LMFDB - Embedded newform 2445.4.a.i.1.43

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			1.43
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)

$f(q)$	$=$	\(q+5.49549 q^{2} +3.00000 q^{3} +22.2004 q^{4} +5.00000 q^{5} +16.4865 q^{6} +22.4164 q^{7} +78.0380 q^{8} +9.00000 q^{9} +27.4774 q^{10} +25.1570 q^{11} +66.6011 q^{12} -37.6667 q^{13} +123.189 q^{14} +15.0000 q^{15} +251.254 q^{16} -106.492 q^{17} +49.4594 q^{18} +112.970 q^{19} +111.002 q^{20} +67.2492 q^{21} +138.250 q^{22} -20.3628 q^{23} +234.114 q^{24} +25.0000 q^{25} -206.997 q^{26} +27.0000 q^{27} +497.653 q^{28} -231.914 q^{29} +82.4323 q^{30} +193.694 q^{31} +756.458 q^{32} +75.4709 q^{33} -585.223 q^{34} +112.082 q^{35} +199.803 q^{36} -209.494 q^{37} +620.825 q^{38} -113.000 q^{39} +390.190 q^{40} -181.292 q^{41} +369.567 q^{42} +313.355 q^{43} +558.494 q^{44} +45.0000 q^{45} -111.903 q^{46} -484.455 q^{47} +753.761 q^{48} +159.495 q^{49} +137.387 q^{50} -319.475 q^{51} -836.214 q^{52} +228.073 q^{53} +148.378 q^{54} +125.785 q^{55} +1749.33 q^{56} +338.910 q^{57} -1274.48 q^{58} +880.632 q^{59} +333.006 q^{60} -508.492 q^{61} +1064.45 q^{62} +201.748 q^{63} +2147.07 q^{64} -188.333 q^{65} +414.749 q^{66} -759.657 q^{67} -2364.15 q^{68} -61.0883 q^{69} +615.945 q^{70} -182.943 q^{71} +702.342 q^{72} -695.324 q^{73} -1151.27 q^{74} +75.0000 q^{75} +2507.97 q^{76} +563.929 q^{77} -620.990 q^{78} -594.878 q^{79} +1256.27 q^{80} +81.0000 q^{81} -996.285 q^{82} +684.446 q^{83} +1492.96 q^{84} -532.458 q^{85} +1722.04 q^{86} -695.742 q^{87} +1963.20 q^{88} +1043.27 q^{89} +247.297 q^{90} -844.351 q^{91} -452.061 q^{92} +581.083 q^{93} -2662.32 q^{94} +564.849 q^{95} +2269.37 q^{96} -546.237 q^{97} +876.503 q^{98} +226.413 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.49549	1.94295	0.971474	−	0.237146i	$-0.0762119\pi$
$2$	5.49549	1.94295	0.971474	+	0.237146i	$0.0762119\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	22.2004	2.77505
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	16.4865	1.12176
$7$	22.4164	1.21037	0.605186	−	0.796084i	$-0.293099\pi$
$7$	22.4164	1.21037	0.605186	+	0.796084i	$0.293099\pi$
$8$	78.0380	3.44882
$9$	9.00000	0.333333
$10$	27.4774	0.868913
$11$	25.1570	0.689555	0.344778	−	0.938684i	$-0.387954\pi$
$11$	25.1570	0.689555	0.344778	+	0.938684i	$0.387954\pi$
$12$	66.6011	1.60217
$13$	−37.6667	−0.803604	−0.401802	−	0.915727i	$-0.631616\pi$
$13$	−37.6667	−0.803604	−0.401802	+	0.915727i	$0.631616\pi$
$14$	123.189	2.35169
$15$	15.0000	0.258199
$16$	251.254	3.92584
$17$	−106.492	−1.51929	−0.759647	−	0.650336i	$-0.774628\pi$
$17$	−106.492	−1.51929	−0.759647	+	0.650336i	$0.774628\pi$
$18$	49.4594	0.647649
$19$	112.970	1.36406	0.682028	−	0.731326i	$-0.261098\pi$
$19$	112.970	1.36406	0.682028	+	0.731326i	$0.261098\pi$
$20$	111.002	1.24104
$21$	67.2492	0.698809
$22$	138.250	1.33977
$23$	−20.3628	−0.184606	−0.0923028	−	0.995731i	$-0.529423\pi$
$23$	−20.3628	−0.184606	−0.0923028	+	0.995731i	$0.529423\pi$
$24$	234.114	1.99118
$25$	25.0000	0.200000
$26$	−206.997	−1.56136
$27$	27.0000	0.192450
$28$	497.653	3.35884
$29$	−231.914	−1.48501	−0.742506	−	0.669839i	$-0.766363\pi$
$29$	−231.914	−1.48501	−0.742506	+	0.669839i	$0.766363\pi$
$30$	82.4323	0.501667
$31$	193.694	1.12221	0.561106	−	0.827744i	$-0.310376\pi$
$31$	193.694	1.12221	0.561106	+	0.827744i	$0.310376\pi$
$32$	756.458	4.17888
$33$	75.4709	0.398115
$34$	−585.223	−2.95191
$35$	112.082	0.541295
$36$	199.803	0.925016
$37$	−209.494	−0.930827	−0.465413	−	0.885093i	$-0.654094\pi$
$37$	−209.494	−0.930827	−0.465413	+	0.885093i	$0.654094\pi$
$38$	620.825	2.65029
$39$	−113.000	−0.463961
$40$	390.190	1.54236
$41$	−181.292	−0.690560	−0.345280	−	0.938500i	$-0.612216\pi$
$41$	−181.292	−0.690560	−0.345280	+	0.938500i	$0.612216\pi$
$42$	369.567	1.35775
$43$	313.355	1.11131	0.555654	−	0.831414i	$-0.312468\pi$
$43$	313.355	1.11131	0.555654	+	0.831414i	$0.312468\pi$
$44$	558.494	1.91355
$45$	45.0000	0.149071
$46$	−111.903	−0.358679
$47$	−484.455	−1.50351	−0.751756	−	0.659441i	$-0.770793\pi$
$47$	−484.455	−1.50351	−0.751756	+	0.659441i	$0.770793\pi$
$48$	753.761	2.26659
$49$	159.495	0.465000
$50$	137.387	0.388590
$51$	−319.475	−0.877165
$52$	−836.214	−2.23004
$53$	228.073	0.591099	0.295550	−	0.955327i	$-0.404497\pi$
$53$	228.073	0.591099	0.295550	+	0.955327i	$0.404497\pi$
$54$	148.378	0.373921
$55$	125.785	0.308379
$56$	1749.33	4.17436
$57$	338.910	0.787538
$58$	−1274.48	−2.88530
$59$	880.632	1.94319	0.971597	−	0.236640i	$-0.0760461\pi$
$59$	880.632	1.94319	0.971597	+	0.236640i	$0.0760461\pi$
$60$	333.006	0.716514
$61$	−508.492	−1.06731	−0.533653	−	0.845703i	$-0.679181\pi$
$61$	−508.492	−1.06731	−0.533653	+	0.845703i	$0.679181\pi$
$62$	1064.45	2.18040
$63$	201.748	0.403457
$64$	2147.07	4.19351
$65$	−188.333	−0.359383
$66$	414.749	0.773517
$67$	−759.657	−1.38518	−0.692588	−	0.721333i	$-0.743530\pi$
$67$	−759.657	−1.38518	−0.692588	+	0.721333i	$0.743530\pi$
$68$	−2364.15	−4.21611
$69$	−61.0883	−0.106582
$70$	615.945	1.05171
$71$	−182.943	−0.305794	−0.152897	−	0.988242i	$-0.548860\pi$
$71$	−182.943	−0.305794	−0.152897	+	0.988242i	$0.548860\pi$
$72$	702.342	1.14961
$73$	−695.324	−1.11482	−0.557408	−	0.830239i	$-0.688204\pi$
$73$	−695.324	−1.11482	−0.557408	+	0.830239i	$0.688204\pi$
$74$	−1151.27	−1.80855
$75$	75.0000	0.115470
$76$	2507.97	3.78532
$77$	563.929	0.834618
$78$	−620.990	−0.901452
$79$	−594.878	−0.847202	−0.423601	−	0.905849i	$-0.639234\pi$
$79$	−594.878	−0.847202	−0.423601	+	0.905849i	$0.639234\pi$
$80$	1256.27	1.75569
$81$	81.0000	0.111111
$82$	−996.285	−1.34172
$83$	684.446	0.905153	0.452577	−	0.891725i	$-0.350505\pi$
$83$	684.446	0.905153	0.452577	+	0.891725i	$0.350505\pi$
$84$	1492.96	1.93923
$85$	−532.458	−0.679449
$86$	1722.04	2.15921
$87$	−695.742	−0.857372
$88$	1963.20	2.37816
$89$	1043.27	1.24255	0.621273	−	0.783594i	$-0.286616\pi$
$89$	1043.27	1.24255	0.621273	+	0.783594i	$0.286616\pi$
$90$	247.297	0.289638
$91$	−844.351	−0.972660
$92$	−452.061	−0.512289
$93$	581.083	0.647909
$94$	−2662.32	−2.92125
$95$	564.849	0.610025
$96$	2269.37	2.41268
$97$	−546.237	−0.571772	−0.285886	−	0.958264i	$-0.592288\pi$
$97$	−546.237	−0.571772	−0.285886	+	0.958264i	$0.592288\pi$
$98$	876.503	0.903471
$99$	226.413	0.229852
$100$	555.009	0.555009
$101$	484.964	0.477780	0.238890	−	0.971047i	$-0.423217\pi$
$101$	484.964	0.477780	0.238890	+	0.971047i	$0.423217\pi$
$102$	−1755.67	−1.70429
$103$	−1872.36	−1.79115	−0.895577	−	0.444907i	$-0.853237\pi$
$103$	−1872.36	−1.79115	−0.895577	+	0.444907i	$0.853237\pi$
$104$	−2939.43	−2.77149
$105$	336.246	0.312517
$106$	1253.37	1.14848
$107$	−662.811	−0.598844	−0.299422	−	0.954121i	$-0.596794\pi$
$107$	−662.811	−0.598844	−0.299422	+	0.954121i	$0.596794\pi$
$108$	599.410	0.534058
$109$	182.954	0.160769	0.0803844	−	0.996764i	$-0.474385\pi$
$109$	182.954	0.160769	0.0803844	+	0.996764i	$0.474385\pi$
$110$	691.249	0.599163
$111$	−628.482	−0.537413
$112$	5632.21	4.75173
$113$	1129.60	0.940388	0.470194	−	0.882563i	$-0.344184\pi$
$113$	1129.60	0.940388	0.470194	+	0.882563i	$0.344184\pi$
$114$	1862.47	1.53015
$115$	−101.814	−0.0825582
$116$	−5148.58	−4.12098
$117$	−339.000	−0.267868
$118$	4839.50	3.77553
$119$	−2387.16	−1.83891
$120$	1170.57	0.890483
$121$	−698.127	−0.524513
$122$	−2794.41	−2.07372
$123$	−543.875	−0.398695
$124$	4300.09	3.11419
$125$	125.000	0.0894427
$126$	1108.70	0.783897
$127$	458.451	0.320323	0.160161	−	0.987091i	$-0.448799\pi$
$127$	458.451	0.320323	0.160161	+	0.987091i	$0.448799\pi$
$128$	5747.56	3.96888
$129$	940.066	0.641614
$130$	−1034.98	−0.698262
$131$	699.653	0.466633	0.233317	−	0.972401i	$-0.425042\pi$
$131$	699.653	0.466633	0.233317	+	0.972401i	$0.425042\pi$
$132$	1675.48	1.10479
$133$	2532.38	1.65102
$134$	−4174.68	−2.69133
$135$	135.000	0.0860663
$136$	−8310.39	−5.23978
$137$	1922.28	1.19877	0.599385	−	0.800461i	$-0.295412\pi$
$137$	1922.28	1.19877	0.599385	+	0.800461i	$0.295412\pi$
$138$	−335.710	−0.207084
$139$	2242.79	1.36857	0.684284	−	0.729216i	$-0.260115\pi$
$139$	2242.79	1.36857	0.684284	+	0.729216i	$0.260115\pi$
$140$	2488.26	1.50212
$141$	−1453.37	−0.868053
$142$	−1005.36	−0.594142
$143$	−947.579	−0.554130
$144$	2261.28	1.30861
$145$	−1159.57	−0.664118
$146$	−3821.14	−2.16603
$147$	478.485	0.268468
$148$	−4650.84	−2.58309
$149$	−2854.96	−1.56971	−0.784857	−	0.619676i	$-0.787264\pi$
$149$	−2854.96	−1.56971	−0.784857	+	0.619676i	$0.787264\pi$
$150$	412.162	0.224352
$151$	−2705.54	−1.45810	−0.729052	−	0.684459i	$-0.760039\pi$
$151$	−2705.54	−1.45810	−0.729052	+	0.684459i	$0.760039\pi$
$152$	8815.94	4.70439
$153$	−958.424	−0.506431
$154$	3099.06	1.62162
$155$	968.472	0.501868
$156$	−2508.64	−1.28751
$157$	2739.23	1.39245	0.696224	−	0.717825i	$-0.254862\pi$
$157$	2739.23	1.39245	0.696224	+	0.717825i	$0.254862\pi$
$158$	−3269.14	−1.64607
$159$	684.220	0.341271
$160$	3782.29	1.86885
$161$	−456.460	−0.223442
$162$	445.134	0.215883
$163$	−163.000	−0.0783260
$163$	−163.000	−0.0783260
$164$	−4024.74	−1.91634
$165$	377.354	0.178042
$166$	3761.37	1.75867
$167$	812.111	0.376306	0.188153	−	0.982140i	$-0.439750\pi$
$167$	812.111	0.376306	0.188153	+	0.982140i	$0.439750\pi$
$168$	5247.99	2.41007
$169$	−778.222	−0.354220
$170$	−2926.11	−1.32013
$171$	1016.73	0.454685
$172$	6956.61	3.08393
$173$	1962.85	0.862616	0.431308	−	0.902205i	$-0.358052\pi$
$173$	1962.85	0.862616	0.431308	+	0.902205i	$0.358052\pi$
$174$	−3823.44	−1.66583
$175$	560.410	0.242074
$176$	6320.78	2.70708
$177$	2641.90	1.12190
$178$	5733.29	2.41420
$179$	−1737.34	−0.725448	−0.362724	−	0.931897i	$-0.618153\pi$
$179$	−1737.34	−0.725448	−0.362724	+	0.931897i	$0.618153\pi$
$180$	999.017	0.413680
$181$	−4572.71	−1.87783	−0.938914	−	0.344152i	$-0.888166\pi$
$181$	−4572.71	−1.87783	−0.938914	+	0.344152i	$0.888166\pi$
$182$	−4640.12	−1.88983
$183$	−1525.48	−0.616210
$184$	−1589.07	−0.636673
$185$	−1047.47	−0.416278
$186$	3193.34	1.25885
$187$	−2679.00	−1.04764
$188$	−10755.1	−4.17232
$189$	605.243	0.232936
$190$	3104.12	1.18525
$191$	812.578	0.307833	0.153916	−	0.988084i	$-0.450811\pi$
$191$	812.578	0.307833	0.153916	+	0.988084i	$0.450811\pi$
$192$	6441.22	2.42112
$193$	3998.70	1.49136	0.745681	−	0.666303i	$-0.232124\pi$
$193$	3998.70	1.49136	0.745681	+	0.666303i	$0.232124\pi$
$194$	−3001.84	−1.11092
$195$	−565.000	−0.207490
$196$	3540.85	1.29040
$197$	−2516.83	−0.910236	−0.455118	−	0.890431i	$-0.650403\pi$
$197$	−2516.83	−0.910236	−0.455118	+	0.890431i	$0.650403\pi$
$198$	1244.25	0.446590
$199$	−1935.04	−0.689303	−0.344652	−	0.938731i	$-0.612003\pi$
$199$	−1935.04	−0.689303	−0.344652	+	0.938731i	$0.612003\pi$
$200$	1950.95	0.689765
$201$	−2278.97	−0.799732
$202$	2665.11	0.928301
$203$	−5198.68	−1.79742
$204$	−7092.46	−2.43417
$205$	−906.458	−0.308828
$206$	−10289.5	−3.48012
$207$	−183.265	−0.0615352
$208$	−9463.89	−3.15482
$209$	2841.98	0.940592
$210$	1847.84	0.607204
$211$	−5724.72	−1.86780	−0.933901	−	0.357532i	$-0.883618\pi$
$211$	−5724.72	−1.86780	−0.933901	+	0.357532i	$0.883618\pi$
$212$	5063.31	1.64033
$213$	−548.830	−0.176550
$214$	−3642.47	−1.16352
$215$	1566.78	0.496992
$216$	2107.03	0.663727
$217$	4341.93	1.35829
$218$	1005.42	0.312365
$219$	−2085.97	−0.643639
$220$	2792.47	0.855765
$221$	4011.18	1.22091
$222$	−3453.81	−1.04417
$223$	−3059.63	−0.918779	−0.459390	−	0.888235i	$-0.651932\pi$
$223$	−3059.63	−0.918779	−0.459390	+	0.888235i	$0.651932\pi$
$224$	16957.1	5.05800
$225$	225.000	0.0666667
$226$	6207.70	1.82712
$227$	3826.00	1.11868	0.559341	−	0.828938i	$-0.311054\pi$
$227$	3826.00	1.11868	0.559341	+	0.828938i	$0.311054\pi$
$228$	7523.92	2.18546
$229$	2753.05	0.794439	0.397220	−	0.917724i	$-0.369975\pi$
$229$	2753.05	0.794439	0.397220	+	0.917724i	$0.369975\pi$
$230$	−559.517	−0.160406
$231$	1691.79	0.481867
$232$	−18098.1	−5.12155
$233$	5780.33	1.62524	0.812622	−	0.582791i	$-0.198039\pi$
$233$	5780.33	1.62524	0.812622	+	0.582791i	$0.198039\pi$
$234$	−1862.97	−0.520454
$235$	−2422.28	−0.672391
$236$	19550.4	5.39246
$237$	−1784.63	−0.489133
$238$	−13118.6	−3.57291
$239$	−2583.61	−0.699246	−0.349623	−	0.936891i	$-0.613690\pi$
$239$	−2583.61	−0.699246	−0.349623	+	0.936891i	$0.613690\pi$
$240$	3768.81	1.01365
$241$	7086.86	1.89421	0.947106	−	0.320921i	$-0.103992\pi$
$241$	7086.86	1.89421	0.947106	+	0.320921i	$0.103992\pi$
$242$	−3836.55	−1.01910
$243$	243.000	0.0641500
$244$	−11288.7	−2.96183
$245$	797.476	0.207954
$246$	−2988.86	−0.774644
$247$	−4255.20	−1.09616
$248$	15115.5	3.87031
$249$	2053.34	0.522591
$250$	686.936	0.173783
$251$	−6017.71	−1.51329	−0.756643	−	0.653829i	$-0.773162\pi$
$251$	−6017.71	−1.51329	−0.756643	+	0.653829i	$0.773162\pi$
$252$	4478.87	1.11961
$253$	−512.265	−0.127296
$254$	2519.41	0.622370
$255$	−1597.37	−0.392280
$256$	14409.0	3.51783
$257$	5495.03	1.33374	0.666869	−	0.745175i	$-0.267634\pi$
$257$	5495.03	1.33374	0.666869	+	0.745175i	$0.267634\pi$
$258$	5166.12	1.24662
$259$	−4696.10	−1.12665
$260$	−4181.07	−0.997304
$261$	−2087.23	−0.495004
$262$	3844.94	0.906645
$263$	4398.70	1.03131	0.515656	−	0.856795i	$-0.327548\pi$
$263$	4398.70	1.03131	0.515656	+	0.856795i	$0.327548\pi$
$264$	5889.60	1.37303
$265$	1140.37	0.264348
$266$	13916.7	3.20784
$267$	3129.82	0.717385
$268$	−16864.7	−3.84393
$269$	−8418.16	−1.90804	−0.954022	−	0.299736i	$-0.903101\pi$
$269$	−8418.16	−1.90804	−0.954022	+	0.299736i	$0.903101\pi$
$270$	741.891	0.167222
$271$	3841.71	0.861133	0.430567	−	0.902559i	$-0.358314\pi$
$271$	3841.71	0.861133	0.430567	+	0.902559i	$0.358314\pi$
$272$	−26756.4	−5.96450
$273$	−2533.05	−0.561565
$274$	10563.9	2.32915
$275$	628.924	0.137911
$276$	−1356.18	−0.295770
$277$	1428.10	0.309769	0.154885	−	0.987933i	$-0.450499\pi$
$277$	1428.10	0.309769	0.154885	+	0.987933i	$0.450499\pi$
$278$	12325.2	2.65906
$279$	1743.25	0.374070
$280$	8746.66	1.86683
$281$	3514.70	0.746154	0.373077	−	0.927800i	$-0.378303\pi$
$281$	3514.70	0.746154	0.373077	+	0.927800i	$0.378303\pi$
$282$	−7986.96	−1.68658
$283$	3927.32	0.824928	0.412464	−	0.910974i	$-0.364668\pi$
$283$	3927.32	0.824928	0.412464	+	0.910974i	$0.364668\pi$
$284$	−4061.41	−0.848593
$285$	1694.55	0.352198
$286$	−5207.41	−1.07664
$287$	−4063.90	−0.835835
$288$	6808.12	1.39296
$289$	6427.45	1.30825
$290$	−6372.40	−1.29035
$291$	−1638.71	−0.330113
$292$	−15436.5	−3.09367
$293$	−2732.80	−0.544887	−0.272444	−	0.962172i	$-0.587832\pi$
$293$	−2732.80	−0.544887	−0.272444	+	0.962172i	$0.587832\pi$
$294$	2629.51	0.521619
$295$	4403.16	0.869023
$296$	−16348.5	−3.21026
$297$	679.238	0.132705
$298$	−15689.4	−3.04987
$299$	766.998	0.148350
$300$	1665.03	0.320435
$301$	7024.30	1.34510
$302$	−14868.2	−2.83302
$303$	1454.89	0.275846
$304$	28384.1	5.35507
$305$	−2542.46	−0.477314
$306$	−5267.01	−0.983970
$307$	3771.71	0.701182	0.350591	−	0.936529i	$-0.385981\pi$
$307$	3771.71	0.701182	0.350591	+	0.936529i	$0.385981\pi$
$308$	12519.4	2.31611
$309$	−5617.07	−1.03412
$310$	5322.23	0.975104
$311$	10651.8	1.94216	0.971078	−	0.238761i	$-0.0767412\pi$
$311$	10651.8	1.94216	0.971078	+	0.238761i	$0.0767412\pi$
$312$	−8818.29	−1.60012
$313$	−1649.24	−0.297828	−0.148914	−	0.988850i	$-0.547578\pi$
$313$	−1649.24	−0.297828	−0.148914	+	0.988850i	$0.547578\pi$
$314$	15053.4	2.70545
$315$	1008.74	0.180432
$316$	−13206.5	−2.35103
$317$	5831.26	1.03317	0.516587	−	0.856235i	$-0.327202\pi$
$317$	5831.26	1.03317	0.516587	+	0.856235i	$0.327202\pi$
$318$	3760.12	0.663073
$319$	−5834.25	−1.02400
$320$	10735.4	1.87539
$321$	−1988.43	−0.345743
$322$	−2508.47	−0.434135
$323$	−12030.3	−2.07240
$324$	1798.23	0.308339
$325$	−941.667	−0.160721
$326$	−895.764	−0.152183
$327$	548.861	0.0928199
$328$	−14147.6	−2.38162
$329$	−10859.7	−1.81981
$330$	2073.75	0.345927
$331$	143.474	0.0238250	0.0119125	−	0.999929i	$-0.496208\pi$
$331$	143.474	0.0238250	0.0119125	+	0.999929i	$0.496208\pi$
$332$	15195.0	2.51184
$333$	−1885.45	−0.310276
$334$	4462.95	0.731142
$335$	−3798.28	−0.619470
$336$	16896.6	2.74341
$337$	7254.79	1.17268	0.586341	−	0.810064i	$-0.300568\pi$
$337$	7254.79	1.17268	0.586341	+	0.810064i	$0.300568\pi$
$338$	−4276.71	−0.688232
$339$	3388.80	0.542933
$340$	−11820.8	−1.88550
$341$	4872.76	0.773827
$342$	5587.42	0.883430
$343$	−4113.52	−0.647549
$344$	24453.6	3.83271
$345$	−305.441	−0.0476650
$346$	10786.8	1.67602
$347$	7561.95	1.16988	0.584938	−	0.811078i	$-0.301119\pi$
$347$	7561.95	1.16988	0.584938	+	0.811078i	$0.301119\pi$
$348$	−15445.7	−2.37925
$349$	−6381.95	−0.978848	−0.489424	−	0.872046i	$-0.662793\pi$
$349$	−6381.95	−0.978848	−0.489424	+	0.872046i	$0.662793\pi$
$350$	3079.73	0.470338
$351$	−1017.00	−0.154654
$352$	19030.2	2.88157
$353$	−26.6159	−0.00401309	−0.00200655	−	0.999998i	$-0.500639\pi$
$353$	−26.6159	−0.00401309	−0.00200655	+	0.999998i	$0.500639\pi$
$354$	14518.5	2.17980
$355$	−914.717	−0.136755
$356$	23161.0	3.44813
$357$	−7161.47	−1.06170
$358$	−9547.56	−1.40951
$359$	−7956.45	−1.16971	−0.584854	−	0.811138i	$-0.698848\pi$
$359$	−7956.45	−1.16971	−0.584854	+	0.811138i	$0.698848\pi$
$360$	3511.71	0.514120
$361$	5903.20	0.860650
$362$	−25129.3	−3.64852
$363$	−2094.38	−0.302828
$364$	−18744.9	−2.69918
$365$	−3476.62	−0.498561
$366$	−8383.23	−1.19726
$367$	7866.70	1.11891	0.559453	−	0.828862i	$-0.311011\pi$
$367$	7866.70	1.11891	0.559453	+	0.828862i	$0.311011\pi$
$368$	−5116.22	−0.724732
$369$	−1631.62	−0.230187
$370$	−5756.36	−0.808807
$371$	5112.58	0.715450
$372$	12900.3	1.79798
$373$	−6938.55	−0.963176	−0.481588	−	0.876398i	$-0.659940\pi$
$373$	−6938.55	−0.963176	−0.481588	+	0.876398i	$0.659940\pi$
$374$	−14722.4	−2.03550
$375$	375.000	0.0516398
$376$	−37805.9	−5.18535
$377$	8735.43	1.19336
$378$	3326.10	0.452583
$379$	8453.34	1.14570	0.572848	−	0.819662i	$-0.305839\pi$
$379$	8453.34	1.14570	0.572848	+	0.819662i	$0.305839\pi$
$380$	12539.9	1.69285
$381$	1375.35	0.184938
$382$	4465.51	0.598104
$383$	9542.92	1.27316	0.636580	−	0.771210i	$-0.280348\pi$
$383$	9542.92	1.27316	0.636580	+	0.771210i	$0.280348\pi$
$384$	17242.7	2.29144
$385$	2819.64	0.373253
$386$	21974.8	2.89764
$387$	2820.20	0.370436
$388$	−12126.7	−1.58670
$389$	7460.92	0.972451	0.486226	−	0.873833i	$-0.338373\pi$
$389$	7460.92	0.972451	0.486226	+	0.873833i	$0.338373\pi$
$390$	−3104.95	−0.403142
$391$	2168.46	0.280470
$392$	12446.7	1.60370
$393$	2098.96	0.269411
$394$	−13831.2	−1.76854
$395$	−2974.39	−0.378880
$396$	5026.45	0.637850
$397$	305.727	0.0386498	0.0193249	−	0.999813i	$-0.493848\pi$
$397$	305.727	0.0386498	0.0193249	+	0.999813i	$0.493848\pi$
$398$	−10634.0	−1.33928
$399$	7597.14	0.953214
$400$	6281.34	0.785168
$401$	−792.130	−0.0986461	−0.0493230	−	0.998783i	$-0.515706\pi$
$401$	−792.130	−0.0986461	−0.0493230	+	0.998783i	$0.515706\pi$
$402$	−12524.1	−1.55384
$403$	−7295.82	−0.901814
$404$	10766.4	1.32586
$405$	405.000	0.0496904
$406$	−28569.3	−3.49229
$407$	−5270.23	−0.641857
$408$	−24931.2	−3.02519
$409$	−10514.6	−1.27119	−0.635594	−	0.772024i	$-0.719245\pi$
$409$	−10514.6	−1.27119	−0.635594	+	0.772024i	$0.719245\pi$
$410$	−4981.43	−0.600037
$411$	5766.84	0.692110
$412$	−41567.0	−4.97053
$413$	19740.6	2.35199
$414$	−1007.13	−0.119560
$415$	3422.23	0.404797
$416$	−28493.3	−3.35816
$417$	6728.37	0.790143
$418$	15618.1	1.82752
$419$	−3176.06	−0.370312	−0.185156	−	0.982709i	$-0.559279\pi$
$419$	−3176.06	−0.370312	−0.185156	+	0.982709i	$0.559279\pi$
$420$	7464.79	0.867249
$421$	−8668.63	−1.00352	−0.501762	−	0.865006i	$-0.667315\pi$
$421$	−8668.63	−1.00352	−0.501762	+	0.865006i	$0.667315\pi$
$422$	−31460.1	−3.62904
$423$	−4360.10	−0.501171
$424$	17798.4	2.03860
$425$	−2662.29	−0.303859
$426$	−3016.09	−0.343028
$427$	−11398.6	−1.29184
$428$	−14714.7	−1.66182
$429$	−2842.74	−0.319927
$430$	8610.20	0.965630
$431$	−13520.7	−1.51106	−0.755531	−	0.655113i	$-0.772621\pi$
$431$	−13520.7	−1.51106	−0.755531	+	0.655113i	$0.772621\pi$
$432$	6783.85	0.755528
$433$	−10213.1	−1.13351	−0.566754	−	0.823887i	$-0.691801\pi$
$433$	−10213.1	−1.13351	−0.566754	+	0.823887i	$0.691801\pi$
$434$	23861.0	2.63909
$435$	−3478.71	−0.383429
$436$	4061.64	0.446141
$437$	−2300.38	−0.251813
$438$	−11463.4	−1.25056
$439$	−5215.08	−0.566975	−0.283487	−	0.958976i	$-0.591491\pi$
$439$	−5215.08	−0.566975	−0.283487	+	0.958976i	$0.591491\pi$
$440$	9815.99	1.06354
$441$	1435.46	0.155000
$442$	22043.4	2.37217
$443$	−1106.70	−0.118692	−0.0593462	−	0.998237i	$-0.518902\pi$
$443$	−1106.70	−0.118692	−0.0593462	+	0.998237i	$0.518902\pi$
$444$	−13952.5	−1.49135
$445$	5216.36	0.555684
$446$	−16814.1	−1.78514
$447$	−8564.88	−0.906275
$448$	48129.7	5.07570
$449$	−2110.07	−0.221782	−0.110891	−	0.993833i	$-0.535371\pi$
$449$	−2110.07	−0.221782	−0.110891	+	0.993833i	$0.535371\pi$
$450$	1236.48	0.129530
$451$	−4560.74	−0.476180
$452$	25077.5	2.60962
$453$	−8116.61	−0.841836
$454$	21025.7	2.17354
$455$	−4221.76	−0.434987
$456$	26447.8	2.71608
$457$	9631.05	0.985824	0.492912	−	0.870079i	$-0.335933\pi$
$457$	9631.05	0.985824	0.492912	+	0.870079i	$0.335933\pi$
$458$	15129.3	1.54355
$459$	−2875.27	−0.292388
$460$	−2260.31	−0.229103
$461$	−10383.6	−1.04905	−0.524526	−	0.851394i	$-0.675757\pi$
$461$	−10383.6	−1.04905	−0.524526	+	0.851394i	$0.675757\pi$
$462$	9297.19	0.936243
$463$	−14144.1	−1.41972	−0.709862	−	0.704341i	$-0.751243\pi$
$463$	−14144.1	−1.41972	−0.709862	+	0.704341i	$0.751243\pi$
$464$	−58269.3	−5.82992
$465$	2905.42	0.289754
$466$	31765.7	3.15777
$467$	11687.4	1.15809	0.579047	−	0.815294i	$-0.303425\pi$
$467$	11687.4	1.15809	0.579047	+	0.815294i	$0.303425\pi$
$468$	−7525.93	−0.743347
$469$	−17028.8	−1.67658
$470$	−13311.6	−1.30642
$471$	8217.68	0.803930
$472$	68722.7	6.70174
$473$	7883.07	0.766308
$474$	−9807.43	−0.950359
$475$	2824.25	0.272811
$476$	−52995.8	−5.10306
$477$	2052.66	0.197033
$478$	−14198.2	−1.35860
$479$	−13205.9	−1.25970	−0.629848	−	0.776719i	$-0.716883\pi$
$479$	−13205.9	−1.25970	−0.629848	+	0.776719i	$0.716883\pi$
$480$	11346.9	1.07898
$481$	7890.94	0.748016
$482$	38945.8	3.68036
$483$	−1369.38	−0.129004
$484$	−15498.7	−1.45555
$485$	−2731.18	−0.255704
$486$	1335.40	0.124640
$487$	−3356.25	−0.312292	−0.156146	−	0.987734i	$-0.549907\pi$
$487$	−3356.25	−0.312292	−0.156146	+	0.987734i	$0.549907\pi$
$488$	−39681.7	−3.68095
$489$	−489.000	−0.0452216
$490$	4382.52	0.404045
$491$	−11743.5	−1.07938	−0.539690	−	0.841864i	$-0.681459\pi$
$491$	−11743.5	−1.07938	−0.539690	+	0.841864i	$0.681459\pi$
$492$	−12074.2	−1.10640
$493$	24696.9	2.25617
$494$	−23384.4	−2.12978
$495$	1132.06	0.102793
$496$	48666.5	4.40562
$497$	−4100.93	−0.370125
$498$	11284.1	1.01537
$499$	−7169.93	−0.643227	−0.321613	−	0.946871i	$-0.604225\pi$
$499$	−7169.93	−0.643227	−0.321613	+	0.946871i	$0.604225\pi$
$500$	2775.05	0.248208
$501$	2436.33	0.217260
$502$	−33070.3	−2.94023
$503$	10671.4	0.945955	0.472978	−	0.881074i	$-0.343179\pi$
$503$	10671.4	0.945955	0.472978	+	0.881074i	$0.343179\pi$
$504$	15744.0	1.39145
$505$	2424.82	0.213670
$506$	−2815.15	−0.247329
$507$	−2334.67	−0.204509
$508$	10177.8	0.888910
$509$	6806.16	0.592687	0.296344	−	0.955081i	$-0.404233\pi$
$509$	6806.16	0.592687	0.296344	+	0.955081i	$0.404233\pi$
$510$	−8778.34	−0.762180
$511$	−15586.7	−1.34934
$512$	33204.2	2.86608
$513$	3050.19	0.262513
$514$	30197.9	2.59138
$515$	−9361.78	−0.801028
$516$	20869.8	1.78051
$517$	−12187.4	−1.03676
$518$	−25807.4	−2.18902
$519$	5888.55	0.498032
$520$	−14697.2	−1.23945
$521$	1533.35	0.128939	0.0644694	−	0.997920i	$-0.479465\pi$
$521$	1533.35	0.128939	0.0644694	+	0.997920i	$0.479465\pi$
$522$	−11470.3	−0.961767
$523$	−2199.30	−0.183879	−0.0919394	−	0.995765i	$-0.529307\pi$
$523$	−2199.30	−0.183879	−0.0919394	+	0.995765i	$0.529307\pi$
$524$	15532.6	1.29493
$525$	1681.23	0.139762
$526$	24173.0	2.00379
$527$	−20626.8	−1.70497
$528$	18962.3	1.56294
$529$	−11752.4	−0.965921
$530$	6266.87	0.513614
$531$	7925.69	0.647732
$532$	56219.8	4.58165
$533$	6828.65	0.554937
$534$	17199.9	1.39384
$535$	−3314.05	−0.267811
$536$	−59282.1	−4.77723
$537$	−5212.03	−0.418838
$538$	−46261.9	−3.70723
$539$	4012.41	0.320643
$540$	2997.05	0.238838
$541$	5101.81	0.405441	0.202721	−	0.979237i	$-0.435022\pi$
$541$	5101.81	0.405441	0.202721	+	0.979237i	$0.435022\pi$
$542$	21112.1	1.67314
$543$	−13718.1	−1.08416
$544$	−80556.4	−6.34894
$545$	914.769	0.0718980
$546$	−13920.4	−1.09109
$547$	1884.24	0.147284	0.0736419	−	0.997285i	$-0.476538\pi$
$547$	1884.24	0.147284	0.0736419	+	0.997285i	$0.476538\pi$
$548$	42675.4	3.32664
$549$	−4576.43	−0.355769
$550$	3456.24	0.267954
$551$	−26199.3	−2.02564
$552$	−4767.21	−0.367583
$553$	−13335.0	−1.02543
$554$	7848.10	0.601866
$555$	−3142.41	−0.240338
$556$	49790.8	3.79784
$557$	−5431.84	−0.413203	−0.206602	−	0.978425i	$-0.566240\pi$
$557$	−5431.84	−0.413203	−0.206602	+	0.978425i	$0.566240\pi$
$558$	9580.01	0.726799
$559$	−11803.1	−0.893052
$560$	28161.0	2.12504
$561$	−8037.01	−0.604853
$562$	19315.0	1.44974
$563$	231.448	0.0173257	0.00866286	−	0.999962i	$-0.497242\pi$
$563$	231.448	0.0173257	0.00866286	+	0.999962i	$0.497242\pi$
$564$	−32265.3	−2.40889
$565$	5648.00	0.420554
$566$	21582.5	1.60279
$567$	1815.73	0.134486
$568$	−14276.5	−1.05463
$569$	−2946.71	−0.217105	−0.108552	−	0.994091i	$-0.534621\pi$
$569$	−2946.71	−0.217105	−0.108552	+	0.994091i	$0.534621\pi$
$570$	9312.37	0.684302
$571$	−18764.1	−1.37522	−0.687612	−	0.726078i	$-0.741341\pi$
$571$	−18764.1	−1.37522	−0.687612	+	0.726078i	$0.741341\pi$
$572$	−21036.6	−1.53774
$573$	2437.73	0.177727
$574$	−22333.1	−1.62398
$575$	−509.069	−0.0369211
$576$	19323.7	1.39784
$577$	8333.10	0.601233	0.300617	−	0.953745i	$-0.402808\pi$
$577$	8333.10	0.601233	0.300617	+	0.953745i	$0.402808\pi$
$578$	35321.9	2.54187
$579$	11996.1	0.861038
$580$	−25742.9	−1.84296
$581$	15342.8	1.09557
$582$	−9005.51	−0.641392
$583$	5737.63	0.407596
$584$	−54261.7	−3.84480
$585$	−1695.00	−0.119794
$586$	−15018.1	−1.05869
$587$	−12081.1	−0.849469	−0.424735	−	0.905318i	$-0.639633\pi$
$587$	−12081.1	−0.849469	−0.424735	+	0.905318i	$0.639633\pi$
$588$	10622.6	0.745012
$589$	21881.6	1.53076
$590$	24197.5	1.68847
$591$	−7550.48	−0.525525
$592$	−52636.1	−3.65428
$593$	−14540.3	−1.00691	−0.503456	−	0.864021i	$-0.667938\pi$
$593$	−14540.3	−1.00691	−0.503456	+	0.864021i	$0.667938\pi$
$594$	3732.74	0.257839
$595$	−11935.8	−0.822386
$596$	−63381.2	−4.35603
$597$	−5805.12	−0.397969
$598$	4215.03	0.288236
$599$	22538.5	1.53739	0.768695	−	0.639615i	$-0.220906\pi$
$599$	22538.5	1.53739	0.768695	+	0.639615i	$0.220906\pi$
$600$	5852.85	0.398236
$601$	6682.72	0.453567	0.226784	−	0.973945i	$-0.427179\pi$
$601$	6682.72	0.453567	0.226784	+	0.973945i	$0.427179\pi$
$602$	38601.9	2.61345
$603$	−6836.91	−0.461726
$604$	−60064.0	−4.04630
$605$	−3490.64	−0.234570
$606$	7995.34	0.535955
$607$	24275.6	1.62326	0.811629	−	0.584174i	$-0.198581\pi$
$607$	24275.6	1.62326	0.811629	+	0.584174i	$0.198581\pi$
$608$	85457.0	5.70023
$609$	−15596.0	−1.03774
$610$	−13972.1	−0.927396
$611$	18247.8	1.20823
$612$	−21277.4	−1.40537
$613$	−21018.5	−1.38488	−0.692438	−	0.721478i	$-0.743463\pi$
$613$	−21018.5	−1.38488	−0.692438	+	0.721478i	$0.743463\pi$
$614$	20727.4	1.36236
$615$	−2719.37	−0.178302
$616$	44007.9	2.87845
$617$	−1743.55	−0.113765	−0.0568824	−	0.998381i	$-0.518116\pi$
$617$	−1743.55	−0.113765	−0.0568824	+	0.998381i	$0.518116\pi$
$618$	−30868.5	−2.00925
$619$	12839.3	0.833694	0.416847	−	0.908977i	$-0.363135\pi$
$619$	12839.3	0.833694	0.416847	+	0.908977i	$0.363135\pi$
$620$	21500.4	1.39271
$621$	−549.795	−0.0355274
$622$	58537.1	3.77351
$623$	23386.4	1.50394
$624$	−28391.7	−1.82144
$625$	625.000	0.0400000
$626$	−9063.35	−0.578665
$627$	8525.94	0.543051
$628$	60811.9	3.86411
$629$	22309.3	1.41420
$630$	5543.51	0.350569
$631$	−22703.0	−1.43231	−0.716157	−	0.697939i	$-0.754101\pi$
$631$	−22703.0	−1.43231	−0.716157	+	0.697939i	$0.754101\pi$
$632$	−46423.1	−2.92185
$633$	−17174.2	−1.07838
$634$	32045.6	2.00740
$635$	2292.26	0.143253
$636$	15189.9	0.947044
$637$	−6007.65	−0.373676
$638$	−32062.1	−1.98958
$639$	−1646.49	−0.101931
$640$	28737.8	1.77494
$641$	28392.3	1.74950	0.874750	−	0.484575i	$-0.161026\pi$
$641$	28392.3	1.74950	0.874750	+	0.484575i	$0.161026\pi$
$642$	−10927.4	−0.671761
$643$	2565.39	0.157339	0.0786697	−	0.996901i	$-0.474933\pi$
$643$	2565.39	0.157339	0.0786697	+	0.996901i	$0.474933\pi$
$644$	−10133.6	−0.620061
$645$	4700.33	0.286938
$646$	−66112.6	−4.02657
$647$	22127.6	1.34455	0.672276	−	0.740300i	$-0.265317\pi$
$647$	22127.6	1.34455	0.672276	+	0.740300i	$0.265317\pi$
$648$	6321.08	0.383203
$649$	22154.0	1.33994
$650$	−5174.92	−0.312272
$651$	13025.8	0.784211
$652$	−3618.66	−0.217358
$653$	−16673.0	−0.999181	−0.499591	−	0.866262i	$-0.666516\pi$
$653$	−16673.0	−0.999181	−0.499591	+	0.866262i	$0.666516\pi$
$654$	3016.26	0.180344
$655$	3498.27	0.208685
$656$	−45550.2	−2.71103
$657$	−6257.92	−0.371605
$658$	−59679.6	−3.53579
$659$	5436.88	0.321382	0.160691	−	0.987005i	$-0.448628\pi$
$659$	5436.88	0.321382	0.160691	+	0.987005i	$0.448628\pi$
$660$	8377.41	0.494076
$661$	12724.7	0.748766	0.374383	−	0.927274i	$-0.377854\pi$
$661$	12724.7	0.748766	0.374383	+	0.927274i	$0.377854\pi$
$662$	788.461	0.0462907
$663$	12033.5	0.704893
$664$	53412.8	3.12172
$665$	12661.9	0.738357
$666$	−10361.4	−0.602849
$667$	4722.41	0.274142
$668$	18029.2	1.04427
$669$	−9178.88	−0.530457
$670$	−20873.4	−1.20360
$671$	−12792.1	−0.735967
$672$	50871.2	2.92024
$673$	−7280.55	−0.417005	−0.208503	−	0.978022i	$-0.566859\pi$
$673$	−7280.55	−0.417005	−0.208503	+	0.978022i	$0.566859\pi$
$674$	39868.6	2.27846
$675$	675.000	0.0384900
$676$	−17276.8	−0.982978
$677$	3893.02	0.221006	0.110503	−	0.993876i	$-0.464754\pi$
$677$	3893.02	0.221006	0.110503	+	0.993876i	$0.464754\pi$
$678$	18623.1	1.05489
$679$	−12244.7	−0.692057
$680$	−41551.9	−2.34330
$681$	11478.0	0.645871
$682$	26778.2	1.50351
$683$	−6334.82	−0.354898	−0.177449	−	0.984130i	$-0.556784\pi$
$683$	−6334.82	−0.354898	−0.177449	+	0.984130i	$0.556784\pi$
$684$	22571.8	1.26177
$685$	9611.40	0.536106
$686$	−22605.8	−1.25815
$687$	8259.15	0.458670
$688$	78731.7	4.36282
$689$	−8590.76	−0.475010
$690$	−1678.55	−0.0926106
$691$	14817.5	0.815754	0.407877	−	0.913037i	$-0.366269\pi$
$691$	14817.5	0.815754	0.407877	+	0.913037i	$0.366269\pi$
$692$	43576.0	2.39380
$693$	5075.36	0.278206
$694$	41556.6	2.27301
$695$	11213.9	0.612042
$696$	−54294.3	−2.95693
$697$	19306.0	1.04916
$698$	−35071.9	−1.90185
$699$	17341.0	0.938335
$700$	12441.3	0.671768
$701$	−23498.2	−1.26607	−0.633034	−	0.774124i	$-0.718191\pi$
$701$	−23498.2	−1.26607	−0.633034	+	0.774124i	$0.718191\pi$
$702$	−5588.91	−0.300484
$703$	−23666.5	−1.26970
$704$	54013.9	2.89165
$705$	−7266.83	−0.388205
$706$	−146.267	−0.00779723
$707$	10871.2	0.578291
$708$	58651.1	3.11334
$709$	26260.6	1.39103	0.695513	−	0.718514i	$-0.255177\pi$
$709$	26260.6	1.39103	0.695513	+	0.718514i	$0.255177\pi$
$710$	−5026.81	−0.265708
$711$	−5353.90	−0.282401
$712$	81414.9	4.28533
$713$	−3944.15	−0.207167
$714$	−39355.8	−2.06282
$715$	−4737.89	−0.247814
$716$	−38569.7	−2.01315
$717$	−7750.83	−0.403710
$718$	−43724.6	−2.27268
$719$	9321.17	0.483478	0.241739	−	0.970341i	$-0.422282\pi$
$719$	9321.17	0.483478	0.241739	+	0.970341i	$0.422282\pi$
$720$	11306.4	0.585230
$721$	−41971.5	−2.16796
$722$	32440.9	1.67220
$723$	21260.6	1.09362
$724$	−101516.	−5.21106
$725$	−5797.85	−0.297002
$726$	−11509.6	−0.588379
$727$	−8754.08	−0.446590	−0.223295	−	0.974751i	$-0.571681\pi$
$727$	−8754.08	−0.446590	−0.223295	+	0.974751i	$0.571681\pi$
$728$	−65891.5	−3.35453
$729$	729.000	0.0370370
$730$	−19105.7	−0.968677
$731$	−33369.7	−1.68840
$732$	−33866.1	−1.71001
$733$	−27850.2	−1.40337	−0.701686	−	0.712486i	$-0.747569\pi$
$733$	−27850.2	−1.40337	−0.701686	+	0.712486i	$0.747569\pi$
$734$	43231.3	2.17398
$735$	2392.43	0.120063
$736$	−15403.6	−0.771445
$737$	−19110.7	−0.955156
$738$	−8966.57	−0.447241
$739$	29999.4	1.49330	0.746648	−	0.665220i	$-0.231662\pi$
$739$	29999.4	1.49330	0.746648	+	0.665220i	$0.231662\pi$
$740$	−23254.2	−1.15519
$741$	−12765.6	−0.632869
$742$	28096.1	1.39008
$743$	3127.81	0.154439	0.0772196	−	0.997014i	$-0.475396\pi$
$743$	3127.81	0.154439	0.0772196	+	0.997014i	$0.475396\pi$
$744$	45346.6	2.23452
$745$	−14274.8	−0.701998
$746$	−38130.7	−1.87140
$747$	6160.02	0.301718
$748$	−59474.9	−2.90724
$749$	−14857.8	−0.724825
$750$	2060.81	0.100333
$751$	−23109.3	−1.12286	−0.561432	−	0.827523i	$-0.689750\pi$
$751$	−23109.3	−1.12286	−0.561432	+	0.827523i	$0.689750\pi$
$752$	−121721.	−5.90255
$753$	−18053.1	−0.873696
$754$	48005.4	2.31864
$755$	−13527.7	−0.652083
$756$	13436.6	0.646409
$757$	−31546.8	−1.51465	−0.757324	−	0.653039i	$-0.773494\pi$
$757$	−31546.8	−1.51465	−0.757324	+	0.653039i	$0.773494\pi$
$758$	46455.2	2.22603
$759$	−1536.80	−0.0734943
$760$	44079.7	2.10387
$761$	−27261.4	−1.29859	−0.649293	−	0.760538i	$-0.724935\pi$
$761$	−27261.4	−1.29859	−0.649293	+	0.760538i	$0.724935\pi$
$762$	7558.24	0.359326
$763$	4101.17	0.194590
$764$	18039.5	0.854251
$765$	−4792.12	−0.226483
$766$	52443.0	2.47368
$767$	−33170.5	−1.56156
$768$	43227.1	2.03102
$769$	21933.4	1.02853	0.514265	−	0.857631i	$-0.328065\pi$
$769$	21933.4	1.02853	0.514265	+	0.857631i	$0.328065\pi$
$770$	15495.3	0.725211
$771$	16485.1	0.770034
$772$	88772.7	4.13860
$773$	32769.2	1.52474	0.762372	−	0.647139i	$-0.224035\pi$
$773$	32769.2	1.52474	0.762372	+	0.647139i	$0.224035\pi$
$774$	15498.4	0.719738
$775$	4842.36	0.224442
$776$	−42627.2	−1.97194
$777$	−14088.3	−0.650470
$778$	41001.4	1.88942
$779$	−20480.5	−0.941963
$780$	−12543.2	−0.575794
$781$	−4602.30	−0.210862
$782$	11916.8	0.544939
$783$	−6261.68	−0.285791
$784$	40073.7	1.82552
$785$	13696.1	0.622721
$786$	11534.8	0.523452
$787$	−5072.60	−0.229757	−0.114878	−	0.993380i	$-0.536648\pi$
$787$	−5072.60	−0.229757	−0.114878	+	0.993380i	$0.536648\pi$
$788$	−55874.5	−2.52595
$789$	13196.1	0.595429
$790$	−16345.7	−0.736145
$791$	25321.6	1.13822
$792$	17668.8	0.792719
$793$	19153.2	0.857692
$794$	1680.12	0.0750946
$795$	3421.10	0.152621
$796$	−42958.6	−1.91285
$797$	−6558.49	−0.291485	−0.145743	−	0.989323i	$-0.546557\pi$
$797$	−6558.49	−0.291485	−0.145743	+	0.989323i	$0.546557\pi$
$798$	41750.0	1.85205
$799$	51590.4	2.28428
$800$	18911.4	0.835776
$801$	9389.45	0.414182
$802$	−4353.14	−0.191664
$803$	−17492.2	−0.768727
$804$	−50594.0	−2.21929
$805$	−2282.30	−0.0999261
$806$	−40094.1	−1.75218
$807$	−25254.5	−1.10161
$808$	37845.6	1.64778
$809$	−12699.6	−0.551908	−0.275954	−	0.961171i	$-0.588994\pi$
$809$	−12699.6	−0.551908	−0.275954	+	0.961171i	$0.588994\pi$
$810$	2225.67	0.0965459
$811$	−4972.17	−0.215286	−0.107643	−	0.994190i	$-0.534330\pi$
$811$	−4972.17	−0.215286	−0.107643	+	0.994190i	$0.534330\pi$
$812$	−115413.	−4.98792
$813$	11525.1	0.497176
$814$	−28962.5	−1.24709
$815$	−815.000	−0.0350285
$816$	−80269.2	−3.44361
$817$	35399.7	1.51589
$818$	−57783.1	−2.46985
$819$	−7599.16	−0.324220
$820$	−20123.7	−0.857012
$821$	−9880.31	−0.420007	−0.210003	−	0.977701i	$-0.567347\pi$
$821$	−9880.31	−0.420007	−0.210003	+	0.977701i	$0.567347\pi$
$822$	31691.6	1.34473
$823$	−29672.0	−1.25674	−0.628372	−	0.777913i	$-0.716278\pi$
$823$	−29672.0	−1.25674	−0.628372	+	0.777913i	$0.716278\pi$
$824$	−146115.	−6.17737
$825$	1886.77	0.0796230
$826$	108484.	4.56979
$827$	−13947.9	−0.586477	−0.293239	−	0.956039i	$-0.594733\pi$
$827$	−13947.9	−0.586477	−0.293239	+	0.956039i	$0.594733\pi$
$828$	−4068.55	−0.170763
$829$	−12196.0	−0.510958	−0.255479	−	0.966815i	$-0.582233\pi$
$829$	−12196.0	−0.510958	−0.255479	+	0.966815i	$0.582233\pi$
$830$	18806.8	0.786499
$831$	4284.30	0.178846
$832$	−80873.1	−3.36992
$833$	−16984.9	−0.706472
$834$	36975.7	1.53521
$835$	4060.56	0.168289
$836$	63093.0	2.61019
$837$	5229.75	0.215970
$838$	−17454.0	−0.719497
$839$	−14848.4	−0.610994	−0.305497	−	0.952193i	$-0.598823\pi$
$839$	−14848.4	−0.610994	−0.305497	+	0.952193i	$0.598823\pi$
$840$	26240.0	1.07782
$841$	29395.1	1.20526
$842$	−47638.4	−1.94979
$843$	10544.1	0.430792
$844$	−127091.	−5.18324
$845$	−3891.11	−0.158412
$846$	−23960.9	−0.973749
$847$	−15649.5	−0.634856
$848$	57304.3	2.32056
$849$	11781.9	0.476273
$850$	−14630.6	−0.590382
$851$	4265.88	0.171836
$852$	−12184.2	−0.489936
$853$	−28353.2	−1.13809	−0.569047	−	0.822305i	$-0.692688\pi$
$853$	−28353.2	−1.13809	−0.569047	+	0.822305i	$0.692688\pi$
$854$	−62640.6	−2.50997
$855$	5083.65	0.203342
$856$	−51724.4	−2.06531
$857$	13253.9	0.528292	0.264146	−	0.964483i	$-0.414910\pi$
$857$	13253.9	0.528292	0.264146	+	0.964483i	$0.414910\pi$
$858$	−15622.2	−0.621601
$859$	11306.3	0.449088	0.224544	−	0.974464i	$-0.427911\pi$
$859$	11306.3	0.449088	0.224544	+	0.974464i	$0.427911\pi$
$860$	34783.0	1.37918
$861$	−12191.7	−0.482570
$862$	−74302.7	−2.93592
$863$	−18807.7	−0.741856	−0.370928	−	0.928662i	$-0.620960\pi$
$863$	−18807.7	−0.741856	−0.370928	+	0.928662i	$0.620960\pi$
$864$	20424.4	0.804226
$865$	9814.24	0.385774
$866$	−56125.8	−2.20235
$867$	19282.3	0.755320
$868$	96392.5	3.76933
$869$	−14965.3	−0.584193
$870$	−19117.2	−0.744982
$871$	28613.7	1.11313
$872$	14277.3	0.554463
$873$	−4916.13	−0.190591
$874$	−12641.7	−0.489259
$875$	2802.05	0.108259
$876$	−46309.4	−1.78613
$877$	17186.5	0.661739	0.330870	−	0.943676i	$-0.392658\pi$
$877$	17186.5	0.661739	0.330870	+	0.943676i	$0.392658\pi$
$878$	−28659.4	−1.10160
$879$	−8198.41	−0.314591
$880$	31603.9	1.21064
$881$	14081.1	0.538485	0.269242	−	0.963072i	$-0.413227\pi$
$881$	14081.1	0.538485	0.269242	+	0.963072i	$0.413227\pi$
$882$	7888.53	0.301157
$883$	−15332.8	−0.584359	−0.292180	−	0.956363i	$-0.594381\pi$
$883$	−15332.8	−0.584359	−0.292180	+	0.956363i	$0.594381\pi$
$884$	89049.7	3.38808
$885$	13209.5	0.501731
$886$	−6081.84	−0.230613
$887$	7942.82	0.300669	0.150335	−	0.988635i	$-0.451965\pi$
$887$	7942.82	0.300669	0.150335	+	0.988635i	$0.451965\pi$
$888$	−49045.5	−1.85344
$889$	10276.8	0.387709
$890$	28666.5	1.07966
$891$	2037.71	0.0766173
$892$	−67924.9	−2.54966
$893$	−54728.9	−2.05088
$894$	−47068.2	−1.76085
$895$	−8686.72	−0.324430
$896$	128840.	4.80383
$897$	2300.99	0.0856498
$898$	−11595.9	−0.430912
$899$	−44920.5	−1.66650
$900$	4995.09	0.185003
$901$	−24287.9	−0.898054
$902$	−25063.5	−0.925192
$903$	21072.9	0.776591
$904$	88151.7	3.24323
$905$	−22863.5	−0.839790
$906$	−44604.7	−1.63564
$907$	215.041	0.00787247	0.00393624	−	0.999992i	$-0.498747\pi$
$907$	215.041	0.00787247	0.00393624	+	0.999992i	$0.498747\pi$
$908$	84938.7	3.10439
$909$	4364.68	0.159260
$910$	−23200.6	−0.845157
$911$	5254.93	0.191112	0.0955562	−	0.995424i	$-0.469537\pi$
$911$	5254.93	0.191112	0.0955562	+	0.995424i	$0.469537\pi$
$912$	85152.3	3.09175
$913$	17218.6	0.624153
$914$	52927.3	1.91540
$915$	−7627.38	−0.275577
$916$	61118.7	2.20461
$917$	15683.7	0.564800
$918$	−15801.0	−0.568095
$919$	−12312.7	−0.441957	−0.220979	−	0.975279i	$-0.570925\pi$
$919$	−12312.7	−0.441957	−0.220979	+	0.975279i	$0.570925\pi$
$920$	−7945.35	−0.284729
$921$	11315.1	0.404828
$922$	−57063.0	−2.03825
$923$	6890.87	0.245737
$924$	37558.3	1.33720
$925$	−5237.35	−0.186165
$926$	−77728.7	−2.75845
$927$	−16851.2	−0.597051
$928$	−175433.	−6.20569
$929$	−14735.1	−0.520392	−0.260196	−	0.965556i	$-0.583787\pi$
$929$	−14735.1	−0.520392	−0.260196	+	0.965556i	$0.583787\pi$
$930$	15966.7	0.562976
$931$	18018.1	0.634287
$932$	128326.	4.51013
$933$	31955.5	1.12130
$934$	64228.2	2.25012
$935$	−13395.0	−0.468518
$936$	−26454.9	−0.923830
$937$	−12185.4	−0.424844	−0.212422	−	0.977178i	$-0.568135\pi$
$937$	−12185.4	−0.424844	−0.212422	+	0.977178i	$0.568135\pi$
$938$	−93581.4	−3.25751
$939$	−4947.71	−0.171951
$940$	−53775.5	−1.86592
$941$	−16561.2	−0.573728	−0.286864	−	0.957971i	$-0.592613\pi$
$941$	−16561.2	−0.573728	−0.286864	+	0.957971i	$0.592613\pi$
$942$	45160.2	1.56199
$943$	3691.60	0.127481
$944$	221262.	7.62867
$945$	3026.21	0.104172
$946$	43321.3	1.48890
$947$	−24404.1	−0.837409	−0.418705	−	0.908122i	$-0.637516\pi$
$947$	−24404.1	−0.837409	−0.418705	+	0.908122i	$0.637516\pi$
$948$	−39619.5	−1.35737
$949$	26190.5	0.895870
$950$	15520.6	0.530058
$951$	17493.8	0.596503
$952$	−186289.	−6.34208
$953$	23346.2	0.793553	0.396777	−	0.917915i	$-0.370129\pi$
$953$	23346.2	0.793553	0.396777	+	0.917915i	$0.370129\pi$
$954$	11280.4	0.382825
$955$	4062.89	0.137667
$956$	−57357.1	−1.94044
$957$	−17502.8	−0.591206
$958$	−72573.0	−2.44752
$959$	43090.6	1.45096
$960$	32206.1	1.08276
$961$	7726.54	0.259358
$962$	43364.5	1.45336
$963$	−5965.30	−0.199615
$964$	157331.	5.25653
$965$	19993.5	0.666958
$966$	−7525.41	−0.250648
$967$	11091.3	0.368845	0.184423	−	0.982847i	$-0.440958\pi$
$967$	11091.3	0.368845	0.184423	+	0.982847i	$0.440958\pi$
$968$	−54480.5	−1.80895
$969$	−36091.0	−1.19650
$970$	−15009.2	−0.496820
$971$	18824.3	0.622144	0.311072	−	0.950386i	$-0.399312\pi$
$971$	18824.3	0.622144	0.311072	+	0.950386i	$0.399312\pi$
$972$	5394.69	0.178019
$973$	50275.3	1.65648
$974$	−18444.2	−0.606766
$975$	−2825.00	−0.0927922
$976$	−127761.	−4.19008
$977$	13255.3	0.434059	0.217030	−	0.976165i	$-0.430363\pi$
$977$	13255.3	0.434059	0.217030	+	0.976165i	$0.430363\pi$
$978$	−2687.29	−0.0878632
$979$	26245.6	0.856805
$980$	17704.3	0.577083
$981$	1646.58	0.0535896
$982$	−64536.1	−2.09718
$983$	36348.3	1.17938	0.589691	−	0.807629i	$-0.299250\pi$
$983$	36348.3	1.17938	0.589691	+	0.807629i	$0.299250\pi$
$984$	−42442.9	−1.37503
$985$	−12584.1	−0.407070
$986$	135721.	4.38362
$987$	−32579.2	−1.05067
$988$	−94467.0	−3.04190
$989$	−6380.78	−0.205154
$990$	6221.24	0.199721
$991$	21190.9	0.679264	0.339632	−	0.940558i	$-0.389697\pi$
$991$	21190.9	0.679264	0.339632	+	0.940558i	$0.389697\pi$
$992$	146522.	4.68959
$993$	430.423	0.0137553
$994$	−22536.6	−0.719133
$995$	−9675.20	−0.308266
$996$	45584.9	1.45021
$997$	30519.1	0.969458	0.484729	−	0.874664i	$-0.338918\pi$
$997$	30519.1	0.969458	0.484729	+	0.874664i	$0.338918\pi$
$998$	−39402.3	−1.24976
$999$	−5656.34	−0.179138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2445.4.a.i.1.43	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2445.4.a.i.1.43	✓	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)

\(f(q)\)	\(=\)	\(q+5.49549 q^{2} +3.00000 q^{3} +22.2004 q^{4} +5.00000 q^{5} +16.4865 q^{6} +22.4164 q^{7} +78.0380 q^{8} +9.00000 q^{9} +27.4774 q^{10} +25.1570 q^{11} +66.6011 q^{12} -37.6667 q^{13} +123.189 q^{14} +15.0000 q^{15} +251.254 q^{16} -106.492 q^{17} +49.4594 q^{18} +112.970 q^{19} +111.002 q^{20} +67.2492 q^{21} +138.250 q^{22} -20.3628 q^{23} +234.114 q^{24} +25.0000 q^{25} -206.997 q^{26} +27.0000 q^{27} +497.653 q^{28} -231.914 q^{29} +82.4323 q^{30} +193.694 q^{31} +756.458 q^{32} +75.4709 q^{33} -585.223 q^{34} +112.082 q^{35} +199.803 q^{36} -209.494 q^{37} +620.825 q^{38} -113.000 q^{39} +390.190 q^{40} -181.292 q^{41} +369.567 q^{42} +313.355 q^{43} +558.494 q^{44} +45.0000 q^{45} -111.903 q^{46} -484.455 q^{47} +753.761 q^{48} +159.495 q^{49} +137.387 q^{50} -319.475 q^{51} -836.214 q^{52} +228.073 q^{53} +148.378 q^{54} +125.785 q^{55} +1749.33 q^{56} +338.910 q^{57} -1274.48 q^{58} +880.632 q^{59} +333.006 q^{60} -508.492 q^{61} +1064.45 q^{62} +201.748 q^{63} +2147.07 q^{64} -188.333 q^{65} +414.749 q^{66} -759.657 q^{67} -2364.15 q^{68} -61.0883 q^{69} +615.945 q^{70} -182.943 q^{71} +702.342 q^{72} -695.324 q^{73} -1151.27 q^{74} +75.0000 q^{75} +2507.97 q^{76} +563.929 q^{77} -620.990 q^{78} -594.878 q^{79} +1256.27 q^{80} +81.0000 q^{81} -996.285 q^{82} +684.446 q^{83} +1492.96 q^{84} -532.458 q^{85} +1722.04 q^{86} -695.742 q^{87} +1963.20 q^{88} +1043.27 q^{89} +247.297 q^{90} -844.351 q^{91} -452.061 q^{92} +581.083 q^{93} -2662.32 q^{94} +564.849 q^{95} +2269.37 q^{96} -546.237 q^{97} +876.503 q^{98} +226.413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 18 q^{2} + 129 q^{3} + 198 q^{4} + 215 q^{5} + 54 q^{6} + 137 q^{7} + 201 q^{8} + 387 q^{9} + 90 q^{10} + 137 q^{11} + 594 q^{12} + 212 q^{13} + 246 q^{14} + 645 q^{15} + 930 q^{16} + 547 q^{17}+ \cdots + 1233 q^{99}+O(q^{100}) \) 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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