LMFDB - Embedded newform 2445.4.a.i.1.38

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			1.38
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)

$f(q)$	$=$	\(q+4.84451 q^{2} +3.00000 q^{3} +15.4693 q^{4} +5.00000 q^{5} +14.5335 q^{6} +15.7615 q^{7} +36.1851 q^{8} +9.00000 q^{9} +24.2226 q^{10} +26.9542 q^{11} +46.4079 q^{12} -46.0879 q^{13} +76.3567 q^{14} +15.0000 q^{15} +51.5448 q^{16} -16.2823 q^{17} +43.6006 q^{18} -46.2772 q^{19} +77.3465 q^{20} +47.2845 q^{21} +130.580 q^{22} +120.968 q^{23} +108.555 q^{24} +25.0000 q^{25} -223.273 q^{26} +27.0000 q^{27} +243.819 q^{28} +252.330 q^{29} +72.6677 q^{30} +140.270 q^{31} -39.7714 q^{32} +80.8625 q^{33} -78.8798 q^{34} +78.8074 q^{35} +139.224 q^{36} -118.054 q^{37} -224.191 q^{38} -138.264 q^{39} +180.926 q^{40} +56.1615 q^{41} +229.070 q^{42} +302.457 q^{43} +416.962 q^{44} +45.0000 q^{45} +586.032 q^{46} +454.721 q^{47} +154.634 q^{48} -94.5755 q^{49} +121.113 q^{50} -48.8469 q^{51} -712.948 q^{52} -278.643 q^{53} +130.802 q^{54} +134.771 q^{55} +570.331 q^{56} -138.832 q^{57} +1222.42 q^{58} -142.379 q^{59} +232.039 q^{60} +367.047 q^{61} +679.540 q^{62} +141.853 q^{63} -605.031 q^{64} -230.440 q^{65} +391.739 q^{66} -91.7792 q^{67} -251.876 q^{68} +362.905 q^{69} +381.784 q^{70} +144.053 q^{71} +325.666 q^{72} +306.477 q^{73} -571.912 q^{74} +75.0000 q^{75} -715.876 q^{76} +424.838 q^{77} -669.820 q^{78} +775.060 q^{79} +257.724 q^{80} +81.0000 q^{81} +272.075 q^{82} -906.110 q^{83} +731.457 q^{84} -81.4115 q^{85} +1465.26 q^{86} +756.991 q^{87} +975.340 q^{88} -590.430 q^{89} +218.003 q^{90} -726.414 q^{91} +1871.29 q^{92} +420.810 q^{93} +2202.90 q^{94} -231.386 q^{95} -119.314 q^{96} +817.740 q^{97} -458.172 q^{98} +242.588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.84451	1.71279	0.856397	−	0.516318i	$-0.172698\pi$
$2$	4.84451	1.71279	0.856397	+	0.516318i	$0.172698\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	15.4693	1.93366
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	14.5335	0.988882
$7$	15.7615	0.851040	0.425520	−	0.904949i	$-0.360091\pi$
$7$	15.7615	0.851040	0.425520	+	0.904949i	$0.360091\pi$
$8$	36.1851	1.59917
$9$	9.00000	0.333333
$10$	24.2226	0.765985
$11$	26.9542	0.738817	0.369409	−	0.929267i	$-0.379560\pi$
$11$	26.9542	0.738817	0.369409	+	0.929267i	$0.379560\pi$
$12$	46.4079	1.11640
$13$	−46.0879	−0.983268	−0.491634	−	0.870802i	$-0.663600\pi$
$13$	−46.0879	−0.983268	−0.491634	+	0.870802i	$0.663600\pi$
$14$	76.3567	1.45766
$15$	15.0000	0.258199
$16$	51.5448	0.805388
$17$	−16.2823	−0.232296	−0.116148	−	0.993232i	$-0.537055\pi$
$17$	−16.2823	−0.232296	−0.116148	+	0.993232i	$0.537055\pi$
$18$	43.6006	0.570931
$19$	−46.2772	−0.558775	−0.279387	−	0.960178i	$-0.590131\pi$
$19$	−46.2772	−0.558775	−0.279387	+	0.960178i	$0.590131\pi$
$20$	77.3465	0.864760
$21$	47.2845	0.491348
$22$	130.580	1.26544
$23$	120.968	1.09668	0.548340	−	0.836256i	$-0.315260\pi$
$23$	120.968	1.09668	0.548340	+	0.836256i	$0.315260\pi$
$24$	108.555	0.923282
$25$	25.0000	0.200000
$26$	−223.273	−1.68414
$27$	27.0000	0.192450
$28$	243.819	1.64562
$29$	252.330	1.61574	0.807872	−	0.589358i	$-0.200619\pi$
$29$	252.330	1.61574	0.807872	+	0.589358i	$0.200619\pi$
$30$	72.6677	0.442241
$31$	140.270	0.812685	0.406343	−	0.913721i	$-0.366804\pi$
$31$	140.270	0.812685	0.406343	+	0.913721i	$0.366804\pi$
$32$	−39.7714	−0.219708
$33$	80.8625	0.426556
$34$	−78.8798	−0.397876
$35$	78.8074	0.380597
$36$	139.224	0.644554
$37$	−118.054	−0.524537	−0.262269	−	0.964995i	$-0.584471\pi$
$37$	−118.054	−0.524537	−0.262269	+	0.964995i	$0.584471\pi$
$38$	−224.191	−0.957066
$39$	−138.264	−0.567690
$40$	180.926	0.715171
$41$	56.1615	0.213926	0.106963	−	0.994263i	$-0.465887\pi$
$41$	56.1615	0.213926	0.106963	+	0.994263i	$0.465887\pi$
$42$	229.070	0.841578
$43$	302.457	1.07266	0.536329	−	0.844009i	$-0.319811\pi$
$43$	302.457	1.07266	0.536329	+	0.844009i	$0.319811\pi$
$44$	416.962	1.42862
$45$	45.0000	0.149071
$46$	586.032	1.87839
$47$	454.721	1.41123	0.705615	−	0.708595i	$-0.250671\pi$
$47$	454.721	1.41123	0.705615	+	0.708595i	$0.250671\pi$
$48$	154.634	0.464991
$49$	−94.5755	−0.275730
$50$	121.113	0.342559
$51$	−48.8469	−0.134116
$52$	−712.948	−1.90131
$53$	−278.643	−0.722162	−0.361081	−	0.932534i	$-0.617592\pi$
$53$	−278.643	−0.722162	−0.361081	+	0.932534i	$0.617592\pi$
$54$	130.802	0.329627
$55$	134.771	0.330409
$56$	570.331	1.36096
$57$	−138.832	−0.322609
$58$	1222.42	2.76744
$59$	−142.379	−0.314172	−0.157086	−	0.987585i	$-0.550210\pi$
$59$	−142.379	−0.314172	−0.157086	+	0.987585i	$0.550210\pi$
$60$	232.039	0.499269
$61$	367.047	0.770418	0.385209	−	0.922829i	$-0.374129\pi$
$61$	367.047	0.770418	0.385209	+	0.922829i	$0.374129\pi$
$62$	679.540	1.39196
$63$	141.853	0.283680
$64$	−605.031	−1.18170
$65$	−230.440	−0.439731
$66$	391.739	0.730603
$67$	−91.7792	−0.167352	−0.0836762	−	0.996493i	$-0.526666\pi$
$67$	−91.7792	−0.167352	−0.0836762	+	0.996493i	$0.526666\pi$
$68$	−251.876	−0.449183
$69$	362.905	0.633168
$70$	381.784	0.651884
$71$	144.053	0.240788	0.120394	−	0.992726i	$-0.461584\pi$
$71$	144.053	0.240788	0.120394	+	0.992726i	$0.461584\pi$
$72$	325.666	0.533057
$73$	306.477	0.491376	0.245688	−	0.969349i	$-0.420986\pi$
$73$	306.477	0.491376	0.245688	+	0.969349i	$0.420986\pi$
$74$	−571.912	−0.898424
$75$	75.0000	0.115470
$76$	−715.876	−1.08048
$77$	424.838	0.628763
$78$	−669.820	−0.972336
$79$	775.060	1.10381	0.551905	−	0.833907i	$-0.313901\pi$
$79$	775.060	1.10381	0.551905	+	0.833907i	$0.313901\pi$
$80$	257.724	0.360180
$81$	81.0000	0.111111
$82$	272.075	0.366411
$83$	−906.110	−1.19830	−0.599148	−	0.800638i	$-0.704494\pi$
$83$	−906.110	−1.19830	−0.599148	+	0.800638i	$0.704494\pi$
$84$	731.457	0.950102
$85$	−81.4115	−0.103886
$86$	1465.26	1.83724
$87$	756.991	0.932850
$88$	975.340	1.18149
$89$	−590.430	−0.703207	−0.351603	−	0.936149i	$-0.614363\pi$
$89$	−590.430	−0.703207	−0.351603	+	0.936149i	$0.614363\pi$
$90$	218.003	0.255328
$91$	−726.414	−0.836801
$92$	1871.29	2.12061
$93$	420.810	0.469204
$94$	2202.90	2.41715
$95$	−231.386	−0.249892
$96$	−119.314	−0.126848
$97$	817.740	0.855969	0.427984	−	0.903786i	$-0.359224\pi$
$97$	817.740	0.855969	0.427984	+	0.903786i	$0.359224\pi$
$98$	−458.172	−0.472269
$99$	242.588	0.246272
$100$	386.732	0.386732
$101$	64.6001	0.0636430	0.0318215	−	0.999494i	$-0.489869\pi$
$101$	64.6001	0.0636430	0.0318215	+	0.999494i	$0.489869\pi$
$102$	−236.640	−0.229714
$103$	341.269	0.326469	0.163234	−	0.986587i	$-0.447807\pi$
$103$	341.269	0.326469	0.163234	+	0.986587i	$0.447807\pi$
$104$	−1667.70	−1.57241
$105$	236.422	0.219738
$106$	−1349.89	−1.23691
$107$	−1117.40	−1.00956	−0.504780	−	0.863248i	$-0.668426\pi$
$107$	−1117.40	−1.00956	−0.504780	+	0.863248i	$0.668426\pi$
$108$	417.671	0.372133
$109$	1608.79	1.41371	0.706853	−	0.707361i	$-0.250114\pi$
$109$	1608.79	1.41371	0.706853	+	0.707361i	$0.250114\pi$
$110$	652.899	0.565923
$111$	−354.161	−0.302842
$112$	812.423	0.685417
$113$	−478.557	−0.398397	−0.199199	−	0.979959i	$-0.563834\pi$
$113$	−478.557	−0.398397	−0.199199	+	0.979959i	$0.563834\pi$
$114$	−672.572	−0.552562
$115$	604.842	0.490450
$116$	3903.38	3.12430
$117$	−414.791	−0.327756
$118$	−689.756	−0.538112
$119$	−256.633	−0.197694
$120$	542.777	0.412904
$121$	−604.473	−0.454149
$122$	1778.16	1.31957
$123$	168.484	0.123510
$124$	2169.88	1.57146
$125$	125.000	0.0894427
$126$	687.210	0.485886
$127$	−328.111	−0.229253	−0.114627	−	0.993409i	$-0.536567\pi$
$127$	−328.111	−0.229253	−0.114627	+	0.993409i	$0.536567\pi$
$128$	−2612.91	−1.80430
$129$	907.372	0.619300
$130$	−1116.37	−0.753168
$131$	−2319.69	−1.54712	−0.773559	−	0.633725i	$-0.781525\pi$
$131$	−2319.69	−1.54712	−0.773559	+	0.633725i	$0.781525\pi$
$132$	1250.89	0.824816
$133$	−729.398	−0.475540
$134$	−444.625	−0.286640
$135$	135.000	0.0860663
$136$	−589.177	−0.371482
$137$	−2430.11	−1.51546	−0.757732	−	0.652566i	$-0.773693\pi$
$137$	−2430.11	−1.51546	−0.757732	+	0.652566i	$0.773693\pi$
$138$	1758.10	1.08449
$139$	−1599.43	−0.975982	−0.487991	−	0.872849i	$-0.662270\pi$
$139$	−1599.43	−0.975982	−0.487991	+	0.872849i	$0.662270\pi$
$140$	1219.10	0.735946
$141$	1364.16	0.814775
$142$	697.867	0.412421
$143$	−1242.26	−0.726455
$144$	463.903	0.268463
$145$	1261.65	0.722583
$146$	1484.73	0.841626
$147$	−283.727	−0.159193
$148$	−1826.21	−1.01428
$149$	−1755.40	−0.965153	−0.482577	−	0.875854i	$-0.660299\pi$
$149$	−1755.40	−0.965153	−0.482577	+	0.875854i	$0.660299\pi$
$150$	363.338	0.197776
$151$	−401.169	−0.216203	−0.108102	−	0.994140i	$-0.534477\pi$
$151$	−401.169	−0.216203	−0.108102	+	0.994140i	$0.534477\pi$
$152$	−1674.55	−0.893577
$153$	−146.541	−0.0774322
$154$	2058.13	1.07694
$155$	701.350	0.363444
$156$	−2138.84	−1.09772
$157$	1051.79	0.534665	0.267332	−	0.963604i	$-0.413858\pi$
$157$	1051.79	0.534665	0.267332	+	0.963604i	$0.413858\pi$
$158$	3754.79	1.89060
$159$	−835.930	−0.416940
$160$	−198.857	−0.0982564
$161$	1906.64	0.933319
$162$	392.405	0.190310
$163$	−163.000	−0.0783260
$163$	−163.000	−0.0783260
$164$	868.779	0.413660
$165$	404.313	0.190762
$166$	−4389.66	−2.05243
$167$	525.714	0.243599	0.121799	−	0.992555i	$-0.461134\pi$
$167$	525.714	0.243599	0.121799	+	0.992555i	$0.461134\pi$
$168$	1710.99	0.785750
$169$	−72.9053	−0.0331840
$170$	−394.399	−0.177936
$171$	−416.495	−0.186258
$172$	4678.80	2.07416
$173$	2053.14	0.902297	0.451148	−	0.892449i	$-0.351015\pi$
$173$	2053.14	0.902297	0.451148	+	0.892449i	$0.351015\pi$
$174$	3667.25	1.59778
$175$	394.037	0.170208
$176$	1389.35	0.595034
$177$	−427.136	−0.181387
$178$	−2860.34	−1.20445
$179$	−3846.65	−1.60621	−0.803106	−	0.595837i	$-0.796821\pi$
$179$	−3846.65	−1.60621	−0.803106	+	0.595837i	$0.796821\pi$
$180$	696.118	0.288253
$181$	547.476	0.224826	0.112413	−	0.993662i	$-0.464142\pi$
$181$	547.476	0.224826	0.112413	+	0.993662i	$0.464142\pi$
$182$	−3519.12	−1.43327
$183$	1101.14	0.444801
$184$	4377.25	1.75378
$185$	−590.268	−0.234580
$186$	2038.62	0.803650
$187$	−438.876	−0.171625
$188$	7034.21	2.72884
$189$	425.560	0.163783
$190$	−1120.95	−0.428013
$191$	−3775.32	−1.43022	−0.715111	−	0.699011i	$-0.753624\pi$
$191$	−3775.32	−1.43022	−0.715111	+	0.699011i	$0.753624\pi$
$192$	−1815.09	−0.682256
$193$	−2498.60	−0.931883	−0.465941	−	0.884816i	$-0.654284\pi$
$193$	−2498.60	−0.931883	−0.465941	+	0.884816i	$0.654284\pi$
$194$	3961.55	1.46610
$195$	−691.319	−0.253879
$196$	−1463.02	−0.533169
$197$	643.441	0.232707	0.116354	−	0.993208i	$-0.462879\pi$
$197$	643.441	0.232707	0.116354	+	0.993208i	$0.462879\pi$
$198$	1175.22	0.421814
$199$	−1534.19	−0.546513	−0.273257	−	0.961941i	$-0.588101\pi$
$199$	−1534.19	−0.546513	−0.273257	+	0.961941i	$0.588101\pi$
$200$	904.628	0.319834
$201$	−275.337	−0.0966209
$202$	312.956	0.109007
$203$	3977.10	1.37506
$204$	−755.628	−0.259336
$205$	280.807	0.0956705
$206$	1653.28	0.559173
$207$	1088.71	0.365560
$208$	−2375.59	−0.791912
$209$	−1247.36	−0.412832
$210$	1145.35	0.376365
$211$	1052.21	0.343305	0.171653	−	0.985158i	$-0.445089\pi$
$211$	1052.21	0.343305	0.171653	+	0.985158i	$0.445089\pi$
$212$	−4310.41	−1.39642
$213$	432.160	0.139019
$214$	−5413.24	−1.72917
$215$	1512.29	0.479707
$216$	976.998	0.307761
$217$	2210.86	0.691628
$218$	7793.79	2.42139
$219$	919.432	0.283696
$220$	2084.81	0.638900
$221$	750.417	0.228410
$222$	−1715.74	−0.518705
$223$	−951.556	−0.285744	−0.142872	−	0.989741i	$-0.545634\pi$
$223$	−951.556	−0.285744	−0.142872	+	0.989741i	$0.545634\pi$
$224$	−626.856	−0.186980
$225$	225.000	0.0666667
$226$	−2318.38	−0.682372
$227$	1960.76	0.573305	0.286652	−	0.958035i	$-0.407458\pi$
$227$	1960.76	0.573305	0.286652	+	0.958035i	$0.407458\pi$
$228$	−2147.63	−0.623816
$229$	2315.63	0.668214	0.334107	−	0.942535i	$-0.391565\pi$
$229$	2315.63	0.668214	0.334107	+	0.942535i	$0.391565\pi$
$230$	2930.16	0.840040
$231$	1274.51	0.363017
$232$	9130.60	2.58385
$233$	−3411.34	−0.959159	−0.479580	−	0.877498i	$-0.659211\pi$
$233$	−3411.34	−0.959159	−0.479580	+	0.877498i	$0.659211\pi$
$234$	−2009.46	−0.561378
$235$	2273.60	0.631122
$236$	−2202.50	−0.607502
$237$	2325.18	0.637285
$238$	−1243.26	−0.338608
$239$	3568.39	0.965774	0.482887	−	0.875683i	$-0.339588\pi$
$239$	3568.39	0.965774	0.482887	+	0.875683i	$0.339588\pi$
$240$	773.172	0.207950
$241$	−2250.56	−0.601540	−0.300770	−	0.953697i	$-0.597244\pi$
$241$	−2250.56	−0.601540	−0.300770	+	0.953697i	$0.597244\pi$
$242$	−2928.37	−0.777864
$243$	243.000	0.0641500
$244$	5677.96	1.48973
$245$	−472.878	−0.123310
$246$	816.225	0.211547
$247$	2132.82	0.549425
$248$	5075.69	1.29962
$249$	−2718.33	−0.691836
$250$	605.564	0.153197
$251$	2478.94	0.623384	0.311692	−	0.950183i	$-0.399104\pi$
$251$	2478.94	0.623384	0.311692	+	0.950183i	$0.399104\pi$
$252$	2194.37	0.548542
$253$	3260.60	0.810246
$254$	−1589.54	−0.392664
$255$	−244.235	−0.0599787
$256$	−7818.03	−1.90870
$257$	4861.37	1.17994	0.589969	−	0.807426i	$-0.299140\pi$
$257$	4861.37	1.17994	0.589969	+	0.807426i	$0.299140\pi$
$258$	4395.78	1.06073
$259$	−1860.70	−0.446402
$260$	−3564.74	−0.850291
$261$	2270.97	0.538581
$262$	−11237.8	−2.64989
$263$	−1625.64	−0.381146	−0.190573	−	0.981673i	$-0.561035\pi$
$263$	−1625.64	−0.381146	−0.190573	+	0.981673i	$0.561035\pi$
$264$	2926.02	0.682136
$265$	−1393.22	−0.322961
$266$	−3533.58	−0.814502
$267$	−1771.29	−0.405997
$268$	−1419.76	−0.323603
$269$	5427.97	1.23029	0.615147	−	0.788412i	$-0.289096\pi$
$269$	5427.97	1.23029	0.615147	+	0.788412i	$0.289096\pi$
$270$	654.009	0.147414
$271$	4029.24	0.903169	0.451585	−	0.892228i	$-0.350859\pi$
$271$	4029.24	0.903169	0.451585	+	0.892228i	$0.350859\pi$
$272$	−839.269	−0.187089
$273$	−2179.24	−0.483127
$274$	−11772.7	−2.59568
$275$	673.854	0.147763
$276$	5613.88	1.22433
$277$	−7824.82	−1.69728	−0.848642	−	0.528968i	$-0.822579\pi$
$277$	−7824.82	−1.69728	−0.848642	+	0.528968i	$0.822579\pi$
$278$	−7748.43	−1.67166
$279$	1262.43	0.270895
$280$	2851.66	0.608639
$281$	344.407	0.0731161	0.0365580	−	0.999332i	$-0.488361\pi$
$281$	344.407	0.0731161	0.0365580	+	0.999332i	$0.488361\pi$
$282$	6608.70	1.39554
$283$	−2344.33	−0.492425	−0.246212	−	0.969216i	$-0.579186\pi$
$283$	−2344.33	−0.492425	−0.246212	+	0.969216i	$0.579186\pi$
$284$	2228.40	0.465603
$285$	−694.158	−0.144275
$286$	−6018.15	−1.24427
$287$	885.189	0.182059
$288$	−357.942	−0.0732360
$289$	−4647.89	−0.946038
$290$	6112.09	1.23764
$291$	2453.22	0.494194
$292$	4740.99	0.950156
$293$	−6896.49	−1.37508	−0.687538	−	0.726148i	$-0.741309\pi$
$293$	−6896.49	−1.37508	−0.687538	+	0.726148i	$0.741309\pi$
$294$	−1374.52	−0.272665
$295$	−711.894	−0.140502
$296$	−4271.78	−0.838825
$297$	727.763	0.142185
$298$	−8504.05	−1.65311
$299$	−5575.18	−1.07833
$300$	1160.20	0.223280
$301$	4767.18	0.912876
$302$	−1943.47	−0.370311
$303$	193.800	0.0367443
$304$	−2385.35	−0.450030
$305$	1835.23	0.344542
$306$	−709.919	−0.132625
$307$	7202.79	1.33904	0.669519	−	0.742795i	$-0.266500\pi$
$307$	7202.79	1.33904	0.669519	+	0.742795i	$0.266500\pi$
$308$	6571.94	1.21582
$309$	1023.81	0.188487
$310$	3397.70	0.622504
$311$	−397.871	−0.0725441	−0.0362721	−	0.999342i	$-0.511548\pi$
$311$	−397.871	−0.0725441	−0.0362721	+	0.999342i	$0.511548\pi$
$312$	−5003.09	−0.907833
$313$	2983.62	0.538800	0.269400	−	0.963028i	$-0.413175\pi$
$313$	2983.62	0.538800	0.269400	+	0.963028i	$0.413175\pi$
$314$	5095.43	0.915770
$315$	709.267	0.126866
$316$	11989.6	2.13440
$317$	8915.41	1.57962	0.789810	−	0.613352i	$-0.210179\pi$
$317$	8915.41	1.57962	0.789810	+	0.613352i	$0.210179\pi$
$318$	−4049.67	−0.714133
$319$	6801.36	1.19374
$320$	−3025.16	−0.528473
$321$	−3352.19	−0.582869
$322$	9236.74	1.59858
$323$	753.500	0.129801
$324$	1253.01	0.214851
$325$	−1152.20	−0.196654
$326$	−789.655	−0.134156
$327$	4826.36	0.816203
$328$	2032.21	0.342104
$329$	7167.08	1.20101
$330$	1958.70	0.326736
$331$	−9869.21	−1.63885	−0.819427	−	0.573183i	$-0.805708\pi$
$331$	−9869.21	−1.63885	−0.819427	+	0.573183i	$0.805708\pi$
$332$	−14016.9	−2.31710
$333$	−1062.48	−0.174846
$334$	2546.83	0.417234
$335$	−458.896	−0.0748423
$336$	2437.27	0.395726
$337$	10502.4	1.69763	0.848815	−	0.528691i	$-0.177317\pi$
$337$	10502.4	1.69763	0.848815	+	0.528691i	$0.177317\pi$
$338$	−353.191	−0.0568374
$339$	−1435.67	−0.230015
$340$	−1259.38	−0.200881
$341$	3780.86	0.600426
$342$	−2017.71	−0.319022
$343$	−6896.84	−1.08570
$344$	10944.5	1.71536
$345$	1814.52	0.283162
$346$	9946.46	1.54545
$347$	3008.79	0.465477	0.232738	−	0.972539i	$-0.425231\pi$
$347$	3008.79	0.465477	0.232738	+	0.972539i	$0.425231\pi$
$348$	11710.1	1.80382
$349$	8801.79	1.35000	0.674998	−	0.737819i	$-0.264144\pi$
$349$	8801.79	1.35000	0.674998	+	0.737819i	$0.264144\pi$
$350$	1908.92	0.291531
$351$	−1244.37	−0.189230
$352$	−1072.00	−0.162324
$353$	2271.49	0.342491	0.171245	−	0.985228i	$-0.445221\pi$
$353$	2271.49	0.342491	0.171245	+	0.985228i	$0.445221\pi$
$354$	−2069.27	−0.310679
$355$	720.266	0.107684
$356$	−9133.53	−1.35976
$357$	−769.900	−0.114138
$358$	−18635.1	−2.75111
$359$	−5336.90	−0.784599	−0.392299	−	0.919838i	$-0.628320\pi$
$359$	−5336.90	−0.784599	−0.392299	+	0.919838i	$0.628320\pi$
$360$	1628.33	0.238390
$361$	−4717.42	−0.687771
$362$	2652.25	0.385081
$363$	−1813.42	−0.262203
$364$	−11237.1	−1.61809
$365$	1532.39	0.219750
$366$	5334.49	0.761853
$367$	−6828.44	−0.971231	−0.485615	−	0.874173i	$-0.661404\pi$
$367$	−6828.44	−0.971231	−0.485615	+	0.874173i	$0.661404\pi$
$368$	6235.29	0.883253
$369$	505.453	0.0713086
$370$	−2859.56	−0.401787
$371$	−4391.83	−0.614589
$372$	6509.64	0.907282
$373$	−1845.13	−0.256131	−0.128066	−	0.991766i	$-0.540877\pi$
$373$	−1845.13	−0.256131	−0.128066	+	0.991766i	$0.540877\pi$
$374$	−2126.14	−0.293958
$375$	375.000	0.0516398
$376$	16454.1	2.25680
$377$	−11629.4	−1.58871
$378$	2061.63	0.280526
$379$	−5578.19	−0.756022	−0.378011	−	0.925801i	$-0.623392\pi$
$379$	−5578.19	−0.756022	−0.378011	+	0.925801i	$0.623392\pi$
$380$	−3579.38	−0.483206
$381$	−984.334	−0.132360
$382$	−18289.6	−2.44967
$383$	11614.8	1.54957	0.774786	−	0.632224i	$-0.217858\pi$
$383$	11614.8	1.54957	0.774786	+	0.632224i	$0.217858\pi$
$384$	−7838.73	−1.04172
$385$	2124.19	0.281191
$386$	−12104.5	−1.59612
$387$	2722.12	0.357553
$388$	12649.9	1.65515
$389$	−7872.19	−1.02606	−0.513028	−	0.858372i	$-0.671476\pi$
$389$	−7872.19	−1.02606	−0.513028	+	0.858372i	$0.671476\pi$
$390$	−3349.10	−0.434842
$391$	−1969.64	−0.254755
$392$	−3422.23	−0.440940
$393$	−6959.07	−0.893229
$394$	3117.16	0.398579
$395$	3875.30	0.493639
$396$	3752.66	0.476208
$397$	7238.89	0.915138	0.457569	−	0.889174i	$-0.348720\pi$
$397$	7238.89	0.915138	0.457569	+	0.889174i	$0.348720\pi$
$398$	−7432.42	−0.936064
$399$	−2188.19	−0.274553
$400$	1288.62	0.161078
$401$	−1971.45	−0.245510	−0.122755	−	0.992437i	$-0.539173\pi$
$401$	−1971.45	−0.245510	−0.122755	+	0.992437i	$0.539173\pi$
$402$	−1333.88	−0.165492
$403$	−6464.75	−0.799087
$404$	999.318	0.123064
$405$	405.000	0.0496904
$406$	19267.1	2.35520
$407$	−3182.03	−0.387537
$408$	−1767.53	−0.214475
$409$	−10259.0	−1.24028	−0.620140	−	0.784491i	$-0.712924\pi$
$409$	−10259.0	−1.24028	−0.620140	+	0.784491i	$0.712924\pi$
$410$	1360.38	0.163864
$411$	−7290.34	−0.874954
$412$	5279.20	0.631280
$413$	−2244.10	−0.267373
$414$	5274.29	0.626129
$415$	−4530.55	−0.535894
$416$	1832.98	0.216032
$417$	−4798.28	−0.563483
$418$	−6042.87	−0.707097
$419$	−2139.62	−0.249468	−0.124734	−	0.992190i	$-0.539808\pi$
$419$	−2139.62	−0.249468	−0.124734	+	0.992190i	$0.539808\pi$
$420$	3657.29	0.424898
$421$	4986.75	0.577290	0.288645	−	0.957436i	$-0.406795\pi$
$421$	4986.75	0.577290	0.288645	+	0.957436i	$0.406795\pi$
$422$	5097.46	0.588011
$423$	4092.49	0.470410
$424$	−10082.7	−1.15486
$425$	−407.058	−0.0464593
$426$	2093.60	0.238111
$427$	5785.20	0.655657
$428$	−17285.3	−1.95215
$429$	−3726.78	−0.419419
$430$	7326.29	0.821640
$431$	11769.3	1.31533	0.657665	−	0.753310i	$-0.271544\pi$
$431$	11769.3	1.31533	0.657665	+	0.753310i	$0.271544\pi$
$432$	1391.71	0.154997
$433$	−10199.1	−1.13195	−0.565977	−	0.824421i	$-0.691501\pi$
$433$	−10199.1	−1.13195	−0.565977	+	0.824421i	$0.691501\pi$
$434$	10710.6	1.18462
$435$	3784.96	0.417183
$436$	24886.8	2.73363
$437$	−5598.08	−0.612797
$438$	4454.20	0.485913
$439$	−2448.88	−0.266238	−0.133119	−	0.991100i	$-0.542499\pi$
$439$	−2448.88	−0.266238	−0.133119	+	0.991100i	$0.542499\pi$
$440$	4876.70	0.528381
$441$	−851.180	−0.0919101
$442$	3635.41	0.391219
$443$	−4871.61	−0.522476	−0.261238	−	0.965274i	$-0.584131\pi$
$443$	−4871.61	−0.522476	−0.261238	+	0.965274i	$0.584131\pi$
$444$	−5478.62	−0.585594
$445$	−2952.15	−0.314484
$446$	−4609.82	−0.489420
$447$	−5266.20	−0.557232
$448$	−9536.20	−1.00568
$449$	−5041.31	−0.529876	−0.264938	−	0.964265i	$-0.585351\pi$
$449$	−5041.31	−0.529876	−0.264938	+	0.964265i	$0.585351\pi$
$450$	1090.02	0.114186
$451$	1513.79	0.158052
$452$	−7402.94	−0.770365
$453$	−1203.51	−0.124825
$454$	9498.92	0.981952
$455$	−3632.07	−0.374229
$456$	−5023.64	−0.515907
$457$	−7699.19	−0.788081	−0.394040	−	0.919093i	$-0.628923\pi$
$457$	−7699.19	−0.788081	−0.394040	+	0.919093i	$0.628923\pi$
$458$	11218.1	1.14451
$459$	−439.622	−0.0447055
$460$	9356.47	0.948365
$461$	1723.01	0.174075	0.0870376	−	0.996205i	$-0.472260\pi$
$461$	1723.01	0.174075	0.0870376	+	0.996205i	$0.472260\pi$
$462$	6174.40	0.621773
$463$	−10957.2	−1.09984	−0.549918	−	0.835219i	$-0.685341\pi$
$463$	−10957.2	−1.09984	−0.549918	+	0.835219i	$0.685341\pi$
$464$	13006.3	1.30130
$465$	2104.05	0.209834
$466$	−16526.3	−1.64284
$467$	7424.58	0.735693	0.367847	−	0.929886i	$-0.380095\pi$
$467$	7424.58	0.735693	0.367847	+	0.929886i	$0.380095\pi$
$468$	−6416.53	−0.633769
$469$	−1446.58	−0.142424
$470$	11014.5	1.08098
$471$	3155.38	0.308689
$472$	−5151.99	−0.502415
$473$	8152.49	0.792499
$474$	11264.4	1.09154
$475$	−1156.93	−0.111755
$476$	−3969.94	−0.382273
$477$	−2507.79	−0.240721
$478$	17287.1	1.65417
$479$	−12616.2	−1.20344	−0.601720	−	0.798707i	$-0.705518\pi$
$479$	−12616.2	−1.20344	−0.601720	+	0.798707i	$0.705518\pi$
$480$	−596.571	−0.0567283
$481$	5440.84	0.515761
$482$	−10902.8	−1.03031
$483$	5719.92	0.538852
$484$	−9350.77	−0.878171
$485$	4088.70	0.382801
$486$	1177.22	0.109876
$487$	6001.79	0.558454	0.279227	−	0.960225i	$-0.409922\pi$
$487$	6001.79	0.558454	0.279227	+	0.960225i	$0.409922\pi$
$488$	13281.6	1.23203
$489$	−489.000	−0.0452216
$490$	−2290.86	−0.211205
$491$	1796.86	0.165155	0.0825776	−	0.996585i	$-0.473685\pi$
$491$	1796.86	0.165155	0.0825776	+	0.996585i	$0.473685\pi$
$492$	2606.34	0.238827
$493$	−4108.52	−0.375332
$494$	10332.5	0.941052
$495$	1212.94	0.110136
$496$	7230.19	0.654527
$497$	2270.49	0.204921
$498$	−13169.0	−1.18497
$499$	4287.29	0.384620	0.192310	−	0.981334i	$-0.438402\pi$
$499$	4287.29	0.384620	0.192310	+	0.981334i	$0.438402\pi$
$500$	1933.66	0.172952
$501$	1577.14	0.140642
$502$	12009.3	1.06773
$503$	−4110.76	−0.364393	−0.182197	−	0.983262i	$-0.558321\pi$
$503$	−4110.76	−0.364393	−0.182197	+	0.983262i	$0.558321\pi$
$504$	5132.98	0.453653
$505$	323.000	0.0284620
$506$	15796.0	1.38778
$507$	−218.716	−0.0191588
$508$	−5075.65	−0.443299
$509$	18481.3	1.60937	0.804684	−	0.593703i	$-0.202335\pi$
$509$	18481.3	1.60937	0.804684	+	0.593703i	$0.202335\pi$
$510$	−1183.20	−0.102731
$511$	4830.54	0.418181
$512$	−16971.2	−1.46490
$513$	−1249.48	−0.107536
$514$	23551.0	2.02099
$515$	1706.35	0.146001
$516$	14036.4	1.19752
$517$	12256.6	1.04264
$518$	−9014.18	−0.764595
$519$	6159.42	0.520941
$520$	−8338.48	−0.703205
$521$	−11576.6	−0.973473	−0.486736	−	0.873549i	$-0.661813\pi$
$521$	−11576.6	−0.973473	−0.486736	+	0.873549i	$0.661813\pi$
$522$	11001.8	0.922479
$523$	3296.33	0.275599	0.137800	−	0.990460i	$-0.455997\pi$
$523$	3296.33	0.275599	0.137800	+	0.990460i	$0.455997\pi$
$524$	−35884.0	−2.99160
$525$	1182.11	0.0982697
$526$	−7875.45	−0.652825
$527$	−2283.92	−0.188784
$528$	4168.04	0.343543
$529$	2466.33	0.202707
$530$	−6749.45	−0.553165
$531$	−1281.41	−0.104724
$532$	−11283.3	−0.919534
$533$	−2588.37	−0.210346
$534$	−8581.03	−0.695389
$535$	−5586.98	−0.451489
$536$	−3321.04	−0.267625
$537$	−11539.9	−0.927347
$538$	26295.9	2.10724
$539$	−2549.20	−0.203714
$540$	2088.36	0.166423
$541$	10164.3	0.807758	0.403879	−	0.914812i	$-0.367662\pi$
$541$	10164.3	0.807758	0.403879	+	0.914812i	$0.367662\pi$
$542$	19519.7	1.54694
$543$	1642.43	0.129803
$544$	647.570	0.0510374
$545$	8043.94	0.632228
$546$	−10557.4	−0.827497
$547$	−20329.9	−1.58911	−0.794554	−	0.607194i	$-0.792295\pi$
$547$	−20329.9	−1.58911	−0.794554	+	0.607194i	$0.792295\pi$
$548$	−37592.2	−2.93040
$549$	3303.42	0.256806
$550$	3264.50	0.253088
$551$	−11677.2	−0.902837
$552$	13131.8	1.01254
$553$	12216.1	0.939387
$554$	−37907.4	−2.90710
$555$	−1770.80	−0.135435
$556$	−24742.0	−1.88722
$557$	20258.8	1.54110	0.770550	−	0.637379i	$-0.219981\pi$
$557$	20258.8	1.54110	0.770550	+	0.637379i	$0.219981\pi$
$558$	6115.86	0.463987
$559$	−13939.6	−1.05471
$560$	4062.11	0.306528
$561$	−1316.63	−0.0990875
$562$	1668.48	0.125233
$563$	−4951.12	−0.370630	−0.185315	−	0.982679i	$-0.559331\pi$
$563$	−4951.12	−0.370630	−0.185315	+	0.982679i	$0.559331\pi$
$564$	21102.6	1.57550
$565$	−2392.79	−0.178169
$566$	−11357.2	−0.843422
$567$	1276.68	0.0945600
$568$	5212.58	0.385062
$569$	−11311.5	−0.833399	−0.416699	−	0.909044i	$-0.636813\pi$
$569$	−11311.5	−0.833399	−0.416699	+	0.909044i	$0.636813\pi$
$570$	−3362.86	−0.247113
$571$	−11038.8	−0.809033	−0.404516	−	0.914531i	$-0.632560\pi$
$571$	−11038.8	−0.809033	−0.404516	+	0.914531i	$0.632560\pi$
$572$	−19216.9	−1.40472
$573$	−11325.9	−0.825739
$574$	4288.31	0.311830
$575$	3024.21	0.219336
$576$	−5445.28	−0.393901
$577$	−4307.84	−0.310811	−0.155405	−	0.987851i	$-0.549668\pi$
$577$	−4307.84	−0.310811	−0.155405	+	0.987851i	$0.549668\pi$
$578$	−22516.7	−1.62037
$579$	−7495.81	−0.538023
$580$	19516.9	1.39723
$581$	−14281.6	−1.01980
$582$	11884.7	0.846452
$583$	−7510.60	−0.533546
$584$	11089.9	0.785795
$585$	−2073.96	−0.146577
$586$	−33410.2	−2.35522
$587$	7377.25	0.518725	0.259363	−	0.965780i	$-0.416488\pi$
$587$	7377.25	0.518725	0.259363	+	0.965780i	$0.416488\pi$
$588$	−4389.05	−0.307826
$589$	−6491.31	−0.454108
$590$	−3448.78	−0.240651
$591$	1930.32	0.134354
$592$	−6085.05	−0.422456
$593$	12570.5	0.870504	0.435252	−	0.900309i	$-0.356659\pi$
$593$	12570.5	0.870504	0.435252	+	0.900309i	$0.356659\pi$
$594$	3525.66	0.243534
$595$	−1283.17	−0.0884113
$596$	−27154.8	−1.86628
$597$	−4602.58	−0.315529
$598$	−27009.0	−1.84696
$599$	−18299.9	−1.24827	−0.624137	−	0.781315i	$-0.714549\pi$
$599$	−18299.9	−1.24827	−0.624137	+	0.781315i	$0.714549\pi$
$600$	2713.88	0.184656
$601$	11723.7	0.795704	0.397852	−	0.917450i	$-0.369756\pi$
$601$	11723.7	0.795704	0.397852	+	0.917450i	$0.369756\pi$
$602$	23094.7	1.56357
$603$	−826.012	−0.0557841
$604$	−6205.80	−0.418064
$605$	−3022.36	−0.203102
$606$	938.868	0.0629355
$607$	14922.0	0.997802	0.498901	−	0.866659i	$-0.333737\pi$
$607$	14922.0	0.997802	0.498901	+	0.866659i	$0.333737\pi$
$608$	1840.51	0.122767
$609$	11931.3	0.793893
$610$	8890.81	0.590129
$611$	−20957.1	−1.38762
$612$	−2266.88	−0.149728
$613$	−19552.1	−1.28826	−0.644128	−	0.764918i	$-0.722779\pi$
$613$	−19552.1	−1.28826	−0.644128	+	0.764918i	$0.722779\pi$
$614$	34894.0	2.29350
$615$	842.422	0.0552354
$616$	15372.8	1.00550
$617$	13849.0	0.903630	0.451815	−	0.892112i	$-0.350777\pi$
$617$	13849.0	0.903630	0.451815	+	0.892112i	$0.350777\pi$
$618$	4959.85	0.322839
$619$	6762.52	0.439109	0.219555	−	0.975600i	$-0.429540\pi$
$619$	6762.52	0.439109	0.219555	+	0.975600i	$0.429540\pi$
$620$	10849.4	0.702778
$621$	3266.14	0.211056
$622$	−1927.49	−0.124253
$623$	−9306.05	−0.598457
$624$	−7126.78	−0.457211
$625$	625.000	0.0400000
$626$	14454.2	0.922853
$627$	−3742.09	−0.238349
$628$	16270.5	1.03386
$629$	1922.18	0.121848
$630$	3436.05	0.217295
$631$	1900.69	0.119913	0.0599565	−	0.998201i	$-0.480904\pi$
$631$	1900.69	0.119913	0.0599565	+	0.998201i	$0.480904\pi$
$632$	28045.6	1.76518
$633$	3156.64	0.198207
$634$	43190.8	2.70556
$635$	−1640.56	−0.102525
$636$	−12931.2	−0.806222
$637$	4358.79	0.271117
$638$	32949.3	2.04463
$639$	1296.48	0.0802628
$640$	−13064.6	−0.806909
$641$	−5898.99	−0.363489	−0.181744	−	0.983346i	$-0.558174\pi$
$641$	−5898.99	−0.363489	−0.181744	+	0.983346i	$0.558174\pi$
$642$	−16239.7	−0.998335
$643$	−26636.0	−1.63362	−0.816812	−	0.576904i	$-0.804261\pi$
$643$	−26636.0	−1.63362	−0.816812	+	0.576904i	$0.804261\pi$
$644$	29494.4	1.80472
$645$	4536.86	0.276959
$646$	3650.34	0.222323
$647$	10787.0	0.655458	0.327729	−	0.944772i	$-0.393717\pi$
$647$	10787.0	0.655458	0.327729	+	0.944772i	$0.393717\pi$
$648$	2930.99	0.177686
$649$	−3837.70	−0.232116
$650$	−5581.84	−0.336827
$651$	6632.59	0.399311
$652$	−2521.50	−0.151456
$653$	7447.40	0.446308	0.223154	−	0.974783i	$-0.428365\pi$
$653$	7447.40	0.446308	0.223154	+	0.974783i	$0.428365\pi$
$654$	23381.4	1.39799
$655$	−11598.5	−0.691892
$656$	2894.83	0.172293
$657$	2758.30	0.163792
$658$	34721.0	2.05709
$659$	−16225.0	−0.959086	−0.479543	−	0.877518i	$-0.659198\pi$
$659$	−16225.0	−0.959086	−0.479543	+	0.877518i	$0.659198\pi$
$660$	6254.43	0.368869
$661$	−5757.05	−0.338764	−0.169382	−	0.985550i	$-0.554177\pi$
$661$	−5757.05	−0.338764	−0.169382	+	0.985550i	$0.554177\pi$
$662$	−47811.5	−2.80702
$663$	2251.25	0.131872
$664$	−32787.7	−1.91628
$665$	−3646.99	−0.212668
$666$	−5147.21	−0.299475
$667$	30524.0	1.77195
$668$	8132.43	0.471038
$669$	−2854.67	−0.164974
$670$	−2223.13	−0.128189
$671$	9893.44	0.569198
$672$	−1880.57	−0.107953
$673$	379.132	0.0217154	0.0108577	−	0.999941i	$-0.496544\pi$
$673$	379.132	0.0217154	0.0108577	+	0.999941i	$0.496544\pi$
$674$	50878.9	2.90769
$675$	675.000	0.0384900
$676$	−1127.79	−0.0641667
$677$	−25951.7	−1.47327	−0.736637	−	0.676288i	$-0.763587\pi$
$677$	−25951.7	−1.47327	−0.736637	+	0.676288i	$0.763587\pi$
$678$	−6955.13	−0.393968
$679$	12888.8	0.728464
$680$	−2945.89	−0.166132
$681$	5882.28	0.330998
$682$	18316.4	1.02841
$683$	4956.26	0.277666	0.138833	−	0.990316i	$-0.455665\pi$
$683$	4956.26	0.277666	0.138833	+	0.990316i	$0.455665\pi$
$684$	−6442.88	−0.360161
$685$	−12150.6	−0.677736
$686$	−33411.8	−1.85958
$687$	6946.89	0.385794
$688$	15590.1	0.863906
$689$	12842.1	0.710079
$690$	8790.49	0.484997
$691$	−15169.1	−0.835110	−0.417555	−	0.908652i	$-0.637113\pi$
$691$	−15169.1	−0.835110	−0.417555	+	0.908652i	$0.637113\pi$
$692$	31760.6	1.74474
$693$	3823.54	0.209588
$694$	14576.1	0.797266
$695$	−7997.13	−0.436472
$696$	27391.8	1.49179
$697$	−914.439	−0.0496942
$698$	42640.4	2.31227
$699$	−10234.0	−0.553771
$700$	6095.48	0.329125
$701$	−17562.2	−0.946243	−0.473122	−	0.880997i	$-0.656873\pi$
$701$	−17562.2	−0.946243	−0.473122	+	0.880997i	$0.656873\pi$
$702$	−6028.38	−0.324112
$703$	5463.19	0.293098
$704$	−16308.1	−0.873062
$705$	6820.81	0.364378
$706$	11004.3	0.586616
$707$	1018.19	0.0541628
$708$	−6607.50	−0.350742
$709$	20947.6	1.10960	0.554799	−	0.831985i	$-0.312795\pi$
$709$	20947.6	1.10960	0.554799	+	0.831985i	$0.312795\pi$
$710$	3489.34	0.184440
$711$	6975.54	0.367937
$712$	−21364.8	−1.12455
$713$	16968.2	0.891255
$714$	−3729.79	−0.195496
$715$	−6211.31	−0.324881
$716$	−59504.9	−3.10587
$717$	10705.2	0.557590
$718$	−25854.7	−1.34386
$719$	−5947.86	−0.308509	−0.154254	−	0.988031i	$-0.549298\pi$
$719$	−5947.86	−0.308509	−0.154254	+	0.988031i	$0.549298\pi$
$720$	2319.52	0.120060
$721$	5378.91	0.277838
$722$	−22853.6	−1.17801
$723$	−6751.67	−0.347299
$724$	8469.07	0.434738
$725$	6308.26	0.323149
$726$	−8785.12	−0.449100
$727$	250.346	0.0127714	0.00638571	−	0.999980i	$-0.497967\pi$
$727$	250.346	0.0127714	0.00638571	+	0.999980i	$0.497967\pi$
$728$	−26285.4	−1.33819
$729$	729.000	0.0370370
$730$	7423.67	0.376387
$731$	−4924.70	−0.249175
$732$	17033.9	0.860095
$733$	33867.7	1.70659	0.853297	−	0.521425i	$-0.174599\pi$
$733$	33867.7	1.70659	0.853297	+	0.521425i	$0.174599\pi$
$734$	−33080.5	−1.66352
$735$	−1418.63	−0.0711933
$736$	−4811.08	−0.240949
$737$	−2473.83	−0.123643
$738$	2448.68	0.122137
$739$	−4981.93	−0.247988	−0.123994	−	0.992283i	$-0.539570\pi$
$739$	−4981.93	−0.247988	−0.123994	+	0.992283i	$0.539570\pi$
$740$	−9131.03	−0.453599
$741$	6398.46	0.317211
$742$	−21276.3	−1.05266
$743$	−20421.2	−1.00832	−0.504160	−	0.863610i	$-0.668198\pi$
$743$	−20421.2	−1.00832	−0.504160	+	0.863610i	$0.668198\pi$
$744$	15227.1	0.750337
$745$	−8776.99	−0.431630
$746$	−8938.74	−0.438700
$747$	−8154.99	−0.399432
$748$	−6789.11	−0.331864
$749$	−17611.8	−0.859175
$750$	1816.69	0.0884483
$751$	−18280.2	−0.888219	−0.444110	−	0.895972i	$-0.646480\pi$
$751$	−18280.2	−0.888219	−0.444110	+	0.895972i	$0.646480\pi$
$752$	23438.5	1.13659
$753$	7436.83	0.359911
$754$	−56338.7	−2.72113
$755$	−2005.85	−0.0966890
$756$	6583.12	0.316701
$757$	−2640.61	−0.126783	−0.0633914	−	0.997989i	$-0.520192\pi$
$757$	−2640.61	−0.126783	−0.0633914	+	0.997989i	$0.520192\pi$
$758$	−27023.6	−1.29491
$759$	9781.80	0.467796
$760$	−8372.73	−0.399620
$761$	−2099.35	−0.100002	−0.0500010	−	0.998749i	$-0.515922\pi$
$761$	−2099.35	−0.100002	−0.0500010	+	0.998749i	$0.515922\pi$
$762$	−4768.62	−0.226705
$763$	25356.9	1.20312
$764$	−58401.5	−2.76556
$765$	−732.704	−0.0346287
$766$	56267.8	2.65410
$767$	6561.94	0.308915
$768$	−23454.1	−1.10199
$769$	26384.5	1.23726	0.618628	−	0.785684i	$-0.287689\pi$
$769$	26384.5	1.23726	0.618628	+	0.785684i	$0.287689\pi$
$770$	10290.7	0.481623
$771$	14584.1	0.681238
$772$	−38651.6	−1.80195
$773$	−10316.6	−0.480030	−0.240015	−	0.970769i	$-0.577152\pi$
$773$	−10316.6	−0.480030	−0.240015	+	0.970769i	$0.577152\pi$
$774$	13187.3	0.612414
$775$	3506.75	0.162537
$776$	29590.0	1.36884
$777$	−5582.10	−0.257731
$778$	−38136.9	−1.75742
$779$	−2599.00	−0.119536
$780$	−10694.2	−0.490916
$781$	3882.83	0.177899
$782$	−9541.96	−0.436343
$783$	6812.92	0.310950
$784$	−4874.88	−0.222070
$785$	5258.97	0.239109
$786$	−33713.3	−1.52992
$787$	−23248.5	−1.05301	−0.526505	−	0.850172i	$-0.676498\pi$
$787$	−23248.5	−1.05301	−0.526505	+	0.850172i	$0.676498\pi$
$788$	9953.59	0.449977
$789$	−4876.93	−0.220055
$790$	18773.9	0.845502
$791$	−7542.77	−0.339052
$792$	8778.06	0.393832
$793$	−16916.4	−0.757528
$794$	35068.9	1.56744
$795$	−4179.65	−0.186461
$796$	−23732.9	−1.05677
$797$	−9816.09	−0.436266	−0.218133	−	0.975919i	$-0.569997\pi$
$797$	−9816.09	−0.436266	−0.218133	+	0.975919i	$0.569997\pi$
$798$	−10600.7	−0.470253
$799$	−7403.91	−0.327824
$800$	−994.285	−0.0439416
$801$	−5313.87	−0.234402
$802$	−9550.72	−0.420508
$803$	8260.84	0.363037
$804$	−4259.28	−0.186832
$805$	9533.20	0.417393
$806$	−31318.6	−1.36867
$807$	16283.9	0.710311
$808$	2337.56	0.101776
$809$	7428.86	0.322849	0.161424	−	0.986885i	$-0.448391\pi$
$809$	7428.86	0.322849	0.161424	+	0.986885i	$0.448391\pi$
$810$	1962.03	0.0851094
$811$	−5086.79	−0.220248	−0.110124	−	0.993918i	$-0.535125\pi$
$811$	−5086.79	−0.220248	−0.110124	+	0.993918i	$0.535125\pi$
$812$	61523.0	2.65891
$813$	12087.7	0.521445
$814$	−15415.4	−0.663771
$815$	−815.000	−0.0350285
$816$	−2517.81	−0.108016
$817$	−13996.9	−0.599375
$818$	−49699.8	−2.12434
$819$	−6537.72	−0.278934
$820$	4343.89	0.184994
$821$	−23528.2	−1.00017	−0.500085	−	0.865976i	$-0.666698\pi$
$821$	−23528.2	−1.00017	−0.500085	+	0.865976i	$0.666698\pi$
$822$	−35318.2	−1.49862
$823$	11046.2	0.467859	0.233929	−	0.972254i	$-0.424842\pi$
$823$	11046.2	0.467859	0.233929	+	0.972254i	$0.424842\pi$
$824$	12348.9	0.522079
$825$	2021.56	0.0853113
$826$	−10871.6	−0.457955
$827$	7848.11	0.329994	0.164997	−	0.986294i	$-0.447238\pi$
$827$	7848.11	0.329994	0.164997	+	0.986294i	$0.447238\pi$
$828$	16841.7	0.706870
$829$	18904.7	0.792025	0.396013	−	0.918245i	$-0.370394\pi$
$829$	18904.7	0.792025	0.396013	+	0.918245i	$0.370394\pi$
$830$	−21948.3	−0.917876
$831$	−23474.4	−0.979927
$832$	27884.6	1.16193
$833$	1539.91	0.0640512
$834$	−23245.3	−0.965131
$835$	2628.57	0.108941
$836$	−19295.8	−0.798279
$837$	3787.29	0.156401
$838$	−10365.4	−0.427288
$839$	8809.68	0.362507	0.181254	−	0.983436i	$-0.441984\pi$
$839$	8809.68	0.362507	0.181254	+	0.983436i	$0.441984\pi$
$840$	8554.97	0.351398
$841$	39281.7	1.61063
$842$	24158.4	0.988779
$843$	1033.22	0.0422136
$844$	16277.0	0.663836
$845$	−364.527	−0.0148403
$846$	19826.1	0.805716
$847$	−9527.39	−0.386499
$848$	−14362.6	−0.581620
$849$	−7033.00	−0.284301
$850$	−1972.00	−0.0795752
$851$	−14280.7	−0.575249
$852$	6685.21	0.268816
$853$	2123.70	0.0852453	0.0426227	−	0.999091i	$-0.486429\pi$
$853$	2123.70	0.0852453	0.0426227	+	0.999091i	$0.486429\pi$
$854$	28026.5	1.12301
$855$	−2082.47	−0.0832972
$856$	−40433.1	−1.61446
$857$	−13890.7	−0.553673	−0.276836	−	0.960917i	$-0.589286\pi$
$857$	−13890.7	−0.553673	−0.276836	+	0.960917i	$0.589286\pi$
$858$	−18054.4	−0.718378
$859$	28314.6	1.12466	0.562330	−	0.826913i	$-0.309905\pi$
$859$	28314.6	1.12466	0.562330	+	0.826913i	$0.309905\pi$
$860$	23394.0	0.927592
$861$	2655.57	0.105112
$862$	57016.6	2.25289
$863$	−1284.21	−0.0506548	−0.0253274	−	0.999679i	$-0.508063\pi$
$863$	−1284.21	−0.0506548	−0.0253274	+	0.999679i	$0.508063\pi$
$864$	−1073.83	−0.0422828
$865$	10265.7	0.403519
$866$	−49409.5	−1.93880
$867$	−13943.7	−0.546195
$868$	34200.5	1.33737
$869$	20891.1	0.815514
$870$	18336.3	0.714549
$871$	4229.91	0.164552
$872$	58214.1	2.26076
$873$	7359.66	0.285323
$874$	−27120.0	−1.04960
$875$	1970.19	0.0761194
$876$	14223.0	0.548573
$877$	1377.53	0.0530399	0.0265200	−	0.999648i	$-0.491557\pi$
$877$	1377.53	0.0530399	0.0265200	+	0.999648i	$0.491557\pi$
$878$	−11863.6	−0.456011
$879$	−20689.5	−0.793901
$880$	6946.74	0.266107
$881$	14924.1	0.570721	0.285360	−	0.958420i	$-0.407887\pi$
$881$	14924.1	0.570721	0.285360	+	0.958420i	$0.407887\pi$
$882$	−4123.55	−0.157423
$883$	−14101.3	−0.537425	−0.268713	−	0.963220i	$-0.586598\pi$
$883$	−14101.3	−0.537425	−0.268713	+	0.963220i	$0.586598\pi$
$884$	11608.4	0.441667
$885$	−2135.68	−0.0811188
$886$	−23600.6	−0.894894
$887$	−9476.93	−0.358742	−0.179371	−	0.983782i	$-0.557406\pi$
$887$	−9476.93	−0.358742	−0.179371	+	0.983782i	$0.557406\pi$
$888$	−12815.3	−0.484296
$889$	−5171.52	−0.195104
$890$	−14301.7	−0.538646
$891$	2183.29	0.0820908
$892$	−14719.9	−0.552532
$893$	−21043.2	−0.788560
$894$	−25512.2	−0.954423
$895$	−19233.2	−0.718320
$896$	−41183.4	−1.53554
$897$	−16725.5	−0.622574
$898$	−24422.7	−0.907568
$899$	35394.4	1.31309
$900$	3480.59	0.128911
$901$	4536.95	0.167756
$902$	7333.56	0.270710
$903$	14301.5	0.527049
$904$	−17316.6	−0.637105
$905$	2737.38	0.100545
$906$	−5830.40	−0.213799
$907$	18397.4	0.673511	0.336755	−	0.941592i	$-0.390670\pi$
$907$	18397.4	0.673511	0.336755	+	0.941592i	$0.390670\pi$
$908$	30331.6	1.10858
$909$	581.401	0.0212143
$910$	−17595.6	−0.640977
$911$	−1154.31	−0.0419801	−0.0209900	−	0.999780i	$-0.506682\pi$
$911$	−1154.31	−0.0419801	−0.0209900	+	0.999780i	$0.506682\pi$
$912$	−7156.05	−0.259825
$913$	−24423.5	−0.885321
$914$	−37298.8	−1.34982
$915$	5505.70	0.198921
$916$	35821.1	1.29210
$917$	−36561.8	−1.31666
$918$	−2129.76	−0.0765713
$919$	−4601.91	−0.165183	−0.0825913	−	0.996583i	$-0.526320\pi$
$919$	−4601.91	−0.165183	−0.0825913	+	0.996583i	$0.526320\pi$
$920$	21886.3	0.784314
$921$	21608.4	0.773094
$922$	8347.15	0.298155
$923$	−6639.11	−0.236759
$924$	19715.8	0.701952
$925$	−2951.34	−0.104907
$926$	−53082.3	−1.88379
$927$	3071.42	0.108823
$928$	−10035.5	−0.354992
$929$	−22664.2	−0.800418	−0.400209	−	0.916424i	$-0.631062\pi$
$929$	−22664.2	−0.800418	−0.400209	+	0.916424i	$0.631062\pi$
$930$	10193.1	0.359403
$931$	4376.69	0.154071
$932$	−52771.0	−1.85469
$933$	−1193.61	−0.0418834
$934$	35968.5	1.26009
$935$	−2194.38	−0.0767529
$936$	−15009.3	−0.524138
$937$	−44534.9	−1.55271	−0.776356	−	0.630295i	$-0.782934\pi$
$937$	−44534.9	−1.55271	−0.776356	+	0.630295i	$0.782934\pi$
$938$	−7007.96	−0.243942
$939$	8950.87	0.311076
$940$	35171.1	1.22038
$941$	31605.6	1.09491	0.547456	−	0.836834i	$-0.315596\pi$
$941$	31605.6	1.09491	0.547456	+	0.836834i	$0.315596\pi$
$942$	15286.3	0.528720
$943$	6793.76	0.234608
$944$	−7338.89	−0.253030
$945$	2127.80	0.0732459
$946$	39494.8	1.35739
$947$	43788.2	1.50256	0.751281	−	0.659982i	$-0.229436\pi$
$947$	43788.2	1.50256	0.751281	+	0.659982i	$0.229436\pi$
$948$	35968.9	1.23229
$949$	−14124.9	−0.483155
$950$	−5604.76	−0.191413
$951$	26746.2	0.911994
$952$	−9286.31	−0.316146
$953$	20943.2	0.711876	0.355938	−	0.934510i	$-0.384161\pi$
$953$	20943.2	0.711876	0.355938	+	0.934510i	$0.384161\pi$
$954$	−12149.0	−0.412305
$955$	−18876.6	−0.639614
$956$	55200.5	1.86748
$957$	20404.1	0.689206
$958$	−61119.2	−2.06124
$959$	−38302.2	−1.28972
$960$	−9075.47	−0.305114
$961$	−10115.3	−0.339543
$962$	26358.2	0.883392
$963$	−10056.6	−0.336520
$964$	−34814.5	−1.16317
$965$	−12493.0	−0.416751
$966$	27710.2	0.922942
$967$	−21785.0	−0.724466	−0.362233	−	0.932088i	$-0.617985\pi$
$967$	−21785.0	−0.724466	−0.362233	+	0.932088i	$0.617985\pi$
$968$	−21872.9	−0.726262
$969$	2260.50	0.0749409
$970$	19807.8	0.655659
$971$	−20986.9	−0.693617	−0.346808	−	0.937936i	$-0.612735\pi$
$971$	−20986.9	−0.693617	−0.346808	+	0.937936i	$0.612735\pi$
$972$	3759.04	0.124044
$973$	−25209.3	−0.830600
$974$	29075.7	0.956516
$975$	−3456.59	−0.113538
$976$	18919.4	0.620486
$977$	−51490.4	−1.68611	−0.843053	−	0.537831i	$-0.819244\pi$
$977$	−51490.4	−1.68611	−0.843053	+	0.537831i	$0.819244\pi$
$978$	−2368.97	−0.0774552
$979$	−15914.5	−0.519541
$980$	−7315.08	−0.238441
$981$	14479.1	0.471235
$982$	8704.91	0.282877
$983$	−42893.6	−1.39175	−0.695876	−	0.718162i	$-0.744984\pi$
$983$	−42893.6	−1.39175	−0.695876	+	0.718162i	$0.744984\pi$
$984$	6096.63	0.197514
$985$	3217.21	0.104070
$986$	−19903.8	−0.642866
$987$	21501.2	0.693406
$988$	32993.2	1.06240
$989$	36587.8	1.17636
$990$	5876.09	0.188641
$991$	−14254.6	−0.456925	−0.228462	−	0.973553i	$-0.573370\pi$
$991$	−14254.6	−0.456925	−0.228462	+	0.973553i	$0.573370\pi$
$992$	−5578.73	−0.178553
$993$	−29607.6	−0.946193
$994$	10999.4	0.350987
$995$	−7670.97	−0.244408
$996$	−42050.7	−1.33778
$997$	1167.52	0.0370870	0.0185435	−	0.999828i	$-0.494097\pi$
$997$	1167.52	0.0370870	0.0185435	+	0.999828i	$0.494097\pi$
$998$	20769.8	0.658775
$999$	−3187.44	−0.100947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2445.4.a.i.1.38	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2445.4.a.i.1.38	✓	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)

\(f(q)\)	\(=\)	\(q+4.84451 q^{2} +3.00000 q^{3} +15.4693 q^{4} +5.00000 q^{5} +14.5335 q^{6} +15.7615 q^{7} +36.1851 q^{8} +9.00000 q^{9} +24.2226 q^{10} +26.9542 q^{11} +46.4079 q^{12} -46.0879 q^{13} +76.3567 q^{14} +15.0000 q^{15} +51.5448 q^{16} -16.2823 q^{17} +43.6006 q^{18} -46.2772 q^{19} +77.3465 q^{20} +47.2845 q^{21} +130.580 q^{22} +120.968 q^{23} +108.555 q^{24} +25.0000 q^{25} -223.273 q^{26} +27.0000 q^{27} +243.819 q^{28} +252.330 q^{29} +72.6677 q^{30} +140.270 q^{31} -39.7714 q^{32} +80.8625 q^{33} -78.8798 q^{34} +78.8074 q^{35} +139.224 q^{36} -118.054 q^{37} -224.191 q^{38} -138.264 q^{39} +180.926 q^{40} +56.1615 q^{41} +229.070 q^{42} +302.457 q^{43} +416.962 q^{44} +45.0000 q^{45} +586.032 q^{46} +454.721 q^{47} +154.634 q^{48} -94.5755 q^{49} +121.113 q^{50} -48.8469 q^{51} -712.948 q^{52} -278.643 q^{53} +130.802 q^{54} +134.771 q^{55} +570.331 q^{56} -138.832 q^{57} +1222.42 q^{58} -142.379 q^{59} +232.039 q^{60} +367.047 q^{61} +679.540 q^{62} +141.853 q^{63} -605.031 q^{64} -230.440 q^{65} +391.739 q^{66} -91.7792 q^{67} -251.876 q^{68} +362.905 q^{69} +381.784 q^{70} +144.053 q^{71} +325.666 q^{72} +306.477 q^{73} -571.912 q^{74} +75.0000 q^{75} -715.876 q^{76} +424.838 q^{77} -669.820 q^{78} +775.060 q^{79} +257.724 q^{80} +81.0000 q^{81} +272.075 q^{82} -906.110 q^{83} +731.457 q^{84} -81.4115 q^{85} +1465.26 q^{86} +756.991 q^{87} +975.340 q^{88} -590.430 q^{89} +218.003 q^{90} -726.414 q^{91} +1871.29 q^{92} +420.810 q^{93} +2202.90 q^{94} -231.386 q^{95} -119.314 q^{96} +817.740 q^{97} -458.172 q^{98} +242.588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 18 q^{2} + 129 q^{3} + 198 q^{4} + 215 q^{5} + 54 q^{6} + 137 q^{7} + 201 q^{8} + 387 q^{9} + 90 q^{10} + 137 q^{11} + 594 q^{12} + 212 q^{13} + 246 q^{14} + 645 q^{15} + 930 q^{16} + 547 q^{17}+ \cdots + 1233 q^{99}+O(q^{100}) \) 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

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