LMFDB - Embedded newform 4730.2.a.be.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 $ x^12 - 3x^11 - 26x^10 + 79x^9 + 247x^8 - 766x^7 - 1023x^6 + 3281x^5 + 1634x^4 - 5557x^3 - 483x^2 + 1648*x + 392
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.94615$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.94615 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.94615 q^{6} -1.80392 q^{7} +1.00000 q^{8} +0.787492 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.94615 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.94615 q^{6} -1.80392 q^{7} +1.00000 q^{8} +0.787492 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.94615 q^{12} -3.07092 q^{13} -1.80392 q^{14} -1.94615 q^{15} +1.00000 q^{16} -2.66744 q^{17} +0.787492 q^{18} -7.67236 q^{19} +1.00000 q^{20} +3.51070 q^{21} -1.00000 q^{22} +5.07092 q^{23} -1.94615 q^{24} +1.00000 q^{25} -3.07092 q^{26} +4.30587 q^{27} -1.80392 q^{28} +6.04298 q^{29} -1.94615 q^{30} -6.12573 q^{31} +1.00000 q^{32} +1.94615 q^{33} -2.66744 q^{34} -1.80392 q^{35} +0.787492 q^{36} +6.64486 q^{37} -7.67236 q^{38} +5.97647 q^{39} +1.00000 q^{40} +3.25559 q^{41} +3.51070 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.787492 q^{45} +5.07092 q^{46} -9.42291 q^{47} -1.94615 q^{48} -3.74586 q^{49} +1.00000 q^{50} +5.19123 q^{51} -3.07092 q^{52} +8.46618 q^{53} +4.30587 q^{54} -1.00000 q^{55} -1.80392 q^{56} +14.9316 q^{57} +6.04298 q^{58} +4.12176 q^{59} -1.94615 q^{60} +8.30029 q^{61} -6.12573 q^{62} -1.42058 q^{63} +1.00000 q^{64} -3.07092 q^{65} +1.94615 q^{66} +6.38267 q^{67} -2.66744 q^{68} -9.86877 q^{69} -1.80392 q^{70} +7.02540 q^{71} +0.787492 q^{72} -6.73478 q^{73} +6.64486 q^{74} -1.94615 q^{75} -7.67236 q^{76} +1.80392 q^{77} +5.97647 q^{78} +15.7403 q^{79} +1.00000 q^{80} -10.7423 q^{81} +3.25559 q^{82} +8.30389 q^{83} +3.51070 q^{84} -2.66744 q^{85} +1.00000 q^{86} -11.7605 q^{87} -1.00000 q^{88} +0.597136 q^{89} +0.787492 q^{90} +5.53971 q^{91} +5.07092 q^{92} +11.9216 q^{93} -9.42291 q^{94} -7.67236 q^{95} -1.94615 q^{96} +11.1598 q^{97} -3.74586 q^{98} -0.787492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * 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
$3$	−1.94615	−1.12361	−0.561805	−	0.827270i	$-0.689893\pi$
$3$	−1.94615	−1.12361	−0.561805	+	0.827270i	$0.689893\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.94615	−0.794512
$7$	−1.80392	−0.681819	−0.340910	−	0.940096i	$-0.610735\pi$
$7$	−1.80392	−0.681819	−0.340910	+	0.940096i	$0.610735\pi$
$8$	1.00000	0.353553
$9$	0.787492	0.262497
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.94615	−0.561805
$13$	−3.07092	−0.851721	−0.425860	−	0.904789i	$-0.640029\pi$
$13$	−3.07092	−0.851721	−0.425860	+	0.904789i	$0.640029\pi$
$14$	−1.80392	−0.482119
$15$	−1.94615	−0.502493
$16$	1.00000	0.250000
$17$	−2.66744	−0.646949	−0.323474	−	0.946237i	$-0.604851\pi$
$17$	−2.66744	−0.646949	−0.323474	+	0.946237i	$0.604851\pi$
$18$	0.787492	0.185614
$19$	−7.67236	−1.76016	−0.880081	−	0.474824i	$-0.842512\pi$
$19$	−7.67236	−1.76016	−0.880081	+	0.474824i	$0.842512\pi$
$20$	1.00000	0.223607
$21$	3.51070	0.766098
$22$	−1.00000	−0.213201
$23$	5.07092	1.05736	0.528680	−	0.848821i	$-0.322687\pi$
$23$	5.07092	1.05736	0.528680	+	0.848821i	$0.322687\pi$
$24$	−1.94615	−0.397256
$25$	1.00000	0.200000
$26$	−3.07092	−0.602258
$27$	4.30587	0.828665
$28$	−1.80392	−0.340910
$29$	6.04298	1.12215	0.561077	−	0.827764i	$-0.310387\pi$
$29$	6.04298	1.12215	0.561077	+	0.827764i	$0.310387\pi$
$30$	−1.94615	−0.355316
$31$	−6.12573	−1.10021	−0.550107	−	0.835094i	$-0.685413\pi$
$31$	−6.12573	−1.10021	−0.550107	+	0.835094i	$0.685413\pi$
$32$	1.00000	0.176777
$33$	1.94615	0.338781
$34$	−2.66744	−0.457462
$35$	−1.80392	−0.304919
$36$	0.787492	0.131249
$37$	6.64486	1.09241	0.546204	−	0.837652i	$-0.316072\pi$
$37$	6.64486	1.09241	0.546204	+	0.837652i	$0.316072\pi$
$38$	−7.67236	−1.24462
$39$	5.97647	0.957001
$40$	1.00000	0.158114
$41$	3.25559	0.508437	0.254219	−	0.967147i	$-0.418182\pi$
$41$	3.25559	0.508437	0.254219	+	0.967147i	$0.418182\pi$
$42$	3.51070	0.541713
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	0.787492	0.117392
$46$	5.07092	0.747667
$47$	−9.42291	−1.37447	−0.687236	−	0.726434i	$-0.741176\pi$
$47$	−9.42291	−1.37447	−0.687236	+	0.726434i	$0.741176\pi$
$48$	−1.94615	−0.280902
$49$	−3.74586	−0.535122
$50$	1.00000	0.141421
$51$	5.19123	0.726917
$52$	−3.07092	−0.425860
$53$	8.46618	1.16292	0.581460	−	0.813575i	$-0.302482\pi$
$53$	8.46618	1.16292	0.581460	+	0.813575i	$0.302482\pi$
$54$	4.30587	0.585954
$55$	−1.00000	−0.134840
$56$	−1.80392	−0.241060
$57$	14.9316	1.97773
$58$	6.04298	0.793483
$59$	4.12176	0.536607	0.268304	−	0.963334i	$-0.413537\pi$
$59$	4.12176	0.536607	0.268304	+	0.963334i	$0.413537\pi$
$60$	−1.94615	−0.251247
$61$	8.30029	1.06274	0.531372	−	0.847139i	$-0.321677\pi$
$61$	8.30029	1.06274	0.531372	+	0.847139i	$0.321677\pi$
$62$	−6.12573	−0.777968
$63$	−1.42058	−0.178976
$64$	1.00000	0.125000
$65$	−3.07092	−0.380901
$66$	1.94615	0.239554
$67$	6.38267	0.779767	0.389883	−	0.920864i	$-0.372515\pi$
$67$	6.38267	0.779767	0.389883	+	0.920864i	$0.372515\pi$
$68$	−2.66744	−0.323474
$69$	−9.86877	−1.18806
$70$	−1.80392	−0.215610
$71$	7.02540	0.833762	0.416881	−	0.908961i	$-0.363123\pi$
$71$	7.02540	0.833762	0.416881	+	0.908961i	$0.363123\pi$
$72$	0.787492	0.0928068
$73$	−6.73478	−0.788246	−0.394123	−	0.919058i	$-0.628952\pi$
$73$	−6.73478	−0.788246	−0.394123	+	0.919058i	$0.628952\pi$
$74$	6.64486	0.772449
$75$	−1.94615	−0.224722
$76$	−7.67236	−0.880081
$77$	1.80392	0.205576
$78$	5.97647	0.676702
$79$	15.7403	1.77093	0.885464	−	0.464708i	$-0.153841\pi$
$79$	15.7403	1.77093	0.885464	+	0.464708i	$0.153841\pi$
$80$	1.00000	0.111803
$81$	−10.7423	−1.19359
$82$	3.25559	0.359519
$83$	8.30389	0.911470	0.455735	−	0.890115i	$-0.349376\pi$
$83$	8.30389	0.911470	0.455735	+	0.890115i	$0.349376\pi$
$84$	3.51070	0.383049
$85$	−2.66744	−0.289324
$86$	1.00000	0.107833
$87$	−11.7605	−1.26086
$88$	−1.00000	−0.106600
$89$	0.597136	0.0632963	0.0316482	−	0.999499i	$-0.489924\pi$
$89$	0.597136	0.0632963	0.0316482	+	0.999499i	$0.489924\pi$
$90$	0.787492	0.0830089
$91$	5.53971	0.580720
$92$	5.07092	0.528680
$93$	11.9216	1.23621
$94$	−9.42291	−0.971899
$95$	−7.67236	−0.787168
$96$	−1.94615	−0.198628
$97$	11.1598	1.13311	0.566553	−	0.824025i	$-0.308277\pi$
$97$	11.1598	1.13311	0.566553	+	0.824025i	$0.308277\pi$
$98$	−3.74586	−0.378389
$99$	−0.787492	−0.0791459
$100$	1.00000	0.100000
$101$	2.12892	0.211835	0.105918	−	0.994375i	$-0.466222\pi$
$101$	2.12892	0.211835	0.105918	+	0.994375i	$0.466222\pi$
$102$	5.19123	0.514008
$103$	−14.9767	−1.47570	−0.737850	−	0.674965i	$-0.764159\pi$
$103$	−14.9767	−1.47570	−0.737850	+	0.674965i	$0.764159\pi$
$104$	−3.07092	−0.301129
$105$	3.51070	0.342610
$106$	8.46618	0.822308
$107$	8.15661	0.788529	0.394265	−	0.918997i	$-0.370999\pi$
$107$	8.15661	0.788529	0.394265	+	0.918997i	$0.370999\pi$
$108$	4.30587	0.414332
$109$	1.25351	0.120064	0.0600320	−	0.998196i	$-0.480880\pi$
$109$	1.25351	0.120064	0.0600320	+	0.998196i	$0.480880\pi$
$110$	−1.00000	−0.0953463
$111$	−12.9319	−1.22744
$112$	−1.80392	−0.170455
$113$	11.4892	1.08082	0.540408	−	0.841403i	$-0.318270\pi$
$113$	11.4892	1.08082	0.540408	+	0.841403i	$0.318270\pi$
$114$	14.9316	1.39847
$115$	5.07092	0.472866
$116$	6.04298	0.561077
$117$	−2.41833	−0.223574
$118$	4.12176	0.379439
$119$	4.81185	0.441102
$120$	−1.94615	−0.177658
$121$	1.00000	0.0909091
$122$	8.30029	0.751473
$123$	−6.33585	−0.571285
$124$	−6.12573	−0.550107
$125$	1.00000	0.0894427
$126$	−1.42058	−0.126555
$127$	−19.9054	−1.76632	−0.883159	−	0.469073i	$-0.844588\pi$
$127$	−19.9054	−1.76632	−0.883159	+	0.469073i	$0.844588\pi$
$128$	1.00000	0.0883883
$129$	−1.94615	−0.171349
$130$	−3.07092	−0.269338
$131$	−2.04693	−0.178841	−0.0894206	−	0.995994i	$-0.528502\pi$
$131$	−2.04693	−0.178841	−0.0894206	+	0.995994i	$0.528502\pi$
$132$	1.94615	0.169390
$133$	13.8404	1.20011
$134$	6.38267	0.551379
$135$	4.30587	0.370590
$136$	−2.66744	−0.228731
$137$	−2.08422	−0.178067	−0.0890335	−	0.996029i	$-0.528378\pi$
$137$	−2.08422	−0.178067	−0.0890335	+	0.996029i	$0.528378\pi$
$138$	−9.86877	−0.840085
$139$	−20.3274	−1.72415	−0.862075	−	0.506781i	$-0.830835\pi$
$139$	−20.3274	−1.72415	−0.862075	+	0.506781i	$0.830835\pi$
$140$	−1.80392	−0.152459
$141$	18.3384	1.54437
$142$	7.02540	0.589559
$143$	3.07092	0.256804
$144$	0.787492	0.0656243
$145$	6.04298	0.501842
$146$	−6.73478	−0.557374
$147$	7.28999	0.601268
$148$	6.64486	0.546204
$149$	17.2922	1.41663	0.708316	−	0.705895i	$-0.249455\pi$
$149$	17.2922	1.41663	0.708316	+	0.705895i	$0.249455\pi$
$150$	−1.94615	−0.158902
$151$	−2.41168	−0.196260	−0.0981298	−	0.995174i	$-0.531286\pi$
$151$	−2.41168	−0.196260	−0.0981298	+	0.995174i	$0.531286\pi$
$152$	−7.67236	−0.622311
$153$	−2.10059	−0.169822
$154$	1.80392	0.145364
$155$	−6.12573	−0.492030
$156$	5.97647	0.478501
$157$	−12.7552	−1.01798	−0.508989	−	0.860773i	$-0.669981\pi$
$157$	−12.7552	−1.01798	−0.508989	+	0.860773i	$0.669981\pi$
$158$	15.7403	1.25223
$159$	−16.4764	−1.30667
$160$	1.00000	0.0790569
$161$	−9.14756	−0.720929
$162$	−10.7423	−0.843997
$163$	−1.86939	−0.146422	−0.0732108	−	0.997316i	$-0.523325\pi$
$163$	−1.86939	−0.146422	−0.0732108	+	0.997316i	$0.523325\pi$
$164$	3.25559	0.254219
$165$	1.94615	0.151507
$166$	8.30389	0.644507
$167$	25.2636	1.95496	0.977480	−	0.211029i	$-0.0676814\pi$
$167$	25.2636	1.95496	0.977480	+	0.211029i	$0.0676814\pi$
$168$	3.51070	0.270857
$169$	−3.56943	−0.274572
$170$	−2.66744	−0.204583
$171$	−6.04193	−0.462038
$172$	1.00000	0.0762493
$173$	22.5713	1.71606	0.858032	−	0.513596i	$-0.171687\pi$
$173$	22.5713	1.71606	0.858032	+	0.513596i	$0.171687\pi$
$174$	−11.7605	−0.891564
$175$	−1.80392	−0.136364
$176$	−1.00000	−0.0753778
$177$	−8.02155	−0.602937
$178$	0.597136	0.0447572
$179$	−17.0575	−1.27494	−0.637469	−	0.770476i	$-0.720019\pi$
$179$	−17.0575	−1.27494	−0.637469	+	0.770476i	$0.720019\pi$
$180$	0.787492	0.0586962
$181$	−11.8662	−0.882007	−0.441004	−	0.897505i	$-0.645377\pi$
$181$	−11.8662	−0.882007	−0.441004	+	0.897505i	$0.645377\pi$
$182$	5.53971	0.410631
$183$	−16.1536	−1.19411
$184$	5.07092	0.373833
$185$	6.64486	0.488540
$186$	11.9216	0.874132
$187$	2.66744	0.195062
$188$	−9.42291	−0.687236
$189$	−7.76746	−0.565000
$190$	−7.67236	−0.556612
$191$	−9.03514	−0.653760	−0.326880	−	0.945066i	$-0.605997\pi$
$191$	−9.03514	−0.653760	−0.326880	+	0.945066i	$0.605997\pi$
$192$	−1.94615	−0.140451
$193$	19.0304	1.36984	0.684918	−	0.728621i	$-0.259838\pi$
$193$	19.0304	1.36984	0.684918	+	0.728621i	$0.259838\pi$
$194$	11.1598	0.801227
$195$	5.97647	0.427984
$196$	−3.74586	−0.267561
$197$	−8.57050	−0.610623	−0.305311	−	0.952253i	$-0.598761\pi$
$197$	−8.57050	−0.610623	−0.305311	+	0.952253i	$0.598761\pi$
$198$	−0.787492	−0.0559646
$199$	−7.56214	−0.536066	−0.268033	−	0.963410i	$-0.586374\pi$
$199$	−7.56214	−0.536066	−0.268033	+	0.963410i	$0.586374\pi$
$200$	1.00000	0.0707107
$201$	−12.4216	−0.876153
$202$	2.12892	0.149790
$203$	−10.9011	−0.765106
$204$	5.19123	0.363459
$205$	3.25559	0.227380
$206$	−14.9767	−1.04348
$207$	3.99331	0.277554
$208$	−3.07092	−0.212930
$209$	7.67236	0.530709
$210$	3.51070	0.242262
$211$	21.6038	1.48727	0.743635	−	0.668586i	$-0.233100\pi$
$211$	21.6038	1.48727	0.743635	+	0.668586i	$0.233100\pi$
$212$	8.46618	0.581460
$213$	−13.6725	−0.936822
$214$	8.15661	0.557574
$215$	1.00000	0.0681994
$216$	4.30587	0.292977
$217$	11.0504	0.750147
$218$	1.25351	0.0848981
$219$	13.1069	0.885681
$220$	−1.00000	−0.0674200
$221$	8.19150	0.551020
$222$	−12.9319	−0.867931
$223$	12.6642	0.848060	0.424030	−	0.905648i	$-0.360615\pi$
$223$	12.6642	0.848060	0.424030	+	0.905648i	$0.360615\pi$
$224$	−1.80392	−0.120530
$225$	0.787492	0.0524995
$226$	11.4892	0.764252
$227$	24.1290	1.60150	0.800751	−	0.598998i	$-0.204434\pi$
$227$	24.1290	1.60150	0.800751	+	0.598998i	$0.204434\pi$
$228$	14.9316	0.988867
$229$	−24.5929	−1.62515	−0.812573	−	0.582860i	$-0.801934\pi$
$229$	−24.5929	−1.62515	−0.812573	+	0.582860i	$0.801934\pi$
$230$	5.07092	0.334367
$231$	−3.51070	−0.230987
$232$	6.04298	0.396741
$233$	26.9616	1.76631	0.883157	−	0.469077i	$-0.155413\pi$
$233$	26.9616	1.76631	0.883157	+	0.469077i	$0.155413\pi$
$234$	−2.41833	−0.158091
$235$	−9.42291	−0.614683
$236$	4.12176	0.268304
$237$	−30.6330	−1.98983
$238$	4.81185	0.311906
$239$	15.3401	0.992270	0.496135	−	0.868245i	$-0.334752\pi$
$239$	15.3401	0.992270	0.496135	+	0.868245i	$0.334752\pi$
$240$	−1.94615	−0.125623
$241$	−11.2781	−0.726487	−0.363244	−	0.931694i	$-0.618331\pi$
$241$	−11.2781	−0.726487	−0.363244	+	0.931694i	$0.618331\pi$
$242$	1.00000	0.0642824
$243$	7.98856	0.512467
$244$	8.30029	0.531372
$245$	−3.74586	−0.239314
$246$	−6.33585	−0.403959
$247$	23.5612	1.49917
$248$	−6.12573	−0.388984
$249$	−16.1606	−1.02414
$250$	1.00000	0.0632456
$251$	−1.91281	−0.120736	−0.0603678	−	0.998176i	$-0.519227\pi$
$251$	−1.91281	−0.120736	−0.0603678	+	0.998176i	$0.519227\pi$
$252$	−1.42058	−0.0894879
$253$	−5.07092	−0.318806
$254$	−19.9054	−1.24898
$255$	5.19123	0.325087
$256$	1.00000	0.0625000
$257$	14.3787	0.896920	0.448460	−	0.893803i	$-0.351973\pi$
$257$	14.3787	0.896920	0.448460	+	0.893803i	$0.351973\pi$
$258$	−1.94615	−0.121162
$259$	−11.9868	−0.744825
$260$	−3.07092	−0.190451
$261$	4.75880	0.294562
$262$	−2.04693	−0.126460
$263$	13.3732	0.824624	0.412312	−	0.911043i	$-0.364721\pi$
$263$	13.3732	0.824624	0.412312	+	0.911043i	$0.364721\pi$
$264$	1.94615	0.119777
$265$	8.46618	0.520073
$266$	13.8404	0.848607
$267$	−1.16212	−0.0711203
$268$	6.38267	0.389883
$269$	3.86207	0.235475	0.117737	−	0.993045i	$-0.462436\pi$
$269$	3.86207	0.235475	0.117737	+	0.993045i	$0.462436\pi$
$270$	4.30587	0.262047
$271$	17.8656	1.08526	0.542630	−	0.839972i	$-0.317429\pi$
$271$	17.8656	1.08526	0.542630	+	0.839972i	$0.317429\pi$
$272$	−2.66744	−0.161737
$273$	−10.7811	−0.652502
$274$	−2.08422	−0.125912
$275$	−1.00000	−0.0603023
$276$	−9.86877	−0.594030
$277$	3.55770	0.213762	0.106881	−	0.994272i	$-0.465914\pi$
$277$	3.55770	0.213762	0.106881	+	0.994272i	$0.465914\pi$
$278$	−20.3274	−1.21916
$279$	−4.82396	−0.288803
$280$	−1.80392	−0.107805
$281$	18.7205	1.11677	0.558385	−	0.829582i	$-0.311421\pi$
$281$	18.7205	1.11677	0.558385	+	0.829582i	$0.311421\pi$
$282$	18.3384	1.09203
$283$	22.2481	1.32251	0.661255	−	0.750161i	$-0.270024\pi$
$283$	22.2481	1.32251	0.661255	+	0.750161i	$0.270024\pi$
$284$	7.02540	0.416881
$285$	14.9316	0.884469
$286$	3.07092	0.181588
$287$	−5.87283	−0.346662
$288$	0.787492	0.0464034
$289$	−9.88478	−0.581458
$290$	6.04298	0.354856
$291$	−21.7186	−1.27317
$292$	−6.73478	−0.394123
$293$	16.1883	0.945728	0.472864	−	0.881135i	$-0.343220\pi$
$293$	16.1883	0.945728	0.472864	+	0.881135i	$0.343220\pi$
$294$	7.28999	0.425161
$295$	4.12176	0.239978
$296$	6.64486	0.386225
$297$	−4.30587	−0.249852
$298$	17.2922	1.00171
$299$	−15.5724	−0.900576
$300$	−1.94615	−0.112361
$301$	−1.80392	−0.103976
$302$	−2.41168	−0.138777
$303$	−4.14319	−0.238020
$304$	−7.67236	−0.440040
$305$	8.30029	0.475273
$306$	−2.10059	−0.120082
$307$	9.08961	0.518771	0.259386	−	0.965774i	$-0.416480\pi$
$307$	9.08961	0.518771	0.259386	+	0.965774i	$0.416480\pi$
$308$	1.80392	0.102788
$309$	29.1469	1.65811
$310$	−6.12573	−0.347918
$311$	12.2692	0.695724	0.347862	−	0.937546i	$-0.386908\pi$
$311$	12.2692	0.695724	0.347862	+	0.937546i	$0.386908\pi$
$312$	5.97647	0.338351
$313$	29.4204	1.66294	0.831471	−	0.555568i	$-0.187499\pi$
$313$	29.4204	1.66294	0.831471	+	0.555568i	$0.187499\pi$
$314$	−12.7552	−0.719819
$315$	−1.42058	−0.0800404
$316$	15.7403	0.885464
$317$	−31.2392	−1.75457	−0.877285	−	0.479969i	$-0.840648\pi$
$317$	−31.2392	−1.75457	−0.877285	+	0.479969i	$0.840648\pi$
$318$	−16.4764	−0.923953
$319$	−6.04298	−0.338342
$320$	1.00000	0.0559017
$321$	−15.8740	−0.885998
$322$	−9.14756	−0.509774
$323$	20.4656	1.13873
$324$	−10.7423	−0.596796
$325$	−3.07092	−0.170344
$326$	−1.86939	−0.103536
$327$	−2.43951	−0.134905
$328$	3.25559	0.179760
$329$	16.9982	0.937142
$330$	1.94615	0.107132
$331$	−0.985673	−0.0541775	−0.0270887	−	0.999633i	$-0.508624\pi$
$331$	−0.985673	−0.0541775	−0.0270887	+	0.999633i	$0.508624\pi$
$332$	8.30389	0.455735
$333$	5.23277	0.286754
$334$	25.2636	1.38237
$335$	6.38267	0.348722
$336$	3.51070	0.191525
$337$	21.8560	1.19057	0.595287	−	0.803513i	$-0.297038\pi$
$337$	21.8560	1.19057	0.595287	+	0.803513i	$0.297038\pi$
$338$	−3.56943	−0.194151
$339$	−22.3597	−1.21441
$340$	−2.66744	−0.144662
$341$	6.12573	0.331727
$342$	−6.04193	−0.326710
$343$	19.3847	1.04668
$344$	1.00000	0.0539164
$345$	−9.86877	−0.531317
$346$	22.5713	1.21344
$347$	−21.7521	−1.16771	−0.583856	−	0.811857i	$-0.698457\pi$
$347$	−21.7521	−1.16771	−0.583856	+	0.811857i	$0.698457\pi$
$348$	−11.7605	−0.630431
$349$	−34.1659	−1.82886	−0.914429	−	0.404746i	$-0.867360\pi$
$349$	−34.1659	−1.82886	−0.914429	+	0.404746i	$0.867360\pi$
$350$	−1.80392	−0.0964238
$351$	−13.2230	−0.705791
$352$	−1.00000	−0.0533002
$353$	−0.428704	−0.0228176	−0.0114088	−	0.999935i	$-0.503632\pi$
$353$	−0.428704	−0.0228176	−0.0114088	+	0.999935i	$0.503632\pi$
$354$	−8.02155	−0.426341
$355$	7.02540	0.372870
$356$	0.597136	0.0316482
$357$	−9.36458	−0.495626
$358$	−17.0575	−0.901517
$359$	−23.1249	−1.22049	−0.610243	−	0.792214i	$-0.708928\pi$
$359$	−23.1249	−1.22049	−0.610243	+	0.792214i	$0.708928\pi$
$360$	0.787492	0.0415045
$361$	39.8652	2.09817
$362$	−11.8662	−0.623673
$363$	−1.94615	−0.102146
$364$	5.53971	0.290360
$365$	−6.73478	−0.352514
$366$	−16.1536	−0.844362
$367$	−1.79699	−0.0938023	−0.0469011	−	0.998900i	$-0.514935\pi$
$367$	−1.79699	−0.0938023	−0.0469011	+	0.998900i	$0.514935\pi$
$368$	5.07092	0.264340
$369$	2.56375	0.133463
$370$	6.64486	0.345450
$371$	−15.2723	−0.792901
$372$	11.9216	0.618105
$373$	21.7123	1.12422	0.562110	−	0.827063i	$-0.309990\pi$
$373$	21.7123	1.12422	0.562110	+	0.827063i	$0.309990\pi$
$374$	2.66744	0.137930
$375$	−1.94615	−0.100499
$376$	−9.42291	−0.485949
$377$	−18.5575	−0.955762
$378$	−7.76746	−0.399515
$379$	13.5210	0.694525	0.347262	−	0.937768i	$-0.387111\pi$
$379$	13.5210	0.694525	0.347262	+	0.937768i	$0.387111\pi$
$380$	−7.67236	−0.393584
$381$	38.7389	1.98465
$382$	−9.03514	−0.462278
$383$	10.8496	0.554389	0.277194	−	0.960814i	$-0.410595\pi$
$383$	10.8496	0.554389	0.277194	+	0.960814i	$0.410595\pi$
$384$	−1.94615	−0.0993139
$385$	1.80392	0.0919365
$386$	19.0304	0.968620
$387$	0.787492	0.0400305
$388$	11.1598	0.566553
$389$	15.3610	0.778834	0.389417	−	0.921062i	$-0.372677\pi$
$389$	15.3610	0.778834	0.389417	+	0.921062i	$0.372677\pi$
$390$	5.97647	0.302630
$391$	−13.5264	−0.684058
$392$	−3.74586	−0.189194
$393$	3.98363	0.200948
$394$	−8.57050	−0.431775
$395$	15.7403	0.791983
$396$	−0.787492	−0.0395730
$397$	−10.9909	−0.551618	−0.275809	−	0.961212i	$-0.588946\pi$
$397$	−10.9909	−0.551618	−0.275809	+	0.961212i	$0.588946\pi$
$398$	−7.56214	−0.379056
$399$	−26.9354	−1.34846
$400$	1.00000	0.0500000
$401$	19.2341	0.960503	0.480251	−	0.877131i	$-0.340545\pi$
$401$	19.2341	0.960503	0.480251	+	0.877131i	$0.340545\pi$
$402$	−12.4216	−0.619534
$403$	18.8116	0.937075
$404$	2.12892	0.105918
$405$	−10.7423	−0.533791
$406$	−10.9011	−0.541012
$407$	−6.64486	−0.329373
$408$	5.19123	0.257004
$409$	8.25725	0.408295	0.204147	−	0.978940i	$-0.434558\pi$
$409$	8.25725	0.408295	0.204147	+	0.978940i	$0.434558\pi$
$410$	3.25559	0.160782
$411$	4.05620	0.200078
$412$	−14.9767	−0.737850
$413$	−7.43534	−0.365869
$414$	3.99331	0.196261
$415$	8.30389	0.407622
$416$	−3.07092	−0.150564
$417$	39.5602	1.93727
$418$	7.67236	0.375268
$419$	−22.5936	−1.10377	−0.551884	−	0.833921i	$-0.686091\pi$
$419$	−22.5936	−1.10377	−0.551884	+	0.833921i	$0.686091\pi$
$420$	3.51070	0.171305
$421$	−1.06066	−0.0516933	−0.0258467	−	0.999666i	$-0.508228\pi$
$421$	−1.06066	−0.0516933	−0.0258467	+	0.999666i	$0.508228\pi$
$422$	21.6038	1.05166
$423$	−7.42047	−0.360795
$424$	8.46618	0.411154
$425$	−2.66744	−0.129390
$426$	−13.6725	−0.662433
$427$	−14.9731	−0.724599
$428$	8.15661	0.394265
$429$	−5.97647	−0.288547
$430$	1.00000	0.0482243
$431$	−29.3695	−1.41468	−0.707338	−	0.706875i	$-0.750104\pi$
$431$	−29.3695	−1.41468	−0.707338	+	0.706875i	$0.750104\pi$
$432$	4.30587	0.207166
$433$	−28.5671	−1.37285	−0.686424	−	0.727202i	$-0.740821\pi$
$433$	−28.5671	−1.37285	−0.686424	+	0.727202i	$0.740821\pi$
$434$	11.0504	0.530434
$435$	−11.7605	−0.563875
$436$	1.25351	0.0600320
$437$	−38.9060	−1.86113
$438$	13.1069	0.626271
$439$	−1.69956	−0.0811158	−0.0405579	−	0.999177i	$-0.512914\pi$
$439$	−1.69956	−0.0811158	−0.0405579	+	0.999177i	$0.512914\pi$
$440$	−1.00000	−0.0476731
$441$	−2.94983	−0.140468
$442$	8.19150	0.389630
$443$	−31.1897	−1.48187	−0.740933	−	0.671579i	$-0.765616\pi$
$443$	−31.1897	−1.48187	−0.740933	+	0.671579i	$0.765616\pi$
$444$	−12.9319	−0.613720
$445$	0.597136	0.0283070
$446$	12.6642	0.599669
$447$	−33.6532	−1.59174
$448$	−1.80392	−0.0852274
$449$	20.9363	0.988047	0.494024	−	0.869449i	$-0.335526\pi$
$449$	20.9363	0.988047	0.494024	+	0.869449i	$0.335526\pi$
$450$	0.787492	0.0371227
$451$	−3.25559	−0.153300
$452$	11.4892	0.540408
$453$	4.69348	0.220519
$454$	24.1290	1.13243
$455$	5.53971	0.259706
$456$	14.9316	0.699234
$457$	21.5884	1.00986	0.504931	−	0.863160i	$-0.331518\pi$
$457$	21.5884	1.00986	0.504931	+	0.863160i	$0.331518\pi$
$458$	−24.5929	−1.14915
$459$	−11.4856	−0.536103
$460$	5.07092	0.236433
$461$	40.7731	1.89899	0.949496	−	0.313779i	$-0.101595\pi$
$461$	40.7731	1.89899	0.949496	+	0.313779i	$0.101595\pi$
$462$	−3.51070	−0.163333
$463$	−32.9637	−1.53196	−0.765978	−	0.642867i	$-0.777745\pi$
$463$	−32.9637	−1.53196	−0.765978	+	0.642867i	$0.777745\pi$
$464$	6.04298	0.280538
$465$	11.9216	0.552850
$466$	26.9616	1.24897
$467$	6.01996	0.278571	0.139285	−	0.990252i	$-0.455519\pi$
$467$	6.01996	0.278571	0.139285	+	0.990252i	$0.455519\pi$
$468$	−2.41833	−0.111787
$469$	−11.5138	−0.531660
$470$	−9.42291	−0.434646
$471$	24.8236	1.14381
$472$	4.12176	0.189719
$473$	−1.00000	−0.0459800
$474$	−30.6330	−1.40702
$475$	−7.67236	−0.352032
$476$	4.81185	0.220551
$477$	6.66705	0.305263
$478$	15.3401	0.701641
$479$	−21.0217	−0.960507	−0.480253	−	0.877130i	$-0.659455\pi$
$479$	−21.0217	−0.960507	−0.480253	+	0.877130i	$0.659455\pi$
$480$	−1.94615	−0.0888291
$481$	−20.4059	−0.930427
$482$	−11.2781	−0.513704
$483$	17.8025	0.810042
$484$	1.00000	0.0454545
$485$	11.1598	0.506740
$486$	7.98856	0.362369
$487$	−35.6027	−1.61331	−0.806656	−	0.591021i	$-0.798725\pi$
$487$	−35.6027	−1.61331	−0.806656	+	0.591021i	$0.798725\pi$
$488$	8.30029	0.375737
$489$	3.63810	0.164521
$490$	−3.74586	−0.169221
$491$	−39.5063	−1.78290	−0.891448	−	0.453123i	$-0.850310\pi$
$491$	−39.5063	−1.78290	−0.891448	+	0.453123i	$0.850310\pi$
$492$	−6.33585	−0.285642
$493$	−16.1193	−0.725976
$494$	23.5612	1.06007
$495$	−0.787492	−0.0353951
$496$	−6.12573	−0.275053
$497$	−12.6733	−0.568475
$498$	−16.1606	−0.724173
$499$	−29.3492	−1.31385	−0.656924	−	0.753956i	$-0.728143\pi$
$499$	−29.3492	−1.31385	−0.656924	+	0.753956i	$0.728143\pi$
$500$	1.00000	0.0447214
$501$	−49.1668	−2.19661
$502$	−1.91281	−0.0853729
$503$	41.1545	1.83499	0.917494	−	0.397749i	$-0.130209\pi$
$503$	41.1545	1.83499	0.917494	+	0.397749i	$0.130209\pi$
$504$	−1.42058	−0.0632775
$505$	2.12892	0.0947355
$506$	−5.07092	−0.225430
$507$	6.94664	0.308511
$508$	−19.9054	−0.883159
$509$	−30.5730	−1.35513	−0.677563	−	0.735465i	$-0.736964\pi$
$509$	−30.5730	−1.35513	−0.677563	+	0.735465i	$0.736964\pi$
$510$	5.19123	0.229871
$511$	12.1490	0.537442
$512$	1.00000	0.0441942
$513$	−33.0362	−1.45858
$514$	14.3787	0.634218
$515$	−14.9767	−0.659953
$516$	−1.94615	−0.0856744
$517$	9.42291	0.414419
$518$	−11.9868	−0.526671
$519$	−43.9271	−1.92819
$520$	−3.07092	−0.134669
$521$	−17.6279	−0.772291	−0.386145	−	0.922438i	$-0.626194\pi$
$521$	−17.6279	−0.772291	−0.386145	+	0.922438i	$0.626194\pi$
$522$	4.75880	0.208287
$523$	−32.4427	−1.41862	−0.709309	−	0.704898i	$-0.750993\pi$
$523$	−32.4427	−1.41862	−0.709309	+	0.704898i	$0.750993\pi$
$524$	−2.04693	−0.0894206
$525$	3.51070	0.153220
$526$	13.3732	0.583097
$527$	16.3400	0.711782
$528$	1.94615	0.0846952
$529$	2.71426	0.118011
$530$	8.46618	0.367747
$531$	3.24585	0.140858
$532$	13.8404	0.600056
$533$	−9.99765	−0.433046
$534$	−1.16212	−0.0502896
$535$	8.15661	0.352641
$536$	6.38267	0.275689
$537$	33.1964	1.43253
$538$	3.86207	0.166506
$539$	3.74586	0.161345
$540$	4.30587	0.185295
$541$	37.1940	1.59909	0.799547	−	0.600603i	$-0.205073\pi$
$541$	37.1940	1.59909	0.799547	+	0.600603i	$0.205073\pi$
$542$	17.8656	0.767395
$543$	23.0934	0.991032
$544$	−2.66744	−0.114365
$545$	1.25351	0.0536943
$546$	−10.7811	−0.461389
$547$	−17.0694	−0.729835	−0.364917	−	0.931040i	$-0.618903\pi$
$547$	−17.0694	−0.729835	−0.364917	+	0.931040i	$0.618903\pi$
$548$	−2.08422	−0.0890335
$549$	6.53641	0.278967
$550$	−1.00000	−0.0426401
$551$	−46.3640	−1.97517
$552$	−9.86877	−0.420043
$553$	−28.3944	−1.20745
$554$	3.55770	0.151152
$555$	−12.9319	−0.548928
$556$	−20.3274	−0.862075
$557$	−26.4689	−1.12152	−0.560762	−	0.827977i	$-0.689492\pi$
$557$	−26.4689	−1.12152	−0.560762	+	0.827977i	$0.689492\pi$
$558$	−4.82396	−0.204215
$559$	−3.07092	−0.129886
$560$	−1.80392	−0.0762297
$561$	−5.19123	−0.219174
$562$	18.7205	0.789675
$563$	36.0976	1.52133	0.760665	−	0.649144i	$-0.224873\pi$
$563$	36.0976	1.52133	0.760665	+	0.649144i	$0.224873\pi$
$564$	18.3384	0.772185
$565$	11.4892	0.483356
$566$	22.2481	0.935155
$567$	19.3784	0.813814
$568$	7.02540	0.294779
$569$	−8.84730	−0.370898	−0.185449	−	0.982654i	$-0.559374\pi$
$569$	−8.84730	−0.370898	−0.185449	+	0.982654i	$0.559374\pi$
$570$	14.9316	0.625414
$571$	13.6973	0.573213	0.286606	−	0.958048i	$-0.407473\pi$
$571$	13.6973	0.573213	0.286606	+	0.958048i	$0.407473\pi$
$572$	3.07092	0.128402
$573$	17.5837	0.734570
$574$	−5.87283	−0.245127
$575$	5.07092	0.211472
$576$	0.787492	0.0328122
$577$	30.5780	1.27298	0.636489	−	0.771286i	$-0.280386\pi$
$577$	30.5780	1.27298	0.636489	+	0.771286i	$0.280386\pi$
$578$	−9.88478	−0.411153
$579$	−37.0359	−1.53916
$580$	6.04298	0.250921
$581$	−14.9796	−0.621458
$582$	−21.7186	−0.900265
$583$	−8.46618	−0.350633
$584$	−6.73478	−0.278687
$585$	−2.41833	−0.0999855
$586$	16.1883	0.668731
$587$	−2.42159	−0.0999496	−0.0499748	−	0.998750i	$-0.515914\pi$
$587$	−2.42159	−0.0999496	−0.0499748	+	0.998750i	$0.515914\pi$
$588$	7.28999	0.300634
$589$	46.9988	1.93655
$590$	4.12176	0.169690
$591$	16.6795	0.686101
$592$	6.64486	0.273102
$593$	22.8268	0.937384	0.468692	−	0.883362i	$-0.344725\pi$
$593$	22.8268	0.937384	0.468692	+	0.883362i	$0.344725\pi$
$594$	−4.30587	−0.176672
$595$	4.81185	0.197267
$596$	17.2922	0.708316
$597$	14.7171	0.602329
$598$	−15.5724	−0.636803
$599$	−35.7442	−1.46047	−0.730234	−	0.683198i	$-0.760589\pi$
$599$	−35.7442	−1.46047	−0.730234	+	0.683198i	$0.760589\pi$
$600$	−1.94615	−0.0794512
$601$	42.0642	1.71583	0.857917	−	0.513789i	$-0.171758\pi$
$601$	42.0642	1.71583	0.857917	+	0.513789i	$0.171758\pi$
$602$	−1.80392	−0.0735225
$603$	5.02630	0.204687
$604$	−2.41168	−0.0981298
$605$	1.00000	0.0406558
$606$	−4.14319	−0.168305
$607$	6.69034	0.271553	0.135776	−	0.990740i	$-0.456647\pi$
$607$	6.69034	0.271553	0.135776	+	0.990740i	$0.456647\pi$
$608$	−7.67236	−0.311155
$609$	21.2151	0.859680
$610$	8.30029	0.336069
$611$	28.9370	1.17067
$612$	−2.10059	−0.0849111
$613$	−25.1359	−1.01523	−0.507616	−	0.861584i	$-0.669473\pi$
$613$	−25.1359	−1.01523	−0.507616	+	0.861584i	$0.669473\pi$
$614$	9.08961	0.366827
$615$	−6.33585	−0.255486
$616$	1.80392	0.0726822
$617$	25.6461	1.03247	0.516236	−	0.856446i	$-0.327333\pi$
$617$	25.6461	1.03247	0.516236	+	0.856446i	$0.327333\pi$
$618$	29.1469	1.17246
$619$	4.84131	0.194589	0.0972944	−	0.995256i	$-0.468981\pi$
$619$	4.84131	0.194589	0.0972944	+	0.995256i	$0.468981\pi$
$620$	−6.12573	−0.246015
$621$	21.8347	0.876197
$622$	12.2692	0.491951
$623$	−1.07719	−0.0431566
$624$	5.97647	0.239250
$625$	1.00000	0.0400000
$626$	29.4204	1.17588
$627$	−14.9316	−0.596309
$628$	−12.7552	−0.508989
$629$	−17.7247	−0.706732
$630$	−1.42058	−0.0565971
$631$	−39.1491	−1.55850	−0.779250	−	0.626713i	$-0.784400\pi$
$631$	−39.1491	−1.55850	−0.779250	+	0.626713i	$0.784400\pi$
$632$	15.7403	0.626117
$633$	−42.0443	−1.67111
$634$	−31.2392	−1.24067
$635$	−19.9054	−0.789922
$636$	−16.4764	−0.653333
$637$	11.5032	0.455775
$638$	−6.04298	−0.239244
$639$	5.53245	0.218860
$640$	1.00000	0.0395285
$641$	−14.7411	−0.582238	−0.291119	−	0.956687i	$-0.594028\pi$
$641$	−14.7411	−0.582238	−0.291119	+	0.956687i	$0.594028\pi$
$642$	−15.8740	−0.626495
$643$	−4.07803	−0.160822	−0.0804109	−	0.996762i	$-0.525623\pi$
$643$	−4.07803	−0.160822	−0.0804109	+	0.996762i	$0.525623\pi$
$644$	−9.14756	−0.360464
$645$	−1.94615	−0.0766295
$646$	20.4656	0.805206
$647$	8.68125	0.341295	0.170648	−	0.985332i	$-0.445414\pi$
$647$	8.68125	0.341295	0.170648	+	0.985332i	$0.445414\pi$
$648$	−10.7423	−0.421999
$649$	−4.12176	−0.161793
$650$	−3.07092	−0.120452
$651$	−21.5056	−0.842872
$652$	−1.86939	−0.0732108
$653$	−27.7927	−1.08761	−0.543807	−	0.839210i	$-0.683018\pi$
$653$	−27.7927	−1.08761	−0.543807	+	0.839210i	$0.683018\pi$
$654$	−2.43951	−0.0953923
$655$	−2.04693	−0.0799802
$656$	3.25559	0.127109
$657$	−5.30358	−0.206913
$658$	16.9982	0.662659
$659$	8.71197	0.339370	0.169685	−	0.985498i	$-0.445725\pi$
$659$	8.71197	0.339370	0.169685	+	0.985498i	$0.445725\pi$
$660$	1.94615	0.0757537
$661$	40.5867	1.57864	0.789320	−	0.613982i	$-0.210433\pi$
$661$	40.5867	1.57864	0.789320	+	0.613982i	$0.210433\pi$
$662$	−0.985673	−0.0383093
$663$	−15.9419	−0.619131
$664$	8.30389	0.322253
$665$	13.8404	0.536706
$666$	5.23277	0.202766
$667$	30.6435	1.18652
$668$	25.2636	0.977480
$669$	−24.6465	−0.952888
$670$	6.38267	0.246584
$671$	−8.30029	−0.320429
$672$	3.51070	0.135428
$673$	−24.1766	−0.931940	−0.465970	−	0.884801i	$-0.654295\pi$
$673$	−24.1766	−0.931940	−0.465970	+	0.884801i	$0.654295\pi$
$674$	21.8560	0.841863
$675$	4.30587	0.165733
$676$	−3.56943	−0.137286
$677$	34.0871	1.31007	0.655036	−	0.755597i	$-0.272653\pi$
$677$	34.0871	1.31007	0.655036	+	0.755597i	$0.272653\pi$
$678$	−22.3597	−0.858721
$679$	−20.1314	−0.772573
$680$	−2.66744	−0.102292
$681$	−46.9587	−1.79946
$682$	6.12573	0.234566
$683$	−13.8590	−0.530301	−0.265150	−	0.964207i	$-0.585422\pi$
$683$	−13.8590	−0.530301	−0.265150	+	0.964207i	$0.585422\pi$
$684$	−6.04193	−0.231019
$685$	−2.08422	−0.0796340
$686$	19.3847	0.740112
$687$	47.8615	1.82603
$688$	1.00000	0.0381246
$689$	−25.9990	−0.990482
$690$	−9.86877	−0.375698
$691$	15.2366	0.579628	0.289814	−	0.957083i	$-0.406407\pi$
$691$	15.2366	0.579628	0.289814	+	0.957083i	$0.406407\pi$
$692$	22.5713	0.858032
$693$	1.42058	0.0539632
$694$	−21.7521	−0.825697
$695$	−20.3274	−0.771063
$696$	−11.7605	−0.445782
$697$	−8.68407	−0.328933
$698$	−34.1659	−1.29320
$699$	−52.4713	−1.98465
$700$	−1.80392	−0.0681819
$701$	20.2220	0.763774	0.381887	−	0.924209i	$-0.375274\pi$
$701$	20.2220	0.763774	0.381887	+	0.924209i	$0.375274\pi$
$702$	−13.2230	−0.499070
$703$	−50.9818	−1.92281
$704$	−1.00000	−0.0376889
$705$	18.3384	0.690663
$706$	−0.428704	−0.0161345
$707$	−3.84040	−0.144433
$708$	−8.02155	−0.301468
$709$	9.28908	0.348859	0.174429	−	0.984670i	$-0.444192\pi$
$709$	9.28908	0.348859	0.174429	+	0.984670i	$0.444192\pi$
$710$	7.02540	0.263659
$711$	12.3954	0.464864
$712$	0.597136	0.0223786
$713$	−31.0631	−1.16332
$714$	−9.36458	−0.350461
$715$	3.07092	0.114846
$716$	−17.0575	−0.637469
$717$	−29.8541	−1.11492
$718$	−23.1249	−0.863014
$719$	−6.92118	−0.258117	−0.129058	−	0.991637i	$-0.541195\pi$
$719$	−6.92118	−0.258117	−0.129058	+	0.991637i	$0.541195\pi$
$720$	0.787492	0.0293481
$721$	27.0169	1.00616
$722$	39.8652	1.48363
$723$	21.9489	0.816287
$724$	−11.8662	−0.441004
$725$	6.04298	0.224431
$726$	−1.94615	−0.0722283
$727$	41.6626	1.54518	0.772591	−	0.634904i	$-0.218960\pi$
$727$	41.6626	1.54518	0.772591	+	0.634904i	$0.218960\pi$
$728$	5.53971	0.205315
$729$	16.6801	0.617780
$730$	−6.73478	−0.249265
$731$	−2.66744	−0.0986587
$732$	−16.1536	−0.597054
$733$	−47.2017	−1.74344	−0.871718	−	0.490008i	$-0.836994\pi$
$733$	−47.2017	−1.74344	−0.871718	+	0.490008i	$0.836994\pi$
$734$	−1.79699	−0.0663282
$735$	7.28999	0.268895
$736$	5.07092	0.186917
$737$	−6.38267	−0.235109
$738$	2.56375	0.0943729
$739$	40.8354	1.50215	0.751076	−	0.660215i	$-0.229535\pi$
$739$	40.8354	1.50215	0.751076	+	0.660215i	$0.229535\pi$
$740$	6.64486	0.244270
$741$	−45.8537	−1.68448
$742$	−15.2723	−0.560665
$743$	−2.26473	−0.0830851	−0.0415425	−	0.999137i	$-0.513227\pi$
$743$	−2.26473	−0.0830851	−0.0415425	+	0.999137i	$0.513227\pi$
$744$	11.9216	0.437066
$745$	17.2922	0.633537
$746$	21.7123	0.794943
$747$	6.53924	0.239258
$748$	2.66744	0.0975312
$749$	−14.7139	−0.537634
$750$	−1.94615	−0.0710633
$751$	−10.0313	−0.366047	−0.183023	−	0.983109i	$-0.558588\pi$
$751$	−10.0313	−0.366047	−0.183023	+	0.983109i	$0.558588\pi$
$752$	−9.42291	−0.343618
$753$	3.72261	0.135660
$754$	−18.5575	−0.675826
$755$	−2.41168	−0.0877700
$756$	−7.76746	−0.282500
$757$	−49.7002	−1.80639	−0.903193	−	0.429235i	$-0.858783\pi$
$757$	−49.7002	−1.80639	−0.903193	+	0.429235i	$0.858783\pi$
$758$	13.5210	0.491103
$759$	9.86877	0.358214
$760$	−7.67236	−0.278306
$761$	2.24241	0.0812871	0.0406436	−	0.999174i	$-0.487059\pi$
$761$	2.24241	0.0812871	0.0406436	+	0.999174i	$0.487059\pi$
$762$	38.7389	1.40336
$763$	−2.26123	−0.0818620
$764$	−9.03514	−0.326880
$765$	−2.10059	−0.0759468
$766$	10.8496	0.392012
$767$	−12.6576	−0.457040
$768$	−1.94615	−0.0702256
$769$	−30.0095	−1.08217	−0.541086	−	0.840967i	$-0.681987\pi$
$769$	−30.0095	−1.08217	−0.541086	+	0.840967i	$0.681987\pi$
$770$	1.80392	0.0650089
$771$	−27.9831	−1.00779
$772$	19.0304	0.684918
$773$	9.54302	0.343238	0.171619	−	0.985163i	$-0.445100\pi$
$773$	9.54302	0.343238	0.171619	+	0.985163i	$0.445100\pi$
$774$	0.787492	0.0283058
$775$	−6.12573	−0.220043
$776$	11.1598	0.400613
$777$	23.3281	0.836892
$778$	15.3610	0.550719
$779$	−24.9780	−0.894931
$780$	5.97647	0.213992
$781$	−7.02540	−0.251389
$782$	−13.5264	−0.483702
$783$	26.0203	0.929889
$784$	−3.74586	−0.133781
$785$	−12.7552	−0.455253
$786$	3.98363	0.142091
$787$	2.67784	0.0954547	0.0477273	−	0.998860i	$-0.484802\pi$
$787$	2.67784	0.0954547	0.0477273	+	0.998860i	$0.484802\pi$
$788$	−8.57050	−0.305311
$789$	−26.0261	−0.926555
$790$	15.7403	0.560016
$791$	−20.7257	−0.736921
$792$	−0.787492	−0.0279823
$793$	−25.4896	−0.905161
$794$	−10.9909	−0.390053
$795$	−16.4764	−0.584359
$796$	−7.56214	−0.268033
$797$	47.7000	1.68962	0.844810	−	0.535066i	$-0.179713\pi$
$797$	47.7000	1.68962	0.844810	+	0.535066i	$0.179713\pi$
$798$	−26.9354	−0.953503
$799$	25.1350	0.889213
$800$	1.00000	0.0353553
$801$	0.470240	0.0166151
$802$	19.2341	0.679178
$803$	6.73478	0.237665
$804$	−12.4216	−0.438077
$805$	−9.14756	−0.322409
$806$	18.8116	0.662612
$807$	−7.51617	−0.264582
$808$	2.12892	0.0748950
$809$	−15.3779	−0.540660	−0.270330	−	0.962768i	$-0.587133\pi$
$809$	−15.3779	−0.540660	−0.270330	+	0.962768i	$0.587133\pi$
$810$	−10.7423	−0.377447
$811$	−36.9989	−1.29921	−0.649603	−	0.760273i	$-0.725065\pi$
$811$	−36.9989	−1.29921	−0.649603	+	0.760273i	$0.725065\pi$
$812$	−10.9011	−0.382553
$813$	−34.7692	−1.21941
$814$	−6.64486	−0.232902
$815$	−1.86939	−0.0654818
$816$	5.19123	0.181729
$817$	−7.67236	−0.268422
$818$	8.25725	0.288708
$819$	4.36248	0.152437
$820$	3.25559	0.113690
$821$	−8.86426	−0.309365	−0.154682	−	0.987964i	$-0.549435\pi$
$821$	−8.86426	−0.309365	−0.154682	+	0.987964i	$0.549435\pi$
$822$	4.05620	0.141476
$823$	37.0194	1.29042	0.645208	−	0.764007i	$-0.276771\pi$
$823$	37.0194	1.29042	0.645208	+	0.764007i	$0.276771\pi$
$824$	−14.9767	−0.521739
$825$	1.94615	0.0677562
$826$	−7.43534	−0.258709
$827$	14.6619	0.509844	0.254922	−	0.966962i	$-0.417950\pi$
$827$	14.6619	0.509844	0.254922	+	0.966962i	$0.417950\pi$
$828$	3.99331	0.138777
$829$	33.3015	1.15661	0.578305	−	0.815821i	$-0.303714\pi$
$829$	33.3015	1.15661	0.578305	+	0.815821i	$0.303714\pi$
$830$	8.30389	0.288232
$831$	−6.92382	−0.240185
$832$	−3.07092	−0.106465
$833$	9.99184	0.346197
$834$	39.5602	1.36986
$835$	25.2636	0.874285
$836$	7.67236	0.265354
$837$	−26.3766	−0.911708
$838$	−22.5936	−0.780482
$839$	32.5997	1.12547	0.562734	−	0.826638i	$-0.309750\pi$
$839$	32.5997	1.12547	0.562734	+	0.826638i	$0.309750\pi$
$840$	3.51070	0.121131
$841$	7.51764	0.259229
$842$	−1.06066	−0.0365527
$843$	−36.4328	−1.25481
$844$	21.6038	0.743635
$845$	−3.56943	−0.122792
$846$	−7.42047	−0.255121
$847$	−1.80392	−0.0619836
$848$	8.46618	0.290730
$849$	−43.2980	−1.48598
$850$	−2.66744	−0.0914923
$851$	33.6956	1.15507
$852$	−13.6725	−0.468411
$853$	−4.22582	−0.144689	−0.0723447	−	0.997380i	$-0.523048\pi$
$853$	−4.22582	−0.144689	−0.0723447	+	0.997380i	$0.523048\pi$
$854$	−14.9731	−0.512369
$855$	−6.04193	−0.206629
$856$	8.15661	0.278787
$857$	39.9084	1.36324	0.681622	−	0.731704i	$-0.261275\pi$
$857$	39.9084	1.36324	0.681622	+	0.731704i	$0.261275\pi$
$858$	−5.97647	−0.204033
$859$	−29.3527	−1.00150	−0.500751	−	0.865591i	$-0.666943\pi$
$859$	−29.3527	−1.00150	−0.500751	+	0.865591i	$0.666943\pi$
$860$	1.00000	0.0340997
$861$	11.4294	0.389513
$862$	−29.3695	−1.00033
$863$	50.9961	1.73593	0.867964	−	0.496627i	$-0.165428\pi$
$863$	50.9961	1.73593	0.867964	+	0.496627i	$0.165428\pi$
$864$	4.30587	0.146489
$865$	22.5713	0.767447
$866$	−28.5671	−0.970750
$867$	19.2372	0.653331
$868$	11.0504	0.375073
$869$	−15.7403	−0.533955
$870$	−11.7605	−0.398720
$871$	−19.6007	−0.664144
$872$	1.25351	0.0424490
$873$	8.78825	0.297437
$874$	−38.9060	−1.31601
$875$	−1.80392	−0.0609838
$876$	13.1069	0.442840
$877$	11.5551	0.390189	0.195095	−	0.980784i	$-0.437499\pi$
$877$	11.5551	0.390189	0.195095	+	0.980784i	$0.437499\pi$
$878$	−1.69956	−0.0573575
$879$	−31.5047	−1.06263
$880$	−1.00000	−0.0337100
$881$	37.7598	1.27216	0.636080	−	0.771623i	$-0.280555\pi$
$881$	37.7598	1.27216	0.636080	+	0.771623i	$0.280555\pi$
$882$	−2.94983	−0.0993260
$883$	1.39066	0.0467994	0.0233997	−	0.999726i	$-0.492551\pi$
$883$	1.39066	0.0467994	0.0233997	+	0.999726i	$0.492551\pi$
$884$	8.19150	0.275510
$885$	−8.02155	−0.269641
$886$	−31.1897	−1.04784
$887$	4.55277	0.152867	0.0764335	−	0.997075i	$-0.475647\pi$
$887$	4.55277	0.152867	0.0764335	+	0.997075i	$0.475647\pi$
$888$	−12.9319	−0.433965
$889$	35.9078	1.20431
$890$	0.597136	0.0200160
$891$	10.7423	0.359882
$892$	12.6642	0.424030
$893$	72.2960	2.41929
$894$	−33.6532	−1.12553
$895$	−17.0575	−0.570170
$896$	−1.80392	−0.0602649
$897$	30.3062	1.01190
$898$	20.9363	0.698655
$899$	−37.0177	−1.23461
$900$	0.787492	0.0262497
$901$	−22.5830	−0.752349
$902$	−3.25559	−0.108399
$903$	3.51070	0.116829
$904$	11.4892	0.382126
$905$	−11.8662	−0.394446
$906$	4.69348	0.155931
$907$	0.175942	0.00584205	0.00292103	−	0.999996i	$-0.499070\pi$
$907$	0.175942	0.00584205	0.00292103	+	0.999996i	$0.499070\pi$
$908$	24.1290	0.800751
$909$	1.67650	0.0556061
$910$	5.53971	0.183640
$911$	−6.53460	−0.216501	−0.108251	−	0.994124i	$-0.534525\pi$
$911$	−6.53460	−0.216501	−0.108251	+	0.994124i	$0.534525\pi$
$912$	14.9316	0.494433
$913$	−8.30389	−0.274819
$914$	21.5884	0.714080
$915$	−16.1536	−0.534022
$916$	−24.5929	−0.812573
$917$	3.69251	0.121937
$918$	−11.4856	−0.379082
$919$	−57.6333	−1.90115	−0.950573	−	0.310502i	$-0.899503\pi$
$919$	−57.6333	−1.90115	−0.950573	+	0.310502i	$0.899503\pi$
$920$	5.07092	0.167183
$921$	−17.6897	−0.582896
$922$	40.7731	1.34279
$923$	−21.5745	−0.710132
$924$	−3.51070	−0.115494
$925$	6.64486	0.218482
$926$	−32.9637	−1.08326
$927$	−11.7940	−0.387367
$928$	6.04298	0.198371
$929$	3.38631	0.111101	0.0555506	−	0.998456i	$-0.482309\pi$
$929$	3.38631	0.111101	0.0555506	+	0.998456i	$0.482309\pi$
$930$	11.9216	0.390924
$931$	28.7396	0.941902
$932$	26.9616	0.883157
$933$	−23.8777	−0.781722
$934$	6.01996	0.196979
$935$	2.66744	0.0872345
$936$	−2.41833	−0.0790455
$937$	−16.5132	−0.539463	−0.269731	−	0.962936i	$-0.586935\pi$
$937$	−16.5132	−0.539463	−0.269731	+	0.962936i	$0.586935\pi$
$938$	−11.5138	−0.375941
$939$	−57.2565	−1.86850
$940$	−9.42291	−0.307341
$941$	0.179492	0.00585126	0.00292563	−	0.999996i	$-0.499069\pi$
$941$	0.179492	0.00585126	0.00292563	+	0.999996i	$0.499069\pi$
$942$	24.8236	0.808795
$943$	16.5088	0.537601
$944$	4.12176	0.134152
$945$	−7.76746	−0.252675
$946$	−1.00000	−0.0325128
$947$	−18.5996	−0.604405	−0.302202	−	0.953244i	$-0.597722\pi$
$947$	−18.5996	−0.604405	−0.302202	+	0.953244i	$0.597722\pi$
$948$	−30.6330	−0.994915
$949$	20.6820	0.671366
$950$	−7.67236	−0.248924
$951$	60.7962	1.97145
$952$	4.81185	0.155953
$953$	27.6162	0.894576	0.447288	−	0.894390i	$-0.352390\pi$
$953$	27.6162	0.894576	0.447288	+	0.894390i	$0.352390\pi$
$954$	6.66705	0.215854
$955$	−9.03514	−0.292370
$956$	15.3401	0.496135
$957$	11.7605	0.380164
$958$	−21.0217	−0.679181
$959$	3.75978	0.121410
$960$	−1.94615	−0.0628117
$961$	6.52456	0.210470
$962$	−20.4059	−0.657911
$963$	6.42326	0.206987
$964$	−11.2781	−0.363244
$965$	19.0304	0.612609
$966$	17.8025	0.572786
$967$	−7.41969	−0.238601	−0.119301	−	0.992858i	$-0.538065\pi$
$967$	−7.41969	−0.238601	−0.119301	+	0.992858i	$0.538065\pi$
$968$	1.00000	0.0321412
$969$	−39.8290	−1.27949
$970$	11.1598	0.358319
$971$	−25.2446	−0.810138	−0.405069	−	0.914286i	$-0.632752\pi$
$971$	−25.2446	−0.810138	−0.405069	+	0.914286i	$0.632752\pi$
$972$	7.98856	0.256233
$973$	36.6691	1.17556
$974$	−35.6027	−1.14078
$975$	5.97647	0.191400
$976$	8.30029	0.265686
$977$	−44.8974	−1.43640	−0.718198	−	0.695839i	$-0.755033\pi$
$977$	−44.8974	−1.43640	−0.718198	+	0.695839i	$0.755033\pi$
$978$	3.63810	0.116334
$979$	−0.597136	−0.0190846
$980$	−3.74586	−0.119657
$981$	0.987125	0.0315165
$982$	−39.5063	−1.26070
$983$	−35.5289	−1.13320	−0.566598	−	0.823995i	$-0.691741\pi$
$983$	−35.5289	−1.13320	−0.566598	+	0.823995i	$0.691741\pi$
$984$	−6.33585	−0.201980
$985$	−8.57050	−0.273079
$986$	−16.1193	−0.513342
$987$	−33.0810	−1.05298
$988$	23.5612	0.749583
$989$	5.07092	0.161246
$990$	−0.787492	−0.0250281
$991$	30.8147	0.978860	0.489430	−	0.872043i	$-0.337205\pi$
$991$	30.8147	0.978860	0.489430	+	0.872043i	$0.337205\pi$
$992$	−6.12573	−0.194492
$993$	1.91827	0.0608743
$994$	−12.6733	−0.401972
$995$	−7.56214	−0.239736
$996$	−16.1606	−0.512068
$997$	−56.7452	−1.79714	−0.898569	−	0.438832i	$-0.855392\pi$
$997$	−56.7452	−1.79714	−0.898569	+	0.438832i	$0.855392\pi$
$998$	−29.3492	−0.929031
$999$	28.6119	0.905240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.be.1.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.be.1.4	✓	12	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.94615 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.94615 q^{6} -1.80392 q^{7} +1.00000 q^{8} +0.787492 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.94615 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.94615 q^{6} -1.80392 q^{7} +1.00000 q^{8} +0.787492 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.94615 q^{12} -3.07092 q^{13} -1.80392 q^{14} -1.94615 q^{15} +1.00000 q^{16} -2.66744 q^{17} +0.787492 q^{18} -7.67236 q^{19} +1.00000 q^{20} +3.51070 q^{21} -1.00000 q^{22} +5.07092 q^{23} -1.94615 q^{24} +1.00000 q^{25} -3.07092 q^{26} +4.30587 q^{27} -1.80392 q^{28} +6.04298 q^{29} -1.94615 q^{30} -6.12573 q^{31} +1.00000 q^{32} +1.94615 q^{33} -2.66744 q^{34} -1.80392 q^{35} +0.787492 q^{36} +6.64486 q^{37} -7.67236 q^{38} +5.97647 q^{39} +1.00000 q^{40} +3.25559 q^{41} +3.51070 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.787492 q^{45} +5.07092 q^{46} -9.42291 q^{47} -1.94615 q^{48} -3.74586 q^{49} +1.00000 q^{50} +5.19123 q^{51} -3.07092 q^{52} +8.46618 q^{53} +4.30587 q^{54} -1.00000 q^{55} -1.80392 q^{56} +14.9316 q^{57} +6.04298 q^{58} +4.12176 q^{59} -1.94615 q^{60} +8.30029 q^{61} -6.12573 q^{62} -1.42058 q^{63} +1.00000 q^{64} -3.07092 q^{65} +1.94615 q^{66} +6.38267 q^{67} -2.66744 q^{68} -9.86877 q^{69} -1.80392 q^{70} +7.02540 q^{71} +0.787492 q^{72} -6.73478 q^{73} +6.64486 q^{74} -1.94615 q^{75} -7.67236 q^{76} +1.80392 q^{77} +5.97647 q^{78} +15.7403 q^{79} +1.00000 q^{80} -10.7423 q^{81} +3.25559 q^{82} +8.30389 q^{83} +3.51070 q^{84} -2.66744 q^{85} +1.00000 q^{86} -11.7605 q^{87} -1.00000 q^{88} +0.597136 q^{89} +0.787492 q^{90} +5.53971 q^{91} +5.07092 q^{92} +11.9216 q^{93} -9.42291 q^{94} -7.67236 q^{95} -1.94615 q^{96} +11.1598 q^{97} -3.74586 q^{98} -0.787492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

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