LMFDB - Embedded newform 4030.2.a.q.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 48x^{6} + 66x^{5} - 202x^{4} - 75x^{3} + 210x^{2} + 68x - 16 $ x^9 - 3x^8 - 16x^7 + 48x^6 + 66x^5 - 202x^4 - 75x^3 + 210x^2 + 68x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.90335$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.90335 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.90335 q^{6} -3.95405 q^{7} +1.00000 q^{8} +0.622734 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.90335 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.90335 q^{6} -3.95405 q^{7} +1.00000 q^{8} +0.622734 q^{9} -1.00000 q^{10} +0.890437 q^{11} +1.90335 q^{12} +1.00000 q^{13} -3.95405 q^{14} -1.90335 q^{15} +1.00000 q^{16} +6.51985 q^{17} +0.622734 q^{18} -4.03070 q^{19} -1.00000 q^{20} -7.52593 q^{21} +0.890437 q^{22} +6.24153 q^{23} +1.90335 q^{24} +1.00000 q^{25} +1.00000 q^{26} -4.52477 q^{27} -3.95405 q^{28} +4.15488 q^{29} -1.90335 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.69481 q^{33} +6.51985 q^{34} +3.95405 q^{35} +0.622734 q^{36} +6.70344 q^{37} -4.03070 q^{38} +1.90335 q^{39} -1.00000 q^{40} +1.92050 q^{41} -7.52593 q^{42} +11.3340 q^{43} +0.890437 q^{44} -0.622734 q^{45} +6.24153 q^{46} +11.7535 q^{47} +1.90335 q^{48} +8.63451 q^{49} +1.00000 q^{50} +12.4095 q^{51} +1.00000 q^{52} -4.78854 q^{53} -4.52477 q^{54} -0.890437 q^{55} -3.95405 q^{56} -7.67182 q^{57} +4.15488 q^{58} -13.0061 q^{59} -1.90335 q^{60} +4.43837 q^{61} +1.00000 q^{62} -2.46232 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.69481 q^{66} +4.30947 q^{67} +6.51985 q^{68} +11.8798 q^{69} +3.95405 q^{70} +6.03915 q^{71} +0.622734 q^{72} +9.31710 q^{73} +6.70344 q^{74} +1.90335 q^{75} -4.03070 q^{76} -3.52083 q^{77} +1.90335 q^{78} +1.27976 q^{79} -1.00000 q^{80} -10.4804 q^{81} +1.92050 q^{82} +2.95491 q^{83} -7.52593 q^{84} -6.51985 q^{85} +11.3340 q^{86} +7.90818 q^{87} +0.890437 q^{88} -15.7998 q^{89} -0.622734 q^{90} -3.95405 q^{91} +6.24153 q^{92} +1.90335 q^{93} +11.7535 q^{94} +4.03070 q^{95} +1.90335 q^{96} -10.1253 q^{97} +8.63451 q^{98} +0.554505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.90335	1.09890	0.549449	−	0.835527i	$-0.314838\pi$
$3$	1.90335	1.09890	0.549449	+	0.835527i	$0.314838\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.90335	0.777039
$7$	−3.95405	−1.49449	−0.747245	−	0.664548i	$-0.768624\pi$
$7$	−3.95405	−1.49449	−0.747245	+	0.664548i	$0.768624\pi$
$8$	1.00000	0.353553
$9$	0.622734	0.207578
$10$	−1.00000	−0.316228
$11$	0.890437	0.268477	0.134238	−	0.990949i	$-0.457141\pi$
$11$	0.890437	0.268477	0.134238	+	0.990949i	$0.457141\pi$
$12$	1.90335	0.549449
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.95405	−1.05676
$15$	−1.90335	−0.491442
$16$	1.00000	0.250000
$17$	6.51985	1.58130	0.790648	−	0.612271i	$-0.209744\pi$
$17$	6.51985	1.58130	0.790648	+	0.612271i	$0.209744\pi$
$18$	0.622734	0.146780
$19$	−4.03070	−0.924705	−0.462353	−	0.886696i	$-0.652995\pi$
$19$	−4.03070	−0.924705	−0.462353	+	0.886696i	$0.652995\pi$
$20$	−1.00000	−0.223607
$21$	−7.52593	−1.64229
$22$	0.890437	0.189842
$23$	6.24153	1.30145	0.650724	−	0.759314i	$-0.274465\pi$
$23$	6.24153	1.30145	0.650724	+	0.759314i	$0.274465\pi$
$24$	1.90335	0.388519
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−4.52477	−0.870791
$28$	−3.95405	−0.747245
$29$	4.15488	0.771542	0.385771	−	0.922595i	$-0.373935\pi$
$29$	4.15488	0.771542	0.385771	+	0.922595i	$0.373935\pi$
$30$	−1.90335	−0.347502
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	1.69481	0.295029
$34$	6.51985	1.11814
$35$	3.95405	0.668356
$36$	0.622734	0.103789
$37$	6.70344	1.10204	0.551019	−	0.834493i	$-0.314239\pi$
$37$	6.70344	1.10204	0.551019	+	0.834493i	$0.314239\pi$
$38$	−4.03070	−0.653865
$39$	1.90335	0.304780
$40$	−1.00000	−0.158114
$41$	1.92050	0.299932	0.149966	−	0.988691i	$-0.452084\pi$
$41$	1.92050	0.299932	0.149966	+	0.988691i	$0.452084\pi$
$42$	−7.52593	−1.16128
$43$	11.3340	1.72842	0.864209	−	0.503133i	$-0.167819\pi$
$43$	11.3340	1.72842	0.864209	+	0.503133i	$0.167819\pi$
$44$	0.890437	0.134238
$45$	−0.622734	−0.0928317
$46$	6.24153	0.920263
$47$	11.7535	1.71442	0.857210	−	0.514968i	$-0.172196\pi$
$47$	11.7535	1.71442	0.857210	+	0.514968i	$0.172196\pi$
$48$	1.90335	0.274725
$49$	8.63451	1.23350
$50$	1.00000	0.141421
$51$	12.4095	1.73768
$52$	1.00000	0.138675
$53$	−4.78854	−0.657756	−0.328878	−	0.944372i	$-0.606670\pi$
$53$	−4.78854	−0.657756	−0.328878	+	0.944372i	$0.606670\pi$
$54$	−4.52477	−0.615743
$55$	−0.890437	−0.120066
$56$	−3.95405	−0.528382
$57$	−7.67182	−1.01616
$58$	4.15488	0.545563
$59$	−13.0061	−1.69325	−0.846623	−	0.532194i	$-0.821368\pi$
$59$	−13.0061	−1.69325	−0.846623	+	0.532194i	$0.821368\pi$
$60$	−1.90335	−0.245721
$61$	4.43837	0.568274	0.284137	−	0.958784i	$-0.408293\pi$
$61$	4.43837	0.568274	0.284137	+	0.958784i	$0.408293\pi$
$62$	1.00000	0.127000
$63$	−2.46232	−0.310223
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	1.69481	0.208617
$67$	4.30947	0.526486	0.263243	−	0.964730i	$-0.415208\pi$
$67$	4.30947	0.526486	0.263243	+	0.964730i	$0.415208\pi$
$68$	6.51985	0.790648
$69$	11.8798	1.43016
$70$	3.95405	0.472599
$71$	6.03915	0.716715	0.358357	−	0.933584i	$-0.383337\pi$
$71$	6.03915	0.716715	0.358357	+	0.933584i	$0.383337\pi$
$72$	0.622734	0.0733899
$73$	9.31710	1.09048	0.545242	−	0.838279i	$-0.316438\pi$
$73$	9.31710	1.09048	0.545242	+	0.838279i	$0.316438\pi$
$74$	6.70344	0.779259
$75$	1.90335	0.219780
$76$	−4.03070	−0.462353
$77$	−3.52083	−0.401236
$78$	1.90335	0.215512
$79$	1.27976	0.143984	0.0719920	−	0.997405i	$-0.477064\pi$
$79$	1.27976	0.143984	0.0719920	+	0.997405i	$0.477064\pi$
$80$	−1.00000	−0.111803
$81$	−10.4804	−1.16449
$82$	1.92050	0.212084
$83$	2.95491	0.324343	0.162172	−	0.986763i	$-0.448150\pi$
$83$	2.95491	0.324343	0.162172	+	0.986763i	$0.448150\pi$
$84$	−7.52593	−0.821147
$85$	−6.51985	−0.707177
$86$	11.3340	1.22218
$87$	7.90818	0.847846
$88$	0.890437	0.0949209
$89$	−15.7998	−1.67478	−0.837388	−	0.546609i	$-0.815918\pi$
$89$	−15.7998	−1.67478	−0.837388	+	0.546609i	$0.815918\pi$
$90$	−0.622734	−0.0656419
$91$	−3.95405	−0.414497
$92$	6.24153	0.650724
$93$	1.90335	0.197368
$94$	11.7535	1.21228
$95$	4.03070	0.413541
$96$	1.90335	0.194260
$97$	−10.1253	−1.02807	−0.514036	−	0.857768i	$-0.671850\pi$
$97$	−10.1253	−1.02807	−0.514036	+	0.857768i	$0.671850\pi$
$98$	8.63451	0.872217
$99$	0.554505	0.0557299
$100$	1.00000	0.100000
$101$	−12.8420	−1.27783	−0.638916	−	0.769277i	$-0.720617\pi$
$101$	−12.8420	−1.27783	−0.638916	+	0.769277i	$0.720617\pi$
$102$	12.4095	1.22873
$103$	12.7500	1.25630	0.628150	−	0.778092i	$-0.283813\pi$
$103$	12.7500	1.25630	0.628150	+	0.778092i	$0.283813\pi$
$104$	1.00000	0.0980581
$105$	7.52593	0.734456
$106$	−4.78854	−0.465104
$107$	−4.58679	−0.443422	−0.221711	−	0.975112i	$-0.571164\pi$
$107$	−4.58679	−0.443422	−0.221711	+	0.975112i	$0.571164\pi$
$108$	−4.52477	−0.435396
$109$	1.31502	0.125956	0.0629780	−	0.998015i	$-0.479940\pi$
$109$	1.31502	0.125956	0.0629780	+	0.998015i	$0.479940\pi$
$110$	−0.890437	−0.0848998
$111$	12.7590	1.21103
$112$	−3.95405	−0.373623
$113$	3.49691	0.328962	0.164481	−	0.986380i	$-0.447405\pi$
$113$	3.49691	0.328962	0.164481	+	0.986380i	$0.447405\pi$
$114$	−7.67182	−0.718532
$115$	−6.24153	−0.582025
$116$	4.15488	0.385771
$117$	0.622734	0.0575718
$118$	−13.0061	−1.19731
$119$	−25.7798	−2.36323
$120$	−1.90335	−0.173751
$121$	−10.2071	−0.927920
$122$	4.43837	0.401831
$123$	3.65539	0.329595
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	−2.46232	−0.219361
$127$	−12.5208	−1.11104	−0.555522	−	0.831502i	$-0.687482\pi$
$127$	−12.5208	−1.11104	−0.555522	+	0.831502i	$0.687482\pi$
$128$	1.00000	0.0883883
$129$	21.5725	1.89936
$130$	−1.00000	−0.0877058
$131$	4.58738	0.400801	0.200401	−	0.979714i	$-0.435776\pi$
$131$	4.58738	0.400801	0.200401	+	0.979714i	$0.435776\pi$
$132$	1.69481	0.147514
$133$	15.9376	1.38196
$134$	4.30947	0.372281
$135$	4.52477	0.389430
$136$	6.51985	0.559072
$137$	0.250363	0.0213899	0.0106950	−	0.999943i	$-0.496596\pi$
$137$	0.250363	0.0213899	0.0106950	+	0.999943i	$0.496596\pi$
$138$	11.8798	1.01128
$139$	21.6580	1.83701	0.918505	−	0.395409i	$-0.129397\pi$
$139$	21.6580	1.83701	0.918505	+	0.395409i	$0.129397\pi$
$140$	3.95405	0.334178
$141$	22.3709	1.88397
$142$	6.03915	0.506794
$143$	0.890437	0.0744621
$144$	0.622734	0.0518945
$145$	−4.15488	−0.345044
$146$	9.31710	0.771089
$147$	16.4345	1.35549
$148$	6.70344	0.551019
$149$	5.15108	0.421993	0.210997	−	0.977487i	$-0.432329\pi$
$149$	5.15108	0.421993	0.210997	+	0.977487i	$0.432329\pi$
$150$	1.90335	0.155408
$151$	12.8148	1.04286	0.521429	−	0.853295i	$-0.325399\pi$
$151$	12.8148	1.04286	0.521429	+	0.853295i	$0.325399\pi$
$152$	−4.03070	−0.326933
$153$	4.06013	0.328242
$154$	−3.52083	−0.283717
$155$	−1.00000	−0.0803219
$156$	1.90335	0.152390
$157$	−7.40349	−0.590862	−0.295431	−	0.955364i	$-0.595463\pi$
$157$	−7.40349	−0.590862	−0.295431	+	0.955364i	$0.595463\pi$
$158$	1.27976	0.101812
$159$	−9.11425	−0.722807
$160$	−1.00000	−0.0790569
$161$	−24.6793	−1.94500
$162$	−10.4804	−0.823418
$163$	19.5138	1.52844	0.764218	−	0.644957i	$-0.223125\pi$
$163$	19.5138	1.52844	0.764218	+	0.644957i	$0.223125\pi$
$164$	1.92050	0.149966
$165$	−1.69481	−0.131941
$166$	2.95491	0.229345
$167$	−21.0792	−1.63116	−0.815581	−	0.578643i	$-0.803582\pi$
$167$	−21.0792	−1.63116	−0.815581	+	0.578643i	$0.803582\pi$
$168$	−7.52593	−0.580638
$169$	1.00000	0.0769231
$170$	−6.51985	−0.500049
$171$	−2.51005	−0.191948
$172$	11.3340	0.864209
$173$	−5.10968	−0.388482	−0.194241	−	0.980954i	$-0.562224\pi$
$173$	−5.10968	−0.388482	−0.194241	+	0.980954i	$0.562224\pi$
$174$	7.90818	0.599518
$175$	−3.95405	−0.298898
$176$	0.890437	0.0671192
$177$	−24.7551	−1.86070
$178$	−15.7998	−1.18425
$179$	−9.68063	−0.723564	−0.361782	−	0.932263i	$-0.617832\pi$
$179$	−9.68063	−0.723564	−0.361782	+	0.932263i	$0.617832\pi$
$180$	−0.622734	−0.0464158
$181$	10.3455	0.768978	0.384489	−	0.923130i	$-0.374378\pi$
$181$	10.3455	0.768978	0.384489	+	0.923130i	$0.374378\pi$
$182$	−3.95405	−0.293094
$183$	8.44775	0.624476
$184$	6.24153	0.460132
$185$	−6.70344	−0.492847
$186$	1.90335	0.139560
$187$	5.80551	0.424541
$188$	11.7535	0.857210
$189$	17.8911	1.30139
$190$	4.03070	0.292417
$191$	1.23706	0.0895105	0.0447553	−	0.998998i	$-0.485749\pi$
$191$	1.23706	0.0895105	0.0447553	+	0.998998i	$0.485749\pi$
$192$	1.90335	0.137362
$193$	−21.7637	−1.56659	−0.783293	−	0.621652i	$-0.786462\pi$
$193$	−21.7637	−1.56659	−0.783293	+	0.621652i	$0.786462\pi$
$194$	−10.1253	−0.726957
$195$	−1.90335	−0.136302
$196$	8.63451	0.616751
$197$	−7.63890	−0.544249	−0.272124	−	0.962262i	$-0.587726\pi$
$197$	−7.63890	−0.544249	−0.272124	+	0.962262i	$0.587726\pi$
$198$	0.554505	0.0394070
$199$	17.2500	1.22282	0.611410	−	0.791314i	$-0.290603\pi$
$199$	17.2500	1.22282	0.611410	+	0.791314i	$0.290603\pi$
$200$	1.00000	0.0707107
$201$	8.20242	0.578554
$202$	−12.8420	−0.903563
$203$	−16.4286	−1.15306
$204$	12.4095	0.868841
$205$	−1.92050	−0.134134
$206$	12.7500	0.888338
$207$	3.88681	0.270152
$208$	1.00000	0.0693375
$209$	−3.58908	−0.248262
$210$	7.52593	0.519339
$211$	18.3640	1.26423	0.632113	−	0.774876i	$-0.282188\pi$
$211$	18.3640	1.26423	0.632113	+	0.774876i	$0.282188\pi$
$212$	−4.78854	−0.328878
$213$	11.4946	0.787597
$214$	−4.58679	−0.313547
$215$	−11.3340	−0.772972
$216$	−4.52477	−0.307871
$217$	−3.95405	−0.268418
$218$	1.31502	0.0890644
$219$	17.7337	1.19833
$220$	−0.890437	−0.0600332
$221$	6.51985	0.438572
$222$	12.7590	0.856326
$223$	2.72322	0.182360	0.0911800	−	0.995834i	$-0.470936\pi$
$223$	2.72322	0.182360	0.0911800	+	0.995834i	$0.470936\pi$
$224$	−3.95405	−0.264191
$225$	0.622734	0.0415156
$226$	3.49691	0.232611
$227$	−22.0157	−1.46124	−0.730618	−	0.682787i	$-0.760768\pi$
$227$	−22.0157	−1.46124	−0.730618	+	0.682787i	$0.760768\pi$
$228$	−7.67182	−0.508079
$229$	−24.9366	−1.64786	−0.823929	−	0.566692i	$-0.808223\pi$
$229$	−24.9366	−1.64786	−0.823929	+	0.566692i	$0.808223\pi$
$230$	−6.24153	−0.411554
$231$	−6.70137	−0.440918
$232$	4.15488	0.272781
$233$	16.3518	1.07124	0.535622	−	0.844458i	$-0.320077\pi$
$233$	16.3518	1.07124	0.535622	+	0.844458i	$0.320077\pi$
$234$	0.622734	0.0407094
$235$	−11.7535	−0.766712
$236$	−13.0061	−0.846623
$237$	2.43583	0.158224
$238$	−25.7798	−1.67106
$239$	−3.75790	−0.243078	−0.121539	−	0.992587i	$-0.538783\pi$
$239$	−3.75790	−0.243078	−0.121539	+	0.992587i	$0.538783\pi$
$240$	−1.90335	−0.122861
$241$	−19.2153	−1.23777	−0.618883	−	0.785483i	$-0.712415\pi$
$241$	−19.2153	−1.23777	−0.618883	+	0.785483i	$0.712415\pi$
$242$	−10.2071	−0.656139
$243$	−6.37356	−0.408864
$244$	4.43837	0.284137
$245$	−8.63451	−0.551639
$246$	3.65539	0.233059
$247$	−4.03070	−0.256467
$248$	1.00000	0.0635001
$249$	5.62422	0.356420
$250$	−1.00000	−0.0632456
$251$	4.58237	0.289237	0.144618	−	0.989488i	$-0.453805\pi$
$251$	4.58237	0.289237	0.144618	+	0.989488i	$0.453805\pi$
$252$	−2.46232	−0.155112
$253$	5.55769	0.349409
$254$	−12.5208	−0.785627
$255$	−12.4095	−0.777115
$256$	1.00000	0.0625000
$257$	1.23534	0.0770581	0.0385291	−	0.999257i	$-0.487733\pi$
$257$	1.23534	0.0770581	0.0385291	+	0.999257i	$0.487733\pi$
$258$	21.5725	1.34305
$259$	−26.5057	−1.64699
$260$	−1.00000	−0.0620174
$261$	2.58738	0.160155
$262$	4.58738	0.283409
$263$	2.09717	0.129317	0.0646585	−	0.997907i	$-0.479404\pi$
$263$	2.09717	0.129317	0.0646585	+	0.997907i	$0.479404\pi$
$264$	1.69481	0.104308
$265$	4.78854	0.294157
$266$	15.9376	0.977195
$267$	−30.0725	−1.84041
$268$	4.30947	0.263243
$269$	19.7169	1.20216	0.601081	−	0.799188i	$-0.294737\pi$
$269$	19.7169	1.20216	0.601081	+	0.799188i	$0.294737\pi$
$270$	4.52477	0.275368
$271$	2.53069	0.153728	0.0768642	−	0.997042i	$-0.475509\pi$
$271$	2.53069	0.153728	0.0768642	+	0.997042i	$0.475509\pi$
$272$	6.51985	0.395324
$273$	−7.52593	−0.455490
$274$	0.250363	0.0151250
$275$	0.890437	0.0536954
$276$	11.8798	0.715080
$277$	−14.3941	−0.864858	−0.432429	−	0.901668i	$-0.642343\pi$
$277$	−14.3941	−0.864858	−0.432429	+	0.901668i	$0.642343\pi$
$278$	21.6580	1.29896
$279$	0.622734	0.0372821
$280$	3.95405	0.236300
$281$	19.3021	1.15147	0.575734	−	0.817637i	$-0.304716\pi$
$281$	19.3021	1.15147	0.575734	+	0.817637i	$0.304716\pi$
$282$	22.3709	1.33217
$283$	−29.9074	−1.77781	−0.888904	−	0.458093i	$-0.848533\pi$
$283$	−29.9074	−1.77781	−0.888904	+	0.458093i	$0.848533\pi$
$284$	6.03915	0.358357
$285$	7.67182	0.454439
$286$	0.890437	0.0526526
$287$	−7.59377	−0.448246
$288$	0.622734	0.0366949
$289$	25.5084	1.50049
$290$	−4.15488	−0.243983
$291$	−19.2720	−1.12975
$292$	9.31710	0.545242
$293$	8.61012	0.503008	0.251504	−	0.967856i	$-0.419075\pi$
$293$	8.61012	0.503008	0.251504	+	0.967856i	$0.419075\pi$
$294$	16.4345	0.958478
$295$	13.0061	0.757242
$296$	6.70344	0.389629
$297$	−4.02902	−0.233787
$298$	5.15108	0.298394
$299$	6.24153	0.360957
$300$	1.90335	0.109890
$301$	−44.8152	−2.58310
$302$	12.8148	0.737411
$303$	−24.4429	−1.40421
$304$	−4.03070	−0.231176
$305$	−4.43837	−0.254140
$306$	4.06013	0.232102
$307$	8.60434	0.491076	0.245538	−	0.969387i	$-0.421035\pi$
$307$	8.60434	0.491076	0.245538	+	0.969387i	$0.421035\pi$
$308$	−3.52083	−0.200618
$309$	24.2678	1.38055
$310$	−1.00000	−0.0567962
$311$	18.5453	1.05160	0.525802	−	0.850607i	$-0.323765\pi$
$311$	18.5453	1.05160	0.525802	+	0.850607i	$0.323765\pi$
$312$	1.90335	0.107756
$313$	−31.1218	−1.75911	−0.879553	−	0.475800i	$-0.842158\pi$
$313$	−31.1218	−1.75911	−0.879553	+	0.475800i	$0.842158\pi$
$314$	−7.40349	−0.417803
$315$	2.46232	0.138736
$316$	1.27976	0.0719920
$317$	20.2539	1.13757	0.568787	−	0.822485i	$-0.307413\pi$
$317$	20.2539	1.13757	0.568787	+	0.822485i	$0.307413\pi$
$318$	−9.11425	−0.511102
$319$	3.69966	0.207141
$320$	−1.00000	−0.0559017
$321$	−8.73026	−0.487276
$322$	−24.6793	−1.37532
$323$	−26.2795	−1.46223
$324$	−10.4804	−0.582245
$325$	1.00000	0.0554700
$326$	19.5138	1.08077
$327$	2.50294	0.138413
$328$	1.92050	0.106042
$329$	−46.4738	−2.56218
$330$	−1.69481	−0.0932963
$331$	6.16575	0.338900	0.169450	−	0.985539i	$-0.445801\pi$
$331$	6.16575	0.338900	0.169450	+	0.985539i	$0.445801\pi$
$332$	2.95491	0.162172
$333$	4.17446	0.228759
$334$	−21.0792	−1.15341
$335$	−4.30947	−0.235451
$336$	−7.52593	−0.410573
$337$	−35.3138	−1.92366	−0.961832	−	0.273642i	$-0.911772\pi$
$337$	−35.3138	−1.92366	−0.961832	+	0.273642i	$0.911772\pi$
$338$	1.00000	0.0543928
$339$	6.65584	0.361496
$340$	−6.51985	−0.353588
$341$	0.890437	0.0482199
$342$	−2.51005	−0.135728
$343$	−6.46294	−0.348966
$344$	11.3340	0.611088
$345$	−11.8798	−0.639587
$346$	−5.10968	−0.274698
$347$	35.9848	1.93177	0.965883	−	0.258980i	$-0.0833863\pi$
$347$	35.9848	1.93177	0.965883	+	0.258980i	$0.0833863\pi$
$348$	7.90818	0.423923
$349$	−24.6167	−1.31770	−0.658850	−	0.752274i	$-0.728957\pi$
$349$	−24.6167	−1.31770	−0.658850	+	0.752274i	$0.728957\pi$
$350$	−3.95405	−0.211353
$351$	−4.52477	−0.241514
$352$	0.890437	0.0474605
$353$	−22.3388	−1.18897	−0.594487	−	0.804106i	$-0.702645\pi$
$353$	−22.3388	−1.18897	−0.594487	+	0.804106i	$0.702645\pi$
$354$	−24.7551	−1.31572
$355$	−6.03915	−0.320525
$356$	−15.7998	−0.837388
$357$	−49.0679	−2.59695
$358$	−9.68063	−0.511637
$359$	−28.7921	−1.51959	−0.759795	−	0.650163i	$-0.774701\pi$
$359$	−28.7921	−1.51959	−0.759795	+	0.650163i	$0.774701\pi$
$360$	−0.622734	−0.0328209
$361$	−2.75349	−0.144920
$362$	10.3455	0.543750
$363$	−19.4277	−1.01969
$364$	−3.95405	−0.207249
$365$	−9.31710	−0.487679
$366$	8.44775	0.441571
$367$	12.0902	0.631101	0.315551	−	0.948909i	$-0.397811\pi$
$367$	12.0902	0.631101	0.315551	+	0.948909i	$0.397811\pi$
$368$	6.24153	0.325362
$369$	1.19596	0.0622593
$370$	−6.70344	−0.348495
$371$	18.9341	0.983010
$372$	1.90335	0.0986840
$373$	33.5697	1.73817	0.869085	−	0.494662i	$-0.164708\pi$
$373$	33.5697	1.73817	0.869085	+	0.494662i	$0.164708\pi$
$374$	5.80551	0.300196
$375$	−1.90335	−0.0982885
$376$	11.7535	0.606139
$377$	4.15488	0.213987
$378$	17.8911	0.920221
$379$	0.618322	0.0317611	0.0158805	−	0.999874i	$-0.494945\pi$
$379$	0.618322	0.0317611	0.0158805	+	0.999874i	$0.494945\pi$
$380$	4.03070	0.206770
$381$	−23.8315	−1.22093
$382$	1.23706	0.0632935
$383$	−31.1016	−1.58922	−0.794610	−	0.607121i	$-0.792324\pi$
$383$	−31.1016	−1.58922	−0.794610	+	0.607121i	$0.792324\pi$
$384$	1.90335	0.0971298
$385$	3.52083	0.179438
$386$	−21.7637	−1.10774
$387$	7.05806	0.358781
$388$	−10.1253	−0.514036
$389$	17.2196	0.873071	0.436535	−	0.899687i	$-0.356205\pi$
$389$	17.2196	0.873071	0.436535	+	0.899687i	$0.356205\pi$
$390$	−1.90335	−0.0963798
$391$	40.6938	2.05797
$392$	8.63451	0.436109
$393$	8.73138	0.440440
$394$	−7.63890	−0.384842
$395$	−1.27976	−0.0643916
$396$	0.554505	0.0278649
$397$	0.881149	0.0442236	0.0221118	−	0.999756i	$-0.492961\pi$
$397$	0.881149	0.0442236	0.0221118	+	0.999756i	$0.492961\pi$
$398$	17.2500	0.864665
$399$	30.3348	1.51864
$400$	1.00000	0.0500000
$401$	14.1568	0.706955	0.353478	−	0.935443i	$-0.384999\pi$
$401$	14.1568	0.706955	0.353478	+	0.935443i	$0.384999\pi$
$402$	8.20242	0.409100
$403$	1.00000	0.0498135
$404$	−12.8420	−0.638916
$405$	10.4804	0.520775
$406$	−16.4286	−0.815338
$407$	5.96899	0.295872
$408$	12.4095	0.614364
$409$	11.3669	0.562055	0.281027	−	0.959700i	$-0.409325\pi$
$409$	11.3669	0.562055	0.281027	+	0.959700i	$0.409325\pi$
$410$	−1.92050	−0.0948469
$411$	0.476527	0.0235053
$412$	12.7500	0.628150
$413$	51.4266	2.53054
$414$	3.88681	0.191026
$415$	−2.95491	−0.145051
$416$	1.00000	0.0490290
$417$	41.2228	2.01869
$418$	−3.58908	−0.175548
$419$	−5.39008	−0.263323	−0.131661	−	0.991295i	$-0.542031\pi$
$419$	−5.39008	−0.263323	−0.131661	+	0.991295i	$0.542031\pi$
$420$	7.52593	0.367228
$421$	3.78858	0.184644	0.0923220	−	0.995729i	$-0.470571\pi$
$421$	3.78858	0.184644	0.0923220	+	0.995729i	$0.470571\pi$
$422$	18.3640	0.893943
$423$	7.31928	0.355876
$424$	−4.78854	−0.232552
$425$	6.51985	0.316259
$426$	11.4946	0.556915
$427$	−17.5495	−0.849281
$428$	−4.58679	−0.221711
$429$	1.69481	0.0818263
$430$	−11.3340	−0.546574
$431$	−28.3877	−1.36739	−0.683694	−	0.729769i	$-0.739628\pi$
$431$	−28.3877	−1.36739	−0.683694	+	0.729769i	$0.739628\pi$
$432$	−4.52477	−0.217698
$433$	−38.9416	−1.87142	−0.935708	−	0.352776i	$-0.885238\pi$
$433$	−38.9416	−1.87142	−0.935708	+	0.352776i	$0.885238\pi$
$434$	−3.95405	−0.189800
$435$	−7.90818	−0.379168
$436$	1.31502	0.0629780
$437$	−25.1577	−1.20346
$438$	17.7337	0.847348
$439$	2.58726	0.123483	0.0617415	−	0.998092i	$-0.480335\pi$
$439$	2.58726	0.123483	0.0617415	+	0.998092i	$0.480335\pi$
$440$	−0.890437	−0.0424499
$441$	5.37700	0.256048
$442$	6.51985	0.310117
$443$	21.8374	1.03752	0.518762	−	0.854918i	$-0.326393\pi$
$443$	21.8374	1.03752	0.518762	+	0.854918i	$0.326393\pi$
$444$	12.7590	0.605514
$445$	15.7998	0.748983
$446$	2.72322	0.128948
$447$	9.80431	0.463728
$448$	−3.95405	−0.186811
$449$	6.29037	0.296861	0.148430	−	0.988923i	$-0.452578\pi$
$449$	6.29037	0.296861	0.148430	+	0.988923i	$0.452578\pi$
$450$	0.622734	0.0293559
$451$	1.71009	0.0805249
$452$	3.49691	0.164481
$453$	24.3911	1.14599
$454$	−22.0157	−1.03325
$455$	3.95405	0.185369
$456$	−7.67182	−0.359266
$457$	−14.5589	−0.681034	−0.340517	−	0.940238i	$-0.610602\pi$
$457$	−14.5589	−0.681034	−0.340517	+	0.940238i	$0.610602\pi$
$458$	−24.9366	−1.16521
$459$	−29.5008	−1.37698
$460$	−6.24153	−0.291013
$461$	−6.70788	−0.312417	−0.156209	−	0.987724i	$-0.549927\pi$
$461$	−6.70788	−0.312417	−0.156209	+	0.987724i	$0.549927\pi$
$462$	−6.70137	−0.311776
$463$	−12.1870	−0.566380	−0.283190	−	0.959064i	$-0.591393\pi$
$463$	−12.1870	−0.566380	−0.283190	+	0.959064i	$0.591393\pi$
$464$	4.15488	0.192885
$465$	−1.90335	−0.0882657
$466$	16.3518	0.757485
$467$	−20.2313	−0.936194	−0.468097	−	0.883677i	$-0.655060\pi$
$467$	−20.2313	−0.936194	−0.468097	+	0.883677i	$0.655060\pi$
$468$	0.622734	0.0287859
$469$	−17.0399	−0.786828
$470$	−11.7535	−0.542147
$471$	−14.0914	−0.649298
$472$	−13.0061	−0.598653
$473$	10.0922	0.464040
$474$	2.43583	0.111881
$475$	−4.03070	−0.184941
$476$	−25.7798	−1.18162
$477$	−2.98198	−0.136536
$478$	−3.75790	−0.171882
$479$	38.1651	1.74381	0.871905	−	0.489675i	$-0.162885\pi$
$479$	38.1651	1.74381	0.871905	+	0.489675i	$0.162885\pi$
$480$	−1.90335	−0.0868756
$481$	6.70344	0.305650
$482$	−19.2153	−0.875233
$483$	−46.9733	−2.13736
$484$	−10.2071	−0.463960
$485$	10.1253	0.459768
$486$	−6.37356	−0.289111
$487$	39.9186	1.80888	0.904441	−	0.426598i	$-0.140288\pi$
$487$	39.9186	1.80888	0.904441	+	0.426598i	$0.140288\pi$
$488$	4.43837	0.200915
$489$	37.1415	1.67960
$490$	−8.63451	−0.390067
$491$	−29.5033	−1.33146	−0.665732	−	0.746191i	$-0.731880\pi$
$491$	−29.5033	−1.33146	−0.665732	+	0.746191i	$0.731880\pi$
$492$	3.65539	0.164798
$493$	27.0892	1.22004
$494$	−4.03070	−0.181350
$495$	−0.554505	−0.0249232
$496$	1.00000	0.0449013
$497$	−23.8791	−1.07112
$498$	5.62422	0.252027
$499$	−18.2721	−0.817969	−0.408985	−	0.912541i	$-0.634117\pi$
$499$	−18.2721	−0.817969	−0.408985	+	0.912541i	$0.634117\pi$
$500$	−1.00000	−0.0447214
$501$	−40.1211	−1.79248
$502$	4.58237	0.204521
$503$	12.5197	0.558225	0.279113	−	0.960258i	$-0.409960\pi$
$503$	12.5197	0.558225	0.279113	+	0.960258i	$0.409960\pi$
$504$	−2.46232	−0.109680
$505$	12.8420	0.571464
$506$	5.55769	0.247069
$507$	1.90335	0.0845307
$508$	−12.5208	−0.555522
$509$	44.2266	1.96031	0.980155	−	0.198233i	$-0.0635202\pi$
$509$	44.2266	1.96031	0.980155	+	0.198233i	$0.0635202\pi$
$510$	−12.4095	−0.549504
$511$	−36.8403	−1.62972
$512$	1.00000	0.0441942
$513$	18.2380	0.805225
$514$	1.23534	0.0544883
$515$	−12.7500	−0.561834
$516$	21.5725	0.949678
$517$	10.4657	0.460282
$518$	−26.5057	−1.16459
$519$	−9.72550	−0.426902
$520$	−1.00000	−0.0438529
$521$	−3.46613	−0.151854	−0.0759269	−	0.997113i	$-0.524192\pi$
$521$	−3.46613	−0.151854	−0.0759269	+	0.997113i	$0.524192\pi$
$522$	2.58738	0.113247
$523$	−28.6597	−1.25320	−0.626601	−	0.779340i	$-0.715554\pi$
$523$	−28.6597	−1.25320	−0.626601	+	0.779340i	$0.715554\pi$
$524$	4.58738	0.200401
$525$	−7.52593	−0.328459
$526$	2.09717	0.0914410
$527$	6.51985	0.284009
$528$	1.69481	0.0737572
$529$	15.9567	0.693768
$530$	4.78854	0.208001
$531$	−8.09932	−0.351480
$532$	15.9376	0.690981
$533$	1.92050	0.0831863
$534$	−30.0725	−1.30137
$535$	4.58679	0.198304
$536$	4.30947	0.186141
$537$	−18.4256	−0.795124
$538$	19.7169	0.850057
$539$	7.68849	0.331167
$540$	4.52477	0.194715
$541$	−10.4289	−0.448375	−0.224187	−	0.974546i	$-0.571973\pi$
$541$	−10.4289	−0.448375	−0.224187	+	0.974546i	$0.571973\pi$
$542$	2.53069	0.108702
$543$	19.6912	0.845029
$544$	6.51985	0.279536
$545$	−1.31502	−0.0563293
$546$	−7.52593	−0.322080
$547$	−31.8970	−1.36382	−0.681909	−	0.731437i	$-0.738850\pi$
$547$	−31.8970	−1.36382	−0.681909	+	0.731437i	$0.738850\pi$
$548$	0.250363	0.0106950
$549$	2.76392	0.117961
$550$	0.890437	0.0379684
$551$	−16.7471	−0.713449
$552$	11.8798	0.505638
$553$	−5.06023	−0.215183
$554$	−14.3941	−0.611547
$555$	−12.7590	−0.541588
$556$	21.6580	0.918505
$557$	4.61243	0.195435	0.0977176	−	0.995214i	$-0.468846\pi$
$557$	4.61243	0.195435	0.0977176	+	0.995214i	$0.468846\pi$
$558$	0.622734	0.0263624
$559$	11.3340	0.479377
$560$	3.95405	0.167089
$561$	11.0499	0.466528
$562$	19.3021	0.814210
$563$	34.4538	1.45206	0.726028	−	0.687665i	$-0.241364\pi$
$563$	34.4538	1.45206	0.726028	+	0.687665i	$0.241364\pi$
$564$	22.3709	0.941986
$565$	−3.49691	−0.147116
$566$	−29.9074	−1.25710
$567$	41.4400	1.74032
$568$	6.03915	0.253397
$569$	−33.9231	−1.42213	−0.711065	−	0.703127i	$-0.751787\pi$
$569$	−33.9231	−1.42213	−0.711065	+	0.703127i	$0.751787\pi$
$570$	7.67182	0.321337
$571$	−3.13719	−0.131287	−0.0656436	−	0.997843i	$-0.520910\pi$
$571$	−3.13719	−0.131287	−0.0656436	+	0.997843i	$0.520910\pi$
$572$	0.890437	0.0372310
$573$	2.35456	0.0983630
$574$	−7.59377	−0.316958
$575$	6.24153	0.260290
$576$	0.622734	0.0259472
$577$	−24.1041	−1.00347	−0.501733	−	0.865022i	$-0.667304\pi$
$577$	−24.1041	−1.00347	−0.501733	+	0.865022i	$0.667304\pi$
$578$	25.5084	1.06101
$579$	−41.4239	−1.72152
$580$	−4.15488	−0.172522
$581$	−11.6839	−0.484728
$582$	−19.2720	−0.798852
$583$	−4.26389	−0.176592
$584$	9.31710	0.385544
$585$	−0.622734	−0.0257469
$586$	8.61012	0.355681
$587$	12.3317	0.508985	0.254493	−	0.967075i	$-0.418092\pi$
$587$	12.3317	0.508985	0.254493	+	0.967075i	$0.418092\pi$
$588$	16.4345	0.677747
$589$	−4.03070	−0.166082
$590$	13.0061	0.535451
$591$	−14.5395	−0.598074
$592$	6.70344	0.275510
$593$	41.5322	1.70552	0.852762	−	0.522299i	$-0.174925\pi$
$593$	41.5322	1.70552	0.852762	+	0.522299i	$0.174925\pi$
$594$	−4.02902	−0.165313
$595$	25.7798	1.05687
$596$	5.15108	0.210997
$597$	32.8328	1.34376
$598$	6.24153	0.255235
$599$	33.2244	1.35751	0.678757	−	0.734363i	$-0.262519\pi$
$599$	33.2244	1.35751	0.678757	+	0.734363i	$0.262519\pi$
$600$	1.90335	0.0777039
$601$	6.12225	0.249732	0.124866	−	0.992174i	$-0.460150\pi$
$601$	6.12225	0.249732	0.124866	+	0.992174i	$0.460150\pi$
$602$	−44.8152	−1.82653
$603$	2.68365	0.109287
$604$	12.8148	0.521429
$605$	10.2071	0.414979
$606$	−24.4429	−0.992924
$607$	−21.5570	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$607$	−21.5570	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$608$	−4.03070	−0.163466
$609$	−31.2694	−1.26710
$610$	−4.43837	−0.179704
$611$	11.7535	0.475494
$612$	4.06013	0.164121
$613$	14.9193	0.602585	0.301293	−	0.953532i	$-0.402582\pi$
$613$	14.9193	0.602585	0.301293	+	0.953532i	$0.402582\pi$
$614$	8.60434	0.347243
$615$	−3.65539	−0.147399
$616$	−3.52083	−0.141858
$617$	31.8692	1.28301	0.641503	−	0.767120i	$-0.278311\pi$
$617$	31.8692	1.28301	0.641503	+	0.767120i	$0.278311\pi$
$618$	24.2678	0.976193
$619$	38.0120	1.52783	0.763915	−	0.645317i	$-0.223275\pi$
$619$	38.0120	1.52783	0.763915	+	0.645317i	$0.223275\pi$
$620$	−1.00000	−0.0401610
$621$	−28.2414	−1.13329
$622$	18.5453	0.743597
$623$	62.4732	2.50294
$624$	1.90335	0.0761949
$625$	1.00000	0.0400000
$626$	−31.1218	−1.24388
$627$	−6.83127	−0.272815
$628$	−7.40349	−0.295431
$629$	43.7054	1.74265
$630$	2.46232	0.0981012
$631$	13.7119	0.545862	0.272931	−	0.962034i	$-0.412007\pi$
$631$	13.7119	0.545862	0.272931	+	0.962034i	$0.412007\pi$
$632$	1.27976	0.0509061
$633$	34.9530	1.38926
$634$	20.2539	0.804387
$635$	12.5208	0.496874
$636$	−9.11425	−0.361404
$637$	8.63451	0.342112
$638$	3.69966	0.146471
$639$	3.76078	0.148774
$640$	−1.00000	−0.0395285
$641$	−43.5965	−1.72196	−0.860978	−	0.508642i	$-0.830148\pi$
$641$	−43.5965	−1.72196	−0.860978	+	0.508642i	$0.830148\pi$
$642$	−8.73026	−0.344556
$643$	18.3494	0.723629	0.361815	−	0.932250i	$-0.382157\pi$
$643$	18.3494	0.723629	0.361815	+	0.932250i	$0.382157\pi$
$644$	−24.6793	−0.972501
$645$	−21.5725	−0.849418
$646$	−26.2795	−1.03395
$647$	−10.7148	−0.421243	−0.210621	−	0.977568i	$-0.567549\pi$
$647$	−10.7148	−0.421243	−0.210621	+	0.977568i	$0.567549\pi$
$648$	−10.4804	−0.411709
$649$	−11.5811	−0.454597
$650$	1.00000	0.0392232
$651$	−7.52593	−0.294965
$652$	19.5138	0.764218
$653$	−6.58182	−0.257567	−0.128783	−	0.991673i	$-0.541107\pi$
$653$	−6.58182	−0.257567	−0.128783	+	0.991673i	$0.541107\pi$
$654$	2.50294	0.0978727
$655$	−4.58738	−0.179244
$656$	1.92050	0.0749831
$657$	5.80207	0.226360
$658$	−46.4738	−1.81174
$659$	−27.2389	−1.06108	−0.530539	−	0.847660i	$-0.678010\pi$
$659$	−27.2389	−1.06108	−0.530539	+	0.847660i	$0.678010\pi$
$660$	−1.69481	−0.0659704
$661$	4.70788	0.183115	0.0915577	−	0.995800i	$-0.470815\pi$
$661$	4.70788	0.183115	0.0915577	+	0.995800i	$0.470815\pi$
$662$	6.16575	0.239639
$663$	12.4095	0.481947
$664$	2.95491	0.114673
$665$	−15.9376	−0.618033
$666$	4.17446	0.161757
$667$	25.9328	1.00412
$668$	−21.0792	−0.815581
$669$	5.18323	0.200395
$670$	−4.30947	−0.166489
$671$	3.95208	0.152569
$672$	−7.52593	−0.290319
$673$	42.5504	1.64020	0.820099	−	0.572221i	$-0.193918\pi$
$673$	42.5504	1.64020	0.820099	+	0.572221i	$0.193918\pi$
$674$	−35.3138	−1.36024
$675$	−4.52477	−0.174158
$676$	1.00000	0.0384615
$677$	31.3051	1.20315	0.601577	−	0.798815i	$-0.294539\pi$
$677$	31.3051	1.20315	0.601577	+	0.798815i	$0.294539\pi$
$678$	6.65584	0.255616
$679$	40.0361	1.53644
$680$	−6.51985	−0.250025
$681$	−41.9036	−1.60575
$682$	0.890437	0.0340966
$683$	1.63343	0.0625013	0.0312507	−	0.999512i	$-0.490051\pi$
$683$	1.63343	0.0625013	0.0312507	+	0.999512i	$0.490051\pi$
$684$	−2.51005	−0.0959742
$685$	−0.250363	−0.00956586
$686$	−6.46294	−0.246756
$687$	−47.4631	−1.81083
$688$	11.3340	0.432105
$689$	−4.78854	−0.182429
$690$	−11.8798	−0.452256
$691$	−1.85039	−0.0703921	−0.0351961	−	0.999380i	$-0.511206\pi$
$691$	−1.85039	−0.0703921	−0.0351961	+	0.999380i	$0.511206\pi$
$692$	−5.10968	−0.194241
$693$	−2.19254	−0.0832877
$694$	35.9848	1.36596
$695$	−21.6580	−0.821536
$696$	7.90818	0.299759
$697$	12.5214	0.474282
$698$	−24.6167	−0.931754
$699$	31.1232	1.17719
$700$	−3.95405	−0.149449
$701$	0.371718	0.0140396	0.00701980	−	0.999975i	$-0.497766\pi$
$701$	0.371718	0.0140396	0.00701980	+	0.999975i	$0.497766\pi$
$702$	−4.52477	−0.170776
$703$	−27.0195	−1.01906
$704$	0.890437	0.0335596
$705$	−22.3709	−0.842538
$706$	−22.3388	−0.840731
$707$	50.7781	1.90971
$708$	−24.7551	−0.930352
$709$	13.6695	0.513371	0.256685	−	0.966495i	$-0.417370\pi$
$709$	13.6695	0.513371	0.256685	+	0.966495i	$0.417370\pi$
$710$	−6.03915	−0.226645
$711$	0.796949	0.0298879
$712$	−15.7998	−0.592123
$713$	6.24153	0.233747
$714$	−49.0679	−1.83632
$715$	−0.890437	−0.0333005
$716$	−9.68063	−0.361782
$717$	−7.15258	−0.267118
$718$	−28.7921	−1.07451
$719$	−40.8848	−1.52475	−0.762374	−	0.647137i	$-0.775966\pi$
$719$	−40.8848	−1.52475	−0.762374	+	0.647137i	$0.775966\pi$
$720$	−0.622734	−0.0232079
$721$	−50.4143	−1.87753
$722$	−2.75349	−0.102474
$723$	−36.5734	−1.36018
$724$	10.3455	0.384489
$725$	4.15488	0.154308
$726$	−19.4277	−0.721030
$727$	−20.5959	−0.763861	−0.381931	−	0.924191i	$-0.624741\pi$
$727$	−20.5959	−0.763861	−0.381931	+	0.924191i	$0.624741\pi$
$728$	−3.95405	−0.146547
$729$	19.3101	0.715189
$730$	−9.31710	−0.344841
$731$	73.8959	2.73314
$732$	8.44775	0.312238
$733$	−4.46510	−0.164922	−0.0824612	−	0.996594i	$-0.526278\pi$
$733$	−4.46510	−0.164922	−0.0824612	+	0.996594i	$0.526278\pi$
$734$	12.0902	0.446256
$735$	−16.4345	−0.606195
$736$	6.24153	0.230066
$737$	3.83731	0.141349
$738$	1.19596	0.0440240
$739$	10.0032	0.367973	0.183986	−	0.982929i	$-0.441100\pi$
$739$	10.0032	0.367973	0.183986	+	0.982929i	$0.441100\pi$
$740$	−6.70344	−0.246423
$741$	−7.67182	−0.281831
$742$	18.9341	0.695093
$743$	18.6306	0.683491	0.341745	−	0.939793i	$-0.388982\pi$
$743$	18.6306	0.683491	0.341745	+	0.939793i	$0.388982\pi$
$744$	1.90335	0.0697801
$745$	−5.15108	−0.188721
$746$	33.5697	1.22907
$747$	1.84012	0.0673265
$748$	5.80551	0.212271
$749$	18.1364	0.662690
$750$	−1.90335	−0.0695004
$751$	−34.2912	−1.25131	−0.625653	−	0.780102i	$-0.715167\pi$
$751$	−34.2912	−1.25131	−0.625653	+	0.780102i	$0.715167\pi$
$752$	11.7535	0.428605
$753$	8.72185	0.317842
$754$	4.15488	0.151312
$755$	−12.8148	−0.466380
$756$	17.8911	0.650695
$757$	−40.9998	−1.49016	−0.745082	−	0.666973i	$-0.767590\pi$
$757$	−40.9998	−1.49016	−0.745082	+	0.666973i	$0.767590\pi$
$758$	0.618322	0.0224585
$759$	10.5782	0.383965
$760$	4.03070	0.146209
$761$	−8.92625	−0.323576	−0.161788	−	0.986826i	$-0.551726\pi$
$761$	−8.92625	−0.323576	−0.161788	+	0.986826i	$0.551726\pi$
$762$	−23.8315	−0.863325
$763$	−5.19966	−0.188240
$764$	1.23706	0.0447553
$765$	−4.06013	−0.146794
$766$	−31.1016	−1.12375
$767$	−13.0061	−0.469622
$768$	1.90335	0.0686812
$769$	−14.4575	−0.521350	−0.260675	−	0.965427i	$-0.583945\pi$
$769$	−14.4575	−0.521350	−0.260675	+	0.965427i	$0.583945\pi$
$770$	3.52083	0.126882
$771$	2.35127	0.0846791
$772$	−21.7637	−0.783293
$773$	−33.2690	−1.19660	−0.598302	−	0.801271i	$-0.704158\pi$
$773$	−33.2690	−1.19660	−0.598302	+	0.801271i	$0.704158\pi$
$774$	7.05806	0.253697
$775$	1.00000	0.0359211
$776$	−10.1253	−0.363479
$777$	−50.4496	−1.80987
$778$	17.2196	0.617354
$779$	−7.74097	−0.277349
$780$	−1.90335	−0.0681508
$781$	5.37748	0.192421
$782$	40.6938	1.45521
$783$	−18.7999	−0.671852
$784$	8.63451	0.308375
$785$	7.40349	0.264242
$786$	8.73138	0.311438
$787$	−3.09916	−0.110473	−0.0552365	−	0.998473i	$-0.517591\pi$
$787$	−3.09916	−0.110473	−0.0552365	+	0.998473i	$0.517591\pi$
$788$	−7.63890	−0.272124
$789$	3.99164	0.142106
$790$	−1.27976	−0.0455318
$791$	−13.8270	−0.491631
$792$	0.554505	0.0197035
$793$	4.43837	0.157611
$794$	0.881149	0.0312708
$795$	9.11425	0.323249
$796$	17.2500	0.611410
$797$	13.8344	0.490038	0.245019	−	0.969518i	$-0.421206\pi$
$797$	13.8344	0.490038	0.245019	+	0.969518i	$0.421206\pi$
$798$	30.3348	1.07384
$799$	76.6308	2.71100
$800$	1.00000	0.0353553
$801$	−9.83907	−0.347647
$802$	14.1568	0.499893
$803$	8.29629	0.292770
$804$	8.20242	0.289277
$805$	24.6793	0.869831
$806$	1.00000	0.0352235
$807$	37.5282	1.32105
$808$	−12.8420	−0.451782
$809$	−49.4339	−1.73800	−0.869002	−	0.494809i	$-0.835238\pi$
$809$	−49.4339	−1.73800	−0.869002	+	0.494809i	$0.835238\pi$
$810$	10.4804	0.368244
$811$	−28.6375	−1.00560	−0.502800	−	0.864403i	$-0.667697\pi$
$811$	−28.6375	−1.00560	−0.502800	+	0.864403i	$0.667697\pi$
$812$	−16.4286	−0.576531
$813$	4.81678	0.168932
$814$	5.96899	0.209213
$815$	−19.5138	−0.683538
$816$	12.4095	0.434421
$817$	−45.6839	−1.59828
$818$	11.3669	0.397433
$819$	−2.46232	−0.0860404
$820$	−1.92050	−0.0670669
$821$	8.90171	0.310672	0.155336	−	0.987862i	$-0.450354\pi$
$821$	8.90171	0.310672	0.155336	+	0.987862i	$0.450354\pi$
$822$	0.476527	0.0166208
$823$	46.9273	1.63578	0.817891	−	0.575374i	$-0.195143\pi$
$823$	46.9273	1.63578	0.817891	+	0.575374i	$0.195143\pi$
$824$	12.7500	0.444169
$825$	1.69481	0.0590058
$826$	51.4266	1.78936
$827$	−52.2187	−1.81582	−0.907910	−	0.419165i	$-0.862323\pi$
$827$	−52.2187	−1.81582	−0.907910	+	0.419165i	$0.862323\pi$
$828$	3.88681	0.135076
$829$	28.2538	0.981296	0.490648	−	0.871358i	$-0.336760\pi$
$829$	28.2538	0.981296	0.490648	+	0.871358i	$0.336760\pi$
$830$	−2.95491	−0.102566
$831$	−27.3970	−0.950392
$832$	1.00000	0.0346688
$833$	56.2957	1.95053
$834$	41.2228	1.42743
$835$	21.0792	0.729478
$836$	−3.58908	−0.124131
$837$	−4.52477	−0.156399
$838$	−5.39008	−0.186197
$839$	5.11990	0.176759	0.0883793	−	0.996087i	$-0.471831\pi$
$839$	5.11990	0.176759	0.0883793	+	0.996087i	$0.471831\pi$
$840$	7.52593	0.259669
$841$	−11.7370	−0.404723
$842$	3.78858	0.130563
$843$	36.7386	1.26535
$844$	18.3640	0.632113
$845$	−1.00000	−0.0344010
$846$	7.31928	0.251642
$847$	40.3595	1.38677
$848$	−4.78854	−0.164439
$849$	−56.9241	−1.95363
$850$	6.51985	0.223629
$851$	41.8397	1.43425
$852$	11.4946	0.393799
$853$	−29.0840	−0.995818	−0.497909	−	0.867229i	$-0.665899\pi$
$853$	−29.0840	−0.995818	−0.497909	+	0.867229i	$0.665899\pi$
$854$	−17.5495	−0.600532
$855$	2.51005	0.0858419
$856$	−4.58679	−0.156773
$857$	23.8415	0.814409	0.407204	−	0.913337i	$-0.366504\pi$
$857$	23.8415	0.814409	0.407204	+	0.913337i	$0.366504\pi$
$858$	1.69481	0.0578599
$859$	−13.4117	−0.457601	−0.228800	−	0.973473i	$-0.573480\pi$
$859$	−13.4117	−0.457601	−0.228800	+	0.973473i	$0.573480\pi$
$860$	−11.3340	−0.386486
$861$	−14.4536	−0.492577
$862$	−28.3877	−0.966889
$863$	−25.3865	−0.864166	−0.432083	−	0.901834i	$-0.642221\pi$
$863$	−25.3865	−0.864166	−0.432083	+	0.901834i	$0.642221\pi$
$864$	−4.52477	−0.153936
$865$	5.10968	0.173734
$866$	−38.9416	−1.32329
$867$	48.5514	1.64889
$868$	−3.95405	−0.134209
$869$	1.13954	0.0386564
$870$	−7.90818	−0.268113
$871$	4.30947	0.146021
$872$	1.31502	0.0445322
$873$	−6.30539	−0.213405
$874$	−25.1577	−0.850972
$875$	3.95405	0.133671
$876$	17.7337	0.599166
$877$	−21.8032	−0.736242	−0.368121	−	0.929778i	$-0.619999\pi$
$877$	−21.8032	−0.736242	−0.368121	+	0.929778i	$0.619999\pi$
$878$	2.58726	0.0873156
$879$	16.3881	0.552755
$880$	−0.890437	−0.0300166
$881$	−20.2161	−0.681097	−0.340549	−	0.940227i	$-0.610613\pi$
$881$	−20.2161	−0.681097	−0.340549	+	0.940227i	$0.610613\pi$
$882$	5.37700	0.181053
$883$	−45.1916	−1.52082	−0.760409	−	0.649445i	$-0.775001\pi$
$883$	−45.1916	−1.52082	−0.760409	+	0.649445i	$0.775001\pi$
$884$	6.51985	0.219286
$885$	24.7551	0.832133
$886$	21.8374	0.733641
$887$	8.07164	0.271019	0.135510	−	0.990776i	$-0.456733\pi$
$887$	8.07164	0.271019	0.135510	+	0.990776i	$0.456733\pi$
$888$	12.7590	0.428163
$889$	49.5080	1.66045
$890$	15.7998	0.529611
$891$	−9.33214	−0.312638
$892$	2.72322	0.0911800
$893$	−47.3747	−1.58533
$894$	9.80431	0.327905
$895$	9.68063	0.323588
$896$	−3.95405	−0.132096
$897$	11.8798	0.396655
$898$	6.29037	0.209912
$899$	4.15488	0.138573
$900$	0.622734	0.0207578
$901$	−31.2205	−1.04011
$902$	1.71009	0.0569397
$903$	−85.2989	−2.83857
$904$	3.49691	0.116306
$905$	−10.3455	−0.343897
$906$	24.3911	0.810340
$907$	−29.2993	−0.972868	−0.486434	−	0.873717i	$-0.661703\pi$
$907$	−29.2993	−0.972868	−0.486434	+	0.873717i	$0.661703\pi$
$908$	−22.0157	−0.730618
$909$	−7.99718	−0.265250
$910$	3.95405	0.131075
$911$	−19.3569	−0.641321	−0.320661	−	0.947194i	$-0.603905\pi$
$911$	−19.3569	−0.641321	−0.320661	+	0.947194i	$0.603905\pi$
$912$	−7.67182	−0.254039
$913$	2.63116	0.0870787
$914$	−14.5589	−0.481564
$915$	−8.44775	−0.279274
$916$	−24.9366	−0.823929
$917$	−18.1387	−0.598993
$918$	−29.5008	−0.973671
$919$	41.0812	1.35514	0.677572	−	0.735457i	$-0.263032\pi$
$919$	41.0812	1.35514	0.677572	+	0.735457i	$0.263032\pi$
$920$	−6.24153	−0.205777
$921$	16.3771	0.539642
$922$	−6.70788	−0.220912
$923$	6.03915	0.198781
$924$	−6.70137	−0.220459
$925$	6.70344	0.220408
$926$	−12.1870	−0.400491
$927$	7.93988	0.260780
$928$	4.15488	0.136391
$929$	20.3840	0.668777	0.334389	−	0.942435i	$-0.391470\pi$
$929$	20.3840	0.668777	0.334389	+	0.942435i	$0.391470\pi$
$930$	−1.90335	−0.0624132
$931$	−34.8031	−1.14063
$932$	16.3518	0.535622
$933$	35.2981	1.15561
$934$	−20.2313	−0.661989
$935$	−5.80551	−0.189861
$936$	0.622734	0.0203547
$937$	16.7456	0.547054	0.273527	−	0.961864i	$-0.411810\pi$
$937$	16.7456	0.547054	0.273527	+	0.961864i	$0.411810\pi$
$938$	−17.0399	−0.556371
$939$	−59.2356	−1.93308
$940$	−11.7535	−0.383356
$941$	32.6549	1.06452	0.532259	−	0.846582i	$-0.321343\pi$
$941$	32.6549	1.06452	0.532259	+	0.846582i	$0.321343\pi$
$942$	−14.0914	−0.459123
$943$	11.9869	0.390347
$944$	−13.0061	−0.423311
$945$	−17.8911	−0.581999
$946$	10.0922	0.328126
$947$	−8.24789	−0.268020	−0.134010	−	0.990980i	$-0.542785\pi$
$947$	−8.24789	−0.268020	−0.134010	+	0.990980i	$0.542785\pi$
$948$	2.43583	0.0791120
$949$	9.31710	0.302446
$950$	−4.03070	−0.130773
$951$	38.5503	1.25008
$952$	−25.7798	−0.835528
$953$	31.1992	1.01064	0.505321	−	0.862932i	$-0.331374\pi$
$953$	31.1992	1.01064	0.505321	+	0.862932i	$0.331374\pi$
$954$	−2.98198	−0.0965453
$955$	−1.23706	−0.0400303
$956$	−3.75790	−0.121539
$957$	7.04174	0.227627
$958$	38.1651	1.23306
$959$	−0.989946	−0.0319670
$960$	−1.90335	−0.0614303
$961$	1.00000	0.0322581
$962$	6.70344	0.216128
$963$	−2.85635	−0.0920446
$964$	−19.2153	−0.618883
$965$	21.7637	0.700599
$966$	−46.9733	−1.51134
$967$	−59.8091	−1.92333	−0.961665	−	0.274228i	$-0.911578\pi$
$967$	−59.8091	−1.92333	−0.961665	+	0.274228i	$0.911578\pi$
$968$	−10.2071	−0.328069
$969$	−50.0191	−1.60684
$970$	10.1253	0.325105
$971$	27.8519	0.893811	0.446906	−	0.894581i	$-0.352526\pi$
$971$	27.8519	0.893811	0.446906	+	0.894581i	$0.352526\pi$
$972$	−6.37356	−0.204432
$973$	−85.6369	−2.74539
$974$	39.9186	1.27907
$975$	1.90335	0.0609559
$976$	4.43837	0.142069
$977$	−13.7742	−0.440674	−0.220337	−	0.975424i	$-0.570716\pi$
$977$	−13.7742	−0.440674	−0.220337	+	0.975424i	$0.570716\pi$
$978$	37.1415	1.18765
$979$	−14.0687	−0.449639
$980$	−8.63451	−0.275819
$981$	0.818907	0.0261457
$982$	−29.5033	−0.941487
$983$	42.6393	1.35998	0.679992	−	0.733220i	$-0.261983\pi$
$983$	42.6393	1.35998	0.679992	+	0.733220i	$0.261983\pi$
$984$	3.65539	0.116530
$985$	7.63890	0.243396
$986$	27.0892	0.862695
$987$	−88.4558	−2.81558
$988$	−4.03070	−0.128234
$989$	70.7415	2.24945
$990$	−0.554505	−0.0176233
$991$	−33.2433	−1.05601	−0.528005	−	0.849241i	$-0.677060\pi$
$991$	−33.2433	−1.05601	−0.528005	+	0.849241i	$0.677060\pi$
$992$	1.00000	0.0317500
$993$	11.7356	0.372417
$994$	−23.8791	−0.757399
$995$	−17.2500	−0.546862
$996$	5.62422	0.178210
$997$	17.9606	0.568818	0.284409	−	0.958703i	$-0.408203\pi$
$997$	17.9606	0.568818	0.284409	+	0.958703i	$0.408203\pi$
$998$	−18.2721	−0.578392
$999$	−30.3315	−0.959646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.q.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.q.1.7	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.90335 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.90335 q^{6} -3.95405 q^{7} +1.00000 q^{8} +0.622734 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.90335 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.90335 q^{6} -3.95405 q^{7} +1.00000 q^{8} +0.622734 q^{9} -1.00000 q^{10} +0.890437 q^{11} +1.90335 q^{12} +1.00000 q^{13} -3.95405 q^{14} -1.90335 q^{15} +1.00000 q^{16} +6.51985 q^{17} +0.622734 q^{18} -4.03070 q^{19} -1.00000 q^{20} -7.52593 q^{21} +0.890437 q^{22} +6.24153 q^{23} +1.90335 q^{24} +1.00000 q^{25} +1.00000 q^{26} -4.52477 q^{27} -3.95405 q^{28} +4.15488 q^{29} -1.90335 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.69481 q^{33} +6.51985 q^{34} +3.95405 q^{35} +0.622734 q^{36} +6.70344 q^{37} -4.03070 q^{38} +1.90335 q^{39} -1.00000 q^{40} +1.92050 q^{41} -7.52593 q^{42} +11.3340 q^{43} +0.890437 q^{44} -0.622734 q^{45} +6.24153 q^{46} +11.7535 q^{47} +1.90335 q^{48} +8.63451 q^{49} +1.00000 q^{50} +12.4095 q^{51} +1.00000 q^{52} -4.78854 q^{53} -4.52477 q^{54} -0.890437 q^{55} -3.95405 q^{56} -7.67182 q^{57} +4.15488 q^{58} -13.0061 q^{59} -1.90335 q^{60} +4.43837 q^{61} +1.00000 q^{62} -2.46232 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.69481 q^{66} +4.30947 q^{67} +6.51985 q^{68} +11.8798 q^{69} +3.95405 q^{70} +6.03915 q^{71} +0.622734 q^{72} +9.31710 q^{73} +6.70344 q^{74} +1.90335 q^{75} -4.03070 q^{76} -3.52083 q^{77} +1.90335 q^{78} +1.27976 q^{79} -1.00000 q^{80} -10.4804 q^{81} +1.92050 q^{82} +2.95491 q^{83} -7.52593 q^{84} -6.51985 q^{85} +11.3340 q^{86} +7.90818 q^{87} +0.890437 q^{88} -15.7998 q^{89} -0.622734 q^{90} -3.95405 q^{91} +6.24153 q^{92} +1.90335 q^{93} +11.7535 q^{94} +4.03070 q^{95} +1.90335 q^{96} -10.1253 q^{97} +8.63451 q^{98} +0.554505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

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