LMFDB - Embedded newform 2445.4.a.i.1.7

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			1.7
Character	$\chi$	$=$	2445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.77545 q^{2} +3.00000 q^{3} +6.25402 q^{4} +5.00000 q^{5} -11.3264 q^{6} +32.7551 q^{7} +6.59184 q^{8} +9.00000 q^{9} -18.8773 q^{10} +21.2025 q^{11} +18.7621 q^{12} +86.1026 q^{13} -123.665 q^{14} +15.0000 q^{15} -74.9194 q^{16} -7.19926 q^{17} -33.9791 q^{18} -127.944 q^{19} +31.2701 q^{20} +98.2653 q^{21} -80.0490 q^{22} -94.1959 q^{23} +19.7755 q^{24} +25.0000 q^{25} -325.076 q^{26} +27.0000 q^{27} +204.851 q^{28} -100.851 q^{29} -56.6318 q^{30} +50.8189 q^{31} +230.120 q^{32} +63.6075 q^{33} +27.1805 q^{34} +163.775 q^{35} +56.2862 q^{36} -427.996 q^{37} +483.047 q^{38} +258.308 q^{39} +32.9592 q^{40} +512.557 q^{41} -370.996 q^{42} -343.112 q^{43} +132.601 q^{44} +45.0000 q^{45} +355.632 q^{46} +223.400 q^{47} -224.758 q^{48} +729.896 q^{49} -94.3863 q^{50} -21.5978 q^{51} +538.488 q^{52} +572.127 q^{53} -101.937 q^{54} +106.013 q^{55} +215.916 q^{56} -383.832 q^{57} +380.759 q^{58} -365.686 q^{59} +93.8104 q^{60} +724.106 q^{61} -191.864 q^{62} +294.796 q^{63} -269.450 q^{64} +430.513 q^{65} -240.147 q^{66} -69.2625 q^{67} -45.0244 q^{68} -282.588 q^{69} -618.326 q^{70} +850.949 q^{71} +59.3266 q^{72} -459.931 q^{73} +1615.88 q^{74} +75.0000 q^{75} -800.166 q^{76} +694.490 q^{77} -975.228 q^{78} +89.2693 q^{79} -374.597 q^{80} +81.0000 q^{81} -1935.13 q^{82} -277.978 q^{83} +614.554 q^{84} -35.9963 q^{85} +1295.40 q^{86} -302.554 q^{87} +139.764 q^{88} +117.845 q^{89} -169.895 q^{90} +2820.30 q^{91} -589.104 q^{92} +152.457 q^{93} -843.436 q^{94} -639.721 q^{95} +690.359 q^{96} -457.227 q^{97} -2755.69 q^{98} +190.823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 18 q^{2} + 129 q^{3} + 198 q^{4} + 215 q^{5} + 54 q^{6} + 137 q^{7} + 201 q^{8} + 387 q^{9} + 90 q^{10} + 137 q^{11} + 594 q^{12} + 212 q^{13} + 246 q^{14} + 645 q^{15} + 930 q^{16} + 547 q^{17}+ \cdots + 1233 q^{99}+O(q^{100}) $ 43 * q + 18 * q^2 + 129 * q^3 + 198 * q^4 + 215 * q^5 + 54 * q^6 + 137 * q^7 + 201 * q^8 + 387 * q^9 + 90 * q^10 + 137 * q^11 + 594 * q^12 + 212 * q^13 + 246 * q^14 + 645 * q^15 + 930 * q^16 + 547 * q^17 + 162 * q^18 + 563 * q^19 + 990 * q^20 + 411 * q^21 + 279 * q^22 + 793 * q^23 + 603 * q^24 + 1075 * q^25 + 520 * q^26 + 1161 * q^27 + 833 * q^28 + 699 * q^29 + 270 * q^30 + 1130 * q^31 + 1651 * q^32 + 411 * q^33 + 651 * q^34 + 685 * q^35 + 1782 * q^36 + 644 * q^37 + 1122 * q^38 + 636 * q^39 + 1005 * q^40 + 1447 * q^41 + 738 * q^42 + 1629 * q^43 + 1828 * q^44 + 1935 * q^45 + 435 * q^46 + 1962 * q^47 + 2790 * q^48 + 3050 * q^49 + 450 * q^50 + 1641 * q^51 + 2284 * q^52 + 1995 * q^53 + 486 * q^54 + 685 * q^55 - 662 * q^56 + 1689 * q^57 - 130 * q^58 + 1935 * q^59 + 2970 * q^60 + 2152 * q^61 + 1975 * q^62 + 1233 * q^63 + 6187 * q^64 + 1060 * q^65 + 837 * q^66 + 2968 * q^67 + 2412 * q^68 + 2379 * q^69 + 1230 * q^70 + 1835 * q^71 + 1809 * q^72 + 1095 * q^73 + 2874 * q^74 + 3225 * q^75 + 2866 * q^76 + 4658 * q^77 + 1560 * q^78 + 2262 * q^79 + 4650 * q^80 + 3483 * q^81 + 746 * q^82 + 5285 * q^83 + 2499 * q^84 + 2735 * q^85 + 2389 * q^86 + 2097 * q^87 + 4391 * q^88 + 3012 * q^89 + 810 * q^90 + 3560 * q^91 + 5808 * q^92 + 3390 * q^93 + 887 * q^94 + 2815 * q^95 + 4953 * q^96 + 1108 * q^97 + 2858 * q^98 + 1233 * q^99

Coefficient data

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

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

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

$2$	−3.77545	−1.33482	−0.667412	−	0.744689i	$-0.732598\pi$
$2$	−3.77545	−1.33482	−0.667412	+	0.744689i	$0.732598\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	6.25402	0.781753
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−11.3264	−0.770661
$7$	32.7551	1.76861	0.884304	−	0.466911i	$-0.154633\pi$
$7$	32.7551	1.76861	0.884304	+	0.466911i	$0.154633\pi$
$8$	6.59184	0.291321
$9$	9.00000	0.333333
$10$	−18.8773	−0.596951
$11$	21.2025	0.581163	0.290582	−	0.956850i	$-0.406151\pi$
$11$	21.2025	0.581163	0.290582	+	0.956850i	$0.406151\pi$
$12$	18.7621	0.451345
$13$	86.1026	1.83697	0.918483	−	0.395460i	$-0.129415\pi$
$13$	86.1026	1.83697	0.918483	+	0.395460i	$0.129415\pi$
$14$	−123.665	−2.36078
$15$	15.0000	0.258199
$16$	−74.9194	−1.17062
$17$	−7.19926	−0.102710	−0.0513552	−	0.998680i	$-0.516354\pi$
$17$	−7.19926	−0.102710	−0.0513552	+	0.998680i	$0.516354\pi$
$18$	−33.9791	−0.444941
$19$	−127.944	−1.54486	−0.772431	−	0.635098i	$-0.780960\pi$
$19$	−127.944	−1.54486	−0.772431	+	0.635098i	$0.780960\pi$
$20$	31.2701	0.349611
$21$	98.2653	1.02111
$22$	−80.0490	−0.775750
$23$	−94.1959	−0.853966	−0.426983	−	0.904260i	$-0.640424\pi$
$23$	−94.1959	−0.853966	−0.426983	+	0.904260i	$0.640424\pi$
$24$	19.7755	0.168194
$25$	25.0000	0.200000
$26$	−325.076	−2.45203
$27$	27.0000	0.192450
$28$	204.851	1.38262
$29$	−100.851	−0.645780	−0.322890	−	0.946436i	$-0.604654\pi$
$29$	−100.851	−0.645780	−0.322890	+	0.946436i	$0.604654\pi$
$30$	−56.6318	−0.344650
$31$	50.8189	0.294430	0.147215	−	0.989104i	$-0.452969\pi$
$31$	50.8189	0.294430	0.147215	+	0.989104i	$0.452969\pi$
$32$	230.120	1.27124
$33$	63.6075	0.335535
$34$	27.1805	0.137100
$35$	163.775	0.790946
$36$	56.2862	0.260584
$37$	−427.996	−1.90168	−0.950839	−	0.309687i	$-0.899776\pi$
$37$	−427.996	−1.90168	−0.950839	+	0.309687i	$0.899776\pi$
$38$	483.047	2.06212
$39$	258.308	1.06057
$40$	32.9592	0.130283
$41$	512.557	1.95239	0.976194	−	0.216897i	$-0.0695936\pi$
$41$	512.557	1.95239	0.976194	+	0.216897i	$0.0695936\pi$
$42$	−370.996	−1.36300
$43$	−343.112	−1.21684	−0.608419	−	0.793616i	$-0.708196\pi$
$43$	−343.112	−1.21684	−0.608419	+	0.793616i	$0.708196\pi$
$44$	132.601	0.454326
$45$	45.0000	0.149071
$46$	355.632	1.13989
$47$	223.400	0.693324	0.346662	−	0.937990i	$-0.387315\pi$
$47$	223.400	0.693324	0.346662	+	0.937990i	$0.387315\pi$
$48$	−224.758	−0.675855
$49$	729.896	2.12798
$50$	−94.3863	−0.266965
$51$	−21.5978	−0.0592999
$52$	538.488	1.43605
$53$	572.127	1.48279	0.741393	−	0.671071i	$-0.234165\pi$
$53$	572.127	1.48279	0.741393	+	0.671071i	$0.234165\pi$
$54$	−101.937	−0.256887
$55$	106.013	0.259904
$56$	215.916	0.515233
$57$	−383.832	−0.891927
$58$	380.759	0.862002
$59$	−365.686	−0.806919	−0.403459	−	0.914998i	$-0.632192\pi$
$59$	−365.686	−0.806919	−0.403459	+	0.914998i	$0.632192\pi$
$60$	93.8104	0.201848
$61$	724.106	1.51987	0.759937	−	0.649997i	$-0.225230\pi$
$61$	724.106	1.51987	0.759937	+	0.649997i	$0.225230\pi$
$62$	−191.864	−0.393013
$63$	294.796	0.589536
$64$	−269.450	−0.526270
$65$	430.513	0.821516
$66$	−240.147	−0.447880
$67$	−69.2625	−0.126295	−0.0631474	−	0.998004i	$-0.520114\pi$
$67$	−69.2625	−0.126295	−0.0631474	+	0.998004i	$0.520114\pi$
$68$	−45.0244	−0.0802942
$69$	−282.588	−0.493037
$70$	−618.326	−1.05577
$71$	850.949	1.42238	0.711191	−	0.702999i	$-0.248156\pi$
$71$	850.949	1.42238	0.711191	+	0.702999i	$0.248156\pi$
$72$	59.3266	0.0971070
$73$	−459.931	−0.737409	−0.368705	−	0.929547i	$-0.620199\pi$
$73$	−459.931	−0.737409	−0.368705	+	0.929547i	$0.620199\pi$
$74$	1615.88	2.53840
$75$	75.0000	0.115470
$76$	−800.166	−1.20770
$77$	694.490	1.02785
$78$	−975.228	−1.41568
$79$	89.2693	0.127134	0.0635670	−	0.997978i	$-0.479752\pi$
$79$	89.2693	0.127134	0.0635670	+	0.997978i	$0.479752\pi$
$80$	−374.597	−0.523515
$81$	81.0000	0.111111
$82$	−1935.13	−2.60609
$83$	−277.978	−0.367615	−0.183807	−	0.982962i	$-0.558842\pi$
$83$	−277.978	−0.367615	−0.183807	+	0.982962i	$0.558842\pi$
$84$	614.554	0.798253
$85$	−35.9963	−0.0459335
$86$	1295.40	1.62426
$87$	−302.554	−0.372841
$88$	139.764	0.169305
$89$	117.845	0.140354	0.0701770	−	0.997535i	$-0.477644\pi$
$89$	117.845	0.140354	0.0701770	+	0.997535i	$0.477644\pi$
$90$	−169.895	−0.198984
$91$	2820.30	3.24888
$92$	−589.104	−0.667590
$93$	152.457	0.169989
$94$	−843.436	−0.925465
$95$	−639.721	−0.690884
$96$	690.359	0.733953
$97$	−457.227	−0.478601	−0.239301	−	0.970946i	$-0.576918\pi$
$97$	−457.227	−0.478601	−0.239301	+	0.970946i	$0.576918\pi$
$98$	−2755.69	−2.84047
$99$	190.823	0.193721
$100$	156.351	0.156351
$101$	−815.241	−0.803164	−0.401582	−	0.915823i	$-0.631540\pi$
$101$	−815.241	−0.803164	−0.401582	+	0.915823i	$0.631540\pi$
$102$	81.5414	0.0791549
$103$	52.9557	0.0506590	0.0253295	−	0.999679i	$-0.491936\pi$
$103$	52.9557	0.0506590	0.0253295	+	0.999679i	$0.491936\pi$
$104$	567.575	0.535147
$105$	491.326	0.456653
$106$	−2160.04	−1.97926
$107$	1700.31	1.53622	0.768109	−	0.640319i	$-0.221198\pi$
$107$	1700.31	1.53622	0.768109	+	0.640319i	$0.221198\pi$
$108$	168.859	0.150448
$109$	1381.66	1.21412	0.607059	−	0.794657i	$-0.292349\pi$
$109$	1381.66	1.21412	0.607059	+	0.794657i	$0.292349\pi$
$110$	−400.245	−0.346926
$111$	−1283.99	−1.09793
$112$	−2453.99	−2.07036
$113$	324.256	0.269942	0.134971	−	0.990850i	$-0.456906\pi$
$113$	324.256	0.269942	0.134971	+	0.990850i	$0.456906\pi$
$114$	1449.14	1.19056
$115$	−470.980	−0.381905
$116$	−630.727	−0.504841
$117$	774.923	0.612322
$118$	1380.63	1.07709
$119$	−235.813	−0.181655
$120$	98.8777	0.0752188
$121$	−881.454	−0.662249
$122$	−2733.83	−2.02876
$123$	1537.67	1.12721
$124$	317.823	0.230172
$125$	125.000	0.0894427
$126$	−1112.99	−0.786927
$127$	1619.13	1.13130	0.565649	−	0.824646i	$-0.308626\pi$
$127$	1619.13	1.13130	0.565649	+	0.824646i	$0.308626\pi$
$128$	−823.661	−0.568766
$129$	−1029.34	−0.702542
$130$	−1625.38	−1.09658
$131$	1901.53	1.26823	0.634114	−	0.773240i	$-0.281365\pi$
$131$	1901.53	1.26823	0.634114	+	0.773240i	$0.281365\pi$
$132$	397.803	0.262305
$133$	−4190.82	−2.73226
$134$	261.497	0.168581
$135$	135.000	0.0860663
$136$	−47.4564	−0.0299217
$137$	759.777	0.473811	0.236906	−	0.971533i	$-0.423867\pi$
$137$	759.777	0.473811	0.236906	+	0.971533i	$0.423867\pi$
$138$	1066.90	0.658118
$139$	1589.42	0.969878	0.484939	−	0.874548i	$-0.338842\pi$
$139$	1589.42	0.969878	0.484939	+	0.874548i	$0.338842\pi$
$140$	1024.26	0.618324
$141$	670.200	0.400291
$142$	−3212.72	−1.89863
$143$	1825.59	1.06758
$144$	−674.274	−0.390205
$145$	−504.257	−0.288802
$146$	1736.45	0.984311
$147$	2189.69	1.22859
$148$	−2676.70	−1.48664
$149$	−2986.59	−1.64209	−0.821044	−	0.570864i	$-0.806608\pi$
$149$	−2986.59	−1.64209	−0.821044	+	0.570864i	$0.806608\pi$
$150$	−283.159	−0.154132
$151$	305.033	0.164392	0.0821961	−	0.996616i	$-0.473807\pi$
$151$	305.033	0.164392	0.0821961	+	0.996616i	$0.473807\pi$
$152$	−843.388	−0.450051
$153$	−64.7934	−0.0342368
$154$	−2622.01	−1.37200
$155$	254.094	0.131673
$156$	1615.46	0.829106
$157$	−1726.10	−0.877436	−0.438718	−	0.898625i	$-0.644567\pi$
$157$	−1726.10	−0.877436	−0.438718	+	0.898625i	$0.644567\pi$
$158$	−337.032	−0.169701
$159$	1716.38	0.856087
$160$	1150.60	0.568517
$161$	−3085.40	−1.51033
$162$	−305.811	−0.148314
$163$	−163.000	−0.0783260
$163$	−163.000	−0.0783260
$164$	3205.54	1.52629
$165$	318.038	0.150056
$166$	1049.49	0.490701
$167$	3464.07	1.60514	0.802569	−	0.596560i	$-0.203466\pi$
$167$	3464.07	1.60514	0.802569	+	0.596560i	$0.203466\pi$
$168$	647.749	0.297470
$169$	5216.66	2.37445
$170$	135.902	0.0613131
$171$	−1151.50	−0.514954
$172$	−2145.83	−0.951268
$173$	2329.24	1.02363	0.511817	−	0.859094i	$-0.328972\pi$
$173$	2329.24	1.02363	0.511817	+	0.859094i	$0.328972\pi$
$174$	1142.28	0.497677
$175$	818.877	0.353722
$176$	−1588.48	−0.680319
$177$	−1097.06	−0.465875
$178$	−444.916	−0.187348
$179$	−1247.42	−0.520875	−0.260438	−	0.965491i	$-0.583867\pi$
$179$	−1247.42	−0.520875	−0.260438	+	0.965491i	$0.583867\pi$
$180$	281.431	0.116537
$181$	1987.28	0.816097	0.408048	−	0.912960i	$-0.366209\pi$
$181$	1987.28	0.816097	0.408048	+	0.912960i	$0.366209\pi$
$182$	−10647.9	−4.33667
$183$	2172.32	0.877499
$184$	−620.925	−0.248778
$185$	−2139.98	−0.850456
$186$	−575.593	−0.226906
$187$	−152.642	−0.0596916
$188$	1397.15	0.542008
$189$	884.388	0.340369
$190$	2415.23	0.922207
$191$	−1359.36	−0.514974	−0.257487	−	0.966282i	$-0.582894\pi$
$191$	−1359.36	−0.514974	−0.257487	+	0.966282i	$0.582894\pi$
$192$	−808.351	−0.303842
$193$	−248.396	−0.0926420	−0.0463210	−	0.998927i	$-0.514750\pi$
$193$	−248.396	−0.0926420	−0.0463210	+	0.998927i	$0.514750\pi$
$194$	1726.24	0.638848
$195$	1291.54	0.474303
$196$	4564.79	1.66355
$197$	751.521	0.271795	0.135898	−	0.990723i	$-0.456608\pi$
$197$	751.521	0.271795	0.135898	+	0.990723i	$0.456608\pi$
$198$	−720.441	−0.258583
$199$	1501.33	0.534806	0.267403	−	0.963585i	$-0.413834\pi$
$199$	1501.33	0.534806	0.267403	+	0.963585i	$0.413834\pi$
$200$	164.796	0.0582642
$201$	−207.787	−0.0729164
$202$	3077.90	1.07208
$203$	−3303.39	−1.14213
$204$	−135.073	−0.0463579
$205$	2562.78	0.873135
$206$	−199.932	−0.0676209
$207$	−847.764	−0.284655
$208$	−6450.75	−2.15038
$209$	−2712.74	−0.897818
$210$	−1854.98	−0.609551
$211$	−1915.48	−0.624961	−0.312481	−	0.949924i	$-0.601160\pi$
$211$	−1915.48	−0.624961	−0.312481	+	0.949924i	$0.601160\pi$
$212$	3578.10	1.15917
$213$	2552.85	0.821212
$214$	−6419.44	−2.05058
$215$	−1715.56	−0.544187
$216$	177.980	0.0560648
$217$	1664.58	0.520732
$218$	−5216.38	−1.62063
$219$	−1379.79	−0.425743
$220$	663.005	0.203181
$221$	−619.875	−0.188676
$222$	4847.63	1.46555
$223$	−1503.45	−0.451472	−0.225736	−	0.974188i	$-0.572479\pi$
$223$	−1503.45	−0.451472	−0.225736	+	0.974188i	$0.572479\pi$
$224$	7537.59	2.24833
$225$	225.000	0.0666667
$226$	−1224.21	−0.360325
$227$	2371.97	0.693539	0.346769	−	0.937950i	$-0.387279\pi$
$227$	2371.97	0.693539	0.346769	+	0.937950i	$0.387279\pi$
$228$	−2400.50	−0.697267
$229$	−387.837	−0.111917	−0.0559585	−	0.998433i	$-0.517821\pi$
$229$	−387.837	−0.111917	−0.0559585	+	0.998433i	$0.517821\pi$
$230$	1778.16	0.509776
$231$	2083.47	0.593430
$232$	−664.796	−0.188129
$233$	1371.53	0.385629	0.192815	−	0.981235i	$-0.438238\pi$
$233$	1371.53	0.385629	0.192815	+	0.981235i	$0.438238\pi$
$234$	−2925.68	−0.817342
$235$	1117.00	0.310064
$236$	−2287.01	−0.630811
$237$	267.808	0.0734008
$238$	890.299	0.242477
$239$	3626.80	0.981581	0.490791	−	0.871278i	$-0.336708\pi$
$239$	3626.80	0.981581	0.490791	+	0.871278i	$0.336708\pi$
$240$	−1123.79	−0.302252
$241$	−251.342	−0.0671799	−0.0335899	−	0.999436i	$-0.510694\pi$
$241$	−251.342	−0.0671799	−0.0335899	+	0.999436i	$0.510694\pi$
$242$	3327.88	0.883985
$243$	243.000	0.0641500
$244$	4528.58	1.18817
$245$	3649.48	0.951660
$246$	−5805.40	−1.50463
$247$	−11016.3	−2.83786
$248$	334.990	0.0857738
$249$	−833.933	−0.212242
$250$	−471.931	−0.119390
$251$	6602.93	1.66045	0.830225	−	0.557428i	$-0.188212\pi$
$251$	6602.93	1.66045	0.830225	+	0.557428i	$0.188212\pi$
$252$	1843.66	0.460872
$253$	−1997.19	−0.496294
$254$	−6112.96	−1.51008
$255$	−107.989	−0.0265197
$256$	5265.29	1.28547
$257$	6121.53	1.48580	0.742900	−	0.669402i	$-0.233450\pi$
$257$	6121.53	1.48580	0.742900	+	0.669402i	$0.233450\pi$
$258$	3886.21	0.937770
$259$	−14019.0	−3.36332
$260$	2692.44	0.642223
$261$	−907.662	−0.215260
$262$	−7179.15	−1.69286
$263$	−2600.34	−0.609673	−0.304836	−	0.952405i	$-0.598602\pi$
$263$	−2600.34	−0.609673	−0.304836	+	0.952405i	$0.598602\pi$
$264$	419.291	0.0977484
$265$	2860.64	0.663122
$266$	15822.2	3.64708
$267$	353.534	0.0810334
$268$	−433.169	−0.0987314
$269$	−3033.20	−0.687500	−0.343750	−	0.939061i	$-0.611697\pi$
$269$	−3033.20	−0.687500	−0.343750	+	0.939061i	$0.611697\pi$
$270$	−509.686	−0.114883
$271$	−4136.07	−0.927116	−0.463558	−	0.886067i	$-0.653427\pi$
$271$	−4136.07	−0.927116	−0.463558	+	0.886067i	$0.653427\pi$
$272$	539.364	0.120234
$273$	8460.90	1.87574
$274$	−2868.50	−0.632454
$275$	530.063	0.116233
$276$	−1767.31	−0.385433
$277$	4911.53	1.06536	0.532681	−	0.846316i	$-0.321184\pi$
$277$	4911.53	1.06536	0.532681	+	0.846316i	$0.321184\pi$
$278$	−6000.79	−1.29462
$279$	457.370	0.0981435
$280$	1079.58	0.230419
$281$	−3364.80	−0.714331	−0.357166	−	0.934041i	$-0.616257\pi$
$281$	−3364.80	−0.714331	−0.357166	+	0.934041i	$0.616257\pi$
$282$	−2530.31	−0.534318
$283$	5311.30	1.11563	0.557816	−	0.829964i	$-0.311639\pi$
$283$	5311.30	1.11563	0.557816	+	0.829964i	$0.311639\pi$
$284$	5321.86	1.11195
$285$	−1919.16	−0.398882
$286$	−6892.43	−1.42503
$287$	16788.9	3.45301
$288$	2071.08	0.423748
$289$	−4861.17	−0.989451
$290$	1903.80	0.385499
$291$	−1371.68	−0.276321
$292$	−2876.42	−0.576472
$293$	−407.544	−0.0812594	−0.0406297	−	0.999174i	$-0.512936\pi$
$293$	−407.544	−0.0812594	−0.0406297	+	0.999174i	$0.512936\pi$
$294$	−8267.06	−1.63995
$295$	−1828.43	−0.360865
$296$	−2821.28	−0.553999
$297$	572.468	0.111845
$298$	11275.7	2.19190
$299$	−8110.52	−1.56871
$300$	469.052	0.0902691
$301$	−11238.7	−2.15211
$302$	−1151.64	−0.219435
$303$	−2445.72	−0.463707
$304$	9585.49	1.80844
$305$	3620.53	0.679708
$306$	244.624	0.0457001
$307$	−3175.67	−0.590375	−0.295187	−	0.955439i	$-0.595382\pi$
$307$	−3175.67	−0.590375	−0.295187	+	0.955439i	$0.595382\pi$
$308$	4343.36	0.803525
$309$	158.867	0.0292480
$310$	−959.321	−0.175761
$311$	2069.64	0.377359	0.188679	−	0.982039i	$-0.439579\pi$
$311$	2069.64	0.377359	0.188679	+	0.982039i	$0.439579\pi$
$312$	1702.72	0.308967
$313$	−7919.10	−1.43008	−0.715038	−	0.699085i	$-0.753591\pi$
$313$	−7919.10	−1.43008	−0.715038	+	0.699085i	$0.753591\pi$
$314$	6516.79	1.17122
$315$	1473.98	0.263649
$316$	558.292	0.0993873
$317$	1453.94	0.257607	0.128804	−	0.991670i	$-0.458886\pi$
$317$	1453.94	0.257607	0.128804	+	0.991670i	$0.458886\pi$
$318$	−6480.11	−1.14273
$319$	−2138.30	−0.375304
$320$	−1347.25	−0.235355
$321$	5100.93	0.886936
$322$	11648.8	2.01603
$323$	921.104	0.158674
$324$	506.576	0.0868615
$325$	2152.57	0.367393
$326$	615.398	0.104551
$327$	4144.97	0.700971
$328$	3378.70	0.568772
$329$	7317.49	1.22622
$330$	−1200.74	−0.200298
$331$	−1907.33	−0.316726	−0.158363	−	0.987381i	$-0.550622\pi$
$331$	−1907.33	−0.316726	−0.158363	+	0.987381i	$0.550622\pi$
$332$	−1738.48	−0.287384
$333$	−3851.96	−0.633892
$334$	−13078.4	−2.14257
$335$	−346.312	−0.0564808
$336$	−7361.97	−1.19532
$337$	−9830.05	−1.58895	−0.794476	−	0.607296i	$-0.792254\pi$
$337$	−9830.05	−1.58895	−0.794476	+	0.607296i	$0.792254\pi$
$338$	−19695.2	−3.16947
$339$	972.768	0.155851
$340$	−225.122	−0.0359087
$341$	1077.49	0.171112
$342$	4347.42	0.687373
$343$	12672.8	1.99495
$344$	−2261.74	−0.354491
$345$	−1412.94	−0.220493
$346$	−8793.93	−1.36637
$347$	22.8857	0.00354055	0.00177027	−	0.999998i	$-0.499437\pi$
$347$	22.8857	0.00354055	0.00177027	+	0.999998i	$0.499437\pi$
$348$	−1892.18	−0.291470
$349$	−1628.07	−0.249710	−0.124855	−	0.992175i	$-0.539847\pi$
$349$	−1628.07	−0.249710	−0.124855	+	0.992175i	$0.539847\pi$
$350$	−3091.63	−0.472156
$351$	2324.77	0.353524
$352$	4879.11	0.738800
$353$	−4228.11	−0.637506	−0.318753	−	0.947838i	$-0.603264\pi$
$353$	−4228.11	−0.637506	−0.318753	+	0.947838i	$0.603264\pi$
$354$	4141.88	0.621861
$355$	4254.75	0.636108
$356$	737.003	0.109722
$357$	−707.438	−0.104878
$358$	4709.58	0.695277
$359$	−9812.45	−1.44257	−0.721283	−	0.692641i	$-0.756447\pi$
$359$	−9812.45	−1.44257	−0.721283	+	0.692641i	$0.756447\pi$
$360$	296.633	0.0434276
$361$	9510.69	1.38660
$362$	−7502.88	−1.08934
$363$	−2644.36	−0.382350
$364$	17638.2	2.53982
$365$	−2299.66	−0.329779
$366$	−8201.48	−1.17131
$367$	5667.20	0.806064	0.403032	−	0.915186i	$-0.367956\pi$
$367$	5667.20	0.806064	0.403032	+	0.915186i	$0.367956\pi$
$368$	7057.10	0.999665
$369$	4613.01	0.650796
$370$	8079.38	1.13521
$371$	18740.1	2.62247
$372$	953.468	0.132890
$373$	−14244.7	−1.97738	−0.988690	−	0.149974i	$-0.952081\pi$
$373$	−14244.7	−1.97738	−0.988690	+	0.149974i	$0.952081\pi$
$374$	576.294	0.0796777
$375$	375.000	0.0516398
$376$	1472.62	0.201980
$377$	−8683.56	−1.18628
$378$	−3338.96	−0.454332
$379$	473.981	0.0642395	0.0321197	−	0.999484i	$-0.489774\pi$
$379$	473.981	0.0642395	0.0321197	+	0.999484i	$0.489774\pi$
$380$	−4000.83	−0.540100
$381$	4857.40	0.653155
$382$	5132.21	0.687399
$383$	−12146.4	−1.62050	−0.810250	−	0.586085i	$-0.800669\pi$
$383$	−12146.4	−1.62050	−0.810250	+	0.586085i	$0.800669\pi$
$384$	−2470.98	−0.328377
$385$	3472.45	0.459669
$386$	937.806	0.123661
$387$	−3088.01	−0.405613
$388$	−2859.51	−0.374148
$389$	−53.1945	−0.00693334	−0.00346667	−	0.999994i	$-0.501103\pi$
$389$	−53.1945	−0.00693334	−0.00346667	+	0.999994i	$0.501103\pi$
$390$	−4876.14	−0.633110
$391$	678.142	0.0877112
$392$	4811.36	0.619925
$393$	5704.60	0.732212
$394$	−2837.33	−0.362798
$395$	446.346	0.0568560
$396$	1193.41	0.151442
$397$	12532.7	1.58438	0.792189	−	0.610276i	$-0.208941\pi$
$397$	12532.7	1.58438	0.792189	+	0.610276i	$0.208941\pi$
$398$	−5668.20	−0.713872
$399$	−12572.5	−1.57747
$400$	−1872.98	−0.234123
$401$	−13.8913	−0.00172993	−0.000864963	−	1.00000i	$-0.500275\pi$
$401$	−13.8913	−0.00172993	−0.000864963		1.00000i	$0.500275\pi$
$402$	784.491	0.0973305
$403$	4375.64	0.540859
$404$	−5098.54	−0.627876
$405$	405.000	0.0496904
$406$	12471.8	1.52454
$407$	−9074.58	−1.10519
$408$	−142.369	−0.0172753
$409$	−14497.0	−1.75265	−0.876323	−	0.481725i	$-0.840011\pi$
$409$	−14497.0	−1.75265	−0.876323	+	0.481725i	$0.840011\pi$
$410$	−9675.67	−1.16548
$411$	2279.33	0.273555
$412$	331.186	0.0396029
$413$	−11978.1	−1.42712
$414$	3200.69	0.379964
$415$	−1389.89	−0.164402
$416$	19813.9	2.33523
$417$	4768.27	0.559960
$418$	10241.8	1.19843
$419$	15040.0	1.75359	0.876794	−	0.480865i	$-0.159677\pi$
$419$	15040.0	1.75359	0.876794	+	0.480865i	$0.159677\pi$
$420$	3072.77	0.356990
$421$	10385.7	1.20230	0.601149	−	0.799137i	$-0.294710\pi$
$421$	10385.7	1.20230	0.601149	+	0.799137i	$0.294710\pi$
$422$	7231.79	0.834213
$423$	2010.60	0.231108
$424$	3771.37	0.431967
$425$	−179.982	−0.0205421
$426$	−9638.15	−1.09617
$427$	23718.2	2.68806
$428$	10633.8	1.20094
$429$	5476.77	0.616366
$430$	6477.01	0.726393
$431$	8860.70	0.990267	0.495133	−	0.868817i	$-0.335119\pi$
$431$	8860.70	0.990267	0.495133	+	0.868817i	$0.335119\pi$
$432$	−2022.82	−0.225285
$433$	−1239.54	−0.137571	−0.0687857	−	0.997631i	$-0.521912\pi$
$433$	−1239.54	−0.137571	−0.0687857	+	0.997631i	$0.521912\pi$
$434$	−6284.53	−0.695085
$435$	−1512.77	−0.166740
$436$	8640.92	0.949140
$437$	12051.8	1.31926
$438$	5209.34	0.568292
$439$	8917.74	0.969523	0.484761	−	0.874647i	$-0.338906\pi$
$439$	8917.74	0.969523	0.484761	+	0.874647i	$0.338906\pi$
$440$	698.818	0.0757156
$441$	6569.07	0.709326
$442$	2340.31	0.251849
$443$	11596.7	1.24373	0.621867	−	0.783123i	$-0.286375\pi$
$443$	11596.7	1.24373	0.621867	+	0.783123i	$0.286375\pi$
$444$	−8030.09	−0.858313
$445$	589.223	0.0627682
$446$	5676.19	0.602636
$447$	−8959.78	−0.948060
$448$	−8825.87	−0.930766
$449$	14474.6	1.52138	0.760691	−	0.649114i	$-0.224860\pi$
$449$	14474.6	1.52138	0.760691	+	0.649114i	$0.224860\pi$
$450$	−849.476	−0.0889882
$451$	10867.5	1.13466
$452$	2027.90	0.211028
$453$	915.099	0.0949119
$454$	−8955.26	−0.925752
$455$	14101.5	1.45294
$456$	−2530.16	−0.259837
$457$	−9837.33	−1.00694	−0.503469	−	0.864013i	$-0.667943\pi$
$457$	−9837.33	−1.00694	−0.503469	+	0.864013i	$0.667943\pi$
$458$	1464.26	0.149389
$459$	−194.380	−0.0197666
$460$	−2945.52	−0.298555
$461$	5498.93	0.555555	0.277778	−	0.960645i	$-0.410402\pi$
$461$	5498.93	0.555555	0.277778	+	0.960645i	$0.410402\pi$
$462$	−7866.04	−0.792124
$463$	−2230.40	−0.223878	−0.111939	−	0.993715i	$-0.535706\pi$
$463$	−2230.40	−0.223878	−0.111939	+	0.993715i	$0.535706\pi$
$464$	7555.72	0.755960
$465$	762.283	0.0760216
$466$	−5178.13	−0.514747
$467$	4322.37	0.428298	0.214149	−	0.976801i	$-0.431302\pi$
$467$	4322.37	0.428298	0.214149	+	0.976801i	$0.431302\pi$
$468$	4846.39	0.478685
$469$	−2268.70	−0.223366
$470$	−4217.18	−0.413881
$471$	−5178.29	−0.506588
$472$	−2410.54	−0.235072
$473$	−7274.83	−0.707182
$474$	−1011.10	−0.0979771
$475$	−3198.60	−0.308973
$476$	−1474.78	−0.142009
$477$	5149.14	0.494262
$478$	−13692.8	−1.31024
$479$	−7257.95	−0.692326	−0.346163	−	0.938174i	$-0.612516\pi$
$479$	−7257.95	−0.692326	−0.346163	+	0.938174i	$0.612516\pi$
$480$	3451.79	0.328234
$481$	−36851.5	−3.49332
$482$	948.929	0.0896733
$483$	−9256.19	−0.871990
$484$	−5512.63	−0.517715
$485$	−2286.13	−0.214037
$486$	−917.434	−0.0856290
$487$	18440.2	1.71582	0.857912	−	0.513797i	$-0.171762\pi$
$487$	18440.2	1.71582	0.857912	+	0.513797i	$0.171762\pi$
$488$	4773.19	0.442771
$489$	−489.000	−0.0452216
$490$	−13778.4	−1.27030
$491$	−13967.3	−1.28378	−0.641890	−	0.766796i	$-0.721850\pi$
$491$	−13967.3	−1.28378	−0.641890	+	0.766796i	$0.721850\pi$
$492$	9616.63	0.881202
$493$	726.055	0.0663284
$494$	41591.6	3.78804
$495$	954.113	0.0866347
$496$	−3807.32	−0.344665
$497$	27872.9	2.51564
$498$	3148.47	0.283306
$499$	−13128.5	−1.17778	−0.588890	−	0.808213i	$-0.700435\pi$
$499$	−13128.5	−1.17778	−0.588890	+	0.808213i	$0.700435\pi$
$500$	781.753	0.0699221
$501$	10392.2	0.926727
$502$	−24929.0	−2.21641
$503$	−9742.72	−0.863631	−0.431815	−	0.901962i	$-0.642127\pi$
$503$	−9742.72	−0.863631	−0.431815	+	0.901962i	$0.642127\pi$
$504$	1943.25	0.171744
$505$	−4076.21	−0.359186
$506$	7540.29	0.662464
$507$	15650.0	1.37089
$508$	10126.1	0.884396
$509$	21290.0	1.85395	0.926976	−	0.375120i	$-0.122398\pi$
$509$	21290.0	1.85395	0.926976	+	0.375120i	$0.122398\pi$
$510$	407.707	0.0353992
$511$	−15065.1	−1.30419
$512$	−13289.6	−1.14711
$513$	−3454.49	−0.297309
$514$	−23111.5	−1.98328
$515$	264.779	0.0226554
$516$	−6437.49	−0.549215
$517$	4736.64	0.402935
$518$	52928.2	4.48944
$519$	6987.72	0.590996
$520$	2837.87	0.239325
$521$	−19364.8	−1.62838	−0.814190	−	0.580599i	$-0.802818\pi$
$521$	−19364.8	−1.62838	−0.814190	+	0.580599i	$0.802818\pi$
$522$	3426.83	0.287334
$523$	−1716.85	−0.143543	−0.0717713	−	0.997421i	$-0.522865\pi$
$523$	−1716.85	−0.143543	−0.0717713	+	0.997421i	$0.522865\pi$
$524$	11892.2	0.991441
$525$	2456.63	0.204221
$526$	9817.46	0.813805
$527$	−365.859	−0.0302411
$528$	−4765.44	−0.392782
$529$	−3294.12	−0.270742
$530$	−10800.2	−0.885151
$531$	−3291.17	−0.268973
$532$	−26209.5	−2.13595
$533$	44132.5	3.58647
$534$	−1334.75	−0.108165
$535$	8501.56	0.687018
$536$	−456.567	−0.0367924
$537$	−3742.27	−0.300728
$538$	11451.7	0.917691
$539$	15475.6	1.23670
$540$	844.293	0.0672826
$541$	20997.4	1.66867	0.834334	−	0.551259i	$-0.185852\pi$
$541$	20997.4	1.66867	0.834334	+	0.551259i	$0.185852\pi$
$542$	15615.5	1.23754
$543$	5961.84	0.471174
$544$	−1656.69	−0.130570
$545$	6908.29	0.542970
$546$	−31943.7	−2.50378
$547$	9570.97	0.748126	0.374063	−	0.927403i	$-0.377964\pi$
$547$	9570.97	0.748126	0.374063	+	0.927403i	$0.377964\pi$
$548$	4751.67	0.370403
$549$	6516.95	0.506624
$550$	−2001.23	−0.155150
$551$	12903.3	0.997642
$552$	−1862.77	−0.143632
$553$	2924.02	0.224850
$554$	−18543.2	−1.42207
$555$	−6419.93	−0.491011
$556$	9940.29	0.758205
$557$	−19843.7	−1.50953	−0.754763	−	0.655998i	$-0.772248\pi$
$557$	−19843.7	−1.50953	−0.754763	+	0.655998i	$0.772248\pi$
$558$	−1726.78	−0.131004
$559$	−29542.8	−2.23529
$560$	−12270.0	−0.925893
$561$	−457.927	−0.0344629
$562$	12703.6	0.953506
$563$	12522.0	0.937367	0.468684	−	0.883366i	$-0.344728\pi$
$563$	12522.0	0.937367	0.468684	+	0.883366i	$0.344728\pi$
$564$	4191.45	0.312929
$565$	1621.28	0.120722
$566$	−20052.6	−1.48917
$567$	2653.16	0.196512
$568$	5609.32	0.414370
$569$	−6590.03	−0.485533	−0.242767	−	0.970085i	$-0.578055\pi$
$569$	−6590.03	−0.485533	−0.242767	+	0.970085i	$0.578055\pi$
$570$	7245.70	0.532437
$571$	−2448.44	−0.179447	−0.0897233	−	0.995967i	$-0.528598\pi$
$571$	−2448.44	−0.179447	−0.0897233	+	0.995967i	$0.528598\pi$
$572$	11417.3	0.834582
$573$	−4078.09	−0.297320
$574$	−63385.5	−4.60916
$575$	−2354.90	−0.170793
$576$	−2425.05	−0.175423
$577$	−20698.0	−1.49336	−0.746681	−	0.665182i	$-0.768354\pi$
$577$	−20698.0	−1.49336	−0.746681	+	0.665182i	$0.768354\pi$
$578$	18353.1	1.32074
$579$	−745.187	−0.0534869
$580$	−3153.63	−0.225772
$581$	−9105.19	−0.650167
$582$	5178.71	0.368839
$583$	12130.5	0.861741
$584$	−3031.79	−0.214823
$585$	3874.62	0.273839
$586$	1538.66	0.108467
$587$	−12515.6	−0.880027	−0.440013	−	0.897991i	$-0.645026\pi$
$587$	−12515.6	−0.880027	−0.440013	+	0.897991i	$0.645026\pi$
$588$	13694.4	0.960453
$589$	−6501.98	−0.454855
$590$	6903.14	0.481691
$591$	2254.56	0.156921
$592$	32065.2	2.22613
$593$	11434.9	0.791865	0.395933	−	0.918280i	$-0.370421\pi$
$593$	11434.9	0.791865	0.395933	+	0.918280i	$0.370421\pi$
$594$	−2161.32	−0.149293
$595$	−1179.06	−0.0812384
$596$	−18678.2	−1.28371
$597$	4503.99	0.308771
$598$	30620.9	2.09395
$599$	−3264.92	−0.222706	−0.111353	−	0.993781i	$-0.535518\pi$
$599$	−3264.92	−0.222706	−0.111353	+	0.993781i	$0.535518\pi$
$600$	494.388	0.0336389
$601$	−442.933	−0.0300626	−0.0150313	−	0.999887i	$-0.504785\pi$
$601$	−442.933	−0.0300626	−0.0150313	+	0.999887i	$0.504785\pi$
$602$	42431.0	2.87269
$603$	−623.362	−0.0420983
$604$	1907.68	0.128514
$605$	−4407.27	−0.296167
$606$	9233.71	0.618967
$607$	2406.06	0.160888	0.0804441	−	0.996759i	$-0.474366\pi$
$607$	2406.06	0.160888	0.0804441	+	0.996759i	$0.474366\pi$
$608$	−29442.4	−1.96390
$609$	−9910.18	−0.659410
$610$	−13669.1	−0.907290
$611$	19235.3	1.27361
$612$	−405.219	−0.0267647
$613$	−4856.19	−0.319967	−0.159984	−	0.987120i	$-0.551144\pi$
$613$	−4856.19	−0.319967	−0.159984	+	0.987120i	$0.551144\pi$
$614$	11989.6	0.788046
$615$	7688.35	0.504105
$616$	4577.97	0.299435
$617$	−12642.4	−0.824898	−0.412449	−	0.910981i	$-0.635327\pi$
$617$	−12642.4	−0.824898	−0.412449	+	0.910981i	$0.635327\pi$
$618$	−599.795	−0.0390409
$619$	−10767.3	−0.699152	−0.349576	−	0.936908i	$-0.613674\pi$
$619$	−10767.3	−0.699152	−0.349576	+	0.936908i	$0.613674\pi$
$620$	1589.11	0.102936
$621$	−2543.29	−0.164346
$622$	−7813.82	−0.503707
$623$	3860.01	0.248231
$624$	−19352.3	−1.24152
$625$	625.000	0.0400000
$626$	29898.2	1.90890
$627$	−8138.21	−0.518355
$628$	−10795.0	−0.685938
$629$	3081.25	0.195322
$630$	−5564.94	−0.351924
$631$	25250.1	1.59301	0.796505	−	0.604631i	$-0.206680\pi$
$631$	25250.1	1.59301	0.796505	+	0.604631i	$0.206680\pi$
$632$	588.449	0.0370368
$633$	−5746.43	−0.360822
$634$	−5489.28	−0.343860
$635$	8095.67	0.505932
$636$	10734.3	0.669249
$637$	62846.0	3.90902
$638$	8073.05	0.500964
$639$	7658.54	0.474127
$640$	−4118.31	−0.254360
$641$	20857.5	1.28521	0.642605	−	0.766197i	$-0.277853\pi$
$641$	20857.5	1.28521	0.642605	+	0.766197i	$0.277853\pi$
$642$	−19258.3	−1.18390
$643$	−28316.4	−1.73669	−0.868343	−	0.495964i	$-0.834815\pi$
$643$	−28316.4	−1.73669	−0.868343	+	0.495964i	$0.834815\pi$
$644$	−19296.2	−1.18071
$645$	−5146.68	−0.314186
$646$	−3477.58	−0.211801
$647$	−14154.0	−0.860047	−0.430024	−	0.902818i	$-0.641495\pi$
$647$	−14154.0	−0.860047	−0.430024	+	0.902818i	$0.641495\pi$
$648$	533.939	0.0323690
$649$	−7753.45	−0.468952
$650$	−8126.90	−0.490405
$651$	4993.73	0.300645
$652$	−1019.41	−0.0612316
$653$	17708.9	1.06126	0.530629	−	0.847604i	$-0.321956\pi$
$653$	17708.9	1.06126	0.530629	+	0.847604i	$0.321956\pi$
$654$	−15649.1	−0.935673
$655$	9507.67	0.567169
$656$	−38400.4	−2.28550
$657$	−4139.38	−0.245803
$658$	−27626.8	−1.63679
$659$	−2406.09	−0.142227	−0.0711137	−	0.997468i	$-0.522655\pi$
$659$	−2406.09	−0.142227	−0.0711137	+	0.997468i	$0.522655\pi$
$660$	1989.02	0.117307
$661$	6218.55	0.365921	0.182960	−	0.983120i	$-0.441432\pi$
$661$	6218.55	0.365921	0.182960	+	0.983120i	$0.441432\pi$
$662$	7201.02	0.422773
$663$	−1859.63	−0.108932
$664$	−1832.39	−0.107094
$665$	−20954.1	−1.22190
$666$	14542.9	0.846134
$667$	9499.79	0.551474
$668$	21664.4	1.25482
$669$	−4510.35	−0.260658
$670$	1307.48	0.0753919
$671$	15352.9	0.883295
$672$	22612.8	1.29808
$673$	−6295.21	−0.360569	−0.180284	−	0.983615i	$-0.557702\pi$
$673$	−6295.21	−0.360569	−0.180284	+	0.983615i	$0.557702\pi$
$674$	37112.8	2.12097
$675$	675.000	0.0384900
$676$	32625.1	1.85623
$677$	−19351.8	−1.09860	−0.549299	−	0.835626i	$-0.685105\pi$
$677$	−19351.8	−1.09860	−0.549299	+	0.835626i	$0.685105\pi$
$678$	−3672.64	−0.208034
$679$	−14976.5	−0.846459
$680$	−237.282	−0.0133814
$681$	7115.91	0.400415
$682$	−4068.00	−0.228404
$683$	26713.5	1.49658	0.748291	−	0.663371i	$-0.230875\pi$
$683$	26713.5	1.49658	0.748291	+	0.663371i	$0.230875\pi$
$684$	−7201.49	−0.402567
$685$	3798.89	0.211895
$686$	−47845.6	−2.66291
$687$	−1163.51	−0.0646153
$688$	25705.7	1.42445
$689$	49261.6	2.72383
$690$	5334.48	0.294319
$691$	23406.1	1.28858	0.644290	−	0.764782i	$-0.277153\pi$
$691$	23406.1	1.28858	0.644290	+	0.764782i	$0.277153\pi$
$692$	14567.1	0.800230
$693$	6250.41	0.342617
$694$	−86.4039	−0.00472601
$695$	7947.11	0.433743
$696$	−1994.39	−0.108617
$697$	−3690.03	−0.200531
$698$	6146.70	0.333318
$699$	4114.58	0.222643
$700$	5121.28	0.276523
$701$	30870.0	1.66326	0.831630	−	0.555330i	$-0.187408\pi$
$701$	30870.0	1.66326	0.831630	+	0.555330i	$0.187408\pi$
$702$	−8777.05	−0.471893
$703$	54759.5	2.93783
$704$	−5713.02	−0.305849
$705$	3351.00	0.179016
$706$	15963.0	0.850958
$707$	−26703.3	−1.42048
$708$	−6861.02	−0.364199
$709$	−10012.4	−0.530357	−0.265179	−	0.964199i	$-0.585431\pi$
$709$	−10012.4	−0.530357	−0.265179	+	0.964199i	$0.585431\pi$
$710$	−16063.6	−0.849092
$711$	803.424	0.0423780
$712$	776.813	0.0408881
$713$	−4786.93	−0.251433
$714$	2670.90	0.139994
$715$	9127.96	0.477435
$716$	−7801.41	−0.407196
$717$	10880.4	0.566716
$718$	37046.4	1.92557
$719$	13607.5	0.705807	0.352903	−	0.935660i	$-0.385194\pi$
$719$	13607.5	0.705807	0.352903	+	0.935660i	$0.385194\pi$
$720$	−3371.37	−0.174505
$721$	1734.57	0.0895960
$722$	−35907.2	−1.85087
$723$	−754.026	−0.0387863
$724$	12428.5	0.637986
$725$	−2521.28	−0.129156
$726$	9983.65	0.510369
$727$	−33157.4	−1.69153	−0.845764	−	0.533557i	$-0.820855\pi$
$727$	−33157.4	−1.69153	−0.845764	+	0.533557i	$0.820855\pi$
$728$	18591.0	0.946466
$729$	729.000	0.0370370
$730$	8682.23	0.440197
$731$	2470.15	0.124982
$732$	13585.7	0.685988
$733$	−34722.1	−1.74965	−0.874823	−	0.484442i	$-0.839023\pi$
$733$	−34722.1	−1.74965	−0.874823	+	0.484442i	$0.839023\pi$
$734$	−21396.2	−1.07595
$735$	10948.4	0.549441
$736$	−21676.3	−1.08560
$737$	−1468.54	−0.0733979
$738$	−17416.2	−0.868698
$739$	−3501.25	−0.174283	−0.0871417	−	0.996196i	$-0.527773\pi$
$739$	−3501.25	−0.174283	−0.0871417	+	0.996196i	$0.527773\pi$
$740$	−13383.5	−0.664846
$741$	−33049.0	−1.63844
$742$	−70752.2	−3.50053
$743$	34415.6	1.69931	0.849655	−	0.527339i	$-0.176810\pi$
$743$	34415.6	1.69931	0.849655	+	0.527339i	$0.176810\pi$
$744$	1004.97	0.0495215
$745$	−14933.0	−0.734364
$746$	53780.2	2.63945
$747$	−2501.80	−0.122538
$748$	−954.630	−0.0466641
$749$	55693.9	2.71697
$750$	−1415.79	−0.0689300
$751$	−33212.9	−1.61379	−0.806895	−	0.590695i	$-0.798854\pi$
$751$	−33212.9	−1.61379	−0.806895	+	0.590695i	$0.798854\pi$
$752$	−16737.0	−0.811616
$753$	19808.8	0.958662
$754$	32784.4	1.58347
$755$	1525.17	0.0735185
$756$	5530.98	0.266084
$757$	21895.2	1.05125	0.525623	−	0.850717i	$-0.323832\pi$
$757$	21895.2	1.05125	0.525623	+	0.850717i	$0.323832\pi$
$758$	−1789.49	−0.0857484
$759$	−5991.57	−0.286535
$760$	−4216.94	−0.201269
$761$	−39965.7	−1.90375	−0.951876	−	0.306483i	$-0.900848\pi$
$761$	−39965.7	−1.90375	−0.951876	+	0.306483i	$0.900848\pi$
$762$	−18338.9	−0.871847
$763$	45256.3	2.14730
$764$	−8501.49	−0.402582
$765$	−323.967	−0.0153112
$766$	45858.1	2.16308
$767$	−31486.5	−1.48228
$768$	15795.9	0.742168
$769$	25480.5	1.19487	0.597433	−	0.801919i	$-0.296188\pi$
$769$	25480.5	1.19487	0.597433	+	0.801919i	$0.296188\pi$
$770$	−13110.1	−0.613577
$771$	18364.6	0.857827
$772$	−1553.47	−0.0724232
$773$	26819.5	1.24790	0.623952	−	0.781463i	$-0.285526\pi$
$773$	26819.5	1.24790	0.623952	+	0.781463i	$0.285526\pi$
$774$	11658.6	0.541422
$775$	1270.47	0.0588861
$776$	−3013.97	−0.139427
$777$	−42057.1	−1.94182
$778$	200.833	0.00925478
$779$	−65578.6	−3.01617
$780$	8077.32	0.370788
$781$	18042.3	0.826636
$782$	−2560.29	−0.117079
$783$	−2722.99	−0.124280
$784$	−54683.4	−2.49104
$785$	−8630.48	−0.392401
$786$	−21537.5	−0.977373
$787$	−8520.16	−0.385910	−0.192955	−	0.981208i	$-0.561807\pi$
$787$	−8520.16	−0.385910	−0.192955	+	0.981208i	$0.561807\pi$
$788$	4700.03	0.212477
$789$	−7801.02	−0.351995
$790$	−1685.16	−0.0758927
$791$	10621.0	0.477422
$792$	1257.87	0.0564350
$793$	62347.4	2.79196
$794$	−47316.6	−2.11486
$795$	8581.91	0.382854
$796$	9389.35	0.418086
$797$	22379.9	0.994652	0.497326	−	0.867564i	$-0.334315\pi$
$797$	22379.9	0.994652	0.497326	+	0.867564i	$0.334315\pi$
$798$	47466.7	2.10564
$799$	−1608.32	−0.0712117
$800$	5752.99	0.254249
$801$	1060.60	0.0467847
$802$	52.4461	0.00230915
$803$	−9751.69	−0.428555
$804$	−1299.51	−0.0570026
$805$	−15427.0	−0.675441
$806$	−16520.0	−0.721951
$807$	−9099.60	−0.396928
$808$	−5373.94	−0.233979
$809$	−13903.5	−0.604229	−0.302114	−	0.953272i	$-0.597692\pi$
$809$	−13903.5	−0.604229	−0.302114	+	0.953272i	$0.597692\pi$
$810$	−1529.06	−0.0663279
$811$	41656.6	1.80365	0.901825	−	0.432101i	$-0.142227\pi$
$811$	41656.6	1.80365	0.901825	+	0.432101i	$0.142227\pi$
$812$	−20659.5	−0.892865
$813$	−12408.2	−0.535271
$814$	34260.6	1.47523
$815$	−815.000	−0.0350285
$816$	1618.09	0.0694174
$817$	43899.1	1.87985
$818$	54732.8	2.33947
$819$	25382.7	1.08296
$820$	16027.7	0.682576
$821$	−12794.7	−0.543896	−0.271948	−	0.962312i	$-0.587668\pi$
$821$	−12794.7	−0.543896	−0.271948	+	0.962312i	$0.587668\pi$
$822$	−8605.50	−0.365148
$823$	26549.9	1.12451	0.562255	−	0.826964i	$-0.309934\pi$
$823$	26549.9	1.12451	0.562255	+	0.826964i	$0.309934\pi$
$824$	349.076	0.0147580
$825$	1590.19	0.0671070
$826$	45222.6	1.90496
$827$	−26056.1	−1.09560	−0.547800	−	0.836610i	$-0.684534\pi$
$827$	−26056.1	−1.09560	−0.547800	+	0.836610i	$0.684534\pi$
$828$	−5301.93	−0.222530
$829$	−22533.5	−0.944056	−0.472028	−	0.881584i	$-0.656478\pi$
$829$	−22533.5	−0.944056	−0.472028	+	0.881584i	$0.656478\pi$
$830$	5247.45	0.219448
$831$	14734.6	0.615087
$832$	−23200.4	−0.966740
$833$	−5254.72	−0.218566
$834$	−18002.4	−0.747447
$835$	17320.4	0.717839
$836$	−16965.5	−0.701872
$837$	1372.11	0.0566632
$838$	−56782.9	−2.34073
$839$	−11993.9	−0.493536	−0.246768	−	0.969075i	$-0.579369\pi$
$839$	−11993.9	−0.493536	−0.246768	+	0.969075i	$0.579369\pi$
$840$	3238.75	0.133033
$841$	−14218.0	−0.582968
$842$	−39210.7	−1.60486
$843$	−10094.4	−0.412419
$844$	−11979.4	−0.488565
$845$	26083.3	1.06188
$846$	−7590.92	−0.308488
$847$	−28872.1	−1.17126
$848$	−42863.4	−1.73577
$849$	15933.9	0.644111
$850$	679.512	0.0274201
$851$	40315.5	1.62397
$852$	15965.6	0.641985
$853$	−30160.1	−1.21062	−0.605311	−	0.795989i	$-0.706951\pi$
$853$	−30160.1	−1.21062	−0.605311	+	0.795989i	$0.706951\pi$
$854$	−89546.7	−3.58809
$855$	−5757.48	−0.230295
$856$	11208.2	0.447533
$857$	3603.45	0.143631	0.0718153	−	0.997418i	$-0.477121\pi$
$857$	3603.45	0.143631	0.0718153	+	0.997418i	$0.477121\pi$
$858$	−20677.3	−0.822740
$859$	−22064.0	−0.876384	−0.438192	−	0.898881i	$-0.644381\pi$
$859$	−22064.0	−0.876384	−0.438192	+	0.898881i	$0.644381\pi$
$860$	−10729.2	−0.425420
$861$	50366.6	1.99360
$862$	−33453.1	−1.32183
$863$	−6743.64	−0.265998	−0.132999	−	0.991116i	$-0.542461\pi$
$863$	−6743.64	−0.265998	−0.132999	+	0.991116i	$0.542461\pi$
$864$	6213.23	0.244651
$865$	11646.2	0.457783
$866$	4679.81	0.183633
$867$	−14583.5	−0.571260
$868$	10410.3	0.407084
$869$	1892.73	0.0738856
$870$	5711.39	0.222568
$871$	−5963.68	−0.231999
$872$	9107.67	0.353698
$873$	−4115.04	−0.159534
$874$	−45501.0	−1.76098
$875$	4094.39	0.158189
$876$	−8629.26	−0.332826
$877$	−16977.9	−0.653709	−0.326854	−	0.945075i	$-0.605989\pi$
$877$	−16977.9	−0.653709	−0.326854	+	0.945075i	$0.605989\pi$
$878$	−33668.5	−1.29414
$879$	−1222.63	−0.0469151
$880$	−7942.39	−0.304248
$881$	−25076.2	−0.958956	−0.479478	−	0.877554i	$-0.659174\pi$
$881$	−25076.2	−0.958956	−0.479478	+	0.877554i	$0.659174\pi$
$882$	−24801.2	−0.946825
$883$	−7927.87	−0.302145	−0.151073	−	0.988523i	$-0.548273\pi$
$883$	−7927.87	−0.302145	−0.151073	+	0.988523i	$0.548273\pi$
$884$	−3876.72	−0.147498
$885$	−5485.28	−0.208346
$886$	−43782.6	−1.66016
$887$	−13138.5	−0.497347	−0.248673	−	0.968587i	$-0.579995\pi$
$887$	−13138.5	−0.497347	−0.248673	+	0.968587i	$0.579995\pi$
$888$	−8463.84	−0.319851
$889$	53034.9	2.00082
$890$	−2224.58	−0.0837845
$891$	1717.40	0.0645737
$892$	−9402.60	−0.352940
$893$	−28582.7	−1.07109
$894$	33827.2	1.26549
$895$	−6237.11	−0.232943
$896$	−26979.1	−1.00592
$897$	−24331.5	−0.905693
$898$	−54648.3	−2.03078
$899$	−5125.15	−0.190137
$900$	1407.16	0.0521169
$901$	−4118.89	−0.152298
$902$	−41029.7	−1.51457
$903$	−33716.0	−1.24252
$904$	2137.44	0.0786397
$905$	9936.41	0.364969
$906$	−3454.91	−0.126691
$907$	4798.94	0.175685	0.0878424	−	0.996134i	$-0.472003\pi$
$907$	4798.94	0.175685	0.0878424	+	0.996134i	$0.472003\pi$
$908$	14834.4	0.542176
$909$	−7337.17	−0.267721
$910$	−53239.5	−1.93942
$911$	−24790.8	−0.901597	−0.450799	−	0.892626i	$-0.648861\pi$
$911$	−24790.8	−0.901597	−0.450799	+	0.892626i	$0.648861\pi$
$912$	28756.5	1.04410
$913$	−5893.83	−0.213644
$914$	37140.3	1.34408
$915$	10861.6	0.392430
$916$	−2425.54	−0.0874914
$917$	62285.0	2.24300
$918$	733.873	0.0263850
$919$	−32784.4	−1.17678	−0.588389	−	0.808578i	$-0.700238\pi$
$919$	−32784.4	−1.17678	−0.588389	+	0.808578i	$0.700238\pi$
$920$	−3104.62	−0.111257
$921$	−9527.01	−0.340853
$922$	−20761.0	−0.741568
$923$	73268.9	2.61287
$924$	13030.1	0.463916
$925$	−10699.9	−0.380335
$926$	8420.76	0.298837
$927$	476.601	0.0168863
$928$	−23207.9	−0.820944
$929$	−46792.5	−1.65254	−0.826271	−	0.563273i	$-0.809542\pi$
$929$	−46792.5	−1.65254	−0.826271	+	0.563273i	$0.809542\pi$
$930$	−2877.96	−0.101475
$931$	−93385.9	−3.28743
$932$	8577.55	0.301467
$933$	6208.92	0.217868
$934$	−16318.9	−0.571702
$935$	−763.212	−0.0266949
$936$	5108.17	0.178382
$937$	−51286.0	−1.78809	−0.894044	−	0.447978i	$-0.852144\pi$
$937$	−51286.0	−1.78809	−0.894044	+	0.447978i	$0.852144\pi$
$938$	8565.36	0.298154
$939$	−23757.3	−0.825655
$940$	6985.75	0.242393
$941$	8570.73	0.296916	0.148458	−	0.988919i	$-0.452569\pi$
$941$	8570.73	0.296916	0.148458	+	0.988919i	$0.452569\pi$
$942$	19550.4	0.676205
$943$	−48280.8	−1.66727
$944$	27396.9	0.944592
$945$	4421.94	0.152218
$946$	27465.8	0.943963
$947$	−57512.7	−1.97351	−0.986754	−	0.162225i	$-0.948133\pi$
$947$	−57512.7	−1.97351	−0.986754	+	0.162225i	$0.948133\pi$
$948$	1674.88	0.0573813
$949$	−39601.3	−1.35460
$950$	12076.2	0.412424
$951$	4361.83	0.148730
$952$	−1554.44	−0.0529198
$953$	−30430.8	−1.03437	−0.517183	−	0.855875i	$-0.673019\pi$
$953$	−30430.8	−1.03437	−0.517183	+	0.855875i	$0.673019\pi$
$954$	−19440.3	−0.659753
$955$	−6796.81	−0.230303
$956$	22682.1	0.767354
$957$	−6414.90	−0.216682
$958$	27402.0	0.924133
$959$	24886.6	0.837987
$960$	−4041.75	−0.135882
$961$	−27208.4	−0.913311
$962$	139131.	4.66296
$963$	15302.8	0.512073
$964$	−1571.90	−0.0525181
$965$	−1241.98	−0.0414308
$966$	34946.3	1.16395
$967$	−20090.4	−0.668110	−0.334055	−	0.942554i	$-0.608417\pi$
$967$	−20090.4	−0.668110	−0.334055	+	0.942554i	$0.608417\pi$
$968$	−5810.40	−0.192927
$969$	2763.31	0.0916102
$970$	8631.18	0.285702
$971$	−13214.3	−0.436734	−0.218367	−	0.975867i	$-0.570073\pi$
$971$	−13214.3	−0.436734	−0.218367	+	0.975867i	$0.570073\pi$
$972$	1519.73	0.0501495
$973$	52061.7	1.71534
$974$	−69620.1	−2.29032
$975$	6457.70	0.212115
$976$	−54249.6	−1.77919
$977$	27115.3	0.887919	0.443959	−	0.896047i	$-0.353573\pi$
$977$	27115.3	0.887919	0.443959	+	0.896047i	$0.353573\pi$
$978$	1846.20	0.0603628
$979$	2498.60	0.0815686
$980$	22823.9	0.743963
$981$	12434.9	0.404706
$982$	52732.9	1.71362
$983$	30597.4	0.992784	0.496392	−	0.868099i	$-0.334658\pi$
$983$	30597.4	0.992784	0.496392	+	0.868099i	$0.334658\pi$
$984$	10136.1	0.328381
$985$	3757.60	0.121550
$986$	−2741.19	−0.0885367
$987$	21952.5	0.707958
$988$	−68896.3	−2.21851
$989$	32319.7	1.03914
$990$	−3602.21	−0.115642
$991$	−33635.4	−1.07817	−0.539084	−	0.842252i	$-0.681230\pi$
$991$	−33635.4	−1.07817	−0.539084	+	0.842252i	$0.681230\pi$
$992$	11694.4	0.374293
$993$	−5721.98	−0.182862
$994$	−105233.	−3.35793
$995$	7506.65	0.239173
$996$	−5215.44	−0.165921
$997$	−9979.80	−0.317015	−0.158507	−	0.987358i	$-0.550668\pi$
$997$	−9979.80	−0.317015	−0.158507	+	0.987358i	$0.550668\pi$
$998$	49566.0	1.57213
$999$	−11555.9	−0.365978

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2445.4.a.i.1.7	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2445.4.a.i.1.7	✓	43	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-3.77545 q^{2} +3.00000 q^{3} +6.25402 q^{4} +5.00000 q^{5} -11.3264 q^{6} +32.7551 q^{7} +6.59184 q^{8} +9.00000 q^{9} -18.8773 q^{10} +21.2025 q^{11} +18.7621 q^{12} +86.1026 q^{13} -123.665 q^{14} +15.0000 q^{15} -74.9194 q^{16} -7.19926 q^{17} -33.9791 q^{18} -127.944 q^{19} +31.2701 q^{20} +98.2653 q^{21} -80.0490 q^{22} -94.1959 q^{23} +19.7755 q^{24} +25.0000 q^{25} -325.076 q^{26} +27.0000 q^{27} +204.851 q^{28} -100.851 q^{29} -56.6318 q^{30} +50.8189 q^{31} +230.120 q^{32} +63.6075 q^{33} +27.1805 q^{34} +163.775 q^{35} +56.2862 q^{36} -427.996 q^{37} +483.047 q^{38} +258.308 q^{39} +32.9592 q^{40} +512.557 q^{41} -370.996 q^{42} -343.112 q^{43} +132.601 q^{44} +45.0000 q^{45} +355.632 q^{46} +223.400 q^{47} -224.758 q^{48} +729.896 q^{49} -94.3863 q^{50} -21.5978 q^{51} +538.488 q^{52} +572.127 q^{53} -101.937 q^{54} +106.013 q^{55} +215.916 q^{56} -383.832 q^{57} +380.759 q^{58} -365.686 q^{59} +93.8104 q^{60} +724.106 q^{61} -191.864 q^{62} +294.796 q^{63} -269.450 q^{64} +430.513 q^{65} -240.147 q^{66} -69.2625 q^{67} -45.0244 q^{68} -282.588 q^{69} -618.326 q^{70} +850.949 q^{71} +59.3266 q^{72} -459.931 q^{73} +1615.88 q^{74} +75.0000 q^{75} -800.166 q^{76} +694.490 q^{77} -975.228 q^{78} +89.2693 q^{79} -374.597 q^{80} +81.0000 q^{81} -1935.13 q^{82} -277.978 q^{83} +614.554 q^{84} -35.9963 q^{85} +1295.40 q^{86} -302.554 q^{87} +139.764 q^{88} +117.845 q^{89} -169.895 q^{90} +2820.30 q^{91} -589.104 q^{92} +152.457 q^{93} -843.436 q^{94} -639.721 q^{95} +690.359 q^{96} -457.227 q^{97} -2755.69 q^{98} +190.823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 18 q^{2} + 129 q^{3} + 198 q^{4} + 215 q^{5} + 54 q^{6} + 137 q^{7} + 201 q^{8} + 387 q^{9} + 90 q^{10} + 137 q^{11} + 594 q^{12} + 212 q^{13} + 246 q^{14} + 645 q^{15} + 930 q^{16} + 547 q^{17}+ \cdots + 1233 q^{99}+O(q^{100}) \) 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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