LMFDB - Embedded newform 231.4.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,4,Mod(1,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, 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("231.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.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:	$13.6294412113$
Analytic rank:	$0$
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} - 28x^{3} - 11x^{2} + 108x - 64 $ x^5 - 28x^3 - 11x^2 + 108*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.767088$ of defining polynomial
Character	$\chi$	$=$	231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.232912 q^{2} +3.00000 q^{3} -7.94575 q^{4} +7.75746 q^{5} +0.698736 q^{6} -7.00000 q^{7} -3.71396 q^{8} +9.00000 q^{9} +1.80680 q^{10} +11.0000 q^{11} -23.8373 q^{12} +59.4737 q^{13} -1.63038 q^{14} +23.2724 q^{15} +62.7010 q^{16} -45.4400 q^{17} +2.09621 q^{18} +111.752 q^{19} -61.6388 q^{20} -21.0000 q^{21} +2.56203 q^{22} +105.326 q^{23} -11.1419 q^{24} -64.8219 q^{25} +13.8521 q^{26} +27.0000 q^{27} +55.6203 q^{28} +10.0244 q^{29} +5.42041 q^{30} +315.364 q^{31} +44.3154 q^{32} +33.0000 q^{33} -10.5835 q^{34} -54.3022 q^{35} -71.5118 q^{36} -182.176 q^{37} +26.0283 q^{38} +178.421 q^{39} -28.8108 q^{40} +487.944 q^{41} -4.89115 q^{42} -358.348 q^{43} -87.4033 q^{44} +69.8171 q^{45} +24.5317 q^{46} +205.857 q^{47} +188.103 q^{48} +49.0000 q^{49} -15.0978 q^{50} -136.320 q^{51} -472.563 q^{52} +134.518 q^{53} +6.28862 q^{54} +85.3320 q^{55} +25.9977 q^{56} +335.255 q^{57} +2.33481 q^{58} -891.997 q^{59} -184.916 q^{60} +654.613 q^{61} +73.4520 q^{62} -63.0000 q^{63} -491.286 q^{64} +461.364 q^{65} +7.68609 q^{66} -102.298 q^{67} +361.055 q^{68} +315.978 q^{69} -12.6476 q^{70} +119.126 q^{71} -33.4256 q^{72} -346.254 q^{73} -42.4310 q^{74} -194.466 q^{75} -887.951 q^{76} -77.0000 q^{77} +41.5564 q^{78} -774.834 q^{79} +486.400 q^{80} +81.0000 q^{81} +113.648 q^{82} +1040.89 q^{83} +166.861 q^{84} -352.499 q^{85} -83.4636 q^{86} +30.0732 q^{87} -40.8535 q^{88} +502.925 q^{89} +16.2612 q^{90} -416.316 q^{91} -836.896 q^{92} +946.091 q^{93} +47.9465 q^{94} +866.908 q^{95} +132.946 q^{96} -939.285 q^{97} +11.4127 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 15 q^{3} + 21 q^{4} + 7 q^{5} + 15 q^{6} - 35 q^{7} + 60 q^{8} + 45 q^{9} + 55 q^{10} + 55 q^{11} + 63 q^{12} + 111 q^{13} - 35 q^{14} + 21 q^{15} + 201 q^{16} + 136 q^{17} + 45 q^{18} + 111 q^{19}+ \cdots + 495 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 15 * q^3 + 21 * q^4 + 7 * q^5 + 15 * q^6 - 35 * q^7 + 60 * q^8 + 45 * q^9 + 55 * q^10 + 55 * q^11 + 63 * q^12 + 111 * q^13 - 35 * q^14 + 21 * q^15 + 201 * q^16 + 136 * q^17 + 45 * q^18 + 111 * q^19 + 219 * q^20 - 105 * q^21 + 55 * q^22 - 28 * q^23 + 180 * q^24 + 190 * q^25 - q^26 + 135 * q^27 - 147 * q^28 + 61 * q^29 + 165 * q^30 - 280 * q^31 + 535 * q^32 + 165 * q^33 - 572 * q^34 - 49 * q^35 + 189 * q^36 - 41 * q^37 + 267 * q^38 + 333 * q^39 - 336 * q^40 + 426 * q^41 - 105 * q^42 + 424 * q^43 + 231 * q^44 + 63 * q^45 + 140 * q^46 + 75 * q^47 + 603 * q^48 + 245 * q^49 + 490 * q^50 + 408 * q^51 - 269 * q^52 + 1500 * q^53 + 135 * q^54 + 77 * q^55 - 420 * q^56 + 333 * q^57 - 1767 * q^58 + 757 * q^59 + 657 * q^60 + 658 * q^61 - 568 * q^62 - 315 * q^63 - 748 * q^64 + 537 * q^65 + 165 * q^66 - 583 * q^67 - 1650 * q^68 - 84 * q^69 - 385 * q^70 - 764 * q^71 + 540 * q^72 + 875 * q^73 - 825 * q^74 + 570 * q^75 + 213 * q^76 - 385 * q^77 - 3 * q^78 - 244 * q^79 - 2577 * q^80 + 405 * q^81 - 2006 * q^82 + 924 * q^83 - 441 * q^84 - 1402 * q^85 + 1272 * q^86 + 183 * q^87 + 660 * q^88 - 1110 * q^89 + 495 * q^90 - 777 * q^91 - 2046 * q^92 - 840 * q^93 - 3349 * q^94 + 1923 * q^95 + 1605 * q^96 - 852 * q^97 + 245 * q^98 + 495 * 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 $

$2$	0.232912	0.0823468	0.0411734	−	0.999152i	$-0.486890\pi$
$2$	0.232912	0.0823468	0.0411734	+	0.999152i	$0.486890\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.94575	−0.993219
$5$	7.75746	0.693848	0.346924	−	0.937893i	$-0.387226\pi$
$5$	7.75746	0.693848	0.346924	+	0.937893i	$0.387226\pi$
$6$	0.698736	0.0475429
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−3.71396	−0.164135
$9$	9.00000	0.333333
$10$	1.80680	0.0571362
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−23.8373	−0.573435
$13$	59.4737	1.26885	0.634424	−	0.772985i	$-0.281237\pi$
$13$	59.4737	1.26885	0.634424	+	0.772985i	$0.281237\pi$
$14$	−1.63038	−0.0311242
$15$	23.2724	0.400593
$16$	62.7010	0.979703
$17$	−45.4400	−0.648284	−0.324142	−	0.946008i	$-0.605076\pi$
$17$	−45.4400	−0.648284	−0.324142	+	0.946008i	$0.605076\pi$
$18$	2.09621	0.0274489
$19$	111.752	1.34935	0.674673	−	0.738117i	$-0.264285\pi$
$19$	111.752	1.34935	0.674673	+	0.738117i	$0.264285\pi$
$20$	−61.6388	−0.689143
$21$	−21.0000	−0.218218
$22$	2.56203	0.0248285
$23$	105.326	0.954871	0.477435	−	0.878667i	$-0.341567\pi$
$23$	105.326	0.954871	0.477435	+	0.878667i	$0.341567\pi$
$24$	−11.1419	−0.0947635
$25$	−64.8219	−0.518575
$26$	13.8521	0.104486
$27$	27.0000	0.192450
$28$	55.6203	0.375401
$29$	10.0244	0.0641892	0.0320946	−	0.999485i	$-0.489782\pi$
$29$	10.0244	0.0641892	0.0320946	+	0.999485i	$0.489782\pi$
$30$	5.42041	0.0329876
$31$	315.364	1.82713	0.913565	−	0.406694i	$-0.133318\pi$
$31$	315.364	1.82713	0.913565	+	0.406694i	$0.133318\pi$
$32$	44.3154	0.244811
$33$	33.0000	0.174078
$34$	−10.5835	−0.0533841
$35$	−54.3022	−0.262250
$36$	−71.5118	−0.331073
$37$	−182.176	−0.809448	−0.404724	−	0.914439i	$-0.632632\pi$
$37$	−182.176	−0.809448	−0.404724	+	0.914439i	$0.632632\pi$
$38$	26.0283	0.111114
$39$	178.421	0.732570
$40$	−28.8108	−0.113885
$41$	487.944	1.85864	0.929318	−	0.369280i	$-0.120396\pi$
$41$	487.944	1.85864	0.929318	+	0.369280i	$0.120396\pi$
$42$	−4.89115	−0.0179695
$43$	−358.348	−1.27087	−0.635437	−	0.772152i	$-0.719180\pi$
$43$	−358.348	−1.27087	−0.635437	+	0.772152i	$0.719180\pi$
$44$	−87.4033	−0.299467
$45$	69.8171	0.231283
$46$	24.5317	0.0786305
$47$	205.857	0.638879	0.319439	−	0.947607i	$-0.396505\pi$
$47$	205.857	0.638879	0.319439	+	0.947607i	$0.396505\pi$
$48$	188.103	0.565632
$49$	49.0000	0.142857
$50$	−15.0978	−0.0427030
$51$	−136.320	−0.374287
$52$	−472.563	−1.26024
$53$	134.518	0.348632	0.174316	−	0.984690i	$-0.444229\pi$
$53$	134.518	0.348632	0.174316	+	0.984690i	$0.444229\pi$
$54$	6.28862	0.0158476
$55$	85.3320	0.209203
$56$	25.9977	0.0620373
$57$	335.255	0.779046
$58$	2.33481	0.00528578
$59$	−891.997	−1.96827	−0.984137	−	0.177410i	$-0.943228\pi$
$59$	−891.997	−1.96827	−0.984137	+	0.177410i	$0.943228\pi$
$60$	−184.916	−0.397877
$61$	654.613	1.37401	0.687005	−	0.726653i	$-0.258925\pi$
$61$	654.613	1.37401	0.687005	+	0.726653i	$0.258925\pi$
$62$	73.4520	0.150458
$63$	−63.0000	−0.125988
$64$	−491.286	−0.959544
$65$	461.364	0.880388
$66$	7.68609	0.0143347
$67$	−102.298	−0.186532	−0.0932659	−	0.995641i	$-0.529731\pi$
$67$	−102.298	−0.186532	−0.0932659	+	0.995641i	$0.529731\pi$
$68$	361.055	0.643888
$69$	315.978	0.551295
$70$	−12.6476	−0.0215954
$71$	119.126	0.199122	0.0995608	−	0.995031i	$-0.468256\pi$
$71$	119.126	0.199122	0.0995608	+	0.995031i	$0.468256\pi$
$72$	−33.4256	−0.0547117
$73$	−346.254	−0.555151	−0.277575	−	0.960704i	$-0.589531\pi$
$73$	−346.254	−0.555151	−0.277575	+	0.960704i	$0.589531\pi$
$74$	−42.4310	−0.0666554
$75$	−194.466	−0.299399
$76$	−887.951	−1.34020
$77$	−77.0000	−0.113961
$78$	41.5564	0.0603248
$79$	−774.834	−1.10349	−0.551744	−	0.834013i	$-0.686038\pi$
$79$	−774.834	−1.10349	−0.551744	+	0.834013i	$0.686038\pi$
$80$	486.400	0.679765
$81$	81.0000	0.111111
$82$	113.648	0.153053
$83$	1040.89	1.37653	0.688265	−	0.725459i	$-0.258373\pi$
$83$	1040.89	1.37653	0.688265	+	0.725459i	$0.258373\pi$
$84$	166.861	0.216738
$85$	−352.499	−0.449811
$86$	−83.4636	−0.104652
$87$	30.0732	0.0370597
$88$	−40.8535	−0.0494886
$89$	502.925	0.598988	0.299494	−	0.954098i	$-0.403182\pi$
$89$	502.925	0.598988	0.299494	+	0.954098i	$0.403182\pi$
$90$	16.2612	0.0190454
$91$	−416.316	−0.479579
$92$	−836.896	−0.948396
$93$	946.091	1.05489
$94$	47.9465	0.0526096
$95$	866.908	0.936241
$96$	132.946	0.141341
$97$	−939.285	−0.983195	−0.491598	−	0.870822i	$-0.663587\pi$
$97$	−939.285	−0.983195	−0.491598	+	0.870822i	$0.663587\pi$
$98$	11.4127	0.0117638
$99$	99.0000	0.100504
$100$	515.058	0.515058
$101$	−664.250	−0.654409	−0.327205	−	0.944953i	$-0.606107\pi$
$101$	−664.250	−0.654409	−0.327205	+	0.944953i	$0.606107\pi$
$102$	−31.7506	−0.0308213
$103$	−1500.66	−1.43558	−0.717789	−	0.696261i	$-0.754846\pi$
$103$	−1500.66	−1.43558	−0.717789	+	0.696261i	$0.754846\pi$
$104$	−220.882	−0.208263
$105$	−162.907	−0.151410
$106$	31.3309	0.0287087
$107$	−1090.60	−0.985353	−0.492676	−	0.870213i	$-0.663981\pi$
$107$	−1090.60	−0.985353	−0.492676	+	0.870213i	$0.663981\pi$
$108$	−214.535	−0.191145
$109$	525.673	0.461930	0.230965	−	0.972962i	$-0.425812\pi$
$109$	525.673	0.461930	0.230965	+	0.972962i	$0.425812\pi$
$110$	19.8748	0.0172272
$111$	−546.528	−0.467335
$112$	−438.907	−0.370293
$113$	−1978.09	−1.64675	−0.823377	−	0.567494i	$-0.807913\pi$
$113$	−1978.09	−1.64675	−0.823377	+	0.567494i	$0.807913\pi$
$114$	78.0848	0.0641519
$115$	817.063	0.662535
$116$	−79.6515	−0.0637539
$117$	535.263	0.422949
$118$	−207.757	−0.162081
$119$	318.080	0.245028
$120$	−86.4325	−0.0657515
$121$	121.000	0.0909091
$122$	152.467	0.113145
$123$	1463.83	1.07308
$124$	−2505.80	−1.81474
$125$	−1472.53	−1.05366
$126$	−14.6734	−0.0103747
$127$	−2464.93	−1.72226	−0.861131	−	0.508383i	$-0.830243\pi$
$127$	−2464.93	−1.72226	−0.861131	+	0.508383i	$0.830243\pi$
$128$	−468.950	−0.323826
$129$	−1075.05	−0.733740
$130$	107.457	0.0724971
$131$	−552.047	−0.368188	−0.184094	−	0.982909i	$-0.558935\pi$
$131$	−552.047	−0.368188	−0.184094	+	0.982909i	$0.558935\pi$
$132$	−262.210	−0.172897
$133$	−782.261	−0.510005
$134$	−23.8263	−0.0153603
$135$	209.451	0.133531
$136$	168.762	0.106406
$137$	794.265	0.495318	0.247659	−	0.968847i	$-0.420339\pi$
$137$	794.265	0.495318	0.247659	+	0.968847i	$0.420339\pi$
$138$	73.5951	0.0453974
$139$	430.970	0.262982	0.131491	−	0.991317i	$-0.458024\pi$
$139$	430.970	0.262982	0.131491	+	0.991317i	$0.458024\pi$
$140$	431.472	0.260472
$141$	617.571	0.368857
$142$	27.7458	0.0163970
$143$	654.210	0.382572
$144$	564.309	0.326568
$145$	77.7640	0.0445376
$146$	−80.6468	−0.0457149
$147$	147.000	0.0824786
$148$	1447.53	0.803959
$149$	2645.94	1.45479	0.727397	−	0.686217i	$-0.240730\pi$
$149$	2645.94	1.45479	0.727397	+	0.686217i	$0.240730\pi$
$150$	−45.2933	−0.0246546
$151$	−538.071	−0.289984	−0.144992	−	0.989433i	$-0.546316\pi$
$151$	−538.071	−0.289984	−0.144992	+	0.989433i	$0.546316\pi$
$152$	−415.041	−0.221475
$153$	−408.960	−0.216095
$154$	−17.9342	−0.00938429
$155$	2446.42	1.26775
$156$	−1417.69	−0.727602
$157$	2052.43	1.04332	0.521661	−	0.853153i	$-0.325313\pi$
$157$	2052.43	1.04332	0.521661	+	0.853153i	$0.325313\pi$
$158$	−180.468	−0.0908688
$159$	403.554	0.201283
$160$	343.775	0.169861
$161$	−737.283	−0.360907
$162$	18.8659	0.00914964
$163$	2191.90	1.05327	0.526634	−	0.850092i	$-0.323454\pi$
$163$	2191.90	1.05327	0.526634	+	0.850092i	$0.323454\pi$
$164$	−3877.08	−1.84603
$165$	255.996	0.120783
$166$	242.435	0.113353
$167$	40.0010	0.0185351	0.00926757	−	0.999957i	$-0.497050\pi$
$167$	40.0010	0.0185351	0.00926757	+	0.999957i	$0.497050\pi$
$168$	77.9931	0.0358172
$169$	1340.12	0.609975
$170$	−82.1012	−0.0370405
$171$	1005.76	0.449782
$172$	2847.35	1.26226
$173$	4251.43	1.86838	0.934192	−	0.356770i	$-0.116122\pi$
$173$	4251.43	1.86838	0.934192	+	0.356770i	$0.116122\pi$
$174$	7.00442	0.00305174
$175$	453.753	0.196003
$176$	689.711	0.295392
$177$	−2675.99	−1.13638
$178$	117.137	0.0493247
$179$	4768.34	1.99108	0.995538	−	0.0943649i	$-0.0300820\pi$
$179$	4768.34	1.99108	0.995538	+	0.0943649i	$0.0300820\pi$
$180$	−554.749	−0.229714
$181$	−2955.03	−1.21351	−0.606756	−	0.794888i	$-0.707530\pi$
$181$	−2955.03	−1.21351	−0.606756	+	0.794888i	$0.707530\pi$
$182$	−96.9648	−0.0394918
$183$	1963.84	0.793285
$184$	−391.177	−0.156728
$185$	−1413.22	−0.561634
$186$	220.356	0.0868671
$187$	−499.840	−0.195465
$188$	−1635.69	−0.634547
$189$	−189.000	−0.0727393
$190$	201.913	0.0770965
$191$	715.502	0.271057	0.135529	−	0.990773i	$-0.456727\pi$
$191$	715.502	0.271057	0.135529	+	0.990773i	$0.456727\pi$
$192$	−1473.86	−0.553993
$193$	1799.38	0.671098	0.335549	−	0.942023i	$-0.391078\pi$
$193$	1799.38	0.671098	0.335549	+	0.942023i	$0.391078\pi$
$194$	−218.771	−0.0809630
$195$	1384.09	0.508292
$196$	−389.342	−0.141888
$197$	2978.55	1.07722	0.538612	−	0.842554i	$-0.318949\pi$
$197$	2978.55	1.07722	0.538612	+	0.842554i	$0.318949\pi$
$198$	23.0583	0.00827616
$199$	−2303.16	−0.820434	−0.410217	−	0.911988i	$-0.634547\pi$
$199$	−2303.16	−0.820434	−0.410217	+	0.911988i	$0.634547\pi$
$200$	240.745	0.0851164
$201$	−306.893	−0.107694
$202$	−154.712	−0.0538885
$203$	−70.1709	−0.0242612
$204$	1083.17	0.371749
$205$	3785.21	1.28961
$206$	−349.522	−0.118215
$207$	947.935	0.318290
$208$	3729.06	1.24309
$209$	1229.27	0.406843
$210$	−37.9429	−0.0124681
$211$	−4258.59	−1.38945	−0.694724	−	0.719277i	$-0.744473\pi$
$211$	−4258.59	−1.38945	−0.694724	+	0.719277i	$0.744473\pi$
$212$	−1068.85	−0.346268
$213$	357.377	0.114963
$214$	−254.015	−0.0811406
$215$	−2779.87	−0.881794
$216$	−100.277	−0.0315878
$217$	−2207.55	−0.690590
$218$	122.435	0.0380384
$219$	−1038.76	−0.320517
$220$	−678.027	−0.207784
$221$	−2702.49	−0.822574
$222$	−127.293	−0.0384835
$223$	−2739.54	−0.822660	−0.411330	−	0.911486i	$-0.634936\pi$
$223$	−2739.54	−0.822660	−0.411330	+	0.911486i	$0.634936\pi$
$224$	−310.208	−0.0925297
$225$	−583.397	−0.172858
$226$	−460.721	−0.135605
$227$	3373.57	0.986395	0.493198	−	0.869917i	$-0.335828\pi$
$227$	3373.57	0.986395	0.493198	+	0.869917i	$0.335828\pi$
$228$	−2663.85	−0.773763
$229$	349.100	0.100739	0.0503693	−	0.998731i	$-0.483960\pi$
$229$	349.100	0.100739	0.0503693	+	0.998731i	$0.483960\pi$
$230$	190.304	0.0545576
$231$	−231.000	−0.0657952
$232$	−37.2302	−0.0105357
$233$	2210.59	0.621548	0.310774	−	0.950484i	$-0.399412\pi$
$233$	2210.59	0.621548	0.310774	+	0.950484i	$0.399412\pi$
$234$	124.669	0.0348285
$235$	1596.93	0.443285
$236$	7087.59	1.95493
$237$	−2324.50	−0.637100
$238$	74.0847	0.0201773
$239$	−4073.04	−1.10236	−0.551178	−	0.834388i	$-0.685821\pi$
$239$	−4073.04	−1.10236	−0.551178	+	0.834388i	$0.685821\pi$
$240$	1459.20	0.392463
$241$	1967.60	0.525910	0.262955	−	0.964808i	$-0.415303\pi$
$241$	1967.60	0.525910	0.262955	+	0.964808i	$0.415303\pi$
$242$	28.1823	0.00748607
$243$	243.000	0.0641500
$244$	−5201.39	−1.36469
$245$	380.115	0.0991211
$246$	340.944	0.0883650
$247$	6646.28	1.71212
$248$	−1171.25	−0.299896
$249$	3122.66	0.794740
$250$	−342.971	−0.0867655
$251$	−7019.95	−1.76532	−0.882660	−	0.470011i	$-0.844250\pi$
$251$	−7019.95	−1.76532	−0.882660	+	0.470011i	$0.844250\pi$
$252$	500.582	0.125134
$253$	1158.59	0.287904
$254$	−574.112	−0.141823
$255$	−1057.50	−0.259698
$256$	3821.07	0.932878
$257$	−2810.13	−0.682066	−0.341033	−	0.940051i	$-0.610777\pi$
$257$	−2810.13	−0.682066	−0.341033	+	0.940051i	$0.610777\pi$
$258$	−250.391	−0.0604211
$259$	1275.23	0.305943
$260$	−3665.89	−0.874418
$261$	90.2197	0.0213964
$262$	−128.578	−0.0303191
$263$	5388.34	1.26334	0.631672	−	0.775236i	$-0.282369\pi$
$263$	5388.34	1.26334	0.631672	+	0.775236i	$0.282369\pi$
$264$	−122.561	−0.0285723
$265$	1043.52	0.241898
$266$	−182.198	−0.0419973
$267$	1508.77	0.345826
$268$	812.831	0.185267
$269$	−839.014	−0.190169	−0.0950847	−	0.995469i	$-0.530312\pi$
$269$	−839.014	−0.190169	−0.0950847	+	0.995469i	$0.530312\pi$
$270$	48.7837	0.0109959
$271$	3831.43	0.858830	0.429415	−	0.903107i	$-0.358720\pi$
$271$	3831.43	0.858830	0.429415	+	0.903107i	$0.358720\pi$
$272$	−2849.14	−0.635126
$273$	−1248.95	−0.276885
$274$	184.994	0.0407879
$275$	−713.040	−0.156356
$276$	−2510.69	−0.547556
$277$	−800.595	−0.173657	−0.0868287	−	0.996223i	$-0.527673\pi$
$277$	−800.595	−0.173657	−0.0868287	+	0.996223i	$0.527673\pi$
$278$	100.378	0.0216557
$279$	2838.27	0.609043
$280$	201.676	0.0430444
$281$	3988.10	0.846655	0.423327	−	0.905977i	$-0.360862\pi$
$281$	3988.10	0.846655	0.423327	+	0.905977i	$0.360862\pi$
$282$	143.840	0.0303742
$283$	218.036	0.0457982	0.0228991	−	0.999738i	$-0.492710\pi$
$283$	218.036	0.0457982	0.0228991	+	0.999738i	$0.492710\pi$
$284$	−946.544	−0.197771
$285$	2600.73	0.540539
$286$	152.373	0.0315036
$287$	−3415.61	−0.702498
$288$	398.839	0.0816035
$289$	−2848.20	−0.579728
$290$	18.1122	0.00366752
$291$	−2817.86	−0.567648
$292$	2751.25	0.551386
$293$	2886.47	0.575527	0.287763	−	0.957702i	$-0.407088\pi$
$293$	2886.47	0.575527	0.287763	+	0.957702i	$0.407088\pi$
$294$	34.2380	0.00679185
$295$	−6919.63	−1.36568
$296$	676.594	0.132859
$297$	297.000	0.0580259
$298$	616.272	0.119798
$299$	6264.13	1.21159
$300$	1545.18	0.297369
$301$	2508.44	0.480345
$302$	−125.323	−0.0238792
$303$	−1992.75	−0.377823
$304$	7006.94	1.32196
$305$	5078.13	0.953354
$306$	−95.2517	−0.0177947
$307$	1453.05	0.270130	0.135065	−	0.990837i	$-0.456876\pi$
$307$	1453.05	0.270130	0.135065	+	0.990837i	$0.456876\pi$
$308$	611.823	0.113188
$309$	−4501.98	−0.828831
$310$	569.800	0.104395
$311$	−10772.3	−1.96412	−0.982062	−	0.188556i	$-0.939619\pi$
$311$	−10772.3	−1.96412	−0.982062	+	0.188556i	$0.939619\pi$
$312$	−662.647	−0.120240
$313$	−2382.11	−0.430175	−0.215087	−	0.976595i	$-0.569004\pi$
$313$	−2382.11	−0.430175	−0.215087	+	0.976595i	$0.569004\pi$
$314$	478.035	0.0859142
$315$	−488.720	−0.0874166
$316$	6156.64	1.09601
$317$	−7870.28	−1.39444	−0.697222	−	0.716855i	$-0.745581\pi$
$317$	−7870.28	−1.39444	−0.697222	+	0.716855i	$0.745581\pi$
$318$	93.9926	0.0165750
$319$	110.269	0.0193538
$320$	−3811.13	−0.665777
$321$	−3271.81	−0.568894
$322$	−171.722	−0.0297195
$323$	−5078.00	−0.874760
$324$	−643.606	−0.110358
$325$	−3855.19	−0.657993
$326$	510.519	0.0867333
$327$	1577.02	0.266695
$328$	−1812.20	−0.305068
$329$	−1441.00	−0.241474
$330$	59.6245	0.00994613
$331$	−6237.15	−1.03572	−0.517862	−	0.855464i	$-0.673272\pi$
$331$	−6237.15	−1.03572	−0.517862	+	0.855464i	$0.673272\pi$
$332$	−8270.62	−1.36720
$333$	−1639.59	−0.269816
$334$	9.31670	0.00152631
$335$	−793.569	−0.129425
$336$	−1316.72	−0.213789
$337$	−5496.22	−0.888422	−0.444211	−	0.895922i	$-0.646516\pi$
$337$	−5496.22	−0.888422	−0.444211	+	0.895922i	$0.646516\pi$
$338$	312.129	0.0502295
$339$	−5934.28	−0.950754
$340$	2800.87	0.446760
$341$	3469.00	0.550900
$342$	234.255	0.0370381
$343$	−343.000	−0.0539949
$344$	1330.89	0.208595
$345$	2451.19	0.382515
$346$	990.210	0.153855
$347$	−10566.3	−1.63466	−0.817332	−	0.576167i	$-0.804548\pi$
$347$	−10566.3	−1.63466	−0.817332	+	0.576167i	$0.804548\pi$
$348$	−238.955	−0.0368084
$349$	−2553.15	−0.391596	−0.195798	−	0.980644i	$-0.562730\pi$
$349$	−2553.15	−0.391596	−0.195798	+	0.980644i	$0.562730\pi$
$350$	105.684	0.0161402
$351$	1605.79	0.244190
$352$	487.470	0.0738132
$353$	1724.64	0.260037	0.130019	−	0.991512i	$-0.458496\pi$
$353$	1724.64	0.260037	0.130019	+	0.991512i	$0.458496\pi$
$354$	−623.270	−0.0935775
$355$	924.113	0.138160
$356$	−3996.11	−0.594926
$357$	954.241	0.141467
$358$	1110.60	0.163959
$359$	2686.78	0.394994	0.197497	−	0.980303i	$-0.436719\pi$
$359$	2686.78	0.394994	0.197497	+	0.980303i	$0.436719\pi$
$360$	−259.298	−0.0379616
$361$	5629.43	0.820736
$362$	−688.262	−0.0999289
$363$	363.000	0.0524864
$364$	3307.94	0.476327
$365$	−2686.05	−0.385190
$366$	457.401	0.0653245
$367$	−2379.21	−0.338403	−0.169201	−	0.985582i	$-0.554119\pi$
$367$	−2379.21	−0.338403	−0.169201	+	0.985582i	$0.554119\pi$
$368$	6604.05	0.935490
$369$	4391.50	0.619545
$370$	−329.157	−0.0462487
$371$	−941.627	−0.131770
$372$	−7517.41	−1.04774
$373$	9982.30	1.38569	0.692847	−	0.721085i	$-0.256356\pi$
$373$	9982.30	1.38569	0.692847	+	0.721085i	$0.256356\pi$
$374$	−116.419	−0.0160959
$375$	−4417.60	−0.608331
$376$	−764.543	−0.104863
$377$	596.189	0.0814464
$378$	−44.0203	−0.00598985
$379$	−1197.67	−0.162323	−0.0811613	−	0.996701i	$-0.525863\pi$
$379$	−1197.67	−0.162323	−0.0811613	+	0.996701i	$0.525863\pi$
$380$	−6888.24	−0.929893
$381$	−7394.79	−0.994349
$382$	166.649	0.0223207
$383$	−3954.76	−0.527621	−0.263811	−	0.964575i	$-0.584979\pi$
$383$	−3954.76	−0.527621	−0.263811	+	0.964575i	$0.584979\pi$
$384$	−1406.85	−0.186961
$385$	−597.324	−0.0790713
$386$	419.096	0.0552627
$387$	−3225.14	−0.423625
$388$	7463.33	0.976528
$389$	−14191.8	−1.84976	−0.924878	−	0.380263i	$-0.875833\pi$
$389$	−14191.8	−1.84976	−0.924878	+	0.380263i	$0.875833\pi$
$390$	322.372	0.0418562
$391$	−4786.03	−0.619027
$392$	−181.984	−0.0234479
$393$	−1656.14	−0.212573
$394$	693.740	0.0887059
$395$	−6010.74	−0.765654
$396$	−786.629	−0.0998223
$397$	−8724.90	−1.10300	−0.551499	−	0.834176i	$-0.685944\pi$
$397$	−8724.90	−1.10300	−0.551499	+	0.834176i	$0.685944\pi$
$398$	−536.432	−0.0675601
$399$	−2346.78	−0.294452
$400$	−4064.40	−0.508049
$401$	9736.18	1.21247	0.606236	−	0.795285i	$-0.292679\pi$
$401$	9736.18	1.21247	0.606236	+	0.795285i	$0.292679\pi$
$402$	−71.4789	−0.00886827
$403$	18755.8	2.31835
$404$	5277.97	0.649972
$405$	628.354	0.0770942
$406$	−16.3436	−0.00199784
$407$	−2003.94	−0.244058
$408$	506.287	0.0614337
$409$	−10284.9	−1.24342	−0.621708	−	0.783249i	$-0.713561\pi$
$409$	−10284.9	−1.24342	−0.621708	+	0.783249i	$0.713561\pi$
$410$	881.620	0.106195
$411$	2382.79	0.285972
$412$	11923.9	1.42584
$413$	6243.98	0.743938
$414$	220.785	0.0262102
$415$	8074.62	0.955103
$416$	2635.60	0.310627
$417$	1292.91	0.151832
$418$	286.311	0.0335022
$419$	12837.5	1.49679	0.748393	−	0.663255i	$-0.230826\pi$
$419$	12837.5	1.49679	0.748393	+	0.663255i	$0.230826\pi$
$420$	1294.42	0.150383
$421$	3108.45	0.359849	0.179925	−	0.983680i	$-0.442415\pi$
$421$	3108.45	0.359849	0.179925	+	0.983680i	$0.442415\pi$
$422$	−991.876	−0.114417
$423$	1852.71	0.212960
$424$	−499.594	−0.0572227
$425$	2945.51	0.336184
$426$	83.2374	0.00946682
$427$	−4582.29	−0.519327
$428$	8665.67	0.978671
$429$	1962.63	0.220878
$430$	−647.465	−0.0726129
$431$	−414.489	−0.0463231	−0.0231615	−	0.999732i	$-0.507373\pi$
$431$	−414.489	−0.0463231	−0.0231615	+	0.999732i	$0.507373\pi$
$432$	1692.93	0.188544
$433$	7591.87	0.842591	0.421296	−	0.906923i	$-0.361575\pi$
$433$	7591.87	0.842591	0.421296	+	0.906923i	$0.361575\pi$
$434$	−514.164	−0.0568679
$435$	233.292	0.0257138
$436$	−4176.87	−0.458797
$437$	11770.4	1.28845
$438$	−241.940	−0.0263935
$439$	−1585.71	−0.172396	−0.0861982	−	0.996278i	$-0.527472\pi$
$439$	−1585.71	−0.172396	−0.0861982	+	0.996278i	$0.527472\pi$
$440$	−316.919	−0.0343376
$441$	441.000	0.0476190
$442$	−629.441	−0.0677363
$443$	3305.39	0.354501	0.177250	−	0.984166i	$-0.443280\pi$
$443$	3305.39	0.354501	0.177250	+	0.984166i	$0.443280\pi$
$444$	4342.58	0.464166
$445$	3901.42	0.415606
$446$	−638.072	−0.0677434
$447$	7937.83	0.839925
$448$	3439.00	0.362673
$449$	−2470.77	−0.259694	−0.129847	−	0.991534i	$-0.541449\pi$
$449$	−2470.77	−0.259694	−0.129847	+	0.991534i	$0.541449\pi$
$450$	−135.880	−0.0142343
$451$	5367.39	0.560400
$452$	15717.4	1.63559
$453$	−1614.21	−0.167422
$454$	785.745	0.0812265
$455$	−3229.55	−0.332755
$456$	−1245.12	−0.127869
$457$	2916.85	0.298566	0.149283	−	0.988795i	$-0.452303\pi$
$457$	2916.85	0.298566	0.149283	+	0.988795i	$0.452303\pi$
$458$	81.3095	0.00829551
$459$	−1226.88	−0.124762
$460$	−6492.18	−0.658042
$461$	−6185.85	−0.624954	−0.312477	−	0.949925i	$-0.601159\pi$
$461$	−6185.85	−0.624954	−0.312477	+	0.949925i	$0.601159\pi$
$462$	−53.8026	−0.00541802
$463$	−19037.0	−1.91086	−0.955428	−	0.295224i	$-0.904606\pi$
$463$	−19037.0	−1.91086	−0.955428	+	0.295224i	$0.904606\pi$
$464$	628.541	0.0628864
$465$	7339.26	0.731936
$466$	514.873	0.0511825
$467$	−3241.03	−0.321150	−0.160575	−	0.987024i	$-0.551335\pi$
$467$	−3241.03	−0.321150	−0.160575	+	0.987024i	$0.551335\pi$
$468$	−4253.07	−0.420081
$469$	716.083	0.0705024
$470$	371.943	0.0365031
$471$	6157.28	0.602362
$472$	3312.84	0.323063
$473$	−3941.83	−0.383183
$474$	−541.404	−0.0524631
$475$	−7243.95	−0.699737
$476$	−2527.39	−0.243367
$477$	1210.66	0.116211
$478$	−948.659	−0.0907754
$479$	17662.0	1.68475	0.842377	−	0.538889i	$-0.181156\pi$
$479$	17662.0	1.68475	0.842377	+	0.538889i	$0.181156\pi$
$480$	1031.33	0.0980695
$481$	−10834.7	−1.02707
$482$	458.278	0.0433070
$483$	−2211.85	−0.208370
$484$	−961.436	−0.0902926
$485$	−7286.46	−0.682188
$486$	56.5976	0.00528255
$487$	−11143.6	−1.03689	−0.518445	−	0.855111i	$-0.673489\pi$
$487$	−11143.6	−1.03689	−0.518445	+	0.855111i	$0.673489\pi$
$488$	−2431.20	−0.225523
$489$	6575.70	0.608105
$490$	88.5334	0.00816231
$491$	7223.60	0.663944	0.331972	−	0.943289i	$-0.392286\pi$
$491$	7223.60	0.663944	0.331972	+	0.943289i	$0.392286\pi$
$492$	−11631.3	−1.06581
$493$	−455.510	−0.0416128
$494$	1548.00	0.140987
$495$	767.988	0.0697344
$496$	19773.6	1.79004
$497$	−833.880	−0.0752609
$498$	727.304	0.0654443
$499$	−13771.3	−1.23545	−0.617725	−	0.786394i	$-0.711946\pi$
$499$	−13771.3	−1.23545	−0.617725	+	0.786394i	$0.711946\pi$
$500$	11700.4	1.04652
$501$	120.003	0.0107013
$502$	−1635.03	−0.145368
$503$	−16826.6	−1.49157	−0.745787	−	0.666185i	$-0.767926\pi$
$503$	−16826.6	−1.49157	−0.745787	+	0.666185i	$0.767926\pi$
$504$	233.979	0.0206791
$505$	−5152.89	−0.454061
$506$	269.849	0.0237080
$507$	4020.35	0.352169
$508$	19585.7	1.71058
$509$	17447.3	1.51932	0.759662	−	0.650318i	$-0.225364\pi$
$509$	17447.3	1.51932	0.759662	+	0.650318i	$0.225364\pi$
$510$	−246.304	−0.0213853
$511$	2423.78	0.209827
$512$	4641.57	0.400645
$513$	3017.29	0.259682
$514$	−654.513	−0.0561660
$515$	−11641.3	−0.996073
$516$	8542.04	0.728764
$517$	2264.43	0.192629
$518$	297.017	0.0251934
$519$	12754.3	1.07871
$520$	−1713.49	−0.144503
$521$	−1688.35	−0.141973	−0.0709866	−	0.997477i	$-0.522615\pi$
$521$	−1688.35	−0.141973	−0.0709866	+	0.997477i	$0.522615\pi$
$522$	21.0132	0.00176193
$523$	−21089.3	−1.76323	−0.881616	−	0.471967i	$-0.843544\pi$
$523$	−21089.3	−1.76323	−0.881616	+	0.471967i	$0.843544\pi$
$524$	4386.43	0.365691
$525$	1361.26	0.113162
$526$	1255.01	0.104032
$527$	−14330.1	−1.18450
$528$	2069.13	0.170544
$529$	−1073.40	−0.0882223
$530$	243.048	0.0199195
$531$	−8027.98	−0.656091
$532$	6215.66	0.506547
$533$	29019.8	2.35833
$534$	351.411	0.0284776
$535$	−8460.32	−0.683685
$536$	379.928	0.0306164
$537$	14305.0	1.14955
$538$	−195.416	−0.0156598
$539$	539.000	0.0430730
$540$	−1664.25	−0.132626
$541$	15205.5	1.20838	0.604191	−	0.796840i	$-0.293496\pi$
$541$	15205.5	1.20838	0.604191	+	0.796840i	$0.293496\pi$
$542$	892.386	0.0707219
$543$	−8865.10	−0.700622
$544$	−2013.70	−0.158707
$545$	4077.88	0.320509
$546$	−290.895	−0.0228006
$547$	−6915.32	−0.540544	−0.270272	−	0.962784i	$-0.587114\pi$
$547$	−6915.32	−0.540544	−0.270272	+	0.962784i	$0.587114\pi$
$548$	−6311.03	−0.491960
$549$	5891.52	0.458003
$550$	−166.076	−0.0128754
$551$	1120.24	0.0866135
$552$	−1173.53	−0.0904869
$553$	5423.84	0.417080
$554$	−186.468	−0.0143001
$555$	−4239.67	−0.324259
$556$	−3424.38	−0.261198
$557$	−2243.06	−0.170631	−0.0853156	−	0.996354i	$-0.527190\pi$
$557$	−2243.06	−0.170631	−0.0853156	+	0.996354i	$0.527190\pi$
$558$	661.068	0.0501527
$559$	−21312.3	−1.61255
$560$	−3404.80	−0.256927
$561$	−1499.52	−0.112852
$562$	928.875	0.0697193
$563$	−1533.10	−0.114765	−0.0573824	−	0.998352i	$-0.518275\pi$
$563$	−1533.10	−0.114765	−0.0573824	+	0.998352i	$0.518275\pi$
$564$	−4907.06	−0.366356
$565$	−15345.0	−1.14260
$566$	50.7832	0.00377134
$567$	−567.000	−0.0419961
$568$	−442.428	−0.0326828
$569$	8226.60	0.606110	0.303055	−	0.952973i	$-0.401993\pi$
$569$	8226.60	0.606110	0.303055	+	0.952973i	$0.401993\pi$
$570$	605.740	0.0445117
$571$	565.628	0.0414550	0.0207275	−	0.999785i	$-0.493402\pi$
$571$	565.628	0.0414550	0.0207275	+	0.999785i	$0.493402\pi$
$572$	−5198.19	−0.379978
$573$	2146.51	0.156495
$574$	−795.536	−0.0578485
$575$	−6827.44	−0.495172
$576$	−4421.58	−0.319848
$577$	−7258.21	−0.523680	−0.261840	−	0.965111i	$-0.584329\pi$
$577$	−7258.21	−0.523680	−0.261840	+	0.965111i	$0.584329\pi$
$578$	−663.380	−0.0477387
$579$	5398.13	0.387458
$580$	−617.893	−0.0442356
$581$	−7286.20	−0.520279
$582$	−656.312	−0.0467440
$583$	1479.70	0.105116
$584$	1285.97	0.0911198
$585$	4152.28	0.293463
$586$	672.293	0.0473928
$587$	17458.6	1.22758	0.613792	−	0.789468i	$-0.289643\pi$
$587$	17458.6	1.22758	0.613792	+	0.789468i	$0.289643\pi$
$588$	−1168.03	−0.0819193
$589$	35242.4	2.46543
$590$	−1611.66	−0.112460
$591$	8935.65	0.621935
$592$	−11422.6	−0.793019
$593$	−13482.3	−0.933648	−0.466824	−	0.884350i	$-0.654602\pi$
$593$	−13482.3	−0.933648	−0.466824	+	0.884350i	$0.654602\pi$
$594$	69.1748	0.00477825
$595$	2467.49	0.170012
$596$	−21024.0	−1.44493
$597$	−6909.47	−0.473678
$598$	1458.99	0.0997702
$599$	−5040.45	−0.343819	−0.171909	−	0.985113i	$-0.554994\pi$
$599$	−5040.45	−0.343819	−0.171909	+	0.985113i	$0.554994\pi$
$600$	722.236	0.0491420
$601$	13587.9	0.922234	0.461117	−	0.887339i	$-0.347449\pi$
$601$	13587.9	0.922234	0.461117	+	0.887339i	$0.347449\pi$
$602$	584.245	0.0395549
$603$	−920.678	−0.0621773
$604$	4275.38	0.288018
$605$	938.652	0.0630771
$606$	−464.135	−0.0311125
$607$	−24238.0	−1.62074	−0.810371	−	0.585917i	$-0.800735\pi$
$607$	−24238.0	−1.62074	−0.810371	+	0.585917i	$0.800735\pi$
$608$	4952.32	0.330334
$609$	−210.513	−0.0140072
$610$	1182.76	0.0785056
$611$	12243.1	0.810640
$612$	3249.50	0.214629
$613$	−7239.20	−0.476979	−0.238490	−	0.971145i	$-0.576652\pi$
$613$	−7239.20	−0.476979	−0.238490	+	0.971145i	$0.576652\pi$
$614$	338.433	0.0222444
$615$	11355.6	0.744557
$616$	285.975	0.0187049
$617$	25095.8	1.63747	0.818736	−	0.574170i	$-0.194675\pi$
$617$	25095.8	1.63747	0.818736	+	0.574170i	$0.194675\pi$
$618$	−1048.57	−0.0682516
$619$	9983.31	0.648244	0.324122	−	0.946015i	$-0.394931\pi$
$619$	9983.31	0.648244	0.324122	+	0.946015i	$0.394931\pi$
$620$	−19438.7	−1.25915
$621$	2843.81	0.183765
$622$	−2509.00	−0.161739
$623$	−3520.47	−0.226396
$624$	11187.2	0.717701
$625$	−3320.39	−0.212505
$626$	−554.821	−0.0354235
$627$	3687.80	0.234891
$628$	−16308.1	−1.03625
$629$	8278.09	0.524752
$630$	−113.829	−0.00719848
$631$	10735.0	0.677264	0.338632	−	0.940919i	$-0.390036\pi$
$631$	10735.0	0.677264	0.338632	+	0.940919i	$0.390036\pi$
$632$	2877.70	0.181121
$633$	−12775.8	−0.802198
$634$	−1833.08	−0.114828
$635$	−19121.6	−1.19499
$636$	−3206.54	−0.199918
$637$	2914.21	0.181264
$638$	25.6829	0.00159372
$639$	1072.13	0.0663738
$640$	−3637.86	−0.224686
$641$	12831.2	0.790643	0.395322	−	0.918543i	$-0.370633\pi$
$641$	12831.2	0.790643	0.395322	+	0.918543i	$0.370633\pi$
$642$	−762.044	−0.0468466
$643$	−16536.8	−1.01423	−0.507113	−	0.861880i	$-0.669287\pi$
$643$	−16536.8	−1.01423	−0.507113	+	0.861880i	$0.669287\pi$
$644$	5858.27	0.358460
$645$	−8339.62	−0.509104
$646$	−1182.73	−0.0720337
$647$	−6600.54	−0.401073	−0.200536	−	0.979686i	$-0.564268\pi$
$647$	−6600.54	−0.401073	−0.200536	+	0.979686i	$0.564268\pi$
$648$	−300.830	−0.0182372
$649$	−9811.97	−0.593457
$650$	−897.920	−0.0541836
$651$	−6622.64	−0.398712
$652$	−17416.3	−1.04613
$653$	−22720.9	−1.36162	−0.680810	−	0.732460i	$-0.738372\pi$
$653$	−22720.9	−1.36162	−0.680810	+	0.732460i	$0.738372\pi$
$654$	367.306	0.0219615
$655$	−4282.48	−0.255466
$656$	30594.6	1.82091
$657$	−3116.29	−0.185050
$658$	−335.626	−0.0198846
$659$	916.372	0.0541681	0.0270841	−	0.999633i	$-0.491378\pi$
$659$	916.372	0.0541681	0.0270841	+	0.999633i	$0.491378\pi$
$660$	−2034.08	−0.119964
$661$	−10592.7	−0.623312	−0.311656	−	0.950195i	$-0.600884\pi$
$661$	−10592.7	−0.623312	−0.311656	+	0.950195i	$0.600884\pi$
$662$	−1452.71	−0.0852886
$663$	−8107.46	−0.474913
$664$	−3865.80	−0.225937
$665$	−6068.36	−0.353866
$666$	−381.879	−0.0222185
$667$	1055.83	0.0612924
$668$	−317.838	−0.0184095
$669$	−8218.62	−0.474963
$670$	−184.832	−0.0106577
$671$	7200.74	0.414279
$672$	−930.624	−0.0534220
$673$	10778.2	0.617336	0.308668	−	0.951170i	$-0.400117\pi$
$673$	10778.2	0.617336	0.308668	+	0.951170i	$0.400117\pi$
$674$	−1280.14	−0.0731587
$675$	−1750.19	−0.0997998
$676$	−10648.2	−0.605839
$677$	24654.1	1.39960	0.699802	−	0.714336i	$-0.253271\pi$
$677$	24654.1	1.39960	0.699802	+	0.714336i	$0.253271\pi$
$678$	−1382.16	−0.0782915
$679$	6575.00	0.371613
$680$	1309.17	0.0738298
$681$	10120.7	0.569495
$682$	807.972	0.0453649
$683$	−21152.8	−1.18505	−0.592524	−	0.805553i	$-0.701868\pi$
$683$	−21152.8	−1.18505	−0.592524	+	0.805553i	$0.701868\pi$
$684$	−7991.56	−0.446732
$685$	6161.48	0.343676
$686$	−79.8888	−0.00444631
$687$	1047.30	0.0581615
$688$	−22468.8	−1.24508
$689$	8000.29	0.442361
$690$	570.911	0.0314989
$691$	3359.89	0.184973	0.0924865	−	0.995714i	$-0.470519\pi$
$691$	3359.89	0.184973	0.0924865	+	0.995714i	$0.470519\pi$
$692$	−33780.8	−1.85572
$693$	−693.000	−0.0379869
$694$	−2461.02	−0.134609
$695$	3343.23	0.182469
$696$	−111.691	−0.00608279
$697$	−22172.2	−1.20492
$698$	−594.659	−0.0322467
$699$	6631.77	0.358851
$700$	−3605.41	−0.194674
$701$	−20003.4	−1.07777	−0.538887	−	0.842378i	$-0.681155\pi$
$701$	−20003.4	−1.07777	−0.538887	+	0.842378i	$0.681155\pi$
$702$	374.007	0.0201083
$703$	−20358.5	−1.09223
$704$	−5404.15	−0.289313
$705$	4790.78	0.255931
$706$	401.688	0.0214132
$707$	4649.75	0.247344
$708$	21262.8	1.12868
$709$	6330.56	0.335331	0.167665	−	0.985844i	$-0.446377\pi$
$709$	6330.56	0.335331	0.167665	+	0.985844i	$0.446377\pi$
$710$	215.237	0.0113770
$711$	−6973.50	−0.367830
$712$	−1867.84	−0.0983149
$713$	33216.1	1.74467
$714$	222.254	0.0116494
$715$	5075.01	0.265447
$716$	−37888.0	−1.97757
$717$	−12219.1	−0.636445
$718$	625.784	0.0325265
$719$	−111.791	−0.00579845	−0.00289923	−	0.999996i	$-0.500923\pi$
$719$	−111.791	−0.00579845	−0.00289923	+	0.999996i	$0.500923\pi$
$720$	4377.60	0.226588
$721$	10504.6	0.542597
$722$	1311.16	0.0675849
$723$	5902.80	0.303634
$724$	23480.0	1.20528
$725$	−649.801	−0.0332869
$726$	84.5470	0.00432209
$727$	−17266.8	−0.880867	−0.440433	−	0.897785i	$-0.645175\pi$
$727$	−17266.8	−0.880867	−0.440433	+	0.897785i	$0.645175\pi$
$728$	1546.18	0.0787159
$729$	729.000	0.0370370
$730$	−625.614	−0.0317192
$731$	16283.4	0.823888
$732$	−15604.2	−0.787906
$733$	−858.639	−0.0432668	−0.0216334	−	0.999766i	$-0.506887\pi$
$733$	−858.639	−0.0432668	−0.0216334	+	0.999766i	$0.506887\pi$
$734$	−554.146	−0.0278664
$735$	1140.35	0.0572276
$736$	4667.58	0.233762
$737$	−1125.27	−0.0562415
$738$	1022.83	0.0510176
$739$	16141.2	0.803471	0.401736	−	0.915756i	$-0.368407\pi$
$739$	16141.2	0.803471	0.401736	+	0.915756i	$0.368407\pi$
$740$	11229.1	0.557825
$741$	19938.8	0.988490
$742$	−219.316	−0.0108509
$743$	1249.50	0.0616953	0.0308476	−	0.999524i	$-0.490179\pi$
$743$	1249.50	0.0616953	0.0308476	+	0.999524i	$0.490179\pi$
$744$	−3513.74	−0.173145
$745$	20525.8	1.00941
$746$	2325.00	0.114107
$747$	9367.97	0.458843
$748$	3971.61	0.194140
$749$	7634.23	0.372428
$750$	−1028.91	−0.0500941
$751$	82.9863	0.00403224	0.00201612	−	0.999998i	$-0.499358\pi$
$751$	82.9863	0.00403224	0.00201612	+	0.999998i	$0.499358\pi$
$752$	12907.4	0.625912
$753$	−21059.9	−1.01921
$754$	138.859	0.00670685
$755$	−4174.06	−0.201205
$756$	1501.75	0.0722461
$757$	−3439.65	−0.165147	−0.0825735	−	0.996585i	$-0.526314\pi$
$757$	−3439.65	−0.165147	−0.0825735	+	0.996585i	$0.526314\pi$
$758$	−278.952	−0.0133667
$759$	3475.76	0.166222
$760$	−3219.66	−0.153670
$761$	5651.24	0.269195	0.134597	−	0.990900i	$-0.457026\pi$
$761$	5651.24	0.269195	0.134597	+	0.990900i	$0.457026\pi$
$762$	−1722.34	−0.0818814
$763$	−3679.71	−0.174593
$764$	−5685.20	−0.269219
$765$	−3172.49	−0.149937
$766$	−921.111	−0.0434479
$767$	−53050.3	−2.49744
$768$	11463.2	0.538597
$769$	14381.1	0.674378	0.337189	−	0.941437i	$-0.390524\pi$
$769$	14381.1	0.674378	0.337189	+	0.941437i	$0.390524\pi$
$770$	−139.124	−0.00651127
$771$	−8430.39	−0.393791
$772$	−14297.4	−0.666547
$773$	−31316.0	−1.45713	−0.728563	−	0.684979i	$-0.759811\pi$
$773$	−31316.0	−1.45713	−0.728563	+	0.684979i	$0.759811\pi$
$774$	−751.172	−0.0348841
$775$	−20442.5	−0.947503
$776$	3488.46	0.161377
$777$	3825.70	0.176636
$778$	−3305.45	−0.152321
$779$	54528.6	2.50794
$780$	−10997.7	−0.504845
$781$	1310.38	0.0600374
$782$	−1114.72	−0.0509749
$783$	270.659	0.0123532
$784$	3072.35	0.139958
$785$	15921.6	0.723907
$786$	−385.735	−0.0175047
$787$	29847.6	1.35191	0.675954	−	0.736944i	$-0.263732\pi$
$787$	29847.6	1.35191	0.675954	+	0.736944i	$0.263732\pi$
$788$	−23666.8	−1.06992
$789$	16165.0	0.729391
$790$	−1399.97	−0.0630491
$791$	13846.6	0.622415
$792$	−367.682	−0.0164962
$793$	38932.2	1.74341
$794$	−2032.13	−0.0908283
$795$	3130.56	0.139660
$796$	18300.3	0.814871
$797$	7581.40	0.336947	0.168474	−	0.985706i	$-0.446116\pi$
$797$	7581.40	0.336947	0.168474	+	0.985706i	$0.446116\pi$
$798$	−546.594	−0.0242471
$799$	−9354.15	−0.414175
$800$	−2872.61	−0.126953
$801$	4526.32	0.199663
$802$	2267.67	0.0998432
$803$	−3808.80	−0.167384
$804$	2438.49	0.106964
$805$	−5719.44	−0.250415
$806$	4368.46	0.190909
$807$	−2517.04	−0.109794
$808$	2467.00	0.107412
$809$	−25260.6	−1.09779	−0.548896	−	0.835891i	$-0.684952\pi$
$809$	−25260.6	−1.09779	−0.548896	+	0.835891i	$0.684952\pi$
$810$	146.351	0.00634846
$811$	−25594.8	−1.10821	−0.554103	−	0.832448i	$-0.686939\pi$
$811$	−25594.8	−1.10821	−0.554103	+	0.832448i	$0.686939\pi$
$812$	557.561	0.0240967
$813$	11494.3	0.495846
$814$	−466.741	−0.0200974
$815$	17003.6	0.730808
$816$	−8547.41	−0.366690
$817$	−40046.0	−1.71485
$818$	−2395.48	−0.102391
$819$	−3746.84	−0.159860
$820$	−30076.3	−1.28087
$821$	−19077.2	−0.810959	−0.405480	−	0.914104i	$-0.632895\pi$
$821$	−19077.2	−0.810959	−0.405480	+	0.914104i	$0.632895\pi$
$822$	554.981	0.0235489
$823$	13889.2	0.588270	0.294135	−	0.955764i	$-0.404969\pi$
$823$	13889.2	0.588270	0.294135	+	0.955764i	$0.404969\pi$
$824$	5573.39	0.235629
$825$	−2139.12	−0.0902723
$826$	1454.30	0.0612609
$827$	1354.92	0.0569714	0.0284857	−	0.999594i	$-0.490931\pi$
$827$	1354.92	0.0569714	0.0284857	+	0.999594i	$0.490931\pi$
$828$	−7532.06	−0.316132
$829$	29760.9	1.24685	0.623426	−	0.781882i	$-0.285740\pi$
$829$	29760.9	1.24685	0.623426	+	0.781882i	$0.285740\pi$
$830$	1880.68	0.0786496
$831$	−2401.79	−0.100261
$832$	−29218.6	−1.21752
$833$	−2226.56	−0.0926120
$834$	301.134	0.0125029
$835$	310.306	0.0128606
$836$	−9767.46	−0.404084
$837$	8514.82	0.351631
$838$	2990.01	0.123256
$839$	33789.1	1.39038	0.695191	−	0.718825i	$-0.255320\pi$
$839$	33789.1	1.39038	0.695191	+	0.718825i	$0.255320\pi$
$840$	605.028	0.0248517
$841$	−24288.5	−0.995880
$842$	723.995	0.0296324
$843$	11964.3	0.488816
$844$	33837.7	1.38003
$845$	10395.9	0.423230
$846$	431.519	0.0175365
$847$	−847.000	−0.0343604
$848$	8434.42	0.341556
$849$	654.108	0.0264416
$850$	686.044	0.0276837
$851$	−19187.9	−0.772918
$852$	−2839.63	−0.114183
$853$	22293.3	0.894851	0.447426	−	0.894321i	$-0.352341\pi$
$853$	22293.3	0.894851	0.447426	+	0.894321i	$0.352341\pi$
$854$	−1067.27	−0.0427649
$855$	7802.18	0.312080
$856$	4050.46	0.161731
$857$	−43972.3	−1.75270	−0.876352	−	0.481672i	$-0.840030\pi$
$857$	−43972.3	−1.75270	−0.876352	+	0.481672i	$0.840030\pi$
$858$	457.120	0.0181886
$859$	−34582.5	−1.37362	−0.686810	−	0.726837i	$-0.740990\pi$
$859$	−34582.5	−1.37362	−0.686810	+	0.726837i	$0.740990\pi$
$860$	22088.2	0.875814
$861$	−10246.8	−0.405588
$862$	−96.5395	−0.00381456
$863$	48984.4	1.93215	0.966077	−	0.258254i	$-0.0831472\pi$
$863$	48984.4	1.93215	0.966077	+	0.258254i	$0.0831472\pi$
$864$	1196.52	0.0471138
$865$	32980.3	1.29638
$866$	1768.24	0.0693847
$867$	−8544.61	−0.334706
$868$	17540.6	0.685907
$869$	−8523.17	−0.332714
$870$	54.3365	0.00211745
$871$	−6084.01	−0.236681
$872$	−1952.33	−0.0758189
$873$	−8453.57	−0.327732
$874$	2741.46	0.106100
$875$	10307.7	0.398246
$876$	8253.76	0.318343
$877$	3914.98	0.150741	0.0753703	−	0.997156i	$-0.475986\pi$
$877$	3914.98	0.150741	0.0753703	+	0.997156i	$0.475986\pi$
$878$	−369.332	−0.0141963
$879$	8659.41	0.332281
$880$	5350.40	0.204957
$881$	4908.77	0.187719	0.0938597	−	0.995585i	$-0.470079\pi$
$881$	4908.77	0.187719	0.0938597	+	0.995585i	$0.470079\pi$
$882$	102.714	0.00392128
$883$	8791.82	0.335072	0.167536	−	0.985866i	$-0.446419\pi$
$883$	8791.82	0.335072	0.167536	+	0.985866i	$0.446419\pi$
$884$	21473.3	0.816996
$885$	−20758.9	−0.788477
$886$	769.865	0.0291920
$887$	−10011.0	−0.378958	−0.189479	−	0.981885i	$-0.560680\pi$
$887$	−10011.0	−0.378958	−0.189479	+	0.981885i	$0.560680\pi$
$888$	2029.78	0.0767061
$889$	17254.5	0.650954
$890$	908.686	0.0342239
$891$	891.000	0.0335013
$892$	21767.7	0.817082
$893$	23004.8	0.862069
$894$	1848.82	0.0691651
$895$	36990.2	1.38150
$896$	3282.65	0.122395
$897$	18792.4	0.699509
$898$	−575.471	−0.0213850
$899$	3161.34	0.117282
$900$	4635.53	0.171686
$901$	−6112.51	−0.226012
$902$	1250.13	0.0461471
$903$	7525.32	0.277328
$904$	7346.55	0.270290
$905$	−22923.5	−0.841993
$906$	−375.969	−0.0137867
$907$	−44587.3	−1.63230	−0.816150	−	0.577840i	$-0.803896\pi$
$907$	−44587.3	−1.63230	−0.816150	+	0.577840i	$0.803896\pi$
$908$	−26805.5	−0.979706
$909$	−5978.25	−0.218136
$910$	−752.201	−0.0274013
$911$	22201.6	0.807434	0.403717	−	0.914884i	$-0.367718\pi$
$911$	22201.6	0.807434	0.403717	+	0.914884i	$0.367718\pi$
$912$	21020.8	0.763233
$913$	11449.7	0.415039
$914$	679.370	0.0245860
$915$	15234.4	0.550419
$916$	−2773.86	−0.100056
$917$	3864.33	0.139162
$918$	−285.755	−0.0102738
$919$	−4755.83	−0.170708	−0.0853538	−	0.996351i	$-0.527202\pi$
$919$	−4755.83	−0.170708	−0.0853538	+	0.996351i	$0.527202\pi$
$920$	−3034.54	−0.108745
$921$	4359.15	0.155960
$922$	−1440.76	−0.0514630
$923$	7084.84	0.252655
$924$	1835.47	0.0653490
$925$	11809.0	0.419759
$926$	−4433.95	−0.157353
$927$	−13505.9	−0.478526
$928$	444.236	0.0157142
$929$	−22020.9	−0.777699	−0.388849	−	0.921301i	$-0.627127\pi$
$929$	−22020.9	−0.777699	−0.388849	+	0.921301i	$0.627127\pi$
$930$	1709.40	0.0602726
$931$	5475.83	0.192764
$932$	−17564.8	−0.617333
$933$	−32317.0	−1.13399
$934$	−754.874	−0.0264457
$935$	−3877.49	−0.135623
$936$	−1987.94	−0.0694209
$937$	29862.2	1.04115	0.520573	−	0.853817i	$-0.325718\pi$
$937$	29862.2	1.04115	0.520573	+	0.853817i	$0.325718\pi$
$938$	166.784	0.00580565
$939$	−7146.32	−0.248362
$940$	−12688.8	−0.440279
$941$	−8090.56	−0.280281	−0.140141	−	0.990132i	$-0.544755\pi$
$941$	−8090.56	−0.280281	−0.140141	+	0.990132i	$0.544755\pi$
$942$	1434.10	0.0496026
$943$	51393.3	1.77476
$944$	−55929.1	−1.92832
$945$	−1466.16	−0.0504700
$946$	−918.099	−0.0315539
$947$	4398.75	0.150940	0.0754700	−	0.997148i	$-0.475954\pi$
$947$	4398.75	0.150940	0.0754700	+	0.997148i	$0.475954\pi$
$948$	18469.9	0.632779
$949$	−20593.0	−0.704402
$950$	−1687.20	−0.0576211
$951$	−23610.8	−0.805083
$952$	−1181.34	−0.0402178
$953$	−4288.91	−0.145783	−0.0728917	−	0.997340i	$-0.523223\pi$
$953$	−4288.91	−0.145783	−0.0728917	+	0.997340i	$0.523223\pi$
$954$	281.978	0.00956957
$955$	5550.48	0.188073
$956$	32363.3	1.09488
$957$	330.806	0.0111739
$958$	4113.69	0.138734
$959$	−5559.85	−0.187213
$960$	−11433.4	−0.384387
$961$	69663.3	2.33840
$962$	−2523.53	−0.0845756
$963$	−9815.44	−0.328451
$964$	−15634.1	−0.522344
$965$	13958.6	0.465640
$966$	−515.166	−0.0171586
$967$	34271.8	1.13972	0.569858	−	0.821743i	$-0.306998\pi$
$967$	34271.8	1.13972	0.569858	+	0.821743i	$0.306998\pi$
$968$	−449.389	−0.0149214
$969$	−15234.0	−0.505043
$970$	−1697.10	−0.0561760
$971$	36628.3	1.21056	0.605282	−	0.796011i	$-0.293060\pi$
$971$	36628.3	1.21056	0.605282	+	0.796011i	$0.293060\pi$
$972$	−1930.82	−0.0637150
$973$	−3016.79	−0.0993977
$974$	−2595.48	−0.0853845
$975$	−11565.6	−0.379892
$976$	41044.9	1.34612
$977$	29087.7	0.952504	0.476252	−	0.879309i	$-0.341995\pi$
$977$	29087.7	0.952504	0.476252	+	0.879309i	$0.341995\pi$
$978$	1531.56	0.0500755
$979$	5532.17	0.180602
$980$	−3020.30	−0.0984490
$981$	4731.06	0.153977
$982$	1682.46	0.0546737
$983$	−32900.7	−1.06752	−0.533758	−	0.845637i	$-0.679221\pi$
$983$	−32900.7	−1.06752	−0.533758	+	0.845637i	$0.679221\pi$
$984$	−5436.61	−0.176131
$985$	23106.0	0.747429
$986$	−106.094	−0.00342668
$987$	−4322.99	−0.139415
$988$	−52809.7	−1.70051
$989$	−37743.5	−1.21352
$990$	178.874	0.00574240
$991$	7288.46	0.233628	0.116814	−	0.993154i	$-0.462732\pi$
$991$	7288.46	0.233628	0.116814	+	0.993154i	$0.462732\pi$
$992$	13975.5	0.447301
$993$	−18711.4	−0.597976
$994$	−194.221	−0.00619749
$995$	−17866.6	−0.569257
$996$	−24811.8	−0.789351
$997$	2983.80	0.0947822	0.0473911	−	0.998876i	$-0.484909\pi$
$997$	2983.80	0.0947822	0.0473911	+	0.998876i	$0.484909\pi$
$998$	−3207.51	−0.101735
$999$	−4918.76	−0.155778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.a.l.1.3	✓	5
3.2	odd	2		693.4.a.n.1.3		5
7.6	odd	2		1617.4.a.p.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.l.1.3	✓	5	1.1	even	1	trivial
693.4.a.n.1.3		5	3.2	odd	2
1617.4.a.p.1.3		5	7.6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.a (trivial)

\(f(q)\)	\(=\)	\(q+0.232912 q^{2} +3.00000 q^{3} -7.94575 q^{4} +7.75746 q^{5} +0.698736 q^{6} -7.00000 q^{7} -3.71396 q^{8} +9.00000 q^{9} +1.80680 q^{10} +11.0000 q^{11} -23.8373 q^{12} +59.4737 q^{13} -1.63038 q^{14} +23.2724 q^{15} +62.7010 q^{16} -45.4400 q^{17} +2.09621 q^{18} +111.752 q^{19} -61.6388 q^{20} -21.0000 q^{21} +2.56203 q^{22} +105.326 q^{23} -11.1419 q^{24} -64.8219 q^{25} +13.8521 q^{26} +27.0000 q^{27} +55.6203 q^{28} +10.0244 q^{29} +5.42041 q^{30} +315.364 q^{31} +44.3154 q^{32} +33.0000 q^{33} -10.5835 q^{34} -54.3022 q^{35} -71.5118 q^{36} -182.176 q^{37} +26.0283 q^{38} +178.421 q^{39} -28.8108 q^{40} +487.944 q^{41} -4.89115 q^{42} -358.348 q^{43} -87.4033 q^{44} +69.8171 q^{45} +24.5317 q^{46} +205.857 q^{47} +188.103 q^{48} +49.0000 q^{49} -15.0978 q^{50} -136.320 q^{51} -472.563 q^{52} +134.518 q^{53} +6.28862 q^{54} +85.3320 q^{55} +25.9977 q^{56} +335.255 q^{57} +2.33481 q^{58} -891.997 q^{59} -184.916 q^{60} +654.613 q^{61} +73.4520 q^{62} -63.0000 q^{63} -491.286 q^{64} +461.364 q^{65} +7.68609 q^{66} -102.298 q^{67} +361.055 q^{68} +315.978 q^{69} -12.6476 q^{70} +119.126 q^{71} -33.4256 q^{72} -346.254 q^{73} -42.4310 q^{74} -194.466 q^{75} -887.951 q^{76} -77.0000 q^{77} +41.5564 q^{78} -774.834 q^{79} +486.400 q^{80} +81.0000 q^{81} +113.648 q^{82} +1040.89 q^{83} +166.861 q^{84} -352.499 q^{85} -83.4636 q^{86} +30.0732 q^{87} -40.8535 q^{88} +502.925 q^{89} +16.2612 q^{90} -416.316 q^{91} -836.896 q^{92} +946.091 q^{93} +47.9465 q^{94} +866.908 q^{95} +132.946 q^{96} -939.285 q^{97} +11.4127 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 15 q^{3} + 21 q^{4} + 7 q^{5} + 15 q^{6} - 35 q^{7} + 60 q^{8} + 45 q^{9} + 55 q^{10} + 55 q^{11} + 63 q^{12} + 111 q^{13} - 35 q^{14} + 21 q^{15} + 201 q^{16} + 136 q^{17} + 45 q^{18} + 111 q^{19}+ \cdots + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 15 * q^3 + 21 * q^4 + 7 * q^5 + 15 * q^6 - 35 * q^7 + 60 * q^8 + 45 * q^9 + 55 * q^10 + 55 * q^11 + 63 * q^12 + 111 * q^13 - 35 * q^14 + 21 * q^15 + 201 * q^16 + 136 * q^17 + 45 * q^18 + 111 * q^19 + 219 * q^20 - 105 * q^21 + 55 * q^22 - 28 * q^23 + 180 * q^24 + 190 * q^25 - q^26 + 135 * q^27 - 147 * q^28 + 61 * q^29 + 165 * q^30 - 280 * q^31 + 535 * q^32 + 165 * q^33 - 572 * q^34 - 49 * q^35 + 189 * q^36 - 41 * q^37 + 267 * q^38 + 333 * q^39 - 336 * q^40 + 426 * q^41 - 105 * q^42 + 424 * q^43 + 231 * q^44 + 63 * q^45 + 140 * q^46 + 75 * q^47 + 603 * q^48 + 245 * q^49 + 490 * q^50 + 408 * q^51 - 269 * q^52 + 1500 * q^53 + 135 * q^54 + 77 * q^55 - 420 * q^56 + 333 * q^57 - 1767 * q^58 + 757 * q^59 + 657 * q^60 + 658 * q^61 - 568 * q^62 - 315 * q^63 - 748 * q^64 + 537 * q^65 + 165 * q^66 - 583 * q^67 - 1650 * q^68 - 84 * q^69 - 385 * q^70 - 764 * q^71 + 540 * q^72 + 875 * q^73 - 825 * q^74 + 570 * q^75 + 213 * q^76 - 385 * q^77 - 3 * q^78 - 244 * q^79 - 2577 * q^80 + 405 * q^81 - 2006 * q^82 + 924 * q^83 - 441 * q^84 - 1402 * q^85 + 1272 * q^86 + 183 * q^87 + 660 * q^88 - 1110 * q^89 + 495 * q^90 - 777 * q^91 - 2046 * q^92 - 840 * q^93 - 3349 * q^94 + 1923 * q^95 + 1605 * q^96 - 852 * q^97 + 245 * q^98 + 495 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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