LMFDB - Embedded newform 4017.2.a.k.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.15421 q^{2} +1.00000 q^{3} -0.667790 q^{4} +1.41297 q^{5} +1.15421 q^{6} +4.47597 q^{7} -3.07920 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.15421 q^{2} +1.00000 q^{3} -0.667790 q^{4} +1.41297 q^{5} +1.15421 q^{6} +4.47597 q^{7} -3.07920 q^{8} +1.00000 q^{9} +1.63087 q^{10} -4.25189 q^{11} -0.667790 q^{12} +1.00000 q^{13} +5.16622 q^{14} +1.41297 q^{15} -2.21848 q^{16} +3.52940 q^{17} +1.15421 q^{18} +1.74665 q^{19} -0.943569 q^{20} +4.47597 q^{21} -4.90759 q^{22} +0.540588 q^{23} -3.07920 q^{24} -3.00351 q^{25} +1.15421 q^{26} +1.00000 q^{27} -2.98901 q^{28} +8.90335 q^{29} +1.63087 q^{30} -3.80675 q^{31} +3.59780 q^{32} -4.25189 q^{33} +4.07368 q^{34} +6.32442 q^{35} -0.667790 q^{36} +3.33884 q^{37} +2.01601 q^{38} +1.00000 q^{39} -4.35083 q^{40} -4.87337 q^{41} +5.16622 q^{42} +6.15118 q^{43} +2.83937 q^{44} +1.41297 q^{45} +0.623954 q^{46} +9.02290 q^{47} -2.21848 q^{48} +13.0343 q^{49} -3.46669 q^{50} +3.52940 q^{51} -0.667790 q^{52} +0.00882258 q^{53} +1.15421 q^{54} -6.00780 q^{55} -13.7824 q^{56} +1.74665 q^{57} +10.2764 q^{58} +11.6957 q^{59} -0.943569 q^{60} +0.522484 q^{61} -4.39380 q^{62} +4.47597 q^{63} +8.58959 q^{64} +1.41297 q^{65} -4.90759 q^{66} +11.0045 q^{67} -2.35690 q^{68} +0.540588 q^{69} +7.29973 q^{70} -10.7002 q^{71} -3.07920 q^{72} +3.79170 q^{73} +3.85373 q^{74} -3.00351 q^{75} -1.16640 q^{76} -19.0313 q^{77} +1.15421 q^{78} -11.3797 q^{79} -3.13465 q^{80} +1.00000 q^{81} -5.62491 q^{82} -15.8692 q^{83} -2.98901 q^{84} +4.98694 q^{85} +7.09977 q^{86} +8.90335 q^{87} +13.0924 q^{88} +0.259341 q^{89} +1.63087 q^{90} +4.47597 q^{91} -0.360999 q^{92} -3.80675 q^{93} +10.4144 q^{94} +2.46797 q^{95} +3.59780 q^{96} -6.09251 q^{97} +15.0444 q^{98} -4.25189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	1.15421	0.816153	0.408076	−	0.912948i	$-0.366200\pi$
$2$	1.15421	0.816153	0.408076	+	0.912948i	$0.366200\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.667790	−0.333895
$5$	1.41297	0.631901	0.315950	−	0.948776i	$-0.397677\pi$
$5$	1.41297	0.631901	0.315950	+	0.948776i	$0.397677\pi$
$6$	1.15421	0.471206
$7$	4.47597	1.69176	0.845878	−	0.533376i	$-0.179077\pi$
$7$	4.47597	1.69176	0.845878	+	0.533376i	$0.179077\pi$
$8$	−3.07920	−1.08866
$9$	1.00000	0.333333
$10$	1.63087	0.515727
$11$	−4.25189	−1.28199	−0.640996	−	0.767544i	$-0.721479\pi$
$11$	−4.25189	−1.28199	−0.640996	+	0.767544i	$0.721479\pi$
$12$	−0.667790	−0.192774
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	5.16622	1.38073
$15$	1.41297	0.364828
$16$	−2.21848	−0.554619
$17$	3.52940	0.856004	0.428002	−	0.903778i	$-0.359218\pi$
$17$	3.52940	0.856004	0.428002	+	0.903778i	$0.359218\pi$
$18$	1.15421	0.272051
$19$	1.74665	0.400709	0.200354	−	0.979723i	$-0.435791\pi$
$19$	1.74665	0.400709	0.200354	+	0.979723i	$0.435791\pi$
$20$	−0.943569	−0.210988
$21$	4.47597	0.976736
$22$	−4.90759	−1.04630
$23$	0.540588	0.112720	0.0563602	−	0.998411i	$-0.482050\pi$
$23$	0.540588	0.112720	0.0563602	+	0.998411i	$0.482050\pi$
$24$	−3.07920	−0.628539
$25$	−3.00351	−0.600702
$26$	1.15421	0.226360
$27$	1.00000	0.192450
$28$	−2.98901	−0.564869
$29$	8.90335	1.65331	0.826655	−	0.562709i	$-0.190241\pi$
$29$	8.90335	1.65331	0.826655	+	0.562709i	$0.190241\pi$
$30$	1.63087	0.297755
$31$	−3.80675	−0.683712	−0.341856	−	0.939752i	$-0.611056\pi$
$31$	−3.80675	−0.683712	−0.341856	+	0.939752i	$0.611056\pi$
$32$	3.59780	0.636008
$33$	−4.25189	−0.740159
$34$	4.07368	0.698630
$35$	6.32442	1.06902
$36$	−0.667790	−0.111298
$37$	3.33884	0.548901	0.274451	−	0.961601i	$-0.411504\pi$
$37$	3.33884	0.548901	0.274451	+	0.961601i	$0.411504\pi$
$38$	2.01601	0.327040
$39$	1.00000	0.160128
$40$	−4.35083	−0.687926
$41$	−4.87337	−0.761092	−0.380546	−	0.924762i	$-0.624264\pi$
$41$	−4.87337	−0.761092	−0.380546	+	0.924762i	$0.624264\pi$
$42$	5.16622	0.797166
$43$	6.15118	0.938046	0.469023	−	0.883186i	$-0.344606\pi$
$43$	6.15118	0.938046	0.469023	+	0.883186i	$0.344606\pi$
$44$	2.83937	0.428051
$45$	1.41297	0.210634
$46$	0.623954	0.0919970
$47$	9.02290	1.31613	0.658063	−	0.752963i	$-0.271376\pi$
$47$	9.02290	1.31613	0.658063	+	0.752963i	$0.271376\pi$
$48$	−2.21848	−0.320209
$49$	13.0343	1.86204
$50$	−3.46669	−0.490264
$51$	3.52940	0.494214
$52$	−0.667790	−0.0926058
$53$	0.00882258	0.00121188	0.000605938	−	1.00000i	$-0.499807\pi$
$53$	0.00882258	0.00121188	0.000605938		1.00000i	$0.499807\pi$
$54$	1.15421	0.157069
$55$	−6.00780	−0.810092
$56$	−13.7824	−1.84175
$57$	1.74665	0.231349
$58$	10.2764	1.34935
$59$	11.6957	1.52265	0.761327	−	0.648368i	$-0.224548\pi$
$59$	11.6957	1.52265	0.761327	+	0.648368i	$0.224548\pi$
$60$	−0.943569	−0.121814
$61$	0.522484	0.0668972	0.0334486	−	0.999440i	$-0.489351\pi$
$61$	0.522484	0.0668972	0.0334486	+	0.999440i	$0.489351\pi$
$62$	−4.39380	−0.558014
$63$	4.47597	0.563919
$64$	8.58959	1.07370
$65$	1.41297	0.175258
$66$	−4.90759	−0.604082
$67$	11.0045	1.34441	0.672204	−	0.740366i	$-0.265348\pi$
$67$	11.0045	1.34441	0.672204	+	0.740366i	$0.265348\pi$
$68$	−2.35690	−0.285816
$69$	0.540588	0.0650791
$70$	7.29973	0.872485
$71$	−10.7002	−1.26988	−0.634940	−	0.772562i	$-0.718975\pi$
$71$	−10.7002	−1.26988	−0.634940	+	0.772562i	$0.718975\pi$
$72$	−3.07920	−0.362887
$73$	3.79170	0.443785	0.221892	−	0.975071i	$-0.428777\pi$
$73$	3.79170	0.443785	0.221892	+	0.975071i	$0.428777\pi$
$74$	3.85373	0.447987
$75$	−3.00351	−0.346815
$76$	−1.16640	−0.133795
$77$	−19.0313	−2.16882
$78$	1.15421	0.130689
$79$	−11.3797	−1.28032	−0.640159	−	0.768242i	$-0.721132\pi$
$79$	−11.3797	−1.28032	−0.640159	+	0.768242i	$0.721132\pi$
$80$	−3.13465	−0.350464
$81$	1.00000	0.111111
$82$	−5.62491	−0.621168
$83$	−15.8692	−1.74187	−0.870936	−	0.491396i	$-0.836487\pi$
$83$	−15.8692	−1.74187	−0.870936	+	0.491396i	$0.836487\pi$
$84$	−2.98901	−0.326127
$85$	4.98694	0.540910
$86$	7.09977	0.765588
$87$	8.90335	0.954539
$88$	13.0924	1.39566
$89$	0.259341	0.0274901	0.0137451	−	0.999906i	$-0.495625\pi$
$89$	0.259341	0.0274901	0.0137451	+	0.999906i	$0.495625\pi$
$90$	1.63087	0.171909
$91$	4.47597	0.469209
$92$	−0.360999	−0.0376368
$93$	−3.80675	−0.394742
$94$	10.4144	1.07416
$95$	2.46797	0.253208
$96$	3.59780	0.367199
$97$	−6.09251	−0.618600	−0.309300	−	0.950964i	$-0.600095\pi$
$97$	−6.09251	−0.618600	−0.309300	+	0.950964i	$0.600095\pi$
$98$	15.0444	1.51971
$99$	−4.25189	−0.427331
$100$	2.00571	0.200571
$101$	−1.83817	−0.182905	−0.0914525	−	0.995809i	$-0.529151\pi$
$101$	−1.83817	−0.182905	−0.0914525	+	0.995809i	$0.529151\pi$
$102$	4.07368	0.403354
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−3.07920	−0.301940
$105$	6.32442	0.617200
$106$	0.0101831	0.000989075 0
$107$	8.57570	0.829044	0.414522	−	0.910039i	$-0.363949\pi$
$107$	8.57570	0.829044	0.414522	+	0.910039i	$0.363949\pi$
$108$	−0.667790	−0.0642581
$109$	7.58500	0.726511	0.363255	−	0.931690i	$-0.381665\pi$
$109$	7.58500	0.726511	0.363255	+	0.931690i	$0.381665\pi$
$110$	−6.93429	−0.661158
$111$	3.33884	0.316908
$112$	−9.92983	−0.938280
$113$	−18.2783	−1.71948	−0.859741	−	0.510731i	$-0.829375\pi$
$113$	−18.2783	−1.71948	−0.859741	+	0.510731i	$0.829375\pi$
$114$	2.01601	0.188816
$115$	0.763836	0.0712281
$116$	−5.94557	−0.552032
$117$	1.00000	0.0924500
$118$	13.4994	1.24272
$119$	15.7975	1.44815
$120$	−4.35083	−0.397174
$121$	7.07855	0.643504
$122$	0.603058	0.0545983
$123$	−4.87337	−0.439417
$124$	2.54211	0.228288
$125$	−11.3087	−1.01148
$126$	5.16622	0.460244
$127$	16.8485	1.49507	0.747533	−	0.664225i	$-0.231238\pi$
$127$	16.8485	1.49507	0.747533	+	0.664225i	$0.231238\pi$
$128$	2.71861	0.240294
$129$	6.15118	0.541581
$130$	1.63087	0.143037
$131$	−14.7931	−1.29248	−0.646240	−	0.763135i	$-0.723659\pi$
$131$	−14.7931	−1.29248	−0.646240	+	0.763135i	$0.723659\pi$
$132$	2.83937	0.247135
$133$	7.81795	0.677902
$134$	12.7015	1.09724
$135$	1.41297	0.121609
$136$	−10.8677	−0.931899
$137$	4.58039	0.391330	0.195665	−	0.980671i	$-0.437314\pi$
$137$	4.58039	0.391330	0.195665	+	0.980671i	$0.437314\pi$
$138$	0.623954	0.0531145
$139$	−6.14892	−0.521545	−0.260772	−	0.965400i	$-0.583977\pi$
$139$	−6.14892	−0.521545	−0.260772	+	0.965400i	$0.583977\pi$
$140$	−4.22338	−0.356941
$141$	9.02290	0.759865
$142$	−12.3503	−1.03642
$143$	−4.25189	−0.355561
$144$	−2.21848	−0.184873
$145$	12.5802	1.04473
$146$	4.37643	0.362196
$147$	13.0343	1.07505
$148$	−2.22964	−0.183275
$149$	12.4162	1.01718	0.508589	−	0.861009i	$-0.330167\pi$
$149$	12.4162	1.01718	0.508589	+	0.861009i	$0.330167\pi$
$150$	−3.46669	−0.283054
$151$	9.28484	0.755589	0.377795	−	0.925889i	$-0.376683\pi$
$151$	9.28484	0.755589	0.377795	+	0.925889i	$0.376683\pi$
$152$	−5.37828	−0.436236
$153$	3.52940	0.285335
$154$	−21.9662	−1.77009
$155$	−5.37883	−0.432038
$156$	−0.667790	−0.0534660
$157$	3.62767	0.289519	0.144760	−	0.989467i	$-0.453759\pi$
$157$	3.62767	0.289519	0.144760	+	0.989467i	$0.453759\pi$
$158$	−13.1346	−1.04494
$159$	0.00882258	0.000699676 0
$160$	5.08360	0.401894
$161$	2.41965	0.190695
$162$	1.15421	0.0906836
$163$	−3.51331	−0.275184	−0.137592	−	0.990489i	$-0.543936\pi$
$163$	−3.51331	−0.275184	−0.137592	+	0.990489i	$0.543936\pi$
$164$	3.25439	0.254125
$165$	−6.00780	−0.467707
$166$	−18.3165	−1.42163
$167$	18.2461	1.41193	0.705964	−	0.708248i	$-0.250514\pi$
$167$	18.2461	1.41193	0.705964	+	0.708248i	$0.250514\pi$
$168$	−13.7824	−1.06334
$169$	1.00000	0.0769231
$170$	5.75600	0.441465
$171$	1.74665	0.133570
$172$	−4.10769	−0.313209
$173$	11.0132	0.837321	0.418661	−	0.908143i	$-0.362500\pi$
$173$	11.0132	0.837321	0.418661	+	0.908143i	$0.362500\pi$
$174$	10.2764	0.779050
$175$	−13.4436	−1.01624
$176$	9.43271	0.711017
$177$	11.6957	0.879105
$178$	0.299335	0.0224361
$179$	−11.8186	−0.883364	−0.441682	−	0.897172i	$-0.645618\pi$
$179$	−11.8186	−0.883364	−0.441682	+	0.897172i	$0.645618\pi$
$180$	−0.943569	−0.0703295
$181$	−10.0461	−0.746720	−0.373360	−	0.927686i	$-0.621794\pi$
$181$	−10.0461	−0.746720	−0.373360	+	0.927686i	$0.621794\pi$
$182$	5.16622	0.382946
$183$	0.522484	0.0386231
$184$	−1.66458	−0.122714
$185$	4.71768	0.346851
$186$	−4.39380	−0.322169
$187$	−15.0066	−1.09739
$188$	−6.02540	−0.439448
$189$	4.47597	0.325579
$190$	2.84856	0.206657
$191$	−7.05674	−0.510608	−0.255304	−	0.966861i	$-0.582176\pi$
$191$	−7.05674	−0.510608	−0.255304	+	0.966861i	$0.582176\pi$
$192$	8.58959	0.619900
$193$	2.57382	0.185267	0.0926337	−	0.995700i	$-0.470471\pi$
$193$	2.57382	0.185267	0.0926337	+	0.995700i	$0.470471\pi$
$194$	−7.03205	−0.504872
$195$	1.41297	0.101185
$196$	−8.70416	−0.621726
$197$	−13.8902	−0.989638	−0.494819	−	0.868996i	$-0.664766\pi$
$197$	−13.8902	−0.989638	−0.494819	+	0.868996i	$0.664766\pi$
$198$	−4.90759	−0.348767
$199$	21.9911	1.55891	0.779454	−	0.626459i	$-0.215497\pi$
$199$	21.9911	1.55891	0.779454	+	0.626459i	$0.215497\pi$
$200$	9.24840	0.653961
$201$	11.0045	0.776194
$202$	−2.12164	−0.149278
$203$	39.8511	2.79700
$204$	−2.35690	−0.165016
$205$	−6.88594	−0.480935
$206$	1.15421	0.0804179
$207$	0.540588	0.0375734
$208$	−2.21848	−0.153824
$209$	−7.42656	−0.513706
$210$	7.29973	0.503730
$211$	6.50534	0.447846	0.223923	−	0.974607i	$-0.428114\pi$
$211$	6.50534	0.447846	0.223923	+	0.974607i	$0.428114\pi$
$212$	−0.00589163	−0.000404639 0
$213$	−10.7002	−0.733165
$214$	9.89819	0.676626
$215$	8.69145	0.592752
$216$	−3.07920	−0.209513
$217$	−17.0389	−1.15667
$218$	8.75471	0.592944
$219$	3.79170	0.256219
$220$	4.01195	0.270486
$221$	3.52940	0.237413
$222$	3.85373	0.258645
$223$	−3.17728	−0.212766	−0.106383	−	0.994325i	$-0.533927\pi$
$223$	−3.17728	−0.212766	−0.106383	+	0.994325i	$0.533927\pi$
$224$	16.1037	1.07597
$225$	−3.00351	−0.200234
$226$	−21.0971	−1.40336
$227$	8.39690	0.557322	0.278661	−	0.960390i	$-0.410109\pi$
$227$	8.39690	0.557322	0.278661	+	0.960390i	$0.410109\pi$
$228$	−1.16640	−0.0772464
$229$	−2.58221	−0.170637	−0.0853187	−	0.996354i	$-0.527191\pi$
$229$	−2.58221	−0.170637	−0.0853187	+	0.996354i	$0.527191\pi$
$230$	0.881630	0.0581330
$231$	−19.0313	−1.25217
$232$	−27.4152	−1.79990
$233$	−14.5019	−0.950049	−0.475024	−	0.879973i	$-0.657561\pi$
$233$	−14.5019	−0.950049	−0.475024	+	0.879973i	$0.657561\pi$
$234$	1.15421	0.0754533
$235$	12.7491	0.831660
$236$	−7.81029	−0.508407
$237$	−11.3797	−0.739192
$238$	18.2336	1.18191
$239$	−19.0647	−1.23319	−0.616596	−	0.787280i	$-0.711489\pi$
$239$	−19.0647	−1.23319	−0.616596	+	0.787280i	$0.711489\pi$
$240$	−3.13465	−0.202341
$241$	−23.9614	−1.54349	−0.771745	−	0.635932i	$-0.780616\pi$
$241$	−23.9614	−1.54349	−0.771745	+	0.635932i	$0.780616\pi$
$242$	8.17016	0.525198
$243$	1.00000	0.0641500
$244$	−0.348910	−0.0223367
$245$	18.4171	1.17662
$246$	−5.62491	−0.358631
$247$	1.74665	0.111137
$248$	11.7217	0.744332
$249$	−15.8692	−1.00567
$250$	−13.0527	−0.825526
$251$	−3.84295	−0.242565	−0.121282	−	0.992618i	$-0.538701\pi$
$251$	−3.84295	−0.242565	−0.121282	+	0.992618i	$0.538701\pi$
$252$	−2.98901	−0.188290
$253$	−2.29852	−0.144507
$254$	19.4468	1.22020
$255$	4.98694	0.312294
$256$	−14.0413	−0.877582
$257$	−26.0629	−1.62576	−0.812880	−	0.582432i	$-0.802101\pi$
$257$	−26.0629	−1.62576	−0.812880	+	0.582432i	$0.802101\pi$
$258$	7.09977	0.442013
$259$	14.9445	0.928607
$260$	−0.943569	−0.0585177
$261$	8.90335	0.551103
$262$	−17.0744	−1.05486
$263$	−13.4102	−0.826906	−0.413453	−	0.910525i	$-0.635677\pi$
$263$	−13.4102	−0.826906	−0.413453	+	0.910525i	$0.635677\pi$
$264$	13.0924	0.805782
$265$	0.0124661	0.000765785 0
$266$	9.02358	0.553271
$267$	0.259341	0.0158714
$268$	−7.34866	−0.448891
$269$	−17.2766	−1.05337	−0.526686	−	0.850060i	$-0.676566\pi$
$269$	−17.2766	−1.05337	−0.526686	+	0.850060i	$0.676566\pi$
$270$	1.63087	0.0992518
$271$	21.5430	1.30865	0.654323	−	0.756215i	$-0.272954\pi$
$271$	21.5430	1.30865	0.654323	+	0.756215i	$0.272954\pi$
$272$	−7.82988	−0.474756
$273$	4.47597	0.270898
$274$	5.28676	0.319385
$275$	12.7706	0.770095
$276$	−0.360999	−0.0217296
$277$	−11.0490	−0.663872	−0.331936	−	0.943302i	$-0.607702\pi$
$277$	−11.0490	−0.663872	−0.331936	+	0.943302i	$0.607702\pi$
$278$	−7.09717	−0.425660
$279$	−3.80675	−0.227904
$280$	−19.4742	−1.16380
$281$	25.8935	1.54468	0.772339	−	0.635210i	$-0.219087\pi$
$281$	25.8935	1.54468	0.772339	+	0.635210i	$0.219087\pi$
$282$	10.4144	0.620166
$283$	5.77887	0.343518	0.171759	−	0.985139i	$-0.445055\pi$
$283$	5.77887	0.343518	0.171759	+	0.985139i	$0.445055\pi$
$284$	7.14548	0.424007
$285$	2.46797	0.146190
$286$	−4.90759	−0.290192
$287$	−21.8130	−1.28758
$288$	3.59780	0.212003
$289$	−4.54337	−0.267257
$290$	14.5202	0.852657
$291$	−6.09251	−0.357149
$292$	−2.53206	−0.148178
$293$	−25.0219	−1.46179	−0.730896	−	0.682489i	$-0.760898\pi$
$293$	−25.0219	−1.46179	−0.730896	+	0.682489i	$0.760898\pi$
$294$	15.0444	0.877404
$295$	16.5257	0.962166
$296$	−10.2809	−0.597568
$297$	−4.25189	−0.246720
$298$	14.3310	0.830172
$299$	0.540588	0.0312630
$300$	2.00571	0.115800
$301$	27.5325	1.58695
$302$	10.7167	0.616676
$303$	−1.83817	−0.105600
$304$	−3.87490	−0.222241
$305$	0.738256	0.0422724
$306$	4.07368	0.232877
$307$	16.9094	0.965072	0.482536	−	0.875876i	$-0.339716\pi$
$307$	16.9094	0.965072	0.482536	+	0.875876i	$0.339716\pi$
$308$	12.7089	0.724158
$309$	1.00000	0.0568880
$310$	−6.20833	−0.352609
$311$	−14.9387	−0.847095	−0.423547	−	0.905874i	$-0.639215\pi$
$311$	−14.9387	−0.847095	−0.423547	+	0.905874i	$0.639215\pi$
$312$	−3.07920	−0.174325
$313$	5.13323	0.290147	0.145074	−	0.989421i	$-0.453658\pi$
$313$	5.13323	0.290147	0.145074	+	0.989421i	$0.453658\pi$
$314$	4.18711	0.236292
$315$	6.32442	0.356341
$316$	7.59926	0.427492
$317$	5.02425	0.282190	0.141095	−	0.989996i	$-0.454938\pi$
$317$	5.02425	0.282190	0.141095	+	0.989996i	$0.454938\pi$
$318$	0.0101831	0.000571043 0
$319$	−37.8560	−2.11953
$320$	12.1369	0.678471
$321$	8.57570	0.478649
$322$	2.79280	0.155637
$323$	6.16462	0.343008
$324$	−0.667790	−0.0370994
$325$	−3.00351	−0.166605
$326$	−4.05511	−0.224592
$327$	7.58500	0.419451
$328$	15.0061	0.828572
$329$	40.3862	2.22656
$330$	−6.93429	−0.381720
$331$	3.56591	0.196000	0.0980001	−	0.995186i	$-0.468755\pi$
$331$	3.56591	0.196000	0.0980001	+	0.995186i	$0.468755\pi$
$332$	10.5973	0.581603
$333$	3.33884	0.182967
$334$	21.0599	1.15235
$335$	15.5490	0.849532
$336$	−9.92983	−0.541716
$337$	−7.32495	−0.399015	−0.199508	−	0.979896i	$-0.563934\pi$
$337$	−7.32495	−0.399015	−0.199508	+	0.979896i	$0.563934\pi$
$338$	1.15421	0.0627810
$339$	−18.2783	−0.992743
$340$	−3.33023	−0.180607
$341$	16.1859	0.876514
$342$	2.01601	0.109013
$343$	27.0093	1.45836
$344$	−18.9407	−1.02121
$345$	0.763836	0.0411235
$346$	12.7116	0.683382
$347$	27.4456	1.47336	0.736679	−	0.676242i	$-0.236393\pi$
$347$	27.4456	1.47336	0.736679	+	0.676242i	$0.236393\pi$
$348$	−5.94557	−0.318716
$349$	−16.3163	−0.873392	−0.436696	−	0.899609i	$-0.643851\pi$
$349$	−16.3163	−0.873392	−0.436696	+	0.899609i	$0.643851\pi$
$350$	−15.5168	−0.829408
$351$	1.00000	0.0533761
$352$	−15.2975	−0.815357
$353$	5.89303	0.313655	0.156827	−	0.987626i	$-0.449873\pi$
$353$	5.89303	0.313655	0.156827	+	0.987626i	$0.449873\pi$
$354$	13.4994	0.717484
$355$	−15.1191	−0.802438
$356$	−0.173186	−0.00917882
$357$	15.7975	0.836090
$358$	−13.6412	−0.720960
$359$	−5.13445	−0.270986	−0.135493	−	0.990778i	$-0.543262\pi$
$359$	−5.13445	−0.270986	−0.135493	+	0.990778i	$0.543262\pi$
$360$	−4.35083	−0.229309
$361$	−15.9492	−0.839432
$362$	−11.5953	−0.609438
$363$	7.07855	0.371527
$364$	−2.98901	−0.156667
$365$	5.35757	0.280428
$366$	0.603058	0.0315224
$367$	2.01925	0.105404	0.0527019	−	0.998610i	$-0.483217\pi$
$367$	2.01925	0.105404	0.0527019	+	0.998610i	$0.483217\pi$
$368$	−1.19928	−0.0625169
$369$	−4.87337	−0.253697
$370$	5.44522	0.283083
$371$	0.0394896	0.00205020
$372$	2.54211	0.131802
$373$	4.90259	0.253846	0.126923	−	0.991913i	$-0.459490\pi$
$373$	4.90259	0.253846	0.126923	+	0.991913i	$0.459490\pi$
$374$	−17.3208	−0.895638
$375$	−11.3087	−0.583981
$376$	−27.7833	−1.43282
$377$	8.90335	0.458546
$378$	5.16622	0.265722
$379$	3.48508	0.179017	0.0895084	−	0.995986i	$-0.471470\pi$
$379$	3.48508	0.179017	0.0895084	+	0.995986i	$0.471470\pi$
$380$	−1.64808	−0.0845450
$381$	16.8485	0.863177
$382$	−8.14499	−0.416734
$383$	−27.7930	−1.42016	−0.710079	−	0.704122i	$-0.751341\pi$
$383$	−27.7930	−1.42016	−0.710079	+	0.704122i	$0.751341\pi$
$384$	2.71861	0.138734
$385$	−26.8907	−1.37048
$386$	2.97073	0.151206
$387$	6.15118	0.312682
$388$	4.06851	0.206548
$389$	27.2914	1.38373	0.691863	−	0.722028i	$-0.256790\pi$
$389$	27.2914	1.38373	0.691863	+	0.722028i	$0.256790\pi$
$390$	1.63087	0.0825825
$391$	1.90795	0.0964891
$392$	−40.1352	−2.02713
$393$	−14.7931	−0.746213
$394$	−16.0323	−0.807696
$395$	−16.0792	−0.809034
$396$	2.83937	0.142684
$397$	0.673430	0.0337985	0.0168993	−	0.999857i	$-0.494621\pi$
$397$	0.673430	0.0337985	0.0168993	+	0.999857i	$0.494621\pi$
$398$	25.3824	1.27231
$399$	7.81795	0.391387
$400$	6.66321	0.333161
$401$	13.8539	0.691832	0.345916	−	0.938265i	$-0.387568\pi$
$401$	13.8539	0.691832	0.345916	+	0.938265i	$0.387568\pi$
$402$	12.7015	0.633493
$403$	−3.80675	−0.189628
$404$	1.22751	0.0610710
$405$	1.41297	0.0702112
$406$	45.9967	2.28278
$407$	−14.1964	−0.703687
$408$	−10.8677	−0.538032
$409$	20.5942	1.01832	0.509160	−	0.860672i	$-0.329956\pi$
$409$	20.5942	1.01832	0.509160	+	0.860672i	$0.329956\pi$
$410$	−7.94785	−0.392516
$411$	4.58039	0.225934
$412$	−0.667790	−0.0328997
$413$	52.3497	2.57596
$414$	0.623954	0.0306657
$415$	−22.4228	−1.10069
$416$	3.59780	0.176397
$417$	−6.14892	−0.301114
$418$	−8.57184	−0.419262
$419$	0.825971	0.0403513	0.0201757	−	0.999796i	$-0.493577\pi$
$419$	0.825971	0.0403513	0.0201757	+	0.999796i	$0.493577\pi$
$420$	−4.22338	−0.206080
$421$	−23.2649	−1.13386	−0.566932	−	0.823765i	$-0.691870\pi$
$421$	−23.2649	−1.13386	−0.566932	+	0.823765i	$0.691870\pi$
$422$	7.50855	0.365510
$423$	9.02290	0.438708
$424$	−0.0271665	−0.00131932
$425$	−10.6006	−0.514203
$426$	−12.3503	−0.598375
$427$	2.33862	0.113174
$428$	−5.72677	−0.276814
$429$	−4.25189	−0.205283
$430$	10.0318	0.483776
$431$	−21.4477	−1.03310	−0.516549	−	0.856258i	$-0.672783\pi$
$431$	−21.4477	−1.03310	−0.516549	+	0.856258i	$0.672783\pi$
$432$	−2.21848	−0.106736
$433$	39.1903	1.88337	0.941683	−	0.336502i	$-0.109244\pi$
$433$	39.1903	1.88337	0.941683	+	0.336502i	$0.109244\pi$
$434$	−19.6665	−0.944023
$435$	12.5802	0.603174
$436$	−5.06519	−0.242578
$437$	0.944217	0.0451680
$438$	4.37643	0.209114
$439$	11.8417	0.565173	0.282587	−	0.959242i	$-0.408808\pi$
$439$	11.8417	0.565173	0.282587	+	0.959242i	$0.408808\pi$
$440$	18.4992	0.881916
$441$	13.0343	0.620680
$442$	4.07368	0.193765
$443$	−0.840763	−0.0399459	−0.0199729	−	0.999801i	$-0.506358\pi$
$443$	−0.840763	−0.0399459	−0.0199729	+	0.999801i	$0.506358\pi$
$444$	−2.22964	−0.105814
$445$	0.366442	0.0173710
$446$	−3.66726	−0.173650
$447$	12.4162	0.587268
$448$	38.4467	1.81644
$449$	−0.303683	−0.0143317	−0.00716584	−	0.999974i	$-0.502281\pi$
$449$	−0.303683	−0.0143317	−0.00716584	+	0.999974i	$0.502281\pi$
$450$	−3.46669	−0.163421
$451$	20.7210	0.975715
$452$	12.2061	0.574126
$453$	9.28484	0.436240
$454$	9.69182	0.454860
$455$	6.32442	0.296493
$456$	−5.37828	−0.251861
$457$	−39.0628	−1.82728	−0.913641	−	0.406522i	$-0.866741\pi$
$457$	−39.0628	−1.82728	−0.913641	+	0.406522i	$0.866741\pi$
$458$	−2.98043	−0.139266
$459$	3.52940	0.164738
$460$	−0.510082	−0.0237827
$461$	−12.8806	−0.599910	−0.299955	−	0.953953i	$-0.596972\pi$
$461$	−12.8806	−0.599910	−0.299955	+	0.953953i	$0.596972\pi$
$462$	−21.9662	−1.02196
$463$	30.4050	1.41304	0.706521	−	0.707692i	$-0.250264\pi$
$463$	30.4050	1.41304	0.706521	+	0.707692i	$0.250264\pi$
$464$	−19.7519	−0.916957
$465$	−5.37883	−0.249437
$466$	−16.7383	−0.775385
$467$	−15.3040	−0.708185	−0.354092	−	0.935210i	$-0.615210\pi$
$467$	−15.3040	−0.708185	−0.354092	+	0.935210i	$0.615210\pi$
$468$	−0.667790	−0.0308686
$469$	49.2556	2.27441
$470$	14.7152	0.678762
$471$	3.62767	0.167154
$472$	−36.0135	−1.65766
$473$	−26.1541	−1.20257
$474$	−13.1346	−0.603294
$475$	−5.24608	−0.240706
$476$	−10.5494	−0.483530
$477$	0.00882258	0.000403958 0
$478$	−22.0047	−1.00647
$479$	−29.2604	−1.33694	−0.668470	−	0.743739i	$-0.733050\pi$
$479$	−29.2604	−1.33694	−0.668470	+	0.743739i	$0.733050\pi$
$480$	5.08360	0.232034
$481$	3.33884	0.152238
$482$	−27.6566	−1.25972
$483$	2.41965	0.110098
$484$	−4.72698	−0.214863
$485$	−8.60854	−0.390894
$486$	1.15421	0.0523562
$487$	−16.5687	−0.750798	−0.375399	−	0.926863i	$-0.622494\pi$
$487$	−16.5687	−0.750798	−0.375399	+	0.926863i	$0.622494\pi$
$488$	−1.60883	−0.0728285
$489$	−3.51331	−0.158877
$490$	21.2573	0.960305
$491$	34.4476	1.55460	0.777299	−	0.629132i	$-0.216589\pi$
$491$	34.4476	1.55460	0.777299	+	0.629132i	$0.216589\pi$
$492$	3.25439	0.146719
$493$	31.4234	1.41524
$494$	2.01601	0.0907045
$495$	−6.00780	−0.270031
$496$	8.44518	0.379200
$497$	−47.8937	−2.14833
$498$	−18.3165	−0.820781
$499$	−30.0665	−1.34596	−0.672981	−	0.739660i	$-0.734986\pi$
$499$	−30.0665	−1.34596	−0.672981	+	0.739660i	$0.734986\pi$
$500$	7.55186	0.337730
$501$	18.2461	0.815177
$502$	−4.43558	−0.197970
$503$	−31.6490	−1.41116	−0.705580	−	0.708630i	$-0.749313\pi$
$503$	−31.6490	−1.41116	−0.705580	+	0.708630i	$0.749313\pi$
$504$	−13.7824	−0.613917
$505$	−2.59729	−0.115578
$506$	−2.65298	−0.117939
$507$	1.00000	0.0444116
$508$	−11.2513	−0.499195
$509$	6.36381	0.282071	0.141035	−	0.990005i	$-0.454957\pi$
$509$	6.36381	0.282071	0.141035	+	0.990005i	$0.454957\pi$
$510$	5.75600	0.254880
$511$	16.9715	0.750776
$512$	−21.6439	−0.956535
$513$	1.74665	0.0771165
$514$	−30.0822	−1.32687
$515$	1.41297	0.0622630
$516$	−4.10769	−0.180831
$517$	−38.3644	−1.68726
$518$	17.2492	0.757885
$519$	11.0132	0.483428
$520$	−4.35083	−0.190796
$521$	−9.21569	−0.403747	−0.201873	−	0.979412i	$-0.564703\pi$
$521$	−9.21569	−0.403747	−0.201873	+	0.979412i	$0.564703\pi$
$522$	10.2764	0.449784
$523$	−35.8706	−1.56851	−0.784256	−	0.620437i	$-0.786955\pi$
$523$	−35.8706	−1.56851	−0.784256	+	0.620437i	$0.786955\pi$
$524$	9.87868	0.431552
$525$	−13.4436	−0.586727
$526$	−15.4782	−0.674882
$527$	−13.4355	−0.585261
$528$	9.43271	0.410506
$529$	−22.7078	−0.987294
$530$	0.0143885	0.000624997 0
$531$	11.6957	0.507551
$532$	−5.22075	−0.226348
$533$	−4.87337	−0.211089
$534$	0.299335	0.0129535
$535$	12.1172	0.523873
$536$	−33.8849	−1.46361
$537$	−11.8186	−0.510010
$538$	−19.9409	−0.859713
$539$	−55.4203	−2.38712
$540$	−0.943569	−0.0406048
$541$	−12.7392	−0.547703	−0.273851	−	0.961772i	$-0.588298\pi$
$541$	−12.7392	−0.547703	−0.273851	+	0.961772i	$0.588298\pi$
$542$	24.8653	1.06805
$543$	−10.0461	−0.431119
$544$	12.6981	0.544426
$545$	10.7174	0.459083
$546$	5.16622	0.221094
$547$	31.2421	1.33581	0.667907	−	0.744245i	$-0.267190\pi$
$547$	31.2421	1.33581	0.667907	+	0.744245i	$0.267190\pi$
$548$	−3.05874	−0.130663
$549$	0.522484	0.0222991
$550$	14.7400	0.628515
$551$	15.5510	0.662496
$552$	−1.66458	−0.0708492
$553$	−50.9353	−2.16599
$554$	−12.7530	−0.541821
$555$	4.71768	0.200255
$556$	4.10619	0.174141
$557$	−38.0536	−1.61238	−0.806191	−	0.591656i	$-0.798475\pi$
$557$	−38.0536	−1.61238	−0.806191	+	0.591656i	$0.798475\pi$
$558$	−4.39380	−0.186005
$559$	6.15118	0.260167
$560$	−14.0306	−0.592900
$561$	−15.0066	−0.633579
$562$	29.8867	1.26069
$563$	5.97461	0.251800	0.125900	−	0.992043i	$-0.459818\pi$
$563$	5.97461	0.251800	0.125900	+	0.992043i	$0.459818\pi$
$564$	−6.02540	−0.253715
$565$	−25.8268	−1.08654
$566$	6.67006	0.280363
$567$	4.47597	0.187973
$568$	32.9481	1.38247
$569$	−11.5735	−0.485185	−0.242593	−	0.970128i	$-0.577998\pi$
$569$	−11.5735	−0.485185	−0.242593	+	0.970128i	$0.577998\pi$
$570$	2.84856	0.119313
$571$	−23.8147	−0.996612	−0.498306	−	0.867001i	$-0.666044\pi$
$571$	−23.8147	−0.996612	−0.498306	+	0.867001i	$0.666044\pi$
$572$	2.83937	0.118720
$573$	−7.05674	−0.294800
$574$	−25.1769	−1.05086
$575$	−1.62366	−0.0677113
$576$	8.58959	0.357900
$577$	38.4579	1.60102	0.800511	−	0.599318i	$-0.204561\pi$
$577$	38.4579	1.60102	0.800511	+	0.599318i	$0.204561\pi$
$578$	−5.24402	−0.218122
$579$	2.57382	0.106964
$580$	−8.40093	−0.348829
$581$	−71.0301	−2.94682
$582$	−7.03205	−0.291488
$583$	−0.0375126	−0.00155361
$584$	−11.6754	−0.483132
$585$	1.41297	0.0584192
$586$	−28.8806	−1.19305
$587$	−26.3360	−1.08700	−0.543502	−	0.839408i	$-0.682902\pi$
$587$	−26.3360	−1.08700	−0.543502	+	0.839408i	$0.682902\pi$
$588$	−8.70416	−0.358954
$589$	−6.64906	−0.273970
$590$	19.0742	0.785274
$591$	−13.8902	−0.571368
$592$	−7.40713	−0.304431
$593$	16.4484	0.675456	0.337728	−	0.941244i	$-0.390342\pi$
$593$	16.4484	0.675456	0.337728	+	0.941244i	$0.390342\pi$
$594$	−4.90759	−0.201361
$595$	22.3214	0.915087
$596$	−8.29144	−0.339631
$597$	21.9911	0.900036
$598$	0.623954	0.0255154
$599$	−35.6269	−1.45567	−0.727837	−	0.685750i	$-0.759474\pi$
$599$	−35.6269	−1.45567	−0.727837	+	0.685750i	$0.759474\pi$
$600$	9.24840	0.377564
$601$	41.2474	1.68252	0.841258	−	0.540634i	$-0.181815\pi$
$601$	41.2474	1.68252	0.841258	+	0.540634i	$0.181815\pi$
$602$	31.7784	1.29519
$603$	11.0045	0.448136
$604$	−6.20032	−0.252288
$605$	10.0018	0.406631
$606$	−2.12164	−0.0861859
$607$	43.4774	1.76469	0.882346	−	0.470602i	$-0.155963\pi$
$607$	43.4774	1.76469	0.882346	+	0.470602i	$0.155963\pi$
$608$	6.28410	0.254854
$609$	39.8511	1.61485
$610$	0.852105	0.0345007
$611$	9.02290	0.365027
$612$	−2.35690	−0.0952718
$613$	−44.7152	−1.80603	−0.903015	−	0.429609i	$-0.858652\pi$
$613$	−44.7152	−1.80603	−0.903015	+	0.429609i	$0.858652\pi$
$614$	19.5171	0.787646
$615$	−6.88594	−0.277668
$616$	58.6012	2.36111
$617$	45.0392	1.81321	0.906606	−	0.421978i	$-0.138664\pi$
$617$	45.0392	1.81321	0.906606	+	0.421978i	$0.138664\pi$
$618$	1.15421	0.0464293
$619$	−19.4631	−0.782286	−0.391143	−	0.920330i	$-0.627920\pi$
$619$	−19.4631	−0.782286	−0.391143	+	0.920330i	$0.627920\pi$
$620$	3.59193	0.144255
$621$	0.540588	0.0216930
$622$	−17.2424	−0.691358
$623$	1.16080	0.0465066
$624$	−2.21848	−0.0888101
$625$	−0.961402	−0.0384561
$626$	5.92485	0.236805
$627$	−7.42656	−0.296588
$628$	−2.42252	−0.0966691
$629$	11.7841	0.469862
$630$	7.29973	0.290828
$631$	−4.48966	−0.178731	−0.0893653	−	0.995999i	$-0.528484\pi$
$631$	−4.48966	−0.178731	−0.0893653	+	0.995999i	$0.528484\pi$
$632$	35.0404	1.39383
$633$	6.50534	0.258564
$634$	5.79906	0.230310
$635$	23.8065	0.944733
$636$	−0.00589163	−0.000233618 0
$637$	13.0343	0.516437
$638$	−43.6940	−1.72986
$639$	−10.7002	−0.423293
$640$	3.84133	0.151842
$641$	−25.1297	−0.992565	−0.496282	−	0.868161i	$-0.665302\pi$
$641$	−25.1297	−0.992565	−0.496282	+	0.868161i	$0.665302\pi$
$642$	9.89819	0.390650
$643$	4.27415	0.168556	0.0842781	−	0.996442i	$-0.473142\pi$
$643$	4.27415	0.168556	0.0842781	+	0.996442i	$0.473142\pi$
$644$	−1.61582	−0.0636722
$645$	8.69145	0.342225
$646$	7.11529	0.279947
$647$	−47.0127	−1.84826	−0.924129	−	0.382080i	$-0.875208\pi$
$647$	−47.0127	−1.84826	−0.924129	+	0.382080i	$0.875208\pi$
$648$	−3.07920	−0.120962
$649$	−49.7289	−1.95203
$650$	−3.46669	−0.135975
$651$	−17.0389	−0.667807
$652$	2.34615	0.0918825
$653$	−40.0360	−1.56673	−0.783365	−	0.621562i	$-0.786498\pi$
$653$	−40.0360	−1.56673	−0.783365	+	0.621562i	$0.786498\pi$
$654$	8.75471	0.342336
$655$	−20.9022	−0.816718
$656$	10.8115	0.422116
$657$	3.79170	0.147928
$658$	46.6143	1.81722
$659$	−26.5759	−1.03525	−0.517624	−	0.855608i	$-0.673183\pi$
$659$	−26.5759	−1.03525	−0.517624	+	0.855608i	$0.673183\pi$
$660$	4.01195	0.156165
$661$	−8.39901	−0.326684	−0.163342	−	0.986570i	$-0.552227\pi$
$661$	−8.39901	−0.326684	−0.163342	+	0.986570i	$0.552227\pi$
$662$	4.11583	0.159966
$663$	3.52940	0.137070
$664$	48.8645	1.89631
$665$	11.0465	0.428367
$666$	3.85373	0.149329
$667$	4.81304	0.186362
$668$	−12.1846	−0.471436
$669$	−3.17728	−0.122841
$670$	17.9469	0.693348
$671$	−2.22154	−0.0857617
$672$	16.1037	0.621212
$673$	−21.0824	−0.812667	−0.406334	−	0.913725i	$-0.633193\pi$
$673$	−21.0824	−0.812667	−0.406334	+	0.913725i	$0.633193\pi$
$674$	−8.45456	−0.325657
$675$	−3.00351	−0.115605
$676$	−0.667790	−0.0256842
$677$	38.1911	1.46780	0.733902	−	0.679255i	$-0.237697\pi$
$677$	38.1911	1.46780	0.733902	+	0.679255i	$0.237697\pi$
$678$	−21.0971	−0.810230
$679$	−27.2699	−1.04652
$680$	−15.3558	−0.588868
$681$	8.39690	0.321770
$682$	18.6820	0.715369
$683$	−3.48089	−0.133193	−0.0665963	−	0.997780i	$-0.521214\pi$
$683$	−3.48089	−0.133193	−0.0665963	+	0.997780i	$0.521214\pi$
$684$	−1.16640	−0.0445982
$685$	6.47197	0.247281
$686$	31.1745	1.19025
$687$	−2.58221	−0.0985176
$688$	−13.6462	−0.520258
$689$	0.00882258	0.000336114 0
$690$	0.881630	0.0335631
$691$	33.0989	1.25914	0.629570	−	0.776944i	$-0.283231\pi$
$691$	33.0989	1.25914	0.629570	+	0.776944i	$0.283231\pi$
$692$	−7.35453	−0.279577
$693$	−19.0313	−0.722940
$694$	31.6781	1.20249
$695$	−8.68826	−0.329565
$696$	−27.4152	−1.03917
$697$	−17.2000	−0.651498
$698$	−18.8325	−0.712821
$699$	−14.5019	−0.548511
$700$	8.97750	0.339318
$701$	−14.5242	−0.548570	−0.274285	−	0.961648i	$-0.588441\pi$
$701$	−14.5242	−0.548570	−0.274285	+	0.961648i	$0.588441\pi$
$702$	1.15421	0.0435630
$703$	5.83178	0.219950
$704$	−36.5220	−1.37647
$705$	12.7491	0.480159
$706$	6.80182	0.255990
$707$	−8.22760	−0.309431
$708$	−7.81029	−0.293529
$709$	9.65565	0.362626	0.181313	−	0.983425i	$-0.441965\pi$
$709$	9.65565	0.362626	0.181313	+	0.983425i	$0.441965\pi$
$710$	−17.4507	−0.654912
$711$	−11.3797	−0.426773
$712$	−0.798564	−0.0299275
$713$	−2.05788	−0.0770683
$714$	18.2336	0.682377
$715$	−6.00780	−0.224679
$716$	7.89235	0.294951
$717$	−19.0647	−0.711983
$718$	−5.92625	−0.221166
$719$	−4.93863	−0.184180	−0.0920899	−	0.995751i	$-0.529355\pi$
$719$	−4.93863	−0.184180	−0.0920899	+	0.995751i	$0.529355\pi$
$720$	−3.13465	−0.116821
$721$	4.47597	0.166694
$722$	−18.4088	−0.685105
$723$	−23.9614	−0.891134
$724$	6.70868	0.249326
$725$	−26.7413	−0.993146
$726$	8.17016	0.303223
$727$	−20.7519	−0.769646	−0.384823	−	0.922990i	$-0.625737\pi$
$727$	−20.7519	−0.769646	−0.384823	+	0.922990i	$0.625737\pi$
$728$	−13.7824	−0.510810
$729$	1.00000	0.0370370
$730$	6.18378	0.228872
$731$	21.7099	0.802971
$732$	−0.348910	−0.0128961
$733$	7.14207	0.263798	0.131899	−	0.991263i	$-0.457892\pi$
$733$	7.14207	0.263798	0.131899	+	0.991263i	$0.457892\pi$
$734$	2.33064	0.0860256
$735$	18.4171	0.679324
$736$	1.94493	0.0716910
$737$	−46.7897	−1.72352
$738$	−5.62491	−0.207056
$739$	39.9654	1.47015	0.735076	−	0.677984i	$-0.237146\pi$
$739$	39.9654	1.47015	0.735076	+	0.677984i	$0.237146\pi$
$740$	−3.15042	−0.115812
$741$	1.74665	0.0641648
$742$	0.0455794	0.00167327
$743$	3.73427	0.136997	0.0684985	−	0.997651i	$-0.478179\pi$
$743$	3.73427	0.136997	0.0684985	+	0.997651i	$0.478179\pi$
$744$	11.7217	0.429740
$745$	17.5438	0.642755
$746$	5.65864	0.207177
$747$	−15.8692	−0.580624
$748$	10.0213	0.366413
$749$	38.3845	1.40254
$750$	−13.0527	−0.476617
$751$	19.8046	0.722681	0.361341	−	0.932434i	$-0.382319\pi$
$751$	19.8046	0.722681	0.361341	+	0.932434i	$0.382319\pi$
$752$	−20.0171	−0.729948
$753$	−3.84295	−0.140045
$754$	10.2764	0.374243
$755$	13.1192	0.477457
$756$	−2.98901	−0.108709
$757$	−46.5341	−1.69131	−0.845655	−	0.533731i	$-0.820790\pi$
$757$	−46.5341	−1.69131	−0.845655	+	0.533731i	$0.820790\pi$
$758$	4.02253	0.146105
$759$	−2.29852	−0.0834309
$760$	−7.59937	−0.275658
$761$	20.9730	0.760272	0.380136	−	0.924931i	$-0.375877\pi$
$761$	20.9730	0.760272	0.380136	+	0.924931i	$0.375877\pi$
$762$	19.4468	0.704484
$763$	33.9502	1.22908
$764$	4.71242	0.170490
$765$	4.98694	0.180303
$766$	−32.0791	−1.15906
$767$	11.6957	0.422308
$768$	−14.0413	−0.506672
$769$	12.4877	0.450317	0.225158	−	0.974322i	$-0.427710\pi$
$769$	12.4877	0.450317	0.225158	+	0.974322i	$0.427710\pi$
$770$	−31.0376	−1.11852
$771$	−26.0629	−0.938633
$772$	−1.71877	−0.0618598
$773$	6.60759	0.237659	0.118829	−	0.992915i	$-0.462086\pi$
$773$	6.60759	0.237659	0.118829	+	0.992915i	$0.462086\pi$
$774$	7.09977	0.255196
$775$	11.4336	0.410707
$776$	18.7600	0.673446
$777$	14.9445	0.536132
$778$	31.5001	1.12933
$779$	−8.51207	−0.304977
$780$	−0.943569	−0.0337852
$781$	45.4960	1.62798
$782$	2.20218	0.0787498
$783$	8.90335	0.318180
$784$	−28.9162	−1.03272
$785$	5.12580	0.182948
$786$	−17.0744	−0.609024
$787$	−28.2338	−1.00643	−0.503214	−	0.864162i	$-0.667849\pi$
$787$	−28.2338	−1.00643	−0.503214	+	0.864162i	$0.667849\pi$
$788$	9.27576	0.330435
$789$	−13.4102	−0.477415
$790$	−18.5589	−0.660295
$791$	−81.8132	−2.90894
$792$	13.0924	0.465219
$793$	0.522484	0.0185540
$794$	0.777283	0.0275847
$795$	0.0124661	0.000442126 0
$796$	−14.6854	−0.520512
$797$	−41.8872	−1.48372	−0.741860	−	0.670555i	$-0.766056\pi$
$797$	−41.8872	−1.48372	−0.741860	+	0.670555i	$0.766056\pi$
$798$	9.02358	0.319431
$799$	31.8454	1.12661
$800$	−10.8060	−0.382051
$801$	0.259341	0.00916338
$802$	15.9904	0.564641
$803$	−16.1219	−0.568929
$804$	−7.34866	−0.259167
$805$	3.41890	0.120501
$806$	−4.39380	−0.154765
$807$	−17.2766	−0.608165
$808$	5.66010	0.199122
$809$	36.0137	1.26617	0.633087	−	0.774081i	$-0.281787\pi$
$809$	36.0137	1.26617	0.633087	+	0.774081i	$0.281787\pi$
$810$	1.63087	0.0573030
$811$	11.3841	0.399751	0.199876	−	0.979821i	$-0.435946\pi$
$811$	11.3841	0.399751	0.199876	+	0.979821i	$0.435946\pi$
$812$	−26.6122	−0.933904
$813$	21.5430	0.755547
$814$	−16.3856	−0.574316
$815$	−4.96421	−0.173889
$816$	−7.82988	−0.274101
$817$	10.7440	0.375883
$818$	23.7701	0.831104
$819$	4.47597	0.156403
$820$	4.59836	0.160582
$821$	−43.9197	−1.53281	−0.766403	−	0.642360i	$-0.777956\pi$
$821$	−43.9197	−1.53281	−0.766403	+	0.642360i	$0.777956\pi$
$822$	5.28676	0.184397
$823$	−11.0843	−0.386375	−0.193187	−	0.981162i	$-0.561883\pi$
$823$	−11.0843	−0.386375	−0.193187	+	0.981162i	$0.561883\pi$
$824$	−3.07920	−0.107269
$825$	12.7706	0.444614
$826$	60.4227	2.10238
$827$	−3.59837	−0.125127	−0.0625637	−	0.998041i	$-0.519928\pi$
$827$	−3.59837	−0.125127	−0.0625637	+	0.998041i	$0.519928\pi$
$828$	−0.360999	−0.0125456
$829$	23.2513	0.807551	0.403776	−	0.914858i	$-0.367698\pi$
$829$	23.2513	0.807551	0.403776	+	0.914858i	$0.367698\pi$
$830$	−25.8807	−0.898331
$831$	−11.0490	−0.383287
$832$	8.58959	0.297790
$833$	46.0031	1.59391
$834$	−7.09717	−0.245755
$835$	25.7813	0.892198
$836$	4.95938	0.171524
$837$	−3.80675	−0.131581
$838$	0.953347	0.0329328
$839$	7.21203	0.248987	0.124494	−	0.992220i	$-0.460269\pi$
$839$	7.21203	0.248987	0.124494	+	0.992220i	$0.460269\pi$
$840$	−19.4742	−0.671922
$841$	50.2696	1.73344
$842$	−26.8527	−0.925406
$843$	25.8935	0.891820
$844$	−4.34420	−0.149533
$845$	1.41297	0.0486077
$846$	10.4144	0.358053
$847$	31.6833	1.08865
$848$	−0.0195727	−0.000672129 0
$849$	5.77887	0.198330
$850$	−12.2353	−0.419668
$851$	1.80493	0.0618723
$852$	7.14548	0.244800
$853$	−55.2499	−1.89172	−0.945860	−	0.324575i	$-0.894779\pi$
$853$	−55.2499	−1.89172	−0.945860	+	0.324575i	$0.894779\pi$
$854$	2.69927	0.0923671
$855$	2.46797	0.0844027
$856$	−26.4063	−0.902549
$857$	37.0191	1.26455	0.632275	−	0.774744i	$-0.282121\pi$
$857$	37.0191	1.26455	0.632275	+	0.774744i	$0.282121\pi$
$858$	−4.90759	−0.167542
$859$	47.4569	1.61921	0.809604	−	0.586977i	$-0.199682\pi$
$859$	47.4569	1.61921	0.809604	+	0.586977i	$0.199682\pi$
$860$	−5.80406	−0.197917
$861$	−21.8130	−0.743387
$862$	−24.7552	−0.843165
$863$	−42.0552	−1.43158	−0.715788	−	0.698318i	$-0.753932\pi$
$863$	−42.0552	−1.43158	−0.715788	+	0.698318i	$0.753932\pi$
$864$	3.59780	0.122400
$865$	15.5614	0.529104
$866$	45.2340	1.53711
$867$	−4.54337	−0.154301
$868$	11.3784	0.386208
$869$	48.3853	1.64136
$870$	14.5202	0.492282
$871$	11.0045	0.372872
$872$	−23.3557	−0.790925
$873$	−6.09251	−0.206200
$874$	1.08983	0.0368640
$875$	−50.6175	−1.71119
$876$	−2.53206	−0.0855503
$877$	−30.6066	−1.03351	−0.516755	−	0.856133i	$-0.672860\pi$
$877$	−30.6066	−1.03351	−0.516755	+	0.856133i	$0.672860\pi$
$878$	13.6678	0.461267
$879$	−25.0219	−0.843966
$880$	13.3282	0.449292
$881$	22.6588	0.763396	0.381698	−	0.924287i	$-0.375340\pi$
$881$	22.6588	0.763396	0.381698	+	0.924287i	$0.375340\pi$
$882$	15.0444	0.506570
$883$	−26.6596	−0.897166	−0.448583	−	0.893741i	$-0.648071\pi$
$883$	−26.6596	−0.897166	−0.448583	+	0.893741i	$0.648071\pi$
$884$	−2.35690	−0.0792710
$885$	16.5257	0.555507
$886$	−0.970421	−0.0326019
$887$	−17.2691	−0.579841	−0.289920	−	0.957051i	$-0.593629\pi$
$887$	−17.2691	−0.579841	−0.289920	+	0.957051i	$0.593629\pi$
$888$	−10.2809	−0.345006
$889$	75.4135	2.52929
$890$	0.422953	0.0141774
$891$	−4.25189	−0.142444
$892$	2.12176	0.0710416
$893$	15.7598	0.527383
$894$	14.3310	0.479300
$895$	−16.6994	−0.558198
$896$	12.1684	0.406519
$897$	0.540588	0.0180497
$898$	−0.350515	−0.0116968
$899$	−33.8928	−1.13039
$900$	2.00571	0.0668571
$901$	0.0311384	0.00103737
$902$	23.9165	0.796332
$903$	27.5325	0.916223
$904$	56.2827	1.87193
$905$	−14.1949	−0.471853
$906$	10.7167	0.356038
$907$	−24.7082	−0.820423	−0.410212	−	0.911990i	$-0.634545\pi$
$907$	−24.7082	−0.820423	−0.410212	+	0.911990i	$0.634545\pi$
$908$	−5.60737	−0.186087
$909$	−1.83817	−0.0609683
$910$	7.29973	0.241984
$911$	27.8706	0.923393	0.461696	−	0.887038i	$-0.347241\pi$
$911$	27.8706	0.923393	0.461696	+	0.887038i	$0.347241\pi$
$912$	−3.87490	−0.128311
$913$	67.4741	2.23307
$914$	−45.0869	−1.49134
$915$	0.738256	0.0244060
$916$	1.72438	0.0569750
$917$	−66.2134	−2.18656
$918$	4.07368	0.134451
$919$	−28.2456	−0.931738	−0.465869	−	0.884854i	$-0.654258\pi$
$919$	−28.2456	−0.931738	−0.465869	+	0.884854i	$0.654258\pi$
$920$	−2.35200	−0.0775433
$921$	16.9094	0.557185
$922$	−14.8670	−0.489618
$923$	−10.7002	−0.352201
$924$	12.7089	0.418093
$925$	−10.0282	−0.329726
$926$	35.0939	1.15326
$927$	1.00000	0.0328443
$928$	32.0325	1.05152
$929$	14.2536	0.467647	0.233823	−	0.972279i	$-0.424876\pi$
$929$	14.2536	0.467647	0.233823	+	0.972279i	$0.424876\pi$
$930$	−6.20833	−0.203579
$931$	22.7663	0.746136
$932$	9.68420	0.317217
$933$	−14.9387	−0.489070
$934$	−17.6641	−0.577987
$935$	−21.2039	−0.693442
$936$	−3.07920	−0.100647
$937$	2.20182	0.0719305	0.0359652	−	0.999353i	$-0.488549\pi$
$937$	2.20182	0.0719305	0.0359652	+	0.999353i	$0.488549\pi$
$938$	56.8515	1.85627
$939$	5.13323	0.167517
$940$	−8.51373	−0.277687
$941$	16.4851	0.537399	0.268699	−	0.963224i	$-0.413406\pi$
$941$	16.4851	0.537399	0.268699	+	0.963224i	$0.413406\pi$
$942$	4.18711	0.136423
$943$	−2.63448	−0.0857906
$944$	−25.9467	−0.844493
$945$	6.32442	0.205733
$946$	−30.1874	−0.981478
$947$	−11.0097	−0.357768	−0.178884	−	0.983870i	$-0.557249\pi$
$947$	−11.0097	−0.357768	−0.178884	+	0.983870i	$0.557249\pi$
$948$	7.59926	0.246813
$949$	3.79170	0.123084
$950$	−6.05509	−0.196453
$951$	5.02425	0.162922
$952$	−48.6435	−1.57655
$953$	24.5322	0.794676	0.397338	−	0.917672i	$-0.369934\pi$
$953$	24.5322	0.794676	0.397338	+	0.917672i	$0.369934\pi$
$954$	0.0101831	0.000329692 0
$955$	−9.97099	−0.322654
$956$	12.7312	0.411756
$957$	−37.8560	−1.22371
$958$	−33.7727	−1.09115
$959$	20.5017	0.662034
$960$	12.1369	0.391715
$961$	−16.5087	−0.532537
$962$	3.85373	0.124249
$963$	8.57570	0.276348
$964$	16.0012	0.515364
$965$	3.63673	0.117071
$966$	2.79280	0.0898568
$967$	−2.86798	−0.0922281	−0.0461141	−	0.998936i	$-0.514684\pi$
$967$	−2.86798	−0.0922281	−0.0461141	+	0.998936i	$0.514684\pi$
$968$	−21.7963	−0.700558
$969$	6.16462	0.198036
$970$	−9.93610	−0.319029
$971$	−39.3993	−1.26439	−0.632193	−	0.774811i	$-0.717845\pi$
$971$	−39.3993	−1.26439	−0.632193	+	0.774811i	$0.717845\pi$
$972$	−0.667790	−0.0214194
$973$	−27.5224	−0.882327
$974$	−19.1238	−0.612765
$975$	−3.00351	−0.0961892
$976$	−1.15912	−0.0371025
$977$	−10.1149	−0.323606	−0.161803	−	0.986823i	$-0.551731\pi$
$977$	−10.1149	−0.323606	−0.161803	+	0.986823i	$0.551731\pi$
$978$	−4.05511	−0.129668
$979$	−1.10269	−0.0352421
$980$	−12.2987	−0.392869
$981$	7.58500	0.242170
$982$	39.7599	1.26879
$983$	−31.1085	−0.992208	−0.496104	−	0.868263i	$-0.665236\pi$
$983$	−31.1085	−0.992208	−0.496104	+	0.868263i	$0.665236\pi$
$984$	15.0061	0.478376
$985$	−19.6265	−0.625353
$986$	36.2694	1.15505
$987$	40.3862	1.28551
$988$	−1.16640	−0.0371080
$989$	3.32525	0.105737
$990$	−6.93429	−0.220386
$991$	−23.7044	−0.752994	−0.376497	−	0.926418i	$-0.622872\pi$
$991$	−23.7044	−0.752994	−0.376497	+	0.926418i	$0.622872\pi$
$992$	−13.6959	−0.434847
$993$	3.56591	0.113161
$994$	−55.2796	−1.75336
$995$	31.0728	0.985075
$996$	10.5973	0.335788
$997$	26.2737	0.832096	0.416048	−	0.909343i	$-0.363415\pi$
$997$	26.2737	0.832096	0.416048	+	0.909343i	$0.363415\pi$
$998$	−34.7032	−1.09851
$999$	3.33884	0.105636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.20	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.20	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.15421 q^{2} +1.00000 q^{3} -0.667790 q^{4} +1.41297 q^{5} +1.15421 q^{6} +4.47597 q^{7} -3.07920 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.15421 q^{2} +1.00000 q^{3} -0.667790 q^{4} +1.41297 q^{5} +1.15421 q^{6} +4.47597 q^{7} -3.07920 q^{8} +1.00000 q^{9} +1.63087 q^{10} -4.25189 q^{11} -0.667790 q^{12} +1.00000 q^{13} +5.16622 q^{14} +1.41297 q^{15} -2.21848 q^{16} +3.52940 q^{17} +1.15421 q^{18} +1.74665 q^{19} -0.943569 q^{20} +4.47597 q^{21} -4.90759 q^{22} +0.540588 q^{23} -3.07920 q^{24} -3.00351 q^{25} +1.15421 q^{26} +1.00000 q^{27} -2.98901 q^{28} +8.90335 q^{29} +1.63087 q^{30} -3.80675 q^{31} +3.59780 q^{32} -4.25189 q^{33} +4.07368 q^{34} +6.32442 q^{35} -0.667790 q^{36} +3.33884 q^{37} +2.01601 q^{38} +1.00000 q^{39} -4.35083 q^{40} -4.87337 q^{41} +5.16622 q^{42} +6.15118 q^{43} +2.83937 q^{44} +1.41297 q^{45} +0.623954 q^{46} +9.02290 q^{47} -2.21848 q^{48} +13.0343 q^{49} -3.46669 q^{50} +3.52940 q^{51} -0.667790 q^{52} +0.00882258 q^{53} +1.15421 q^{54} -6.00780 q^{55} -13.7824 q^{56} +1.74665 q^{57} +10.2764 q^{58} +11.6957 q^{59} -0.943569 q^{60} +0.522484 q^{61} -4.39380 q^{62} +4.47597 q^{63} +8.58959 q^{64} +1.41297 q^{65} -4.90759 q^{66} +11.0045 q^{67} -2.35690 q^{68} +0.540588 q^{69} +7.29973 q^{70} -10.7002 q^{71} -3.07920 q^{72} +3.79170 q^{73} +3.85373 q^{74} -3.00351 q^{75} -1.16640 q^{76} -19.0313 q^{77} +1.15421 q^{78} -11.3797 q^{79} -3.13465 q^{80} +1.00000 q^{81} -5.62491 q^{82} -15.8692 q^{83} -2.98901 q^{84} +4.98694 q^{85} +7.09977 q^{86} +8.90335 q^{87} +13.0924 q^{88} +0.259341 q^{89} +1.63087 q^{90} +4.47597 q^{91} -0.360999 q^{92} -3.80675 q^{93} +10.4144 q^{94} +2.46797 q^{95} +3.59780 q^{96} -6.09251 q^{97} +15.0444 q^{98} -4.25189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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