LMFDB - Embedded newform 7381.2.a.t.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21081 q^{2} -2.81493 q^{3} -0.533929 q^{4} -2.26742 q^{5} +3.40836 q^{6} -3.92521 q^{7} +3.06812 q^{8} +4.92385 q^{9} +O(q^{10})$	\(q-1.21081 q^{2} -2.81493 q^{3} -0.533929 q^{4} -2.26742 q^{5} +3.40836 q^{6} -3.92521 q^{7} +3.06812 q^{8} +4.92385 q^{9} +2.74542 q^{10} +1.50298 q^{12} +2.95188 q^{13} +4.75270 q^{14} +6.38264 q^{15} -2.64706 q^{16} -3.73179 q^{17} -5.96187 q^{18} +2.93218 q^{19} +1.21064 q^{20} +11.0492 q^{21} -5.11069 q^{23} -8.63655 q^{24} +0.141196 q^{25} -3.57417 q^{26} -5.41551 q^{27} +2.09579 q^{28} -8.80274 q^{29} -7.72819 q^{30} -6.16475 q^{31} -2.93114 q^{32} +4.51851 q^{34} +8.90011 q^{35} -2.62899 q^{36} +4.31741 q^{37} -3.55032 q^{38} -8.30934 q^{39} -6.95671 q^{40} -12.0299 q^{41} -13.3785 q^{42} +11.0718 q^{43} -11.1644 q^{45} +6.18810 q^{46} -8.12434 q^{47} +7.45130 q^{48} +8.40731 q^{49} -0.170962 q^{50} +10.5047 q^{51} -1.57609 q^{52} +4.50506 q^{53} +6.55718 q^{54} -12.0430 q^{56} -8.25388 q^{57} +10.6585 q^{58} +3.62460 q^{59} -3.40788 q^{60} -1.00000 q^{61} +7.46436 q^{62} -19.3272 q^{63} +8.84318 q^{64} -6.69315 q^{65} +3.06274 q^{67} +1.99251 q^{68} +14.3863 q^{69} -10.7764 q^{70} -5.53575 q^{71} +15.1070 q^{72} -4.59485 q^{73} -5.22758 q^{74} -0.397458 q^{75} -1.56557 q^{76} +10.0611 q^{78} -9.63707 q^{79} +6.00200 q^{80} +0.472760 q^{81} +14.5660 q^{82} -9.35549 q^{83} -5.89950 q^{84} +8.46154 q^{85} -13.4059 q^{86} +24.7791 q^{87} +15.8661 q^{89} +13.5181 q^{90} -11.5868 q^{91} +2.72875 q^{92} +17.3534 q^{93} +9.83707 q^{94} -6.64847 q^{95} +8.25095 q^{96} +13.2688 q^{97} -10.1797 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) $ 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9	\( 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9} + 2 q^{10} - 27 q^{12} - 3 q^{13} - 39 q^{14} - 28 q^{15} + 23 q^{16} + 4 q^{17} - 34 q^{18} - 3 q^{19} - 37 q^{20} + 9 q^{21} - 52 q^{23} + 3 q^{24} + 24 q^{25} - 47 q^{26} - 48 q^{27} - 9 q^{28} - 2 q^{29} + 31 q^{30} - 41 q^{31} + 22 q^{32} + 11 q^{34} + 11 q^{35} - 22 q^{36} - 21 q^{37} - 4 q^{38} - 4 q^{39} - 96 q^{40} - 6 q^{41} - 8 q^{42} + 19 q^{43} - 8 q^{45} - q^{46} - 47 q^{47} - 35 q^{48} + 30 q^{49} + 20 q^{50} - 30 q^{51} + 44 q^{52} - 48 q^{53} + 46 q^{54} - 89 q^{56} - 19 q^{57} - 45 q^{58} - 135 q^{59} - 10 q^{60} - 54 q^{61} - 41 q^{62} + 34 q^{63} - 45 q^{64} + 11 q^{65} - 55 q^{67} + 41 q^{68} - 37 q^{69} - 38 q^{70} - 113 q^{71} - 72 q^{72} - 42 q^{73} + 51 q^{74} - 85 q^{75} + 34 q^{76} + 13 q^{78} - 15 q^{79} - 93 q^{80} - 38 q^{81} + 5 q^{82} - 23 q^{83} - 74 q^{84} + 9 q^{85} - 106 q^{86} + 70 q^{87} - 66 q^{89} - 7 q^{90} - 121 q^{91} - 133 q^{92} - 15 q^{93} + 17 q^{94} - 47 q^{95} + 34 q^{96} - 7 q^{97} + 61 q^{98}+O(q^{100}) \) 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9 + 2 * q^10 - 27 * q^12 - 3 * q^13 - 39 * q^14 - 28 * q^15 + 23 * q^16 + 4 * q^17 - 34 * q^18 - 3 * q^19 - 37 * q^20 + 9 * q^21 - 52 * q^23 + 3 * q^24 + 24 * q^25 - 47 * q^26 - 48 * q^27 - 9 * q^28 - 2 * q^29 + 31 * q^30 - 41 * q^31 + 22 * q^32 + 11 * q^34 + 11 * q^35 - 22 * q^36 - 21 * q^37 - 4 * q^38 - 4 * q^39 - 96 * q^40 - 6 * q^41 - 8 * q^42 + 19 * q^43 - 8 * q^45 - q^46 - 47 * q^47 - 35 * q^48 + 30 * q^49 + 20 * q^50 - 30 * q^51 + 44 * q^52 - 48 * q^53 + 46 * q^54 - 89 * q^56 - 19 * q^57 - 45 * q^58 - 135 * q^59 - 10 * q^60 - 54 * q^61 - 41 * q^62 + 34 * q^63 - 45 * q^64 + 11 * q^65 - 55 * q^67 + 41 * q^68 - 37 * q^69 - 38 * q^70 - 113 * q^71 - 72 * q^72 - 42 * q^73 + 51 * q^74 - 85 * q^75 + 34 * q^76 + 13 * q^78 - 15 * q^79 - 93 * q^80 - 38 * q^81 + 5 * q^82 - 23 * q^83 - 74 * q^84 + 9 * q^85 - 106 * q^86 + 70 * q^87 - 66 * q^89 - 7 * q^90 - 121 * q^91 - 133 * q^92 - 15 * q^93 + 17 * q^94 - 47 * q^95 + 34 * q^96 - 7 * q^97 + 61 * q^98

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 $

$2$	−1.21081	−0.856175	−0.428087	−	0.903737i	$-0.640812\pi$
$2$	−1.21081	−0.856175	−0.428087	+	0.903737i	$0.640812\pi$
$3$	−2.81493	−1.62520	−0.812601	−	0.582820i	$-0.801949\pi$
$3$	−2.81493	−1.62520	−0.812601	+	0.582820i	$0.801949\pi$
$4$	−0.533929	−0.266965
$5$	−2.26742	−1.01402	−0.507011	−	0.861940i	$-0.669250\pi$
$5$	−2.26742	−1.01402	−0.507011	+	0.861940i	$0.669250\pi$
$6$	3.40836	1.39146
$7$	−3.92521	−1.48359	−0.741796	−	0.670626i	$-0.766026\pi$
$7$	−3.92521	−1.48359	−0.741796	+	0.670626i	$0.766026\pi$
$8$	3.06812	1.08474
$9$	4.92385	1.64128
$10$	2.74542	0.868180
$11$	0	0
$11$	0	0
$12$	1.50298	0.433872
$13$	2.95188	0.818703	0.409352	−	0.912377i	$-0.365755\pi$
$13$	2.95188	0.818703	0.409352	+	0.912377i	$0.365755\pi$
$14$	4.75270	1.27021
$15$	6.38264	1.64799
$16$	−2.64706	−0.661765
$17$	−3.73179	−0.905092	−0.452546	−	0.891741i	$-0.649484\pi$
$17$	−3.73179	−0.905092	−0.452546	+	0.891741i	$0.649484\pi$
$18$	−5.96187	−1.40523
$19$	2.93218	0.672687	0.336344	−	0.941739i	$-0.390810\pi$
$19$	2.93218	0.672687	0.336344	+	0.941739i	$0.390810\pi$
$20$	1.21064	0.270708
$21$	11.0492	2.41114
$22$	0	0
$23$	−5.11069	−1.06565	−0.532826	−	0.846225i	$-0.678870\pi$
$23$	−5.11069	−1.06565	−0.532826	+	0.846225i	$0.678870\pi$
$24$	−8.63655	−1.76293
$25$	0.141196	0.0282392
$26$	−3.57417	−0.700953
$27$	−5.41551	−1.04222
$28$	2.09579	0.396067
$29$	−8.80274	−1.63463	−0.817313	−	0.576193i	$-0.804538\pi$
$29$	−8.80274	−1.63463	−0.817313	+	0.576193i	$0.804538\pi$
$30$	−7.72819	−1.41097
$31$	−6.16475	−1.10722	−0.553611	−	0.832776i	$-0.686750\pi$
$31$	−6.16475	−1.10722	−0.553611	+	0.832776i	$0.686750\pi$
$32$	−2.93114	−0.518157
$33$	0	0
$34$	4.51851	0.774917
$35$	8.90011	1.50439
$36$	−2.62899	−0.438165
$37$	4.31741	0.709778	0.354889	−	0.934909i	$-0.384519\pi$
$37$	4.31741	0.709778	0.354889	+	0.934909i	$0.384519\pi$
$38$	−3.55032	−0.575938
$39$	−8.30934	−1.33056
$40$	−6.95671	−1.09995
$41$	−12.0299	−1.87876	−0.939378	−	0.342884i	$-0.888596\pi$
$41$	−12.0299	−1.87876	−0.939378	+	0.342884i	$0.888596\pi$
$42$	−13.3785	−2.06435
$43$	11.0718	1.68843	0.844217	−	0.536002i	$-0.180066\pi$
$43$	11.0718	1.68843	0.844217	+	0.536002i	$0.180066\pi$
$44$	0	0
$45$	−11.1644	−1.66430
$46$	6.18810	0.912385
$47$	−8.12434	−1.18506	−0.592529	−	0.805549i	$-0.701870\pi$
$47$	−8.12434	−1.18506	−0.592529	+	0.805549i	$0.701870\pi$
$48$	7.45130	1.07550
$49$	8.40731	1.20104
$50$	−0.170962	−0.0241777
$51$	10.5047	1.47096
$52$	−1.57609	−0.218565
$53$	4.50506	0.618818	0.309409	−	0.950929i	$-0.399869\pi$
$53$	4.50506	0.618818	0.309409	+	0.950929i	$0.399869\pi$
$54$	6.55718	0.892319
$55$	0	0
$56$	−12.0430	−1.60932
$57$	−8.25388	−1.09325
$58$	10.6585	1.39953
$59$	3.62460	0.471882	0.235941	−	0.971767i	$-0.424183\pi$
$59$	3.62460	0.471882	0.235941	+	0.971767i	$0.424183\pi$
$60$	−3.40788	−0.439955
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	7.46436	0.947975
$63$	−19.3272	−2.43499
$64$	8.84318	1.10540
$65$	−6.69315	−0.830183
$66$	0	0
$67$	3.06274	0.374174	0.187087	−	0.982343i	$-0.440095\pi$
$67$	3.06274	0.374174	0.187087	+	0.982343i	$0.440095\pi$
$68$	1.99251	0.241628
$69$	14.3863	1.73190
$70$	−10.7764	−1.28802
$71$	−5.53575	−0.656973	−0.328486	−	0.944509i	$-0.606539\pi$
$71$	−5.53575	−0.656973	−0.328486	+	0.944509i	$0.606539\pi$
$72$	15.1070	1.78037
$73$	−4.59485	−0.537787	−0.268893	−	0.963170i	$-0.586658\pi$
$73$	−4.59485	−0.537787	−0.268893	+	0.963170i	$0.586658\pi$
$74$	−5.22758	−0.607694
$75$	−0.397458	−0.0458945
$76$	−1.56557	−0.179584
$77$	0	0
$78$	10.0611	1.13919
$79$	−9.63707	−1.08426	−0.542128	−	0.840296i	$-0.682381\pi$
$79$	−9.63707	−1.08426	−0.542128	+	0.840296i	$0.682381\pi$
$80$	6.00200	0.671044
$81$	0.472760	0.0525289
$82$	14.5660	1.60854
$83$	−9.35549	−1.02690	−0.513449	−	0.858120i	$-0.671632\pi$
$83$	−9.35549	−1.02690	−0.513449	+	0.858120i	$0.671632\pi$
$84$	−5.89950	−0.643688
$85$	8.46154	0.917783
$86$	−13.4059	−1.44559
$87$	24.7791	2.65660
$88$	0	0
$89$	15.8661	1.68180	0.840902	−	0.541188i	$-0.182025\pi$
$89$	15.8661	1.68180	0.840902	+	0.541188i	$0.182025\pi$
$90$	13.5181	1.42493
$91$	−11.5868	−1.21462
$92$	2.72875	0.284492
$93$	17.3534	1.79946
$94$	9.83707	1.01462
$95$	−6.64847	−0.682119
$96$	8.25095	0.842109
$97$	13.2688	1.34724	0.673620	−	0.739077i	$-0.264738\pi$
$97$	13.2688	1.34724	0.673620	+	0.739077i	$0.264738\pi$
$98$	−10.1797	−1.02830
$99$	0	0
$100$	−0.0753888	−0.00753888
$101$	7.15445	0.711894	0.355947	−	0.934506i	$-0.384158\pi$
$101$	7.15445	0.711894	0.355947	+	0.934506i	$0.384158\pi$
$102$	−12.7193	−1.25940
$103$	7.34143	0.723373	0.361687	−	0.932300i	$-0.382201\pi$
$103$	7.34143	0.723373	0.361687	+	0.932300i	$0.382201\pi$
$104$	9.05671	0.888083
$105$	−25.0532	−2.44494
$106$	−5.45479	−0.529816
$107$	−0.445546	−0.0430725	−0.0215363	−	0.999768i	$-0.506856\pi$
$107$	−0.445546	−0.0430725	−0.0215363	+	0.999768i	$0.506856\pi$
$108$	2.89150	0.278235
$109$	2.54339	0.243613	0.121806	−	0.992554i	$-0.461131\pi$
$109$	2.54339	0.243613	0.121806	+	0.992554i	$0.461131\pi$
$110$	0	0
$111$	−12.1532	−1.15353
$112$	10.3903	0.981789
$113$	1.57234	0.147913	0.0739566	−	0.997261i	$-0.476437\pi$
$113$	1.57234	0.147913	0.0739566	+	0.997261i	$0.476437\pi$
$114$	9.99391	0.936016
$115$	11.5881	1.08059
$116$	4.70004	0.436388
$117$	14.5346	1.34372
$118$	−4.38871	−0.404014
$119$	14.6481	1.34279
$120$	19.5827	1.78765
$121$	0	0
$122$	1.21081	0.109622
$123$	33.8634	3.05336
$124$	3.29154	0.295589
$125$	11.0170	0.985386
$126$	23.4016	2.08478
$127$	1.86310	0.165323	0.0826617	−	0.996578i	$-0.473658\pi$
$127$	1.86310	0.165323	0.0826617	+	0.996578i	$0.473658\pi$
$128$	−4.84518	−0.428257
$129$	−31.1664	−2.74405
$130$	8.10416	0.710782
$131$	14.9839	1.30915	0.654576	−	0.755996i	$-0.272847\pi$
$131$	14.9839	1.30915	0.654576	+	0.755996i	$0.272847\pi$
$132$	0	0
$133$	−11.5094	−0.997993
$134$	−3.70841	−0.320358
$135$	12.2792	1.05683
$136$	−11.4496	−0.981793
$137$	−14.0379	−1.19934	−0.599668	−	0.800249i	$-0.704701\pi$
$137$	−14.0379	−1.19934	−0.599668	+	0.800249i	$0.704701\pi$
$138$	−17.4191	−1.48281
$139$	14.0558	1.19220	0.596099	−	0.802911i	$-0.296717\pi$
$139$	14.0558	1.19220	0.596099	+	0.802911i	$0.296717\pi$
$140$	−4.75203	−0.401620
$141$	22.8695	1.92596
$142$	6.70277	0.562484
$143$	0	0
$144$	−13.0337	−1.08614
$145$	19.9595	1.65755
$146$	5.56351	0.460439
$147$	−23.6660	−1.95194
$148$	−2.30519	−0.189486
$149$	21.8868	1.79304	0.896519	−	0.443004i	$-0.146087\pi$
$149$	21.8868	1.79304	0.896519	+	0.443004i	$0.146087\pi$
$150$	0.481248	0.0392937
$151$	3.92092	0.319080	0.159540	−	0.987191i	$-0.448999\pi$
$151$	3.92092	0.319080	0.159540	+	0.987191i	$0.448999\pi$
$152$	8.99626	0.729693
$153$	−18.3748	−1.48551
$154$	0	0
$155$	13.9781	1.12275
$156$	4.43660	0.355212
$157$	5.85697	0.467437	0.233719	−	0.972304i	$-0.424911\pi$
$157$	5.85697	0.467437	0.233719	+	0.972304i	$0.424911\pi$
$158$	11.6687	0.928312
$159$	−12.6814	−1.00570
$160$	6.64612	0.525422
$161$	20.0606	1.58099
$162$	−0.572424	−0.0449739
$163$	2.56336	0.200778	0.100389	−	0.994948i	$-0.467991\pi$
$163$	2.56336	0.200778	0.100389	+	0.994948i	$0.467991\pi$
$164$	6.42312	0.501561
$165$	0	0
$166$	11.3278	0.879204
$167$	3.04462	0.235600	0.117800	−	0.993037i	$-0.462416\pi$
$167$	3.04462	0.235600	0.117800	+	0.993037i	$0.462416\pi$
$168$	33.9003	2.61546
$169$	−4.28642	−0.329725
$170$	−10.2454	−0.785783
$171$	14.4376	1.10407
$172$	−5.91156	−0.450752
$173$	−1.10132	−0.0837316	−0.0418658	−	0.999123i	$-0.513330\pi$
$173$	−1.10132	−0.0837316	−0.0418658	+	0.999123i	$0.513330\pi$
$174$	−30.0029	−2.27451
$175$	−0.554225	−0.0418955
$176$	0	0
$177$	−10.2030	−0.766905
$178$	−19.2109	−1.43992
$179$	−24.5831	−1.83743	−0.918713	−	0.394926i	$-0.870770\pi$
$179$	−24.5831	−1.83743	−0.918713	+	0.394926i	$0.870770\pi$
$180$	5.96102	0.444308
$181$	1.96420	0.145998	0.0729989	−	0.997332i	$-0.476743\pi$
$181$	1.96420	0.145998	0.0729989	+	0.997332i	$0.476743\pi$
$182$	14.0294	1.03993
$183$	2.81493	0.208086
$184$	−15.6802	−1.15596
$185$	−9.78938	−0.719730
$186$	−21.0117	−1.54065
$187$	0	0
$188$	4.33783	0.316368
$189$	21.2571	1.54622
$190$	8.05007	0.584013
$191$	−0.589077	−0.0426241	−0.0213121	−	0.999773i	$-0.506784\pi$
$191$	−0.589077	−0.0426241	−0.0213121	+	0.999773i	$0.506784\pi$
$192$	−24.8930	−1.79650
$193$	5.76222	0.414773	0.207387	−	0.978259i	$-0.433504\pi$
$193$	5.76222	0.414773	0.207387	+	0.978259i	$0.433504\pi$
$194$	−16.0660	−1.15347
$195$	18.8408	1.34922
$196$	−4.48891	−0.320636
$197$	1.97857	0.140967	0.0704836	−	0.997513i	$-0.477546\pi$
$197$	1.97857	0.140967	0.0704836	+	0.997513i	$0.477546\pi$
$198$	0	0
$199$	−3.79762	−0.269206	−0.134603	−	0.990900i	$-0.542976\pi$
$199$	−3.79762	−0.269206	−0.134603	+	0.990900i	$0.542976\pi$
$200$	0.433206	0.0306323
$201$	−8.62142	−0.608108
$202$	−8.66271	−0.609506
$203$	34.5526	2.42512
$204$	−5.60879	−0.392694
$205$	27.2769	1.90510
$206$	−8.88911	−0.619334
$207$	−25.1643	−1.74904
$208$	−7.81380	−0.541789
$209$	0	0
$210$	30.3348	2.09330
$211$	−20.7773	−1.43037	−0.715185	−	0.698935i	$-0.753658\pi$
$211$	−20.7773	−1.43037	−0.715185	+	0.698935i	$0.753658\pi$
$212$	−2.40538	−0.165202
$213$	15.5828	1.06771
$214$	0.539473	0.0368776
$215$	−25.1044	−1.71211
$216$	−16.6154	−1.13054
$217$	24.1980	1.64266
$218$	−3.07957	−0.208575
$219$	12.9342	0.874012
$220$	0	0
$221$	−11.0158	−0.741002
$222$	14.7153	0.987626
$223$	−3.26428	−0.218593	−0.109296	−	0.994009i	$-0.534860\pi$
$223$	−3.26428	−0.218593	−0.109296	+	0.994009i	$0.534860\pi$
$224$	11.5053	0.768733
$225$	0.695229	0.0463486
$226$	−1.90381	−0.126640
$227$	−4.96289	−0.329399	−0.164699	−	0.986344i	$-0.552665\pi$
$227$	−4.96289	−0.329399	−0.164699	+	0.986344i	$0.552665\pi$
$228$	4.40699	0.291860
$229$	−10.0462	−0.663869	−0.331934	−	0.943302i	$-0.607701\pi$
$229$	−10.0462	−0.663869	−0.331934	+	0.943302i	$0.607701\pi$
$230$	−14.0310	−0.925178
$231$	0	0
$232$	−27.0078	−1.77315
$233$	3.47083	0.227381	0.113691	−	0.993516i	$-0.463733\pi$
$233$	3.47083	0.227381	0.113691	+	0.993516i	$0.463733\pi$
$234$	−17.5987	−1.15046
$235$	18.4213	1.20167
$236$	−1.93528	−0.125976
$237$	27.1277	1.76213
$238$	−17.7361	−1.14966
$239$	15.3376	0.992108	0.496054	−	0.868292i	$-0.334782\pi$
$239$	15.3376	0.992108	0.496054	+	0.868292i	$0.334782\pi$
$240$	−16.8952	−1.09058
$241$	−20.0740	−1.29308	−0.646540	−	0.762880i	$-0.723785\pi$
$241$	−20.0740	−1.29308	−0.646540	+	0.762880i	$0.723785\pi$
$242$	0	0
$243$	14.9158	0.956846
$244$	0.533929	0.0341813
$245$	−19.0629	−1.21788
$246$	−41.0023	−2.61421
$247$	8.65542	0.550731
$248$	−18.9142	−1.20105
$249$	26.3351	1.66892
$250$	−13.3395	−0.843663
$251$	−20.1366	−1.27101	−0.635504	−	0.772098i	$-0.719208\pi$
$251$	−20.1366	−1.27101	−0.635504	+	0.772098i	$0.719208\pi$
$252$	10.3193	0.650058
$253$	0	0
$254$	−2.25587	−0.141546
$255$	−23.8187	−1.49158
$256$	−11.8198	−0.738735
$257$	11.3545	0.708274	0.354137	−	0.935194i	$-0.384775\pi$
$257$	11.3545	0.708274	0.354137	+	0.935194i	$0.384775\pi$
$258$	37.7367	2.34938
$259$	−16.9468	−1.05302
$260$	3.57367	0.221629
$261$	−43.3434	−2.68289
$262$	−18.1428	−1.12086
$263$	−28.3466	−1.74793	−0.873963	−	0.485993i	$-0.838458\pi$
$263$	−28.3466	−1.74793	−0.873963	+	0.485993i	$0.838458\pi$
$264$	0	0
$265$	−10.2149	−0.627494
$266$	13.9358	0.854456
$267$	−44.6620	−2.73327
$268$	−1.63529	−0.0998912
$269$	−3.64867	−0.222463	−0.111232	−	0.993795i	$-0.535480\pi$
$269$	−3.64867	−0.222463	−0.111232	+	0.993795i	$0.535480\pi$
$270$	−14.8679	−0.904831
$271$	8.34160	0.506716	0.253358	−	0.967373i	$-0.418465\pi$
$271$	8.34160	0.506716	0.253358	+	0.967373i	$0.418465\pi$
$272$	9.87828	0.598959
$273$	32.6159	1.97401
$274$	16.9973	1.02684
$275$	0	0
$276$	−7.68124	−0.462357
$277$	22.0045	1.32212	0.661062	−	0.750331i	$-0.270106\pi$
$277$	22.0045	1.32212	0.661062	+	0.750331i	$0.270106\pi$
$278$	−17.0190	−1.02073
$279$	−30.3543	−1.81726
$280$	27.3066	1.63188
$281$	26.2329	1.56492	0.782462	−	0.622698i	$-0.213964\pi$
$281$	26.2329	1.56492	0.782462	+	0.622698i	$0.213964\pi$
$282$	−27.6907	−1.64896
$283$	33.4347	1.98748	0.993742	−	0.111696i	$-0.0356281\pi$
$283$	33.4347	1.98748	0.993742	+	0.111696i	$0.0356281\pi$
$284$	2.95570	0.175389
$285$	18.7150	1.10858
$286$	0	0
$287$	47.2200	2.78731
$288$	−14.4325	−0.850442
$289$	−3.07373	−0.180808
$290$	−24.1672	−1.41915
$291$	−37.3507	−2.18954
$292$	2.45333	0.143570
$293$	28.7356	1.67875	0.839377	−	0.543550i	$-0.182920\pi$
$293$	28.7356	1.67875	0.839377	+	0.543550i	$0.182920\pi$
$294$	28.6551	1.67120
$295$	−8.21849	−0.478499
$296$	13.2463	0.769927
$297$	0	0
$298$	−26.5009	−1.53515
$299$	−15.0861	−0.872454
$300$	0.212214	0.0122522
$301$	−43.4592	−2.50495
$302$	−4.74750	−0.273188
$303$	−20.1393	−1.15697
$304$	−7.76165	−0.445161
$305$	2.26742	0.129832
$306$	22.2484	1.27186
$307$	−16.8046	−0.959091	−0.479545	−	0.877517i	$-0.659198\pi$
$307$	−16.8046	−0.959091	−0.479545	+	0.877517i	$0.659198\pi$
$308$	0	0
$309$	−20.6657	−1.17563
$310$	−16.9249	−0.961267
$311$	29.0962	1.64989	0.824947	−	0.565209i	$-0.191205\pi$
$311$	29.0962	1.64989	0.824947	+	0.565209i	$0.191205\pi$
$312$	−25.4940	−1.44332
$313$	9.47033	0.535294	0.267647	−	0.963517i	$-0.413754\pi$
$313$	9.47033	0.535294	0.267647	+	0.963517i	$0.413754\pi$
$314$	−7.09170	−0.400208
$315$	43.8228	2.46914
$316$	5.14552	0.289458
$317$	25.3648	1.42463	0.712314	−	0.701861i	$-0.247647\pi$
$317$	25.3648	1.42463	0.712314	+	0.701861i	$0.247647\pi$
$318$	15.3549	0.861059
$319$	0	0
$320$	−20.0512	−1.12090
$321$	1.25418	0.0700016
$322$	−24.2896	−1.35361
$323$	−10.9423	−0.608844
$324$	−0.252420	−0.0140234
$325$	0.416794	0.0231196
$326$	−3.10375	−0.171901
$327$	−7.15947	−0.395920
$328$	−36.9092	−2.03797
$329$	31.8898	1.75814
$330$	0	0
$331$	−19.8505	−1.09108	−0.545541	−	0.838084i	$-0.683676\pi$
$331$	−19.8505	−1.09108	−0.545541	+	0.838084i	$0.683676\pi$
$332$	4.99517	0.274145
$333$	21.2583	1.16495
$334$	−3.68647	−0.201715
$335$	−6.94453	−0.379420
$336$	−29.2479	−1.59561
$337$	6.76244	0.368373	0.184187	−	0.982891i	$-0.441035\pi$
$337$	6.76244	0.368373	0.184187	+	0.982891i	$0.441035\pi$
$338$	5.19006	0.282302
$339$	−4.42603	−0.240389
$340$	−4.51786	−0.245016
$341$	0	0
$342$	−17.4812	−0.945277
$343$	−5.52398	−0.298267
$344$	33.9696	1.83152
$345$	−32.6197	−1.75619
$346$	1.33349	0.0716889
$347$	33.6001	1.80375	0.901873	−	0.432001i	$-0.142192\pi$
$347$	33.6001	1.80375	0.901873	+	0.432001i	$0.142192\pi$
$348$	−13.2303	−0.709218
$349$	23.8529	1.27682	0.638408	−	0.769698i	$-0.279593\pi$
$349$	23.8529	1.27682	0.638408	+	0.769698i	$0.279593\pi$
$350$	0.671064	0.0358699
$351$	−15.9859	−0.853266
$352$	0	0
$353$	−0.240868	−0.0128201	−0.00641005	−	0.999979i	$-0.502040\pi$
$353$	−0.240868	−0.0128201	−0.00641005	+	0.999979i	$0.502040\pi$
$354$	12.3539	0.656604
$355$	12.5519	0.666184
$356$	−8.47138	−0.448982
$357$	−41.2334	−2.18230
$358$	29.7655	1.57316
$359$	−9.70471	−0.512195	−0.256097	−	0.966651i	$-0.582437\pi$
$359$	−9.70471	−0.512195	−0.256097	+	0.966651i	$0.582437\pi$
$360$	−34.2538	−1.80533
$361$	−10.4023	−0.547492
$362$	−2.37828	−0.125000
$363$	0	0
$364$	6.18651	0.324261
$365$	10.4185	0.545327
$366$	−3.40836	−0.178158
$367$	3.34349	0.174529	0.0872643	−	0.996185i	$-0.472188\pi$
$367$	3.34349	0.174529	0.0872643	+	0.996185i	$0.472188\pi$
$368$	13.5283	0.705212
$369$	−59.2335	−3.08357
$370$	11.8531	0.616214
$371$	−17.6833	−0.918073
$372$	−9.26547	−0.480392
$373$	20.7368	1.07371	0.536856	−	0.843674i	$-0.319612\pi$
$373$	20.7368	1.07371	0.536856	+	0.843674i	$0.319612\pi$
$374$	0	0
$375$	−31.0120	−1.60145
$376$	−24.9264	−1.28548
$377$	−25.9846	−1.33827
$378$	−25.7383	−1.32384
$379$	24.5502	1.26106	0.630530	−	0.776165i	$-0.282837\pi$
$379$	24.5502	1.26106	0.630530	+	0.776165i	$0.282837\pi$
$380$	3.54982	0.182102
$381$	−5.24450	−0.268684
$382$	0.713263	0.0364937
$383$	−23.8093	−1.21660	−0.608299	−	0.793708i	$-0.708148\pi$
$383$	−23.8093	−1.21660	−0.608299	+	0.793708i	$0.708148\pi$
$384$	13.6389	0.696005
$385$	0	0
$386$	−6.97697	−0.355119
$387$	54.5159	2.77120
$388$	−7.08459	−0.359666
$389$	−0.0340703	−0.00172743	−0.000863715	−	1.00000i	$-0.500275\pi$
$389$	−0.0340703	−0.00172743	−0.000863715		1.00000i	$0.500275\pi$
$390$	−22.8127	−1.15516
$391$	19.0720	0.964514
$392$	25.7946	1.30282
$393$	−42.1788	−2.12764
$394$	−2.39568	−0.120693
$395$	21.8513	1.09946
$396$	0	0
$397$	21.1040	1.05918	0.529589	−	0.848254i	$-0.322346\pi$
$397$	21.1040	1.05918	0.529589	+	0.848254i	$0.322346\pi$
$398$	4.59821	0.230487
$399$	32.3982	1.62194
$400$	−0.373755	−0.0186877
$401$	−14.3662	−0.717413	−0.358707	−	0.933450i	$-0.616782\pi$
$401$	−14.3662	−0.717413	−0.358707	+	0.933450i	$0.616782\pi$
$402$	10.4389	0.520647
$403$	−18.1976	−0.906486
$404$	−3.81997	−0.190051
$405$	−1.07195	−0.0532654
$406$	−41.8368	−2.07633
$407$	0	0
$408$	32.2298	1.59561
$409$	−21.1611	−1.04635	−0.523175	−	0.852225i	$-0.675253\pi$
$409$	−21.1611	−1.04635	−0.523175	+	0.852225i	$0.675253\pi$
$410$	−33.0272	−1.63110
$411$	39.5157	1.94917
$412$	−3.91981	−0.193115
$413$	−14.2273	−0.700081
$414$	30.4693	1.49748
$415$	21.2128	1.04130
$416$	−8.65236	−0.424217
$417$	−39.5661	−1.93756
$418$	0	0
$419$	−15.3410	−0.749457	−0.374729	−	0.927135i	$-0.622264\pi$
$419$	−15.3410	−0.749457	−0.374729	+	0.927135i	$0.622264\pi$
$420$	13.3767	0.652714
$421$	2.52923	0.123267	0.0616335	−	0.998099i	$-0.480369\pi$
$421$	2.52923	0.123267	0.0616335	+	0.998099i	$0.480369\pi$
$422$	25.1575	1.22465
$423$	−40.0031	−1.94502
$424$	13.8221	0.671258
$425$	−0.526915	−0.0255591
$426$	−18.8678	−0.914150
$427$	3.92521	0.189954
$428$	0.237890	0.0114988
$429$	0	0
$430$	30.3968	1.46586
$431$	−36.1237	−1.74002	−0.870009	−	0.493036i	$-0.835887\pi$
$431$	−36.1237	−1.74002	−0.870009	+	0.493036i	$0.835887\pi$
$432$	14.3352	0.689702
$433$	2.00591	0.0963980	0.0481990	−	0.998838i	$-0.484652\pi$
$433$	2.00591	0.0963980	0.0481990	+	0.998838i	$0.484652\pi$
$434$	−29.2992	−1.40641
$435$	−56.1847	−2.69385
$436$	−1.35799	−0.0650360
$437$	−14.9854	−0.716851
$438$	−15.6609	−0.748307
$439$	34.7624	1.65912	0.829560	−	0.558417i	$-0.188591\pi$
$439$	34.7624	1.65912	0.829560	+	0.558417i	$0.188591\pi$
$440$	0	0
$441$	41.3963	1.97125
$442$	13.3381	0.634427
$443$	−27.1693	−1.29085	−0.645427	−	0.763822i	$-0.723321\pi$
$443$	−27.1693	−1.29085	−0.645427	+	0.763822i	$0.723321\pi$
$444$	6.48896	0.307952
$445$	−35.9751	−1.70538
$446$	3.95244	0.187153
$447$	−61.6100	−2.91405
$448$	−34.7114	−1.63996
$449$	22.2169	1.04848	0.524240	−	0.851571i	$-0.324350\pi$
$449$	22.2169	1.04848	0.524240	+	0.851571i	$0.324350\pi$
$450$	−0.841793	−0.0396825
$451$	0	0
$452$	−0.839518	−0.0394876
$453$	−11.0371	−0.518569
$454$	6.00914	0.282023
$455$	26.2720	1.23165
$456$	−25.3239	−1.18590
$457$	−11.0675	−0.517715	−0.258858	−	0.965915i	$-0.583346\pi$
$457$	−11.0675	−0.517715	−0.258858	+	0.965915i	$0.583346\pi$
$458$	12.1640	0.568388
$459$	20.2096	0.943302
$460$	−6.18722	−0.288481
$461$	15.8081	0.736256	0.368128	−	0.929775i	$-0.379999\pi$
$461$	15.8081	0.736256	0.368128	+	0.929775i	$0.379999\pi$
$462$	0	0
$463$	−12.9373	−0.601249	−0.300625	−	0.953743i	$-0.597195\pi$
$463$	−12.9373	−0.601249	−0.300625	+	0.953743i	$0.597195\pi$
$464$	23.3014	1.08174
$465$	−39.3474	−1.82469
$466$	−4.20252	−0.194678
$467$	5.58174	0.258292	0.129146	−	0.991626i	$-0.458776\pi$
$467$	5.58174	0.258292	0.129146	+	0.991626i	$0.458776\pi$
$468$	−7.76045	−0.358727
$469$	−12.0219	−0.555121
$470$	−22.3048	−1.02884
$471$	−16.4870	−0.759680
$472$	11.1207	0.511871
$473$	0	0
$474$	−32.8466	−1.50870
$475$	0.414012	0.0189962
$476$	−7.82104	−0.358477
$477$	22.1822	1.01566
$478$	−18.5710	−0.849418
$479$	−21.6490	−0.989167	−0.494583	−	0.869130i	$-0.664679\pi$
$479$	−21.6490	−0.989167	−0.494583	+	0.869130i	$0.664679\pi$
$480$	−18.7084	−0.853917
$481$	12.7445	0.581097
$482$	24.3059	1.10710
$483$	−56.4691	−2.56943
$484$	0	0
$485$	−30.0859	−1.36613
$486$	−18.0602	−0.819228
$487$	40.9755	1.85678	0.928389	−	0.371609i	$-0.121194\pi$
$487$	40.9755	1.85678	0.928389	+	0.371609i	$0.121194\pi$
$488$	−3.06812	−0.138887
$489$	−7.21568	−0.326304
$490$	23.0816	1.04272
$491$	25.6534	1.15772	0.578862	−	0.815426i	$-0.303497\pi$
$491$	25.6534	1.15772	0.578862	+	0.815426i	$0.303497\pi$
$492$	−18.0807	−0.815139
$493$	32.8500	1.47949
$494$	−10.4801	−0.471522
$495$	0	0
$496$	16.3185	0.732721
$497$	21.7290	0.974679
$498$	−31.8869	−1.42889
$499$	−33.0211	−1.47823	−0.739113	−	0.673581i	$-0.764755\pi$
$499$	−33.0211	−1.47823	−0.739113	+	0.673581i	$0.764755\pi$
$500$	−5.88227	−0.263063
$501$	−8.57040	−0.382897
$502$	24.3816	1.08821
$503$	7.43758	0.331625	0.165813	−	0.986157i	$-0.446975\pi$
$503$	7.43758	0.331625	0.165813	+	0.986157i	$0.446975\pi$
$504$	−59.2980	−2.64134
$505$	−16.2221	−0.721876
$506$	0	0
$507$	12.0660	0.535869
$508$	−0.994763	−0.0441355
$509$	25.5332	1.13174	0.565869	−	0.824495i	$-0.308541\pi$
$509$	25.5332	1.13174	0.565869	+	0.824495i	$0.308541\pi$
$510$	28.8400	1.27706
$511$	18.0358	0.797856
$512$	24.0019	1.06074
$513$	−15.8792	−0.701085
$514$	−13.7482	−0.606406
$515$	−16.6461	−0.733516
$516$	16.6406	0.732564
$517$	0	0
$518$	20.5194	0.901569
$519$	3.10013	0.136081
$520$	−20.5354	−0.900535
$521$	−4.82078	−0.211202	−0.105601	−	0.994409i	$-0.533677\pi$
$521$	−4.82078	−0.211202	−0.105601	+	0.994409i	$0.533677\pi$
$522$	52.4808	2.29702
$523$	2.79000	0.121998	0.0609991	−	0.998138i	$-0.480571\pi$
$523$	2.79000	0.121998	0.0609991	+	0.998138i	$0.480571\pi$
$524$	−8.00036	−0.349497
$525$	1.56011	0.0680887
$526$	34.3224	1.49653
$527$	23.0056	1.00214
$528$	0	0
$529$	3.11916	0.135616
$530$	12.3683	0.537245
$531$	17.8470	0.774493
$532$	6.14522	0.266429
$533$	−35.5108	−1.53814
$534$	54.0774	2.34016
$535$	1.01024	0.0436765
$536$	9.39686	0.405882
$537$	69.1997	2.98619
$538$	4.41786	0.190467
$539$	0	0
$540$	−6.55625	−0.282136
$541$	6.18018	0.265707	0.132853	−	0.991136i	$-0.457586\pi$
$541$	6.18018	0.265707	0.132853	+	0.991136i	$0.457586\pi$
$542$	−10.1001	−0.433838
$543$	−5.52909	−0.237276
$544$	10.9384	0.468980
$545$	−5.76693	−0.247028
$546$	−39.4918	−1.69009
$547$	−31.1943	−1.33377	−0.666885	−	0.745160i	$-0.732373\pi$
$547$	−31.1943	−1.33377	−0.666885	+	0.745160i	$0.732373\pi$
$548$	7.49523	0.320181
$549$	−4.92385	−0.210145
$550$	0	0
$551$	−25.8112	−1.09959
$552$	44.1387	1.87867
$553$	37.8276	1.60859
$554$	−26.6434	−1.13197
$555$	27.5565	1.16971
$556$	−7.50480	−0.318275
$557$	29.6299	1.25546	0.627729	−	0.778432i	$-0.283985\pi$
$557$	29.6299	1.25546	0.627729	+	0.778432i	$0.283985\pi$
$558$	36.7534	1.55590
$559$	32.6826	1.38233
$560$	−23.5591	−0.995555
$561$	0	0
$562$	−31.7632	−1.33985
$563$	−1.54906	−0.0652853	−0.0326426	−	0.999467i	$-0.510392\pi$
$563$	−1.54906	−0.0652853	−0.0326426	+	0.999467i	$0.510392\pi$
$564$	−12.2107	−0.514163
$565$	−3.56515	−0.149987
$566$	−40.4832	−1.70163
$567$	−1.85568	−0.0779314
$568$	−16.9843	−0.712647
$569$	19.0578	0.798946	0.399473	−	0.916745i	$-0.369193\pi$
$569$	19.0578	0.798946	0.399473	+	0.916745i	$0.369193\pi$
$570$	−22.6604	−0.949140
$571$	19.3022	0.807772	0.403886	−	0.914809i	$-0.367659\pi$
$571$	19.3022	0.807772	0.403886	+	0.914809i	$0.367659\pi$
$572$	0	0
$573$	1.65821	0.0692728
$574$	−57.1746	−2.38642
$575$	−0.721610	−0.0300932
$576$	43.5425	1.81427
$577$	4.33295	0.180383	0.0901915	−	0.995924i	$-0.471252\pi$
$577$	4.33295	0.180383	0.0901915	+	0.995924i	$0.471252\pi$
$578$	3.72172	0.154803
$579$	−16.2203	−0.674091
$580$	−10.6570	−0.442506
$581$	36.7223	1.52350
$582$	45.2248	1.87463
$583$	0	0
$584$	−14.0975	−0.583360
$585$	−32.9561	−1.36257
$586$	−34.7935	−1.43731
$587$	−30.4454	−1.25662	−0.628308	−	0.777965i	$-0.716252\pi$
$587$	−30.4454	−1.25662	−0.628308	+	0.777965i	$0.716252\pi$
$588$	12.6360	0.521099
$589$	−18.0761	−0.744814
$590$	9.95106	0.409679
$591$	−5.56954	−0.229100
$592$	−11.4284	−0.469706
$593$	30.8122	1.26531	0.632654	−	0.774435i	$-0.281966\pi$
$593$	30.8122	1.26531	0.632654	+	0.774435i	$0.281966\pi$
$594$	0	0
$595$	−33.2134	−1.36161
$596$	−11.6860	−0.478678
$597$	10.6900	0.437514
$598$	18.2665	0.746973
$599$	−39.1044	−1.59776	−0.798881	−	0.601489i	$-0.794575\pi$
$599$	−39.1044	−1.59776	−0.798881	+	0.601489i	$0.794575\pi$
$600$	−1.21945	−0.0497837
$601$	−35.8332	−1.46167	−0.730833	−	0.682556i	$-0.760868\pi$
$601$	−35.8332	−1.46167	−0.730833	+	0.682556i	$0.760868\pi$
$602$	52.6210	2.14467
$603$	15.0805	0.614125
$604$	−2.09349	−0.0851831
$605$	0	0
$606$	24.3849	0.990571
$607$	14.5678	0.591288	0.295644	−	0.955298i	$-0.404466\pi$
$607$	14.5678	0.591288	0.295644	+	0.955298i	$0.404466\pi$
$608$	−8.59461	−0.348557
$609$	−97.2633	−3.94131
$610$	−2.74542	−0.111159
$611$	−23.9821	−0.970210
$612$	9.81084	0.396580
$613$	16.4183	0.663130	0.331565	−	0.943432i	$-0.392423\pi$
$613$	16.4183	0.663130	0.331565	+	0.943432i	$0.392423\pi$
$614$	20.3473	0.821149
$615$	−76.7825	−3.09617
$616$	0	0
$617$	−16.1400	−0.649771	−0.324886	−	0.945753i	$-0.605326\pi$
$617$	−16.1400	−0.649771	−0.324886	+	0.945753i	$0.605326\pi$
$618$	25.0223	1.00654
$619$	−17.5201	−0.704192	−0.352096	−	0.935964i	$-0.614531\pi$
$619$	−17.5201	−0.704192	−0.352096	+	0.935964i	$0.614531\pi$
$620$	−7.46331	−0.299734
$621$	27.6770	1.11064
$622$	−35.2301	−1.41260
$623$	−62.2778	−2.49511
$624$	21.9953	0.880518
$625$	−25.6860	−1.02744
$626$	−11.4668	−0.458306
$627$	0	0
$628$	−3.12721	−0.124789
$629$	−16.1117	−0.642414
$630$	−53.0613	−2.11401
$631$	−13.5926	−0.541114	−0.270557	−	0.962704i	$-0.587208\pi$
$631$	−13.5926	−0.541114	−0.270557	+	0.962704i	$0.587208\pi$
$632$	−29.5677	−1.17614
$633$	58.4868	2.32464
$634$	−30.7120	−1.21973
$635$	−4.22443	−0.167641
$636$	6.77100	0.268487
$637$	24.8173	0.983299
$638$	0	0
$639$	−27.2572	−1.07828
$640$	10.9861	0.434262
$641$	−42.4702	−1.67747	−0.838736	−	0.544538i	$-0.816705\pi$
$641$	−42.4702	−1.67747	−0.838736	+	0.544538i	$0.816705\pi$
$642$	−1.51858	−0.0599336
$643$	22.4929	0.887035	0.443518	−	0.896266i	$-0.353730\pi$
$643$	22.4929	0.887035	0.443518	+	0.896266i	$0.353730\pi$
$644$	−10.7109	−0.422069
$645$	70.6673	2.78252
$646$	13.2490	0.521277
$647$	16.4258	0.645766	0.322883	−	0.946439i	$-0.395348\pi$
$647$	16.4258	0.645766	0.322883	+	0.946439i	$0.395348\pi$
$648$	1.45048	0.0569803
$649$	0	0
$650$	−0.504660	−0.0197944
$651$	−68.1156	−2.66966
$652$	−1.36865	−0.0536005
$653$	11.5957	0.453774	0.226887	−	0.973921i	$-0.427145\pi$
$653$	11.5957	0.453774	0.226887	+	0.973921i	$0.427145\pi$
$654$	8.66879	0.338977
$655$	−33.9749	−1.32751
$656$	31.8439	1.24330
$657$	−22.6244	−0.882660
$658$	−38.6126	−1.50528
$659$	−17.1541	−0.668229	−0.334115	−	0.942532i	$-0.608437\pi$
$659$	−17.1541	−0.668229	−0.334115	+	0.942532i	$0.608437\pi$
$660$	0	0
$661$	18.7477	0.729202	0.364601	−	0.931164i	$-0.381205\pi$
$661$	18.7477	0.729202	0.364601	+	0.931164i	$0.381205\pi$
$662$	24.0352	0.934156
$663$	31.0087	1.20428
$664$	−28.7037	−1.11392
$665$	26.0967	1.01199
$666$	−25.7398	−0.997398
$667$	44.9881	1.74194
$668$	−1.62561	−0.0628968
$669$	9.18874	0.355257
$670$	8.40853	0.324850
$671$	0	0
$672$	−32.3868	−1.24935
$673$	−19.1197	−0.737010	−0.368505	−	0.929626i	$-0.620130\pi$
$673$	−19.1197	−0.737010	−0.368505	+	0.929626i	$0.620130\pi$
$674$	−8.18805	−0.315392
$675$	−0.764650	−0.0294314
$676$	2.28865	0.0880248
$677$	29.7222	1.14232	0.571159	−	0.820840i	$-0.306494\pi$
$677$	29.7222	1.14232	0.571159	+	0.820840i	$0.306494\pi$
$678$	5.35910	0.205815
$679$	−52.0828	−1.99876
$680$	25.9610	0.995559
$681$	13.9702	0.535340
$682$	0	0
$683$	−48.0821	−1.83981	−0.919906	−	0.392139i	$-0.871735\pi$
$683$	−48.0821	−1.83981	−0.919906	+	0.392139i	$0.871735\pi$
$684$	−7.70866	−0.294748
$685$	31.8298	1.21615
$686$	6.68851	0.255369
$687$	28.2793	1.07892
$688$	−29.3077	−1.11735
$689$	13.2984	0.506628
$690$	39.4964	1.50360
$691$	−31.0527	−1.18130	−0.590650	−	0.806928i	$-0.701129\pi$
$691$	−31.0527	−1.18130	−0.590650	+	0.806928i	$0.701129\pi$
$692$	0.588025	0.0223534
$693$	0	0
$694$	−40.6834	−1.54432
$695$	−31.8704	−1.20891
$696$	76.0252	2.88173
$697$	44.8931	1.70045
$698$	−28.8814	−1.09318
$699$	−9.77014	−0.369541
$700$	0.295917	0.0111846
$701$	−14.9119	−0.563215	−0.281608	−	0.959530i	$-0.590868\pi$
$701$	−14.9119	−0.563215	−0.281608	+	0.959530i	$0.590868\pi$
$702$	19.3560	0.730545
$703$	12.6594	0.477458
$704$	0	0
$705$	−51.8547	−1.95296
$706$	0.291646	0.0109762
$707$	−28.0827	−1.05616
$708$	5.44768	0.204736
$709$	23.2629	0.873655	0.436828	−	0.899545i	$-0.356102\pi$
$709$	23.2629	0.873655	0.436828	+	0.899545i	$0.356102\pi$
$710$	−15.1980	−0.570370
$711$	−47.4515	−1.77957
$712$	48.6791	1.82432
$713$	31.5061	1.17991
$714$	49.9259	1.86843
$715$	0	0
$716$	13.1256	0.490528
$717$	−43.1744	−1.61238
$718$	11.7506	0.438528
$719$	29.9450	1.11676	0.558381	−	0.829585i	$-0.311423\pi$
$719$	29.9450	1.11676	0.558381	+	0.829585i	$0.311423\pi$
$720$	29.5530	1.10137
$721$	−28.8167	−1.07319
$722$	12.5953	0.468749
$723$	56.5069	2.10152
$724$	−1.04874	−0.0389763
$725$	−1.24291	−0.0461606
$726$	0	0
$727$	−6.61898	−0.245484	−0.122742	−	0.992439i	$-0.539169\pi$
$727$	−6.61898	−0.245484	−0.122742	+	0.992439i	$0.539169\pi$
$728$	−35.5495	−1.31755
$729$	−43.4051	−1.60760
$730$	−12.6148	−0.466895
$731$	−41.3176	−1.52819
$732$	−1.50298	−0.0555516
$733$	−19.3661	−0.715305	−0.357652	−	0.933855i	$-0.616423\pi$
$733$	−19.3661	−0.715305	−0.357652	+	0.933855i	$0.616423\pi$
$734$	−4.04834	−0.149427
$735$	53.6608	1.97931
$736$	14.9801	0.552175
$737$	0	0
$738$	71.7207	2.64008
$739$	5.84586	0.215044	0.107522	−	0.994203i	$-0.465708\pi$
$739$	5.84586	0.215044	0.107522	+	0.994203i	$0.465708\pi$
$740$	5.22684	0.192142
$741$	−24.3644	−0.895050
$742$	21.4112	0.786031
$743$	39.0274	1.43177	0.715887	−	0.698216i	$-0.246022\pi$
$743$	39.0274	1.43177	0.715887	+	0.698216i	$0.246022\pi$
$744$	53.2421	1.95195
$745$	−49.6266	−1.81818
$746$	−25.1084	−0.919285
$747$	−46.0650	−1.68543
$748$	0	0
$749$	1.74886	0.0639020
$750$	37.5498	1.37112
$751$	17.8300	0.650626	0.325313	−	0.945606i	$-0.394530\pi$
$751$	17.8300	0.650626	0.325313	+	0.945606i	$0.394530\pi$
$752$	21.5056	0.784230
$753$	56.6831	2.06565
$754$	31.4625	1.14580
$755$	−8.89037	−0.323554
$756$	−11.3498	−0.412787
$757$	46.9823	1.70760	0.853800	−	0.520601i	$-0.174292\pi$
$757$	46.9823	1.70760	0.853800	+	0.520601i	$0.174292\pi$
$758$	−29.7258	−1.07969
$759$	0	0
$760$	−20.3983	−0.739924
$761$	−6.53645	−0.236946	−0.118473	−	0.992957i	$-0.537800\pi$
$761$	−6.53645	−0.236946	−0.118473	+	0.992957i	$0.537800\pi$
$762$	6.35011	0.230040
$763$	−9.98335	−0.361422
$764$	0.314526	0.0113791
$765$	41.6634	1.50634
$766$	28.8286	1.04162
$767$	10.6994	0.386332
$768$	33.2718	1.20059
$769$	22.7589	0.820706	0.410353	−	0.911927i	$-0.365405\pi$
$769$	22.7589	0.820706	0.410353	+	0.911927i	$0.365405\pi$
$770$	0	0
$771$	−31.9621	−1.15109
$772$	−3.07662	−0.110730
$773$	−25.9917	−0.934858	−0.467429	−	0.884031i	$-0.654820\pi$
$773$	−25.9917	−0.934858	−0.467429	+	0.884031i	$0.654820\pi$
$774$	−66.0086	−2.37263
$775$	−0.870439	−0.0312671
$776$	40.7102	1.46141
$777$	47.7040	1.71137
$778$	0.0412527	0.00147898
$779$	−35.2738	−1.26381
$780$	−10.0596	−0.360193
$781$	0	0
$782$	−23.0927	−0.825793
$783$	47.6713	1.70363
$784$	−22.2547	−0.794809
$785$	−13.2802	−0.473991
$786$	51.0707	1.82163
$787$	9.45003	0.336857	0.168429	−	0.985714i	$-0.446131\pi$
$787$	9.45003	0.336857	0.168429	+	0.985714i	$0.446131\pi$
$788$	−1.05642	−0.0376333
$789$	79.7938	2.84073
$790$	−26.4579	−0.941328
$791$	−6.17177	−0.219443
$792$	0	0
$793$	−2.95188	−0.104824
$794$	−25.5530	−0.906842
$795$	28.7542	1.01981
$796$	2.02766	0.0718685
$797$	−13.9753	−0.495030	−0.247515	−	0.968884i	$-0.579614\pi$
$797$	−13.9753	−0.495030	−0.247515	+	0.968884i	$0.579614\pi$
$798$	−39.2282	−1.38866
$799$	30.3183	1.07259
$800$	−0.413865	−0.0146323
$801$	78.1223	2.76032
$802$	17.3948	0.614231
$803$	0	0
$804$	4.60323	0.162343
$805$	−45.4857	−1.60316
$806$	22.0339	0.776110
$807$	10.2708	0.361548
$808$	21.9507	0.772223
$809$	−20.2412	−0.711641	−0.355821	−	0.934554i	$-0.615799\pi$
$809$	−20.2412	−0.711641	−0.355821	+	0.934554i	$0.615799\pi$
$810$	1.29793	0.0456045
$811$	−40.7155	−1.42972	−0.714858	−	0.699270i	$-0.753509\pi$
$811$	−40.7155	−1.42972	−0.714858	+	0.699270i	$0.753509\pi$
$812$	−18.4487	−0.647421
$813$	−23.4810	−0.823516
$814$	0	0
$815$	−5.81221	−0.203593
$816$	−27.8067	−0.973429
$817$	32.4645	1.13579
$818$	25.6222	0.895859
$819$	−57.0514	−1.99354
$820$	−14.5639	−0.508594
$821$	22.4572	0.783760	0.391880	−	0.920016i	$-0.371825\pi$
$821$	22.4572	0.783760	0.391880	+	0.920016i	$0.371825\pi$
$822$	−47.8462	−1.66883
$823$	30.3663	1.05850	0.529252	−	0.848465i	$-0.322473\pi$
$823$	30.3663	1.05850	0.529252	+	0.848465i	$0.322473\pi$
$824$	22.5244	0.784674
$825$	0	0
$826$	17.2266	0.599392
$827$	−36.9929	−1.28637	−0.643184	−	0.765712i	$-0.722387\pi$
$827$	−36.9929	−1.28637	−0.643184	+	0.765712i	$0.722387\pi$
$828$	13.4359	0.466932
$829$	−38.7783	−1.34683	−0.673414	−	0.739266i	$-0.735173\pi$
$829$	−38.7783	−1.34683	−0.673414	+	0.739266i	$0.735173\pi$
$830$	−25.6848	−0.891532
$831$	−61.9413	−2.14872
$832$	26.1040	0.904993
$833$	−31.3743	−1.08706
$834$	47.9072	1.65889
$835$	−6.90343	−0.238903
$836$	0	0
$837$	33.3853	1.15396
$838$	18.5751	0.641666
$839$	−4.73129	−0.163342	−0.0816711	−	0.996659i	$-0.526026\pi$
$839$	−4.73129	−0.163342	−0.0816711	+	0.996659i	$0.526026\pi$
$840$	−76.8662	−2.65214
$841$	48.4882	1.67201
$842$	−3.06242	−0.105538
$843$	−73.8439	−2.54332
$844$	11.0936	0.381858
$845$	9.71912	0.334348
$846$	48.4363	1.66527
$847$	0	0
$848$	−11.9252	−0.409512
$849$	−94.1164	−3.23007
$850$	0.637996	0.0218831
$851$	−22.0649	−0.756376
$852$	−8.32010	−0.285042
$853$	21.6068	0.739804	0.369902	−	0.929071i	$-0.379391\pi$
$853$	21.6068	0.739804	0.369902	+	0.929071i	$0.379391\pi$
$854$	−4.75270	−0.162634
$855$	−32.7361	−1.11955
$856$	−1.36699	−0.0467226
$857$	2.16317	0.0738926	0.0369463	−	0.999317i	$-0.488237\pi$
$857$	2.16317	0.0738926	0.0369463	+	0.999317i	$0.488237\pi$
$858$	0	0
$859$	−5.69173	−0.194199	−0.0970996	−	0.995275i	$-0.530957\pi$
$859$	−5.69173	−0.194199	−0.0970996	+	0.995275i	$0.530957\pi$
$860$	13.4040	0.457072
$861$	−132.921	−4.52994
$862$	43.7391	1.48976
$863$	−3.13842	−0.106833	−0.0534166	−	0.998572i	$-0.517011\pi$
$863$	−3.13842	−0.106833	−0.0534166	+	0.998572i	$0.517011\pi$
$864$	15.8736	0.540031
$865$	2.49715	0.0849056
$866$	−2.42879	−0.0825335
$867$	8.65236	0.293850
$868$	−12.9200	−0.438533
$869$	0	0
$870$	68.0292	2.30641
$871$	9.04084	0.306337
$872$	7.80342	0.264257
$873$	65.3335	2.21120
$874$	18.1446	0.613750
$875$	−43.2439	−1.46191
$876$	−6.90595	−0.233330
$877$	45.8347	1.54773	0.773864	−	0.633352i	$-0.218321\pi$
$877$	45.8347	1.54773	0.773864	+	0.633352i	$0.218321\pi$
$878$	−42.0909	−1.42050
$879$	−80.8889	−2.72832
$880$	0	0
$881$	10.4493	0.352045	0.176022	−	0.984386i	$-0.443677\pi$
$881$	10.4493	0.352045	0.176022	+	0.984386i	$0.443677\pi$
$882$	−50.1233	−1.68774
$883$	30.1762	1.01551	0.507755	−	0.861501i	$-0.330475\pi$
$883$	30.1762	1.01551	0.507755	+	0.861501i	$0.330475\pi$
$884$	5.88165	0.197821
$885$	23.1345	0.777658
$886$	32.8970	1.10520
$887$	−4.08350	−0.137111	−0.0685553	−	0.997647i	$-0.521839\pi$
$887$	−4.08350	−0.137111	−0.0685553	+	0.997647i	$0.521839\pi$
$888$	−37.2875	−1.25129
$889$	−7.31306	−0.245272
$890$	43.5592	1.46011
$891$	0	0
$892$	1.74290	0.0583565
$893$	−23.8220	−0.797173
$894$	74.5982	2.49494
$895$	55.7402	1.86319
$896$	19.0184	0.635359
$897$	42.4665	1.41791
$898$	−26.9005	−0.897681
$899$	54.2666	1.80989
$900$	−0.371203	−0.0123734
$901$	−16.8119	−0.560087
$902$	0	0
$903$	122.335	4.07104
$904$	4.82412	0.160448
$905$	−4.45367	−0.148045
$906$	13.3639	0.443986
$907$	−25.1026	−0.833520	−0.416760	−	0.909017i	$-0.636834\pi$
$907$	−25.1026	−0.833520	−0.416760	+	0.909017i	$0.636834\pi$
$908$	2.64983	0.0879378
$909$	35.2274	1.16842
$910$	−31.8106	−1.05451
$911$	−15.3025	−0.506995	−0.253497	−	0.967336i	$-0.581581\pi$
$911$	−15.3025	−0.506995	−0.253497	+	0.967336i	$0.581581\pi$
$912$	21.8485	0.723477
$913$	0	0
$914$	13.4007	0.443255
$915$	−6.38264	−0.211004
$916$	5.36394	0.177230
$917$	−58.8151	−1.94225
$918$	−24.4700	−0.807631
$919$	−10.4394	−0.344364	−0.172182	−	0.985065i	$-0.555082\pi$
$919$	−10.4394	−0.344364	−0.172182	+	0.985065i	$0.555082\pi$
$920$	35.5536	1.17217
$921$	47.3039	1.55872
$922$	−19.1407	−0.630364
$923$	−16.3409	−0.537866
$924$	0	0
$925$	0.609602	0.0200436
$926$	15.6647	0.514775
$927$	36.1481	1.18726
$928$	25.8020	0.846993
$929$	54.5638	1.79018	0.895090	−	0.445886i	$-0.147111\pi$
$929$	54.5638	1.79018	0.895090	+	0.445886i	$0.147111\pi$
$930$	47.6423	1.56225
$931$	24.6517	0.807927
$932$	−1.85318	−0.0607028
$933$	−81.9039	−2.68141
$934$	−6.75845	−0.221143
$935$	0	0
$936$	44.5939	1.45760
$937$	18.1571	0.593165	0.296583	−	0.955007i	$-0.404153\pi$
$937$	18.1571	0.593165	0.296583	+	0.955007i	$0.404153\pi$
$938$	14.5563	0.475281
$939$	−26.6583	−0.869962
$940$	−9.83567	−0.320804
$941$	21.9846	0.716677	0.358338	−	0.933592i	$-0.383343\pi$
$941$	21.9846	0.716677	0.358338	+	0.933592i	$0.383343\pi$
$942$	19.9627	0.650419
$943$	61.4811	2.00210
$944$	−9.59453	−0.312275
$945$	−48.1987	−1.56790
$946$	0	0
$947$	−25.1265	−0.816502	−0.408251	−	0.912870i	$-0.633861\pi$
$947$	−25.1265	−0.816502	−0.408251	+	0.912870i	$0.633861\pi$
$948$	−14.4843	−0.470428
$949$	−13.5634	−0.440288
$950$	−0.501292	−0.0162640
$951$	−71.4001	−2.31531
$952$	44.9420	1.45658
$953$	−16.7130	−0.541386	−0.270693	−	0.962666i	$-0.587253\pi$
$953$	−16.7130	−0.541386	−0.270693	+	0.962666i	$0.587253\pi$
$954$	−26.8586	−0.869579
$955$	1.33569	0.0432218
$956$	−8.18921	−0.264858
$957$	0	0
$958$	26.2129	0.846900
$959$	55.1017	1.77933
$960$	56.4428	1.82168
$961$	7.00411	0.225939
$962$	−15.4312	−0.497521
$963$	−2.19380	−0.0706942
$964$	10.7181	0.345207
$965$	−13.0654	−0.420589
$966$	68.3736	2.19989
$967$	−18.4452	−0.593157	−0.296578	−	0.955009i	$-0.595846\pi$
$967$	−18.4452	−0.593157	−0.296578	+	0.955009i	$0.595846\pi$
$968$	0	0
$969$	30.8018	0.989495
$970$	36.4284	1.16965
$971$	−8.03044	−0.257709	−0.128855	−	0.991664i	$-0.541130\pi$
$971$	−8.03044	−0.257709	−0.128855	+	0.991664i	$0.541130\pi$
$972$	−7.96396	−0.255444
$973$	−55.1720	−1.76873
$974$	−49.6137	−1.58973
$975$	−1.17325	−0.0375740
$976$	2.64706	0.0847303
$977$	−51.9494	−1.66201	−0.831004	−	0.556266i	$-0.812233\pi$
$977$	−51.9494	−1.66201	−0.831004	+	0.556266i	$0.812233\pi$
$978$	8.73684	0.279373
$979$	0	0
$980$	10.1782	0.325132
$981$	12.5233	0.399837
$982$	−31.0616	−0.991214
$983$	49.9499	1.59316	0.796578	−	0.604536i	$-0.206641\pi$
$983$	49.9499	1.59316	0.796578	+	0.604536i	$0.206641\pi$
$984$	103.897	3.31211
$985$	−4.48625	−0.142944
$986$	−39.7752	−1.26670
$987$	−89.7676	−2.85734
$988$	−4.62138	−0.147026
$989$	−56.5845	−1.79928
$990$	0	0
$991$	−14.3042	−0.454388	−0.227194	−	0.973849i	$-0.572955\pi$
$991$	−14.3042	−0.454388	−0.227194	+	0.973849i	$0.572955\pi$
$992$	18.0697	0.573714
$993$	55.8778	1.77323
$994$	−26.3098	−0.834496
$995$	8.61079	0.272981
$996$	−14.0611	−0.445542
$997$	−41.9452	−1.32842	−0.664209	−	0.747547i	$-0.731232\pi$
$997$	−41.9452	−1.32842	−0.664209	+	0.747547i	$0.731232\pi$
$998$	39.9824	1.26562
$999$	−23.3810	−0.739742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.t.1.17		54
11.5	even	5		671.2.j.b.245.20	✓	108
11.9	even	5		671.2.j.b.367.20	yes	108
11.10	odd	2		7381.2.a.s.1.38		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.b.245.20	✓	108	11.5	even	5
671.2.j.b.367.20	yes	108	11.9	even	5
7381.2.a.s.1.38		54	11.10	odd	2
7381.2.a.t.1.17		54	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21081 q^{2} -2.81493 q^{3} -0.533929 q^{4} -2.26742 q^{5} +3.40836 q^{6} -3.92521 q^{7} +3.06812 q^{8} +4.92385 q^{9} +O(q^{10})\)	\(q-1.21081 q^{2} -2.81493 q^{3} -0.533929 q^{4} -2.26742 q^{5} +3.40836 q^{6} -3.92521 q^{7} +3.06812 q^{8} +4.92385 q^{9} +2.74542 q^{10} +1.50298 q^{12} +2.95188 q^{13} +4.75270 q^{14} +6.38264 q^{15} -2.64706 q^{16} -3.73179 q^{17} -5.96187 q^{18} +2.93218 q^{19} +1.21064 q^{20} +11.0492 q^{21} -5.11069 q^{23} -8.63655 q^{24} +0.141196 q^{25} -3.57417 q^{26} -5.41551 q^{27} +2.09579 q^{28} -8.80274 q^{29} -7.72819 q^{30} -6.16475 q^{31} -2.93114 q^{32} +4.51851 q^{34} +8.90011 q^{35} -2.62899 q^{36} +4.31741 q^{37} -3.55032 q^{38} -8.30934 q^{39} -6.95671 q^{40} -12.0299 q^{41} -13.3785 q^{42} +11.0718 q^{43} -11.1644 q^{45} +6.18810 q^{46} -8.12434 q^{47} +7.45130 q^{48} +8.40731 q^{49} -0.170962 q^{50} +10.5047 q^{51} -1.57609 q^{52} +4.50506 q^{53} +6.55718 q^{54} -12.0430 q^{56} -8.25388 q^{57} +10.6585 q^{58} +3.62460 q^{59} -3.40788 q^{60} -1.00000 q^{61} +7.46436 q^{62} -19.3272 q^{63} +8.84318 q^{64} -6.69315 q^{65} +3.06274 q^{67} +1.99251 q^{68} +14.3863 q^{69} -10.7764 q^{70} -5.53575 q^{71} +15.1070 q^{72} -4.59485 q^{73} -5.22758 q^{74} -0.397458 q^{75} -1.56557 q^{76} +10.0611 q^{78} -9.63707 q^{79} +6.00200 q^{80} +0.472760 q^{81} +14.5660 q^{82} -9.35549 q^{83} -5.89950 q^{84} +8.46154 q^{85} -13.4059 q^{86} +24.7791 q^{87} +15.8661 q^{89} +13.5181 q^{90} -11.5868 q^{91} +2.72875 q^{92} +17.3534 q^{93} +9.83707 q^{94} -6.64847 q^{95} +8.25095 q^{96} +13.2688 q^{97} -10.1797 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) \) 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9	\( 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9} + 2 q^{10} - 27 q^{12} - 3 q^{13} - 39 q^{14} - 28 q^{15} + 23 q^{16} + 4 q^{17} - 34 q^{18} - 3 q^{19} - 37 q^{20} + 9 q^{21} - 52 q^{23} + 3 q^{24} + 24 q^{25} - 47 q^{26} - 48 q^{27} - 9 q^{28} - 2 q^{29} + 31 q^{30} - 41 q^{31} + 22 q^{32} + 11 q^{34} + 11 q^{35} - 22 q^{36} - 21 q^{37} - 4 q^{38} - 4 q^{39} - 96 q^{40} - 6 q^{41} - 8 q^{42} + 19 q^{43} - 8 q^{45} - q^{46} - 47 q^{47} - 35 q^{48} + 30 q^{49} + 20 q^{50} - 30 q^{51} + 44 q^{52} - 48 q^{53} + 46 q^{54} - 89 q^{56} - 19 q^{57} - 45 q^{58} - 135 q^{59} - 10 q^{60} - 54 q^{61} - 41 q^{62} + 34 q^{63} - 45 q^{64} + 11 q^{65} - 55 q^{67} + 41 q^{68} - 37 q^{69} - 38 q^{70} - 113 q^{71} - 72 q^{72} - 42 q^{73} + 51 q^{74} - 85 q^{75} + 34 q^{76} + 13 q^{78} - 15 q^{79} - 93 q^{80} - 38 q^{81} + 5 q^{82} - 23 q^{83} - 74 q^{84} + 9 q^{85} - 106 q^{86} + 70 q^{87} - 66 q^{89} - 7 q^{90} - 121 q^{91} - 133 q^{92} - 15 q^{93} + 17 q^{94} - 47 q^{95} + 34 q^{96} - 7 q^{97} + 61 q^{98}+O(q^{100}) \) 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9 + 2 * q^10 - 27 * q^12 - 3 * q^13 - 39 * q^14 - 28 * q^15 + 23 * q^16 + 4 * q^17 - 34 * q^18 - 3 * q^19 - 37 * q^20 + 9 * q^21 - 52 * q^23 + 3 * q^24 + 24 * q^25 - 47 * q^26 - 48 * q^27 - 9 * q^28 - 2 * q^29 + 31 * q^30 - 41 * q^31 + 22 * q^32 + 11 * q^34 + 11 * q^35 - 22 * q^36 - 21 * q^37 - 4 * q^38 - 4 * q^39 - 96 * q^40 - 6 * q^41 - 8 * q^42 + 19 * q^43 - 8 * q^45 - q^46 - 47 * q^47 - 35 * q^48 + 30 * q^49 + 20 * q^50 - 30 * q^51 + 44 * q^52 - 48 * q^53 + 46 * q^54 - 89 * q^56 - 19 * q^57 - 45 * q^58 - 135 * q^59 - 10 * q^60 - 54 * q^61 - 41 * q^62 + 34 * q^63 - 45 * q^64 + 11 * q^65 - 55 * q^67 + 41 * q^68 - 37 * q^69 - 38 * q^70 - 113 * q^71 - 72 * q^72 - 42 * q^73 + 51 * q^74 - 85 * q^75 + 34 * q^76 + 13 * q^78 - 15 * q^79 - 93 * q^80 - 38 * q^81 + 5 * q^82 - 23 * q^83 - 74 * q^84 + 9 * q^85 - 106 * q^86 + 70 * q^87 - 66 * q^89 - 7 * q^90 - 121 * q^91 - 133 * q^92 - 15 * q^93 + 17 * q^94 - 47 * q^95 + 34 * q^96 - 7 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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