LMFDB - Embedded newform 6034.2.a.o.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.28274 q^{3} +1.00000 q^{4} -1.76478 q^{5} +1.28274 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.35459 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.28274 q^{3} +1.00000 q^{4} -1.76478 q^{5} +1.28274 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.35459 q^{9} +1.76478 q^{10} +2.36672 q^{11} -1.28274 q^{12} +4.94017 q^{13} +1.00000 q^{14} +2.26375 q^{15} +1.00000 q^{16} -5.35042 q^{17} +1.35459 q^{18} -3.39930 q^{19} -1.76478 q^{20} +1.28274 q^{21} -2.36672 q^{22} -1.24459 q^{23} +1.28274 q^{24} -1.88554 q^{25} -4.94017 q^{26} +5.58579 q^{27} -1.00000 q^{28} +3.78205 q^{29} -2.26375 q^{30} +7.86724 q^{31} -1.00000 q^{32} -3.03588 q^{33} +5.35042 q^{34} +1.76478 q^{35} -1.35459 q^{36} -2.11108 q^{37} +3.39930 q^{38} -6.33694 q^{39} +1.76478 q^{40} -6.47654 q^{41} -1.28274 q^{42} -3.36808 q^{43} +2.36672 q^{44} +2.39055 q^{45} +1.24459 q^{46} +7.31384 q^{47} -1.28274 q^{48} +1.00000 q^{49} +1.88554 q^{50} +6.86318 q^{51} +4.94017 q^{52} -6.54196 q^{53} -5.58579 q^{54} -4.17675 q^{55} +1.00000 q^{56} +4.36040 q^{57} -3.78205 q^{58} -4.49931 q^{59} +2.26375 q^{60} -1.67013 q^{61} -7.86724 q^{62} +1.35459 q^{63} +1.00000 q^{64} -8.71833 q^{65} +3.03588 q^{66} +15.0278 q^{67} -5.35042 q^{68} +1.59648 q^{69} -1.76478 q^{70} +0.648743 q^{71} +1.35459 q^{72} +15.2602 q^{73} +2.11108 q^{74} +2.41865 q^{75} -3.39930 q^{76} -2.36672 q^{77} +6.33694 q^{78} -1.47332 q^{79} -1.76478 q^{80} -3.10134 q^{81} +6.47654 q^{82} -0.837870 q^{83} +1.28274 q^{84} +9.44234 q^{85} +3.36808 q^{86} -4.85138 q^{87} -2.36672 q^{88} -0.643328 q^{89} -2.39055 q^{90} -4.94017 q^{91} -1.24459 q^{92} -10.0916 q^{93} -7.31384 q^{94} +5.99902 q^{95} +1.28274 q^{96} -16.5885 q^{97} -1.00000 q^{98} -3.20593 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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
$3$	−1.28274	−0.740589	−0.370294	−	0.928914i	$-0.620743\pi$
$3$	−1.28274	−0.740589	−0.370294	+	0.928914i	$0.620743\pi$
$4$	1.00000	0.500000
$5$	−1.76478	−0.789235	−0.394618	−	0.918845i	$-0.629123\pi$
$5$	−1.76478	−0.789235	−0.394618	+	0.918845i	$0.629123\pi$
$6$	1.28274	0.523675
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−1.35459	−0.451529
$10$	1.76478	0.558074
$11$	2.36672	0.713593	0.356796	−	0.934182i	$-0.383869\pi$
$11$	2.36672	0.713593	0.356796	+	0.934182i	$0.383869\pi$
$12$	−1.28274	−0.370294
$13$	4.94017	1.37016	0.685078	−	0.728470i	$-0.259768\pi$
$13$	4.94017	1.37016	0.685078	+	0.728470i	$0.259768\pi$
$14$	1.00000	0.267261
$15$	2.26375	0.584499
$16$	1.00000	0.250000
$17$	−5.35042	−1.29767	−0.648834	−	0.760930i	$-0.724743\pi$
$17$	−5.35042	−1.29767	−0.648834	+	0.760930i	$0.724743\pi$
$18$	1.35459	0.319279
$19$	−3.39930	−0.779852	−0.389926	−	0.920846i	$-0.627499\pi$
$19$	−3.39930	−0.779852	−0.389926	+	0.920846i	$0.627499\pi$
$20$	−1.76478	−0.394618
$21$	1.28274	0.279916
$22$	−2.36672	−0.504586
$23$	−1.24459	−0.259514	−0.129757	−	0.991546i	$-0.541420\pi$
$23$	−1.24459	−0.259514	−0.129757	+	0.991546i	$0.541420\pi$
$24$	1.28274	0.261838
$25$	−1.88554	−0.377108
$26$	−4.94017	−0.968847
$27$	5.58579	1.07499
$28$	−1.00000	−0.188982
$29$	3.78205	0.702310	0.351155	−	0.936317i	$-0.385789\pi$
$29$	3.78205	0.702310	0.351155	+	0.936317i	$0.385789\pi$
$30$	−2.26375	−0.413303
$31$	7.86724	1.41300	0.706499	−	0.707714i	$-0.250274\pi$
$31$	7.86724	1.41300	0.706499	+	0.707714i	$0.250274\pi$
$32$	−1.00000	−0.176777
$33$	−3.03588	−0.528479
$34$	5.35042	0.917590
$35$	1.76478	0.298303
$36$	−1.35459	−0.225764
$37$	−2.11108	−0.347060	−0.173530	−	0.984829i	$-0.555517\pi$
$37$	−2.11108	−0.347060	−0.173530	+	0.984829i	$0.555517\pi$
$38$	3.39930	0.551439
$39$	−6.33694	−1.01472
$40$	1.76478	0.279037
$41$	−6.47654	−1.01147	−0.505733	−	0.862690i	$-0.668778\pi$
$41$	−6.47654	−1.01147	−0.505733	+	0.862690i	$0.668778\pi$
$42$	−1.28274	−0.197931
$43$	−3.36808	−0.513628	−0.256814	−	0.966461i	$-0.582673\pi$
$43$	−3.36808	−0.513628	−0.256814	+	0.966461i	$0.582673\pi$
$44$	2.36672	0.356796
$45$	2.39055	0.356362
$46$	1.24459	0.183504
$47$	7.31384	1.06683	0.533417	−	0.845852i	$-0.320908\pi$
$47$	7.31384	1.06683	0.533417	+	0.845852i	$0.320908\pi$
$48$	−1.28274	−0.185147
$49$	1.00000	0.142857
$50$	1.88554	0.266656
$51$	6.86318	0.961038
$52$	4.94017	0.685078
$53$	−6.54196	−0.898608	−0.449304	−	0.893379i	$-0.648328\pi$
$53$	−6.54196	−0.898608	−0.449304	+	0.893379i	$0.648328\pi$
$54$	−5.58579	−0.760130
$55$	−4.17675	−0.563193
$56$	1.00000	0.133631
$57$	4.36040	0.577549
$58$	−3.78205	−0.496608
$59$	−4.49931	−0.585760	−0.292880	−	0.956149i	$-0.594614\pi$
$59$	−4.49931	−0.585760	−0.292880	+	0.956149i	$0.594614\pi$
$60$	2.26375	0.292249
$61$	−1.67013	−0.213839	−0.106919	−	0.994268i	$-0.534099\pi$
$61$	−1.67013	−0.213839	−0.106919	+	0.994268i	$0.534099\pi$
$62$	−7.86724	−0.999140
$63$	1.35459	0.170662
$64$	1.00000	0.125000
$65$	−8.71833	−1.08138
$66$	3.03588	0.373691
$67$	15.0278	1.83594	0.917970	−	0.396650i	$-0.129827\pi$
$67$	15.0278	1.83594	0.917970	+	0.396650i	$0.129827\pi$
$68$	−5.35042	−0.648834
$69$	1.59648	0.192193
$70$	−1.76478	−0.210932
$71$	0.648743	0.0769917	0.0384958	−	0.999259i	$-0.487743\pi$
$71$	0.648743	0.0769917	0.0384958	+	0.999259i	$0.487743\pi$
$72$	1.35459	0.159639
$73$	15.2602	1.78608	0.893038	−	0.449982i	$-0.148570\pi$
$73$	15.2602	1.78608	0.893038	+	0.449982i	$0.148570\pi$
$74$	2.11108	0.245408
$75$	2.41865	0.279282
$76$	−3.39930	−0.389926
$77$	−2.36672	−0.269713
$78$	6.33694	0.717517
$79$	−1.47332	−0.165761	−0.0828807	−	0.996559i	$-0.526412\pi$
$79$	−1.47332	−0.165761	−0.0828807	+	0.996559i	$0.526412\pi$
$80$	−1.76478	−0.197309
$81$	−3.10134	−0.344593
$82$	6.47654	0.715214
$83$	−0.837870	−0.0919682	−0.0459841	−	0.998942i	$-0.514642\pi$
$83$	−0.837870	−0.0919682	−0.0459841	+	0.998942i	$0.514642\pi$
$84$	1.28274	0.139958
$85$	9.44234	1.02417
$86$	3.36808	0.363190
$87$	−4.85138	−0.520123
$88$	−2.36672	−0.252293
$89$	−0.643328	−0.0681927	−0.0340963	−	0.999419i	$-0.510855\pi$
$89$	−0.643328	−0.0681927	−0.0340963	+	0.999419i	$0.510855\pi$
$90$	−2.39055	−0.251986
$91$	−4.94017	−0.517870
$92$	−1.24459	−0.129757
$93$	−10.0916	−1.04645
$94$	−7.31384	−0.754365
$95$	5.99902	0.615486
$96$	1.28274	0.130919
$97$	−16.5885	−1.68431	−0.842153	−	0.539239i	$-0.818712\pi$
$97$	−16.5885	−1.68431	−0.842153	+	0.539239i	$0.818712\pi$
$98$	−1.00000	−0.101015
$99$	−3.20593	−0.322208
$100$	−1.88554	−0.188554
$101$	6.91224	0.687794	0.343897	−	0.939007i	$-0.388253\pi$
$101$	6.91224	0.687794	0.343897	+	0.939007i	$0.388253\pi$
$102$	−6.86318	−0.679556
$103$	14.0029	1.37974	0.689872	−	0.723931i	$-0.257667\pi$
$103$	14.0029	1.37974	0.689872	+	0.723931i	$0.257667\pi$
$104$	−4.94017	−0.484423
$105$	−2.26375	−0.220920
$106$	6.54196	0.635412
$107$	−11.0683	−1.07001	−0.535006	−	0.844848i	$-0.679691\pi$
$107$	−11.0683	−1.07001	−0.535006	+	0.844848i	$0.679691\pi$
$108$	5.58579	0.537493
$109$	19.5719	1.87464	0.937322	−	0.348464i	$-0.113297\pi$
$109$	19.5719	1.87464	0.937322	+	0.348464i	$0.113297\pi$
$110$	4.17675	0.398237
$111$	2.70796	0.257029
$112$	−1.00000	−0.0944911
$113$	4.86853	0.457993	0.228996	−	0.973427i	$-0.426456\pi$
$113$	4.86853	0.457993	0.228996	+	0.973427i	$0.426456\pi$
$114$	−4.36040	−0.408389
$115$	2.19643	0.204818
$116$	3.78205	0.351155
$117$	−6.69188	−0.618665
$118$	4.49931	0.414195
$119$	5.35042	0.490472
$120$	−2.26375	−0.206651
$121$	−5.39864	−0.490785
$122$	1.67013	0.151207
$123$	8.30770	0.749080
$124$	7.86724	0.706499
$125$	12.1515	1.08686
$126$	−1.35459	−0.120676
$127$	15.6595	1.38955	0.694777	−	0.719226i	$-0.255503\pi$
$127$	15.6595	1.38955	0.694777	+	0.719226i	$0.255503\pi$
$128$	−1.00000	−0.0883883
$129$	4.32037	0.380387
$130$	8.71833	0.764648
$131$	−4.65890	−0.407050	−0.203525	−	0.979070i	$-0.565240\pi$
$131$	−4.65890	−0.407050	−0.203525	+	0.979070i	$0.565240\pi$
$132$	−3.03588	−0.264239
$133$	3.39930	0.294756
$134$	−15.0278	−1.29821
$135$	−9.85771	−0.848416
$136$	5.35042	0.458795
$137$	18.0724	1.54403	0.772015	−	0.635604i	$-0.219249\pi$
$137$	18.0724	1.54403	0.772015	+	0.635604i	$0.219249\pi$
$138$	−1.59648	−0.135901
$139$	−13.0157	−1.10398	−0.551988	−	0.833852i	$-0.686131\pi$
$139$	−13.0157	−1.10398	−0.551988	+	0.833852i	$0.686131\pi$
$140$	1.76478	0.149151
$141$	−9.38174	−0.790085
$142$	−0.648743	−0.0544413
$143$	11.6920	0.977734
$144$	−1.35459	−0.112882
$145$	−6.67451	−0.554288
$146$	−15.2602	−1.26295
$147$	−1.28274	−0.105798
$148$	−2.11108	−0.173530
$149$	−8.77608	−0.718965	−0.359482	−	0.933152i	$-0.617047\pi$
$149$	−8.77608	−0.718965	−0.359482	+	0.933152i	$0.617047\pi$
$150$	−2.41865	−0.197482
$151$	−19.4312	−1.58129	−0.790645	−	0.612275i	$-0.790254\pi$
$151$	−19.4312	−1.58129	−0.790645	+	0.612275i	$0.790254\pi$
$152$	3.39930	0.275719
$153$	7.24760	0.585934
$154$	2.36672	0.190716
$155$	−13.8840	−1.11519
$156$	−6.33694	−0.507361
$157$	−13.7910	−1.10064	−0.550321	−	0.834953i	$-0.685495\pi$
$157$	−13.7910	−1.10064	−0.550321	+	0.834953i	$0.685495\pi$
$158$	1.47332	0.117211
$159$	8.39162	0.665499
$160$	1.76478	0.139518
$161$	1.24459	0.0980872
$162$	3.10134	0.243664
$163$	−11.4558	−0.897291	−0.448646	−	0.893710i	$-0.648093\pi$
$163$	−11.4558	−0.897291	−0.448646	+	0.893710i	$0.648093\pi$
$164$	−6.47654	−0.505733
$165$	5.35767	0.417094
$166$	0.837870	0.0650314
$167$	10.3489	0.800821	0.400411	−	0.916336i	$-0.368867\pi$
$167$	10.3489	0.800821	0.400411	+	0.916336i	$0.368867\pi$
$168$	−1.28274	−0.0989653
$169$	11.4053	0.877328
$170$	−9.44234	−0.724194
$171$	4.60464	0.352125
$172$	−3.36808	−0.256814
$173$	−10.2289	−0.777687	−0.388844	−	0.921304i	$-0.627125\pi$
$173$	−10.2289	−0.777687	−0.388844	+	0.921304i	$0.627125\pi$
$174$	4.85138	0.367782
$175$	1.88554	0.142533
$176$	2.36672	0.178398
$177$	5.77143	0.433807
$178$	0.643328	0.0482195
$179$	10.5878	0.791371	0.395686	−	0.918386i	$-0.370507\pi$
$179$	10.5878	0.791371	0.395686	+	0.918386i	$0.370507\pi$
$180$	2.39055	0.178181
$181$	1.37579	0.102262	0.0511308	−	0.998692i	$-0.483717\pi$
$181$	1.37579	0.102262	0.0511308	+	0.998692i	$0.483717\pi$
$182$	4.94017	0.366190
$183$	2.14234	0.158367
$184$	1.24459	0.0917522
$185$	3.72560	0.273912
$186$	10.0916	0.739952
$187$	−12.6630	−0.926007
$188$	7.31384	0.533417
$189$	−5.58579	−0.406306
$190$	−5.99902	−0.435215
$191$	16.0093	1.15839	0.579195	−	0.815189i	$-0.303367\pi$
$191$	16.0093	1.15839	0.579195	+	0.815189i	$0.303367\pi$
$192$	−1.28274	−0.0925736
$193$	26.4523	1.90408	0.952041	−	0.305972i	$-0.0989814\pi$
$193$	26.4523	1.90408	0.952041	+	0.305972i	$0.0989814\pi$
$194$	16.5885	1.19098
$195$	11.1833	0.800854
$196$	1.00000	0.0714286
$197$	16.5486	1.17904	0.589521	−	0.807753i	$-0.299317\pi$
$197$	16.5486	1.17904	0.589521	+	0.807753i	$0.299317\pi$
$198$	3.20593	0.227835
$199$	−23.8069	−1.68763	−0.843814	−	0.536635i	$-0.819695\pi$
$199$	−23.8069	−1.68763	−0.843814	+	0.536635i	$0.819695\pi$
$200$	1.88554	0.133328
$201$	−19.2767	−1.35968
$202$	−6.91224	−0.486344
$203$	−3.78205	−0.265448
$204$	6.86318	0.480519
$205$	11.4297	0.798285
$206$	−14.0029	−0.975626
$207$	1.68590	0.117178
$208$	4.94017	0.342539
$209$	−8.04518	−0.556497
$210$	2.26375	0.156214
$211$	−4.20544	−0.289514	−0.144757	−	0.989467i	$-0.546240\pi$
$211$	−4.20544	−0.289514	−0.144757	+	0.989467i	$0.546240\pi$
$212$	−6.54196	−0.449304
$213$	−0.832167	−0.0570192
$214$	11.0683	0.756612
$215$	5.94394	0.405373
$216$	−5.58579	−0.380065
$217$	−7.86724	−0.534063
$218$	−19.5719	−1.32557
$219$	−19.5749	−1.32275
$220$	−4.17675	−0.281596
$221$	−26.4320	−1.77801
$222$	−2.70796	−0.181747
$223$	18.9711	1.27040	0.635198	−	0.772349i	$-0.280919\pi$
$223$	18.9711	1.27040	0.635198	+	0.772349i	$0.280919\pi$
$224$	1.00000	0.0668153
$225$	2.55412	0.170275
$226$	−4.86853	−0.323850
$227$	−26.8122	−1.77959	−0.889794	−	0.456363i	$-0.849152\pi$
$227$	−26.8122	−1.77959	−0.889794	+	0.456363i	$0.849152\pi$
$228$	4.36040	0.288775
$229$	−18.5409	−1.22522	−0.612609	−	0.790386i	$-0.709880\pi$
$229$	−18.5409	−1.22522	−0.612609	+	0.790386i	$0.709880\pi$
$230$	−2.19643	−0.144828
$231$	3.03588	0.199746
$232$	−3.78205	−0.248304
$233$	−6.06736	−0.397486	−0.198743	−	0.980052i	$-0.563686\pi$
$233$	−6.06736	−0.397486	−0.198743	+	0.980052i	$0.563686\pi$
$234$	6.69188	0.437462
$235$	−12.9074	−0.841983
$236$	−4.49931	−0.292880
$237$	1.88988	0.122761
$238$	−5.35042	−0.346816
$239$	9.17090	0.593216	0.296608	−	0.954999i	$-0.404145\pi$
$239$	9.17090	0.593216	0.296608	+	0.954999i	$0.404145\pi$
$240$	2.26375	0.146125
$241$	2.12269	0.136735	0.0683673	−	0.997660i	$-0.478221\pi$
$241$	2.12269	0.136735	0.0683673	+	0.997660i	$0.478221\pi$
$242$	5.39864	0.347037
$243$	−12.7792	−0.819784
$244$	−1.67013	−0.106919
$245$	−1.76478	−0.112748
$246$	−8.30770	−0.529680
$247$	−16.7931	−1.06852
$248$	−7.86724	−0.499570
$249$	1.07477	0.0681106
$250$	−12.1515	−0.768527
$251$	−13.0219	−0.821933	−0.410966	−	0.911651i	$-0.634809\pi$
$251$	−13.0219	−0.821933	−0.410966	+	0.911651i	$0.634809\pi$
$252$	1.35459	0.0853309
$253$	−2.94559	−0.185188
$254$	−15.6595	−0.982563
$255$	−12.1120	−0.758485
$256$	1.00000	0.0625000
$257$	−22.9745	−1.43311	−0.716556	−	0.697530i	$-0.754283\pi$
$257$	−22.9745	−1.43311	−0.716556	+	0.697530i	$0.754283\pi$
$258$	−4.32037	−0.268974
$259$	2.11108	0.131176
$260$	−8.71833	−0.540688
$261$	−5.12312	−0.317113
$262$	4.65890	0.287828
$263$	−21.4910	−1.32519	−0.662597	−	0.748976i	$-0.730546\pi$
$263$	−21.4910	−1.32519	−0.662597	+	0.748976i	$0.730546\pi$
$264$	3.03588	0.186845
$265$	11.5451	0.709213
$266$	−3.39930	−0.208424
$267$	0.825221	0.0505027
$268$	15.0278	0.917970
$269$	8.05620	0.491195	0.245598	−	0.969372i	$-0.421016\pi$
$269$	8.05620	0.491195	0.245598	+	0.969372i	$0.421016\pi$
$270$	9.85771	0.599921
$271$	4.13954	0.251459	0.125730	−	0.992065i	$-0.459873\pi$
$271$	4.13954	0.251459	0.125730	+	0.992065i	$0.459873\pi$
$272$	−5.35042	−0.324417
$273$	6.33694	0.383529
$274$	−18.0724	−1.09179
$275$	−4.46254	−0.269102
$276$	1.59648	0.0960967
$277$	20.4894	1.23109	0.615545	−	0.788102i	$-0.288936\pi$
$277$	20.4894	1.23109	0.615545	+	0.788102i	$0.288936\pi$
$278$	13.0157	0.780629
$279$	−10.6568	−0.638009
$280$	−1.76478	−0.105466
$281$	−31.8472	−1.89985	−0.949923	−	0.312484i	$-0.898839\pi$
$281$	−31.8472	−1.89985	−0.949923	+	0.312484i	$0.898839\pi$
$282$	9.38174	0.558674
$283$	−3.26317	−0.193975	−0.0969875	−	0.995286i	$-0.530921\pi$
$283$	−3.26317	−0.193975	−0.0969875	+	0.995286i	$0.530921\pi$
$284$	0.648743	0.0384958
$285$	−7.69517	−0.455822
$286$	−11.6920	−0.691362
$287$	6.47654	0.382298
$288$	1.35459	0.0798197
$289$	11.6270	0.683942
$290$	6.67451	0.391941
$291$	21.2787	1.24738
$292$	15.2602	0.893038
$293$	−13.0408	−0.761854	−0.380927	−	0.924605i	$-0.624395\pi$
$293$	−13.0408	−0.761854	−0.380927	+	0.924605i	$0.624395\pi$
$294$	1.28274	0.0748107
$295$	7.94031	0.462303
$296$	2.11108	0.122704
$297$	13.2200	0.767102
$298$	8.77608	0.508385
$299$	−6.14847	−0.355575
$300$	2.41865	0.139641
$301$	3.36808	0.194133
$302$	19.4312	1.11814
$303$	−8.86659	−0.509372
$304$	−3.39930	−0.194963
$305$	2.94743	0.168769
$306$	−7.24760	−0.414318
$307$	−23.2581	−1.32741	−0.663706	−	0.747994i	$-0.731017\pi$
$307$	−23.2581	−1.32741	−0.663706	+	0.747994i	$0.731017\pi$
$308$	−2.36672	−0.134856
$309$	−17.9620	−1.02182
$310$	13.8840	0.788557
$311$	−23.6930	−1.34351	−0.671753	−	0.740775i	$-0.734458\pi$
$311$	−23.6930	−1.34351	−0.671753	+	0.740775i	$0.734458\pi$
$312$	6.33694	0.358758
$313$	1.20377	0.0680413	0.0340207	−	0.999421i	$-0.489169\pi$
$313$	1.20377	0.0680413	0.0340207	+	0.999421i	$0.489169\pi$
$314$	13.7910	0.778272
$315$	−2.39055	−0.134692
$316$	−1.47332	−0.0828807
$317$	−7.36645	−0.413741	−0.206870	−	0.978368i	$-0.566328\pi$
$317$	−7.36645	−0.413741	−0.206870	+	0.978368i	$0.566328\pi$
$318$	−8.39162	−0.470579
$319$	8.95106	0.501163
$320$	−1.76478	−0.0986544
$321$	14.1977	0.792438
$322$	−1.24459	−0.0693581
$323$	18.1877	1.01199
$324$	−3.10134	−0.172297
$325$	−9.31488	−0.516697
$326$	11.4558	0.634481
$327$	−25.1055	−1.38834
$328$	6.47654	0.357607
$329$	−7.31384	−0.403225
$330$	−5.35767	−0.294930
$331$	9.29064	0.510660	0.255330	−	0.966854i	$-0.417816\pi$
$331$	9.29064	0.510660	0.255330	+	0.966854i	$0.417816\pi$
$332$	−0.837870	−0.0459841
$333$	2.85964	0.156707
$334$	−10.3489	−0.566266
$335$	−26.5208	−1.44899
$336$	1.28274	0.0699790
$337$	20.8623	1.13644	0.568220	−	0.822876i	$-0.307632\pi$
$337$	20.8623	1.13644	0.568220	+	0.822876i	$0.307632\pi$
$338$	−11.4053	−0.620364
$339$	−6.24504	−0.339184
$340$	9.44234	0.512083
$341$	18.6195	1.00831
$342$	−4.60464	−0.248990
$343$	−1.00000	−0.0539949
$344$	3.36808	0.181595
$345$	−2.81744	−0.151686
$346$	10.2289	0.549908
$347$	−17.4634	−0.937485	−0.468742	−	0.883335i	$-0.655293\pi$
$347$	−17.4634	−0.937485	−0.468742	+	0.883335i	$0.655293\pi$
$348$	−4.85138	−0.260061
$349$	−21.5597	−1.15406	−0.577031	−	0.816722i	$-0.695789\pi$
$349$	−21.5597	−1.15406	−0.577031	+	0.816722i	$0.695789\pi$
$350$	−1.88554	−0.100786
$351$	27.5947	1.47290
$352$	−2.36672	−0.126147
$353$	−28.2149	−1.50173	−0.750863	−	0.660458i	$-0.770362\pi$
$353$	−28.2149	−1.50173	−0.750863	+	0.660458i	$0.770362\pi$
$354$	−5.77143	−0.306748
$355$	−1.14489	−0.0607645
$356$	−0.643328	−0.0340963
$357$	−6.86318	−0.363238
$358$	−10.5878	−0.559584
$359$	−4.40090	−0.232271	−0.116135	−	0.993233i	$-0.537051\pi$
$359$	−4.40090	−0.232271	−0.116135	+	0.993233i	$0.537051\pi$
$360$	−2.39055	−0.125993
$361$	−7.44479	−0.391831
$362$	−1.37579	−0.0723098
$363$	6.92503	0.363470
$364$	−4.94017	−0.258935
$365$	−26.9310	−1.40963
$366$	−2.14234	−0.111982
$367$	13.3941	0.699164	0.349582	−	0.936906i	$-0.386324\pi$
$367$	13.3941	0.699164	0.349582	+	0.936906i	$0.386324\pi$
$368$	−1.24459	−0.0648786
$369$	8.77303	0.456706
$370$	−3.72560	−0.193685
$371$	6.54196	0.339642
$372$	−10.0916	−0.523225
$373$	24.4728	1.26715	0.633575	−	0.773681i	$-0.281587\pi$
$373$	24.4728	1.26715	0.633575	+	0.773681i	$0.281587\pi$
$374$	12.6630	0.654786
$375$	−15.5872	−0.804918
$376$	−7.31384	−0.377183
$377$	18.6840	0.962274
$378$	5.58579	0.287302
$379$	−5.19054	−0.266620	−0.133310	−	0.991074i	$-0.542561\pi$
$379$	−5.19054	−0.266620	−0.133310	+	0.991074i	$0.542561\pi$
$380$	5.99902	0.307743
$381$	−20.0870	−1.02909
$382$	−16.0093	−0.819105
$383$	10.5773	0.540474	0.270237	−	0.962794i	$-0.412898\pi$
$383$	10.5773	0.540474	0.270237	+	0.962794i	$0.412898\pi$
$384$	1.28274	0.0654594
$385$	4.17675	0.212867
$386$	−26.4523	−1.34639
$387$	4.56236	0.231918
$388$	−16.5885	−0.842153
$389$	−23.6982	−1.20155	−0.600774	−	0.799419i	$-0.705141\pi$
$389$	−23.6982	−1.20155	−0.600774	+	0.799419i	$0.705141\pi$
$390$	−11.1833	−0.566289
$391$	6.65907	0.336764
$392$	−1.00000	−0.0505076
$393$	5.97614	0.301456
$394$	−16.5486	−0.833709
$395$	2.60009	0.130825
$396$	−3.20593	−0.161104
$397$	−9.29264	−0.466384	−0.233192	−	0.972431i	$-0.574917\pi$
$397$	−9.29264	−0.466384	−0.233192	+	0.972431i	$0.574917\pi$
$398$	23.8069	1.19333
$399$	−4.36040	−0.218293
$400$	−1.88554	−0.0942770
$401$	10.6783	0.533247	0.266623	−	0.963801i	$-0.414092\pi$
$401$	10.6783	0.533247	0.266623	+	0.963801i	$0.414092\pi$
$402$	19.2767	0.961436
$403$	38.8655	1.93603
$404$	6.91224	0.343897
$405$	5.47319	0.271965
$406$	3.78205	0.187700
$407$	−4.99634	−0.247660
$408$	−6.86318	−0.339778
$409$	21.9436	1.08504	0.542522	−	0.840042i	$-0.317470\pi$
$409$	21.9436	1.08504	0.542522	+	0.840042i	$0.317470\pi$
$410$	−11.4297	−0.564472
$411$	−23.1822	−1.14349
$412$	14.0029	0.689872
$413$	4.49931	0.221397
$414$	−1.68590	−0.0828575
$415$	1.47866	0.0725846
$416$	−4.94017	−0.242212
$417$	16.6957	0.817592
$418$	8.04518	0.393503
$419$	−24.3460	−1.18938	−0.594691	−	0.803955i	$-0.702725\pi$
$419$	−24.3460	−1.18938	−0.594691	+	0.803955i	$0.702725\pi$
$420$	−2.26375	−0.110460
$421$	28.7539	1.40138	0.700691	−	0.713465i	$-0.252875\pi$
$421$	28.7539	1.40138	0.700691	+	0.713465i	$0.252875\pi$
$422$	4.20544	0.204717
$423$	−9.90723	−0.481706
$424$	6.54196	0.317706
$425$	10.0884	0.489361
$426$	0.832167	0.0403186
$427$	1.67013	0.0808235
$428$	−11.0683	−0.535006
$429$	−14.9978	−0.724098
$430$	−5.94394	−0.286642
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.58579	0.268746
$433$	−26.0839	−1.25351	−0.626757	−	0.779215i	$-0.715618\pi$
$433$	−26.0839	−1.25351	−0.626757	+	0.779215i	$0.715618\pi$
$434$	7.86724	0.377639
$435$	8.56164	0.410499
$436$	19.5719	0.937322
$437$	4.23072	0.202383
$438$	19.5749	0.935323
$439$	4.79078	0.228651	0.114326	−	0.993443i	$-0.463529\pi$
$439$	4.79078	0.228651	0.114326	+	0.993443i	$0.463529\pi$
$440$	4.17675	0.199119
$441$	−1.35459	−0.0645041
$442$	26.4320	1.25724
$443$	10.1371	0.481628	0.240814	−	0.970571i	$-0.422586\pi$
$443$	10.1371	0.481628	0.240814	+	0.970571i	$0.422586\pi$
$444$	2.70796	0.128514
$445$	1.13534	0.0538201
$446$	−18.9711	−0.898305
$447$	11.2574	0.532457
$448$	−1.00000	−0.0472456
$449$	−12.9747	−0.612313	−0.306156	−	0.951981i	$-0.599043\pi$
$449$	−12.9747	−0.612313	−0.306156	+	0.951981i	$0.599043\pi$
$450$	−2.55412	−0.120403
$451$	−15.3282	−0.721775
$452$	4.86853	0.228996
$453$	24.9251	1.17108
$454$	26.8122	1.25836
$455$	8.71833	0.408721
$456$	−4.36040	−0.204195
$457$	−28.5057	−1.33344	−0.666719	−	0.745309i	$-0.732302\pi$
$457$	−28.5057	−1.33344	−0.666719	+	0.745309i	$0.732302\pi$
$458$	18.5409	0.866360
$459$	−29.8863	−1.39497
$460$	2.19643	0.102409
$461$	23.9692	1.11636	0.558179	−	0.829720i	$-0.311500\pi$
$461$	23.9692	1.11636	0.558179	+	0.829720i	$0.311500\pi$
$462$	−3.03588	−0.141242
$463$	16.3785	0.761173	0.380587	−	0.924745i	$-0.375722\pi$
$463$	16.3785	0.761173	0.380587	+	0.924745i	$0.375722\pi$
$464$	3.78205	0.175577
$465$	17.8095	0.825895
$466$	6.06736	0.281065
$467$	−38.7760	−1.79434	−0.897169	−	0.441687i	$-0.854380\pi$
$467$	−38.7760	−1.79434	−0.897169	+	0.441687i	$0.854380\pi$
$468$	−6.69188	−0.309332
$469$	−15.0278	−0.693920
$470$	12.9074	0.595372
$471$	17.6902	0.815123
$472$	4.49931	0.207097
$473$	−7.97131	−0.366521
$474$	−1.88988	−0.0868052
$475$	6.40951	0.294088
$476$	5.35042	0.245236
$477$	8.86165	0.405747
$478$	−9.17090	−0.419467
$479$	−5.45138	−0.249080	−0.124540	−	0.992215i	$-0.539745\pi$
$479$	−5.45138	−0.249080	−0.124540	+	0.992215i	$0.539745\pi$
$480$	−2.26375	−0.103326
$481$	−10.4291	−0.475526
$482$	−2.12269	−0.0966859
$483$	−1.59648	−0.0726423
$484$	−5.39864	−0.245393
$485$	29.2751	1.32931
$486$	12.7792	0.579675
$487$	−21.9090	−0.992792	−0.496396	−	0.868096i	$-0.665344\pi$
$487$	−21.9090	−0.992792	−0.496396	+	0.868096i	$0.665344\pi$
$488$	1.67013	0.0756034
$489$	14.6948	0.664524
$490$	1.76478	0.0797248
$491$	2.20050	0.0993073	0.0496536	−	0.998766i	$-0.484188\pi$
$491$	2.20050	0.0993073	0.0496536	+	0.998766i	$0.484188\pi$
$492$	8.30770	0.374540
$493$	−20.2356	−0.911365
$494$	16.7931	0.755557
$495$	5.65776	0.254298
$496$	7.86724	0.353249
$497$	−0.648743	−0.0291001
$498$	−1.07477	−0.0481615
$499$	−21.7806	−0.975035	−0.487517	−	0.873113i	$-0.662097\pi$
$499$	−21.7806	−0.975035	−0.487517	+	0.873113i	$0.662097\pi$
$500$	12.1515	0.543431
$501$	−13.2749	−0.593079
$502$	13.0219	0.581194
$503$	30.0912	1.34170	0.670850	−	0.741593i	$-0.265929\pi$
$503$	30.0912	1.34170	0.670850	+	0.741593i	$0.265929\pi$
$504$	−1.35459	−0.0603380
$505$	−12.1986	−0.542831
$506$	2.94559	0.130947
$507$	−14.6299	−0.649739
$508$	15.6595	0.694777
$509$	32.4535	1.43847	0.719237	−	0.694764i	$-0.244491\pi$
$509$	32.4535	1.43847	0.719237	+	0.694764i	$0.244491\pi$
$510$	12.1120	0.536330
$511$	−15.2602	−0.675073
$512$	−1.00000	−0.0441942
$513$	−18.9877	−0.838329
$514$	22.9745	1.01336
$515$	−24.7120	−1.08894
$516$	4.32037	0.190194
$517$	17.3098	0.761285
$518$	−2.11108	−0.0927557
$519$	13.1210	0.575946
$520$	8.71833	0.382324
$521$	9.63645	0.422180	0.211090	−	0.977467i	$-0.432299\pi$
$521$	9.63645	0.422180	0.211090	+	0.977467i	$0.432299\pi$
$522$	5.12312	0.224233
$523$	17.0286	0.744608	0.372304	−	0.928111i	$-0.378568\pi$
$523$	17.0286	0.744608	0.372304	+	0.928111i	$0.378568\pi$
$524$	−4.65890	−0.203525
$525$	−2.41865	−0.105559
$526$	21.4910	0.937053
$527$	−42.0930	−1.83360
$528$	−3.03588	−0.132120
$529$	−21.4510	−0.932652
$530$	−11.5451	−0.501489
$531$	6.09470	0.264487
$532$	3.39930	0.147378
$533$	−31.9952	−1.38587
$534$	−0.825221	−0.0357108
$535$	19.5331	0.844491
$536$	−15.0278	−0.649103
$537$	−13.5814	−0.586081
$538$	−8.05620	−0.347327
$539$	2.36672	0.101942
$540$	−9.85771	−0.424208
$541$	9.40783	0.404474	0.202237	−	0.979337i	$-0.435179\pi$
$541$	9.40783	0.404474	0.202237	+	0.979337i	$0.435179\pi$
$542$	−4.13954	−0.177808
$543$	−1.76477	−0.0757337
$544$	5.35042	0.229397
$545$	−34.5401	−1.47953
$546$	−6.33694	−0.271196
$547$	−26.9560	−1.15255	−0.576277	−	0.817254i	$-0.695495\pi$
$547$	−26.9560	−1.15255	−0.576277	+	0.817254i	$0.695495\pi$
$548$	18.0724	0.772015
$549$	2.26234	0.0965543
$550$	4.46254	0.190284
$551$	−12.8563	−0.547698
$552$	−1.59648	−0.0679506
$553$	1.47332	0.0626519
$554$	−20.4894	−0.870512
$555$	−4.77897	−0.202856
$556$	−13.0157	−0.551988
$557$	14.5825	0.617882	0.308941	−	0.951081i	$-0.400026\pi$
$557$	14.5825	0.617882	0.308941	+	0.951081i	$0.400026\pi$
$558$	10.6568	0.451140
$559$	−16.6389	−0.703751
$560$	1.76478	0.0745757
$561$	16.2432	0.685790
$562$	31.8472	1.34339
$563$	19.2027	0.809299	0.404649	−	0.914472i	$-0.367394\pi$
$563$	19.2027	0.809299	0.404649	+	0.914472i	$0.367394\pi$
$564$	−9.38174	−0.395042
$565$	−8.59190	−0.361464
$566$	3.26317	0.137161
$567$	3.10134	0.130244
$568$	−0.648743	−0.0272207
$569$	−41.6935	−1.74788	−0.873940	−	0.486033i	$-0.838443\pi$
$569$	−41.6935	−1.74788	−0.873940	+	0.486033i	$0.838443\pi$
$570$	7.69517	0.322315
$571$	7.03713	0.294495	0.147247	−	0.989100i	$-0.452959\pi$
$571$	7.03713	0.294495	0.147247	+	0.989100i	$0.452959\pi$
$572$	11.6920	0.488867
$573$	−20.5357	−0.857890
$574$	−6.47654	−0.270326
$575$	2.34672	0.0978649
$576$	−1.35459	−0.0564411
$577$	−17.5072	−0.728834	−0.364417	−	0.931236i	$-0.618732\pi$
$577$	−17.5072	−0.728834	−0.364417	+	0.931236i	$0.618732\pi$
$578$	−11.6270	−0.483620
$579$	−33.9314	−1.41014
$580$	−6.67451	−0.277144
$581$	0.837870	0.0347607
$582$	−21.2787	−0.882029
$583$	−15.4830	−0.641240
$584$	−15.2602	−0.631473
$585$	11.8097	0.488272
$586$	13.0408	0.538712
$587$	−10.1835	−0.420319	−0.210160	−	0.977667i	$-0.567398\pi$
$587$	−10.1835	−0.420319	−0.210160	+	0.977667i	$0.567398\pi$
$588$	−1.28274	−0.0528992
$589$	−26.7431	−1.10193
$590$	−7.94031	−0.326897
$591$	−21.2276	−0.873185
$592$	−2.11108	−0.0867650
$593$	−30.7605	−1.26318	−0.631591	−	0.775302i	$-0.717598\pi$
$593$	−30.7605	−1.26318	−0.631591	+	0.775302i	$0.717598\pi$
$594$	−13.2200	−0.542423
$595$	−9.44234	−0.387098
$596$	−8.77608	−0.359482
$597$	30.5380	1.24984
$598$	6.14847	0.251430
$599$	−6.19889	−0.253280	−0.126640	−	0.991949i	$-0.540419\pi$
$599$	−6.19889	−0.253280	−0.126640	+	0.991949i	$0.540419\pi$
$600$	−2.41865	−0.0987410
$601$	−19.9073	−0.812036	−0.406018	−	0.913865i	$-0.633083\pi$
$601$	−19.9073	−0.812036	−0.406018	+	0.913865i	$0.633083\pi$
$602$	−3.36808	−0.137273
$603$	−20.3565	−0.828979
$604$	−19.4312	−0.790645
$605$	9.52742	0.387345
$606$	8.86659	0.360181
$607$	−41.9365	−1.70215	−0.851074	−	0.525045i	$-0.824048\pi$
$607$	−41.9365	−1.70215	−0.851074	+	0.525045i	$0.824048\pi$
$608$	3.39930	0.137860
$609$	4.85138	0.196588
$610$	−2.94743	−0.119338
$611$	36.1316	1.46173
$612$	7.24760	0.292967
$613$	45.0877	1.82108	0.910538	−	0.413425i	$-0.135667\pi$
$613$	45.0877	1.82108	0.910538	+	0.413425i	$0.135667\pi$
$614$	23.2581	0.938621
$615$	−14.6613	−0.591200
$616$	2.36672	0.0953579
$617$	−14.2713	−0.574541	−0.287271	−	0.957849i	$-0.592748\pi$
$617$	−14.2713	−0.574541	−0.287271	+	0.957849i	$0.592748\pi$
$618$	17.9620	0.722538
$619$	−20.8680	−0.838757	−0.419379	−	0.907811i	$-0.637752\pi$
$619$	−20.8680	−0.838757	−0.419379	+	0.907811i	$0.637752\pi$
$620$	−13.8840	−0.557594
$621$	−6.95200	−0.278974
$622$	23.6930	0.950002
$623$	0.643328	0.0257744
$624$	−6.33694	−0.253680
$625$	−12.0170	−0.480682
$626$	−1.20377	−0.0481125
$627$	10.3199	0.412135
$628$	−13.7910	−0.550321
$629$	11.2952	0.450368
$630$	2.39055	0.0952418
$631$	−5.28471	−0.210381	−0.105191	−	0.994452i	$-0.533545\pi$
$631$	−5.28471	−0.210381	−0.105191	+	0.994452i	$0.533545\pi$
$632$	1.47332	0.0586055
$633$	5.39447	0.214411
$634$	7.36645	0.292559
$635$	−27.6356	−1.09668
$636$	8.39162	0.332749
$637$	4.94017	0.195737
$638$	−8.95106	−0.354376
$639$	−0.878779	−0.0347639
$640$	1.76478	0.0697592
$641$	−36.2049	−1.43001	−0.715004	−	0.699120i	$-0.753575\pi$
$641$	−36.2049	−1.43001	−0.715004	+	0.699120i	$0.753575\pi$
$642$	−14.1977	−0.560339
$643$	−2.44686	−0.0964948	−0.0482474	−	0.998835i	$-0.515364\pi$
$643$	−2.44686	−0.0964948	−0.0482474	+	0.998835i	$0.515364\pi$
$644$	1.24459	0.0490436
$645$	−7.62451	−0.300215
$646$	−18.1877	−0.715584
$647$	−19.7206	−0.775298	−0.387649	−	0.921807i	$-0.626713\pi$
$647$	−19.7206	−0.775298	−0.387649	+	0.921807i	$0.626713\pi$
$648$	3.10134	0.121832
$649$	−10.6486	−0.417994
$650$	9.31488	0.365360
$651$	10.0916	0.395521
$652$	−11.4558	−0.448646
$653$	2.67482	0.104674	0.0523370	−	0.998629i	$-0.483333\pi$
$653$	2.67482	0.104674	0.0523370	+	0.998629i	$0.483333\pi$
$654$	25.1055	0.981705
$655$	8.22195	0.321258
$656$	−6.47654	−0.252866
$657$	−20.6713	−0.806464
$658$	7.31384	0.285123
$659$	−34.4384	−1.34153	−0.670764	−	0.741670i	$-0.734034\pi$
$659$	−34.4384	−1.34153	−0.670764	+	0.741670i	$0.734034\pi$
$660$	5.35767	0.208547
$661$	19.1907	0.746432	0.373216	−	0.927745i	$-0.378255\pi$
$661$	19.1907	0.746432	0.373216	+	0.927745i	$0.378255\pi$
$662$	−9.29064	−0.361091
$663$	33.9053	1.31677
$664$	0.837870	0.0325157
$665$	−5.99902	−0.232632
$666$	−2.85964	−0.110809
$667$	−4.70710	−0.182260
$668$	10.3489	0.400411
$669$	−24.3349	−0.940841
$670$	26.5208	1.02459
$671$	−3.95274	−0.152594
$672$	−1.28274	−0.0494827
$673$	11.7927	0.454573	0.227287	−	0.973828i	$-0.427015\pi$
$673$	11.7927	0.454573	0.227287	+	0.973828i	$0.427015\pi$
$674$	−20.8623	−0.803585
$675$	−10.5322	−0.405385
$676$	11.4053	0.438664
$677$	−39.4171	−1.51492	−0.757461	−	0.652880i	$-0.773561\pi$
$677$	−39.4171	−1.51492	−0.757461	+	0.652880i	$0.773561\pi$
$678$	6.24504	0.239839
$679$	16.5885	0.636608
$680$	−9.44234	−0.362097
$681$	34.3930	1.31794
$682$	−18.6195	−0.712979
$683$	13.1785	0.504263	0.252131	−	0.967693i	$-0.418869\pi$
$683$	13.1785	0.504263	0.252131	+	0.967693i	$0.418869\pi$
$684$	4.60464	0.176063
$685$	−31.8939	−1.21860
$686$	1.00000	0.0381802
$687$	23.7831	0.907383
$688$	−3.36808	−0.128407
$689$	−32.3184	−1.23123
$690$	2.81744	0.107258
$691$	−17.9918	−0.684440	−0.342220	−	0.939620i	$-0.611179\pi$
$691$	−17.9918	−0.684440	−0.342220	+	0.939620i	$0.611179\pi$
$692$	−10.2289	−0.388844
$693$	3.20593	0.121783
$694$	17.4634	0.662902
$695$	22.9699	0.871297
$696$	4.85138	0.183891
$697$	34.6522	1.31255
$698$	21.5597	0.816045
$699$	7.78283	0.294374
$700$	1.88554	0.0712667
$701$	−39.3750	−1.48717	−0.743586	−	0.668641i	$-0.766876\pi$
$701$	−39.3750	−1.48717	−0.743586	+	0.668641i	$0.766876\pi$
$702$	−27.5947	−1.04150
$703$	7.17619	0.270655
$704$	2.36672	0.0891991
$705$	16.5567	0.623563
$706$	28.2149	1.06188
$707$	−6.91224	−0.259962
$708$	5.77143	0.216904
$709$	−49.2324	−1.84896	−0.924480	−	0.381230i	$-0.875501\pi$
$709$	−49.2324	−1.84896	−0.924480	+	0.381230i	$0.875501\pi$
$710$	1.14489	0.0429670
$711$	1.99574	0.0748460
$712$	0.643328	0.0241098
$713$	−9.79146	−0.366693
$714$	6.86318	0.256848
$715$	−20.6338	−0.771662
$716$	10.5878	0.395686
$717$	−11.7638	−0.439329
$718$	4.40090	0.164240
$719$	−5.48669	−0.204619	−0.102310	−	0.994753i	$-0.532623\pi$
$719$	−5.48669	−0.204619	−0.102310	+	0.994753i	$0.532623\pi$
$720$	2.39055	0.0890906
$721$	−14.0029	−0.521494
$722$	7.44479	0.277066
$723$	−2.72285	−0.101264
$724$	1.37579	0.0511308
$725$	−7.13121	−0.264847
$726$	−6.92503	−0.257012
$727$	−37.1879	−1.37922	−0.689612	−	0.724179i	$-0.742219\pi$
$727$	−37.1879	−1.37922	−0.689612	+	0.724179i	$0.742219\pi$
$728$	4.94017	0.183095
$729$	25.6963	0.951716
$730$	26.9310	0.996761
$731$	18.0207	0.666519
$732$	2.14234	0.0791833
$733$	9.13911	0.337561	0.168780	−	0.985654i	$-0.446017\pi$
$733$	9.13911	0.337561	0.168780	+	0.985654i	$0.446017\pi$
$734$	−13.3941	−0.494384
$735$	2.26375	0.0834998
$736$	1.24459	0.0458761
$737$	35.5666	1.31011
$738$	−8.77303	−0.322940
$739$	38.0118	1.39829	0.699143	−	0.714982i	$-0.253565\pi$
$739$	38.0118	1.39829	0.699143	+	0.714982i	$0.253565\pi$
$740$	3.72560	0.136956
$741$	21.5411	0.791333
$742$	−6.54196	−0.240163
$743$	−14.5802	−0.534895	−0.267447	−	0.963572i	$-0.586180\pi$
$743$	−14.5802	−0.534895	−0.267447	+	0.963572i	$0.586180\pi$
$744$	10.0916	0.369976
$745$	15.4879	0.567432
$746$	−24.4728	−0.896011
$747$	1.13497	0.0415263
$748$	−12.6630	−0.463003
$749$	11.0683	0.404426
$750$	15.5872	0.569163
$751$	−26.8444	−0.979566	−0.489783	−	0.871844i	$-0.662924\pi$
$751$	−26.8444	−0.979566	−0.489783	+	0.871844i	$0.662924\pi$
$752$	7.31384	0.266708
$753$	16.7036	0.608714
$754$	−18.6840	−0.680431
$755$	34.2919	1.24801
$756$	−5.58579	−0.203153
$757$	23.2941	0.846637	0.423318	−	0.905981i	$-0.360865\pi$
$757$	23.2941	0.846637	0.423318	+	0.905981i	$0.360865\pi$
$758$	5.19054	0.188529
$759$	3.77842	0.137148
$760$	−5.99902	−0.217607
$761$	−42.6062	−1.54447	−0.772237	−	0.635335i	$-0.780862\pi$
$761$	−42.6062	−1.54447	−0.772237	+	0.635335i	$0.780862\pi$
$762$	20.0870	0.727675
$763$	−19.5719	−0.708549
$764$	16.0093	0.579195
$765$	−12.7905	−0.462440
$766$	−10.5773	−0.382173
$767$	−22.2273	−0.802583
$768$	−1.28274	−0.0462868
$769$	−15.4921	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$769$	−15.4921	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$770$	−4.17675	−0.150520
$771$	29.4703	1.06135
$772$	26.4523	0.952041
$773$	48.9074	1.75908	0.879539	−	0.475827i	$-0.157851\pi$
$773$	48.9074	1.75908	0.879539	+	0.475827i	$0.157851\pi$
$774$	−4.56236	−0.163991
$775$	−14.8340	−0.532852
$776$	16.5885	0.595492
$777$	−2.70796	−0.0971477
$778$	23.6982	0.849622
$779$	22.0157	0.788794
$780$	11.1833	0.400427
$781$	1.53539	0.0549407
$782$	−6.65907	−0.238128
$783$	21.1258	0.754973
$784$	1.00000	0.0357143
$785$	24.3382	0.868666
$786$	−5.97614	−0.213162
$787$	−41.5754	−1.48200	−0.741002	−	0.671503i	$-0.765649\pi$
$787$	−41.5754	−1.48200	−0.741002	+	0.671503i	$0.765649\pi$
$788$	16.5486	0.589521
$789$	27.5673	0.981423
$790$	−2.60009	−0.0925071
$791$	−4.86853	−0.173105
$792$	3.20593	0.113918
$793$	−8.25075	−0.292993
$794$	9.29264	0.329783
$795$	−14.8094	−0.525235
$796$	−23.8069	−0.843814
$797$	16.3431	0.578901	0.289451	−	0.957193i	$-0.406527\pi$
$797$	16.3431	0.578901	0.289451	+	0.957193i	$0.406527\pi$
$798$	4.36040	0.154357
$799$	−39.1321	−1.38440
$800$	1.88554	0.0666639
$801$	0.871444	0.0307909
$802$	−10.6783	−0.377062
$803$	36.1167	1.27453
$804$	−19.2767	−0.679838
$805$	−2.19643	−0.0774139
$806$	−38.8655	−1.36898
$807$	−10.3340	−0.363773
$808$	−6.91224	−0.243172
$809$	−10.6470	−0.374328	−0.187164	−	0.982329i	$-0.559930\pi$
$809$	−10.6470	−0.374328	−0.187164	+	0.982329i	$0.559930\pi$
$810$	−5.47319	−0.192308
$811$	15.6221	0.548565	0.274282	−	0.961649i	$-0.411560\pi$
$811$	15.6221	0.548565	0.274282	+	0.961649i	$0.411560\pi$
$812$	−3.78205	−0.132724
$813$	−5.30994	−0.186228
$814$	4.99634	0.175122
$815$	20.2171	0.708174
$816$	6.86318	0.240259
$817$	11.4491	0.400554
$818$	−21.9436	−0.767242
$819$	6.69188	0.233833
$820$	11.4297	0.399142
$821$	−3.00875	−0.105006	−0.0525030	−	0.998621i	$-0.516720\pi$
$821$	−3.00875	−0.105006	−0.0525030	+	0.998621i	$0.516720\pi$
$822$	23.1822	0.808571
$823$	−24.9371	−0.869253	−0.434626	−	0.900611i	$-0.643120\pi$
$823$	−24.9371	−0.869253	−0.434626	+	0.900611i	$0.643120\pi$
$824$	−14.0029	−0.487813
$825$	5.72427	0.199294
$826$	−4.49931	−0.156551
$827$	−43.1803	−1.50153	−0.750763	−	0.660572i	$-0.770314\pi$
$827$	−43.1803	−1.50153	−0.750763	+	0.660572i	$0.770314\pi$
$828$	1.68590	0.0585891
$829$	5.76088	0.200084	0.100042	−	0.994983i	$-0.468102\pi$
$829$	5.76088	0.200084	0.100042	+	0.994983i	$0.468102\pi$
$830$	−1.47866	−0.0513250
$831$	−26.2825	−0.911731
$832$	4.94017	0.171270
$833$	−5.35042	−0.185381
$834$	−16.6957	−0.578125
$835$	−18.2636	−0.632036
$836$	−8.04518	−0.278248
$837$	43.9447	1.51895
$838$	24.3460	0.841020
$839$	−3.07097	−0.106022	−0.0530108	−	0.998594i	$-0.516882\pi$
$839$	−3.07097	−0.106022	−0.0530108	+	0.998594i	$0.516882\pi$
$840$	2.26375	0.0781069
$841$	−14.6961	−0.506761
$842$	−28.7539	−0.990926
$843$	40.8516	1.40700
$844$	−4.20544	−0.144757
$845$	−20.1278	−0.692418
$846$	9.90723	0.340618
$847$	5.39864	0.185499
$848$	−6.54196	−0.224652
$849$	4.18578	0.143656
$850$	−10.0884	−0.346030
$851$	2.62743	0.0900670
$852$	−0.832167	−0.0285096
$853$	11.1954	0.383323	0.191661	−	0.981461i	$-0.438612\pi$
$853$	11.1954	0.383323	0.191661	+	0.981461i	$0.438612\pi$
$854$	−1.67013	−0.0571508
$855$	−8.12619	−0.277910
$856$	11.0683	0.378306
$857$	−2.37830	−0.0812411	−0.0406205	−	0.999175i	$-0.512933\pi$
$857$	−2.37830	−0.0812411	−0.0406205	+	0.999175i	$0.512933\pi$
$858$	14.9978	0.512015
$859$	−28.3059	−0.965784	−0.482892	−	0.875680i	$-0.660414\pi$
$859$	−28.3059	−0.965784	−0.482892	+	0.875680i	$0.660414\pi$
$860$	5.94394	0.202687
$861$	−8.30770	−0.283126
$862$	1.00000	0.0340601
$863$	7.22569	0.245965	0.122983	−	0.992409i	$-0.460754\pi$
$863$	7.22569	0.245965	0.122983	+	0.992409i	$0.460754\pi$
$864$	−5.58579	−0.190032
$865$	18.0518	0.613778
$866$	26.0839	0.886368
$867$	−14.9144	−0.506520
$868$	−7.86724	−0.267031
$869$	−3.48694	−0.118286
$870$	−8.56164	−0.290267
$871$	74.2399	2.51552
$872$	−19.5719	−0.662787
$873$	22.4705	0.760512
$874$	−4.23072	−0.143106
$875$	−12.1515	−0.410795
$876$	−19.5749	−0.661373
$877$	27.4947	0.928431	0.464216	−	0.885722i	$-0.346336\pi$
$877$	27.4947	0.928431	0.464216	+	0.885722i	$0.346336\pi$
$878$	−4.79078	−0.161681
$879$	16.7280	0.564221
$880$	−4.17675	−0.140798
$881$	29.8097	1.00431	0.502157	−	0.864777i	$-0.332540\pi$
$881$	29.8097	1.00431	0.502157	+	0.864777i	$0.332540\pi$
$882$	1.35459	0.0456113
$883$	4.54446	0.152933	0.0764666	−	0.997072i	$-0.475636\pi$
$883$	4.54446	0.152933	0.0764666	+	0.997072i	$0.475636\pi$
$884$	−26.4320	−0.889004
$885$	−10.1853	−0.342376
$886$	−10.1371	−0.340563
$887$	25.8321	0.867358	0.433679	−	0.901067i	$-0.357215\pi$
$887$	25.8321	0.867358	0.433679	+	0.901067i	$0.357215\pi$
$888$	−2.70796	−0.0908733
$889$	−15.6595	−0.525202
$890$	−1.13534	−0.0380565
$891$	−7.34000	−0.245899
$892$	18.9711	0.635198
$893$	−24.8619	−0.831972
$894$	−11.2574	−0.376504
$895$	−18.6852	−0.624578
$896$	1.00000	0.0334077
$897$	7.88687	0.263335
$898$	12.9747	0.432970
$899$	29.7543	0.992362
$900$	2.55412	0.0851375
$901$	35.0023	1.16609
$902$	15.3282	0.510372
$903$	−4.32037	−0.143773
$904$	−4.86853	−0.161925
$905$	−2.42797	−0.0807084
$906$	−24.9251	−0.828082
$907$	24.6584	0.818770	0.409385	−	0.912362i	$-0.365743\pi$
$907$	24.6584	0.818770	0.409385	+	0.912362i	$0.365743\pi$
$908$	−26.8122	−0.889794
$909$	−9.36323	−0.310559
$910$	−8.71833	−0.289010
$911$	38.1864	1.26517	0.632585	−	0.774491i	$-0.281994\pi$
$911$	38.1864	1.26517	0.632585	+	0.774491i	$0.281994\pi$
$912$	4.36040	0.144387
$913$	−1.98300	−0.0656279
$914$	28.5057	0.942884
$915$	−3.78077	−0.124988
$916$	−18.5409	−0.612609
$917$	4.65890	0.153850
$918$	29.8863	0.986396
$919$	−55.3857	−1.82701	−0.913503	−	0.406831i	$-0.866634\pi$
$919$	−55.3857	−1.82701	−0.913503	+	0.406831i	$0.866634\pi$
$920$	−2.19643	−0.0724141
$921$	29.8341	0.983066
$922$	−23.9692	−0.789385
$923$	3.20490	0.105491
$924$	3.03588	0.0998731
$925$	3.98053	0.130879
$926$	−16.3785	−0.538231
$927$	−18.9681	−0.622994
$928$	−3.78205	−0.124152
$929$	−53.6631	−1.76063	−0.880315	−	0.474389i	$-0.842669\pi$
$929$	−53.6631	−1.76063	−0.880315	+	0.474389i	$0.842669\pi$
$930$	−17.8095	−0.583996
$931$	−3.39930	−0.111407
$932$	−6.06736	−0.198743
$933$	30.3919	0.994985
$934$	38.7760	1.26879
$935$	22.3474	0.730837
$936$	6.69188	0.218731
$937$	17.2298	0.562873	0.281436	−	0.959580i	$-0.409189\pi$
$937$	17.2298	0.562873	0.281436	+	0.959580i	$0.409189\pi$
$938$	15.0278	0.490676
$939$	−1.54413	−0.0503906
$940$	−12.9074	−0.420991
$941$	5.70883	0.186103	0.0930513	−	0.995661i	$-0.470338\pi$
$941$	5.70883	0.186103	0.0930513	+	0.995661i	$0.470338\pi$
$942$	−17.6902	−0.576379
$943$	8.06062	0.262490
$944$	−4.49931	−0.146440
$945$	9.85771	0.320671
$946$	7.97131	0.259170
$947$	33.2532	1.08058	0.540292	−	0.841478i	$-0.318314\pi$
$947$	33.2532	1.08058	0.540292	+	0.841478i	$0.318314\pi$
$948$	1.88988	0.0613805
$949$	75.3881	2.44720
$950$	−6.40951	−0.207952
$951$	9.44921	0.306412
$952$	−5.35042	−0.173408
$953$	22.6022	0.732156	0.366078	−	0.930584i	$-0.380700\pi$
$953$	22.6022	0.732156	0.366078	+	0.930584i	$0.380700\pi$
$954$	−8.86165	−0.286906
$955$	−28.2529	−0.914241
$956$	9.17090	0.296608
$957$	−11.4819	−0.371156
$958$	5.45138	0.176126
$959$	−18.0724	−0.583589
$960$	2.26375	0.0730623
$961$	30.8934	0.996562
$962$	10.4291	0.336248
$963$	14.9929	0.483141
$964$	2.12269	0.0683673
$965$	−46.6827	−1.50277
$966$	1.59648	0.0513658
$967$	4.75173	0.152805	0.0764027	−	0.997077i	$-0.475657\pi$
$967$	4.75173	0.152805	0.0764027	+	0.997077i	$0.475657\pi$
$968$	5.39864	0.173519
$969$	−23.3300	−0.749467
$970$	−29.2751	−0.939966
$971$	−28.7669	−0.923172	−0.461586	−	0.887095i	$-0.652719\pi$
$971$	−28.7669	−0.923172	−0.461586	+	0.887095i	$0.652719\pi$
$972$	−12.7792	−0.409892
$973$	13.0157	0.417264
$974$	21.9090	0.702010
$975$	11.9485	0.382660
$976$	−1.67013	−0.0534597
$977$	41.6203	1.33155	0.665775	−	0.746153i	$-0.268101\pi$
$977$	41.6203	1.33155	0.665775	+	0.746153i	$0.268101\pi$
$978$	−14.6948	−0.469889
$979$	−1.52258	−0.0486618
$980$	−1.76478	−0.0563739
$981$	−26.5118	−0.846455
$982$	−2.20050	−0.0702208
$983$	15.4867	0.493949	0.246974	−	0.969022i	$-0.420564\pi$
$983$	15.4867	0.493949	0.246974	+	0.969022i	$0.420564\pi$
$984$	−8.30770	−0.264840
$985$	−29.2048	−0.930541
$986$	20.2356	0.644432
$987$	9.38174	0.298624
$988$	−16.7931	−0.534259
$989$	4.19188	0.133294
$990$	−5.65776	−0.179816
$991$	12.3845	0.393407	0.196703	−	0.980463i	$-0.436976\pi$
$991$	12.3845	0.393407	0.196703	+	0.980463i	$0.436976\pi$
$992$	−7.86724	−0.249785
$993$	−11.9174	−0.378189
$994$	0.648743	0.0205769
$995$	42.0141	1.33194
$996$	1.07477	0.0340553
$997$	−25.0925	−0.794686	−0.397343	−	0.917670i	$-0.630068\pi$
$997$	−25.0925	−0.794686	−0.397343	+	0.917670i	$0.630068\pi$
$998$	21.7806	0.689454
$999$	−11.7921	−0.373084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.8	✓	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.28274 q^{3} +1.00000 q^{4} -1.76478 q^{5} +1.28274 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.35459 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.28274 q^{3} +1.00000 q^{4} -1.76478 q^{5} +1.28274 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.35459 q^{9} +1.76478 q^{10} +2.36672 q^{11} -1.28274 q^{12} +4.94017 q^{13} +1.00000 q^{14} +2.26375 q^{15} +1.00000 q^{16} -5.35042 q^{17} +1.35459 q^{18} -3.39930 q^{19} -1.76478 q^{20} +1.28274 q^{21} -2.36672 q^{22} -1.24459 q^{23} +1.28274 q^{24} -1.88554 q^{25} -4.94017 q^{26} +5.58579 q^{27} -1.00000 q^{28} +3.78205 q^{29} -2.26375 q^{30} +7.86724 q^{31} -1.00000 q^{32} -3.03588 q^{33} +5.35042 q^{34} +1.76478 q^{35} -1.35459 q^{36} -2.11108 q^{37} +3.39930 q^{38} -6.33694 q^{39} +1.76478 q^{40} -6.47654 q^{41} -1.28274 q^{42} -3.36808 q^{43} +2.36672 q^{44} +2.39055 q^{45} +1.24459 q^{46} +7.31384 q^{47} -1.28274 q^{48} +1.00000 q^{49} +1.88554 q^{50} +6.86318 q^{51} +4.94017 q^{52} -6.54196 q^{53} -5.58579 q^{54} -4.17675 q^{55} +1.00000 q^{56} +4.36040 q^{57} -3.78205 q^{58} -4.49931 q^{59} +2.26375 q^{60} -1.67013 q^{61} -7.86724 q^{62} +1.35459 q^{63} +1.00000 q^{64} -8.71833 q^{65} +3.03588 q^{66} +15.0278 q^{67} -5.35042 q^{68} +1.59648 q^{69} -1.76478 q^{70} +0.648743 q^{71} +1.35459 q^{72} +15.2602 q^{73} +2.11108 q^{74} +2.41865 q^{75} -3.39930 q^{76} -2.36672 q^{77} +6.33694 q^{78} -1.47332 q^{79} -1.76478 q^{80} -3.10134 q^{81} +6.47654 q^{82} -0.837870 q^{83} +1.28274 q^{84} +9.44234 q^{85} +3.36808 q^{86} -4.85138 q^{87} -2.36672 q^{88} -0.643328 q^{89} -2.39055 q^{90} -4.94017 q^{91} -1.24459 q^{92} -10.0916 q^{93} -7.31384 q^{94} +5.99902 q^{95} +1.28274 q^{96} -16.5885 q^{97} -1.00000 q^{98} -3.20593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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