LMFDB - Embedded newform 1617.4.a.z.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 45 x^{8} + 168 x^{7} + 651 x^{6} - 2176 x^{5} - 3439 x^{4} + 8716 x^{3} + 7840 x^{2} + \cdots - 4032 $ x^10 - 4x^9 - 45x^8 + 168x^7 + 651x^6 - 2176x^5 - 3439x^4 + 8716x^3 + 7840x^2 - 9216*x - 4032
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.53481$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.53481 q^{2} +3.00000 q^{3} +4.49490 q^{4} -15.9961 q^{5} +10.6044 q^{6} -12.3899 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.53481 q^{2} +3.00000 q^{3} +4.49490 q^{4} -15.9961 q^{5} +10.6044 q^{6} -12.3899 q^{8} +9.00000 q^{9} -56.5431 q^{10} -11.0000 q^{11} +13.4847 q^{12} -25.4845 q^{13} -47.9882 q^{15} -79.7551 q^{16} +58.2343 q^{17} +31.8133 q^{18} +8.86464 q^{19} -71.9007 q^{20} -38.8829 q^{22} +84.2132 q^{23} -37.1696 q^{24} +130.874 q^{25} -90.0829 q^{26} +27.0000 q^{27} +151.367 q^{29} -169.629 q^{30} -228.235 q^{31} -182.800 q^{32} -33.0000 q^{33} +205.847 q^{34} +40.4541 q^{36} +303.455 q^{37} +31.3349 q^{38} -76.4535 q^{39} +198.189 q^{40} -106.618 q^{41} +182.255 q^{43} -49.4439 q^{44} -143.965 q^{45} +297.678 q^{46} +25.4865 q^{47} -239.265 q^{48} +462.616 q^{50} +174.703 q^{51} -114.550 q^{52} -4.48318 q^{53} +95.4399 q^{54} +175.957 q^{55} +26.5939 q^{57} +535.054 q^{58} +233.761 q^{59} -215.702 q^{60} +381.181 q^{61} -806.768 q^{62} -8.12377 q^{64} +407.652 q^{65} -116.649 q^{66} +891.507 q^{67} +261.757 q^{68} +252.640 q^{69} -355.079 q^{71} -111.509 q^{72} -259.945 q^{73} +1072.65 q^{74} +392.623 q^{75} +39.8457 q^{76} -270.249 q^{78} +1203.33 q^{79} +1275.77 q^{80} +81.0000 q^{81} -376.876 q^{82} +686.630 q^{83} -931.520 q^{85} +644.239 q^{86} +454.101 q^{87} +136.289 q^{88} +296.459 q^{89} -508.888 q^{90} +378.530 q^{92} -684.705 q^{93} +90.0899 q^{94} -141.799 q^{95} -548.401 q^{96} +1871.92 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9} + 44 q^{10} - 110 q^{11} + 78 q^{12} + 82 q^{13} + 60 q^{15} - 10 q^{16} + 164 q^{17} + 36 q^{18} - 76 q^{19} + 356 q^{20} - 44 q^{22} + 140 q^{23} + 108 q^{24} + 472 q^{25} + 360 q^{26} + 270 q^{27} + 40 q^{29} + 132 q^{30} + 24 q^{31} + 112 q^{32} - 330 q^{33} - 262 q^{34} + 234 q^{36} + 412 q^{37} + 16 q^{38} + 246 q^{39} + 828 q^{40} - 228 q^{41} + 530 q^{43} - 286 q^{44} + 180 q^{45} + 1422 q^{46} + 768 q^{47} - 30 q^{48} + 670 q^{50} + 492 q^{51} + 952 q^{52} + 136 q^{53} + 108 q^{54} - 220 q^{55} - 228 q^{57} + 1708 q^{58} + 608 q^{59} + 1068 q^{60} + 1618 q^{61} + 164 q^{62} - 1238 q^{64} + 2764 q^{65} - 132 q^{66} + 1002 q^{67} + 2816 q^{68} + 420 q^{69} + 812 q^{71} + 324 q^{72} + 134 q^{73} + 342 q^{74} + 1416 q^{75} - 450 q^{76} + 1080 q^{78} + 1262 q^{79} - 1316 q^{80} + 810 q^{81} + 982 q^{82} + 1078 q^{83} - 1402 q^{85} + 1692 q^{86} + 120 q^{87} - 396 q^{88} + 2880 q^{89} + 396 q^{90} + 2364 q^{92} + 72 q^{93} - 2362 q^{94} + 2866 q^{95} + 336 q^{96} - 1030 q^{97} - 990 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9 + 44 * q^10 - 110 * q^11 + 78 * q^12 + 82 * q^13 + 60 * q^15 - 10 * q^16 + 164 * q^17 + 36 * q^18 - 76 * q^19 + 356 * q^20 - 44 * q^22 + 140 * q^23 + 108 * q^24 + 472 * q^25 + 360 * q^26 + 270 * q^27 + 40 * q^29 + 132 * q^30 + 24 * q^31 + 112 * q^32 - 330 * q^33 - 262 * q^34 + 234 * q^36 + 412 * q^37 + 16 * q^38 + 246 * q^39 + 828 * q^40 - 228 * q^41 + 530 * q^43 - 286 * q^44 + 180 * q^45 + 1422 * q^46 + 768 * q^47 - 30 * q^48 + 670 * q^50 + 492 * q^51 + 952 * q^52 + 136 * q^53 + 108 * q^54 - 220 * q^55 - 228 * q^57 + 1708 * q^58 + 608 * q^59 + 1068 * q^60 + 1618 * q^61 + 164 * q^62 - 1238 * q^64 + 2764 * q^65 - 132 * q^66 + 1002 * q^67 + 2816 * q^68 + 420 * q^69 + 812 * q^71 + 324 * q^72 + 134 * q^73 + 342 * q^74 + 1416 * q^75 - 450 * q^76 + 1080 * q^78 + 1262 * q^79 - 1316 * q^80 + 810 * q^81 + 982 * q^82 + 1078 * q^83 - 1402 * q^85 + 1692 * q^86 + 120 * q^87 - 396 * q^88 + 2880 * q^89 + 396 * q^90 + 2364 * q^92 + 72 * q^93 - 2362 * q^94 + 2866 * q^95 + 336 * q^96 - 1030 * q^97 - 990 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	3.53481	1.24974	0.624872	−	0.780727i	$-0.285151\pi$
$2$	3.53481	1.24974	0.624872	+	0.780727i	$0.285151\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.49490	0.561862
$5$	−15.9961	−1.43073	−0.715366	−	0.698750i	$-0.753740\pi$
$5$	−15.9961	−1.43073	−0.715366	+	0.698750i	$0.753740\pi$
$6$	10.6044	0.721541
$7$	0	0
$7$	0	0
$8$	−12.3899	−0.547560
$9$	9.00000	0.333333
$10$	−56.5431	−1.78805
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	13.4847	0.324391
$13$	−25.4845	−0.543702	−0.271851	−	0.962339i	$-0.587636\pi$
$13$	−25.4845	−0.543702	−0.271851	+	0.962339i	$0.587636\pi$
$14$	0	0
$15$	−47.9882	−0.826033
$16$	−79.7551	−1.24617
$17$	58.2343	0.830818	0.415409	−	0.909635i	$-0.363639\pi$
$17$	58.2343	0.830818	0.415409	+	0.909635i	$0.363639\pi$
$18$	31.8133	0.416582
$19$	8.86464	0.107036	0.0535181	−	0.998567i	$-0.482957\pi$
$19$	8.86464	0.107036	0.0535181	+	0.998567i	$0.482957\pi$
$20$	−71.9007	−0.803874
$21$	0	0
$22$	−38.8829	−0.376812
$23$	84.2132	0.763464	0.381732	−	0.924273i	$-0.375328\pi$
$23$	84.2132	0.763464	0.381732	+	0.924273i	$0.375328\pi$
$24$	−37.1696	−0.316134
$25$	130.874	1.04699
$26$	−90.0829	−0.679489
$27$	27.0000	0.192450
$28$	0	0
$29$	151.367	0.969247	0.484624	−	0.874723i	$-0.338957\pi$
$29$	151.367	0.969247	0.484624	+	0.874723i	$0.338957\pi$
$30$	−169.629	−1.03233
$31$	−228.235	−1.32233	−0.661165	−	0.750240i	$-0.729938\pi$
$31$	−228.235	−1.32233	−0.661165	+	0.750240i	$0.729938\pi$
$32$	−182.800	−1.00984
$33$	−33.0000	−0.174078
$34$	205.847	1.03831
$35$	0	0
$36$	40.4541	0.187287
$37$	303.455	1.34831	0.674157	−	0.738588i	$-0.264507\pi$
$37$	303.455	1.34831	0.674157	+	0.738588i	$0.264507\pi$
$38$	31.3349	0.133768
$39$	−76.4535	−0.313907
$40$	198.189	0.783412
$41$	−106.618	−0.406122	−0.203061	−	0.979166i	$-0.565089\pi$
$41$	−106.618	−0.406122	−0.203061	+	0.979166i	$0.565089\pi$
$42$	0	0
$43$	182.255	0.646365	0.323182	−	0.946337i	$-0.395247\pi$
$43$	182.255	0.646365	0.323182	+	0.946337i	$0.395247\pi$
$44$	−49.4439	−0.169408
$45$	−143.965	−0.476911
$46$	297.678	0.954135
$47$	25.4865	0.0790976	0.0395488	−	0.999218i	$-0.487408\pi$
$47$	25.4865	0.0790976	0.0395488	+	0.999218i	$0.487408\pi$
$48$	−239.265	−0.719478
$49$	0	0
$50$	462.616	1.30848
$51$	174.703	0.479673
$52$	−114.550	−0.305486
$53$	−4.48318	−0.0116191	−0.00580955	−	0.999983i	$-0.501849\pi$
$53$	−4.48318	−0.0116191	−0.00580955	+	0.999983i	$0.501849\pi$
$54$	95.4399	0.240514
$55$	175.957	0.431382
$56$	0	0
$57$	26.5939	0.0617974
$58$	535.054	1.21131
$59$	233.761	0.515815	0.257908	−	0.966170i	$-0.416967\pi$
$59$	233.761	0.515815	0.257908	+	0.966170i	$0.416967\pi$
$60$	−215.702	−0.464117
$61$	381.181	0.800086	0.400043	−	0.916496i	$-0.368995\pi$
$61$	381.181	0.800086	0.400043	+	0.916496i	$0.368995\pi$
$62$	−806.768	−1.65258
$63$	0	0
$64$	−8.12377	−0.0158667
$65$	407.652	0.777892
$66$	−116.649	−0.217553
$67$	891.507	1.62560	0.812798	−	0.582546i	$-0.197943\pi$
$67$	891.507	1.62560	0.812798	+	0.582546i	$0.197943\pi$
$68$	261.757	0.466805
$69$	252.640	0.440786
$70$	0	0
$71$	−355.079	−0.593523	−0.296762	−	0.954952i	$-0.595907\pi$
$71$	−355.079	−0.593523	−0.296762	+	0.954952i	$0.595907\pi$
$72$	−111.509	−0.182520
$73$	−259.945	−0.416770	−0.208385	−	0.978047i	$-0.566821\pi$
$73$	−259.945	−0.416770	−0.208385	+	0.978047i	$0.566821\pi$
$74$	1072.65	1.68505
$75$	392.623	0.604482
$76$	39.8457	0.0601396
$77$	0	0
$78$	−270.249	−0.392303
$79$	1203.33	1.71374	0.856869	−	0.515534i	$-0.172407\pi$
$79$	1203.33	1.71374	0.856869	+	0.515534i	$0.172407\pi$
$80$	1275.77	1.78294
$81$	81.0000	0.111111
$82$	−376.876	−0.507549
$83$	686.630	0.908041	0.454020	−	0.890991i	$-0.349989\pi$
$83$	686.630	0.908041	0.454020	+	0.890991i	$0.349989\pi$
$84$	0	0
$85$	−931.520	−1.18868
$86$	644.239	0.807791
$87$	454.101	0.559595
$88$	136.289	0.165096
$89$	296.459	0.353086	0.176543	−	0.984293i	$-0.443509\pi$
$89$	296.459	0.353086	0.176543	+	0.984293i	$0.443509\pi$
$90$	−508.888	−0.596017
$91$	0	0
$92$	378.530	0.428962
$93$	−684.705	−0.763448
$94$	90.0899	0.0988518
$95$	−141.799	−0.153140
$96$	−548.401	−0.583030
$97$	1871.92	1.95943	0.979715	−	0.200398i	$-0.0642235\pi$
$97$	1871.92	1.95943	0.979715	+	0.200398i	$0.0642235\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	588.266	0.588266
$101$	−640.972	−0.631476	−0.315738	−	0.948846i	$-0.602252\pi$
$101$	−640.972	−0.631476	−0.315738	+	0.948846i	$0.602252\pi$
$102$	617.542	0.599469
$103$	−1782.13	−1.70484	−0.852421	−	0.522856i	$-0.824867\pi$
$103$	−1782.13	−1.70484	−0.852421	+	0.522856i	$0.824867\pi$
$104$	315.750	0.297710
$105$	0	0
$106$	−15.8472	−0.0145209
$107$	−63.8552	−0.0576927	−0.0288463	−	0.999584i	$-0.509183\pi$
$107$	−63.8552	−0.0576927	−0.0288463	+	0.999584i	$0.509183\pi$
$108$	121.362	0.108130
$109$	−620.187	−0.544983	−0.272491	−	0.962158i	$-0.587848\pi$
$109$	−620.187	−0.544983	−0.272491	+	0.962158i	$0.587848\pi$
$110$	621.974	0.539117
$111$	910.364	0.778450
$112$	0	0
$113$	482.690	0.401838	0.200919	−	0.979608i	$-0.435607\pi$
$113$	482.690	0.401838	0.200919	+	0.979608i	$0.435607\pi$
$114$	94.0046	0.0772310
$115$	−1347.08	−1.09231
$116$	680.380	0.544583
$117$	−229.361	−0.181234
$118$	826.302	0.644638
$119$	0	0
$120$	594.568	0.452303
$121$	121.000	0.0909091
$122$	1347.40	0.999903
$123$	−319.855	−0.234475
$124$	−1025.89	−0.742967
$125$	−93.9646	−0.0672356
$126$	0	0
$127$	2575.01	1.79918	0.899588	−	0.436739i	$-0.143867\pi$
$127$	2575.01	1.79918	0.899588	+	0.436739i	$0.143867\pi$
$128$	1433.69	0.990009
$129$	546.766	0.373179
$130$	1440.97	0.972167
$131$	−2280.94	−1.52127	−0.760637	−	0.649177i	$-0.775113\pi$
$131$	−2280.94	−1.52127	−0.760637	+	0.649177i	$0.775113\pi$
$132$	−148.332	−0.0978077
$133$	0	0
$134$	3151.31	2.03158
$135$	−431.894	−0.275344
$136$	−721.516	−0.454923
$137$	31.0836	0.0193843	0.00969216	−	0.999953i	$-0.496915\pi$
$137$	31.0836	0.0193843	0.00969216	+	0.999953i	$0.496915\pi$
$138$	893.034	0.550870
$139$	−1794.21	−1.09484	−0.547421	−	0.836857i	$-0.684390\pi$
$139$	−1794.21	−1.09484	−0.547421	+	0.836857i	$0.684390\pi$
$140$	0	0
$141$	76.4594	0.0456670
$142$	−1255.14	−0.741753
$143$	280.330	0.163932
$144$	−717.796	−0.415391
$145$	−2421.28	−1.38673
$146$	−918.856	−0.520857
$147$	0	0
$148$	1364.00	0.757567
$149$	322.019	0.177052	0.0885262	−	0.996074i	$-0.471784\pi$
$149$	322.019	0.177052	0.0885262	+	0.996074i	$0.471784\pi$
$150$	1387.85	0.755448
$151$	2520.51	1.35838	0.679192	−	0.733961i	$-0.262330\pi$
$151$	2520.51	1.35838	0.679192	+	0.733961i	$0.262330\pi$
$152$	−109.832	−0.0586088
$153$	524.109	0.276939
$154$	0	0
$155$	3650.86	1.89190
$156$	−343.651	−0.176372
$157$	−791.804	−0.402502	−0.201251	−	0.979540i	$-0.564501\pi$
$157$	−791.804	−0.402502	−0.201251	+	0.979540i	$0.564501\pi$
$158$	4253.55	2.14173
$159$	−13.4495	−0.00670829
$160$	2924.08	1.44481
$161$	0	0
$162$	286.320	0.138861
$163$	−2841.88	−1.36560	−0.682801	−	0.730604i	$-0.739239\pi$
$163$	−2841.88	−1.36560	−0.682801	+	0.730604i	$0.739239\pi$
$164$	−479.239	−0.228185
$165$	527.870	0.249058
$166$	2427.11	1.13482
$167$	3208.10	1.48653	0.743264	−	0.668999i	$-0.233277\pi$
$167$	3208.10	1.48653	0.743264	+	0.668999i	$0.233277\pi$
$168$	0	0
$169$	−1547.54	−0.704388
$170$	−3292.75	−1.48554
$171$	79.7818	0.0356788
$172$	819.220	0.363168
$173$	−1823.32	−0.801296	−0.400648	−	0.916232i	$-0.631215\pi$
$173$	−1823.32	−0.801296	−0.400648	+	0.916232i	$0.631215\pi$
$174$	1605.16	0.699351
$175$	0	0
$176$	877.306	0.375735
$177$	701.283	0.297806
$178$	1047.93	0.441267
$179$	2247.65	0.938530	0.469265	−	0.883057i	$-0.344519\pi$
$179$	2247.65	0.938530	0.469265	+	0.883057i	$0.344519\pi$
$180$	−647.106	−0.267958
$181$	−777.610	−0.319333	−0.159667	−	0.987171i	$-0.551042\pi$
$181$	−777.610	−0.319333	−0.159667	+	0.987171i	$0.551042\pi$
$182$	0	0
$183$	1143.54	0.461930
$184$	−1043.39	−0.418043
$185$	−4854.08	−1.92908
$186$	−2420.30	−0.954115
$187$	−640.578	−0.250501
$188$	114.559	0.0444419
$189$	0	0
$190$	−501.234	−0.191386
$191$	3733.33	1.41431	0.707157	−	0.707056i	$-0.249977\pi$
$191$	3733.33	1.41431	0.707157	+	0.707056i	$0.249977\pi$
$192$	−24.3713	−0.00916067
$193$	−4886.94	−1.82264	−0.911321	−	0.411698i	$-0.864936\pi$
$193$	−4886.94	−1.82264	−0.911321	+	0.411698i	$0.864936\pi$
$194$	6616.88	2.44879
$195$	1222.96	0.449116
$196$	0	0
$197$	4294.65	1.55320	0.776601	−	0.629993i	$-0.216942\pi$
$197$	4294.65	1.55320	0.776601	+	0.629993i	$0.216942\pi$
$198$	−349.946	−0.125604
$199$	3246.08	1.15633	0.578163	−	0.815921i	$-0.303770\pi$
$199$	3246.08	1.15633	0.578163	+	0.815921i	$0.303770\pi$
$200$	−1621.52	−0.573292
$201$	2674.52	0.938538
$202$	−2265.71	−0.789184
$203$	0	0
$204$	785.272	0.269510
$205$	1705.48	0.581052
$206$	−6299.50	−2.13062
$207$	757.919	0.254488
$208$	2032.52	0.677547
$209$	−97.5111	−0.0322726
$210$	0	0
$211$	−1086.12	−0.354367	−0.177184	−	0.984178i	$-0.556699\pi$
$211$	−1086.12	−0.354367	−0.177184	+	0.984178i	$0.556699\pi$
$212$	−20.1514	−0.00652833
$213$	−1065.24	−0.342671
$214$	−225.716	−0.0721012
$215$	−2915.37	−0.924775
$216$	−334.527	−0.105378
$217$	0	0
$218$	−2192.24	−0.681089
$219$	−779.835	−0.240623
$220$	790.908	0.242377
$221$	−1484.07	−0.451717
$222$	3217.96	0.972863
$223$	−1928.44	−0.579093	−0.289546	−	0.957164i	$-0.593504\pi$
$223$	−1928.44	−0.579093	−0.289546	+	0.957164i	$0.593504\pi$
$224$	0	0
$225$	1177.87	0.348998
$226$	1706.22	0.502194
$227$	−429.010	−0.125438	−0.0627189	−	0.998031i	$-0.519977\pi$
$227$	−429.010	−0.125438	−0.0627189	+	0.998031i	$0.519977\pi$
$228$	119.537	0.0347216
$229$	3413.54	0.985036	0.492518	−	0.870302i	$-0.336077\pi$
$229$	3413.54	0.985036	0.492518	+	0.870302i	$0.336077\pi$
$230$	−4761.68	−1.36511
$231$	0	0
$232$	−1875.42	−0.530721
$233$	−3037.33	−0.854002	−0.427001	−	0.904251i	$-0.640430\pi$
$233$	−3037.33	−0.854002	−0.427001	+	0.904251i	$0.640430\pi$
$234$	−810.747	−0.226496
$235$	−407.683	−0.113167
$236$	1050.73	0.289817
$237$	3609.99	0.989427
$238$	0	0
$239$	601.549	0.162807	0.0814036	−	0.996681i	$-0.474060\pi$
$239$	601.549	0.162807	0.0814036	+	0.996681i	$0.474060\pi$
$240$	3827.30	1.02938
$241$	−1610.82	−0.430547	−0.215274	−	0.976554i	$-0.569064\pi$
$241$	−1610.82	−0.430547	−0.215274	+	0.976554i	$0.569064\pi$
$242$	427.712	0.113613
$243$	243.000	0.0641500
$244$	1713.37	0.449538
$245$	0	0
$246$	−1130.63	−0.293034
$247$	−225.911	−0.0581959
$248$	2827.81	0.724056
$249$	2059.89	0.524258
$250$	−332.147	−0.0840273
$251$	6565.71	1.65109	0.825546	−	0.564335i	$-0.190867\pi$
$251$	6565.71	1.65109	0.825546	+	0.564335i	$0.190867\pi$
$252$	0	0
$253$	−926.346	−0.230193
$254$	9102.19	2.24851
$255$	−2794.56	−0.686283
$256$	5132.80	1.25312
$257$	−5020.87	−1.21865	−0.609326	−	0.792920i	$-0.708560\pi$
$257$	−5020.87	−1.21865	−0.609326	+	0.792920i	$0.708560\pi$
$258$	1932.72	0.466379
$259$	0	0
$260$	1832.35	0.437068
$261$	1362.30	0.323082
$262$	−8062.71	−1.90121
$263$	−2953.30	−0.692428	−0.346214	−	0.938156i	$-0.612533\pi$
$263$	−2953.30	−0.692428	−0.346214	+	0.938156i	$0.612533\pi$
$264$	408.866	0.0953180
$265$	71.7132	0.0166238
$266$	0	0
$267$	889.378	0.203854
$268$	4007.23	0.913361
$269$	2508.32	0.568531	0.284266	−	0.958746i	$-0.408250\pi$
$269$	2508.32	0.568531	0.284266	+	0.958746i	$0.408250\pi$
$270$	−1526.66	−0.344110
$271$	5857.45	1.31297	0.656485	−	0.754339i	$-0.272043\pi$
$271$	5857.45	1.31297	0.656485	+	0.754339i	$0.272043\pi$
$272$	−4644.48	−1.03534
$273$	0	0
$274$	109.875	0.0242255
$275$	−1439.62	−0.315681
$276$	1135.59	0.247661
$277$	−5169.49	−1.12132	−0.560658	−	0.828048i	$-0.689452\pi$
$277$	−5169.49	−1.12132	−0.560658	+	0.828048i	$0.689452\pi$
$278$	−6342.20	−1.36827
$279$	−2054.12	−0.440777
$280$	0	0
$281$	4954.97	1.05192	0.525958	−	0.850510i	$-0.323707\pi$
$281$	4954.97	1.05192	0.525958	+	0.850510i	$0.323707\pi$
$282$	270.270	0.0570721
$283$	−4391.59	−0.922449	−0.461224	−	0.887284i	$-0.652590\pi$
$283$	−4391.59	−0.922449	−0.461224	+	0.887284i	$0.652590\pi$
$284$	−1596.05	−0.333478
$285$	−425.398	−0.0884155
$286$	990.912	0.204874
$287$	0	0
$288$	−1645.20	−0.336613
$289$	−1521.76	−0.309742
$290$	−8558.77	−1.73306
$291$	5615.76	1.13128
$292$	−1168.43	−0.234168
$293$	8257.12	1.64637	0.823185	−	0.567774i	$-0.192195\pi$
$293$	8257.12	1.64637	0.823185	+	0.567774i	$0.192195\pi$
$294$	0	0
$295$	−3739.26	−0.737993
$296$	−3759.77	−0.738283
$297$	−297.000	−0.0580259
$298$	1138.28	0.221270
$299$	−2146.13	−0.415097
$300$	1764.80	0.339636
$301$	0	0
$302$	8909.52	1.69763
$303$	−1922.91	−0.364583
$304$	−707.000	−0.133386
$305$	−6097.40	−1.14471
$306$	1852.63	0.346103
$307$	−10153.6	−1.88761	−0.943803	−	0.330509i	$-0.892780\pi$
$307$	−10153.6	−1.88761	−0.943803	+	0.330509i	$0.892780\pi$
$308$	0	0
$309$	−5346.40	−0.984291
$310$	12905.1	2.36439
$311$	−9344.62	−1.70381	−0.851904	−	0.523697i	$-0.824552\pi$
$311$	−9344.62	−1.70381	−0.851904	+	0.523697i	$0.824552\pi$
$312$	947.250	0.171883
$313$	−5167.02	−0.933090	−0.466545	−	0.884497i	$-0.654501\pi$
$313$	−5167.02	−0.933090	−0.466545	+	0.884497i	$0.654501\pi$
$314$	−2798.88	−0.503025
$315$	0	0
$316$	5408.85	0.962884
$317$	6572.10	1.16444	0.582218	−	0.813033i	$-0.302185\pi$
$317$	6572.10	1.16444	0.582218	+	0.813033i	$0.302185\pi$
$318$	−47.5416	−0.00838365
$319$	−1665.04	−0.292239
$320$	129.948	0.0227011
$321$	−191.566	−0.0333089
$322$	0	0
$323$	516.227	0.0889276
$324$	364.087	0.0624291
$325$	−3335.27	−0.569253
$326$	−10045.5	−1.70666
$327$	−1860.56	−0.314646
$328$	1320.99	0.222376
$329$	0	0
$330$	1865.92	0.311260
$331$	−8431.25	−1.40007	−0.700035	−	0.714108i	$-0.746832\pi$
$331$	−8431.25	−1.40007	−0.700035	+	0.714108i	$0.746832\pi$
$332$	3086.33	0.510194
$333$	2731.09	0.449438
$334$	11340.0	1.85778
$335$	−14260.6	−2.32579
$336$	0	0
$337$	5331.53	0.861801	0.430900	−	0.902400i	$-0.358196\pi$
$337$	5331.53	0.861801	0.430900	+	0.902400i	$0.358196\pi$
$338$	−5470.26	−0.880305
$339$	1448.07	0.232001
$340$	−4187.09	−0.667873
$341$	2510.59	0.398698
$342$	282.014	0.0445893
$343$	0	0
$344$	−2258.12	−0.353924
$345$	−4041.24	−0.630647
$346$	−6445.08	−1.00142
$347$	−10849.2	−1.67843	−0.839214	−	0.543801i	$-0.816984\pi$
$347$	−10849.2	−1.67843	−0.839214	+	0.543801i	$0.816984\pi$
$348$	2041.14	0.314415
$349$	1502.96	0.230520	0.115260	−	0.993335i	$-0.463230\pi$
$349$	1502.96	0.230520	0.115260	+	0.993335i	$0.463230\pi$
$350$	0	0
$351$	−688.082	−0.104636
$352$	2010.80	0.304478
$353$	6524.16	0.983700	0.491850	−	0.870680i	$-0.336321\pi$
$353$	6524.16	0.983700	0.491850	+	0.870680i	$0.336321\pi$
$354$	2478.90	0.372182
$355$	5679.87	0.849173
$356$	1332.55	0.198386
$357$	0	0
$358$	7945.01	1.17292
$359$	5294.33	0.778340	0.389170	−	0.921166i	$-0.372762\pi$
$359$	5294.33	0.778340	0.389170	+	0.921166i	$0.372762\pi$
$360$	1783.70	0.261137
$361$	−6780.42	−0.988543
$362$	−2748.70	−0.399085
$363$	363.000	0.0524864
$364$	0	0
$365$	4158.10	0.596287
$366$	4042.21	0.577294
$367$	4402.33	0.626157	0.313079	−	0.949727i	$-0.398640\pi$
$367$	4402.33	0.626157	0.313079	+	0.949727i	$0.398640\pi$
$368$	−6716.43	−0.951408
$369$	−959.566	−0.135374
$370$	−17158.3	−2.41085
$371$	0	0
$372$	−3077.68	−0.428952
$373$	12479.9	1.73240	0.866202	−	0.499694i	$-0.166554\pi$
$373$	12479.9	1.73240	0.866202	+	0.499694i	$0.166554\pi$
$374$	−2264.32	−0.313062
$375$	−281.894	−0.0388185
$376$	−315.774	−0.0433107
$377$	−3857.52	−0.526982
$378$	0	0
$379$	6716.24	0.910264	0.455132	−	0.890424i	$-0.349592\pi$
$379$	6716.24	0.910264	0.455132	+	0.890424i	$0.349592\pi$
$380$	−637.374	−0.0860437
$381$	7725.04	1.03875
$382$	13196.6	1.76753
$383$	−3168.43	−0.422713	−0.211357	−	0.977409i	$-0.567788\pi$
$383$	−3168.43	−0.422713	−0.211357	+	0.977409i	$0.567788\pi$
$384$	4301.06	0.571582
$385$	0	0
$386$	−17274.4	−2.27784
$387$	1640.30	0.215455
$388$	8414.09	1.10093
$389$	1253.47	0.163377	0.0816884	−	0.996658i	$-0.473969\pi$
$389$	1253.47	0.163377	0.0816884	+	0.996658i	$0.473969\pi$
$390$	4322.92	0.561281
$391$	4904.10	0.634299
$392$	0	0
$393$	−6842.83	−0.878308
$394$	15180.8	1.94111
$395$	−19248.6	−2.45190
$396$	−444.995	−0.0564693
$397$	6976.59	0.881978	0.440989	−	0.897513i	$-0.354628\pi$
$397$	6976.59	0.881978	0.440989	+	0.897513i	$0.354628\pi$
$398$	11474.3	1.44511
$399$	0	0
$400$	−10437.9	−1.30474
$401$	−12477.3	−1.55383	−0.776917	−	0.629603i	$-0.783218\pi$
$401$	−12477.3	−1.55383	−0.776917	+	0.629603i	$0.783218\pi$
$402$	9453.93	1.17293
$403$	5816.46	0.718954
$404$	−2881.10	−0.354802
$405$	−1295.68	−0.158970
$406$	0	0
$407$	−3338.00	−0.406532
$408$	−2164.55	−0.262650
$409$	−129.934	−0.0157086	−0.00785432	−	0.999969i	$-0.502500\pi$
$409$	−129.934	−0.0157086	−0.00785432	+	0.999969i	$0.502500\pi$
$410$	6028.54	0.726167
$411$	93.2508	0.0111915
$412$	−8010.50	−0.957886
$413$	0	0
$414$	2679.10	0.318045
$415$	−10983.4	−1.29916
$416$	4658.57	0.549051
$417$	−5382.64	−0.632108
$418$	−344.683	−0.0403326
$419$	16687.2	1.94564	0.972819	−	0.231568i	$-0.0743856\pi$
$419$	16687.2	1.94564	0.972819	+	0.231568i	$0.0743856\pi$
$420$	0	0
$421$	−6673.48	−0.772554	−0.386277	−	0.922383i	$-0.626239\pi$
$421$	−6673.48	−0.772554	−0.386277	+	0.922383i	$0.626239\pi$
$422$	−3839.22	−0.442868
$423$	229.378	0.0263659
$424$	55.5460	0.00636215
$425$	7621.37	0.869861
$426$	−3765.42	−0.428251
$427$	0	0
$428$	−287.023	−0.0324153
$429$	840.989	0.0946464
$430$	−10305.3	−1.15573
$431$	13274.4	1.48354	0.741768	−	0.670657i	$-0.233988\pi$
$431$	13274.4	1.48354	0.741768	+	0.670657i	$0.233988\pi$
$432$	−2153.39	−0.239826
$433$	−3377.93	−0.374903	−0.187451	−	0.982274i	$-0.560023\pi$
$433$	−3377.93	−0.374903	−0.187451	+	0.982274i	$0.560023\pi$
$434$	0	0
$435$	−7263.84	−0.800631
$436$	−2787.68	−0.306205
$437$	746.520	0.0817183
$438$	−2756.57	−0.300717
$439$	7532.26	0.818895	0.409448	−	0.912334i	$-0.365721\pi$
$439$	7532.26	0.818895	0.409448	+	0.912334i	$0.365721\pi$
$440$	−2180.08	−0.236208
$441$	0	0
$442$	−5245.92	−0.564532
$443$	−6055.78	−0.649478	−0.324739	−	0.945804i	$-0.605277\pi$
$443$	−6055.78	−0.649478	−0.324739	+	0.945804i	$0.605277\pi$
$444$	4091.99	0.437381
$445$	−4742.19	−0.505171
$446$	−6816.66	−0.723718
$447$	966.056	0.102221
$448$	0	0
$449$	11091.6	1.16580	0.582899	−	0.812544i	$-0.301918\pi$
$449$	11091.6	1.16580	0.582899	+	0.812544i	$0.301918\pi$
$450$	4163.54	0.436158
$451$	1172.80	0.122450
$452$	2169.64	0.225777
$453$	7561.52	0.784263
$454$	−1516.47	−0.156765
$455$	0	0
$456$	−329.496	−0.0338378
$457$	−5837.50	−0.597521	−0.298760	−	0.954328i	$-0.596573\pi$
$457$	−5837.50	−0.597521	−0.298760	+	0.954328i	$0.596573\pi$
$458$	12066.2	1.23104
$459$	1572.33	0.159891
$460$	−6054.99	−0.613729
$461$	10153.5	1.02580	0.512902	−	0.858447i	$-0.328570\pi$
$461$	10153.5	1.02580	0.512902	+	0.858447i	$0.328570\pi$
$462$	0	0
$463$	−16764.9	−1.68279	−0.841396	−	0.540419i	$-0.818266\pi$
$463$	−16764.9	−1.68279	−0.841396	+	0.540419i	$0.818266\pi$
$464$	−12072.3	−1.20785
$465$	10952.6	1.09229
$466$	−10736.4	−1.06728
$467$	10061.3	0.996959	0.498479	−	0.866902i	$-0.333892\pi$
$467$	10061.3	0.996959	0.498479	+	0.866902i	$0.333892\pi$
$468$	−1030.95	−0.101829
$469$	0	0
$470$	−1441.08	−0.141430
$471$	−2375.41	−0.232385
$472$	−2896.27	−0.282440
$473$	−2004.81	−0.194886
$474$	12760.6	1.23653
$475$	1160.15	0.112066
$476$	0	0
$477$	−40.3486	−0.00387303
$478$	2126.36	0.203468
$479$	−6645.91	−0.633944	−0.316972	−	0.948435i	$-0.602666\pi$
$479$	−6645.91	−0.633944	−0.316972	+	0.948435i	$0.602666\pi$
$480$	8772.25	0.834160
$481$	−7733.39	−0.733082
$482$	−5693.94	−0.538074
$483$	0	0
$484$	543.883	0.0510784
$485$	−29943.4	−2.80342
$486$	858.959	0.0801712
$487$	−4418.21	−0.411105	−0.205552	−	0.978646i	$-0.565899\pi$
$487$	−4418.21	−0.411105	−0.205552	+	0.978646i	$0.565899\pi$
$488$	−4722.79	−0.438095
$489$	−8525.64	−0.788431
$490$	0	0
$491$	5231.74	0.480866	0.240433	−	0.970666i	$-0.422711\pi$
$491$	5231.74	0.480866	0.240433	+	0.970666i	$0.422711\pi$
$492$	−1437.72	−0.131742
$493$	8814.76	0.805268
$494$	−798.553	−0.0727300
$495$	1583.61	0.143794
$496$	18202.9	1.64785
$497$	0	0
$498$	7281.32	0.655188
$499$	22173.1	1.98919	0.994595	−	0.103830i	$-0.0331099\pi$
$499$	22173.1	1.98919	0.994595	+	0.103830i	$0.0331099\pi$
$500$	−422.361	−0.0377771
$501$	9624.29	0.858247
$502$	23208.6	2.06344
$503$	9463.88	0.838914	0.419457	−	0.907775i	$-0.362221\pi$
$503$	9463.88	0.838914	0.419457	+	0.907775i	$0.362221\pi$
$504$	0	0
$505$	10253.0	0.903473
$506$	−3274.46	−0.287683
$507$	−4642.62	−0.406678
$508$	11574.4	1.01089
$509$	−1452.02	−0.126443	−0.0632215	−	0.998000i	$-0.520137\pi$
$509$	−1452.02	−0.126443	−0.0632215	+	0.998000i	$0.520137\pi$
$510$	−9878.25	−0.857679
$511$	0	0
$512$	6674.00	0.576078
$513$	239.345	0.0205991
$514$	−17747.8	−1.52300
$515$	28507.1	2.43917
$516$	2457.66	0.209675
$517$	−280.351	−0.0238488
$518$	0	0
$519$	−5469.95	−0.462628
$520$	−5050.76	−0.425943
$521$	20252.7	1.70305	0.851523	−	0.524317i	$-0.175679\pi$
$521$	20252.7	1.70305	0.851523	+	0.524317i	$0.175679\pi$
$522$	4815.49	0.403771
$523$	7204.86	0.602383	0.301192	−	0.953564i	$-0.402616\pi$
$523$	7204.86	0.602383	0.301192	+	0.953564i	$0.402616\pi$
$524$	−10252.6	−0.854747
$525$	0	0
$526$	−10439.4	−0.865358
$527$	−13291.1	−1.09862
$528$	2631.92	0.216931
$529$	−5075.13	−0.417123
$530$	253.493	0.0207755
$531$	2103.85	0.171938
$532$	0	0
$533$	2717.12	0.220810
$534$	3143.79	0.254766
$535$	1021.43	0.0825428
$536$	−11045.7	−0.890112
$537$	6742.94	0.541861
$538$	8866.43	0.710519
$539$	0	0
$540$	−1941.32	−0.154706
$541$	11861.5	0.942633	0.471316	−	0.881964i	$-0.343779\pi$
$541$	11861.5	0.942633	0.471316	+	0.881964i	$0.343779\pi$
$542$	20705.0	1.64088
$543$	−2332.83	−0.184367
$544$	−10645.2	−0.838991
$545$	9920.55	0.779724
$546$	0	0
$547$	6844.15	0.534981	0.267490	−	0.963561i	$-0.413806\pi$
$547$	6844.15	0.534981	0.267490	+	0.963561i	$0.413806\pi$
$548$	139.718	0.0108913
$549$	3430.63	0.266695
$550$	−5088.77	−0.394520
$551$	1341.82	0.103745
$552$	−3130.17	−0.241357
$553$	0	0
$554$	−18273.2	−1.40136
$555$	−14562.2	−1.11375
$556$	−8064.80	−0.615151
$557$	−10415.1	−0.792281	−0.396141	−	0.918190i	$-0.629651\pi$
$557$	−10415.1	−0.792281	−0.396141	+	0.918190i	$0.629651\pi$
$558$	−7260.91	−0.550858
$559$	−4644.69	−0.351430
$560$	0	0
$561$	−1921.73	−0.144627
$562$	17514.9	1.31463
$563$	−17768.7	−1.33012	−0.665062	−	0.746788i	$-0.731595\pi$
$563$	−17768.7	−1.33012	−0.665062	+	0.746788i	$0.731595\pi$
$564$	343.677	0.0256586
$565$	−7721.14	−0.574922
$566$	−15523.5	−1.15283
$567$	0	0
$568$	4399.39	0.324990
$569$	11578.1	0.853040	0.426520	−	0.904478i	$-0.359739\pi$
$569$	11578.1	0.853040	0.426520	+	0.904478i	$0.359739\pi$
$570$	−1503.70	−0.110497
$571$	−2374.45	−0.174024	−0.0870121	−	0.996207i	$-0.527732\pi$
$571$	−2374.45	−0.174024	−0.0870121	+	0.996207i	$0.527732\pi$
$572$	1260.05	0.0921074
$573$	11200.0	0.816555
$574$	0	0
$575$	11021.3	0.799342
$576$	−73.1139	−0.00528891
$577$	21264.9	1.53426	0.767131	−	0.641491i	$-0.221684\pi$
$577$	21264.9	1.53426	0.767131	+	0.641491i	$0.221684\pi$
$578$	−5379.15	−0.387099
$579$	−14660.8	−1.05230
$580$	−10883.4	−0.779153
$581$	0	0
$582$	19850.7	1.41381
$583$	49.3150	0.00350329
$584$	3220.69	0.228207
$585$	3668.87	0.259297
$586$	29187.4	2.05754
$587$	12179.7	0.856406	0.428203	−	0.903683i	$-0.359147\pi$
$587$	12179.7	0.856406	0.428203	+	0.903683i	$0.359147\pi$
$588$	0	0
$589$	−2023.22	−0.141537
$590$	−13217.6	−0.922304
$591$	12883.9	0.896742
$592$	−24202.0	−1.68023
$593$	15555.2	1.07719	0.538596	−	0.842564i	$-0.318955\pi$
$593$	15555.2	1.07719	0.538596	+	0.842564i	$0.318955\pi$
$594$	−1049.84	−0.0725176
$595$	0	0
$596$	1447.44	0.0994790
$597$	9738.25	0.667605
$598$	−7586.18	−0.518766
$599$	−22146.0	−1.51062	−0.755310	−	0.655367i	$-0.772514\pi$
$599$	−22146.0	−1.51062	−0.755310	+	0.655367i	$0.772514\pi$
$600$	−4864.55	−0.330991
$601$	19865.8	1.34833	0.674164	−	0.738582i	$-0.264504\pi$
$601$	19865.8	1.34833	0.674164	+	0.738582i	$0.264504\pi$
$602$	0	0
$603$	8023.56	0.541865
$604$	11329.4	0.763224
$605$	−1935.52	−0.130067
$606$	−6797.14	−0.455635
$607$	−16342.5	−1.09279	−0.546393	−	0.837529i	$-0.684000\pi$
$607$	−16342.5	−1.09279	−0.546393	+	0.837529i	$0.684000\pi$
$608$	−1620.46	−0.108089
$609$	0	0
$610$	−21553.2	−1.43059
$611$	−649.510	−0.0430055
$612$	2355.82	0.155602
$613$	−24276.5	−1.59954	−0.799769	−	0.600308i	$-0.795045\pi$
$613$	−24276.5	−1.59954	−0.799769	+	0.600308i	$0.795045\pi$
$614$	−35891.0	−2.35903
$615$	5116.43	0.335470
$616$	0	0
$617$	19821.5	1.29333	0.646663	−	0.762775i	$-0.276164\pi$
$617$	19821.5	1.29333	0.646663	+	0.762775i	$0.276164\pi$
$618$	−18898.5	−1.23011
$619$	−6708.85	−0.435625	−0.217812	−	0.975991i	$-0.569892\pi$
$619$	−6708.85	−0.435625	−0.217812	+	0.975991i	$0.569892\pi$
$620$	16410.3	1.06299
$621$	2273.76	0.146929
$622$	−33031.5	−2.12933
$623$	0	0
$624$	6097.56	0.391182
$625$	−14856.2	−0.950798
$626$	−18264.4	−1.16612
$627$	−292.533	−0.0186326
$628$	−3559.08	−0.226151
$629$	17671.5	1.12020
$630$	0	0
$631$	−28096.3	−1.77258	−0.886288	−	0.463134i	$-0.846725\pi$
$631$	−28096.3	−1.77258	−0.886288	+	0.463134i	$0.846725\pi$
$632$	−14909.1	−0.938375
$633$	−3258.35	−0.204594
$634$	23231.1	1.45525
$635$	−41190.1	−2.57414
$636$	−60.4543	−0.00376913
$637$	0	0
$638$	−5885.60	−0.365224
$639$	−3195.71	−0.197841
$640$	−22933.3	−1.41644
$641$	2723.62	0.167826	0.0839131	−	0.996473i	$-0.473258\pi$
$641$	2723.62	0.167826	0.0839131	+	0.996473i	$0.473258\pi$
$642$	−677.149	−0.0416276
$643$	19080.8	1.17025	0.585127	−	0.810942i	$-0.301045\pi$
$643$	19080.8	1.17025	0.585127	+	0.810942i	$0.301045\pi$
$644$	0	0
$645$	−8746.11	−0.533919
$646$	1824.76	0.111137
$647$	11695.8	0.710678	0.355339	−	0.934737i	$-0.384365\pi$
$647$	11695.8	0.710678	0.355339	+	0.934737i	$0.384365\pi$
$648$	−1003.58	−0.0608400
$649$	−2571.37	−0.155524
$650$	−11789.5	−0.711421
$651$	0	0
$652$	−12774.0	−0.767281
$653$	−4131.71	−0.247605	−0.123803	−	0.992307i	$-0.539509\pi$
$653$	−4131.71	−0.247605	−0.123803	+	0.992307i	$0.539509\pi$
$654$	−6576.73	−0.393227
$655$	36486.1	2.17654
$656$	8503.36	0.506098
$657$	−2339.50	−0.138923
$658$	0	0
$659$	−8762.84	−0.517985	−0.258992	−	0.965879i	$-0.583390\pi$
$659$	−8762.84	−0.517985	−0.258992	+	0.965879i	$0.583390\pi$
$660$	2372.72	0.139937
$661$	8697.31	0.511779	0.255890	−	0.966706i	$-0.417632\pi$
$661$	8697.31	0.511779	0.255890	+	0.966706i	$0.417632\pi$
$662$	−29802.9	−1.74973
$663$	−4452.22	−0.260799
$664$	−8507.26	−0.497207
$665$	0	0
$666$	9653.89	0.561683
$667$	12747.1	0.739985
$668$	14420.1	0.835224
$669$	−5785.31	−0.334339
$670$	−50408.6	−2.90665
$671$	−4192.99	−0.241235
$672$	0	0
$673$	7057.26	0.404216	0.202108	−	0.979363i	$-0.435221\pi$
$673$	7057.26	0.404216	0.202108	+	0.979363i	$0.435221\pi$
$674$	18845.9	1.07703
$675$	3533.60	0.201494
$676$	−6956.03	−0.395769
$677$	−22357.9	−1.26925	−0.634627	−	0.772819i	$-0.718846\pi$
$677$	−22357.9	−1.26925	−0.634627	+	0.772819i	$0.718846\pi$
$678$	5118.65	0.289942
$679$	0	0
$680$	11541.4	0.650873
$681$	−1287.03	−0.0724215
$682$	8874.45	0.498270
$683$	17143.0	0.960408	0.480204	−	0.877157i	$-0.340563\pi$
$683$	17143.0	0.960408	0.480204	+	0.877157i	$0.340563\pi$
$684$	358.611	0.0200465
$685$	−497.216	−0.0277338
$686$	0	0
$687$	10240.6	0.568711
$688$	−14535.8	−0.805483
$689$	114.252	0.00631733
$690$	−14285.0	−0.788148
$691$	−35434.8	−1.95080	−0.975401	−	0.220438i	$-0.929251\pi$
$691$	−35434.8	−1.95080	−0.975401	+	0.220438i	$0.929251\pi$
$692$	−8195.62	−0.450218
$693$	0	0
$694$	−38349.8	−2.09761
$695$	28700.3	1.56643
$696$	−5626.26	−0.306412
$697$	−6208.86	−0.337413
$698$	5312.67	0.288091
$699$	−9112.00	−0.493058
$700$	0	0
$701$	1325.58	0.0714217	0.0357109	−	0.999362i	$-0.488630\pi$
$701$	1325.58	0.0714217	0.0357109	+	0.999362i	$0.488630\pi$
$702$	−2432.24	−0.130768
$703$	2690.02	0.144318
$704$	89.3615	0.00478400
$705$	−1223.05	−0.0653372
$706$	23061.7	1.22937
$707$	0	0
$708$	3152.20	0.167326
$709$	20161.8	1.06797	0.533986	−	0.845493i	$-0.320694\pi$
$709$	20161.8	1.06797	0.533986	+	0.845493i	$0.320694\pi$
$710$	20077.3	1.06125
$711$	10830.0	0.571246
$712$	−3673.10	−0.193336
$713$	−19220.4	−1.00955
$714$	0	0
$715$	−4484.17	−0.234543
$716$	10102.9	0.527325
$717$	1804.65	0.0939968
$718$	18714.5	0.972726
$719$	26554.1	1.37733	0.688666	−	0.725079i	$-0.258197\pi$
$719$	26554.1	1.37733	0.688666	+	0.725079i	$0.258197\pi$
$720$	11481.9	0.594313
$721$	0	0
$722$	−23967.5	−1.23543
$723$	−4832.45	−0.248577
$724$	−3495.28	−0.179421
$725$	19810.1	1.01480
$726$	1283.14	0.0655946
$727$	4014.42	0.204796	0.102398	−	0.994744i	$-0.467349\pi$
$727$	4014.42	0.204796	0.102398	+	0.994744i	$0.467349\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	14698.1	0.745206
$731$	10613.5	0.537011
$732$	5140.11	0.259541
$733$	−30822.6	−1.55315	−0.776576	−	0.630024i	$-0.783045\pi$
$733$	−30822.6	−1.55315	−0.776576	+	0.630024i	$0.783045\pi$
$734$	15561.4	0.782537
$735$	0	0
$736$	−15394.2	−0.770975
$737$	−9806.58	−0.490136
$738$	−3391.89	−0.169183
$739$	−11151.0	−0.555068	−0.277534	−	0.960716i	$-0.589517\pi$
$739$	−11151.0	−0.555068	−0.277534	+	0.960716i	$0.589517\pi$
$740$	−21818.6	−1.08387
$741$	−677.733	−0.0335994
$742$	0	0
$743$	−12379.5	−0.611250	−0.305625	−	0.952152i	$-0.598865\pi$
$743$	−12379.5	−0.611250	−0.305625	+	0.952152i	$0.598865\pi$
$744$	8483.42	0.418034
$745$	−5151.03	−0.253314
$746$	44114.2	2.16506
$747$	6179.67	0.302680
$748$	−2879.33	−0.140747
$749$	0	0
$750$	−996.441	−0.0485132
$751$	11836.0	0.575101	0.287550	−	0.957766i	$-0.407159\pi$
$751$	11836.0	0.575101	0.287550	+	0.957766i	$0.407159\pi$
$752$	−2032.68	−0.0985692
$753$	19697.1	0.953258
$754$	−13635.6	−0.658593
$755$	−40318.2	−1.94348
$756$	0	0
$757$	−15338.3	−0.736435	−0.368217	−	0.929740i	$-0.620032\pi$
$757$	−15338.3	−0.736435	−0.368217	+	0.929740i	$0.620032\pi$
$758$	23740.7	1.13760
$759$	−2779.04	−0.132902
$760$	1756.88	0.0838535
$761$	−8981.72	−0.427841	−0.213921	−	0.976851i	$-0.568623\pi$
$761$	−8981.72	−0.427841	−0.213921	+	0.976851i	$0.568623\pi$
$762$	27306.6	1.29818
$763$	0	0
$764$	16780.9	0.794650
$765$	−8383.68	−0.396226
$766$	−11199.8	−0.528284
$767$	−5957.29	−0.280450
$768$	15398.4	0.723492
$769$	7635.45	0.358051	0.179026	−	0.983844i	$-0.442705\pi$
$769$	7635.45	0.358051	0.179026	+	0.983844i	$0.442705\pi$
$770$	0	0
$771$	−15062.6	−0.703589
$772$	−21966.3	−1.02407
$773$	22066.2	1.02674	0.513368	−	0.858169i	$-0.328398\pi$
$773$	22066.2	1.02674	0.513368	+	0.858169i	$0.328398\pi$
$774$	5798.15	0.269264
$775$	−29870.1	−1.38447
$776$	−23192.9	−1.07291
$777$	0	0
$778$	4430.79	0.204179
$779$	−945.135	−0.0434698
$780$	5497.06	0.252341
$781$	3905.87	0.178954
$782$	17335.1	0.792712
$783$	4086.91	0.186532
$784$	0	0
$785$	12665.7	0.575872
$786$	−24188.1	−1.09766
$787$	−9757.00	−0.441931	−0.220965	−	0.975282i	$-0.570921\pi$
$787$	−9757.00	−0.441931	−0.220965	+	0.975282i	$0.570921\pi$
$788$	19304.0	0.872686
$789$	−8859.91	−0.399774
$790$	−68040.0	−3.06425
$791$	0	0
$792$	1226.60	0.0550319
$793$	−9714.21	−0.435009
$794$	24660.9	1.10225
$795$	215.140	0.00959776
$796$	14590.8	0.649696
$797$	14559.5	0.647082	0.323541	−	0.946214i	$-0.395127\pi$
$797$	14559.5	0.647082	0.323541	+	0.946214i	$0.395127\pi$
$798$	0	0
$799$	1484.19	0.0657156
$800$	−23923.8	−1.05729
$801$	2668.13	0.117695
$802$	−44105.0	−1.94190
$803$	2859.39	0.125661
$804$	12021.7	0.527329
$805$	0	0
$806$	20560.1	0.898509
$807$	7524.96	0.328242
$808$	7941.56	0.345771
$809$	2957.68	0.128537	0.0642685	−	0.997933i	$-0.479529\pi$
$809$	2957.68	0.128537	0.0642685	+	0.997933i	$0.479529\pi$
$810$	−4579.99	−0.198672
$811$	−8182.97	−0.354307	−0.177154	−	0.984183i	$-0.556689\pi$
$811$	−8182.97	−0.354307	−0.177154	+	0.984183i	$0.556689\pi$
$812$	0	0
$813$	17572.4	0.758044
$814$	−11799.2	−0.508061
$815$	45458.9	1.95381
$816$	−13933.5	−0.597755
$817$	1615.63	0.0691845
$818$	−459.293	−0.0196318
$819$	0	0
$820$	7665.94	0.326471
$821$	22532.9	0.957862	0.478931	−	0.877852i	$-0.341024\pi$
$821$	22532.9	0.957862	0.478931	+	0.877852i	$0.341024\pi$
$822$	329.624	0.0139866
$823$	47047.5	1.99268	0.996339	−	0.0854869i	$-0.0272446\pi$
$823$	47047.5	1.99268	0.996339	+	0.0854869i	$0.0272446\pi$
$824$	22080.4	0.933504
$825$	−4318.85	−0.182258
$826$	0	0
$827$	−4918.98	−0.206831	−0.103416	−	0.994638i	$-0.532977\pi$
$827$	−4918.98	−0.206831	−0.103416	+	0.994638i	$0.532977\pi$
$828$	3406.77	0.142987
$829$	8011.55	0.335648	0.167824	−	0.985817i	$-0.446326\pi$
$829$	8011.55	0.335648	0.167824	+	0.985817i	$0.446326\pi$
$830$	−38824.2	−1.62362
$831$	−15508.5	−0.647392
$832$	207.030	0.00862678
$833$	0	0
$834$	−19026.6	−0.789973
$835$	−51317.0	−2.12682
$836$	−438.302	−0.0181328
$837$	−6162.35	−0.254483
$838$	58986.0	2.43155
$839$	−8110.25	−0.333727	−0.166864	−	0.985980i	$-0.553364\pi$
$839$	−8110.25	−0.333727	−0.166864	+	0.985980i	$0.553364\pi$
$840$	0	0
$841$	−1477.00	−0.0605600
$842$	−23589.5	−0.965496
$843$	14864.9	0.607325
$844$	−4881.99	−0.199105
$845$	24754.6	1.00779
$846$	810.809	0.0329506
$847$	0	0
$848$	357.556	0.0144794
$849$	−13174.8	−0.532576
$850$	26940.1	1.08710
$851$	25554.9	1.02939
$852$	−4788.14	−0.192534
$853$	−2100.50	−0.0843138	−0.0421569	−	0.999111i	$-0.513423\pi$
$853$	−2100.50	−0.0843138	−0.0421569	+	0.999111i	$0.513423\pi$
$854$	0	0
$855$	−1276.20	−0.0510467
$856$	791.159	0.0315902
$857$	−18533.2	−0.738720	−0.369360	−	0.929286i	$-0.620423\pi$
$857$	−18533.2	−0.738720	−0.369360	+	0.929286i	$0.620423\pi$
$858$	2972.74	0.118284
$859$	−17003.1	−0.675363	−0.337682	−	0.941260i	$-0.609643\pi$
$859$	−17003.1	−0.675363	−0.337682	+	0.941260i	$0.609643\pi$
$860$	−13104.3	−0.519596
$861$	0	0
$862$	46922.4	1.85404
$863$	37721.2	1.48788	0.743942	−	0.668244i	$-0.232954\pi$
$863$	37721.2	1.48788	0.743942	+	0.668244i	$0.232954\pi$
$864$	−4935.61	−0.194343
$865$	29165.9	1.14644
$866$	−11940.3	−0.468533
$867$	−4565.29	−0.178830
$868$	0	0
$869$	−13236.6	−0.516711
$870$	−25676.3	−1.00058
$871$	−22719.6	−0.883840
$872$	7684.04	0.298411
$873$	16847.3	0.653143
$874$	2638.81	0.102127
$875$	0	0
$876$	−3505.28	−0.135197
$877$	−37503.7	−1.44403	−0.722013	−	0.691880i	$-0.756783\pi$
$877$	−37503.7	−1.44403	−0.722013	+	0.691880i	$0.756783\pi$
$878$	26625.1	1.02341
$879$	24771.4	0.950532
$880$	−14033.4	−0.537577
$881$	35044.8	1.34017	0.670086	−	0.742284i	$-0.266257\pi$
$881$	35044.8	1.34017	0.670086	+	0.742284i	$0.266257\pi$
$882$	0	0
$883$	−7183.12	−0.273761	−0.136881	−	0.990588i	$-0.543708\pi$
$883$	−7183.12	−0.273761	−0.136881	+	0.990588i	$0.543708\pi$
$884$	−6670.76	−0.253803
$885$	−11217.8	−0.426081
$886$	−21406.1	−0.811682
$887$	39557.4	1.49741	0.748707	−	0.662901i	$-0.230675\pi$
$887$	39557.4	1.49741	0.748707	+	0.662901i	$0.230675\pi$
$888$	−11279.3	−0.426248
$889$	0	0
$890$	−16762.7	−0.631335
$891$	−891.000	−0.0335013
$892$	−8668.13	−0.325370
$893$	225.929	0.00846631
$894$	3414.83	0.127750
$895$	−35953.5	−1.34279
$896$	0	0
$897$	−6438.40	−0.239656
$898$	39206.6	1.45695
$899$	−34547.3	−1.28166
$900$	5294.40	0.196089
$901$	−261.075	−0.00965335
$902$	4145.64	0.153032
$903$	0	0
$904$	−5980.47	−0.220030
$905$	12438.7	0.456880
$906$	26728.6	0.980129
$907$	7135.63	0.261229	0.130614	−	0.991433i	$-0.458305\pi$
$907$	7135.63	0.261229	0.130614	+	0.991433i	$0.458305\pi$
$908$	−1928.35	−0.0704787
$909$	−5768.74	−0.210492
$910$	0	0
$911$	28859.4	1.04957	0.524783	−	0.851236i	$-0.324146\pi$
$911$	28859.4	1.04957	0.524783	+	0.851236i	$0.324146\pi$
$912$	−2121.00	−0.0770103
$913$	−7552.93	−0.273785
$914$	−20634.5	−0.746748
$915$	−18292.2	−0.660898
$916$	15343.5	0.553455
$917$	0	0
$918$	5557.88	0.199823
$919$	−29929.1	−1.07429	−0.537144	−	0.843491i	$-0.680497\pi$
$919$	−29929.1	−1.07429	−0.537144	+	0.843491i	$0.680497\pi$
$920$	16690.2	0.598107
$921$	−30460.7	−1.08981
$922$	35890.7	1.28199
$923$	9049.02	0.322700
$924$	0	0
$925$	39714.4	1.41168
$926$	−59260.9	−2.10306
$927$	−16039.2	−0.568281
$928$	−27669.9	−0.978783
$929$	3385.44	0.119562	0.0597809	−	0.998212i	$-0.480960\pi$
$929$	3385.44	0.119562	0.0597809	+	0.998212i	$0.480960\pi$
$930$	38715.4	1.36508
$931$	0	0
$932$	−13652.5	−0.479831
$933$	−28033.8	−0.983694
$934$	35564.7	1.24594
$935$	10246.7	0.358400
$936$	2841.75	0.0992366
$937$	−15337.3	−0.534735	−0.267367	−	0.963595i	$-0.586154\pi$
$937$	−15337.3	−0.534735	−0.267367	+	0.963595i	$0.586154\pi$
$938$	0	0
$939$	−15501.1	−0.538720
$940$	−1832.50	−0.0635845
$941$	16906.2	0.585683	0.292841	−	0.956161i	$-0.405399\pi$
$941$	16906.2	0.585683	0.292841	+	0.956161i	$0.405399\pi$
$942$	−8396.63	−0.290421
$943$	−8978.69	−0.310060
$944$	−18643.6	−0.642795
$945$	0	0
$946$	−7086.63	−0.243558
$947$	8945.48	0.306958	0.153479	−	0.988152i	$-0.450952\pi$
$947$	8945.48	0.306958	0.153479	+	0.988152i	$0.450952\pi$
$948$	16226.5	0.555922
$949$	6624.57	0.226599
$950$	4100.92	0.140054
$951$	19716.3	0.672287
$952$	0	0
$953$	−49292.5	−1.67549	−0.837745	−	0.546061i	$-0.816127\pi$
$953$	−49292.5	−1.67549	−0.837745	+	0.546061i	$0.816127\pi$
$954$	−142.625	−0.00484030
$955$	−59718.5	−2.02350
$956$	2703.90	0.0914753
$957$	−4995.11	−0.168724
$958$	−23492.0	−0.792269
$959$	0	0
$960$	389.845	0.0131065
$961$	22300.3	0.748557
$962$	−27336.1	−0.916165
$963$	−574.697	−0.0192309
$964$	−7240.46	−0.241908
$965$	78171.8	2.60771
$966$	0	0
$967$	24090.9	0.801151	0.400575	−	0.916264i	$-0.368810\pi$
$967$	24090.9	0.801151	0.400575	+	0.916264i	$0.368810\pi$
$968$	−1499.18	−0.0497782
$969$	1548.68	0.0513424
$970$	−105844.	−3.50356
$971$	18828.5	0.622283	0.311141	−	0.950364i	$-0.399289\pi$
$971$	18828.5	0.622283	0.311141	+	0.950364i	$0.399289\pi$
$972$	1092.26	0.0360435
$973$	0	0
$974$	−15617.5	−0.513776
$975$	−10005.8	−0.328658
$976$	−30401.1	−0.997045
$977$	43722.0	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$977$	43722.0	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$978$	−30136.5	−0.985338
$979$	−3261.05	−0.106459
$980$	0	0
$981$	−5581.68	−0.181661
$982$	18493.2	0.600960
$983$	39122.8	1.26940	0.634702	−	0.772757i	$-0.281123\pi$
$983$	39122.8	1.26940	0.634702	+	0.772757i	$0.281123\pi$
$984$	3962.97	0.128389
$985$	−68697.4	−2.22222
$986$	31158.5	1.00638
$987$	0	0
$988$	−1015.45	−0.0326981
$989$	15348.3	0.493476
$990$	5597.77	0.179706
$991$	−16229.0	−0.520213	−0.260106	−	0.965580i	$-0.583758\pi$
$991$	−16229.0	−0.520213	−0.260106	+	0.965580i	$0.583758\pi$
$992$	41721.4	1.33534
$993$	−25293.7	−0.808331
$994$	0	0
$995$	−51924.6	−1.65439
$996$	9258.99	0.294561
$997$	−29520.8	−0.937748	−0.468874	−	0.883265i	$-0.655340\pi$
$997$	−29520.8	−0.937748	−0.468874	+	0.883265i	$0.655340\pi$
$998$	78377.9	2.48598
$999$	8193.27	0.259483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.z.1.8		10
7.3	odd	6		231.4.i.b.100.3	yes	20
7.5	odd	6		231.4.i.b.67.3	✓	20
7.6	odd	2		1617.4.a.y.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.i.b.67.3	✓	20	7.5	odd	6
231.4.i.b.100.3	yes	20	7.3	odd	6
1617.4.a.y.1.8		10	7.6	odd	2
1617.4.a.z.1.8		10	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+3.53481 q^{2} +3.00000 q^{3} +4.49490 q^{4} -15.9961 q^{5} +10.6044 q^{6} -12.3899 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.53481 q^{2} +3.00000 q^{3} +4.49490 q^{4} -15.9961 q^{5} +10.6044 q^{6} -12.3899 q^{8} +9.00000 q^{9} -56.5431 q^{10} -11.0000 q^{11} +13.4847 q^{12} -25.4845 q^{13} -47.9882 q^{15} -79.7551 q^{16} +58.2343 q^{17} +31.8133 q^{18} +8.86464 q^{19} -71.9007 q^{20} -38.8829 q^{22} +84.2132 q^{23} -37.1696 q^{24} +130.874 q^{25} -90.0829 q^{26} +27.0000 q^{27} +151.367 q^{29} -169.629 q^{30} -228.235 q^{31} -182.800 q^{32} -33.0000 q^{33} +205.847 q^{34} +40.4541 q^{36} +303.455 q^{37} +31.3349 q^{38} -76.4535 q^{39} +198.189 q^{40} -106.618 q^{41} +182.255 q^{43} -49.4439 q^{44} -143.965 q^{45} +297.678 q^{46} +25.4865 q^{47} -239.265 q^{48} +462.616 q^{50} +174.703 q^{51} -114.550 q^{52} -4.48318 q^{53} +95.4399 q^{54} +175.957 q^{55} +26.5939 q^{57} +535.054 q^{58} +233.761 q^{59} -215.702 q^{60} +381.181 q^{61} -806.768 q^{62} -8.12377 q^{64} +407.652 q^{65} -116.649 q^{66} +891.507 q^{67} +261.757 q^{68} +252.640 q^{69} -355.079 q^{71} -111.509 q^{72} -259.945 q^{73} +1072.65 q^{74} +392.623 q^{75} +39.8457 q^{76} -270.249 q^{78} +1203.33 q^{79} +1275.77 q^{80} +81.0000 q^{81} -376.876 q^{82} +686.630 q^{83} -931.520 q^{85} +644.239 q^{86} +454.101 q^{87} +136.289 q^{88} +296.459 q^{89} -508.888 q^{90} +378.530 q^{92} -684.705 q^{93} +90.0899 q^{94} -141.799 q^{95} -548.401 q^{96} +1871.92 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9} + 44 q^{10} - 110 q^{11} + 78 q^{12} + 82 q^{13} + 60 q^{15} - 10 q^{16} + 164 q^{17} + 36 q^{18} - 76 q^{19} + 356 q^{20} - 44 q^{22} + 140 q^{23} + 108 q^{24} + 472 q^{25} + 360 q^{26} + 270 q^{27} + 40 q^{29} + 132 q^{30} + 24 q^{31} + 112 q^{32} - 330 q^{33} - 262 q^{34} + 234 q^{36} + 412 q^{37} + 16 q^{38} + 246 q^{39} + 828 q^{40} - 228 q^{41} + 530 q^{43} - 286 q^{44} + 180 q^{45} + 1422 q^{46} + 768 q^{47} - 30 q^{48} + 670 q^{50} + 492 q^{51} + 952 q^{52} + 136 q^{53} + 108 q^{54} - 220 q^{55} - 228 q^{57} + 1708 q^{58} + 608 q^{59} + 1068 q^{60} + 1618 q^{61} + 164 q^{62} - 1238 q^{64} + 2764 q^{65} - 132 q^{66} + 1002 q^{67} + 2816 q^{68} + 420 q^{69} + 812 q^{71} + 324 q^{72} + 134 q^{73} + 342 q^{74} + 1416 q^{75} - 450 q^{76} + 1080 q^{78} + 1262 q^{79} - 1316 q^{80} + 810 q^{81} + 982 q^{82} + 1078 q^{83} - 1402 q^{85} + 1692 q^{86} + 120 q^{87} - 396 q^{88} + 2880 q^{89} + 396 q^{90} + 2364 q^{92} + 72 q^{93} - 2362 q^{94} + 2866 q^{95} + 336 q^{96} - 1030 q^{97} - 990 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9 + 44 * q^10 - 110 * q^11 + 78 * q^12 + 82 * q^13 + 60 * q^15 - 10 * q^16 + 164 * q^17 + 36 * q^18 - 76 * q^19 + 356 * q^20 - 44 * q^22 + 140 * q^23 + 108 * q^24 + 472 * q^25 + 360 * q^26 + 270 * q^27 + 40 * q^29 + 132 * q^30 + 24 * q^31 + 112 * q^32 - 330 * q^33 - 262 * q^34 + 234 * q^36 + 412 * q^37 + 16 * q^38 + 246 * q^39 + 828 * q^40 - 228 * q^41 + 530 * q^43 - 286 * q^44 + 180 * q^45 + 1422 * q^46 + 768 * q^47 - 30 * q^48 + 670 * q^50 + 492 * q^51 + 952 * q^52 + 136 * q^53 + 108 * q^54 - 220 * q^55 - 228 * q^57 + 1708 * q^58 + 608 * q^59 + 1068 * q^60 + 1618 * q^61 + 164 * q^62 - 1238 * q^64 + 2764 * q^65 - 132 * q^66 + 1002 * q^67 + 2816 * q^68 + 420 * q^69 + 812 * q^71 + 324 * q^72 + 134 * q^73 + 342 * q^74 + 1416 * q^75 - 450 * q^76 + 1080 * q^78 + 1262 * q^79 - 1316 * q^80 + 810 * q^81 + 982 * q^82 + 1078 * q^83 - 1402 * q^85 + 1692 * q^86 + 120 * q^87 - 396 * q^88 + 2880 * q^89 + 396 * q^90 + 2364 * q^92 + 72 * q^93 - 2362 * q^94 + 2866 * q^95 + 336 * q^96 - 1030 * q^97 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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