LMFDB - Embedded newform 4017.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65538 q^{2} +1.00000 q^{3} +5.05105 q^{4} -1.68203 q^{5} -2.65538 q^{6} -3.96430 q^{7} -8.10171 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65538 q^{2} +1.00000 q^{3} +5.05105 q^{4} -1.68203 q^{5} -2.65538 q^{6} -3.96430 q^{7} -8.10171 q^{8} +1.00000 q^{9} +4.46642 q^{10} -5.81798 q^{11} +5.05105 q^{12} -1.00000 q^{13} +10.5267 q^{14} -1.68203 q^{15} +11.4110 q^{16} -3.34963 q^{17} -2.65538 q^{18} -4.92265 q^{19} -8.49600 q^{20} -3.96430 q^{21} +15.4490 q^{22} +2.84741 q^{23} -8.10171 q^{24} -2.17079 q^{25} +2.65538 q^{26} +1.00000 q^{27} -20.0239 q^{28} -9.70385 q^{29} +4.46642 q^{30} +8.23300 q^{31} -14.0972 q^{32} -5.81798 q^{33} +8.89454 q^{34} +6.66805 q^{35} +5.05105 q^{36} +1.17976 q^{37} +13.0715 q^{38} -1.00000 q^{39} +13.6273 q^{40} -4.01432 q^{41} +10.5267 q^{42} -5.10473 q^{43} -29.3869 q^{44} -1.68203 q^{45} -7.56096 q^{46} -0.541846 q^{47} +11.4110 q^{48} +8.71564 q^{49} +5.76427 q^{50} -3.34963 q^{51} -5.05105 q^{52} -12.5492 q^{53} -2.65538 q^{54} +9.78600 q^{55} +32.1176 q^{56} -4.92265 q^{57} +25.7674 q^{58} -3.30260 q^{59} -8.49600 q^{60} -10.0355 q^{61} -21.8618 q^{62} -3.96430 q^{63} +14.6114 q^{64} +1.68203 q^{65} +15.4490 q^{66} -12.0308 q^{67} -16.9191 q^{68} +2.84741 q^{69} -17.7062 q^{70} -13.8283 q^{71} -8.10171 q^{72} +9.72233 q^{73} -3.13270 q^{74} -2.17079 q^{75} -24.8646 q^{76} +23.0642 q^{77} +2.65538 q^{78} -9.63575 q^{79} -19.1936 q^{80} +1.00000 q^{81} +10.6595 q^{82} +7.71568 q^{83} -20.0239 q^{84} +5.63416 q^{85} +13.5550 q^{86} -9.70385 q^{87} +47.1356 q^{88} -15.8964 q^{89} +4.46642 q^{90} +3.96430 q^{91} +14.3824 q^{92} +8.23300 q^{93} +1.43881 q^{94} +8.28003 q^{95} -14.0972 q^{96} +12.2772 q^{97} -23.1433 q^{98} -5.81798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	−2.65538	−1.87764	−0.938819	−	0.344410i	$-0.888079\pi$
$2$	−2.65538	−1.87764	−0.938819	+	0.344410i	$0.888079\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.05105	2.52553
$5$	−1.68203	−0.752225	−0.376113	−	0.926574i	$-0.622739\pi$
$5$	−1.68203	−0.752225	−0.376113	+	0.926574i	$0.622739\pi$
$6$	−2.65538	−1.08406
$7$	−3.96430	−1.49836	−0.749181	−	0.662365i	$-0.769553\pi$
$7$	−3.96430	−1.49836	−0.749181	+	0.662365i	$0.769553\pi$
$8$	−8.10171	−2.86439
$9$	1.00000	0.333333
$10$	4.46642	1.41241
$11$	−5.81798	−1.75419	−0.877094	−	0.480319i	$-0.840521\pi$
$11$	−5.81798	−1.75419	−0.877094	+	0.480319i	$0.840521\pi$
$12$	5.05105	1.45811
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	10.5267	2.81338
$15$	−1.68203	−0.434297
$16$	11.4110	2.85275
$17$	−3.34963	−0.812404	−0.406202	−	0.913783i	$-0.633147\pi$
$17$	−3.34963	−0.812404	−0.406202	+	0.913783i	$0.633147\pi$
$18$	−2.65538	−0.625879
$19$	−4.92265	−1.12933	−0.564667	−	0.825319i	$-0.690995\pi$
$19$	−4.92265	−1.12933	−0.564667	+	0.825319i	$0.690995\pi$
$20$	−8.49600	−1.89976
$21$	−3.96430	−0.865080
$22$	15.4490	3.29373
$23$	2.84741	0.593726	0.296863	−	0.954920i	$-0.404059\pi$
$23$	2.84741	0.593726	0.296863	+	0.954920i	$0.404059\pi$
$24$	−8.10171	−1.65375
$25$	−2.17079	−0.434158
$26$	2.65538	0.520763
$27$	1.00000	0.192450
$28$	−20.0239	−3.78415
$29$	−9.70385	−1.80196	−0.900980	−	0.433861i	$-0.857151\pi$
$29$	−9.70385	−1.80196	−0.900980	+	0.433861i	$0.857151\pi$
$30$	4.46642	0.815453
$31$	8.23300	1.47869	0.739345	−	0.673326i	$-0.235135\pi$
$31$	8.23300	1.47869	0.739345	+	0.673326i	$0.235135\pi$
$32$	−14.0972	−2.49206
$33$	−5.81798	−1.01278
$34$	8.89454	1.52540
$35$	6.66805	1.12711
$36$	5.05105	0.841842
$37$	1.17976	0.193951	0.0969753	−	0.995287i	$-0.469083\pi$
$37$	1.17976	0.193951	0.0969753	+	0.995287i	$0.469083\pi$
$38$	13.0715	2.12048
$39$	−1.00000	−0.160128
$40$	13.6273	2.15466
$41$	−4.01432	−0.626931	−0.313465	−	0.949600i	$-0.601490\pi$
$41$	−4.01432	−0.626931	−0.313465	+	0.949600i	$0.601490\pi$
$42$	10.5267	1.62431
$43$	−5.10473	−0.778464	−0.389232	−	0.921140i	$-0.627260\pi$
$43$	−5.10473	−0.778464	−0.389232	+	0.921140i	$0.627260\pi$
$44$	−29.3869	−4.43025
$45$	−1.68203	−0.250742
$46$	−7.56096	−1.11480
$47$	−0.541846	−0.0790363	−0.0395182	−	0.999219i	$-0.512582\pi$
$47$	−0.541846	−0.0790363	−0.0395182	+	0.999219i	$0.512582\pi$
$48$	11.4110	1.64704
$49$	8.71564	1.24509
$50$	5.76427	0.815191
$51$	−3.34963	−0.469041
$52$	−5.05105	−0.700455
$53$	−12.5492	−1.72377	−0.861885	−	0.507105i	$-0.830716\pi$
$53$	−12.5492	−1.72377	−0.861885	+	0.507105i	$0.830716\pi$
$54$	−2.65538	−0.361352
$55$	9.78600	1.31954
$56$	32.1176	4.29189
$57$	−4.92265	−0.652021
$58$	25.7674	3.38343
$59$	−3.30260	−0.429962	−0.214981	−	0.976618i	$-0.568969\pi$
$59$	−3.30260	−0.429962	−0.214981	+	0.976618i	$0.568969\pi$
$60$	−8.49600	−1.09683
$61$	−10.0355	−1.28491	−0.642455	−	0.766324i	$-0.722084\pi$
$61$	−10.0355	−1.28491	−0.642455	+	0.766324i	$0.722084\pi$
$62$	−21.8618	−2.77645
$63$	−3.96430	−0.499454
$64$	14.6114	1.82643
$65$	1.68203	0.208630
$66$	15.4490	1.90164
$67$	−12.0308	−1.46980	−0.734899	−	0.678177i	$-0.762770\pi$
$67$	−12.0308	−1.46980	−0.734899	+	0.678177i	$0.762770\pi$
$68$	−16.9191	−2.05175
$69$	2.84741	0.342788
$70$	−17.7062	−2.11630
$71$	−13.8283	−1.64112	−0.820560	−	0.571560i	$-0.806338\pi$
$71$	−13.8283	−1.64112	−0.820560	+	0.571560i	$0.806338\pi$
$72$	−8.10171	−0.954795
$73$	9.72233	1.13791	0.568956	−	0.822368i	$-0.307347\pi$
$73$	9.72233	1.13791	0.568956	+	0.822368i	$0.307347\pi$
$74$	−3.13270	−0.364169
$75$	−2.17079	−0.250661
$76$	−24.8646	−2.85216
$77$	23.0642	2.62841
$78$	2.65538	0.300663
$79$	−9.63575	−1.08411	−0.542053	−	0.840344i	$-0.682353\pi$
$79$	−9.63575	−1.08411	−0.542053	+	0.840344i	$0.682353\pi$
$80$	−19.1936	−2.14591
$81$	1.00000	0.111111
$82$	10.6595	1.17715
$83$	7.71568	0.846906	0.423453	−	0.905918i	$-0.360818\pi$
$83$	7.71568	0.846906	0.423453	+	0.905918i	$0.360818\pi$
$84$	−20.0239	−2.18478
$85$	5.63416	0.611110
$86$	13.5550	1.46167
$87$	−9.70385	−1.04036
$88$	47.1356	5.02467
$89$	−15.8964	−1.68501	−0.842507	−	0.538686i	$-0.818921\pi$
$89$	−15.8964	−1.68501	−0.842507	+	0.538686i	$0.818921\pi$
$90$	4.46642	0.470802
$91$	3.96430	0.415571
$92$	14.3824	1.49947
$93$	8.23300	0.853723
$94$	1.43881	0.148402
$95$	8.28003	0.849514
$96$	−14.0972	−1.43879
$97$	12.2772	1.24656	0.623281	−	0.781998i	$-0.285799\pi$
$97$	12.2772	1.24656	0.623281	+	0.781998i	$0.285799\pi$
$98$	−23.1433	−2.33783
$99$	−5.81798	−0.584729
$100$	−10.9648	−1.09648
$101$	6.76868	0.673508	0.336754	−	0.941593i	$-0.390671\pi$
$101$	6.76868	0.673508	0.336754	+	0.941593i	$0.390671\pi$
$102$	8.89454	0.880690
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	8.10171	0.794438
$105$	6.66805	0.650735
$106$	33.3230	3.23662
$107$	5.70856	0.551867	0.275934	−	0.961177i	$-0.411013\pi$
$107$	5.70856	0.551867	0.275934	+	0.961177i	$0.411013\pi$
$108$	5.05105	0.486038
$109$	−6.23736	−0.597431	−0.298716	−	0.954342i	$-0.596558\pi$
$109$	−6.23736	−0.597431	−0.298716	+	0.954342i	$0.596558\pi$
$110$	−25.9856	−2.47763
$111$	1.17976	0.111977
$112$	−45.2367	−4.27446
$113$	0.806799	0.0758972	0.0379486	−	0.999280i	$-0.487918\pi$
$113$	0.806799	0.0758972	0.0379486	+	0.999280i	$0.487918\pi$
$114$	13.0715	1.22426
$115$	−4.78942	−0.446616
$116$	−49.0147	−4.55090
$117$	−1.00000	−0.0924500
$118$	8.76966	0.807312
$119$	13.2789	1.21728
$120$	13.6273	1.24400
$121$	22.8489	2.07717
$122$	26.6480	2.41259
$123$	−4.01432	−0.361959
$124$	41.5853	3.73447
$125$	12.0615	1.07881
$126$	10.5267	0.937794
$127$	0.540913	0.0479983	0.0239991	−	0.999712i	$-0.492360\pi$
$127$	0.540913	0.0479983	0.0239991	+	0.999712i	$0.492360\pi$
$128$	−10.6045	−0.937310
$129$	−5.10473	−0.449446
$130$	−4.46642	−0.391731
$131$	0.726567	0.0634804	0.0317402	−	0.999496i	$-0.489895\pi$
$131$	0.726567	0.0634804	0.0317402	+	0.999496i	$0.489895\pi$
$132$	−29.3869	−2.55780
$133$	19.5149	1.69215
$134$	31.9464	2.75975
$135$	−1.68203	−0.144766
$136$	27.1377	2.32704
$137$	0.284269	0.0242867	0.0121434	−	0.999926i	$-0.496135\pi$
$137$	0.284269	0.0242867	0.0121434	+	0.999926i	$0.496135\pi$
$138$	−7.56096	−0.643632
$139$	9.85489	0.835881	0.417940	−	0.908474i	$-0.362752\pi$
$139$	9.85489	0.835881	0.417940	+	0.908474i	$0.362752\pi$
$140$	33.6807	2.84654
$141$	−0.541846	−0.0456316
$142$	36.7195	3.08143
$143$	5.81798	0.486524
$144$	11.4110	0.950918
$145$	16.3221	1.35548
$146$	−25.8165	−2.13659
$147$	8.71564	0.718854
$148$	5.95901	0.489827
$149$	−4.06009	−0.332615	−0.166308	−	0.986074i	$-0.553184\pi$
$149$	−4.06009	−0.332615	−0.166308	+	0.986074i	$0.553184\pi$
$150$	5.76427	0.470651
$151$	−9.00916	−0.733155	−0.366578	−	0.930387i	$-0.619471\pi$
$151$	−9.00916	−0.733155	−0.366578	+	0.930387i	$0.619471\pi$
$152$	39.8819	3.23485
$153$	−3.34963	−0.270801
$154$	−61.2442	−4.93520
$155$	−13.8481	−1.11231
$156$	−5.05105	−0.404408
$157$	1.67449	0.133639	0.0668193	−	0.997765i	$-0.478715\pi$
$157$	1.67449	0.133639	0.0668193	+	0.997765i	$0.478715\pi$
$158$	25.5866	2.03556
$159$	−12.5492	−0.995219
$160$	23.7119	1.87459
$161$	−11.2880	−0.889617
$162$	−2.65538	−0.208626
$163$	10.6622	0.835125	0.417562	−	0.908648i	$-0.362884\pi$
$163$	10.6622	0.835125	0.417562	+	0.908648i	$0.362884\pi$
$164$	−20.2765	−1.58333
$165$	9.78600	0.761839
$166$	−20.4881	−1.59018
$167$	−14.0597	−1.08797	−0.543985	−	0.839095i	$-0.683085\pi$
$167$	−14.0597	−1.08797	−0.543985	+	0.839095i	$0.683085\pi$
$168$	32.1176	2.47792
$169$	1.00000	0.0769231
$170$	−14.9608	−1.14744
$171$	−4.92265	−0.376445
$172$	−25.7843	−1.96603
$173$	−12.4649	−0.947692	−0.473846	−	0.880608i	$-0.657135\pi$
$173$	−12.4649	−0.947692	−0.473846	+	0.880608i	$0.657135\pi$
$174$	25.7674	1.95342
$175$	8.60564	0.650525
$176$	−66.3891	−5.00427
$177$	−3.30260	−0.248238
$178$	42.2110	3.16385
$179$	3.86258	0.288703	0.144352	−	0.989526i	$-0.453890\pi$
$179$	3.86258	0.288703	0.144352	+	0.989526i	$0.453890\pi$
$180$	−8.49600	−0.633255
$181$	15.3135	1.13825	0.569123	−	0.822252i	$-0.307283\pi$
$181$	15.3135	1.13825	0.569123	+	0.822252i	$0.307283\pi$
$182$	−10.5267	−0.780292
$183$	−10.0355	−0.741843
$184$	−23.0689	−1.70066
$185$	−1.98438	−0.145895
$186$	−21.8618	−1.60298
$187$	19.4881	1.42511
$188$	−2.73689	−0.199608
$189$	−3.96430	−0.288360
$190$	−21.9866	−1.59508
$191$	23.0894	1.67069	0.835346	−	0.549725i	$-0.185267\pi$
$191$	23.0894	1.67069	0.835346	+	0.549725i	$0.185267\pi$
$192$	14.6114	1.05449
$193$	2.81909	0.202922	0.101461	−	0.994840i	$-0.467648\pi$
$193$	2.81909	0.202922	0.101461	+	0.994840i	$0.467648\pi$
$194$	−32.6007	−2.34059
$195$	1.68203	0.120452
$196$	44.0231	3.14451
$197$	12.9161	0.920237	0.460118	−	0.887858i	$-0.347807\pi$
$197$	12.9161	0.920237	0.460118	+	0.887858i	$0.347807\pi$
$198$	15.4490	1.09791
$199$	−12.0839	−0.856605	−0.428302	−	0.903635i	$-0.640888\pi$
$199$	−12.0839	−0.856605	−0.428302	+	0.903635i	$0.640888\pi$
$200$	17.5871	1.24359
$201$	−12.0308	−0.848588
$202$	−17.9734	−1.26461
$203$	38.4689	2.69999
$204$	−16.9191	−1.18458
$205$	6.75219	0.471593
$206$	2.65538	0.185009
$207$	2.84741	0.197909
$208$	−11.4110	−0.791212
$209$	28.6399	1.98106
$210$	−17.7062	−1.22184
$211$	−17.7462	−1.22170	−0.610849	−	0.791747i	$-0.709172\pi$
$211$	−17.7462	−1.22170	−0.610849	+	0.791747i	$0.709172\pi$
$212$	−63.3868	−4.35342
$213$	−13.8283	−0.947502
$214$	−15.1584	−1.03621
$215$	8.58629	0.585580
$216$	−8.10171	−0.551251
$217$	−32.6380	−2.21562
$218$	16.5626	1.12176
$219$	9.72233	0.656974
$220$	49.4296	3.33254
$221$	3.34963	0.225320
$222$	−3.13270	−0.210253
$223$	7.21459	0.483125	0.241562	−	0.970385i	$-0.422340\pi$
$223$	7.21459	0.483125	0.241562	+	0.970385i	$0.422340\pi$
$224$	55.8855	3.73400
$225$	−2.17079	−0.144719
$226$	−2.14236	−0.142508
$227$	−21.6840	−1.43922	−0.719610	−	0.694378i	$-0.755680\pi$
$227$	−21.6840	−1.43922	−0.719610	+	0.694378i	$0.755680\pi$
$228$	−24.8646	−1.64670
$229$	0.430424	0.0284432	0.0142216	−	0.999899i	$-0.495473\pi$
$229$	0.430424	0.0284432	0.0142216	+	0.999899i	$0.495473\pi$
$230$	12.7177	0.838583
$231$	23.0642	1.51751
$232$	78.6178	5.16151
$233$	7.24840	0.474859	0.237429	−	0.971405i	$-0.423695\pi$
$233$	7.24840	0.474859	0.237429	+	0.971405i	$0.423695\pi$
$234$	2.65538	0.173588
$235$	0.911399	0.0594531
$236$	−16.6816	−1.08588
$237$	−9.63575	−0.625909
$238$	−35.2606	−2.28560
$239$	−6.60802	−0.427437	−0.213719	−	0.976895i	$-0.568558\pi$
$239$	−6.60802	−0.427437	−0.213719	+	0.976895i	$0.568558\pi$
$240$	−19.1936	−1.23894
$241$	−8.08043	−0.520506	−0.260253	−	0.965540i	$-0.583806\pi$
$241$	−8.08043	−0.520506	−0.260253	+	0.965540i	$0.583806\pi$
$242$	−60.6726	−3.90018
$243$	1.00000	0.0641500
$244$	−50.6896	−3.24507
$245$	−14.6599	−0.936588
$246$	10.6595	0.679628
$247$	4.92265	0.313221
$248$	−66.7014	−4.23554
$249$	7.71568	0.488962
$250$	−32.0278	−2.02561
$251$	−27.4927	−1.73532	−0.867662	−	0.497155i	$-0.834378\pi$
$251$	−27.4927	−1.73532	−0.867662	+	0.497155i	$0.834378\pi$
$252$	−20.0239	−1.26138
$253$	−16.5662	−1.04151
$254$	−1.43633	−0.0901234
$255$	5.63416	0.352825
$256$	−1.06393	−0.0664955
$257$	27.1853	1.69577	0.847885	−	0.530179i	$-0.177875\pi$
$257$	27.1853	1.69577	0.847885	+	0.530179i	$0.177875\pi$
$258$	13.5550	0.843898
$259$	−4.67690	−0.290608
$260$	8.49600	0.526900
$261$	−9.70385	−0.600653
$262$	−1.92931	−0.119193
$263$	27.9707	1.72475	0.862374	−	0.506271i	$-0.168977\pi$
$263$	27.9707	1.72475	0.862374	+	0.506271i	$0.168977\pi$
$264$	47.1356	2.90099
$265$	21.1081	1.29666
$266$	−51.8194	−3.17725
$267$	−15.8964	−0.972843
$268$	−60.7682	−3.71201
$269$	−7.88511	−0.480764	−0.240382	−	0.970678i	$-0.577273\pi$
$269$	−7.88511	−0.480764	−0.240382	+	0.970678i	$0.577273\pi$
$270$	4.46642	0.271818
$271$	−26.9486	−1.63701	−0.818506	−	0.574498i	$-0.805197\pi$
$271$	−26.9486	−1.63701	−0.818506	+	0.574498i	$0.805197\pi$
$272$	−38.2226	−2.31759
$273$	3.96430	0.239930
$274$	−0.754842	−0.0456017
$275$	12.6296	0.761594
$276$	14.3824	0.865720
$277$	−5.67687	−0.341090	−0.170545	−	0.985350i	$-0.554553\pi$
$277$	−5.67687	−0.341090	−0.170545	+	0.985350i	$0.554553\pi$
$278$	−26.1685	−1.56948
$279$	8.23300	0.492897
$280$	−54.0226	−3.22847
$281$	17.9736	1.07222	0.536108	−	0.844150i	$-0.319894\pi$
$281$	17.9736	1.07222	0.536108	+	0.844150i	$0.319894\pi$
$282$	1.43881	0.0856797
$283$	1.86764	0.111020	0.0555098	−	0.998458i	$-0.482322\pi$
$283$	1.86764	0.111020	0.0555098	+	0.998458i	$0.482322\pi$
$284$	−69.8476	−4.14469
$285$	8.28003	0.490467
$286$	−15.4490	−0.913516
$287$	15.9139	0.939370
$288$	−14.0972	−0.830685
$289$	−5.78001	−0.340000
$290$	−43.3415	−2.54510
$291$	12.2772	0.719702
$292$	49.1080	2.87383
$293$	8.53310	0.498509	0.249254	−	0.968438i	$-0.419814\pi$
$293$	8.53310	0.498509	0.249254	+	0.968438i	$0.419814\pi$
$294$	−23.1433	−1.34975
$295$	5.55506	0.323428
$296$	−9.55804	−0.555550
$297$	−5.81798	−0.337594
$298$	10.7811	0.624531
$299$	−2.84741	−0.164670
$300$	−10.9648	−0.633051
$301$	20.2367	1.16642
$302$	23.9228	1.37660
$303$	6.76868	0.388850
$304$	−56.1725	−3.22171
$305$	16.8799	0.966541
$306$	8.89454	0.508467
$307$	3.27781	0.187075	0.0935373	−	0.995616i	$-0.470183\pi$
$307$	3.27781	0.187075	0.0935373	+	0.995616i	$0.470183\pi$
$308$	116.498	6.63812
$309$	−1.00000	−0.0568880
$310$	36.7721	2.08851
$311$	22.8796	1.29738	0.648690	−	0.761053i	$-0.275317\pi$
$311$	22.8796	1.29738	0.648690	+	0.761053i	$0.275317\pi$
$312$	8.10171	0.458669
$313$	−16.1170	−0.910988	−0.455494	−	0.890239i	$-0.650537\pi$
$313$	−16.1170	−0.910988	−0.455494	+	0.890239i	$0.650537\pi$
$314$	−4.44640	−0.250925
$315$	6.66805	0.375702
$316$	−48.6706	−2.73794
$317$	−23.7671	−1.33489	−0.667446	−	0.744658i	$-0.732613\pi$
$317$	−23.7671	−1.33489	−0.667446	+	0.744658i	$0.732613\pi$
$318$	33.3230	1.86866
$319$	56.4568	3.16098
$320$	−24.5768	−1.37388
$321$	5.70856	0.318621
$322$	29.9739	1.67038
$323$	16.4890	0.917475
$324$	5.05105	0.280614
$325$	2.17079	0.120414
$326$	−28.3121	−1.56806
$327$	−6.23736	−0.344927
$328$	32.5228	1.79577
$329$	2.14804	0.118425
$330$	−25.9856	−1.43046
$331$	−33.1498	−1.82208	−0.911038	−	0.412323i	$-0.864718\pi$
$331$	−33.1498	−1.82208	−0.911038	+	0.412323i	$0.864718\pi$
$332$	38.9723	2.13888
$333$	1.17976	0.0646502
$334$	37.3338	2.04281
$335$	20.2361	1.10562
$336$	−45.2367	−2.46786
$337$	−25.1340	−1.36914	−0.684569	−	0.728948i	$-0.740010\pi$
$337$	−25.1340	−1.36914	−0.684569	+	0.728948i	$0.740010\pi$
$338$	−2.65538	−0.144434
$339$	0.806799	0.0438193
$340$	28.4584	1.54337
$341$	−47.8995	−2.59390
$342$	13.0715	0.706827
$343$	−6.80129	−0.367235
$344$	41.3570	2.22982
$345$	−4.78942	−0.257854
$346$	33.0992	1.77942
$347$	−16.8926	−0.906841	−0.453421	−	0.891297i	$-0.649796\pi$
$347$	−16.8926	−0.906841	−0.453421	+	0.891297i	$0.649796\pi$
$348$	−49.0147	−2.62746
$349$	18.4837	0.989409	0.494705	−	0.869061i	$-0.335276\pi$
$349$	18.4837	0.989409	0.494705	+	0.869061i	$0.335276\pi$
$350$	−22.8513	−1.22145
$351$	−1.00000	−0.0533761
$352$	82.0173	4.37153
$353$	−0.880285	−0.0468528	−0.0234264	−	0.999726i	$-0.507458\pi$
$353$	−0.880285	−0.0468528	−0.0234264	+	0.999726i	$0.507458\pi$
$354$	8.76966	0.466102
$355$	23.2596	1.23449
$356$	−80.2934	−4.25554
$357$	13.2789	0.702794
$358$	−10.2566	−0.542080
$359$	30.7540	1.62313	0.811567	−	0.584259i	$-0.198615\pi$
$359$	30.7540	1.62313	0.811567	+	0.584259i	$0.198615\pi$
$360$	13.6273	0.718221
$361$	5.23252	0.275396
$362$	−40.6633	−2.13722
$363$	22.8489	1.19926
$364$	20.0239	1.04954
$365$	−16.3532	−0.855966
$366$	26.6480	1.39291
$367$	36.6357	1.91237	0.956183	−	0.292771i	$-0.0945772\pi$
$367$	36.6357	1.91237	0.956183	+	0.292771i	$0.0945772\pi$
$368$	32.4919	1.69376
$369$	−4.01432	−0.208977
$370$	5.26929	0.273937
$371$	49.7488	2.58283
$372$	41.5853	2.15610
$373$	−27.4813	−1.42293	−0.711464	−	0.702723i	$-0.751967\pi$
$373$	−27.4813	−1.42293	−0.711464	+	0.702723i	$0.751967\pi$
$374$	−51.7482	−2.67584
$375$	12.0615	0.622851
$376$	4.38987	0.226391
$377$	9.70385	0.499774
$378$	10.5267	0.541436
$379$	0.856816	0.0440117	0.0220058	−	0.999758i	$-0.492995\pi$
$379$	0.856816	0.0440117	0.0220058	+	0.999758i	$0.492995\pi$
$380$	41.8229	2.14547
$381$	0.540913	0.0277118
$382$	−61.3112	−3.13695
$383$	−5.07553	−0.259347	−0.129674	−	0.991557i	$-0.541393\pi$
$383$	−5.07553	−0.259347	−0.129674	+	0.991557i	$0.541393\pi$
$384$	−10.6045	−0.541156
$385$	−38.7946	−1.97716
$386$	−7.48575	−0.381014
$387$	−5.10473	−0.259488
$388$	62.0128	3.14822
$389$	−33.8764	−1.71760	−0.858800	−	0.512311i	$-0.828790\pi$
$389$	−33.8764	−1.71760	−0.858800	+	0.512311i	$0.828790\pi$
$390$	−4.46642	−0.226166
$391$	−9.53776	−0.482345
$392$	−70.6115	−3.56642
$393$	0.726567	0.0366504
$394$	−34.2973	−1.72787
$395$	16.2076	0.815492
$396$	−29.3869	−1.47675
$397$	0.477051	0.0239425	0.0119713	−	0.999928i	$-0.496189\pi$
$397$	0.477051	0.0239425	0.0119713	+	0.999928i	$0.496189\pi$
$398$	32.0874	1.60839
$399$	19.5149	0.976965
$400$	−24.7709	−1.23855
$401$	−11.2558	−0.562089	−0.281044	−	0.959695i	$-0.590681\pi$
$401$	−11.2558	−0.562089	−0.281044	+	0.959695i	$0.590681\pi$
$402$	31.9464	1.59334
$403$	−8.23300	−0.410115
$404$	34.1889	1.70096
$405$	−1.68203	−0.0835806
$406$	−102.150	−5.06960
$407$	−6.86380	−0.340226
$408$	27.1377	1.34352
$409$	28.3076	1.39972	0.699859	−	0.714281i	$-0.253246\pi$
$409$	28.3076	1.39972	0.699859	+	0.714281i	$0.253246\pi$
$410$	−17.9296	−0.885481
$411$	0.284269	0.0140219
$412$	−5.05105	−0.248847
$413$	13.0925	0.644238
$414$	−7.56096	−0.371601
$415$	−12.9780	−0.637064
$416$	14.0972	0.691172
$417$	9.85489	0.482596
$418$	−76.0499	−3.71972
$419$	25.7342	1.25720	0.628598	−	0.777730i	$-0.283629\pi$
$419$	25.7342	1.25720	0.628598	+	0.777730i	$0.283629\pi$
$420$	33.6807	1.64345
$421$	−14.3098	−0.697419	−0.348710	−	0.937231i	$-0.613380\pi$
$421$	−14.3098	−0.697419	−0.348710	+	0.937231i	$0.613380\pi$
$422$	47.1229	2.29391
$423$	−0.541846	−0.0263454
$424$	101.670	4.93754
$425$	7.27133	0.352711
$426$	36.7195	1.77907
$427$	39.7835	1.92526
$428$	28.8342	1.39376
$429$	5.81798	0.280895
$430$	−22.7999	−1.09951
$431$	1.02334	0.0492926	0.0246463	−	0.999696i	$-0.492154\pi$
$431$	1.02334	0.0492926	0.0246463	+	0.999696i	$0.492154\pi$
$432$	11.4110	0.549013
$433$	−15.6800	−0.753532	−0.376766	−	0.926308i	$-0.622964\pi$
$433$	−15.6800	−0.753532	−0.376766	+	0.926308i	$0.622964\pi$
$434$	86.6665	4.16012
$435$	16.3221	0.782586
$436$	−31.5053	−1.50883
$437$	−14.0168	−0.670515
$438$	−25.8165	−1.23356
$439$	23.7168	1.13194	0.565970	−	0.824426i	$-0.308502\pi$
$439$	23.7168	1.13194	0.565970	+	0.824426i	$0.308502\pi$
$440$	−79.2833	−3.77968
$441$	8.71564	0.415030
$442$	−8.89454	−0.423070
$443$	−16.6780	−0.792396	−0.396198	−	0.918165i	$-0.629671\pi$
$443$	−16.6780	−0.792396	−0.396198	+	0.918165i	$0.629671\pi$
$444$	5.95901	0.282802
$445$	26.7381	1.26751
$446$	−19.1575	−0.907133
$447$	−4.06009	−0.192036
$448$	−57.9239	−2.73665
$449$	−17.9276	−0.846055	−0.423027	−	0.906117i	$-0.639033\pi$
$449$	−17.9276	−0.846055	−0.423027	+	0.906117i	$0.639033\pi$
$450$	5.76427	0.271730
$451$	23.3552	1.09975
$452$	4.07518	0.191680
$453$	−9.00916	−0.423287
$454$	57.5794	2.70234
$455$	−6.66805	−0.312603
$456$	39.8819	1.86764
$457$	−21.2374	−0.993443	−0.496721	−	0.867910i	$-0.665463\pi$
$457$	−21.2374	−0.993443	−0.496721	+	0.867910i	$0.665463\pi$
$458$	−1.14294	−0.0534061
$459$	−3.34963	−0.156347
$460$	−24.1916	−1.12794
$461$	−11.1107	−0.517479	−0.258739	−	0.965947i	$-0.583307\pi$
$461$	−11.1107	−0.517479	−0.258739	+	0.965947i	$0.583307\pi$
$462$	−61.2442	−2.84934
$463$	3.46776	0.161161	0.0805803	−	0.996748i	$-0.474323\pi$
$463$	3.46776	0.161161	0.0805803	+	0.996748i	$0.474323\pi$
$464$	−110.731	−5.14055
$465$	−13.8481	−0.642191
$466$	−19.2473	−0.891613
$467$	6.43694	0.297866	0.148933	−	0.988847i	$-0.452416\pi$
$467$	6.43694	0.297866	0.148933	+	0.988847i	$0.452416\pi$
$468$	−5.05105	−0.233485
$469$	47.6937	2.20229
$470$	−2.42011	−0.111631
$471$	1.67449	0.0771563
$472$	26.7567	1.23158
$473$	29.6992	1.36557
$474$	25.5866	1.17523
$475$	10.6860	0.490309
$476$	67.0724	3.07426
$477$	−12.5492	−0.574590
$478$	17.5468	0.802573
$479$	16.8970	0.772042	0.386021	−	0.922490i	$-0.373849\pi$
$479$	16.8970	0.772042	0.386021	+	0.922490i	$0.373849\pi$
$480$	23.7119	1.08229
$481$	−1.17976	−0.0537922
$482$	21.4566	0.977322
$483$	−11.2880	−0.513621
$484$	115.411	5.24596
$485$	−20.6506	−0.937695
$486$	−2.65538	−0.120451
$487$	42.2499	1.91453	0.957263	−	0.289219i	$-0.0933956\pi$
$487$	42.2499	1.91453	0.957263	+	0.289219i	$0.0933956\pi$
$488$	81.3044	3.68048
$489$	10.6622	0.482160
$490$	38.9277	1.75857
$491$	−8.34720	−0.376704	−0.188352	−	0.982102i	$-0.560315\pi$
$491$	−8.34720	−0.376704	−0.188352	+	0.982102i	$0.560315\pi$
$492$	−20.2765	−0.914136
$493$	32.5043	1.46392
$494$	−13.0715	−0.588116
$495$	9.78600	0.439848
$496$	93.9469	4.21834
$497$	54.8196	2.45899
$498$	−20.4881	−0.918093
$499$	−3.98168	−0.178244	−0.0891222	−	0.996021i	$-0.528406\pi$
$499$	−3.98168	−0.178244	−0.0891222	+	0.996021i	$0.528406\pi$
$500$	60.9230	2.72456
$501$	−14.0597	−0.628139
$502$	73.0036	3.25831
$503$	−12.3772	−0.551870	−0.275935	−	0.961176i	$-0.588988\pi$
$503$	−12.3772	−0.551870	−0.275935	+	0.961176i	$0.588988\pi$
$504$	32.1176	1.43063
$505$	−11.3851	−0.506630
$506$	43.9895	1.95557
$507$	1.00000	0.0444116
$508$	2.73218	0.121221
$509$	19.9921	0.886134	0.443067	−	0.896488i	$-0.353890\pi$
$509$	19.9921	0.886134	0.443067	+	0.896488i	$0.353890\pi$
$510$	−14.9608	−0.662477
$511$	−38.5422	−1.70501
$512$	24.0340	1.06216
$513$	−4.92265	−0.217340
$514$	−72.1873	−3.18404
$515$	1.68203	0.0741189
$516$	−25.7843	−1.13509
$517$	3.15245	0.138645
$518$	12.4190	0.545658
$519$	−12.4649	−0.547150
$520$	−13.6273	−0.597596
$521$	3.01624	0.132144	0.0660720	−	0.997815i	$-0.478953\pi$
$521$	3.01624	0.132144	0.0660720	+	0.997815i	$0.478953\pi$
$522$	25.7674	1.12781
$523$	−12.2041	−0.533647	−0.266824	−	0.963745i	$-0.585974\pi$
$523$	−12.2041	−0.533647	−0.266824	+	0.963745i	$0.585974\pi$
$524$	3.66993	0.160321
$525$	8.60564	0.375581
$526$	−74.2729	−3.23845
$527$	−27.5775	−1.20129
$528$	−66.3891	−2.88922
$529$	−14.8922	−0.647489
$530$	−56.0501	−2.43466
$531$	−3.30260	−0.143321
$532$	98.5705	4.27357
$533$	4.01432	0.173879
$534$	42.2110	1.82665
$535$	−9.60195	−0.415128
$536$	97.4701	4.21007
$537$	3.86258	0.166683
$538$	20.9380	0.902701
$539$	−50.7074	−2.18412
$540$	−8.49600	−0.365610
$541$	−18.7574	−0.806445	−0.403223	−	0.915102i	$-0.632110\pi$
$541$	−18.7574	−0.806445	−0.403223	+	0.915102i	$0.632110\pi$
$542$	71.5589	3.07372
$543$	15.3135	0.657167
$544$	47.2203	2.02456
$545$	10.4914	0.449403
$546$	−10.5267	−0.450502
$547$	−10.9578	−0.468520	−0.234260	−	0.972174i	$-0.575267\pi$
$547$	−10.9578	−0.468520	−0.234260	+	0.972174i	$0.575267\pi$
$548$	1.43586	0.0613367
$549$	−10.0355	−0.428303
$550$	−33.5364	−1.43000
$551$	47.7687	2.03502
$552$	−23.0689	−0.981877
$553$	38.1989	1.62438
$554$	15.0743	0.640444
$555$	−1.98438	−0.0842323
$556$	49.7776	2.11104
$557$	11.9355	0.505725	0.252863	−	0.967502i	$-0.418628\pi$
$557$	11.9355	0.505725	0.252863	+	0.967502i	$0.418628\pi$
$558$	−21.8618	−0.925482
$559$	5.10473	0.215907
$560$	76.0892	3.21536
$561$	19.4881	0.822787
$562$	−47.7268	−2.01323
$563$	19.3844	0.816953	0.408476	−	0.912769i	$-0.366060\pi$
$563$	19.3844	0.816953	0.408476	+	0.912769i	$0.366060\pi$
$564$	−2.73689	−0.115244
$565$	−1.35706	−0.0570918
$566$	−4.95930	−0.208455
$567$	−3.96430	−0.166485
$568$	112.033	4.70080
$569$	−26.0460	−1.09190	−0.545952	−	0.837816i	$-0.683832\pi$
$569$	−26.0460	−1.09190	−0.545952	+	0.837816i	$0.683832\pi$
$570$	−21.9866	−0.920919
$571$	−1.46534	−0.0613226	−0.0306613	−	0.999530i	$-0.509761\pi$
$571$	−1.46534	−0.0613226	−0.0306613	+	0.999530i	$0.509761\pi$
$572$	29.3869	1.22873
$573$	23.0894	0.964574
$574$	−42.2576	−1.76380
$575$	−6.18113	−0.257771
$576$	14.6114	0.608809
$577$	26.7011	1.11158	0.555791	−	0.831322i	$-0.312416\pi$
$577$	26.7011	1.11158	0.555791	+	0.831322i	$0.312416\pi$
$578$	15.3481	0.638398
$579$	2.81909	0.117157
$580$	82.4439	3.42330
$581$	−30.5873	−1.26897
$582$	−32.6007	−1.35134
$583$	73.0112	3.02381
$584$	−78.7674	−3.25942
$585$	1.68203	0.0695432
$586$	−22.6586	−0.936019
$587$	6.04506	0.249506	0.124753	−	0.992188i	$-0.460186\pi$
$587$	6.04506	0.249506	0.124753	+	0.992188i	$0.460186\pi$
$588$	44.0231	1.81548
$589$	−40.5282	−1.66994
$590$	−14.7508	−0.607281
$591$	12.9161	0.531299
$592$	13.4622	0.553294
$593$	47.7797	1.96208	0.981039	−	0.193812i	$-0.0620851\pi$
$593$	47.7797	1.96208	0.981039	+	0.193812i	$0.0620851\pi$
$594$	15.4490	0.633879
$595$	−22.3355	−0.915665
$596$	−20.5077	−0.840028
$597$	−12.0839	−0.494561
$598$	7.56096	0.309191
$599$	5.97385	0.244085	0.122042	−	0.992525i	$-0.461056\pi$
$599$	5.97385	0.244085	0.122042	+	0.992525i	$0.461056\pi$
$600$	17.5871	0.717990
$601$	−40.6492	−1.65811	−0.829057	−	0.559164i	$-0.811122\pi$
$601$	−40.6492	−1.65811	−0.829057	+	0.559164i	$0.811122\pi$
$602$	−53.7361	−2.19012
$603$	−12.0308	−0.489932
$604$	−45.5057	−1.85160
$605$	−38.4325	−1.56250
$606$	−17.9734	−0.730120
$607$	29.4571	1.19563	0.597813	−	0.801636i	$-0.296037\pi$
$607$	29.4571	1.19563	0.597813	+	0.801636i	$0.296037\pi$
$608$	69.3956	2.81436
$609$	38.4689	1.55884
$610$	−44.8226	−1.81481
$611$	0.541846	0.0219207
$612$	−16.9191	−0.683915
$613$	−30.3335	−1.22516	−0.612579	−	0.790410i	$-0.709868\pi$
$613$	−30.3335	−1.22516	−0.612579	+	0.790410i	$0.709868\pi$
$614$	−8.70384	−0.351258
$615$	6.75219	0.272274
$616$	−186.859	−7.52878
$617$	1.72397	0.0694045	0.0347023	−	0.999398i	$-0.488952\pi$
$617$	1.72397	0.0694045	0.0347023	+	0.999398i	$0.488952\pi$
$618$	2.65538	0.106815
$619$	34.1857	1.37404	0.687020	−	0.726639i	$-0.258919\pi$
$619$	34.1857	1.37404	0.687020	+	0.726639i	$0.258919\pi$
$620$	−69.9476	−2.80916
$621$	2.84741	0.114263
$622$	−60.7539	−2.43601
$623$	63.0179	2.52476
$624$	−11.4110	−0.456806
$625$	−9.43374	−0.377350
$626$	42.7968	1.71051
$627$	28.6399	1.14377
$628$	8.45792	0.337508
$629$	−3.95174	−0.157566
$630$	−17.7062	−0.705432
$631$	3.04624	0.121269	0.0606344	−	0.998160i	$-0.480688\pi$
$631$	3.04624	0.121269	0.0606344	+	0.998160i	$0.480688\pi$
$632$	78.0660	3.10530
$633$	−17.7462	−0.705347
$634$	63.1107	2.50644
$635$	−0.909830	−0.0361055
$636$	−63.3868	−2.51345
$637$	−8.71564	−0.345326
$638$	−149.914	−5.93517
$639$	−13.8283	−0.547040
$640$	17.8370	0.705068
$641$	−26.0708	−1.02973	−0.514867	−	0.857270i	$-0.672159\pi$
$641$	−26.0708	−1.02973	−0.514867	+	0.857270i	$0.672159\pi$
$642$	−15.1584	−0.598255
$643$	−38.4368	−1.51580	−0.757900	−	0.652371i	$-0.773775\pi$
$643$	−38.4368	−1.51580	−0.757900	+	0.652371i	$0.773775\pi$
$644$	−57.0162	−2.24675
$645$	8.58629	0.338085
$646$	−43.7847	−1.72269
$647$	10.6231	0.417637	0.208819	−	0.977954i	$-0.433038\pi$
$647$	10.6231	0.417637	0.208819	+	0.977954i	$0.433038\pi$
$648$	−8.10171	−0.318265
$649$	19.2145	0.754233
$650$	−5.76427	−0.226093
$651$	−32.6380	−1.27919
$652$	53.8551	2.10913
$653$	−37.3251	−1.46064	−0.730321	−	0.683104i	$-0.760630\pi$
$653$	−37.3251	−1.46064	−0.730321	+	0.683104i	$0.760630\pi$
$654$	16.5626	0.647648
$655$	−1.22210	−0.0477516
$656$	−45.8074	−1.78848
$657$	9.72233	0.379304
$658$	−5.70386	−0.222359
$659$	−9.67737	−0.376977	−0.188488	−	0.982075i	$-0.560359\pi$
$659$	−9.67737	−0.376977	−0.188488	+	0.982075i	$0.560359\pi$
$660$	49.4296	1.92404
$661$	−20.8394	−0.810558	−0.405279	−	0.914193i	$-0.632826\pi$
$661$	−20.8394	−0.810558	−0.405279	+	0.914193i	$0.632826\pi$
$662$	88.0253	3.42120
$663$	3.34963	0.130089
$664$	−62.5102	−2.42587
$665$	−32.8245	−1.27288
$666$	−3.13270	−0.121390
$667$	−27.6309	−1.06987
$668$	−71.0161	−2.74769
$669$	7.21459	0.278932
$670$	−53.7347	−2.07595
$671$	58.3861	2.25397
$672$	55.8855	2.15583
$673$	−43.7207	−1.68531	−0.842655	−	0.538454i	$-0.819009\pi$
$673$	−43.7207	−1.68531	−0.842655	+	0.538454i	$0.819009\pi$
$674$	66.7405	2.57075
$675$	−2.17079	−0.0835537
$676$	5.05105	0.194271
$677$	−22.5253	−0.865719	−0.432859	−	0.901461i	$-0.642495\pi$
$677$	−22.5253	−0.865719	−0.432859	+	0.901461i	$0.642495\pi$
$678$	−2.14236	−0.0822768
$679$	−48.6705	−1.86780
$680$	−45.6463	−1.75046
$681$	−21.6840	−0.830935
$682$	127.191	4.87041
$683$	12.8181	0.490470	0.245235	−	0.969464i	$-0.421135\pi$
$683$	12.8181	0.490470	0.245235	+	0.969464i	$0.421135\pi$
$684$	−24.8646	−0.950721
$685$	−0.478148	−0.0182691
$686$	18.0600	0.689535
$687$	0.430424	0.0164217
$688$	−58.2502	−2.22077
$689$	12.5492	0.478088
$690$	12.7177	0.484156
$691$	−24.6081	−0.936138	−0.468069	−	0.883692i	$-0.655050\pi$
$691$	−24.6081	−0.936138	−0.468069	+	0.883692i	$0.655050\pi$
$692$	−62.9610	−2.39342
$693$	23.0642	0.876136
$694$	44.8562	1.70272
$695$	−16.5762	−0.628770
$696$	78.6178	2.98000
$697$	13.4465	0.509321
$698$	−49.0812	−1.85775
$699$	7.24840	0.274160
$700$	43.4675	1.64292
$701$	33.7603	1.27511	0.637555	−	0.770405i	$-0.279946\pi$
$701$	33.7603	1.27511	0.637555	+	0.770405i	$0.279946\pi$
$702$	2.65538	0.100221
$703$	−5.80753	−0.219035
$704$	−85.0089	−3.20389
$705$	0.911399	0.0343253
$706$	2.33749	0.0879727
$707$	−26.8330	−1.00916
$708$	−16.6816	−0.626933
$709$	34.1317	1.28184	0.640921	−	0.767607i	$-0.278553\pi$
$709$	34.1317	1.28184	0.640921	+	0.767607i	$0.278553\pi$
$710$	−61.7631	−2.31793
$711$	−9.63575	−0.361369
$712$	128.788	4.82653
$713$	23.4427	0.877938
$714$	−35.2606	−1.31959
$715$	−9.78600	−0.365976
$716$	19.5101	0.729127
$717$	−6.60802	−0.246781
$718$	−81.6636	−3.04766
$719$	−1.09618	−0.0408807	−0.0204404	−	0.999791i	$-0.506507\pi$
$719$	−1.09618	−0.0408807	−0.0204404	+	0.999791i	$0.506507\pi$
$720$	−19.1936	−0.715305
$721$	3.96430	0.147638
$722$	−13.8943	−0.517094
$723$	−8.08043	−0.300514
$724$	77.3495	2.87467
$725$	21.0650	0.782335
$726$	−60.6726	−2.25177
$727$	−51.4495	−1.90816	−0.954078	−	0.299559i	$-0.903161\pi$
$727$	−51.4495	−1.90816	−0.954078	+	0.299559i	$0.903161\pi$
$728$	−32.1176	−1.19036
$729$	1.00000	0.0370370
$730$	43.4240	1.60719
$731$	17.0989	0.632427
$732$	−50.6896	−1.87354
$733$	−25.2924	−0.934195	−0.467098	−	0.884206i	$-0.654700\pi$
$733$	−25.2924	−0.934195	−0.467098	+	0.884206i	$0.654700\pi$
$734$	−97.2816	−3.59073
$735$	−14.6599	−0.540740
$736$	−40.1405	−1.47960
$737$	69.9950	2.57830
$738$	10.6595	0.392383
$739$	−2.71963	−0.100043	−0.0500216	−	0.998748i	$-0.515929\pi$
$739$	−2.71963	−0.100043	−0.0500216	+	0.998748i	$0.515929\pi$
$740$	−10.0232	−0.368460
$741$	4.92265	0.180838
$742$	−132.102	−4.84962
$743$	48.2922	1.77167	0.885834	−	0.464001i	$-0.153587\pi$
$743$	48.2922	1.77167	0.885834	+	0.464001i	$0.153587\pi$
$744$	−66.7014	−2.44539
$745$	6.82917	0.250202
$746$	72.9733	2.67174
$747$	7.71568	0.282302
$748$	98.4352	3.59915
$749$	−22.6304	−0.826898
$750$	−32.0278	−1.16949
$751$	−40.5131	−1.47834	−0.739172	−	0.673516i	$-0.764783\pi$
$751$	−40.5131	−1.47834	−0.739172	+	0.673516i	$0.764783\pi$
$752$	−6.18301	−0.225471
$753$	−27.4927	−1.00189
$754$	−25.7674	−0.938394
$755$	15.1536	0.551498
$756$	−20.0239	−0.728261
$757$	−6.37994	−0.231883	−0.115941	−	0.993256i	$-0.536988\pi$
$757$	−6.37994	−0.231883	−0.115941	+	0.993256i	$0.536988\pi$
$758$	−2.27517	−0.0826380
$759$	−16.5662	−0.601314
$760$	−67.0824	−2.43333
$761$	−48.6125	−1.76220	−0.881100	−	0.472930i	$-0.843197\pi$
$761$	−48.6125	−1.76220	−0.881100	+	0.472930i	$0.843197\pi$
$762$	−1.43633	−0.0520328
$763$	24.7268	0.895169
$764$	116.626	4.21938
$765$	5.63416	0.203703
$766$	13.4775	0.486961
$767$	3.30260	0.119250
$768$	−1.06393	−0.0383912
$769$	−38.7527	−1.39746	−0.698729	−	0.715387i	$-0.746251\pi$
$769$	−38.7527	−1.39746	−0.698729	+	0.715387i	$0.746251\pi$
$770$	103.014	3.71238
$771$	27.1853	0.979054
$772$	14.2393	0.512485
$773$	−9.78755	−0.352034	−0.176017	−	0.984387i	$-0.556321\pi$
$773$	−9.78755	−0.352034	−0.176017	+	0.984387i	$0.556321\pi$
$774$	13.5550	0.487225
$775$	−17.8721	−0.641985
$776$	−99.4663	−3.57063
$777$	−4.67690	−0.167783
$778$	89.9547	3.22503
$779$	19.7611	0.708015
$780$	8.49600	0.304206
$781$	80.4530	2.87883
$782$	25.3264	0.905670
$783$	−9.70385	−0.346787
$784$	99.4543	3.55194
$785$	−2.81653	−0.100526
$786$	−1.92931	−0.0688163
$787$	37.7472	1.34554	0.672772	−	0.739850i	$-0.265104\pi$
$787$	37.7472	1.34554	0.672772	+	0.739850i	$0.265104\pi$
$788$	65.2401	2.32408
$789$	27.9707	0.995784
$790$	−43.0373	−1.53120
$791$	−3.19839	−0.113722
$792$	47.1356	1.67489
$793$	10.0355	0.356370
$794$	−1.26675	−0.0449554
$795$	21.1081	0.748628
$796$	−61.0364	−2.16338
$797$	47.4530	1.68087	0.840437	−	0.541910i	$-0.182299\pi$
$797$	47.4530	1.68087	0.840437	+	0.541910i	$0.182299\pi$
$798$	−51.8194	−1.83439
$799$	1.81498	0.0642094
$800$	30.6020	1.08195
$801$	−15.8964	−0.561671
$802$	29.8885	1.05540
$803$	−56.5643	−1.99611
$804$	−60.7682	−2.14313
$805$	18.9867	0.669192
$806$	21.8618	0.770048
$807$	−7.88511	−0.277569
$808$	−54.8378	−1.92919
$809$	−10.5047	−0.369325	−0.184663	−	0.982802i	$-0.559119\pi$
$809$	−10.5047	−0.369325	−0.184663	+	0.982802i	$0.559119\pi$
$810$	4.46642	0.156934
$811$	−33.8554	−1.18882	−0.594412	−	0.804160i	$-0.702615\pi$
$811$	−33.8554	−1.18882	−0.594412	+	0.804160i	$0.702615\pi$
$812$	194.309	6.81889
$813$	−26.9486	−0.945129
$814$	18.2260	0.638821
$815$	−17.9340	−0.628202
$816$	−38.2226	−1.33806
$817$	25.1288	0.879146
$818$	−75.1674	−2.62817
$819$	3.96430	0.138524
$820$	34.1056	1.19102
$821$	−1.29726	−0.0452747	−0.0226374	−	0.999744i	$-0.507206\pi$
$821$	−1.29726	−0.0452747	−0.0226374	+	0.999744i	$0.507206\pi$
$822$	−0.754842	−0.0263281
$823$	−41.9591	−1.46260	−0.731301	−	0.682055i	$-0.761086\pi$
$823$	−41.9591	−1.46260	−0.731301	+	0.682055i	$0.761086\pi$
$824$	8.10171	0.282236
$825$	12.6296	0.439706
$826$	−34.7655	−1.20965
$827$	11.9878	0.416857	0.208429	−	0.978038i	$-0.433165\pi$
$827$	11.9878	0.416857	0.208429	+	0.978038i	$0.433165\pi$
$828$	14.3824	0.499824
$829$	22.5657	0.783738	0.391869	−	0.920021i	$-0.371829\pi$
$829$	22.5657	0.783738	0.391869	+	0.920021i	$0.371829\pi$
$830$	34.4615	1.19618
$831$	−5.67687	−0.196928
$832$	−14.6114	−0.506559
$833$	−29.1941	−1.01152
$834$	−26.1685	−0.906141
$835$	23.6487	0.818398
$836$	144.662	5.00323
$837$	8.23300	0.284574
$838$	−68.3341	−2.36056
$839$	−25.0365	−0.864357	−0.432178	−	0.901788i	$-0.642255\pi$
$839$	−25.0365	−0.864357	−0.432178	+	0.901788i	$0.642255\pi$
$840$	−54.0226	−1.86396
$841$	65.1647	2.24706
$842$	37.9981	1.30950
$843$	17.9736	0.619044
$844$	−89.6369	−3.08543
$845$	−1.68203	−0.0578635
$846$	1.43881	0.0494672
$847$	−90.5798	−3.11236
$848$	−143.200	−4.91749
$849$	1.86764	0.0640972
$850$	−19.3081	−0.662264
$851$	3.35925	0.115154
$852$	−69.8476	−2.39294
$853$	16.3310	0.559164	0.279582	−	0.960122i	$-0.409804\pi$
$853$	16.3310	0.559164	0.279582	+	0.960122i	$0.409804\pi$
$854$	−105.640	−3.61494
$855$	8.28003	0.283171
$856$	−46.2491	−1.58076
$857$	0.548010	0.0187197	0.00935984	−	0.999956i	$-0.497021\pi$
$857$	0.548010	0.0187197	0.00935984	+	0.999956i	$0.497021\pi$
$858$	−15.4490	−0.527419
$859$	49.2010	1.67872	0.839358	−	0.543579i	$-0.182931\pi$
$859$	49.2010	1.67872	0.839358	+	0.543579i	$0.182931\pi$
$860$	43.3698	1.47890
$861$	15.9139	0.542346
$862$	−2.71736	−0.0925537
$863$	20.9444	0.712956	0.356478	−	0.934304i	$-0.383977\pi$
$863$	20.9444	0.712956	0.356478	+	0.934304i	$0.383977\pi$
$864$	−14.0972	−0.479596
$865$	20.9664	0.712877
$866$	41.6364	1.41486
$867$	−5.78001	−0.196299
$868$	−164.856	−5.59559
$869$	56.0606	1.90173
$870$	−43.3415	−1.46941
$871$	12.0308	0.407648
$872$	50.5333	1.71127
$873$	12.2772	0.415520
$874$	37.2200	1.25899
$875$	−47.8152	−1.61645
$876$	49.1080	1.65920
$877$	−43.5498	−1.47057	−0.735285	−	0.677758i	$-0.762952\pi$
$877$	−43.5498	−1.47057	−0.735285	+	0.677758i	$0.762952\pi$
$878$	−62.9770	−2.12537
$879$	8.53310	0.287814
$880$	111.668	3.76433
$881$	−56.6167	−1.90746	−0.953732	−	0.300658i	$-0.902794\pi$
$881$	−56.6167	−1.90746	−0.953732	+	0.300658i	$0.902794\pi$
$882$	−23.1433	−0.779277
$883$	−10.5586	−0.355325	−0.177663	−	0.984091i	$-0.556854\pi$
$883$	−10.5586	−0.355325	−0.177663	+	0.984091i	$0.556854\pi$
$884$	16.9191	0.569052
$885$	5.55506	0.186731
$886$	44.2865	1.48783
$887$	−4.78812	−0.160769	−0.0803847	−	0.996764i	$-0.525615\pi$
$887$	−4.78812	−0.160769	−0.0803847	+	0.996764i	$0.525615\pi$
$888$	−9.55804	−0.320747
$889$	−2.14434	−0.0719188
$890$	−70.9999	−2.37992
$891$	−5.81798	−0.194910
$892$	36.4413	1.22014
$893$	2.66732	0.0892584
$894$	10.7811	0.360573
$895$	−6.49697	−0.217170
$896$	42.0392	1.40443
$897$	−2.84741	−0.0950723
$898$	47.6046	1.58858
$899$	−79.8918	−2.66454
$900$	−10.9648	−0.365492
$901$	42.0352	1.40040
$902$	−62.0170	−2.06494
$903$	20.2367	0.673434
$904$	−6.53645	−0.217399
$905$	−25.7578	−0.856218
$906$	23.9228	0.794781
$907$	−38.4364	−1.27626	−0.638131	−	0.769928i	$-0.720292\pi$
$907$	−38.4364	−1.27626	−0.638131	+	0.769928i	$0.720292\pi$
$908$	−109.527	−3.63479
$909$	6.76868	0.224503
$910$	17.7062	0.586955
$911$	−37.9023	−1.25576	−0.627880	−	0.778310i	$-0.716077\pi$
$911$	−37.9023	−1.25576	−0.627880	+	0.778310i	$0.716077\pi$
$912$	−56.1725	−1.86006
$913$	−44.8897	−1.48563
$914$	56.3934	1.86533
$915$	16.8799	0.558033
$916$	2.17409	0.0718341
$917$	−2.88033	−0.0951167
$918$	8.89454	0.293563
$919$	47.7362	1.57467	0.787335	−	0.616525i	$-0.211460\pi$
$919$	47.7362	1.57467	0.787335	+	0.616525i	$0.211460\pi$
$920$	38.8025	1.27928
$921$	3.27781	0.108008
$922$	29.5032	0.971638
$923$	13.8283	0.455165
$924$	116.498	3.83252
$925$	−2.56100	−0.0842051
$926$	−9.20823	−0.302601
$927$	−1.00000	−0.0328443
$928$	136.797	4.49059
$929$	−20.7412	−0.680496	−0.340248	−	0.940336i	$-0.610511\pi$
$929$	−20.7412	−0.680496	−0.340248	+	0.940336i	$0.610511\pi$
$930$	36.7721	1.20580
$931$	−42.9041	−1.40612
$932$	36.6121	1.19927
$933$	22.8796	0.749043
$934$	−17.0925	−0.559285
$935$	−32.7794	−1.07200
$936$	8.10171	0.264813
$937$	−16.8433	−0.550248	−0.275124	−	0.961409i	$-0.588719\pi$
$937$	−16.8433	−0.550248	−0.275124	+	0.961409i	$0.588719\pi$
$938$	−126.645	−4.13510
$939$	−16.1170	−0.525959
$940$	4.60352	0.150150
$941$	20.1170	0.655794	0.327897	−	0.944714i	$-0.393660\pi$
$941$	20.1170	0.655794	0.327897	+	0.944714i	$0.393660\pi$
$942$	−4.44640	−0.144872
$943$	−11.4304	−0.372225
$944$	−37.6860	−1.22658
$945$	6.66805	0.216912
$946$	−78.8628	−2.56405
$947$	−28.7844	−0.935368	−0.467684	−	0.883896i	$-0.654911\pi$
$947$	−28.7844	−0.935368	−0.467684	+	0.883896i	$0.654911\pi$
$948$	−48.6706	−1.58075
$949$	−9.72233	−0.315600
$950$	−28.3755	−0.920623
$951$	−23.7671	−0.770700
$952$	−107.582	−3.48675
$953$	−12.7736	−0.413776	−0.206888	−	0.978365i	$-0.566334\pi$
$953$	−12.7736	−0.413776	−0.206888	+	0.978365i	$0.566334\pi$
$954$	33.3230	1.07887
$955$	−38.8370	−1.25674
$956$	−33.3775	−1.07950
$957$	56.4568	1.82499
$958$	−44.8679	−1.44962
$959$	−1.12693	−0.0363903
$960$	−24.5768	−0.793212
$961$	36.7823	1.18653
$962$	3.13270	0.101002
$963$	5.70856	0.183956
$964$	−40.8147	−1.31455
$965$	−4.74178	−0.152643
$966$	29.9739	0.964394
$967$	−23.2601	−0.747993	−0.373996	−	0.927430i	$-0.622013\pi$
$967$	−23.2601	−0.747993	−0.373996	+	0.927430i	$0.622013\pi$
$968$	−185.115	−5.94983
$969$	16.4890	0.529705
$970$	54.8352	1.76065
$971$	−24.3601	−0.781751	−0.390876	−	0.920443i	$-0.627828\pi$
$971$	−24.3601	−0.781751	−0.390876	+	0.920443i	$0.627828\pi$
$972$	5.05105	0.162013
$973$	−39.0677	−1.25245
$974$	−112.190	−3.59479
$975$	2.17079	0.0695208
$976$	−114.515	−3.66553
$977$	−28.3186	−0.905991	−0.452996	−	0.891513i	$-0.649645\pi$
$977$	−28.3186	−0.905991	−0.452996	+	0.891513i	$0.649645\pi$
$978$	−28.3121	−0.905321
$979$	92.4849	2.95583
$980$	−74.0481	−2.36538
$981$	−6.23736	−0.199144
$982$	22.1650	0.707313
$983$	38.9329	1.24177	0.620883	−	0.783903i	$-0.286774\pi$
$983$	38.9329	1.24177	0.620883	+	0.783903i	$0.286774\pi$
$984$	32.5228	1.03679
$985$	−21.7253	−0.692225
$986$	−86.3113	−2.74871
$987$	2.14804	0.0683727
$988$	24.8646	0.791048
$989$	−14.5353	−0.462195
$990$	−25.9856	−0.825875
$991$	−0.641772	−0.0203866	−0.0101933	−	0.999948i	$-0.503245\pi$
$991$	−0.641772	−0.0203866	−0.0101933	+	0.999948i	$0.503245\pi$
$992$	−116.062	−3.68498
$993$	−33.1498	−1.05198
$994$	−145.567	−4.61710
$995$	20.3254	0.644360
$996$	38.9723	1.23489
$997$	36.0288	1.14104	0.570522	−	0.821282i	$-0.306741\pi$
$997$	36.0288	1.14104	0.570522	+	0.821282i	$0.306741\pi$
$998$	10.5729	0.334679
$999$	1.17976	0.0373258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.3	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65538 q^{2} +1.00000 q^{3} +5.05105 q^{4} -1.68203 q^{5} -2.65538 q^{6} -3.96430 q^{7} -8.10171 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65538 q^{2} +1.00000 q^{3} +5.05105 q^{4} -1.68203 q^{5} -2.65538 q^{6} -3.96430 q^{7} -8.10171 q^{8} +1.00000 q^{9} +4.46642 q^{10} -5.81798 q^{11} +5.05105 q^{12} -1.00000 q^{13} +10.5267 q^{14} -1.68203 q^{15} +11.4110 q^{16} -3.34963 q^{17} -2.65538 q^{18} -4.92265 q^{19} -8.49600 q^{20} -3.96430 q^{21} +15.4490 q^{22} +2.84741 q^{23} -8.10171 q^{24} -2.17079 q^{25} +2.65538 q^{26} +1.00000 q^{27} -20.0239 q^{28} -9.70385 q^{29} +4.46642 q^{30} +8.23300 q^{31} -14.0972 q^{32} -5.81798 q^{33} +8.89454 q^{34} +6.66805 q^{35} +5.05105 q^{36} +1.17976 q^{37} +13.0715 q^{38} -1.00000 q^{39} +13.6273 q^{40} -4.01432 q^{41} +10.5267 q^{42} -5.10473 q^{43} -29.3869 q^{44} -1.68203 q^{45} -7.56096 q^{46} -0.541846 q^{47} +11.4110 q^{48} +8.71564 q^{49} +5.76427 q^{50} -3.34963 q^{51} -5.05105 q^{52} -12.5492 q^{53} -2.65538 q^{54} +9.78600 q^{55} +32.1176 q^{56} -4.92265 q^{57} +25.7674 q^{58} -3.30260 q^{59} -8.49600 q^{60} -10.0355 q^{61} -21.8618 q^{62} -3.96430 q^{63} +14.6114 q^{64} +1.68203 q^{65} +15.4490 q^{66} -12.0308 q^{67} -16.9191 q^{68} +2.84741 q^{69} -17.7062 q^{70} -13.8283 q^{71} -8.10171 q^{72} +9.72233 q^{73} -3.13270 q^{74} -2.17079 q^{75} -24.8646 q^{76} +23.0642 q^{77} +2.65538 q^{78} -9.63575 q^{79} -19.1936 q^{80} +1.00000 q^{81} +10.6595 q^{82} +7.71568 q^{83} -20.0239 q^{84} +5.63416 q^{85} +13.5550 q^{86} -9.70385 q^{87} +47.1356 q^{88} -15.8964 q^{89} +4.46642 q^{90} +3.96430 q^{91} +14.3824 q^{92} +8.23300 q^{93} +1.43881 q^{94} +8.28003 q^{95} -14.0972 q^{96} +12.2772 q^{97} -23.1433 q^{98} -5.81798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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