LMFDB - Embedded newform 6037.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.60200 q^{2} -2.50808 q^{3} +4.77039 q^{4} +0.421972 q^{5} +6.52603 q^{6} -1.06326 q^{7} -7.20855 q^{8} +3.29049 q^{9} +O(q^{10})$	\(q-2.60200 q^{2} -2.50808 q^{3} +4.77039 q^{4} +0.421972 q^{5} +6.52603 q^{6} -1.06326 q^{7} -7.20855 q^{8} +3.29049 q^{9} -1.09797 q^{10} -2.57042 q^{11} -11.9645 q^{12} +3.70300 q^{13} +2.76660 q^{14} -1.05834 q^{15} +9.21585 q^{16} -5.32295 q^{17} -8.56184 q^{18} -7.54727 q^{19} +2.01297 q^{20} +2.66674 q^{21} +6.68822 q^{22} +4.06815 q^{23} +18.0797 q^{24} -4.82194 q^{25} -9.63520 q^{26} -0.728563 q^{27} -5.07216 q^{28} -2.06786 q^{29} +2.75380 q^{30} -5.40445 q^{31} -9.56252 q^{32} +6.44682 q^{33} +13.8503 q^{34} -0.448665 q^{35} +15.6969 q^{36} -8.73603 q^{37} +19.6380 q^{38} -9.28743 q^{39} -3.04181 q^{40} -5.87862 q^{41} -6.93885 q^{42} -5.00492 q^{43} -12.2619 q^{44} +1.38849 q^{45} -10.5853 q^{46} +4.68277 q^{47} -23.1141 q^{48} -5.86948 q^{49} +12.5467 q^{50} +13.3504 q^{51} +17.6648 q^{52} -10.3864 q^{53} +1.89572 q^{54} -1.08464 q^{55} +7.66455 q^{56} +18.9292 q^{57} +5.38057 q^{58} +12.4664 q^{59} -5.04870 q^{60} -10.1115 q^{61} +14.0624 q^{62} -3.49864 q^{63} +6.44995 q^{64} +1.56256 q^{65} -16.7746 q^{66} -10.2037 q^{67} -25.3926 q^{68} -10.2033 q^{69} +1.16743 q^{70} -6.16132 q^{71} -23.7196 q^{72} +11.7691 q^{73} +22.7311 q^{74} +12.0938 q^{75} -36.0035 q^{76} +2.73302 q^{77} +24.1659 q^{78} -0.169344 q^{79} +3.88883 q^{80} -8.04416 q^{81} +15.2962 q^{82} +4.24867 q^{83} +12.7214 q^{84} -2.24614 q^{85} +13.0228 q^{86} +5.18637 q^{87} +18.5290 q^{88} -4.85615 q^{89} -3.61286 q^{90} -3.93724 q^{91} +19.4067 q^{92} +13.5548 q^{93} -12.1846 q^{94} -3.18474 q^{95} +23.9836 q^{96} -8.55369 q^{97} +15.2724 q^{98} -8.45792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60200	−1.83989	−0.919945	−	0.392047i	$-0.871767\pi$
$2$	−2.60200	−1.83989	−0.919945	+	0.392047i	$0.871767\pi$
$3$	−2.50808	−1.44804	−0.724022	−	0.689777i	$-0.757708\pi$
$3$	−2.50808	−1.44804	−0.724022	+	0.689777i	$0.757708\pi$
$4$	4.77039	2.38520
$5$	0.421972	0.188712	0.0943558	−	0.995539i	$-0.469921\pi$
$5$	0.421972	0.188712	0.0943558	+	0.995539i	$0.469921\pi$
$6$	6.52603	2.66424
$7$	−1.06326	−0.401874	−0.200937	−	0.979604i	$-0.564399\pi$
$7$	−1.06326	−0.401874	−0.200937	+	0.979604i	$0.564399\pi$
$8$	−7.20855	−2.54861
$9$	3.29049	1.09683
$10$	−1.09797	−0.347209
$11$	−2.57042	−0.775010	−0.387505	−	0.921868i	$-0.626663\pi$
$11$	−2.57042	−0.775010	−0.387505	+	0.921868i	$0.626663\pi$
$12$	−11.9645	−3.45387
$13$	3.70300	1.02703	0.513514	−	0.858081i	$-0.328344\pi$
$13$	3.70300	1.02703	0.513514	+	0.858081i	$0.328344\pi$
$14$	2.76660	0.739404
$15$	−1.05834	−0.273263
$16$	9.21585	2.30396
$17$	−5.32295	−1.29101	−0.645503	−	0.763758i	$-0.723352\pi$
$17$	−5.32295	−1.29101	−0.645503	+	0.763758i	$0.723352\pi$
$18$	−8.56184	−2.01804
$19$	−7.54727	−1.73146	−0.865732	−	0.500508i	$-0.833146\pi$
$19$	−7.54727	−1.73146	−0.865732	+	0.500508i	$0.833146\pi$
$20$	2.01297	0.450114
$21$	2.66674	0.581931
$22$	6.68822	1.42593
$23$	4.06815	0.848268	0.424134	−	0.905599i	$-0.360579\pi$
$23$	4.06815	0.848268	0.424134	+	0.905599i	$0.360579\pi$
$24$	18.0797	3.69049
$25$	−4.82194	−0.964388
$26$	−9.63520	−1.88962
$27$	−0.728563	−0.140212
$28$	−5.07216	−0.958548
$29$	−2.06786	−0.383992	−0.191996	−	0.981396i	$-0.561496\pi$
$29$	−2.06786	−0.383992	−0.191996	+	0.981396i	$0.561496\pi$
$30$	2.75380	0.502773
$31$	−5.40445	−0.970668	−0.485334	−	0.874329i	$-0.661302\pi$
$31$	−5.40445	−0.970668	−0.485334	+	0.874329i	$0.661302\pi$
$32$	−9.56252	−1.69043
$33$	6.44682	1.12225
$34$	13.8503	2.37531
$35$	−0.448665	−0.0758383
$36$	15.6969	2.61615
$37$	−8.73603	−1.43619	−0.718097	−	0.695943i	$-0.754987\pi$
$37$	−8.73603	−1.43619	−0.718097	+	0.695943i	$0.754987\pi$
$38$	19.6380	3.18570
$39$	−9.28743	−1.48718
$40$	−3.04181	−0.480952
$41$	−5.87862	−0.918087	−0.459043	−	0.888414i	$-0.651808\pi$
$41$	−5.87862	−0.918087	−0.459043	+	0.888414i	$0.651808\pi$
$42$	−6.93885	−1.07069
$43$	−5.00492	−0.763243	−0.381622	−	0.924319i	$-0.624634\pi$
$43$	−5.00492	−0.763243	−0.381622	+	0.924319i	$0.624634\pi$
$44$	−12.2619	−1.84855
$45$	1.38849	0.206984
$46$	−10.5853	−1.56072
$47$	4.68277	0.683052	0.341526	−	0.939872i	$-0.389056\pi$
$47$	4.68277	0.683052	0.341526	+	0.939872i	$0.389056\pi$
$48$	−23.1141	−3.33624
$49$	−5.86948	−0.838497
$50$	12.5467	1.77437
$51$	13.3504	1.86943
$52$	17.6648	2.44966
$53$	−10.3864	−1.42668	−0.713339	−	0.700820i	$-0.752818\pi$
$53$	−10.3864	−1.42668	−0.713339	+	0.700820i	$0.752818\pi$
$54$	1.89572	0.257975
$55$	−1.08464	−0.146253
$56$	7.66455	1.02422
$57$	18.9292	2.50723
$58$	5.38057	0.706504
$59$	12.4664	1.62299	0.811496	−	0.584358i	$-0.198654\pi$
$59$	12.4664	1.62299	0.811496	+	0.584358i	$0.198654\pi$
$60$	−5.04870	−0.651785
$61$	−10.1115	−1.29465	−0.647325	−	0.762214i	$-0.724112\pi$
$61$	−10.1115	−1.29465	−0.647325	+	0.762214i	$0.724112\pi$
$62$	14.0624	1.78592
$63$	−3.49864	−0.440787
$64$	6.44995	0.806243
$65$	1.56256	0.193812
$66$	−16.7746	−2.06481
$67$	−10.2037	−1.24659	−0.623293	−	0.781989i	$-0.714205\pi$
$67$	−10.2037	−1.24659	−0.623293	+	0.781989i	$0.714205\pi$
$68$	−25.3926	−3.07930
$69$	−10.2033	−1.22833
$70$	1.16743	0.139534
$71$	−6.16132	−0.731214	−0.365607	−	0.930769i	$-0.619139\pi$
$71$	−6.16132	−0.731214	−0.365607	+	0.930769i	$0.619139\pi$
$72$	−23.7196	−2.79539
$73$	11.7691	1.37747	0.688733	−	0.725015i	$-0.258167\pi$
$73$	11.7691	1.37747	0.688733	+	0.725015i	$0.258167\pi$
$74$	22.7311	2.64244
$75$	12.0938	1.39648
$76$	−36.0035	−4.12988
$77$	2.73302	0.311456
$78$	24.1659	2.73625
$79$	−0.169344	−0.0190526	−0.00952632	−	0.999955i	$-0.503032\pi$
$79$	−0.169344	−0.0190526	−0.00952632	+	0.999955i	$0.503032\pi$
$80$	3.88883	0.434785
$81$	−8.04416	−0.893796
$82$	15.2962	1.68918
$83$	4.24867	0.466352	0.233176	−	0.972435i	$-0.425088\pi$
$83$	4.24867	0.466352	0.233176	+	0.972435i	$0.425088\pi$
$84$	12.7214	1.38802
$85$	−2.24614	−0.243628
$86$	13.0228	1.40428
$87$	5.18637	0.556037
$88$	18.5290	1.97520
$89$	−4.85615	−0.514751	−0.257376	−	0.966311i	$-0.582858\pi$
$89$	−4.85615	−0.514751	−0.257376	+	0.966311i	$0.582858\pi$
$90$	−3.61286	−0.380828
$91$	−3.93724	−0.412735
$92$	19.4067	2.02329
$93$	13.5548	1.40557
$94$	−12.1846	−1.25674
$95$	−3.18474	−0.326747
$96$	23.9836	2.44782
$97$	−8.55369	−0.868496	−0.434248	−	0.900793i	$-0.642986\pi$
$97$	−8.55369	−0.868496	−0.434248	+	0.900793i	$0.642986\pi$
$98$	15.2724	1.54274
$99$	−8.45792	−0.850053
$100$	−23.0025	−2.30025
$101$	9.07104	0.902602	0.451301	−	0.892372i	$-0.350960\pi$
$101$	9.07104	0.902602	0.451301	+	0.892372i	$0.350960\pi$
$102$	−34.7377	−3.43955
$103$	−1.04588	−0.103054	−0.0515270	−	0.998672i	$-0.516409\pi$
$103$	−1.04588	−0.103054	−0.0515270	+	0.998672i	$0.516409\pi$
$104$	−26.6933	−2.61749
$105$	1.12529	0.109817
$106$	27.0253	2.62493
$107$	9.99804	0.966547	0.483273	−	0.875469i	$-0.339448\pi$
$107$	9.99804	0.966547	0.483273	+	0.875469i	$0.339448\pi$
$108$	−3.47553	−0.334433
$109$	−2.85821	−0.273767	−0.136883	−	0.990587i	$-0.543709\pi$
$109$	−2.85821	−0.273767	−0.136883	+	0.990587i	$0.543709\pi$
$110$	2.82224	0.269090
$111$	21.9107	2.07967
$112$	−9.79883	−0.925902
$113$	10.9654	1.03154	0.515770	−	0.856727i	$-0.327506\pi$
$113$	10.9654	1.03154	0.515770	+	0.856727i	$0.327506\pi$
$114$	−49.2537	−4.61303
$115$	1.71665	0.160078
$116$	−9.86451	−0.915897
$117$	12.1847	1.12647
$118$	−32.4376	−2.98613
$119$	5.65967	0.518821
$120$	7.62911	0.696439
$121$	−4.39296	−0.399360
$122$	26.3102	2.38201
$123$	14.7441	1.32943
$124$	−25.7813	−2.31523
$125$	−4.14458	−0.370703
$126$	9.10344	0.810999
$127$	−13.6068	−1.20741	−0.603704	−	0.797208i	$-0.706309\pi$
$127$	−13.6068	−1.20741	−0.603704	+	0.797208i	$0.706309\pi$
$128$	2.34229	0.207031
$129$	12.5528	1.10521
$130$	−4.06578	−0.356593
$131$	2.43434	0.212689	0.106345	−	0.994329i	$-0.466085\pi$
$131$	2.43434	0.212689	0.106345	+	0.994329i	$0.466085\pi$
$132$	30.7539	2.67678
$133$	8.02470	0.695830
$134$	26.5501	2.29358
$135$	−0.307433	−0.0264596
$136$	38.3708	3.29027
$137$	4.34294	0.371042	0.185521	−	0.982640i	$-0.440603\pi$
$137$	4.34294	0.371042	0.185521	+	0.982640i	$0.440603\pi$
$138$	26.5489	2.25999
$139$	10.8969	0.924263	0.462132	−	0.886811i	$-0.347085\pi$
$139$	10.8969	0.924263	0.462132	+	0.886811i	$0.347085\pi$
$140$	−2.14031	−0.180889
$141$	−11.7448	−0.989089
$142$	16.0317	1.34535
$143$	−9.51825	−0.795956
$144$	30.3246	2.52705
$145$	−0.872580	−0.0724638
$146$	−30.6231	−2.53439
$147$	14.7212	1.21418
$148$	−41.6743	−3.42560
$149$	−18.8882	−1.54738	−0.773690	−	0.633564i	$-0.781591\pi$
$149$	−18.8882	−1.54738	−0.773690	+	0.633564i	$0.781591\pi$
$150$	−31.4681	−2.56936
$151$	−1.76685	−0.143784	−0.0718920	−	0.997412i	$-0.522904\pi$
$151$	−1.76685	−0.143784	−0.0718920	+	0.997412i	$0.522904\pi$
$152$	54.4049	4.41282
$153$	−17.5151	−1.41601
$154$	−7.11130	−0.573045
$155$	−2.28053	−0.183176
$156$	−44.3047	−3.54721
$157$	4.33460	0.345939	0.172969	−	0.984927i	$-0.444664\pi$
$157$	4.33460	0.345939	0.172969	+	0.984927i	$0.444664\pi$
$158$	0.440632	0.0350548
$159$	26.0499	2.06589
$160$	−4.03512	−0.319004
$161$	−4.32549	−0.340897
$162$	20.9309	1.64449
$163$	−4.06005	−0.318007	−0.159004	−	0.987278i	$-0.550828\pi$
$163$	−4.06005	−0.318007	−0.159004	+	0.987278i	$0.550828\pi$
$164$	−28.0433	−2.18982
$165$	2.72038	0.211781
$166$	−11.0550	−0.858037
$167$	21.6107	1.67229	0.836144	−	0.548510i	$-0.184805\pi$
$167$	21.6107	1.67229	0.836144	+	0.548510i	$0.184805\pi$
$168$	−19.2233	−1.48311
$169$	0.712206	0.0547851
$170$	5.84445	0.448248
$171$	−24.8342	−1.89912
$172$	−23.8754	−1.82048
$173$	−16.2724	−1.23717	−0.618584	−	0.785718i	$-0.712294\pi$
$173$	−16.2724	−1.23717	−0.618584	+	0.785718i	$0.712294\pi$
$174$	−13.4949	−1.02305
$175$	5.12697	0.387562
$176$	−23.6886	−1.78559
$177$	−31.2669	−2.35016
$178$	12.6357	0.947086
$179$	−4.86042	−0.363285	−0.181642	−	0.983365i	$-0.558141\pi$
$179$	−4.86042	−0.363285	−0.181642	+	0.983365i	$0.558141\pi$
$180$	6.62366	0.493698
$181$	−1.15380	−0.0857610	−0.0428805	−	0.999080i	$-0.513653\pi$
$181$	−1.15380	−0.0857610	−0.0428805	+	0.999080i	$0.513653\pi$
$182$	10.2447	0.759388
$183$	25.3606	1.87471
$184$	−29.3255	−2.16190
$185$	−3.68636	−0.271027
$186$	−35.2696	−2.58609
$187$	13.6822	1.00054
$188$	22.3386	1.62921
$189$	0.774651	0.0563475
$190$	8.28668	0.601179
$191$	−19.4965	−1.41071	−0.705357	−	0.708852i	$-0.749213\pi$
$191$	−19.4965	−1.41071	−0.705357	+	0.708852i	$0.749213\pi$
$192$	−16.1770	−1.16748
$193$	−13.0698	−0.940784	−0.470392	−	0.882458i	$-0.655887\pi$
$193$	−13.0698	−0.940784	−0.470392	+	0.882458i	$0.655887\pi$
$194$	22.2567	1.59794
$195$	−3.91904	−0.280648
$196$	−27.9997	−1.99998
$197$	3.07879	0.219355	0.109677	−	0.993967i	$-0.465018\pi$
$197$	3.07879	0.219355	0.109677	+	0.993967i	$0.465018\pi$
$198$	22.0075	1.56400
$199$	9.40233	0.666513	0.333257	−	0.942836i	$-0.391852\pi$
$199$	9.40233	0.666513	0.333257	+	0.942836i	$0.391852\pi$
$200$	34.7592	2.45785
$201$	25.5918	1.80511
$202$	−23.6028	−1.66069
$203$	2.19867	0.154316
$204$	63.6867	4.45896
$205$	−2.48062	−0.173254
$206$	2.72139	0.189608
$207$	13.3862	0.930405
$208$	34.1263	2.36623
$209$	19.3996	1.34190
$210$	−2.92800	−0.202051
$211$	−13.2029	−0.908926	−0.454463	−	0.890766i	$-0.650169\pi$
$211$	−13.2029	−0.908926	−0.454463	+	0.890766i	$0.650169\pi$
$212$	−49.5470	−3.40290
$213$	15.4531	1.05883
$214$	−26.0149	−1.77834
$215$	−2.11194	−0.144033
$216$	5.25188	0.357345
$217$	5.74633	0.390086
$218$	7.43705	0.503700
$219$	−29.5178	−1.99463
$220$	−5.17418	−0.348843
$221$	−19.7109	−1.32590
$222$	−57.0116	−3.82637
$223$	8.33033	0.557840	0.278920	−	0.960314i	$-0.410023\pi$
$223$	8.33033	0.557840	0.278920	+	0.960314i	$0.410023\pi$
$224$	10.1674	0.679340
$225$	−15.8665	−1.05777
$226$	−28.5320	−1.89792
$227$	10.4967	0.696693	0.348346	−	0.937366i	$-0.386743\pi$
$227$	10.4967	0.696693	0.348346	+	0.937366i	$0.386743\pi$
$228$	90.2997	5.98024
$229$	−24.3460	−1.60883	−0.804415	−	0.594067i	$-0.797521\pi$
$229$	−24.3460	−1.60883	−0.804415	+	0.594067i	$0.797521\pi$
$230$	−4.46671	−0.294526
$231$	−6.85463	−0.451002
$232$	14.9063	0.978646
$233$	−25.0042	−1.63808	−0.819041	−	0.573735i	$-0.805494\pi$
$233$	−25.0042	−1.63808	−0.819041	+	0.573735i	$0.805494\pi$
$234$	−31.7045	−2.07259
$235$	1.97600	0.128900
$236$	59.4698	3.87115
$237$	0.424728	0.0275890
$238$	−14.7265	−0.954574
$239$	0.610822	0.0395108	0.0197554	−	0.999805i	$-0.493711\pi$
$239$	0.610822	0.0395108	0.0197554	+	0.999805i	$0.493711\pi$
$240$	−9.75352	−0.629587
$241$	−0.802165	−0.0516720	−0.0258360	−	0.999666i	$-0.508225\pi$
$241$	−0.802165	−0.0516720	−0.0258360	+	0.999666i	$0.508225\pi$
$242$	11.4305	0.734779
$243$	22.3611	1.43447
$244$	−48.2360	−3.08799
$245$	−2.47676	−0.158234
$246$	−38.3641	−2.44600
$247$	−27.9476	−1.77826
$248$	38.9583	2.47385
$249$	−10.6560	−0.675298
$250$	10.7842	0.682053
$251$	−4.14027	−0.261332	−0.130666	−	0.991426i	$-0.541712\pi$
$251$	−4.14027	−0.261332	−0.130666	+	0.991426i	$0.541712\pi$
$252$	−16.6899	−1.05136
$253$	−10.4568	−0.657416
$254$	35.4049	2.22150
$255$	5.63350	0.352784
$256$	−18.9945	−1.18716
$257$	−13.2371	−0.825709	−0.412854	−	0.910797i	$-0.635468\pi$
$257$	−13.2371	−0.825709	−0.412854	+	0.910797i	$0.635468\pi$
$258$	−32.6623	−2.03346
$259$	9.28865	0.577169
$260$	7.45404	0.462280
$261$	−6.80427	−0.421174
$262$	−6.33414	−0.391324
$263$	−22.9404	−1.41456	−0.707281	−	0.706932i	$-0.750079\pi$
$263$	−22.9404	−1.41456	−0.707281	+	0.706932i	$0.750079\pi$
$264$	−46.4722	−2.86017
$265$	−4.38276	−0.269231
$266$	−20.8803	−1.28025
$267$	12.1796	0.745382
$268$	−48.6758	−2.97335
$269$	−0.280355	−0.0170936	−0.00854679	−	0.999963i	$-0.502721\pi$
$269$	−0.280355	−0.0170936	−0.00854679	+	0.999963i	$0.502721\pi$
$270$	0.799941	0.0486828
$271$	−32.1628	−1.95375	−0.976874	−	0.213816i	$-0.931411\pi$
$271$	−32.1628	−1.95375	−0.976874	+	0.213816i	$0.931411\pi$
$272$	−49.0555	−2.97443
$273$	9.87494	0.597659
$274$	−11.3003	−0.682677
$275$	12.3944	0.747410
$276$	−48.6736	−2.92980
$277$	13.7852	0.828274	0.414137	−	0.910215i	$-0.364083\pi$
$277$	13.7852	0.828274	0.414137	+	0.910215i	$0.364083\pi$
$278$	−28.3537	−1.70054
$279$	−17.7833	−1.06466
$280$	3.23423	0.193282
$281$	−16.2375	−0.968650	−0.484325	−	0.874888i	$-0.660935\pi$
$281$	−16.2375	−0.968650	−0.484325	+	0.874888i	$0.660935\pi$
$282$	30.5599	1.81981
$283$	−8.19036	−0.486867	−0.243433	−	0.969918i	$-0.578274\pi$
$283$	−8.19036	−0.486867	−0.243433	+	0.969918i	$0.578274\pi$
$284$	−29.3919	−1.74409
$285$	7.98759	0.473144
$286$	24.7665	1.46447
$287$	6.25050	0.368955
$288$	−31.4653	−1.85411
$289$	11.3338	0.666696
$290$	2.27045	0.133326
$291$	21.4534	1.25762
$292$	56.1431	3.28553
$293$	8.36765	0.488843	0.244422	−	0.969669i	$-0.421402\pi$
$293$	8.36765	0.488843	0.244422	+	0.969669i	$0.421402\pi$
$294$	−38.3044	−2.23396
$295$	5.26049	0.306278
$296$	62.9741	3.66030
$297$	1.87271	0.108666
$298$	49.1470	2.84701
$299$	15.0644	0.871194
$300$	57.6923	3.33087
$301$	5.32152	0.306728
$302$	4.59733	0.264547
$303$	−22.7509	−1.30701
$304$	−69.5546	−3.98923
$305$	−4.26679	−0.244316
$306$	45.5743	2.60531
$307$	9.47421	0.540722	0.270361	−	0.962759i	$-0.412857\pi$
$307$	9.47421	0.540722	0.270361	+	0.962759i	$0.412857\pi$
$308$	13.0376	0.742884
$309$	2.62317	0.149227
$310$	5.93393	0.337024
$311$	−4.92648	−0.279355	−0.139678	−	0.990197i	$-0.544607\pi$
$311$	−4.92648	−0.279355	−0.139678	+	0.990197i	$0.544607\pi$
$312$	66.9489	3.79024
$313$	13.6944	0.774051	0.387025	−	0.922069i	$-0.373503\pi$
$313$	13.6944	0.774051	0.387025	+	0.922069i	$0.373503\pi$
$314$	−11.2786	−0.636490
$315$	−1.47633	−0.0831816
$316$	−0.807835	−0.0454443
$317$	16.7011	0.938026	0.469013	−	0.883191i	$-0.344610\pi$
$317$	16.7011	0.938026	0.469013	+	0.883191i	$0.344610\pi$
$318$	−67.7817	−3.80101
$319$	5.31527	0.297598
$320$	2.72170	0.152148
$321$	−25.0759	−1.39960
$322$	11.2549	0.627212
$323$	40.1738	2.23533
$324$	−38.3738	−2.13188
$325$	−17.8556	−0.990453
$326$	10.5642	0.585099
$327$	7.16862	0.396426
$328$	42.3764	2.33984
$329$	−4.97899	−0.274501
$330$	−7.07842	−0.389654
$331$	2.46233	0.135342	0.0676710	−	0.997708i	$-0.478443\pi$
$331$	2.46233	0.135342	0.0676710	+	0.997708i	$0.478443\pi$
$332$	20.2678	1.11234
$333$	−28.7458	−1.57526
$334$	−56.2310	−3.07683
$335$	−4.30569	−0.235245
$336$	24.5763	1.34075
$337$	0.572821	0.0312035	0.0156018	−	0.999878i	$-0.495034\pi$
$337$	0.572821	0.0312035	0.0156018	+	0.999878i	$0.495034\pi$
$338$	−1.85316	−0.100799
$339$	−27.5022	−1.49371
$340$	−10.7150	−0.581100
$341$	13.8917	0.752277
$342$	64.6185	3.49417
$343$	13.6836	0.738844
$344$	36.0782	1.94521
$345$	−4.30549	−0.231800
$346$	42.3408	2.27625
$347$	0.813396	0.0436654	0.0218327	−	0.999762i	$-0.493050\pi$
$347$	0.813396	0.0436654	0.0218327	+	0.999762i	$0.493050\pi$
$348$	24.7410	1.32626
$349$	19.5749	1.04782	0.523910	−	0.851774i	$-0.324473\pi$
$349$	19.5749	1.04782	0.523910	+	0.851774i	$0.324473\pi$
$350$	−13.3404	−0.713072
$351$	−2.69787	−0.144002
$352$	24.5797	1.31010
$353$	−28.9414	−1.54040	−0.770198	−	0.637805i	$-0.779842\pi$
$353$	−28.9414	−1.54040	−0.770198	+	0.637805i	$0.779842\pi$
$354$	81.3563	4.32404
$355$	−2.59990	−0.137989
$356$	−23.1657	−1.22778
$357$	−14.1949	−0.751276
$358$	12.6468	0.668404
$359$	−28.5449	−1.50654	−0.753272	−	0.657709i	$-0.771525\pi$
$359$	−28.5449	−1.50654	−0.753272	+	0.657709i	$0.771525\pi$
$360$	−10.0090	−0.527522
$361$	37.9614	1.99797
$362$	3.00217	0.157791
$363$	11.0179	0.578291
$364$	−18.7822	−0.984455
$365$	4.96622	0.259944
$366$	−65.9882	−3.44926
$367$	26.8132	1.39964	0.699819	−	0.714320i	$-0.253264\pi$
$367$	26.8132	1.39964	0.699819	+	0.714320i	$0.253264\pi$
$368$	37.4915	1.95438
$369$	−19.3435	−1.00698
$370$	9.59190	0.498659
$371$	11.0434	0.573344
$372$	64.6618	3.35256
$373$	−25.0671	−1.29793	−0.648963	−	0.760820i	$-0.724797\pi$
$373$	−25.0671	−1.29793	−0.648963	+	0.760820i	$0.724797\pi$
$374$	−35.6011	−1.84089
$375$	10.3950	0.536794
$376$	−33.7560	−1.74083
$377$	−7.65729	−0.394371
$378$	−2.01564	−0.103673
$379$	−0.889645	−0.0456980	−0.0228490	−	0.999739i	$-0.507274\pi$
$379$	−0.889645	−0.0456980	−0.0228490	+	0.999739i	$0.507274\pi$
$380$	−15.1925	−0.779356
$381$	34.1270	1.74838
$382$	50.7297	2.59556
$383$	−30.3780	−1.55224	−0.776122	−	0.630582i	$-0.782816\pi$
$383$	−30.3780	−1.55224	−0.776122	+	0.630582i	$0.782816\pi$
$384$	−5.87466	−0.299790
$385$	1.15326	0.0587754
$386$	34.0076	1.73094
$387$	−16.4686	−0.837147
$388$	−40.8045	−2.07153
$389$	−18.9050	−0.958524	−0.479262	−	0.877672i	$-0.659096\pi$
$389$	−18.9050	−0.958524	−0.479262	+	0.877672i	$0.659096\pi$
$390$	10.1973	0.516362
$391$	−21.6546	−1.09512
$392$	42.3105	2.13700
$393$	−6.10552	−0.307983
$394$	−8.01101	−0.403589
$395$	−0.0714583	−0.00359546
$396$	−40.3476	−2.02754
$397$	−23.0434	−1.15652	−0.578258	−	0.815854i	$-0.696267\pi$
$397$	−23.0434	−1.15652	−0.578258	+	0.815854i	$0.696267\pi$
$398$	−24.4648	−1.22631
$399$	−20.1266	−1.00759
$400$	−44.4383	−2.22191
$401$	−32.5008	−1.62301	−0.811506	−	0.584343i	$-0.801352\pi$
$401$	−32.5008	−1.62301	−0.811506	+	0.584343i	$0.801352\pi$
$402$	−66.5899	−3.32120
$403$	−20.0127	−0.996903
$404$	43.2724	2.15288
$405$	−3.39441	−0.168670
$406$	−5.72094	−0.283925
$407$	22.4552	1.11306
$408$	−96.2371	−4.76445
$409$	−8.06276	−0.398678	−0.199339	−	0.979931i	$-0.563879\pi$
$409$	−8.06276	−0.398678	−0.199339	+	0.979931i	$0.563879\pi$
$410$	6.45456	0.318768
$411$	−10.8924	−0.537285
$412$	−4.98928	−0.245804
$413$	−13.2550	−0.652238
$414$	−34.8308	−1.71184
$415$	1.79282	0.0880061
$416$	−35.4100	−1.73612
$417$	−27.3303	−1.33837
$418$	−50.4778	−2.46895
$419$	9.49540	0.463880	0.231940	−	0.972730i	$-0.425493\pi$
$419$	9.49540	0.463880	0.231940	+	0.972730i	$0.425493\pi$
$420$	5.36808	0.261935
$421$	7.72704	0.376593	0.188296	−	0.982112i	$-0.439703\pi$
$421$	7.72704	0.376593	0.188296	+	0.982112i	$0.439703\pi$
$422$	34.3540	1.67232
$423$	15.4086	0.749191
$424$	74.8707	3.63604
$425$	25.6670	1.24503
$426$	−40.2089	−1.94813
$427$	10.7512	0.520286
$428$	47.6946	2.30540
$429$	23.8726	1.15258
$430$	5.49526	0.265005
$431$	24.2334	1.16728	0.583641	−	0.812012i	$-0.301628\pi$
$431$	24.2334	1.16728	0.583641	+	0.812012i	$0.301628\pi$
$432$	−6.71433	−0.323043
$433$	−18.0024	−0.865141	−0.432571	−	0.901600i	$-0.642393\pi$
$433$	−18.0024	−0.865141	−0.432571	+	0.901600i	$0.642393\pi$
$434$	−14.9519	−0.717716
$435$	2.18850	0.104931
$436$	−13.6348	−0.652987
$437$	−30.7034	−1.46875
$438$	76.8054	3.66990
$439$	−34.0158	−1.62349	−0.811743	−	0.584015i	$-0.801481\pi$
$439$	−34.0158	−1.62349	−0.811743	+	0.584015i	$0.801481\pi$
$440$	7.81871	0.372742
$441$	−19.3134	−0.919688
$442$	51.2877	2.43951
$443$	3.31827	0.157656	0.0788280	−	0.996888i	$-0.474882\pi$
$443$	3.31827	0.157656	0.0788280	+	0.996888i	$0.474882\pi$
$444$	104.523	4.96042
$445$	−2.04916	−0.0971396
$446$	−21.6755	−1.02637
$447$	47.3731	2.24067
$448$	−6.85796	−0.324008
$449$	23.7116	1.11902	0.559511	−	0.828823i	$-0.310989\pi$
$449$	23.7116	1.11902	0.559511	+	0.828823i	$0.310989\pi$
$450$	41.2847	1.94618
$451$	15.1105	0.711526
$452$	52.3093	2.46042
$453$	4.43140	0.208205
$454$	−27.3125	−1.28184
$455$	−1.66141	−0.0778880
$456$	−136.452	−6.38996
$457$	18.3282	0.857357	0.428678	−	0.903457i	$-0.358979\pi$
$457$	18.3282	0.857357	0.428678	+	0.903457i	$0.358979\pi$
$458$	63.3483	2.96007
$459$	3.87811	0.181015
$460$	8.18907	0.381818
$461$	−36.6549	−1.70719	−0.853595	−	0.520938i	$-0.825582\pi$
$461$	−36.6549	−1.70719	−0.853595	+	0.520938i	$0.825582\pi$
$462$	17.8357	0.829794
$463$	32.5430	1.51240	0.756202	−	0.654339i	$-0.227053\pi$
$463$	32.5430	1.51240	0.756202	+	0.654339i	$0.227053\pi$
$464$	−19.0571	−0.884704
$465$	5.71976	0.265247
$466$	65.0610	3.01389
$467$	3.23763	0.149820	0.0749098	−	0.997190i	$-0.476133\pi$
$467$	3.23763	0.149820	0.0749098	+	0.997190i	$0.476133\pi$
$468$	58.1256	2.68686
$469$	10.8492	0.500970
$470$	−5.14154	−0.237162
$471$	−10.8715	−0.500934
$472$	−89.8650	−4.13637
$473$	12.8647	0.591521
$474$	−1.10514	−0.0507608
$475$	36.3925	1.66980
$476$	26.9989	1.23749
$477$	−34.1762	−1.56482
$478$	−1.58936	−0.0726955
$479$	29.1690	1.33277	0.666383	−	0.745610i	$-0.267842\pi$
$479$	29.1690	1.33277	0.666383	+	0.745610i	$0.267842\pi$
$480$	10.1204	0.461931
$481$	−32.3495	−1.47501
$482$	2.08723	0.0950708
$483$	10.8487	0.493633
$484$	−20.9561	−0.952552
$485$	−3.60942	−0.163895
$486$	−58.1836	−2.63926
$487$	−5.90908	−0.267766	−0.133883	−	0.990997i	$-0.542745\pi$
$487$	−5.90908	−0.267766	−0.133883	+	0.990997i	$0.542745\pi$
$488$	72.8896	3.29956
$489$	10.1829	0.460488
$490$	6.44452	0.291134
$491$	3.33601	0.150552	0.0752759	−	0.997163i	$-0.476016\pi$
$491$	3.33601	0.150552	0.0752759	+	0.997163i	$0.476016\pi$
$492$	70.3351	3.17095
$493$	11.0071	0.495736
$494$	72.7195	3.27180
$495$	−3.56901	−0.160415
$496$	−49.8066	−2.23638
$497$	6.55107	0.293856
$498$	27.7269	1.24247
$499$	3.78987	0.169658	0.0848289	−	0.996396i	$-0.472966\pi$
$499$	3.78987	0.169658	0.0848289	+	0.996396i	$0.472966\pi$
$500$	−19.7713	−0.884199
$501$	−54.2015	−2.42154
$502$	10.7730	0.480822
$503$	20.3327	0.906589	0.453295	−	0.891361i	$-0.350249\pi$
$503$	20.3327	0.906589	0.453295	+	0.891361i	$0.350249\pi$
$504$	25.2201	1.12339
$505$	3.82773	0.170332
$506$	27.2087	1.20957
$507$	−1.78627	−0.0793312
$508$	−64.9098	−2.87991
$509$	32.4268	1.43729	0.718647	−	0.695375i	$-0.244762\pi$
$509$	32.4268	1.43729	0.718647	+	0.695375i	$0.244762\pi$
$510$	−14.6584	−0.649083
$511$	−12.5136	−0.553568
$512$	44.7391	1.97721
$513$	5.49866	0.242772
$514$	34.4429	1.51921
$515$	−0.441334	−0.0194475
$516$	59.8816	2.63614
$517$	−12.0367	−0.529372
$518$	−24.1691	−1.06193
$519$	40.8126	1.79147
$520$	−11.2638	−0.493951
$521$	−33.7507	−1.47865	−0.739323	−	0.673351i	$-0.764855\pi$
$521$	−33.7507	−1.47865	−0.739323	+	0.673351i	$0.764855\pi$
$522$	17.7047	0.774913
$523$	−0.964432	−0.0421717	−0.0210858	−	0.999778i	$-0.506712\pi$
$523$	−0.964432	−0.0421717	−0.0210858	+	0.999778i	$0.506712\pi$
$524$	11.6127	0.507305
$525$	−12.8589	−0.561207
$526$	59.6908	2.60264
$527$	28.7676	1.25314
$528$	59.4129	2.58562
$529$	−6.45015	−0.280441
$530$	11.4039	0.495355
$531$	41.0206	1.78014
$532$	38.2810	1.65969
$533$	−21.7685	−0.942900
$534$	−31.6914	−1.37142
$535$	4.21889	0.182399
$536$	73.5542	3.17706
$537$	12.1903	0.526052
$538$	0.729484	0.0314503
$539$	15.0870	0.649844
$540$	−1.46658	−0.0631114
$541$	24.4964	1.05318	0.526591	−	0.850119i	$-0.323470\pi$
$541$	24.4964	1.05318	0.526591	+	0.850119i	$0.323470\pi$
$542$	83.6874	3.59468
$543$	2.89382	0.124186
$544$	50.9008	2.18236
$545$	−1.20608	−0.0516629
$546$	−25.6946	−1.09963
$547$	44.4606	1.90100	0.950500	−	0.310725i	$-0.100572\pi$
$547$	44.4606	1.90100	0.950500	+	0.310725i	$0.100572\pi$
$548$	20.7175	0.885008
$549$	−33.2719	−1.42001
$550$	−32.2502	−1.37515
$551$	15.6067	0.664869
$552$	73.5507	3.13053
$553$	0.180056	0.00765676
$554$	−35.8691	−1.52393
$555$	9.24570	0.392458
$556$	51.9825	2.20455
$557$	13.4324	0.569151	0.284575	−	0.958654i	$-0.408147\pi$
$557$	13.4324	0.569151	0.284575	+	0.958654i	$0.408147\pi$
$558$	46.2720	1.95885
$559$	−18.5332	−0.783872
$560$	−4.13483	−0.174729
$561$	−34.3161	−1.44883
$562$	42.2500	1.78221
$563$	−6.80148	−0.286648	−0.143324	−	0.989676i	$-0.545779\pi$
$563$	−6.80148	−0.286648	−0.143324	+	0.989676i	$0.545779\pi$
$564$	−56.0272	−2.35917
$565$	4.62710	0.194664
$566$	21.3113	0.895781
$567$	8.55302	0.359193
$568$	44.4142	1.86358
$569$	38.6875	1.62187	0.810933	−	0.585139i	$-0.198960\pi$
$569$	38.6875	1.62187	0.810933	+	0.585139i	$0.198960\pi$
$570$	−20.7837	−0.870533
$571$	15.5090	0.649030	0.324515	−	0.945881i	$-0.394799\pi$
$571$	15.5090	0.649030	0.324515	+	0.945881i	$0.394799\pi$
$572$	−45.4058	−1.89851
$573$	48.8987	2.04277
$574$	−16.2638	−0.678837
$575$	−19.6164	−0.818059
$576$	21.2235	0.884311
$577$	16.8797	0.702711	0.351356	−	0.936242i	$-0.385721\pi$
$577$	16.8797	0.702711	0.351356	+	0.936242i	$0.385721\pi$
$578$	−29.4906	−1.22665
$579$	32.7801	1.36230
$580$	−4.16255	−0.172840
$581$	−4.51743	−0.187415
$582$	−55.8216	−2.31388
$583$	26.6973	1.10569
$584$	−84.8380	−3.51062
$585$	5.14159	0.212579
$586$	−21.7726	−0.899418
$587$	−1.92631	−0.0795073	−0.0397537	−	0.999210i	$-0.512657\pi$
$587$	−1.92631	−0.0795073	−0.0397537	+	0.999210i	$0.512657\pi$
$588$	70.2257	2.89606
$589$	40.7889	1.68068
$590$	−13.6878	−0.563517
$591$	−7.72187	−0.317635
$592$	−80.5099	−3.30894
$593$	38.1126	1.56510	0.782549	−	0.622589i	$-0.213919\pi$
$593$	38.1126	1.56510	0.782549	+	0.622589i	$0.213919\pi$
$594$	−4.87279	−0.199933
$595$	2.38822	0.0979077
$596$	−90.1040	−3.69080
$597$	−23.5818	−0.965140
$598$	−39.1974	−1.60290
$599$	22.1264	0.904061	0.452030	−	0.892002i	$-0.350700\pi$
$599$	22.1264	0.904061	0.452030	+	0.892002i	$0.350700\pi$
$600$	−87.1790	−3.55907
$601$	21.1754	0.863761	0.431881	−	0.901931i	$-0.357850\pi$
$601$	21.1754	0.863761	0.431881	+	0.901931i	$0.357850\pi$
$602$	−13.8466	−0.564345
$603$	−33.5753	−1.36729
$604$	−8.42855	−0.342953
$605$	−1.85371	−0.0753639
$606$	59.1979	2.40475
$607$	−25.5581	−1.03737	−0.518685	−	0.854965i	$-0.673578\pi$
$607$	−25.5581	−1.03737	−0.518685	+	0.854965i	$0.673578\pi$
$608$	72.1709	2.92692
$609$	−5.51445	−0.223457
$610$	11.1022	0.449514
$611$	17.3403	0.701513
$612$	−83.5539	−3.37747
$613$	24.8431	1.00340	0.501701	−	0.865041i	$-0.332708\pi$
$613$	24.8431	1.00340	0.501701	+	0.865041i	$0.332708\pi$
$614$	−24.6519	−0.994868
$615$	6.22159	0.250879
$616$	−19.7011	−0.793779
$617$	7.68846	0.309526	0.154763	−	0.987952i	$-0.450539\pi$
$617$	7.68846	0.309526	0.154763	+	0.987952i	$0.450539\pi$
$618$	−6.82547	−0.274561
$619$	8.41073	0.338056	0.169028	−	0.985611i	$-0.445937\pi$
$619$	8.41073	0.338056	0.169028	+	0.985611i	$0.445937\pi$
$620$	−10.8790	−0.436912
$621$	−2.96390	−0.118937
$622$	12.8187	0.513983
$623$	5.16334	0.206865
$624$	−85.5916	−3.42641
$625$	22.3608	0.894432
$626$	−35.6327	−1.42417
$627$	−48.6559	−1.94313
$628$	20.6777	0.825132
$629$	46.5015	1.85413
$630$	3.84140	0.153045
$631$	10.2435	0.407787	0.203893	−	0.978993i	$-0.434640\pi$
$631$	10.2435	0.407787	0.203893	+	0.978993i	$0.434640\pi$
$632$	1.22072	0.0485577
$633$	33.1140	1.31616
$634$	−43.4562	−1.72586
$635$	−5.74169	−0.227852
$636$	124.268	4.92755
$637$	−21.7347	−0.861160
$638$	−13.8303	−0.547547
$639$	−20.2737	−0.802016
$640$	0.988381	0.0390692
$641$	48.7454	1.92533	0.962665	−	0.270697i	$-0.0872541\pi$
$641$	48.7454	1.92533	0.962665	+	0.270697i	$0.0872541\pi$
$642$	65.2475	2.57511
$643$	−28.6616	−1.13030	−0.565151	−	0.824988i	$-0.691182\pi$
$643$	−28.6616	−1.13030	−0.565151	+	0.824988i	$0.691182\pi$
$644$	−20.6343	−0.813105
$645$	5.29692	0.208566
$646$	−104.532	−4.11276
$647$	−5.39033	−0.211916	−0.105958	−	0.994371i	$-0.533791\pi$
$647$	−5.39033	−0.211916	−0.105958	+	0.994371i	$0.533791\pi$
$648$	57.9867	2.27793
$649$	−32.0439	−1.25783
$650$	46.4603	1.82232
$651$	−14.4123	−0.564862
$652$	−19.3680	−0.758510
$653$	−38.6182	−1.51125	−0.755623	−	0.655007i	$-0.772666\pi$
$653$	−38.6182	−1.51125	−0.755623	+	0.655007i	$0.772666\pi$
$654$	−18.6527	−0.729380
$655$	1.02722	0.0401369
$656$	−54.1765	−2.11524
$657$	38.7260	1.51084
$658$	12.9553	0.505051
$659$	−18.5992	−0.724522	−0.362261	−	0.932077i	$-0.617995\pi$
$659$	−18.5992	−0.724522	−0.362261	+	0.932077i	$0.617995\pi$
$660$	12.9773	0.505140
$661$	−47.1983	−1.83580	−0.917901	−	0.396809i	$-0.870117\pi$
$661$	−47.1983	−1.83580	−0.917901	+	0.396809i	$0.870117\pi$
$662$	−6.40698	−0.249014
$663$	49.4366	1.91996
$664$	−30.6268	−1.18855
$665$	3.38620	0.131311
$666$	74.7964	2.89830
$667$	−8.41237	−0.325728
$668$	103.092	3.98873
$669$	−20.8932	−0.807777
$670$	11.2034	0.432825
$671$	25.9909	1.00337
$672$	−25.5008	−0.983713
$673$	34.1681	1.31708	0.658542	−	0.752544i	$-0.271174\pi$
$673$	34.1681	1.31708	0.658542	+	0.752544i	$0.271174\pi$
$674$	−1.49048	−0.0574111
$675$	3.51309	0.135219
$676$	3.39750	0.130673
$677$	15.0137	0.577023	0.288511	−	0.957476i	$-0.406840\pi$
$677$	15.0137	0.577023	0.288511	+	0.957476i	$0.406840\pi$
$678$	71.5606	2.74827
$679$	9.09478	0.349026
$680$	16.1914	0.620912
$681$	−26.3267	−1.00884
$682$	−36.1461	−1.38411
$683$	16.0899	0.615663	0.307831	−	0.951441i	$-0.400397\pi$
$683$	16.0899	0.615663	0.307831	+	0.951441i	$0.400397\pi$
$684$	−118.469	−4.52977
$685$	1.83260	0.0700200
$686$	−35.6046	−1.35939
$687$	61.0619	2.32966
$688$	−46.1246	−1.75848
$689$	−38.4607	−1.46524
$690$	11.2029	0.426486
$691$	8.37173	0.318476	0.159238	−	0.987240i	$-0.449096\pi$
$691$	8.37173	0.318476	0.159238	+	0.987240i	$0.449096\pi$
$692$	−77.6258	−2.95089
$693$	8.99295	0.341614
$694$	−2.11646	−0.0803395
$695$	4.59819	0.174419
$696$	−37.3862	−1.41712
$697$	31.2916	1.18526
$698$	−50.9338	−1.92787
$699$	62.7127	2.37201
$700$	24.4576	0.924412
$701$	51.2471	1.93557	0.967787	−	0.251769i	$-0.0810122\pi$
$701$	51.2471	1.93557	0.967787	+	0.251769i	$0.0810122\pi$
$702$	7.01985	0.264947
$703$	65.9332	2.48672
$704$	−16.5790	−0.624846
$705$	−4.95597	−0.186653
$706$	75.3055	2.83416
$707$	−9.64486	−0.362732
$708$	−149.155	−5.60560
$709$	−41.5781	−1.56150	−0.780749	−	0.624845i	$-0.785162\pi$
$709$	−41.5781	−1.56150	−0.780749	+	0.624845i	$0.785162\pi$
$710$	6.76495	0.253884
$711$	−0.557223	−0.0208975
$712$	35.0058	1.31190
$713$	−21.9861	−0.823387
$714$	36.9352	1.38226
$715$	−4.01644	−0.150206
$716$	−23.1861	−0.866505
$717$	−1.53199	−0.0572133
$718$	74.2738	2.77187
$719$	−19.1472	−0.714070	−0.357035	−	0.934091i	$-0.616212\pi$
$719$	−19.1472	−0.714070	−0.357035	+	0.934091i	$0.616212\pi$
$720$	12.7961	0.476884
$721$	1.11205	0.0414147
$722$	−98.7753	−3.67604
$723$	2.01190	0.0748233
$724$	−5.50406	−0.204557
$725$	9.97111	0.370318
$726$	−28.6686	−1.06399
$727$	−40.1138	−1.48774	−0.743869	−	0.668326i	$-0.767011\pi$
$727$	−40.1138	−1.48774	−0.743869	+	0.668326i	$0.767011\pi$
$728$	28.3818	1.05190
$729$	−31.9511	−1.18337
$730$	−12.9221	−0.478268
$731$	26.6410	0.985352
$732$	120.980	4.47155
$733$	−40.5800	−1.49886	−0.749429	−	0.662085i	$-0.769672\pi$
$733$	−40.5800	−1.49886	−0.749429	+	0.662085i	$0.769672\pi$
$734$	−69.7679	−2.57518
$735$	6.21192	0.229130
$736$	−38.9018	−1.43394
$737$	26.2279	0.966116
$738$	50.3318	1.85274
$739$	−11.1808	−0.411293	−0.205647	−	0.978626i	$-0.565930\pi$
$739$	−11.1808	−0.411293	−0.205647	+	0.978626i	$0.565930\pi$
$740$	−17.5854	−0.646451
$741$	70.0948	2.57500
$742$	−28.7349	−1.05489
$743$	46.1368	1.69260	0.846298	−	0.532711i	$-0.178827\pi$
$743$	46.1368	1.69260	0.846298	+	0.532711i	$0.178827\pi$
$744$	−97.7106	−3.58224
$745$	−7.97028	−0.292009
$746$	65.2246	2.38804
$747$	13.9802	0.511508
$748$	65.2695	2.38649
$749$	−10.6305	−0.388430
$750$	−27.0477	−0.987642
$751$	36.1428	1.31887	0.659434	−	0.751762i	$-0.270796\pi$
$751$	36.1428	1.31887	0.659434	+	0.751762i	$0.270796\pi$
$752$	43.1557	1.57373
$753$	10.3842	0.378420
$754$	19.9243	0.725599
$755$	−0.745560	−0.0271337
$756$	3.69539	0.134400
$757$	−10.0781	−0.366294	−0.183147	−	0.983086i	$-0.558628\pi$
$757$	−10.0781	−0.366294	−0.183147	+	0.983086i	$0.558628\pi$
$758$	2.31485	0.0840793
$759$	26.2266	0.951966
$760$	22.9574	0.832751
$761$	4.37255	0.158505	0.0792523	−	0.996855i	$-0.474747\pi$
$761$	4.37255	0.158505	0.0792523	+	0.996855i	$0.474747\pi$
$762$	−88.7984	−3.21683
$763$	3.03901	0.110020
$764$	−93.0057	−3.36483
$765$	−7.39088	−0.267218
$766$	79.0436	2.85596
$767$	46.1632	1.66686
$768$	47.6399	1.71906
$769$	24.0729	0.868091	0.434045	−	0.900891i	$-0.357086\pi$
$769$	24.0729	0.868091	0.434045	+	0.900891i	$0.357086\pi$
$770$	−3.00077	−0.108140
$771$	33.1998	1.19566
$772$	−62.3480	−2.24395
$773$	−16.2792	−0.585523	−0.292761	−	0.956186i	$-0.594574\pi$
$773$	−16.2792	−0.585523	−0.292761	+	0.956186i	$0.594574\pi$
$774$	42.8513	1.54026
$775$	26.0599	0.936101
$776$	61.6597	2.21346
$777$	−23.2967	−0.835765
$778$	49.1909	1.76358
$779$	44.3676	1.58963
$780$	−18.6953	−0.669401
$781$	15.8372	0.566698
$782$	56.3451	2.01490
$783$	1.50657	0.0538403
$784$	−54.0923	−1.93187
$785$	1.82908	0.0652827
$786$	15.8866	0.566655
$787$	−8.51539	−0.303541	−0.151770	−	0.988416i	$-0.548497\pi$
$787$	−8.51539	−0.303541	−0.151770	+	0.988416i	$0.548497\pi$
$788$	14.6870	0.523204
$789$	57.5363	2.04835
$790$	0.185934	0.00661524
$791$	−11.6591	−0.414549
$792$	60.9693	2.16645
$793$	−37.4430	−1.32964
$794$	59.9590	2.12786
$795$	10.9923	0.389858
$796$	44.8528	1.58976
$797$	−13.1161	−0.464596	−0.232298	−	0.972645i	$-0.574624\pi$
$797$	−13.1161	−0.464596	−0.232298	+	0.972645i	$0.574624\pi$
$798$	52.3694	1.85386
$799$	−24.9262	−0.881824
$800$	46.1099	1.63023
$801$	−15.9791	−0.564594
$802$	84.5670	2.98617
$803$	−30.2514	−1.06755
$804$	122.083	4.30554
$805$	−1.82524	−0.0643312
$806$	52.0730	1.83419
$807$	0.703155	0.0247522
$808$	−65.3891	−2.30038
$809$	−53.5738	−1.88356	−0.941778	−	0.336236i	$-0.890846\pi$
$809$	−53.5738	−1.88356	−0.941778	+	0.336236i	$0.890846\pi$
$810$	8.83225	0.310334
$811$	−41.1700	−1.44567	−0.722837	−	0.691019i	$-0.757162\pi$
$811$	−41.1700	−1.44567	−0.722837	+	0.691019i	$0.757162\pi$
$812$	10.4885	0.368075
$813$	80.6669	2.82911
$814$	−58.4284	−2.04792
$815$	−1.71323	−0.0600117
$816$	123.035	4.30710
$817$	37.7735	1.32153
$818$	20.9793	0.733523
$819$	−12.9554	−0.452700
$820$	−11.8335	−0.413244
$821$	23.5848	0.823116	0.411558	−	0.911384i	$-0.364985\pi$
$821$	23.5848	0.823116	0.411558	+	0.911384i	$0.364985\pi$
$822$	28.3421	0.988545
$823$	19.0603	0.664400	0.332200	−	0.943209i	$-0.392209\pi$
$823$	19.0603	0.664400	0.332200	+	0.943209i	$0.392209\pi$
$824$	7.53931	0.262644
$825$	−31.0862	−1.08228
$826$	34.4896	1.20005
$827$	−4.98841	−0.173464	−0.0867320	−	0.996232i	$-0.527642\pi$
$827$	−4.98841	−0.173464	−0.0867320	+	0.996232i	$0.527642\pi$
$828$	63.8574	2.21920
$829$	−1.17639	−0.0408578	−0.0204289	−	0.999791i	$-0.506503\pi$
$829$	−1.17639	−0.0408578	−0.0204289	+	0.999791i	$0.506503\pi$
$830$	−4.66491	−0.161922
$831$	−34.5745	−1.19938
$832$	23.8842	0.828034
$833$	31.2430	1.08250
$834$	71.1135	2.46246
$835$	9.11912	0.315580
$836$	92.5439	3.20070
$837$	3.93748	0.136099
$838$	−24.7070	−0.853489
$839$	−15.9012	−0.548972	−0.274486	−	0.961591i	$-0.588508\pi$
$839$	−15.9012	−0.548972	−0.274486	+	0.961591i	$0.588508\pi$
$840$	−8.11171	−0.279881
$841$	−24.7239	−0.852550
$842$	−20.1057	−0.692890
$843$	40.7251	1.40265
$844$	−62.9831	−2.16797
$845$	0.300531	0.0103386
$846$	−40.0931	−1.37843
$847$	4.67085	0.160492
$848$	−95.7192	−3.28701
$849$	20.5421	0.705004
$850$	−66.7854	−2.29072
$851$	−35.5395	−1.21828
$852$	73.7174	2.52552
$853$	16.5186	0.565587	0.282793	−	0.959181i	$-0.408739\pi$
$853$	16.5186	0.565587	0.282793	+	0.959181i	$0.408739\pi$
$854$	−27.9746	−0.957269
$855$	−10.4793	−0.358386
$856$	−72.0714	−2.46335
$857$	−20.9190	−0.714580	−0.357290	−	0.933994i	$-0.616299\pi$
$857$	−20.9190	−0.714580	−0.357290	+	0.933994i	$0.616299\pi$
$858$	−62.1164	−2.12062
$859$	19.8204	0.676264	0.338132	−	0.941099i	$-0.390205\pi$
$859$	19.8204	0.676264	0.338132	+	0.941099i	$0.390205\pi$
$860$	−10.0748	−0.343547
$861$	−15.6768	−0.534263
$862$	−63.0552	−2.14767
$863$	15.3542	0.522662	0.261331	−	0.965249i	$-0.415839\pi$
$863$	15.3542	0.522662	0.261331	+	0.965249i	$0.415839\pi$
$864$	6.96690	0.237019
$865$	−6.86651	−0.233468
$866$	46.8423	1.59176
$867$	−28.4262	−0.965404
$868$	27.4122	0.930432
$869$	0.435283	0.0147660
$870$	−5.69448	−0.193061
$871$	−37.7844	−1.28028
$872$	20.6035	0.697723
$873$	−28.1458	−0.952591
$874$	79.8903	2.70233
$875$	4.40676	0.148976
$876$	−140.812	−4.75759
$877$	−0.156434	−0.00528242	−0.00264121	−	0.999997i	$-0.500841\pi$
$877$	−0.156434	−0.00528242	−0.00264121	+	0.999997i	$0.500841\pi$
$878$	88.5090	2.98703
$879$	−20.9868	−0.707866
$880$	−9.99592	−0.336962
$881$	−13.3979	−0.451388	−0.225694	−	0.974198i	$-0.572465\pi$
$881$	−13.3979	−0.451388	−0.225694	+	0.974198i	$0.572465\pi$
$882$	50.2535	1.69212
$883$	−11.0318	−0.371250	−0.185625	−	0.982621i	$-0.559431\pi$
$883$	−11.0318	−0.371250	−0.185625	+	0.982621i	$0.559431\pi$
$884$	−94.0287	−3.16253
$885$	−13.1938	−0.443503
$886$	−8.63414	−0.290070
$887$	−36.8627	−1.23773	−0.618864	−	0.785498i	$-0.712407\pi$
$887$	−36.8627	−1.23773	−0.618864	+	0.785498i	$0.712407\pi$
$888$	−157.944	−5.30027
$889$	14.4675	0.485226
$890$	5.33191	0.178726
$891$	20.6768	0.692700
$892$	39.7390	1.33056
$893$	−35.3421	−1.18268
$894$	−123.265	−4.12259
$895$	−2.05096	−0.0685561
$896$	−2.49046	−0.0832004
$897$	−37.7827	−1.26153
$898$	−61.6976	−2.05888
$899$	11.1757	0.372729
$900$	−75.6895	−2.52298
$901$	55.2861	1.84185
$902$	−39.3175	−1.30913
$903$	−13.3468	−0.444155
$904$	−79.0448	−2.62899
$905$	−0.486870	−0.0161841
$906$	−11.5305	−0.383075
$907$	−21.4514	−0.712283	−0.356141	−	0.934432i	$-0.615908\pi$
$907$	−21.4514	−0.712283	−0.356141	+	0.934432i	$0.615908\pi$
$908$	50.0735	1.66175
$909$	29.8481	0.990000
$910$	4.32298	0.143305
$911$	−21.3522	−0.707430	−0.353715	−	0.935353i	$-0.615082\pi$
$911$	−21.3522	−0.707430	−0.353715	+	0.935353i	$0.615082\pi$
$912$	174.449	5.77657
$913$	−10.9208	−0.361427
$914$	−47.6899	−1.57744
$915$	10.7015	0.353780
$916$	−116.140	−3.83738
$917$	−2.58833	−0.0854742
$918$	−10.0908	−0.333047
$919$	26.7724	0.883140	0.441570	−	0.897227i	$-0.354422\pi$
$919$	26.7724	0.883140	0.441570	+	0.897227i	$0.354422\pi$
$920$	−12.3745	−0.407976
$921$	−23.7621	−0.782988
$922$	95.3760	3.14104
$923$	−22.8154	−0.750977
$924$	−32.6993	−1.07573
$925$	42.1246	1.38505
$926$	−84.6769	−2.78266
$927$	−3.44147	−0.113033
$928$	19.7740	0.649112
$929$	−10.9798	−0.360236	−0.180118	−	0.983645i	$-0.557648\pi$
$929$	−10.9798	−0.360236	−0.180118	+	0.983645i	$0.557648\pi$
$930$	−14.8828	−0.488026
$931$	44.2986	1.45183
$932$	−119.280	−3.90715
$933$	12.3560	0.404518
$934$	−8.42430	−0.275652
$935$	5.77351	0.188814
$936$	−87.8338	−2.87094
$937$	49.0691	1.60302	0.801509	−	0.597983i	$-0.204031\pi$
$937$	49.0691	1.60302	0.801509	+	0.597983i	$0.204031\pi$
$938$	−28.2296	−0.921730
$939$	−34.3466	−1.12086
$940$	9.42628	0.307451
$941$	−16.4162	−0.535153	−0.267576	−	0.963537i	$-0.586223\pi$
$941$	−16.4162	−0.535153	−0.267576	+	0.963537i	$0.586223\pi$
$942$	28.2877	0.921664
$943$	−23.9151	−0.778784
$944$	114.889	3.73931
$945$	0.326881	0.0106334
$946$	−33.4740	−1.08833
$947$	37.3421	1.21345	0.606727	−	0.794910i	$-0.292482\pi$
$947$	37.3421	1.21345	0.606727	+	0.794910i	$0.292482\pi$
$948$	2.02612	0.0658053
$949$	43.5809	1.41470
$950$	−94.6932	−3.07225
$951$	−41.8877	−1.35830
$952$	−40.7981	−1.32227
$953$	22.6614	0.734074	0.367037	−	0.930206i	$-0.380372\pi$
$953$	22.6614	0.734074	0.367037	+	0.930206i	$0.380372\pi$
$954$	88.9264	2.87910
$955$	−8.22696	−0.266218
$956$	2.91386	0.0942410
$957$	−13.3311	−0.430934
$958$	−75.8977	−2.45214
$959$	−4.61766	−0.149112
$960$	−6.82625	−0.220316
$961$	−1.79190	−0.0578033
$962$	84.1733	2.71386
$963$	32.8984	1.06014
$964$	−3.82664	−0.123248
$965$	−5.51509	−0.177537
$966$	−28.2283	−0.908231
$967$	−43.1014	−1.38605	−0.693024	−	0.720914i	$-0.743722\pi$
$967$	−43.1014	−1.38605	−0.693024	+	0.720914i	$0.743722\pi$
$968$	31.6669	1.01781
$969$	−100.759	−3.23685
$970$	9.39170	0.301549
$971$	−56.4626	−1.81197	−0.905986	−	0.423308i	$-0.860869\pi$
$971$	−56.4626	−1.81197	−0.905986	+	0.423308i	$0.860869\pi$
$972$	106.671	3.42148
$973$	−11.5862	−0.371437
$974$	15.3754	0.492660
$975$	44.7834	1.43422
$976$	−93.1865	−2.98283
$977$	−43.3163	−1.38581	−0.692906	−	0.721028i	$-0.743670\pi$
$977$	−43.3163	−1.38581	−0.692906	+	0.721028i	$0.743670\pi$
$978$	−26.4960	−0.847248
$979$	12.4823	0.398937
$980$	−11.8151	−0.377420
$981$	−9.40489	−0.300275
$982$	−8.68028	−0.276999
$983$	−51.5548	−1.64434	−0.822171	−	0.569241i	$-0.807237\pi$
$983$	−51.5548	−1.64434	−0.822171	+	0.569241i	$0.807237\pi$
$984$	−106.283	−3.38819
$985$	1.29916	0.0413948
$986$	−28.6405	−0.912100
$987$	12.4877	0.397489
$988$	−133.321	−4.24150
$989$	−20.3608	−0.647435
$990$	9.28654	0.295146
$991$	−29.5822	−0.939709	−0.469855	−	0.882744i	$-0.655694\pi$
$991$	−29.5822	−0.939709	−0.469855	+	0.882744i	$0.655694\pi$
$992$	51.6802	1.64085
$993$	−6.17573	−0.195981
$994$	−17.0459	−0.540662
$995$	3.96752	0.125779
$996$	−50.8334	−1.61072
$997$	−27.1639	−0.860289	−0.430144	−	0.902760i	$-0.641537\pi$
$997$	−27.1639	−0.860289	−0.430144	+	0.902760i	$0.641537\pi$
$998$	−9.86123	−0.312152
$999$	6.36475	0.201372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.7	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.60200 q^{2} -2.50808 q^{3} +4.77039 q^{4} +0.421972 q^{5} +6.52603 q^{6} -1.06326 q^{7} -7.20855 q^{8} +3.29049 q^{9} +O(q^{10})\)	\(q-2.60200 q^{2} -2.50808 q^{3} +4.77039 q^{4} +0.421972 q^{5} +6.52603 q^{6} -1.06326 q^{7} -7.20855 q^{8} +3.29049 q^{9} -1.09797 q^{10} -2.57042 q^{11} -11.9645 q^{12} +3.70300 q^{13} +2.76660 q^{14} -1.05834 q^{15} +9.21585 q^{16} -5.32295 q^{17} -8.56184 q^{18} -7.54727 q^{19} +2.01297 q^{20} +2.66674 q^{21} +6.68822 q^{22} +4.06815 q^{23} +18.0797 q^{24} -4.82194 q^{25} -9.63520 q^{26} -0.728563 q^{27} -5.07216 q^{28} -2.06786 q^{29} +2.75380 q^{30} -5.40445 q^{31} -9.56252 q^{32} +6.44682 q^{33} +13.8503 q^{34} -0.448665 q^{35} +15.6969 q^{36} -8.73603 q^{37} +19.6380 q^{38} -9.28743 q^{39} -3.04181 q^{40} -5.87862 q^{41} -6.93885 q^{42} -5.00492 q^{43} -12.2619 q^{44} +1.38849 q^{45} -10.5853 q^{46} +4.68277 q^{47} -23.1141 q^{48} -5.86948 q^{49} +12.5467 q^{50} +13.3504 q^{51} +17.6648 q^{52} -10.3864 q^{53} +1.89572 q^{54} -1.08464 q^{55} +7.66455 q^{56} +18.9292 q^{57} +5.38057 q^{58} +12.4664 q^{59} -5.04870 q^{60} -10.1115 q^{61} +14.0624 q^{62} -3.49864 q^{63} +6.44995 q^{64} +1.56256 q^{65} -16.7746 q^{66} -10.2037 q^{67} -25.3926 q^{68} -10.2033 q^{69} +1.16743 q^{70} -6.16132 q^{71} -23.7196 q^{72} +11.7691 q^{73} +22.7311 q^{74} +12.0938 q^{75} -36.0035 q^{76} +2.73302 q^{77} +24.1659 q^{78} -0.169344 q^{79} +3.88883 q^{80} -8.04416 q^{81} +15.2962 q^{82} +4.24867 q^{83} +12.7214 q^{84} -2.24614 q^{85} +13.0228 q^{86} +5.18637 q^{87} +18.5290 q^{88} -4.85615 q^{89} -3.61286 q^{90} -3.93724 q^{91} +19.4067 q^{92} +13.5548 q^{93} -12.1846 q^{94} -3.18474 q^{95} +23.9836 q^{96} -8.55369 q^{97} +15.2724 q^{98} -8.45792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 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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