LMFDB - Embedded newform 4013.2.a.c.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.39764 q^{2} -0.316927 q^{3} +3.74866 q^{4} -2.45861 q^{5} +0.759875 q^{6} +1.72271 q^{7} -4.19265 q^{8} -2.89956 q^{9} +O(q^{10})$	\(q-2.39764 q^{2} -0.316927 q^{3} +3.74866 q^{4} -2.45861 q^{5} +0.759875 q^{6} +1.72271 q^{7} -4.19265 q^{8} -2.89956 q^{9} +5.89485 q^{10} +1.31818 q^{11} -1.18805 q^{12} -5.85869 q^{13} -4.13043 q^{14} +0.779199 q^{15} +2.55512 q^{16} -7.44659 q^{17} +6.95208 q^{18} +2.22092 q^{19} -9.21648 q^{20} -0.545972 q^{21} -3.16051 q^{22} -1.17179 q^{23} +1.32876 q^{24} +1.04475 q^{25} +14.0470 q^{26} +1.86973 q^{27} +6.45784 q^{28} -7.80883 q^{29} -1.86823 q^{30} -8.13081 q^{31} +2.25904 q^{32} -0.417766 q^{33} +17.8542 q^{34} -4.23546 q^{35} -10.8694 q^{36} -5.39667 q^{37} -5.32495 q^{38} +1.85677 q^{39} +10.3081 q^{40} -6.28336 q^{41} +1.30904 q^{42} +4.06230 q^{43} +4.94140 q^{44} +7.12888 q^{45} +2.80953 q^{46} +5.83162 q^{47} -0.809786 q^{48} -4.03228 q^{49} -2.50494 q^{50} +2.36002 q^{51} -21.9622 q^{52} -0.446823 q^{53} -4.48293 q^{54} -3.24088 q^{55} -7.22270 q^{56} -0.703868 q^{57} +18.7227 q^{58} -5.83679 q^{59} +2.92095 q^{60} +11.9984 q^{61} +19.4947 q^{62} -4.99509 q^{63} -10.5266 q^{64} +14.4042 q^{65} +1.00165 q^{66} -2.80463 q^{67} -27.9147 q^{68} +0.371372 q^{69} +10.1551 q^{70} -5.59150 q^{71} +12.1568 q^{72} +7.25360 q^{73} +12.9393 q^{74} -0.331110 q^{75} +8.32546 q^{76} +2.27084 q^{77} -4.45187 q^{78} -2.78957 q^{79} -6.28204 q^{80} +8.10611 q^{81} +15.0652 q^{82} -11.8777 q^{83} -2.04666 q^{84} +18.3082 q^{85} -9.73991 q^{86} +2.47483 q^{87} -5.52665 q^{88} +3.96733 q^{89} -17.0924 q^{90} -10.0928 q^{91} -4.39265 q^{92} +2.57687 q^{93} -13.9821 q^{94} -5.46037 q^{95} -0.715951 q^{96} +14.8294 q^{97} +9.66794 q^{98} -3.82213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.39764	−1.69538	−0.847692	−	0.530488i	$-0.822009\pi$
$2$	−2.39764	−1.69538	−0.847692	+	0.530488i	$0.822009\pi$
$3$	−0.316927	−0.182978	−0.0914889	−	0.995806i	$-0.529163\pi$
$3$	−0.316927	−0.182978	−0.0914889	+	0.995806i	$0.529163\pi$
$4$	3.74866	1.87433
$5$	−2.45861	−1.09952	−0.549761	−	0.835322i	$-0.685281\pi$
$5$	−2.45861	−1.09952	−0.549761	+	0.835322i	$0.685281\pi$
$6$	0.759875	0.310218
$7$	1.72271	0.651122	0.325561	−	0.945521i	$-0.394447\pi$
$7$	1.72271	0.651122	0.325561	+	0.945521i	$0.394447\pi$
$8$	−4.19265	−1.48232
$9$	−2.89956	−0.966519
$10$	5.89485	1.86411
$11$	1.31818	0.397446	0.198723	−	0.980056i	$-0.436321\pi$
$11$	1.31818	0.397446	0.198723	+	0.980056i	$0.436321\pi$
$12$	−1.18805	−0.342960
$13$	−5.85869	−1.62491	−0.812453	−	0.583026i	$-0.801869\pi$
$13$	−5.85869	−1.62491	−0.812453	+	0.583026i	$0.801869\pi$
$14$	−4.13043	−1.10390
$15$	0.779199	0.201188
$16$	2.55512	0.638780
$17$	−7.44659	−1.80606	−0.903031	−	0.429575i	$-0.858663\pi$
$17$	−7.44659	−1.80606	−0.903031	+	0.429575i	$0.858663\pi$
$18$	6.95208	1.63862
$19$	2.22092	0.509513	0.254757	−	0.967005i	$-0.418005\pi$
$19$	2.22092	0.509513	0.254757	+	0.967005i	$0.418005\pi$
$20$	−9.21648	−2.06087
$21$	−0.545972	−0.119141
$22$	−3.16051	−0.673823
$23$	−1.17179	−0.244335	−0.122168	−	0.992509i	$-0.538985\pi$
$23$	−1.17179	−0.244335	−0.122168	+	0.992509i	$0.538985\pi$
$24$	1.32876	0.271232
$25$	1.04475	0.208951
$26$	14.0470	2.75484
$27$	1.86973	0.359829
$28$	6.45784	1.22042
$29$	−7.80883	−1.45006	−0.725031	−	0.688716i	$-0.758175\pi$
$29$	−7.80883	−1.45006	−0.725031	+	0.688716i	$0.758175\pi$
$30$	−1.86823	−0.341091
$31$	−8.13081	−1.46034	−0.730168	−	0.683267i	$-0.760558\pi$
$31$	−8.13081	−1.46034	−0.730168	+	0.683267i	$0.760558\pi$
$32$	2.25904	0.399346
$33$	−0.417766	−0.0727237
$34$	17.8542	3.06197
$35$	−4.23546	−0.715924
$36$	−10.8694	−1.81157
$37$	−5.39667	−0.887208	−0.443604	−	0.896223i	$-0.646300\pi$
$37$	−5.39667	−0.887208	−0.443604	+	0.896223i	$0.646300\pi$
$38$	−5.32495	−0.863821
$39$	1.85677	0.297322
$40$	10.3081	1.62985
$41$	−6.28336	−0.981296	−0.490648	−	0.871358i	$-0.663240\pi$
$41$	−6.28336	−0.981296	−0.490648	+	0.871358i	$0.663240\pi$
$42$	1.30904	0.201990
$43$	4.06230	0.619494	0.309747	−	0.950819i	$-0.399756\pi$
$43$	4.06230	0.619494	0.309747	+	0.950819i	$0.399756\pi$
$44$	4.94140	0.744944
$45$	7.12888	1.06271
$46$	2.80953	0.414243
$47$	5.83162	0.850629	0.425315	−	0.905046i	$-0.360163\pi$
$47$	5.83162	0.850629	0.425315	+	0.905046i	$0.360163\pi$
$48$	−0.809786	−0.116883
$49$	−4.03228	−0.576040
$50$	−2.50494	−0.354252
$51$	2.36002	0.330469
$52$	−21.9622	−3.04561
$53$	−0.446823	−0.0613758	−0.0306879	−	0.999529i	$-0.509770\pi$
$53$	−0.446823	−0.0613758	−0.0306879	+	0.999529i	$0.509770\pi$
$54$	−4.48293	−0.610049
$55$	−3.24088	−0.437001
$56$	−7.22270	−0.965174
$57$	−0.703868	−0.0932296
$58$	18.7227	2.45841
$59$	−5.83679	−0.759885	−0.379943	−	0.925010i	$-0.624056\pi$
$59$	−5.83679	−0.759885	−0.379943	+	0.925010i	$0.624056\pi$
$60$	2.92095	0.377093
$61$	11.9984	1.53624	0.768120	−	0.640306i	$-0.221193\pi$
$61$	11.9984	1.53624	0.768120	+	0.640306i	$0.221193\pi$
$62$	19.4947	2.47583
$63$	−4.99509	−0.629322
$64$	−10.5266	−1.31582
$65$	14.4042	1.78662
$66$	1.00165	0.123295
$67$	−2.80463	−0.342640	−0.171320	−	0.985215i	$-0.554803\pi$
$67$	−2.80463	−0.342640	−0.171320	+	0.985215i	$0.554803\pi$
$68$	−27.9147	−3.38515
$69$	0.371372	0.0447079
$70$	10.1551	1.21377
$71$	−5.59150	−0.663589	−0.331795	−	0.943352i	$-0.607654\pi$
$71$	−5.59150	−0.663589	−0.331795	+	0.943352i	$0.607654\pi$
$72$	12.1568	1.43269
$73$	7.25360	0.848970	0.424485	−	0.905435i	$-0.360455\pi$
$73$	7.25360	0.848970	0.424485	+	0.905435i	$0.360455\pi$
$74$	12.9393	1.50416
$75$	−0.331110	−0.0382333
$76$	8.32546	0.954996
$77$	2.27084	0.258786
$78$	−4.45187	−0.504075
$79$	−2.78957	−0.313851	−0.156926	−	0.987610i	$-0.550158\pi$
$79$	−2.78957	−0.313851	−0.156926	+	0.987610i	$0.550158\pi$
$80$	−6.28204	−0.702353
$81$	8.10611	0.900678
$82$	15.0652	1.66367
$83$	−11.8777	−1.30375	−0.651873	−	0.758328i	$-0.726017\pi$
$83$	−11.8777	−1.30375	−0.651873	+	0.758328i	$0.726017\pi$
$84$	−2.04666	−0.223309
$85$	18.3082	1.98581
$86$	−9.73991	−1.05028
$87$	2.47483	0.265329
$88$	−5.52665	−0.589143
$89$	3.96733	0.420536	0.210268	−	0.977644i	$-0.432566\pi$
$89$	3.96733	0.420536	0.210268	+	0.977644i	$0.432566\pi$
$90$	−17.0924	−1.80170
$91$	−10.0928	−1.05801
$92$	−4.39265	−0.457965
$93$	2.57687	0.267209
$94$	−13.9821	−1.44214
$95$	−5.46037	−0.560222
$96$	−0.715951	−0.0730714
$97$	14.8294	1.50570	0.752850	−	0.658192i	$-0.228679\pi$
$97$	14.8294	1.50570	0.752850	+	0.658192i	$0.228679\pi$
$98$	9.66794	0.976609
$99$	−3.82213	−0.384139
$100$	3.91643	0.391643
$101$	−15.6448	−1.55671	−0.778356	−	0.627823i	$-0.783946\pi$
$101$	−15.6448	−1.55671	−0.778356	+	0.627823i	$0.783946\pi$
$102$	−5.65847	−0.560272
$103$	5.43445	0.535472	0.267736	−	0.963492i	$-0.413725\pi$
$103$	5.43445	0.535472	0.267736	+	0.963492i	$0.413725\pi$
$104$	24.5634	2.40864
$105$	1.34233	0.130998
$106$	1.07132	0.104056
$107$	−17.2648	−1.66905	−0.834524	−	0.550971i	$-0.814257\pi$
$107$	−17.2648	−1.66905	−0.834524	+	0.550971i	$0.814257\pi$
$108$	7.00897	0.674438
$109$	2.16404	0.207278	0.103639	−	0.994615i	$-0.466951\pi$
$109$	2.16404	0.207278	0.103639	+	0.994615i	$0.466951\pi$
$110$	7.77046	0.740884
$111$	1.71035	0.162339
$112$	4.40173	0.415924
$113$	1.15218	0.108388	0.0541941	−	0.998530i	$-0.482741\pi$
$113$	1.15218	0.108388	0.0541941	+	0.998530i	$0.482741\pi$
$114$	1.68762	0.158060
$115$	2.88098	0.268652
$116$	−29.2726	−2.71789
$117$	16.9876	1.57050
$118$	13.9945	1.28830
$119$	−12.8283	−1.17597
$120$	−3.26690	−0.298226
$121$	−9.26241	−0.842037
$122$	−28.7678	−2.60452
$123$	1.99136	0.179555
$124$	−30.4796	−2.73715
$125$	9.72440	0.869777
$126$	11.9764	1.06694
$127$	6.37659	0.565831	0.282915	−	0.959145i	$-0.408698\pi$
$127$	6.37659	0.565831	0.282915	+	0.959145i	$0.408698\pi$
$128$	20.7209	1.83148
$129$	−1.28745	−0.113354
$130$	−34.5361	−3.02901
$131$	−14.7188	−1.28598	−0.642992	−	0.765873i	$-0.722307\pi$
$131$	−14.7188	−1.28598	−0.642992	+	0.765873i	$0.722307\pi$
$132$	−1.56606	−0.136308
$133$	3.82599	0.331756
$134$	6.72448	0.580906
$135$	−4.59693	−0.395640
$136$	31.2209	2.67717
$137$	−10.8371	−0.925874	−0.462937	−	0.886391i	$-0.653204\pi$
$137$	−10.8371	−0.925874	−0.462937	+	0.886391i	$0.653204\pi$
$138$	−0.890415	−0.0757971
$139$	6.37819	0.540991	0.270496	−	0.962721i	$-0.412812\pi$
$139$	6.37819	0.540991	0.270496	+	0.962721i	$0.412812\pi$
$140$	−15.8773	−1.34188
$141$	−1.84820	−0.155646
$142$	13.4064	1.12504
$143$	−7.72279	−0.645812
$144$	−7.40872	−0.617393
$145$	19.1988	1.59438
$146$	−17.3915	−1.43933
$147$	1.27794	0.105402
$148$	−20.2303	−1.66292
$149$	−8.35233	−0.684249	−0.342125	−	0.939655i	$-0.611146\pi$
$149$	−8.35233	−0.684249	−0.342125	+	0.939655i	$0.611146\pi$
$150$	0.793882	0.0648202
$151$	11.0222	0.896976	0.448488	−	0.893789i	$-0.351963\pi$
$151$	11.0222	0.896976	0.448488	+	0.893789i	$0.351963\pi$
$152$	−9.31152	−0.755264
$153$	21.5918	1.74559
$154$	−5.44464	−0.438741
$155$	19.9905	1.60567
$156$	6.96041	0.557279
$157$	−13.8390	−1.10447	−0.552236	−	0.833688i	$-0.686225\pi$
$157$	−13.8390	−1.10447	−0.552236	+	0.833688i	$0.686225\pi$
$158$	6.68837	0.532098
$159$	0.141610	0.0112304
$160$	−5.55410	−0.439090
$161$	−2.01865	−0.159092
$162$	−19.4355	−1.52700
$163$	15.3411	1.20161	0.600804	−	0.799397i	$-0.294847\pi$
$163$	15.3411	1.20161	0.600804	+	0.799397i	$0.294847\pi$
$164$	−23.5542	−1.83927
$165$	1.02712	0.0799614
$166$	28.4784	2.21035
$167$	−4.61183	−0.356874	−0.178437	−	0.983951i	$-0.557104\pi$
$167$	−4.61183	−0.356874	−0.178437	+	0.983951i	$0.557104\pi$
$168$	2.28907	0.176605
$169$	21.3242	1.64032
$170$	−43.8965	−3.36671
$171$	−6.43968	−0.492454
$172$	15.2282	1.16114
$173$	9.53392	0.724851	0.362425	−	0.932013i	$-0.381949\pi$
$173$	9.53392	0.724851	0.362425	+	0.932013i	$0.381949\pi$
$174$	−5.93373	−0.449835
$175$	1.79981	0.136053
$176$	3.36810	0.253880
$177$	1.84983	0.139042
$178$	−9.51222	−0.712971
$179$	−4.56903	−0.341505	−0.170752	−	0.985314i	$-0.554620\pi$
$179$	−4.56903	−0.341505	−0.170752	+	0.985314i	$0.554620\pi$
$180$	26.7237	1.99187
$181$	5.85275	0.435031	0.217516	−	0.976057i	$-0.430205\pi$
$181$	5.85275	0.435031	0.217516	+	0.976057i	$0.430205\pi$
$182$	24.1989	1.79374
$183$	−3.80262	−0.281098
$184$	4.91291	0.362184
$185$	13.2683	0.975505
$186$	−6.17840	−0.453022
$187$	−9.81593	−0.717812
$188$	21.8607	1.59436
$189$	3.22099	0.234293
$190$	13.0920	0.949791
$191$	−25.6135	−1.85333	−0.926663	−	0.375892i	$-0.877336\pi$
$191$	−25.6135	−1.85333	−0.926663	+	0.375892i	$0.877336\pi$
$192$	3.33616	0.240767
$193$	−1.97922	−0.142468	−0.0712338	−	0.997460i	$-0.522694\pi$
$193$	−1.97922	−0.142468	−0.0712338	+	0.997460i	$0.522694\pi$
$194$	−35.5555	−2.55274
$195$	−4.56508	−0.326912
$196$	−15.1156	−1.07969
$197$	12.1530	0.865869	0.432934	−	0.901425i	$-0.357478\pi$
$197$	12.1530	0.865869	0.432934	+	0.901425i	$0.357478\pi$
$198$	9.16409	0.651263
$199$	−25.8978	−1.83584	−0.917922	−	0.396761i	$-0.870134\pi$
$199$	−25.8978	−1.83584	−0.917922	+	0.396761i	$0.870134\pi$
$200$	−4.38028	−0.309733
$201$	0.888861	0.0626954
$202$	37.5105	2.63923
$203$	−13.4523	−0.944168
$204$	8.84691	0.619408
$205$	15.4483	1.07896
$206$	−13.0298	−0.907831
$207$	3.39768	0.236155
$208$	−14.9696	−1.03796
$209$	2.92757	0.202504
$210$	−3.21842	−0.222092
$211$	−12.4266	−0.855482	−0.427741	−	0.903901i	$-0.640690\pi$
$211$	−12.4266	−0.855482	−0.427741	+	0.903901i	$0.640690\pi$
$212$	−1.67499	−0.115038
$213$	1.77210	0.121422
$214$	41.3946	2.82968
$215$	−9.98759	−0.681148
$216$	−7.83910	−0.533383
$217$	−14.0070	−0.950858
$218$	−5.18859	−0.351416
$219$	−2.29886	−0.155343
$220$	−12.1490	−0.819083
$221$	43.6272	2.93468
$222$	−4.10080	−0.275227
$223$	4.48447	0.300303	0.150151	−	0.988663i	$-0.452024\pi$
$223$	4.48447	0.300303	0.150151	+	0.988663i	$0.452024\pi$
$224$	3.89167	0.260023
$225$	−3.02932	−0.201955
$226$	−2.76252	−0.183760
$227$	19.9312	1.32288	0.661441	−	0.749997i	$-0.269945\pi$
$227$	19.9312	1.32288	0.661441	+	0.749997i	$0.269945\pi$
$228$	−2.63856	−0.174743
$229$	−14.2494	−0.941624	−0.470812	−	0.882234i	$-0.656039\pi$
$229$	−14.2494	−0.941624	−0.470812	+	0.882234i	$0.656039\pi$
$230$	−6.90753	−0.455469
$231$	−0.719689	−0.0473520
$232$	32.7396	2.14946
$233$	−25.2137	−1.65181	−0.825903	−	0.563813i	$-0.809334\pi$
$233$	−25.2137	−1.65181	−0.825903	+	0.563813i	$0.809334\pi$
$234$	−40.7301	−2.66261
$235$	−14.3377	−0.935286
$236$	−21.8801	−1.42428
$237$	0.884089	0.0574277
$238$	30.7576	1.99372
$239$	−2.79535	−0.180816	−0.0904082	−	0.995905i	$-0.528817\pi$
$239$	−2.79535	−0.180816	−0.0904082	+	0.995905i	$0.528817\pi$
$240$	1.99095	0.128515
$241$	1.12615	0.0725415	0.0362707	−	0.999342i	$-0.488452\pi$
$241$	1.12615	0.0725415	0.0362707	+	0.999342i	$0.488452\pi$
$242$	22.2079	1.42758
$243$	−8.17822	−0.524633
$244$	44.9779	2.87942
$245$	9.91379	0.633369
$246$	−4.77457	−0.304415
$247$	−13.0117	−0.827912
$248$	34.0896	2.16469
$249$	3.76436	0.238557
$250$	−23.3156	−1.47461
$251$	6.88020	0.434275	0.217137	−	0.976141i	$-0.430328\pi$
$251$	6.88020	0.434275	0.217137	+	0.976141i	$0.430328\pi$
$252$	−18.7249	−1.17956
$253$	−1.54463	−0.0971101
$254$	−15.2887	−0.959301
$255$	−5.80237	−0.363358
$256$	−28.6279	−1.78924
$257$	−2.00590	−0.125125	−0.0625623	−	0.998041i	$-0.519927\pi$
$257$	−2.00590	−0.125125	−0.0625623	+	0.998041i	$0.519927\pi$
$258$	3.08684	0.192178
$259$	−9.29689	−0.577681
$260$	53.9965	3.34872
$261$	22.6421	1.40151
$262$	35.2902	2.18024
$263$	16.7730	1.03427	0.517134	−	0.855904i	$-0.326999\pi$
$263$	16.7730	1.03427	0.517134	+	0.855904i	$0.326999\pi$
$264$	1.75154	0.107800
$265$	1.09856	0.0674841
$266$	−9.17333	−0.562453
$267$	−1.25735	−0.0769488
$268$	−10.5136	−0.642220
$269$	9.36855	0.571210	0.285605	−	0.958347i	$-0.407805\pi$
$269$	9.36855	0.571210	0.285605	+	0.958347i	$0.407805\pi$
$270$	11.0218	0.670763
$271$	−18.8559	−1.14541	−0.572707	−	0.819760i	$-0.694107\pi$
$271$	−18.8559	−1.14541	−0.572707	+	0.819760i	$0.694107\pi$
$272$	−19.0269	−1.15368
$273$	3.19868	0.193593
$274$	25.9834	1.56971
$275$	1.37717	0.0830466
$276$	1.39215	0.0837974
$277$	−1.10026	−0.0661080	−0.0330540	−	0.999454i	$-0.510523\pi$
$277$	−1.10026	−0.0661080	−0.0330540	+	0.999454i	$0.510523\pi$
$278$	−15.2926	−0.917188
$279$	23.5757	1.41144
$280$	17.7578	1.06123
$281$	1.43852	0.0858148	0.0429074	−	0.999079i	$-0.486338\pi$
$281$	1.43852	0.0858148	0.0429074	+	0.999079i	$0.486338\pi$
$282$	4.43130	0.263880
$283$	9.19786	0.546756	0.273378	−	0.961907i	$-0.411859\pi$
$283$	9.19786	0.546756	0.273378	+	0.961907i	$0.411859\pi$
$284$	−20.9606	−1.24378
$285$	1.73054	0.102508
$286$	18.5164	1.09490
$287$	−10.8244	−0.638944
$288$	−6.55022	−0.385975
$289$	38.4516	2.26186
$290$	−46.0318	−2.70308
$291$	−4.69984	−0.275509
$292$	27.1913	1.59125
$293$	14.5082	0.847576	0.423788	−	0.905762i	$-0.360700\pi$
$293$	14.5082	0.847576	0.423788	+	0.905762i	$0.360700\pi$
$294$	−3.06403	−0.178698
$295$	14.3504	0.835511
$296$	22.6263	1.31513
$297$	2.46463	0.143013
$298$	20.0258	1.16007
$299$	6.86516	0.397022
$300$	−1.24122	−0.0716619
$301$	6.99815	0.403367
$302$	−26.4273	−1.52072
$303$	4.95825	0.284844
$304$	5.67471	0.325467
$305$	−29.4994	−1.68913
$306$	−51.7693	−2.95945
$307$	5.57451	0.318154	0.159077	−	0.987266i	$-0.449148\pi$
$307$	5.57451	0.318154	0.159077	+	0.987266i	$0.449148\pi$
$308$	8.51259	0.485050
$309$	−1.72232	−0.0979794
$310$	−47.9299	−2.72223
$311$	0.894022	0.0506954	0.0253477	−	0.999679i	$-0.491931\pi$
$311$	0.894022	0.0506954	0.0253477	+	0.999679i	$0.491931\pi$
$312$	−7.78479	−0.440727
$313$	4.41311	0.249443	0.124722	−	0.992192i	$-0.460196\pi$
$313$	4.41311	0.249443	0.124722	+	0.992192i	$0.460196\pi$
$314$	33.1809	1.87251
$315$	12.2810	0.691954
$316$	−10.4571	−0.588260
$317$	−13.9641	−0.784300	−0.392150	−	0.919901i	$-0.628269\pi$
$317$	−13.9641	−0.784300	−0.392150	+	0.919901i	$0.628269\pi$
$318$	−0.339529	−0.0190399
$319$	−10.2934	−0.576321
$320$	25.8808	1.44678
$321$	5.47167	0.305399
$322$	4.84000	0.269723
$323$	−16.5383	−0.920213
$324$	30.3870	1.68817
$325$	−6.12088	−0.339526
$326$	−36.7824	−2.03719
$327$	−0.685844	−0.0379272
$328$	26.3439	1.45460
$329$	10.0462	0.553864
$330$	−2.46267	−0.135565
$331$	7.30618	0.401584	0.200792	−	0.979634i	$-0.435648\pi$
$331$	7.30618	0.401584	0.200792	+	0.979634i	$0.435648\pi$
$332$	−44.5254	−2.44365
$333$	15.6480	0.857503
$334$	11.0575	0.605039
$335$	6.89548	0.376740
$336$	−1.39502	−0.0761048
$337$	−32.1259	−1.75001	−0.875005	−	0.484114i	$-0.839142\pi$
$337$	−32.1259	−1.75001	−0.875005	+	0.484114i	$0.839142\pi$
$338$	−51.1276	−2.78098
$339$	−0.365158	−0.0198326
$340$	68.6313	3.72206
$341$	−10.7179	−0.580404
$342$	15.4400	0.834900
$343$	−19.0054	−1.02619
$344$	−17.0318	−0.918291
$345$	−0.913058	−0.0491574
$346$	−22.8589	−1.22890
$347$	17.6296	0.946406	0.473203	−	0.880954i	$-0.343098\pi$
$347$	17.6296	0.946406	0.473203	+	0.880954i	$0.343098\pi$
$348$	9.27728	0.497314
$349$	−16.7039	−0.894137	−0.447068	−	0.894500i	$-0.647532\pi$
$349$	−16.7039	−0.894137	−0.447068	+	0.894500i	$0.647532\pi$
$350$	−4.31528	−0.230661
$351$	−10.9541	−0.584689
$352$	2.97782	0.158718
$353$	8.89638	0.473507	0.236753	−	0.971570i	$-0.423917\pi$
$353$	8.89638	0.473507	0.236753	+	0.971570i	$0.423917\pi$
$354$	−4.43523	−0.235730
$355$	13.7473	0.729632
$356$	14.8722	0.788223
$357$	4.06563	0.215176
$358$	10.9549	0.578982
$359$	−0.461297	−0.0243463	−0.0121732	−	0.999926i	$-0.503875\pi$
$359$	−0.461297	−0.0243463	−0.0121732	+	0.999926i	$0.503875\pi$
$360$	−29.8888	−1.57528
$361$	−14.0675	−0.740396
$362$	−14.0328	−0.737545
$363$	2.93550	0.154074
$364$	−37.8345	−1.98306
$365$	−17.8338	−0.933462
$366$	9.11729	0.476568
$367$	−16.7506	−0.874376	−0.437188	−	0.899370i	$-0.644026\pi$
$367$	−16.7506	−0.874376	−0.437188	+	0.899370i	$0.644026\pi$
$368$	−2.99407	−0.156077
$369$	18.2190	0.948441
$370$	−31.8126	−1.65386
$371$	−0.769745	−0.0399632
$372$	9.65981	0.500838
$373$	−24.7730	−1.28270	−0.641349	−	0.767249i	$-0.721625\pi$
$373$	−24.7730	−1.28270	−0.641349	+	0.767249i	$0.721625\pi$
$374$	23.5350	1.21697
$375$	−3.08192	−0.159150
$376$	−24.4499	−1.26091
$377$	45.7495	2.35622
$378$	−7.72277	−0.397216
$379$	20.8200	1.06945	0.534725	−	0.845026i	$-0.320415\pi$
$379$	20.8200	1.06945	0.534725	+	0.845026i	$0.320415\pi$
$380$	−20.4690	−1.05004
$381$	−2.02091	−0.103534
$382$	61.4118	3.14210
$383$	17.0441	0.870912	0.435456	−	0.900210i	$-0.356587\pi$
$383$	17.0441	0.870912	0.435456	+	0.900210i	$0.356587\pi$
$384$	−6.56700	−0.335121
$385$	−5.58310	−0.284541
$386$	4.74545	0.241537
$387$	−11.7789	−0.598753
$388$	55.5904	2.82218
$389$	16.2639	0.824613	0.412306	−	0.911045i	$-0.364723\pi$
$389$	16.2639	0.824613	0.412306	+	0.911045i	$0.364723\pi$
$390$	10.9454	0.554242
$391$	8.72585	0.441285
$392$	16.9059	0.853878
$393$	4.66477	0.235306
$394$	−29.1386	−1.46798
$395$	6.85846	0.345086
$396$	−14.3279	−0.720003
$397$	10.3854	0.521231	0.260615	−	0.965443i	$-0.416075\pi$
$397$	10.3854	0.521231	0.260615	+	0.965443i	$0.416075\pi$
$398$	62.0934	3.11246
$399$	−1.21256	−0.0607039
$400$	2.66947	0.133474
$401$	−2.65065	−0.132367	−0.0661835	−	0.997807i	$-0.521082\pi$
$401$	−2.65065	−0.132367	−0.0661835	+	0.997807i	$0.521082\pi$
$402$	−2.13117	−0.106293
$403$	47.6358	2.37291
$404$	−58.6469	−2.91779
$405$	−19.9297	−0.990317
$406$	32.2538	1.60073
$407$	−7.11378	−0.352617
$408$	−9.89473	−0.489862
$409$	30.9306	1.52942	0.764709	−	0.644375i	$-0.222883\pi$
$409$	30.9306	1.52942	0.764709	+	0.644375i	$0.222883\pi$
$410$	−37.0395	−1.82925
$411$	3.43456	0.169414
$412$	20.3719	1.00365
$413$	−10.0551	−0.494778
$414$	−8.14639	−0.400373
$415$	29.2026	1.43350
$416$	−13.2350	−0.648900
$417$	−2.02142	−0.0989894
$418$	−7.01924	−0.343322
$419$	26.0461	1.27243	0.636217	−	0.771510i	$-0.280498\pi$
$419$	26.0461	1.27243	0.636217	+	0.771510i	$0.280498\pi$
$420$	5.03194	0.245534
$421$	−0.978836	−0.0477055	−0.0238528	−	0.999715i	$-0.507593\pi$
$421$	−0.978836	−0.0477055	−0.0238528	+	0.999715i	$0.507593\pi$
$422$	29.7944	1.45037
$423$	−16.9091	−0.822149
$424$	1.87337	0.0909788
$425$	−7.77985	−0.377378
$426$	−4.24884	−0.205857
$427$	20.6698	1.00028
$428$	−64.7197	−3.12835
$429$	2.44756	0.118169
$430$	23.9466	1.15481
$431$	24.1082	1.16125	0.580626	−	0.814171i	$-0.302808\pi$
$431$	24.1082	1.16125	0.580626	+	0.814171i	$0.302808\pi$
$432$	4.77738	0.229852
$433$	−22.3266	−1.07295	−0.536474	−	0.843917i	$-0.680244\pi$
$433$	−22.3266	−1.07295	−0.536474	+	0.843917i	$0.680244\pi$
$434$	33.5837	1.61207
$435$	−6.08463	−0.291736
$436$	8.11226	0.388507
$437$	−2.60245	−0.124492
$438$	5.51183	0.263365
$439$	29.1688	1.39215	0.696075	−	0.717969i	$-0.254928\pi$
$439$	29.1688	1.39215	0.696075	+	0.717969i	$0.254928\pi$
$440$	13.5879	0.647777
$441$	11.6918	0.556753
$442$	−104.602	−4.97542
$443$	31.5607	1.49949	0.749747	−	0.661725i	$-0.230175\pi$
$443$	31.5607	1.49949	0.749747	+	0.661725i	$0.230175\pi$
$444$	6.41152	0.304277
$445$	−9.75411	−0.462389
$446$	−10.7521	−0.509128
$447$	2.64708	0.125202
$448$	−18.1343	−0.856763
$449$	26.1367	1.23347	0.616733	−	0.787172i	$-0.288456\pi$
$449$	26.1367	1.23347	0.616733	+	0.787172i	$0.288456\pi$
$450$	7.26322	0.342391
$451$	−8.28259	−0.390012
$452$	4.31914	0.203155
$453$	−3.49324	−0.164127
$454$	−47.7879	−2.24280
$455$	24.8142	1.16331
$456$	2.95107	0.138196
$457$	33.5883	1.57119	0.785596	−	0.618739i	$-0.212356\pi$
$457$	33.5883	1.57119	0.785596	+	0.618739i	$0.212356\pi$
$458$	34.1648	1.59641
$459$	−13.9231	−0.649874
$460$	10.7998	0.503543
$461$	−40.3301	−1.87836	−0.939180	−	0.343426i	$-0.888413\pi$
$461$	−40.3301	−1.87836	−0.939180	+	0.343426i	$0.888413\pi$
$462$	1.72555	0.0802799
$463$	13.6447	0.634123	0.317061	−	0.948405i	$-0.397304\pi$
$463$	13.6447	0.634123	0.317061	+	0.948405i	$0.397304\pi$
$464$	−19.9525	−0.926271
$465$	−6.33551	−0.293802
$466$	60.4533	2.80045
$467$	−20.9111	−0.967650	−0.483825	−	0.875165i	$-0.660753\pi$
$467$	−20.9111	−0.967650	−0.483825	+	0.875165i	$0.660753\pi$
$468$	63.6807	2.94364
$469$	−4.83155	−0.223100
$470$	34.3765	1.58567
$471$	4.38595	0.202094
$472$	24.4716	1.12640
$473$	5.35483	0.246215
$474$	−2.11972	−0.0973621
$475$	2.32031	0.106463
$476$	−48.0889	−2.20415
$477$	1.29559	0.0593209
$478$	6.70224	0.306553
$479$	38.6442	1.76570	0.882849	−	0.469657i	$-0.155623\pi$
$479$	38.6442	1.76570	0.882849	+	0.469657i	$0.155623\pi$
$480$	1.76024	0.0803437
$481$	31.6174	1.44163
$482$	−2.70009	−0.122986
$483$	0.639765	0.0291103
$484$	−34.7216	−1.57825
$485$	−36.4597	−1.65555
$486$	19.6084	0.889455
$487$	−4.26731	−0.193370	−0.0966852	−	0.995315i	$-0.530824\pi$
$487$	−4.26731	−0.193370	−0.0966852	+	0.995315i	$0.530824\pi$
$488$	−50.3051	−2.27720
$489$	−4.86200	−0.219867
$490$	−23.7697	−1.07380
$491$	−1.49540	−0.0674863	−0.0337432	−	0.999431i	$-0.510743\pi$
$491$	−1.49540	−0.0674863	−0.0337432	+	0.999431i	$0.510743\pi$
$492$	7.46495	0.336546
$493$	58.1491	2.61890
$494$	31.1972	1.40363
$495$	9.39713	0.422370
$496$	−20.7752	−0.932834
$497$	−9.63252	−0.432078
$498$	−9.02556	−0.404445
$499$	−17.2631	−0.772802	−0.386401	−	0.922331i	$-0.626282\pi$
$499$	−17.2631	−0.772802	−0.386401	+	0.922331i	$0.626282\pi$
$500$	36.4534	1.63025
$501$	1.46161	0.0653000
$502$	−16.4962	−0.736262
$503$	21.2963	0.949553	0.474777	−	0.880106i	$-0.342529\pi$
$503$	21.2963	0.949553	0.474777	+	0.880106i	$0.342529\pi$
$504$	20.9426	0.932859
$505$	38.4644	1.71164
$506$	3.70346	0.164639
$507$	−6.75821	−0.300142
$508$	23.9037	1.06055
$509$	22.1525	0.981893	0.490946	−	0.871190i	$-0.336651\pi$
$509$	22.1525	0.981893	0.490946	+	0.871190i	$0.336651\pi$
$510$	13.9120	0.616032
$511$	12.4958	0.552783
$512$	27.1976	1.20197
$513$	4.15251	0.183338
$514$	4.80942	0.212134
$515$	−13.3612	−0.588764
$516$	−4.82621	−0.212462
$517$	7.68712	0.338079
$518$	22.2906	0.979391
$519$	−3.02155	−0.132632
$520$	−60.3917	−2.64835
$521$	30.0635	1.31710	0.658552	−	0.752535i	$-0.271169\pi$
$521$	30.0635	1.31710	0.658552	+	0.752535i	$0.271169\pi$
$522$	−54.2876	−2.37610
$523$	27.8356	1.21717	0.608583	−	0.793490i	$-0.291738\pi$
$523$	27.8356	1.21717	0.608583	+	0.793490i	$0.291738\pi$
$524$	−55.1756	−2.41036
$525$	−0.570406	−0.0248946
$526$	−40.2156	−1.75348
$527$	60.5468	2.63746
$528$	−1.06744	−0.0464545
$529$	−21.6269	−0.940300
$530$	−2.63395	−0.114412
$531$	16.9241	0.734444
$532$	14.3423	0.621819
$533$	36.8122	1.59451
$534$	3.01468	0.130458
$535$	42.4473	1.83516
$536$	11.7588	0.507903
$537$	1.44805	0.0624878
$538$	−22.4624	−0.968421
$539$	−5.31526	−0.228945
$540$	−17.2323	−0.741560
$541$	4.13399	0.177734	0.0888670	−	0.996044i	$-0.471675\pi$
$541$	4.13399	0.177734	0.0888670	+	0.996044i	$0.471675\pi$
$542$	45.2096	1.94192
$543$	−1.85489	−0.0796010
$544$	−16.8221	−0.721244
$545$	−5.32054	−0.227907
$546$	−7.66927	−0.328214
$547$	41.2325	1.76298	0.881488	−	0.472206i	$-0.156542\pi$
$547$	41.2325	1.76298	0.881488	+	0.472206i	$0.156542\pi$
$548$	−40.6245	−1.73539
$549$	−34.7901	−1.48480
$550$	−3.30196	−0.140796
$551$	−17.3428	−0.738826
$552$	−1.55703	−0.0662716
$553$	−4.80561	−0.204355
$554$	2.63801	0.112078
$555$	−4.20508	−0.178496
$556$	23.9097	1.01400
$557$	16.3474	0.692663	0.346331	−	0.938112i	$-0.387427\pi$
$557$	16.3474	0.692663	0.346331	+	0.938112i	$0.387427\pi$
$558$	−56.5261	−2.39294
$559$	−23.7997	−1.00662
$560$	−10.8221	−0.457318
$561$	3.11093	0.131344
$562$	−3.44904	−0.145489
$563$	−10.5134	−0.443088	−0.221544	−	0.975150i	$-0.571110\pi$
$563$	−10.5134	−0.443088	−0.221544	+	0.975150i	$0.571110\pi$
$564$	−6.92825	−0.291732
$565$	−2.83277	−0.119175
$566$	−22.0531	−0.926962
$567$	13.9645	0.586452
$568$	23.4432	0.983654
$569$	−33.8485	−1.41900	−0.709501	−	0.704704i	$-0.751080\pi$
$569$	−33.8485	−1.41900	−0.709501	+	0.704704i	$0.751080\pi$
$570$	−4.14919	−0.173791
$571$	1.21018	0.0506444	0.0253222	−	0.999679i	$-0.491939\pi$
$571$	1.21018	0.0506444	0.0253222	+	0.999679i	$0.491939\pi$
$572$	−28.9501	−1.21046
$573$	8.11760	0.339117
$574$	25.9530	1.08326
$575$	−1.22423	−0.0510541
$576$	30.5225	1.27177
$577$	12.0441	0.501401	0.250700	−	0.968065i	$-0.419339\pi$
$577$	12.0441	0.501401	0.250700	+	0.968065i	$0.419339\pi$
$578$	−92.1930	−3.83472
$579$	0.627268	0.0260684
$580$	71.9699	2.98839
$581$	−20.4618	−0.848899
$582$	11.2685	0.467094
$583$	−0.588992	−0.0243936
$584$	−30.4118	−1.25845
$585$	−41.7658	−1.72680
$586$	−34.7853	−1.43697
$587$	−30.0503	−1.24031	−0.620154	−	0.784480i	$-0.712930\pi$
$587$	−30.0503	−1.24031	−0.620154	+	0.784480i	$0.712930\pi$
$588$	4.79055	0.197559
$589$	−18.0579	−0.744061
$590$	−34.4070	−1.41651
$591$	−3.85162	−0.158435
$592$	−13.7892	−0.566731
$593$	6.32716	0.259825	0.129913	−	0.991525i	$-0.458530\pi$
$593$	6.32716	0.259825	0.129913	+	0.991525i	$0.458530\pi$
$594$	−5.90930	−0.242461
$595$	31.5397	1.29300
$596$	−31.3100	−1.28251
$597$	8.20769	0.335918
$598$	−16.4601	−0.673106
$599$	−37.9882	−1.55216	−0.776079	−	0.630636i	$-0.782794\pi$
$599$	−37.9882	−1.55216	−0.776079	+	0.630636i	$0.782794\pi$
$600$	1.38823	0.0566742
$601$	23.9352	0.976336	0.488168	−	0.872750i	$-0.337665\pi$
$601$	23.9352	0.976336	0.488168	+	0.872750i	$0.337665\pi$
$602$	−16.7790	−0.683862
$603$	8.13218	0.331168
$604$	41.3185	1.68123
$605$	22.7726	0.925839
$606$	−11.8881	−0.482920
$607$	−19.7729	−0.802559	−0.401279	−	0.915956i	$-0.631434\pi$
$607$	−19.7729	−0.802559	−0.401279	+	0.915956i	$0.631434\pi$
$608$	5.01714	0.203472
$609$	4.26340	0.172762
$610$	70.7288	2.86373
$611$	−34.1656	−1.38219
$612$	80.9403	3.27182
$613$	−27.2775	−1.10173	−0.550863	−	0.834596i	$-0.685701\pi$
$613$	−27.2775	−1.10173	−0.550863	+	0.834596i	$0.685701\pi$
$614$	−13.3656	−0.539393
$615$	−4.89599	−0.197425
$616$	−9.52081	−0.383604
$617$	3.16648	0.127478	0.0637388	−	0.997967i	$-0.479698\pi$
$617$	3.16648	0.127478	0.0637388	+	0.997967i	$0.479698\pi$
$618$	4.12950	0.166113
$619$	−32.8049	−1.31854	−0.659270	−	0.751906i	$-0.729135\pi$
$619$	−32.8049	−1.31854	−0.659270	+	0.751906i	$0.729135\pi$
$620$	74.9374	3.00956
$621$	−2.19093	−0.0879190
$622$	−2.14354	−0.0859481
$623$	6.83455	0.273821
$624$	4.74428	0.189923
$625$	−29.1323	−1.16529
$626$	−10.5810	−0.422903
$627$	−0.927824	−0.0370537
$628$	−51.8777	−2.07015
$629$	40.1868	1.60235
$630$	−29.4453	−1.17313
$631$	8.68468	0.345732	0.172866	−	0.984945i	$-0.444697\pi$
$631$	8.68468	0.345732	0.172866	+	0.984945i	$0.444697\pi$
$632$	11.6957	0.465229
$633$	3.93832	0.156534
$634$	33.4807	1.32969
$635$	−15.6775	−0.622144
$636$	0.530848	0.0210495
$637$	23.6238	0.936011
$638$	24.6799	0.977086
$639$	16.2129	0.641372
$640$	−50.9445	−2.01376
$641$	20.1443	0.795650	0.397825	−	0.917461i	$-0.369765\pi$
$641$	20.1443	0.795650	0.397825	+	0.917461i	$0.369765\pi$
$642$	−13.1191	−0.517768
$643$	−5.84165	−0.230372	−0.115186	−	0.993344i	$-0.536746\pi$
$643$	−5.84165	−0.230372	−0.115186	+	0.993344i	$0.536746\pi$
$644$	−7.56724	−0.298191
$645$	3.16534	0.124635
$646$	39.6527	1.56011
$647$	−35.7973	−1.40734	−0.703668	−	0.710529i	$-0.748456\pi$
$647$	−35.7973	−1.40734	−0.703668	+	0.710529i	$0.748456\pi$
$648$	−33.9860	−1.33510
$649$	−7.69393	−0.302013
$650$	14.6757	0.575626
$651$	4.43919	0.173986
$652$	57.5085	2.25221
$653$	−17.2329	−0.674374	−0.337187	−	0.941438i	$-0.609476\pi$
$653$	−17.2329	−0.674374	−0.337187	+	0.941438i	$0.609476\pi$
$654$	1.64440	0.0643013
$655$	36.1876	1.41397
$656$	−16.0547	−0.626832
$657$	−21.0322	−0.820546
$658$	−24.0871	−0.939012
$659$	21.6584	0.843691	0.421845	−	0.906668i	$-0.361382\pi$
$659$	21.6584	0.843691	0.421845	+	0.906668i	$0.361382\pi$
$660$	3.85033	0.149874
$661$	−0.404780	−0.0157441	−0.00787206	−	0.999969i	$-0.502506\pi$
$661$	−0.404780	−0.0157441	−0.00787206	+	0.999969i	$0.502506\pi$
$662$	−17.5176	−0.680839
$663$	−13.8266	−0.536982
$664$	49.7990	1.93257
$665$	−9.40661	−0.364773
$666$	−37.5181	−1.45380
$667$	9.15032	0.354302
$668$	−17.2882	−0.668900
$669$	−1.42125	−0.0549487
$670$	−16.5328	−0.638720
$671$	15.8160	0.610572
$672$	−1.23337	−0.0475784
$673$	21.3509	0.823016	0.411508	−	0.911406i	$-0.365002\pi$
$673$	21.3509	0.823016	0.411508	+	0.911406i	$0.365002\pi$
$674$	77.0262	2.96694
$675$	1.95341	0.0751866
$676$	79.9371	3.07450
$677$	−3.71286	−0.142697	−0.0713484	−	0.997451i	$-0.522730\pi$
$677$	−3.71286	−0.142697	−0.0713484	+	0.997451i	$0.522730\pi$
$678$	0.875515	0.0336239
$679$	25.5468	0.980394
$680$	−76.7599	−2.94361
$681$	−6.31674	−0.242058
$682$	25.6975	0.984009
$683$	−31.5780	−1.20830	−0.604149	−	0.796871i	$-0.706487\pi$
$683$	−31.5780	−1.20830	−0.604149	+	0.796871i	$0.706487\pi$
$684$	−24.1401	−0.923022
$685$	26.6441	1.01802
$686$	45.5680	1.73979
$687$	4.51600	0.172296
$688$	10.3797	0.395721
$689$	2.61779	0.0997300
$690$	2.18918	0.0833407
$691$	0.752503	0.0286266	0.0143133	−	0.999898i	$-0.495444\pi$
$691$	0.752503	0.0286266	0.0143133	+	0.999898i	$0.495444\pi$
$692$	35.7394	1.35861
$693$	−6.58442	−0.250121
$694$	−42.2693	−1.60452
$695$	−15.6815	−0.594832
$696$	−10.3761	−0.393304
$697$	46.7896	1.77228
$698$	40.0498	1.51591
$699$	7.99090	0.302244
$700$	6.74686	0.255007
$701$	47.5913	1.79750	0.898750	−	0.438462i	$-0.144476\pi$
$701$	47.5913	1.79750	0.898750	+	0.438462i	$0.144476\pi$
$702$	26.2640	0.991273
$703$	−11.9856	−0.452044
$704$	−13.8759	−0.522969
$705$	4.54399	0.171137
$706$	−21.3303	−0.802776
$707$	−26.9514	−1.01361
$708$	6.93440	0.260611
$709$	22.0899	0.829602	0.414801	−	0.909912i	$-0.363851\pi$
$709$	22.0899	0.829602	0.414801	+	0.909912i	$0.363851\pi$
$710$	−32.9610	−1.23701
$711$	8.08852	0.303343
$712$	−16.6336	−0.623371
$713$	9.52761	0.356812
$714$	−9.74789	−0.364806
$715$	18.9873	0.710086
$716$	−17.1277	−0.640093
$717$	0.885922	0.0330854
$718$	1.10602	0.0412764
$719$	9.63281	0.359243	0.179622	−	0.983736i	$-0.442513\pi$
$719$	9.63281	0.359243	0.179622	+	0.983736i	$0.442513\pi$
$720$	18.2151	0.678838
$721$	9.36196	0.348658
$722$	33.7288	1.25526
$723$	−0.356906	−0.0132735
$724$	21.9399	0.815392
$725$	−8.15830	−0.302992
$726$	−7.03827	−0.261215
$727$	−20.3417	−0.754430	−0.377215	−	0.926126i	$-0.623118\pi$
$727$	−20.3417	−0.754430	−0.377215	+	0.926126i	$0.623118\pi$
$728$	42.3155	1.56832
$729$	−21.7264	−0.804682
$730$	42.7589	1.58258
$731$	−30.2502	−1.11885
$732$	−14.2547	−0.526869
$733$	−35.2902	−1.30347	−0.651736	−	0.758446i	$-0.725959\pi$
$733$	−35.2902	−1.30347	−0.651736	+	0.758446i	$0.725959\pi$
$734$	40.1619	1.48240
$735$	−3.14195	−0.115892
$736$	−2.64713	−0.0975743
$737$	−3.69700	−0.136181
$738$	−43.6824	−1.60797
$739$	−26.9971	−0.993104	−0.496552	−	0.868007i	$-0.665401\pi$
$739$	−26.9971	−0.993104	−0.496552	+	0.868007i	$0.665401\pi$
$740$	49.7383	1.82842
$741$	4.12374	0.151489
$742$	1.84557	0.0677529
$743$	−9.23421	−0.338770	−0.169385	−	0.985550i	$-0.554178\pi$
$743$	−9.23421	−0.338770	−0.169385	+	0.985550i	$0.554178\pi$
$744$	−10.8039	−0.396090
$745$	20.5351	0.752348
$746$	59.3966	2.17467
$747$	34.4401	1.26010
$748$	−36.7966	−1.34542
$749$	−29.7422	−1.08675
$750$	7.38933	0.269820
$751$	−28.5403	−1.04145	−0.520726	−	0.853724i	$-0.674339\pi$
$751$	−28.5403	−1.04145	−0.520726	+	0.853724i	$0.674339\pi$
$752$	14.9005	0.543365
$753$	−2.18052	−0.0794626
$754$	−109.691	−3.99469
$755$	−27.0993	−0.986246
$756$	12.0744	0.439142
$757$	5.42608	0.197214	0.0986071	−	0.995126i	$-0.468561\pi$
$757$	5.42608	0.197214	0.0986071	+	0.995126i	$0.468561\pi$
$758$	−49.9187	−1.81313
$759$	0.489535	0.0177690
$760$	22.8934	0.830430
$761$	3.98220	0.144354	0.0721772	−	0.997392i	$-0.477005\pi$
$761$	3.98220	0.144354	0.0721772	+	0.997392i	$0.477005\pi$
$762$	4.84541	0.175531
$763$	3.72802	0.134963
$764$	−96.0162	−3.47374
$765$	−53.0858	−1.91932
$766$	−40.8655	−1.47653
$767$	34.1959	1.23474
$768$	9.07295	0.327392
$769$	−52.0690	−1.87765	−0.938827	−	0.344388i	$-0.888087\pi$
$769$	−52.0690	−1.87765	−0.938827	+	0.344388i	$0.888087\pi$
$770$	13.3862	0.482406
$771$	0.635723	0.0228950
$772$	−7.41943	−0.267031
$773$	28.4037	1.02161	0.510804	−	0.859697i	$-0.329348\pi$
$773$	28.4037	1.02161	0.510804	+	0.859697i	$0.329348\pi$
$774$	28.2414	1.01512
$775$	−8.49469	−0.305138
$776$	−62.1745	−2.23193
$777$	2.94643	0.105703
$778$	−38.9949	−1.39804
$779$	−13.9548	−0.499983
$780$	−17.1129	−0.612741
$781$	−7.37060	−0.263741
$782$	−20.9214	−0.748148
$783$	−14.6004	−0.521775
$784$	−10.3030	−0.367963
$785$	34.0247	1.21439
$786$	−11.1844	−0.398935
$787$	23.4048	0.834290	0.417145	−	0.908840i	$-0.363031\pi$
$787$	23.4048	0.834290	0.417145	+	0.908840i	$0.363031\pi$
$788$	45.5576	1.62292
$789$	−5.31582	−0.189248
$790$	−16.4441	−0.585054
$791$	1.98487	0.0705740
$792$	16.0249	0.569418
$793$	−70.2949	−2.49625
$794$	−24.9005	−0.883686
$795$	−0.348164	−0.0123481
$796$	−97.0819	−3.44098
$797$	40.2926	1.42724	0.713619	−	0.700534i	$-0.247055\pi$
$797$	40.2926	1.42724	0.713619	+	0.700534i	$0.247055\pi$
$798$	2.90727	0.102916
$799$	−43.4257	−1.53629
$800$	2.36014	0.0834436
$801$	−11.5035	−0.406456
$802$	6.35529	0.224413
$803$	9.56154	0.337419
$804$	3.33204	0.117512
$805$	4.96308	0.174926
$806$	−114.213	−4.02300
$807$	−2.96914	−0.104519
$808$	65.5930	2.30755
$809$	−8.85900	−0.311466	−0.155733	−	0.987799i	$-0.549774\pi$
$809$	−8.85900	−0.311466	−0.155733	+	0.987799i	$0.549774\pi$
$810$	47.7843	1.67897
$811$	−34.4578	−1.20998	−0.604988	−	0.796234i	$-0.706822\pi$
$811$	−34.4578	−1.20998	−0.604988	+	0.796234i	$0.706822\pi$
$812$	−50.4282	−1.76968
$813$	5.97594	0.209585
$814$	17.0563	0.597821
$815$	−37.7177	−1.32119
$816$	6.03014	0.211097
$817$	9.02202	0.315641
$818$	−74.1603	−2.59295
$819$	29.2647	1.02259
$820$	57.9105	2.02232
$821$	−45.6000	−1.59145	−0.795725	−	0.605658i	$-0.792910\pi$
$821$	−45.6000	−1.59145	−0.795725	+	0.605658i	$0.792910\pi$
$822$	−8.23483	−0.287223
$823$	22.5036	0.784425	0.392212	−	0.919875i	$-0.371710\pi$
$823$	22.5036	0.784425	0.392212	+	0.919875i	$0.371710\pi$
$824$	−22.7847	−0.793743
$825$	−0.436463	−0.0151957
$826$	24.1084	0.838840
$827$	11.3072	0.393190	0.196595	−	0.980485i	$-0.437012\pi$
$827$	11.3072	0.393190	0.196595	+	0.980485i	$0.437012\pi$
$828$	12.7367	0.442632
$829$	−25.2486	−0.876921	−0.438460	−	0.898750i	$-0.644476\pi$
$829$	−25.2486	−0.876921	−0.438460	+	0.898750i	$0.644476\pi$
$830$	−70.0172	−2.43033
$831$	0.348700	0.0120963
$832$	61.6720	2.13809
$833$	30.0267	1.04036
$834$	4.84663	0.167825
$835$	11.3387	0.392391
$836$	10.9744	0.379559
$837$	−15.2024	−0.525472
$838$	−62.4490	−2.15726
$839$	−55.5513	−1.91784	−0.958921	−	0.283672i	$-0.908447\pi$
$839$	−55.5513	−1.91784	−0.958921	+	0.283672i	$0.908447\pi$
$840$	−5.62792	−0.194182
$841$	31.9778	1.10268
$842$	2.34689	0.0808792
$843$	−0.455905	−0.0157022
$844$	−46.5830	−1.60345
$845$	−52.4278	−1.80357
$846$	40.5419	1.39386
$847$	−15.9564	−0.548269
$848$	−1.14169	−0.0392057
$849$	−2.91505	−0.100044
$850$	18.6532	0.639801
$851$	6.32378	0.216776
$852$	6.64298	0.227585
$853$	3.31467	0.113492	0.0567461	−	0.998389i	$-0.481927\pi$
$853$	3.31467	0.113492	0.0567461	+	0.998389i	$0.481927\pi$
$854$	−49.5585	−1.69586
$855$	15.8326	0.541465
$856$	72.3851	2.47407
$857$	22.1081	0.755198	0.377599	−	0.925969i	$-0.376750\pi$
$857$	22.1081	0.755198	0.377599	+	0.925969i	$0.376750\pi$
$858$	−5.86836	−0.200342
$859$	7.57946	0.258608	0.129304	−	0.991605i	$-0.458726\pi$
$859$	7.57946	0.258608	0.129304	+	0.991605i	$0.458726\pi$
$860$	−37.4401	−1.27670
$861$	3.43054	0.116912
$862$	−57.8027	−1.96877
$863$	−51.1594	−1.74149	−0.870743	−	0.491738i	$-0.836362\pi$
$863$	−51.1594	−1.74149	−0.870743	+	0.491738i	$0.836362\pi$
$864$	4.22379	0.143696
$865$	−23.4402	−0.796990
$866$	53.5310	1.81906
$867$	−12.1863	−0.413870
$868$	−52.5075	−1.78222
$869$	−3.67715	−0.124739
$870$	14.5887	0.494604
$871$	16.4314	0.556758
$872$	−9.07307	−0.307253
$873$	−42.9988	−1.45529
$874$	6.23973	0.211062
$875$	16.7523	0.566331
$876$	−8.61764	−0.291163
$877$	−25.9157	−0.875112	−0.437556	−	0.899191i	$-0.644156\pi$
$877$	−25.9157	−0.875112	−0.437556	+	0.899191i	$0.644156\pi$
$878$	−69.9361	−2.36023
$879$	−4.59802	−0.155087
$880$	−8.28085	−0.279147
$881$	3.63835	0.122579	0.0612895	−	0.998120i	$-0.480479\pi$
$881$	3.63835	0.122579	0.0612895	+	0.998120i	$0.480479\pi$
$882$	−28.0327	−0.943911
$883$	−13.0158	−0.438018	−0.219009	−	0.975723i	$-0.570282\pi$
$883$	−13.0158	−0.438018	−0.219009	+	0.975723i	$0.570282\pi$
$884$	163.543	5.50056
$885$	−4.54802	−0.152880
$886$	−75.6710	−2.54222
$887$	−20.0329	−0.672640	−0.336320	−	0.941748i	$-0.609182\pi$
$887$	−20.0329	−0.672640	−0.336320	+	0.941748i	$0.609182\pi$
$888$	−7.17089	−0.240639
$889$	10.9850	0.368425
$890$	23.3868	0.783928
$891$	10.6853	0.357971
$892$	16.8108	0.562866
$893$	12.9515	0.433407
$894$	−6.34672	−0.212266
$895$	11.2334	0.375493
$896$	35.6960	1.19252
$897$	−2.17575	−0.0726462
$898$	−62.6662	−2.09120
$899$	63.4921	2.11758
$900$	−11.3559	−0.378530
$901$	3.32730	0.110849
$902$	19.8586	0.661220
$903$	−2.21790	−0.0738071
$904$	−4.83069	−0.160667
$905$	−14.3896	−0.478327
$906$	8.37551	0.278258
$907$	−6.75194	−0.224195	−0.112097	−	0.993697i	$-0.535757\pi$
$907$	−6.75194	−0.224195	−0.112097	+	0.993697i	$0.535757\pi$
$908$	74.7154	2.47952
$909$	45.3629	1.50459
$910$	−59.4955	−1.97226
$911$	−57.5089	−1.90536	−0.952678	−	0.303981i	$-0.901684\pi$
$911$	−57.5089	−1.90536	−0.952678	+	0.303981i	$0.901684\pi$
$912$	−1.79847	−0.0595532
$913$	−15.6569	−0.518169
$914$	−80.5324	−2.66378
$915$	9.34914	0.309073
$916$	−53.4160	−1.76491
$917$	−25.3561	−0.837332
$918$	33.3825	1.10179
$919$	−33.3230	−1.09922	−0.549611	−	0.835420i	$-0.685224\pi$
$919$	−33.3230	−1.09922	−0.549611	+	0.835420i	$0.685224\pi$
$920$	−12.0789	−0.398230
$921$	−1.76671	−0.0582151
$922$	96.6969	3.18454
$923$	32.7588	1.07827
$924$	−2.69787	−0.0887533
$925$	−5.63820	−0.185383
$926$	−32.7150	−1.07508
$927$	−15.7575	−0.517544
$928$	−17.6405	−0.579077
$929$	−40.1759	−1.31813	−0.659064	−	0.752086i	$-0.729048\pi$
$929$	−40.1759	−1.31813	−0.659064	+	0.752086i	$0.729048\pi$
$930$	15.1903	0.498108
$931$	−8.95536	−0.293500
$932$	−94.5176	−3.09603
$933$	−0.283340	−0.00927612
$934$	50.1372	1.64054
$935$	24.1335	0.789251
$936$	−71.2230	−2.32800
$937$	7.15920	0.233881	0.116940	−	0.993139i	$-0.462691\pi$
$937$	7.15920	0.233881	0.116940	+	0.993139i	$0.462691\pi$
$938$	11.5843	0.378241
$939$	−1.39863	−0.0456426
$940$	−53.7470	−1.75303
$941$	−30.0216	−0.978675	−0.489337	−	0.872095i	$-0.662761\pi$
$941$	−30.0216	−0.978675	−0.489337	+	0.872095i	$0.662761\pi$
$942$	−10.5159	−0.342627
$943$	7.36279	0.239765
$944$	−14.9137	−0.485400
$945$	−7.91916	−0.257610
$946$	−12.8389	−0.417430
$947$	33.6017	1.09191	0.545954	−	0.837815i	$-0.316167\pi$
$947$	33.6017	1.09191	0.545954	+	0.837815i	$0.316167\pi$
$948$	3.31415	0.107638
$949$	−42.4966	−1.37950
$950$	−5.56326	−0.180496
$951$	4.42558	0.143509
$952$	53.7845	1.74316
$953$	52.7230	1.70787	0.853933	−	0.520382i	$-0.174211\pi$
$953$	52.7230	1.70787	0.853933	+	0.520382i	$0.174211\pi$
$954$	−3.10635	−0.100572
$955$	62.9735	2.03778
$956$	−10.4788	−0.338909
$957$	3.26226	0.105454
$958$	−92.6547	−2.99354
$959$	−18.6691	−0.602857
$960$	−8.20231	−0.264728
$961$	35.1100	1.13258
$962$	−75.8070	−2.44412
$963$	50.0602	1.61317
$964$	4.22154	0.135967
$965$	4.86613	0.156646
$966$	−1.53392	−0.0493532
$967$	−19.6112	−0.630654	−0.315327	−	0.948983i	$-0.602114\pi$
$967$	−19.6112	−0.630654	−0.315327	+	0.948983i	$0.602114\pi$
$968$	38.8340	1.24817
$969$	5.24141	0.168378
$970$	87.4172	2.80680
$971$	9.87024	0.316751	0.158376	−	0.987379i	$-0.449374\pi$
$971$	9.87024	0.316751	0.158376	+	0.987379i	$0.449374\pi$
$972$	−30.6574	−0.983335
$973$	10.9878	0.352252
$974$	10.2315	0.327837
$975$	1.93987	0.0621256
$976$	30.6574	0.981319
$977$	17.6805	0.565648	0.282824	−	0.959172i	$-0.408729\pi$
$977$	17.6805	0.565648	0.282824	+	0.959172i	$0.408729\pi$
$978$	11.6573	0.372760
$979$	5.22965	0.167140
$980$	37.1634	1.18714
$981$	−6.27477	−0.200338
$982$	3.58542	0.114415
$983$	42.0208	1.34025	0.670127	−	0.742247i	$-0.266240\pi$
$983$	42.0208	1.34025	0.670127	+	0.742247i	$0.266240\pi$
$984$	−8.34909	−0.266159
$985$	−29.8796	−0.952043
$986$	−139.420	−4.44005
$987$	−3.18390	−0.101345
$988$	−48.7762	−1.55178
$989$	−4.76016	−0.151364
$990$	−22.5309	−0.716079
$991$	−2.91463	−0.0925863	−0.0462932	−	0.998928i	$-0.514741\pi$
$991$	−2.91463	−0.0925863	−0.0462932	+	0.998928i	$0.514741\pi$
$992$	−18.3678	−0.583179
$993$	−2.31552	−0.0734809
$994$	23.0953	0.732538
$995$	63.6725	2.01855
$996$	14.1113	0.447134
$997$	−48.4339	−1.53392	−0.766958	−	0.641697i	$-0.778231\pi$
$997$	−48.4339	−1.53392	−0.766958	+	0.641697i	$0.778231\pi$
$998$	41.3906	1.31020
$999$	−10.0903	−0.319243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.16	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.39764 q^{2} -0.316927 q^{3} +3.74866 q^{4} -2.45861 q^{5} +0.759875 q^{6} +1.72271 q^{7} -4.19265 q^{8} -2.89956 q^{9} +O(q^{10})\)	\(q-2.39764 q^{2} -0.316927 q^{3} +3.74866 q^{4} -2.45861 q^{5} +0.759875 q^{6} +1.72271 q^{7} -4.19265 q^{8} -2.89956 q^{9} +5.89485 q^{10} +1.31818 q^{11} -1.18805 q^{12} -5.85869 q^{13} -4.13043 q^{14} +0.779199 q^{15} +2.55512 q^{16} -7.44659 q^{17} +6.95208 q^{18} +2.22092 q^{19} -9.21648 q^{20} -0.545972 q^{21} -3.16051 q^{22} -1.17179 q^{23} +1.32876 q^{24} +1.04475 q^{25} +14.0470 q^{26} +1.86973 q^{27} +6.45784 q^{28} -7.80883 q^{29} -1.86823 q^{30} -8.13081 q^{31} +2.25904 q^{32} -0.417766 q^{33} +17.8542 q^{34} -4.23546 q^{35} -10.8694 q^{36} -5.39667 q^{37} -5.32495 q^{38} +1.85677 q^{39} +10.3081 q^{40} -6.28336 q^{41} +1.30904 q^{42} +4.06230 q^{43} +4.94140 q^{44} +7.12888 q^{45} +2.80953 q^{46} +5.83162 q^{47} -0.809786 q^{48} -4.03228 q^{49} -2.50494 q^{50} +2.36002 q^{51} -21.9622 q^{52} -0.446823 q^{53} -4.48293 q^{54} -3.24088 q^{55} -7.22270 q^{56} -0.703868 q^{57} +18.7227 q^{58} -5.83679 q^{59} +2.92095 q^{60} +11.9984 q^{61} +19.4947 q^{62} -4.99509 q^{63} -10.5266 q^{64} +14.4042 q^{65} +1.00165 q^{66} -2.80463 q^{67} -27.9147 q^{68} +0.371372 q^{69} +10.1551 q^{70} -5.59150 q^{71} +12.1568 q^{72} +7.25360 q^{73} +12.9393 q^{74} -0.331110 q^{75} +8.32546 q^{76} +2.27084 q^{77} -4.45187 q^{78} -2.78957 q^{79} -6.28204 q^{80} +8.10611 q^{81} +15.0652 q^{82} -11.8777 q^{83} -2.04666 q^{84} +18.3082 q^{85} -9.73991 q^{86} +2.47483 q^{87} -5.52665 q^{88} +3.96733 q^{89} -17.0924 q^{90} -10.0928 q^{91} -4.39265 q^{92} +2.57687 q^{93} -13.9821 q^{94} -5.46037 q^{95} -0.715951 q^{96} +14.8294 q^{97} +9.66794 q^{98} -3.82213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 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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