LMFDB - Embedded newform 6031.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29692 q^{2} -1.19284 q^{3} +3.27585 q^{4} +2.94374 q^{5} +2.73987 q^{6} +2.63830 q^{7} -2.93052 q^{8} -1.57712 q^{9} +O(q^{10})$	\(q-2.29692 q^{2} -1.19284 q^{3} +3.27585 q^{4} +2.94374 q^{5} +2.73987 q^{6} +2.63830 q^{7} -2.93052 q^{8} -1.57712 q^{9} -6.76154 q^{10} +4.30647 q^{11} -3.90758 q^{12} -6.74114 q^{13} -6.05996 q^{14} -3.51143 q^{15} +0.179482 q^{16} -1.72197 q^{17} +3.62252 q^{18} -5.57632 q^{19} +9.64325 q^{20} -3.14708 q^{21} -9.89162 q^{22} -4.11633 q^{23} +3.49566 q^{24} +3.66561 q^{25} +15.4839 q^{26} +5.45979 q^{27} +8.64266 q^{28} +8.78933 q^{29} +8.06547 q^{30} -5.48288 q^{31} +5.44879 q^{32} -5.13695 q^{33} +3.95523 q^{34} +7.76646 q^{35} -5.16641 q^{36} -1.00000 q^{37} +12.8084 q^{38} +8.04114 q^{39} -8.62670 q^{40} +0.771431 q^{41} +7.22859 q^{42} -2.64739 q^{43} +14.1073 q^{44} -4.64264 q^{45} +9.45488 q^{46} +4.92276 q^{47} -0.214094 q^{48} -0.0393921 q^{49} -8.41962 q^{50} +2.05404 q^{51} -22.0830 q^{52} +11.9147 q^{53} -12.5407 q^{54} +12.6771 q^{55} -7.73158 q^{56} +6.65168 q^{57} -20.1884 q^{58} -5.07050 q^{59} -11.5029 q^{60} -0.629197 q^{61} +12.5937 q^{62} -4.16091 q^{63} -12.8744 q^{64} -19.8442 q^{65} +11.7992 q^{66} +11.6624 q^{67} -5.64091 q^{68} +4.91014 q^{69} -17.8390 q^{70} +10.8562 q^{71} +4.62179 q^{72} +2.00568 q^{73} +2.29692 q^{74} -4.37251 q^{75} -18.2672 q^{76} +11.3617 q^{77} -18.4699 q^{78} -5.31075 q^{79} +0.528349 q^{80} -1.78132 q^{81} -1.77192 q^{82} -5.43224 q^{83} -10.3093 q^{84} -5.06903 q^{85} +6.08085 q^{86} -10.4843 q^{87} -12.6202 q^{88} -13.9163 q^{89} +10.6638 q^{90} -17.7851 q^{91} -13.4845 q^{92} +6.54022 q^{93} -11.3072 q^{94} -16.4152 q^{95} -6.49956 q^{96} -5.34872 q^{97} +0.0904806 q^{98} -6.79182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.29692	−1.62417	−0.812084	−	0.583540i	$-0.801667\pi$
$2$	−2.29692	−1.62417	−0.812084	+	0.583540i	$0.801667\pi$
$3$	−1.19284	−0.688689	−0.344345	−	0.938843i	$-0.611899\pi$
$3$	−1.19284	−0.688689	−0.344345	+	0.938843i	$0.611899\pi$
$4$	3.27585	1.63792
$5$	2.94374	1.31648	0.658241	−	0.752808i	$-0.271301\pi$
$5$	2.94374	1.31648	0.658241	+	0.752808i	$0.271301\pi$
$6$	2.73987	1.11855
$7$	2.63830	0.997182	0.498591	−	0.866837i	$-0.333851\pi$
$7$	2.63830	0.997182	0.498591	+	0.866837i	$0.333851\pi$
$8$	−2.93052	−1.03610
$9$	−1.57712	−0.525707
$10$	−6.76154	−2.13819
$11$	4.30647	1.29845	0.649224	−	0.760597i	$-0.275094\pi$
$11$	4.30647	1.29845	0.649224	+	0.760597i	$0.275094\pi$
$12$	−3.90758	−1.12802
$13$	−6.74114	−1.86966	−0.934828	−	0.355100i	$-0.884447\pi$
$13$	−6.74114	−1.86966	−0.934828	+	0.355100i	$0.884447\pi$
$14$	−6.05996	−1.61959
$15$	−3.51143	−0.906646
$16$	0.179482	0.0448706
$17$	−1.72197	−0.417639	−0.208820	−	0.977954i	$-0.566962\pi$
$17$	−1.72197	−0.417639	−0.208820	+	0.977954i	$0.566962\pi$
$18$	3.62252	0.853837
$19$	−5.57632	−1.27930	−0.639648	−	0.768668i	$-0.720920\pi$
$19$	−5.57632	−1.27930	−0.639648	+	0.768668i	$0.720920\pi$
$20$	9.64325	2.15630
$21$	−3.14708	−0.686749
$22$	−9.89162	−2.10890
$23$	−4.11633	−0.858313	−0.429157	−	0.903230i	$-0.641189\pi$
$23$	−4.11633	−0.858313	−0.429157	+	0.903230i	$0.641189\pi$
$24$	3.49566	0.713548
$25$	3.66561	0.733122
$26$	15.4839	3.03664
$27$	5.45979	1.05074
$28$	8.64266	1.63331
$29$	8.78933	1.63214	0.816069	−	0.577955i	$-0.196149\pi$
$29$	8.78933	1.63214	0.816069	+	0.577955i	$0.196149\pi$
$30$	8.06547	1.47255
$31$	−5.48288	−0.984754	−0.492377	−	0.870382i	$-0.663872\pi$
$31$	−5.48288	−0.984754	−0.492377	+	0.870382i	$0.663872\pi$
$32$	5.44879	0.963218
$33$	−5.13695	−0.894228
$34$	3.95523	0.678316
$35$	7.76646	1.31277
$36$	−5.16641	−0.861068
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	12.8084	2.07779
$39$	8.04114	1.28761
$40$	−8.62670	−1.36400
$41$	0.771431	0.120477	0.0602386	−	0.998184i	$-0.480814\pi$
$41$	0.771431	0.120477	0.0602386	+	0.998184i	$0.480814\pi$
$42$	7.22859	1.11540
$43$	−2.64739	−0.403724	−0.201862	−	0.979414i	$-0.564699\pi$
$43$	−2.64739	−0.403724	−0.201862	+	0.979414i	$0.564699\pi$
$44$	14.1073	2.12676
$45$	−4.64264	−0.692084
$46$	9.45488	1.39405
$47$	4.92276	0.718058	0.359029	−	0.933326i	$-0.383108\pi$
$47$	4.92276	0.718058	0.359029	+	0.933326i	$0.383108\pi$
$48$	−0.214094	−0.0309019
$49$	−0.0393921	−0.00562744
$50$	−8.41962	−1.19071
$51$	2.05404	0.287624
$52$	−22.0830	−3.06235
$53$	11.9147	1.63661	0.818307	−	0.574782i	$-0.194913\pi$
$53$	11.9147	1.63661	0.818307	+	0.574782i	$0.194913\pi$
$54$	−12.5407	−1.70658
$55$	12.6771	1.70938
$56$	−7.73158	−1.03318
$57$	6.65168	0.881037
$58$	−20.1884	−2.65087
$59$	−5.07050	−0.660123	−0.330061	−	0.943959i	$-0.607069\pi$
$59$	−5.07050	−0.660123	−0.330061	+	0.943959i	$0.607069\pi$
$60$	−11.5029	−1.48502
$61$	−0.629197	−0.0805604	−0.0402802	−	0.999188i	$-0.512825\pi$
$61$	−0.629197	−0.0805604	−0.0402802	+	0.999188i	$0.512825\pi$
$62$	12.5937	1.59941
$63$	−4.16091	−0.524226
$64$	−12.8744	−1.60930
$65$	−19.8442	−2.46137
$66$	11.7992	1.45238
$67$	11.6624	1.42479	0.712395	−	0.701779i	$-0.247611\pi$
$67$	11.6624	1.42479	0.712395	+	0.701779i	$0.247611\pi$
$68$	−5.64091	−0.684061
$69$	4.91014	0.591111
$70$	−17.8390	−2.13216
$71$	10.8562	1.28839	0.644196	−	0.764860i	$-0.277192\pi$
$71$	10.8562	1.28839	0.644196	+	0.764860i	$0.277192\pi$
$72$	4.62179	0.544683
$73$	2.00568	0.234748	0.117374	−	0.993088i	$-0.462552\pi$
$73$	2.00568	0.234748	0.117374	+	0.993088i	$0.462552\pi$
$74$	2.29692	0.267012
$75$	−4.37251	−0.504893
$76$	−18.2672	−2.09539
$77$	11.3617	1.29479
$78$	−18.4699	−2.09130
$79$	−5.31075	−0.597506	−0.298753	−	0.954330i	$-0.596571\pi$
$79$	−5.31075	−0.597506	−0.298753	+	0.954330i	$0.596571\pi$
$80$	0.528349	0.0590713
$81$	−1.78132	−0.197925
$82$	−1.77192	−0.195675
$83$	−5.43224	−0.596266	−0.298133	−	0.954524i	$-0.596364\pi$
$83$	−5.43224	−0.596266	−0.298133	+	0.954524i	$0.596364\pi$
$84$	−10.3093	−1.12484
$85$	−5.06903	−0.549814
$86$	6.08085	0.655715
$87$	−10.4843	−1.12404
$88$	−12.6202	−1.34532
$89$	−13.9163	−1.47512	−0.737560	−	0.675282i	$-0.764022\pi$
$89$	−13.9163	−1.47512	−0.737560	+	0.675282i	$0.764022\pi$
$90$	10.6638	1.12406
$91$	−17.7851	−1.86439
$92$	−13.4845	−1.40585
$93$	6.54022	0.678189
$94$	−11.3072	−1.16625
$95$	−16.4152	−1.68417
$96$	−6.49956	−0.663358
$97$	−5.34872	−0.543080	−0.271540	−	0.962427i	$-0.587533\pi$
$97$	−5.34872	−0.543080	−0.271540	+	0.962427i	$0.587533\pi$
$98$	0.0904806	0.00913992
$99$	−6.79182	−0.682604
$100$	12.0080	1.20080
$101$	−4.80534	−0.478149	−0.239075	−	0.971001i	$-0.576844\pi$
$101$	−4.80534	−0.478149	−0.239075	+	0.971001i	$0.576844\pi$
$102$	−4.71797	−0.467149
$103$	7.61135	0.749969	0.374984	−	0.927031i	$-0.377648\pi$
$103$	7.61135	0.749969	0.374984	+	0.927031i	$0.377648\pi$
$104$	19.7551	1.93714
$105$	−9.26418	−0.904092
$106$	−27.3672	−2.65814
$107$	−1.21490	−0.117448	−0.0587242	−	0.998274i	$-0.518703\pi$
$107$	−1.21490	−0.117448	−0.0587242	+	0.998274i	$0.518703\pi$
$108$	17.8855	1.72103
$109$	5.12492	0.490879	0.245439	−	0.969412i	$-0.421068\pi$
$109$	5.12492	0.490879	0.245439	+	0.969412i	$0.421068\pi$
$110$	−29.1184	−2.77633
$111$	1.19284	0.113220
$112$	0.473528	0.0447441
$113$	−12.8915	−1.21273	−0.606365	−	0.795187i	$-0.707373\pi$
$113$	−12.8915	−1.21273	−0.606365	+	0.795187i	$0.707373\pi$
$114$	−15.2784	−1.43095
$115$	−12.1174	−1.12995
$116$	28.7925	2.67332
$117$	10.6316	0.982892
$118$	11.6465	1.07215
$119$	−4.54307	−0.416462
$120$	10.2903	0.939372
$121$	7.54566	0.685969
$122$	1.44522	0.130844
$123$	−0.920197	−0.0829713
$124$	−17.9611	−1.61295
$125$	−3.92809	−0.351339
$126$	9.55729	0.851431
$127$	7.63348	0.677362	0.338681	−	0.940901i	$-0.390019\pi$
$127$	7.63348	0.677362	0.338681	+	0.940901i	$0.390019\pi$
$128$	18.6739	1.65056
$129$	3.15793	0.278040
$130$	45.5805	3.99768
$131$	−5.17801	−0.452405	−0.226203	−	0.974080i	$-0.572631\pi$
$131$	−5.17801	−0.452405	−0.226203	+	0.974080i	$0.572631\pi$
$132$	−16.8279	−1.46468
$133$	−14.7120	−1.27569
$134$	−26.7876	−2.31410
$135$	16.0722	1.38328
$136$	5.04627	0.432714
$137$	16.7635	1.43221	0.716103	−	0.697995i	$-0.245924\pi$
$137$	16.7635	1.43221	0.716103	+	0.697995i	$0.245924\pi$
$138$	−11.2782	−0.960064
$139$	−21.7476	−1.84461	−0.922304	−	0.386465i	$-0.873696\pi$
$139$	−21.7476	−1.84461	−0.922304	+	0.386465i	$0.873696\pi$
$140$	25.4417	2.15022
$141$	−5.87209	−0.494519
$142$	−24.9358	−2.09257
$143$	−29.0305	−2.42765
$144$	−0.283065	−0.0235888
$145$	25.8735	2.14868
$146$	−4.60690	−0.381270
$147$	0.0469887	0.00387556
$148$	−3.27585	−0.269273
$149$	−14.8671	−1.21796	−0.608980	−	0.793186i	$-0.708421\pi$
$149$	−14.8671	−1.21796	−0.608980	+	0.793186i	$0.708421\pi$
$150$	10.0433	0.820032
$151$	−10.1461	−0.825678	−0.412839	−	0.910804i	$-0.635463\pi$
$151$	−10.1461	−0.825678	−0.412839	+	0.910804i	$0.635463\pi$
$152$	16.3415	1.32547
$153$	2.71576	0.219556
$154$	−26.0970	−2.10296
$155$	−16.1402	−1.29641
$156$	26.3415	2.10901
$157$	7.49603	0.598248	0.299124	−	0.954214i	$-0.403306\pi$
$157$	7.49603	0.598248	0.299124	+	0.954214i	$0.403306\pi$
$158$	12.1984	0.970451
$159$	−14.2124	−1.12712
$160$	16.0398	1.26806
$161$	−10.8601	−0.855895
$162$	4.09156	0.321463
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	2.52709	0.197332
$165$	−15.1218	−1.17723
$166$	12.4774	0.968436
$167$	−12.9026	−0.998436	−0.499218	−	0.866476i	$-0.666379\pi$
$167$	−12.9026	−0.998436	−0.499218	+	0.866476i	$0.666379\pi$
$168$	9.22258	0.711537
$169$	32.4430	2.49562
$170$	11.6432	0.892991
$171$	8.79454	0.672535
$172$	−8.67246	−0.661269
$173$	−13.7866	−1.04818	−0.524089	−	0.851663i	$-0.675594\pi$
$173$	−13.7866	−1.04818	−0.524089	+	0.851663i	$0.675594\pi$
$174$	24.0816	1.82562
$175$	9.67097	0.731057
$176$	0.772935	0.0582621
$177$	6.04832	0.454619
$178$	31.9645	2.39584
$179$	15.5932	1.16549	0.582745	−	0.812655i	$-0.301979\pi$
$179$	15.5932	1.16549	0.582745	+	0.812655i	$0.301979\pi$
$180$	−15.2086	−1.13358
$181$	−1.64268	−0.122100	−0.0610499	−	0.998135i	$-0.519445\pi$
$181$	−1.64268	−0.122100	−0.0610499	+	0.998135i	$0.519445\pi$
$182$	40.8510	3.02808
$183$	0.750534	0.0554811
$184$	12.0630	0.889295
$185$	−2.94374	−0.216428
$186$	−15.0224	−1.10149
$187$	−7.41561	−0.542283
$188$	16.1262	1.17612
$189$	14.4046	1.04778
$190$	37.7045	2.73537
$191$	−14.0792	−1.01873	−0.509367	−	0.860549i	$-0.670120\pi$
$191$	−14.0792	−1.01873	−0.509367	+	0.860549i	$0.670120\pi$
$192$	15.3572	1.10831
$193$	21.6392	1.55762	0.778811	−	0.627259i	$-0.215823\pi$
$193$	21.6392	1.55762	0.778811	+	0.627259i	$0.215823\pi$
$194$	12.2856	0.882054
$195$	23.6710	1.69512
$196$	−0.129043	−0.00921733
$197$	−2.43924	−0.173788	−0.0868942	−	0.996218i	$-0.527694\pi$
$197$	−2.43924	−0.173788	−0.0868942	+	0.996218i	$0.527694\pi$
$198$	15.6003	1.10866
$199$	−11.3066	−0.801503	−0.400752	−	0.916187i	$-0.631251\pi$
$199$	−11.3066	−0.801503	−0.400752	+	0.916187i	$0.631251\pi$
$200$	−10.7422	−0.759585
$201$	−13.9114	−0.981237
$202$	11.0375	0.776595
$203$	23.1889	1.62754
$204$	6.72873	0.471105
$205$	2.27089	0.158606
$206$	−17.4827	−1.21808
$207$	6.49195	0.451222
$208$	−1.20992	−0.0838926
$209$	−24.0142	−1.66110
$210$	21.2791	1.46840
$211$	−0.966681	−0.0665491	−0.0332745	−	0.999446i	$-0.510594\pi$
$211$	−0.966681	−0.0665491	−0.0332745	+	0.999446i	$0.510594\pi$
$212$	39.0308	2.68065
$213$	−12.9497	−0.887302
$214$	2.79052	0.190756
$215$	−7.79324	−0.531495
$216$	−16.0000	−1.08867
$217$	−14.4655	−0.981979
$218$	−11.7715	−0.797270
$219$	−2.39247	−0.161668
$220$	41.5283	2.79984
$221$	11.6080	0.780842
$222$	−2.73987	−0.183888
$223$	−9.70305	−0.649764	−0.324882	−	0.945755i	$-0.605325\pi$
$223$	−9.70305	−0.649764	−0.324882	+	0.945755i	$0.605325\pi$
$224$	14.3755	0.960504
$225$	−5.78112	−0.385408
$226$	29.6107	1.96968
$227$	−9.73382	−0.646057	−0.323028	−	0.946389i	$-0.604701\pi$
$227$	−9.73382	−0.646057	−0.323028	+	0.946389i	$0.604701\pi$
$228$	21.7899	1.44307
$229$	−1.02371	−0.0676485	−0.0338242	−	0.999428i	$-0.510769\pi$
$229$	−1.02371	−0.0676485	−0.0338242	+	0.999428i	$0.510769\pi$
$230$	27.8327	1.83523
$231$	−13.5528	−0.891708
$232$	−25.7573	−1.69105
$233$	23.2700	1.52447	0.762234	−	0.647302i	$-0.224103\pi$
$233$	23.2700	1.52447	0.762234	+	0.647302i	$0.224103\pi$
$234$	−24.4200	−1.59638
$235$	14.4913	0.945310
$236$	−16.6102	−1.08123
$237$	6.33490	0.411496
$238$	10.4351	0.676405
$239$	−9.24285	−0.597870	−0.298935	−	0.954273i	$-0.596631\pi$
$239$	−9.24285	−0.597870	−0.298935	+	0.954273i	$0.596631\pi$
$240$	−0.630239	−0.0406817
$241$	−1.70632	−0.109914	−0.0549568	−	0.998489i	$-0.517502\pi$
$241$	−1.70632	−0.109914	−0.0549568	+	0.998489i	$0.517502\pi$
$242$	−17.3318	−1.11413
$243$	−14.2545	−0.914429
$244$	−2.06115	−0.131952
$245$	−0.115960	−0.00740842
$246$	2.11362	0.134759
$247$	37.5908	2.39184
$248$	16.0677	1.02030
$249$	6.47982	0.410642
$250$	9.02252	0.570634
$251$	−16.4934	−1.04106	−0.520529	−	0.853844i	$-0.674265\pi$
$251$	−16.4934	−1.04106	−0.520529	+	0.853844i	$0.674265\pi$
$252$	−13.6305	−0.858642
$253$	−17.7268	−1.11448
$254$	−17.5335	−1.10015
$255$	6.04657	0.378651
$256$	−17.1437	−1.07148
$257$	−5.84439	−0.364563	−0.182281	−	0.983246i	$-0.558348\pi$
$257$	−5.84439	−0.364563	−0.182281	+	0.983246i	$0.558348\pi$
$258$	−7.25351	−0.451584
$259$	−2.63830	−0.163936
$260$	−65.0065	−4.03153
$261$	−13.8618	−0.858027
$262$	11.8935	0.734782
$263$	−21.2129	−1.30804	−0.654020	−	0.756477i	$-0.726919\pi$
$263$	−21.2129	−1.30804	−0.654020	+	0.756477i	$0.726919\pi$
$264$	15.0539	0.926505
$265$	35.0739	2.15457
$266$	33.7923	2.07194
$267$	16.5999	1.01590
$268$	38.2043	2.33370
$269$	−12.7728	−0.778770	−0.389385	−	0.921075i	$-0.627312\pi$
$269$	−12.7728	−0.778770	−0.389385	+	0.921075i	$0.627312\pi$
$270$	−36.9166	−2.24667
$271$	−3.56361	−0.216474	−0.108237	−	0.994125i	$-0.534521\pi$
$271$	−3.56361	−0.216474	−0.108237	+	0.994125i	$0.534521\pi$
$272$	−0.309063	−0.0187397
$273$	21.2149	1.28398
$274$	−38.5045	−2.32614
$275$	15.7858	0.951922
$276$	16.0849	0.968195
$277$	−22.7289	−1.36565	−0.682823	−	0.730584i	$-0.739248\pi$
$277$	−22.7289	−1.36565	−0.682823	+	0.730584i	$0.739248\pi$
$278$	49.9525	2.99595
$279$	8.64717	0.517692
$280$	−22.7598	−1.36016
$281$	−12.9534	−0.772732	−0.386366	−	0.922346i	$-0.626270\pi$
$281$	−12.9534	−0.772732	−0.386366	+	0.922346i	$0.626270\pi$
$282$	13.4877	0.803182
$283$	−26.1804	−1.55627	−0.778133	−	0.628100i	$-0.783833\pi$
$283$	−26.1804	−1.55627	−0.778133	+	0.628100i	$0.783833\pi$
$284$	35.5632	2.11029
$285$	19.5808	1.15987
$286$	66.6808	3.94292
$287$	2.03526	0.120138
$288$	−8.59340	−0.506371
$289$	−14.0348	−0.825578
$290$	−59.4294	−3.48982
$291$	6.38019	0.374014
$292$	6.57032	0.384499
$293$	4.83835	0.282660	0.141330	−	0.989963i	$-0.454862\pi$
$293$	4.83835	0.282660	0.141330	+	0.989963i	$0.454862\pi$
$294$	−0.107929	−0.00629456
$295$	−14.9262	−0.869039
$296$	2.93052	0.170333
$297$	23.5124	1.36433
$298$	34.1485	1.97817
$299$	27.7487	1.60475
$300$	−14.3237	−0.826977
$301$	−6.98461	−0.402586
$302$	23.3048	1.34104
$303$	5.73203	0.329296
$304$	−1.00085	−0.0574027
$305$	−1.85219	−0.106056
$306$	−6.23788	−0.356596
$307$	−14.3057	−0.816470	−0.408235	−	0.912877i	$-0.633856\pi$
$307$	−14.3057	−0.816470	−0.408235	+	0.912877i	$0.633856\pi$
$308$	37.2193	2.12077
$309$	−9.07916	−0.516495
$310$	37.0727	2.10559
$311$	16.5631	0.939210	0.469605	−	0.882877i	$-0.344396\pi$
$311$	16.5631	0.939210	0.469605	+	0.882877i	$0.344396\pi$
$312$	−23.5647	−1.33409
$313$	−32.1966	−1.81986	−0.909930	−	0.414762i	$-0.863865\pi$
$313$	−32.1966	−1.81986	−0.909930	+	0.414762i	$0.863865\pi$
$314$	−17.2178	−0.971656
$315$	−12.2487	−0.690134
$316$	−17.3972	−0.978670
$317$	−4.08441	−0.229404	−0.114702	−	0.993400i	$-0.536591\pi$
$317$	−4.08441	−0.229404	−0.114702	+	0.993400i	$0.536591\pi$
$318$	32.6448	1.83063
$319$	37.8510	2.11925
$320$	−37.8989	−2.11861
$321$	1.44918	0.0808854
$322$	24.9448	1.39012
$323$	9.60226	0.534284
$324$	−5.83534	−0.324185
$325$	−24.7104	−1.37069
$326$	2.29692	0.127215
$327$	−6.11324	−0.338063
$328$	−2.26069	−0.124826
$329$	12.9877	0.716035
$330$	34.7337	1.91203
$331$	−15.1163	−0.830869	−0.415434	−	0.909623i	$-0.636370\pi$
$331$	−15.1163	−0.830869	−0.415434	+	0.909623i	$0.636370\pi$
$332$	−17.7952	−0.976638
$333$	1.57712	0.0864257
$334$	29.6363	1.62163
$335$	34.3311	1.87571
$336$	−0.564845	−0.0308148
$337$	26.3601	1.43593	0.717964	−	0.696080i	$-0.245074\pi$
$337$	26.3601	1.43593	0.717964	+	0.696080i	$0.245074\pi$
$338$	−74.5190	−4.05330
$339$	15.3775	0.835193
$340$	−16.6054	−0.900553
$341$	−23.6118	−1.27865
$342$	−20.2004	−1.09231
$343$	−18.5720	−1.00279
$344$	7.75824	0.418296
$345$	14.4542	0.778187
$346$	31.6668	1.70242
$347$	7.41803	0.398221	0.199110	−	0.979977i	$-0.436195\pi$
$347$	7.41803	0.398221	0.199110	+	0.979977i	$0.436195\pi$
$348$	−34.3450	−1.84108
$349$	−7.97234	−0.426749	−0.213375	−	0.976970i	$-0.568445\pi$
$349$	−7.97234	−0.426749	−0.213375	+	0.976970i	$0.568445\pi$
$350$	−22.2135	−1.18736
$351$	−36.8053	−1.96452
$352$	23.4650	1.25069
$353$	18.6798	0.994226	0.497113	−	0.867686i	$-0.334394\pi$
$353$	18.6798	0.994226	0.497113	+	0.867686i	$0.334394\pi$
$354$	−13.8925	−0.738379
$355$	31.9578	1.69614
$356$	−45.5875	−2.41613
$357$	5.41917	0.286813
$358$	−35.8163	−1.89295
$359$	6.42551	0.339125	0.169563	−	0.985519i	$-0.445764\pi$
$359$	6.42551	0.339125	0.169563	+	0.985519i	$0.445764\pi$
$360$	13.6054	0.717065
$361$	12.0954	0.636598
$362$	3.77312	0.198311
$363$	−9.00080	−0.472419
$364$	−58.2614	−3.05373
$365$	5.90422	0.309041
$366$	−1.72392	−0.0901107
$367$	2.54553	0.132876	0.0664378	−	0.997791i	$-0.478837\pi$
$367$	2.54553	0.132876	0.0664378	+	0.997791i	$0.478837\pi$
$368$	−0.738808	−0.0385130
$369$	−1.21664	−0.0633357
$370$	6.76154	0.351516
$371$	31.4346	1.63200
$372$	21.4248	1.11082
$373$	−20.2667	−1.04937	−0.524684	−	0.851297i	$-0.675817\pi$
$373$	−20.2667	−1.04937	−0.524684	+	0.851297i	$0.675817\pi$
$374$	17.0331	0.880759
$375$	4.68560	0.241964
$376$	−14.4263	−0.743977
$377$	−59.2501	−3.05154
$378$	−33.0861	−1.70177
$379$	14.9509	0.767976	0.383988	−	0.923338i	$-0.374550\pi$
$379$	14.9509	0.767976	0.383988	+	0.923338i	$0.374550\pi$
$380$	−53.7738	−2.75854
$381$	−9.10556	−0.466492
$382$	32.3388	1.65460
$383$	21.0449	1.07534	0.537672	−	0.843154i	$-0.319304\pi$
$383$	21.0449	1.07534	0.537672	+	0.843154i	$0.319304\pi$
$384$	−22.2751	−1.13672
$385$	33.4460	1.70457
$386$	−49.7035	−2.52984
$387$	4.17526	0.212240
$388$	−17.5216	−0.889524
$389$	−37.2400	−1.88814	−0.944071	−	0.329743i	$-0.893038\pi$
$389$	−37.2400	−1.88814	−0.944071	+	0.329743i	$0.893038\pi$
$390$	−54.3705	−2.75316
$391$	7.08819	0.358465
$392$	0.115439	0.00583057
$393$	6.17656	0.311566
$394$	5.60273	0.282262
$395$	−15.6335	−0.786606
$396$	−22.2490	−1.11805
$397$	13.8848	0.696856	0.348428	−	0.937335i	$-0.386716\pi$
$397$	13.8848	0.696856	0.348428	+	0.937335i	$0.386716\pi$
$398$	25.9704	1.30178
$399$	17.5491	0.878555
$400$	0.657912	0.0328956
$401$	18.3962	0.918662	0.459331	−	0.888265i	$-0.348089\pi$
$401$	18.3962	0.918662	0.459331	+	0.888265i	$0.348089\pi$
$402$	31.9535	1.59369
$403$	36.9609	1.84115
$404$	−15.7416	−0.783172
$405$	−5.24375	−0.260564
$406$	−53.2630	−2.64340
$407$	−4.30647	−0.213464
$408$	−6.01942	−0.298006
$409$	8.92397	0.441262	0.220631	−	0.975357i	$-0.429188\pi$
$409$	8.92397	0.441262	0.220631	+	0.975357i	$0.429188\pi$
$410$	−5.21606	−0.257603
$411$	−19.9963	−0.986345
$412$	24.9336	1.22839
$413$	−13.3775	−0.658263
$414$	−14.9115	−0.732860
$415$	−15.9911	−0.784973
$416$	−36.7310	−1.80089
$417$	25.9415	1.27036
$418$	55.1588	2.69791
$419$	8.39621	0.410182	0.205091	−	0.978743i	$-0.434251\pi$
$419$	8.39621	0.410182	0.205091	+	0.978743i	$0.434251\pi$
$420$	−30.3480	−1.48083
$421$	−29.4136	−1.43353	−0.716766	−	0.697314i	$-0.754379\pi$
$421$	−29.4136	−1.43353	−0.716766	+	0.697314i	$0.754379\pi$
$422$	2.22039	0.108087
$423$	−7.76379	−0.377488
$424$	−34.9164	−1.69569
$425$	−6.31207	−0.306181
$426$	29.7446	1.44113
$427$	−1.66001	−0.0803334
$428$	−3.97981	−0.192371
$429$	34.6289	1.67190
$430$	17.9005	0.863237
$431$	37.7111	1.81648	0.908240	−	0.418450i	$-0.137426\pi$
$431$	37.7111	1.81648	0.908240	+	0.418450i	$0.137426\pi$
$432$	0.979937	0.0471472
$433$	−13.9736	−0.671530	−0.335765	−	0.941946i	$-0.608995\pi$
$433$	−13.9736	−0.671530	−0.335765	+	0.941946i	$0.608995\pi$
$434$	33.2260	1.59490
$435$	−30.8631	−1.47977
$436$	16.7885	0.804022
$437$	22.9540	1.09804
$438$	5.49532	0.262576
$439$	3.64510	0.173971	0.0869856	−	0.996210i	$-0.472277\pi$
$439$	3.64510	0.173971	0.0869856	+	0.996210i	$0.472277\pi$
$440$	−37.1506	−1.77108
$441$	0.0621262	0.00295839
$442$	−26.6628	−1.26822
$443$	−16.9218	−0.803980	−0.401990	−	0.915644i	$-0.631681\pi$
$443$	−16.9218	−0.803980	−0.401990	+	0.915644i	$0.631681\pi$
$444$	3.90758	0.185445
$445$	−40.9658	−1.94197
$446$	22.2871	1.05533
$447$	17.7341	0.838795
$448$	−33.9665	−1.60477
$449$	1.09058	0.0514675	0.0257338	−	0.999669i	$-0.491808\pi$
$449$	1.09058	0.0514675	0.0257338	+	0.999669i	$0.491808\pi$
$450$	13.2788	0.625967
$451$	3.32214	0.156433
$452$	−42.2305	−1.98636
$453$	12.1027	0.568635
$454$	22.3578	1.04930
$455$	−52.3548	−2.45443
$456$	−19.4929	−0.912839
$457$	−8.37145	−0.391600	−0.195800	−	0.980644i	$-0.562730\pi$
$457$	−8.37145	−0.391600	−0.195800	+	0.980644i	$0.562730\pi$
$458$	2.35138	0.109873
$459$	−9.40160	−0.438829
$460$	−39.6948	−1.85078
$461$	18.5093	0.862065	0.431032	−	0.902336i	$-0.358149\pi$
$461$	18.5093	0.862065	0.431032	+	0.902336i	$0.358149\pi$
$462$	31.1297	1.44828
$463$	−17.8802	−0.830964	−0.415482	−	0.909601i	$-0.636387\pi$
$463$	−17.8802	−0.830964	−0.415482	+	0.909601i	$0.636387\pi$
$464$	1.57753	0.0732350
$465$	19.2527	0.892823
$466$	−53.4493	−2.47599
$467$	−31.6586	−1.46498	−0.732492	−	0.680775i	$-0.761643\pi$
$467$	−31.6586	−1.46498	−0.732492	+	0.680775i	$0.761643\pi$
$468$	34.8275	1.60990
$469$	30.7689	1.42077
$470$	−33.2854	−1.53534
$471$	−8.94160	−0.412007
$472$	14.8592	0.683950
$473$	−11.4009	−0.524215
$474$	−14.5508	−0.668339
$475$	−20.4406	−0.937880
$476$	−14.8824	−0.682134
$477$	−18.7910	−0.860380
$478$	21.2301	0.971042
$479$	−27.1543	−1.24071	−0.620357	−	0.784320i	$-0.713012\pi$
$479$	−27.1543	−1.24071	−0.620357	+	0.784320i	$0.713012\pi$
$480$	−19.1330	−0.873298
$481$	6.74114	0.307370
$482$	3.91928	0.178518
$483$	12.9544	0.589446
$484$	24.7184	1.12357
$485$	−15.7452	−0.714955
$486$	32.7416	1.48519
$487$	29.7771	1.34933	0.674665	−	0.738124i	$-0.264288\pi$
$487$	29.7771	1.34933	0.674665	+	0.738124i	$0.264288\pi$
$488$	1.84388	0.0834683
$489$	1.19284	0.0539423
$490$	0.266351	0.0120325
$491$	31.5685	1.42467	0.712334	−	0.701841i	$-0.247638\pi$
$491$	31.5685	1.42467	0.712334	+	0.701841i	$0.247638\pi$
$492$	−3.01442	−0.135901
$493$	−15.1350	−0.681644
$494$	−86.3431	−3.88476
$495$	−19.9934	−0.898635
$496$	−0.984079	−0.0441865
$497$	28.6418	1.28476
$498$	−14.8836	−0.666952
$499$	−29.7147	−1.33021	−0.665107	−	0.746748i	$-0.731614\pi$
$499$	−29.7147	−1.33021	−0.665107	+	0.746748i	$0.731614\pi$
$500$	−12.8678	−0.575467
$501$	15.3908	0.687612
$502$	37.8841	1.69085
$503$	−7.02749	−0.313340	−0.156670	−	0.987651i	$-0.550076\pi$
$503$	−7.02749	−0.313340	−0.156670	+	0.987651i	$0.550076\pi$
$504$	12.1936	0.543148
$505$	−14.1457	−0.629475
$506$	40.7171	1.81010
$507$	−38.6995	−1.71870
$508$	25.0061	1.10947
$509$	4.98194	0.220821	0.110410	−	0.993886i	$-0.464783\pi$
$509$	4.98194	0.220821	0.110410	+	0.993886i	$0.464783\pi$
$510$	−13.8885	−0.614993
$511$	5.29159	0.234086
$512$	2.02991	0.0897104
$513$	−30.4456	−1.34420
$514$	13.4241	0.592111
$515$	22.4058	0.987320
$516$	10.3449	0.455409
$517$	21.1997	0.932362
$518$	6.05996	0.266259
$519$	16.4453	0.721869
$520$	58.1538	2.55021
$521$	0.0709506	0.00310840	0.00155420	−	0.999999i	$-0.499505\pi$
$521$	0.0709506	0.00310840	0.00155420	+	0.999999i	$0.499505\pi$
$522$	31.8396	1.39358
$523$	−2.41048	−0.105403	−0.0527016	−	0.998610i	$-0.516783\pi$
$523$	−2.41048	−0.105403	−0.0527016	+	0.998610i	$0.516783\pi$
$524$	−16.9624	−0.741005
$525$	−11.5360	−0.503471
$526$	48.7243	2.12448
$527$	9.44135	0.411272
$528$	−0.921991	−0.0401245
$529$	−6.05586	−0.263298
$530$	−80.5619	−3.49939
$531$	7.99679	0.347031
$532$	−48.1942	−2.08948
$533$	−5.20032	−0.225251
$534$	−38.1287	−1.64999
$535$	−3.57634	−0.154619
$536$	−34.1769	−1.47622
$537$	−18.6003	−0.802660
$538$	29.3381	1.26485
$539$	−0.169641	−0.00730695
$540$	52.6502	2.26570
$541$	−8.71507	−0.374690	−0.187345	−	0.982294i	$-0.559988\pi$
$541$	−8.71507	−0.374690	−0.187345	+	0.982294i	$0.559988\pi$
$542$	8.18533	0.351590
$543$	1.95947	0.0840887
$544$	−9.38265	−0.402278
$545$	15.0864	0.646232
$546$	−48.7290	−2.08541
$547$	38.2909	1.63720	0.818599	−	0.574365i	$-0.194751\pi$
$547$	38.2909	1.63720	0.818599	+	0.574365i	$0.194751\pi$
$548$	54.9148	2.34584
$549$	0.992321	0.0423512
$550$	−36.2588	−1.54608
$551$	−49.0121	−2.08799
$552$	−14.3893	−0.612448
$553$	−14.0113	−0.595823
$554$	52.2064	2.21804
$555$	3.51143	0.149052
$556$	−71.2418	−3.02133
$557$	−3.56915	−0.151230	−0.0756149	−	0.997137i	$-0.524092\pi$
$557$	−3.56915	−0.151230	−0.0756149	+	0.997137i	$0.524092\pi$
$558$	−19.8619	−0.840820
$559$	17.8465	0.754825
$560$	1.39394	0.0589048
$561$	8.84567	0.373464
$562$	29.7528	1.25505
$563$	9.36304	0.394605	0.197303	−	0.980343i	$-0.436782\pi$
$563$	9.36304	0.394605	0.197303	+	0.980343i	$0.436782\pi$
$564$	−19.2361	−0.809984
$565$	−37.9492	−1.59653
$566$	60.1344	2.52764
$567$	−4.69966	−0.197367
$568$	−31.8143	−1.33490
$569$	−40.5221	−1.69877	−0.849387	−	0.527771i	$-0.823028\pi$
$569$	−40.5221	−1.69877	−0.849387	+	0.527771i	$0.823028\pi$
$570$	−44.9756	−1.88382
$571$	6.33740	0.265212	0.132606	−	0.991169i	$-0.457666\pi$
$571$	6.33740	0.265212	0.132606	+	0.991169i	$0.457666\pi$
$572$	−95.0995	−3.97631
$573$	16.7943	0.701591
$574$	−4.67484	−0.195124
$575$	−15.0889	−0.629249
$576$	20.3045	0.846021
$577$	−16.4313	−0.684042	−0.342021	−	0.939692i	$-0.611111\pi$
$577$	−16.4313	−0.684042	−0.342021	+	0.939692i	$0.611111\pi$
$578$	32.2369	1.34088
$579$	−25.8122	−1.07272
$580$	84.7577	3.51937
$581$	−14.3319	−0.594586
$582$	−14.6548	−0.607461
$583$	51.3104	2.12506
$584$	−5.87770	−0.243221
$585$	31.2967	1.29396
$586$	−11.1133	−0.459087
$587$	14.0169	0.578541	0.289271	−	0.957247i	$-0.406587\pi$
$587$	14.0169	0.578541	0.289271	+	0.957247i	$0.406587\pi$
$588$	0.153928	0.00634787
$589$	30.5743	1.25979
$590$	34.2844	1.41147
$591$	2.90963	0.119686
$592$	−0.179482	−0.00737668
$593$	−30.7740	−1.26374	−0.631868	−	0.775076i	$-0.717712\pi$
$593$	−30.7740	−1.26374	−0.631868	+	0.775076i	$0.717712\pi$
$594$	−54.0062	−2.21590
$595$	−13.3736	−0.548265
$596$	−48.7023	−1.99492
$597$	13.4870	0.551987
$598$	−63.7367	−2.60639
$599$	−26.6167	−1.08753	−0.543764	−	0.839238i	$-0.683001\pi$
$599$	−26.6167	−1.08753	−0.543764	+	0.839238i	$0.683001\pi$
$600$	12.8137	0.523118
$601$	−21.4677	−0.875686	−0.437843	−	0.899051i	$-0.644257\pi$
$601$	−21.4677	−0.875686	−0.437843	+	0.899051i	$0.644257\pi$
$602$	16.0431	0.653868
$603$	−18.3930	−0.749022
$604$	−33.2371	−1.35240
$605$	22.2125	0.903065
$606$	−13.1660	−0.534833
$607$	14.6582	0.594958	0.297479	−	0.954728i	$-0.403854\pi$
$607$	14.6582	0.594958	0.297479	+	0.954728i	$0.403854\pi$
$608$	−30.3842	−1.23224
$609$	−27.6607	−1.12087
$610$	4.25434	0.172253
$611$	−33.1850	−1.34252
$612$	8.89640	0.359616
$613$	−33.7357	−1.36257	−0.681286	−	0.732018i	$-0.738579\pi$
$613$	−33.7357	−1.36257	−0.681286	+	0.732018i	$0.738579\pi$
$614$	32.8591	1.32608
$615$	−2.70882	−0.109230
$616$	−33.2958	−1.34153
$617$	−48.9003	−1.96865	−0.984326	−	0.176357i	$-0.943569\pi$
$617$	−48.9003	−1.96865	−0.984326	+	0.176357i	$0.943569\pi$
$618$	20.8541	0.838876
$619$	−11.9029	−0.478419	−0.239210	−	0.970968i	$-0.576888\pi$
$619$	−11.9029	−0.478419	−0.239210	+	0.970968i	$0.576888\pi$
$620$	−52.8727	−2.12342
$621$	−22.4743	−0.901863
$622$	−38.0442	−1.52544
$623$	−36.7152	−1.47096
$624$	1.44324	0.0577759
$625$	−29.8913	−1.19565
$626$	73.9531	2.95576
$627$	28.6453	1.14398
$628$	24.5558	0.979885
$629$	1.72197	0.0686594
$630$	28.1342	1.12089
$631$	35.5014	1.41329	0.706643	−	0.707570i	$-0.250209\pi$
$631$	35.5014	1.41329	0.706643	+	0.707570i	$0.250209\pi$
$632$	15.5633	0.619074
$633$	1.15310	0.0458316
$634$	9.38158	0.372590
$635$	22.4710	0.891734
$636$	−46.5577	−1.84613
$637$	0.265548	0.0105214
$638$	−86.9407	−3.44201
$639$	−17.1215	−0.677317
$640$	54.9711	2.17293
$641$	−27.8073	−1.09832	−0.549162	−	0.835716i	$-0.685053\pi$
$641$	−27.8073	−1.09832	−0.549162	+	0.835716i	$0.685053\pi$
$642$	−3.32866	−0.131372
$643$	−14.1684	−0.558748	−0.279374	−	0.960182i	$-0.590127\pi$
$643$	−14.1684	−0.558748	−0.279374	+	0.960182i	$0.590127\pi$
$644$	−35.5760	−1.40189
$645$	9.29613	0.366035
$646$	−22.0556	−0.867767
$647$	−0.145172	−0.00570729	−0.00285365	−	0.999996i	$-0.500908\pi$
$647$	−0.145172	−0.00570729	−0.00285365	+	0.999996i	$0.500908\pi$
$648$	5.22020	0.205069
$649$	−21.8359	−0.857136
$650$	56.7579	2.22623
$651$	17.2550	0.676278
$652$	−3.27585	−0.128292
$653$	−15.6645	−0.612998	−0.306499	−	0.951871i	$-0.599158\pi$
$653$	−15.6645	−0.612998	−0.306499	+	0.951871i	$0.599158\pi$
$654$	14.0416	0.549071
$655$	−15.2427	−0.595583
$656$	0.138458	0.00540588
$657$	−3.16321	−0.123409
$658$	−29.8317	−1.16296
$659$	0.336171	0.0130954	0.00654769	−	0.999979i	$-0.497916\pi$
$659$	0.336171	0.0130954	0.00654769	+	0.999979i	$0.497916\pi$
$660$	−49.5368	−1.92822
$661$	−9.48554	−0.368945	−0.184472	−	0.982838i	$-0.559058\pi$
$661$	−9.48554	−0.368945	−0.184472	+	0.982838i	$0.559058\pi$
$662$	34.7210	1.34947
$663$	−13.8466	−0.537757
$664$	15.9193	0.617789
$665$	−43.3083	−1.67942
$666$	−3.62252	−0.140370
$667$	−36.1797	−1.40089
$668$	−42.2671	−1.63536
$669$	11.5742	0.447486
$670$	−78.8558	−3.04647
$671$	−2.70962	−0.104604
$672$	−17.1478	−0.661489
$673$	37.1614	1.43247	0.716233	−	0.697861i	$-0.245865\pi$
$673$	37.1614	1.43247	0.716233	+	0.697861i	$0.245865\pi$
$674$	−60.5472	−2.33219
$675$	20.0135	0.770320
$676$	106.278	4.08763
$677$	27.7100	1.06498	0.532491	−	0.846436i	$-0.321256\pi$
$677$	27.7100	1.06498	0.532491	+	0.846436i	$0.321256\pi$
$678$	−35.3210	−1.35649
$679$	−14.1115	−0.541550
$680$	14.8549	0.569660
$681$	11.6109	0.444932
$682$	54.2345	2.07675
$683$	6.68002	0.255604	0.127802	−	0.991800i	$-0.459208\pi$
$683$	6.68002	0.255604	0.127802	+	0.991800i	$0.459208\pi$
$684$	28.8096	1.10156
$685$	49.3475	1.88547
$686$	42.6584	1.62871
$687$	1.22112	0.0465888
$688$	−0.475160	−0.0181153
$689$	−80.3189	−3.05991
$690$	−33.2001	−1.26391
$691$	−43.6454	−1.66035	−0.830175	−	0.557503i	$-0.811760\pi$
$691$	−43.6454	−1.66035	−0.830175	+	0.557503i	$0.811760\pi$
$692$	−45.1629	−1.71684
$693$	−17.9188	−0.680681
$694$	−17.0386	−0.646778
$695$	−64.0193	−2.42839
$696$	30.7245	1.16461
$697$	−1.32838	−0.0503160
$698$	18.3118	0.693113
$699$	−27.7575	−1.04988
$700$	31.6806	1.19742
$701$	−3.85529	−0.145612	−0.0728061	−	0.997346i	$-0.523195\pi$
$701$	−3.85529	−0.145612	−0.0728061	+	0.997346i	$0.523195\pi$
$702$	84.5388	3.19071
$703$	5.57632	0.210315
$704$	−55.4432	−2.08959
$705$	−17.2859	−0.651025
$706$	−42.9060	−1.61479
$707$	−12.6779	−0.476802
$708$	19.8134	0.744632
$709$	0.985285	0.0370032	0.0185016	−	0.999829i	$-0.494110\pi$
$709$	0.985285	0.0370032	0.0185016	+	0.999829i	$0.494110\pi$
$710$	−73.4046	−2.75482
$711$	8.37570	0.314113
$712$	40.7819	1.52837
$713$	22.5693	0.845227
$714$	−12.4474	−0.465833
$715$	−85.4583	−3.19596
$716$	51.0809	1.90898
$717$	11.0253	0.411747
$718$	−14.7589	−0.550797
$719$	5.98634	0.223253	0.111626	−	0.993750i	$-0.464394\pi$
$719$	5.98634	0.223253	0.111626	+	0.993750i	$0.464394\pi$
$720$	−0.833271	−0.0310542
$721$	20.0810	0.747856
$722$	−27.7821	−1.03394
$723$	2.03537	0.0756963
$724$	−5.38118	−0.199990
$725$	32.2183	1.19656
$726$	20.6741	0.767289
$727$	27.5329	1.02114	0.510569	−	0.859837i	$-0.329435\pi$
$727$	27.5329	1.02114	0.510569	+	0.859837i	$0.329435\pi$
$728$	52.1197	1.93169
$729$	22.3474	0.827682
$730$	−13.5615	−0.501934
$731$	4.55873	0.168611
$732$	2.45864	0.0908738
$733$	−3.83694	−0.141720	−0.0708602	−	0.997486i	$-0.522574\pi$
$733$	−3.83694	−0.141720	−0.0708602	+	0.997486i	$0.522574\pi$
$734$	−5.84688	−0.215812
$735$	0.138322	0.00510210
$736$	−22.4290	−0.826743
$737$	50.2238	1.85002
$738$	2.79453	0.102868
$739$	12.9405	0.476025	0.238012	−	0.971262i	$-0.423504\pi$
$739$	12.9405	0.476025	0.238012	+	0.971262i	$0.423504\pi$
$740$	−9.64325	−0.354493
$741$	−44.8400	−1.64724
$742$	−72.2028	−2.65065
$743$	35.9578	1.31916	0.659581	−	0.751633i	$-0.270734\pi$
$743$	35.9578	1.31916	0.659581	+	0.751633i	$0.270734\pi$
$744$	−19.1663	−0.702669
$745$	−43.7649	−1.60342
$746$	46.5510	1.70435
$747$	8.56730	0.313461
$748$	−24.2924	−0.888218
$749$	−3.20525	−0.117117
$750$	−10.7625	−0.392990
$751$	0.180518	0.00658720	0.00329360	−	0.999995i	$-0.498952\pi$
$751$	0.180518	0.00658720	0.00329360	+	0.999995i	$0.498952\pi$
$752$	0.883548	0.0322197
$753$	19.6741	0.716965
$754$	136.093	4.95621
$755$	−29.8675	−1.08699
$756$	47.1871	1.71618
$757$	−13.1591	−0.478277	−0.239139	−	0.970985i	$-0.576865\pi$
$757$	−13.1591	−0.478277	−0.239139	+	0.970985i	$0.576865\pi$
$758$	−34.3411	−1.24732
$759$	21.1453	0.767528
$760$	48.1052	1.74496
$761$	−52.1544	−1.89059	−0.945297	−	0.326210i	$-0.894228\pi$
$761$	−52.1544	−1.89059	−0.945297	+	0.326210i	$0.894228\pi$
$762$	20.9147	0.757661
$763$	13.5211	0.489495
$764$	−46.1213	−1.66861
$765$	7.99448	0.289041
$766$	−48.3385	−1.74654
$767$	34.1810	1.23420
$768$	20.4498	0.737917
$769$	51.5595	1.85928	0.929642	−	0.368465i	$-0.120117\pi$
$769$	51.5595	1.85928	0.929642	+	0.368465i	$0.120117\pi$
$770$	−76.8229	−2.76850
$771$	6.97144	0.251070
$772$	70.8866	2.55127
$773$	8.79414	0.316303	0.158152	−	0.987415i	$-0.449447\pi$
$773$	8.79414	0.316303	0.158152	+	0.987415i	$0.449447\pi$
$774$	−9.59025	−0.344714
$775$	−20.0981	−0.721945
$776$	15.6745	0.562683
$777$	3.14708	0.112901
$778$	85.5373	3.06666
$779$	−4.30174	−0.154126
$780$	77.5427	2.77647
$781$	46.7518	1.67291
$782$	−16.2810	−0.582208
$783$	47.9879	1.71495
$784$	−0.00707019	−0.000252507 0
$785$	22.0664	0.787582
$786$	−14.1871	−0.506036
$787$	36.8748	1.31445	0.657223	−	0.753696i	$-0.271731\pi$
$787$	36.8748	1.31445	0.657223	+	0.753696i	$0.271731\pi$
$788$	−7.99056	−0.284652
$789$	25.3036	0.900833
$790$	35.9089	1.27758
$791$	−34.0116	−1.20931
$792$	19.9036	0.707243
$793$	4.24151	0.150620
$794$	−31.8922	−1.13181
$795$	−41.8377	−1.48383
$796$	−37.0387	−1.31280
$797$	28.2991	1.00240	0.501202	−	0.865330i	$-0.332891\pi$
$797$	28.2991	1.00240	0.501202	+	0.865330i	$0.332891\pi$
$798$	−40.3089	−1.42692
$799$	−8.47684	−0.299889
$800$	19.9731	0.706157
$801$	21.9476	0.775481
$802$	−42.2546	−1.49206
$803$	8.63741	0.304808
$804$	−45.5717	−1.60719
$805$	−31.9693	−1.12677
$806$	−84.8962	−2.99034
$807$	15.2359	0.536330
$808$	14.0822	0.495409
$809$	22.1590	0.779068	0.389534	−	0.921012i	$-0.372636\pi$
$809$	22.1590	0.779068	0.389534	+	0.921012i	$0.372636\pi$
$810$	12.0445	0.423200
$811$	−21.5216	−0.755725	−0.377863	−	0.925862i	$-0.623341\pi$
$811$	−21.5216	−0.755725	−0.377863	+	0.925862i	$0.623341\pi$
$812$	75.9632	2.66578
$813$	4.25083	0.149083
$814$	9.89162	0.346701
$815$	−2.94374	−0.103115
$816$	0.368664	0.0129058
$817$	14.7627	0.516482
$818$	−20.4976	−0.716683
$819$	28.0493	0.980123
$820$	7.43910	0.259784
$821$	−12.2501	−0.427533	−0.213766	−	0.976885i	$-0.568573\pi$
$821$	−12.2501	−0.427533	−0.213766	+	0.976885i	$0.568573\pi$
$822$	45.9299	1.60199
$823$	−39.5115	−1.37729	−0.688643	−	0.725101i	$-0.741793\pi$
$823$	−39.5115	−1.37729	−0.688643	+	0.725101i	$0.741793\pi$
$824$	−22.3052	−0.777040
$825$	−18.8301	−0.655578
$826$	30.7270	1.06913
$827$	−5.78528	−0.201174	−0.100587	−	0.994928i	$-0.532072\pi$
$827$	−5.78528	−0.201174	−0.100587	+	0.994928i	$0.532072\pi$
$828$	21.2666	0.739067
$829$	11.1637	0.387732	0.193866	−	0.981028i	$-0.437897\pi$
$829$	11.1637	0.387732	0.193866	+	0.981028i	$0.437897\pi$
$830$	36.7303	1.27493
$831$	27.1120	0.940505
$832$	86.7882	3.00884
$833$	0.0678320	0.00235024
$834$	−59.5856	−2.06328
$835$	−37.9820	−1.31442
$836$	−78.6670	−2.72076
$837$	−29.9354	−1.03472
$838$	−19.2854	−0.666204
$839$	−37.9784	−1.31116	−0.655580	−	0.755126i	$-0.727576\pi$
$839$	−37.9784	−1.31116	−0.655580	+	0.755126i	$0.727576\pi$
$840$	27.1489	0.936726
$841$	48.2523	1.66387
$842$	67.5608	2.32830
$843$	15.4513	0.532172
$844$	−3.16670	−0.109002
$845$	95.5038	3.28543
$846$	17.8328	0.613105
$847$	19.9077	0.684036
$848$	2.13848	0.0734358
$849$	31.2292	1.07178
$850$	14.4983	0.497289
$851$	4.11633	0.141106
$852$	−42.4214	−1.45333
$853$	−22.3239	−0.764356	−0.382178	−	0.924089i	$-0.624826\pi$
$853$	−22.3239	−0.764356	−0.382178	+	0.924089i	$0.624826\pi$
$854$	3.81291	0.130475
$855$	25.8888	0.885380
$856$	3.56028	0.121688
$857$	−12.5551	−0.428872	−0.214436	−	0.976738i	$-0.568791\pi$
$857$	−12.5551	−0.428872	−0.214436	+	0.976738i	$0.568791\pi$
$858$	−79.5398	−2.71545
$859$	1.95037	0.0665457	0.0332729	−	0.999446i	$-0.489407\pi$
$859$	1.95037	0.0665457	0.0332729	+	0.999446i	$0.489407\pi$
$860$	−25.5295	−0.870548
$861$	−2.42775	−0.0827376
$862$	−86.6194	−2.95027
$863$	15.1992	0.517387	0.258694	−	0.965959i	$-0.416708\pi$
$863$	15.1992	0.517387	0.258694	+	0.965959i	$0.416708\pi$
$864$	29.7493	1.01209
$865$	−40.5843	−1.37991
$866$	32.0963	1.09068
$867$	16.7414	0.568566
$868$	−47.3866	−1.60841
$869$	−22.8706	−0.775831
$870$	70.8901	2.40340
$871$	−78.6179	−2.66387
$872$	−15.0187	−0.508597
$873$	8.43558	0.285501
$874$	−52.7234	−1.78340
$875$	−10.3635	−0.350349
$876$	−7.83737	−0.264800
$877$	9.08254	0.306695	0.153348	−	0.988172i	$-0.450995\pi$
$877$	9.08254	0.306695	0.153348	+	0.988172i	$0.450995\pi$
$878$	−8.37251	−0.282559
$879$	−5.77140	−0.194665
$880$	2.27532	0.0767010
$881$	27.2737	0.918874	0.459437	−	0.888210i	$-0.348051\pi$
$881$	27.2737	0.918874	0.459437	+	0.888210i	$0.348051\pi$
$882$	−0.142699	−0.00480492
$883$	29.7002	0.999490	0.499745	−	0.866173i	$-0.333427\pi$
$883$	29.7002	0.999490	0.499745	+	0.866173i	$0.333427\pi$
$884$	38.0262	1.27896
$885$	17.8047	0.598498
$886$	38.8681	1.30580
$887$	46.6539	1.56648	0.783242	−	0.621717i	$-0.213564\pi$
$887$	46.6539	1.56648	0.783242	+	0.621717i	$0.213564\pi$
$888$	−3.49566	−0.117307
$889$	20.1394	0.675453
$890$	94.0953	3.15408
$891$	−7.67120	−0.256995
$892$	−31.7857	−1.06426
$893$	−27.4509	−0.918609
$894$	−40.7339	−1.36234
$895$	45.9023	1.53435
$896$	49.2673	1.64591
$897$	−33.0999	−1.10517
$898$	−2.50497	−0.0835919
$899$	−48.1908	−1.60725
$900$	−18.9381	−0.631269
$901$	−20.5168	−0.683514
$902$	−7.63069	−0.254074
$903$	8.33155	0.277257
$904$	37.7788	1.25650
$905$	−4.83564	−0.160742
$906$	−27.7990	−0.923560
$907$	22.2362	0.738341	0.369171	−	0.929362i	$-0.379642\pi$
$907$	22.2362	0.738341	0.369171	+	0.929362i	$0.379642\pi$
$908$	−31.8865	−1.05819
$909$	7.57861	0.251367
$910$	120.255	3.98641
$911$	54.0357	1.79028	0.895141	−	0.445784i	$-0.147075\pi$
$911$	54.0357	1.79028	0.895141	+	0.445784i	$0.147075\pi$
$912$	1.19386	0.0395326
$913$	−23.3938	−0.774221
$914$	19.2286	0.636024
$915$	2.20938	0.0730398
$916$	−3.35351	−0.110803
$917$	−13.6611	−0.451130
$918$	21.5947	0.712733
$919$	−14.1375	−0.466352	−0.233176	−	0.972435i	$-0.574912\pi$
$919$	−14.1375	−0.466352	−0.233176	+	0.972435i	$0.574912\pi$
$920$	35.5103	1.17074
$921$	17.0645	0.562294
$922$	−42.5144	−1.40014
$923$	−73.1831	−2.40885
$924$	−44.3969	−1.46055
$925$	−3.66561	−0.120525
$926$	41.0694	1.34963
$927$	−12.0040	−0.394264
$928$	47.8912	1.57210
$929$	6.55141	0.214945	0.107472	−	0.994208i	$-0.465724\pi$
$929$	6.55141	0.214945	0.107472	+	0.994208i	$0.465724\pi$
$930$	−44.2220	−1.45010
$931$	0.219663	0.00719917
$932$	76.2289	2.49696
$933$	−19.7573	−0.646824
$934$	72.7173	2.37938
$935$	−21.8296	−0.713905
$936$	−31.1561	−1.01837
$937$	−20.0870	−0.656213	−0.328107	−	0.944641i	$-0.606410\pi$
$937$	−20.0870	−0.656213	−0.328107	+	0.944641i	$0.606410\pi$
$938$	−70.6737	−2.30758
$939$	38.4055	1.25332
$940$	47.4714	1.54835
$941$	−34.8929	−1.13748	−0.568738	−	0.822519i	$-0.692568\pi$
$941$	−34.8929	−1.13748	−0.568738	+	0.822519i	$0.692568\pi$
$942$	20.5381	0.669169
$943$	−3.17546	−0.103407
$944$	−0.910065	−0.0296201
$945$	42.4033	1.37938
$946$	26.1870	0.851413
$947$	50.5705	1.64332	0.821660	−	0.569979i	$-0.193048\pi$
$947$	50.5705	1.64332	0.821660	+	0.569979i	$0.193048\pi$
$948$	20.7522	0.673999
$949$	−13.5206	−0.438897
$950$	46.9505	1.52328
$951$	4.87207	0.157988
$952$	13.3136	0.431495
$953$	−12.6234	−0.408911	−0.204456	−	0.978876i	$-0.565542\pi$
$953$	−12.6234	−0.408911	−0.204456	+	0.978876i	$0.565542\pi$
$954$	43.1614	1.39740
$955$	−41.4455	−1.34114
$956$	−30.2782	−0.979266
$957$	−45.1503	−1.45950
$958$	62.3714	2.01513
$959$	44.2272	1.42817
$960$	45.2075	1.45907
$961$	−0.938054	−0.0302598
$962$	−15.4839	−0.499220
$963$	1.91604	0.0617435
$964$	−5.58964	−0.180030
$965$	63.7001	2.05058
$966$	−29.7552	−0.957359
$967$	38.5842	1.24078	0.620391	−	0.784292i	$-0.286974\pi$
$967$	38.5842	1.24078	0.620391	+	0.784292i	$0.286974\pi$
$968$	−22.1127	−0.710730
$969$	−11.4540	−0.367956
$970$	36.1656	1.16121
$971$	36.1469	1.16001	0.580005	−	0.814613i	$-0.303051\pi$
$971$	36.1469	1.16001	0.580005	+	0.814613i	$0.303051\pi$
$972$	−46.6957	−1.49777
$973$	−57.3766	−1.83941
$974$	−68.3957	−2.19154
$975$	29.4757	0.943977
$976$	−0.112930	−0.00361479
$977$	−10.1059	−0.323316	−0.161658	−	0.986847i	$-0.551684\pi$
$977$	−10.1059	−0.323316	−0.161658	+	0.986847i	$0.551684\pi$
$978$	−2.73987	−0.0876114
$979$	−59.9299	−1.91537
$980$	−0.379868	−0.0121344
$981$	−8.08263	−0.258058
$982$	−72.5104	−2.31390
$983$	−54.4293	−1.73602	−0.868012	−	0.496543i	$-0.834602\pi$
$983$	−54.4293	−1.73602	−0.868012	+	0.496543i	$0.834602\pi$
$984$	2.69666	0.0859663
$985$	−7.18048	−0.228789
$986$	34.7638	1.10711
$987$	−15.4923	−0.493125
$988$	123.142	3.91766
$989$	10.8975	0.346521
$990$	45.9232	1.45953
$991$	24.4730	0.777410	0.388705	−	0.921362i	$-0.372923\pi$
$991$	24.4730	0.777410	0.388705	+	0.921362i	$0.372923\pi$
$992$	−29.8750	−0.948533
$993$	18.0314	0.572210
$994$	−65.7881	−2.08667
$995$	−33.2837	−1.05516
$996$	21.2269	0.672600
$997$	−1.94965	−0.0617461	−0.0308730	−	0.999523i	$-0.509829\pi$
$997$	−1.94965	−0.0617461	−0.0308730	+	0.999523i	$0.509829\pi$
$998$	68.2524	2.16049
$999$	−5.45979	−0.172740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.14	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.14	✓	110	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29692 q^{2} -1.19284 q^{3} +3.27585 q^{4} +2.94374 q^{5} +2.73987 q^{6} +2.63830 q^{7} -2.93052 q^{8} -1.57712 q^{9} +O(q^{10})\)	\(q-2.29692 q^{2} -1.19284 q^{3} +3.27585 q^{4} +2.94374 q^{5} +2.73987 q^{6} +2.63830 q^{7} -2.93052 q^{8} -1.57712 q^{9} -6.76154 q^{10} +4.30647 q^{11} -3.90758 q^{12} -6.74114 q^{13} -6.05996 q^{14} -3.51143 q^{15} +0.179482 q^{16} -1.72197 q^{17} +3.62252 q^{18} -5.57632 q^{19} +9.64325 q^{20} -3.14708 q^{21} -9.89162 q^{22} -4.11633 q^{23} +3.49566 q^{24} +3.66561 q^{25} +15.4839 q^{26} +5.45979 q^{27} +8.64266 q^{28} +8.78933 q^{29} +8.06547 q^{30} -5.48288 q^{31} +5.44879 q^{32} -5.13695 q^{33} +3.95523 q^{34} +7.76646 q^{35} -5.16641 q^{36} -1.00000 q^{37} +12.8084 q^{38} +8.04114 q^{39} -8.62670 q^{40} +0.771431 q^{41} +7.22859 q^{42} -2.64739 q^{43} +14.1073 q^{44} -4.64264 q^{45} +9.45488 q^{46} +4.92276 q^{47} -0.214094 q^{48} -0.0393921 q^{49} -8.41962 q^{50} +2.05404 q^{51} -22.0830 q^{52} +11.9147 q^{53} -12.5407 q^{54} +12.6771 q^{55} -7.73158 q^{56} +6.65168 q^{57} -20.1884 q^{58} -5.07050 q^{59} -11.5029 q^{60} -0.629197 q^{61} +12.5937 q^{62} -4.16091 q^{63} -12.8744 q^{64} -19.8442 q^{65} +11.7992 q^{66} +11.6624 q^{67} -5.64091 q^{68} +4.91014 q^{69} -17.8390 q^{70} +10.8562 q^{71} +4.62179 q^{72} +2.00568 q^{73} +2.29692 q^{74} -4.37251 q^{75} -18.2672 q^{76} +11.3617 q^{77} -18.4699 q^{78} -5.31075 q^{79} +0.528349 q^{80} -1.78132 q^{81} -1.77192 q^{82} -5.43224 q^{83} -10.3093 q^{84} -5.06903 q^{85} +6.08085 q^{86} -10.4843 q^{87} -12.6202 q^{88} -13.9163 q^{89} +10.6638 q^{90} -17.7851 q^{91} -13.4845 q^{92} +6.54022 q^{93} -11.3072 q^{94} -16.4152 q^{95} -6.49956 q^{96} -5.34872 q^{97} +0.0904806 q^{98} -6.79182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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