LMFDB - Embedded newform 6011.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63588 q^{2} +1.89916 q^{3} +4.94785 q^{4} -3.80955 q^{5} -5.00596 q^{6} -0.400599 q^{7} -7.77017 q^{8} +0.606822 q^{9} +O(q^{10})$	\(q-2.63588 q^{2} +1.89916 q^{3} +4.94785 q^{4} -3.80955 q^{5} -5.00596 q^{6} -0.400599 q^{7} -7.77017 q^{8} +0.606822 q^{9} +10.0415 q^{10} -1.47140 q^{11} +9.39678 q^{12} -6.12624 q^{13} +1.05593 q^{14} -7.23496 q^{15} +10.5855 q^{16} -1.43021 q^{17} -1.59951 q^{18} +2.30309 q^{19} -18.8491 q^{20} -0.760803 q^{21} +3.87844 q^{22} -6.11313 q^{23} -14.7568 q^{24} +9.51266 q^{25} +16.1480 q^{26} -4.54504 q^{27} -1.98210 q^{28} -2.17668 q^{29} +19.0705 q^{30} +5.13764 q^{31} -12.3618 q^{32} -2.79444 q^{33} +3.76985 q^{34} +1.52610 q^{35} +3.00246 q^{36} -2.72072 q^{37} -6.07066 q^{38} -11.6347 q^{39} +29.6009 q^{40} -8.61711 q^{41} +2.00538 q^{42} -9.33387 q^{43} -7.28028 q^{44} -2.31172 q^{45} +16.1135 q^{46} +10.4171 q^{47} +20.1036 q^{48} -6.83952 q^{49} -25.0742 q^{50} -2.71620 q^{51} -30.3117 q^{52} -8.87847 q^{53} +11.9802 q^{54} +5.60538 q^{55} +3.11272 q^{56} +4.37394 q^{57} +5.73746 q^{58} +4.55063 q^{59} -35.7975 q^{60} +13.4258 q^{61} -13.5422 q^{62} -0.243092 q^{63} +11.4131 q^{64} +23.3382 q^{65} +7.36579 q^{66} -15.0823 q^{67} -7.07645 q^{68} -11.6098 q^{69} -4.02262 q^{70} -12.5632 q^{71} -4.71511 q^{72} +8.32218 q^{73} +7.17148 q^{74} +18.0661 q^{75} +11.3953 q^{76} +0.589443 q^{77} +30.6677 q^{78} -12.3376 q^{79} -40.3261 q^{80} -10.4522 q^{81} +22.7136 q^{82} +1.34195 q^{83} -3.76434 q^{84} +5.44844 q^{85} +24.6029 q^{86} -4.13387 q^{87} +11.4331 q^{88} -0.288726 q^{89} +6.09340 q^{90} +2.45417 q^{91} -30.2469 q^{92} +9.75721 q^{93} -27.4581 q^{94} -8.77373 q^{95} -23.4771 q^{96} -11.4653 q^{97} +18.0281 q^{98} -0.892880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.63588	−1.86385	−0.931923	−	0.362655i	$-0.881870\pi$
$2$	−2.63588	−1.86385	−0.931923	+	0.362655i	$0.881870\pi$
$3$	1.89916	1.09648	0.548241	−	0.836320i	$-0.315298\pi$
$3$	1.89916	1.09648	0.548241	+	0.836320i	$0.315298\pi$
$4$	4.94785	2.47393
$5$	−3.80955	−1.70368	−0.851841	−	0.523800i	$-0.824514\pi$
$5$	−3.80955	−1.70368	−0.851841	+	0.523800i	$0.824514\pi$
$6$	−5.00596	−2.04368
$7$	−0.400599	−0.151412	−0.0757061	−	0.997130i	$-0.524121\pi$
$7$	−0.400599	−0.151412	−0.0757061	+	0.997130i	$0.524121\pi$
$8$	−7.77017	−2.74717
$9$	0.606822	0.202274
$10$	10.0415	3.17540
$11$	−1.47140	−0.443645	−0.221822	−	0.975087i	$-0.571201\pi$
$11$	−1.47140	−0.443645	−0.221822	+	0.975087i	$0.571201\pi$
$12$	9.39678	2.71262
$13$	−6.12624	−1.69911	−0.849557	−	0.527498i	$-0.823130\pi$
$13$	−6.12624	−1.69911	−0.849557	+	0.527498i	$0.823130\pi$
$14$	1.05593	0.282209
$15$	−7.23496	−1.86806
$16$	10.5855	2.64638
$17$	−1.43021	−0.346876	−0.173438	−	0.984845i	$-0.555488\pi$
$17$	−1.43021	−0.346876	−0.173438	+	0.984845i	$0.555488\pi$
$18$	−1.59951	−0.377008
$19$	2.30309	0.528365	0.264182	−	0.964473i	$-0.414898\pi$
$19$	2.30309	0.528365	0.264182	+	0.964473i	$0.414898\pi$
$20$	−18.8491	−4.21478
$21$	−0.760803	−0.166021
$22$	3.87844	0.826886
$23$	−6.11313	−1.27468	−0.637338	−	0.770584i	$-0.719964\pi$
$23$	−6.11313	−1.27468	−0.637338	+	0.770584i	$0.719964\pi$
$24$	−14.7568	−3.01223
$25$	9.51266	1.90253
$26$	16.1480	3.16689
$27$	−4.54504	−0.874693
$28$	−1.98210	−0.374582
$29$	−2.17668	−0.404199	−0.202100	−	0.979365i	$-0.564776\pi$
$29$	−2.17668	−0.404199	−0.202100	+	0.979365i	$0.564776\pi$
$30$	19.0705	3.48177
$31$	5.13764	0.922747	0.461373	−	0.887206i	$-0.347357\pi$
$31$	5.13764	0.922747	0.461373	+	0.887206i	$0.347357\pi$
$32$	−12.3618	−2.18528
$33$	−2.79444	−0.486449
$34$	3.76985	0.646524
$35$	1.52610	0.257958
$36$	3.00246	0.500411
$37$	−2.72072	−0.447283	−0.223642	−	0.974671i	$-0.571795\pi$
$37$	−2.72072	−0.447283	−0.223642	+	0.974671i	$0.571795\pi$
$38$	−6.07066	−0.984791
$39$	−11.6347	−1.86305
$40$	29.6009	4.68031
$41$	−8.61711	−1.34577	−0.672883	−	0.739749i	$-0.734944\pi$
$41$	−8.61711	−1.34577	−0.672883	+	0.739749i	$0.734944\pi$
$42$	2.00538	0.309437
$43$	−9.33387	−1.42340	−0.711701	−	0.702483i	$-0.752075\pi$
$43$	−9.33387	−1.42340	−0.711701	+	0.702483i	$0.752075\pi$
$44$	−7.28028	−1.09754
$45$	−2.31172	−0.344611
$46$	16.1135	2.37580
$47$	10.4171	1.51948	0.759742	−	0.650225i	$-0.225325\pi$
$47$	10.4171	1.51948	0.759742	+	0.650225i	$0.225325\pi$
$48$	20.1036	2.90171
$49$	−6.83952	−0.977074
$50$	−25.0742	−3.54603
$51$	−2.71620	−0.380344
$52$	−30.3117	−4.20348
$53$	−8.87847	−1.21955	−0.609776	−	0.792574i	$-0.708741\pi$
$53$	−8.87847	−1.21955	−0.609776	+	0.792574i	$0.708741\pi$
$54$	11.9802	1.63029
$55$	5.60538	0.755830
$56$	3.11272	0.415955
$57$	4.37394	0.579343
$58$	5.73746	0.753366
$59$	4.55063	0.592441	0.296221	−	0.955120i	$-0.404274\pi$
$59$	4.55063	0.592441	0.296221	+	0.955120i	$0.404274\pi$
$60$	−35.7975	−4.62144
$61$	13.4258	1.71900	0.859498	−	0.511140i	$-0.170777\pi$
$61$	13.4258	1.71900	0.859498	+	0.511140i	$0.170777\pi$
$62$	−13.5422	−1.71986
$63$	−0.243092	−0.0306267
$64$	11.4131	1.42664
$65$	23.3382	2.89475
$66$	7.36579	0.906666
$67$	−15.0823	−1.84260	−0.921299	−	0.388856i	$-0.872870\pi$
$67$	−15.0823	−1.84260	−0.921299	+	0.388856i	$0.872870\pi$
$68$	−7.07645	−0.858145
$69$	−11.6098	−1.39766
$70$	−4.02262	−0.480795
$71$	−12.5632	−1.49098	−0.745489	−	0.666518i	$-0.767784\pi$
$71$	−12.5632	−1.49098	−0.745489	+	0.666518i	$0.767784\pi$
$72$	−4.71511	−0.555681
$73$	8.32218	0.974037	0.487019	−	0.873392i	$-0.338084\pi$
$73$	8.32218	0.974037	0.487019	+	0.873392i	$0.338084\pi$
$74$	7.17148	0.833667
$75$	18.0661	2.08609
$76$	11.3953	1.30714
$77$	0.589443	0.0671732
$78$	30.6677	3.47244
$79$	−12.3376	−1.38809	−0.694045	−	0.719932i	$-0.744173\pi$
$79$	−12.3376	−1.38809	−0.694045	+	0.719932i	$0.744173\pi$
$80$	−40.3261	−4.50859
$81$	−10.4522	−1.16136
$82$	22.7136	2.50830
$83$	1.34195	0.147298	0.0736491	−	0.997284i	$-0.476536\pi$
$83$	1.34195	0.147298	0.0736491	+	0.997284i	$0.476536\pi$
$84$	−3.76434	−0.410723
$85$	5.44844	0.590967
$86$	24.6029	2.65300
$87$	−4.13387	−0.443197
$88$	11.4331	1.21877
$89$	−0.288726	−0.0306049	−0.0153024	−	0.999883i	$-0.504871\pi$
$89$	−0.288726	−0.0306049	−0.0153024	+	0.999883i	$0.504871\pi$
$90$	6.09340	0.642301
$91$	2.45417	0.257266
$92$	−30.2469	−3.15345
$93$	9.75721	1.01178
$94$	−27.4581	−2.83209
$95$	−8.77373	−0.900166
$96$	−23.4771	−2.39612
$97$	−11.4653	−1.16412	−0.582060	−	0.813146i	$-0.697753\pi$
$97$	−11.4653	−1.16412	−0.582060	+	0.813146i	$0.697753\pi$
$98$	18.0281	1.82112
$99$	−0.892880	−0.0897378
$100$	47.0672	4.70672
$101$	8.53067	0.848834	0.424417	−	0.905467i	$-0.360479\pi$
$101$	8.53067	0.848834	0.424417	+	0.905467i	$0.360479\pi$
$102$	7.15956	0.708902
$103$	15.6472	1.54177	0.770883	−	0.636977i	$-0.219815\pi$
$103$	15.6472	1.54177	0.770883	+	0.636977i	$0.219815\pi$
$104$	47.6019	4.66775
$105$	2.89832	0.282847
$106$	23.4026	2.27306
$107$	−14.4810	−1.39993	−0.699964	−	0.714178i	$-0.746801\pi$
$107$	−14.4810	−1.39993	−0.699964	+	0.714178i	$0.746801\pi$
$108$	−22.4882	−2.16392
$109$	17.8532	1.71002	0.855012	−	0.518608i	$-0.173550\pi$
$109$	17.8532	1.71002	0.855012	+	0.518608i	$0.173550\pi$
$110$	−14.7751	−1.40875
$111$	−5.16709	−0.490438
$112$	−4.24055	−0.400694
$113$	−19.4550	−1.83018	−0.915088	−	0.403255i	$-0.867879\pi$
$113$	−19.4550	−1.83018	−0.915088	+	0.403255i	$0.867879\pi$
$114$	−11.5292	−1.07981
$115$	23.2883	2.17164
$116$	−10.7699	−0.999959
$117$	−3.71754	−0.343686
$118$	−11.9949	−1.10422
$119$	0.572939	0.0525213
$120$	56.2169	5.13187
$121$	−8.83497	−0.803179
$122$	−35.3887	−3.20394
$123$	−16.3653	−1.47561
$124$	25.4203	2.28281
$125$	−17.1912	−1.53763
$126$	0.640761	0.0570836
$127$	−20.8718	−1.85207	−0.926035	−	0.377439i	$-0.876805\pi$
$127$	−20.8718	−1.85207	−0.926035	+	0.377439i	$0.876805\pi$
$128$	−5.36005	−0.473766
$129$	−17.7265	−1.56073
$130$	−61.5167	−5.39537
$131$	−0.602799	−0.0526668	−0.0263334	−	0.999653i	$-0.508383\pi$
$131$	−0.602799	−0.0526668	−0.0263334	+	0.999653i	$0.508383\pi$
$132$	−13.8264	−1.20344
$133$	−0.922615	−0.0800009
$134$	39.7551	3.43432
$135$	17.3145	1.49020
$136$	11.1130	0.952928
$137$	−4.95421	−0.423267	−0.211633	−	0.977349i	$-0.567878\pi$
$137$	−4.95421	−0.423267	−0.211633	+	0.977349i	$0.567878\pi$
$138$	30.6021	2.60502
$139$	−4.25811	−0.361168	−0.180584	−	0.983560i	$-0.557799\pi$
$139$	−4.25811	−0.361168	−0.180584	+	0.983560i	$0.557799\pi$
$140$	7.55092	0.638169
$141$	19.7837	1.66609
$142$	33.1150	2.77895
$143$	9.01417	0.753803
$144$	6.42353	0.535294
$145$	8.29217	0.688627
$146$	−21.9362	−1.81546
$147$	−12.9894	−1.07134
$148$	−13.4617	−1.10655
$149$	−22.3495	−1.83094	−0.915472	−	0.402381i	$-0.868183\pi$
$149$	−22.3495	−1.83094	−0.915472	+	0.402381i	$0.868183\pi$
$150$	−47.6200	−3.88816
$151$	14.1402	1.15071	0.575357	−	0.817902i	$-0.304863\pi$
$151$	14.1402	1.15071	0.575357	+	0.817902i	$0.304863\pi$
$152$	−17.8954	−1.45151
$153$	−0.867881	−0.0701640
$154$	−1.55370	−0.125201
$155$	−19.5721	−1.57207
$156$	−57.5669	−4.60904
$157$	15.5423	1.24041	0.620204	−	0.784441i	$-0.287050\pi$
$157$	15.5423	1.24041	0.620204	+	0.784441i	$0.287050\pi$
$158$	32.5204	2.58719
$159$	−16.8617	−1.33722
$160$	47.0929	3.72302
$161$	2.44891	0.193001
$162$	27.5508	2.16460
$163$	13.5162	1.05867	0.529334	−	0.848414i	$-0.322442\pi$
$163$	13.5162	1.05867	0.529334	+	0.848414i	$0.322442\pi$
$164$	−42.6362	−3.32932
$165$	10.6455	0.828754
$166$	−3.53722	−0.274541
$167$	4.23111	0.327413	0.163707	−	0.986509i	$-0.447655\pi$
$167$	4.23111	0.327413	0.163707	+	0.986509i	$0.447655\pi$
$168$	5.91157	0.456088
$169$	24.5308	1.88699
$170$	−14.3614	−1.10147
$171$	1.39756	0.106874
$172$	−46.1826	−3.52139
$173$	−8.17953	−0.621878	−0.310939	−	0.950430i	$-0.600643\pi$
$173$	−8.17953	−0.621878	−0.310939	+	0.950430i	$0.600643\pi$
$174$	10.8964	0.826052
$175$	−3.81076	−0.288067
$176$	−15.5756	−1.17405
$177$	8.64238	0.649601
$178$	0.761045	0.0570428
$179$	5.39480	0.403227	0.201613	−	0.979465i	$-0.435382\pi$
$179$	5.39480	0.403227	0.201613	+	0.979465i	$0.435382\pi$
$180$	−11.4380	−0.852541
$181$	−4.11446	−0.305825	−0.152913	−	0.988240i	$-0.548865\pi$
$181$	−4.11446	−0.305825	−0.152913	+	0.988240i	$0.548865\pi$
$182$	−6.46888	−0.479505
$183$	25.4978	1.88485
$184$	47.5001	3.50175
$185$	10.3647	0.762028
$186$	−25.7188	−1.88579
$187$	2.10441	0.153890
$188$	51.5420	3.75909
$189$	1.82074	0.132439
$190$	23.1265	1.67777
$191$	21.8528	1.58121	0.790606	−	0.612325i	$-0.209766\pi$
$191$	21.8528	1.58121	0.790606	+	0.612325i	$0.209766\pi$
$192$	21.6754	1.56429
$193$	5.40184	0.388833	0.194417	−	0.980919i	$-0.437719\pi$
$193$	5.40184	0.388833	0.194417	+	0.980919i	$0.437719\pi$
$194$	30.2210	2.16974
$195$	44.3231	3.17404
$196$	−33.8409	−2.41721
$197$	8.46568	0.603154	0.301577	−	0.953442i	$-0.402487\pi$
$197$	8.46568	0.603154	0.301577	+	0.953442i	$0.402487\pi$
$198$	2.35352	0.167257
$199$	10.9767	0.778114	0.389057	−	0.921214i	$-0.372801\pi$
$199$	10.9767	0.778114	0.389057	+	0.921214i	$0.372801\pi$
$200$	−73.9151	−5.22658
$201$	−28.6438	−2.02038
$202$	−22.4858	−1.58210
$203$	0.871976	0.0612007
$204$	−13.4393	−0.940942
$205$	32.8273	2.29276
$206$	−41.2441	−2.87362
$207$	−3.70958	−0.257834
$208$	−64.8495	−4.49650
$209$	−3.38877	−0.234406
$210$	−7.63961	−0.527183
$211$	20.2377	1.39322	0.696611	−	0.717449i	$-0.254690\pi$
$211$	20.2377	1.39322	0.696611	+	0.717449i	$0.254690\pi$
$212$	−43.9293	−3.01708
$213$	−23.8596	−1.63483
$214$	38.1701	2.60925
$215$	35.5578	2.42502
$216$	35.3157	2.40293
$217$	−2.05813	−0.139715
$218$	−47.0588	−3.18722
$219$	15.8052	1.06801
$220$	27.7346	1.86987
$221$	8.76179	0.589382
$222$	13.6198	0.914102
$223$	−12.7637	−0.854722	−0.427361	−	0.904081i	$-0.640557\pi$
$223$	−12.7637	−0.854722	−0.427361	+	0.904081i	$0.640557\pi$
$224$	4.95212	0.330878
$225$	5.77249	0.384833
$226$	51.2811	3.41117
$227$	19.0161	1.26214	0.631071	−	0.775725i	$-0.282615\pi$
$227$	19.0161	1.26214	0.631071	+	0.775725i	$0.282615\pi$
$228$	21.6416	1.43325
$229$	17.5922	1.16252	0.581262	−	0.813717i	$-0.302559\pi$
$229$	17.5922	1.16252	0.581262	+	0.813717i	$0.302559\pi$
$230$	−61.3850	−4.04761
$231$	1.11945	0.0736543
$232$	16.9132	1.11040
$233$	−6.68699	−0.438079	−0.219040	−	0.975716i	$-0.570292\pi$
$233$	−6.68699	−0.438079	−0.219040	+	0.975716i	$0.570292\pi$
$234$	9.79897	0.640579
$235$	−39.6843	−2.58872
$236$	22.5158	1.46566
$237$	−23.4311	−1.52202
$238$	−1.51020	−0.0978916
$239$	−9.82172	−0.635314	−0.317657	−	0.948206i	$-0.602896\pi$
$239$	−9.82172	−0.635314	−0.317657	+	0.948206i	$0.602896\pi$
$240$	−76.5858	−4.94359
$241$	14.8277	0.955133	0.477567	−	0.878596i	$-0.341519\pi$
$241$	14.8277	0.955133	0.477567	+	0.878596i	$0.341519\pi$
$242$	23.2879	1.49700
$243$	−6.21539	−0.398717
$244$	66.4288	4.25267
$245$	26.0555	1.66462
$246$	43.1369	2.75031
$247$	−14.1093	−0.897752
$248$	−39.9203	−2.53494
$249$	2.54858	0.161510
$250$	45.3139	2.86591
$251$	−19.1036	−1.20581	−0.602905	−	0.797813i	$-0.705990\pi$
$251$	−19.1036	−1.20581	−0.602905	+	0.797813i	$0.705990\pi$
$252$	−1.20278	−0.0757683
$253$	8.99488	0.565503
$254$	55.0154	3.45197
$255$	10.3475	0.647985
$256$	−8.69786	−0.543616
$257$	14.3120	0.892761	0.446380	−	0.894843i	$-0.352713\pi$
$257$	14.3120	0.892761	0.446380	+	0.894843i	$0.352713\pi$
$258$	46.7250	2.90897
$259$	1.08992	0.0677241
$260$	115.474	7.16139
$261$	−1.32086	−0.0817590
$262$	1.58890	0.0981628
$263$	23.8071	1.46801	0.734006	−	0.679143i	$-0.237649\pi$
$263$	23.8071	1.46801	0.734006	+	0.679143i	$0.237649\pi$
$264$	21.7132	1.33636
$265$	33.8230	2.07773
$266$	2.43190	0.149109
$267$	−0.548337	−0.0335577
$268$	−74.6250	−4.55845
$269$	−0.273513	−0.0166764	−0.00833818	−	0.999965i	$-0.502654\pi$
$269$	−0.273513	−0.0166764	−0.00833818	+	0.999965i	$0.502654\pi$
$270$	−45.6390	−2.77750
$271$	1.27792	0.0776278	0.0388139	−	0.999246i	$-0.487642\pi$
$271$	1.27792	0.0776278	0.0388139	+	0.999246i	$0.487642\pi$
$272$	−15.1395	−0.917966
$273$	4.66086	0.282088
$274$	13.0587	0.788904
$275$	−13.9970	−0.844049
$276$	−57.4437	−3.45771
$277$	2.89353	0.173856	0.0869278	−	0.996215i	$-0.472295\pi$
$277$	2.89353	0.173856	0.0869278	+	0.996215i	$0.472295\pi$
$278$	11.2239	0.673162
$279$	3.11763	0.186648
$280$	−11.8581	−0.708655
$281$	28.2596	1.68583	0.842914	−	0.538048i	$-0.180838\pi$
$281$	28.2596	1.68583	0.842914	+	0.538048i	$0.180838\pi$
$282$	−52.1474	−3.10533
$283$	−12.1775	−0.723874	−0.361937	−	0.932202i	$-0.617885\pi$
$283$	−12.1775	−0.723874	−0.361937	+	0.932202i	$0.617885\pi$
$284$	−62.1608	−3.68857
$285$	−16.6627	−0.987016
$286$	−23.7602	−1.40497
$287$	3.45200	0.203765
$288$	−7.50141	−0.442025
$289$	−14.9545	−0.879677
$290$	−21.8571	−1.28350
$291$	−21.7744	−1.27644
$292$	41.1769	2.40970
$293$	16.2397	0.948734	0.474367	−	0.880327i	$-0.342677\pi$
$293$	16.2397	0.948734	0.474367	+	0.880327i	$0.342677\pi$
$294$	34.2384	1.99682
$295$	−17.3358	−1.00933
$296$	21.1404	1.22876
$297$	6.68758	0.388053
$298$	58.9106	3.41260
$299$	37.4505	2.16582
$300$	89.3884	5.16084
$301$	3.73914	0.215520
$302$	−37.2719	−2.14475
$303$	16.2011	0.930731
$304$	24.3794	1.39825
$305$	−51.1462	−2.92862
$306$	2.28763	0.130775
$307$	−14.0721	−0.803140	−0.401570	−	0.915828i	$-0.631535\pi$
$307$	−14.0721	−0.803140	−0.401570	+	0.915828i	$0.631535\pi$
$308$	2.91647	0.166182
$309$	29.7166	1.69052
$310$	51.5896	2.93009
$311$	−19.3924	−1.09964	−0.549820	−	0.835283i	$-0.685304\pi$
$311$	−19.3924	−1.09964	−0.549820	+	0.835283i	$0.685304\pi$
$312$	90.4039	5.11811
$313$	−19.7590	−1.11684	−0.558421	−	0.829558i	$-0.688593\pi$
$313$	−19.7590	−1.11684	−0.558421	+	0.829558i	$0.688593\pi$
$314$	−40.9675	−2.31193
$315$	0.926072	0.0521782
$316$	−61.0446	−3.43403
$317$	6.07034	0.340944	0.170472	−	0.985362i	$-0.445471\pi$
$317$	6.07034	0.340944	0.170472	+	0.985362i	$0.445471\pi$
$318$	44.4453	2.49237
$319$	3.20277	0.179321
$320$	−43.4789	−2.43055
$321$	−27.5017	−1.53500
$322$	−6.45504	−0.359725
$323$	−3.29389	−0.183277
$324$	−51.7161	−2.87312
$325$	−58.2769	−3.23262
$326$	−35.6269	−1.97319
$327$	33.9061	1.87501
$328$	66.9564	3.69705
$329$	−4.17306	−0.230068
$330$	−28.0603	−1.54467
$331$	22.1647	1.21828	0.609141	−	0.793062i	$-0.291514\pi$
$331$	22.1647	1.21828	0.609141	+	0.793062i	$0.291514\pi$
$332$	6.63977	0.364405
$333$	−1.65099	−0.0904737
$334$	−11.1527	−0.610248
$335$	57.4568	3.13920
$336$	−8.05350	−0.439354
$337$	17.8852	0.974268	0.487134	−	0.873327i	$-0.338042\pi$
$337$	17.8852	0.974268	0.487134	+	0.873327i	$0.338042\pi$
$338$	−64.6602	−3.51705
$339$	−36.9483	−2.00676
$340$	26.9581	1.46201
$341$	−7.55953	−0.409372
$342$	−3.68381	−0.199198
$343$	5.54410	0.299353
$344$	72.5258	3.91033
$345$	44.2282	2.38117
$346$	21.5602	1.15909
$347$	16.8852	0.906447	0.453223	−	0.891397i	$-0.350274\pi$
$347$	16.8852	0.906447	0.453223	+	0.891397i	$0.350274\pi$
$348$	−20.4538	−1.09644
$349$	−12.8466	−0.687663	−0.343831	−	0.939031i	$-0.611725\pi$
$349$	−12.8466	−0.687663	−0.343831	+	0.939031i	$0.611725\pi$
$350$	10.0447	0.536912
$351$	27.8440	1.48620
$352$	18.1892	0.969487
$353$	−4.58315	−0.243936	−0.121968	−	0.992534i	$-0.538921\pi$
$353$	−4.58315	−0.243936	−0.121968	+	0.992534i	$0.538921\pi$
$354$	−22.7803	−1.21076
$355$	47.8601	2.54015
$356$	−1.42857	−0.0757141
$357$	1.08811	0.0575886
$358$	−14.2200	−0.751553
$359$	1.70451	0.0899606	0.0449803	−	0.998988i	$-0.485677\pi$
$359$	1.70451	0.0899606	0.0449803	+	0.998988i	$0.485677\pi$
$360$	17.9624	0.946704
$361$	−13.6958	−0.720831
$362$	10.8452	0.570011
$363$	−16.7791	−0.880672
$364$	12.1428	0.636458
$365$	−31.7037	−1.65945
$366$	−67.2090	−3.51307
$367$	−19.3790	−1.01158	−0.505788	−	0.862658i	$-0.668798\pi$
$367$	−19.3790	−1.01158	−0.505788	+	0.862658i	$0.668798\pi$
$368$	−64.7107	−3.37328
$369$	−5.22905	−0.272213
$370$	−27.3201	−1.42030
$371$	3.55671	0.184655
$372$	48.2772	2.50306
$373$	20.5683	1.06499	0.532493	−	0.846434i	$-0.321255\pi$
$373$	20.5683	1.06499	0.532493	+	0.846434i	$0.321255\pi$
$374$	−5.54697	−0.286827
$375$	−32.6489	−1.68598
$376$	−80.9423	−4.17428
$377$	13.3349	0.686780
$378$	−4.79924	−0.246846
$379$	−27.1474	−1.39447	−0.697235	−	0.716842i	$-0.745587\pi$
$379$	−27.1474	−1.39447	−0.697235	+	0.716842i	$0.745587\pi$
$380$	−43.4111	−2.22694
$381$	−39.6389	−2.03076
$382$	−57.6013	−2.94714
$383$	11.9960	0.612966	0.306483	−	0.951876i	$-0.400848\pi$
$383$	11.9960	0.612966	0.306483	+	0.951876i	$0.400848\pi$
$384$	−10.1796	−0.519476
$385$	−2.24551	−0.114442
$386$	−14.2386	−0.724726
$387$	−5.66399	−0.287917
$388$	−56.7284	−2.87995
$389$	−12.3396	−0.625643	−0.312821	−	0.949812i	$-0.601274\pi$
$389$	−12.3396	−0.625643	−0.312821	+	0.949812i	$0.601274\pi$
$390$	−116.830	−5.91593
$391$	8.74304	0.442155
$392$	53.1443	2.68419
$393$	−1.14481	−0.0577482
$394$	−22.3145	−1.12419
$395$	47.0007	2.36486
$396$	−4.41783	−0.222005
$397$	−6.49610	−0.326030	−0.163015	−	0.986624i	$-0.552122\pi$
$397$	−6.49610	−0.326030	−0.163015	+	0.986624i	$0.552122\pi$
$398$	−28.9331	−1.45029
$399$	−1.75220	−0.0877196
$400$	100.697	5.03483
$401$	−39.2560	−1.96035	−0.980176	−	0.198126i	$-0.936514\pi$
$401$	−39.2560	−1.96035	−0.980176	+	0.198126i	$0.936514\pi$
$402$	75.5015	3.76567
$403$	−31.4744	−1.56785
$404$	42.2085	2.09995
$405$	39.8183	1.97859
$406$	−2.29842	−0.114069
$407$	4.00327	0.198435
$408$	21.1053	1.04487
$409$	13.0971	0.647611	0.323806	−	0.946124i	$-0.395038\pi$
$409$	13.0971	0.647611	0.323806	+	0.946124i	$0.395038\pi$
$410$	−86.5287	−4.27335
$411$	−9.40885	−0.464104
$412$	77.4201	3.81421
$413$	−1.82298	−0.0897028
$414$	9.77800	0.480563
$415$	−5.11223	−0.250949
$416$	75.7314	3.71304
$417$	−8.08685	−0.396015
$418$	8.93239	0.436897
$419$	29.7444	1.45311	0.726554	−	0.687109i	$-0.241120\pi$
$419$	29.7444	1.45311	0.726554	+	0.687109i	$0.241120\pi$
$420$	14.3404	0.699742
$421$	15.7868	0.769403	0.384701	−	0.923041i	$-0.374304\pi$
$421$	15.7868	0.769403	0.384701	+	0.923041i	$0.374304\pi$
$422$	−53.3442	−2.59675
$423$	6.32130	0.307352
$424$	68.9873	3.35032
$425$	−13.6051	−0.659943
$426$	62.8909	3.04707
$427$	−5.37835	−0.260277
$428$	−71.6497	−3.46332
$429$	17.1194	0.826531
$430$	−93.7261	−4.51987
$431$	1.16451	0.0560926	0.0280463	−	0.999607i	$-0.491071\pi$
$431$	1.16451	0.0560926	0.0280463	+	0.999607i	$0.491071\pi$
$432$	−48.1116	−2.31477
$433$	−29.6381	−1.42432	−0.712159	−	0.702018i	$-0.752282\pi$
$433$	−29.6381	−1.42432	−0.712159	+	0.702018i	$0.752282\pi$
$434$	5.42498	0.260408
$435$	15.7482	0.755068
$436$	88.3348	4.23047
$437$	−14.0791	−0.673494
$438$	−41.6605	−1.99062
$439$	10.7716	0.514102	0.257051	−	0.966398i	$-0.417249\pi$
$439$	10.7716	0.514102	0.257051	+	0.966398i	$0.417249\pi$
$440$	−43.5548	−2.07639
$441$	−4.15037	−0.197637
$442$	−23.0950	−1.09852
$443$	−12.0222	−0.571190	−0.285595	−	0.958350i	$-0.592191\pi$
$443$	−12.0222	−0.571190	−0.285595	+	0.958350i	$0.592191\pi$
$444$	−25.5660	−1.21331
$445$	1.09991	0.0521409
$446$	33.6436	1.59307
$447$	−42.4454	−2.00760
$448$	−4.57209	−0.216011
$449$	34.0229	1.60564	0.802821	−	0.596221i	$-0.203332\pi$
$449$	34.0229	1.60564	0.802821	+	0.596221i	$0.203332\pi$
$450$	−15.2156	−0.717269
$451$	12.6792	0.597042
$452$	−96.2606	−4.52772
$453$	26.8546	1.26174
$454$	−50.1241	−2.35244
$455$	−9.34926	−0.438300
$456$	−33.9863	−1.59155
$457$	−34.8750	−1.63138	−0.815691	−	0.578488i	$-0.803643\pi$
$457$	−34.8750	−1.63138	−0.815691	+	0.578488i	$0.803643\pi$
$458$	−46.3708	−2.16677
$459$	6.50034	0.303410
$460$	115.227	5.37248
$461$	6.56624	0.305820	0.152910	−	0.988240i	$-0.451135\pi$
$461$	6.56624	0.305820	0.152910	+	0.988240i	$0.451135\pi$
$462$	−2.95073	−0.137280
$463$	−4.36795	−0.202996	−0.101498	−	0.994836i	$-0.532364\pi$
$463$	−4.36795	−0.202996	−0.101498	+	0.994836i	$0.532364\pi$
$464$	−23.0413	−1.06967
$465$	−37.1706	−1.72374
$466$	17.6261	0.816513
$467$	−20.7495	−0.960173	−0.480087	−	0.877221i	$-0.659395\pi$
$467$	−20.7495	−0.960173	−0.480087	+	0.877221i	$0.659395\pi$
$468$	−18.3938	−0.850254
$469$	6.04196	0.278992
$470$	104.603	4.82497
$471$	29.5173	1.36009
$472$	−35.3592	−1.62754
$473$	13.7339	0.631485
$474$	61.7616	2.83680
$475$	21.9085	1.00523
$476$	2.83482	0.129934
$477$	−5.38765	−0.246684
$478$	25.8889	1.18413
$479$	−17.3922	−0.794671	−0.397336	−	0.917673i	$-0.630065\pi$
$479$	−17.3922	−0.794671	−0.397336	+	0.917673i	$0.630065\pi$
$480$	89.4371	4.08223
$481$	16.6678	0.759985
$482$	−39.0839	−1.78022
$483$	4.65089	0.211623
$484$	−43.7141	−1.98701
$485$	43.6774	1.98329
$486$	16.3830	0.743148
$487$	−26.6667	−1.20838	−0.604192	−	0.796839i	$-0.706504\pi$
$487$	−26.6667	−1.20838	−0.604192	+	0.796839i	$0.706504\pi$
$488$	−104.321	−4.72237
$489$	25.6694	1.16081
$490$	−68.6791	−3.10260
$491$	−43.8681	−1.97974	−0.989870	−	0.141979i	$-0.954653\pi$
$491$	−43.8681	−1.97974	−0.989870	+	0.141979i	$0.954653\pi$
$492$	−80.9730	−3.65055
$493$	3.11310	0.140207
$494$	37.1903	1.67327
$495$	3.40147	0.152885
$496$	54.3846	2.44194
$497$	5.03280	0.225752
$498$	−6.71776	−0.301030
$499$	−26.7454	−1.19729	−0.598645	−	0.801014i	$-0.704294\pi$
$499$	−26.7454	−1.19729	−0.598645	+	0.801014i	$0.704294\pi$
$500$	−85.0596	−3.80398
$501$	8.03557	0.359003
$502$	50.3548	2.24745
$503$	16.3179	0.727578	0.363789	−	0.931481i	$-0.381483\pi$
$503$	16.3179	0.727578	0.363789	+	0.931481i	$0.381483\pi$
$504$	1.88887	0.0841369
$505$	−32.4980	−1.44614
$506$	−23.7094	−1.05401
$507$	46.5880	2.06905
$508$	−103.270	−4.58188
$509$	−11.9197	−0.528333	−0.264167	−	0.964477i	$-0.585097\pi$
$509$	−11.9197	−0.528333	−0.264167	+	0.964477i	$0.585097\pi$
$510$	−27.2747	−1.20774
$511$	−3.33386	−0.147481
$512$	33.6466	1.48698
$513$	−10.4676	−0.462157
$514$	−37.7248	−1.66397
$515$	−59.6088	−2.62668
$516$	−87.7083	−3.86114
$517$	−15.3277	−0.674111
$518$	−2.87289	−0.126227
$519$	−15.5343	−0.681878
$520$	−181.342	−7.95237
$521$	28.7114	1.25787	0.628934	−	0.777459i	$-0.283492\pi$
$521$	28.7114	1.25787	0.628934	+	0.777459i	$0.283492\pi$
$522$	3.48162	0.152386
$523$	−14.1626	−0.619286	−0.309643	−	0.950853i	$-0.600210\pi$
$523$	−14.1626	−0.619286	−0.309643	+	0.950853i	$0.600210\pi$
$524$	−2.98256	−0.130294
$525$	−7.23726	−0.315860
$526$	−62.7527	−2.73615
$527$	−7.34788	−0.320079
$528$	−29.5806	−1.28733
$529$	14.3704	0.624799
$530$	−89.1532	−3.87257
$531$	2.76142	0.119835
$532$	−4.56496	−0.197916
$533$	52.7905	2.28661
$534$	1.44535	0.0625464
$535$	55.1660	2.38503
$536$	117.192	5.06193
$537$	10.2456	0.442131
$538$	0.720946	0.0310822
$539$	10.0637	0.433474
$540$	85.6698	3.68664
$541$	−42.8721	−1.84321	−0.921607	−	0.388124i	$-0.873123\pi$
$541$	−42.8721	−1.84321	−0.921607	+	0.388124i	$0.873123\pi$
$542$	−3.36843	−0.144686
$543$	−7.81402	−0.335332
$544$	17.6799	0.758021
$545$	−68.0125	−2.91334
$546$	−12.2855	−0.525769
$547$	−15.2490	−0.652000	−0.326000	−	0.945370i	$-0.605701\pi$
$547$	−15.2490	−0.652000	−0.326000	+	0.945370i	$0.605701\pi$
$548$	−24.5127	−1.04713
$549$	8.14706	0.347708
$550$	36.8943	1.57318
$551$	−5.01309	−0.213565
$552$	90.2104	3.83961
$553$	4.94243	0.210174
$554$	−7.62700	−0.324040
$555$	19.6843	0.835551
$556$	−21.0685	−0.893503
$557$	32.6505	1.38345	0.691724	−	0.722162i	$-0.256852\pi$
$557$	32.6505	1.38345	0.691724	+	0.722162i	$0.256852\pi$
$558$	−8.21769	−0.347883
$559$	57.1815	2.41852
$560$	16.1546	0.682656
$561$	3.99662	0.168737
$562$	−74.4889	−3.14213
$563$	41.6963	1.75729	0.878645	−	0.477475i	$-0.158448\pi$
$563$	41.6963	1.75729	0.878645	+	0.477475i	$0.158448\pi$
$564$	97.8868	4.12178
$565$	74.1149	3.11804
$566$	32.0983	1.34919
$567$	4.18715	0.175844
$568$	97.6182	4.09597
$569$	−13.5734	−0.569026	−0.284513	−	0.958672i	$-0.591832\pi$
$569$	−13.5734	−0.569026	−0.284513	+	0.958672i	$0.591832\pi$
$570$	43.9210	1.83965
$571$	23.0331	0.963907	0.481953	−	0.876197i	$-0.339927\pi$
$571$	23.0331	0.963907	0.481953	+	0.876197i	$0.339927\pi$
$572$	44.6008	1.86485
$573$	41.5020	1.73377
$574$	−9.09906	−0.379787
$575$	−58.1522	−2.42511
$576$	6.92574	0.288573
$577$	7.38647	0.307503	0.153751	−	0.988110i	$-0.450864\pi$
$577$	7.38647	0.307503	0.153751	+	0.988110i	$0.450864\pi$
$578$	39.4183	1.63958
$579$	10.2590	0.426349
$580$	41.0284	1.70361
$581$	−0.537584	−0.0223028
$582$	57.3946	2.37908
$583$	13.0638	0.541048
$584$	−64.6648	−2.67585
$585$	14.1621	0.585532
$586$	−42.8059	−1.76829
$587$	16.4509	0.679003	0.339501	−	0.940606i	$-0.389742\pi$
$587$	16.4509	0.679003	0.339501	+	0.940606i	$0.389742\pi$
$588$	−64.2694	−2.65043
$589$	11.8324	0.487547
$590$	45.6951	1.88124
$591$	16.0777	0.661348
$592$	−28.8002	−1.18368
$593$	0.465066	0.0190980	0.00954899	−	0.999954i	$-0.496960\pi$
$593$	0.465066	0.0190980	0.00954899	+	0.999954i	$0.496960\pi$
$594$	−17.6276	−0.723271
$595$	−2.18264	−0.0894795
$596$	−110.582	−4.52962
$597$	20.8465	0.853189
$598$	−98.7150	−4.03675
$599$	36.9525	1.50984	0.754919	−	0.655818i	$-0.227676\pi$
$599$	36.9525	1.50984	0.754919	+	0.655818i	$0.227676\pi$
$600$	−140.377	−5.73086
$601$	−17.7495	−0.724019	−0.362009	−	0.932174i	$-0.617909\pi$
$601$	−17.7495	−0.724019	−0.362009	+	0.932174i	$0.617909\pi$
$602$	−9.85591	−0.401697
$603$	−9.15227	−0.372709
$604$	69.9636	2.84678
$605$	33.6573	1.36836
$606$	−42.7042	−1.73474
$607$	29.8588	1.21193	0.605966	−	0.795491i	$-0.292787\pi$
$607$	29.8588	1.21193	0.605966	+	0.795491i	$0.292787\pi$
$608$	−28.4703	−1.15462
$609$	1.65602	0.0671055
$610$	134.815	5.45850
$611$	−63.8174	−2.58178
$612$	−4.29414	−0.173580
$613$	10.2126	0.412483	0.206242	−	0.978501i	$-0.433877\pi$
$613$	10.2126	0.412483	0.206242	+	0.978501i	$0.433877\pi$
$614$	37.0924	1.49693
$615$	62.3444	2.51397
$616$	−4.58007	−0.184536
$617$	−22.4613	−0.904258	−0.452129	−	0.891953i	$-0.649335\pi$
$617$	−22.4613	−0.904258	−0.452129	+	0.891953i	$0.649335\pi$
$618$	−78.3294	−3.15087
$619$	16.7749	0.674241	0.337120	−	0.941462i	$-0.390547\pi$
$619$	16.7749	0.674241	0.337120	+	0.941462i	$0.390547\pi$
$620$	−96.8397	−3.88918
$621$	27.7844	1.11495
$622$	51.1159	2.04956
$623$	0.115663	0.00463395
$624$	−123.160	−4.93033
$625$	17.9275	0.717099
$626$	52.0822	2.08162
$627$	−6.43583	−0.257022
$628$	76.9008	3.06868
$629$	3.89119	0.155152
$630$	−2.44101	−0.0972522
$631$	−4.25387	−0.169344	−0.0846720	−	0.996409i	$-0.526984\pi$
$631$	−4.25387	−0.169344	−0.0846720	+	0.996409i	$0.526984\pi$
$632$	95.8653	3.81332
$633$	38.4347	1.52764
$634$	−16.0007	−0.635468
$635$	79.5120	3.15534
$636$	−83.4290	−3.30818
$637$	41.9005	1.66016
$638$	−8.44212	−0.334227
$639$	−7.62362	−0.301586
$640$	20.4194	0.807146
$641$	−14.6472	−0.578531	−0.289266	−	0.957249i	$-0.593411\pi$
$641$	−14.6472	−0.578531	−0.289266	+	0.957249i	$0.593411\pi$
$642$	72.4912	2.86100
$643$	31.2224	1.23129	0.615646	−	0.788023i	$-0.288895\pi$
$643$	31.2224	1.23129	0.615646	+	0.788023i	$0.288895\pi$
$644$	12.1169	0.477471
$645$	67.5301	2.65900
$646$	8.68230	0.341600
$647$	−0.431308	−0.0169565	−0.00847823	−	0.999964i	$-0.502699\pi$
$647$	−0.431308	−0.0169565	−0.00847823	+	0.999964i	$0.502699\pi$
$648$	81.2157	3.19045
$649$	−6.69581	−0.262833
$650$	153.611	6.02511
$651$	−3.90873	−0.153195
$652$	66.8759	2.61906
$653$	19.8512	0.776838	0.388419	−	0.921483i	$-0.373021\pi$
$653$	19.8512	0.776838	0.388419	+	0.921483i	$0.373021\pi$
$654$	−89.3723	−3.49473
$655$	2.29639	0.0897274
$656$	−91.2166	−3.56141
$657$	5.05008	0.197022
$658$	10.9997	0.428812
$659$	36.7481	1.43150	0.715751	−	0.698355i	$-0.246084\pi$
$659$	36.7481	1.43150	0.715751	+	0.698355i	$0.246084\pi$
$660$	52.6725	2.05028
$661$	−29.8388	−1.16059	−0.580297	−	0.814405i	$-0.697064\pi$
$661$	−29.8388	−1.16059	−0.580297	+	0.814405i	$0.697064\pi$
$662$	−58.4235	−2.27069
$663$	16.6401	0.646247
$664$	−10.4272	−0.404654
$665$	3.51475	0.136296
$666$	4.35181	0.168629
$667$	13.3063	0.515223
$668$	20.9349	0.809996
$669$	−24.2404	−0.937188
$670$	−151.449	−5.85099
$671$	−19.7547	−0.762623
$672$	9.40489	0.362802
$673$	−34.5156	−1.33048	−0.665239	−	0.746631i	$-0.731670\pi$
$673$	−34.5156	−1.33048	−0.665239	+	0.746631i	$0.731670\pi$
$674$	−47.1431	−1.81589
$675$	−43.2354	−1.66413
$676$	121.375	4.66826
$677$	48.3923	1.85987	0.929934	−	0.367727i	$-0.119864\pi$
$677$	48.3923	1.85987	0.929934	+	0.367727i	$0.119864\pi$
$678$	97.3912	3.74029
$679$	4.59297	0.176262
$680$	−42.3353	−1.62349
$681$	36.1147	1.38392
$682$	19.9260	0.763006
$683$	10.7325	0.410666	0.205333	−	0.978692i	$-0.434172\pi$
$683$	10.7325	0.410666	0.205333	+	0.978692i	$0.434172\pi$
$684$	6.91494	0.264399
$685$	18.8733	0.721112
$686$	−14.6136	−0.557948
$687$	33.4104	1.27469
$688$	−98.8039	−3.76686
$689$	54.3916	2.07216
$690$	−116.580	−4.43813
$691$	14.9053	0.567023	0.283511	−	0.958969i	$-0.408501\pi$
$691$	14.9053	0.567023	0.283511	+	0.958969i	$0.408501\pi$
$692$	−40.4711	−1.53848
$693$	0.357687	0.0135874
$694$	−44.5074	−1.68948
$695$	16.2215	0.615316
$696$	32.1209	1.21754
$697$	12.3242	0.466814
$698$	33.8621	1.28170
$699$	−12.6997	−0.480346
$700$	−18.8551	−0.712655
$701$	−34.5173	−1.30370	−0.651850	−	0.758348i	$-0.726007\pi$
$701$	−34.5173	−1.30370	−0.651850	+	0.758348i	$0.726007\pi$
$702$	−73.3933	−2.77005
$703$	−6.26605	−0.236329
$704$	−16.7933	−0.632923
$705$	−75.3670	−2.83848
$706$	12.0806	0.454660
$707$	−3.41738	−0.128524
$708$	42.7612	1.60707
$709$	31.9093	1.19838	0.599189	−	0.800608i	$-0.295490\pi$
$709$	31.9093	1.19838	0.599189	+	0.800608i	$0.295490\pi$
$710$	−126.153	−4.73445
$711$	−7.48673	−0.280774
$712$	2.24345	0.0840768
$713$	−31.4070	−1.17620
$714$	−2.86811	−0.107336
$715$	−34.3399	−1.28424
$716$	26.6927	0.997552
$717$	−18.6531	−0.696611
$718$	−4.49288	−0.167673
$719$	−24.6786	−0.920355	−0.460178	−	0.887827i	$-0.652214\pi$
$719$	−24.6786	−0.920355	−0.460178	+	0.887827i	$0.652214\pi$
$720$	−24.4707	−0.911971
$721$	−6.26826	−0.233442
$722$	36.1004	1.34352
$723$	28.1601	1.04729
$724$	−20.3577	−0.756588
$725$	−20.7060	−0.769002
$726$	44.2275	1.64144
$727$	9.45140	0.350533	0.175267	−	0.984521i	$-0.443921\pi$
$727$	9.45140	0.350533	0.175267	+	0.984521i	$0.443921\pi$
$728$	−19.0693	−0.706755
$729$	19.5527	0.724173
$730$	83.5672	3.09296
$731$	13.3494	0.493744
$732$	126.159	4.66297
$733$	−7.44025	−0.274812	−0.137406	−	0.990515i	$-0.543877\pi$
$733$	−7.44025	−0.274812	−0.137406	+	0.990515i	$0.543877\pi$
$734$	51.0807	1.88542
$735$	49.4836	1.82523
$736$	75.5693	2.78552
$737$	22.1922	0.817459
$738$	13.7831	0.507364
$739$	5.43365	0.199880	0.0999401	−	0.994993i	$-0.468135\pi$
$739$	5.43365	0.199880	0.0999401	+	0.994993i	$0.468135\pi$
$740$	51.2830	1.88520
$741$	−26.7958	−0.984369
$742$	−9.37504	−0.344169
$743$	−8.86315	−0.325158	−0.162579	−	0.986696i	$-0.551981\pi$
$743$	−8.86315	−0.325158	−0.162579	+	0.986696i	$0.551981\pi$
$744$	−75.8152	−2.77952
$745$	85.1416	3.11935
$746$	−54.2155	−1.98497
$747$	0.814325	0.0297946
$748$	10.4123	0.380712
$749$	5.80106	0.211966
$750$	86.0586	3.14242
$751$	15.1869	0.554177	0.277089	−	0.960844i	$-0.410630\pi$
$751$	15.1869	0.554177	0.277089	+	0.960844i	$0.410630\pi$
$752$	110.270	4.02113
$753$	−36.2809	−1.32215
$754$	−35.1491	−1.28005
$755$	−53.8678	−1.96045
$756$	9.00873	0.327645
$757$	−29.3899	−1.06819	−0.534097	−	0.845423i	$-0.679348\pi$
$757$	−29.3899	−1.06819	−0.534097	+	0.845423i	$0.679348\pi$
$758$	71.5573	2.59908
$759$	17.0827	0.620065
$760$	68.1734	2.47291
$761$	−29.1212	−1.05564	−0.527822	−	0.849355i	$-0.676991\pi$
$761$	−29.1212	−1.05564	−0.527822	+	0.849355i	$0.676991\pi$
$762$	104.483	3.78503
$763$	−7.15196	−0.258918
$764$	108.124	3.91180
$765$	3.30623	0.119537
$766$	−31.6199	−1.14247
$767$	−27.8782	−1.00662
$768$	−16.5187	−0.596065
$769$	−5.30589	−0.191335	−0.0956677	−	0.995413i	$-0.530499\pi$
$769$	−5.30589	−0.191335	−0.0956677	+	0.995413i	$0.530499\pi$
$770$	5.91889	0.213302
$771$	27.1809	0.978896
$772$	26.7275	0.961944
$773$	22.4900	0.808909	0.404454	−	0.914558i	$-0.367461\pi$
$773$	22.4900	0.808909	0.404454	+	0.914558i	$0.367461\pi$
$774$	14.9296	0.536633
$775$	48.8726	1.75556
$776$	89.0870	3.19804
$777$	2.06993	0.0742583
$778$	32.5257	1.16610
$779$	−19.8460	−0.711055
$780$	219.304	7.85234
$781$	18.4855	0.661464
$782$	−23.0456	−0.824108
$783$	9.89309	0.353550
$784$	−72.3999	−2.58571
$785$	−59.2090	−2.11326
$786$	3.01759	0.107634
$787$	33.2246	1.18433	0.592165	−	0.805817i	$-0.298273\pi$
$787$	33.2246	1.18433	0.592165	+	0.805817i	$0.298273\pi$
$788$	41.8869	1.49216
$789$	45.2137	1.60965
$790$	−123.888	−4.40774
$791$	7.79367	0.277111
$792$	6.93783	0.246525
$793$	−82.2496	−2.92077
$794$	17.1229	0.607670
$795$	64.2353	2.27819
$796$	54.3108	1.92500
$797$	39.5662	1.40151	0.700753	−	0.713404i	$-0.252847\pi$
$797$	39.5662	1.40151	0.700753	+	0.713404i	$0.252847\pi$
$798$	4.61858	0.163496
$799$	−14.8985	−0.527073
$800$	−117.594	−4.15756
$801$	−0.175205	−0.00619057
$802$	103.474	3.65380
$803$	−12.2453	−0.432127
$804$	−141.725	−4.99826
$805$	−9.32926	−0.328813
$806$	82.9626	2.92223
$807$	−0.519445	−0.0182853
$808$	−66.2848	−2.33189
$809$	−29.0057	−1.01979	−0.509894	−	0.860237i	$-0.670315\pi$
$809$	−29.0057	−1.01979	−0.509894	+	0.860237i	$0.670315\pi$
$810$	−104.956	−3.68778
$811$	51.8903	1.82212	0.911058	−	0.412279i	$-0.135267\pi$
$811$	51.8903	1.82212	0.911058	+	0.412279i	$0.135267\pi$
$812$	4.31441	0.151406
$813$	2.42697	0.0851176
$814$	−10.5521	−0.369852
$815$	−51.4905	−1.80363
$816$	−28.7524	−1.00653
$817$	−21.4967	−0.752075
$818$	−34.5224	−1.20705
$819$	1.48924	0.0520383
$820$	162.425	5.67211
$821$	−13.6905	−0.477802	−0.238901	−	0.971044i	$-0.576787\pi$
$821$	−13.6905	−0.477802	−0.238901	+	0.971044i	$0.576787\pi$
$822$	24.8006	0.865019
$823$	−27.6816	−0.964921	−0.482460	−	0.875918i	$-0.660257\pi$
$823$	−27.6816	−0.964921	−0.482460	+	0.875918i	$0.660257\pi$
$824$	−121.582	−4.23550
$825$	−26.5825	−0.925485
$826$	4.80514	0.167192
$827$	−7.97363	−0.277270	−0.138635	−	0.990344i	$-0.544272\pi$
$827$	−7.97363	−0.277270	−0.138635	+	0.990344i	$0.544272\pi$
$828$	−18.3545	−0.637861
$829$	6.65254	0.231052	0.115526	−	0.993304i	$-0.463145\pi$
$829$	6.65254	0.231052	0.115526	+	0.993304i	$0.463145\pi$
$830$	13.4752	0.467731
$831$	5.49529	0.190630
$832$	−69.9197	−2.42403
$833$	9.78193	0.338924
$834$	21.3159	0.738111
$835$	−16.1186	−0.557808
$836$	−16.7671	−0.579904
$837$	−23.3507	−0.807120
$838$	−78.4026	−2.70837
$839$	7.08795	0.244703	0.122352	−	0.992487i	$-0.460956\pi$
$839$	7.08795	0.244703	0.122352	+	0.992487i	$0.460956\pi$
$840$	−22.5204	−0.777028
$841$	−24.2621	−0.836623
$842$	−41.6121	−1.43405
$843$	53.6697	1.84848
$844$	100.133	3.44673
$845$	−93.4513	−3.21482
$846$	−16.6622	−0.572857
$847$	3.53928	0.121611
$848$	−93.9833	−3.22740
$849$	−23.1270	−0.793716
$850$	35.8613	1.23003
$851$	16.6321	0.570141
$852$	−118.054	−4.04445
$853$	−40.8200	−1.39765	−0.698826	−	0.715292i	$-0.746294\pi$
$853$	−40.8200	−1.39765	−0.698826	+	0.715292i	$0.746294\pi$
$854$	14.1767	0.485116
$855$	−5.32409	−0.182080
$856$	112.520	3.84584
$857$	−22.9371	−0.783515	−0.391758	−	0.920068i	$-0.628133\pi$
$857$	−22.9371	−0.783515	−0.391758	+	0.920068i	$0.628133\pi$
$858$	−45.1246	−1.54053
$859$	1.43303	0.0488945	0.0244472	−	0.999701i	$-0.492217\pi$
$859$	1.43303	0.0488945	0.0244472	+	0.999701i	$0.492217\pi$
$860$	175.935	5.99933
$861$	6.55592	0.223425
$862$	−3.06951	−0.104548
$863$	−35.6040	−1.21197	−0.605987	−	0.795475i	$-0.707222\pi$
$863$	−35.6040	−1.21197	−0.605987	+	0.795475i	$0.707222\pi$
$864$	56.1848	1.91145
$865$	31.1603	1.05948
$866$	78.1225	2.65471
$867$	−28.4011	−0.964550
$868$	−10.1833	−0.345645
$869$	18.1536	0.615818
$870$	−41.5103	−1.40733
$871$	92.3978	3.13078
$872$	−138.722	−4.69773
$873$	−6.95737	−0.235471
$874$	37.1107	1.25529
$875$	6.88678	0.232816
$876$	78.2017	2.64219
$877$	0.531398	0.0179440	0.00897201	−	0.999960i	$-0.497144\pi$
$877$	0.531398	0.0179440	0.00897201	+	0.999960i	$0.497144\pi$
$878$	−28.3927	−0.958207
$879$	30.8419	1.04027
$880$	59.3359	2.00021
$881$	−46.7749	−1.57589	−0.787944	−	0.615748i	$-0.788854\pi$
$881$	−46.7749	−1.57589	−0.787944	+	0.615748i	$0.788854\pi$
$882$	10.9399	0.368365
$883$	−18.1801	−0.611808	−0.305904	−	0.952062i	$-0.598959\pi$
$883$	−18.1801	−0.611808	−0.305904	+	0.952062i	$0.598959\pi$
$884$	43.3520	1.45809
$885$	−32.9236	−1.10671
$886$	31.6889	1.06461
$887$	−7.55199	−0.253571	−0.126785	−	0.991930i	$-0.540466\pi$
$887$	−7.55199	−0.253571	−0.126785	+	0.991930i	$0.540466\pi$
$888$	40.1492	1.34732
$889$	8.36121	0.280426
$890$	−2.89924	−0.0971827
$891$	15.3794	0.515231
$892$	−63.1530	−2.11452
$893$	23.9914	0.802842
$894$	111.881	3.74186
$895$	−20.5518	−0.686970
$896$	2.14723	0.0717339
$897$	71.1246	2.37478
$898$	−89.6803	−2.99267
$899$	−11.1830	−0.372974
$900$	28.5614	0.952048
$901$	12.6980	0.423033
$902$	−33.4209	−1.11279
$903$	7.10123	0.236314
$904$	151.169	5.02781
$905$	15.6742	0.521029
$906$	−70.7853	−2.35169
$907$	33.6647	1.11782	0.558909	−	0.829229i	$-0.311220\pi$
$907$	33.6647	1.11782	0.558909	+	0.829229i	$0.311220\pi$
$908$	94.0888	3.12245
$909$	5.17660	0.171697
$910$	24.6435	0.816925
$911$	−48.7269	−1.61439	−0.807197	−	0.590282i	$-0.799016\pi$
$911$	−48.7269	−1.61439	−0.807197	+	0.590282i	$0.799016\pi$
$912$	46.3005	1.53316
$913$	−1.97455	−0.0653481
$914$	91.9261	3.04065
$915$	−97.1349	−3.21118
$916$	87.0434	2.87600
$917$	0.241481	0.00797439
$918$	−17.1341	−0.565510
$919$	−36.5493	−1.20565	−0.602825	−	0.797873i	$-0.705958\pi$
$919$	−36.5493	−1.20565	−0.602825	+	0.797873i	$0.705958\pi$
$920$	−180.954	−5.96587
$921$	−26.7253	−0.880629
$922$	−17.3078	−0.570002
$923$	76.9651	2.53334
$924$	5.53886	0.182215
$925$	−25.8813	−0.850971
$926$	11.5134	0.378353
$927$	9.49507	0.311859
$928$	26.9077	0.883288
$929$	−7.75912	−0.254568	−0.127284	−	0.991866i	$-0.540626\pi$
$929$	−7.75912	−0.254568	−0.127284	+	0.991866i	$0.540626\pi$
$930$	97.9771	3.21279
$931$	−15.7520	−0.516252
$932$	−33.0862	−1.08378
$933$	−36.8293	−1.20574
$934$	54.6932	1.78962
$935$	−8.01686	−0.262179
$936$	28.8859	0.944165
$937$	11.0429	0.360756	0.180378	−	0.983597i	$-0.442268\pi$
$937$	11.0429	0.360756	0.180378	+	0.983597i	$0.442268\pi$
$938$	−15.9259	−0.519998
$939$	−37.5255	−1.22460
$940$	−196.352	−6.40429
$941$	50.4264	1.64385	0.821926	−	0.569594i	$-0.192899\pi$
$941$	50.4264	1.64385	0.821926	+	0.569594i	$0.192899\pi$
$942$	−77.8040	−2.53499
$943$	52.6775	1.71542
$944$	48.1708	1.56783
$945$	−6.93619	−0.225634
$946$	−36.2008	−1.17699
$947$	48.4583	1.57468	0.787342	−	0.616516i	$-0.211456\pi$
$947$	48.4583	1.57468	0.787342	+	0.616516i	$0.211456\pi$
$948$	−115.934	−3.76535
$949$	−50.9837	−1.65500
$950$	−57.7482	−1.87360
$951$	11.5286	0.373839
$952$	−4.45184	−0.144285
$953$	0.343841	0.0111381	0.00556906	−	0.999984i	$-0.498227\pi$
$953$	0.343841	0.0111381	0.00556906	+	0.999984i	$0.498227\pi$
$954$	14.2012	0.459780
$955$	−83.2493	−2.69388
$956$	−48.5964	−1.57172
$957$	6.08259	0.196622
$958$	45.8438	1.48115
$959$	1.98465	0.0640877
$960$	−82.5736	−2.66505
$961$	−4.60470	−0.148539
$962$	−43.9342	−1.41650
$963$	−8.78737	−0.283169
$964$	73.3650	2.36293
$965$	−20.5786	−0.662448
$966$	−12.2592	−0.394432
$967$	44.9484	1.44544	0.722721	−	0.691140i	$-0.242891\pi$
$967$	44.9484	1.44544	0.722721	+	0.691140i	$0.242891\pi$
$968$	68.6493	2.20647
$969$	−6.25564	−0.200960
$970$	−115.128	−3.69655
$971$	24.3133	0.780251	0.390126	−	0.920762i	$-0.372432\pi$
$971$	24.3133	0.780251	0.390126	+	0.920762i	$0.372432\pi$
$972$	−30.7528	−0.986397
$973$	1.70580	0.0546853
$974$	70.2902	2.25224
$975$	−110.677	−3.54451
$976$	142.119	4.54912
$977$	−51.6960	−1.65390	−0.826951	−	0.562274i	$-0.809926\pi$
$977$	−51.6960	−1.65390	−0.826951	+	0.562274i	$0.809926\pi$
$978$	−67.6614	−2.16357
$979$	0.424832	0.0135777
$980$	128.919	4.11816
$981$	10.8337	0.345893
$982$	115.631	3.68993
$983$	7.02481	0.224057	0.112028	−	0.993705i	$-0.464265\pi$
$983$	7.02481	0.224057	0.112028	+	0.993705i	$0.464265\pi$
$984$	127.161	4.05375
$985$	−32.2504	−1.02758
$986$	−8.20576	−0.261324
$987$	−7.92533	−0.252266
$988$	−69.8106	−2.22097
$989$	57.0592	1.81438
$990$	−8.96585	−0.284954
$991$	57.6543	1.83145	0.915724	−	0.401807i	$-0.131618\pi$
$991$	57.6543	1.83145	0.915724	+	0.401807i	$0.131618\pi$
$992$	−63.5104	−2.01646
$993$	42.0944	1.33583
$994$	−13.2659	−0.420767
$995$	−41.8161	−1.32566
$996$	12.6100	0.399564
$997$	−3.94363	−0.124896	−0.0624480	−	0.998048i	$-0.519891\pi$
$997$	−3.94363	−0.124896	−0.0624480	+	0.998048i	$0.519891\pi$
$998$	70.4977	2.23157
$999$	12.3658	0.391235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.11	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.11	✓	275	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63588 q^{2} +1.89916 q^{3} +4.94785 q^{4} -3.80955 q^{5} -5.00596 q^{6} -0.400599 q^{7} -7.77017 q^{8} +0.606822 q^{9} +O(q^{10})\)	\(q-2.63588 q^{2} +1.89916 q^{3} +4.94785 q^{4} -3.80955 q^{5} -5.00596 q^{6} -0.400599 q^{7} -7.77017 q^{8} +0.606822 q^{9} +10.0415 q^{10} -1.47140 q^{11} +9.39678 q^{12} -6.12624 q^{13} +1.05593 q^{14} -7.23496 q^{15} +10.5855 q^{16} -1.43021 q^{17} -1.59951 q^{18} +2.30309 q^{19} -18.8491 q^{20} -0.760803 q^{21} +3.87844 q^{22} -6.11313 q^{23} -14.7568 q^{24} +9.51266 q^{25} +16.1480 q^{26} -4.54504 q^{27} -1.98210 q^{28} -2.17668 q^{29} +19.0705 q^{30} +5.13764 q^{31} -12.3618 q^{32} -2.79444 q^{33} +3.76985 q^{34} +1.52610 q^{35} +3.00246 q^{36} -2.72072 q^{37} -6.07066 q^{38} -11.6347 q^{39} +29.6009 q^{40} -8.61711 q^{41} +2.00538 q^{42} -9.33387 q^{43} -7.28028 q^{44} -2.31172 q^{45} +16.1135 q^{46} +10.4171 q^{47} +20.1036 q^{48} -6.83952 q^{49} -25.0742 q^{50} -2.71620 q^{51} -30.3117 q^{52} -8.87847 q^{53} +11.9802 q^{54} +5.60538 q^{55} +3.11272 q^{56} +4.37394 q^{57} +5.73746 q^{58} +4.55063 q^{59} -35.7975 q^{60} +13.4258 q^{61} -13.5422 q^{62} -0.243092 q^{63} +11.4131 q^{64} +23.3382 q^{65} +7.36579 q^{66} -15.0823 q^{67} -7.07645 q^{68} -11.6098 q^{69} -4.02262 q^{70} -12.5632 q^{71} -4.71511 q^{72} +8.32218 q^{73} +7.17148 q^{74} +18.0661 q^{75} +11.3953 q^{76} +0.589443 q^{77} +30.6677 q^{78} -12.3376 q^{79} -40.3261 q^{80} -10.4522 q^{81} +22.7136 q^{82} +1.34195 q^{83} -3.76434 q^{84} +5.44844 q^{85} +24.6029 q^{86} -4.13387 q^{87} +11.4331 q^{88} -0.288726 q^{89} +6.09340 q^{90} +2.45417 q^{91} -30.2469 q^{92} +9.75721 q^{93} -27.4581 q^{94} -8.77373 q^{95} -23.4771 q^{96} -11.4653 q^{97} +18.0281 q^{98} -0.892880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more