LMFDB - Embedded newform 65.4.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,4,Mod(1,65)] 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("65.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,1] 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:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.56155 q^{2} +8.24621 q^{3} -1.43845 q^{4} -5.00000 q^{5} +21.1231 q^{6} +24.8769 q^{7} -24.1771 q^{8} +41.0000 q^{9} -12.8078 q^{10} -38.8769 q^{11} -11.8617 q^{12} -13.0000 q^{13} +63.7235 q^{14} -41.2311 q^{15} -50.4233 q^{16} -79.9697 q^{17} +105.024 q^{18} +128.354 q^{19} +7.19224 q^{20} +205.140 q^{21} -99.5852 q^{22} -101.939 q^{23} -199.369 q^{24} +25.0000 q^{25} -33.3002 q^{26} +115.447 q^{27} -35.7841 q^{28} +117.723 q^{29} -105.616 q^{30} -298.756 q^{31} +64.2547 q^{32} -320.587 q^{33} -204.847 q^{34} -124.384 q^{35} -58.9763 q^{36} +254.216 q^{37} +328.786 q^{38} -107.201 q^{39} +120.885 q^{40} +219.633 q^{41} +525.477 q^{42} -104.462 q^{43} +55.9224 q^{44} -205.000 q^{45} -261.123 q^{46} +308.816 q^{47} -415.801 q^{48} +275.860 q^{49} +64.0388 q^{50} -659.447 q^{51} +18.6998 q^{52} -0.0909300 q^{53} +295.723 q^{54} +194.384 q^{55} -601.451 q^{56} +1058.44 q^{57} +301.555 q^{58} -349.710 q^{59} +59.3087 q^{60} +442.000 q^{61} -765.278 q^{62} +1019.95 q^{63} +567.978 q^{64} +65.0000 q^{65} -821.201 q^{66} +228.074 q^{67} +115.032 q^{68} -840.614 q^{69} -318.617 q^{70} +964.328 q^{71} -991.260 q^{72} +662.682 q^{73} +651.187 q^{74} +206.155 q^{75} -184.631 q^{76} -967.136 q^{77} -274.600 q^{78} -65.2614 q^{79} +252.116 q^{80} -155.000 q^{81} +562.600 q^{82} -92.4185 q^{83} -295.083 q^{84} +399.848 q^{85} -267.585 q^{86} +970.773 q^{87} +939.930 q^{88} -178.614 q^{89} -525.118 q^{90} -323.400 q^{91} +146.634 q^{92} -2463.60 q^{93} +791.049 q^{94} -641.771 q^{95} +529.858 q^{96} -1707.46 q^{97} +706.630 q^{98} -1593.95 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 7 q^{4} - 10 q^{5} + 34 q^{6} + 58 q^{7} - 3 q^{8} + 82 q^{9} - 5 q^{10} - 86 q^{11} + 34 q^{12} - 26 q^{13} + 12 q^{14} - 39 q^{16} - 28 q^{17} + 41 q^{18} + 166 q^{19} + 35 q^{20} - 68 q^{21}+ \cdots - 3526 q^{99}+O(q^{100}) $ 2 * q + q^2 - 7 * q^4 - 10 * q^5 + 34 * q^6 + 58 * q^7 - 3 * q^8 + 82 * q^9 - 5 * q^10 - 86 * q^11 + 34 * q^12 - 26 * q^13 + 12 * q^14 - 39 * q^16 - 28 * q^17 + 41 * q^18 + 166 * q^19 + 35 * q^20 - 68 * q^21 - 26 * q^22 + 60 * q^23 - 374 * q^24 + 50 * q^25 - 13 * q^26 - 220 * q^28 + 120 * q^29 - 170 * q^30 - 78 * q^31 - 123 * q^32 + 68 * q^33 - 286 * q^34 - 290 * q^35 - 287 * q^36 + 360 * q^37 + 270 * q^38 + 15 * q^40 - 72 * q^41 + 952 * q^42 - 44 * q^43 + 318 * q^44 - 410 * q^45 - 514 * q^46 + 362 * q^47 - 510 * q^48 + 1030 * q^49 + 25 * q^50 - 1088 * q^51 + 91 * q^52 - 396 * q^53 + 476 * q^54 + 430 * q^55 + 100 * q^56 + 748 * q^57 + 298 * q^58 + 18 * q^59 - 170 * q^60 + 884 * q^61 - 1110 * q^62 + 2378 * q^63 + 769 * q^64 + 130 * q^65 - 1428 * q^66 + 1322 * q^67 - 174 * q^68 - 2176 * q^69 - 60 * q^70 + 634 * q^71 - 123 * q^72 - 60 * q^73 + 486 * q^74 - 394 * q^76 - 2528 * q^77 - 442 * q^78 - 180 * q^79 + 195 * q^80 - 310 * q^81 + 1018 * q^82 + 714 * q^83 + 1224 * q^84 + 140 * q^85 - 362 * q^86 + 952 * q^87 - 58 * q^88 - 852 * q^89 - 205 * q^90 - 754 * q^91 - 754 * q^92 - 4284 * q^93 + 708 * q^94 - 830 * q^95 + 2074 * q^96 + 32 * q^97 - 471 * q^98 - 3526 * 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 $

$2$	2.56155	0.905646	0.452823	−	0.891601i	$-0.350417\pi$
$2$	2.56155	0.905646	0.452823	+	0.891601i	$0.350417\pi$
$3$	8.24621	1.58698	0.793492	−	0.608581i	$-0.208261\pi$
$3$	8.24621	1.58698	0.793492	+	0.608581i	$0.208261\pi$
$4$	−1.43845	−0.179806
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	21.1231	1.43725
$7$	24.8769	1.34323	0.671613	−	0.740902i	$-0.265602\pi$
$7$	24.8769	1.34323	0.671613	+	0.740902i	$0.265602\pi$
$8$	−24.1771	−1.06849
$9$	41.0000	1.51852
$10$	−12.8078	−0.405017
$11$	−38.8769	−1.06562	−0.532810	−	0.846235i	$-0.678864\pi$
$11$	−38.8769	−1.06562	−0.532810	+	0.846235i	$0.678864\pi$
$12$	−11.8617	−0.285349
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	63.7235	1.21649
$15$	−41.2311	−0.709721
$16$	−50.4233	−0.787864
$17$	−79.9697	−1.14091	−0.570456	−	0.821328i	$-0.693233\pi$
$17$	−79.9697	−1.14091	−0.570456	+	0.821328i	$0.693233\pi$
$18$	105.024	1.37524
$19$	128.354	1.54981	0.774907	−	0.632075i	$-0.217797\pi$
$19$	128.354	1.54981	0.774907	+	0.632075i	$0.217797\pi$
$20$	7.19224	0.0804116
$21$	205.140	2.13168
$22$	−99.5852	−0.965075
$23$	−101.939	−0.924167	−0.462083	−	0.886837i	$-0.652898\pi$
$23$	−101.939	−0.924167	−0.462083	+	0.886837i	$0.652898\pi$
$24$	−199.369	−1.69567
$25$	25.0000	0.200000
$26$	−33.3002	−0.251181
$27$	115.447	0.822881
$28$	−35.7841	−0.241520
$29$	117.723	0.753817	0.376909	−	0.926250i	$-0.376987\pi$
$29$	117.723	0.753817	0.376909	+	0.926250i	$0.376987\pi$
$30$	−105.616	−0.642756
$31$	−298.756	−1.73091	−0.865453	−	0.500990i	$-0.832969\pi$
$31$	−298.756	−1.73091	−0.865453	+	0.500990i	$0.832969\pi$
$32$	64.2547	0.354961
$33$	−320.587	−1.69112
$34$	−204.847	−1.03326
$35$	−124.384	−0.600709
$36$	−58.9763	−0.273039
$37$	254.216	1.12954	0.564768	−	0.825250i	$-0.308966\pi$
$37$	254.216	1.12954	0.564768	+	0.825250i	$0.308966\pi$
$38$	328.786	1.40358
$39$	−107.201	−0.440150
$40$	120.885	0.477842
$41$	219.633	0.836606	0.418303	−	0.908308i	$-0.362625\pi$
$41$	219.633	0.836606	0.418303	+	0.908308i	$0.362625\pi$
$42$	525.477	1.93055
$43$	−104.462	−0.370473	−0.185236	−	0.982694i	$-0.559305\pi$
$43$	−104.462	−0.370473	−0.185236	+	0.982694i	$0.559305\pi$
$44$	55.9224	0.191605
$45$	−205.000	−0.679102
$46$	−261.123	−0.836967
$47$	308.816	0.958415	0.479207	−	0.877702i	$-0.340924\pi$
$47$	308.816	0.958415	0.479207	+	0.877702i	$0.340924\pi$
$48$	−415.801	−1.25033
$49$	275.860	0.804256
$50$	64.0388	0.181129
$51$	−659.447	−1.81061
$52$	18.6998	0.0498692
$53$	−0.0909300	−0.000235664 0	−0.000117832	−	1.00000i	$-0.500038\pi$
$53$	−0.0909300	−0.000235664 0	−0.000117832		1.00000i	$0.500038\pi$
$54$	295.723	0.745238
$55$	194.384	0.476560
$56$	−601.451	−1.43522
$57$	1058.44	2.45953
$58$	301.555	0.682691
$59$	−349.710	−0.771668	−0.385834	−	0.922568i	$-0.626086\pi$
$59$	−349.710	−0.771668	−0.385834	+	0.922568i	$0.626086\pi$
$60$	59.3087	0.127612
$61$	442.000	0.927743	0.463871	−	0.885903i	$-0.346460\pi$
$61$	442.000	0.927743	0.463871	+	0.885903i	$0.346460\pi$
$62$	−765.278	−1.56759
$63$	1019.95	2.03971
$64$	567.978	1.10933
$65$	65.0000	0.124035
$66$	−821.201	−1.53156
$67$	228.074	0.415876	0.207938	−	0.978142i	$-0.433325\pi$
$67$	228.074	0.415876	0.207938	+	0.978142i	$0.433325\pi$
$68$	115.032	0.205143
$69$	−840.614	−1.46664
$70$	−318.617	−0.544029
$71$	964.328	1.61190	0.805948	−	0.591986i	$-0.201656\pi$
$71$	964.328	1.61190	0.805948	+	0.591986i	$0.201656\pi$
$72$	−991.260	−1.62252
$73$	662.682	1.06248	0.531240	−	0.847221i	$-0.321726\pi$
$73$	662.682	1.06248	0.531240	+	0.847221i	$0.321726\pi$
$74$	651.187	1.02296
$75$	206.155	0.317397
$76$	−184.631	−0.278666
$77$	−967.136	−1.43137
$78$	−274.600	−0.398620
$79$	−65.2614	−0.0929428	−0.0464714	−	0.998920i	$-0.514798\pi$
$79$	−65.2614	−0.0929428	−0.0464714	+	0.998920i	$0.514798\pi$
$80$	252.116	0.352343
$81$	−155.000	−0.212620
$82$	562.600	0.757669
$83$	−92.4185	−0.122220	−0.0611099	−	0.998131i	$-0.519464\pi$
$83$	−92.4185	−0.122220	−0.0611099	+	0.998131i	$0.519464\pi$
$84$	−295.083	−0.383288
$85$	399.848	0.510231
$86$	−267.585	−0.335517
$87$	970.773	1.19630
$88$	939.930	1.13860
$89$	−178.614	−0.212730	−0.106365	−	0.994327i	$-0.533921\pi$
$89$	−178.614	−0.212730	−0.106365	+	0.994327i	$0.533921\pi$
$90$	−525.118	−0.615026
$91$	−323.400	−0.372544
$92$	146.634	0.166171
$93$	−2463.60	−2.74692
$94$	791.049	0.867984
$95$	−641.771	−0.693098
$96$	529.858	0.563317
$97$	−1707.46	−1.78728	−0.893640	−	0.448785i	$-0.851857\pi$
$97$	−1707.46	−1.78728	−0.893640	+	0.448785i	$0.851857\pi$
$98$	706.630	0.728371
$99$	−1593.95	−1.61816
$100$	−35.9612	−0.0359612
$101$	−1364.04	−1.34383	−0.671915	−	0.740628i	$-0.734528\pi$
$101$	−1364.04	−1.34383	−0.671915	+	0.740628i	$0.734528\pi$
$102$	−1689.21	−1.63977
$103$	355.167	0.339763	0.169882	−	0.985464i	$-0.445661\pi$
$103$	355.167	0.339763	0.169882	+	0.985464i	$0.445661\pi$
$104$	314.302	0.296345
$105$	−1025.70	−0.953316
$106$	−0.232922	−0.000213428 0
$107$	325.905	0.294453	0.147226	−	0.989103i	$-0.452965\pi$
$107$	325.905	0.294453	0.147226	+	0.989103i	$0.452965\pi$
$108$	−166.064	−0.147959
$109$	1738.93	1.52807	0.764034	−	0.645176i	$-0.223216\pi$
$109$	1738.93	1.52807	0.764034	+	0.645176i	$0.223216\pi$
$110$	497.926	0.431594
$111$	2096.32	1.79256
$112$	−1254.37	−1.05828
$113$	−1628.89	−1.35605	−0.678024	−	0.735040i	$-0.737164\pi$
$113$	−1628.89	−1.35605	−0.678024	+	0.735040i	$0.737164\pi$
$114$	2711.24	2.22746
$115$	509.697	0.413300
$116$	−169.339	−0.135541
$117$	−533.000	−0.421161
$118$	−895.801	−0.698857
$119$	−1989.40	−1.53250
$120$	996.847	0.758327
$121$	180.413	0.135547
$122$	1132.21	0.840206
$123$	1811.14	1.32768
$124$	429.744	0.311227
$125$	−125.000	−0.0894427
$126$	2612.66	1.84726
$127$	165.333	0.115519	0.0577596	−	0.998331i	$-0.481604\pi$
$127$	165.333	0.115519	0.0577596	+	0.998331i	$0.481604\pi$
$128$	940.868	0.649702
$129$	−861.417	−0.587934
$130$	166.501	0.112332
$131$	−1867.49	−1.24552	−0.622760	−	0.782413i	$-0.713989\pi$
$131$	−1867.49	−1.24552	−0.622760	+	0.782413i	$0.713989\pi$
$132$	461.148	0.304074
$133$	3193.05	2.08175
$134$	584.223	0.376636
$135$	−577.235	−0.368003
$136$	1933.43	1.21905
$137$	1740.80	1.08560	0.542798	−	0.839864i	$-0.317365\pi$
$137$	1740.80	1.08560	0.542798	+	0.839864i	$0.317365\pi$
$138$	−2153.28	−1.32825
$139$	−985.511	−0.601367	−0.300683	−	0.953724i	$-0.597215\pi$
$139$	−985.511	−0.601367	−0.300683	+	0.953724i	$0.597215\pi$
$140$	178.920	0.108011
$141$	2546.56	1.52099
$142$	2470.18	1.45981
$143$	505.400	0.295550
$144$	−2067.35	−1.19639
$145$	−588.617	−0.337117
$146$	1697.49	0.962230
$147$	2274.80	1.27634
$148$	−365.676	−0.203097
$149$	−2496.90	−1.37285	−0.686423	−	0.727202i	$-0.740820\pi$
$149$	−2496.90	−1.37285	−0.686423	+	0.727202i	$0.740820\pi$
$150$	528.078	0.287449
$151$	357.710	0.192782	0.0963909	−	0.995344i	$-0.469270\pi$
$151$	357.710	0.192782	0.0963909	+	0.995344i	$0.469270\pi$
$152$	−3103.23	−1.65595
$153$	−3278.76	−1.73250
$154$	−2477.37	−1.29631
$155$	1493.78	0.774085
$156$	154.203	0.0791416
$157$	−3218.32	−1.63599	−0.817993	−	0.575228i	$-0.804913\pi$
$157$	−3218.32	−1.63599	−0.817993	+	0.575228i	$0.804913\pi$
$158$	−167.170	−0.0841732
$159$	−0.749828	−0.000373995 0
$160$	−321.274	−0.158743
$161$	−2535.94	−1.24136
$162$	−397.041	−0.192558
$163$	−2901.51	−1.39425	−0.697127	−	0.716948i	$-0.745539\pi$
$163$	−2901.51	−1.39425	−0.697127	+	0.716948i	$0.745539\pi$
$164$	−315.930	−0.150427
$165$	1602.94	0.756293
$166$	−236.735	−0.110688
$167$	531.036	0.246065	0.123032	−	0.992403i	$-0.460738\pi$
$167$	531.036	0.246065	0.123032	+	0.992403i	$0.460738\pi$
$168$	−4959.69	−2.27767
$169$	169.000	0.0769231
$170$	1024.23	0.462089
$171$	5262.52	2.35342
$172$	150.263	0.0666132
$173$	809.826	0.355895	0.177948	−	0.984040i	$-0.443054\pi$
$173$	809.826	0.355895	0.177948	+	0.984040i	$0.443054\pi$
$174$	2486.69	1.08342
$175$	621.922	0.268645
$176$	1960.30	0.839564
$177$	−2883.78	−1.22462
$178$	−457.528	−0.192658
$179$	−1831.87	−0.764919	−0.382459	−	0.923972i	$-0.624923\pi$
$179$	−1831.87	−0.764919	−0.382459	+	0.923972i	$0.624923\pi$
$180$	294.882	0.122107
$181$	1046.76	0.429863	0.214931	−	0.976629i	$-0.431047\pi$
$181$	1046.76	0.429863	0.214931	+	0.976629i	$0.431047\pi$
$182$	−828.405	−0.337393
$183$	3644.83	1.47231
$184$	2464.60	0.987459
$185$	−1271.08	−0.505144
$186$	−6310.65	−2.48774
$187$	3108.97	1.21578
$188$	−444.216	−0.172329
$189$	2871.96	1.10531
$190$	−1643.93	−0.627701
$191$	759.973	0.287904	0.143952	−	0.989585i	$-0.454019\pi$
$191$	759.973	0.287904	0.143952	+	0.989585i	$0.454019\pi$
$192$	4683.67	1.76049
$193$	−411.618	−0.153518	−0.0767588	−	0.997050i	$-0.524457\pi$
$193$	−411.618	−0.153518	−0.0767588	+	0.997050i	$0.524457\pi$
$194$	−4373.74	−1.61864
$195$	536.004	0.196841
$196$	−396.810	−0.144610
$197$	−805.204	−0.291210	−0.145605	−	0.989343i	$-0.546513\pi$
$197$	−805.204	−0.291210	−0.145605	+	0.989343i	$0.546513\pi$
$198$	−4082.99	−1.46548
$199$	2932.02	1.04445	0.522225	−	0.852808i	$-0.325102\pi$
$199$	2932.02	1.04445	0.522225	+	0.852808i	$0.325102\pi$
$200$	−604.427	−0.213697
$201$	1880.75	0.659988
$202$	−3494.05	−1.21703
$203$	2928.59	1.01255
$204$	948.580	0.325558
$205$	−1098.16	−0.374142
$206$	909.778	0.307705
$207$	−4179.51	−1.40336
$208$	655.503	0.218514
$209$	−4990.01	−1.65151
$210$	−2627.39	−0.863366
$211$	−3922.57	−1.27982	−0.639908	−	0.768452i	$-0.721027\pi$
$211$	−3922.57	−1.27982	−0.639908	+	0.768452i	$0.721027\pi$
$212$	0.130798	4.23738e−5 0
$213$	7952.05	2.55805
$214$	834.824	0.266670
$215$	522.311	0.165680
$216$	−2791.17	−0.879237
$217$	−7432.11	−2.32500
$218$	4454.37	1.38389
$219$	5464.61	1.68614
$220$	−279.612	−0.0856883
$221$	1039.61	0.316432
$222$	5369.83	1.62342
$223$	6115.27	1.83636	0.918181	−	0.396162i	$-0.129658\pi$
$223$	6115.27	1.83636	0.918181	+	0.396162i	$0.129658\pi$
$224$	1598.46	0.476792
$225$	1025.00	0.303704
$226$	−4172.50	−1.22810
$227$	4216.13	1.23275	0.616376	−	0.787452i	$-0.288600\pi$
$227$	4216.13	1.23275	0.616376	+	0.787452i	$0.288600\pi$
$228$	−1522.50	−0.442238
$229$	−299.451	−0.0864116	−0.0432058	−	0.999066i	$-0.513757\pi$
$229$	−299.451	−0.0864116	−0.0432058	+	0.999066i	$0.513757\pi$
$230$	1305.62	0.374303
$231$	−7975.21	−2.27156
$232$	−2846.21	−0.805443
$233$	1223.17	0.343916	0.171958	−	0.985104i	$-0.444991\pi$
$233$	1223.17	0.343916	0.171958	+	0.985104i	$0.444991\pi$
$234$	−1365.31	−0.381423
$235$	−1544.08	−0.428616
$236$	503.040	0.138750
$237$	−538.159	−0.147499
$238$	−5095.95	−1.38790
$239$	−48.7253	−0.0131874	−0.00659368	−	0.999978i	$-0.502099\pi$
$239$	−48.7253	−0.0131874	−0.00659368	+	0.999978i	$0.502099\pi$
$240$	2079.01	0.559163
$241$	−4499.83	−1.20274	−0.601368	−	0.798972i	$-0.705378\pi$
$241$	−4499.83	−1.20274	−0.601368	+	0.798972i	$0.705378\pi$
$242$	462.137	0.122757
$243$	−4395.23	−1.16031
$244$	−635.794	−0.166814
$245$	−1379.30	−0.359674
$246$	4639.32	1.20241
$247$	−1668.60	−0.429841
$248$	7223.04	1.84945
$249$	−762.103	−0.193961
$250$	−320.194	−0.0810034
$251$	−110.288	−0.0277343	−0.0138671	−	0.999904i	$-0.504414\pi$
$251$	−110.288	−0.0277343	−0.0138671	+	0.999904i	$0.504414\pi$
$252$	−1467.15	−0.366753
$253$	3963.09	0.984811
$254$	423.510	0.104620
$255$	3297.23	0.809729
$256$	−2133.74	−0.520933
$257$	7453.76	1.80916	0.904578	−	0.426308i	$-0.140186\pi$
$257$	7453.76	1.80916	0.904578	+	0.426308i	$0.140186\pi$
$258$	−2206.56	−0.532460
$259$	6324.10	1.51722
$260$	−93.4991	−0.0223022
$261$	4826.66	1.14469
$262$	−4783.67	−1.12800
$263$	−225.156	−0.0527897	−0.0263948	−	0.999652i	$-0.508403\pi$
$263$	−225.156	−0.0527897	−0.0263948	+	0.999652i	$0.508403\pi$
$264$	7750.86	1.80694
$265$	0.454650	0.000105392 0
$266$	8179.17	1.88533
$267$	−1472.89	−0.337600
$268$	−328.072	−0.0747769
$269$	−2742.09	−0.621517	−0.310758	−	0.950489i	$-0.600583\pi$
$269$	−2742.09	−0.621517	−0.310758	+	0.950489i	$0.600583\pi$
$270$	−1478.62	−0.333281
$271$	6749.69	1.51297	0.756484	−	0.654012i	$-0.226916\pi$
$271$	6749.69	1.51297	0.756484	+	0.654012i	$0.226916\pi$
$272$	4032.34	0.898883
$273$	−2666.82	−0.591221
$274$	4459.15	0.983164
$275$	−971.922	−0.213124
$276$	1209.18	0.263710
$277$	1511.65	0.327893	0.163946	−	0.986469i	$-0.447578\pi$
$277$	1511.65	0.327893	0.163946	+	0.986469i	$0.447578\pi$
$278$	−2524.44	−0.544625
$279$	−12249.0	−2.62841
$280$	3007.25	0.641849
$281$	−5593.69	−1.18751	−0.593757	−	0.804645i	$-0.702356\pi$
$281$	−5593.69	−1.18751	−0.593757	+	0.804645i	$0.702356\pi$
$282$	6523.16	1.37748
$283$	−3221.02	−0.676572	−0.338286	−	0.941043i	$-0.609847\pi$
$283$	−3221.02	−0.676572	−0.338286	+	0.941043i	$0.609847\pi$
$284$	−1387.13	−0.289828
$285$	−5292.18	−1.09994
$286$	1294.61	0.267664
$287$	5463.78	1.12375
$288$	2634.44	0.539014
$289$	1482.15	0.301679
$290$	−1507.77	−0.305309
$291$	−14080.1	−2.83638
$292$	−953.233	−0.191040
$293$	7809.84	1.55719	0.778594	−	0.627528i	$-0.215933\pi$
$293$	7809.84	1.55719	0.778594	+	0.627528i	$0.215933\pi$
$294$	5827.02	1.15591
$295$	1748.55	0.345100
$296$	−6146.20	−1.20689
$297$	−4488.22	−0.876878
$298$	−6395.94	−1.24331
$299$	1325.21	0.256318
$300$	−296.543	−0.0570698
$301$	−2598.69	−0.497628
$302$	916.294	0.174592
$303$	−11248.1	−2.13264
$304$	−6472.04	−1.22104
$305$	−2210.00	−0.414899
$306$	−8398.71	−1.56903
$307$	8581.07	1.59527	0.797634	−	0.603141i	$-0.206084\pi$
$307$	8581.07	1.59527	0.797634	+	0.603141i	$0.206084\pi$
$308$	1391.17	0.257369
$309$	2928.78	0.539199
$310$	3826.39	0.701047
$311$	9251.84	1.68689	0.843447	−	0.537213i	$-0.180523\pi$
$311$	9251.84	1.68689	0.843447	+	0.537213i	$0.180523\pi$
$312$	2591.80	0.470294
$313$	4386.17	0.792081	0.396040	−	0.918233i	$-0.370384\pi$
$313$	4386.17	0.792081	0.396040	+	0.918233i	$0.370384\pi$
$314$	−8243.89	−1.48162
$315$	−5099.76	−0.912188
$316$	93.8750	0.0167117
$317$	−587.686	−0.104125	−0.0520626	−	0.998644i	$-0.516580\pi$
$317$	−587.686	−0.104125	−0.0520626	+	0.998644i	$0.516580\pi$
$318$	−1.92072	−0.000338707 0
$319$	−4576.72	−0.803283
$320$	−2839.89	−0.496109
$321$	2687.48	0.467292
$322$	−6495.93	−1.12424
$323$	−10264.4	−1.76820
$324$	222.959	0.0382303
$325$	−325.000	−0.0554700
$326$	−7432.36	−1.26270
$327$	14339.6	2.42502
$328$	−5310.07	−0.893902
$329$	7682.39	1.28737
$330$	4106.00	0.684934
$331$	−6559.71	−1.08929	−0.544644	−	0.838668i	$-0.683335\pi$
$331$	−6559.71	−1.08929	−0.544644	+	0.838668i	$0.683335\pi$
$332$	132.939	0.0219759
$333$	10422.9	1.71522
$334$	1360.28	0.222847
$335$	−1140.37	−0.185985
$336$	−10343.8	−1.67947
$337$	3316.98	0.536165	0.268083	−	0.963396i	$-0.413610\pi$
$337$	3316.98	0.536165	0.268083	+	0.963396i	$0.413610\pi$
$338$	432.902	0.0696651
$339$	−13432.2	−2.15203
$340$	−575.161	−0.0917426
$341$	11614.7	1.84449
$342$	13480.2	2.13137
$343$	−1670.24	−0.262928
$344$	2525.59	0.395845
$345$	4203.07	0.655900
$346$	2074.41	0.322315
$347$	−3729.06	−0.576906	−0.288453	−	0.957494i	$-0.593141\pi$
$347$	−3729.06	−0.576906	−0.288453	+	0.957494i	$0.593141\pi$
$348$	−1396.41	−0.215101
$349$	3748.22	0.574892	0.287446	−	0.957797i	$-0.407194\pi$
$349$	3748.22	0.574892	0.287446	+	0.957797i	$0.407194\pi$
$350$	1593.09	0.243297
$351$	−1500.81	−0.228226
$352$	−2498.02	−0.378253
$353$	−3353.90	−0.505694	−0.252847	−	0.967506i	$-0.581367\pi$
$353$	−3353.90	−0.505694	−0.252847	+	0.967506i	$0.581367\pi$
$354$	−7386.97	−1.10908
$355$	−4821.64	−0.720862
$356$	256.926	0.0382502
$357$	−16405.0	−2.43206
$358$	−4692.44	−0.692746
$359$	−1041.87	−0.153169	−0.0765843	−	0.997063i	$-0.524401\pi$
$359$	−1041.87	−0.153169	−0.0765843	+	0.997063i	$0.524401\pi$
$360$	4956.30	0.725611
$361$	9615.79	1.40192
$362$	2681.33	0.389303
$363$	1487.72	0.215111
$364$	465.193	0.0669856
$365$	−3313.41	−0.475155
$366$	9336.41	1.33339
$367$	1099.95	0.156449	0.0782247	−	0.996936i	$-0.475075\pi$
$367$	1099.95	0.156449	0.0782247	+	0.996936i	$0.475075\pi$
$368$	5140.12	0.728117
$369$	9004.93	1.27040
$370$	−3255.94	−0.457481
$371$	−2.26206	−0.000316550 0
$372$	3543.76	0.493913
$373$	2967.14	0.411884	0.205942	−	0.978564i	$-0.433974\pi$
$373$	2967.14	0.411884	0.205942	+	0.978564i	$0.433974\pi$
$374$	7963.80	1.10106
$375$	−1030.78	−0.141944
$376$	−7466.28	−1.02405
$377$	−1530.41	−0.209071
$378$	7356.68	1.00102
$379$	−9221.67	−1.24983	−0.624915	−	0.780693i	$-0.714866\pi$
$379$	−9221.67	−1.24983	−0.624915	+	0.780693i	$0.714866\pi$
$380$	923.153	0.124623
$381$	1363.37	0.183327
$382$	1946.71	0.260739
$383$	−11048.0	−1.47395	−0.736976	−	0.675918i	$-0.763747\pi$
$383$	−11048.0	−1.47395	−0.736976	+	0.675918i	$0.763747\pi$
$384$	7758.60	1.03107
$385$	4835.68	0.640128
$386$	−1054.38	−0.139032
$387$	−4282.95	−0.562570
$388$	2456.09	0.321363
$389$	−201.382	−0.0262480	−0.0131240	−	0.999914i	$-0.504178\pi$
$389$	−201.382	−0.0262480	−0.0131240	+	0.999914i	$0.504178\pi$
$390$	1373.00	0.178268
$391$	8152.06	1.05439
$392$	−6669.49	−0.859337
$393$	−15399.7	−1.97662
$394$	−2062.57	−0.263733
$395$	326.307	0.0415653
$396$	2292.82	0.290955
$397$	−4354.09	−0.550443	−0.275221	−	0.961381i	$-0.588751\pi$
$397$	−4354.09	−0.550443	−0.275221	+	0.961381i	$0.588751\pi$
$398$	7510.53	0.945902
$399$	26330.6	3.30370
$400$	−1260.58	−0.157573
$401$	4241.31	0.528182	0.264091	−	0.964498i	$-0.414928\pi$
$401$	4241.31	0.528182	0.264091	+	0.964498i	$0.414928\pi$
$402$	4817.63	0.597715
$403$	3883.82	0.480067
$404$	1962.10	0.241629
$405$	775.000	0.0950866
$406$	7501.75	0.917009
$407$	−9883.12	−1.20366
$408$	15943.5	1.93461
$409$	−1622.25	−0.196124	−0.0980622	−	0.995180i	$-0.531264\pi$
$409$	−1622.25	−0.196124	−0.0980622	+	0.995180i	$0.531264\pi$
$410$	−2813.00	−0.338840
$411$	14355.0	1.72282
$412$	−510.889	−0.0610914
$413$	−8699.70	−1.03652
$414$	−10706.0	−1.27095
$415$	462.093	0.0546584
$416$	−835.311	−0.0984483
$417$	−8126.73	−0.954359
$418$	−12782.2	−1.49569
$419$	−6344.39	−0.739723	−0.369861	−	0.929087i	$-0.620595\pi$
$419$	−6344.39	−0.739723	−0.369861	+	0.929087i	$0.620595\pi$
$420$	1475.42	0.171412
$421$	−7050.55	−0.816206	−0.408103	−	0.912936i	$-0.633810\pi$
$421$	−7050.55	−0.816206	−0.408103	+	0.912936i	$0.633810\pi$
$422$	−10047.9	−1.15906
$423$	12661.5	1.45537
$424$	2.19842	0.000251804 0
$425$	−1999.24	−0.228182
$426$	20369.6	2.31669
$427$	10995.6	1.24617
$428$	−468.798	−0.0529444
$429$	4167.63	0.469033
$430$	1337.93	0.150048
$431$	−2749.74	−0.307309	−0.153655	−	0.988125i	$-0.549104\pi$
$431$	−2749.74	−0.307309	−0.153655	+	0.988125i	$0.549104\pi$
$432$	−5821.22	−0.648318
$433$	−12718.7	−1.41160	−0.705798	−	0.708413i	$-0.749411\pi$
$433$	−12718.7	−1.41160	−0.705798	+	0.708413i	$0.749411\pi$
$434$	−19037.7	−2.10562
$435$	−4853.86	−0.535000
$436$	−2501.36	−0.274756
$437$	−13084.3	−1.43229
$438$	13997.9	1.52704
$439$	17656.7	1.91961	0.959807	−	0.280660i	$-0.0905535\pi$
$439$	17656.7	1.91961	0.959807	+	0.280660i	$0.0905535\pi$
$440$	−4699.65	−0.509198
$441$	11310.3	1.22128
$442$	2663.01	0.286575
$443$	18355.7	1.96864	0.984319	−	0.176397i	$-0.0564444\pi$
$443$	18355.7	1.96864	0.984319	+	0.176397i	$0.0564444\pi$
$444$	−3015.44	−0.322312
$445$	893.068	0.0951360
$446$	15664.6	1.66309
$447$	−20590.0	−2.17869
$448$	14129.5	1.49008
$449$	−2675.78	−0.281242	−0.140621	−	0.990063i	$-0.544910\pi$
$449$	−2675.78	−0.281242	−0.140621	+	0.990063i	$0.544910\pi$
$450$	2625.59	0.275048
$451$	−8538.63	−0.891504
$452$	2343.08	0.243825
$453$	2949.75	0.305942
$454$	10799.9	1.11644
$455$	1617.00	0.166607
$456$	−25589.9	−2.62797
$457$	6114.51	0.625875	0.312937	−	0.949774i	$-0.398687\pi$
$457$	6114.51	0.625875	0.312937	+	0.949774i	$0.398687\pi$
$458$	−767.059	−0.0782583
$459$	−9232.26	−0.938834
$460$	−733.172	−0.0743137
$461$	−13983.6	−1.41275	−0.706377	−	0.707836i	$-0.749671\pi$
$461$	−13983.6	−1.41275	−0.706377	+	0.707836i	$0.749671\pi$
$462$	−20428.9	−2.05723
$463$	−5068.98	−0.508802	−0.254401	−	0.967099i	$-0.581878\pi$
$463$	−5068.98	−0.508802	−0.254401	+	0.967099i	$0.581878\pi$
$464$	−5936.01	−0.593905
$465$	12318.0	1.22846
$466$	3133.21	0.311466
$467$	2449.21	0.242689	0.121345	−	0.992610i	$-0.461279\pi$
$467$	2449.21	0.242689	0.121345	+	0.992610i	$0.461279\pi$
$468$	766.692	0.0757273
$469$	5673.77	0.558615
$470$	−3955.25	−0.388174
$471$	−26538.9	−2.59628
$472$	8454.97	0.824516
$473$	4061.16	0.394783
$474$	−1378.52	−0.133582
$475$	3208.85	0.309963
$476$	2861.64	0.275553
$477$	−3.72813	−0.000357860 0
$478$	−124.813	−0.0119431
$479$	−14106.1	−1.34556	−0.672780	−	0.739842i	$-0.734900\pi$
$479$	−14106.1	−1.34556	−0.672780	+	0.739842i	$0.734900\pi$
$480$	−2649.29	−0.251923
$481$	−3304.81	−0.313277
$482$	−11526.6	−1.08925
$483$	−20911.9	−1.97003
$484$	−259.514	−0.0243721
$485$	8537.29	0.799296
$486$	−11258.6	−1.05083
$487$	11324.4	1.05371	0.526855	−	0.849955i	$-0.323371\pi$
$487$	11324.4	1.05371	0.526855	+	0.849955i	$0.323371\pi$
$488$	−10686.3	−0.991280
$489$	−23926.4	−2.21266
$490$	−3533.15	−0.325737
$491$	−11824.8	−1.08686	−0.543430	−	0.839455i	$-0.682875\pi$
$491$	−11824.8	−1.08686	−0.543430	+	0.839455i	$0.682875\pi$
$492$	−2605.22	−0.238725
$493$	−9414.31	−0.860039
$494$	−4274.22	−0.389284
$495$	7969.76	0.723665
$496$	15064.2	1.36372
$497$	23989.5	2.16514
$498$	−1952.17	−0.175660
$499$	11462.3	1.02830	0.514150	−	0.857700i	$-0.328108\pi$
$499$	11462.3	1.02830	0.514150	+	0.857700i	$0.328108\pi$
$500$	179.806	0.0160823
$501$	4379.03	0.390501
$502$	−282.508	−0.0251174
$503$	−13165.2	−1.16701	−0.583506	−	0.812109i	$-0.698320\pi$
$503$	−13165.2	−1.16701	−0.583506	+	0.812109i	$0.698320\pi$
$504$	−24659.5	−2.17941
$505$	6820.19	0.600979
$506$	10151.7	0.891890
$507$	1393.61	0.122076
$508$	−237.823	−0.0207710
$509$	8849.94	0.770661	0.385331	−	0.922779i	$-0.374087\pi$
$509$	8849.94	0.770661	0.385331	+	0.922779i	$0.374087\pi$
$510$	8446.04	0.733327
$511$	16485.5	1.42715
$512$	−12992.6	−1.12148
$513$	14818.1	1.27531
$514$	19093.2	1.63845
$515$	−1775.83	−0.151947
$516$	1239.10	0.105714
$517$	−12005.8	−1.02131
$518$	16199.5	1.37407
$519$	6677.99	0.564800
$520$	−1571.51	−0.132529
$521$	20509.2	1.72461	0.862306	−	0.506387i	$-0.169019\pi$
$521$	20509.2	1.72461	0.862306	+	0.506387i	$0.169019\pi$
$522$	12363.8	1.03668
$523$	434.056	0.0362906	0.0181453	−	0.999835i	$-0.494224\pi$
$523$	434.056	0.0362906	0.0181453	+	0.999835i	$0.494224\pi$
$524$	2686.28	0.223952
$525$	5128.50	0.426336
$526$	−576.748	−0.0478087
$527$	23891.4	1.97481
$528$	16165.1	1.33237
$529$	−1775.36	−0.145916
$530$	1.16461	9.54479e−5 0
$531$	−14338.1	−1.17179
$532$	−4593.04	−0.374311
$533$	−2855.22	−0.232033
$534$	−3772.88	−0.305746
$535$	−1629.53	−0.131683
$536$	−5514.16	−0.444357
$537$	−15106.0	−1.21391
$538$	−7024.00	−0.562874
$539$	−10724.6	−0.857032
$540$	830.322	0.0661692
$541$	−5500.16	−0.437099	−0.218549	−	0.975826i	$-0.570132\pi$
$541$	−5500.16	−0.437099	−0.218549	+	0.975826i	$0.570132\pi$
$542$	17289.7	1.37021
$543$	8631.82	0.682185
$544$	−5138.43	−0.404979
$545$	−8694.66	−0.683373
$546$	−6831.20	−0.535437
$547$	8536.10	0.667235	0.333617	−	0.942709i	$-0.391731\pi$
$547$	8536.10	0.667235	0.333617	+	0.942709i	$0.391731\pi$
$548$	−2504.05	−0.195196
$549$	18122.0	1.40879
$550$	−2489.63	−0.193015
$551$	15110.3	1.16828
$552$	20323.6	1.56708
$553$	−1623.50	−0.124843
$554$	3872.18	0.296955
$555$	−10481.6	−0.801655
$556$	1417.61	0.108129
$557$	−4701.29	−0.357630	−0.178815	−	0.983883i	$-0.557226\pi$
$557$	−4701.29	−0.357630	−0.178815	+	0.983883i	$0.557226\pi$
$558$	−31376.4	−2.38041
$559$	1358.01	0.102751
$560$	6271.87	0.473277
$561$	25637.2	1.92942
$562$	−14328.5	−1.07547
$563$	14613.9	1.09396	0.546981	−	0.837145i	$-0.315777\pi$
$563$	14613.9	1.09396	0.546981	+	0.837145i	$0.315777\pi$
$564$	−3663.10	−0.273483
$565$	8144.47	0.606443
$566$	−8250.82	−0.612735
$567$	−3855.92	−0.285597
$568$	−23314.6	−1.72229
$569$	−10789.3	−0.794921	−0.397461	−	0.917619i	$-0.630108\pi$
$569$	−10789.3	−0.794921	−0.397461	+	0.917619i	$0.630108\pi$
$570$	−13556.2	−0.996152
$571$	−1553.39	−0.113848	−0.0569240	−	0.998379i	$-0.518129\pi$
$571$	−1553.39	−0.113848	−0.0569240	+	0.998379i	$0.518129\pi$
$572$	−726.991	−0.0531416
$573$	6266.90	0.456900
$574$	13995.8	1.01772
$575$	−2548.48	−0.184833
$576$	23287.1	1.68454
$577$	11828.6	0.853431	0.426715	−	0.904386i	$-0.359671\pi$
$577$	11828.6	0.853431	0.426715	+	0.904386i	$0.359671\pi$
$578$	3796.61	0.273215
$579$	−3394.29	−0.243630
$580$	846.695	0.0606157
$581$	−2299.09	−0.164169
$582$	−36066.8	−2.56876
$583$	3.53507	0.000251128 0
$584$	−16021.7	−1.13525
$585$	2665.00	0.188349
$586$	20005.3	1.41026
$587$	2823.97	0.198565	0.0992825	−	0.995059i	$-0.468345\pi$
$587$	2823.97	0.198565	0.0992825	+	0.995059i	$0.468345\pi$
$588$	−3272.18	−0.229494
$589$	−38346.5	−2.68258
$590$	4479.01	0.312539
$591$	−6639.89	−0.462146
$592$	−12818.4	−0.889921
$593$	2016.22	0.139623	0.0698115	−	0.997560i	$-0.477760\pi$
$593$	2016.22	0.139623	0.0698115	+	0.997560i	$0.477760\pi$
$594$	−11496.8	−0.794141
$595$	9946.99	0.685356
$596$	3591.66	0.246846
$597$	24178.1	1.65753
$598$	3394.60	0.232133
$599$	9247.60	0.630796	0.315398	−	0.948960i	$-0.397862\pi$
$599$	9247.60	0.630796	0.315398	+	0.948960i	$0.397862\pi$
$600$	−4984.23	−0.339134
$601$	8105.84	0.550156	0.275078	−	0.961422i	$-0.411296\pi$
$601$	8105.84	0.550156	0.275078	+	0.961422i	$0.411296\pi$
$602$	−6656.69	−0.450675
$603$	9351.03	0.631515
$604$	−514.547	−0.0346633
$605$	−902.065	−0.0606184
$606$	−28812.7	−1.93141
$607$	11059.6	0.739534	0.369767	−	0.929124i	$-0.379437\pi$
$607$	11059.6	0.739534	0.369767	+	0.929124i	$0.379437\pi$
$608$	8247.36	0.550123
$609$	24149.8	1.60690
$610$	−5661.03	−0.375752
$611$	−4014.61	−0.265816
$612$	4716.32	0.311513
$613$	−12579.3	−0.828831	−0.414416	−	0.910088i	$-0.636014\pi$
$613$	−12579.3	−0.828831	−0.414416	+	0.910088i	$0.636014\pi$
$614$	21980.9	1.44475
$615$	−9055.68	−0.593757
$616$	23382.5	1.52940
$617$	16915.6	1.10372	0.551862	−	0.833935i	$-0.313917\pi$
$617$	16915.6	1.10372	0.551862	+	0.833935i	$0.313917\pi$
$618$	7502.22	0.488323
$619$	10313.7	0.669697	0.334849	−	0.942272i	$-0.391315\pi$
$619$	10313.7	0.669697	0.334849	+	0.942272i	$0.391315\pi$
$620$	−2148.72	−0.139185
$621$	−11768.6	−0.760479
$622$	23699.1	1.52773
$623$	−4443.35	−0.285745
$624$	5405.41	0.346778
$625$	625.000	0.0400000
$626$	11235.4	0.717344
$627$	−41148.7	−2.62093
$628$	4629.38	0.294160
$629$	−20329.6	−1.28870
$630$	−13063.3	−0.826119
$631$	−20558.9	−1.29705	−0.648524	−	0.761194i	$-0.724613\pi$
$631$	−20558.9	−1.29705	−0.648524	+	0.761194i	$0.724613\pi$
$632$	1577.83	0.0993080
$633$	−32346.4	−2.03105
$634$	−1505.39	−0.0943006
$635$	−826.666	−0.0516618
$636$	1.07859	6.72465e−5 0
$637$	−3586.18	−0.223061
$638$	−11723.5	−0.727490
$639$	39537.4	2.44769
$640$	−4704.34	−0.290555
$641$	−5651.22	−0.348221	−0.174111	−	0.984726i	$-0.555705\pi$
$641$	−5651.22	−0.348221	−0.174111	+	0.984726i	$0.555705\pi$
$642$	6884.13	0.423201
$643$	2197.26	0.134761	0.0673805	−	0.997727i	$-0.478536\pi$
$643$	2197.26	0.134761	0.0673805	+	0.997727i	$0.478536\pi$
$644$	3647.81	0.223205
$645$	4307.08	0.262932
$646$	−26292.9	−1.60136
$647$	23529.6	1.42974	0.714872	−	0.699255i	$-0.246485\pi$
$647$	23529.6	1.42974	0.714872	+	0.699255i	$0.246485\pi$
$648$	3747.45	0.227182
$649$	13595.6	0.822305
$650$	−832.505	−0.0502362
$651$	−61286.8	−3.68974
$652$	4173.66	0.250695
$653$	26577.6	1.59275	0.796373	−	0.604806i	$-0.206749\pi$
$653$	26577.6	1.59275	0.796373	+	0.604806i	$0.206749\pi$
$654$	36731.6	2.19621
$655$	9337.44	0.557014
$656$	−11074.6	−0.659132
$657$	27170.0	1.61340
$658$	19678.8	1.16590
$659$	−454.595	−0.0268718	−0.0134359	−	0.999910i	$-0.504277\pi$
$659$	−454.595	−0.0268718	−0.0134359	+	0.999910i	$0.504277\pi$
$660$	−2305.74	−0.135986
$661$	−21367.3	−1.25732	−0.628662	−	0.777679i	$-0.716397\pi$
$661$	−21367.3	−1.25732	−0.628662	+	0.777679i	$0.716397\pi$
$662$	−16803.0	−0.986508
$663$	8572.81	0.502173
$664$	2234.41	0.130590
$665$	−15965.3	−0.930987
$666$	26698.7	1.55338
$667$	−12000.7	−0.696653
$668$	−763.867	−0.0442439
$669$	50427.8	2.91428
$670$	−2921.12	−0.168437
$671$	−17183.6	−0.988622
$672$	13181.2	0.756662
$673$	−18710.7	−1.07169	−0.535843	−	0.844318i	$-0.680006\pi$
$673$	−18710.7	−1.07169	−0.535843	+	0.844318i	$0.680006\pi$
$674$	8496.63	0.485576
$675$	2886.17	0.164576
$676$	−243.098	−0.0138312
$677$	−29181.5	−1.65662	−0.828312	−	0.560267i	$-0.810699\pi$
$677$	−29181.5	−1.65662	−0.828312	+	0.560267i	$0.810699\pi$
$678$	−34407.3	−1.94897
$679$	−42476.3	−2.40072
$680$	−9667.17	−0.545175
$681$	34767.1	1.95636
$682$	29751.6	1.67045
$683$	21953.8	1.22992	0.614961	−	0.788557i	$-0.289172\pi$
$683$	21953.8	1.22992	0.614961	+	0.788557i	$0.289172\pi$
$684$	−7569.86	−0.423159
$685$	−8704.00	−0.485493
$686$	−4278.40	−0.238120
$687$	−2469.33	−0.137134
$688$	5267.32	0.291882
$689$	1.18209	6.53614e−5 0
$690$	10766.4	0.594013
$691$	2242.59	0.123462	0.0617309	−	0.998093i	$-0.480338\pi$
$691$	2242.59	0.123462	0.0617309	+	0.998093i	$0.480338\pi$
$692$	−1164.89	−0.0639921
$693$	−39652.6	−2.17356
$694$	−9552.18	−0.522472
$695$	4927.56	0.268939
$696$	−23470.4	−1.27823
$697$	−17563.9	−0.954493
$698$	9601.25	0.520649
$699$	10086.5	0.545788
$700$	−894.602	−0.0483040
$701$	16013.4	0.862794	0.431397	−	0.902162i	$-0.358021\pi$
$701$	16013.4	0.862794	0.431397	+	0.902162i	$0.358021\pi$
$702$	−3844.41	−0.206692
$703$	32629.7	1.75057
$704$	−22081.2	−1.18213
$705$	−12732.8	−0.680207
$706$	−8591.19	−0.457980
$707$	−33933.0	−1.80507
$708$	4148.17	0.220195
$709$	−34333.3	−1.81864	−0.909318	−	0.416102i	$-0.863396\pi$
$709$	−34333.3	−1.81864	−0.909318	+	0.416102i	$0.863396\pi$
$710$	−12350.9	−0.652845
$711$	−2675.72	−0.141135
$712$	4318.36	0.227300
$713$	30455.0	1.59965
$714$	−42022.3	−2.20258
$715$	−2527.00	−0.132174
$716$	2635.05	0.137537
$717$	−401.799	−0.0209281
$718$	−2668.79	−0.138717
$719$	−4359.43	−0.226119	−0.113059	−	0.993588i	$-0.536065\pi$
$719$	−4359.43	−0.226119	−0.113059	+	0.993588i	$0.536065\pi$
$720$	10336.8	0.535040
$721$	8835.44	0.456379
$722$	24631.4	1.26965
$723$	−37106.5	−1.90872
$724$	−1505.71	−0.0772919
$725$	2943.09	0.150763
$726$	3810.88	0.194814
$727$	−9626.47	−0.491095	−0.245547	−	0.969385i	$-0.578968\pi$
$727$	−9626.47	−0.491095	−0.245547	+	0.969385i	$0.578968\pi$
$728$	7818.86	0.398058
$729$	−32059.0	−1.62877
$730$	−8487.47	−0.430322
$731$	8353.80	0.422677
$732$	−5242.89	−0.264731
$733$	−11224.3	−0.565590	−0.282795	−	0.959180i	$-0.591262\pi$
$733$	−11224.3	−0.565590	−0.282795	+	0.959180i	$0.591262\pi$
$734$	2817.58	0.141688
$735$	−11374.0	−0.570797
$736$	−6550.09	−0.328043
$737$	−8866.81	−0.443165
$738$	23066.6	1.15053
$739$	20190.6	1.00504	0.502519	−	0.864566i	$-0.332407\pi$
$739$	20190.6	1.00504	0.502519	+	0.864566i	$0.332407\pi$
$740$	1828.38	0.0908279
$741$	−13759.7	−0.682151
$742$	−5.79437	−0.000286682 0
$743$	−19756.1	−0.975479	−0.487739	−	0.872989i	$-0.662178\pi$
$743$	−19756.1	−0.975479	−0.487739	+	0.872989i	$0.662178\pi$
$744$	59562.7	2.93505
$745$	12484.5	0.613956
$746$	7600.49	0.373021
$747$	−3789.16	−0.185593
$748$	−4472.09	−0.218604
$749$	8107.51	0.395517
$750$	−2640.39	−0.128551
$751$	17597.3	0.855040	0.427520	−	0.904006i	$-0.359387\pi$
$751$	17597.3	0.855040	0.427520	+	0.904006i	$0.359387\pi$
$752$	−15571.5	−0.755100
$753$	−909.456	−0.0440138
$754$	−3920.21	−0.189345
$755$	−1788.55	−0.0862146
$756$	−4131.17	−0.198742
$757$	29920.3	1.43655	0.718277	−	0.695757i	$-0.244931\pi$
$757$	29920.3	1.43655	0.718277	+	0.695757i	$0.244931\pi$
$758$	−23621.8	−1.13190
$759$	32680.4	1.56288
$760$	15516.1	0.740565
$761$	13040.7	0.621190	0.310595	−	0.950542i	$-0.399472\pi$
$761$	13040.7	0.621190	0.310595	+	0.950542i	$0.399472\pi$
$762$	3492.35	0.166030
$763$	43259.2	2.05254
$764$	−1093.18	−0.0517669
$765$	16393.8	0.774796
$766$	−28299.9	−1.33488
$767$	4546.23	0.214022
$768$	−17595.3	−0.826712
$769$	23856.2	1.11869	0.559347	−	0.828934i	$-0.311052\pi$
$769$	23856.2	1.11869	0.559347	+	0.828934i	$0.311052\pi$
$770$	12386.9	0.579729
$771$	61465.3	2.87110
$772$	592.090	0.0276034
$773$	−20701.3	−0.963224	−0.481612	−	0.876384i	$-0.659949\pi$
$773$	−20701.3	−0.963224	−0.481612	+	0.876384i	$0.659949\pi$
$774$	−10971.0	−0.509489
$775$	−7468.89	−0.346181
$776$	41281.4	1.90968
$777$	52149.9	2.40781
$778$	−515.851	−0.0237714
$779$	28190.8	1.29658
$780$	−771.013	−0.0353932
$781$	−37490.1	−1.71767
$782$	20881.9	0.954906
$783$	13590.8	0.620302
$784$	−13909.8	−0.633644
$785$	16091.6	0.731635
$786$	−39447.2	−1.79012
$787$	−4082.21	−0.184899	−0.0924493	−	0.995717i	$-0.529470\pi$
$787$	−4082.21	−0.184899	−0.0924493	+	0.995717i	$0.529470\pi$
$788$	1158.24	0.0523613
$789$	−1856.68	−0.0837764
$790$	835.852	0.0376434
$791$	−40521.8	−1.82148
$792$	38537.1	1.72899
$793$	−5746.00	−0.257310
$794$	−11153.2	−0.498506
$795$	3.74914	0.000167256 0
$796$	−4217.56	−0.187798
$797$	17269.3	0.767514	0.383757	−	0.923434i	$-0.374630\pi$
$797$	17269.3	0.767514	0.383757	+	0.923434i	$0.374630\pi$
$798$	67447.2	2.99199
$799$	−24695.9	−1.09347
$800$	1606.37	0.0709921
$801$	−7323.16	−0.323035
$802$	10864.3	0.478346
$803$	−25763.0	−1.13220
$804$	−2705.35	−0.118670
$805$	12679.7	0.555155
$806$	9948.62	0.434771
$807$	−22611.8	−0.986337
$808$	32978.5	1.43586
$809$	−35166.8	−1.52831	−0.764153	−	0.645034i	$-0.776843\pi$
$809$	−35166.8	−1.52831	−0.764153	+	0.645034i	$0.776843\pi$
$810$	1985.20	0.0861147
$811$	−40718.1	−1.76302	−0.881509	−	0.472167i	$-0.843472\pi$
$811$	−40718.1	−1.76302	−0.881509	+	0.472167i	$0.843472\pi$
$812$	−4212.63	−0.182062
$813$	55659.3	2.40106
$814$	−25316.1	−1.09009
$815$	14507.5	0.623529
$816$	33251.5	1.42651
$817$	−13408.1	−0.574164
$818$	−4155.47	−0.177619
$819$	−13259.4	−0.565715
$820$	1579.65	0.0672729
$821$	−30057.8	−1.27774	−0.638870	−	0.769314i	$-0.720598\pi$
$821$	−30057.8	−1.27774	−0.638870	+	0.769314i	$0.720598\pi$
$822$	36771.1	1.56027
$823$	4548.10	0.192633	0.0963163	−	0.995351i	$-0.469294\pi$
$823$	4548.10	0.192633	0.0963163	+	0.995351i	$0.469294\pi$
$824$	−8586.89	−0.363032
$825$	−8014.68	−0.338225
$826$	−22284.7	−0.938724
$827$	9335.94	0.392554	0.196277	−	0.980548i	$-0.437115\pi$
$827$	9335.94	0.392554	0.196277	+	0.980548i	$0.437115\pi$
$828$	6012.01	0.252333
$829$	−22765.0	−0.953751	−0.476876	−	0.878971i	$-0.658231\pi$
$829$	−22765.0	−0.953751	−0.476876	+	0.878971i	$0.658231\pi$
$830$	1183.67	0.0495011
$831$	12465.4	0.520361
$832$	−7383.72	−0.307673
$833$	−22060.4	−0.917585
$834$	−20817.1	−0.864312
$835$	−2655.18	−0.110043
$836$	7177.87	0.296952
$837$	−34490.4	−1.42433
$838$	−16251.5	−0.669927
$839$	28521.3	1.17362	0.586808	−	0.809726i	$-0.300384\pi$
$839$	28521.3	1.17362	0.586808	+	0.809726i	$0.300384\pi$
$840$	24798.4	1.01860
$841$	−10530.2	−0.431760
$842$	−18060.3	−0.739193
$843$	−46126.7	−1.88456
$844$	5642.41	0.230118
$845$	−845.000	−0.0344010
$846$	32433.0	1.31805
$847$	4488.11	0.182070
$848$	4.58499	0.000185671 0
$849$	−26561.2	−1.07371
$850$	−5121.16	−0.206652
$851$	−25914.6	−1.04388
$852$	−11438.6	−0.459953
$853$	5037.10	0.202189	0.101094	−	0.994877i	$-0.467766\pi$
$853$	5037.10	0.202189	0.101094	+	0.994877i	$0.467766\pi$
$854$	28165.8	1.12859
$855$	−26312.6	−1.05248
$856$	−7879.44	−0.314619
$857$	−27178.6	−1.08332	−0.541658	−	0.840599i	$-0.682203\pi$
$857$	−27178.6	−1.08332	−0.541658	+	0.840599i	$0.682203\pi$
$858$	10675.6	0.424778
$859$	21916.5	0.870525	0.435262	−	0.900304i	$-0.356656\pi$
$859$	21916.5	0.870525	0.435262	+	0.900304i	$0.356656\pi$
$860$	−751.316	−0.0297903
$861$	45055.4	1.78337
$862$	−7043.60	−0.278313
$863$	38533.9	1.51994	0.759971	−	0.649957i	$-0.225213\pi$
$863$	38533.9	1.51994	0.759971	+	0.649957i	$0.225213\pi$
$864$	7418.01	0.292090
$865$	−4049.13	−0.159161
$866$	−32579.6	−1.27841
$867$	12222.1	0.478761
$868$	10690.7	0.418048
$869$	2537.16	0.0990417
$870$	−12433.4	−0.484520
$871$	−2964.96	−0.115343
$872$	−42042.3	−1.63272
$873$	−70005.8	−2.71402
$874$	−33516.2	−1.29714
$875$	−3109.61	−0.120142
$876$	−7860.56	−0.303178
$877$	4812.41	0.185295	0.0926475	−	0.995699i	$-0.470467\pi$
$877$	4812.41	0.185295	0.0926475	+	0.995699i	$0.470467\pi$
$878$	45228.7	1.73849
$879$	64401.6	2.47123
$880$	−9801.51	−0.375464
$881$	−18910.3	−0.723160	−0.361580	−	0.932341i	$-0.617763\pi$
$881$	−18910.3	−0.723160	−0.361580	+	0.932341i	$0.617763\pi$
$882$	28971.8	1.10605
$883$	−35174.6	−1.34057	−0.670283	−	0.742106i	$-0.733827\pi$
$883$	−35174.6	−1.34057	−0.670283	+	0.742106i	$0.733827\pi$
$884$	−1495.42	−0.0568963
$885$	14418.9	0.547669
$886$	47019.2	1.78289
$887$	38502.7	1.45749	0.728745	−	0.684785i	$-0.240104\pi$
$887$	38502.7	1.45749	0.728745	+	0.684785i	$0.240104\pi$
$888$	−50682.9	−1.91532
$889$	4112.98	0.155168
$890$	2287.64	0.0861595
$891$	6025.92	0.226572
$892$	−8796.49	−0.330189
$893$	39637.9	1.48536
$894$	−52742.3	−1.97312
$895$	9159.36	0.342082
$896$	23405.9	0.872696
$897$	10928.0	0.406772
$898$	−6854.14	−0.254706
$899$	−35170.6	−1.30479
$900$	−1474.41	−0.0546077
$901$	7.27164	0.000268872 0
$902$	−21872.2	−0.807387
$903$	−21429.4	−0.789728
$904$	39381.9	1.44892
$905$	−5233.81	−0.192240
$906$	7555.95	0.277075
$907$	−52947.3	−1.93835	−0.969176	−	0.246368i	$-0.920763\pi$
$907$	−52947.3	−1.93835	−0.969176	+	0.246368i	$0.920763\pi$
$908$	−6064.69	−0.221656
$909$	−55925.5	−2.04063
$910$	4142.03	0.150887
$911$	11565.8	0.420627	0.210314	−	0.977634i	$-0.432551\pi$
$911$	11565.8	0.420627	0.210314	+	0.977634i	$0.432551\pi$
$912$	−53369.8	−1.93778
$913$	3592.94	0.130240
$914$	15662.6	0.566821
$915$	−18224.1	−0.658438
$916$	430.744	0.0155373
$917$	−46457.3	−1.67302
$918$	−23648.9	−0.850251
$919$	−31800.9	−1.14148	−0.570738	−	0.821132i	$-0.693343\pi$
$919$	−31800.9	−1.14148	−0.570738	+	0.821132i	$0.693343\pi$
$920$	−12323.0	−0.441605
$921$	70761.3	2.53167
$922$	−35819.6	−1.27945
$923$	−12536.3	−0.447060
$924$	11471.9	0.408440
$925$	6355.40	0.225907
$926$	−12984.5	−0.460794
$927$	14561.8	0.515937
$928$	7564.29	0.267575
$929$	39306.1	1.38815	0.694075	−	0.719903i	$-0.255814\pi$
$929$	39306.1	1.38815	0.694075	+	0.719903i	$0.255814\pi$
$930$	31553.2	1.11255
$931$	35407.8	1.24645
$932$	−1759.46	−0.0618380
$933$	76292.6	2.67707
$934$	6273.78	0.219791
$935$	−15544.9	−0.543713
$936$	12886.4	0.450005
$937$	2554.39	0.0890589	0.0445294	−	0.999008i	$-0.485821\pi$
$937$	2554.39	0.0890589	0.0445294	+	0.999008i	$0.485821\pi$
$938$	14533.7	0.505907
$939$	36169.3	1.25702
$940$	2221.08	0.0770677
$941$	17871.8	0.619133	0.309567	−	0.950878i	$-0.399816\pi$
$941$	17871.8	0.619133	0.309567	+	0.950878i	$0.399816\pi$
$942$	−67980.9	−2.35131
$943$	−22389.2	−0.773163
$944$	17633.5	0.607969
$945$	−14359.8	−0.494312
$946$	10402.9	0.357534
$947$	13013.0	0.446532	0.223266	−	0.974758i	$-0.428328\pi$
$947$	13013.0	0.446532	0.223266	+	0.974758i	$0.428328\pi$
$948$	774.113	0.0265211
$949$	−8614.86	−0.294679
$950$	8219.65	0.280716
$951$	−4846.18	−0.165245
$952$	48097.8	1.63746
$953$	−11984.0	−0.407345	−0.203672	−	0.979039i	$-0.565288\pi$
$953$	−11984.0	−0.407345	−0.203672	+	0.979039i	$0.565288\pi$
$954$	−9.54980	−0.000324094 0
$955$	−3799.87	−0.128755
$956$	70.0888	0.00237117
$957$	−37740.6	−1.27480
$958$	−36133.5	−1.21860
$959$	43305.7	1.45820
$960$	−23418.3	−0.787316
$961$	59463.9	1.99604
$962$	−8465.44	−0.283718
$963$	13362.1	0.447132
$964$	6472.77	0.216259
$965$	2058.09	0.0686551
$966$	−53566.8	−1.78415
$967$	34643.6	1.15208	0.576041	−	0.817421i	$-0.304597\pi$
$967$	34643.6	1.15208	0.576041	+	0.817421i	$0.304597\pi$
$968$	−4361.86	−0.144830
$969$	−84642.8	−2.80611
$970$	21868.7	0.723879
$971$	11097.6	0.366776	0.183388	−	0.983041i	$-0.441294\pi$
$971$	11097.6	0.366776	0.183388	+	0.983041i	$0.441294\pi$
$972$	6322.31	0.208630
$973$	−24516.5	−0.807771
$974$	29008.0	0.954288
$975$	−2680.02	−0.0880300
$976$	−22287.1	−0.730935
$977$	6609.39	0.216431	0.108215	−	0.994127i	$-0.465486\pi$
$977$	6609.39	0.216431	0.108215	+	0.994127i	$0.465486\pi$
$978$	−61288.8	−2.00389
$979$	6943.94	0.226690
$980$	1984.05	0.0646716
$981$	71296.2	2.32040
$982$	−30290.0	−0.984309
$983$	30211.3	0.980254	0.490127	−	0.871651i	$-0.336950\pi$
$983$	30211.3	0.980254	0.490127	+	0.871651i	$0.336950\pi$
$984$	−43788.0	−1.41861
$985$	4026.02	0.130233
$986$	−24115.3	−0.778891
$987$	63350.6	2.04303
$988$	2400.20	0.0772880
$989$	10648.8	0.342378
$990$	20415.0	0.655384
$991$	36910.1	1.18313	0.591567	−	0.806256i	$-0.298509\pi$
$991$	36910.1	1.18313	0.591567	+	0.806256i	$0.298509\pi$
$992$	−19196.5	−0.614403
$993$	−54092.7	−1.72868
$994$	61450.3	1.96085
$995$	−14660.1	−0.467092
$996$	1096.24	0.0348753
$997$	−42912.3	−1.36313	−0.681567	−	0.731755i	$-0.738701\pi$
$997$	−42912.3	−1.36313	−0.681567	+	0.731755i	$0.738701\pi$
$998$	29361.2	0.931275
$999$	29348.5	0.929473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.a.c.1.2	✓	2
3.2	odd	2		585.4.a.h.1.1		2
4.3	odd	2		1040.4.a.k.1.1		2
5.2	odd	4		325.4.b.f.274.4		4
5.3	odd	4		325.4.b.f.274.1		4
5.4	even	2		325.4.a.g.1.1		2
13.12	even	2		845.4.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.a.c.1.2	✓	2	1.1	even	1	trivial
325.4.a.g.1.1		2	5.4	even	2
325.4.b.f.274.1		4	5.3	odd	4
325.4.b.f.274.4		4	5.2	odd	4
585.4.a.h.1.1		2	3.2	odd	2
845.4.a.d.1.1		2	13.12	even	2
1040.4.a.k.1.1		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.a (trivial)

\(f(q)\)	\(=\)	\(q+2.56155 q^{2} +8.24621 q^{3} -1.43845 q^{4} -5.00000 q^{5} +21.1231 q^{6} +24.8769 q^{7} -24.1771 q^{8} +41.0000 q^{9} -12.8078 q^{10} -38.8769 q^{11} -11.8617 q^{12} -13.0000 q^{13} +63.7235 q^{14} -41.2311 q^{15} -50.4233 q^{16} -79.9697 q^{17} +105.024 q^{18} +128.354 q^{19} +7.19224 q^{20} +205.140 q^{21} -99.5852 q^{22} -101.939 q^{23} -199.369 q^{24} +25.0000 q^{25} -33.3002 q^{26} +115.447 q^{27} -35.7841 q^{28} +117.723 q^{29} -105.616 q^{30} -298.756 q^{31} +64.2547 q^{32} -320.587 q^{33} -204.847 q^{34} -124.384 q^{35} -58.9763 q^{36} +254.216 q^{37} +328.786 q^{38} -107.201 q^{39} +120.885 q^{40} +219.633 q^{41} +525.477 q^{42} -104.462 q^{43} +55.9224 q^{44} -205.000 q^{45} -261.123 q^{46} +308.816 q^{47} -415.801 q^{48} +275.860 q^{49} +64.0388 q^{50} -659.447 q^{51} +18.6998 q^{52} -0.0909300 q^{53} +295.723 q^{54} +194.384 q^{55} -601.451 q^{56} +1058.44 q^{57} +301.555 q^{58} -349.710 q^{59} +59.3087 q^{60} +442.000 q^{61} -765.278 q^{62} +1019.95 q^{63} +567.978 q^{64} +65.0000 q^{65} -821.201 q^{66} +228.074 q^{67} +115.032 q^{68} -840.614 q^{69} -318.617 q^{70} +964.328 q^{71} -991.260 q^{72} +662.682 q^{73} +651.187 q^{74} +206.155 q^{75} -184.631 q^{76} -967.136 q^{77} -274.600 q^{78} -65.2614 q^{79} +252.116 q^{80} -155.000 q^{81} +562.600 q^{82} -92.4185 q^{83} -295.083 q^{84} +399.848 q^{85} -267.585 q^{86} +970.773 q^{87} +939.930 q^{88} -178.614 q^{89} -525.118 q^{90} -323.400 q^{91} +146.634 q^{92} -2463.60 q^{93} +791.049 q^{94} -641.771 q^{95} +529.858 q^{96} -1707.46 q^{97} +706.630 q^{98} -1593.95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 7 q^{4} - 10 q^{5} + 34 q^{6} + 58 q^{7} - 3 q^{8} + 82 q^{9} - 5 q^{10} - 86 q^{11} + 34 q^{12} - 26 q^{13} + 12 q^{14} - 39 q^{16} - 28 q^{17} + 41 q^{18} + 166 q^{19} + 35 q^{20} - 68 q^{21}+ \cdots - 3526 q^{99}+O(q^{100}) \) 2 * q + q^2 - 7 * q^4 - 10 * q^5 + 34 * q^6 + 58 * q^7 - 3 * q^8 + 82 * q^9 - 5 * q^10 - 86 * q^11 + 34 * q^12 - 26 * q^13 + 12 * q^14 - 39 * q^16 - 28 * q^17 + 41 * q^18 + 166 * q^19 + 35 * q^20 - 68 * q^21 - 26 * q^22 + 60 * q^23 - 374 * q^24 + 50 * q^25 - 13 * q^26 - 220 * q^28 + 120 * q^29 - 170 * q^30 - 78 * q^31 - 123 * q^32 + 68 * q^33 - 286 * q^34 - 290 * q^35 - 287 * q^36 + 360 * q^37 + 270 * q^38 + 15 * q^40 - 72 * q^41 + 952 * q^42 - 44 * q^43 + 318 * q^44 - 410 * q^45 - 514 * q^46 + 362 * q^47 - 510 * q^48 + 1030 * q^49 + 25 * q^50 - 1088 * q^51 + 91 * q^52 - 396 * q^53 + 476 * q^54 + 430 * q^55 + 100 * q^56 + 748 * q^57 + 298 * q^58 + 18 * q^59 - 170 * q^60 + 884 * q^61 - 1110 * q^62 + 2378 * q^63 + 769 * q^64 + 130 * q^65 - 1428 * q^66 + 1322 * q^67 - 174 * q^68 - 2176 * q^69 - 60 * q^70 + 634 * q^71 - 123 * q^72 - 60 * q^73 + 486 * q^74 - 394 * q^76 - 2528 * q^77 - 442 * q^78 - 180 * q^79 + 195 * q^80 - 310 * q^81 + 1018 * q^82 + 714 * q^83 + 1224 * q^84 + 140 * q^85 - 362 * q^86 + 952 * q^87 - 58 * q^88 - 852 * q^89 - 205 * q^90 - 754 * q^91 - 754 * q^92 - 4284 * q^93 + 708 * q^94 - 830 * q^95 + 2074 * q^96 + 32 * q^97 - 471 * q^98 - 3526 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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