0.329334i	−0.0171685	+	0.0195769i	0.743192	+	0.669078i	$0.233311\pi$
$284$		0			0
$285$	−0.0242567	+	0.0905273i	−0.00143684	+	0.00536237i
$286$		0			0
$287$	4.54459	+	0.177926i	0.268259	+	0.0105026i
$288$		0			0
$289$	−4.55069	−	16.3796i	−0.267687	−	0.963506i
$290$		0			0
$291$	2.60626	−	1.99985i	0.152781	−	0.117233i
$292$		0			0
$293$	0.0902951	−	0.0902951i	0.00527510	−	0.00527510i	−0.704464	−	0.709739i	$-0.748813\pi$
$293$	0.0902951	−	0.0902951i	0.00527510	−	0.00527510i	0.709739	+	0.704464i	$0.248813\pi$
$294$		0			0
$295$	10.0115	+	1.99142i	0.582894	+	0.115945i
$296$		0			0
$297$	2.25515	−	17.1296i	0.130857	−	0.993958i
$298$		0			0
$299$	−13.7564	+	27.8952i	−0.795551	+	1.61322i
$300$		0			0
$301$	19.1340	+	4.59086i	1.10286	+	0.264613i
$302$		0			0
$303$	31.3265	−	27.4726i	1.79966	−	1.57826i
$304$		0			0
$305$	−6.52955	−	3.76984i	−0.373881	−	0.215860i
$306$		0			0
$307$			9.94904i			0.567822i	0.958851	+	0.283911i	$0.0916320\pi$
$307$			9.94904i			0.567822i	−0.958851	+	0.283911i	$0.908368\pi$
$308$		0			0
$309$	−23.0480	+	4.58454i	−1.31116	+	0.260805i
$310$		0			0
$311$	−5.80504	+	2.86273i	−0.329173	+	0.162330i	−0.599364	−	0.800476i	$-0.704580\pi$
$311$	−5.80504	+	2.86273i	−0.329173	+	0.162330i	0.270191	+	0.962807i	$0.412913\pi$
$312$		0			0
$313$	12.3724	+	6.10140i	0.699330	+	0.344871i	0.756955	−	0.653467i	$-0.226686\pi$
$313$	12.3724	+	6.10140i	0.699330	+	0.344871i	−0.0576251	+	0.998338i	$0.518353\pi$
$314$		0			0
$315$	13.2875	−	3.00860i	0.748668	−	0.169516i
$316$		0			0
$317$	−26.3903	+	8.95828i	−1.48222	+	0.503147i	−0.941197	−	0.337858i	$-0.890298\pi$
$317$	−26.3903	+	8.95828i	−1.48222	+	0.503147i	−0.541027	+	0.841005i	$0.681964\pi$
$318$		0			0
$319$	−6.31120	−	23.5537i	−0.353359	−	1.31876i
$320$		0			0
$321$	−23.2843	−	9.64468i	−1.29960	−	0.538314i
$322$		0			0
$323$	0.0609558	−	0.106708i	0.00339167	−	0.00593740i
$324$		0			0
$325$	−13.8618	−	18.0650i	−0.768913	−	1.00207i
$326$		0			0
$327$	−46.4782	−	12.4538i	−2.57025	−	0.688696i
$328$		0			0
$329$	−12.4677	+	10.0990i	−0.687369	+	0.556778i
$330$		0			0
$331$	−8.42474	+	10.9793i	−0.463066	+	0.603479i	−0.965265	−	0.261273i	$-0.915858\pi$
$331$	−8.42474	+	10.9793i	−0.463066	+	0.603479i	0.502199	+	0.864752i	$0.332524\pi$
$332$		0			0
$333$	−3.04878	−	46.5154i	−0.167072	−	2.54903i
$334$		0			0
$335$	0.271734	−	0.406679i	0.0148464	−	0.0222192i
$336$		0			0
$337$	−3.87026	−	19.4571i	−0.210827	−	1.05990i	−0.930698	−	0.365789i	$-0.880799\pi$
$337$	−3.87026	−	19.4571i	−0.210827	−	1.05990i	0.719871	−	0.694108i	$-0.244201\pi$
$338$		0			0
$339$	6.88598	−	11.9269i	0.373995	−	0.647778i
$340$		0			0
$341$	29.5727	−	17.0738i	1.60145	−	0.924597i
$342$		0			0
$343$	−5.71574	+	17.6162i	−0.308621	+	0.951185i
$344$		0			0
$345$	15.7627	+	1.03314i	0.848636	+	0.0556225i
$346$		0			0
$347$	35.4079	−	2.32076i	1.90080	−	0.124585i	0.930468	−	0.366372i	$-0.119400\pi$
$347$	35.4079	−	2.32076i	1.90080	−	0.124585i	0.970329	+	0.241787i	$0.0777336\pi$
$348$		0			0
$349$	3.83349	+	9.25486i	0.205202	+	0.495401i	0.992656	−	0.120972i	$-0.0386012\pi$
$349$	3.83349	+	9.25486i	0.205202	+	0.495401i	−0.787454	+	0.616373i	$0.788601\pi$
$350$		0			0
$351$	−4.88293	+	24.5482i	−0.260632	+	1.31028i
$352$		0			0
$353$	−30.0638	+	8.05556i	−1.60013	+	0.428754i	−0.945083	−	0.326831i	$-0.894019\pi$
$353$	−30.0638	+	8.05556i	−1.60013	+	0.428754i	−0.655050	+	0.755585i	$0.727353\pi$
$354$		0			0
$355$	−0.396544	−	3.01205i	−0.0210464	−	0.159863i
$356$		0			0
$357$	−29.8137	−	1.03002i	−1.57791	−	0.0545144i
$358$		0			0
$359$	−0.312279	−	2.37199i	−0.0164815	−	0.125189i	0.981226	−	0.192860i	$-0.0617764\pi$
$359$	−0.312279	−	2.37199i	−0.0164815	−	0.125189i	−0.997708	+	0.0676713i	$0.978443\pi$
$360$		0			0
$361$	−18.3517	+	4.91733i	−0.965881	+	0.258807i
$362$		0			0
$363$	3.87583	−	19.4851i	0.203428	−	1.02270i
$364$		0			0
$365$	−6.49694	−	15.6850i	−0.340065	−	0.820991i
$366$		0			0
$367$	10.6366	−	0.697158i	0.555225	−	0.0363914i	0.214791	−	0.976660i	$-0.431093\pi$
$367$	10.6366	−	0.697158i	0.555225	−	0.0363914i	0.340433	+	0.940269i	$0.389426\pi$
$368$		0			0
$369$	7.68179	+	0.503491i	0.399898	+	0.0262107i
$370$		0			0
$371$	10.5982	−	0.278995i	0.550229	−	0.0144847i
$372$		0			0
$373$	6.90833	−	3.98853i	0.357700	−	0.206518i	−0.310372	−	0.950615i	$-0.600453\pi$
$373$	6.90833	−	3.98853i	0.357700	−	0.206518i	0.668071	+	0.744097i	$0.267120\pi$
$374$		0			0
$375$	−13.6434	+	23.6310i	−0.704542	+	1.22030i
$376$		0			0
$377$	6.89158	+	34.6463i	0.354934	+	1.78438i
$378$		0			0
$379$	−1.69584	+	2.53800i	−0.0871093	+	0.130368i	−0.872465	−	0.488676i	$-0.837480\pi$
$379$	−1.69584	+	2.53800i	−0.0871093	+	0.130368i	0.785356	+	0.619044i	$0.212480\pi$
$380$		0			0
$381$	0.322079	+	4.91397i	0.0165006	+	0.251751i
$382$		0			0
$383$	0.547009	−	0.712876i	0.0279508	−	0.0364262i	−0.779169	−	0.626814i	$-0.784359\pi$
$383$	0.547009	−	0.712876i	0.0279508	−	0.0364262i	0.807120	+	0.590388i	$0.201025\pi$
$384$		0			0
$385$	12.8412	−	2.03567i	0.654447	−	0.103747i
$386$		0			0
$387$	32.1713	+	8.62029i	1.63536	+	0.438194i
$388$		0			0
$389$	13.5010	+	17.5948i	0.684527	+	0.892093i	0.998352	−	0.0573878i	$-0.0182771\pi$
$389$	13.5010	+	17.5948i	0.684527	+	0.892093i	−0.313825	+	0.949481i	$0.601610\pi$
$390$		0			0
$391$	−19.6443	−	6.56781i	−0.993457	−	0.332149i
$392$		0			0
$393$	22.5345	+	9.33409i	1.13671	+	0.470842i
$394$		0			0
$395$	3.31970	+	12.3893i	0.167032	+	0.623373i
$396$		0			0
$397$	5.44903	−	1.84969i	0.273479	−	0.0928335i	−0.181331	−	0.983422i	$-0.558041\pi$
$397$	5.44903	−	1.84969i	0.273479	−	0.0928335i	0.454810	+	0.890589i	$0.349707\pi$
$398$		0			0
$399$	−0.146405	−	0.158336i	−0.00732940	−	0.00792669i
$400$		0			0
$401$	−1.87640	−	0.925338i	−0.0937029	−	0.0462092i	0.394833	−	0.918753i	$-0.370802\pi$
$401$	−1.87640	−	0.925338i	−0.0937029	−	0.0462092i	−0.488536	+	0.872544i	$0.662469\pi$
$402$		0			0
$403$	−44.3668	+	21.8793i	−2.21007	+	1.08988i
$404$		0			0
$405$	−2.68361	+	0.533803i	−0.133350	+	0.0265249i
$406$		0			0
$407$		−	44.4857i		−	2.20508i
$408$		0			0
$409$	9.12284	+	5.26707i	0.451095	+	0.260440i	0.708293	−	0.705919i	$-0.249466\pi$
$409$	9.12284	+	5.26707i	0.451095	+	0.260440i	−0.257197	+	0.966359i	$0.582799\pi$
$410$		0			0
$411$	18.5536	−	16.2711i	0.915183	−	0.802594i
$412$		0			0
$413$	−16.1654	+	17.0395i	−0.795448	+	0.838461i
$414$		0			0
$415$	−5.24740	+	10.6407i	−0.257585	+	0.522330i
$416$		0			0
$417$	−3.39732	+	25.8052i	−0.166368	+	1.26369i
$418$		0			0
$419$	1.14775	+	0.228302i	0.0560714	+	0.0111533i	0.223046	−	0.974808i	$-0.428400\pi$
$419$	1.14775	+	0.228302i	0.0560714	+	0.0111533i	−0.166975	+	0.985961i	$0.553400\pi$
$420$		0			0
$421$	8.49055	−	8.49055i	0.413804	−	0.413804i	−0.469257	−	0.883061i	$-0.655478\pi$
$421$	8.49055	−	8.49055i	0.413804	−	0.413804i	0.883061	+	0.469257i	$0.155478\pi$
$422$		0			0
$423$	−21.5460	+	16.5328i	−1.04760	+	0.803853i
$424$		0			0
$425$	10.6733	−	10.7719i	0.517733	−	0.522514i
$426$		0			0
$427$	15.3522	−	8.07990i	0.742944	−	0.391014i
$428$		0			0
$429$	−18.7276	+	69.8923i	−0.904176	+	3.37443i
$430$		0			0
$431$	−14.9204	+	17.0134i	−0.718689	+	0.819508i	−0.989713	−	0.143065i	$-0.954304\pi$
$431$	−14.9204	+	17.0134i	−0.718689	+	0.819508i	0.271024	+	0.962572i	$0.412638\pi$
$432$		0			0
$433$	21.8605	−	9.05491i	1.05055	−	0.435151i	0.210461	−	0.977602i	$-0.432504\pi$
$433$	21.8605	−	9.05491i	1.05055	−	0.435151i	0.840087	+	0.542451i	$0.182504\pi$
$434$		0			0
$435$	14.9174	−	9.96749i	0.715235	−	0.477905i
$436$		0			0
$437$	−0.0662254	−	0.134292i	−0.00316799	−	0.00642405i
$438$		0			0
$439$	2.47282	+	2.81971i	0.118021	+	0.134577i	0.807833	−	0.589411i	$-0.200640\pi$
$439$	2.47282	+	2.81971i	0.118021	+	0.134577i	−0.689812	+	0.723989i	$0.742307\pi$
$440$		0			0
$441$	−10.4560	+	29.5530i	−0.497907	+	1.40729i
$442$		0			0
$443$	−5.09566	−	8.82594i	−0.242102	−	0.419333i	0.719211	−	0.694792i	$-0.244504\pi$
$443$	−5.09566	−	8.82594i	−0.242102	−	0.419333i	−0.961313	+	0.275459i	$0.911170\pi$
$444$		0			0
$445$	0.547744	−	1.61360i	0.0259655	−	0.0764920i
$446$		0			0
$447$	−43.9005	−	29.3334i	−2.07642	−	1.38742i
$448$		0			0
$449$	16.4777	+	24.6606i	0.777629	+	1.16380i	0.982727	+	0.185063i	$0.0592488\pi$
$449$	16.4777	+	24.6606i	0.777629	+	1.16380i	−0.205098	+	0.978742i	$0.565751\pi$
$450$		0			0
$451$	7.28375	+	0.958924i	0.342979	+	0.0451540i
$452$		0			0
$453$	−6.66997	−	19.6491i	−0.313382	−	0.923195i
$454$		0			0
$455$	−18.7556	+	1.72602i	−0.879275	+	0.0809171i
$456$		0			0
$457$	−6.21335	+	0.818003i	−0.290648	+	0.0382646i	−0.274440	−	0.961604i	$-0.588493\pi$
$457$	−6.21335	+	0.818003i	−0.290648	+	0.0382646i	−0.0162077	+	0.999869i	$0.505159\pi$
$458$		0			0
$459$	−16.6376	−	1.01370i	−0.776575	−	0.0473157i
$460$		0			0
$461$	−15.5445	+	37.5278i	−0.723981	+	1.74785i	−0.0623027	+	0.998057i	$0.519844\pi$
$461$	−15.5445	+	37.5278i	−0.723981	+	1.74785i	−0.661678	+	0.749788i	$0.730156\pi$
$462$		0			0
$463$	20.5115	+	20.5115i	0.953249	+	0.953249i	0.998955	−	0.0457059i	$-0.0145537\pi$
$463$	20.5115	+	20.5115i	0.953249	+	0.953249i	−0.0457059	+	0.998955i	$0.514554\pi$
$464$		0			0
$465$	18.8893	+	16.5655i	0.875971	+	0.768206i
$466$		0			0
$467$	−5.46455	−	4.19310i	−0.252869	−	0.194033i	0.474546	−	0.880230i	$-0.342612\pi$
$467$	−5.46455	−	4.19310i	−0.252869	−	0.194033i	−0.727416	+	0.686197i	$0.759279\pi$
$468$		0			0
$469$	0.457895	+	1.02806i	0.0211436	+	0.0474716i
$470$		0			0
$471$	1.59977	−	24.4077i	0.0737134	−	1.12465i
$472$		0			0
$473$	30.0979	+	10.2169i	1.38390	+	0.469772i
$474$		0			0
$475$	0.109621			0.00502974
$476$		0			0
$477$	17.9451			0.821652
$478$		0			0
$479$	34.9158	+	11.8523i	1.59534	+	0.541546i	0.970892	−	0.239518i	$-0.0769893\pi$
$479$	34.9158	+	11.8523i	1.59534	+	0.541546i	0.624451	+	0.781064i	$0.285323\pi$
$480$		0			0
$481$	−4.21489	+	64.3068i	−0.192183	+	2.93214i
$482$		0			0
$483$	−21.3604	+	29.4086i	−0.971932	+	1.33814i
$484$		0			0
$485$	1.09585	+	0.840878i	0.0497601	+	0.0381823i
$486$		0			0
$487$	−8.79309	−	7.71134i	−0.398453	−	0.349434i	0.436549	−	0.899680i	$-0.356200\pi$
$487$	−8.79309	−	7.71134i	−0.398453	−	0.349434i	−0.835002	+	0.550246i	$0.814534\pi$
$488$		0			0
$489$	8.77289	+	8.77289i	0.396724	+	0.396724i
$490$		0			0
$491$	−1.80411	+	4.35552i	−0.0814185	+	0.196562i	−0.959346	−	0.282231i	$-0.908926\pi$
$491$	−1.80411	+	4.35552i	−0.0814185	+	0.196562i	0.877928	+	0.478793i	$0.158926\pi$
$492$		0			0
$493$	−22.2417	+	7.66422i	−1.00171	+	0.345179i
$494$		0			0
$495$	21.8187	−	2.87249i	0.980677	−	0.129109i
$496$		0			0
$497$	6.34874	+	2.92574i	0.284780	+	0.131237i
$498$		0			0
$499$	6.10563	+	17.9866i	0.273326	+	0.805191i	0.993747	+	0.111655i	$0.0356151\pi$
$499$	6.10563	+	17.9866i	0.273326	+	0.805191i	−0.720421	+	0.693537i	$0.756052\pi$
$500$		0			0
$501$	54.0324	+	7.11350i	2.41399	+	0.317808i
$502$		0			0
$503$	−10.0737	−	15.0764i	−0.449166	−	0.672224i	0.535924	−	0.844266i	$-0.319963\pi$
$503$	−10.0737	−	15.0764i	−0.449166	−	0.672224i	−0.985090	+	0.172042i	$0.944963\pi$
$504$		0			0
$505$	14.5669	+	9.73331i	0.648220	+	0.433127i
$506$		0			0
$507$	22.2666	−	65.5953i	0.988895	−	2.91319i
$508$		0			0
$509$	4.65355	+	8.06018i	0.206265	+	0.357261i	0.950535	−	0.310617i	$-0.100536\pi$
$509$	4.65355	+	8.06018i	0.206265	+	0.357261i	−0.744270	+	0.667879i	$0.767202\pi$
$510$		0			0
$511$	38.5011	+	6.61019i	1.70319	+	0.292418i
$512$		0			0
$513$	−0.0794474	−	0.0905924i	−0.00350769	−	0.00399975i
$514$		0			0
$515$	−4.37019	−	8.86188i	−0.192574	−	0.390501i
$516$		0			0
$517$	−21.5496	+	14.3990i	−0.947751	+	0.633267i
$518$		0			0
$519$	−32.7788	+	13.5774i	−1.43883	+	0.595983i
$520$		0			0
$521$	15.1779	−	17.3071i	0.664957	−	0.758238i	−0.316777	−	0.948500i	$-0.602601\pi$
$521$	15.1779	−	17.3071i	0.664957	−	0.758238i	0.981733	+	0.190262i	$0.0609339\pi$
$522$		0			0
$523$	−7.58564	+	28.3100i	−0.331697	+	1.23791i	0.575709	+	0.817654i	$0.304726\pi$
$523$	−7.58564	+	28.3100i	−0.331697	+	1.23791i	−0.907406	+	0.420255i	$0.861941\pi$
$524$		0			0
$525$	−12.3933	−	23.5479i	−0.540890	−	1.02772i
$526$		0			0
$527$	−18.4284	−	27.3075i	−0.802754	−	1.18953i
$528$		0			0
$529$	−1.77507	+	1.36206i	−0.0771772	+	0.0592201i
$530$		0			0
$531$	−28.1118	+	28.1118i	−1.21995	+	1.21995i
$532$		0			0
$533$	−10.4383	−	2.07630i	−0.452131	−	0.0899344i
$534$		0			0
$535$	1.38319	−	10.5064i	0.0598004	−	0.454229i
$536$		0			0
$537$	−0.953595	+	1.93370i	−0.0411506	+	0.0834453i
$538$		0			0
$539$	−11.8016	+	27.4900i	−0.508331	+	1.18408i
$540$		0			0
$541$	2.65307	−	2.32668i	0.114064	−	0.100032i	−0.600414	−	0.799689i	$-0.704997\pi$
$541$	2.65307	−	2.32668i	0.114064	−	0.100032i	0.714478	+	0.699658i	$0.246664\pi$
$542$		0			0
$543$	5.07764	+	2.93158i	0.217902	+	0.125806i
$544$		0			0
$545$		−	20.2321i		−	0.866647i
$546$		0			0
$547$	−17.3972	+	3.46053i	−0.743852	+	0.147961i	−0.552445	−	0.833549i	$-0.686305\pi$
$547$	−17.3972	+	3.46053i	−0.743852	+	0.147961i	−0.191407	+	0.981511i	$0.561305\pi$
$548$		0			0
$549$	26.3367	−	12.9878i	1.12402	−	0.554307i
$550$		0			0
$551$	−0.152523	−	0.0752160i	−0.00649769	−	0.00320431i
$552$		0			0
$553$	−28.1868	−	8.74795i	−1.19863	−	0.372001i
$554$		0			0
$555$	30.9934	−	10.5209i	1.31560	−	0.446585i
$556$		0			0
$557$	−4.83306	−	18.0372i	−0.204783	−	0.764262i	−0.989515	−	0.144427i	$-0.953866\pi$
$557$	−4.83306	−	18.0372i	−0.204783	−	0.764262i	0.784732	−	0.619835i	$-0.212801\pi$
$558$		0			0
$559$	−42.5404	−	17.6208i	−1.79927	−	0.745280i
$560$		0			0
$561$	−47.8037	−	6.07007i	−2.01827	−	0.256279i
$562$		0			0
$563$	2.00615	+	2.61447i	0.0845492	+	0.110187i	0.833713	−	0.552198i	$-0.186211\pi$
$563$	2.00615	+	2.61447i	0.0845492	+	0.110187i	−0.749163	+	0.662385i	$0.769544\pi$
$564$		0			0
$565$	5.59338	+	1.49874i	0.235315	+	0.0630526i
$566$		0			0
$567$	2.25543	−	5.87803i	0.0947191	−	0.246854i
$568$		0			0
$569$	9.53239	−	12.4229i	0.399619	−	0.520793i	−0.549592	−	0.835433i	$-0.685217\pi$
$569$	9.53239	−	12.4229i	0.399619	−	0.520793i	0.949211	+	0.314640i	$0.101884\pi$
$570$		0			0
$571$	1.71726	+	26.2003i	0.0718650	+	1.09645i	0.869703	+	0.493576i	$0.164310\pi$
$571$	1.71726	+	26.2003i	0.0718650	+	1.09645i	−0.797838	+	0.602872i	$0.794023\pi$
$572$		0			0
$573$	−4.16766	+	6.23735i	−0.174107	+	0.260569i
$574$		0			0
$575$	−3.60458	−	18.1214i	−0.150321	−	0.755716i
$576$		0			0
$577$	1.43655	−	2.48818i	0.0598044	−	0.103584i	−0.834573	−	0.550897i	$-0.814286\pi$
$577$	1.43655	−	2.48818i	0.0598044	−	0.103584i	0.894378	+	0.447313i	$0.147619\pi$
$578$		0			0
$579$	−11.2701	+	6.50679i	−0.468369	+	0.270413i
$580$		0			0
$581$	−14.2670	−	23.2744i	−0.591896	−	0.965585i
$582$		0			0
$583$	17.0887	+	1.12005i	0.707742	+	0.0463879i
$584$		0			0
$585$	−31.8124	+	2.08510i	−1.31528	+	0.0862081i
$586$		0			0
$587$	−8.15694	−	19.6926i	−0.336673	−	0.812801i	−0.998031	−	0.0627299i	$-0.980019\pi$
$587$	−8.15694	−	19.6926i	−0.336673	−	0.812801i	0.661357	−	0.750071i	$-0.269981\pi$
$588$		0			0
$589$	0.0464605	−	0.233573i	0.00191437	−	0.00962419i
$590$		0			0
$591$	23.8101	−	6.37991i	0.979418	−	0.262434i
$592$		0			0
$593$	−5.47281	−	41.5702i	−0.224742	−	1.70708i	−0.616782	−	0.787134i	$-0.711564\pi$
$593$	−5.47281	−	41.5702i	−0.224742	−	1.70708i	0.392041	−	0.919948i	$-0.371769\pi$
$594$		0			0
$595$	−2.82617	−	12.2207i	−0.115861	−	0.501001i
$596$		0			0
$597$	−2.40759	−	18.2874i	−0.0985360	−	0.748455i
$598$		0			0
$599$	33.6185	−	9.00806i	1.37362	−	0.368059i	0.504818	−	0.863226i	$-0.331560\pi$
$599$	33.6185	−	9.00806i	1.37362	−	0.368059i	0.868798	+	0.495166i	$0.164893\pi$
$600$		0			0
$601$	−0.504002	+	2.53379i	−0.0205587	+	0.103355i	−0.989702	−	0.143142i	$-0.954280\pi$
$601$	−0.504002	+	2.53379i	−0.0205587	+	0.103355i	0.969144	+	0.246497i	$0.0792796\pi$
$602$		0			0
$603$	0.728992	+	1.75994i	0.0296868	+	0.0716704i
$604$		0			0
$605$	8.33552	−	0.546339i	0.338887	−	0.0222118i
$606$		0			0
$607$	0.198445	+	0.0130068i	0.00805465	+	0.000527930i	0.0694299	−	0.997587i	$-0.477882\pi$
$607$	0.198445	+	0.0130068i	0.00805465	+	0.000527930i	−0.0613753	+	0.998115i	$0.519549\pi$
$608$		0			0
$609$	1.08636	+	41.2675i	0.0440215	+	1.67224i
$610$		0			0
$611$	32.5155	−	18.7729i	1.31544	−	0.759468i
$612$		0			0
$613$	2.20077	−	3.81185i	0.0888883	−	0.153959i	−0.818153	−	0.575000i	$-0.805002\pi$
$613$	2.20077	−	3.81185i	0.0888883	−	0.153959i	0.907041	+	0.421041i	$0.138335\pi$
$614$		0			0
$615$	1.05452	+	5.30141i	0.0425222	+	0.213774i
$616$		0			0
$617$	19.2067	−	28.7448i	0.773232	−	1.15722i	−0.210503	−	0.977593i	$-0.567510\pi$
$617$	19.2067	−	28.7448i	0.773232	−	1.15722i	0.983734	−	0.179630i	$-0.0574899\pi$
$618$		0			0
$619$	−2.43824	−	37.2003i	−0.0980011	−	1.49521i	−0.709917	−	0.704285i	$-0.751268\pi$
$619$	−2.43824	−	37.2003i	−0.0980011	−	1.49521i	0.611916	−	0.790923i	$-0.290399\pi$
$620$		0			0
$621$	−12.3634	+	16.1124i	−0.496128	+	0.646567i
$622$		0			0
$623$	2.46795	+	3.04680i	0.0988763	+	0.122067i
$624$		0			0
$625$	6.68041	+	1.79001i	0.267216	+	0.0716004i
$626$		0			0
$627$	−0.212057	−	0.276359i	−0.00846876	−	0.0110367i
$628$		0			0
$629$	−42.8125	+	3.00377i	−1.70705	+	0.119768i
$630$		0			0
$631$	−30.2915	−	12.5472i	−1.20589	−	0.499494i	−0.312989	−	0.949757i	$-0.601330\pi$
$631$	−30.2915	−	12.5472i	−1.20589	−	0.499494i	−0.892896	+	0.450262i	$0.851330\pi$
$632$		0			0
$633$	−0.981974	−	3.66478i	−0.0390300	−	0.145662i
$634$		0			0
$635$	−1.96073	+	0.665577i	−0.0778090	+	0.0264126i
$636$		0			0
$637$	19.6645	−	38.6203i	0.779137	−	1.53019i
$638$		0			0
$639$	10.6121	+	5.23332i	0.419809	+	0.207027i
$640$		0			0
$641$	9.84141	−	4.85324i	0.388712	−	0.191692i	−0.237423	−	0.971406i	$-0.576303\pi$
$641$	9.84141	−	4.85324i	0.388712	−	0.191692i	0.626135	+	0.779715i	$0.284636\pi$
$642$		0			0
$643$	14.8543	−	2.95470i	0.585796	−	0.116522i	0.106710	−	0.994290i	$-0.465968\pi$
$643$	14.8543	−	2.95470i	0.585796	−	0.116522i	0.479086	+	0.877768i	$0.340968\pi$
$644$		0			0
$645$			23.3857i			0.920810i
$646$		0			0
$647$	−7.44867	−	4.30049i	−0.292838	−	0.169070i	0.346383	−	0.938093i	$-0.387410\pi$
$647$	−7.44867	−	4.30049i	−0.292838	−	0.169070i	−0.639221	+	0.769023i	$0.720743\pi$
$648$		0			0
$649$	−28.5248	+	25.0156i	−1.11970	+	0.981947i
$650$		0			0
$651$	−55.4270	+	16.4266i	−2.17236	+	0.643809i
$652$		0			0
$653$	9.98260	−	20.2427i	0.390650	−	0.792159i	−0.609350	−	0.792901i	$-0.708570\pi$
$653$	9.98260	−	20.2427i	0.390650	−	0.792159i	1.00000		0.000742347i	$0.000236296\pi$
$654$		0			0
$655$	−1.33864	+	10.1680i	−0.0523051	+	0.397297i
$656$		0			0
$657$	64.8516	+	12.8998i	2.53010	+	0.503269i
$658$		0			0
$659$	23.1166	−	23.1166i	0.900496	−	0.900496i	−0.0949828	−	0.995479i	$-0.530280\pi$
$659$	23.1166	−	23.1166i	0.900496	−	0.900496i	0.995479	+	0.0949828i	$0.0302796\pi$
$660$		0			0
$661$	10.2658	−	7.87726i	0.399295	−	0.306390i	−0.389523	−	0.921017i	$-0.627360\pi$
$661$	10.2658	−	7.87726i	0.399295	−	0.306390i	0.788818	+	0.614627i	$0.210693\pi$
$662$		0			0
$663$	68.5280	+	13.3039i	2.66141	+	0.516681i
$664$		0			0
$665$	0.0483743	−	0.0766922i	0.00187588	−	0.00297400i
$666$		0			0
$667$	−7.41868	+	27.6869i	−0.287252	+	1.07204i
$668$		0			0
$669$	19.6789	−	22.4394i	0.760829	−	0.867559i
$670$		0			0
$671$	25.8904	−	10.7242i	0.999489	−	0.414002i
$672$		0			0
$673$	0.725460	−	0.484737i	0.0279644	−	0.0186852i	−0.541509	−	0.840695i	$-0.682147\pi$
$673$	0.725460	−	0.484737i	0.0279644	−	0.0186852i	0.569474	+	0.822009i	$0.307147\pi$
$674$		0			0
$675$	−6.57615	−	13.3351i	−0.253116	−	0.513269i
$676$		0			0
$677$	30.7484	+	35.0619i	1.18176	+	1.34754i	0.924494	+	0.381197i	$0.124488\pi$
$677$	30.7484	+	35.0619i	1.18176	+	1.34754i	0.257265	+	0.966341i	$0.417179\pi$
$678$		0			0
$679$	−2.98172	+	1.10048i	−0.114428	+	0.0422327i
$680$		0			0
$681$	−25.6581	−	44.4412i	−0.983221	−	1.70299i
$682$		0			0
$683$	−2.75931	+	8.12867i	−0.105582	+	0.311035i	−0.986863	−	0.161557i	$-0.948348\pi$
$683$	−2.75931	+	8.12867i	−0.105582	+	0.311035i	0.881281	+	0.472592i	$0.156682\pi$
$684$		0			0
$685$	8.62750	+	5.76471i	0.329640	+	0.220258i
$686$		0			0
$687$	−6.92017	−	10.3568i	−0.264021	−	0.395135i
$688$		0			0
$689$	−24.5966	−	3.23821i	−0.937058	−	0.123366i
$690$		0			0
$691$	−9.20369	−	27.1132i	−0.350125	−	1.03143i	−0.969236	−	0.246131i	$-0.920841\pi$
$691$	−9.20369	−	27.1132i	−0.350125	−	1.03143i	0.619112	−	0.785303i	$-0.287493\pi$
$692$		0			0
$693$	−21.1935	+	45.9890i	−0.805074	+	1.74698i
$694$		0			0
$695$	−10.8503	+	1.42847i	−0.411577	+	0.0541851i
$696$		0			0
$697$	0.431043	−	7.07454i	0.0163269	−	0.267967i
$698$		0			0
$699$	18.1406	−	43.7954i	0.686142	−	1.65649i
$700$		0			0
$701$	−8.05499	−	8.05499i	−0.304233	−	0.304233i	0.538434	−	0.842667i	$-0.319016\pi$
$701$	−8.05499	−	8.05499i	−0.304233	−	0.304233i	−0.842667	+	0.538434i	$0.819016\pi$
$702$		0			0
$703$	−0.233257	−	0.204561i	−0.00879745	−	0.00771516i
$704$		0			0
$705$	−15.1283	−	11.6084i	−0.569765	−	0.437196i
$706$		0			0
$707$	−36.8245	+	16.4014i	−1.38493	+	0.616840i
$708$		0			0
$709$	2.63622	−	40.2209i	0.0990052	−	1.51053i	−0.602647	−	0.798008i	$-0.705887\pi$
$709$	2.63622	−	40.2209i	0.0990052	−	1.51053i	0.701653	−	0.712519i	$-0.252446\pi$
$710$		0			0
$711$	−47.3041	−	16.0576i	−1.77404	−	0.602206i
$712$		0			0
$713$	−40.1397			−1.50324
$714$		0			0
$715$	−30.4243			−1.13780
$716$		0			0
$717$	60.1500	+	20.4182i	2.24634	+	0.762531i
$718$		0			0
$719$	0.0859315	−	1.31106i	0.00320470	−	0.0488943i	−0.995957	−	0.0898307i	$-0.971367\pi$
$719$	0.0859315	−	1.31106i	0.00320470	−	0.0488943i	0.999162	+	0.0409363i	$0.0130341\pi$
$720$		0			0
$721$	22.6114	+	2.37338i	0.842093	+	0.0883893i
$722$		0			0
$723$	38.2877	+	29.3792i	1.42393	+	1.09262i
$724$		0			0
$725$	−15.7772	−	13.8362i	−0.585950	−	0.513864i
$726$		0			0
$727$	−31.1201	−	31.1201i	−1.15418	−	1.15418i	−0.985706	−	0.168473i	$-0.946117\pi$
$727$	−31.1201	−	31.1201i	−1.15418	−	1.15418i	−0.168473	−	0.985706i	$-0.553883\pi$
$728$		0			0
$729$	16.7702	−	40.4869i	0.621119	−	1.49951i
$730$		0			0
$731$	7.80031	−	29.6557i	0.288505	−	1.09686i
$732$		0			0
$733$	3.97625	−	0.523484i	0.146866	−	0.0193353i	−0.0567345	−	0.998389i	$-0.518069\pi$
$733$	3.97625	−	0.523484i	0.146866	−	0.0193353i	0.203601	+	0.979054i	$0.434736\pi$
$734$		0			0
$735$	−21.9435	−	1.72086i	−0.809398	−	0.0634749i
$736$		0			0
$737$	0.584353	+	1.72145i	0.0215249	+	0.0634104i
$738$		0			0
$739$	7.16495	+	0.943284i	0.263567	+	0.0346993i	0.261152	−	0.965298i	$-0.415898\pi$
$739$	7.16495	+	0.943284i	0.263567	+	0.0346993i	0.00241557	+	0.999997i	$0.499231\pi$
$740$		0			0
$741$	0.280358	+	0.419585i	0.0102992	+	0.0154138i
$742$		0			0
$743$	−15.4817	−	10.3446i	−0.567970	−	0.379505i	0.238176	−	0.971222i	$-0.423450\pi$
$743$	−15.4817	−	10.3446i	−0.567970	−	0.379505i	−0.806146	+	0.591717i	$0.798450\pi$
$744$		0			0
$745$	7.13604	−	21.0221i	0.261444	−	0.770190i
$746$		0			0
$747$	−23.1039	−	40.0172i	−0.845328	−	1.46415i
$748$		0			0
$749$	18.7492	+	15.5891i	0.685080	+	0.569614i
$750$		0			0
$751$	23.9568	+	27.3175i	0.874195	+	0.996829i	0.999989	+	0.00477219i	$0.00151904\pi$
$751$	23.9568	+	27.3175i	0.874195	+	0.996829i	−0.125793	+	0.992056i	$0.540148\pi$
$752$		0			0
$753$	−14.4078	−	29.2161i	−0.525049	−	1.06469i
$754$		0			0
$755$	7.25448	−	4.84729i	0.264017	−	0.176411i
$756$		0			0
$757$	−14.3922	+	5.96145i	−0.523094	+	0.216673i	−0.628575	−	0.777749i	$-0.716362\pi$
$757$	−14.3922	+	5.96145i	−0.523094	+	0.216673i	0.105481	+	0.994421i	$0.466362\pi$
$758$		0			0
$759$	−38.7120	+	44.1426i	−1.40516	+	1.60227i
$760$		0			0
$761$	−13.6829	+	51.0654i	−0.496006	+	1.85112i	0.0283137	+	0.999599i	$0.490986\pi$
$761$	−13.6829	+	51.0654i	−0.496006	+	1.85112i	−0.524320	+	0.851521i	$0.675680\pi$
$762$		0			0
$763$	39.3751	+	24.8362i	1.42547	+	0.899130i
$764$		0			0
$765$	−4.23769	−	20.8041i	−0.153214	−	0.752173i
$766$		0			0
$767$	43.6045	−	33.4589i	1.57447	−	1.20813i
$768$		0			0
$769$	24.5040	−	24.5040i	0.883638	−	0.883638i	−0.110264	−	0.993902i	$-0.535170\pi$
$769$	24.5040	−	24.5040i	0.883638	−	0.883638i	0.993902	+	0.110264i	$0.0351697\pi$
$770$		0			0
$771$	52.6410	+	10.4709i	1.89582	+	0.377102i
$772$		0			0
$773$	−0.175448	+	1.33266i	−0.00631044	+	0.0479325i	−0.994310	−	0.106522i	$-0.966029\pi$
$773$	−0.175448	+	1.33266i	−0.00631044	+	0.0479325i	0.988000	+	0.154454i	$0.0493619\pi$
$774$		0			0
$775$	12.9973	−	26.3560i	0.466877	−	0.946734i
$776$		0			0
$777$	−17.5711	+	73.2335i	−0.630358	+	2.62724i
$778$		0			0
$779$	0.0385213	−	0.0337822i	0.00138017	−	0.00121037i
$780$		0			0
$781$	9.77902	+	5.64592i	0.349921	+	0.202027i
$782$		0			0
$783$			23.0663i			0.824322i
$784$		0			0
$785$	10.0871	−	2.00646i	0.360025	−	0.0716135i
$786$		0			0
$787$	−35.4923	+	17.5028i	−1.26516	+	0.623909i	−0.946115	−	0.323830i	$-0.895030\pi$
$787$	−35.4923	+	17.5028i	−1.26516	+	0.623909i	−0.319047	+	0.947739i	$0.603363\pi$
$788$		0			0
$789$	−22.5494	−	11.1201i	−0.802778	−	0.395886i
$790$		0			0
$791$	−9.78304	+	9.04587i	−0.347845	+	0.321634i
$792$		0			0
$793$	−38.4423	+	13.0494i	−1.36512	+	0.463397i
$794$		0			0
$795$	3.26112	+	12.1707i	0.115660	+	0.431650i
$796$		0			0
$797$	32.1033	+	13.2976i	1.13716	+	0.471027i	0.870209	−	0.492684i	$-0.163984\pi$
$797$	32.1033	+	13.2976i	1.13716	+	0.471027i	0.266950	+	0.963710i	$0.413984\pi$
$798$		0			0
$799$	15.3125	+	19.7668i	0.541717	+	0.699300i
$800$		0			0
$801$	4.04020	+	5.26529i	0.142753	+	0.186040i
$802$		0			0
$803$	60.9514	+	16.3319i	2.15093	+	0.576340i
$804$		0			0
$805$	−14.2687	−	5.47496i	−0.502905	−	0.192967i
$806$		0			0
$807$	31.7001	−	41.3124i	1.11590	−	1.45427i
$808$		0			0
$809$	−0.264510	−	4.03565i	−0.00929968	−	0.141886i	−0.999984	−	0.00570524i	$-0.998184\pi$
$809$	−0.264510	−	4.03565i	−0.00929968	−	0.141886i	0.990684	−	0.136181i	$-0.0434827\pi$
$810$		0			0
$811$	−28.0629	+	41.9992i	−0.985423	+	1.47479i	−0.108537	+	0.994092i	$0.534617\pi$
$811$	−28.0629	+	41.9992i	−0.985423	+	1.47479i	−0.876886	+	0.480698i	$0.840383\pi$
$812$		0			0
$813$	−2.73238	−	13.7366i	−0.0958286	−	0.481763i
$814$		0			0
$815$	−2.60833	+	4.51776i	−0.0913659	+	0.158250i
$816$		0			0
$817$	0.191972	−	0.110835i	0.00671625	−	0.00387763i
$818$		0			0
$819$	34.9938	−	64.4719i	1.22278	−	2.25283i
$820$		0			0
$821$	−7.46164	−	0.489062i	−0.260413	−	0.0170684i	−0.0653625	−	0.997862i	$-0.520820\pi$
$821$	−7.46164	−	0.489062i	−0.260413	−	0.0170684i	−0.195050	+	0.980793i	$0.562487\pi$
$822$		0			0
$823$	−41.1354	+	2.69616i	−1.43389	+	0.0939821i	−0.762436	−	0.647064i	$-0.775997\pi$
$823$	−41.1354	+	2.69616i	−1.43389	+	0.0939821i	−0.671454	+	0.741046i	$0.734330\pi$
$824$		0			0
$825$	−16.4492	−	39.7120i	−0.572689	−	1.38259i
$826$		0			0
$827$	−6.53804	+	32.8689i	−0.227350	+	1.14297i	0.683412	+	0.730033i	$0.260495\pi$
$827$	−6.53804	+	32.8689i	−0.227350	+	1.14297i	−0.910762	+	0.412932i	$0.864505\pi$
$828$		0			0
$829$	42.5244	−	11.3944i	1.47693	−	0.395743i	0.571630	−	0.820511i	$-0.306311\pi$
$829$	42.5244	−	11.3944i	1.47693	−	0.395743i	0.905302	+	0.424769i	$0.139645\pi$
$830$		0			0
$831$	11.4202	+	86.7448i	0.396161	+	3.00914i
$832$		0			0
$833$	27.2529	+	9.50153i	0.944257	+	0.329208i
$834$		0			0
$835$	2.99102	+	22.7190i	0.103508	+	0.786224i
$836$		0			0
$837$	−31.2008	+	8.36022i	−1.07846	+	0.288971i
$838$		0			0
$839$	3.17053	−	15.9394i	0.109459	−	0.550288i	−0.886671	−	0.462400i	$-0.846988\pi$
$839$	3.17053	−	15.9394i	0.109459	−	0.550288i	0.996130	−	0.0878875i	$-0.0280116\pi$
$840$		0			0
$841$	1.36038	+	3.28425i	0.0469097	+	0.113250i
$842$		0			0
$843$	−70.7386	+	4.63645i	−2.43637	+	0.159688i
$844$		0			0
$845$	29.0643	+	1.90497i	0.999841	+	0.0655331i
$846$		0			0
$847$	−9.16912	+	16.8930i	−0.315055	+	0.580450i
$848$		0			0
$849$	1.03740	−	0.598940i	0.0356033	−	0.0205556i
$850$		0			0
$851$	−26.1460	+	45.2862i	−0.896273	+	1.55239i
$852$		0			0
$853$	8.99834	+	45.2377i	0.308097	+	1.54891i	0.755846	+	0.654750i	$0.227226\pi$
$853$	8.99834	+	45.2377i	0.308097	+	1.54891i	−0.447749	+	0.894160i	$0.647774\pi$
$854$		0			0
$855$	0.0852683	−	0.127613i	0.00291611	−	0.00436427i
$856$		0			0
$857$	3.28971	+	50.1913i	0.112374	+	1.71450i	0.566915	+	0.823776i	$0.308137\pi$
$857$	3.28971	+	50.1913i	0.112374	+	1.71450i	−0.454541	+	0.890726i	$0.650197\pi$
$858$		0			0
$859$	22.9302	−	29.8832i	0.782368	−	1.01960i	−0.216691	−	0.976240i	$-0.569526\pi$
$859$	22.9302	−	29.8832i	0.782368	−	1.01960i	0.999059	−	0.0433621i	$-0.0138069\pi$
$860$		0			0
$861$	−11.6119	−	4.45555i	−0.395734	−	0.151845i
$862$		0			0
$863$	14.5047	+	3.88651i	0.493745	+	0.132298i	0.497095	−	0.867696i	$-0.334400\pi$
$863$	14.5047	+	3.88651i	0.493745	+	0.132298i	−0.00335077	+	0.999994i	$0.501067\pi$
$864$		0			0
$865$	−9.08156	−	11.8353i	−0.308782	−	0.402413i
$866$		0			0
$867$	−2.61396	+	46.4155i	−0.0887748	+	1.57635i
$868$		0			0
$869$	−44.0442	−	18.2437i	−1.49410	−	0.618876i
$870$		0			0
$871$	−0.681616	−	2.54383i	−0.0230957	−	0.0861942i
$872$		0			0
$873$	−5.09426	+	1.72927i	−0.172415	+	0.0585269i
$874$		0			0
$875$	19.3834	−	17.9228i	0.655279	−	0.605903i
$876$		0			0
$877$	38.2818	+	18.8785i	1.29268	+	0.637481i	0.952975	−	0.303050i	$-0.0980049\pi$
$877$	38.2818	+	18.8785i	1.29268	+	0.637481i	0.339708	+	0.940531i	$0.389672\pi$
$878$		0			0
$879$	−0.313193	+	0.154450i	−0.0105637	+	0.00520946i
$880$		0			0
$881$	45.2662	−	9.00400i	1.52506	−	0.303352i	0.639831	−	0.768516i	$-0.279004\pi$
$881$	45.2662	−	9.00400i	1.52506	−	0.303352i	0.885225	+	0.465164i	$0.154004\pi$
$882$		0			0
$883$			34.0584i			1.14615i	0.819501	+	0.573077i	$0.194251\pi$
$883$			34.0584i			1.14615i	−0.819501	+	0.573077i	$0.805749\pi$
$884$		0			0
$885$	−24.1746	−	13.9572i	−0.812620	−	0.469166i
$886$		0			0
$887$	5.46830	−	4.79557i	0.183608	−	0.161020i	−0.562608	−	0.826724i	$-0.690202\pi$
$887$	5.46830	−	4.79557i	0.183608	−	0.161020i	0.746216	+	0.665704i	$0.231869\pi$
$888$		0			0
$889$	1.11159	−	4.63294i	0.0372815	−	0.155384i
$890$		0			0
$891$	4.49803	−	9.12109i	0.150690	−	0.305568i
$892$		0			0
$893$	−0.0235928	+	0.179205i	−0.000789502	+	0.00599686i
$894$		0			0
$895$	−0.889134	−	0.176860i	−0.0297205	−	0.00591177i
$896$		0			0
$897$	60.1430	−	60.1430i	2.00812	−	2.00812i
$898$		0			0
$899$	−36.1681	+	27.7528i	−1.20627	+	0.925607i
$900$		0			0
$901$	−0.0759399	−	16.5216i	−0.00252993	−	0.550414i
$902$		0			0
$903$	−45.5124	−	28.7074i	−1.51456	−	0.955322i
$904$		0			0
$905$	−0.638062	+	2.38128i	−0.0212099	+	0.0791564i
$906$		0			0
$907$	−5.92048	+	6.75101i	−0.196586	+	0.224164i	−0.841732	−	0.539896i	$-0.818463\pi$
$907$	−5.92048	+	6.75101i	−0.196586	+	0.224164i	0.645145	+	0.764060i	$0.276797\pi$
$908$		0			0
$909$	−63.0398	+	26.1119i	−2.09090	+	0.866078i
$910$		0			0
$911$	47.9240	−	32.0218i	1.58779	−	1.06093i	0.628773	−	0.777589i	$-0.283557\pi$
$911$	47.9240	−	32.0218i	1.58779	−	1.06093i	0.959019	−	0.283341i	$-0.0914427\pi$
$912$		0			0
$913$	−19.5036	−	39.5494i	−0.645475	−	1.30889i
$914$		0			0
$915$	13.5947	+	15.5017i	0.449425	+	0.512471i
$916$		0			0
$917$	−18.1454	−	15.0871i	−0.599214	−	0.498220i
$918$		0			0
$919$	−13.8523	−	23.9929i	−0.456946	−	0.791454i	0.541852	−	0.840474i	$-0.317723\pi$
$919$	−13.8523	−	23.9929i	−0.456946	−	0.791454i	−0.998798	+	0.0490204i	$0.984390\pi$
$920$		0			0
$921$	8.74545	−	25.7633i	0.288172	−	0.848929i
$922$		0			0
$923$	−13.6012	−	9.08805i	−0.447690	−	0.299137i
$924$		0			0
$925$	−21.2690	−	31.8314i	−0.699322	−	1.04661i
$926$		0			0
$927$	38.1541	+	5.02308i	1.25315	+	0.164980i
$928$		0			0
$929$	−11.4199	−	33.6418i	−0.374674	−	1.10375i	−0.956823	−	0.290671i	$-0.906121\pi$
$929$	−11.4199	−	33.6418i	−0.374674	−	1.10375i	0.582149	−	0.813082i	$-0.302212\pi$
$930$		0			0
$931$	0.0898735	+	0.188289i	0.00294548	+	0.00617093i
$932$		0			0
$933$	17.5487	−	2.31033i	0.574518	−	0.0756367i
$934$		0			0
$935$	−2.73695	−	20.0757i	−0.0895078	−	0.656546i
$936$		0			0
$937$	−2.15841	+	5.21087i	−0.0705122	+	0.170232i	−0.955206	−	0.295940i	$-0.904367\pi$
$937$	−2.15841	+	5.21087i	−0.0705122	+	0.170232i	0.884694	+	0.466172i	$0.154367\pi$
$938$		0			0
$939$	−26.6754	−	26.6754i	−0.870518	−	0.870518i
$940$		0			0
$941$	−34.2075	−	29.9992i	−1.11513	−	0.977944i	−0.115250	−	0.993336i	$-0.536767\pi$
$941$	−34.2075	−	29.9992i	−1.11513	−	0.977944i	−0.999882	+	0.0153921i	$0.995100\pi$
$942$		0			0
$943$	−6.85122	−	5.25713i	−0.223106	−	0.171196i
$944$		0			0
$945$	−12.2314	−	1.28386i	−0.397888	−	0.0417639i
$946$		0			0
$947$	3.33790	−	50.9265i	0.108467	−	1.65489i	−0.503493	−	0.864000i	$-0.667952\pi$
$947$	3.33790	−	50.9265i	0.108467	−	1.65489i	0.611960	−	0.790889i	$-0.290381\pi$
$948$		0			0
$949$	−86.5616	−	29.3837i	−2.80991	−	0.953835i
$950$		0			0
$951$	76.2127			2.47137
$952$		0			0
$953$	24.8379			0.804579			0.402290	−	0.915512i	$-0.368214\pi$
$953$	24.8379			0.804579			0.402290	+	0.915512i	$0.368214\pi$
$954$		0			0
$955$	−2.98680	−	1.01388i	−0.0966507	−	0.0328085i
$956$		0			0
$957$	−4.36130	+	66.5406i	−0.140981	+	2.15095i
$958$		0			0
$959$	−21.8099	+	9.71403i	−0.704279	+	0.313682i
$960$		0			0
$961$	−26.0549	−	19.9927i	−0.840482	−	0.644924i
$962$		0			0
$963$	31.0303	+	27.2129i	0.999938	+	0.876923i
$964$		0			0
$965$	−3.86916	−	3.86916i	−0.124553	−	0.124553i
$966$		0			0
$967$	−15.7208	+	37.9534i	−0.505548	+	1.22050i	0.440875	+	0.897569i	$0.354668\pi$
$967$	−15.7208	+	37.9534i	−0.505548	+	1.22050i	−0.946422	+	0.322931i	$0.895332\pi$
$968$		0			0
$969$	−0.251646	+	0.222742i	−0.00808402	+	0.00715550i
$970$		0			0
$971$	−42.0289	+	5.53321i	−1.34877	+	0.177569i	−0.770065	−	0.637966i	$-0.779776\pi$
$971$	−42.0289	+	5.53321i	−1.34877	+	0.177569i	−0.578708	+	0.815535i	$0.696443\pi$
$972$		0			0
$973$	10.5394	−	22.8701i	0.337878	−	0.733182i
$974$		0			0
$975$	20.0158	+	58.9646i	0.641018	+	1.88838i
$976$		0			0
$977$	−31.0353	−	4.08588i	−0.992909	−	0.130719i	−0.383471	−	0.923553i	$-0.625271\pi$
$977$	−31.0353	−	4.08588i	−0.992909	−	0.130719i	−0.609438	+	0.792834i	$0.708605\pi$
$978$		0			0
$979$	3.51875	+	5.26618i	0.112460	+	0.168308i
$980$		0			0
$981$	65.5186	+	43.7781i	2.09185	+	1.39773i
$982$		0			0
$983$	−1.78254	+	5.25120i	−0.0568543	+	0.167487i	−0.971647	−	0.236436i	$-0.924021\pi$
$983$	−1.78254	+	5.25120i	−0.0568543	+	0.167487i	0.914793	+	0.403924i	$0.132354\pi$
$984$		0			0
$985$	5.18231	+	8.97602i	0.165122	+	0.286000i
$986$		0			0
$987$	41.1628	−	15.1923i	1.31023	−	0.483575i
$988$		0			0
$989$	−24.6347	−	28.0904i	−0.783336	−	0.893224i
$990$		0			0
$991$	−1.24362	−	2.52181i	−0.0395048	−	0.0801078i	0.876226	−	0.481901i	$-0.160054\pi$
$991$	−1.24362	−	2.52181i	−0.0395048	−	0.0801078i	−0.915730	+	0.401794i	$0.868387\pi$
$992$		0			0
$993$	31.4672	−	21.0257i	0.998580	−	0.667230i
$994$		0			0
$995$	7.16531	−	2.96797i	0.227156	−	0.0940909i
$996$		0			0
$997$	14.3641	−	16.3791i	0.454916	−	0.518732i	−0.478228	−	0.878236i	$-0.658721\pi$
$997$	14.3641	−	16.3791i	0.454916	−	0.518732i	0.933144	+	0.359504i	$0.117054\pi$
$998$		0			0
$999$	−10.8913	+	40.6468i	−0.344585	+	1.28601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.1	yes	192
7.5	odd	6	inner	476.2.bl.a.397.1	yes	192
17.3	odd	16	inner	476.2.bl.a.241.1	yes	192
119.54	even	48	inner	476.2.bl.a.173.1	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.1	✓	192	119.54	even	48	inner
476.2.bl.a.241.1	yes	192	17.3	odd	16	inner
476.2.bl.a.397.1	yes	192	7.5	odd	6	inner
476.2.bl.a.465.1	yes	192	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.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.58952 - 0.879025i) q^{3} +(0.0752031 - 1.14738i) q^{5} +(2.14067 + 1.55484i) q^{7} +(3.55289 + 2.72623i) q^{9} +O(q^{10})\)	\(q+(-2.58952 - 0.879025i) q^{3} +(0.0752031 - 1.14738i) q^{5} +(2.14067 + 1.55484i) q^{7} +(3.55289 + 2.72623i) q^{9} +(3.21317 + 2.81787i) q^{11} +(-4.37784 - 4.37784i) q^{13} +(-1.20331 + 2.90506i) q^{15} +(2.49493 - 3.28258i) q^{17} +(0.0295505 - 0.00389040i) q^{19} +(-4.17659 - 5.90799i) q^{21} +(-1.61481 - 4.75708i) q^{23} +(3.64640 + 0.480058i) q^{25} +(-2.24599 - 3.36137i) q^{27} +(-4.74410 - 3.16991i) q^{29} +(2.56833 - 7.56606i) q^{31} +(-5.84359 - 10.1214i) q^{33} +(1.94497 - 2.33923i) q^{35} +(-6.86319 - 7.82597i) q^{37} +(7.48830 + 15.1848i) q^{39} +(1.42931 - 0.955031i) q^{41} +(6.87109 - 2.84610i) q^{43} +(3.39520 - 3.87148i) q^{45} +(-1.56957 + 5.85772i) q^{47} +(2.16497 + 6.65679i) q^{49} +(-9.34614 + 6.30722i) q^{51} +(3.17906 - 2.43938i) q^{53} +(3.47480 - 3.47480i) q^{55} +(-0.0799415 - 0.0159014i) q^{57} +(-1.15874 + 8.80152i) q^{59} +(2.90016 - 5.88094i) q^{61} +(3.36674 + 11.3601i) q^{63} +(-5.35227 + 4.69381i) q^{65} +(0.368382 + 0.212686i) q^{67} +13.7380i q^{69} +(2.59138 - 0.515457i) q^{71} +(13.2423 - 6.53037i) q^{73} +(-9.02047 - 4.44840i) q^{75} +(2.49701 + 11.0281i) q^{77} +(-10.5629 + 3.58563i) q^{79} +(-0.615892 - 2.29854i) q^{81} +(-9.53271 - 3.94858i) q^{83} +(-3.57873 - 3.10948i) q^{85} +(9.49854 + 12.3787i) q^{87} +(1.43148 + 0.383563i) q^{89} +(-2.56470 - 16.1784i) q^{91} +(-13.3015 + 17.3349i) q^{93} +(-0.00224147 - 0.0341982i) q^{95} +(-0.667402 + 0.998837i) q^{97} +(3.73387 + 18.7714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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