LMFDB - Embedded newform 4015.2.a.g.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96967 q^{2} +2.18511 q^{3} +1.87958 q^{4} -1.00000 q^{5} -4.30394 q^{6} +1.92639 q^{7} +0.237186 q^{8} +1.77472 q^{9} +O(q^{10})$	\(q-1.96967 q^{2} +2.18511 q^{3} +1.87958 q^{4} -1.00000 q^{5} -4.30394 q^{6} +1.92639 q^{7} +0.237186 q^{8} +1.77472 q^{9} +1.96967 q^{10} -1.00000 q^{11} +4.10710 q^{12} +1.43841 q^{13} -3.79434 q^{14} -2.18511 q^{15} -4.22634 q^{16} -7.20159 q^{17} -3.49561 q^{18} +4.56506 q^{19} -1.87958 q^{20} +4.20938 q^{21} +1.96967 q^{22} -0.678385 q^{23} +0.518279 q^{24} +1.00000 q^{25} -2.83319 q^{26} -2.67737 q^{27} +3.62080 q^{28} -8.50180 q^{29} +4.30394 q^{30} -0.232871 q^{31} +7.85010 q^{32} -2.18511 q^{33} +14.1847 q^{34} -1.92639 q^{35} +3.33573 q^{36} +9.23742 q^{37} -8.99165 q^{38} +3.14309 q^{39} -0.237186 q^{40} -6.82080 q^{41} -8.29106 q^{42} +1.35964 q^{43} -1.87958 q^{44} -1.77472 q^{45} +1.33619 q^{46} -3.95817 q^{47} -9.23503 q^{48} -3.28903 q^{49} -1.96967 q^{50} -15.7363 q^{51} +2.70361 q^{52} -5.34615 q^{53} +5.27353 q^{54} +1.00000 q^{55} +0.456913 q^{56} +9.97518 q^{57} +16.7457 q^{58} +1.88506 q^{59} -4.10710 q^{60} -5.04258 q^{61} +0.458678 q^{62} +3.41880 q^{63} -7.00939 q^{64} -1.43841 q^{65} +4.30394 q^{66} -10.2362 q^{67} -13.5360 q^{68} -1.48235 q^{69} +3.79434 q^{70} -6.04853 q^{71} +0.420940 q^{72} -1.00000 q^{73} -18.1946 q^{74} +2.18511 q^{75} +8.58041 q^{76} -1.92639 q^{77} -6.19083 q^{78} -0.0160830 q^{79} +4.22634 q^{80} -11.1745 q^{81} +13.4347 q^{82} +1.00209 q^{83} +7.91186 q^{84} +7.20159 q^{85} -2.67803 q^{86} -18.5774 q^{87} -0.237186 q^{88} +4.39239 q^{89} +3.49561 q^{90} +2.77094 q^{91} -1.27508 q^{92} -0.508850 q^{93} +7.79627 q^{94} -4.56506 q^{95} +17.1534 q^{96} -8.96721 q^{97} +6.47828 q^{98} -1.77472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−1.96967	−1.39276	−0.696382	−	0.717672i	$-0.745208\pi$
$2$	−1.96967	−1.39276	−0.696382	+	0.717672i	$0.745208\pi$
$3$	2.18511	1.26158	0.630788	−	0.775955i	$-0.282732\pi$
$3$	2.18511	1.26158	0.630788	+	0.775955i	$0.282732\pi$
$4$	1.87958	0.939790
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.30394	−1.75708
$7$	1.92639	0.728107	0.364053	−	0.931378i	$-0.381393\pi$
$7$	1.92639	0.728107	0.364053	+	0.931378i	$0.381393\pi$
$8$	0.237186	0.0838581
$9$	1.77472	0.591574
$10$	1.96967	0.622863
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.10710	1.18562
$13$	1.43841	0.398943	0.199472	−	0.979904i	$-0.436077\pi$
$13$	1.43841	0.398943	0.199472	+	0.979904i	$0.436077\pi$
$14$	−3.79434	−1.01408
$15$	−2.18511	−0.564194
$16$	−4.22634	−1.05658
$17$	−7.20159	−1.74664	−0.873322	−	0.487144i	$-0.838039\pi$
$17$	−7.20159	−1.74664	−0.873322	+	0.487144i	$0.838039\pi$
$18$	−3.49561	−0.823922
$19$	4.56506	1.04730	0.523649	−	0.851934i	$-0.324570\pi$
$19$	4.56506	1.04730	0.523649	+	0.851934i	$0.324570\pi$
$20$	−1.87958	−0.420287
$21$	4.20938	0.918562
$22$	1.96967	0.419934
$23$	−0.678385	−0.141453	−0.0707266	−	0.997496i	$-0.522532\pi$
$23$	−0.678385	−0.141453	−0.0707266	+	0.997496i	$0.522532\pi$
$24$	0.518279	0.105793
$25$	1.00000	0.200000
$26$	−2.83319	−0.555633
$27$	−2.67737	−0.515261
$28$	3.62080	0.684267
$29$	−8.50180	−1.57874	−0.789372	−	0.613915i	$-0.789594\pi$
$29$	−8.50180	−1.57874	−0.789372	+	0.613915i	$0.789594\pi$
$30$	4.30394	0.785789
$31$	−0.232871	−0.0418249	−0.0209124	−	0.999781i	$-0.506657\pi$
$31$	−0.232871	−0.0418249	−0.0209124	+	0.999781i	$0.506657\pi$
$32$	7.85010	1.38771
$33$	−2.18511	−0.380379
$34$	14.1847	2.43266
$35$	−1.92639	−0.325619
$36$	3.33573	0.555955
$37$	9.23742	1.51862	0.759311	−	0.650728i	$-0.225536\pi$
$37$	9.23742	1.51862	0.759311	+	0.650728i	$0.225536\pi$
$38$	−8.99165	−1.45864
$39$	3.14309	0.503297
$40$	−0.237186	−0.0375025
$41$	−6.82080	−1.06523	−0.532615	−	0.846358i	$-0.678791\pi$
$41$	−6.82080	−1.06523	−0.532615	+	0.846358i	$0.678791\pi$
$42$	−8.29106	−1.27934
$43$	1.35964	0.207343	0.103671	−	0.994612i	$-0.466941\pi$
$43$	1.35964	0.207343	0.103671	+	0.994612i	$0.466941\pi$
$44$	−1.87958	−0.283357
$45$	−1.77472	−0.264560
$46$	1.33619	0.197011
$47$	−3.95817	−0.577359	−0.288679	−	0.957426i	$-0.593216\pi$
$47$	−3.95817	−0.577359	−0.288679	+	0.957426i	$0.593216\pi$
$48$	−9.23503	−1.33296
$49$	−3.28903	−0.469861
$50$	−1.96967	−0.278553
$51$	−15.7363	−2.20352
$52$	2.70361	0.374923
$53$	−5.34615	−0.734351	−0.367175	−	0.930152i	$-0.619675\pi$
$53$	−5.34615	−0.734351	−0.367175	+	0.930152i	$0.619675\pi$
$54$	5.27353	0.717637
$55$	1.00000	0.134840
$56$	0.456913	0.0610576
$57$	9.97518	1.32125
$58$	16.7457	2.19882
$59$	1.88506	0.245413	0.122707	−	0.992443i	$-0.460843\pi$
$59$	1.88506	0.245413	0.122707	+	0.992443i	$0.460843\pi$
$60$	−4.10710	−0.530224
$61$	−5.04258	−0.645637	−0.322818	−	0.946461i	$-0.604630\pi$
$61$	−5.04258	−0.645637	−0.322818	+	0.946461i	$0.604630\pi$
$62$	0.458678	0.0582522
$63$	3.41880	0.430729
$64$	−7.00939	−0.876173
$65$	−1.43841	−0.178413
$66$	4.30394	0.529779
$67$	−10.2362	−1.25055	−0.625277	−	0.780403i	$-0.715014\pi$
$67$	−10.2362	−1.25055	−0.625277	+	0.780403i	$0.715014\pi$
$68$	−13.5360	−1.64148
$69$	−1.48235	−0.178454
$70$	3.79434	0.453510
$71$	−6.04853	−0.717829	−0.358914	−	0.933371i	$-0.616853\pi$
$71$	−6.04853	−0.717829	−0.358914	+	0.933371i	$0.616853\pi$
$72$	0.420940	0.0496082
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−18.1946	−2.11508
$75$	2.18511	0.252315
$76$	8.58041	0.984240
$77$	−1.92639	−0.219532
$78$	−6.19083	−0.700974
$79$	−0.0160830	−0.00180948	−0.000904742	−	1.00000i	$-0.500288\pi$
$79$	−0.0160830	−0.00180948	−0.000904742		1.00000i	$0.500288\pi$
$80$	4.22634	0.472519
$81$	−11.1745	−1.24161
$82$	13.4347	1.48361
$83$	1.00209	0.109994	0.0549970	−	0.998487i	$-0.482485\pi$
$83$	1.00209	0.109994	0.0549970	+	0.998487i	$0.482485\pi$
$84$	7.91186	0.863255
$85$	7.20159	0.781123
$86$	−2.67803	−0.288779
$87$	−18.5774	−1.99171
$88$	−0.237186	−0.0252842
$89$	4.39239	0.465593	0.232796	−	0.972525i	$-0.425212\pi$
$89$	4.39239	0.465593	0.232796	+	0.972525i	$0.425212\pi$
$90$	3.49561	0.368469
$91$	2.77094	0.290473
$92$	−1.27508	−0.132936
$93$	−0.508850	−0.0527653
$94$	7.79627	0.804124
$95$	−4.56506	−0.468366
$96$	17.1534	1.75071
$97$	−8.96721	−0.910482	−0.455241	−	0.890368i	$-0.650447\pi$
$97$	−8.96721	−0.910482	−0.455241	+	0.890368i	$0.650447\pi$
$98$	6.47828	0.654405
$99$	−1.77472	−0.178366
$100$	1.87958	0.187958
$101$	−9.12936	−0.908405	−0.454203	−	0.890898i	$-0.650076\pi$
$101$	−9.12936	−0.908405	−0.454203	+	0.890898i	$0.650076\pi$
$102$	30.9952	3.06899
$103$	−10.1241	−0.997559	−0.498780	−	0.866729i	$-0.666218\pi$
$103$	−10.1241	−0.997559	−0.498780	+	0.866729i	$0.666218\pi$
$104$	0.341171	0.0334546
$105$	−4.20938	−0.410793
$106$	10.5301	1.02278
$107$	18.4228	1.78100	0.890498	−	0.454988i	$-0.150356\pi$
$107$	18.4228	1.78100	0.890498	+	0.454988i	$0.150356\pi$
$108$	−5.03234	−0.484237
$109$	2.51379	0.240777	0.120389	−	0.992727i	$-0.461586\pi$
$109$	2.51379	0.240777	0.120389	+	0.992727i	$0.461586\pi$
$110$	−1.96967	−0.187800
$111$	20.1848	1.91586
$112$	−8.14157	−0.769306
$113$	14.1953	1.33538	0.667692	−	0.744438i	$-0.267282\pi$
$113$	14.1953	1.33538	0.667692	+	0.744438i	$0.267282\pi$
$114$	−19.6478	−1.84018
$115$	0.678385	0.0632598
$116$	−15.9798	−1.48369
$117$	2.55278	0.236004
$118$	−3.71293	−0.341803
$119$	−13.8731	−1.27174
$120$	−0.518279	−0.0473122
$121$	1.00000	0.0909091
$122$	9.93220	0.899219
$123$	−14.9042	−1.34387
$124$	−0.437700	−0.0393066
$125$	−1.00000	−0.0894427
$126$	−6.73389	−0.599903
$127$	1.87273	0.166178	0.0830889	−	0.996542i	$-0.473521\pi$
$127$	1.87273	0.166178	0.0830889	+	0.996542i	$0.473521\pi$
$128$	−1.89405	−0.167412
$129$	2.97096	0.261579
$130$	2.83319	0.248487
$131$	−5.42147	−0.473676	−0.236838	−	0.971549i	$-0.576111\pi$
$131$	−5.42147	−0.473676	−0.236838	+	0.971549i	$0.576111\pi$
$132$	−4.10710	−0.357477
$133$	8.79409	0.762544
$134$	20.1619	1.74172
$135$	2.67737	0.230432
$136$	−1.70812	−0.146470
$137$	15.7050	1.34177	0.670884	−	0.741563i	$-0.265915\pi$
$137$	15.7050	1.34177	0.670884	+	0.741563i	$0.265915\pi$
$138$	2.91973	0.248544
$139$	−1.80874	−0.153415	−0.0767077	−	0.997054i	$-0.524441\pi$
$139$	−1.80874	−0.153415	−0.0767077	+	0.997054i	$0.524441\pi$
$140$	−3.62080	−0.306014
$141$	−8.64906	−0.728382
$142$	11.9136	0.999765
$143$	−1.43841	−0.120286
$144$	−7.50057	−0.625048
$145$	8.50180	0.706036
$146$	1.96967	0.163011
$147$	−7.18690	−0.592765
$148$	17.3625	1.42719
$149$	17.6683	1.44744	0.723722	−	0.690091i	$-0.242430\pi$
$149$	17.6683	1.44744	0.723722	+	0.690091i	$0.242430\pi$
$150$	−4.30394	−0.351415
$151$	10.6828	0.869354	0.434677	−	0.900586i	$-0.356863\pi$
$151$	10.6828	0.869354	0.434677	+	0.900586i	$0.356863\pi$
$152$	1.08277	0.0878244
$153$	−12.7808	−1.03327
$154$	3.79434	0.305757
$155$	0.232871	0.0187047
$156$	5.90769	0.472994
$157$	−20.5748	−1.64205	−0.821024	−	0.570894i	$-0.806597\pi$
$157$	−20.5748	−1.64205	−0.821024	+	0.570894i	$0.806597\pi$
$158$	0.0316782	0.00252018
$159$	−11.6820	−0.926439
$160$	−7.85010	−0.620605
$161$	−1.30683	−0.102993
$162$	22.0101	1.72928
$163$	−11.2176	−0.878629	−0.439315	−	0.898333i	$-0.644779\pi$
$163$	−11.2176	−0.878629	−0.439315	+	0.898333i	$0.644779\pi$
$164$	−12.8202	−1.00109
$165$	2.18511	0.170111
$166$	−1.97379	−0.153196
$167$	1.21513	0.0940297	0.0470148	−	0.998894i	$-0.485029\pi$
$167$	1.21513	0.0940297	0.0470148	+	0.998894i	$0.485029\pi$
$168$	0.998407	0.0770288
$169$	−10.9310	−0.840844
$170$	−14.1847	−1.08792
$171$	8.10171	0.619554
$172$	2.55555	0.194859
$173$	−21.8344	−1.66004	−0.830020	−	0.557733i	$-0.811671\pi$
$173$	−21.8344	−1.66004	−0.830020	+	0.557733i	$0.811671\pi$
$174$	36.5912	2.77397
$175$	1.92639	0.145621
$176$	4.22634	0.318572
$177$	4.11906	0.309607
$178$	−8.65155	−0.648461
$179$	−12.0042	−0.897233	−0.448617	−	0.893724i	$-0.648083\pi$
$179$	−12.0042	−0.897233	−0.448617	+	0.893724i	$0.648083\pi$
$180$	−3.33573	−0.248631
$181$	−9.69012	−0.720261	−0.360130	−	0.932902i	$-0.617268\pi$
$181$	−9.69012	−0.720261	−0.360130	+	0.932902i	$0.617268\pi$
$182$	−5.45782	−0.404560
$183$	−11.0186	−0.814520
$184$	−0.160904	−0.0118620
$185$	−9.23742	−0.679148
$186$	1.00226	0.0734895
$187$	7.20159	0.526633
$188$	−7.43970	−0.542596
$189$	−5.15766	−0.375165
$190$	8.99165	0.652323
$191$	−27.3483	−1.97886	−0.989428	−	0.145026i	$-0.953673\pi$
$191$	−27.3483	−1.97886	−0.989428	+	0.145026i	$0.953673\pi$
$192$	−15.3163	−1.10536
$193$	6.03000	0.434049	0.217025	−	0.976166i	$-0.430365\pi$
$193$	6.03000	0.434049	0.217025	+	0.976166i	$0.430365\pi$
$194$	17.6624	1.26809
$195$	−3.14309	−0.225081
$196$	−6.18199	−0.441571
$197$	5.77903	0.411739	0.205869	−	0.978579i	$-0.433998\pi$
$197$	5.77903	0.411739	0.205869	+	0.978579i	$0.433998\pi$
$198$	3.49561	0.248422
$199$	0.124961	0.00885823	0.00442911	−	0.999990i	$-0.498590\pi$
$199$	0.124961	0.00885823	0.00442911	+	0.999990i	$0.498590\pi$
$200$	0.237186	0.0167716
$201$	−22.3673	−1.57767
$202$	17.9818	1.26519
$203$	−16.3778	−1.14949
$204$	−29.5776	−2.07085
$205$	6.82080	0.476385
$206$	19.9411	1.38936
$207$	−1.20394	−0.0836799
$208$	−6.07921	−0.421517
$209$	−4.56506	−0.315772
$210$	8.29106	0.572138
$211$	−22.3294	−1.53722	−0.768610	−	0.639718i	$-0.779051\pi$
$211$	−22.3294	−1.53722	−0.768610	+	0.639718i	$0.779051\pi$
$212$	−10.0485	−0.690136
$213$	−13.2167	−0.905595
$214$	−36.2867	−2.48051
$215$	−1.35964	−0.0927265
$216$	−0.635037	−0.0432088
$217$	−0.448600	−0.0304530
$218$	−4.95132	−0.335346
$219$	−2.18511	−0.147656
$220$	1.87958	0.126721
$221$	−10.3588	−0.696811
$222$	−39.7573	−2.66833
$223$	−16.3273	−1.09336	−0.546678	−	0.837343i	$-0.684108\pi$
$223$	−16.3273	−1.09336	−0.546678	+	0.837343i	$0.684108\pi$
$224$	15.1223	1.01040
$225$	1.77472	0.118315
$226$	−27.9600	−1.85987
$227$	21.8098	1.44757	0.723784	−	0.690027i	$-0.242401\pi$
$227$	21.8098	1.44757	0.723784	+	0.690027i	$0.242401\pi$
$228$	18.7492	1.24169
$229$	23.6416	1.56228	0.781141	−	0.624355i	$-0.214638\pi$
$229$	23.6416	1.56228	0.781141	+	0.624355i	$0.214638\pi$
$230$	−1.33619	−0.0881059
$231$	−4.20938	−0.276957
$232$	−2.01651	−0.132390
$233$	4.69883	0.307830	0.153915	−	0.988084i	$-0.450812\pi$
$233$	4.69883	0.307830	0.153915	+	0.988084i	$0.450812\pi$
$234$	−5.02811	−0.328698
$235$	3.95817	0.258203
$236$	3.54311	0.230637
$237$	−0.0351433	−0.00228280
$238$	27.3253	1.77124
$239$	14.0257	0.907247	0.453623	−	0.891193i	$-0.350131\pi$
$239$	14.0257	0.907247	0.453623	+	0.891193i	$0.350131\pi$
$240$	9.23503	0.596119
$241$	25.2435	1.62608	0.813039	−	0.582209i	$-0.197812\pi$
$241$	25.2435	1.62608	0.813039	+	0.582209i	$0.197812\pi$
$242$	−1.96967	−0.126615
$243$	−16.3855	−1.05113
$244$	−9.47794	−0.606763
$245$	3.28903	0.210128
$246$	29.3563	1.87169
$247$	6.56643	0.417812
$248$	−0.0552339	−0.00350735
$249$	2.18969	0.138766
$250$	1.96967	0.124573
$251$	1.63599	0.103263	0.0516315	−	0.998666i	$-0.483558\pi$
$251$	1.63599	0.103263	0.0516315	+	0.998666i	$0.483558\pi$
$252$	6.42591	0.404794
$253$	0.678385	0.0426497
$254$	−3.68865	−0.231446
$255$	15.7363	0.985445
$256$	17.7494	1.10934
$257$	−26.7738	−1.67010	−0.835051	−	0.550172i	$-0.814562\pi$
$257$	−26.7738	−1.67010	−0.835051	+	0.550172i	$0.814562\pi$
$258$	−5.85180	−0.364317
$259$	17.7949	1.10572
$260$	−2.70361	−0.167671
$261$	−15.0883	−0.933943
$262$	10.6785	0.659719
$263$	10.7726	0.664268	0.332134	−	0.943232i	$-0.392231\pi$
$263$	10.7726	0.664268	0.332134	+	0.943232i	$0.392231\pi$
$264$	−0.518279	−0.0318979
$265$	5.34615	0.328412
$266$	−17.3214	−1.06204
$267$	9.59788	0.587381
$268$	−19.2398	−1.17526
$269$	17.1568	1.04607	0.523034	−	0.852312i	$-0.324800\pi$
$269$	17.1568	1.04607	0.523034	+	0.852312i	$0.324800\pi$
$270$	−5.27353	−0.320937
$271$	27.4210	1.66570	0.832852	−	0.553496i	$-0.186706\pi$
$271$	27.4210	1.66570	0.832852	+	0.553496i	$0.186706\pi$
$272$	30.4364	1.84548
$273$	6.05481	0.366454
$274$	−30.9336	−1.86876
$275$	−1.00000	−0.0603023
$276$	−2.78619	−0.167709
$277$	19.9402	1.19809	0.599044	−	0.800716i	$-0.295547\pi$
$277$	19.9402	1.19809	0.599044	+	0.800716i	$0.295547\pi$
$278$	3.56262	0.213672
$279$	−0.413281	−0.0247425
$280$	−0.456913	−0.0273058
$281$	−3.44347	−0.205420	−0.102710	−	0.994711i	$-0.532751\pi$
$281$	−3.44347	−0.205420	−0.102710	+	0.994711i	$0.532751\pi$
$282$	17.0357	1.01446
$283$	8.11096	0.482147	0.241073	−	0.970507i	$-0.422501\pi$
$283$	8.11096	0.482147	0.241073	+	0.970507i	$0.422501\pi$
$284$	−11.3687	−0.674608
$285$	−9.97518	−0.590879
$286$	2.83319	0.167530
$287$	−13.1395	−0.775601
$288$	13.9317	0.820935
$289$	34.8630	2.05076
$290$	−16.7457	−0.983341
$291$	−19.5944	−1.14864
$292$	−1.87958	−0.109994
$293$	−15.8015	−0.923133	−0.461567	−	0.887106i	$-0.652712\pi$
$293$	−15.8015	−0.923133	−0.461567	+	0.887106i	$0.652712\pi$
$294$	14.1558	0.825582
$295$	−1.88506	−0.109752
$296$	2.19099	0.127349
$297$	2.67737	0.155357
$298$	−34.8007	−2.01595
$299$	−0.975796	−0.0564318
$300$	4.10710	0.237123
$301$	2.61919	0.150968
$302$	−21.0415	−1.21080
$303$	−19.9487	−1.14602
$304$	−19.2935	−1.10656
$305$	5.04258	0.288738
$306$	25.1739	1.43910
$307$	−27.7691	−1.58487	−0.792434	−	0.609957i	$-0.791187\pi$
$307$	−27.7691	−1.58487	−0.792434	+	0.609957i	$0.791187\pi$
$308$	−3.62080	−0.206314
$309$	−22.1223	−1.25850
$310$	−0.458678	−0.0260512
$311$	−16.6005	−0.941327	−0.470664	−	0.882313i	$-0.655985\pi$
$311$	−16.6005	−0.941327	−0.470664	+	0.882313i	$0.655985\pi$
$312$	0.745498	0.0422055
$313$	10.8299	0.612140	0.306070	−	0.952009i	$-0.400986\pi$
$313$	10.8299	0.612140	0.306070	+	0.952009i	$0.400986\pi$
$314$	40.5255	2.28698
$315$	−3.41880	−0.192628
$316$	−0.0302294	−0.00170054
$317$	−20.1485	−1.13166	−0.565828	−	0.824524i	$-0.691443\pi$
$317$	−20.1485	−1.13166	−0.565828	+	0.824524i	$0.691443\pi$
$318$	23.0095	1.29031
$319$	8.50180	0.476009
$320$	7.00939	0.391837
$321$	40.2558	2.24686
$322$	2.57403	0.143445
$323$	−32.8757	−1.82926
$324$	−21.0034	−1.16686
$325$	1.43841	0.0797886
$326$	22.0949	1.22372
$327$	5.49291	0.303759
$328$	−1.61780	−0.0893281
$329$	−7.62498	−0.420379
$330$	−4.30394	−0.236924
$331$	−2.78104	−0.152860	−0.0764298	−	0.997075i	$-0.524352\pi$
$331$	−2.78104	−0.152860	−0.0764298	+	0.997075i	$0.524352\pi$
$332$	1.88351	0.103371
$333$	16.3938	0.898376
$334$	−2.39340	−0.130961
$335$	10.2362	0.559264
$336$	−17.7903	−0.970538
$337$	6.41230	0.349300	0.174650	−	0.984631i	$-0.444121\pi$
$337$	6.41230	0.349300	0.174650	+	0.984631i	$0.444121\pi$
$338$	21.5304	1.17110
$339$	31.0184	1.68469
$340$	13.5360	0.734091
$341$	0.232871	0.0126107
$342$	−15.9577	−0.862892
$343$	−19.8207	−1.07022
$344$	0.322487	0.0173874
$345$	1.48235	0.0798070
$346$	43.0065	2.31204
$347$	−19.7071	−1.05793	−0.528966	−	0.848643i	$-0.677420\pi$
$347$	−19.7071	−1.05793	−0.528966	+	0.848643i	$0.677420\pi$
$348$	−34.9177	−1.87179
$349$	−24.0456	−1.28713	−0.643565	−	0.765391i	$-0.722545\pi$
$349$	−24.0456	−1.28713	−0.643565	+	0.765391i	$0.722545\pi$
$350$	−3.79434	−0.202816
$351$	−3.85116	−0.205560
$352$	−7.85010	−0.418412
$353$	−25.5331	−1.35899	−0.679496	−	0.733680i	$-0.737801\pi$
$353$	−25.5331	−1.35899	−0.679496	+	0.733680i	$0.737801\pi$
$354$	−8.11317	−0.431210
$355$	6.04853	0.321023
$356$	8.25586	0.437560
$357$	−30.3142	−1.60440
$358$	23.6442	1.24963
$359$	23.4642	1.23840	0.619198	−	0.785235i	$-0.287458\pi$
$359$	23.4642	1.23840	0.619198	+	0.785235i	$0.287458\pi$
$360$	−0.420940	−0.0221855
$361$	1.83982	0.0968325
$362$	19.0863	1.00315
$363$	2.18511	0.114689
$364$	5.20820	0.272984
$365$	1.00000	0.0523424
$366$	21.7030	1.13443
$367$	4.64840	0.242645	0.121322	−	0.992613i	$-0.461287\pi$
$367$	4.64840	0.242645	0.121322	+	0.992613i	$0.461287\pi$
$368$	2.86709	0.149457
$369$	−12.1050	−0.630162
$370$	18.1946	0.945893
$371$	−10.2988	−0.534686
$372$	−0.956424	−0.0495883
$373$	−4.24591	−0.219845	−0.109922	−	0.993940i	$-0.535060\pi$
$373$	−4.24591	−0.219845	−0.109922	+	0.993940i	$0.535060\pi$
$374$	−14.1847	−0.733475
$375$	−2.18511	−0.112839
$376$	−0.938825	−0.0484162
$377$	−12.2291	−0.629829
$378$	10.1589	0.522516
$379$	17.6094	0.904532	0.452266	−	0.891883i	$-0.350616\pi$
$379$	17.6094	0.904532	0.452266	+	0.891883i	$0.350616\pi$
$380$	−8.58041	−0.440166
$381$	4.09213	0.209646
$382$	53.8670	2.75608
$383$	−27.8257	−1.42183	−0.710913	−	0.703280i	$-0.751718\pi$
$383$	−27.8257	−1.42183	−0.710913	+	0.703280i	$0.751718\pi$
$384$	−4.13872	−0.211203
$385$	1.92639	0.0981779
$386$	−11.8771	−0.604528
$387$	2.41298	0.122658
$388$	−16.8546	−0.855662
$389$	−2.48385	−0.125936	−0.0629680	−	0.998016i	$-0.520057\pi$
$389$	−2.48385	−0.125936	−0.0629680	+	0.998016i	$0.520057\pi$
$390$	6.19083	0.313485
$391$	4.88546	0.247068
$392$	−0.780112	−0.0394016
$393$	−11.8465	−0.597578
$394$	−11.3828	−0.573455
$395$	0.0160830	0.000809226 0
$396$	−3.33573	−0.167627
$397$	−26.2139	−1.31564	−0.657819	−	0.753176i	$-0.728521\pi$
$397$	−26.2139	−1.31564	−0.657819	+	0.753176i	$0.728521\pi$
$398$	−0.246131	−0.0123374
$399$	19.2161	0.962007
$400$	−4.22634	−0.211317
$401$	22.7569	1.13643	0.568214	−	0.822881i	$-0.307635\pi$
$401$	22.7569	1.13643	0.568214	+	0.822881i	$0.307635\pi$
$402$	44.0561	2.19732
$403$	−0.334964	−0.0166858
$404$	−17.1594	−0.853710
$405$	11.1745	0.555267
$406$	32.2587	1.60097
$407$	−9.23742	−0.457882
$408$	−3.73244	−0.184783
$409$	−21.6082	−1.06845	−0.534227	−	0.845341i	$-0.679397\pi$
$409$	−21.6082	−1.06845	−0.534227	+	0.845341i	$0.679397\pi$
$410$	−13.4347	−0.663492
$411$	34.3172	1.69274
$412$	−19.0291	−0.937496
$413$	3.63135	0.178687
$414$	2.37137	0.116546
$415$	−1.00209	−0.0491908
$416$	11.2917	0.553619
$417$	−3.95231	−0.193545
$418$	8.99165	0.439796
$419$	16.5712	0.809558	0.404779	−	0.914415i	$-0.367348\pi$
$419$	16.5712	0.809558	0.404779	+	0.914415i	$0.367348\pi$
$420$	−7.91186	−0.386059
$421$	32.7830	1.59775	0.798874	−	0.601499i	$-0.205429\pi$
$421$	32.7830	1.59775	0.798874	+	0.601499i	$0.205429\pi$
$422$	43.9815	2.14098
$423$	−7.02465	−0.341550
$424$	−1.26804	−0.0615812
$425$	−7.20159	−0.349329
$426$	26.0325	1.26128
$427$	−9.71398	−0.470092
$428$	34.6271	1.67376
$429$	−3.14309	−0.151750
$430$	2.67803	0.129146
$431$	6.96591	0.335536	0.167768	−	0.985827i	$-0.446344\pi$
$431$	6.96591	0.335536	0.167768	+	0.985827i	$0.446344\pi$
$432$	11.3155	0.544417
$433$	−12.6925	−0.609961	−0.304980	−	0.952359i	$-0.598650\pi$
$433$	−12.6925	−0.609961	−0.304980	+	0.952359i	$0.598650\pi$
$434$	0.883592	0.0424138
$435$	18.5774	0.890718
$436$	4.72487	0.226280
$437$	−3.09687	−0.148144
$438$	4.30394	0.205650
$439$	−30.3578	−1.44890	−0.724449	−	0.689329i	$-0.757905\pi$
$439$	−30.3578	−1.44890	−0.724449	+	0.689329i	$0.757905\pi$
$440$	0.237186	0.0113074
$441$	−5.83710	−0.277957
$442$	20.4035	0.970493
$443$	−39.0805	−1.85677	−0.928385	−	0.371619i	$-0.878803\pi$
$443$	−39.0805	−1.85677	−0.928385	+	0.371619i	$0.878803\pi$
$444$	37.9390	1.80050
$445$	−4.39239	−0.208219
$446$	32.1593	1.52279
$447$	38.6073	1.82606
$448$	−13.5028	−0.637948
$449$	2.28287	0.107735	0.0538677	−	0.998548i	$-0.482845\pi$
$449$	2.28287	0.107735	0.0538677	+	0.998548i	$0.482845\pi$
$450$	−3.49561	−0.164784
$451$	6.82080	0.321179
$452$	26.6812	1.25498
$453$	23.3431	1.09676
$454$	−42.9580	−2.01612
$455$	−2.77094	−0.129904
$456$	2.36598	0.110797
$457$	10.6666	0.498962	0.249481	−	0.968380i	$-0.419740\pi$
$457$	10.6666	0.498962	0.249481	+	0.968380i	$0.419740\pi$
$458$	−46.5661	−2.17589
$459$	19.2814	0.899977
$460$	1.27508	0.0594509
$461$	19.1981	0.894144	0.447072	−	0.894498i	$-0.352467\pi$
$461$	19.1981	0.894144	0.447072	+	0.894498i	$0.352467\pi$
$462$	8.29106	0.385735
$463$	2.29606	0.106707	0.0533535	−	0.998576i	$-0.483009\pi$
$463$	2.29606	0.106707	0.0533535	+	0.998576i	$0.483009\pi$
$464$	35.9315	1.66808
$465$	0.508850	0.0235973
$466$	−9.25511	−0.428735
$467$	−8.92770	−0.413125	−0.206562	−	0.978433i	$-0.566228\pi$
$467$	−8.92770	−0.413125	−0.206562	+	0.978433i	$0.566228\pi$
$468$	4.79815	0.221794
$469$	−19.7189	−0.910536
$470$	−7.79627	−0.359615
$471$	−44.9583	−2.07157
$472$	0.447109	0.0205799
$473$	−1.35964	−0.0625162
$474$	0.0692205	0.00317940
$475$	4.56506	0.209460
$476$	−26.0756	−1.19517
$477$	−9.48793	−0.434422
$478$	−27.6259	−1.26358
$479$	−38.8746	−1.77622	−0.888112	−	0.459626i	$-0.847983\pi$
$479$	−38.8746	−1.77622	−0.888112	+	0.459626i	$0.847983\pi$
$480$	−17.1534	−0.782940
$481$	13.2872	0.605844
$482$	−49.7213	−2.26474
$483$	−2.85558	−0.129933
$484$	1.87958	0.0854355
$485$	8.96721	0.407180
$486$	32.2739	1.46397
$487$	23.7817	1.07765	0.538825	−	0.842417i	$-0.318868\pi$
$487$	23.7817	1.07765	0.538825	+	0.842417i	$0.318868\pi$
$488$	−1.19603	−0.0541418
$489$	−24.5117	−1.10846
$490$	−6.47828	−0.292659
$491$	−13.6168	−0.614517	−0.307259	−	0.951626i	$-0.599412\pi$
$491$	−13.6168	−0.614517	−0.307259	+	0.951626i	$0.599412\pi$
$492$	−28.0137	−1.26295
$493$	61.2265	2.75750
$494$	−12.9337	−0.581914
$495$	1.77472	0.0797678
$496$	0.984192	0.0441915
$497$	−11.6518	−0.522656
$498$	−4.31295	−0.193268
$499$	−39.7920	−1.78133	−0.890667	−	0.454656i	$-0.849762\pi$
$499$	−39.7920	−1.78133	−0.890667	+	0.454656i	$0.849762\pi$
$500$	−1.87958	−0.0840574
$501$	2.65520	0.118626
$502$	−3.22236	−0.143821
$503$	−5.88066	−0.262206	−0.131103	−	0.991369i	$-0.541852\pi$
$503$	−5.88066	−0.262206	−0.131103	+	0.991369i	$0.541852\pi$
$504$	0.810893	0.0361201
$505$	9.12936	0.406251
$506$	−1.33619	−0.0594010
$507$	−23.8854	−1.06079
$508$	3.51994	0.156172
$509$	−8.51758	−0.377535	−0.188768	−	0.982022i	$-0.560449\pi$
$509$	−8.51758	−0.377535	−0.188768	+	0.982022i	$0.560449\pi$
$510$	−30.9952	−1.37249
$511$	−1.92639	−0.0852184
$512$	−31.1723	−1.37763
$513$	−12.2224	−0.539632
$514$	52.7354	2.32606
$515$	10.1241	0.446122
$516$	5.58416	0.245829
$517$	3.95817	0.174080
$518$	−35.0499	−1.54000
$519$	−47.7107	−2.09427
$520$	−0.341171	−0.0149613
$521$	−1.41385	−0.0619418	−0.0309709	−	0.999520i	$-0.509860\pi$
$521$	−1.41385	−0.0619418	−0.0309709	+	0.999520i	$0.509860\pi$
$522$	29.7189	1.30076
$523$	−38.6239	−1.68891	−0.844453	−	0.535629i	$-0.820075\pi$
$523$	−38.6239	−1.68891	−0.844453	+	0.535629i	$0.820075\pi$
$524$	−10.1901	−0.445156
$525$	4.20938	0.183712
$526$	−21.2184	−0.925168
$527$	1.67704	0.0730532
$528$	9.23503	0.401903
$529$	−22.5398	−0.979991
$530$	−10.5301	−0.457400
$531$	3.34545	0.145180
$532$	16.5292	0.716632
$533$	−9.81111	−0.424966
$534$	−18.9046	−0.818082
$535$	−18.4228	−0.796485
$536$	−2.42789	−0.104869
$537$	−26.2305	−1.13193
$538$	−33.7931	−1.45692
$539$	3.28903	0.141668
$540$	5.03234	0.216557
$541$	4.47001	0.192181	0.0960903	−	0.995373i	$-0.469366\pi$
$541$	4.47001	0.192181	0.0960903	+	0.995373i	$0.469366\pi$
$542$	−54.0101	−2.31993
$543$	−21.1740	−0.908664
$544$	−56.5332	−2.42384
$545$	−2.51379	−0.107679
$546$	−11.9259	−0.510383
$547$	−21.1152	−0.902821	−0.451410	−	0.892316i	$-0.649079\pi$
$547$	−21.1152	−0.902821	−0.451410	+	0.892316i	$0.649079\pi$
$548$	29.5188	1.26098
$549$	−8.94918	−0.381942
$550$	1.96967	0.0839868
$551$	−38.8113	−1.65342
$552$	−0.351593	−0.0149648
$553$	−0.0309822	−0.00131750
$554$	−39.2754	−1.66865
$555$	−20.1848	−0.856797
$556$	−3.39968	−0.144178
$557$	−16.0242	−0.678968	−0.339484	−	0.940612i	$-0.610252\pi$
$557$	−16.0242	−0.678968	−0.339484	+	0.940612i	$0.610252\pi$
$558$	0.814026	0.0344604
$559$	1.95571	0.0827179
$560$	8.14157	0.344044
$561$	15.7363	0.664387
$562$	6.78249	0.286102
$563$	39.2080	1.65242	0.826210	−	0.563363i	$-0.190493\pi$
$563$	39.2080	1.65242	0.826210	+	0.563363i	$0.190493\pi$
$564$	−16.2566	−0.684526
$565$	−14.1953	−0.597202
$566$	−15.9759	−0.671516
$567$	−21.5265	−0.904027
$568$	−1.43463	−0.0601957
$569$	28.9177	1.21230	0.606148	−	0.795352i	$-0.292714\pi$
$569$	28.9177	1.21230	0.606148	+	0.795352i	$0.292714\pi$
$570$	19.6478	0.822955
$571$	28.9108	1.20988	0.604939	−	0.796272i	$-0.293197\pi$
$571$	28.9108	1.20988	0.604939	+	0.796272i	$0.293197\pi$
$572$	−2.70361	−0.113043
$573$	−59.7592	−2.49648
$574$	25.8804	1.08023
$575$	−0.678385	−0.0282906
$576$	−12.4397	−0.518321
$577$	−35.7558	−1.48854	−0.744268	−	0.667881i	$-0.767201\pi$
$577$	−35.7558	−1.48854	−0.744268	+	0.667881i	$0.767201\pi$
$578$	−68.6684	−2.85623
$579$	13.1762	0.547586
$580$	15.9798	0.663526
$581$	1.93042	0.0800873
$582$	38.5943	1.59979
$583$	5.34615	0.221415
$584$	−0.237186	−0.00981484
$585$	−2.55278	−0.105544
$586$	31.1237	1.28571
$587$	21.3686	0.881976	0.440988	−	0.897513i	$-0.354628\pi$
$587$	21.3686	0.881976	0.440988	+	0.897513i	$0.354628\pi$
$588$	−13.5083	−0.557075
$589$	−1.06307	−0.0438031
$590$	3.71293	0.152859
$591$	12.6278	0.519440
$592$	−39.0404	−1.60455
$593$	−22.5580	−0.926347	−0.463174	−	0.886268i	$-0.653289\pi$
$593$	−22.5580	−0.926347	−0.463174	+	0.886268i	$0.653289\pi$
$594$	−5.27353	−0.216376
$595$	13.8731	0.568740
$596$	33.2090	1.36029
$597$	0.273053	0.0111753
$598$	1.92199	0.0785961
$599$	−9.15524	−0.374073	−0.187037	−	0.982353i	$-0.559888\pi$
$599$	−9.15524	−0.374073	−0.187037	+	0.982353i	$0.559888\pi$
$600$	0.518279	0.0211587
$601$	16.8471	0.687209	0.343604	−	0.939114i	$-0.388352\pi$
$601$	16.8471	0.687209	0.343604	+	0.939114i	$0.388352\pi$
$602$	−5.15893	−0.210262
$603$	−18.1664	−0.739794
$604$	20.0792	0.817011
$605$	−1.00000	−0.0406558
$606$	39.2922	1.59614
$607$	11.7254	0.475918	0.237959	−	0.971275i	$-0.423522\pi$
$607$	11.7254	0.475918	0.237959	+	0.971275i	$0.423522\pi$
$608$	35.8362	1.45335
$609$	−35.7873	−1.45017
$610$	−9.93220	−0.402143
$611$	−5.69347	−0.230333
$612$	−24.0226	−0.971055
$613$	12.7576	0.515275	0.257637	−	0.966242i	$-0.417056\pi$
$613$	12.7576	0.515275	0.257637	+	0.966242i	$0.417056\pi$
$614$	54.6959	2.20735
$615$	14.9042	0.600996
$616$	−0.456913	−0.0184096
$617$	8.68066	0.349470	0.174735	−	0.984615i	$-0.444093\pi$
$617$	8.68066	0.349470	0.174735	+	0.984615i	$0.444093\pi$
$618$	43.5736	1.75279
$619$	30.5902	1.22952	0.614762	−	0.788713i	$-0.289252\pi$
$619$	30.5902	1.22952	0.614762	+	0.788713i	$0.289252\pi$
$620$	0.437700	0.0175785
$621$	1.81629	0.0728853
$622$	32.6974	1.31105
$623$	8.46146	0.339001
$624$	−13.2838	−0.531776
$625$	1.00000	0.0400000
$626$	−21.3312	−0.852566
$627$	−9.97518	−0.398370
$628$	−38.6720	−1.54318
$629$	−66.5241	−2.65249
$630$	6.73389	0.268285
$631$	10.6579	0.424284	0.212142	−	0.977239i	$-0.431956\pi$
$631$	10.6579	0.424284	0.212142	+	0.977239i	$0.431956\pi$
$632$	−0.00381468	−0.000151740 0
$633$	−48.7923	−1.93932
$634$	39.6859	1.57613
$635$	−1.87273	−0.0743170
$636$	−21.9572	−0.870658
$637$	−4.73097	−0.187448
$638$	−16.7457	−0.662968
$639$	−10.7345	−0.424648
$640$	1.89405	0.0748690
$641$	6.47432	0.255720	0.127860	−	0.991792i	$-0.459189\pi$
$641$	6.47432	0.255720	0.127860	+	0.991792i	$0.459189\pi$
$642$	−79.2905	−3.12935
$643$	−26.6951	−1.05275	−0.526376	−	0.850252i	$-0.676450\pi$
$643$	−26.6951	−1.05275	−0.526376	+	0.850252i	$0.676450\pi$
$644$	−2.45630	−0.0967918
$645$	−2.97096	−0.116981
$646$	64.7542	2.54772
$647$	18.1448	0.713346	0.356673	−	0.934229i	$-0.383911\pi$
$647$	18.1448	0.713346	0.356673	+	0.934229i	$0.383911\pi$
$648$	−2.65045	−0.104119
$649$	−1.88506	−0.0739949
$650$	−2.83319	−0.111127
$651$	−0.980243	−0.0384187
$652$	−21.0844	−0.825727
$653$	−42.3150	−1.65591	−0.827957	−	0.560791i	$-0.810497\pi$
$653$	−42.3150	−1.65591	−0.827957	+	0.560791i	$0.810497\pi$
$654$	−10.8192	−0.423064
$655$	5.42147	0.211834
$656$	28.8270	1.12551
$657$	−1.77472	−0.0692384
$658$	15.0187	0.585488
$659$	33.3030	1.29730	0.648650	−	0.761087i	$-0.275334\pi$
$659$	33.3030	1.29730	0.648650	+	0.761087i	$0.275334\pi$
$660$	4.10710	0.159869
$661$	38.9960	1.51677	0.758383	−	0.651809i	$-0.225990\pi$
$661$	38.9960	1.51677	0.758383	+	0.651809i	$0.225990\pi$
$662$	5.47771	0.212897
$663$	−22.6352	−0.879080
$664$	0.237683	0.00922388
$665$	−8.79409	−0.341020
$666$	−32.2904	−1.25123
$667$	5.76750	0.223318
$668$	2.28394	0.0883682
$669$	−35.6770	−1.37935
$670$	−20.1619	−0.778923
$671$	5.04258	0.194667
$672$	33.0440	1.27470
$673$	30.8132	1.18776	0.593881	−	0.804553i	$-0.297595\pi$
$673$	30.8132	1.18776	0.593881	+	0.804553i	$0.297595\pi$
$674$	−12.6301	−0.486492
$675$	−2.67737	−0.103052
$676$	−20.5456	−0.790217
$677$	−31.8264	−1.22319	−0.611593	−	0.791172i	$-0.709471\pi$
$677$	−31.8264	−1.22319	−0.611593	+	0.791172i	$0.709471\pi$
$678$	−61.0958	−2.34637
$679$	−17.2743	−0.662928
$680$	1.70812	0.0655034
$681$	47.6569	1.82622
$682$	−0.458678	−0.0175637
$683$	−33.4390	−1.27951	−0.639754	−	0.768580i	$-0.720964\pi$
$683$	−33.4390	−1.27951	−0.639754	+	0.768580i	$0.720964\pi$
$684$	15.2278	0.582250
$685$	−15.7050	−0.600057
$686$	39.0401	1.49056
$687$	51.6596	1.97094
$688$	−5.74629	−0.219075
$689$	−7.68996	−0.292964
$690$	−2.91973	−0.111152
$691$	−16.4919	−0.627381	−0.313691	−	0.949525i	$-0.601565\pi$
$691$	−16.4919	−0.627381	−0.313691	+	0.949525i	$0.601565\pi$
$692$	−41.0396	−1.56009
$693$	−3.41880	−0.129870
$694$	38.8164	1.47345
$695$	1.80874	0.0686095
$696$	−4.40630	−0.167021
$697$	49.1206	1.86058
$698$	47.3617	1.79267
$699$	10.2675	0.388351
$700$	3.62080	0.136853
$701$	−6.47429	−0.244531	−0.122265	−	0.992497i	$-0.539016\pi$
$701$	−6.47429	−0.244531	−0.122265	+	0.992497i	$0.539016\pi$
$702$	7.58550	0.286296
$703$	42.1694	1.59045
$704$	7.00939	0.264176
$705$	8.64906	0.325742
$706$	50.2917	1.89275
$707$	−17.5867	−0.661416
$708$	7.74210	0.290966
$709$	45.8774	1.72296	0.861482	−	0.507789i	$-0.169537\pi$
$709$	45.8774	1.72296	0.861482	+	0.507789i	$0.169537\pi$
$710$	−11.9136	−0.447109
$711$	−0.0285429	−0.00107044
$712$	1.04182	0.0390437
$713$	0.157976	0.00591626
$714$	59.7089	2.23455
$715$	1.43841	0.0537935
$716$	−22.5628	−0.843211
$717$	30.6477	1.14456
$718$	−46.2167	−1.72479
$719$	1.42014	0.0529624	0.0264812	−	0.999649i	$-0.491570\pi$
$719$	1.42014	0.0529624	0.0264812	+	0.999649i	$0.491570\pi$
$720$	7.50057	0.279530
$721$	−19.5030	−0.726329
$722$	−3.62382	−0.134865
$723$	55.1599	2.05142
$724$	−18.2134	−0.676894
$725$	−8.50180	−0.315749
$726$	−4.30394	−0.159734
$727$	−19.4334	−0.720747	−0.360373	−	0.932808i	$-0.617351\pi$
$727$	−19.4334	−0.720747	−0.360373	+	0.932808i	$0.617351\pi$
$728$	0.657228	0.0243585
$729$	−2.28057	−0.0844654
$730$	−1.96967	−0.0729006
$731$	−9.79155	−0.362154
$732$	−20.7104	−0.765478
$733$	−12.5146	−0.462236	−0.231118	−	0.972926i	$-0.574238\pi$
$733$	−12.5146	−0.462236	−0.231118	+	0.972926i	$0.574238\pi$
$734$	−9.15579	−0.337946
$735$	7.18690	0.265093
$736$	−5.32539	−0.196297
$737$	10.2362	0.377056
$738$	23.8428	0.877667
$739$	−38.2296	−1.40630	−0.703149	−	0.711042i	$-0.748223\pi$
$739$	−38.2296	−1.40630	−0.703149	+	0.711042i	$0.748223\pi$
$740$	−17.3625	−0.638257
$741$	14.3484	0.527102
$742$	20.2851	0.744690
$743$	1.89433	0.0694963	0.0347481	−	0.999396i	$-0.488937\pi$
$743$	1.89433	0.0694963	0.0347481	+	0.999396i	$0.488937\pi$
$744$	−0.120692	−0.00442479
$745$	−17.6683	−0.647317
$746$	8.36302	0.306192
$747$	1.77843	0.0650695
$748$	13.5360	0.494924
$749$	35.4894	1.29675
$750$	4.30394	0.157158
$751$	8.33431	0.304123	0.152062	−	0.988371i	$-0.451409\pi$
$751$	8.33431	0.304123	0.152062	+	0.988371i	$0.451409\pi$
$752$	16.7286	0.610029
$753$	3.57483	0.130274
$754$	24.0872	0.877203
$755$	−10.6828	−0.388787
$756$	−9.69424	−0.352576
$757$	−3.69219	−0.134195	−0.0670975	−	0.997746i	$-0.521374\pi$
$757$	−3.69219	−0.134195	−0.0670975	+	0.997746i	$0.521374\pi$
$758$	−34.6845	−1.25980
$759$	1.48235	0.0538059
$760$	−1.08277	−0.0392762
$761$	−9.17779	−0.332695	−0.166347	−	0.986067i	$-0.553197\pi$
$761$	−9.17779	−0.332695	−0.166347	+	0.986067i	$0.553197\pi$
$762$	−8.06012	−0.291987
$763$	4.84253	0.175312
$764$	−51.4034	−1.85971
$765$	12.7808	0.462091
$766$	54.8073	1.98027
$767$	2.71148	0.0979059
$768$	38.7845	1.39952
$769$	26.6045	0.959381	0.479691	−	0.877438i	$-0.340749\pi$
$769$	26.6045	0.959381	0.479691	+	0.877438i	$0.340749\pi$
$770$	−3.79434	−0.136739
$771$	−58.5038	−2.10696
$772$	11.3339	0.407915
$773$	47.4271	1.70583	0.852917	−	0.522047i	$-0.174831\pi$
$773$	47.4271	1.70583	0.852917	+	0.522047i	$0.174831\pi$
$774$	−4.75275	−0.170834
$775$	−0.232871	−0.00836498
$776$	−2.12690	−0.0763513
$777$	38.8838	1.39495
$778$	4.89235	0.175399
$779$	−31.1374	−1.11561
$780$	−5.90769	−0.211529
$781$	6.04853	0.216433
$782$	−9.62271	−0.344108
$783$	22.7625	0.813465
$784$	13.9005	0.496448
$785$	20.5748	0.734346
$786$	23.3337	0.832285
$787$	−8.41331	−0.299902	−0.149951	−	0.988693i	$-0.547912\pi$
$787$	−8.41331	−0.299902	−0.149951	+	0.988693i	$0.547912\pi$
$788$	10.8621	0.386948
$789$	23.5394	0.838024
$790$	−0.0316782	−0.00112706
$791$	27.3457	0.972301
$792$	−0.420940	−0.0149574
$793$	−7.25330	−0.257572
$794$	51.6326	1.83237
$795$	11.6820	0.414316
$796$	0.234874	0.00832487
$797$	−13.2655	−0.469889	−0.234945	−	0.972009i	$-0.575491\pi$
$797$	−13.2655	−0.469889	−0.234945	+	0.972009i	$0.575491\pi$
$798$	−37.8492	−1.33985
$799$	28.5052	1.00844
$800$	7.85010	0.277543
$801$	7.79527	0.275432
$802$	−44.8236	−1.58277
$803$	1.00000	0.0352892
$804$	−42.0411	−1.48268
$805$	1.30683	0.0460599
$806$	0.659767	0.0232393
$807$	37.4895	1.31969
$808$	−2.16536	−0.0761771
$809$	35.2045	1.23772	0.618862	−	0.785500i	$-0.287594\pi$
$809$	35.2045	1.23772	0.618862	+	0.785500i	$0.287594\pi$
$810$	−22.0101	−0.773355
$811$	−8.85227	−0.310845	−0.155423	−	0.987848i	$-0.549674\pi$
$811$	−8.85227	−0.310845	−0.155423	+	0.987848i	$0.549674\pi$
$812$	−30.7833	−1.08028
$813$	59.9179	2.10141
$814$	18.1946	0.637721
$815$	11.2176	0.392935
$816$	66.5069	2.32821
$817$	6.20683	0.217150
$818$	42.5608	1.48811
$819$	4.91764	0.171836
$820$	12.8202	0.447702
$821$	−5.24978	−0.183219	−0.0916093	−	0.995795i	$-0.529201\pi$
$821$	−5.24978	−0.183219	−0.0916093	+	0.995795i	$0.529201\pi$
$822$	−67.5933	−2.35759
$823$	8.64428	0.301321	0.150660	−	0.988586i	$-0.451860\pi$
$823$	8.64428	0.301321	0.150660	+	0.988586i	$0.451860\pi$
$824$	−2.40130	−0.0836534
$825$	−2.18511	−0.0760759
$826$	−7.15254	−0.248869
$827$	35.1828	1.22343	0.611713	−	0.791080i	$-0.290481\pi$
$827$	35.1828	1.22343	0.611713	+	0.791080i	$0.290481\pi$
$828$	−2.26291	−0.0786416
$829$	−27.8530	−0.967375	−0.483687	−	0.875241i	$-0.660703\pi$
$829$	−27.8530	−0.967375	−0.483687	+	0.875241i	$0.660703\pi$
$830$	1.97379	0.0685111
$831$	43.5715	1.51148
$832$	−10.0824	−0.349543
$833$	23.6862	0.820679
$834$	7.78472	0.269563
$835$	−1.21513	−0.0420514
$836$	−8.58041	−0.296760
$837$	0.623483	0.0215507
$838$	−32.6398	−1.12752
$839$	−34.0568	−1.17577	−0.587885	−	0.808945i	$-0.700039\pi$
$839$	−34.0568	−1.17577	−0.587885	+	0.808945i	$0.700039\pi$
$840$	−0.998407	−0.0344483
$841$	43.2806	1.49243
$842$	−64.5716	−2.22528
$843$	−7.52438	−0.259153
$844$	−41.9699	−1.44466
$845$	10.9310	0.376037
$846$	13.8362	0.475699
$847$	1.92639	0.0661915
$848$	22.5947	0.775904
$849$	17.7234	0.608265
$850$	14.1847	0.486532
$851$	−6.26653	−0.214814
$852$	−24.8419	−0.851069
$853$	4.04262	0.138417	0.0692084	−	0.997602i	$-0.477953\pi$
$853$	4.04262	0.138417	0.0692084	+	0.997602i	$0.477953\pi$
$854$	19.1333	0.654727
$855$	−8.10171	−0.277073
$856$	4.36963	0.149351
$857$	11.1735	0.381680	0.190840	−	0.981621i	$-0.438879\pi$
$857$	11.1735	0.381680	0.190840	+	0.981621i	$0.438879\pi$
$858$	6.19083	0.211352
$859$	−19.6993	−0.672130	−0.336065	−	0.941839i	$-0.609096\pi$
$859$	−19.6993	−0.672130	−0.336065	+	0.941839i	$0.609096\pi$
$860$	−2.55555	−0.0871434
$861$	−28.7113	−0.978479
$862$	−13.7205	−0.467322
$863$	27.9850	0.952620	0.476310	−	0.879278i	$-0.341974\pi$
$863$	27.9850	0.952620	0.476310	+	0.879278i	$0.341974\pi$
$864$	−21.0177	−0.715035
$865$	21.8344	0.742393
$866$	24.9999	0.849531
$867$	76.1795	2.58719
$868$	−0.843180	−0.0286194
$869$	0.0160830	0.000545580 0
$870$	−36.5912	−1.24056
$871$	−14.7239	−0.498900
$872$	0.596236	0.0201911
$873$	−15.9143	−0.538617
$874$	6.09980	0.206329
$875$	−1.92639	−0.0651238
$876$	−4.10710	−0.138766
$877$	−53.9036	−1.82020	−0.910098	−	0.414394i	$-0.863994\pi$
$877$	−53.9036	−1.82020	−0.910098	+	0.414394i	$0.863994\pi$
$878$	59.7946	2.01797
$879$	−34.5281	−1.16460
$880$	−4.22634	−0.142470
$881$	36.8384	1.24112	0.620558	−	0.784160i	$-0.286906\pi$
$881$	36.8384	1.24112	0.620558	+	0.784160i	$0.286906\pi$
$882$	11.4971	0.387129
$883$	13.9681	0.470065	0.235032	−	0.971988i	$-0.424480\pi$
$883$	13.9681	0.470065	0.235032	+	0.971988i	$0.424480\pi$
$884$	−19.4703	−0.654856
$885$	−4.11906	−0.138461
$886$	76.9755	2.58604
$887$	17.4010	0.584268	0.292134	−	0.956377i	$-0.405635\pi$
$887$	17.4010	0.584268	0.292134	+	0.956377i	$0.405635\pi$
$888$	4.78756	0.160660
$889$	3.60760	0.120995
$890$	8.65155	0.290000
$891$	11.1745	0.374361
$892$	−30.6884	−1.02752
$893$	−18.0693	−0.604667
$894$	−76.0434	−2.54327
$895$	12.0042	0.401255
$896$	−3.64868	−0.121894
$897$	−2.13223	−0.0711929
$898$	−4.49650	−0.150050
$899$	1.97982	0.0660308
$900$	3.33573	0.111191
$901$	38.5008	1.28265
$902$	−13.4347	−0.447326
$903$	5.72323	0.190457
$904$	3.36694	0.111983
$905$	9.69012	0.322111
$906$	−45.9782	−1.52752
$907$	−5.13083	−0.170367	−0.0851833	−	0.996365i	$-0.527148\pi$
$907$	−5.13083	−0.170367	−0.0851833	+	0.996365i	$0.527148\pi$
$908$	40.9933	1.36041
$909$	−16.2021	−0.537389
$910$	5.45782	0.180925
$911$	7.18939	0.238195	0.119097	−	0.992883i	$-0.462000\pi$
$911$	7.18939	0.238195	0.119097	+	0.992883i	$0.462000\pi$
$912$	−42.1585	−1.39601
$913$	−1.00209	−0.0331644
$914$	−21.0096	−0.694936
$915$	11.0186	0.364264
$916$	44.4363	1.46822
$917$	−10.4439	−0.344887
$918$	−37.9778	−1.25346
$919$	−1.19355	−0.0393715	−0.0196858	−	0.999806i	$-0.506267\pi$
$919$	−1.19355	−0.0393715	−0.0196858	+	0.999806i	$0.506267\pi$
$920$	0.160904	0.00530484
$921$	−60.6787	−1.99943
$922$	−37.8138	−1.24533
$923$	−8.70027	−0.286373
$924$	−7.91186	−0.260281
$925$	9.23742	0.303724
$926$	−4.52247	−0.148618
$927$	−17.9675	−0.590130
$928$	−66.7399	−2.19085
$929$	14.1385	0.463869	0.231935	−	0.972731i	$-0.425494\pi$
$929$	14.1385	0.463869	0.231935	+	0.972731i	$0.425494\pi$
$930$	−1.00226	−0.0328655
$931$	−15.0146	−0.492084
$932$	8.83182	0.289296
$933$	−36.2739	−1.18756
$934$	17.5846	0.575385
$935$	−7.20159	−0.235517
$936$	0.605484	0.0197909
$937$	38.7167	1.26482	0.632409	−	0.774635i	$-0.282066\pi$
$937$	38.7167	1.26482	0.632409	+	0.774635i	$0.282066\pi$
$938$	38.8397	1.26816
$939$	23.6645	0.772261
$940$	7.43970	0.242656
$941$	39.4575	1.28628	0.643140	−	0.765749i	$-0.277631\pi$
$941$	39.4575	1.28628	0.643140	+	0.765749i	$0.277631\pi$
$942$	88.5527	2.88520
$943$	4.62713	0.150680
$944$	−7.96688	−0.259300
$945$	5.15766	0.167779
$946$	2.67803	0.0870702
$947$	0.240923	0.00782895	0.00391447	−	0.999992i	$-0.498754\pi$
$947$	0.240923	0.00782895	0.00391447	+	0.999992i	$0.498754\pi$
$948$	−0.0660546	−0.00214535
$949$	−1.43841	−0.0466928
$950$	−8.99165	−0.291728
$951$	−44.0269	−1.42767
$952$	−3.29050	−0.106646
$953$	18.9910	0.615180	0.307590	−	0.951519i	$-0.400477\pi$
$953$	18.9910	0.615180	0.307590	+	0.951519i	$0.400477\pi$
$954$	18.6880	0.605048
$955$	27.3483	0.884971
$956$	26.3624	0.852622
$957$	18.5774	0.600522
$958$	76.5699	2.47386
$959$	30.2539	0.976950
$960$	15.3163	0.494332
$961$	−30.9458	−0.998251
$962$	−26.1713	−0.843797
$963$	32.6952	1.05359
$964$	47.4472	1.52817
$965$	−6.03000	−0.194113
$966$	5.62454	0.180967
$967$	6.07050	0.195214	0.0976071	−	0.995225i	$-0.468881\pi$
$967$	6.07050	0.195214	0.0976071	+	0.995225i	$0.468881\pi$
$968$	0.237186	0.00762346
$969$	−71.8372	−2.30774
$970$	−17.6624	−0.567105
$971$	3.88124	0.124555	0.0622774	−	0.998059i	$-0.480164\pi$
$971$	3.88124	0.124555	0.0622774	+	0.998059i	$0.480164\pi$
$972$	−30.7978	−0.987841
$973$	−3.48434	−0.111703
$974$	−46.8419	−1.50091
$975$	3.14309	0.100659
$976$	21.3117	0.682170
$977$	−44.6555	−1.42866	−0.714328	−	0.699811i	$-0.753268\pi$
$977$	−44.6555	−1.42866	−0.714328	+	0.699811i	$0.753268\pi$
$978$	48.2798	1.54382
$979$	−4.39239	−0.140382
$980$	6.18199	0.197476
$981$	4.46127	0.142437
$982$	26.8205	0.855877
$983$	56.1124	1.78971	0.894854	−	0.446359i	$-0.147280\pi$
$983$	56.1124	1.78971	0.894854	+	0.446359i	$0.147280\pi$
$984$	−3.53508	−0.112694
$985$	−5.77903	−0.184135
$986$	−120.596	−3.84055
$987$	−16.6614	−0.530340
$988$	12.3421	0.392656
$989$	−0.922358	−0.0293293
$990$	−3.49561	−0.111098
$991$	1.19739	0.0380364	0.0190182	−	0.999819i	$-0.493946\pi$
$991$	1.19739	0.0380364	0.0190182	+	0.999819i	$0.493946\pi$
$992$	−1.82806	−0.0580410
$993$	−6.07688	−0.192844
$994$	22.9502	0.727936
$995$	−0.124961	−0.00396152
$996$	4.11569	0.130411
$997$	54.9592	1.74058	0.870288	−	0.492543i	$-0.163933\pi$
$997$	54.9592	1.74058	0.870288	+	0.492543i	$0.163933\pi$
$998$	78.3769	2.48098
$999$	−24.7320	−0.782486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.8	✓	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96967 q^{2} +2.18511 q^{3} +1.87958 q^{4} -1.00000 q^{5} -4.30394 q^{6} +1.92639 q^{7} +0.237186 q^{8} +1.77472 q^{9} +O(q^{10})\)	\(q-1.96967 q^{2} +2.18511 q^{3} +1.87958 q^{4} -1.00000 q^{5} -4.30394 q^{6} +1.92639 q^{7} +0.237186 q^{8} +1.77472 q^{9} +1.96967 q^{10} -1.00000 q^{11} +4.10710 q^{12} +1.43841 q^{13} -3.79434 q^{14} -2.18511 q^{15} -4.22634 q^{16} -7.20159 q^{17} -3.49561 q^{18} +4.56506 q^{19} -1.87958 q^{20} +4.20938 q^{21} +1.96967 q^{22} -0.678385 q^{23} +0.518279 q^{24} +1.00000 q^{25} -2.83319 q^{26} -2.67737 q^{27} +3.62080 q^{28} -8.50180 q^{29} +4.30394 q^{30} -0.232871 q^{31} +7.85010 q^{32} -2.18511 q^{33} +14.1847 q^{34} -1.92639 q^{35} +3.33573 q^{36} +9.23742 q^{37} -8.99165 q^{38} +3.14309 q^{39} -0.237186 q^{40} -6.82080 q^{41} -8.29106 q^{42} +1.35964 q^{43} -1.87958 q^{44} -1.77472 q^{45} +1.33619 q^{46} -3.95817 q^{47} -9.23503 q^{48} -3.28903 q^{49} -1.96967 q^{50} -15.7363 q^{51} +2.70361 q^{52} -5.34615 q^{53} +5.27353 q^{54} +1.00000 q^{55} +0.456913 q^{56} +9.97518 q^{57} +16.7457 q^{58} +1.88506 q^{59} -4.10710 q^{60} -5.04258 q^{61} +0.458678 q^{62} +3.41880 q^{63} -7.00939 q^{64} -1.43841 q^{65} +4.30394 q^{66} -10.2362 q^{67} -13.5360 q^{68} -1.48235 q^{69} +3.79434 q^{70} -6.04853 q^{71} +0.420940 q^{72} -1.00000 q^{73} -18.1946 q^{74} +2.18511 q^{75} +8.58041 q^{76} -1.92639 q^{77} -6.19083 q^{78} -0.0160830 q^{79} +4.22634 q^{80} -11.1745 q^{81} +13.4347 q^{82} +1.00209 q^{83} +7.91186 q^{84} +7.20159 q^{85} -2.67803 q^{86} -18.5774 q^{87} -0.237186 q^{88} +4.39239 q^{89} +3.49561 q^{90} +2.77094 q^{91} -1.27508 q^{92} -0.508850 q^{93} +7.79627 q^{94} -4.56506 q^{95} +17.1534 q^{96} -8.96721 q^{97} +6.47828 q^{98} -1.77472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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