LMFDB - Embedded newform 6026.2.a.g.1.10

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:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.104929 q^{3} +1.00000 q^{4} -0.922657 q^{5} -0.104929 q^{6} +4.49446 q^{7} +1.00000 q^{8} -2.98899 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.104929 q^{3} +1.00000 q^{4} -0.922657 q^{5} -0.104929 q^{6} +4.49446 q^{7} +1.00000 q^{8} -2.98899 q^{9} -0.922657 q^{10} -2.62570 q^{11} -0.104929 q^{12} -2.06888 q^{13} +4.49446 q^{14} +0.0968138 q^{15} +1.00000 q^{16} +3.36673 q^{17} -2.98899 q^{18} -1.41096 q^{19} -0.922657 q^{20} -0.471600 q^{21} -2.62570 q^{22} -1.00000 q^{23} -0.104929 q^{24} -4.14870 q^{25} -2.06888 q^{26} +0.628421 q^{27} +4.49446 q^{28} -6.36048 q^{29} +0.0968138 q^{30} -4.17734 q^{31} +1.00000 q^{32} +0.275513 q^{33} +3.36673 q^{34} -4.14684 q^{35} -2.98899 q^{36} -5.57655 q^{37} -1.41096 q^{38} +0.217087 q^{39} -0.922657 q^{40} -0.924886 q^{41} -0.471600 q^{42} +2.50020 q^{43} -2.62570 q^{44} +2.75781 q^{45} -1.00000 q^{46} -7.26050 q^{47} -0.104929 q^{48} +13.2001 q^{49} -4.14870 q^{50} -0.353269 q^{51} -2.06888 q^{52} +1.40099 q^{53} +0.628421 q^{54} +2.42262 q^{55} +4.49446 q^{56} +0.148051 q^{57} -6.36048 q^{58} +1.75225 q^{59} +0.0968138 q^{60} -2.76783 q^{61} -4.17734 q^{62} -13.4339 q^{63} +1.00000 q^{64} +1.90887 q^{65} +0.275513 q^{66} +1.77430 q^{67} +3.36673 q^{68} +0.104929 q^{69} -4.14684 q^{70} -13.7655 q^{71} -2.98899 q^{72} -5.44434 q^{73} -5.57655 q^{74} +0.435321 q^{75} -1.41096 q^{76} -11.8011 q^{77} +0.217087 q^{78} -5.27667 q^{79} -0.922657 q^{80} +8.90103 q^{81} -0.924886 q^{82} +12.7384 q^{83} -0.471600 q^{84} -3.10634 q^{85} +2.50020 q^{86} +0.667401 q^{87} -2.62570 q^{88} -0.332849 q^{89} +2.75781 q^{90} -9.29850 q^{91} -1.00000 q^{92} +0.438325 q^{93} -7.26050 q^{94} +1.30183 q^{95} -0.104929 q^{96} -7.74399 q^{97} +13.2001 q^{98} +7.84819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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
$3$	−0.104929	−0.0605810	−0.0302905	−	0.999541i	$-0.509643\pi$
$3$	−0.104929	−0.0605810	−0.0302905	+	0.999541i	$0.509643\pi$
$4$	1.00000	0.500000
$5$	−0.922657	−0.412625	−0.206312	−	0.978486i	$-0.566146\pi$
$5$	−0.922657	−0.412625	−0.206312	+	0.978486i	$0.566146\pi$
$6$	−0.104929	−0.0428372
$7$	4.49446	1.69874	0.849372	−	0.527794i	$-0.176981\pi$
$7$	4.49446	1.69874	0.849372	+	0.527794i	$0.176981\pi$
$8$	1.00000	0.353553
$9$	−2.98899	−0.996330
$10$	−0.922657	−0.291770
$11$	−2.62570	−0.791678	−0.395839	−	0.918320i	$-0.629546\pi$
$11$	−2.62570	−0.791678	−0.395839	+	0.918320i	$0.629546\pi$
$12$	−0.104929	−0.0302905
$13$	−2.06888	−0.573805	−0.286902	−	0.957960i	$-0.592626\pi$
$13$	−2.06888	−0.573805	−0.286902	+	0.957960i	$0.592626\pi$
$14$	4.49446	1.20119
$15$	0.0968138	0.0249972
$16$	1.00000	0.250000
$17$	3.36673	0.816552	0.408276	−	0.912859i	$-0.366130\pi$
$17$	3.36673	0.816552	0.408276	+	0.912859i	$0.366130\pi$
$18$	−2.98899	−0.704512
$19$	−1.41096	−0.323697	−0.161848	−	0.986816i	$-0.551746\pi$
$19$	−1.41096	−0.323697	−0.161848	+	0.986816i	$0.551746\pi$
$20$	−0.922657	−0.206312
$21$	−0.471600	−0.102912
$22$	−2.62570	−0.559801
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.104929	−0.0214186
$25$	−4.14870	−0.829741
$26$	−2.06888	−0.405741
$27$	0.628421	0.120940
$28$	4.49446	0.849372
$29$	−6.36048	−1.18111	−0.590556	−	0.806997i	$-0.701092\pi$
$29$	−6.36048	−1.18111	−0.590556	+	0.806997i	$0.701092\pi$
$30$	0.0968138	0.0176757
$31$	−4.17734	−0.750272	−0.375136	−	0.926970i	$-0.622404\pi$
$31$	−4.17734	−0.750272	−0.375136	+	0.926970i	$0.622404\pi$
$32$	1.00000	0.176777
$33$	0.275513	0.0479606
$34$	3.36673	0.577389
$35$	−4.14684	−0.700944
$36$	−2.98899	−0.498165
$37$	−5.57655	−0.916780	−0.458390	−	0.888751i	$-0.651574\pi$
$37$	−5.57655	−0.916780	−0.458390	+	0.888751i	$0.651574\pi$
$38$	−1.41096	−0.228888
$39$	0.217087	0.0347617
$40$	−0.922657	−0.145885
$41$	−0.924886	−0.144443	−0.0722215	−	0.997389i	$-0.523009\pi$
$41$	−0.924886	−0.144443	−0.0722215	+	0.997389i	$0.523009\pi$
$42$	−0.471600	−0.0727695
$43$	2.50020	0.381277	0.190639	−	0.981660i	$-0.438944\pi$
$43$	2.50020	0.381277	0.190639	+	0.981660i	$0.438944\pi$
$44$	−2.62570	−0.395839
$45$	2.75781	0.411110
$46$	−1.00000	−0.147442
$47$	−7.26050	−1.05905	−0.529526	−	0.848294i	$-0.677630\pi$
$47$	−7.26050	−1.05905	−0.529526	+	0.848294i	$0.677630\pi$
$48$	−0.104929	−0.0151452
$49$	13.2001	1.88573
$50$	−4.14870	−0.586715
$51$	−0.353269	−0.0494675
$52$	−2.06888	−0.286902
$53$	1.40099	0.192441	0.0962203	−	0.995360i	$-0.469325\pi$
$53$	1.40099	0.192441	0.0962203	+	0.995360i	$0.469325\pi$
$54$	0.628421	0.0855172
$55$	2.42262	0.326666
$56$	4.49446	0.600597
$57$	0.148051	0.0196099
$58$	−6.36048	−0.835172
$59$	1.75225	0.228124	0.114062	−	0.993474i	$-0.463614\pi$
$59$	1.75225	0.228124	0.114062	+	0.993474i	$0.463614\pi$
$60$	0.0968138	0.0124986
$61$	−2.76783	−0.354384	−0.177192	−	0.984176i	$-0.556701\pi$
$61$	−2.76783	−0.354384	−0.177192	+	0.984176i	$0.556701\pi$
$62$	−4.17734	−0.530523
$63$	−13.4339	−1.69251
$64$	1.00000	0.125000
$65$	1.90887	0.236766
$66$	0.275513	0.0339133
$67$	1.77430	0.216766	0.108383	−	0.994109i	$-0.465433\pi$
$67$	1.77430	0.216766	0.108383	+	0.994109i	$0.465433\pi$
$68$	3.36673	0.408276
$69$	0.104929	0.0126320
$70$	−4.14684	−0.495642
$71$	−13.7655	−1.63366	−0.816830	−	0.576879i	$-0.804270\pi$
$71$	−13.7655	−1.63366	−0.816830	+	0.576879i	$0.804270\pi$
$72$	−2.98899	−0.352256
$73$	−5.44434	−0.637212	−0.318606	−	0.947887i	$-0.603215\pi$
$73$	−5.44434	−0.637212	−0.318606	+	0.947887i	$0.603215\pi$
$74$	−5.57655	−0.648261
$75$	0.435321	0.0502665
$76$	−1.41096	−0.161848
$77$	−11.8011	−1.34486
$78$	0.217087	0.0245802
$79$	−5.27667	−0.593672	−0.296836	−	0.954928i	$-0.595932\pi$
$79$	−5.27667	−0.593672	−0.296836	+	0.954928i	$0.595932\pi$
$80$	−0.922657	−0.103156
$81$	8.90103	0.989003
$82$	−0.924886	−0.102137
$83$	12.7384	1.39822	0.699110	−	0.715014i	$-0.253580\pi$
$83$	12.7384	1.39822	0.699110	+	0.715014i	$0.253580\pi$
$84$	−0.471600	−0.0514558
$85$	−3.10634	−0.336930
$86$	2.50020	0.269604
$87$	0.667401	0.0715529
$88$	−2.62570	−0.279900
$89$	−0.332849	−0.0352819	−0.0176410	−	0.999844i	$-0.505616\pi$
$89$	−0.332849	−0.0352819	−0.0176410	+	0.999844i	$0.505616\pi$
$90$	2.75781	0.290699
$91$	−9.29850	−0.974748
$92$	−1.00000	−0.104257
$93$	0.438325	0.0454522
$94$	−7.26050	−0.748863
$95$	1.30183	0.133565
$96$	−0.104929	−0.0107093
$97$	−7.74399	−0.786283	−0.393141	−	0.919478i	$-0.628612\pi$
$97$	−7.74399	−0.786283	−0.393141	+	0.919478i	$0.628612\pi$
$98$	13.2001	1.33341
$99$	7.84819	0.788773
$100$	−4.14870	−0.414870
$101$	−4.95703	−0.493243	−0.246621	−	0.969112i	$-0.579320\pi$
$101$	−4.95703	−0.493243	−0.246621	+	0.969112i	$0.579320\pi$
$102$	−0.353269	−0.0349788
$103$	−9.93749	−0.979170	−0.489585	−	0.871955i	$-0.662852\pi$
$103$	−9.93749	−0.979170	−0.489585	+	0.871955i	$0.662852\pi$
$104$	−2.06888	−0.202871
$105$	0.435125	0.0424639
$106$	1.40099	0.136076
$107$	17.1607	1.65898	0.829492	−	0.558519i	$-0.188630\pi$
$107$	17.1607	1.65898	0.829492	+	0.558519i	$0.188630\pi$
$108$	0.628421	0.0604698
$109$	−11.7647	−1.12686	−0.563428	−	0.826165i	$-0.690518\pi$
$109$	−11.7647	−1.12686	−0.563428	+	0.826165i	$0.690518\pi$
$110$	2.42262	0.230988
$111$	0.585144	0.0555394
$112$	4.49446	0.424686
$113$	17.2476	1.62251	0.811257	−	0.584690i	$-0.198784\pi$
$113$	17.2476	1.62251	0.811257	+	0.584690i	$0.198784\pi$
$114$	0.148051	0.0138663
$115$	0.922657	0.0860382
$116$	−6.36048	−0.590556
$117$	6.18387	0.571699
$118$	1.75225	0.161308
$119$	15.1316	1.38711
$120$	0.0968138	0.00883785
$121$	−4.10570	−0.373246
$122$	−2.76783	−0.250587
$123$	0.0970477	0.00875050
$124$	−4.17734	−0.375136
$125$	8.44112	0.754996
$126$	−13.4339	−1.19679
$127$	−13.3680	−1.18622	−0.593111	−	0.805121i	$-0.702101\pi$
$127$	−13.3680	−1.18622	−0.593111	+	0.805121i	$0.702101\pi$
$128$	1.00000	0.0883883
$129$	−0.262345	−0.0230982
$130$	1.90887	0.167419
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.275513	0.0239803
$133$	−6.34150	−0.549878
$134$	1.77430	0.153277
$135$	−0.579817	−0.0499027
$136$	3.36673	0.288695
$137$	1.94428	0.166111	0.0830555	−	0.996545i	$-0.473532\pi$
$137$	1.94428	0.166111	0.0830555	+	0.996545i	$0.473532\pi$
$138$	0.104929	0.00893218
$139$	−10.6273	−0.901400	−0.450700	−	0.892675i	$-0.648826\pi$
$139$	−10.6273	−0.901400	−0.450700	+	0.892675i	$0.648826\pi$
$140$	−4.14684	−0.350472
$141$	0.761839	0.0641585
$142$	−13.7655	−1.15517
$143$	5.43226	0.454269
$144$	−2.98899	−0.249082
$145$	5.86855	0.487356
$146$	−5.44434	−0.450577
$147$	−1.38508	−0.114240
$148$	−5.57655	−0.458390
$149$	20.5570	1.68410	0.842048	−	0.539402i	$-0.181350\pi$
$149$	20.5570	1.68410	0.842048	+	0.539402i	$0.181350\pi$
$150$	0.435321	0.0355438
$151$	7.69548	0.626249	0.313124	−	0.949712i	$-0.398624\pi$
$151$	7.69548	0.626249	0.313124	+	0.949712i	$0.398624\pi$
$152$	−1.41096	−0.114444
$153$	−10.0631	−0.813555
$154$	−11.8011	−0.950959
$155$	3.85425	0.309581
$156$	0.217087	0.0173808
$157$	−6.60981	−0.527521	−0.263760	−	0.964588i	$-0.584963\pi$
$157$	−6.60981	−0.527521	−0.263760	+	0.964588i	$0.584963\pi$
$158$	−5.27667	−0.419790
$159$	−0.147005	−0.0116582
$160$	−0.922657	−0.0729425
$161$	−4.49446	−0.354213
$162$	8.90103	0.699331
$163$	8.14277	0.637791	0.318895	−	0.947790i	$-0.396688\pi$
$163$	8.14277	0.637791	0.318895	+	0.947790i	$0.396688\pi$
$164$	−0.924886	−0.0722215
$165$	−0.254204	−0.0197898
$166$	12.7384	0.988691
$167$	−23.9719	−1.85500	−0.927501	−	0.373820i	$-0.878048\pi$
$167$	−23.9719	−1.85500	−0.927501	+	0.373820i	$0.878048\pi$
$168$	−0.471600	−0.0363848
$169$	−8.71972	−0.670748
$170$	−3.10634	−0.238245
$171$	4.21735	0.322509
$172$	2.50020	0.190639
$173$	−14.3175	−1.08854	−0.544268	−	0.838911i	$-0.683193\pi$
$173$	−14.3175	−1.08854	−0.544268	+	0.838911i	$0.683193\pi$
$174$	0.667401	0.0505956
$175$	−18.6462	−1.40952
$176$	−2.62570	−0.197920
$177$	−0.183863	−0.0138200
$178$	−0.332849	−0.0249481
$179$	−6.19888	−0.463326	−0.231663	−	0.972796i	$-0.574417\pi$
$179$	−6.19888	−0.463326	−0.231663	+	0.972796i	$0.574417\pi$
$180$	2.75781	0.205555
$181$	11.6292	0.864388	0.432194	−	0.901781i	$-0.357740\pi$
$181$	11.6292	0.864388	0.432194	+	0.901781i	$0.357740\pi$
$182$	−9.29850	−0.689251
$183$	0.290426	0.0214689
$184$	−1.00000	−0.0737210
$185$	5.14525	0.378286
$186$	0.438325	0.0321396
$187$	−8.84002	−0.646446
$188$	−7.26050	−0.529526
$189$	2.82441	0.205446
$190$	1.30183	0.0944449
$191$	−22.3031	−1.61380	−0.806900	−	0.590689i	$-0.798856\pi$
$191$	−22.3031	−1.61380	−0.806900	+	0.590689i	$0.798856\pi$
$192$	−0.104929	−0.00757262
$193$	18.8087	1.35388	0.676941	−	0.736037i	$-0.263305\pi$
$193$	18.8087	1.35388	0.676941	+	0.736037i	$0.263305\pi$
$194$	−7.74399	−0.555986
$195$	−0.200296	−0.0143435
$196$	13.2001	0.942866
$197$	0.621917	0.0443098	0.0221549	−	0.999755i	$-0.492947\pi$
$197$	0.621917	0.0443098	0.0221549	+	0.999755i	$0.492947\pi$
$198$	7.84819	0.557746
$199$	−12.8832	−0.913268	−0.456634	−	0.889655i	$-0.650945\pi$
$199$	−12.8832	−0.913268	−0.456634	+	0.889655i	$0.650945\pi$
$200$	−4.14870	−0.293358
$201$	−0.186177	−0.0131319
$202$	−4.95703	−0.348775
$203$	−28.5869	−2.00641
$204$	−0.353269	−0.0247338
$205$	0.853353	0.0596007
$206$	−9.93749	−0.692378
$207$	2.98899	0.207749
$208$	−2.06888	−0.143451
$209$	3.70476	0.256264
$210$	0.435125	0.0300265
$211$	1.02730	0.0707221	0.0353610	−	0.999375i	$-0.488742\pi$
$211$	1.02730	0.0707221	0.0353610	+	0.999375i	$0.488742\pi$
$212$	1.40099	0.0962203
$213$	1.44440	0.0989687
$214$	17.1607	1.17308
$215$	−2.30683	−0.157325
$216$	0.628421	0.0427586
$217$	−18.7749	−1.27452
$218$	−11.7647	−0.796808
$219$	0.571271	0.0386029
$220$	2.42262	0.163333
$221$	−6.96537	−0.468542
$222$	0.585144	0.0392723
$223$	12.2314	0.819076	0.409538	−	0.912293i	$-0.365690\pi$
$223$	12.2314	0.819076	0.409538	+	0.912293i	$0.365690\pi$
$224$	4.49446	0.300298
$225$	12.4004	0.826696
$226$	17.2476	1.14729
$227$	−6.97219	−0.462761	−0.231380	−	0.972863i	$-0.574324\pi$
$227$	−6.97219	−0.462761	−0.231380	+	0.972863i	$0.574324\pi$
$228$	0.148051	0.00980493
$229$	10.4119	0.688035	0.344017	−	0.938963i	$-0.388212\pi$
$229$	10.4119	0.688035	0.344017	+	0.938963i	$0.388212\pi$
$230$	0.922657	0.0608382
$231$	1.23828	0.0814729
$232$	−6.36048	−0.417586
$233$	−4.03144	−0.264108	−0.132054	−	0.991242i	$-0.542157\pi$
$233$	−4.03144	−0.264108	−0.132054	+	0.991242i	$0.542157\pi$
$234$	6.18387	0.404252
$235$	6.69895	0.436991
$236$	1.75225	0.114062
$237$	0.553678	0.0359652
$238$	15.1316	0.980837
$239$	5.53535	0.358052	0.179026	−	0.983844i	$-0.442705\pi$
$239$	5.53535	0.358052	0.179026	+	0.983844i	$0.442705\pi$
$240$	0.0968138	0.00624930
$241$	24.7841	1.59648	0.798241	−	0.602338i	$-0.205764\pi$
$241$	24.7841	1.59648	0.798241	+	0.602338i	$0.205764\pi$
$242$	−4.10570	−0.263925
$243$	−2.81924	−0.180854
$244$	−2.76783	−0.177192
$245$	−12.1792	−0.778100
$246$	0.0970477	0.00618754
$247$	2.91911	0.185739
$248$	−4.17734	−0.265261
$249$	−1.33663	−0.0847055
$250$	8.44112	0.533863
$251$	−1.82366	−0.115108	−0.0575541	−	0.998342i	$-0.518330\pi$
$251$	−1.82366	−0.115108	−0.0575541	+	0.998342i	$0.518330\pi$
$252$	−13.4339	−0.846255
$253$	2.62570	0.165076
$254$	−13.3680	−0.838786
$255$	0.325946	0.0204115
$256$	1.00000	0.0625000
$257$	3.31104	0.206537	0.103269	−	0.994654i	$-0.467070\pi$
$257$	3.31104	0.206537	0.103269	+	0.994654i	$0.467070\pi$
$258$	−0.262345	−0.0163329
$259$	−25.0636	−1.55737
$260$	1.90887	0.118383
$261$	19.0114	1.17678
$262$	1.00000	0.0617802
$263$	7.17574	0.442475	0.221238	−	0.975220i	$-0.428990\pi$
$263$	7.17574	0.442475	0.221238	+	0.975220i	$0.428990\pi$
$264$	0.275513	0.0169566
$265$	−1.29263	−0.0794058
$266$	−6.34150	−0.388823
$267$	0.0349256	0.00213741
$268$	1.77430	0.108383
$269$	7.38289	0.450143	0.225072	−	0.974342i	$-0.427738\pi$
$269$	7.38289	0.450143	0.225072	+	0.974342i	$0.427738\pi$
$270$	−0.579817	−0.0352865
$271$	−30.0110	−1.82304	−0.911520	−	0.411256i	$-0.865090\pi$
$271$	−30.0110	−1.82304	−0.911520	+	0.411256i	$0.865090\pi$
$272$	3.36673	0.204138
$273$	0.975686	0.0590512
$274$	1.94428	0.117458
$275$	10.8932	0.656888
$276$	0.104929	0.00631600
$277$	−14.8705	−0.893484	−0.446742	−	0.894663i	$-0.647416\pi$
$277$	−14.8705	−0.893484	−0.446742	+	0.894663i	$0.647416\pi$
$278$	−10.6273	−0.637386
$279$	12.4860	0.747519
$280$	−4.14684	−0.247821
$281$	16.2176	0.967459	0.483730	−	0.875217i	$-0.339282\pi$
$281$	16.2176	0.967459	0.483730	+	0.875217i	$0.339282\pi$
$282$	0.761839	0.0453669
$283$	−3.55924	−0.211575	−0.105787	−	0.994389i	$-0.533736\pi$
$283$	−3.55924	−0.211575	−0.105787	+	0.994389i	$0.533736\pi$
$284$	−13.7655	−0.816830
$285$	−0.136601	−0.00809152
$286$	5.43226	0.321217
$287$	−4.15686	−0.245372
$288$	−2.98899	−0.176128
$289$	−5.66513	−0.333243
$290$	5.86855	0.344613
$291$	0.812572	0.0476338
$292$	−5.44434	−0.318606
$293$	−6.76805	−0.395394	−0.197697	−	0.980263i	$-0.563346\pi$
$293$	−6.76805	−0.395394	−0.197697	+	0.980263i	$0.563346\pi$
$294$	−1.38508	−0.0807796
$295$	−1.61673	−0.0941297
$296$	−5.57655	−0.324131
$297$	−1.65004	−0.0957453
$298$	20.5570	1.19084
$299$	2.06888	0.119647
$300$	0.435321	0.0251333
$301$	11.2371	0.647693
$302$	7.69548	0.442825
$303$	0.520138	0.0298811
$304$	−1.41096	−0.0809242
$305$	2.55376	0.146228
$306$	−10.0631	−0.575270
$307$	17.3144	0.988187	0.494093	−	0.869409i	$-0.335500\pi$
$307$	17.3144	0.988187	0.494093	+	0.869409i	$0.335500\pi$
$308$	−11.8011	−0.672429
$309$	1.04273	0.0593191
$310$	3.85425	0.218907
$311$	−1.81503	−0.102921	−0.0514604	−	0.998675i	$-0.516388\pi$
$311$	−1.81503	−0.102921	−0.0514604	+	0.998675i	$0.516388\pi$
$312$	0.217087	0.0122901
$313$	−0.341200	−0.0192857	−0.00964287	−	0.999954i	$-0.503069\pi$
$313$	−0.341200	−0.0192857	−0.00964287	+	0.999954i	$0.503069\pi$
$314$	−6.60981	−0.373013
$315$	12.3949	0.698372
$316$	−5.27667	−0.296836
$317$	15.3180	0.860345	0.430173	−	0.902747i	$-0.358453\pi$
$317$	15.3180	0.860345	0.430173	+	0.902747i	$0.358453\pi$
$318$	−0.147005	−0.00824362
$319$	16.7007	0.935061
$320$	−0.922657	−0.0515781
$321$	−1.80066	−0.100503
$322$	−4.49446	−0.250466
$323$	−4.75033	−0.264315
$324$	8.90103	0.494502
$325$	8.58318	0.476109
$326$	8.14277	0.450986
$327$	1.23447	0.0682661
$328$	−0.924886	−0.0510683
$329$	−32.6320	−1.79906
$330$	−0.254204	−0.0139935
$331$	2.91722	0.160345	0.0801726	−	0.996781i	$-0.474453\pi$
$331$	2.91722	0.160345	0.0801726	+	0.996781i	$0.474453\pi$
$332$	12.7384	0.699110
$333$	16.6683	0.913415
$334$	−23.9719	−1.31168
$335$	−1.63707	−0.0894429
$336$	−0.471600	−0.0257279
$337$	−14.7290	−0.802337	−0.401169	−	0.916004i	$-0.631396\pi$
$337$	−14.7290	−0.802337	−0.401169	+	0.916004i	$0.631396\pi$
$338$	−8.71972	−0.474290
$339$	−1.80977	−0.0982935
$340$	−3.10634	−0.168465
$341$	10.9684	0.593974
$342$	4.21735	0.228048
$343$	27.8662	1.50463
$344$	2.50020	0.134802
$345$	−0.0968138	−0.00521228
$346$	−14.3175	−0.769712
$347$	−0.0630938	−0.00338705	−0.00169353	−	0.999999i	$-0.500539\pi$
$347$	−0.0630938	−0.00338705	−0.00169353	+	0.999999i	$0.500539\pi$
$348$	0.667401	0.0357765
$349$	−31.5735	−1.69009	−0.845047	−	0.534693i	$-0.820427\pi$
$349$	−31.5735	−1.69009	−0.845047	+	0.534693i	$0.820427\pi$
$350$	−18.6462	−0.996679
$351$	−1.30013	−0.0693957
$352$	−2.62570	−0.139950
$353$	−14.5219	−0.772921	−0.386461	−	0.922306i	$-0.626302\pi$
$353$	−14.5219	−0.772921	−0.386461	+	0.922306i	$0.626302\pi$
$354$	−0.183863	−0.00977220
$355$	12.7008	0.674088
$356$	−0.332849	−0.0176410
$357$	−1.58775	−0.0840327
$358$	−6.19888	−0.327621
$359$	−29.2666	−1.54463	−0.772317	−	0.635237i	$-0.780902\pi$
$359$	−29.2666	−1.54463	−0.772317	+	0.635237i	$0.780902\pi$
$360$	2.75781	0.145350
$361$	−17.0092	−0.895220
$362$	11.6292	0.611215
$363$	0.430809	0.0226116
$364$	−9.29850	−0.487374
$365$	5.02326	0.262929
$366$	0.290426	0.0151808
$367$	0.888116	0.0463593	0.0231796	−	0.999731i	$-0.492621\pi$
$367$	0.888116	0.0463593	0.0231796	+	0.999731i	$0.492621\pi$
$368$	−1.00000	−0.0521286
$369$	2.76448	0.143913
$370$	5.14525	0.267489
$371$	6.29668	0.326908
$372$	0.438325	0.0227261
$373$	27.2211	1.40946	0.704728	−	0.709477i	$-0.251069\pi$
$373$	27.2211	1.40946	0.704728	+	0.709477i	$0.251069\pi$
$374$	−8.84002	−0.457107
$375$	−0.885721	−0.0457384
$376$	−7.26050	−0.374432
$377$	13.1591	0.677728
$378$	2.82441	0.145272
$379$	3.22953	0.165890	0.0829450	−	0.996554i	$-0.473567\pi$
$379$	3.22953	0.165890	0.0829450	+	0.996554i	$0.473567\pi$
$380$	1.30183	0.0667827
$381$	1.40270	0.0718625
$382$	−22.3031	−1.14113
$383$	−26.7849	−1.36865	−0.684323	−	0.729179i	$-0.739902\pi$
$383$	−26.7849	−1.36865	−0.684323	+	0.729179i	$0.739902\pi$
$384$	−0.104929	−0.00535465
$385$	10.8884	0.554922
$386$	18.8087	0.957339
$387$	−7.47308	−0.379878
$388$	−7.74399	−0.393141
$389$	27.8018	1.40961	0.704804	−	0.709402i	$-0.251035\pi$
$389$	27.8018	1.40961	0.704804	+	0.709402i	$0.251035\pi$
$390$	−0.200296	−0.0101424
$391$	−3.36673	−0.170263
$392$	13.2001	0.666707
$393$	−0.104929	−0.00529299
$394$	0.621917	0.0313317
$395$	4.86856	0.244964
$396$	7.84819	0.394386
$397$	12.2162	0.613114	0.306557	−	0.951852i	$-0.400823\pi$
$397$	12.2162	0.613114	0.306557	+	0.951852i	$0.400823\pi$
$398$	−12.8832	−0.645778
$399$	0.665410	0.0333122
$400$	−4.14870	−0.207435
$401$	10.9786	0.548244	0.274122	−	0.961695i	$-0.411613\pi$
$401$	10.9786	0.548244	0.274122	+	0.961695i	$0.411613\pi$
$402$	−0.186177	−0.00928564
$403$	8.64242	0.430510
$404$	−4.95703	−0.246621
$405$	−8.21260	−0.408087
$406$	−28.5869	−1.41874
$407$	14.6424	0.725795
$408$	−0.353269	−0.0174894
$409$	−10.9712	−0.542491	−0.271246	−	0.962510i	$-0.587436\pi$
$409$	−10.9712	−0.542491	−0.271246	+	0.962510i	$0.587436\pi$
$410$	0.853353	0.0421441
$411$	−0.204012	−0.0100632
$412$	−9.93749	−0.489585
$413$	7.87543	0.387524
$414$	2.98899	0.146901
$415$	−11.7532	−0.576940
$416$	−2.06888	−0.101435
$417$	1.11512	0.0546077
$418$	3.70476	0.181206
$419$	35.0121	1.71045	0.855227	−	0.518254i	$-0.173418\pi$
$419$	35.0121	1.71045	0.855227	+	0.518254i	$0.173418\pi$
$420$	0.435125	0.0212319
$421$	−21.6550	−1.05540	−0.527701	−	0.849430i	$-0.676946\pi$
$421$	−21.6550	−1.05540	−0.527701	+	0.849430i	$0.676946\pi$
$422$	1.02730	0.0500081
$423$	21.7016	1.05517
$424$	1.40099	0.0680380
$425$	−13.9676	−0.677527
$426$	1.44440	0.0699814
$427$	−12.4399	−0.602008
$428$	17.1607	0.829492
$429$	−0.570004	−0.0275200
$430$	−2.30683	−0.111245
$431$	32.7824	1.57907	0.789536	−	0.613705i	$-0.210321\pi$
$431$	32.7824	1.57907	0.789536	+	0.613705i	$0.210321\pi$
$432$	0.628421	0.0302349
$433$	−38.3958	−1.84518	−0.922592	−	0.385777i	$-0.873934\pi$
$433$	−38.3958	−1.84518	−0.922592	+	0.385777i	$0.873934\pi$
$434$	−18.7749	−0.901222
$435$	−0.615783	−0.0295245
$436$	−11.7647	−0.563428
$437$	1.41096	0.0674954
$438$	0.571271	0.0272964
$439$	−2.57434	−0.122866	−0.0614332	−	0.998111i	$-0.519567\pi$
$439$	−2.57434	−0.122866	−0.0614332	+	0.998111i	$0.519567\pi$
$440$	2.42262	0.115494
$441$	−39.4551	−1.87881
$442$	−6.96537	−0.331309
$443$	6.85752	0.325811	0.162905	−	0.986642i	$-0.447913\pi$
$443$	6.85752	0.325811	0.162905	+	0.986642i	$0.447913\pi$
$444$	0.585144	0.0277697
$445$	0.307106	0.0145582
$446$	12.2314	0.579174
$447$	−2.15703	−0.102024
$448$	4.49446	0.212343
$449$	12.6949	0.599109	0.299555	−	0.954079i	$-0.403162\pi$
$449$	12.6949	0.599109	0.299555	+	0.954079i	$0.403162\pi$
$450$	12.4004	0.584562
$451$	2.42847	0.114352
$452$	17.2476	0.811257
$453$	−0.807481	−0.0379388
$454$	−6.97219	−0.327221
$455$	8.57933	0.402205
$456$	0.148051	0.00693314
$457$	−16.8525	−0.788326	−0.394163	−	0.919041i	$-0.628965\pi$
$457$	−16.8525	−0.788326	−0.394163	+	0.919041i	$0.628965\pi$
$458$	10.4119	0.486514
$459$	2.11572	0.0987535
$460$	0.922657	0.0430191
$461$	37.4821	1.74572	0.872858	−	0.487975i	$-0.162264\pi$
$461$	37.4821	1.74572	0.872858	+	0.487975i	$0.162264\pi$
$462$	1.23828	0.0576100
$463$	−1.17079	−0.0544112	−0.0272056	−	0.999630i	$-0.508661\pi$
$463$	−1.17079	−0.0544112	−0.0272056	+	0.999630i	$0.508661\pi$
$464$	−6.36048	−0.295278
$465$	−0.404424	−0.0187547
$466$	−4.03144	−0.186753
$467$	−7.36079	−0.340617	−0.170308	−	0.985391i	$-0.554476\pi$
$467$	−7.36079	−0.340617	−0.170308	+	0.985391i	$0.554476\pi$
$468$	6.18387	0.285849
$469$	7.97453	0.368230
$470$	6.69895	0.309000
$471$	0.693563	0.0319577
$472$	1.75225	0.0806540
$473$	−6.56478	−0.301849
$474$	0.553678	0.0254313
$475$	5.85366	0.268584
$476$	15.1316	0.693557
$477$	−4.18754	−0.191734
$478$	5.53535	0.253181
$479$	8.66283	0.395815	0.197907	−	0.980221i	$-0.436585\pi$
$479$	8.66283	0.395815	0.197907	+	0.980221i	$0.436585\pi$
$480$	0.0968138	0.00441893
$481$	11.5372	0.526053
$482$	24.7841	1.12888
$483$	0.471600	0.0214586
$484$	−4.10570	−0.186623
$485$	7.14505	0.324440
$486$	−2.81924	−0.127883
$487$	−35.3904	−1.60369	−0.801845	−	0.597532i	$-0.796148\pi$
$487$	−35.3904	−1.60369	−0.801845	+	0.597532i	$0.796148\pi$
$488$	−2.76783	−0.125294
$489$	−0.854415	−0.0386380
$490$	−12.1792	−0.550200
$491$	11.5517	0.521321	0.260660	−	0.965431i	$-0.416060\pi$
$491$	11.5517	0.521321	0.260660	+	0.965431i	$0.416060\pi$
$492$	0.0970477	0.00437525
$493$	−21.4140	−0.964439
$494$	2.91911	0.131337
$495$	−7.24119	−0.325467
$496$	−4.17734	−0.187568
$497$	−61.8682	−2.77517
$498$	−1.33663	−0.0598958
$499$	−12.9095	−0.577910	−0.288955	−	0.957343i	$-0.593308\pi$
$499$	−12.9095	−0.577910	−0.288955	+	0.957343i	$0.593308\pi$
$500$	8.44112	0.377498
$501$	2.51536	0.112378
$502$	−1.82366	−0.0813938
$503$	0.499263	0.0222610	0.0111305	−	0.999938i	$-0.496457\pi$
$503$	0.499263	0.0222610	0.0111305	+	0.999938i	$0.496457\pi$
$504$	−13.4339	−0.598393
$505$	4.57364	0.203524
$506$	2.62570	0.116727
$507$	0.914955	0.0406346
$508$	−13.3680	−0.593111
$509$	2.59603	0.115067	0.0575336	−	0.998344i	$-0.481676\pi$
$509$	2.59603	0.115067	0.0575336	+	0.998344i	$0.481676\pi$
$510$	0.325946	0.0144331
$511$	−24.4693	−1.08246
$512$	1.00000	0.0441942
$513$	−0.886677	−0.0391478
$514$	3.31104	0.146044
$515$	9.16890	0.404030
$516$	−0.262345	−0.0115491
$517$	19.0639	0.838429
$518$	−25.0636	−1.10123
$519$	1.50232	0.0659446
$520$	1.90887	0.0837095
$521$	17.5923	0.770734	0.385367	−	0.922763i	$-0.374075\pi$
$521$	17.5923	0.770734	0.385367	+	0.922763i	$0.374075\pi$
$522$	19.0114	0.832107
$523$	−4.82154	−0.210831	−0.105416	−	0.994428i	$-0.533617\pi$
$523$	−4.82154	−0.210831	−0.105416	+	0.994428i	$0.533617\pi$
$524$	1.00000	0.0436852
$525$	1.95653	0.0853900
$526$	7.17574	0.312877
$527$	−14.0640	−0.612636
$528$	0.275513	0.0119902
$529$	1.00000	0.0434783
$530$	−1.29263	−0.0561484
$531$	−5.23747	−0.227287
$532$	−6.34150	−0.274939
$533$	1.91348	0.0828821
$534$	0.0349256	0.00151138
$535$	−15.8334	−0.684538
$536$	1.77430	0.0766383
$537$	0.650444	0.0280687
$538$	7.38289	0.318299
$539$	−34.6596	−1.49289
$540$	−0.579817	−0.0249513
$541$	−11.7232	−0.504018	−0.252009	−	0.967725i	$-0.581091\pi$
$541$	−11.7232	−0.504018	−0.252009	+	0.967725i	$0.581091\pi$
$542$	−30.0110	−1.28908
$543$	−1.22024	−0.0523655
$544$	3.36673	0.144347
$545$	10.8548	0.464969
$546$	0.975686	0.0417555
$547$	−25.6970	−1.09872	−0.549361	−	0.835585i	$-0.685129\pi$
$547$	−25.6970	−1.09872	−0.549361	+	0.835585i	$0.685129\pi$
$548$	1.94428	0.0830555
$549$	8.27301	0.353084
$550$	10.8932	0.464490
$551$	8.97440	0.382322
$552$	0.104929	0.00446609
$553$	−23.7158	−1.00850
$554$	−14.8705	−0.631789
$555$	−0.539888	−0.0229169
$556$	−10.6273	−0.450700
$557$	−36.2207	−1.53472	−0.767360	−	0.641216i	$-0.778430\pi$
$557$	−36.2207	−1.53472	−0.767360	+	0.641216i	$0.778430\pi$
$558$	12.4860	0.528576
$559$	−5.17263	−0.218779
$560$	−4.14684	−0.175236
$561$	0.927578	0.0391624
$562$	16.2176	0.684097
$563$	1.16134	0.0489446	0.0244723	−	0.999701i	$-0.492209\pi$
$563$	1.16134	0.0489446	0.0244723	+	0.999701i	$0.492209\pi$
$564$	0.761839	0.0320792
$565$	−15.9136	−0.669489
$566$	−3.55924	−0.149606
$567$	40.0053	1.68006
$568$	−13.7655	−0.577586
$569$	−28.3199	−1.18723	−0.593616	−	0.804748i	$-0.702300\pi$
$569$	−28.3199	−1.18723	−0.593616	+	0.804748i	$0.702300\pi$
$570$	−0.136601	−0.00572157
$571$	−6.75947	−0.282875	−0.141437	−	0.989947i	$-0.545172\pi$
$571$	−6.75947	−0.282875	−0.141437	+	0.989947i	$0.545172\pi$
$572$	5.43226	0.227134
$573$	2.34025	0.0977655
$574$	−4.15686	−0.173504
$575$	4.14870	0.173013
$576$	−2.98899	−0.124541
$577$	−9.27256	−0.386022	−0.193011	−	0.981197i	$-0.561825\pi$
$577$	−9.27256	−0.386022	−0.193011	+	0.981197i	$0.561825\pi$
$578$	−5.66513	−0.235638
$579$	−1.97359	−0.0820195
$580$	5.86855	0.243678
$581$	57.2521	2.37522
$582$	0.812572	0.0336822
$583$	−3.67858	−0.152351
$584$	−5.44434	−0.225288
$585$	−5.70559	−0.235897
$586$	−6.76805	−0.279586
$587$	−40.9161	−1.68879	−0.844394	−	0.535723i	$-0.820039\pi$
$587$	−40.9161	−1.68879	−0.844394	+	0.535723i	$0.820039\pi$
$588$	−1.38508	−0.0571198
$589$	5.89406	0.242861
$590$	−1.61673	−0.0665597
$591$	−0.0652574	−0.00268433
$592$	−5.57655	−0.229195
$593$	−24.7167	−1.01499	−0.507496	−	0.861654i	$-0.669429\pi$
$593$	−24.7167	−1.01499	−0.507496	+	0.861654i	$0.669429\pi$
$594$	−1.65004	−0.0677021
$595$	−13.9613	−0.572357
$596$	20.5570	0.842048
$597$	1.35183	0.0553267
$598$	2.06888	0.0846029
$599$	−34.5998	−1.41371	−0.706855	−	0.707358i	$-0.749887\pi$
$599$	−34.5998	−1.41371	−0.706855	+	0.707358i	$0.749887\pi$
$600$	0.435321	0.0177719
$601$	13.4788	0.549812	0.274906	−	0.961471i	$-0.411353\pi$
$601$	13.4788	0.549812	0.274906	+	0.961471i	$0.411353\pi$
$602$	11.2371	0.457988
$603$	−5.30338	−0.215970
$604$	7.69548	0.313124
$605$	3.78816	0.154010
$606$	0.520138	0.0211292
$607$	−18.4913	−0.750540	−0.375270	−	0.926916i	$-0.622450\pi$
$607$	−18.4913	−0.750540	−0.375270	+	0.926916i	$0.622450\pi$
$608$	−1.41096	−0.0572220
$609$	2.99961	0.121550
$610$	2.55376	0.103399
$611$	15.0211	0.607690
$612$	−10.0631	−0.406778
$613$	17.0909	0.690295	0.345147	−	0.938549i	$-0.387829\pi$
$613$	17.0909	0.690295	0.345147	+	0.938549i	$0.387829\pi$
$614$	17.3144	0.698754
$615$	−0.0895418	−0.00361067
$616$	−11.8011	−0.475479
$617$	−44.8127	−1.80409	−0.902045	−	0.431642i	$-0.857934\pi$
$617$	−44.8127	−1.80409	−0.902045	+	0.431642i	$0.857934\pi$
$618$	1.04273	0.0419449
$619$	46.8054	1.88127	0.940634	−	0.339423i	$-0.110232\pi$
$619$	46.8054	1.88127	0.940634	+	0.339423i	$0.110232\pi$
$620$	3.85425	0.154790
$621$	−0.628421	−0.0252177
$622$	−1.81503	−0.0727760
$623$	−1.49598	−0.0599350
$624$	0.217087	0.00869042
$625$	12.9553	0.518210
$626$	−0.341200	−0.0136371
$627$	−0.388738	−0.0155247
$628$	−6.60981	−0.263760
$629$	−18.7748	−0.748599
$630$	12.3949	0.493823
$631$	15.7987	0.628938	0.314469	−	0.949268i	$-0.398174\pi$
$631$	15.7987	0.628938	0.314469	+	0.949268i	$0.398174\pi$
$632$	−5.27667	−0.209895
$633$	−0.107794	−0.00428441
$634$	15.3180	0.608356
$635$	12.3341	0.489465
$636$	−0.147005	−0.00582912
$637$	−27.3095	−1.08204
$638$	16.7007	0.661188
$639$	41.1448	1.62766
$640$	−0.922657	−0.0364712
$641$	48.4106	1.91210	0.956051	−	0.293199i	$-0.0947199\pi$
$641$	48.4106	1.91210	0.956051	+	0.293199i	$0.0947199\pi$
$642$	−1.80066	−0.0710663
$643$	39.4557	1.55598	0.777991	−	0.628276i	$-0.216239\pi$
$643$	39.4557	1.55598	0.777991	+	0.628276i	$0.216239\pi$
$644$	−4.49446	−0.177106
$645$	0.242054	0.00953087
$646$	−4.75033	−0.186899
$647$	31.2628	1.22907	0.614533	−	0.788891i	$-0.289344\pi$
$647$	31.2628	1.22907	0.614533	+	0.788891i	$0.289344\pi$
$648$	8.90103	0.349665
$649$	−4.60089	−0.180601
$650$	8.58318	0.336660
$651$	1.97003	0.0772117
$652$	8.14277	0.318895
$653$	−30.4142	−1.19020	−0.595100	−	0.803652i	$-0.702887\pi$
$653$	−30.4142	−1.19020	−0.595100	+	0.803652i	$0.702887\pi$
$654$	1.23447	0.0482714
$655$	−0.922657	−0.0360512
$656$	−0.924886	−0.0361107
$657$	16.2731	0.634873
$658$	−32.6320	−1.27213
$659$	−17.7627	−0.691938	−0.345969	−	0.938246i	$-0.612450\pi$
$659$	−17.7627	−0.691938	−0.345969	+	0.938246i	$0.612450\pi$
$660$	−0.254204	−0.00989488
$661$	−10.1809	−0.395992	−0.197996	−	0.980203i	$-0.563443\pi$
$661$	−10.1809	−0.395992	−0.197996	+	0.980203i	$0.563443\pi$
$662$	2.91722	0.113381
$663$	0.730872	0.0283847
$664$	12.7384	0.494345
$665$	5.85103	0.226893
$666$	16.6683	0.645882
$667$	6.36048	0.246279
$668$	−23.9719	−0.927501
$669$	−1.28343	−0.0496204
$670$	−1.63707	−0.0632457
$671$	7.26749	0.280558
$672$	−0.471600	−0.0181924
$673$	23.5152	0.906445	0.453223	−	0.891397i	$-0.350274\pi$
$673$	23.5152	0.906445	0.453223	+	0.891397i	$0.350274\pi$
$674$	−14.7290	−0.567338
$675$	−2.60713	−0.100349
$676$	−8.71972	−0.335374
$677$	33.7749	1.29808	0.649038	−	0.760756i	$-0.275171\pi$
$677$	33.7749	1.29808	0.649038	+	0.760756i	$0.275171\pi$
$678$	−1.80977	−0.0695040
$679$	−34.8050	−1.33569
$680$	−3.10634	−0.119123
$681$	0.731588	0.0280345
$682$	10.9684	0.420003
$683$	−20.9082	−0.800031	−0.400016	−	0.916508i	$-0.630995\pi$
$683$	−20.9082	−0.800031	−0.400016	+	0.916508i	$0.630995\pi$
$684$	4.21735	0.161254
$685$	−1.79390	−0.0685415
$686$	27.8662	1.06394
$687$	−1.09251	−0.0416818
$688$	2.50020	0.0953193
$689$	−2.89848	−0.110423
$690$	−0.0968138	−0.00368564
$691$	19.0903	0.726229	0.363114	−	0.931745i	$-0.381713\pi$
$691$	19.0903	0.726229	0.363114	+	0.931745i	$0.381713\pi$
$692$	−14.3175	−0.544268
$693$	35.2733	1.33992
$694$	−0.0630938	−0.00239501
$695$	9.80540	0.371940
$696$	0.667401	0.0252978
$697$	−3.11384	−0.117945
$698$	−31.5735	−1.19508
$699$	0.423016	0.0159999
$700$	−18.6462	−0.704759
$701$	40.1206	1.51533	0.757667	−	0.652642i	$-0.226339\pi$
$701$	40.1206	1.51533	0.757667	+	0.652642i	$0.226339\pi$
$702$	−1.30013	−0.0490702
$703$	7.86830	0.296759
$704$	−2.62570	−0.0989598
$705$	−0.702917	−0.0264734
$706$	−14.5219	−0.546538
$707$	−22.2791	−0.837893
$708$	−0.183863	−0.00690999
$709$	−29.8132	−1.11966	−0.559830	−	0.828607i	$-0.689134\pi$
$709$	−29.8132	−1.11966	−0.559830	+	0.828607i	$0.689134\pi$
$710$	12.7008	0.476653
$711$	15.7719	0.591493
$712$	−0.332849	−0.0124740
$713$	4.17734	0.156443
$714$	−1.58775	−0.0594201
$715$	−5.01212	−0.187443
$716$	−6.19888	−0.231663
$717$	−0.580820	−0.0216911
$718$	−29.2666	−1.09222
$719$	31.8977	1.18959	0.594793	−	0.803879i	$-0.297234\pi$
$719$	31.8977	1.18959	0.594793	+	0.803879i	$0.297234\pi$
$720$	2.75781	0.102778
$721$	−44.6636	−1.66336
$722$	−17.0092	−0.633016
$723$	−2.60058	−0.0967165
$724$	11.6292	0.432194
$725$	26.3878	0.980017
$726$	0.430809	0.0159888
$727$	12.9040	0.478583	0.239291	−	0.970948i	$-0.423085\pi$
$727$	12.9040	0.478583	0.239291	+	0.970948i	$0.423085\pi$
$728$	−9.29850	−0.344625
$729$	−26.4073	−0.978047
$730$	5.02326	0.185919
$731$	8.41751	0.311333
$732$	0.290426	0.0107345
$733$	14.1017	0.520859	0.260430	−	0.965493i	$-0.416136\pi$
$733$	14.1017	0.520859	0.260430	+	0.965493i	$0.416136\pi$
$734$	0.888116	0.0327810
$735$	1.27795	0.0471381
$736$	−1.00000	−0.0368605
$737$	−4.65879	−0.171609
$738$	2.76448	0.101762
$739$	42.6642	1.56943	0.784715	−	0.619857i	$-0.212809\pi$
$739$	42.6642	1.56943	0.784715	+	0.619857i	$0.212809\pi$
$740$	5.14525	0.189143
$741$	−0.306301	−0.0112522
$742$	6.29668	0.231159
$743$	−12.3252	−0.452167	−0.226084	−	0.974108i	$-0.572592\pi$
$743$	−12.3252	−0.452167	−0.226084	+	0.974108i	$0.572592\pi$
$744$	0.438325	0.0160698
$745$	−18.9671	−0.694900
$746$	27.2211	0.996636
$747$	−38.0749	−1.39309
$748$	−8.84002	−0.323223
$749$	77.1278	2.81819
$750$	−0.885721	−0.0323420
$751$	31.3378	1.14353	0.571766	−	0.820417i	$-0.306259\pi$
$751$	31.3378	1.14353	0.571766	+	0.820417i	$0.306259\pi$
$752$	−7.26050	−0.264763
$753$	0.191355	0.00697337
$754$	13.1591	0.479226
$755$	−7.10029	−0.258406
$756$	2.82441	0.102723
$757$	−0.135578	−0.00492768	−0.00246384	−	0.999997i	$-0.500784\pi$
$757$	−0.135578	−0.00492768	−0.00246384	+	0.999997i	$0.500784\pi$
$758$	3.22953	0.117302
$759$	−0.275513	−0.0100005
$760$	1.30183	0.0472225
$761$	47.3009	1.71466	0.857329	−	0.514769i	$-0.172122\pi$
$761$	47.3009	1.71466	0.857329	+	0.514769i	$0.172122\pi$
$762$	1.40270	0.0508145
$763$	−52.8761	−1.91424
$764$	−22.3031	−0.806900
$765$	9.28481	0.335693
$766$	−26.7849	−0.967779
$767$	−3.62521	−0.130899
$768$	−0.104929	−0.00378631
$769$	8.33290	0.300492	0.150246	−	0.988649i	$-0.451993\pi$
$769$	8.33290	0.300492	0.150246	+	0.988649i	$0.451993\pi$
$770$	10.8884	0.392389
$771$	−0.347426	−0.0125122
$772$	18.8087	0.676941
$773$	−8.79868	−0.316466	−0.158233	−	0.987402i	$-0.550580\pi$
$773$	−8.79868	−0.316466	−0.158233	+	0.987402i	$0.550580\pi$
$774$	−7.47308	−0.268614
$775$	17.3305	0.622531
$776$	−7.74399	−0.277993
$777$	2.62990	0.0943473
$778$	27.8018	0.996743
$779$	1.30498	0.0467557
$780$	−0.200296	−0.00717176
$781$	36.1440	1.29333
$782$	−3.36673	−0.120394
$783$	−3.99706	−0.142843
$784$	13.2001	0.471433
$785$	6.09859	0.217668
$786$	−0.104929	−0.00374271
$787$	−24.2596	−0.864760	−0.432380	−	0.901691i	$-0.642326\pi$
$787$	−24.2596	−0.864760	−0.432380	+	0.901691i	$0.642326\pi$
$788$	0.621917	0.0221549
$789$	−0.752946	−0.0268056
$790$	4.86856	0.173216
$791$	77.5184	2.75624
$792$	7.84819	0.278873
$793$	5.72631	0.203347
$794$	12.2162	0.433537
$795$	0.135635	0.00481048
$796$	−12.8832	−0.456634
$797$	54.2627	1.92208	0.961041	−	0.276406i	$-0.0891433\pi$
$797$	54.2627	1.92208	0.961041	+	0.276406i	$0.0891433\pi$
$798$	0.665410	0.0235553
$799$	−24.4441	−0.864772
$800$	−4.14870	−0.146679
$801$	0.994883	0.0351524
$802$	10.9786	0.387667
$803$	14.2952	0.504467
$804$	−0.186177	−0.00656594
$805$	4.14684	0.146157
$806$	8.64242	0.304416
$807$	−0.774682	−0.0272701
$808$	−4.95703	−0.174388
$809$	26.9769	0.948457	0.474229	−	0.880402i	$-0.342727\pi$
$809$	26.9769	0.948457	0.474229	+	0.880402i	$0.342727\pi$
$810$	−8.21260	−0.288561
$811$	10.0780	0.353887	0.176944	−	0.984221i	$-0.443379\pi$
$811$	10.0780	0.353887	0.176944	+	0.984221i	$0.443379\pi$
$812$	−28.5869	−1.00320
$813$	3.14904	0.110442
$814$	14.6424	0.513214
$815$	−7.51298	−0.263168
$816$	−0.353269	−0.0123669
$817$	−3.52769	−0.123418
$818$	−10.9712	−0.383599
$819$	27.7931	0.971170
$820$	0.853353	0.0298004
$821$	14.1336	0.493267	0.246633	−	0.969109i	$-0.420676\pi$
$821$	14.1336	0.493267	0.246633	+	0.969109i	$0.420676\pi$
$822$	−0.204012	−0.00711573
$823$	38.7543	1.35089	0.675446	−	0.737410i	$-0.263951\pi$
$823$	38.7543	1.35089	0.675446	+	0.737410i	$0.263951\pi$
$824$	−9.93749	−0.346189
$825$	−1.14302	−0.0397949
$826$	7.87543	0.274021
$827$	46.4378	1.61480	0.807400	−	0.590005i	$-0.200874\pi$
$827$	46.4378	1.61480	0.807400	+	0.590005i	$0.200874\pi$
$828$	2.98899	0.103875
$829$	−45.9314	−1.59526	−0.797631	−	0.603145i	$-0.793914\pi$
$829$	−45.9314	−1.59526	−0.797631	+	0.603145i	$0.793914\pi$
$830$	−11.7532	−0.407958
$831$	1.56036	0.0541282
$832$	−2.06888	−0.0717256
$833$	44.4413	1.53980
$834$	1.11512	0.0386135
$835$	22.1179	0.765420
$836$	3.70476	0.128132
$837$	−2.62513	−0.0907377
$838$	35.0121	1.20947
$839$	−3.72011	−0.128433	−0.0642163	−	0.997936i	$-0.520455\pi$
$839$	−3.72011	−0.128433	−0.0642163	+	0.997936i	$0.520455\pi$
$840$	0.435125	0.0150133
$841$	11.4557	0.395026
$842$	−21.6550	−0.746282
$843$	−1.70170	−0.0586096
$844$	1.02730	0.0353610
$845$	8.04532	0.276767
$846$	21.7016	0.746115
$847$	−18.4529	−0.634049
$848$	1.40099	0.0481102
$849$	0.373469	0.0128174
$850$	−13.9676	−0.479084
$851$	5.57655	0.191162
$852$	1.44440	0.0494843
$853$	3.56729	0.122142	0.0610708	−	0.998133i	$-0.480548\pi$
$853$	3.56729	0.122142	0.0610708	+	0.998133i	$0.480548\pi$
$854$	−12.4399	−0.425684
$855$	−3.89117	−0.133075
$856$	17.1607	0.586539
$857$	48.8357	1.66820	0.834098	−	0.551617i	$-0.185989\pi$
$857$	48.8357	1.66820	0.834098	+	0.551617i	$0.185989\pi$
$858$	−0.570004	−0.0194596
$859$	−8.44172	−0.288028	−0.144014	−	0.989576i	$-0.546001\pi$
$859$	−8.44172	−0.288028	−0.144014	+	0.989576i	$0.546001\pi$
$860$	−2.30683	−0.0786623
$861$	0.436177	0.0148649
$862$	32.7824	1.11657
$863$	6.15788	0.209617	0.104808	−	0.994492i	$-0.466577\pi$
$863$	6.15788	0.209617	0.104808	+	0.994492i	$0.466577\pi$
$864$	0.628421	0.0213793
$865$	13.2101	0.449157
$866$	−38.3958	−1.30474
$867$	0.594438	0.0201882
$868$	−18.7749	−0.637260
$869$	13.8550	0.469997
$870$	−0.615783	−0.0208770
$871$	−3.67083	−0.124381
$872$	−11.7647	−0.398404
$873$	23.1467	0.783397
$874$	1.41096	0.0477265
$875$	37.9382	1.28255
$876$	0.571271	0.0193015
$877$	−11.7323	−0.396171	−0.198086	−	0.980185i	$-0.563472\pi$
$877$	−11.7323	−0.396171	−0.198086	+	0.980185i	$0.563472\pi$
$878$	−2.57434	−0.0868797
$879$	0.710167	0.0239533
$880$	2.42262	0.0816665
$881$	−32.8076	−1.10532	−0.552658	−	0.833408i	$-0.686386\pi$
$881$	−32.8076	−1.10532	−0.552658	+	0.833408i	$0.686386\pi$
$882$	−39.4551	−1.32852
$883$	44.1112	1.48446	0.742230	−	0.670145i	$-0.233768\pi$
$883$	44.1112	1.48446	0.742230	+	0.670145i	$0.233768\pi$
$884$	−6.96537	−0.234271
$885$	0.169642	0.00570247
$886$	6.85752	0.230383
$887$	15.0465	0.505211	0.252605	−	0.967569i	$-0.418713\pi$
$887$	15.0465	0.505211	0.252605	+	0.967569i	$0.418713\pi$
$888$	0.585144	0.0196362
$889$	−60.0821	−2.01509
$890$	0.307106	0.0102942
$891$	−23.3714	−0.782972
$892$	12.2314	0.409538
$893$	10.2443	0.342812
$894$	−2.15703	−0.0721420
$895$	5.71944	0.191180
$896$	4.49446	0.150149
$897$	−0.217087	−0.00724831
$898$	12.6949	0.423634
$899$	26.5699	0.886156
$900$	12.4004	0.413348
$901$	4.71675	0.157138
$902$	2.42847	0.0808593
$903$	−1.17910	−0.0392379
$904$	17.2476	0.573645
$905$	−10.7297	−0.356668
$906$	−0.807481	−0.0268268
$907$	15.9616	0.529997	0.264998	−	0.964249i	$-0.414629\pi$
$907$	15.9616	0.529997	0.264998	+	0.964249i	$0.414629\pi$
$908$	−6.97219	−0.231380
$909$	14.8165	0.491433
$910$	8.57933	0.284402
$911$	−12.4841	−0.413616	−0.206808	−	0.978382i	$-0.566308\pi$
$911$	−12.4841	−0.413616	−0.206808	+	0.978382i	$0.566308\pi$
$912$	0.148051	0.00490247
$913$	−33.4472	−1.10694
$914$	−16.8525	−0.557431
$915$	−0.267964	−0.00885862
$916$	10.4119	0.344017
$917$	4.49446	0.148420
$918$	2.11572	0.0698293
$919$	−4.85021	−0.159994	−0.0799969	−	0.996795i	$-0.525491\pi$
$919$	−4.85021	−0.159994	−0.0799969	+	0.996795i	$0.525491\pi$
$920$	0.922657	0.0304191
$921$	−1.81679	−0.0598653
$922$	37.4821	1.23441
$923$	28.4791	0.937402
$924$	1.23828	0.0407364
$925$	23.1355	0.760690
$926$	−1.17079	−0.0384745
$927$	29.7031	0.975577
$928$	−6.36048	−0.208793
$929$	48.7242	1.59859	0.799294	−	0.600940i	$-0.205207\pi$
$929$	48.7242	1.59859	0.799294	+	0.600940i	$0.205207\pi$
$930$	−0.404424	−0.0132616
$931$	−18.6249	−0.610406
$932$	−4.03144	−0.132054
$933$	0.190450	0.00623505
$934$	−7.36079	−0.240852
$935$	8.15631	0.266740
$936$	6.18387	0.202126
$937$	−15.8277	−0.517069	−0.258535	−	0.966002i	$-0.583240\pi$
$937$	−15.8277	−0.517069	−0.258535	+	0.966002i	$0.583240\pi$
$938$	7.97453	0.260378
$939$	0.0358019	0.00116835
$940$	6.69895	0.218496
$941$	7.45855	0.243142	0.121571	−	0.992583i	$-0.461207\pi$
$941$	7.45855	0.243142	0.121571	+	0.992583i	$0.461207\pi$
$942$	0.693563	0.0225975
$943$	0.924886	0.0301184
$944$	1.75225	0.0570310
$945$	−2.60596	−0.0847719
$946$	−6.56478	−0.213439
$947$	−25.4360	−0.826559	−0.413280	−	0.910604i	$-0.635617\pi$
$947$	−25.4360	−0.826559	−0.413280	+	0.910604i	$0.635617\pi$
$948$	0.553678	0.0179826
$949$	11.2637	0.365635
$950$	5.85366	0.189918
$951$	−1.60731	−0.0521206
$952$	15.1316	0.490419
$953$	−31.0700	−1.00646	−0.503228	−	0.864154i	$-0.667854\pi$
$953$	−31.0700	−1.00646	−0.503228	+	0.864154i	$0.667854\pi$
$954$	−4.18754	−0.135577
$955$	20.5782	0.665894
$956$	5.53535	0.179026
$957$	−1.75240	−0.0566469
$958$	8.66283	0.279883
$959$	8.73848	0.282180
$960$	0.0968138	0.00312465
$961$	−13.5498	−0.437092
$962$	11.5372	0.371975
$963$	−51.2930	−1.65289
$964$	24.7841	0.798241
$965$	−17.3540	−0.558645
$966$	0.471600	0.0151735
$967$	−2.89990	−0.0932545	−0.0466273	−	0.998912i	$-0.514847\pi$
$967$	−2.89990	−0.0932545	−0.0466273	+	0.998912i	$0.514847\pi$
$968$	−4.10570	−0.131962
$969$	0.498449	0.0160125
$970$	7.14505	0.229414
$971$	35.6839	1.14515	0.572576	−	0.819852i	$-0.305944\pi$
$971$	35.6839	1.14515	0.572576	+	0.819852i	$0.305944\pi$
$972$	−2.81924	−0.0904272
$973$	−47.7641	−1.53125
$974$	−35.3904	−1.13398
$975$	−0.900628	−0.0288432
$976$	−2.76783	−0.0885960
$977$	−26.4373	−0.845804	−0.422902	−	0.906175i	$-0.638989\pi$
$977$	−26.4373	−0.845804	−0.422902	+	0.906175i	$0.638989\pi$
$978$	−0.854415	−0.0273212
$979$	0.873962	0.0279319
$980$	−12.1792	−0.389050
$981$	35.1647	1.12272
$982$	11.5517	0.368629
$983$	−5.87858	−0.187498	−0.0937488	−	0.995596i	$-0.529885\pi$
$983$	−5.87858	−0.187498	−0.0937488	+	0.995596i	$0.529885\pi$
$984$	0.0970477	0.00309377
$985$	−0.573816	−0.0182833
$986$	−21.4140	−0.681962
$987$	3.42405	0.108989
$988$	2.91911	0.0928694
$989$	−2.50020	−0.0795018
$990$	−7.24119	−0.230140
$991$	12.5285	0.397981	0.198990	−	0.980001i	$-0.436234\pi$
$991$	12.5285	0.397981	0.198990	+	0.980001i	$0.436234\pi$
$992$	−4.17734	−0.132631
$993$	−0.306102	−0.00971387
$994$	−61.8682	−1.96234
$995$	11.8868	0.376837
$996$	−1.33663	−0.0423528
$997$	3.21764	0.101904	0.0509518	−	0.998701i	$-0.483774\pi$
$997$	3.21764	0.101904	0.0509518	+	0.998701i	$0.483774\pi$
$998$	−12.9095	−0.408644
$999$	−3.50442	−0.110875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.10	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.104929 q^{3} +1.00000 q^{4} -0.922657 q^{5} -0.104929 q^{6} +4.49446 q^{7} +1.00000 q^{8} -2.98899 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.104929 q^{3} +1.00000 q^{4} -0.922657 q^{5} -0.104929 q^{6} +4.49446 q^{7} +1.00000 q^{8} -2.98899 q^{9} -0.922657 q^{10} -2.62570 q^{11} -0.104929 q^{12} -2.06888 q^{13} +4.49446 q^{14} +0.0968138 q^{15} +1.00000 q^{16} +3.36673 q^{17} -2.98899 q^{18} -1.41096 q^{19} -0.922657 q^{20} -0.471600 q^{21} -2.62570 q^{22} -1.00000 q^{23} -0.104929 q^{24} -4.14870 q^{25} -2.06888 q^{26} +0.628421 q^{27} +4.49446 q^{28} -6.36048 q^{29} +0.0968138 q^{30} -4.17734 q^{31} +1.00000 q^{32} +0.275513 q^{33} +3.36673 q^{34} -4.14684 q^{35} -2.98899 q^{36} -5.57655 q^{37} -1.41096 q^{38} +0.217087 q^{39} -0.922657 q^{40} -0.924886 q^{41} -0.471600 q^{42} +2.50020 q^{43} -2.62570 q^{44} +2.75781 q^{45} -1.00000 q^{46} -7.26050 q^{47} -0.104929 q^{48} +13.2001 q^{49} -4.14870 q^{50} -0.353269 q^{51} -2.06888 q^{52} +1.40099 q^{53} +0.628421 q^{54} +2.42262 q^{55} +4.49446 q^{56} +0.148051 q^{57} -6.36048 q^{58} +1.75225 q^{59} +0.0968138 q^{60} -2.76783 q^{61} -4.17734 q^{62} -13.4339 q^{63} +1.00000 q^{64} +1.90887 q^{65} +0.275513 q^{66} +1.77430 q^{67} +3.36673 q^{68} +0.104929 q^{69} -4.14684 q^{70} -13.7655 q^{71} -2.98899 q^{72} -5.44434 q^{73} -5.57655 q^{74} +0.435321 q^{75} -1.41096 q^{76} -11.8011 q^{77} +0.217087 q^{78} -5.27667 q^{79} -0.922657 q^{80} +8.90103 q^{81} -0.924886 q^{82} +12.7384 q^{83} -0.471600 q^{84} -3.10634 q^{85} +2.50020 q^{86} +0.667401 q^{87} -2.62570 q^{88} -0.332849 q^{89} +2.75781 q^{90} -9.29850 q^{91} -1.00000 q^{92} +0.438325 q^{93} -7.26050 q^{94} +1.30183 q^{95} -0.104929 q^{96} -7.74399 q^{97} +13.2001 q^{98} +7.84819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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