LMFDB - Embedded newform 4013.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43054 q^{2} +3.05350 q^{3} +3.90754 q^{4} -3.60333 q^{5} -7.42166 q^{6} -4.38981 q^{7} -4.63635 q^{8} +6.32386 q^{9} +O(q^{10})$	\(q-2.43054 q^{2} +3.05350 q^{3} +3.90754 q^{4} -3.60333 q^{5} -7.42166 q^{6} -4.38981 q^{7} -4.63635 q^{8} +6.32386 q^{9} +8.75804 q^{10} -5.21796 q^{11} +11.9317 q^{12} +6.11691 q^{13} +10.6696 q^{14} -11.0028 q^{15} +3.45377 q^{16} -4.72373 q^{17} -15.3704 q^{18} +6.16848 q^{19} -14.0801 q^{20} -13.4043 q^{21} +12.6825 q^{22} -3.32672 q^{23} -14.1571 q^{24} +7.98396 q^{25} -14.8674 q^{26} +10.1494 q^{27} -17.1534 q^{28} -8.94966 q^{29} +26.7427 q^{30} -7.12998 q^{31} +0.878162 q^{32} -15.9330 q^{33} +11.4812 q^{34} +15.8179 q^{35} +24.7107 q^{36} -4.39436 q^{37} -14.9927 q^{38} +18.6780 q^{39} +16.7063 q^{40} +0.767924 q^{41} +32.5797 q^{42} +7.55171 q^{43} -20.3894 q^{44} -22.7869 q^{45} +8.08573 q^{46} -6.57599 q^{47} +10.5461 q^{48} +12.2705 q^{49} -19.4054 q^{50} -14.4239 q^{51} +23.9020 q^{52} +11.1367 q^{53} -24.6686 q^{54} +18.8020 q^{55} +20.3527 q^{56} +18.8354 q^{57} +21.7525 q^{58} +6.34111 q^{59} -42.9937 q^{60} -0.451493 q^{61} +17.3297 q^{62} -27.7606 q^{63} -9.04195 q^{64} -22.0412 q^{65} +38.7259 q^{66} -3.02569 q^{67} -18.4582 q^{68} -10.1581 q^{69} -38.4461 q^{70} +2.67080 q^{71} -29.3196 q^{72} -9.29932 q^{73} +10.6807 q^{74} +24.3790 q^{75} +24.1036 q^{76} +22.9058 q^{77} -45.3976 q^{78} -2.53748 q^{79} -12.4451 q^{80} +12.0196 q^{81} -1.86647 q^{82} -7.38597 q^{83} -52.3778 q^{84} +17.0212 q^{85} -18.3548 q^{86} -27.3278 q^{87} +24.1923 q^{88} +8.01497 q^{89} +55.3846 q^{90} -26.8521 q^{91} -12.9993 q^{92} -21.7714 q^{93} +15.9832 q^{94} -22.2270 q^{95} +2.68147 q^{96} -2.59110 q^{97} -29.8239 q^{98} -32.9976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.43054	−1.71865	−0.859327	−	0.511427i	$-0.829117\pi$
$2$	−2.43054	−1.71865	−0.859327	+	0.511427i	$0.829117\pi$
$3$	3.05350	1.76294	0.881470	−	0.472241i	$-0.156555\pi$
$3$	3.05350	1.76294	0.881470	+	0.472241i	$0.156555\pi$
$4$	3.90754	1.95377
$5$	−3.60333	−1.61146	−0.805728	−	0.592285i	$-0.798226\pi$
$5$	−3.60333	−1.61146	−0.805728	+	0.592285i	$0.798226\pi$
$6$	−7.42166	−3.02988
$7$	−4.38981	−1.65919	−0.829597	−	0.558363i	$-0.811430\pi$
$7$	−4.38981	−1.65919	−0.829597	+	0.558363i	$0.811430\pi$
$8$	−4.63635	−1.63920
$9$	6.32386	2.10795
$10$	8.75804	2.76954
$11$	−5.21796	−1.57327	−0.786636	−	0.617417i	$-0.788179\pi$
$11$	−5.21796	−1.57327	−0.786636	+	0.617417i	$0.788179\pi$
$12$	11.9317	3.44437
$13$	6.11691	1.69652	0.848262	−	0.529576i	$-0.177649\pi$
$13$	6.11691	1.69652	0.848262	+	0.529576i	$0.177649\pi$
$14$	10.6696	2.85158
$15$	−11.0028	−2.84090
$16$	3.45377	0.863443
$17$	−4.72373	−1.14567	−0.572837	−	0.819669i	$-0.694157\pi$
$17$	−4.72373	−1.14567	−0.572837	+	0.819669i	$0.694157\pi$
$18$	−15.3704	−3.62284
$19$	6.16848	1.41515	0.707573	−	0.706640i	$-0.249790\pi$
$19$	6.16848	1.41515	0.707573	+	0.706640i	$0.249790\pi$
$20$	−14.0801	−3.14841
$21$	−13.4043	−2.92506
$22$	12.6825	2.70391
$23$	−3.32672	−0.693669	−0.346835	−	0.937926i	$-0.612743\pi$
$23$	−3.32672	−0.693669	−0.346835	+	0.937926i	$0.612743\pi$
$24$	−14.1571	−2.88980
$25$	7.98396	1.59679
$26$	−14.8674	−2.91574
$27$	10.1494	1.95326
$28$	−17.1534	−3.24168
$29$	−8.94966	−1.66191	−0.830955	−	0.556340i	$-0.812205\pi$
$29$	−8.94966	−1.66191	−0.830955	+	0.556340i	$0.812205\pi$
$30$	26.7427	4.88252
$31$	−7.12998	−1.28058	−0.640291	−	0.768132i	$-0.721186\pi$
$31$	−7.12998	−1.28058	−0.640291	+	0.768132i	$0.721186\pi$
$32$	0.878162	0.155239
$33$	−15.9330	−2.77358
$34$	11.4812	1.96902
$35$	15.8179	2.67372
$36$	24.7107	4.11845
$37$	−4.39436	−0.722428	−0.361214	−	0.932483i	$-0.617638\pi$
$37$	−4.39436	−0.722428	−0.361214	+	0.932483i	$0.617638\pi$
$38$	−14.9927	−2.43214
$39$	18.6780	2.99087
$40$	16.7063	2.64150
$41$	0.767924	0.119930	0.0599648	−	0.998200i	$-0.480901\pi$
$41$	0.767924	0.119930	0.0599648	+	0.998200i	$0.480901\pi$
$42$	32.5797	5.02716
$43$	7.55171	1.15163	0.575813	−	0.817582i	$-0.304686\pi$
$43$	7.55171	1.15163	0.575813	+	0.817582i	$0.304686\pi$
$44$	−20.3894	−3.07381
$45$	−22.7869	−3.39688
$46$	8.08573	1.19218
$47$	−6.57599	−0.959207	−0.479604	−	0.877485i	$-0.659220\pi$
$47$	−6.57599	−0.959207	−0.479604	+	0.877485i	$0.659220\pi$
$48$	10.5461	1.52220
$49$	12.2705	1.75292
$50$	−19.4054	−2.74433
$51$	−14.4239	−2.01975
$52$	23.9020	3.31462
$53$	11.1367	1.52974	0.764872	−	0.644182i	$-0.222802\pi$
$53$	11.1367	1.52974	0.764872	+	0.644182i	$0.222802\pi$
$54$	−24.6686	−3.35697
$55$	18.8020	2.53526
$56$	20.3527	2.71974
$57$	18.8354	2.49482
$58$	21.7525	2.85625
$59$	6.34111	0.825542	0.412771	−	0.910835i	$-0.364561\pi$
$59$	6.34111	0.825542	0.412771	+	0.910835i	$0.364561\pi$
$60$	−42.9937	−5.55046
$61$	−0.451493	−0.0578078	−0.0289039	−	0.999582i	$-0.509202\pi$
$61$	−0.451493	−0.0578078	−0.0289039	+	0.999582i	$0.509202\pi$
$62$	17.3297	2.20088
$63$	−27.7606	−3.49750
$64$	−9.04195	−1.13024
$65$	−22.0412	−2.73388
$66$	38.7259	4.76683
$67$	−3.02569	−0.369647	−0.184824	−	0.982772i	$-0.559171\pi$
$67$	−3.02569	−0.369647	−0.184824	+	0.982772i	$0.559171\pi$
$68$	−18.4582	−2.23838
$69$	−10.1581	−1.22290
$70$	−38.4461	−4.59519
$71$	2.67080	0.316966	0.158483	−	0.987362i	$-0.449340\pi$
$71$	2.67080	0.316966	0.158483	+	0.987362i	$0.449340\pi$
$72$	−29.3196	−3.45535
$73$	−9.29932	−1.08840	−0.544201	−	0.838955i	$-0.683167\pi$
$73$	−9.29932	−1.08840	−0.544201	+	0.838955i	$0.683167\pi$
$74$	10.6807	1.24160
$75$	24.3790	2.81505
$76$	24.1036	2.76487
$77$	22.9058	2.61036
$78$	−45.3976	−5.14027
$79$	−2.53748	−0.285489	−0.142744	−	0.989760i	$-0.545593\pi$
$79$	−2.53748	−0.285489	−0.142744	+	0.989760i	$0.545593\pi$
$80$	−12.4451	−1.39140
$81$	12.0196	1.33552
$82$	−1.86647	−0.206117
$83$	−7.38597	−0.810715	−0.405357	−	0.914158i	$-0.632853\pi$
$83$	−7.38597	−0.810715	−0.405357	+	0.914158i	$0.632853\pi$
$84$	−52.3778	−5.71488
$85$	17.0212	1.84620
$86$	−18.3548	−1.97925
$87$	−27.3278	−2.92984
$88$	24.1923	2.57890
$89$	8.01497	0.849585	0.424792	−	0.905291i	$-0.360347\pi$
$89$	8.01497	0.849585	0.424792	+	0.905291i	$0.360347\pi$
$90$	55.3846	5.83805
$91$	−26.8521	−2.81486
$92$	−12.9993	−1.35527
$93$	−21.7714	−2.25759
$94$	15.9832	1.64854
$95$	−22.2270	−2.28045
$96$	2.68147	0.273676
$97$	−2.59110	−0.263087	−0.131543	−	0.991310i	$-0.541993\pi$
$97$	−2.59110	−0.263087	−0.131543	+	0.991310i	$0.541993\pi$
$98$	−29.8239	−3.01266
$99$	−32.9976	−3.31639
$100$	31.1976	3.11976
$101$	2.59743	0.258454	0.129227	−	0.991615i	$-0.458750\pi$
$101$	2.59743	0.258454	0.129227	+	0.991615i	$0.458750\pi$
$102$	35.0579	3.47125
$103$	9.04055	0.890792	0.445396	−	0.895334i	$-0.353063\pi$
$103$	9.04055	0.890792	0.445396	+	0.895334i	$0.353063\pi$
$104$	−28.3601	−2.78094
$105$	48.3000	4.71360
$106$	−27.0682	−2.62910
$107$	4.22353	0.408304	0.204152	−	0.978939i	$-0.434556\pi$
$107$	4.22353	0.408304	0.204152	+	0.978939i	$0.434556\pi$
$108$	39.6592	3.81621
$109$	−3.37688	−0.323447	−0.161723	−	0.986836i	$-0.551705\pi$
$109$	−3.37688	−0.323447	−0.161723	+	0.986836i	$0.551705\pi$
$110$	−45.6991	−4.35723
$111$	−13.4182	−1.27360
$112$	−15.1614	−1.43262
$113$	6.95475	0.654248	0.327124	−	0.944981i	$-0.393920\pi$
$113$	6.95475	0.654248	0.327124	+	0.944981i	$0.393920\pi$
$114$	−45.7804	−4.28772
$115$	11.9873	1.11782
$116$	−34.9711	−3.24699
$117$	38.6825	3.57620
$118$	−15.4123	−1.41882
$119$	20.7363	1.90089
$120$	51.0126	4.65680
$121$	16.2271	1.47519
$122$	1.09737	0.0993515
$123$	2.34486	0.211429
$124$	−27.8607	−2.50196
$125$	−10.7522	−0.961706
$126$	67.4732	6.01099
$127$	−6.76963	−0.600707	−0.300354	−	0.953828i	$-0.597105\pi$
$127$	−6.76963	−0.600707	−0.300354	+	0.953828i	$0.597105\pi$
$128$	20.2205	1.78726
$129$	23.0592	2.03025
$130$	53.5721	4.69859
$131$	16.2878	1.42307	0.711536	−	0.702650i	$-0.248000\pi$
$131$	16.2878	1.42307	0.711536	+	0.702650i	$0.248000\pi$
$132$	−62.2589	−5.41894
$133$	−27.0785	−2.34800
$134$	7.35407	0.635295
$135$	−36.5717	−3.14759
$136$	21.9009	1.87798
$137$	16.7109	1.42771	0.713856	−	0.700293i	$-0.246947\pi$
$137$	16.7109	1.42771	0.713856	+	0.700293i	$0.246947\pi$
$138$	24.6898	2.10173
$139$	11.4452	0.970773	0.485386	−	0.874300i	$-0.338679\pi$
$139$	11.4452	0.970773	0.485386	+	0.874300i	$0.338679\pi$
$140$	61.8091	5.22383
$141$	−20.0798	−1.69102
$142$	−6.49150	−0.544755
$143$	−31.9178	−2.66910
$144$	21.8412	1.82010
$145$	32.2485	2.67810
$146$	22.6024	1.87059
$147$	37.4678	3.09029
$148$	−17.1711	−1.41146
$149$	10.6958	0.876236	0.438118	−	0.898917i	$-0.355645\pi$
$149$	10.6958	0.876236	0.438118	+	0.898917i	$0.355645\pi$
$150$	−59.2543	−4.83809
$151$	4.43686	0.361067	0.180533	−	0.983569i	$-0.442218\pi$
$151$	4.43686	0.361067	0.180533	+	0.983569i	$0.442218\pi$
$152$	−28.5992	−2.31970
$153$	−29.8722	−2.41503
$154$	−55.6736	−4.48631
$155$	25.6917	2.06360
$156$	72.9849	5.84347
$157$	−14.4748	−1.15522	−0.577609	−	0.816314i	$-0.696014\pi$
$157$	−14.4748	−1.15522	−0.577609	+	0.816314i	$0.696014\pi$
$158$	6.16745	0.490656
$159$	34.0059	2.69685
$160$	−3.16431	−0.250160
$161$	14.6037	1.15093
$162$	−29.2143	−2.29529
$163$	−5.31927	−0.416637	−0.208319	−	0.978061i	$-0.566799\pi$
$163$	−5.31927	−0.416637	−0.208319	+	0.978061i	$0.566799\pi$
$164$	3.00069	0.234315
$165$	57.4119	4.46951
$166$	17.9519	1.39334
$167$	18.2204	1.40994	0.704969	−	0.709238i	$-0.250961\pi$
$167$	18.2204	1.40994	0.704969	+	0.709238i	$0.250961\pi$
$168$	62.1470	4.79474
$169$	24.4166	1.87820
$170$	−41.3706	−3.17298
$171$	39.0086	2.98306
$172$	29.5086	2.25001
$173$	7.90904	0.601314	0.300657	−	0.953732i	$-0.402794\pi$
$173$	7.90904	0.601314	0.300657	+	0.953732i	$0.402794\pi$
$174$	66.4213	5.03539
$175$	−35.0481	−2.64939
$176$	−18.0216	−1.35843
$177$	19.3626	1.45538
$178$	−19.4807	−1.46014
$179$	−16.6376	−1.24356	−0.621778	−	0.783194i	$-0.713589\pi$
$179$	−16.6376	−1.24356	−0.621778	+	0.783194i	$0.713589\pi$
$180$	−89.0408	−6.63671
$181$	4.49669	0.334236	0.167118	−	0.985937i	$-0.446554\pi$
$181$	4.49669	0.334236	0.167118	+	0.985937i	$0.446554\pi$
$182$	65.2651	4.83777
$183$	−1.37863	−0.101912
$184$	15.4238	1.13706
$185$	15.8343	1.16416
$186$	52.9163	3.88001
$187$	24.6482	1.80246
$188$	−25.6959	−1.87407
$189$	−44.5540	−3.24083
$190$	54.0238	3.91930
$191$	14.3222	1.03632	0.518159	−	0.855284i	$-0.326617\pi$
$191$	14.3222	1.03632	0.518159	+	0.855284i	$0.326617\pi$
$192$	−27.6096	−1.99255
$193$	−2.65543	−0.191142	−0.0955710	−	0.995423i	$-0.530468\pi$
$193$	−2.65543	−0.191142	−0.0955710	+	0.995423i	$0.530468\pi$
$194$	6.29779	0.452155
$195$	−67.3029	−4.81966
$196$	47.9472	3.42480
$197$	2.85745	0.203585	0.101792	−	0.994806i	$-0.467542\pi$
$197$	2.85745	0.203585	0.101792	+	0.994806i	$0.467542\pi$
$198$	80.2021	5.69972
$199$	−20.0287	−1.41980	−0.709898	−	0.704305i	$-0.751259\pi$
$199$	−20.0287	−1.41980	−0.709898	+	0.704305i	$0.751259\pi$
$200$	−37.0165	−2.61746
$201$	−9.23895	−0.651665
$202$	−6.31316	−0.444193
$203$	39.2873	2.75743
$204$	−56.3620	−3.94613
$205$	−2.76708	−0.193261
$206$	−21.9734	−1.53096
$207$	−21.0377	−1.46222
$208$	21.1264	1.46485
$209$	−32.1868	−2.22641
$210$	−117.395	−8.10105
$211$	22.2194	1.52965	0.764823	−	0.644240i	$-0.222826\pi$
$211$	22.2194	1.52965	0.764823	+	0.644240i	$0.222826\pi$
$212$	43.5171	2.98877
$213$	8.15530	0.558792
$214$	−10.2655	−0.701733
$215$	−27.2113	−1.85580
$216$	−47.0562	−3.20177
$217$	31.2993	2.12473
$218$	8.20766	0.555893
$219$	−28.3955	−1.91879
$220$	73.4695	4.95331
$221$	−28.8946	−1.94366
$222$	32.6134	2.18887
$223$	25.8181	1.72891	0.864454	−	0.502711i	$-0.167664\pi$
$223$	25.8181	1.72891	0.864454	+	0.502711i	$0.167664\pi$
$224$	−3.85497	−0.257571
$225$	50.4895	3.36597
$226$	−16.9038	−1.12443
$227$	23.7558	1.57673	0.788364	−	0.615209i	$-0.210928\pi$
$227$	23.7558	1.57673	0.788364	+	0.615209i	$0.210928\pi$
$228$	73.6002	4.87429
$229$	−20.0499	−1.32494	−0.662469	−	0.749090i	$-0.730491\pi$
$229$	−20.0499	−1.32494	−0.662469	+	0.749090i	$0.730491\pi$
$230$	−29.1355	−1.92114
$231$	69.9430	4.60191
$232$	41.4937	2.72420
$233$	15.9261	1.04336	0.521678	−	0.853143i	$-0.325306\pi$
$233$	15.9261	1.04336	0.521678	+	0.853143i	$0.325306\pi$
$234$	−94.0194	−6.14624
$235$	23.6955	1.54572
$236$	24.7781	1.61292
$237$	−7.74819	−0.503299
$238$	−50.4005	−3.26698
$239$	6.85242	0.443246	0.221623	−	0.975132i	$-0.428865\pi$
$239$	6.85242	0.443246	0.221623	+	0.975132i	$0.428865\pi$
$240$	−38.0010	−2.45295
$241$	−3.48151	−0.224264	−0.112132	−	0.993693i	$-0.535768\pi$
$241$	−3.48151	−0.224264	−0.112132	+	0.993693i	$0.535768\pi$
$242$	−39.4406	−2.53533
$243$	6.25376	0.401179
$244$	−1.76423	−0.112943
$245$	−44.2145	−2.82476
$246$	−5.69927	−0.363372
$247$	37.7320	2.40083
$248$	33.0571	2.09913
$249$	−22.5530	−1.42924
$250$	26.1337	1.65284
$251$	−27.5610	−1.73963	−0.869816	−	0.493376i	$-0.835763\pi$
$251$	−27.5610	−1.73963	−0.869816	+	0.493376i	$0.835763\pi$
$252$	−108.475	−6.83331
$253$	17.3587	1.09133
$254$	16.4539	1.03241
$255$	51.9741	3.25474
$256$	−31.0629	−1.94143
$257$	−12.1629	−0.758698	−0.379349	−	0.925254i	$-0.623852\pi$
$257$	−12.1629	−0.758698	−0.379349	+	0.925254i	$0.623852\pi$
$258$	−56.0463	−3.48929
$259$	19.2904	1.19865
$260$	−86.1269	−5.34136
$261$	−56.5964	−3.50323
$262$	−39.5882	−2.44577
$263$	−6.97665	−0.430199	−0.215099	−	0.976592i	$-0.569008\pi$
$263$	−6.97665	−0.430199	−0.215099	+	0.976592i	$0.569008\pi$
$264$	73.8711	4.54645
$265$	−40.1292	−2.46512
$266$	65.8153	4.03540
$267$	24.4737	1.49777
$268$	−11.8230	−0.722205
$269$	25.5991	1.56080	0.780402	−	0.625278i	$-0.215014\pi$
$269$	25.5991	1.56080	0.780402	+	0.625278i	$0.215014\pi$
$270$	88.8890	5.40961
$271$	18.4328	1.11971	0.559856	−	0.828590i	$-0.310856\pi$
$271$	18.4328	1.11971	0.559856	+	0.828590i	$0.310856\pi$
$272$	−16.3147	−0.989223
$273$	−81.9928	−4.96243
$274$	−40.6166	−2.45374
$275$	−41.6600	−2.51219
$276$	−39.6933	−2.38926
$277$	−18.6470	−1.12039	−0.560196	−	0.828360i	$-0.689274\pi$
$277$	−18.6470	−1.12039	−0.560196	+	0.828360i	$0.689274\pi$
$278$	−27.8182	−1.66842
$279$	−45.0890	−2.69941
$280$	−73.3374	−4.38275
$281$	−25.2239	−1.50473	−0.752367	−	0.658744i	$-0.771088\pi$
$281$	−25.2239	−1.50473	−0.752367	+	0.658744i	$0.771088\pi$
$282$	48.8048	2.90628
$283$	2.37033	0.140901	0.0704507	−	0.997515i	$-0.477556\pi$
$283$	2.37033	0.140901	0.0704507	+	0.997515i	$0.477556\pi$
$284$	10.4363	0.619278
$285$	−67.8703	−4.02029
$286$	77.5775	4.58725
$287$	−3.37104	−0.198986
$288$	5.55338	0.327236
$289$	5.31365	0.312568
$290$	−78.3814	−4.60272
$291$	−7.91194	−0.463806
$292$	−36.3374	−2.12649
$293$	6.03233	0.352412	0.176206	−	0.984353i	$-0.443617\pi$
$293$	6.03233	0.352412	0.176206	+	0.984353i	$0.443617\pi$
$294$	−91.0671	−5.31114
$295$	−22.8491	−1.33033
$296$	20.3738	1.18420
$297$	−52.9592	−3.07300
$298$	−25.9967	−1.50595
$299$	−20.3492	−1.17683
$300$	95.2620	5.49995
$301$	−33.1506	−1.91077
$302$	−10.7840	−0.620548
$303$	7.93125	0.455639
$304$	21.3045	1.22190
$305$	1.62688	0.0931547
$306$	72.6057	4.15059
$307$	25.4172	1.45063	0.725317	−	0.688415i	$-0.241693\pi$
$307$	25.4172	1.45063	0.725317	+	0.688415i	$0.241693\pi$
$308$	89.5054	5.10005
$309$	27.6053	1.57041
$310$	−62.4447	−3.54662
$311$	19.6538	1.11447	0.557233	−	0.830356i	$-0.311863\pi$
$311$	19.6538	1.11447	0.557233	+	0.830356i	$0.311863\pi$
$312$	−86.5976	−4.90263
$313$	15.7452	0.889969	0.444984	−	0.895538i	$-0.353209\pi$
$313$	15.7452	0.889969	0.444984	+	0.895538i	$0.353209\pi$
$314$	35.1817	1.98542
$315$	100.030	5.63608
$316$	−9.91529	−0.557779
$317$	17.8797	1.00422	0.502112	−	0.864803i	$-0.332556\pi$
$317$	17.8797	1.00422	0.502112	+	0.864803i	$0.332556\pi$
$318$	−82.6529	−4.63494
$319$	46.6989	2.61464
$320$	32.5811	1.82134
$321$	12.8966	0.719816
$322$	−35.4949	−1.97805
$323$	−29.1382	−1.62130
$324$	46.9672	2.60929
$325$	48.8372	2.70900
$326$	12.9287	0.716055
$327$	−10.3113	−0.570217
$328$	−3.56036	−0.196588
$329$	28.8674	1.59151
$330$	−139.542	−7.68154
$331$	33.2686	1.82861	0.914304	−	0.405028i	$-0.132738\pi$
$331$	33.2686	1.82861	0.914304	+	0.405028i	$0.132738\pi$
$332$	−28.8609	−1.58395
$333$	−27.7893	−1.52285
$334$	−44.2855	−2.42320
$335$	10.9026	0.595670
$336$	−46.2954	−2.52562
$337$	−13.4475	−0.732531	−0.366266	−	0.930510i	$-0.619364\pi$
$337$	−13.4475	−0.732531	−0.366266	+	0.930510i	$0.619364\pi$
$338$	−59.3455	−3.22797
$339$	21.2363	1.15340
$340$	66.5108	3.60705
$341$	37.2039	2.01471
$342$	−94.8121	−5.12685
$343$	−23.1363	−1.24924
$344$	−35.0124	−1.88774
$345$	36.6031	1.97064
$346$	−19.2233	−1.03345
$347$	−1.76466	−0.0947317	−0.0473658	−	0.998878i	$-0.515083\pi$
$347$	−1.76466	−0.0947317	−0.0473658	+	0.998878i	$0.515083\pi$
$348$	−106.784	−5.72424
$349$	−9.72749	−0.520701	−0.260350	−	0.965514i	$-0.583838\pi$
$349$	−9.72749	−0.520701	−0.260350	+	0.965514i	$0.583838\pi$
$350$	85.1859	4.55338
$351$	62.0830	3.31375
$352$	−4.58221	−0.244233
$353$	8.73423	0.464876	0.232438	−	0.972611i	$-0.425330\pi$
$353$	8.73423	0.464876	0.232438	+	0.972611i	$0.425330\pi$
$354$	−47.0616	−2.50129
$355$	−9.62378	−0.510777
$356$	31.3188	1.65989
$357$	63.3183	3.35116
$358$	40.4385	2.13724
$359$	24.4685	1.29140	0.645699	−	0.763592i	$-0.276566\pi$
$359$	24.4685	1.29140	0.645699	+	0.763592i	$0.276566\pi$
$360$	105.648	5.56815
$361$	19.0501	1.00264
$362$	−10.9294	−0.574436
$363$	49.5493	2.60067
$364$	−104.925	−5.49959
$365$	33.5085	1.75391
$366$	3.35083	0.175151
$367$	−11.0243	−0.575461	−0.287731	−	0.957711i	$-0.592901\pi$
$367$	−11.0243	−0.575461	−0.287731	+	0.957711i	$0.592901\pi$
$368$	−11.4897	−0.598944
$369$	4.85625	0.252806
$370$	−38.4860	−2.00079
$371$	−48.8881	−2.53814
$372$	−85.0725	−4.41081
$373$	8.84812	0.458138	0.229069	−	0.973410i	$-0.426432\pi$
$373$	8.84812	0.458138	0.229069	+	0.973410i	$0.426432\pi$
$374$	−59.9086	−3.09780
$375$	−32.8318	−1.69543
$376$	30.4886	1.57233
$377$	−54.7442	−2.81947
$378$	108.290	5.56986
$379$	−11.9817	−0.615456	−0.307728	−	0.951474i	$-0.599569\pi$
$379$	−11.9817	−0.615456	−0.307728	+	0.951474i	$0.599569\pi$
$380$	−86.8530	−4.45546
$381$	−20.6711	−1.05901
$382$	−34.8107	−1.78107
$383$	8.91941	0.455761	0.227880	−	0.973689i	$-0.426820\pi$
$383$	8.91941	0.455761	0.227880	+	0.973689i	$0.426820\pi$
$384$	61.7434	3.15083
$385$	−82.5372	−4.20649
$386$	6.45413	0.328507
$387$	47.7560	2.42757
$388$	−10.1248	−0.514011
$389$	−21.0029	−1.06489	−0.532444	−	0.846465i	$-0.678726\pi$
$389$	−21.0029	−1.06489	−0.532444	+	0.846465i	$0.678726\pi$
$390$	163.582	8.28332
$391$	15.7145	0.794718
$392$	−56.8901	−2.87338
$393$	49.7348	2.50879
$394$	−6.94515	−0.349891
$395$	9.14337	0.460053
$396$	−128.939	−6.47945
$397$	7.93316	0.398154	0.199077	−	0.979984i	$-0.436206\pi$
$397$	7.93316	0.398154	0.199077	+	0.979984i	$0.436206\pi$
$398$	48.6806	2.44014
$399$	−82.6841	−4.13938
$400$	27.5748	1.37874
$401$	8.58034	0.428482	0.214241	−	0.976781i	$-0.431272\pi$
$401$	8.58034	0.428482	0.214241	+	0.976781i	$0.431272\pi$
$402$	22.4557	1.11999
$403$	−43.6134	−2.17254
$404$	10.1496	0.504959
$405$	−43.3107	−2.15213
$406$	−95.4895	−4.73906
$407$	22.9296	1.13658
$408$	66.8743	3.31077
$409$	−15.4987	−0.766359	−0.383180	−	0.923674i	$-0.625171\pi$
$409$	−15.4987	−0.766359	−0.383180	+	0.923674i	$0.625171\pi$
$410$	6.72551	0.332149
$411$	51.0269	2.51697
$412$	35.3263	1.74040
$413$	−27.8363	−1.36973
$414$	51.1331	2.51305
$415$	26.6140	1.30643
$416$	5.37164	0.263366
$417$	34.9481	1.71141
$418$	78.2315	3.82643
$419$	−12.9913	−0.634667	−0.317333	−	0.948314i	$-0.602787\pi$
$419$	−12.9913	−0.634667	−0.317333	+	0.948314i	$0.602787\pi$
$420$	188.734	9.20929
$421$	−35.4719	−1.72879	−0.864396	−	0.502811i	$-0.832299\pi$
$421$	−35.4719	−1.72879	−0.864396	+	0.502811i	$0.832299\pi$
$422$	−54.0052	−2.62893
$423$	−41.5857	−2.02196
$424$	−51.6337	−2.50755
$425$	−37.7141	−1.82940
$426$	−19.8218	−0.960370
$427$	1.98197	0.0959143
$428$	16.5036	0.797732
$429$	−97.4609	−4.70545
$430$	66.1382	3.18947
$431$	9.18056	0.442212	0.221106	−	0.975250i	$-0.429033\pi$
$431$	9.18056	0.442212	0.221106	+	0.975250i	$0.429033\pi$
$432$	35.0538	1.68652
$433$	−2.37393	−0.114084	−0.0570420	−	0.998372i	$-0.518167\pi$
$433$	−2.37393	−0.114084	−0.0570420	+	0.998372i	$0.518167\pi$
$434$	−76.0742	−3.65168
$435$	98.4709	4.72132
$436$	−13.1953	−0.631940
$437$	−20.5208	−0.981643
$438$	69.0164	3.29773
$439$	−4.55511	−0.217404	−0.108702	−	0.994074i	$-0.534669\pi$
$439$	−4.55511	−0.217404	−0.108702	+	0.994074i	$0.534669\pi$
$440$	−87.1726	−4.15579
$441$	77.5967	3.69508
$442$	70.2296	3.34048
$443$	−7.83071	−0.372048	−0.186024	−	0.982545i	$-0.559560\pi$
$443$	−7.83071	−0.372048	−0.186024	+	0.982545i	$0.559560\pi$
$444$	−52.4320	−2.48831
$445$	−28.8805	−1.36907
$446$	−62.7520	−2.97139
$447$	32.6597	1.54475
$448$	39.6925	1.87529
$449$	25.6881	1.21230	0.606149	−	0.795351i	$-0.292714\pi$
$449$	25.6881	1.21230	0.606149	+	0.795351i	$0.292714\pi$
$450$	−122.717	−5.78493
$451$	−4.00699	−0.188682
$452$	27.1760	1.27825
$453$	13.5480	0.636538
$454$	−57.7395	−2.70985
$455$	96.7568	4.53603
$456$	−87.3277	−4.08949
$457$	8.80508	0.411884	0.205942	−	0.978564i	$-0.433974\pi$
$457$	8.80508	0.411884	0.205942	+	0.978564i	$0.433974\pi$
$458$	48.7322	2.27711
$459$	−47.9431	−2.23779
$460$	46.8407	2.18396
$461$	12.4247	0.578674	0.289337	−	0.957227i	$-0.406565\pi$
$461$	12.4247	0.578674	0.289337	+	0.957227i	$0.406565\pi$
$462$	−169.999	−7.90909
$463$	5.71488	0.265593	0.132797	−	0.991143i	$-0.457604\pi$
$463$	5.71488	0.265593	0.132797	+	0.991143i	$0.457604\pi$
$464$	−30.9101	−1.43496
$465$	78.4495	3.63801
$466$	−38.7091	−1.79317
$467$	−35.3140	−1.63414	−0.817069	−	0.576540i	$-0.804403\pi$
$467$	−35.3140	−1.63414	−0.817069	+	0.576540i	$0.804403\pi$
$468$	151.153	6.98706
$469$	13.2822	0.613316
$470$	−57.5928	−2.65656
$471$	−44.1989	−2.03658
$472$	−29.3996	−1.35323
$473$	−39.4045	−1.81182
$474$	18.8323	0.864997
$475$	49.2489	2.25969
$476$	81.0279	3.71391
$477$	70.4270	3.22463
$478$	−16.6551	−0.761787
$479$	26.1264	1.19375	0.596874	−	0.802335i	$-0.296409\pi$
$479$	26.1264	1.19375	0.596874	+	0.802335i	$0.296409\pi$
$480$	−9.66221	−0.441017
$481$	−26.8799	−1.22562
$482$	8.46196	0.385432
$483$	44.5923	2.02902
$484$	63.4078	2.88217
$485$	9.33660	0.423953
$486$	−15.2000	−0.689487
$487$	3.25878	0.147670	0.0738348	−	0.997270i	$-0.476476\pi$
$487$	3.25878	0.147670	0.0738348	+	0.997270i	$0.476476\pi$
$488$	2.09328	0.0947584
$489$	−16.2424	−0.734506
$490$	107.465	4.85478
$491$	−17.6282	−0.795550	−0.397775	−	0.917483i	$-0.630218\pi$
$491$	−17.6282	−0.795550	−0.397775	+	0.917483i	$0.630218\pi$
$492$	9.16261	0.413083
$493$	42.2758	1.90401
$494$	−91.7093	−4.12619
$495$	118.901	5.34421
$496$	−24.6253	−1.10571
$497$	−11.7243	−0.525908
$498$	54.8161	2.45637
$499$	−24.7331	−1.10720	−0.553602	−	0.832781i	$-0.686747\pi$
$499$	−24.7331	−1.10720	−0.553602	+	0.832781i	$0.686747\pi$
$500$	−42.0146	−1.87895
$501$	55.6361	2.48564
$502$	66.9881	2.98983
$503$	29.8129	1.32929	0.664645	−	0.747159i	$-0.268583\pi$
$503$	29.8129	1.32929	0.664645	+	0.747159i	$0.268583\pi$
$504$	128.708	5.73310
$505$	−9.35939	−0.416487
$506$	−42.1910	−1.87562
$507$	74.5560	3.31115
$508$	−26.4526	−1.17364
$509$	14.6401	0.648909	0.324454	−	0.945901i	$-0.394819\pi$
$509$	14.6401	0.648909	0.324454	+	0.945901i	$0.394819\pi$
$510$	−126.325	−5.59378
$511$	40.8223	1.80587
$512$	35.0587	1.54939
$513$	62.6064	2.76414
$514$	29.5623	1.30394
$515$	−32.5761	−1.43547
$516$	90.1045	3.96663
$517$	34.3132	1.50909
$518$	−46.8862	−2.06006
$519$	24.1503	1.06008
$520$	102.191	4.48136
$521$	−28.7508	−1.25959	−0.629797	−	0.776760i	$-0.716862\pi$
$521$	−28.7508	−1.25959	−0.629797	+	0.776760i	$0.716862\pi$
$522$	137.560	6.02083
$523$	13.4026	0.586054	0.293027	−	0.956104i	$-0.405337\pi$
$523$	13.4026	0.586054	0.293027	+	0.956104i	$0.405337\pi$
$524$	63.6452	2.78035
$525$	−107.019	−4.67071
$526$	16.9570	0.739362
$527$	33.6801	1.46713
$528$	−55.0290	−2.39483
$529$	−11.9329	−0.518823
$530$	97.5357	4.23668
$531$	40.1003	1.74021
$532$	−105.810	−4.58745
$533$	4.69732	0.203464
$534$	−59.4844	−2.57414
$535$	−15.2188	−0.657965
$536$	14.0282	0.605924
$537$	−50.8030	−2.19231
$538$	−62.2197	−2.68248
$539$	−64.0267	−2.75782
$540$	−142.905	−6.14966
$541$	−22.4239	−0.964077	−0.482039	−	0.876150i	$-0.660104\pi$
$541$	−22.4239	−0.964077	−0.482039	+	0.876150i	$0.660104\pi$
$542$	−44.8017	−1.92440
$543$	13.7306	0.589238
$544$	−4.14820	−0.177853
$545$	12.1680	0.521220
$546$	199.287	8.52870
$547$	34.4422	1.47264	0.736321	−	0.676633i	$-0.236561\pi$
$547$	34.4422	1.47264	0.736321	+	0.676633i	$0.236561\pi$
$548$	65.2986	2.78942
$549$	−2.85518	−0.121856
$550$	101.256	4.31758
$551$	−55.2058	−2.35184
$552$	47.0967	2.00457
$553$	11.1391	0.473681
$554$	45.3224	1.92556
$555$	48.3501	2.05235
$556$	44.7227	1.89667
$557$	−26.1547	−1.10821	−0.554104	−	0.832447i	$-0.686939\pi$
$557$	−26.1547	−1.10821	−0.554104	+	0.832447i	$0.686939\pi$
$558$	109.591	4.63935
$559$	46.1931	1.95376
$560$	54.6315	2.30860
$561$	75.2634	3.17762
$562$	61.3079	2.58612
$563$	1.78628	0.0752828	0.0376414	−	0.999291i	$-0.488016\pi$
$563$	1.78628	0.0752828	0.0376414	+	0.999291i	$0.488016\pi$
$564$	−78.4625	−3.30387
$565$	−25.0603	−1.05429
$566$	−5.76119	−0.242161
$567$	−52.7640	−2.21588
$568$	−12.3828	−0.519570
$569$	1.19423	0.0500648	0.0250324	−	0.999687i	$-0.492031\pi$
$569$	1.19423	0.0500648	0.0250324	+	0.999687i	$0.492031\pi$
$570$	164.962	6.90948
$571$	18.1429	0.759257	0.379628	−	0.925139i	$-0.376052\pi$
$571$	18.1429	0.759257	0.379628	+	0.925139i	$0.376052\pi$
$572$	−124.720	−5.21480
$573$	43.7329	1.82697
$574$	8.19346	0.341989
$575$	−26.5604	−1.10765
$576$	−57.1801	−2.38250
$577$	35.0910	1.46086	0.730429	−	0.682989i	$-0.239320\pi$
$577$	35.0910	1.46086	0.730429	+	0.682989i	$0.239320\pi$
$578$	−12.9151	−0.537195
$579$	−8.10835	−0.336972
$580$	126.012	5.23238
$581$	32.4230	1.34513
$582$	19.2303	0.797122
$583$	−58.1109	−2.40671
$584$	43.1149	1.78411
$585$	−139.386	−5.76289
$586$	−14.6618	−0.605675
$587$	17.7395	0.732189	0.366095	−	0.930578i	$-0.380695\pi$
$587$	17.7395	0.732189	0.366095	+	0.930578i	$0.380695\pi$
$588$	146.407	6.03772
$589$	−43.9811	−1.81221
$590$	55.5357	2.28637
$591$	8.72521	0.358907
$592$	−15.1771	−0.623775
$593$	−23.8691	−0.980188	−0.490094	−	0.871670i	$-0.663038\pi$
$593$	−23.8691	−0.980188	−0.490094	+	0.871670i	$0.663038\pi$
$594$	128.720	5.28143
$595$	−74.7197	−3.06321
$596$	41.7943	1.71196
$597$	−61.1576	−2.50301
$598$	49.4597	2.02256
$599$	−34.1939	−1.39713	−0.698563	−	0.715549i	$-0.746177\pi$
$599$	−34.1939	−1.39713	−0.698563	+	0.715549i	$0.746177\pi$
$600$	−113.030	−4.61442
$601$	25.0591	1.02218	0.511091	−	0.859527i	$-0.329242\pi$
$601$	25.0591	1.02218	0.511091	+	0.859527i	$0.329242\pi$
$602$	80.5740	3.28395
$603$	−19.1341	−0.779199
$604$	17.3372	0.705441
$605$	−58.4714	−2.37720
$606$	−19.2772	−0.783085
$607$	13.6189	0.552772	0.276386	−	0.961047i	$-0.410863\pi$
$607$	13.6189	0.552772	0.276386	+	0.961047i	$0.410863\pi$
$608$	5.41693	0.219685
$609$	119.964	4.86118
$610$	−3.95420	−0.160101
$611$	−40.2247	−1.62732
$612$	−116.727	−4.71840
$613$	−4.76830	−0.192590	−0.0962949	−	0.995353i	$-0.530699\pi$
$613$	−4.76830	−0.192590	−0.0962949	+	0.995353i	$0.530699\pi$
$614$	−61.7775	−2.49314
$615$	−8.44928	−0.340708
$616$	−106.200	−4.27890
$617$	3.22759	0.129938	0.0649690	−	0.997887i	$-0.479305\pi$
$617$	3.22759	0.129938	0.0649690	+	0.997887i	$0.479305\pi$
$618$	−67.0959	−2.69899
$619$	−40.5064	−1.62809	−0.814044	−	0.580803i	$-0.802739\pi$
$619$	−40.5064	−1.62809	−0.814044	+	0.580803i	$0.802739\pi$
$620$	100.391	4.03180
$621$	−33.7643	−1.35491
$622$	−47.7694	−1.91538
$623$	−35.1842	−1.40963
$624$	64.5095	2.58244
$625$	−1.17613	−0.0470452
$626$	−38.2693	−1.52955
$627$	−98.2825	−3.92503
$628$	−56.5610	−2.25703
$629$	20.7578	0.827667
$630$	−243.128	−9.68646
$631$	−38.6113	−1.53709	−0.768546	−	0.639794i	$-0.779020\pi$
$631$	−38.6113	−1.53709	−0.768546	+	0.639794i	$0.779020\pi$
$632$	11.7646	0.467972
$633$	67.8469	2.69667
$634$	−43.4574	−1.72591
$635$	24.3932	0.968014
$636$	132.879	5.26901
$637$	75.0572	2.97388
$638$	−113.504	−4.49365
$639$	16.8898	0.668150
$640$	−72.8612	−2.88009
$641$	−26.8877	−1.06200	−0.531000	−	0.847372i	$-0.678183\pi$
$641$	−26.8877	−1.06200	−0.531000	+	0.847372i	$0.678183\pi$
$642$	−31.3456	−1.23711
$643$	−2.28068	−0.0899414	−0.0449707	−	0.998988i	$-0.514319\pi$
$643$	−2.28068	−0.0899414	−0.0449707	+	0.998988i	$0.514319\pi$
$644$	57.0644	2.24865
$645$	−83.0897	−3.27165
$646$	70.8217	2.78644
$647$	−14.5559	−0.572253	−0.286127	−	0.958192i	$-0.592368\pi$
$647$	−14.5559	−0.572253	−0.286127	+	0.958192i	$0.592368\pi$
$648$	−55.7273	−2.18917
$649$	−33.0876	−1.29880
$650$	−118.701	−4.65583
$651$	95.5724	3.74578
$652$	−20.7852	−0.814013
$653$	−20.7337	−0.811373	−0.405687	−	0.914012i	$-0.632968\pi$
$653$	−20.7337	−0.811373	−0.405687	+	0.914012i	$0.632968\pi$
$654$	25.0621	0.980005
$655$	−58.6903	−2.29322
$656$	2.65223	0.103552
$657$	−58.8076	−2.29430
$658$	−70.1634	−2.73525
$659$	11.5941	0.451643	0.225821	−	0.974169i	$-0.427493\pi$
$659$	11.5941	0.451643	0.225821	+	0.974169i	$0.427493\pi$
$660$	224.339	8.73239
$661$	4.42233	0.172009	0.0860043	−	0.996295i	$-0.472590\pi$
$661$	4.42233	0.172009	0.0860043	+	0.996295i	$0.472590\pi$
$662$	−80.8608	−3.14274
$663$	−88.2298	−3.42656
$664$	34.2439	1.32892
$665$	97.5725	3.78370
$666$	67.5431	2.61724
$667$	29.7730	1.15282
$668$	71.1970	2.75469
$669$	78.8356	3.04796
$670$	−26.4991	−1.02375
$671$	2.35587	0.0909474
$672$	−11.7711	−0.454082
$673$	32.2214	1.24204	0.621021	−	0.783794i	$-0.286718\pi$
$673$	32.2214	1.24204	0.621021	+	0.783794i	$0.286718\pi$
$674$	32.6847	1.25897
$675$	81.0326	3.11894
$676$	95.4086	3.66956
$677$	0.992295	0.0381370	0.0190685	−	0.999818i	$-0.493930\pi$
$677$	0.992295	0.0381370	0.0190685	+	0.999818i	$0.493930\pi$
$678$	−51.6158	−1.98229
$679$	11.3745	0.436512
$680$	−78.9160	−3.02629
$681$	72.5384	2.77968
$682$	−90.4257	−3.46258
$683$	−27.8896	−1.06717	−0.533584	−	0.845747i	$-0.679155\pi$
$683$	−27.8896	−1.06717	−0.533584	+	0.845747i	$0.679155\pi$
$684$	152.428	5.82821
$685$	−60.2150	−2.30070
$686$	56.2338	2.14701
$687$	−61.2225	−2.33578
$688$	26.0819	0.994363
$689$	68.1222	2.59525
$690$	−88.9654	−3.38685
$691$	−0.435917	−0.0165831	−0.00829153	−	0.999966i	$-0.502639\pi$
$691$	−0.435917	−0.0165831	−0.00829153	+	0.999966i	$0.502639\pi$
$692$	30.9049	1.17483
$693$	144.853	5.50253
$694$	4.28907	0.162811
$695$	−41.2410	−1.56436
$696$	126.701	4.80259
$697$	−3.62747	−0.137400
$698$	23.6431	0.894904
$699$	48.6304	1.83937
$700$	−136.952	−5.17629
$701$	−11.7486	−0.443739	−0.221869	−	0.975076i	$-0.571216\pi$
$701$	−11.7486	−0.443739	−0.221869	+	0.975076i	$0.571216\pi$
$702$	−150.895	−5.69518
$703$	−27.1065	−1.02234
$704$	47.1805	1.77818
$705$	72.3541	2.72501
$706$	−21.2289	−0.798961
$707$	−11.4022	−0.428825
$708$	75.6600	2.84348
$709$	−20.4752	−0.768964	−0.384482	−	0.923132i	$-0.625620\pi$
$709$	−20.4752	−0.768964	−0.384482	+	0.923132i	$0.625620\pi$
$710$	23.3910	0.877849
$711$	−16.0467	−0.601797
$712$	−37.1602	−1.39264
$713$	23.7195	0.888300
$714$	−153.898	−5.75948
$715$	115.010	4.30113
$716$	−65.0122	−2.42962
$717$	20.9239	0.781416
$718$	−59.4717	−2.21947
$719$	−33.0149	−1.23125	−0.615624	−	0.788040i	$-0.711096\pi$
$719$	−33.0149	−1.23125	−0.615624	+	0.788040i	$0.711096\pi$
$720$	−78.7009	−2.93301
$721$	−39.6863	−1.47800
$722$	−46.3021	−1.72319
$723$	−10.6308	−0.395364
$724$	17.5710	0.653020
$725$	−71.4537	−2.65373
$726$	−120.432	−4.46964
$727$	15.6875	0.581819	0.290909	−	0.956751i	$-0.406042\pi$
$727$	15.6875	0.581819	0.290909	+	0.956751i	$0.406042\pi$
$728$	124.496	4.61411
$729$	−16.9631	−0.628263
$730$	−81.4438	−3.01437
$731$	−35.6723	−1.31939
$732$	−5.38707	−0.199112
$733$	−13.6226	−0.503163	−0.251582	−	0.967836i	$-0.580951\pi$
$733$	−13.6226	−0.503163	−0.251582	+	0.967836i	$0.580951\pi$
$734$	26.7949	0.989018
$735$	−135.009	−4.97988
$736$	−2.92140	−0.107684
$737$	15.7879	0.581556
$738$	−11.8033	−0.434486
$739$	−1.25824	−0.0462850	−0.0231425	−	0.999732i	$-0.507367\pi$
$739$	−1.25824	−0.0462850	−0.0231425	+	0.999732i	$0.507367\pi$
$740$	61.8732	2.27450
$741$	115.215	4.23252
$742$	118.825	4.36219
$743$	20.7205	0.760161	0.380081	−	0.924953i	$-0.375896\pi$
$743$	20.7205	0.760161	0.380081	+	0.924953i	$0.375896\pi$
$744$	100.940	3.70063
$745$	−38.5406	−1.41202
$746$	−21.5057	−0.787381
$747$	−46.7078	−1.70895
$748$	96.3139	3.52158
$749$	−18.5405	−0.677456
$750$	79.7992	2.91385
$751$	29.8984	1.09101	0.545503	−	0.838109i	$-0.316339\pi$
$751$	29.8984	1.09101	0.545503	+	0.838109i	$0.316339\pi$
$752$	−22.7120	−0.828220
$753$	−84.1574	−3.06687
$754$	133.058	4.84569
$755$	−15.9875	−0.581843
$756$	−174.096	−6.33183
$757$	21.7485	0.790461	0.395231	−	0.918582i	$-0.370665\pi$
$757$	21.7485	0.790461	0.395231	+	0.918582i	$0.370665\pi$
$758$	29.1219	1.05776
$759$	53.0047	1.92395
$760$	103.052	3.73810
$761$	−17.4254	−0.631672	−0.315836	−	0.948814i	$-0.602285\pi$
$761$	−17.4254	−0.631672	−0.315836	+	0.948814i	$0.602285\pi$
$762$	50.2419	1.82007
$763$	14.8239	0.536660
$764$	55.9646	2.02473
$765$	107.639	3.89171
$766$	−21.6790	−0.783295
$767$	38.7880	1.40055
$768$	−94.8507	−3.42263
$769$	−51.4998	−1.85713	−0.928565	−	0.371170i	$-0.878957\pi$
$769$	−51.4998	−1.85713	−0.928565	+	0.371170i	$0.878957\pi$
$770$	200.610	7.22949
$771$	−37.1393	−1.33754
$772$	−10.3762	−0.373447
$773$	2.85471	0.102677	0.0513384	−	0.998681i	$-0.483651\pi$
$773$	2.85471	0.102677	0.0513384	+	0.998681i	$0.483651\pi$
$774$	−116.073	−4.17216
$775$	−56.9255	−2.04482
$776$	12.0133	0.431251
$777$	58.9033	2.11314
$778$	51.0484	1.83017
$779$	4.73692	0.169718
$780$	−262.988	−9.41650
$781$	−13.9361	−0.498674
$782$	−38.1948	−1.36585
$783$	−90.8338	−3.24613
$784$	42.3793	1.51355
$785$	52.1576	1.86158
$786$	−120.883	−4.31174
$787$	34.9060	1.24427	0.622133	−	0.782912i	$-0.286266\pi$
$787$	34.9060	1.24427	0.622133	+	0.782912i	$0.286266\pi$
$788$	11.1656	0.397757
$789$	−21.3032	−0.758414
$790$	−22.2233	−0.790671
$791$	−30.5301	−1.08552
$792$	152.989	5.43621
$793$	−2.76174	−0.0980724
$794$	−19.2819	−0.684288
$795$	−122.535	−4.34585
$796$	−78.2628	−2.77395
$797$	2.96355	0.104974	0.0524872	−	0.998622i	$-0.483285\pi$
$797$	2.96355	0.104974	0.0524872	+	0.998622i	$0.483285\pi$
$798$	200.967	7.11416
$799$	31.0632	1.09894
$800$	7.01122	0.247884
$801$	50.6856	1.79089
$802$	−20.8549	−0.736412
$803$	48.5234	1.71235
$804$	−36.1015	−1.27320
$805$	−52.6218	−1.85468
$806$	106.004	3.73384
$807$	78.1668	2.75160
$808$	−12.0426	−0.423657
$809$	18.6026	0.654031	0.327016	−	0.945019i	$-0.393957\pi$
$809$	18.6026	0.654031	0.327016	+	0.945019i	$0.393957\pi$
$810$	105.269	3.69876
$811$	14.2630	0.500842	0.250421	−	0.968137i	$-0.419431\pi$
$811$	14.2630	0.500842	0.250421	+	0.968137i	$0.419431\pi$
$812$	153.517	5.38738
$813$	56.2845	1.97398
$814$	−55.7313	−1.95338
$815$	19.1671	0.671393
$816$	−49.8169	−1.74394
$817$	46.5826	1.62972
$818$	37.6701	1.31711
$819$	−169.809	−5.93360
$820$	−10.8125	−0.377588
$821$	−11.8581	−0.413852	−0.206926	−	0.978357i	$-0.566346\pi$
$821$	−11.8581	−0.413852	−0.206926	+	0.978357i	$0.566346\pi$
$822$	−124.023	−4.32580
$823$	−34.0340	−1.18635	−0.593175	−	0.805074i	$-0.702126\pi$
$823$	−34.0340	−1.18635	−0.593175	+	0.805074i	$0.702126\pi$
$824$	−41.9152	−1.46018
$825$	−127.209	−4.42884
$826$	67.6573	2.35410
$827$	10.0912	0.350907	0.175454	−	0.984488i	$-0.443861\pi$
$827$	10.0912	0.350907	0.175454	+	0.984488i	$0.443861\pi$
$828$	−82.2057	−2.85684
$829$	6.44215	0.223745	0.111873	−	0.993723i	$-0.464315\pi$
$829$	6.44215	0.223745	0.111873	+	0.993723i	$0.464315\pi$
$830$	−64.6866	−2.24530
$831$	−56.9387	−1.97518
$832$	−55.3088	−1.91749
$833$	−57.9623	−2.00828
$834$	−84.9427	−2.94133
$835$	−65.6541	−2.27206
$836$	−125.771	−4.34989
$837$	−72.3651	−2.50130
$838$	31.5759	1.09077
$839$	37.5787	1.29736	0.648680	−	0.761062i	$-0.275322\pi$
$839$	37.5787	1.29736	0.648680	+	0.761062i	$0.275322\pi$
$840$	−223.936	−7.72652
$841$	51.0963	1.76194
$842$	86.2158	2.97119
$843$	−77.0213	−2.65276
$844$	86.8231	2.98857
$845$	−87.9809	−3.02663
$846$	101.076	3.47506
$847$	−71.2337	−2.44762
$848$	38.4636	1.32085
$849$	7.23780	0.248401
$850$	91.6658	3.14411
$851$	14.6188	0.501126
$852$	31.8671	1.09175
$853$	−2.23495	−0.0765233	−0.0382617	−	0.999268i	$-0.512182\pi$
$853$	−2.23495	−0.0765233	−0.0382617	+	0.999268i	$0.512182\pi$
$854$	−4.81726	−0.164843
$855$	−140.561	−4.80708
$856$	−19.5818	−0.669291
$857$	34.4773	1.17772	0.588861	−	0.808234i	$-0.299576\pi$
$857$	34.4773	1.17772	0.588861	+	0.808234i	$0.299576\pi$
$858$	236.883	8.08704
$859$	38.7933	1.32361	0.661805	−	0.749676i	$-0.269791\pi$
$859$	38.7933	1.32361	0.661805	+	0.749676i	$0.269791\pi$
$860$	−106.329	−3.62579
$861$	−10.2935	−0.350801
$862$	−22.3137	−0.760009
$863$	−41.5052	−1.41285	−0.706426	−	0.707787i	$-0.749694\pi$
$863$	−41.5052	−1.41285	−0.706426	+	0.707787i	$0.749694\pi$
$864$	8.91283	0.303221
$865$	−28.4989	−0.968991
$866$	5.76995	0.196071
$867$	16.2252	0.551038
$868$	122.303	4.15124
$869$	13.2405	0.449152
$870$	−239.338	−8.11431
$871$	−18.5079	−0.627115
$872$	15.6564	0.530193
$873$	−16.3858	−0.554575
$874$	49.8767	1.68710
$875$	47.2001	1.59566
$876$	−110.956	−3.74887
$877$	18.9049	0.638374	0.319187	−	0.947692i	$-0.396590\pi$
$877$	18.9049	0.638374	0.319187	+	0.947692i	$0.396590\pi$
$878$	11.0714	0.373642
$879$	18.4197	0.621281
$880$	64.9378	2.18905
$881$	24.0629	0.810701	0.405350	−	0.914161i	$-0.367150\pi$
$881$	24.0629	0.810701	0.405350	+	0.914161i	$0.367150\pi$
$882$	−188.602	−6.35056
$883$	33.4339	1.12514	0.562571	−	0.826749i	$-0.309812\pi$
$883$	33.4339	1.12514	0.562571	+	0.826749i	$0.309812\pi$
$884$	−112.907	−3.79747
$885$	−69.7697	−2.34528
$886$	19.0329	0.639422
$887$	−1.86619	−0.0626607	−0.0313303	−	0.999509i	$-0.509974\pi$
$887$	−1.86619	−0.0626607	−0.0313303	+	0.999509i	$0.509974\pi$
$888$	62.2113	2.08768
$889$	29.7174	0.996689
$890$	70.1954	2.35296
$891$	−62.7180	−2.10113
$892$	100.885	3.37789
$893$	−40.5639	−1.35742
$894$	−79.3808	−2.65489
$895$	59.9509	2.00394
$896$	−88.7643	−2.96541
$897$	−62.1364	−2.07467
$898$	−62.4361	−2.08352
$899$	63.8109	2.12821
$900$	197.290	6.57632
$901$	−52.6068	−1.75259
$902$	9.73917	0.324279
$903$	−101.225	−3.36857
$904$	−32.2447	−1.07244
$905$	−16.2030	−0.538607
$906$	−32.9289	−1.09399
$907$	39.0677	1.29722	0.648611	−	0.761120i	$-0.275350\pi$
$907$	39.0677	1.29722	0.648611	+	0.761120i	$0.275350\pi$
$908$	92.8267	3.08056
$909$	16.4258	0.544809
$910$	−235.172	−7.79586
$911$	−4.53801	−0.150351	−0.0751755	−	0.997170i	$-0.523952\pi$
$911$	−4.53801	−0.150351	−0.0751755	+	0.997170i	$0.523952\pi$
$912$	65.0533	2.15413
$913$	38.5396	1.27548
$914$	−21.4011	−0.707886
$915$	4.96767	0.164226
$916$	−78.3459	−2.58862
$917$	−71.5004	−2.36115
$918$	116.528	3.84599
$919$	24.3084	0.801859	0.400930	−	0.916109i	$-0.368687\pi$
$919$	24.3084	0.801859	0.400930	+	0.916109i	$0.368687\pi$
$920$	−55.5771	−1.83232
$921$	77.6113	2.55738
$922$	−30.1987	−0.994540
$923$	16.3371	0.537741
$924$	273.305	8.99107
$925$	−35.0844	−1.15357
$926$	−13.8903	−0.456463
$927$	57.1712	1.87775
$928$	−7.85925	−0.257993
$929$	−34.9767	−1.14755	−0.573773	−	0.819014i	$-0.694521\pi$
$929$	−34.9767	−1.14755	−0.573773	+	0.819014i	$0.694521\pi$
$930$	−190.675	−6.25247
$931$	75.6900	2.48064
$932$	62.2319	2.03847
$933$	60.0129	1.96473
$934$	85.8322	2.80852
$935$	−88.8156	−2.90458
$936$	−179.346	−5.86209
$937$	−50.3865	−1.64606	−0.823028	−	0.568001i	$-0.807717\pi$
$937$	−50.3865	−1.64606	−0.823028	+	0.568001i	$0.807717\pi$
$938$	−32.2830	−1.05408
$939$	48.0778	1.56896
$940$	92.5909	3.01998
$941$	−21.6113	−0.704507	−0.352253	−	0.935905i	$-0.614584\pi$
$941$	−21.6113	−0.704507	−0.352253	+	0.935905i	$0.614584\pi$
$942$	107.427	3.50017
$943$	−2.55467	−0.0831915
$944$	21.9007	0.712808
$945$	160.543	5.22246
$946$	95.7743	3.11389
$947$	−8.52961	−0.277175	−0.138587	−	0.990350i	$-0.544256\pi$
$947$	−8.52961	−0.277175	−0.138587	+	0.990350i	$0.544256\pi$
$948$	−30.2764	−0.983330
$949$	−56.8831	−1.84650
$950$	−119.702	−3.88363
$951$	54.5957	1.77039
$952$	−96.1407	−3.11594
$953$	−3.11453	−0.100890	−0.0504448	−	0.998727i	$-0.516064\pi$
$953$	−3.11453	−0.100890	−0.0504448	+	0.998727i	$0.516064\pi$
$954$	−171.176	−5.54202
$955$	−51.6076	−1.66998
$956$	26.7761	0.866001
$957$	142.595	4.60945
$958$	−63.5014	−2.05164
$959$	−73.3579	−2.36885
$960$	99.4864	3.21091
$961$	19.8366	0.639891
$962$	65.3327	2.10641
$963$	26.7090	0.860687
$964$	−13.6041	−0.438160
$965$	9.56838	0.308017
$966$	−108.384	−3.48718
$967$	41.3067	1.32833	0.664167	−	0.747584i	$-0.268786\pi$
$967$	41.3067	1.32833	0.664167	+	0.747584i	$0.268786\pi$
$968$	−75.2343	−2.41812
$969$	−88.9736	−2.85824
$970$	−22.6930	−0.728628
$971$	−37.0840	−1.19008	−0.595041	−	0.803696i	$-0.702864\pi$
$971$	−37.0840	−1.19008	−0.595041	+	0.803696i	$0.702864\pi$
$972$	24.4368	0.783810
$973$	−50.2425	−1.61070
$974$	−7.92061	−0.253793
$975$	149.124	4.77580
$976$	−1.55935	−0.0499137
$977$	27.5075	0.880042	0.440021	−	0.897988i	$-0.354971\pi$
$977$	27.5075	0.880042	0.440021	+	0.897988i	$0.354971\pi$
$978$	39.4778	1.26236
$979$	−41.8217	−1.33663
$980$	−172.770	−5.51892
$981$	−21.3549	−0.681811
$982$	42.8461	1.36728
$983$	−40.7643	−1.30018	−0.650090	−	0.759857i	$-0.725269\pi$
$983$	−40.7643	−1.30018	−0.650090	+	0.759857i	$0.725269\pi$
$984$	−10.8716	−0.346573
$985$	−10.2963	−0.328068
$986$	−102.753	−3.27232
$987$	88.1465	2.80574
$988$	147.439	4.69067
$989$	−25.1224	−0.798847
$990$	−288.995	−9.18485
$991$	51.6623	1.64111	0.820553	−	0.571570i	$-0.193666\pi$
$991$	51.6623	1.64111	0.820553	+	0.571570i	$0.193666\pi$
$992$	−6.26128	−0.198796
$993$	101.586	3.22372
$994$	28.4965	0.903853
$995$	72.1699	2.28794
$996$	−88.1269	−2.79241
$997$	−14.0872	−0.446146	−0.223073	−	0.974802i	$-0.571609\pi$
$997$	−14.0872	−0.446146	−0.223073	+	0.974802i	$0.571609\pi$
$998$	60.1148	1.90290
$999$	−44.6002	−1.41109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.14	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.14	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43054 q^{2} +3.05350 q^{3} +3.90754 q^{4} -3.60333 q^{5} -7.42166 q^{6} -4.38981 q^{7} -4.63635 q^{8} +6.32386 q^{9} +O(q^{10})\)	\(q-2.43054 q^{2} +3.05350 q^{3} +3.90754 q^{4} -3.60333 q^{5} -7.42166 q^{6} -4.38981 q^{7} -4.63635 q^{8} +6.32386 q^{9} +8.75804 q^{10} -5.21796 q^{11} +11.9317 q^{12} +6.11691 q^{13} +10.6696 q^{14} -11.0028 q^{15} +3.45377 q^{16} -4.72373 q^{17} -15.3704 q^{18} +6.16848 q^{19} -14.0801 q^{20} -13.4043 q^{21} +12.6825 q^{22} -3.32672 q^{23} -14.1571 q^{24} +7.98396 q^{25} -14.8674 q^{26} +10.1494 q^{27} -17.1534 q^{28} -8.94966 q^{29} +26.7427 q^{30} -7.12998 q^{31} +0.878162 q^{32} -15.9330 q^{33} +11.4812 q^{34} +15.8179 q^{35} +24.7107 q^{36} -4.39436 q^{37} -14.9927 q^{38} +18.6780 q^{39} +16.7063 q^{40} +0.767924 q^{41} +32.5797 q^{42} +7.55171 q^{43} -20.3894 q^{44} -22.7869 q^{45} +8.08573 q^{46} -6.57599 q^{47} +10.5461 q^{48} +12.2705 q^{49} -19.4054 q^{50} -14.4239 q^{51} +23.9020 q^{52} +11.1367 q^{53} -24.6686 q^{54} +18.8020 q^{55} +20.3527 q^{56} +18.8354 q^{57} +21.7525 q^{58} +6.34111 q^{59} -42.9937 q^{60} -0.451493 q^{61} +17.3297 q^{62} -27.7606 q^{63} -9.04195 q^{64} -22.0412 q^{65} +38.7259 q^{66} -3.02569 q^{67} -18.4582 q^{68} -10.1581 q^{69} -38.4461 q^{70} +2.67080 q^{71} -29.3196 q^{72} -9.29932 q^{73} +10.6807 q^{74} +24.3790 q^{75} +24.1036 q^{76} +22.9058 q^{77} -45.3976 q^{78} -2.53748 q^{79} -12.4451 q^{80} +12.0196 q^{81} -1.86647 q^{82} -7.38597 q^{83} -52.3778 q^{84} +17.0212 q^{85} -18.3548 q^{86} -27.3278 q^{87} +24.1923 q^{88} +8.01497 q^{89} +55.3846 q^{90} -26.8521 q^{91} -12.9993 q^{92} -21.7714 q^{93} +15.9832 q^{94} -22.2270 q^{95} +2.68147 q^{96} -2.59110 q^{97} -29.8239 q^{98} -32.9976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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