LMFDB - Embedded newform 507.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,4,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("507.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	507.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:	$29.9139683729$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.5054412.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 29x^{2} + 48 $ x^4 - 29*x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.21898$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.21898 q^{2} -3.00000 q^{3} +19.2377 q^{4} +5.83936 q^{5} +15.6569 q^{6} +31.3139 q^{7} -58.6495 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.21898 q^{2} -3.00000 q^{3} +19.2377 q^{4} +5.83936 q^{5} +15.6569 q^{6} +31.3139 q^{7} -58.6495 q^{8} +9.00000 q^{9} -30.4755 q^{10} +16.2773 q^{11} -57.7132 q^{12} -163.426 q^{14} -17.5181 q^{15} +152.189 q^{16} -54.0000 q^{17} -46.9708 q^{18} -66.3500 q^{19} +112.336 q^{20} -93.9416 q^{21} -84.9510 q^{22} -182.853 q^{23} +175.949 q^{24} -90.9019 q^{25} -27.0000 q^{27} +602.408 q^{28} -164.853 q^{29} +91.4264 q^{30} +58.9055 q^{31} -325.073 q^{32} -48.8319 q^{33} +281.825 q^{34} +182.853 q^{35} +173.140 q^{36} +110.366 q^{37} +346.279 q^{38} -342.475 q^{40} -55.0357 q^{41} +490.279 q^{42} -113.147 q^{43} +313.139 q^{44} +52.5542 q^{45} +954.305 q^{46} -514.089 q^{47} -456.566 q^{48} +637.559 q^{49} +474.415 q^{50} +162.000 q^{51} +242.559 q^{53} +140.912 q^{54} +95.0490 q^{55} -1836.54 q^{56} +199.050 q^{57} +860.364 q^{58} +265.036 q^{59} -337.008 q^{60} -468.098 q^{61} -307.426 q^{62} +281.825 q^{63} +479.042 q^{64} +254.853 q^{66} -852.919 q^{67} -1038.84 q^{68} +548.559 q^{69} -954.305 q^{70} -165.619 q^{71} -527.846 q^{72} -315.325 q^{73} -576.000 q^{74} +272.706 q^{75} -1276.42 q^{76} +509.706 q^{77} +479.608 q^{79} +888.684 q^{80} +81.0000 q^{81} +287.230 q^{82} -574.235 q^{83} -1807.22 q^{84} -315.325 q^{85} +590.512 q^{86} +494.559 q^{87} -954.657 q^{88} -66.7144 q^{89} -274.279 q^{90} -3517.68 q^{92} -176.716 q^{93} +2683.02 q^{94} -387.441 q^{95} +975.220 q^{96} +1438.25 q^{97} -3327.40 q^{98} +146.496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{3} + 26 q^{4} + 36 q^{9}+O(q^{10}) $ 4 * q - 12 * q^3 + 26 * q^4 + 36 * q^9	$ 4 q - 12 q^{3} + 26 q^{4} + 36 q^{9} - 20 q^{10} - 78 q^{12} - 348 q^{14} + 354 q^{16} - 216 q^{17} - 136 q^{22} - 120 q^{23} + 44 q^{25} - 108 q^{27} - 48 q^{29} + 60 q^{30} + 120 q^{35} + 234 q^{36} + 468 q^{38} - 1268 q^{40} + 1044 q^{42} - 1064 q^{43} - 1062 q^{48} + 716 q^{49} + 648 q^{51} - 864 q^{53} + 584 q^{55} - 3372 q^{56} - 2280 q^{61} - 924 q^{62} + 1050 q^{64} + 408 q^{66} - 1404 q^{68} + 360 q^{69} - 2304 q^{74} - 132 q^{75} + 816 q^{77} + 288 q^{79} + 324 q^{81} + 28 q^{82} + 144 q^{87} - 2392 q^{88} - 180 q^{90} - 8568 q^{92} + 6656 q^{94} - 3384 q^{95}+O(q^{100}) $ 4 * q - 12 * q^3 + 26 * q^4 + 36 * q^9 - 20 * q^10 - 78 * q^12 - 348 * q^14 + 354 * q^16 - 216 * q^17 - 136 * q^22 - 120 * q^23 + 44 * q^25 - 108 * q^27 - 48 * q^29 + 60 * q^30 + 120 * q^35 + 234 * q^36 + 468 * q^38 - 1268 * q^40 + 1044 * q^42 - 1064 * q^43 - 1062 * q^48 + 716 * q^49 + 648 * q^51 - 864 * q^53 + 584 * q^55 - 3372 * q^56 - 2280 * q^61 - 924 * q^62 + 1050 * q^64 + 408 * q^66 - 1404 * q^68 + 360 * q^69 - 2304 * q^74 - 132 * q^75 + 816 * q^77 + 288 * q^79 + 324 * q^81 + 28 * q^82 + 144 * q^87 - 2392 * q^88 - 180 * q^90 - 8568 * q^92 + 6656 * q^94 - 3384 * q^95

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 $

$2$	−5.21898	−1.84519	−0.922594	−	0.385773i	$-0.873935\pi$
$2$	−5.21898	−1.84519	−0.922594	+	0.385773i	$0.873935\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	19.2377	2.40472
$5$	5.83936	0.522288	0.261144	−	0.965300i	$-0.415900\pi$
$5$	5.83936	0.522288	0.261144	+	0.965300i	$0.415900\pi$
$6$	15.6569	1.06532
$7$	31.3139	1.69079	0.845395	−	0.534141i	$-0.179365\pi$
$7$	31.3139	1.69079	0.845395	+	0.534141i	$0.179365\pi$
$8$	−58.6495	−2.59197
$9$	9.00000	0.333333
$10$	−30.4755	−0.963719
$11$	16.2773	0.446163	0.223082	−	0.974800i	$-0.428388\pi$
$11$	16.2773	0.446163	0.223082	+	0.974800i	$0.428388\pi$
$12$	−57.7132	−1.38836
$13$	0	0
$13$	0	0
$14$	−163.426	−3.11983
$15$	−17.5181	−0.301543
$16$	152.189	2.37795
$17$	−54.0000	−0.770407	−0.385204	−	0.922832i	$-0.625869\pi$
$17$	−54.0000	−0.770407	−0.385204	+	0.922832i	$0.625869\pi$
$18$	−46.9708	−0.615063
$19$	−66.3500	−0.801144	−0.400572	−	0.916265i	$-0.631189\pi$
$19$	−66.3500	−0.801144	−0.400572	+	0.916265i	$0.631189\pi$
$20$	112.336	1.25595
$21$	−93.9416	−0.976178
$22$	−84.9510	−0.823255
$23$	−182.853	−1.65772	−0.828858	−	0.559459i	$-0.811009\pi$
$23$	−182.853	−1.65772	−0.828858	+	0.559459i	$0.811009\pi$
$24$	175.949	1.49647
$25$	−90.9019	−0.727215
$26$	0	0
$27$	−27.0000	−0.192450
$28$	602.408	4.06587
$29$	−164.853	−1.05560	−0.527800	−	0.849369i	$-0.676983\pi$
$29$	−164.853	−1.05560	−0.527800	+	0.849369i	$0.676983\pi$
$30$	91.4264	0.556404
$31$	58.9055	0.341282	0.170641	−	0.985333i	$-0.445416\pi$
$31$	58.9055	0.341282	0.170641	+	0.985333i	$0.445416\pi$
$32$	−325.073	−1.79579
$33$	−48.8319	−0.257592
$34$	281.825	1.42155
$35$	182.853	0.883079
$36$	173.140	0.801572
$37$	110.366	0.490382	0.245191	−	0.969475i	$-0.421149\pi$
$37$	110.366	0.490382	0.245191	+	0.969475i	$0.421149\pi$
$38$	346.279	1.47826
$39$	0	0
$40$	−342.475	−1.35375
$41$	−55.0357	−0.209637	−0.104819	−	0.994491i	$-0.533426\pi$
$41$	−55.0357	−0.209637	−0.104819	+	0.994491i	$0.533426\pi$
$42$	490.279	1.80123
$43$	−113.147	−0.401274	−0.200637	−	0.979666i	$-0.564301\pi$
$43$	−113.147	−0.401274	−0.200637	+	0.979666i	$0.564301\pi$
$44$	313.139	1.07290
$45$	52.5542	0.174096
$46$	954.305	3.05880
$47$	−514.089	−1.59548	−0.797740	−	0.603001i	$-0.793971\pi$
$47$	−514.089	−1.59548	−0.797740	+	0.603001i	$0.793971\pi$
$48$	−456.566	−1.37291
$49$	637.559	1.85877
$50$	474.415	1.34185
$51$	162.000	0.444795
$52$	0	0
$53$	242.559	0.628641	0.314321	−	0.949317i	$-0.398223\pi$
$53$	242.559	0.628641	0.314321	+	0.949317i	$0.398223\pi$
$54$	140.912	0.355107
$55$	95.0490	0.233026
$56$	−1836.54	−4.38247
$57$	199.050	0.462541
$58$	860.364	1.94778
$59$	265.036	0.584825	0.292413	−	0.956292i	$-0.405542\pi$
$59$	265.036	0.584825	0.292413	+	0.956292i	$0.405542\pi$
$60$	−337.008	−0.725126
$61$	−468.098	−0.982522	−0.491261	−	0.871013i	$-0.663464\pi$
$61$	−468.098	−0.982522	−0.491261	+	0.871013i	$0.663464\pi$
$62$	−307.426	−0.629729
$63$	281.825	0.563597
$64$	479.042	0.935628
$65$	0	0
$66$	254.853	0.475306
$67$	−852.919	−1.55523	−0.777617	−	0.628739i	$-0.783572\pi$
$67$	−852.919	−1.55523	−0.777617	+	0.628739i	$0.783572\pi$
$68$	−1038.84	−1.85261
$69$	548.559	0.957083
$70$	−954.305	−1.62945
$71$	−165.619	−0.276836	−0.138418	−	0.990374i	$-0.544202\pi$
$71$	−165.619	−0.276836	−0.138418	+	0.990374i	$0.544202\pi$
$72$	−527.846	−0.863989
$73$	−315.325	−0.505562	−0.252781	−	0.967524i	$-0.581345\pi$
$73$	−315.325	−0.505562	−0.252781	+	0.967524i	$0.581345\pi$
$74$	−576.000	−0.904846
$75$	272.706	0.419858
$76$	−1276.42	−1.92653
$77$	509.706	0.754368
$78$	0	0
$79$	479.608	0.683039	0.341519	−	0.939875i	$-0.389058\pi$
$79$	479.608	0.683039	0.341519	+	0.939875i	$0.389058\pi$
$80$	888.684	1.24197
$81$	81.0000	0.111111
$82$	287.230	0.386820
$83$	−574.235	−0.759404	−0.379702	−	0.925109i	$-0.623973\pi$
$83$	−574.235	−0.759404	−0.379702	+	0.925109i	$0.623973\pi$
$84$	−1807.22	−2.34743
$85$	−315.325	−0.402374
$86$	590.512	0.740426
$87$	494.559	0.609451
$88$	−954.657	−1.15644
$89$	−66.7144	−0.0794575	−0.0397287	−	0.999211i	$-0.512649\pi$
$89$	−66.7144	−0.0794575	−0.0397287	+	0.999211i	$0.512649\pi$
$90$	−274.279	−0.321240
$91$	0	0
$92$	−3517.68	−3.98634
$93$	−176.716	−0.197039
$94$	2683.02	2.94396
$95$	−387.441	−0.418428
$96$	975.220	1.03680
$97$	1438.25	1.50549	0.752744	−	0.658313i	$-0.228730\pi$
$97$	1438.25	1.50549	0.752744	+	0.658313i	$0.228730\pi$
$98$	−3327.40	−3.42978
$99$	146.496	0.148721
$100$	−1748.75	−1.74875
$101$	−896.264	−0.882986	−0.441493	−	0.897265i	$-0.645551\pi$
$101$	−896.264	−0.882986	−0.441493	+	0.897265i	$0.645551\pi$
$102$	−845.475	−0.820730
$103$	−22.2644	−0.0212988	−0.0106494	−	0.999943i	$-0.503390\pi$
$103$	−22.2644	−0.0212988	−0.0106494	+	0.999943i	$0.503390\pi$
$104$	0	0
$105$	−548.559	−0.509846
$106$	−1265.91	−1.15996
$107$	−351.441	−0.317524	−0.158762	−	0.987317i	$-0.550750\pi$
$107$	−351.441	−0.317524	−0.158762	+	0.987317i	$0.550750\pi$
$108$	−519.419	−0.462788
$109$	−967.008	−0.849748	−0.424874	−	0.905252i	$-0.639682\pi$
$109$	−967.008	−0.849748	−0.424874	+	0.905252i	$0.639682\pi$
$110$	−496.059	−0.429976
$111$	−331.099	−0.283122
$112$	4765.62	4.02061
$113$	48.2943	0.0402048	0.0201024	−	0.999798i	$-0.493601\pi$
$113$	48.2943	0.0402048	0.0201024	+	0.999798i	$0.493601\pi$
$114$	−1038.84	−0.853474
$115$	−1067.74	−0.865805
$116$	−3171.40	−2.53842
$117$	0	0
$118$	−1383.22	−1.07911
$119$	−1690.95	−1.30260
$120$	1027.43	0.781590
$121$	−1066.05	−0.800938
$122$	2442.99	1.81294
$123$	165.107	0.121034
$124$	1133.21	0.820686
$125$	−1260.73	−0.902104
$126$	−1470.84	−1.03994
$127$	−1763.02	−1.23183	−0.615916	−	0.787812i	$-0.711214\pi$
$127$	−1763.02	−1.23183	−0.615916	+	0.787812i	$0.711214\pi$
$128$	100.479	0.0693844
$129$	339.441	0.231676
$130$	0	0
$131$	955.970	0.637584	0.318792	−	0.947825i	$-0.396723\pi$
$131$	955.970	0.637584	0.318792	+	0.947825i	$0.396723\pi$
$132$	−939.416	−0.619437
$133$	−2077.68	−1.35457
$134$	4451.37	2.86970
$135$	−157.663	−0.100514
$136$	3167.07	1.99687
$137$	−15.9215	−0.00992894	−0.00496447	−	0.999988i	$-0.501580\pi$
$137$	−15.9215	−0.00992894	−0.00496447	+	0.999988i	$0.501580\pi$
$138$	−2862.92	−1.76600
$139$	2074.26	1.26573	0.632866	−	0.774261i	$-0.281878\pi$
$139$	2074.26	1.26573	0.632866	+	0.774261i	$0.281878\pi$
$140$	3517.68	2.12356
$141$	1542.27	0.921151
$142$	864.362	0.510815
$143$	0	0
$144$	1369.70	0.792649
$145$	−962.635	−0.551327
$146$	1645.68	0.932857
$147$	−1912.68	−1.07316
$148$	2123.20	1.17923
$149$	2764.08	1.51975	0.759873	−	0.650071i	$-0.225261\pi$
$149$	2764.08	1.51975	0.759873	+	0.650071i	$0.225261\pi$
$150$	−1423.25	−0.774717
$151$	1618.46	0.872239	0.436120	−	0.899889i	$-0.356352\pi$
$151$	1618.46	0.872239	0.436120	+	0.899889i	$0.356352\pi$
$152$	3891.40	2.07654
$153$	−486.000	−0.256802
$154$	−2660.14	−1.39195
$155$	343.970	0.178247
$156$	0	0
$157$	−1109.97	−0.564237	−0.282119	−	0.959380i	$-0.591037\pi$
$157$	−1109.97	−0.564237	−0.282119	+	0.959380i	$0.591037\pi$
$158$	−2503.06	−1.26034
$159$	−727.676	−0.362946
$160$	−1898.22	−0.937921
$161$	−5725.83	−2.80285
$162$	−422.737	−0.205021
$163$	−233.201	−0.112060	−0.0560299	−	0.998429i	$-0.517844\pi$
$163$	−233.201	−0.112060	−0.0560299	+	0.998429i	$0.517844\pi$
$164$	−1058.76	−0.504119
$165$	−285.147	−0.134537
$166$	2996.92	1.40124
$167$	−215.405	−0.0998118	−0.0499059	−	0.998754i	$-0.515892\pi$
$167$	−215.405	−0.0998118	−0.0499059	+	0.998754i	$0.515892\pi$
$168$	5509.63	2.53022
$169$	0	0
$170$	1645.68	0.742456
$171$	−597.150	−0.267048
$172$	−2176.69	−0.964950
$173$	−1383.15	−0.607854	−0.303927	−	0.952695i	$-0.598298\pi$
$173$	−1383.15	−0.607854	−0.303927	+	0.952695i	$0.598298\pi$
$174$	−2581.09	−1.12455
$175$	−2846.49	−1.22957
$176$	2477.22	1.06095
$177$	−795.107	−0.337649
$178$	348.181	0.146614
$179$	3642.79	1.52109	0.760545	−	0.649285i	$-0.224932\pi$
$179$	3642.79	1.52109	0.760545	+	0.649285i	$0.224932\pi$
$180$	1011.02	0.418652
$181$	2621.97	1.07674	0.538369	−	0.842709i	$-0.319041\pi$
$181$	2621.97	1.07674	0.538369	+	0.842709i	$0.319041\pi$
$182$	0	0
$183$	1404.29	0.567259
$184$	10724.2	4.29674
$185$	644.469	0.256121
$186$	922.279	0.363574
$187$	−878.975	−0.343727
$188$	−9889.91	−3.83668
$189$	−845.475	−0.325393
$190$	2022.05	0.772078
$191$	−3419.32	−1.29536	−0.647679	−	0.761913i	$-0.724260\pi$
$191$	−3419.32	−1.29536	−0.647679	+	0.761913i	$0.724260\pi$
$192$	−1437.12	−0.540185
$193$	1698.39	0.633435	0.316718	−	0.948520i	$-0.397419\pi$
$193$	1698.39	0.633435	0.316718	+	0.948520i	$0.397419\pi$
$194$	−7506.20	−2.77791
$195$	0	0
$196$	12265.2	4.46982
$197$	2293.72	0.829548	0.414774	−	0.909925i	$-0.363861\pi$
$197$	2293.72	0.829548	0.414774	+	0.909925i	$0.363861\pi$
$198$	−764.559	−0.274418
$199$	900.981	0.320949	0.160474	−	0.987040i	$-0.448698\pi$
$199$	900.981	0.320949	0.160474	+	0.987040i	$0.448698\pi$
$200$	5331.35	1.88492
$201$	2558.76	0.897915
$202$	4677.58	1.62928
$203$	−5162.18	−1.78480
$204$	3116.51	1.06961
$205$	−321.373	−0.109491
$206$	116.197	0.0393002
$207$	−1645.68	−0.552572
$208$	0	0
$209$	−1080.00	−0.357441
$210$	2862.92	0.940762
$211$	431.019	0.140628	0.0703142	−	0.997525i	$-0.477600\pi$
$211$	431.019	0.140628	0.0703142	+	0.997525i	$0.477600\pi$
$212$	4666.28	1.51170
$213$	496.857	0.159831
$214$	1834.17	0.585892
$215$	−660.706	−0.209580
$216$	1583.54	0.498824
$217$	1844.56	0.577036
$218$	5046.79	1.56794
$219$	945.976	0.291886
$220$	1828.53	0.560361
$221$	0	0
$222$	1728.00	0.522413
$223$	−4104.30	−1.23249	−0.616243	−	0.787556i	$-0.711346\pi$
$223$	−4104.30	−1.23249	−0.616243	+	0.787556i	$0.711346\pi$
$224$	−10179.3	−3.03631
$225$	−818.117	−0.242405
$226$	−252.047	−0.0741854
$227$	1809.11	0.528963	0.264482	−	0.964391i	$-0.414799\pi$
$227$	1809.11	0.528963	0.264482	+	0.964391i	$0.414799\pi$
$228$	3829.27	1.11228
$229$	−5249.33	−1.51478	−0.757392	−	0.652961i	$-0.773527\pi$
$229$	−5249.33	−1.51478	−0.757392	+	0.652961i	$0.773527\pi$
$230$	5572.53	1.59757
$231$	−1529.12	−0.435535
$232$	9668.54	2.73608
$233$	−2808.88	−0.789768	−0.394884	−	0.918731i	$-0.629215\pi$
$233$	−2808.88	−0.789768	−0.394884	+	0.918731i	$0.629215\pi$
$234$	0	0
$235$	−3001.95	−0.833300
$236$	5098.69	1.40634
$237$	−1438.82	−0.394353
$238$	8825.03	2.40354
$239$	6712.01	1.81659	0.908293	−	0.418334i	$-0.137386\pi$
$239$	6712.01	1.81659	0.908293	+	0.418334i	$0.137386\pi$
$240$	−2666.05	−0.717054
$241$	2519.11	0.673321	0.336661	−	0.941626i	$-0.390703\pi$
$241$	2519.11	0.673321	0.336661	+	0.941626i	$0.390703\pi$
$242$	5563.69	1.47788
$243$	−243.000	−0.0641500
$244$	−9005.15	−2.36269
$245$	3722.93	0.970814
$246$	−861.691	−0.223331
$247$	0	0
$248$	−3454.78	−0.884591
$249$	1722.71	0.438442
$250$	6579.71	1.66455
$251$	828.000	0.208219	0.104109	−	0.994566i	$-0.466801\pi$
$251$	828.000	0.208219	0.104109	+	0.994566i	$0.466801\pi$
$252$	5421.67	1.35529
$253$	−2976.35	−0.739612
$254$	9201.16	2.27296
$255$	945.976	0.232311
$256$	−4356.73	−1.06366
$257$	−5840.76	−1.41765	−0.708826	−	0.705383i	$-0.750775\pi$
$257$	−5840.76	−1.41765	−0.708826	+	0.705383i	$0.750775\pi$
$258$	−1771.54	−0.427485
$259$	3456.00	0.829133
$260$	0	0
$261$	−1483.68	−0.351867
$262$	−4989.19	−1.17646
$263$	−4064.06	−0.952854	−0.476427	−	0.879214i	$-0.658068\pi$
$263$	−4064.06	−0.952854	−0.476427	+	0.879214i	$0.658068\pi$
$264$	2863.97	0.667671
$265$	1416.39	0.328332
$266$	10843.3	2.49943
$267$	200.143	0.0458748
$268$	−16408.2	−3.73990
$269$	1845.44	0.418285	0.209142	−	0.977885i	$-0.432933\pi$
$269$	1845.44	0.418285	0.209142	+	0.977885i	$0.432933\pi$
$270$	822.838	0.185468
$271$	−2106.78	−0.472242	−0.236121	−	0.971724i	$-0.575876\pi$
$271$	−2106.78	−0.472242	−0.236121	+	0.971724i	$0.575876\pi$
$272$	−8218.19	−1.83199
$273$	0	0
$274$	83.0939	0.0183208
$275$	−1479.64	−0.324457
$276$	10553.0	2.30151
$277$	−4781.94	−1.03725	−0.518626	−	0.855001i	$-0.673556\pi$
$277$	−4781.94	−1.03725	−0.518626	+	0.855001i	$0.673556\pi$
$278$	−10825.5	−2.33551
$279$	530.149	0.113761
$280$	−10724.2	−2.28891
$281$	5865.81	1.24528	0.622642	−	0.782507i	$-0.286059\pi$
$281$	5865.81	1.24528	0.622642	+	0.782507i	$0.286059\pi$
$282$	−8049.06	−1.69970
$283$	−6407.02	−1.34579	−0.672894	−	0.739739i	$-0.734949\pi$
$283$	−6407.02	−1.34579	−0.672894	+	0.739739i	$0.734949\pi$
$284$	−3186.14	−0.665713
$285$	1162.32	0.241579
$286$	0	0
$287$	−1723.38	−0.354453
$288$	−2925.66	−0.598598
$289$	−1997.00	−0.406473
$290$	5023.97	1.01730
$291$	−4314.75	−0.869194
$292$	−6066.15	−1.21573
$293$	−3010.24	−0.600204	−0.300102	−	0.953907i	$-0.597021\pi$
$293$	−3010.24	−0.600204	−0.300102	+	0.953907i	$0.597021\pi$
$294$	9982.21	1.98019
$295$	1547.64	0.305447
$296$	−6472.94	−1.27105
$297$	−439.487	−0.0858641
$298$	−14425.7	−2.80422
$299$	0	0
$300$	5246.24	1.00964
$301$	−3543.07	−0.678470
$302$	−8446.69	−1.60944
$303$	2688.79	0.509792
$304$	−10097.7	−1.90508
$305$	−2733.39	−0.513159
$306$	2536.42	0.473849
$307$	−3341.84	−0.621266	−0.310633	−	0.950530i	$-0.600541\pi$
$307$	−3341.84	−0.621266	−0.310633	+	0.950530i	$0.600541\pi$
$308$	9805.59	1.81404
$309$	66.7931	0.0122968
$310$	−1795.17	−0.328900
$311$	8755.20	1.59634	0.798170	−	0.602432i	$-0.205801\pi$
$311$	8755.20	1.59634	0.798170	+	0.602432i	$0.205801\pi$
$312$	0	0
$313$	1948.93	0.351949	0.175974	−	0.984395i	$-0.443692\pi$
$313$	1948.93	0.351949	0.175974	+	0.984395i	$0.443692\pi$
$314$	5792.91	1.04112
$315$	1645.68	0.294360
$316$	9226.57	1.64252
$317$	−1940.43	−0.343802	−0.171901	−	0.985114i	$-0.554991\pi$
$317$	−1940.43	−0.343802	−0.171901	+	0.985114i	$0.554991\pi$
$318$	3797.72	0.669704
$319$	−2683.36	−0.470970
$320$	2797.29	0.488667
$321$	1054.32	0.183323
$322$	29883.0	5.17178
$323$	3582.90	0.617207
$324$	1558.26	0.267191
$325$	0	0
$326$	1217.07	0.206771
$327$	2901.02	0.490602
$328$	3227.82	0.543373
$329$	−16098.1	−2.69762
$330$	1488.18	0.248247
$331$	−7402.13	−1.22918	−0.614589	−	0.788848i	$-0.710678\pi$
$331$	−7402.13	−1.22918	−0.614589	+	0.788848i	$0.710678\pi$
$332$	−11047.0	−1.82615
$333$	993.298	0.163461
$334$	1124.20	0.184171
$335$	−4980.50	−0.812280
$336$	−14296.9	−2.32130
$337$	−5494.05	−0.888071	−0.444035	−	0.896009i	$-0.646454\pi$
$337$	−5494.05	−0.888071	−0.444035	+	0.896009i	$0.646454\pi$
$338$	0	0
$339$	−144.883	−0.0232122
$340$	−6066.15	−0.967597
$341$	958.823	0.152267
$342$	3116.51	0.492754
$343$	9223.77	1.45200
$344$	6636.03	1.04009
$345$	3203.23	0.499873
$346$	7218.62	1.12160
$347$	3410.76	0.527664	0.263832	−	0.964569i	$-0.415014\pi$
$347$	3410.76	0.527664	0.263832	+	0.964569i	$0.415014\pi$
$348$	9514.19	1.46556
$349$	−12629.8	−1.93712	−0.968562	−	0.248773i	$-0.919973\pi$
$349$	−12629.8	−1.93712	−0.968562	+	0.248773i	$0.919973\pi$
$350$	14855.8	2.26878
$351$	0	0
$352$	−5291.32	−0.801217
$353$	2981.78	0.449586	0.224793	−	0.974407i	$-0.427829\pi$
$353$	2981.78	0.449586	0.224793	+	0.974407i	$0.427829\pi$
$354$	4149.65	0.623026
$355$	−967.109	−0.144588
$356$	−1283.43	−0.191073
$357$	5072.85	0.752055
$358$	−19011.7	−2.80670
$359$	8942.30	1.31464	0.657321	−	0.753611i	$-0.271690\pi$
$359$	8942.30	1.31464	0.657321	+	0.753611i	$0.271690\pi$
$360$	−3082.28	−0.451251
$361$	−2456.68	−0.358168
$362$	−13684.0	−1.98678
$363$	3198.15	0.462422
$364$	0	0
$365$	−1841.30	−0.264049
$366$	−7328.98	−1.04670
$367$	−4735.26	−0.673511	−0.336756	−	0.941592i	$-0.609330\pi$
$367$	−4735.26	−0.673511	−0.336756	+	0.941592i	$0.609330\pi$
$368$	−27828.1	−3.94196
$369$	−495.321	−0.0698792
$370$	−3363.47	−0.472590
$371$	7595.45	1.06290
$372$	−3399.62	−0.473823
$373$	−8304.01	−1.15272	−0.576361	−	0.817195i	$-0.695528\pi$
$373$	−8304.01	−1.15272	−0.576361	+	0.817195i	$0.695528\pi$
$374$	4587.35	0.634241
$375$	3782.18	0.520830
$376$	30151.1	4.13543
$377$	0	0
$378$	4412.51	0.600411
$379$	4088.11	0.554069	0.277035	−	0.960860i	$-0.410648\pi$
$379$	4088.11	0.554069	0.277035	+	0.960860i	$0.410648\pi$
$380$	−7453.50	−1.00620
$381$	5289.06	0.711198
$382$	17845.4	2.39018
$383$	13951.5	1.86132	0.930662	−	0.365879i	$-0.119232\pi$
$383$	13951.5	1.86132	0.930662	+	0.365879i	$0.119232\pi$
$384$	−301.438	−0.0400591
$385$	2976.35	0.393997
$386$	−8863.88	−1.16881
$387$	−1018.32	−0.133758
$388$	27668.7	3.62027
$389$	−2804.26	−0.365506	−0.182753	−	0.983159i	$-0.558501\pi$
$389$	−2804.26	−0.365506	−0.182753	+	0.983159i	$0.558501\pi$
$390$	0	0
$391$	9874.06	1.27712
$392$	−37392.5	−4.81787
$393$	−2867.91	−0.368109
$394$	−11970.9	−1.53067
$395$	2800.60	0.356743
$396$	2818.25	0.357632
$397$	6556.18	0.828830	0.414415	−	0.910088i	$-0.363986\pi$
$397$	6556.18	0.828830	0.414415	+	0.910088i	$0.363986\pi$
$398$	−4702.20	−0.592211
$399$	6233.03	0.782059
$400$	−13834.2	−1.72928
$401$	−4730.95	−0.589157	−0.294579	−	0.955627i	$-0.595179\pi$
$401$	−4730.95	−0.589157	−0.294579	+	0.955627i	$0.595179\pi$
$402$	−13354.1	−1.65682
$403$	0	0
$404$	−17242.1	−2.12333
$405$	472.988	0.0580320
$406$	26941.3	3.29329
$407$	1796.47	0.218790
$408$	−9501.22	−1.15289
$409$	−12314.4	−1.48878	−0.744389	−	0.667746i	$-0.767259\pi$
$409$	−12314.4	−1.48878	−0.744389	+	0.667746i	$0.767259\pi$
$410$	1677.24	0.202032
$411$	47.7645	0.00573247
$412$	−428.316	−0.0512175
$413$	8299.29	0.988817
$414$	8588.75	1.01960
$415$	−3353.16	−0.396627
$416$	0	0
$417$	−6222.79	−0.730771
$418$	5636.50	0.659546
$419$	−5499.85	−0.641254	−0.320627	−	0.947206i	$-0.603894\pi$
$419$	−5499.85	−0.641254	−0.320627	+	0.947206i	$0.603894\pi$
$420$	−10553.0	−1.22604
$421$	12629.7	1.46208	0.731039	−	0.682336i	$-0.239036\pi$
$421$	12629.7	1.46208	0.731039	+	0.682336i	$0.239036\pi$
$422$	−2249.48	−0.259486
$423$	−4626.80	−0.531827
$424$	−14225.9	−1.62942
$425$	4908.70	0.560252
$426$	−2593.09	−0.294919
$427$	−14658.0	−1.66124
$428$	−6760.94	−0.763557
$429$	0	0
$430$	3448.21	0.386715
$431$	7191.15	0.803679	0.401840	−	0.915710i	$-0.368371\pi$
$431$	7191.15	0.803679	0.401840	+	0.915710i	$0.368371\pi$
$432$	−4109.09	−0.457636
$433$	6062.68	0.672873	0.336436	−	0.941706i	$-0.390778\pi$
$433$	6062.68	0.672873	0.336436	+	0.941706i	$0.390778\pi$
$434$	−9626.71	−1.06474
$435$	2887.90	0.318309
$436$	−18603.0	−2.04340
$437$	12132.3	1.32807
$438$	−4937.03	−0.538585
$439$	11864.3	1.28986	0.644932	−	0.764240i	$-0.276886\pi$
$439$	11864.3	1.28986	0.644932	+	0.764240i	$0.276886\pi$
$440$	−5574.58	−0.603995
$441$	5738.03	0.619590
$442$	0	0
$443$	10560.5	1.13261	0.566303	−	0.824197i	$-0.308373\pi$
$443$	10560.5	1.13261	0.566303	+	0.824197i	$0.308373\pi$
$444$	−6369.60	−0.680829
$445$	−389.569	−0.0414997
$446$	21420.3	2.27417
$447$	−8292.24	−0.877426
$448$	15000.6	1.58195
$449$	−12659.7	−1.33062	−0.665308	−	0.746569i	$-0.731700\pi$
$449$	−12659.7	−1.33062	−0.665308	+	0.746569i	$0.731700\pi$
$450$	4269.74	0.447283
$451$	−895.834	−0.0935325
$452$	929.072	0.0966812
$453$	−4855.37	−0.503587
$454$	−9441.69	−0.976037
$455$	0	0
$456$	−11674.2	−1.19889
$457$	−1544.24	−0.158067	−0.0790336	−	0.996872i	$-0.525183\pi$
$457$	−1544.24	−0.158067	−0.0790336	+	0.996872i	$0.525183\pi$
$458$	27396.1	2.79506
$459$	1458.00	0.148265
$460$	−20541.0	−2.08202
$461$	−13196.8	−1.33327	−0.666635	−	0.745384i	$-0.732266\pi$
$461$	−13196.8	−1.33327	−0.666635	+	0.745384i	$0.732266\pi$
$462$	7980.43	0.803643
$463$	16309.2	1.63705	0.818524	−	0.574472i	$-0.194792\pi$
$463$	16309.2	1.63705	0.818524	+	0.574472i	$0.194792\pi$
$464$	−25088.7	−2.51016
$465$	−1031.91	−0.102911
$466$	14659.5	1.45727
$467$	−14260.8	−1.41308	−0.706541	−	0.707672i	$-0.749745\pi$
$467$	−14260.8	−1.41308	−0.706541	+	0.707672i	$0.749745\pi$
$468$	0	0
$469$	−26708.2	−2.62957
$470$	15667.1	1.53760
$471$	3329.91	0.325763
$472$	−15544.2	−1.51585
$473$	−1841.73	−0.179034
$474$	7509.19	0.727655
$475$	6031.34	0.582604
$476$	−32530.0	−3.13238
$477$	2183.03	0.209547
$478$	−35029.9	−3.35194
$479$	18011.5	1.71809	0.859046	−	0.511899i	$-0.171058\pi$
$479$	18011.5	1.71809	0.859046	+	0.511899i	$0.171058\pi$
$480$	5694.66	0.541509
$481$	0	0
$482$	−13147.2	−1.24240
$483$	17177.5	1.61823
$484$	−20508.4	−1.92603
$485$	8398.46	0.786298
$486$	1268.21	0.118369
$487$	−14043.3	−1.30670	−0.653351	−	0.757055i	$-0.726637\pi$
$487$	−14043.3	−1.30670	−0.653351	+	0.757055i	$0.726637\pi$
$488$	27453.7	2.54666
$489$	699.604	0.0646977
$490$	−19429.9	−1.79133
$491$	−12966.1	−1.19176	−0.595878	−	0.803075i	$-0.703196\pi$
$491$	−12966.1	−1.19176	−0.595878	+	0.803075i	$0.703196\pi$
$492$	3176.29	0.291053
$493$	8902.06	0.813242
$494$	0	0
$495$	855.441	0.0776752
$496$	8964.75	0.811551
$497$	−5186.17	−0.468072
$498$	−8990.76	−0.809007
$499$	−10215.5	−0.916453	−0.458227	−	0.888835i	$-0.651515\pi$
$499$	−10215.5	−0.916453	−0.458227	+	0.888835i	$0.651515\pi$
$500$	−24253.6	−2.16930
$501$	646.216	0.0576264
$502$	−4321.31	−0.384203
$503$	−16632.0	−1.47432	−0.737161	−	0.675717i	$-0.763834\pi$
$503$	−16632.0	−1.47432	−0.737161	+	0.675717i	$0.763834\pi$
$504$	−16528.9	−1.46082
$505$	−5233.61	−0.461173
$506$	15533.5	1.36472
$507$	0	0
$508$	−33916.5	−2.96221
$509$	15235.3	1.32671	0.663354	−	0.748306i	$-0.269132\pi$
$509$	15235.3	1.32671	0.663354	+	0.748306i	$0.269132\pi$
$510$	−4937.03	−0.428657
$511$	−9874.06	−0.854799
$512$	21933.9	1.89326
$513$	1791.45	0.154180
$514$	30482.8	2.61584
$515$	−130.009	−0.0111241
$516$	6530.08	0.557114
$517$	−8367.99	−0.711845
$518$	−18036.8	−1.52991
$519$	4149.44	0.350945
$520$	0	0
$521$	2680.23	0.225380	0.112690	−	0.993630i	$-0.464053\pi$
$521$	2680.23	0.225380	0.112690	+	0.993630i	$0.464053\pi$
$522$	7743.27	0.649260
$523$	−2410.38	−0.201527	−0.100764	−	0.994910i	$-0.532129\pi$
$523$	−2410.38	−0.201527	−0.100764	+	0.994910i	$0.532129\pi$
$524$	18390.7	1.53321
$525$	8539.47	0.709892
$526$	21210.2	1.75819
$527$	−3180.90	−0.262926
$528$	−7431.67	−0.612541
$529$	21268.2	1.74802
$530$	−7392.09	−0.605834
$531$	2385.32	0.194942
$532$	−39969.8	−3.25735
$533$	0	0
$534$	−1044.54	−0.0846476
$535$	−2052.19	−0.165839
$536$	50023.3	4.03111
$537$	−10928.4	−0.878202
$538$	−9631.32	−0.771814
$539$	10377.7	0.829315
$540$	−3033.07	−0.241709
$541$	−9969.58	−0.792284	−0.396142	−	0.918189i	$-0.629651\pi$
$541$	−9969.58	−0.792284	−0.396142	+	0.918189i	$0.629651\pi$
$542$	10995.2	0.871375
$543$	−7865.91	−0.621655
$544$	17554.0	1.38349
$545$	−5646.70	−0.443813
$546$	0	0
$547$	16848.8	1.31701	0.658505	−	0.752576i	$-0.271189\pi$
$547$	16848.8	1.31701	0.658505	+	0.752576i	$0.271189\pi$
$548$	−306.293	−0.0238763
$549$	−4212.88	−0.327507
$550$	7722.20	0.598683
$551$	10938.0	0.845688
$552$	−32172.7	−2.48073
$553$	15018.4	1.15488
$554$	24956.8	1.91393
$555$	−1933.41	−0.147871
$556$	39904.2	3.04373
$557$	3800.83	0.289132	0.144566	−	0.989495i	$-0.453821\pi$
$557$	3800.83	0.289132	0.144566	+	0.989495i	$0.453821\pi$
$558$	−2766.84	−0.209910
$559$	0	0
$560$	27828.1	2.09992
$561$	2636.92	0.198451
$562$	−30613.5	−2.29778
$563$	−15750.2	−1.17903	−0.589513	−	0.807759i	$-0.700680\pi$
$563$	−15750.2	−1.17903	−0.589513	+	0.807759i	$0.700680\pi$
$564$	29669.7	2.21511
$565$	282.007	0.0209985
$566$	33438.1	2.48323
$567$	2536.42	0.187866
$568$	9713.48	0.717550
$569$	17753.2	1.30800	0.654002	−	0.756493i	$-0.273089\pi$
$569$	17753.2	1.30800	0.654002	+	0.756493i	$0.273089\pi$
$570$	−6066.15	−0.445759
$571$	25293.1	1.85374	0.926868	−	0.375388i	$-0.122491\pi$
$571$	25293.1	1.85374	0.926868	+	0.375388i	$0.122491\pi$
$572$	0	0
$573$	10258.0	0.747875
$574$	8994.29	0.654032
$575$	16621.7	1.20552
$576$	4311.37	0.311876
$577$	18488.8	1.33396	0.666982	−	0.745073i	$-0.267586\pi$
$577$	18488.8	1.33396	0.666982	+	0.745073i	$0.267586\pi$
$578$	10422.3	0.750018
$579$	−5095.18	−0.365714
$580$	−18518.9	−1.32579
$581$	−17981.5	−1.28399
$582$	22518.6	1.60383
$583$	3948.20	0.280477
$584$	18493.7	1.31040
$585$	0	0
$586$	15710.4	1.10749
$587$	17376.7	1.22183	0.610914	−	0.791697i	$-0.290802\pi$
$587$	17376.7	1.22183	0.610914	+	0.791697i	$0.290802\pi$
$588$	−36795.6	−2.58065
$589$	−3908.38	−0.273416
$590$	−8077.09	−0.563608
$591$	−6881.16	−0.478940
$592$	16796.5	1.16610
$593$	−7991.09	−0.553381	−0.276690	−	0.960959i	$-0.589238\pi$
$593$	−7991.09	−0.553381	−0.276690	+	0.960959i	$0.589238\pi$
$594$	2293.68	0.158435
$595$	−9874.06	−0.680331
$596$	53174.7	3.65456
$597$	−2702.94	−0.185300
$598$	0	0
$599$	10386.5	0.708480	0.354240	−	0.935154i	$-0.384740\pi$
$599$	10386.5	0.708480	0.354240	+	0.935154i	$0.384740\pi$
$600$	−15994.1	−1.08826
$601$	−9241.77	−0.627254	−0.313627	−	0.949546i	$-0.601544\pi$
$601$	−9241.77	−0.627254	−0.313627	+	0.949546i	$0.601544\pi$
$602$	18491.2	1.25190
$603$	−7676.27	−0.518411
$604$	31135.4	2.09749
$605$	−6225.04	−0.418320
$606$	−14032.8	−0.940663
$607$	18921.5	1.26524	0.632619	−	0.774463i	$-0.281980\pi$
$607$	18921.5	1.26524	0.632619	+	0.774463i	$0.281980\pi$
$608$	21568.6	1.43869
$609$	15486.5	1.03045
$610$	14265.5	0.946875
$611$	0	0
$612$	−9349.54	−0.617537
$613$	−17138.1	−1.12921	−0.564603	−	0.825363i	$-0.690971\pi$
$613$	−17138.1	−1.12921	−0.564603	+	0.825363i	$0.690971\pi$
$614$	17441.0	1.14635
$615$	964.120	0.0632147
$616$	−29894.0	−1.95530
$617$	−18825.8	−1.22836	−0.614180	−	0.789166i	$-0.710513\pi$
$617$	−18825.8	−1.22836	−0.614180	+	0.789166i	$0.710513\pi$
$618$	−348.592	−0.0226900
$619$	−1392.83	−0.0904404	−0.0452202	−	0.998977i	$-0.514399\pi$
$619$	−1392.83	−0.0904404	−0.0452202	+	0.998977i	$0.514399\pi$
$620$	6617.21	0.428635
$621$	4937.03	0.319028
$622$	−45693.2	−2.94555
$623$	−2089.09	−0.134346
$624$	0	0
$625$	4000.90	0.256057
$626$	−10171.4	−0.649412
$627$	3240.00	0.206369
$628$	−21353.3	−1.35683
$629$	−5959.79	−0.377794
$630$	−8588.75	−0.543149
$631$	−25488.4	−1.60804	−0.804022	−	0.594599i	$-0.797311\pi$
$631$	−25488.4	−1.60804	−0.804022	+	0.594599i	$0.797311\pi$
$632$	−28128.8	−1.77041
$633$	−1293.06	−0.0811918
$634$	10127.1	0.634379
$635$	−10294.9	−0.643371
$636$	−13998.8	−0.872783
$637$	0	0
$638$	14004.4	0.869028
$639$	−1490.57	−0.0922787
$640$	586.735	0.0362387
$641$	−6066.41	−0.373805	−0.186902	−	0.982379i	$-0.559845\pi$
$641$	−6066.41	−0.373805	−0.186902	+	0.982379i	$0.559845\pi$
$642$	−5502.50	−0.338265
$643$	1598.78	0.0980554	0.0490277	−	0.998797i	$-0.484388\pi$
$643$	1598.78	0.0980554	0.0490277	+	0.998797i	$0.484388\pi$
$644$	−110152.	−6.74006
$645$	1982.12	0.121001
$646$	−18699.1	−1.13886
$647$	23067.2	1.40164	0.700822	−	0.713336i	$-0.252817\pi$
$647$	23067.2	1.40164	0.700822	+	0.713336i	$0.252817\pi$
$648$	−4750.61	−0.287996
$649$	4314.07	0.260928
$650$	0	0
$651$	−5533.68	−0.333152
$652$	−4486.26	−0.269472
$653$	−23743.9	−1.42293	−0.711463	−	0.702723i	$-0.751967\pi$
$653$	−23743.9	−1.42293	−0.711463	+	0.702723i	$0.751967\pi$
$654$	−15140.4	−0.905253
$655$	5582.25	0.333002
$656$	−8375.81	−0.498507
$657$	−2837.93	−0.168521
$658$	84015.7	4.97762
$659$	−7497.65	−0.443197	−0.221598	−	0.975138i	$-0.571127\pi$
$659$	−7497.65	−0.443197	−0.221598	+	0.975138i	$0.571127\pi$
$660$	−5485.59	−0.323524
$661$	−1255.26	−0.0738638	−0.0369319	−	0.999318i	$-0.511758\pi$
$661$	−1255.26	−0.0738638	−0.0369319	+	0.999318i	$0.511758\pi$
$662$	38631.5	2.26806
$663$	0	0
$664$	33678.6	1.96835
$665$	−12132.3	−0.707474
$666$	−5184.00	−0.301615
$667$	30143.8	1.74989
$668$	−4143.91	−0.240019
$669$	12312.9	0.711576
$670$	25993.1	1.49881
$671$	−7619.38	−0.438365
$672$	30537.9	1.75301
$673$	1505.97	0.0862569	0.0431284	−	0.999070i	$-0.486268\pi$
$673$	1505.97	0.0862569	0.0431284	+	0.999070i	$0.486268\pi$
$674$	28673.3	1.63866
$675$	2454.35	0.139953
$676$	0	0
$677$	−16201.4	−0.919751	−0.459876	−	0.887983i	$-0.652106\pi$
$677$	−16201.4	−0.919751	−0.459876	+	0.887983i	$0.652106\pi$
$678$	756.140	0.0428310
$679$	45037.2	2.54546
$680$	18493.7	1.04294
$681$	−5427.32	−0.305397
$682$	−5004.08	−0.280962
$683$	29090.4	1.62974	0.814870	−	0.579644i	$-0.196808\pi$
$683$	29090.4	1.62974	0.814870	+	0.579644i	$0.196808\pi$
$684$	−11487.8	−0.642175
$685$	−92.9712	−0.00518576
$686$	−48138.7	−2.67922
$687$	15748.0	0.874561
$688$	−17219.7	−0.954208
$689$	0	0
$690$	−16717.6	−0.922359
$691$	940.952	0.0518025	0.0259012	−	0.999665i	$-0.491754\pi$
$691$	940.952	0.0518025	0.0259012	+	0.999665i	$0.491754\pi$
$692$	−26608.6	−1.46172
$693$	4587.35	0.251456
$694$	−17800.7	−0.973639
$695$	12112.4	0.661077
$696$	−29005.6	−1.57968
$697$	2971.93	0.161506
$698$	65914.5	3.57436
$699$	8426.65	0.455973
$700$	−54760.1	−2.95676
$701$	−30713.9	−1.65485	−0.827424	−	0.561578i	$-0.810195\pi$
$701$	−30713.9	−1.65485	−0.827424	+	0.561578i	$0.810195\pi$
$702$	0	0
$703$	−7322.81	−0.392866
$704$	7797.51	0.417443
$705$	9005.85	0.481106
$706$	−15561.8	−0.829571
$707$	−28065.5	−1.49294
$708$	−15296.1	−0.811951
$709$	25640.5	1.35818	0.679089	−	0.734056i	$-0.262375\pi$
$709$	25640.5	1.35818	0.679089	+	0.734056i	$0.262375\pi$
$710$	5047.32	0.266792
$711$	4316.47	0.227680
$712$	3912.77	0.205951
$713$	−10771.0	−0.565748
$714$	−26475.1	−1.38768
$715$	0	0
$716$	70079.1	3.65779
$717$	−20136.0	−1.04881
$718$	−46669.7	−2.42576
$719$	20842.5	1.08108	0.540538	−	0.841319i	$-0.318221\pi$
$719$	20842.5	1.08108	0.540538	+	0.841319i	$0.318221\pi$
$720$	7998.16	0.413991
$721$	−697.183	−0.0360117
$722$	12821.3	0.660888
$723$	−7557.34	−0.388742
$724$	50440.8	2.58925
$725$	14985.4	0.767649
$726$	−16691.1	−0.853255
$727$	−263.608	−0.0134480	−0.00672398	−	0.999977i	$-0.502140\pi$
$727$	−263.608	−0.0134480	−0.00672398	+	0.999977i	$0.502140\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	9609.69	0.487220
$731$	6109.94	0.309144
$732$	27015.4	1.36410
$733$	21835.5	1.10029	0.550146	−	0.835069i	$-0.314572\pi$
$733$	21835.5	1.10029	0.550146	+	0.835069i	$0.314572\pi$
$734$	24713.2	1.24275
$735$	−11168.8	−0.560500
$736$	59440.6	2.97692
$737$	−13883.2	−0.693888
$738$	2585.07	0.128940
$739$	−19536.4	−0.972476	−0.486238	−	0.873826i	$-0.661631\pi$
$739$	−19536.4	−0.972476	−0.486238	+	0.873826i	$0.661631\pi$
$740$	12398.1	0.615897
$741$	0	0
$742$	−39640.5	−1.96125
$743$	−30353.1	−1.49872	−0.749360	−	0.662163i	$-0.769639\pi$
$743$	−30353.1	−1.49872	−0.749360	+	0.662163i	$0.769639\pi$
$744$	10364.3	0.510719
$745$	16140.5	0.793746
$746$	43338.4	2.12699
$747$	−5168.12	−0.253135
$748$	−16909.5	−0.826567
$749$	−11005.0	−0.536867
$750$	−19739.1	−0.961029
$751$	−3904.20	−0.189702	−0.0948510	−	0.995491i	$-0.530237\pi$
$751$	−3904.20	−0.189702	−0.0948510	+	0.995491i	$0.530237\pi$
$752$	−78238.5	−3.79397
$753$	−2484.00	−0.120215
$754$	0	0
$755$	9450.74	0.455560
$756$	−16265.0	−0.782478
$757$	−2900.52	−0.139262	−0.0696308	−	0.997573i	$-0.522182\pi$
$757$	−2900.52	−0.139262	−0.0696308	+	0.997573i	$0.522182\pi$
$758$	−21335.8	−1.02236
$759$	8929.06	0.427015
$760$	22723.3	1.08455
$761$	−33518.7	−1.59665	−0.798325	−	0.602227i	$-0.794280\pi$
$761$	−33518.7	−1.59665	−0.798325	+	0.602227i	$0.794280\pi$
$762$	−27603.5	−1.31229
$763$	−30280.8	−1.43675
$764$	−65780.0	−3.11497
$765$	−2837.93	−0.134125
$766$	−72812.5	−3.43449
$767$	0	0
$768$	13070.2	0.614102
$769$	−552.769	−0.0259211	−0.0129606	−	0.999916i	$-0.504126\pi$
$769$	−552.769	−0.0259211	−0.0129606	+	0.999916i	$0.504126\pi$
$770$	−15533.5	−0.726999
$771$	17522.3	0.818482
$772$	32673.3	1.52323
$773$	36498.8	1.69828	0.849141	−	0.528166i	$-0.177120\pi$
$773$	36498.8	1.69828	0.849141	+	0.528166i	$0.177120\pi$
$774$	5314.61	0.246809
$775$	−5354.62	−0.248185
$776$	−84352.8	−3.90218
$777$	−10368.0	−0.478700
$778$	14635.4	0.674427
$779$	3651.62	0.167950
$780$	0	0
$781$	−2695.83	−0.123514
$782$	−51532.5	−2.35652
$783$	4451.03	0.203150
$784$	97029.2	4.42006
$785$	−6481.51	−0.294694
$786$	14967.6	0.679231
$787$	4284.79	0.194074	0.0970371	−	0.995281i	$-0.469063\pi$
$787$	4284.79	0.194074	0.0970371	+	0.995281i	$0.469063\pi$
$788$	44126.0	1.99483
$789$	12192.2	0.550131
$790$	−14616.3	−0.658258
$791$	1512.28	0.0679779
$792$	−8591.91	−0.385480
$793$	0	0
$794$	−34216.6	−1.52935
$795$	−4249.16	−0.189562
$796$	17332.8	0.771792
$797$	−29538.5	−1.31281	−0.656405	−	0.754409i	$-0.727924\pi$
$797$	−29538.5	−1.31281	−0.656405	+	0.754409i	$0.727924\pi$
$798$	−32530.0	−1.44305
$799$	27760.8	1.22917
$800$	29549.8	1.30593
$801$	−600.430	−0.0264858
$802$	24690.7	1.08711
$803$	−5132.65	−0.225563
$804$	49224.7	2.15923
$805$	−33435.2	−1.46389
$806$	0	0
$807$	−5536.32	−0.241497
$808$	52565.5	2.28867
$809$	−895.586	−0.0389211	−0.0194605	−	0.999811i	$-0.506195\pi$
$809$	−895.586	−0.0389211	−0.0194605	+	0.999811i	$0.506195\pi$
$810$	−2468.51	−0.107080
$811$	−20139.7	−0.872011	−0.436006	−	0.899944i	$-0.643607\pi$
$811$	−20139.7	−0.872011	−0.436006	+	0.899944i	$0.643607\pi$
$812$	−99308.7	−4.29194
$813$	6320.33	0.272649
$814$	−9375.73	−0.403709
$815$	−1361.75	−0.0585274
$816$	24654.6	1.05770
$817$	7507.31	0.321478
$818$	64268.8	2.74707
$819$	0	0
$820$	−6182.49	−0.263295
$821$	17263.2	0.733848	0.366924	−	0.930251i	$-0.380411\pi$
$821$	17263.2	0.733848	0.366924	+	0.930251i	$0.380411\pi$
$822$	−249.282	−0.0105775
$823$	12114.5	0.513104	0.256552	−	0.966530i	$-0.417413\pi$
$823$	12114.5	0.513104	0.256552	+	0.966530i	$0.417413\pi$
$824$	1305.79	0.0552057
$825$	4438.92	0.187325
$826$	−43313.8	−1.82455
$827$	−31450.9	−1.32243	−0.661217	−	0.750194i	$-0.729960\pi$
$827$	−31450.9	−1.32243	−0.661217	+	0.750194i	$0.729960\pi$
$828$	−31659.1	−1.32878
$829$	13760.4	0.576499	0.288250	−	0.957555i	$-0.406927\pi$
$829$	13760.4	0.576499	0.288250	+	0.957555i	$0.406927\pi$
$830$	17500.1	0.731852
$831$	14345.8	0.598858
$832$	0	0
$833$	−34428.2	−1.43201
$834$	32476.6	1.34841
$835$	−1257.83	−0.0521305
$836$	−20776.8	−0.859545
$837$	−1590.45	−0.0656797
$838$	28703.6	1.18323
$839$	9846.21	0.405160	0.202580	−	0.979266i	$-0.435067\pi$
$839$	9846.21	0.405160	0.202580	+	0.979266i	$0.435067\pi$
$840$	32172.7	1.32150
$841$	2787.47	0.114292
$842$	−65914.2	−2.69781
$843$	−17597.4	−0.718965
$844$	8291.83	0.338171
$845$	0	0
$846$	24147.2	0.981320
$847$	−33382.1	−1.35422
$848$	36914.7	1.49488
$849$	19221.1	0.776991
$850$	−25618.4	−1.03377
$851$	−20180.8	−0.812914
$852$	9558.41	0.384349
$853$	27574.5	1.10684	0.553420	−	0.832903i	$-0.313323\pi$
$853$	27574.5	1.10684	0.553420	+	0.832903i	$0.313323\pi$
$854$	76499.6	3.06530
$855$	−3486.97	−0.139476
$856$	20611.9	0.823013
$857$	−8046.95	−0.320745	−0.160373	−	0.987057i	$-0.551270\pi$
$857$	−8046.95	−0.320745	−0.160373	+	0.987057i	$0.551270\pi$
$858$	0	0
$859$	2898.13	0.115114	0.0575570	−	0.998342i	$-0.481669\pi$
$859$	2898.13	0.115114	0.0575570	+	0.998342i	$0.481669\pi$
$860$	−12710.5	−0.503982
$861$	5170.14	0.204644
$862$	−37530.5	−1.48294
$863$	4961.16	0.195689	0.0978447	−	0.995202i	$-0.468805\pi$
$863$	4961.16	0.195689	0.0978447	+	0.995202i	$0.468805\pi$
$864$	8776.98	0.345601
$865$	−8076.69	−0.317475
$866$	−31641.0	−1.24158
$867$	5991.00	0.234677
$868$	35485.1	1.38761
$869$	7806.72	0.304747
$870$	−15071.9	−0.587340
$871$	0	0
$872$	56714.5	2.20252
$873$	12944.3	0.501829
$874$	−63318.2	−2.45054
$875$	−39478.3	−1.52527
$876$	18198.4	0.701904
$877$	1386.66	0.0533913	0.0266957	−	0.999644i	$-0.491502\pi$
$877$	1386.66	0.0533913	0.0266957	+	0.999644i	$0.491502\pi$
$878$	−61919.3	−2.38004
$879$	9030.71	0.346528
$880$	14465.4	0.554123
$881$	9030.36	0.345335	0.172668	−	0.984980i	$-0.444761\pi$
$881$	9030.36	0.345335	0.172668	+	0.984980i	$0.444761\pi$
$882$	−29946.6	−1.14326
$883$	15512.7	0.591216	0.295608	−	0.955309i	$-0.404478\pi$
$883$	15512.7	0.591216	0.295608	+	0.955309i	$0.404478\pi$
$884$	0	0
$885$	−4642.91	−0.176350
$886$	−55115.0	−2.08987
$887$	7431.21	0.281303	0.140651	−	0.990059i	$-0.455080\pi$
$887$	7431.21	0.281303	0.140651	+	0.990059i	$0.455080\pi$
$888$	19418.8	0.733843
$889$	−55207.0	−2.08277
$890$	2033.15	0.0765747
$891$	1318.46	0.0495737
$892$	−78957.5	−2.96378
$893$	34109.8	1.27821
$894$	43277.0	1.61902
$895$	21271.6	0.794447
$896$	3146.40	0.117315
$897$	0	0
$898$	66070.5	2.45524
$899$	−9710.74	−0.360257
$900$	−15738.7	−0.582916
$901$	−13098.2	−0.484310
$902$	4675.34	0.172585
$903$	10629.2	0.391715
$904$	−2832.44	−0.104210
$905$	15310.6	0.562367
$906$	25340.1	0.929213
$907$	10550.2	0.386234	0.193117	−	0.981176i	$-0.438140\pi$
$907$	10550.2	0.386234	0.193117	+	0.981176i	$0.438140\pi$
$908$	34803.1	1.27201
$909$	−8066.38	−0.294329
$910$	0	0
$911$	35703.3	1.29847	0.649234	−	0.760589i	$-0.275090\pi$
$911$	35703.3	1.29847	0.649234	+	0.760589i	$0.275090\pi$
$912$	30293.2	1.09990
$913$	−9347.01	−0.338818
$914$	8059.38	0.291664
$915$	8200.18	0.296273
$916$	−100985.	−3.64263
$917$	29935.1	1.07802
$918$	−7609.27	−0.273577
$919$	−42896.6	−1.53975	−0.769873	−	0.638197i	$-0.779681\pi$
$919$	−42896.6	−1.53975	−0.769873	+	0.638197i	$0.779681\pi$
$920$	62622.6	2.24414
$921$	10025.5	0.358688
$922$	68874.0	2.46013
$923$	0	0
$924$	−29416.8	−1.04734
$925$	−10032.5	−0.356613
$926$	−85117.5	−3.02066
$927$	−200.379	−0.00709959
$928$	53589.3	1.89564
$929$	10366.7	0.366114	0.183057	−	0.983102i	$-0.441401\pi$
$929$	10366.7	0.366114	0.183057	+	0.983102i	$0.441401\pi$
$930$	5385.52	0.189890
$931$	−42302.0	−1.48914
$932$	−54036.6	−1.89917
$933$	−26265.6	−0.921648
$934$	74426.6	2.60740
$935$	−5132.65	−0.179525
$936$	0	0
$937$	20289.8	0.707405	0.353702	−	0.935358i	$-0.384923\pi$
$937$	20289.8	0.707405	0.353702	+	0.935358i	$0.384923\pi$
$938$	139390.	4.85206
$939$	−5846.79	−0.203198
$940$	−57750.7	−2.00385
$941$	−37089.1	−1.28488	−0.642438	−	0.766337i	$-0.722077\pi$
$941$	−37089.1	−1.28488	−0.642438	+	0.766337i	$0.722077\pi$
$942$	−17378.7	−0.601093
$943$	10063.4	0.347519
$944$	40335.4	1.39068
$945$	−4937.03	−0.169949
$946$	9611.96	0.330351
$947$	−23458.2	−0.804952	−0.402476	−	0.915430i	$-0.631850\pi$
$947$	−23458.2	−0.804952	−0.402476	+	0.915430i	$0.631850\pi$
$948$	−27679.7	−0.948307
$949$	0	0
$950$	−31477.5	−1.07501
$951$	5821.28	0.198494
$952$	99173.4	3.37629
$953$	34695.5	1.17933	0.589663	−	0.807649i	$-0.299260\pi$
$953$	34695.5	1.17933	0.589663	+	0.807649i	$0.299260\pi$
$954$	−11393.2	−0.386654
$955$	−19966.6	−0.676550
$956$	129124.	4.36838
$957$	8050.09	0.271915
$958$	−94001.6	−3.17020
$959$	−498.563	−0.0167878
$960$	−8391.88	−0.282132
$961$	−26321.1	−0.883527
$962$	0	0
$963$	−3162.97	−0.105841
$964$	48462.1	1.61915
$965$	9917.53	0.330836
$966$	−89649.0	−2.98593
$967$	−6289.66	−0.209164	−0.104582	−	0.994516i	$-0.533351\pi$
$967$	−6289.66	−0.209164	−0.104582	+	0.994516i	$0.533351\pi$
$968$	62523.3	2.07601
$969$	−10748.7	−0.356345
$970$	−43831.4	−1.45087
$971$	−20185.9	−0.667145	−0.333573	−	0.942724i	$-0.608254\pi$
$971$	−20185.9	−0.667145	−0.333573	+	0.942724i	$0.608254\pi$
$972$	−4674.77	−0.154263
$973$	64953.2	2.14009
$974$	73291.8	2.41111
$975$	0	0
$976$	−71239.2	−2.33639
$977$	−44244.0	−1.44881	−0.724406	−	0.689373i	$-0.757886\pi$
$977$	−44244.0	−1.44881	−0.724406	+	0.689373i	$0.757886\pi$
$978$	−3651.22	−0.119379
$979$	−1085.93	−0.0354510
$980$	71620.8	2.33453
$981$	−8703.07	−0.283249
$982$	67669.9	2.19901
$983$	−8835.11	−0.286670	−0.143335	−	0.989674i	$-0.545783\pi$
$983$	−8835.11	−0.286670	−0.143335	+	0.989674i	$0.545783\pi$
$984$	−9683.46	−0.313717
$985$	13393.9	0.433263
$986$	−46459.6	−1.50058
$987$	48294.3	1.55747
$988$	0	0
$989$	20689.3	0.665198
$990$	−4464.53	−0.143325
$991$	34915.1	1.11919	0.559594	−	0.828767i	$-0.310957\pi$
$991$	34915.1	1.11919	0.559594	+	0.828767i	$0.310957\pi$
$992$	−19148.6	−0.612872
$993$	22206.4	0.709666
$994$	27066.5	0.863680
$995$	5261.15	0.167628
$996$	33141.0	1.05433
$997$	37962.8	1.20591	0.602956	−	0.797774i	$-0.293989\pi$
$997$	37962.8	1.20591	0.602956	+	0.797774i	$0.293989\pi$
$998$	53314.6	1.69103
$999$	−2979.89	−0.0943740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.j.1.1		4
3.2	odd	2		1521.4.a.x.1.4		4
13.5	odd	4		39.4.b.a.25.4	yes	4
13.8	odd	4		39.4.b.a.25.1	✓	4
13.12	even	2	inner	507.4.a.j.1.4		4
39.5	even	4		117.4.b.d.64.1		4
39.8	even	4		117.4.b.d.64.4		4
39.38	odd	2		1521.4.a.x.1.1		4
52.31	even	4		624.4.c.e.337.2		4
52.47	even	4		624.4.c.e.337.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.b.a.25.1	✓	4	13.8	odd	4
39.4.b.a.25.4	yes	4	13.5	odd	4
117.4.b.d.64.1		4	39.5	even	4
117.4.b.d.64.4		4	39.8	even	4
507.4.a.j.1.1		4	1.1	even	1	trivial
507.4.a.j.1.4		4	13.12	even	2	inner
624.4.c.e.337.2		4	52.31	even	4
624.4.c.e.337.3		4	52.47	even	4
1521.4.a.x.1.1		4	39.38	odd	2
1521.4.a.x.1.4		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q-5.21898 q^{2} -3.00000 q^{3} +19.2377 q^{4} +5.83936 q^{5} +15.6569 q^{6} +31.3139 q^{7} -58.6495 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.21898 q^{2} -3.00000 q^{3} +19.2377 q^{4} +5.83936 q^{5} +15.6569 q^{6} +31.3139 q^{7} -58.6495 q^{8} +9.00000 q^{9} -30.4755 q^{10} +16.2773 q^{11} -57.7132 q^{12} -163.426 q^{14} -17.5181 q^{15} +152.189 q^{16} -54.0000 q^{17} -46.9708 q^{18} -66.3500 q^{19} +112.336 q^{20} -93.9416 q^{21} -84.9510 q^{22} -182.853 q^{23} +175.949 q^{24} -90.9019 q^{25} -27.0000 q^{27} +602.408 q^{28} -164.853 q^{29} +91.4264 q^{30} +58.9055 q^{31} -325.073 q^{32} -48.8319 q^{33} +281.825 q^{34} +182.853 q^{35} +173.140 q^{36} +110.366 q^{37} +346.279 q^{38} -342.475 q^{40} -55.0357 q^{41} +490.279 q^{42} -113.147 q^{43} +313.139 q^{44} +52.5542 q^{45} +954.305 q^{46} -514.089 q^{47} -456.566 q^{48} +637.559 q^{49} +474.415 q^{50} +162.000 q^{51} +242.559 q^{53} +140.912 q^{54} +95.0490 q^{55} -1836.54 q^{56} +199.050 q^{57} +860.364 q^{58} +265.036 q^{59} -337.008 q^{60} -468.098 q^{61} -307.426 q^{62} +281.825 q^{63} +479.042 q^{64} +254.853 q^{66} -852.919 q^{67} -1038.84 q^{68} +548.559 q^{69} -954.305 q^{70} -165.619 q^{71} -527.846 q^{72} -315.325 q^{73} -576.000 q^{74} +272.706 q^{75} -1276.42 q^{76} +509.706 q^{77} +479.608 q^{79} +888.684 q^{80} +81.0000 q^{81} +287.230 q^{82} -574.235 q^{83} -1807.22 q^{84} -315.325 q^{85} +590.512 q^{86} +494.559 q^{87} -954.657 q^{88} -66.7144 q^{89} -274.279 q^{90} -3517.68 q^{92} -176.716 q^{93} +2683.02 q^{94} -387.441 q^{95} +975.220 q^{96} +1438.25 q^{97} -3327.40 q^{98} +146.496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{3} + 26 q^{4} + 36 q^{9}+O(q^{10}) \) 4 * q - 12 * q^3 + 26 * q^4 + 36 * q^9	\( 4 q - 12 q^{3} + 26 q^{4} + 36 q^{9} - 20 q^{10} - 78 q^{12} - 348 q^{14} + 354 q^{16} - 216 q^{17} - 136 q^{22} - 120 q^{23} + 44 q^{25} - 108 q^{27} - 48 q^{29} + 60 q^{30} + 120 q^{35} + 234 q^{36} + 468 q^{38} - 1268 q^{40} + 1044 q^{42} - 1064 q^{43} - 1062 q^{48} + 716 q^{49} + 648 q^{51} - 864 q^{53} + 584 q^{55} - 3372 q^{56} - 2280 q^{61} - 924 q^{62} + 1050 q^{64} + 408 q^{66} - 1404 q^{68} + 360 q^{69} - 2304 q^{74} - 132 q^{75} + 816 q^{77} + 288 q^{79} + 324 q^{81} + 28 q^{82} + 144 q^{87} - 2392 q^{88} - 180 q^{90} - 8568 q^{92} + 6656 q^{94} - 3384 q^{95}+O(q^{100}) \) 4 * q - 12 * q^3 + 26 * q^4 + 36 * q^9 - 20 * q^10 - 78 * q^12 - 348 * q^14 + 354 * q^16 - 216 * q^17 - 136 * q^22 - 120 * q^23 + 44 * q^25 - 108 * q^27 - 48 * q^29 + 60 * q^30 + 120 * q^35 + 234 * q^36 + 468 * q^38 - 1268 * q^40 + 1044 * q^42 - 1064 * q^43 - 1062 * q^48 + 716 * q^49 + 648 * q^51 - 864 * q^53 + 584 * q^55 - 3372 * q^56 - 2280 * q^61 - 924 * q^62 + 1050 * q^64 + 408 * q^66 - 1404 * q^68 + 360 * q^69 - 2304 * q^74 - 132 * q^75 + 816 * q^77 + 288 * q^79 + 324 * q^81 + 28 * q^82 + 144 * q^87 - 2392 * q^88 - 180 * q^90 - 8568 * q^92 + 6656 * q^94 - 3384 * q^95

Introduction

L-functions

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