LMFDB - Embedded newform 605.2.a.j.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(1,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.83094932229$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.35567$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.35567 q^{2} +0.575493 q^{3} -0.162147 q^{4} -1.00000 q^{5} +0.780181 q^{6} -3.64941 q^{7} -2.93117 q^{8} -2.66881 q^{9} -1.35567 q^{10} -0.0933146 q^{12} -2.83095 q^{13} -4.94742 q^{14} -0.575493 q^{15} -3.64941 q^{16} +3.69195 q^{17} -3.61803 q^{18} -0.0951243 q^{19} +0.162147 q^{20} -2.10021 q^{21} +1.16215 q^{23} -1.68687 q^{24} +1.00000 q^{25} -3.83785 q^{26} -3.26236 q^{27} +0.591742 q^{28} -6.75389 q^{29} -0.780181 q^{30} +6.77837 q^{31} +0.914918 q^{32} +5.00509 q^{34} +3.64941 q^{35} +0.432740 q^{36} +9.83980 q^{37} -0.128958 q^{38} -1.62920 q^{39} +2.93117 q^{40} -8.31822 q^{41} -2.84720 q^{42} -2.96862 q^{43} +2.66881 q^{45} +1.57549 q^{46} -2.22491 q^{47} -2.10021 q^{48} +6.31822 q^{49} +1.35567 q^{50} +2.12469 q^{51} +0.459031 q^{52} +2.99393 q^{53} -4.42270 q^{54} +10.6970 q^{56} -0.0547434 q^{57} -9.15607 q^{58} -8.50860 q^{59} +0.0933146 q^{60} -8.48037 q^{61} +9.18926 q^{62} +9.73958 q^{63} +8.53916 q^{64} +2.83095 q^{65} -13.4153 q^{67} -0.598640 q^{68} +0.668808 q^{69} +4.94742 q^{70} +8.30309 q^{71} +7.82272 q^{72} -1.32003 q^{73} +13.3396 q^{74} +0.575493 q^{75} +0.0154241 q^{76} -2.20866 q^{78} -13.8661 q^{79} +3.64941 q^{80} +6.12896 q^{81} -11.2768 q^{82} -10.6445 q^{83} +0.340544 q^{84} -3.69195 q^{85} -4.02448 q^{86} -3.88682 q^{87} -12.1612 q^{89} +3.61803 q^{90} +10.3313 q^{91} -0.188439 q^{92} +3.90091 q^{93} -3.01625 q^{94} +0.0951243 q^{95} +0.526529 q^{96} -4.33133 q^{97} +8.56545 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 4 q^{5} - q^{6} - 3 q^{7} - 3 q^{8} + q^{10} + 8 q^{12} - q^{13} + 2 q^{14} - 3 q^{16} + q^{17} - 10 q^{18} - 20 q^{19} + q^{20} - 10 q^{21} + 5 q^{23} - 11 q^{24} + 4 q^{25}+ \cdots + 8 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 4 * q^5 - q^6 - 3 * q^7 - 3 * q^8 + q^10 + 8 * q^12 - q^13 + 2 * q^14 - 3 * q^16 + q^17 - 10 * q^18 - 20 * q^19 + q^20 - 10 * q^21 + 5 * q^23 - 11 * q^24 + 4 * q^25 - 15 * q^26 - 15 * q^27 - 13 * q^28 - 12 * q^29 + q^30 - 5 * q^31 + 8 * q^32 + 2 * q^34 + 3 * q^35 + 7 * q^37 + 20 * q^38 - 7 * q^39 + 3 * q^40 - 11 * q^41 + 12 * q^42 - 19 * q^43 + 4 * q^46 + 5 * q^47 - 10 * q^48 + 3 * q^49 - q^50 - 7 * q^51 + 11 * q^52 - 11 * q^53 + 8 * q^54 + 11 * q^56 + 5 * q^57 - 14 * q^58 + 9 * q^59 - 8 * q^60 - 12 * q^61 + 35 * q^62 + 5 * q^63 - 3 * q^64 + q^65 - 19 * q^67 + 3 * q^68 - 8 * q^69 - 2 * q^70 + 5 * q^71 + 25 * q^72 - 11 * q^73 - 8 * q^78 - 34 * q^79 + 3 * q^80 + 4 * q^81 - 6 * q^82 + 11 * q^83 - 11 * q^84 - q^85 + q^86 + 19 * q^87 - 8 * q^89 + 10 * q^90 - 8 * q^91 - 12 * q^92 - 5 * q^93 + q^94 + 20 * q^95 + 34 * q^96 + 32 * q^97 + 8 * q^98

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 $

$2$	1.35567	0.958606	0.479303	−	0.877649i	$-0.340889\pi$
$2$	1.35567	0.958606	0.479303	+	0.877649i	$0.340889\pi$
$3$	0.575493	0.332261	0.166131	−	0.986104i	$-0.446873\pi$
$3$	0.575493	0.332261	0.166131	+	0.986104i	$0.446873\pi$
$4$	−0.162147	−0.0810736
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.780181	0.318508
$7$	−3.64941	−1.37935	−0.689674	−	0.724120i	$-0.742246\pi$
$7$	−3.64941	−1.37935	−0.689674	+	0.724120i	$0.742246\pi$
$8$	−2.93117	−1.03632
$9$	−2.66881	−0.889603
$10$	−1.35567	−0.428702
$11$	0	0
$11$	0	0
$12$	−0.0933146	−0.0269376
$13$	−2.83095	−0.785166	−0.392583	−	0.919717i	$-0.628418\pi$
$13$	−2.83095	−0.785166	−0.392583	+	0.919717i	$0.628418\pi$
$14$	−4.94742	−1.32225
$15$	−0.575493	−0.148592
$16$	−3.64941	−0.912353
$17$	3.69195	0.895431	0.447715	−	0.894176i	$-0.352238\pi$
$17$	3.69195	0.895431	0.447715	+	0.894176i	$0.352238\pi$
$18$	−3.61803	−0.852779
$19$	−0.0951243	−0.0218230	−0.0109115	−	0.999940i	$-0.503473\pi$
$19$	−0.0951243	−0.0218230	−0.0109115	+	0.999940i	$0.503473\pi$
$20$	0.162147	0.0362572
$21$	−2.10021	−0.458304
$22$	0	0
$23$	1.16215	0.242324	0.121162	−	0.992633i	$-0.461338\pi$
$23$	1.16215	0.242324	0.121162	+	0.992633i	$0.461338\pi$
$24$	−1.68687	−0.344330
$25$	1.00000	0.200000
$26$	−3.83785	−0.752665
$27$	−3.26236	−0.627841
$28$	0.591742	0.111829
$29$	−6.75389	−1.25417	−0.627083	−	0.778953i	$-0.715751\pi$
$29$	−6.75389	−1.25417	−0.627083	+	0.778953i	$0.715751\pi$
$30$	−0.780181	−0.142441
$31$	6.77837	1.21743	0.608716	−	0.793388i	$-0.291685\pi$
$31$	6.77837	1.21743	0.608716	+	0.793388i	$0.291685\pi$
$32$	0.914918	0.161736
$33$	0	0
$34$	5.00509	0.858366
$35$	3.64941	0.616864
$36$	0.432740	0.0721233
$37$	9.83980	1.61765	0.808826	−	0.588048i	$-0.200103\pi$
$37$	9.83980	1.61765	0.808826	+	0.588048i	$0.200103\pi$
$38$	−0.128958	−0.0209197
$39$	−1.62920	−0.260880
$40$	2.93117	0.463458
$41$	−8.31822	−1.29909	−0.649544	−	0.760324i	$-0.725040\pi$
$41$	−8.31822	−1.29909	−0.649544	+	0.760324i	$0.725040\pi$
$42$	−2.84720	−0.439333
$43$	−2.96862	−0.452710	−0.226355	−	0.974045i	$-0.572681\pi$
$43$	−2.96862	−0.452710	−0.226355	+	0.974045i	$0.572681\pi$
$44$	0	0
$45$	2.66881	0.397842
$46$	1.57549	0.232294
$47$	−2.22491	−0.324536	−0.162268	−	0.986747i	$-0.551881\pi$
$47$	−2.22491	−0.324536	−0.162268	+	0.986747i	$0.551881\pi$
$48$	−2.10021	−0.303140
$49$	6.31822	0.902603
$50$	1.35567	0.191721
$51$	2.12469	0.297517
$52$	0.459031	0.0636562
$53$	2.99393	0.411248	0.205624	−	0.978631i	$-0.434078\pi$
$53$	2.99393	0.411248	0.205624	+	0.978631i	$0.434078\pi$
$54$	−4.42270	−0.601853
$55$	0	0
$56$	10.6970	1.42945
$57$	−0.0547434	−0.00725094
$58$	−9.15607	−1.20225
$59$	−8.50860	−1.10773	−0.553863	−	0.832608i	$-0.686847\pi$
$59$	−8.50860	−1.10773	−0.553863	+	0.832608i	$0.686847\pi$
$60$	0.0933146	0.0120469
$61$	−8.48037	−1.08580	−0.542900	−	0.839797i	$-0.682674\pi$
$61$	−8.48037	−1.08580	−0.542900	+	0.839797i	$0.682674\pi$
$62$	9.18926	1.16704
$63$	9.73958	1.22707
$64$	8.53916	1.06739
$65$	2.83095	0.351137
$66$	0	0
$67$	−13.4153	−1.63894	−0.819469	−	0.573123i	$-0.805732\pi$
$67$	−13.4153	−1.63894	−0.819469	+	0.573123i	$0.805732\pi$
$68$	−0.598640	−0.0725958
$69$	0.668808	0.0805150
$70$	4.94742	0.591329
$71$	8.30309	0.985396	0.492698	−	0.870200i	$-0.336011\pi$
$71$	8.30309	0.985396	0.492698	+	0.870200i	$0.336011\pi$
$72$	7.82272	0.921917
$73$	−1.32003	−0.154498	−0.0772490	−	0.997012i	$-0.524614\pi$
$73$	−1.32003	−0.154498	−0.0772490	+	0.997012i	$0.524614\pi$
$74$	13.3396	1.55069
$75$	0.575493	0.0664522
$76$	0.0154241	0.00176927
$77$	0	0
$78$	−2.20866	−0.250081
$79$	−13.8661	−1.56006	−0.780028	−	0.625744i	$-0.784795\pi$
$79$	−13.8661	−1.56006	−0.780028	+	0.625744i	$0.784795\pi$
$80$	3.64941	0.408017
$81$	6.12896	0.680995
$82$	−11.2768	−1.24531
$83$	−10.6445	−1.16838	−0.584191	−	0.811616i	$-0.698588\pi$
$83$	−10.6445	−1.16838	−0.584191	+	0.811616i	$0.698588\pi$
$84$	0.340544	0.0371564
$85$	−3.69195	−0.400449
$86$	−4.02448	−0.433971
$87$	−3.88682	−0.416710
$88$	0	0
$89$	−12.1612	−1.28908	−0.644540	−	0.764570i	$-0.722951\pi$
$89$	−12.1612	−1.28908	−0.644540	+	0.764570i	$0.722951\pi$
$90$	3.61803	0.381374
$91$	10.3313	1.08302
$92$	−0.188439	−0.0196461
$93$	3.90091	0.404505
$94$	−3.01625	−0.311102
$95$	0.0951243	0.00975955
$96$	0.526529	0.0537387
$97$	−4.33133	−0.439780	−0.219890	−	0.975525i	$-0.570570\pi$
$97$	−4.33133	−0.439780	−0.219890	+	0.975525i	$0.570570\pi$
$98$	8.56545	0.865241
$99$	0	0
$100$	−0.162147	−0.0162147
$101$	9.90570	0.985654	0.492827	−	0.870127i	$-0.335964\pi$
$101$	9.90570	0.985654	0.492827	+	0.870127i	$0.335964\pi$
$102$	2.88039	0.285201
$103$	4.06590	0.400625	0.200313	−	0.979732i	$-0.435804\pi$
$103$	4.06590	0.400625	0.200313	+	0.979732i	$0.435804\pi$
$104$	8.29800	0.813686
$105$	2.10021	0.204960
$106$	4.05879	0.394225
$107$	1.93858	0.187409	0.0937046	−	0.995600i	$-0.470129\pi$
$107$	1.93858	0.187409	0.0937046	+	0.995600i	$0.470129\pi$
$108$	0.528983	0.0509014
$109$	6.12664	0.586825	0.293413	−	0.955986i	$-0.405209\pi$
$109$	6.12664	0.586825	0.293413	+	0.955986i	$0.405209\pi$
$110$	0	0
$111$	5.66273	0.537483
$112$	13.3182	1.25845
$113$	5.78527	0.544232	0.272116	−	0.962264i	$-0.412276\pi$
$113$	5.78527	0.544232	0.272116	+	0.962264i	$0.412276\pi$
$114$	−0.0742142	−0.00695080
$115$	−1.16215	−0.108371
$116$	1.09512	0.101680
$117$	7.55527	0.698485
$118$	−11.5349	−1.06187
$119$	−13.4735	−1.23511
$120$	1.68687	0.153989
$121$	0	0
$122$	−11.4966	−1.04085
$123$	−4.78708	−0.431636
$124$	−1.09909	−0.0987016
$125$	−1.00000	−0.0894427
$126$	13.2037	1.17628
$127$	2.43783	0.216322	0.108161	−	0.994133i	$-0.465504\pi$
$127$	2.43783	0.216322	0.108161	+	0.994133i	$0.465504\pi$
$128$	9.74648	0.861475
$129$	−1.70842	−0.150418
$130$	3.83785	0.336602
$131$	7.04156	0.615224	0.307612	−	0.951512i	$-0.400470\pi$
$131$	7.04156	0.615224	0.307612	+	0.951512i	$0.400470\pi$
$132$	0	0
$133$	0.347148	0.0301016
$134$	−18.1868	−1.57110
$135$	3.26236	0.280779
$136$	−10.8217	−0.927956
$137$	−9.57286	−0.817864	−0.408932	−	0.912565i	$-0.634099\pi$
$137$	−9.57286	−0.817864	−0.408932	+	0.912565i	$0.634099\pi$
$138$	0.906685	0.0771822
$139$	0.515502	0.0437243	0.0218621	−	0.999761i	$-0.493041\pi$
$139$	0.515502	0.0437243	0.0218621	+	0.999761i	$0.493041\pi$
$140$	−0.591742	−0.0500113
$141$	−1.28042	−0.107831
$142$	11.2563	0.944607
$143$	0	0
$144$	9.73958	0.811632
$145$	6.75389	0.560880
$146$	−1.78953	−0.148103
$147$	3.63609	0.299900
$148$	−1.59550	−0.131149
$149$	−8.15983	−0.668479	−0.334240	−	0.942488i	$-0.608479\pi$
$149$	−8.15983	−0.668479	−0.334240	+	0.942488i	$0.608479\pi$
$150$	0.780181	0.0637015
$151$	1.94023	0.157893	0.0789466	−	0.996879i	$-0.474844\pi$
$151$	1.94023	0.157893	0.0789466	+	0.996879i	$0.474844\pi$
$152$	0.278825	0.0226157
$153$	−9.85312	−0.796577
$154$	0	0
$155$	−6.77837	−0.544452
$156$	0.264169	0.0211505
$157$	21.2745	1.69789	0.848944	−	0.528483i	$-0.177239\pi$
$157$	21.2745	1.69789	0.848944	+	0.528483i	$0.177239\pi$
$158$	−18.7979	−1.49548
$159$	1.72298	0.136642
$160$	−0.914918	−0.0723306
$161$	−4.24116	−0.334250
$162$	8.30887	0.652807
$163$	−15.9810	−1.25173	−0.625863	−	0.779933i	$-0.715253\pi$
$163$	−15.9810	−1.25173	−0.625863	+	0.779933i	$0.715253\pi$
$164$	1.34878	0.105322
$165$	0	0
$166$	−14.4304	−1.12002
$167$	17.7090	1.37037	0.685183	−	0.728371i	$-0.259722\pi$
$167$	17.7090	1.37037	0.685183	+	0.728371i	$0.259722\pi$
$168$	6.15607	0.474951
$169$	−4.98569	−0.383515
$170$	−5.00509	−0.383873
$171$	0.253869	0.0194138
$172$	0.481353	0.0367029
$173$	15.8855	1.20775	0.603875	−	0.797079i	$-0.293622\pi$
$173$	15.8855	1.20775	0.603875	+	0.797079i	$0.293622\pi$
$174$	−5.26926	−0.399461
$175$	−3.64941	−0.275870
$176$	0	0
$177$	−4.89664	−0.368054
$178$	−16.4866	−1.23572
$179$	−16.8810	−1.26175	−0.630874	−	0.775885i	$-0.717304\pi$
$179$	−16.8810	−1.26175	−0.630874	+	0.775885i	$0.717304\pi$
$180$	−0.432740	−0.0322545
$181$	−24.0874	−1.79040	−0.895200	−	0.445664i	$-0.852968\pi$
$181$	−24.0874	−1.79040	−0.895200	+	0.445664i	$0.852968\pi$
$182$	14.0059	1.03819
$183$	−4.88039	−0.360769
$184$	−3.40645	−0.251127
$185$	−9.83980	−0.723436
$186$	5.28836	0.387761
$187$	0	0
$188$	0.360762	0.0263113
$189$	11.9057	0.866012
$190$	0.128958	0.00935557
$191$	5.38279	0.389485	0.194743	−	0.980854i	$-0.437613\pi$
$191$	5.38279	0.389485	0.194743	+	0.980854i	$0.437613\pi$
$192$	4.91423	0.354654
$193$	18.2840	1.31611	0.658057	−	0.752968i	$-0.271378\pi$
$193$	18.2840	1.31611	0.658057	+	0.752968i	$0.271378\pi$
$194$	−5.87187	−0.421576
$195$	1.62920	0.116669
$196$	−1.02448	−0.0731773
$197$	2.64566	0.188496	0.0942478	−	0.995549i	$-0.469955\pi$
$197$	2.64566	0.188496	0.0942478	+	0.995549i	$0.469955\pi$
$198$	0	0
$199$	6.52800	0.462757	0.231379	−	0.972864i	$-0.425676\pi$
$199$	6.52800	0.462757	0.231379	+	0.972864i	$0.425676\pi$
$200$	−2.93117	−0.207265
$201$	−7.72041	−0.544555
$202$	13.4289	0.944854
$203$	24.6477	1.72993
$204$	−0.344513	−0.0241208
$205$	8.31822	0.580970
$206$	5.51204	0.384042
$207$	−3.10155	−0.215572
$208$	10.3313	0.716349
$209$	0	0
$210$	2.84720	0.196476
$211$	−27.4478	−1.88958	−0.944792	−	0.327671i	$-0.893736\pi$
$211$	−27.4478	−1.88958	−0.944792	+	0.327671i	$0.893736\pi$
$212$	−0.485457	−0.0333413
$213$	4.77837	0.327409
$214$	2.62808	0.179652
$215$	2.96862	0.202458
$216$	9.56252	0.650647
$217$	−24.7371	−1.67926
$218$	8.30573	0.562535
$219$	−0.759669	−0.0513337
$220$	0	0
$221$	−10.4518	−0.703061
$222$	7.67682	0.515235
$223$	−5.08194	−0.340312	−0.170156	−	0.985417i	$-0.554427\pi$
$223$	−5.08194	−0.340312	−0.170156	+	0.985417i	$0.554427\pi$
$224$	−3.33892	−0.223091
$225$	−2.66881	−0.177921
$226$	7.84294	0.521705
$227$	3.73980	0.248219	0.124110	−	0.992269i	$-0.460393\pi$
$227$	3.73980	0.248219	0.124110	+	0.992269i	$0.460393\pi$
$228$	0.00887649	0.000587860 0
$229$	26.9241	1.77920	0.889598	−	0.456745i	$-0.150985\pi$
$229$	26.9241	1.77920	0.889598	+	0.456745i	$0.150985\pi$
$230$	−1.57549	−0.103885
$231$	0	0
$232$	19.7968	1.29972
$233$	18.3167	1.19997	0.599984	−	0.800012i	$-0.295174\pi$
$233$	18.3167	1.19997	0.599984	+	0.800012i	$0.295174\pi$
$234$	10.2425	0.669573
$235$	2.22491	0.145137
$236$	1.37965	0.0898073
$237$	−7.97984	−0.518346
$238$	−18.2656	−1.18399
$239$	−10.9559	−0.708676	−0.354338	−	0.935117i	$-0.615294\pi$
$239$	−10.9559	−0.708676	−0.354338	+	0.935117i	$0.615294\pi$
$240$	2.10021	0.135568
$241$	−9.99444	−0.643798	−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444	−0.643798	−0.321899	+	0.946774i	$0.604321\pi$
$242$	0	0
$243$	13.3143	0.854110
$244$	1.37507	0.0880297
$245$	−6.31822	−0.403656
$246$	−6.48972	−0.413769
$247$	0.269293	0.0171347
$248$	−19.8685	−1.26165
$249$	−6.12581	−0.388208
$250$	−1.35567	−0.0857404
$251$	9.65743	0.609572	0.304786	−	0.952421i	$-0.401415\pi$
$251$	9.65743	0.609572	0.304786	+	0.952421i	$0.401415\pi$
$252$	−1.57925	−0.0994832
$253$	0	0
$254$	3.30490	0.207368
$255$	−2.12469	−0.133054
$256$	−3.86526	−0.241579
$257$	10.4276	0.650454	0.325227	−	0.945636i	$-0.394559\pi$
$257$	10.4276	0.650454	0.325227	+	0.945636i	$0.394559\pi$
$258$	−2.31606	−0.144192
$259$	−35.9095	−2.23131
$260$	−0.459031	−0.0284679
$261$	18.0248	1.11571
$262$	9.54606	0.589757
$263$	−10.9619	−0.675937	−0.337968	−	0.941157i	$-0.609740\pi$
$263$	−10.9619	−0.675937	−0.337968	+	0.941157i	$0.609740\pi$
$264$	0	0
$265$	−2.99393	−0.183915
$266$	0.470620	0.0288555
$267$	−6.99867	−0.428311
$268$	2.17525	0.132875
$269$	−0.0893449	−0.00544746	−0.00272373	−	0.999996i	$-0.500867\pi$
$269$	−0.0893449	−0.00544746	−0.00272373	+	0.999996i	$0.500867\pi$
$270$	4.42270	0.269157
$271$	−13.3996	−0.813965	−0.406982	−	0.913436i	$-0.633419\pi$
$271$	−13.3996	−0.813965	−0.406982	+	0.913436i	$0.633419\pi$
$272$	−13.4735	−0.816949
$273$	5.94561	0.359844
$274$	−12.9777	−0.784010
$275$	0	0
$276$	−0.108445	−0.00652764
$277$	−3.90669	−0.234730	−0.117365	−	0.993089i	$-0.537445\pi$
$277$	−3.90669	−0.234730	−0.117365	+	0.993089i	$0.537445\pi$
$278$	0.698853	0.0419144
$279$	−18.0902	−1.08303
$280$	−10.6970	−0.639271
$281$	−1.53743	−0.0917155	−0.0458577	−	0.998948i	$-0.514602\pi$
$281$	−1.53743	−0.0917155	−0.0458577	+	0.998948i	$0.514602\pi$
$282$	−1.73583	−0.103367
$283$	−5.41170	−0.321692	−0.160846	−	0.986980i	$-0.551422\pi$
$283$	−5.41170	−0.321692	−0.160846	+	0.986980i	$0.551422\pi$
$284$	−1.34632	−0.0798896
$285$	0.0547434	0.00324272
$286$	0	0
$287$	30.3566	1.79190
$288$	−2.44174	−0.143881
$289$	−3.36947	−0.198204
$290$	9.15607	0.537663
$291$	−2.49265	−0.146122
$292$	0.214039	0.0125257
$293$	11.4165	0.666958	0.333479	−	0.942757i	$-0.391777\pi$
$293$	11.4165	0.666958	0.333479	+	0.942757i	$0.391777\pi$
$294$	4.92936	0.287486
$295$	8.50860	0.495390
$296$	−28.8421	−1.67641
$297$	0	0
$298$	−11.0621	−0.640808
$299$	−3.28999	−0.190265
$300$	−0.0933146	−0.00538752
$301$	10.8337	0.624445
$302$	2.63031	0.151358
$303$	5.70066	0.327494
$304$	0.347148	0.0199103
$305$	8.48037	0.485585
$306$	−13.3576	−0.763604
$307$	−4.25008	−0.242565	−0.121282	−	0.992618i	$-0.538701\pi$
$307$	−4.25008	−0.242565	−0.121282	+	0.992618i	$0.538701\pi$
$308$	0	0
$309$	2.33990	0.133112
$310$	−9.18926	−0.521915
$311$	−16.6195	−0.942404	−0.471202	−	0.882025i	$-0.656180\pi$
$311$	−16.6195	−0.942404	−0.471202	+	0.882025i	$0.656180\pi$
$312$	4.77544	0.270356
$313$	−26.5770	−1.50222	−0.751109	−	0.660178i	$-0.770481\pi$
$313$	−26.5770	−1.50222	−0.751109	+	0.660178i	$0.770481\pi$
$314$	28.8413	1.62761
$315$	−9.73958	−0.548763
$316$	2.24835	0.126479
$317$	5.79694	0.325589	0.162794	−	0.986660i	$-0.447949\pi$
$317$	5.79694	0.325589	0.162794	+	0.986660i	$0.447949\pi$
$318$	2.33581	0.130985
$319$	0	0
$320$	−8.53916	−0.477353
$321$	1.11564	0.0622688
$322$	−5.74963	−0.320414
$323$	−0.351195	−0.0195410
$324$	−0.993793	−0.0552107
$325$	−2.83095	−0.157033
$326$	−21.6650	−1.19991
$327$	3.52584	0.194979
$328$	24.3821	1.34628
$329$	8.11961	0.447648
$330$	0	0
$331$	−12.9230	−0.710311	−0.355155	−	0.934807i	$-0.615572\pi$
$331$	−12.9230	−0.710311	−0.355155	+	0.934807i	$0.615572\pi$
$332$	1.72597	0.0947249
$333$	−26.2605	−1.43907
$334$	24.0077	1.31364
$335$	13.4153	0.732956
$336$	7.66454	0.418135
$337$	13.3854	0.729148	0.364574	−	0.931174i	$-0.381215\pi$
$337$	13.3854	0.729148	0.364574	+	0.931174i	$0.381215\pi$
$338$	−6.75898	−0.367640
$339$	3.32938	0.180827
$340$	0.598640	0.0324658
$341$	0	0
$342$	0.344163	0.0186102
$343$	2.48809	0.134344
$344$	8.70152	0.469155
$345$	−0.668808	−0.0360074
$346$	21.5355	1.15776
$347$	−8.44899	−0.453565	−0.226783	−	0.973945i	$-0.572821\pi$
$347$	−8.44899	−0.453565	−0.226783	+	0.973945i	$0.572821\pi$
$348$	0.630236	0.0337842
$349$	−10.3988	−0.556636	−0.278318	−	0.960489i	$-0.589777\pi$
$349$	−10.3988	−0.556636	−0.278318	+	0.960489i	$0.589777\pi$
$350$	−4.94742	−0.264451
$351$	9.23559	0.492959
$352$	0	0
$353$	19.1073	1.01698	0.508489	−	0.861069i	$-0.330204\pi$
$353$	19.1073	1.01698	0.508489	+	0.861069i	$0.330204\pi$
$354$	−6.63825	−0.352819
$355$	−8.30309	−0.440682
$356$	1.97190	0.104510
$357$	−7.75389	−0.410379
$358$	−22.8852	−1.20952
$359$	−4.41417	−0.232971	−0.116486	−	0.993192i	$-0.537163\pi$
$359$	−4.41417	−0.232971	−0.116486	+	0.993192i	$0.537163\pi$
$360$	−7.82272	−0.412294
$361$	−18.9910	−0.999524
$362$	−32.6546	−1.71629
$363$	0	0
$364$	−1.67520	−0.0878041
$365$	1.32003	0.0690936
$366$	−6.61622	−0.345836
$367$	−29.3617	−1.53267	−0.766335	−	0.642442i	$-0.777922\pi$
$367$	−29.3617	−1.53267	−0.766335	+	0.642442i	$0.777922\pi$
$368$	−4.24116	−0.221086
$369$	22.1997	1.15567
$370$	−13.3396	−0.693491
$371$	−10.9261	−0.567254
$372$	−0.632521	−0.0327947
$373$	−4.96478	−0.257067	−0.128533	−	0.991705i	$-0.541027\pi$
$373$	−4.96478	−0.257067	−0.128533	+	0.991705i	$0.541027\pi$
$374$	0	0
$375$	−0.575493	−0.0297183
$376$	6.52157	0.336325
$377$	19.1200	0.984728
$378$	16.1403	0.830165
$379$	7.92315	0.406985	0.203492	−	0.979077i	$-0.434771\pi$
$379$	7.92315	0.406985	0.203492	+	0.979077i	$0.434771\pi$
$380$	−0.0154241	−0.000791242 0
$381$	1.40295	0.0718755
$382$	7.29731	0.373363
$383$	−24.5155	−1.25268	−0.626342	−	0.779549i	$-0.715449\pi$
$383$	−24.5155	−1.25268	−0.626342	+	0.779549i	$0.715449\pi$
$384$	5.60903	0.286235
$385$	0	0
$386$	24.7872	1.26164
$387$	7.92268	0.402732
$388$	0.702312	0.0356545
$389$	5.46094	0.276881	0.138440	−	0.990371i	$-0.455791\pi$
$389$	5.46094	0.276881	0.138440	+	0.990371i	$0.455791\pi$
$390$	2.20866	0.111840
$391$	4.29059	0.216985
$392$	−18.5198	−0.935389
$393$	4.05237	0.204415
$394$	3.58665	0.180693
$395$	13.8661	0.697679
$396$	0	0
$397$	−6.43455	−0.322941	−0.161470	−	0.986878i	$-0.551624\pi$
$397$	−6.43455	−0.322941	−0.161470	+	0.986878i	$0.551624\pi$
$398$	8.84984	0.443602
$399$	0.199781	0.0100016
$400$	−3.64941	−0.182471
$401$	−14.7026	−0.734213	−0.367107	−	0.930179i	$-0.619652\pi$
$401$	−14.7026	−0.734213	−0.367107	+	0.930179i	$0.619652\pi$
$402$	−10.4664	−0.522014
$403$	−19.1893	−0.955885
$404$	−1.60618	−0.0799105
$405$	−6.12896	−0.304550
$406$	33.4143	1.65832
$407$	0	0
$408$	−6.22784	−0.308324
$409$	4.39576	0.217356	0.108678	−	0.994077i	$-0.465338\pi$
$409$	4.39576	0.217356	0.108678	+	0.994077i	$0.465338\pi$
$410$	11.2768	0.556921
$411$	−5.50911	−0.271745
$412$	−0.659275	−0.0324802
$413$	31.0514	1.52794
$414$	−4.20469	−0.206649
$415$	10.6445	0.522516
$416$	−2.59009	−0.126990
$417$	0.296668	0.0145279
$418$	0	0
$419$	17.8526	0.872159	0.436079	−	0.899908i	$-0.356367\pi$
$419$	17.8526	0.872159	0.436079	+	0.899908i	$0.356367\pi$
$420$	−0.340544	−0.0166168
$421$	−4.82854	−0.235328	−0.117664	−	0.993053i	$-0.537541\pi$
$421$	−4.82854	−0.235328	−0.117664	+	0.993053i	$0.537541\pi$
$422$	−37.2103	−1.81137
$423$	5.93785	0.288708
$424$	−8.77570	−0.426186
$425$	3.69195	0.179086
$426$	6.47792	0.313856
$427$	30.9484	1.49770
$428$	−0.314335	−0.0151939
$429$	0	0
$430$	4.02448	0.194078
$431$	−24.8739	−1.19814	−0.599068	−	0.800698i	$-0.704462\pi$
$431$	−24.8739	−1.19814	−0.599068	+	0.800698i	$0.704462\pi$
$432$	11.9057	0.572813
$433$	−21.2502	−1.02122	−0.510611	−	0.859812i	$-0.670581\pi$
$433$	−21.2502	−1.02122	−0.510611	+	0.859812i	$0.670581\pi$
$434$	−33.5354	−1.60975
$435$	3.88682	0.186359
$436$	−0.993417	−0.0475761
$437$	−0.110548	−0.00528825
$438$	−1.02986	−0.0492088
$439$	−15.9119	−0.759434	−0.379717	−	0.925103i	$-0.623979\pi$
$439$	−15.9119	−0.759434	−0.379717	+	0.925103i	$0.623979\pi$
$440$	0	0
$441$	−16.8621	−0.802958
$442$	−14.1692	−0.673959
$443$	26.2876	1.24896	0.624481	−	0.781040i	$-0.285310\pi$
$443$	26.2876	1.24896	0.624481	+	0.781040i	$0.285310\pi$
$444$	−0.918197	−0.0435757
$445$	12.1612	0.576494
$446$	−6.88945	−0.326225
$447$	−4.69592	−0.222110
$448$	−31.1629	−1.47231
$449$	−8.18961	−0.386492	−0.193246	−	0.981150i	$-0.561902\pi$
$449$	−8.18961	−0.386492	−0.193246	+	0.981150i	$0.561902\pi$
$450$	−3.61803	−0.170556
$451$	0	0
$452$	−0.938065	−0.0441229
$453$	1.11659	0.0524618
$454$	5.06995	0.237945
$455$	−10.3313	−0.484340
$456$	0.160462	0.00751432
$457$	11.9164	0.557425	0.278713	−	0.960375i	$-0.410092\pi$
$457$	11.9164	0.557425	0.278713	+	0.960375i	$0.410092\pi$
$458$	36.5003	1.70555
$459$	−12.0445	−0.562188
$460$	0.188439	0.00878601
$461$	6.96172	0.324240	0.162120	−	0.986771i	$-0.448167\pi$
$461$	6.96172	0.324240	0.162120	+	0.986771i	$0.448167\pi$
$462$	0	0
$463$	12.4762	0.579817	0.289909	−	0.957054i	$-0.406375\pi$
$463$	12.4762	0.579817	0.289909	+	0.957054i	$0.406375\pi$
$464$	24.6477	1.14424
$465$	−3.90091	−0.180900
$466$	24.8315	1.15030
$467$	−6.14617	−0.284411	−0.142205	−	0.989837i	$-0.545419\pi$
$467$	−6.14617	−0.284411	−0.142205	+	0.989837i	$0.545419\pi$
$468$	−1.22507	−0.0566287
$469$	48.9579	2.26067
$470$	3.01625	0.139129
$471$	12.2433	0.564142
$472$	24.9401	1.14796
$473$	0	0
$474$	−10.8181	−0.496890
$475$	−0.0951243	−0.00436460
$476$	2.18469	0.100135
$477$	−7.99022	−0.365847
$478$	−14.8526	−0.679341
$479$	22.1942	1.01408	0.507039	−	0.861923i	$-0.330740\pi$
$479$	22.1942	1.01408	0.507039	+	0.861923i	$0.330740\pi$
$480$	−0.526529	−0.0240327
$481$	−27.8560	−1.27013
$482$	−13.5492	−0.617149
$483$	−2.44076	−0.111058
$484$	0	0
$485$	4.33133	0.196675
$486$	18.0498	0.818755
$487$	−34.2306	−1.55114	−0.775569	−	0.631263i	$-0.782537\pi$
$487$	−34.2306	−1.55114	−0.775569	+	0.631263i	$0.782537\pi$
$488$	24.8574	1.12524
$489$	−9.19693	−0.415900
$490$	−8.56545	−0.386948
$491$	−16.9957	−0.767007	−0.383503	−	0.923539i	$-0.625283\pi$
$491$	−16.9957	−0.767007	−0.383503	+	0.923539i	$0.625283\pi$
$492$	0.776212	0.0349943
$493$	−24.9351	−1.12302
$494$	0.365073	0.0164254
$495$	0	0
$496$	−24.7371	−1.11073
$497$	−30.3014	−1.35920
$498$	−8.30461	−0.372138
$499$	5.22946	0.234103	0.117051	−	0.993126i	$-0.462656\pi$
$499$	5.22946	0.234103	0.117051	+	0.993126i	$0.462656\pi$
$500$	0.162147	0.00725144
$501$	10.1914	0.455319
$502$	13.0923	0.584339
$503$	41.9448	1.87023	0.935113	−	0.354350i	$-0.115298\pi$
$503$	41.9448	1.87023	0.935113	+	0.354350i	$0.115298\pi$
$504$	−28.5484	−1.27164
$505$	−9.90570	−0.440798
$506$	0	0
$507$	−2.86923	−0.127427
$508$	−0.395287	−0.0175380
$509$	20.3678	0.902787	0.451393	−	0.892325i	$-0.350927\pi$
$509$	20.3678	0.902787	0.451393	+	0.892325i	$0.350927\pi$
$510$	−2.88039	−0.127546
$511$	4.81734	0.213107
$512$	−24.7330	−1.09305
$513$	0.310330	0.0137014
$514$	14.1364	0.623529
$515$	−4.06590	−0.179165
$516$	0.277016	0.0121949
$517$	0	0
$518$	−48.6816	−2.13895
$519$	9.14199	0.401289
$520$	−8.29800	−0.363891
$521$	14.4779	0.634287	0.317143	−	0.948378i	$-0.397276\pi$
$521$	14.4779	0.634287	0.317143	+	0.948378i	$0.397276\pi$
$522$	24.4358	1.06953
$523$	11.1601	0.487998	0.243999	−	0.969775i	$-0.421541\pi$
$523$	11.1601	0.487998	0.243999	+	0.969775i	$0.421541\pi$
$524$	−1.14177	−0.0498784
$525$	−2.10021	−0.0916608
$526$	−14.8607	−0.647958
$527$	25.0254	1.09013
$528$	0	0
$529$	−21.6494	−0.941279
$530$	−4.05879	−0.176303
$531$	22.7078	0.985436
$532$	−0.0562891	−0.00244044
$533$	23.5485	1.02000
$534$	−9.48791	−0.410582
$535$	−1.93858	−0.0838119
$536$	39.3225	1.69847
$537$	−9.71492	−0.419230
$538$	−0.121123	−0.00522197
$539$	0	0
$540$	−0.528983	−0.0227638
$541$	10.6808	0.459203	0.229602	−	0.973285i	$-0.426258\pi$
$541$	10.6808	0.459203	0.229602	+	0.973285i	$0.426258\pi$
$542$	−18.1654	−0.780272
$543$	−13.8621	−0.594880
$544$	3.37784	0.144824
$545$	−6.12664	−0.262436
$546$	8.06031	0.344949
$547$	1.74760	0.0747220	0.0373610	−	0.999302i	$-0.488105\pi$
$547$	1.74760	0.0747220	0.0373610	+	0.999302i	$0.488105\pi$
$548$	1.55221	0.0663072
$549$	22.6325	0.965930
$550$	0	0
$551$	0.642459	0.0273697
$552$	−1.96039	−0.0834396
$553$	50.6031	2.15186
$554$	−5.29619	−0.225014
$555$	−5.66273	−0.240370
$556$	−0.0835872	−0.00354489
$557$	−19.4844	−0.825579	−0.412790	−	0.910826i	$-0.635446\pi$
$557$	−19.4844	−0.825579	−0.412790	+	0.910826i	$0.635446\pi$
$558$	−24.5244	−1.03820
$559$	8.40403	0.355453
$560$	−13.3182	−0.562798
$561$	0	0
$562$	−2.08426	−0.0879191
$563$	−14.6892	−0.619074	−0.309537	−	0.950887i	$-0.600174\pi$
$563$	−14.6892	−0.619074	−0.309537	+	0.950887i	$0.600174\pi$
$564$	0.207616	0.00874222
$565$	−5.78527	−0.243388
$566$	−7.33650	−0.308376
$567$	−22.3671	−0.939330
$568$	−24.3377	−1.02119
$569$	19.9335	0.835658	0.417829	−	0.908526i	$-0.362791\pi$
$569$	19.9335	0.835658	0.417829	+	0.908526i	$0.362791\pi$
$570$	0.0742142	0.00310849
$571$	5.24422	0.219464	0.109732	−	0.993961i	$-0.465001\pi$
$571$	5.24422	0.219464	0.109732	+	0.993961i	$0.465001\pi$
$572$	0	0
$573$	3.09776	0.129411
$574$	41.1537	1.71772
$575$	1.16215	0.0484649
$576$	−22.7894	−0.949557
$577$	37.6004	1.56533	0.782663	−	0.622446i	$-0.213861\pi$
$577$	37.6004	1.56533	0.782663	+	0.622446i	$0.213861\pi$
$578$	−4.56790	−0.190000
$579$	10.5223	0.437294
$580$	−1.09512	−0.0454726
$581$	38.8460	1.61161
$582$	−3.37922	−0.140073
$583$	0	0
$584$	3.86923	0.160110
$585$	−7.55527	−0.312372
$586$	15.4770	0.639351
$587$	25.5711	1.05543	0.527716	−	0.849421i	$-0.323048\pi$
$587$	25.5711	1.05543	0.527716	+	0.849421i	$0.323048\pi$
$588$	−0.589582	−0.0243140
$589$	−0.644788	−0.0265680
$590$	11.5349	0.474884
$591$	1.52256	0.0626297
$592$	−35.9095	−1.47587
$593$	40.2260	1.65188	0.825942	−	0.563754i	$-0.190644\pi$
$593$	40.2260	1.65188	0.825942	+	0.563754i	$0.190644\pi$
$594$	0	0
$595$	13.4735	0.552358
$596$	1.32309	0.0541960
$597$	3.75682	0.153756
$598$	−4.46015	−0.182389
$599$	4.92997	0.201433	0.100716	−	0.994915i	$-0.467886\pi$
$599$	4.92997	0.201433	0.100716	+	0.994915i	$0.467886\pi$
$600$	−1.68687	−0.0688660
$601$	46.0896	1.88003	0.940017	−	0.341127i	$-0.110809\pi$
$601$	46.0896	1.88003	0.940017	+	0.341127i	$0.110809\pi$
$602$	14.6870	0.598597
$603$	35.8028	1.45800
$604$	−0.314602	−0.0128010
$605$	0	0
$606$	7.72824	0.313938
$607$	−45.1365	−1.83203	−0.916016	−	0.401141i	$-0.868614\pi$
$607$	−45.1365	−1.83203	−0.916016	+	0.401141i	$0.868614\pi$
$608$	−0.0870310	−0.00352957
$609$	14.1846	0.574789
$610$	11.4966	0.465484
$611$	6.29861	0.254815
$612$	1.59766	0.0645814
$613$	4.73418	0.191212	0.0956059	−	0.995419i	$-0.469521\pi$
$613$	4.73418	0.191212	0.0956059	+	0.995419i	$0.469521\pi$
$614$	−5.76172	−0.232524
$615$	4.78708	0.193034
$616$	0	0
$617$	17.8468	0.718486	0.359243	−	0.933244i	$-0.383035\pi$
$617$	17.8468	0.718486	0.359243	+	0.933244i	$0.383035\pi$
$618$	3.17214	0.127602
$619$	0.356952	0.0143471	0.00717356	−	0.999974i	$-0.497717\pi$
$619$	0.356952	0.0143471	0.00717356	+	0.999974i	$0.497717\pi$
$620$	1.09909	0.0441407
$621$	−3.79134	−0.152141
$622$	−22.5306	−0.903394
$623$	44.3811	1.77809
$624$	5.94561	0.238015
$625$	1.00000	0.0400000
$626$	−36.0297	−1.44004
$627$	0	0
$628$	−3.44960	−0.137654
$629$	36.3281	1.44850
$630$	−13.2037	−0.526048
$631$	−31.9922	−1.27359	−0.636795	−	0.771033i	$-0.719740\pi$
$631$	−31.9922	−1.27359	−0.636795	+	0.771033i	$0.719740\pi$
$632$	40.6438	1.61672
$633$	−15.7960	−0.627835
$634$	7.85876	0.312111
$635$	−2.43783	−0.0967422
$636$	−0.279377	−0.0110780
$637$	−17.8866	−0.708693
$638$	0	0
$639$	−22.1594	−0.876610
$640$	−9.74648	−0.385264
$641$	1.01285	0.0400050	0.0200025	−	0.999800i	$-0.493633\pi$
$641$	1.01285	0.0400050	0.0200025	+	0.999800i	$0.493633\pi$
$642$	1.51244	0.0596912
$643$	−14.9724	−0.590455	−0.295228	−	0.955427i	$-0.595395\pi$
$643$	−14.9724	−0.590455	−0.295228	+	0.955427i	$0.595395\pi$
$644$	0.687692	0.0270988
$645$	1.70842	0.0672690
$646$	−0.476106	−0.0187321
$647$	17.8873	0.703224	0.351612	−	0.936146i	$-0.385634\pi$
$647$	17.8873	0.703224	0.351612	+	0.936146i	$0.385634\pi$
$648$	−17.9650	−0.705732
$649$	0	0
$650$	−3.83785	−0.150533
$651$	−14.2360	−0.557954
$652$	2.59127	0.101482
$653$	45.7642	1.79089	0.895446	−	0.445169i	$-0.146856\pi$
$653$	45.7642	1.79089	0.895446	+	0.445169i	$0.146856\pi$
$654$	4.77989	0.186908
$655$	−7.04156	−0.275136
$656$	30.3566	1.18523
$657$	3.52291	0.137442
$658$	11.0075	0.429119
$659$	−9.54036	−0.371640	−0.185820	−	0.982584i	$-0.559494\pi$
$659$	−9.54036	−0.371640	−0.185820	+	0.982584i	$0.559494\pi$
$660$	0	0
$661$	15.7769	0.613651	0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769	0.613651	0.306825	+	0.951766i	$0.400733\pi$
$662$	−17.5193	−0.680908
$663$	−6.01491	−0.233600
$664$	31.2007	1.21082
$665$	−0.347148	−0.0134618
$666$	−35.6007	−1.37950
$667$	−7.84901	−0.303915
$668$	−2.87147	−0.111100
$669$	−2.92462	−0.113072
$670$	18.1868	0.702616
$671$	0	0
$672$	−1.92152	−0.0741243
$673$	47.3031	1.82340	0.911700	−	0.410856i	$-0.134770\pi$
$673$	47.3031	1.82340	0.911700	+	0.410856i	$0.134770\pi$
$674$	18.1462	0.698966
$675$	−3.26236	−0.125568
$676$	0.808416	0.0310929
$677$	27.5431	1.05857	0.529284	−	0.848445i	$-0.322461\pi$
$677$	27.5431	1.05857	0.529284	+	0.848445i	$0.322461\pi$
$678$	4.51356	0.173342
$679$	15.8068	0.606609
$680$	10.8217	0.414995
$681$	2.15223	0.0824736
$682$	0	0
$683$	−27.1617	−1.03931	−0.519656	−	0.854375i	$-0.673940\pi$
$683$	−27.1617	−1.03931	−0.519656	+	0.854375i	$0.673940\pi$
$684$	−0.0411641	−0.00157395
$685$	9.57286	0.365760
$686$	3.37304	0.128783
$687$	15.4946	0.591157
$688$	10.8337	0.413032
$689$	−8.47567	−0.322897
$690$	−0.906685	−0.0345169
$691$	−7.52680	−0.286333	−0.143166	−	0.989699i	$-0.545728\pi$
$691$	−7.52680	−0.286333	−0.143166	+	0.989699i	$0.545728\pi$
$692$	−2.57579	−0.0979167
$693$	0	0
$694$	−11.4541	−0.434791
$695$	−0.515502	−0.0195541
$696$	11.3929	0.431847
$697$	−30.7105	−1.16324
$698$	−14.0974	−0.533595
$699$	10.5411	0.398702
$700$	0.591742	0.0223658
$701$	−31.8207	−1.20185	−0.600926	−	0.799305i	$-0.705201\pi$
$701$	−31.8207	−1.20185	−0.600926	+	0.799305i	$0.705201\pi$
$702$	12.5205	0.472554
$703$	−0.936004	−0.0353021
$704$	0	0
$705$	1.28042	0.0482234
$706$	25.9032	0.974882
$707$	−36.1500	−1.35956
$708$	0.793977	0.0298395
$709$	−14.4381	−0.542235	−0.271118	−	0.962546i	$-0.587393\pi$
$709$	−14.4381	−0.542235	−0.271118	+	0.962546i	$0.587393\pi$
$710$	−11.2563	−0.422441
$711$	37.0059	1.38783
$712$	35.6464	1.33591
$713$	7.87747	0.295013
$714$	−10.5117	−0.393392
$715$	0	0
$716$	2.73721	0.102294
$717$	−6.30503	−0.235465
$718$	−5.98418	−0.223328
$719$	5.41004	0.201761	0.100880	−	0.994899i	$-0.467834\pi$
$719$	5.41004	0.201761	0.100880	+	0.994899i	$0.467834\pi$
$720$	−9.73958	−0.362973
$721$	−14.8382	−0.552602
$722$	−25.7455	−0.958150
$723$	−5.75173	−0.213909
$724$	3.90570	0.145154
$725$	−6.75389	−0.250833
$726$	0	0
$727$	−16.7753	−0.622161	−0.311080	−	0.950384i	$-0.600691\pi$
$727$	−16.7753	−0.622161	−0.311080	+	0.950384i	$0.600691\pi$
$728$	−30.2828	−1.12236
$729$	−10.7246	−0.397208
$730$	1.78953	0.0662336
$731$	−10.9600	−0.405371
$732$	0.791342	0.0292488
$733$	−14.0851	−0.520243	−0.260122	−	0.965576i	$-0.583763\pi$
$733$	−14.0851	−0.520243	−0.260122	+	0.965576i	$0.583763\pi$
$734$	−39.8049	−1.46923
$735$	−3.63609	−0.134119
$736$	1.06327	0.0391926
$737$	0	0
$738$	30.0956	1.10783
$739$	−36.3457	−1.33700	−0.668499	−	0.743713i	$-0.733063\pi$
$739$	−36.3457	−1.33700	−0.668499	+	0.743713i	$0.733063\pi$
$740$	1.59550	0.0586516
$741$	0.154976	0.00569319
$742$	−14.8122	−0.543773
$743$	−1.95716	−0.0718012	−0.0359006	−	0.999355i	$-0.511430\pi$
$743$	−1.95716	−0.0718012	−0.0359006	+	0.999355i	$0.511430\pi$
$744$	−11.4342	−0.419198
$745$	8.15983	0.298953
$746$	−6.73063	−0.246426
$747$	28.4080	1.03939
$748$	0	0
$749$	−7.07466	−0.258503
$750$	−0.780181	−0.0284882
$751$	18.7106	0.682759	0.341379	−	0.939926i	$-0.389106\pi$
$751$	18.7106	0.682759	0.341379	+	0.939926i	$0.389106\pi$
$752$	8.11961	0.296092
$753$	5.55778	0.202537
$754$	25.9204	0.943967
$755$	−1.94023	−0.0706120
$756$	−1.93048	−0.0702107
$757$	−14.5470	−0.528721	−0.264361	−	0.964424i	$-0.585161\pi$
$757$	−14.5470	−0.528721	−0.264361	+	0.964424i	$0.585161\pi$
$758$	10.7412	0.390138
$759$	0	0
$760$	−0.278825	−0.0101141
$761$	13.1406	0.476345	0.238173	−	0.971223i	$-0.423452\pi$
$761$	13.1406	0.476345	0.238173	+	0.971223i	$0.423452\pi$
$762$	1.90195	0.0689003
$763$	−22.3586	−0.809437
$764$	−0.872805	−0.0315770
$765$	9.85312	0.356240
$766$	−33.2350	−1.20083
$767$	24.0875	0.869748
$768$	−2.22443	−0.0802673
$769$	38.9767	1.40554	0.702768	−	0.711419i	$-0.251947\pi$
$769$	38.9767	1.40554	0.702768	+	0.711419i	$0.251947\pi$
$770$	0	0
$771$	6.00099	0.216121
$772$	−2.96471	−0.106702
$773$	−38.7539	−1.39388	−0.696940	−	0.717129i	$-0.745456\pi$
$773$	−38.7539	−1.39388	−0.696940	+	0.717129i	$0.745456\pi$
$774$	10.7406	0.386062
$775$	6.77837	0.243486
$776$	12.6958	0.455754
$777$	−20.6657	−0.741377
$778$	7.40326	0.265420
$779$	0.791265	0.0283500
$780$	−0.264169	−0.00945878
$781$	0	0
$782$	5.81665	0.208003
$783$	22.0336	0.787417
$784$	−23.0578	−0.823493
$785$	−21.2745	−0.759319
$786$	5.49369	0.195953
$787$	−21.3842	−0.762265	−0.381132	−	0.924521i	$-0.624466\pi$
$787$	−21.3842	−0.762265	−0.381132	+	0.924521i	$0.624466\pi$
$788$	−0.428986	−0.0152820
$789$	−6.30847	−0.224588
$790$	18.7979	0.668799
$791$	−21.1128	−0.750686
$792$	0	0
$793$	24.0075	0.852533
$794$	−8.72315	−0.309573
$795$	−1.72298	−0.0611080
$796$	−1.05850	−0.0375174
$797$	−2.22456	−0.0787978	−0.0393989	−	0.999224i	$-0.512544\pi$
$797$	−2.22456	−0.0787978	−0.0393989	+	0.999224i	$0.512544\pi$
$798$	0.270838	0.00958757
$799$	−8.21426	−0.290599
$800$	0.914918	0.0323472
$801$	32.4558	1.14677
$802$	−19.9319	−0.703821
$803$	0	0
$804$	1.25184	0.0441491
$805$	4.24116	0.149481
$806$	−26.0144	−0.916318
$807$	−0.0514174	−0.00180998
$808$	−29.0353	−1.02146
$809$	21.1682	0.744234	0.372117	−	0.928186i	$-0.378632\pi$
$809$	21.1682	0.744234	0.372117	+	0.928186i	$0.378632\pi$
$810$	−8.30887	−0.291944
$811$	−36.7172	−1.28932	−0.644658	−	0.764471i	$-0.723000\pi$
$811$	−36.7172	−1.28932	−0.644658	+	0.764471i	$0.723000\pi$
$812$	−3.99656	−0.140252
$813$	−7.71135	−0.270449
$814$	0	0
$815$	15.9810	0.559788
$816$	−7.75389	−0.271440
$817$	0.282388	0.00987951
$818$	5.95922	0.208359
$819$	−27.5723	−0.963455
$820$	−1.34878	−0.0471013
$821$	−39.6693	−1.38447	−0.692235	−	0.721673i	$-0.743374\pi$
$821$	−39.6693	−1.38447	−0.692235	+	0.721673i	$0.743374\pi$
$822$	−7.46856	−0.260496
$823$	−45.9283	−1.60096	−0.800480	−	0.599359i	$-0.795422\pi$
$823$	−45.9283	−1.60096	−0.800480	+	0.599359i	$0.795422\pi$
$824$	−11.9178	−0.415178
$825$	0	0
$826$	42.0956	1.46469
$827$	−39.6949	−1.38033	−0.690164	−	0.723653i	$-0.742462\pi$
$827$	−39.6949	−1.38033	−0.690164	+	0.723653i	$0.742462\pi$
$828$	0.502907	0.0174772
$829$	7.65584	0.265898	0.132949	−	0.991123i	$-0.457555\pi$
$829$	7.65584	0.265898	0.132949	+	0.991123i	$0.457555\pi$
$830$	14.4304	0.500887
$831$	−2.24827	−0.0779916
$832$	−24.1740	−0.838082
$833$	23.3266	0.808218
$834$	0.402185	0.0139265
$835$	−17.7090	−0.612846
$836$	0	0
$837$	−22.1135	−0.764354
$838$	24.2024	0.836057
$839$	27.5886	0.952465	0.476233	−	0.879319i	$-0.342002\pi$
$839$	27.5886	0.952465	0.476233	+	0.879319i	$0.342002\pi$
$840$	−6.15607	−0.212405
$841$	16.6150	0.572932
$842$	−6.54592	−0.225587
$843$	−0.884781	−0.0304735
$844$	4.45058	0.153195
$845$	4.98569	0.171513
$846$	8.04979	0.276757
$847$	0	0
$848$	−10.9261	−0.375203
$849$	−3.11439	−0.106886
$850$	5.00509	0.171673
$851$	11.4353	0.391997
$852$	−0.774800	−0.0265442
$853$	42.1496	1.44318	0.721588	−	0.692323i	$-0.243413\pi$
$853$	42.1496	1.44318	0.721588	+	0.692323i	$0.243413\pi$
$854$	41.9559	1.43570
$855$	−0.253869	−0.00868212
$856$	−5.68229	−0.194217
$857$	−45.0850	−1.54008	−0.770038	−	0.637998i	$-0.779763\pi$
$857$	−45.0850	−1.54008	−0.770038	+	0.637998i	$0.779763\pi$
$858$	0	0
$859$	−11.8257	−0.403488	−0.201744	−	0.979438i	$-0.564661\pi$
$859$	−11.8257	−0.403488	−0.201744	+	0.979438i	$0.564661\pi$
$860$	−0.481353	−0.0164140
$861$	17.4700	0.595377
$862$	−33.7210	−1.14854
$863$	27.8713	0.948750	0.474375	−	0.880323i	$-0.342674\pi$
$863$	27.8713	0.948750	0.474375	+	0.880323i	$0.342674\pi$
$864$	−2.98479	−0.101545
$865$	−15.8855	−0.540123
$866$	−28.8084	−0.978950
$867$	−1.93911	−0.0658555
$868$	4.01105	0.136144
$869$	0	0
$870$	5.26926	0.178645
$871$	37.9781	1.28684
$872$	−17.9582	−0.608141
$873$	11.5595	0.391229
$874$	−0.149868	−0.00506935
$875$	3.64941	0.123373
$876$	0.123178	0.00416181
$877$	−11.4471	−0.386543	−0.193271	−	0.981145i	$-0.561910\pi$
$877$	−11.4471	−0.386543	−0.193271	+	0.981145i	$0.561910\pi$
$878$	−21.5714	−0.727998
$879$	6.57011	0.221604
$880$	0	0
$881$	47.0037	1.58360	0.791798	−	0.610783i	$-0.209145\pi$
$881$	47.0037	1.58360	0.791798	+	0.610783i	$0.209145\pi$
$882$	−22.8595	−0.769721
$883$	−46.9146	−1.57880	−0.789401	−	0.613877i	$-0.789609\pi$
$883$	−46.9146	−1.57880	−0.789401	+	0.613877i	$0.789609\pi$
$884$	1.69472	0.0569997
$885$	4.89664	0.164599
$886$	35.6374	1.19726
$887$	−27.8427	−0.934866	−0.467433	−	0.884029i	$-0.654821\pi$
$887$	−27.8427	−0.934866	−0.467433	+	0.884029i	$0.654821\pi$
$888$	−16.5984	−0.557007
$889$	−8.89664	−0.298384
$890$	16.4866	0.552631
$891$	0	0
$892$	0.824022	0.0275903
$893$	0.211643	0.00708236
$894$	−6.36614	−0.212916
$895$	16.8810	0.564271
$896$	−35.5689	−1.18828
$897$	−1.89336	−0.0632176
$898$	−11.1024	−0.370494
$899$	−45.7804	−1.52686
$900$	0.432740	0.0144247
$901$	11.0534	0.368244
$902$	0	0
$903$	6.23473	0.207479
$904$	−16.9576	−0.564001
$905$	24.0874	0.800691
$906$	1.51373	0.0502902
$907$	−28.6233	−0.950421	−0.475210	−	0.879872i	$-0.657628\pi$
$907$	−28.6233	−0.950421	−0.475210	+	0.879872i	$0.657628\pi$
$908$	−0.606398	−0.0201240
$909$	−26.4364	−0.876840
$910$	−14.0059	−0.464292
$911$	5.12823	0.169906	0.0849529	−	0.996385i	$-0.472926\pi$
$911$	5.12823	0.169906	0.0849529	+	0.996385i	$0.472926\pi$
$912$	0.199781	0.00661542
$913$	0	0
$914$	16.1547	0.534351
$915$	4.88039	0.161341
$916$	−4.36567	−0.144246
$917$	−25.6976	−0.848608
$918$	−16.3284	−0.538917
$919$	35.2810	1.16381	0.581906	−	0.813256i	$-0.302307\pi$
$919$	35.2810	1.16381	0.581906	+	0.813256i	$0.302307\pi$
$920$	3.40645	0.112307
$921$	−2.44589	−0.0805949
$922$	9.43783	0.310818
$923$	−23.5057	−0.773699
$924$	0	0
$925$	9.83980	0.323531
$926$	16.9136	0.555817
$927$	−10.8511	−0.356397
$928$	−6.17926	−0.202844
$929$	−59.1427	−1.94041	−0.970204	−	0.242289i	$-0.922102\pi$
$929$	−59.1427	−1.94041	−0.970204	+	0.242289i	$0.922102\pi$
$930$	−5.28836	−0.173412
$931$	−0.601017	−0.0196975
$932$	−2.97000	−0.0972857
$933$	−9.56439	−0.313124
$934$	−8.33220	−0.272638
$935$	0	0
$936$	−22.1458	−0.723857
$937$	14.4425	0.471817	0.235909	−	0.971775i	$-0.424193\pi$
$937$	14.4425	0.471817	0.235909	+	0.971775i	$0.424193\pi$
$938$	66.3710	2.16709
$939$	−15.2949	−0.499129
$940$	−0.360762	−0.0117668
$941$	−18.6591	−0.608269	−0.304135	−	0.952629i	$-0.598367\pi$
$941$	−18.6591	−0.608269	−0.304135	+	0.952629i	$0.598367\pi$
$942$	16.5979	0.540790
$943$	−9.66700	−0.314801
$944$	31.0514	1.01064
$945$	−11.9057	−0.387292
$946$	0	0
$947$	−0.991391	−0.0322159	−0.0161079	−	0.999870i	$-0.505128\pi$
$947$	−0.991391	−0.0322159	−0.0161079	+	0.999870i	$0.505128\pi$
$948$	1.29391	0.0420242
$949$	3.73695	0.121306
$950$	−0.128958	−0.00418394
$951$	3.33610	0.108180
$952$	39.4930	1.27998
$953$	−8.26404	−0.267699	−0.133849	−	0.991002i	$-0.542734\pi$
$953$	−8.26404	−0.267699	−0.133849	+	0.991002i	$0.542734\pi$
$954$	−10.8321	−0.350703
$955$	−5.38279	−0.174183
$956$	1.77646	0.0574549
$957$	0	0
$958$	30.0881	0.972101
$959$	34.9353	1.12812
$960$	−4.91423	−0.158606
$961$	14.9463	0.482139
$962$	−37.7637	−1.21755
$963$	−5.17368	−0.166720
$964$	1.62057	0.0521950
$965$	−18.2840	−0.588584
$966$	−3.30887	−0.106461
$967$	7.36029	0.236691	0.118345	−	0.992972i	$-0.462241\pi$
$967$	7.36029	0.236691	0.118345	+	0.992972i	$0.462241\pi$
$968$	0	0
$969$	−0.202110	−0.00649271
$970$	5.87187	0.188534
$971$	−4.97733	−0.159730	−0.0798650	−	0.996806i	$-0.525449\pi$
$971$	−4.97733	−0.159730	−0.0798650	+	0.996806i	$0.525449\pi$
$972$	−2.15887	−0.0692457
$973$	−1.88128	−0.0603111
$974$	−46.4056	−1.48693
$975$	−1.62920	−0.0521760
$976$	30.9484	0.990633
$977$	10.3368	0.330704	0.165352	−	0.986235i	$-0.447124\pi$
$977$	10.3368	0.330704	0.165352	+	0.986235i	$0.447124\pi$
$978$	−12.4680	−0.398684
$979$	0	0
$980$	1.02448	0.0327259
$981$	−16.3508	−0.522041
$982$	−23.0407	−0.735258
$983$	−29.0614	−0.926913	−0.463457	−	0.886120i	$-0.653391\pi$
$983$	−29.0614	−0.926913	−0.463457	+	0.886120i	$0.653391\pi$
$984$	14.0317	0.447315
$985$	−2.64566	−0.0842978
$986$	−33.8038	−1.07653
$987$	4.67278	0.148736
$988$	−0.0436651	−0.00138917
$989$	−3.44997	−0.109703
$990$	0	0
$991$	7.70381	0.244719	0.122360	−	0.992486i	$-0.460954\pi$
$991$	7.70381	0.244719	0.122360	+	0.992486i	$0.460954\pi$
$992$	6.20166	0.196903
$993$	−7.43708	−0.236009
$994$	−41.0788	−1.30294
$995$	−6.52800	−0.206951
$996$	0.993283	0.0314734
$997$	−2.86418	−0.0907095	−0.0453547	−	0.998971i	$-0.514442\pi$
$997$	−2.86418	−0.0907095	−0.0453547	+	0.998971i	$0.514442\pi$
$998$	7.08945	0.224413
$999$	−32.1010	−1.01563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.j.1.4		4
3.2	odd	2		5445.2.a.bp.1.1		4
4.3	odd	2		9680.2.a.cn.1.2		4
5.4	even	2		3025.2.a.bd.1.1		4
11.2	odd	10		605.2.g.k.81.2		8
11.3	even	5		605.2.g.m.251.2		8
11.4	even	5		605.2.g.m.511.2		8
11.5	even	5		55.2.g.b.36.1	yes	8
11.6	odd	10		605.2.g.k.366.2		8
11.7	odd	10		605.2.g.e.511.1		8
11.8	odd	10		605.2.g.e.251.1		8
11.9	even	5		55.2.g.b.26.1	✓	8
11.10	odd	2		605.2.a.k.1.1		4
33.5	odd	10		495.2.n.e.91.2		8
33.20	odd	10		495.2.n.e.136.2		8
33.32	even	2		5445.2.a.bi.1.4		4
44.27	odd	10		880.2.bo.h.641.1		8
44.31	odd	10		880.2.bo.h.81.1		8
44.43	even	2		9680.2.a.cm.1.2		4
55.9	even	10		275.2.h.a.26.2		8
55.27	odd	20		275.2.z.a.124.1		16
55.38	odd	20		275.2.z.a.124.4		16
55.42	odd	20		275.2.z.a.224.4		16
55.49	even	10		275.2.h.a.201.2		8
55.53	odd	20		275.2.z.a.224.1		16
55.54	odd	2		3025.2.a.w.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	11.9	even	5
55.2.g.b.36.1	yes	8	11.5	even	5
275.2.h.a.26.2		8	55.9	even	10
275.2.h.a.201.2		8	55.49	even	10
275.2.z.a.124.1		16	55.27	odd	20
275.2.z.a.124.4		16	55.38	odd	20
275.2.z.a.224.1		16	55.53	odd	20
275.2.z.a.224.4		16	55.42	odd	20
495.2.n.e.91.2		8	33.5	odd	10
495.2.n.e.136.2		8	33.20	odd	10
605.2.a.j.1.4		4	1.1	even	1	trivial
605.2.a.k.1.1		4	11.10	odd	2
605.2.g.e.251.1		8	11.8	odd	10
605.2.g.e.511.1		8	11.7	odd	10
605.2.g.k.81.2		8	11.2	odd	10
605.2.g.k.366.2		8	11.6	odd	10
605.2.g.m.251.2		8	11.3	even	5
605.2.g.m.511.2		8	11.4	even	5
880.2.bo.h.81.1		8	44.31	odd	10
880.2.bo.h.641.1		8	44.27	odd	10
3025.2.a.w.1.4		4	55.54	odd	2
3025.2.a.bd.1.1		4	5.4	even	2
5445.2.a.bi.1.4		4	33.32	even	2
5445.2.a.bp.1.1		4	3.2	odd	2
9680.2.a.cm.1.2		4	44.43	even	2
9680.2.a.cn.1.2		4	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+1.35567 q^{2} +0.575493 q^{3} -0.162147 q^{4} -1.00000 q^{5} +0.780181 q^{6} -3.64941 q^{7} -2.93117 q^{8} -2.66881 q^{9} -1.35567 q^{10} -0.0933146 q^{12} -2.83095 q^{13} -4.94742 q^{14} -0.575493 q^{15} -3.64941 q^{16} +3.69195 q^{17} -3.61803 q^{18} -0.0951243 q^{19} +0.162147 q^{20} -2.10021 q^{21} +1.16215 q^{23} -1.68687 q^{24} +1.00000 q^{25} -3.83785 q^{26} -3.26236 q^{27} +0.591742 q^{28} -6.75389 q^{29} -0.780181 q^{30} +6.77837 q^{31} +0.914918 q^{32} +5.00509 q^{34} +3.64941 q^{35} +0.432740 q^{36} +9.83980 q^{37} -0.128958 q^{38} -1.62920 q^{39} +2.93117 q^{40} -8.31822 q^{41} -2.84720 q^{42} -2.96862 q^{43} +2.66881 q^{45} +1.57549 q^{46} -2.22491 q^{47} -2.10021 q^{48} +6.31822 q^{49} +1.35567 q^{50} +2.12469 q^{51} +0.459031 q^{52} +2.99393 q^{53} -4.42270 q^{54} +10.6970 q^{56} -0.0547434 q^{57} -9.15607 q^{58} -8.50860 q^{59} +0.0933146 q^{60} -8.48037 q^{61} +9.18926 q^{62} +9.73958 q^{63} +8.53916 q^{64} +2.83095 q^{65} -13.4153 q^{67} -0.598640 q^{68} +0.668808 q^{69} +4.94742 q^{70} +8.30309 q^{71} +7.82272 q^{72} -1.32003 q^{73} +13.3396 q^{74} +0.575493 q^{75} +0.0154241 q^{76} -2.20866 q^{78} -13.8661 q^{79} +3.64941 q^{80} +6.12896 q^{81} -11.2768 q^{82} -10.6445 q^{83} +0.340544 q^{84} -3.69195 q^{85} -4.02448 q^{86} -3.88682 q^{87} -12.1612 q^{89} +3.61803 q^{90} +10.3313 q^{91} -0.188439 q^{92} +3.90091 q^{93} -3.01625 q^{94} +0.0951243 q^{95} +0.526529 q^{96} -4.33133 q^{97} +8.56545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 4 q^{5} - q^{6} - 3 q^{7} - 3 q^{8} + q^{10} + 8 q^{12} - q^{13} + 2 q^{14} - 3 q^{16} + q^{17} - 10 q^{18} - 20 q^{19} + q^{20} - 10 q^{21} + 5 q^{23} - 11 q^{24} + 4 q^{25}+ \cdots + 8 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 4 * q^5 - q^6 - 3 * q^7 - 3 * q^8 + q^10 + 8 * q^12 - q^13 + 2 * q^14 - 3 * q^16 + q^17 - 10 * q^18 - 20 * q^19 + q^20 - 10 * q^21 + 5 * q^23 - 11 * q^24 + 4 * q^25 - 15 * q^26 - 15 * q^27 - 13 * q^28 - 12 * q^29 + q^30 - 5 * q^31 + 8 * q^32 + 2 * q^34 + 3 * q^35 + 7 * q^37 + 20 * q^38 - 7 * q^39 + 3 * q^40 - 11 * q^41 + 12 * q^42 - 19 * q^43 + 4 * q^46 + 5 * q^47 - 10 * q^48 + 3 * q^49 - q^50 - 7 * q^51 + 11 * q^52 - 11 * q^53 + 8 * q^54 + 11 * q^56 + 5 * q^57 - 14 * q^58 + 9 * q^59 - 8 * q^60 - 12 * q^61 + 35 * q^62 + 5 * q^63 - 3 * q^64 + q^65 - 19 * q^67 + 3 * q^68 - 8 * q^69 - 2 * q^70 + 5 * q^71 + 25 * q^72 - 11 * q^73 - 8 * q^78 - 34 * q^79 + 3 * q^80 + 4 * q^81 - 6 * q^82 + 11 * q^83 - 11 * q^84 - q^85 + q^86 + 19 * q^87 - 8 * q^89 + 10 * q^90 - 8 * q^91 - 12 * q^92 - 5 * q^93 + q^94 + 20 * q^95 + 34 * q^96 + 32 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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