LMFDB - Embedded newform 161.4.a.a.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(1,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.49930751092$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 18x^{3} - 4x^{2} + 44x + 24 $ x^5 - x^4 - 18x^3 - 4x^2 + 44*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.74375$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.743749 q^{2} +0.765559 q^{3} -7.44684 q^{4} +3.68128 q^{5} +0.569384 q^{6} +7.00000 q^{7} -11.4886 q^{8} -26.4139 q^{9} +2.73795 q^{10} -1.75087 q^{11} -5.70100 q^{12} -35.3722 q^{13} +5.20625 q^{14} +2.81824 q^{15} +51.0301 q^{16} -72.1754 q^{17} -19.6453 q^{18} -104.019 q^{19} -27.4139 q^{20} +5.35892 q^{21} -1.30221 q^{22} -23.0000 q^{23} -8.79519 q^{24} -111.448 q^{25} -26.3080 q^{26} -40.8915 q^{27} -52.1279 q^{28} -33.5283 q^{29} +2.09606 q^{30} +39.4051 q^{31} +129.862 q^{32} -1.34039 q^{33} -53.6804 q^{34} +25.7689 q^{35} +196.700 q^{36} +276.575 q^{37} -77.3642 q^{38} -27.0795 q^{39} -42.2926 q^{40} -357.944 q^{41} +3.98569 q^{42} +63.6398 q^{43} +13.0384 q^{44} -97.2370 q^{45} -17.1062 q^{46} +483.948 q^{47} +39.0665 q^{48} +49.0000 q^{49} -82.8895 q^{50} -55.2545 q^{51} +263.411 q^{52} -535.285 q^{53} -30.4130 q^{54} -6.44544 q^{55} -80.4200 q^{56} -79.6329 q^{57} -24.9366 q^{58} +82.9537 q^{59} -20.9869 q^{60} +598.451 q^{61} +29.3075 q^{62} -184.897 q^{63} -311.656 q^{64} -130.215 q^{65} -0.996918 q^{66} -748.468 q^{67} +537.478 q^{68} -17.6079 q^{69} +19.1656 q^{70} +707.079 q^{71} +303.458 q^{72} +954.119 q^{73} +205.703 q^{74} -85.3202 q^{75} +774.614 q^{76} -12.2561 q^{77} -20.1404 q^{78} +272.311 q^{79} +187.856 q^{80} +681.871 q^{81} -266.221 q^{82} -505.317 q^{83} -39.9070 q^{84} -265.698 q^{85} +47.3321 q^{86} -25.6679 q^{87} +20.1150 q^{88} -297.219 q^{89} -72.3199 q^{90} -247.605 q^{91} +171.277 q^{92} +30.1669 q^{93} +359.936 q^{94} -382.924 q^{95} +99.4172 q^{96} -634.517 q^{97} +36.4437 q^{98} +46.2473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 11 q^{3} - 4 q^{5} + 35 q^{7} + 18 q^{8} + 14 q^{9} + 26 q^{10} - 36 q^{11} - 28 q^{12} - 69 q^{13} - 28 q^{14} - 88 q^{15} - 124 q^{16} - 42 q^{17} - 94 q^{18} - 140 q^{19} - 168 q^{20}+ \cdots - 990 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 11 * q^3 - 4 * q^5 + 35 * q^7 + 18 * q^8 + 14 * q^9 + 26 * q^10 - 36 * q^11 - 28 * q^12 - 69 * q^13 - 28 * q^14 - 88 * q^15 - 124 * q^16 - 42 * q^17 - 94 * q^18 - 140 * q^19 - 168 * q^20 - 77 * q^21 - 346 * q^22 - 115 * q^23 + 18 * q^24 - 357 * q^25 + 68 * q^26 - 35 * q^27 - 383 * q^29 + 184 * q^30 - 319 * q^31 - 50 * q^32 - 108 * q^33 - 376 * q^34 - 28 * q^35 - 180 * q^36 - 154 * q^37 + 8 * q^38 - 235 * q^39 + 90 * q^40 + 277 * q^41 - 718 * q^43 + 422 * q^44 + 470 * q^45 + 92 * q^46 + 53 * q^47 + 248 * q^48 + 245 * q^49 - 60 * q^50 + 232 * q^51 + 178 * q^52 + 450 * q^53 + 468 * q^54 - 206 * q^55 + 126 * q^56 - 560 * q^57 + 1738 * q^58 + 936 * q^59 + 944 * q^60 - 522 * q^61 + 788 * q^62 + 98 * q^63 - 252 * q^64 + 264 * q^65 + 2310 * q^66 - 810 * q^67 + 1326 * q^68 + 253 * q^69 + 182 * q^70 - 1373 * q^71 + 1590 * q^72 + 459 * q^73 + 330 * q^74 + 333 * q^75 + 1168 * q^76 - 252 * q^77 + 462 * q^78 - 728 * q^79 + 1368 * q^80 - 895 * q^81 + 1034 * q^82 - 500 * q^83 - 196 * q^84 - 1432 * q^85 + 3138 * q^86 + 1803 * q^87 - 722 * q^88 - 586 * q^89 - 1024 * q^90 - 483 * q^91 + 2149 * q^93 + 316 * q^94 - 188 * q^95 + 1210 * q^96 - 2150 * q^97 - 196 * q^98 - 990 * 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 $

$2$	0.743749	0.262955	0.131478	−	0.991319i	$-0.458028\pi$
$2$	0.743749	0.262955	0.131478	+	0.991319i	$0.458028\pi$
$3$	0.765559	0.147332	0.0736660	−	0.997283i	$-0.476530\pi$
$3$	0.765559	0.147332	0.0736660	+	0.997283i	$0.476530\pi$
$4$	−7.44684	−0.930855
$5$	3.68128	0.329263	0.164632	−	0.986355i	$-0.447356\pi$
$5$	3.68128	0.329263	0.164632	+	0.986355i	$0.447356\pi$
$6$	0.569384	0.0387417
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−11.4886	−0.507728
$9$	−26.4139	−0.978293
$10$	2.73795	0.0865815
$11$	−1.75087	−0.0479915	−0.0239958	−	0.999712i	$-0.507639\pi$
$11$	−1.75087	−0.0479915	−0.0239958	+	0.999712i	$0.507639\pi$
$12$	−5.70100	−0.137145
$13$	−35.3722	−0.754652	−0.377326	−	0.926080i	$-0.623156\pi$
$13$	−35.3722	−0.754652	−0.377326	+	0.926080i	$0.623156\pi$
$14$	5.20625	0.0993877
$15$	2.81824	0.0485110
$16$	51.0301	0.797345
$17$	−72.1754	−1.02971	−0.514856	−	0.857277i	$-0.672155\pi$
$17$	−72.1754	−1.02971	−0.514856	+	0.857277i	$0.672155\pi$
$18$	−19.6453	−0.257247
$19$	−104.019	−1.25598	−0.627991	−	0.778221i	$-0.716122\pi$
$19$	−104.019	−1.25598	−0.627991	+	0.778221i	$0.716122\pi$
$20$	−27.4139	−0.306496
$21$	5.35892	0.0556862
$22$	−1.30221	−0.0126196
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−8.79519	−0.0748046
$25$	−111.448	−0.891586
$26$	−26.3080	−0.198440
$27$	−40.8915	−0.291466
$28$	−52.1279	−0.351830
$29$	−33.5283	−0.214691	−0.107346	−	0.994222i	$-0.534235\pi$
$29$	−33.5283	−0.214691	−0.107346	+	0.994222i	$0.534235\pi$
$30$	2.09606	0.0127562
$31$	39.4051	0.228302	0.114151	−	0.993463i	$-0.463585\pi$
$31$	39.4051	0.228302	0.114151	+	0.993463i	$0.463585\pi$
$32$	129.862	0.717394
$33$	−1.34039	−0.00707069
$34$	−53.6804	−0.270768
$35$	25.7689	0.124450
$36$	196.700	0.910649
$37$	276.575	1.22888	0.614442	−	0.788962i	$-0.289381\pi$
$37$	276.575	1.22888	0.614442	+	0.788962i	$0.289381\pi$
$38$	−77.3642	−0.330267
$39$	−27.0795	−0.111184
$40$	−42.2926	−0.167176
$41$	−357.944	−1.36345	−0.681725	−	0.731608i	$-0.738770\pi$
$41$	−357.944	−1.36345	−0.681725	+	0.731608i	$0.738770\pi$
$42$	3.98569	0.0146430
$43$	63.6398	0.225697	0.112849	−	0.993612i	$-0.464002\pi$
$43$	63.6398	0.225697	0.112849	+	0.993612i	$0.464002\pi$
$44$	13.0384	0.0446732
$45$	−97.2370	−0.322116
$46$	−17.1062	−0.0548299
$47$	483.948	1.50194	0.750969	−	0.660338i	$-0.229587\pi$
$47$	483.948	1.50194	0.750969	+	0.660338i	$0.229587\pi$
$48$	39.0665	0.117474
$49$	49.0000	0.142857
$50$	−82.8895	−0.234447
$51$	−55.2545	−0.151709
$52$	263.411	0.702471
$53$	−535.285	−1.38730	−0.693652	−	0.720310i	$-0.743999\pi$
$53$	−535.285	−1.38730	−0.693652	+	0.720310i	$0.743999\pi$
$54$	−30.4130	−0.0766424
$55$	−6.44544	−0.0158019
$56$	−80.4200	−0.191903
$57$	−79.6329	−0.185046
$58$	−24.9366	−0.0564542
$59$	82.9537	0.183045	0.0915225	−	0.995803i	$-0.470827\pi$
$59$	82.9537	0.183045	0.0915225	+	0.995803i	$0.470827\pi$
$60$	−20.9869	−0.0451567
$61$	598.451	1.25613	0.628063	−	0.778162i	$-0.283848\pi$
$61$	598.451	1.25613	0.628063	+	0.778162i	$0.283848\pi$
$62$	29.3075	0.0600332
$63$	−184.897	−0.369760
$64$	−311.656	−0.608702
$65$	−130.215	−0.248479
$66$	−0.996918	−0.00185927
$67$	−748.468	−1.36477	−0.682387	−	0.730991i	$-0.739058\pi$
$67$	−748.468	−1.36477	−0.682387	+	0.730991i	$0.739058\pi$
$68$	537.478	0.958512
$69$	−17.6079	−0.0307208
$70$	19.1656	0.0327247
$71$	707.079	1.18190	0.590950	−	0.806708i	$-0.298753\pi$
$71$	707.079	1.18190	0.590950	+	0.806708i	$0.298753\pi$
$72$	303.458	0.496707
$73$	954.119	1.52974	0.764871	−	0.644183i	$-0.222803\pi$
$73$	954.119	1.52974	0.764871	+	0.644183i	$0.222803\pi$
$74$	205.703	0.323142
$75$	−85.3202	−0.131359
$76$	774.614	1.16914
$77$	−12.2561	−0.0181391
$78$	−20.1404	−0.0292365
$79$	272.311	0.387815	0.193907	−	0.981020i	$-0.437884\pi$
$79$	272.311	0.387815	0.193907	+	0.981020i	$0.437884\pi$
$80$	187.856	0.262537
$81$	681.871	0.935351
$82$	−266.221	−0.358526
$83$	−505.317	−0.668262	−0.334131	−	0.942527i	$-0.608443\pi$
$83$	−505.317	−0.668262	−0.334131	+	0.942527i	$0.608443\pi$
$84$	−39.9070	−0.0518358
$85$	−265.698	−0.339047
$86$	47.3321	0.0593482
$87$	−25.6679	−0.0316309
$88$	20.1150	0.0243667
$89$	−297.219	−0.353990	−0.176995	−	0.984212i	$-0.556638\pi$
$89$	−297.219	−0.353990	−0.176995	+	0.984212i	$0.556638\pi$
$90$	−72.3199	−0.0847021
$91$	−247.605	−0.285232
$92$	171.277	0.194097
$93$	30.1669	0.0336362
$94$	359.936	0.394942
$95$	−382.924	−0.413549
$96$	99.4172	0.105695
$97$	−634.517	−0.664180	−0.332090	−	0.943248i	$-0.607754\pi$
$97$	−634.517	−0.664180	−0.332090	+	0.943248i	$0.607754\pi$
$98$	36.4437	0.0375650
$99$	46.2473	0.0469498
$100$	829.937	0.829937
$101$	1277.73	1.25880	0.629400	−	0.777082i	$-0.283301\pi$
$101$	1277.73	1.25880	0.629400	+	0.777082i	$0.283301\pi$
$102$	−41.0955	−0.0398928
$103$	−791.108	−0.756798	−0.378399	−	0.925643i	$-0.623525\pi$
$103$	−791.108	−0.756798	−0.378399	+	0.925643i	$0.623525\pi$
$104$	406.376	0.383158
$105$	19.7277	0.0183354
$106$	−398.118	−0.364799
$107$	−291.571	−0.263433	−0.131716	−	0.991287i	$-0.542049\pi$
$107$	−291.571	−0.263433	−0.131716	+	0.991287i	$0.542049\pi$
$108$	304.512	0.271312
$109$	−11.7810	−0.0103524	−0.00517621	−	0.999987i	$-0.501648\pi$
$109$	−11.7810	−0.0103524	−0.00517621	+	0.999987i	$0.501648\pi$
$110$	−4.79379	−0.00415518
$111$	211.735	0.181054
$112$	357.210	0.301368
$113$	−1776.98	−1.47933	−0.739665	−	0.672976i	$-0.765016\pi$
$113$	−1776.98	−1.47933	−0.739665	+	0.672976i	$0.765016\pi$
$114$	−59.2269	−0.0486588
$115$	−84.6694	−0.0686562
$116$	249.680	0.199846
$117$	934.318	0.738271
$118$	61.6968	0.0481326
$119$	−505.228	−0.389195
$120$	−32.3775	−0.0246304
$121$	−1327.93	−0.997697
$122$	445.097	0.330305
$123$	−274.027	−0.200880
$124$	−293.443	−0.212516
$125$	−870.431	−0.622830
$126$	−137.517	−0.0972303
$127$	−1909.68	−1.33431	−0.667153	−	0.744921i	$-0.732487\pi$
$127$	−1909.68	−1.33431	−0.667153	+	0.744921i	$0.732487\pi$
$128$	−1270.69	−0.877456
$129$	48.7200	0.0332524
$130$	−96.8472	−0.0653389
$131$	−40.3906	−0.0269385	−0.0134693	−	0.999909i	$-0.504288\pi$
$131$	−40.3906	−0.0269385	−0.0134693	+	0.999909i	$0.504288\pi$
$132$	9.98170	0.00658178
$133$	−728.134	−0.474716
$134$	−556.672	−0.358874
$135$	−150.533	−0.0959690
$136$	829.193	0.522814
$137$	1304.12	0.813274	0.406637	−	0.913590i	$-0.366701\pi$
$137$	1304.12	0.813274	0.406637	+	0.913590i	$0.366701\pi$
$138$	−13.0958	−0.00807820
$139$	−815.579	−0.497673	−0.248836	−	0.968546i	$-0.580048\pi$
$139$	−815.579	−0.497673	−0.248836	+	0.968546i	$0.580048\pi$
$140$	−191.897	−0.115845
$141$	370.491	0.221283
$142$	525.890	0.310787
$143$	61.9321	0.0362169
$144$	−1347.90	−0.780037
$145$	−123.427	−0.0706900
$146$	709.626	0.402254
$147$	37.5124	0.0210474
$148$	−2059.61	−1.14391
$149$	2381.79	1.30956	0.654778	−	0.755821i	$-0.272762\pi$
$149$	2381.79	1.30956	0.654778	+	0.755821i	$0.272762\pi$
$150$	−63.4569	−0.0345415
$151$	−2417.34	−1.30279	−0.651393	−	0.758740i	$-0.725815\pi$
$151$	−2417.34	−1.30279	−0.651393	+	0.758740i	$0.725815\pi$
$152$	1195.03	0.637697
$153$	1906.44	1.00736
$154$	−9.11546	−0.00476977
$155$	145.061	0.0751715
$156$	201.657	0.103496
$157$	−2608.92	−1.32621	−0.663104	−	0.748527i	$-0.730761\pi$
$157$	−2608.92	−1.32621	−0.663104	+	0.748527i	$0.730761\pi$
$158$	202.531	0.101978
$159$	−409.793	−0.204394
$160$	478.059	0.236212
$161$	−161.000	−0.0788110
$162$	507.141	0.245955
$163$	−781.664	−0.375612	−0.187806	−	0.982206i	$-0.560138\pi$
$163$	−781.664	−0.375612	−0.187806	+	0.982206i	$0.560138\pi$
$164$	2665.55	1.26917
$165$	−4.93436	−0.00232812
$166$	−375.829	−0.175723
$167$	−117.042	−0.0542332	−0.0271166	−	0.999632i	$-0.508633\pi$
$167$	−117.042	−0.0542332	−0.0271166	+	0.999632i	$0.508633\pi$
$168$	−61.5663	−0.0282735
$169$	−945.809	−0.430500
$170$	−197.612	−0.0891540
$171$	2747.55	1.22872
$172$	−473.915	−0.210091
$173$	1632.35	0.717369	0.358685	−	0.933459i	$-0.383225\pi$
$173$	1632.35	0.717369	0.358685	+	0.933459i	$0.383225\pi$
$174$	−19.0905	−0.00831750
$175$	−780.137	−0.336988
$176$	−89.3470	−0.0382658
$177$	63.5060	0.0269684
$178$	−221.056	−0.0930836
$179$	−4213.76	−1.75951	−0.879753	−	0.475431i	$-0.842292\pi$
$179$	−4213.76	−1.75951	−0.879753	+	0.475431i	$0.842292\pi$
$180$	724.108	0.299843
$181$	−2110.23	−0.866587	−0.433293	−	0.901253i	$-0.642649\pi$
$181$	−2110.23	−0.866587	−0.433293	+	0.901253i	$0.642649\pi$
$182$	−184.156	−0.0750031
$183$	458.149	0.185068
$184$	264.237	0.105869
$185$	1018.15	0.404627
$186$	22.4366	0.00884481
$187$	126.370	0.0494175
$188$	−3603.88	−1.39809
$189$	−286.241	−0.110164
$190$	−284.799	−0.108745
$191$	3578.43	1.35563	0.677817	−	0.735230i	$-0.262926\pi$
$191$	3578.43	1.35563	0.677817	+	0.735230i	$0.262926\pi$
$192$	−238.591	−0.0896813
$193$	−2293.68	−0.855455	−0.427727	−	0.903908i	$-0.640686\pi$
$193$	−2293.68	−0.855455	−0.427727	+	0.903908i	$0.640686\pi$
$194$	−471.922	−0.174649
$195$	−99.6872	−0.0366090
$196$	−364.895	−0.132979
$197$	216.209	0.0781940	0.0390970	−	0.999235i	$-0.487552\pi$
$197$	216.209	0.0781940	0.0390970	+	0.999235i	$0.487552\pi$
$198$	34.3964	0.0123457
$199$	3761.17	1.33981	0.669905	−	0.742447i	$-0.266335\pi$
$199$	3761.17	1.33981	0.669905	+	0.742447i	$0.266335\pi$
$200$	1280.38	0.452683
$201$	−572.996	−0.201075
$202$	950.310	0.331008
$203$	−234.698	−0.0811457
$204$	411.472	0.141219
$205$	−1317.69	−0.448934
$206$	−588.386	−0.199004
$207$	607.520	0.203988
$208$	−1805.04	−0.601718
$209$	182.124	0.0602765
$210$	14.6724	0.00482140
$211$	−4232.10	−1.38080	−0.690402	−	0.723426i	$-0.742566\pi$
$211$	−4232.10	−1.38080	−0.690402	+	0.723426i	$0.742566\pi$
$212$	3986.18	1.29138
$213$	541.311	0.174132
$214$	−216.856	−0.0692709
$215$	234.276	0.0743138
$216$	469.785	0.147985
$217$	275.836	0.0862900
$218$	−8.76210	−0.00272222
$219$	730.435	0.225380
$220$	47.9981	0.0147092
$221$	2553.00	0.777074
$222$	157.478	0.0476091
$223$	1055.59	0.316985	0.158493	−	0.987360i	$-0.449337\pi$
$223$	1055.59	0.316985	0.158493	+	0.987360i	$0.449337\pi$
$224$	909.035	0.271149
$225$	2943.78	0.872232
$226$	−1321.63	−0.388997
$227$	3677.25	1.07519	0.537594	−	0.843204i	$-0.319333\pi$
$227$	3677.25	1.07519	0.537594	+	0.843204i	$0.319333\pi$
$228$	593.013	0.172251
$229$	3094.27	0.892906	0.446453	−	0.894807i	$-0.352687\pi$
$229$	3094.27	0.892906	0.446453	+	0.894807i	$0.352687\pi$
$230$	−62.9728	−0.0180535
$231$	−9.38276	−0.00267247
$232$	385.192	0.109005
$233$	2985.42	0.839404	0.419702	−	0.907662i	$-0.362135\pi$
$233$	2985.42	0.839404	0.419702	+	0.907662i	$0.362135\pi$
$234$	694.898	0.194132
$235$	1781.55	0.494533
$236$	−617.743	−0.170388
$237$	208.470	0.0571375
$238$	−375.763	−0.102341
$239$	−522.153	−0.141319	−0.0706596	−	0.997500i	$-0.522510\pi$
$239$	−522.153	−0.141319	−0.0706596	+	0.997500i	$0.522510\pi$
$240$	143.815	0.0386800
$241$	4849.16	1.29611	0.648054	−	0.761594i	$-0.275583\pi$
$241$	4849.16	1.29611	0.648054	+	0.761594i	$0.275583\pi$
$242$	−987.651	−0.262350
$243$	1626.08	0.429273
$244$	−4456.56	−1.16927
$245$	180.383	0.0470376
$246$	−203.808	−0.0528224
$247$	3679.39	0.947829
$248$	−452.708	−0.115915
$249$	−386.850	−0.0984564
$250$	−647.383	−0.163776
$251$	−1246.53	−0.313467	−0.156734	−	0.987641i	$-0.550096\pi$
$251$	−1246.53	−0.313467	−0.156734	+	0.987641i	$0.550096\pi$
$252$	1376.90	0.344193
$253$	40.2700	0.0100069
$254$	−1420.32	−0.350862
$255$	−203.407	−0.0499524
$256$	1548.17	0.377971
$257$	7059.92	1.71356	0.856781	−	0.515680i	$-0.172461\pi$
$257$	7059.92	1.71356	0.856781	+	0.515680i	$0.172461\pi$
$258$	36.2355	0.00874389
$259$	1936.03	0.464475
$260$	969.688	0.231298
$261$	885.613	0.210031
$262$	−30.0405	−0.00708362
$263$	−5184.11	−1.21546	−0.607730	−	0.794144i	$-0.707920\pi$
$263$	−5184.11	−1.21546	−0.607730	+	0.794144i	$0.707920\pi$
$264$	15.3992	0.00358999
$265$	−1970.53	−0.456789
$266$	−541.550	−0.124829
$267$	−227.539	−0.0521541
$268$	5573.72	1.27041
$269$	−5061.41	−1.14721	−0.573606	−	0.819132i	$-0.694456\pi$
$269$	−5061.41	−1.14721	−0.573606	+	0.819132i	$0.694456\pi$
$270$	−111.959	−0.0252356
$271$	−2988.65	−0.669916	−0.334958	−	0.942233i	$-0.608722\pi$
$271$	−2988.65	−0.669916	−0.334958	+	0.942233i	$0.608722\pi$
$272$	−3683.12	−0.821036
$273$	−189.557	−0.0420237
$274$	969.939	0.213855
$275$	195.131	0.0427886
$276$	131.123	0.0285966
$277$	5689.81	1.23418	0.617090	−	0.786893i	$-0.288312\pi$
$277$	5689.81	1.23418	0.617090	+	0.786893i	$0.288312\pi$
$278$	−606.587	−0.130866
$279$	−1040.84	−0.223346
$280$	−296.048	−0.0631867
$281$	−74.8343	−0.0158870	−0.00794349	−	0.999968i	$-0.502529\pi$
$281$	−74.8343	−0.0158870	−0.00794349	+	0.999968i	$0.502529\pi$
$282$	275.552	0.0581876
$283$	−1782.86	−0.374487	−0.187243	−	0.982314i	$-0.559955\pi$
$283$	−1782.86	−0.374487	−0.187243	+	0.982314i	$0.559955\pi$
$284$	−5265.50	−1.10018
$285$	−293.151	−0.0609289
$286$	46.0619	0.00952343
$287$	−2505.61	−0.515336
$288$	−3430.17	−0.701822
$289$	296.288	0.0603070
$290$	−91.7987	−0.0185883
$291$	−485.760	−0.0978549
$292$	−7105.17	−1.42397
$293$	8117.63	1.61856	0.809279	−	0.587425i	$-0.199858\pi$
$293$	8117.63	1.61856	0.809279	+	0.587425i	$0.199858\pi$
$294$	27.8998	0.00553453
$295$	305.376	0.0602700
$296$	−3177.46	−0.623939
$297$	71.5957	0.0139879
$298$	1771.46	0.344355
$299$	813.560	0.157356
$300$	635.366	0.122276
$301$	445.479	0.0853055
$302$	−1797.90	−0.342574
$303$	978.177	0.185461
$304$	−5308.11	−1.00145
$305$	2203.06	0.413597
$306$	1417.91	0.264891
$307$	−6758.21	−1.25639	−0.628194	−	0.778056i	$-0.716206\pi$
$307$	−6758.21	−1.25639	−0.628194	+	0.778056i	$0.716206\pi$
$308$	91.2691	0.0168849
$309$	−605.640	−0.111501
$310$	107.889	0.0197667
$311$	3035.80	0.553519	0.276759	−	0.960939i	$-0.410740\pi$
$311$	3035.80	0.553519	0.276759	+	0.960939i	$0.410740\pi$
$312$	311.105	0.0564514
$313$	−9613.39	−1.73604	−0.868020	−	0.496529i	$-0.834608\pi$
$313$	−9613.39	−1.73604	−0.868020	+	0.496529i	$0.834608\pi$
$314$	−1940.38	−0.348733
$315$	−680.659	−0.121748
$316$	−2027.86	−0.360999
$317$	−3088.93	−0.547291	−0.273646	−	0.961831i	$-0.588230\pi$
$317$	−3088.93	−0.547291	−0.273646	+	0.961831i	$0.588230\pi$
$318$	−304.783	−0.0537465
$319$	58.7037	0.0103034
$320$	−1147.29	−0.200423
$321$	−223.215	−0.0388120
$322$	−119.744	−0.0207238
$323$	7507.63	1.29330
$324$	−5077.78	−0.870676
$325$	3942.17	0.672837
$326$	−581.363	−0.0987690
$327$	−9.01905	−0.00152524
$328$	4112.27	0.692262
$329$	3387.64	0.567679
$330$	−3.66993	−0.000612191 0
$331$	−10197.5	−1.69336	−0.846682	−	0.532099i	$-0.821403\pi$
$331$	−10197.5	−1.69336	−0.846682	+	0.532099i	$0.821403\pi$
$332$	3763.01	0.622055
$333$	−7305.44	−1.20221
$334$	−87.0496	−0.0142609
$335$	−2755.32	−0.449370
$336$	273.466	0.0444011
$337$	1343.64	0.217189	0.108594	−	0.994086i	$-0.465365\pi$
$337$	1343.64	0.217189	0.108594	+	0.994086i	$0.465365\pi$
$338$	−703.445	−0.113202
$339$	−1360.38	−0.217952
$340$	1978.61	0.315603
$341$	−68.9932	−0.0109566
$342$	2043.49	0.323098
$343$	343.000	0.0539949
$344$	−731.131	−0.114593
$345$	−64.8194	−0.0101152
$346$	1214.06	0.188636
$347$	2586.63	0.400165	0.200083	−	0.979779i	$-0.435879\pi$
$347$	2586.63	0.400165	0.200083	+	0.979779i	$0.435879\pi$
$348$	191.145	0.0294438
$349$	1884.25	0.289002	0.144501	−	0.989505i	$-0.453842\pi$
$349$	1884.25	0.289002	0.144501	+	0.989505i	$0.453842\pi$
$350$	−580.227	−0.0886126
$351$	1446.42	0.219955
$352$	−227.372	−0.0344289
$353$	−7042.58	−1.06187	−0.530933	−	0.847414i	$-0.678158\pi$
$353$	−7042.58	−1.06187	−0.530933	+	0.847414i	$0.678158\pi$
$354$	47.2326	0.00709148
$355$	2602.95	0.389156
$356$	2213.34	0.329514
$357$	−386.782	−0.0573408
$358$	−3133.98	−0.462671
$359$	−1845.66	−0.271337	−0.135669	−	0.990754i	$-0.543318\pi$
$359$	−1845.66	−0.271337	−0.135669	+	0.990754i	$0.543318\pi$
$360$	1117.11	0.163547
$361$	3960.99	0.577489
$362$	−1569.48	−0.227873
$363$	−1016.61	−0.146993
$364$	1843.88	0.265509
$365$	3512.38	0.503688
$366$	340.748	0.0486645
$367$	−7279.14	−1.03534	−0.517668	−	0.855582i	$-0.673200\pi$
$367$	−7279.14	−1.03534	−0.517668	+	0.855582i	$0.673200\pi$
$368$	−1173.69	−0.166258
$369$	9454.70	1.33385
$370$	757.249	0.106399
$371$	−3747.00	−0.524352
$372$	−224.648	−0.0313104
$373$	−8404.65	−1.16669	−0.583346	−	0.812224i	$-0.698257\pi$
$373$	−8404.65	−1.16669	−0.583346	+	0.812224i	$0.698257\pi$
$374$	93.9874	0.0129946
$375$	−666.367	−0.0917628
$376$	−5559.87	−0.762576
$377$	1185.97	0.162017
$378$	−212.891	−0.0289681
$379$	−2614.55	−0.354355	−0.177177	−	0.984179i	$-0.556697\pi$
$379$	−2614.55	−0.354355	−0.177177	+	0.984179i	$0.556697\pi$
$380$	2851.57	0.384954
$381$	−1461.97	−0.196586
$382$	2661.46	0.356471
$383$	6160.12	0.821848	0.410924	−	0.911670i	$-0.365206\pi$
$383$	6160.12	0.821848	0.410924	+	0.911670i	$0.365206\pi$
$384$	−972.790	−0.129277
$385$	−45.1181	−0.00597254
$386$	−1705.92	−0.224946
$387$	−1680.98	−0.220798
$388$	4725.14	0.618255
$389$	−1298.49	−0.169244	−0.0846220	−	0.996413i	$-0.526968\pi$
$389$	−1298.49	−0.169244	−0.0846220	+	0.996413i	$0.526968\pi$
$390$	−74.1423	−0.00962651
$391$	1660.03	0.214710
$392$	−562.940	−0.0725326
$393$	−30.9214	−0.00396890
$394$	160.805	0.0205615
$395$	1002.45	0.127693
$396$	−344.396	−0.0437034
$397$	6963.08	0.880269	0.440135	−	0.897932i	$-0.354931\pi$
$397$	6963.08	0.880269	0.440135	+	0.897932i	$0.354931\pi$
$398$	2797.37	0.352310
$399$	−557.430	−0.0699409
$400$	−5687.21	−0.710901
$401$	4633.09	0.576971	0.288486	−	0.957484i	$-0.406848\pi$
$401$	4633.09	0.576971	0.288486	+	0.957484i	$0.406848\pi$
$402$	−426.166	−0.0528737
$403$	−1393.84	−0.172289
$404$	−9515.04	−1.17176
$405$	2510.16	0.307977
$406$	−174.557	−0.0213377
$407$	−484.248	−0.0589761
$408$	634.796	0.0770272
$409$	−4361.04	−0.527236	−0.263618	−	0.964627i	$-0.584916\pi$
$409$	−4361.04	−0.527236	−0.263618	+	0.964627i	$0.584916\pi$
$410$	−980.032	−0.118050
$411$	998.382	0.119821
$412$	5891.25	0.704469
$413$	580.676	0.0691845
$414$	451.843	0.0536398
$415$	−1860.21	−0.220034
$416$	−4593.51	−0.541383
$417$	−624.374	−0.0733231
$418$	135.455	0.0158500
$419$	−4893.57	−0.570565	−0.285282	−	0.958444i	$-0.592087\pi$
$419$	−4893.57	−0.570565	−0.285282	+	0.958444i	$0.592087\pi$
$420$	−146.909	−0.0170676
$421$	11321.3	1.31061	0.655303	−	0.755366i	$-0.272541\pi$
$421$	11321.3	1.31061	0.655303	+	0.755366i	$0.272541\pi$
$422$	−3147.62	−0.363089
$423$	−12783.0	−1.46934
$424$	6149.67	0.704373
$425$	8043.82	0.918076
$426$	402.600	0.0457888
$427$	4189.15	0.474771
$428$	2171.29	0.245217
$429$	47.4127	0.00533591
$430$	174.242	0.0195412
$431$	10591.2	1.18367	0.591836	−	0.806059i	$-0.298403\pi$
$431$	10591.2	1.18367	0.591836	+	0.806059i	$0.298403\pi$
$432$	−2086.70	−0.232399
$433$	9650.08	1.07102	0.535512	−	0.844528i	$-0.320119\pi$
$433$	9650.08	1.07102	0.535512	+	0.844528i	$0.320119\pi$
$434$	205.153	0.0226904
$435$	−94.4906	−0.0104149
$436$	87.7311	0.00963660
$437$	2392.44	0.261890
$438$	543.261	0.0592648
$439$	−15618.9	−1.69806	−0.849030	−	0.528344i	$-0.822813\pi$
$439$	−15618.9	−1.69806	−0.849030	+	0.528344i	$0.822813\pi$
$440$	74.0489	0.00802305
$441$	−1294.28	−0.139756
$442$	1898.79	0.204336
$443$	−1018.48	−0.109232	−0.0546158	−	0.998507i	$-0.517393\pi$
$443$	−1018.48	−0.109232	−0.0546158	+	0.998507i	$0.517393\pi$
$444$	−1576.76	−0.168535
$445$	−1094.15	−0.116556
$446$	785.096	0.0833529
$447$	1823.40	0.192939
$448$	−2181.59	−0.230068
$449$	−4780.78	−0.502492	−0.251246	−	0.967923i	$-0.580840\pi$
$449$	−4780.78	−0.502492	−0.251246	+	0.967923i	$0.580840\pi$
$450$	2189.44	0.229358
$451$	626.713	0.0654341
$452$	13232.9	1.37704
$453$	−1850.62	−0.191942
$454$	2734.96	0.282726
$455$	−911.504	−0.0939164
$456$	914.868	0.0939531
$457$	6633.99	0.679048	0.339524	−	0.940597i	$-0.389734\pi$
$457$	6633.99	0.679048	0.339524	+	0.940597i	$0.389734\pi$
$458$	2301.37	0.234794
$459$	2951.36	0.300126
$460$	630.519	0.0639089
$461$	14006.3	1.41505	0.707524	−	0.706689i	$-0.249812\pi$
$461$	14006.3	1.41505	0.707524	+	0.706689i	$0.249812\pi$
$462$	−6.97842	−0.000702740 0
$463$	7939.96	0.796979	0.398489	−	0.917173i	$-0.369535\pi$
$463$	7939.96	0.796979	0.398489	+	0.917173i	$0.369535\pi$
$464$	−1710.95	−0.171183
$465$	111.053	0.0110752
$466$	2220.40	0.220726
$467$	9069.00	0.898636	0.449318	−	0.893372i	$-0.351667\pi$
$467$	9069.00	0.898636	0.449318	+	0.893372i	$0.351667\pi$
$468$	−6957.71	−0.687223
$469$	−5239.27	−0.515836
$470$	1325.02	0.130040
$471$	−1997.28	−0.195393
$472$	−953.020	−0.0929371
$473$	−111.425	−0.0108316
$474$	155.050	0.0150246
$475$	11592.8	1.11981
$476$	3762.35	0.362284
$477$	14139.0	1.35719
$478$	−388.351	−0.0371606
$479$	−20962.2	−1.99956	−0.999778	−	0.0210851i	$-0.993288\pi$
$479$	−20962.2	−1.99956	−0.999778	+	0.0210851i	$0.993288\pi$
$480$	365.982	0.0348015
$481$	−9783.08	−0.927380
$482$	3606.56	0.340818
$483$	−123.255	−0.0116114
$484$	9888.91	0.928711
$485$	−2335.83	−0.218690
$486$	1209.40	0.112880
$487$	−13091.6	−1.21815	−0.609075	−	0.793112i	$-0.708459\pi$
$487$	−13091.6	−1.21815	−0.609075	+	0.793112i	$0.708459\pi$
$488$	−6875.35	−0.637771
$489$	−598.410	−0.0553396
$490$	134.159	0.0123688
$491$	−19625.2	−1.80381	−0.901906	−	0.431932i	$-0.857832\pi$
$491$	−19625.2	−1.80381	−0.901906	+	0.431932i	$0.857832\pi$
$492$	2040.64	0.186990
$493$	2419.92	0.221070
$494$	2736.54	0.249236
$495$	170.249	0.0154589
$496$	2010.84	0.182035
$497$	4949.55	0.446716
$498$	−287.720	−0.0258896
$499$	−3088.96	−0.277116	−0.138558	−	0.990354i	$-0.544247\pi$
$499$	−3088.96	−0.277116	−0.138558	+	0.990354i	$0.544247\pi$
$500$	6481.96	0.579764
$501$	−89.6022	−0.00799029
$502$	−927.106	−0.0824278
$503$	−12928.1	−1.14600	−0.572999	−	0.819556i	$-0.694220\pi$
$503$	−12928.1	−1.14600	−0.572999	+	0.819556i	$0.694220\pi$
$504$	2124.21	0.187738
$505$	4703.67	0.414477
$506$	29.9508	0.00263137
$507$	−724.073	−0.0634264
$508$	14221.1	1.24204
$509$	9427.54	0.820960	0.410480	−	0.911870i	$-0.365361\pi$
$509$	9427.54	0.820960	0.410480	+	0.911870i	$0.365361\pi$
$510$	−151.284	−0.0131352
$511$	6678.83	0.578188
$512$	11317.0	0.976845
$513$	4253.50	0.366076
$514$	5250.81	0.450590
$515$	−2912.29	−0.249186
$516$	−362.810	−0.0309532
$517$	−847.330	−0.0720803
$518$	1439.92	0.122136
$519$	1249.66	0.105691
$520$	1495.98	0.126160
$521$	−10000.5	−0.840943	−0.420472	−	0.907306i	$-0.638135\pi$
$521$	−10000.5	−0.840943	−0.420472	+	0.907306i	$0.638135\pi$
$522$	658.675	0.0552287
$523$	3563.89	0.297969	0.148985	−	0.988840i	$-0.452400\pi$
$523$	3563.89	0.297969	0.148985	+	0.988840i	$0.452400\pi$
$524$	300.782	0.0250758
$525$	−597.241	−0.0496491
$526$	−3855.68	−0.319612
$527$	−2844.08	−0.235085
$528$	−68.4004	−0.00563778
$529$	529.000	0.0434783
$530$	−1465.58	−0.120115
$531$	−2191.13	−0.179072
$532$	5422.30	0.441892
$533$	12661.3	1.02893
$534$	−169.232	−0.0137142
$535$	−1073.36	−0.0867387
$536$	8598.83	0.692934
$537$	−3225.89	−0.259231
$538$	−3764.42	−0.301665
$539$	−85.7926	−0.00685594
$540$	1120.99	0.0893332
$541$	−15756.4	−1.25216	−0.626080	−	0.779759i	$-0.715342\pi$
$541$	−15756.4	−1.25216	−0.626080	+	0.779759i	$0.715342\pi$
$542$	−2222.80	−0.176158
$543$	−1615.51	−0.127676
$544$	−9372.86	−0.738709
$545$	−43.3691	−0.00340867
$546$	−140.983	−0.0110504
$547$	3866.97	0.302266	0.151133	−	0.988513i	$-0.451708\pi$
$547$	3866.97	0.302266	0.151133	+	0.988513i	$0.451708\pi$
$548$	−9711.58	−0.757040
$549$	−15807.4	−1.22886
$550$	145.129	0.0112515
$551$	3487.59	0.269648
$552$	202.289	0.0155978
$553$	1906.18	0.146580
$554$	4231.79	0.324534
$555$	779.455	0.0596145
$556$	6073.49	0.463261
$557$	−6348.96	−0.482970	−0.241485	−	0.970405i	$-0.577634\pi$
$557$	−6348.96	−0.482970	−0.241485	+	0.970405i	$0.577634\pi$
$558$	−774.126	−0.0587301
$559$	−2251.08	−0.170323
$560$	1314.99	0.0992295
$561$	96.7435	0.00728077
$562$	−55.6580	−0.00417756
$563$	−9962.84	−0.745797	−0.372898	−	0.927872i	$-0.621636\pi$
$563$	−9962.84	−0.745797	−0.372898	+	0.927872i	$0.621636\pi$
$564$	−2758.99	−0.205983
$565$	−6541.56	−0.487089
$566$	−1326.00	−0.0984732
$567$	4773.10	0.353529
$568$	−8123.33	−0.600084
$569$	−4834.24	−0.356172	−0.178086	−	0.984015i	$-0.556991\pi$
$569$	−4834.24	−0.356172	−0.178086	+	0.984015i	$0.556991\pi$
$570$	−218.031	−0.0160216
$571$	−21810.2	−1.59847	−0.799237	−	0.601015i	$-0.794763\pi$
$571$	−21810.2	−1.59847	−0.799237	+	0.601015i	$0.794763\pi$
$572$	−461.198	−0.0337127
$573$	2739.50	0.199728
$574$	−1863.54	−0.135510
$575$	2563.31	0.185908
$576$	8232.05	0.595489
$577$	−25561.3	−1.84424	−0.922122	−	0.386899i	$-0.873546\pi$
$577$	−25561.3	−1.84424	−0.922122	+	0.386899i	$0.873546\pi$
$578$	220.364	0.0158580
$579$	−1755.95	−0.126036
$580$	919.140	0.0658021
$581$	−3537.22	−0.252579
$582$	−361.284	−0.0257315
$583$	937.215	0.0665789
$584$	−10961.5	−0.776693
$585$	3439.48	0.243086
$586$	6037.49	0.425608
$587$	12649.4	0.889431	0.444715	−	0.895672i	$-0.353305\pi$
$587$	12649.4	0.889431	0.444715	+	0.895672i	$0.353305\pi$
$588$	−279.349	−0.0195921
$589$	−4098.89	−0.286743
$590$	227.123	0.0158483
$591$	165.520	0.0115205
$592$	14113.7	0.979845
$593$	21508.7	1.48947	0.744734	−	0.667361i	$-0.232576\pi$
$593$	21508.7	1.48947	0.744734	+	0.667361i	$0.232576\pi$
$594$	53.2493	0.00367819
$595$	−1859.88	−0.128148
$596$	−17736.8	−1.21901
$597$	2879.40	0.197397
$598$	605.085	0.0413775
$599$	−15364.6	−1.04805	−0.524025	−	0.851703i	$-0.675570\pi$
$599$	−15364.6	−1.04805	−0.524025	+	0.851703i	$0.675570\pi$
$600$	980.208	0.0666947
$601$	−2580.16	−0.175120	−0.0875599	−	0.996159i	$-0.527907\pi$
$601$	−2580.16	−0.175120	−0.0875599	+	0.996159i	$0.527907\pi$
$602$	331.324	0.0224315
$603$	19770.0	1.33515
$604$	18001.6	1.21270
$605$	−4888.50	−0.328505
$606$	727.519	0.0487680
$607$	17447.1	1.16665	0.583325	−	0.812239i	$-0.301752\pi$
$607$	17447.1	1.16665	0.583325	+	0.812239i	$0.301752\pi$
$608$	−13508.2	−0.901033
$609$	−179.675	−0.0119554
$610$	1638.53	0.108757
$611$	−17118.3	−1.13344
$612$	−14196.9	−0.937706
$613$	15641.9	1.03062	0.515312	−	0.857003i	$-0.327676\pi$
$613$	15641.9	1.03062	0.515312	+	0.857003i	$0.327676\pi$
$614$	−5026.41	−0.330374
$615$	−1008.77	−0.0661424
$616$	140.805	0.00920973
$617$	17719.7	1.15619	0.578093	−	0.815971i	$-0.303797\pi$
$617$	17719.7	1.15619	0.578093	+	0.815971i	$0.303797\pi$
$618$	−450.444	−0.0293196
$619$	−3795.98	−0.246484	−0.123242	−	0.992377i	$-0.539329\pi$
$619$	−3795.98	−0.246484	−0.123242	+	0.992377i	$0.539329\pi$
$620$	−1080.25	−0.0699737
$621$	940.505	0.0607748
$622$	2257.87	0.145551
$623$	−2080.53	−0.133796
$624$	−1381.87	−0.0886523
$625$	10726.7	0.686510
$626$	−7149.95	−0.456501
$627$	139.427	0.00888065
$628$	19428.2	1.23451
$629$	−19961.9	−1.26540
$630$	−506.240	−0.0320144
$631$	−10497.6	−0.662287	−0.331143	−	0.943580i	$-0.607434\pi$
$631$	−10497.6	−0.662287	−0.331143	+	0.943580i	$0.607434\pi$
$632$	−3128.47	−0.196905
$633$	−3239.92	−0.203437
$634$	−2297.39	−0.143913
$635$	−7030.06	−0.439338
$636$	3051.66	0.190261
$637$	−1733.24	−0.107807
$638$	43.6608	0.00270932
$639$	−18676.7	−1.15624
$640$	−4677.77	−0.288914
$641$	−9034.71	−0.556708	−0.278354	−	0.960479i	$-0.589789\pi$
$641$	−9034.71	−0.556708	−0.278354	+	0.960479i	$0.589789\pi$
$642$	−166.016	−0.0102058
$643$	12838.6	0.787413	0.393706	−	0.919236i	$-0.371193\pi$
$643$	12838.6	0.787413	0.393706	+	0.919236i	$0.371193\pi$
$644$	1198.94	0.0733616
$645$	179.352	0.0109488
$646$	5583.79	0.340080
$647$	13518.1	0.821407	0.410703	−	0.911769i	$-0.365283\pi$
$647$	13518.1	0.821407	0.410703	+	0.911769i	$0.365283\pi$
$648$	−7833.73	−0.474904
$649$	−145.241	−0.00878461
$650$	2931.98	0.176926
$651$	211.168	0.0127133
$652$	5820.93	0.349640
$653$	−18505.2	−1.10898	−0.554490	−	0.832190i	$-0.687087\pi$
$653$	−18505.2	−1.10898	−0.554490	+	0.832190i	$0.687087\pi$
$654$	−6.70791	−0.000401070 0
$655$	−148.689	−0.00886987
$656$	−18265.9	−1.08714
$657$	−25202.0	−1.49654
$658$	2519.55	0.149274
$659$	14918.6	0.881860	0.440930	−	0.897542i	$-0.354649\pi$
$659$	14918.6	0.881860	0.440930	+	0.897542i	$0.354649\pi$
$660$	36.7454	0.00216714
$661$	25666.1	1.51028	0.755140	−	0.655564i	$-0.227569\pi$
$661$	25666.1	1.51028	0.755140	+	0.655564i	$0.227569\pi$
$662$	−7584.36	−0.445279
$663$	1954.47	0.114488
$664$	5805.37	0.339296
$665$	−2680.46	−0.156307
$666$	−5433.42	−0.316127
$667$	771.151	0.0447662
$668$	871.589	0.0504832
$669$	808.119	0.0467021
$670$	−2049.27	−0.118164
$671$	−1047.81	−0.0602835
$672$	695.921	0.0399490
$673$	−15116.4	−0.865819	−0.432910	−	0.901437i	$-0.642513\pi$
$673$	−15116.4	−0.865819	−0.432910	+	0.901437i	$0.642513\pi$
$674$	999.331	0.0571110
$675$	4557.29	0.259867
$676$	7043.28	0.400733
$677$	−29368.6	−1.66725	−0.833624	−	0.552333i	$-0.813738\pi$
$677$	−29368.6	−1.66725	−0.833624	+	0.552333i	$0.813738\pi$
$678$	−1011.78	−0.0573117
$679$	−4441.62	−0.251036
$680$	3052.49	0.172143
$681$	2815.16	0.158410
$682$	−51.3136	−0.00288109
$683$	−6749.84	−0.378148	−0.189074	−	0.981963i	$-0.560549\pi$
$683$	−6749.84	−0.378148	−0.189074	+	0.981963i	$0.560549\pi$
$684$	−20460.6	−1.14376
$685$	4800.83	0.267781
$686$	255.106	0.0141982
$687$	2368.85	0.131554
$688$	3247.54	0.179958
$689$	18934.2	1.04693
$690$	−48.2094	−0.00265986
$691$	30766.9	1.69382	0.846909	−	0.531738i	$-0.178461\pi$
$691$	30766.9	1.69382	0.846909	+	0.531738i	$0.178461\pi$
$692$	−12155.8	−0.667767
$693$	323.731	0.0177454
$694$	1923.80	0.105226
$695$	−3002.37	−0.163866
$696$	294.888	0.0160599
$697$	25834.8	1.40396
$698$	1401.41	0.0759946
$699$	2285.51	0.123671
$700$	5809.56	0.313687
$701$	−10999.3	−0.592638	−0.296319	−	0.955089i	$-0.595759\pi$
$701$	−10999.3	−0.592638	−0.296319	+	0.955089i	$0.595759\pi$
$702$	1075.78	0.0578384
$703$	−28769.2	−1.54346
$704$	545.668	0.0292126
$705$	1363.88	0.0728605
$706$	−5237.91	−0.279223
$707$	8944.10	0.475782
$708$	−472.919	−0.0251036
$709$	−36465.8	−1.93160	−0.965798	−	0.259297i	$-0.916509\pi$
$709$	−36465.8	−1.93160	−0.965798	+	0.259297i	$0.916509\pi$
$710$	1935.95	0.102331
$711$	−7192.80	−0.379397
$712$	3414.62	0.179731
$713$	−906.317	−0.0476043
$714$	−287.669	−0.0150781
$715$	227.989	0.0119249
$716$	31379.2	1.63784
$717$	−399.739	−0.0208208
$718$	−1372.71	−0.0713496
$719$	−15388.3	−0.798171	−0.399086	−	0.916914i	$-0.630672\pi$
$719$	−15388.3	−0.798171	−0.399086	+	0.916914i	$0.630672\pi$
$720$	−4962.01	−0.256838
$721$	−5537.76	−0.286043
$722$	2945.99	0.151854
$723$	3712.32	0.190958
$724$	15714.5	0.806666
$725$	3736.67	0.191416
$726$	−756.105	−0.0386525
$727$	9502.16	0.484753	0.242377	−	0.970182i	$-0.422073\pi$
$727$	9502.16	0.484753	0.242377	+	0.970182i	$0.422073\pi$
$728$	2844.63	0.144820
$729$	−17165.7	−0.872105
$730$	2612.33	0.132447
$731$	−4593.23	−0.232403
$732$	−3411.76	−0.172271
$733$	−16753.4	−0.844203	−0.422102	−	0.906548i	$-0.638707\pi$
$733$	−16753.4	−0.844203	−0.422102	+	0.906548i	$0.638707\pi$
$734$	−5413.86	−0.272247
$735$	138.094	0.00693015
$736$	−2986.83	−0.149587
$737$	1310.47	0.0654976
$738$	7031.93	0.350744
$739$	37612.2	1.87224	0.936121	−	0.351679i	$-0.114389\pi$
$739$	37612.2	1.87224	0.936121	+	0.351679i	$0.114389\pi$
$740$	−7582.00	−0.376649
$741$	2816.79	0.139645
$742$	−2786.83	−0.137881
$743$	7355.49	0.363185	0.181593	−	0.983374i	$-0.441875\pi$
$743$	7355.49	0.363185	0.181593	+	0.983374i	$0.441875\pi$
$744$	−346.575	−0.0170780
$745$	8768.03	0.431189
$746$	−6250.96	−0.306788
$747$	13347.4	0.653756
$748$	−941.055	−0.0460005
$749$	−2041.00	−0.0995681
$750$	−495.610	−0.0241295
$751$	6945.20	0.337462	0.168731	−	0.985662i	$-0.446033\pi$
$751$	6945.20	0.337462	0.168731	+	0.985662i	$0.446033\pi$
$752$	24695.9	1.19756
$753$	−954.293	−0.0461837
$754$	882.064	0.0426033
$755$	−8898.92	−0.428960
$756$	2131.59	0.102546
$757$	22667.4	1.08832	0.544161	−	0.838981i	$-0.316848\pi$
$757$	22667.4	1.08832	0.544161	+	0.838981i	$0.316848\pi$
$758$	−1944.57	−0.0931794
$759$	30.8291	0.00147434
$760$	4399.25	0.209970
$761$	20257.6	0.964961	0.482481	−	0.875907i	$-0.339736\pi$
$761$	20257.6	0.964961	0.482481	+	0.875907i	$0.339736\pi$
$762$	−1087.34	−0.0516932
$763$	−82.4669	−0.00391285
$764$	−26648.0	−1.26190
$765$	7018.12	0.331687
$766$	4581.59	0.216109
$767$	−2934.25	−0.138135
$768$	1185.22	0.0556872
$769$	30242.2	1.41815	0.709077	−	0.705131i	$-0.249112\pi$
$769$	30242.2	1.41815	0.709077	+	0.705131i	$0.249112\pi$
$770$	−33.5565	−0.00157051
$771$	5404.78	0.252462
$772$	17080.7	0.796304
$773$	17990.0	0.837068	0.418534	−	0.908201i	$-0.362544\pi$
$773$	17990.0	0.837068	0.418534	+	0.908201i	$0.362544\pi$
$774$	−1250.23	−0.0580600
$775$	−4391.63	−0.203551
$776$	7289.70	0.337223
$777$	1482.14	0.0684320
$778$	−965.749	−0.0445036
$779$	37233.1	1.71247
$780$	742.354	0.0340776
$781$	−1238.00	−0.0567212
$782$	1234.65	0.0564591
$783$	1371.02	0.0625752
$784$	2500.47	0.113906
$785$	−9604.16	−0.436672
$786$	−22.9978	−0.00104364
$787$	8660.54	0.392268	0.196134	−	0.980577i	$-0.437161\pi$
$787$	8660.54	0.392268	0.196134	+	0.980577i	$0.437161\pi$
$788$	−1610.07	−0.0727873
$789$	−3968.75	−0.179076
$790$	745.573	0.0335776
$791$	−12438.9	−0.559134
$792$	−531.316	−0.0238377
$793$	−21168.5	−0.947939
$794$	5178.79	0.231471
$795$	−1508.56	−0.0672995
$796$	−28008.8	−1.24717
$797$	15720.0	0.698660	0.349330	−	0.937000i	$-0.386409\pi$
$797$	15720.0	0.698660	0.349330	+	0.937000i	$0.386409\pi$
$798$	−414.588	−0.0183913
$799$	−34929.1	−1.54656
$800$	−14472.9	−0.639618
$801$	7850.72	0.346306
$802$	3445.86	0.151718
$803$	−1670.54	−0.0734147
$804$	4267.01	0.187171
$805$	−592.686	−0.0259496
$806$	−1036.67	−0.0453042
$807$	−3874.81	−0.169021
$808$	−14679.3	−0.639128
$809$	17588.8	0.764386	0.382193	−	0.924083i	$-0.375169\pi$
$809$	17588.8	0.764386	0.382193	+	0.924083i	$0.375169\pi$
$810$	1866.93	0.0809841
$811$	20188.6	0.874126	0.437063	−	0.899431i	$-0.356019\pi$
$811$	20188.6	0.874126	0.437063	+	0.899431i	$0.356019\pi$
$812$	1747.76	0.0755348
$813$	−2287.99	−0.0987001
$814$	−360.159	−0.0155081
$815$	−2877.52	−0.123675
$816$	−2819.64	−0.120965
$817$	−6619.76	−0.283471
$818$	−3243.52	−0.138639
$819$	6540.23	0.279040
$820$	9812.63	0.417893
$821$	32375.1	1.37625	0.688124	−	0.725593i	$-0.258434\pi$
$821$	32375.1	1.37625	0.688124	+	0.725593i	$0.258434\pi$
$822$	742.546	0.0315076
$823$	−24971.2	−1.05764	−0.528822	−	0.848733i	$-0.677366\pi$
$823$	−24971.2	−1.05764	−0.528822	+	0.848733i	$0.677366\pi$
$824$	9088.70	0.384248
$825$	149.385	0.00630412
$826$	431.878	0.0181924
$827$	41806.8	1.75788	0.878939	−	0.476935i	$-0.158252\pi$
$827$	41806.8	1.75788	0.878939	+	0.476935i	$0.158252\pi$
$828$	−4524.10	−0.189883
$829$	3995.99	0.167414	0.0837072	−	0.996490i	$-0.473324\pi$
$829$	3995.99	0.167414	0.0837072	+	0.996490i	$0.473324\pi$
$830$	−1383.53	−0.0578592
$831$	4355.89	0.181834
$832$	11023.9	0.459359
$833$	−3536.59	−0.147102
$834$	−464.378	−0.0192807
$835$	−430.862	−0.0178570
$836$	−1356.25	−0.0561086
$837$	−1611.33	−0.0665422
$838$	−3639.59	−0.150033
$839$	5773.08	0.237555	0.118778	−	0.992921i	$-0.462102\pi$
$839$	5773.08	0.237555	0.118778	+	0.992921i	$0.462102\pi$
$840$	−226.643	−0.00930942
$841$	−23264.9	−0.953908
$842$	8420.19	0.344631
$843$	−57.2901	−0.00234066
$844$	31515.7	1.28533
$845$	−3481.79	−0.141748
$846$	−9507.32	−0.386369
$847$	−9295.54	−0.377094
$848$	−27315.7	−1.10616
$849$	−1364.88	−0.0551739
$850$	5982.59	0.241413
$851$	−6361.24	−0.256240
$852$	−4031.06	−0.162091
$853$	42543.4	1.70769	0.853844	−	0.520528i	$-0.174265\pi$
$853$	42543.4	1.70769	0.853844	+	0.520528i	$0.174265\pi$
$854$	3115.68	0.124844
$855$	10114.5	0.404572
$856$	3349.74	0.133752
$857$	16117.9	0.642449	0.321224	−	0.947003i	$-0.395906\pi$
$857$	16117.9	0.642449	0.321224	+	0.947003i	$0.395906\pi$
$858$	35.2631	0.00140310
$859$	−3569.97	−0.141800	−0.0708998	−	0.997483i	$-0.522587\pi$
$859$	−3569.97	−0.141800	−0.0708998	+	0.997483i	$0.522587\pi$
$860$	−1744.61	−0.0691754
$861$	−1918.19	−0.0759254
$862$	7877.23	0.311253
$863$	1181.61	0.0466075	0.0233038	−	0.999728i	$-0.492582\pi$
$863$	1181.61	0.0466075	0.0233038	+	0.999728i	$0.492582\pi$
$864$	−5310.26	−0.209096
$865$	6009.12	0.236204
$866$	7177.24	0.281631
$867$	226.826	0.00888514
$868$	−2054.10	−0.0803235
$869$	−476.781	−0.0186118
$870$	−70.2774	−0.00273865
$871$	26474.9	1.02993
$872$	135.347	0.00525622
$873$	16760.1	0.649763
$874$	1779.38	0.0688654
$875$	−6093.02	−0.235408
$876$	−5439.43	−0.209796
$877$	−3434.54	−0.132242	−0.0661210	−	0.997812i	$-0.521062\pi$
$877$	−3434.54	−0.132242	−0.0661210	+	0.997812i	$0.521062\pi$
$878$	−11616.5	−0.446514
$879$	6214.53	0.238465
$880$	−328.911	−0.0125995
$881$	−22864.7	−0.874382	−0.437191	−	0.899369i	$-0.644027\pi$
$881$	−22864.7	−0.874382	−0.437191	+	0.899369i	$0.644027\pi$
$882$	−962.622	−0.0367496
$883$	581.005	0.0221431	0.0110716	−	0.999939i	$-0.496476\pi$
$883$	581.005	0.0221431	0.0110716	+	0.999939i	$0.496476\pi$
$884$	−19011.8	−0.723343
$885$	233.783	0.00887970
$886$	−757.496	−0.0287230
$887$	3694.06	0.139836	0.0699179	−	0.997553i	$-0.477726\pi$
$887$	3694.06	0.139836	0.0699179	+	0.997553i	$0.477726\pi$
$888$	−2432.53	−0.0919262
$889$	−13367.8	−0.504320
$890$	−813.770	−0.0306490
$891$	−1193.87	−0.0448889
$892$	−7860.83	−0.295067
$893$	−50339.9	−1.88641
$894$	1356.15	0.0507344
$895$	−15512.0	−0.579341
$896$	−8894.84	−0.331647
$897$	622.829	0.0231835
$898$	−3555.70	−0.132133
$899$	−1321.18	−0.0490144
$900$	−21921.9	−0.811921
$901$	38634.4	1.42852
$902$	466.118	0.0172062
$903$	341.040	0.0125682
$904$	20415.0	0.751097
$905$	−7768.34	−0.285335
$906$	−1376.40	−0.0504722
$907$	14220.8	0.520611	0.260305	−	0.965526i	$-0.416177\pi$
$907$	14220.8	0.520611	0.260305	+	0.965526i	$0.416177\pi$
$908$	−27383.9	−1.00084
$909$	−33749.8	−1.23148
$910$	−677.930	−0.0246958
$911$	−11795.4	−0.428978	−0.214489	−	0.976726i	$-0.568809\pi$
$911$	−11795.4	−0.428978	−0.214489	+	0.976726i	$0.568809\pi$
$912$	−4063.67	−0.147546
$913$	884.744	0.0320709
$914$	4934.02	0.178559
$915$	1686.58	0.0609360
$916$	−23042.6	−0.831166
$917$	−282.734	−0.0101818
$918$	2195.07	0.0789196
$919$	3834.29	0.137630	0.0688149	−	0.997629i	$-0.478078\pi$
$919$	3834.29	0.137630	0.0688149	+	0.997629i	$0.478078\pi$
$920$	972.731	0.0348587
$921$	−5173.81	−0.185106
$922$	10417.2	0.372094
$923$	−25010.9	−0.891923
$924$	69.8719	0.00248768
$925$	−30823.8	−1.09566
$926$	5905.34	0.209570
$927$	20896.3	0.740370
$928$	−4354.06	−0.154018
$929$	14037.9	0.495770	0.247885	−	0.968790i	$-0.420265\pi$
$929$	14037.9	0.495770	0.247885	+	0.968790i	$0.420265\pi$
$930$	82.5955	0.00291227
$931$	−5096.94	−0.179426
$932$	−22231.9	−0.781363
$933$	2324.08	0.0815510
$934$	6745.06	0.236301
$935$	465.202	0.0162714
$936$	−10734.0	−0.374841
$937$	−7139.64	−0.248924	−0.124462	−	0.992224i	$-0.539720\pi$
$937$	−7139.64	−0.248924	−0.124462	+	0.992224i	$0.539720\pi$
$938$	−3896.71	−0.135642
$939$	−7359.62	−0.255774
$940$	−13266.9	−0.460338
$941$	−3840.24	−0.133037	−0.0665187	−	0.997785i	$-0.521189\pi$
$941$	−3840.24	−0.133037	−0.0665187	+	0.997785i	$0.521189\pi$
$942$	−1485.48	−0.0513795
$943$	8232.71	0.284299
$944$	4233.14	0.145950
$945$	−1053.73	−0.0362729
$946$	−82.8723	−0.00284821
$947$	20395.9	0.699871	0.349936	−	0.936774i	$-0.386203\pi$
$947$	20395.9	0.699871	0.349936	+	0.936774i	$0.386203\pi$
$948$	−1552.44	−0.0531867
$949$	−33749.3	−1.15442
$950$	8622.10	0.294461
$951$	−2364.76	−0.0806335
$952$	5804.35	0.197605
$953$	−8495.21	−0.288758	−0.144379	−	0.989522i	$-0.546119\pi$
$953$	−8495.21	−0.288758	−0.144379	+	0.989522i	$0.546119\pi$
$954$	10515.9	0.356880
$955$	13173.2	0.446361
$956$	3888.39	0.131548
$957$	44.9411	0.00151802
$958$	−15590.6	−0.525793
$959$	9128.85	0.307389
$960$	−878.319	−0.0295288
$961$	−28238.2	−0.947878
$962$	−7276.16	−0.243859
$963$	7701.55	0.257714
$964$	−36110.9	−1.20649
$965$	−8443.68	−0.281670
$966$	−91.6709	−0.00305327
$967$	17879.3	0.594582	0.297291	−	0.954787i	$-0.403917\pi$
$967$	17879.3	0.594582	0.297291	+	0.954787i	$0.403917\pi$
$968$	15256.1	0.506559
$969$	5747.53	0.190544
$970$	−1737.27	−0.0575057
$971$	−15764.1	−0.521003	−0.260502	−	0.965473i	$-0.583888\pi$
$971$	−15764.1	−0.521003	−0.260502	+	0.965473i	$0.583888\pi$
$972$	−12109.2	−0.399591
$973$	−5709.06	−0.188103
$974$	−9736.91	−0.320319
$975$	3017.96	0.0991304
$976$	30539.0	1.00157
$977$	−9121.70	−0.298699	−0.149350	−	0.988784i	$-0.547718\pi$
$977$	−9121.70	−0.298699	−0.149350	+	0.988784i	$0.547718\pi$
$978$	−445.067	−0.0145518
$979$	520.392	0.0169885
$980$	−1343.28	−0.0437852
$981$	311.182	0.0101277
$982$	−14596.2	−0.474322
$983$	20076.3	0.651409	0.325704	−	0.945472i	$-0.394399\pi$
$983$	20076.3	0.651409	0.325704	+	0.945472i	$0.394399\pi$
$984$	3148.18	0.101992
$985$	795.924	0.0257464
$986$	1799.81	0.0581315
$987$	2593.44	0.0836373
$988$	−27399.8	−0.882291
$989$	−1463.72	−0.0470611
$990$	126.623	0.00406499
$991$	−19128.2	−0.613146	−0.306573	−	0.951847i	$-0.599182\pi$
$991$	−19128.2	−0.613146	−0.306573	+	0.951847i	$0.599182\pi$
$992$	5117.23	0.163783
$993$	−7806.77	−0.249487
$994$	3681.23	0.117466
$995$	13845.9	0.441150
$996$	2880.81	0.0916486
$997$	−1697.22	−0.0539132	−0.0269566	−	0.999637i	$-0.508582\pi$
$997$	−1697.22	−0.0539132	−0.0269566	+	0.999637i	$0.508582\pi$
$998$	−2297.41	−0.0728690
$999$	−11309.6	−0.358178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.a.1.4	✓	5
3.2	odd	2		1449.4.a.e.1.2		5
7.6	odd	2		1127.4.a.d.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.a.1.4	✓	5	1.1	even	1	trivial
1127.4.a.d.1.4		5	7.6	odd	2
1449.4.a.e.1.2		5	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+0.743749 q^{2} +0.765559 q^{3} -7.44684 q^{4} +3.68128 q^{5} +0.569384 q^{6} +7.00000 q^{7} -11.4886 q^{8} -26.4139 q^{9} +2.73795 q^{10} -1.75087 q^{11} -5.70100 q^{12} -35.3722 q^{13} +5.20625 q^{14} +2.81824 q^{15} +51.0301 q^{16} -72.1754 q^{17} -19.6453 q^{18} -104.019 q^{19} -27.4139 q^{20} +5.35892 q^{21} -1.30221 q^{22} -23.0000 q^{23} -8.79519 q^{24} -111.448 q^{25} -26.3080 q^{26} -40.8915 q^{27} -52.1279 q^{28} -33.5283 q^{29} +2.09606 q^{30} +39.4051 q^{31} +129.862 q^{32} -1.34039 q^{33} -53.6804 q^{34} +25.7689 q^{35} +196.700 q^{36} +276.575 q^{37} -77.3642 q^{38} -27.0795 q^{39} -42.2926 q^{40} -357.944 q^{41} +3.98569 q^{42} +63.6398 q^{43} +13.0384 q^{44} -97.2370 q^{45} -17.1062 q^{46} +483.948 q^{47} +39.0665 q^{48} +49.0000 q^{49} -82.8895 q^{50} -55.2545 q^{51} +263.411 q^{52} -535.285 q^{53} -30.4130 q^{54} -6.44544 q^{55} -80.4200 q^{56} -79.6329 q^{57} -24.9366 q^{58} +82.9537 q^{59} -20.9869 q^{60} +598.451 q^{61} +29.3075 q^{62} -184.897 q^{63} -311.656 q^{64} -130.215 q^{65} -0.996918 q^{66} -748.468 q^{67} +537.478 q^{68} -17.6079 q^{69} +19.1656 q^{70} +707.079 q^{71} +303.458 q^{72} +954.119 q^{73} +205.703 q^{74} -85.3202 q^{75} +774.614 q^{76} -12.2561 q^{77} -20.1404 q^{78} +272.311 q^{79} +187.856 q^{80} +681.871 q^{81} -266.221 q^{82} -505.317 q^{83} -39.9070 q^{84} -265.698 q^{85} +47.3321 q^{86} -25.6679 q^{87} +20.1150 q^{88} -297.219 q^{89} -72.3199 q^{90} -247.605 q^{91} +171.277 q^{92} +30.1669 q^{93} +359.936 q^{94} -382.924 q^{95} +99.4172 q^{96} -634.517 q^{97} +36.4437 q^{98} +46.2473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 11 q^{3} - 4 q^{5} + 35 q^{7} + 18 q^{8} + 14 q^{9} + 26 q^{10} - 36 q^{11} - 28 q^{12} - 69 q^{13} - 28 q^{14} - 88 q^{15} - 124 q^{16} - 42 q^{17} - 94 q^{18} - 140 q^{19} - 168 q^{20}+ \cdots - 990 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 11 * q^3 - 4 * q^5 + 35 * q^7 + 18 * q^8 + 14 * q^9 + 26 * q^10 - 36 * q^11 - 28 * q^12 - 69 * q^13 - 28 * q^14 - 88 * q^15 - 124 * q^16 - 42 * q^17 - 94 * q^18 - 140 * q^19 - 168 * q^20 - 77 * q^21 - 346 * q^22 - 115 * q^23 + 18 * q^24 - 357 * q^25 + 68 * q^26 - 35 * q^27 - 383 * q^29 + 184 * q^30 - 319 * q^31 - 50 * q^32 - 108 * q^33 - 376 * q^34 - 28 * q^35 - 180 * q^36 - 154 * q^37 + 8 * q^38 - 235 * q^39 + 90 * q^40 + 277 * q^41 - 718 * q^43 + 422 * q^44 + 470 * q^45 + 92 * q^46 + 53 * q^47 + 248 * q^48 + 245 * q^49 - 60 * q^50 + 232 * q^51 + 178 * q^52 + 450 * q^53 + 468 * q^54 - 206 * q^55 + 126 * q^56 - 560 * q^57 + 1738 * q^58 + 936 * q^59 + 944 * q^60 - 522 * q^61 + 788 * q^62 + 98 * q^63 - 252 * q^64 + 264 * q^65 + 2310 * q^66 - 810 * q^67 + 1326 * q^68 + 253 * q^69 + 182 * q^70 - 1373 * q^71 + 1590 * q^72 + 459 * q^73 + 330 * q^74 + 333 * q^75 + 1168 * q^76 - 252 * q^77 + 462 * q^78 - 728 * q^79 + 1368 * q^80 - 895 * q^81 + 1034 * q^82 - 500 * q^83 - 196 * q^84 - 1432 * q^85 + 3138 * q^86 + 1803 * q^87 - 722 * q^88 - 586 * q^89 - 1024 * q^90 - 483 * q^91 + 2149 * q^93 + 316 * q^94 - 188 * q^95 + 1210 * q^96 - 2150 * q^97 - 196 * q^98 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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