LMFDB - Embedded newform 383.2.a.c.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [383,2,Mod(1,383)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(383, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("383.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	383.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:	$3.05827039742$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	383.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.44206 q^{2} -1.30351 q^{3} +3.96367 q^{4} +4.41754 q^{5} -3.18325 q^{6} -1.22662 q^{7} +4.79540 q^{8} -1.30086 q^{9} +10.7879 q^{10} -4.93420 q^{11} -5.16667 q^{12} +2.75972 q^{13} -2.99548 q^{14} -5.75830 q^{15} +3.78332 q^{16} -3.42121 q^{17} -3.17679 q^{18} +2.87116 q^{19} +17.5097 q^{20} +1.59891 q^{21} -12.0496 q^{22} -6.71149 q^{23} -6.25084 q^{24} +14.5147 q^{25} +6.73941 q^{26} +5.60622 q^{27} -4.86191 q^{28} +5.97613 q^{29} -14.0621 q^{30} -0.194994 q^{31} -0.351691 q^{32} +6.43177 q^{33} -8.35481 q^{34} -5.41865 q^{35} -5.15619 q^{36} -4.58157 q^{37} +7.01154 q^{38} -3.59732 q^{39} +21.1839 q^{40} -8.40654 q^{41} +3.90464 q^{42} +2.87579 q^{43} -19.5575 q^{44} -5.74663 q^{45} -16.3899 q^{46} -3.79223 q^{47} -4.93159 q^{48} -5.49540 q^{49} +35.4457 q^{50} +4.45958 q^{51} +10.9386 q^{52} +9.85864 q^{53} +13.6907 q^{54} -21.7970 q^{55} -5.88213 q^{56} -3.74258 q^{57} +14.5941 q^{58} -0.738043 q^{59} -22.8240 q^{60} -3.24433 q^{61} -0.476188 q^{62} +1.59567 q^{63} -8.42549 q^{64} +12.1912 q^{65} +15.7068 q^{66} +9.93407 q^{67} -13.5605 q^{68} +8.74849 q^{69} -13.2327 q^{70} +12.8706 q^{71} -6.23816 q^{72} -7.87147 q^{73} -11.1885 q^{74} -18.9200 q^{75} +11.3803 q^{76} +6.05238 q^{77} -8.78488 q^{78} -6.52390 q^{79} +16.7130 q^{80} -3.40516 q^{81} -20.5293 q^{82} -4.20664 q^{83} +6.33755 q^{84} -15.1133 q^{85} +7.02286 q^{86} -7.78994 q^{87} -23.6614 q^{88} -11.1609 q^{89} -14.0336 q^{90} -3.38513 q^{91} -26.6021 q^{92} +0.254177 q^{93} -9.26086 q^{94} +12.6835 q^{95} +0.458433 q^{96} +9.67947 q^{97} -13.4201 q^{98} +6.41872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} + 2 q^{3} + 29 q^{4} + 3 q^{5} + q^{6} + 17 q^{7} + 15 q^{8} + 34 q^{9} + q^{10} - 7 q^{12} + 28 q^{13} - 8 q^{14} - 2 q^{15} + 35 q^{16} + 16 q^{17} + 19 q^{18} + 13 q^{19} - 4 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) $ 24 * q + 5 * q^2 + 2 * q^3 + 29 * q^4 + 3 * q^5 + q^6 + 17 * q^7 + 15 * q^8 + 34 * q^9 + q^10 - 7 * q^12 + 28 * q^13 - 8 * q^14 - 2 * q^15 + 35 * q^16 + 16 * q^17 + 19 * q^18 + 13 * q^19 - 4 * q^20 - 4 * q^21 + 12 * q^22 + 7 * q^23 - 11 * q^24 + 67 * q^25 - 14 * q^26 - 10 * q^27 + 39 * q^28 - 2 * q^29 - 17 * q^30 + 20 * q^32 + 24 * q^33 - 18 * q^34 - 10 * q^35 + 20 * q^36 + 35 * q^37 - 5 * q^38 - 12 * q^39 - 36 * q^40 - 36 * q^42 + 34 * q^43 - 36 * q^44 - 27 * q^45 - 17 * q^46 - 3 * q^47 - 56 * q^48 + 49 * q^49 - 20 * q^50 - 28 * q^51 + 29 * q^52 - 9 * q^53 - 53 * q^54 + 10 * q^55 - 47 * q^56 + 47 * q^57 + 12 * q^58 - 6 * q^59 - 83 * q^60 + 3 * q^61 - 58 * q^62 + 13 * q^63 + 15 * q^64 + 8 * q^65 - 71 * q^66 + 42 * q^67 - 23 * q^68 - 30 * q^69 - 59 * q^70 - 13 * q^71 + 16 * q^72 + 83 * q^73 - 45 * q^74 - 65 * q^75 + 4 * q^76 - 21 * q^77 - 60 * q^78 - 3 * q^79 - 93 * q^80 + 28 * q^81 - 13 * q^82 - 23 * q^83 - 148 * q^84 + 52 * q^85 - 43 * q^86 - 5 * q^87 - 25 * q^88 - 38 * q^89 - 142 * q^90 - 17 * q^91 - 61 * q^92 + 17 * q^93 - 71 * q^94 - 66 * q^95 - 101 * q^96 + 63 * q^97 - 29 * q^98 - 54 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.44206	1.72680	0.863399	−	0.504521i	$-0.168331\pi$
$2$	2.44206	1.72680	0.863399	+	0.504521i	$0.168331\pi$
$3$	−1.30351	−0.752581	−0.376291	−	0.926502i	$-0.622801\pi$
$3$	−1.30351	−0.752581	−0.376291	+	0.926502i	$0.622801\pi$
$4$	3.96367	1.98183
$5$	4.41754	1.97558	0.987792	−	0.155776i	$-0.0497879\pi$
$5$	4.41754	1.97558	0.987792	+	0.155776i	$0.0497879\pi$
$6$	−3.18325	−1.29956
$7$	−1.22662	−0.463619	−0.231809	−	0.972761i	$-0.574465\pi$
$7$	−1.22662	−0.463619	−0.231809	+	0.972761i	$0.574465\pi$
$8$	4.79540	1.69543
$9$	−1.30086	−0.433622
$10$	10.7879	3.41144
$11$	−4.93420	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$11$	−4.93420	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$12$	−5.16667	−1.49149
$13$	2.75972	0.765409	0.382705	−	0.923871i	$-0.374993\pi$
$13$	2.75972	0.765409	0.382705	+	0.923871i	$0.374993\pi$
$14$	−2.99548	−0.800576
$15$	−5.75830	−1.48679
$16$	3.78332	0.945830
$17$	−3.42121	−0.829766	−0.414883	−	0.909875i	$-0.636177\pi$
$17$	−3.42121	−0.829766	−0.414883	+	0.909875i	$0.636177\pi$
$18$	−3.17679	−0.748777
$19$	2.87116	0.658689	0.329344	−	0.944210i	$-0.393172\pi$
$19$	2.87116	0.658689	0.329344	+	0.944210i	$0.393172\pi$
$20$	17.5097	3.91528
$21$	1.59891	0.348911
$22$	−12.0496	−2.56899
$23$	−6.71149	−1.39944	−0.699721	−	0.714416i	$-0.746693\pi$
$23$	−6.71149	−1.39944	−0.699721	+	0.714416i	$0.746693\pi$
$24$	−6.25084	−1.27595
$25$	14.5147	2.90293
$26$	6.73941	1.32171
$27$	5.60622	1.07892
$28$	−4.86191	−0.918815
$29$	5.97613	1.10974	0.554870	−	0.831937i	$-0.312768\pi$
$29$	5.97613	1.10974	0.554870	+	0.831937i	$0.312768\pi$
$30$	−14.0621	−2.56738
$31$	−0.194994	−0.0350220	−0.0175110	−	0.999847i	$-0.505574\pi$
$31$	−0.194994	−0.0350220	−0.0175110	+	0.999847i	$0.505574\pi$
$32$	−0.351691	−0.0621709
$33$	6.43177	1.11963
$34$	−8.35481	−1.43284
$35$	−5.41865	−0.915918
$36$	−5.15619	−0.859366
$37$	−4.58157	−0.753206	−0.376603	−	0.926375i	$-0.622908\pi$
$37$	−4.58157	−0.753206	−0.376603	+	0.926375i	$0.622908\pi$
$38$	7.01154	1.13742
$39$	−3.59732	−0.576032
$40$	21.1839	3.34946
$41$	−8.40654	−1.31288	−0.656441	−	0.754378i	$-0.727939\pi$
$41$	−8.40654	−1.31288	−0.656441	+	0.754378i	$0.727939\pi$
$42$	3.90464	0.602499
$43$	2.87579	0.438554	0.219277	−	0.975663i	$-0.429630\pi$
$43$	2.87579	0.438554	0.219277	+	0.975663i	$0.429630\pi$
$44$	−19.5575	−2.94840
$45$	−5.74663	−0.856656
$46$	−16.3899	−2.41656
$47$	−3.79223	−0.553153	−0.276577	−	0.960992i	$-0.589200\pi$
$47$	−3.79223	−0.553153	−0.276577	+	0.960992i	$0.589200\pi$
$48$	−4.93159	−0.711814
$49$	−5.49540	−0.785058
$50$	35.4457	5.01278
$51$	4.45958	0.624466
$52$	10.9386	1.51691
$53$	9.85864	1.35419	0.677094	−	0.735897i	$-0.263239\pi$
$53$	9.85864	1.35419	0.677094	+	0.735897i	$0.263239\pi$
$54$	13.6907	1.86307
$55$	−21.7970	−2.93911
$56$	−5.88213	−0.786033
$57$	−3.74258	−0.495717
$58$	14.5941	1.91630
$59$	−0.738043	−0.0960850	−0.0480425	−	0.998845i	$-0.515298\pi$
$59$	−0.738043	−0.0960850	−0.0480425	+	0.998845i	$0.515298\pi$
$60$	−22.8240	−2.94657
$61$	−3.24433	−0.415394	−0.207697	−	0.978193i	$-0.566597\pi$
$61$	−3.24433	−0.415394	−0.207697	+	0.978193i	$0.566597\pi$
$62$	−0.476188	−0.0604760
$63$	1.59567	0.201035
$64$	−8.42549	−1.05319
$65$	12.1912	1.51213
$66$	15.7068	1.93337
$67$	9.93407	1.21364	0.606820	−	0.794839i	$-0.292445\pi$
$67$	9.93407	1.21364	0.606820	+	0.794839i	$0.292445\pi$
$68$	−13.5605	−1.64446
$69$	8.74849	1.05319
$70$	−13.2327	−1.58161
$71$	12.8706	1.52745	0.763727	−	0.645539i	$-0.223367\pi$
$71$	12.8706	1.52745	0.763727	+	0.645539i	$0.223367\pi$
$72$	−6.23816	−0.735174
$73$	−7.87147	−0.921286	−0.460643	−	0.887586i	$-0.652381\pi$
$73$	−7.87147	−0.921286	−0.460643	+	0.887586i	$0.652381\pi$
$74$	−11.1885	−1.30063
$75$	−18.9200	−2.18469
$76$	11.3803	1.30541
$77$	6.05238	0.689733
$78$	−8.78488	−0.994692
$79$	−6.52390	−0.733997	−0.366998	−	0.930222i	$-0.619615\pi$
$79$	−6.52390	−0.733997	−0.366998	+	0.930222i	$0.619615\pi$
$80$	16.7130	1.86857
$81$	−3.40516	−0.378351
$82$	−20.5293	−2.26708
$83$	−4.20664	−0.461738	−0.230869	−	0.972985i	$-0.574157\pi$
$83$	−4.20664	−0.461738	−0.230869	+	0.972985i	$0.574157\pi$
$84$	6.33755	0.691483
$85$	−15.1133	−1.63927
$86$	7.02286	0.757294
$87$	−7.78994	−0.835169
$88$	−23.6614	−2.52232
$89$	−11.1609	−1.18305	−0.591524	−	0.806287i	$-0.701474\pi$
$89$	−11.1609	−1.18305	−0.591524	+	0.806287i	$0.701474\pi$
$90$	−14.0336	−1.47927
$91$	−3.38513	−0.354858
$92$	−26.6021	−2.77346
$93$	0.254177	0.0263569
$94$	−9.26086	−0.955185
$95$	12.6835	1.30130
$96$	0.458433	0.0467886
$97$	9.67947	0.982801	0.491401	−	0.870934i	$-0.336485\pi$
$97$	9.67947	0.982801	0.491401	+	0.870934i	$0.336485\pi$
$98$	−13.4201	−1.35564
$99$	6.41872	0.645106
$100$	57.5313	5.75313
$101$	18.4717	1.83800	0.919002	−	0.394253i	$-0.128996\pi$
$101$	18.4717	1.83800	0.919002	+	0.394253i	$0.128996\pi$
$102$	10.8906	1.07833
$103$	7.23595	0.712980	0.356490	−	0.934299i	$-0.383973\pi$
$103$	7.23595	0.712980	0.356490	+	0.934299i	$0.383973\pi$
$104$	13.2340	1.29770
$105$	7.06325	0.689303
$106$	24.0754	2.33841
$107$	−5.16239	−0.499067	−0.249533	−	0.968366i	$-0.580277\pi$
$107$	−5.16239	−0.499067	−0.249533	+	0.968366i	$0.580277\pi$
$108$	22.2212	2.13823
$109$	9.36439	0.896946	0.448473	−	0.893796i	$-0.351968\pi$
$109$	9.36439	0.896946	0.448473	+	0.893796i	$0.351968\pi$
$110$	−53.2297	−5.07525
$111$	5.97212	0.566849
$112$	−4.64070	−0.438505
$113$	−1.59371	−0.149924	−0.0749620	−	0.997186i	$-0.523884\pi$
$113$	−1.59371	−0.149924	−0.0749620	+	0.997186i	$0.523884\pi$
$114$	−9.13961	−0.856003
$115$	−29.6483	−2.76472
$116$	23.6874	2.19932
$117$	−3.59003	−0.331898
$118$	−1.80235	−0.165919
$119$	4.19653	0.384695
$120$	−27.6133	−2.52074
$121$	13.3463	1.21330
$122$	−7.92286	−0.717302
$123$	10.9580	0.988050
$124$	−0.772893	−0.0694078
$125$	42.0315	3.75941
$126$	3.89672	0.347147
$127$	17.2146	1.52754	0.763772	−	0.645486i	$-0.223345\pi$
$127$	17.2146	1.52754	0.763772	+	0.645486i	$0.223345\pi$
$128$	−19.8722	−1.75647
$129$	−3.74862	−0.330047
$130$	29.7716	2.61114
$131$	−3.66928	−0.320587	−0.160293	−	0.987069i	$-0.551244\pi$
$131$	−3.66928	−0.320587	−0.160293	+	0.987069i	$0.551244\pi$
$132$	25.4934	2.21891
$133$	−3.52182	−0.305381
$134$	24.2596	2.09571
$135$	24.7657	2.13149
$136$	−16.4061	−1.40681
$137$	−19.7407	−1.68656	−0.843279	−	0.537476i	$-0.819378\pi$
$137$	−19.7407	−1.68656	−0.843279	+	0.537476i	$0.819378\pi$
$138$	21.3643	1.81865
$139$	−4.32368	−0.366730	−0.183365	−	0.983045i	$-0.558699\pi$
$139$	−4.32368	−0.366730	−0.183365	+	0.983045i	$0.558699\pi$
$140$	−21.4777	−1.81520
$141$	4.94320	0.416293
$142$	31.4307	2.63761
$143$	−13.6170	−1.13871
$144$	−4.92159	−0.410132
$145$	26.3998	2.19238
$146$	−19.2226	−1.59087
$147$	7.16331	0.590819
$148$	−18.1598	−1.49273
$149$	−1.16167	−0.0951676	−0.0475838	−	0.998867i	$-0.515152\pi$
$149$	−1.16167	−0.0951676	−0.0475838	+	0.998867i	$0.515152\pi$
$150$	−46.2038	−3.77253
$151$	20.2459	1.64758	0.823792	−	0.566892i	$-0.191854\pi$
$151$	20.2459	1.64758	0.823792	+	0.566892i	$0.191854\pi$
$152$	13.7683	1.11676
$153$	4.45054	0.359804
$154$	14.7803	1.19103
$155$	−0.861396	−0.0691890
$156$	−14.2586	−1.14160
$157$	6.68344	0.533397	0.266698	−	0.963780i	$-0.414067\pi$
$157$	6.68344	0.533397	0.266698	+	0.963780i	$0.414067\pi$
$158$	−15.9318	−1.26746
$159$	−12.8508	−1.01914
$160$	−1.55361	−0.122824
$161$	8.23245	0.648808
$162$	−8.31560	−0.653335
$163$	−0.00663327	−0.000519558 0	−0.000259779	−	1.00000i	$-0.500083\pi$
$163$	−0.00663327	−0.000519558 0	−0.000259779		1.00000i	$0.500083\pi$
$164$	−33.3207	−2.60191
$165$	28.4126	2.21192
$166$	−10.2729	−0.797329
$167$	12.2768	0.950007	0.475004	−	0.879984i	$-0.342447\pi$
$167$	12.2768	0.950007	0.475004	+	0.879984i	$0.342447\pi$
$168$	7.66741	0.591553
$169$	−5.38394	−0.414149
$170$	−36.9077	−2.83069
$171$	−3.73499	−0.285622
$172$	11.3987	0.869141
$173$	6.44792	0.490226	0.245113	−	0.969494i	$-0.421175\pi$
$173$	6.44792	0.490226	0.245113	+	0.969494i	$0.421175\pi$
$174$	−19.0235	−1.44217
$175$	−17.8040	−1.34586
$176$	−18.6676	−1.40713
$177$	0.962045	0.0723117
$178$	−27.2555	−2.04289
$179$	5.75748	0.430334	0.215167	−	0.976577i	$-0.430970\pi$
$179$	5.75748	0.430334	0.215167	+	0.976577i	$0.430970\pi$
$180$	−22.7777	−1.69775
$181$	−11.7080	−0.870249	−0.435124	−	0.900370i	$-0.643296\pi$
$181$	−11.7080	−0.870249	−0.435124	+	0.900370i	$0.643296\pi$
$182$	−8.26670	−0.612769
$183$	4.22902	0.312618
$184$	−32.1843	−2.37265
$185$	−20.2393	−1.48802
$186$	0.620716	0.0455131
$187$	16.8809	1.23446
$188$	−15.0311	−1.09626
$189$	−6.87670	−0.500206
$190$	30.9738	2.24707
$191$	−13.9644	−1.01043	−0.505213	−	0.862995i	$-0.668586\pi$
$191$	−13.9644	−1.01043	−0.505213	+	0.862995i	$0.668586\pi$
$192$	10.9827	0.792608
$193$	−8.89789	−0.640484	−0.320242	−	0.947336i	$-0.603764\pi$
$193$	−8.89789	−0.640484	−0.320242	+	0.947336i	$0.603764\pi$
$194$	23.6379	1.69710
$195$	−15.8913	−1.13800
$196$	−21.7819	−1.55585
$197$	20.7045	1.47513	0.737567	−	0.675274i	$-0.235974\pi$
$197$	20.7045	1.47513	0.737567	+	0.675274i	$0.235974\pi$
$198$	15.6749	1.11397
$199$	−12.8212	−0.908870	−0.454435	−	0.890780i	$-0.650159\pi$
$199$	−12.8212	−0.908870	−0.454435	+	0.890780i	$0.650159\pi$
$200$	69.6036	4.92172
$201$	−12.9491	−0.913362
$202$	45.1091	3.17386
$203$	−7.33044	−0.514496
$204$	17.6763	1.23759
$205$	−37.1363	−2.59371
$206$	17.6706	1.23117
$207$	8.73074	0.606829
$208$	10.4409	0.723947
$209$	−14.1669	−0.979942
$210$	17.2489	1.19029
$211$	19.3376	1.33125	0.665627	−	0.746285i	$-0.268164\pi$
$211$	19.3376	1.33125	0.665627	+	0.746285i	$0.268164\pi$
$212$	39.0764	2.68377
$213$	−16.7769	−1.14953
$214$	−12.6069	−0.861788
$215$	12.7039	0.866400
$216$	26.8840	1.82923
$217$	0.239184	0.0162369
$218$	22.8684	1.54884
$219$	10.2605	0.693342
$220$	−86.3961	−5.82482
$221$	−9.44159	−0.635110
$222$	14.5843	0.978833
$223$	1.42361	0.0953321	0.0476660	−	0.998863i	$-0.484822\pi$
$223$	1.42361	0.0953321	0.0476660	+	0.998863i	$0.484822\pi$
$224$	0.431392	0.0288236
$225$	−18.8816	−1.25878
$226$	−3.89195	−0.258888
$227$	0.569455	0.0377960	0.0188980	−	0.999821i	$-0.493984\pi$
$227$	0.569455	0.0377960	0.0188980	+	0.999821i	$0.493984\pi$
$228$	−14.8343	−0.982428
$229$	20.8298	1.37647	0.688236	−	0.725486i	$-0.258385\pi$
$229$	20.8298	1.37647	0.688236	+	0.725486i	$0.258385\pi$
$230$	−72.4030	−4.77411
$231$	−7.88934	−0.519080
$232$	28.6579	1.88148
$233$	0.611253	0.0400445	0.0200223	−	0.999800i	$-0.493626\pi$
$233$	0.611253	0.0400445	0.0200223	+	0.999800i	$0.493626\pi$
$234$	−8.76706	−0.573121
$235$	−16.7523	−1.09280
$236$	−2.92536	−0.190424
$237$	8.50397	0.552392
$238$	10.2482	0.664291
$239$	−23.1736	−1.49898	−0.749488	−	0.662017i	$-0.769700\pi$
$239$	−23.1736	−1.49898	−0.749488	+	0.662017i	$0.769700\pi$
$240$	−21.7855	−1.40625
$241$	−20.3842	−1.31306	−0.656530	−	0.754300i	$-0.727977\pi$
$241$	−20.3842	−1.31306	−0.656530	+	0.754300i	$0.727977\pi$
$242$	32.5925	2.09512
$243$	−12.3800	−0.794177
$244$	−12.8595	−0.823242
$245$	−24.2762	−1.55095
$246$	26.7601	1.70616
$247$	7.92360	0.504166
$248$	−0.935075	−0.0593773
$249$	5.48339	0.347496
$250$	102.643	6.49174
$251$	9.66207	0.609864	0.304932	−	0.952374i	$-0.401366\pi$
$251$	9.66207	0.609864	0.304932	+	0.952374i	$0.401366\pi$
$252$	6.32469	0.398418
$253$	33.1158	2.08197
$254$	42.0390	2.63776
$255$	19.7004	1.23369
$256$	−31.6781	−1.97988
$257$	−25.9262	−1.61723	−0.808617	−	0.588335i	$-0.799784\pi$
$257$	−25.9262	−1.61723	−0.808617	+	0.588335i	$0.799784\pi$
$258$	−9.15436	−0.569925
$259$	5.61985	0.349200
$260$	48.3218	2.99679
$261$	−7.77414	−0.481207
$262$	−8.96062	−0.553589
$263$	5.20973	0.321246	0.160623	−	0.987016i	$-0.448650\pi$
$263$	5.20973	0.321246	0.160623	+	0.987016i	$0.448650\pi$
$264$	30.8429	1.89825
$265$	43.5509	2.67531
$266$	−8.60050	−0.527331
$267$	14.5483	0.890340
$268$	39.3753	2.40523
$269$	2.05246	0.125140	0.0625702	−	0.998041i	$-0.480070\pi$
$269$	2.05246	0.125140	0.0625702	+	0.998041i	$0.480070\pi$
$270$	60.4793	3.68066
$271$	−6.32559	−0.384252	−0.192126	−	0.981370i	$-0.561538\pi$
$271$	−6.32559	−0.384252	−0.192126	+	0.981370i	$0.561538\pi$
$272$	−12.9435	−0.784817
$273$	4.41255	0.267060
$274$	−48.2079	−2.91235
$275$	−71.6182	−4.31874
$276$	34.6761	2.08726
$277$	−1.02544	−0.0616129	−0.0308065	−	0.999525i	$-0.509808\pi$
$277$	−1.02544	−0.0616129	−0.0308065	+	0.999525i	$0.509808\pi$
$278$	−10.5587	−0.633269
$279$	0.253661	0.0151863
$280$	−25.9846	−1.55287
$281$	31.0337	1.85132	0.925658	−	0.378361i	$-0.123512\pi$
$281$	31.0337	1.85132	0.925658	+	0.378361i	$0.123512\pi$
$282$	12.0716	0.718854
$283$	−18.0620	−1.07368	−0.536839	−	0.843685i	$-0.680382\pi$
$283$	−18.0620	−1.07368	−0.536839	+	0.843685i	$0.680382\pi$
$284$	51.0146	3.02716
$285$	−16.5330	−0.979330
$286$	−33.2536	−1.96633
$287$	10.3116	0.608677
$288$	0.457503	0.0269586
$289$	−5.29531	−0.311489
$290$	64.4700	3.78581
$291$	−12.6173	−0.739638
$292$	−31.1999	−1.82583
$293$	3.31959	0.193932	0.0969662	−	0.995288i	$-0.469086\pi$
$293$	3.31959	0.193932	0.0969662	+	0.995288i	$0.469086\pi$
$294$	17.4932	1.02023
$295$	−3.26033	−0.189824
$296$	−21.9704	−1.27701
$297$	−27.6622	−1.60512
$298$	−2.83687	−0.164335
$299$	−18.5219	−1.07115
$300$	−74.9926	−4.32970
$301$	−3.52750	−0.203322
$302$	49.4416	2.84505
$303$	−24.0780	−1.38325
$304$	10.8625	0.623007
$305$	−14.3320	−0.820647
$306$	10.8685	0.621310
$307$	25.6866	1.46601	0.733006	−	0.680222i	$-0.238117\pi$
$307$	25.6866	1.46601	0.733006	+	0.680222i	$0.238117\pi$
$308$	23.9896	1.36694
$309$	−9.43213	−0.536575
$310$	−2.10358	−0.119475
$311$	15.0042	0.850811	0.425406	−	0.905003i	$-0.360131\pi$
$311$	15.0042	0.850811	0.425406	+	0.905003i	$0.360131\pi$
$312$	−17.2506	−0.976622
$313$	−12.6102	−0.712772	−0.356386	−	0.934339i	$-0.615991\pi$
$313$	−12.6102	−0.712772	−0.356386	+	0.934339i	$0.615991\pi$
$314$	16.3214	0.921069
$315$	7.04893	0.397162
$316$	−25.8586	−1.45466
$317$	−5.63738	−0.316627	−0.158313	−	0.987389i	$-0.550606\pi$
$317$	−5.63738	−0.316627	−0.158313	+	0.987389i	$0.550606\pi$
$318$	−31.3825	−1.75984
$319$	−29.4874	−1.65098
$320$	−37.2200	−2.08066
$321$	6.72922	0.375588
$322$	20.1042	1.12036
$323$	−9.82284	−0.546557
$324$	−13.4969	−0.749828
$325$	40.0565	2.22193
$326$	−0.0161989	−0.000897172 0
$327$	−12.2066	−0.675024
$328$	−40.3127	−2.22590
$329$	4.65163	0.256452
$330$	69.3853	3.81954
$331$	−7.28945	−0.400664	−0.200332	−	0.979728i	$-0.564202\pi$
$331$	−7.28945	−0.400664	−0.200332	+	0.979728i	$0.564202\pi$
$332$	−16.6737	−0.915089
$333$	5.96001	0.326606
$334$	29.9807	1.64047
$335$	43.8842	2.39765
$336$	6.04919	0.330010
$337$	4.75243	0.258881	0.129441	−	0.991587i	$-0.458682\pi$
$337$	4.75243	0.258881	0.129441	+	0.991587i	$0.458682\pi$
$338$	−13.1479	−0.715152
$339$	2.07742	0.112830
$340$	−59.9043	−3.24877
$341$	0.962141	0.0521028
$342$	−9.12107	−0.493211
$343$	15.3271	0.827586
$344$	13.7905	0.743537
$345$	38.6468	2.08067
$346$	15.7462	0.846522
$347$	−21.8331	−1.17206	−0.586031	−	0.810289i	$-0.699310\pi$
$347$	−21.8331	−1.17206	−0.586031	+	0.810289i	$0.699310\pi$
$348$	−30.8767	−1.65517
$349$	−20.8788	−1.11762	−0.558809	−	0.829297i	$-0.688741\pi$
$349$	−20.8788	−1.11762	−0.558809	+	0.829297i	$0.688741\pi$
$350$	−43.4785	−2.32402
$351$	15.4716	0.825813
$352$	1.73531	0.0924926
$353$	0.0487347	0.00259388	0.00129694	−	0.999999i	$-0.499587\pi$
$353$	0.0487347	0.00259388	0.00129694	+	0.999999i	$0.499587\pi$
$354$	2.34937	0.124868
$355$	56.8562	3.01761
$356$	−44.2379	−2.34460
$357$	−5.47021	−0.289514
$358$	14.0601	0.743100
$359$	−34.2870	−1.80960	−0.904800	−	0.425837i	$-0.859980\pi$
$359$	−34.2870	−1.80960	−0.904800	+	0.425837i	$0.859980\pi$
$360$	−27.5573	−1.45240
$361$	−10.7565	−0.566129
$362$	−28.5917	−1.50274
$363$	−17.3970	−0.913106
$364$	−13.4175	−0.703270
$365$	−34.7725	−1.82008
$366$	10.3275	0.539828
$367$	17.7340	0.925706	0.462853	−	0.886435i	$-0.346826\pi$
$367$	17.7340	0.925706	0.462853	+	0.886435i	$0.346826\pi$
$368$	−25.3917	−1.32363
$369$	10.9358	0.569294
$370$	−49.4256	−2.56951
$371$	−12.0928	−0.627827
$372$	1.00747	0.0522350
$373$	19.0851	0.988188	0.494094	−	0.869408i	$-0.335500\pi$
$373$	19.0851	0.988188	0.494094	+	0.869408i	$0.335500\pi$
$374$	41.2243	2.13166
$375$	−54.7884	−2.82926
$376$	−18.1852	−0.937832
$377$	16.4925	0.849405
$378$	−16.7933	−0.863755
$379$	1.87124	0.0961189	0.0480594	−	0.998844i	$-0.484696\pi$
$379$	1.87124	0.0961189	0.0480594	+	0.998844i	$0.484696\pi$
$380$	50.2730	2.57895
$381$	−22.4393	−1.14960
$382$	−34.1018	−1.74480
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	25.9036	1.32189
$385$	26.7367	1.36263
$386$	−21.7292	−1.10599
$387$	−3.74101	−0.190166
$388$	38.3662	1.94775
$389$	−26.3435	−1.33567	−0.667833	−	0.744311i	$-0.732778\pi$
$389$	−26.3435	−1.33567	−0.667833	+	0.744311i	$0.732778\pi$
$390$	−38.8076	−1.96510
$391$	22.9614	1.16121
$392$	−26.3526	−1.33101
$393$	4.78294	0.241268
$394$	50.5617	2.54726
$395$	−28.8196	−1.45007
$396$	25.4417	1.27849
$397$	22.8068	1.14464	0.572321	−	0.820030i	$-0.306043\pi$
$397$	22.8068	1.14464	0.572321	+	0.820030i	$0.306043\pi$
$398$	−31.3101	−1.56944
$399$	4.59072	0.229824
$400$	54.9136	2.74568
$401$	−1.73361	−0.0865726	−0.0432863	−	0.999063i	$-0.513783\pi$
$401$	−1.73361	−0.0865726	−0.0432863	+	0.999063i	$0.513783\pi$
$402$	−31.6226	−1.57719
$403$	−0.538130	−0.0268062
$404$	73.2157	3.64262
$405$	−15.0424	−0.747464
$406$	−17.9014	−0.888431
$407$	22.6064	1.12056
$408$	21.3854	1.05874
$409$	−17.4437	−0.862533	−0.431267	−	0.902224i	$-0.641933\pi$
$409$	−17.4437	−0.862533	−0.431267	+	0.902224i	$0.641933\pi$
$410$	−90.6890	−4.47881
$411$	25.7321	1.26927
$412$	28.6809	1.41301
$413$	0.905298	0.0445468
$414$	21.3210	1.04787
$415$	−18.5830	−0.912203
$416$	−0.970571	−0.0475861
$417$	5.63596	0.275994
$418$	−34.5963	−1.69216
$419$	−27.0556	−1.32175	−0.660876	−	0.750495i	$-0.729815\pi$
$419$	−27.0556	−1.32175	−0.660876	+	0.750495i	$0.729815\pi$
$420$	27.9964	1.36608
$421$	−17.0036	−0.828703	−0.414351	−	0.910117i	$-0.635991\pi$
$421$	−17.0036	−0.828703	−0.414351	+	0.910117i	$0.635991\pi$
$422$	47.2235	2.29881
$423$	4.93318	0.239859
$424$	47.2761	2.29593
$425$	−49.6578	−2.40876
$426$	−40.9702	−1.98501
$427$	3.97957	0.192585
$428$	−20.4620	−0.989067
$429$	17.7499	0.856973
$430$	31.0238	1.49610
$431$	−10.8218	−0.521265	−0.260633	−	0.965438i	$-0.583931\pi$
$431$	−10.8218	−0.521265	−0.260633	+	0.965438i	$0.583931\pi$
$432$	21.2101	1.02047
$433$	3.71372	0.178470	0.0892351	−	0.996011i	$-0.471558\pi$
$433$	3.71372	0.178470	0.0892351	+	0.996011i	$0.471558\pi$
$434$	0.584102	0.0280378
$435$	−34.4124	−1.64995
$436$	37.1173	1.77760
$437$	−19.2697	−0.921797
$438$	25.0568	1.19726
$439$	13.8548	0.661251	0.330626	−	0.943762i	$-0.392740\pi$
$439$	13.8548	0.661251	0.330626	+	0.943762i	$0.392740\pi$
$440$	−104.525	−4.98305
$441$	7.14878	0.340418
$442$	−23.0570	−1.09671
$443$	19.5049	0.926705	0.463352	−	0.886174i	$-0.346646\pi$
$443$	19.5049	0.926705	0.463352	+	0.886174i	$0.346646\pi$
$444$	23.6715	1.12340
$445$	−49.3035	−2.33721
$446$	3.47655	0.164619
$447$	1.51424	0.0716213
$448$	10.3349	0.488277
$449$	12.8651	0.607140	0.303570	−	0.952809i	$-0.401821\pi$
$449$	12.8651	0.607140	0.303570	+	0.952809i	$0.401821\pi$
$450$	−46.1101	−2.17365
$451$	41.4795	1.95319
$452$	−6.31695	−0.297124
$453$	−26.3906	−1.23994
$454$	1.39064	0.0652662
$455$	−14.9540	−0.701052
$456$	−17.9471	−0.840452
$457$	17.1052	0.800145	0.400073	−	0.916483i	$-0.368985\pi$
$457$	17.1052	0.800145	0.400073	+	0.916483i	$0.368985\pi$
$458$	50.8677	2.37689
$459$	−19.1801	−0.895248
$460$	−117.516	−5.47921
$461$	−19.8511	−0.924558	−0.462279	−	0.886734i	$-0.652968\pi$
$461$	−19.8511	−0.924558	−0.462279	+	0.886734i	$0.652968\pi$
$462$	−19.2662	−0.896347
$463$	36.6304	1.70236	0.851180	−	0.524874i	$-0.175888\pi$
$463$	36.6304	1.70236	0.851180	+	0.524874i	$0.175888\pi$
$464$	22.6096	1.04962
$465$	1.12284	0.0520703
$466$	1.49272	0.0691488
$467$	−15.8665	−0.734215	−0.367107	−	0.930179i	$-0.619652\pi$
$467$	−15.8665	−0.734215	−0.367107	+	0.930179i	$0.619652\pi$
$468$	−14.2297	−0.657766
$469$	−12.1853	−0.562666
$470$	−40.9102	−1.88705
$471$	−8.71192	−0.401424
$472$	−3.53921	−0.162905
$473$	−14.1897	−0.652444
$474$	20.7672	0.953870
$475$	41.6739	1.91213
$476$	16.6336	0.762402
$477$	−12.8248	−0.587205
$478$	−56.5914	−2.58843
$479$	−38.7555	−1.77078	−0.885391	−	0.464847i	$-0.846109\pi$
$479$	−38.7555	−1.77078	−0.885391	+	0.464847i	$0.846109\pi$
$480$	2.02515	0.0924349
$481$	−12.6439	−0.576511
$482$	−49.7794	−2.26739
$483$	−10.7311	−0.488281
$484$	52.9002	2.40456
$485$	42.7595	1.94161
$486$	−30.2327	−1.37138
$487$	22.7319	1.03008	0.515041	−	0.857165i	$-0.327777\pi$
$487$	22.7319	1.03008	0.515041	+	0.857165i	$0.327777\pi$
$488$	−15.5579	−0.704271
$489$	0.00864652	0.000391009 0
$490$	−59.2839	−2.67817
$491$	−7.38185	−0.333138	−0.166569	−	0.986030i	$-0.553269\pi$
$491$	−7.38185	−0.333138	−0.166569	+	0.986030i	$0.553269\pi$
$492$	43.4339	1.95815
$493$	−20.4456	−0.920824
$494$	19.3499	0.870594
$495$	28.3550	1.27446
$496$	−0.737726	−0.0331249
$497$	−15.7873	−0.708157
$498$	13.3908	0.600055
$499$	3.32458	0.148828	0.0744142	−	0.997227i	$-0.476291\pi$
$499$	3.32458	0.148828	0.0744142	+	0.997227i	$0.476291\pi$
$500$	166.599	7.45052
$501$	−16.0029	−0.714958
$502$	23.5954	1.05311
$503$	14.6797	0.654536	0.327268	−	0.944932i	$-0.393872\pi$
$503$	14.6797	0.654536	0.327268	+	0.944932i	$0.393872\pi$
$504$	7.65186	0.340841
$505$	81.5996	3.63113
$506$	80.8709	3.59515
$507$	7.01801	0.311681
$508$	68.2328	3.02734
$509$	−30.9528	−1.37196	−0.685980	−	0.727620i	$-0.740626\pi$
$509$	−30.9528	−1.37196	−0.685980	+	0.727620i	$0.740626\pi$
$510$	48.1096	2.13033
$511$	9.65530	0.427125
$512$	−37.6156	−1.66239
$513$	16.0963	0.710670
$514$	−63.3135	−2.79264
$515$	31.9651	1.40855
$516$	−14.8583	−0.654099
$517$	18.7116	0.822935
$518$	13.7240	0.602999
$519$	−8.40492	−0.368935
$520$	58.4616	2.56371
$521$	25.7946	1.13008	0.565041	−	0.825063i	$-0.308860\pi$
$521$	25.7946	1.13008	0.565041	+	0.825063i	$0.308860\pi$
$522$	−18.9849	−0.830948
$523$	−29.0590	−1.27066	−0.635331	−	0.772240i	$-0.719136\pi$
$523$	−29.0590	−1.27066	−0.635331	+	0.772240i	$0.719136\pi$
$524$	−14.5438	−0.635350
$525$	23.2077	1.01287
$526$	12.7225	0.554726
$527$	0.667117	0.0290601
$528$	24.3334	1.05898
$529$	22.0441	0.958440
$530$	106.354	4.61973
$531$	0.960094	0.0416645
$532$	−13.9593	−0.605213
$533$	−23.1997	−1.00489
$534$	35.5278	1.53744
$535$	−22.8051	−0.985949
$536$	47.6378	2.05764
$537$	−7.50492	−0.323861
$538$	5.01222	0.216092
$539$	27.1154	1.16794
$540$	98.1629	4.22426
$541$	−7.48017	−0.321598	−0.160799	−	0.986987i	$-0.551407\pi$
$541$	−7.48017	−0.321598	−0.160799	+	0.986987i	$0.551407\pi$
$542$	−15.4475	−0.663527
$543$	15.2615	0.654933
$544$	1.20321	0.0515873
$545$	41.3676	1.77199
$546$	10.7757	0.461158
$547$	−39.8193	−1.70255	−0.851276	−	0.524718i	$-0.824171\pi$
$547$	−39.8193	−1.70255	−0.851276	+	0.524718i	$0.824171\pi$
$548$	−78.2454	−3.34248
$549$	4.22044	0.180124
$550$	−174.896	−7.45760
$551$	17.1584	0.730973
$552$	41.9525	1.78562
$553$	8.00235	0.340295
$554$	−2.50420	−0.106393
$555$	26.3821	1.11986
$556$	−17.1376	−0.726798
$557$	38.5971	1.63541	0.817707	−	0.575635i	$-0.195245\pi$
$557$	38.5971	1.63541	0.817707	+	0.575635i	$0.195245\pi$
$558$	0.619457	0.0262237
$559$	7.93638	0.335673
$560$	−20.5005	−0.866303
$561$	−22.0044	−0.929028
$562$	75.7863	3.19685
$563$	17.6178	0.742500	0.371250	−	0.928533i	$-0.378929\pi$
$563$	17.6178	0.742500	0.371250	+	0.928533i	$0.378929\pi$
$564$	19.5932	0.825023
$565$	−7.04029	−0.296187
$566$	−44.1086	−1.85402
$567$	4.17683	0.175411
$568$	61.7194	2.58969
$569$	3.57925	0.150050	0.0750250	−	0.997182i	$-0.476096\pi$
$569$	3.57925	0.150050	0.0750250	+	0.997182i	$0.476096\pi$
$570$	−40.3746	−1.69111
$571$	−9.34854	−0.391224	−0.195612	−	0.980681i	$-0.562669\pi$
$571$	−9.34854	−0.391224	−0.195612	+	0.980681i	$0.562669\pi$
$572$	−53.9733	−2.25674
$573$	18.2027	0.760427
$574$	25.1817	1.05106
$575$	−97.4151	−4.06249
$576$	10.9604	0.456684
$577$	−30.6054	−1.27412	−0.637060	−	0.770814i	$-0.719850\pi$
$577$	−30.6054	−1.27412	−0.637060	+	0.770814i	$0.719850\pi$
$578$	−12.9315	−0.537878
$579$	11.5985	0.482016
$580$	104.640	4.34494
$581$	5.15995	0.214071
$582$	−30.8122	−1.27720
$583$	−48.6444	−2.01465
$584$	−37.7468	−1.56197
$585$	−15.8591	−0.655693
$586$	8.10664	0.334882
$587$	−28.0845	−1.15917	−0.579587	−	0.814911i	$-0.696786\pi$
$587$	−28.0845	−1.15917	−0.579587	+	0.814911i	$0.696786\pi$
$588$	28.3930	1.17091
$589$	−0.559860	−0.0230686
$590$	−7.96194	−0.327788
$591$	−26.9885	−1.11016
$592$	−17.3335	−0.712404
$593$	12.8428	0.527391	0.263696	−	0.964606i	$-0.415059\pi$
$593$	12.8428	0.527391	0.263696	+	0.964606i	$0.415059\pi$
$594$	−67.5527	−2.77172
$595$	18.5383	0.759998
$596$	−4.60447	−0.188606
$597$	16.7125	0.683998
$598$	−45.2315	−1.84965
$599$	15.2335	0.622425	0.311213	−	0.950340i	$-0.399265\pi$
$599$	15.2335	0.622425	0.311213	+	0.950340i	$0.399265\pi$
$600$	−90.7289	−3.70399
$601$	−37.6906	−1.53743	−0.768716	−	0.639590i	$-0.779104\pi$
$601$	−37.6906	−1.53743	−0.768716	+	0.639590i	$0.779104\pi$
$602$	−8.61438	−0.351096
$603$	−12.9229	−0.526260
$604$	80.2478	3.26524
$605$	58.9578	2.39697
$606$	−58.8001	−2.38859
$607$	10.9735	0.445400	0.222700	−	0.974887i	$-0.428513\pi$
$607$	10.9735	0.445400	0.222700	+	0.974887i	$0.428513\pi$
$608$	−1.00976	−0.0409512
$609$	9.55530	0.387200
$610$	−34.9996	−1.41709
$611$	−10.4655	−0.423389
$612$	17.6404	0.713072
$613$	15.1246	0.610876	0.305438	−	0.952212i	$-0.401197\pi$
$613$	15.1246	0.610876	0.305438	+	0.952212i	$0.401197\pi$
$614$	62.7283	2.53151
$615$	48.4074	1.95198
$616$	29.0236	1.16939
$617$	27.6660	1.11379	0.556896	−	0.830582i	$-0.311992\pi$
$617$	27.6660	1.11379	0.556896	+	0.830582i	$0.311992\pi$
$618$	−23.0338	−0.926557
$619$	−28.4029	−1.14161	−0.570805	−	0.821086i	$-0.693369\pi$
$619$	−28.4029	−1.14161	−0.570805	+	0.821086i	$0.693369\pi$
$620$	−3.41429	−0.137121
$621$	−37.6261	−1.50988
$622$	36.6412	1.46918
$623$	13.6901	0.548484
$624$	−13.6098	−0.544829
$625$	113.102	4.52410
$626$	−30.7949	−1.23081
$627$	18.4666	0.737486
$628$	26.4909	1.05710
$629$	15.6745	0.624985
$630$	17.2139	0.685819
$631$	32.6756	1.30079	0.650397	−	0.759594i	$-0.274603\pi$
$631$	32.6756	1.30079	0.650397	+	0.759594i	$0.274603\pi$
$632$	−31.2847	−1.24444
$633$	−25.2067	−1.00188
$634$	−13.7668	−0.546751
$635$	76.0460	3.01779
$636$	−50.9364	−2.01976
$637$	−15.1658	−0.600890
$638$	−72.0101	−2.85091
$639$	−16.7429	−0.662337
$640$	−87.7862	−3.47005
$641$	−25.2343	−0.996696	−0.498348	−	0.866977i	$-0.666060\pi$
$641$	−25.2343	−0.996696	−0.498348	+	0.866977i	$0.666060\pi$
$642$	16.4332	0.648565
$643$	12.6574	0.499158	0.249579	−	0.968354i	$-0.419708\pi$
$643$	12.6574	0.499158	0.249579	+	0.968354i	$0.419708\pi$
$644$	32.6307	1.28583
$645$	−16.5597	−0.652036
$646$	−23.9880	−0.943794
$647$	−31.2847	−1.22993	−0.614965	−	0.788555i	$-0.710830\pi$
$647$	−31.2847	−1.22993	−0.614965	+	0.788555i	$0.710830\pi$
$648$	−16.3291	−0.641466
$649$	3.64165	0.142947
$650$	97.8204	3.83683
$651$	−0.311779	−0.0122196
$652$	−0.0262921	−0.00102968
$653$	−10.8026	−0.422738	−0.211369	−	0.977406i	$-0.567792\pi$
$653$	−10.8026	−0.422738	−0.211369	+	0.977406i	$0.567792\pi$
$654$	−29.8092	−1.16563
$655$	−16.2092	−0.633346
$656$	−31.8046	−1.24176
$657$	10.2397	0.399489
$658$	11.3596	0.442842
$659$	−18.4059	−0.716993	−0.358496	−	0.933531i	$-0.616710\pi$
$659$	−18.4059	−0.716993	−0.358496	+	0.933531i	$0.616710\pi$
$660$	112.618	4.38365
$661$	0.369038	0.0143539	0.00717696	−	0.999974i	$-0.497715\pi$
$661$	0.369038	0.0143539	0.00717696	+	0.999974i	$0.497715\pi$
$662$	−17.8013	−0.691866
$663$	12.3072	0.477972
$664$	−20.1725	−0.782844
$665$	−15.5578	−0.603305
$666$	14.5547	0.563983
$667$	−40.1088	−1.55302
$668$	48.6611	1.88276
$669$	−1.85569	−0.0717451
$670$	107.168	4.14026
$671$	16.0082	0.617989
$672$	−0.562323	−0.0216921
$673$	14.7123	0.567117	0.283558	−	0.958955i	$-0.408485\pi$
$673$	14.7123	0.567117	0.283558	+	0.958955i	$0.408485\pi$
$674$	11.6057	0.447036
$675$	81.3724	3.13202
$676$	−21.3401	−0.820774
$677$	−36.7312	−1.41169	−0.705847	−	0.708365i	$-0.749433\pi$
$677$	−36.7312	−1.41169	−0.705847	+	0.708365i	$0.749433\pi$
$678$	5.07319	0.194835
$679$	−11.8730	−0.455645
$680$	−72.4745	−2.77927
$681$	−0.742289	−0.0284446
$682$	2.34961	0.0899711
$683$	−17.8681	−0.683704	−0.341852	−	0.939754i	$-0.611054\pi$
$683$	−17.8681	−0.683704	−0.341852	+	0.939754i	$0.611054\pi$
$684$	−14.8042	−0.566054
$685$	−87.2051	−3.33194
$686$	37.4298	1.42908
$687$	−27.1518	−1.03591
$688$	10.8800	0.414797
$689$	27.2071	1.03651
$690$	94.3779	3.59291
$691$	−5.78876	−0.220215	−0.110107	−	0.993920i	$-0.535119\pi$
$691$	−5.78876	−0.220215	−0.110107	+	0.993920i	$0.535119\pi$
$692$	25.5574	0.971547
$693$	−7.87334	−0.299083
$694$	−53.3178	−2.02391
$695$	−19.1001	−0.724506
$696$	−37.3558	−1.41597
$697$	28.7606	1.08938
$698$	−50.9874	−1.92990
$699$	−0.796774	−0.0301367
$700$	−70.5691	−2.66726
$701$	26.5640	1.00331	0.501655	−	0.865068i	$-0.332725\pi$
$701$	26.5640	1.00331	0.501655	+	0.865068i	$0.332725\pi$
$702$	37.7826	1.42601
$703$	−13.1544	−0.496128
$704$	41.5730	1.56684
$705$	21.8368	0.822422
$706$	0.119013	0.00447911
$707$	−22.6578	−0.852134
$708$	3.81323	0.143310
$709$	0.790245	0.0296783	0.0148391	−	0.999890i	$-0.495276\pi$
$709$	0.790245	0.0296783	0.0148391	+	0.999890i	$0.495276\pi$
$710$	138.846	5.21081
$711$	8.48672	0.318277
$712$	−53.5207	−2.00577
$713$	1.30870	0.0490113
$714$	−13.3586	−0.499933
$715$	−60.1537	−2.24962
$716$	22.8207	0.852850
$717$	30.2070	1.12810
$718$	−83.7310	−3.12481
$719$	−19.8774	−0.741303	−0.370652	−	0.928772i	$-0.620866\pi$
$719$	−19.8774	−0.741303	−0.370652	+	0.928772i	$0.620866\pi$
$720$	−21.7413	−0.810251
$721$	−8.87577	−0.330551
$722$	−26.2679	−0.977591
$723$	26.5710	0.988185
$724$	−46.4066	−1.72469
$725$	86.7416	3.22150
$726$	−42.4846	−1.57675
$727$	−33.9031	−1.25740	−0.628698	−	0.777650i	$-0.716412\pi$
$727$	−33.9031	−1.25740	−0.628698	+	0.777650i	$0.716412\pi$
$728$	−16.2330	−0.601636
$729$	26.3529	0.976033
$730$	−84.9167	−3.14291
$731$	−9.83869	−0.363897
$732$	16.7624	0.619557
$733$	22.3552	0.825707	0.412853	−	0.910797i	$-0.364532\pi$
$733$	22.3552	0.825707	0.412853	+	0.910797i	$0.364532\pi$
$734$	43.3075	1.59851
$735$	31.6442	1.16721
$736$	2.36037	0.0870046
$737$	−49.0166	−1.80555
$738$	26.7058	0.983056
$739$	17.1333	0.630259	0.315130	−	0.949049i	$-0.397952\pi$
$739$	17.1333	0.630259	0.315130	+	0.949049i	$0.397952\pi$
$740$	−80.2218	−2.94901
$741$	−10.3285	−0.379426
$742$	−29.5314	−1.08413
$743$	−31.7065	−1.16320	−0.581600	−	0.813475i	$-0.697573\pi$
$743$	−31.7065	−1.16320	−0.581600	+	0.813475i	$0.697573\pi$
$744$	1.21888	0.0446863
$745$	−5.13172	−0.188012
$746$	46.6070	1.70640
$747$	5.47227	0.200220
$748$	66.9104	2.44649
$749$	6.33229	0.231377
$750$	−133.797	−4.88556
$751$	−46.4121	−1.69360	−0.846801	−	0.531909i	$-0.821475\pi$
$751$	−46.4121	−1.69360	−0.846801	+	0.531909i	$0.821475\pi$
$752$	−14.3472	−0.523189
$753$	−12.5946	−0.458972
$754$	40.2756	1.46675
$755$	89.4369	3.25494
$756$	−27.2569	−0.991325
$757$	−3.57900	−0.130081	−0.0650404	−	0.997883i	$-0.520718\pi$
$757$	−3.57900	−0.130081	−0.0650404	+	0.997883i	$0.520718\pi$
$758$	4.56967	0.165978
$759$	−43.1668	−1.56685
$760$	60.8222	2.20625
$761$	−28.1771	−1.02142	−0.510709	−	0.859754i	$-0.670617\pi$
$761$	−28.1771	−1.02142	−0.510709	+	0.859754i	$0.670617\pi$
$762$	−54.7982	−1.98513
$763$	−11.4865	−0.415841
$764$	−55.3501	−2.00249
$765$	19.6604	0.710824
$766$	2.44206	0.0882353
$767$	−2.03679	−0.0735443
$768$	41.2927	1.49002
$769$	12.0775	0.435527	0.217764	−	0.976002i	$-0.430124\pi$
$769$	12.0775	0.435527	0.217764	+	0.976002i	$0.430124\pi$
$770$	65.2926	2.35298
$771$	33.7951	1.21710
$772$	−35.2683	−1.26933
$773$	−4.95998	−0.178398	−0.0891991	−	0.996014i	$-0.528431\pi$
$773$	−4.95998	−0.178398	−0.0891991	+	0.996014i	$0.528431\pi$
$774$	−9.13579	−0.328379
$775$	−2.83028	−0.101667
$776$	46.4169	1.66627
$777$	−7.32552	−0.262802
$778$	−64.3323	−2.30643
$779$	−24.1365	−0.864780
$780$	−62.9879	−2.25533
$781$	−63.5058	−2.27242
$782$	56.0733	2.00518
$783$	33.5035	1.19732
$784$	−20.7909	−0.742531
$785$	29.5244	1.05377
$786$	11.6802	0.416620
$787$	10.7172	0.382026	0.191013	−	0.981588i	$-0.438823\pi$
$787$	10.7172	0.382026	0.191013	+	0.981588i	$0.438823\pi$
$788$	82.0657	2.92347
$789$	−6.79092	−0.241763
$790$	−70.3793	−2.50398
$791$	1.95488	0.0695076
$792$	30.7803	1.09373
$793$	−8.95346	−0.317947
$794$	55.6957	1.97657
$795$	−56.7690	−2.01339
$796$	−50.8189	−1.80123
$797$	−13.8652	−0.491132	−0.245566	−	0.969380i	$-0.578974\pi$
$797$	−13.8652	−0.491132	−0.245566	+	0.969380i	$0.578974\pi$
$798$	11.2108	0.396859
$799$	12.9740	0.458988
$800$	−5.10469	−0.180478
$801$	14.5188	0.512995
$802$	−4.23359	−0.149493
$803$	38.8394	1.37061
$804$	−51.3261	−1.81013
$805$	36.3672	1.28178
$806$	−1.31415	−0.0462889
$807$	−2.67539	−0.0941783
$808$	88.5792	3.11620
$809$	−26.5096	−0.932028	−0.466014	−	0.884777i	$-0.654310\pi$
$809$	−26.5096	−0.932028	−0.466014	+	0.884777i	$0.654310\pi$
$810$	−36.7345	−1.29072
$811$	−39.1324	−1.37412	−0.687062	−	0.726599i	$-0.741100\pi$
$811$	−39.1324	−1.37412	−0.687062	+	0.726599i	$0.741100\pi$
$812$	−29.0554	−1.01965
$813$	8.24547	0.289181
$814$	55.2062	1.93498
$815$	−0.0293027	−0.00102643
$816$	16.8720	0.590639
$817$	8.25684	0.288870
$818$	−42.5985	−1.48942
$819$	4.40360	0.153874
$820$	−147.196	−5.14030
$821$	20.6885	0.722034	0.361017	−	0.932559i	$-0.382430\pi$
$821$	20.6885	0.722034	0.361017	+	0.932559i	$0.382430\pi$
$822$	62.8394	2.19178
$823$	48.9776	1.70725	0.853626	−	0.520886i	$-0.174398\pi$
$823$	48.9776	1.70725	0.853626	+	0.520886i	$0.174398\pi$
$824$	34.6992	1.20881
$825$	93.3550	3.25020
$826$	2.21079	0.0769234
$827$	−37.4455	−1.30211	−0.651053	−	0.759032i	$-0.725673\pi$
$827$	−37.4455	−1.30211	−0.651053	+	0.759032i	$0.725673\pi$
$828$	34.6058	1.20263
$829$	14.8501	0.515764	0.257882	−	0.966176i	$-0.416975\pi$
$829$	14.8501	0.515764	0.257882	+	0.966176i	$0.416975\pi$
$830$	−45.3808	−1.57519
$831$	1.33667	0.0463687
$832$	−23.2520	−0.806118
$833$	18.8009	0.651414
$834$	13.7634	0.476586
$835$	54.2333	1.87682
$836$	−56.1527	−1.94208
$837$	−1.09318	−0.0377858
$838$	−66.0714	−2.28240
$839$	−34.2367	−1.18198	−0.590991	−	0.806678i	$-0.701263\pi$
$839$	−34.2367	−1.18198	−0.590991	+	0.806678i	$0.701263\pi$
$840$	33.8711	1.16866
$841$	6.71414	0.231522
$842$	−41.5237	−1.43100
$843$	−40.4527	−1.39327
$844$	76.6477	2.63832
$845$	−23.7838	−0.818186
$846$	12.0471	0.414189
$847$	−16.3708	−0.562508
$848$	37.2984	1.28083
$849$	23.5440	0.808029
$850$	−121.267	−4.15944
$851$	30.7492	1.05407
$852$	−66.4980	−2.27818
$853$	38.4698	1.31718	0.658591	−	0.752501i	$-0.271153\pi$
$853$	38.4698	1.31718	0.658591	+	0.752501i	$0.271153\pi$
$854$	9.71835	0.332555
$855$	−16.4995	−0.564270
$856$	−24.7557	−0.846132
$857$	25.0469	0.855585	0.427793	−	0.903877i	$-0.359291\pi$
$857$	25.0469	0.855585	0.427793	+	0.903877i	$0.359291\pi$
$858$	43.3463	1.47982
$859$	−39.5530	−1.34953	−0.674766	−	0.738032i	$-0.735756\pi$
$859$	−39.5530	−1.34953	−0.674766	+	0.738032i	$0.735756\pi$
$860$	50.3541	1.71706
$861$	−13.4413	−0.458079
$862$	−26.4274	−0.900120
$863$	28.7031	0.977066	0.488533	−	0.872545i	$-0.337532\pi$
$863$	28.7031	0.977066	0.488533	+	0.872545i	$0.337532\pi$
$864$	−1.97166	−0.0670772
$865$	28.4840	0.968484
$866$	9.06914	0.308182
$867$	6.90248	0.234420
$868$	0.948046	0.0321788
$869$	32.1902	1.09198
$870$	−84.0372	−2.84913
$871$	27.4153	0.928931
$872$	44.9059	1.52071
$873$	−12.5917	−0.426164
$874$	−47.0579	−1.59176
$875$	−51.5567	−1.74293
$876$	40.6693	1.37409
$877$	19.0593	0.643588	0.321794	−	0.946810i	$-0.395714\pi$
$877$	19.0593	0.643588	0.321794	+	0.946810i	$0.395714\pi$
$878$	33.8342	1.14185
$879$	−4.32711	−0.145950
$880$	−82.4651	−2.77990
$881$	34.6912	1.16878	0.584388	−	0.811475i	$-0.301335\pi$
$881$	34.6912	1.16878	0.584388	+	0.811475i	$0.301335\pi$
$882$	17.4578	0.587833
$883$	11.5748	0.389525	0.194762	−	0.980850i	$-0.437606\pi$
$883$	11.5748	0.389525	0.194762	+	0.980850i	$0.437606\pi$
$884$	−37.4233	−1.25868
$885$	4.24987	0.142858
$886$	47.6321	1.60023
$887$	25.6422	0.860980	0.430490	−	0.902595i	$-0.358341\pi$
$887$	25.6422	0.860980	0.430490	+	0.902595i	$0.358341\pi$
$888$	28.6387	0.961051
$889$	−21.1157	−0.708199
$890$	−120.402	−4.03589
$891$	16.8017	0.562878
$892$	5.64272	0.188932
$893$	−10.8881	−0.364356
$894$	3.69788	0.123676
$895$	25.4339	0.850162
$896$	24.3756	0.814333
$897$	24.1434	0.806124
$898$	31.4173	1.04841
$899$	−1.16531	−0.0388653
$900$	−74.8405	−2.49468
$901$	−33.7285	−1.12366
$902$	101.296	3.37277
$903$	4.59813	0.153016
$904$	−7.64248	−0.254185
$905$	−51.7206	−1.71925
$906$	−64.4476	−2.14113
$907$	34.4910	1.14525	0.572627	−	0.819816i	$-0.305924\pi$
$907$	34.4910	1.14525	0.572627	+	0.819816i	$0.305924\pi$
$908$	2.25713	0.0749055
$909$	−24.0292	−0.796998
$910$	−36.5185	−1.21058
$911$	8.69842	0.288191	0.144096	−	0.989564i	$-0.453973\pi$
$911$	8.69842	0.288191	0.144096	+	0.989564i	$0.453973\pi$
$912$	−14.1594	−0.468864
$913$	20.7564	0.686936
$914$	41.7718	1.38169
$915$	18.6819	0.617603
$916$	82.5624	2.72794
$917$	4.50082	0.148630
$918$	−46.8389	−1.54591
$919$	57.4064	1.89366	0.946831	−	0.321732i	$-0.104265\pi$
$919$	57.4064	1.89366	0.946831	+	0.321732i	$0.104265\pi$
$920$	−142.175	−4.68738
$921$	−33.4827	−1.10329
$922$	−48.4776	−1.59653
$923$	35.5192	1.16913
$924$	−31.2707	−1.02873
$925$	−66.5000	−2.18651
$926$	89.4537	2.93963
$927$	−9.41300	−0.309163
$928$	−2.10175	−0.0689935
$929$	−35.1129	−1.15202	−0.576008	−	0.817444i	$-0.695390\pi$
$929$	−35.1129	−1.15202	−0.576008	+	0.817444i	$0.695390\pi$
$930$	2.74204	0.0899150
$931$	−15.7782	−0.517108
$932$	2.42280	0.0793616
$933$	−19.5581	−0.640304
$934$	−38.7470	−1.26784
$935$	74.5722	2.43877
$936$	−17.2156	−0.562709
$937$	−5.40809	−0.176675	−0.0883373	−	0.996091i	$-0.528155\pi$
$937$	−5.40809	−0.176675	−0.0883373	+	0.996091i	$0.528155\pi$
$938$	−29.7573	−0.971611
$939$	16.4375	0.536419
$940$	−66.4006	−2.16575
$941$	19.5106	0.636026	0.318013	−	0.948086i	$-0.396984\pi$
$941$	19.5106	0.636026	0.318013	+	0.948086i	$0.396984\pi$
$942$	−21.2751	−0.693179
$943$	56.4204	1.83730
$944$	−2.79225	−0.0908800
$945$	−30.3781	−0.988200
$946$	−34.6521	−1.12664
$947$	15.1064	0.490893	0.245446	−	0.969410i	$-0.421065\pi$
$947$	15.1064	0.490893	0.245446	+	0.969410i	$0.421065\pi$
$948$	33.7069	1.09475
$949$	−21.7231	−0.705160
$950$	101.770	3.30186
$951$	7.34837	0.238287
$952$	20.1240	0.652223
$953$	9.54005	0.309033	0.154516	−	0.987990i	$-0.450618\pi$
$953$	9.54005	0.309033	0.154516	+	0.987990i	$0.450618\pi$
$954$	−31.3188	−1.01399
$955$	−61.6881	−1.99618
$956$	−91.8525	−2.97072
$957$	38.4371	1.24249
$958$	−94.6432	−3.05778
$959$	24.2143	0.781920
$960$	48.5165	1.56586
$961$	−30.9620	−0.998773
$962$	−30.8771	−0.995518
$963$	6.71557	0.216406
$964$	−80.7961	−2.60227
$965$	−39.3068	−1.26533
$966$	−26.2059	−0.843162
$967$	46.1794	1.48503	0.742514	−	0.669831i	$-0.233633\pi$
$967$	46.1794	1.48503	0.742514	+	0.669831i	$0.233633\pi$
$968$	64.0007	2.05706
$969$	12.8042	0.411329
$970$	104.421	3.35276
$971$	6.72490	0.215812	0.107906	−	0.994161i	$-0.465585\pi$
$971$	6.72490	0.215812	0.107906	+	0.994161i	$0.465585\pi$
$972$	−49.0702	−1.57393
$973$	5.30352	0.170023
$974$	55.5128	1.77875
$975$	−52.2140	−1.67218
$976$	−12.2743	−0.392892
$977$	26.3977	0.844538	0.422269	−	0.906470i	$-0.361234\pi$
$977$	26.3977	0.844538	0.422269	+	0.906470i	$0.361234\pi$
$978$	0.0211153	0.000675194 0
$979$	55.0698	1.76004
$980$	−96.2226	−3.07372
$981$	−12.1818	−0.388935
$982$	−18.0269	−0.575262
$983$	27.9249	0.890667	0.445333	−	0.895365i	$-0.353085\pi$
$983$	27.9249	0.890667	0.445333	+	0.895365i	$0.353085\pi$
$984$	52.5480	1.67517
$985$	91.4630	2.91425
$986$	−49.9295	−1.59008
$987$	−6.06343	−0.193001
$988$	31.4065	0.999173
$989$	−19.3008	−0.613731
$990$	69.2446	2.20074
$991$	50.4571	1.60282	0.801412	−	0.598113i	$-0.204083\pi$
$991$	50.4571	1.60282	0.801412	+	0.598113i	$0.204083\pi$
$992$	0.0685779	0.00217735
$993$	9.50186	0.301532
$994$	−38.5535	−1.22284
$995$	−56.6381	−1.79555
$996$	21.7343	0.688678
$997$	−11.1734	−0.353864	−0.176932	−	0.984223i	$-0.556617\pi$
$997$	−11.1734	−0.353864	−0.176932	+	0.984223i	$0.556617\pi$
$998$	8.11882	0.256997
$999$	−25.6853	−0.812646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	383.2.a.c.1.21	✓	24
3.2	odd	2		3447.2.a.j.1.4		24
4.3	odd	2		6128.2.a.p.1.16		24
5.4	even	2		9575.2.a.e.1.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
383.2.a.c.1.21	✓	24	1.1	even	1	trivial
3447.2.a.j.1.4		24	3.2	odd	2
6128.2.a.p.1.16		24	4.3	odd	2
9575.2.a.e.1.4		24	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	383.a (trivial)

\(f(q)\)	\(=\)	\(q+2.44206 q^{2} -1.30351 q^{3} +3.96367 q^{4} +4.41754 q^{5} -3.18325 q^{6} -1.22662 q^{7} +4.79540 q^{8} -1.30086 q^{9} +10.7879 q^{10} -4.93420 q^{11} -5.16667 q^{12} +2.75972 q^{13} -2.99548 q^{14} -5.75830 q^{15} +3.78332 q^{16} -3.42121 q^{17} -3.17679 q^{18} +2.87116 q^{19} +17.5097 q^{20} +1.59891 q^{21} -12.0496 q^{22} -6.71149 q^{23} -6.25084 q^{24} +14.5147 q^{25} +6.73941 q^{26} +5.60622 q^{27} -4.86191 q^{28} +5.97613 q^{29} -14.0621 q^{30} -0.194994 q^{31} -0.351691 q^{32} +6.43177 q^{33} -8.35481 q^{34} -5.41865 q^{35} -5.15619 q^{36} -4.58157 q^{37} +7.01154 q^{38} -3.59732 q^{39} +21.1839 q^{40} -8.40654 q^{41} +3.90464 q^{42} +2.87579 q^{43} -19.5575 q^{44} -5.74663 q^{45} -16.3899 q^{46} -3.79223 q^{47} -4.93159 q^{48} -5.49540 q^{49} +35.4457 q^{50} +4.45958 q^{51} +10.9386 q^{52} +9.85864 q^{53} +13.6907 q^{54} -21.7970 q^{55} -5.88213 q^{56} -3.74258 q^{57} +14.5941 q^{58} -0.738043 q^{59} -22.8240 q^{60} -3.24433 q^{61} -0.476188 q^{62} +1.59567 q^{63} -8.42549 q^{64} +12.1912 q^{65} +15.7068 q^{66} +9.93407 q^{67} -13.5605 q^{68} +8.74849 q^{69} -13.2327 q^{70} +12.8706 q^{71} -6.23816 q^{72} -7.87147 q^{73} -11.1885 q^{74} -18.9200 q^{75} +11.3803 q^{76} +6.05238 q^{77} -8.78488 q^{78} -6.52390 q^{79} +16.7130 q^{80} -3.40516 q^{81} -20.5293 q^{82} -4.20664 q^{83} +6.33755 q^{84} -15.1133 q^{85} +7.02286 q^{86} -7.78994 q^{87} -23.6614 q^{88} -11.1609 q^{89} -14.0336 q^{90} -3.38513 q^{91} -26.6021 q^{92} +0.254177 q^{93} -9.26086 q^{94} +12.6835 q^{95} +0.458433 q^{96} +9.67947 q^{97} -13.4201 q^{98} +6.41872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} + 2 q^{3} + 29 q^{4} + 3 q^{5} + q^{6} + 17 q^{7} + 15 q^{8} + 34 q^{9} + q^{10} - 7 q^{12} + 28 q^{13} - 8 q^{14} - 2 q^{15} + 35 q^{16} + 16 q^{17} + 19 q^{18} + 13 q^{19} - 4 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) \) 24 * q + 5 * q^2 + 2 * q^3 + 29 * q^4 + 3 * q^5 + q^6 + 17 * q^7 + 15 * q^8 + 34 * q^9 + q^10 - 7 * q^12 + 28 * q^13 - 8 * q^14 - 2 * q^15 + 35 * q^16 + 16 * q^17 + 19 * q^18 + 13 * q^19 - 4 * q^20 - 4 * q^21 + 12 * q^22 + 7 * q^23 - 11 * q^24 + 67 * q^25 - 14 * q^26 - 10 * q^27 + 39 * q^28 - 2 * q^29 - 17 * q^30 + 20 * q^32 + 24 * q^33 - 18 * q^34 - 10 * q^35 + 20 * q^36 + 35 * q^37 - 5 * q^38 - 12 * q^39 - 36 * q^40 - 36 * q^42 + 34 * q^43 - 36 * q^44 - 27 * q^45 - 17 * q^46 - 3 * q^47 - 56 * q^48 + 49 * q^49 - 20 * q^50 - 28 * q^51 + 29 * q^52 - 9 * q^53 - 53 * q^54 + 10 * q^55 - 47 * q^56 + 47 * q^57 + 12 * q^58 - 6 * q^59 - 83 * q^60 + 3 * q^61 - 58 * q^62 + 13 * q^63 + 15 * q^64 + 8 * q^65 - 71 * q^66 + 42 * q^67 - 23 * q^68 - 30 * q^69 - 59 * q^70 - 13 * q^71 + 16 * q^72 + 83 * q^73 - 45 * q^74 - 65 * q^75 + 4 * q^76 - 21 * q^77 - 60 * q^78 - 3 * q^79 - 93 * q^80 + 28 * q^81 - 13 * q^82 - 23 * q^83 - 148 * q^84 + 52 * q^85 - 43 * q^86 - 5 * q^87 - 25 * q^88 - 38 * q^89 - 142 * q^90 - 17 * q^91 - 61 * q^92 + 17 * q^93 - 71 * q^94 - 66 * q^95 - 101 * q^96 + 63 * q^97 - 29 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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