LMFDB - Embedded newform 8031.2.a.c.1.1

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:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.78421 q^{2} -1.00000 q^{3} +5.75185 q^{4} +0.686525 q^{5} +2.78421 q^{6} -0.869505 q^{7} -10.4459 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.78421 q^{2} -1.00000 q^{3} +5.75185 q^{4} +0.686525 q^{5} +2.78421 q^{6} -0.869505 q^{7} -10.4459 q^{8} +1.00000 q^{9} -1.91143 q^{10} +2.22695 q^{11} -5.75185 q^{12} -3.80567 q^{13} +2.42089 q^{14} -0.686525 q^{15} +17.5801 q^{16} -0.299722 q^{17} -2.78421 q^{18} +2.18096 q^{19} +3.94879 q^{20} +0.869505 q^{21} -6.20029 q^{22} -3.87886 q^{23} +10.4459 q^{24} -4.52868 q^{25} +10.5958 q^{26} -1.00000 q^{27} -5.00126 q^{28} +9.71234 q^{29} +1.91143 q^{30} -7.55494 q^{31} -28.0548 q^{32} -2.22695 q^{33} +0.834490 q^{34} -0.596937 q^{35} +5.75185 q^{36} +1.51764 q^{37} -6.07225 q^{38} +3.80567 q^{39} -7.17141 q^{40} -0.0945292 q^{41} -2.42089 q^{42} +0.236414 q^{43} +12.8091 q^{44} +0.686525 q^{45} +10.7996 q^{46} +7.48238 q^{47} -17.5801 q^{48} -6.24396 q^{49} +12.6088 q^{50} +0.299722 q^{51} -21.8896 q^{52} +11.1258 q^{53} +2.78421 q^{54} +1.52885 q^{55} +9.08280 q^{56} -2.18096 q^{57} -27.0412 q^{58} +3.85149 q^{59} -3.94879 q^{60} -2.22450 q^{61} +21.0346 q^{62} -0.869505 q^{63} +42.9503 q^{64} -2.61269 q^{65} +6.20029 q^{66} -8.37705 q^{67} -1.72395 q^{68} +3.87886 q^{69} +1.66200 q^{70} -12.7059 q^{71} -10.4459 q^{72} +0.299545 q^{73} -4.22545 q^{74} +4.52868 q^{75} +12.5445 q^{76} -1.93634 q^{77} -10.5958 q^{78} +0.626397 q^{79} +12.0692 q^{80} +1.00000 q^{81} +0.263190 q^{82} -14.3255 q^{83} +5.00126 q^{84} -0.205767 q^{85} -0.658227 q^{86} -9.71234 q^{87} -23.2626 q^{88} +7.65192 q^{89} -1.91143 q^{90} +3.30905 q^{91} -22.3106 q^{92} +7.55494 q^{93} -20.8326 q^{94} +1.49728 q^{95} +28.0548 q^{96} -11.3724 q^{97} +17.3845 q^{98} +2.22695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.78421	−1.96874	−0.984368	−	0.176122i	$-0.943645\pi$
$2$	−2.78421	−1.96874	−0.984368	+	0.176122i	$0.943645\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.75185	2.87592
$5$	0.686525	0.307023	0.153512	−	0.988147i	$-0.450942\pi$
$5$	0.686525	0.307023	0.153512	+	0.988147i	$0.450942\pi$
$6$	2.78421	1.13665
$7$	−0.869505	−0.328642	−0.164321	−	0.986407i	$-0.552543\pi$
$7$	−0.869505	−0.328642	−0.164321	+	0.986407i	$0.552543\pi$
$8$	−10.4459	−3.69320
$9$	1.00000	0.333333
$10$	−1.91143	−0.604448
$11$	2.22695	0.671449	0.335725	−	0.941960i	$-0.391019\pi$
$11$	2.22695	0.671449	0.335725	+	0.941960i	$0.391019\pi$
$12$	−5.75185	−1.66042
$13$	−3.80567	−1.05550	−0.527751	−	0.849399i	$-0.676965\pi$
$13$	−3.80567	−1.05550	−0.527751	+	0.849399i	$0.676965\pi$
$14$	2.42089	0.647009
$15$	−0.686525	−0.177260
$16$	17.5801	4.39502
$17$	−0.299722	−0.0726932	−0.0363466	−	0.999339i	$-0.511572\pi$
$17$	−0.299722	−0.0726932	−0.0363466	+	0.999339i	$0.511572\pi$
$18$	−2.78421	−0.656246
$19$	2.18096	0.500346	0.250173	−	0.968201i	$-0.419513\pi$
$19$	2.18096	0.500346	0.250173	+	0.968201i	$0.419513\pi$
$20$	3.94879	0.882976
$21$	0.869505	0.189741
$22$	−6.20029	−1.32191
$23$	−3.87886	−0.808797	−0.404399	−	0.914583i	$-0.632519\pi$
$23$	−3.87886	−0.808797	−0.404399	+	0.914583i	$0.632519\pi$
$24$	10.4459	2.13227
$25$	−4.52868	−0.905737
$26$	10.5958	2.07801
$27$	−1.00000	−0.192450
$28$	−5.00126	−0.945149
$29$	9.71234	1.80354	0.901768	−	0.432220i	$-0.142269\pi$
$29$	9.71234	1.80354	0.901768	+	0.432220i	$0.142269\pi$
$30$	1.91143	0.348978
$31$	−7.55494	−1.35691	−0.678453	−	0.734643i	$-0.737349\pi$
$31$	−7.55494	−1.35691	−0.678453	+	0.734643i	$0.737349\pi$
$32$	−28.0548	−4.95943
$33$	−2.22695	−0.387661
$34$	0.834490	0.143114
$35$	−0.596937	−0.100901
$36$	5.75185	0.958641
$37$	1.51764	0.249499	0.124750	−	0.992188i	$-0.460187\pi$
$37$	1.51764	0.249499	0.124750	+	0.992188i	$0.460187\pi$
$38$	−6.07225	−0.985049
$39$	3.80567	0.609395
$40$	−7.17141	−1.13390
$41$	−0.0945292	−0.0147630	−0.00738149	−	0.999973i	$-0.502350\pi$
$41$	−0.0945292	−0.0147630	−0.00738149	+	0.999973i	$0.502350\pi$
$42$	−2.42089	−0.373551
$43$	0.236414	0.0360528	0.0180264	−	0.999838i	$-0.494262\pi$
$43$	0.236414	0.0360528	0.0180264	+	0.999838i	$0.494262\pi$
$44$	12.8091	1.93104
$45$	0.686525	0.102341
$46$	10.7996	1.59231
$47$	7.48238	1.09142	0.545709	−	0.837975i	$-0.316260\pi$
$47$	7.48238	1.09142	0.545709	+	0.837975i	$0.316260\pi$
$48$	−17.5801	−2.53746
$49$	−6.24396	−0.891995
$50$	12.6088	1.78316
$51$	0.299722	0.0419694
$52$	−21.8896	−3.03554
$53$	11.1258	1.52825	0.764126	−	0.645067i	$-0.223170\pi$
$53$	11.1258	1.52825	0.764126	+	0.645067i	$0.223170\pi$
$54$	2.78421	0.378884
$55$	1.52885	0.206151
$56$	9.08280	1.21374
$57$	−2.18096	−0.288875
$58$	−27.0412	−3.55069
$59$	3.85149	0.501421	0.250710	−	0.968062i	$-0.419336\pi$
$59$	3.85149	0.501421	0.250710	+	0.968062i	$0.419336\pi$
$60$	−3.94879	−0.509787
$61$	−2.22450	−0.284818	−0.142409	−	0.989808i	$-0.545485\pi$
$61$	−2.22450	−0.284818	−0.142409	+	0.989808i	$0.545485\pi$
$62$	21.0346	2.67139
$63$	−0.869505	−0.109547
$64$	42.9503	5.36879
$65$	−2.61269	−0.324064
$66$	6.20029	0.763203
$67$	−8.37705	−1.02342	−0.511710	−	0.859158i	$-0.670988\pi$
$67$	−8.37705	−1.02342	−0.511710	+	0.859158i	$0.670988\pi$
$68$	−1.72395	−0.209060
$69$	3.87886	0.466959
$70$	1.66200	0.198647
$71$	−12.7059	−1.50791	−0.753956	−	0.656925i	$-0.771857\pi$
$71$	−12.7059	−1.50791	−0.753956	+	0.656925i	$0.771857\pi$
$72$	−10.4459	−1.23107
$73$	0.299545	0.0350590	0.0175295	−	0.999846i	$-0.494420\pi$
$73$	0.299545	0.0350590	0.0175295	+	0.999846i	$0.494420\pi$
$74$	−4.22545	−0.491198
$75$	4.52868	0.522927
$76$	12.5445	1.43896
$77$	−1.93634	−0.220666
$78$	−10.5958	−1.19974
$79$	0.626397	0.0704752	0.0352376	−	0.999379i	$-0.488781\pi$
$79$	0.626397	0.0704752	0.0352376	+	0.999379i	$0.488781\pi$
$80$	12.0692	1.34937
$81$	1.00000	0.111111
$82$	0.263190	0.0290644
$83$	−14.3255	−1.57243	−0.786215	−	0.617953i	$-0.787962\pi$
$83$	−14.3255	−1.57243	−0.786215	+	0.617953i	$0.787962\pi$
$84$	5.00126	0.545682
$85$	−0.205767	−0.0223185
$86$	−0.658227	−0.0709784
$87$	−9.71234	−1.04127
$88$	−23.2626	−2.47980
$89$	7.65192	0.811102	0.405551	−	0.914072i	$-0.367080\pi$
$89$	7.65192	0.811102	0.405551	+	0.914072i	$0.367080\pi$
$90$	−1.91143	−0.201483
$91$	3.30905	0.346882
$92$	−22.3106	−2.32604
$93$	7.55494	0.783411
$94$	−20.8326	−2.14871
$95$	1.49728	0.153618
$96$	28.0548	2.86333
$97$	−11.3724	−1.15469	−0.577344	−	0.816501i	$-0.695911\pi$
$97$	−11.3724	−1.15469	−0.577344	+	0.816501i	$0.695911\pi$
$98$	17.3845	1.75610
$99$	2.22695	0.223816
$100$	−26.0483	−2.60483
$101$	−1.38459	−0.137771	−0.0688857	−	0.997625i	$-0.521944\pi$
$101$	−1.38459	−0.137771	−0.0688857	+	0.997625i	$0.521944\pi$
$102$	−0.834490	−0.0826268
$103$	16.7745	1.65284	0.826421	−	0.563053i	$-0.190373\pi$
$103$	16.7745	1.65284	0.826421	+	0.563053i	$0.190373\pi$
$104$	39.7538	3.89818
$105$	0.596937	0.0582551
$106$	−30.9767	−3.00873
$107$	11.5747	1.11897	0.559483	−	0.828842i	$-0.311000\pi$
$107$	11.5747	1.11897	0.559483	+	0.828842i	$0.311000\pi$
$108$	−5.75185	−0.553472
$109$	−5.24837	−0.502702	−0.251351	−	0.967896i	$-0.580875\pi$
$109$	−5.24837	−0.502702	−0.251351	+	0.967896i	$0.580875\pi$
$110$	−4.25666	−0.405856
$111$	−1.51764	−0.144048
$112$	−15.2859	−1.44439
$113$	−9.95720	−0.936695	−0.468347	−	0.883544i	$-0.655150\pi$
$113$	−9.95720	−0.936695	−0.468347	+	0.883544i	$0.655150\pi$
$114$	6.07225	0.568718
$115$	−2.66293	−0.248320
$116$	55.8639	5.18683
$117$	−3.80567	−0.351834
$118$	−10.7234	−0.987165
$119$	0.260610	0.0238900
$120$	7.17141	0.654657
$121$	−6.04071	−0.549156
$122$	6.19349	0.560732
$123$	0.0945292	0.00852341
$124$	−43.4549	−3.90236
$125$	−6.54168	−0.585106
$126$	2.42089	0.215670
$127$	−5.78014	−0.512905	−0.256452	−	0.966557i	$-0.582554\pi$
$127$	−5.78014	−0.512905	−0.256452	+	0.966557i	$0.582554\pi$
$128$	−63.4734	−5.61031
$129$	−0.236414	−0.0208151
$130$	7.27428	0.637997
$131$	5.71377	0.499214	0.249607	−	0.968347i	$-0.419699\pi$
$131$	5.71377	0.499214	0.249607	+	0.968347i	$0.419699\pi$
$132$	−12.8091	−1.11488
$133$	−1.89635	−0.164435
$134$	23.3235	2.01484
$135$	−0.686525	−0.0590867
$136$	3.13088	0.268471
$137$	9.74933	0.832941	0.416471	−	0.909149i	$-0.363267\pi$
$137$	9.74933	0.832941	0.416471	+	0.909149i	$0.363267\pi$
$138$	−10.7996	−0.919320
$139$	7.21278	0.611780	0.305890	−	0.952067i	$-0.401046\pi$
$139$	7.21278	0.611780	0.305890	+	0.952067i	$0.401046\pi$
$140$	−3.43349	−0.290183
$141$	−7.48238	−0.630130
$142$	35.3759	2.96868
$143$	−8.47501	−0.708716
$144$	17.5801	1.46501
$145$	6.66777	0.553728
$146$	−0.833996	−0.0690220
$147$	6.24396	0.514993
$148$	8.72926	0.717540
$149$	22.1198	1.81212	0.906061	−	0.423148i	$-0.139075\pi$
$149$	22.1198	1.81212	0.906061	+	0.423148i	$0.139075\pi$
$150$	−12.6088	−1.02951
$151$	10.9791	0.893470	0.446735	−	0.894666i	$-0.352587\pi$
$151$	10.9791	0.893470	0.446735	+	0.894666i	$0.352587\pi$
$152$	−22.7822	−1.84788
$153$	−0.299722	−0.0242311
$154$	5.39118	0.434434
$155$	−5.18666	−0.416602
$156$	21.8896	1.75257
$157$	7.30752	0.583204	0.291602	−	0.956540i	$-0.405812\pi$
$157$	7.30752	0.583204	0.291602	+	0.956540i	$0.405812\pi$
$158$	−1.74402	−0.138747
$159$	−11.1258	−0.882337
$160$	−19.2603	−1.52266
$161$	3.37268	0.265805
$162$	−2.78421	−0.218749
$163$	6.22922	0.487911	0.243955	−	0.969786i	$-0.421555\pi$
$163$	6.22922	0.487911	0.243955	+	0.969786i	$0.421555\pi$
$164$	−0.543718	−0.0424572
$165$	−1.52885	−0.119021
$166$	39.8853	3.09570
$167$	−23.3983	−1.81061	−0.905307	−	0.424757i	$-0.860360\pi$
$167$	−23.3983	−1.81061	−0.905307	+	0.424757i	$0.860360\pi$
$168$	−9.08280	−0.700753
$169$	1.48310	0.114085
$170$	0.572898	0.0439393
$171$	2.18096	0.166782
$172$	1.35982	0.103685
$173$	−0.840182	−0.0638779	−0.0319389	−	0.999490i	$-0.510168\pi$
$173$	−0.840182	−0.0638779	−0.0319389	+	0.999490i	$0.510168\pi$
$174$	27.0412	2.04999
$175$	3.93771	0.297663
$176$	39.1498	2.95103
$177$	−3.85149	−0.289495
$178$	−21.3046	−1.59685
$179$	−6.15207	−0.459827	−0.229914	−	0.973211i	$-0.573844\pi$
$179$	−6.15207	−0.459827	−0.229914	+	0.973211i	$0.573844\pi$
$180$	3.94879	0.294325
$181$	−8.07676	−0.600341	−0.300170	−	0.953886i	$-0.597043\pi$
$181$	−8.07676	−0.600341	−0.300170	+	0.953886i	$0.597043\pi$
$182$	−9.21309	−0.682920
$183$	2.22450	0.164440
$184$	40.5183	2.98705
$185$	1.04190	0.0766021
$186$	−21.0346	−1.54233
$187$	−0.667464	−0.0488098
$188$	43.0375	3.13883
$189$	0.869505	0.0632472
$190$	−4.16875	−0.302433
$191$	14.6553	1.06042	0.530210	−	0.847866i	$-0.322113\pi$
$191$	14.6553	1.06042	0.530210	+	0.847866i	$0.322113\pi$
$192$	−42.9503	−3.09967
$193$	−6.90986	−0.497383	−0.248691	−	0.968583i	$-0.580000\pi$
$193$	−6.90986	−0.497383	−0.248691	+	0.968583i	$0.580000\pi$
$194$	31.6631	2.27328
$195$	2.61269	0.187098
$196$	−35.9143	−2.56531
$197$	26.9165	1.91772	0.958860	−	0.283880i	$-0.0916217\pi$
$197$	26.9165	1.91772	0.958860	+	0.283880i	$0.0916217\pi$
$198$	−6.20029	−0.440636
$199$	20.2656	1.43659	0.718295	−	0.695739i	$-0.244923\pi$
$199$	20.2656	1.43659	0.718295	+	0.695739i	$0.244923\pi$
$200$	47.3064	3.34507
$201$	8.37705	0.590871
$202$	3.85498	0.271236
$203$	−8.44493	−0.592718
$204$	1.72395	0.120701
$205$	−0.0648967	−0.00453258
$206$	−46.7038	−3.25401
$207$	−3.87886	−0.269599
$208$	−66.9039	−4.63895
$209$	4.85687	0.335957
$210$	−1.66200	−0.114689
$211$	5.34902	0.368242	0.184121	−	0.982904i	$-0.441056\pi$
$211$	5.34902	0.368242	0.184121	+	0.982904i	$0.441056\pi$
$212$	63.9942	4.39514
$213$	12.7059	0.870593
$214$	−32.2264	−2.20295
$215$	0.162304	0.0110690
$216$	10.4459	0.710757
$217$	6.56905	0.445936
$218$	14.6126	0.989689
$219$	−0.299545	−0.0202414
$220$	8.79374	0.592874
$221$	1.14064	0.0767279
$222$	4.22545	0.283593
$223$	8.26567	0.553510	0.276755	−	0.960940i	$-0.410741\pi$
$223$	8.26567	0.553510	0.276755	+	0.960940i	$0.410741\pi$
$224$	24.3937	1.62988
$225$	−4.52868	−0.301912
$226$	27.7230	1.84411
$227$	14.0707	0.933907	0.466954	−	0.884282i	$-0.345351\pi$
$227$	14.0707	0.933907	0.466954	+	0.884282i	$0.345351\pi$
$228$	−12.5445	−0.830782
$229$	5.75987	0.380623	0.190311	−	0.981724i	$-0.439050\pi$
$229$	5.75987	0.380623	0.190311	+	0.981724i	$0.439050\pi$
$230$	7.41417	0.488876
$231$	1.93634	0.127402
$232$	−101.455	−6.66082
$233$	1.43900	0.0942719	0.0471359	−	0.998888i	$-0.484991\pi$
$233$	1.43900	0.0942719	0.0471359	+	0.998888i	$0.484991\pi$
$234$	10.5958	0.692669
$235$	5.13684	0.335091
$236$	22.1532	1.44205
$237$	−0.626397	−0.0406889
$238$	−0.725593	−0.0470332
$239$	−5.89698	−0.381444	−0.190722	−	0.981644i	$-0.561083\pi$
$239$	−5.89698	−0.381444	−0.190722	+	0.981644i	$0.561083\pi$
$240$	−12.0692	−0.779061
$241$	26.5558	1.71061	0.855304	−	0.518127i	$-0.173370\pi$
$241$	26.5558	1.71061	0.855304	+	0.518127i	$0.173370\pi$
$242$	16.8186	1.08114
$243$	−1.00000	−0.0641500
$244$	−12.7950	−0.819115
$245$	−4.28664	−0.273863
$246$	−0.263190	−0.0167804
$247$	−8.29999	−0.528116
$248$	78.9185	5.01133
$249$	14.3255	0.907843
$250$	18.2134	1.15192
$251$	−5.25237	−0.331527	−0.165763	−	0.986166i	$-0.553009\pi$
$251$	−5.25237	−0.331527	−0.165763	+	0.986166i	$0.553009\pi$
$252$	−5.00126	−0.315050
$253$	−8.63800	−0.543066
$254$	16.0932	1.00977
$255$	0.205767	0.0128856
$256$	90.8229	5.67643
$257$	2.34980	0.146577	0.0732883	−	0.997311i	$-0.476651\pi$
$257$	2.34980	0.146577	0.0732883	+	0.997311i	$0.476651\pi$
$258$	0.658227	0.0409794
$259$	−1.31960	−0.0819958
$260$	−15.0278	−0.931983
$261$	9.71234	0.601179
$262$	−15.9084	−0.982822
$263$	−16.3351	−1.00727	−0.503633	−	0.863918i	$-0.668004\pi$
$263$	−16.3351	−1.00727	−0.503633	+	0.863918i	$0.668004\pi$
$264$	23.2626	1.43171
$265$	7.63818	0.469209
$266$	5.27985	0.323728
$267$	−7.65192	−0.468290
$268$	−48.1835	−2.94328
$269$	6.60993	0.403014	0.201507	−	0.979487i	$-0.435416\pi$
$269$	6.60993	0.403014	0.201507	+	0.979487i	$0.435416\pi$
$270$	1.91143	0.116326
$271$	−13.7505	−0.835281	−0.417641	−	0.908612i	$-0.637143\pi$
$271$	−13.7505	−0.835281	−0.417641	+	0.908612i	$0.637143\pi$
$272$	−5.26913	−0.319488
$273$	−3.30905	−0.200273
$274$	−27.1442	−1.63984
$275$	−10.0851	−0.608156
$276$	22.3106	1.34294
$277$	−22.0401	−1.32426	−0.662129	−	0.749390i	$-0.730347\pi$
$277$	−22.0401	−1.32426	−0.662129	+	0.749390i	$0.730347\pi$
$278$	−20.0819	−1.20443
$279$	−7.55494	−0.452302
$280$	6.23557	0.372647
$281$	−18.2026	−1.08587	−0.542937	−	0.839773i	$-0.682688\pi$
$281$	−18.2026	−1.08587	−0.542937	+	0.839773i	$0.682688\pi$
$282$	20.8326	1.24056
$283$	0.932514	0.0554322	0.0277161	−	0.999616i	$-0.491177\pi$
$283$	0.932514	0.0554322	0.0277161	+	0.999616i	$0.491177\pi$
$284$	−73.0823	−4.33664
$285$	−1.49728	−0.0886913
$286$	23.5963	1.39528
$287$	0.0821936	0.00485173
$288$	−28.0548	−1.65314
$289$	−16.9102	−0.994716
$290$	−18.5645	−1.09014
$291$	11.3724	0.666659
$292$	1.72294	0.100827
$293$	−2.74485	−0.160356	−0.0801779	−	0.996781i	$-0.525549\pi$
$293$	−2.74485	−0.160356	−0.0801779	+	0.996781i	$0.525549\pi$
$294$	−17.3845	−1.01389
$295$	2.64414	0.153948
$296$	−15.8532	−0.921450
$297$	−2.22695	−0.129220
$298$	−61.5861	−3.56759
$299$	14.7616	0.853687
$300$	26.0483	1.50390
$301$	−0.205563	−0.0118484
$302$	−30.5683	−1.75901
$303$	1.38459	0.0795424
$304$	38.3413	2.19903
$305$	−1.52718	−0.0874459
$306$	0.834490	0.0477046
$307$	−19.1635	−1.09372	−0.546860	−	0.837224i	$-0.684177\pi$
$307$	−19.1635	−1.09372	−0.546860	+	0.837224i	$0.684177\pi$
$308$	−11.1375	−0.634620
$309$	−16.7745	−0.954269
$310$	14.4408	0.820180
$311$	−5.15624	−0.292383	−0.146192	−	0.989256i	$-0.546702\pi$
$311$	−5.15624	−0.292383	−0.146192	+	0.989256i	$0.546702\pi$
$312$	−39.7538	−2.25062
$313$	15.7490	0.890187	0.445093	−	0.895484i	$-0.353171\pi$
$313$	15.7490	0.890187	0.445093	+	0.895484i	$0.353171\pi$
$314$	−20.3457	−1.14817
$315$	−0.596937	−0.0336336
$316$	3.60294	0.202681
$317$	9.57558	0.537818	0.268909	−	0.963166i	$-0.413337\pi$
$317$	9.57558	0.537818	0.268909	+	0.963166i	$0.413337\pi$
$318$	30.9767	1.73709
$319$	21.6289	1.21098
$320$	29.4865	1.64834
$321$	−11.5747	−0.646035
$322$	−9.39027	−0.523299
$323$	−0.653680	−0.0363717
$324$	5.75185	0.319547
$325$	17.2347	0.956007
$326$	−17.3435	−0.960567
$327$	5.24837	0.290235
$328$	0.987447	0.0545227
$329$	−6.50597	−0.358686
$330$	4.25666	0.234321
$331$	−0.0231720	−0.00127365	−0.000636824	−	1.00000i	$-0.500203\pi$
$331$	−0.0231720	−0.00127365	−0.000636824		1.00000i	$0.500203\pi$
$332$	−82.3982	−4.52219
$333$	1.51764	0.0831664
$334$	65.1459	3.56462
$335$	−5.75106	−0.314214
$336$	15.2859	0.833917
$337$	2.27377	0.123860	0.0619301	−	0.998080i	$-0.480274\pi$
$337$	2.27377	0.123860	0.0619301	+	0.998080i	$0.480274\pi$
$338$	−4.12928	−0.224603
$339$	9.95720	0.540801
$340$	−1.18354	−0.0641864
$341$	−16.8244	−0.911094
$342$	−6.07225	−0.328350
$343$	11.5157	0.621789
$344$	−2.46957	−0.133150
$345$	2.66293	0.143367
$346$	2.33925	0.125759
$347$	−2.59685	−0.139406	−0.0697030	−	0.997568i	$-0.522205\pi$
$347$	−2.59685	−0.139406	−0.0697030	+	0.997568i	$0.522205\pi$
$348$	−55.8639	−2.99462
$349$	19.9879	1.06993	0.534965	−	0.844874i	$-0.320325\pi$
$349$	19.9879	1.06993	0.534965	+	0.844874i	$0.320325\pi$
$350$	−10.9634	−0.586020
$351$	3.80567	0.203132
$352$	−62.4764	−3.33000
$353$	25.0727	1.33448	0.667242	−	0.744841i	$-0.267475\pi$
$353$	25.0727	1.33448	0.667242	+	0.744841i	$0.267475\pi$
$354$	10.7234	0.569940
$355$	−8.72291	−0.462964
$356$	44.0127	2.33267
$357$	−0.260610	−0.0137929
$358$	17.1287	0.905279
$359$	−14.0158	−0.739726	−0.369863	−	0.929086i	$-0.620595\pi$
$359$	−14.0158	−0.739726	−0.369863	+	0.929086i	$0.620595\pi$
$360$	−7.17141	−0.377966
$361$	−14.2434	−0.749654
$362$	22.4874	1.18191
$363$	6.04071	0.317055
$364$	19.0331	0.997607
$365$	0.205645	0.0107640
$366$	−6.19349	−0.323739
$367$	−31.8525	−1.66268	−0.831342	−	0.555761i	$-0.812427\pi$
$367$	−31.8525	−1.66268	−0.831342	+	0.555761i	$0.812427\pi$
$368$	−68.1905	−3.55468
$369$	−0.0945292	−0.00492099
$370$	−2.90088	−0.150809
$371$	−9.67398	−0.502248
$372$	43.4549	2.25303
$373$	23.1440	1.19835	0.599176	−	0.800618i	$-0.295495\pi$
$373$	23.1440	1.19835	0.599176	+	0.800618i	$0.295495\pi$
$374$	1.85836	0.0960937
$375$	6.54168	0.337811
$376$	−78.1606	−4.03082
$377$	−36.9619	−1.90364
$378$	−2.42089	−0.124517
$379$	−9.17228	−0.471148	−0.235574	−	0.971856i	$-0.575697\pi$
$379$	−9.17228	−0.471148	−0.235574	+	0.971856i	$0.575697\pi$
$380$	8.61214	0.441793
$381$	5.78014	0.296126
$382$	−40.8035	−2.08769
$383$	−12.3590	−0.631515	−0.315758	−	0.948840i	$-0.602259\pi$
$383$	−12.3590	−0.631515	−0.315758	+	0.948840i	$0.602259\pi$
$384$	63.4734	3.23911
$385$	−1.32935	−0.0677497
$386$	19.2385	0.979216
$387$	0.236414	0.0120176
$388$	−65.4120	−3.32079
$389$	25.2655	1.28101	0.640506	−	0.767954i	$-0.278725\pi$
$389$	25.2655	1.28101	0.640506	+	0.767954i	$0.278725\pi$
$390$	−7.27428	−0.368347
$391$	1.16258	0.0587941
$392$	65.2241	3.29431
$393$	−5.71377	−0.288222
$394$	−74.9412	−3.77549
$395$	0.430038	0.0216375
$396$	12.8091	0.643679
$397$	10.1059	0.507200	0.253600	−	0.967309i	$-0.418385\pi$
$397$	10.1059	0.507200	0.253600	+	0.967309i	$0.418385\pi$
$398$	−56.4237	−2.82827
$399$	1.89635	0.0949363
$400$	−79.6145	−3.98073
$401$	−19.4977	−0.973666	−0.486833	−	0.873495i	$-0.661848\pi$
$401$	−19.4977	−0.973666	−0.486833	+	0.873495i	$0.661848\pi$
$402$	−23.3235	−1.16327
$403$	28.7516	1.43222
$404$	−7.96393	−0.396220
$405$	0.686525	0.0341137
$406$	23.5125	1.16691
$407$	3.37971	0.167526
$408$	−3.13088	−0.155002
$409$	−7.16194	−0.354135	−0.177068	−	0.984199i	$-0.556661\pi$
$409$	−7.16194	−0.354135	−0.177068	+	0.984199i	$0.556661\pi$
$410$	0.180686	0.00892346
$411$	−9.74933	−0.480899
$412$	96.4845	4.75345
$413$	−3.34888	−0.164788
$414$	10.7996	0.530770
$415$	−9.83483	−0.482773
$416$	106.767	5.23469
$417$	−7.21278	−0.353211
$418$	−13.5226	−0.661410
$419$	7.57726	0.370174	0.185087	−	0.982722i	$-0.440743\pi$
$419$	7.57726	0.370174	0.185087	+	0.982722i	$0.440743\pi$
$420$	3.43349	0.167537
$421$	−29.6974	−1.44736	−0.723681	−	0.690135i	$-0.757551\pi$
$421$	−29.6974	−1.44736	−0.723681	+	0.690135i	$0.757551\pi$
$422$	−14.8928	−0.724972
$423$	7.48238	0.363806
$424$	−116.220	−5.64414
$425$	1.35735	0.0658409
$426$	−35.3759	−1.71397
$427$	1.93421	0.0936032
$428$	66.5758	3.21806
$429$	8.47501	0.409178
$430$	−0.451889	−0.0217920
$431$	14.5765	0.702123	0.351062	−	0.936352i	$-0.385821\pi$
$431$	14.5765	0.702123	0.351062	+	0.936352i	$0.385821\pi$
$432$	−17.5801	−0.845821
$433$	−2.38592	−0.114660	−0.0573301	−	0.998355i	$-0.518259\pi$
$433$	−2.38592	−0.114660	−0.0573301	+	0.998355i	$0.518259\pi$
$434$	−18.2897	−0.877931
$435$	−6.66777	−0.319695
$436$	−30.1878	−1.44573
$437$	−8.45961	−0.404678
$438$	0.833996	0.0398499
$439$	40.4030	1.92833	0.964165	−	0.265303i	$-0.0854721\pi$
$439$	40.4030	1.92833	0.964165	+	0.265303i	$0.0854721\pi$
$440$	−15.9703	−0.761356
$441$	−6.24396	−0.297332
$442$	−3.17579	−0.151057
$443$	−20.8445	−0.990350	−0.495175	−	0.868793i	$-0.664896\pi$
$443$	−20.8445	−0.990350	−0.495175	+	0.868793i	$0.664896\pi$
$444$	−8.72926	−0.414272
$445$	5.25324	0.249027
$446$	−23.0134	−1.08972
$447$	−22.1198	−1.04623
$448$	−37.3455	−1.76441
$449$	7.22437	0.340939	0.170470	−	0.985363i	$-0.445472\pi$
$449$	7.22437	0.340939	0.170470	+	0.985363i	$0.445472\pi$
$450$	12.6088	0.594386
$451$	−0.210511	−0.00991260
$452$	−57.2723	−2.69386
$453$	−10.9791	−0.515845
$454$	−39.1759	−1.83862
$455$	2.27174	0.106501
$456$	22.7822	1.06687
$457$	4.48175	0.209647	0.104824	−	0.994491i	$-0.466572\pi$
$457$	4.48175	0.209647	0.104824	+	0.994491i	$0.466572\pi$
$458$	−16.0367	−0.749346
$459$	0.299722	0.0139898
$460$	−15.3168	−0.714149
$461$	8.57285	0.399277	0.199639	−	0.979870i	$-0.436023\pi$
$461$	8.57285	0.399277	0.199639	+	0.979870i	$0.436023\pi$
$462$	−5.39118	−0.250821
$463$	−20.3132	−0.944035	−0.472017	−	0.881589i	$-0.656474\pi$
$463$	−20.3132	−0.944035	−0.472017	+	0.881589i	$0.656474\pi$
$464$	170.744	7.92657
$465$	5.18666	0.240525
$466$	−4.00648	−0.185596
$467$	38.7590	1.79355	0.896776	−	0.442485i	$-0.145903\pi$
$467$	38.7590	1.79355	0.896776	+	0.442485i	$0.145903\pi$
$468$	−21.8896	−1.01185
$469$	7.28388	0.336338
$470$	−14.3021	−0.659706
$471$	−7.30752	−0.336713
$472$	−40.2324	−1.85185
$473$	0.526481	0.0242076
$474$	1.74402	0.0801057
$475$	−9.87686	−0.453181
$476$	1.49899	0.0687059
$477$	11.1258	0.509418
$478$	16.4185	0.750963
$479$	6.20041	0.283304	0.141652	−	0.989917i	$-0.454759\pi$
$479$	6.20041	0.283304	0.141652	+	0.989917i	$0.454759\pi$
$480$	19.2603	0.879109
$481$	−5.77565	−0.263347
$482$	−73.9370	−3.36774
$483$	−3.37268	−0.153462
$484$	−34.7453	−1.57933
$485$	−7.80741	−0.354516
$486$	2.78421	0.126295
$487$	−35.2518	−1.59741	−0.798705	−	0.601722i	$-0.794481\pi$
$487$	−35.2518	−1.59741	−0.798705	+	0.601722i	$0.794481\pi$
$488$	23.2370	1.05189
$489$	−6.22922	−0.281695
$490$	11.9349	0.539165
$491$	34.4519	1.55479	0.777395	−	0.629012i	$-0.216540\pi$
$491$	34.4519	1.55479	0.777395	+	0.629012i	$0.216540\pi$
$492$	0.543718	0.0245127
$493$	−2.91100	−0.131105
$494$	23.1090	1.03972
$495$	1.52885	0.0687169
$496$	−132.816	−5.96363
$497$	11.0478	0.495563
$498$	−39.8853	−1.78730
$499$	−33.1741	−1.48508	−0.742539	−	0.669803i	$-0.766378\pi$
$499$	−33.1741	−1.48508	−0.742539	+	0.669803i	$0.766378\pi$
$500$	−37.6268	−1.68272
$501$	23.3983	1.04536
$502$	14.6237	0.652689
$503$	16.7358	0.746211	0.373105	−	0.927789i	$-0.378293\pi$
$503$	16.7358	0.746211	0.373105	+	0.927789i	$0.378293\pi$
$504$	9.08280	0.404580
$505$	−0.950553	−0.0422991
$506$	24.0500	1.06915
$507$	−1.48310	−0.0658670
$508$	−33.2465	−1.47508
$509$	7.34898	0.325738	0.162869	−	0.986648i	$-0.447925\pi$
$509$	7.34898	0.325738	0.162869	+	0.986648i	$0.447925\pi$
$510$	−0.572898	−0.0253684
$511$	−0.260455	−0.0115219
$512$	−125.924	−5.56509
$513$	−2.18096	−0.0962916
$514$	−6.54236	−0.288571
$515$	11.5161	0.507461
$516$	−1.35982	−0.0598626
$517$	16.6629	0.732832
$518$	3.67404	0.161428
$519$	0.840182	0.0368799
$520$	27.2920	1.19683
$521$	3.14474	0.137774	0.0688868	−	0.997624i	$-0.478055\pi$
$521$	3.14474	0.137774	0.0688868	+	0.997624i	$0.478055\pi$
$522$	−27.0412	−1.18356
$523$	12.0213	0.525654	0.262827	−	0.964843i	$-0.415345\pi$
$523$	12.0213	0.525654	0.262827	+	0.964843i	$0.415345\pi$
$524$	32.8647	1.43570
$525$	−3.93771	−0.171856
$526$	45.4805	1.98304
$527$	2.26438	0.0986379
$528$	−39.1498	−1.70378
$529$	−7.95448	−0.345847
$530$	−21.2663	−0.923750
$531$	3.85149	0.167140
$532$	−10.9075	−0.472901
$533$	0.359747	0.0155824
$534$	21.3046	0.921940
$535$	7.94631	0.343549
$536$	87.5062	3.77969
$537$	6.15207	0.265481
$538$	−18.4035	−0.793429
$539$	−13.9050	−0.598929
$540$	−3.94879	−0.169929
$541$	24.0324	1.03323	0.516617	−	0.856217i	$-0.327191\pi$
$541$	24.0324	1.03323	0.516617	+	0.856217i	$0.327191\pi$
$542$	38.2842	1.64445
$543$	8.07676	0.346607
$544$	8.40862	0.360517
$545$	−3.60314	−0.154341
$546$	9.21309	0.394284
$547$	34.3383	1.46820	0.734100	−	0.679042i	$-0.237605\pi$
$547$	34.3383	1.46820	0.734100	+	0.679042i	$0.237605\pi$
$548$	56.0767	2.39548
$549$	−2.22450	−0.0949394
$550$	28.0792	1.19730
$551$	21.1822	0.902392
$552$	−40.5183	−1.72457
$553$	−0.544655	−0.0231611
$554$	61.3642	2.60712
$555$	−1.04190	−0.0442262
$556$	41.4868	1.75943
$557$	38.9197	1.64908	0.824540	−	0.565803i	$-0.191434\pi$
$557$	38.9197	1.64908	0.824540	+	0.565803i	$0.191434\pi$
$558$	21.0346	0.890464
$559$	−0.899712	−0.0380538
$560$	−10.4942	−0.443460
$561$	0.667464	0.0281804
$562$	50.6799	2.13780
$563$	−35.4794	−1.49528	−0.747639	−	0.664105i	$-0.768813\pi$
$563$	−35.4794	−1.49528	−0.747639	+	0.664105i	$0.768813\pi$
$564$	−43.0375	−1.81221
$565$	−6.83587	−0.287587
$566$	−2.59632	−0.109131
$567$	−0.869505	−0.0365158
$568$	132.725	5.56902
$569$	−42.6041	−1.78606	−0.893028	−	0.450001i	$-0.851424\pi$
$569$	−42.6041	−1.78606	−0.893028	+	0.450001i	$0.851424\pi$
$570$	4.16875	0.174610
$571$	15.7535	0.659264	0.329632	−	0.944110i	$-0.393075\pi$
$571$	15.7535	0.659264	0.329632	+	0.944110i	$0.393075\pi$
$572$	−48.7470	−2.03821
$573$	−14.6553	−0.612234
$574$	−0.228845	−0.00955179
$575$	17.5661	0.732557
$576$	42.9503	1.78960
$577$	−8.23573	−0.342858	−0.171429	−	0.985196i	$-0.554838\pi$
$577$	−8.23573	−0.342858	−0.171429	+	0.985196i	$0.554838\pi$
$578$	47.0815	1.95833
$579$	6.90986	0.287164
$580$	38.3520	1.59248
$581$	12.4561	0.516766
$582$	−31.6631	−1.31248
$583$	24.7767	1.02614
$584$	−3.12903	−0.129480
$585$	−2.61269	−0.108021
$586$	7.64225	0.315698
$587$	−2.60754	−0.107625	−0.0538124	−	0.998551i	$-0.517137\pi$
$587$	−2.60754	−0.107625	−0.0538124	+	0.998551i	$0.517137\pi$
$588$	35.9143	1.48108
$589$	−16.4770	−0.678922
$590$	−7.36186	−0.303083
$591$	−26.9165	−1.10720
$592$	26.6803	1.09655
$593$	−35.9804	−1.47754	−0.738770	−	0.673958i	$-0.764593\pi$
$593$	−35.9804	−1.47754	−0.738770	+	0.673958i	$0.764593\pi$
$594$	6.20029	0.254401
$595$	0.178915	0.00733480
$596$	127.229	5.21152
$597$	−20.2656	−0.829415
$598$	−41.0995	−1.68069
$599$	−17.0692	−0.697431	−0.348715	−	0.937229i	$-0.613382\pi$
$599$	−17.0692	−0.697431	−0.348715	+	0.937229i	$0.613382\pi$
$600$	−47.3064	−1.93128
$601$	−39.2736	−1.60200	−0.801001	−	0.598663i	$-0.795699\pi$
$601$	−39.2736	−1.60200	−0.801001	+	0.598663i	$0.795699\pi$
$602$	0.572331	0.0233265
$603$	−8.37705	−0.341140
$604$	63.1504	2.56955
$605$	−4.14710	−0.168604
$606$	−3.85498	−0.156598
$607$	22.3652	0.907775	0.453888	−	0.891059i	$-0.350037\pi$
$607$	22.3652	0.907775	0.453888	+	0.891059i	$0.350037\pi$
$608$	−61.1862	−2.48143
$609$	8.44493	0.342206
$610$	4.25199	0.172158
$611$	−28.4755	−1.15199
$612$	−1.72395	−0.0696867
$613$	−2.92401	−0.118100	−0.0590498	−	0.998255i	$-0.518807\pi$
$613$	−2.92401	−0.118100	−0.0590498	+	0.998255i	$0.518807\pi$
$614$	53.3553	2.15325
$615$	0.0648967	0.00261689
$616$	20.2269	0.814965
$617$	6.14031	0.247200	0.123600	−	0.992332i	$-0.460556\pi$
$617$	6.14031	0.247200	0.123600	+	0.992332i	$0.460556\pi$
$618$	46.7038	1.87870
$619$	−10.0688	−0.404699	−0.202349	−	0.979313i	$-0.564858\pi$
$619$	−10.0688	−0.404699	−0.202349	+	0.979313i	$0.564858\pi$
$620$	−29.8329	−1.19812
$621$	3.87886	0.155653
$622$	14.3561	0.575626
$623$	−6.65338	−0.266562
$624$	66.9039	2.67830
$625$	18.1524	0.726095
$626$	−43.8486	−1.75254
$627$	−4.85687	−0.193965
$628$	42.0317	1.67725
$629$	−0.454871	−0.0181369
$630$	1.66200	0.0662157
$631$	−8.88530	−0.353718	−0.176859	−	0.984236i	$-0.556594\pi$
$631$	−8.88530	−0.353718	−0.176859	+	0.984236i	$0.556594\pi$
$632$	−6.54331	−0.260279
$633$	−5.34902	−0.212605
$634$	−26.6605	−1.05882
$635$	−3.96822	−0.157474
$636$	−63.9942	−2.53753
$637$	23.7624	0.941502
$638$	−60.2194	−2.38411
$639$	−12.7059	−0.502637
$640$	−43.5761	−1.72250
$641$	1.82731	0.0721746	0.0360873	−	0.999349i	$-0.488511\pi$
$641$	1.82731	0.0721746	0.0360873	+	0.999349i	$0.488511\pi$
$642$	32.2264	1.27187
$643$	33.2737	1.31219	0.656094	−	0.754679i	$-0.272208\pi$
$643$	33.2737	1.31219	0.656094	+	0.754679i	$0.272208\pi$
$644$	19.3992	0.764434
$645$	−0.162304	−0.00639072
$646$	1.81999	0.0716064
$647$	−4.08848	−0.160735	−0.0803673	−	0.996765i	$-0.525609\pi$
$647$	−4.08848	−0.160735	−0.0803673	+	0.996765i	$0.525609\pi$
$648$	−10.4459	−0.410356
$649$	8.57705	0.336679
$650$	−47.9850	−1.88213
$651$	−6.56905	−0.257462
$652$	35.8296	1.40319
$653$	17.1880	0.672617	0.336309	−	0.941752i	$-0.390821\pi$
$653$	17.1880	0.672617	0.336309	+	0.941752i	$0.390821\pi$
$654$	−14.6126	−0.571397
$655$	3.92265	0.153271
$656$	−1.66183	−0.0648835
$657$	0.299545	0.0116863
$658$	18.1140	0.706157
$659$	44.2832	1.72503	0.862513	−	0.506034i	$-0.168889\pi$
$659$	44.2832	1.72503	0.862513	+	0.506034i	$0.168889\pi$
$660$	−8.79374	−0.342296
$661$	−9.77603	−0.380244	−0.190122	−	0.981761i	$-0.560888\pi$
$661$	−9.77603	−0.380244	−0.190122	+	0.981761i	$0.560888\pi$
$662$	0.0645158	0.00250748
$663$	−1.14064	−0.0442988
$664$	149.644	5.80730
$665$	−1.30189	−0.0504853
$666$	−4.22545	−0.163733
$667$	−37.6728	−1.45870
$668$	−134.583	−5.20719
$669$	−8.26567	−0.319569
$670$	16.0122	0.618604
$671$	−4.95384	−0.191241
$672$	−24.3937	−0.941009
$673$	7.86842	0.303305	0.151653	−	0.988434i	$-0.451541\pi$
$673$	7.86842	0.303305	0.151653	+	0.988434i	$0.451541\pi$
$674$	−6.33067	−0.243848
$675$	4.52868	0.174309
$676$	8.53059	0.328100
$677$	−0.799995	−0.0307463	−0.0153731	−	0.999882i	$-0.504894\pi$
$677$	−0.799995	−0.0307463	−0.0153731	+	0.999882i	$0.504894\pi$
$678$	−27.7230	−1.06469
$679$	9.88831	0.379479
$680$	2.14943	0.0824268
$681$	−14.0707	−0.539192
$682$	46.8428	1.79370
$683$	48.1906	1.84396	0.921980	−	0.387237i	$-0.126570\pi$
$683$	48.1906	1.84396	0.921980	+	0.387237i	$0.126570\pi$
$684$	12.5445	0.479652
$685$	6.69316	0.255733
$686$	−32.0621	−1.22414
$687$	−5.75987	−0.219753
$688$	4.15617	0.158452
$689$	−42.3413	−1.61307
$690$	−7.41417	−0.282253
$691$	9.38634	0.357073	0.178537	−	0.983933i	$-0.442864\pi$
$691$	9.38634	0.357073	0.178537	+	0.983933i	$0.442864\pi$
$692$	−4.83260	−0.183708
$693$	−1.93634	−0.0735555
$694$	7.23018	0.274454
$695$	4.95176	0.187831
$696$	101.455	3.84563
$697$	0.0283325	0.00107317
$698$	−55.6507	−2.10641
$699$	−1.43900	−0.0544279
$700$	22.6491	0.856056
$701$	33.4097	1.26187	0.630934	−	0.775837i	$-0.282672\pi$
$701$	33.4097	1.26187	0.630934	+	0.775837i	$0.282672\pi$
$702$	−10.5958	−0.399912
$703$	3.30991	0.124836
$704$	95.6481	3.60487
$705$	−5.13684	−0.193465
$706$	−69.8077	−2.62725
$707$	1.20390	0.0452774
$708$	−22.1532	−0.832567
$709$	−5.01117	−0.188199	−0.0940993	−	0.995563i	$-0.529997\pi$
$709$	−5.01117	−0.188199	−0.0940993	+	0.995563i	$0.529997\pi$
$710$	24.2865	0.911454
$711$	0.626397	0.0234917
$712$	−79.9316	−2.99556
$713$	29.3045	1.09746
$714$	0.725593	0.0271546
$715$	−5.81831	−0.217593
$716$	−35.3858	−1.32243
$717$	5.89698	0.220227
$718$	39.0230	1.45633
$719$	12.3130	0.459198	0.229599	−	0.973285i	$-0.426259\pi$
$719$	12.3130	0.459198	0.229599	+	0.973285i	$0.426259\pi$
$720$	12.0692	0.449791
$721$	−14.5855	−0.543193
$722$	39.6568	1.47587
$723$	−26.5558	−0.987620
$724$	−46.4563	−1.72653
$725$	−43.9841	−1.63353
$726$	−16.8186	−0.624198
$727$	−24.4402	−0.906438	−0.453219	−	0.891399i	$-0.649724\pi$
$727$	−24.4402	−0.906438	−0.453219	+	0.891399i	$0.649724\pi$
$728$	−34.5661	−1.28111
$729$	1.00000	0.0370370
$730$	−0.572560	−0.0211914
$731$	−0.0708584	−0.00262079
$732$	12.7950	0.472917
$733$	45.4128	1.67736	0.838680	−	0.544625i	$-0.183328\pi$
$733$	45.4128	1.67736	0.838680	+	0.544625i	$0.183328\pi$
$734$	88.6841	3.27339
$735$	4.28664	0.158115
$736$	108.820	4.01117
$737$	−18.6552	−0.687174
$738$	0.263190	0.00968814
$739$	48.8473	1.79688	0.898439	−	0.439099i	$-0.144702\pi$
$739$	48.8473	1.79688	0.898439	+	0.439099i	$0.144702\pi$
$740$	5.99286	0.220302
$741$	8.29999	0.304908
$742$	26.9344	0.988794
$743$	−22.9169	−0.840741	−0.420370	−	0.907353i	$-0.638100\pi$
$743$	−22.9169	−0.840741	−0.420370	+	0.907353i	$0.638100\pi$
$744$	−78.9185	−2.89329
$745$	15.1858	0.556364
$746$	−64.4379	−2.35924
$747$	−14.3255	−0.524143
$748$	−3.83915	−0.140373
$749$	−10.0642	−0.367739
$750$	−18.2134	−0.665061
$751$	−51.7192	−1.88726	−0.943631	−	0.331000i	$-0.892614\pi$
$751$	−51.7192	−1.88726	−0.943631	+	0.331000i	$0.892614\pi$
$752$	131.541	4.79680
$753$	5.25237	0.191407
$754$	102.910	3.74776
$755$	7.53746	0.274316
$756$	5.00126	0.181894
$757$	7.51114	0.272997	0.136498	−	0.990640i	$-0.456415\pi$
$757$	7.51114	0.272997	0.136498	+	0.990640i	$0.456415\pi$
$758$	25.5376	0.927567
$759$	8.63800	0.313540
$760$	−15.6405	−0.567342
$761$	−11.1040	−0.402520	−0.201260	−	0.979538i	$-0.564504\pi$
$761$	−11.1040	−0.402520	−0.201260	+	0.979538i	$0.564504\pi$
$762$	−16.0932	−0.582994
$763$	4.56348	0.165209
$764$	84.2951	3.04969
$765$	−0.205767	−0.00743951
$766$	34.4101	1.24329
$767$	−14.6575	−0.529251
$768$	−90.8229	−3.27729
$769$	25.9981	0.937514	0.468757	−	0.883327i	$-0.344702\pi$
$769$	25.9981	0.937514	0.468757	+	0.883327i	$0.344702\pi$
$770$	3.70118	0.133381
$771$	−2.34980	−0.0846261
$772$	−39.7445	−1.43044
$773$	27.7804	0.999193	0.499597	−	0.866258i	$-0.333482\pi$
$773$	27.7804	0.999193	0.499597	+	0.866258i	$0.333482\pi$
$774$	−0.658227	−0.0236595
$775$	34.2139	1.22900
$776$	118.795	4.26449
$777$	1.31960	0.0473403
$778$	−70.3445	−2.52197
$779$	−0.206164	−0.00738659
$780$	15.0278	0.538081
$781$	−28.2953	−1.01249
$782$	−3.23686	−0.115750
$783$	−9.71234	−0.347091
$784$	−109.769	−3.92033
$785$	5.01680	0.179057
$786$	15.9084	0.567432
$787$	28.8431	1.02815	0.514073	−	0.857746i	$-0.328136\pi$
$787$	28.8431	1.02815	0.514073	+	0.857746i	$0.328136\pi$
$788$	154.820	5.51522
$789$	16.3351	0.581546
$790$	−1.19732	−0.0425986
$791$	8.65783	0.307837
$792$	−23.2626	−0.826599
$793$	8.46571	0.300626
$794$	−28.1369	−0.998543
$795$	−7.63818	−0.270898
$796$	116.565	4.13152
$797$	13.2454	0.469176	0.234588	−	0.972095i	$-0.424626\pi$
$797$	13.2454	0.469176	0.234588	+	0.972095i	$0.424626\pi$
$798$	−5.27985	−0.186905
$799$	−2.24263	−0.0793387
$800$	127.051	4.49194
$801$	7.65192	0.270367
$802$	54.2856	1.91689
$803$	0.667070	0.0235404
$804$	48.1835	1.69930
$805$	2.31543	0.0816083
$806$	−80.0506	−2.81966
$807$	−6.60993	−0.232680
$808$	14.4633	0.508817
$809$	17.7721	0.624835	0.312418	−	0.949945i	$-0.398861\pi$
$809$	17.7721	0.624835	0.312418	+	0.949945i	$0.398861\pi$
$810$	−1.91143	−0.0671609
$811$	−46.7495	−1.64160	−0.820799	−	0.571217i	$-0.806471\pi$
$811$	−46.7495	−1.64160	−0.820799	+	0.571217i	$0.806471\pi$
$812$	−48.5739	−1.70461
$813$	13.7505	0.482250
$814$	−9.40984	−0.329815
$815$	4.27652	0.149800
$816$	5.26913	0.184456
$817$	0.515608	0.0180388
$818$	19.9404	0.697199
$819$	3.30905	0.115627
$820$	−0.373276	−0.0130354
$821$	−30.4414	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$821$	−30.4414	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$822$	27.1442	0.946763
$823$	30.1095	1.04955	0.524776	−	0.851241i	$-0.324149\pi$
$823$	30.1095	1.04955	0.524776	+	0.851241i	$0.324149\pi$
$824$	−175.226	−6.10428
$825$	10.0851	0.351119
$826$	9.32401	0.324424
$827$	−25.9516	−0.902424	−0.451212	−	0.892417i	$-0.649008\pi$
$827$	−25.9516	−0.902424	−0.451212	+	0.892417i	$0.649008\pi$
$828$	−22.3106	−0.775347
$829$	5.67216	0.197002	0.0985011	−	0.995137i	$-0.468595\pi$
$829$	5.67216	0.197002	0.0985011	+	0.995137i	$0.468595\pi$
$830$	27.3823	0.950453
$831$	22.0401	0.764561
$832$	−163.455	−5.66677
$833$	1.87145	0.0648420
$834$	20.0819	0.695380
$835$	−16.0635	−0.555901
$836$	27.9360	0.966186
$837$	7.55494	0.261137
$838$	−21.0967	−0.728774
$839$	36.2216	1.25051	0.625254	−	0.780421i	$-0.284995\pi$
$839$	36.2216	1.25051	0.625254	+	0.780421i	$0.284995\pi$
$840$	−6.23557	−0.215148
$841$	65.3296	2.25274
$842$	82.6839	2.84947
$843$	18.2026	0.626930
$844$	30.7668	1.05904
$845$	1.01819	0.0350268
$846$	−20.8326	−0.716238
$847$	5.25243	0.180476
$848$	195.593	6.71670
$849$	−0.932514	−0.0320038
$850$	−3.77914	−0.129623
$851$	−5.88672	−0.201794
$852$	73.0823	2.50376
$853$	45.2133	1.54808	0.774038	−	0.633140i	$-0.218234\pi$
$853$	45.2133	1.54808	0.774038	+	0.633140i	$0.218234\pi$
$854$	−5.38527	−0.184280
$855$	1.49728	0.0512059
$856$	−120.908	−4.13257
$857$	52.2052	1.78330	0.891648	−	0.452730i	$-0.149550\pi$
$857$	52.2052	1.78330	0.891648	+	0.452730i	$0.149550\pi$
$858$	−23.5963	−0.805563
$859$	45.7298	1.56028	0.780140	−	0.625606i	$-0.215148\pi$
$859$	45.7298	1.56028	0.780140	+	0.625606i	$0.215148\pi$
$860$	0.933548	0.0318337
$861$	−0.0821936	−0.00280115
$862$	−40.5840	−1.38230
$863$	−16.9860	−0.578209	−0.289105	−	0.957298i	$-0.593358\pi$
$863$	−16.9860	−0.578209	−0.289105	+	0.957298i	$0.593358\pi$
$864$	28.0548	0.954442
$865$	−0.576806	−0.0196120
$866$	6.64292	0.225736
$867$	16.9102	0.574299
$868$	37.7842	1.28248
$869$	1.39495	0.0473205
$870$	18.5645	0.629395
$871$	31.8803	1.08022
$872$	54.8242	1.85658
$873$	−11.3724	−0.384896
$874$	23.5534	0.796705
$875$	5.68802	0.192290
$876$	−1.72294	−0.0582126
$877$	−17.4876	−0.590514	−0.295257	−	0.955418i	$-0.595405\pi$
$877$	−17.4876	−0.590514	−0.295257	+	0.955418i	$0.595405\pi$
$878$	−112.491	−3.79637
$879$	2.74485	0.0925815
$880$	26.8774	0.906036
$881$	38.4451	1.29525	0.647624	−	0.761960i	$-0.275763\pi$
$881$	38.4451	1.29525	0.647624	+	0.761960i	$0.275763\pi$
$882$	17.3845	0.585367
$883$	−15.2721	−0.513945	−0.256973	−	0.966419i	$-0.582725\pi$
$883$	−15.2721	−0.513945	−0.256973	+	0.966419i	$0.582725\pi$
$884$	6.56080	0.220663
$885$	−2.64414	−0.0888819
$886$	58.0354	1.94974
$887$	−35.1747	−1.18105	−0.590525	−	0.807019i	$-0.701079\pi$
$887$	−35.1747	−1.18105	−0.590525	+	0.807019i	$0.701079\pi$
$888$	15.8532	0.532000
$889$	5.02586	0.168562
$890$	−14.6261	−0.490269
$891$	2.22695	0.0746055
$892$	47.5429	1.59185
$893$	16.3187	0.546086
$894$	61.5861	2.05975
$895$	−4.22355	−0.141178
$896$	55.1904	1.84378
$897$	−14.7616	−0.492877
$898$	−20.1142	−0.671220
$899$	−73.3761	−2.44723
$900$	−26.0483	−0.868277
$901$	−3.33466	−0.111094
$902$	0.586109	0.0195153
$903$	0.205563	0.00684070
$904$	104.012	3.45940
$905$	−5.54490	−0.184319
$906$	30.5683	1.01556
$907$	11.4906	0.381540	0.190770	−	0.981635i	$-0.438901\pi$
$907$	11.4906	0.381540	0.190770	+	0.981635i	$0.438901\pi$
$908$	80.9327	2.68585
$909$	−1.38459	−0.0459238
$910$	−6.32502	−0.209672
$911$	−31.0129	−1.02750	−0.513751	−	0.857939i	$-0.671745\pi$
$911$	−31.0129	−1.02750	−0.513751	+	0.857939i	$0.671745\pi$
$912$	−38.3413	−1.26961
$913$	−31.9022	−1.05581
$914$	−12.4781	−0.412740
$915$	1.52718	0.0504869
$916$	33.1299	1.09464
$917$	−4.96815	−0.164063
$918$	−0.834490	−0.0275423
$919$	4.79484	0.158167	0.0790837	−	0.996868i	$-0.474801\pi$
$919$	4.79484	0.158167	0.0790837	+	0.996868i	$0.474801\pi$
$920$	27.8169	0.917095
$921$	19.1635	0.631459
$922$	−23.8687	−0.786072
$923$	48.3544	1.59160
$924$	11.1375	0.366398
$925$	−6.87293	−0.225980
$926$	56.5563	1.85856
$927$	16.7745	0.550947
$928$	−272.477	−8.94451
$929$	12.8367	0.421160	0.210580	−	0.977577i	$-0.432465\pi$
$929$	12.8367	0.421160	0.210580	+	0.977577i	$0.432465\pi$
$930$	−14.4408	−0.473531
$931$	−13.6178	−0.446306
$932$	8.27690	0.271119
$933$	5.15624	0.168808
$934$	−107.913	−3.53103
$935$	−0.458231	−0.0149858
$936$	39.7538	1.29939
$937$	31.8576	1.04074	0.520372	−	0.853940i	$-0.325793\pi$
$937$	31.8576	1.04074	0.520372	+	0.853940i	$0.325793\pi$
$938$	−20.2799	−0.662162
$939$	−15.7490	−0.513949
$940$	29.5464	0.963696
$941$	0.409229	0.0133405	0.00667024	−	0.999978i	$-0.497877\pi$
$941$	0.409229	0.0133405	0.00667024	+	0.999978i	$0.497877\pi$
$942$	20.3457	0.662899
$943$	0.366665	0.0119403
$944$	67.7094	2.20375
$945$	0.596937	0.0194184
$946$	−1.46583	−0.0476584
$947$	14.3019	0.464750	0.232375	−	0.972626i	$-0.425350\pi$
$947$	14.3019	0.464750	0.232375	+	0.972626i	$0.425350\pi$
$948$	−3.60294	−0.117018
$949$	−1.13997	−0.0370049
$950$	27.4993	0.892195
$951$	−9.57558	−0.310509
$952$	−2.72231	−0.0882307
$953$	20.3278	0.658483	0.329241	−	0.944246i	$-0.393207\pi$
$953$	20.3278	0.658483	0.329241	+	0.944246i	$0.393207\pi$
$954$	−30.9767	−1.00291
$955$	10.0612	0.325574
$956$	−33.9186	−1.09700
$957$	−21.6289	−0.699162
$958$	−17.2633	−0.557751
$959$	−8.47709	−0.273739
$960$	−29.4865	−0.951672
$961$	26.0771	0.841196
$962$	16.0806	0.518461
$963$	11.5747	0.372989
$964$	152.745	4.91958
$965$	−4.74380	−0.152708
$966$	9.39027	0.302127
$967$	47.2068	1.51807	0.759034	−	0.651052i	$-0.225672\pi$
$967$	47.2068	1.51807	0.759034	+	0.651052i	$0.225672\pi$
$968$	63.1010	2.02814
$969$	0.653680	0.0209992
$970$	21.7375	0.697949
$971$	5.26820	0.169065	0.0845323	−	0.996421i	$-0.473060\pi$
$971$	5.26820	0.169065	0.0845323	+	0.996421i	$0.473060\pi$
$972$	−5.75185	−0.184491
$973$	−6.27154	−0.201056
$974$	98.1485	3.14488
$975$	−17.2347	−0.551951
$976$	−39.1069	−1.25178
$977$	−38.2709	−1.22439	−0.612197	−	0.790706i	$-0.709714\pi$
$977$	−38.2709	−1.22439	−0.612197	+	0.790706i	$0.709714\pi$
$978$	17.3435	0.554584
$979$	17.0404	0.544614
$980$	−24.6561	−0.787610
$981$	−5.24837	−0.167567
$982$	−95.9214	−3.06097
$983$	−23.2795	−0.742502	−0.371251	−	0.928533i	$-0.621071\pi$
$983$	−23.2795	−0.742502	−0.371251	+	0.928533i	$0.621071\pi$
$984$	−0.987447	−0.0314787
$985$	18.4788	0.588785
$986$	8.10485	0.258111
$987$	6.50597	0.207087
$988$	−47.7403	−1.51882
$989$	−0.917015	−0.0291594
$990$	−4.25666	−0.135285
$991$	50.5803	1.60673	0.803367	−	0.595484i	$-0.203040\pi$
$991$	50.5803	1.60673	0.803367	+	0.595484i	$0.203040\pi$
$992$	211.952	6.72948
$993$	0.0231720	0.000735341 0
$994$	−30.7595	−0.975632
$995$	13.9128	0.441067
$996$	82.3982	2.61089
$997$	22.2272	0.703942	0.351971	−	0.936011i	$-0.385512\pi$
$997$	22.2272	0.703942	0.351971	+	0.936011i	$0.385512\pi$
$998$	92.3638	2.92373
$999$	−1.51764	−0.0480161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.1	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.1	✓	121	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)

\(f(q)\)	\(=\)	\(q-2.78421 q^{2} -1.00000 q^{3} +5.75185 q^{4} +0.686525 q^{5} +2.78421 q^{6} -0.869505 q^{7} -10.4459 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.78421 q^{2} -1.00000 q^{3} +5.75185 q^{4} +0.686525 q^{5} +2.78421 q^{6} -0.869505 q^{7} -10.4459 q^{8} +1.00000 q^{9} -1.91143 q^{10} +2.22695 q^{11} -5.75185 q^{12} -3.80567 q^{13} +2.42089 q^{14} -0.686525 q^{15} +17.5801 q^{16} -0.299722 q^{17} -2.78421 q^{18} +2.18096 q^{19} +3.94879 q^{20} +0.869505 q^{21} -6.20029 q^{22} -3.87886 q^{23} +10.4459 q^{24} -4.52868 q^{25} +10.5958 q^{26} -1.00000 q^{27} -5.00126 q^{28} +9.71234 q^{29} +1.91143 q^{30} -7.55494 q^{31} -28.0548 q^{32} -2.22695 q^{33} +0.834490 q^{34} -0.596937 q^{35} +5.75185 q^{36} +1.51764 q^{37} -6.07225 q^{38} +3.80567 q^{39} -7.17141 q^{40} -0.0945292 q^{41} -2.42089 q^{42} +0.236414 q^{43} +12.8091 q^{44} +0.686525 q^{45} +10.7996 q^{46} +7.48238 q^{47} -17.5801 q^{48} -6.24396 q^{49} +12.6088 q^{50} +0.299722 q^{51} -21.8896 q^{52} +11.1258 q^{53} +2.78421 q^{54} +1.52885 q^{55} +9.08280 q^{56} -2.18096 q^{57} -27.0412 q^{58} +3.85149 q^{59} -3.94879 q^{60} -2.22450 q^{61} +21.0346 q^{62} -0.869505 q^{63} +42.9503 q^{64} -2.61269 q^{65} +6.20029 q^{66} -8.37705 q^{67} -1.72395 q^{68} +3.87886 q^{69} +1.66200 q^{70} -12.7059 q^{71} -10.4459 q^{72} +0.299545 q^{73} -4.22545 q^{74} +4.52868 q^{75} +12.5445 q^{76} -1.93634 q^{77} -10.5958 q^{78} +0.626397 q^{79} +12.0692 q^{80} +1.00000 q^{81} +0.263190 q^{82} -14.3255 q^{83} +5.00126 q^{84} -0.205767 q^{85} -0.658227 q^{86} -9.71234 q^{87} -23.2626 q^{88} +7.65192 q^{89} -1.91143 q^{90} +3.30905 q^{91} -22.3106 q^{92} +7.55494 q^{93} -20.8326 q^{94} +1.49728 q^{95} +28.0548 q^{96} -11.3724 q^{97} +17.3845 q^{98} +2.22695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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