LMFDB - Embedded newform 7381.2.a.v.1.25

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:	$0$
Dimension:	$64$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q-0.577732 q^{2} -2.58243 q^{3} -1.66623 q^{4} +0.399552 q^{5} +1.49196 q^{6} +2.97468 q^{7} +2.11810 q^{8} +3.66897 q^{9} +O(q^{10})$	\(q-0.577732 q^{2} -2.58243 q^{3} -1.66623 q^{4} +0.399552 q^{5} +1.49196 q^{6} +2.97468 q^{7} +2.11810 q^{8} +3.66897 q^{9} -0.230834 q^{10} +4.30292 q^{12} -3.72597 q^{13} -1.71857 q^{14} -1.03182 q^{15} +2.10876 q^{16} +3.82933 q^{17} -2.11968 q^{18} +2.13680 q^{19} -0.665744 q^{20} -7.68191 q^{21} -8.40500 q^{23} -5.46985 q^{24} -4.84036 q^{25} +2.15261 q^{26} -1.72757 q^{27} -4.95648 q^{28} +3.73888 q^{29} +0.596114 q^{30} +8.81932 q^{31} -5.45449 q^{32} -2.21233 q^{34} +1.18854 q^{35} -6.11333 q^{36} +5.56087 q^{37} -1.23450 q^{38} +9.62207 q^{39} +0.846290 q^{40} +11.0833 q^{41} +4.43809 q^{42} +5.51311 q^{43} +1.46594 q^{45} +4.85584 q^{46} +1.53544 q^{47} -5.44573 q^{48} +1.84871 q^{49} +2.79643 q^{50} -9.88900 q^{51} +6.20830 q^{52} -12.6597 q^{53} +0.998071 q^{54} +6.30066 q^{56} -5.51816 q^{57} -2.16007 q^{58} +7.81419 q^{59} +1.71924 q^{60} +1.00000 q^{61} -5.09521 q^{62} +10.9140 q^{63} -1.06628 q^{64} -1.48872 q^{65} -8.73758 q^{67} -6.38053 q^{68} +21.7054 q^{69} -0.686657 q^{70} +5.18643 q^{71} +7.77123 q^{72} +14.7332 q^{73} -3.21270 q^{74} +12.4999 q^{75} -3.56040 q^{76} -5.55898 q^{78} -7.78500 q^{79} +0.842559 q^{80} -6.54558 q^{81} -6.40320 q^{82} +1.04278 q^{83} +12.7998 q^{84} +1.53002 q^{85} -3.18510 q^{86} -9.65541 q^{87} +1.87457 q^{89} -0.846923 q^{90} -11.0836 q^{91} +14.0046 q^{92} -22.7753 q^{93} -0.887073 q^{94} +0.853764 q^{95} +14.0859 q^{96} -10.8318 q^{97} -1.06806 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * 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 $

$2$	−0.577732	−0.408518	−0.204259	−	0.978917i	$-0.565479\pi$
$2$	−0.577732	−0.408518	−0.204259	+	0.978917i	$0.565479\pi$
$3$	−2.58243	−1.49097	−0.745485	−	0.666523i	$-0.767782\pi$
$3$	−2.58243	−1.49097	−0.745485	+	0.666523i	$0.767782\pi$
$4$	−1.66623	−0.833113
$5$	0.399552	0.178685	0.0893425	−	0.996001i	$-0.471523\pi$
$5$	0.399552	0.178685	0.0893425	+	0.996001i	$0.471523\pi$
$6$	1.49196	0.609088
$7$	2.97468	1.12432	0.562161	−	0.827028i	$-0.309970\pi$
$7$	2.97468	1.12432	0.562161	+	0.827028i	$0.309970\pi$
$8$	2.11810	0.748860
$9$	3.66897	1.22299
$10$	−0.230834	−0.0729961
$11$	0	0
$11$	0	0
$12$	4.30292	1.24215
$13$	−3.72597	−1.03340	−0.516699	−	0.856167i	$-0.672839\pi$
$13$	−3.72597	−1.03340	−0.516699	+	0.856167i	$0.672839\pi$
$14$	−1.71857	−0.459306
$15$	−1.03182	−0.266414
$16$	2.10876	0.527190
$17$	3.82933	0.928749	0.464375	−	0.885639i	$-0.346279\pi$
$17$	3.82933	0.928749	0.464375	+	0.885639i	$0.346279\pi$
$18$	−2.11968	−0.499614
$19$	2.13680	0.490217	0.245108	−	0.969496i	$-0.421176\pi$
$19$	2.13680	0.490217	0.245108	+	0.969496i	$0.421176\pi$
$20$	−0.665744	−0.148865
$21$	−7.68191	−1.67633
$22$	0	0
$23$	−8.40500	−1.75256	−0.876282	−	0.481798i	$-0.839984\pi$
$23$	−8.40500	−1.75256	−0.876282	+	0.481798i	$0.839984\pi$
$24$	−5.46985	−1.11653
$25$	−4.84036	−0.968072
$26$	2.15261	0.422162
$27$	−1.72757	−0.332470
$28$	−4.95648	−0.936688
$29$	3.73888	0.694292	0.347146	−	0.937811i	$-0.387151\pi$
$29$	3.73888	0.694292	0.347146	+	0.937811i	$0.387151\pi$
$30$	0.596114	0.108835
$31$	8.81932	1.58400	0.791998	−	0.610523i	$-0.209041\pi$
$31$	8.81932	1.58400	0.791998	+	0.610523i	$0.209041\pi$
$32$	−5.45449	−0.964227
$33$	0	0
$34$	−2.21233	−0.379411
$35$	1.18854	0.200900
$36$	−6.11333	−1.01889
$37$	5.56087	0.914202	0.457101	−	0.889415i	$-0.348888\pi$
$37$	5.56087	0.914202	0.457101	+	0.889415i	$0.348888\pi$
$38$	−1.23450	−0.200262
$39$	9.62207	1.54076
$40$	0.846290	0.133810
$41$	11.0833	1.73093	0.865463	−	0.500972i	$-0.167024\pi$
$41$	11.0833	1.73093	0.865463	+	0.500972i	$0.167024\pi$
$42$	4.43809	0.684812
$43$	5.51311	0.840742	0.420371	−	0.907352i	$-0.361900\pi$
$43$	5.51311	0.840742	0.420371	+	0.907352i	$0.361900\pi$
$44$	0	0
$45$	1.46594	0.218530
$46$	4.85584	0.715955
$47$	1.53544	0.223967	0.111983	−	0.993710i	$-0.464280\pi$
$47$	1.53544	0.223967	0.111983	+	0.993710i	$0.464280\pi$
$48$	−5.44573	−0.786024
$49$	1.84871	0.264101
$50$	2.79643	0.395475
$51$	−9.88900	−1.38474
$52$	6.20830	0.860937
$53$	−12.6597	−1.73895	−0.869473	−	0.493980i	$-0.835542\pi$
$53$	−12.6597	−1.73895	−0.869473	+	0.493980i	$0.835542\pi$
$54$	0.998071	0.135820
$55$	0	0
$56$	6.30066	0.841960
$57$	−5.51816	−0.730898
$58$	−2.16007	−0.283631
$59$	7.81419	1.01732	0.508661	−	0.860967i	$-0.330141\pi$
$59$	7.81419	1.01732	0.508661	+	0.860967i	$0.330141\pi$
$60$	1.71924	0.221953
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−5.09521	−0.647092
$63$	10.9140	1.37503
$64$	−1.06628	−0.133285
$65$	−1.48872	−0.184653
$66$	0	0
$67$	−8.73758	−1.06747	−0.533733	−	0.845653i	$-0.679211\pi$
$67$	−8.73758	−1.06747	−0.533733	+	0.845653i	$0.679211\pi$
$68$	−6.38053	−0.773753
$69$	21.7054	2.61302
$70$	−0.686657	−0.0820712
$71$	5.18643	0.615516	0.307758	−	0.951465i	$-0.400421\pi$
$71$	5.18643	0.615516	0.307758	+	0.951465i	$0.400421\pi$
$72$	7.77123	0.915848
$73$	14.7332	1.72439	0.862194	−	0.506578i	$-0.169090\pi$
$73$	14.7332	1.72439	0.862194	+	0.506578i	$0.169090\pi$
$74$	−3.21270	−0.373468
$75$	12.4999	1.44337
$76$	−3.56040	−0.408406
$77$	0	0
$78$	−5.55898	−0.629430
$79$	−7.78500	−0.875881	−0.437941	−	0.899004i	$-0.644292\pi$
$79$	−7.78500	−0.875881	−0.437941	+	0.899004i	$0.644292\pi$
$80$	0.842559	0.0942009
$81$	−6.54558	−0.727286
$82$	−6.40320	−0.707115
$83$	1.04278	0.114459	0.0572297	−	0.998361i	$-0.481773\pi$
$83$	1.04278	0.114459	0.0572297	+	0.998361i	$0.481773\pi$
$84$	12.7998	1.39657
$85$	1.53002	0.165954
$86$	−3.18510	−0.343458
$87$	−9.65541	−1.03517
$88$	0	0
$89$	1.87457	0.198704	0.0993521	−	0.995052i	$-0.468323\pi$
$89$	1.87457	0.198704	0.0993521	+	0.995052i	$0.468323\pi$
$90$	−0.846923	−0.0892735
$91$	−11.0836	−1.16187
$92$	14.0046	1.46008
$93$	−22.7753	−2.36169
$94$	−0.887073	−0.0914946
$95$	0.853764	0.0875944
$96$	14.0859	1.43763
$97$	−10.8318	−1.09980	−0.549901	−	0.835230i	$-0.685335\pi$
$97$	−10.8318	−1.09980	−0.549901	+	0.835230i	$0.685335\pi$
$98$	−1.06806	−0.107890
$99$	0	0
$100$	8.06513	0.806513
$101$	16.4758	1.63940	0.819700	−	0.572793i	$-0.194140\pi$
$101$	16.4758	1.63940	0.819700	+	0.572793i	$0.194140\pi$
$102$	5.71319	0.565690
$103$	−13.5539	−1.33550	−0.667752	−	0.744384i	$-0.732743\pi$
$103$	−13.5539	−1.33550	−0.667752	+	0.744384i	$0.732743\pi$
$104$	−7.89196	−0.773870
$105$	−3.06932	−0.299535
$106$	7.31393	0.710391
$107$	15.1972	1.46917	0.734583	−	0.678519i	$-0.237378\pi$
$107$	15.1972	1.46917	0.734583	+	0.678519i	$0.237378\pi$
$108$	2.87852	0.276985
$109$	15.9166	1.52454	0.762269	−	0.647260i	$-0.224085\pi$
$109$	15.9166	1.52454	0.762269	+	0.647260i	$0.224085\pi$
$110$	0	0
$111$	−14.3606	−1.36305
$112$	6.27288	0.592731
$113$	2.69919	0.253918	0.126959	−	0.991908i	$-0.459478\pi$
$113$	2.69919	0.253918	0.126959	+	0.991908i	$0.459478\pi$
$114$	3.18802	0.298585
$115$	−3.35824	−0.313157
$116$	−6.22981	−0.578424
$117$	−13.6705	−1.26383
$118$	−4.51451	−0.415594
$119$	11.3910	1.04421
$120$	−2.18549	−0.199507
$121$	0	0
$122$	−0.577732	−0.0523054
$123$	−28.6220	−2.58076
$124$	−14.6950	−1.31965
$125$	−3.93173	−0.351665
$126$	−6.30537	−0.561727
$127$	−4.11458	−0.365110	−0.182555	−	0.983196i	$-0.558437\pi$
$127$	−4.11458	−0.365110	−0.182555	+	0.983196i	$0.558437\pi$
$128$	11.5250	1.01868
$129$	−14.2373	−1.25352
$130$	0.860080	0.0754340
$131$	−8.73454	−0.763140	−0.381570	−	0.924340i	$-0.624617\pi$
$131$	−8.73454	−0.763140	−0.381570	+	0.924340i	$0.624617\pi$
$132$	0	0
$133$	6.35631	0.551162
$134$	5.04798	0.436079
$135$	−0.690253	−0.0594075
$136$	8.11089	0.695503
$137$	−15.5233	−1.32624	−0.663122	−	0.748512i	$-0.730769\pi$
$137$	−15.5233	−1.32624	−0.663122	+	0.748512i	$0.730769\pi$
$138$	−12.5399	−1.06747
$139$	6.57490	0.557676	0.278838	−	0.960338i	$-0.410051\pi$
$139$	6.57490	0.557676	0.278838	+	0.960338i	$0.410051\pi$
$140$	−1.98037	−0.167372
$141$	−3.96517	−0.333928
$142$	−2.99637	−0.251450
$143$	0	0
$144$	7.73697	0.644747
$145$	1.49388	0.124060
$146$	−8.51183	−0.704444
$147$	−4.77417	−0.393767
$148$	−9.26567	−0.761633
$149$	−9.40437	−0.770436	−0.385218	−	0.922826i	$-0.625874\pi$
$149$	−9.40437	−0.770436	−0.385218	+	0.922826i	$0.625874\pi$
$150$	−7.22160	−0.589641
$151$	−2.43521	−0.198175	−0.0990874	−	0.995079i	$-0.531592\pi$
$151$	−2.43521	−0.198175	−0.0990874	+	0.995079i	$0.531592\pi$
$152$	4.52596	0.367104
$153$	14.0497	1.13585
$154$	0	0
$155$	3.52378	0.283037
$156$	−16.0325	−1.28363
$157$	−2.37104	−0.189230	−0.0946148	−	0.995514i	$-0.530162\pi$
$157$	−2.37104	−0.189230	−0.0946148	+	0.995514i	$0.530162\pi$
$158$	4.49765	0.357814
$159$	32.6929	2.59272
$160$	−2.17935	−0.172293
$161$	−25.0022	−1.97045
$162$	3.78159	0.297110
$163$	−20.5932	−1.61298	−0.806492	−	0.591245i	$-0.798637\pi$
$163$	−20.5932	−1.61298	−0.806492	+	0.591245i	$0.798637\pi$
$164$	−18.4673	−1.44206
$165$	0	0
$166$	−0.602445	−0.0467588
$167$	−14.6414	−1.13299	−0.566495	−	0.824066i	$-0.691701\pi$
$167$	−14.6414	−1.13299	−0.566495	+	0.824066i	$0.691701\pi$
$168$	−16.2710	−1.25534
$169$	0.882841	0.0679109
$170$	−0.883940	−0.0677951
$171$	7.83987	0.599530
$172$	−9.18609	−0.700433
$173$	−18.1835	−1.38247	−0.691234	−	0.722631i	$-0.742933\pi$
$173$	−18.1835	−1.38247	−0.691234	+	0.722631i	$0.742933\pi$
$174$	5.57824	0.422885
$175$	−14.3985	−1.08842
$176$	0	0
$177$	−20.1796	−1.51679
$178$	−1.08300	−0.0811743
$179$	25.4494	1.90218	0.951089	−	0.308917i	$-0.0999666\pi$
$179$	25.4494	1.90218	0.951089	+	0.308917i	$0.0999666\pi$
$180$	−2.44259	−0.182060
$181$	−19.1196	−1.42115	−0.710576	−	0.703620i	$-0.751566\pi$
$181$	−19.1196	−1.42115	−0.710576	+	0.703620i	$0.751566\pi$
$182$	6.40333	0.474646
$183$	−2.58243	−0.190899
$184$	−17.8026	−1.31243
$185$	2.22186	0.163354
$186$	13.1580	0.964794
$187$	0	0
$188$	−2.55839	−0.186590
$189$	−5.13896	−0.373804
$190$	−0.493247	−0.0357839
$191$	−12.2455	−0.886055	−0.443027	−	0.896508i	$-0.646096\pi$
$191$	−12.2455	−0.886055	−0.443027	+	0.896508i	$0.646096\pi$
$192$	2.75360	0.198724
$193$	−5.76439	−0.414930	−0.207465	−	0.978242i	$-0.566521\pi$
$193$	−5.76439	−0.414930	−0.207465	+	0.978242i	$0.566521\pi$
$194$	6.25788	0.449289
$195$	3.84452	0.275312
$196$	−3.08037	−0.220026
$197$	2.84841	0.202941	0.101470	−	0.994839i	$-0.467645\pi$
$197$	2.84841	0.202941	0.101470	+	0.994839i	$0.467645\pi$
$198$	0	0
$199$	19.7963	1.40332	0.701661	−	0.712511i	$-0.252442\pi$
$199$	19.7963	1.40332	0.701661	+	0.712511i	$0.252442\pi$
$200$	−10.2523	−0.724950
$201$	22.5642	1.59156
$202$	−9.51858	−0.669725
$203$	11.1220	0.780609
$204$	16.4773	1.15364
$205$	4.42837	0.309291
$206$	7.83051	0.545578
$207$	−30.8377	−2.14337
$208$	−7.85717	−0.544797
$209$	0	0
$210$	1.77325	0.122366
$211$	−3.39036	−0.233402	−0.116701	−	0.993167i	$-0.537232\pi$
$211$	−3.39036	−0.233402	−0.116701	+	0.993167i	$0.537232\pi$
$212$	21.0939	1.44874
$213$	−13.3936	−0.917716
$214$	−8.77990	−0.600182
$215$	2.20277	0.150228
$216$	−3.65915	−0.248974
$217$	26.2346	1.78092
$218$	−9.19556	−0.622802
$219$	−38.0475	−2.57101
$220$	0	0
$221$	−14.2680	−0.959767
$222$	8.29658	0.556830
$223$	20.9291	1.40152	0.700758	−	0.713399i	$-0.252845\pi$
$223$	20.9291	1.40152	0.700758	+	0.713399i	$0.252845\pi$
$224$	−16.2254	−1.08410
$225$	−17.7591	−1.18394
$226$	−1.55941	−0.103730
$227$	−14.0592	−0.933145	−0.466572	−	0.884483i	$-0.654511\pi$
$227$	−14.0592	−0.933145	−0.466572	+	0.884483i	$0.654511\pi$
$228$	9.19450	0.608920
$229$	1.27055	0.0839606	0.0419803	−	0.999118i	$-0.486633\pi$
$229$	1.27055	0.0839606	0.0419803	+	0.999118i	$0.486633\pi$
$230$	1.94016	0.127930
$231$	0	0
$232$	7.91931	0.519928
$233$	4.96087	0.324997	0.162499	−	0.986709i	$-0.448045\pi$
$233$	4.96087	0.324997	0.162499	+	0.986709i	$0.448045\pi$
$234$	7.89787	0.516300
$235$	0.613488	0.0400195
$236$	−13.0202	−0.847543
$237$	20.1043	1.30591
$238$	−6.58096	−0.426580
$239$	−20.7043	−1.33925	−0.669626	−	0.742699i	$-0.733545\pi$
$239$	−20.7043	−1.33925	−0.669626	+	0.742699i	$0.733545\pi$
$240$	−2.17585	−0.140451
$241$	−16.9402	−1.09121	−0.545607	−	0.838041i	$-0.683701\pi$
$241$	−16.9402	−1.09121	−0.545607	+	0.838041i	$0.683701\pi$
$242$	0	0
$243$	22.0862	1.41683
$244$	−1.66623	−0.106669
$245$	0.738656	0.0471910
$246$	16.5358	1.05429
$247$	−7.96167	−0.506589
$248$	18.6802	1.18619
$249$	−2.69290	−0.170656
$250$	2.27149	0.143662
$251$	1.35792	0.0857111	0.0428556	−	0.999081i	$-0.486354\pi$
$251$	1.35792	0.0857111	0.0428556	+	0.999081i	$0.486354\pi$
$252$	−18.1852	−1.14556
$253$	0	0
$254$	2.37713	0.149154
$255$	−3.95117	−0.247432
$256$	−4.52580	−0.282863
$257$	8.48464	0.529257	0.264629	−	0.964350i	$-0.414751\pi$
$257$	8.48464	0.529257	0.264629	+	0.964350i	$0.414751\pi$
$258$	8.22532	0.512086
$259$	16.5418	1.02786
$260$	2.48054	0.153837
$261$	13.7178	0.849112
$262$	5.04623	0.311757
$263$	−11.6870	−0.720650	−0.360325	−	0.932827i	$-0.617334\pi$
$263$	−11.6870	−0.720650	−0.360325	+	0.932827i	$0.617334\pi$
$264$	0	0
$265$	−5.05822	−0.310724
$266$	−3.67224	−0.225160
$267$	−4.84096	−0.296262
$268$	14.5588	0.889319
$269$	24.4076	1.48816	0.744078	−	0.668093i	$-0.232889\pi$
$269$	24.4076	1.48816	0.744078	+	0.668093i	$0.232889\pi$
$270$	0.398781	0.0242691
$271$	26.5226	1.61113	0.805567	−	0.592505i	$-0.201861\pi$
$271$	26.5226	1.61113	0.805567	+	0.592505i	$0.201861\pi$
$272$	8.07513	0.489627
$273$	28.6226	1.73232
$274$	8.96830	0.541795
$275$	0	0
$276$	−36.1660	−2.17694
$277$	8.75001	0.525737	0.262869	−	0.964832i	$-0.415331\pi$
$277$	8.75001	0.525737	0.262869	+	0.964832i	$0.415331\pi$
$278$	−3.79853	−0.227821
$279$	32.3578	1.93721
$280$	2.51744	0.150446
$281$	−0.809825	−0.0483101	−0.0241551	−	0.999708i	$-0.507690\pi$
$281$	−0.809825	−0.0483101	−0.0241551	+	0.999708i	$0.507690\pi$
$282$	2.29081	0.136416
$283$	23.0214	1.36848	0.684240	−	0.729256i	$-0.260134\pi$
$283$	23.0214	1.36848	0.684240	+	0.729256i	$0.260134\pi$
$284$	−8.64176	−0.512794
$285$	−2.20479	−0.130601
$286$	0	0
$287$	32.9694	1.94612
$288$	−20.0124	−1.17924
$289$	−2.33622	−0.137425
$290$	−0.863060	−0.0506806
$291$	27.9724	1.63977
$292$	−24.5488	−1.43661
$293$	−12.4595	−0.727889	−0.363945	−	0.931421i	$-0.618570\pi$
$293$	−12.4595	−0.727889	−0.363945	+	0.931421i	$0.618570\pi$
$294$	2.75819	0.160861
$295$	3.12218	0.181780
$296$	11.7785	0.684610
$297$	0	0
$298$	5.43321	0.314737
$299$	31.3168	1.81110
$300$	−20.8277	−1.20249
$301$	16.3997	0.945265
$302$	1.40690	0.0809580
$303$	−42.5476	−2.44430
$304$	4.50600	0.258437
$305$	0.399552	0.0228783
$306$	−8.11696	−0.464016
$307$	−1.59312	−0.0909239	−0.0454619	−	0.998966i	$-0.514476\pi$
$307$	−1.59312	−0.0909239	−0.0454619	+	0.998966i	$0.514476\pi$
$308$	0	0
$309$	35.0020	1.99120
$310$	−2.03580	−0.115626
$311$	4.68928	0.265905	0.132952	−	0.991122i	$-0.457554\pi$
$311$	4.68928	0.265905	0.132952	+	0.991122i	$0.457554\pi$
$312$	20.3805	1.15382
$313$	24.0099	1.35712	0.678561	−	0.734544i	$-0.262604\pi$
$313$	24.0099	1.35712	0.678561	+	0.734544i	$0.262604\pi$
$314$	1.36983	0.0773037
$315$	4.36071	0.245698
$316$	12.9716	0.729708
$317$	5.69700	0.319975	0.159988	−	0.987119i	$-0.448855\pi$
$317$	5.69700	0.319975	0.159988	+	0.987119i	$0.448855\pi$
$318$	−18.8877	−1.05917
$319$	0	0
$320$	−0.426035	−0.0238161
$321$	−39.2457	−2.19048
$322$	14.4446	0.804964
$323$	8.18253	0.455288
$324$	10.9064	0.605911
$325$	18.0350	1.00040
$326$	11.8974	0.658934
$327$	−41.1037	−2.27304
$328$	23.4756	1.29622
$329$	4.56744	0.251811
$330$	0	0
$331$	8.90369	0.489391	0.244696	−	0.969600i	$-0.421312\pi$
$331$	8.90369	0.489391	0.244696	+	0.969600i	$0.421312\pi$
$332$	−1.73750	−0.0953576
$333$	20.4027	1.11806
$334$	8.45883	0.462847
$335$	−3.49112	−0.190740
$336$	−16.1993	−0.883744
$337$	1.84168	0.100323	0.0501614	−	0.998741i	$-0.484026\pi$
$337$	1.84168	0.100323	0.0501614	+	0.998741i	$0.484026\pi$
$338$	−0.510046	−0.0277428
$339$	−6.97048	−0.378584
$340$	−2.54935	−0.138258
$341$	0	0
$342$	−4.52934	−0.244919
$343$	−15.3234	−0.827387
$344$	11.6773	0.629598
$345$	8.67242	0.466908
$346$	10.5052	0.564764
$347$	23.8002	1.27766	0.638830	−	0.769348i	$-0.279419\pi$
$347$	23.8002	1.27766	0.638830	+	0.769348i	$0.279419\pi$
$348$	16.0881	0.862412
$349$	14.9408	0.799764	0.399882	−	0.916567i	$-0.369051\pi$
$349$	14.9408	0.799764	0.399882	+	0.916567i	$0.369051\pi$
$350$	8.31848	0.444642
$351$	6.43686	0.343574
$352$	0	0
$353$	6.97200	0.371082	0.185541	−	0.982637i	$-0.440596\pi$
$353$	6.97200	0.371082	0.185541	+	0.982637i	$0.440596\pi$
$354$	11.6584	0.619638
$355$	2.07225	0.109984
$356$	−3.12346	−0.165543
$357$	−29.4166	−1.55689
$358$	−14.7029	−0.777075
$359$	−2.06096	−0.108773	−0.0543867	−	0.998520i	$-0.517320\pi$
$359$	−2.06096	−0.108773	−0.0543867	+	0.998520i	$0.517320\pi$
$360$	3.10501	0.163648
$361$	−14.4341	−0.759688
$362$	11.0460	0.580567
$363$	0	0
$364$	18.4677	0.967971
$365$	5.88667	0.308122
$366$	1.49196	0.0779858
$367$	7.50846	0.391939	0.195969	−	0.980610i	$-0.437215\pi$
$367$	7.50846	0.391939	0.195969	+	0.980610i	$0.437215\pi$
$368$	−17.7241	−0.923934
$369$	40.6644	2.11690
$370$	−1.28364	−0.0667332
$371$	−37.6586	−1.95514
$372$	37.9488	1.96755
$373$	23.2634	1.20453	0.602267	−	0.798295i	$-0.294264\pi$
$373$	23.2634	1.20453	0.602267	+	0.798295i	$0.294264\pi$
$374$	0	0
$375$	10.1534	0.524322
$376$	3.25221	0.167720
$377$	−13.9309	−0.717480
$378$	2.96894	0.152706
$379$	−7.05373	−0.362326	−0.181163	−	0.983453i	$-0.557986\pi$
$379$	−7.05373	−0.362326	−0.181163	+	0.983453i	$0.557986\pi$
$380$	−1.42256	−0.0729760
$381$	10.6256	0.544368
$382$	7.07463	0.361970
$383$	4.34339	0.221937	0.110969	−	0.993824i	$-0.464605\pi$
$383$	4.34339	0.221937	0.110969	+	0.993824i	$0.464605\pi$
$384$	−29.7626	−1.51882
$385$	0	0
$386$	3.33027	0.169506
$387$	20.2274	1.02822
$388$	18.0482	0.916259
$389$	21.6381	1.09710	0.548548	−	0.836119i	$-0.315181\pi$
$389$	21.6381	1.09710	0.548548	+	0.836119i	$0.315181\pi$
$390$	−2.22110	−0.112470
$391$	−32.1855	−1.62769
$392$	3.91575	0.197775
$393$	22.5564	1.13782
$394$	−1.64562	−0.0829051
$395$	−3.11051	−0.156507
$396$	0	0
$397$	27.4196	1.37615	0.688075	−	0.725639i	$-0.258456\pi$
$397$	27.4196	1.37615	0.688075	+	0.725639i	$0.258456\pi$
$398$	−11.4370	−0.573283
$399$	−16.4147	−0.821765
$400$	−10.2071	−0.510357
$401$	−12.0668	−0.602585	−0.301293	−	0.953532i	$-0.597418\pi$
$401$	−12.0668	−0.602585	−0.301293	+	0.953532i	$0.597418\pi$
$402$	−13.0361	−0.650181
$403$	−32.8605	−1.63690
$404$	−27.4523	−1.36581
$405$	−2.61530	−0.129955
$406$	−6.42551	−0.318893
$407$	0	0
$408$	−20.9458	−1.03697
$409$	2.44383	0.120839	0.0604197	−	0.998173i	$-0.480756\pi$
$409$	2.44383	0.120839	0.0604197	+	0.998173i	$0.480756\pi$
$410$	−2.55841	−0.126351
$411$	40.0879	1.97739
$412$	22.5838	1.11263
$413$	23.2447	1.14380
$414$	17.8159	0.875605
$415$	0.416643	0.0204522
$416$	20.3233	0.996430
$417$	−16.9792	−0.831477
$418$	0	0
$419$	−12.2239	−0.597179	−0.298589	−	0.954382i	$-0.596516\pi$
$419$	−12.2239	−0.597179	−0.298589	+	0.954382i	$0.596516\pi$
$420$	5.11418	0.249547
$421$	−26.8620	−1.30917	−0.654587	−	0.755986i	$-0.727158\pi$
$421$	−26.8620	−1.30917	−0.654587	+	0.755986i	$0.727158\pi$
$422$	1.95872	0.0953491
$423$	5.63348	0.273909
$424$	−26.8145	−1.30223
$425$	−18.5353	−0.899096
$426$	7.73792	0.374904
$427$	2.97468	0.143955
$428$	−25.3219	−1.22398
$429$	0	0
$430$	−1.27261	−0.0613709
$431$	10.3849	0.500222	0.250111	−	0.968217i	$-0.419533\pi$
$431$	10.3849	0.500222	0.250111	+	0.968217i	$0.419533\pi$
$432$	−3.64302	−0.175275
$433$	−16.2130	−0.779147	−0.389573	−	0.920995i	$-0.627378\pi$
$433$	−16.2130	−0.779147	−0.389573	+	0.920995i	$0.627378\pi$
$434$	−15.1566	−0.727540
$435$	−3.85784	−0.184969
$436$	−26.5207	−1.27011
$437$	−17.9598	−0.859136
$438$	21.9813	1.05031
$439$	−15.9981	−0.763548	−0.381774	−	0.924256i	$-0.624687\pi$
$439$	−15.9981	−0.763548	−0.381774	+	0.924256i	$0.624687\pi$
$440$	0	0
$441$	6.78286	0.322993
$442$	8.24306	0.392083
$443$	0.482975	0.0229468	0.0114734	−	0.999934i	$-0.496348\pi$
$443$	0.482975	0.0229468	0.0114734	+	0.999934i	$0.496348\pi$
$444$	23.9280	1.13557
$445$	0.748989	0.0355055
$446$	−12.0914	−0.572545
$447$	24.2862	1.14870
$448$	−3.17185	−0.149856
$449$	−31.5263	−1.48782	−0.743910	−	0.668280i	$-0.767031\pi$
$449$	−31.5263	−1.48782	−0.743910	+	0.668280i	$0.767031\pi$
$450$	10.2600	0.483662
$451$	0	0
$452$	−4.49746	−0.211543
$453$	6.28878	0.295472
$454$	8.12248	0.381207
$455$	−4.42846	−0.207609
$456$	−11.6880	−0.547340
$457$	−9.06611	−0.424095	−0.212047	−	0.977259i	$-0.568013\pi$
$457$	−9.06611	−0.424095	−0.212047	+	0.977259i	$0.568013\pi$
$458$	−0.734040	−0.0342994
$459$	−6.61543	−0.308782
$460$	5.59558	0.260895
$461$	13.0274	0.606748	0.303374	−	0.952872i	$-0.401887\pi$
$461$	13.0274	0.606748	0.303374	+	0.952872i	$0.401887\pi$
$462$	0	0
$463$	2.42007	0.112470	0.0562352	−	0.998418i	$-0.482090\pi$
$463$	2.42007	0.112470	0.0562352	+	0.998418i	$0.482090\pi$
$464$	7.88439	0.366024
$465$	−9.09992	−0.421999
$466$	−2.86605	−0.132767
$467$	41.7281	1.93095	0.965474	−	0.260499i	$-0.0838870\pi$
$467$	41.7281	1.93095	0.965474	+	0.260499i	$0.0838870\pi$
$468$	22.7781	1.05292
$469$	−25.9915	−1.20018
$470$	−0.354432	−0.0163487
$471$	6.12305	0.282135
$472$	16.5512	0.761831
$473$	0	0
$474$	−11.6149	−0.533489
$475$	−10.3429	−0.474565
$476$	−18.9800	−0.869948
$477$	−46.4481	−2.12671
$478$	11.9616	0.547109
$479$	15.3849	0.702955	0.351478	−	0.936196i	$-0.385679\pi$
$479$	15.3849	0.702955	0.351478	+	0.936196i	$0.385679\pi$
$480$	5.62803	0.256883
$481$	−20.7196	−0.944734
$482$	9.78690	0.445781
$483$	64.5665	2.93788
$484$	0	0
$485$	−4.32787	−0.196518
$486$	−12.7599	−0.578802
$487$	−0.215661	−0.00977254	−0.00488627	−	0.999988i	$-0.501555\pi$
$487$	−0.215661	−0.00977254	−0.00488627	+	0.999988i	$0.501555\pi$
$488$	2.11810	0.0958817
$489$	53.1806	2.40491
$490$	−0.426745	−0.0192784
$491$	−11.4165	−0.515217	−0.257609	−	0.966249i	$-0.582935\pi$
$491$	−11.4165	−0.515217	−0.257609	+	0.966249i	$0.582935\pi$
$492$	47.6907	2.15006
$493$	14.3174	0.644823
$494$	4.59971	0.206951
$495$	0	0
$496$	18.5978	0.835067
$497$	15.4280	0.692039
$498$	1.55577	0.0697159
$499$	33.8808	1.51671	0.758357	−	0.651840i	$-0.226003\pi$
$499$	33.8808	1.51671	0.758357	+	0.651840i	$0.226003\pi$
$500$	6.55116	0.292977
$501$	37.8106	1.68925
$502$	−0.784514	−0.0350146
$503$	−8.41876	−0.375374	−0.187687	−	0.982229i	$-0.560099\pi$
$503$	−8.41876	−0.375374	−0.187687	+	0.982229i	$0.560099\pi$
$504$	23.1169	1.02971
$505$	6.58293	0.292936
$506$	0	0
$507$	−2.27988	−0.101253
$508$	6.85583	0.304178
$509$	28.0497	1.24328	0.621641	−	0.783302i	$-0.286466\pi$
$509$	28.0497	1.24328	0.621641	+	0.783302i	$0.286466\pi$
$510$	2.28272	0.101080
$511$	43.8265	1.93877
$512$	−20.4353	−0.903122
$513$	−3.69147	−0.162983
$514$	−4.90185	−0.216211
$515$	−5.41548	−0.238635
$516$	23.7225	1.04432
$517$	0	0
$518$	−9.55674	−0.419899
$519$	46.9578	2.06122
$520$	−3.15325	−0.138279
$521$	−6.24300	−0.273511	−0.136755	−	0.990605i	$-0.543667\pi$
$521$	−6.24300	−0.273511	−0.136755	+	0.990605i	$0.543667\pi$
$522$	−7.92523	−0.346878
$523$	22.1584	0.968918	0.484459	−	0.874814i	$-0.339016\pi$
$523$	22.1584	0.968918	0.484459	+	0.874814i	$0.339016\pi$
$524$	14.5537	0.635782
$525$	37.1832	1.62281
$526$	6.75194	0.294399
$527$	33.7721	1.47114
$528$	0	0
$529$	47.6441	2.07148
$530$	2.92229	0.126936
$531$	28.6700	1.24417
$532$	−10.5910	−0.459180
$533$	−41.2962	−1.78874
$534$	2.79678	0.121028
$535$	6.07206	0.262518
$536$	−18.5070	−0.799382
$537$	−65.7214	−2.83609
$538$	−14.1010	−0.607939
$539$	0	0
$540$	1.15012	0.0494931
$541$	24.8182	1.06702	0.533510	−	0.845794i	$-0.320873\pi$
$541$	24.8182	1.06702	0.533510	+	0.845794i	$0.320873\pi$
$542$	−15.3230	−0.658178
$543$	49.3752	2.11889
$544$	−20.8871	−0.895525
$545$	6.35953	0.272412
$546$	−16.5362	−0.707683
$547$	33.9809	1.45292	0.726460	−	0.687209i	$-0.241164\pi$
$547$	33.9809	1.45292	0.726460	+	0.687209i	$0.241164\pi$
$548$	25.8653	1.10491
$549$	3.66897	0.156588
$550$	0	0
$551$	7.98925	0.340354
$552$	45.9741	1.95679
$553$	−23.1579	−0.984773
$554$	−5.05516	−0.214773
$555$	−5.73780	−0.243556
$556$	−10.9553	−0.464607
$557$	5.79531	0.245555	0.122778	−	0.992434i	$-0.460820\pi$
$557$	5.79531	0.245555	0.122778	+	0.992434i	$0.460820\pi$
$558$	−18.6941	−0.791386
$559$	−20.5417	−0.868821
$560$	2.50634	0.105912
$561$	0	0
$562$	0.467862	0.0197356
$563$	36.4950	1.53808	0.769040	−	0.639200i	$-0.220734\pi$
$563$	36.4950	1.53808	0.769040	+	0.639200i	$0.220734\pi$
$564$	6.60687	0.278199
$565$	1.07847	0.0453714
$566$	−13.3002	−0.559050
$567$	−19.4710	−0.817704
$568$	10.9854	0.460935
$569$	12.9162	0.541477	0.270738	−	0.962653i	$-0.412732\pi$
$569$	12.9162	0.541477	0.270738	+	0.962653i	$0.412732\pi$
$570$	1.27378	0.0533527
$571$	15.9782	0.668667	0.334334	−	0.942455i	$-0.391489\pi$
$571$	15.9782	0.668667	0.334334	+	0.942455i	$0.391489\pi$
$572$	0	0
$573$	31.6233	1.32108
$574$	−19.0475	−0.795026
$575$	40.6832	1.69661
$576$	−3.91216	−0.163006
$577$	6.34721	0.264238	0.132119	−	0.991234i	$-0.457822\pi$
$577$	6.34721	0.264238	0.132119	+	0.991234i	$0.457822\pi$
$578$	1.34971	0.0561406
$579$	14.8862	0.618647
$580$	−2.48913	−0.103356
$581$	3.10192	0.128689
$582$	−16.1606	−0.669877
$583$	0	0
$584$	31.2063	1.29133
$585$	−5.46206	−0.225828
$586$	7.19823	0.297356
$587$	−25.9523	−1.07117	−0.535584	−	0.844482i	$-0.679908\pi$
$587$	−25.9523	−1.07117	−0.535584	+	0.844482i	$0.679908\pi$
$588$	7.95485	0.328052
$589$	18.8452	0.776502
$590$	−1.80378	−0.0742605
$591$	−7.35584	−0.302579
$592$	11.7265	0.481958
$593$	13.6873	0.562068	0.281034	−	0.959698i	$-0.409323\pi$
$593$	13.6873	0.562068	0.281034	+	0.959698i	$0.409323\pi$
$594$	0	0
$595$	4.55131	0.186585
$596$	15.6698	0.641860
$597$	−51.1226	−2.09231
$598$	−18.0927	−0.739866
$599$	−5.35950	−0.218983	−0.109492	−	0.993988i	$-0.534922\pi$
$599$	−5.35950	−0.218983	−0.109492	+	0.993988i	$0.534922\pi$
$600$	26.4760	1.08088
$601$	−34.3605	−1.40160	−0.700798	−	0.713360i	$-0.747172\pi$
$601$	−34.3605	−1.40160	−0.700798	+	0.713360i	$0.747172\pi$
$602$	−9.47466	−0.386158
$603$	−32.0579	−1.30550
$604$	4.05761	0.165102
$605$	0	0
$606$	24.5811	0.998540
$607$	−8.88162	−0.360494	−0.180247	−	0.983621i	$-0.557690\pi$
$607$	−8.88162	−0.360494	−0.180247	+	0.983621i	$0.557690\pi$
$608$	−11.6552	−0.472680
$609$	−28.7217	−1.16386
$610$	−0.230834	−0.00934620
$611$	−5.72100	−0.231447
$612$	−23.4100	−0.946292
$613$	−44.9512	−1.81556	−0.907781	−	0.419444i	$-0.862225\pi$
$613$	−44.9512	−1.81556	−0.907781	+	0.419444i	$0.862225\pi$
$614$	0.920394	0.0371441
$615$	−11.4360	−0.461143
$616$	0	0
$617$	4.10205	0.165142	0.0825711	−	0.996585i	$-0.473687\pi$
$617$	4.10205	0.165142	0.0825711	+	0.996585i	$0.473687\pi$
$618$	−20.2218	−0.813440
$619$	5.19446	0.208783	0.104392	−	0.994536i	$-0.466710\pi$
$619$	5.19446	0.208783	0.104392	+	0.994536i	$0.466710\pi$
$620$	−5.87141	−0.235801
$621$	14.5202	0.582676
$622$	−2.70915	−0.108627
$623$	5.57625	0.223408
$624$	20.2906	0.812275
$625$	22.6309	0.905234
$626$	−13.8713	−0.554409
$627$	0	0
$628$	3.95069	0.157650
$629$	21.2944	0.849064
$630$	−2.51932	−0.100372
$631$	8.00395	0.318632	0.159316	−	0.987228i	$-0.449071\pi$
$631$	8.00395	0.318632	0.159316	+	0.987228i	$0.449071\pi$
$632$	−16.4894	−0.655913
$633$	8.75540	0.347996
$634$	−3.29134	−0.130716
$635$	−1.64399	−0.0652398
$636$	−54.4737	−2.16002
$637$	−6.88824	−0.272922
$638$	0	0
$639$	19.0289	0.752770
$640$	4.60484	0.182022
$641$	21.9021	0.865082	0.432541	−	0.901614i	$-0.357617\pi$
$641$	21.9021	0.865082	0.432541	+	0.901614i	$0.357617\pi$
$642$	22.6735	0.894852
$643$	−16.5821	−0.653935	−0.326968	−	0.945036i	$-0.606027\pi$
$643$	−16.5821	−0.653935	−0.326968	+	0.945036i	$0.606027\pi$
$644$	41.6593	1.64161
$645$	−5.68852	−0.223985
$646$	−4.72731	−0.185994
$647$	41.7329	1.64069	0.820345	−	0.571868i	$-0.193781\pi$
$647$	41.7329	1.64069	0.820345	+	0.571868i	$0.193781\pi$
$648$	−13.8642	−0.544636
$649$	0	0
$650$	−10.4194	−0.408683
$651$	−67.7492	−2.65530
$652$	34.3129	1.34380
$653$	19.5135	0.763623	0.381812	−	0.924240i	$-0.375300\pi$
$653$	19.5135	0.763623	0.381812	+	0.924240i	$0.375300\pi$
$654$	23.7469	0.928578
$655$	−3.48990	−0.136362
$656$	23.3721	0.912527
$657$	54.0556	2.10891
$658$	−2.63876	−0.102869
$659$	−13.7535	−0.535760	−0.267880	−	0.963452i	$-0.586323\pi$
$659$	−13.7535	−0.535760	−0.267880	+	0.963452i	$0.586323\pi$
$660$	0	0
$661$	−33.7577	−1.31302	−0.656512	−	0.754316i	$-0.727969\pi$
$661$	−33.7577	−1.31302	−0.656512	+	0.754316i	$0.727969\pi$
$662$	−5.14395	−0.199925
$663$	36.8461	1.43098
$664$	2.20870	0.0857141
$665$	2.53967	0.0984843
$666$	−11.7873	−0.456748
$667$	−31.4253	−1.21679
$668$	24.3959	0.943908
$669$	−54.0481	−2.08962
$670$	2.01693	0.0779208
$671$	0	0
$672$	41.9009	1.61636
$673$	−19.6608	−0.757869	−0.378935	−	0.925423i	$-0.623710\pi$
$673$	−19.6608	−0.757869	−0.378935	+	0.925423i	$0.623710\pi$
$674$	−1.06400	−0.0409837
$675$	8.36204	0.321855
$676$	−1.47101	−0.0565774
$677$	−14.6142	−0.561670	−0.280835	−	0.959756i	$-0.590611\pi$
$677$	−14.6142	−0.561670	−0.280835	+	0.959756i	$0.590611\pi$
$678$	4.02707	0.154659
$679$	−32.2211	−1.23653
$680$	3.24072	0.124276
$681$	36.3071	1.39129
$682$	0	0
$683$	−18.4992	−0.707851	−0.353925	−	0.935274i	$-0.615153\pi$
$683$	−18.4992	−0.707851	−0.353925	+	0.935274i	$0.615153\pi$
$684$	−13.0630	−0.499476
$685$	−6.20236	−0.236980
$686$	8.85284	0.338003
$687$	−3.28112	−0.125183
$688$	11.6258	0.443230
$689$	47.1697	1.79702
$690$	−5.01034	−0.190740
$691$	−6.87925	−0.261699	−0.130849	−	0.991402i	$-0.541770\pi$
$691$	−6.87925	−0.261699	−0.130849	+	0.991402i	$0.541770\pi$
$692$	30.2979	1.15175
$693$	0	0
$694$	−13.7501	−0.521948
$695$	2.62701	0.0996483
$696$	−20.4511	−0.775196
$697$	42.4418	1.60760
$698$	−8.63179	−0.326718
$699$	−12.8111	−0.484561
$700$	23.9912	0.906781
$701$	−0.963721	−0.0363993	−0.0181996	−	0.999834i	$-0.505793\pi$
$701$	−0.963721	−0.0363993	−0.0181996	+	0.999834i	$0.505793\pi$
$702$	−3.71878	−0.140356
$703$	11.8825	0.448157
$704$	0	0
$705$	−1.58429	−0.0596679
$706$	−4.02795	−0.151594
$707$	49.0101	1.84321
$708$	33.6238	1.26366
$709$	−31.7803	−1.19353	−0.596766	−	0.802415i	$-0.703548\pi$
$709$	−31.7803	−1.19353	−0.596766	+	0.802415i	$0.703548\pi$
$710$	−1.19720	−0.0449303
$711$	−28.5629	−1.07119
$712$	3.97052	0.148802
$713$	−74.1264	−2.77606
$714$	16.9949	0.636018
$715$	0	0
$716$	−42.4044	−1.58473
$717$	53.4676	1.99678
$718$	1.19068	0.0444360
$719$	18.7549	0.699440	0.349720	−	0.936854i	$-0.386277\pi$
$719$	18.7549	0.699440	0.349720	+	0.936854i	$0.386277\pi$
$720$	3.09132	0.115207
$721$	−40.3184	−1.50154
$722$	8.33902	0.310346
$723$	43.7470	1.62697
$724$	31.8576	1.18398
$725$	−18.0975	−0.672125
$726$	0	0
$727$	−33.2521	−1.23325	−0.616625	−	0.787257i	$-0.711501\pi$
$727$	−33.2521	−1.23325	−0.616625	+	0.787257i	$0.711501\pi$
$728$	−23.4760	−0.870080
$729$	−37.3995	−1.38517
$730$	−3.40092	−0.125874
$731$	21.1115	0.780838
$732$	4.30292	0.159040
$733$	−12.2406	−0.452116	−0.226058	−	0.974114i	$-0.572584\pi$
$733$	−12.2406	−0.452116	−0.226058	+	0.974114i	$0.572584\pi$
$734$	−4.33788	−0.160114
$735$	−1.90753	−0.0703603
$736$	45.8450	1.68987
$737$	0	0
$738$	−23.4931	−0.864795
$739$	23.5401	0.865935	0.432967	−	0.901410i	$-0.357466\pi$
$739$	23.5401	0.865935	0.432967	+	0.901410i	$0.357466\pi$
$740$	−3.70212	−0.136093
$741$	20.5605	0.755308
$742$	21.7566	0.798709
$743$	11.3637	0.416892	0.208446	−	0.978034i	$-0.433159\pi$
$743$	11.3637	0.416892	0.208446	+	0.978034i	$0.433159\pi$
$744$	−48.2403	−1.76858
$745$	−3.75753	−0.137665
$746$	−13.4400	−0.492074
$747$	3.82591	0.139983
$748$	0	0
$749$	45.2067	1.65182
$750$	−5.86597	−0.214195
$751$	−18.7127	−0.682838	−0.341419	−	0.939911i	$-0.610907\pi$
$751$	−18.7127	−0.682838	−0.341419	+	0.939911i	$0.610907\pi$
$752$	3.23787	0.118073
$753$	−3.50674	−0.127793
$754$	8.04835	0.293104
$755$	−0.972994	−0.0354109
$756$	8.56266	0.311421
$757$	−6.69094	−0.243186	−0.121593	−	0.992580i	$-0.538800\pi$
$757$	−6.69094	−0.243186	−0.121593	+	0.992580i	$0.538800\pi$
$758$	4.07517	0.148017
$759$	0	0
$760$	1.80836	0.0655959
$761$	26.0474	0.944216	0.472108	−	0.881541i	$-0.343493\pi$
$761$	26.0474	0.944216	0.472108	+	0.881541i	$0.343493\pi$
$762$	−6.13878	−0.222384
$763$	47.3469	1.71407
$764$	20.4038	0.738183
$765$	5.61358	0.202960
$766$	−2.50932	−0.0906653
$767$	−29.1154	−1.05130
$768$	11.6876	0.421740
$769$	−3.45334	−0.124531	−0.0622653	−	0.998060i	$-0.519832\pi$
$769$	−3.45334	−0.124531	−0.0622653	+	0.998060i	$0.519832\pi$
$770$	0	0
$771$	−21.9110	−0.789106
$772$	9.60477	0.345683
$773$	13.0636	0.469865	0.234932	−	0.972012i	$-0.424513\pi$
$773$	13.0636	0.469865	0.234932	+	0.972012i	$0.424513\pi$
$774$	−11.6860	−0.420046
$775$	−42.6887	−1.53342
$776$	−22.9428	−0.823598
$777$	−42.7181	−1.53250
$778$	−12.5010	−0.448184
$779$	23.6829	0.848529
$780$	−6.40583	−0.229366
$781$	0	0
$782$	18.5946	0.664942
$783$	−6.45916	−0.230832
$784$	3.89848	0.139232
$785$	−0.947353	−0.0338125
$786$	−13.0315	−0.464820
$787$	50.1924	1.78917	0.894583	−	0.446902i	$-0.147473\pi$
$787$	50.1924	1.78917	0.894583	+	0.446902i	$0.147473\pi$
$788$	−4.74610	−0.169073
$789$	30.1808	1.07447
$790$	1.79704	0.0639360
$791$	8.02922	0.285486
$792$	0	0
$793$	−3.72597	−0.132313
$794$	−15.8412	−0.562183
$795$	13.0625	0.463280
$796$	−32.9851	−1.16913
$797$	4.72067	0.167215	0.0836073	−	0.996499i	$-0.473356\pi$
$797$	4.72067	0.167215	0.0836073	+	0.996499i	$0.473356\pi$
$798$	9.48333	0.335706
$799$	5.87971	0.208009
$800$	26.4017	0.933441
$801$	6.87774	0.243013
$802$	6.97135	0.246167
$803$	0	0
$804$	−37.5971	−1.32595
$805$	−9.98967	−0.352090
$806$	18.9846	0.668703
$807$	−63.0310	−2.21880
$808$	34.8973	1.22768
$809$	1.42195	0.0499931	0.0249966	−	0.999688i	$-0.492043\pi$
$809$	1.42195	0.0499931	0.0249966	+	0.999688i	$0.492043\pi$
$810$	1.51094	0.0530891
$811$	29.1343	1.02304	0.511522	−	0.859270i	$-0.329082\pi$
$811$	29.1343	1.02304	0.511522	+	0.859270i	$0.329082\pi$
$812$	−18.5317	−0.650335
$813$	−68.4929	−2.40215
$814$	0	0
$815$	−8.22806	−0.288216
$816$	−20.8535	−0.730019
$817$	11.7804	0.412146
$818$	−1.41188	−0.0493651
$819$	−40.6652	−1.42096
$820$	−7.37866	−0.257674
$821$	−38.4025	−1.34026	−0.670128	−	0.742245i	$-0.733761\pi$
$821$	−38.4025	−1.34026	−0.670128	+	0.742245i	$0.733761\pi$
$822$	−23.1600	−0.807799
$823$	−14.8780	−0.518616	−0.259308	−	0.965795i	$-0.583494\pi$
$823$	−14.8780	−0.518616	−0.259308	+	0.965795i	$0.583494\pi$
$824$	−28.7084	−1.00011
$825$	0	0
$826$	−13.4292	−0.467262
$827$	4.76748	0.165782	0.0828908	−	0.996559i	$-0.473585\pi$
$827$	4.76748	0.165782	0.0828908	+	0.996559i	$0.473585\pi$
$828$	51.3825	1.78567
$829$	23.3096	0.809576	0.404788	−	0.914410i	$-0.367345\pi$
$829$	23.3096	0.809576	0.404788	+	0.914410i	$0.367345\pi$
$830$	−0.240708	−0.00835510
$831$	−22.5963	−0.783858
$832$	3.97293	0.137737
$833$	7.07932	0.245284
$834$	9.80946	0.339674
$835$	−5.85002	−0.202448
$836$	0	0
$837$	−15.2360	−0.526632
$838$	7.06217	0.243959
$839$	30.2730	1.04514	0.522570	−	0.852596i	$-0.324973\pi$
$839$	30.2730	1.04514	0.522570	+	0.852596i	$0.324973\pi$
$840$	−6.50112	−0.224310
$841$	−15.0208	−0.517958
$842$	15.5191	0.534822
$843$	2.09132	0.0720289
$844$	5.64911	0.194450
$845$	0.352741	0.0121347
$846$	−3.25464	−0.111897
$847$	0	0
$848$	−26.6963	−0.916754
$849$	−59.4513	−2.04036
$850$	10.7085	0.367297
$851$	−46.7392	−1.60220
$852$	22.3168	0.764561
$853$	−42.1183	−1.44210	−0.721052	−	0.692881i	$-0.756341\pi$
$853$	−42.1183	−1.44210	−0.721052	+	0.692881i	$0.756341\pi$
$854$	−1.71857	−0.0588082
$855$	3.13243	0.107127
$856$	32.1891	1.10020
$857$	54.9133	1.87580	0.937902	−	0.346901i	$-0.112766\pi$
$857$	54.9133	1.87580	0.937902	+	0.346901i	$0.112766\pi$
$858$	0	0
$859$	39.1387	1.33540	0.667698	−	0.744433i	$-0.267280\pi$
$859$	39.1387	1.33540	0.667698	+	0.744433i	$0.267280\pi$
$860$	−3.67032	−0.125157
$861$	−85.1412	−2.90161
$862$	−5.99968	−0.204350
$863$	33.8189	1.15121	0.575604	−	0.817729i	$-0.304767\pi$
$863$	33.8189	1.15121	0.575604	+	0.817729i	$0.304767\pi$
$864$	9.42300	0.320577
$865$	−7.26527	−0.247026
$866$	9.36677	0.318296
$867$	6.03315	0.204896
$868$	−43.7128	−1.48371
$869$	0	0
$870$	2.22880	0.0755633
$871$	32.5560	1.10312
$872$	33.7130	1.14167
$873$	−39.7415	−1.34505
$874$	10.3760	0.350973
$875$	−11.6956	−0.395385
$876$	63.3957	2.14194
$877$	−46.1200	−1.55736	−0.778681	−	0.627420i	$-0.784111\pi$
$877$	−46.1200	−1.55736	−0.778681	+	0.627420i	$0.784111\pi$
$878$	9.24263	0.311924
$879$	32.1757	1.08526
$880$	0	0
$881$	−0.397406	−0.0133889	−0.00669447	−	0.999978i	$-0.502131\pi$
$881$	−0.397406	−0.0133889	−0.00669447	+	0.999978i	$0.502131\pi$
$882$	−3.91868	−0.131949
$883$	−24.4062	−0.821334	−0.410667	−	0.911785i	$-0.634704\pi$
$883$	−24.4062	−0.821334	−0.410667	+	0.911785i	$0.634704\pi$
$884$	23.7737	0.799594
$885$	−8.06281	−0.271029
$886$	−0.279030	−0.00937420
$887$	−5.37039	−0.180320	−0.0901601	−	0.995927i	$-0.528738\pi$
$887$	−5.37039	−0.180320	−0.0901601	+	0.995927i	$0.528738\pi$
$888$	−30.4171	−1.02073
$889$	−12.2396	−0.410502
$890$	−0.432715	−0.0145046
$891$	0	0
$892$	−34.8726	−1.16762
$893$	3.28093	0.109792
$894$	−14.0309	−0.469263
$895$	10.1684	0.339891
$896$	34.2832	1.14532
$897$	−80.8735	−2.70029
$898$	18.2138	0.607801
$899$	32.9744	1.09976
$900$	29.5907	0.986357
$901$	−48.4783	−1.61504
$902$	0	0
$903$	−42.3512	−1.40936
$904$	5.71714	0.190149
$905$	−7.63929	−0.253939
$906$	−3.63323	−0.120706
$907$	−36.0688	−1.19765	−0.598823	−	0.800881i	$-0.704365\pi$
$907$	−36.0688	−1.19765	−0.598823	+	0.800881i	$0.704365\pi$
$908$	23.4259	0.777415
$909$	60.4491	2.00497
$910$	2.55846	0.0848122
$911$	−36.6550	−1.21443	−0.607217	−	0.794536i	$-0.707714\pi$
$911$	−36.6550	−1.21443	−0.607217	+	0.794536i	$0.707714\pi$
$912$	−11.6365	−0.385322
$913$	0	0
$914$	5.23778	0.173250
$915$	−1.03182	−0.0341108
$916$	−2.11703	−0.0699486
$917$	−25.9825	−0.858016
$918$	3.82195	0.126143
$919$	23.9036	0.788507	0.394253	−	0.919002i	$-0.371003\pi$
$919$	23.9036	0.788507	0.394253	+	0.919002i	$0.371003\pi$
$920$	−7.11307	−0.234511
$921$	4.11412	0.135565
$922$	−7.52636	−0.247868
$923$	−19.3245	−0.636073
$924$	0	0
$925$	−26.9166	−0.885013
$926$	−1.39815	−0.0459462
$927$	−49.7288	−1.63331
$928$	−20.3937	−0.669455
$929$	−42.0859	−1.38079	−0.690397	−	0.723431i	$-0.742564\pi$
$929$	−42.0859	−1.38079	−0.690397	+	0.723431i	$0.742564\pi$
$930$	5.25732	0.172394
$931$	3.95033	0.129467
$932$	−8.26592	−0.270759
$933$	−12.1098	−0.396456
$934$	−24.1077	−0.788828
$935$	0	0
$936$	−28.9554	−0.946435
$937$	45.3487	1.48148	0.740739	−	0.671793i	$-0.234476\pi$
$937$	45.3487	1.48148	0.740739	+	0.671793i	$0.234476\pi$
$938$	15.0161	0.490294
$939$	−62.0041	−2.02343
$940$	−1.02221	−0.0333408
$941$	23.8945	0.778938	0.389469	−	0.921040i	$-0.372659\pi$
$941$	23.8945	0.778938	0.389469	+	0.921040i	$0.372659\pi$
$942$	−3.53748	−0.115257
$943$	−93.1555	−3.03356
$944$	16.4782	0.536321
$945$	−2.05328	−0.0667932
$946$	0	0
$947$	37.3965	1.21522	0.607612	−	0.794234i	$-0.292127\pi$
$947$	37.3965	1.21522	0.607612	+	0.794234i	$0.292127\pi$
$948$	−33.4982	−1.08797
$949$	−54.8954	−1.78198
$950$	5.97543	0.193868
$951$	−14.7121	−0.477073
$952$	24.1273	0.781970
$953$	−35.7070	−1.15666	−0.578332	−	0.815802i	$-0.696296\pi$
$953$	−35.7070	−1.15666	−0.578332	+	0.815802i	$0.696296\pi$
$954$	26.8346	0.868801
$955$	−4.89272	−0.158325
$956$	34.4981	1.11575
$957$	0	0
$958$	−8.88837	−0.287170
$959$	−46.1768	−1.49113
$960$	1.10021	0.0355090
$961$	46.7804	1.50905
$962$	11.9704	0.385941
$963$	55.7580	1.79678
$964$	28.2262	0.909105
$965$	−2.30317	−0.0741417
$966$	−37.3021	−1.20018
$967$	10.9377	0.351732	0.175866	−	0.984414i	$-0.443727\pi$
$967$	10.9377	0.351732	0.175866	+	0.984414i	$0.443727\pi$
$968$	0	0
$969$	−21.1309	−0.678821
$970$	2.50035	0.0802813
$971$	35.5660	1.14137	0.570683	−	0.821170i	$-0.306678\pi$
$971$	35.5660	1.14137	0.570683	+	0.821170i	$0.306678\pi$
$972$	−36.8006	−1.18038
$973$	19.5582	0.627007
$974$	0.124594	0.00399226
$975$	−46.5743	−1.49157
$976$	2.10876	0.0674997
$977$	15.8326	0.506530	0.253265	−	0.967397i	$-0.418496\pi$
$977$	15.8326	0.506530	0.253265	+	0.967397i	$0.418496\pi$
$978$	−30.7242	−0.982450
$979$	0	0
$980$	−1.23077	−0.0393154
$981$	58.3977	1.86449
$982$	6.59565	0.210476
$983$	35.9127	1.14544	0.572719	−	0.819752i	$-0.305888\pi$
$983$	35.9127	1.14544	0.572719	+	0.819752i	$0.305888\pi$
$984$	−60.6241	−1.93263
$985$	1.13809	0.0362625
$986$	−8.27162	−0.263422
$987$	−11.7951	−0.375443
$988$	13.2659	0.422046
$989$	−46.3377	−1.47345
$990$	0	0
$991$	41.1944	1.30858	0.654291	−	0.756243i	$-0.272967\pi$
$991$	41.1944	1.30858	0.654291	+	0.756243i	$0.272967\pi$
$992$	−48.1049	−1.52733
$993$	−22.9932	−0.729667
$994$	−8.91323	−0.282710
$995$	7.90965	0.250753
$996$	4.48698	0.142175
$997$	−28.4340	−0.900512	−0.450256	−	0.892899i	$-0.648667\pi$
$997$	−28.4340	−0.900512	−0.450256	+	0.892899i	$0.648667\pi$
$998$	−19.5740	−0.619605
$999$	−9.60678	−0.303945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.25		64
11.5	even	5		671.2.j.c.245.20	✓	128
11.9	even	5		671.2.j.c.367.20	yes	128
11.10	odd	2		7381.2.a.u.1.40		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.20	✓	128	11.5	even	5
671.2.j.c.367.20	yes	128	11.9	even	5
7381.2.a.u.1.40		64	11.10	odd	2
7381.2.a.v.1.25		64	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)

\(f(q)\)	\(=\)	\(q-0.577732 q^{2} -2.58243 q^{3} -1.66623 q^{4} +0.399552 q^{5} +1.49196 q^{6} +2.97468 q^{7} +2.11810 q^{8} +3.66897 q^{9} +O(q^{10})\)	\(q-0.577732 q^{2} -2.58243 q^{3} -1.66623 q^{4} +0.399552 q^{5} +1.49196 q^{6} +2.97468 q^{7} +2.11810 q^{8} +3.66897 q^{9} -0.230834 q^{10} +4.30292 q^{12} -3.72597 q^{13} -1.71857 q^{14} -1.03182 q^{15} +2.10876 q^{16} +3.82933 q^{17} -2.11968 q^{18} +2.13680 q^{19} -0.665744 q^{20} -7.68191 q^{21} -8.40500 q^{23} -5.46985 q^{24} -4.84036 q^{25} +2.15261 q^{26} -1.72757 q^{27} -4.95648 q^{28} +3.73888 q^{29} +0.596114 q^{30} +8.81932 q^{31} -5.45449 q^{32} -2.21233 q^{34} +1.18854 q^{35} -6.11333 q^{36} +5.56087 q^{37} -1.23450 q^{38} +9.62207 q^{39} +0.846290 q^{40} +11.0833 q^{41} +4.43809 q^{42} +5.51311 q^{43} +1.46594 q^{45} +4.85584 q^{46} +1.53544 q^{47} -5.44573 q^{48} +1.84871 q^{49} +2.79643 q^{50} -9.88900 q^{51} +6.20830 q^{52} -12.6597 q^{53} +0.998071 q^{54} +6.30066 q^{56} -5.51816 q^{57} -2.16007 q^{58} +7.81419 q^{59} +1.71924 q^{60} +1.00000 q^{61} -5.09521 q^{62} +10.9140 q^{63} -1.06628 q^{64} -1.48872 q^{65} -8.73758 q^{67} -6.38053 q^{68} +21.7054 q^{69} -0.686657 q^{70} +5.18643 q^{71} +7.77123 q^{72} +14.7332 q^{73} -3.21270 q^{74} +12.4999 q^{75} -3.56040 q^{76} -5.55898 q^{78} -7.78500 q^{79} +0.842559 q^{80} -6.54558 q^{81} -6.40320 q^{82} +1.04278 q^{83} +12.7998 q^{84} +1.53002 q^{85} -3.18510 q^{86} -9.65541 q^{87} +1.87457 q^{89} -0.846923 q^{90} -11.0836 q^{91} +14.0046 q^{92} -22.7753 q^{93} -0.887073 q^{94} +0.853764 q^{95} +14.0859 q^{96} -10.8318 q^{97} -1.06806 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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