LMFDB - Embedded newform 322.4.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,4,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, 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("322.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.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:	$18.9986150218$
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} - 92x^{3} - 28x^{2} + 1593x - 1782 $ x^5 - 92x^3 - 28x^2 + 1593*x - 1782
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			$1.26012$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -0.260120 q^{3} +4.00000 q^{4} +15.2484 q^{5} -0.520240 q^{6} -7.00000 q^{7} +8.00000 q^{8} -26.9323 q^{9} +30.4969 q^{10} +63.1379 q^{11} -1.04048 q^{12} +40.8864 q^{13} -14.0000 q^{14} -3.96643 q^{15} +16.0000 q^{16} -57.0717 q^{17} -53.8647 q^{18} +34.4579 q^{19} +60.9938 q^{20} +1.82084 q^{21} +126.276 q^{22} +23.0000 q^{23} -2.08096 q^{24} +107.515 q^{25} +81.7727 q^{26} +14.0289 q^{27} -28.0000 q^{28} +180.951 q^{29} -7.93285 q^{30} -5.92805 q^{31} +32.0000 q^{32} -16.4234 q^{33} -114.143 q^{34} -106.739 q^{35} -107.729 q^{36} -161.864 q^{37} +68.9158 q^{38} -10.6354 q^{39} +121.988 q^{40} -104.432 q^{41} +3.64168 q^{42} +16.5725 q^{43} +252.552 q^{44} -410.676 q^{45} +46.0000 q^{46} +333.754 q^{47} -4.16192 q^{48} +49.0000 q^{49} +215.030 q^{50} +14.8455 q^{51} +163.545 q^{52} +296.103 q^{53} +28.0578 q^{54} +962.756 q^{55} -56.0000 q^{56} -8.96319 q^{57} +361.902 q^{58} -805.644 q^{59} -15.8657 q^{60} +715.603 q^{61} -11.8561 q^{62} +188.526 q^{63} +64.0000 q^{64} +623.454 q^{65} -32.8469 q^{66} +301.232 q^{67} -228.287 q^{68} -5.98276 q^{69} -213.478 q^{70} -871.046 q^{71} -215.459 q^{72} +894.771 q^{73} -323.728 q^{74} -27.9668 q^{75} +137.832 q^{76} -441.966 q^{77} -21.2707 q^{78} -1246.19 q^{79} +243.975 q^{80} +723.524 q^{81} -208.863 q^{82} -1223.93 q^{83} +7.28336 q^{84} -870.255 q^{85} +33.1451 q^{86} -47.0690 q^{87} +505.104 q^{88} -86.3579 q^{89} -821.353 q^{90} -286.205 q^{91} +92.0000 q^{92} +1.54200 q^{93} +667.507 q^{94} +525.429 q^{95} -8.32384 q^{96} +343.939 q^{97} +98.0000 q^{98} -1700.45 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} + 5 q^{3} + 20 q^{4} + 22 q^{5} + 10 q^{6} - 35 q^{7} + 40 q^{8} + 54 q^{9} + 44 q^{10} + 42 q^{11} + 20 q^{12} + 107 q^{13} - 70 q^{14} + 122 q^{15} + 80 q^{16} + 218 q^{17} + 108 q^{18}+ \cdots - 2616 q^{99}+O(q^{100}) $ 5 * q + 10 * q^2 + 5 * q^3 + 20 * q^4 + 22 * q^5 + 10 * q^6 - 35 * q^7 + 40 * q^8 + 54 * q^9 + 44 * q^10 + 42 * q^11 + 20 * q^12 + 107 * q^13 - 70 * q^14 + 122 * q^15 + 80 * q^16 + 218 * q^17 + 108 * q^18 + 194 * q^19 + 88 * q^20 - 35 * q^21 + 84 * q^22 + 115 * q^23 + 40 * q^24 + 219 * q^25 + 214 * q^26 + 203 * q^27 - 140 * q^28 + 33 * q^29 + 244 * q^30 + 19 * q^31 + 160 * q^32 + 240 * q^33 + 436 * q^34 - 154 * q^35 + 216 * q^36 + 214 * q^37 + 388 * q^38 - 243 * q^39 + 176 * q^40 + 395 * q^41 - 70 * q^42 - 284 * q^43 + 168 * q^44 + 470 * q^45 + 230 * q^46 - 493 * q^47 + 80 * q^48 + 245 * q^49 + 438 * q^50 - 244 * q^51 + 428 * q^52 - 70 * q^53 + 406 * q^54 - 186 * q^55 - 280 * q^56 + 22 * q^57 + 66 * q^58 + 226 * q^59 + 488 * q^60 + 1606 * q^61 + 38 * q^62 - 378 * q^63 + 320 * q^64 + 362 * q^65 + 480 * q^66 + 298 * q^67 + 872 * q^68 + 115 * q^69 - 308 * q^70 - 969 * q^71 + 432 * q^72 + 697 * q^73 + 428 * q^74 + 1065 * q^75 + 776 * q^76 - 294 * q^77 - 486 * q^78 + 186 * q^79 + 352 * q^80 - 335 * q^81 + 790 * q^82 - 1104 * q^83 - 140 * q^84 - 1344 * q^85 - 568 * q^86 - 1603 * q^87 + 336 * q^88 - 814 * q^89 + 940 * q^90 - 749 * q^91 + 460 * q^92 - 3423 * q^93 - 986 * q^94 - 2812 * q^95 + 160 * q^96 - 256 * q^97 + 490 * q^98 - 2616 * q^99

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−0.260120	−0.0500601	−0.0250301	−	0.999687i	$-0.507968\pi$
$3$	−0.260120	−0.0500601	−0.0250301	+	0.999687i	$0.507968\pi$
$4$	4.00000	0.500000
$5$	15.2484	1.36386	0.681931	−	0.731416i	$-0.261140\pi$
$5$	15.2484	1.36386	0.681931	+	0.731416i	$0.261140\pi$
$6$	−0.520240	−0.0353978
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	−26.9323	−0.997494
$10$	30.4969	0.964397
$11$	63.1379	1.73062	0.865309	−	0.501238i	$-0.167122\pi$
$11$	63.1379	1.73062	0.865309	+	0.501238i	$0.167122\pi$
$12$	−1.04048	−0.0250301
$13$	40.8864	0.872295	0.436148	−	0.899875i	$-0.356343\pi$
$13$	40.8864	0.872295	0.436148	+	0.899875i	$0.356343\pi$
$14$	−14.0000	−0.267261
$15$	−3.96643	−0.0682751
$16$	16.0000	0.250000
$17$	−57.0717	−0.814231	−0.407115	−	0.913377i	$-0.633465\pi$
$17$	−57.0717	−0.814231	−0.407115	+	0.913377i	$0.633465\pi$
$18$	−53.8647	−0.705335
$19$	34.4579	0.416062	0.208031	−	0.978122i	$-0.433294\pi$
$19$	34.4579	0.416062	0.208031	+	0.978122i	$0.433294\pi$
$20$	60.9938	0.681931
$21$	1.82084	0.0189209
$22$	126.276	1.22373
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−2.08096	−0.0176989
$25$	107.515	0.860121
$26$	81.7727	0.616806
$27$	14.0289	0.0999948
$28$	−28.0000	−0.188982
$29$	180.951	1.15868	0.579340	−	0.815086i	$-0.303310\pi$
$29$	180.951	1.15868	0.579340	+	0.815086i	$0.303310\pi$
$30$	−7.93285	−0.0482778
$31$	−5.92805	−0.0343455	−0.0171727	−	0.999853i	$-0.505467\pi$
$31$	−5.92805	−0.0343455	−0.0171727	+	0.999853i	$0.505467\pi$
$32$	32.0000	0.176777
$33$	−16.4234	−0.0866350
$34$	−114.143	−0.575748
$35$	−106.739	−0.515492
$36$	−107.729	−0.498747
$37$	−161.864	−0.719196	−0.359598	−	0.933107i	$-0.617086\pi$
$37$	−161.864	−0.719196	−0.359598	+	0.933107i	$0.617086\pi$
$38$	68.9158	0.294200
$39$	−10.6354	−0.0436672
$40$	121.988	0.482198
$41$	−104.432	−0.397792	−0.198896	−	0.980021i	$-0.563736\pi$
$41$	−104.432	−0.397792	−0.198896	+	0.980021i	$0.563736\pi$
$42$	3.64168	0.0133791
$43$	16.5725	0.0587742	0.0293871	−	0.999568i	$-0.490644\pi$
$43$	16.5725	0.0587742	0.0293871	+	0.999568i	$0.490644\pi$
$44$	252.552	0.865309
$45$	−410.676	−1.36044
$46$	46.0000	0.147442
$47$	333.754	1.03581	0.517904	−	0.855439i	$-0.326713\pi$
$47$	333.754	1.03581	0.517904	+	0.855439i	$0.326713\pi$
$48$	−4.16192	−0.0125150
$49$	49.0000	0.142857
$50$	215.030	0.608198
$51$	14.8455	0.0407605
$52$	163.545	0.436148
$53$	296.103	0.767412	0.383706	−	0.923455i	$-0.374648\pi$
$53$	296.103	0.767412	0.383706	+	0.923455i	$0.374648\pi$
$54$	28.0578	0.0707070
$55$	962.756	2.36033
$56$	−56.0000	−0.133631
$57$	−8.96319	−0.0208281
$58$	361.902	0.819311
$59$	−805.644	−1.77773	−0.888864	−	0.458171i	$-0.848505\pi$
$59$	−805.644	−1.77773	−0.888864	+	0.458171i	$0.848505\pi$
$60$	−15.8657	−0.0341376
$61$	715.603	1.50202	0.751012	−	0.660288i	$-0.229566\pi$
$61$	715.603	1.50202	0.751012	+	0.660288i	$0.229566\pi$
$62$	−11.8561	−0.0242859
$63$	188.526	0.377017
$64$	64.0000	0.125000
$65$	623.454	1.18969
$66$	−32.8469	−0.0612602
$67$	301.232	0.549275	0.274637	−	0.961548i	$-0.411442\pi$
$67$	301.232	0.549275	0.274637	+	0.961548i	$0.411442\pi$
$68$	−228.287	−0.407115
$69$	−5.98276	−0.0104383
$70$	−213.478	−0.364508
$71$	−871.046	−1.45597	−0.727987	−	0.685591i	$-0.759544\pi$
$71$	−871.046	−1.45597	−0.727987	+	0.685591i	$0.759544\pi$
$72$	−215.459	−0.352667
$73$	894.771	1.43459	0.717295	−	0.696770i	$-0.245380\pi$
$73$	894.771	1.43459	0.717295	+	0.696770i	$0.245380\pi$
$74$	−323.728	−0.508548
$75$	−27.9668	−0.0430578
$76$	137.832	0.208031
$77$	−441.966	−0.654112
$78$	−21.2707	−0.0308774
$79$	−1246.19	−1.77477	−0.887386	−	0.461028i	$-0.847481\pi$
$79$	−1246.19	−1.77477	−0.887386	+	0.461028i	$0.847481\pi$
$80$	243.975	0.340966
$81$	723.524	0.992488
$82$	−208.863	−0.281281
$83$	−1223.93	−1.61860	−0.809300	−	0.587395i	$-0.800154\pi$
$83$	−1223.93	−1.61860	−0.809300	+	0.587395i	$0.800154\pi$
$84$	7.28336	0.00946047
$85$	−870.255	−1.11050
$86$	33.1451	0.0415596
$87$	−47.0690	−0.0580037
$88$	505.104	0.611866
$89$	−86.3579	−0.102853	−0.0514265	−	0.998677i	$-0.516377\pi$
$89$	−86.3579	−0.102853	−0.0514265	+	0.998677i	$0.516377\pi$
$90$	−821.353	−0.961980
$91$	−286.205	−0.329697
$92$	92.0000	0.104257
$93$	1.54200	0.00171934
$94$	667.507	0.732426
$95$	525.429	0.567452
$96$	−8.32384	−0.00884946
$97$	343.939	0.360018	0.180009	−	0.983665i	$-0.442387\pi$
$97$	343.939	0.360018	0.180009	+	0.983665i	$0.442387\pi$
$98$	98.0000	0.101015
$99$	−1700.45	−1.72628
$100$	430.061	0.430061
$101$	458.505	0.451713	0.225856	−	0.974161i	$-0.427482\pi$
$101$	458.505	0.451713	0.225856	+	0.974161i	$0.427482\pi$
$102$	29.6910	0.0288220
$103$	−574.886	−0.549954	−0.274977	−	0.961451i	$-0.588670\pi$
$103$	−574.886	−0.549954	−0.274977	+	0.961451i	$0.588670\pi$
$104$	327.091	0.308403
$105$	27.7650	0.0258056
$106$	592.205	0.542642
$107$	−1451.76	−1.31165	−0.655825	−	0.754913i	$-0.727679\pi$
$107$	−1451.76	−1.31165	−0.655825	+	0.754913i	$0.727679\pi$
$108$	56.1155	0.0499974
$109$	−1812.89	−1.59306	−0.796530	−	0.604598i	$-0.793334\pi$
$109$	−1812.89	−1.59306	−0.796530	+	0.604598i	$0.793334\pi$
$110$	1925.51	1.66900
$111$	42.1040	0.0360030
$112$	−112.000	−0.0944911
$113$	−1693.79	−1.41007	−0.705035	−	0.709173i	$-0.749069\pi$
$113$	−1693.79	−1.41007	−0.705035	+	0.709173i	$0.749069\pi$
$114$	−17.9264	−0.0147277
$115$	350.714	0.284385
$116$	723.804	0.579340
$117$	−1101.17	−0.870109
$118$	−1611.29	−1.25704
$119$	399.502	0.307750
$120$	−31.7314	−0.0241389
$121$	2655.40	1.99504
$122$	1431.21	1.06209
$123$	27.1647	0.0199135
$124$	−23.7122	−0.0171727
$125$	−266.616	−0.190775
$126$	377.053	0.266591
$127$	251.950	0.176039	0.0880194	−	0.996119i	$-0.471946\pi$
$127$	251.950	0.176039	0.0880194	+	0.996119i	$0.471946\pi$
$128$	128.000	0.0883883
$129$	−4.31085	−0.00294224
$130$	1246.91	0.841238
$131$	−1844.44	−1.23015	−0.615074	−	0.788469i	$-0.710874\pi$
$131$	−1844.44	−1.23015	−0.615074	+	0.788469i	$0.710874\pi$
$132$	−65.6938	−0.0433175
$133$	−241.205	−0.157257
$134$	602.465	0.388396
$135$	213.919	0.136379
$136$	−456.574	−0.287874
$137$	−1169.93	−0.729592	−0.364796	−	0.931087i	$-0.618861\pi$
$137$	−1169.93	−0.729592	−0.364796	+	0.931087i	$0.618861\pi$
$138$	−11.9655	−0.00738096
$139$	−1618.44	−0.987585	−0.493792	−	0.869580i	$-0.664390\pi$
$139$	−1618.44	−0.987585	−0.493792	+	0.869580i	$0.664390\pi$
$140$	−426.957	−0.257746
$141$	−86.8160	−0.0518526
$142$	−1742.09	−1.02953
$143$	2581.48	1.50961
$144$	−430.917	−0.249373
$145$	2759.22	1.58028
$146$	1789.54	1.01441
$147$	−12.7459	−0.00715144
$148$	−647.455	−0.359598
$149$	−1745.63	−0.959785	−0.479892	−	0.877327i	$-0.659324\pi$
$149$	−1745.63	−0.959785	−0.479892	+	0.877327i	$0.659324\pi$
$150$	−55.9337	−0.0304464
$151$	−2520.41	−1.35833	−0.679167	−	0.733984i	$-0.737659\pi$
$151$	−2520.41	−1.35833	−0.679167	+	0.733984i	$0.737659\pi$
$152$	275.663	0.147100
$153$	1537.07	0.812190
$154$	−883.931	−0.462527
$155$	−90.3936	−0.0468425
$156$	−42.5414	−0.0218336
$157$	1122.56	0.570635	0.285318	−	0.958433i	$-0.407901\pi$
$157$	1122.56	0.570635	0.285318	+	0.958433i	$0.407901\pi$
$158$	−2492.37	−1.25495
$159$	−77.0222	−0.0384167
$160$	487.950	0.241099
$161$	−161.000	−0.0788110
$162$	1447.05	0.701795
$163$	149.438	0.0718091	0.0359045	−	0.999355i	$-0.488569\pi$
$163$	149.438	0.0718091	0.0359045	+	0.999355i	$0.488569\pi$
$164$	−417.726	−0.198896
$165$	−250.432	−0.118158
$166$	−2447.86	−1.14452
$167$	1950.78	0.903927	0.451963	−	0.892037i	$-0.350724\pi$
$167$	1950.78	0.903927	0.451963	+	0.892037i	$0.350724\pi$
$168$	14.5667	0.00668956
$169$	−525.306	−0.239101
$170$	−1740.51	−0.785241
$171$	−928.032	−0.415020
$172$	66.2902	0.0293871
$173$	2850.79	1.25284	0.626420	−	0.779486i	$-0.284520\pi$
$173$	2850.79	1.25284	0.626420	+	0.779486i	$0.284520\pi$
$174$	−94.1379	−0.0410148
$175$	−752.606	−0.325095
$176$	1010.21	0.432655
$177$	209.564	0.0889933
$178$	−172.716	−0.0727280
$179$	1847.62	0.771493	0.385747	−	0.922605i	$-0.373944\pi$
$179$	1847.62	0.771493	0.385747	+	0.922605i	$0.373944\pi$
$180$	−1642.71	−0.680222
$181$	3260.42	1.33892	0.669461	−	0.742847i	$-0.266525\pi$
$181$	3260.42	1.33892	0.669461	+	0.742847i	$0.266525\pi$
$182$	−572.409	−0.233131
$183$	−186.143	−0.0751915
$184$	184.000	0.0737210
$185$	−2468.17	−0.980884
$186$	3.08401	0.00121576
$187$	−3603.39	−1.40912
$188$	1335.01	0.517904
$189$	−98.2021	−0.0377945
$190$	1050.86	0.401249
$191$	1616.13	0.612247	0.306123	−	0.951992i	$-0.400968\pi$
$191$	1616.13	0.612247	0.306123	+	0.951992i	$0.400968\pi$
$192$	−16.6477	−0.00625751
$193$	−4746.87	−1.77040	−0.885200	−	0.465211i	$-0.845979\pi$
$193$	−4746.87	−1.77040	−0.885200	+	0.465211i	$0.845979\pi$
$194$	687.878	0.254571
$195$	−162.173	−0.0595560
$196$	196.000	0.0714286
$197$	−1471.77	−0.532280	−0.266140	−	0.963934i	$-0.585748\pi$
$197$	−1471.77	−0.532280	−0.266140	+	0.963934i	$0.585748\pi$
$198$	−3400.90	−1.22067
$199$	3296.74	1.17437	0.587184	−	0.809453i	$-0.300236\pi$
$199$	3296.74	1.17437	0.587184	+	0.809453i	$0.300236\pi$
$200$	860.121	0.304099
$201$	−78.3566	−0.0274967
$202$	917.011	0.319409
$203$	−1266.66	−0.437940
$204$	59.3820	0.0203802
$205$	−1592.42	−0.542533
$206$	−1149.77	−0.388876
$207$	−619.444	−0.207992
$208$	654.182	0.218074
$209$	2175.60	0.720045
$210$	55.5300	0.0182473
$211$	−2436.09	−0.794821	−0.397410	−	0.917641i	$-0.630091\pi$
$211$	−2436.09	−0.794821	−0.397410	+	0.917641i	$0.630091\pi$
$212$	1184.41	0.383706
$213$	226.577	0.0728862
$214$	−2903.51	−0.927477
$215$	252.706	0.0801599
$216$	112.231	0.0353535
$217$	41.4964	0.0129814
$218$	−3625.79	−1.12646
$219$	−232.748	−0.0718157
$220$	3851.02	1.18016
$221$	−2333.45	−0.710250
$222$	84.2080	0.0254580
$223$	1464.12	0.439662	0.219831	−	0.975538i	$-0.429449\pi$
$223$	1464.12	0.439662	0.219831	+	0.975538i	$0.429449\pi$
$224$	−224.000	−0.0668153
$225$	−2895.64	−0.857966
$226$	−3387.57	−0.997070
$227$	−3419.39	−0.999794	−0.499897	−	0.866085i	$-0.666629\pi$
$227$	−3419.39	−0.999794	−0.499897	+	0.866085i	$0.666629\pi$
$228$	−35.8527	−0.0104141
$229$	−3437.40	−0.991922	−0.495961	−	0.868345i	$-0.665184\pi$
$229$	−3437.40	−0.991922	−0.495961	+	0.868345i	$0.665184\pi$
$230$	701.429	0.201091
$231$	114.964	0.0327449
$232$	1447.61	0.409656
$233$	3049.48	0.857415	0.428708	−	0.903443i	$-0.358969\pi$
$233$	3049.48	0.857415	0.428708	+	0.903443i	$0.358969\pi$
$234$	−2202.33	−0.615260
$235$	5089.22	1.41270
$236$	−3222.58	−0.888864
$237$	324.158	0.0888453
$238$	799.004	0.217612
$239$	1961.10	0.530767	0.265383	−	0.964143i	$-0.414501\pi$
$239$	1961.10	0.530767	0.265383	+	0.964143i	$0.414501\pi$
$240$	−63.4628	−0.0170688
$241$	6121.70	1.63624	0.818119	−	0.575049i	$-0.195017\pi$
$241$	6121.70	1.63624	0.818119	+	0.575049i	$0.195017\pi$
$242$	5310.80	1.41071
$243$	−566.983	−0.149679
$244$	2862.41	0.751012
$245$	747.174	0.194838
$246$	54.3295	0.0140810
$247$	1408.86	0.362929
$248$	−47.4244	−0.0121430
$249$	318.369	0.0810273
$250$	−533.233	−0.134898
$251$	4112.95	1.03429	0.517145	−	0.855898i	$-0.326995\pi$
$251$	4112.95	1.03429	0.517145	+	0.855898i	$0.326995\pi$
$252$	754.105	0.188509
$253$	1452.17	0.360859
$254$	503.899	0.124478
$255$	226.371	0.0555917
$256$	256.000	0.0625000
$257$	−2135.52	−0.518328	−0.259164	−	0.965833i	$-0.583447\pi$
$257$	−2135.52	−0.518328	−0.259164	+	0.965833i	$0.583447\pi$
$258$	−8.62170	−0.00208048
$259$	1133.05	0.271830
$260$	2493.81	0.594845
$261$	−4873.43	−1.15578
$262$	−3688.88	−0.869846
$263$	7005.80	1.64257	0.821286	−	0.570517i	$-0.193257\pi$
$263$	7005.80	1.64257	0.821286	+	0.570517i	$0.193257\pi$
$264$	−131.388	−0.0306301
$265$	4515.10	1.04664
$266$	−482.410	−0.111197
$267$	22.4634	0.00514883
$268$	1204.93	0.274637
$269$	6566.34	1.48831	0.744157	−	0.668004i	$-0.232851\pi$
$269$	6566.34	1.48831	0.744157	+	0.668004i	$0.232851\pi$
$270$	427.837	0.0964346
$271$	−5759.43	−1.29100	−0.645499	−	0.763761i	$-0.723351\pi$
$271$	−5759.43	−1.29100	−0.645499	+	0.763761i	$0.723351\pi$
$272$	−913.147	−0.203558
$273$	74.4475	0.0165046
$274$	−2339.87	−0.515900
$275$	6788.29	1.48854
$276$	−23.9310	−0.00521913
$277$	356.886	0.0774123	0.0387061	−	0.999251i	$-0.487676\pi$
$277$	356.886	0.0774123	0.0387061	+	0.999251i	$0.487676\pi$
$278$	−3236.88	−0.698328
$279$	159.656	0.0342594
$280$	−853.913	−0.182254
$281$	−925.745	−0.196531	−0.0982657	−	0.995160i	$-0.531329\pi$
$281$	−925.745	−0.196531	−0.0982657	+	0.995160i	$0.531329\pi$
$282$	−173.632	−0.0366654
$283$	6928.18	1.45526	0.727629	−	0.685971i	$-0.240622\pi$
$283$	6928.18	1.45526	0.727629	+	0.685971i	$0.240622\pi$
$284$	−3484.19	−0.727987
$285$	−136.675	−0.0284067
$286$	5162.96	1.06746
$287$	731.021	0.150351
$288$	−861.835	−0.176334
$289$	−1655.82	−0.337028
$290$	5518.44	1.11743
$291$	−89.4655	−0.0180225
$292$	3579.08	0.717295
$293$	148.190	0.0295472	0.0147736	−	0.999891i	$-0.495297\pi$
$293$	148.190	0.0295472	0.0147736	+	0.999891i	$0.495297\pi$
$294$	−25.4918	−0.00505684
$295$	−12284.8	−2.42458
$296$	−1294.91	−0.254274
$297$	885.755	0.173053
$298$	−3491.27	−0.678670
$299$	940.386	0.181886
$300$	−111.867	−0.0215289
$301$	−116.008	−0.0222145
$302$	−5040.83	−0.960487
$303$	−119.266	−0.0226128
$304$	551.326	0.104016
$305$	10911.8	2.04856
$306$	3074.15	0.574305
$307$	−10096.8	−1.87705	−0.938527	−	0.345207i	$-0.887809\pi$
$307$	−10096.8	−1.87705	−0.938527	+	0.345207i	$0.887809\pi$
$308$	−1767.86	−0.327056
$309$	149.539	0.0275308
$310$	−180.787	−0.0331227
$311$	−1063.81	−0.193965	−0.0969826	−	0.995286i	$-0.530919\pi$
$311$	−1063.81	−0.193965	−0.0969826	+	0.995286i	$0.530919\pi$
$312$	−85.0829	−0.0154387
$313$	1953.88	0.352844	0.176422	−	0.984315i	$-0.443548\pi$
$313$	1953.88	0.352844	0.176422	+	0.984315i	$0.443548\pi$
$314$	2245.11	0.403500
$315$	2874.73	0.514200
$316$	−4984.75	−0.887386
$317$	−2939.51	−0.520819	−0.260409	−	0.965498i	$-0.583858\pi$
$317$	−2939.51	−0.520819	−0.260409	+	0.965498i	$0.583858\pi$
$318$	−154.044	−0.0271647
$319$	11424.9	2.00523
$320$	975.901	0.170483
$321$	377.631	0.0656614
$322$	−322.000	−0.0557278
$323$	−1966.57	−0.338771
$324$	2894.10	0.496244
$325$	4395.90	0.750280
$326$	298.876	0.0507767
$327$	471.570	0.0797488
$328$	−835.452	−0.140641
$329$	−2336.27	−0.391498
$330$	−500.864	−0.0835505
$331$	−8808.46	−1.46271	−0.731354	−	0.681998i	$-0.761111\pi$
$331$	−8808.46	−1.46271	−0.731354	+	0.681998i	$0.761111\pi$
$332$	−4895.72	−0.809300
$333$	4359.37	0.717393
$334$	3901.56	0.639173
$335$	4593.33	0.749135
$336$	29.1334	0.00473024
$337$	3966.73	0.641191	0.320596	−	0.947216i	$-0.396117\pi$
$337$	3966.73	0.641191	0.320596	+	0.947216i	$0.396117\pi$
$338$	−1050.61	−0.169070
$339$	440.587	0.0705883
$340$	−3481.02	−0.555250
$341$	−374.285	−0.0594389
$342$	−1856.06	−0.293463
$343$	−343.000	−0.0539949
$344$	132.580	0.0207798
$345$	−91.2278	−0.0142363
$346$	5701.57	0.885891
$347$	5747.24	0.889129	0.444565	−	0.895747i	$-0.353358\pi$
$347$	5747.24	0.889129	0.444565	+	0.895747i	$0.353358\pi$
$348$	−188.276	−0.0290018
$349$	8367.21	1.28334	0.641671	−	0.766980i	$-0.278241\pi$
$349$	8367.21	1.28334	0.641671	+	0.766980i	$0.278241\pi$
$350$	−1505.21	−0.229877
$351$	573.590	0.0872249
$352$	2020.41	0.305933
$353$	4056.10	0.611571	0.305785	−	0.952100i	$-0.401081\pi$
$353$	4056.10	0.611571	0.305785	+	0.952100i	$0.401081\pi$
$354$	419.128	0.0629278
$355$	−13282.1	−1.98575
$356$	−345.431	−0.0514265
$357$	−103.918	−0.0154060
$358$	3695.23	0.545528
$359$	−2580.13	−0.379315	−0.189658	−	0.981850i	$-0.560738\pi$
$359$	−2580.13	−0.379315	−0.189658	+	0.981850i	$0.560738\pi$
$360$	−3285.41	−0.480990
$361$	−5671.65	−0.826892
$362$	6520.83	0.946761
$363$	−690.722	−0.0998720
$364$	−1144.82	−0.164848
$365$	13643.9	1.95658
$366$	−372.285	−0.0531684
$367$	938.253	0.133451	0.0667254	−	0.997771i	$-0.478745\pi$
$367$	938.253	0.133451	0.0667254	+	0.997771i	$0.478745\pi$
$368$	368.000	0.0521286
$369$	2812.59	0.396795
$370$	−4936.34	−0.693590
$371$	−2072.72	−0.290054
$372$	6.16802	0.000859669 0
$373$	10951.6	1.52025	0.760125	−	0.649777i	$-0.225138\pi$
$373$	10951.6	1.52025	0.760125	+	0.649777i	$0.225138\pi$
$374$	−7206.78	−0.996401
$375$	69.3522	0.00955023
$376$	2670.03	0.366213
$377$	7398.42	1.01071
$378$	−196.404	−0.0267247
$379$	9520.76	1.29037	0.645183	−	0.764028i	$-0.276781\pi$
$379$	9520.76	1.29037	0.645183	+	0.764028i	$0.276781\pi$
$380$	2101.72	0.283726
$381$	−65.5371	−0.00881252
$382$	3232.26	0.432924
$383$	−3099.25	−0.413484	−0.206742	−	0.978396i	$-0.566286\pi$
$383$	−3099.25	−0.413484	−0.206742	+	0.978396i	$0.566286\pi$
$384$	−33.2954	−0.00442473
$385$	−6739.29	−0.892119
$386$	−9493.74	−1.25186
$387$	−446.337	−0.0586269
$388$	1375.76	0.180009
$389$	4368.35	0.569368	0.284684	−	0.958621i	$-0.408111\pi$
$389$	4368.35	0.569368	0.284684	+	0.958621i	$0.408111\pi$
$390$	−324.345	−0.0421125
$391$	−1312.65	−0.169779
$392$	392.000	0.0505076
$393$	479.775	0.0615813
$394$	−2943.54	−0.376379
$395$	−19002.4	−2.42054
$396$	−6801.81	−0.863141
$397$	6306.06	0.797210	0.398605	−	0.917123i	$-0.369495\pi$
$397$	6306.06	0.797210	0.398605	+	0.917123i	$0.369495\pi$
$398$	6593.47	0.830404
$399$	62.7423	0.00787229
$400$	1720.24	0.215030
$401$	−83.0874	−0.0103471	−0.00517355	−	0.999987i	$-0.501647\pi$
$401$	−83.0874	−0.0103471	−0.00517355	+	0.999987i	$0.501647\pi$
$402$	−156.713	−0.0194431
$403$	−242.376	−0.0299594
$404$	1834.02	0.225856
$405$	11032.6	1.35362
$406$	−2533.31	−0.309671
$407$	−10219.7	−1.24465
$408$	118.764	0.0144110
$409$	1594.33	0.192750	0.0963749	−	0.995345i	$-0.469275\pi$
$409$	1594.33	0.192750	0.0963749	+	0.995345i	$0.469275\pi$
$410$	−3184.84	−0.383629
$411$	304.323	0.0365235
$412$	−2299.55	−0.274977
$413$	5639.51	0.671918
$414$	−1238.89	−0.147072
$415$	−18663.0	−2.20755
$416$	1308.36	0.154201
$417$	420.988	0.0494386
$418$	4351.20	0.509149
$419$	−3260.67	−0.380177	−0.190089	−	0.981767i	$-0.560878\pi$
$419$	−3260.67	−0.380177	−0.190089	+	0.981767i	$0.560878\pi$
$420$	111.060	0.0129028
$421$	−7104.66	−0.822471	−0.411235	−	0.911529i	$-0.634903\pi$
$421$	−7104.66	−0.822471	−0.411235	+	0.911529i	$0.634903\pi$
$422$	−4872.18	−0.562023
$423$	−8988.76	−1.03321
$424$	2368.82	0.271321
$425$	−6136.08	−0.700337
$426$	453.153	0.0515384
$427$	−5009.22	−0.567712
$428$	−5807.02	−0.655825
$429$	−671.495	−0.0755712
$430$	505.411	0.0566816
$431$	10760.4	1.20258	0.601290	−	0.799031i	$-0.294654\pi$
$431$	10760.4	1.20258	0.601290	+	0.799031i	$0.294654\pi$
$432$	224.462	0.0249987
$433$	−11537.4	−1.28049	−0.640245	−	0.768171i	$-0.721167\pi$
$433$	−11537.4	−1.28049	−0.640245	+	0.768171i	$0.721167\pi$
$434$	82.9927	0.00917921
$435$	−717.729	−0.0791091
$436$	−7251.57	−0.796530
$437$	792.532	0.0867550
$438$	−465.496	−0.0507814
$439$	−10785.2	−1.17255	−0.586277	−	0.810111i	$-0.699407\pi$
$439$	−10785.2	−1.17255	−0.586277	+	0.810111i	$0.699407\pi$
$440$	7702.05	0.834501
$441$	−1319.68	−0.142499
$442$	−4666.91	−0.502222
$443$	2483.46	0.266349	0.133175	−	0.991093i	$-0.457483\pi$
$443$	2483.46	0.266349	0.133175	+	0.991093i	$0.457483\pi$
$444$	168.416	0.0180015
$445$	−1316.82	−0.140277
$446$	2928.24	0.310888
$447$	454.074	0.0480469
$448$	−448.000	−0.0472456
$449$	−3010.79	−0.316454	−0.158227	−	0.987403i	$-0.550578\pi$
$449$	−3010.79	−0.316454	−0.158227	+	0.987403i	$0.550578\pi$
$450$	−5791.27	−0.606674
$451$	−6593.59	−0.688426
$452$	−6775.14	−0.705035
$453$	655.610	0.0679983
$454$	−6838.79	−0.706961
$455$	−4364.17	−0.449661
$456$	−71.7055	−0.00736385
$457$	−12906.5	−1.32110	−0.660549	−	0.750783i	$-0.729677\pi$
$457$	−12906.5	−1.32110	−0.660549	+	0.750783i	$0.729677\pi$
$458$	−6874.81	−0.701395
$459$	−800.652	−0.0814188
$460$	1402.86	0.142193
$461$	1928.01	0.194786	0.0973931	−	0.995246i	$-0.468950\pi$
$461$	1928.01	0.194786	0.0973931	+	0.995246i	$0.468950\pi$
$462$	229.928	0.0231542
$463$	2880.38	0.289121	0.144560	−	0.989496i	$-0.453823\pi$
$463$	2880.38	0.289121	0.144560	+	0.989496i	$0.453823\pi$
$464$	2895.22	0.289670
$465$	23.5132	0.00234494
$466$	6098.95	0.606284
$467$	6861.47	0.679895	0.339947	−	0.940444i	$-0.389591\pi$
$467$	6861.47	0.679895	0.339947	+	0.940444i	$0.389591\pi$
$468$	−4404.66	−0.435055
$469$	−2108.63	−0.207606
$470$	10178.4	0.998929
$471$	−291.999	−0.0285661
$472$	−6445.16	−0.628522
$473$	1046.36	0.101716
$474$	648.316	0.0628231
$475$	3704.75	0.357864
$476$	1598.01	0.153875
$477$	−7974.73	−0.765488
$478$	3922.21	0.375309
$479$	−4580.05	−0.436885	−0.218443	−	0.975850i	$-0.570098\pi$
$479$	−4580.05	−0.436885	−0.218443	+	0.975850i	$0.570098\pi$
$480$	−126.926	−0.0120695
$481$	−6618.02	−0.627351
$482$	12243.4	1.15700
$483$	41.8793	0.00394529
$484$	10621.6	0.997521
$485$	5244.54	0.491015
$486$	−1133.97	−0.105839
$487$	8844.29	0.822943	0.411471	−	0.911423i	$-0.365015\pi$
$487$	8844.29	0.822943	0.411471	+	0.911423i	$0.365015\pi$
$488$	5724.82	0.531046
$489$	−38.8718	−0.00359477
$490$	1494.35	0.137771
$491$	−4687.22	−0.430817	−0.215408	−	0.976524i	$-0.569108\pi$
$491$	−4687.22	−0.430817	−0.215408	+	0.976524i	$0.569108\pi$
$492$	108.659	0.00995675
$493$	−10327.2	−0.943434
$494$	2817.72	0.256630
$495$	−25929.3	−2.35441
$496$	−94.8488	−0.00858637
$497$	6097.32	0.550307
$498$	636.738	0.0572950
$499$	−10245.1	−0.919107	−0.459553	−	0.888150i	$-0.651991\pi$
$499$	−10245.1	−0.919107	−0.459553	+	0.888150i	$0.651991\pi$
$500$	−1066.47	−0.0953876
$501$	−507.436	−0.0452507
$502$	8225.89	0.731354
$503$	−10020.9	−0.888286	−0.444143	−	0.895956i	$-0.646492\pi$
$503$	−10020.9	−0.888286	−0.444143	+	0.895956i	$0.646492\pi$
$504$	1508.21	0.133296
$505$	6991.50	0.616074
$506$	2904.35	0.255166
$507$	136.643	0.0119694
$508$	1007.80	0.0880194
$509$	−15666.6	−1.36427	−0.682133	−	0.731228i	$-0.738947\pi$
$509$	−15666.6	−1.36427	−0.682133	+	0.731228i	$0.738947\pi$
$510$	452.741	0.0393093
$511$	−6263.40	−0.542224
$512$	512.000	0.0441942
$513$	483.406	0.0416041
$514$	−4271.05	−0.366513
$515$	−8766.13	−0.750062
$516$	−17.2434	−0.00147112
$517$	21072.5	1.79259
$518$	2266.09	0.192213
$519$	−741.546	−0.0627173
$520$	4987.63	0.420619
$521$	12571.8	1.05716	0.528581	−	0.848883i	$-0.322724\pi$
$521$	12571.8	1.05716	0.528581	+	0.848883i	$0.322724\pi$
$522$	−9746.86	−0.817258
$523$	12266.4	1.02557	0.512785	−	0.858517i	$-0.328614\pi$
$523$	12266.4	1.02557	0.512785	+	0.858517i	$0.328614\pi$
$524$	−7377.76	−0.615074
$525$	195.768	0.0162743
$526$	14011.6	1.16147
$527$	338.324	0.0279651
$528$	−262.775	−0.0216587
$529$	529.000	0.0434783
$530$	9030.21	0.740089
$531$	21697.9	1.77327
$532$	−964.821	−0.0786284
$533$	−4269.83	−0.346992
$534$	44.9268	0.00364077
$535$	−22137.0	−1.78891
$536$	2409.86	0.194198
$537$	−480.602	−0.0386210
$538$	13132.7	1.05240
$539$	3093.76	0.247231
$540$	855.675	0.0681896
$541$	−17141.8	−1.36226	−0.681131	−	0.732161i	$-0.738512\pi$
$541$	−17141.8	−1.36226	−0.681131	+	0.732161i	$0.738512\pi$
$542$	−11518.9	−0.912874
$543$	−848.100	−0.0670266
$544$	−1826.29	−0.143937
$545$	−27643.8	−2.17272
$546$	148.895	0.0116705
$547$	−13619.5	−1.06459	−0.532294	−	0.846560i	$-0.678670\pi$
$547$	−13619.5	−1.06459	−0.532294	+	0.846560i	$0.678670\pi$
$548$	−4679.73	−0.364796
$549$	−19272.8	−1.49826
$550$	13576.6	1.05256
$551$	6235.19	0.482083
$552$	−47.8621	−0.00369048
$553$	8723.31	0.670801
$554$	713.772	0.0547387
$555$	642.021	0.0491032
$556$	−6473.76	−0.493792
$557$	−14755.1	−1.12243	−0.561214	−	0.827671i	$-0.689666\pi$
$557$	−14755.1	−1.12243	−0.561214	+	0.827671i	$0.689666\pi$
$558$	319.313	0.0242251
$559$	677.591	0.0512684
$560$	−1707.83	−0.128873
$561$	937.314	0.0705409
$562$	−1851.49	−0.138969
$563$	21018.7	1.57341	0.786706	−	0.617327i	$-0.211785\pi$
$563$	21018.7	1.57341	0.786706	+	0.617327i	$0.211785\pi$
$564$	−347.264	−0.0259263
$565$	−25827.6	−1.92314
$566$	13856.4	1.02902
$567$	−5064.67	−0.375125
$568$	−6968.37	−0.514765
$569$	13750.9	1.01313	0.506563	−	0.862203i	$-0.330916\pi$
$569$	13750.9	1.01313	0.506563	+	0.862203i	$0.330916\pi$
$570$	−273.349	−0.0200866
$571$	10636.3	0.779535	0.389768	−	0.920913i	$-0.372555\pi$
$571$	10636.3	0.779535	0.389768	+	0.920913i	$0.372555\pi$
$572$	10325.9	0.754805
$573$	−420.388	−0.0306491
$574$	1462.04	0.106314
$575$	2472.85	0.179348
$576$	−1723.67	−0.124687
$577$	7290.64	0.526019	0.263010	−	0.964793i	$-0.415285\pi$
$577$	7290.64	0.526019	0.263010	+	0.964793i	$0.415285\pi$
$578$	−3311.64	−0.238315
$579$	1234.76	0.0886264
$580$	11036.9	0.790141
$581$	8567.52	0.611774
$582$	−178.931	−0.0127439
$583$	18695.3	1.32810
$584$	7158.17	0.507204
$585$	−16791.1	−1.18671
$586$	296.379	0.0208930
$587$	−6315.96	−0.444102	−0.222051	−	0.975035i	$-0.571275\pi$
$587$	−6315.96	−0.444102	−0.222051	+	0.975035i	$0.571275\pi$
$588$	−50.9835	−0.00357572
$589$	−204.268	−0.0142899
$590$	−24569.7	−1.71444
$591$	382.836	0.0266460
$592$	−2589.82	−0.179799
$593$	19795.1	1.37081	0.685403	−	0.728164i	$-0.259626\pi$
$593$	19795.1	1.37081	0.685403	+	0.728164i	$0.259626\pi$
$594$	1771.51	0.122367
$595$	6091.79	0.419729
$596$	−6982.54	−0.479892
$597$	−857.547	−0.0587890
$598$	1880.77	0.128613
$599$	27201.1	1.85544	0.927720	−	0.373277i	$-0.121766\pi$
$599$	27201.1	1.85544	0.927720	+	0.373277i	$0.121766\pi$
$600$	−223.735	−0.0152232
$601$	11695.1	0.793763	0.396882	−	0.917870i	$-0.370092\pi$
$601$	11695.1	0.793763	0.396882	+	0.917870i	$0.370092\pi$
$602$	−232.016	−0.0157081
$603$	−8112.89	−0.547898
$604$	−10081.7	−0.679167
$605$	40490.7	2.72096
$606$	−238.533	−0.0159897
$607$	−4523.78	−0.302495	−0.151247	−	0.988496i	$-0.548329\pi$
$607$	−4523.78	−0.302495	−0.151247	+	0.988496i	$0.548329\pi$
$608$	1102.65	0.0735501
$609$	329.483	0.0219233
$610$	21823.7	1.44855
$611$	13646.0	0.903530
$612$	6148.30	0.406095
$613$	27979.4	1.84352	0.921758	−	0.387765i	$-0.126753\pi$
$613$	27979.4	1.84352	0.921758	+	0.387765i	$0.126753\pi$
$614$	−20193.6	−1.32728
$615$	414.220	0.0271593
$616$	−3535.72	−0.231264
$617$	27419.8	1.78911	0.894553	−	0.446961i	$-0.147494\pi$
$617$	27419.8	1.78911	0.894553	+	0.446961i	$0.147494\pi$
$618$	299.079	0.0194672
$619$	4941.83	0.320887	0.160443	−	0.987045i	$-0.448708\pi$
$619$	4941.83	0.320887	0.160443	+	0.987045i	$0.448708\pi$
$620$	−361.574	−0.0234213
$621$	322.664	0.0208504
$622$	−2127.62	−0.137154
$623$	604.505	0.0388748
$624$	−170.166	−0.0109168
$625$	−17504.9	−1.12031
$626$	3907.77	0.249498
$627$	−565.917	−0.0360455
$628$	4490.22	0.285318
$629$	9237.84	0.585591
$630$	5749.47	0.363594
$631$	−13077.3	−0.825037	−0.412519	−	0.910949i	$-0.635351\pi$
$631$	−13077.3	−0.825037	−0.412519	+	0.910949i	$0.635351\pi$
$632$	−9969.49	−0.627477
$633$	633.675	0.0397888
$634$	−5879.03	−0.368274
$635$	3841.84	0.240093
$636$	−308.089	−0.0192084
$637$	2003.43	0.124614
$638$	22849.7	1.41792
$639$	23459.3	1.45233
$640$	1951.80	0.120550
$641$	−1272.72	−0.0784235	−0.0392117	−	0.999231i	$-0.512485\pi$
$641$	−1272.72	−0.0784235	−0.0392117	+	0.999231i	$0.512485\pi$
$642$	755.262	0.0464296
$643$	113.036	0.00693269	0.00346634	−	0.999994i	$-0.498897\pi$
$643$	113.036	0.00693269	0.00346634	+	0.999994i	$0.498897\pi$
$644$	−644.000	−0.0394055
$645$	−65.7338	−0.00401281
$646$	−3933.14	−0.239547
$647$	−1829.78	−0.111184	−0.0555919	−	0.998454i	$-0.517705\pi$
$647$	−1829.78	−0.111184	−0.0555919	+	0.998454i	$0.517705\pi$
$648$	5788.19	0.350898
$649$	−50866.7	−3.07657
$650$	8791.81	0.530528
$651$	−10.7940	−0.000649849 0
$652$	597.751	0.0359045
$653$	1936.86	0.116072	0.0580361	−	0.998314i	$-0.481516\pi$
$653$	1936.86	0.116072	0.0580361	+	0.998314i	$0.481516\pi$
$654$	943.139	0.0563909
$655$	−28124.8	−1.67775
$656$	−1670.90	−0.0994480
$657$	−24098.3	−1.43099
$658$	−4672.55	−0.276831
$659$	−22889.3	−1.35302	−0.676509	−	0.736434i	$-0.736508\pi$
$659$	−22889.3	−1.35302	−0.676509	+	0.736434i	$0.736508\pi$
$660$	−1001.73	−0.0590791
$661$	17818.0	1.04847	0.524237	−	0.851573i	$-0.324351\pi$
$661$	17818.0	1.04847	0.524237	+	0.851573i	$0.324351\pi$
$662$	−17616.9	−1.03429
$663$	606.978	0.0355552
$664$	−9791.45	−0.572262
$665$	−3678.01	−0.214477
$666$	8718.74	0.507274
$667$	4161.87	0.241602
$668$	7803.11	0.451963
$669$	−380.847	−0.0220095
$670$	9186.65	0.529718
$671$	45181.7	2.59943
$672$	58.2669	0.00334478
$673$	20993.6	1.20244	0.601222	−	0.799082i	$-0.294681\pi$
$673$	20993.6	1.20244	0.601222	+	0.799082i	$0.294681\pi$
$674$	7933.46	0.453391
$675$	1508.32	0.0860076
$676$	−2101.22	−0.119551
$677$	5364.75	0.304555	0.152278	−	0.988338i	$-0.451339\pi$
$677$	5364.75	0.304555	0.152278	+	0.988338i	$0.451339\pi$
$678$	881.175	0.0499134
$679$	−2407.57	−0.136074
$680$	−6962.04	−0.392621
$681$	889.453	0.0500498
$682$	−748.570	−0.0420297
$683$	−31720.5	−1.77709	−0.888543	−	0.458793i	$-0.848282\pi$
$683$	−31720.5	−1.77709	−0.888543	+	0.458793i	$0.848282\pi$
$684$	−3712.13	−0.207510
$685$	−17839.7	−0.995063
$686$	−686.000	−0.0381802
$687$	894.138	0.0496557
$688$	265.161	0.0146935
$689$	12106.6	0.669409
$690$	−182.456	−0.0100666
$691$	−12501.1	−0.688228	−0.344114	−	0.938928i	$-0.611821\pi$
$691$	−12501.1	−0.688228	−0.344114	+	0.938928i	$0.611821\pi$
$692$	11403.1	0.626420
$693$	11903.2	0.652473
$694$	11494.5	0.628709
$695$	−24678.7	−1.34693
$696$	−376.552	−0.0205074
$697$	5960.09	0.323894
$698$	16734.4	0.907460
$699$	−793.230	−0.0429223
$700$	−3010.43	−0.162548
$701$	−4917.13	−0.264932	−0.132466	−	0.991188i	$-0.542290\pi$
$701$	−4917.13	−0.264932	−0.132466	+	0.991188i	$0.542290\pi$
$702$	1147.18	0.0616773
$703$	−5577.48	−0.299230
$704$	4040.83	0.216327
$705$	−1323.81	−0.0707199
$706$	8112.20	0.432446
$707$	−3209.54	−0.170731
$708$	838.257	0.0444966
$709$	2043.21	0.108229	0.0541145	−	0.998535i	$-0.482766\pi$
$709$	2043.21	0.108229	0.0541145	+	0.998535i	$0.482766\pi$
$710$	−26564.2	−1.40414
$711$	33562.7	1.77032
$712$	−690.863	−0.0363640
$713$	−136.345	−0.00716153
$714$	−207.837	−0.0108937
$715$	39363.6	2.05890
$716$	7390.46	0.385747
$717$	−510.122	−0.0265703
$718$	−5160.27	−0.268216
$719$	24690.8	1.28069	0.640343	−	0.768089i	$-0.278792\pi$
$719$	24690.8	1.28069	0.640343	+	0.768089i	$0.278792\pi$
$720$	−6570.82	−0.340111
$721$	4024.21	0.207863
$722$	−11343.3	−0.584701
$723$	−1592.38	−0.0819103
$724$	13041.7	0.669461
$725$	19455.0	0.996606
$726$	−1381.44	−0.0706202
$727$	−23243.0	−1.18574	−0.592872	−	0.805297i	$-0.702006\pi$
$727$	−23243.0	−1.18574	−0.592872	+	0.805297i	$0.702006\pi$
$728$	−2289.64	−0.116565
$729$	−19387.7	−0.984995
$730$	27287.7	1.38351
$731$	−945.823	−0.0478557
$732$	−744.570	−0.0375958
$733$	−35315.4	−1.77954	−0.889772	−	0.456406i	$-0.849137\pi$
$733$	−35315.4	−1.77954	−0.889772	+	0.456406i	$0.849137\pi$
$734$	1876.51	0.0943639
$735$	−194.355	−0.00975359
$736$	736.000	0.0368605
$737$	19019.2	0.950585
$738$	5625.17	0.280576
$739$	10783.2	0.536763	0.268382	−	0.963313i	$-0.413511\pi$
$739$	10783.2	0.536763	0.268382	+	0.963313i	$0.413511\pi$
$740$	−9872.69	−0.490442
$741$	−366.472	−0.0181683
$742$	−4145.44	−0.205099
$743$	−4972.73	−0.245534	−0.122767	−	0.992436i	$-0.539177\pi$
$743$	−4972.73	−0.245534	−0.122767	+	0.992436i	$0.539177\pi$
$744$	12.3360	0.000607878 0
$745$	−26618.2	−1.30901
$746$	21903.2	1.07498
$747$	32963.3	1.61454
$748$	−14413.6	−0.704562
$749$	10162.3	0.495757
$750$	138.704	0.00675303
$751$	−29604.7	−1.43847	−0.719234	−	0.694768i	$-0.755507\pi$
$751$	−29604.7	−1.43847	−0.719234	+	0.694768i	$0.755507\pi$
$752$	5340.06	0.258952
$753$	−1069.86	−0.0517767
$754$	14796.8	0.714681
$755$	−38432.4	−1.85258
$756$	−392.809	−0.0188972
$757$	−9958.05	−0.478113	−0.239056	−	0.971006i	$-0.576838\pi$
$757$	−9958.05	−0.478113	−0.239056	+	0.971006i	$0.576838\pi$
$758$	19041.5	0.912426
$759$	−377.739	−0.0180646
$760$	4203.44	0.200625
$761$	28654.4	1.36494	0.682472	−	0.730911i	$-0.260905\pi$
$761$	28654.4	1.36494	0.682472	+	0.730911i	$0.260905\pi$
$762$	−131.074	−0.00623139
$763$	12690.2	0.602120
$764$	6464.52	0.306123
$765$	23438.0	1.10772
$766$	−6198.50	−0.292377
$767$	−32939.9	−1.55070
$768$	−66.5907	−0.00312876
$769$	1580.21	0.0741011	0.0370506	−	0.999313i	$-0.488204\pi$
$769$	1580.21	0.0741011	0.0370506	+	0.999313i	$0.488204\pi$
$770$	−13478.6	−0.630824
$771$	555.493	0.0259476
$772$	−18987.5	−0.885200
$773$	36297.7	1.68892	0.844461	−	0.535617i	$-0.179921\pi$
$773$	36297.7	1.68892	0.844461	+	0.535617i	$0.179921\pi$
$774$	−892.675	−0.0414555
$775$	−637.356	−0.0295413
$776$	2751.51	0.127286
$777$	−294.728	−0.0136079
$778$	8736.69	0.402604
$779$	−3598.49	−0.165506
$780$	−648.691	−0.0297780
$781$	−54996.1	−2.51974
$782$	−2625.30	−0.120052
$783$	2538.54	0.115862
$784$	784.000	0.0357143
$785$	17117.2	0.778268
$786$	959.551	0.0435446
$787$	3840.61	0.173956	0.0869778	−	0.996210i	$-0.472279\pi$
$787$	3840.61	0.173956	0.0869778	+	0.996210i	$0.472279\pi$
$788$	−5887.07	−0.266140
$789$	−1822.35	−0.0822273
$790$	−38004.8	−1.71158
$791$	11856.5	0.532956
$792$	−13603.6	−0.610333
$793$	29258.4	1.31021
$794$	12612.1	0.563712
$795$	−1174.47	−0.0523951
$796$	13186.9	0.587184
$797$	−24193.7	−1.07526	−0.537632	−	0.843179i	$-0.680681\pi$
$797$	−24193.7	−1.07526	−0.537632	+	0.843179i	$0.680681\pi$
$798$	125.485	0.00556655
$799$	−19047.9	−0.843386
$800$	3440.49	0.152049
$801$	2325.82	0.102595
$802$	−166.175	−0.00731650
$803$	56494.0	2.48273
$804$	−313.426	−0.0137484
$805$	−2455.00	−0.107487
$806$	−484.753	−0.0211845
$807$	−1708.04	−0.0745052
$808$	3668.04	0.159705
$809$	−16476.8	−0.716063	−0.358031	−	0.933710i	$-0.616552\pi$
$809$	−16476.8	−0.716063	−0.358031	+	0.933710i	$0.616552\pi$
$810$	22065.2	0.957152
$811$	2891.58	0.125200	0.0625999	−	0.998039i	$-0.480061\pi$
$811$	2891.58	0.125200	0.0625999	+	0.998039i	$0.480061\pi$
$812$	−5066.63	−0.218970
$813$	1498.14	0.0646275
$814$	−20439.5	−0.880103
$815$	2278.70	0.0979377
$816$	237.528	0.0101901
$817$	571.055	0.0244537
$818$	3188.66	0.136295
$819$	7708.16	0.328870
$820$	−6369.68	−0.271267
$821$	36315.1	1.54373	0.771867	−	0.635785i	$-0.219323\pi$
$821$	36315.1	1.54373	0.771867	+	0.635785i	$0.219323\pi$
$822$	608.646	0.0258260
$823$	−18744.4	−0.793913	−0.396956	−	0.917838i	$-0.629934\pi$
$823$	−18744.4	−0.793913	−0.396956	+	0.917838i	$0.629934\pi$
$824$	−4599.09	−0.194438
$825$	−1765.77	−0.0745166
$826$	11279.0	0.475118
$827$	25294.4	1.06357	0.531784	−	0.846880i	$-0.321522\pi$
$827$	25294.4	1.06357	0.531784	+	0.846880i	$0.321522\pi$
$828$	−2477.78	−0.103996
$829$	−39438.4	−1.65230	−0.826148	−	0.563453i	$-0.809473\pi$
$829$	−39438.4	−1.65230	−0.826148	+	0.563453i	$0.809473\pi$
$830$	−37326.1	−1.56097
$831$	−92.8332	−0.00387527
$832$	2616.73	0.109037
$833$	−2796.51	−0.116319
$834$	841.977	0.0349584
$835$	29746.3	1.23283
$836$	8702.40	0.360023
$837$	−83.1639	−0.00343437
$838$	−6521.34	−0.268826
$839$	−30165.0	−1.24125	−0.620627	−	0.784106i	$-0.713122\pi$
$839$	−30165.0	−1.24125	−0.620627	+	0.784106i	$0.713122\pi$
$840$	222.120	0.00912365
$841$	8354.24	0.342541
$842$	−14209.3	−0.581574
$843$	240.805	0.00983838
$844$	−9744.35	−0.397410
$845$	−8010.10	−0.326101
$846$	−17977.5	−0.730591
$847$	−18587.8	−0.754055
$848$	4737.64	0.191853
$849$	−1802.16	−0.0728503
$850$	−12272.2	−0.495213
$851$	−3722.87	−0.149963
$852$	906.306	0.0364431
$853$	8977.27	0.360347	0.180173	−	0.983635i	$-0.442334\pi$
$853$	8977.27	0.360347	0.180173	+	0.983635i	$0.442334\pi$
$854$	−10018.4	−0.401433
$855$	−14151.0	−0.566030
$856$	−11614.0	−0.463738
$857$	−40593.6	−1.61803	−0.809015	−	0.587789i	$-0.799999\pi$
$857$	−40593.6	−1.61803	−0.809015	+	0.587789i	$0.799999\pi$
$858$	−1342.99	−0.0534369
$859$	−14117.7	−0.560755	−0.280377	−	0.959890i	$-0.590460\pi$
$859$	−14117.7	−0.560755	−0.280377	+	0.959890i	$0.590460\pi$
$860$	1010.82	0.0400799
$861$	−190.153	−0.00752660
$862$	21520.9	0.850352
$863$	−7080.02	−0.279266	−0.139633	−	0.990203i	$-0.544592\pi$
$863$	−7080.02	−0.279266	−0.139633	+	0.990203i	$0.544592\pi$
$864$	448.924	0.0176767
$865$	43470.1	1.70870
$866$	−23074.8	−0.905443
$867$	430.712	0.0168717
$868$	165.985	0.00649068
$869$	−78681.7	−3.07145
$870$	−1435.46	−0.0559386
$871$	12316.3	0.479129
$872$	−14503.1	−0.563232
$873$	−9263.09	−0.359116
$874$	1585.06	0.0613450
$875$	1866.31	0.0721062
$876$	−930.991	−0.0359079
$877$	−29775.4	−1.14646	−0.573229	−	0.819395i	$-0.694309\pi$
$877$	−29775.4	−1.14646	−0.573229	+	0.819395i	$0.694309\pi$
$878$	−21570.5	−0.829120
$879$	−38.5471	−0.00147914
$880$	15404.1	0.590082
$881$	32974.9	1.26101	0.630506	−	0.776184i	$-0.282847\pi$
$881$	32974.9	1.26101	0.630506	+	0.776184i	$0.282847\pi$
$882$	−2639.37	−0.100762
$883$	−8286.80	−0.315825	−0.157912	−	0.987453i	$-0.550476\pi$
$883$	−8286.80	−0.315825	−0.157912	+	0.987453i	$0.550476\pi$
$884$	−9333.82	−0.355125
$885$	3195.53	0.121375
$886$	4966.91	0.188337
$887$	−13354.7	−0.505533	−0.252767	−	0.967527i	$-0.581341\pi$
$887$	−13354.7	−0.505533	−0.252767	+	0.967527i	$0.581341\pi$
$888$	336.832	0.0127290
$889$	−1763.65	−0.0665364
$890$	−2633.65	−0.0991911
$891$	45681.8	1.71762
$892$	5856.48	0.219831
$893$	11500.4	0.430960
$894$	908.149	0.0339743
$895$	28173.3	1.05221
$896$	−896.000	−0.0334077
$897$	−244.613	−0.00910524
$898$	−6021.57	−0.223767
$899$	−1072.69	−0.0397954
$900$	−11582.5	−0.428983
$901$	−16899.1	−0.624850
$902$	−13187.2	−0.486791
$903$	30.1759	0.00111206
$904$	−13550.3	−0.498535
$905$	49716.3	1.82611
$906$	1311.22	0.0480821
$907$	53901.6	1.97329	0.986645	−	0.162885i	$-0.0520801\pi$
$907$	53901.6	1.97329	0.986645	+	0.162885i	$0.0520801\pi$
$908$	−13677.6	−0.499897
$909$	−12348.6	−0.450581
$910$	−8728.35	−0.317958
$911$	−14861.5	−0.540488	−0.270244	−	0.962792i	$-0.587104\pi$
$911$	−14861.5	−0.540488	−0.270244	+	0.962792i	$0.587104\pi$
$912$	−143.411	−0.00520703
$913$	−77276.5	−2.80118
$914$	−25813.1	−0.934158
$915$	−2838.38	−0.102551
$916$	−13749.6	−0.495961
$917$	12911.1	0.464952
$918$	−1601.30	−0.0575718
$919$	39976.2	1.43492	0.717460	−	0.696599i	$-0.245304\pi$
$919$	39976.2	1.43492	0.717460	+	0.696599i	$0.245304\pi$
$920$	2805.71	0.100545
$921$	2626.38	0.0939655
$922$	3856.02	0.137735
$923$	−35613.9	−1.27004
$924$	459.856	0.0163725
$925$	−17402.8	−0.618596
$926$	5760.77	0.204439
$927$	15483.0	0.548576
$928$	5790.43	0.204828
$929$	−7480.52	−0.264185	−0.132093	−	0.991237i	$-0.542170\pi$
$929$	−7480.52	−0.264185	−0.132093	+	0.991237i	$0.542170\pi$
$930$	47.0264	0.00165812
$931$	1688.44	0.0594375
$932$	12197.9	0.428708
$933$	276.718	0.00970992
$934$	13722.9	0.480758
$935$	−54946.1	−1.92185
$936$	−8809.32	−0.307630
$937$	−18057.0	−0.629558	−0.314779	−	0.949165i	$-0.601930\pi$
$937$	−18057.0	−0.629558	−0.314779	+	0.949165i	$0.601930\pi$
$938$	−4217.25	−0.146800
$939$	−508.244	−0.0176634
$940$	20356.9	0.706350
$941$	−18921.5	−0.655496	−0.327748	−	0.944765i	$-0.606290\pi$
$941$	−18921.5	−0.655496	−0.327748	+	0.944765i	$0.606290\pi$
$942$	−583.999	−0.0201993
$943$	−2401.93	−0.0829453
$944$	−12890.3	−0.444432
$945$	−1497.43	−0.0515465
$946$	2092.71	0.0719238
$947$	−10147.2	−0.348193	−0.174097	−	0.984729i	$-0.555701\pi$
$947$	−10147.2	−0.348193	−0.174097	+	0.984729i	$0.555701\pi$
$948$	1296.63	0.0444226
$949$	36583.9	1.25139
$950$	7409.49	0.253048
$951$	764.626	0.0260722
$952$	3196.02	0.108806
$953$	6284.28	0.213607	0.106804	−	0.994280i	$-0.465938\pi$
$953$	6284.28	0.213607	0.106804	+	0.994280i	$0.465938\pi$
$954$	−15949.5	−0.541282
$955$	24643.5	0.835020
$956$	7844.42	0.265383
$957$	−2971.84	−0.100382
$958$	−9160.11	−0.308925
$959$	8189.53	0.275760
$960$	−253.851	−0.00853439
$961$	−29755.9	−0.998820
$962$	−13236.0	−0.443604
$963$	39099.2	1.30836
$964$	24486.8	0.818119
$965$	−72382.4	−2.41458
$966$	83.7586	0.00278974
$967$	−10750.9	−0.357524	−0.178762	−	0.983892i	$-0.557209\pi$
$967$	−10750.9	−0.357524	−0.178762	+	0.983892i	$0.557209\pi$
$968$	21243.2	0.705354
$969$	511.544	0.0169589
$970$	10489.1	0.347200
$971$	21337.3	0.705198	0.352599	−	0.935774i	$-0.385298\pi$
$971$	21337.3	0.705198	0.352599	+	0.935774i	$0.385298\pi$
$972$	−2267.93	−0.0748394
$973$	11329.1	0.373272
$974$	17688.6	0.581908
$975$	−1143.46	−0.0375591
$976$	11449.6	0.375506
$977$	−713.051	−0.0233496	−0.0116748	−	0.999932i	$-0.503716\pi$
$977$	−713.051	−0.0233496	−0.0116748	+	0.999932i	$0.503716\pi$
$978$	−77.7435	−0.00254189
$979$	−5452.46	−0.177999
$980$	2988.70	0.0974188
$981$	48825.4	1.58907
$982$	−9374.43	−0.304634
$983$	31306.7	1.01580	0.507898	−	0.861417i	$-0.330423\pi$
$983$	31306.7	1.01580	0.507898	+	0.861417i	$0.330423\pi$
$984$	217.318	0.00704049
$985$	−22442.2	−0.725956
$986$	−20654.4	−0.667108
$987$	607.712	0.0195985
$988$	5635.43	0.181465
$989$	381.168	0.0122553
$990$	−51858.5	−1.66482
$991$	13538.1	0.433956	0.216978	−	0.976176i	$-0.430380\pi$
$991$	13538.1	0.433956	0.216978	+	0.976176i	$0.430380\pi$
$992$	−189.698	−0.00607148
$993$	2291.26	0.0732234
$994$	12194.6	0.389125
$995$	50270.1	1.60168
$996$	1273.48	0.0405137
$997$	44983.5	1.42893	0.714464	−	0.699672i	$-0.246671\pi$
$997$	44983.5	1.42893	0.714464	+	0.699672i	$0.246671\pi$
$998$	−20490.2	−0.649907
$999$	−2270.77	−0.0719158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.a.h.1.3	✓	5
7.6	odd	2		2254.4.a.l.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.a.h.1.3	✓	5	1.1	even	1	trivial
2254.4.a.l.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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -0.260120 q^{3} +4.00000 q^{4} +15.2484 q^{5} -0.520240 q^{6} -7.00000 q^{7} +8.00000 q^{8} -26.9323 q^{9} +30.4969 q^{10} +63.1379 q^{11} -1.04048 q^{12} +40.8864 q^{13} -14.0000 q^{14} -3.96643 q^{15} +16.0000 q^{16} -57.0717 q^{17} -53.8647 q^{18} +34.4579 q^{19} +60.9938 q^{20} +1.82084 q^{21} +126.276 q^{22} +23.0000 q^{23} -2.08096 q^{24} +107.515 q^{25} +81.7727 q^{26} +14.0289 q^{27} -28.0000 q^{28} +180.951 q^{29} -7.93285 q^{30} -5.92805 q^{31} +32.0000 q^{32} -16.4234 q^{33} -114.143 q^{34} -106.739 q^{35} -107.729 q^{36} -161.864 q^{37} +68.9158 q^{38} -10.6354 q^{39} +121.988 q^{40} -104.432 q^{41} +3.64168 q^{42} +16.5725 q^{43} +252.552 q^{44} -410.676 q^{45} +46.0000 q^{46} +333.754 q^{47} -4.16192 q^{48} +49.0000 q^{49} +215.030 q^{50} +14.8455 q^{51} +163.545 q^{52} +296.103 q^{53} +28.0578 q^{54} +962.756 q^{55} -56.0000 q^{56} -8.96319 q^{57} +361.902 q^{58} -805.644 q^{59} -15.8657 q^{60} +715.603 q^{61} -11.8561 q^{62} +188.526 q^{63} +64.0000 q^{64} +623.454 q^{65} -32.8469 q^{66} +301.232 q^{67} -228.287 q^{68} -5.98276 q^{69} -213.478 q^{70} -871.046 q^{71} -215.459 q^{72} +894.771 q^{73} -323.728 q^{74} -27.9668 q^{75} +137.832 q^{76} -441.966 q^{77} -21.2707 q^{78} -1246.19 q^{79} +243.975 q^{80} +723.524 q^{81} -208.863 q^{82} -1223.93 q^{83} +7.28336 q^{84} -870.255 q^{85} +33.1451 q^{86} -47.0690 q^{87} +505.104 q^{88} -86.3579 q^{89} -821.353 q^{90} -286.205 q^{91} +92.0000 q^{92} +1.54200 q^{93} +667.507 q^{94} +525.429 q^{95} -8.32384 q^{96} +343.939 q^{97} +98.0000 q^{98} -1700.45 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 5 q^{3} + 20 q^{4} + 22 q^{5} + 10 q^{6} - 35 q^{7} + 40 q^{8} + 54 q^{9} + 44 q^{10} + 42 q^{11} + 20 q^{12} + 107 q^{13} - 70 q^{14} + 122 q^{15} + 80 q^{16} + 218 q^{17} + 108 q^{18}+ \cdots - 2616 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 5 * q^3 + 20 * q^4 + 22 * q^5 + 10 * q^6 - 35 * q^7 + 40 * q^8 + 54 * q^9 + 44 * q^10 + 42 * q^11 + 20 * q^12 + 107 * q^13 - 70 * q^14 + 122 * q^15 + 80 * q^16 + 218 * q^17 + 108 * q^18 + 194 * q^19 + 88 * q^20 - 35 * q^21 + 84 * q^22 + 115 * q^23 + 40 * q^24 + 219 * q^25 + 214 * q^26 + 203 * q^27 - 140 * q^28 + 33 * q^29 + 244 * q^30 + 19 * q^31 + 160 * q^32 + 240 * q^33 + 436 * q^34 - 154 * q^35 + 216 * q^36 + 214 * q^37 + 388 * q^38 - 243 * q^39 + 176 * q^40 + 395 * q^41 - 70 * q^42 - 284 * q^43 + 168 * q^44 + 470 * q^45 + 230 * q^46 - 493 * q^47 + 80 * q^48 + 245 * q^49 + 438 * q^50 - 244 * q^51 + 428 * q^52 - 70 * q^53 + 406 * q^54 - 186 * q^55 - 280 * q^56 + 22 * q^57 + 66 * q^58 + 226 * q^59 + 488 * q^60 + 1606 * q^61 + 38 * q^62 - 378 * q^63 + 320 * q^64 + 362 * q^65 + 480 * q^66 + 298 * q^67 + 872 * q^68 + 115 * q^69 - 308 * q^70 - 969 * q^71 + 432 * q^72 + 697 * q^73 + 428 * q^74 + 1065 * q^75 + 776 * q^76 - 294 * q^77 - 486 * q^78 + 186 * q^79 + 352 * q^80 - 335 * q^81 + 790 * q^82 - 1104 * q^83 - 140 * q^84 - 1344 * q^85 - 568 * q^86 - 1603 * q^87 + 336 * q^88 - 814 * q^89 + 940 * q^90 - 749 * q^91 + 460 * q^92 - 3423 * q^93 - 986 * q^94 - 2812 * q^95 + 160 * q^96 - 256 * q^97 + 490 * q^98 - 2616 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more