LMFDB - Embedded newform 2303.4.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.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:	$135.881398743$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 130 x^{18} + 379 x^{17} + 6970 x^{16} - 19652 x^{15} - 199330 x^{14} + \cdots - 19267584 $ x^20 - 3x^19 - 130x^18 + 379x^17 + 6970x^16 - 19652x^15 - 199330x^14 + 540440x^13 + 3283799x^12 - 8520033x^11 - 31283236x^10 + 77759541x^9 + 161161774x^8 - 391970848x^7 - 357939064x^6 + 946653568x^5 + 47744512x^4 - 707974144x^3 + 258494464x^2 + 38535168*x - 19267584
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 329)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-3.72716$ of defining polynomial
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.72716 q^{2} +2.16417 q^{3} +5.89176 q^{4} +2.35387 q^{5} -8.06620 q^{6} +7.85777 q^{8} -22.3164 q^{9} +O(q^{10})$	\(q-3.72716 q^{2} +2.16417 q^{3} +5.89176 q^{4} +2.35387 q^{5} -8.06620 q^{6} +7.85777 q^{8} -22.3164 q^{9} -8.77327 q^{10} +8.53037 q^{11} +12.7507 q^{12} +37.7582 q^{13} +5.09417 q^{15} -76.4213 q^{16} -94.2359 q^{17} +83.1769 q^{18} +59.3157 q^{19} +13.8684 q^{20} -31.7941 q^{22} -179.894 q^{23} +17.0055 q^{24} -119.459 q^{25} -140.731 q^{26} -106.729 q^{27} -136.005 q^{29} -18.9868 q^{30} +12.7872 q^{31} +221.972 q^{32} +18.4611 q^{33} +351.233 q^{34} -131.483 q^{36} +264.157 q^{37} -221.079 q^{38} +81.7150 q^{39} +18.4962 q^{40} +178.019 q^{41} +312.523 q^{43} +50.2589 q^{44} -52.5299 q^{45} +670.496 q^{46} +47.0000 q^{47} -165.388 q^{48} +445.244 q^{50} -203.942 q^{51} +222.462 q^{52} -438.712 q^{53} +397.796 q^{54} +20.0794 q^{55} +128.369 q^{57} +506.914 q^{58} -369.054 q^{59} +30.0136 q^{60} -884.447 q^{61} -47.6599 q^{62} -215.958 q^{64} +88.8780 q^{65} -68.8077 q^{66} +251.059 q^{67} -555.215 q^{68} -389.321 q^{69} +852.664 q^{71} -175.357 q^{72} -860.257 q^{73} -984.555 q^{74} -258.530 q^{75} +349.474 q^{76} -304.565 q^{78} +1060.45 q^{79} -179.886 q^{80} +371.564 q^{81} -663.507 q^{82} +878.587 q^{83} -221.819 q^{85} -1164.83 q^{86} -294.338 q^{87} +67.0297 q^{88} -664.121 q^{89} +195.788 q^{90} -1059.89 q^{92} +27.6735 q^{93} -175.177 q^{94} +139.622 q^{95} +480.385 q^{96} +1334.06 q^{97} -190.367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9	\( 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9} - 68 q^{10} + 62 q^{11} + 6 q^{13} + 420 q^{15} + 957 q^{16} + 138 q^{17} + 120 q^{18} - 182 q^{19} - 787 q^{20} + 521 q^{22} + 326 q^{23} + 18 q^{24} + 678 q^{25} - 118 q^{26} - 68 q^{27} + 528 q^{29} + 877 q^{30} - 1092 q^{31} + 254 q^{32} + 424 q^{33} - 234 q^{34} + 2608 q^{36} + 904 q^{37} + 166 q^{38} + 606 q^{39} - 323 q^{40} + 8 q^{41} - 18 q^{43} + 98 q^{44} - 316 q^{45} + 1382 q^{46} + 940 q^{47} - 937 q^{48} + 892 q^{50} + 756 q^{51} - 761 q^{52} + 992 q^{53} - 384 q^{54} - 1060 q^{55} + 1554 q^{57} - 938 q^{58} - 2140 q^{59} + 5830 q^{60} + 186 q^{61} - 69 q^{62} + 7086 q^{64} + 662 q^{65} - 3617 q^{66} + 2852 q^{67} - 1163 q^{68} - 628 q^{69} + 3448 q^{71} - 355 q^{72} + 304 q^{73} + 1512 q^{74} - 4930 q^{75} - 339 q^{76} + 1054 q^{78} + 4248 q^{79} - 5945 q^{80} + 5696 q^{81} - 3665 q^{82} + 274 q^{83} + 232 q^{85} - 5730 q^{86} - 3756 q^{87} + 1976 q^{88} + 3168 q^{89} + 13306 q^{90} - 4214 q^{92} - 374 q^{93} + 141 q^{94} + 6100 q^{95} + 11433 q^{96} + 4112 q^{97} + 7252 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9 - 68 * q^10 + 62 * q^11 + 6 * q^13 + 420 * q^15 + 957 * q^16 + 138 * q^17 + 120 * q^18 - 182 * q^19 - 787 * q^20 + 521 * q^22 + 326 * q^23 + 18 * q^24 + 678 * q^25 - 118 * q^26 - 68 * q^27 + 528 * q^29 + 877 * q^30 - 1092 * q^31 + 254 * q^32 + 424 * q^33 - 234 * q^34 + 2608 * q^36 + 904 * q^37 + 166 * q^38 + 606 * q^39 - 323 * q^40 + 8 * q^41 - 18 * q^43 + 98 * q^44 - 316 * q^45 + 1382 * q^46 + 940 * q^47 - 937 * q^48 + 892 * q^50 + 756 * q^51 - 761 * q^52 + 992 * q^53 - 384 * q^54 - 1060 * q^55 + 1554 * q^57 - 938 * q^58 - 2140 * q^59 + 5830 * q^60 + 186 * q^61 - 69 * q^62 + 7086 * q^64 + 662 * q^65 - 3617 * q^66 + 2852 * q^67 - 1163 * q^68 - 628 * q^69 + 3448 * q^71 - 355 * q^72 + 304 * q^73 + 1512 * q^74 - 4930 * q^75 - 339 * q^76 + 1054 * q^78 + 4248 * q^79 - 5945 * q^80 + 5696 * q^81 - 3665 * q^82 + 274 * q^83 + 232 * q^85 - 5730 * q^86 - 3756 * q^87 + 1976 * q^88 + 3168 * q^89 + 13306 * q^90 - 4214 * q^92 - 374 * q^93 + 141 * q^94 + 6100 * q^95 + 11433 * q^96 + 4112 * q^97 + 7252 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.72716	−1.31775	−0.658876	−	0.752252i	$-0.728968\pi$
$2$	−3.72716	−1.31775	−0.658876	+	0.752252i	$0.728968\pi$
$3$	2.16417	0.416494	0.208247	−	0.978076i	$-0.433224\pi$
$3$	2.16417	0.416494	0.208247	+	0.978076i	$0.433224\pi$
$4$	5.89176	0.736469
$5$	2.35387	0.210537	0.105268	−	0.994444i	$-0.466430\pi$
$5$	2.35387	0.210537	0.105268	+	0.994444i	$0.466430\pi$
$6$	−8.06620	−0.548835
$7$	0	0
$7$	0	0
$8$	7.85777	0.347268
$9$	−22.3164	−0.826533
$10$	−8.77327	−0.277435
$11$	8.53037	0.233819	0.116909	−	0.993143i	$-0.462701\pi$
$11$	8.53037	0.233819	0.116909	+	0.993143i	$0.462701\pi$
$12$	12.7507	0.306735
$13$	37.7582	0.805557	0.402778	−	0.915298i	$-0.368045\pi$
$13$	37.7582	0.805557	0.402778	+	0.915298i	$0.368045\pi$
$14$	0	0
$15$	5.09417	0.0876873
$16$	−76.4213	−1.19408
$17$	−94.2359	−1.34445	−0.672223	−	0.740349i	$-0.734660\pi$
$17$	−94.2359	−1.34445	−0.672223	+	0.740349i	$0.734660\pi$
$18$	83.1769	1.08917
$19$	59.3157	0.716208	0.358104	−	0.933682i	$-0.383423\pi$
$19$	59.3157	0.716208	0.358104	+	0.933682i	$0.383423\pi$
$20$	13.8684	0.155054
$21$	0	0
$22$	−31.7941	−0.308115
$23$	−179.894	−1.63089	−0.815447	−	0.578831i	$-0.803509\pi$
$23$	−179.894	−1.63089	−0.815447	+	0.578831i	$0.803509\pi$
$24$	17.0055	0.144635
$25$	−119.459	−0.955674
$26$	−140.731	−1.06152
$27$	−106.729	−0.760740
$28$	0	0
$29$	−136.005	−0.870881	−0.435441	−	0.900218i	$-0.643407\pi$
$29$	−136.005	−0.870881	−0.435441	+	0.900218i	$0.643407\pi$
$30$	−18.9868	−0.115550
$31$	12.7872	0.0740853	0.0370426	−	0.999314i	$-0.488206\pi$
$31$	12.7872	0.0740853	0.0370426	+	0.999314i	$0.488206\pi$
$32$	221.972	1.22624
$33$	18.4611	0.0973840
$34$	351.233	1.77165
$35$	0	0
$36$	−131.483	−0.608716
$37$	264.157	1.17371	0.586853	−	0.809694i	$-0.300367\pi$
$37$	264.157	1.17371	0.586853	+	0.809694i	$0.300367\pi$
$38$	−221.079	−0.943785
$39$	81.7150	0.335509
$40$	18.4962	0.0731126
$41$	178.019	0.678095	0.339048	−	0.940769i	$-0.389895\pi$
$41$	178.019	0.678095	0.339048	+	0.940769i	$0.389895\pi$
$42$	0	0
$43$	312.523	1.10836	0.554178	−	0.832398i	$-0.313033\pi$
$43$	312.523	1.10836	0.554178	+	0.832398i	$0.313033\pi$
$44$	50.2589	0.172200
$45$	−52.5299	−0.174016
$46$	670.496	2.14911
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−165.388	−0.497328
$49$	0	0
$50$	445.244	1.25934
$51$	−203.942	−0.559953
$52$	222.462	0.593268
$53$	−438.712	−1.13701	−0.568507	−	0.822678i	$-0.692479\pi$
$53$	−438.712	−1.13701	−0.568507	+	0.822678i	$0.692479\pi$
$54$	397.796	1.00247
$55$	20.0794	0.0492274
$56$	0	0
$57$	128.369	0.298296
$58$	506.914	1.14760
$59$	−369.054	−0.814351	−0.407175	−	0.913350i	$-0.633486\pi$
$59$	−369.054	−0.814351	−0.407175	+	0.913350i	$0.633486\pi$
$60$	30.0136	0.0645790
$61$	−884.447	−1.85642	−0.928212	−	0.372052i	$-0.878654\pi$
$61$	−884.447	−1.85642	−0.928212	+	0.372052i	$0.878654\pi$
$62$	−47.6599	−0.0976260
$63$	0	0
$64$	−215.958	−0.421792
$65$	88.8780	0.169599
$66$	−68.8077	−0.128328
$67$	251.059	0.457787	0.228894	−	0.973451i	$-0.426489\pi$
$67$	251.059	0.457787	0.228894	+	0.973451i	$0.426489\pi$
$68$	−555.215	−0.990143
$69$	−389.321	−0.679258
$70$	0	0
$71$	852.664	1.42525	0.712624	−	0.701546i	$-0.247507\pi$
$71$	852.664	1.42525	0.712624	+	0.701546i	$0.247507\pi$
$72$	−175.357	−0.287028
$73$	−860.257	−1.37925	−0.689626	−	0.724165i	$-0.742225\pi$
$73$	−860.257	−1.37925	−0.689626	+	0.724165i	$0.742225\pi$
$74$	−984.555	−1.54665
$75$	−258.530	−0.398032
$76$	349.474	0.527466
$77$	0	0
$78$	−304.565	−0.442118
$79$	1060.45	1.51025	0.755123	−	0.655583i	$-0.227577\pi$
$79$	1060.45	1.51025	0.755123	+	0.655583i	$0.227577\pi$
$80$	−179.886	−0.251398
$81$	371.564	0.509689
$82$	−663.507	−0.893561
$83$	878.587	1.16190	0.580949	−	0.813940i	$-0.302682\pi$
$83$	878.587	1.16190	0.580949	+	0.813940i	$0.302682\pi$
$84$	0	0
$85$	−221.819	−0.283055
$86$	−1164.83	−1.46054
$87$	−294.338	−0.362717
$88$	67.0297	0.0811977
$89$	−664.121	−0.790974	−0.395487	−	0.918472i	$-0.629424\pi$
$89$	−664.121	−0.790974	−0.395487	+	0.918472i	$0.629424\pi$
$90$	195.788	0.229309
$91$	0	0
$92$	−1059.89	−1.20110
$93$	27.6735	0.0308561
$94$	−175.177	−0.192214
$95$	139.622	0.150788
$96$	480.385	0.510720
$97$	1334.06	1.39643	0.698214	−	0.715890i	$-0.253979\pi$
$97$	1334.06	1.39643	0.698214	+	0.715890i	$0.253979\pi$
$98$	0	0
$99$	−190.367	−0.193259
$100$	−703.825	−0.703825
$101$	−757.562	−0.746339	−0.373170	−	0.927763i	$-0.621729\pi$
$101$	−757.562	−0.746339	−0.373170	+	0.927763i	$0.621729\pi$
$102$	760.126	0.737879
$103$	1179.85	1.12868	0.564339	−	0.825543i	$-0.309131\pi$
$103$	1179.85	1.12868	0.564339	+	0.825543i	$0.309131\pi$
$104$	296.695	0.279744
$105$	0	0
$106$	1635.15	1.49830
$107$	−11.4090	−0.0103079	−0.00515395	−	0.999987i	$-0.501641\pi$
$107$	−11.4090	−0.0103079	−0.00515395	+	0.999987i	$0.501641\pi$
$108$	−628.820	−0.560262
$109$	1787.32	1.57059	0.785293	−	0.619124i	$-0.212512\pi$
$109$	1787.32	1.57059	0.785293	+	0.619124i	$0.212512\pi$
$110$	−74.8393	−0.0648695
$111$	571.679	0.488841
$112$	0	0
$113$	−1056.46	−0.879501	−0.439750	−	0.898120i	$-0.644933\pi$
$113$	−1056.46	−0.879501	−0.439750	+	0.898120i	$0.644933\pi$
$114$	−478.453	−0.393081
$115$	−423.448	−0.343363
$116$	−801.310	−0.641377
$117$	−842.626	−0.665819
$118$	1375.52	1.07311
$119$	0	0
$120$	40.0288	0.0304510
$121$	−1258.23	−0.945329
$122$	3296.48	2.44631
$123$	385.263	0.282423
$124$	75.3389	0.0545615
$125$	−575.426	−0.411741
$126$	0	0
$127$	497.941	0.347914	0.173957	−	0.984753i	$-0.444345\pi$
$127$	497.941	0.347914	0.173957	+	0.984753i	$0.444345\pi$
$128$	−970.869	−0.670418
$129$	676.352	0.461624
$130$	−331.263	−0.223490
$131$	2782.27	1.85563	0.927816	−	0.373038i	$-0.121684\pi$
$131$	2782.27	1.85563	0.927816	+	0.373038i	$0.121684\pi$
$132$	108.769	0.0717204
$133$	0	0
$134$	−935.738	−0.603250
$135$	−251.226	−0.160164
$136$	−740.485	−0.466883
$137$	1667.84	1.04010	0.520048	−	0.854137i	$-0.325914\pi$
$137$	1667.84	1.04010	0.520048	+	0.854137i	$0.325914\pi$
$138$	1451.06	0.895093
$139$	−2292.34	−1.39881	−0.699403	−	0.714727i	$-0.746551\pi$
$139$	−2292.34	−1.39881	−0.699403	+	0.714727i	$0.746551\pi$
$140$	0	0
$141$	101.716	0.0607519
$142$	−3178.02	−1.87812
$143$	322.091	0.188354
$144$	1705.45	0.986948
$145$	−320.139	−0.183352
$146$	3206.32	1.81751
$147$	0	0
$148$	1556.35	0.864398
$149$	114.532	0.0629718	0.0314859	−	0.999504i	$-0.489976\pi$
$149$	114.532	0.0629718	0.0314859	+	0.999504i	$0.489976\pi$
$150$	963.583	0.524508
$151$	−1335.25	−0.719610	−0.359805	−	0.933028i	$-0.617157\pi$
$151$	−1335.25	−0.719610	−0.359805	+	0.933028i	$0.617157\pi$
$152$	466.089	0.248716
$153$	2103.01	1.11123
$154$	0	0
$155$	30.0994	0.0155977
$156$	481.445	0.247092
$157$	291.162	0.148008	0.0740039	−	0.997258i	$-0.476422\pi$
$157$	291.162	0.148008	0.0740039	+	0.997258i	$0.476422\pi$
$158$	−3952.45	−1.99013
$159$	−949.446	−0.473560
$160$	522.495	0.258168
$161$	0	0
$162$	−1384.88	−0.671644
$163$	−1220.98	−0.586714	−0.293357	−	0.956003i	$-0.594772\pi$
$163$	−1220.98	−0.586714	−0.293357	+	0.956003i	$0.594772\pi$
$164$	1048.85	0.499397
$165$	43.4552	0.0205029
$166$	−3274.64	−1.53109
$167$	−2078.65	−0.963179	−0.481589	−	0.876397i	$-0.659940\pi$
$167$	−2078.65	−0.963179	−0.481589	+	0.876397i	$0.659940\pi$
$168$	0	0
$169$	−771.319	−0.351078
$170$	826.757	0.372996
$171$	−1323.71	−0.591970
$172$	1841.31	0.816271
$173$	−2465.12	−1.08335	−0.541675	−	0.840588i	$-0.682210\pi$
$173$	−2465.12	−1.08335	−0.541675	+	0.840588i	$0.682210\pi$
$174$	1097.05	0.477970
$175$	0	0
$176$	−651.902	−0.279199
$177$	−798.693	−0.339172
$178$	2475.29	1.04231
$179$	2015.19	0.841464	0.420732	−	0.907185i	$-0.361773\pi$
$179$	2015.19	0.841464	0.420732	+	0.907185i	$0.361773\pi$
$180$	−309.493	−0.128157
$181$	4322.63	1.77513	0.887565	−	0.460683i	$-0.152395\pi$
$181$	4322.63	1.77513	0.887565	+	0.460683i	$0.152395\pi$
$182$	0	0
$183$	−1914.09	−0.773189
$184$	−1413.57	−0.566357
$185$	621.791	0.247108
$186$	−103.144	−0.0406606
$187$	−803.868	−0.314356
$188$	276.913	0.107425
$189$	0	0
$190$	−520.393	−0.198701
$191$	−198.945	−0.0753672	−0.0376836	−	0.999290i	$-0.511998\pi$
$191$	−198.945	−0.0753672	−0.0376836	+	0.999290i	$0.511998\pi$
$192$	−467.368	−0.175674
$193$	4577.70	1.70731	0.853653	−	0.520843i	$-0.174382\pi$
$193$	4577.70	1.70731	0.853653	+	0.520843i	$0.174382\pi$
$194$	−4972.27	−1.84014
$195$	192.347	0.0706371
$196$	0	0
$197$	−777.728	−0.281273	−0.140637	−	0.990061i	$-0.544915\pi$
$197$	−777.728	−0.281273	−0.140637	+	0.990061i	$0.544915\pi$
$198$	709.530	0.254667
$199$	−2026.90	−0.722025	−0.361012	−	0.932561i	$-0.617569\pi$
$199$	−2026.90	−0.722025	−0.361012	+	0.932561i	$0.617569\pi$
$200$	−938.684	−0.331875
$201$	543.333	0.190666
$202$	2823.56	0.983490
$203$	0	0
$204$	−1201.58	−0.412388
$205$	419.034	0.142764
$206$	−4397.48	−1.48732
$207$	4014.59	1.34799
$208$	−2885.53	−0.961901
$209$	505.985	0.167463
$210$	0	0
$211$	2525.08	0.823855	0.411928	−	0.911217i	$-0.364856\pi$
$211$	2525.08	0.823855	0.411928	+	0.911217i	$0.364856\pi$
$212$	−2584.79	−0.837377
$213$	1845.31	0.593607
$214$	42.5231	0.0135833
$215$	735.640	0.233350
$216$	−838.651	−0.264180
$217$	0	0
$218$	−6661.62	−2.06964
$219$	−1861.74	−0.574450
$220$	118.303	0.0362545
$221$	−3558.18	−1.08303
$222$	−2130.74	−0.644171
$223$	−3688.76	−1.10770	−0.553851	−	0.832616i	$-0.686842\pi$
$223$	−3688.76	−1.10770	−0.553851	+	0.832616i	$0.686842\pi$
$224$	0	0
$225$	2665.90	0.789896
$226$	3937.61	1.15896
$227$	−579.301	−0.169381	−0.0846906	−	0.996407i	$-0.526990\pi$
$227$	−579.301	−0.169381	−0.0846906	+	0.996407i	$0.526990\pi$
$228$	756.319	0.219686
$229$	−4621.47	−1.33360	−0.666802	−	0.745235i	$-0.732337\pi$
$229$	−4621.47	−1.33360	−0.666802	+	0.745235i	$0.732337\pi$
$230$	1578.26	0.452467
$231$	0	0
$232$	−1068.70	−0.302429
$233$	−4779.77	−1.34392	−0.671959	−	0.740588i	$-0.734547\pi$
$233$	−4779.77	−1.34392	−0.671959	+	0.740588i	$0.734547\pi$
$234$	3140.61	0.877384
$235$	110.632	0.0307099
$236$	−2174.37	−0.599744
$237$	2294.98	0.629008
$238$	0	0
$239$	3494.72	0.945834	0.472917	−	0.881107i	$-0.343201\pi$
$239$	3494.72	0.945834	0.472917	+	0.881107i	$0.343201\pi$
$240$	−389.303	−0.104706
$241$	5210.63	1.39272	0.696362	−	0.717691i	$-0.254801\pi$
$241$	5210.63	1.39272	0.696362	+	0.717691i	$0.254801\pi$
$242$	4689.64	1.24571
$243$	3685.80	0.973022
$244$	−5210.95	−1.36720
$245$	0	0
$246$	−1435.94	−0.372163
$247$	2239.65	0.576947
$248$	100.479	0.0257274
$249$	1901.41	0.483923
$250$	2144.71	0.542573
$251$	1226.33	0.308388	0.154194	−	0.988041i	$-0.450722\pi$
$251$	1226.33	0.308388	0.154194	+	0.988041i	$0.450722\pi$
$252$	0	0
$253$	−1534.57	−0.381334
$254$	−1855.91	−0.458464
$255$	−480.054	−0.117891
$256$	5346.25	1.30524
$257$	564.618	0.137042	0.0685212	−	0.997650i	$-0.478172\pi$
$257$	564.618	0.137042	0.0685212	+	0.997650i	$0.478172\pi$
$258$	−2520.88	−0.608306
$259$	0	0
$260$	523.647	0.124905
$261$	3035.15	0.719812
$262$	−10370.0	−2.44526
$263$	7442.16	1.74488	0.872439	−	0.488723i	$-0.162537\pi$
$263$	7442.16	1.74488	0.872439	+	0.488723i	$0.162537\pi$
$264$	145.063	0.0338183
$265$	−1032.67	−0.239383
$266$	0	0
$267$	−1437.27	−0.329436
$268$	1479.18	0.337146
$269$	2112.16	0.478738	0.239369	−	0.970929i	$-0.423060\pi$
$269$	2112.16	0.478738	0.239369	+	0.970929i	$0.423060\pi$
$270$	936.361	0.211056
$271$	−6205.77	−1.39105	−0.695523	−	0.718503i	$-0.744827\pi$
$271$	−6205.77	−1.39105	−0.695523	+	0.718503i	$0.744827\pi$
$272$	7201.63	1.60538
$273$	0	0
$274$	−6216.32	−1.37059
$275$	−1019.03	−0.223454
$276$	−2293.79	−0.500252
$277$	−536.786	−0.116434	−0.0582172	−	0.998304i	$-0.518542\pi$
$277$	−536.786	−0.116434	−0.0582172	+	0.998304i	$0.518542\pi$
$278$	8543.95	1.84328
$279$	−285.363	−0.0612339
$280$	0	0
$281$	1893.63	0.402009	0.201005	−	0.979590i	$-0.435579\pi$
$281$	1893.63	0.402009	0.201005	+	0.979590i	$0.435579\pi$
$282$	−379.111	−0.0800559
$283$	91.1443	0.0191448	0.00957238	−	0.999954i	$-0.496953\pi$
$283$	91.1443	0.0191448	0.00957238	+	0.999954i	$0.496953\pi$
$284$	5023.69	1.04965
$285$	302.164	0.0628023
$286$	−1200.49	−0.248204
$287$	0	0
$288$	−4953.62	−1.01352
$289$	3967.41	0.807533
$290$	1193.21	0.241613
$291$	2887.13	0.581603
$292$	−5068.42	−1.01578
$293$	7455.77	1.48659	0.743294	−	0.668964i	$-0.233262\pi$
$293$	7455.77	1.48659	0.743294	+	0.668964i	$0.233262\pi$
$294$	0	0
$295$	−868.705	−0.171451
$296$	2075.68	0.407590
$297$	−910.437	−0.177875
$298$	−426.878	−0.0829811
$299$	−6792.49	−1.31378
$300$	−1523.19	−0.293139
$301$	0	0
$302$	4976.70	0.948267
$303$	−1639.49	−0.310846
$304$	−4532.98	−0.855212
$305$	−2081.88	−0.390845
$306$	−7838.25	−1.46432
$307$	−2084.76	−0.387569	−0.193785	−	0.981044i	$-0.562076\pi$
$307$	−2084.76	−0.387569	−0.193785	+	0.981044i	$0.562076\pi$
$308$	0	0
$309$	2553.38	0.470087
$310$	−112.185	−0.0205539
$311$	−364.176	−0.0664003	−0.0332002	−	0.999449i	$-0.510570\pi$
$311$	−364.176	−0.0664003	−0.0332002	+	0.999449i	$0.510570\pi$
$312$	642.098	0.116512
$313$	−5918.99	−1.06888	−0.534442	−	0.845205i	$-0.679478\pi$
$313$	−5918.99	−1.06888	−0.534442	+	0.845205i	$0.679478\pi$
$314$	−1085.21	−0.195038
$315$	0	0
$316$	6247.88	1.11225
$317$	−10038.6	−1.77863	−0.889315	−	0.457295i	$-0.848819\pi$
$317$	−10038.6	−1.77863	−0.889315	+	0.457295i	$0.848819\pi$
$318$	3538.74	0.624034
$319$	−1160.18	−0.203628
$320$	−508.337	−0.0888028
$321$	−24.6909	−0.00429318
$322$	0	0
$323$	−5589.67	−0.962903
$324$	2189.16	0.375371
$325$	−4510.57	−0.769850
$326$	4550.78	0.773143
$327$	3868.05	0.654140
$328$	1398.83	0.235481
$329$	0	0
$330$	−161.965	−0.0270177
$331$	3149.30	0.522965	0.261482	−	0.965208i	$-0.415789\pi$
$331$	3149.30	0.522965	0.261482	+	0.965208i	$0.415789\pi$
$332$	5176.42	0.855702
$333$	−5895.02	−0.970106
$334$	7747.48	1.26923
$335$	590.961	0.0963810
$336$	0	0
$337$	−11139.5	−1.80062	−0.900310	−	0.435249i	$-0.856660\pi$
$337$	−11139.5	−1.80062	−0.900310	+	0.435249i	$0.856660\pi$
$338$	2874.83	0.462634
$339$	−2286.36	−0.366307
$340$	−1306.91	−0.208461
$341$	109.079	0.0173225
$342$	4933.70	0.780069
$343$	0	0
$344$	2455.74	0.384897
$345$	−916.412	−0.143009
$346$	9187.90	1.42759
$347$	−2603.95	−0.402846	−0.201423	−	0.979504i	$-0.564557\pi$
$347$	−2603.95	−0.402846	−0.201423	+	0.979504i	$0.564557\pi$
$348$	−1734.17	−0.267130
$349$	−10140.5	−1.55533	−0.777663	−	0.628681i	$-0.783595\pi$
$349$	−10140.5	−1.55533	−0.777663	+	0.628681i	$0.783595\pi$
$350$	0	0
$351$	−4029.89	−0.612819
$352$	1893.51	0.286717
$353$	3969.70	0.598543	0.299271	−	0.954168i	$-0.403256\pi$
$353$	3969.70	0.598543	0.299271	+	0.954168i	$0.403256\pi$
$354$	2976.86	0.446944
$355$	2007.06	0.300067
$356$	−3912.84	−0.582528
$357$	0	0
$358$	−7510.93	−1.10884
$359$	10246.3	1.50635	0.753174	−	0.657821i	$-0.228522\pi$
$359$	10246.3	1.50635	0.753174	+	0.657821i	$0.228522\pi$
$360$	−412.768	−0.0604300
$361$	−3340.64	−0.487045
$362$	−16111.2	−2.33918
$363$	−2723.02	−0.393724
$364$	0	0
$365$	−2024.94	−0.290383
$366$	7134.13	1.01887
$367$	11536.9	1.64092	0.820462	−	0.571701i	$-0.193716\pi$
$367$	11536.9	1.64092	0.820462	+	0.571701i	$0.193716\pi$
$368$	13747.8	1.94742
$369$	−3972.74	−0.560468
$370$	−2317.52	−0.325627
$371$	0	0
$372$	163.046	0.0227245
$373$	12974.0	1.80098	0.900490	−	0.434876i	$-0.143208\pi$
$373$	12974.0	1.80098	0.900490	+	0.434876i	$0.143208\pi$
$374$	2996.15	0.414244
$375$	−1245.32	−0.171488
$376$	369.315	0.0506542
$377$	−5135.31	−0.701544
$378$	0	0
$379$	3652.29	0.495001	0.247500	−	0.968888i	$-0.420391\pi$
$379$	3652.29	0.495001	0.247500	+	0.968888i	$0.420391\pi$
$380$	822.617	0.111051
$381$	1077.63	0.144904
$382$	741.500	0.0993153
$383$	10847.5	1.44721	0.723603	−	0.690216i	$-0.242485\pi$
$383$	10847.5	1.44721	0.723603	+	0.690216i	$0.242485\pi$
$384$	−2101.12	−0.279225
$385$	0	0
$386$	−17061.8	−2.24980
$387$	−6974.39	−0.916093
$388$	7859.97	1.02843
$389$	−3102.59	−0.404390	−0.202195	−	0.979345i	$-0.564808\pi$
$389$	−3102.59	−0.404390	−0.202195	+	0.979345i	$0.564808\pi$
$390$	−716.907	−0.0930821
$391$	16952.5	2.19265
$392$	0	0
$393$	6021.29	0.772859
$394$	2898.72	0.370648
$395$	2496.15	0.317962
$396$	−1121.60	−0.142329
$397$	15502.5	1.95982	0.979911	−	0.199437i	$-0.0639113\pi$
$397$	15502.5	1.95982	0.979911	+	0.199437i	$0.0639113\pi$
$398$	7554.58	0.951449
$399$	0	0
$400$	9129.23	1.14115
$401$	−11907.7	−1.48290	−0.741451	−	0.671007i	$-0.765862\pi$
$401$	−11907.7	−1.48290	−0.741451	+	0.671007i	$0.765862\pi$
$402$	−2025.09	−0.251250
$403$	482.820	0.0596799
$404$	−4463.37	−0.549656
$405$	874.613	0.107308
$406$	0	0
$407$	2253.36	0.274434
$408$	−1602.53	−0.194454
$409$	2455.08	0.296812	0.148406	−	0.988927i	$-0.452586\pi$
$409$	2455.08	0.296812	0.148406	+	0.988927i	$0.452586\pi$
$410$	−1561.81	−0.188128
$411$	3609.48	0.433194
$412$	6951.37	0.831237
$413$	0	0
$414$	−14963.0	−1.77631
$415$	2068.08	0.244622
$416$	8381.28	0.987803
$417$	−4961.01	−0.582594
$418$	−1885.89	−0.220674
$419$	5909.50	0.689017	0.344508	−	0.938783i	$-0.388046\pi$
$419$	5909.50	0.689017	0.344508	+	0.938783i	$0.388046\pi$
$420$	0	0
$421$	14081.1	1.63010	0.815050	−	0.579390i	$-0.196709\pi$
$421$	14081.1	1.63010	0.815050	+	0.579390i	$0.196709\pi$
$422$	−9411.38	−1.08564
$423$	−1048.87	−0.120562
$424$	−3447.30	−0.394849
$425$	11257.4	1.28485
$426$	−6877.76	−0.782227
$427$	0	0
$428$	−67.2188	−0.00759146
$429$	697.059	0.0784483
$430$	−2741.85	−0.307497
$431$	8491.71	0.949028	0.474514	−	0.880248i	$-0.342624\pi$
$431$	8491.71	0.949028	0.474514	+	0.880248i	$0.342624\pi$
$432$	8156.35	0.908386
$433$	6296.94	0.698872	0.349436	−	0.936960i	$-0.386373\pi$
$433$	6296.94	0.698872	0.349436	+	0.936960i	$0.386373\pi$
$434$	0	0
$435$	−692.834	−0.0763652
$436$	10530.4	1.15669
$437$	−10670.6	−1.16806
$438$	6939.01	0.756983
$439$	9761.68	1.06127	0.530637	−	0.847599i	$-0.321953\pi$
$439$	9761.68	1.06127	0.530637	+	0.847599i	$0.321953\pi$
$440$	157.779	0.0170951
$441$	0	0
$442$	13261.9	1.42716
$443$	12303.2	1.31951	0.659756	−	0.751480i	$-0.270660\pi$
$443$	12303.2	1.31951	0.659756	+	0.751480i	$0.270660\pi$
$444$	3368.19	0.360016
$445$	−1563.26	−0.166529
$446$	13748.6	1.45968
$447$	247.865	0.0262273
$448$	0	0
$449$	16428.2	1.72671	0.863355	−	0.504597i	$-0.168359\pi$
$449$	16428.2	1.72671	0.863355	+	0.504597i	$0.168359\pi$
$450$	−9936.25	−1.04089
$451$	1518.57	0.158551
$452$	−6224.42	−0.647725
$453$	−2889.70	−0.299713
$454$	2159.15	0.223202
$455$	0	0
$456$	1008.69	0.103589
$457$	15831.6	1.62050	0.810250	−	0.586084i	$-0.199331\pi$
$457$	15831.6	1.62050	0.810250	+	0.586084i	$0.199331\pi$
$458$	17225.0	1.75736
$459$	10057.7	1.02277
$460$	−2494.85	−0.252877
$461$	9339.50	0.943566	0.471783	−	0.881715i	$-0.343611\pi$
$461$	9339.50	0.943566	0.471783	+	0.881715i	$0.343611\pi$
$462$	0	0
$463$	6716.69	0.674193	0.337096	−	0.941470i	$-0.390555\pi$
$463$	6716.69	0.674193	0.337096	+	0.941470i	$0.390555\pi$
$464$	10393.7	1.03990
$465$	65.1400	0.00649633
$466$	17815.0	1.77095
$467$	6202.10	0.614559	0.307279	−	0.951619i	$-0.400581\pi$
$467$	6202.10	0.614559	0.307279	+	0.951619i	$0.400581\pi$
$468$	−4964.55	−0.490355
$469$	0	0
$470$	−412.344	−0.0404681
$471$	630.122	0.0616443
$472$	−2899.94	−0.282798
$473$	2665.94	0.259154
$474$	−8553.76	−0.828876
$475$	−7085.81	−0.684462
$476$	0	0
$477$	9790.47	0.939780
$478$	−13025.4	−1.24637
$479$	−7263.21	−0.692828	−0.346414	−	0.938082i	$-0.612601\pi$
$479$	−7263.21	−0.692828	−0.346414	+	0.938082i	$0.612601\pi$
$480$	1130.77	0.107525
$481$	9974.08	0.945486
$482$	−19420.9	−1.83526
$483$	0	0
$484$	−7413.20	−0.696206
$485$	3140.21	0.293999
$486$	−13737.6	−1.28220
$487$	−4251.31	−0.395576	−0.197788	−	0.980245i	$-0.563376\pi$
$487$	−4251.31	−0.395576	−0.197788	+	0.980245i	$0.563376\pi$
$488$	−6949.78	−0.644676
$489$	−2642.40	−0.244363
$490$	0	0
$491$	−241.842	−0.0222285	−0.0111142	−	0.999938i	$-0.503538\pi$
$491$	−241.842	−0.0222285	−0.0111142	+	0.999938i	$0.503538\pi$
$492$	2269.87	0.207996
$493$	12816.6	1.17085
$494$	−8347.56	−0.760272
$495$	−448.100	−0.0406881
$496$	−977.211	−0.0884639
$497$	0	0
$498$	−7086.86	−0.637691
$499$	17230.7	1.54580	0.772899	−	0.634529i	$-0.218806\pi$
$499$	17230.7	1.54580	0.772899	+	0.634529i	$0.218806\pi$
$500$	−3390.27	−0.303235
$501$	−4498.55	−0.401158
$502$	−4570.74	−0.406379
$503$	−13388.0	−1.18676	−0.593380	−	0.804922i	$-0.702207\pi$
$503$	−13388.0	−1.18676	−0.593380	+	0.804922i	$0.702207\pi$
$504$	0	0
$505$	−1783.20	−0.157132
$506$	5719.58	0.502503
$507$	−1669.26	−0.146222
$508$	2933.74	0.256228
$509$	2121.60	0.184751	0.0923756	−	0.995724i	$-0.470554\pi$
$509$	2121.60	0.184751	0.0923756	+	0.995724i	$0.470554\pi$
$510$	1789.24	0.155351
$511$	0	0
$512$	−12159.4	−1.04956
$513$	−6330.70	−0.544848
$514$	−2104.42	−0.180588
$515$	2777.21	0.237628
$516$	3984.90	0.339972
$517$	400.928	0.0341059
$518$	0	0
$519$	−5334.93	−0.451209
$520$	698.383	0.0588964
$521$	−14229.1	−1.19653	−0.598263	−	0.801300i	$-0.704142\pi$
$521$	−14229.1	−1.19653	−0.598263	+	0.801300i	$0.704142\pi$
$522$	−11312.5	−0.948533
$523$	−6336.82	−0.529808	−0.264904	−	0.964275i	$-0.585340\pi$
$523$	−6336.82	−0.529808	−0.264904	+	0.964275i	$0.585340\pi$
$524$	16392.4	1.36662
$525$	0	0
$526$	−27738.1	−2.29932
$527$	−1205.01	−0.0996036
$528$	−1410.82	−0.116285
$529$	20195.0	1.65982
$530$	3848.94	0.315448
$531$	8235.94	0.673087
$532$	0	0
$533$	6721.68	0.546244
$534$	5356.93	0.434114
$535$	−26.8552	−0.00217019
$536$	1972.76	0.158975
$537$	4361.20	0.350465
$538$	−7872.35	−0.630857
$539$	0	0
$540$	−1480.16	−0.117956
$541$	−15809.8	−1.25640	−0.628202	−	0.778050i	$-0.716209\pi$
$541$	−15809.8	−1.25640	−0.628202	+	0.778050i	$0.716209\pi$
$542$	23129.9	1.83305
$543$	9354.89	0.739331
$544$	−20917.8	−1.64861
$545$	4207.12	0.330666
$546$	0	0
$547$	23211.4	1.81435	0.907174	−	0.420755i	$-0.138235\pi$
$547$	23211.4	1.81435	0.907174	+	0.420755i	$0.138235\pi$
$548$	9826.51	0.765999
$549$	19737.7	1.53440
$550$	3798.10	0.294457
$551$	−8067.25	−0.623732
$552$	−3059.20	−0.235884
$553$	0	0
$554$	2000.69	0.153432
$555$	1345.66	0.102919
$556$	−13505.9	−1.03018
$557$	−23601.9	−1.79541	−0.897706	−	0.440595i	$-0.854768\pi$
$557$	−23601.9	−1.79541	−0.897706	+	0.440595i	$0.854768\pi$
$558$	1063.60	0.0806911
$559$	11800.3	0.892844
$560$	0	0
$561$	−1739.70	−0.130927
$562$	−7057.88	−0.529748
$563$	14266.8	1.06799	0.533993	−	0.845489i	$-0.320691\pi$
$563$	14266.8	1.06799	0.533993	+	0.845489i	$0.320691\pi$
$564$	599.285	0.0447419
$565$	−2486.78	−0.185167
$566$	−339.710	−0.0252280
$567$	0	0
$568$	6700.04	0.494943
$569$	−17103.1	−1.26010	−0.630052	−	0.776553i	$-0.716966\pi$
$569$	−17103.1	−1.26010	−0.630052	+	0.776553i	$0.716966\pi$
$570$	−1126.22	−0.0827579
$571$	13527.4	0.991426	0.495713	−	0.868487i	$-0.334907\pi$
$571$	13527.4	0.991426	0.495713	+	0.868487i	$0.334907\pi$
$572$	1897.68	0.138717
$573$	−430.549	−0.0313900
$574$	0	0
$575$	21490.1	1.55860
$576$	4819.40	0.348625
$577$	−7792.53	−0.562231	−0.281116	−	0.959674i	$-0.590704\pi$
$577$	−7792.53	−0.562231	−0.281116	+	0.959674i	$0.590704\pi$
$578$	−14787.2	−1.06413
$579$	9906.90	0.711082
$580$	−1886.18	−0.135033
$581$	0	0
$582$	−10760.8	−0.766409
$583$	−3742.38	−0.265855
$584$	−6759.70	−0.478970
$585$	−1983.43	−0.140179
$586$	−27788.9	−1.95895
$587$	−11701.4	−0.822775	−0.411387	−	0.911461i	$-0.634956\pi$
$587$	−11701.4	−0.822775	−0.411387	+	0.911461i	$0.634956\pi$
$588$	0	0
$589$	758.480	0.0530605
$590$	3237.81	0.225929
$591$	−1683.13	−0.117149
$592$	−20187.2	−1.40150
$593$	25814.9	1.78767	0.893837	−	0.448391i	$-0.148003\pi$
$593$	25814.9	1.78767	0.893837	+	0.448391i	$0.148003\pi$
$594$	3393.35	0.234395
$595$	0	0
$596$	674.792	0.0463768
$597$	−4386.54	−0.300719
$598$	25316.7	1.73123
$599$	911.463	0.0621726	0.0310863	−	0.999517i	$-0.490103\pi$
$599$	911.463	0.0621726	0.0310863	+	0.999517i	$0.490103\pi$
$600$	−2031.47	−0.138224
$601$	9063.56	0.615159	0.307579	−	0.951522i	$-0.400481\pi$
$601$	9063.56	0.615159	0.307579	+	0.951522i	$0.400481\pi$
$602$	0	0
$603$	−5602.73	−0.378376
$604$	−7866.97	−0.529971
$605$	−2961.72	−0.199026
$606$	6110.65	0.409617
$607$	−8974.93	−0.600134	−0.300067	−	0.953918i	$-0.597009\pi$
$607$	−8974.93	−0.600134	−0.300067	+	0.953918i	$0.597009\pi$
$608$	13166.5	0.878241
$609$	0	0
$610$	7759.49	0.515037
$611$	1774.63	0.117503
$612$	12390.4	0.818386
$613$	−19818.8	−1.30583	−0.652915	−	0.757431i	$-0.726454\pi$
$613$	−19818.8	−1.30583	−0.652915	+	0.757431i	$0.726454\pi$
$614$	7770.26	0.510720
$615$	906.859	0.0594603
$616$	0	0
$617$	−9941.32	−0.648659	−0.324329	−	0.945944i	$-0.605139\pi$
$617$	−9941.32	−0.648659	−0.324329	+	0.945944i	$0.605139\pi$
$618$	−9516.88	−0.619458
$619$	14453.3	0.938492	0.469246	−	0.883067i	$-0.344526\pi$
$619$	14453.3	0.938492	0.469246	+	0.883067i	$0.344526\pi$
$620$	177.338	0.0114872
$621$	19199.9	1.24069
$622$	1357.34	0.0874991
$623$	0	0
$624$	−6244.76	−0.400626
$625$	13577.9	0.868988
$626$	22061.0	1.40852
$627$	1095.04	0.0697473
$628$	1715.45	0.109003
$629$	−24893.1	−1.57798
$630$	0	0
$631$	17871.6	1.12750	0.563752	−	0.825944i	$-0.309357\pi$
$631$	17871.6	1.12750	0.563752	+	0.825944i	$0.309357\pi$
$632$	8332.74	0.524460
$633$	5464.69	0.343131
$634$	37415.6	2.34379
$635$	1172.09	0.0732487
$636$	−5593.90	−0.348762
$637$	0	0
$638$	4324.17	0.268331
$639$	−19028.4	−1.17801
$640$	−2285.30	−0.141148
$641$	8453.28	0.520881	0.260440	−	0.965490i	$-0.416132\pi$
$641$	8453.28	0.520881	0.260440	+	0.965490i	$0.416132\pi$
$642$	92.0269	0.00565734
$643$	12562.7	0.770491	0.385245	−	0.922814i	$-0.374117\pi$
$643$	12562.7	0.770491	0.385245	+	0.922814i	$0.374117\pi$
$644$	0	0
$645$	1592.05	0.0971888
$646$	20833.6	1.26887
$647$	−7875.80	−0.478562	−0.239281	−	0.970950i	$-0.576912\pi$
$647$	−7875.80	−0.478562	−0.239281	+	0.970950i	$0.576912\pi$
$648$	2919.66	0.176999
$649$	−3148.17	−0.190410
$650$	16811.6	1.01447
$651$	0	0
$652$	−7193.70	−0.432097
$653$	4201.64	0.251796	0.125898	−	0.992043i	$-0.459819\pi$
$653$	4201.64	0.251796	0.125898	+	0.992043i	$0.459819\pi$
$654$	−14416.9	−0.861993
$655$	6549.10	0.390679
$656$	−13604.4	−0.809702
$657$	19197.8	1.14000
$658$	0	0
$659$	27.4503	0.00162263	0.000811314	−	1.00000i	$-0.499742\pi$
$659$	27.4503	0.00162263	0.000811314		1.00000i	$0.499742\pi$
$660$	256.027	0.0150998
$661$	1193.11	0.0702067	0.0351033	−	0.999384i	$-0.488824\pi$
$661$	1193.11	0.0702067	0.0351033	+	0.999384i	$0.488824\pi$
$662$	−11738.0	−0.689138
$663$	−7700.49	−0.451074
$664$	6903.74	0.403490
$665$	0	0
$666$	21971.7	1.27836
$667$	24466.6	1.42032
$668$	−12246.9	−0.709352
$669$	−7983.08	−0.461351
$670$	−2202.61	−0.127006
$671$	−7544.67	−0.434066
$672$	0	0
$673$	−3163.50	−0.181194	−0.0905972	−	0.995888i	$-0.528878\pi$
$673$	−3163.50	−0.181194	−0.0905972	+	0.995888i	$0.528878\pi$
$674$	41518.9	2.37277
$675$	12749.7	0.727019
$676$	−4544.42	−0.258558
$677$	−12377.3	−0.702655	−0.351327	−	0.936253i	$-0.614270\pi$
$677$	−12377.3	−0.702655	−0.351327	+	0.936253i	$0.614270\pi$
$678$	8521.63	0.482701
$679$	0	0
$680$	−1743.01	−0.0982959
$681$	−1253.70	−0.0705462
$682$	−406.557	−0.0228268
$683$	15155.2	0.849044	0.424522	−	0.905418i	$-0.360442\pi$
$683$	15155.2	0.849044	0.424522	+	0.905418i	$0.360442\pi$
$684$	−7798.99	−0.435968
$685$	3925.88	0.218979
$686$	0	0
$687$	−10001.6	−0.555438
$688$	−23883.4	−1.32347
$689$	−16565.0	−0.915930
$690$	3415.62	0.188450
$691$	−1668.51	−0.0918566	−0.0459283	−	0.998945i	$-0.514625\pi$
$691$	−1668.51	−0.0918566	−0.0459283	+	0.998945i	$0.514625\pi$
$692$	−14523.9	−0.797854
$693$	0	0
$694$	9705.36	0.530851
$695$	−5395.89	−0.294500
$696$	−2312.84	−0.125960
$697$	−16775.8	−0.911662
$698$	37795.4	2.04953
$699$	−10344.2	−0.559734
$700$	0	0
$701$	25511.7	1.37455	0.687277	−	0.726395i	$-0.258806\pi$
$701$	25511.7	1.37455	0.687277	+	0.726395i	$0.258806\pi$
$702$	15020.1	0.807543
$703$	15668.6	0.840618
$704$	−1842.20	−0.0986229
$705$	239.426	0.0127905
$706$	−14795.7	−0.788731
$707$	0	0
$708$	−4705.70	−0.249790
$709$	23404.0	1.23971	0.619855	−	0.784717i	$-0.287192\pi$
$709$	23404.0	1.23971	0.619855	+	0.784717i	$0.287192\pi$
$710$	−7480.65	−0.395414
$711$	−23665.3	−1.24827
$712$	−5218.51	−0.274680
$713$	−2300.34	−0.120825
$714$	0	0
$715$	758.162	0.0396555
$716$	11873.0	0.619713
$717$	7563.14	0.393934
$718$	−38189.7	−1.98499
$719$	10877.8	0.564218	0.282109	−	0.959382i	$-0.408966\pi$
$719$	10877.8	0.564218	0.282109	+	0.959382i	$0.408966\pi$
$720$	4014.40	0.207789
$721$	0	0
$722$	12451.1	0.641805
$723$	11276.7	0.580061
$724$	25467.9	1.30733
$725$	16247.1	0.832279
$726$	10149.2	0.518830
$727$	−16496.8	−0.841585	−0.420792	−	0.907157i	$-0.638248\pi$
$727$	−16496.8	−0.841585	−0.420792	+	0.907157i	$0.638248\pi$
$728$	0	0
$729$	−2055.53	−0.104432
$730$	7547.27	0.382653
$731$	−29450.9	−1.49013
$732$	−11277.4	−0.569430
$733$	22800.7	1.14892	0.574462	−	0.818531i	$-0.305211\pi$
$733$	22800.7	1.14892	0.574462	+	0.818531i	$0.305211\pi$
$734$	−42999.8	−2.16233
$735$	0	0
$736$	−39931.6	−1.99986
$737$	2141.63	0.107039
$738$	14807.1	0.738558
$739$	10560.6	0.525682	0.262841	−	0.964839i	$-0.415340\pi$
$739$	10560.6	0.525682	0.262841	+	0.964839i	$0.415340\pi$
$740$	3663.44	0.181988
$741$	4846.98	0.240295
$742$	0	0
$743$	−6096.81	−0.301037	−0.150518	−	0.988607i	$-0.548094\pi$
$743$	−6096.81	−0.301037	−0.150518	+	0.988607i	$0.548094\pi$
$744$	217.452	0.0107153
$745$	269.593	0.0132579
$746$	−48356.1	−2.37325
$747$	−19606.9	−0.960347
$748$	−4736.19	−0.231514
$749$	0	0
$750$	4641.50	0.225978
$751$	13717.9	0.666544	0.333272	−	0.942831i	$-0.391847\pi$
$751$	13717.9	0.666544	0.333272	+	0.942831i	$0.391847\pi$
$752$	−3591.80	−0.174175
$753$	2653.99	0.128442
$754$	19140.2	0.924461
$755$	−3143.01	−0.151504
$756$	0	0
$757$	34603.4	1.66140	0.830701	−	0.556719i	$-0.187940\pi$
$757$	34603.4	1.66140	0.830701	+	0.556719i	$0.187940\pi$
$758$	−13612.7	−0.652288
$759$	−3321.06	−0.158823
$760$	1097.12	0.0523639
$761$	−19052.1	−0.907541	−0.453771	−	0.891119i	$-0.649921\pi$
$761$	−19052.1	−0.907541	−0.453771	+	0.891119i	$0.649921\pi$
$762$	−4016.49	−0.190948
$763$	0	0
$764$	−1172.13	−0.0555056
$765$	4950.21	0.233954
$766$	−40430.3	−1.90706
$767$	−13934.8	−0.656006
$768$	11570.2	0.543623
$769$	−15039.1	−0.705234	−0.352617	−	0.935768i	$-0.614708\pi$
$769$	−15039.1	−0.705234	−0.352617	+	0.935768i	$0.614708\pi$
$770$	0	0
$771$	1221.93	0.0570773
$772$	26970.7	1.25738
$773$	14312.9	0.665977	0.332988	−	0.942931i	$-0.391943\pi$
$773$	14312.9	0.665977	0.332988	+	0.942931i	$0.391943\pi$
$774$	25994.7	1.20718
$775$	−1527.55	−0.0708014
$776$	10482.8	0.484934
$777$	0	0
$778$	11563.9	0.532886
$779$	10559.3	0.485658
$780$	1133.26	0.0520220
$781$	7273.54	0.333250
$782$	−63184.8	−2.88937
$783$	14515.7	0.662514
$784$	0	0
$785$	685.357	0.0311611
$786$	−22442.3	−1.01844
$787$	−10732.6	−0.486119	−0.243059	−	0.970011i	$-0.578151\pi$
$787$	−10732.6	−0.486119	−0.243059	+	0.970011i	$0.578151\pi$
$788$	−4582.18	−0.207149
$789$	16106.1	0.726731
$790$	−9303.57	−0.418995
$791$	0	0
$792$	−1495.86	−0.0671125
$793$	−33395.1	−1.49545
$794$	−57780.4	−2.58256
$795$	−2234.87	−0.0997017
$796$	−11942.0	−0.531749
$797$	−8760.66	−0.389358	−0.194679	−	0.980867i	$-0.562367\pi$
$797$	−8760.66	−0.389358	−0.194679	+	0.980867i	$0.562367\pi$
$798$	0	0
$799$	−4429.09	−0.196108
$800$	−26516.7	−1.17188
$801$	14820.8	0.653766
$802$	44382.1	1.95410
$803$	−7338.31	−0.322495
$804$	3201.19	0.140419
$805$	0	0
$806$	−1799.55	−0.0786433
$807$	4571.05	0.199391
$808$	−5952.75	−0.259180
$809$	−16842.5	−0.731953	−0.365976	−	0.930624i	$-0.619265\pi$
$809$	−16842.5	−0.731953	−0.365976	+	0.930624i	$0.619265\pi$
$810$	−3259.83	−0.141406
$811$	−590.949	−0.0255870	−0.0127935	−	0.999918i	$-0.504072\pi$
$811$	−590.949	−0.0255870	−0.0127935	+	0.999918i	$0.504072\pi$
$812$	0	0
$813$	−13430.3	−0.579362
$814$	−8398.63	−0.361636
$815$	−2874.02	−0.123525
$816$	15585.5	0.668630
$817$	18537.5	0.793815
$818$	−9150.49	−0.391124
$819$	0	0
$820$	2468.85	0.105141
$821$	17329.6	0.736672	0.368336	−	0.929693i	$-0.379928\pi$
$821$	17329.6	0.736672	0.368336	+	0.929693i	$0.379928\pi$
$822$	−13453.1	−0.570842
$823$	11220.3	0.475232	0.237616	−	0.971359i	$-0.423634\pi$
$823$	11220.3	0.475232	0.237616	+	0.971359i	$0.423634\pi$
$824$	9270.97	0.391953
$825$	−2205.35	−0.0930674
$826$	0	0
$827$	−32763.5	−1.37763	−0.688814	−	0.724938i	$-0.741868\pi$
$827$	−32763.5	−1.37763	−0.688814	+	0.724938i	$0.741868\pi$
$828$	23653.0	0.992752
$829$	13107.6	0.549153	0.274576	−	0.961565i	$-0.411462\pi$
$829$	13107.6	0.549153	0.274576	+	0.961565i	$0.411462\pi$
$830$	−7708.08	−0.322351
$831$	−1161.69	−0.0484942
$832$	−8154.17	−0.339778
$833$	0	0
$834$	18490.5	0.767715
$835$	−4892.88	−0.202785
$836$	2981.14	0.123331
$837$	−1364.76	−0.0563596
$838$	−22025.7	−0.907953
$839$	−17234.7	−0.709185	−0.354593	−	0.935021i	$-0.615380\pi$
$839$	−17234.7	−0.709185	−0.354593	+	0.935021i	$0.615380\pi$
$840$	0	0
$841$	−5891.56	−0.241566
$842$	−52482.7	−2.14807
$843$	4098.13	0.167434
$844$	14877.1	0.606744
$845$	−1815.59	−0.0739149
$846$	3909.31	0.158871
$847$	0	0
$848$	33526.9	1.35769
$849$	197.251	0.00797367
$850$	−41958.0	−1.69312
$851$	−47520.3	−1.91419
$852$	10872.1	0.437174
$853$	−8402.54	−0.337277	−0.168639	−	0.985678i	$-0.553937\pi$
$853$	−8402.54	−0.337277	−0.168639	+	0.985678i	$0.553937\pi$
$854$	0	0
$855$	−3115.85	−0.124631
$856$	−89.6490	−0.00357960
$857$	30538.4	1.21724	0.608619	−	0.793463i	$-0.291724\pi$
$857$	30538.4	1.21724	0.608619	+	0.793463i	$0.291724\pi$
$858$	−2598.05	−0.103375
$859$	47171.8	1.87367	0.936834	−	0.349774i	$-0.113742\pi$
$859$	47171.8	1.87367	0.936834	+	0.349774i	$0.113742\pi$
$860$	4334.21	0.171855
$861$	0	0
$862$	−31650.0	−1.25058
$863$	−27257.3	−1.07515	−0.537573	−	0.843217i	$-0.680659\pi$
$863$	−27257.3	−1.07515	−0.537573	+	0.843217i	$0.680659\pi$
$864$	−23690.9	−0.932846
$865$	−5802.58	−0.228085
$866$	−23469.7	−0.920940
$867$	8586.13	0.336333
$868$	0	0
$869$	9045.99	0.353124
$870$	2582.31	0.100630
$871$	9479.53	0.368774
$872$	14044.3	0.545414
$873$	−29771.4	−1.15419
$874$	39771.0	1.53921
$875$	0	0
$876$	−10968.9	−0.423065
$877$	−16759.3	−0.645293	−0.322647	−	0.946520i	$-0.604573\pi$
$877$	−16759.3	−0.645293	−0.322647	+	0.946520i	$0.604573\pi$
$878$	−36383.4	−1.39850
$879$	16135.5	0.619155
$880$	−1534.49	−0.0587816
$881$	16666.3	0.637348	0.318674	−	0.947864i	$-0.396763\pi$
$881$	16666.3	0.637348	0.318674	+	0.947864i	$0.396763\pi$
$882$	0	0
$883$	−17376.9	−0.662263	−0.331132	−	0.943585i	$-0.607430\pi$
$883$	−17376.9	−0.662263	−0.331132	+	0.943585i	$0.607430\pi$
$884$	−20963.9	−0.797616
$885$	−1880.02	−0.0714082
$886$	−45856.2	−1.73879
$887$	−43205.1	−1.63550	−0.817748	−	0.575576i	$-0.804778\pi$
$887$	−43205.1	−1.63550	−0.817748	+	0.575576i	$0.804778\pi$
$888$	4492.12	0.169759
$889$	0	0
$890$	5826.51	0.219444
$891$	3169.58	0.119175
$892$	−21733.3	−0.815788
$893$	2787.84	0.104470
$894$	−923.835	−0.0345611
$895$	4743.49	0.177159
$896$	0	0
$897$	−14700.1	−0.547181
$898$	−61230.5	−2.27538
$899$	−1739.12	−0.0645195
$900$	15706.8	0.581734
$901$	41342.5	1.52865
$902$	−5659.96	−0.208931
$903$	0	0
$904$	−8301.44	−0.305422
$905$	10174.9	0.373730
$906$	10770.4	0.394947
$907$	14225.5	0.520783	0.260392	−	0.965503i	$-0.416148\pi$
$907$	14225.5	0.520783	0.260392	+	0.965503i	$0.416148\pi$
$908$	−3413.10	−0.124744
$909$	16906.1	0.616874
$910$	0	0
$911$	10288.8	0.374184	0.187092	−	0.982342i	$-0.440094\pi$
$911$	10288.8	0.374184	0.187092	+	0.982342i	$0.440094\pi$
$912$	−9810.12	−0.356190
$913$	7494.68	0.271673
$914$	−59006.8	−2.13542
$915$	−4505.52	−0.162785
$916$	−27228.6	−0.982159
$917$	0	0
$918$	−37486.7	−1.34776
$919$	−20976.8	−0.752950	−0.376475	−	0.926427i	$-0.622864\pi$
$919$	−20976.8	−0.752950	−0.376475	+	0.926427i	$0.622864\pi$
$920$	−3327.36	−0.119239
$921$	−4511.77	−0.161420
$922$	−34809.8	−1.24339
$923$	32195.1	1.14812
$924$	0	0
$925$	−31556.0	−1.12168
$926$	−25034.2	−0.888418
$927$	−26329.9	−0.932889
$928$	−30189.4	−1.06791
$929$	7296.24	0.257677	0.128839	−	0.991666i	$-0.458875\pi$
$929$	7296.24	0.257677	0.128839	+	0.991666i	$0.458875\pi$
$930$	−242.787	−0.00856055
$931$	0	0
$932$	−28161.2	−0.989755
$933$	−788.136	−0.0276553
$934$	−23116.2	−0.809836
$935$	−1892.20	−0.0661836
$936$	−6621.17	−0.231218
$937$	−57014.5	−1.98782	−0.993908	−	0.110213i	$-0.964847\pi$
$937$	−57014.5	−1.98782	−0.993908	+	0.110213i	$0.964847\pi$
$938$	0	0
$939$	−12809.7	−0.445184
$940$	651.817	0.0226169
$941$	−16717.1	−0.579130	−0.289565	−	0.957158i	$-0.593511\pi$
$941$	−16717.1	−0.579130	−0.289565	+	0.957158i	$0.593511\pi$
$942$	−2348.57	−0.0812319
$943$	−32024.6	−1.10590
$944$	28203.5	0.972401
$945$	0	0
$946$	−9936.40	−0.341501
$947$	8921.02	0.306119	0.153059	−	0.988217i	$-0.451087\pi$
$947$	8921.02	0.306119	0.153059	+	0.988217i	$0.451087\pi$
$948$	13521.5	0.463245
$949$	−32481.7	−1.11107
$950$	26410.0	0.901951
$951$	−21725.3	−0.740789
$952$	0	0
$953$	1128.59	0.0383618	0.0191809	−	0.999816i	$-0.493894\pi$
$953$	1128.59	0.0383618	0.0191809	+	0.999816i	$0.493894\pi$
$954$	−36490.7	−1.23840
$955$	−468.290	−0.0158676
$956$	20590.0	0.696578
$957$	−2510.81	−0.0848099
$958$	27071.2	0.912976
$959$	0	0
$960$	−1100.13	−0.0369858
$961$	−29627.5	−0.994511
$962$	−37175.0	−1.24592
$963$	254.607	0.00851982
$964$	30699.8	1.02570
$965$	10775.3	0.359451
$966$	0	0
$967$	27190.7	0.904235	0.452118	−	0.891958i	$-0.350669\pi$
$967$	27190.7	0.904235	0.452118	+	0.891958i	$0.350669\pi$
$968$	−9886.91	−0.328282
$969$	−12097.0	−0.401043
$970$	−11704.1	−0.387418
$971$	30689.0	1.01427	0.507136	−	0.861866i	$-0.330704\pi$
$971$	30689.0	1.01427	0.507136	+	0.861866i	$0.330704\pi$
$972$	21715.9	0.716601
$973$	0	0
$974$	15845.3	0.521271
$975$	−9761.61	−0.320638
$976$	67590.6	2.21672
$977$	−12479.0	−0.408637	−0.204319	−	0.978904i	$-0.565498\pi$
$977$	−12479.0	−0.408637	−0.204319	+	0.978904i	$0.565498\pi$
$978$	9848.65	0.322009
$979$	−5665.20	−0.184944
$980$	0	0
$981$	−39886.5	−1.29814
$982$	901.386	0.0292916
$983$	−29214.1	−0.947899	−0.473949	−	0.880552i	$-0.657172\pi$
$983$	−29214.1	−0.947899	−0.473949	+	0.880552i	$0.657172\pi$
$984$	3027.31	0.0980763
$985$	−1830.67	−0.0592183
$986$	−47769.5	−1.54289
$987$	0	0
$988$	13195.5	0.424904
$989$	−56221.2	−1.80761
$990$	1670.14	0.0536168
$991$	36949.0	1.18438	0.592191	−	0.805798i	$-0.298263\pi$
$991$	36949.0	1.18438	0.592191	+	0.805798i	$0.298263\pi$
$992$	2838.40	0.0908460
$993$	6815.61	0.217812
$994$	0	0
$995$	−4771.06	−0.152013
$996$	11202.6	0.356395
$997$	21649.2	0.687699	0.343850	−	0.939025i	$-0.388269\pi$
$997$	21649.2	0.687699	0.343850	+	0.939025i	$0.388269\pi$
$998$	−64221.7	−2.03698
$999$	−28193.1	−0.892884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.e.1.4		20
7.6	odd	2		329.4.a.c.1.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
329.4.a.c.1.4	✓	20	7.6	odd	2
2303.4.a.e.1.4		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-3.72716 q^{2} +2.16417 q^{3} +5.89176 q^{4} +2.35387 q^{5} -8.06620 q^{6} +7.85777 q^{8} -22.3164 q^{9} +O(q^{10})\)	\(q-3.72716 q^{2} +2.16417 q^{3} +5.89176 q^{4} +2.35387 q^{5} -8.06620 q^{6} +7.85777 q^{8} -22.3164 q^{9} -8.77327 q^{10} +8.53037 q^{11} +12.7507 q^{12} +37.7582 q^{13} +5.09417 q^{15} -76.4213 q^{16} -94.2359 q^{17} +83.1769 q^{18} +59.3157 q^{19} +13.8684 q^{20} -31.7941 q^{22} -179.894 q^{23} +17.0055 q^{24} -119.459 q^{25} -140.731 q^{26} -106.729 q^{27} -136.005 q^{29} -18.9868 q^{30} +12.7872 q^{31} +221.972 q^{32} +18.4611 q^{33} +351.233 q^{34} -131.483 q^{36} +264.157 q^{37} -221.079 q^{38} +81.7150 q^{39} +18.4962 q^{40} +178.019 q^{41} +312.523 q^{43} +50.2589 q^{44} -52.5299 q^{45} +670.496 q^{46} +47.0000 q^{47} -165.388 q^{48} +445.244 q^{50} -203.942 q^{51} +222.462 q^{52} -438.712 q^{53} +397.796 q^{54} +20.0794 q^{55} +128.369 q^{57} +506.914 q^{58} -369.054 q^{59} +30.0136 q^{60} -884.447 q^{61} -47.6599 q^{62} -215.958 q^{64} +88.8780 q^{65} -68.8077 q^{66} +251.059 q^{67} -555.215 q^{68} -389.321 q^{69} +852.664 q^{71} -175.357 q^{72} -860.257 q^{73} -984.555 q^{74} -258.530 q^{75} +349.474 q^{76} -304.565 q^{78} +1060.45 q^{79} -179.886 q^{80} +371.564 q^{81} -663.507 q^{82} +878.587 q^{83} -221.819 q^{85} -1164.83 q^{86} -294.338 q^{87} +67.0297 q^{88} -664.121 q^{89} +195.788 q^{90} -1059.89 q^{92} +27.6735 q^{93} -175.177 q^{94} +139.622 q^{95} +480.385 q^{96} +1334.06 q^{97} -190.367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9	\( 20 q + 3 q^{2} - 2 q^{3} + 109 q^{4} + 4 q^{5} - q^{6} + 12 q^{8} + 278 q^{9} - 68 q^{10} + 62 q^{11} + 6 q^{13} + 420 q^{15} + 957 q^{16} + 138 q^{17} + 120 q^{18} - 182 q^{19} - 787 q^{20} + 521 q^{22} + 326 q^{23} + 18 q^{24} + 678 q^{25} - 118 q^{26} - 68 q^{27} + 528 q^{29} + 877 q^{30} - 1092 q^{31} + 254 q^{32} + 424 q^{33} - 234 q^{34} + 2608 q^{36} + 904 q^{37} + 166 q^{38} + 606 q^{39} - 323 q^{40} + 8 q^{41} - 18 q^{43} + 98 q^{44} - 316 q^{45} + 1382 q^{46} + 940 q^{47} - 937 q^{48} + 892 q^{50} + 756 q^{51} - 761 q^{52} + 992 q^{53} - 384 q^{54} - 1060 q^{55} + 1554 q^{57} - 938 q^{58} - 2140 q^{59} + 5830 q^{60} + 186 q^{61} - 69 q^{62} + 7086 q^{64} + 662 q^{65} - 3617 q^{66} + 2852 q^{67} - 1163 q^{68} - 628 q^{69} + 3448 q^{71} - 355 q^{72} + 304 q^{73} + 1512 q^{74} - 4930 q^{75} - 339 q^{76} + 1054 q^{78} + 4248 q^{79} - 5945 q^{80} + 5696 q^{81} - 3665 q^{82} + 274 q^{83} + 232 q^{85} - 5730 q^{86} - 3756 q^{87} + 1976 q^{88} + 3168 q^{89} + 13306 q^{90} - 4214 q^{92} - 374 q^{93} + 141 q^{94} + 6100 q^{95} + 11433 q^{96} + 4112 q^{97} + 7252 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - 2 * q^3 + 109 * q^4 + 4 * q^5 - q^6 + 12 * q^8 + 278 * q^9 - 68 * q^10 + 62 * q^11 + 6 * q^13 + 420 * q^15 + 957 * q^16 + 138 * q^17 + 120 * q^18 - 182 * q^19 - 787 * q^20 + 521 * q^22 + 326 * q^23 + 18 * q^24 + 678 * q^25 - 118 * q^26 - 68 * q^27 + 528 * q^29 + 877 * q^30 - 1092 * q^31 + 254 * q^32 + 424 * q^33 - 234 * q^34 + 2608 * q^36 + 904 * q^37 + 166 * q^38 + 606 * q^39 - 323 * q^40 + 8 * q^41 - 18 * q^43 + 98 * q^44 - 316 * q^45 + 1382 * q^46 + 940 * q^47 - 937 * q^48 + 892 * q^50 + 756 * q^51 - 761 * q^52 + 992 * q^53 - 384 * q^54 - 1060 * q^55 + 1554 * q^57 - 938 * q^58 - 2140 * q^59 + 5830 * q^60 + 186 * q^61 - 69 * q^62 + 7086 * q^64 + 662 * q^65 - 3617 * q^66 + 2852 * q^67 - 1163 * q^68 - 628 * q^69 + 3448 * q^71 - 355 * q^72 + 304 * q^73 + 1512 * q^74 - 4930 * q^75 - 339 * q^76 + 1054 * q^78 + 4248 * q^79 - 5945 * q^80 + 5696 * q^81 - 3665 * q^82 + 274 * q^83 + 232 * q^85 - 5730 * q^86 - 3756 * q^87 + 1976 * q^88 + 3168 * q^89 + 13306 * q^90 - 4214 * q^92 - 374 * q^93 + 141 * q^94 + 6100 * q^95 + 11433 * q^96 + 4112 * q^97 + 7252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more