LMFDB - Embedded newform 1250.4.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,4,Mod(1,1250)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1250.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$73.7523875072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 125 x^{14} + 990 x^{13} + 6166 x^{12} - 47880 x^{11} - 151199 x^{10} + \cdots - 45086320 $ x^16 - 8x^15 - 125x^14 + 990x^13 + 6166x^12 - 47880x^11 - 151199x^10 + 1143340x^9 + 1899751x^8 - 14035110x^7 - 11070230x^6 + 83435508x^5 + 14900696x^4 - 193725880x^3 + 78433160x^2 + 82757040*x - 45086320
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{15} $
Twist minimal:	no (minimal twist has level 50)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.09423$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -7.50360 q^{3} +4.00000 q^{4} -15.0072 q^{6} +17.5556 q^{7} +8.00000 q^{8} +29.3040 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -7.50360 q^{3} +4.00000 q^{4} -15.0072 q^{6} +17.5556 q^{7} +8.00000 q^{8} +29.3040 q^{9} +48.7111 q^{11} -30.0144 q^{12} +81.1475 q^{13} +35.1112 q^{14} +16.0000 q^{16} -35.2812 q^{17} +58.6081 q^{18} +43.9132 q^{19} -131.730 q^{21} +97.4223 q^{22} +92.2684 q^{23} -60.0288 q^{24} +162.295 q^{26} -17.2886 q^{27} +70.2224 q^{28} -287.916 q^{29} +117.286 q^{31} +32.0000 q^{32} -365.509 q^{33} -70.5624 q^{34} +117.216 q^{36} -68.2623 q^{37} +87.8265 q^{38} -608.898 q^{39} +168.528 q^{41} -263.461 q^{42} -19.3756 q^{43} +194.845 q^{44} +184.537 q^{46} -296.281 q^{47} -120.058 q^{48} -34.8008 q^{49} +264.736 q^{51} +324.590 q^{52} +708.338 q^{53} -34.5772 q^{54} +140.445 q^{56} -329.507 q^{57} -575.831 q^{58} -670.470 q^{59} -82.3896 q^{61} +234.573 q^{62} +514.450 q^{63} +64.0000 q^{64} -731.018 q^{66} -144.783 q^{67} -141.125 q^{68} -692.345 q^{69} +195.518 q^{71} +234.432 q^{72} +219.427 q^{73} -136.525 q^{74} +175.653 q^{76} +855.153 q^{77} -1217.80 q^{78} +524.490 q^{79} -661.482 q^{81} +337.056 q^{82} +457.172 q^{83} -526.921 q^{84} -38.7512 q^{86} +2160.40 q^{87} +389.689 q^{88} -840.318 q^{89} +1424.59 q^{91} +369.073 q^{92} -880.070 q^{93} -592.562 q^{94} -240.115 q^{96} +1660.10 q^{97} -69.6015 q^{98} +1427.43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) $ 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9} + 72 q^{11} + 48 q^{12} + 202 q^{13} + 112 q^{14} + 256 q^{16} + 216 q^{17} + 424 q^{18} + 100 q^{19} + 192 q^{21} + 144 q^{22} + 292 q^{23} + 96 q^{24} + 404 q^{26} + 570 q^{27} + 224 q^{28} + 400 q^{29} + 102 q^{31} + 512 q^{32} + 664 q^{33} + 432 q^{34} + 848 q^{36} + 646 q^{37} + 200 q^{38} + 104 q^{39} + 532 q^{41} + 384 q^{42} + 902 q^{43} + 288 q^{44} + 584 q^{46} + 776 q^{47} + 192 q^{48} + 1038 q^{49} + 442 q^{51} + 808 q^{52} + 632 q^{53} + 1140 q^{54} + 448 q^{56} + 1400 q^{57} + 800 q^{58} + 1000 q^{59} + 662 q^{61} + 204 q^{62} + 932 q^{63} + 1024 q^{64} + 1328 q^{66} + 1326 q^{67} + 864 q^{68} + 1854 q^{69} + 1292 q^{71} + 1696 q^{72} + 2272 q^{73} + 1292 q^{74} + 400 q^{76} + 2582 q^{77} + 208 q^{78} + 320 q^{79} + 2956 q^{81} + 1064 q^{82} + 2842 q^{83} + 768 q^{84} + 1804 q^{86} + 2920 q^{87} + 576 q^{88} + 2780 q^{89} + 812 q^{91} + 1168 q^{92} + 2824 q^{93} + 1552 q^{94} + 384 q^{96} + 3796 q^{97} + 2076 q^{98} + 1054 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9 + 72 * q^11 + 48 * q^12 + 202 * q^13 + 112 * q^14 + 256 * q^16 + 216 * q^17 + 424 * q^18 + 100 * q^19 + 192 * q^21 + 144 * q^22 + 292 * q^23 + 96 * q^24 + 404 * q^26 + 570 * q^27 + 224 * q^28 + 400 * q^29 + 102 * q^31 + 512 * q^32 + 664 * q^33 + 432 * q^34 + 848 * q^36 + 646 * q^37 + 200 * q^38 + 104 * q^39 + 532 * q^41 + 384 * q^42 + 902 * q^43 + 288 * q^44 + 584 * q^46 + 776 * q^47 + 192 * q^48 + 1038 * q^49 + 442 * q^51 + 808 * q^52 + 632 * q^53 + 1140 * q^54 + 448 * q^56 + 1400 * q^57 + 800 * q^58 + 1000 * q^59 + 662 * q^61 + 204 * q^62 + 932 * q^63 + 1024 * q^64 + 1328 * q^66 + 1326 * q^67 + 864 * q^68 + 1854 * q^69 + 1292 * q^71 + 1696 * q^72 + 2272 * q^73 + 1292 * q^74 + 400 * q^76 + 2582 * q^77 + 208 * q^78 + 320 * q^79 + 2956 * q^81 + 1064 * q^82 + 2842 * q^83 + 768 * q^84 + 1804 * q^86 + 2920 * q^87 + 576 * q^88 + 2780 * q^89 + 812 * q^91 + 1168 * q^92 + 2824 * q^93 + 1552 * q^94 + 384 * q^96 + 3796 * q^97 + 2076 * q^98 + 1054 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−7.50360	−1.44407	−0.722034	−	0.691857i	$-0.756793\pi$
$3$	−7.50360	−1.44407	−0.722034	+	0.691857i	$0.756793\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−15.0072	−1.02111
$7$	17.5556	0.947914	0.473957	−	0.880548i	$-0.342825\pi$
$7$	17.5556	0.947914	0.473957	+	0.880548i	$0.342825\pi$
$8$	8.00000	0.353553
$9$	29.3040	1.08533
$10$	0	0
$11$	48.7111	1.33518	0.667589	−	0.744530i	$-0.267326\pi$
$11$	48.7111	1.33518	0.667589	+	0.744530i	$0.267326\pi$
$12$	−30.0144	−0.722034
$13$	81.1475	1.73125	0.865625	−	0.500693i	$-0.166921\pi$
$13$	81.1475	1.73125	0.865625	+	0.500693i	$0.166921\pi$
$14$	35.1112	0.670276
$15$	0	0
$16$	16.0000	0.250000
$17$	−35.2812	−0.503350	−0.251675	−	0.967812i	$-0.580981\pi$
$17$	−35.2812	−0.503350	−0.251675	+	0.967812i	$0.580981\pi$
$18$	58.6081	0.767448
$19$	43.9132	0.530231	0.265115	−	0.964217i	$-0.414590\pi$
$19$	43.9132	0.530231	0.265115	+	0.964217i	$0.414590\pi$
$20$	0	0
$21$	−131.730	−1.36885
$22$	97.4223	0.944114
$23$	92.2684	0.836491	0.418245	−	0.908334i	$-0.362645\pi$
$23$	92.2684	0.836491	0.418245	+	0.908334i	$0.362645\pi$
$24$	−60.0288	−0.510555
$25$	0	0
$26$	162.295	1.22418
$27$	−17.2886	−0.123229
$28$	70.2224	0.473957
$29$	−287.916	−1.84361	−0.921804	−	0.387657i	$-0.873284\pi$
$29$	−287.916	−1.84361	−0.921804	+	0.387657i	$0.873284\pi$
$30$	0	0
$31$	117.286	0.679524	0.339762	−	0.940511i	$-0.389653\pi$
$31$	117.286	0.679524	0.339762	+	0.940511i	$0.389653\pi$
$32$	32.0000	0.176777
$33$	−365.509	−1.92809
$34$	−70.5624	−0.355922
$35$	0	0
$36$	117.216	0.542667
$37$	−68.2623	−0.303304	−0.151652	−	0.988434i	$-0.548459\pi$
$37$	−68.2623	−0.303304	−0.151652	+	0.988434i	$0.548459\pi$
$38$	87.8265	0.374930
$39$	−608.898	−2.50004
$40$	0	0
$41$	168.528	0.641943	0.320972	−	0.947089i	$-0.395991\pi$
$41$	168.528	0.641943	0.320972	+	0.947089i	$0.395991\pi$
$42$	−263.461	−0.967925
$43$	−19.3756	−0.0687151	−0.0343576	−	0.999410i	$-0.510939\pi$
$43$	−19.3756	−0.0687151	−0.0343576	+	0.999410i	$0.510939\pi$
$44$	194.845	0.667589
$45$	0	0
$46$	184.537	0.591488
$47$	−296.281	−0.919511	−0.459755	−	0.888046i	$-0.652063\pi$
$47$	−296.281	−0.919511	−0.459755	+	0.888046i	$0.652063\pi$
$48$	−120.058	−0.361017
$49$	−34.8008	−0.101460
$50$	0	0
$51$	264.736	0.726872
$52$	324.590	0.865625
$53$	708.338	1.83580	0.917902	−	0.396806i	$-0.129882\pi$
$53$	708.338	1.83580	0.917902	+	0.396806i	$0.129882\pi$
$54$	−34.5772	−0.0871363
$55$	0	0
$56$	140.445	0.335138
$57$	−329.507	−0.765690
$58$	−575.831	−1.30363
$59$	−670.470	−1.47945	−0.739726	−	0.672908i	$-0.765045\pi$
$59$	−670.470	−1.47945	−0.739726	+	0.672908i	$0.765045\pi$
$60$	0	0
$61$	−82.3896	−0.172933	−0.0864665	−	0.996255i	$-0.527558\pi$
$61$	−82.3896	−0.172933	−0.0864665	+	0.996255i	$0.527558\pi$
$62$	234.573	0.480496
$63$	514.450	1.02880
$64$	64.0000	0.125000
$65$	0	0
$66$	−731.018	−1.36337
$67$	−144.783	−0.264001	−0.132001	−	0.991250i	$-0.542140\pi$
$67$	−144.783	−0.264001	−0.132001	+	0.991250i	$0.542140\pi$
$68$	−141.125	−0.251675
$69$	−692.345	−1.20795
$70$	0	0
$71$	195.518	0.326813	0.163406	−	0.986559i	$-0.447752\pi$
$71$	195.518	0.326813	0.163406	+	0.986559i	$0.447752\pi$
$72$	234.432	0.383724
$73$	219.427	0.351807	0.175904	−	0.984407i	$-0.443715\pi$
$73$	219.427	0.351807	0.175904	+	0.984407i	$0.443715\pi$
$74$	−136.525	−0.214468
$75$	0	0
$76$	175.653	0.265115
$77$	855.153	1.26563
$78$	−1217.80	−1.76780
$79$	524.490	0.746959	0.373480	−	0.927638i	$-0.378165\pi$
$79$	524.490	0.746959	0.373480	+	0.927638i	$0.378165\pi$
$80$	0	0
$81$	−661.482	−0.907383
$82$	337.056	0.453922
$83$	457.172	0.604592	0.302296	−	0.953214i	$-0.402247\pi$
$83$	457.172	0.604592	0.302296	+	0.953214i	$0.402247\pi$
$84$	−526.921	−0.684426
$85$	0	0
$86$	−38.7512	−0.0485889
$87$	2160.40	2.66230
$88$	389.689	0.472057
$89$	−840.318	−1.00083	−0.500413	−	0.865787i	$-0.666818\pi$
$89$	−840.318	−1.00083	−0.500413	+	0.865787i	$0.666818\pi$
$90$	0	0
$91$	1424.59	1.64108
$92$	369.073	0.418245
$93$	−880.070	−0.981279
$94$	−592.562	−0.650192
$95$	0	0
$96$	−240.115	−0.255278
$97$	1660.10	1.73770	0.868852	−	0.495072i	$-0.164858\pi$
$97$	1660.10	1.73770	0.868852	+	0.495072i	$0.164858\pi$
$98$	−69.6015	−0.0717430
$99$	1427.43	1.44912
$100$	0	0
$101$	−1405.27	−1.38445	−0.692225	−	0.721682i	$-0.743369\pi$
$101$	−1405.27	−1.38445	−0.692225	+	0.721682i	$0.743369\pi$
$102$	529.472	0.513976
$103$	1825.45	1.74628	0.873140	−	0.487469i	$-0.162080\pi$
$103$	1825.45	1.74628	0.873140	+	0.487469i	$0.162080\pi$
$104$	649.180	0.612089
$105$	0	0
$106$	1416.68	1.29811
$107$	−426.043	−0.384926	−0.192463	−	0.981304i	$-0.561648\pi$
$107$	−426.043	−0.384926	−0.192463	+	0.981304i	$0.561648\pi$
$108$	−69.1544	−0.0616147
$109$	602.503	0.529444	0.264722	−	0.964325i	$-0.414720\pi$
$109$	602.503	0.529444	0.264722	+	0.964325i	$0.414720\pi$
$110$	0	0
$111$	512.213	0.437992
$112$	280.890	0.236978
$113$	329.777	0.274538	0.137269	−	0.990534i	$-0.456168\pi$
$113$	329.777	0.274538	0.137269	+	0.990534i	$0.456168\pi$
$114$	−659.015	−0.541425
$115$	0	0
$116$	−1151.66	−0.921804
$117$	2377.95	1.87899
$118$	−1340.94	−1.04613
$119$	−619.383	−0.477132
$120$	0	0
$121$	1041.78	0.782701
$122$	−164.779	−0.122282
$123$	−1264.57	−0.927010
$124$	469.145	0.339762
$125$	0	0
$126$	1028.90	0.727474
$127$	−1681.25	−1.17470	−0.587349	−	0.809334i	$-0.699828\pi$
$127$	−1681.25	−1.17470	−0.587349	+	0.809334i	$0.699828\pi$
$128$	128.000	0.0883883
$129$	145.387	0.0992294
$130$	0	0
$131$	1937.42	1.29216	0.646081	−	0.763269i	$-0.276407\pi$
$131$	1937.42	1.29216	0.646081	+	0.763269i	$0.276407\pi$
$132$	−1462.04	−0.964045
$133$	770.923	0.502613
$134$	−289.566	−0.186677
$135$	0	0
$136$	−282.250	−0.177961
$137$	1634.20	1.01912	0.509559	−	0.860436i	$-0.329808\pi$
$137$	1634.20	1.01912	0.509559	+	0.860436i	$0.329808\pi$
$138$	−1384.69	−0.854150
$139$	−848.951	−0.518037	−0.259018	−	0.965872i	$-0.583399\pi$
$139$	−848.951	−0.518037	−0.259018	+	0.965872i	$0.583399\pi$
$140$	0	0
$141$	2223.17	1.32784
$142$	391.036	0.231092
$143$	3952.79	2.31153
$144$	468.865	0.271334
$145$	0	0
$146$	438.853	0.248765
$147$	261.131	0.146515
$148$	−273.049	−0.151652
$149$	1780.43	0.978918	0.489459	−	0.872026i	$-0.337194\pi$
$149$	1780.43	0.978918	0.489459	+	0.872026i	$0.337194\pi$
$150$	0	0
$151$	−754.290	−0.406511	−0.203256	−	0.979126i	$-0.565152\pi$
$151$	−754.290	−0.406511	−0.203256	+	0.979126i	$0.565152\pi$
$152$	351.306	0.187465
$153$	−1033.88	−0.546303
$154$	1710.31	0.894938
$155$	0	0
$156$	−2435.59	−1.25002
$157$	2609.52	1.32651	0.663257	−	0.748392i	$-0.269174\pi$
$157$	2609.52	1.32651	0.663257	+	0.748392i	$0.269174\pi$
$158$	1048.98	0.528180
$159$	−5315.08	−2.65103
$160$	0	0
$161$	1619.83	0.792921
$162$	−1322.96	−0.641617
$163$	−2044.28	−0.982335	−0.491168	−	0.871065i	$-0.663430\pi$
$163$	−2044.28	−0.982335	−0.491168	+	0.871065i	$0.663430\pi$
$164$	674.112	0.320972
$165$	0	0
$166$	914.344	0.427511
$167$	−2722.79	−1.26165	−0.630826	−	0.775924i	$-0.717284\pi$
$167$	−2722.79	−1.26165	−0.630826	+	0.775924i	$0.717284\pi$
$168$	−1053.84	−0.483962
$169$	4387.91	1.99723
$170$	0	0
$171$	1286.84	0.575478
$172$	−77.5024	−0.0343576
$173$	−322.662	−0.141801	−0.0709005	−	0.997483i	$-0.522587\pi$
$173$	−322.662	−0.141801	−0.0709005	+	0.997483i	$0.522587\pi$
$174$	4320.81	1.88253
$175$	0	0
$176$	779.378	0.333795
$177$	5030.94	2.13643
$178$	−1680.64	−0.707691
$179$	712.669	0.297583	0.148792	−	0.988869i	$-0.452462\pi$
$179$	712.669	0.297583	0.148792	+	0.988869i	$0.452462\pi$
$180$	0	0
$181$	−2437.52	−1.00099	−0.500496	−	0.865739i	$-0.666849\pi$
$181$	−2437.52	−1.00099	−0.500496	+	0.865739i	$0.666849\pi$
$182$	2849.19	1.16042
$183$	618.219	0.249727
$184$	738.147	0.295744
$185$	0	0
$186$	−1760.14	−0.693869
$187$	−1718.59	−0.672062
$188$	−1185.12	−0.459755
$189$	−303.512	−0.116811
$190$	0	0
$191$	−3151.01	−1.19371	−0.596857	−	0.802348i	$-0.703584\pi$
$191$	−3151.01	−1.19371	−0.596857	+	0.802348i	$0.703584\pi$
$192$	−480.231	−0.180509
$193$	−1244.43	−0.464123	−0.232061	−	0.972701i	$-0.574547\pi$
$193$	−1244.43	−0.464123	−0.232061	+	0.972701i	$0.574547\pi$
$194$	3320.19	1.22874
$195$	0	0
$196$	−139.203	−0.0507300
$197$	783.364	0.283311	0.141656	−	0.989916i	$-0.454757\pi$
$197$	783.364	0.283311	0.141656	+	0.989916i	$0.454757\pi$
$198$	2854.87	1.02468
$199$	2234.72	0.796055	0.398028	−	0.917373i	$-0.369695\pi$
$199$	2234.72	0.796055	0.398028	+	0.917373i	$0.369695\pi$
$200$	0	0
$201$	1086.40	0.381236
$202$	−2810.54	−0.978954
$203$	−5054.53	−1.74758
$204$	1058.94	0.363436
$205$	0	0
$206$	3650.90	1.23481
$207$	2703.84	0.907872
$208$	1298.36	0.432813
$209$	2139.06	0.707953
$210$	0	0
$211$	1884.39	0.614818	0.307409	−	0.951578i	$-0.400538\pi$
$211$	1884.39	0.614818	0.307409	+	0.951578i	$0.400538\pi$
$212$	2833.35	0.917902
$213$	−1467.09	−0.471940
$214$	−852.086	−0.272184
$215$	0	0
$216$	−138.309	−0.0435681
$217$	2059.03	0.644130
$218$	1205.01	0.374373
$219$	−1646.49	−0.508034
$220$	0	0
$221$	−2862.98	−0.871425
$222$	1024.43	0.309707
$223$	4237.15	1.27238	0.636190	−	0.771532i	$-0.280509\pi$
$223$	4237.15	1.27238	0.636190	+	0.771532i	$0.280509\pi$
$224$	561.779	0.167569
$225$	0	0
$226$	659.554	0.194128
$227$	831.714	0.243184	0.121592	−	0.992580i	$-0.461200\pi$
$227$	831.714	0.243184	0.121592	+	0.992580i	$0.461200\pi$
$228$	−1318.03	−0.382845
$229$	2223.51	0.641632	0.320816	−	0.947141i	$-0.396043\pi$
$229$	2223.51	0.641632	0.320816	+	0.947141i	$0.396043\pi$
$230$	0	0
$231$	−6416.73	−1.82766
$232$	−2303.33	−0.651814
$233$	56.8486	0.0159840	0.00799201	−	0.999968i	$-0.497456\pi$
$233$	56.8486	0.0159840	0.00799201	+	0.999968i	$0.497456\pi$
$234$	4755.90	1.32864
$235$	0	0
$236$	−2681.88	−0.739726
$237$	−3935.57	−1.07866
$238$	−1238.77	−0.337383
$239$	−6258.27	−1.69378	−0.846891	−	0.531767i	$-0.821528\pi$
$239$	−6258.27	−1.69378	−0.846891	+	0.531767i	$0.821528\pi$
$240$	0	0
$241$	1043.84	0.279002	0.139501	−	0.990222i	$-0.455450\pi$
$241$	1043.84	0.279002	0.139501	+	0.990222i	$0.455450\pi$
$242$	2083.55	0.553453
$243$	5430.29	1.43355
$244$	−329.558	−0.0864665
$245$	0	0
$246$	−2529.14	−0.655495
$247$	3563.45	0.917962
$248$	938.291	0.240248
$249$	−3430.44	−0.873073
$250$	0	0
$251$	583.680	0.146779	0.0733895	−	0.997303i	$-0.476618\pi$
$251$	583.680	0.146779	0.0733895	+	0.997303i	$0.476618\pi$
$252$	2057.80	0.514402
$253$	4494.50	1.11686
$254$	−3362.49	−0.830636
$255$	0	0
$256$	256.000	0.0625000
$257$	1166.67	0.283171	0.141586	−	0.989926i	$-0.454780\pi$
$257$	1166.67	0.283171	0.141586	+	0.989926i	$0.454780\pi$
$258$	290.774	0.0701658
$259$	−1198.39	−0.287506
$260$	0	0
$261$	−8437.09	−2.00093
$262$	3874.84	0.913696
$263$	755.944	0.177238	0.0886189	−	0.996066i	$-0.471755\pi$
$263$	755.944	0.177238	0.0886189	+	0.996066i	$0.471755\pi$
$264$	−2924.07	−0.681683
$265$	0	0
$266$	1541.85	0.355401
$267$	6305.41	1.44526
$268$	−579.133	−0.132001
$269$	591.088	0.133975	0.0669875	−	0.997754i	$-0.478661\pi$
$269$	591.088	0.133975	0.0669875	+	0.997754i	$0.478661\pi$
$270$	0	0
$271$	−6086.80	−1.36438	−0.682189	−	0.731175i	$-0.738972\pi$
$271$	−6086.80	−1.36438	−0.682189	+	0.731175i	$0.738972\pi$
$272$	−564.499	−0.125837
$273$	−10689.6	−2.36983
$274$	3268.40	0.720626
$275$	0	0
$276$	−2769.38	−0.603975
$277$	6295.26	1.36551	0.682754	−	0.730648i	$-0.260782\pi$
$277$	6295.26	1.36551	0.682754	+	0.730648i	$0.260782\pi$
$278$	−1697.90	−0.366307
$279$	3436.96	0.737511
$280$	0	0
$281$	3746.17	0.795295	0.397648	−	0.917538i	$-0.369827\pi$
$281$	3746.17	0.795295	0.397648	+	0.917538i	$0.369827\pi$
$282$	4446.35	0.938922
$283$	−4358.81	−0.915562	−0.457781	−	0.889065i	$-0.651356\pi$
$283$	−4358.81	−0.915562	−0.457781	+	0.889065i	$0.651356\pi$
$284$	782.072	0.163406
$285$	0	0
$286$	7905.57	1.63450
$287$	2958.61	0.608507
$288$	937.729	0.191862
$289$	−3668.24	−0.746639
$290$	0	0
$291$	−12456.7	−2.50936
$292$	877.706	0.175904
$293$	5733.91	1.14327	0.571635	−	0.820508i	$-0.306309\pi$
$293$	5733.91	1.14327	0.571635	+	0.820508i	$0.306309\pi$
$294$	522.262	0.103602
$295$	0	0
$296$	−546.098	−0.107234
$297$	−842.147	−0.164533
$298$	3560.87	0.692200
$299$	7487.34	1.44817
$300$	0	0
$301$	−340.150	−0.0651360
$302$	−1508.58	−0.287447
$303$	10544.6	1.99924
$304$	702.612	0.132558
$305$	0	0
$306$	−2067.76	−0.386295
$307$	390.524	0.0726006	0.0363003	−	0.999341i	$-0.488443\pi$
$307$	390.524	0.0726006	0.0363003	+	0.999341i	$0.488443\pi$
$308$	3420.61	0.632817
$309$	−13697.4	−2.52175
$310$	0	0
$311$	6462.72	1.17835	0.589176	−	0.808005i	$-0.299453\pi$
$311$	6462.72	1.17835	0.589176	+	0.808005i	$0.299453\pi$
$312$	−4871.19	−0.883899
$313$	9997.72	1.80545	0.902723	−	0.430222i	$-0.141565\pi$
$313$	9997.72	1.80545	0.902723	+	0.430222i	$0.141565\pi$
$314$	5219.05	0.937987
$315$	0	0
$316$	2097.96	0.373480
$317$	−1098.51	−0.194633	−0.0973165	−	0.995253i	$-0.531026\pi$
$317$	−1098.51	−0.194633	−0.0973165	+	0.995253i	$0.531026\pi$
$318$	−10630.2	−1.87456
$319$	−14024.7	−2.46154
$320$	0	0
$321$	3196.86	0.555860
$322$	3239.65	0.560680
$323$	−1549.31	−0.266892
$324$	−2645.93	−0.453692
$325$	0	0
$326$	−4088.57	−0.694616
$327$	−4520.95	−0.764553
$328$	1348.22	0.226961
$329$	−5201.39	−0.871617
$330$	0	0
$331$	4282.91	0.711208	0.355604	−	0.934637i	$-0.384275\pi$
$331$	4282.91	0.711208	0.355604	+	0.934637i	$0.384275\pi$
$332$	1828.69	0.302296
$333$	−2000.36	−0.329186
$334$	−5445.59	−0.892123
$335$	0	0
$336$	−2107.68	−0.342213
$337$	−1217.84	−0.196854	−0.0984270	−	0.995144i	$-0.531381\pi$
$337$	−1217.84	−0.196854	−0.0984270	+	0.995144i	$0.531381\pi$
$338$	8775.82	1.41225
$339$	−2474.51	−0.396452
$340$	0	0
$341$	5713.15	0.907286
$342$	2573.67	0.406924
$343$	−6632.52	−1.04409
$344$	−155.005	−0.0242945
$345$	0	0
$346$	−645.325	−0.100268
$347$	−9259.57	−1.43251	−0.716254	−	0.697840i	$-0.754145\pi$
$347$	−9259.57	−1.43251	−0.716254	+	0.697840i	$0.754145\pi$
$348$	8641.62	1.33115
$349$	−6276.46	−0.962668	−0.481334	−	0.876537i	$-0.659848\pi$
$349$	−6276.46	−0.962668	−0.481334	+	0.876537i	$0.659848\pi$
$350$	0	0
$351$	−1402.93	−0.213341
$352$	1558.76	0.236028
$353$	−2326.41	−0.350772	−0.175386	−	0.984500i	$-0.556117\pi$
$353$	−2326.41	−0.350772	−0.175386	+	0.984500i	$0.556117\pi$
$354$	10061.9	1.51069
$355$	0	0
$356$	−3361.27	−0.500413
$357$	4647.60	0.689012
$358$	1425.34	0.210423
$359$	4884.26	0.718053	0.359027	−	0.933327i	$-0.383109\pi$
$359$	4884.26	0.718053	0.359027	+	0.933327i	$0.383109\pi$
$360$	0	0
$361$	−4930.63	−0.718855
$362$	−4875.04	−0.707808
$363$	−7817.07	−1.13027
$364$	5698.37	0.820538
$365$	0	0
$366$	1236.44	0.176584
$367$	−2177.26	−0.309679	−0.154839	−	0.987940i	$-0.549486\pi$
$367$	−2177.26	−0.309679	−0.154839	+	0.987940i	$0.549486\pi$
$368$	1476.29	0.209123
$369$	4938.55	0.696723
$370$	0	0
$371$	12435.3	1.74018
$372$	−3520.28	−0.490640
$373$	−9517.86	−1.32122	−0.660612	−	0.750728i	$-0.729703\pi$
$373$	−9517.86	−1.32122	−0.660612	+	0.750728i	$0.729703\pi$
$374$	−3437.18	−0.475220
$375$	0	0
$376$	−2370.25	−0.325096
$377$	−23363.6	−3.19175
$378$	−607.023	−0.0825977
$379$	2031.52	0.275336	0.137668	−	0.990478i	$-0.456039\pi$
$379$	2031.52	0.275336	0.137668	+	0.990478i	$0.456039\pi$
$380$	0	0
$381$	12615.4	1.69634
$382$	−6302.02	−0.844083
$383$	−13745.0	−1.83378	−0.916892	−	0.399136i	$-0.869310\pi$
$383$	−13745.0	−1.83378	−0.916892	+	0.399136i	$0.869310\pi$
$384$	−960.461	−0.127639
$385$	0	0
$386$	−2488.85	−0.328184
$387$	−567.783	−0.0745789
$388$	6640.39	0.868852
$389$	−525.711	−0.0685208	−0.0342604	−	0.999413i	$-0.510908\pi$
$389$	−525.711	−0.0685208	−0.0342604	+	0.999413i	$0.510908\pi$
$390$	0	0
$391$	−3255.34	−0.421048
$392$	−278.406	−0.0358715
$393$	−14537.6	−1.86597
$394$	1566.73	0.200331
$395$	0	0
$396$	5709.73	0.724558
$397$	12734.7	1.60991	0.804956	−	0.593334i	$-0.202189\pi$
$397$	12734.7	1.60991	0.804956	+	0.593334i	$0.202189\pi$
$398$	4469.44	0.562896
$399$	−5784.70	−0.725808
$400$	0	0
$401$	972.854	0.121152	0.0605761	−	0.998164i	$-0.480706\pi$
$401$	972.854	0.121152	0.0605761	+	0.998164i	$0.480706\pi$
$402$	2172.79	0.269574
$403$	9517.49	1.17643
$404$	−5621.07	−0.692225
$405$	0	0
$406$	−10109.1	−1.23573
$407$	−3325.13	−0.404965
$408$	2117.89	0.256988
$409$	1315.98	0.159098	0.0795492	−	0.996831i	$-0.474652\pi$
$409$	1315.98	0.159098	0.0795492	+	0.996831i	$0.474652\pi$
$410$	0	0
$411$	−12262.4	−1.47168
$412$	7301.80	0.873140
$413$	−11770.5	−1.40239
$414$	5407.67	0.641963
$415$	0	0
$416$	2596.72	0.306045
$417$	6370.19	0.748081
$418$	4278.13	0.500598
$419$	−6970.11	−0.812678	−0.406339	−	0.913722i	$-0.633195\pi$
$419$	−6970.11	−0.812678	−0.406339	+	0.913722i	$0.633195\pi$
$420$	0	0
$421$	−5042.42	−0.583735	−0.291868	−	0.956459i	$-0.594277\pi$
$421$	−5042.42	−0.583735	−0.291868	+	0.956459i	$0.594277\pi$
$422$	3768.77	0.434742
$423$	−8682.22	−0.997977
$424$	5666.70	0.649055
$425$	0	0
$426$	−2934.18	−0.333712
$427$	−1446.40	−0.163925
$428$	−1704.17	−0.192463
$429$	−29660.1	−3.33801
$430$	0	0
$431$	279.158	0.0311986	0.0155993	−	0.999878i	$-0.495034\pi$
$431$	279.158	0.0311986	0.0155993	+	0.999878i	$0.495034\pi$
$432$	−276.617	−0.0308073
$433$	−564.644	−0.0626675	−0.0313338	−	0.999509i	$-0.509975\pi$
$433$	−564.644	−0.0626675	−0.0313338	+	0.999509i	$0.509975\pi$
$434$	4118.06	0.455469
$435$	0	0
$436$	2410.01	0.264722
$437$	4051.80	0.443533
$438$	−3292.98	−0.359234
$439$	3005.50	0.326753	0.163377	−	0.986564i	$-0.447761\pi$
$439$	3005.50	0.326753	0.163377	+	0.986564i	$0.447761\pi$
$440$	0	0
$441$	−1019.80	−0.110118
$442$	−5725.96	−0.616190
$443$	−3052.29	−0.327356	−0.163678	−	0.986514i	$-0.552336\pi$
$443$	−3052.29	−0.327356	−0.163678	+	0.986514i	$0.552336\pi$
$444$	2048.85	0.218996
$445$	0	0
$446$	8474.31	0.899709
$447$	−13359.7	−1.41362
$448$	1123.56	0.118489
$449$	−15746.8	−1.65509	−0.827546	−	0.561398i	$-0.810264\pi$
$449$	−15746.8	−1.65509	−0.827546	+	0.561398i	$0.810264\pi$
$450$	0	0
$451$	8209.20	0.857109
$452$	1319.11	0.137269
$453$	5659.89	0.587030
$454$	1663.43	0.171957
$455$	0	0
$456$	−2636.06	−0.270712
$457$	−5363.96	−0.549050	−0.274525	−	0.961580i	$-0.588521\pi$
$457$	−5363.96	−0.549050	−0.274525	+	0.961580i	$0.588521\pi$
$458$	4447.02	0.453703
$459$	609.962	0.0620275
$460$	0	0
$461$	8588.46	0.867688	0.433844	−	0.900988i	$-0.357157\pi$
$461$	8588.46	0.867688	0.433844	+	0.900988i	$0.357157\pi$
$462$	−12833.5	−1.29235
$463$	11709.2	1.17532	0.587661	−	0.809107i	$-0.300049\pi$
$463$	11709.2	1.17532	0.587661	+	0.809107i	$0.300049\pi$
$464$	−4606.65	−0.460902
$465$	0	0
$466$	113.697	0.0113024
$467$	−11689.9	−1.15834	−0.579168	−	0.815208i	$-0.696623\pi$
$467$	−11689.9	−1.15834	−0.579168	+	0.815208i	$0.696623\pi$
$468$	9511.79	0.939493
$469$	−2541.76	−0.250250
$470$	0	0
$471$	−19580.8	−1.91558
$472$	−5363.76	−0.523066
$473$	−943.807	−0.0917470
$474$	−7871.13	−0.762728
$475$	0	0
$476$	−2477.53	−0.238566
$477$	20757.2	1.99246
$478$	−12516.5	−1.19768
$479$	−3253.71	−0.310367	−0.155184	−	0.987886i	$-0.549597\pi$
$479$	−3253.71	−0.310367	−0.155184	+	0.987886i	$0.549597\pi$
$480$	0	0
$481$	−5539.31	−0.525095
$482$	2087.67	0.197284
$483$	−12154.5	−1.14503
$484$	4167.10	0.391351
$485$	0	0
$486$	10860.6	1.01368
$487$	−3321.92	−0.309098	−0.154549	−	0.987985i	$-0.549392\pi$
$487$	−3321.92	−0.309098	−0.154549	+	0.987985i	$0.549392\pi$
$488$	−659.117	−0.0611410
$489$	15339.5	1.41856
$490$	0	0
$491$	12129.3	1.11484	0.557421	−	0.830230i	$-0.311791\pi$
$491$	12129.3	1.11484	0.557421	+	0.830230i	$0.311791\pi$
$492$	−5058.27	−0.463505
$493$	10158.0	0.927980
$494$	7126.89	0.649097
$495$	0	0
$496$	1876.58	0.169881
$497$	3432.44	0.309790
$498$	−6860.88	−0.617356
$499$	−13271.3	−1.19060	−0.595298	−	0.803505i	$-0.702966\pi$
$499$	−13271.3	−1.19060	−0.595298	+	0.803505i	$0.702966\pi$
$500$	0	0
$501$	20430.8	1.82191
$502$	1167.36	0.103788
$503$	−15097.1	−1.33826	−0.669131	−	0.743144i	$-0.733334\pi$
$503$	−15097.1	−1.33826	−0.669131	+	0.743144i	$0.733334\pi$
$504$	4115.60	0.363737
$505$	0	0
$506$	8988.99	0.789742
$507$	−32925.1	−2.88413
$508$	−6724.99	−0.587349
$509$	13497.3	1.17536	0.587679	−	0.809094i	$-0.300042\pi$
$509$	13497.3	1.17536	0.587679	+	0.809094i	$0.300042\pi$
$510$	0	0
$511$	3852.17	0.333483
$512$	512.000	0.0441942
$513$	−759.198	−0.0653400
$514$	2333.35	0.200232
$515$	0	0
$516$	581.547	0.0496147
$517$	−14432.2	−1.22771
$518$	−2396.77	−0.203297
$519$	2421.13	0.204770
$520$	0	0
$521$	5142.95	0.432470	0.216235	−	0.976341i	$-0.430622\pi$
$521$	5142.95	0.432470	0.216235	+	0.976341i	$0.430622\pi$
$522$	−16874.2	−1.41487
$523$	5299.97	0.443120	0.221560	−	0.975147i	$-0.428885\pi$
$523$	5299.97	0.443120	0.221560	+	0.975147i	$0.428885\pi$
$524$	7749.68	0.646081
$525$	0	0
$526$	1511.89	0.125326
$527$	−4138.00	−0.342038
$528$	−5848.14	−0.482022
$529$	−3653.55	−0.300283
$530$	0	0
$531$	−19647.5	−1.60570
$532$	3083.69	0.251307
$533$	13675.6	1.11136
$534$	12610.8	1.02195
$535$	0	0
$536$	−1158.27	−0.0933385
$537$	−5347.58	−0.429730
$538$	1182.18	0.0947346
$539$	−1695.19	−0.135467
$540$	0	0
$541$	9208.73	0.731819	0.365910	−	0.930650i	$-0.380758\pi$
$541$	9208.73	0.731819	0.365910	+	0.930650i	$0.380758\pi$
$542$	−12173.6	−0.964762
$543$	18290.2	1.44550
$544$	−1129.00	−0.0889805
$545$	0	0
$546$	−21379.2	−1.67572
$547$	−5879.35	−0.459566	−0.229783	−	0.973242i	$-0.573802\pi$
$547$	−5879.35	−0.459566	−0.229783	+	0.973242i	$0.573802\pi$
$548$	6536.81	0.509559
$549$	−2414.35	−0.187690
$550$	0	0
$551$	−12643.3	−0.977537
$552$	−5538.76	−0.427075
$553$	9207.74	0.708053
$554$	12590.5	0.965560
$555$	0	0
$556$	−3395.81	−0.259018
$557$	4520.00	0.343840	0.171920	−	0.985111i	$-0.445003\pi$
$557$	4520.00	0.343840	0.171920	+	0.985111i	$0.445003\pi$
$558$	6873.93	0.521499
$559$	−1572.28	−0.118963
$560$	0	0
$561$	12895.6	0.970504
$562$	7492.35	0.562359
$563$	−11818.8	−0.884730	−0.442365	−	0.896835i	$-0.645860\pi$
$563$	−11818.8	−0.884730	−0.442365	+	0.896835i	$0.645860\pi$
$564$	8892.69	0.663918
$565$	0	0
$566$	−8717.61	−0.647400
$567$	−11612.7	−0.860121
$568$	1564.14	0.115546
$569$	14631.3	1.07799	0.538995	−	0.842309i	$-0.318804\pi$
$569$	14631.3	1.07799	0.538995	+	0.842309i	$0.318804\pi$
$570$	0	0
$571$	16417.3	1.20322	0.601612	−	0.798788i	$-0.294525\pi$
$571$	16417.3	1.20322	0.601612	+	0.798788i	$0.294525\pi$
$572$	15811.1	1.15576
$573$	23643.9	1.72380
$574$	5917.23	0.430279
$575$	0	0
$576$	1875.46	0.135667
$577$	11835.6	0.853939	0.426969	−	0.904266i	$-0.359581\pi$
$577$	11835.6	0.853939	0.426969	+	0.904266i	$0.359581\pi$
$578$	−7336.47	−0.527953
$579$	9337.67	0.670225
$580$	0	0
$581$	8025.93	0.573101
$582$	−24913.4	−1.77439
$583$	34503.9	2.45113
$584$	1755.41	0.124383
$585$	0	0
$586$	11467.8	0.808415
$587$	11721.6	0.824192	0.412096	−	0.911141i	$-0.364797\pi$
$587$	11721.6	0.824192	0.412096	+	0.911141i	$0.364797\pi$
$588$	1044.52	0.0732576
$589$	5150.42	0.360305
$590$	0	0
$591$	−5878.05	−0.409121
$592$	−1092.20	−0.0758260
$593$	14778.5	1.02341	0.511704	−	0.859162i	$-0.329015\pi$
$593$	14778.5	1.02341	0.511704	+	0.859162i	$0.329015\pi$
$594$	−1684.29	−0.116342
$595$	0	0
$596$	7121.73	0.489459
$597$	−16768.4	−1.14956
$598$	14974.7	1.02401
$599$	20533.0	1.40059	0.700296	−	0.713853i	$-0.253051\pi$
$599$	20533.0	1.40059	0.700296	+	0.713853i	$0.253051\pi$
$600$	0	0
$601$	−10892.6	−0.739302	−0.369651	−	0.929171i	$-0.620523\pi$
$601$	−10892.6	−0.739302	−0.369651	+	0.929171i	$0.620523\pi$
$602$	−680.301	−0.0460581
$603$	−4242.73	−0.286530
$604$	−3017.16	−0.203256
$605$	0	0
$606$	21089.2	1.41368
$607$	15269.0	1.02101	0.510504	−	0.859876i	$-0.329459\pi$
$607$	15269.0	1.02101	0.510504	+	0.859876i	$0.329459\pi$
$608$	1405.22	0.0937325
$609$	37927.2	2.52363
$610$	0	0
$611$	−24042.4	−1.59190
$612$	−4135.53	−0.273152
$613$	−25875.1	−1.70487	−0.852436	−	0.522831i	$-0.824876\pi$
$613$	−25875.1	−1.70487	−0.852436	+	0.522831i	$0.824876\pi$
$614$	781.048	0.0513364
$615$	0	0
$616$	6841.23	0.447469
$617$	15654.5	1.02144	0.510718	−	0.859748i	$-0.329380\pi$
$617$	15654.5	1.02144	0.510718	+	0.859748i	$0.329380\pi$
$618$	−27394.9	−1.78315
$619$	15075.0	0.978861	0.489431	−	0.872042i	$-0.337205\pi$
$619$	15075.0	0.978861	0.489431	+	0.872042i	$0.337205\pi$
$620$	0	0
$621$	−1595.19	−0.103080
$622$	12925.4	0.833220
$623$	−14752.3	−0.948696
$624$	−9742.37	−0.625011
$625$	0	0
$626$	19995.4	1.27664
$627$	−16050.7	−1.02233
$628$	10438.1	0.663257
$629$	2408.38	0.152668
$630$	0	0
$631$	17033.7	1.07464	0.537321	−	0.843378i	$-0.319436\pi$
$631$	17033.7	1.07464	0.537321	+	0.843378i	$0.319436\pi$
$632$	4195.92	0.264090
$633$	−14139.7	−0.887839
$634$	−2197.03	−0.137626
$635$	0	0
$636$	−21260.3	−1.32551
$637$	−2823.99	−0.175653
$638$	−28049.4	−1.74057
$639$	5729.47	0.354701
$640$	0	0
$641$	−16960.4	−1.04508	−0.522540	−	0.852615i	$-0.675015\pi$
$641$	−16960.4	−1.04508	−0.522540	+	0.852615i	$0.675015\pi$
$642$	6393.71	0.393053
$643$	−1422.26	−0.0872296	−0.0436148	−	0.999048i	$-0.513887\pi$
$643$	−1422.26	−0.0872296	−0.0436148	+	0.999048i	$0.513887\pi$
$644$	6479.31	0.396460
$645$	0	0
$646$	−3098.62	−0.188721
$647$	6827.02	0.414834	0.207417	−	0.978253i	$-0.433494\pi$
$647$	6827.02	0.414834	0.207417	+	0.978253i	$0.433494\pi$
$648$	−5291.86	−0.320808
$649$	−32659.3	−1.97533
$650$	0	0
$651$	−15450.2	−0.930168
$652$	−8177.13	−0.491168
$653$	−1984.59	−0.118933	−0.0594664	−	0.998230i	$-0.518940\pi$
$653$	−1984.59	−0.118933	−0.0594664	+	0.998230i	$0.518940\pi$
$654$	−9041.89	−0.540621
$655$	0	0
$656$	2696.45	0.160486
$657$	6430.08	0.381829
$658$	−10402.8	−0.616326
$659$	6249.93	0.369442	0.184721	−	0.982791i	$-0.440862\pi$
$659$	6249.93	0.369442	0.184721	+	0.982791i	$0.440862\pi$
$660$	0	0
$661$	15487.5	0.911339	0.455669	−	0.890149i	$-0.349400\pi$
$661$	15487.5	0.911339	0.455669	+	0.890149i	$0.349400\pi$
$662$	8565.81	0.502900
$663$	21482.7	1.25840
$664$	3657.38	0.213756
$665$	0	0
$666$	−4000.72	−0.232770
$667$	−26565.5	−1.54216
$668$	−10891.2	−0.630826
$669$	−31793.9	−1.83740
$670$	0	0
$671$	−4013.29	−0.230896
$672$	−4215.37	−0.241981
$673$	−12065.3	−0.691060	−0.345530	−	0.938408i	$-0.612301\pi$
$673$	−12065.3	−0.691060	−0.345530	+	0.938408i	$0.612301\pi$
$674$	−2435.67	−0.139197
$675$	0	0
$676$	17551.6	0.998614
$677$	3903.82	0.221619	0.110810	−	0.993842i	$-0.464656\pi$
$677$	3903.82	0.221619	0.110810	+	0.993842i	$0.464656\pi$
$678$	−4949.03	−0.280334
$679$	29144.0	1.64719
$680$	0	0
$681$	−6240.85	−0.351175
$682$	11426.3	0.641548
$683$	−3362.57	−0.188382	−0.0941912	−	0.995554i	$-0.530026\pi$
$683$	−3362.57	−0.188382	−0.0941912	+	0.995554i	$0.530026\pi$
$684$	5147.34	0.287739
$685$	0	0
$686$	−13265.0	−0.738282
$687$	−16684.3	−0.926561
$688$	−310.010	−0.0171788
$689$	57479.8	3.17824
$690$	0	0
$691$	29273.8	1.61162	0.805808	−	0.592178i	$-0.201732\pi$
$691$	29273.8	1.61162	0.805808	+	0.592178i	$0.201732\pi$
$692$	−1290.65	−0.0709005
$693$	25059.5	1.37364
$694$	−18519.1	−1.01294
$695$	0	0
$696$	17283.2	0.941264
$697$	−5945.88	−0.323122
$698$	−12552.9	−0.680709
$699$	−426.569	−0.0230820
$700$	0	0
$701$	14151.6	0.762478	0.381239	−	0.924477i	$-0.375498\pi$
$701$	14151.6	0.762478	0.381239	+	0.924477i	$0.375498\pi$
$702$	−2805.85	−0.150855
$703$	−2997.62	−0.160821
$704$	3117.51	0.166897
$705$	0	0
$706$	−4652.82	−0.248033
$707$	−24670.3	−1.31234
$708$	20123.7	1.06822
$709$	−15017.2	−0.795465	−0.397732	−	0.917501i	$-0.630203\pi$
$709$	−15017.2	−0.795465	−0.397732	+	0.917501i	$0.630203\pi$
$710$	0	0
$711$	15369.7	0.810701
$712$	−6722.54	−0.353845
$713$	10821.8	0.568415
$714$	9295.21	0.487205
$715$	0	0
$716$	2850.68	0.148792
$717$	46959.6	2.44594
$718$	9768.51	0.507740
$719$	−10839.8	−0.562247	−0.281123	−	0.959672i	$-0.590707\pi$
$719$	−10839.8	−0.562247	−0.281123	+	0.959672i	$0.590707\pi$
$720$	0	0
$721$	32046.9	1.65532
$722$	−9861.26	−0.508307
$723$	−7832.53	−0.402898
$724$	−9750.08	−0.500496
$725$	0	0
$726$	−15634.1	−0.799225
$727$	−34838.2	−1.77727	−0.888636	−	0.458613i	$-0.848346\pi$
$727$	−34838.2	−1.77727	−0.888636	+	0.458613i	$0.848346\pi$
$728$	11396.7	0.580208
$729$	−22886.7	−1.16277
$730$	0	0
$731$	683.594	0.0345878
$732$	2472.88	0.124864
$733$	17153.2	0.864349	0.432175	−	0.901790i	$-0.357746\pi$
$733$	17153.2	0.864349	0.432175	+	0.901790i	$0.357746\pi$
$734$	−4354.52	−0.218976
$735$	0	0
$736$	2952.59	0.147872
$737$	−7052.55	−0.352489
$738$	9877.11	0.492658
$739$	−29004.5	−1.44377	−0.721887	−	0.692011i	$-0.756725\pi$
$739$	−29004.5	−1.44377	−0.721887	+	0.692011i	$0.756725\pi$
$740$	0	0
$741$	−26738.7	−1.32560
$742$	24870.6	1.23050
$743$	−25985.4	−1.28306	−0.641529	−	0.767099i	$-0.721699\pi$
$743$	−25985.4	−1.28306	−0.641529	+	0.767099i	$0.721699\pi$
$744$	−7040.56	−0.346935
$745$	0	0
$746$	−19035.7	−0.934246
$747$	13397.0	0.656185
$748$	−6874.35	−0.336031
$749$	−7479.44	−0.364877
$750$	0	0
$751$	−7278.21	−0.353643	−0.176821	−	0.984243i	$-0.556581\pi$
$751$	−7278.21	−0.353643	−0.176821	+	0.984243i	$0.556581\pi$
$752$	−4740.49	−0.229878
$753$	−4379.70	−0.211959
$754$	−46727.3	−2.25690
$755$	0	0
$756$	−1214.05	−0.0584054
$757$	−4538.05	−0.217884	−0.108942	−	0.994048i	$-0.534746\pi$
$757$	−4538.05	−0.217884	−0.108942	+	0.994048i	$0.534746\pi$
$758$	4063.05	0.194692
$759$	−33724.9	−1.61283
$760$	0	0
$761$	21279.8	1.01366	0.506828	−	0.862047i	$-0.330818\pi$
$761$	21279.8	1.01366	0.506828	+	0.862047i	$0.330818\pi$
$762$	25230.8	1.19950
$763$	10577.3	0.501867
$764$	−12604.0	−0.596857
$765$	0	0
$766$	−27490.1	−1.29668
$767$	−54406.9	−2.56130
$768$	−1920.92	−0.0902543
$769$	−16807.0	−0.788137	−0.394069	−	0.919081i	$-0.628933\pi$
$769$	−16807.0	−0.788137	−0.394069	+	0.919081i	$0.628933\pi$
$770$	0	0
$771$	−8754.25	−0.408919
$772$	−4977.70	−0.232061
$773$	2841.95	0.132235	0.0661175	−	0.997812i	$-0.478939\pi$
$773$	2841.95	0.132235	0.0661175	+	0.997812i	$0.478939\pi$
$774$	−1135.57	−0.0527353
$775$	0	0
$776$	13280.8	0.614371
$777$	8992.21	0.415179
$778$	−1051.42	−0.0484515
$779$	7400.61	0.340378
$780$	0	0
$781$	9523.91	0.436354
$782$	−6510.68	−0.297726
$783$	4977.66	0.227186
$784$	−556.812	−0.0253650
$785$	0	0
$786$	−29075.2	−1.31944
$787$	−11438.9	−0.518110	−0.259055	−	0.965863i	$-0.583411\pi$
$787$	−11438.9	−0.518110	−0.259055	+	0.965863i	$0.583411\pi$
$788$	3133.46	0.141656
$789$	−5672.31	−0.255944
$790$	0	0
$791$	5789.43	0.260238
$792$	11419.5	0.512340
$793$	−6685.71	−0.299390
$794$	25469.4	1.13838
$795$	0	0
$796$	8938.87	0.398028
$797$	−2017.56	−0.0896681	−0.0448341	−	0.998994i	$-0.514276\pi$
$797$	−2017.56	−0.0896681	−0.0448341	+	0.998994i	$0.514276\pi$
$798$	−11569.4	−0.513224
$799$	10453.1	0.462836
$800$	0	0
$801$	−24624.7	−1.08623
$802$	1945.71	0.0856675
$803$	10688.5	0.469726
$804$	4345.58	0.190618
$805$	0	0
$806$	19035.0	0.831859
$807$	−4435.29	−0.193469
$808$	−11242.1	−0.489477
$809$	−27472.3	−1.19391	−0.596956	−	0.802274i	$-0.703623\pi$
$809$	−27472.3	−1.19391	−0.596956	+	0.802274i	$0.703623\pi$
$810$	0	0
$811$	3009.03	0.130285	0.0651426	−	0.997876i	$-0.479250\pi$
$811$	3009.03	0.130285	0.0651426	+	0.997876i	$0.479250\pi$
$812$	−20218.1	−0.873790
$813$	45672.9	1.97026
$814$	−6650.27	−0.286354
$815$	0	0
$816$	4235.78	0.181718
$817$	−850.845	−0.0364349
$818$	2631.97	0.112500
$819$	41746.3	1.78112
$820$	0	0
$821$	−25216.8	−1.07195	−0.535975	−	0.844234i	$-0.680056\pi$
$821$	−25216.8	−1.07195	−0.535975	+	0.844234i	$0.680056\pi$
$822$	−24524.8	−1.04063
$823$	20180.8	0.854748	0.427374	−	0.904075i	$-0.359439\pi$
$823$	20180.8	0.854748	0.427374	+	0.904075i	$0.359439\pi$
$824$	14603.6	0.617403
$825$	0	0
$826$	−23541.0	−0.991642
$827$	10558.6	0.443965	0.221982	−	0.975051i	$-0.428747\pi$
$827$	10558.6	0.443965	0.221982	+	0.975051i	$0.428747\pi$
$828$	10815.3	0.453936
$829$	8082.99	0.338641	0.169321	−	0.985561i	$-0.445843\pi$
$829$	8082.99	0.338641	0.169321	+	0.985561i	$0.445843\pi$
$830$	0	0
$831$	−47237.1	−1.97189
$832$	5193.44	0.216406
$833$	1227.81	0.0510699
$834$	12740.4	0.528973
$835$	0	0
$836$	8556.26	0.353976
$837$	−2027.72	−0.0837373
$838$	−13940.2	−0.574650
$839$	12888.5	0.530346	0.265173	−	0.964201i	$-0.414571\pi$
$839$	12888.5	0.530346	0.265173	+	0.964201i	$0.414571\pi$
$840$	0	0
$841$	58506.5	2.39889
$842$	−10084.8	−0.412763
$843$	−28109.8	−1.14846
$844$	7537.55	0.307409
$845$	0	0
$846$	−17364.4	−0.705676
$847$	18289.0	0.741933
$848$	11333.4	0.458951
$849$	32706.8	1.32214
$850$	0	0
$851$	−6298.45	−0.253711
$852$	−5868.36	−0.235970
$853$	19087.7	0.766180	0.383090	−	0.923711i	$-0.374860\pi$
$853$	19087.7	0.766180	0.383090	+	0.923711i	$0.374860\pi$
$854$	−2892.80	−0.115913
$855$	0	0
$856$	−3408.34	−0.136092
$857$	8564.22	0.341363	0.170682	−	0.985326i	$-0.445403\pi$
$857$	8564.22	0.341363	0.170682	+	0.985326i	$0.445403\pi$
$858$	−59320.3	−2.36033
$859$	27182.8	1.07971	0.539853	−	0.841760i	$-0.318480\pi$
$859$	27182.8	1.07971	0.539853	+	0.841760i	$0.318480\pi$
$860$	0	0
$861$	−22200.3	−0.878725
$862$	558.317	0.0220607
$863$	−24351.3	−0.960518	−0.480259	−	0.877127i	$-0.659457\pi$
$863$	−24351.3	−0.960518	−0.480259	+	0.877127i	$0.659457\pi$
$864$	−553.235	−0.0217841
$865$	0	0
$866$	−1129.29	−0.0443126
$867$	27525.0	1.07820
$868$	8236.13	0.322065
$869$	25548.5	0.997323
$870$	0	0
$871$	−11748.8	−0.457052
$872$	4820.03	0.187187
$873$	48647.5	1.88599
$874$	8103.60	0.313625
$875$	0	0
$876$	−6585.96	−0.254017
$877$	−32602.1	−1.25530	−0.627649	−	0.778496i	$-0.715983\pi$
$877$	−32602.1	−1.25530	−0.627649	+	0.778496i	$0.715983\pi$
$878$	6011.00	0.231050
$879$	−43024.9	−1.65096
$880$	0	0
$881$	−16468.7	−0.629789	−0.314894	−	0.949127i	$-0.601969\pi$
$881$	−16468.7	−0.629789	−0.314894	+	0.949127i	$0.601969\pi$
$882$	−2039.61	−0.0778652
$883$	−24207.2	−0.922577	−0.461289	−	0.887250i	$-0.652613\pi$
$883$	−24207.2	−0.922577	−0.461289	+	0.887250i	$0.652613\pi$
$884$	−11451.9	−0.435712
$885$	0	0
$886$	−6104.58	−0.231476
$887$	−5153.96	−0.195099	−0.0975496	−	0.995231i	$-0.531100\pi$
$887$	−5153.96	−0.195099	−0.0975496	+	0.995231i	$0.531100\pi$
$888$	4097.70	0.154854
$889$	−29515.3	−1.11351
$890$	0	0
$891$	−32221.6	−1.21152
$892$	16948.6	0.636190
$893$	−13010.6	−0.487553
$894$	−26719.3	−0.999584
$895$	0	0
$896$	2247.12	0.0837845
$897$	−56182.0	−2.09126
$898$	−31493.6	−1.17033
$899$	−33768.6	−1.25278
$900$	0	0
$901$	−24991.0	−0.924052
$902$	16418.4	0.606067
$903$	2552.35	0.0940609
$904$	2638.22	0.0970639
$905$	0	0
$906$	11319.8	0.415093
$907$	−7000.87	−0.256296	−0.128148	−	0.991755i	$-0.540903\pi$
$907$	−7000.87	−0.256296	−0.128148	+	0.991755i	$0.540903\pi$
$908$	3326.86	0.121592
$909$	−41180.0	−1.50259
$910$	0	0
$911$	−24182.2	−0.879465	−0.439733	−	0.898129i	$-0.644927\pi$
$911$	−24182.2	−0.879465	−0.439733	+	0.898129i	$0.644927\pi$
$912$	−5272.12	−0.191422
$913$	22269.4	0.807239
$914$	−10727.9	−0.388237
$915$	0	0
$916$	8894.05	0.320816
$917$	34012.6	1.22486
$918$	1219.92	0.0438600
$919$	−42910.8	−1.54026	−0.770129	−	0.637888i	$-0.779808\pi$
$919$	−42910.8	−1.54026	−0.770129	+	0.637888i	$0.779808\pi$
$920$	0	0
$921$	−2930.34	−0.104840
$922$	17176.9	0.613548
$923$	15865.8	0.565795
$924$	−25666.9	−0.913831
$925$	0	0
$926$	23418.5	0.831078
$927$	53493.0	1.89530
$928$	−9213.30	−0.325907
$929$	40871.7	1.44344	0.721720	−	0.692185i	$-0.243352\pi$
$929$	40871.7	1.44344	0.721720	+	0.692185i	$0.243352\pi$
$930$	0	0
$931$	−1528.21	−0.0537972
$932$	227.394	0.00799201
$933$	−48493.7	−1.70162
$934$	−23379.8	−0.819068
$935$	0	0
$936$	19023.6	0.664322
$937$	−6821.09	−0.237818	−0.118909	−	0.992905i	$-0.537940\pi$
$937$	−6821.09	−0.237818	−0.118909	+	0.992905i	$0.537940\pi$
$938$	−5083.51	−0.176954
$939$	−75018.9	−2.60719
$940$	0	0
$941$	−57042.7	−1.97613	−0.988065	−	0.154038i	$-0.950772\pi$
$941$	−57042.7	−1.97613	−0.988065	+	0.154038i	$0.950772\pi$
$942$	−39161.7	−1.35452
$943$	15549.8	0.536979
$944$	−10727.5	−0.369863
$945$	0	0
$946$	−1887.61	−0.0648749
$947$	56084.8	1.92451	0.962254	−	0.272151i	$-0.0877352\pi$
$947$	56084.8	1.92451	0.962254	+	0.272151i	$0.0877352\pi$
$948$	−15742.3	−0.539330
$949$	17805.9	0.609067
$950$	0	0
$951$	8242.80	0.281063
$952$	−4955.06	−0.168692
$953$	−29090.1	−0.988793	−0.494397	−	0.869236i	$-0.664611\pi$
$953$	−29090.1	−0.988793	−0.494397	+	0.869236i	$0.664611\pi$
$954$	41514.3	1.40888
$955$	0	0
$956$	−25033.1	−0.846891
$957$	105236.	3.55464
$958$	−6507.42	−0.219463
$959$	28689.4	0.966036
$960$	0	0
$961$	−16034.9	−0.538247
$962$	−11078.6	−0.371298
$963$	−12484.8	−0.417774
$964$	4175.34	0.139501
$965$	0	0
$966$	−24309.1	−0.809660
$967$	−27577.0	−0.917079	−0.458540	−	0.888674i	$-0.651627\pi$
$967$	−27577.0	−0.917079	−0.458540	+	0.888674i	$0.651627\pi$
$968$	8334.20	0.276727
$969$	11625.4	0.385410
$970$	0	0
$971$	−6007.74	−0.198556	−0.0992779	−	0.995060i	$-0.531653\pi$
$971$	−6007.74	−0.198556	−0.0992779	+	0.995060i	$0.531653\pi$
$972$	21721.2	0.716777
$973$	−14903.9	−0.491054
$974$	−6643.84	−0.218565
$975$	0	0
$976$	−1318.23	−0.0432332
$977$	12376.0	0.405265	0.202632	−	0.979255i	$-0.435050\pi$
$977$	12376.0	0.405265	0.202632	+	0.979255i	$0.435050\pi$
$978$	30679.0	1.00307
$979$	−40932.8	−1.33628
$980$	0	0
$981$	17655.8	0.574624
$982$	24258.6	0.788313
$983$	25902.6	0.840453	0.420227	−	0.907419i	$-0.361951\pi$
$983$	25902.6	0.840453	0.420227	+	0.907419i	$0.361951\pi$
$984$	−10116.5	−0.327748
$985$	0	0
$986$	20316.0	0.656181
$987$	39029.1	1.25867
$988$	14253.8	0.458981
$989$	−1787.75	−0.0574796
$990$	0	0
$991$	28196.9	0.903838	0.451919	−	0.892059i	$-0.350740\pi$
$991$	28196.9	0.903838	0.451919	+	0.892059i	$0.350740\pi$
$992$	3753.16	0.120124
$993$	−32137.2	−1.02703
$994$	6864.87	0.219055
$995$	0	0
$996$	−13721.8	−0.436536
$997$	−4915.28	−0.156137	−0.0780684	−	0.996948i	$-0.524875\pi$
$997$	−4915.28	−0.156137	−0.0780684	+	0.996948i	$0.524875\pi$
$998$	−26542.7	−0.841878
$999$	1180.16	0.0373760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.4.a.n.1.2		16
5.4	even	2		1250.4.a.m.1.15		16
25.2	odd	20		250.4.e.b.149.8		32
25.9	even	10		250.4.d.d.151.2		32
25.11	even	5		250.4.d.c.101.7		32
25.12	odd	20		50.4.e.a.19.1	✓	32
25.13	odd	20		250.4.e.b.99.8		32
25.14	even	10		250.4.d.d.101.2		32
25.16	even	5		250.4.d.c.151.7		32
25.23	odd	20		50.4.e.a.29.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.19.1	✓	32	25.12	odd	20
50.4.e.a.29.1	yes	32	25.23	odd	20
250.4.d.c.101.7		32	25.11	even	5
250.4.d.c.151.7		32	25.16	even	5
250.4.d.d.101.2		32	25.14	even	10
250.4.d.d.151.2		32	25.9	even	10
250.4.e.b.99.8		32	25.13	odd	20
250.4.e.b.149.8		32	25.2	odd	20
1250.4.a.m.1.15		16	5.4	even	2
1250.4.a.n.1.2		16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -7.50360 q^{3} +4.00000 q^{4} -15.0072 q^{6} +17.5556 q^{7} +8.00000 q^{8} +29.3040 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -7.50360 q^{3} +4.00000 q^{4} -15.0072 q^{6} +17.5556 q^{7} +8.00000 q^{8} +29.3040 q^{9} +48.7111 q^{11} -30.0144 q^{12} +81.1475 q^{13} +35.1112 q^{14} +16.0000 q^{16} -35.2812 q^{17} +58.6081 q^{18} +43.9132 q^{19} -131.730 q^{21} +97.4223 q^{22} +92.2684 q^{23} -60.0288 q^{24} +162.295 q^{26} -17.2886 q^{27} +70.2224 q^{28} -287.916 q^{29} +117.286 q^{31} +32.0000 q^{32} -365.509 q^{33} -70.5624 q^{34} +117.216 q^{36} -68.2623 q^{37} +87.8265 q^{38} -608.898 q^{39} +168.528 q^{41} -263.461 q^{42} -19.3756 q^{43} +194.845 q^{44} +184.537 q^{46} -296.281 q^{47} -120.058 q^{48} -34.8008 q^{49} +264.736 q^{51} +324.590 q^{52} +708.338 q^{53} -34.5772 q^{54} +140.445 q^{56} -329.507 q^{57} -575.831 q^{58} -670.470 q^{59} -82.3896 q^{61} +234.573 q^{62} +514.450 q^{63} +64.0000 q^{64} -731.018 q^{66} -144.783 q^{67} -141.125 q^{68} -692.345 q^{69} +195.518 q^{71} +234.432 q^{72} +219.427 q^{73} -136.525 q^{74} +175.653 q^{76} +855.153 q^{77} -1217.80 q^{78} +524.490 q^{79} -661.482 q^{81} +337.056 q^{82} +457.172 q^{83} -526.921 q^{84} -38.7512 q^{86} +2160.40 q^{87} +389.689 q^{88} -840.318 q^{89} +1424.59 q^{91} +369.073 q^{92} -880.070 q^{93} -592.562 q^{94} -240.115 q^{96} +1660.10 q^{97} -69.6015 q^{98} +1427.43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9} + 72 q^{11} + 48 q^{12} + 202 q^{13} + 112 q^{14} + 256 q^{16} + 216 q^{17} + 424 q^{18} + 100 q^{19} + 192 q^{21} + 144 q^{22} + 292 q^{23} + 96 q^{24} + 404 q^{26} + 570 q^{27} + 224 q^{28} + 400 q^{29} + 102 q^{31} + 512 q^{32} + 664 q^{33} + 432 q^{34} + 848 q^{36} + 646 q^{37} + 200 q^{38} + 104 q^{39} + 532 q^{41} + 384 q^{42} + 902 q^{43} + 288 q^{44} + 584 q^{46} + 776 q^{47} + 192 q^{48} + 1038 q^{49} + 442 q^{51} + 808 q^{52} + 632 q^{53} + 1140 q^{54} + 448 q^{56} + 1400 q^{57} + 800 q^{58} + 1000 q^{59} + 662 q^{61} + 204 q^{62} + 932 q^{63} + 1024 q^{64} + 1328 q^{66} + 1326 q^{67} + 864 q^{68} + 1854 q^{69} + 1292 q^{71} + 1696 q^{72} + 2272 q^{73} + 1292 q^{74} + 400 q^{76} + 2582 q^{77} + 208 q^{78} + 320 q^{79} + 2956 q^{81} + 1064 q^{82} + 2842 q^{83} + 768 q^{84} + 1804 q^{86} + 2920 q^{87} + 576 q^{88} + 2780 q^{89} + 812 q^{91} + 1168 q^{92} + 2824 q^{93} + 1552 q^{94} + 384 q^{96} + 3796 q^{97} + 2076 q^{98} + 1054 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9 + 72 * q^11 + 48 * q^12 + 202 * q^13 + 112 * q^14 + 256 * q^16 + 216 * q^17 + 424 * q^18 + 100 * q^19 + 192 * q^21 + 144 * q^22 + 292 * q^23 + 96 * q^24 + 404 * q^26 + 570 * q^27 + 224 * q^28 + 400 * q^29 + 102 * q^31 + 512 * q^32 + 664 * q^33 + 432 * q^34 + 848 * q^36 + 646 * q^37 + 200 * q^38 + 104 * q^39 + 532 * q^41 + 384 * q^42 + 902 * q^43 + 288 * q^44 + 584 * q^46 + 776 * q^47 + 192 * q^48 + 1038 * q^49 + 442 * q^51 + 808 * q^52 + 632 * q^53 + 1140 * q^54 + 448 * q^56 + 1400 * q^57 + 800 * q^58 + 1000 * q^59 + 662 * q^61 + 204 * q^62 + 932 * q^63 + 1024 * q^64 + 1328 * q^66 + 1326 * q^67 + 864 * q^68 + 1854 * q^69 + 1292 * q^71 + 1696 * q^72 + 2272 * q^73 + 1292 * q^74 + 400 * q^76 + 2582 * q^77 + 208 * q^78 + 320 * q^79 + 2956 * q^81 + 1064 * q^82 + 2842 * q^83 + 768 * q^84 + 1804 * q^86 + 2920 * q^87 + 576 * q^88 + 2780 * q^89 + 812 * q^91 + 1168 * q^92 + 2824 * q^93 + 1552 * q^94 + 384 * q^96 + 3796 * q^97 + 2076 * q^98 + 1054 * q^99

Introduction

L-functions

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Database

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