LMFDB - Embedded newform 2303.4.a.h.1.15

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:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-0.936762 q^{2} +3.03943 q^{3} -7.12248 q^{4} +14.9851 q^{5} -2.84722 q^{6} +14.1662 q^{8} -17.7619 q^{9} +O(q^{10})$	\(q-0.936762 q^{2} +3.03943 q^{3} -7.12248 q^{4} +14.9851 q^{5} -2.84722 q^{6} +14.1662 q^{8} -17.7619 q^{9} -14.0375 q^{10} -41.4851 q^{11} -21.6483 q^{12} -22.8208 q^{13} +45.5461 q^{15} +43.7095 q^{16} +91.4044 q^{17} +16.6386 q^{18} +115.223 q^{19} -106.731 q^{20} +38.8616 q^{22} -176.873 q^{23} +43.0571 q^{24} +99.5526 q^{25} +21.3777 q^{26} -136.051 q^{27} +206.003 q^{29} -42.6659 q^{30} -193.096 q^{31} -154.275 q^{32} -126.091 q^{33} -85.6242 q^{34} +126.508 q^{36} +270.584 q^{37} -107.936 q^{38} -69.3623 q^{39} +212.281 q^{40} +106.243 q^{41} -395.950 q^{43} +295.476 q^{44} -266.163 q^{45} +165.688 q^{46} +47.0000 q^{47} +132.852 q^{48} -93.2571 q^{50} +277.817 q^{51} +162.541 q^{52} +81.1559 q^{53} +127.447 q^{54} -621.657 q^{55} +350.211 q^{57} -192.975 q^{58} -361.827 q^{59} -324.401 q^{60} +589.352 q^{61} +180.885 q^{62} -205.157 q^{64} -341.972 q^{65} +118.117 q^{66} -172.157 q^{67} -651.026 q^{68} -537.593 q^{69} +373.316 q^{71} -251.617 q^{72} +112.377 q^{73} -253.473 q^{74} +302.583 q^{75} -820.670 q^{76} +64.9759 q^{78} +1308.00 q^{79} +654.990 q^{80} +66.0540 q^{81} -99.5245 q^{82} -1045.64 q^{83} +1369.70 q^{85} +370.911 q^{86} +626.131 q^{87} -587.684 q^{88} -1169.89 q^{89} +249.331 q^{90} +1259.77 q^{92} -586.903 q^{93} -44.0278 q^{94} +1726.62 q^{95} -468.907 q^{96} +1882.40 q^{97} +736.852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * 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 $

$2$	−0.936762	−0.331195	−0.165598	−	0.986193i	$-0.552955\pi$
$2$	−0.936762	−0.331195	−0.165598	+	0.986193i	$0.552955\pi$
$3$	3.03943	0.584939	0.292469	−	0.956275i	$-0.405523\pi$
$3$	3.03943	0.584939	0.292469	+	0.956275i	$0.405523\pi$
$4$	−7.12248	−0.890310
$5$	14.9851	1.34031	0.670153	−	0.742223i	$-0.266228\pi$
$5$	14.9851	1.34031	0.670153	+	0.742223i	$0.266228\pi$
$6$	−2.84722	−0.193729
$7$	0	0
$7$	0	0
$8$	14.1662	0.626062
$9$	−17.7619	−0.657847
$10$	−14.0375	−0.443903
$11$	−41.4851	−1.13711	−0.568555	−	0.822645i	$-0.692497\pi$
$11$	−41.4851	−1.13711	−0.568555	+	0.822645i	$0.692497\pi$
$12$	−21.6483	−0.520777
$13$	−22.8208	−0.486873	−0.243437	−	0.969917i	$-0.578275\pi$
$13$	−22.8208	−0.486873	−0.243437	+	0.969917i	$0.578275\pi$
$14$	0	0
$15$	45.5461	0.783997
$16$	43.7095	0.682961
$17$	91.4044	1.30405	0.652024	−	0.758198i	$-0.273920\pi$
$17$	91.4044	1.30405	0.652024	+	0.758198i	$0.273920\pi$
$18$	16.6386	0.217876
$19$	115.223	1.39126	0.695628	−	0.718402i	$-0.255126\pi$
$19$	115.223	1.39126	0.695628	+	0.718402i	$0.255126\pi$
$20$	−106.731	−1.19329
$21$	0	0
$22$	38.8616	0.376606
$23$	−176.873	−1.60350	−0.801751	−	0.597658i	$-0.796098\pi$
$23$	−176.873	−1.60350	−0.801751	+	0.597658i	$0.796098\pi$
$24$	43.0571	0.366208
$25$	99.5526	0.796421
$26$	21.3777	0.161250
$27$	−136.051	−0.969739
$28$	0	0
$29$	206.003	1.31909	0.659547	−	0.751663i	$-0.270748\pi$
$29$	206.003	1.31909	0.659547	+	0.751663i	$0.270748\pi$
$30$	−42.6659	−0.259656
$31$	−193.096	−1.11875	−0.559373	−	0.828916i	$-0.688958\pi$
$31$	−193.096	−1.11875	−0.559373	+	0.828916i	$0.688958\pi$
$32$	−154.275	−0.852255
$33$	−126.091	−0.665140
$34$	−85.6242	−0.431895
$35$	0	0
$36$	126.508	0.585687
$37$	270.584	1.20226	0.601132	−	0.799150i	$-0.294717\pi$
$37$	270.584	1.20226	0.601132	+	0.799150i	$0.294717\pi$
$38$	−107.936	−0.460778
$39$	−69.3623	−0.284791
$40$	212.281	0.839115
$41$	106.243	0.404692	0.202346	−	0.979314i	$-0.435143\pi$
$41$	106.243	0.404692	0.202346	+	0.979314i	$0.435143\pi$
$42$	0	0
$43$	−395.950	−1.40423	−0.702114	−	0.712064i	$-0.747760\pi$
$43$	−395.950	−1.40423	−0.702114	+	0.712064i	$0.747760\pi$
$44$	295.476	1.01238
$45$	−266.163	−0.881716
$46$	165.688	0.531072
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	132.852	0.399490
$49$	0	0
$50$	−93.2571	−0.263771
$51$	277.817	0.762788
$52$	162.541	0.433468
$53$	81.1559	0.210332	0.105166	−	0.994455i	$-0.466463\pi$
$53$	81.1559	0.210332	0.105166	+	0.994455i	$0.466463\pi$
$54$	127.447	0.321173
$55$	−621.657	−1.52408
$56$	0	0
$57$	350.211	0.813799
$58$	−192.975	−0.436878
$59$	−361.827	−0.798405	−0.399203	−	0.916863i	$-0.630713\pi$
$59$	−361.827	−0.798405	−0.399203	+	0.916863i	$0.630713\pi$
$60$	−324.401	−0.698000
$61$	589.352	1.23703	0.618514	−	0.785773i	$-0.287735\pi$
$61$	589.352	1.23703	0.618514	+	0.785773i	$0.287735\pi$
$62$	180.885	0.370524
$63$	0	0
$64$	−205.157	−0.400698
$65$	−341.972	−0.652559
$66$	118.117	0.220291
$67$	−172.157	−0.313915	−0.156957	−	0.987605i	$-0.550169\pi$
$67$	−172.157	−0.313915	−0.156957	+	0.987605i	$0.550169\pi$
$68$	−651.026	−1.16101
$69$	−537.593	−0.937950
$70$	0	0
$71$	373.316	0.624006	0.312003	−	0.950081i	$-0.399000\pi$
$71$	373.316	0.624006	0.312003	+	0.950081i	$0.399000\pi$
$72$	−251.617	−0.411853
$73$	112.377	0.180174	0.0900870	−	0.995934i	$-0.471285\pi$
$73$	112.377	0.180174	0.0900870	+	0.995934i	$0.471285\pi$
$74$	−253.473	−0.398184
$75$	302.583	0.465857
$76$	−820.670	−1.23865
$77$	0	0
$78$	64.9759	0.0943215
$79$	1308.00	1.86281	0.931404	−	0.363986i	$-0.118584\pi$
$79$	1308.00	1.86281	0.931404	+	0.363986i	$0.118584\pi$
$80$	654.990	0.915377
$81$	66.0540	0.0906091
$82$	−99.5245	−0.134032
$83$	−1045.64	−1.38282	−0.691409	−	0.722464i	$-0.743010\pi$
$83$	−1045.64	−1.38282	−0.691409	+	0.722464i	$0.743010\pi$
$84$	0	0
$85$	1369.70	1.74782
$86$	370.911	0.465074
$87$	626.131	0.771589
$88$	−587.684	−0.711901
$89$	−1169.89	−1.39335	−0.696676	−	0.717386i	$-0.745338\pi$
$89$	−1169.89	−1.39335	−0.696676	+	0.717386i	$0.745338\pi$
$90$	249.331	0.292020
$91$	0	0
$92$	1259.77	1.42761
$93$	−586.903	−0.654398
$94$	−44.0278	−0.0483098
$95$	1726.62	1.86471
$96$	−468.907	−0.498517
$97$	1882.40	1.97040	0.985198	−	0.171418i	$-0.0548349\pi$
$97$	1882.40	1.97040	0.985198	+	0.171418i	$0.0548349\pi$
$98$	0	0
$99$	736.852	0.748044
$100$	−709.061	−0.709061
$101$	71.8967	0.0708316	0.0354158	−	0.999373i	$-0.488724\pi$
$101$	71.8967	0.0708316	0.0354158	+	0.999373i	$0.488724\pi$
$102$	−260.249	−0.252632
$103$	1145.71	1.09602	0.548009	−	0.836473i	$-0.315386\pi$
$103$	1145.71	1.09602	0.548009	+	0.836473i	$0.315386\pi$
$104$	−323.283	−0.304813
$105$	0	0
$106$	−76.0237	−0.0696611
$107$	713.786	0.644900	0.322450	−	0.946587i	$-0.395494\pi$
$107$	713.786	0.644900	0.322450	+	0.946587i	$0.395494\pi$
$108$	969.017	0.863368
$109$	1608.79	1.41371	0.706853	−	0.707360i	$-0.250114\pi$
$109$	1608.79	1.41371	0.706853	+	0.707360i	$0.250114\pi$
$110$	582.345	0.504767
$111$	822.422	0.703251
$112$	0	0
$113$	1429.82	1.19032	0.595159	−	0.803608i	$-0.297089\pi$
$113$	1429.82	1.19032	0.595159	+	0.803608i	$0.297089\pi$
$114$	−328.064	−0.269527
$115$	−2650.45	−2.14918
$116$	−1467.25	−1.17440
$117$	405.340	0.320288
$118$	338.946	0.264428
$119$	0	0
$120$	645.214	0.490831
$121$	390.010	0.293020
$122$	−552.082	−0.409698
$123$	322.918	0.236720
$124$	1375.32	0.996031
$125$	−381.331	−0.272859
$126$	0	0
$127$	−598.709	−0.418322	−0.209161	−	0.977881i	$-0.567073\pi$
$127$	−598.709	−0.418322	−0.209161	+	0.977881i	$0.567073\pi$
$128$	1426.38	0.984965
$129$	−1203.46	−0.821387
$130$	320.346	0.216125
$131$	−1895.10	−1.26393	−0.631967	−	0.774995i	$-0.717752\pi$
$131$	−1895.10	−1.26393	−0.631967	+	0.774995i	$0.717752\pi$
$132$	898.080	0.592180
$133$	0	0
$134$	161.270	0.103967
$135$	−2038.73	−1.29975
$136$	1294.85	0.816415
$137$	1991.33	1.24183	0.620916	−	0.783877i	$-0.286761\pi$
$137$	1991.33	1.24183	0.620916	+	0.783877i	$0.286761\pi$
$138$	503.597	0.310645
$139$	−2114.28	−1.29015	−0.645076	−	0.764118i	$-0.723174\pi$
$139$	−2114.28	−1.29015	−0.645076	+	0.764118i	$0.723174\pi$
$140$	0	0
$141$	142.853	0.0853221
$142$	−349.708	−0.206668
$143$	946.723	0.553629
$144$	−776.362	−0.449284
$145$	3086.97	1.76799
$146$	−105.270	−0.0596728
$147$	0	0
$148$	−1927.23	−1.07039
$149$	235.469	0.129466	0.0647329	−	0.997903i	$-0.479380\pi$
$149$	235.469	0.129466	0.0647329	+	0.997903i	$0.479380\pi$
$150$	−283.448	−0.154290
$151$	2781.97	1.49929	0.749647	−	0.661838i	$-0.230223\pi$
$151$	2781.97	1.49929	0.749647	+	0.661838i	$0.230223\pi$
$152$	1632.26	0.871012
$153$	−1623.51	−0.857864
$154$	0	0
$155$	−2893.56	−1.49946
$156$	494.031	0.253552
$157$	2321.33	1.18001	0.590007	−	0.807398i	$-0.299125\pi$
$157$	2321.33	1.18001	0.590007	+	0.807398i	$0.299125\pi$
$158$	−1225.29	−0.616954
$159$	246.668	0.123032
$160$	−2311.82	−1.14228
$161$	0	0
$162$	−61.8769	−0.0300093
$163$	−3535.60	−1.69896	−0.849478	−	0.527624i	$-0.823083\pi$
$163$	−3535.60	−1.69896	−0.849478	+	0.527624i	$0.823083\pi$
$164$	−756.714	−0.360301
$165$	−1889.48	−0.891491
$166$	979.516	0.457983
$167$	75.7784	0.0351132	0.0175566	−	0.999846i	$-0.494411\pi$
$167$	75.7784	0.0351132	0.0175566	+	0.999846i	$0.494411\pi$
$168$	0	0
$169$	−1676.21	−0.762954
$170$	−1283.08	−0.578871
$171$	−2046.57	−0.915233
$172$	2820.14	1.25020
$173$	551.395	0.242322	0.121161	−	0.992633i	$-0.461338\pi$
$173$	551.395	0.242322	0.121161	+	0.992633i	$0.461338\pi$
$174$	−586.535	−0.255547
$175$	0	0
$176$	−1813.29	−0.776602
$177$	−1099.75	−0.467018
$178$	1095.91	0.461472
$179$	−3780.51	−1.57860	−0.789298	−	0.614010i	$-0.789555\pi$
$179$	−3780.51	−1.57860	−0.789298	+	0.614010i	$0.789555\pi$
$180$	1895.74	0.785000
$181$	1508.76	0.619585	0.309793	−	0.950804i	$-0.399740\pi$
$181$	1508.76	0.619585	0.309793	+	0.950804i	$0.399740\pi$
$182$	0	0
$183$	1791.29	0.723586
$184$	−2505.61	−1.00389
$185$	4054.73	1.61140
$186$	549.789	0.216734
$187$	−3791.92	−1.48285
$188$	−334.756	−0.129865
$189$	0	0
$190$	−1617.43	−0.617583
$191$	3779.81	1.43192	0.715962	−	0.698140i	$-0.245989\pi$
$191$	3779.81	1.43192	0.715962	+	0.698140i	$0.245989\pi$
$192$	−623.561	−0.234384
$193$	1608.17	0.599786	0.299893	−	0.953973i	$-0.403049\pi$
$193$	1608.17	0.599786	0.299893	+	0.953973i	$0.403049\pi$
$194$	−1763.36	−0.652586
$195$	−1039.40	−0.381707
$196$	0	0
$197$	508.934	0.184061	0.0920305	−	0.995756i	$-0.470664\pi$
$197$	508.934	0.184061	0.0920305	+	0.995756i	$0.470664\pi$
$198$	−690.255	−0.247749
$199$	3064.31	1.09157	0.545786	−	0.837924i	$-0.316231\pi$
$199$	3064.31	1.09157	0.545786	+	0.837924i	$0.316231\pi$
$200$	1410.28	0.498609
$201$	−523.258	−0.183621
$202$	−67.3501	−0.0234591
$203$	0	0
$204$	−1978.75	−0.679118
$205$	1592.06	0.542411
$206$	−1073.25	−0.362996
$207$	3141.59	1.05486
$208$	−997.486	−0.332515
$209$	−4780.01	−1.58201
$210$	0	0
$211$	−4485.58	−1.46351	−0.731754	−	0.681569i	$-0.761298\pi$
$211$	−4485.58	−1.46351	−0.731754	+	0.681569i	$0.761298\pi$
$212$	−578.031	−0.187261
$213$	1134.67	0.365005
$214$	−668.647	−0.213588
$215$	−5933.34	−1.88210
$216$	−1927.31	−0.607116
$217$	0	0
$218$	−1507.05	−0.468213
$219$	341.561	0.105391
$220$	4427.74	1.35690
$221$	−2085.92	−0.634906
$222$	−770.414	−0.232913
$223$	−2873.19	−0.862795	−0.431397	−	0.902162i	$-0.641979\pi$
$223$	−2873.19	−0.862795	−0.431397	+	0.902162i	$0.641979\pi$
$224$	0	0
$225$	−1768.24	−0.523923
$226$	−1339.40	−0.394228
$227$	1820.50	0.532294	0.266147	−	0.963932i	$-0.414249\pi$
$227$	1820.50	0.532294	0.266147	+	0.963932i	$0.414249\pi$
$228$	−2494.37	−0.724533
$229$	6047.19	1.74502	0.872510	−	0.488596i	$-0.162491\pi$
$229$	6047.19	1.74502	0.872510	+	0.488596i	$0.162491\pi$
$230$	2482.84	0.711800
$231$	0	0
$232$	2918.27	0.825834
$233$	1730.68	0.486611	0.243306	−	0.969950i	$-0.421768\pi$
$233$	1730.68	0.486611	0.243306	+	0.969950i	$0.421768\pi$
$234$	−379.707	−0.106078
$235$	704.299	0.195504
$236$	2577.11	0.710828
$237$	3975.59	1.08963
$238$	0	0
$239$	1758.63	0.475967	0.237984	−	0.971269i	$-0.423514\pi$
$239$	1758.63	0.475967	0.237984	+	0.971269i	$0.423514\pi$
$240$	1990.80	0.535439
$241$	2494.13	0.666643	0.333322	−	0.942813i	$-0.391830\pi$
$241$	2494.13	0.666643	0.333322	+	0.942813i	$0.391830\pi$
$242$	−365.346	−0.0970469
$243$	3874.13	1.02274
$244$	−4197.64	−1.10134
$245$	0	0
$246$	−302.498	−0.0784006
$247$	−2629.47	−0.677366
$248$	−2735.44	−0.700404
$249$	−3178.15	−0.808864
$250$	357.217	0.0903695
$251$	−2937.34	−0.738659	−0.369329	−	0.929299i	$-0.620413\pi$
$251$	−2937.34	−0.738659	−0.369329	+	0.929299i	$0.620413\pi$
$252$	0	0
$253$	7337.58	1.82336
$254$	560.848	0.138546
$255$	4163.11	1.02237
$256$	305.078	0.0744820
$257$	5222.40	1.26756	0.633782	−	0.773512i	$-0.281502\pi$
$257$	5222.40	1.26756	0.633782	+	0.773512i	$0.281502\pi$
$258$	1127.36	0.272040
$259$	0	0
$260$	2435.69	0.580980
$261$	−3658.99	−0.867762
$262$	1775.26	0.418609
$263$	3800.47	0.891054	0.445527	−	0.895269i	$-0.353016\pi$
$263$	3800.47	0.891054	0.445527	+	0.895269i	$0.353016\pi$
$264$	−1786.22	−0.416419
$265$	1216.13	0.281910
$266$	0	0
$267$	−3555.81	−0.815025
$268$	1226.18	0.279481
$269$	7226.82	1.63802	0.819010	−	0.573780i	$-0.194523\pi$
$269$	7226.82	1.63802	0.819010	+	0.573780i	$0.194523\pi$
$270$	1909.80	0.430470
$271$	−941.619	−0.211068	−0.105534	−	0.994416i	$-0.533655\pi$
$271$	−941.619	−0.211068	−0.105534	+	0.994416i	$0.533655\pi$
$272$	3995.24	0.890614
$273$	0	0
$274$	−1865.40	−0.411289
$275$	−4129.94	−0.905618
$276$	3828.99	0.835066
$277$	−6556.65	−1.42221	−0.711103	−	0.703088i	$-0.751804\pi$
$277$	−6556.65	−1.42221	−0.711103	+	0.703088i	$0.751804\pi$
$278$	1980.58	0.427293
$279$	3429.75	0.735964
$280$	0	0
$281$	−2315.21	−0.491508	−0.245754	−	0.969332i	$-0.579036\pi$
$281$	−2315.21	−0.491508	−0.245754	+	0.969332i	$0.579036\pi$
$282$	−133.819	−0.0282583
$283$	960.091	0.201666	0.100833	−	0.994903i	$-0.467849\pi$
$283$	960.091	0.201666	0.100833	+	0.994903i	$0.467849\pi$
$284$	−2658.93	−0.555558
$285$	5247.94	1.09074
$286$	−886.854	−0.183359
$287$	0	0
$288$	2740.21	0.560653
$289$	3441.76	0.700541
$290$	−2891.75	−0.585550
$291$	5721.42	1.15256
$292$	−800.401	−0.160411
$293$	−2720.16	−0.542367	−0.271184	−	0.962528i	$-0.587415\pi$
$293$	−2720.16	−0.542367	−0.271184	+	0.962528i	$0.587415\pi$
$294$	0	0
$295$	−5422.01	−1.07011
$296$	3833.14	0.752692
$297$	5644.07	1.10270
$298$	−220.579	−0.0428785
$299$	4036.38	0.780702
$300$	−2155.14	−0.414757
$301$	0	0
$302$	−2606.04	−0.496559
$303$	218.525	0.0414322
$304$	5036.32	0.950173
$305$	8831.48	1.65800
$306$	1520.84	0.284121
$307$	7591.73	1.41135	0.705673	−	0.708538i	$-0.250645\pi$
$307$	7591.73	1.41135	0.705673	+	0.708538i	$0.250645\pi$
$308$	0	0
$309$	3482.30	0.641103
$310$	2710.58	0.496615
$311$	2086.57	0.380446	0.190223	−	0.981741i	$-0.439079\pi$
$311$	2086.57	0.380446	0.190223	+	0.981741i	$0.439079\pi$
$312$	−982.597	−0.178297
$313$	3068.41	0.554110	0.277055	−	0.960854i	$-0.410641\pi$
$313$	3068.41	0.554110	0.277055	+	0.960854i	$0.410641\pi$
$314$	−2174.53	−0.390815
$315$	0	0
$316$	−9316.23	−1.65848
$317$	−1401.18	−0.248259	−0.124129	−	0.992266i	$-0.539614\pi$
$317$	−1401.18	−0.248259	−0.124129	+	0.992266i	$0.539614\pi$
$318$	−231.069	−0.0407475
$319$	−8546.03	−1.49996
$320$	−3074.30	−0.537058
$321$	2169.50	0.377227
$322$	0	0
$323$	10531.8	1.81426
$324$	−470.468	−0.0806701
$325$	−2271.87	−0.387756
$326$	3312.02	0.562686
$327$	4889.80	0.826932
$328$	1505.06	0.253362
$329$	0	0
$330$	1770.00	0.295258
$331$	4623.89	0.767831	0.383915	−	0.923368i	$-0.374575\pi$
$331$	4623.89	0.767831	0.383915	+	0.923368i	$0.374575\pi$
$332$	7447.54	1.23114
$333$	−4806.08	−0.790905
$334$	−70.9863	−0.0116293
$335$	−2579.78	−0.420742
$336$	0	0
$337$	6400.10	1.03453	0.517264	−	0.855826i	$-0.326951\pi$
$337$	6400.10	1.03453	0.517264	+	0.855826i	$0.326951\pi$
$338$	1570.21	0.252687
$339$	4345.83	0.696263
$340$	−9755.67	−1.55610
$341$	8010.62	1.27214
$342$	1917.15	0.303121
$343$	0	0
$344$	−5609.09	−0.879134
$345$	−8055.87	−1.25714
$346$	−516.526	−0.0802561
$347$	5580.16	0.863282	0.431641	−	0.902046i	$-0.357935\pi$
$347$	5580.16	0.863282	0.431641	+	0.902046i	$0.357935\pi$
$348$	−4459.60	−0.686953
$349$	−918.489	−0.140876	−0.0704378	−	0.997516i	$-0.522440\pi$
$349$	−918.489	−0.140876	−0.0704378	+	0.997516i	$0.522440\pi$
$350$	0	0
$351$	3104.78	0.472140
$352$	6400.09	0.969108
$353$	−1777.06	−0.267942	−0.133971	−	0.990985i	$-0.542773\pi$
$353$	−1777.06	−0.267942	−0.133971	+	0.990985i	$0.542773\pi$
$354$	1030.20	0.154674
$355$	5594.16	0.836359
$356$	8332.53	1.24051
$357$	0	0
$358$	3541.44	0.522824
$359$	6525.38	0.959321	0.479661	−	0.877454i	$-0.340760\pi$
$359$	6525.38	0.959321	0.479661	+	0.877454i	$0.340760\pi$
$360$	−3770.51	−0.552009
$361$	6417.23	0.935593
$362$	−1413.34	−0.205204
$363$	1185.41	0.171399
$364$	0	0
$365$	1683.97	0.241488
$366$	−1678.02	−0.239648
$367$	6714.82	0.955070	0.477535	−	0.878613i	$-0.341530\pi$
$367$	6714.82	0.955070	0.477535	+	0.878613i	$0.341530\pi$
$368$	−7731.02	−1.09513
$369$	−1887.07	−0.266225
$370$	−3798.31	−0.533689
$371$	0	0
$372$	4180.20	0.582617
$373$	−3531.26	−0.490192	−0.245096	−	0.969499i	$-0.578820\pi$
$373$	−3531.26	−0.490192	−0.245096	+	0.969499i	$0.578820\pi$
$374$	3552.12	0.491112
$375$	−1159.03	−0.159606
$376$	665.810	0.0913205
$377$	−4701.15	−0.642232
$378$	0	0
$379$	−4338.51	−0.588005	−0.294003	−	0.955805i	$-0.594987\pi$
$379$	−4338.51	−0.588005	−0.294003	+	0.955805i	$0.594987\pi$
$380$	−12297.8	−1.66017
$381$	−1819.74	−0.244693
$382$	−3540.78	−0.474246
$383$	13445.9	1.79387	0.896935	−	0.442162i	$-0.145789\pi$
$383$	13445.9	1.79387	0.896935	+	0.442162i	$0.145789\pi$
$384$	4335.39	0.576144
$385$	0	0
$386$	−1506.47	−0.198646
$387$	7032.81	0.923767
$388$	−13407.3	−1.75426
$389$	−4020.65	−0.524049	−0.262024	−	0.965061i	$-0.584390\pi$
$389$	−4020.65	−0.524049	−0.262024	+	0.965061i	$0.584390\pi$
$390$	973.670	0.126420
$391$	−16167.0	−2.09104
$392$	0	0
$393$	−5760.02	−0.739324
$394$	−476.750	−0.0609602
$395$	19600.5	2.49673
$396$	−5248.21	−0.665991
$397$	−9928.35	−1.25514	−0.627569	−	0.778561i	$-0.715950\pi$
$397$	−9928.35	−1.25514	−0.627569	+	0.778561i	$0.715950\pi$
$398$	−2870.53	−0.361524
$399$	0	0
$400$	4351.39	0.543924
$401$	11104.8	1.38291	0.691456	−	0.722418i	$-0.256969\pi$
$401$	11104.8	1.38291	0.691456	+	0.722418i	$0.256969\pi$
$402$	490.168	0.0608144
$403$	4406.62	0.544688
$404$	−512.083	−0.0630621
$405$	989.825	0.121444
$406$	0	0
$407$	−11225.2	−1.36711
$408$	3935.60	0.477553
$409$	−15219.0	−1.83993	−0.919967	−	0.391996i	$-0.871785\pi$
$409$	−15219.0	−1.83993	−0.919967	+	0.391996i	$0.871785\pi$
$410$	−1491.38	−0.179644
$411$	6052.51	0.726395
$412$	−8160.27	−0.975795
$413$	0	0
$414$	−2942.92	−0.349364
$415$	−15669.0	−1.85340
$416$	3520.67	0.414940
$417$	−6426.22	−0.754660
$418$	4477.74	0.523955
$419$	−1096.02	−0.127790	−0.0638951	−	0.997957i	$-0.520352\pi$
$419$	−1096.02	−0.127790	−0.0638951	+	0.997957i	$0.520352\pi$
$420$	0	0
$421$	4026.91	0.466175	0.233088	−	0.972456i	$-0.425117\pi$
$421$	4026.91	0.466175	0.233088	+	0.972456i	$0.425117\pi$
$422$	4201.92	0.484707
$423$	−834.808	−0.0959568
$424$	1149.67	0.131681
$425$	9099.54	1.03857
$426$	−1062.91	−0.120888
$427$	0	0
$428$	−5083.92	−0.574160
$429$	2877.50	0.323839
$430$	5558.13	0.623341
$431$	14438.1	1.61359	0.806794	−	0.590832i	$-0.201201\pi$
$431$	14438.1	1.61359	0.806794	+	0.590832i	$0.201201\pi$
$432$	−5946.70	−0.662294
$433$	5548.48	0.615803	0.307902	−	0.951418i	$-0.400373\pi$
$433$	5548.48	0.615803	0.307902	+	0.951418i	$0.400373\pi$
$434$	0	0
$435$	9382.62	1.03417
$436$	−11458.6	−1.25864
$437$	−20379.7	−2.23088
$438$	−319.962	−0.0349049
$439$	−8781.22	−0.954681	−0.477341	−	0.878718i	$-0.658399\pi$
$439$	−8781.22	−0.954681	−0.477341	+	0.878718i	$0.658399\pi$
$440$	−8806.49	−0.954166
$441$	0	0
$442$	1954.01	0.210278
$443$	9829.78	1.05424	0.527118	−	0.849792i	$-0.323272\pi$
$443$	9829.78	1.05424	0.527118	+	0.849792i	$0.323272\pi$
$444$	−5857.68	−0.626111
$445$	−17530.9	−1.86752
$446$	2691.50	0.285754
$447$	715.693	0.0757296
$448$	0	0
$449$	−372.354	−0.0391369	−0.0195684	−	0.999809i	$-0.506229\pi$
$449$	−372.354	−0.0391369	−0.0195684	+	0.999809i	$0.506229\pi$
$450$	1656.42	0.173521
$451$	−4407.50	−0.460180
$452$	−10183.8	−1.05975
$453$	8455.60	0.876995
$454$	−1705.37	−0.176293
$455$	0	0
$456$	4961.14	0.509489
$457$	12941.1	1.32463	0.662317	−	0.749224i	$-0.269573\pi$
$457$	12941.1	1.32463	0.662317	+	0.749224i	$0.269573\pi$
$458$	−5664.78	−0.577943
$459$	−12435.6	−1.26459
$460$	18877.8	1.91344
$461$	1383.28	0.139752	0.0698761	−	0.997556i	$-0.477740\pi$
$461$	1383.28	0.139752	0.0698761	+	0.997556i	$0.477740\pi$
$462$	0	0
$463$	6374.36	0.639831	0.319915	−	0.947446i	$-0.396346\pi$
$463$	6374.36	0.639831	0.319915	+	0.947446i	$0.396346\pi$
$464$	9004.27	0.900889
$465$	−8794.79	−0.877094
$466$	−1621.23	−0.161163
$467$	−11187.0	−1.10851	−0.554254	−	0.832348i	$-0.686996\pi$
$467$	−11187.0	−1.10851	−0.554254	+	0.832348i	$0.686996\pi$
$468$	−2887.03	−0.285156
$469$	0	0
$470$	−659.760	−0.0647499
$471$	7055.52	0.690236
$472$	−5125.71	−0.499851
$473$	16426.0	1.59676
$474$	−3724.18	−0.360880
$475$	11470.7	1.10803
$476$	0	0
$477$	−1441.48	−0.138366
$478$	−1647.42	−0.157638
$479$	11700.2	1.11607	0.558034	−	0.829818i	$-0.311556\pi$
$479$	11700.2	1.11607	0.558034	+	0.829818i	$0.311556\pi$
$480$	−7026.61	−0.668166
$481$	−6174.95	−0.585350
$482$	−2336.41	−0.220789
$483$	0	0
$484$	−2777.84	−0.260879
$485$	28207.9	2.64093
$486$	−3629.14	−0.338727
$487$	−15511.5	−1.44331	−0.721654	−	0.692254i	$-0.756618\pi$
$487$	−15511.5	−1.44331	−0.721654	+	0.692254i	$0.756618\pi$
$488$	8348.85	0.774457
$489$	−10746.2	−0.993785
$490$	0	0
$491$	17307.0	1.59075	0.795373	−	0.606121i	$-0.207275\pi$
$491$	17307.0	1.59075	0.795373	+	0.606121i	$0.207275\pi$
$492$	−2299.98	−0.210754
$493$	18829.5	1.72016
$494$	2463.19	0.224340
$495$	11041.8	1.00261
$496$	−8440.15	−0.764060
$497$	0	0
$498$	2977.17	0.267892
$499$	−15385.8	−1.38029	−0.690145	−	0.723671i	$-0.742453\pi$
$499$	−15385.8	−1.38029	−0.690145	+	0.723671i	$0.742453\pi$
$500$	2716.02	0.242929
$501$	230.323	0.0205391
$502$	2751.59	0.244640
$503$	−6602.99	−0.585313	−0.292657	−	0.956218i	$-0.594539\pi$
$503$	−6602.99	−0.585313	−0.292657	+	0.956218i	$0.594539\pi$
$504$	0	0
$505$	1077.38	0.0949361
$506$	−6873.57	−0.603888
$507$	−5094.73	−0.446281
$508$	4264.29	0.372436
$509$	14032.9	1.22200	0.610998	−	0.791632i	$-0.290768\pi$
$509$	14032.9	1.22200	0.610998	+	0.791632i	$0.290768\pi$
$510$	−3899.85	−0.338604
$511$	0	0
$512$	−11696.8	−1.00963
$513$	−15676.1	−1.34915
$514$	−4892.14	−0.419812
$515$	17168.5	1.46900
$516$	8571.63	0.731289
$517$	−1949.80	−0.165865
$518$	0	0
$519$	1675.93	0.141744
$520$	−4844.43	−0.408543
$521$	4312.94	0.362674	0.181337	−	0.983421i	$-0.441957\pi$
$521$	4312.94	0.362674	0.181337	+	0.983421i	$0.441957\pi$
$522$	3427.60	0.287399
$523$	5461.31	0.456609	0.228304	−	0.973590i	$-0.426682\pi$
$523$	5461.31	0.456609	0.228304	+	0.973590i	$0.426682\pi$
$524$	13497.8	1.12529
$525$	0	0
$526$	−3560.14	−0.295113
$527$	−17649.9	−1.45890
$528$	−5511.37	−0.454264
$529$	19117.0	1.57122
$530$	−1139.22	−0.0933672
$531$	6426.73	0.525228
$532$	0	0
$533$	−2424.55	−0.197034
$534$	3330.94	0.269933
$535$	10696.1	0.864363
$536$	−2438.80	−0.196530
$537$	−11490.6	−0.923382
$538$	−6769.81	−0.542504
$539$	0	0
$540$	14520.8	1.15718
$541$	22204.0	1.76455	0.882277	−	0.470731i	$-0.156010\pi$
$541$	22204.0	1.76455	0.882277	+	0.470731i	$0.156010\pi$
$542$	882.073	0.0699046
$543$	4585.76	0.362419
$544$	−14101.4	−1.11138
$545$	24107.8	1.89480
$546$	0	0
$547$	18174.5	1.42063	0.710314	−	0.703885i	$-0.248553\pi$
$547$	18174.5	1.42063	0.710314	+	0.703885i	$0.248553\pi$
$548$	−14183.2	−1.10561
$549$	−10468.0	−0.813775
$550$	3868.78	0.299937
$551$	23736.1	1.83520
$552$	−7615.63	−0.587215
$553$	0	0
$554$	6142.03	0.471028
$555$	12324.1	0.942571
$556$	15058.9	1.14864
$557$	20048.3	1.52509	0.762544	−	0.646936i	$-0.223950\pi$
$557$	20048.3	1.52509	0.762544	+	0.646936i	$0.223950\pi$
$558$	−3212.86	−0.243748
$559$	9035.90	0.683681
$560$	0	0
$561$	−11525.3	−0.867374
$562$	2168.80	0.162785
$563$	−3549.57	−0.265713	−0.132856	−	0.991135i	$-0.542415\pi$
$563$	−3549.57	−0.265713	−0.132856	+	0.991135i	$0.542415\pi$
$564$	−1017.47	−0.0759631
$565$	21425.9	1.59539
$566$	−899.377	−0.0667909
$567$	0	0
$568$	5288.45	0.390666
$569$	−5702.84	−0.420168	−0.210084	−	0.977683i	$-0.567374\pi$
$569$	−5702.84	−0.420168	−0.210084	+	0.977683i	$0.567374\pi$
$570$	−4916.07	−0.361248
$571$	−4723.87	−0.346213	−0.173107	−	0.984903i	$-0.555381\pi$
$571$	−4723.87	−0.346213	−0.173107	+	0.984903i	$0.555381\pi$
$572$	−6743.01	−0.492901
$573$	11488.5	0.837587
$574$	0	0
$575$	−17608.2	−1.27706
$576$	3643.97	0.263598
$577$	16257.0	1.17294	0.586470	−	0.809971i	$-0.300517\pi$
$577$	16257.0	1.17294	0.586470	+	0.809971i	$0.300517\pi$
$578$	−3224.11	−0.232016
$579$	4887.92	0.350838
$580$	−21986.8	−1.57406
$581$	0	0
$582$	−5359.61	−0.381723
$583$	−3366.75	−0.239171
$584$	1591.95	0.112800
$585$	6074.05	0.429284
$586$	2548.14	0.179630
$587$	3709.64	0.260840	0.130420	−	0.991459i	$-0.458367\pi$
$587$	3709.64	0.260840	0.130420	+	0.991459i	$0.458367\pi$
$588$	0	0
$589$	−22249.1	−1.55646
$590$	5079.14	0.354415
$591$	1546.87	0.107664
$592$	11827.1	0.821099
$593$	−27520.3	−1.90577	−0.952887	−	0.303326i	$-0.901903\pi$
$593$	−27520.3	−1.90577	−0.952887	+	0.303326i	$0.901903\pi$
$594$	−5287.15	−0.365209
$595$	0	0
$596$	−1677.13	−0.115265
$597$	9313.75	0.638503
$598$	−3781.13	−0.258565
$599$	4864.73	0.331832	0.165916	−	0.986140i	$-0.446942\pi$
$599$	4864.73	0.331832	0.165916	+	0.986140i	$0.446942\pi$
$600$	4286.44	0.291655
$601$	−12611.3	−0.855947	−0.427974	−	0.903791i	$-0.640772\pi$
$601$	−12611.3	−0.855947	−0.427974	+	0.903791i	$0.640772\pi$
$602$	0	0
$603$	3057.82	0.206508
$604$	−19814.5	−1.33484
$605$	5844.33	0.392737
$606$	−204.706	−0.0137221
$607$	−2162.72	−0.144617	−0.0723083	−	0.997382i	$-0.523037\pi$
$607$	−2162.72	−0.144617	−0.0723083	+	0.997382i	$0.523037\pi$
$608$	−17775.9	−1.18571
$609$	0	0
$610$	−8273.00	−0.549121
$611$	−1072.58	−0.0710178
$612$	11563.4	0.763764
$613$	2878.41	0.189654	0.0948271	−	0.995494i	$-0.469770\pi$
$613$	2878.41	0.189654	0.0948271	+	0.995494i	$0.469770\pi$
$614$	−7111.65	−0.467431
$615$	4838.96	0.317277
$616$	0	0
$617$	−15943.5	−1.04029	−0.520147	−	0.854077i	$-0.674123\pi$
$617$	−15943.5	−1.04029	−0.520147	+	0.854077i	$0.674123\pi$
$618$	−3262.08	−0.212330
$619$	5335.05	0.346420	0.173210	−	0.984885i	$-0.444586\pi$
$619$	5335.05	0.346420	0.173210	+	0.984885i	$0.444586\pi$
$620$	20609.3	1.33499
$621$	24063.7	1.55498
$622$	−1954.62	−0.126002
$623$	0	0
$624$	−3031.79	−0.194501
$625$	−18158.4	−1.16213
$626$	−2874.37	−0.183519
$627$	−14528.5	−0.925380
$628$	−16533.6	−1.05058
$629$	24732.6	1.56781
$630$	0	0
$631$	−18563.2	−1.17114	−0.585570	−	0.810622i	$-0.699129\pi$
$631$	−18563.2	−1.17114	−0.585570	+	0.810622i	$0.699129\pi$
$632$	18529.4	1.16623
$633$	−13633.6	−0.856062
$634$	1312.57	0.0822222
$635$	−8971.70	−0.560679
$636$	−1756.88	−0.109536
$637$	0	0
$638$	8005.60	0.496778
$639$	−6630.78	−0.410500
$640$	21374.4	1.32015
$641$	−4942.47	−0.304549	−0.152274	−	0.988338i	$-0.548660\pi$
$641$	−4942.47	−0.304549	−0.152274	+	0.988338i	$0.548660\pi$
$642$	−2032.31	−0.124936
$643$	−4048.57	−0.248305	−0.124152	−	0.992263i	$-0.539621\pi$
$643$	−4048.57	−0.248305	−0.124152	+	0.992263i	$0.539621\pi$
$644$	0	0
$645$	−18034.0	−1.10091
$646$	−9865.83	−0.600876
$647$	19646.9	1.19382	0.596909	−	0.802309i	$-0.296395\pi$
$647$	19646.9	1.19382	0.596909	+	0.802309i	$0.296395\pi$
$648$	935.732	0.0567269
$649$	15010.4	0.907875
$650$	2128.20	0.128423
$651$	0	0
$652$	25182.2	1.51260
$653$	−12358.3	−0.740610	−0.370305	−	0.928910i	$-0.620747\pi$
$653$	−12358.3	−0.740610	−0.370305	+	0.928910i	$0.620747\pi$
$654$	−4580.58	−0.273876
$655$	−28398.2	−1.69406
$656$	4643.83	0.276389
$657$	−1996.02	−0.118527
$658$	0	0
$659$	−5204.28	−0.307633	−0.153816	−	0.988099i	$-0.549156\pi$
$659$	−5204.28	−0.307633	−0.153816	+	0.988099i	$0.549156\pi$
$660$	13457.8	0.793703
$661$	−32688.5	−1.92350	−0.961752	−	0.273922i	$-0.911679\pi$
$661$	−32688.5	−1.92350	−0.961752	+	0.273922i	$0.911679\pi$
$662$	−4331.49	−0.254302
$663$	−6340.02	−0.371381
$664$	−14812.7	−0.865729
$665$	0	0
$666$	4502.15	0.261944
$667$	−36436.3	−2.11517
$668$	−539.730	−0.0312616
$669$	−8732.87	−0.504682
$670$	2416.64	0.139348
$671$	−24449.3	−1.40664
$672$	0	0
$673$	−16667.9	−0.954684	−0.477342	−	0.878718i	$-0.658400\pi$
$673$	−16667.9	−0.954684	−0.477342	+	0.878718i	$0.658400\pi$
$674$	−5995.37	−0.342631
$675$	−13544.2	−0.772320
$676$	11938.8	0.679265
$677$	−15905.4	−0.902943	−0.451472	−	0.892286i	$-0.649101\pi$
$677$	−15905.4	−0.902943	−0.451472	+	0.892286i	$0.649101\pi$
$678$	−4071.01	−0.230599
$679$	0	0
$680$	19403.4	1.09425
$681$	5533.28	0.311359
$682$	−7504.04	−0.421326
$683$	7692.02	0.430933	0.215466	−	0.976511i	$-0.430873\pi$
$683$	7692.02	0.430933	0.215466	+	0.976511i	$0.430873\pi$
$684$	14576.6	0.814841
$685$	29840.3	1.66443
$686$	0	0
$687$	18380.0	1.02073
$688$	−17306.8	−0.959033
$689$	−1852.04	−0.102405
$690$	7546.43	0.416359
$691$	−558.465	−0.0307453	−0.0153727	−	0.999882i	$-0.504893\pi$
$691$	−558.465	−0.0307453	−0.0153727	+	0.999882i	$0.504893\pi$
$692$	−3927.30	−0.215742
$693$	0	0
$694$	−5227.28	−0.285915
$695$	−31682.7	−1.72920
$696$	8869.87	0.483062
$697$	9711.08	0.527738
$698$	860.405	0.0466573
$699$	5260.27	0.284638
$700$	0	0
$701$	−26991.5	−1.45428	−0.727142	−	0.686487i	$-0.759152\pi$
$701$	−26991.5	−1.45428	−0.727142	+	0.686487i	$0.759152\pi$
$702$	−2908.44	−0.156371
$703$	31177.4	1.67266
$704$	8510.96	0.455638
$705$	2140.67	0.114358
$706$	1664.68	0.0887411
$707$	0	0
$708$	7832.94	0.415791
$709$	21561.3	1.14210	0.571052	−	0.820914i	$-0.306535\pi$
$709$	21561.3	1.14210	0.571052	+	0.820914i	$0.306535\pi$
$710$	−5240.40	−0.276998
$711$	−23232.6	−1.22544
$712$	−16572.9	−0.872324
$713$	34153.5	1.79391
$714$	0	0
$715$	14186.7	0.742032
$716$	26926.6	1.40544
$717$	5345.23	0.278412
$718$	−6112.73	−0.317723
$719$	26892.8	1.39490	0.697448	−	0.716635i	$-0.254319\pi$
$719$	26892.8	1.39490	0.697448	+	0.716635i	$0.254319\pi$
$720$	−11633.8	−0.602177
$721$	0	0
$722$	−6011.42	−0.309864
$723$	7580.74	0.389946
$724$	−10746.1	−0.551623
$725$	20508.1	1.05055
$726$	−1110.44	−0.0567665
$727$	19376.2	0.988476	0.494238	−	0.869327i	$-0.335447\pi$
$727$	19376.2	0.988476	0.494238	+	0.869327i	$0.335447\pi$
$728$	0	0
$729$	9991.70	0.507631
$730$	−1577.48	−0.0799798
$731$	−36191.6	−1.83118
$732$	−12758.4	−0.644216
$733$	−20089.2	−1.01229	−0.506147	−	0.862447i	$-0.668931\pi$
$733$	−20089.2	−1.01229	−0.506147	+	0.862447i	$0.668931\pi$
$734$	−6290.19	−0.316315
$735$	0	0
$736$	27287.0	1.36659
$737$	7141.93	0.356956
$738$	1767.74	0.0881726
$739$	10471.8	0.521263	0.260631	−	0.965438i	$-0.416069\pi$
$739$	10471.8	0.521263	0.260631	+	0.965438i	$0.416069\pi$
$740$	−28879.7	−1.43465
$741$	−7992.10	−0.396217
$742$	0	0
$743$	−7888.43	−0.389500	−0.194750	−	0.980853i	$-0.562390\pi$
$743$	−7888.43	−0.389500	−0.194750	+	0.980853i	$0.562390\pi$
$744$	−8314.17	−0.409694
$745$	3528.53	0.173524
$746$	3307.95	0.162349
$747$	18572.5	0.909682
$748$	27007.8	1.32019
$749$	0	0
$750$	1085.74	0.0528606
$751$	3380.98	0.164279	0.0821395	−	0.996621i	$-0.473825\pi$
$751$	3380.98	0.164279	0.0821395	+	0.996621i	$0.473825\pi$
$752$	2054.35	0.0996201
$753$	−8927.85	−0.432070
$754$	4403.86	0.212704
$755$	41688.0	2.00951
$756$	0	0
$757$	−2910.35	−0.139734	−0.0698668	−	0.997556i	$-0.522257\pi$
$757$	−2910.35	−0.139734	−0.0698668	+	0.997556i	$0.522257\pi$
$758$	4064.15	0.194745
$759$	22302.1	1.06655
$760$	24459.6	1.16742
$761$	−12925.9	−0.615719	−0.307860	−	0.951432i	$-0.599613\pi$
$761$	−12925.9	−0.615719	−0.307860	+	0.951432i	$0.599613\pi$
$762$	1704.66	0.0810410
$763$	0	0
$764$	−26921.6	−1.27485
$765$	−24328.5	−1.14980
$766$	−12595.6	−0.594122
$767$	8257.20	0.388722
$768$	927.264	0.0435674
$769$	32132.4	1.50680	0.753398	−	0.657565i	$-0.228414\pi$
$769$	32132.4	1.50680	0.753398	+	0.657565i	$0.228414\pi$
$770$	0	0
$771$	15873.1	0.741447
$772$	−11454.2	−0.533995
$773$	−33550.4	−1.56109	−0.780547	−	0.625098i	$-0.785059\pi$
$773$	−33550.4	−1.56109	−0.780547	+	0.625098i	$0.785059\pi$
$774$	−6588.07	−0.305947
$775$	−19223.2	−0.890993
$776$	26666.3	1.23359
$777$	0	0
$778$	3766.39	0.173562
$779$	12241.6	0.563030
$780$	7403.10	0.339838
$781$	−15487.0	−0.709563
$782$	15144.6	0.692544
$783$	−28026.8	−1.27918
$784$	0	0
$785$	34785.3	1.58158
$786$	5395.77	0.244861
$787$	−26048.2	−1.17982	−0.589909	−	0.807470i	$-0.700836\pi$
$787$	−26048.2	−1.17982	−0.589909	+	0.807470i	$0.700836\pi$
$788$	−3624.87	−0.163871
$789$	11551.3	0.521212
$790$	−18361.0	−0.826907
$791$	0	0
$792$	10438.4	0.468322
$793$	−13449.5	−0.602277
$794$	9300.50	0.415696
$795$	3696.33	0.164900
$796$	−21825.5	−0.971838
$797$	−30359.1	−1.34928	−0.674640	−	0.738147i	$-0.735701\pi$
$797$	−30359.1	−1.34928	−0.674640	+	0.738147i	$0.735701\pi$
$798$	0	0
$799$	4296.01	0.190215
$800$	−15358.4	−0.678754
$801$	20779.5	0.916612
$802$	−10402.6	−0.458014
$803$	−4661.95	−0.204878
$804$	3726.89	0.163479
$805$	0	0
$806$	−4127.95	−0.180398
$807$	21965.4	0.958141
$808$	1018.50	0.0443450
$809$	−3108.05	−0.135072	−0.0675361	−	0.997717i	$-0.521514\pi$
$809$	−3108.05	−0.135072	−0.0675361	+	0.997717i	$0.521514\pi$
$810$	−927.230	−0.0402217
$811$	−16109.0	−0.697490	−0.348745	−	0.937218i	$-0.613392\pi$
$811$	−16109.0	−0.697490	−0.348745	+	0.937218i	$0.613392\pi$
$812$	0	0
$813$	−2861.99	−0.123462
$814$	10515.3	0.452780
$815$	−52981.3	−2.27712
$816$	12143.3	0.520954
$817$	−45622.4	−1.95364
$818$	14256.6	0.609378
$819$	0	0
$820$	−11339.4	−0.482914
$821$	−32591.8	−1.38546	−0.692730	−	0.721197i	$-0.743592\pi$
$821$	−32591.8	−1.38546	−0.692730	+	0.721197i	$0.743592\pi$
$822$	−5669.76	−0.240579
$823$	7335.80	0.310705	0.155352	−	0.987859i	$-0.450349\pi$
$823$	7335.80	0.310705	0.155352	+	0.987859i	$0.450349\pi$
$824$	16230.3	0.686175
$825$	−12552.7	−0.529731
$826$	0	0
$827$	−23298.9	−0.979663	−0.489831	−	0.871817i	$-0.662942\pi$
$827$	−23298.9	−0.979663	−0.489831	+	0.871817i	$0.662942\pi$
$828$	−22375.9	−0.939151
$829$	14257.0	0.597307	0.298653	−	0.954362i	$-0.403463\pi$
$829$	14257.0	0.597307	0.298653	+	0.954362i	$0.403463\pi$
$830$	14678.1	0.613837
$831$	−19928.5	−0.831904
$832$	4681.86	0.195089
$833$	0	0
$834$	6019.84	0.249940
$835$	1135.55	0.0470625
$836$	34045.5	1.40848
$837$	26270.9	1.08489
$838$	1026.71	0.0423235
$839$	22037.1	0.906799	0.453399	−	0.891307i	$-0.350211\pi$
$839$	22037.1	0.906799	0.453399	+	0.891307i	$0.350211\pi$
$840$	0	0
$841$	18048.1	0.740008
$842$	−3772.26	−0.154395
$843$	−7036.91	−0.287502
$844$	31948.4	1.30297
$845$	−25118.1	−1.02259
$846$	782.016	0.0317805
$847$	0	0
$848$	3547.28	0.143649
$849$	2918.13	0.117962
$850$	−8524.11	−0.343970
$851$	−47859.0	−1.92783
$852$	−8081.64	−0.324968
$853$	9082.05	0.364553	0.182276	−	0.983247i	$-0.441653\pi$
$853$	9082.05	0.364553	0.182276	+	0.983247i	$0.441653\pi$
$854$	0	0
$855$	−30668.0	−1.22669
$856$	10111.6	0.403747
$857$	−45446.3	−1.81145	−0.905727	−	0.423861i	$-0.860674\pi$
$857$	−45446.3	−1.81145	−0.905727	+	0.423861i	$0.860674\pi$
$858$	−2695.53	−0.107254
$859$	−38680.8	−1.53640	−0.768202	−	0.640208i	$-0.778848\pi$
$859$	−38680.8	−1.53640	−0.768202	+	0.640208i	$0.778848\pi$
$860$	42260.1	1.67565
$861$	0	0
$862$	−13525.0	−0.534413
$863$	32679.4	1.28901	0.644507	−	0.764599i	$-0.277063\pi$
$863$	32679.4	1.28901	0.644507	+	0.764599i	$0.277063\pi$
$864$	20989.2	0.826465
$865$	8262.70	0.324786
$866$	−5197.60	−0.203951
$867$	10461.0	0.409774
$868$	0	0
$869$	−54262.6	−2.11822
$870$	−8789.28	−0.342511
$871$	3928.75	0.152837
$872$	22790.4	0.885068
$873$	−33434.9	−1.29622
$874$	19091.0	0.738858
$875$	0	0
$876$	−2432.76	−0.0938304
$877$	33643.4	1.29539	0.647694	−	0.761900i	$-0.275733\pi$
$877$	33643.4	1.29539	0.647694	+	0.761900i	$0.275733\pi$
$878$	8225.92	0.316186
$879$	−8267.74	−0.317252
$880$	−27172.3	−1.04088
$881$	−15468.7	−0.591548	−0.295774	−	0.955258i	$-0.595577\pi$
$881$	−15468.7	−0.591548	−0.295774	+	0.955258i	$0.595577\pi$
$882$	0	0
$883$	26313.9	1.00287	0.501435	−	0.865195i	$-0.332806\pi$
$883$	26313.9	1.00287	0.501435	+	0.865195i	$0.332806\pi$
$884$	14856.9	0.565263
$885$	−16479.8	−0.625947
$886$	−9208.17	−0.349158
$887$	16439.7	0.622314	0.311157	−	0.950359i	$-0.399284\pi$
$887$	16439.7	0.622314	0.311157	+	0.950359i	$0.399284\pi$
$888$	11650.6	0.440278
$889$	0	0
$890$	16422.3	0.618513
$891$	−2740.25	−0.103033
$892$	20464.3	0.768155
$893$	5415.46	0.202936
$894$	−670.434	−0.0250813
$895$	−56651.3	−2.11580
$896$	0	0
$897$	12268.3	0.456663
$898$	348.807	0.0129620
$899$	−39778.4	−1.47573
$900$	12594.2	0.466453
$901$	7418.00	0.274283
$902$	4128.78	0.152409
$903$	0	0
$904$	20255.0	0.745213
$905$	22608.8	0.830434
$906$	−7920.89	−0.290457
$907$	14210.5	0.520234	0.260117	−	0.965577i	$-0.416239\pi$
$907$	14210.5	0.520234	0.260117	+	0.965577i	$0.416239\pi$
$908$	−12966.5	−0.473907
$909$	−1277.02	−0.0465964
$910$	0	0
$911$	40479.3	1.47216	0.736081	−	0.676893i	$-0.236674\pi$
$911$	40479.3	1.47216	0.736081	+	0.676893i	$0.236674\pi$
$912$	15307.5	0.555793
$913$	43378.4	1.57242
$914$	−12122.7	−0.438713
$915$	26842.7	0.969827
$916$	−43071.0	−1.55361
$917$	0	0
$918$	11649.2	0.418825
$919$	41679.9	1.49608	0.748038	−	0.663656i	$-0.230996\pi$
$919$	41679.9	1.49608	0.748038	+	0.663656i	$0.230996\pi$
$920$	−37546.8	−1.34552
$921$	23074.5	0.825551
$922$	−1295.80	−0.0462853
$923$	−8519.37	−0.303812
$924$	0	0
$925$	26937.4	0.957508
$926$	−5971.26	−0.211909
$927$	−20349.9	−0.721012
$928$	−31781.0	−1.12420
$929$	−7489.65	−0.264508	−0.132254	−	0.991216i	$-0.542221\pi$
$929$	−7489.65	−0.264508	−0.132254	+	0.991216i	$0.542221\pi$
$930$	8238.63	0.290489
$931$	0	0
$932$	−12326.7	−0.433235
$933$	6342.00	0.222538
$934$	10479.6	0.367133
$935$	−56822.2	−1.98747
$936$	5742.11	0.200520
$937$	−17951.6	−0.625884	−0.312942	−	0.949772i	$-0.601315\pi$
$937$	−17951.6	−0.625884	−0.312942	+	0.949772i	$0.601315\pi$
$938$	0	0
$939$	9326.21	0.324121
$940$	−5016.35	−0.174059
$941$	3270.38	0.113296	0.0566480	−	0.998394i	$-0.481959\pi$
$941$	3270.38	0.113296	0.0566480	+	0.998394i	$0.481959\pi$
$942$	−6609.34	−0.228603
$943$	−18791.5	−0.648925
$944$	−15815.3	−0.545280
$945$	0	0
$946$	−15387.3	−0.528840
$947$	15171.0	0.520581	0.260290	−	0.965530i	$-0.416182\pi$
$947$	15171.0	0.520581	0.260290	+	0.965530i	$0.416182\pi$
$948$	−28316.0	−0.970107
$949$	−2564.53	−0.0877219
$950$	−10745.3	−0.366973
$951$	−4258.79	−0.145216
$952$	0	0
$953$	−48992.6	−1.66529	−0.832647	−	0.553804i	$-0.813176\pi$
$953$	−48992.6	−1.66529	−0.832647	+	0.553804i	$0.813176\pi$
$954$	1350.32	0.0458263
$955$	56640.7	1.91922
$956$	−12525.8	−0.423758
$957$	−25975.1	−0.877382
$958$	−10960.3	−0.369637
$959$	0	0
$960$	−9344.11	−0.314146
$961$	7495.22	0.251594
$962$	5784.46	0.193865
$963$	−12678.2	−0.424245
$964$	−17764.4	−0.593519
$965$	24098.6	0.803896
$966$	0	0
$967$	−23005.3	−0.765048	−0.382524	−	0.923946i	$-0.624945\pi$
$967$	−23005.3	−0.765048	−0.382524	+	0.923946i	$0.624945\pi$
$968$	5524.94	0.183449
$969$	32010.8	1.06123
$970$	−26424.1	−0.874666
$971$	59842.8	1.97780	0.988901	−	0.148576i	$-0.0474689\pi$
$971$	59842.8	1.97780	0.988901	+	0.148576i	$0.0474689\pi$
$972$	−27593.4	−0.910555
$973$	0	0
$974$	14530.5	0.478017
$975$	−6905.19	−0.226814
$976$	25760.3	0.844842
$977$	−29245.5	−0.957671	−0.478836	−	0.877905i	$-0.658941\pi$
$977$	−29245.5	−0.957671	−0.478836	+	0.877905i	$0.658941\pi$
$978$	10066.6	0.329137
$979$	48533.0	1.58439
$980$	0	0
$981$	−28575.1	−0.930002
$982$	−16212.6	−0.526847
$983$	−10612.8	−0.344348	−0.172174	−	0.985067i	$-0.555079\pi$
$983$	−10612.8	−0.344348	−0.172174	+	0.985067i	$0.555079\pi$
$984$	4574.51	0.148201
$985$	7626.41	0.246698
$986$	−17638.8	−0.569710
$987$	0	0
$988$	18728.4	0.603065
$989$	70032.8	2.25168
$990$	−10343.5	−0.332059
$991$	−28415.0	−0.910828	−0.455414	−	0.890280i	$-0.650509\pi$
$991$	−28415.0	−0.910828	−0.455414	+	0.890280i	$0.650509\pi$
$992$	29789.9	0.953458
$993$	14054.0	0.449134
$994$	0	0
$995$	45918.9	1.46304
$996$	22636.3	0.720139
$997$	6719.79	0.213458	0.106729	−	0.994288i	$-0.465962\pi$
$997$	6719.79	0.213458	0.106729	+	0.994288i	$0.465962\pi$
$998$	14412.9	0.457146
$999$	−36813.1	−1.16588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.15	yes	35
7.6	odd	2		2303.4.a.g.1.15	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.15	✓	35	7.6	odd	2
2303.4.a.h.1.15	yes	35	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)

\(f(q)\)	\(=\)	\(q-0.936762 q^{2} +3.03943 q^{3} -7.12248 q^{4} +14.9851 q^{5} -2.84722 q^{6} +14.1662 q^{8} -17.7619 q^{9} +O(q^{10})\)	\(q-0.936762 q^{2} +3.03943 q^{3} -7.12248 q^{4} +14.9851 q^{5} -2.84722 q^{6} +14.1662 q^{8} -17.7619 q^{9} -14.0375 q^{10} -41.4851 q^{11} -21.6483 q^{12} -22.8208 q^{13} +45.5461 q^{15} +43.7095 q^{16} +91.4044 q^{17} +16.6386 q^{18} +115.223 q^{19} -106.731 q^{20} +38.8616 q^{22} -176.873 q^{23} +43.0571 q^{24} +99.5526 q^{25} +21.3777 q^{26} -136.051 q^{27} +206.003 q^{29} -42.6659 q^{30} -193.096 q^{31} -154.275 q^{32} -126.091 q^{33} -85.6242 q^{34} +126.508 q^{36} +270.584 q^{37} -107.936 q^{38} -69.3623 q^{39} +212.281 q^{40} +106.243 q^{41} -395.950 q^{43} +295.476 q^{44} -266.163 q^{45} +165.688 q^{46} +47.0000 q^{47} +132.852 q^{48} -93.2571 q^{50} +277.817 q^{51} +162.541 q^{52} +81.1559 q^{53} +127.447 q^{54} -621.657 q^{55} +350.211 q^{57} -192.975 q^{58} -361.827 q^{59} -324.401 q^{60} +589.352 q^{61} +180.885 q^{62} -205.157 q^{64} -341.972 q^{65} +118.117 q^{66} -172.157 q^{67} -651.026 q^{68} -537.593 q^{69} +373.316 q^{71} -251.617 q^{72} +112.377 q^{73} -253.473 q^{74} +302.583 q^{75} -820.670 q^{76} +64.9759 q^{78} +1308.00 q^{79} +654.990 q^{80} +66.0540 q^{81} -99.5245 q^{82} -1045.64 q^{83} +1369.70 q^{85} +370.911 q^{86} +626.131 q^{87} -587.684 q^{88} -1169.89 q^{89} +249.331 q^{90} +1259.77 q^{92} -586.903 q^{93} -44.0278 q^{94} +1726.62 q^{95} -468.907 q^{96} +1882.40 q^{97} +736.852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

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Database

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