LMFDB - Embedded newform 1011.4.a.c.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1011,4,Mod(1,1011)] 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("1011.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1011 = 3 \cdot 337 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1011.a (trivial)

Newform invariants

comment:select newform

sage:traces = [46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$59.6509310158$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1011.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.92365 q^{2} -3.00000 q^{3} +7.39501 q^{4} -14.7876 q^{5} +11.7709 q^{6} -6.54928 q^{7} +2.37377 q^{8} +9.00000 q^{9} +58.0213 q^{10} +46.3738 q^{11} -22.1850 q^{12} +23.3184 q^{13} +25.6971 q^{14} +44.3628 q^{15} -68.4739 q^{16} +85.8596 q^{17} -35.3128 q^{18} +117.556 q^{19} -109.354 q^{20} +19.6478 q^{21} -181.954 q^{22} +129.043 q^{23} -7.12130 q^{24} +93.6729 q^{25} -91.4934 q^{26} -27.0000 q^{27} -48.4320 q^{28} -230.128 q^{29} -174.064 q^{30} +54.5606 q^{31} +249.677 q^{32} -139.121 q^{33} -336.883 q^{34} +96.8481 q^{35} +66.5551 q^{36} +43.0375 q^{37} -461.247 q^{38} -69.9553 q^{39} -35.1023 q^{40} -198.894 q^{41} -77.0912 q^{42} +214.068 q^{43} +342.934 q^{44} -133.088 q^{45} -506.319 q^{46} +547.429 q^{47} +205.422 q^{48} -300.107 q^{49} -367.539 q^{50} -257.579 q^{51} +172.440 q^{52} -279.728 q^{53} +105.938 q^{54} -685.756 q^{55} -15.5465 q^{56} -352.667 q^{57} +902.939 q^{58} +678.355 q^{59} +328.063 q^{60} -163.613 q^{61} -214.077 q^{62} -58.9435 q^{63} -431.855 q^{64} -344.824 q^{65} +545.863 q^{66} -780.052 q^{67} +634.933 q^{68} -387.129 q^{69} -379.998 q^{70} +643.207 q^{71} +21.3639 q^{72} -566.903 q^{73} -168.864 q^{74} -281.019 q^{75} +869.326 q^{76} -303.715 q^{77} +274.480 q^{78} +76.9672 q^{79} +1012.56 q^{80} +81.0000 q^{81} +780.389 q^{82} +725.192 q^{83} +145.296 q^{84} -1269.66 q^{85} -839.926 q^{86} +690.383 q^{87} +110.081 q^{88} +984.294 q^{89} +522.192 q^{90} -152.719 q^{91} +954.273 q^{92} -163.682 q^{93} -2147.92 q^{94} -1738.37 q^{95} -749.032 q^{96} -760.823 q^{97} +1177.51 q^{98} +417.364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) $ 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * 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 $

$2$	−3.92365	−1.38722	−0.693609	−	0.720351i	$-0.743981\pi$
$2$	−3.92365	−1.38722	−0.693609	+	0.720351i	$0.743981\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	7.39501	0.924376
$5$	−14.7876	−1.32264	−0.661321	−	0.750103i	$-0.730004\pi$
$5$	−14.7876	−1.32264	−0.661321	+	0.750103i	$0.730004\pi$
$6$	11.7709	0.800911
$7$	−6.54928	−0.353628	−0.176814	−	0.984244i	$-0.556579\pi$
$7$	−6.54928	−0.353628	−0.176814	+	0.984244i	$0.556579\pi$
$8$	2.37377	0.104907
$9$	9.00000	0.333333
$10$	58.0213	1.83479
$11$	46.3738	1.27111	0.635555	−	0.772056i	$-0.280771\pi$
$11$	46.3738	1.27111	0.635555	+	0.772056i	$0.280771\pi$
$12$	−22.1850	−0.533689
$13$	23.3184	0.497490	0.248745	−	0.968569i	$-0.419982\pi$
$13$	23.3184	0.497490	0.248745	+	0.968569i	$0.419982\pi$
$14$	25.6971	0.490559
$15$	44.3628	0.763628
$16$	−68.4739	−1.06990
$17$	85.8596	1.22494	0.612471	−	0.790493i	$-0.290176\pi$
$17$	85.8596	1.22494	0.612471	+	0.790493i	$0.290176\pi$
$18$	−35.3128	−0.462406
$19$	117.556	1.41943	0.709714	−	0.704490i	$-0.248824\pi$
$19$	117.556	1.41943	0.709714	+	0.704490i	$0.248824\pi$
$20$	−109.354	−1.22262
$21$	19.6478	0.204167
$22$	−181.954	−1.76331
$23$	129.043	1.16988	0.584941	−	0.811076i	$-0.301118\pi$
$23$	129.043	1.16988	0.584941	+	0.811076i	$0.301118\pi$
$24$	−7.12130	−0.0605679
$25$	93.6729	0.749383
$26$	−91.4934	−0.690128
$27$	−27.0000	−0.192450
$28$	−48.4320	−0.326885
$29$	−230.128	−1.47357	−0.736787	−	0.676125i	$-0.763658\pi$
$29$	−230.128	−1.47357	−0.736787	+	0.676125i	$0.763658\pi$
$30$	−174.064	−1.05932
$31$	54.5606	0.316109	0.158054	−	0.987430i	$-0.449478\pi$
$31$	54.5606	0.316109	0.158054	+	0.987430i	$0.449478\pi$
$32$	249.677	1.37929
$33$	−139.121	−0.733876
$34$	−336.883	−1.69926
$35$	96.8481	0.467723
$36$	66.5551	0.308125
$37$	43.0375	0.191225	0.0956125	−	0.995419i	$-0.469519\pi$
$37$	43.0375	0.191225	0.0956125	+	0.995419i	$0.469519\pi$
$38$	−461.247	−1.96906
$39$	−69.9553	−0.287226
$40$	−35.1023	−0.138754
$41$	−198.894	−0.757610	−0.378805	−	0.925477i	$-0.623665\pi$
$41$	−198.894	−0.757610	−0.378805	+	0.925477i	$0.623665\pi$
$42$	−77.0912	−0.283225
$43$	214.068	0.759187	0.379593	−	0.925153i	$-0.376064\pi$
$43$	214.068	0.759187	0.379593	+	0.925153i	$0.376064\pi$
$44$	342.934	1.17498
$45$	−133.088	−0.440881
$46$	−506.319	−1.62288
$47$	547.429	1.69895	0.849477	−	0.527626i	$-0.176918\pi$
$47$	547.429	1.69895	0.849477	+	0.527626i	$0.176918\pi$
$48$	205.422	0.617710
$49$	−300.107	−0.874947
$50$	−367.539	−1.03956
$51$	−257.579	−0.707221
$52$	172.440	0.459868
$53$	−279.728	−0.724973	−0.362486	−	0.931989i	$-0.618072\pi$
$53$	−279.728	−0.724973	−0.362486	+	0.931989i	$0.618072\pi$
$54$	105.938	0.266970
$55$	−685.756	−1.68122
$56$	−15.5465	−0.0370979
$57$	−352.667	−0.819507
$58$	902.939	2.04417
$59$	678.355	1.49685	0.748426	−	0.663218i	$-0.230810\pi$
$59$	678.355	1.49685	0.748426	+	0.663218i	$0.230810\pi$
$60$	328.063	0.705880
$61$	−163.613	−0.343419	−0.171709	−	0.985148i	$-0.554929\pi$
$61$	−163.613	−0.343419	−0.171709	+	0.985148i	$0.554929\pi$
$62$	−214.077	−0.438512
$63$	−58.9435	−0.117876
$64$	−431.855	−0.843466
$65$	−344.824	−0.658002
$66$	545.863	1.01805
$67$	−780.052	−1.42237	−0.711183	−	0.703007i	$-0.751840\pi$
$67$	−780.052	−1.42237	−0.711183	+	0.703007i	$0.751840\pi$
$68$	634.933	1.13231
$69$	−387.129	−0.675432
$70$	−379.998	−0.648834
$71$	643.207	1.07513	0.537567	−	0.843221i	$-0.319343\pi$
$71$	643.207	1.07513	0.537567	+	0.843221i	$0.319343\pi$
$72$	21.3639	0.0349689
$73$	−566.903	−0.908918	−0.454459	−	0.890768i	$-0.650167\pi$
$73$	−566.903	−0.908918	−0.454459	+	0.890768i	$0.650167\pi$
$74$	−168.864	−0.265271
$75$	−281.019	−0.432656
$76$	869.326	1.31209
$77$	−303.715	−0.449500
$78$	274.480	0.398446
$79$	76.9672	0.109614	0.0548069	−	0.998497i	$-0.482546\pi$
$79$	76.9672	0.109614	0.0548069	+	0.998497i	$0.482546\pi$
$80$	1012.56	1.41510
$81$	81.0000	0.111111
$82$	780.389	1.05097
$83$	725.192	0.959038	0.479519	−	0.877532i	$-0.340811\pi$
$83$	725.192	0.959038	0.479519	+	0.877532i	$0.340811\pi$
$84$	145.296	0.188727
$85$	−1269.66	−1.62016
$86$	−839.926	−1.05316
$87$	690.383	0.850768
$88$	110.081	0.133348
$89$	984.294	1.17230	0.586152	−	0.810201i	$-0.300642\pi$
$89$	984.294	1.17230	0.586152	+	0.810201i	$0.300642\pi$
$90$	522.192	0.611598
$91$	−152.719	−0.175926
$92$	954.273	1.08141
$93$	−163.682	−0.182506
$94$	−2147.92	−2.35682
$95$	−1738.37	−1.87740
$96$	−749.032	−0.796331
$97$	−760.823	−0.796390	−0.398195	−	0.917301i	$-0.630363\pi$
$97$	−760.823	−0.796390	−0.398195	+	0.917301i	$0.630363\pi$
$98$	1177.51	1.21374
$99$	417.364	0.423703
$100$	692.712	0.692712
$101$	764.006	0.752688	0.376344	−	0.926480i	$-0.377181\pi$
$101$	764.006	0.752688	0.376344	+	0.926480i	$0.377181\pi$
$102$	1010.65	0.981070
$103$	−582.206	−0.556956	−0.278478	−	0.960443i	$-0.589830\pi$
$103$	−582.206	−0.556956	−0.278478	+	0.960443i	$0.589830\pi$
$104$	55.3526	0.0521901
$105$	−290.544	−0.270040
$106$	1097.55	1.00570
$107$	451.239	0.407691	0.203845	−	0.979003i	$-0.434656\pi$
$107$	451.239	0.407691	0.203845	+	0.979003i	$0.434656\pi$
$108$	−199.665	−0.177896
$109$	416.569	0.366055	0.183028	−	0.983108i	$-0.441410\pi$
$109$	416.569	0.366055	0.183028	+	0.983108i	$0.441410\pi$
$110$	2690.67	2.33223
$111$	−129.113	−0.110404
$112$	448.455	0.378348
$113$	−1206.44	−1.00436	−0.502180	−	0.864763i	$-0.667469\pi$
$113$	−1206.44	−1.00436	−0.502180	+	0.864763i	$0.667469\pi$
$114$	1383.74	1.13684
$115$	−1908.23	−1.54734
$116$	−1701.80	−1.36214
$117$	209.866	0.165830
$118$	−2661.63	−2.07646
$119$	−562.319	−0.433174
$120$	105.307	0.0801097
$121$	819.525	0.615721
$122$	641.961	0.476397
$123$	596.682	0.437406
$124$	403.476	0.292204
$125$	463.253	0.331477
$126$	231.274	0.163520
$127$	−1451.82	−1.01439	−0.507197	−	0.861830i	$-0.669318\pi$
$127$	−1451.82	−1.01439	−0.507197	+	0.861830i	$0.669318\pi$
$128$	−302.973	−0.209213
$129$	−642.203	−0.438317
$130$	1352.97	0.912792
$131$	−1201.41	−0.801281	−0.400640	−	0.916235i	$-0.631212\pi$
$131$	−1201.41	−0.801281	−0.400640	+	0.916235i	$0.631212\pi$
$132$	−1028.80	−0.678377
$133$	−769.905	−0.501949
$134$	3060.65	1.97313
$135$	399.265	0.254543
$136$	203.811	0.128505
$137$	−994.959	−0.620475	−0.310237	−	0.950659i	$-0.600409\pi$
$137$	−994.959	−0.620475	−0.310237	+	0.950659i	$0.600409\pi$
$138$	1518.96	0.936972
$139$	−2294.67	−1.40023	−0.700114	−	0.714031i	$-0.746868\pi$
$139$	−2294.67	−1.40023	−0.700114	+	0.714031i	$0.746868\pi$
$140$	716.192	0.432352
$141$	−1642.29	−0.980891
$142$	−2523.72	−1.49145
$143$	1081.36	0.632365
$144$	−616.265	−0.356635
$145$	3403.03	1.94901
$146$	2224.33	1.26087
$147$	900.321	0.505151
$148$	318.263	0.176764
$149$	−66.9449	−0.0368077	−0.0184038	−	0.999831i	$-0.505858\pi$
$149$	−66.9449	−0.0368077	−0.0184038	+	0.999831i	$0.505858\pi$
$150$	1102.62	0.600189
$151$	1284.29	0.692148	0.346074	−	0.938207i	$-0.387515\pi$
$151$	1284.29	0.692148	0.346074	+	0.938207i	$0.387515\pi$
$152$	279.050	0.148908
$153$	772.737	0.408314
$154$	1191.67	0.623555
$155$	−806.820	−0.418099
$156$	−517.320	−0.265505
$157$	3167.73	1.61027	0.805134	−	0.593093i	$-0.202093\pi$
$157$	3167.73	1.61027	0.805134	+	0.593093i	$0.202093\pi$
$158$	−301.992	−0.152058
$159$	839.183	0.418563
$160$	−3692.13	−1.82430
$161$	−845.138	−0.413703
$162$	−317.815	−0.154135
$163$	−338.948	−0.162874	−0.0814370	−	0.996678i	$-0.525951\pi$
$163$	−338.948	−0.162874	−0.0814370	+	0.996678i	$0.525951\pi$
$164$	−1470.82	−0.700316
$165$	2057.27	0.970655
$166$	−2845.40	−1.33040
$167$	1772.47	0.821304	0.410652	−	0.911792i	$-0.365301\pi$
$167$	1772.47	0.821304	0.410652	+	0.911792i	$0.365301\pi$
$168$	46.6394	0.0214185
$169$	−1653.25	−0.752503
$170$	4981.69	2.24752
$171$	1058.00	0.473143
$172$	1583.03	0.701774
$173$	−960.710	−0.422205	−0.211102	−	0.977464i	$-0.567705\pi$
$173$	−960.710	−0.422205	−0.211102	+	0.977464i	$0.567705\pi$
$174$	−2708.82	−1.18020
$175$	−613.490	−0.265003
$176$	−3175.39	−1.35997
$177$	−2035.07	−0.864208
$178$	−3862.02	−1.62624
$179$	2462.03	1.02805	0.514024	−	0.857776i	$-0.328154\pi$
$179$	2462.03	1.02805	0.514024	+	0.857776i	$0.328154\pi$
$180$	−984.189	−0.407540
$181$	2387.03	0.980255	0.490128	−	0.871651i	$-0.336950\pi$
$181$	2387.03	0.980255	0.490128	+	0.871651i	$0.336950\pi$
$182$	599.216	0.244048
$183$	490.840	0.198273
$184$	306.318	0.122729
$185$	−636.421	−0.252922
$186$	642.230	0.253175
$187$	3981.63	1.55704
$188$	4048.25	1.57047
$189$	176.831	0.0680557
$190$	6820.74	2.60436
$191$	3188.19	1.20780	0.603899	−	0.797061i	$-0.293613\pi$
$191$	3188.19	1.20780	0.603899	+	0.797061i	$0.293613\pi$
$192$	1295.56	0.486975
$193$	387.169	0.144399	0.0721996	−	0.997390i	$-0.476998\pi$
$193$	387.169	0.144399	0.0721996	+	0.997390i	$0.476998\pi$
$194$	2985.20	1.10477
$195$	1034.47	0.379897
$196$	−2219.29	−0.808781
$197$	−511.432	−0.184965	−0.0924823	−	0.995714i	$-0.529480\pi$
$197$	−511.432	−0.184965	−0.0924823	+	0.995714i	$0.529480\pi$
$198$	−1637.59	−0.587769
$199$	2642.38	0.941272	0.470636	−	0.882327i	$-0.344024\pi$
$199$	2642.38	0.941272	0.470636	+	0.882327i	$0.344024\pi$
$200$	222.358	0.0786153
$201$	2340.15	0.821203
$202$	−2997.69	−1.04414
$203$	1507.17	0.521096
$204$	−1904.80	−0.653738
$205$	2941.16	1.00205
$206$	2284.37	0.772620
$207$	1161.39	0.389961
$208$	−1596.71	−0.532267
$209$	5451.50	1.80425
$210$	1139.99	0.374605
$211$	3585.37	1.16980	0.584898	−	0.811107i	$-0.301134\pi$
$211$	3585.37	1.16980	0.584898	+	0.811107i	$0.301134\pi$
$212$	−2068.59	−0.670147
$213$	−1929.62	−0.620729
$214$	−1770.50	−0.565556
$215$	−3165.55	−1.00413
$216$	−64.0917	−0.0201893
$217$	−357.333	−0.111785
$218$	−1634.47	−0.507799
$219$	1700.71	0.524764
$220$	−5071.17	−1.55408
$221$	2002.11	0.609397
$222$	506.592	0.153154
$223$	1218.19	0.365811	0.182906	−	0.983130i	$-0.441450\pi$
$223$	1218.19	0.365811	0.182906	+	0.983130i	$0.441450\pi$
$224$	−1635.21	−0.487754
$225$	843.056	0.249794
$226$	4733.66	1.39327
$227$	−1445.19	−0.422557	−0.211279	−	0.977426i	$-0.567763\pi$
$227$	−1445.19	−0.422557	−0.211279	+	0.977426i	$0.567763\pi$
$228$	−2607.98	−0.757533
$229$	2876.63	0.830101	0.415050	−	0.909798i	$-0.363764\pi$
$229$	2876.63	0.830101	0.415050	+	0.909798i	$0.363764\pi$
$230$	7487.23	2.14649
$231$	911.144	0.259519
$232$	−546.270	−0.154588
$233$	2519.58	0.708426	0.354213	−	0.935165i	$-0.384749\pi$
$233$	2519.58	0.708426	0.354213	+	0.935165i	$0.384749\pi$
$234$	−823.440	−0.230043
$235$	−8095.16	−2.24711
$236$	5016.44	1.38366
$237$	−230.902	−0.0632856
$238$	2206.34	0.600907
$239$	6388.18	1.72894	0.864470	−	0.502684i	$-0.167654\pi$
$239$	6388.18	1.72894	0.864470	+	0.502684i	$0.167654\pi$
$240$	−3037.69	−0.817009
$241$	−2480.02	−0.662872	−0.331436	−	0.943478i	$-0.607533\pi$
$241$	−2480.02	−0.662872	−0.331436	+	0.943478i	$0.607533\pi$
$242$	−3215.53	−0.854140
$243$	−243.000	−0.0641500
$244$	−1209.92	−0.317448
$245$	4437.86	1.15724
$246$	−2341.17	−0.606778
$247$	2741.22	0.706152
$248$	129.514	0.0331619
$249$	−2175.57	−0.553701
$250$	−1817.64	−0.459831
$251$	2077.93	0.522542	0.261271	−	0.965266i	$-0.415858\pi$
$251$	2077.93	0.522542	0.261271	+	0.965266i	$0.415858\pi$
$252$	−435.888	−0.108962
$253$	5984.20	1.48705
$254$	5696.42	1.40719
$255$	3808.97	0.935400
$256$	4643.60	1.13369
$257$	−3713.06	−0.901223	−0.450611	−	0.892720i	$-0.648794\pi$
$257$	−3713.06	−0.901223	−0.450611	+	0.892720i	$0.648794\pi$
$258$	2519.78	0.608041
$259$	−281.865	−0.0676225
$260$	−2549.97	−0.608241
$261$	−2071.15	−0.491191
$262$	4713.91	1.11155
$263$	−5716.06	−1.34018	−0.670090	−	0.742279i	$-0.733745\pi$
$263$	−5716.06	−1.34018	−0.670090	+	0.742279i	$0.733745\pi$
$264$	−330.242	−0.0769885
$265$	4136.50	0.958880
$266$	3020.84	0.696314
$267$	−2952.88	−0.676830
$268$	−5768.49	−1.31480
$269$	−5156.84	−1.16884	−0.584420	−	0.811451i	$-0.698678\pi$
$269$	−5156.84	−1.16884	−0.584420	+	0.811451i	$0.698678\pi$
$270$	−1566.58	−0.353106
$271$	10.5166	0.00235734	0.00117867	−	0.999999i	$-0.499625\pi$
$271$	10.5166	0.00235734	0.00117867	+	0.999999i	$0.499625\pi$
$272$	−5879.14	−1.31057
$273$	458.157	0.101571
$274$	3903.87	0.860735
$275$	4343.96	0.952548
$276$	−2862.82	−0.624353
$277$	−3777.76	−0.819435	−0.409718	−	0.912212i	$-0.634373\pi$
$277$	−3777.76	−0.819435	−0.409718	+	0.912212i	$0.634373\pi$
$278$	9003.49	1.94242
$279$	491.046	0.105370
$280$	229.895	0.0490673
$281$	6305.66	1.33866	0.669331	−	0.742964i	$-0.266581\pi$
$281$	6305.66	1.33866	0.669331	+	0.742964i	$0.266581\pi$
$282$	6443.76	1.36071
$283$	−2614.26	−0.549122	−0.274561	−	0.961570i	$-0.588533\pi$
$283$	−2614.26	−0.549122	−0.274561	+	0.961570i	$0.588533\pi$
$284$	4756.52	0.993829
$285$	5215.10	1.08392
$286$	−4242.89	−0.877229
$287$	1302.61	0.267912
$288$	2247.10	0.459762
$289$	2458.87	0.500483
$290$	−13352.3	−2.70370
$291$	2282.47	0.459796
$292$	−4192.26	−0.840182
$293$	−655.808	−0.130760	−0.0653801	−	0.997860i	$-0.520826\pi$
$293$	−655.808	−0.130760	−0.0653801	+	0.997860i	$0.520826\pi$
$294$	−3532.54	−0.700755
$295$	−10031.2	−1.97980
$296$	102.161	0.0200608
$297$	−1252.09	−0.244625
$298$	262.668	0.0510603
$299$	3009.08	0.582005
$300$	−2078.14	−0.399937
$301$	−1401.99	−0.268470
$302$	−5039.12	−0.960161
$303$	−2292.02	−0.434564
$304$	−8049.50	−1.51865
$305$	2419.45	0.454220
$306$	−3031.95	−0.566421
$307$	−639.986	−0.118977	−0.0594885	−	0.998229i	$-0.518947\pi$
$307$	−639.986	−0.118977	−0.0594885	+	0.998229i	$0.518947\pi$
$308$	−2245.97	−0.415507
$309$	1746.62	0.321559
$310$	3165.68	0.579995
$311$	−1808.14	−0.329679	−0.164840	−	0.986320i	$-0.552711\pi$
$311$	−1808.14	−0.329679	−0.164840	+	0.986320i	$0.552711\pi$
$312$	−166.058	−0.0301320
$313$	−8084.23	−1.45990	−0.729949	−	0.683502i	$-0.760456\pi$
$313$	−8084.23	−1.45990	−0.729949	+	0.683502i	$0.760456\pi$
$314$	−12429.0	−2.23379
$315$	871.633	0.155908
$316$	569.173	0.101324
$317$	−7187.04	−1.27339	−0.636695	−	0.771116i	$-0.719699\pi$
$317$	−7187.04	−1.27339	−0.636695	+	0.771116i	$0.719699\pi$
$318$	−3292.66	−0.580639
$319$	−10671.9	−1.87307
$320$	6386.09	1.11560
$321$	−1353.72	−0.235380
$322$	3316.02	0.573897
$323$	10093.3	1.73872
$324$	598.996	0.102708
$325$	2184.31	0.372811
$326$	1329.91	0.225942
$327$	−1249.71	−0.211342
$328$	−472.128	−0.0794784
$329$	−3585.27	−0.600797
$330$	−8072.00	−1.34651
$331$	11873.0	1.97159	0.985797	−	0.167944i	$-0.0537127\pi$
$331$	11873.0	1.97159	0.985797	+	0.167944i	$0.0537127\pi$
$332$	5362.80	0.886512
$333$	387.338	0.0637417
$334$	−6954.54	−1.13933
$335$	11535.1	1.88128
$336$	−1345.36	−0.218439
$337$	−337.000	−0.0544735
$337$	−337.000	−0.0544735
$338$	6486.77	1.04389
$339$	3619.33	0.579868
$340$	−9389.13	−1.49764
$341$	2530.18	0.401809
$342$	−4151.23	−0.656353
$343$	4211.89	0.663034
$344$	508.147	0.0796438
$345$	5724.70	0.893355
$346$	3769.49	0.585690
$347$	−8308.23	−1.28533	−0.642665	−	0.766148i	$-0.722171\pi$
$347$	−8308.23	−1.28533	−0.642665	+	0.766148i	$0.722171\pi$
$348$	5105.39	0.786430
$349$	1423.22	0.218290	0.109145	−	0.994026i	$-0.465189\pi$
$349$	1423.22	0.218290	0.109145	+	0.994026i	$0.465189\pi$
$350$	2407.12	0.367617
$351$	−629.598	−0.0957420
$352$	11578.5	1.75322
$353$	−5587.90	−0.842532	−0.421266	−	0.906937i	$-0.638414\pi$
$353$	−5587.90	−0.842532	−0.421266	+	0.906937i	$0.638414\pi$
$354$	7984.88	1.19885
$355$	−9511.48	−1.42202
$356$	7278.87	1.08365
$357$	1686.96	0.250093
$358$	−9660.13	−1.42613
$359$	−4075.45	−0.599148	−0.299574	−	0.954073i	$-0.596845\pi$
$359$	−4075.45	−0.599148	−0.299574	+	0.954073i	$0.596845\pi$
$360$	−315.921	−0.0462514
$361$	6960.36	1.01478
$362$	−9365.85	−1.35983
$363$	−2458.57	−0.355487
$364$	−1129.36	−0.162622
$365$	8383.13	1.20217
$366$	−1925.88	−0.275048
$367$	5626.07	0.800214	0.400107	−	0.916468i	$-0.368973\pi$
$367$	5626.07	0.800214	0.400107	+	0.916468i	$0.368973\pi$
$368$	−8836.07	−1.25166
$369$	−1790.04	−0.252537
$370$	2497.09	0.350859
$371$	1832.01	0.256370
$372$	−1210.43	−0.168704
$373$	−2799.44	−0.388604	−0.194302	−	0.980942i	$-0.562244\pi$
$373$	−2799.44	−0.388604	−0.194302	+	0.980942i	$0.562244\pi$
$374$	−15622.5	−2.15995
$375$	−1389.76	−0.191378
$376$	1299.47	0.178232
$377$	−5366.22	−0.733088
$378$	−693.821	−0.0944082
$379$	12841.0	1.74037	0.870184	−	0.492726i	$-0.164000\pi$
$379$	12841.0	1.74037	0.870184	+	0.492726i	$0.164000\pi$
$380$	−12855.2	−1.73542
$381$	4355.45	0.585660
$382$	−12509.3	−1.67548
$383$	6318.66	0.842998	0.421499	−	0.906829i	$-0.361504\pi$
$383$	6318.66	0.842998	0.421499	+	0.906829i	$0.361504\pi$
$384$	908.920	0.120789
$385$	4491.21	0.594528
$386$	−1519.12	−0.200313
$387$	1926.61	0.253062
$388$	−5626.29	−0.736164
$389$	7291.35	0.950350	0.475175	−	0.879891i	$-0.342385\pi$
$389$	7291.35	0.950350	0.475175	+	0.879891i	$0.342385\pi$
$390$	−4058.90	−0.527001
$391$	11079.6	1.43304
$392$	−712.384	−0.0917879
$393$	3604.23	0.462620
$394$	2006.68	0.256586
$395$	−1138.16	−0.144980
$396$	3086.41	0.391661
$397$	−8403.88	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$397$	−8403.88	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$398$	−10367.8	−1.30575
$399$	2309.72	0.289801
$400$	−6414.15	−0.801768
$401$	−3146.51	−0.391844	−0.195922	−	0.980620i	$-0.562770\pi$
$401$	−3146.51	−0.391844	−0.195922	+	0.980620i	$0.562770\pi$
$402$	−9181.94	−1.13919
$403$	1272.27	0.157261
$404$	5649.83	0.695767
$405$	−1197.79	−0.146960
$406$	−5913.60	−0.722875
$407$	1995.81	0.243068
$408$	−611.433	−0.0741922
$409$	−14642.5	−1.77023	−0.885116	−	0.465371i	$-0.845921\pi$
$409$	−14642.5	−1.77023	−0.885116	+	0.465371i	$0.845921\pi$
$410$	−11540.1	−1.39006
$411$	2984.88	0.358231
$412$	−4305.42	−0.514837
$413$	−4442.74	−0.529329
$414$	−4556.87	−0.540961
$415$	−10723.8	−1.26846
$416$	5822.09	0.686181
$417$	6884.02	0.808422
$418$	−21389.8	−2.50289
$419$	−15631.1	−1.82250	−0.911252	−	0.411848i	$-0.864883\pi$
$419$	−15631.1	−1.82250	−0.911252	+	0.411848i	$0.864883\pi$
$420$	−2148.58	−0.249619
$421$	5623.63	0.651019	0.325509	−	0.945539i	$-0.394464\pi$
$421$	5623.63	0.651019	0.325509	+	0.945539i	$0.394464\pi$
$422$	−14067.7	−1.62276
$423$	4926.87	0.566318
$424$	−664.009	−0.0760545
$425$	8042.72	0.917951
$426$	7571.15	0.861088
$427$	1071.55	0.121442
$428$	3336.92	0.376860
$429$	−3244.09	−0.365096
$430$	12420.5	1.39295
$431$	1957.99	0.218824	0.109412	−	0.993996i	$-0.465103\pi$
$431$	1957.99	0.218824	0.109412	+	0.993996i	$0.465103\pi$
$432$	1848.80	0.205903
$433$	3436.49	0.381402	0.190701	−	0.981648i	$-0.438924\pi$
$433$	3436.49	0.381402	0.190701	+	0.981648i	$0.438924\pi$
$434$	1402.05	0.155070
$435$	−10209.1	−1.12526
$436$	3080.53	0.338373
$437$	15169.7	1.66056
$438$	−6672.99	−0.727963
$439$	15147.3	1.64679	0.823397	−	0.567466i	$-0.192076\pi$
$439$	15147.3	1.64679	0.823397	+	0.567466i	$0.192076\pi$
$440$	−1627.83	−0.176372
$441$	−2700.96	−0.291649
$442$	−7855.59	−0.845367
$443$	−5013.85	−0.537731	−0.268866	−	0.963178i	$-0.586649\pi$
$443$	−5013.85	−0.537731	−0.268866	+	0.963178i	$0.586649\pi$
$444$	−954.789	−0.102055
$445$	−14555.3	−1.55054
$446$	−4779.74	−0.507460
$447$	200.835	0.0212509
$448$	2828.34	0.298273
$449$	−13335.6	−1.40166	−0.700830	−	0.713328i	$-0.747187\pi$
$449$	−13335.6	−1.40166	−0.700830	+	0.713328i	$0.747187\pi$
$450$	−3307.85	−0.346519
$451$	−9223.45	−0.963005
$452$	−8921.67	−0.928407
$453$	−3852.88	−0.399612
$454$	5670.41	0.586179
$455$	2258.35	0.232688
$456$	−837.150	−0.0859718
$457$	−8086.28	−0.827703	−0.413852	−	0.910344i	$-0.635817\pi$
$457$	−8086.28	−0.827703	−0.413852	+	0.910344i	$0.635817\pi$
$458$	−11286.9	−1.15153
$459$	−2318.21	−0.235740
$460$	−14111.4	−1.43032
$461$	1182.39	0.119457	0.0597283	−	0.998215i	$-0.480977\pi$
$461$	1182.39	0.119457	0.0597283	+	0.998215i	$0.480977\pi$
$462$	−3575.01	−0.360010
$463$	−14246.8	−1.43003	−0.715014	−	0.699110i	$-0.753580\pi$
$463$	−14246.8	−1.43003	−0.715014	+	0.699110i	$0.753580\pi$
$464$	15757.7	1.57658
$465$	2420.46	0.241390
$466$	−9885.94	−0.982741
$467$	−7653.01	−0.758327	−0.379164	−	0.925330i	$-0.623788\pi$
$467$	−7653.01	−0.758327	−0.379164	+	0.925330i	$0.623788\pi$
$468$	1551.96	0.153289
$469$	5108.78	0.502988
$470$	31762.6	3.11723
$471$	−9503.18	−0.929689
$472$	1610.26	0.157030
$473$	9927.13	0.965010
$474$	905.977	0.0877909
$475$	11011.8	1.06370
$476$	−4158.35	−0.400415
$477$	−2517.55	−0.241658
$478$	−25065.0	−2.39842
$479$	−4361.64	−0.416051	−0.208026	−	0.978123i	$-0.566704\pi$
$479$	−4361.64	−0.416051	−0.208026	+	0.978123i	$0.566704\pi$
$480$	11076.4	1.05326
$481$	1003.57	0.0951326
$482$	9730.72	0.919548
$483$	2535.41	0.238852
$484$	6060.39	0.569158
$485$	11250.7	1.05334
$486$	953.446	0.0889901
$487$	19190.9	1.78568	0.892839	−	0.450376i	$-0.148710\pi$
$487$	19190.9	1.78568	0.892839	+	0.450376i	$0.148710\pi$
$488$	−388.380	−0.0360269
$489$	1016.84	0.0940353
$490$	−17412.6	−1.60535
$491$	1264.48	0.116223	0.0581114	−	0.998310i	$-0.481492\pi$
$491$	1264.48	0.116223	0.0581114	+	0.998310i	$0.481492\pi$
$492$	4412.47	0.404328
$493$	−19758.7	−1.80504
$494$	−10755.6	−0.979587
$495$	−6171.80	−0.560408
$496$	−3735.98	−0.338206
$497$	−4212.54	−0.380198
$498$	8536.19	0.768104
$499$	−10159.2	−0.911399	−0.455699	−	0.890134i	$-0.650611\pi$
$499$	−10159.2	−0.911399	−0.455699	+	0.890134i	$0.650611\pi$
$500$	3425.76	0.306409
$501$	−5317.40	−0.474180
$502$	−8153.08	−0.724880
$503$	9185.99	0.814280	0.407140	−	0.913366i	$-0.366526\pi$
$503$	9185.99	0.814280	0.407140	+	0.913366i	$0.366526\pi$
$504$	−139.918	−0.0123660
$505$	−11297.8	−0.995537
$506$	−23479.9	−2.06286
$507$	4959.75	0.434458
$508$	−10736.2	−0.937681
$509$	13806.5	1.20228	0.601141	−	0.799143i	$-0.294713\pi$
$509$	13806.5	1.20228	0.601141	+	0.799143i	$0.294713\pi$
$510$	−14945.1	−1.29760
$511$	3712.81	0.321419
$512$	−15796.1	−1.36346
$513$	−3174.01	−0.273169
$514$	14568.7	1.25019
$515$	8609.42	0.736653
$516$	−4749.10	−0.405169
$517$	25386.4	2.15956
$518$	1105.94	0.0938072
$519$	2882.13	0.243760
$520$	−818.531	−0.0690288
$521$	−7767.10	−0.653134	−0.326567	−	0.945174i	$-0.605892\pi$
$521$	−7767.10	−0.653134	−0.326567	+	0.945174i	$0.605892\pi$
$522$	8126.46	0.681389
$523$	11785.0	0.985317	0.492659	−	0.870223i	$-0.336025\pi$
$523$	11785.0	0.985317	0.492659	+	0.870223i	$0.336025\pi$
$524$	−8884.45	−0.740685
$525$	1840.47	0.152999
$526$	22427.8	1.85912
$527$	4684.55	0.387215
$528$	9526.18	0.785177
$529$	4485.06	0.368625
$530$	−16230.2	−1.33018
$531$	6105.20	0.498951
$532$	−5693.46	−0.463990
$533$	−4637.90	−0.376903
$534$	11586.1	0.938911
$535$	−6672.73	−0.539229
$536$	−1851.66	−0.149216
$537$	−7386.08	−0.593544
$538$	20233.6	1.62144
$539$	−13917.1	−1.11215
$540$	2952.57	0.235293
$541$	653.476	0.0519319	0.0259659	−	0.999663i	$-0.491734\pi$
$541$	653.476	0.0519319	0.0259659	+	0.999663i	$0.491734\pi$
$542$	−41.2635	−0.00327015
$543$	−7161.08	−0.565951
$544$	21437.2	1.68954
$545$	−6160.05	−0.484160
$546$	−1797.65	−0.140901
$547$	−377.550	−0.0295116	−0.0147558	−	0.999891i	$-0.504697\pi$
$547$	−377.550	−0.0295116	−0.0147558	+	0.999891i	$0.504697\pi$
$548$	−7357.73	−0.573552
$549$	−1472.52	−0.114473
$550$	−17044.2	−1.32139
$551$	−27052.8	−2.09163
$552$	−918.953	−0.0708573
$553$	−504.080	−0.0387625
$554$	14822.6	1.13674
$555$	1909.26	0.146025
$556$	−16969.1	−1.29434
$557$	24625.5	1.87328	0.936639	−	0.350296i	$-0.113919\pi$
$557$	24625.5	1.87328	0.936639	+	0.350296i	$0.113919\pi$
$558$	−1926.69	−0.146171
$559$	4991.73	0.377688
$560$	−6631.57	−0.500419
$561$	−11944.9	−0.898955
$562$	−24741.2	−1.85702
$563$	12242.1	0.916419	0.458210	−	0.888844i	$-0.348491\pi$
$563$	12242.1	0.916419	0.458210	+	0.888844i	$0.348491\pi$
$564$	−12144.7	−0.906712
$565$	17840.4	1.32841
$566$	10257.4	0.761753
$567$	−530.492	−0.0392920
$568$	1526.82	0.112789
$569$	5235.14	0.385709	0.192854	−	0.981227i	$-0.438225\pi$
$569$	5235.14	0.385709	0.192854	+	0.981227i	$0.438225\pi$
$570$	−20462.2	−1.50363
$571$	−18525.1	−1.35771	−0.678855	−	0.734272i	$-0.737523\pi$
$571$	−18525.1	−1.35771	−0.678855	+	0.734272i	$0.737523\pi$
$572$	7996.70	0.584543
$573$	−9564.57	−0.697322
$574$	−5110.99	−0.371652
$575$	12087.8	0.876690
$576$	−3886.69	−0.281155
$577$	1870.70	0.134971	0.0674856	−	0.997720i	$-0.478502\pi$
$577$	1870.70	0.134971	0.0674856	+	0.997720i	$0.478502\pi$
$578$	−9647.76	−0.694280
$579$	−1161.51	−0.0833689
$580$	25165.5	1.80162
$581$	−4749.48	−0.339142
$582$	−8955.60	−0.637838
$583$	−12972.0	−0.921520
$584$	−1345.70	−0.0953516
$585$	−3103.41	−0.219334
$586$	2573.16	0.181393
$587$	19930.0	1.40136	0.700681	−	0.713475i	$-0.252880\pi$
$587$	19930.0	1.40136	0.700681	+	0.713475i	$0.252880\pi$
$588$	6657.88	0.466950
$589$	6413.91	0.448694
$590$	39359.0	2.74642
$591$	1534.30	0.106789
$592$	−2946.95	−0.204593
$593$	10254.1	0.710094	0.355047	−	0.934848i	$-0.384465\pi$
$593$	10254.1	0.710094	0.355047	+	0.934848i	$0.384465\pi$
$594$	4912.76	0.339349
$595$	8315.34	0.572934
$596$	−495.058	−0.0340241
$597$	−7927.13	−0.543444
$598$	−11806.6	−0.807368
$599$	8945.20	0.610169	0.305084	−	0.952325i	$-0.401315\pi$
$599$	8945.20	0.610169	0.305084	+	0.952325i	$0.401315\pi$
$600$	−667.073	−0.0453886
$601$	21885.1	1.48538	0.742689	−	0.669637i	$-0.233550\pi$
$601$	21885.1	1.48538	0.742689	+	0.669637i	$0.233550\pi$
$602$	5500.91	0.372426
$603$	−7020.46	−0.474122
$604$	9497.37	0.639806
$605$	−12118.8	−0.814379
$606$	8993.07	0.602836
$607$	15323.4	1.02464	0.512321	−	0.858794i	$-0.328786\pi$
$607$	15323.4	1.02464	0.512321	+	0.858794i	$0.328786\pi$
$608$	29351.0	1.95780
$609$	−4521.51	−0.300855
$610$	−9493.06	−0.630103
$611$	12765.2	0.845213
$612$	5714.39	0.377436
$613$	21199.5	1.39680	0.698401	−	0.715707i	$-0.253895\pi$
$613$	21199.5	1.39680	0.698401	+	0.715707i	$0.253895\pi$
$614$	2511.08	0.165047
$615$	−8823.48	−0.578532
$616$	−720.948	−0.0471556
$617$	17302.6	1.12898	0.564488	−	0.825441i	$-0.309074\pi$
$617$	17302.6	1.12898	0.564488	+	0.825441i	$0.309074\pi$
$618$	−6853.11	−0.446072
$619$	−29715.1	−1.92948	−0.964742	−	0.263196i	$-0.915223\pi$
$619$	−29715.1	−1.92948	−0.964742	+	0.263196i	$0.915223\pi$
$620$	−5966.44	−0.386481
$621$	−3484.16	−0.225144
$622$	7094.50	0.457337
$623$	−6446.42	−0.414559
$624$	4790.12	0.307305
$625$	−18559.5	−1.18781
$626$	31719.7	2.02520
$627$	−16354.5	−1.04168
$628$	23425.4	1.48849
$629$	3695.19	0.234240
$630$	−3419.98	−0.216278
$631$	1679.57	0.105963	0.0529816	−	0.998595i	$-0.483128\pi$
$631$	1679.57	0.105963	0.0529816	+	0.998595i	$0.483128\pi$
$632$	182.702	0.0114992
$633$	−10756.1	−0.675382
$634$	28199.4	1.76647
$635$	21468.9	1.34168
$636$	6205.77	0.386910
$637$	−6998.03	−0.435278
$638$	41872.7	2.59836
$639$	5788.86	0.358378
$640$	4480.25	0.276715
$641$	−13554.0	−0.835183	−0.417592	−	0.908635i	$-0.637126\pi$
$641$	−13554.0	−0.835183	−0.417592	+	0.908635i	$0.637126\pi$
$642$	5311.51	0.326524
$643$	−1425.09	−0.0874031	−0.0437015	−	0.999045i	$-0.513915\pi$
$643$	−1425.09	−0.0874031	−0.0437015	+	0.999045i	$0.513915\pi$
$644$	−6249.80	−0.382417
$645$	9496.64	0.579736
$646$	−39602.5	−2.41198
$647$	−447.780	−0.0272088	−0.0136044	−	0.999907i	$-0.504331\pi$
$647$	−447.780	−0.0272088	−0.0136044	+	0.999907i	$0.504331\pi$
$648$	192.275	0.0116563
$649$	31457.9	1.90266
$650$	−8570.45	−0.517170
$651$	1072.00	0.0645390
$652$	−2506.52	−0.150557
$653$	28906.3	1.73230	0.866148	−	0.499787i	$-0.166588\pi$
$653$	28906.3	1.73230	0.866148	+	0.499787i	$0.166588\pi$
$654$	4903.40	0.293178
$655$	17766.0	1.05981
$656$	13619.0	0.810570
$657$	−5102.13	−0.302973
$658$	14067.3	0.833437
$659$	23567.0	1.39308	0.696539	−	0.717519i	$-0.254722\pi$
$659$	23567.0	1.39308	0.696539	+	0.717519i	$0.254722\pi$
$660$	15213.5	0.897251
$661$	3928.17	0.231147	0.115573	−	0.993299i	$-0.463129\pi$
$661$	3928.17	0.231147	0.115573	+	0.993299i	$0.463129\pi$
$662$	−46585.3	−2.73503
$663$	−6006.34	−0.351835
$664$	1721.44	0.100609
$665$	11385.0	0.663900
$666$	−1519.78	−0.0884237
$667$	−29696.3	−1.72391
$668$	13107.4	0.759193
$669$	−3654.56	−0.211201
$670$	−45259.6	−2.60975
$671$	−7587.36	−0.436523
$672$	4905.62	0.281605
$673$	−11501.5	−0.658768	−0.329384	−	0.944196i	$-0.606841\pi$
$673$	−11501.5	−0.658768	−0.329384	+	0.944196i	$0.606841\pi$
$674$	1322.27	0.0755666
$675$	−2529.17	−0.144219
$676$	−12225.8	−0.695596
$677$	15479.8	0.878784	0.439392	−	0.898296i	$-0.355194\pi$
$677$	15479.8	0.878784	0.439392	+	0.898296i	$0.355194\pi$
$678$	−14201.0	−0.804403
$679$	4982.84	0.281626
$680$	−3013.87	−0.169966
$681$	4335.56	0.243963
$682$	−9927.54	−0.557397
$683$	16028.0	0.897945	0.448972	−	0.893546i	$-0.351790\pi$
$683$	16028.0	0.897945	0.448972	+	0.893546i	$0.351790\pi$
$684$	7823.93	0.437362
$685$	14713.0	0.820667
$686$	−16526.0	−0.919773
$687$	−8629.89	−0.479259
$688$	−14658.1	−0.812257
$689$	−6522.81	−0.360667
$690$	−22461.7	−1.23928
$691$	−9452.10	−0.520369	−0.260184	−	0.965559i	$-0.583783\pi$
$691$	−9452.10	−0.520369	−0.260184	+	0.965559i	$0.583783\pi$
$692$	−7104.46	−0.390276
$693$	−2733.43	−0.149833
$694$	32598.6	1.78303
$695$	33932.7	1.85200
$696$	1638.81	0.0892513
$697$	−17077.0	−0.928028
$698$	−5584.20	−0.302815
$699$	−7558.74	−0.409010
$700$	−4536.76	−0.244962
$701$	7678.28	0.413701	0.206851	−	0.978373i	$-0.433679\pi$
$701$	7678.28	0.413701	0.206851	+	0.978373i	$0.433679\pi$
$702$	2470.32	0.132815
$703$	5059.31	0.271430
$704$	−20026.7	−1.07214
$705$	24285.5	1.29737
$706$	21925.0	1.16878
$707$	−5003.69	−0.266171
$708$	−15049.3	−0.798854
$709$	14526.9	0.769491	0.384746	−	0.923023i	$-0.374289\pi$
$709$	14526.9	0.769491	0.384746	+	0.923023i	$0.374289\pi$
$710$	37319.7	1.97265
$711$	692.705	0.0365379
$712$	2336.49	0.122983
$713$	7040.66	0.369810
$714$	−6619.02	−0.346934
$715$	−15990.8	−0.836393
$716$	18206.7	0.950303
$717$	−19164.5	−0.998205
$718$	15990.6	0.831149
$719$	−22424.9	−1.16315	−0.581577	−	0.813491i	$-0.697564\pi$
$719$	−22424.9	−1.16315	−0.581577	+	0.813491i	$0.697564\pi$
$720$	9113.08	0.471701
$721$	3813.03	0.196955
$722$	−27310.0	−1.40772
$723$	7440.06	0.382709
$724$	17652.1	0.906125
$725$	−21556.7	−1.10427
$726$	9646.58	0.493138
$727$	−14350.5	−0.732093	−0.366046	−	0.930597i	$-0.619289\pi$
$727$	−14350.5	−0.732093	−0.366046	+	0.930597i	$0.619289\pi$
$728$	−362.520	−0.0184559
$729$	729.000	0.0370370
$730$	−32892.5	−1.66768
$731$	18379.8	0.929960
$732$	3629.77	0.183279
$733$	15024.2	0.757071	0.378535	−	0.925587i	$-0.376428\pi$
$733$	15024.2	0.757071	0.378535	+	0.925587i	$0.376428\pi$
$734$	−22074.7	−1.11007
$735$	−13313.6	−0.668134
$736$	32219.1	1.61360
$737$	−36173.9	−1.80798
$738$	7023.50	0.350324
$739$	−37847.2	−1.88394	−0.941970	−	0.335697i	$-0.891028\pi$
$739$	−37847.2	−1.88394	−0.941970	+	0.335697i	$0.891028\pi$
$740$	−4706.34	−0.233795
$741$	−8223.65	−0.407697
$742$	−7188.18	−0.355642
$743$	22381.6	1.10512	0.552558	−	0.833475i	$-0.313652\pi$
$743$	22381.6	1.10512	0.552558	+	0.833475i	$0.313652\pi$
$744$	−388.543	−0.0191461
$745$	989.954	0.0486834
$746$	10984.0	0.539079
$747$	6526.72	0.319679
$748$	29444.2	1.43929
$749$	−2955.29	−0.144171
$750$	5452.92	0.265483
$751$	20159.1	0.979513	0.489757	−	0.871859i	$-0.337086\pi$
$751$	20159.1	0.979513	0.489757	+	0.871859i	$0.337086\pi$
$752$	−37484.6	−1.81772
$753$	−6233.80	−0.301690
$754$	21055.1	1.01695
$755$	−18991.6	−0.915465
$756$	1307.66	0.0629091
$757$	−31425.6	−1.50883	−0.754413	−	0.656399i	$-0.772079\pi$
$757$	−31425.6	−1.50883	−0.754413	+	0.656399i	$0.772079\pi$
$758$	−50383.7	−2.41427
$759$	−17952.6	−0.858548
$760$	−4126.48	−0.196951
$761$	−27384.6	−1.30446	−0.652228	−	0.758023i	$-0.726166\pi$
$761$	−27384.6	−1.30446	−0.652228	+	0.758023i	$0.726166\pi$
$762$	−17089.3	−0.812439
$763$	−2728.22	−0.129447
$764$	23576.7	1.11646
$765$	−11426.9	−0.540054
$766$	−24792.2	−1.16942
$767$	15818.2	0.744670
$768$	−13930.8	−0.654537
$769$	18052.5	0.846541	0.423270	−	0.906003i	$-0.360882\pi$
$769$	18052.5	0.846541	0.423270	+	0.906003i	$0.360882\pi$
$770$	−17621.9	−0.824740
$771$	11139.2	0.520321
$772$	2863.12	0.133479
$773$	−31434.2	−1.46262	−0.731312	−	0.682043i	$-0.761092\pi$
$773$	−31434.2	−1.46262	−0.731312	+	0.682043i	$0.761092\pi$
$774$	−7559.34	−0.351053
$775$	5110.85	0.236887
$776$	−1806.02	−0.0835467
$777$	845.594	0.0390419
$778$	−28608.7	−1.31834
$779$	−23381.1	−1.07537
$780$	7649.92	0.351168
$781$	29827.9	1.36662
$782$	−43472.3	−1.98794
$783$	6213.44	0.283589
$784$	20549.5	0.936110
$785$	−46843.1	−2.12981
$786$	−14141.7	−0.641755
$787$	10803.1	0.489310	0.244655	−	0.969610i	$-0.421325\pi$
$787$	10803.1	0.489310	0.244655	+	0.969610i	$0.421325\pi$
$788$	−3782.04	−0.170977
$789$	17148.2	0.773754
$790$	4465.74	0.201119
$791$	7901.34	0.355170
$792$	990.725	0.0444493
$793$	−3815.21	−0.170847
$794$	32973.9	1.47380
$795$	−12409.5	−0.553609
$796$	19540.4	0.870090
$797$	1835.25	0.0815659	0.0407829	−	0.999168i	$-0.487015\pi$
$797$	1835.25	0.0815659	0.0407829	+	0.999168i	$0.487015\pi$
$798$	−9062.51	−0.402017
$799$	47002.1	2.08112
$800$	23388.0	1.03361
$801$	8858.65	0.390768
$802$	12345.8	0.543573
$803$	−26289.4	−1.15533
$804$	17305.5	0.759101
$805$	12497.6	0.547181
$806$	−4991.93	−0.218156
$807$	15470.5	0.674830
$808$	1813.57	0.0789620
$809$	451.777	0.0196337	0.00981684	−	0.999952i	$-0.496875\pi$
$809$	451.777	0.0196337	0.00981684	+	0.999952i	$0.496875\pi$
$810$	4699.73	0.203866
$811$	36021.1	1.55965	0.779823	−	0.626000i	$-0.215309\pi$
$811$	36021.1	1.55965	0.779823	+	0.626000i	$0.215309\pi$
$812$	11145.5	0.481689
$813$	−31.5498	−0.00136101
$814$	−7830.86	−0.337189
$815$	5012.22	0.215424
$816$	17637.4	0.756659
$817$	25164.9	1.07761
$818$	57452.0	2.45570
$819$	−1374.47	−0.0586421
$820$	21749.9	0.926268
$821$	−29084.4	−1.23636	−0.618181	−	0.786036i	$-0.712130\pi$
$821$	−29084.4	−1.23636	−0.618181	+	0.786036i	$0.712130\pi$
$822$	−11711.6	−0.496945
$823$	15063.0	0.637987	0.318993	−	0.947757i	$-0.396655\pi$
$823$	15063.0	0.637987	0.318993	+	0.947757i	$0.396655\pi$
$824$	−1382.02	−0.0584284
$825$	−13031.9	−0.549954
$826$	17431.7	0.734295
$827$	18118.8	0.761852	0.380926	−	0.924606i	$-0.375605\pi$
$827$	18118.8	0.761852	0.380926	+	0.924606i	$0.375605\pi$
$828$	8588.46	0.360470
$829$	41061.9	1.72031	0.860157	−	0.510029i	$-0.170365\pi$
$829$	41061.9	1.72031	0.860157	+	0.510029i	$0.170365\pi$
$830$	42076.6	1.75964
$831$	11333.3	0.473101
$832$	−10070.2	−0.419616
$833$	−25767.1	−1.07176
$834$	−27010.5	−1.12146
$835$	−26210.5	−1.08629
$836$	40313.9	1.66781
$837$	−1473.14	−0.0608352
$838$	61331.0	2.52821
$839$	−23657.8	−0.973489	−0.486745	−	0.873544i	$-0.661816\pi$
$839$	−23657.8	−0.973489	−0.486745	+	0.873544i	$0.661816\pi$
$840$	−689.685	−0.0283290
$841$	28569.7	1.17142
$842$	−22065.1	−0.903105
$843$	−18917.0	−0.772877
$844$	26513.8	1.08133
$845$	24447.6	0.995293
$846$	−19331.3	−0.785607
$847$	−5367.30	−0.217736
$848$	19154.0	0.775652
$849$	7842.78	0.317036
$850$	−31556.8	−1.27340
$851$	5553.69	0.223711
$852$	−14269.6	−0.573788
$853$	−20282.3	−0.814130	−0.407065	−	0.913399i	$-0.633448\pi$
$853$	−20282.3	−0.814130	−0.407065	+	0.913399i	$0.633448\pi$
$854$	−4204.38	−0.168467
$855$	−15645.3	−0.625799
$856$	1071.14	0.0427695
$857$	16170.4	0.644540	0.322270	−	0.946648i	$-0.395554\pi$
$857$	16170.4	0.644540	0.322270	+	0.946648i	$0.395554\pi$
$858$	12728.7	0.506468
$859$	12437.0	0.494000	0.247000	−	0.969015i	$-0.420555\pi$
$859$	12437.0	0.494000	0.247000	+	0.969015i	$0.420555\pi$
$860$	−23409.2	−0.928196
$861$	−3907.83	−0.154679
$862$	−7682.48	−0.303557
$863$	−48647.3	−1.91886	−0.959429	−	0.281951i	$-0.909018\pi$
$863$	−48647.3	−1.91886	−0.959429	+	0.281951i	$0.909018\pi$
$864$	−6741.29	−0.265444
$865$	14206.6	0.558426
$866$	−13483.6	−0.529088
$867$	−7376.62	−0.288954
$868$	−2642.48	−0.103331
$869$	3569.26	0.139331
$870$	40056.9	1.56098
$871$	−18189.6	−0.707613
$872$	988.837	0.0384017
$873$	−6847.41	−0.265463
$874$	−59520.7	−2.30357
$875$	−3033.97	−0.117219
$876$	12576.8	0.485079
$877$	−17642.2	−0.679288	−0.339644	−	0.940554i	$-0.610307\pi$
$877$	−17642.2	−0.679288	−0.339644	+	0.940554i	$0.610307\pi$
$878$	−59432.8	−2.28446
$879$	1967.42	0.0754944
$880$	46956.4	1.79875
$881$	−3691.47	−0.141168	−0.0705838	−	0.997506i	$-0.522486\pi$
$881$	−3691.47	−0.141168	−0.0705838	+	0.997506i	$0.522486\pi$
$882$	10597.6	0.404581
$883$	21575.1	0.822265	0.411133	−	0.911576i	$-0.365133\pi$
$883$	21575.1	0.822265	0.411133	+	0.911576i	$0.365133\pi$
$884$	14805.6	0.563312
$885$	30093.7	1.14304
$886$	19672.6	0.745951
$887$	−26651.9	−1.00889	−0.504444	−	0.863444i	$-0.668303\pi$
$887$	−26651.9	−1.00889	−0.504444	+	0.863444i	$0.668303\pi$
$888$	−306.483	−0.0115821
$889$	9508.36	0.358718
$890$	57110.0	2.15094
$891$	3756.27	0.141234
$892$	9008.51	0.338147
$893$	64353.5	2.41154
$894$	−788.005	−0.0294797
$895$	−36407.5	−1.35974
$896$	1984.26	0.0739837
$897$	−9027.24	−0.336021
$898$	52324.1	1.94441
$899$	−12555.9	−0.465810
$900$	6234.41	0.230904
$901$	−24017.3	−0.888050
$902$	36189.6	1.33590
$903$	4205.97	0.155001
$904$	−2863.82	−0.105364
$905$	−35298.4	−1.29653
$906$	15117.4	0.554349
$907$	−12962.7	−0.474552	−0.237276	−	0.971442i	$-0.576255\pi$
$907$	−12962.7	−0.474552	−0.237276	+	0.971442i	$0.576255\pi$
$908$	−10687.2	−0.390602
$909$	6876.05	0.250896
$910$	−8860.96	−0.322789
$911$	23784.0	0.864981	0.432490	−	0.901639i	$-0.357635\pi$
$911$	23784.0	0.864981	0.432490	+	0.901639i	$0.357635\pi$
$912$	24148.5	0.876795
$913$	33629.9	1.21904
$914$	31727.7	1.14821
$915$	−7258.34	−0.262244
$916$	21272.7	0.767326
$917$	7868.38	0.283355
$918$	9095.84	0.327023
$919$	21180.0	0.760243	0.380121	−	0.924937i	$-0.375882\pi$
$919$	21180.0	0.760243	0.380121	+	0.924937i	$0.375882\pi$
$920$	−4529.70	−0.162326
$921$	1919.96	0.0686914
$922$	−4639.29	−0.165712
$923$	14998.6	0.534869
$924$	6737.92	0.239893
$925$	4031.45	0.143301
$926$	55899.3	1.98376
$927$	−5239.85	−0.185652
$928$	−57457.6	−2.03248
$929$	−20064.4	−0.708601	−0.354301	−	0.935132i	$-0.615281\pi$
$929$	−20064.4	−0.708601	−0.354301	+	0.935132i	$0.615281\pi$
$930$	−9497.03	−0.334860
$931$	−35279.3	−1.24193
$932$	18632.3	0.654852
$933$	5424.42	0.190340
$934$	30027.7	1.05197
$935$	−58878.8	−2.05940
$936$	498.173	0.0173967
$937$	37342.0	1.30193	0.650965	−	0.759108i	$-0.274364\pi$
$937$	37342.0	1.30193	0.650965	+	0.759108i	$0.274364\pi$
$938$	−20045.0	−0.697754
$939$	24252.7	0.842872
$940$	−59863.8	−2.07717
$941$	21762.7	0.753925	0.376963	−	0.926228i	$-0.376969\pi$
$941$	21762.7	0.753925	0.376963	+	0.926228i	$0.376969\pi$
$942$	37287.1	1.28968
$943$	−25665.8	−0.886314
$944$	−46449.6	−1.60149
$945$	−2614.90	−0.0900134
$946$	−38950.5	−1.33868
$947$	51864.3	1.77969	0.889843	−	0.456267i	$-0.150814\pi$
$947$	51864.3	1.77969	0.889843	+	0.456267i	$0.150814\pi$
$948$	−1707.52	−0.0584997
$949$	−13219.3	−0.452178
$950$	−43206.4	−1.47558
$951$	21561.1	0.735192
$952$	−1334.81	−0.0454428
$953$	35726.9	1.21438	0.607191	−	0.794556i	$-0.292296\pi$
$953$	35726.9	1.21438	0.607191	+	0.794556i	$0.292296\pi$
$954$	9877.97	0.335232
$955$	−47145.7	−1.59748
$956$	47240.6	1.59819
$957$	32015.6	1.08142
$958$	17113.5	0.577154
$959$	6516.26	0.219417
$960$	−19158.3	−0.644094
$961$	−26814.1	−0.900075
$962$	−3937.65	−0.131970
$963$	4061.15	0.135897
$964$	−18339.8	−0.612743
$965$	−5725.30	−0.190989
$966$	−9948.07	−0.331339
$967$	−19765.5	−0.657306	−0.328653	−	0.944451i	$-0.606595\pi$
$967$	−19765.5	−0.657306	−0.328653	+	0.944451i	$0.606595\pi$
$968$	1945.36	0.0645933
$969$	−30279.9	−1.00385
$970$	−44143.9	−1.46121
$971$	7309.79	0.241589	0.120794	−	0.992678i	$-0.461456\pi$
$971$	7309.79	0.241589	0.120794	+	0.992678i	$0.461456\pi$
$972$	−1796.99	−0.0592988
$973$	15028.5	0.495160
$974$	−75298.5	−2.47713
$975$	−6552.92	−0.215242
$976$	11203.2	0.367425
$977$	−2680.70	−0.0877823	−0.0438911	−	0.999036i	$-0.513975\pi$
$977$	−2680.70	−0.0877823	−0.0438911	+	0.999036i	$0.513975\pi$
$978$	−3989.74	−0.130448
$979$	45645.4	1.49013
$980$	32818.0	1.06973
$981$	3749.12	0.122018
$982$	−4961.39	−0.161226
$983$	42906.7	1.39218	0.696090	−	0.717955i	$-0.254921\pi$
$983$	42906.7	1.39218	0.696090	+	0.717955i	$0.254921\pi$
$984$	1416.38	0.0458868
$985$	7562.85	0.244642
$986$	77526.0	2.50399
$987$	10755.8	0.346870
$988$	20271.3	0.652750
$989$	27623.9	0.888159
$990$	24216.0	0.777409
$991$	55984.3	1.79455	0.897275	−	0.441473i	$-0.145544\pi$
$991$	55984.3	1.79455	0.897275	+	0.441473i	$0.145544\pi$
$992$	13622.5	0.436004
$993$	−35618.9	−1.13830
$994$	16528.5	0.527417
$995$	−39074.4	−1.24497
$996$	−16088.4	−0.511828
$997$	9218.93	0.292845	0.146422	−	0.989222i	$-0.453224\pi$
$997$	9218.93	0.292845	0.146422	+	0.989222i	$0.453224\pi$
$998$	39861.1	1.26431
$999$	−1162.01	−0.0368013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1011.4.a.c.1.10	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1011.4.a.c.1.10	✓	46	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:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1011.a (trivial)

\(f(q)\)	\(=\)	\(q-3.92365 q^{2} -3.00000 q^{3} +7.39501 q^{4} -14.7876 q^{5} +11.7709 q^{6} -6.54928 q^{7} +2.37377 q^{8} +9.00000 q^{9} +58.0213 q^{10} +46.3738 q^{11} -22.1850 q^{12} +23.3184 q^{13} +25.6971 q^{14} +44.3628 q^{15} -68.4739 q^{16} +85.8596 q^{17} -35.3128 q^{18} +117.556 q^{19} -109.354 q^{20} +19.6478 q^{21} -181.954 q^{22} +129.043 q^{23} -7.12130 q^{24} +93.6729 q^{25} -91.4934 q^{26} -27.0000 q^{27} -48.4320 q^{28} -230.128 q^{29} -174.064 q^{30} +54.5606 q^{31} +249.677 q^{32} -139.121 q^{33} -336.883 q^{34} +96.8481 q^{35} +66.5551 q^{36} +43.0375 q^{37} -461.247 q^{38} -69.9553 q^{39} -35.1023 q^{40} -198.894 q^{41} -77.0912 q^{42} +214.068 q^{43} +342.934 q^{44} -133.088 q^{45} -506.319 q^{46} +547.429 q^{47} +205.422 q^{48} -300.107 q^{49} -367.539 q^{50} -257.579 q^{51} +172.440 q^{52} -279.728 q^{53} +105.938 q^{54} -685.756 q^{55} -15.5465 q^{56} -352.667 q^{57} +902.939 q^{58} +678.355 q^{59} +328.063 q^{60} -163.613 q^{61} -214.077 q^{62} -58.9435 q^{63} -431.855 q^{64} -344.824 q^{65} +545.863 q^{66} -780.052 q^{67} +634.933 q^{68} -387.129 q^{69} -379.998 q^{70} +643.207 q^{71} +21.3639 q^{72} -566.903 q^{73} -168.864 q^{74} -281.019 q^{75} +869.326 q^{76} -303.715 q^{77} +274.480 q^{78} +76.9672 q^{79} +1012.56 q^{80} +81.0000 q^{81} +780.389 q^{82} +725.192 q^{83} +145.296 q^{84} -1269.66 q^{85} -839.926 q^{86} +690.383 q^{87} +110.081 q^{88} +984.294 q^{89} +522.192 q^{90} -152.719 q^{91} +954.273 q^{92} -163.682 q^{93} -2147.92 q^{94} -1738.37 q^{95} -749.032 q^{96} -760.823 q^{97} +1177.51 q^{98} +417.364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) \) 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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