LMFDB - Embedded newform 6037.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46237 q^{2} -0.199276 q^{3} +4.06325 q^{4} -0.688498 q^{5} +0.490692 q^{6} +0.363231 q^{7} -5.08049 q^{8} -2.96029 q^{9} +O(q^{10})$	\(q-2.46237 q^{2} -0.199276 q^{3} +4.06325 q^{4} -0.688498 q^{5} +0.490692 q^{6} +0.363231 q^{7} -5.08049 q^{8} -2.96029 q^{9} +1.69534 q^{10} +0.608305 q^{11} -0.809710 q^{12} +1.23967 q^{13} -0.894407 q^{14} +0.137201 q^{15} +4.38352 q^{16} +0.714168 q^{17} +7.28932 q^{18} -3.65294 q^{19} -2.79754 q^{20} -0.0723833 q^{21} -1.49787 q^{22} -8.98401 q^{23} +1.01242 q^{24} -4.52597 q^{25} -3.05251 q^{26} +1.18774 q^{27} +1.47590 q^{28} -4.08453 q^{29} -0.337840 q^{30} -2.25338 q^{31} -0.632868 q^{32} -0.121221 q^{33} -1.75854 q^{34} -0.250084 q^{35} -12.0284 q^{36} -1.99307 q^{37} +8.99489 q^{38} -0.247036 q^{39} +3.49791 q^{40} +1.90939 q^{41} +0.178234 q^{42} -9.31067 q^{43} +2.47170 q^{44} +2.03815 q^{45} +22.1219 q^{46} +10.6828 q^{47} -0.873533 q^{48} -6.86806 q^{49} +11.1446 q^{50} -0.142317 q^{51} +5.03708 q^{52} +7.83367 q^{53} -2.92466 q^{54} -0.418817 q^{55} -1.84539 q^{56} +0.727945 q^{57} +10.0576 q^{58} +2.96694 q^{59} +0.557484 q^{60} +4.72291 q^{61} +5.54865 q^{62} -1.07527 q^{63} -7.20869 q^{64} -0.853508 q^{65} +0.298490 q^{66} -5.88429 q^{67} +2.90185 q^{68} +1.79030 q^{69} +0.615798 q^{70} -5.19133 q^{71} +15.0397 q^{72} -16.0982 q^{73} +4.90767 q^{74} +0.901919 q^{75} -14.8428 q^{76} +0.220955 q^{77} +0.608294 q^{78} +14.5062 q^{79} -3.01805 q^{80} +8.64418 q^{81} -4.70161 q^{82} -12.9259 q^{83} -0.294112 q^{84} -0.491704 q^{85} +22.9263 q^{86} +0.813951 q^{87} -3.09049 q^{88} +11.5823 q^{89} -5.01868 q^{90} +0.450285 q^{91} -36.5043 q^{92} +0.449045 q^{93} -26.3051 q^{94} +2.51504 q^{95} +0.126116 q^{96} -13.6450 q^{97} +16.9117 q^{98} -1.80076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.46237	−1.74116	−0.870578	−	0.492030i	$-0.836255\pi$
$2$	−2.46237	−1.74116	−0.870578	+	0.492030i	$0.836255\pi$
$3$	−0.199276	−0.115052	−0.0575261	−	0.998344i	$-0.518321\pi$
$3$	−0.199276	−0.115052	−0.0575261	+	0.998344i	$0.518321\pi$
$4$	4.06325	2.03163
$5$	−0.688498	−0.307906	−0.153953	−	0.988078i	$-0.549200\pi$
$5$	−0.688498	−0.307906	−0.153953	+	0.988078i	$0.549200\pi$
$6$	0.490692	0.200324
$7$	0.363231	0.137288	0.0686441	−	0.997641i	$-0.478133\pi$
$7$	0.363231	0.137288	0.0686441	+	0.997641i	$0.478133\pi$
$8$	−5.08049	−1.79622
$9$	−2.96029	−0.986763
$10$	1.69534	0.536112
$11$	0.608305	0.183411	0.0917054	−	0.995786i	$-0.470768\pi$
$11$	0.608305	0.183411	0.0917054	+	0.995786i	$0.470768\pi$
$12$	−0.809710	−0.233743
$13$	1.23967	0.343821	0.171911	−	0.985113i	$-0.445006\pi$
$13$	1.23967	0.343821	0.171911	+	0.985113i	$0.445006\pi$
$14$	−0.894407	−0.239040
$15$	0.137201	0.0354253
$16$	4.38352	1.09588
$17$	0.714168	0.173211	0.0866056	−	0.996243i	$-0.472398\pi$
$17$	0.714168	0.173211	0.0866056	+	0.996243i	$0.472398\pi$
$18$	7.28932	1.71811
$19$	−3.65294	−0.838042	−0.419021	−	0.907976i	$-0.637627\pi$
$19$	−3.65294	−0.838042	−0.419021	+	0.907976i	$0.637627\pi$
$20$	−2.79754	−0.625550
$21$	−0.0723833	−0.0157953
$22$	−1.49787	−0.319347
$23$	−8.98401	−1.87330	−0.936648	−	0.350273i	$-0.886089\pi$
$23$	−8.98401	−1.87330	−0.936648	+	0.350273i	$0.886089\pi$
$24$	1.01242	0.206660
$25$	−4.52597	−0.905194
$26$	−3.05251	−0.598647
$27$	1.18774	0.228582
$28$	1.47590	0.278919
$29$	−4.08453	−0.758479	−0.379239	−	0.925299i	$-0.623814\pi$
$29$	−4.08453	−0.758479	−0.379239	+	0.925299i	$0.623814\pi$
$30$	−0.337840	−0.0616809
$31$	−2.25338	−0.404719	−0.202359	−	0.979311i	$-0.564861\pi$
$31$	−2.25338	−0.404719	−0.202359	+	0.979311i	$0.564861\pi$
$32$	−0.632868	−0.111876
$33$	−0.121221	−0.0211018
$34$	−1.75854	−0.301588
$35$	−0.250084	−0.0422719
$36$	−12.0284	−2.00473
$37$	−1.99307	−0.327659	−0.163829	−	0.986489i	$-0.552385\pi$
$37$	−1.99307	−0.327659	−0.163829	+	0.986489i	$0.552385\pi$
$38$	8.99489	1.45916
$39$	−0.247036	−0.0395574
$40$	3.49791	0.553068
$41$	1.90939	0.298196	0.149098	−	0.988822i	$-0.452363\pi$
$41$	1.90939	0.298196	0.149098	+	0.988822i	$0.452363\pi$
$42$	0.178234	0.0275021
$43$	−9.31067	−1.41986	−0.709932	−	0.704270i	$-0.751274\pi$
$43$	−9.31067	−1.41986	−0.709932	+	0.704270i	$0.751274\pi$
$44$	2.47170	0.372622
$45$	2.03815	0.303830
$46$	22.1219	3.26170
$47$	10.6828	1.55825	0.779126	−	0.626867i	$-0.215663\pi$
$47$	10.6828	1.55825	0.779126	+	0.626867i	$0.215663\pi$
$48$	−0.873533	−0.126084
$49$	−6.86806	−0.981152
$50$	11.1446	1.57608
$51$	−0.142317	−0.0199283
$52$	5.03708	0.698517
$53$	7.83367	1.07604	0.538019	−	0.842933i	$-0.319173\pi$
$53$	7.83367	1.07604	0.538019	+	0.842933i	$0.319173\pi$
$54$	−2.92466	−0.397996
$55$	−0.418817	−0.0564732
$56$	−1.84539	−0.246601
$57$	0.727945	0.0964187
$58$	10.0576	1.32063
$59$	2.96694	0.386262	0.193131	−	0.981173i	$-0.438136\pi$
$59$	2.96694	0.386262	0.193131	+	0.981173i	$0.438136\pi$
$60$	0.557484	0.0719709
$61$	4.72291	0.604707	0.302353	−	0.953196i	$-0.402228\pi$
$61$	4.72291	0.604707	0.302353	+	0.953196i	$0.402228\pi$
$62$	5.54865	0.704679
$63$	−1.07527	−0.135471
$64$	−7.20869	−0.901087
$65$	−0.853508	−0.105865
$66$	0.298490	0.0367416
$67$	−5.88429	−0.718880	−0.359440	−	0.933168i	$-0.617032\pi$
$67$	−5.88429	−0.718880	−0.359440	+	0.933168i	$0.617032\pi$
$68$	2.90185	0.351901
$69$	1.79030	0.215527
$70$	0.615798	0.0736019
$71$	−5.19133	−0.616098	−0.308049	−	0.951370i	$-0.599676\pi$
$71$	−5.19133	−0.616098	−0.308049	+	0.951370i	$0.599676\pi$
$72$	15.0397	1.77245
$73$	−16.0982	−1.88415	−0.942076	−	0.335398i	$-0.891129\pi$
$73$	−16.0982	−1.88415	−0.942076	+	0.335398i	$0.891129\pi$
$74$	4.90767	0.570505
$75$	0.901919	0.104145
$76$	−14.8428	−1.70259
$77$	0.220955	0.0251802
$78$	0.608294	0.0688757
$79$	14.5062	1.63208	0.816038	−	0.577998i	$-0.196166\pi$
$79$	14.5062	1.63208	0.816038	+	0.577998i	$0.196166\pi$
$80$	−3.01805	−0.337428
$81$	8.64418	0.960464
$82$	−4.70161	−0.519206
$83$	−12.9259	−1.41881	−0.709404	−	0.704803i	$-0.751036\pi$
$83$	−12.9259	−1.41881	−0.709404	+	0.704803i	$0.751036\pi$
$84$	−0.294112	−0.0320902
$85$	−0.491704	−0.0533328
$86$	22.9263	2.47221
$87$	0.813951	0.0872647
$88$	−3.09049	−0.329447
$89$	11.5823	1.22772	0.613859	−	0.789416i	$-0.289616\pi$
$89$	11.5823	1.22772	0.613859	+	0.789416i	$0.289616\pi$
$90$	−5.01868	−0.529016
$91$	0.450285	0.0472027
$92$	−36.5043	−3.80584
$93$	0.449045	0.0465638
$94$	−26.3051	−2.71316
$95$	2.51504	0.258038
$96$	0.126116	0.0128716
$97$	−13.6450	−1.38544	−0.692722	−	0.721204i	$-0.743589\pi$
$97$	−13.6450	−1.38544	−0.692722	+	0.721204i	$0.743589\pi$
$98$	16.9117	1.70834
$99$	−1.80076	−0.180983
$100$	−18.3902	−1.83902
$101$	8.25853	0.821755	0.410877	−	0.911691i	$-0.365222\pi$
$101$	8.25853	0.821755	0.410877	+	0.911691i	$0.365222\pi$
$102$	0.350436	0.0346984
$103$	11.8042	1.16310	0.581551	−	0.813510i	$-0.302446\pi$
$103$	11.8042	1.16310	0.581551	+	0.813510i	$0.302446\pi$
$104$	−6.29811	−0.617580
$105$	0.0498358	0.00486347
$106$	−19.2894	−1.87355
$107$	5.57492	0.538948	0.269474	−	0.963008i	$-0.413150\pi$
$107$	5.57492	0.538948	0.269474	+	0.963008i	$0.413150\pi$
$108$	4.82611	0.464392
$109$	−10.2275	−0.979618	−0.489809	−	0.871830i	$-0.662933\pi$
$109$	−10.2275	−0.979618	−0.489809	+	0.871830i	$0.662933\pi$
$110$	1.03128	0.0983288
$111$	0.397172	0.0376979
$112$	1.59223	0.150452
$113$	0.255742	0.0240581	0.0120291	−	0.999928i	$-0.496171\pi$
$113$	0.255742	0.0240581	0.0120291	+	0.999928i	$0.496171\pi$
$114$	−1.79247	−0.167880
$115$	6.18548	0.576799
$116$	−16.5965	−1.54095
$117$	−3.66977	−0.339270
$118$	−7.30569	−0.672543
$119$	0.259408	0.0237799
$120$	−0.697051	−0.0636317
$121$	−10.6300	−0.966360
$122$	−11.6295	−1.05289
$123$	−0.380495	−0.0343081
$124$	−9.15605	−0.822238
$125$	6.55862	0.586620
$126$	2.64770	0.235876
$127$	14.6336	1.29852	0.649261	−	0.760566i	$-0.275078\pi$
$127$	14.6336	1.29852	0.649261	+	0.760566i	$0.275078\pi$
$128$	19.0162	1.68081
$129$	1.85540	0.163359
$130$	2.10165	0.184327
$131$	2.22423	0.194331	0.0971657	−	0.995268i	$-0.469022\pi$
$131$	2.22423	0.194331	0.0971657	+	0.995268i	$0.469022\pi$
$132$	−0.492551	−0.0428710
$133$	−1.32686	−0.115053
$134$	14.4893	1.25168
$135$	−0.817760	−0.0703816
$136$	−3.62832	−0.311126
$137$	3.75673	0.320959	0.160479	−	0.987039i	$-0.448696\pi$
$137$	3.75673	0.320959	0.160479	+	0.987039i	$0.448696\pi$
$138$	−4.40838	−0.375266
$139$	0.575436	0.0488079	0.0244039	−	0.999702i	$-0.492231\pi$
$139$	0.575436	0.0488079	0.0244039	+	0.999702i	$0.492231\pi$
$140$	−1.01615	−0.0858807
$141$	−2.12884	−0.179280
$142$	12.7830	1.07272
$143$	0.754094	0.0630605
$144$	−12.9765	−1.08137
$145$	2.81219	0.233540
$146$	39.6397	3.28061
$147$	1.36864	0.112884
$148$	−8.09835	−0.665680
$149$	8.71682	0.714109	0.357055	−	0.934083i	$-0.383781\pi$
$149$	8.71682	0.714109	0.357055	+	0.934083i	$0.383781\pi$
$150$	−2.22086	−0.181332
$151$	1.59710	0.129970	0.0649851	−	0.997886i	$-0.479300\pi$
$151$	1.59710	0.129970	0.0649851	+	0.997886i	$0.479300\pi$
$152$	18.5587	1.50531
$153$	−2.11414	−0.170918
$154$	−0.544072	−0.0438426
$155$	1.55145	0.124615
$156$	−1.00377	−0.0803659
$157$	9.73833	0.777204	0.388602	−	0.921406i	$-0.372958\pi$
$157$	9.73833	0.777204	0.388602	+	0.921406i	$0.372958\pi$
$158$	−35.7196	−2.84170
$159$	−1.56107	−0.123801
$160$	0.435729	0.0344474
$161$	−3.26327	−0.257182
$162$	−21.2851	−1.67232
$163$	6.99321	0.547751	0.273875	−	0.961765i	$-0.411694\pi$
$163$	6.99321	0.547751	0.273875	+	0.961765i	$0.411694\pi$
$164$	7.75832	0.605823
$165$	0.0834603	0.00649738
$166$	31.8284	2.47037
$167$	−1.83769	−0.142205	−0.0711025	−	0.997469i	$-0.522652\pi$
$167$	−1.83769	−0.142205	−0.0711025	+	0.997469i	$0.522652\pi$
$168$	0.367743	0.0283720
$169$	−11.4632	−0.881787
$170$	1.21076	0.0928607
$171$	10.8138	0.826949
$172$	−37.8316	−2.88463
$173$	13.0373	0.991204	0.495602	−	0.868550i	$-0.334948\pi$
$173$	13.0373	0.991204	0.495602	+	0.868550i	$0.334948\pi$
$174$	−2.00425	−0.151942
$175$	−1.64397	−0.124273
$176$	2.66652	0.200996
$177$	−0.591240	−0.0444403
$178$	−28.5198	−2.13765
$179$	−12.8342	−0.959269	−0.479635	−	0.877468i	$-0.659231\pi$
$179$	−12.8342	−0.959269	−0.479635	+	0.877468i	$0.659231\pi$
$180$	8.28154	0.617269
$181$	8.53462	0.634373	0.317187	−	0.948363i	$-0.397262\pi$
$181$	8.53462	0.634373	0.317187	+	0.948363i	$0.397262\pi$
$182$	−1.10877	−0.0821872
$183$	−0.941164	−0.0695729
$184$	45.6432	3.36486
$185$	1.37223	0.100888
$186$	−1.10571	−0.0810749
$187$	0.434432	0.0317688
$188$	43.4071	3.16579
$189$	0.431425	0.0313816
$190$	−6.19297	−0.449285
$191$	13.3780	0.968000	0.484000	−	0.875068i	$-0.339184\pi$
$191$	13.3780	0.968000	0.484000	+	0.875068i	$0.339184\pi$
$192$	1.43652	0.103672
$193$	17.5520	1.26342	0.631711	−	0.775204i	$-0.282353\pi$
$193$	17.5520	1.26342	0.631711	+	0.775204i	$0.282353\pi$
$194$	33.5991	2.41228
$195$	0.170084	0.0121800
$196$	−27.9067	−1.99333
$197$	−4.38499	−0.312417	−0.156209	−	0.987724i	$-0.549927\pi$
$197$	−4.38499	−0.312417	−0.156209	+	0.987724i	$0.549927\pi$
$198$	4.43413	0.315120
$199$	−3.34431	−0.237072	−0.118536	−	0.992950i	$-0.537820\pi$
$199$	−3.34431	−0.237072	−0.118536	+	0.992950i	$0.537820\pi$
$200$	22.9941	1.62593
$201$	1.17260	0.0827088
$202$	−20.3355	−1.43080
$203$	−1.48363	−0.104130
$204$	−0.578270	−0.0404870
$205$	−1.31461	−0.0918162
$206$	−29.0663	−2.02514
$207$	26.5953	1.84850
$208$	5.43410	0.376787
$209$	−2.22210	−0.153706
$210$	−0.122714	−0.00846807
$211$	−21.5889	−1.48624	−0.743121	−	0.669157i	$-0.766655\pi$
$211$	−21.5889	−1.48624	−0.743121	+	0.669157i	$0.766655\pi$
$212$	31.8302	2.18611
$213$	1.03451	0.0708835
$214$	−13.7275	−0.938393
$215$	6.41038	0.437185
$216$	−6.03432	−0.410584
$217$	−0.818497	−0.0555632
$218$	25.1839	1.70567
$219$	3.20799	0.216776
$220$	−1.70176	−0.114733
$221$	0.885330	0.0595537
$222$	−0.977983	−0.0656379
$223$	12.1800	0.815636	0.407818	−	0.913063i	$-0.366290\pi$
$223$	12.1800	0.815636	0.407818	+	0.913063i	$0.366290\pi$
$224$	−0.229877	−0.0153593
$225$	13.3982	0.893212
$226$	−0.629730	−0.0418890
$227$	−16.3201	−1.08321	−0.541603	−	0.840635i	$-0.682182\pi$
$227$	−16.3201	−1.08321	−0.541603	+	0.840635i	$0.682182\pi$
$228$	2.95783	0.195887
$229$	−1.05865	−0.0699574	−0.0349787	−	0.999388i	$-0.511136\pi$
$229$	−1.05865	−0.0699574	−0.0349787	+	0.999388i	$0.511136\pi$
$230$	−15.2309	−1.00430
$231$	−0.0440311	−0.00289703
$232$	20.7514	1.36240
$233$	−18.7423	−1.22785	−0.613923	−	0.789366i	$-0.710410\pi$
$233$	−18.7423	−1.22785	−0.613923	+	0.789366i	$0.710410\pi$
$234$	9.03632	0.590723
$235$	−7.35512	−0.479795
$236$	12.0554	0.784741
$237$	−2.89075	−0.187774
$238$	−0.638757	−0.0414045
$239$	−8.37904	−0.541995	−0.270997	−	0.962580i	$-0.587354\pi$
$239$	−8.37904	−0.541995	−0.270997	+	0.962580i	$0.587354\pi$
$240$	0.601426	0.0388219
$241$	−7.94408	−0.511723	−0.255862	−	0.966713i	$-0.582359\pi$
$241$	−7.94408	−0.511723	−0.255862	+	0.966713i	$0.582359\pi$
$242$	26.1749	1.68259
$243$	−5.28581	−0.339085
$244$	19.1904	1.22854
$245$	4.72865	0.302102
$246$	0.936919	0.0597358
$247$	−4.52843	−0.288137
$248$	11.4483	0.726966
$249$	2.57584	0.163237
$250$	−16.1497	−1.02140
$251$	15.6797	0.989693	0.494847	−	0.868980i	$-0.335224\pi$
$251$	15.6797	0.989693	0.494847	+	0.868980i	$0.335224\pi$
$252$	−4.36909	−0.275227
$253$	−5.46501	−0.343583
$254$	−36.0333	−2.26093
$255$	0.0979849	0.00613605
$256$	−32.4075	−2.02547
$257$	−2.31076	−0.144141	−0.0720707	−	0.997400i	$-0.522961\pi$
$257$	−2.31076	−0.144141	−0.0720707	+	0.997400i	$0.522961\pi$
$258$	−4.56867	−0.284433
$259$	−0.723944	−0.0449837
$260$	−3.46802	−0.215077
$261$	12.0914	0.748439
$262$	−5.47686	−0.338362
$263$	0.559168	0.0344798	0.0172399	−	0.999851i	$-0.494512\pi$
$263$	0.559168	0.0344798	0.0172399	+	0.999851i	$0.494512\pi$
$264$	0.615861	0.0379036
$265$	−5.39347	−0.331318
$266$	3.26722	0.200326
$267$	−2.30807	−0.141252
$268$	−23.9094	−1.46050
$269$	−11.9395	−0.727965	−0.363982	−	0.931406i	$-0.618583\pi$
$269$	−11.9395	−0.727965	−0.363982	+	0.931406i	$0.618583\pi$
$270$	2.01363	0.122545
$271$	−6.23189	−0.378560	−0.189280	−	0.981923i	$-0.560615\pi$
$271$	−6.23189	−0.378560	−0.189280	+	0.981923i	$0.560615\pi$
$272$	3.13057	0.189819
$273$	−0.0897311	−0.00543077
$274$	−9.25044	−0.558839
$275$	−2.75317	−0.166022
$276$	7.27445	0.437870
$277$	−26.6442	−1.60089	−0.800447	−	0.599404i	$-0.795404\pi$
$277$	−26.6442	−1.60089	−0.800447	+	0.599404i	$0.795404\pi$
$278$	−1.41694	−0.0849821
$279$	6.67065	0.399362
$280$	1.27055	0.0759297
$281$	11.9020	0.710012	0.355006	−	0.934864i	$-0.384479\pi$
$281$	11.9020	0.710012	0.355006	+	0.934864i	$0.384479\pi$
$282$	5.24198	0.312155
$283$	9.26386	0.550679	0.275340	−	0.961347i	$-0.411210\pi$
$283$	9.26386	0.550679	0.275340	+	0.961347i	$0.411210\pi$
$284$	−21.0937	−1.25168
$285$	−0.501189	−0.0296879
$286$	−1.85686	−0.109798
$287$	0.693547	0.0409388
$288$	1.87347	0.110395
$289$	−16.4900	−0.969998
$290$	−6.92466	−0.406630
$291$	2.71914	0.159399
$292$	−65.4111	−3.82790
$293$	14.7360	0.860886	0.430443	−	0.902618i	$-0.358357\pi$
$293$	14.7360	0.860886	0.430443	+	0.902618i	$0.358357\pi$
$294$	−3.37010	−0.196548
$295$	−2.04273	−0.118932
$296$	10.1258	0.588548
$297$	0.722511	0.0419243
$298$	−21.4640	−1.24338
$299$	−11.1372	−0.644079
$300$	3.66473	0.211583
$301$	−3.38192	−0.194931
$302$	−3.93265	−0.226299
$303$	−1.64573	−0.0945447
$304$	−16.0128	−0.918395
$305$	−3.25172	−0.186193
$306$	5.20580	0.297596
$307$	29.3661	1.67601	0.838006	−	0.545661i	$-0.183721\pi$
$307$	29.3661	1.67601	0.838006	+	0.545661i	$0.183721\pi$
$308$	0.897796	0.0511567
$309$	−2.35230	−0.133817
$310$	−3.82024	−0.216975
$311$	−19.6726	−1.11553	−0.557764	−	0.829999i	$-0.688341\pi$
$311$	−19.6726	−1.11553	−0.557764	+	0.829999i	$0.688341\pi$
$312$	1.25506	0.0710540
$313$	−7.33952	−0.414854	−0.207427	−	0.978250i	$-0.566509\pi$
$313$	−7.33952	−0.414854	−0.207427	+	0.978250i	$0.566509\pi$
$314$	−23.9794	−1.35323
$315$	0.740320	0.0417123
$316$	58.9424	3.31577
$317$	16.3228	0.916781	0.458390	−	0.888751i	$-0.348426\pi$
$317$	16.3228	0.916781	0.458390	+	0.888751i	$0.348426\pi$
$318$	3.84392	0.215556
$319$	−2.48464	−0.139113
$320$	4.96317	0.277450
$321$	−1.11095	−0.0620072
$322$	8.03536	0.447793
$323$	−2.60882	−0.145158
$324$	35.1235	1.95130
$325$	−5.61069	−0.311225
$326$	−17.2199	−0.953720
$327$	2.03810	0.112707
$328$	−9.70061	−0.535627
$329$	3.88034	0.213930
$330$	−0.205510	−0.0113129
$331$	4.51222	0.248014	0.124007	−	0.992281i	$-0.460425\pi$
$331$	4.51222	0.248014	0.124007	+	0.992281i	$0.460425\pi$
$332$	−52.5214	−2.88249
$333$	5.90006	0.323321
$334$	4.52508	0.247601
$335$	4.05132	0.221347
$336$	−0.317294	−0.0173098
$337$	2.41213	0.131397	0.0656986	−	0.997840i	$-0.479072\pi$
$337$	2.41213	0.131397	0.0656986	+	0.997840i	$0.479072\pi$
$338$	28.2267	1.53533
$339$	−0.0509633	−0.00276794
$340$	−1.99792	−0.108352
$341$	−1.37074	−0.0742298
$342$	−26.6275	−1.43985
$343$	−5.03731	−0.271989
$344$	47.3028	2.55039
$345$	−1.23262	−0.0663620
$346$	−32.1025	−1.72584
$347$	−4.17830	−0.224303	−0.112151	−	0.993691i	$-0.535774\pi$
$347$	−4.17830	−0.224303	−0.112151	+	0.993691i	$0.535774\pi$
$348$	3.30729	0.177289
$349$	6.84288	0.366291	0.183146	−	0.983086i	$-0.441372\pi$
$349$	6.84288	0.366291	0.183146	+	0.983086i	$0.441372\pi$
$350$	4.04806	0.216378
$351$	1.47241	0.0785912
$352$	−0.384977	−0.0205193
$353$	−26.3267	−1.40123	−0.700613	−	0.713541i	$-0.747090\pi$
$353$	−26.3267	−1.40123	−0.700613	+	0.713541i	$0.747090\pi$
$354$	1.45585	0.0773776
$355$	3.57423	0.189700
$356$	47.0617	2.49427
$357$	−0.0516938	−0.00273593
$358$	31.6024	1.67024
$359$	−17.5566	−0.926602	−0.463301	−	0.886201i	$-0.653335\pi$
$359$	−17.5566	−0.926602	−0.463301	+	0.886201i	$0.653335\pi$
$360$	−10.3548	−0.545747
$361$	−5.65601	−0.297685
$362$	−21.0154	−1.10454
$363$	2.11830	0.111182
$364$	1.82962	0.0958982
$365$	11.0836	0.580142
$366$	2.31749	0.121137
$367$	28.1724	1.47059	0.735293	−	0.677750i	$-0.237045\pi$
$367$	28.1724	1.47059	0.735293	+	0.677750i	$0.237045\pi$
$368$	−39.3816	−2.05291
$369$	−5.65233	−0.294249
$370$	−3.37892	−0.175662
$371$	2.84543	0.147727
$372$	1.82459	0.0946003
$373$	5.57630	0.288730	0.144365	−	0.989525i	$-0.453886\pi$
$373$	5.57630	0.288730	0.144365	+	0.989525i	$0.453886\pi$
$374$	−1.06973	−0.0553145
$375$	−1.30698	−0.0674920
$376$	−54.2741	−2.79897
$377$	−5.06346	−0.260781
$378$	−1.06233	−0.0546402
$379$	−15.0356	−0.772327	−0.386163	−	0.922430i	$-0.626200\pi$
$379$	−15.0356	−0.772327	−0.386163	+	0.922430i	$0.626200\pi$
$380$	10.2193	0.524237
$381$	−2.91613	−0.149398
$382$	−32.9416	−1.68544
$383$	23.8340	1.21786	0.608929	−	0.793224i	$-0.291599\pi$
$383$	23.8340	1.21786	0.608929	+	0.793224i	$0.291599\pi$
$384$	−3.78948	−0.193381
$385$	−0.152127	−0.00775312
$386$	−43.2195	−2.19982
$387$	27.5623	1.40107
$388$	−55.4433	−2.81471
$389$	8.34022	0.422866	0.211433	−	0.977392i	$-0.432187\pi$
$389$	8.34022	0.422866	0.211433	+	0.977392i	$0.432187\pi$
$390$	−0.418809	−0.0212072
$391$	−6.41609	−0.324476
$392$	34.8931	1.76237
$393$	−0.443236	−0.0223583
$394$	10.7975	0.543968
$395$	−9.98750	−0.502526
$396$	−7.31694	−0.367690
$397$	11.7351	0.588967	0.294483	−	0.955657i	$-0.404852\pi$
$397$	11.7351	0.588967	0.294483	+	0.955657i	$0.404852\pi$
$398$	8.23493	0.412780
$399$	0.264412	0.0132372
$400$	−19.8397	−0.991985
$401$	17.5279	0.875301	0.437650	−	0.899145i	$-0.355811\pi$
$401$	17.5279	0.875301	0.437650	+	0.899145i	$0.355811\pi$
$402$	−2.88737	−0.144009
$403$	−2.79344	−0.139151
$404$	33.5565	1.66950
$405$	−5.95150	−0.295733
$406$	3.65324	0.181307
$407$	−1.21239	−0.0600961
$408$	0.723039	0.0357958
$409$	34.8728	1.72435	0.862176	−	0.506610i	$-0.169101\pi$
$409$	34.8728	1.72435	0.862176	+	0.506610i	$0.169101\pi$
$410$	3.23705	0.159866
$411$	−0.748627	−0.0369270
$412$	47.9634	2.36299
$413$	1.07768	0.0530293
$414$	−65.4873	−3.21853
$415$	8.89949	0.436859
$416$	−0.784545	−0.0384655
$417$	−0.114671	−0.00561546
$418$	5.47163	0.267626
$419$	−10.3102	−0.503686	−0.251843	−	0.967768i	$-0.581037\pi$
$419$	−10.3102	−0.503686	−0.251843	+	0.967768i	$0.581037\pi$
$420$	0.202495	0.00988076
$421$	−5.72609	−0.279073	−0.139536	−	0.990217i	$-0.544561\pi$
$421$	−5.72609	−0.279073	−0.139536	+	0.990217i	$0.544561\pi$
$422$	53.1598	2.58778
$423$	−31.6243	−1.53763
$424$	−39.7989	−1.93280
$425$	−3.23230	−0.156790
$426$	−2.54734	−0.123419
$427$	1.71551	0.0830191
$428$	22.6523	1.09494
$429$	−0.150273	−0.00725526
$430$	−15.7847	−0.761207
$431$	−5.94644	−0.286430	−0.143215	−	0.989692i	$-0.545744\pi$
$431$	−5.94644	−0.286430	−0.143215	+	0.989692i	$0.545744\pi$
$432$	5.20651	0.250498
$433$	24.9052	1.19687	0.598435	−	0.801172i	$-0.295790\pi$
$433$	24.9052	1.19687	0.598435	+	0.801172i	$0.295790\pi$
$434$	2.01544	0.0967442
$435$	−0.560404	−0.0268693
$436$	−41.5570	−1.99022
$437$	32.8181	1.56990
$438$	−7.89926	−0.377441
$439$	−2.94598	−0.140604	−0.0703019	−	0.997526i	$-0.522396\pi$
$439$	−2.94598	−0.140604	−0.0703019	+	0.997526i	$0.522396\pi$
$440$	2.12779	0.101439
$441$	20.3315	0.968164
$442$	−2.18001	−0.103692
$443$	−12.1746	−0.578431	−0.289216	−	0.957264i	$-0.593394\pi$
$443$	−12.1746	−0.578431	−0.289216	+	0.957264i	$0.593394\pi$
$444$	1.61381	0.0765880
$445$	−7.97438	−0.378022
$446$	−29.9917	−1.42015
$447$	−1.73706	−0.0821599
$448$	−2.61842	−0.123709
$449$	24.3684	1.15001	0.575007	−	0.818149i	$-0.304999\pi$
$449$	24.3684	1.15001	0.575007	+	0.818149i	$0.304999\pi$
$450$	−32.9912	−1.55522
$451$	1.16149	0.0546923
$452$	1.03914	0.0488772
$453$	−0.318264	−0.0149534
$454$	40.1862	1.88603
$455$	−0.310020	−0.0145340
$456$	−3.69832	−0.173190
$457$	−13.3343	−0.623753	−0.311877	−	0.950123i	$-0.600958\pi$
$457$	−13.3343	−0.623753	−0.311877	+	0.950123i	$0.600958\pi$
$458$	2.60678	0.121807
$459$	0.848250	0.0395929
$460$	25.1332	1.17184
$461$	20.2808	0.944573	0.472286	−	0.881445i	$-0.343429\pi$
$461$	20.2808	0.944573	0.472286	+	0.881445i	$0.343429\pi$
$462$	0.108421	0.00504419
$463$	23.5324	1.09364	0.546822	−	0.837249i	$-0.315837\pi$
$463$	23.5324	1.09364	0.546822	+	0.837249i	$0.315837\pi$
$464$	−17.9046	−0.831202
$465$	−0.309167	−0.0143373
$466$	46.1503	2.13787
$467$	14.0058	0.648109	0.324055	−	0.946038i	$-0.394954\pi$
$467$	14.0058	0.648109	0.324055	+	0.946038i	$0.394954\pi$
$468$	−14.9112	−0.689271
$469$	−2.13735	−0.0986939
$470$	18.1110	0.835398
$471$	−1.94062	−0.0894190
$472$	−15.0735	−0.693813
$473$	−5.66373	−0.260418
$474$	7.11808	0.326944
$475$	16.5331	0.758591
$476$	1.05404	0.0483118
$477$	−23.1899	−1.06179
$478$	20.6323	0.943698
$479$	−36.0014	−1.64494	−0.822472	−	0.568805i	$-0.807406\pi$
$479$	−36.0014	−1.64494	−0.822472	+	0.568805i	$0.807406\pi$
$480$	−0.0868304	−0.00396325
$481$	−2.47074	−0.112656
$482$	19.5612	0.890990
$483$	0.650292	0.0295893
$484$	−43.1922	−1.96328
$485$	9.39460	0.426587
$486$	13.0156	0.590400
$487$	−1.23392	−0.0559143	−0.0279572	−	0.999609i	$-0.508900\pi$
$487$	−1.23392	−0.0559143	−0.0279572	+	0.999609i	$0.508900\pi$
$488$	−23.9947	−1.08619
$489$	−1.39358	−0.0630200
$490$	−11.6437	−0.526008
$491$	4.38378	0.197837	0.0989187	−	0.995096i	$-0.468462\pi$
$491$	4.38378	0.197837	0.0989187	+	0.995096i	$0.468462\pi$
$492$	−1.54605	−0.0697013
$493$	−2.91704	−0.131377
$494$	11.1507	0.501692
$495$	1.23982	0.0557257
$496$	−9.87774	−0.443524
$497$	−1.88565	−0.0845830
$498$	−6.34266	−0.284221
$499$	−32.9660	−1.47576	−0.737881	−	0.674931i	$-0.764173\pi$
$499$	−32.9660	−1.47576	−0.737881	+	0.674931i	$0.764173\pi$
$500$	26.6493	1.19179
$501$	0.366209	0.0163610
$502$	−38.6092	−1.72321
$503$	3.32925	0.148444	0.0742220	−	0.997242i	$-0.476353\pi$
$503$	3.32925	0.148444	0.0742220	+	0.997242i	$0.476353\pi$
$504$	5.46289	0.243336
$505$	−5.68599	−0.253023
$506$	13.4569	0.598231
$507$	2.28435	0.101452
$508$	59.4600	2.63811
$509$	−25.5006	−1.13029	−0.565147	−	0.824990i	$-0.691180\pi$
$509$	−25.5006	−1.13029	−0.565147	+	0.824990i	$0.691180\pi$
$510$	−0.241275	−0.0106838
$511$	−5.84736	−0.258672
$512$	41.7667	1.84584
$513$	−4.33876	−0.191561
$514$	5.68995	0.250973
$515$	−8.12717	−0.358126
$516$	7.53895	0.331884
$517$	6.49842	0.285800
$518$	1.78262	0.0783237
$519$	−2.59802	−0.114040
$520$	4.33624	0.190157
$521$	−7.13807	−0.312724	−0.156362	−	0.987700i	$-0.549977\pi$
$521$	−7.13807	−0.312724	−0.156362	+	0.987700i	$0.549977\pi$
$522$	−29.7735	−1.30315
$523$	−10.2309	−0.447367	−0.223683	−	0.974662i	$-0.571808\pi$
$523$	−10.2309	−0.447367	−0.223683	+	0.974662i	$0.571808\pi$
$524$	9.03759	0.394809
$525$	0.327605	0.0142978
$526$	−1.37688	−0.0600347
$527$	−1.60929	−0.0701019
$528$	−0.531374	−0.0231251
$529$	57.7124	2.50924
$530$	13.2807	0.576877
$531$	−8.78299	−0.381149
$532$	−5.39137	−0.233746
$533$	2.36700	0.102526
$534$	5.68332	0.245942
$535$	−3.83832	−0.165945
$536$	29.8951	1.29127
$537$	2.55754	0.110366
$538$	29.3995	1.26750
$539$	−4.17788	−0.179954
$540$	−3.32277	−0.142989
$541$	−14.3939	−0.618841	−0.309420	−	0.950925i	$-0.600135\pi$
$541$	−14.3939	−0.618841	−0.309420	+	0.950925i	$0.600135\pi$
$542$	15.3452	0.659132
$543$	−1.70075	−0.0729861
$544$	−0.451974	−0.0193782
$545$	7.04163	0.301630
$546$	0.220951	0.00945583
$547$	−0.0309924	−0.00132514	−0.000662569	−	1.00000i	$-0.500211\pi$
$547$	−0.0309924	−0.00132514	−0.000662569		1.00000i	$0.500211\pi$
$548$	15.2645	0.652068
$549$	−13.9812	−0.596702
$550$	6.77931	0.289071
$551$	14.9206	0.635637
$552$	−9.09560	−0.387135
$553$	5.26910	0.224065
$554$	65.6078	2.78741
$555$	−0.273452	−0.0116074
$556$	2.33814	0.0991594
$557$	12.4387	0.527043	0.263522	−	0.964654i	$-0.415116\pi$
$557$	12.4387	0.527043	0.263522	+	0.964654i	$0.415116\pi$
$558$	−16.4256	−0.695351
$559$	−11.5421	−0.488180
$560$	−1.09625	−0.0463249
$561$	−0.0865720	−0.00365507
$562$	−29.3070	−1.23624
$563$	35.7047	1.50477	0.752387	−	0.658721i	$-0.228902\pi$
$563$	35.7047	1.50477	0.752387	+	0.658721i	$0.228902\pi$
$564$	−8.65001	−0.364231
$565$	−0.176078	−0.00740764
$566$	−22.8110	−0.958819
$567$	3.13983	0.131860
$568$	26.3745	1.10665
$569$	27.5053	1.15308	0.576541	−	0.817068i	$-0.304402\pi$
$569$	27.5053	1.15308	0.576541	+	0.817068i	$0.304402\pi$
$570$	1.23411	0.0516912
$571$	20.8980	0.874556	0.437278	−	0.899326i	$-0.355943\pi$
$571$	20.8980	0.874556	0.437278	+	0.899326i	$0.355943\pi$
$572$	3.06408	0.128116
$573$	−2.66592	−0.111371
$574$	−1.70777	−0.0712809
$575$	40.6614	1.69570
$576$	21.3398	0.889159
$577$	6.99681	0.291281	0.145641	−	0.989338i	$-0.453476\pi$
$577$	6.99681	0.291281	0.145641	+	0.989338i	$0.453476\pi$
$578$	40.6044	1.68892
$579$	−3.49770	−0.145360
$580$	11.4267	0.474466
$581$	−4.69510	−0.194786
$582$	−6.69551	−0.277538
$583$	4.76526	0.197357
$584$	81.7868	3.38436
$585$	2.52663	0.104463
$586$	−36.2854	−1.49894
$587$	15.0302	0.620363	0.310181	−	0.950677i	$-0.399610\pi$
$587$	15.0302	0.620363	0.310181	+	0.950677i	$0.399610\pi$
$588$	5.56114	0.229338
$589$	8.23147	0.339172
$590$	5.02995	0.207080
$591$	0.873825	0.0359443
$592$	−8.73667	−0.359075
$593$	16.5479	0.679542	0.339771	−	0.940508i	$-0.389650\pi$
$593$	16.5479	0.679542	0.339771	+	0.940508i	$0.389650\pi$
$594$	−1.77909	−0.0729968
$595$	−0.178602	−0.00732196
$596$	35.4186	1.45080
$597$	0.666443	0.0272757
$598$	27.4238	1.12144
$599$	15.3528	0.627299	0.313650	−	0.949539i	$-0.398448\pi$
$599$	15.3528	0.627299	0.313650	+	0.949539i	$0.398448\pi$
$600$	−4.58219	−0.187067
$601$	−4.00835	−0.163504	−0.0817521	−	0.996653i	$-0.526052\pi$
$601$	−4.00835	−0.163504	−0.0817521	+	0.996653i	$0.526052\pi$
$602$	8.32754	0.339405
$603$	17.4192	0.709365
$604$	6.48943	0.264051
$605$	7.31871	0.297548
$606$	4.05239	0.164617
$607$	30.4854	1.23736	0.618682	−	0.785642i	$-0.287667\pi$
$607$	30.4854	1.23736	0.618682	+	0.785642i	$0.287667\pi$
$608$	2.31183	0.0937571
$609$	0.295652	0.0119804
$610$	8.00692	0.324191
$611$	13.2432	0.535761
$612$	−8.59030	−0.347242
$613$	0.946597	0.0382327	0.0191163	−	0.999817i	$-0.493915\pi$
$613$	0.946597	0.0382327	0.0191163	+	0.999817i	$0.493915\pi$
$614$	−72.3101	−2.91820
$615$	0.261970	0.0105637
$616$	−1.12256	−0.0452292
$617$	32.1592	1.29468	0.647341	−	0.762201i	$-0.275881\pi$
$617$	32.1592	1.29468	0.647341	+	0.762201i	$0.275881\pi$
$618$	5.79222	0.232997
$619$	−42.7938	−1.72003	−0.860014	−	0.510270i	$-0.829545\pi$
$619$	−42.7938	−1.72003	−0.860014	+	0.510270i	$0.829545\pi$
$620$	6.30393	0.253172
$621$	−10.6707	−0.428201
$622$	48.4411	1.94231
$623$	4.20704	0.168551
$624$	−1.08289	−0.0433502
$625$	18.1143	0.724570
$626$	18.0726	0.722326
$627$	0.442812	0.0176842
$628$	39.5693	1.57899
$629$	−1.42339	−0.0567542
$630$	−1.82294	−0.0726277
$631$	13.5830	0.540730	0.270365	−	0.962758i	$-0.412856\pi$
$631$	13.5830	0.540730	0.270365	+	0.962758i	$0.412856\pi$
$632$	−73.6986	−2.93157
$633$	4.30216	0.170996
$634$	−40.1928	−1.59626
$635$	−10.0752	−0.399822
$636$	−6.34300	−0.251516
$637$	−8.51410	−0.337341
$638$	6.11810	0.242218
$639$	15.3678	0.607943
$640$	−13.0926	−0.517531
$641$	−38.1110	−1.50529	−0.752647	−	0.658424i	$-0.771223\pi$
$641$	−38.1110	−1.50529	−0.752647	+	0.658424i	$0.771223\pi$
$642$	2.73557	0.107964
$643$	−4.72788	−0.186449	−0.0932246	−	0.995645i	$-0.529717\pi$
$643$	−4.72788	−0.186449	−0.0932246	+	0.995645i	$0.529717\pi$
$644$	−13.2595	−0.522497
$645$	−1.27744	−0.0502991
$646$	6.42386	0.252743
$647$	24.7026	0.971159	0.485579	−	0.874193i	$-0.338609\pi$
$647$	24.7026	0.971159	0.485579	+	0.874193i	$0.338609\pi$
$648$	−43.9166	−1.72521
$649$	1.80480	0.0708446
$650$	13.8156	0.541892
$651$	0.163107	0.00639267
$652$	28.4152	1.11283
$653$	−15.7362	−0.615805	−0.307902	−	0.951418i	$-0.599627\pi$
$653$	−15.7362	−0.615805	−0.307902	+	0.951418i	$0.599627\pi$
$654$	−5.01856	−0.196241
$655$	−1.53138	−0.0598358
$656$	8.36983	0.326787
$657$	47.6554	1.85921
$658$	−9.55481	−0.372485
$659$	−5.03185	−0.196013	−0.0980066	−	0.995186i	$-0.531247\pi$
$659$	−5.03185	−0.196013	−0.0980066	+	0.995186i	$0.531247\pi$
$660$	0.339120	0.0132002
$661$	25.0643	0.974888	0.487444	−	0.873154i	$-0.337929\pi$
$661$	25.0643	0.974888	0.487444	+	0.873154i	$0.337929\pi$
$662$	−11.1107	−0.431831
$663$	−0.176425	−0.00685179
$664$	65.6701	2.54850
$665$	0.913541	0.0354256
$666$	−14.5281	−0.562953
$667$	36.6955	1.42085
$668$	−7.46702	−0.288908
$669$	−2.42719	−0.0938407
$670$	−9.97585	−0.385401
$671$	2.87297	0.110910
$672$	0.0458091	0.00176712
$673$	−12.4768	−0.480945	−0.240472	−	0.970656i	$-0.577302\pi$
$673$	−12.4768	−0.480945	−0.240472	+	0.970656i	$0.577302\pi$
$674$	−5.93956	−0.228783
$675$	−5.37570	−0.206911
$676$	−46.5780	−1.79146
$677$	15.5776	0.598696	0.299348	−	0.954144i	$-0.403231\pi$
$677$	15.5776	0.598696	0.299348	+	0.954144i	$0.403231\pi$
$678$	0.125490	0.00481942
$679$	−4.95630	−0.190205
$680$	2.49810	0.0957976
$681$	3.25222	0.124625
$682$	3.37527	0.129246
$683$	25.3107	0.968488	0.484244	−	0.874933i	$-0.339095\pi$
$683$	25.3107	0.968488	0.484244	+	0.874933i	$0.339095\pi$
$684$	43.9391	1.68005
$685$	−2.58650	−0.0988251
$686$	12.4037	0.473575
$687$	0.210963	0.00804876
$688$	−40.8136	−1.55600
$689$	9.71113	0.369965
$690$	3.03516	0.115547
$691$	31.9905	1.21698	0.608489	−	0.793563i	$-0.291776\pi$
$691$	31.9905	1.21698	0.608489	+	0.793563i	$0.291776\pi$
$692$	52.9737	2.01376
$693$	−0.654090	−0.0248468
$694$	10.2885	0.390546
$695$	−0.396187	−0.0150282
$696$	−4.13527	−0.156747
$697$	1.36362	0.0516509
$698$	−16.8497	−0.637770
$699$	3.73489	0.141267
$700$	−6.67987	−0.252475
$701$	23.1733	0.875244	0.437622	−	0.899159i	$-0.355821\pi$
$701$	23.1733	0.875244	0.437622	+	0.899159i	$0.355821\pi$
$702$	−3.62561	−0.136840
$703$	7.28057	0.274592
$704$	−4.38508	−0.165269
$705$	1.46570	0.0552015
$706$	64.8259	2.43975
$707$	2.99975	0.112817
$708$	−2.40236	−0.0902862
$709$	−43.4701	−1.63255	−0.816277	−	0.577660i	$-0.803966\pi$
$709$	−43.4701	−1.63255	−0.816277	+	0.577660i	$0.803966\pi$
$710$	−8.80106	−0.330298
$711$	−42.9426	−1.61047
$712$	−58.8436	−2.20526
$713$	20.2444	0.758158
$714$	0.127289	0.00476368
$715$	−0.519193	−0.0194167
$716$	−52.1484	−1.94888
$717$	1.66974	0.0623577
$718$	43.2308	1.61336
$719$	39.6940	1.48034	0.740169	−	0.672421i	$-0.234746\pi$
$719$	39.6940	1.48034	0.740169	+	0.672421i	$0.234746\pi$
$720$	8.93430	0.332962
$721$	4.28764	0.159680
$722$	13.9272	0.518316
$723$	1.58307	0.0588749
$724$	34.6783	1.28881
$725$	18.4865	0.686570
$726$	−5.21604	−0.193585
$727$	36.2404	1.34408	0.672041	−	0.740514i	$-0.265418\pi$
$727$	36.2404	1.34408	0.672041	+	0.740514i	$0.265418\pi$
$728$	−2.28767	−0.0847865
$729$	−24.8792	−0.921452
$730$	−27.2919	−1.01012
$731$	−6.64939	−0.245936
$732$	−3.82419	−0.141346
$733$	33.0965	1.22245	0.611224	−	0.791457i	$-0.290677\pi$
$733$	33.0965	1.22245	0.611224	+	0.791457i	$0.290677\pi$
$734$	−69.3707	−2.56052
$735$	−0.942308	−0.0347576
$736$	5.68569	0.209577
$737$	−3.57944	−0.131850
$738$	13.9181	0.512333
$739$	−43.7389	−1.60896	−0.804480	−	0.593980i	$-0.797556\pi$
$739$	−43.7389	−1.60896	−0.804480	+	0.593980i	$0.797556\pi$
$740$	5.57570	0.204967
$741$	0.902409	0.0331508
$742$	−7.00649	−0.257216
$743$	−9.83063	−0.360651	−0.180325	−	0.983607i	$-0.557715\pi$
$743$	−9.83063	−0.360651	−0.180325	+	0.983607i	$0.557715\pi$
$744$	−2.28137	−0.0836391
$745$	−6.00151	−0.219878
$746$	−13.7309	−0.502724
$747$	38.2645	1.40003
$748$	1.76521	0.0645424
$749$	2.02498	0.0739912
$750$	3.21826	0.117514
$751$	37.0100	1.35051	0.675257	−	0.737583i	$-0.264033\pi$
$751$	37.0100	1.35051	0.675257	+	0.737583i	$0.264033\pi$
$752$	46.8285	1.70766
$753$	−3.12459	−0.113866
$754$	12.4681	0.454061
$755$	−1.09960	−0.0400186
$756$	1.75299	0.0637557
$757$	15.6212	0.567760	0.283880	−	0.958860i	$-0.408378\pi$
$757$	15.6212	0.567760	0.283880	+	0.958860i	$0.408378\pi$
$758$	37.0232	1.34474
$759$	1.08905	0.0395299
$760$	−12.7777	−0.463494
$761$	−34.9672	−1.26756	−0.633780	−	0.773513i	$-0.718498\pi$
$761$	−34.9672	−1.26756	−0.633780	+	0.773513i	$0.718498\pi$
$762$	7.18058	0.260125
$763$	−3.71495	−0.134490
$764$	54.3583	1.96661
$765$	1.45559	0.0526268
$766$	−58.6880	−2.12048
$767$	3.67801	0.132805
$768$	6.45804	0.233034
$769$	−36.1481	−1.30353	−0.651767	−	0.758419i	$-0.725972\pi$
$769$	−36.1481	−1.30353	−0.651767	+	0.758419i	$0.725972\pi$
$770$	0.374593	0.0134994
$771$	0.460481	0.0165838
$772$	71.3183	2.56680
$773$	30.5228	1.09783	0.548915	−	0.835878i	$-0.315041\pi$
$773$	30.5228	1.09783	0.548915	+	0.835878i	$0.315041\pi$
$774$	−67.8685	−2.43948
$775$	10.1987	0.366349
$776$	69.3235	2.48857
$777$	0.144265	0.00517548
$778$	−20.5367	−0.736276
$779$	−6.97487	−0.249901
$780$	0.691094	0.0247451
$781$	−3.15791	−0.112999
$782$	15.7988	0.564963
$783$	−4.85138	−0.173374
$784$	−30.1063	−1.07523
$785$	−6.70483	−0.239306
$786$	1.09141	0.0389293
$787$	−0.816266	−0.0290967	−0.0145484	−	0.999894i	$-0.504631\pi$
$787$	−0.816266	−0.0290967	−0.0145484	+	0.999894i	$0.504631\pi$
$788$	−17.8173	−0.634716
$789$	−0.111429	−0.00396698
$790$	24.5929	0.874976
$791$	0.0928932	0.00330290
$792$	9.14873	0.325086
$793$	5.85483	0.207911
$794$	−28.8961	−1.02548
$795$	1.07479	0.0381189
$796$	−13.5888	−0.481642
$797$	24.9704	0.884496	0.442248	−	0.896893i	$-0.354181\pi$
$797$	24.9704	0.884496	0.442248	+	0.896893i	$0.354181\pi$
$798$	−0.651079	−0.0230480
$799$	7.62934	0.269907
$800$	2.86434	0.101270
$801$	−34.2869	−1.21147
$802$	−43.1601	−1.52404
$803$	−9.79262	−0.345574
$804$	4.76457	0.168033
$805$	2.24675	0.0791877
$806$	6.87847	0.242284
$807$	2.37926	0.0837540
$808$	−41.9574	−1.47606
$809$	10.8063	0.379930	0.189965	−	0.981791i	$-0.439163\pi$
$809$	10.8063	0.379930	0.189965	+	0.981791i	$0.439163\pi$
$810$	14.6548	0.514917
$811$	37.7034	1.32395	0.661973	−	0.749527i	$-0.269719\pi$
$811$	37.7034	1.32395	0.661973	+	0.749527i	$0.269719\pi$
$812$	−6.02836	−0.211554
$813$	1.24187	0.0435542
$814$	2.98536	0.104637
$815$	−4.81482	−0.168656
$816$	−0.623849	−0.0218391
$817$	34.0114	1.18991
$818$	−85.8698	−3.00237
$819$	−1.33297	−0.0465778
$820$	−5.34159	−0.186536
$821$	−14.7813	−0.515871	−0.257935	−	0.966162i	$-0.583042\pi$
$821$	−14.7813	−0.515871	−0.257935	+	0.966162i	$0.583042\pi$
$822$	1.84339	0.0642957
$823$	−47.3909	−1.65194	−0.825972	−	0.563711i	$-0.809373\pi$
$823$	−47.3909	−1.65194	−0.825972	+	0.563711i	$0.809373\pi$
$824$	−59.9711	−2.08919
$825$	0.548641	0.0191012
$826$	−2.65365	−0.0923323
$827$	−51.8766	−1.80393	−0.901963	−	0.431814i	$-0.857874\pi$
$827$	−51.8766	−1.80393	−0.901963	+	0.431814i	$0.857874\pi$
$828$	108.063	3.75546
$829$	8.10315	0.281434	0.140717	−	0.990050i	$-0.455059\pi$
$829$	8.10315	0.281434	0.140717	+	0.990050i	$0.455059\pi$
$830$	−21.9138	−0.760640
$831$	5.30955	0.184186
$832$	−8.93637	−0.309813
$833$	−4.90495	−0.169947
$834$	0.282362	0.00977739
$835$	1.26525	0.0437858
$836$	−9.02896	−0.312273
$837$	−2.67644	−0.0925113
$838$	25.3875	0.876997
$839$	37.3711	1.29020	0.645098	−	0.764100i	$-0.276817\pi$
$839$	37.3711	1.29020	0.645098	+	0.764100i	$0.276817\pi$
$840$	−0.253190	−0.00873589
$841$	−12.3166	−0.424710
$842$	14.0997	0.485909
$843$	−2.37178	−0.0816885
$844$	−87.7212	−3.01949
$845$	7.89241	0.271507
$846$	77.8706	2.67725
$847$	−3.86113	−0.132670
$848$	34.3391	1.17921
$849$	−1.84607	−0.0633569
$850$	7.95912	0.272996
$851$	17.9058	0.613801
$852$	4.20348	0.144009
$853$	2.04739	0.0701012	0.0350506	−	0.999386i	$-0.488841\pi$
$853$	2.04739	0.0701012	0.0350506	+	0.999386i	$0.488841\pi$
$854$	−4.22420	−0.144549
$855$	−7.44526	−0.254623
$856$	−28.3233	−0.968071
$857$	11.0282	0.376716	0.188358	−	0.982100i	$-0.439683\pi$
$857$	11.0282	0.376716	0.188358	+	0.982100i	$0.439683\pi$
$858$	0.370028	0.0126325
$859$	−14.4955	−0.494579	−0.247290	−	0.968942i	$-0.579540\pi$
$859$	−14.4955	−0.494579	−0.247290	+	0.968942i	$0.579540\pi$
$860$	26.0470	0.888196
$861$	−0.138208	−0.00471010
$862$	14.6423	0.498719
$863$	3.55962	0.121171	0.0605854	−	0.998163i	$-0.480703\pi$
$863$	3.55962	0.121171	0.0605854	+	0.998163i	$0.480703\pi$
$864$	−0.751686	−0.0255729
$865$	−8.97613	−0.305197
$866$	−61.3259	−2.08394
$867$	3.28606	0.111600
$868$	−3.32576	−0.112884
$869$	8.82420	0.299340
$870$	1.37992	0.0467837
$871$	−7.29455	−0.247166
$872$	51.9608	1.75961
$873$	40.3933	1.36711
$874$	−80.8101	−2.73344
$875$	2.38229	0.0805361
$876$	13.0349	0.440408
$877$	−47.7955	−1.61394	−0.806970	−	0.590592i	$-0.798894\pi$
$877$	−47.7955	−1.61394	−0.806970	+	0.590592i	$0.798894\pi$
$878$	7.25408	0.244813
$879$	−2.93653	−0.0990468
$880$	−1.83589	−0.0618880
$881$	45.5872	1.53587	0.767936	−	0.640527i	$-0.221284\pi$
$881$	45.5872	1.53587	0.767936	+	0.640527i	$0.221284\pi$
$882$	−50.0635	−1.68573
$883$	7.88523	0.265359	0.132680	−	0.991159i	$-0.457642\pi$
$883$	7.88523	0.265359	0.132680	+	0.991159i	$0.457642\pi$
$884$	3.59732	0.120991
$885$	0.407068	0.0136834
$886$	29.9783	1.00714
$887$	26.1885	0.879322	0.439661	−	0.898164i	$-0.355099\pi$
$887$	26.1885	0.879322	0.439661	+	0.898164i	$0.355099\pi$
$888$	−2.01783	−0.0677138
$889$	5.31537	0.178272
$890$	19.6358	0.658195
$891$	5.25829	0.176159
$892$	49.4906	1.65707
$893$	−39.0238	−1.30588
$894$	4.27727	0.143053
$895$	8.83629	0.295365
$896$	6.90726	0.230755
$897$	2.21937	0.0741028
$898$	−60.0038	−2.00235
$899$	9.20400	0.306971
$900$	54.4402	1.81467
$901$	5.59456	0.186382
$902$	−2.86001	−0.0952279
$903$	0.673937	0.0224272
$904$	−1.29929	−0.0432138
$905$	−5.87607	−0.195327
$906$	0.783684	0.0260362
$907$	35.4269	1.17633	0.588165	−	0.808741i	$-0.299851\pi$
$907$	35.4269	1.17633	0.588165	+	0.808741i	$0.299851\pi$
$908$	−66.3128	−2.20067
$909$	−24.4476	−0.810877
$910$	0.763384	0.0253059
$911$	−12.8829	−0.426830	−0.213415	−	0.976962i	$-0.568459\pi$
$911$	−12.8829	−0.426830	−0.213415	+	0.976962i	$0.568459\pi$
$912$	3.19096	0.105663
$913$	−7.86291	−0.260225
$914$	32.8340	1.08605
$915$	0.647990	0.0214219
$916$	−4.30155	−0.142127
$917$	0.807907	0.0266794
$918$	−2.08870	−0.0689374
$919$	−24.6257	−0.812328	−0.406164	−	0.913800i	$-0.633134\pi$
$919$	−24.6257	−0.812328	−0.406164	+	0.913800i	$0.633134\pi$
$920$	−31.4252	−1.03606
$921$	−5.85197	−0.192829
$922$	−49.9389	−1.64465
$923$	−6.43552	−0.211828
$924$	−0.178910	−0.00588569
$925$	9.02057	0.296595
$926$	−57.9455	−1.90421
$927$	−34.9438	−1.14771
$928$	2.58497	0.0848558
$929$	43.4827	1.42662	0.713310	−	0.700848i	$-0.247195\pi$
$929$	43.4827	1.42662	0.713310	+	0.700848i	$0.247195\pi$
$930$	0.761283	0.0249634
$931$	25.0886	0.822247
$932$	−76.1546	−2.49453
$933$	3.92028	0.128344
$934$	−34.4873	−1.12846
$935$	−0.299106	−0.00978180
$936$	18.6442	0.609405
$937$	46.0292	1.50371	0.751854	−	0.659330i	$-0.229160\pi$
$937$	46.0292	1.50371	0.751854	+	0.659330i	$0.229160\pi$
$938$	5.26295	0.171841
$939$	1.46259	0.0477299
$940$	−29.8857	−0.974764
$941$	−28.2566	−0.921140	−0.460570	−	0.887623i	$-0.652355\pi$
$941$	−28.2566	−0.921140	−0.460570	+	0.887623i	$0.652355\pi$
$942$	4.77852	0.155693
$943$	−17.1539	−0.558609
$944$	13.0056	0.423297
$945$	−0.297036	−0.00966257
$946$	13.9462	0.453429
$947$	43.5512	1.41522	0.707612	−	0.706601i	$-0.249772\pi$
$947$	43.5512	1.41522	0.707612	+	0.706601i	$0.249772\pi$
$948$	−11.7458	−0.381487
$949$	−19.9564	−0.647812
$950$	−40.7106	−1.32083
$951$	−3.25275	−0.105478
$952$	−1.31792	−0.0427140
$953$	−36.6249	−1.18640	−0.593199	−	0.805056i	$-0.702135\pi$
$953$	−36.6249	−1.18640	−0.593199	+	0.805056i	$0.702135\pi$
$954$	57.1021	1.84875
$955$	−9.21075	−0.298053
$956$	−34.0462	−1.10113
$957$	0.495130	0.0160053
$958$	88.6486	2.86411
$959$	1.36456	0.0440639
$960$	−0.989043	−0.0319212
$961$	−25.9223	−0.836203
$962$	6.08387	0.196152
$963$	−16.5034	−0.531814
$964$	−32.2788	−1.03963
$965$	−12.0845	−0.389015
$966$	−1.60126	−0.0515196
$967$	−17.1291	−0.550835	−0.275418	−	0.961325i	$-0.588816\pi$
$967$	−17.1291	−0.550835	−0.275418	+	0.961325i	$0.588816\pi$
$968$	54.0054	1.73580
$969$	0.519875	0.0167008
$970$	−23.1329	−0.742754
$971$	9.58860	0.307713	0.153856	−	0.988093i	$-0.450831\pi$
$971$	9.58860	0.307713	0.153856	+	0.988093i	$0.450831\pi$
$972$	−21.4776	−0.688895
$973$	0.209016	0.00670075
$974$	3.03837	0.0973556
$975$	1.11808	0.0358071
$976$	20.7030	0.662686
$977$	3.91750	0.125332	0.0626659	−	0.998035i	$-0.480040\pi$
$977$	3.91750	0.125332	0.0626659	+	0.998035i	$0.480040\pi$
$978$	3.43151	0.109728
$979$	7.04555	0.225177
$980$	19.2137	0.613759
$981$	30.2764	0.966651
$982$	−10.7945	−0.344466
$983$	17.0680	0.544383	0.272192	−	0.962243i	$-0.412252\pi$
$983$	17.0680	0.544383	0.272192	+	0.962243i	$0.412252\pi$
$984$	1.93310	0.0616251
$985$	3.01906	0.0961952
$986$	7.18283	0.228748
$987$	−0.773259	−0.0246131
$988$	−18.4001	−0.585387
$989$	83.6472	2.65983
$990$	−3.05289	−0.0970272
$991$	30.1671	0.958288	0.479144	−	0.877736i	$-0.340947\pi$
$991$	30.1671	0.958288	0.479144	+	0.877736i	$0.340947\pi$
$992$	1.42609	0.0452785
$993$	−0.899178	−0.0285346
$994$	4.64317	0.147272
$995$	2.30255	0.0729959
$996$	10.4663	0.331637
$997$	13.1035	0.414993	0.207497	−	0.978236i	$-0.433468\pi$
$997$	13.1035	0.414993	0.207497	+	0.978236i	$0.433468\pi$
$998$	81.1745	2.56953
$999$	−2.36726	−0.0748967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.15	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.15	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46237 q^{2} -0.199276 q^{3} +4.06325 q^{4} -0.688498 q^{5} +0.490692 q^{6} +0.363231 q^{7} -5.08049 q^{8} -2.96029 q^{9} +O(q^{10})\)	\(q-2.46237 q^{2} -0.199276 q^{3} +4.06325 q^{4} -0.688498 q^{5} +0.490692 q^{6} +0.363231 q^{7} -5.08049 q^{8} -2.96029 q^{9} +1.69534 q^{10} +0.608305 q^{11} -0.809710 q^{12} +1.23967 q^{13} -0.894407 q^{14} +0.137201 q^{15} +4.38352 q^{16} +0.714168 q^{17} +7.28932 q^{18} -3.65294 q^{19} -2.79754 q^{20} -0.0723833 q^{21} -1.49787 q^{22} -8.98401 q^{23} +1.01242 q^{24} -4.52597 q^{25} -3.05251 q^{26} +1.18774 q^{27} +1.47590 q^{28} -4.08453 q^{29} -0.337840 q^{30} -2.25338 q^{31} -0.632868 q^{32} -0.121221 q^{33} -1.75854 q^{34} -0.250084 q^{35} -12.0284 q^{36} -1.99307 q^{37} +8.99489 q^{38} -0.247036 q^{39} +3.49791 q^{40} +1.90939 q^{41} +0.178234 q^{42} -9.31067 q^{43} +2.47170 q^{44} +2.03815 q^{45} +22.1219 q^{46} +10.6828 q^{47} -0.873533 q^{48} -6.86806 q^{49} +11.1446 q^{50} -0.142317 q^{51} +5.03708 q^{52} +7.83367 q^{53} -2.92466 q^{54} -0.418817 q^{55} -1.84539 q^{56} +0.727945 q^{57} +10.0576 q^{58} +2.96694 q^{59} +0.557484 q^{60} +4.72291 q^{61} +5.54865 q^{62} -1.07527 q^{63} -7.20869 q^{64} -0.853508 q^{65} +0.298490 q^{66} -5.88429 q^{67} +2.90185 q^{68} +1.79030 q^{69} +0.615798 q^{70} -5.19133 q^{71} +15.0397 q^{72} -16.0982 q^{73} +4.90767 q^{74} +0.901919 q^{75} -14.8428 q^{76} +0.220955 q^{77} +0.608294 q^{78} +14.5062 q^{79} -3.01805 q^{80} +8.64418 q^{81} -4.70161 q^{82} -12.9259 q^{83} -0.294112 q^{84} -0.491704 q^{85} +22.9263 q^{86} +0.813951 q^{87} -3.09049 q^{88} +11.5823 q^{89} -5.01868 q^{90} +0.450285 q^{91} -36.5043 q^{92} +0.449045 q^{93} -26.3051 q^{94} +2.51504 q^{95} +0.126116 q^{96} -13.6450 q^{97} +16.9117 q^{98} -1.80076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

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