LMFDB - Embedded newform 6026.2.a.i.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.694821 q^{3} +1.00000 q^{4} +0.658132 q^{5} -0.694821 q^{6} -2.75018 q^{7} -1.00000 q^{8} -2.51722 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.694821 q^{3} +1.00000 q^{4} +0.658132 q^{5} -0.694821 q^{6} -2.75018 q^{7} -1.00000 q^{8} -2.51722 q^{9} -0.658132 q^{10} -3.14857 q^{11} +0.694821 q^{12} -1.49529 q^{13} +2.75018 q^{14} +0.457284 q^{15} +1.00000 q^{16} +7.27942 q^{17} +2.51722 q^{18} +5.41346 q^{19} +0.658132 q^{20} -1.91089 q^{21} +3.14857 q^{22} +1.00000 q^{23} -0.694821 q^{24} -4.56686 q^{25} +1.49529 q^{26} -3.83348 q^{27} -2.75018 q^{28} +7.88069 q^{29} -0.457284 q^{30} -1.13470 q^{31} -1.00000 q^{32} -2.18769 q^{33} -7.27942 q^{34} -1.80998 q^{35} -2.51722 q^{36} -0.745843 q^{37} -5.41346 q^{38} -1.03896 q^{39} -0.658132 q^{40} +0.571803 q^{41} +1.91089 q^{42} +5.56529 q^{43} -3.14857 q^{44} -1.65666 q^{45} -1.00000 q^{46} +0.938950 q^{47} +0.694821 q^{48} +0.563515 q^{49} +4.56686 q^{50} +5.05790 q^{51} -1.49529 q^{52} -10.5215 q^{53} +3.83348 q^{54} -2.07217 q^{55} +2.75018 q^{56} +3.76139 q^{57} -7.88069 q^{58} -6.71876 q^{59} +0.457284 q^{60} +12.7225 q^{61} +1.13470 q^{62} +6.92283 q^{63} +1.00000 q^{64} -0.984094 q^{65} +2.18769 q^{66} +6.08507 q^{67} +7.27942 q^{68} +0.694821 q^{69} +1.80998 q^{70} -8.32793 q^{71} +2.51722 q^{72} +8.52483 q^{73} +0.745843 q^{74} -3.17315 q^{75} +5.41346 q^{76} +8.65916 q^{77} +1.03896 q^{78} +0.159145 q^{79} +0.658132 q^{80} +4.88809 q^{81} -0.571803 q^{82} -1.60969 q^{83} -1.91089 q^{84} +4.79082 q^{85} -5.56529 q^{86} +5.47567 q^{87} +3.14857 q^{88} -15.4922 q^{89} +1.65666 q^{90} +4.11231 q^{91} +1.00000 q^{92} -0.788414 q^{93} -0.938950 q^{94} +3.56277 q^{95} -0.694821 q^{96} -9.93497 q^{97} -0.563515 q^{98} +7.92566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.694821	0.401155	0.200578	−	0.979678i	$-0.435718\pi$
$3$	0.694821	0.401155	0.200578	+	0.979678i	$0.435718\pi$
$4$	1.00000	0.500000
$5$	0.658132	0.294325	0.147163	−	0.989112i	$-0.452986\pi$
$5$	0.658132	0.294325	0.147163	+	0.989112i	$0.452986\pi$
$6$	−0.694821	−0.283660
$7$	−2.75018	−1.03947	−0.519736	−	0.854327i	$-0.673970\pi$
$7$	−2.75018	−1.03947	−0.519736	+	0.854327i	$0.673970\pi$
$8$	−1.00000	−0.353553
$9$	−2.51722	−0.839075
$10$	−0.658132	−0.208119
$11$	−3.14857	−0.949330	−0.474665	−	0.880166i	$-0.657431\pi$
$11$	−3.14857	−0.949330	−0.474665	+	0.880166i	$0.657431\pi$
$12$	0.694821	0.200578
$13$	−1.49529	−0.414718	−0.207359	−	0.978265i	$-0.566487\pi$
$13$	−1.49529	−0.414718	−0.207359	+	0.978265i	$0.566487\pi$
$14$	2.75018	0.735018
$15$	0.457284	0.118070
$16$	1.00000	0.250000
$17$	7.27942	1.76552	0.882759	−	0.469825i	$-0.155683\pi$
$17$	7.27942	1.76552	0.882759	+	0.469825i	$0.155683\pi$
$18$	2.51722	0.593315
$19$	5.41346	1.24193	0.620967	−	0.783837i	$-0.286740\pi$
$19$	5.41346	1.24193	0.620967	+	0.783837i	$0.286740\pi$
$20$	0.658132	0.147163
$21$	−1.91089	−0.416990
$22$	3.14857	0.671278
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.694821	−0.141830
$25$	−4.56686	−0.913373
$26$	1.49529	0.293250
$27$	−3.83348	−0.737754
$28$	−2.75018	−0.519736
$29$	7.88069	1.46341	0.731703	−	0.681623i	$-0.238726\pi$
$29$	7.88069	1.46341	0.731703	+	0.681623i	$0.238726\pi$
$30$	−0.457284	−0.0834882
$31$	−1.13470	−0.203798	−0.101899	−	0.994795i	$-0.532492\pi$
$31$	−1.13470	−0.203798	−0.101899	+	0.994795i	$0.532492\pi$
$32$	−1.00000	−0.176777
$33$	−2.18769	−0.380829
$34$	−7.27942	−1.24841
$35$	−1.80998	−0.305943
$36$	−2.51722	−0.419537
$37$	−0.745843	−0.122616	−0.0613079	−	0.998119i	$-0.519527\pi$
$37$	−0.745843	−0.122616	−0.0613079	+	0.998119i	$0.519527\pi$
$38$	−5.41346	−0.878179
$39$	−1.03896	−0.166366
$40$	−0.658132	−0.104060
$41$	0.571803	0.0893006	0.0446503	−	0.999003i	$-0.485783\pi$
$41$	0.571803	0.0893006	0.0446503	+	0.999003i	$0.485783\pi$
$42$	1.91089	0.294856
$43$	5.56529	0.848698	0.424349	−	0.905499i	$-0.360503\pi$
$43$	5.56529	0.848698	0.424349	+	0.905499i	$0.360503\pi$
$44$	−3.14857	−0.474665
$45$	−1.65666	−0.246961
$46$	−1.00000	−0.147442
$47$	0.938950	0.136960	0.0684799	−	0.997652i	$-0.478185\pi$
$47$	0.938950	0.136960	0.0684799	+	0.997652i	$0.478185\pi$
$48$	0.694821	0.100289
$49$	0.563515	0.0805022
$50$	4.56686	0.645852
$51$	5.05790	0.708247
$52$	−1.49529	−0.207359
$53$	−10.5215	−1.44523	−0.722617	−	0.691248i	$-0.757061\pi$
$53$	−10.5215	−1.44523	−0.722617	+	0.691248i	$0.757061\pi$
$54$	3.83348	0.521671
$55$	−2.07217	−0.279412
$56$	2.75018	0.367509
$57$	3.76139	0.498208
$58$	−7.88069	−1.03478
$59$	−6.71876	−0.874707	−0.437354	−	0.899290i	$-0.644084\pi$
$59$	−6.71876	−0.874707	−0.437354	+	0.899290i	$0.644084\pi$
$60$	0.457284	0.0590351
$61$	12.7225	1.62895	0.814473	−	0.580201i	$-0.197026\pi$
$61$	12.7225	1.62895	0.814473	+	0.580201i	$0.197026\pi$
$62$	1.13470	0.144107
$63$	6.92283	0.872195
$64$	1.00000	0.125000
$65$	−0.984094	−0.122062
$66$	2.18769	0.269287
$67$	6.08507	0.743410	0.371705	−	0.928351i	$-0.378773\pi$
$67$	6.08507	0.743410	0.371705	+	0.928351i	$0.378773\pi$
$68$	7.27942	0.882759
$69$	0.694821	0.0836466
$70$	1.80998	0.216334
$71$	−8.32793	−0.988343	−0.494172	−	0.869364i	$-0.664529\pi$
$71$	−8.32793	−0.988343	−0.494172	+	0.869364i	$0.664529\pi$
$72$	2.51722	0.296658
$73$	8.52483	0.997756	0.498878	−	0.866672i	$-0.333746\pi$
$73$	8.52483	0.997756	0.498878	+	0.866672i	$0.333746\pi$
$74$	0.745843	0.0867025
$75$	−3.17315	−0.366404
$76$	5.41346	0.620967
$77$	8.65916	0.986802
$78$	1.03896	0.117639
$79$	0.159145	0.0179053	0.00895263	−	0.999960i	$-0.497150\pi$
$79$	0.159145	0.0179053	0.00895263	+	0.999960i	$0.497150\pi$
$80$	0.658132	0.0735813
$81$	4.88809	0.543121
$82$	−0.571803	−0.0631451
$83$	−1.60969	−0.176687	−0.0883433	−	0.996090i	$-0.528157\pi$
$83$	−1.60969	−0.176687	−0.0883433	+	0.996090i	$0.528157\pi$
$84$	−1.91089	−0.208495
$85$	4.79082	0.519637
$86$	−5.56529	−0.600120
$87$	5.47567	0.587053
$88$	3.14857	0.335639
$89$	−15.4922	−1.64217	−0.821084	−	0.570808i	$-0.806630\pi$
$89$	−15.4922	−1.64217	−0.821084	+	0.570808i	$0.806630\pi$
$90$	1.65666	0.174628
$91$	4.11231	0.431087
$92$	1.00000	0.104257
$93$	−0.788414	−0.0817548
$94$	−0.938950	−0.0968452
$95$	3.56277	0.365532
$96$	−0.694821	−0.0709149
$97$	−9.93497	−1.00874	−0.504372	−	0.863487i	$-0.668276\pi$
$97$	−9.93497	−1.00874	−0.504372	+	0.863487i	$0.668276\pi$
$98$	−0.563515	−0.0569236
$99$	7.92566	0.796559
$100$	−4.56686	−0.456686
$101$	13.8875	1.38186	0.690931	−	0.722921i	$-0.257201\pi$
$101$	13.8875	1.38186	0.690931	+	0.722921i	$0.257201\pi$
$102$	−5.05790	−0.500806
$103$	−5.75577	−0.567133	−0.283566	−	0.958953i	$-0.591518\pi$
$103$	−5.75577	−0.567133	−0.283566	+	0.958953i	$0.591518\pi$
$104$	1.49529	0.146625
$105$	−1.25761	−0.122731
$106$	10.5215	1.02194
$107$	−16.1338	−1.55971	−0.779856	−	0.625959i	$-0.784708\pi$
$107$	−16.1338	−1.55971	−0.779856	+	0.625959i	$0.784708\pi$
$108$	−3.83348	−0.368877
$109$	−8.74861	−0.837965	−0.418983	−	0.907994i	$-0.637613\pi$
$109$	−8.74861	−0.837965	−0.418983	+	0.907994i	$0.637613\pi$
$110$	2.07217	0.197574
$111$	−0.518227	−0.0491880
$112$	−2.75018	−0.259868
$113$	−5.92802	−0.557661	−0.278831	−	0.960340i	$-0.589947\pi$
$113$	−5.92802	−0.557661	−0.278831	+	0.960340i	$0.589947\pi$
$114$	−3.76139	−0.352286
$115$	0.658132	0.0613711
$116$	7.88069	0.731703
$117$	3.76397	0.347979
$118$	6.71876	0.618512
$119$	−20.0198	−1.83521
$120$	−0.457284	−0.0417441
$121$	−1.08649	−0.0987720
$122$	−12.7225	−1.15184
$123$	0.397301	0.0358234
$124$	−1.13470	−0.101899
$125$	−6.29625	−0.563154
$126$	−6.92283	−0.616735
$127$	5.50278	0.488293	0.244146	−	0.969738i	$-0.421492\pi$
$127$	5.50278	0.488293	0.244146	+	0.969738i	$0.421492\pi$
$128$	−1.00000	−0.0883883
$129$	3.86688	0.340460
$130$	0.984094	0.0863108
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.18769	−0.190414
$133$	−14.8880	−1.29095
$134$	−6.08507	−0.525670
$135$	−2.52294	−0.217140
$136$	−7.27942	−0.624205
$137$	4.71028	0.402426	0.201213	−	0.979547i	$-0.435512\pi$
$137$	4.71028	0.402426	0.201213	+	0.979547i	$0.435512\pi$
$138$	−0.694821	−0.0591471
$139$	−7.19628	−0.610380	−0.305190	−	0.952291i	$-0.598720\pi$
$139$	−7.19628	−0.610380	−0.305190	+	0.952291i	$0.598720\pi$
$140$	−1.80998	−0.152972
$141$	0.652402	0.0549422
$142$	8.32793	0.698864
$143$	4.70801	0.393704
$144$	−2.51722	−0.209769
$145$	5.18653	0.430718
$146$	−8.52483	−0.705520
$147$	0.391542	0.0322939
$148$	−0.745843	−0.0613079
$149$	−21.7636	−1.78295	−0.891473	−	0.453074i	$-0.850327\pi$
$149$	−21.7636	−1.78295	−0.891473	+	0.453074i	$0.850327\pi$
$150$	3.17315	0.259087
$151$	−24.1261	−1.96336	−0.981678	−	0.190548i	$-0.938974\pi$
$151$	−24.1261	−1.96336	−0.981678	+	0.190548i	$0.938974\pi$
$152$	−5.41346	−0.439090
$153$	−18.3239	−1.48140
$154$	−8.65916	−0.697775
$155$	−0.746783	−0.0599830
$156$	−1.03896	−0.0831830
$157$	4.29518	0.342793	0.171396	−	0.985202i	$-0.445172\pi$
$157$	4.29518	0.342793	0.171396	+	0.985202i	$0.445172\pi$
$158$	−0.159145	−0.0126609
$159$	−7.31054	−0.579763
$160$	−0.658132	−0.0520299
$161$	−2.75018	−0.216745
$162$	−4.88809	−0.384044
$163$	−12.5454	−0.982628	−0.491314	−	0.870983i	$-0.663483\pi$
$163$	−12.5454	−0.982628	−0.491314	+	0.870983i	$0.663483\pi$
$164$	0.571803	0.0446503
$165$	−1.43979	−0.112088
$166$	1.60969	0.124936
$167$	−0.118125	−0.00914077	−0.00457038	−	0.999990i	$-0.501455\pi$
$167$	−0.118125	−0.00914077	−0.00457038	+	0.999990i	$0.501455\pi$
$168$	1.91089	0.147428
$169$	−10.7641	−0.828009
$170$	−4.79082	−0.367439
$171$	−13.6269	−1.04207
$172$	5.56529	0.424349
$173$	1.22616	0.0932232	0.0466116	−	0.998913i	$-0.485158\pi$
$173$	1.22616	0.0932232	0.0466116	+	0.998913i	$0.485158\pi$
$174$	−5.47567	−0.415109
$175$	12.5597	0.949425
$176$	−3.14857	−0.237333
$177$	−4.66833	−0.350893
$178$	15.4922	1.16119
$179$	21.1353	1.57972	0.789862	−	0.613284i	$-0.210152\pi$
$179$	21.1353	1.57972	0.789862	+	0.613284i	$0.210152\pi$
$180$	−1.65666	−0.123480
$181$	3.70932	0.275712	0.137856	−	0.990452i	$-0.455979\pi$
$181$	3.70932	0.275712	0.137856	+	0.990452i	$0.455979\pi$
$182$	−4.11231	−0.304825
$183$	8.83985	0.653460
$184$	−1.00000	−0.0737210
$185$	−0.490863	−0.0360890
$186$	0.788414	0.0578093
$187$	−22.9198	−1.67606
$188$	0.938950	0.0684799
$189$	10.5428	0.766875
$190$	−3.56277	−0.258470
$191$	−14.9726	−1.08338	−0.541689	−	0.840579i	$-0.682215\pi$
$191$	−14.9726	−1.08338	−0.541689	+	0.840579i	$0.682215\pi$
$192$	0.694821	0.0501444
$193$	4.67809	0.336736	0.168368	−	0.985724i	$-0.446150\pi$
$193$	4.67809	0.336736	0.168368	+	0.985724i	$0.446150\pi$
$194$	9.93497	0.713290
$195$	−0.683770	−0.0489658
$196$	0.563515	0.0402511
$197$	−16.3000	−1.16133	−0.580664	−	0.814144i	$-0.697207\pi$
$197$	−16.3000	−1.16133	−0.580664	+	0.814144i	$0.697207\pi$
$198$	−7.92566	−0.563252
$199$	−27.1378	−1.92375	−0.961875	−	0.273490i	$-0.911822\pi$
$199$	−27.1378	−1.92375	−0.961875	+	0.273490i	$0.911822\pi$
$200$	4.56686	0.322926
$201$	4.22804	0.298223
$202$	−13.8875	−0.977124
$203$	−21.6733	−1.52117
$204$	5.05790	0.354124
$205$	0.376322	0.0262834
$206$	5.75577	0.401023
$207$	−2.51722	−0.174959
$208$	−1.49529	−0.103679
$209$	−17.0447	−1.17900
$210$	1.25761	0.0867837
$211$	13.6348	0.938658	0.469329	−	0.883023i	$-0.344496\pi$
$211$	13.6348	0.938658	0.469329	+	0.883023i	$0.344496\pi$
$212$	−10.5215	−0.722617
$213$	−5.78642	−0.396479
$214$	16.1338	1.10288
$215$	3.66269	0.249793
$216$	3.83348	0.260836
$217$	3.12064	0.211843
$218$	8.74861	0.592531
$219$	5.92323	0.400255
$220$	−2.07217	−0.139706
$221$	−10.8848	−0.732192
$222$	0.518227	0.0347811
$223$	−21.2600	−1.42367	−0.711836	−	0.702346i	$-0.752136\pi$
$223$	−21.2600	−1.42367	−0.711836	+	0.702346i	$0.752136\pi$
$224$	2.75018	0.183754
$225$	11.4958	0.766388
$226$	5.92802	0.394326
$227$	−0.670276	−0.0444878	−0.0222439	−	0.999753i	$-0.507081\pi$
$227$	−0.670276	−0.0444878	−0.0222439	+	0.999753i	$0.507081\pi$
$228$	3.76139	0.249104
$229$	11.9142	0.787314	0.393657	−	0.919257i	$-0.371210\pi$
$229$	11.9142	0.787314	0.393657	+	0.919257i	$0.371210\pi$
$230$	−0.658132	−0.0433959
$231$	6.01656	0.395861
$232$	−7.88069	−0.517392
$233$	−0.864723	−0.0566499	−0.0283250	−	0.999599i	$-0.509017\pi$
$233$	−0.864723	−0.0566499	−0.0283250	+	0.999599i	$0.509017\pi$
$234$	−3.76397	−0.246058
$235$	0.617952	0.0403108
$236$	−6.71876	−0.437354
$237$	0.110578	0.00718279
$238$	20.0198	1.29769
$239$	22.8758	1.47971	0.739855	−	0.672767i	$-0.234894\pi$
$239$	22.8758	1.47971	0.739855	+	0.672767i	$0.234894\pi$
$240$	0.457284	0.0295175
$241$	−11.8143	−0.761025	−0.380513	−	0.924776i	$-0.624252\pi$
$241$	−11.8143	−0.761025	−0.380513	+	0.924776i	$0.624252\pi$
$242$	1.08649	0.0698423
$243$	14.8968	0.955630
$244$	12.7225	0.814473
$245$	0.370867	0.0236938
$246$	−0.397301	−0.0253310
$247$	−8.09467	−0.515051
$248$	1.13470	0.0720536
$249$	−1.11845	−0.0708787
$250$	6.29625	0.398210
$251$	−20.0470	−1.26536	−0.632679	−	0.774414i	$-0.718045\pi$
$251$	−20.0470	−1.26536	−0.632679	+	0.774414i	$0.718045\pi$
$252$	6.92283	0.436097
$253$	−3.14857	−0.197949
$254$	−5.50278	−0.345275
$255$	3.32876	0.208455
$256$	1.00000	0.0625000
$257$	−3.31472	−0.206767	−0.103383	−	0.994642i	$-0.532967\pi$
$257$	−3.31472	−0.206767	−0.103383	+	0.994642i	$0.532967\pi$
$258$	−3.86688	−0.240741
$259$	2.05121	0.127456
$260$	−0.984094	−0.0610309
$261$	−19.8374	−1.22791
$262$	−1.00000	−0.0617802
$263$	−13.7906	−0.850366	−0.425183	−	0.905107i	$-0.639790\pi$
$263$	−13.7906	−0.850366	−0.425183	+	0.905107i	$0.639790\pi$
$264$	2.18769	0.134643
$265$	−6.92451	−0.425369
$266$	14.8880	0.912843
$267$	−10.7643	−0.658764
$268$	6.08507	0.371705
$269$	5.73083	0.349415	0.174708	−	0.984620i	$-0.444102\pi$
$269$	5.73083	0.349415	0.174708	+	0.984620i	$0.444102\pi$
$270$	2.52294	0.153541
$271$	−2.53205	−0.153811	−0.0769056	−	0.997038i	$-0.524504\pi$
$271$	−2.53205	−0.153811	−0.0769056	+	0.997038i	$0.524504\pi$
$272$	7.27942	0.441380
$273$	2.85732	0.172933
$274$	−4.71028	−0.284558
$275$	14.3791	0.867092
$276$	0.694821	0.0418233
$277$	4.29884	0.258292	0.129146	−	0.991626i	$-0.458776\pi$
$277$	4.29884	0.258292	0.129146	+	0.991626i	$0.458776\pi$
$278$	7.19628	0.431604
$279$	2.85630	0.171002
$280$	1.80998	0.108167
$281$	1.97574	0.117863	0.0589314	−	0.998262i	$-0.481231\pi$
$281$	1.97574	0.117863	0.0589314	+	0.998262i	$0.481231\pi$
$282$	−0.652402	−0.0388500
$283$	−12.8507	−0.763893	−0.381946	−	0.924185i	$-0.624746\pi$
$283$	−12.8507	−0.763893	−0.381946	+	0.924185i	$0.624746\pi$
$284$	−8.32793	−0.494172
$285$	2.47549	0.146635
$286$	−4.70801	−0.278391
$287$	−1.57256	−0.0928255
$288$	2.51722	0.148329
$289$	35.9900	2.11706
$290$	−5.18653	−0.304563
$291$	−6.90303	−0.404663
$292$	8.52483	0.498878
$293$	29.0896	1.69943	0.849717	−	0.527239i	$-0.176773\pi$
$293$	29.0896	1.69943	0.849717	+	0.527239i	$0.176773\pi$
$294$	−0.391542	−0.0228352
$295$	−4.42183	−0.257449
$296$	0.745843	0.0433512
$297$	12.0700	0.700372
$298$	21.7636	1.26073
$299$	−1.49529	−0.0864746
$300$	−3.17315	−0.183202
$301$	−15.3056	−0.882198
$302$	24.1261	1.38830
$303$	9.64936	0.554341
$304$	5.41346	0.310483
$305$	8.37306	0.479440
$306$	18.3239	1.04751
$307$	0.792769	0.0452457	0.0226228	−	0.999744i	$-0.492798\pi$
$307$	0.792769	0.0452457	0.0226228	+	0.999744i	$0.492798\pi$
$308$	8.65916	0.493401
$309$	−3.99923	−0.227508
$310$	0.746783	0.0424144
$311$	13.7086	0.777346	0.388673	−	0.921376i	$-0.372934\pi$
$311$	13.7086	0.777346	0.388673	+	0.921376i	$0.372934\pi$
$312$	1.03896	0.0588193
$313$	20.3914	1.15259	0.576295	−	0.817241i	$-0.304498\pi$
$313$	20.3914	1.15259	0.576295	+	0.817241i	$0.304498\pi$
$314$	−4.29518	−0.242391
$315$	4.55613	0.256709
$316$	0.159145	0.00895263
$317$	18.9589	1.06484	0.532420	−	0.846481i	$-0.321283\pi$
$317$	18.9589	1.06484	0.532420	+	0.846481i	$0.321283\pi$
$318$	7.31054	0.409955
$319$	−24.8129	−1.38926
$320$	0.658132	0.0367907
$321$	−11.2101	−0.625687
$322$	2.75018	0.153262
$323$	39.4069	2.19266
$324$	4.88809	0.271560
$325$	6.82876	0.378792
$326$	12.5454	0.694823
$327$	−6.07872	−0.336154
$328$	−0.571803	−0.0315725
$329$	−2.58228	−0.142366
$330$	1.43979	0.0792579
$331$	−30.7041	−1.68765	−0.843825	−	0.536619i	$-0.819701\pi$
$331$	−30.7041	−1.68765	−0.843825	+	0.536619i	$0.819701\pi$
$332$	−1.60969	−0.0883433
$333$	1.87745	0.102884
$334$	0.118125	0.00646350
$335$	4.00478	0.218804
$336$	−1.91089	−0.104247
$337$	−32.2210	−1.75519	−0.877594	−	0.479405i	$-0.840853\pi$
$337$	−32.2210	−1.75519	−0.877594	+	0.479405i	$0.840853\pi$
$338$	10.7641	0.585491
$339$	−4.11891	−0.223709
$340$	4.79082	0.259819
$341$	3.57269	0.193472
$342$	13.6269	0.736858
$343$	17.7015	0.955792
$344$	−5.56529	−0.300060
$345$	0.457284	0.0246193
$346$	−1.22616	−0.0659187
$347$	−20.2439	−1.08675	−0.543374	−	0.839491i	$-0.682853\pi$
$347$	−20.2439	−1.08675	−0.543374	+	0.839491i	$0.682853\pi$
$348$	5.47567	0.293527
$349$	−11.9773	−0.641133	−0.320566	−	0.947226i	$-0.603873\pi$
$349$	−11.9773	−0.641133	−0.320566	+	0.947226i	$0.603873\pi$
$350$	−12.5597	−0.671345
$351$	5.73215	0.305960
$352$	3.14857	0.167819
$353$	−5.21454	−0.277542	−0.138771	−	0.990325i	$-0.544315\pi$
$353$	−5.21454	−0.277542	−0.138771	+	0.990325i	$0.544315\pi$
$354$	4.66833	0.248119
$355$	−5.48087	−0.290894
$356$	−15.4922	−0.821084
$357$	−13.9101	−0.736203
$358$	−21.1353	−1.11703
$359$	25.9486	1.36951	0.684757	−	0.728772i	$-0.259908\pi$
$359$	25.9486	1.36951	0.684757	+	0.728772i	$0.259908\pi$
$360$	1.65666	0.0873139
$361$	10.3056	0.542398
$362$	−3.70932	−0.194958
$363$	−0.754917	−0.0396229
$364$	4.11231	0.215544
$365$	5.61046	0.293665
$366$	−8.83985	−0.462066
$367$	−25.0750	−1.30891	−0.654453	−	0.756103i	$-0.727101\pi$
$367$	−25.0750	−1.30891	−0.654453	+	0.756103i	$0.727101\pi$
$368$	1.00000	0.0521286
$369$	−1.43936	−0.0749299
$370$	0.490863	0.0255187
$371$	28.9360	1.50228
$372$	−0.788414	−0.0408774
$373$	24.6352	1.27556	0.637782	−	0.770217i	$-0.279852\pi$
$373$	24.6352	1.27556	0.637782	+	0.770217i	$0.279852\pi$
$374$	22.9198	1.18515
$375$	−4.37477	−0.225912
$376$	−0.938950	−0.0484226
$377$	−11.7839	−0.606900
$378$	−10.5428	−0.542262
$379$	−22.2957	−1.14525	−0.572626	−	0.819817i	$-0.694075\pi$
$379$	−22.2957	−1.14525	−0.572626	+	0.819817i	$0.694075\pi$
$380$	3.56277	0.182766
$381$	3.82345	0.195881
$382$	14.9726	0.766064
$383$	4.31212	0.220339	0.110169	−	0.993913i	$-0.464861\pi$
$383$	4.31212	0.220339	0.110169	+	0.993913i	$0.464861\pi$
$384$	−0.694821	−0.0354574
$385$	5.69886	0.290441
$386$	−4.67809	−0.238108
$387$	−14.0091	−0.712121
$388$	−9.93497	−0.504372
$389$	1.19665	0.0606723	0.0303362	−	0.999540i	$-0.490342\pi$
$389$	1.19665	0.0606723	0.0303362	+	0.999540i	$0.490342\pi$
$390$	0.683770	0.0346240
$391$	7.27942	0.368136
$392$	−0.563515	−0.0284618
$393$	0.694821	0.0350491
$394$	16.3000	0.821182
$395$	0.104739	0.00526997
$396$	7.92566	0.398279
$397$	1.15769	0.0581026	0.0290513	−	0.999578i	$-0.490751\pi$
$397$	1.15769	0.0581026	0.0290513	+	0.999578i	$0.490751\pi$
$398$	27.1378	1.36030
$399$	−10.3445	−0.517873
$400$	−4.56686	−0.228343
$401$	−5.23220	−0.261284	−0.130642	−	0.991430i	$-0.541704\pi$
$401$	−5.23220	−0.261284	−0.130642	+	0.991430i	$0.541704\pi$
$402$	−4.22804	−0.210875
$403$	1.69670	0.0845187
$404$	13.8875	0.690931
$405$	3.21700	0.159854
$406$	21.6733	1.07563
$407$	2.34834	0.116403
$408$	−5.05790	−0.250403
$409$	16.2341	0.802724	0.401362	−	0.915919i	$-0.368537\pi$
$409$	16.2341	0.802724	0.401362	+	0.915919i	$0.368537\pi$
$410$	−0.376322	−0.0185852
$411$	3.27280	0.161435
$412$	−5.75577	−0.283566
$413$	18.4778	0.909234
$414$	2.51722	0.123715
$415$	−1.05939	−0.0520033
$416$	1.49529	0.0733124
$417$	−5.00012	−0.244857
$418$	17.0447	0.833682
$419$	0.0219989	0.00107472	0.000537359	−	1.00000i	$-0.499829\pi$
$419$	0.0219989	0.00107472	0.000537359		1.00000i	$0.499829\pi$
$420$	−1.25761	−0.0613653
$421$	−37.9389	−1.84903	−0.924514	−	0.381149i	$-0.875529\pi$
$421$	−37.9389	−1.84903	−0.924514	+	0.381149i	$0.875529\pi$
$422$	−13.6348	−0.663731
$423$	−2.36355	−0.114920
$424$	10.5215	0.510968
$425$	−33.2441	−1.61258
$426$	5.78642	0.280353
$427$	−34.9892	−1.69324
$428$	−16.1338	−0.779856
$429$	3.27123	0.157936
$430$	−3.66269	−0.176631
$431$	20.0758	0.967015	0.483508	−	0.875340i	$-0.339363\pi$
$431$	20.0758	0.967015	0.483508	+	0.875340i	$0.339363\pi$
$432$	−3.83348	−0.184439
$433$	−13.8363	−0.664928	−0.332464	−	0.943116i	$-0.607880\pi$
$433$	−13.8363	−0.664928	−0.332464	+	0.943116i	$0.607880\pi$
$434$	−3.12064	−0.149795
$435$	3.60371	0.172785
$436$	−8.74861	−0.418983
$437$	5.41346	0.258961
$438$	−5.92323	−0.283023
$439$	0.455439	0.0217369	0.0108685	−	0.999941i	$-0.496540\pi$
$439$	0.455439	0.0217369	0.0108685	+	0.999941i	$0.496540\pi$
$440$	2.07217	0.0987871
$441$	−1.41849	−0.0675473
$442$	10.8848	0.517738
$443$	22.5855	1.07307	0.536534	−	0.843879i	$-0.319733\pi$
$443$	22.5855	1.07307	0.536534	+	0.843879i	$0.319733\pi$
$444$	−0.518227	−0.0245940
$445$	−10.1959	−0.483332
$446$	21.2600	1.00669
$447$	−15.1218	−0.715238
$448$	−2.75018	−0.129934
$449$	28.3401	1.33745	0.668725	−	0.743510i	$-0.266840\pi$
$449$	28.3401	1.33745	0.668725	+	0.743510i	$0.266840\pi$
$450$	−11.4958	−0.541918
$451$	−1.80036	−0.0847758
$452$	−5.92802	−0.278831
$453$	−16.7633	−0.787610
$454$	0.670276	0.0314576
$455$	2.70644	0.126880
$456$	−3.76139	−0.176143
$457$	1.31355	0.0614455	0.0307227	−	0.999528i	$-0.490219\pi$
$457$	1.31355	0.0614455	0.0307227	+	0.999528i	$0.490219\pi$
$458$	−11.9142	−0.556715
$459$	−27.9055	−1.30252
$460$	0.658132	0.0306855
$461$	−28.5051	−1.32761	−0.663807	−	0.747904i	$-0.731060\pi$
$461$	−28.5051	−1.32761	−0.663807	+	0.747904i	$0.731060\pi$
$462$	−6.01656	−0.279916
$463$	−14.6572	−0.681178	−0.340589	−	0.940212i	$-0.610626\pi$
$463$	−14.6572	−0.681178	−0.340589	+	0.940212i	$0.610626\pi$
$464$	7.88069	0.365852
$465$	−0.518880	−0.0240625
$466$	0.864723	0.0400575
$467$	−14.3089	−0.662136	−0.331068	−	0.943607i	$-0.607409\pi$
$467$	−14.3089	−0.662136	−0.331068	+	0.943607i	$0.607409\pi$
$468$	3.76397	0.173989
$469$	−16.7351	−0.772754
$470$	−0.617952	−0.0285040
$471$	2.98438	0.137513
$472$	6.71876	0.309256
$473$	−17.5227	−0.805695
$474$	−0.110578	−0.00507900
$475$	−24.7225	−1.13435
$476$	−20.0198	−0.917604
$477$	26.4849	1.21266
$478$	−22.8758	−1.04631
$479$	−31.9334	−1.45907	−0.729537	−	0.683942i	$-0.760264\pi$
$479$	−31.9334	−1.45907	−0.729537	+	0.683942i	$0.760264\pi$
$480$	−0.457284	−0.0208721
$481$	1.11525	0.0508509
$482$	11.8143	0.538126
$483$	−1.91089	−0.0869483
$484$	−1.08649	−0.0493860
$485$	−6.53852	−0.296899
$486$	−14.8968	−0.675732
$487$	16.7752	0.760156	0.380078	−	0.924954i	$-0.375897\pi$
$487$	16.7752	0.760156	0.380078	+	0.924954i	$0.375897\pi$
$488$	−12.7225	−0.575919
$489$	−8.71677	−0.394186
$490$	−0.370867	−0.0167541
$491$	7.83418	0.353552	0.176776	−	0.984251i	$-0.443433\pi$
$491$	7.83418	0.353552	0.176776	+	0.984251i	$0.443433\pi$
$492$	0.397301	0.0179117
$493$	57.3668	2.58367
$494$	8.09467	0.364196
$495$	5.21613	0.234448
$496$	−1.13470	−0.0509496
$497$	22.9033	1.02735
$498$	1.11845	0.0501188
$499$	−23.9829	−1.07362	−0.536811	−	0.843703i	$-0.680371\pi$
$499$	−23.9829	−1.07362	−0.536811	+	0.843703i	$0.680371\pi$
$500$	−6.29625	−0.281577
$501$	−0.0820756	−0.00366687
$502$	20.0470	0.894743
$503$	17.6562	0.787253	0.393626	−	0.919271i	$-0.371220\pi$
$503$	17.6562	0.787253	0.393626	+	0.919271i	$0.371220\pi$
$504$	−6.92283	−0.308367
$505$	9.13983	0.406717
$506$	3.14857	0.139971
$507$	−7.47914	−0.332160
$508$	5.50278	0.244146
$509$	32.5101	1.44098	0.720492	−	0.693464i	$-0.243916\pi$
$509$	32.5101	1.44098	0.720492	+	0.693464i	$0.243916\pi$
$510$	−3.32876	−0.147400
$511$	−23.4449	−1.03714
$512$	−1.00000	−0.0441942
$513$	−20.7524	−0.916241
$514$	3.31472	0.146206
$515$	−3.78805	−0.166922
$516$	3.86688	0.170230
$517$	−2.95635	−0.130020
$518$	−2.05121	−0.0901248
$519$	0.851962	0.0373970
$520$	0.984094	0.0431554
$521$	−19.2640	−0.843973	−0.421987	−	0.906602i	$-0.638667\pi$
$521$	−19.2640	−0.843973	−0.421987	+	0.906602i	$0.638667\pi$
$522$	19.8374	0.868261
$523$	8.62009	0.376930	0.188465	−	0.982080i	$-0.439649\pi$
$523$	8.62009	0.376930	0.188465	+	0.982080i	$0.439649\pi$
$524$	1.00000	0.0436852
$525$	8.72676	0.380867
$526$	13.7906	0.601300
$527$	−8.25997	−0.359810
$528$	−2.18769	−0.0952072
$529$	1.00000	0.0434783
$530$	6.92451	0.300782
$531$	16.9126	0.733945
$532$	−14.8880	−0.645477
$533$	−0.855009	−0.0370345
$534$	10.7643	0.465816
$535$	−10.6182	−0.459063
$536$	−6.08507	−0.262835
$537$	14.6852	0.633715
$538$	−5.73083	−0.247074
$539$	−1.77427	−0.0764232
$540$	−2.52294	−0.108570
$541$	−27.5731	−1.18546	−0.592730	−	0.805401i	$-0.701950\pi$
$541$	−27.5731	−1.18546	−0.592730	+	0.805401i	$0.701950\pi$
$542$	2.53205	0.108761
$543$	2.57732	0.110603
$544$	−7.27942	−0.312103
$545$	−5.75774	−0.246634
$546$	−2.85732	−0.122282
$547$	−13.4317	−0.574300	−0.287150	−	0.957886i	$-0.592708\pi$
$547$	−13.4317	−0.574300	−0.287150	+	0.957886i	$0.592708\pi$
$548$	4.71028	0.201213
$549$	−32.0253	−1.36681
$550$	−14.3791	−0.613127
$551$	42.6618	1.81745
$552$	−0.694821	−0.0295736
$553$	−0.437679	−0.0186120
$554$	−4.29884	−0.182640
$555$	−0.341062	−0.0144773
$556$	−7.19628	−0.305190
$557$	19.0470	0.807049	0.403525	−	0.914969i	$-0.367785\pi$
$557$	19.0470	0.807049	0.403525	+	0.914969i	$0.367785\pi$
$558$	−2.85630	−0.120917
$559$	−8.32169	−0.351970
$560$	−1.80998	−0.0764858
$561$	−15.9252	−0.672360
$562$	−1.97574	−0.0833415
$563$	−16.4054	−0.691407	−0.345704	−	0.938344i	$-0.612360\pi$
$563$	−16.4054	−0.691407	−0.345704	+	0.938344i	$0.612360\pi$
$564$	0.652402	0.0274711
$565$	−3.90142	−0.164134
$566$	12.8507	0.540154
$567$	−13.4431	−0.564559
$568$	8.32793	0.349432
$569$	17.2800	0.724413	0.362207	−	0.932098i	$-0.382023\pi$
$569$	17.2800	0.724413	0.362207	+	0.932098i	$0.382023\pi$
$570$	−2.47549	−0.103687
$571$	45.6655	1.91104	0.955521	−	0.294922i	$-0.0952937\pi$
$571$	45.6655	1.91104	0.955521	+	0.294922i	$0.0952937\pi$
$572$	4.70801	0.196852
$573$	−10.4033	−0.434603
$574$	1.57256	0.0656375
$575$	−4.56686	−0.190451
$576$	−2.51722	−0.104884
$577$	−24.0912	−1.00293	−0.501465	−	0.865178i	$-0.667205\pi$
$577$	−24.0912	−1.00293	−0.501465	+	0.865178i	$0.667205\pi$
$578$	−35.9900	−1.49699
$579$	3.25044	0.135083
$580$	5.18653	0.215359
$581$	4.42695	0.183661
$582$	6.90303	0.286140
$583$	33.1276	1.37201
$584$	−8.52483	−0.352760
$585$	2.47719	0.102419
$586$	−29.0896	−1.20168
$587$	15.1134	0.623797	0.311899	−	0.950115i	$-0.399035\pi$
$587$	15.1134	0.623797	0.311899	+	0.950115i	$0.399035\pi$
$588$	0.391542	0.0161469
$589$	−6.14266	−0.253104
$590$	4.42183	0.182044
$591$	−11.3256	−0.465872
$592$	−0.745843	−0.0306540
$593$	−23.9030	−0.981578	−0.490789	−	0.871278i	$-0.663291\pi$
$593$	−23.9030	−0.981578	−0.490789	+	0.871278i	$0.663291\pi$
$594$	−12.0700	−0.495238
$595$	−13.1756	−0.540148
$596$	−21.7636	−0.891473
$597$	−18.8559	−0.771722
$598$	1.49529	0.0611468
$599$	−17.9812	−0.734692	−0.367346	−	0.930084i	$-0.619734\pi$
$599$	−17.9812	−0.734692	−0.367346	+	0.930084i	$0.619734\pi$
$600$	3.17315	0.129543
$601$	−21.4257	−0.873971	−0.436986	−	0.899469i	$-0.643954\pi$
$601$	−21.4257	−0.873971	−0.436986	+	0.899469i	$0.643954\pi$
$602$	15.3056	0.623808
$603$	−15.3175	−0.623777
$604$	−24.1261	−0.981678
$605$	−0.715054	−0.0290711
$606$	−9.64936	−0.391978
$607$	8.29982	0.336879	0.168440	−	0.985712i	$-0.446127\pi$
$607$	8.29982	0.336879	0.168440	+	0.985712i	$0.446127\pi$
$608$	−5.41346	−0.219545
$609$	−15.0591	−0.610225
$610$	−8.37306	−0.339015
$611$	−1.40400	−0.0567997
$612$	−18.3239	−0.740701
$613$	−12.5208	−0.505709	−0.252854	−	0.967504i	$-0.581369\pi$
$613$	−12.5208	−0.505709	−0.252854	+	0.967504i	$0.581369\pi$
$614$	−0.792769	−0.0319935
$615$	0.261476	0.0105437
$616$	−8.65916	−0.348887
$617$	−17.7025	−0.712675	−0.356337	−	0.934357i	$-0.615975\pi$
$617$	−17.7025	−0.712675	−0.356337	+	0.934357i	$0.615975\pi$
$618$	3.99923	0.160873
$619$	16.2196	0.651920	0.325960	−	0.945384i	$-0.394313\pi$
$619$	16.2196	0.651920	0.325960	+	0.945384i	$0.394313\pi$
$620$	−0.746783	−0.0299915
$621$	−3.83348	−0.153832
$622$	−13.7086	−0.549667
$623$	42.6063	1.70699
$624$	−1.03896	−0.0415915
$625$	18.6905	0.747622
$626$	−20.3914	−0.815005
$627$	−11.8430	−0.472964
$628$	4.29518	0.171396
$629$	−5.42930	−0.216481
$630$	−4.55613	−0.181521
$631$	−23.3358	−0.928984	−0.464492	−	0.885577i	$-0.653763\pi$
$631$	−23.3358	−0.928984	−0.464492	+	0.885577i	$0.653763\pi$
$632$	−0.159145	−0.00633047
$633$	9.47374	0.376547
$634$	−18.9589	−0.752955
$635$	3.62155	0.143717
$636$	−7.31054	−0.289882
$637$	−0.842616	−0.0333857
$638$	24.8129	0.982352
$639$	20.9633	0.829293
$640$	−0.658132	−0.0260149
$641$	39.9053	1.57617	0.788083	−	0.615570i	$-0.211074\pi$
$641$	39.9053	1.57617	0.788083	+	0.615570i	$0.211074\pi$
$642$	11.2101	0.442427
$643$	−34.2542	−1.35085	−0.675426	−	0.737427i	$-0.736040\pi$
$643$	−34.2542	−1.35085	−0.675426	+	0.737427i	$0.736040\pi$
$644$	−2.75018	−0.108372
$645$	2.54492	0.100206
$646$	−39.4069	−1.55044
$647$	−35.6578	−1.40185	−0.700926	−	0.713234i	$-0.747230\pi$
$647$	−35.6578	−1.40185	−0.700926	+	0.713234i	$0.747230\pi$
$648$	−4.88809	−0.192022
$649$	21.1545	0.830386
$650$	−6.82876	−0.267846
$651$	2.16829	0.0849818
$652$	−12.5454	−0.491314
$653$	−29.8576	−1.16842	−0.584210	−	0.811603i	$-0.698596\pi$
$653$	−29.8576	−1.16842	−0.584210	+	0.811603i	$0.698596\pi$
$654$	6.07872	0.237697
$655$	0.658132	0.0257153
$656$	0.571803	0.0223252
$657$	−21.4589	−0.837192
$658$	2.58228	0.100668
$659$	33.4901	1.30459	0.652295	−	0.757966i	$-0.273807\pi$
$659$	33.4901	1.30459	0.652295	+	0.757966i	$0.273807\pi$
$660$	−1.43979	−0.0560438
$661$	33.6795	1.30998	0.654991	−	0.755637i	$-0.272672\pi$
$661$	33.6795	1.30998	0.654991	+	0.755637i	$0.272672\pi$
$662$	30.7041	1.19335
$663$	−7.56300	−0.293722
$664$	1.60969	0.0624681
$665$	−9.79827	−0.379961
$666$	−1.87745	−0.0727498
$667$	7.88069	0.305141
$668$	−0.118125	−0.00457038
$669$	−14.7719	−0.571114
$670$	−4.00478	−0.154718
$671$	−40.0576	−1.54641
$672$	1.91089	0.0737140
$673$	0.514315	0.0198254	0.00991270	−	0.999951i	$-0.496845\pi$
$673$	0.514315	0.0198254	0.00991270	+	0.999951i	$0.496845\pi$
$674$	32.2210	1.24111
$675$	17.5070	0.673845
$676$	−10.7641	−0.414005
$677$	48.4923	1.86371	0.931856	−	0.362829i	$-0.118189\pi$
$677$	48.4923	1.86371	0.931856	+	0.362829i	$0.118189\pi$
$678$	4.11891	0.158186
$679$	27.3230	1.04856
$680$	−4.79082	−0.183719
$681$	−0.465722	−0.0178465
$682$	−3.57269	−0.136805
$683$	−18.3406	−0.701784	−0.350892	−	0.936416i	$-0.614122\pi$
$683$	−18.3406	−0.701784	−0.350892	+	0.936416i	$0.614122\pi$
$684$	−13.6269	−0.521037
$685$	3.09998	0.118444
$686$	−17.7015	−0.675847
$687$	8.27825	0.315835
$688$	5.56529	0.212175
$689$	15.7326	0.599364
$690$	−0.457284	−0.0174085
$691$	−6.76233	−0.257251	−0.128625	−	0.991693i	$-0.541057\pi$
$691$	−6.76233	−0.257251	−0.128625	+	0.991693i	$0.541057\pi$
$692$	1.22616	0.0466116
$693$	−21.7970	−0.828001
$694$	20.2439	0.768447
$695$	−4.73610	−0.179650
$696$	−5.47567	−0.207555
$697$	4.16239	0.157662
$698$	11.9773	0.453349
$699$	−0.600828	−0.0227254
$700$	12.5597	0.474713
$701$	11.8954	0.449284	0.224642	−	0.974441i	$-0.427879\pi$
$701$	11.8954	0.449284	0.224642	+	0.974441i	$0.427879\pi$
$702$	−5.73215	−0.216346
$703$	−4.03759	−0.152281
$704$	−3.14857	−0.118666
$705$	0.429366	0.0161709
$706$	5.21454	0.196252
$707$	−38.1933	−1.43641
$708$	−4.66833	−0.175447
$709$	−29.8736	−1.12193	−0.560963	−	0.827841i	$-0.689569\pi$
$709$	−29.8736	−1.12193	−0.560963	+	0.827841i	$0.689569\pi$
$710$	5.48087	0.205693
$711$	−0.400605	−0.0150239
$712$	15.4922	0.580594
$713$	−1.13470	−0.0424949
$714$	13.9101	0.520574
$715$	3.09849	0.115877
$716$	21.1353	0.789862
$717$	15.8946	0.593593
$718$	−25.9486	−0.968392
$719$	10.2261	0.381368	0.190684	−	0.981651i	$-0.438929\pi$
$719$	10.2261	0.381368	0.190684	+	0.981651i	$0.438929\pi$
$720$	−1.65666	−0.0617402
$721$	15.8294	0.589519
$722$	−10.3056	−0.383533
$723$	−8.20882	−0.305289
$724$	3.70932	0.137856
$725$	−35.9900	−1.33664
$726$	0.754917	0.0280176
$727$	−28.7802	−1.06740	−0.533700	−	0.845674i	$-0.679199\pi$
$727$	−28.7802	−1.06740	−0.533700	+	0.845674i	$0.679199\pi$
$728$	−4.11231	−0.152412
$729$	−4.31365	−0.159765
$730$	−5.61046	−0.207653
$731$	40.5121	1.49839
$732$	8.83985	0.326730
$733$	3.54184	0.130821	0.0654104	−	0.997858i	$-0.479164\pi$
$733$	3.54184	0.130821	0.0654104	+	0.997858i	$0.479164\pi$
$734$	25.0750	0.925536
$735$	0.257686	0.00950491
$736$	−1.00000	−0.0368605
$737$	−19.1593	−0.705742
$738$	1.43936	0.0529834
$739$	−29.6310	−1.08999	−0.544997	−	0.838438i	$-0.683469\pi$
$739$	−29.6310	−1.08999	−0.544997	+	0.838438i	$0.683469\pi$
$740$	−0.490863	−0.0180445
$741$	−5.62435	−0.206616
$742$	−28.9360	−1.06227
$743$	46.9697	1.72315	0.861576	−	0.507629i	$-0.169478\pi$
$743$	46.9697	1.72315	0.861576	+	0.507629i	$0.169478\pi$
$744$	0.788414	0.0289047
$745$	−14.3233	−0.524766
$746$	−24.6352	−0.901960
$747$	4.05195	0.148253
$748$	−22.9198	−0.838030
$749$	44.3709	1.62128
$750$	4.37477	0.159744
$751$	−12.1831	−0.444567	−0.222284	−	0.974982i	$-0.571351\pi$
$751$	−12.1831	−0.444567	−0.222284	+	0.974982i	$0.571351\pi$
$752$	0.938950	0.0342400
$753$	−13.9291	−0.507605
$754$	11.7839	0.429143
$755$	−15.8782	−0.577865
$756$	10.5428	0.383437
$757$	37.3316	1.35684	0.678419	−	0.734675i	$-0.262665\pi$
$757$	37.3316	1.35684	0.678419	+	0.734675i	$0.262665\pi$
$758$	22.2957	0.809815
$759$	−2.18769	−0.0794083
$760$	−3.56277	−0.129235
$761$	18.3068	0.663620	0.331810	−	0.943346i	$-0.392341\pi$
$761$	18.3068	0.663620	0.331810	+	0.943346i	$0.392341\pi$
$762$	−3.82345	−0.138509
$763$	24.0603	0.871041
$764$	−14.9726	−0.541689
$765$	−12.0596	−0.436014
$766$	−4.31212	−0.155803
$767$	10.0465	0.362756
$768$	0.694821	0.0250722
$769$	43.7609	1.57806	0.789029	−	0.614356i	$-0.210584\pi$
$769$	43.7609	1.57806	0.789029	+	0.614356i	$0.210584\pi$
$770$	−5.69886	−0.205373
$771$	−2.30314	−0.0829455
$772$	4.67809	0.168368
$773$	−34.1896	−1.22972	−0.614858	−	0.788638i	$-0.710787\pi$
$773$	−34.1896	−1.22972	−0.614858	+	0.788638i	$0.710787\pi$
$774$	14.0091	0.503546
$775$	5.18202	0.186144
$776$	9.93497	0.356645
$777$	1.42522	0.0511295
$778$	−1.19665	−0.0429018
$779$	3.09543	0.110905
$780$	−0.683770	−0.0244829
$781$	26.2211	0.938264
$782$	−7.27942	−0.260312
$783$	−30.2105	−1.07963
$784$	0.563515	0.0201255
$785$	2.82679	0.100893
$786$	−0.694821	−0.0247834
$787$	21.7507	0.775328	0.387664	−	0.921801i	$-0.373282\pi$
$787$	21.7507	0.775328	0.387664	+	0.921801i	$0.373282\pi$
$788$	−16.3000	−0.580664
$789$	−9.58201	−0.341129
$790$	−0.104739	−0.00372643
$791$	16.3031	0.579673
$792$	−7.92566	−0.281626
$793$	−19.0237	−0.675552
$794$	−1.15769	−0.0410847
$795$	−4.81130	−0.170639
$796$	−27.1378	−0.961875
$797$	50.4341	1.78647	0.893234	−	0.449592i	$-0.148431\pi$
$797$	50.4341	1.78647	0.893234	+	0.449592i	$0.148431\pi$
$798$	10.3445	0.366192
$799$	6.83501	0.241805
$800$	4.56686	0.161463
$801$	38.9973	1.37790
$802$	5.23220	0.184755
$803$	−26.8411	−0.947200
$804$	4.22804	0.149111
$805$	−1.80998	−0.0637935
$806$	−1.69670	−0.0597638
$807$	3.98190	0.140170
$808$	−13.8875	−0.488562
$809$	−36.9337	−1.29852	−0.649260	−	0.760567i	$-0.724921\pi$
$809$	−36.9337	−1.29852	−0.649260	+	0.760567i	$0.724921\pi$
$810$	−3.21700	−0.113034
$811$	10.1298	0.355706	0.177853	−	0.984057i	$-0.443085\pi$
$811$	10.1298	0.355706	0.177853	+	0.984057i	$0.443085\pi$
$812$	−21.6733	−0.760585
$813$	−1.75932	−0.0617021
$814$	−2.34834	−0.0823093
$815$	−8.25649	−0.289212
$816$	5.05790	0.177062
$817$	30.1275	1.05403
$818$	−16.2341	−0.567612
$819$	−10.3516	−0.361714
$820$	0.376322	0.0131417
$821$	9.05774	0.316117	0.158059	−	0.987430i	$-0.449477\pi$
$821$	9.05774	0.316117	0.158059	+	0.987430i	$0.449477\pi$
$822$	−3.27280	−0.114152
$823$	23.9357	0.834346	0.417173	−	0.908827i	$-0.363021\pi$
$823$	23.9357	0.834346	0.417173	+	0.908827i	$0.363021\pi$
$824$	5.75577	0.200512
$825$	9.99090	0.347839
$826$	−18.4778	−0.642925
$827$	15.7423	0.547412	0.273706	−	0.961813i	$-0.411750\pi$
$827$	15.7423	0.547412	0.273706	+	0.961813i	$0.411750\pi$
$828$	−2.51722	−0.0874796
$829$	32.4219	1.12606	0.563030	−	0.826436i	$-0.309636\pi$
$829$	32.4219	1.12606	0.563030	+	0.826436i	$0.309636\pi$
$830$	1.05939	0.0367719
$831$	2.98692	0.103615
$832$	−1.49529	−0.0518397
$833$	4.10206	0.142128
$834$	5.00012	0.173140
$835$	−0.0777416	−0.00269036
$836$	−17.0447	−0.589502
$837$	4.34986	0.150353
$838$	−0.0219989	−0.000759940 0
$839$	−22.8462	−0.788739	−0.394370	−	0.918952i	$-0.629037\pi$
$839$	−22.8462	−0.788739	−0.394370	+	0.918952i	$0.629037\pi$
$840$	1.25761	0.0433918
$841$	33.1052	1.14156
$842$	37.9389	1.30746
$843$	1.37279	0.0472812
$844$	13.6348	0.469329
$845$	−7.08421	−0.243704
$846$	2.36355	0.0812604
$847$	2.98805	0.102671
$848$	−10.5215	−0.361309
$849$	−8.92891	−0.306439
$850$	33.2441	1.14026
$851$	−0.745843	−0.0255672
$852$	−5.78642	−0.198239
$853$	24.8542	0.850993	0.425496	−	0.904960i	$-0.360099\pi$
$853$	24.8542	0.850993	0.425496	+	0.904960i	$0.360099\pi$
$854$	34.9892	1.19730
$855$	−8.96829	−0.306709
$856$	16.1338	0.551441
$857$	−3.63255	−0.124086	−0.0620428	−	0.998073i	$-0.519762\pi$
$857$	−3.63255	−0.124086	−0.0620428	+	0.998073i	$0.519762\pi$
$858$	−3.27123	−0.111678
$859$	−20.6635	−0.705031	−0.352515	−	0.935806i	$-0.614674\pi$
$859$	−20.6635	−0.705031	−0.352515	+	0.935806i	$0.614674\pi$
$860$	3.66269	0.124897
$861$	−1.09265	−0.0372374
$862$	−20.0758	−0.683783
$863$	3.63896	0.123872	0.0619358	−	0.998080i	$-0.480273\pi$
$863$	3.63896	0.123872	0.0619358	+	0.998080i	$0.480273\pi$
$864$	3.83348	0.130418
$865$	0.806974	0.0274379
$866$	13.8363	0.470175
$867$	25.0066	0.849268
$868$	3.12064	0.105921
$869$	−0.501081	−0.0169980
$870$	−3.60371	−0.122177
$871$	−9.09892	−0.308305
$872$	8.74861	0.296265
$873$	25.0086	0.846411
$874$	−5.41346	−0.183113
$875$	17.3159	0.585383
$876$	5.92323	0.200128
$877$	8.42961	0.284648	0.142324	−	0.989820i	$-0.454543\pi$
$877$	8.42961	0.284648	0.142324	+	0.989820i	$0.454543\pi$
$878$	−0.455439	−0.0153703
$879$	20.2121	0.681737
$880$	−2.07217	−0.0698530
$881$	−35.6407	−1.20077	−0.600383	−	0.799713i	$-0.704985\pi$
$881$	−35.6407	−1.20077	−0.600383	+	0.799713i	$0.704985\pi$
$882$	1.41849	0.0477632
$883$	2.87396	0.0967166	0.0483583	−	0.998830i	$-0.484601\pi$
$883$	2.87396	0.0967166	0.0483583	+	0.998830i	$0.484601\pi$
$884$	−10.8848	−0.366096
$885$	−3.07238	−0.103277
$886$	−22.5855	−0.758773
$887$	−18.9107	−0.634960	−0.317480	−	0.948265i	$-0.602837\pi$
$887$	−18.9107	−0.634960	−0.317480	+	0.948265i	$0.602837\pi$
$888$	0.518227	0.0173906
$889$	−15.1337	−0.507567
$890$	10.1959	0.341767
$891$	−15.3905	−0.515601
$892$	−21.2600	−0.711836
$893$	5.08297	0.170095
$894$	15.1218	0.505750
$895$	13.9098	0.464953
$896$	2.75018	0.0918772
$897$	−1.03896	−0.0346897
$898$	−28.3401	−0.945720
$899$	−8.94222	−0.298240
$900$	11.4958	0.383194
$901$	−76.5902	−2.55159
$902$	1.80036	0.0599455
$903$	−10.6346	−0.353898
$904$	5.92802	0.197163
$905$	2.44122	0.0811490
$906$	16.7633	0.556925
$907$	−50.3508	−1.67187	−0.835935	−	0.548829i	$-0.815074\pi$
$907$	−50.3508	−1.67187	−0.835935	+	0.548829i	$0.815074\pi$
$908$	−0.670276	−0.0222439
$909$	−34.9580	−1.15948
$910$	−2.70644	−0.0897177
$911$	26.6345	0.882441	0.441221	−	0.897399i	$-0.354546\pi$
$911$	26.6345	0.882441	0.441221	+	0.897399i	$0.354546\pi$
$912$	3.76139	0.124552
$913$	5.06823	0.167734
$914$	−1.31355	−0.0434485
$915$	5.81778	0.192330
$916$	11.9142	0.393657
$917$	−2.75018	−0.0908191
$918$	27.9055	0.921020
$919$	−45.9429	−1.51552	−0.757759	−	0.652535i	$-0.773706\pi$
$919$	−45.9429	−1.51552	−0.757759	+	0.652535i	$0.773706\pi$
$920$	−0.658132	−0.0216980
$921$	0.550832	0.0181505
$922$	28.5051	0.938764
$923$	12.4526	0.409883
$924$	6.01656	0.197930
$925$	3.40616	0.111994
$926$	14.6572	0.481665
$927$	14.4886	0.475867
$928$	−7.88069	−0.258696
$929$	−48.2511	−1.58307	−0.791533	−	0.611126i	$-0.790717\pi$
$929$	−48.2511	−1.58307	−0.791533	+	0.611126i	$0.790717\pi$
$930$	0.518880	0.0170148
$931$	3.05057	0.0999783
$932$	−0.864723	−0.0283250
$933$	9.52506	0.311836
$934$	14.3089	0.468201
$935$	−15.0842	−0.493307
$936$	−3.76397	−0.123029
$937$	−37.0743	−1.21116	−0.605582	−	0.795783i	$-0.707060\pi$
$937$	−37.0743	−1.21116	−0.605582	+	0.795783i	$0.707060\pi$
$938$	16.7351	0.546420
$939$	14.1684	0.462368
$940$	0.617952	0.0201554
$941$	−33.1354	−1.08018	−0.540092	−	0.841606i	$-0.681610\pi$
$941$	−33.1354	−1.08018	−0.540092	+	0.841606i	$0.681610\pi$
$942$	−2.98438	−0.0972364
$943$	0.571803	0.0186205
$944$	−6.71876	−0.218677
$945$	6.93854	0.225711
$946$	17.5227	0.569712
$947$	−47.0830	−1.52999	−0.764996	−	0.644035i	$-0.777259\pi$
$947$	−47.0830	−1.52999	−0.764996	+	0.644035i	$0.777259\pi$
$948$	0.110578	0.00359139
$949$	−12.7471	−0.413787
$950$	24.7225	0.802105
$951$	13.1731	0.427166
$952$	20.0198	0.648844
$953$	−19.1754	−0.621153	−0.310576	−	0.950548i	$-0.600522\pi$
$953$	−19.1754	−0.621153	−0.310576	+	0.950548i	$0.600522\pi$
$954$	−26.4849	−0.857480
$955$	−9.85393	−0.318866
$956$	22.8758	0.739855
$957$	−17.2405	−0.557307
$958$	31.9334	1.03172
$959$	−12.9541	−0.418311
$960$	0.457284	0.0147588
$961$	−29.7125	−0.958466
$962$	−1.11525	−0.0359570
$963$	40.6123	1.30871
$964$	−11.8143	−0.380513
$965$	3.07880	0.0991100
$966$	1.91089	0.0614818
$967$	−1.68616	−0.0542232	−0.0271116	−	0.999632i	$-0.508631\pi$
$967$	−1.68616	−0.0542232	−0.0271116	+	0.999632i	$0.508631\pi$
$968$	1.08649	0.0349212
$969$	27.3807	0.879595
$970$	6.53852	0.209939
$971$	−34.8390	−1.11804	−0.559018	−	0.829155i	$-0.688822\pi$
$971$	−34.8390	−1.11804	−0.559018	+	0.829155i	$0.688822\pi$
$972$	14.8968	0.477815
$973$	19.7911	0.634473
$974$	−16.7752	−0.537511
$975$	4.74477	0.151954
$976$	12.7225	0.407237
$977$	24.0490	0.769396	0.384698	−	0.923042i	$-0.374306\pi$
$977$	24.0490	0.769396	0.384698	+	0.923042i	$0.374306\pi$
$978$	8.71677	0.278732
$979$	48.7782	1.55896
$980$	0.370867	0.0118469
$981$	22.0222	0.703115
$982$	−7.83418	−0.249999
$983$	−37.5531	−1.19776	−0.598878	−	0.800840i	$-0.704387\pi$
$983$	−37.5531	−1.19776	−0.598878	+	0.800840i	$0.704387\pi$
$984$	−0.397301	−0.0126655
$985$	−10.7275	−0.341808
$986$	−57.3668	−1.82693
$987$	−1.79423	−0.0571108
$988$	−8.09467	−0.257526
$989$	5.56529	0.176966
$990$	−5.21613	−0.165779
$991$	14.1581	0.449748	0.224874	−	0.974388i	$-0.427803\pi$
$991$	14.1581	0.449748	0.224874	+	0.974388i	$0.427803\pi$
$992$	1.13470	0.0360268
$993$	−21.3339	−0.677009
$994$	−22.9033	−0.726450
$995$	−17.8603	−0.566208
$996$	−1.11845	−0.0354394
$997$	28.2854	0.895808	0.447904	−	0.894082i	$-0.352171\pi$
$997$	28.2854	0.895808	0.447904	+	0.894082i	$0.352171\pi$
$998$	23.9829	0.759165
$999$	2.85918	0.0904603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.16	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.16	✓	25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.694821 q^{3} +1.00000 q^{4} +0.658132 q^{5} -0.694821 q^{6} -2.75018 q^{7} -1.00000 q^{8} -2.51722 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.694821 q^{3} +1.00000 q^{4} +0.658132 q^{5} -0.694821 q^{6} -2.75018 q^{7} -1.00000 q^{8} -2.51722 q^{9} -0.658132 q^{10} -3.14857 q^{11} +0.694821 q^{12} -1.49529 q^{13} +2.75018 q^{14} +0.457284 q^{15} +1.00000 q^{16} +7.27942 q^{17} +2.51722 q^{18} +5.41346 q^{19} +0.658132 q^{20} -1.91089 q^{21} +3.14857 q^{22} +1.00000 q^{23} -0.694821 q^{24} -4.56686 q^{25} +1.49529 q^{26} -3.83348 q^{27} -2.75018 q^{28} +7.88069 q^{29} -0.457284 q^{30} -1.13470 q^{31} -1.00000 q^{32} -2.18769 q^{33} -7.27942 q^{34} -1.80998 q^{35} -2.51722 q^{36} -0.745843 q^{37} -5.41346 q^{38} -1.03896 q^{39} -0.658132 q^{40} +0.571803 q^{41} +1.91089 q^{42} +5.56529 q^{43} -3.14857 q^{44} -1.65666 q^{45} -1.00000 q^{46} +0.938950 q^{47} +0.694821 q^{48} +0.563515 q^{49} +4.56686 q^{50} +5.05790 q^{51} -1.49529 q^{52} -10.5215 q^{53} +3.83348 q^{54} -2.07217 q^{55} +2.75018 q^{56} +3.76139 q^{57} -7.88069 q^{58} -6.71876 q^{59} +0.457284 q^{60} +12.7225 q^{61} +1.13470 q^{62} +6.92283 q^{63} +1.00000 q^{64} -0.984094 q^{65} +2.18769 q^{66} +6.08507 q^{67} +7.27942 q^{68} +0.694821 q^{69} +1.80998 q^{70} -8.32793 q^{71} +2.51722 q^{72} +8.52483 q^{73} +0.745843 q^{74} -3.17315 q^{75} +5.41346 q^{76} +8.65916 q^{77} +1.03896 q^{78} +0.159145 q^{79} +0.658132 q^{80} +4.88809 q^{81} -0.571803 q^{82} -1.60969 q^{83} -1.91089 q^{84} +4.79082 q^{85} -5.56529 q^{86} +5.47567 q^{87} +3.14857 q^{88} -15.4922 q^{89} +1.65666 q^{90} +4.11231 q^{91} +1.00000 q^{92} -0.788414 q^{93} -0.938950 q^{94} +3.56277 q^{95} -0.694821 q^{96} -9.93497 q^{97} -0.563515 q^{98} +7.92566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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