LMFDB - Embedded newform 6026.2.a.i.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.489389 q^{3} +1.00000 q^{4} +2.70694 q^{5} -0.489389 q^{6} +1.75684 q^{7} -1.00000 q^{8} -2.76050 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.489389 q^{3} +1.00000 q^{4} +2.70694 q^{5} -0.489389 q^{6} +1.75684 q^{7} -1.00000 q^{8} -2.76050 q^{9} -2.70694 q^{10} +1.86326 q^{11} +0.489389 q^{12} -5.77826 q^{13} -1.75684 q^{14} +1.32475 q^{15} +1.00000 q^{16} +0.411409 q^{17} +2.76050 q^{18} -3.30662 q^{19} +2.70694 q^{20} +0.859779 q^{21} -1.86326 q^{22} +1.00000 q^{23} -0.489389 q^{24} +2.32751 q^{25} +5.77826 q^{26} -2.81912 q^{27} +1.75684 q^{28} -8.95375 q^{29} -1.32475 q^{30} +4.04733 q^{31} -1.00000 q^{32} +0.911859 q^{33} -0.411409 q^{34} +4.75566 q^{35} -2.76050 q^{36} +8.37793 q^{37} +3.30662 q^{38} -2.82781 q^{39} -2.70694 q^{40} -9.32536 q^{41} -0.859779 q^{42} -4.95120 q^{43} +1.86326 q^{44} -7.47250 q^{45} -1.00000 q^{46} -10.3867 q^{47} +0.489389 q^{48} -3.91351 q^{49} -2.32751 q^{50} +0.201339 q^{51} -5.77826 q^{52} +8.33584 q^{53} +2.81912 q^{54} +5.04373 q^{55} -1.75684 q^{56} -1.61822 q^{57} +8.95375 q^{58} +13.2744 q^{59} +1.32475 q^{60} +9.35245 q^{61} -4.04733 q^{62} -4.84976 q^{63} +1.00000 q^{64} -15.6414 q^{65} -0.911859 q^{66} +6.28748 q^{67} +0.411409 q^{68} +0.489389 q^{69} -4.75566 q^{70} -4.46886 q^{71} +2.76050 q^{72} -13.5354 q^{73} -8.37793 q^{74} +1.13906 q^{75} -3.30662 q^{76} +3.27346 q^{77} +2.82781 q^{78} -7.13291 q^{79} +2.70694 q^{80} +6.90185 q^{81} +9.32536 q^{82} +6.71368 q^{83} +0.859779 q^{84} +1.11366 q^{85} +4.95120 q^{86} -4.38187 q^{87} -1.86326 q^{88} +3.92441 q^{89} +7.47250 q^{90} -10.1515 q^{91} +1.00000 q^{92} +1.98072 q^{93} +10.3867 q^{94} -8.95081 q^{95} -0.489389 q^{96} -9.59770 q^{97} +3.91351 q^{98} -5.14353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.489389	0.282549	0.141274	−	0.989970i	$-0.454880\pi$
$3$	0.489389	0.282549	0.141274	+	0.989970i	$0.454880\pi$
$4$	1.00000	0.500000
$5$	2.70694	1.21058	0.605290	−	0.796005i	$-0.293057\pi$
$5$	2.70694	1.21058	0.605290	+	0.796005i	$0.293057\pi$
$6$	−0.489389	−0.199792
$7$	1.75684	0.664024	0.332012	−	0.943275i	$-0.392273\pi$
$7$	1.75684	0.664024	0.332012	+	0.943275i	$0.392273\pi$
$8$	−1.00000	−0.353553
$9$	−2.76050	−0.920166
$10$	−2.70694	−0.856009
$11$	1.86326	0.561794	0.280897	−	0.959738i	$-0.409368\pi$
$11$	1.86326	0.561794	0.280897	+	0.959738i	$0.409368\pi$
$12$	0.489389	0.141274
$13$	−5.77826	−1.60260	−0.801300	−	0.598263i	$-0.795858\pi$
$13$	−5.77826	−1.60260	−0.801300	+	0.598263i	$0.795858\pi$
$14$	−1.75684	−0.469536
$15$	1.32475	0.342048
$16$	1.00000	0.250000
$17$	0.411409	0.0997814	0.0498907	−	0.998755i	$-0.484113\pi$
$17$	0.411409	0.0997814	0.0498907	+	0.998755i	$0.484113\pi$
$18$	2.76050	0.650656
$19$	−3.30662	−0.758590	−0.379295	−	0.925276i	$-0.623833\pi$
$19$	−3.30662	−0.758590	−0.379295	+	0.925276i	$0.623833\pi$
$20$	2.70694	0.605290
$21$	0.859779	0.187619
$22$	−1.86326	−0.397249
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.489389	−0.0998961
$25$	2.32751	0.465502
$26$	5.77826	1.13321
$27$	−2.81912	−0.542541
$28$	1.75684	0.332012
$29$	−8.95375	−1.66267	−0.831335	−	0.555772i	$-0.812423\pi$
$29$	−8.95375	−1.66267	−0.831335	+	0.555772i	$0.812423\pi$
$30$	−1.32475	−0.241864
$31$	4.04733	0.726921	0.363461	−	0.931610i	$-0.381595\pi$
$31$	4.04733	0.726921	0.363461	+	0.931610i	$0.381595\pi$
$32$	−1.00000	−0.176777
$33$	0.911859	0.158734
$34$	−0.411409	−0.0705561
$35$	4.75566	0.803854
$36$	−2.76050	−0.460083
$37$	8.37793	1.37732	0.688662	−	0.725083i	$-0.258198\pi$
$37$	8.37793	1.37732	0.688662	+	0.725083i	$0.258198\pi$
$38$	3.30662	0.536404
$39$	−2.82781	−0.452813
$40$	−2.70694	−0.428004
$41$	−9.32536	−1.45638	−0.728188	−	0.685377i	$-0.759637\pi$
$41$	−9.32536	−1.45638	−0.728188	+	0.685377i	$0.759637\pi$
$42$	−0.859779	−0.132667
$43$	−4.95120	−0.755050	−0.377525	−	0.925999i	$-0.623225\pi$
$43$	−4.95120	−0.755050	−0.377525	+	0.925999i	$0.623225\pi$
$44$	1.86326	0.280897
$45$	−7.47250	−1.11393
$46$	−1.00000	−0.147442
$47$	−10.3867	−1.51506	−0.757529	−	0.652802i	$-0.773593\pi$
$47$	−10.3867	−1.51506	−0.757529	+	0.652802i	$0.773593\pi$
$48$	0.489389	0.0706372
$49$	−3.91351	−0.559072
$50$	−2.32751	−0.329160
$51$	0.201339	0.0281931
$52$	−5.77826	−0.801300
$53$	8.33584	1.14502	0.572508	−	0.819899i	$-0.305971\pi$
$53$	8.33584	1.14502	0.572508	+	0.819899i	$0.305971\pi$
$54$	2.81912	0.383634
$55$	5.04373	0.680097
$56$	−1.75684	−0.234768
$57$	−1.61822	−0.214339
$58$	8.95375	1.17568
$59$	13.2744	1.72818	0.864089	−	0.503340i	$-0.167896\pi$
$59$	13.2744	1.72818	0.864089	+	0.503340i	$0.167896\pi$
$60$	1.32475	0.171024
$61$	9.35245	1.19746	0.598729	−	0.800951i	$-0.295672\pi$
$61$	9.35245	1.19746	0.598729	+	0.800951i	$0.295672\pi$
$62$	−4.04733	−0.514011
$63$	−4.84976	−0.611012
$64$	1.00000	0.125000
$65$	−15.6414	−1.94007
$66$	−0.911859	−0.112242
$67$	6.28748	0.768138	0.384069	−	0.923304i	$-0.374523\pi$
$67$	6.28748	0.768138	0.384069	+	0.923304i	$0.374523\pi$
$68$	0.411409	0.0498907
$69$	0.489389	0.0589155
$70$	−4.75566	−0.568410
$71$	−4.46886	−0.530356	−0.265178	−	0.964199i	$-0.585431\pi$
$71$	−4.46886	−0.530356	−0.265178	+	0.964199i	$0.585431\pi$
$72$	2.76050	0.325328
$73$	−13.5354	−1.58420	−0.792100	−	0.610391i	$-0.791012\pi$
$73$	−13.5354	−1.58420	−0.792100	+	0.610391i	$0.791012\pi$
$74$	−8.37793	−0.973915
$75$	1.13906	0.131527
$76$	−3.30662	−0.379295
$77$	3.27346	0.373045
$78$	2.82781	0.320187
$79$	−7.13291	−0.802515	−0.401257	−	0.915965i	$-0.631427\pi$
$79$	−7.13291	−0.802515	−0.401257	+	0.915965i	$0.631427\pi$
$80$	2.70694	0.302645
$81$	6.90185	0.766872
$82$	9.32536	1.02981
$83$	6.71368	0.736922	0.368461	−	0.929643i	$-0.379885\pi$
$83$	6.71368	0.736922	0.368461	+	0.929643i	$0.379885\pi$
$84$	0.859779	0.0938096
$85$	1.11366	0.120793
$86$	4.95120	0.533901
$87$	−4.38187	−0.469785
$88$	−1.86326	−0.198624
$89$	3.92441	0.415987	0.207993	−	0.978130i	$-0.433307\pi$
$89$	3.92441	0.415987	0.207993	+	0.978130i	$0.433307\pi$
$90$	7.47250	0.787670
$91$	−10.1515	−1.06416
$92$	1.00000	0.104257
$93$	1.98072	0.205391
$94$	10.3867	1.07131
$95$	−8.95081	−0.918333
$96$	−0.489389	−0.0499481
$97$	−9.59770	−0.974499	−0.487250	−	0.873263i	$-0.662000\pi$
$97$	−9.59770	−0.974499	−0.487250	+	0.873263i	$0.662000\pi$
$98$	3.91351	0.395324
$99$	−5.14353	−0.516944
$100$	2.32751	0.232751
$101$	−15.0579	−1.49831	−0.749156	−	0.662393i	$-0.769541\pi$
$101$	−15.0579	−1.49831	−0.749156	+	0.662393i	$0.769541\pi$
$102$	−0.201339	−0.0199355
$103$	−13.5851	−1.33858	−0.669288	−	0.743003i	$-0.733401\pi$
$103$	−13.5851	−1.33858	−0.669288	+	0.743003i	$0.733401\pi$
$104$	5.77826	0.566605
$105$	2.32737	0.227128
$106$	−8.33584	−0.809648
$107$	−3.55479	−0.343655	−0.171827	−	0.985127i	$-0.554967\pi$
$107$	−3.55479	−0.343655	−0.171827	+	0.985127i	$0.554967\pi$
$108$	−2.81912	−0.271270
$109$	−14.6600	−1.40418	−0.702088	−	0.712090i	$-0.747749\pi$
$109$	−14.6600	−1.40418	−0.702088	+	0.712090i	$0.747749\pi$
$110$	−5.04373	−0.480901
$111$	4.10007	0.389161
$112$	1.75684	0.166006
$113$	−15.2325	−1.43295	−0.716477	−	0.697611i	$-0.754246\pi$
$113$	−15.2325	−1.43295	−0.716477	+	0.697611i	$0.754246\pi$
$114$	1.61822	0.151560
$115$	2.70694	0.252423
$116$	−8.95375	−0.831335
$117$	15.9509	1.47466
$118$	−13.2744	−1.22201
$119$	0.722781	0.0662572
$120$	−1.32475	−0.120932
$121$	−7.52826	−0.684387
$122$	−9.35245	−0.846731
$123$	−4.56373	−0.411497
$124$	4.04733	0.363461
$125$	−7.23426	−0.647052
$126$	4.84976	0.432051
$127$	10.2391	0.908571	0.454285	−	0.890856i	$-0.349895\pi$
$127$	10.2391	0.908571	0.454285	+	0.890856i	$0.349895\pi$
$128$	−1.00000	−0.0883883
$129$	−2.42306	−0.213339
$130$	15.6414	1.37184
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.911859	0.0793672
$133$	−5.80920	−0.503722
$134$	−6.28748	−0.543155
$135$	−7.63119	−0.656789
$136$	−0.411409	−0.0352780
$137$	−10.9035	−0.931545	−0.465773	−	0.884904i	$-0.654223\pi$
$137$	−10.9035	−0.931545	−0.465773	+	0.884904i	$0.654223\pi$
$138$	−0.489389	−0.0416596
$139$	3.79529	0.321912	0.160956	−	0.986962i	$-0.448542\pi$
$139$	3.79529	0.321912	0.160956	+	0.986962i	$0.448542\pi$
$140$	4.75566	0.401927
$141$	−5.08314	−0.428078
$142$	4.46886	0.375019
$143$	−10.7664	−0.900331
$144$	−2.76050	−0.230042
$145$	−24.2372	−2.01279
$146$	13.5354	1.12020
$147$	−1.91523	−0.157965
$148$	8.37793	0.688662
$149$	17.9850	1.47339	0.736695	−	0.676225i	$-0.236385\pi$
$149$	17.9850	1.47339	0.736695	+	0.676225i	$0.236385\pi$
$150$	−1.13906	−0.0930037
$151$	−19.3200	−1.57224	−0.786120	−	0.618074i	$-0.787913\pi$
$151$	−19.3200	−1.57224	−0.786120	+	0.618074i	$0.787913\pi$
$152$	3.30662	0.268202
$153$	−1.13569	−0.0918155
$154$	−3.27346	−0.263783
$155$	10.9559	0.879996
$156$	−2.82781	−0.226406
$157$	−1.36425	−0.108879	−0.0544396	−	0.998517i	$-0.517337\pi$
$157$	−1.36425	−0.108879	−0.0544396	+	0.998517i	$0.517337\pi$
$158$	7.13291	0.567464
$159$	4.07947	0.323523
$160$	−2.70694	−0.214002
$161$	1.75684	0.138459
$162$	−6.90185	−0.542260
$163$	11.9751	0.937959	0.468979	−	0.883209i	$-0.344622\pi$
$163$	11.9751	0.937959	0.468979	+	0.883209i	$0.344622\pi$
$164$	−9.32536	−0.728188
$165$	2.46835	0.192161
$166$	−6.71368	−0.521083
$167$	−8.16434	−0.631775	−0.315888	−	0.948797i	$-0.602302\pi$
$167$	−8.16434	−0.631775	−0.315888	+	0.948797i	$0.602302\pi$
$168$	−0.859779	−0.0663334
$169$	20.3882	1.56833
$170$	−1.11366	−0.0854138
$171$	9.12791	0.698029
$172$	−4.95120	−0.377525
$173$	−21.4495	−1.63078	−0.815389	−	0.578913i	$-0.803477\pi$
$173$	−21.4495	−1.63078	−0.815389	+	0.578913i	$0.803477\pi$
$174$	4.38187	0.332188
$175$	4.08907	0.309105
$176$	1.86326	0.140449
$177$	6.49634	0.488295
$178$	−3.92441	−0.294147
$179$	−9.37898	−0.701018	−0.350509	−	0.936559i	$-0.613991\pi$
$179$	−9.37898	−0.701018	−0.350509	+	0.936559i	$0.613991\pi$
$180$	−7.47250	−0.556967
$181$	18.5444	1.37839	0.689197	−	0.724574i	$-0.257964\pi$
$181$	18.5444	1.37839	0.689197	+	0.724574i	$0.257964\pi$
$182$	10.1515	0.752478
$183$	4.57699	0.338341
$184$	−1.00000	−0.0737210
$185$	22.6785	1.66736
$186$	−1.98072	−0.145233
$187$	0.766563	0.0560566
$188$	−10.3867	−0.757529
$189$	−4.95276	−0.360260
$190$	8.95081	0.649360
$191$	6.37074	0.460971	0.230485	−	0.973076i	$-0.425969\pi$
$191$	6.37074	0.460971	0.230485	+	0.973076i	$0.425969\pi$
$192$	0.489389	0.0353186
$193$	−7.98381	−0.574687	−0.287344	−	0.957828i	$-0.592772\pi$
$193$	−7.98381	−0.574687	−0.287344	+	0.957828i	$0.592772\pi$
$194$	9.59770	0.689075
$195$	−7.65472	−0.548166
$196$	−3.91351	−0.279536
$197$	−18.6150	−1.32626	−0.663131	−	0.748503i	$-0.730773\pi$
$197$	−18.6150	−1.32626	−0.663131	+	0.748503i	$0.730773\pi$
$198$	5.14353	0.365535
$199$	1.98994	0.141063	0.0705316	−	0.997510i	$-0.477530\pi$
$199$	1.98994	0.141063	0.0705316	+	0.997510i	$0.477530\pi$
$200$	−2.32751	−0.164580
$201$	3.07702	0.217036
$202$	15.0579	1.05947
$203$	−15.7303	−1.10405
$204$	0.201339	0.0140966
$205$	−25.2432	−1.76306
$206$	13.5851	0.946517
$207$	−2.76050	−0.191868
$208$	−5.77826	−0.400650
$209$	−6.16109	−0.426172
$210$	−2.32737	−0.160604
$211$	27.2622	1.87681	0.938404	−	0.345541i	$-0.112305\pi$
$211$	27.2622	1.87681	0.938404	+	0.345541i	$0.112305\pi$
$212$	8.33584	0.572508
$213$	−2.18701	−0.149852
$214$	3.55479	0.243001
$215$	−13.4026	−0.914048
$216$	2.81912	0.191817
$217$	7.11052	0.482693
$218$	14.6600	0.992902
$219$	−6.62408	−0.447614
$220$	5.04373	0.340048
$221$	−2.37723	−0.159910
$222$	−4.10007	−0.275179
$223$	17.9483	1.20191	0.600955	−	0.799283i	$-0.294787\pi$
$223$	17.9483	1.20191	0.600955	+	0.799283i	$0.294787\pi$
$224$	−1.75684	−0.117384
$225$	−6.42509	−0.428340
$226$	15.2325	1.01325
$227$	18.9955	1.26078	0.630388	−	0.776280i	$-0.282896\pi$
$227$	18.9955	1.26078	0.630388	+	0.776280i	$0.282896\pi$
$228$	−1.61822	−0.107169
$229$	21.4469	1.41725	0.708627	−	0.705583i	$-0.249315\pi$
$229$	21.4469	1.41725	0.708627	+	0.705583i	$0.249315\pi$
$230$	−2.70694	−0.178490
$231$	1.60199	0.105403
$232$	8.95375	0.587842
$233$	6.68967	0.438255	0.219127	−	0.975696i	$-0.429679\pi$
$233$	6.68967	0.438255	0.219127	+	0.975696i	$0.429679\pi$
$234$	−15.9509	−1.04274
$235$	−28.1162	−1.83410
$236$	13.2744	0.864089
$237$	−3.49077	−0.226750
$238$	−0.722781	−0.0468509
$239$	9.43105	0.610044	0.305022	−	0.952345i	$-0.401336\pi$
$239$	9.43105	0.610044	0.305022	+	0.952345i	$0.401336\pi$
$240$	1.32475	0.0855120
$241$	−20.6794	−1.33208	−0.666040	−	0.745916i	$-0.732012\pi$
$241$	−20.6794	−1.33208	−0.666040	+	0.745916i	$0.732012\pi$
$242$	7.52826	0.483935
$243$	11.8351	0.759220
$244$	9.35245	0.598729
$245$	−10.5936	−0.676801
$246$	4.56373	0.290973
$247$	19.1065	1.21572
$248$	−4.04733	−0.257006
$249$	3.28560	0.208217
$250$	7.23426	0.457535
$251$	−20.4131	−1.28846	−0.644231	−	0.764831i	$-0.722822\pi$
$251$	−20.4131	−1.28846	−0.644231	+	0.764831i	$0.722822\pi$
$252$	−4.84976	−0.305506
$253$	1.86326	0.117142
$254$	−10.2391	−0.642457
$255$	0.545012	0.0341300
$256$	1.00000	0.0625000
$257$	19.8981	1.24121	0.620605	−	0.784123i	$-0.286887\pi$
$257$	19.8981	1.24121	0.620605	+	0.784123i	$0.286887\pi$
$258$	2.42306	0.150853
$259$	14.7187	0.914576
$260$	−15.6414	−0.970037
$261$	24.7168	1.52993
$262$	−1.00000	−0.0617802
$263$	−23.2400	−1.43304	−0.716521	−	0.697566i	$-0.754266\pi$
$263$	−23.2400	−1.43304	−0.716521	+	0.697566i	$0.754266\pi$
$264$	−0.911859	−0.0561211
$265$	22.5646	1.38613
$266$	5.80920	0.356185
$267$	1.92056	0.117537
$268$	6.28748	0.384069
$269$	−14.4636	−0.881860	−0.440930	−	0.897542i	$-0.645351\pi$
$269$	−14.4636	−0.881860	−0.440930	+	0.897542i	$0.645351\pi$
$270$	7.63119	0.464420
$271$	−14.5554	−0.884175	−0.442088	−	0.896972i	$-0.645762\pi$
$271$	−14.5554	−0.884175	−0.442088	+	0.896972i	$0.645762\pi$
$272$	0.411409	0.0249453
$273$	−4.96802	−0.300678
$274$	10.9035	0.658702
$275$	4.33676	0.261517
$276$	0.489389	0.0294578
$277$	13.9840	0.840219	0.420110	−	0.907473i	$-0.361992\pi$
$277$	13.9840	0.840219	0.420110	+	0.907473i	$0.361992\pi$
$278$	−3.79529	−0.227626
$279$	−11.1726	−0.668889
$280$	−4.75566	−0.284205
$281$	2.40661	0.143566	0.0717831	−	0.997420i	$-0.477131\pi$
$281$	2.40661	0.143566	0.0717831	+	0.997420i	$0.477131\pi$
$282$	5.08314	0.302697
$283$	1.01250	0.0601869	0.0300935	−	0.999547i	$-0.490420\pi$
$283$	1.01250	0.0601869	0.0300935	+	0.999547i	$0.490420\pi$
$284$	−4.46886	−0.265178
$285$	−4.38043	−0.259474
$286$	10.7664	0.636630
$287$	−16.3832	−0.967069
$288$	2.76050	0.162664
$289$	−16.8307	−0.990044
$290$	24.2372	1.42326
$291$	−4.69701	−0.275344
$292$	−13.5354	−0.792100
$293$	5.73778	0.335205	0.167602	−	0.985855i	$-0.446397\pi$
$293$	5.73778	0.335205	0.167602	+	0.985855i	$0.446397\pi$
$294$	1.91523	0.111698
$295$	35.9329	2.09210
$296$	−8.37793	−0.486957
$297$	−5.25276	−0.304796
$298$	−17.9850	−1.04184
$299$	−5.77826	−0.334165
$300$	1.13906	0.0657636
$301$	−8.69847	−0.501372
$302$	19.3200	1.11174
$303$	−7.36915	−0.423346
$304$	−3.30662	−0.189647
$305$	25.3165	1.44962
$306$	1.13569	0.0649233
$307$	12.1385	0.692780	0.346390	−	0.938091i	$-0.387407\pi$
$307$	12.1385	0.692780	0.346390	+	0.938091i	$0.387407\pi$
$308$	3.27346	0.186522
$309$	−6.64838	−0.378213
$310$	−10.9559	−0.622251
$311$	−7.46737	−0.423436	−0.211718	−	0.977331i	$-0.567906\pi$
$311$	−7.46737	−0.423436	−0.211718	+	0.977331i	$0.567906\pi$
$312$	2.82781	0.160093
$313$	−16.2053	−0.915978	−0.457989	−	0.888958i	$-0.651430\pi$
$313$	−16.2053	−0.915978	−0.457989	+	0.888958i	$0.651430\pi$
$314$	1.36425	0.0769892
$315$	−13.1280	−0.739679
$316$	−7.13291	−0.401257
$317$	31.7233	1.78176	0.890879	−	0.454242i	$-0.150090\pi$
$317$	31.7233	1.78176	0.890879	+	0.454242i	$0.150090\pi$
$318$	−4.07947	−0.228765
$319$	−16.6832	−0.934078
$320$	2.70694	0.151322
$321$	−1.73968	−0.0970993
$322$	−1.75684	−0.0979050
$323$	−1.36037	−0.0756932
$324$	6.90185	0.383436
$325$	−13.4490	−0.746014
$326$	−11.9751	−0.663237
$327$	−7.17446	−0.396748
$328$	9.32536	0.514907
$329$	−18.2478	−1.00603
$330$	−2.46835	−0.135878
$331$	12.6481	0.695204	0.347602	−	0.937642i	$-0.386996\pi$
$331$	12.6481	0.695204	0.347602	+	0.937642i	$0.386996\pi$
$332$	6.71368	0.368461
$333$	−23.1273	−1.26737
$334$	8.16434	0.446733
$335$	17.0198	0.929892
$336$	0.859779	0.0469048
$337$	10.0795	0.549067	0.274534	−	0.961578i	$-0.411477\pi$
$337$	10.0795	0.549067	0.274534	+	0.961578i	$0.411477\pi$
$338$	−20.3882	−1.10897
$339$	−7.45462	−0.404879
$340$	1.11366	0.0603966
$341$	7.54123	0.408380
$342$	−9.12791	−0.493581
$343$	−19.1733	−1.03526
$344$	4.95120	0.266951
$345$	1.32475	0.0713219
$346$	21.4495	1.15313
$347$	−2.43014	−0.130457	−0.0652284	−	0.997870i	$-0.520778\pi$
$347$	−2.43014	−0.130457	−0.0652284	+	0.997870i	$0.520778\pi$
$348$	−4.38187	−0.234893
$349$	−11.8155	−0.632472	−0.316236	−	0.948681i	$-0.602419\pi$
$349$	−11.8155	−0.632472	−0.316236	+	0.948681i	$0.602419\pi$
$350$	−4.08907	−0.218570
$351$	16.2896	0.869476
$352$	−1.86326	−0.0993121
$353$	−12.9583	−0.689699	−0.344849	−	0.938658i	$-0.612070\pi$
$353$	−12.9583	−0.689699	−0.344849	+	0.938658i	$0.612070\pi$
$354$	−6.49634	−0.345276
$355$	−12.0969	−0.642038
$356$	3.92441	0.207993
$357$	0.353721	0.0187209
$358$	9.37898	0.495694
$359$	25.4169	1.34145	0.670727	−	0.741704i	$-0.265982\pi$
$359$	25.4169	1.34145	0.670727	+	0.741704i	$0.265982\pi$
$360$	7.47250	0.393835
$361$	−8.06628	−0.424541
$362$	−18.5444	−0.974671
$363$	−3.68425	−0.193373
$364$	−10.1515	−0.532082
$365$	−36.6395	−1.91780
$366$	−4.57699	−0.239243
$367$	4.09411	0.213711	0.106855	−	0.994275i	$-0.465922\pi$
$367$	4.09411	0.213711	0.106855	+	0.994275i	$0.465922\pi$
$368$	1.00000	0.0521286
$369$	25.7426	1.34011
$370$	−22.6785	−1.17900
$371$	14.6448	0.760318
$372$	1.98072	0.102695
$373$	−14.1480	−0.732556	−0.366278	−	0.930505i	$-0.619368\pi$
$373$	−14.1480	−0.732556	−0.366278	+	0.930505i	$0.619368\pi$
$374$	−0.766563	−0.0396380
$375$	−3.54037	−0.182824
$376$	10.3867	0.535654
$377$	51.7370	2.66459
$378$	4.95276	0.254742
$379$	−15.6164	−0.802159	−0.401080	−	0.916043i	$-0.631365\pi$
$379$	−15.6164	−0.802159	−0.401080	+	0.916043i	$0.631365\pi$
$380$	−8.95081	−0.459167
$381$	5.01089	0.256716
$382$	−6.37074	−0.325955
$383$	21.4338	1.09521	0.547607	−	0.836736i	$-0.315539\pi$
$383$	21.4338	1.09521	0.547607	+	0.836736i	$0.315539\pi$
$384$	−0.489389	−0.0249740
$385$	8.86104	0.451600
$386$	7.98381	0.406365
$387$	13.6678	0.694772
$388$	−9.59770	−0.487250
$389$	−10.1472	−0.514485	−0.257243	−	0.966347i	$-0.582814\pi$
$389$	−10.1472	−0.514485	−0.257243	+	0.966347i	$0.582814\pi$
$390$	7.65472	0.387612
$391$	0.411409	0.0208059
$392$	3.91351	0.197662
$393$	0.489389	0.0246864
$394$	18.6150	0.937809
$395$	−19.3083	−0.971508
$396$	−5.14353	−0.258472
$397$	7.32012	0.367386	0.183693	−	0.982984i	$-0.441195\pi$
$397$	7.32012	0.367386	0.183693	+	0.982984i	$0.441195\pi$
$398$	−1.98994	−0.0997467
$399$	−2.84296	−0.142326
$400$	2.32751	0.116376
$401$	16.9234	0.845114	0.422557	−	0.906336i	$-0.361133\pi$
$401$	16.9234	0.845114	0.422557	+	0.906336i	$0.361133\pi$
$402$	−3.07702	−0.153468
$403$	−23.3865	−1.16496
$404$	−15.0579	−0.749156
$405$	18.6829	0.928359
$406$	15.7303	0.780683
$407$	15.6103	0.773773
$408$	−0.201339	−0.00996777
$409$	2.23908	0.110715	0.0553577	−	0.998467i	$-0.482370\pi$
$409$	2.23908	0.110715	0.0553577	+	0.998467i	$0.482370\pi$
$410$	25.2432	1.24667
$411$	−5.33603	−0.263207
$412$	−13.5851	−0.669288
$413$	23.3210	1.14755
$414$	2.76050	0.135671
$415$	18.1735	0.892103
$416$	5.77826	0.283302
$417$	1.85737	0.0909559
$418$	6.16109	0.301349
$419$	−7.44628	−0.363775	−0.181887	−	0.983319i	$-0.558221\pi$
$419$	−7.44628	−0.363775	−0.181887	+	0.983319i	$0.558221\pi$
$420$	2.32737	0.113564
$421$	22.1005	1.07711	0.538555	−	0.842590i	$-0.318970\pi$
$421$	22.1005	1.07711	0.538555	+	0.842590i	$0.318970\pi$
$422$	−27.2622	−1.32710
$423$	28.6725	1.39410
$424$	−8.33584	−0.404824
$425$	0.957560	0.0464485
$426$	2.18701	0.105961
$427$	16.4308	0.795141
$428$	−3.55479	−0.171827
$429$	−5.26896	−0.254388
$430$	13.4026	0.646330
$431$	−11.7617	−0.566540	−0.283270	−	0.959040i	$-0.591419\pi$
$431$	−11.7617	−0.566540	−0.283270	+	0.959040i	$0.591419\pi$
$432$	−2.81912	−0.135635
$433$	−17.0115	−0.817520	−0.408760	−	0.912642i	$-0.634039\pi$
$433$	−17.0115	−0.817520	−0.408760	+	0.912642i	$0.634039\pi$
$434$	−7.11052	−0.341316
$435$	−11.8614	−0.568712
$436$	−14.6600	−0.702088
$437$	−3.30662	−0.158177
$438$	6.62408	0.316511
$439$	37.3642	1.78329	0.891647	−	0.452731i	$-0.149550\pi$
$439$	37.3642	1.78329	0.891647	+	0.452731i	$0.149550\pi$
$440$	−5.04373	−0.240450
$441$	10.8032	0.514439
$442$	2.37723	0.113073
$443$	16.4430	0.781231	0.390615	−	0.920554i	$-0.372262\pi$
$443$	16.4430	0.781231	0.390615	+	0.920554i	$0.372262\pi$
$444$	4.10007	0.194581
$445$	10.6231	0.503585
$446$	−17.9483	−0.849878
$447$	8.80167	0.416305
$448$	1.75684	0.0830030
$449$	13.3905	0.631939	0.315970	−	0.948769i	$-0.397670\pi$
$449$	13.3905	0.631939	0.315970	+	0.948769i	$0.397670\pi$
$450$	6.42509	0.302882
$451$	−17.3756	−0.818184
$452$	−15.2325	−0.716477
$453$	−9.45500	−0.444235
$454$	−18.9955	−0.891504
$455$	−27.4794	−1.28826
$456$	1.61822	0.0757802
$457$	−7.64751	−0.357736	−0.178868	−	0.983873i	$-0.557243\pi$
$457$	−7.64751	−0.357736	−0.178868	+	0.983873i	$0.557243\pi$
$458$	−21.4469	−1.00215
$459$	−1.15981	−0.0541355
$460$	2.70694	0.126212
$461$	−26.6413	−1.24081	−0.620405	−	0.784282i	$-0.713032\pi$
$461$	−26.6413	−1.24081	−0.620405	+	0.784282i	$0.713032\pi$
$462$	−1.60199	−0.0745315
$463$	−10.0154	−0.465454	−0.232727	−	0.972542i	$-0.574765\pi$
$463$	−10.0154	−0.465454	−0.232727	+	0.972542i	$0.574765\pi$
$464$	−8.95375	−0.415667
$465$	5.36168	0.248642
$466$	−6.68967	−0.309893
$467$	13.7640	0.636920	0.318460	−	0.947936i	$-0.396834\pi$
$467$	13.7640	0.636920	0.318460	+	0.947936i	$0.396834\pi$
$468$	15.9509	0.737329
$469$	11.0461	0.510062
$470$	28.1162	1.29690
$471$	−0.667650	−0.0307637
$472$	−13.2744	−0.611003
$473$	−9.22537	−0.424183
$474$	3.49077	0.160336
$475$	−7.69619	−0.353125
$476$	0.722781	0.0331286
$477$	−23.0111	−1.05360
$478$	−9.43105	−0.431366
$479$	−15.1671	−0.693004	−0.346502	−	0.938049i	$-0.612631\pi$
$479$	−15.1671	−0.693004	−0.346502	+	0.938049i	$0.612631\pi$
$480$	−1.32475	−0.0604661
$481$	−48.4098	−2.20730
$482$	20.6794	0.941923
$483$	0.859779	0.0391213
$484$	−7.52826	−0.342194
$485$	−25.9804	−1.17971
$486$	−11.8351	−0.536849
$487$	−31.5734	−1.43073	−0.715363	−	0.698753i	$-0.753739\pi$
$487$	−31.5734	−1.43073	−0.715363	+	0.698753i	$0.753739\pi$
$488$	−9.35245	−0.423366
$489$	5.86046	0.265019
$490$	10.5936	0.478571
$491$	−7.35504	−0.331928	−0.165964	−	0.986132i	$-0.553074\pi$
$491$	−7.35504	−0.331928	−0.165964	+	0.986132i	$0.553074\pi$
$492$	−4.56373	−0.205749
$493$	−3.68365	−0.165903
$494$	−19.1065	−0.859641
$495$	−13.9232	−0.625802
$496$	4.04733	0.181730
$497$	−7.85109	−0.352169
$498$	−3.28560	−0.147231
$499$	−38.9889	−1.74538	−0.872692	−	0.488271i	$-0.837628\pi$
$499$	−38.9889	−1.74538	−0.872692	+	0.488271i	$0.837628\pi$
$500$	−7.23426	−0.323526
$501$	−3.99554	−0.178507
$502$	20.4131	0.911080
$503$	−15.5334	−0.692598	−0.346299	−	0.938124i	$-0.612562\pi$
$503$	−15.5334	−0.692598	−0.346299	+	0.938124i	$0.612562\pi$
$504$	4.84976	0.216025
$505$	−40.7607	−1.81383
$506$	−1.86326	−0.0828321
$507$	9.97778	0.443129
$508$	10.2391	0.454285
$509$	8.81732	0.390821	0.195410	−	0.980722i	$-0.437396\pi$
$509$	8.81732	0.390821	0.195410	+	0.980722i	$0.437396\pi$
$510$	−0.545012	−0.0241336
$511$	−23.7796	−1.05195
$512$	−1.00000	−0.0441942
$513$	9.32176	0.411566
$514$	−19.8981	−0.877668
$515$	−36.7739	−1.62045
$516$	−2.42306	−0.106669
$517$	−19.3532	−0.851151
$518$	−14.7187	−0.646703
$519$	−10.4972	−0.460775
$520$	15.6414	0.685920
$521$	24.7182	1.08292	0.541462	−	0.840725i	$-0.317871\pi$
$521$	24.7182	1.08292	0.541462	+	0.840725i	$0.317871\pi$
$522$	−24.7168	−1.08183
$523$	−3.27789	−0.143332	−0.0716660	−	0.997429i	$-0.522832\pi$
$523$	−3.27789	−0.143332	−0.0716660	+	0.997429i	$0.522832\pi$
$524$	1.00000	0.0436852
$525$	2.00115	0.0873372
$526$	23.2400	1.01331
$527$	1.66511	0.0725332
$528$	0.911859	0.0396836
$529$	1.00000	0.0434783
$530$	−22.5646	−0.980143
$531$	−36.6439	−1.59021
$532$	−5.80920	−0.251861
$533$	53.8843	2.33399
$534$	−1.92056	−0.0831109
$535$	−9.62261	−0.416022
$536$	−6.28748	−0.271578
$537$	−4.58997	−0.198072
$538$	14.4636	0.623569
$539$	−7.29188	−0.314084
$540$	−7.63119	−0.328394
$541$	−41.7473	−1.79486	−0.897428	−	0.441160i	$-0.854567\pi$
$541$	−41.7473	−1.79486	−0.897428	+	0.441160i	$0.854567\pi$
$542$	14.5554	0.625206
$543$	9.07542	0.389463
$544$	−0.411409	−0.0176390
$545$	−39.6838	−1.69987
$546$	4.96802	0.212612
$547$	−41.8202	−1.78810	−0.894052	−	0.447964i	$-0.852149\pi$
$547$	−41.8202	−1.78810	−0.894052	+	0.447964i	$0.852149\pi$
$548$	−10.9035	−0.465773
$549$	−25.8174	−1.10186
$550$	−4.33676	−0.184920
$551$	29.6066	1.26128
$552$	−0.489389	−0.0208298
$553$	−12.5314	−0.532889
$554$	−13.9840	−0.594125
$555$	11.0986	0.471111
$556$	3.79529	0.160956
$557$	33.5427	1.42125	0.710624	−	0.703572i	$-0.248413\pi$
$557$	33.5427	1.42125	0.710624	+	0.703572i	$0.248413\pi$
$558$	11.1726	0.472976
$559$	28.6093	1.21004
$560$	4.75566	0.200963
$561$	0.375147	0.0158387
$562$	−2.40661	−0.101517
$563$	−43.0222	−1.81317	−0.906585	−	0.422024i	$-0.861320\pi$
$563$	−43.0222	−1.81317	−0.906585	+	0.422024i	$0.861320\pi$
$564$	−5.08314	−0.214039
$565$	−41.2335	−1.73470
$566$	−1.01250	−0.0425586
$567$	12.1255	0.509221
$568$	4.46886	0.187509
$569$	−13.1197	−0.550005	−0.275003	−	0.961443i	$-0.588679\pi$
$569$	−13.1197	−0.550005	−0.275003	+	0.961443i	$0.588679\pi$
$570$	4.38043	0.183476
$571$	−9.01775	−0.377381	−0.188690	−	0.982037i	$-0.560424\pi$
$571$	−9.01775	−0.377381	−0.188690	+	0.982037i	$0.560424\pi$
$572$	−10.7664	−0.450166
$573$	3.11777	0.130247
$574$	16.3832	0.683821
$575$	2.32751	0.0970640
$576$	−2.76050	−0.115021
$577$	19.4321	0.808969	0.404485	−	0.914545i	$-0.367451\pi$
$577$	19.4321	0.808969	0.404485	+	0.914545i	$0.367451\pi$
$578$	16.8307	0.700067
$579$	−3.90719	−0.162377
$580$	−24.2372	−1.00640
$581$	11.7949	0.489334
$582$	4.69701	0.194697
$583$	15.5318	0.643263
$584$	13.5354	0.560099
$585$	43.1780	1.78519
$586$	−5.73778	−0.237026
$587$	14.1535	0.584177	0.292089	−	0.956391i	$-0.405650\pi$
$587$	14.1535	0.584177	0.292089	+	0.956391i	$0.405650\pi$
$588$	−1.91523	−0.0789826
$589$	−13.3830	−0.551435
$590$	−35.9329	−1.47934
$591$	−9.10996	−0.374734
$592$	8.37793	0.344331
$593$	27.4777	1.12837	0.564186	−	0.825648i	$-0.309190\pi$
$593$	27.4777	1.12837	0.564186	+	0.825648i	$0.309190\pi$
$594$	5.25276	0.215524
$595$	1.95652	0.0802096
$596$	17.9850	0.736695
$597$	0.973855	0.0398572
$598$	5.77826	0.236290
$599$	−5.82025	−0.237809	−0.118905	−	0.992906i	$-0.537938\pi$
$599$	−5.82025	−0.237809	−0.118905	+	0.992906i	$0.537938\pi$
$600$	−1.13906	−0.0465019
$601$	28.9690	1.18167	0.590836	−	0.806792i	$-0.298798\pi$
$601$	28.9690	1.18167	0.590836	+	0.806792i	$0.298798\pi$
$602$	8.69847	0.354523
$603$	−17.3566	−0.706814
$604$	−19.3200	−0.786120
$605$	−20.3785	−0.828505
$606$	7.36915	0.299351
$607$	18.7414	0.760689	0.380344	−	0.924845i	$-0.375805\pi$
$607$	18.7414	0.760689	0.380344	+	0.924845i	$0.375805\pi$
$608$	3.30662	0.134101
$609$	−7.69825	−0.311949
$610$	−25.3165	−1.02504
$611$	60.0171	2.42803
$612$	−1.13569	−0.0459077
$613$	−35.1711	−1.42055	−0.710274	−	0.703925i	$-0.751429\pi$
$613$	−35.1711	−1.42055	−0.710274	+	0.703925i	$0.751429\pi$
$614$	−12.1385	−0.489869
$615$	−12.3537	−0.498150
$616$	−3.27346	−0.131891
$617$	17.9312	0.721883	0.360942	−	0.932588i	$-0.382455\pi$
$617$	17.9312	0.721883	0.360942	+	0.932588i	$0.382455\pi$
$618$	6.64838	0.267437
$619$	11.4249	0.459204	0.229602	−	0.973285i	$-0.426258\pi$
$619$	11.4249	0.459204	0.229602	+	0.973285i	$0.426258\pi$
$620$	10.9559	0.439998
$621$	−2.81912	−0.113128
$622$	7.46737	0.299414
$623$	6.89457	0.276225
$624$	−2.82781	−0.113203
$625$	−31.2202	−1.24881
$626$	16.2053	0.647694
$627$	−3.01517	−0.120414
$628$	−1.36425	−0.0544396
$629$	3.44676	0.137431
$630$	13.1280	0.523032
$631$	−45.0572	−1.79370	−0.896850	−	0.442335i	$-0.854150\pi$
$631$	−45.0572	−1.79370	−0.896850	+	0.442335i	$0.854150\pi$
$632$	7.13291	0.283732
$633$	13.3418	0.530290
$634$	−31.7233	−1.25989
$635$	27.7165	1.09990
$636$	4.07947	0.161761
$637$	22.6132	0.895969
$638$	16.6832	0.660493
$639$	12.3363	0.488016
$640$	−2.70694	−0.107001
$641$	46.7212	1.84538	0.922688	−	0.385547i	$-0.125987\pi$
$641$	46.7212	1.84538	0.922688	+	0.385547i	$0.125987\pi$
$642$	1.73968	0.0686596
$643$	−8.38073	−0.330504	−0.165252	−	0.986251i	$-0.552844\pi$
$643$	−8.38073	−0.330504	−0.165252	+	0.986251i	$0.552844\pi$
$644$	1.75684	0.0692293
$645$	−6.55908	−0.258263
$646$	1.36037	0.0535231
$647$	−8.67354	−0.340992	−0.170496	−	0.985358i	$-0.554537\pi$
$647$	−8.67354	−0.340992	−0.170496	+	0.985358i	$0.554537\pi$
$648$	−6.90185	−0.271130
$649$	24.7336	0.970880
$650$	13.4490	0.527512
$651$	3.47981	0.136384
$652$	11.9751	0.468979
$653$	−2.16174	−0.0845954	−0.0422977	−	0.999105i	$-0.513468\pi$
$653$	−2.16174	−0.0845954	−0.0422977	+	0.999105i	$0.513468\pi$
$654$	7.17446	0.280543
$655$	2.70694	0.105769
$656$	−9.32536	−0.364094
$657$	37.3645	1.45773
$658$	18.2478	0.711374
$659$	9.18967	0.357979	0.178989	−	0.983851i	$-0.442717\pi$
$659$	9.18967	0.357979	0.178989	+	0.983851i	$0.442717\pi$
$660$	2.46835	0.0960803
$661$	24.7234	0.961627	0.480814	−	0.876823i	$-0.340341\pi$
$661$	24.7234	0.961627	0.480814	+	0.876823i	$0.340341\pi$
$662$	−12.6481	−0.491583
$663$	−1.16339	−0.0451823
$664$	−6.71368	−0.260541
$665$	−15.7252	−0.609795
$666$	23.1273	0.896164
$667$	−8.95375	−0.346691
$668$	−8.16434	−0.315888
$669$	8.78372	0.339598
$670$	−17.0198	−0.657533
$671$	17.4261	0.672726
$672$	−0.859779	−0.0331667
$673$	11.2109	0.432150	0.216075	−	0.976377i	$-0.430675\pi$
$673$	11.2109	0.432150	0.216075	+	0.976377i	$0.430675\pi$
$674$	−10.0795	−0.388249
$675$	−6.56155	−0.252554
$676$	20.3882	0.784163
$677$	−8.34645	−0.320780	−0.160390	−	0.987054i	$-0.551275\pi$
$677$	−8.34645	−0.320780	−0.160390	+	0.987054i	$0.551275\pi$
$678$	7.45462	0.286293
$679$	−16.8617	−0.647091
$680$	−1.11366	−0.0427069
$681$	9.29620	0.356231
$682$	−7.54123	−0.288769
$683$	23.8569	0.912859	0.456430	−	0.889759i	$-0.349128\pi$
$683$	23.8569	0.912859	0.456430	+	0.889759i	$0.349128\pi$
$684$	9.12791	0.349014
$685$	−29.5150	−1.12771
$686$	19.1733	0.732040
$687$	10.4959	0.400444
$688$	−4.95120	−0.188763
$689$	−48.1666	−1.83500
$690$	−1.32475	−0.0504322
$691$	−18.8652	−0.717665	−0.358833	−	0.933402i	$-0.616825\pi$
$691$	−18.8652	−0.717665	−0.358833	+	0.933402i	$0.616825\pi$
$692$	−21.4495	−0.815389
$693$	−9.03637	−0.343263
$694$	2.43014	0.0922469
$695$	10.2736	0.389700
$696$	4.38187	0.166094
$697$	−3.83654	−0.145319
$698$	11.8155	0.447225
$699$	3.27385	0.123828
$700$	4.08907	0.154552
$701$	21.2911	0.804155	0.402077	−	0.915606i	$-0.368288\pi$
$701$	21.2911	0.804155	0.402077	+	0.915606i	$0.368288\pi$
$702$	−16.2896	−0.614812
$703$	−27.7026	−1.04482
$704$	1.86326	0.0702243
$705$	−13.7597	−0.518222
$706$	12.9583	0.487691
$707$	−26.4543	−0.994915
$708$	6.49634	0.244147
$709$	−24.8977	−0.935052	−0.467526	−	0.883979i	$-0.654855\pi$
$709$	−24.8977	−0.935052	−0.467526	+	0.883979i	$0.654855\pi$
$710$	12.0969	0.453990
$711$	19.6904	0.738447
$712$	−3.92441	−0.147073
$713$	4.04733	0.151574
$714$	−0.353721	−0.0132377
$715$	−29.1440	−1.08992
$716$	−9.37898	−0.350509
$717$	4.61545	0.172367
$718$	−25.4169	−0.948552
$719$	−30.3358	−1.13133	−0.565667	−	0.824634i	$-0.691381\pi$
$719$	−30.3358	−1.13133	−0.565667	+	0.824634i	$0.691381\pi$
$720$	−7.47250	−0.278484
$721$	−23.8668	−0.888847
$722$	8.06628	0.300196
$723$	−10.1203	−0.376378
$724$	18.5444	0.689197
$725$	−20.8400	−0.773977
$726$	3.68425	0.136735
$727$	32.2087	1.19456	0.597278	−	0.802034i	$-0.296249\pi$
$727$	32.2087	1.19456	0.597278	+	0.802034i	$0.296249\pi$
$728$	10.1515	0.376239
$729$	−14.9136	−0.552355
$730$	36.6395	1.35609
$731$	−2.03697	−0.0753400
$732$	4.57699	0.169170
$733$	32.8486	1.21329	0.606646	−	0.794972i	$-0.292515\pi$
$733$	32.8486	1.21329	0.606646	+	0.794972i	$0.292515\pi$
$734$	−4.09411	−0.151116
$735$	−5.18440	−0.191229
$736$	−1.00000	−0.0368605
$737$	11.7152	0.431535
$738$	−25.7426	−0.947599
$739$	−52.9357	−1.94727	−0.973636	−	0.228109i	$-0.926746\pi$
$739$	−52.9357	−1.94727	−0.973636	+	0.228109i	$0.926746\pi$
$740$	22.6785	0.833680
$741$	9.35050	0.343499
$742$	−14.6448	−0.537626
$743$	35.0933	1.28745	0.643724	−	0.765258i	$-0.277388\pi$
$743$	35.0933	1.28745	0.643724	+	0.765258i	$0.277388\pi$
$744$	−1.98072	−0.0726166
$745$	48.6843	1.78365
$746$	14.1480	0.517996
$747$	−18.5331	−0.678091
$748$	0.766563	0.0280283
$749$	−6.24521	−0.228195
$750$	3.54037	0.129276
$751$	−44.5823	−1.62683	−0.813415	−	0.581684i	$-0.802394\pi$
$751$	−44.5823	−1.62683	−0.813415	+	0.581684i	$0.802394\pi$
$752$	−10.3867	−0.378764
$753$	−9.98993	−0.364053
$754$	−51.7370	−1.88415
$755$	−52.2981	−1.90332
$756$	−4.95276	−0.180130
$757$	−22.3479	−0.812248	−0.406124	−	0.913818i	$-0.633120\pi$
$757$	−22.3479	−0.812248	−0.406124	+	0.913818i	$0.633120\pi$
$758$	15.6164	0.567212
$759$	0.911859	0.0330984
$760$	8.95081	0.324680
$761$	6.77441	0.245572	0.122786	−	0.992433i	$-0.460817\pi$
$761$	6.77441	0.245572	0.122786	+	0.992433i	$0.460817\pi$
$762$	−5.01089	−0.181525
$763$	−25.7554	−0.932407
$764$	6.37074	0.230485
$765$	−3.07425	−0.111150
$766$	−21.4338	−0.774433
$767$	−76.7028	−2.76958
$768$	0.489389	0.0176593
$769$	17.2431	0.621801	0.310901	−	0.950442i	$-0.399369\pi$
$769$	17.2431	0.621801	0.310901	+	0.950442i	$0.399369\pi$
$770$	−8.86104	−0.319330
$771$	9.73791	0.350702
$772$	−7.98381	−0.287344
$773$	35.0374	1.26021	0.630105	−	0.776510i	$-0.283012\pi$
$773$	35.0374	1.26021	0.630105	+	0.776510i	$0.283012\pi$
$774$	−13.6678	−0.491278
$775$	9.42020	0.338384
$776$	9.59770	0.344537
$777$	7.20317	0.258412
$778$	10.1472	0.363796
$779$	30.8354	1.10479
$780$	−7.65472	−0.274083
$781$	−8.32666	−0.297951
$782$	−0.411409	−0.0147120
$783$	25.2417	0.902066
$784$	−3.91351	−0.139768
$785$	−3.69294	−0.131807
$786$	−0.489389	−0.0174559
$787$	14.7753	0.526684	0.263342	−	0.964703i	$-0.415175\pi$
$787$	14.7753	0.526684	0.263342	+	0.964703i	$0.415175\pi$
$788$	−18.6150	−0.663131
$789$	−11.3734	−0.404904
$790$	19.3083	0.686960
$791$	−26.7611	−0.951516
$792$	5.14353	0.182767
$793$	−54.0409	−1.91905
$794$	−7.32012	−0.259781
$795$	11.0429	0.391650
$796$	1.98994	0.0705316
$797$	−12.6253	−0.447210	−0.223605	−	0.974680i	$-0.571783\pi$
$797$	−12.6253	−0.447210	−0.223605	+	0.974680i	$0.571783\pi$
$798$	2.84296	0.100640
$799$	−4.27319	−0.151175
$800$	−2.32751	−0.0822900
$801$	−10.8333	−0.382777
$802$	−16.9234	−0.597586
$803$	−25.2200	−0.889995
$804$	3.07702	0.108518
$805$	4.75566	0.167615
$806$	23.3865	0.823754
$807$	−7.07832	−0.249169
$808$	15.0579	0.529733
$809$	43.6519	1.53472	0.767359	−	0.641217i	$-0.221570\pi$
$809$	43.6519	1.53472	0.767359	+	0.641217i	$0.221570\pi$
$810$	−18.6829	−0.656449
$811$	29.0471	1.01998	0.509992	−	0.860179i	$-0.329649\pi$
$811$	29.0471	1.01998	0.509992	+	0.860179i	$0.329649\pi$
$812$	−15.7303	−0.552026
$813$	−7.12323	−0.249823
$814$	−15.6103	−0.547140
$815$	32.4157	1.13547
$816$	0.201339	0.00704828
$817$	16.3717	0.572774
$818$	−2.23908	−0.0782876
$819$	28.0232	0.979208
$820$	−25.2432	−0.881529
$821$	26.1466	0.912524	0.456262	−	0.889845i	$-0.349188\pi$
$821$	26.1466	0.912524	0.456262	+	0.889845i	$0.349188\pi$
$822$	5.33603	0.186115
$823$	10.4056	0.362716	0.181358	−	0.983417i	$-0.441951\pi$
$823$	10.4056	0.362716	0.181358	+	0.983417i	$0.441951\pi$
$824$	13.5851	0.473258
$825$	2.12236	0.0738912
$826$	−23.3210	−0.811441
$827$	−9.15527	−0.318360	−0.159180	−	0.987250i	$-0.550885\pi$
$827$	−9.15527	−0.318360	−0.159180	+	0.987250i	$0.550885\pi$
$828$	−2.76050	−0.0959340
$829$	49.3509	1.71403	0.857015	−	0.515292i	$-0.172317\pi$
$829$	49.3509	1.71403	0.857015	+	0.515292i	$0.172317\pi$
$830$	−18.1735	−0.630812
$831$	6.84363	0.237403
$832$	−5.77826	−0.200325
$833$	−1.61005	−0.0557850
$834$	−1.85737	−0.0643155
$835$	−22.1004	−0.764814
$836$	−6.16109	−0.213086
$837$	−11.4099	−0.394385
$838$	7.44628	0.257227
$839$	−44.8551	−1.54857	−0.774286	−	0.632836i	$-0.781891\pi$
$839$	−44.8551	−1.54857	−0.774286	+	0.632836i	$0.781891\pi$
$840$	−2.32737	−0.0803019
$841$	51.1696	1.76447
$842$	−22.1005	−0.761632
$843$	1.17777	0.0405644
$844$	27.2622	0.938404
$845$	55.1897	1.89858
$846$	−28.6725	−0.985781
$847$	−13.2260	−0.454449
$848$	8.33584	0.286254
$849$	0.495507	0.0170057
$850$	−0.957560	−0.0328440
$851$	8.37793	0.287192
$852$	−2.18701	−0.0749258
$853$	12.5232	0.428787	0.214393	−	0.976747i	$-0.431223\pi$
$853$	12.5232	0.428787	0.214393	+	0.976747i	$0.431223\pi$
$854$	−16.4308	−0.562250
$855$	24.7087	0.845019
$856$	3.55479	0.121500
$857$	9.14815	0.312495	0.156247	−	0.987718i	$-0.450060\pi$
$857$	9.14815	0.312495	0.156247	+	0.987718i	$0.450060\pi$
$858$	5.26896	0.179879
$859$	−7.95805	−0.271525	−0.135763	−	0.990741i	$-0.543348\pi$
$859$	−7.95805	−0.271525	−0.135763	+	0.990741i	$0.543348\pi$
$860$	−13.4026	−0.457024
$861$	−8.01775	−0.273244
$862$	11.7617	0.400604
$863$	−7.31829	−0.249117	−0.124559	−	0.992212i	$-0.539752\pi$
$863$	−7.31829	−0.249117	−0.124559	+	0.992212i	$0.539752\pi$
$864$	2.81912	0.0959086
$865$	−58.0626	−1.97419
$866$	17.0115	0.578074
$867$	−8.23678	−0.279736
$868$	7.11052	0.241347
$869$	−13.2905	−0.450848
$870$	11.8614	0.402140
$871$	−36.3307	−1.23102
$872$	14.6600	0.496451
$873$	26.4944	0.896701
$874$	3.30662	0.111848
$875$	−12.7095	−0.429658
$876$	−6.62408	−0.223807
$877$	−34.1203	−1.15216	−0.576080	−	0.817393i	$-0.695418\pi$
$877$	−34.1203	−1.15216	−0.576080	+	0.817393i	$0.695418\pi$
$878$	−37.3642	−1.26098
$879$	2.80801	0.0947118
$880$	5.04373	0.170024
$881$	24.4209	0.822760	0.411380	−	0.911464i	$-0.365047\pi$
$881$	24.4209	0.822760	0.411380	+	0.911464i	$0.365047\pi$
$882$	−10.8032	−0.363764
$883$	−31.1626	−1.04870	−0.524352	−	0.851502i	$-0.675692\pi$
$883$	−31.1626	−1.04870	−0.524352	+	0.851502i	$0.675692\pi$
$884$	−2.37723	−0.0799548
$885$	17.5852	0.591119
$886$	−16.4430	−0.552414
$887$	56.1470	1.88523	0.942616	−	0.333880i	$-0.108358\pi$
$887$	56.1470	1.88523	0.942616	+	0.333880i	$0.108358\pi$
$888$	−4.10007	−0.137589
$889$	17.9884	0.603313
$890$	−10.6231	−0.356088
$891$	12.8599	0.430824
$892$	17.9483	0.600955
$893$	34.3449	1.14931
$894$	−8.80167	−0.294372
$895$	−25.3883	−0.848637
$896$	−1.75684	−0.0586920
$897$	−2.82781	−0.0944180
$898$	−13.3905	−0.446848
$899$	−36.2388	−1.20863
$900$	−6.42509	−0.214170
$901$	3.42944	0.114251
$902$	17.3756	0.578543
$903$	−4.25694	−0.141662
$904$	15.2325	0.506626
$905$	50.1985	1.66865
$906$	9.45500	0.314121
$907$	−54.1884	−1.79930	−0.899648	−	0.436616i	$-0.856177\pi$
$907$	−54.1884	−1.79930	−0.899648	+	0.436616i	$0.856177\pi$
$908$	18.9955	0.630388
$909$	41.5672	1.37870
$910$	27.4794	0.910934
$911$	−49.4517	−1.63841	−0.819203	−	0.573503i	$-0.805584\pi$
$911$	−49.4517	−1.63841	−0.819203	+	0.573503i	$0.805584\pi$
$912$	−1.61822	−0.0535847
$913$	12.5093	0.413999
$914$	7.64751	0.252957
$915$	12.3896	0.409588
$916$	21.4469	0.708627
$917$	1.75684	0.0580160
$918$	1.15981	0.0382796
$919$	14.6614	0.483635	0.241818	−	0.970322i	$-0.422256\pi$
$919$	14.6614	0.483635	0.241818	+	0.970322i	$0.422256\pi$
$920$	−2.70694	−0.0892451
$921$	5.94044	0.195744
$922$	26.6413	0.877385
$923$	25.8222	0.849949
$924$	1.60199	0.0527017
$925$	19.4997	0.641147
$926$	10.0154	0.329126
$927$	37.5016	1.23171
$928$	8.95375	0.293921
$929$	4.63009	0.151908	0.0759541	−	0.997111i	$-0.475800\pi$
$929$	4.63009	0.151908	0.0759541	+	0.997111i	$0.475800\pi$
$930$	−5.36168	−0.175816
$931$	12.9405	0.424107
$932$	6.68967	0.219127
$933$	−3.65445	−0.119641
$934$	−13.7640	−0.450371
$935$	2.07504	0.0678610
$936$	−15.9509	−0.521370
$937$	−23.2690	−0.760165	−0.380082	−	0.924953i	$-0.624104\pi$
$937$	−23.2690	−0.760165	−0.380082	+	0.924953i	$0.624104\pi$
$938$	−11.0461	−0.360668
$939$	−7.93070	−0.258809
$940$	−28.1162	−0.917049
$941$	−27.5790	−0.899051	−0.449526	−	0.893267i	$-0.648407\pi$
$941$	−27.5790	−0.899051	−0.449526	+	0.893267i	$0.648407\pi$
$942$	0.667650	0.0217532
$943$	−9.32536	−0.303675
$944$	13.2744	0.432044
$945$	−13.4068	−0.436123
$946$	9.22537	0.299943
$947$	−21.0274	−0.683298	−0.341649	−	0.939828i	$-0.610985\pi$
$947$	−21.0274	−0.683298	−0.341649	+	0.939828i	$0.610985\pi$
$948$	−3.49077	−0.113375
$949$	78.2111	2.53884
$950$	7.69619	0.249697
$951$	15.5250	0.503433
$952$	−0.722781	−0.0234255
$953$	19.9440	0.646050	0.323025	−	0.946390i	$-0.395300\pi$
$953$	19.9440	0.646050	0.323025	+	0.946390i	$0.395300\pi$
$954$	23.0111	0.745011
$955$	17.2452	0.558041
$956$	9.43105	0.305022
$957$	−8.16456	−0.263923
$958$	15.1671	0.490028
$959$	−19.1557	−0.618568
$960$	1.32475	0.0427560
$961$	−14.6191	−0.471585
$962$	48.4098	1.56080
$963$	9.81300	0.316220
$964$	−20.6794	−0.666040
$965$	−21.6117	−0.695704
$966$	−0.859779	−0.0276629
$967$	3.81629	0.122724	0.0613618	−	0.998116i	$-0.480456\pi$
$967$	3.81629	0.122724	0.0613618	+	0.998116i	$0.480456\pi$
$968$	7.52826	0.241967
$969$	−0.665751	−0.0213870
$970$	25.9804	0.834180
$971$	5.44289	0.174671	0.0873353	−	0.996179i	$-0.472165\pi$
$971$	5.44289	0.174671	0.0873353	+	0.996179i	$0.472165\pi$
$972$	11.8351	0.379610
$973$	6.66772	0.213757
$974$	31.5734	1.01168
$975$	−6.58177	−0.210785
$976$	9.35245	0.299365
$977$	15.7503	0.503896	0.251948	−	0.967741i	$-0.418929\pi$
$977$	15.7503	0.503896	0.251948	+	0.967741i	$0.418929\pi$
$978$	−5.86046	−0.187397
$979$	7.31220	0.233699
$980$	−10.5936	−0.338401
$981$	40.4690	1.29208
$982$	7.35504	0.234709
$983$	52.0544	1.66028	0.830140	−	0.557556i	$-0.188261\pi$
$983$	52.0544	1.66028	0.830140	+	0.557556i	$0.188261\pi$
$984$	4.56373	0.145486
$985$	−50.3896	−1.60555
$986$	3.68365	0.117311
$987$	−8.93028	−0.284254
$988$	19.1065	0.607858
$989$	−4.95120	−0.157439
$990$	13.9232	0.442509
$991$	−20.9966	−0.666978	−0.333489	−	0.942754i	$-0.608226\pi$
$991$	−20.9966	−0.666978	−0.333489	+	0.942754i	$0.608226\pi$
$992$	−4.04733	−0.128503
$993$	6.18985	0.196429
$994$	7.85109	0.249021
$995$	5.38665	0.170768
$996$	3.28560	0.104108
$997$	−21.9383	−0.694793	−0.347396	−	0.937718i	$-0.612934\pi$
$997$	−21.9383	−0.694793	−0.347396	+	0.937718i	$0.612934\pi$
$998$	38.9889	1.23417
$999$	−23.6184	−0.747254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.15	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.489389 q^{3} +1.00000 q^{4} +2.70694 q^{5} -0.489389 q^{6} +1.75684 q^{7} -1.00000 q^{8} -2.76050 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.489389 q^{3} +1.00000 q^{4} +2.70694 q^{5} -0.489389 q^{6} +1.75684 q^{7} -1.00000 q^{8} -2.76050 q^{9} -2.70694 q^{10} +1.86326 q^{11} +0.489389 q^{12} -5.77826 q^{13} -1.75684 q^{14} +1.32475 q^{15} +1.00000 q^{16} +0.411409 q^{17} +2.76050 q^{18} -3.30662 q^{19} +2.70694 q^{20} +0.859779 q^{21} -1.86326 q^{22} +1.00000 q^{23} -0.489389 q^{24} +2.32751 q^{25} +5.77826 q^{26} -2.81912 q^{27} +1.75684 q^{28} -8.95375 q^{29} -1.32475 q^{30} +4.04733 q^{31} -1.00000 q^{32} +0.911859 q^{33} -0.411409 q^{34} +4.75566 q^{35} -2.76050 q^{36} +8.37793 q^{37} +3.30662 q^{38} -2.82781 q^{39} -2.70694 q^{40} -9.32536 q^{41} -0.859779 q^{42} -4.95120 q^{43} +1.86326 q^{44} -7.47250 q^{45} -1.00000 q^{46} -10.3867 q^{47} +0.489389 q^{48} -3.91351 q^{49} -2.32751 q^{50} +0.201339 q^{51} -5.77826 q^{52} +8.33584 q^{53} +2.81912 q^{54} +5.04373 q^{55} -1.75684 q^{56} -1.61822 q^{57} +8.95375 q^{58} +13.2744 q^{59} +1.32475 q^{60} +9.35245 q^{61} -4.04733 q^{62} -4.84976 q^{63} +1.00000 q^{64} -15.6414 q^{65} -0.911859 q^{66} +6.28748 q^{67} +0.411409 q^{68} +0.489389 q^{69} -4.75566 q^{70} -4.46886 q^{71} +2.76050 q^{72} -13.5354 q^{73} -8.37793 q^{74} +1.13906 q^{75} -3.30662 q^{76} +3.27346 q^{77} +2.82781 q^{78} -7.13291 q^{79} +2.70694 q^{80} +6.90185 q^{81} +9.32536 q^{82} +6.71368 q^{83} +0.859779 q^{84} +1.11366 q^{85} +4.95120 q^{86} -4.38187 q^{87} -1.86326 q^{88} +3.92441 q^{89} +7.47250 q^{90} -10.1515 q^{91} +1.00000 q^{92} +1.98072 q^{93} +10.3867 q^{94} -8.95081 q^{95} -0.489389 q^{96} -9.59770 q^{97} +3.91351 q^{98} -5.14353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more