LMFDB - Embedded newform 6026.2.a.i.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.76687 q^{3} +1.00000 q^{4} -0.379310 q^{5} -1.76687 q^{6} -0.00141487 q^{7} -1.00000 q^{8} +0.121841 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.76687 q^{3} +1.00000 q^{4} -0.379310 q^{5} -1.76687 q^{6} -0.00141487 q^{7} -1.00000 q^{8} +0.121841 q^{9} +0.379310 q^{10} -1.92533 q^{11} +1.76687 q^{12} -0.508617 q^{13} +0.00141487 q^{14} -0.670192 q^{15} +1.00000 q^{16} -3.60561 q^{17} -0.121841 q^{18} +5.47957 q^{19} -0.379310 q^{20} -0.00249990 q^{21} +1.92533 q^{22} +1.00000 q^{23} -1.76687 q^{24} -4.85612 q^{25} +0.508617 q^{26} -5.08534 q^{27} -0.00141487 q^{28} +1.18532 q^{29} +0.670192 q^{30} +7.55554 q^{31} -1.00000 q^{32} -3.40181 q^{33} +3.60561 q^{34} +0.000536675 q^{35} +0.121841 q^{36} -0.946095 q^{37} -5.47957 q^{38} -0.898661 q^{39} +0.379310 q^{40} +7.34729 q^{41} +0.00249990 q^{42} -2.24582 q^{43} -1.92533 q^{44} -0.0462156 q^{45} -1.00000 q^{46} +0.668739 q^{47} +1.76687 q^{48} -7.00000 q^{49} +4.85612 q^{50} -6.37065 q^{51} -0.508617 q^{52} +0.305012 q^{53} +5.08534 q^{54} +0.730296 q^{55} +0.00141487 q^{56} +9.68170 q^{57} -1.18532 q^{58} +8.06109 q^{59} -0.670192 q^{60} -12.9193 q^{61} -7.55554 q^{62} -0.000172390 q^{63} +1.00000 q^{64} +0.192923 q^{65} +3.40181 q^{66} +4.52748 q^{67} -3.60561 q^{68} +1.76687 q^{69} -0.000536675 q^{70} -2.54728 q^{71} -0.121841 q^{72} -10.5179 q^{73} +0.946095 q^{74} -8.58016 q^{75} +5.47957 q^{76} +0.00272410 q^{77} +0.898661 q^{78} -14.5022 q^{79} -0.379310 q^{80} -9.35068 q^{81} -7.34729 q^{82} +9.23516 q^{83} -0.00249990 q^{84} +1.36764 q^{85} +2.24582 q^{86} +2.09432 q^{87} +1.92533 q^{88} -5.09908 q^{89} +0.0462156 q^{90} +0.000719627 q^{91} +1.00000 q^{92} +13.3497 q^{93} -0.668739 q^{94} -2.07845 q^{95} -1.76687 q^{96} -18.6859 q^{97} +7.00000 q^{98} -0.234585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.76687	1.02010	0.510052	−	0.860143i	$-0.329626\pi$
$3$	1.76687	1.02010	0.510052	+	0.860143i	$0.329626\pi$
$4$	1.00000	0.500000
$5$	−0.379310	−0.169632	−0.0848162	−	0.996397i	$-0.527030\pi$
$5$	−0.379310	−0.169632	−0.0848162	+	0.996397i	$0.527030\pi$
$6$	−1.76687	−0.721323
$7$	−0.00141487	−0.000534771 0	−0.000267386	−	1.00000i	$-0.500085\pi$
$7$	−0.00141487	−0.000534771 0	−0.000267386		1.00000i	$0.500085\pi$
$8$	−1.00000	−0.353553
$9$	0.121841	0.0406138
$10$	0.379310	0.119948
$11$	−1.92533	−0.580509	−0.290254	−	0.956950i	$-0.593740\pi$
$11$	−1.92533	−0.580509	−0.290254	+	0.956950i	$0.593740\pi$
$12$	1.76687	0.510052
$13$	−0.508617	−0.141065	−0.0705324	−	0.997509i	$-0.522470\pi$
$13$	−0.508617	−0.141065	−0.0705324	+	0.997509i	$0.522470\pi$
$14$	0.00141487	0.000378141 0
$15$	−0.670192	−0.173043
$16$	1.00000	0.250000
$17$	−3.60561	−0.874488	−0.437244	−	0.899343i	$-0.644045\pi$
$17$	−3.60561	−0.874488	−0.437244	+	0.899343i	$0.644045\pi$
$18$	−0.121841	−0.0287183
$19$	5.47957	1.25710	0.628549	−	0.777770i	$-0.283649\pi$
$19$	5.47957	1.25710	0.628549	+	0.777770i	$0.283649\pi$
$20$	−0.379310	−0.0848162
$21$	−0.00249990	−0.000545523 0
$22$	1.92533	0.410482
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.76687	−0.360662
$25$	−4.85612	−0.971225
$26$	0.508617	0.0997479
$27$	−5.08534	−0.978674
$28$	−0.00141487	−0.000267386 0
$29$	1.18532	0.220109	0.110055	−	0.993926i	$-0.464897\pi$
$29$	1.18532	0.220109	0.110055	+	0.993926i	$0.464897\pi$
$30$	0.670192	0.122360
$31$	7.55554	1.35702	0.678508	−	0.734593i	$-0.262627\pi$
$31$	7.55554	1.35702	0.678508	+	0.734593i	$0.262627\pi$
$32$	−1.00000	−0.176777
$33$	−3.40181	−0.592180
$34$	3.60561	0.618356
$35$	0.000536675 0	9.07146e−5 0
$36$	0.121841	0.0203069
$37$	−0.946095	−0.155537	−0.0777685	−	0.996971i	$-0.524780\pi$
$37$	−0.946095	−0.155537	−0.0777685	+	0.996971i	$0.524780\pi$
$38$	−5.47957	−0.888903
$39$	−0.898661	−0.143901
$40$	0.379310	0.0599741
$41$	7.34729	1.14745	0.573727	−	0.819047i	$-0.305497\pi$
$41$	7.34729	1.14745	0.573727	+	0.819047i	$0.305497\pi$
$42$	0.00249990	0.000385743 0
$43$	−2.24582	−0.342485	−0.171242	−	0.985229i	$-0.554778\pi$
$43$	−2.24582	−0.342485	−0.171242	+	0.985229i	$0.554778\pi$
$44$	−1.92533	−0.290254
$45$	−0.0462156	−0.00688942
$46$	−1.00000	−0.147442
$47$	0.668739	0.0975457	0.0487728	−	0.998810i	$-0.484469\pi$
$47$	0.668739	0.0975457	0.0487728	+	0.998810i	$0.484469\pi$
$48$	1.76687	0.255026
$49$	−7.00000	−1.00000
$50$	4.85612	0.686760
$51$	−6.37065	−0.892069
$52$	−0.508617	−0.0705324
$53$	0.305012	0.0418967	0.0209483	−	0.999781i	$-0.493331\pi$
$53$	0.305012	0.0418967	0.0209483	+	0.999781i	$0.493331\pi$
$54$	5.08534	0.692027
$55$	0.730296	0.0984731
$56$	0.00141487	0.000189070 0
$57$	9.68170	1.28237
$58$	−1.18532	−0.155641
$59$	8.06109	1.04946	0.524732	−	0.851267i	$-0.324165\pi$
$59$	8.06109	1.04946	0.524732	+	0.851267i	$0.324165\pi$
$60$	−0.670192	−0.0865214
$61$	−12.9193	−1.65415	−0.827076	−	0.562091i	$-0.809997\pi$
$61$	−12.9193	−1.65415	−0.827076	+	0.562091i	$0.809997\pi$
$62$	−7.55554	−0.959555
$63$	−0.000172390 0	−2.17191e−5 0
$64$	1.00000	0.125000
$65$	0.192923	0.0239292
$66$	3.40181	0.418734
$67$	4.52748	0.553120	0.276560	−	0.960997i	$-0.410806\pi$
$67$	4.52748	0.553120	0.276560	+	0.960997i	$0.410806\pi$
$68$	−3.60561	−0.437244
$69$	1.76687	0.212707
$70$	−0.000536675 0	−6.41449e−5 0
$71$	−2.54728	−0.302306	−0.151153	−	0.988510i	$-0.548299\pi$
$71$	−2.54728	−0.302306	−0.151153	+	0.988510i	$0.548299\pi$
$72$	−0.121841	−0.0143591
$73$	−10.5179	−1.23103	−0.615513	−	0.788127i	$-0.711051\pi$
$73$	−10.5179	−1.23103	−0.615513	+	0.788127i	$0.711051\pi$
$74$	0.946095	0.109981
$75$	−8.58016	−0.990751
$76$	5.47957	0.628549
$77$	0.00272410	0.000310439 0
$78$	0.898661	0.101753
$79$	−14.5022	−1.63163	−0.815813	−	0.578316i	$-0.803710\pi$
$79$	−14.5022	−1.63163	−0.815813	+	0.578316i	$0.803710\pi$
$80$	−0.379310	−0.0424081
$81$	−9.35068	−1.03896
$82$	−7.34729	−0.811372
$83$	9.23516	1.01369	0.506845	−	0.862037i	$-0.330811\pi$
$83$	9.23516	1.01369	0.506845	+	0.862037i	$0.330811\pi$
$84$	−0.00249990	−0.000272761 0
$85$	1.36764	0.148342
$86$	2.24582	0.242173
$87$	2.09432	0.224535
$88$	1.92533	0.205241
$89$	−5.09908	−0.540501	−0.270251	−	0.962790i	$-0.587107\pi$
$89$	−5.09908	−0.540501	−0.270251	+	0.962790i	$0.587107\pi$
$90$	0.0462156	0.00487155
$91$	0.000719627 0	7.54374e−5 0
$92$	1.00000	0.104257
$93$	13.3497	1.38430
$94$	−0.668739	−0.0689752
$95$	−2.07845	−0.213245
$96$	−1.76687	−0.180331
$97$	−18.6859	−1.89726	−0.948632	−	0.316381i	$-0.897532\pi$
$97$	−18.6859	−1.89726	−0.948632	+	0.316381i	$0.897532\pi$
$98$	7.00000	0.707107
$99$	−0.234585	−0.0235767
$100$	−4.85612	−0.485612
$101$	−13.3930	−1.33265	−0.666325	−	0.745661i	$-0.732134\pi$
$101$	−13.3930	−1.33265	−0.666325	+	0.745661i	$0.732134\pi$
$102$	6.37065	0.630788
$103$	−3.83841	−0.378210	−0.189105	−	0.981957i	$-0.560559\pi$
$103$	−3.83841	−0.378210	−0.189105	+	0.981957i	$0.560559\pi$
$104$	0.508617	0.0498740
$105$	0.000948236 0	9.25384e−5 0
$106$	−0.305012	−0.0296254
$107$	18.1475	1.75438	0.877192	−	0.480139i	$-0.159414\pi$
$107$	18.1475	1.75438	0.877192	+	0.480139i	$0.159414\pi$
$108$	−5.08534	−0.489337
$109$	11.3384	1.08602	0.543009	−	0.839727i	$-0.317285\pi$
$109$	11.3384	1.08602	0.543009	+	0.839727i	$0.317285\pi$
$110$	−0.730296	−0.0696310
$111$	−1.67163	−0.158664
$112$	−0.00141487	−0.000133693 0
$113$	10.4493	0.982985	0.491492	−	0.870882i	$-0.336452\pi$
$113$	10.4493	0.982985	0.491492	+	0.870882i	$0.336452\pi$
$114$	−9.68170	−0.906774
$115$	−0.379310	−0.0353708
$116$	1.18532	0.110055
$117$	−0.0619706	−0.00572918
$118$	−8.06109	−0.742083
$119$	0.00510147	0.000467651 0
$120$	0.670192	0.0611799
$121$	−7.29311	−0.663010
$122$	12.9193	1.16966
$123$	12.9817	1.17052
$124$	7.55554	0.678508
$125$	3.73852	0.334384
$126$	0.000172390 0	1.53577e−5 0
$127$	−21.7549	−1.93043	−0.965216	−	0.261453i	$-0.915798\pi$
$127$	−21.7549	−1.93043	−0.965216	+	0.261453i	$0.915798\pi$
$128$	−1.00000	−0.0883883
$129$	−3.96809	−0.349371
$130$	−0.192923	−0.0169205
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−3.40181	−0.296090
$133$	−0.00775289	−0.000672260 0
$134$	−4.52748	−0.391115
$135$	1.92892	0.166015
$136$	3.60561	0.309178
$137$	−8.79911	−0.751758	−0.375879	−	0.926669i	$-0.622659\pi$
$137$	−8.79911	−0.751758	−0.375879	+	0.926669i	$0.622659\pi$
$138$	−1.76687	−0.150406
$139$	−11.3192	−0.960084	−0.480042	−	0.877246i	$-0.659379\pi$
$139$	−11.3192	−0.960084	−0.480042	+	0.877246i	$0.659379\pi$
$140$	0.000536675 0	4.53573e−5 0
$141$	1.18158	0.0995068
$142$	2.54728	0.213763
$143$	0.979254	0.0818894
$144$	0.121841	0.0101534
$145$	−0.449605	−0.0373377
$146$	10.5179	0.870467
$147$	−12.3681	−1.02010
$148$	−0.946095	−0.0777685
$149$	−14.8851	−1.21943	−0.609716	−	0.792620i	$-0.708716\pi$
$149$	−14.8851	−1.21943	−0.609716	+	0.792620i	$0.708716\pi$
$150$	8.58016	0.700567
$151$	−12.3707	−1.00671	−0.503357	−	0.864079i	$-0.667902\pi$
$151$	−12.3707	−1.00671	−0.503357	+	0.864079i	$0.667902\pi$
$152$	−5.47957	−0.444451
$153$	−0.439312	−0.0355163
$154$	−0.00272410	−0.000219514 0
$155$	−2.86589	−0.230194
$156$	−0.898661	−0.0719505
$157$	−13.5907	−1.08466	−0.542330	−	0.840166i	$-0.682458\pi$
$157$	−13.5907	−1.08466	−0.542330	+	0.840166i	$0.682458\pi$
$158$	14.5022	1.15373
$159$	0.538918	0.0427390
$160$	0.379310	0.0299871
$161$	−0.00141487	−0.000111508 0
$162$	9.35068	0.734659
$163$	−11.3765	−0.891080	−0.445540	−	0.895262i	$-0.646988\pi$
$163$	−11.3765	−0.891080	−0.445540	+	0.895262i	$0.646988\pi$
$164$	7.34729	0.573727
$165$	1.29034	0.100453
$166$	−9.23516	−0.716788
$167$	1.61910	0.125290	0.0626450	−	0.998036i	$-0.480046\pi$
$167$	1.61910	0.125290	0.0626450	+	0.998036i	$0.480046\pi$
$168$	0.00249990	0.000192871 0
$169$	−12.7413	−0.980101
$170$	−1.36764	−0.104893
$171$	0.667638	0.0510556
$172$	−2.24582	−0.171242
$173$	−9.21369	−0.700504	−0.350252	−	0.936656i	$-0.613904\pi$
$173$	−9.21369	−0.700504	−0.350252	+	0.936656i	$0.613904\pi$
$174$	−2.09432	−0.158770
$175$	0.00687080	0.000519383 0
$176$	−1.92533	−0.145127
$177$	14.2429	1.07056
$178$	5.09908	0.382192
$179$	−7.06964	−0.528410	−0.264205	−	0.964467i	$-0.585110\pi$
$179$	−7.06964	−0.528410	−0.264205	+	0.964467i	$0.585110\pi$
$180$	−0.0462156	−0.00344471
$181$	−7.90374	−0.587481	−0.293740	−	0.955885i	$-0.594900\pi$
$181$	−7.90374	−0.587481	−0.293740	+	0.955885i	$0.594900\pi$
$182$	−0.000719627 0	−5.33423e−5 0
$183$	−22.8268	−1.68741
$184$	−1.00000	−0.0737210
$185$	0.358863	0.0263841
$186$	−13.3497	−0.978847
$187$	6.94198	0.507648
$188$	0.668739	0.0487728
$189$	0.00719511	0.000523367 0
$190$	2.07845	0.150787
$191$	−14.0450	−1.01626	−0.508130	−	0.861280i	$-0.669663\pi$
$191$	−14.0450	−1.01626	−0.508130	+	0.861280i	$0.669663\pi$
$192$	1.76687	0.127513
$193$	9.71943	0.699620	0.349810	−	0.936821i	$-0.386246\pi$
$193$	9.71943	0.699620	0.349810	+	0.936821i	$0.386246\pi$
$194$	18.6859	1.34157
$195$	0.340871	0.0244103
$196$	−7.00000	−0.500000
$197$	16.7363	1.19241	0.596206	−	0.802832i	$-0.296674\pi$
$197$	16.7363	1.19241	0.596206	+	0.802832i	$0.296674\pi$
$198$	0.234585	0.0166712
$199$	−4.41855	−0.313223	−0.156611	−	0.987660i	$-0.550057\pi$
$199$	−4.41855	−0.313223	−0.156611	+	0.987660i	$0.550057\pi$
$200$	4.85612	0.343380
$201$	7.99948	0.564240
$202$	13.3930	0.942326
$203$	−0.00167708	−0.000117708 0
$204$	−6.37065	−0.446035
$205$	−2.78690	−0.194645
$206$	3.83841	0.267435
$207$	0.121841	0.00846856
$208$	−0.508617	−0.0352662
$209$	−10.5500	−0.729757
$210$	−0.000948236 0	−6.54345e−5 0
$211$	10.2292	0.704209	0.352105	−	0.935961i	$-0.385466\pi$
$211$	10.2292	0.704209	0.352105	+	0.935961i	$0.385466\pi$
$212$	0.305012	0.0209483
$213$	−4.50072	−0.308384
$214$	−18.1475	−1.24054
$215$	0.851863	0.0580966
$216$	5.08534	0.346014
$217$	−0.0106901	−0.000725693 0
$218$	−11.3384	−0.767931
$219$	−18.5838	−1.25578
$220$	0.730296	0.0492366
$221$	1.83387	0.123360
$222$	1.67163	0.112192
$223$	27.9242	1.86995	0.934973	−	0.354720i	$-0.115424\pi$
$223$	27.9242	1.86995	0.934973	+	0.354720i	$0.115424\pi$
$224$	0.00141487	9.45351e−5 0
$225$	−0.591677	−0.0394451
$226$	−10.4493	−0.695075
$227$	11.2019	0.743497	0.371749	−	0.928333i	$-0.378758\pi$
$227$	11.2019	0.743497	0.371749	+	0.928333i	$0.378758\pi$
$228$	9.68170	0.641186
$229$	12.6638	0.836850	0.418425	−	0.908251i	$-0.362582\pi$
$229$	12.6638	0.836850	0.418425	+	0.908251i	$0.362582\pi$
$230$	0.379310	0.0250109
$231$	0.00481313	0.000316681 0
$232$	−1.18532	−0.0778204
$233$	−22.5854	−1.47962	−0.739810	−	0.672816i	$-0.765085\pi$
$233$	−22.5854	−1.47962	−0.739810	+	0.672816i	$0.765085\pi$
$234$	0.0619706	0.00405114
$235$	−0.253659	−0.0165469
$236$	8.06109	0.524732
$237$	−25.6236	−1.66443
$238$	−0.00510147	−0.000330679 0
$239$	1.23332	0.0797771	0.0398885	−	0.999204i	$-0.487300\pi$
$239$	1.23332	0.0797771	0.0398885	+	0.999204i	$0.487300\pi$
$240$	−0.670192	−0.0432607
$241$	−9.02566	−0.581394	−0.290697	−	0.956815i	$-0.593887\pi$
$241$	−9.02566	−0.581394	−0.290697	+	0.956815i	$0.593887\pi$
$242$	7.29311	0.468819
$243$	−1.26544	−0.0811780
$244$	−12.9193	−0.827076
$245$	2.65517	0.169632
$246$	−12.9817	−0.827685
$247$	−2.78700	−0.177332
$248$	−7.55554	−0.479778
$249$	16.3174	1.03407
$250$	−3.73852	−0.236445
$251$	6.91948	0.436754	0.218377	−	0.975865i	$-0.429924\pi$
$251$	6.91948	0.436754	0.218377	+	0.975865i	$0.429924\pi$
$252$	−0.000172390 0	−1.08595e−5 0
$253$	−1.92533	−0.121044
$254$	21.7549	1.36502
$255$	2.41645	0.151324
$256$	1.00000	0.0625000
$257$	−15.9208	−0.993110	−0.496555	−	0.868005i	$-0.665402\pi$
$257$	−15.9208	−0.993110	−0.496555	+	0.868005i	$0.665402\pi$
$258$	3.96809	0.247042
$259$	0.00133860	8.31768e−5 0
$260$	0.192923	0.0119646
$261$	0.144422	0.00893947
$262$	−1.00000	−0.0617802
$263$	18.2098	1.12286	0.561432	−	0.827523i	$-0.310251\pi$
$263$	18.2098	1.12286	0.561432	+	0.827523i	$0.310251\pi$
$264$	3.40181	0.209367
$265$	−0.115694	−0.00710704
$266$	0.00775289	0.000475360 0
$267$	−9.00942	−0.551368
$268$	4.52748	0.276560
$269$	−10.1764	−0.620466	−0.310233	−	0.950661i	$-0.600407\pi$
$269$	−10.1764	−0.620466	−0.310233	+	0.950661i	$0.600407\pi$
$270$	−1.92892	−0.117390
$271$	11.2418	0.682888	0.341444	−	0.939902i	$-0.389084\pi$
$271$	11.2418	0.682888	0.341444	+	0.939902i	$0.389084\pi$
$272$	−3.60561	−0.218622
$273$	0.00127149	7.69541e−5 0
$274$	8.79911	0.531573
$275$	9.34964	0.563804
$276$	1.76687	0.106353
$277$	−14.6965	−0.883026	−0.441513	−	0.897255i	$-0.645558\pi$
$277$	−14.6965	−0.883026	−0.441513	+	0.897255i	$0.645558\pi$
$278$	11.3192	0.678882
$279$	0.920578	0.0551136
$280$	−0.000536675 0	−3.20725e−5 0
$281$	−13.5224	−0.806678	−0.403339	−	0.915051i	$-0.632150\pi$
$281$	−13.5224	−0.806678	−0.403339	+	0.915051i	$0.632150\pi$
$282$	−1.18158	−0.0703619
$283$	8.72783	0.518816	0.259408	−	0.965768i	$-0.416473\pi$
$283$	8.72783	0.518816	0.259408	+	0.965768i	$0.416473\pi$
$284$	−2.54728	−0.151153
$285$	−3.67236	−0.217532
$286$	−0.979254	−0.0579045
$287$	−0.0103955	−0.000613625 0
$288$	−0.121841	−0.00717957
$289$	−3.99960	−0.235271
$290$	0.449605	0.0264017
$291$	−33.0156	−1.93541
$292$	−10.5179	−0.615513
$293$	4.12146	0.240778	0.120389	−	0.992727i	$-0.461586\pi$
$293$	4.12146	0.240778	0.120389	+	0.992727i	$0.461586\pi$
$294$	12.3681	0.721323
$295$	−3.05765	−0.178023
$296$	0.946095	0.0549906
$297$	9.79096	0.568129
$298$	14.8851	0.862268
$299$	−0.508617	−0.0294141
$300$	−8.58016	−0.495376
$301$	0.00317755	0.000183151 0
$302$	12.3707	0.711854
$303$	−23.6637	−1.35944
$304$	5.47957	0.314275
$305$	4.90043	0.280598
$306$	0.439312	0.0251138
$307$	−17.2682	−0.985549	−0.492774	−	0.870157i	$-0.664017\pi$
$307$	−17.2682	−0.985549	−0.492774	+	0.870157i	$0.664017\pi$
$308$	0.00272410	0.000155220 0
$309$	−6.78199	−0.385814
$310$	2.86589	0.162772
$311$	−1.05410	−0.0597726	−0.0298863	−	0.999553i	$-0.509515\pi$
$311$	−1.05410	−0.0597726	−0.0298863	+	0.999553i	$0.509515\pi$
$312$	0.898661	0.0508767
$313$	0.128938	0.00728802	0.00364401	−	0.999993i	$-0.498840\pi$
$313$	0.128938	0.00728802	0.00364401	+	0.999993i	$0.498840\pi$
$314$	13.5907	0.766970
$315$	6.53892e−5 0	3.68426e−6 0
$316$	−14.5022	−0.815813
$317$	−14.2027	−0.797701	−0.398850	−	0.917016i	$-0.630591\pi$
$317$	−14.2027	−0.797701	−0.398850	+	0.917016i	$0.630591\pi$
$318$	−0.538918	−0.0302210
$319$	−2.28214	−0.127775
$320$	−0.379310	−0.0212041
$321$	32.0643	1.78966
$322$	0.00141487	7.88477e−5 0
$323$	−19.7572	−1.09932
$324$	−9.35068	−0.519482
$325$	2.46991	0.137006
$326$	11.3765	0.630089
$327$	20.0335	1.10785
$328$	−7.34729	−0.405686
$329$	−0.000946181 0	−5.21646e−5 0
$330$	−1.29034	−0.0710309
$331$	−8.05620	−0.442809	−0.221404	−	0.975182i	$-0.571064\pi$
$331$	−8.05620	−0.442809	−0.221404	+	0.975182i	$0.571064\pi$
$332$	9.23516	0.506845
$333$	−0.115274	−0.00631695
$334$	−1.61910	−0.0885934
$335$	−1.71732	−0.0938271
$336$	−0.00249990	−0.000136381 0
$337$	9.93115	0.540984	0.270492	−	0.962722i	$-0.412814\pi$
$337$	9.93115	0.540984	0.270492	+	0.962722i	$0.412814\pi$
$338$	12.7413	0.693036
$339$	18.4625	1.00275
$340$	1.36764	0.0741708
$341$	−14.5469	−0.787759
$342$	−0.667638	−0.0361017
$343$	0.0198082	0.00106954
$344$	2.24582	0.121087
$345$	−0.670192	−0.0360819
$346$	9.21369	0.495331
$347$	2.13350	0.114532	0.0572662	−	0.998359i	$-0.481762\pi$
$347$	2.13350	0.114532	0.0572662	+	0.998359i	$0.481762\pi$
$348$	2.09432	0.112267
$349$	−34.2009	−1.83073	−0.915367	−	0.402621i	$-0.868099\pi$
$349$	−34.2009	−1.83073	−0.915367	+	0.402621i	$0.868099\pi$
$350$	−0.00687080	−0.000367259 0
$351$	2.58649	0.138057
$352$	1.92533	0.102620
$353$	21.9828	1.17002	0.585012	−	0.811025i	$-0.301090\pi$
$353$	21.9828	1.17002	0.585012	+	0.811025i	$0.301090\pi$
$354$	−14.2429	−0.757003
$355$	0.966208	0.0512810
$356$	−5.09908	−0.270251
$357$	0.00901365	0.000477053 0
$358$	7.06964	0.373642
$359$	−16.8272	−0.888104	−0.444052	−	0.896001i	$-0.646460\pi$
$359$	−16.8272	−0.888104	−0.444052	+	0.896001i	$0.646460\pi$
$360$	0.0462156	0.00243578
$361$	11.0256	0.580297
$362$	7.90374	0.415412
$363$	−12.8860	−0.676339
$364$	0.000719627 0	3.77187e−5 0
$365$	3.98954	0.208822
$366$	22.8268	1.19318
$367$	29.5616	1.54310	0.771552	−	0.636166i	$-0.219481\pi$
$367$	29.5616	1.54310	0.771552	+	0.636166i	$0.219481\pi$
$368$	1.00000	0.0521286
$369$	0.895204	0.0466024
$370$	−0.358863	−0.0186564
$371$	−0.000431554 0	−2.24051e−5 0
$372$	13.3497	0.692149
$373$	21.1401	1.09459	0.547296	−	0.836939i	$-0.315657\pi$
$373$	21.1401	1.09459	0.547296	+	0.836939i	$0.315657\pi$
$374$	−6.94198	−0.358961
$375$	6.60550	0.341106
$376$	−0.668739	−0.0344876
$377$	−0.602876	−0.0310497
$378$	−0.00719511	−0.000370076 0
$379$	−15.6054	−0.801594	−0.400797	−	0.916167i	$-0.631267\pi$
$379$	−15.6054	−0.801594	−0.400797	+	0.916167i	$0.631267\pi$
$380$	−2.07845	−0.106622
$381$	−38.4381	−1.96924
$382$	14.0450	0.718605
$383$	20.3815	1.04145	0.520724	−	0.853725i	$-0.325662\pi$
$383$	20.3815	1.04145	0.520724	+	0.853725i	$0.325662\pi$
$384$	−1.76687	−0.0901654
$385$	−0.00103328	−5.26606e−5 0
$386$	−9.71943	−0.494706
$387$	−0.273634	−0.0139096
$388$	−18.6859	−0.948632
$389$	−8.97921	−0.455264	−0.227632	−	0.973747i	$-0.573098\pi$
$389$	−8.97921	−0.455264	−0.227632	+	0.973747i	$0.573098\pi$
$390$	−0.340871	−0.0172607
$391$	−3.60561	−0.182343
$392$	7.00000	0.353553
$393$	1.76687	0.0891270
$394$	−16.7363	−0.843162
$395$	5.50083	0.276777
$396$	−0.234585	−0.0117883
$397$	35.5793	1.78567	0.892836	−	0.450381i	$-0.148712\pi$
$397$	35.5793	1.78567	0.892836	+	0.450381i	$0.148712\pi$
$398$	4.41855	0.221482
$399$	−0.0136984	−0.000685776 0
$400$	−4.85612	−0.242806
$401$	18.2529	0.911508	0.455754	−	0.890106i	$-0.349370\pi$
$401$	18.2529	0.911508	0.455754	+	0.890106i	$0.349370\pi$
$402$	−7.99948	−0.398978
$403$	−3.84287	−0.191427
$404$	−13.3930	−0.666325
$405$	3.54680	0.176242
$406$	0.00167708	8.32322e−5 0
$407$	1.82154	0.0902906
$408$	6.37065	0.315394
$409$	−10.8381	−0.535907	−0.267954	−	0.963432i	$-0.586347\pi$
$409$	−10.8381	−0.535907	−0.267954	+	0.963432i	$0.586347\pi$
$410$	2.78690	0.137635
$411$	−15.5469	−0.766872
$412$	−3.83841	−0.189105
$413$	−0.0114054	−0.000561223 0
$414$	−0.121841	−0.00598818
$415$	−3.50299	−0.171955
$416$	0.508617	0.0249370
$417$	−19.9996	−0.979386
$418$	10.5500	0.516016
$419$	2.87582	0.140493	0.0702465	−	0.997530i	$-0.477621\pi$
$419$	2.87582	0.140493	0.0702465	+	0.997530i	$0.477621\pi$
$420$	0.000948236 0	4.62692e−5 0
$421$	−7.16331	−0.349118	−0.174559	−	0.984647i	$-0.555850\pi$
$421$	−7.16331	−0.349118	−0.174559	+	0.984647i	$0.555850\pi$
$422$	−10.2292	−0.497951
$423$	0.0814801	0.00396170
$424$	−0.305012	−0.0148127
$425$	17.5093	0.849324
$426$	4.50072	0.218061
$427$	0.0182792	0.000884593 0
$428$	18.1475	0.877192
$429$	1.73022	0.0835357
$430$	−0.851863	−0.0410805
$431$	−2.42077	−0.116604	−0.0583021	−	0.998299i	$-0.518569\pi$
$431$	−2.42077	−0.116604	−0.0583021	+	0.998299i	$0.518569\pi$
$432$	−5.08534	−0.244669
$433$	36.5252	1.75529	0.877644	−	0.479312i	$-0.159114\pi$
$433$	36.5252	1.75529	0.877644	+	0.479312i	$0.159114\pi$
$434$	0.0106901	0.000513143 0
$435$	−0.794395	−0.0380883
$436$	11.3384	0.543009
$437$	5.47957	0.262123
$438$	18.5838	0.887968
$439$	6.17395	0.294667	0.147333	−	0.989087i	$-0.452931\pi$
$439$	6.17395	0.294667	0.147333	+	0.989087i	$0.452931\pi$
$440$	−0.730296	−0.0348155
$441$	−0.852890	−0.0406138
$442$	−1.83387	−0.0872283
$443$	11.6133	0.551764	0.275882	−	0.961192i	$-0.411030\pi$
$443$	11.6133	0.551764	0.275882	+	0.961192i	$0.411030\pi$
$444$	−1.67163	−0.0793320
$445$	1.93413	0.0916865
$446$	−27.9242	−1.32225
$447$	−26.3000	−1.24395
$448$	−0.00141487	−6.68464e−5 0
$449$	38.3018	1.80757	0.903786	−	0.427985i	$-0.140776\pi$
$449$	38.3018	1.80757	0.903786	+	0.427985i	$0.140776\pi$
$450$	0.591677	0.0278919
$451$	−14.1459	−0.666107
$452$	10.4493	0.491492
$453$	−21.8575	−1.02695
$454$	−11.2019	−0.525732
$455$	−0.000272962 0	−1.27966e−5 0
$456$	−9.68170	−0.453387
$457$	17.3618	0.812152	0.406076	−	0.913839i	$-0.366897\pi$
$457$	17.3618	0.812152	0.406076	+	0.913839i	$0.366897\pi$
$458$	−12.6638	−0.591742
$459$	18.3357	0.855839
$460$	−0.379310	−0.0176854
$461$	10.5671	0.492158	0.246079	−	0.969250i	$-0.420858\pi$
$461$	10.5671	0.492158	0.246079	+	0.969250i	$0.420858\pi$
$462$	−0.00481313	−0.000223927 0
$463$	−17.5900	−0.817477	−0.408739	−	0.912651i	$-0.634031\pi$
$463$	−17.5900	−0.817477	−0.408739	+	0.912651i	$0.634031\pi$
$464$	1.18532	0.0550273
$465$	−5.06367	−0.234822
$466$	22.5854	1.04625
$467$	−9.62455	−0.445371	−0.222686	−	0.974890i	$-0.571482\pi$
$467$	−9.62455	−0.445371	−0.222686	+	0.974890i	$0.571482\pi$
$468$	−0.0619706	−0.00286459
$469$	−0.00640581	−0.000295793 0
$470$	0.253659	0.0117004
$471$	−24.0131	−1.10647
$472$	−8.06109	−0.371042
$473$	4.32395	0.198816
$474$	25.6236	1.17693
$475$	−26.6095	−1.22093
$476$	0.00510147	0.000233826 0
$477$	0.0371631	0.00170158
$478$	−1.23332	−0.0564109
$479$	−5.59212	−0.255511	−0.127755	−	0.991806i	$-0.540777\pi$
$479$	−5.59212	−0.255511	−0.127755	+	0.991806i	$0.540777\pi$
$480$	0.670192	0.0305899
$481$	0.481199	0.0219408
$482$	9.02566	0.411107
$483$	−0.00249990	−0.000113749 0
$484$	−7.29311	−0.331505
$485$	7.08774	0.321838
$486$	1.26544	0.0574015
$487$	−24.1604	−1.09481	−0.547405	−	0.836868i	$-0.684384\pi$
$487$	−24.1604	−1.09481	−0.547405	+	0.836868i	$0.684384\pi$
$488$	12.9193	0.584831
$489$	−20.1009	−0.908995
$490$	−2.65517	−0.119948
$491$	35.3399	1.59487	0.797434	−	0.603406i	$-0.206190\pi$
$491$	35.3399	1.59487	0.797434	+	0.603406i	$0.206190\pi$
$492$	12.9817	0.585261
$493$	−4.27381	−0.192483
$494$	2.78700	0.125393
$495$	0.0889803	0.00399937
$496$	7.55554	0.339254
$497$	0.00360407	0.000161665 0
$498$	−16.3174	−0.731199
$499$	33.8086	1.51348	0.756740	−	0.653716i	$-0.226791\pi$
$499$	33.8086	1.51348	0.756740	+	0.653716i	$0.226791\pi$
$500$	3.73852	0.167192
$501$	2.86075	0.127809
$502$	−6.91948	−0.308832
$503$	−7.02915	−0.313414	−0.156707	−	0.987645i	$-0.550088\pi$
$503$	−7.02915	−0.313414	−0.156707	+	0.987645i	$0.550088\pi$
$504$	0.000172390 0	7.67886e−6 0
$505$	5.08008	0.226061
$506$	1.92533	0.0855913
$507$	−22.5123	−0.999805
$508$	−21.7549	−0.965216
$509$	−1.58356	−0.0701900	−0.0350950	−	0.999384i	$-0.511173\pi$
$509$	−1.58356	−0.0701900	−0.0350950	+	0.999384i	$0.511173\pi$
$510$	−2.41645	−0.107002
$511$	0.0148815	0.000658318 0
$512$	−1.00000	−0.0441942
$513$	−27.8655	−1.23029
$514$	15.9208	0.702235
$515$	1.45595	0.0641567
$516$	−3.96809	−0.174685
$517$	−1.28754	−0.0566261
$518$	−0.00133860	−5.88148e−5 0
$519$	−16.2794	−0.714587
$520$	−0.192923	−0.00846024
$521$	−34.3233	−1.50373	−0.751866	−	0.659316i	$-0.770846\pi$
$521$	−34.3233	−1.50373	−0.751866	+	0.659316i	$0.770846\pi$
$522$	−0.144422	−0.00632116
$523$	−1.56653	−0.0684998	−0.0342499	−	0.999413i	$-0.510904\pi$
$523$	−1.56653	−0.0684998	−0.0342499	+	0.999413i	$0.510904\pi$
$524$	1.00000	0.0436852
$525$	0.0121398	0.000529825 0
$526$	−18.2098	−0.793984
$527$	−27.2423	−1.18669
$528$	−3.40181	−0.148045
$529$	1.00000	0.0434783
$530$	0.115694	0.00502543
$531$	0.982174	0.0426227
$532$	−0.00775289	−0.000336130 0
$533$	−3.73695	−0.161865
$534$	9.00942	0.389876
$535$	−6.88352	−0.297601
$536$	−4.52748	−0.195557
$537$	−12.4912	−0.539033
$538$	10.1764	0.438736
$539$	13.4773	0.580509
$540$	1.92892	0.0830075
$541$	31.3319	1.34706	0.673532	−	0.739158i	$-0.264776\pi$
$541$	31.3319	1.34706	0.673532	+	0.739158i	$0.264776\pi$
$542$	−11.2418	−0.482875
$543$	−13.9649	−0.599292
$544$	3.60561	0.154589
$545$	−4.30075	−0.184224
$546$	−0.00127149	−5.44148e−5 0
$547$	16.2649	0.695437	0.347719	−	0.937599i	$-0.386956\pi$
$547$	16.2649	0.695437	0.347719	+	0.937599i	$0.386956\pi$
$548$	−8.79911	−0.375879
$549$	−1.57411	−0.0671814
$550$	−9.34964	−0.398670
$551$	6.49507	0.276699
$552$	−1.76687	−0.0752031
$553$	0.0205188	0.000872547 0
$554$	14.6965	0.624394
$555$	0.634065	0.0269146
$556$	−11.3192	−0.480042
$557$	5.38541	0.228187	0.114094	−	0.993470i	$-0.463604\pi$
$557$	5.38541	0.228187	0.114094	+	0.993470i	$0.463604\pi$
$558$	−0.920578	−0.0389712
$559$	1.14226	0.0483126
$560$	0.000536675 0	2.26786e−5 0
$561$	12.2656	0.517854
$562$	13.5224	0.570407
$563$	−15.3128	−0.645356	−0.322678	−	0.946509i	$-0.604583\pi$
$563$	−15.3128	−0.645356	−0.322678	+	0.946509i	$0.604583\pi$
$564$	1.18158	0.0497534
$565$	−3.96351	−0.166746
$566$	−8.72783	−0.366858
$567$	0.0132300	0.000555608 0
$568$	2.54728	0.106881
$569$	−21.7737	−0.912799	−0.456400	−	0.889775i	$-0.650861\pi$
$569$	−21.7737	−0.912799	−0.456400	+	0.889775i	$0.650861\pi$
$570$	3.67236	0.153818
$571$	−3.36689	−0.140900	−0.0704499	−	0.997515i	$-0.522443\pi$
$571$	−3.36689	−0.140900	−0.0704499	+	0.997515i	$0.522443\pi$
$572$	0.979254	0.0409447
$573$	−24.8157	−1.03669
$574$	0.0103955	0.000433899 0
$575$	−4.85612	−0.202514
$576$	0.121841	0.00507672
$577$	22.8252	0.950225	0.475112	−	0.879925i	$-0.342407\pi$
$577$	22.8252	0.950225	0.475112	+	0.879925i	$0.342407\pi$
$578$	3.99960	0.166362
$579$	17.1730	0.713686
$580$	−0.449605	−0.0186688
$581$	−0.0130666	−0.000542093 0
$582$	33.0156	1.36854
$583$	−0.587249	−0.0243214
$584$	10.5179	0.435233
$585$	0.0235060	0.000971855 0
$586$	−4.12146	−0.170256
$587$	−8.35029	−0.344654	−0.172327	−	0.985040i	$-0.555128\pi$
$587$	−8.35029	−0.344654	−0.172327	+	0.985040i	$0.555128\pi$
$588$	−12.3681	−0.510052
$589$	41.4011	1.70590
$590$	3.05765	0.125881
$591$	29.5709	1.21638
$592$	−0.946095	−0.0388843
$593$	−18.5999	−0.763807	−0.381903	−	0.924202i	$-0.624731\pi$
$593$	−18.5999	−0.763807	−0.381903	+	0.924202i	$0.624731\pi$
$594$	−9.79096	−0.401728
$595$	−0.00193504	−7.93288e−5 0
$596$	−14.8851	−0.609716
$597$	−7.80702	−0.319520
$598$	0.508617	0.0207989
$599$	39.1876	1.60116	0.800581	−	0.599225i	$-0.204524\pi$
$599$	39.1876	1.60116	0.800581	+	0.599225i	$0.204524\pi$
$600$	8.58016	0.350283
$601$	−33.6229	−1.37151	−0.685754	−	0.727834i	$-0.740527\pi$
$601$	−33.6229	−1.37151	−0.685754	+	0.727834i	$0.740527\pi$
$602$	−0.00317755	−0.000129507 0
$603$	0.551635	0.0224643
$604$	−12.3707	−0.503357
$605$	2.76635	0.112468
$606$	23.6637	0.961271
$607$	20.5460	0.833936	0.416968	−	0.908921i	$-0.363093\pi$
$607$	20.5460	0.833936	0.416968	+	0.908921i	$0.363093\pi$
$608$	−5.47957	−0.222226
$609$	−0.00296319	−0.000120075 0
$610$	−4.90043	−0.198413
$611$	−0.340132	−0.0137603
$612$	−0.439312	−0.0177581
$613$	34.4490	1.39138	0.695692	−	0.718341i	$-0.255098\pi$
$613$	34.4490	1.39138	0.695692	+	0.718341i	$0.255098\pi$
$614$	17.2682	0.696888
$615$	−4.92409	−0.198559
$616$	−0.00272410	−0.000109757 0
$617$	−6.13888	−0.247142	−0.123571	−	0.992336i	$-0.539435\pi$
$617$	−6.13888	−0.247142	−0.123571	+	0.992336i	$0.539435\pi$
$618$	6.78199	0.272811
$619$	−47.8651	−1.92386	−0.961931	−	0.273293i	$-0.911887\pi$
$619$	−47.8651	−1.92386	−0.961931	+	0.273293i	$0.911887\pi$
$620$	−2.86589	−0.115097
$621$	−5.08534	−0.204068
$622$	1.05410	0.0422656
$623$	0.00721454	0.000289045 0
$624$	−0.898661	−0.0359752
$625$	22.8626	0.914503
$626$	−0.128938	−0.00515341
$627$	−18.6405	−0.744428
$628$	−13.5907	−0.542330
$629$	3.41125	0.136015
$630$	−6.53892e−5 0	−2.60517e−6 0
$631$	9.96437	0.396675	0.198338	−	0.980134i	$-0.436446\pi$
$631$	9.96437	0.396675	0.198338	+	0.980134i	$0.436446\pi$
$632$	14.5022	0.576867
$633$	18.0738	0.718367
$634$	14.2027	0.564059
$635$	8.25183	0.327464
$636$	0.538918	0.0213695
$637$	3.56031	0.141065
$638$	2.28214	0.0903508
$639$	−0.310364	−0.0122778
$640$	0.379310	0.0149935
$641$	−32.2108	−1.27225	−0.636125	−	0.771586i	$-0.719464\pi$
$641$	−32.2108	−1.27225	−0.636125	+	0.771586i	$0.719464\pi$
$642$	−32.0643	−1.26548
$643$	12.3029	0.485179	0.242589	−	0.970129i	$-0.422003\pi$
$643$	12.3029	0.485179	0.242589	+	0.970129i	$0.422003\pi$
$644$	−0.00141487	−5.57538e−5 0
$645$	1.50513	0.0592646
$646$	19.7572	0.777335
$647$	−16.7819	−0.659764	−0.329882	−	0.944022i	$-0.607009\pi$
$647$	−16.7819	−0.659764	−0.329882	+	0.944022i	$0.607009\pi$
$648$	9.35068	0.367329
$649$	−15.5203	−0.609223
$650$	−2.46991	−0.0968776
$651$	−0.0188881	−0.000740283 0
$652$	−11.3765	−0.445540
$653$	−26.3896	−1.03271	−0.516353	−	0.856376i	$-0.672711\pi$
$653$	−26.3896	−1.03271	−0.516353	+	0.856376i	$0.672711\pi$
$654$	−20.0335	−0.783370
$655$	−0.379310	−0.0148209
$656$	7.34729	0.286863
$657$	−1.28151	−0.0499967
$658$	0.000946181 0	3.68860e−5 0
$659$	44.4639	1.73207	0.866035	−	0.499984i	$-0.166661\pi$
$659$	44.4639	1.73207	0.866035	+	0.499984i	$0.166661\pi$
$660$	1.29034	0.0502264
$661$	−10.1306	−0.394035	−0.197018	−	0.980400i	$-0.563126\pi$
$661$	−10.1306	−0.394035	−0.197018	+	0.980400i	$0.563126\pi$
$662$	8.05620	0.313113
$663$	3.24022	0.125840
$664$	−9.23516	−0.358394
$665$	0.00294074	0.000114037 0
$666$	0.115274	0.00446676
$667$	1.18532	0.0458960
$668$	1.61910	0.0626450
$669$	49.3386	1.90754
$670$	1.71732	0.0663457
$671$	24.8740	0.960249
$672$	0.00249990	9.64357e−5 0
$673$	−33.3597	−1.28592	−0.642961	−	0.765899i	$-0.722294\pi$
$673$	−33.3597	−1.28592	−0.642961	+	0.765899i	$0.722294\pi$
$674$	−9.93115	−0.382534
$675$	24.6951	0.950513
$676$	−12.7413	−0.490050
$677$	27.2696	1.04806	0.524028	−	0.851701i	$-0.324429\pi$
$677$	27.2696	1.04806	0.524028	+	0.851701i	$0.324429\pi$
$678$	−18.4625	−0.709050
$679$	0.0264381	0.00101460
$680$	−1.36764	−0.0524467
$681$	19.7924	0.758445
$682$	14.5469	0.557030
$683$	−46.6768	−1.78604	−0.893020	−	0.450018i	$-0.851418\pi$
$683$	−46.6768	−1.78604	−0.893020	+	0.450018i	$0.851418\pi$
$684$	0.667638	0.0255278
$685$	3.33759	0.127523
$686$	−0.0198082	−0.000756281 0
$687$	22.3754	0.853675
$688$	−2.24582	−0.0856212
$689$	−0.155134	−0.00591015
$690$	0.670192	0.0255138
$691$	−32.8833	−1.25094	−0.625470	−	0.780248i	$-0.715093\pi$
$691$	−32.8833	−1.25094	−0.625470	+	0.780248i	$0.715093\pi$
$692$	−9.21369	−0.350252
$693$	0.000331908 0	1.26081e−5 0
$694$	−2.13350	−0.0809867
$695$	4.29349	0.162861
$696$	−2.09432	−0.0793849
$697$	−26.4914	−1.00343
$698$	34.2009	1.29452
$699$	−39.9056	−1.50937
$700$	0.00687080	0.000259692 0
$701$	26.6298	1.00579	0.502897	−	0.864347i	$-0.332268\pi$
$701$	26.6298	1.00579	0.502897	+	0.864347i	$0.332268\pi$
$702$	−2.58649	−0.0976207
$703$	−5.18419	−0.195525
$704$	−1.92533	−0.0725636
$705$	−0.448184	−0.0168796
$706$	−21.9828	−0.827332
$707$	0.0189493	0.000712663 0
$708$	14.2429	0.535282
$709$	−14.3389	−0.538507	−0.269254	−	0.963069i	$-0.586777\pi$
$709$	−14.3389	−0.538507	−0.269254	+	0.963069i	$0.586777\pi$
$710$	−0.966208	−0.0362611
$711$	−1.76697	−0.0662665
$712$	5.09908	0.191096
$713$	7.55554	0.282957
$714$	−0.00901365	−0.000337328 0
$715$	−0.371441	−0.0138911
$716$	−7.06964	−0.264205
$717$	2.17913	0.0813810
$718$	16.8272	0.627985
$719$	51.3498	1.91503	0.957513	−	0.288391i	$-0.0931204\pi$
$719$	51.3498	1.91503	0.957513	+	0.288391i	$0.0931204\pi$
$720$	−0.0462156	−0.00172235
$721$	0.00543086	0.000202256 0
$722$	−11.0256	−0.410332
$723$	−15.9472	−0.593083
$724$	−7.90374	−0.293740
$725$	−5.75608	−0.213776
$726$	12.8860	0.478244
$727$	−21.6817	−0.804129	−0.402065	−	0.915611i	$-0.631707\pi$
$727$	−21.6817	−0.804129	−0.402065	+	0.915611i	$0.631707\pi$
$728$	−0.000719627 0	−2.66712e−5 0
$729$	25.8162	0.956154
$730$	−3.98954	−0.147659
$731$	8.09756	0.299499
$732$	−22.8268	−0.843704
$733$	−47.5951	−1.75797	−0.878983	−	0.476853i	$-0.841778\pi$
$733$	−47.5951	−1.75797	−0.878983	+	0.476853i	$0.841778\pi$
$734$	−29.5616	−1.09114
$735$	4.69134	0.173043
$736$	−1.00000	−0.0368605
$737$	−8.71689	−0.321091
$738$	−0.895204	−0.0329529
$739$	−8.57556	−0.315457	−0.157729	−	0.987482i	$-0.550417\pi$
$739$	−8.57556	−0.315457	−0.157729	+	0.987482i	$0.550417\pi$
$740$	0.358863	0.0131921
$741$	−4.92427	−0.180898
$742$	0.000431554 0	1.58428e−5 0
$743$	−24.1915	−0.887501	−0.443751	−	0.896150i	$-0.646352\pi$
$743$	−24.1915	−0.887501	−0.443751	+	0.896150i	$0.646352\pi$
$744$	−13.3497	−0.489423
$745$	5.64605	0.206855
$746$	−21.1401	−0.773993
$747$	1.12523	0.0411698
$748$	6.94198	0.253824
$749$	−0.0256764	−0.000938195 0
$750$	−6.60550	−0.241199
$751$	−1.13442	−0.0413954	−0.0206977	−	0.999786i	$-0.506589\pi$
$751$	−1.13442	−0.0413954	−0.0206977	+	0.999786i	$0.506589\pi$
$752$	0.668739	0.0243864
$753$	12.2258	0.445535
$754$	0.602876	0.0219554
$755$	4.69233	0.170771
$756$	0.00719511	0.000261684 0
$757$	38.9407	1.41533	0.707663	−	0.706550i	$-0.249750\pi$
$757$	38.9407	1.41533	0.707663	+	0.706550i	$0.249750\pi$
$758$	15.6054	0.566813
$759$	−3.40181	−0.123478
$760$	2.07845	0.0753934
$761$	−13.4093	−0.486088	−0.243044	−	0.970015i	$-0.578146\pi$
$761$	−13.4093	−0.486088	−0.243044	+	0.970015i	$0.578146\pi$
$762$	38.4381	1.39247
$763$	−0.0160423	−0.000580772 0
$764$	−14.0450	−0.508130
$765$	0.166635	0.00602471
$766$	−20.3815	−0.736414
$767$	−4.10000	−0.148043
$768$	1.76687	0.0637565
$769$	36.6950	1.32326	0.661628	−	0.749832i	$-0.269866\pi$
$769$	36.6950	1.32326	0.661628	+	0.749832i	$0.269866\pi$
$770$	0.00103328	3.72367e−5 0
$771$	−28.1300	−1.01308
$772$	9.71943	0.349810
$773$	−6.72378	−0.241838	−0.120919	−	0.992662i	$-0.538584\pi$
$773$	−6.72378	−0.241838	−0.120919	+	0.992662i	$0.538584\pi$
$774$	0.273634	0.00983558
$775$	−36.6907	−1.31797
$776$	18.6859	0.670784
$777$	0.00236514	8.48490e−5 0
$778$	8.97921	0.321920
$779$	40.2599	1.44246
$780$	0.340871	0.0122051
$781$	4.90435	0.175492
$782$	3.60561	0.128936
$783$	−6.02778	−0.215415
$784$	−7.00000	−0.250000
$785$	5.15510	0.183993
$786$	−1.76687	−0.0630223
$787$	26.8116	0.955731	0.477866	−	0.878433i	$-0.341411\pi$
$787$	26.8116	0.955731	0.477866	+	0.878433i	$0.341411\pi$
$788$	16.7363	0.596206
$789$	32.1744	1.14544
$790$	−5.50083	−0.195711
$791$	−0.0147844	−0.000525672 0
$792$	0.234585	0.00833561
$793$	6.57099	0.233343
$794$	−35.5793	−1.26266
$795$	−0.204417	−0.00724992
$796$	−4.41855	−0.156611
$797$	−52.8691	−1.87272	−0.936360	−	0.351040i	$-0.885828\pi$
$797$	−52.8691	−1.87272	−0.936360	+	0.351040i	$0.885828\pi$
$798$	0.0136984	0.000484917 0
$799$	−2.41121	−0.0853025
$800$	4.85612	0.171690
$801$	−0.621279	−0.0219518
$802$	−18.2529	−0.644533
$803$	20.2504	0.714621
$804$	7.99948	0.282120
$805$	0.000536675 0	1.89153e−5 0
$806$	3.84287	0.135359
$807$	−17.9804	−0.632940
$808$	13.3930	0.471163
$809$	−11.4132	−0.401265	−0.200633	−	0.979667i	$-0.564300\pi$
$809$	−11.4132	−0.401265	−0.200633	+	0.979667i	$0.564300\pi$
$810$	−3.54680	−0.124622
$811$	−39.8012	−1.39761	−0.698805	−	0.715312i	$-0.746284\pi$
$811$	−39.8012	−1.39761	−0.698805	+	0.715312i	$0.746284\pi$
$812$	−0.00167708	−5.88541e−5 0
$813$	19.8628	0.696617
$814$	−1.82154	−0.0638451
$815$	4.31523	0.151156
$816$	−6.37065	−0.223017
$817$	−12.3061	−0.430537
$818$	10.8381	0.378944
$819$	8.76804e−5 0	3.06380e−6 0
$820$	−2.78690	−0.0973227
$821$	−2.07902	−0.0725584	−0.0362792	−	0.999342i	$-0.511551\pi$
$821$	−2.07902	−0.0725584	−0.0362792	+	0.999342i	$0.511551\pi$
$822$	15.5469	0.542261
$823$	12.6739	0.441783	0.220891	−	0.975298i	$-0.429103\pi$
$823$	12.6739	0.441783	0.220891	+	0.975298i	$0.429103\pi$
$824$	3.83841	0.133717
$825$	16.5196	0.575140
$826$	0.0114054	0.000396845 0
$827$	−16.3840	−0.569728	−0.284864	−	0.958568i	$-0.591948\pi$
$827$	−16.3840	−0.569728	−0.284864	+	0.958568i	$0.591948\pi$
$828$	0.121841	0.00423428
$829$	−9.78416	−0.339818	−0.169909	−	0.985460i	$-0.554347\pi$
$829$	−9.78416	−0.339818	−0.169909	+	0.985460i	$0.554347\pi$
$830$	3.50299	0.121590
$831$	−25.9668	−0.900779
$832$	−0.508617	−0.0176331
$833$	25.2392	0.874488
$834$	19.9996	0.692530
$835$	−0.614141	−0.0212532
$836$	−10.5500	−0.364878
$837$	−38.4225	−1.32808
$838$	−2.87582	−0.0993435
$839$	−44.3840	−1.53231	−0.766153	−	0.642658i	$-0.777832\pi$
$839$	−44.3840	−1.53231	−0.766153	+	0.642658i	$0.777832\pi$
$840$	−0.000948236 0	−3.27173e−5 0
$841$	−27.5950	−0.951552
$842$	7.16331	0.246864
$843$	−23.8923	−0.822896
$844$	10.2292	0.352105
$845$	4.83290	0.166257
$846$	−0.0814801	−0.00280135
$847$	0.0103188	0.000354559 0
$848$	0.305012	0.0104742
$849$	15.4210	0.529247
$850$	−17.5093	−0.600563
$851$	−0.946095	−0.0324317
$852$	−4.50072	−0.154192
$853$	9.78672	0.335091	0.167545	−	0.985864i	$-0.446416\pi$
$853$	9.78672	0.335091	0.167545	+	0.985864i	$0.446416\pi$
$854$	−0.0182792	−0.000625502 0
$855$	−0.253242	−0.00866068
$856$	−18.1475	−0.620269
$857$	−29.7961	−1.01782	−0.508908	−	0.860821i	$-0.669950\pi$
$857$	−29.7961	−1.01782	−0.508908	+	0.860821i	$0.669950\pi$
$858$	−1.73022	−0.0590687
$859$	23.9499	0.817162	0.408581	−	0.912722i	$-0.366024\pi$
$859$	23.9499	0.817162	0.408581	+	0.912722i	$0.366024\pi$
$860$	0.851863	0.0290483
$861$	−0.0183675	−0.000625962 0
$862$	2.42077	0.0824517
$863$	25.4201	0.865311	0.432655	−	0.901559i	$-0.357577\pi$
$863$	25.4201	0.865311	0.432655	+	0.901559i	$0.357577\pi$
$864$	5.08534	0.173007
$865$	3.49484	0.118828
$866$	−36.5252	−1.24118
$867$	−7.06679	−0.240001
$868$	−0.0106901	−0.000362847 0
$869$	27.9215	0.947173
$870$	0.794395	0.0269325
$871$	−2.30275	−0.0780257
$872$	−11.3384	−0.383966
$873$	−2.27671	−0.0770551
$874$	−5.47957	−0.185349
$875$	−0.00528953	−0.000178819 0
$876$	−18.5838	−0.627888
$877$	−38.1391	−1.28787	−0.643933	−	0.765082i	$-0.722698\pi$
$877$	−38.1391	−1.28787	−0.643933	+	0.765082i	$0.722698\pi$
$878$	−6.17395	−0.208361
$879$	7.28209	0.245619
$880$	0.730296	0.0246183
$881$	−13.3811	−0.450819	−0.225410	−	0.974264i	$-0.572372\pi$
$881$	−13.3811	−0.450819	−0.225410	+	0.974264i	$0.572372\pi$
$882$	0.852890	0.0287183
$883$	11.2906	0.379958	0.189979	−	0.981788i	$-0.439158\pi$
$883$	11.2906	0.379958	0.189979	+	0.981788i	$0.439158\pi$
$884$	1.83387	0.0616798
$885$	−5.40248	−0.181602
$886$	−11.6133	−0.390156
$887$	23.8266	0.800018	0.400009	−	0.916511i	$-0.369007\pi$
$887$	23.8266	0.800018	0.400009	+	0.916511i	$0.369007\pi$
$888$	1.67163	0.0560962
$889$	0.0307804	0.00103234
$890$	−1.93413	−0.0648322
$891$	18.0031	0.603128
$892$	27.9242	0.934973
$893$	3.66440	0.122625
$894$	26.3000	0.879604
$895$	2.68158	0.0896354
$896$	0.00141487	4.72676e−5 0
$897$	−0.898661	−0.0300054
$898$	−38.3018	−1.27815
$899$	8.95577	0.298692
$900$	−0.591677	−0.0197226
$901$	−1.09975	−0.0366381
$902$	14.1459	0.471009
$903$	0.00561434	0.000186833 0
$904$	−10.4493	−0.347538
$905$	2.99797	0.0996558
$906$	21.8575	0.726166
$907$	−12.3276	−0.409330	−0.204665	−	0.978832i	$-0.565611\pi$
$907$	−12.3276	−0.409330	−0.204665	+	0.978832i	$0.565611\pi$
$908$	11.2019	0.371749
$909$	−1.63182	−0.0541240
$910$	0.000272962 0	9.04859e−6 0
$911$	−30.5427	−1.01192	−0.505962	−	0.862556i	$-0.668862\pi$
$911$	−30.5427	−1.01192	−0.505962	+	0.862556i	$0.668862\pi$
$912$	9.68170	0.320593
$913$	−17.7807	−0.588456
$914$	−17.3618	−0.574278
$915$	8.65844	0.286239
$916$	12.6638	0.418425
$917$	−0.00141487	−4.67232e−5 0
$918$	−18.3357	−0.605170
$919$	37.0261	1.22138	0.610688	−	0.791871i	$-0.290893\pi$
$919$	37.0261	1.22138	0.610688	+	0.791871i	$0.290893\pi$
$920$	0.379310	0.0125055
$921$	−30.5107	−1.00536
$922$	−10.5671	−0.348008
$923$	1.29559	0.0426448
$924$	0.00481313	0.000158340 0
$925$	4.59435	0.151061
$926$	17.5900	0.578044
$927$	−0.467677	−0.0153605
$928$	−1.18532	−0.0389102
$929$	−34.1550	−1.12059	−0.560294	−	0.828294i	$-0.689312\pi$
$929$	−34.1550	−1.12059	−0.560294	+	0.828294i	$0.689312\pi$
$930$	5.06367	0.166044
$931$	−38.3569	−1.25710
$932$	−22.5854	−0.739810
$933$	−1.86246	−0.0609743
$934$	9.62455	0.314925
$935$	−2.63316	−0.0861136
$936$	0.0619706	0.00202557
$937$	−44.4718	−1.45283	−0.726416	−	0.687255i	$-0.758815\pi$
$937$	−44.4718	−1.45283	−0.726416	+	0.687255i	$0.758815\pi$
$938$	0.00640581	0.000209157 0
$939$	0.227817	0.00743454
$940$	−0.253659	−0.00827346
$941$	−44.8441	−1.46187	−0.730937	−	0.682444i	$-0.760917\pi$
$941$	−44.8441	−1.46187	−0.730937	+	0.682444i	$0.760917\pi$
$942$	24.0131	0.782390
$943$	7.34729	0.239261
$944$	8.06109	0.262366
$945$	−0.00272917	−8.87801e−5 0
$946$	−4.32395	−0.140584
$947$	13.0581	0.424331	0.212165	−	0.977234i	$-0.431948\pi$
$947$	13.0581	0.424331	0.212165	+	0.977234i	$0.431948\pi$
$948$	−25.6236	−0.832215
$949$	5.34957	0.173655
$950$	26.6095	0.863325
$951$	−25.0943	−0.813738
$952$	−0.00510147	−0.000165340 0
$953$	−25.4899	−0.825699	−0.412850	−	0.910799i	$-0.635466\pi$
$953$	−25.4899	−0.825699	−0.412850	+	0.910799i	$0.635466\pi$
$954$	−0.0371631	−0.00120320
$955$	5.32741	0.172391
$956$	1.23332	0.0398885
$957$	−4.03225	−0.130344
$958$	5.59212	0.180673
$959$	0.0124496	0.000402019 0
$960$	−0.670192	−0.0216304
$961$	26.0862	0.841492
$962$	−0.481199	−0.0155145
$963$	2.21112	0.0712522
$964$	−9.02566	−0.290697
$965$	−3.68667	−0.118678
$966$	0.00249990	8.04330e−5 0
$967$	−7.41726	−0.238523	−0.119261	−	0.992863i	$-0.538053\pi$
$967$	−7.41726	−0.238523	−0.119261	+	0.992863i	$0.538053\pi$
$968$	7.29311	0.234409
$969$	−34.9084	−1.12142
$970$	−7.08774	−0.227574
$971$	55.5575	1.78292	0.891462	−	0.453096i	$-0.149680\pi$
$971$	55.5575	1.78292	0.891462	+	0.453096i	$0.149680\pi$
$972$	−1.26544	−0.0405890
$973$	0.0160152	0.000513425 0
$974$	24.1604	0.774148
$975$	4.36401	0.139760
$976$	−12.9193	−0.413538
$977$	0.424018	0.0135655	0.00678277	−	0.999977i	$-0.497841\pi$
$977$	0.424018	0.0135655	0.00678277	+	0.999977i	$0.497841\pi$
$978$	20.1009	0.642756
$979$	9.81740	0.313766
$980$	2.65517	0.0848162
$981$	1.38148	0.0441074
$982$	−35.3399	−1.12774
$983$	25.9567	0.827891	0.413945	−	0.910302i	$-0.364150\pi$
$983$	25.9567	0.827891	0.413945	+	0.910302i	$0.364150\pi$
$984$	−12.9817	−0.413842
$985$	−6.34824	−0.202272
$986$	4.27381	0.136106
$987$	−0.00167178	−5.32134e−5 0
$988$	−2.78700	−0.0886662
$989$	−2.24582	−0.0714131
$990$	−0.0889803	−0.00282798
$991$	−11.5205	−0.365962	−0.182981	−	0.983116i	$-0.558575\pi$
$991$	−11.5205	−0.365962	−0.182981	+	0.983116i	$0.558575\pi$
$992$	−7.55554	−0.239889
$993$	−14.2343	−0.451711
$994$	−0.00360407	−0.000114314 0
$995$	1.67600	0.0531328
$996$	16.3174	0.517035
$997$	−33.5593	−1.06283	−0.531417	−	0.847110i	$-0.678340\pi$
$997$	−33.5593	−1.06283	−0.531417	+	0.847110i	$0.678340\pi$
$998$	−33.8086	−1.07019
$999$	4.81122	0.152220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.20	✓	25	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.76687 q^{3} +1.00000 q^{4} -0.379310 q^{5} -1.76687 q^{6} -0.00141487 q^{7} -1.00000 q^{8} +0.121841 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.76687 q^{3} +1.00000 q^{4} -0.379310 q^{5} -1.76687 q^{6} -0.00141487 q^{7} -1.00000 q^{8} +0.121841 q^{9} +0.379310 q^{10} -1.92533 q^{11} +1.76687 q^{12} -0.508617 q^{13} +0.00141487 q^{14} -0.670192 q^{15} +1.00000 q^{16} -3.60561 q^{17} -0.121841 q^{18} +5.47957 q^{19} -0.379310 q^{20} -0.00249990 q^{21} +1.92533 q^{22} +1.00000 q^{23} -1.76687 q^{24} -4.85612 q^{25} +0.508617 q^{26} -5.08534 q^{27} -0.00141487 q^{28} +1.18532 q^{29} +0.670192 q^{30} +7.55554 q^{31} -1.00000 q^{32} -3.40181 q^{33} +3.60561 q^{34} +0.000536675 q^{35} +0.121841 q^{36} -0.946095 q^{37} -5.47957 q^{38} -0.898661 q^{39} +0.379310 q^{40} +7.34729 q^{41} +0.00249990 q^{42} -2.24582 q^{43} -1.92533 q^{44} -0.0462156 q^{45} -1.00000 q^{46} +0.668739 q^{47} +1.76687 q^{48} -7.00000 q^{49} +4.85612 q^{50} -6.37065 q^{51} -0.508617 q^{52} +0.305012 q^{53} +5.08534 q^{54} +0.730296 q^{55} +0.00141487 q^{56} +9.68170 q^{57} -1.18532 q^{58} +8.06109 q^{59} -0.670192 q^{60} -12.9193 q^{61} -7.55554 q^{62} -0.000172390 q^{63} +1.00000 q^{64} +0.192923 q^{65} +3.40181 q^{66} +4.52748 q^{67} -3.60561 q^{68} +1.76687 q^{69} -0.000536675 q^{70} -2.54728 q^{71} -0.121841 q^{72} -10.5179 q^{73} +0.946095 q^{74} -8.58016 q^{75} +5.47957 q^{76} +0.00272410 q^{77} +0.898661 q^{78} -14.5022 q^{79} -0.379310 q^{80} -9.35068 q^{81} -7.34729 q^{82} +9.23516 q^{83} -0.00249990 q^{84} +1.36764 q^{85} +2.24582 q^{86} +2.09432 q^{87} +1.92533 q^{88} -5.09908 q^{89} +0.0462156 q^{90} +0.000719627 q^{91} +1.00000 q^{92} +13.3497 q^{93} -0.668739 q^{94} -2.07845 q^{95} -1.76687 q^{96} -18.6859 q^{97} +7.00000 q^{98} -0.234585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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