LMFDB - Embedded newform 4655.2.a.br.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4655,2,Mod(1,4655)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4655, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4655.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4655 = 5 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4655.a (trivial)

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:	yes
Analytic conductor:	$37.1703621409$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.162590 q^{2} -3.34603 q^{3} -1.97356 q^{4} -1.00000 q^{5} +0.544029 q^{6} +0.646060 q^{8} +8.19589 q^{9} +0.162590 q^{10} +0.429014 q^{11} +6.60360 q^{12} -5.75642 q^{13} +3.34603 q^{15} +3.84209 q^{16} +7.07631 q^{17} -1.33257 q^{18} +1.00000 q^{19} +1.97356 q^{20} -0.0697533 q^{22} +3.90187 q^{23} -2.16173 q^{24} +1.00000 q^{25} +0.935934 q^{26} -17.3856 q^{27} +6.42012 q^{29} -0.544029 q^{30} -2.72845 q^{31} -1.91680 q^{32} -1.43549 q^{33} -1.15053 q^{34} -16.1751 q^{36} +7.18753 q^{37} -0.162590 q^{38} +19.2611 q^{39} -0.646060 q^{40} +11.9120 q^{41} -12.2010 q^{43} -0.846688 q^{44} -8.19589 q^{45} -0.634403 q^{46} +3.66097 q^{47} -12.8557 q^{48} -0.162590 q^{50} -23.6775 q^{51} +11.3607 q^{52} -3.66806 q^{53} +2.82671 q^{54} -0.429014 q^{55} -3.34603 q^{57} -1.04385 q^{58} -6.15976 q^{59} -6.60360 q^{60} -7.90953 q^{61} +0.443617 q^{62} -7.37252 q^{64} +5.75642 q^{65} +0.233396 q^{66} +6.45590 q^{67} -13.9656 q^{68} -13.0558 q^{69} -2.64572 q^{71} +5.29504 q^{72} -6.62975 q^{73} -1.16862 q^{74} -3.34603 q^{75} -1.97356 q^{76} -3.13166 q^{78} +1.62292 q^{79} -3.84209 q^{80} +33.5849 q^{81} -1.93676 q^{82} +3.98106 q^{83} -7.07631 q^{85} +1.98375 q^{86} -21.4819 q^{87} +0.277169 q^{88} +0.576435 q^{89} +1.33257 q^{90} -7.70059 q^{92} +9.12945 q^{93} -0.595236 q^{94} -1.00000 q^{95} +6.41368 q^{96} -12.6618 q^{97} +3.51615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) $ 26 * q + 4 * q^2 - 6 * q^3 + 36 * q^4 - 26 * q^5 + 4 * q^6 + 12 * q^8 + 44 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 14 * q^13 + 6 * q^15 + 64 * q^16 - 18 * q^17 + 8 * q^18 + 26 * q^19 - 36 * q^20 + 36 * q^22 + 44 * q^24 + 26 * q^25 + 8 * q^26 - 30 * q^27 + 22 * q^29 - 4 * q^30 + 28 * q^32 - 38 * q^33 + 68 * q^36 + 48 * q^37 + 4 * q^38 + 26 * q^39 - 12 * q^40 - 4 * q^41 + 16 * q^43 + 44 * q^44 - 44 * q^45 + 48 * q^46 - 22 * q^47 - 48 * q^48 + 4 * q^50 + 34 * q^51 - 32 * q^52 + 28 * q^53 + 28 * q^54 - 14 * q^55 - 6 * q^57 + 52 * q^58 + 8 * q^59 + 20 * q^60 + 28 * q^61 + 16 * q^62 + 52 * q^64 + 14 * q^65 + 24 * q^66 + 60 * q^67 - 52 * q^68 + 4 * q^69 + 8 * q^71 + 36 * q^72 + 4 * q^73 + 8 * q^74 - 6 * q^75 + 36 * q^76 - 76 * q^78 + 50 * q^79 - 64 * q^80 + 114 * q^81 + 36 * q^82 - 20 * q^83 + 18 * q^85 + 40 * q^86 - 18 * q^87 + 108 * q^88 + 20 * q^89 - 8 * q^90 - 48 * q^92 + 32 * q^93 + 80 * q^94 - 26 * q^95 + 140 * q^96 - 26 * q^97 + 24 * q^99

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 $

$2$	−0.162590	−0.114968	−0.0574841	−	0.998346i	$-0.518308\pi$
$2$	−0.162590	−0.114968	−0.0574841	+	0.998346i	$0.518308\pi$
$3$	−3.34603	−1.93183	−0.965914	−	0.258862i	$-0.916653\pi$
$3$	−3.34603	−1.93183	−0.965914	+	0.258862i	$0.916653\pi$
$4$	−1.97356	−0.986782
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.544029	0.222099
$7$	0	0
$7$	0	0
$8$	0.646060	0.228417
$9$	8.19589	2.73196
$10$	0.162590	0.0514153
$11$	0.429014	0.129353	0.0646764	−	0.997906i	$-0.479398\pi$
$11$	0.429014	0.129353	0.0646764	+	0.997906i	$0.479398\pi$
$12$	6.60360	1.90629
$13$	−5.75642	−1.59654	−0.798272	−	0.602297i	$-0.794252\pi$
$13$	−5.75642	−1.59654	−0.798272	+	0.602297i	$0.794252\pi$
$14$	0	0
$15$	3.34603	0.863940
$16$	3.84209	0.960522
$17$	7.07631	1.71626	0.858129	−	0.513435i	$-0.171627\pi$
$17$	7.07631	1.71626	0.858129	+	0.513435i	$0.171627\pi$
$18$	−1.33257	−0.314089
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.97356	0.441302
$21$	0	0
$22$	−0.0697533	−0.0148715
$23$	3.90187	0.813596	0.406798	−	0.913518i	$-0.366645\pi$
$23$	3.90187	0.813596	0.406798	+	0.913518i	$0.366645\pi$
$24$	−2.16173	−0.441262
$25$	1.00000	0.200000
$26$	0.935934	0.183552
$27$	−17.3856	−3.34586
$28$	0	0
$29$	6.42012	1.19219	0.596093	−	0.802915i	$-0.296719\pi$
$29$	6.42012	1.19219	0.596093	+	0.802915i	$0.296719\pi$
$30$	−0.544029	−0.0993257
$31$	−2.72845	−0.490043	−0.245022	−	0.969518i	$-0.578795\pi$
$31$	−2.72845	−0.490043	−0.245022	+	0.969518i	$0.578795\pi$
$32$	−1.91680	−0.338846
$33$	−1.43549	−0.249887
$34$	−1.15053	−0.197315
$35$	0	0
$36$	−16.1751	−2.69585
$37$	7.18753	1.18162	0.590812	−	0.806810i	$-0.298808\pi$
$37$	7.18753	1.18162	0.590812	+	0.806810i	$0.298808\pi$
$38$	−0.162590	−0.0263755
$39$	19.2611	3.08425
$40$	−0.646060	−0.102151
$41$	11.9120	1.86034	0.930169	−	0.367131i	$-0.119660\pi$
$41$	11.9120	1.86034	0.930169	+	0.367131i	$0.119660\pi$
$42$	0	0
$43$	−12.2010	−1.86063	−0.930315	−	0.366761i	$-0.880467\pi$
$43$	−12.2010	−1.86063	−0.930315	+	0.366761i	$0.880467\pi$
$44$	−0.846688	−0.127643
$45$	−8.19589	−1.22177
$46$	−0.634403	−0.0935377
$47$	3.66097	0.534007	0.267004	−	0.963696i	$-0.413966\pi$
$47$	3.66097	0.534007	0.267004	+	0.963696i	$0.413966\pi$
$48$	−12.8557	−1.85556
$49$	0	0
$50$	−0.162590	−0.0229936
$51$	−23.6775	−3.31552
$52$	11.3607	1.57544
$53$	−3.66806	−0.503847	−0.251923	−	0.967747i	$-0.581063\pi$
$53$	−3.66806	−0.503847	−0.251923	+	0.967747i	$0.581063\pi$
$54$	2.82671	0.384667
$55$	−0.429014	−0.0578483
$56$	0	0
$57$	−3.34603	−0.443192
$58$	−1.04385	−0.137064
$59$	−6.15976	−0.801933	−0.400967	−	0.916093i	$-0.631326\pi$
$59$	−6.15976	−0.801933	−0.400967	+	0.916093i	$0.631326\pi$
$60$	−6.60360	−0.852521
$61$	−7.90953	−1.01271	−0.506355	−	0.862325i	$-0.669008\pi$
$61$	−7.90953	−1.01271	−0.506355	+	0.862325i	$0.669008\pi$
$62$	0.443617	0.0563394
$63$	0	0
$64$	−7.37252	−0.921565
$65$	5.75642	0.713996
$66$	0.233396	0.0287291
$67$	6.45590	0.788714	0.394357	−	0.918957i	$-0.370967\pi$
$67$	6.45590	0.788714	0.394357	+	0.918957i	$0.370967\pi$
$68$	−13.9656	−1.69357
$69$	−13.0558	−1.57173
$70$	0	0
$71$	−2.64572	−0.313989	−0.156995	−	0.987599i	$-0.550180\pi$
$71$	−2.64572	−0.313989	−0.156995	+	0.987599i	$0.550180\pi$
$72$	5.29504	0.624026
$73$	−6.62975	−0.775954	−0.387977	−	0.921669i	$-0.626826\pi$
$73$	−6.62975	−0.775954	−0.387977	+	0.921669i	$0.626826\pi$
$74$	−1.16862	−0.135849
$75$	−3.34603	−0.386366
$76$	−1.97356	−0.226383
$77$	0	0
$78$	−3.13166	−0.354591
$79$	1.62292	0.182593	0.0912963	−	0.995824i	$-0.470899\pi$
$79$	1.62292	0.182593	0.0912963	+	0.995824i	$0.470899\pi$
$80$	−3.84209	−0.429558
$81$	33.5849	3.73166
$82$	−1.93676	−0.213880
$83$	3.98106	0.436979	0.218489	−	0.975839i	$-0.429887\pi$
$83$	3.98106	0.436979	0.218489	+	0.975839i	$0.429887\pi$
$84$	0	0
$85$	−7.07631	−0.767534
$86$	1.98375	0.213913
$87$	−21.4819	−2.30310
$88$	0.277169	0.0295463
$89$	0.576435	0.0611020	0.0305510	−	0.999533i	$-0.490274\pi$
$89$	0.576435	0.0611020	0.0305510	+	0.999533i	$0.490274\pi$
$90$	1.33257	0.140465
$91$	0	0
$92$	−7.70059	−0.802842
$93$	9.12945	0.946680
$94$	−0.595236	−0.0613939
$95$	−1.00000	−0.102598
$96$	6.41368	0.654593
$97$	−12.6618	−1.28562	−0.642808	−	0.766027i	$-0.722231\pi$
$97$	−12.6618	−1.28562	−0.642808	+	0.766027i	$0.722231\pi$
$98$	0	0
$99$	3.51615	0.353387
$100$	−1.97356	−0.197356
$101$	14.1804	1.41100	0.705501	−	0.708708i	$-0.250722\pi$
$101$	14.1804	1.41100	0.705501	+	0.708708i	$0.250722\pi$
$102$	3.84972	0.381179
$103$	−15.9521	−1.57181	−0.785903	−	0.618350i	$-0.787802\pi$
$103$	−15.9521	−1.57181	−0.785903	+	0.618350i	$0.787802\pi$
$104$	−3.71899	−0.364677
$105$	0	0
$106$	0.596389	0.0579264
$107$	−6.46100	−0.624608	−0.312304	−	0.949982i	$-0.601101\pi$
$107$	−6.46100	−0.624608	−0.312304	+	0.949982i	$0.601101\pi$
$108$	34.3116	3.30163
$109$	−5.10533	−0.489002	−0.244501	−	0.969649i	$-0.578624\pi$
$109$	−5.10533	−0.489002	−0.244501	+	0.969649i	$0.578624\pi$
$110$	0.0697533	0.00665072
$111$	−24.0497	−2.28269
$112$	0	0
$113$	−2.78712	−0.262190	−0.131095	−	0.991370i	$-0.541849\pi$
$113$	−2.78712	−0.262190	−0.131095	+	0.991370i	$0.541849\pi$
$114$	0.544029	0.0509530
$115$	−3.90187	−0.363851
$116$	−12.6705	−1.17643
$117$	−47.1790	−4.36170
$118$	1.00151	0.0921968
$119$	0	0
$120$	2.16173	0.197338
$121$	−10.8159	−0.983268
$122$	1.28601	0.116430
$123$	−39.8578	−3.59386
$124$	5.38477	0.483566
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−1.78740	−0.158606	−0.0793029	−	0.996851i	$-0.525269\pi$
$127$	−1.78740	−0.158606	−0.0793029	+	0.996851i	$0.525269\pi$
$128$	5.03230	0.444797
$129$	40.8248	3.59442
$130$	−0.935934	−0.0820868
$131$	11.6846	1.02089	0.510443	−	0.859912i	$-0.329482\pi$
$131$	11.6846	1.02089	0.510443	+	0.859912i	$0.329482\pi$
$132$	2.83304	0.246584
$133$	0	0
$134$	−1.04966	−0.0906770
$135$	17.3856	1.49631
$136$	4.57172	0.392022
$137$	7.85588	0.671173	0.335587	−	0.942009i	$-0.391065\pi$
$137$	7.85588	0.671173	0.335587	+	0.942009i	$0.391065\pi$
$138$	2.12273	0.180699
$139$	8.34848	0.708109	0.354055	−	0.935225i	$-0.384803\pi$
$139$	8.34848	0.708109	0.354055	+	0.935225i	$0.384803\pi$
$140$	0	0
$141$	−12.2497	−1.03161
$142$	0.430166	0.0360988
$143$	−2.46959	−0.206517
$144$	31.4893	2.62411
$145$	−6.42012	−0.533162
$146$	1.07793	0.0892100
$147$	0	0
$148$	−14.1851	−1.16600
$149$	19.0334	1.55927	0.779637	−	0.626232i	$-0.215404\pi$
$149$	19.0334	1.55927	0.779637	+	0.626232i	$0.215404\pi$
$150$	0.544029	0.0444198
$151$	11.2945	0.919137	0.459569	−	0.888142i	$-0.348004\pi$
$151$	11.2945	0.919137	0.459569	+	0.888142i	$0.348004\pi$
$152$	0.646060	0.0524024
$153$	57.9967	4.68875
$154$	0	0
$155$	2.72845	0.219154
$156$	−38.0131	−3.04348
$157$	−9.39523	−0.749821	−0.374910	−	0.927061i	$-0.622327\pi$
$157$	−9.39523	−0.749821	−0.374910	+	0.927061i	$0.622327\pi$
$158$	−0.263870	−0.0209924
$159$	12.2734	0.973346
$160$	1.91680	0.151537
$161$	0	0
$162$	−5.46056	−0.429022
$163$	23.9250	1.87395	0.936976	−	0.349393i	$-0.113612\pi$
$163$	23.9250	1.87395	0.936976	+	0.349393i	$0.113612\pi$
$164$	−23.5091	−1.83575
$165$	1.43549	0.111753
$166$	−0.647280	−0.0502386
$167$	5.00493	0.387293	0.193646	−	0.981071i	$-0.437969\pi$
$167$	5.00493	0.387293	0.193646	+	0.981071i	$0.437969\pi$
$168$	0	0
$169$	20.1364	1.54895
$170$	1.15053	0.0882420
$171$	8.19589	0.626755
$172$	24.0794	1.83604
$173$	7.41087	0.563438	0.281719	−	0.959497i	$-0.409095\pi$
$173$	7.41087	0.563438	0.281719	+	0.959497i	$0.409095\pi$
$174$	3.49273	0.264783
$175$	0	0
$176$	1.64831	0.124246
$177$	20.6107	1.54920
$178$	−0.0937223	−0.00702478
$179$	−12.4608	−0.931360	−0.465680	−	0.884953i	$-0.654190\pi$
$179$	−12.4608	−0.931360	−0.465680	+	0.884953i	$0.654190\pi$
$180$	16.1751	1.20562
$181$	2.66274	0.197920	0.0989600	−	0.995091i	$-0.468448\pi$
$181$	2.66274	0.197920	0.0989600	+	0.995091i	$0.468448\pi$
$182$	0	0
$183$	26.4655	1.95638
$184$	2.52084	0.185839
$185$	−7.18753	−0.528438
$186$	−1.48435	−0.108838
$187$	3.03584	0.222003
$188$	−7.22516	−0.526949
$189$	0	0
$190$	0.162590	0.0117955
$191$	10.4654	0.757247	0.378623	−	0.925551i	$-0.376398\pi$
$191$	10.4654	0.757247	0.378623	+	0.925551i	$0.376398\pi$
$192$	24.6686	1.78031
$193$	−20.4799	−1.47417	−0.737086	−	0.675799i	$-0.763799\pi$
$193$	−20.4799	−1.47417	−0.737086	+	0.675799i	$0.763799\pi$
$194$	2.05868	0.147805
$195$	−19.2611	−1.37932
$196$	0	0
$197$	−8.24849	−0.587681	−0.293840	−	0.955855i	$-0.594933\pi$
$197$	−8.24849	−0.587681	−0.293840	+	0.955855i	$0.594933\pi$
$198$	−0.571690	−0.0406283
$199$	−21.2610	−1.50715	−0.753575	−	0.657362i	$-0.771672\pi$
$199$	−21.2610	−1.50715	−0.753575	+	0.657362i	$0.771672\pi$
$200$	0.646060	0.0456834
$201$	−21.6016	−1.52366
$202$	−2.30559	−0.162220
$203$	0	0
$204$	46.7291	3.27169
$205$	−11.9120	−0.831969
$206$	2.59364	0.180708
$207$	31.9793	2.22271
$208$	−22.1167	−1.53351
$209$	0.429014	0.0296756
$210$	0	0
$211$	−13.6887	−0.942371	−0.471185	−	0.882034i	$-0.656174\pi$
$211$	−13.6887	−0.942371	−0.471185	+	0.882034i	$0.656174\pi$
$212$	7.23915	0.497187
$213$	8.85264	0.606573
$214$	1.05049	0.0718101
$215$	12.2010	0.832099
$216$	−11.2321	−0.764250
$217$	0	0
$218$	0.830074	0.0562197
$219$	22.1833	1.49901
$220$	0.846688	0.0570837
$221$	−40.7342	−2.74008
$222$	3.91023	0.262437
$223$	16.8583	1.12892	0.564458	−	0.825462i	$-0.309085\pi$
$223$	16.8583	1.12892	0.564458	+	0.825462i	$0.309085\pi$
$224$	0	0
$225$	8.19589	0.546393
$226$	0.453156	0.0301435
$227$	3.95193	0.262299	0.131149	−	0.991363i	$-0.458133\pi$
$227$	3.95193	0.262299	0.131149	+	0.991363i	$0.458133\pi$
$228$	6.60360	0.437334
$229$	17.1650	1.13429	0.567147	−	0.823617i	$-0.308047\pi$
$229$	17.1650	1.13429	0.567147	+	0.823617i	$0.308047\pi$
$230$	0.634403	0.0418313
$231$	0	0
$232$	4.14779	0.272315
$233$	22.2536	1.45788	0.728942	−	0.684576i	$-0.240013\pi$
$233$	22.2536	1.45788	0.728942	+	0.684576i	$0.240013\pi$
$234$	7.67081	0.501457
$235$	−3.66097	−0.238815
$236$	12.1567	0.791333
$237$	−5.43033	−0.352738
$238$	0	0
$239$	17.4276	1.12730	0.563648	−	0.826015i	$-0.309397\pi$
$239$	17.4276	1.12730	0.563648	+	0.826015i	$0.309397\pi$
$240$	12.8557	0.829833
$241$	−7.08256	−0.456228	−0.228114	−	0.973634i	$-0.573256\pi$
$241$	−7.08256	−0.456228	−0.228114	+	0.973634i	$0.573256\pi$
$242$	1.75856	0.113045
$243$	−60.2193	−3.86307
$244$	15.6100	0.999325
$245$	0	0
$246$	6.48046	0.413179
$247$	−5.75642	−0.366272
$248$	−1.76274	−0.111934
$249$	−13.3207	−0.844168
$250$	0.162590	0.0102831
$251$	−10.6832	−0.674318	−0.337159	−	0.941448i	$-0.609466\pi$
$251$	−10.6832	−0.674318	−0.337159	+	0.941448i	$0.609466\pi$
$252$	0	0
$253$	1.67396	0.105241
$254$	0.290612	0.0182346
$255$	23.6775	1.48274
$256$	13.9268	0.870428
$257$	17.5873	1.09707	0.548533	−	0.836129i	$-0.315186\pi$
$257$	17.5873	1.09707	0.548533	+	0.836129i	$0.315186\pi$
$258$	−6.63768	−0.413244
$259$	0	0
$260$	−11.3607	−0.704559
$261$	52.6186	3.25701
$262$	−1.89979	−0.117369
$263$	−10.8490	−0.668980	−0.334490	−	0.942399i	$-0.608564\pi$
$263$	−10.8490	−0.668980	−0.334490	+	0.942399i	$0.608564\pi$
$264$	−0.927415	−0.0570785
$265$	3.66806	0.225327
$266$	0	0
$267$	−1.92877	−0.118039
$268$	−12.7411	−0.778289
$269$	−0.815536	−0.0497241	−0.0248621	−	0.999691i	$-0.507915\pi$
$269$	−0.815536	−0.0497241	−0.0248621	+	0.999691i	$0.507915\pi$
$270$	−2.82671	−0.172028
$271$	−2.68008	−0.162803	−0.0814016	−	0.996681i	$-0.525940\pi$
$271$	−2.68008	−0.162803	−0.0814016	+	0.996681i	$0.525940\pi$
$272$	27.1878	1.64850
$273$	0	0
$274$	−1.27728	−0.0771636
$275$	0.429014	0.0258705
$276$	25.7664	1.55095
$277$	−29.7471	−1.78733	−0.893665	−	0.448735i	$-0.851875\pi$
$277$	−29.7471	−1.78733	−0.893665	+	0.448735i	$0.851875\pi$
$278$	−1.35738	−0.0814100
$279$	−22.3620	−1.33878
$280$	0	0
$281$	13.9492	0.832142	0.416071	−	0.909332i	$-0.363407\pi$
$281$	13.9492	0.832142	0.416071	+	0.909332i	$0.363407\pi$
$282$	1.99167	0.118602
$283$	4.27910	0.254366	0.127183	−	0.991879i	$-0.459406\pi$
$283$	4.27910	0.254366	0.127183	+	0.991879i	$0.459406\pi$
$284$	5.22150	0.309839
$285$	3.34603	0.198201
$286$	0.401529	0.0237429
$287$	0	0
$288$	−15.7099	−0.925715
$289$	33.0742	1.94554
$290$	1.04385	0.0612967
$291$	42.3669	2.48359
$292$	13.0842	0.765697
$293$	−24.1403	−1.41029	−0.705146	−	0.709062i	$-0.749119\pi$
$293$	−24.1403	−1.41029	−0.705146	+	0.709062i	$0.749119\pi$
$294$	0	0
$295$	6.15976	0.358635
$296$	4.64358	0.269903
$297$	−7.45866	−0.432796
$298$	−3.09463	−0.179267
$299$	−22.4608	−1.29894
$300$	6.60360	0.381259
$301$	0	0
$302$	−1.83638	−0.105672
$303$	−47.4480	−2.72582
$304$	3.84209	0.220359
$305$	7.90953	0.452898
$306$	−9.42965	−0.539057
$307$	14.0955	0.804475	0.402238	−	0.915535i	$-0.368233\pi$
$307$	14.0955	0.804475	0.402238	+	0.915535i	$0.368233\pi$
$308$	0	0
$309$	53.3761	3.03646
$310$	−0.443617	−0.0251958
$311$	0.781255	0.0443009	0.0221504	−	0.999755i	$-0.492949\pi$
$311$	0.781255	0.0443009	0.0221504	+	0.999755i	$0.492949\pi$
$312$	12.4439	0.704494
$313$	7.61271	0.430296	0.215148	−	0.976581i	$-0.430977\pi$
$313$	7.61271	0.430296	0.215148	+	0.976581i	$0.430977\pi$
$314$	1.52757	0.0862056
$315$	0	0
$316$	−3.20294	−0.180179
$317$	−5.63539	−0.316515	−0.158258	−	0.987398i	$-0.550588\pi$
$317$	−5.63539	−0.316515	−0.158258	+	0.987398i	$0.550588\pi$
$318$	−1.99553	−0.111904
$319$	2.75433	0.154213
$320$	7.37252	0.412136
$321$	21.6187	1.20664
$322$	0	0
$323$	7.07631	0.393736
$324$	−66.2820	−3.68233
$325$	−5.75642	−0.319309
$326$	−3.88996	−0.215445
$327$	17.0826	0.944668
$328$	7.69586	0.424933
$329$	0	0
$330$	−0.233396	−0.0128480
$331$	−3.71669	−0.204288	−0.102144	−	0.994770i	$-0.532570\pi$
$331$	−3.71669	−0.204288	−0.102144	+	0.994770i	$0.532570\pi$
$332$	−7.85689	−0.431203
$333$	58.9082	3.22815
$334$	−0.813749	−0.0445264
$335$	−6.45590	−0.352724
$336$	0	0
$337$	10.5696	0.575762	0.287881	−	0.957666i	$-0.407049\pi$
$337$	10.5696	0.575762	0.287881	+	0.957666i	$0.407049\pi$
$338$	−3.27396	−0.178080
$339$	9.32577	0.506506
$340$	13.9656	0.757389
$341$	−1.17054	−0.0633885
$342$	−1.33257	−0.0720569
$343$	0	0
$344$	−7.88256	−0.424999
$345$	13.0558	0.702898
$346$	−1.20493	−0.0647775
$347$	−26.0140	−1.39650	−0.698251	−	0.715853i	$-0.746038\pi$
$347$	−26.0140	−1.39650	−0.698251	+	0.715853i	$0.746038\pi$
$348$	42.3959	2.27266
$349$	−4.54860	−0.243481	−0.121741	−	0.992562i	$-0.538848\pi$
$349$	−4.54860	−0.243481	−0.121741	+	0.992562i	$0.538848\pi$
$350$	0	0
$351$	100.079	5.34180
$352$	−0.822337	−0.0438307
$353$	9.75866	0.519401	0.259701	−	0.965689i	$-0.416376\pi$
$353$	9.75866	0.519401	0.259701	+	0.965689i	$0.416376\pi$
$354$	−3.35109	−0.178108
$355$	2.64572	0.140420
$356$	−1.13763	−0.0602943
$357$	0	0
$358$	2.02599	0.107077
$359$	−11.7831	−0.621888	−0.310944	−	0.950428i	$-0.600645\pi$
$359$	−11.7831	−0.621888	−0.310944	+	0.950428i	$0.600645\pi$
$360$	−5.29504	−0.279073
$361$	1.00000	0.0526316
$362$	−0.432934	−0.0227545
$363$	36.1904	1.89951
$364$	0	0
$365$	6.62975	0.347017
$366$	−4.30301	−0.224922
$367$	28.7505	1.50076	0.750382	−	0.661004i	$-0.229869\pi$
$367$	28.7505	1.50076	0.750382	+	0.661004i	$0.229869\pi$
$368$	14.9913	0.781476
$369$	97.6293	5.08238
$370$	1.16862	0.0607536
$371$	0	0
$372$	−18.0176	−0.934167
$373$	31.9527	1.65445	0.827223	−	0.561874i	$-0.189919\pi$
$373$	31.9527	1.65445	0.827223	+	0.561874i	$0.189919\pi$
$374$	−0.493596	−0.0255232
$375$	3.34603	0.172788
$376$	2.36521	0.121976
$377$	−36.9569	−1.90338
$378$	0	0
$379$	−12.8469	−0.659901	−0.329951	−	0.943998i	$-0.607032\pi$
$379$	−12.8469	−0.659901	−0.329951	+	0.943998i	$0.607032\pi$
$380$	1.97356	0.101242
$381$	5.98068	0.306399
$382$	−1.70156	−0.0870593
$383$	2.36576	0.120885	0.0604423	−	0.998172i	$-0.480749\pi$
$383$	2.36576	0.120885	0.0604423	+	0.998172i	$0.480749\pi$
$384$	−16.8382	−0.859272
$385$	0	0
$386$	3.32981	0.169483
$387$	−99.9978	−5.08317
$388$	24.9890	1.26862
$389$	13.4160	0.680219	0.340110	−	0.940386i	$-0.389536\pi$
$389$	13.4160	0.680219	0.340110	+	0.940386i	$0.389536\pi$
$390$	3.13166	0.158578
$391$	27.6108	1.39634
$392$	0	0
$393$	−39.0969	−1.97218
$394$	1.34112	0.0675646
$395$	−1.62292	−0.0816579
$396$	−6.93936	−0.348716
$397$	−17.9615	−0.901461	−0.450730	−	0.892660i	$-0.648836\pi$
$397$	−17.9615	−0.901461	−0.450730	+	0.892660i	$0.648836\pi$
$398$	3.45681	0.173274
$399$	0	0
$400$	3.84209	0.192104
$401$	−15.8829	−0.793152	−0.396576	−	0.918002i	$-0.629802\pi$
$401$	−15.8829	−0.793152	−0.396576	+	0.918002i	$0.629802\pi$
$402$	3.51220	0.175172
$403$	15.7061	0.782376
$404$	−27.9859	−1.39235
$405$	−33.5849	−1.66885
$406$	0	0
$407$	3.08356	0.152846
$408$	−15.2971	−0.757320
$409$	13.4731	0.666201	0.333101	−	0.942891i	$-0.391905\pi$
$409$	13.4731	0.666201	0.333101	+	0.942891i	$0.391905\pi$
$410$	1.93676	0.0956500
$411$	−26.2860	−1.29659
$412$	31.4825	1.55103
$413$	0	0
$414$	−5.19950	−0.255541
$415$	−3.98106	−0.195423
$416$	11.0339	0.540983
$417$	−27.9342	−1.36795
$418$	−0.0697533	−0.00341175
$419$	−10.0858	−0.492723	−0.246362	−	0.969178i	$-0.579235\pi$
$419$	−10.0858	−0.492723	−0.246362	+	0.969178i	$0.579235\pi$
$420$	0	0
$421$	−25.0368	−1.22022	−0.610110	−	0.792317i	$-0.708875\pi$
$421$	−25.0368	−1.22022	−0.610110	+	0.792317i	$0.708875\pi$
$422$	2.22564	0.108343
$423$	30.0049	1.45889
$424$	−2.36979	−0.115087
$425$	7.07631	0.343251
$426$	−1.43935	−0.0697366
$427$	0	0
$428$	12.7512	0.616352
$429$	8.26330	0.398956
$430$	−1.98375	−0.0956650
$431$	14.4877	0.697848	0.348924	−	0.937151i	$-0.386547\pi$
$431$	14.4877	0.697848	0.348924	+	0.937151i	$0.386547\pi$
$432$	−66.7969	−3.21377
$433$	13.1763	0.633211	0.316605	−	0.948557i	$-0.397457\pi$
$433$	13.1763	0.633211	0.316605	+	0.948557i	$0.397457\pi$
$434$	0	0
$435$	21.4819	1.02998
$436$	10.0757	0.482538
$437$	3.90187	0.186652
$438$	−3.60678	−0.172338
$439$	1.46559	0.0699488	0.0349744	−	0.999388i	$-0.488865\pi$
$439$	1.46559	0.0699488	0.0349744	+	0.999388i	$0.488865\pi$
$440$	−0.277169	−0.0132135
$441$	0	0
$442$	6.62296	0.315022
$443$	−28.0706	−1.33367	−0.666837	−	0.745204i	$-0.732352\pi$
$443$	−28.0706	−1.33367	−0.666837	+	0.745204i	$0.732352\pi$
$444$	47.4636	2.25252
$445$	−0.576435	−0.0273256
$446$	−2.74098	−0.129789
$447$	−63.6861	−3.01225
$448$	0	0
$449$	21.9342	1.03514	0.517569	−	0.855642i	$-0.326837\pi$
$449$	21.9342	1.03514	0.517569	+	0.855642i	$0.326837\pi$
$450$	−1.33257	−0.0628178
$451$	5.11041	0.240640
$452$	5.50056	0.258724
$453$	−37.7918	−1.77562
$454$	−0.642542	−0.0301560
$455$	0	0
$456$	−2.16173	−0.101232
$457$	−4.81613	−0.225289	−0.112645	−	0.993635i	$-0.535932\pi$
$457$	−4.81613	−0.225289	−0.112645	+	0.993635i	$0.535932\pi$
$458$	−2.79085	−0.130408
$459$	−123.026	−5.74235
$460$	7.70059	0.359042
$461$	38.2152	1.77986	0.889930	−	0.456098i	$-0.150753\pi$
$461$	38.2152	1.77986	0.889930	+	0.456098i	$0.150753\pi$
$462$	0	0
$463$	−15.7283	−0.730958	−0.365479	−	0.930820i	$-0.619095\pi$
$463$	−15.7283	−0.730958	−0.365479	+	0.930820i	$0.619095\pi$
$464$	24.6667	1.14512
$465$	−9.12945	−0.423368
$466$	−3.61821	−0.167610
$467$	−24.2986	−1.12441	−0.562203	−	0.826999i	$-0.690046\pi$
$467$	−24.2986	−1.12441	−0.562203	+	0.826999i	$0.690046\pi$
$468$	93.1108	4.30405
$469$	0	0
$470$	0.595236	0.0274562
$471$	31.4367	1.44853
$472$	−3.97958	−0.183175
$473$	−5.23439	−0.240678
$474$	0.882915	0.0405536
$475$	1.00000	0.0458831
$476$	0	0
$477$	−30.0630	−1.37649
$478$	−2.83354	−0.129603
$479$	30.0503	1.37303	0.686517	−	0.727113i	$-0.259139\pi$
$479$	30.0503	1.37303	0.686517	+	0.727113i	$0.259139\pi$
$480$	−6.41368	−0.292743
$481$	−41.3745	−1.88651
$482$	1.15155	0.0524517
$483$	0	0
$484$	21.3460	0.970271
$485$	12.6618	0.574945
$486$	9.79103	0.444130
$487$	−35.9313	−1.62820	−0.814101	−	0.580723i	$-0.802770\pi$
$487$	−35.9313	−1.62820	−0.814101	+	0.580723i	$0.802770\pi$
$488$	−5.11003	−0.231320
$489$	−80.0537	−3.62016
$490$	0	0
$491$	31.0852	1.40286	0.701428	−	0.712740i	$-0.252546\pi$
$491$	31.0852	1.40286	0.701428	+	0.712740i	$0.252546\pi$
$492$	78.6619	3.54635
$493$	45.4308	2.04610
$494$	0.935934	0.0421097
$495$	−3.51615	−0.158039
$496$	−10.4829	−0.470697
$497$	0	0
$498$	2.16581	0.0970525
$499$	−17.1058	−0.765762	−0.382881	−	0.923798i	$-0.625068\pi$
$499$	−17.1058	−0.765762	−0.382881	+	0.923798i	$0.625068\pi$
$500$	1.97356	0.0882605
$501$	−16.7466	−0.748183
$502$	1.73698	0.0775251
$503$	1.78210	0.0794601	0.0397301	−	0.999210i	$-0.487350\pi$
$503$	1.78210	0.0794601	0.0397301	+	0.999210i	$0.487350\pi$
$504$	0	0
$505$	−14.1804	−0.631020
$506$	−0.272168	−0.0120994
$507$	−67.3768	−2.99231
$508$	3.52754	0.156509
$509$	13.0626	0.578990	0.289495	−	0.957179i	$-0.406513\pi$
$509$	13.0626	0.578990	0.289495	+	0.957179i	$0.406513\pi$
$510$	−3.84972	−0.170468
$511$	0	0
$512$	−12.3290	−0.544868
$513$	−17.3856	−0.767592
$514$	−2.85951	−0.126128
$515$	15.9521	0.702933
$516$	−80.5703	−3.54691
$517$	1.57061	0.0690753
$518$	0	0
$519$	−24.7970	−1.08847
$520$	3.71899	0.163089
$521$	−18.0147	−0.789238	−0.394619	−	0.918845i	$-0.629123\pi$
$521$	−18.0147	−0.789238	−0.394619	+	0.918845i	$0.629123\pi$
$522$	−8.55524	−0.374453
$523$	3.60602	0.157680	0.0788401	−	0.996887i	$-0.474878\pi$
$523$	3.60602	0.157680	0.0788401	+	0.996887i	$0.474878\pi$
$524$	−23.0602	−1.00739
$525$	0	0
$526$	1.76394	0.0769115
$527$	−19.3073	−0.841041
$528$	−5.51529	−0.240022
$529$	−7.77542	−0.338062
$530$	−0.596389	−0.0259055
$531$	−50.4847	−2.19085
$532$	0	0
$533$	−68.5704	−2.97011
$534$	0.313597	0.0135707
$535$	6.46100	0.279333
$536$	4.17090	0.180156
$537$	41.6940	1.79923
$538$	0.132598	0.00571669
$539$	0	0
$540$	−34.3116	−1.47653
$541$	10.2231	0.439526	0.219763	−	0.975553i	$-0.429472\pi$
$541$	10.2231	0.439526	0.219763	+	0.975553i	$0.429472\pi$
$542$	0.435753	0.0187172
$543$	−8.90960	−0.382347
$544$	−13.5639	−0.581547
$545$	5.10533	0.218688
$546$	0	0
$547$	8.44524	0.361092	0.180546	−	0.983567i	$-0.442213\pi$
$547$	8.44524	0.361092	0.180546	+	0.983567i	$0.442213\pi$
$548$	−15.5041	−0.662302
$549$	−64.8256	−2.76669
$550$	−0.0697533	−0.00297429
$551$	6.42012	0.273506
$552$	−8.43480	−0.359009
$553$	0	0
$554$	4.83657	0.205486
$555$	24.0497	1.02085
$556$	−16.4763	−0.698749
$557$	7.84656	0.332469	0.166235	−	0.986086i	$-0.446839\pi$
$557$	7.84656	0.332469	0.166235	+	0.986086i	$0.446839\pi$
$558$	3.63584	0.153917
$559$	70.2339	2.97058
$560$	0	0
$561$	−10.1580	−0.428871
$562$	−2.26800	−0.0956699
$563$	−29.1855	−1.23002	−0.615012	−	0.788518i	$-0.710849\pi$
$563$	−29.1855	−1.23002	−0.615012	+	0.788518i	$0.710849\pi$
$564$	24.1756	1.01798
$565$	2.78712	0.117255
$566$	−0.695737	−0.0292440
$567$	0	0
$568$	−1.70929	−0.0717204
$569$	26.6848	1.11869	0.559343	−	0.828936i	$-0.311053\pi$
$569$	26.6848	1.11869	0.559343	+	0.828936i	$0.311053\pi$
$570$	−0.544029	−0.0227869
$571$	−4.24457	−0.177630	−0.0888148	−	0.996048i	$-0.528308\pi$
$571$	−4.24457	−0.177630	−0.0888148	+	0.996048i	$0.528308\pi$
$572$	4.87389	0.203788
$573$	−35.0174	−1.46287
$574$	0	0
$575$	3.90187	0.162719
$576$	−60.4244	−2.51768
$577$	−38.4331	−1.59999	−0.799995	−	0.600006i	$-0.795165\pi$
$577$	−38.4331	−1.59999	−0.799995	+	0.600006i	$0.795165\pi$
$578$	−5.37752	−0.223675
$579$	68.5261	2.84785
$580$	12.6705	0.526115
$581$	0	0
$582$	−6.88841	−0.285534
$583$	−1.57365	−0.0651740
$584$	−4.28322	−0.177241
$585$	47.1790	1.95061
$586$	3.92497	0.162139
$587$	33.0878	1.36568	0.682841	−	0.730567i	$-0.260744\pi$
$587$	33.0878	1.36568	0.682841	+	0.730567i	$0.260744\pi$
$588$	0	0
$589$	−2.72845	−0.112424
$590$	−1.00151	−0.0412317
$591$	27.5997	1.13530
$592$	27.6151	1.13497
$593$	38.8212	1.59420	0.797098	−	0.603850i	$-0.206367\pi$
$593$	38.8212	1.59420	0.797098	+	0.603850i	$0.206367\pi$
$594$	1.21270	0.0497577
$595$	0	0
$596$	−37.5636	−1.53866
$597$	71.1397	2.91155
$598$	3.65189	0.149337
$599$	−1.94592	−0.0795083	−0.0397541	−	0.999209i	$-0.512657\pi$
$599$	−1.94592	−0.0795083	−0.0397541	+	0.999209i	$0.512657\pi$
$600$	−2.16173	−0.0882524
$601$	10.5788	0.431518	0.215759	−	0.976447i	$-0.430777\pi$
$601$	10.5788	0.431518	0.215759	+	0.976447i	$0.430777\pi$
$602$	0	0
$603$	52.9118	2.15474
$604$	−22.2905	−0.906988
$605$	10.8159	0.439731
$606$	7.71455	0.313382
$607$	−7.81398	−0.317160	−0.158580	−	0.987346i	$-0.550692\pi$
$607$	−7.81398	−0.317160	−0.158580	+	0.987346i	$0.550692\pi$
$608$	−1.91680	−0.0777367
$609$	0	0
$610$	−1.28601	−0.0520689
$611$	−21.0741	−0.852566
$612$	−114.460	−4.62678
$613$	−7.61718	−0.307655	−0.153827	−	0.988098i	$-0.549160\pi$
$613$	−7.61718	−0.307655	−0.153827	+	0.988098i	$0.549160\pi$
$614$	−2.29179	−0.0924891
$615$	39.8578	1.60722
$616$	0	0
$617$	−5.97061	−0.240368	−0.120184	−	0.992752i	$-0.538348\pi$
$617$	−5.97061	−0.240368	−0.120184	+	0.992752i	$0.538348\pi$
$618$	−8.67840	−0.349097
$619$	−13.6068	−0.546904	−0.273452	−	0.961886i	$-0.588165\pi$
$619$	−13.6068	−0.546904	−0.273452	+	0.961886i	$0.588165\pi$
$620$	−5.38477	−0.216257
$621$	−67.8362	−2.72217
$622$	−0.127024	−0.00509319
$623$	0	0
$624$	74.0029	2.96249
$625$	1.00000	0.0400000
$626$	−1.23775	−0.0494703
$627$	−1.43549	−0.0573281
$628$	18.5421	0.739910
$629$	50.8612	2.02797
$630$	0	0
$631$	−32.1031	−1.27801	−0.639003	−	0.769204i	$-0.720653\pi$
$631$	−32.1031	−1.27801	−0.639003	+	0.769204i	$0.720653\pi$
$632$	1.04850	0.0417072
$633$	45.8028	1.82050
$634$	0.916257	0.0363892
$635$	1.78740	0.0709307
$636$	−24.2224	−0.960481
$637$	0	0
$638$	−0.447825	−0.0177295
$639$	−21.6840	−0.857806
$640$	−5.03230	−0.198919
$641$	−27.3440	−1.08002	−0.540012	−	0.841657i	$-0.681580\pi$
$641$	−27.3440	−1.08002	−0.540012	+	0.841657i	$0.681580\pi$
$642$	−3.51497	−0.138725
$643$	8.25125	0.325397	0.162699	−	0.986676i	$-0.447980\pi$
$643$	8.25125	0.325397	0.162699	+	0.986676i	$0.447980\pi$
$644$	0	0
$645$	−40.8248	−1.60747
$646$	−1.15053	−0.0452672
$647$	33.9053	1.33295	0.666476	−	0.745526i	$-0.267802\pi$
$647$	33.9053	1.33295	0.666476	+	0.745526i	$0.267802\pi$
$648$	21.6979	0.852374
$649$	−2.64263	−0.103732
$650$	0.935934	0.0367104
$651$	0	0
$652$	−47.2176	−1.84918
$653$	5.26328	0.205968	0.102984	−	0.994683i	$-0.467161\pi$
$653$	5.26328	0.205968	0.102984	+	0.994683i	$0.467161\pi$
$654$	−2.77745	−0.108607
$655$	−11.6846	−0.456554
$656$	45.7669	1.78690
$657$	−54.3367	−2.11988
$658$	0	0
$659$	−27.0002	−1.05178	−0.525890	−	0.850553i	$-0.676268\pi$
$659$	−27.0002	−1.05178	−0.525890	+	0.850553i	$0.676268\pi$
$660$	−2.83304	−0.110276
$661$	38.0408	1.47962	0.739808	−	0.672818i	$-0.234916\pi$
$661$	38.0408	1.47962	0.739808	+	0.672818i	$0.234916\pi$
$662$	0.604295	0.0234866
$663$	136.298	5.29336
$664$	2.57201	0.0998133
$665$	0	0
$666$	−9.57787	−0.371135
$667$	25.0505	0.969958
$668$	−9.87754	−0.382174
$669$	−56.4083	−2.18087
$670$	1.04966	0.0405520
$671$	−3.39330	−0.130997
$672$	0	0
$673$	−1.52284	−0.0587011	−0.0293505	−	0.999569i	$-0.509344\pi$
$673$	−1.52284	−0.0587011	−0.0293505	+	0.999569i	$0.509344\pi$
$674$	−1.71850	−0.0661943
$675$	−17.3856	−0.669171
$676$	−39.7404	−1.52848
$677$	−3.81536	−0.146636	−0.0733182	−	0.997309i	$-0.523359\pi$
$677$	−3.81536	−0.146636	−0.0733182	+	0.997309i	$0.523359\pi$
$678$	−1.51627	−0.0582321
$679$	0	0
$680$	−4.57172	−0.175318
$681$	−13.2232	−0.506716
$682$	0.190318	0.00728766
$683$	−37.8095	−1.44674	−0.723370	−	0.690460i	$-0.757408\pi$
$683$	−37.8095	−1.44674	−0.723370	+	0.690460i	$0.757408\pi$
$684$	−16.1751	−0.618471
$685$	−7.85588	−0.300158
$686$	0	0
$687$	−57.4344	−2.19126
$688$	−46.8772	−1.78718
$689$	21.1149	0.804414
$690$	−2.12273	−0.0808109
$691$	−9.57018	−0.364067	−0.182033	−	0.983292i	$-0.558268\pi$
$691$	−9.57018	−0.364067	−0.182033	+	0.983292i	$0.558268\pi$
$692$	−14.6258	−0.555991
$693$	0	0
$694$	4.22960	0.160553
$695$	−8.34848	−0.316676
$696$	−13.8786	−0.526067
$697$	84.2929	3.19282
$698$	0.739555	0.0279926
$699$	−74.4612	−2.81638
$700$	0	0
$701$	−2.19668	−0.0829676	−0.0414838	−	0.999139i	$-0.513208\pi$
$701$	−2.19668	−0.0829676	−0.0414838	+	0.999139i	$0.513208\pi$
$702$	−16.2718	−0.614138
$703$	7.18753	0.271083
$704$	−3.16292	−0.119207
$705$	12.2497	0.461350
$706$	−1.58666	−0.0597146
$707$	0	0
$708$	−40.6766	−1.52872
$709$	10.6911	0.401514	0.200757	−	0.979641i	$-0.435660\pi$
$709$	10.6911	0.401514	0.200757	+	0.979641i	$0.435660\pi$
$710$	−0.430166	−0.0161439
$711$	13.3013	0.498836
$712$	0.372412	0.0139567
$713$	−10.6460	−0.398697
$714$	0	0
$715$	2.46959	0.0923573
$716$	24.5921	0.919050
$717$	−58.3131	−2.17774
$718$	1.91581	0.0714973
$719$	−29.7949	−1.11116	−0.555580	−	0.831463i	$-0.687504\pi$
$719$	−29.7949	−1.11116	−0.555580	+	0.831463i	$0.687504\pi$
$720$	−31.4893	−1.17354
$721$	0	0
$722$	−0.162590	−0.00605096
$723$	23.6984	0.881354
$724$	−5.25509	−0.195304
$725$	6.42012	0.238437
$726$	−5.88419	−0.218383
$727$	−5.53987	−0.205463	−0.102731	−	0.994709i	$-0.532758\pi$
$727$	−5.53987	−0.205463	−0.102731	+	0.994709i	$0.532758\pi$
$728$	0	0
$729$	100.741	3.73113
$730$	−1.07793	−0.0398959
$731$	−86.3379	−3.19332
$732$	−52.2313	−1.93053
$733$	−17.2838	−0.638390	−0.319195	−	0.947689i	$-0.603412\pi$
$733$	−17.2838	−0.638390	−0.319195	+	0.947689i	$0.603412\pi$
$734$	−4.67453	−0.172540
$735$	0	0
$736$	−7.47912	−0.275684
$737$	2.76967	0.102022
$738$	−15.8735	−0.584312
$739$	28.0267	1.03098	0.515489	−	0.856896i	$-0.327610\pi$
$739$	28.0267	1.03098	0.515489	+	0.856896i	$0.327610\pi$
$740$	14.1851	0.521453
$741$	19.2611	0.707575
$742$	0	0
$743$	2.52819	0.0927503	0.0463752	−	0.998924i	$-0.485233\pi$
$743$	2.52819	0.0927503	0.0463752	+	0.998924i	$0.485233\pi$
$744$	5.89818	0.216238
$745$	−19.0334	−0.697329
$746$	−5.19517	−0.190209
$747$	32.6284	1.19381
$748$	−5.99143	−0.219068
$749$	0	0
$750$	−0.544029	−0.0198651
$751$	−20.9658	−0.765054	−0.382527	−	0.923944i	$-0.624946\pi$
$751$	−20.9658	−0.765054	−0.382527	+	0.923944i	$0.624946\pi$
$752$	14.0658	0.512926
$753$	35.7463	1.30267
$754$	6.00881	0.218828
$755$	−11.2945	−0.411051
$756$	0	0
$757$	23.2438	0.844812	0.422406	−	0.906407i	$-0.361186\pi$
$757$	23.2438	0.844812	0.422406	+	0.906407i	$0.361186\pi$
$758$	2.08877	0.0758676
$759$	−5.60111	−0.203307
$760$	−0.646060	−0.0234351
$761$	38.8082	1.40680	0.703398	−	0.710796i	$-0.251665\pi$
$761$	38.8082	1.40680	0.703398	+	0.710796i	$0.251665\pi$
$762$	−0.972396	−0.0352262
$763$	0	0
$764$	−20.6541	−0.747238
$765$	−57.9967	−2.09687
$766$	−0.384648	−0.0138979
$767$	35.4582	1.28032
$768$	−46.5996	−1.68152
$769$	41.2415	1.48721	0.743603	−	0.668622i	$-0.233116\pi$
$769$	41.2415	1.48721	0.743603	+	0.668622i	$0.233116\pi$
$770$	0	0
$771$	−58.8476	−2.11934
$772$	40.4183	1.45469
$773$	−3.23499	−0.116355	−0.0581773	−	0.998306i	$-0.518529\pi$
$773$	−3.23499	−0.116355	−0.0581773	+	0.998306i	$0.518529\pi$
$774$	16.2586	0.584403
$775$	−2.72845	−0.0980087
$776$	−8.18032	−0.293656
$777$	0	0
$778$	−2.18131	−0.0782036
$779$	11.9120	0.426791
$780$	38.0131	1.36109
$781$	−1.13505	−0.0406153
$782$	−4.48923	−0.160535
$783$	−111.618	−3.98888
$784$	0	0
$785$	9.39523	0.335330
$786$	6.35674	0.226738
$787$	21.6620	0.772167	0.386083	−	0.922464i	$-0.373828\pi$
$787$	21.6620	0.772167	0.386083	+	0.922464i	$0.373828\pi$
$788$	16.2789	0.579913
$789$	36.3012	1.29236
$790$	0.263870	0.00938806
$791$	0	0
$792$	2.27165	0.0807195
$793$	45.5305	1.61684
$794$	2.92035	0.103639
$795$	−12.2734	−0.435294
$796$	41.9599	1.48723
$797$	−9.77694	−0.346317	−0.173159	−	0.984894i	$-0.555397\pi$
$797$	−9.77694	−0.346317	−0.173159	+	0.984894i	$0.555397\pi$
$798$	0	0
$799$	25.9062	0.916494
$800$	−1.91680	−0.0677693
$801$	4.72440	0.166928
$802$	2.58239	0.0911872
$803$	−2.84426	−0.100372
$804$	42.6322	1.50352
$805$	0	0
$806$	−2.55365	−0.0899483
$807$	2.72880	0.0960585
$808$	9.16140	0.322297
$809$	5.43414	0.191054	0.0955272	−	0.995427i	$-0.469546\pi$
$809$	5.43414	0.191054	0.0955272	+	0.995427i	$0.469546\pi$
$810$	5.46056	0.191865
$811$	7.75425	0.272289	0.136144	−	0.990689i	$-0.456529\pi$
$811$	7.75425	0.272289	0.136144	+	0.990689i	$0.456529\pi$
$812$	0	0
$813$	8.96761	0.314508
$814$	−0.501354	−0.0175725
$815$	−23.9250	−0.838057
$816$	−90.9711	−3.18462
$817$	−12.2010	−0.426858
$818$	−2.19058	−0.0765919
$819$	0	0
$820$	23.5091	0.820972
$821$	53.8309	1.87871	0.939356	−	0.342944i	$-0.111424\pi$
$821$	53.8309	1.87871	0.939356	+	0.342944i	$0.111424\pi$
$822$	4.27383	0.149067
$823$	26.2581	0.915301	0.457650	−	0.889132i	$-0.348691\pi$
$823$	26.2581	0.915301	0.457650	+	0.889132i	$0.348691\pi$
$824$	−10.3060	−0.359027
$825$	−1.43549	−0.0499775
$826$	0	0
$827$	8.54688	0.297204	0.148602	−	0.988897i	$-0.452523\pi$
$827$	8.54688	0.297204	0.148602	+	0.988897i	$0.452523\pi$
$828$	−63.1132	−2.19333
$829$	−38.6838	−1.34354	−0.671772	−	0.740758i	$-0.734467\pi$
$829$	−38.6838	−1.34354	−0.671772	+	0.740758i	$0.734467\pi$
$830$	0.647280	0.0224674
$831$	99.5346	3.45282
$832$	42.4393	1.47132
$833$	0	0
$834$	4.54182	0.157270
$835$	−5.00493	−0.173203
$836$	−0.846688	−0.0292833
$837$	47.4356	1.63961
$838$	1.63985	0.0566475
$839$	39.7958	1.37390	0.686951	−	0.726704i	$-0.258949\pi$
$839$	39.7958	1.37390	0.686951	+	0.726704i	$0.258949\pi$
$840$	0	0
$841$	12.2180	0.421309
$842$	4.07072	0.140286
$843$	−46.6745	−1.60756
$844$	27.0156	0.929915
$845$	−20.1364	−0.692712
$846$	−4.87849	−0.167726
$847$	0	0
$848$	−14.0930	−0.483956
$849$	−14.3180	−0.491392
$850$	−1.15053	−0.0394630
$851$	28.0448	0.961364
$852$	−17.4713	−0.598556
$853$	16.5832	0.567796	0.283898	−	0.958854i	$-0.408372\pi$
$853$	16.5832	0.567796	0.283898	+	0.958854i	$0.408372\pi$
$854$	0	0
$855$	−8.19589	−0.280293
$856$	−4.17419	−0.142671
$857$	14.6297	0.499740	0.249870	−	0.968279i	$-0.419612\pi$
$857$	14.6297	0.499740	0.249870	+	0.968279i	$0.419612\pi$
$858$	−1.34353	−0.0458673
$859$	55.3776	1.88946	0.944729	−	0.327852i	$-0.106325\pi$
$859$	55.3776	1.88946	0.944729	+	0.327852i	$0.106325\pi$
$860$	−24.0794	−0.821101
$861$	0	0
$862$	−2.35555	−0.0802303
$863$	−49.6705	−1.69080	−0.845401	−	0.534132i	$-0.820638\pi$
$863$	−49.6705	−1.69080	−0.845401	+	0.534132i	$0.820638\pi$
$864$	33.3247	1.13373
$865$	−7.41087	−0.251977
$866$	−2.14232	−0.0727991
$867$	−110.667	−3.75845
$868$	0	0
$869$	0.696256	0.0236189
$870$	−3.49273	−0.118415
$871$	−37.1629	−1.25922
$872$	−3.29835	−0.111696
$873$	−103.775	−3.51225
$874$	−0.634403	−0.0214590
$875$	0	0
$876$	−43.7802	−1.47920
$877$	8.24405	0.278382	0.139191	−	0.990266i	$-0.455550\pi$
$877$	8.24405	0.278382	0.139191	+	0.990266i	$0.455550\pi$
$878$	−0.238290	−0.00804189
$879$	80.7741	2.72444
$880$	−1.64831	−0.0555645
$881$	−31.3524	−1.05629	−0.528145	−	0.849154i	$-0.677112\pi$
$881$	−31.3524	−1.05629	−0.528145	+	0.849154i	$0.677112\pi$
$882$	0	0
$883$	24.0326	0.808761	0.404381	−	0.914591i	$-0.367487\pi$
$883$	24.0326	0.808761	0.404381	+	0.914591i	$0.367487\pi$
$884$	80.3916	2.70386
$885$	−20.6107	−0.692822
$886$	4.56398	0.153330
$887$	−9.30530	−0.312441	−0.156221	−	0.987722i	$-0.549931\pi$
$887$	−9.30530	−0.312441	−0.156221	+	0.987722i	$0.549931\pi$
$888$	−15.5375	−0.521406
$889$	0	0
$890$	0.0937223	0.00314158
$891$	14.4084	0.482700
$892$	−33.2709	−1.11399
$893$	3.66097	0.122510
$894$	10.3547	0.346313
$895$	12.4608	0.416517
$896$	0	0
$897$	75.1544	2.50933
$898$	−3.56627	−0.119008
$899$	−17.5170	−0.584223
$900$	−16.1751	−0.539171
$901$	−25.9563	−0.864731
$902$	−0.830900	−0.0276659
$903$	0	0
$904$	−1.80065	−0.0598886
$905$	−2.66274	−0.0885125
$906$	6.14456	0.204139
$907$	−43.8256	−1.45521	−0.727603	−	0.685999i	$-0.759365\pi$
$907$	−43.8256	−1.45521	−0.727603	+	0.685999i	$0.759365\pi$
$908$	−7.79938	−0.258832
$909$	116.221	3.85481
$910$	0	0
$911$	38.8428	1.28692	0.643459	−	0.765480i	$-0.277499\pi$
$911$	38.8428	1.28692	0.643459	+	0.765480i	$0.277499\pi$
$912$	−12.8557	−0.425695
$913$	1.70793	0.0565244
$914$	0.783053	0.0259011
$915$	−26.4655	−0.874922
$916$	−33.8762	−1.11930
$917$	0	0
$918$	20.0027	0.660188
$919$	−46.0432	−1.51882	−0.759412	−	0.650610i	$-0.774513\pi$
$919$	−46.0432	−1.51882	−0.759412	+	0.650610i	$0.774513\pi$
$920$	−2.52084	−0.0831097
$921$	−47.1641	−1.55411
$922$	−6.21339	−0.204627
$923$	15.2299	0.501297
$924$	0	0
$925$	7.18753	0.236325
$926$	2.55727	0.0840369
$927$	−130.742	−4.29412
$928$	−12.3061	−0.403968
$929$	33.7831	1.10839	0.554193	−	0.832388i	$-0.313027\pi$
$929$	33.7831	1.10839	0.554193	+	0.832388i	$0.313027\pi$
$930$	1.48435	0.0486739
$931$	0	0
$932$	−43.9190	−1.43861
$933$	−2.61410	−0.0855817
$934$	3.95070	0.129271
$935$	−3.03584	−0.0992826
$936$	−30.4805	−0.996285
$937$	−8.10845	−0.264891	−0.132446	−	0.991190i	$-0.542283\pi$
$937$	−8.10845	−0.264891	−0.132446	+	0.991190i	$0.542283\pi$
$938$	0	0
$939$	−25.4723	−0.831257
$940$	7.22516	0.235659
$941$	−19.6784	−0.641498	−0.320749	−	0.947164i	$-0.603935\pi$
$941$	−19.6784	−0.641498	−0.320749	+	0.947164i	$0.603935\pi$
$942$	−5.11128	−0.166534
$943$	46.4790	1.51356
$944$	−23.6663	−0.770274
$945$	0	0
$946$	0.851058	0.0276703
$947$	45.6312	1.48282	0.741408	−	0.671055i	$-0.234159\pi$
$947$	45.6312	1.48282	0.741408	+	0.671055i	$0.234159\pi$
$948$	10.7171	0.348075
$949$	38.1636	1.23884
$950$	−0.162590	−0.00527510
$951$	18.8562	0.611453
$952$	0	0
$953$	−21.0135	−0.680696	−0.340348	−	0.940300i	$-0.610545\pi$
$953$	−21.0135	−0.680696	−0.340348	+	0.940300i	$0.610545\pi$
$954$	4.88793	0.158253
$955$	−10.4654	−0.338651
$956$	−34.3944	−1.11240
$957$	−9.21604	−0.297912
$958$	−4.88587	−0.157855
$959$	0	0
$960$	−24.6686	−0.796177
$961$	−23.5556	−0.759857
$962$	6.72706	0.216889
$963$	−52.9536	−1.70641
$964$	13.9779	0.450197
$965$	20.4799	0.659270
$966$	0	0
$967$	28.6328	0.920769	0.460384	−	0.887720i	$-0.347712\pi$
$967$	28.6328	0.920769	0.460384	+	0.887720i	$0.347712\pi$
$968$	−6.98775	−0.224595
$969$	−23.6775	−0.760631
$970$	−2.05868	−0.0661004
$971$	16.3552	0.524864	0.262432	−	0.964950i	$-0.415475\pi$
$971$	16.3552	0.524864	0.262432	+	0.964950i	$0.415475\pi$
$972$	118.847	3.81201
$973$	0	0
$974$	5.84206	0.187192
$975$	19.2611	0.616850
$976$	−30.3891	−0.972731
$977$	−3.83078	−0.122558	−0.0612788	−	0.998121i	$-0.519518\pi$
$977$	−3.83078	−0.122558	−0.0612788	+	0.998121i	$0.519518\pi$
$978$	13.0159	0.416203
$979$	0.247299	0.00790371
$980$	0	0
$981$	−41.8427	−1.33593
$982$	−5.05413	−0.161284
$983$	52.3305	1.66908	0.834542	−	0.550945i	$-0.185733\pi$
$983$	52.3305	1.66908	0.834542	+	0.550945i	$0.185733\pi$
$984$	−25.7505	−0.820897
$985$	8.24849	0.262819
$986$	−7.38657	−0.235236
$987$	0	0
$988$	11.3607	0.361431
$989$	−47.6066	−1.51380
$990$	0.571690	0.0181695
$991$	0.0540071	0.00171559	0.000857795	−	1.00000i	$-0.499727\pi$
$991$	0.0540071	0.00171559	0.000857795		1.00000i	$0.499727\pi$
$992$	5.22990	0.166049
$993$	12.4361	0.394649
$994$	0	0
$995$	21.2610	0.674018
$996$	26.2893	0.833010
$997$	41.5667	1.31643	0.658215	−	0.752830i	$-0.271312\pi$
$997$	41.5667	1.31643	0.658215	+	0.752830i	$0.271312\pi$
$998$	2.78123	0.0880383
$999$	−124.959	−3.95354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4655.2.a.br.1.12	✓	26
7.6	odd	2		4655.2.a.bs.1.12	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4655.2.a.br.1.12	✓	26	1.1	even	1	trivial
4655.2.a.bs.1.12	yes	26	7.6	odd	2

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:	\( N \)	\(=\)	\( 4655 = 5 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4655.a (trivial)

\(f(q)\)	\(=\)	\(q-0.162590 q^{2} -3.34603 q^{3} -1.97356 q^{4} -1.00000 q^{5} +0.544029 q^{6} +0.646060 q^{8} +8.19589 q^{9} +0.162590 q^{10} +0.429014 q^{11} +6.60360 q^{12} -5.75642 q^{13} +3.34603 q^{15} +3.84209 q^{16} +7.07631 q^{17} -1.33257 q^{18} +1.00000 q^{19} +1.97356 q^{20} -0.0697533 q^{22} +3.90187 q^{23} -2.16173 q^{24} +1.00000 q^{25} +0.935934 q^{26} -17.3856 q^{27} +6.42012 q^{29} -0.544029 q^{30} -2.72845 q^{31} -1.91680 q^{32} -1.43549 q^{33} -1.15053 q^{34} -16.1751 q^{36} +7.18753 q^{37} -0.162590 q^{38} +19.2611 q^{39} -0.646060 q^{40} +11.9120 q^{41} -12.2010 q^{43} -0.846688 q^{44} -8.19589 q^{45} -0.634403 q^{46} +3.66097 q^{47} -12.8557 q^{48} -0.162590 q^{50} -23.6775 q^{51} +11.3607 q^{52} -3.66806 q^{53} +2.82671 q^{54} -0.429014 q^{55} -3.34603 q^{57} -1.04385 q^{58} -6.15976 q^{59} -6.60360 q^{60} -7.90953 q^{61} +0.443617 q^{62} -7.37252 q^{64} +5.75642 q^{65} +0.233396 q^{66} +6.45590 q^{67} -13.9656 q^{68} -13.0558 q^{69} -2.64572 q^{71} +5.29504 q^{72} -6.62975 q^{73} -1.16862 q^{74} -3.34603 q^{75} -1.97356 q^{76} -3.13166 q^{78} +1.62292 q^{79} -3.84209 q^{80} +33.5849 q^{81} -1.93676 q^{82} +3.98106 q^{83} -7.07631 q^{85} +1.98375 q^{86} -21.4819 q^{87} +0.277169 q^{88} +0.576435 q^{89} +1.33257 q^{90} -7.70059 q^{92} +9.12945 q^{93} -0.595236 q^{94} -1.00000 q^{95} +6.41368 q^{96} -12.6618 q^{97} +3.51615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 - 6 * q^3 + 36 * q^4 - 26 * q^5 + 4 * q^6 + 12 * q^8 + 44 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 14 * q^13 + 6 * q^15 + 64 * q^16 - 18 * q^17 + 8 * q^18 + 26 * q^19 - 36 * q^20 + 36 * q^22 + 44 * q^24 + 26 * q^25 + 8 * q^26 - 30 * q^27 + 22 * q^29 - 4 * q^30 + 28 * q^32 - 38 * q^33 + 68 * q^36 + 48 * q^37 + 4 * q^38 + 26 * q^39 - 12 * q^40 - 4 * q^41 + 16 * q^43 + 44 * q^44 - 44 * q^45 + 48 * q^46 - 22 * q^47 - 48 * q^48 + 4 * q^50 + 34 * q^51 - 32 * q^52 + 28 * q^53 + 28 * q^54 - 14 * q^55 - 6 * q^57 + 52 * q^58 + 8 * q^59 + 20 * q^60 + 28 * q^61 + 16 * q^62 + 52 * q^64 + 14 * q^65 + 24 * q^66 + 60 * q^67 - 52 * q^68 + 4 * q^69 + 8 * q^71 + 36 * q^72 + 4 * q^73 + 8 * q^74 - 6 * q^75 + 36 * q^76 - 76 * q^78 + 50 * q^79 - 64 * q^80 + 114 * q^81 + 36 * q^82 - 20 * q^83 + 18 * q^85 + 40 * q^86 - 18 * q^87 + 108 * q^88 + 20 * q^89 - 8 * q^90 - 48 * q^92 + 32 * q^93 + 80 * q^94 - 26 * q^95 + 140 * q^96 - 26 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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