LMFDB - Embedded newform 195.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(1,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("195.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	195.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.77846 q^{2} -1.00000 q^{3} +5.71982 q^{4} -1.00000 q^{5} -2.77846 q^{6} -2.71982 q^{7} +10.3354 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.77846 q^{2} -1.00000 q^{3} +5.71982 q^{4} -1.00000 q^{5} -2.77846 q^{6} -2.71982 q^{7} +10.3354 q^{8} +1.00000 q^{9} -2.77846 q^{10} -2.71982 q^{11} -5.71982 q^{12} +1.00000 q^{13} -7.55691 q^{14} +1.00000 q^{15} +17.2767 q^{16} -2.83709 q^{17} +2.77846 q^{18} -3.55691 q^{19} -5.71982 q^{20} +2.71982 q^{21} -7.55691 q^{22} -4.83709 q^{23} -10.3354 q^{24} +1.00000 q^{25} +2.77846 q^{26} -1.00000 q^{27} -15.5569 q^{28} +6.00000 q^{29} +2.77846 q^{30} +7.55691 q^{31} +27.3319 q^{32} +2.71982 q^{33} -7.88273 q^{34} +2.71982 q^{35} +5.71982 q^{36} -4.27674 q^{37} -9.88273 q^{38} -1.00000 q^{39} -10.3354 q^{40} +2.83709 q^{41} +7.55691 q^{42} +11.1138 q^{43} -15.5569 q^{44} -1.00000 q^{45} -13.4396 q^{46} -11.5569 q^{47} -17.2767 q^{48} +0.397442 q^{49} +2.77846 q^{50} +2.83709 q^{51} +5.71982 q^{52} +1.16291 q^{53} -2.77846 q^{54} +2.71982 q^{55} -28.1104 q^{56} +3.55691 q^{57} +16.6707 q^{58} -2.11727 q^{59} +5.71982 q^{60} +6.60256 q^{61} +20.9966 q^{62} -2.71982 q^{63} +41.3871 q^{64} -1.00000 q^{65} +7.55691 q^{66} +1.88273 q^{67} -16.2277 q^{68} +4.83709 q^{69} +7.55691 q^{70} -6.71982 q^{71} +10.3354 q^{72} +9.11383 q^{73} -11.8827 q^{74} -1.00000 q^{75} -20.3449 q^{76} +7.39744 q^{77} -2.77846 q^{78} +10.2767 q^{79} -17.2767 q^{80} +1.00000 q^{81} +7.88273 q^{82} +2.11727 q^{83} +15.5569 q^{84} +2.83709 q^{85} +30.8793 q^{86} -6.00000 q^{87} -28.1104 q^{88} +1.16291 q^{89} -2.77846 q^{90} -2.71982 q^{91} -27.6673 q^{92} -7.55691 q^{93} -32.1104 q^{94} +3.55691 q^{95} -27.3319 q^{96} -10.8371 q^{97} +1.10428 q^{98} -2.71982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + q^{11} - 8 q^{12} + 3 q^{13} - 6 q^{14} + 3 q^{15} + 26 q^{16} - q^{17} + 6 q^{19} - 8 q^{20} - q^{21} - 6 q^{22} - 7 q^{23} - 6 q^{24} + 3 q^{25} - 3 q^{27} - 30 q^{28} + 18 q^{29} + 6 q^{31} + 22 q^{32} - q^{33} - 22 q^{34} - q^{35} + 8 q^{36} + 13 q^{37} - 28 q^{38} - 3 q^{39} - 6 q^{40} + q^{41} + 6 q^{42} - 30 q^{44} - 3 q^{45} - 22 q^{46} - 18 q^{47} - 26 q^{48} + 12 q^{49} + q^{51} + 8 q^{52} + 11 q^{53} - q^{55} - 16 q^{56} - 6 q^{57} - 8 q^{59} + 8 q^{60} + 9 q^{61} + 28 q^{62} + q^{63} + 30 q^{64} - 3 q^{65} + 6 q^{66} + 4 q^{67} + 18 q^{68} + 7 q^{69} + 6 q^{70} - 11 q^{71} + 6 q^{72} - 6 q^{73} - 34 q^{74} - 3 q^{75} + 4 q^{76} + 33 q^{77} + 5 q^{79} - 26 q^{80} + 3 q^{81} + 22 q^{82} + 8 q^{83} + 30 q^{84} + q^{85} + 56 q^{86} - 18 q^{87} - 16 q^{88} + 11 q^{89} + q^{91} + 2 q^{92} - 6 q^{93} - 28 q^{94} - 6 q^{95} - 22 q^{96} - 25 q^{97} + 10 q^{98} + q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9 + q^11 - 8 * q^12 + 3 * q^13 - 6 * q^14 + 3 * q^15 + 26 * q^16 - q^17 + 6 * q^19 - 8 * q^20 - q^21 - 6 * q^22 - 7 * q^23 - 6 * q^24 + 3 * q^25 - 3 * q^27 - 30 * q^28 + 18 * q^29 + 6 * q^31 + 22 * q^32 - q^33 - 22 * q^34 - q^35 + 8 * q^36 + 13 * q^37 - 28 * q^38 - 3 * q^39 - 6 * q^40 + q^41 + 6 * q^42 - 30 * q^44 - 3 * q^45 - 22 * q^46 - 18 * q^47 - 26 * q^48 + 12 * q^49 + q^51 + 8 * q^52 + 11 * q^53 - q^55 - 16 * q^56 - 6 * q^57 - 8 * q^59 + 8 * q^60 + 9 * q^61 + 28 * q^62 + q^63 + 30 * q^64 - 3 * q^65 + 6 * q^66 + 4 * q^67 + 18 * q^68 + 7 * q^69 + 6 * q^70 - 11 * q^71 + 6 * q^72 - 6 * q^73 - 34 * q^74 - 3 * q^75 + 4 * q^76 + 33 * q^77 + 5 * q^79 - 26 * q^80 + 3 * q^81 + 22 * q^82 + 8 * q^83 + 30 * q^84 + q^85 + 56 * q^86 - 18 * q^87 - 16 * q^88 + 11 * q^89 + q^91 + 2 * q^92 - 6 * q^93 - 28 * q^94 - 6 * q^95 - 22 * q^96 - 25 * q^97 + 10 * q^98 + 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 $

$2$	2.77846	1.96467	0.982333	−	0.187142i	$-0.0599223\pi$
$2$	2.77846	1.96467	0.982333	+	0.187142i	$0.0599223\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.71982	2.85991
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.77846	−1.13430
$7$	−2.71982	−1.02800	−0.513998	−	0.857791i	$-0.671836\pi$
$7$	−2.71982	−1.02800	−0.513998	+	0.857791i	$0.671836\pi$
$8$	10.3354	3.65411
$9$	1.00000	0.333333
$10$	−2.77846	−0.878625
$11$	−2.71982	−0.820058	−0.410029	−	0.912073i	$-0.634481\pi$
$11$	−2.71982	−0.820058	−0.410029	+	0.912073i	$0.634481\pi$
$12$	−5.71982	−1.65117
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−7.55691	−2.01967
$15$	1.00000	0.258199
$16$	17.2767	4.31918
$17$	−2.83709	−0.688095	−0.344048	−	0.938952i	$-0.611798\pi$
$17$	−2.83709	−0.688095	−0.344048	+	0.938952i	$0.611798\pi$
$18$	2.77846	0.654889
$19$	−3.55691	−0.816012	−0.408006	−	0.912979i	$-0.633776\pi$
$19$	−3.55691	−0.816012	−0.408006	+	0.912979i	$0.633776\pi$
$20$	−5.71982	−1.27899
$21$	2.71982	0.593514
$22$	−7.55691	−1.61114
$23$	−4.83709	−1.00860	−0.504302	−	0.863528i	$-0.668250\pi$
$23$	−4.83709	−1.00860	−0.504302	+	0.863528i	$0.668250\pi$
$24$	−10.3354	−2.10970
$25$	1.00000	0.200000
$26$	2.77846	0.544900
$27$	−1.00000	−0.192450
$28$	−15.5569	−2.93998
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	2.77846	0.507275
$31$	7.55691	1.35726	0.678631	−	0.734479i	$-0.262574\pi$
$31$	7.55691	1.35726	0.678631	+	0.734479i	$0.262574\pi$
$32$	27.3319	4.83165
$33$	2.71982	0.473461
$34$	−7.88273	−1.35188
$35$	2.71982	0.459734
$36$	5.71982	0.953304
$37$	−4.27674	−0.703091	−0.351546	−	0.936171i	$-0.614344\pi$
$37$	−4.27674	−0.703091	−0.351546	+	0.936171i	$0.614344\pi$
$38$	−9.88273	−1.60319
$39$	−1.00000	−0.160128
$40$	−10.3354	−1.63417
$41$	2.83709	0.443079	0.221540	−	0.975151i	$-0.428892\pi$
$41$	2.83709	0.443079	0.221540	+	0.975151i	$0.428892\pi$
$42$	7.55691	1.16606
$43$	11.1138	1.69484	0.847421	−	0.530921i	$-0.178154\pi$
$43$	11.1138	1.69484	0.847421	+	0.530921i	$0.178154\pi$
$44$	−15.5569	−2.34529
$45$	−1.00000	−0.149071
$46$	−13.4396	−1.98157
$47$	−11.5569	−1.68575	−0.842875	−	0.538110i	$-0.819138\pi$
$47$	−11.5569	−1.68575	−0.842875	+	0.538110i	$0.819138\pi$
$48$	−17.2767	−2.49368
$49$	0.397442	0.0567775
$50$	2.77846	0.392933
$51$	2.83709	0.397272
$52$	5.71982	0.793197
$53$	1.16291	0.159738	0.0798690	−	0.996805i	$-0.474550\pi$
$53$	1.16291	0.159738	0.0798690	+	0.996805i	$0.474550\pi$
$54$	−2.77846	−0.378100
$55$	2.71982	0.366741
$56$	−28.1104	−3.75641
$57$	3.55691	0.471125
$58$	16.6707	2.18898
$59$	−2.11727	−0.275645	−0.137822	−	0.990457i	$-0.544010\pi$
$59$	−2.11727	−0.275645	−0.137822	+	0.990457i	$0.544010\pi$
$60$	5.71982	0.738426
$61$	6.60256	0.845371	0.422685	−	0.906276i	$-0.361088\pi$
$61$	6.60256	0.845371	0.422685	+	0.906276i	$0.361088\pi$
$62$	20.9966	2.66657
$63$	−2.71982	−0.342666
$64$	41.3871	5.17339
$65$	−1.00000	−0.124035
$66$	7.55691	0.930192
$67$	1.88273	0.230013	0.115006	−	0.993365i	$-0.463311\pi$
$67$	1.88273	0.230013	0.115006	+	0.993365i	$0.463311\pi$
$68$	−16.2277	−1.96789
$69$	4.83709	0.582317
$70$	7.55691	0.903224
$71$	−6.71982	−0.797496	−0.398748	−	0.917060i	$-0.630555\pi$
$71$	−6.71982	−0.797496	−0.398748	+	0.917060i	$0.630555\pi$
$72$	10.3354	1.21804
$73$	9.11383	1.06669	0.533346	−	0.845897i	$-0.320934\pi$
$73$	9.11383	1.06669	0.533346	+	0.845897i	$0.320934\pi$
$74$	−11.8827	−1.38134
$75$	−1.00000	−0.115470
$76$	−20.3449	−2.33372
$77$	7.39744	0.843017
$78$	−2.77846	−0.314598
$79$	10.2767	1.15622	0.578112	−	0.815958i	$-0.303790\pi$
$79$	10.2767	1.15622	0.578112	+	0.815958i	$0.303790\pi$
$80$	−17.2767	−1.93160
$81$	1.00000	0.111111
$82$	7.88273	0.870502
$83$	2.11727	0.232400	0.116200	−	0.993226i	$-0.462929\pi$
$83$	2.11727	0.232400	0.116200	+	0.993226i	$0.462929\pi$
$84$	15.5569	1.69740
$85$	2.83709	0.307726
$86$	30.8793	3.32980
$87$	−6.00000	−0.643268
$88$	−28.1104	−2.99658
$89$	1.16291	0.123268	0.0616341	−	0.998099i	$-0.480369\pi$
$89$	1.16291	0.123268	0.0616341	+	0.998099i	$0.480369\pi$
$90$	−2.77846	−0.292875
$91$	−2.71982	−0.285115
$92$	−27.6673	−2.88452
$93$	−7.55691	−0.783616
$94$	−32.1104	−3.31193
$95$	3.55691	0.364932
$96$	−27.3319	−2.78955
$97$	−10.8371	−1.10034	−0.550170	−	0.835053i	$-0.685437\pi$
$97$	−10.8371	−1.10034	−0.550170	+	0.835053i	$0.685437\pi$
$98$	1.10428	0.111549
$99$	−2.71982	−0.273353
$100$	5.71982	0.571982
$101$	7.67418	0.763610	0.381805	−	0.924243i	$-0.375303\pi$
$101$	7.67418	0.763610	0.381805	+	0.924243i	$0.375303\pi$
$102$	7.88273	0.780507
$103$	3.76547	0.371023	0.185511	−	0.982642i	$-0.440606\pi$
$103$	3.76547	0.371023	0.185511	+	0.982642i	$0.440606\pi$
$104$	10.3354	1.01347
$105$	−2.71982	−0.265428
$106$	3.23109	0.313832
$107$	−12.6026	−1.21834	−0.609168	−	0.793041i	$-0.708496\pi$
$107$	−12.6026	−1.21834	−0.609168	+	0.793041i	$0.708496\pi$
$108$	−5.71982	−0.550390
$109$	11.4396	1.09572	0.547860	−	0.836570i	$-0.315443\pi$
$109$	11.4396	1.09572	0.547860	+	0.836570i	$0.315443\pi$
$110$	7.55691	0.720524
$111$	4.27674	0.405930
$112$	−46.9897	−4.44011
$113$	−13.1138	−1.23365	−0.616823	−	0.787102i	$-0.711580\pi$
$113$	−13.1138	−1.23365	−0.616823	+	0.787102i	$0.711580\pi$
$114$	9.88273	0.925603
$115$	4.83709	0.451061
$116$	34.3189	3.18643
$117$	1.00000	0.0924500
$118$	−5.88273	−0.541550
$119$	7.71639	0.707360
$120$	10.3354	0.943486
$121$	−3.60256	−0.327505
$122$	18.3449	1.66087
$123$	−2.83709	−0.255812
$124$	43.2242	3.88165
$125$	−1.00000	−0.0894427
$126$	−7.55691	−0.673223
$127$	−13.4396	−1.19258	−0.596288	−	0.802771i	$-0.703358\pi$
$127$	−13.4396	−1.19258	−0.596288	+	0.802771i	$0.703358\pi$
$128$	60.3285	5.33234
$129$	−11.1138	−0.978518
$130$	−2.77846	−0.243687
$131$	−9.43965	−0.824746	−0.412373	−	0.911015i	$-0.635300\pi$
$131$	−9.43965	−0.824746	−0.412373	+	0.911015i	$0.635300\pi$
$132$	15.5569	1.35406
$133$	9.67418	0.838858
$134$	5.23109	0.451898
$135$	1.00000	0.0860663
$136$	−29.3224	−2.51437
$137$	1.76547	0.150834	0.0754170	−	0.997152i	$-0.475971\pi$
$137$	1.76547	0.150834	0.0754170	+	0.997152i	$0.475971\pi$
$138$	13.4396	1.14406
$139$	−6.27674	−0.532386	−0.266193	−	0.963920i	$-0.585766\pi$
$139$	−6.27674	−0.532386	−0.266193	+	0.963920i	$0.585766\pi$
$140$	15.5569	1.31480
$141$	11.5569	0.973268
$142$	−18.6707	−1.56681
$143$	−2.71982	−0.227443
$144$	17.2767	1.43973
$145$	−6.00000	−0.498273
$146$	25.3224	2.09570
$147$	−0.397442	−0.0327805
$148$	−24.4622	−2.01078
$149$	−20.8302	−1.70648	−0.853239	−	0.521520i	$-0.825365\pi$
$149$	−20.8302	−1.70648	−0.853239	+	0.521520i	$0.825365\pi$
$150$	−2.77846	−0.226860
$151$	4.99656	0.406614	0.203307	−	0.979115i	$-0.434831\pi$
$151$	4.99656	0.406614	0.203307	+	0.979115i	$0.434831\pi$
$152$	−36.7620	−2.98179
$153$	−2.83709	−0.229365
$154$	20.5535	1.65625
$155$	−7.55691	−0.606986
$156$	−5.71982	−0.457952
$157$	8.87930	0.708645	0.354322	−	0.935123i	$-0.384712\pi$
$157$	8.87930	0.708645	0.354322	+	0.935123i	$0.384712\pi$
$158$	28.5535	2.27159
$159$	−1.16291	−0.0922247
$160$	−27.3319	−2.16078
$161$	13.1560	1.03684
$162$	2.77846	0.218296
$163$	−13.8337	−1.08354	−0.541768	−	0.840528i	$-0.682245\pi$
$163$	−13.8337	−1.08354	−0.541768	+	0.840528i	$0.682245\pi$
$164$	16.2277	1.26717
$165$	−2.71982	−0.211738
$166$	5.88273	0.456589
$167$	−9.88273	−0.764749	−0.382374	−	0.924007i	$-0.624894\pi$
$167$	−9.88273	−0.764749	−0.382374	+	0.924007i	$0.624894\pi$
$168$	28.1104	2.16876
$169$	1.00000	0.0769231
$170$	7.88273	0.604578
$171$	−3.55691	−0.272004
$172$	63.5691	4.84710
$173$	13.1138	0.997026	0.498513	−	0.866882i	$-0.333880\pi$
$173$	13.1138	0.997026	0.498513	+	0.866882i	$0.333880\pi$
$174$	−16.6707	−1.26381
$175$	−2.71982	−0.205599
$176$	−46.9897	−3.54198
$177$	2.11727	0.159143
$178$	3.23109	0.242181
$179$	8.55348	0.639317	0.319658	−	0.947533i	$-0.396432\pi$
$179$	8.55348	0.639317	0.319658	+	0.947533i	$0.396432\pi$
$180$	−5.71982	−0.426331
$181$	3.72326	0.276748	0.138374	−	0.990380i	$-0.455812\pi$
$181$	3.72326	0.276748	0.138374	+	0.990380i	$0.455812\pi$
$182$	−7.55691	−0.560156
$183$	−6.60256	−0.488075
$184$	−49.9931	−3.68554
$185$	4.27674	0.314432
$186$	−20.9966	−1.53954
$187$	7.71639	0.564278
$188$	−66.1035	−4.82109
$189$	2.71982	0.197838
$190$	9.88273	0.716969
$191$	−4.23453	−0.306400	−0.153200	−	0.988195i	$-0.548958\pi$
$191$	−4.23453	−0.306400	−0.153200	+	0.988195i	$0.548958\pi$
$192$	−41.3871	−2.98686
$193$	−23.3906	−1.68369	−0.841845	−	0.539719i	$-0.818530\pi$
$193$	−23.3906	−1.68369	−0.841845	+	0.539719i	$0.818530\pi$
$194$	−30.1104	−2.16180
$195$	1.00000	0.0716115
$196$	2.27330	0.162379
$197$	14.5535	1.03689	0.518446	−	0.855110i	$-0.326511\pi$
$197$	14.5535	1.03689	0.518446	+	0.855110i	$0.326511\pi$
$198$	−7.55691	−0.537047
$199$	−15.1138	−1.07139	−0.535695	−	0.844411i	$-0.679950\pi$
$199$	−15.1138	−1.07139	−0.535695	+	0.844411i	$0.679950\pi$
$200$	10.3354	0.730821
$201$	−1.88273	−0.132798
$202$	21.3224	1.50024
$203$	−16.3189	−1.14537
$204$	16.2277	1.13616
$205$	−2.83709	−0.198151
$206$	10.4622	0.728935
$207$	−4.83709	−0.336201
$208$	17.2767	1.19793
$209$	9.67418	0.669177
$210$	−7.55691	−0.521477
$211$	−18.2277	−1.25484	−0.627422	−	0.778680i	$-0.715890\pi$
$211$	−18.2277	−1.25484	−0.627422	+	0.778680i	$0.715890\pi$
$212$	6.65164	0.456836
$213$	6.71982	0.460435
$214$	−35.0157	−2.39362
$215$	−11.1138	−0.757957
$216$	−10.3354	−0.703233
$217$	−20.5535	−1.39526
$218$	31.7846	2.15272
$219$	−9.11383	−0.615855
$220$	15.5569	1.04885
$221$	−2.83709	−0.190843
$222$	11.8827	0.797517
$223$	10.1173	0.677502	0.338751	−	0.940876i	$-0.389996\pi$
$223$	10.1173	0.677502	0.338751	+	0.940876i	$0.389996\pi$
$224$	−74.3380	−4.96692
$225$	1.00000	0.0666667
$226$	−36.4362	−2.42370
$227$	11.3224	0.751493	0.375746	−	0.926723i	$-0.377386\pi$
$227$	11.3224	0.751493	0.375746	+	0.926723i	$0.377386\pi$
$228$	20.3449	1.34738
$229$	−6.23453	−0.411990	−0.205995	−	0.978553i	$-0.566043\pi$
$229$	−6.23453	−0.411990	−0.205995	+	0.978553i	$0.566043\pi$
$230$	13.4396	0.886184
$231$	−7.39744	−0.486716
$232$	62.0122	4.07130
$233$	6.83709	0.447913	0.223956	−	0.974599i	$-0.428103\pi$
$233$	6.83709	0.447913	0.223956	+	0.974599i	$0.428103\pi$
$234$	2.77846	0.181633
$235$	11.5569	0.753890
$236$	−12.1104	−0.788319
$237$	−10.2767	−0.667546
$238$	21.4396	1.38973
$239$	1.28018	0.0828077	0.0414039	−	0.999142i	$-0.486817\pi$
$239$	1.28018	0.0828077	0.0414039	+	0.999142i	$0.486817\pi$
$240$	17.2767	1.11521
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	−10.0096	−0.643438
$243$	−1.00000	−0.0641500
$244$	37.7655	2.41769
$245$	−0.397442	−0.0253917
$246$	−7.88273	−0.502585
$247$	−3.55691	−0.226321
$248$	78.1035	4.95958
$249$	−2.11727	−0.134176
$250$	−2.77846	−0.175725
$251$	18.2277	1.15052	0.575260	−	0.817971i	$-0.304901\pi$
$251$	18.2277	1.15052	0.575260	+	0.817971i	$0.304901\pi$
$252$	−15.5569	−0.979993
$253$	13.1560	0.827113
$254$	−37.3415	−2.34301
$255$	−2.83709	−0.177665
$256$	84.8459	5.30287
$257$	1.11383	0.0694787	0.0347394	−	0.999396i	$-0.488940\pi$
$257$	1.11383	0.0694787	0.0347394	+	0.999396i	$0.488940\pi$
$258$	−30.8793	−1.92246
$259$	11.6320	0.722776
$260$	−5.71982	−0.354728
$261$	6.00000	0.371391
$262$	−26.2277	−1.62035
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	28.1104	1.73007
$265$	−1.16291	−0.0714370
$266$	26.8793	1.64808
$267$	−1.16291	−0.0711689
$268$	10.7689	0.657816
$269$	15.6742	0.955672	0.477836	−	0.878449i	$-0.341421\pi$
$269$	15.6742	0.955672	0.477836	+	0.878449i	$0.341421\pi$
$270$	2.77846	0.169092
$271$	0.443086	0.0269155	0.0134578	−	0.999909i	$-0.495716\pi$
$271$	0.443086	0.0269155	0.0134578	+	0.999909i	$0.495716\pi$
$272$	−49.0157	−2.97201
$273$	2.71982	0.164611
$274$	4.90528	0.296339
$275$	−2.71982	−0.164012
$276$	27.6673	1.66538
$277$	−4.87930	−0.293168	−0.146584	−	0.989198i	$-0.546828\pi$
$277$	−4.87930	−0.293168	−0.146584	+	0.989198i	$0.546828\pi$
$278$	−17.4396	−1.04596
$279$	7.55691	0.452421
$280$	28.1104	1.67992
$281$	−9.11383	−0.543685	−0.271843	−	0.962342i	$-0.587633\pi$
$281$	−9.11383	−0.543685	−0.271843	+	0.962342i	$0.587633\pi$
$282$	32.1104	1.91215
$283$	33.3415	1.98195	0.990973	−	0.134063i	$-0.0428025\pi$
$283$	33.3415	1.98195	0.990973	+	0.134063i	$0.0428025\pi$
$284$	−38.4362	−2.28077
$285$	−3.55691	−0.210693
$286$	−7.55691	−0.446850
$287$	−7.71639	−0.455484
$288$	27.3319	1.61055
$289$	−8.95092	−0.526525
$290$	−16.6707	−0.978940
$291$	10.8371	0.635281
$292$	52.1295	3.05065
$293$	−29.4328	−1.71948	−0.859740	−	0.510731i	$-0.829375\pi$
$293$	−29.4328	−1.71948	−0.859740	+	0.510731i	$0.829375\pi$
$294$	−1.10428	−0.0644027
$295$	2.11727	0.123272
$296$	−44.2017	−2.56917
$297$	2.71982	0.157820
$298$	−57.8759	−3.35266
$299$	−4.83709	−0.279736
$300$	−5.71982	−0.330234
$301$	−30.2277	−1.74229
$302$	13.8827	0.798862
$303$	−7.67418	−0.440870
$304$	−61.4519	−3.52451
$305$	−6.60256	−0.378061
$306$	−7.88273	−0.450626
$307$	−21.8337	−1.24611	−0.623056	−	0.782177i	$-0.714109\pi$
$307$	−21.8337	−1.24611	−0.623056	+	0.782177i	$0.714109\pi$
$308$	42.3121	2.41095
$309$	−3.76547	−0.214210
$310$	−20.9966	−1.19252
$311$	25.1070	1.42368	0.711842	−	0.702339i	$-0.247861\pi$
$311$	25.1070	1.42368	0.711842	+	0.702339i	$0.247861\pi$
$312$	−10.3354	−0.585125
$313$	8.22766	0.465055	0.232527	−	0.972590i	$-0.425300\pi$
$313$	8.22766	0.465055	0.232527	+	0.972590i	$0.425300\pi$
$314$	24.6707	1.39225
$315$	2.71982	0.153245
$316$	58.7811	3.30670
$317$	27.6742	1.55434	0.777168	−	0.629293i	$-0.216655\pi$
$317$	27.6742	1.55434	0.777168	+	0.629293i	$0.216655\pi$
$318$	−3.23109	−0.181191
$319$	−16.3189	−0.913685
$320$	−41.3871	−2.31361
$321$	12.6026	0.703406
$322$	36.5535	2.03705
$323$	10.0913	0.561494
$324$	5.71982	0.317768
$325$	1.00000	0.0554700
$326$	−38.4362	−2.12878
$327$	−11.4396	−0.632614
$328$	29.3224	1.61906
$329$	31.4328	1.73294
$330$	−7.55691	−0.415994
$331$	−13.2311	−0.727247	−0.363623	−	0.931546i	$-0.618460\pi$
$331$	−13.2311	−0.727247	−0.363623	+	0.931546i	$0.618460\pi$
$332$	12.1104	0.664644
$333$	−4.27674	−0.234364
$334$	−27.4588	−1.50248
$335$	−1.88273	−0.102865
$336$	46.9897	2.56350
$337$	−4.32582	−0.235642	−0.117821	−	0.993035i	$-0.537591\pi$
$337$	−4.32582	−0.235642	−0.117821	+	0.993035i	$0.537591\pi$
$338$	2.77846	0.151128
$339$	13.1138	0.712245
$340$	16.2277	0.880068
$341$	−20.5535	−1.11303
$342$	−9.88273	−0.534397
$343$	17.9578	0.969630
$344$	114.866	6.19314
$345$	−4.83709	−0.260420
$346$	36.4362	1.95882
$347$	6.27674	0.336953	0.168476	−	0.985706i	$-0.446115\pi$
$347$	6.27674	0.336953	0.168476	+	0.985706i	$0.446115\pi$
$348$	−34.3189	−1.83969
$349$	17.6673	0.945709	0.472855	−	0.881140i	$-0.343224\pi$
$349$	17.6673	0.945709	0.472855	+	0.881140i	$0.343224\pi$
$350$	−7.55691	−0.403934
$351$	−1.00000	−0.0533761
$352$	−74.3380	−3.96223
$353$	−13.7655	−0.732662	−0.366331	−	0.930485i	$-0.619386\pi$
$353$	−13.7655	−0.732662	−0.366331	+	0.930485i	$0.619386\pi$
$354$	5.88273	0.312664
$355$	6.71982	0.356651
$356$	6.65164	0.352536
$357$	−7.71639	−0.408394
$358$	23.7655	1.25604
$359$	0.996562	0.0525965	0.0262983	−	0.999654i	$-0.491628\pi$
$359$	0.996562	0.0525965	0.0262983	+	0.999654i	$0.491628\pi$
$360$	−10.3354	−0.544722
$361$	−6.34836	−0.334124
$362$	10.3449	0.543717
$363$	3.60256	0.189085
$364$	−15.5569	−0.815404
$365$	−9.11383	−0.477040
$366$	−18.3449	−0.958905
$367$	14.2277	0.742678	0.371339	−	0.928497i	$-0.378899\pi$
$367$	14.2277	0.742678	0.371339	+	0.928497i	$0.378899\pi$
$368$	−83.5691	−4.35634
$369$	2.83709	0.147693
$370$	11.8827	0.617754
$371$	−3.16291	−0.164210
$372$	−43.2242	−2.24107
$373$	15.6742	0.811578	0.405789	−	0.913967i	$-0.366997\pi$
$373$	15.6742	0.811578	0.405789	+	0.913967i	$0.366997\pi$
$374$	21.4396	1.10862
$375$	1.00000	0.0516398
$376$	−119.445	−6.15991
$377$	6.00000	0.309016
$378$	7.55691	0.388686
$379$	26.2017	1.34589	0.672945	−	0.739693i	$-0.265029\pi$
$379$	26.2017	1.34589	0.672945	+	0.739693i	$0.265029\pi$
$380$	20.3449	1.04367
$381$	13.4396	0.688534
$382$	−11.7655	−0.601974
$383$	22.4362	1.14644	0.573218	−	0.819403i	$-0.305695\pi$
$383$	22.4362	1.14644	0.573218	+	0.819403i	$0.305695\pi$
$384$	−60.3285	−3.07863
$385$	−7.39744	−0.377009
$386$	−64.9897	−3.30789
$387$	11.1138	0.564948
$388$	−61.9862	−3.14687
$389$	31.6742	1.60594	0.802972	−	0.596016i	$-0.203251\pi$
$389$	31.6742	1.60594	0.802972	+	0.596016i	$0.203251\pi$
$390$	2.77846	0.140693
$391$	13.7233	0.694015
$392$	4.10771	0.207471
$393$	9.43965	0.476167
$394$	40.4362	2.03715
$395$	−10.2767	−0.517079
$396$	−15.5569	−0.781764
$397$	17.9509	0.900931	0.450465	−	0.892794i	$-0.351258\pi$
$397$	17.9509	0.900931	0.450465	+	0.892794i	$0.351258\pi$
$398$	−41.9931	−2.10493
$399$	−9.67418	−0.484315
$400$	17.2767	0.863837
$401$	13.5829	0.678297	0.339149	−	0.940733i	$-0.389861\pi$
$401$	13.5829	0.678297	0.339149	+	0.940733i	$0.389861\pi$
$402$	−5.23109	−0.260903
$403$	7.55691	0.376437
$404$	43.8950	2.18386
$405$	−1.00000	−0.0496904
$406$	−45.3415	−2.25026
$407$	11.6320	0.576576
$408$	29.3224	1.45167
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	−7.88273	−0.389300
$411$	−1.76547	−0.0870841
$412$	21.5378	1.06109
$413$	5.75859	0.283362
$414$	−13.4396	−0.660523
$415$	−2.11727	−0.103933
$416$	27.3319	1.34006
$417$	6.27674	0.307373
$418$	26.8793	1.31471
$419$	12.3189	0.601820	0.300910	−	0.953653i	$-0.402710\pi$
$419$	12.3189	0.601820	0.300910	+	0.953653i	$0.402710\pi$
$420$	−15.5569	−0.759100
$421$	22.7880	1.11062	0.555310	−	0.831644i	$-0.312600\pi$
$421$	22.7880	1.11062	0.555310	+	0.831644i	$0.312600\pi$
$422$	−50.6448	−2.46535
$423$	−11.5569	−0.561916
$424$	12.0191	0.583699
$425$	−2.83709	−0.137619
$426$	18.6707	0.904600
$427$	−17.9578	−0.869039
$428$	−72.0844	−3.48433
$429$	2.71982	0.131314
$430$	−30.8793	−1.48913
$431$	−8.99656	−0.433349	−0.216675	−	0.976244i	$-0.569521\pi$
$431$	−8.99656	−0.433349	−0.216675	+	0.976244i	$0.569521\pi$
$432$	−17.2767	−0.831227
$433$	−20.3258	−0.976797	−0.488398	−	0.872621i	$-0.662419\pi$
$433$	−20.3258	−0.976797	−0.488398	+	0.872621i	$0.662419\pi$
$434$	−57.1070	−2.74122
$435$	6.00000	0.287678
$436$	65.4328	3.13366
$437$	17.2051	0.823032
$438$	−25.3224	−1.20995
$439$	−25.3906	−1.21183	−0.605913	−	0.795531i	$-0.707192\pi$
$439$	−25.3906	−1.21183	−0.605913	+	0.795531i	$0.707192\pi$
$440$	28.1104	1.34011
$441$	0.397442	0.0189258
$442$	−7.88273	−0.374943
$443$	10.9284	0.519223	0.259611	−	0.965713i	$-0.416406\pi$
$443$	10.9284	0.519223	0.259611	+	0.965713i	$0.416406\pi$
$444$	24.4622	1.16092
$445$	−1.16291	−0.0551272
$446$	28.1104	1.33107
$447$	20.8302	0.985235
$448$	−112.566	−5.31823
$449$	2.83709	0.133891	0.0669453	−	0.997757i	$-0.478675\pi$
$449$	2.83709	0.133891	0.0669453	+	0.997757i	$0.478675\pi$
$450$	2.77846	0.130978
$451$	−7.71639	−0.363350
$452$	−75.0088	−3.52812
$453$	−4.99656	−0.234759
$454$	31.4588	1.47643
$455$	2.71982	0.127507
$456$	36.7620	1.72154
$457$	−13.7164	−0.641625	−0.320813	−	0.947143i	$-0.603956\pi$
$457$	−13.7164	−0.641625	−0.320813	+	0.947143i	$0.603956\pi$
$458$	−17.3224	−0.809422
$459$	2.83709	0.132424
$460$	27.6673	1.28999
$461$	−19.6251	−0.914032	−0.457016	−	0.889458i	$-0.651082\pi$
$461$	−19.6251	−0.914032	−0.457016	+	0.889458i	$0.651082\pi$
$462$	−20.5535	−0.956234
$463$	27.0388	1.25660	0.628299	−	0.777972i	$-0.283751\pi$
$463$	27.0388	1.25660	0.628299	+	0.777972i	$0.283751\pi$
$464$	103.660	4.81231
$465$	7.55691	0.350444
$466$	18.9966	0.879999
$467$	28.9215	1.33833	0.669164	−	0.743115i	$-0.266652\pi$
$467$	28.9215	1.33833	0.669164	+	0.743115i	$0.266652\pi$
$468$	5.71982	0.264399
$469$	−5.12070	−0.236452
$470$	32.1104	1.48114
$471$	−8.87930	−0.409136
$472$	−21.8827	−1.00723
$473$	−30.2277	−1.38987
$474$	−28.5535	−1.31150
$475$	−3.55691	−0.163202
$476$	44.1364	2.02299
$477$	1.16291	0.0532460
$478$	3.55691	0.162689
$479$	−12.1595	−0.555580	−0.277790	−	0.960642i	$-0.589602\pi$
$479$	−12.1595	−0.555580	−0.277790	+	0.960642i	$0.589602\pi$
$480$	27.3319	1.24753
$481$	−4.27674	−0.195002
$482$	−16.6707	−0.759332
$483$	−13.1560	−0.598620
$484$	−20.6060	−0.936636
$485$	10.8371	0.492087
$486$	−2.77846	−0.126033
$487$	−0.159472	−0.00722636	−0.00361318	−	0.999993i	$-0.501150\pi$
$487$	−0.159472	−0.00722636	−0.00361318	+	0.999993i	$0.501150\pi$
$488$	68.2399	3.08907
$489$	13.8337	0.625579
$490$	−1.10428	−0.0498861
$491$	−42.2277	−1.90571	−0.952854	−	0.303430i	$-0.901868\pi$
$491$	−42.2277	−1.90571	−0.952854	+	0.303430i	$0.901868\pi$
$492$	−16.2277	−0.731599
$493$	−17.0225	−0.766657
$494$	−9.88273	−0.444645
$495$	2.71982	0.122247
$496$	130.559	5.86226
$497$	18.2767	0.819824
$498$	−5.88273	−0.263612
$499$	7.79145	0.348793	0.174397	−	0.984676i	$-0.444203\pi$
$499$	7.79145	0.348793	0.174397	+	0.984676i	$0.444203\pi$
$500$	−5.71982	−0.255798
$501$	9.88273	0.441528
$502$	50.6448	2.26039
$503$	27.3484	1.21940	0.609702	−	0.792631i	$-0.291289\pi$
$503$	27.3484	1.21940	0.609702	+	0.792631i	$0.291289\pi$
$504$	−28.1104	−1.25214
$505$	−7.67418	−0.341497
$506$	36.5535	1.62500
$507$	−1.00000	−0.0444116
$508$	−76.8724	−3.41066
$509$	−33.4819	−1.48406	−0.742029	−	0.670368i	$-0.766136\pi$
$509$	−33.4819	−1.48406	−0.742029	+	0.670368i	$0.766136\pi$
$510$	−7.88273	−0.349053
$511$	−24.7880	−1.09656
$512$	115.084	5.08603
$513$	3.55691	0.157042
$514$	3.09472	0.136502
$515$	−3.76547	−0.165926
$516$	−63.5691	−2.79848
$517$	31.4328	1.38241
$518$	32.3189	1.42001
$519$	−13.1138	−0.575633
$520$	−10.3354	−0.453236
$521$	−17.3484	−0.760045	−0.380023	−	0.924977i	$-0.624084\pi$
$521$	−17.3484	−0.760045	−0.380023	+	0.924977i	$0.624084\pi$
$522$	16.6707	0.729659
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−53.9931	−2.35870
$525$	2.71982	0.118703
$526$	22.2277	0.969172
$527$	−21.4396	−0.933926
$528$	46.9897	2.04496
$529$	0.397442	0.0172801
$530$	−3.23109	−0.140350
$531$	−2.11727	−0.0918815
$532$	55.3346	2.39906
$533$	2.83709	0.122888
$534$	−3.23109	−0.139823
$535$	12.6026	0.544856
$536$	19.4588	0.840490
$537$	−8.55348	−0.369110
$538$	43.5500	1.87758
$539$	−1.08097	−0.0465608
$540$	5.71982	0.246142
$541$	−32.6448	−1.40351	−0.701754	−	0.712419i	$-0.747599\pi$
$541$	−32.6448	−1.40351	−0.701754	+	0.712419i	$0.747599\pi$
$542$	1.23109	0.0528800
$543$	−3.72326	−0.159780
$544$	−77.5432	−3.32464
$545$	−11.4396	−0.490021
$546$	7.55691	0.323406
$547$	34.2277	1.46347	0.731734	−	0.681590i	$-0.238711\pi$
$547$	34.2277	1.46347	0.731734	+	0.681590i	$0.238711\pi$
$548$	10.0982	0.431372
$549$	6.60256	0.281790
$550$	−7.55691	−0.322228
$551$	−21.3415	−0.909178
$552$	49.9931	2.12785
$553$	−27.9509	−1.18859
$554$	−13.5569	−0.575978
$555$	−4.27674	−0.181537
$556$	−35.9018	−1.52258
$557$	6.65164	0.281839	0.140919	−	0.990021i	$-0.454994\pi$
$557$	6.65164	0.281839	0.140919	+	0.990021i	$0.454994\pi$
$558$	20.9966	0.888855
$559$	11.1138	0.470065
$560$	46.9897	1.98568
$561$	−7.71639	−0.325786
$562$	−25.3224	−1.06816
$563$	40.2699	1.69717	0.848586	−	0.529057i	$-0.177454\pi$
$563$	40.2699	1.69717	0.848586	+	0.529057i	$0.177454\pi$
$564$	66.1035	2.78346
$565$	13.1138	0.551703
$566$	92.6379	3.89386
$567$	−2.71982	−0.114222
$568$	−69.4519	−2.91414
$569$	−13.4328	−0.563131	−0.281566	−	0.959542i	$-0.590854\pi$
$569$	−13.4328	−0.563131	−0.281566	+	0.959542i	$0.590854\pi$
$570$	−9.88273	−0.413942
$571$	−35.7164	−1.49468	−0.747342	−	0.664439i	$-0.768670\pi$
$571$	−35.7164	−1.49468	−0.747342	+	0.664439i	$0.768670\pi$
$572$	−15.5569	−0.650467
$573$	4.23453	0.176900
$574$	−21.4396	−0.894874
$575$	−4.83709	−0.201721
$576$	41.3871	1.72446
$577$	−13.7164	−0.571021	−0.285510	−	0.958376i	$-0.592163\pi$
$577$	−13.7164	−0.571021	−0.285510	+	0.958376i	$0.592163\pi$
$578$	−24.8697	−1.03444
$579$	23.3906	0.972079
$580$	−34.3189	−1.42502
$581$	−5.75859	−0.238907
$582$	30.1104	1.24812
$583$	−3.16291	−0.130994
$584$	94.1948	3.89781
$585$	−1.00000	−0.0413449
$586$	−81.7777	−3.37821
$587$	30.6707	1.26592	0.632959	−	0.774186i	$-0.281840\pi$
$587$	30.6707	1.26592	0.632959	+	0.774186i	$0.281840\pi$
$588$	−2.27330	−0.0937493
$589$	−26.8793	−1.10754
$590$	5.88273	0.242188
$591$	−14.5535	−0.598650
$592$	−73.8881	−3.03678
$593$	−45.6673	−1.87533	−0.937666	−	0.347538i	$-0.887018\pi$
$593$	−45.6673	−1.87533	−0.937666	+	0.347538i	$0.887018\pi$
$594$	7.55691	0.310064
$595$	−7.71639	−0.316341
$596$	−119.145	−4.88038
$597$	15.1138	0.618568
$598$	−13.4396	−0.549588
$599$	−40.2208	−1.64338	−0.821688	−	0.569937i	$-0.806968\pi$
$599$	−40.2208	−1.64338	−0.821688	+	0.569937i	$0.806968\pi$
$600$	−10.3354	−0.421940
$601$	17.3974	0.709656	0.354828	−	0.934932i	$-0.384539\pi$
$601$	17.3974	0.709656	0.354828	+	0.934932i	$0.384539\pi$
$602$	−83.9862	−3.42302
$603$	1.88273	0.0766708
$604$	28.5795	1.16288
$605$	3.60256	0.146465
$606$	−21.3224	−0.866163
$607$	−14.2277	−0.577483	−0.288741	−	0.957407i	$-0.593237\pi$
$607$	−14.2277	−0.577483	−0.288741	+	0.957407i	$0.593237\pi$
$608$	−97.2173	−3.94268
$609$	16.3189	0.661277
$610$	−18.3449	−0.742764
$611$	−11.5569	−0.467543
$612$	−16.2277	−0.655964
$613$	−40.8302	−1.64912	−0.824558	−	0.565777i	$-0.808576\pi$
$613$	−40.8302	−1.64912	−0.824558	+	0.565777i	$0.808576\pi$
$614$	−60.6639	−2.44819
$615$	2.83709	0.114403
$616$	76.4553	3.08047
$617$	5.11383	0.205875	0.102937	−	0.994688i	$-0.467176\pi$
$617$	5.11383	0.205875	0.102937	+	0.994688i	$0.467176\pi$
$618$	−10.4622	−0.420851
$619$	11.5569	0.464512	0.232256	−	0.972655i	$-0.425389\pi$
$619$	11.5569	0.464512	0.232256	+	0.972655i	$0.425389\pi$
$620$	−43.2242	−1.73593
$621$	4.83709	0.194106
$622$	69.7586	2.79706
$623$	−3.16291	−0.126719
$624$	−17.2767	−0.691623
$625$	1.00000	0.0400000
$626$	22.8602	0.913677
$627$	−9.67418	−0.386350
$628$	50.7880	2.02666
$629$	12.1335	0.483794
$630$	7.55691	0.301075
$631$	35.2242	1.40225	0.701127	−	0.713036i	$-0.252681\pi$
$631$	35.2242	1.40225	0.701127	+	0.713036i	$0.252681\pi$
$632$	106.214	4.22496
$633$	18.2277	0.724484
$634$	76.8915	3.05375
$635$	13.4396	0.533336
$636$	−6.65164	−0.263755
$637$	0.397442	0.0157472
$638$	−45.3415	−1.79509
$639$	−6.71982	−0.265832
$640$	−60.3285	−2.38469
$641$	−21.9018	−0.865071	−0.432535	−	0.901617i	$-0.642381\pi$
$641$	−21.9018	−0.865071	−0.432535	+	0.901617i	$0.642381\pi$
$642$	35.0157	1.38196
$643$	7.50783	0.296080	0.148040	−	0.988981i	$-0.452704\pi$
$643$	7.50783	0.296080	0.148040	+	0.988981i	$0.452704\pi$
$644$	75.2502	2.96527
$645$	11.1138	0.437607
$646$	28.0382	1.10315
$647$	−14.0422	−0.552056	−0.276028	−	0.961150i	$-0.589018\pi$
$647$	−14.0422	−0.552056	−0.276028	+	0.961150i	$0.589018\pi$
$648$	10.3354	0.406012
$649$	5.75859	0.226044
$650$	2.77846	0.108980
$651$	20.5535	0.805554
$652$	−79.1261	−3.09882
$653$	7.99312	0.312795	0.156398	−	0.987694i	$-0.450012\pi$
$653$	7.99312	0.312795	0.156398	+	0.987694i	$0.450012\pi$
$654$	−31.7846	−1.24288
$655$	9.43965	0.368838
$656$	49.0157	1.91374
$657$	9.11383	0.355564
$658$	87.3346	3.40466
$659$	−25.3415	−0.987164	−0.493582	−	0.869699i	$-0.664313\pi$
$659$	−25.3415	−0.987164	−0.493582	+	0.869699i	$0.664313\pi$
$660$	−15.5569	−0.605552
$661$	27.4396	1.06728	0.533639	−	0.845712i	$-0.320824\pi$
$661$	27.4396	1.06728	0.533639	+	0.845712i	$0.320824\pi$
$662$	−36.7620	−1.42880
$663$	2.83709	0.110183
$664$	21.8827	0.849215
$665$	−9.67418	−0.375149
$666$	−11.8827	−0.460447
$667$	−29.0225	−1.12376
$668$	−56.5275	−2.18711
$669$	−10.1173	−0.391156
$670$	−5.23109	−0.202095
$671$	−17.9578	−0.693253
$672$	74.3380	2.86765
$673$	27.1070	1.04490	0.522448	−	0.852671i	$-0.325019\pi$
$673$	27.1070	1.04490	0.522448	+	0.852671i	$0.325019\pi$
$674$	−12.0191	−0.462959
$675$	−1.00000	−0.0384900
$676$	5.71982	0.219993
$677$	−36.5957	−1.40649	−0.703243	−	0.710949i	$-0.748265\pi$
$677$	−36.5957	−1.40649	−0.703243	+	0.710949i	$0.748265\pi$
$678$	36.4362	1.39932
$679$	29.4750	1.13115
$680$	29.3224	1.12446
$681$	−11.3224	−0.433875
$682$	−57.1070	−2.18674
$683$	−13.4656	−0.515248	−0.257624	−	0.966245i	$-0.582940\pi$
$683$	−13.4656	−0.515248	−0.257624	+	0.966245i	$0.582940\pi$
$684$	−20.3449	−0.777908
$685$	−1.76547	−0.0674550
$686$	49.8950	1.90500
$687$	6.23453	0.237862
$688$	192.011	7.32034
$689$	1.16291	0.0443033
$690$	−13.4396	−0.511639
$691$	29.5500	1.12414	0.562068	−	0.827091i	$-0.310006\pi$
$691$	29.5500	1.12414	0.562068	+	0.827091i	$0.310006\pi$
$692$	75.0088	2.85141
$693$	7.39744	0.281006
$694$	17.4396	0.662000
$695$	6.27674	0.238090
$696$	−62.0122	−2.35057
$697$	−8.04908	−0.304881
$698$	49.0878	1.85800
$699$	−6.83709	−0.258603
$700$	−15.5569	−0.587996
$701$	43.6604	1.64903	0.824516	−	0.565839i	$-0.191448\pi$
$701$	43.6604	1.64903	0.824516	+	0.565839i	$0.191448\pi$
$702$	−2.77846	−0.104866
$703$	15.2120	0.573731
$704$	−112.566	−4.24248
$705$	−11.5569	−0.435259
$706$	−38.2468	−1.43944
$707$	−20.8724	−0.784988
$708$	12.1104	0.455136
$709$	−26.7880	−1.00604	−0.503022	−	0.864273i	$-0.667779\pi$
$709$	−26.7880	−1.00604	−0.503022	+	0.864273i	$0.667779\pi$
$710$	18.6707	0.700700
$711$	10.2767	0.385408
$712$	12.0191	0.450435
$713$	−36.5535	−1.36894
$714$	−21.4396	−0.802359
$715$	2.71982	0.101716
$716$	48.9244	1.82839
$717$	−1.28018	−0.0478091
$718$	2.76891	0.103335
$719$	−34.8793	−1.30078	−0.650389	−	0.759601i	$-0.725394\pi$
$719$	−34.8793	−1.30078	−0.650389	+	0.759601i	$0.725394\pi$
$720$	−17.2767	−0.643866
$721$	−10.2414	−0.381410
$722$	−17.6386	−0.656443
$723$	6.00000	0.223142
$724$	21.2964	0.791475
$725$	6.00000	0.222834
$726$	10.0096	0.371489
$727$	37.4396	1.38856	0.694280	−	0.719705i	$-0.255723\pi$
$727$	37.4396	1.38856	0.694280	+	0.719705i	$0.255723\pi$
$728$	−28.1104	−1.04184
$729$	1.00000	0.0370370
$730$	−25.3224	−0.937223
$731$	−31.5309	−1.16621
$732$	−37.7655	−1.39585
$733$	−47.1560	−1.74175	−0.870874	−	0.491506i	$-0.836446\pi$
$733$	−47.1560	−1.74175	−0.870874	+	0.491506i	$0.836446\pi$
$734$	39.5309	1.45911
$735$	0.397442	0.0146599
$736$	−132.207	−4.87322
$737$	−5.12070	−0.188624
$738$	7.88273	0.290167
$739$	−31.7914	−1.16947	−0.584734	−	0.811225i	$-0.698801\pi$
$739$	−31.7914	−1.16947	−0.584734	+	0.811225i	$0.698801\pi$
$740$	24.4622	0.899248
$741$	3.55691	0.130667
$742$	−8.78801	−0.322618
$743$	16.6776	0.611842	0.305921	−	0.952057i	$-0.401036\pi$
$743$	16.6776	0.611842	0.305921	+	0.952057i	$0.401036\pi$
$744$	−78.1035	−2.86341
$745$	20.8302	0.763160
$746$	43.5500	1.59448
$747$	2.11727	0.0774667
$748$	44.1364	1.61379
$749$	34.2767	1.25244
$750$	2.77846	0.101455
$751$	16.1855	0.590616	0.295308	−	0.955402i	$-0.404578\pi$
$751$	16.1855	0.590616	0.295308	+	0.955402i	$0.404578\pi$
$752$	−199.666	−7.28106
$753$	−18.2277	−0.664253
$754$	16.6707	0.607113
$755$	−4.99656	−0.181844
$756$	15.5569	0.565800
$757$	12.3258	0.447990	0.223995	−	0.974590i	$-0.428090\pi$
$757$	12.3258	0.447990	0.223995	+	0.974590i	$0.428090\pi$
$758$	72.8002	2.64422
$759$	−13.1560	−0.477534
$760$	36.7620	1.33350
$761$	−0.00687569	−0.000249244 0	−0.000124622	−	1.00000i	$-0.500040\pi$
$761$	−0.00687569	−0.000249244 0	−0.000124622		1.00000i	$0.500040\pi$
$762$	37.3415	1.35274
$763$	−31.1138	−1.12640
$764$	−24.2208	−0.876277
$765$	2.83709	0.102575
$766$	62.3380	2.25237
$767$	−2.11727	−0.0764501
$768$	−84.8459	−3.06161
$769$	−20.3258	−0.732968	−0.366484	−	0.930424i	$-0.619439\pi$
$769$	−20.3258	−0.732968	−0.366484	+	0.930424i	$0.619439\pi$
$770$	−20.5535	−0.740696
$771$	−1.11383	−0.0401136
$772$	−133.790	−4.81520
$773$	9.90184	0.356144	0.178072	−	0.984017i	$-0.443014\pi$
$773$	9.90184	0.356144	0.178072	+	0.984017i	$0.443014\pi$
$774$	30.8793	1.10993
$775$	7.55691	0.271452
$776$	−112.005	−4.02076
$777$	−11.6320	−0.417295
$778$	88.0054	3.15514
$779$	−10.0913	−0.361558
$780$	5.71982	0.204803
$781$	18.2767	0.653993
$782$	38.1295	1.36351
$783$	−6.00000	−0.214423
$784$	6.86651	0.245232
$785$	−8.87930	−0.316916
$786$	26.2277	0.935510
$787$	36.3449	1.29556	0.647778	−	0.761829i	$-0.275698\pi$
$787$	36.3449	1.29556	0.647778	+	0.761829i	$0.275698\pi$
$788$	83.2433	2.96542
$789$	−8.00000	−0.284808
$790$	−28.5535	−1.01589
$791$	35.6673	1.26818
$792$	−28.1104	−0.998859
$793$	6.60256	0.234464
$794$	49.8759	1.77003
$795$	1.16291	0.0412442
$796$	−86.4484	−3.06408
$797$	18.8371	0.667244	0.333622	−	0.942707i	$-0.391729\pi$
$797$	18.8371	0.667244	0.333622	+	0.942707i	$0.391729\pi$
$798$	−26.8793	−0.951517
$799$	32.7880	1.15996
$800$	27.3319	0.966330
$801$	1.16291	0.0410894
$802$	37.7395	1.33263
$803$	−24.7880	−0.874750
$804$	−10.7689	−0.379790
$805$	−13.1560	−0.463689
$806$	20.9966	0.739572
$807$	−15.6742	−0.551757
$808$	79.3155	2.79031
$809$	32.2277	1.13306	0.566532	−	0.824040i	$-0.308285\pi$
$809$	32.2277	1.13306	0.566532	+	0.824040i	$0.308285\pi$
$810$	−2.77846	−0.0976250
$811$	−23.0034	−0.807760	−0.403880	−	0.914812i	$-0.632339\pi$
$811$	−23.0034	−0.807760	−0.403880	+	0.914812i	$0.632339\pi$
$812$	−93.3415	−3.27564
$813$	−0.443086	−0.0155397
$814$	32.3189	1.13278
$815$	13.8337	0.484572
$816$	49.0157	1.71589
$817$	−39.5309	−1.38301
$818$	−38.8984	−1.36005
$819$	−2.71982	−0.0950383
$820$	−16.2277	−0.566694
$821$	49.9372	1.74282	0.871410	−	0.490556i	$-0.163206\pi$
$821$	49.9372	1.74282	0.871410	+	0.490556i	$0.163206\pi$
$822$	−4.90528	−0.171091
$823$	28.2345	0.984194	0.492097	−	0.870540i	$-0.336231\pi$
$823$	28.2345	0.984194	0.492097	+	0.870540i	$0.336231\pi$
$824$	38.9175	1.35576
$825$	2.71982	0.0946921
$826$	16.0000	0.556711
$827$	−9.55004	−0.332087	−0.166044	−	0.986118i	$-0.553099\pi$
$827$	−9.55004	−0.332087	−0.166044	+	0.986118i	$0.553099\pi$
$828$	−27.6673	−0.961505
$829$	−37.9862	−1.31932	−0.659658	−	0.751565i	$-0.729299\pi$
$829$	−37.9862	−1.31932	−0.659658	+	0.751565i	$0.729299\pi$
$830$	−5.88273	−0.204193
$831$	4.87930	0.169261
$832$	41.3871	1.43484
$833$	−1.12758	−0.0390683
$834$	17.4396	0.603886
$835$	9.88273	0.342006
$836$	55.3346	1.91379
$837$	−7.55691	−0.261205
$838$	34.2277	1.18237
$839$	−4.72670	−0.163184	−0.0815919	−	0.996666i	$-0.526000\pi$
$839$	−4.72670	−0.163184	−0.0815919	+	0.996666i	$0.526000\pi$
$840$	−28.1104	−0.969901
$841$	7.00000	0.241379
$842$	63.3155	2.18200
$843$	9.11383	0.313897
$844$	−104.259	−3.58874
$845$	−1.00000	−0.0344010
$846$	−32.1104	−1.10398
$847$	9.79832	0.336674
$848$	20.0913	0.689938
$849$	−33.3415	−1.14428
$850$	−7.88273	−0.270376
$851$	20.6870	0.709140
$852$	38.4362	1.31680
$853$	−48.3611	−1.65585	−0.827927	−	0.560836i	$-0.810480\pi$
$853$	−48.3611	−1.65585	−0.827927	+	0.560836i	$0.810480\pi$
$854$	−49.8950	−1.70737
$855$	3.55691	0.121644
$856$	−130.252	−4.45193
$857$	6.83709	0.233551	0.116775	−	0.993158i	$-0.462744\pi$
$857$	6.83709	0.233551	0.116775	+	0.993158i	$0.462744\pi$
$858$	7.55691	0.257989
$859$	12.6026	0.429994	0.214997	−	0.976615i	$-0.431026\pi$
$859$	12.6026	0.429994	0.214997	+	0.976615i	$0.431026\pi$
$860$	−63.5691	−2.16769
$861$	7.71639	0.262974
$862$	−24.9966	−0.851386
$863$	8.20855	0.279422	0.139711	−	0.990192i	$-0.455383\pi$
$863$	8.20855	0.279422	0.139711	+	0.990192i	$0.455383\pi$
$864$	−27.3319	−0.929851
$865$	−13.1138	−0.445884
$866$	−56.4744	−1.91908
$867$	8.95092	0.303989
$868$	−117.562	−3.99032
$869$	−27.9509	−0.948170
$870$	16.6707	0.565191
$871$	1.88273	0.0637940
$872$	118.233	4.00387
$873$	−10.8371	−0.366780
$874$	47.8037	1.61698
$875$	2.71982	0.0919468
$876$	−52.1295	−1.76129
$877$	13.5309	0.456907	0.228454	−	0.973555i	$-0.426633\pi$
$877$	13.5309	0.456907	0.228454	+	0.973555i	$0.426633\pi$
$878$	−70.5466	−2.38083
$879$	29.4328	0.992743
$880$	46.9897	1.58402
$881$	−9.34836	−0.314954	−0.157477	−	0.987523i	$-0.550336\pi$
$881$	−9.34836	−0.314954	−0.157477	+	0.987523i	$0.550336\pi$
$882$	1.10428	0.0371829
$883$	−55.1001	−1.85427	−0.927133	−	0.374733i	$-0.877734\pi$
$883$	−55.1001	−1.85427	−0.927133	+	0.374733i	$0.877734\pi$
$884$	−16.2277	−0.545795
$885$	−2.11727	−0.0711711
$886$	30.3640	1.02010
$887$	0.133492	0.00448223	0.00224112	−	0.999997i	$-0.499287\pi$
$887$	0.133492	0.00448223	0.00224112	+	0.999997i	$0.499287\pi$
$888$	44.2017	1.48331
$889$	36.5535	1.22596
$890$	−3.23109	−0.108307
$891$	−2.71982	−0.0911175
$892$	57.8690	1.93760
$893$	41.1070	1.37559
$894$	57.8759	1.93566
$895$	−8.55348	−0.285911
$896$	−164.083	−5.48162
$897$	4.83709	0.161506
$898$	7.88273	0.263050
$899$	45.3415	1.51222
$900$	5.71982	0.190661
$901$	−3.29928	−0.109915
$902$	−21.4396	−0.713862
$903$	30.2277	1.00591
$904$	−135.536	−4.50787
$905$	−3.72326	−0.123765
$906$	−13.8827	−0.461223
$907$	−58.5466	−1.94401	−0.972004	−	0.234964i	$-0.924503\pi$
$907$	−58.5466	−1.94401	−0.972004	+	0.234964i	$0.924503\pi$
$908$	64.7620	2.14920
$909$	7.67418	0.254537
$910$	7.55691	0.250509
$911$	50.4622	1.67189	0.835943	−	0.548816i	$-0.184921\pi$
$911$	50.4622	1.67189	0.835943	+	0.548816i	$0.184921\pi$
$912$	61.4519	2.03487
$913$	−5.75859	−0.190582
$914$	−38.1104	−1.26058
$915$	6.60256	0.218274
$916$	−35.6604	−1.17825
$917$	25.6742	0.847836
$918$	7.88273	0.260169
$919$	56.9735	1.87938	0.939691	−	0.342026i	$-0.111113\pi$
$919$	56.9735	1.87938	0.939691	+	0.342026i	$0.111113\pi$
$920$	49.9931	1.64822
$921$	21.8337	0.719443
$922$	−54.5275	−1.79577
$923$	−6.71982	−0.221186
$924$	−42.3121	−1.39196
$925$	−4.27674	−0.140618
$926$	75.1261	2.46880
$927$	3.76547	0.123674
$928$	163.992	5.38329
$929$	−36.5957	−1.20067	−0.600333	−	0.799750i	$-0.704965\pi$
$929$	−36.5957	−1.20067	−0.600333	+	0.799750i	$0.704965\pi$
$930$	20.9966	0.688504
$931$	−1.41367	−0.0463311
$932$	39.1070	1.28099
$933$	−25.1070	−0.821965
$934$	80.3572	2.62937
$935$	−7.71639	−0.252353
$936$	10.3354	0.337822
$937$	−47.1070	−1.53892	−0.769459	−	0.638697i	$-0.779474\pi$
$937$	−47.1070	−1.53892	−0.769459	+	0.638697i	$0.779474\pi$
$938$	−14.2277	−0.464549
$939$	−8.22766	−0.268499
$940$	66.1035	2.15606
$941$	−36.3611	−1.18534	−0.592670	−	0.805446i	$-0.701926\pi$
$941$	−36.3611	−1.18534	−0.592670	+	0.805446i	$0.701926\pi$
$942$	−24.6707	−0.803816
$943$	−13.7233	−0.446891
$944$	−36.5795	−1.19056
$945$	−2.71982	−0.0884759
$946$	−83.9862	−2.73063
$947$	44.5795	1.44864	0.724319	−	0.689465i	$-0.242154\pi$
$947$	44.5795	1.44864	0.724319	+	0.689465i	$0.242154\pi$
$948$	−58.7811	−1.90912
$949$	9.11383	0.295847
$950$	−9.88273	−0.320638
$951$	−27.6742	−0.897397
$952$	79.7517	2.58477
$953$	19.8596	0.643317	0.321658	−	0.946856i	$-0.395760\pi$
$953$	19.8596	0.643317	0.321658	+	0.946856i	$0.395760\pi$
$954$	3.23109	0.104611
$955$	4.23453	0.137026
$956$	7.32238	0.236823
$957$	16.3189	0.527517
$958$	−33.7846	−1.09153
$959$	−4.80176	−0.155057
$960$	41.3871	1.33576
$961$	26.1070	0.842160
$962$	−11.8827	−0.383115
$963$	−12.6026	−0.406112
$964$	−34.3189	−1.10534
$965$	23.3906	0.752969
$966$	−36.5535	−1.17609
$967$	47.4068	1.52450	0.762250	−	0.647283i	$-0.224095\pi$
$967$	47.4068	1.52450	0.762250	+	0.647283i	$0.224095\pi$
$968$	−37.2338	−1.19674
$969$	−10.0913	−0.324179
$970$	30.1104	0.966786
$971$	−10.6448	−0.341607	−0.170803	−	0.985305i	$-0.554636\pi$
$971$	−10.6448	−0.341607	−0.170803	+	0.985305i	$0.554636\pi$
$972$	−5.71982	−0.183463
$973$	17.0716	0.547291
$974$	−0.443086	−0.0141974
$975$	−1.00000	−0.0320256
$976$	114.071	3.65131
$977$	−1.21199	−0.0387750	−0.0193875	−	0.999812i	$-0.506172\pi$
$977$	−1.21199	−0.0387750	−0.0193875	+	0.999812i	$0.506172\pi$
$978$	38.4362	1.22905
$979$	−3.16291	−0.101087
$980$	−2.27330	−0.0726179
$981$	11.4396	0.365240
$982$	−117.328	−3.74408
$983$	51.8759	1.65458	0.827291	−	0.561773i	$-0.189881\pi$
$983$	51.8759	1.65458	0.827291	+	0.561773i	$0.189881\pi$
$984$	−29.3224	−0.934763
$985$	−14.5535	−0.463712
$986$	−47.2964	−1.50622
$987$	−31.4328	−1.00052
$988$	−20.3449	−0.647258
$989$	−53.7586	−1.70942
$990$	7.55691	0.240175
$991$	−21.6251	−0.686944	−0.343472	−	0.939163i	$-0.611603\pi$
$991$	−21.6251	−0.686944	−0.343472	+	0.939163i	$0.611603\pi$
$992$	206.545	6.55781
$993$	13.2311	0.419876
$994$	50.7811	1.61068
$995$	15.1138	0.479141
$996$	−12.1104	−0.383732
$997$	23.2051	0.734913	0.367457	−	0.930041i	$-0.380229\pi$
$997$	23.2051	0.734913	0.367457	+	0.930041i	$0.380229\pi$
$998$	21.6482	0.685262
$999$	4.27674	0.135310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.a.e.1.3	✓	3
3.2	odd	2		585.2.a.n.1.1		3
4.3	odd	2		3120.2.a.bj.1.3		3
5.2	odd	4		975.2.c.i.274.6		6
5.3	odd	4		975.2.c.i.274.1		6
5.4	even	2		975.2.a.o.1.1		3
7.6	odd	2		9555.2.a.bq.1.3		3
12.11	even	2		9360.2.a.dd.1.3		3
13.12	even	2		2535.2.a.bc.1.1		3
15.2	even	4		2925.2.c.w.2224.1		6
15.8	even	4		2925.2.c.w.2224.6		6
15.14	odd	2		2925.2.a.bh.1.3		3
39.38	odd	2		7605.2.a.bx.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.3	✓	3	1.1	even	1	trivial
585.2.a.n.1.1		3	3.2	odd	2
975.2.a.o.1.1		3	5.4	even	2
975.2.c.i.274.1		6	5.3	odd	4
975.2.c.i.274.6		6	5.2	odd	4
2535.2.a.bc.1.1		3	13.12	even	2
2925.2.a.bh.1.3		3	15.14	odd	2
2925.2.c.w.2224.1		6	15.2	even	4
2925.2.c.w.2224.6		6	15.8	even	4
3120.2.a.bj.1.3		3	4.3	odd	2
7605.2.a.bx.1.3		3	39.38	odd	2
9360.2.a.dd.1.3		3	12.11	even	2
9555.2.a.bq.1.3		3	7.6	odd	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.a (trivial)

\(f(q)\)	\(=\)	\(q+2.77846 q^{2} -1.00000 q^{3} +5.71982 q^{4} -1.00000 q^{5} -2.77846 q^{6} -2.71982 q^{7} +10.3354 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.77846 q^{2} -1.00000 q^{3} +5.71982 q^{4} -1.00000 q^{5} -2.77846 q^{6} -2.71982 q^{7} +10.3354 q^{8} +1.00000 q^{9} -2.77846 q^{10} -2.71982 q^{11} -5.71982 q^{12} +1.00000 q^{13} -7.55691 q^{14} +1.00000 q^{15} +17.2767 q^{16} -2.83709 q^{17} +2.77846 q^{18} -3.55691 q^{19} -5.71982 q^{20} +2.71982 q^{21} -7.55691 q^{22} -4.83709 q^{23} -10.3354 q^{24} +1.00000 q^{25} +2.77846 q^{26} -1.00000 q^{27} -15.5569 q^{28} +6.00000 q^{29} +2.77846 q^{30} +7.55691 q^{31} +27.3319 q^{32} +2.71982 q^{33} -7.88273 q^{34} +2.71982 q^{35} +5.71982 q^{36} -4.27674 q^{37} -9.88273 q^{38} -1.00000 q^{39} -10.3354 q^{40} +2.83709 q^{41} +7.55691 q^{42} +11.1138 q^{43} -15.5569 q^{44} -1.00000 q^{45} -13.4396 q^{46} -11.5569 q^{47} -17.2767 q^{48} +0.397442 q^{49} +2.77846 q^{50} +2.83709 q^{51} +5.71982 q^{52} +1.16291 q^{53} -2.77846 q^{54} +2.71982 q^{55} -28.1104 q^{56} +3.55691 q^{57} +16.6707 q^{58} -2.11727 q^{59} +5.71982 q^{60} +6.60256 q^{61} +20.9966 q^{62} -2.71982 q^{63} +41.3871 q^{64} -1.00000 q^{65} +7.55691 q^{66} +1.88273 q^{67} -16.2277 q^{68} +4.83709 q^{69} +7.55691 q^{70} -6.71982 q^{71} +10.3354 q^{72} +9.11383 q^{73} -11.8827 q^{74} -1.00000 q^{75} -20.3449 q^{76} +7.39744 q^{77} -2.77846 q^{78} +10.2767 q^{79} -17.2767 q^{80} +1.00000 q^{81} +7.88273 q^{82} +2.11727 q^{83} +15.5569 q^{84} +2.83709 q^{85} +30.8793 q^{86} -6.00000 q^{87} -28.1104 q^{88} +1.16291 q^{89} -2.77846 q^{90} -2.71982 q^{91} -27.6673 q^{92} -7.55691 q^{93} -32.1104 q^{94} +3.55691 q^{95} -27.3319 q^{96} -10.8371 q^{97} +1.10428 q^{98} -2.71982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + q^{11} - 8 q^{12} + 3 q^{13} - 6 q^{14} + 3 q^{15} + 26 q^{16} - q^{17} + 6 q^{19} - 8 q^{20} - q^{21} - 6 q^{22} - 7 q^{23} - 6 q^{24} + 3 q^{25} - 3 q^{27} - 30 q^{28} + 18 q^{29} + 6 q^{31} + 22 q^{32} - q^{33} - 22 q^{34} - q^{35} + 8 q^{36} + 13 q^{37} - 28 q^{38} - 3 q^{39} - 6 q^{40} + q^{41} + 6 q^{42} - 30 q^{44} - 3 q^{45} - 22 q^{46} - 18 q^{47} - 26 q^{48} + 12 q^{49} + q^{51} + 8 q^{52} + 11 q^{53} - q^{55} - 16 q^{56} - 6 q^{57} - 8 q^{59} + 8 q^{60} + 9 q^{61} + 28 q^{62} + q^{63} + 30 q^{64} - 3 q^{65} + 6 q^{66} + 4 q^{67} + 18 q^{68} + 7 q^{69} + 6 q^{70} - 11 q^{71} + 6 q^{72} - 6 q^{73} - 34 q^{74} - 3 q^{75} + 4 q^{76} + 33 q^{77} + 5 q^{79} - 26 q^{80} + 3 q^{81} + 22 q^{82} + 8 q^{83} + 30 q^{84} + q^{85} + 56 q^{86} - 18 q^{87} - 16 q^{88} + 11 q^{89} + q^{91} + 2 q^{92} - 6 q^{93} - 28 q^{94} - 6 q^{95} - 22 q^{96} - 25 q^{97} + 10 q^{98} + q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9 + q^11 - 8 * q^12 + 3 * q^13 - 6 * q^14 + 3 * q^15 + 26 * q^16 - q^17 + 6 * q^19 - 8 * q^20 - q^21 - 6 * q^22 - 7 * q^23 - 6 * q^24 + 3 * q^25 - 3 * q^27 - 30 * q^28 + 18 * q^29 + 6 * q^31 + 22 * q^32 - q^33 - 22 * q^34 - q^35 + 8 * q^36 + 13 * q^37 - 28 * q^38 - 3 * q^39 - 6 * q^40 + q^41 + 6 * q^42 - 30 * q^44 - 3 * q^45 - 22 * q^46 - 18 * q^47 - 26 * q^48 + 12 * q^49 + q^51 + 8 * q^52 + 11 * q^53 - q^55 - 16 * q^56 - 6 * q^57 - 8 * q^59 + 8 * q^60 + 9 * q^61 + 28 * q^62 + q^63 + 30 * q^64 - 3 * q^65 + 6 * q^66 + 4 * q^67 + 18 * q^68 + 7 * q^69 + 6 * q^70 - 11 * q^71 + 6 * q^72 - 6 * q^73 - 34 * q^74 - 3 * q^75 + 4 * q^76 + 33 * q^77 + 5 * q^79 - 26 * q^80 + 3 * q^81 + 22 * q^82 + 8 * q^83 + 30 * q^84 + q^85 + 56 * q^86 - 18 * q^87 - 16 * q^88 + 11 * q^89 + q^91 + 2 * q^92 - 6 * q^93 - 28 * q^94 - 6 * q^95 - 22 * q^96 - 25 * q^97 + 10 * q^98 + q^99

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