LMFDB - Embedded newform 2445.4.a.i.1.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2445,4,Mod(1,2445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2445.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 2445 = 3 \cdot 5 \cdot 163 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [43,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$144.259669964$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	2445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.42592 q^{2} +3.00000 q^{3} +3.73695 q^{4} +5.00000 q^{5} +10.2778 q^{6} -10.7086 q^{7} -14.6049 q^{8} +9.00000 q^{9} +17.1296 q^{10} -4.08636 q^{11} +11.2108 q^{12} +10.8412 q^{13} -36.6870 q^{14} +15.0000 q^{15} -79.9308 q^{16} -119.858 q^{17} +30.8333 q^{18} +113.260 q^{19} +18.6847 q^{20} -32.1259 q^{21} -13.9996 q^{22} +145.152 q^{23} -43.8147 q^{24} +25.0000 q^{25} +37.1411 q^{26} +27.0000 q^{27} -40.0176 q^{28} +122.232 q^{29} +51.3888 q^{30} -82.7471 q^{31} -156.998 q^{32} -12.2591 q^{33} -410.623 q^{34} -53.5432 q^{35} +33.6325 q^{36} +272.936 q^{37} +388.019 q^{38} +32.5236 q^{39} -73.0245 q^{40} +373.899 q^{41} -110.061 q^{42} +239.712 q^{43} -15.2705 q^{44} +45.0000 q^{45} +497.279 q^{46} -562.505 q^{47} -239.792 q^{48} -228.325 q^{49} +85.6481 q^{50} -359.573 q^{51} +40.5130 q^{52} +204.052 q^{53} +92.4999 q^{54} -20.4318 q^{55} +156.399 q^{56} +339.779 q^{57} +418.757 q^{58} -317.885 q^{59} +56.0542 q^{60} +652.164 q^{61} -283.485 q^{62} -96.3777 q^{63} +101.585 q^{64} +54.2060 q^{65} -41.9987 q^{66} +530.550 q^{67} -447.902 q^{68} +435.456 q^{69} -183.435 q^{70} +1056.04 q^{71} -131.444 q^{72} -318.572 q^{73} +935.057 q^{74} +75.0000 q^{75} +423.245 q^{76} +43.7594 q^{77} +111.423 q^{78} -84.6532 q^{79} -399.654 q^{80} +81.0000 q^{81} +1280.95 q^{82} +1175.52 q^{83} -120.053 q^{84} -599.288 q^{85} +821.235 q^{86} +366.696 q^{87} +59.6809 q^{88} +118.715 q^{89} +154.167 q^{90} -116.095 q^{91} +542.425 q^{92} -248.241 q^{93} -1927.10 q^{94} +566.298 q^{95} -470.993 q^{96} -281.113 q^{97} -782.224 q^{98} -36.7773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 18 q^{2} + 129 q^{3} + 198 q^{4} + 215 q^{5} + 54 q^{6} + 137 q^{7} + 201 q^{8} + 387 q^{9} + 90 q^{10} + 137 q^{11} + 594 q^{12} + 212 q^{13} + 246 q^{14} + 645 q^{15} + 930 q^{16} + 547 q^{17}+ \cdots + 1233 q^{99}+O(q^{100}) $ 43 * q + 18 * q^2 + 129 * q^3 + 198 * q^4 + 215 * q^5 + 54 * q^6 + 137 * q^7 + 201 * q^8 + 387 * q^9 + 90 * q^10 + 137 * q^11 + 594 * q^12 + 212 * q^13 + 246 * q^14 + 645 * q^15 + 930 * q^16 + 547 * q^17 + 162 * q^18 + 563 * q^19 + 990 * q^20 + 411 * q^21 + 279 * q^22 + 793 * q^23 + 603 * q^24 + 1075 * q^25 + 520 * q^26 + 1161 * q^27 + 833 * q^28 + 699 * q^29 + 270 * q^30 + 1130 * q^31 + 1651 * q^32 + 411 * q^33 + 651 * q^34 + 685 * q^35 + 1782 * q^36 + 644 * q^37 + 1122 * q^38 + 636 * q^39 + 1005 * q^40 + 1447 * q^41 + 738 * q^42 + 1629 * q^43 + 1828 * q^44 + 1935 * q^45 + 435 * q^46 + 1962 * q^47 + 2790 * q^48 + 3050 * q^49 + 450 * q^50 + 1641 * q^51 + 2284 * q^52 + 1995 * q^53 + 486 * q^54 + 685 * q^55 - 662 * q^56 + 1689 * q^57 - 130 * q^58 + 1935 * q^59 + 2970 * q^60 + 2152 * q^61 + 1975 * q^62 + 1233 * q^63 + 6187 * q^64 + 1060 * q^65 + 837 * q^66 + 2968 * q^67 + 2412 * q^68 + 2379 * q^69 + 1230 * q^70 + 1835 * q^71 + 1809 * q^72 + 1095 * q^73 + 2874 * q^74 + 3225 * q^75 + 2866 * q^76 + 4658 * q^77 + 1560 * q^78 + 2262 * q^79 + 4650 * q^80 + 3483 * q^81 + 746 * q^82 + 5285 * q^83 + 2499 * q^84 + 2735 * q^85 + 2389 * q^86 + 2097 * q^87 + 4391 * q^88 + 3012 * q^89 + 810 * q^90 + 3560 * q^91 + 5808 * q^92 + 3390 * q^93 + 887 * q^94 + 2815 * q^95 + 4953 * q^96 + 1108 * q^97 + 2858 * q^98 + 1233 * 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 $

$2$	3.42592	1.21125	0.605623	−	0.795751i	$-0.292924\pi$
$2$	3.42592	1.21125	0.605623	+	0.795751i	$0.292924\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	3.73695	0.467118
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	10.2778	0.699314
$7$	−10.7086	−0.578212	−0.289106	−	0.957297i	$-0.593358\pi$
$7$	−10.7086	−0.578212	−0.289106	+	0.957297i	$0.593358\pi$
$8$	−14.6049	−0.645451
$9$	9.00000	0.333333
$10$	17.1296	0.541686
$11$	−4.08636	−0.112008	−0.0560038	−	0.998431i	$-0.517836\pi$
$11$	−4.08636	−0.112008	−0.0560038	+	0.998431i	$0.517836\pi$
$12$	11.2108	0.269691
$13$	10.8412	0.231293	0.115647	−	0.993290i	$-0.463106\pi$
$13$	10.8412	0.231293	0.115647	+	0.993290i	$0.463106\pi$
$14$	−36.6870	−0.700357
$15$	15.0000	0.258199
$16$	−79.9308	−1.24892
$17$	−119.858	−1.70999	−0.854993	−	0.518640i	$-0.826439\pi$
$17$	−119.858	−1.70999	−0.854993	+	0.518640i	$0.826439\pi$
$18$	30.8333	0.403749
$19$	113.260	1.36755	0.683777	−	0.729691i	$-0.260336\pi$
$19$	113.260	1.36755	0.683777	+	0.729691i	$0.260336\pi$
$20$	18.6847	0.208902
$21$	−32.1259	−0.333831
$22$	−13.9996	−0.135669
$23$	145.152	1.31592	0.657962	−	0.753051i	$-0.271419\pi$
$23$	145.152	1.31592	0.657962	+	0.753051i	$0.271419\pi$
$24$	−43.8147	−0.372651
$25$	25.0000	0.200000
$26$	37.1411	0.280153
$27$	27.0000	0.192450
$28$	−40.0176	−0.270093
$29$	122.232	0.782686	0.391343	−	0.920245i	$-0.372011\pi$
$29$	122.232	0.782686	0.391343	+	0.920245i	$0.372011\pi$
$30$	51.3888	0.312743
$31$	−82.7471	−0.479413	−0.239707	−	0.970845i	$-0.577051\pi$
$31$	−82.7471	−0.479413	−0.239707	+	0.970845i	$0.577051\pi$
$32$	−156.998	−0.867298
$33$	−12.2591	−0.0646677
$34$	−410.623	−2.07121
$35$	−53.5432	−0.258584
$36$	33.6325	0.155706
$37$	272.936	1.21271	0.606357	−	0.795193i	$-0.292630\pi$
$37$	272.936	1.21271	0.606357	+	0.795193i	$0.292630\pi$
$38$	388.019	1.65645
$39$	32.5236	0.133537
$40$	−73.0245	−0.288655
$41$	373.899	1.42422	0.712112	−	0.702066i	$-0.247739\pi$
$41$	373.899	1.42422	0.712112	+	0.702066i	$0.247739\pi$
$42$	−110.061	−0.404352
$43$	239.712	0.850134	0.425067	−	0.905162i	$-0.360251\pi$
$43$	239.712	0.850134	0.425067	+	0.905162i	$0.360251\pi$
$44$	−15.2705	−0.0523208
$45$	45.0000	0.149071
$46$	497.279	1.59391
$47$	−562.505	−1.74574	−0.872869	−	0.487954i	$-0.837743\pi$
$47$	−562.505	−1.74574	−0.872869	+	0.487954i	$0.837743\pi$
$48$	−239.792	−0.721064
$49$	−228.325	−0.665671
$50$	85.6481	0.242249
$51$	−359.573	−0.987261
$52$	40.5130	0.108041
$53$	204.052	0.528843	0.264421	−	0.964407i	$-0.414819\pi$
$53$	204.052	0.528843	0.264421	+	0.964407i	$0.414819\pi$
$54$	92.4999	0.233105
$55$	−20.4318	−0.0500914
$56$	156.399	0.373208
$57$	339.779	0.789558
$58$	418.757	0.948026
$59$	−317.885	−0.701442	−0.350721	−	0.936480i	$-0.614064\pi$
$59$	−317.885	−0.701442	−0.350721	+	0.936480i	$0.614064\pi$
$60$	56.0542	0.120609
$61$	652.164	1.36887	0.684435	−	0.729074i	$-0.260049\pi$
$61$	652.164	1.36887	0.684435	+	0.729074i	$0.260049\pi$
$62$	−283.485	−0.580688
$63$	−96.3777	−0.192737
$64$	101.585	0.198408
$65$	54.2060	0.103437
$66$	−41.9987	−0.0783285
$67$	530.550	0.967418	0.483709	−	0.875229i	$-0.339289\pi$
$67$	530.550	0.967418	0.483709	+	0.875229i	$0.339289\pi$
$68$	−447.902	−0.798766
$69$	435.456	0.759749
$70$	−183.435	−0.313209
$71$	1056.04	1.76520	0.882602	−	0.470121i	$-0.155790\pi$
$71$	1056.04	1.76520	0.882602	+	0.470121i	$0.155790\pi$
$72$	−131.444	−0.215150
$73$	−318.572	−0.510768	−0.255384	−	0.966840i	$-0.582202\pi$
$73$	−318.572	−0.510768	−0.255384	+	0.966840i	$0.582202\pi$
$74$	935.057	1.46889
$75$	75.0000	0.115470
$76$	423.245	0.638810
$77$	43.7594	0.0647642
$78$	111.423	0.161746
$79$	−84.6532	−0.120560	−0.0602799	−	0.998182i	$-0.519199\pi$
$79$	−84.6532	−0.120560	−0.0602799	+	0.998182i	$0.519199\pi$
$80$	−399.654	−0.558533
$81$	81.0000	0.111111
$82$	1280.95	1.72509
$83$	1175.52	1.55458	0.777289	−	0.629144i	$-0.216594\pi$
$83$	1175.52	1.55458	0.777289	+	0.629144i	$0.216594\pi$
$84$	−120.053	−0.155939
$85$	−599.288	−0.764729
$86$	821.235	1.02972
$87$	366.696	0.451884
$88$	59.6809	0.0722955
$89$	118.715	0.141390	0.0706952	−	0.997498i	$-0.477478\pi$
$89$	118.715	0.141390	0.0706952	+	0.997498i	$0.477478\pi$
$90$	154.167	0.180562
$91$	−116.095	−0.133736
$92$	542.425	0.614692
$93$	−248.241	−0.276789
$94$	−1927.10	−2.11452
$95$	566.298	0.611589
$96$	−470.993	−0.500734
$97$	−281.113	−0.294254	−0.147127	−	0.989118i	$-0.547003\pi$
$97$	−281.113	−0.294254	−0.147127	+	0.989118i	$0.547003\pi$
$98$	−782.224	−0.806291
$99$	−36.7773	−0.0373359
$100$	93.4237	0.0934237
$101$	1723.01	1.69749	0.848744	−	0.528804i	$-0.177359\pi$
$101$	1723.01	1.69749	0.848744	+	0.528804i	$0.177359\pi$
$102$	−1231.87	−1.19582
$103$	153.454	0.146799	0.0733996	−	0.997303i	$-0.476615\pi$
$103$	153.454	0.146799	0.0733996	+	0.997303i	$0.476615\pi$
$104$	−158.335	−0.149288
$105$	−160.630	−0.149294
$106$	699.066	0.640559
$107$	1000.44	0.903886	0.451943	−	0.892047i	$-0.350731\pi$
$107$	1000.44	0.903886	0.451943	+	0.892047i	$0.350731\pi$
$108$	100.898	0.0898970
$109$	324.206	0.284893	0.142447	−	0.989802i	$-0.454503\pi$
$109$	324.206	0.284893	0.142447	+	0.989802i	$0.454503\pi$
$110$	−69.9978	−0.0606730
$111$	818.808	0.700160
$112$	855.950	0.722140
$113$	−53.0372	−0.0441533	−0.0220766	−	0.999756i	$-0.507028\pi$
$113$	−53.0372	−0.0441533	−0.0220766	+	0.999756i	$0.507028\pi$
$114$	1164.06	0.956349
$115$	725.759	0.588499
$116$	456.774	0.365607
$117$	97.5709	0.0770977
$118$	−1089.05	−0.849620
$119$	1283.51	0.988734
$120$	−219.073	−0.166655
$121$	−1314.30	−0.987454
$122$	2234.26	1.65804
$123$	1121.70	0.822276
$124$	−309.221	−0.223943
$125$	125.000	0.0894427
$126$	−330.183	−0.233452
$127$	408.576	0.285475	0.142737	−	0.989761i	$-0.454410\pi$
$127$	408.576	0.285475	0.142737	+	0.989761i	$0.454410\pi$
$128$	1604.00	1.10762
$129$	719.136	0.490825
$130$	185.706	0.125288
$131$	−745.918	−0.497489	−0.248745	−	0.968569i	$-0.580018\pi$
$131$	−745.918	−0.497489	−0.248745	+	0.968569i	$0.580018\pi$
$132$	−45.8115	−0.0302074
$133$	−1212.86	−0.790737
$134$	1817.62	1.17178
$135$	135.000	0.0860663
$136$	1750.51	1.10371
$137$	−932.352	−0.581432	−0.290716	−	0.956809i	$-0.593894\pi$
$137$	−932.352	−0.581432	−0.290716	+	0.956809i	$0.593894\pi$
$138$	1491.84	0.920243
$139$	−1388.41	−0.847216	−0.423608	−	0.905846i	$-0.639237\pi$
$139$	−1388.41	−0.847216	−0.423608	+	0.905846i	$0.639237\pi$
$140$	−200.088	−0.120789
$141$	−1687.51	−1.00790
$142$	3617.93	2.13810
$143$	−44.3011	−0.0259066
$144$	−719.377	−0.416306
$145$	611.159	0.350028
$146$	−1091.40	−0.618666
$147$	−684.975	−0.384325
$148$	1019.95	0.566481
$149$	−2080.19	−1.14373	−0.571866	−	0.820347i	$-0.693780\pi$
$149$	−2080.19	−1.14373	−0.571866	+	0.820347i	$0.693780\pi$
$150$	256.944	0.139863
$151$	−2506.98	−1.35109	−0.675547	−	0.737317i	$-0.736092\pi$
$151$	−2506.98	−1.35109	−0.675547	+	0.737317i	$0.736092\pi$
$152$	−1654.14	−0.882690
$153$	−1078.72	−0.569995
$154$	149.916	0.0784454
$155$	−413.735	−0.214400
$156$	121.539	0.0623776
$157$	1414.04	0.718807	0.359403	−	0.933182i	$-0.382980\pi$
$157$	1414.04	0.718807	0.359403	+	0.933182i	$0.382980\pi$
$158$	−290.015	−0.146028
$159$	612.155	0.305328
$160$	−784.988	−0.387867
$161$	−1554.38	−0.760883
$162$	277.500	0.134583
$163$	−163.000	−0.0783260
$163$	−163.000	−0.0783260
$164$	1397.24	0.665281
$165$	−61.2954	−0.0289203
$166$	4027.24	1.88298
$167$	1087.46	0.503891	0.251946	−	0.967741i	$-0.418930\pi$
$167$	1087.46	0.503891	0.251946	+	0.967741i	$0.418930\pi$
$168$	469.196	0.215472
$169$	−2079.47	−0.946504
$170$	−2053.12	−0.926275
$171$	1019.34	0.455851
$172$	895.791	0.397113
$173$	2328.39	1.02326	0.511631	−	0.859205i	$-0.329042\pi$
$173$	2328.39	1.02326	0.511631	+	0.859205i	$0.329042\pi$
$174$	1256.27	0.547343
$175$	−267.716	−0.115642
$176$	326.626	0.139888
$177$	−953.655	−0.404978
$178$	406.708	0.171259
$179$	−63.5121	−0.0265202	−0.0132601	−	0.999912i	$-0.504221\pi$
$179$	−63.5121	−0.0265202	−0.0132601	+	0.999912i	$0.504221\pi$
$180$	168.163	0.0696339
$181$	4670.81	1.91811	0.959056	−	0.283216i	$-0.0914015\pi$
$181$	4670.81	1.91811	0.959056	+	0.283216i	$0.0914015\pi$
$182$	−397.731	−0.161988
$183$	1956.49	0.790318
$184$	−2119.93	−0.849365
$185$	1364.68	0.542342
$186$	−850.455	−0.335260
$187$	489.782	0.191532
$188$	−2102.05	−0.815467
$189$	−289.133	−0.111277
$190$	1940.09	0.740785
$191$	−58.7646	−0.0222621	−0.0111310	−	0.999938i	$-0.503543\pi$
$191$	−58.7646	−0.0222621	−0.0111310	+	0.999938i	$0.503543\pi$
$192$	304.754	0.114551
$193$	−3275.02	−1.22146	−0.610729	−	0.791840i	$-0.709124\pi$
$193$	−3275.02	−1.22146	−0.610729	+	0.791840i	$0.709124\pi$
$194$	−963.071	−0.356415
$195$	162.618	0.0597196
$196$	−853.239	−0.310947
$197$	−313.918	−0.113531	−0.0567657	−	0.998388i	$-0.518079\pi$
$197$	−313.918	−0.113531	−0.0567657	+	0.998388i	$0.518079\pi$
$198$	−125.996	−0.0452230
$199$	4737.43	1.68757	0.843787	−	0.536678i	$-0.180321\pi$
$199$	4737.43	1.68757	0.843787	+	0.536678i	$0.180321\pi$
$200$	−365.122	−0.129090
$201$	1591.65	0.558539
$202$	5902.91	2.05608
$203$	−1308.94	−0.452558
$204$	−1343.71	−0.461168
$205$	1869.49	0.636932
$206$	525.723	0.177810
$207$	1306.37	0.438641
$208$	−866.547	−0.288866
$209$	−462.820	−0.153177
$210$	−550.305	−0.180832
$211$	−2861.49	−0.933618	−0.466809	−	0.884358i	$-0.654596\pi$
$211$	−2861.49	−0.933618	−0.466809	+	0.884358i	$0.654596\pi$
$212$	762.531	0.247032
$213$	3168.13	1.01914
$214$	3427.42	1.09483
$215$	1198.56	0.380191
$216$	−394.332	−0.124217
$217$	886.109	0.277203
$218$	1110.71	0.345076
$219$	−955.717	−0.294892
$220$	−76.3526	−0.0233986
$221$	−1299.40	−0.395508
$222$	2805.17	0.848067
$223$	6504.69	1.95330	0.976651	−	0.214830i	$-0.0689197\pi$
$223$	6504.69	1.95330	0.976651	+	0.214830i	$0.0689197\pi$
$224$	1681.23	0.501482
$225$	225.000	0.0666667
$226$	−181.701	−0.0534805
$227$	−2575.79	−0.753134	−0.376567	−	0.926389i	$-0.622896\pi$
$227$	−2575.79	−0.753134	−0.376567	+	0.926389i	$0.622896\pi$
$228$	1269.74	0.368817
$229$	974.538	0.281220	0.140610	−	0.990065i	$-0.455094\pi$
$229$	974.538	0.281220	0.140610	+	0.990065i	$0.455094\pi$
$230$	2486.39	0.712817
$231$	131.278	0.0373916
$232$	−1785.18	−0.505186
$233$	4030.63	1.13328	0.566642	−	0.823964i	$-0.308242\pi$
$233$	4030.63	1.13328	0.566642	+	0.823964i	$0.308242\pi$
$234$	334.270	0.0933843
$235$	−2812.52	−0.780718
$236$	−1187.92	−0.327657
$237$	−253.960	−0.0696053
$238$	4397.21	1.19760
$239$	2871.91	0.777273	0.388636	−	0.921391i	$-0.372946\pi$
$239$	2871.91	0.777273	0.388636	+	0.921391i	$0.372946\pi$
$240$	−1198.96	−0.322469
$241$	1102.21	0.294604	0.147302	−	0.989092i	$-0.452941\pi$
$241$	1102.21	0.294604	0.147302	+	0.989092i	$0.452941\pi$
$242$	−4502.70	−1.19605
$243$	243.000	0.0641500
$244$	2437.10	0.639424
$245$	−1141.63	−0.297697
$246$	3842.85	0.995979
$247$	1227.87	0.316306
$248$	1208.51	0.309438
$249$	3526.56	0.897536
$250$	428.240	0.108337
$251$	−3473.25	−0.873426	−0.436713	−	0.899601i	$-0.643857\pi$
$251$	−3473.25	−0.873426	−0.436713	+	0.899601i	$0.643857\pi$
$252$	−360.158	−0.0900312
$253$	−593.143	−0.147394
$254$	1399.75	0.345780
$255$	−1797.87	−0.441516
$256$	4682.51	1.14319
$257$	1895.20	0.459997	0.229999	−	0.973191i	$-0.426128\pi$
$257$	1895.20	0.459997	0.229999	+	0.973191i	$0.426128\pi$
$258$	2463.71	0.594510
$259$	−2922.77	−0.701206
$260$	202.565	0.0483175
$261$	1100.09	0.260895
$262$	−2555.46	−0.602582
$263$	2569.69	0.602487	0.301243	−	0.953547i	$-0.402598\pi$
$263$	2569.69	0.602487	0.301243	+	0.953547i	$0.402598\pi$
$264$	179.043	0.0417398
$265$	1020.26	0.236506
$266$	−4155.15	−0.957777
$267$	356.145	0.0816318
$268$	1982.64	0.451899
$269$	−3920.35	−0.888580	−0.444290	−	0.895883i	$-0.646544\pi$
$269$	−3920.35	−0.888580	−0.444290	+	0.895883i	$0.646544\pi$
$270$	462.500	0.104248
$271$	−6560.01	−1.47045	−0.735226	−	0.677822i	$-0.762924\pi$
$271$	−6560.01	−1.47045	−0.735226	+	0.677822i	$0.762924\pi$
$272$	9580.32	2.13563
$273$	−348.284	−0.0772128
$274$	−3194.17	−0.704258
$275$	−102.159	−0.0224015
$276$	1627.27	0.354893
$277$	−4148.00	−0.899745	−0.449873	−	0.893093i	$-0.648531\pi$
$277$	−4148.00	−0.899745	−0.449873	+	0.893093i	$0.648531\pi$
$278$	−4756.57	−1.02619
$279$	−744.724	−0.159804
$280$	781.993	0.166904
$281$	−2092.49	−0.444226	−0.222113	−	0.975021i	$-0.571295\pi$
$281$	−2092.49	−0.444226	−0.222113	+	0.975021i	$0.571295\pi$
$282$	−5781.29	−1.22082
$283$	1573.97	0.330611	0.165306	−	0.986242i	$-0.447139\pi$
$283$	1573.97	0.330611	0.165306	+	0.986242i	$0.447139\pi$
$284$	3946.38	0.824559
$285$	1698.89	0.353101
$286$	−151.772	−0.0313793
$287$	−4003.95	−0.823504
$288$	−1412.98	−0.289099
$289$	9452.86	1.92405
$290$	2093.79	0.423970
$291$	−843.338	−0.169888
$292$	−1190.49	−0.238589
$293$	2767.59	0.551823	0.275912	−	0.961183i	$-0.411020\pi$
$293$	2767.59	0.551823	0.275912	+	0.961183i	$0.411020\pi$
$294$	−2346.67	−0.465513
$295$	−1589.43	−0.313695
$296$	−3986.20	−0.782747
$297$	−110.332	−0.0215559
$298$	−7126.58	−1.38534
$299$	1573.62	0.304364
$300$	280.271	0.0539382
$301$	−2566.99	−0.491558
$302$	−8588.72	−1.63651
$303$	5169.04	0.980045
$304$	−9052.93	−1.70796
$305$	3260.82	0.612177
$306$	−3695.61	−0.690405
$307$	−8517.20	−1.58339	−0.791697	−	0.610914i	$-0.790802\pi$
$307$	−8517.20	−1.58339	−0.791697	+	0.610914i	$0.790802\pi$
$308$	163.526	0.0302525
$309$	460.363	0.0847545
$310$	−1417.43	−0.259692
$311$	−6654.06	−1.21324	−0.606619	−	0.794993i	$-0.707475\pi$
$311$	−6654.06	−1.21324	−0.606619	+	0.794993i	$0.707475\pi$
$312$	−475.004	−0.0861917
$313$	3216.02	0.580767	0.290384	−	0.956910i	$-0.406217\pi$
$313$	3216.02	0.580767	0.290384	+	0.956910i	$0.406217\pi$
$314$	4844.39	0.870652
$315$	−481.889	−0.0861948
$316$	−316.345	−0.0563157
$317$	−10825.3	−1.91801	−0.959006	−	0.283387i	$-0.908542\pi$
$317$	−10825.3	−1.91801	−0.959006	+	0.283387i	$0.908542\pi$
$318$	2097.20	0.369827
$319$	−499.484	−0.0876668
$320$	507.924	0.0887306
$321$	3001.31	0.521859
$322$	−5325.18	−0.921617
$323$	−13575.0	−2.33850
$324$	302.693	0.0519020
$325$	271.030	0.0462586
$326$	−558.425	−0.0948722
$327$	972.619	0.164483
$328$	−5460.75	−0.919267
$329$	6023.66	1.00941
$330$	−209.993	−0.0350296
$331$	−5185.09	−0.861021	−0.430511	−	0.902585i	$-0.641667\pi$
$331$	−5185.09	−0.861021	−0.430511	+	0.902585i	$0.641667\pi$
$332$	4392.85	0.726172
$333$	2456.42	0.404238
$334$	3725.54	0.610337
$335$	2652.75	0.432643
$336$	2567.85	0.416928
$337$	8131.99	1.31447	0.657237	−	0.753684i	$-0.271725\pi$
$337$	8131.99	1.31447	0.657237	+	0.753684i	$0.271725\pi$
$338$	−7124.10	−1.14645
$339$	−159.112	−0.0254919
$340$	−2239.51	−0.357219
$341$	338.135	0.0536980
$342$	3492.17	0.552149
$343$	6118.11	0.963111
$344$	−3500.97	−0.548720
$345$	2177.28	0.339770
$346$	7976.88	1.23942
$347$	12549.8	1.94152	0.970758	−	0.240060i	$-0.0771672\pi$
$347$	12549.8	1.94152	0.970758	+	0.240060i	$0.0771672\pi$
$348$	1370.32	0.211083
$349$	−3496.22	−0.536241	−0.268121	−	0.963385i	$-0.586403\pi$
$349$	−3496.22	−0.536241	−0.268121	+	0.963385i	$0.586403\pi$
$350$	−917.174	−0.140071
$351$	292.713	0.0445124
$352$	641.549	0.0971440
$353$	5429.43	0.818638	0.409319	−	0.912391i	$-0.365766\pi$
$353$	5429.43	0.818638	0.409319	+	0.912391i	$0.365766\pi$
$354$	−3267.15	−0.490528
$355$	5280.22	0.789423
$356$	443.631	0.0660461
$357$	3850.54	0.570846
$358$	−217.588	−0.0321225
$359$	−2574.80	−0.378531	−0.189266	−	0.981926i	$-0.560611\pi$
$359$	−2574.80	−0.378531	−0.189266	+	0.981926i	$0.560611\pi$
$360$	−657.220	−0.0962182
$361$	5968.74	0.870205
$362$	16001.8	2.32331
$363$	−3942.90	−0.570107
$364$	−433.839	−0.0624708
$365$	−1592.86	−0.228423
$366$	6702.79	0.957270
$367$	−135.374	−0.0192547	−0.00962736	−	0.999954i	$-0.503065\pi$
$367$	−135.374	−0.0192547	−0.00962736	+	0.999954i	$0.503065\pi$
$368$	−11602.1	−1.64348
$369$	3365.09	0.474741
$370$	4675.29	0.656910
$371$	−2185.12	−0.305783
$372$	−927.664	−0.129293
$373$	5706.98	0.792216	0.396108	−	0.918204i	$-0.370361\pi$
$373$	5706.98	0.792216	0.396108	+	0.918204i	$0.370361\pi$
$374$	1677.95	0.231992
$375$	375.000	0.0516398
$376$	8215.32	1.12679
$377$	1325.14	0.181030
$378$	−990.548	−0.134784
$379$	3350.91	0.454154	0.227077	−	0.973877i	$-0.427083\pi$
$379$	3350.91	0.454154	0.227077	+	0.973877i	$0.427083\pi$
$380$	2116.23	0.285684
$381$	1225.73	0.164819
$382$	−201.323	−0.0269649
$383$	−5756.10	−0.767945	−0.383973	−	0.923344i	$-0.625444\pi$
$383$	−5756.10	−0.767945	−0.383973	+	0.923344i	$0.625444\pi$
$384$	4812.01	0.639484
$385$	218.797	0.0289634
$386$	−11220.0	−1.47949
$387$	2157.41	0.283378
$388$	−1050.50	−0.137452
$389$	6224.34	0.811277	0.405638	−	0.914034i	$-0.367049\pi$
$389$	6224.34	0.811277	0.405638	+	0.914034i	$0.367049\pi$
$390$	557.117	0.0723352
$391$	−17397.6	−2.25021
$392$	3334.66	0.429658
$393$	−2237.75	−0.287226
$394$	−1075.46	−0.137515
$395$	−423.266	−0.0539160
$396$	−137.435	−0.0174403
$397$	−1649.89	−0.208579	−0.104289	−	0.994547i	$-0.533257\pi$
$397$	−1649.89	−0.208579	−0.104289	+	0.994547i	$0.533257\pi$
$398$	16230.1	2.04407
$399$	−3638.57	−0.456532
$400$	−1998.27	−0.249784
$401$	−11581.4	−1.44226	−0.721131	−	0.692798i	$-0.756378\pi$
$401$	−11581.4	−1.44226	−0.721131	+	0.692798i	$0.756378\pi$
$402$	5452.87	0.676529
$403$	−897.079	−0.110885
$404$	6438.81	0.792927
$405$	405.000	0.0496904
$406$	−4484.32	−0.548160
$407$	−1115.31	−0.135833
$408$	5251.53	0.637229
$409$	6906.36	0.834958	0.417479	−	0.908687i	$-0.362914\pi$
$409$	6906.36	0.834958	0.417479	+	0.908687i	$0.362914\pi$
$410$	6404.74	0.771482
$411$	−2797.06	−0.335690
$412$	573.451	0.0685726
$413$	3404.12	0.405583
$414$	4475.51	0.531303
$415$	5877.60	0.695228
$416$	−1702.04	−0.200600
$417$	−4165.22	−0.489140
$418$	−1585.58	−0.185535
$419$	3067.91	0.357702	0.178851	−	0.983876i	$-0.442762\pi$
$419$	3067.91	0.357702	0.178851	+	0.983876i	$0.442762\pi$
$420$	−600.264	−0.0697378
$421$	−8383.11	−0.970470	−0.485235	−	0.874384i	$-0.661266\pi$
$421$	−8383.11	−0.970470	−0.485235	+	0.874384i	$0.661266\pi$
$422$	−9803.25	−1.13084
$423$	−5062.54	−0.581913
$424$	−2980.15	−0.341342
$425$	−2996.44	−0.341997
$426$	10853.8	1.23443
$427$	−6983.79	−0.791497
$428$	3738.58	0.422222
$429$	−132.903	−0.0149572
$430$	4106.18	0.460506
$431$	−12295.8	−1.37417	−0.687086	−	0.726576i	$-0.741111\pi$
$431$	−12295.8	−1.37417	−0.687086	+	0.726576i	$0.741111\pi$
$432$	−2158.13	−0.240355
$433$	14342.8	1.59185	0.795923	−	0.605398i	$-0.206986\pi$
$433$	14342.8	1.59185	0.795923	+	0.605398i	$0.206986\pi$
$434$	3035.74	0.335761
$435$	1833.48	0.202089
$436$	1211.54	0.133079
$437$	16439.8	1.79960
$438$	−3274.21	−0.357187
$439$	−9127.69	−0.992348	−0.496174	−	0.868223i	$-0.665262\pi$
$439$	−9127.69	−0.992348	−0.496174	+	0.868223i	$0.665262\pi$
$440$	298.404	0.0323315
$441$	−2054.93	−0.221890
$442$	−4451.65	−0.479058
$443$	4134.66	0.443439	0.221719	−	0.975110i	$-0.428833\pi$
$443$	4134.66	0.443439	0.221719	+	0.975110i	$0.428833\pi$
$444$	3059.84	0.327058
$445$	593.574	0.0632317
$446$	22284.6	2.36593
$447$	−6240.58	−0.660334
$448$	−1087.83	−0.114722
$449$	−12489.0	−1.31268	−0.656340	−	0.754465i	$-0.727896\pi$
$449$	−12489.0	−1.31268	−0.656340	+	0.754465i	$0.727896\pi$
$450$	770.833	0.0807498
$451$	−1527.89	−0.159524
$452$	−198.197	−0.0206248
$453$	−7520.94	−0.780054
$454$	−8824.47	−0.912231
$455$	−580.473	−0.0598088
$456$	−4962.43	−0.509621
$457$	5809.31	0.594635	0.297318	−	0.954779i	$-0.403908\pi$
$457$	5809.31	0.594635	0.297318	+	0.954779i	$0.403908\pi$
$458$	3338.69	0.340626
$459$	−3236.16	−0.329087
$460$	2712.12	0.274899
$461$	10230.2	1.03355	0.516777	−	0.856120i	$-0.327131\pi$
$461$	10230.2	1.03355	0.516777	+	0.856120i	$0.327131\pi$
$462$	449.749	0.0452905
$463$	2184.79	0.219300	0.109650	−	0.993970i	$-0.465027\pi$
$463$	2184.79	0.219300	0.109650	+	0.993970i	$0.465027\pi$
$464$	−9770.09	−0.977511
$465$	−1241.21	−0.123784
$466$	13808.6	1.37269
$467$	6300.86	0.624345	0.312173	−	0.950025i	$-0.398943\pi$
$467$	6300.86	0.624345	0.312173	+	0.950025i	$0.398943\pi$
$468$	364.617	0.0360137
$469$	−5681.47	−0.559373
$470$	−9635.49	−0.945642
$471$	4242.12	0.415003
$472$	4642.68	0.452747
$473$	−979.550	−0.0952215
$474$	−870.046	−0.0843092
$475$	2831.49	0.273511
$476$	4796.42	0.461856
$477$	1836.47	0.176281
$478$	9838.93	0.941469
$479$	−2457.26	−0.234395	−0.117198	−	0.993109i	$-0.537391\pi$
$479$	−2457.26	−0.234395	−0.117198	+	0.993109i	$0.537391\pi$
$480$	−2354.96	−0.223935
$481$	2958.96	0.280492
$482$	3776.09	0.356838
$483$	−4663.14	−0.439296
$484$	−4911.47	−0.461258
$485$	−1405.56	−0.131595
$486$	832.499	0.0777015
$487$	390.131	0.0363008	0.0181504	−	0.999835i	$-0.494222\pi$
$487$	390.131	0.0363008	0.0181504	+	0.999835i	$0.494222\pi$
$488$	−9524.79	−0.883539
$489$	−489.000	−0.0452216
$490$	−3911.12	−0.360584
$491$	−126.371	−0.0116151	−0.00580756	−	0.999983i	$-0.501849\pi$
$491$	−126.371	−0.0116151	−0.00580756	+	0.999983i	$0.501849\pi$
$492$	4191.72	0.384100
$493$	−14650.4	−1.33838
$494$	4206.59	0.383124
$495$	−183.886	−0.0166971
$496$	6614.04	0.598748
$497$	−11308.8	−1.02066
$498$	12081.7	1.08714
$499$	12217.3	1.09604	0.548019	−	0.836466i	$-0.315382\pi$
$499$	12217.3	1.09604	0.548019	+	0.836466i	$0.315382\pi$
$500$	467.118	0.0417803
$501$	3262.37	0.290922
$502$	−11899.1	−1.05793
$503$	229.314	0.0203272	0.0101636	−	0.999948i	$-0.496765\pi$
$503$	229.314	0.0203272	0.0101636	+	0.999948i	$0.496765\pi$
$504$	1407.59	0.124403
$505$	8615.07	0.759139
$506$	−2032.06	−0.178530
$507$	−6238.40	−0.546464
$508$	1526.83	0.133350
$509$	9100.44	0.792476	0.396238	−	0.918148i	$-0.370316\pi$
$509$	9100.44	0.792476	0.396238	+	0.918148i	$0.370316\pi$
$510$	−6159.35	−0.534785
$511$	3411.48	0.295332
$512$	3209.90	0.277068
$513$	3058.01	0.263186
$514$	6492.81	0.557170
$515$	767.272	0.0656506
$516$	2687.37	0.229273
$517$	2298.60	0.195536
$518$	−10013.2	−0.849333
$519$	6985.17	0.590780
$520$	−791.673	−0.0667638
$521$	1463.49	0.123065	0.0615324	−	0.998105i	$-0.480401\pi$
$521$	1463.49	0.123065	0.0615324	+	0.998105i	$0.480401\pi$
$522$	3768.81	0.316009
$523$	6581.97	0.550305	0.275152	−	0.961401i	$-0.411272\pi$
$523$	6581.97	0.550305	0.275152	+	0.961401i	$0.411272\pi$
$524$	−2787.45	−0.232386
$525$	−803.148	−0.0667662
$526$	8803.57	0.729760
$527$	9917.87	0.819790
$528$	979.878	0.0807647
$529$	8902.06	0.731656
$530$	3495.33	0.286467
$531$	−2860.97	−0.233814
$532$	−4532.38	−0.369368
$533$	4053.51	0.329413
$534$	1220.12	0.0988763
$535$	5002.18	0.404230
$536$	−7748.63	−0.624421
$537$	−190.536	−0.0153114
$538$	−13430.8	−1.07629
$539$	933.019	0.0745602
$540$	504.488	0.0402031
$541$	9136.58	0.726085	0.363043	−	0.931773i	$-0.381738\pi$
$541$	9136.58	0.726085	0.363043	+	0.931773i	$0.381738\pi$
$542$	−22474.1	−1.78108
$543$	14012.4	1.10742
$544$	18817.4	1.48307
$545$	1621.03	0.127408
$546$	−1193.19	−0.0935237
$547$	13050.7	1.02012	0.510060	−	0.860139i	$-0.329623\pi$
$547$	13050.7	1.02012	0.510060	+	0.860139i	$0.329623\pi$
$548$	−3484.15	−0.271598
$549$	5869.48	0.456290
$550$	−349.989	−0.0271338
$551$	13843.9	1.07037
$552$	−6359.78	−0.490381
$553$	906.521	0.0697092
$554$	−14210.7	−1.08981
$555$	4094.04	0.313121
$556$	−5188.40	−0.395750
$557$	9698.55	0.737775	0.368888	−	0.929474i	$-0.379739\pi$
$557$	9698.55	0.737775	0.368888	+	0.929474i	$0.379739\pi$
$558$	−2551.37	−0.193563
$559$	2598.77	0.196630
$560$	4279.75	0.322951
$561$	1469.35	0.110581
$562$	−7168.70	−0.538067
$563$	−13284.0	−0.994410	−0.497205	−	0.867633i	$-0.665640\pi$
$563$	−13284.0	−0.994410	−0.497205	+	0.867633i	$0.665640\pi$
$564$	−6306.15	−0.470810
$565$	−265.186	−0.0197460
$566$	5392.31	0.400452
$567$	−867.400	−0.0642458
$568$	−15423.4	−1.13935
$569$	−1695.57	−0.124925	−0.0624623	−	0.998047i	$-0.519895\pi$
$569$	−1695.57	−0.124925	−0.0624623	+	0.998047i	$0.519895\pi$
$570$	5820.28	0.427692
$571$	−23426.9	−1.71696	−0.858480	−	0.512848i	$-0.828591\pi$
$571$	−23426.9	−1.71696	−0.858480	+	0.512848i	$0.828591\pi$
$572$	−165.551	−0.0121014
$573$	−176.294	−0.0128530
$574$	−13717.2	−0.997466
$575$	3628.80	0.263185
$576$	914.262	0.0661359
$577$	−17661.8	−1.27430	−0.637151	−	0.770739i	$-0.719887\pi$
$577$	−17661.8	−1.27430	−0.637151	+	0.770739i	$0.719887\pi$
$578$	32384.8	2.33050
$579$	−9825.07	−0.705209
$580$	2283.87	0.163504
$581$	−12588.2	−0.898876
$582$	−2889.21	−0.205776
$583$	−833.829	−0.0592344
$584$	4652.72	0.329676
$585$	487.854	0.0344791
$586$	9481.54	0.668394
$587$	20055.2	1.41016	0.705081	−	0.709127i	$-0.250911\pi$
$587$	20055.2	1.41016	0.705081	+	0.709127i	$0.250911\pi$
$588$	−2559.72	−0.179525
$589$	−9371.90	−0.655624
$590$	−5445.25	−0.379962
$591$	−941.753	−0.0655474
$592$	−21816.0	−1.51458
$593$	−25146.2	−1.74137	−0.870684	−	0.491843i	$-0.836323\pi$
$593$	−25146.2	−1.74137	−0.870684	+	0.491843i	$0.836323\pi$
$594$	−377.988	−0.0261095
$595$	6417.56	0.442176
$596$	−7773.57	−0.534258
$597$	14212.3	0.974321
$598$	5391.11	0.368660
$599$	−1144.90	−0.0780961	−0.0390480	−	0.999237i	$-0.512433\pi$
$599$	−1144.90	−0.0780961	−0.0390480	+	0.999237i	$0.512433\pi$
$600$	−1095.37	−0.0745303
$601$	−11263.2	−0.764451	−0.382225	−	0.924069i	$-0.624842\pi$
$601$	−11263.2	−0.764451	−0.382225	+	0.924069i	$0.624842\pi$
$602$	−8794.31	−0.595398
$603$	4774.95	0.322473
$604$	−9368.45	−0.631121
$605$	−6571.51	−0.441603
$606$	17708.7	1.18708
$607$	−13547.9	−0.905920	−0.452960	−	0.891531i	$-0.649632\pi$
$607$	−13547.9	−0.905920	−0.452960	+	0.891531i	$0.649632\pi$
$608$	−17781.5	−1.18608
$609$	−3926.81	−0.261285
$610$	11171.3	0.741498
$611$	−6098.23	−0.403777
$612$	−4031.12	−0.266255
$613$	−16496.2	−1.08691	−0.543453	−	0.839439i	$-0.682883\pi$
$613$	−16496.2	−1.08691	−0.543453	+	0.839439i	$0.682883\pi$
$614$	−29179.3	−1.91788
$615$	5608.48	0.367733
$616$	−639.101	−0.0418021
$617$	17387.5	1.13451	0.567255	−	0.823542i	$-0.308005\pi$
$617$	17387.5	1.13451	0.567255	+	0.823542i	$0.308005\pi$
$618$	1577.17	0.102659
$619$	−8428.87	−0.547310	−0.273655	−	0.961828i	$-0.588233\pi$
$619$	−8428.87	−0.547310	−0.273655	+	0.961828i	$0.588233\pi$
$620$	−1546.11	−0.100150
$621$	3919.10	0.253250
$622$	−22796.3	−1.46953
$623$	−1271.27	−0.0817537
$624$	−2599.64	−0.166777
$625$	625.000	0.0400000
$626$	11017.8	0.703452
$627$	−1388.46	−0.0884365
$628$	5284.19	0.335768
$629$	−32713.5	−2.07372
$630$	−1650.91	−0.104403
$631$	16325.3	1.02995	0.514976	−	0.857204i	$-0.327801\pi$
$631$	16325.3	1.02995	0.514976	+	0.857204i	$0.327801\pi$
$632$	1236.35	0.0778155
$633$	−8584.48	−0.539024
$634$	−37086.6	−2.32318
$635$	2042.88	0.127668
$636$	2287.59	0.142624
$637$	−2475.32	−0.153965
$638$	−1711.19	−0.106186
$639$	9504.40	0.588401
$640$	8020.01	0.495342
$641$	−4159.45	−0.256300	−0.128150	−	0.991755i	$-0.540904\pi$
$641$	−4159.45	−0.256300	−0.128150	+	0.991755i	$0.540904\pi$
$642$	10282.3	0.632100
$643$	−5812.02	−0.356460	−0.178230	−	0.983989i	$-0.557037\pi$
$643$	−5812.02	−0.356460	−0.178230	+	0.983989i	$0.557037\pi$
$644$	−5808.63	−0.355422
$645$	3595.68	0.219504
$646$	−46507.0	−2.83250
$647$	−1288.43	−0.0782898	−0.0391449	−	0.999234i	$-0.512463\pi$
$647$	−1288.43	−0.0782898	−0.0391449	+	0.999234i	$0.512463\pi$
$648$	−1183.00	−0.0717168
$649$	1298.99	0.0785669
$650$	928.529	0.0560306
$651$	2658.33	0.160043
$652$	−609.122	−0.0365875
$653$	−9074.23	−0.543801	−0.271901	−	0.962325i	$-0.587652\pi$
$653$	−9074.23	−0.543801	−0.271901	+	0.962325i	$0.587652\pi$
$654$	3332.12	0.199230
$655$	−3729.59	−0.222484
$656$	−29886.0	−1.77874
$657$	−2867.15	−0.170256
$658$	20636.6	1.22264
$659$	7320.66	0.432735	0.216368	−	0.976312i	$-0.430579\pi$
$659$	7320.66	0.432735	0.216368	+	0.976312i	$0.430579\pi$
$660$	−229.058	−0.0135092
$661$	10970.0	0.645509	0.322755	−	0.946483i	$-0.395391\pi$
$661$	10970.0	0.645509	0.322755	+	0.946483i	$0.395391\pi$
$662$	−17763.7	−1.04291
$663$	−3898.21	−0.228347
$664$	−17168.3	−1.00340
$665$	−6064.28	−0.353628
$666$	8415.52	0.489632
$667$	17742.2	1.02996
$668$	4063.77	0.235377
$669$	19514.1	1.12774
$670$	9088.12	0.524037
$671$	−2664.98	−0.153324
$672$	5043.69	0.289531
$673$	14422.4	0.826066	0.413033	−	0.910716i	$-0.364469\pi$
$673$	14422.4	0.826066	0.413033	+	0.910716i	$0.364469\pi$
$674$	27859.6	1.59215
$675$	675.000	0.0384900
$676$	−7770.86	−0.442129
$677$	−27104.0	−1.53869	−0.769343	−	0.638836i	$-0.779416\pi$
$677$	−27104.0	−1.53869	−0.769343	+	0.638836i	$0.779416\pi$
$678$	−545.104	−0.0308770
$679$	3010.34	0.170141
$680$	8752.54	0.493595
$681$	−7727.38	−0.434822
$682$	1158.42	0.0650415
$683$	−12105.7	−0.678204	−0.339102	−	0.940750i	$-0.610123\pi$
$683$	−12105.7	−0.678204	−0.339102	+	0.940750i	$0.610123\pi$
$684$	3809.21	0.212937
$685$	−4661.76	−0.260024
$686$	20960.2	1.16656
$687$	2923.61	0.162362
$688$	−19160.4	−1.06175
$689$	2212.17	0.122318
$690$	7459.18	0.411545
$691$	−11339.8	−0.624293	−0.312146	−	0.950034i	$-0.601048\pi$
$691$	−11339.8	−0.624293	−0.312146	+	0.950034i	$0.601048\pi$
$692$	8701.07	0.477984
$693$	393.834	0.0215881
$694$	42994.5	2.35165
$695$	−6942.03	−0.378887
$696$	−5355.55	−0.291669
$697$	−44814.6	−2.43540
$698$	−11977.8	−0.649520
$699$	12091.9	0.654302
$700$	−1000.44	−0.0540187
$701$	12317.4	0.663652	0.331826	−	0.943341i	$-0.392335\pi$
$701$	12317.4	0.663652	0.331826	+	0.943341i	$0.392335\pi$
$702$	1002.81	0.0539155
$703$	30912.6	1.65845
$704$	−415.112	−0.0222232
$705$	−8437.57	−0.450748
$706$	18600.8	0.991572
$707$	−18451.1	−0.981508
$708$	−3563.76	−0.189173
$709$	18985.8	1.00568	0.502839	−	0.864380i	$-0.332289\pi$
$709$	18985.8	1.00568	0.502839	+	0.864380i	$0.332289\pi$
$710$	18089.6	0.956186
$711$	−761.879	−0.0401866
$712$	−1733.82	−0.0912606
$713$	−12010.9	−0.630872
$714$	13191.6	0.691435
$715$	−221.505	−0.0115858
$716$	−237.341	−0.0123881
$717$	8615.72	0.448759
$718$	−8821.06	−0.458495
$719$	−1067.64	−0.0553772	−0.0276886	−	0.999617i	$-0.508815\pi$
$719$	−1067.64	−0.0553772	−0.0276886	+	0.999617i	$0.508815\pi$
$720$	−3596.89	−0.186178
$721$	−1643.29	−0.0848811
$722$	20448.4	1.05403
$723$	3306.63	0.170090
$724$	17454.6	0.895985
$725$	3055.80	0.156537
$726$	−13508.1	−0.690540
$727$	27735.5	1.41493	0.707465	−	0.706749i	$-0.249839\pi$
$727$	27735.5	1.41493	0.707465	+	0.706749i	$0.249839\pi$
$728$	1695.55	0.0863204
$729$	729.000	0.0370370
$730$	−5457.02	−0.276676
$731$	−28731.3	−1.45372
$732$	7311.31	0.369172
$733$	−25849.9	−1.30258	−0.651289	−	0.758830i	$-0.725771\pi$
$733$	−25849.9	−1.30258	−0.651289	+	0.758830i	$0.725771\pi$
$734$	−463.782	−0.0233222
$735$	−3424.88	−0.171875
$736$	−22788.5	−1.14130
$737$	−2168.02	−0.108358
$738$	11528.5	0.575029
$739$	−3272.45	−0.162894	−0.0814472	−	0.996678i	$-0.525954\pi$
$739$	−3272.45	−0.162894	−0.0814472	+	0.996678i	$0.525954\pi$
$740$	5099.74	0.253338
$741$	3683.61	0.182619
$742$	−7486.04	−0.370379
$743$	−449.977	−0.0222181	−0.0111090	−	0.999938i	$-0.503536\pi$
$743$	−449.977	−0.0222181	−0.0111090	+	0.999938i	$0.503536\pi$
$744$	3625.54	0.178654
$745$	−10401.0	−0.511492
$746$	19551.7	0.959569
$747$	10579.7	0.518193
$748$	1830.29	0.0894679
$749$	−10713.3	−0.522638
$750$	1284.72	0.0625485
$751$	36316.3	1.76458	0.882290	−	0.470705i	$-0.156001\pi$
$751$	36316.3	1.76458	0.882290	+	0.470705i	$0.156001\pi$
$752$	44961.4	2.18029
$753$	−10419.8	−0.504273
$754$	4539.83	0.219272
$755$	−12534.9	−0.604227
$756$	−1080.48	−0.0519795
$757$	−29414.4	−1.41226	−0.706132	−	0.708081i	$-0.749561\pi$
$757$	−29414.4	−1.41226	−0.706132	+	0.708081i	$0.749561\pi$
$758$	11479.9	0.550093
$759$	−1779.43	−0.0850977
$760$	−8270.72	−0.394751
$761$	26678.0	1.27080	0.635399	−	0.772184i	$-0.280836\pi$
$761$	26678.0	1.27080	0.635399	+	0.772184i	$0.280836\pi$
$762$	4199.25	0.199636
$763$	−3471.81	−0.164729
$764$	−219.600	−0.0103990
$765$	−5393.60	−0.254910
$766$	−19720.0	−0.930171
$767$	−3446.26	−0.162239
$768$	14047.5	0.660022
$769$	−17973.0	−0.842811	−0.421406	−	0.906872i	$-0.638463\pi$
$769$	−17973.0	−0.842811	−0.421406	+	0.906872i	$0.638463\pi$
$770$	749.581	0.0350819
$771$	5685.60	0.265580
$772$	−12238.6	−0.570565
$773$	−23142.0	−1.07679	−0.538395	−	0.842692i	$-0.680969\pi$
$773$	−23142.0	−1.07679	−0.538395	+	0.842692i	$0.680969\pi$
$774$	7391.12	0.343241
$775$	−2068.68	−0.0958827
$776$	4105.62	0.189927
$777$	−8768.32	−0.404841
$778$	21324.1	0.982656
$779$	42347.6	1.94770
$780$	607.695	0.0278961
$781$	−4315.38	−0.197716
$782$	−59602.7	−2.72556
$783$	3300.26	0.150628
$784$	18250.2	0.831369
$785$	7070.20	0.321460
$786$	−7666.37	−0.347901
$787$	−17748.9	−0.803912	−0.401956	−	0.915659i	$-0.631669\pi$
$787$	−17748.9	−0.803912	−0.401956	+	0.915659i	$0.631669\pi$
$788$	−1173.09	−0.0530326
$789$	7709.08	0.347846
$790$	−1450.08	−0.0653056
$791$	567.956	0.0255300
$792$	537.128	0.0240985
$793$	7070.25	0.316610
$794$	−5652.41	−0.252640
$795$	3060.78	0.136547
$796$	17703.5	0.788297
$797$	14920.1	0.663107	0.331553	−	0.943436i	$-0.392427\pi$
$797$	14920.1	0.663107	0.331553	+	0.943436i	$0.392427\pi$
$798$	−12465.5	−0.552973
$799$	67420.5	2.98519
$800$	−3924.94	−0.173460
$801$	1068.43	0.0471302
$802$	−39677.0	−1.74694
$803$	1301.80	0.0572100
$804$	5947.91	0.260904
$805$	−7771.89	−0.340277
$806$	−3073.32	−0.134309
$807$	−11761.1	−0.513022
$808$	−25164.4	−1.09565
$809$	−15230.2	−0.661885	−0.330942	−	0.943651i	$-0.607367\pi$
$809$	−15230.2	−0.661885	−0.330942	+	0.943651i	$0.607367\pi$
$810$	1387.50	0.0601873
$811$	−21792.3	−0.943564	−0.471782	−	0.881715i	$-0.656389\pi$
$811$	−21792.3	−0.943564	−0.471782	+	0.881715i	$0.656389\pi$
$812$	−4891.43	−0.211398
$813$	−19680.0	−0.848966
$814$	−3820.98	−0.164527
$815$	−815.000	−0.0350285
$816$	28741.0	1.23301
$817$	27149.7	1.16260
$818$	23660.7	1.01134
$819$	−1044.85	−0.0445788
$820$	6986.20	0.297523
$821$	3261.47	0.138643	0.0693215	−	0.997594i	$-0.477917\pi$
$821$	3261.47	0.138643	0.0693215	+	0.997594i	$0.477917\pi$
$822$	−9582.50	−0.406603
$823$	−19048.7	−0.806800	−0.403400	−	0.915024i	$-0.632172\pi$
$823$	−19048.7	−0.806800	−0.403400	+	0.915024i	$0.632172\pi$
$824$	−2241.19	−0.0947517
$825$	−306.477	−0.0129335
$826$	11662.2	0.491260
$827$	−10660.9	−0.448264	−0.224132	−	0.974559i	$-0.571955\pi$
$827$	−10660.9	−0.448264	−0.224132	+	0.974559i	$0.571955\pi$
$828$	4881.82	0.204897
$829$	−22662.6	−0.949464	−0.474732	−	0.880130i	$-0.657455\pi$
$829$	−22662.6	−0.949464	−0.474732	+	0.880130i	$0.657455\pi$
$830$	20136.2	0.842093
$831$	−12444.0	−0.519468
$832$	1101.30	0.0458903
$833$	27366.5	1.13829
$834$	−14269.7	−0.592470
$835$	5437.28	0.225347
$836$	−1729.53	−0.0715516
$837$	−2234.17	−0.0922632
$838$	10510.4	0.433265
$839$	39026.6	1.60590	0.802948	−	0.596049i	$-0.203264\pi$
$839$	39026.6	1.60590	0.802948	+	0.596049i	$0.203264\pi$
$840$	2345.98	0.0963618
$841$	−9448.37	−0.387403
$842$	−28719.9	−1.17548
$843$	−6277.47	−0.256474
$844$	−10693.2	−0.436110
$845$	−10397.3	−0.423289
$846$	−17343.9	−0.704840
$847$	14074.4	0.570958
$848$	−16310.0	−0.660482
$849$	4721.92	0.190879
$850$	−10265.6	−0.414243
$851$	39617.2	1.59584
$852$	11839.1	0.476059
$853$	3753.51	0.150665	0.0753327	−	0.997158i	$-0.475998\pi$
$853$	3753.51	0.150665	0.0753327	+	0.997158i	$0.475998\pi$
$854$	−23925.9	−0.958699
$855$	5096.68	0.203863
$856$	−14611.3	−0.583414
$857$	8142.87	0.324568	0.162284	−	0.986744i	$-0.448114\pi$
$857$	8142.87	0.324568	0.162284	+	0.986744i	$0.448114\pi$
$858$	−455.316	−0.0181168
$859$	40925.7	1.62557	0.812787	−	0.582561i	$-0.197949\pi$
$859$	40925.7	1.62557	0.812787	+	0.582561i	$0.197949\pi$
$860$	4478.96	0.177594
$861$	−12011.8	−0.475450
$862$	−42124.5	−1.66446
$863$	7535.77	0.297243	0.148621	−	0.988894i	$-0.452516\pi$
$863$	7535.77	0.297243	0.148621	+	0.988894i	$0.452516\pi$
$864$	−4238.94	−0.166911
$865$	11641.9	0.457616
$866$	49137.2	1.92812
$867$	28358.6	1.11085
$868$	3311.34	0.129486
$869$	345.924	0.0135036
$870$	6281.36	0.244779
$871$	5751.81	0.223757
$872$	−4735.00	−0.183885
$873$	−2530.02	−0.0980848
$874$	56321.6	2.17976
$875$	−1338.58	−0.0517169
$876$	−3571.46	−0.137750
$877$	−3008.01	−0.115819	−0.0579095	−	0.998322i	$-0.518443\pi$
$877$	−3008.01	−0.115819	−0.0579095	+	0.998322i	$0.518443\pi$
$878$	−31270.8	−1.20198
$879$	8302.76	0.318595
$880$	1633.13	0.0625600
$881$	−233.414	−0.00892613	−0.00446306	−	0.999990i	$-0.501421\pi$
$881$	−233.414	−0.00892613	−0.00446306	+	0.999990i	$0.501421\pi$
$882$	−7040.02	−0.268764
$883$	−31918.0	−1.21645	−0.608226	−	0.793764i	$-0.708119\pi$
$883$	−31918.0	−1.21645	−0.608226	+	0.793764i	$0.708119\pi$
$884$	−4855.80	−0.184749
$885$	−4768.28	−0.181112
$886$	14165.0	0.537114
$887$	−9470.09	−0.358483	−0.179241	−	0.983805i	$-0.557364\pi$
$887$	−9470.09	−0.358483	−0.179241	+	0.983805i	$0.557364\pi$
$888$	−11958.6	−0.451919
$889$	−4375.30	−0.165065
$890$	2033.54	0.0765892
$891$	−330.995	−0.0124453
$892$	24307.7	0.912424
$893$	−63709.0	−2.38739
$894$	−21379.7	−0.799827
$895$	−317.560	−0.0118602
$896$	−17176.7	−0.640438
$897$	4720.86	0.175725
$898$	−42786.4	−1.58998
$899$	−10114.3	−0.375230
$900$	840.813	0.0311412
$901$	−24457.2	−0.904314
$902$	−5234.42	−0.193223
$903$	−7700.97	−0.283801
$904$	774.603	0.0284988
$905$	23354.0	0.857806
$906$	−25766.2	−0.944838
$907$	−40484.8	−1.48211	−0.741056	−	0.671443i	$-0.765675\pi$
$907$	−40484.8	−1.48211	−0.741056	+	0.671443i	$0.765675\pi$
$908$	−9625.60	−0.351803
$909$	15507.1	0.565829
$910$	−1988.66	−0.0724432
$911$	−3999.61	−0.145459	−0.0727294	−	0.997352i	$-0.523171\pi$
$911$	−3999.61	−0.145459	−0.0727294	+	0.997352i	$0.523171\pi$
$912$	−27158.8	−0.986094
$913$	−4803.60	−0.174125
$914$	19902.3	0.720250
$915$	9782.47	0.353441
$916$	3641.80	0.131363
$917$	7987.76	0.287654
$918$	−11086.8	−0.398605
$919$	35955.1	1.29059	0.645294	−	0.763934i	$-0.276735\pi$
$919$	35955.1	1.29059	0.645294	+	0.763934i	$0.276735\pi$
$920$	−10599.6	−0.379847
$921$	−25551.6	−0.914173
$922$	35047.9	1.25189
$923$	11448.8	0.408279
$924$	490.579	0.0174663
$925$	6823.40	0.242543
$926$	7484.91	0.265626
$927$	1381.09	0.0489331
$928$	−19190.1	−0.678822
$929$	−12055.9	−0.425770	−0.212885	−	0.977077i	$-0.568286\pi$
$929$	−12055.9	−0.425770	−0.212885	+	0.977077i	$0.568286\pi$
$930$	−4252.28	−0.149933
$931$	−25860.0	−0.910341
$932$	15062.2	0.529377
$933$	−19962.2	−0.700463
$934$	21586.3	0.756236
$935$	2448.91	0.0856555
$936$	−1425.01	−0.0497628
$937$	25884.7	0.902470	0.451235	−	0.892405i	$-0.350984\pi$
$937$	25884.7	0.902470	0.451235	+	0.892405i	$0.350984\pi$
$938$	−19464.3	−0.677539
$939$	9648.06	0.335306
$940$	−10510.2	−0.364688
$941$	19029.0	0.659221	0.329611	−	0.944117i	$-0.393083\pi$
$941$	19029.0	0.659221	0.329611	+	0.944117i	$0.393083\pi$
$942$	14533.2	0.502671
$943$	54272.1	1.87417
$944$	25408.8	0.876045
$945$	−1445.67	−0.0497646
$946$	−3355.86	−0.115337
$947$	−48543.6	−1.66574	−0.832869	−	0.553470i	$-0.813303\pi$
$947$	−48543.6	−1.66574	−0.832869	+	0.553470i	$0.813303\pi$
$948$	−949.034	−0.0325139
$949$	−3453.71	−0.118137
$950$	9700.47	0.331289
$951$	−32475.9	−1.10736
$952$	−18745.6	−0.638180
$953$	9775.29	0.332269	0.166135	−	0.986103i	$-0.446871\pi$
$953$	9775.29	0.332269	0.166135	+	0.986103i	$0.446871\pi$
$954$	6291.59	0.213520
$955$	−293.823	−0.00995591
$956$	10732.2	0.363078
$957$	−1498.45	−0.0506145
$958$	−8418.40	−0.283910
$959$	9984.22	0.336191
$960$	1523.77	0.0512286
$961$	−22943.9	−0.770163
$962$	10137.2	0.339745
$963$	9003.93	0.301295
$964$	4118.90	0.137615
$965$	−16375.1	−0.546253
$966$	−15975.5	−0.532096
$967$	32417.0	1.07803	0.539017	−	0.842295i	$-0.318796\pi$
$967$	32417.0	1.07803	0.539017	+	0.842295i	$0.318796\pi$
$968$	19195.2	0.637353
$969$	−40725.1	−1.35013
$970$	−4815.35	−0.159393
$971$	15283.0	0.505103	0.252552	−	0.967583i	$-0.418730\pi$
$971$	15283.0	0.505103	0.252552	+	0.967583i	$0.418730\pi$
$972$	908.078	0.0299657
$973$	14867.9	0.489871
$974$	1336.56	0.0439693
$975$	813.091	0.0267074
$976$	−52128.0	−1.70961
$977$	35469.7	1.16149	0.580745	−	0.814086i	$-0.302761\pi$
$977$	35469.7	1.16149	0.580745	+	0.814086i	$0.302761\pi$
$978$	−1675.28	−0.0547745
$979$	−485.112	−0.0158368
$980$	−4266.19	−0.139060
$981$	2917.86	0.0949644
$982$	−432.936	−0.0140688
$983$	−944.110	−0.0306332	−0.0153166	−	0.999883i	$-0.504876\pi$
$983$	−944.110	−0.0306332	−0.0153166	+	0.999883i	$0.504876\pi$
$984$	−16382.3	−0.530739
$985$	−1569.59	−0.0507728
$986$	−50191.2	−1.62111
$987$	18071.0	0.582782
$988$	4588.49	0.147752
$989$	34794.7	1.11871
$990$	−629.980	−0.0202243
$991$	4351.02	0.139470	0.0697349	−	0.997566i	$-0.477785\pi$
$991$	4351.02	0.139470	0.0697349	+	0.997566i	$0.477785\pi$
$992$	12991.1	0.415794
$993$	−15555.3	−0.497111
$994$	−38743.1	−1.23627
$995$	23687.1	0.754706
$996$	13178.6	0.419256
$997$	14283.2	0.453714	0.226857	−	0.973928i	$-0.427155\pi$
$997$	14283.2	0.453714	0.226857	+	0.973928i	$0.427155\pi$
$998$	41855.6	1.32757
$999$	7369.27	0.233387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2445.4.a.i.1.32	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2445.4.a.i.1.32	✓	43	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2445 = 3 \cdot 5 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2445.a (trivial)

\(f(q)\)	\(=\)	\(q+3.42592 q^{2} +3.00000 q^{3} +3.73695 q^{4} +5.00000 q^{5} +10.2778 q^{6} -10.7086 q^{7} -14.6049 q^{8} +9.00000 q^{9} +17.1296 q^{10} -4.08636 q^{11} +11.2108 q^{12} +10.8412 q^{13} -36.6870 q^{14} +15.0000 q^{15} -79.9308 q^{16} -119.858 q^{17} +30.8333 q^{18} +113.260 q^{19} +18.6847 q^{20} -32.1259 q^{21} -13.9996 q^{22} +145.152 q^{23} -43.8147 q^{24} +25.0000 q^{25} +37.1411 q^{26} +27.0000 q^{27} -40.0176 q^{28} +122.232 q^{29} +51.3888 q^{30} -82.7471 q^{31} -156.998 q^{32} -12.2591 q^{33} -410.623 q^{34} -53.5432 q^{35} +33.6325 q^{36} +272.936 q^{37} +388.019 q^{38} +32.5236 q^{39} -73.0245 q^{40} +373.899 q^{41} -110.061 q^{42} +239.712 q^{43} -15.2705 q^{44} +45.0000 q^{45} +497.279 q^{46} -562.505 q^{47} -239.792 q^{48} -228.325 q^{49} +85.6481 q^{50} -359.573 q^{51} +40.5130 q^{52} +204.052 q^{53} +92.4999 q^{54} -20.4318 q^{55} +156.399 q^{56} +339.779 q^{57} +418.757 q^{58} -317.885 q^{59} +56.0542 q^{60} +652.164 q^{61} -283.485 q^{62} -96.3777 q^{63} +101.585 q^{64} +54.2060 q^{65} -41.9987 q^{66} +530.550 q^{67} -447.902 q^{68} +435.456 q^{69} -183.435 q^{70} +1056.04 q^{71} -131.444 q^{72} -318.572 q^{73} +935.057 q^{74} +75.0000 q^{75} +423.245 q^{76} +43.7594 q^{77} +111.423 q^{78} -84.6532 q^{79} -399.654 q^{80} +81.0000 q^{81} +1280.95 q^{82} +1175.52 q^{83} -120.053 q^{84} -599.288 q^{85} +821.235 q^{86} +366.696 q^{87} +59.6809 q^{88} +118.715 q^{89} +154.167 q^{90} -116.095 q^{91} +542.425 q^{92} -248.241 q^{93} -1927.10 q^{94} +566.298 q^{95} -470.993 q^{96} -281.113 q^{97} -782.224 q^{98} -36.7773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 18 q^{2} + 129 q^{3} + 198 q^{4} + 215 q^{5} + 54 q^{6} + 137 q^{7} + 201 q^{8} + 387 q^{9} + 90 q^{10} + 137 q^{11} + 594 q^{12} + 212 q^{13} + 246 q^{14} + 645 q^{15} + 930 q^{16} + 547 q^{17}+ \cdots + 1233 q^{99}+O(q^{100}) \) 43 * q + 18 * q^2 + 129 * q^3 + 198 * q^4 + 215 * q^5 + 54 * q^6 + 137 * q^7 + 201 * q^8 + 387 * q^9 + 90 * q^10 + 137 * q^11 + 594 * q^12 + 212 * q^13 + 246 * q^14 + 645 * q^15 + 930 * q^16 + 547 * q^17 + 162 * q^18 + 563 * q^19 + 990 * q^20 + 411 * q^21 + 279 * q^22 + 793 * q^23 + 603 * q^24 + 1075 * q^25 + 520 * q^26 + 1161 * q^27 + 833 * q^28 + 699 * q^29 + 270 * q^30 + 1130 * q^31 + 1651 * q^32 + 411 * q^33 + 651 * q^34 + 685 * q^35 + 1782 * q^36 + 644 * q^37 + 1122 * q^38 + 636 * q^39 + 1005 * q^40 + 1447 * q^41 + 738 * q^42 + 1629 * q^43 + 1828 * q^44 + 1935 * q^45 + 435 * q^46 + 1962 * q^47 + 2790 * q^48 + 3050 * q^49 + 450 * q^50 + 1641 * q^51 + 2284 * q^52 + 1995 * q^53 + 486 * q^54 + 685 * q^55 - 662 * q^56 + 1689 * q^57 - 130 * q^58 + 1935 * q^59 + 2970 * q^60 + 2152 * q^61 + 1975 * q^62 + 1233 * q^63 + 6187 * q^64 + 1060 * q^65 + 837 * q^66 + 2968 * q^67 + 2412 * q^68 + 2379 * q^69 + 1230 * q^70 + 1835 * q^71 + 1809 * q^72 + 1095 * q^73 + 2874 * q^74 + 3225 * q^75 + 2866 * q^76 + 4658 * q^77 + 1560 * q^78 + 2262 * q^79 + 4650 * q^80 + 3483 * q^81 + 746 * q^82 + 5285 * q^83 + 2499 * q^84 + 2735 * q^85 + 2389 * q^86 + 2097 * q^87 + 4391 * q^88 + 3012 * q^89 + 810 * q^90 + 3560 * q^91 + 5808 * q^92 + 3390 * q^93 + 887 * q^94 + 2815 * q^95 + 4953 * q^96 + 1108 * q^97 + 2858 * q^98 + 1233 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more