LMFDB - Embedded newform 6037.2.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.65823 q^{2} -1.47107 q^{3} +5.06620 q^{4} -0.123247 q^{5} +3.91044 q^{6} -2.04180 q^{7} -8.15068 q^{8} -0.835960 q^{9} +O(q^{10})$	\(q-2.65823 q^{2} -1.47107 q^{3} +5.06620 q^{4} -0.123247 q^{5} +3.91044 q^{6} -2.04180 q^{7} -8.15068 q^{8} -0.835960 q^{9} +0.327620 q^{10} -1.27617 q^{11} -7.45273 q^{12} +1.33307 q^{13} +5.42757 q^{14} +0.181305 q^{15} +11.5340 q^{16} +2.50462 q^{17} +2.22218 q^{18} -0.794015 q^{19} -0.624396 q^{20} +3.00362 q^{21} +3.39235 q^{22} +6.36334 q^{23} +11.9902 q^{24} -4.98481 q^{25} -3.54361 q^{26} +5.64296 q^{27} -10.3442 q^{28} +5.26622 q^{29} -0.481951 q^{30} +4.00337 q^{31} -14.3587 q^{32} +1.87733 q^{33} -6.65786 q^{34} +0.251646 q^{35} -4.23514 q^{36} +6.53938 q^{37} +2.11068 q^{38} -1.96103 q^{39} +1.00455 q^{40} +5.59187 q^{41} -7.98432 q^{42} +9.30737 q^{43} -6.46532 q^{44} +0.103030 q^{45} -16.9152 q^{46} -1.09584 q^{47} -16.9673 q^{48} -2.83107 q^{49} +13.2508 q^{50} -3.68446 q^{51} +6.75360 q^{52} -3.14381 q^{53} -15.0003 q^{54} +0.157284 q^{55} +16.6420 q^{56} +1.16805 q^{57} -13.9988 q^{58} -8.64986 q^{59} +0.918528 q^{60} -13.0794 q^{61} -10.6419 q^{62} +1.70686 q^{63} +15.1008 q^{64} -0.164297 q^{65} -4.99038 q^{66} -7.37724 q^{67} +12.6889 q^{68} -9.36090 q^{69} -0.668933 q^{70} +3.68520 q^{71} +6.81364 q^{72} -12.4700 q^{73} -17.3832 q^{74} +7.33299 q^{75} -4.02264 q^{76} +2.60567 q^{77} +5.21289 q^{78} +10.4393 q^{79} -1.42154 q^{80} -5.79329 q^{81} -14.8645 q^{82} -2.55002 q^{83} +15.2169 q^{84} -0.308687 q^{85} -24.7412 q^{86} -7.74696 q^{87} +10.4016 q^{88} -4.05771 q^{89} -0.273877 q^{90} -2.72185 q^{91} +32.2380 q^{92} -5.88923 q^{93} +2.91300 q^{94} +0.0978602 q^{95} +21.1226 q^{96} +11.8973 q^{97} +7.52565 q^{98} +1.06682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65823	−1.87965	−0.939827	−	0.341650i	$-0.889014\pi$
$2$	−2.65823	−1.87965	−0.939827	+	0.341650i	$0.889014\pi$
$3$	−1.47107	−0.849321	−0.424661	−	0.905353i	$-0.639607\pi$
$3$	−1.47107	−0.849321	−0.424661	+	0.905353i	$0.639607\pi$
$4$	5.06620	2.53310
$5$	−0.123247	−0.0551179	−0.0275589	−	0.999620i	$-0.508773\pi$
$5$	−0.123247	−0.0551179	−0.0275589	+	0.999620i	$0.508773\pi$
$6$	3.91044	1.59643
$7$	−2.04180	−0.771726	−0.385863	−	0.922556i	$-0.626096\pi$
$7$	−2.04180	−0.771726	−0.385863	+	0.922556i	$0.626096\pi$
$8$	−8.15068	−2.88170
$9$	−0.835960	−0.278653
$10$	0.327620	0.103603
$11$	−1.27617	−0.384779	−0.192389	−	0.981319i	$-0.561624\pi$
$11$	−1.27617	−0.384779	−0.192389	+	0.981319i	$0.561624\pi$
$12$	−7.45273	−2.15142
$13$	1.33307	0.369727	0.184863	−	0.982764i	$-0.440816\pi$
$13$	1.33307	0.369727	0.184863	+	0.982764i	$0.440816\pi$
$14$	5.42757	1.45058
$15$	0.181305	0.0468128
$16$	11.5340	2.88350
$17$	2.50462	0.607459	0.303730	−	0.952758i	$-0.401768\pi$
$17$	2.50462	0.607459	0.303730	+	0.952758i	$0.401768\pi$
$18$	2.22218	0.523772
$19$	−0.794015	−0.182160	−0.0910798	−	0.995844i	$-0.529032\pi$
$19$	−0.794015	−0.182160	−0.0910798	+	0.995844i	$0.529032\pi$
$20$	−0.624396	−0.139619
$21$	3.00362	0.655443
$22$	3.39235	0.723251
$23$	6.36334	1.32685	0.663424	−	0.748244i	$-0.269103\pi$
$23$	6.36334	1.32685	0.663424	+	0.748244i	$0.269103\pi$
$24$	11.9902	2.44749
$25$	−4.98481	−0.996962
$26$	−3.54361	−0.694959
$27$	5.64296	1.08599
$28$	−10.3442	−1.95486
$29$	5.26622	0.977912	0.488956	−	0.872309i	$-0.337378\pi$
$29$	5.26622	0.977912	0.488956	+	0.872309i	$0.337378\pi$
$30$	−0.481951	−0.0879918
$31$	4.00337	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$31$	4.00337	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$32$	−14.3587	−2.53829
$33$	1.87733	0.326801
$34$	−6.65786	−1.14181
$35$	0.251646	0.0425359
$36$	−4.23514	−0.705857
$37$	6.53938	1.07507	0.537534	−	0.843242i	$-0.319356\pi$
$37$	6.53938	1.07507	0.537534	+	0.843242i	$0.319356\pi$
$38$	2.11068	0.342397
$39$	−1.96103	−0.314017
$40$	1.00455	0.158833
$41$	5.59187	0.873303	0.436652	−	0.899631i	$-0.356164\pi$
$41$	5.59187	0.873303	0.436652	+	0.899631i	$0.356164\pi$
$42$	−7.98432	−1.23201
$43$	9.30737	1.41936	0.709680	−	0.704524i	$-0.248839\pi$
$43$	9.30737	1.41936	0.709680	+	0.704524i	$0.248839\pi$
$44$	−6.46532	−0.974684
$45$	0.103030	0.0153588
$46$	−16.9152	−2.49402
$47$	−1.09584	−0.159845	−0.0799224	−	0.996801i	$-0.525467\pi$
$47$	−1.09584	−0.159845	−0.0799224	+	0.996801i	$0.525467\pi$
$48$	−16.9673	−2.44902
$49$	−2.83107	−0.404439
$50$	13.2508	1.87394
$51$	−3.68446	−0.515928
$52$	6.75360	0.936556
$53$	−3.14381	−0.431836	−0.215918	−	0.976412i	$-0.569274\pi$
$53$	−3.14381	−0.431836	−0.215918	+	0.976412i	$0.569274\pi$
$54$	−15.0003	−2.04128
$55$	0.157284	0.0212082
$56$	16.6420	2.22388
$57$	1.16805	0.154712
$58$	−13.9988	−1.83814
$59$	−8.64986	−1.12612	−0.563058	−	0.826418i	$-0.690375\pi$
$59$	−8.64986	−1.12612	−0.563058	+	0.826418i	$0.690375\pi$
$60$	0.918528	0.118581
$61$	−13.0794	−1.67465	−0.837325	−	0.546705i	$-0.815882\pi$
$61$	−13.0794	−1.67465	−0.837325	+	0.546705i	$0.815882\pi$
$62$	−10.6419	−1.35152
$63$	1.70686	0.215044
$64$	15.1008	1.88760
$65$	−0.164297	−0.0203786
$66$	−4.99038	−0.614273
$67$	−7.37724	−0.901274	−0.450637	−	0.892707i	$-0.648803\pi$
$67$	−7.37724	−0.901274	−0.450637	+	0.892707i	$0.648803\pi$
$68$	12.6889	1.53876
$69$	−9.36090	−1.12692
$70$	−0.668933	−0.0799528
$71$	3.68520	0.437353	0.218677	−	0.975797i	$-0.429826\pi$
$71$	3.68520	0.437353	0.218677	+	0.975797i	$0.429826\pi$
$72$	6.81364	0.802996
$73$	−12.4700	−1.45950	−0.729752	−	0.683712i	$-0.760364\pi$
$73$	−12.4700	−1.45950	−0.729752	+	0.683712i	$0.760364\pi$
$74$	−17.3832	−2.02076
$75$	7.33299	0.846741
$76$	−4.02264	−0.461429
$77$	2.60567	0.296944
$78$	5.21289	0.590243
$79$	10.4393	1.17451	0.587256	−	0.809401i	$-0.300208\pi$
$79$	10.4393	1.17451	0.587256	+	0.809401i	$0.300208\pi$
$80$	−1.42154	−0.158932
$81$	−5.79329	−0.643699
$82$	−14.8645	−1.64151
$83$	−2.55002	−0.279901	−0.139950	−	0.990159i	$-0.544694\pi$
$83$	−2.55002	−0.279901	−0.139950	+	0.990159i	$0.544694\pi$
$84$	15.2169	1.66030
$85$	−0.308687	−0.0334818
$86$	−24.7412	−2.66791
$87$	−7.74696	−0.830561
$88$	10.4016	1.10882
$89$	−4.05771	−0.430117	−0.215058	−	0.976601i	$-0.568994\pi$
$89$	−4.05771	−0.430117	−0.215058	+	0.976601i	$0.568994\pi$
$90$	−0.273877	−0.0288692
$91$	−2.72185	−0.285328
$92$	32.2380	3.36104
$93$	−5.88923	−0.610684
$94$	2.91300	0.300453
$95$	0.0978602	0.0100402
$96$	21.1226	2.15582
$97$	11.8973	1.20798	0.603992	−	0.796990i	$-0.293576\pi$
$97$	11.8973	1.20798	0.603992	+	0.796990i	$0.293576\pi$
$98$	7.52565	0.760205
$99$	1.06682	0.107220
$100$	−25.2541	−2.52541
$101$	14.0613	1.39915	0.699574	−	0.714560i	$-0.253373\pi$
$101$	14.0613	1.39915	0.699574	+	0.714560i	$0.253373\pi$
$102$	9.79416	0.969766
$103$	−8.63753	−0.851082	−0.425541	−	0.904939i	$-0.639916\pi$
$103$	−8.63753	−0.851082	−0.425541	+	0.904939i	$0.639916\pi$
$104$	−10.8654	−1.06544
$105$	−0.370188	−0.0361266
$106$	8.35698	0.811702
$107$	−7.53328	−0.728270	−0.364135	−	0.931346i	$-0.618635\pi$
$107$	−7.53328	−0.728270	−0.364135	+	0.931346i	$0.618635\pi$
$108$	28.5884	2.75092
$109$	−10.7117	−1.02599	−0.512997	−	0.858391i	$-0.671465\pi$
$109$	−10.7117	−1.02599	−0.512997	+	0.858391i	$0.671465\pi$
$110$	−0.418098	−0.0398641
$111$	−9.61987	−0.913078
$112$	−23.5501	−2.22527
$113$	5.82344	0.547823	0.273911	−	0.961755i	$-0.411682\pi$
$113$	5.82344	0.547823	0.273911	+	0.961755i	$0.411682\pi$
$114$	−3.10495	−0.290805
$115$	−0.784264	−0.0731330
$116$	26.6797	2.47715
$117$	−1.11439	−0.103026
$118$	22.9933	2.11671
$119$	−5.11392	−0.468792
$120$	−1.47776	−0.134900
$121$	−9.37140	−0.851945
$122$	34.7682	3.14776
$123$	−8.22602	−0.741715
$124$	20.2819	1.82137
$125$	1.23060	0.110068
$126$	−4.53723	−0.404209
$127$	2.17453	0.192958	0.0964791	−	0.995335i	$-0.469242\pi$
$127$	2.17453	0.192958	0.0964791	+	0.995335i	$0.469242\pi$
$128$	−11.4240	−1.00975
$129$	−13.6918	−1.20549
$130$	0.436740	0.0383046
$131$	−12.7862	−1.11714	−0.558568	−	0.829459i	$-0.688649\pi$
$131$	−12.7862	−1.11714	−0.558568	+	0.829459i	$0.688649\pi$
$132$	9.51093	0.827820
$133$	1.62122	0.140577
$134$	19.6104	1.69408
$135$	−0.695479	−0.0598573
$136$	−20.4143	−1.75052
$137$	2.25089	0.192307	0.0961534	−	0.995367i	$-0.469346\pi$
$137$	2.25089	0.192307	0.0961534	+	0.995367i	$0.469346\pi$
$138$	24.8835	2.11822
$139$	−21.9323	−1.86027	−0.930135	−	0.367218i	$-0.880310\pi$
$139$	−21.9323	−1.86027	−0.930135	+	0.367218i	$0.880310\pi$
$140$	1.27489	0.107748
$141$	1.61206	0.135760
$142$	−9.79613	−0.822073
$143$	−1.70122	−0.142263
$144$	−9.64197	−0.803498
$145$	−0.649047	−0.0539004
$146$	33.1482	2.74336
$147$	4.16470	0.343498
$148$	33.1298	2.72326
$149$	17.5974	1.44163	0.720817	−	0.693125i	$-0.243767\pi$
$149$	17.5974	1.44163	0.720817	+	0.693125i	$0.243767\pi$
$150$	−19.4928	−1.59158
$151$	−4.93173	−0.401339	−0.200669	−	0.979659i	$-0.564312\pi$
$151$	−4.93173	−0.401339	−0.200669	+	0.979659i	$0.564312\pi$
$152$	6.47177	0.524930
$153$	−2.09376	−0.169270
$154$	−6.92648	−0.558152
$155$	−0.493404	−0.0396312
$156$	−9.93500	−0.795437
$157$	14.2892	1.14040	0.570201	−	0.821505i	$-0.306865\pi$
$157$	14.2892	1.14040	0.570201	+	0.821505i	$0.306865\pi$
$158$	−27.7501	−2.20768
$159$	4.62476	0.366767
$160$	1.76967	0.139905
$161$	−12.9926	−1.02396
$162$	15.3999	1.20993
$163$	22.8863	1.79260	0.896298	−	0.443451i	$-0.146246\pi$
$163$	22.8863	1.79260	0.896298	+	0.443451i	$0.146246\pi$
$164$	28.3295	2.21217
$165$	−0.231376	−0.0180126
$166$	6.77854	0.526117
$167$	−6.70468	−0.518824	−0.259412	−	0.965767i	$-0.583529\pi$
$167$	−6.70468	−0.518824	−0.259412	+	0.965767i	$0.583529\pi$
$168$	−24.4815	−1.88879
$169$	−11.2229	−0.863302
$170$	0.820563	0.0629343
$171$	0.663765	0.0507594
$172$	47.1530	3.59538
$173$	1.94342	0.147755	0.0738777	−	0.997267i	$-0.476463\pi$
$173$	1.94342	0.147755	0.0738777	+	0.997267i	$0.476463\pi$
$174$	20.5932	1.56117
$175$	10.1780	0.769382
$176$	−14.7193	−1.10951
$177$	12.7245	0.956434
$178$	10.7863	0.808471
$179$	21.5858	1.61340	0.806698	−	0.590965i	$-0.201253\pi$
$179$	21.5858	1.61340	0.806698	+	0.590965i	$0.201253\pi$
$180$	0.521970	0.0389053
$181$	−4.25783	−0.316482	−0.158241	−	0.987400i	$-0.550582\pi$
$181$	−4.25783	−0.316482	−0.158241	+	0.987400i	$0.550582\pi$
$182$	7.23532	0.536318
$183$	19.2407	1.42232
$184$	−51.8656	−3.82358
$185$	−0.805961	−0.0592554
$186$	15.6549	1.14788
$187$	−3.19631	−0.233737
$188$	−5.55175	−0.404903
$189$	−11.5218	−0.838085
$190$	−0.260135	−0.0188722
$191$	13.2374	0.957824	0.478912	−	0.877863i	$-0.341031\pi$
$191$	13.2374	0.957824	0.478912	+	0.877863i	$0.341031\pi$
$192$	−22.2143	−1.60318
$193$	14.8525	1.06911	0.534554	−	0.845134i	$-0.320480\pi$
$193$	14.8525	1.06911	0.534554	+	0.845134i	$0.320480\pi$
$194$	−31.6257	−2.27059
$195$	0.241692	0.0173079
$196$	−14.3428	−1.02448
$197$	22.4429	1.59899	0.799494	−	0.600674i	$-0.205101\pi$
$197$	22.4429	1.59899	0.799494	+	0.600674i	$0.205101\pi$
$198$	−2.83587	−0.201536
$199$	−10.4590	−0.741422	−0.370711	−	0.928748i	$-0.620886\pi$
$199$	−10.4590	−0.741422	−0.370711	+	0.928748i	$0.620886\pi$
$200$	40.6296	2.87295
$201$	10.8524	0.765471
$202$	−37.3781	−2.62992
$203$	−10.7525	−0.754680
$204$	−18.6662	−1.30690
$205$	−0.689183	−0.0481346
$206$	22.9606	1.59974
$207$	−5.31950	−0.369731
$208$	15.3756	1.06611
$209$	1.01330	0.0700912
$210$	0.984046	0.0679056
$211$	−12.2074	−0.840390	−0.420195	−	0.907434i	$-0.638038\pi$
$211$	−12.2074	−0.840390	−0.420195	+	0.907434i	$0.638038\pi$
$212$	−15.9272	−1.09388
$213$	−5.42118	−0.371453
$214$	20.0252	1.36890
$215$	−1.14711	−0.0782321
$216$	−45.9940	−3.12949
$217$	−8.17406	−0.554891
$218$	28.4742	1.92851
$219$	18.3442	1.23959
$220$	0.796833	0.0537225
$221$	3.33883	0.224594
$222$	25.5719	1.71627
$223$	3.99085	0.267247	0.133624	−	0.991032i	$-0.457339\pi$
$223$	3.99085	0.267247	0.133624	+	0.991032i	$0.457339\pi$
$224$	29.3176	1.95886
$225$	4.16710	0.277807
$226$	−15.4801	−1.02972
$227$	23.1676	1.53769	0.768844	−	0.639437i	$-0.220832\pi$
$227$	23.1676	1.53769	0.768844	+	0.639437i	$0.220832\pi$
$228$	5.91758	0.391901
$229$	−14.5876	−0.963973	−0.481986	−	0.876179i	$-0.660085\pi$
$229$	−14.5876	−0.963973	−0.481986	+	0.876179i	$0.660085\pi$
$230$	2.08476	0.137465
$231$	−3.83312	−0.252201
$232$	−42.9233	−2.81805
$233$	−22.0413	−1.44398	−0.721988	−	0.691906i	$-0.756771\pi$
$233$	−22.0413	−1.44398	−0.721988	+	0.691906i	$0.756771\pi$
$234$	2.96232	0.193653
$235$	0.135059	0.00881030
$236$	−43.8219	−2.85256
$237$	−15.3569	−0.997538
$238$	13.5940	0.881167
$239$	−2.97495	−0.192433	−0.0962167	−	0.995360i	$-0.530674\pi$
$239$	−2.97495	−0.192433	−0.0962167	+	0.995360i	$0.530674\pi$
$240$	2.09117	0.134985
$241$	−6.97510	−0.449306	−0.224653	−	0.974439i	$-0.572125\pi$
$241$	−6.97510	−0.449306	−0.224653	+	0.974439i	$0.572125\pi$
$242$	24.9114	1.60136
$243$	−8.40655	−0.539280
$244$	−66.2631	−4.24206
$245$	0.348922	0.0222918
$246$	21.8667	1.39417
$247$	−1.05848	−0.0673493
$248$	−32.6302	−2.07202
$249$	3.75125	0.237726
$250$	−3.27122	−0.206890
$251$	−13.5245	−0.853658	−0.426829	−	0.904332i	$-0.640369\pi$
$251$	−13.5245	−0.853658	−0.426829	+	0.904332i	$0.640369\pi$
$252$	8.64730	0.544728
$253$	−8.12068	−0.510543
$254$	−5.78040	−0.362695
$255$	0.454100	0.0284368
$256$	0.166096	0.0103810
$257$	−7.74036	−0.482830	−0.241415	−	0.970422i	$-0.577612\pi$
$257$	−7.74036	−0.482830	−0.241415	+	0.970422i	$0.577612\pi$
$258$	36.3959	2.26591
$259$	−13.3521	−0.829658
$260$	−0.832363	−0.0516209
$261$	−4.40235	−0.272498
$262$	33.9887	2.09983
$263$	−5.46077	−0.336726	−0.168363	−	0.985725i	$-0.553848\pi$
$263$	−5.46077	−0.336726	−0.168363	+	0.985725i	$0.553848\pi$
$264$	−15.3015	−0.941743
$265$	0.387466	0.0238019
$266$	−4.30957	−0.264237
$267$	5.96917	0.365307
$268$	−37.3746	−2.28302
$269$	−5.03875	−0.307218	−0.153609	−	0.988132i	$-0.549090\pi$
$269$	−5.03875	−0.307218	−0.153609	+	0.988132i	$0.549090\pi$
$270$	1.84875	0.112511
$271$	28.3921	1.72470	0.862349	−	0.506314i	$-0.168992\pi$
$271$	28.3921	1.72470	0.862349	+	0.506314i	$0.168992\pi$
$272$	28.8883	1.75161
$273$	4.00403	0.242335
$274$	−5.98340	−0.361470
$275$	6.36145	0.383610
$276$	−47.4242	−2.85460
$277$	−16.2218	−0.974673	−0.487337	−	0.873214i	$-0.662032\pi$
$277$	−16.2218	−0.974673	−0.487337	+	0.873214i	$0.662032\pi$
$278$	58.3011	3.49666
$279$	−3.34666	−0.200359
$280$	−2.05108	−0.122576
$281$	−10.6618	−0.636031	−0.318016	−	0.948085i	$-0.603016\pi$
$281$	−10.6618	−0.636031	−0.318016	+	0.948085i	$0.603016\pi$
$282$	−4.28522	−0.255181
$283$	−11.0767	−0.658443	−0.329222	−	0.944253i	$-0.606786\pi$
$283$	−11.0767	−0.658443	−0.329222	+	0.944253i	$0.606786\pi$
$284$	18.6700	1.10786
$285$	−0.143959	−0.00852740
$286$	4.52224	0.267406
$287$	−11.4175	−0.673951
$288$	12.0033	0.707302
$289$	−10.7269	−0.630993
$290$	1.72532	0.101314
$291$	−17.5017	−1.02597
$292$	−63.1756	−3.69707
$293$	16.2931	0.951853	0.475926	−	0.879485i	$-0.342113\pi$
$293$	16.2931	0.951853	0.475926	+	0.879485i	$0.342113\pi$
$294$	−11.0707	−0.645659
$295$	1.06607	0.0620691
$296$	−53.3004	−3.09802
$297$	−7.20136	−0.417865
$298$	−46.7780	−2.70977
$299$	8.48277	0.490571
$300$	37.1504	2.14488
$301$	−19.0037	−1.09536
$302$	13.1097	0.754378
$303$	−20.6851	−1.18833
$304$	−9.15818	−0.525258
$305$	1.61200	0.0923031
$306$	5.56570	0.318170
$307$	−6.26009	−0.357282	−0.178641	−	0.983914i	$-0.557170\pi$
$307$	−6.26009	−0.357282	−0.178641	+	0.983914i	$0.557170\pi$
$308$	13.2009	0.752189
$309$	12.7064	0.722842
$310$	1.31158	0.0744929
$311$	−6.34983	−0.360066	−0.180033	−	0.983661i	$-0.557620\pi$
$311$	−6.34983	−0.360066	−0.180033	+	0.983661i	$0.557620\pi$
$312$	15.9838	0.904903
$313$	−12.4130	−0.701624	−0.350812	−	0.936446i	$-0.614094\pi$
$313$	−12.4130	−0.701624	−0.350812	+	0.936446i	$0.614094\pi$
$314$	−37.9840	−2.14356
$315$	−0.210366	−0.0118528
$316$	52.8876	2.97516
$317$	−12.7675	−0.717095	−0.358548	−	0.933511i	$-0.616728\pi$
$317$	−12.7675	−0.717095	−0.358548	+	0.933511i	$0.616728\pi$
$318$	−12.2937	−0.689396
$319$	−6.72057	−0.376280
$320$	−1.86113	−0.104040
$321$	11.0820	0.618535
$322$	34.5375	1.92470
$323$	−1.98871	−0.110655
$324$	−29.3500	−1.63055
$325$	−6.64510	−0.368604
$326$	−60.8372	−3.36946
$327$	15.7576	0.871398
$328$	−45.5776	−2.51660
$329$	2.23748	0.123356
$330$	0.615050	0.0338574
$331$	12.9665	0.712705	0.356352	−	0.934352i	$-0.384020\pi$
$331$	12.9665	0.712705	0.356352	+	0.934352i	$0.384020\pi$
$332$	−12.9189	−0.709017
$333$	−5.46666	−0.299571
$334$	17.8226	0.975210
$335$	0.909225	0.0496763
$336$	34.6438	1.88997
$337$	30.2355	1.64703	0.823517	−	0.567292i	$-0.192009\pi$
$337$	30.2355	1.64703	0.823517	+	0.567292i	$0.192009\pi$
$338$	29.8332	1.62271
$339$	−8.56667	−0.465278
$340$	−1.56387	−0.0848129
$341$	−5.10897	−0.276666
$342$	−1.76444	−0.0954101
$343$	20.0730	1.08384
$344$	−75.8614	−4.09017
$345$	1.15371	0.0621134
$346$	−5.16606	−0.277729
$347$	7.18036	0.385462	0.192731	−	0.981252i	$-0.438266\pi$
$347$	7.18036	0.385462	0.192731	+	0.981252i	$0.438266\pi$
$348$	−39.2477	−2.10390
$349$	26.1025	1.39724	0.698618	−	0.715495i	$-0.253799\pi$
$349$	26.1025	1.39724	0.698618	+	0.715495i	$0.253799\pi$
$350$	−27.0554	−1.44617
$351$	7.52245	0.401519
$352$	18.3241	0.976679
$353$	−3.78779	−0.201604	−0.100802	−	0.994907i	$-0.532141\pi$
$353$	−3.78779	−0.201604	−0.100802	+	0.994907i	$0.532141\pi$
$354$	−33.8247	−1.79776
$355$	−0.454191	−0.0241060
$356$	−20.5572	−1.08953
$357$	7.52292	0.398155
$358$	−57.3800	−3.03263
$359$	30.1551	1.59152	0.795762	−	0.605609i	$-0.207070\pi$
$359$	30.1551	1.59152	0.795762	+	0.605609i	$0.207070\pi$
$360$	−0.839763	−0.0442594
$361$	−18.3695	−0.966818
$362$	11.3183	0.594878
$363$	13.7860	0.723575
$364$	−13.7895	−0.722765
$365$	1.53689	0.0804447
$366$	−51.1464	−2.67346
$367$	−2.14491	−0.111963	−0.0559817	−	0.998432i	$-0.517829\pi$
$367$	−2.14491	−0.111963	−0.0559817	+	0.998432i	$0.517829\pi$
$368$	73.3948	3.82597
$369$	−4.67458	−0.243349
$370$	2.14243	0.111380
$371$	6.41902	0.333259
$372$	−29.8360	−1.54693
$373$	−17.4326	−0.902628	−0.451314	−	0.892365i	$-0.649045\pi$
$373$	−17.4326	−0.902628	−0.451314	+	0.892365i	$0.649045\pi$
$374$	8.49654	0.439346
$375$	−1.81030	−0.0934833
$376$	8.93185	0.460625
$377$	7.02023	0.361560
$378$	30.6275	1.57531
$379$	14.8171	0.761102	0.380551	−	0.924760i	$-0.375734\pi$
$379$	14.8171	0.761102	0.380551	+	0.924760i	$0.375734\pi$
$380$	0.495780	0.0254330
$381$	−3.19888	−0.163884
$382$	−35.1881	−1.80038
$383$	32.0701	1.63871	0.819353	−	0.573289i	$-0.194333\pi$
$383$	32.0701	1.63871	0.819353	+	0.573289i	$0.194333\pi$
$384$	16.8055	0.857602
$385$	−0.321142	−0.0163669
$386$	−39.4815	−2.00955
$387$	−7.78059	−0.395509
$388$	60.2740	3.05995
$389$	−30.4168	−1.54219	−0.771097	−	0.636718i	$-0.780292\pi$
$389$	−30.4168	−1.54219	−0.771097	+	0.636718i	$0.780292\pi$
$390$	−0.642474	−0.0325329
$391$	15.9377	0.806006
$392$	23.0752	1.16547
$393$	18.8094	0.948808
$394$	−59.6584	−3.00554
$395$	−1.28661	−0.0647366
$396$	5.40475	0.271599
$397$	30.6312	1.53733	0.768667	−	0.639650i	$-0.220920\pi$
$397$	30.6312	1.53733	0.768667	+	0.639650i	$0.220920\pi$
$398$	27.8026	1.39362
$399$	−2.38492	−0.119395
$400$	−57.4948	−2.87474
$401$	12.8447	0.641433	0.320717	−	0.947175i	$-0.396076\pi$
$401$	12.8447	0.641433	0.320717	+	0.947175i	$0.396076\pi$
$402$	−28.8483	−1.43882
$403$	5.33677	0.265843
$404$	71.2372	3.54419
$405$	0.714007	0.0354793
$406$	28.5827	1.41854
$407$	−8.34534	−0.413663
$408$	30.0309	1.48675
$409$	−35.3205	−1.74648	−0.873242	−	0.487287i	$-0.837987\pi$
$409$	−35.3205	−1.74648	−0.873242	+	0.487287i	$0.837987\pi$
$410$	1.83201	0.0904764
$411$	−3.31122	−0.163330
$412$	−43.7595	−2.15588
$413$	17.6612	0.869053
$414$	14.1405	0.694966
$415$	0.314283	0.0154275
$416$	−19.1412	−0.938473
$417$	32.2638	1.57997
$418$	−2.69358	−0.131747
$419$	−13.0390	−0.636995	−0.318498	−	0.947924i	$-0.603178\pi$
$419$	−13.0390	−0.636995	−0.318498	+	0.947924i	$0.603178\pi$
$420$	−1.87545	−0.0915124
$421$	−15.0702	−0.734478	−0.367239	−	0.930127i	$-0.619697\pi$
$421$	−15.0702	−0.734478	−0.367239	+	0.930127i	$0.619697\pi$
$422$	32.4500	1.57964
$423$	0.916079	0.0445413
$424$	25.6242	1.24442
$425$	−12.4850	−0.605614
$426$	14.4108	0.698204
$427$	26.7055	1.29237
$428$	−38.1652	−1.84478
$429$	2.50261	0.120827
$430$	3.04928	0.147049
$431$	35.3658	1.70351	0.851755	−	0.523940i	$-0.175539\pi$
$431$	35.3658	1.70351	0.851755	+	0.523940i	$0.175539\pi$
$432$	65.0859	3.13145
$433$	−28.5793	−1.37343	−0.686716	−	0.726926i	$-0.740948\pi$
$433$	−28.5793	−1.37343	−0.686716	+	0.726926i	$0.740948\pi$
$434$	21.7286	1.04300
$435$	0.954792	0.0457788
$436$	−54.2676	−2.59895
$437$	−5.05259	−0.241698
$438$	−48.7632	−2.33000
$439$	38.1836	1.82240	0.911201	−	0.411962i	$-0.135156\pi$
$439$	38.1836	1.82240	0.911201	+	0.411962i	$0.135156\pi$
$440$	−1.28197	−0.0611157
$441$	2.36666	0.112698
$442$	−8.87539	−0.422159
$443$	39.1935	1.86214	0.931071	−	0.364838i	$-0.118876\pi$
$443$	39.1935	1.86214	0.931071	+	0.364838i	$0.118876\pi$
$444$	−48.7362	−2.31292
$445$	0.500102	0.0237071
$446$	−10.6086	−0.502332
$447$	−25.8870	−1.22441
$448$	−30.8327	−1.45671
$449$	14.4712	0.682940	0.341470	−	0.939893i	$-0.389075\pi$
$449$	14.4712	0.682940	0.341470	+	0.939893i	$0.389075\pi$
$450$	−11.0771	−0.522181
$451$	−7.13616	−0.336029
$452$	29.5027	1.38769
$453$	7.25491	0.340865
$454$	−61.5849	−2.89032
$455$	0.335461	0.0157267
$456$	−9.52041	−0.445834
$457$	−2.23754	−0.104668	−0.0523338	−	0.998630i	$-0.516666\pi$
$457$	−2.23754	−0.104668	−0.0523338	+	0.998630i	$0.516666\pi$
$458$	38.7771	1.81194
$459$	14.1335	0.659693
$460$	−3.97324	−0.185253
$461$	−4.76473	−0.221916	−0.110958	−	0.993825i	$-0.535392\pi$
$461$	−4.76473	−0.221916	−0.110958	+	0.993825i	$0.535392\pi$
$462$	10.1893	0.474050
$463$	−20.1966	−0.938617	−0.469309	−	0.883034i	$-0.655497\pi$
$463$	−20.1966	−0.938617	−0.469309	+	0.883034i	$0.655497\pi$
$464$	60.7406	2.81981
$465$	0.725831	0.0336596
$466$	58.5910	2.71418
$467$	19.5488	0.904611	0.452306	−	0.891863i	$-0.350602\pi$
$467$	19.5488	0.904611	0.452306	+	0.891863i	$0.350602\pi$
$468$	−5.64574	−0.260974
$469$	15.0628	0.695537
$470$	−0.359019	−0.0165603
$471$	−21.0204	−0.968568
$472$	70.5022	3.24513
$473$	−11.8778	−0.546140
$474$	40.8222	1.87503
$475$	3.95802	0.181606
$476$	−25.9081	−1.18750
$477$	2.62810	0.120332
$478$	7.90810	0.361708
$479$	−0.979237	−0.0447425	−0.0223712	−	0.999750i	$-0.507122\pi$
$479$	−0.979237	−0.0447425	−0.0223712	+	0.999750i	$0.507122\pi$
$480$	−2.60331	−0.118824
$481$	8.71745	0.397481
$482$	18.5414	0.844540
$483$	19.1130	0.869674
$484$	−47.4774	−2.15806
$485$	−1.46631	−0.0665815
$486$	22.3466	1.01366
$487$	27.8793	1.26333	0.631666	−	0.775241i	$-0.282371\pi$
$487$	27.8793	1.26333	0.631666	+	0.775241i	$0.282371\pi$
$488$	106.606	4.82584
$489$	−33.6674	−1.52249
$490$	−0.927516	−0.0419009
$491$	−3.72056	−0.167907	−0.0839534	−	0.996470i	$-0.526755\pi$
$491$	−3.72056	−0.167907	−0.0839534	+	0.996470i	$0.526755\pi$
$492$	−41.6747	−1.87884
$493$	13.1899	0.594041
$494$	2.81368	0.126593
$495$	−0.131483	−0.00590973
$496$	46.1749	2.07331
$497$	−7.52443	−0.337517
$498$	−9.97169	−0.446842
$499$	39.3383	1.76102	0.880511	−	0.474025i	$-0.157199\pi$
$499$	39.3383	1.76102	0.880511	+	0.474025i	$0.157199\pi$
$500$	6.23447	0.278814
$501$	9.86304	0.440648
$502$	35.9512	1.60458
$503$	35.8281	1.59749	0.798747	−	0.601667i	$-0.205496\pi$
$503$	35.8281	1.59749	0.798747	+	0.601667i	$0.205496\pi$
$504$	−13.9121	−0.619693
$505$	−1.73301	−0.0771181
$506$	21.5867	0.959645
$507$	16.5097	0.733221
$508$	11.0166	0.488783
$509$	−0.332989	−0.0147595	−0.00737974	−	0.999973i	$-0.502349\pi$
$509$	−0.332989	−0.0147595	−0.00737974	+	0.999973i	$0.502349\pi$
$510$	−1.20710	−0.0534514
$511$	25.4612	1.12634
$512$	22.4065	0.990237
$513$	−4.48059	−0.197823
$514$	20.5757	0.907554
$515$	1.06455	0.0469098
$516$	−69.3653	−3.05364
$517$	1.39848	0.0615049
$518$	35.4929	1.55947
$519$	−2.85890	−0.125492
$520$	1.33913	0.0587249
$521$	15.4969	0.678930	0.339465	−	0.940619i	$-0.389754\pi$
$521$	15.4969	0.678930	0.339465	+	0.940619i	$0.389754\pi$
$522$	11.7025	0.512203
$523$	−15.5011	−0.677816	−0.338908	−	0.940820i	$-0.610057\pi$
$523$	−15.5011	−0.677816	−0.338908	+	0.940820i	$0.610057\pi$
$524$	−64.7775	−2.82982
$525$	−14.9725	−0.653452
$526$	14.5160	0.632928
$527$	10.0269	0.436779
$528$	21.6531	0.942331
$529$	17.4921	0.760525
$530$	−1.02998	−0.0447393
$531$	7.23093	0.313796
$532$	8.21341	0.356097
$533$	7.45435	0.322884
$534$	−15.8674	−0.686651
$535$	0.928457	0.0401407
$536$	60.1296	2.59720
$537$	−31.7541	−1.37029
$538$	13.3942	0.577463
$539$	3.61292	0.155620
$540$	−3.52344	−0.151625
$541$	−26.0999	−1.12212	−0.561061	−	0.827774i	$-0.689607\pi$
$541$	−26.0999	−1.12212	−0.561061	+	0.827774i	$0.689607\pi$
$542$	−75.4729	−3.24184
$543$	6.26356	0.268795
$544$	−35.9631	−1.54191
$545$	1.32019	0.0565506
$546$	−10.6437	−0.455506
$547$	−5.71922	−0.244536	−0.122268	−	0.992497i	$-0.539017\pi$
$547$	−5.71922	−0.244536	−0.122268	+	0.992497i	$0.539017\pi$
$548$	11.4035	0.487133
$549$	10.9339	0.466647
$550$	−16.9102	−0.721054
$551$	−4.18146	−0.178136
$552$	76.2977	3.24745
$553$	−21.3149	−0.906401
$554$	43.1213	1.83205
$555$	1.18562	0.0503269
$556$	−111.113	−4.71225
$557$	33.7544	1.43022	0.715110	−	0.699012i	$-0.246377\pi$
$557$	33.7544	1.43022	0.715110	+	0.699012i	$0.246377\pi$
$558$	8.89619	0.376606
$559$	12.4074	0.524776
$560$	2.90248	0.122652
$561$	4.70199	0.198518
$562$	28.3416	1.19552
$563$	−33.3496	−1.40552	−0.702759	−	0.711428i	$-0.748049\pi$
$563$	−33.3496	−1.40552	−0.702759	+	0.711428i	$0.748049\pi$
$564$	8.16700	0.343893
$565$	−0.717723	−0.0301948
$566$	29.4445	1.23765
$567$	11.8287	0.496759
$568$	−30.0369	−1.26032
$569$	18.5066	0.775838	0.387919	−	0.921693i	$-0.373194\pi$
$569$	18.5066	0.775838	0.387919	+	0.921693i	$0.373194\pi$
$570$	0.382677	0.0160286
$571$	−22.2615	−0.931615	−0.465808	−	0.884886i	$-0.654236\pi$
$571$	−22.2615	−0.931615	−0.465808	+	0.884886i	$0.654236\pi$
$572$	−8.61872	−0.360367
$573$	−19.4731	−0.813500
$574$	30.3503	1.26680
$575$	−31.7200	−1.32282
$576$	−12.6237	−0.525986
$577$	−32.7314	−1.36263	−0.681313	−	0.731992i	$-0.738591\pi$
$577$	−32.7314	−1.36263	−0.681313	+	0.731992i	$0.738591\pi$
$578$	28.5146	1.18605
$579$	−21.8491	−0.908016
$580$	−3.28820	−0.136535
$581$	5.20661	0.216007
$582$	46.5236	1.92846
$583$	4.01203	0.166161
$584$	101.639	4.20585
$585$	0.137346	0.00567855
$586$	−43.3108	−1.78915
$587$	−13.5519	−0.559346	−0.279673	−	0.960095i	$-0.590226\pi$
$587$	−13.5519	−0.559346	−0.279673	+	0.960095i	$0.590226\pi$
$588$	21.0992	0.870117
$589$	−3.17874	−0.130978
$590$	−2.83387	−0.116668
$591$	−33.0150	−1.35805
$592$	75.4253	3.09996
$593$	−29.3196	−1.20401	−0.602006	−	0.798491i	$-0.705632\pi$
$593$	−29.3196	−1.20401	−0.602006	+	0.798491i	$0.705632\pi$
$594$	19.1429	0.785442
$595$	0.630276	0.0258388
$596$	89.1520	3.65181
$597$	15.3860	0.629705
$598$	−22.5492	−0.922105
$599$	−33.1465	−1.35433	−0.677165	−	0.735831i	$-0.736792\pi$
$599$	−33.1465	−1.35433	−0.677165	+	0.735831i	$0.736792\pi$
$600$	−59.7689	−2.44006
$601$	0.0735303	0.00299936	0.00149968	−	0.999999i	$-0.499523\pi$
$601$	0.0735303	0.00299936	0.00149968	+	0.999999i	$0.499523\pi$
$602$	50.5164	2.05889
$603$	6.16708	0.251143
$604$	−24.9852	−1.01663
$605$	1.15500	0.0469574
$606$	54.9858	2.23364
$607$	19.8711	0.806542	0.403271	−	0.915081i	$-0.367873\pi$
$607$	19.8711	0.806542	0.403271	+	0.915081i	$0.367873\pi$
$608$	11.4010	0.462373
$609$	15.8177	0.640966
$610$	−4.28509	−0.173498
$611$	−1.46083	−0.0590989
$612$	−10.6074	−0.428779
$613$	21.7731	0.879409	0.439705	−	0.898142i	$-0.355083\pi$
$613$	21.7731	0.879409	0.439705	+	0.898142i	$0.355083\pi$
$614$	16.6408	0.671567
$615$	1.01383	0.0408817
$616$	−21.2380	−0.855704
$617$	18.1435	0.730430	0.365215	−	0.930923i	$-0.380995\pi$
$617$	18.1435	0.730430	0.365215	+	0.930923i	$0.380995\pi$
$618$	−33.7766	−1.35869
$619$	9.55638	0.384103	0.192052	−	0.981385i	$-0.438486\pi$
$619$	9.55638	0.384103	0.192052	+	0.981385i	$0.438486\pi$
$620$	−2.49969	−0.100390
$621$	35.9080	1.44094
$622$	16.8793	0.676799
$623$	8.28502	0.331932
$624$	−22.6186	−0.905468
$625$	24.7724	0.990895
$626$	32.9966	1.31881
$627$	−1.49063	−0.0595299
$628$	72.3920	2.88875
$629$	16.3786	0.653059
$630$	0.559201	0.0222791
$631$	−5.80640	−0.231149	−0.115575	−	0.993299i	$-0.536871\pi$
$631$	−5.80640	−0.231149	−0.115575	+	0.993299i	$0.536871\pi$
$632$	−85.0873	−3.38459
$633$	17.9579	0.713761
$634$	33.9390	1.34789
$635$	−0.268005	−0.0106354
$636$	23.4300	0.929059
$637$	−3.77401	−0.149532
$638$	17.8648	0.707276
$639$	−3.08068	−0.121870
$640$	1.40798	0.0556553
$641$	21.8923	0.864694	0.432347	−	0.901707i	$-0.357686\pi$
$641$	21.8923	0.864694	0.432347	+	0.901707i	$0.357686\pi$
$642$	−29.4585	−1.16263
$643$	33.3216	1.31408	0.657038	−	0.753858i	$-0.271809\pi$
$643$	33.3216	1.31408	0.657038	+	0.753858i	$0.271809\pi$
$644$	−65.8233	−2.59380
$645$	1.68747	0.0664442
$646$	5.28644	0.207992
$647$	−29.5283	−1.16088	−0.580438	−	0.814305i	$-0.697119\pi$
$647$	−29.5283	−1.16088	−0.580438	+	0.814305i	$0.697119\pi$
$648$	47.2193	1.85495
$649$	11.0387	0.433305
$650$	17.6642	0.692848
$651$	12.0246	0.471281
$652$	115.947	4.54083
$653$	38.6693	1.51325	0.756624	−	0.653850i	$-0.226847\pi$
$653$	38.6693	1.51325	0.756624	+	0.653850i	$0.226847\pi$
$654$	−41.8874	−1.63793
$655$	1.57587	0.0615742
$656$	64.4967	2.51817
$657$	10.4244	0.406695
$658$	−5.94775	−0.231867
$659$	−14.2591	−0.555456	−0.277728	−	0.960660i	$-0.589581\pi$
$659$	−14.2591	−0.555456	−0.277728	+	0.960660i	$0.589581\pi$
$660$	−1.17220	−0.0456277
$661$	−21.4216	−0.833202	−0.416601	−	0.909089i	$-0.636779\pi$
$661$	−21.4216	−0.833202	−0.416601	+	0.909089i	$0.636779\pi$
$662$	−34.4681	−1.33964
$663$	−4.91164	−0.190752
$664$	20.7844	0.806591
$665$	−0.199811	−0.00774832
$666$	14.5317	0.563090
$667$	33.5107	1.29754
$668$	−33.9673	−1.31423
$669$	−5.87081	−0.226979
$670$	−2.41693	−0.0933743
$671$	16.6916	0.644370
$672$	−43.1281	−1.66370
$673$	5.83221	0.224815	0.112408	−	0.993662i	$-0.464144\pi$
$673$	5.83221	0.224815	0.112408	+	0.993662i	$0.464144\pi$
$674$	−80.3730	−3.09585
$675$	−28.1291	−1.08269
$676$	−56.8576	−2.18683
$677$	−2.33503	−0.0897423	−0.0448712	−	0.998993i	$-0.514288\pi$
$677$	−2.33503	−0.0897423	−0.0448712	+	0.998993i	$0.514288\pi$
$678$	22.7722	0.874561
$679$	−24.2918	−0.932233
$680$	2.51601	0.0964847
$681$	−34.0811	−1.30599
$682$	13.5808	0.520037
$683$	17.6777	0.676419	0.338209	−	0.941071i	$-0.390179\pi$
$683$	17.6777	0.676419	0.338209	+	0.941071i	$0.390179\pi$
$684$	3.36277	0.128579
$685$	−0.277416	−0.0105995
$686$	−53.3588	−2.03725
$687$	21.4593	0.818723
$688$	107.351	4.09273
$689$	−4.19092	−0.159661
$690$	−3.06682	−0.116752
$691$	25.8715	0.984200	0.492100	−	0.870539i	$-0.336229\pi$
$691$	25.8715	0.984200	0.492100	+	0.870539i	$0.336229\pi$
$692$	9.84575	0.374279
$693$	−2.17824	−0.0827444
$694$	−19.0871	−0.724535
$695$	2.70309	0.102534
$696$	63.1430	2.39343
$697$	14.0055	0.530496
$698$	−69.3866	−2.62632
$699$	32.4243	1.22640
$700$	51.5636	1.94892
$701$	−31.4019	−1.18603	−0.593017	−	0.805190i	$-0.702063\pi$
$701$	−31.4019	−1.18603	−0.593017	+	0.805190i	$0.702063\pi$
$702$	−19.9964	−0.754717
$703$	−5.19237	−0.195834
$704$	−19.2712	−0.726309
$705$	−0.198681	−0.00748277
$706$	10.0688	0.378946
$707$	−28.7102	−1.07976
$708$	64.4650	2.42274
$709$	4.68375	0.175902	0.0879509	−	0.996125i	$-0.471968\pi$
$709$	4.68375	0.175902	0.0879509	+	0.996125i	$0.471968\pi$
$710$	1.20735	0.0453109
$711$	−8.72683	−0.327282
$712$	33.0731	1.23947
$713$	25.4748	0.954038
$714$	−19.9977	−0.748394
$715$	0.209671	0.00784124
$716$	109.358	4.08689
$717$	4.37635	0.163438
$718$	−80.1593	−2.99152
$719$	40.1197	1.49621	0.748106	−	0.663580i	$-0.230964\pi$
$719$	40.1197	1.49621	0.748106	+	0.663580i	$0.230964\pi$
$720$	1.18835	0.0442871
$721$	17.6361	0.656802
$722$	48.8305	1.81728
$723$	10.2608	0.381605
$724$	−21.5711	−0.801682
$725$	−26.2511	−0.974941
$726$	−36.6463	−1.36007
$727$	19.5640	0.725589	0.362794	−	0.931869i	$-0.381823\pi$
$727$	19.5640	0.725589	0.362794	+	0.931869i	$0.381823\pi$
$728$	22.1850	0.822230
$729$	29.7465	1.10172
$730$	−4.08542	−0.151208
$731$	23.3114	0.862203
$732$	97.4775	3.60287
$733$	−15.5232	−0.573361	−0.286681	−	0.958026i	$-0.592552\pi$
$733$	−15.5232	−0.573361	−0.286681	+	0.958026i	$0.592552\pi$
$734$	5.70167	0.210453
$735$	−0.513288	−0.0189329
$736$	−91.3694	−3.36792
$737$	9.41460	0.346791
$738$	12.4261	0.457412
$739$	−36.0840	−1.32737	−0.663686	−	0.748012i	$-0.731009\pi$
$739$	−36.0840	−1.32737	−0.663686	+	0.748012i	$0.731009\pi$
$740$	−4.08316	−0.150100
$741$	1.55709	0.0572012
$742$	−17.0633	−0.626412
$743$	6.71066	0.246190	0.123095	−	0.992395i	$-0.460718\pi$
$743$	6.71066	0.246190	0.123095	+	0.992395i	$0.460718\pi$
$744$	48.0012	1.75981
$745$	−2.16883	−0.0794598
$746$	46.3400	1.69663
$747$	2.13171	0.0779953
$748$	−16.1932	−0.592081
$749$	15.3814	0.562025
$750$	4.81219	0.175716
$751$	46.0707	1.68114	0.840571	−	0.541701i	$-0.182219\pi$
$751$	46.0707	1.68114	0.840571	+	0.541701i	$0.182219\pi$
$752$	−12.6394	−0.460913
$753$	19.8954	0.725030
$754$	−18.6614	−0.679608
$755$	0.607823	0.0221209
$756$	−58.3716	−2.12295
$757$	2.24877	0.0817329	0.0408664	−	0.999165i	$-0.486988\pi$
$757$	2.24877	0.0817329	0.0408664	+	0.999165i	$0.486988\pi$
$758$	−39.3872	−1.43061
$759$	11.9461	0.433615
$760$	−0.797628	−0.0289330
$761$	31.9562	1.15841	0.579206	−	0.815181i	$-0.303363\pi$
$761$	31.9562	1.15841	0.579206	+	0.815181i	$0.303363\pi$
$762$	8.50337	0.308044
$763$	21.8711	0.791786
$764$	67.0633	2.42626
$765$	0.258050	0.00932983
$766$	−85.2498	−3.08020
$767$	−11.5309	−0.416355
$768$	−0.244338	−0.00881679
$769$	2.48880	0.0897486	0.0448743	−	0.998993i	$-0.485711\pi$
$769$	2.48880	0.0897486	0.0448743	+	0.998993i	$0.485711\pi$
$770$	0.853670	0.0307641
$771$	11.3866	0.410078
$772$	75.2459	2.70816
$773$	−2.76538	−0.0994638	−0.0497319	−	0.998763i	$-0.515837\pi$
$773$	−2.76538	−0.0994638	−0.0497319	+	0.998763i	$0.515837\pi$
$774$	20.6826	0.743421
$775$	−19.9560	−0.716842
$776$	−96.9709	−3.48105
$777$	19.6418	0.704646
$778$	80.8550	2.89879
$779$	−4.44003	−0.159081
$780$	1.22446	0.0438428
$781$	−4.70293	−0.168284
$782$	−42.3662	−1.51501
$783$	29.7170	1.06200
$784$	−32.6536	−1.16620
$785$	−1.76110	−0.0628565
$786$	−49.9997	−1.78343
$787$	−21.0935	−0.751900	−0.375950	−	0.926640i	$-0.622684\pi$
$787$	−21.0935	−0.751900	−0.375950	+	0.926640i	$0.622684\pi$
$788$	113.700	4.05040
$789$	8.03316	0.285988
$790$	3.42012	0.121682
$791$	−11.8903	−0.422769
$792$	−8.69535	−0.308976
$793$	−17.4358	−0.619163
$794$	−81.4247	−2.88966
$795$	−0.569989	−0.0202154
$796$	−52.9876	−1.87810
$797$	33.5808	1.18949	0.594747	−	0.803913i	$-0.297252\pi$
$797$	33.5808	1.18949	0.594747	+	0.803913i	$0.297252\pi$
$798$	6.33967	0.224422
$799$	−2.74466	−0.0970991
$800$	71.5755	2.53058
$801$	3.39209	0.119853
$802$	−34.1442	−1.20567
$803$	15.9138	0.561586
$804$	54.9806	1.93902
$805$	1.60131	0.0564386
$806$	−14.1864	−0.499694
$807$	7.41234	0.260927
$808$	−114.609	−4.03193
$809$	−17.8743	−0.628429	−0.314214	−	0.949352i	$-0.601741\pi$
$809$	−17.8743	−0.628429	−0.314214	+	0.949352i	$0.601741\pi$
$810$	−1.89800	−0.0666888
$811$	28.5801	1.00358	0.501791	−	0.864989i	$-0.332674\pi$
$811$	28.5801	1.00358	0.501791	+	0.864989i	$0.332674\pi$
$812$	−54.4745	−1.91168
$813$	−41.7667	−1.46482
$814$	22.1839	0.777544
$815$	−2.82068	−0.0988041
$816$	−42.4966	−1.48768
$817$	−7.39019	−0.258550
$818$	93.8900	3.28279
$819$	2.27536	0.0795076
$820$	−3.49154	−0.121930
$821$	−47.7934	−1.66800	−0.834000	−	0.551764i	$-0.813955\pi$
$821$	−47.7934	−1.66800	−0.834000	+	0.551764i	$0.813955\pi$
$822$	8.80198	0.307004
$823$	−24.8377	−0.865788	−0.432894	−	0.901445i	$-0.642508\pi$
$823$	−24.8377	−0.865788	−0.432894	+	0.901445i	$0.642508\pi$
$824$	70.4018	2.45256
$825$	−9.35813	−0.325808
$826$	−46.9477	−1.63352
$827$	−4.72241	−0.164214	−0.0821072	−	0.996624i	$-0.526165\pi$
$827$	−4.72241	−0.164214	−0.0821072	+	0.996624i	$0.526165\pi$
$828$	−26.9496	−0.936565
$829$	2.58244	0.0896918	0.0448459	−	0.998994i	$-0.485720\pi$
$829$	2.58244	0.0896918	0.0448459	+	0.998994i	$0.485720\pi$
$830$	−0.835437	−0.0289984
$831$	23.8634	0.827811
$832$	20.1304	0.697897
$833$	−7.09075	−0.245680
$834$	−85.7648	−2.96979
$835$	0.826334	0.0285965
$836$	5.13357	0.177548
$837$	22.5908	0.780853
$838$	34.6606	1.19733
$839$	27.9234	0.964024	0.482012	−	0.876165i	$-0.339906\pi$
$839$	27.9234	0.964024	0.482012	+	0.876165i	$0.339906\pi$
$840$	3.01728	0.104106
$841$	−1.26698	−0.0436888
$842$	40.0602	1.38056
$843$	15.6843	0.540195
$844$	−61.8450	−2.12879
$845$	1.38320	0.0475834
$846$	−2.43515	−0.0837222
$847$	19.1345	0.657468
$848$	−36.2608	−1.24520
$849$	16.2946	0.559230
$850$	33.1882	1.13834
$851$	41.6123	1.42645
$852$	−27.4648	−0.940929
$853$	51.7741	1.77271	0.886355	−	0.463006i	$-0.153229\pi$
$853$	51.7741	1.77271	0.886355	+	0.463006i	$0.153229\pi$
$854$	−70.9895	−2.42921
$855$	−0.0818072	−0.00279775
$856$	61.4014	2.09866
$857$	53.7137	1.83482	0.917412	−	0.397939i	$-0.130275\pi$
$857$	53.7137	1.83482	0.917412	+	0.397939i	$0.130275\pi$
$858$	−6.65252	−0.227113
$859$	−1.73783	−0.0592941	−0.0296471	−	0.999560i	$-0.509438\pi$
$859$	−1.73783	−0.0592941	−0.0296471	+	0.999560i	$0.509438\pi$
$860$	−5.81148	−0.198170
$861$	16.7958	0.572401
$862$	−94.0105	−3.20201
$863$	−52.7174	−1.79452	−0.897260	−	0.441502i	$-0.854446\pi$
$863$	−52.7174	−1.79452	−0.897260	+	0.441502i	$0.854446\pi$
$864$	−81.0256	−2.75655
$865$	−0.239521	−0.00814396
$866$	75.9703	2.58158
$867$	15.7800	0.535916
$868$	−41.4114	−1.40560
$869$	−13.3223	−0.451927
$870$	−2.53806	−0.0860482
$871$	−9.83438	−0.333225
$872$	87.3075	2.95661
$873$	−9.94564	−0.336609
$874$	13.4310	0.454309
$875$	−2.51263	−0.0849426
$876$	92.9355	3.14000
$877$	40.5530	1.36938	0.684689	−	0.728836i	$-0.259938\pi$
$877$	40.5530	1.36938	0.684689	+	0.728836i	$0.259938\pi$
$878$	−101.501	−3.42549
$879$	−23.9682	−0.808429
$880$	1.81412	0.0611539
$881$	−27.5684	−0.928802	−0.464401	−	0.885625i	$-0.653730\pi$
$881$	−27.5684	−0.928802	−0.464401	+	0.885625i	$0.653730\pi$
$882$	−6.29114	−0.211834
$883$	25.7517	0.866614	0.433307	−	0.901246i	$-0.357347\pi$
$883$	25.7517	0.866614	0.433307	+	0.901246i	$0.357347\pi$
$884$	16.9152	0.568919
$885$	−1.56826	−0.0527166
$886$	−104.186	−3.50018
$887$	−24.6468	−0.827560	−0.413780	−	0.910377i	$-0.635792\pi$
$887$	−24.6468	−0.827560	−0.413780	+	0.910377i	$0.635792\pi$
$888$	78.4085	2.63122
$889$	−4.43994	−0.148911
$890$	−1.32939	−0.0445612
$891$	7.39321	0.247682
$892$	20.2185	0.676964
$893$	0.870114	0.0291173
$894$	68.8136	2.30147
$895$	−2.66039	−0.0889269
$896$	23.3255	0.779250
$897$	−12.4787	−0.416653
$898$	−38.4679	−1.28369
$899$	21.0826	0.703144
$900$	21.1114	0.703713
$901$	−7.87405	−0.262323
$902$	18.9696	0.631618
$903$	27.9558	0.930310
$904$	−47.4650	−1.57866
$905$	0.524767	0.0174438
$906$	−19.2852	−0.640709
$907$	−44.2748	−1.47012	−0.735060	−	0.678002i	$-0.762846\pi$
$907$	−44.2748	−1.47012	−0.735060	+	0.678002i	$0.762846\pi$
$908$	117.372	3.89512
$909$	−11.7547	−0.389877
$910$	−0.891734	−0.0295607
$911$	−22.9975	−0.761941	−0.380971	−	0.924587i	$-0.624410\pi$
$911$	−22.9975	−0.761941	−0.380971	+	0.924587i	$0.624410\pi$
$912$	13.4723	0.446113
$913$	3.25425	0.107700
$914$	5.94790	0.196739
$915$	−2.37137	−0.0783950
$916$	−73.9035	−2.44184
$917$	26.1068	0.862123
$918$	−37.5700	−1.23999
$919$	35.6080	1.17460	0.587300	−	0.809369i	$-0.300191\pi$
$919$	35.6080	1.17460	0.587300	+	0.809369i	$0.300191\pi$
$920$	6.39229	0.210747
$921$	9.20902	0.303447
$922$	12.6658	0.417125
$923$	4.91263	0.161701
$924$	−19.4194	−0.638850
$925$	−32.5976	−1.07180
$926$	53.6874	1.76428
$927$	7.22063	0.237157
$928$	−75.6161	−2.48222
$929$	−36.3221	−1.19169	−0.595845	−	0.803099i	$-0.703183\pi$
$929$	−36.3221	−1.19169	−0.595845	+	0.803099i	$0.703183\pi$
$930$	−1.92943	−0.0632684
$931$	2.24791	0.0736724
$932$	−111.666	−3.65774
$933$	9.34103	0.305812
$934$	−51.9653	−1.70036
$935$	0.393937	0.0128831
$936$	9.08306	0.296889
$937$	−3.50674	−0.114560	−0.0572801	−	0.998358i	$-0.518243\pi$
$937$	−3.50674	−0.114560	−0.0572801	+	0.998358i	$0.518243\pi$
$938$	−40.0405	−1.30737
$939$	18.2603	0.595904
$940$	0.684238	0.0223174
$941$	26.7201	0.871050	0.435525	−	0.900177i	$-0.356563\pi$
$941$	26.7201	0.871050	0.435525	+	0.900177i	$0.356563\pi$
$942$	55.8771	1.82057
$943$	35.5830	1.15874
$944$	−99.7675	−3.24716
$945$	1.42003	0.0461934
$946$	31.5738	1.02655
$947$	−18.8544	−0.612687	−0.306344	−	0.951921i	$-0.599106\pi$
$947$	−18.8544	−0.612687	−0.306344	+	0.951921i	$0.599106\pi$
$948$	−77.8012	−2.52686
$949$	−16.6234	−0.539618
$950$	−10.5213	−0.341357
$951$	18.7819	0.609044
$952$	41.6819	1.35092
$953$	−48.0782	−1.55741	−0.778703	−	0.627393i	$-0.784122\pi$
$953$	−48.0782	−1.55741	−0.778703	+	0.627393i	$0.784122\pi$
$954$	−6.98610	−0.226183
$955$	−1.63147	−0.0527932
$956$	−15.0717	−0.487453
$957$	9.88642	0.319582
$958$	2.60304	0.0841004
$959$	−4.59586	−0.148408
$960$	2.73785	0.0883638
$961$	−14.9730	−0.483001
$962$	−23.1730	−0.747128
$963$	6.29752	0.202935
$964$	−35.3373	−1.13814
$965$	−1.83053	−0.0589270
$966$	−50.8069	−1.63469
$967$	20.2183	0.650176	0.325088	−	0.945684i	$-0.394606\pi$
$967$	20.2183	0.650176	0.325088	+	0.945684i	$0.394606\pi$
$968$	76.3833	2.45505
$969$	2.92552	0.0939812
$970$	3.89778	0.125150
$971$	−15.5725	−0.499746	−0.249873	−	0.968279i	$-0.580389\pi$
$971$	−15.5725	−0.499746	−0.249873	+	0.968279i	$0.580389\pi$
$972$	−42.5893	−1.36605
$973$	44.7812	1.43562
$974$	−74.1097	−2.37463
$975$	9.77539	0.313063
$976$	−150.858	−4.82886
$977$	−19.1176	−0.611626	−0.305813	−	0.952092i	$-0.598928\pi$
$977$	−19.1176	−0.611626	−0.305813	+	0.952092i	$0.598928\pi$
$978$	89.4957	2.86176
$979$	5.17832	0.165500
$980$	1.76771	0.0564674
$981$	8.95454	0.285896
$982$	9.89013	0.315607
$983$	−16.1669	−0.515644	−0.257822	−	0.966192i	$-0.583005\pi$
$983$	−16.1669	−0.515644	−0.257822	+	0.966192i	$0.583005\pi$
$984$	67.0477	2.13740
$985$	−2.76602	−0.0881328
$986$	−35.0617	−1.11659
$987$	−3.29149	−0.104769
$988$	−5.36246	−0.170603
$989$	59.2259	1.88327
$990$	0.349513	0.0111083
$991$	−20.5614	−0.653153	−0.326576	−	0.945171i	$-0.605895\pi$
$991$	−20.5614	−0.653153	−0.326576	+	0.945171i	$0.605895\pi$
$992$	−57.4832	−1.82509
$993$	−19.0746	−0.605315
$994$	20.0017	0.634415
$995$	1.28905	0.0408656
$996$	19.0046	0.602183
$997$	4.38677	0.138930	0.0694652	−	0.997584i	$-0.477871\pi$
$997$	4.38677	0.138930	0.0694652	+	0.997584i	$0.477871\pi$
$998$	−104.570	−3.31011
$999$	36.9014	1.16751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.3	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.65823 q^{2} -1.47107 q^{3} +5.06620 q^{4} -0.123247 q^{5} +3.91044 q^{6} -2.04180 q^{7} -8.15068 q^{8} -0.835960 q^{9} +O(q^{10})\)	\(q-2.65823 q^{2} -1.47107 q^{3} +5.06620 q^{4} -0.123247 q^{5} +3.91044 q^{6} -2.04180 q^{7} -8.15068 q^{8} -0.835960 q^{9} +0.327620 q^{10} -1.27617 q^{11} -7.45273 q^{12} +1.33307 q^{13} +5.42757 q^{14} +0.181305 q^{15} +11.5340 q^{16} +2.50462 q^{17} +2.22218 q^{18} -0.794015 q^{19} -0.624396 q^{20} +3.00362 q^{21} +3.39235 q^{22} +6.36334 q^{23} +11.9902 q^{24} -4.98481 q^{25} -3.54361 q^{26} +5.64296 q^{27} -10.3442 q^{28} +5.26622 q^{29} -0.481951 q^{30} +4.00337 q^{31} -14.3587 q^{32} +1.87733 q^{33} -6.65786 q^{34} +0.251646 q^{35} -4.23514 q^{36} +6.53938 q^{37} +2.11068 q^{38} -1.96103 q^{39} +1.00455 q^{40} +5.59187 q^{41} -7.98432 q^{42} +9.30737 q^{43} -6.46532 q^{44} +0.103030 q^{45} -16.9152 q^{46} -1.09584 q^{47} -16.9673 q^{48} -2.83107 q^{49} +13.2508 q^{50} -3.68446 q^{51} +6.75360 q^{52} -3.14381 q^{53} -15.0003 q^{54} +0.157284 q^{55} +16.6420 q^{56} +1.16805 q^{57} -13.9988 q^{58} -8.64986 q^{59} +0.918528 q^{60} -13.0794 q^{61} -10.6419 q^{62} +1.70686 q^{63} +15.1008 q^{64} -0.164297 q^{65} -4.99038 q^{66} -7.37724 q^{67} +12.6889 q^{68} -9.36090 q^{69} -0.668933 q^{70} +3.68520 q^{71} +6.81364 q^{72} -12.4700 q^{73} -17.3832 q^{74} +7.33299 q^{75} -4.02264 q^{76} +2.60567 q^{77} +5.21289 q^{78} +10.4393 q^{79} -1.42154 q^{80} -5.79329 q^{81} -14.8645 q^{82} -2.55002 q^{83} +15.2169 q^{84} -0.308687 q^{85} -24.7412 q^{86} -7.74696 q^{87} +10.4016 q^{88} -4.05771 q^{89} -0.273877 q^{90} -2.72185 q^{91} +32.2380 q^{92} -5.88923 q^{93} +2.91300 q^{94} +0.0978602 q^{95} +21.1226 q^{96} +11.8973 q^{97} +7.52565 q^{98} +1.06682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 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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