LMFDB - Embedded newform 8031.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62702 q^{2} +1.00000 q^{3} +4.90122 q^{4} +1.25106 q^{5} -2.62702 q^{6} -3.99448 q^{7} -7.62155 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62702 q^{2} +1.00000 q^{3} +4.90122 q^{4} +1.25106 q^{5} -2.62702 q^{6} -3.99448 q^{7} -7.62155 q^{8} +1.00000 q^{9} -3.28657 q^{10} -1.29893 q^{11} +4.90122 q^{12} -1.60304 q^{13} +10.4936 q^{14} +1.25106 q^{15} +10.2195 q^{16} -2.81866 q^{17} -2.62702 q^{18} +0.251686 q^{19} +6.13174 q^{20} -3.99448 q^{21} +3.41230 q^{22} +3.99565 q^{23} -7.62155 q^{24} -3.43484 q^{25} +4.21123 q^{26} +1.00000 q^{27} -19.5778 q^{28} -0.920308 q^{29} -3.28657 q^{30} +3.81849 q^{31} -11.6037 q^{32} -1.29893 q^{33} +7.40466 q^{34} -4.99735 q^{35} +4.90122 q^{36} +10.5330 q^{37} -0.661183 q^{38} -1.60304 q^{39} -9.53505 q^{40} +1.70074 q^{41} +10.4936 q^{42} +1.07004 q^{43} -6.36632 q^{44} +1.25106 q^{45} -10.4966 q^{46} +5.55956 q^{47} +10.2195 q^{48} +8.95584 q^{49} +9.02338 q^{50} -2.81866 q^{51} -7.85687 q^{52} +5.82837 q^{53} -2.62702 q^{54} -1.62504 q^{55} +30.4441 q^{56} +0.251686 q^{57} +2.41766 q^{58} -11.9278 q^{59} +6.13174 q^{60} -11.0689 q^{61} -10.0312 q^{62} -3.99448 q^{63} +10.0441 q^{64} -2.00551 q^{65} +3.41230 q^{66} +3.28806 q^{67} -13.8149 q^{68} +3.99565 q^{69} +13.1281 q^{70} -2.16584 q^{71} -7.62155 q^{72} -8.82229 q^{73} -27.6704 q^{74} -3.43484 q^{75} +1.23357 q^{76} +5.18853 q^{77} +4.21123 q^{78} -2.86216 q^{79} +12.7853 q^{80} +1.00000 q^{81} -4.46786 q^{82} +8.32413 q^{83} -19.5778 q^{84} -3.52632 q^{85} -2.81101 q^{86} -0.920308 q^{87} +9.89983 q^{88} +14.8820 q^{89} -3.28657 q^{90} +6.40332 q^{91} +19.5835 q^{92} +3.81849 q^{93} -14.6051 q^{94} +0.314875 q^{95} -11.6037 q^{96} +15.1845 q^{97} -23.5271 q^{98} -1.29893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * 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 $

$2$	−2.62702	−1.85758	−0.928791	−	0.370605i	$-0.879150\pi$
$2$	−2.62702	−1.85758	−0.928791	+	0.370605i	$0.879150\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.90122	2.45061
$5$	1.25106	0.559493	0.279747	−	0.960074i	$-0.409750\pi$
$5$	1.25106	0.559493	0.279747	+	0.960074i	$0.409750\pi$
$6$	−2.62702	−1.07248
$7$	−3.99448	−1.50977	−0.754885	−	0.655857i	$-0.772307\pi$
$7$	−3.99448	−1.50977	−0.754885	+	0.655857i	$0.772307\pi$
$8$	−7.62155	−2.69462
$9$	1.00000	0.333333
$10$	−3.28657	−1.03930
$11$	−1.29893	−0.391641	−0.195821	−	0.980640i	$-0.562737\pi$
$11$	−1.29893	−0.391641	−0.195821	+	0.980640i	$0.562737\pi$
$12$	4.90122	1.41486
$13$	−1.60304	−0.444605	−0.222302	−	0.974978i	$-0.571357\pi$
$13$	−1.60304	−0.444605	−0.222302	+	0.974978i	$0.571357\pi$
$14$	10.4936	2.80452
$15$	1.25106	0.323023
$16$	10.2195	2.55487
$17$	−2.81866	−0.683625	−0.341812	−	0.939768i	$-0.611041\pi$
$17$	−2.81866	−0.683625	−0.341812	+	0.939768i	$0.611041\pi$
$18$	−2.62702	−0.619194
$19$	0.251686	0.0577407	0.0288703	−	0.999583i	$-0.490809\pi$
$19$	0.251686	0.0577407	0.0288703	+	0.999583i	$0.490809\pi$
$20$	6.13174	1.37110
$21$	−3.99448	−0.871666
$22$	3.41230	0.727505
$23$	3.99565	0.833150	0.416575	−	0.909101i	$-0.363230\pi$
$23$	3.99565	0.833150	0.416575	+	0.909101i	$0.363230\pi$
$24$	−7.62155	−1.55574
$25$	−3.43484	−0.686968
$26$	4.21123	0.825889
$27$	1.00000	0.192450
$28$	−19.5778	−3.69986
$29$	−0.920308	−0.170897	−0.0854484	−	0.996343i	$-0.527232\pi$
$29$	−0.920308	−0.170897	−0.0854484	+	0.996343i	$0.527232\pi$
$30$	−3.28657	−0.600042
$31$	3.81849	0.685821	0.342911	−	0.939368i	$-0.388587\pi$
$31$	3.81849	0.685821	0.342911	+	0.939368i	$0.388587\pi$
$32$	−11.6037	−2.05126
$33$	−1.29893	−0.226114
$34$	7.40466	1.26989
$35$	−4.99735	−0.844706
$36$	4.90122	0.816870
$37$	10.5330	1.73162	0.865809	−	0.500374i	$-0.166804\pi$
$37$	10.5330	1.73162	0.865809	+	0.500374i	$0.166804\pi$
$38$	−0.661183	−0.107258
$39$	−1.60304	−0.256693
$40$	−9.53505	−1.50762
$41$	1.70074	0.265610	0.132805	−	0.991142i	$-0.457602\pi$
$41$	1.70074	0.265610	0.132805	+	0.991142i	$0.457602\pi$
$42$	10.4936	1.61919
$43$	1.07004	0.163179	0.0815896	−	0.996666i	$-0.474000\pi$
$43$	1.07004	0.163179	0.0815896	+	0.996666i	$0.474000\pi$
$44$	−6.36632	−0.959759
$45$	1.25106	0.186498
$46$	−10.4966	−1.54764
$47$	5.55956	0.810946	0.405473	−	0.914107i	$-0.367107\pi$
$47$	5.55956	0.810946	0.405473	+	0.914107i	$0.367107\pi$
$48$	10.2195	1.47506
$49$	8.95584	1.27941
$50$	9.02338	1.27610
$51$	−2.81866	−0.394691
$52$	−7.85687	−1.08955
$53$	5.82837	0.800589	0.400294	−	0.916387i	$-0.368908\pi$
$53$	5.82837	0.800589	0.400294	+	0.916387i	$0.368908\pi$
$54$	−2.62702	−0.357492
$55$	−1.62504	−0.219121
$56$	30.4441	4.06826
$57$	0.251686	0.0333366
$58$	2.41766	0.317455
$59$	−11.9278	−1.55286	−0.776432	−	0.630201i	$-0.782972\pi$
$59$	−11.9278	−1.55286	−0.776432	+	0.630201i	$0.782972\pi$
$60$	6.13174	0.791604
$61$	−11.0689	−1.41723	−0.708616	−	0.705594i	$-0.750680\pi$
$61$	−11.0689	−1.41723	−0.708616	+	0.705594i	$0.750680\pi$
$62$	−10.0312	−1.27397
$63$	−3.99448	−0.503257
$64$	10.0441	1.25551
$65$	−2.00551	−0.248753
$66$	3.41230	0.420025
$67$	3.28806	0.401700	0.200850	−	0.979622i	$-0.435630\pi$
$67$	3.28806	0.401700	0.200850	+	0.979622i	$0.435630\pi$
$68$	−13.8149	−1.67530
$69$	3.99565	0.481019
$70$	13.1281	1.56911
$71$	−2.16584	−0.257038	−0.128519	−	0.991707i	$-0.541022\pi$
$71$	−2.16584	−0.257038	−0.128519	+	0.991707i	$0.541022\pi$
$72$	−7.62155	−0.898208
$73$	−8.82229	−1.03257	−0.516285	−	0.856417i	$-0.672686\pi$
$73$	−8.82229	−1.03257	−0.516285	+	0.856417i	$0.672686\pi$
$74$	−27.6704	−3.21662
$75$	−3.43484	−0.396621
$76$	1.23357	0.141500
$77$	5.18853	0.591288
$78$	4.21123	0.476827
$79$	−2.86216	−0.322018	−0.161009	−	0.986953i	$-0.551475\pi$
$79$	−2.86216	−0.322018	−0.161009	+	0.986953i	$0.551475\pi$
$80$	12.7853	1.42943
$81$	1.00000	0.111111
$82$	−4.46786	−0.493393
$83$	8.32413	0.913692	0.456846	−	0.889546i	$-0.348979\pi$
$83$	8.32413	0.913692	0.456846	+	0.889546i	$0.348979\pi$
$84$	−19.5778	−2.13611
$85$	−3.52632	−0.382483
$86$	−2.81101	−0.303119
$87$	−0.920308	−0.0986674
$88$	9.89983	1.05533
$89$	14.8820	1.57749	0.788744	−	0.614722i	$-0.210732\pi$
$89$	14.8820	1.57749	0.788744	+	0.614722i	$0.210732\pi$
$90$	−3.28657	−0.346435
$91$	6.40332	0.671251
$92$	19.5835	2.04172
$93$	3.81849	0.395959
$94$	−14.6051	−1.50640
$95$	0.314875	0.0323055
$96$	−11.6037	−1.18430
$97$	15.1845	1.54175	0.770877	−	0.636985i	$-0.219818\pi$
$97$	15.1845	1.54175	0.770877	+	0.636985i	$0.219818\pi$
$98$	−23.5271	−2.37660
$99$	−1.29893	−0.130547
$100$	−16.8349	−1.68349
$101$	−0.610430	−0.0607400	−0.0303700	−	0.999539i	$-0.509669\pi$
$101$	−0.610430	−0.0607400	−0.0303700	+	0.999539i	$0.509669\pi$
$102$	7.40466	0.733171
$103$	4.98348	0.491037	0.245519	−	0.969392i	$-0.421042\pi$
$103$	4.98348	0.491037	0.245519	+	0.969392i	$0.421042\pi$
$104$	12.2177	1.19804
$105$	−4.99735	−0.487691
$106$	−15.3112	−1.48716
$107$	4.45846	0.431016	0.215508	−	0.976502i	$-0.430859\pi$
$107$	4.45846	0.431016	0.215508	+	0.976502i	$0.430859\pi$
$108$	4.90122	0.471620
$109$	−17.6080	−1.68654	−0.843272	−	0.537487i	$-0.819374\pi$
$109$	−17.6080	−1.68654	−0.843272	+	0.537487i	$0.819374\pi$
$110$	4.26901	0.407034
$111$	10.5330	0.999751
$112$	−40.8215	−3.85727
$113$	10.9825	1.03314	0.516572	−	0.856244i	$-0.327208\pi$
$113$	10.9825	1.03314	0.516572	+	0.856244i	$0.327208\pi$
$114$	−0.661183	−0.0619255
$115$	4.99881	0.466141
$116$	−4.51063	−0.418801
$117$	−1.60304	−0.148202
$118$	31.3345	2.88457
$119$	11.2591	1.03212
$120$	−9.53505	−0.870427
$121$	−9.31279	−0.846617
$122$	29.0783	2.63263
$123$	1.70074	0.153350
$124$	18.7152	1.68068
$125$	−10.5525	−0.943847
$126$	10.4936	0.934840
$127$	4.94978	0.439222	0.219611	−	0.975588i	$-0.429521\pi$
$127$	4.94978	0.439222	0.219611	+	0.975588i	$0.429521\pi$
$128$	−3.17866	−0.280957
$129$	1.07004	0.0942116
$130$	5.26852	0.462079
$131$	12.4023	1.08360	0.541799	−	0.840508i	$-0.317743\pi$
$131$	12.4023	1.08360	0.541799	+	0.840508i	$0.317743\pi$
$132$	−6.36632	−0.554117
$133$	−1.00535	−0.0871752
$134$	−8.63779	−0.746191
$135$	1.25106	0.107674
$136$	21.4825	1.84211
$137$	9.80028	0.837294	0.418647	−	0.908149i	$-0.362504\pi$
$137$	9.80028	0.837294	0.418647	+	0.908149i	$0.362504\pi$
$138$	−10.4966	−0.893532
$139$	6.93102	0.587882	0.293941	−	0.955824i	$-0.405033\pi$
$139$	6.93102	0.587882	0.293941	+	0.955824i	$0.405033\pi$
$140$	−24.4931	−2.07004
$141$	5.55956	0.468200
$142$	5.68969	0.477469
$143$	2.08224	0.174126
$144$	10.2195	0.851625
$145$	−1.15136	−0.0956156
$146$	23.1763	1.91808
$147$	8.95584	0.738665
$148$	51.6246	4.24352
$149$	16.8262	1.37845	0.689227	−	0.724545i	$-0.257950\pi$
$149$	16.8262	1.37845	0.689227	+	0.724545i	$0.257950\pi$
$150$	9.02338	0.736756
$151$	−17.9034	−1.45696	−0.728478	−	0.685069i	$-0.759772\pi$
$151$	−17.9034	−1.45696	−0.728478	+	0.685069i	$0.759772\pi$
$152$	−1.91824	−0.155589
$153$	−2.81866	−0.227875
$154$	−13.6304	−1.09837
$155$	4.77718	0.383712
$156$	−7.85687	−0.629053
$157$	−6.77529	−0.540727	−0.270364	−	0.962758i	$-0.587144\pi$
$157$	−6.77529	−0.540727	−0.270364	+	0.962758i	$0.587144\pi$
$158$	7.51894	0.598175
$159$	5.82837	0.462220
$160$	−14.5170	−1.14767
$161$	−15.9605	−1.25786
$162$	−2.62702	−0.206398
$163$	−18.4939	−1.44855	−0.724276	−	0.689510i	$-0.757826\pi$
$163$	−18.4939	−1.44855	−0.724276	+	0.689510i	$0.757826\pi$
$164$	8.33567	0.650907
$165$	−1.62504	−0.126509
$166$	−21.8676	−1.69726
$167$	−8.58908	−0.664643	−0.332321	−	0.943166i	$-0.607832\pi$
$167$	−8.58908	−0.664643	−0.332321	+	0.943166i	$0.607832\pi$
$168$	30.4441	2.34881
$169$	−10.4302	−0.802327
$170$	9.26371	0.710494
$171$	0.251686	0.0192469
$172$	5.24449	0.399889
$173$	−16.7026	−1.26988	−0.634938	−	0.772563i	$-0.718974\pi$
$173$	−16.7026	−1.26988	−0.634938	+	0.772563i	$0.718974\pi$
$174$	2.41766	0.183283
$175$	13.7204	1.03716
$176$	−13.2744	−1.00059
$177$	−11.9278	−0.896546
$178$	−39.0953	−2.93031
$179$	−23.6161	−1.76515	−0.882575	−	0.470172i	$-0.844192\pi$
$179$	−23.6161	−1.76515	−0.882575	+	0.470172i	$0.844192\pi$
$180$	6.13174	0.457033
$181$	−8.42679	−0.626359	−0.313179	−	0.949694i	$-0.601394\pi$
$181$	−8.42679	−0.626359	−0.313179	+	0.949694i	$0.601394\pi$
$182$	−16.8216	−1.24690
$183$	−11.0689	−0.818240
$184$	−30.4530	−2.24503
$185$	13.1775	0.968829
$186$	−10.0312	−0.735526
$187$	3.66123	0.267736
$188$	27.2486	1.98731
$189$	−3.99448	−0.290555
$190$	−0.827182	−0.0600101
$191$	−5.15971	−0.373344	−0.186672	−	0.982422i	$-0.559770\pi$
$191$	−5.15971	−0.373344	−0.186672	+	0.982422i	$0.559770\pi$
$192$	10.0441	0.724872
$193$	−20.0486	−1.44313	−0.721564	−	0.692348i	$-0.756576\pi$
$193$	−20.0486	−1.44313	−0.721564	+	0.692348i	$0.756576\pi$
$194$	−39.8900	−2.86393
$195$	−2.00551	−0.143618
$196$	43.8945	3.13532
$197$	−4.62991	−0.329867	−0.164934	−	0.986305i	$-0.552741\pi$
$197$	−4.62991	−0.329867	−0.164934	+	0.986305i	$0.552741\pi$
$198$	3.41230	0.242502
$199$	−21.8225	−1.54696	−0.773478	−	0.633823i	$-0.781485\pi$
$199$	−21.8225	−1.54696	−0.773478	+	0.633823i	$0.781485\pi$
$200$	26.1788	1.85112
$201$	3.28806	0.231922
$202$	1.60361	0.112830
$203$	3.67615	0.258015
$204$	−13.8149	−0.967233
$205$	2.12773	0.148607
$206$	−13.0917	−0.912141
$207$	3.99565	0.277717
$208$	−16.3823	−1.13591
$209$	−0.326921	−0.0226136
$210$	13.1281	0.905926
$211$	−0.572132	−0.0393872	−0.0196936	−	0.999806i	$-0.506269\pi$
$211$	−0.572132	−0.0393872	−0.0196936	+	0.999806i	$0.506269\pi$
$212$	28.5661	1.96193
$213$	−2.16584	−0.148401
$214$	−11.7124	−0.800647
$215$	1.33869	0.0912977
$216$	−7.62155	−0.518581
$217$	−15.2529	−1.03543
$218$	46.2566	3.13289
$219$	−8.82229	−0.596155
$220$	−7.96468	−0.536979
$221$	4.51844	0.303943
$222$	−27.6704	−1.85712
$223$	−18.2772	−1.22393	−0.611966	−	0.790884i	$-0.709621\pi$
$223$	−18.2772	−1.22393	−0.611966	+	0.790884i	$0.709621\pi$
$224$	46.3507	3.09694
$225$	−3.43484	−0.228989
$226$	−28.8511	−1.91915
$227$	10.0053	0.664076	0.332038	−	0.943266i	$-0.392264\pi$
$227$	10.0053	0.664076	0.332038	+	0.943266i	$0.392264\pi$
$228$	1.23357	0.0816950
$229$	8.53714	0.564150	0.282075	−	0.959392i	$-0.408977\pi$
$229$	8.53714	0.564150	0.282075	+	0.959392i	$0.408977\pi$
$230$	−13.1320	−0.865896
$231$	5.18853	0.341380
$232$	7.01417	0.460503
$233$	−3.79997	−0.248944	−0.124472	−	0.992223i	$-0.539724\pi$
$233$	−3.79997	−0.248944	−0.124472	+	0.992223i	$0.539724\pi$
$234$	4.21123	0.275296
$235$	6.95537	0.453718
$236$	−58.4606	−3.80546
$237$	−2.86216	−0.185917
$238$	−29.5777	−1.91724
$239$	−26.6740	−1.72540	−0.862699	−	0.505718i	$-0.831228\pi$
$239$	−26.6740	−1.72540	−0.862699	+	0.505718i	$0.831228\pi$
$240$	12.7853	0.825284
$241$	−21.0391	−1.35525	−0.677624	−	0.735408i	$-0.736990\pi$
$241$	−21.0391	−1.35525	−0.677624	+	0.735408i	$0.736990\pi$
$242$	24.4649	1.57266
$243$	1.00000	0.0641500
$244$	−54.2513	−3.47308
$245$	11.2043	0.715819
$246$	−4.46786	−0.284860
$247$	−0.403464	−0.0256718
$248$	−29.1028	−1.84803
$249$	8.32413	0.527520
$250$	27.7217	1.75327
$251$	17.7788	1.12219	0.561094	−	0.827752i	$-0.310381\pi$
$251$	17.7788	1.12219	0.561094	+	0.827752i	$0.310381\pi$
$252$	−19.5778	−1.23329
$253$	−5.19005	−0.326296
$254$	−13.0031	−0.815890
$255$	−3.52632	−0.220827
$256$	−11.7378	−0.733614
$257$	−21.6977	−1.35347	−0.676733	−	0.736229i	$-0.736605\pi$
$257$	−21.6977	−1.35347	−0.676733	+	0.736229i	$0.736605\pi$
$258$	−2.81101	−0.175006
$259$	−42.0739	−2.61435
$260$	−9.82945	−0.609597
$261$	−0.920308	−0.0569656
$262$	−32.5812	−2.01287
$263$	24.1397	1.48852	0.744259	−	0.667891i	$-0.232803\pi$
$263$	24.1397	1.48852	0.744259	+	0.667891i	$0.232803\pi$
$264$	9.89983	0.609293
$265$	7.29167	0.447924
$266$	2.64108	0.161935
$267$	14.8820	0.910763
$268$	16.1155	0.984411
$269$	−20.5955	−1.25573	−0.627864	−	0.778323i	$-0.716071\pi$
$269$	−20.5955	−1.25573	−0.627864	+	0.778323i	$0.716071\pi$
$270$	−3.28657	−0.200014
$271$	14.7461	0.895759	0.447880	−	0.894094i	$-0.352179\pi$
$271$	14.7461	0.895759	0.447880	+	0.894094i	$0.352179\pi$
$272$	−28.8053	−1.74658
$273$	6.40332	0.387547
$274$	−25.7455	−1.55534
$275$	4.46160	0.269045
$276$	19.5835	1.17879
$277$	−9.63280	−0.578779	−0.289389	−	0.957211i	$-0.593452\pi$
$277$	−9.63280	−0.578779	−0.289389	+	0.957211i	$0.593452\pi$
$278$	−18.2079	−1.09204
$279$	3.81849	0.228607
$280$	38.0875	2.27616
$281$	−6.20323	−0.370054	−0.185027	−	0.982733i	$-0.559237\pi$
$281$	−6.20323	−0.370054	−0.185027	+	0.982733i	$0.559237\pi$
$282$	−14.6051	−0.869719
$283$	−12.6423	−0.751504	−0.375752	−	0.926720i	$-0.622616\pi$
$283$	−12.6423	−0.751504	−0.375752	+	0.926720i	$0.622616\pi$
$284$	−10.6152	−0.629899
$285$	0.314875	0.0186516
$286$	−5.47007	−0.323452
$287$	−6.79355	−0.401010
$288$	−11.6037	−0.683755
$289$	−9.05517	−0.532657
$290$	3.02465	0.177614
$291$	15.1845	0.890132
$292$	−43.2399	−2.53043
$293$	29.2404	1.70824	0.854121	−	0.520074i	$-0.174096\pi$
$293$	29.2404	1.70824	0.854121	+	0.520074i	$0.174096\pi$
$294$	−23.5271	−1.37213
$295$	−14.9224	−0.868817
$296$	−80.2779	−4.66606
$297$	−1.29893	−0.0753714
$298$	−44.2026	−2.56059
$299$	−6.40520	−0.370422
$300$	−16.8349	−0.971963
$301$	−4.27424	−0.246363
$302$	47.0325	2.70642
$303$	−0.610430	−0.0350683
$304$	2.57210	0.147520
$305$	−13.8480	−0.792932
$306$	7.40466	0.423296
$307$	15.5092	0.885160	0.442580	−	0.896729i	$-0.354063\pi$
$307$	15.5092	0.885160	0.442580	+	0.896729i	$0.354063\pi$
$308$	25.4301	1.44902
$309$	4.98348	0.283500
$310$	−12.5497	−0.712776
$311$	2.81793	0.159790	0.0798952	−	0.996803i	$-0.474541\pi$
$311$	2.81793	0.159790	0.0798952	+	0.996803i	$0.474541\pi$
$312$	12.2177	0.691690
$313$	13.7517	0.777290	0.388645	−	0.921388i	$-0.372943\pi$
$313$	13.7517	0.777290	0.388645	+	0.921388i	$0.372943\pi$
$314$	17.7988	1.00445
$315$	−4.99735	−0.281569
$316$	−14.0281	−0.789140
$317$	−8.37919	−0.470622	−0.235311	−	0.971920i	$-0.575611\pi$
$317$	−8.37919	−0.470622	−0.235311	+	0.971920i	$0.575611\pi$
$318$	−15.3112	−0.858612
$319$	1.19541	0.0669303
$320$	12.5658	0.702452
$321$	4.45846	0.248847
$322$	41.9285	2.33659
$323$	−0.709416	−0.0394730
$324$	4.90122	0.272290
$325$	5.50620	0.305429
$326$	48.5837	2.69080
$327$	−17.6080	−0.973726
$328$	−12.9622	−0.715720
$329$	−22.2075	−1.22434
$330$	4.26901	0.235001
$331$	−6.70615	−0.368603	−0.184302	−	0.982870i	$-0.559002\pi$
$331$	−6.70615	−0.368603	−0.184302	+	0.982870i	$0.559002\pi$
$332$	40.7984	2.23910
$333$	10.5330	0.577206
$334$	22.5637	1.23463
$335$	4.11357	0.224749
$336$	−40.8215	−2.22700
$337$	2.08192	0.113409	0.0567047	−	0.998391i	$-0.481941\pi$
$337$	2.08192	0.113409	0.0567047	+	0.998391i	$0.481941\pi$
$338$	27.4004	1.49039
$339$	10.9825	0.596486
$340$	−17.2833	−0.937317
$341$	−4.95994	−0.268596
$342$	−0.661183	−0.0357527
$343$	−7.81255	−0.421838
$344$	−8.15535	−0.439707
$345$	4.99881	0.269127
$346$	43.8780	2.35890
$347$	−29.1241	−1.56346	−0.781732	−	0.623615i	$-0.785663\pi$
$347$	−29.1241	−1.56346	−0.781732	+	0.623615i	$0.785663\pi$
$348$	−4.51063	−0.241795
$349$	27.8464	1.49058	0.745291	−	0.666739i	$-0.232310\pi$
$349$	27.8464	1.49058	0.745291	+	0.666739i	$0.232310\pi$
$350$	−36.0437	−1.92661
$351$	−1.60304	−0.0855642
$352$	15.0724	0.803359
$353$	22.2178	1.18254	0.591268	−	0.806475i	$-0.298628\pi$
$353$	22.2178	1.18254	0.591268	+	0.806475i	$0.298628\pi$
$354$	31.3345	1.66541
$355$	−2.70960	−0.143811
$356$	72.9399	3.86581
$357$	11.2591	0.595893
$358$	62.0399	3.27891
$359$	1.74663	0.0921835	0.0460917	−	0.998937i	$-0.485323\pi$
$359$	1.74663	0.0921835	0.0460917	+	0.998937i	$0.485323\pi$
$360$	−9.53505	−0.502541
$361$	−18.9367	−0.996666
$362$	22.1373	1.16351
$363$	−9.31279	−0.488795
$364$	31.3841	1.64497
$365$	−11.0372	−0.577716
$366$	29.0783	1.51995
$367$	20.4499	1.06748	0.533739	−	0.845649i	$-0.320786\pi$
$367$	20.4499	1.06748	0.533739	+	0.845649i	$0.320786\pi$
$368$	40.8335	2.12859
$369$	1.70074	0.0885367
$370$	−34.6175	−1.79968
$371$	−23.2813	−1.20870
$372$	18.7152	0.970340
$373$	−6.69342	−0.346572	−0.173286	−	0.984872i	$-0.555439\pi$
$373$	−6.69342	−0.346572	−0.173286	+	0.984872i	$0.555439\pi$
$374$	−9.61811	−0.497341
$375$	−10.5525	−0.544930
$376$	−42.3725	−2.18519
$377$	1.47530	0.0759816
$378$	10.4936	0.539730
$379$	−25.3878	−1.30408	−0.652041	−	0.758184i	$-0.726087\pi$
$379$	−25.3878	−1.30408	−0.652041	+	0.758184i	$0.726087\pi$
$380$	1.54327	0.0791682
$381$	4.94978	0.253585
$382$	13.5547	0.693516
$383$	−8.29476	−0.423842	−0.211921	−	0.977287i	$-0.567972\pi$
$383$	−8.29476	−0.423842	−0.211921	+	0.977287i	$0.567972\pi$
$384$	−3.17866	−0.162211
$385$	6.49119	0.330822
$386$	52.6679	2.68073
$387$	1.07004	0.0543931
$388$	74.4226	3.77823
$389$	−18.4791	−0.936927	−0.468464	−	0.883483i	$-0.655192\pi$
$389$	−18.4791	−0.936927	−0.468464	+	0.883483i	$0.655192\pi$
$390$	5.26852	0.266782
$391$	−11.2624	−0.569562
$392$	−68.2574	−3.44752
$393$	12.4023	0.625615
$394$	12.1628	0.612755
$395$	−3.58074	−0.180167
$396$	−6.36632	−0.319920
$397$	−12.2468	−0.614648	−0.307324	−	0.951605i	$-0.599434\pi$
$397$	−12.2468	−0.614648	−0.307324	+	0.951605i	$0.599434\pi$
$398$	57.3281	2.87360
$399$	−1.00535	−0.0503306
$400$	−35.1023	−1.75512
$401$	−16.7570	−0.836804	−0.418402	−	0.908262i	$-0.637410\pi$
$401$	−16.7570	−0.836804	−0.418402	+	0.908262i	$0.637410\pi$
$402$	−8.63779	−0.430814
$403$	−6.12121	−0.304919
$404$	−2.99185	−0.148850
$405$	1.25106	0.0621659
$406$	−9.65730	−0.479284
$407$	−13.6816	−0.678173
$408$	21.4825	1.06354
$409$	−11.2456	−0.556058	−0.278029	−	0.960573i	$-0.589681\pi$
$409$	−11.2456	−0.556058	−0.278029	+	0.960573i	$0.589681\pi$
$410$	−5.58958	−0.276050
$411$	9.80028	0.483412
$412$	24.4251	1.20334
$413$	47.6452	2.34447
$414$	−10.4966	−0.515881
$415$	10.4140	0.511204
$416$	18.6013	0.912001
$417$	6.93102	0.339414
$418$	0.858828	0.0420067
$419$	−7.06667	−0.345229	−0.172615	−	0.984989i	$-0.555222\pi$
$419$	−7.06667	−0.345229	−0.172615	+	0.984989i	$0.555222\pi$
$420$	−24.4931	−1.19514
$421$	2.50796	0.122230	0.0611152	−	0.998131i	$-0.480534\pi$
$421$	2.50796	0.122230	0.0611152	+	0.998131i	$0.480534\pi$
$422$	1.50300	0.0731649
$423$	5.55956	0.270315
$424$	−44.4212	−2.15729
$425$	9.68163	0.469628
$426$	5.68969	0.275667
$427$	44.2146	2.13970
$428$	21.8519	1.05625
$429$	2.08224	0.100531
$430$	−3.51675	−0.169593
$431$	−10.5693	−0.509106	−0.254553	−	0.967059i	$-0.581928\pi$
$431$	−10.5693	−0.509106	−0.254553	+	0.967059i	$0.581928\pi$
$432$	10.2195	0.491686
$433$	−39.6127	−1.90367	−0.951833	−	0.306617i	$-0.900803\pi$
$433$	−39.6127	−1.90367	−0.951833	+	0.306617i	$0.900803\pi$
$434$	40.0695	1.92340
$435$	−1.15136	−0.0552037
$436$	−86.3008	−4.13306
$437$	1.00565	0.0481066
$438$	23.1763	1.10741
$439$	10.6468	0.508143	0.254072	−	0.967185i	$-0.418230\pi$
$439$	10.6468	0.508143	0.254072	+	0.967185i	$0.418230\pi$
$440$	12.3853	0.590447
$441$	8.95584	0.426469
$442$	−11.8700	−0.564599
$443$	−17.4800	−0.830498	−0.415249	−	0.909708i	$-0.636306\pi$
$443$	−17.4800	−0.830498	−0.415249	+	0.909708i	$0.636306\pi$
$444$	51.6246	2.45000
$445$	18.6183	0.882594
$446$	48.0145	2.27355
$447$	16.8262	0.795851
$448$	−40.1210	−1.89554
$449$	4.03715	0.190525	0.0952625	−	0.995452i	$-0.469631\pi$
$449$	4.03715	0.190525	0.0952625	+	0.995452i	$0.469631\pi$
$450$	9.02338	0.425366
$451$	−2.20913	−0.104024
$452$	53.8275	2.53183
$453$	−17.9034	−0.841174
$454$	−26.2841	−1.23358
$455$	8.01097	0.375560
$456$	−1.91824	−0.0898296
$457$	24.5828	1.14993	0.574966	−	0.818177i	$-0.305015\pi$
$457$	24.5828	1.14993	0.574966	+	0.818177i	$0.305015\pi$
$458$	−22.4272	−1.04795
$459$	−2.81866	−0.131564
$460$	24.5003	1.14233
$461$	9.19961	0.428469	0.214234	−	0.976782i	$-0.431274\pi$
$461$	9.19961	0.428469	0.214234	+	0.976782i	$0.431274\pi$
$462$	−13.6304	−0.634142
$463$	−6.79730	−0.315897	−0.157949	−	0.987447i	$-0.550488\pi$
$463$	−6.79730	−0.315897	−0.157949	+	0.987447i	$0.550488\pi$
$464$	−9.40509	−0.436620
$465$	4.77718	0.221536
$466$	9.98258	0.462434
$467$	2.87554	0.133064	0.0665320	−	0.997784i	$-0.478807\pi$
$467$	2.87554	0.133064	0.0665320	+	0.997784i	$0.478807\pi$
$468$	−7.85687	−0.363184
$469$	−13.1341	−0.606475
$470$	−18.2719	−0.842819
$471$	−6.77529	−0.312189
$472$	90.9081	4.18438
$473$	−1.38990	−0.0639077
$474$	7.51894	0.345356
$475$	−0.864500	−0.0396660
$476$	55.1831	2.52931
$477$	5.82837	0.266863
$478$	70.0731	3.20507
$479$	−14.5723	−0.665825	−0.332912	−	0.942958i	$-0.608031\pi$
$479$	−14.5723	−0.665825	−0.332912	+	0.942958i	$0.608031\pi$
$480$	−14.5170	−0.662606
$481$	−16.8849	−0.769886
$482$	55.2701	2.51748
$483$	−15.9605	−0.726228
$484$	−45.6440	−2.07473
$485$	18.9968	0.862600
$486$	−2.62702	−0.119164
$487$	−22.3514	−1.01284	−0.506420	−	0.862287i	$-0.669031\pi$
$487$	−22.3514	−1.01284	−0.506420	+	0.862287i	$0.669031\pi$
$488$	84.3625	3.81891
$489$	−18.4939	−0.836322
$490$	−29.4340	−1.32969
$491$	41.8791	1.88998	0.944988	−	0.327106i	$-0.106074\pi$
$491$	41.8791	1.88998	0.944988	+	0.327106i	$0.106074\pi$
$492$	8.33567	0.375801
$493$	2.59403	0.116829
$494$	1.05991	0.0476874
$495$	−1.62504	−0.0730402
$496$	39.0230	1.75219
$497$	8.65139	0.388068
$498$	−21.8676	−0.979912
$499$	−14.3614	−0.642903	−0.321451	−	0.946926i	$-0.604171\pi$
$499$	−14.3614	−0.642903	−0.321451	+	0.946926i	$0.604171\pi$
$500$	−51.7202	−2.31300
$501$	−8.58908	−0.383732
$502$	−46.7052	−2.08456
$503$	−11.0030	−0.490599	−0.245300	−	0.969447i	$-0.578886\pi$
$503$	−11.0030	−0.490599	−0.245300	+	0.969447i	$0.578886\pi$
$504$	30.4441	1.35609
$505$	−0.763687	−0.0339836
$506$	13.6344	0.606121
$507$	−10.4302	−0.463224
$508$	24.2599	1.07636
$509$	−20.1784	−0.894391	−0.447195	−	0.894436i	$-0.647577\pi$
$509$	−20.1784	−0.894391	−0.447195	+	0.894436i	$0.647577\pi$
$510$	9.26371	0.410204
$511$	35.2404	1.55894
$512$	37.1928	1.64370
$513$	0.251686	0.0111122
$514$	57.0002	2.51417
$515$	6.23466	0.274732
$516$	5.24449	0.230876
$517$	−7.22147	−0.317600
$518$	110.529	4.85636
$519$	−16.7026	−0.733163
$520$	15.2851	0.670296
$521$	−19.6223	−0.859667	−0.429834	−	0.902908i	$-0.641428\pi$
$521$	−19.6223	−0.859667	−0.429834	+	0.902908i	$0.641428\pi$
$522$	2.41766	0.105818
$523$	−20.3345	−0.889164	−0.444582	−	0.895738i	$-0.646648\pi$
$523$	−20.3345	−0.889164	−0.444582	+	0.895738i	$0.646648\pi$
$524$	60.7866	2.65547
$525$	13.7204	0.598806
$526$	−63.4154	−2.76504
$527$	−10.7630	−0.468844
$528$	−13.2744	−0.577693
$529$	−7.03481	−0.305862
$530$	−19.1553	−0.832055
$531$	−11.9278	−0.517621
$532$	−4.92745	−0.213632
$533$	−2.72636	−0.118092
$534$	−39.0953	−1.69182
$535$	5.57782	0.241150
$536$	−25.0601	−1.08243
$537$	−23.6161	−1.01911
$538$	54.1047	2.33262
$539$	−11.6330	−0.501068
$540$	6.13174	0.263868
$541$	−28.5016	−1.22538	−0.612690	−	0.790323i	$-0.709913\pi$
$541$	−28.5016	−1.22538	−0.612690	+	0.790323i	$0.709913\pi$
$542$	−38.7381	−1.66395
$543$	−8.42679	−0.361628
$544$	32.7069	1.40229
$545$	−22.0288	−0.943609
$546$	−16.8216	−0.719900
$547$	11.2441	0.480762	0.240381	−	0.970679i	$-0.422728\pi$
$547$	11.2441	0.480762	0.240381	+	0.970679i	$0.422728\pi$
$548$	48.0333	2.05188
$549$	−11.0689	−0.472411
$550$	−11.7207	−0.499773
$551$	−0.231628	−0.00986770
$552$	−30.4530	−1.29617
$553$	11.4328	0.486173
$554$	25.3055	1.07513
$555$	13.1775	0.559353
$556$	33.9705	1.44067
$557$	−0.250660	−0.0106208	−0.00531040	−	0.999986i	$-0.501690\pi$
$557$	−0.250660	−0.0106208	−0.00531040	+	0.999986i	$0.501690\pi$
$558$	−10.0312	−0.424656
$559$	−1.71532	−0.0725503
$560$	−51.0704	−2.15812
$561$	3.66123	0.154577
$562$	16.2960	0.687405
$563$	20.6561	0.870551	0.435276	−	0.900297i	$-0.356651\pi$
$563$	20.6561	0.870551	0.435276	+	0.900297i	$0.356651\pi$
$564$	27.2486	1.14737
$565$	13.7398	0.578037
$566$	33.2114	1.39598
$567$	−3.99448	−0.167752
$568$	16.5070	0.692620
$569$	24.9412	1.04559	0.522795	−	0.852459i	$-0.324889\pi$
$569$	24.9412	1.04559	0.522795	+	0.852459i	$0.324889\pi$
$570$	−0.827182	−0.0346469
$571$	4.28712	0.179410	0.0897052	−	0.995968i	$-0.471408\pi$
$571$	4.28712	0.179410	0.0897052	+	0.995968i	$0.471408\pi$
$572$	10.2055	0.426713
$573$	−5.15971	−0.215550
$574$	17.8468	0.744909
$575$	−13.7244	−0.572347
$576$	10.0441	0.418505
$577$	26.7465	1.11347	0.556736	−	0.830690i	$-0.312054\pi$
$577$	26.7465	1.11347	0.556736	+	0.830690i	$0.312054\pi$
$578$	23.7881	0.989454
$579$	−20.0486	−0.833190
$580$	−5.64309	−0.234316
$581$	−33.2505	−1.37946
$582$	−39.8900	−1.65349
$583$	−7.57063	−0.313544
$584$	67.2395	2.78239
$585$	−2.00551	−0.0829177
$586$	−76.8150	−3.17320
$587$	−2.43920	−0.100677	−0.0503383	−	0.998732i	$-0.516030\pi$
$587$	−2.43920	−0.100677	−0.0503383	+	0.998732i	$0.516030\pi$
$588$	43.8945	1.81018
$589$	0.961060	0.0395998
$590$	39.2014	1.61390
$591$	−4.62991	−0.190449
$592$	107.642	4.42407
$593$	3.43534	0.141072	0.0705362	−	0.997509i	$-0.477529\pi$
$593$	3.43534	0.141072	0.0705362	+	0.997509i	$0.477529\pi$
$594$	3.41230	0.140008
$595$	14.0858	0.577462
$596$	82.4687	3.37805
$597$	−21.8225	−0.893136
$598$	16.8266	0.688090
$599$	−13.3446	−0.545247	−0.272623	−	0.962121i	$-0.587891\pi$
$599$	−13.3446	−0.545247	−0.272623	+	0.962121i	$0.587891\pi$
$600$	26.1788	1.06874
$601$	3.29771	0.134516	0.0672582	−	0.997736i	$-0.478575\pi$
$601$	3.29771	0.134516	0.0672582	+	0.997736i	$0.478575\pi$
$602$	11.2285	0.457640
$603$	3.28806	0.133900
$604$	−87.7484	−3.57043
$605$	−11.6509	−0.473676
$606$	1.60361	0.0651422
$607$	1.65124	0.0670218	0.0335109	−	0.999438i	$-0.489331\pi$
$607$	1.65124	0.0670218	0.0335109	+	0.999438i	$0.489331\pi$
$608$	−2.92049	−0.118441
$609$	3.67615	0.148965
$610$	36.3788	1.47294
$611$	−8.91223	−0.360550
$612$	−13.8149	−0.558432
$613$	43.8337	1.77043	0.885213	−	0.465186i	$-0.154013\pi$
$613$	43.8337	1.77043	0.885213	+	0.465186i	$0.154013\pi$
$614$	−40.7431	−1.64426
$615$	2.12773	0.0857983
$616$	−39.5446	−1.59330
$617$	−27.0993	−1.09098	−0.545489	−	0.838118i	$-0.683656\pi$
$617$	−27.0993	−1.09098	−0.545489	+	0.838118i	$0.683656\pi$
$618$	−13.0917	−0.526625
$619$	22.2385	0.893840	0.446920	−	0.894574i	$-0.352521\pi$
$619$	22.2385	0.893840	0.446920	+	0.894574i	$0.352521\pi$
$620$	23.4140	0.940328
$621$	3.99565	0.160340
$622$	−7.40276	−0.296824
$623$	−59.4458	−2.38164
$624$	−16.3823	−0.655817
$625$	3.97230	0.158892
$626$	−36.1259	−1.44388
$627$	−0.326921	−0.0130560
$628$	−33.2072	−1.32511
$629$	−29.6890	−1.18378
$630$	13.1281	0.523037
$631$	10.7718	0.428821	0.214410	−	0.976744i	$-0.431217\pi$
$631$	10.7718	0.428821	0.214410	+	0.976744i	$0.431217\pi$
$632$	21.8141	0.867717
$633$	−0.572132	−0.0227402
$634$	22.0123	0.874219
$635$	6.19249	0.245741
$636$	28.5661	1.13272
$637$	−14.3566	−0.568830
$638$	−3.14037	−0.124328
$639$	−2.16584	−0.0856792
$640$	−3.97671	−0.157193
$641$	10.9502	0.432508	0.216254	−	0.976337i	$-0.430616\pi$
$641$	10.9502	0.432508	0.216254	+	0.976337i	$0.430616\pi$
$642$	−11.7124	−0.462253
$643$	−5.95014	−0.234650	−0.117325	−	0.993094i	$-0.537432\pi$
$643$	−5.95014	−0.234650	−0.117325	+	0.993094i	$0.537432\pi$
$644$	−78.2259	−3.08253
$645$	1.33869	0.0527107
$646$	1.86365	0.0733243
$647$	7.50653	0.295112	0.147556	−	0.989054i	$-0.452859\pi$
$647$	7.50653	0.295112	0.147556	+	0.989054i	$0.452859\pi$
$648$	−7.62155	−0.299403
$649$	15.4933	0.608166
$650$	−14.4649	−0.567359
$651$	−15.2529	−0.597807
$652$	−90.6426	−3.54984
$653$	−35.2316	−1.37872	−0.689359	−	0.724420i	$-0.742108\pi$
$653$	−35.2316	−1.37872	−0.689359	+	0.724420i	$0.742108\pi$
$654$	46.2566	1.80878
$655$	15.5161	0.606265
$656$	17.3807	0.678601
$657$	−8.82229	−0.344190
$658$	58.3396	2.27431
$659$	45.4534	1.77061	0.885306	−	0.465008i	$-0.153949\pi$
$659$	45.4534	1.77061	0.885306	+	0.465008i	$0.153949\pi$
$660$	−7.96468	−0.310025
$661$	36.0197	1.40101	0.700503	−	0.713650i	$-0.252959\pi$
$661$	36.0197	1.40101	0.700503	+	0.713650i	$0.252959\pi$
$662$	17.6172	0.684711
$663$	4.51844	0.175481
$664$	−63.4427	−2.46206
$665$	−1.25776	−0.0487739
$666$	−27.6704	−1.07221
$667$	−3.67722	−0.142383
$668$	−42.0969	−1.62878
$669$	−18.2772	−0.706638
$670$	−10.8064	−0.417489
$671$	14.3777	0.555047
$672$	46.3507	1.78802
$673$	1.07660	0.0415000	0.0207500	−	0.999785i	$-0.493395\pi$
$673$	1.07660	0.0415000	0.0207500	+	0.999785i	$0.493395\pi$
$674$	−5.46923	−0.210667
$675$	−3.43484	−0.132207
$676$	−51.1209	−1.96619
$677$	−4.79745	−0.184381	−0.0921905	−	0.995741i	$-0.529387\pi$
$677$	−4.79745	−0.184381	−0.0921905	+	0.995741i	$0.529387\pi$
$678$	−28.8511	−1.10802
$679$	−60.6542	−2.32769
$680$	26.8760	1.03065
$681$	10.0053	0.383405
$682$	13.0298	0.498939
$683$	13.7927	0.527764	0.263882	−	0.964555i	$-0.414997\pi$
$683$	13.7927	0.527764	0.263882	+	0.964555i	$0.414997\pi$
$684$	1.23357	0.0471666
$685$	12.2608	0.468460
$686$	20.5237	0.783599
$687$	8.53714	0.325712
$688$	10.9353	0.416903
$689$	−9.34315	−0.355946
$690$	−13.1320	−0.499925
$691$	−36.0019	−1.36958	−0.684789	−	0.728741i	$-0.740106\pi$
$691$	−36.0019	−1.36958	−0.684789	+	0.728741i	$0.740106\pi$
$692$	−81.8631	−3.11197
$693$	5.18853	0.197096
$694$	76.5095	2.90426
$695$	8.67116	0.328916
$696$	7.01417	0.265871
$697$	−4.79379	−0.181578
$698$	−73.1529	−2.76888
$699$	−3.79997	−0.143728
$700$	67.2466	2.54168
$701$	0.447761	0.0169117	0.00845585	−	0.999964i	$-0.497308\pi$
$701$	0.447761	0.0169117	0.00845585	+	0.999964i	$0.497308\pi$
$702$	4.21123	0.158942
$703$	2.65101	0.0999849
$704$	−13.0466	−0.491711
$705$	6.95537	0.261954
$706$	−58.3666	−2.19666
$707$	2.43835	0.0917035
$708$	−58.4606	−2.19708
$709$	25.4751	0.956738	0.478369	−	0.878159i	$-0.341228\pi$
$709$	25.4751	0.956738	0.478369	+	0.878159i	$0.341228\pi$
$710$	7.11817	0.267140
$711$	−2.86216	−0.107339
$712$	−113.424	−4.25074
$713$	15.2573	0.571392
$714$	−29.5777	−1.10692
$715$	2.60501	0.0974220
$716$	−115.748	−4.32569
$717$	−26.6740	−0.996159
$718$	−4.58842	−0.171238
$719$	−36.0009	−1.34261	−0.671304	−	0.741182i	$-0.734266\pi$
$719$	−36.0009	−1.34261	−0.671304	+	0.741182i	$0.734266\pi$
$720$	12.7853	0.476478
$721$	−19.9064	−0.741353
$722$	49.7469	1.85139
$723$	−21.0391	−0.782453
$724$	−41.3015	−1.53496
$725$	3.16111	0.117401
$726$	24.4649	0.907976
$727$	−34.1351	−1.26600	−0.633001	−	0.774151i	$-0.718177\pi$
$727$	−34.1351	−1.26600	−0.633001	+	0.774151i	$0.718177\pi$
$728$	−48.8032	−1.80877
$729$	1.00000	0.0370370
$730$	28.9950	1.07315
$731$	−3.01607	−0.111553
$732$	−54.2513	−2.00519
$733$	41.5222	1.53366	0.766829	−	0.641851i	$-0.221833\pi$
$733$	41.5222	1.53366	0.766829	+	0.641851i	$0.221833\pi$
$734$	−53.7224	−1.98293
$735$	11.2043	0.413278
$736$	−46.3643	−1.70901
$737$	−4.27095	−0.157322
$738$	−4.46786	−0.164464
$739$	10.5527	0.388187	0.194093	−	0.980983i	$-0.437823\pi$
$739$	10.5527	0.388187	0.194093	+	0.980983i	$0.437823\pi$
$740$	64.5858	2.37422
$741$	−0.403464	−0.0148216
$742$	61.1604	2.24527
$743$	9.52129	0.349302	0.174651	−	0.984630i	$-0.444120\pi$
$743$	9.52129	0.349302	0.174651	+	0.984630i	$0.444120\pi$
$744$	−29.1028	−1.06696
$745$	21.0506	0.771235
$746$	17.5837	0.643786
$747$	8.32413	0.304564
$748$	17.9445	0.656115
$749$	−17.8092	−0.650734
$750$	27.7217	1.01225
$751$	38.0551	1.38865	0.694325	−	0.719661i	$-0.255703\pi$
$751$	38.0551	1.38865	0.694325	+	0.719661i	$0.255703\pi$
$752$	56.8160	2.07186
$753$	17.7788	0.647896
$754$	−3.87562	−0.141142
$755$	−22.3983	−0.815157
$756$	−19.5778	−0.712038
$757$	1.85049	0.0672571	0.0336285	−	0.999434i	$-0.489294\pi$
$757$	1.85049	0.0672571	0.0336285	+	0.999434i	$0.489294\pi$
$758$	66.6941	2.42244
$759$	−5.19005	−0.188387
$760$	−2.39984	−0.0870512
$761$	21.4859	0.778864	0.389432	−	0.921055i	$-0.372671\pi$
$761$	21.4859	0.778864	0.389432	+	0.921055i	$0.372671\pi$
$762$	−13.0031	−0.471054
$763$	70.3349	2.54629
$764$	−25.2889	−0.914919
$765$	−3.52632	−0.127494
$766$	21.7905	0.787322
$767$	19.1208	0.690411
$768$	−11.7378	−0.423552
$769$	35.9089	1.29491	0.647454	−	0.762105i	$-0.275834\pi$
$769$	35.9089	1.29491	0.647454	+	0.762105i	$0.275834\pi$
$770$	−17.0525	−0.614528
$771$	−21.6977	−0.781424
$772$	−98.2624	−3.53654
$773$	−46.3674	−1.66772	−0.833860	−	0.551975i	$-0.813874\pi$
$773$	−46.3674	−1.66772	−0.833860	+	0.551975i	$0.813874\pi$
$774$	−2.81101	−0.101040
$775$	−13.1159	−0.471137
$776$	−115.729	−4.15444
$777$	−42.0739	−1.50939
$778$	48.5449	1.74042
$779$	0.428051	0.0153365
$780$	−9.82945	−0.351951
$781$	2.81327	0.100667
$782$	29.5864	1.05801
$783$	−0.920308	−0.0328891
$784$	91.5242	3.26872
$785$	−8.47633	−0.302533
$786$	−32.5812	−1.16213
$787$	−21.0375	−0.749904	−0.374952	−	0.927044i	$-0.622341\pi$
$787$	−21.0375	−0.749904	−0.374952	+	0.927044i	$0.622341\pi$
$788$	−22.6922	−0.808375
$789$	24.1397	0.859397
$790$	9.40667	0.334674
$791$	−43.8692	−1.55981
$792$	9.89983	0.351775
$793$	17.7440	0.630108
$794$	32.1725	1.14176
$795$	7.29167	0.258609
$796$	−106.957	−3.79098
$797$	−55.4460	−1.96400	−0.981999	−	0.188885i	$-0.939513\pi$
$797$	−55.4460	−1.96400	−0.981999	+	0.188885i	$0.939513\pi$
$798$	2.64108	0.0934932
$799$	−15.6705	−0.554383
$800$	39.8568	1.40915
$801$	14.8820	0.525829
$802$	44.0209	1.55443
$803$	11.4595	0.404397
$804$	16.1155	0.568350
$805$	−19.9676	−0.703766
$806$	16.0805	0.566412
$807$	−20.5955	−0.724995
$808$	4.65242	0.163672
$809$	26.1374	0.918942	0.459471	−	0.888193i	$-0.348039\pi$
$809$	26.1374	0.918942	0.459471	+	0.888193i	$0.348039\pi$
$810$	−3.28657	−0.115478
$811$	−1.57898	−0.0554454	−0.0277227	−	0.999616i	$-0.508826\pi$
$811$	−1.57898	−0.0554454	−0.0277227	+	0.999616i	$0.508826\pi$
$812$	18.0176	0.632294
$813$	14.7461	0.517167
$814$	35.9419	1.25976
$815$	−23.1370	−0.810455
$816$	−28.8053	−1.00839
$817$	0.269313	0.00942208
$818$	29.5423	1.03292
$819$	6.40332	0.223750
$820$	10.4285	0.364178
$821$	−38.4449	−1.34174	−0.670868	−	0.741577i	$-0.734078\pi$
$821$	−38.4449	−1.34174	−0.670868	+	0.741577i	$0.734078\pi$
$822$	−25.7455	−0.897977
$823$	−40.7090	−1.41903	−0.709514	−	0.704692i	$-0.751085\pi$
$823$	−40.7090	−1.41903	−0.709514	+	0.704692i	$0.751085\pi$
$824$	−37.9818	−1.32316
$825$	4.46160	0.155333
$826$	−125.165	−4.35504
$827$	−5.34297	−0.185793	−0.0928967	−	0.995676i	$-0.529613\pi$
$827$	−5.34297	−0.185793	−0.0928967	+	0.995676i	$0.529613\pi$
$828$	19.5835	0.680575
$829$	3.06732	0.106533	0.0532663	−	0.998580i	$-0.483037\pi$
$829$	3.06732	0.106533	0.0532663	+	0.998580i	$0.483037\pi$
$830$	−27.3578	−0.949603
$831$	−9.63280	−0.334158
$832$	−16.1012	−0.558208
$833$	−25.2434	−0.874634
$834$	−18.2079	−0.630489
$835$	−10.7455	−0.371863
$836$	−1.60231	−0.0554172
$837$	3.81849	0.131986
$838$	18.5643	0.641292
$839$	17.1770	0.593015	0.296507	−	0.955031i	$-0.404178\pi$
$839$	17.1770	0.593015	0.296507	+	0.955031i	$0.404178\pi$
$840$	38.0875	1.31414
$841$	−28.1530	−0.970794
$842$	−6.58844	−0.227053
$843$	−6.20323	−0.213651
$844$	−2.80414	−0.0965226
$845$	−13.0489	−0.448896
$846$	−14.6051	−0.502133
$847$	37.1997	1.27820
$848$	59.5631	2.04540
$849$	−12.6423	−0.433881
$850$	−25.4338	−0.872373
$851$	42.0862	1.44270
$852$	−10.6152	−0.363672
$853$	3.79394	0.129902	0.0649510	−	0.997888i	$-0.479311\pi$
$853$	3.79394	0.129902	0.0649510	+	0.997888i	$0.479311\pi$
$854$	−116.153	−3.97466
$855$	0.314875	0.0107685
$856$	−33.9804	−1.16142
$857$	−16.2492	−0.555063	−0.277531	−	0.960717i	$-0.589516\pi$
$857$	−16.2492	−0.555063	−0.277531	+	0.960717i	$0.589516\pi$
$858$	−5.47007	−0.186745
$859$	49.8350	1.70035	0.850174	−	0.526502i	$-0.176497\pi$
$859$	49.8350	1.70035	0.850174	+	0.526502i	$0.176497\pi$
$860$	6.56120	0.223735
$861$	−6.79355	−0.231523
$862$	27.7658	0.945705
$863$	48.9115	1.66497	0.832483	−	0.554051i	$-0.186919\pi$
$863$	48.9115	1.66497	0.832483	+	0.554051i	$0.186919\pi$
$864$	−11.6037	−0.394766
$865$	−20.8960	−0.710487
$866$	104.063	3.53622
$867$	−9.05517	−0.307530
$868$	−74.7576	−2.53744
$869$	3.71773	0.126115
$870$	3.02465	0.102545
$871$	−5.27091	−0.178598
$872$	134.200	4.54460
$873$	15.1845	0.513918
$874$	−2.64185	−0.0893620
$875$	42.1518	1.42499
$876$	−43.2399	−1.46094
$877$	−3.82146	−0.129041	−0.0645207	−	0.997916i	$-0.520552\pi$
$877$	−3.82146	−0.129041	−0.0645207	+	0.997916i	$0.520552\pi$
$878$	−27.9693	−0.943918
$879$	29.2404	0.986254
$880$	−16.6071	−0.559825
$881$	−12.4998	−0.421130	−0.210565	−	0.977580i	$-0.567530\pi$
$881$	−12.4998	−0.421130	−0.210565	+	0.977580i	$0.567530\pi$
$882$	−23.5271	−0.792200
$883$	−11.5998	−0.390364	−0.195182	−	0.980767i	$-0.562530\pi$
$883$	−11.5998	−0.390364	−0.195182	+	0.980767i	$0.562530\pi$
$884$	22.1458	0.744845
$885$	−14.9224	−0.501612
$886$	45.9201	1.54272
$887$	40.2191	1.35043	0.675213	−	0.737623i	$-0.264052\pi$
$887$	40.2191	1.35043	0.675213	+	0.737623i	$0.264052\pi$
$888$	−80.2779	−2.69395
$889$	−19.7718	−0.663124
$890$	−48.9107	−1.63949
$891$	−1.29893	−0.0435157
$892$	−89.5806	−2.99938
$893$	1.39926	0.0468246
$894$	−44.2026	−1.47836
$895$	−29.5453	−0.987589
$896$	12.6971	0.424180
$897$	−6.40520	−0.213863
$898$	−10.6057	−0.353916
$899$	−3.51419	−0.117205
$900$	−16.8349	−0.561163
$901$	−16.4282	−0.547302
$902$	5.80342	0.193233
$903$	−4.27424	−0.142238
$904$	−83.7035	−2.78394
$905$	−10.5425	−0.350443
$906$	47.0325	1.56255
$907$	−16.7508	−0.556202	−0.278101	−	0.960552i	$-0.589705\pi$
$907$	−16.7508	−0.556202	−0.278101	+	0.960552i	$0.589705\pi$
$908$	49.0383	1.62739
$909$	−0.610430	−0.0202467
$910$	−21.0450	−0.697634
$911$	55.1864	1.82841	0.914203	−	0.405257i	$-0.132818\pi$
$911$	55.1864	1.82841	0.914203	+	0.405257i	$0.132818\pi$
$912$	2.57210	0.0851708
$913$	−10.8124	−0.357839
$914$	−64.5793	−2.13609
$915$	−13.8480	−0.457799
$916$	41.8424	1.38251
$917$	−49.5409	−1.63598
$918$	7.40466	0.244390
$919$	28.8977	0.953247	0.476623	−	0.879108i	$-0.341861\pi$
$919$	28.8977	0.953247	0.476623	+	0.879108i	$0.341861\pi$
$920$	−38.0987	−1.25608
$921$	15.5092	0.511047
$922$	−24.1675	−0.795915
$923$	3.47194	0.114280
$924$	25.4301	0.836590
$925$	−36.1792	−1.18957
$926$	17.8566	0.586805
$927$	4.98348	0.163679
$928$	10.6790	0.350555
$929$	33.1220	1.08670	0.543348	−	0.839507i	$-0.317156\pi$
$929$	33.1220	1.08670	0.543348	+	0.839507i	$0.317156\pi$
$930$	−12.5497	−0.411522
$931$	2.25406	0.0738738
$932$	−18.6245	−0.610065
$933$	2.81793	0.0922550
$934$	−7.55409	−0.247177
$935$	4.58044	0.149796
$936$	12.2177	0.399347
$937$	−54.8615	−1.79225	−0.896123	−	0.443806i	$-0.853628\pi$
$937$	−54.8615	−1.79225	−0.896123	+	0.443806i	$0.853628\pi$
$938$	34.5034	1.12658
$939$	13.7517	0.448769
$940$	34.0898	1.11189
$941$	−14.3137	−0.466614	−0.233307	−	0.972403i	$-0.574955\pi$
$941$	−14.3137	−0.466614	−0.233307	+	0.972403i	$0.574955\pi$
$942$	17.7988	0.579917
$943$	6.79554	0.221293
$944$	−121.896	−3.96737
$945$	−4.99735	−0.162564
$946$	3.65129	0.118714
$947$	32.9083	1.06938	0.534688	−	0.845049i	$-0.320429\pi$
$947$	32.9083	1.06938	0.534688	+	0.845049i	$0.320429\pi$
$948$	−14.0281	−0.455610
$949$	14.1425	0.459086
$950$	2.27106	0.0736828
$951$	−8.37919	−0.271714
$952$	−85.8115	−2.78117
$953$	−10.0863	−0.326727	−0.163363	−	0.986566i	$-0.552234\pi$
$953$	−10.0863	−0.326727	−0.163363	+	0.986566i	$0.552234\pi$
$954$	−15.3112	−0.495720
$955$	−6.45513	−0.208883
$956$	−130.735	−4.22828
$957$	1.19541	0.0386422
$958$	38.2816	1.23682
$959$	−39.1470	−1.26412
$960$	12.5658	0.405561
$961$	−16.4191	−0.529650
$962$	44.3570	1.43013
$963$	4.45846	0.143672
$964$	−103.117	−3.32118
$965$	−25.0821	−0.807420
$966$	41.9285	1.34903
$967$	−20.7906	−0.668582	−0.334291	−	0.942470i	$-0.608497\pi$
$967$	−20.7906	−0.668582	−0.334291	+	0.942470i	$0.608497\pi$
$968$	70.9779	2.28131
$969$	−0.709416	−0.0227897
$970$	−49.9049	−1.60235
$971$	−33.3538	−1.07037	−0.535187	−	0.844733i	$-0.679759\pi$
$971$	−33.3538	−1.07037	−0.535187	+	0.844733i	$0.679759\pi$
$972$	4.90122	0.157207
$973$	−27.6858	−0.887566
$974$	58.7176	1.88143
$975$	5.50620	0.176340
$976$	−113.119	−3.62085
$977$	−20.9382	−0.669874	−0.334937	−	0.942241i	$-0.608715\pi$
$977$	−20.9382	−0.669874	−0.334937	+	0.942241i	$0.608715\pi$
$978$	48.5837	1.55354
$979$	−19.3306	−0.617809
$980$	54.9149	1.75419
$981$	−17.6080	−0.562181
$982$	−110.017	−3.51078
$983$	50.9756	1.62587	0.812934	−	0.582356i	$-0.197869\pi$
$983$	50.9756	1.62587	0.812934	+	0.582356i	$0.197869\pi$
$984$	−12.9622	−0.413221
$985$	−5.79231	−0.184558
$986$	−6.81457	−0.217020
$987$	−22.2075	−0.706874
$988$	−1.97746	−0.0629115
$989$	4.27549	0.135953
$990$	4.26901	0.135678
$991$	−20.6452	−0.655817	−0.327909	−	0.944709i	$-0.606344\pi$
$991$	−20.6452	−0.655817	−0.327909	+	0.944709i	$0.606344\pi$
$992$	−44.3086	−1.40680
$993$	−6.70615	−0.212813
$994$	−22.7273	−0.720868
$995$	−27.3014	−0.865511
$996$	40.7984	1.29275
$997$	−41.3330	−1.30903	−0.654514	−	0.756050i	$-0.727127\pi$
$997$	−41.3330	−1.30903	−0.654514	+	0.756050i	$0.727127\pi$
$998$	37.7275	1.19424
$999$	10.5330	0.333250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.a.1.4	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.a.1.4	✓	92	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62702 q^{2} +1.00000 q^{3} +4.90122 q^{4} +1.25106 q^{5} -2.62702 q^{6} -3.99448 q^{7} -7.62155 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62702 q^{2} +1.00000 q^{3} +4.90122 q^{4} +1.25106 q^{5} -2.62702 q^{6} -3.99448 q^{7} -7.62155 q^{8} +1.00000 q^{9} -3.28657 q^{10} -1.29893 q^{11} +4.90122 q^{12} -1.60304 q^{13} +10.4936 q^{14} +1.25106 q^{15} +10.2195 q^{16} -2.81866 q^{17} -2.62702 q^{18} +0.251686 q^{19} +6.13174 q^{20} -3.99448 q^{21} +3.41230 q^{22} +3.99565 q^{23} -7.62155 q^{24} -3.43484 q^{25} +4.21123 q^{26} +1.00000 q^{27} -19.5778 q^{28} -0.920308 q^{29} -3.28657 q^{30} +3.81849 q^{31} -11.6037 q^{32} -1.29893 q^{33} +7.40466 q^{34} -4.99735 q^{35} +4.90122 q^{36} +10.5330 q^{37} -0.661183 q^{38} -1.60304 q^{39} -9.53505 q^{40} +1.70074 q^{41} +10.4936 q^{42} +1.07004 q^{43} -6.36632 q^{44} +1.25106 q^{45} -10.4966 q^{46} +5.55956 q^{47} +10.2195 q^{48} +8.95584 q^{49} +9.02338 q^{50} -2.81866 q^{51} -7.85687 q^{52} +5.82837 q^{53} -2.62702 q^{54} -1.62504 q^{55} +30.4441 q^{56} +0.251686 q^{57} +2.41766 q^{58} -11.9278 q^{59} +6.13174 q^{60} -11.0689 q^{61} -10.0312 q^{62} -3.99448 q^{63} +10.0441 q^{64} -2.00551 q^{65} +3.41230 q^{66} +3.28806 q^{67} -13.8149 q^{68} +3.99565 q^{69} +13.1281 q^{70} -2.16584 q^{71} -7.62155 q^{72} -8.82229 q^{73} -27.6704 q^{74} -3.43484 q^{75} +1.23357 q^{76} +5.18853 q^{77} +4.21123 q^{78} -2.86216 q^{79} +12.7853 q^{80} +1.00000 q^{81} -4.46786 q^{82} +8.32413 q^{83} -19.5778 q^{84} -3.52632 q^{85} -2.81101 q^{86} -0.920308 q^{87} +9.89983 q^{88} +14.8820 q^{89} -3.28657 q^{90} +6.40332 q^{91} +19.5835 q^{92} +3.81849 q^{93} -14.6051 q^{94} +0.314875 q^{95} -11.6037 q^{96} +15.1845 q^{97} -23.5271 q^{98} -1.29893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * q^99

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