LMFDB - Embedded newform 6037.2.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.46629 q^{2} +1.74062 q^{3} +4.08257 q^{4} -1.65001 q^{5} -4.29287 q^{6} +1.73775 q^{7} -5.13620 q^{8} +0.0297629 q^{9} +O(q^{10})$	\(q-2.46629 q^{2} +1.74062 q^{3} +4.08257 q^{4} -1.65001 q^{5} -4.29287 q^{6} +1.73775 q^{7} -5.13620 q^{8} +0.0297629 q^{9} +4.06940 q^{10} -0.125496 q^{11} +7.10620 q^{12} -4.53339 q^{13} -4.28578 q^{14} -2.87205 q^{15} +4.50221 q^{16} -4.82577 q^{17} -0.0734039 q^{18} -2.48015 q^{19} -6.73629 q^{20} +3.02476 q^{21} +0.309508 q^{22} +7.67658 q^{23} -8.94018 q^{24} -2.27746 q^{25} +11.1806 q^{26} -5.17006 q^{27} +7.09447 q^{28} +8.80551 q^{29} +7.08329 q^{30} +3.57464 q^{31} -0.831329 q^{32} -0.218440 q^{33} +11.9017 q^{34} -2.86731 q^{35} +0.121509 q^{36} +0.599906 q^{37} +6.11677 q^{38} -7.89092 q^{39} +8.47480 q^{40} -8.54751 q^{41} -7.45993 q^{42} -2.63683 q^{43} -0.512344 q^{44} -0.0491093 q^{45} -18.9326 q^{46} -5.43328 q^{47} +7.83664 q^{48} -3.98023 q^{49} +5.61686 q^{50} -8.39984 q^{51} -18.5079 q^{52} +8.47546 q^{53} +12.7508 q^{54} +0.207069 q^{55} -8.92542 q^{56} -4.31701 q^{57} -21.7169 q^{58} +9.52056 q^{59} -11.7253 q^{60} -14.8053 q^{61} -8.81608 q^{62} +0.0517205 q^{63} -6.95412 q^{64} +7.48016 q^{65} +0.538736 q^{66} +0.474532 q^{67} -19.7015 q^{68} +13.3620 q^{69} +7.07160 q^{70} +6.07265 q^{71} -0.152868 q^{72} +14.6881 q^{73} -1.47954 q^{74} -3.96419 q^{75} -10.1254 q^{76} -0.218080 q^{77} +19.4613 q^{78} +9.87498 q^{79} -7.42870 q^{80} -9.08840 q^{81} +21.0806 q^{82} -1.54007 q^{83} +12.3488 q^{84} +7.96259 q^{85} +6.50318 q^{86} +15.3271 q^{87} +0.644570 q^{88} +0.501250 q^{89} +0.121117 q^{90} -7.87790 q^{91} +31.3401 q^{92} +6.22210 q^{93} +13.4000 q^{94} +4.09229 q^{95} -1.44703 q^{96} -15.8986 q^{97} +9.81639 q^{98} -0.00373512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.46629	−1.74393	−0.871964	−	0.489571i	$-0.837154\pi$
$2$	−2.46629	−1.74393	−0.871964	+	0.489571i	$0.837154\pi$
$3$	1.74062	1.00495	0.502474	−	0.864592i	$-0.332423\pi$
$3$	1.74062	1.00495	0.502474	+	0.864592i	$0.332423\pi$
$4$	4.08257	2.04128
$5$	−1.65001	−0.737908	−0.368954	−	0.929448i	$-0.620284\pi$
$5$	−1.65001	−0.737908	−0.368954	+	0.929448i	$0.620284\pi$
$6$	−4.29287	−1.75256
$7$	1.73775	0.656807	0.328404	−	0.944538i	$-0.393489\pi$
$7$	1.73775	0.656807	0.328404	+	0.944538i	$0.393489\pi$
$8$	−5.13620	−1.81592
$9$	0.0297629	0.00992098
$10$	4.06940	1.28686
$11$	−0.125496	−0.0378383	−0.0189192	−	0.999821i	$-0.506023\pi$
$11$	−0.125496	−0.0378383	−0.0189192	+	0.999821i	$0.506023\pi$
$12$	7.10620	2.05138
$13$	−4.53339	−1.25734	−0.628669	−	0.777673i	$-0.716400\pi$
$13$	−4.53339	−1.25734	−0.628669	+	0.777673i	$0.716400\pi$
$14$	−4.28578	−1.14542
$15$	−2.87205	−0.741560
$16$	4.50221	1.12555
$17$	−4.82577	−1.17042	−0.585211	−	0.810881i	$-0.698988\pi$
$17$	−4.82577	−1.17042	−0.585211	+	0.810881i	$0.698988\pi$
$18$	−0.0734039	−0.0173015
$19$	−2.48015	−0.568986	−0.284493	−	0.958678i	$-0.591825\pi$
$19$	−2.48015	−0.568986	−0.284493	+	0.958678i	$0.591825\pi$
$20$	−6.73629	−1.50628
$21$	3.02476	0.660057
$22$	0.309508	0.0659873
$23$	7.67658	1.60068	0.800339	−	0.599548i	$-0.204653\pi$
$23$	7.67658	1.60068	0.800339	+	0.599548i	$0.204653\pi$
$24$	−8.94018	−1.82491
$25$	−2.27746	−0.455491
$26$	11.1806	2.19270
$27$	−5.17006	−0.994978
$28$	7.09447	1.34073
$29$	8.80551	1.63514	0.817571	−	0.575828i	$-0.195320\pi$
$29$	8.80551	1.63514	0.817571	+	0.575828i	$0.195320\pi$
$30$	7.08329	1.29323
$31$	3.57464	0.642024	0.321012	−	0.947075i	$-0.395977\pi$
$31$	3.57464	0.642024	0.321012	+	0.947075i	$0.395977\pi$
$32$	−0.831329	−0.146960
$33$	−0.218440	−0.0380256
$34$	11.9017	2.04113
$35$	−2.86731	−0.484663
$36$	0.121509	0.0202515
$37$	0.599906	0.0986240	0.0493120	−	0.998783i	$-0.484297\pi$
$37$	0.599906	0.0986240	0.0493120	+	0.998783i	$0.484297\pi$
$38$	6.11677	0.992271
$39$	−7.89092	−1.26356
$40$	8.47480	1.33998
$41$	−8.54751	−1.33490	−0.667448	−	0.744656i	$-0.732614\pi$
$41$	−8.54751	−1.33490	−0.667448	+	0.744656i	$0.732614\pi$
$42$	−7.45993	−1.15109
$43$	−2.63683	−0.402113	−0.201056	−	0.979580i	$-0.564437\pi$
$43$	−2.63683	−0.402113	−0.201056	+	0.979580i	$0.564437\pi$
$44$	−0.512344	−0.0772387
$45$	−0.0491093	−0.00732078
$46$	−18.9326	−2.79146
$47$	−5.43328	−0.792526	−0.396263	−	0.918137i	$-0.629693\pi$
$47$	−5.43328	−0.792526	−0.396263	+	0.918137i	$0.629693\pi$
$48$	7.83664	1.13112
$49$	−3.98023	−0.568605
$50$	5.61686	0.794343
$51$	−8.39984	−1.17621
$52$	−18.5079	−2.56658
$53$	8.47546	1.16419	0.582097	−	0.813119i	$-0.302232\pi$
$53$	8.47546	1.16419	0.582097	+	0.813119i	$0.302232\pi$
$54$	12.7508	1.73517
$55$	0.207069	0.0279212
$56$	−8.92542	−1.19271
$57$	−4.31701	−0.571802
$58$	−21.7169	−2.85157
$59$	9.52056	1.23947	0.619736	−	0.784811i	$-0.287240\pi$
$59$	9.52056	1.23947	0.619736	+	0.784811i	$0.287240\pi$
$60$	−11.7253	−1.51373
$61$	−14.8053	−1.89563	−0.947815	−	0.318821i	$-0.896713\pi$
$61$	−14.8053	−1.89563	−0.947815	+	0.318821i	$0.896713\pi$
$62$	−8.81608	−1.11964
$63$	0.0517205	0.00651617
$64$	−6.95412	−0.869265
$65$	7.48016	0.927800
$66$	0.538736	0.0663138
$67$	0.474532	0.0579733	0.0289867	−	0.999580i	$-0.490772\pi$
$67$	0.474532	0.0579733	0.0289867	+	0.999580i	$0.490772\pi$
$68$	−19.7015	−2.38916
$69$	13.3620	1.60860
$70$	7.07160	0.845218
$71$	6.07265	0.720691	0.360345	−	0.932819i	$-0.382659\pi$
$71$	6.07265	0.720691	0.360345	+	0.932819i	$0.382659\pi$
$72$	−0.152868	−0.0180157
$73$	14.6881	1.71911	0.859553	−	0.511046i	$-0.170742\pi$
$73$	14.6881	1.71911	0.859553	+	0.511046i	$0.170742\pi$
$74$	−1.47954	−0.171993
$75$	−3.96419	−0.457745
$76$	−10.1254	−1.16146
$77$	−0.218080	−0.0248525
$78$	19.4613	2.20355
$79$	9.87498	1.11102	0.555511	−	0.831509i	$-0.312523\pi$
$79$	9.87498	1.11102	0.555511	+	0.831509i	$0.312523\pi$
$80$	−7.42870	−0.830554
$81$	−9.08840	−1.00982
$82$	21.0806	2.32796
$83$	−1.54007	−0.169045	−0.0845226	−	0.996422i	$-0.526937\pi$
$83$	−1.54007	−0.169045	−0.0845226	+	0.996422i	$0.526937\pi$
$84$	12.3488	1.34736
$85$	7.96259	0.863664
$86$	6.50318	0.701256
$87$	15.3271	1.64323
$88$	0.644570	0.0687114
$89$	0.501250	0.0531324	0.0265662	−	0.999647i	$-0.491543\pi$
$89$	0.501250	0.0531324	0.0265662	+	0.999647i	$0.491543\pi$
$90$	0.121117	0.0127669
$91$	−7.87790	−0.825828
$92$	31.3401	3.26743
$93$	6.22210	0.645201
$94$	13.4000	1.38211
$95$	4.09229	0.419860
$96$	−1.44703	−0.147687
$97$	−15.8986	−1.61426	−0.807129	−	0.590375i	$-0.798980\pi$
$97$	−15.8986	−1.61426	−0.807129	+	0.590375i	$0.798980\pi$
$98$	9.81639	0.991605
$99$	−0.00373512	−0.000375393 0
$100$	−9.29786	−0.929786
$101$	11.3060	1.12498	0.562492	−	0.826802i	$-0.309843\pi$
$101$	11.3060	1.12498	0.562492	+	0.826802i	$0.309843\pi$
$102$	20.7164	2.05123
$103$	1.94479	0.191626	0.0958130	−	0.995399i	$-0.469455\pi$
$103$	1.94479	0.191626	0.0958130	+	0.995399i	$0.469455\pi$
$104$	23.2844	2.28323
$105$	−4.99090	−0.487062
$106$	−20.9029	−2.03027
$107$	−2.43108	−0.235022	−0.117511	−	0.993072i	$-0.537491\pi$
$107$	−2.43108	−0.235022	−0.117511	+	0.993072i	$0.537491\pi$
$108$	−21.1071	−2.03103
$109$	0.100580	0.00963384	0.00481692	−	0.999988i	$-0.498467\pi$
$109$	0.100580	0.00963384	0.00481692	+	0.999988i	$0.498467\pi$
$110$	−0.510692	−0.0486926
$111$	1.04421	0.0991120
$112$	7.82370	0.739270
$113$	4.51665	0.424890	0.212445	−	0.977173i	$-0.431857\pi$
$113$	4.51665	0.424890	0.212445	+	0.977173i	$0.431857\pi$
$114$	10.6470	0.997181
$115$	−12.6665	−1.18115
$116$	35.9491	3.33779
$117$	−0.134927	−0.0124740
$118$	−23.4804	−2.16155
$119$	−8.38598	−0.768741
$120$	14.7514	1.34661
$121$	−10.9843	−0.998568
$122$	36.5142	3.30584
$123$	−14.8780	−1.34150
$124$	14.5937	1.31055
$125$	12.0079	1.07402
$126$	−0.127558	−0.0113637
$127$	16.7858	1.48950	0.744750	−	0.667344i	$-0.232569\pi$
$127$	16.7858	1.48950	0.744750	+	0.667344i	$0.232569\pi$
$128$	18.8135	1.66289
$129$	−4.58972	−0.404103
$130$	−18.4482	−1.61802
$131$	0.432090	0.0377519	0.0188759	−	0.999822i	$-0.493991\pi$
$131$	0.432090	0.0377519	0.0188759	+	0.999822i	$0.493991\pi$
$132$	−0.891796	−0.0776209
$133$	−4.30988	−0.373714
$134$	−1.17033	−0.101101
$135$	8.53067	0.734203
$136$	24.7861	2.12539
$137$	−7.71688	−0.659298	−0.329649	−	0.944104i	$-0.606930\pi$
$137$	−7.71688	−0.659298	−0.329649	+	0.944104i	$0.606930\pi$
$138$	−32.9545	−2.80528
$139$	2.24124	0.190100	0.0950499	−	0.995473i	$-0.469699\pi$
$139$	2.24124	0.190100	0.0950499	+	0.995473i	$0.469699\pi$
$140$	−11.7060	−0.989335
$141$	−9.45729	−0.796447
$142$	−14.9769	−1.25683
$143$	0.568921	0.0475755
$144$	0.133999	0.0111666
$145$	−14.5292	−1.20659
$146$	−36.2249	−2.99800
$147$	−6.92808	−0.571418
$148$	2.44916	0.201319
$149$	6.23594	0.510868	0.255434	−	0.966826i	$-0.417782\pi$
$149$	6.23594	0.510868	0.255434	+	0.966826i	$0.417782\pi$
$150$	9.77682	0.798274
$151$	18.5315	1.50807	0.754036	−	0.656833i	$-0.228104\pi$
$151$	18.5315	1.50807	0.754036	+	0.656833i	$0.228104\pi$
$152$	12.7386	1.03323
$153$	−0.143629	−0.0116117
$154$	0.537847	0.0433409
$155$	−5.89820	−0.473755
$156$	−32.2152	−2.57928
$157$	−3.66361	−0.292388	−0.146194	−	0.989256i	$-0.546702\pi$
$157$	−3.66361	−0.292388	−0.146194	+	0.989256i	$0.546702\pi$
$158$	−24.3545	−1.93754
$159$	14.7526	1.16995
$160$	1.37170	0.108443
$161$	13.3400	1.05134
$162$	22.4146	1.76106
$163$	−4.48176	−0.351039	−0.175519	−	0.984476i	$-0.556160\pi$
$163$	−4.48176	−0.351039	−0.175519	+	0.984476i	$0.556160\pi$
$164$	−34.8958	−2.72490
$165$	0.360429	0.0280594
$166$	3.79826	0.294802
$167$	19.5008	1.50902	0.754509	−	0.656290i	$-0.227875\pi$
$167$	19.5008	1.50902	0.754509	+	0.656290i	$0.227875\pi$
$168$	−15.5358	−1.19861
$169$	7.55166	0.580897
$170$	−19.6380	−1.50617
$171$	−0.0738167	−0.00564490
$172$	−10.7650	−0.820826
$173$	24.4602	1.85967	0.929836	−	0.367975i	$-0.119949\pi$
$173$	24.4602	1.85967	0.929836	+	0.367975i	$0.119949\pi$
$174$	−37.8009	−2.86568
$175$	−3.95764	−0.299170
$176$	−0.565007	−0.0425890
$177$	16.5717	1.24560
$178$	−1.23623	−0.0926591
$179$	2.83534	0.211924	0.105962	−	0.994370i	$-0.466208\pi$
$179$	2.83534	0.211924	0.105962	+	0.994370i	$0.466208\pi$
$180$	−0.200492	−0.0149438
$181$	−1.89165	−0.140606	−0.0703028	−	0.997526i	$-0.522397\pi$
$181$	−1.89165	−0.140606	−0.0703028	+	0.997526i	$0.522397\pi$
$182$	19.4291	1.44018
$183$	−25.7705	−1.90501
$184$	−39.4284	−2.90670
$185$	−0.989853	−0.0727755
$186$	−15.3455	−1.12518
$187$	0.605613	0.0442868
$188$	−22.1817	−1.61777
$189$	−8.98426	−0.653509
$190$	−10.0927	−0.732205
$191$	−16.7142	−1.20940	−0.604700	−	0.796453i	$-0.706707\pi$
$191$	−16.7142	−1.20940	−0.604700	+	0.796453i	$0.706707\pi$
$192$	−12.1045	−0.873566
$193$	16.9962	1.22341	0.611707	−	0.791085i	$-0.290483\pi$
$193$	16.9962	1.22341	0.611707	+	0.791085i	$0.290483\pi$
$194$	39.2105	2.81515
$195$	13.0201	0.932391
$196$	−16.2496	−1.16068
$197$	11.1822	0.796700	0.398350	−	0.917233i	$-0.369583\pi$
$197$	11.1822	0.796700	0.398350	+	0.917233i	$0.369583\pi$
$198$	0.00921186	0.000654659 0
$199$	4.79004	0.339557	0.169779	−	0.985482i	$-0.445695\pi$
$199$	4.79004	0.339557	0.169779	+	0.985482i	$0.445695\pi$
$200$	11.6975	0.827136
$201$	0.825981	0.0582602
$202$	−27.8837	−1.96189
$203$	15.3018	1.07397
$204$	−34.2929	−2.40098
$205$	14.1035	0.985032
$206$	−4.79641	−0.334182
$207$	0.228478	0.0158803
$208$	−20.4103	−1.41520
$209$	0.311248	0.0215295
$210$	12.3090	0.849400
$211$	22.4184	1.54335	0.771673	−	0.636020i	$-0.219420\pi$
$211$	22.4184	1.54335	0.771673	+	0.636020i	$0.219420\pi$
$212$	34.6016	2.37645
$213$	10.5702	0.724257
$214$	5.99574	0.409860
$215$	4.35081	0.296722
$216$	26.5545	1.80680
$217$	6.21182	0.421686
$218$	−0.248060	−0.0168007
$219$	25.5663	1.72761
$220$	0.845374	0.0569951
$221$	21.8771	1.47162
$222$	−2.57532	−0.172844
$223$	1.09376	0.0732436	0.0366218	−	0.999329i	$-0.488340\pi$
$223$	1.09376	0.0732436	0.0366218	+	0.999329i	$0.488340\pi$
$224$	−1.44464	−0.0965241
$225$	−0.0677838	−0.00451892
$226$	−11.1393	−0.740978
$227$	−5.26043	−0.349147	−0.174573	−	0.984644i	$-0.555855\pi$
$227$	−5.26043	−0.349147	−0.174573	+	0.984644i	$0.555855\pi$
$228$	−17.6245	−1.16721
$229$	−13.1708	−0.870353	−0.435176	−	0.900345i	$-0.643314\pi$
$229$	−13.1708	−0.870353	−0.435176	+	0.900345i	$0.643314\pi$
$230$	31.2391	2.05985
$231$	−0.379594	−0.0249754
$232$	−45.2269	−2.96929
$233$	1.00202	0.0656443	0.0328221	−	0.999461i	$-0.489551\pi$
$233$	1.00202	0.0656443	0.0328221	+	0.999461i	$0.489551\pi$
$234$	0.332769	0.0217538
$235$	8.96499	0.584811
$236$	38.8683	2.53011
$237$	17.1886	1.11652
$238$	20.6822	1.34063
$239$	−16.2579	−1.05164	−0.525819	−	0.850597i	$-0.676241\pi$
$239$	−16.2579	−1.05164	−0.525819	+	0.850597i	$0.676241\pi$
$240$	−12.9306	−0.834664
$241$	12.4059	0.799132	0.399566	−	0.916705i	$-0.369161\pi$
$241$	12.4059	0.799132	0.399566	+	0.916705i	$0.369161\pi$
$242$	27.0903	1.74143
$243$	−0.309294	−0.0198412
$244$	−60.4438	−3.86952
$245$	6.56744	0.419578
$246$	36.6933	2.33948
$247$	11.2435	0.715408
$248$	−18.3601	−1.16587
$249$	−2.68069	−0.169882
$250$	−29.6149	−1.87301
$251$	−6.49175	−0.409755	−0.204878	−	0.978788i	$-0.565680\pi$
$251$	−6.49175	−0.409755	−0.204878	+	0.978788i	$0.565680\pi$
$252$	0.211152	0.0133013
$253$	−0.963376	−0.0605669
$254$	−41.3986	−2.59758
$255$	13.8599	0.867938
$256$	−32.4912	−2.03070
$257$	1.57408	0.0981883	0.0490941	−	0.998794i	$-0.484367\pi$
$257$	1.57408	0.0981883	0.0490941	+	0.998794i	$0.484367\pi$
$258$	11.3196	0.704726
$259$	1.04249	0.0647769
$260$	30.5382	1.89390
$261$	0.262078	0.0162222
$262$	−1.06566	−0.0658365
$263$	21.0899	1.30046	0.650231	−	0.759737i	$-0.274672\pi$
$263$	21.0899	1.30046	0.650231	+	0.759737i	$0.274672\pi$
$264$	1.12195	0.0690514
$265$	−13.9846	−0.859068
$266$	10.6294	0.651730
$267$	0.872487	0.0533953
$268$	1.93731	0.118340
$269$	16.6059	1.01248	0.506240	−	0.862392i	$-0.331035\pi$
$269$	16.6059	1.01248	0.506240	+	0.862392i	$0.331035\pi$
$270$	−21.0391	−1.28040
$271$	−8.33485	−0.506306	−0.253153	−	0.967426i	$-0.581468\pi$
$271$	−8.33485	−0.506306	−0.253153	+	0.967426i	$0.581468\pi$
$272$	−21.7266	−1.31737
$273$	−13.7124	−0.829914
$274$	19.0320	1.14977
$275$	0.285810	0.0172350
$276$	54.5513	3.28360
$277$	−7.90450	−0.474935	−0.237468	−	0.971395i	$-0.576317\pi$
$277$	−7.90450	−0.474935	−0.237468	+	0.971395i	$0.576317\pi$
$278$	−5.52755	−0.331520
$279$	0.106392	0.00636951
$280$	14.7271	0.880111
$281$	20.8491	1.24375	0.621876	−	0.783116i	$-0.286371\pi$
$281$	20.8491	1.24375	0.621876	+	0.783116i	$0.286371\pi$
$282$	23.3244	1.38895
$283$	0.918012	0.0545701	0.0272851	−	0.999628i	$-0.491314\pi$
$283$	0.918012	0.0545701	0.0272851	+	0.999628i	$0.491314\pi$
$284$	24.7920	1.47113
$285$	7.12312	0.421937
$286$	−1.40312	−0.0829683
$287$	−14.8534	−0.876770
$288$	−0.0247428	−0.00145798
$289$	6.28809	0.369888
$290$	35.8332	2.10420
$291$	−27.6734	−1.62225
$292$	59.9649	3.50918
$293$	−7.59314	−0.443596	−0.221798	−	0.975093i	$-0.571193\pi$
$293$	−7.59314	−0.443596	−0.221798	+	0.975093i	$0.571193\pi$
$294$	17.0866	0.996512
$295$	−15.7091	−0.914616
$296$	−3.08124	−0.179093
$297$	0.648819	0.0376483
$298$	−15.3796	−0.890917
$299$	−34.8010	−2.01259
$300$	−16.1841	−0.934387
$301$	−4.58215	−0.264111
$302$	−45.7040	−2.62997
$303$	19.6794	1.13055
$304$	−11.1662	−0.640424
$305$	24.4290	1.39880
$306$	0.354231	0.0202500
$307$	8.27524	0.472293	0.236146	−	0.971717i	$-0.424116\pi$
$307$	8.27524	0.472293	0.236146	+	0.971717i	$0.424116\pi$
$308$	−0.890324	−0.0507309
$309$	3.38514	0.192574
$310$	14.5467	0.826195
$311$	−7.80741	−0.442718	−0.221359	−	0.975192i	$-0.571049\pi$
$311$	−7.80741	−0.442718	−0.221359	+	0.975192i	$0.571049\pi$
$312$	40.5294	2.29452
$313$	−23.5840	−1.33305	−0.666525	−	0.745483i	$-0.732219\pi$
$313$	−23.5840	−1.33305	−0.666525	+	0.745483i	$0.732219\pi$
$314$	9.03550	0.509903
$315$	−0.0853395	−0.00480834
$316$	40.3153	2.26791
$317$	−18.1603	−1.01998	−0.509992	−	0.860179i	$-0.670351\pi$
$317$	−18.1603	−1.01998	−0.509992	+	0.860179i	$0.670351\pi$
$318$	−36.3840	−2.04032
$319$	−1.10505	−0.0618710
$320$	11.4744	0.641438
$321$	−4.23159	−0.236184
$322$	−32.9001	−1.83345
$323$	11.9687	0.665954
$324$	−37.1040	−2.06133
$325$	10.3246	0.572706
$326$	11.0533	0.612186
$327$	0.175072	0.00968151
$328$	43.9017	2.42407
$329$	−9.44168	−0.520536
$330$	−0.888921	−0.0489335
$331$	23.6804	1.30160	0.650798	−	0.759251i	$-0.274435\pi$
$331$	23.6804	1.30160	0.650798	+	0.759251i	$0.274435\pi$
$332$	−6.28745	−0.345069
$333$	0.0178550	0.000978447 0
$334$	−48.0945	−2.63162
$335$	−0.782984	−0.0427790
$336$	13.6181	0.742928
$337$	−23.9191	−1.30296	−0.651479	−	0.758667i	$-0.725851\pi$
$337$	−23.9191	−1.30296	−0.651479	+	0.758667i	$0.725851\pi$
$338$	−18.6246	−1.01304
$339$	7.86177	0.426993
$340$	32.5078	1.76298
$341$	−0.448601	−0.0242931
$342$	0.182053	0.00984430
$343$	−19.0809	−1.03027
$344$	13.5433	0.730205
$345$	−22.0475	−1.18700
$346$	−60.3257	−3.24313
$347$	−19.3555	−1.03906	−0.519528	−	0.854454i	$-0.673892\pi$
$347$	−19.3555	−1.03906	−0.519528	+	0.854454i	$0.673892\pi$
$348$	62.5737	3.35430
$349$	32.2745	1.72762	0.863808	−	0.503821i	$-0.168073\pi$
$349$	32.2745	1.72762	0.863808	+	0.503821i	$0.168073\pi$
$350$	9.76068	0.521730
$351$	23.4379	1.25102
$352$	0.104328	0.00556070
$353$	35.5987	1.89473	0.947365	−	0.320156i	$-0.103735\pi$
$353$	35.5987	1.89473	0.947365	+	0.320156i	$0.103735\pi$
$354$	−40.8705	−2.17224
$355$	−10.0200	−0.531804
$356$	2.04639	0.108458
$357$	−14.5968	−0.772545
$358$	−6.99277	−0.369579
$359$	−5.29711	−0.279571	−0.139785	−	0.990182i	$-0.544641\pi$
$359$	−5.29711	−0.279571	−0.139785	+	0.990182i	$0.544641\pi$
$360$	0.252235	0.0132940
$361$	−12.8488	−0.676255
$362$	4.66536	0.245206
$363$	−19.1194	−1.00351
$364$	−32.1620	−1.68575
$365$	−24.2355	−1.26854
$366$	63.5574	3.32220
$367$	29.8064	1.55588	0.777941	−	0.628337i	$-0.216264\pi$
$367$	29.8064	1.55588	0.777941	+	0.628337i	$0.216264\pi$
$368$	34.5615	1.80165
$369$	−0.254399	−0.0132435
$370$	2.44126	0.126915
$371$	14.7282	0.764651
$372$	25.4021	1.31704
$373$	37.5011	1.94174	0.970868	−	0.239617i	$-0.0770217\pi$
$373$	37.5011	1.94174	0.970868	+	0.239617i	$0.0770217\pi$
$374$	−1.49361	−0.0772330
$375$	20.9012	1.07933
$376$	27.9064	1.43916
$377$	−39.9188	−2.05592
$378$	22.1577	1.13967
$379$	−29.3343	−1.50680	−0.753401	−	0.657561i	$-0.771588\pi$
$379$	−29.3343	−1.50680	−0.753401	+	0.657561i	$0.771588\pi$
$380$	16.7070	0.857052
$381$	29.2177	1.49687
$382$	41.2221	2.10911
$383$	9.17459	0.468800	0.234400	−	0.972140i	$-0.424688\pi$
$383$	9.17459	0.468800	0.234400	+	0.972140i	$0.424688\pi$
$384$	32.7472	1.67112
$385$	0.359834	0.0183388
$386$	−41.9175	−2.13354
$387$	−0.0784798	−0.00398935
$388$	−64.9071	−3.29516
$389$	−3.64091	−0.184601	−0.0923007	−	0.995731i	$-0.529422\pi$
$389$	−3.64091	−0.184601	−0.0923007	+	0.995731i	$0.529422\pi$
$390$	−32.1114	−1.62602
$391$	−37.0454	−1.87347
$392$	20.4433	1.03254
$393$	0.752105	0.0379387
$394$	−27.5786	−1.38939
$395$	−16.2939	−0.819833
$396$	−0.0152489	−0.000766284 0
$397$	3.62355	0.181861	0.0909304	−	0.995857i	$-0.471016\pi$
$397$	3.62355	0.181861	0.0909304	+	0.995857i	$0.471016\pi$
$398$	−11.8136	−0.592163
$399$	−7.50187	−0.375563
$400$	−10.2536	−0.512679
$401$	12.1954	0.609008	0.304504	−	0.952511i	$-0.401509\pi$
$401$	12.1954	0.609008	0.304504	+	0.952511i	$0.401509\pi$
$402$	−2.03710	−0.101602
$403$	−16.2053	−0.807241
$404$	46.1573	2.29641
$405$	14.9960	0.745157
$406$	−37.7385	−1.87293
$407$	−0.0752855	−0.00373177
$408$	43.1433	2.13591
$409$	1.74983	0.0865236	0.0432618	−	0.999064i	$-0.486225\pi$
$409$	1.74983	0.0865236	0.0432618	+	0.999064i	$0.486225\pi$
$410$	−34.7833	−1.71782
$411$	−13.4322	−0.662560
$412$	7.93974	0.391163
$413$	16.5443	0.814093
$414$	−0.563491	−0.0276941
$415$	2.54114	0.124740
$416$	3.76874	0.184778
$417$	3.90116	0.191041
$418$	−0.767627	−0.0375459
$419$	−17.2661	−0.843506	−0.421753	−	0.906711i	$-0.638585\pi$
$419$	−17.2661	−0.843506	−0.421753	+	0.906711i	$0.638585\pi$
$420$	−20.3757	−0.994230
$421$	−6.04640	−0.294683	−0.147342	−	0.989086i	$-0.547072\pi$
$421$	−6.04640	−0.294683	−0.147342	+	0.989086i	$0.547072\pi$
$422$	−55.2902	−2.69148
$423$	−0.161711	−0.00786263
$424$	−43.5317	−2.11408
$425$	10.9905	0.533117
$426$	−26.0691	−1.26305
$427$	−25.7280	−1.24506
$428$	−9.92505	−0.479745
$429$	0.990275	0.0478109
$430$	−10.7303	−0.517462
$431$	0.529026	0.0254823	0.0127411	−	0.999919i	$-0.495944\pi$
$431$	0.529026	0.0254823	0.0127411	+	0.999919i	$0.495944\pi$
$432$	−23.2767	−1.11990
$433$	−7.25091	−0.348456	−0.174228	−	0.984705i	$-0.555743\pi$
$433$	−7.25091	−0.348456	−0.174228	+	0.984705i	$0.555743\pi$
$434$	−15.3201	−0.735390
$435$	−25.2898	−1.21256
$436$	0.410625	0.0196654
$437$	−19.0391	−0.910763
$438$	−63.0539	−3.01283
$439$	−16.9987	−0.811303	−0.405652	−	0.914028i	$-0.632955\pi$
$439$	−16.9987	−0.811303	−0.405652	+	0.914028i	$0.632955\pi$
$440$	−1.06355	−0.0507027
$441$	−0.118463	−0.00564112
$442$	−53.9553	−2.56639
$443$	13.5396	0.643286	0.321643	−	0.946861i	$-0.395765\pi$
$443$	13.5396	0.643286	0.321643	+	0.946861i	$0.395765\pi$
$444$	4.26305	0.202316
$445$	−0.827070	−0.0392069
$446$	−2.69752	−0.127731
$447$	10.8544	0.513396
$448$	−12.0845	−0.570939
$449$	23.6345	1.11538	0.557691	−	0.830049i	$-0.311687\pi$
$449$	23.6345	1.11538	0.557691	+	0.830049i	$0.311687\pi$
$450$	0.167174	0.00788067
$451$	1.07267	0.0505103
$452$	18.4395	0.867321
$453$	32.2563	1.51554
$454$	12.9737	0.608887
$455$	12.9986	0.609385
$456$	22.1730	1.03835
$457$	18.5854	0.869388	0.434694	−	0.900578i	$-0.356857\pi$
$457$	18.5854	0.869388	0.434694	+	0.900578i	$0.356857\pi$
$458$	32.4830	1.51783
$459$	24.9495	1.16454
$460$	−51.7116	−2.41107
$461$	−9.11275	−0.424423	−0.212212	−	0.977224i	$-0.568067\pi$
$461$	−9.11275	−0.424423	−0.212212	+	0.977224i	$0.568067\pi$
$462$	0.936187	0.0435554
$463$	−40.8728	−1.89952	−0.949760	−	0.312979i	$-0.898673\pi$
$463$	−40.8728	−1.89952	−0.949760	+	0.312979i	$0.898673\pi$
$464$	39.6442	1.84044
$465$	−10.2665	−0.476099
$466$	−2.47126	−0.114479
$467$	−11.2511	−0.520641	−0.260320	−	0.965522i	$-0.583828\pi$
$467$	−11.2511	−0.520641	−0.260320	+	0.965522i	$0.583828\pi$
$468$	−0.550849	−0.0254630
$469$	0.824617	0.0380773
$470$	−22.1102	−1.01987
$471$	−6.37695	−0.293834
$472$	−48.8995	−2.25078
$473$	0.330910	0.0152153
$474$	−42.3920	−1.94713
$475$	5.64844	0.259168
$476$	−34.2363	−1.56922
$477$	0.252255	0.0115499
$478$	40.0967	1.83398
$479$	−2.81971	−0.128836	−0.0644179	−	0.997923i	$-0.520519\pi$
$479$	−2.81971	−0.128836	−0.0644179	+	0.997923i	$0.520519\pi$
$480$	2.38762	0.108979
$481$	−2.71961	−0.124004
$482$	−30.5964	−1.39363
$483$	23.2198	1.05654
$484$	−44.8439	−2.03836
$485$	26.2329	1.19117
$486$	0.762808	0.0346017
$487$	17.3655	0.786908	0.393454	−	0.919344i	$-0.371280\pi$
$487$	17.3655	0.786908	0.393454	+	0.919344i	$0.371280\pi$
$488$	76.0432	3.44231
$489$	−7.80105	−0.352776
$490$	−16.1972	−0.731714
$491$	−7.85222	−0.354366	−0.177183	−	0.984178i	$-0.556698\pi$
$491$	−7.85222	−0.354366	−0.177183	+	0.984178i	$0.556698\pi$
$492$	−60.7403	−2.73839
$493$	−42.4934	−1.91381
$494$	−27.7297	−1.24762
$495$	0.00616299	0.000277006 0
$496$	16.0938	0.722632
$497$	10.5527	0.473355
$498$	6.61134	0.296261
$499$	−12.3009	−0.550665	−0.275332	−	0.961349i	$-0.588788\pi$
$499$	−12.3009	−0.550665	−0.275332	+	0.961349i	$0.588788\pi$
$500$	49.0230	2.19238
$501$	33.9435	1.51648
$502$	16.0105	0.714584
$503$	9.07881	0.404804	0.202402	−	0.979303i	$-0.435125\pi$
$503$	9.07881	0.404804	0.202402	+	0.979303i	$0.435125\pi$
$504$	−0.265647	−0.0118329
$505$	−18.6550	−0.830136
$506$	2.37596	0.105624
$507$	13.1446	0.583771
$508$	68.5292	3.04049
$509$	40.1244	1.77848	0.889242	−	0.457437i	$-0.151232\pi$
$509$	40.1244	1.77848	0.889242	+	0.457437i	$0.151232\pi$
$510$	−34.1824	−1.51362
$511$	25.5241	1.12912
$512$	42.5057	1.87850
$513$	12.8225	0.566129
$514$	−3.88213	−0.171233
$515$	−3.20893	−0.141402
$516$	−18.7378	−0.824888
$517$	0.681853	0.0299878
$518$	−2.57107	−0.112966
$519$	42.5759	1.86887
$520$	−38.4196	−1.68481
$521$	10.2632	0.449637	0.224819	−	0.974401i	$-0.427821\pi$
$521$	10.2632	0.449637	0.224819	+	0.974401i	$0.427821\pi$
$522$	−0.646359	−0.0282904
$523$	3.22833	0.141165	0.0705825	−	0.997506i	$-0.477514\pi$
$523$	3.22833	0.141165	0.0705825	+	0.997506i	$0.477514\pi$
$524$	1.76403	0.0770622
$525$	−6.88876	−0.300650
$526$	−52.0138	−2.26791
$527$	−17.2504	−0.751439
$528$	−0.983463	−0.0427997
$529$	35.9298	1.56217
$530$	34.4901	1.49815
$531$	0.283360	0.0122968
$532$	−17.5954	−0.762856
$533$	38.7492	1.67842
$534$	−2.15180	−0.0931176
$535$	4.01132	0.173424
$536$	−2.43729	−0.105275
$537$	4.93526	0.212972
$538$	−40.9549	−1.76569
$539$	0.499501	0.0215150
$540$	34.8270	1.49872
$541$	31.8910	1.37110	0.685551	−	0.728024i	$-0.259561\pi$
$541$	31.8910	1.37110	0.685551	+	0.728024i	$0.259561\pi$
$542$	20.5561	0.882961
$543$	−3.29265	−0.141301
$544$	4.01180	0.172005
$545$	−0.165959	−0.00710889
$546$	33.8188	1.44731
$547$	−24.4679	−1.04617	−0.523086	−	0.852280i	$-0.675219\pi$
$547$	−24.4679	−1.04617	−0.523086	+	0.852280i	$0.675219\pi$
$548$	−31.5047	−1.34581
$549$	−0.440651	−0.0188065
$550$	−0.704890	−0.0300566
$551$	−21.8390	−0.930373
$552$	−68.6300	−2.92109
$553$	17.1602	0.729727
$554$	19.4947	0.828253
$555$	−1.72296	−0.0731356
$556$	9.15003	0.388048
$557$	27.4325	1.16235	0.581176	−	0.813778i	$-0.302593\pi$
$557$	27.4325	1.16235	0.581176	+	0.813778i	$0.302593\pi$
$558$	−0.262393	−0.0111080
$559$	11.9538	0.505591
$560$	−12.9092	−0.545514
$561$	1.05414	0.0445059
$562$	−51.4198	−2.16901
$563$	−7.14384	−0.301077	−0.150539	−	0.988604i	$-0.548101\pi$
$563$	−7.14384	−0.301077	−0.150539	+	0.988604i	$0.548101\pi$
$564$	−38.6100	−1.62577
$565$	−7.45253	−0.313530
$566$	−2.26408	−0.0951664
$567$	−15.7934	−0.663259
$568$	−31.1903	−1.30872
$569$	−13.3297	−0.558810	−0.279405	−	0.960173i	$-0.590137\pi$
$569$	−13.3297	−0.558810	−0.279405	+	0.960173i	$0.590137\pi$
$570$	−17.5677	−0.735828
$571$	−19.5998	−0.820225	−0.410113	−	0.912035i	$-0.634511\pi$
$571$	−19.5998	−0.820225	−0.410113	+	0.912035i	$0.634511\pi$
$572$	2.32266	0.0971151
$573$	−29.0932	−1.21538
$574$	36.6328	1.52902
$575$	−17.4831	−0.729094
$576$	−0.206975	−0.00862396
$577$	0.515089	0.0214435	0.0107217	−	0.999943i	$-0.496587\pi$
$577$	0.515089	0.0214435	0.0107217	+	0.999943i	$0.496587\pi$
$578$	−15.5082	−0.645057
$579$	29.5840	1.22947
$580$	−59.3164	−2.46298
$581$	−2.67626	−0.111030
$582$	68.2506	2.82908
$583$	−1.06363	−0.0440511
$584$	−75.4408	−3.12176
$585$	0.222632	0.00920468
$586$	18.7269	0.773600
$587$	27.3392	1.12841	0.564204	−	0.825635i	$-0.309183\pi$
$587$	27.3392	1.12841	0.564204	+	0.825635i	$0.309183\pi$
$588$	−28.2843	−1.16643
$589$	−8.86566	−0.365303
$590$	38.7430	1.59502
$591$	19.4640	0.800643
$592$	2.70090	0.111006
$593$	31.8551	1.30813	0.654066	−	0.756438i	$-0.273062\pi$
$593$	31.8551	1.30813	0.654066	+	0.756438i	$0.273062\pi$
$594$	−1.60017	−0.0656559
$595$	13.8370	0.567261
$596$	25.4586	1.04283
$597$	8.33765	0.341237
$598$	85.8291	3.50981
$599$	36.2383	1.48066	0.740329	−	0.672245i	$-0.234670\pi$
$599$	36.2383	1.48066	0.740329	+	0.672245i	$0.234670\pi$
$600$	20.3609	0.831229
$601$	15.1943	0.619789	0.309895	−	0.950771i	$-0.399706\pi$
$601$	15.1943	0.619789	0.309895	+	0.950771i	$0.399706\pi$
$602$	11.3009	0.460590
$603$	0.0141235	0.000575152 0
$604$	75.6561	3.07840
$605$	18.1242	0.736852
$606$	−48.5350	−1.97160
$607$	26.2706	1.06629	0.533145	−	0.846024i	$-0.321010\pi$
$607$	26.2706	1.06629	0.533145	+	0.846024i	$0.321010\pi$
$608$	2.06182	0.0836180
$609$	26.6346	1.07929
$610$	−60.2489	−2.43941
$611$	24.6312	0.996472
$612$	−0.586376	−0.0237028
$613$	−19.6689	−0.794418	−0.397209	−	0.917728i	$-0.630021\pi$
$613$	−19.6689	−0.794418	−0.397209	+	0.917728i	$0.630021\pi$
$614$	−20.4091	−0.823644
$615$	24.5489	0.989906
$616$	1.12010	0.0451301
$617$	−25.8944	−1.04247	−0.521234	−	0.853414i	$-0.674528\pi$
$617$	−25.8944	−1.04247	−0.521234	+	0.853414i	$0.674528\pi$
$618$	−8.34873	−0.335835
$619$	−23.6024	−0.948662	−0.474331	−	0.880347i	$-0.657310\pi$
$619$	−23.6024	−0.948662	−0.474331	+	0.880347i	$0.657310\pi$
$620$	−24.0798	−0.967068
$621$	−39.6884	−1.59264
$622$	19.2553	0.772068
$623$	0.871047	0.0348978
$624$	−35.5266	−1.42220
$625$	−8.42592	−0.337037
$626$	58.1650	2.32474
$627$	0.541765	0.0216360
$628$	−14.9569	−0.596846
$629$	−2.89501	−0.115432
$630$	0.210472	0.00838539
$631$	−5.64748	−0.224822	−0.112411	−	0.993662i	$-0.535857\pi$
$631$	−5.64748	−0.224822	−0.112411	+	0.993662i	$0.535857\pi$
$632$	−50.7199	−2.01753
$633$	39.0219	1.55098
$634$	44.7884	1.77878
$635$	−27.6968	−1.09911
$636$	60.2283	2.38821
$637$	18.0440	0.714928
$638$	2.72537	0.107899
$639$	0.180740	0.00714996
$640$	−31.0425	−1.22706
$641$	−31.7014	−1.25213	−0.626066	−	0.779770i	$-0.715336\pi$
$641$	−31.7014	−1.25213	−0.626066	+	0.779770i	$0.715336\pi$
$642$	10.4363	0.411889
$643$	22.1341	0.872885	0.436442	−	0.899732i	$-0.356238\pi$
$643$	22.1341	0.872885	0.436442	+	0.899732i	$0.356238\pi$
$644$	54.4612	2.14607
$645$	7.57311	0.298191
$646$	−29.5181	−1.16138
$647$	−13.4886	−0.530293	−0.265146	−	0.964208i	$-0.585420\pi$
$647$	−13.4886	−0.530293	−0.265146	+	0.964208i	$0.585420\pi$
$648$	46.6799	1.83376
$649$	−1.19479	−0.0468995
$650$	−25.4634	−0.998758
$651$	10.8124	0.423773
$652$	−18.2971	−0.716569
$653$	−0.373916	−0.0146325	−0.00731623	−	0.999973i	$-0.502329\pi$
$653$	−0.373916	−0.0146325	−0.00731623	+	0.999973i	$0.502329\pi$
$654$	−0.431778	−0.0168839
$655$	−0.712954	−0.0278574
$656$	−38.4827	−1.50250
$657$	0.437160	0.0170552
$658$	23.2859	0.907778
$659$	1.69672	0.0660948	0.0330474	−	0.999454i	$-0.489479\pi$
$659$	1.69672	0.0660948	0.0330474	+	0.999454i	$0.489479\pi$
$660$	1.47148	0.0572771
$661$	19.9670	0.776625	0.388312	−	0.921528i	$-0.373058\pi$
$661$	19.9670	0.776625	0.388312	+	0.921528i	$0.373058\pi$
$662$	−58.4027	−2.26989
$663$	38.0798	1.47890
$664$	7.91013	0.306973
$665$	7.11136	0.275767
$666$	−0.0440355	−0.00170634
$667$	67.5962	2.61733
$668$	79.6133	3.08033
$669$	1.90382	0.0736060
$670$	1.93106	0.0746035
$671$	1.85800	0.0717274
$672$	−2.51457	−0.0970017
$673$	22.4269	0.864492	0.432246	−	0.901756i	$-0.357721\pi$
$673$	22.4269	0.864492	0.432246	+	0.901756i	$0.357721\pi$
$674$	58.9914	2.27226
$675$	11.7746	0.453204
$676$	30.8301	1.18577
$677$	−30.6427	−1.17769	−0.588847	−	0.808245i	$-0.700418\pi$
$677$	−30.6427	−1.17769	−0.588847	+	0.808245i	$0.700418\pi$
$678$	−19.3894	−0.744645
$679$	−27.6278	−1.06026
$680$	−40.8975	−1.56835
$681$	−9.15641	−0.350874
$682$	1.10638	0.0423654
$683$	11.5216	0.440864	0.220432	−	0.975402i	$-0.429253\pi$
$683$	11.5216	0.440864	0.220432	+	0.975402i	$0.429253\pi$
$684$	−0.301361	−0.0115228
$685$	12.7330	0.486502
$686$	47.0589	1.79672
$687$	−22.9254	−0.874659
$688$	−11.8716	−0.452599
$689$	−38.4226	−1.46378
$690$	54.3754	2.07004
$691$	−1.06234	−0.0404132	−0.0202066	−	0.999796i	$-0.506432\pi$
$691$	−1.06234	−0.0404132	−0.0202066	+	0.999796i	$0.506432\pi$
$692$	99.8602	3.79611
$693$	−0.00649069	−0.000246561 0
$694$	47.7361	1.81204
$695$	−3.69808	−0.140276
$696$	−78.7228	−2.98398
$697$	41.2483	1.56239
$698$	−79.5982	−3.01284
$699$	1.74413	0.0659691
$700$	−16.1573	−0.610690
$701$	−36.9495	−1.39556	−0.697781	−	0.716311i	$-0.745829\pi$
$701$	−36.9495	−1.39556	−0.697781	+	0.716311i	$0.745829\pi$
$702$	−57.8046	−2.18169
$703$	−1.48786	−0.0561157
$704$	0.872711	0.0328915
$705$	15.6047	0.587705
$706$	−87.7967	−3.30427
$707$	19.6469	0.738898
$708$	67.6550	2.54263
$709$	26.4047	0.991648	0.495824	−	0.868423i	$-0.334866\pi$
$709$	26.4047	0.991648	0.495824	+	0.868423i	$0.334866\pi$
$710$	24.7121	0.927427
$711$	0.293909	0.0110224
$712$	−2.57452	−0.0964843
$713$	27.4410	1.02767
$714$	35.9999	1.34726
$715$	−0.938727	−0.0351064
$716$	11.5755	0.432596
$717$	−28.2989	−1.05684
$718$	13.0642	0.487551
$719$	−32.3558	−1.20667	−0.603334	−	0.797488i	$-0.706162\pi$
$719$	−32.3558	−1.20667	−0.603334	+	0.797488i	$0.706162\pi$
$720$	−0.221100	−0.00823991
$721$	3.37956	0.125861
$722$	31.6889	1.17934
$723$	21.5939	0.803086
$724$	−7.72280	−0.287016
$725$	−20.0542	−0.744793
$726$	47.1540	1.75005
$727$	32.0291	1.18789	0.593947	−	0.804504i	$-0.297569\pi$
$727$	32.0291	1.18789	0.593947	+	0.804504i	$0.297569\pi$
$728$	40.4625	1.49964
$729$	26.7268	0.989883
$730$	59.7716	2.21225
$731$	12.7247	0.470642
$732$	−105.210	−3.88866
$733$	43.2615	1.59790	0.798949	−	0.601398i	$-0.205390\pi$
$733$	43.2615	1.59790	0.798949	+	0.601398i	$0.205390\pi$
$734$	−73.5111	−2.71335
$735$	11.4314	0.421654
$736$	−6.38176	−0.235235
$737$	−0.0595516	−0.00219361
$738$	0.627421	0.0230957
$739$	2.59385	0.0954164	0.0477082	−	0.998861i	$-0.484808\pi$
$739$	2.59385	0.0954164	0.0477082	+	0.998861i	$0.484808\pi$
$740$	−4.04114	−0.148555
$741$	19.5707	0.718948
$742$	−36.3240	−1.33350
$743$	−1.66035	−0.0609124	−0.0304562	−	0.999536i	$-0.509696\pi$
$743$	−1.66035	−0.0609124	−0.0304562	+	0.999536i	$0.509696\pi$
$744$	−31.9579	−1.17163
$745$	−10.2894	−0.376974
$746$	−92.4885	−3.38625
$747$	−0.0458372	−0.00167709
$748$	2.47245	0.0904019
$749$	−4.22461	−0.154364
$750$	−51.5483	−1.88228
$751$	31.1455	1.13652	0.568258	−	0.822850i	$-0.307617\pi$
$751$	31.1455	1.13652	0.568258	+	0.822850i	$0.307617\pi$
$752$	−24.4618	−0.892029
$753$	−11.2997	−0.411783
$754$	98.4513	3.58538
$755$	−30.5772	−1.11282
$756$	−36.6788	−1.33400
$757$	−19.7791	−0.718884	−0.359442	−	0.933167i	$-0.617033\pi$
$757$	−19.7791	−0.718884	−0.359442	+	0.933167i	$0.617033\pi$
$758$	72.3468	2.62775
$759$	−1.67687	−0.0608666
$760$	−21.0188	−0.762432
$761$	38.3531	1.39030	0.695149	−	0.718866i	$-0.255338\pi$
$761$	38.3531	1.39030	0.695149	+	0.718866i	$0.255338\pi$
$762$	−72.0593	−2.61043
$763$	0.174783	0.00632758
$764$	−68.2370	−2.46873
$765$	0.236990	0.00856840
$766$	−22.6272	−0.817552
$767$	−43.1604	−1.55843
$768$	−56.5549	−2.04075
$769$	7.24954	0.261425	0.130713	−	0.991420i	$-0.458273\pi$
$769$	7.24954	0.261425	0.130713	+	0.991420i	$0.458273\pi$
$770$	−0.887454	−0.0319816
$771$	2.73987	0.0986741
$772$	69.3881	2.49733
$773$	0.878836	0.0316095	0.0158048	−	0.999875i	$-0.494969\pi$
$773$	0.878836	0.0316095	0.0158048	+	0.999875i	$0.494969\pi$
$774$	0.193554	0.00695714
$775$	−8.14108	−0.292436
$776$	81.6584	2.93137
$777$	1.81457	0.0650974
$778$	8.97952	0.321931
$779$	21.1991	0.759538
$780$	53.1555	1.90327
$781$	−0.762090	−0.0272697
$782$	91.3646	3.26719
$783$	−45.5250	−1.62693
$784$	−17.9198	−0.639994
$785$	6.04500	0.215755
$786$	−1.85491	−0.0661623
$787$	−35.5312	−1.26655	−0.633276	−	0.773926i	$-0.718290\pi$
$787$	−35.5312	−1.26655	−0.633276	+	0.773926i	$0.718290\pi$
$788$	45.6521	1.62629
$789$	36.7096	1.30690
$790$	40.1853	1.42973
$791$	7.84879	0.279071
$792$	0.0191843	0.000681685 0
$793$	67.1184	2.38345
$794$	−8.93672	−0.317152
$795$	−24.3419	−0.863319
$796$	19.5557	0.693132
$797$	34.5344	1.22327	0.611636	−	0.791139i	$-0.290512\pi$
$797$	34.5344	1.22327	0.611636	+	0.791139i	$0.290512\pi$
$798$	18.5018	0.654955
$799$	26.2198	0.927590
$800$	1.89331	0.0669388
$801$	0.0149187	0.000527126 0
$802$	−30.0773	−1.06207
$803$	−1.84328	−0.0650481
$804$	3.37212	0.118925
$805$	−22.0111	−0.775790
$806$	39.9668	1.40777
$807$	28.9046	1.01749
$808$	−58.0697	−2.04288
$809$	0.249494	0.00877175	0.00438588	−	0.999990i	$-0.498604\pi$
$809$	0.249494	0.00877175	0.00438588	+	0.999990i	$0.498604\pi$
$810$	−36.9844	−1.29950
$811$	−42.6669	−1.49824	−0.749119	−	0.662435i	$-0.769523\pi$
$811$	−42.6669	−1.49824	−0.749119	+	0.662435i	$0.769523\pi$
$812$	62.4704	2.19228
$813$	−14.5078	−0.508811
$814$	0.185676	0.00650793
$815$	7.39497	0.259034
$816$	−37.8178	−1.32389
$817$	6.53975	0.228797
$818$	−4.31559	−0.150891
$819$	−0.234469	−0.00819302
$820$	57.5785	2.01073
$821$	−35.5510	−1.24074	−0.620369	−	0.784310i	$-0.713017\pi$
$821$	−35.5510	−1.24074	−0.620369	+	0.784310i	$0.713017\pi$
$822$	33.1276	1.15546
$823$	1.88372	0.0656624	0.0328312	−	0.999461i	$-0.489548\pi$
$823$	1.88372	0.0656624	0.0328312	+	0.999461i	$0.489548\pi$
$824$	−9.98884	−0.347978
$825$	0.497488	0.0173203
$826$	−40.8031	−1.41972
$827$	−54.9009	−1.90909	−0.954546	−	0.298064i	$-0.903659\pi$
$827$	−54.9009	−1.90909	−0.954546	+	0.298064i	$0.903659\pi$
$828$	0.932775	0.0324162
$829$	31.1984	1.08356	0.541782	−	0.840519i	$-0.317750\pi$
$829$	31.1984	1.08356	0.541782	+	0.840519i	$0.317750\pi$
$830$	−6.26719	−0.217537
$831$	−13.7587	−0.477285
$832$	31.5258	1.09296
$833$	19.2077	0.665507
$834$	−9.62137	−0.333161
$835$	−32.1766	−1.11352
$836$	1.27069	0.0439478
$837$	−18.4811	−0.638800
$838$	42.5832	1.47101
$839$	−30.7617	−1.06201	−0.531006	−	0.847368i	$-0.678186\pi$
$839$	−30.7617	−1.06201	−0.531006	+	0.847368i	$0.678186\pi$
$840$	25.6342	0.884466
$841$	48.5370	1.67369
$842$	14.9121	0.513907
$843$	36.2903	1.24991
$844$	91.5245	3.15040
$845$	−12.4603	−0.428649
$846$	0.398824	0.0137119
$847$	−19.0879	−0.655867
$848$	38.1583	1.31036
$849$	1.59791	0.0548402
$850$	−27.1057	−0.929717
$851$	4.60523	0.157865
$852$	43.1535	1.47841
$853$	−13.7046	−0.469235	−0.234618	−	0.972088i	$-0.575384\pi$
$853$	−13.7046	−0.469235	−0.234618	+	0.972088i	$0.575384\pi$
$854$	63.4525	2.17130
$855$	0.121799	0.00416542
$856$	12.4865	0.426781
$857$	19.8086	0.676648	0.338324	−	0.941030i	$-0.390140\pi$
$857$	19.8086	0.676648	0.338324	+	0.941030i	$0.390140\pi$
$858$	−2.44230	−0.0833788
$859$	−1.40390	−0.0479003	−0.0239502	−	0.999713i	$-0.507624\pi$
$859$	−1.40390	−0.0479003	−0.0239502	+	0.999713i	$0.507624\pi$
$860$	17.7624	0.605694
$861$	−25.8542	−0.881108
$862$	−1.30473	−0.0444392
$863$	47.7147	1.62423	0.812114	−	0.583498i	$-0.198317\pi$
$863$	47.7147	1.62423	0.812114	+	0.583498i	$0.198317\pi$
$864$	4.29802	0.146222
$865$	−40.3596	−1.37227
$866$	17.8828	0.607683
$867$	10.9452	0.371718
$868$	25.3602	0.860780
$869$	−1.23927	−0.0420392
$870$	62.3720	2.11461
$871$	−2.15124	−0.0728920
$872$	−0.516600	−0.0174943
$873$	−0.473189	−0.0160150
$874$	46.9558	1.58831
$875$	20.8667	0.705423
$876$	104.376	3.52655
$877$	28.2516	0.953990	0.476995	−	0.878906i	$-0.341726\pi$
$877$	28.2516	0.953990	0.476995	+	0.878906i	$0.341726\pi$
$878$	41.9236	1.41485
$879$	−13.2168	−0.445791
$880$	0.932269	0.0314268
$881$	−25.0078	−0.842534	−0.421267	−	0.906937i	$-0.638415\pi$
$881$	−25.0078	−0.842534	−0.421267	+	0.906937i	$0.638415\pi$
$882$	0.292165	0.00983770
$883$	43.7692	1.47295	0.736475	−	0.676465i	$-0.236489\pi$
$883$	43.7692	1.47295	0.736475	+	0.676465i	$0.236489\pi$
$884$	89.3148	3.00398
$885$	−27.3435	−0.919142
$886$	−33.3925	−1.12184
$887$	10.6167	0.356475	0.178237	−	0.983988i	$-0.442961\pi$
$887$	10.6167	0.356475	0.178237	+	0.983988i	$0.442961\pi$
$888$	−5.36327	−0.179980
$889$	29.1695	0.978314
$890$	2.03979	0.0683739
$891$	1.14055	0.0382100
$892$	4.46534	0.149511
$893$	13.4754	0.450936
$894$	−26.7701	−0.895326
$895$	−4.67836	−0.156380
$896$	32.6931	1.09220
$897$	−60.5753	−2.02255
$898$	−58.2895	−1.94515
$899$	31.4765	1.04980
$900$	−0.276732	−0.00922439
$901$	−40.9006	−1.36260
$902$	−2.64552	−0.0880862
$903$	−7.97578	−0.265417
$904$	−23.1984	−0.771567
$905$	3.12125	0.103754
$906$	−79.5534	−2.64298
$907$	33.8126	1.12273	0.561365	−	0.827569i	$-0.310277\pi$
$907$	33.8126	1.12273	0.561365	+	0.827569i	$0.310277\pi$
$908$	−21.4760	−0.712707
$909$	0.336499	0.0111610
$910$	−32.0583	−1.06272
$911$	29.9735	0.993065	0.496532	−	0.868018i	$-0.334606\pi$
$911$	29.9735	0.993065	0.496532	+	0.868018i	$0.334606\pi$
$912$	−19.4361	−0.643593
$913$	0.193272	0.00639638
$914$	−45.8369	−1.51615
$915$	42.5217	1.40572
$916$	−53.7708	−1.77664
$917$	0.750863	0.0247957
$918$	−61.5327	−2.03088
$919$	−15.7052	−0.518068	−0.259034	−	0.965868i	$-0.583404\pi$
$919$	−15.7052	−0.518068	−0.259034	+	0.965868i	$0.583404\pi$
$920$	65.0575	2.14488
$921$	14.4041	0.474630
$922$	22.4746	0.740163
$923$	−27.5297	−0.906151
$924$	−1.54972	−0.0509819
$925$	−1.36626	−0.0449223
$926$	100.804	3.31263
$927$	0.0578827	0.00190112
$928$	−7.32027	−0.240300
$929$	7.38567	0.242316	0.121158	−	0.992633i	$-0.461339\pi$
$929$	7.38567	0.242316	0.121158	+	0.992633i	$0.461339\pi$
$930$	25.3202	0.830283
$931$	9.87159	0.323528
$932$	4.09080	0.133999
$933$	−13.5897	−0.444908
$934$	27.7485	0.907960
$935$	−0.999269	−0.0326796
$936$	0.693013	0.0226518
$937$	−31.8439	−1.04030	−0.520148	−	0.854076i	$-0.674123\pi$
$937$	−31.8439	−1.04030	−0.520148	+	0.854076i	$0.674123\pi$
$938$	−2.03374	−0.0664040
$939$	−41.0509	−1.33965
$940$	36.6002	1.19377
$941$	28.0486	0.914360	0.457180	−	0.889374i	$-0.348860\pi$
$941$	28.0486	0.914360	0.457180	+	0.889374i	$0.348860\pi$
$942$	15.7274	0.512426
$943$	−65.6156	−2.13674
$944$	42.8635	1.39509
$945$	14.8241	0.482230
$946$	−0.816119	−0.0265343
$947$	59.9734	1.94887	0.974437	−	0.224662i	$-0.0721279\pi$
$947$	59.9734	1.94887	0.974437	+	0.224662i	$0.0721279\pi$
$948$	70.1736	2.27913
$949$	−66.5867	−2.16150
$950$	−13.9307	−0.451971
$951$	−31.6102	−1.02503
$952$	43.0721	1.39597
$953$	−31.6692	−1.02587	−0.512933	−	0.858429i	$-0.671441\pi$
$953$	−31.6692	−1.02587	−0.512933	+	0.858429i	$0.671441\pi$
$954$	−0.622132	−0.0201423
$955$	27.5787	0.892426
$956$	−66.3740	−2.14669
$957$	−1.92348	−0.0621772
$958$	6.95421	0.224680
$959$	−13.4100	−0.433032
$960$	19.9726	0.644612
$961$	−18.2219	−0.587805
$962$	6.70734	0.216253
$963$	−0.0723562	−0.00233164
$964$	50.6477	1.63125
$965$	−28.0440	−0.902767
$966$	−57.2667	−1.84253
$967$	−23.3765	−0.751738	−0.375869	−	0.926673i	$-0.622656\pi$
$967$	−23.3765	−0.751738	−0.375869	+	0.926673i	$0.622656\pi$
$968$	56.4173	1.81332
$969$	20.8329	0.669249
$970$	−64.6978	−2.07732
$971$	49.5848	1.59125	0.795625	−	0.605789i	$-0.207143\pi$
$971$	49.5848	1.59125	0.795625	+	0.605789i	$0.207143\pi$
$972$	−1.26271	−0.0405016
$973$	3.89472	0.124859
$974$	−42.8284	−1.37231
$975$	17.9712	0.575540
$976$	−66.6567	−2.13363
$977$	7.93951	0.254007	0.127004	−	0.991902i	$-0.459464\pi$
$977$	7.93951	0.254007	0.127004	+	0.991902i	$0.459464\pi$
$978$	19.2396	0.615215
$979$	−0.0629047	−0.00201044
$980$	26.8120	0.856477
$981$	0.00299357	9.55772e−5 0
$982$	19.3658	0.617988
$983$	8.21675	0.262074	0.131037	−	0.991377i	$-0.458169\pi$
$983$	8.21675	0.262074	0.131037	+	0.991377i	$0.458169\pi$
$984$	76.4163	2.43606
$985$	−18.4508	−0.587892
$986$	104.801	3.33754
$987$	−16.4344	−0.523112
$988$	45.9024	1.46035
$989$	−20.2418	−0.643653
$990$	−0.0151997	−0.000483078 0
$991$	−1.00672	−0.0319795	−0.0159897	−	0.999872i	$-0.505090\pi$
$991$	−1.00672	−0.0319795	−0.0159897	+	0.999872i	$0.505090\pi$
$992$	−2.97170	−0.0943516
$993$	41.2187	1.30804
$994$	−26.0261	−0.825496
$995$	−7.90364	−0.250562
$996$	−10.9441	−0.346776
$997$	42.0400	1.33142	0.665710	−	0.746211i	$-0.268129\pi$
$997$	42.0400	1.33142	0.665710	+	0.746211i	$0.268129\pi$
$998$	30.3376	0.960319
$999$	−3.10155	−0.0981287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.14	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.46629 q^{2} +1.74062 q^{3} +4.08257 q^{4} -1.65001 q^{5} -4.29287 q^{6} +1.73775 q^{7} -5.13620 q^{8} +0.0297629 q^{9} +O(q^{10})\)	\(q-2.46629 q^{2} +1.74062 q^{3} +4.08257 q^{4} -1.65001 q^{5} -4.29287 q^{6} +1.73775 q^{7} -5.13620 q^{8} +0.0297629 q^{9} +4.06940 q^{10} -0.125496 q^{11} +7.10620 q^{12} -4.53339 q^{13} -4.28578 q^{14} -2.87205 q^{15} +4.50221 q^{16} -4.82577 q^{17} -0.0734039 q^{18} -2.48015 q^{19} -6.73629 q^{20} +3.02476 q^{21} +0.309508 q^{22} +7.67658 q^{23} -8.94018 q^{24} -2.27746 q^{25} +11.1806 q^{26} -5.17006 q^{27} +7.09447 q^{28} +8.80551 q^{29} +7.08329 q^{30} +3.57464 q^{31} -0.831329 q^{32} -0.218440 q^{33} +11.9017 q^{34} -2.86731 q^{35} +0.121509 q^{36} +0.599906 q^{37} +6.11677 q^{38} -7.89092 q^{39} +8.47480 q^{40} -8.54751 q^{41} -7.45993 q^{42} -2.63683 q^{43} -0.512344 q^{44} -0.0491093 q^{45} -18.9326 q^{46} -5.43328 q^{47} +7.83664 q^{48} -3.98023 q^{49} +5.61686 q^{50} -8.39984 q^{51} -18.5079 q^{52} +8.47546 q^{53} +12.7508 q^{54} +0.207069 q^{55} -8.92542 q^{56} -4.31701 q^{57} -21.7169 q^{58} +9.52056 q^{59} -11.7253 q^{60} -14.8053 q^{61} -8.81608 q^{62} +0.0517205 q^{63} -6.95412 q^{64} +7.48016 q^{65} +0.538736 q^{66} +0.474532 q^{67} -19.7015 q^{68} +13.3620 q^{69} +7.07160 q^{70} +6.07265 q^{71} -0.152868 q^{72} +14.6881 q^{73} -1.47954 q^{74} -3.96419 q^{75} -10.1254 q^{76} -0.218080 q^{77} +19.4613 q^{78} +9.87498 q^{79} -7.42870 q^{80} -9.08840 q^{81} +21.0806 q^{82} -1.54007 q^{83} +12.3488 q^{84} +7.96259 q^{85} +6.50318 q^{86} +15.3271 q^{87} +0.644570 q^{88} +0.501250 q^{89} +0.121117 q^{90} -7.87790 q^{91} +31.3401 q^{92} +6.22210 q^{93} +13.4000 q^{94} +4.09229 q^{95} -1.44703 q^{96} -15.8986 q^{97} +9.81639 q^{98} -0.00373512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 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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