LMFDB - Embedded newform 8034.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + \cdots - 180 $ x^13 - 5x^12 - 25x^11 + 134x^10 + 196x^9 - 1151x^8 - 801x^7 + 4263x^6 + 2205x^5 - 6840x^4 - 3579x^3 + 3559x^2 + 1839x - 180
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.14079$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.27728 q^{5} -1.00000 q^{6} -2.14079 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.27728 q^{5} -1.00000 q^{6} -2.14079 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.27728 q^{10} +5.64607 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.14079 q^{14} +4.27728 q^{15} +1.00000 q^{16} -6.07608 q^{17} +1.00000 q^{18} +3.39182 q^{19} -4.27728 q^{20} +2.14079 q^{21} +5.64607 q^{22} -8.51171 q^{23} -1.00000 q^{24} +13.2951 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.14079 q^{28} -6.42956 q^{29} +4.27728 q^{30} +3.39182 q^{31} +1.00000 q^{32} -5.64607 q^{33} -6.07608 q^{34} +9.15675 q^{35} +1.00000 q^{36} +4.53681 q^{37} +3.39182 q^{38} -1.00000 q^{39} -4.27728 q^{40} +4.61293 q^{41} +2.14079 q^{42} -2.65673 q^{43} +5.64607 q^{44} -4.27728 q^{45} -8.51171 q^{46} -5.99956 q^{47} -1.00000 q^{48} -2.41703 q^{49} +13.2951 q^{50} +6.07608 q^{51} +1.00000 q^{52} -13.6836 q^{53} -1.00000 q^{54} -24.1498 q^{55} -2.14079 q^{56} -3.39182 q^{57} -6.42956 q^{58} +0.100702 q^{59} +4.27728 q^{60} -1.98798 q^{61} +3.39182 q^{62} -2.14079 q^{63} +1.00000 q^{64} -4.27728 q^{65} -5.64607 q^{66} -7.85593 q^{67} -6.07608 q^{68} +8.51171 q^{69} +9.15675 q^{70} +3.83076 q^{71} +1.00000 q^{72} +3.15864 q^{73} +4.53681 q^{74} -13.2951 q^{75} +3.39182 q^{76} -12.0870 q^{77} -1.00000 q^{78} +3.26874 q^{79} -4.27728 q^{80} +1.00000 q^{81} +4.61293 q^{82} +15.6894 q^{83} +2.14079 q^{84} +25.9891 q^{85} -2.65673 q^{86} +6.42956 q^{87} +5.64607 q^{88} -7.32723 q^{89} -4.27728 q^{90} -2.14079 q^{91} -8.51171 q^{92} -3.39182 q^{93} -5.99956 q^{94} -14.5078 q^{95} -1.00000 q^{96} -6.52315 q^{97} -2.41703 q^{98} +5.64607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−4.27728	−1.91286	−0.956429	−	0.291965i	$-0.905691\pi$
$5$	−4.27728	−1.91286	−0.956429	+	0.291965i	$0.905691\pi$
$6$	−1.00000	−0.408248
$7$	−2.14079	−0.809141	−0.404571	−	0.914507i	$-0.632579\pi$
$7$	−2.14079	−0.809141	−0.404571	+	0.914507i	$0.632579\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.27728	−1.35259
$11$	5.64607	1.70235	0.851177	−	0.524878i	$-0.175889\pi$
$11$	5.64607	1.70235	0.851177	+	0.524878i	$0.175889\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.14079	−0.572149
$15$	4.27728	1.10439
$16$	1.00000	0.250000
$17$	−6.07608	−1.47367	−0.736833	−	0.676075i	$-0.763680\pi$
$17$	−6.07608	−1.47367	−0.736833	+	0.676075i	$0.763680\pi$
$18$	1.00000	0.235702
$19$	3.39182	0.778136	0.389068	−	0.921209i	$-0.372797\pi$
$19$	3.39182	0.778136	0.389068	+	0.921209i	$0.372797\pi$
$20$	−4.27728	−0.956429
$21$	2.14079	0.467158
$22$	5.64607	1.20375
$23$	−8.51171	−1.77481	−0.887407	−	0.460986i	$-0.847496\pi$
$23$	−8.51171	−1.77481	−0.887407	+	0.460986i	$0.847496\pi$
$24$	−1.00000	−0.204124
$25$	13.2951	2.65903
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−2.14079	−0.404571
$29$	−6.42956	−1.19394	−0.596970	−	0.802264i	$-0.703629\pi$
$29$	−6.42956	−1.19394	−0.596970	+	0.802264i	$0.703629\pi$
$30$	4.27728	0.780921
$31$	3.39182	0.609188	0.304594	−	0.952482i	$-0.401479\pi$
$31$	3.39182	0.609188	0.304594	+	0.952482i	$0.401479\pi$
$32$	1.00000	0.176777
$33$	−5.64607	−0.982855
$34$	−6.07608	−1.04204
$35$	9.15675	1.54777
$36$	1.00000	0.166667
$37$	4.53681	0.745847	0.372924	−	0.927862i	$-0.378355\pi$
$37$	4.53681	0.745847	0.372924	+	0.927862i	$0.378355\pi$
$38$	3.39182	0.550225
$39$	−1.00000	−0.160128
$40$	−4.27728	−0.676297
$41$	4.61293	0.720419	0.360210	−	0.932871i	$-0.382705\pi$
$41$	4.61293	0.720419	0.360210	+	0.932871i	$0.382705\pi$
$42$	2.14079	0.330331
$43$	−2.65673	−0.405147	−0.202573	−	0.979267i	$-0.564930\pi$
$43$	−2.65673	−0.405147	−0.202573	+	0.979267i	$0.564930\pi$
$44$	5.64607	0.851177
$45$	−4.27728	−0.637619
$46$	−8.51171	−1.25498
$47$	−5.99956	−0.875125	−0.437563	−	0.899188i	$-0.644158\pi$
$47$	−5.99956	−0.875125	−0.437563	+	0.899188i	$0.644158\pi$
$48$	−1.00000	−0.144338
$49$	−2.41703	−0.345290
$50$	13.2951	1.88022
$51$	6.07608	0.850821
$52$	1.00000	0.138675
$53$	−13.6836	−1.87959	−0.939796	−	0.341735i	$-0.888985\pi$
$53$	−13.6836	−1.87959	−0.939796	+	0.341735i	$0.888985\pi$
$54$	−1.00000	−0.136083
$55$	−24.1498	−3.25636
$56$	−2.14079	−0.286075
$57$	−3.39182	−0.449257
$58$	−6.42956	−0.844243
$59$	0.100702	0.0131103	0.00655513	−	0.999979i	$-0.497913\pi$
$59$	0.100702	0.0131103	0.00655513	+	0.999979i	$0.497913\pi$
$60$	4.27728	0.552195
$61$	−1.98798	−0.254535	−0.127267	−	0.991868i	$-0.540621\pi$
$61$	−1.98798	−0.254535	−0.127267	+	0.991868i	$0.540621\pi$
$62$	3.39182	0.430761
$63$	−2.14079	−0.269714
$64$	1.00000	0.125000
$65$	−4.27728	−0.530531
$66$	−5.64607	−0.694983
$67$	−7.85593	−0.959755	−0.479877	−	0.877336i	$-0.659319\pi$
$67$	−7.85593	−0.959755	−0.479877	+	0.877336i	$0.659319\pi$
$68$	−6.07608	−0.736833
$69$	8.51171	1.02469
$70$	9.15675	1.09444
$71$	3.83076	0.454628	0.227314	−	0.973822i	$-0.427006\pi$
$71$	3.83076	0.454628	0.227314	+	0.973822i	$0.427006\pi$
$72$	1.00000	0.117851
$73$	3.15864	0.369691	0.184846	−	0.982768i	$-0.440821\pi$
$73$	3.15864	0.369691	0.184846	+	0.982768i	$0.440821\pi$
$74$	4.53681	0.527394
$75$	−13.2951	−1.53519
$76$	3.39182	0.389068
$77$	−12.0870	−1.37745
$78$	−1.00000	−0.113228
$79$	3.26874	0.367762	0.183881	−	0.982949i	$-0.441134\pi$
$79$	3.26874	0.367762	0.183881	+	0.982949i	$0.441134\pi$
$80$	−4.27728	−0.478215
$81$	1.00000	0.111111
$82$	4.61293	0.509413
$83$	15.6894	1.72214	0.861070	−	0.508487i	$-0.169795\pi$
$83$	15.6894	1.72214	0.861070	+	0.508487i	$0.169795\pi$
$84$	2.14079	0.233579
$85$	25.9891	2.81891
$86$	−2.65673	−0.286482
$87$	6.42956	0.689322
$88$	5.64607	0.601873
$89$	−7.32723	−0.776685	−0.388343	−	0.921515i	$-0.626952\pi$
$89$	−7.32723	−0.776685	−0.388343	+	0.921515i	$0.626952\pi$
$90$	−4.27728	−0.450865
$91$	−2.14079	−0.224415
$92$	−8.51171	−0.887407
$93$	−3.39182	−0.351715
$94$	−5.99956	−0.618807
$95$	−14.5078	−1.48846
$96$	−1.00000	−0.102062
$97$	−6.52315	−0.662326	−0.331163	−	0.943574i	$-0.607441\pi$
$97$	−6.52315	−0.662326	−0.331163	+	0.943574i	$0.607441\pi$
$98$	−2.41703	−0.244157
$99$	5.64607	0.567452
$100$	13.2951	1.32951
$101$	−15.2239	−1.51483	−0.757417	−	0.652932i	$-0.773539\pi$
$101$	−15.2239	−1.51483	−0.757417	+	0.652932i	$0.773539\pi$
$102$	6.07608	0.601621
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−9.15675	−0.893607
$106$	−13.6836	−1.32907
$107$	−1.42869	−0.138116	−0.0690581	−	0.997613i	$-0.521999\pi$
$107$	−1.42869	−0.138116	−0.0690581	+	0.997613i	$0.521999\pi$
$108$	−1.00000	−0.0962250
$109$	9.69578	0.928687	0.464344	−	0.885655i	$-0.346290\pi$
$109$	9.69578	0.928687	0.464344	+	0.885655i	$0.346290\pi$
$110$	−24.1498	−2.30260
$111$	−4.53681	−0.430615
$112$	−2.14079	−0.202285
$113$	8.55748	0.805020	0.402510	−	0.915416i	$-0.368138\pi$
$113$	8.55748	0.805020	0.402510	+	0.915416i	$0.368138\pi$
$114$	−3.39182	−0.317673
$115$	36.4070	3.39497
$116$	−6.42956	−0.596970
$117$	1.00000	0.0924500
$118$	0.100702	0.00927036
$119$	13.0076	1.19240
$120$	4.27728	0.390461
$121$	20.8781	1.89801
$122$	−1.98798	−0.179983
$123$	−4.61293	−0.415934
$124$	3.39182	0.304594
$125$	−35.4806	−3.17348
$126$	−2.14079	−0.190716
$127$	16.6114	1.47402	0.737011	−	0.675880i	$-0.236236\pi$
$127$	16.6114	1.47402	0.737011	+	0.675880i	$0.236236\pi$
$128$	1.00000	0.0883883
$129$	2.65673	0.233912
$130$	−4.27728	−0.375142
$131$	5.56624	0.486325	0.243162	−	0.969986i	$-0.421815\pi$
$131$	5.56624	0.486325	0.243162	+	0.969986i	$0.421815\pi$
$132$	−5.64607	−0.491427
$133$	−7.26116	−0.629622
$134$	−7.85593	−0.678649
$135$	4.27728	0.368130
$136$	−6.07608	−0.521019
$137$	18.2104	1.55582	0.777908	−	0.628378i	$-0.216281\pi$
$137$	18.2104	1.55582	0.777908	+	0.628378i	$0.216281\pi$
$138$	8.51171	0.724565
$139$	−0.868351	−0.0736525	−0.0368263	−	0.999322i	$-0.511725\pi$
$139$	−0.868351	−0.0736525	−0.0368263	+	0.999322i	$0.511725\pi$
$140$	9.15675	0.773886
$141$	5.99956	0.505254
$142$	3.83076	0.321470
$143$	5.64607	0.472148
$144$	1.00000	0.0833333
$145$	27.5010	2.28384
$146$	3.15864	0.261411
$147$	2.41703	0.199353
$148$	4.53681	0.372924
$149$	9.39696	0.769829	0.384915	−	0.922952i	$-0.374231\pi$
$149$	9.39696	0.769829	0.384915	+	0.922952i	$0.374231\pi$
$150$	−13.2951	−1.08554
$151$	6.83407	0.556149	0.278074	−	0.960560i	$-0.410304\pi$
$151$	6.83407	0.556149	0.278074	+	0.960560i	$0.410304\pi$
$152$	3.39182	0.275113
$153$	−6.07608	−0.491222
$154$	−12.0870	−0.974001
$155$	−14.5078	−1.16529
$156$	−1.00000	−0.0800641
$157$	−18.1555	−1.44897	−0.724483	−	0.689293i	$-0.757921\pi$
$157$	−18.1555	−1.44897	−0.724483	+	0.689293i	$0.757921\pi$
$158$	3.26874	0.260047
$159$	13.6836	1.08518
$160$	−4.27728	−0.338149
$161$	18.2218	1.43608
$162$	1.00000	0.0785674
$163$	7.54505	0.590974	0.295487	−	0.955347i	$-0.404518\pi$
$163$	7.54505	0.590974	0.295487	+	0.955347i	$0.404518\pi$
$164$	4.61293	0.360210
$165$	24.1498	1.88006
$166$	15.6894	1.21774
$167$	8.92695	0.690788	0.345394	−	0.938458i	$-0.387745\pi$
$167$	8.92695	0.690788	0.345394	+	0.938458i	$0.387745\pi$
$168$	2.14079	0.165165
$169$	1.00000	0.0769231
$170$	25.9891	1.99327
$171$	3.39182	0.259379
$172$	−2.65673	−0.202573
$173$	16.2335	1.23421	0.617105	−	0.786881i	$-0.288305\pi$
$173$	16.2335	1.23421	0.617105	+	0.786881i	$0.288305\pi$
$174$	6.42956	0.487424
$175$	−28.4620	−2.15153
$176$	5.64607	0.425589
$177$	−0.100702	−0.00756921
$178$	−7.32723	−0.549199
$179$	−3.61131	−0.269922	−0.134961	−	0.990851i	$-0.543091\pi$
$179$	−3.61131	−0.269922	−0.134961	+	0.990851i	$0.543091\pi$
$180$	−4.27728	−0.318810
$181$	4.01150	0.298173	0.149086	−	0.988824i	$-0.452367\pi$
$181$	4.01150	0.298173	0.149086	+	0.988824i	$0.452367\pi$
$182$	−2.14079	−0.158686
$183$	1.98798	0.146956
$184$	−8.51171	−0.627492
$185$	−19.4052	−1.42670
$186$	−3.39182	−0.248700
$187$	−34.3060	−2.50870
$188$	−5.99956	−0.437563
$189$	2.14079	0.155719
$190$	−14.5078	−1.05250
$191$	22.0004	1.59189	0.795945	−	0.605369i	$-0.206974\pi$
$191$	22.0004	1.59189	0.795945	+	0.605369i	$0.206974\pi$
$192$	−1.00000	−0.0721688
$193$	12.5347	0.902270	0.451135	−	0.892456i	$-0.351019\pi$
$193$	12.5347	0.902270	0.451135	+	0.892456i	$0.351019\pi$
$194$	−6.52315	−0.468335
$195$	4.27728	0.306302
$196$	−2.41703	−0.172645
$197$	−1.47488	−0.105081	−0.0525406	−	0.998619i	$-0.516732\pi$
$197$	−1.47488	−0.105081	−0.0525406	+	0.998619i	$0.516732\pi$
$198$	5.64607	0.401249
$199$	−5.86202	−0.415548	−0.207774	−	0.978177i	$-0.566622\pi$
$199$	−5.86202	−0.415548	−0.207774	+	0.978177i	$0.566622\pi$
$200$	13.2951	0.940108
$201$	7.85593	0.554115
$202$	−15.2239	−1.07115
$203$	13.7643	0.966066
$204$	6.07608	0.425411
$205$	−19.7308	−1.37806
$206$	1.00000	0.0696733
$207$	−8.51171	−0.591605
$208$	1.00000	0.0693375
$209$	19.1504	1.32466
$210$	−9.15675	−0.631876
$211$	10.3608	0.713270	0.356635	−	0.934244i	$-0.383924\pi$
$211$	10.3608	0.713270	0.356635	+	0.934244i	$0.383924\pi$
$212$	−13.6836	−0.939796
$213$	−3.83076	−0.262479
$214$	−1.42869	−0.0976629
$215$	11.3636	0.774988
$216$	−1.00000	−0.0680414
$217$	−7.26116	−0.492920
$218$	9.69578	0.656681
$219$	−3.15864	−0.213441
$220$	−24.1498	−1.62818
$221$	−6.07608	−0.408721
$222$	−4.53681	−0.304491
$223$	−16.0141	−1.07238	−0.536191	−	0.844097i	$-0.680137\pi$
$223$	−16.0141	−1.07238	−0.536191	+	0.844097i	$0.680137\pi$
$224$	−2.14079	−0.143037
$225$	13.2951	0.886342
$226$	8.55748	0.569235
$227$	12.4891	0.828929	0.414465	−	0.910065i	$-0.363969\pi$
$227$	12.4891	0.828929	0.414465	+	0.910065i	$0.363969\pi$
$228$	−3.39182	−0.224629
$229$	−1.97084	−0.130237	−0.0651183	−	0.997878i	$-0.520742\pi$
$229$	−1.97084	−0.130237	−0.0651183	+	0.997878i	$0.520742\pi$
$230$	36.4070	2.40061
$231$	12.0870	0.795269
$232$	−6.42956	−0.422121
$233$	−24.0527	−1.57574	−0.787872	−	0.615839i	$-0.788817\pi$
$233$	−24.0527	−1.57574	−0.787872	+	0.615839i	$0.788817\pi$
$234$	1.00000	0.0653720
$235$	25.6618	1.67399
$236$	0.100702	0.00655513
$237$	−3.26874	−0.212327
$238$	13.0076	0.843157
$239$	−4.27172	−0.276315	−0.138157	−	0.990410i	$-0.544118\pi$
$239$	−4.27172	−0.276315	−0.138157	+	0.990410i	$0.544118\pi$
$240$	4.27728	0.276097
$241$	−7.49584	−0.482849	−0.241425	−	0.970420i	$-0.577615\pi$
$241$	−7.49584	−0.482849	−0.241425	+	0.970420i	$0.577615\pi$
$242$	20.8781	1.34210
$243$	−1.00000	−0.0641500
$244$	−1.98798	−0.127267
$245$	10.3383	0.660491
$246$	−4.61293	−0.294110
$247$	3.39182	0.215816
$248$	3.39182	0.215381
$249$	−15.6894	−0.994278
$250$	−35.4806	−2.24399
$251$	18.8336	1.18876	0.594382	−	0.804183i	$-0.297397\pi$
$251$	18.8336	1.18876	0.594382	+	0.804183i	$0.297397\pi$
$252$	−2.14079	−0.134857
$253$	−48.0577	−3.02136
$254$	16.6114	1.04229
$255$	−25.9891	−1.62750
$256$	1.00000	0.0625000
$257$	3.11482	0.194297	0.0971486	−	0.995270i	$-0.469028\pi$
$257$	3.11482	0.194297	0.0971486	+	0.995270i	$0.469028\pi$
$258$	2.65673	0.165401
$259$	−9.71235	−0.603496
$260$	−4.27728	−0.265266
$261$	−6.42956	−0.397980
$262$	5.56624	0.343884
$263$	23.0982	1.42430	0.712148	−	0.702030i	$-0.247723\pi$
$263$	23.0982	1.42430	0.712148	+	0.702030i	$0.247723\pi$
$264$	−5.64607	−0.347492
$265$	58.5288	3.59539
$266$	−7.26116	−0.445210
$267$	7.32723	0.448419
$268$	−7.85593	−0.479877
$269$	−24.8798	−1.51695	−0.758473	−	0.651704i	$-0.774054\pi$
$269$	−24.8798	−1.51695	−0.758473	+	0.651704i	$0.774054\pi$
$270$	4.27728	0.260307
$271$	20.5256	1.24684	0.623419	−	0.781888i	$-0.285743\pi$
$271$	20.5256	1.24684	0.623419	+	0.781888i	$0.285743\pi$
$272$	−6.07608	−0.368416
$273$	2.14079	0.129566
$274$	18.2104	1.10013
$275$	75.0652	4.52660
$276$	8.51171	0.512345
$277$	27.5111	1.65298	0.826490	−	0.562952i	$-0.190334\pi$
$277$	27.5111	1.65298	0.826490	+	0.562952i	$0.190334\pi$
$278$	−0.868351	−0.0520802
$279$	3.39182	0.203063
$280$	9.15675	0.547220
$281$	−7.60620	−0.453748	−0.226874	−	0.973924i	$-0.572851\pi$
$281$	−7.60620	−0.453748	−0.226874	+	0.973924i	$0.572851\pi$
$282$	5.99956	0.357268
$283$	−9.07187	−0.539267	−0.269633	−	0.962963i	$-0.586903\pi$
$283$	−9.07187	−0.539267	−0.269633	+	0.962963i	$0.586903\pi$
$284$	3.83076	0.227314
$285$	14.5078	0.859365
$286$	5.64607	0.333859
$287$	−9.87531	−0.582921
$288$	1.00000	0.0589256
$289$	19.9187	1.17169
$290$	27.5010	1.61492
$291$	6.52315	0.382394
$292$	3.15864	0.184846
$293$	−21.2646	−1.24229	−0.621145	−	0.783695i	$-0.713332\pi$
$293$	−21.2646	−1.24229	−0.621145	+	0.783695i	$0.713332\pi$
$294$	2.41703	0.140964
$295$	−0.430730	−0.0250781
$296$	4.53681	0.263697
$297$	−5.64607	−0.327618
$298$	9.39696	0.544351
$299$	−8.51171	−0.492245
$300$	−13.2951	−0.767595
$301$	5.68748	0.327821
$302$	6.83407	0.393257
$303$	15.2239	0.874590
$304$	3.39182	0.194534
$305$	8.50315	0.486889
$306$	−6.07608	−0.347346
$307$	−10.2841	−0.586943	−0.293471	−	0.955968i	$-0.594811\pi$
$307$	−10.2841	−0.586943	−0.293471	+	0.955968i	$0.594811\pi$
$308$	−12.0870	−0.688723
$309$	−1.00000	−0.0568880
$310$	−14.5078	−0.823985
$311$	11.8628	0.672680	0.336340	−	0.941741i	$-0.390811\pi$
$311$	11.8628	0.672680	0.336340	+	0.941741i	$0.390811\pi$
$312$	−1.00000	−0.0566139
$313$	10.0467	0.567873	0.283936	−	0.958843i	$-0.408360\pi$
$313$	10.0467	0.567873	0.283936	+	0.958843i	$0.408360\pi$
$314$	−18.1555	−1.02457
$315$	9.15675	0.515924
$316$	3.26874	0.183881
$317$	30.5597	1.71641	0.858203	−	0.513310i	$-0.171581\pi$
$317$	30.5597	1.71641	0.858203	+	0.513310i	$0.171581\pi$
$318$	13.6836	0.767340
$319$	−36.3018	−2.03251
$320$	−4.27728	−0.239107
$321$	1.42869	0.0797414
$322$	18.2218	1.01546
$323$	−20.6089	−1.14671
$324$	1.00000	0.0555556
$325$	13.2951	0.737481
$326$	7.54505	0.417882
$327$	−9.69578	−0.536178
$328$	4.61293	0.254707
$329$	12.8438	0.708100
$330$	24.1498	1.32940
$331$	3.61802	0.198864	0.0994321	−	0.995044i	$-0.468297\pi$
$331$	3.61802	0.198864	0.0994321	+	0.995044i	$0.468297\pi$
$332$	15.6894	0.861070
$333$	4.53681	0.248616
$334$	8.92695	0.488461
$335$	33.6020	1.83587
$336$	2.14079	0.116790
$337$	18.7014	1.01873	0.509365	−	0.860550i	$-0.329880\pi$
$337$	18.7014	1.01873	0.509365	+	0.860550i	$0.329880\pi$
$338$	1.00000	0.0543928
$339$	−8.55748	−0.464778
$340$	25.9891	1.40946
$341$	19.1504	1.03705
$342$	3.39182	0.183408
$343$	20.1599	1.08853
$344$	−2.65673	−0.143241
$345$	−36.4070	−1.96009
$346$	16.2335	0.872718
$347$	17.4950	0.939179	0.469590	−	0.882885i	$-0.344402\pi$
$347$	17.4950	0.939179	0.469590	+	0.882885i	$0.344402\pi$
$348$	6.42956	0.344661
$349$	−20.4362	−1.09393	−0.546963	−	0.837157i	$-0.684216\pi$
$349$	−20.4362	−1.09393	−0.546963	+	0.837157i	$0.684216\pi$
$350$	−28.4620	−1.52136
$351$	−1.00000	−0.0533761
$352$	5.64607	0.300937
$353$	−0.541050	−0.0287972	−0.0143986	−	0.999896i	$-0.504583\pi$
$353$	−0.541050	−0.0287972	−0.0143986	+	0.999896i	$0.504583\pi$
$354$	−0.100702	−0.00535224
$355$	−16.3852	−0.869638
$356$	−7.32723	−0.388343
$357$	−13.0076	−0.688435
$358$	−3.61131	−0.190864
$359$	−16.4361	−0.867464	−0.433732	−	0.901042i	$-0.642804\pi$
$359$	−16.4361	−0.867464	−0.433732	+	0.901042i	$0.642804\pi$
$360$	−4.27728	−0.225432
$361$	−7.49558	−0.394504
$362$	4.01150	0.210840
$363$	−20.8781	−1.09582
$364$	−2.14079	−0.112208
$365$	−13.5104	−0.707167
$366$	1.98798	0.103913
$367$	14.3975	0.751541	0.375771	−	0.926713i	$-0.377378\pi$
$367$	14.3975	0.751541	0.375771	+	0.926713i	$0.377378\pi$
$368$	−8.51171	−0.443704
$369$	4.61293	0.240140
$370$	−19.4052	−1.00883
$371$	29.2938	1.52086
$372$	−3.39182	−0.175858
$373$	11.0628	0.572808	0.286404	−	0.958109i	$-0.407540\pi$
$373$	11.0628	0.572808	0.286404	+	0.958109i	$0.407540\pi$
$374$	−34.3060	−1.77392
$375$	35.4806	1.83221
$376$	−5.99956	−0.309403
$377$	−6.42956	−0.331139
$378$	2.14079	0.110110
$379$	27.1919	1.39675	0.698377	−	0.715730i	$-0.253906\pi$
$379$	27.1919	1.39675	0.698377	+	0.715730i	$0.253906\pi$
$380$	−14.5078	−0.744232
$381$	−16.6114	−0.851028
$382$	22.0004	1.12564
$383$	−10.2183	−0.522132	−0.261066	−	0.965321i	$-0.584074\pi$
$383$	−10.2183	−0.522132	−0.261066	+	0.965321i	$0.584074\pi$
$384$	−1.00000	−0.0510310
$385$	51.6996	2.63486
$386$	12.5347	0.638001
$387$	−2.65673	−0.135049
$388$	−6.52315	−0.331163
$389$	20.7818	1.05368	0.526839	−	0.849965i	$-0.323377\pi$
$389$	20.7818	1.05368	0.526839	+	0.849965i	$0.323377\pi$
$390$	4.27728	0.216589
$391$	51.7178	2.61548
$392$	−2.41703	−0.122079
$393$	−5.56624	−0.280780
$394$	−1.47488	−0.0743036
$395$	−13.9813	−0.703476
$396$	5.64607	0.283726
$397$	−23.1114	−1.15993	−0.579963	−	0.814642i	$-0.696933\pi$
$397$	−23.1114	−1.15993	−0.579963	+	0.814642i	$0.696933\pi$
$398$	−5.86202	−0.293837
$399$	7.26116	0.363513
$400$	13.2951	0.664756
$401$	18.7174	0.934704	0.467352	−	0.884071i	$-0.345208\pi$
$401$	18.7174	0.934704	0.467352	+	0.884071i	$0.345208\pi$
$402$	7.85593	0.391818
$403$	3.39182	0.168958
$404$	−15.2239	−0.757417
$405$	−4.27728	−0.212540
$406$	13.7643	0.683112
$407$	25.6152	1.26970
$408$	6.07608	0.300811
$409$	16.7184	0.826671	0.413335	−	0.910579i	$-0.364364\pi$
$409$	16.7184	0.826671	0.413335	+	0.910579i	$0.364364\pi$
$410$	−19.7308	−0.974435
$411$	−18.2104	−0.898251
$412$	1.00000	0.0492665
$413$	−0.215581	−0.0106081
$414$	−8.51171	−0.418328
$415$	−67.1081	−3.29421
$416$	1.00000	0.0490290
$417$	0.868351	0.0425233
$418$	19.1504	0.936679
$419$	−0.375740	−0.0183561	−0.00917806	−	0.999958i	$-0.502922\pi$
$419$	−0.375740	−0.0183561	−0.00917806	+	0.999958i	$0.502922\pi$
$420$	−9.15675	−0.446803
$421$	−17.6135	−0.858430	−0.429215	−	0.903202i	$-0.641210\pi$
$421$	−17.6135	−0.858430	−0.429215	+	0.903202i	$0.641210\pi$
$422$	10.3608	0.504358
$423$	−5.99956	−0.291708
$424$	−13.6836	−0.664536
$425$	−80.7823	−3.91851
$426$	−3.83076	−0.185601
$427$	4.25584	0.205955
$428$	−1.42869	−0.0690581
$429$	−5.64607	−0.272595
$430$	11.3636	0.548000
$431$	38.1357	1.83693	0.918465	−	0.395501i	$-0.129429\pi$
$431$	38.1357	1.83693	0.918465	+	0.395501i	$0.129429\pi$
$432$	−1.00000	−0.0481125
$433$	−33.1341	−1.59232	−0.796162	−	0.605084i	$-0.793140\pi$
$433$	−33.1341	−1.59232	−0.796162	+	0.605084i	$0.793140\pi$
$434$	−7.26116	−0.348547
$435$	−27.5010	−1.31857
$436$	9.69578	0.464344
$437$	−28.8702	−1.38105
$438$	−3.15864	−0.150926
$439$	38.5264	1.83876	0.919382	−	0.393365i	$-0.128689\pi$
$439$	38.5264	1.83876	0.919382	+	0.393365i	$0.128689\pi$
$440$	−24.1498	−1.15130
$441$	−2.41703	−0.115097
$442$	−6.07608	−0.289010
$443$	−36.6885	−1.74312	−0.871562	−	0.490284i	$-0.836893\pi$
$443$	−36.6885	−1.74312	−0.871562	+	0.490284i	$0.836893\pi$
$444$	−4.53681	−0.215308
$445$	31.3406	1.48569
$446$	−16.0141	−0.758289
$447$	−9.39696	−0.444461
$448$	−2.14079	−0.101143
$449$	15.8187	0.746531	0.373266	−	0.927725i	$-0.378238\pi$
$449$	15.8187	0.746531	0.373266	+	0.927725i	$0.378238\pi$
$450$	13.2951	0.626738
$451$	26.0450	1.22641
$452$	8.55748	0.402510
$453$	−6.83407	−0.321093
$454$	12.4891	0.586141
$455$	9.15675	0.429275
$456$	−3.39182	−0.158836
$457$	−8.59896	−0.402243	−0.201121	−	0.979566i	$-0.564459\pi$
$457$	−8.59896	−0.402243	−0.201121	+	0.979566i	$0.564459\pi$
$458$	−1.97084	−0.0920912
$459$	6.07608	0.283607
$460$	36.4070	1.69748
$461$	5.80201	0.270227	0.135113	−	0.990830i	$-0.456860\pi$
$461$	5.80201	0.270227	0.135113	+	0.990830i	$0.456860\pi$
$462$	12.0870	0.562340
$463$	−9.29261	−0.431864	−0.215932	−	0.976408i	$-0.569279\pi$
$463$	−9.29261	−0.431864	−0.215932	+	0.976408i	$0.569279\pi$
$464$	−6.42956	−0.298485
$465$	14.5078	0.672781
$466$	−24.0527	−1.11422
$467$	30.9688	1.43306	0.716532	−	0.697554i	$-0.245728\pi$
$467$	30.9688	1.43306	0.716532	+	0.697554i	$0.245728\pi$
$468$	1.00000	0.0462250
$469$	16.8179	0.776577
$470$	25.6618	1.18369
$471$	18.1555	0.836561
$472$	0.100702	0.00463518
$473$	−15.0001	−0.689704
$474$	−3.26874	−0.150138
$475$	45.0946	2.06908
$476$	13.0076	0.596202
$477$	−13.6836	−0.626531
$478$	−4.27172	−0.195384
$479$	0.294271	0.0134456	0.00672278	−	0.999977i	$-0.497860\pi$
$479$	0.294271	0.0134456	0.00672278	+	0.999977i	$0.497860\pi$
$480$	4.27728	0.195230
$481$	4.53681	0.206861
$482$	−7.49584	−0.341426
$483$	−18.2218	−0.829119
$484$	20.8781	0.949005
$485$	27.9014	1.26694
$486$	−1.00000	−0.0453609
$487$	5.79774	0.262721	0.131360	−	0.991335i	$-0.458066\pi$
$487$	5.79774	0.262721	0.131360	+	0.991335i	$0.458066\pi$
$488$	−1.98798	−0.0899916
$489$	−7.54505	−0.341199
$490$	10.3383	0.467038
$491$	−27.9075	−1.25945	−0.629724	−	0.776819i	$-0.716832\pi$
$491$	−27.9075	−1.25945	−0.629724	+	0.776819i	$0.716832\pi$
$492$	−4.61293	−0.207967
$493$	39.0665	1.75947
$494$	3.39182	0.152605
$495$	−24.1498	−1.08545
$496$	3.39182	0.152297
$497$	−8.20085	−0.367858
$498$	−15.6894	−0.703061
$499$	12.6617	0.566815	0.283407	−	0.959000i	$-0.408535\pi$
$499$	12.6617	0.566815	0.283407	+	0.959000i	$0.408535\pi$
$500$	−35.4806	−1.58674
$501$	−8.92695	−0.398827
$502$	18.8336	0.840584
$503$	−17.9878	−0.802036	−0.401018	−	0.916070i	$-0.631343\pi$
$503$	−17.9878	−0.802036	−0.401018	+	0.916070i	$0.631343\pi$
$504$	−2.14079	−0.0953582
$505$	65.1168	2.89766
$506$	−48.0577	−2.13643
$507$	−1.00000	−0.0444116
$508$	16.6114	0.737011
$509$	20.8919	0.926016	0.463008	−	0.886354i	$-0.346770\pi$
$509$	20.8919	0.926016	0.463008	+	0.886354i	$0.346770\pi$
$510$	−25.9891	−1.15082
$511$	−6.76198	−0.299132
$512$	1.00000	0.0441942
$513$	−3.39182	−0.149752
$514$	3.11482	0.137389
$515$	−4.27728	−0.188480
$516$	2.65673	0.116956
$517$	−33.8739	−1.48977
$518$	−9.71235	−0.426736
$519$	−16.2335	−0.712571
$520$	−4.27728	−0.187571
$521$	39.5370	1.73215	0.866073	−	0.499918i	$-0.166636\pi$
$521$	39.5370	1.73215	0.866073	+	0.499918i	$0.166636\pi$
$522$	−6.42956	−0.281414
$523$	−0.461122	−0.0201635	−0.0100817	−	0.999949i	$-0.503209\pi$
$523$	−0.461122	−0.0201635	−0.0100817	+	0.999949i	$0.503209\pi$
$524$	5.56624	0.243162
$525$	28.4620	1.24219
$526$	23.0982	1.00713
$527$	−20.6089	−0.897740
$528$	−5.64607	−0.245714
$529$	49.4492	2.14997
$530$	58.5288	2.54233
$531$	0.100702	0.00437009
$532$	−7.26116	−0.314811
$533$	4.61293	0.199808
$534$	7.32723	0.317080
$535$	6.11089	0.264197
$536$	−7.85593	−0.339325
$537$	3.61131	0.155839
$538$	−24.8798	−1.07264
$539$	−13.6467	−0.587806
$540$	4.27728	0.184065
$541$	−0.829649	−0.0356694	−0.0178347	−	0.999841i	$-0.505677\pi$
$541$	−0.829649	−0.0356694	−0.0178347	+	0.999841i	$0.505677\pi$
$542$	20.5256	0.881648
$543$	−4.01150	−0.172150
$544$	−6.07608	−0.260510
$545$	−41.4716	−1.77645
$546$	2.14079	0.0916172
$547$	10.2127	0.436665	0.218332	−	0.975874i	$-0.429938\pi$
$547$	10.2127	0.436665	0.218332	+	0.975874i	$0.429938\pi$
$548$	18.2104	0.777908
$549$	−1.98798	−0.0848449
$550$	75.0652	3.20079
$551$	−21.8079	−0.929048
$552$	8.51171	0.362283
$553$	−6.99768	−0.297571
$554$	27.5111	1.16883
$555$	19.4052	0.823706
$556$	−0.868351	−0.0368263
$557$	−11.6483	−0.493554	−0.246777	−	0.969072i	$-0.579371\pi$
$557$	−11.6483	−0.493554	−0.246777	+	0.969072i	$0.579371\pi$
$558$	3.39182	0.143587
$559$	−2.65673	−0.112368
$560$	9.15675	0.386943
$561$	34.3060	1.44840
$562$	−7.60620	−0.320848
$563$	−14.2393	−0.600115	−0.300057	−	0.953921i	$-0.597006\pi$
$563$	−14.2393	−0.600115	−0.300057	+	0.953921i	$0.597006\pi$
$564$	5.99956	0.252627
$565$	−36.6027	−1.53989
$566$	−9.07187	−0.381319
$567$	−2.14079	−0.0899046
$568$	3.83076	0.160735
$569$	−27.7535	−1.16349	−0.581744	−	0.813372i	$-0.697629\pi$
$569$	−27.7535	−1.16349	−0.581744	+	0.813372i	$0.697629\pi$
$570$	14.5078	0.607663
$571$	32.8620	1.37523	0.687617	−	0.726074i	$-0.258657\pi$
$571$	32.8620	1.37523	0.687617	+	0.726074i	$0.258657\pi$
$572$	5.64607	0.236074
$573$	−22.0004	−0.919078
$574$	−9.87531	−0.412187
$575$	−113.164	−4.71928
$576$	1.00000	0.0416667
$577$	35.7465	1.48815	0.744074	−	0.668097i	$-0.232891\pi$
$577$	35.7465	1.48815	0.744074	+	0.668097i	$0.232891\pi$
$578$	19.9187	0.828510
$579$	−12.5347	−0.520926
$580$	27.5010	1.14192
$581$	−33.5877	−1.39345
$582$	6.52315	0.270393
$583$	−77.2588	−3.19973
$584$	3.15864	0.130706
$585$	−4.27728	−0.176844
$586$	−21.2646	−0.878432
$587$	−19.9553	−0.823644	−0.411822	−	0.911264i	$-0.635107\pi$
$587$	−19.9553	−0.823644	−0.411822	+	0.911264i	$0.635107\pi$
$588$	2.41703	0.0996767
$589$	11.5044	0.474032
$590$	−0.430730	−0.0177329
$591$	1.47488	0.0606687
$592$	4.53681	0.186462
$593$	5.87399	0.241216	0.120608	−	0.992700i	$-0.461516\pi$
$593$	5.87399	0.241216	0.120608	+	0.992700i	$0.461516\pi$
$594$	−5.64607	−0.231661
$595$	−55.6371	−2.28090
$596$	9.39696	0.384915
$597$	5.86202	0.239917
$598$	−8.51171	−0.348070
$599$	−10.4582	−0.427309	−0.213655	−	0.976909i	$-0.568537\pi$
$599$	−10.4582	−0.427309	−0.213655	+	0.976909i	$0.568537\pi$
$600$	−13.2951	−0.542771
$601$	−1.73507	−0.0707749	−0.0353875	−	0.999374i	$-0.511267\pi$
$601$	−1.73507	−0.0707749	−0.0353875	+	0.999374i	$0.511267\pi$
$602$	5.68748	0.231805
$603$	−7.85593	−0.319918
$604$	6.83407	0.278074
$605$	−89.3016	−3.63063
$606$	15.2239	0.618428
$607$	−40.8934	−1.65981	−0.829905	−	0.557905i	$-0.811606\pi$
$607$	−40.8934	−1.65981	−0.829905	+	0.557905i	$0.811606\pi$
$608$	3.39182	0.137556
$609$	−13.7643	−0.557759
$610$	8.50315	0.344282
$611$	−5.99956	−0.242716
$612$	−6.07608	−0.245611
$613$	8.57576	0.346372	0.173186	−	0.984889i	$-0.444594\pi$
$613$	8.57576	0.346372	0.173186	+	0.984889i	$0.444594\pi$
$614$	−10.2841	−0.415031
$615$	19.7308	0.795623
$616$	−12.0870	−0.487001
$617$	40.3264	1.62348	0.811740	−	0.584019i	$-0.198521\pi$
$617$	40.3264	1.62348	0.811740	+	0.584019i	$0.198521\pi$
$618$	−1.00000	−0.0402259
$619$	19.2293	0.772893	0.386446	−	0.922312i	$-0.373702\pi$
$619$	19.2293	0.772893	0.386446	+	0.922312i	$0.373702\pi$
$620$	−14.5078	−0.582645
$621$	8.51171	0.341563
$622$	11.8628	0.475657
$623$	15.6860	0.628448
$624$	−1.00000	−0.0400320
$625$	85.2848	3.41139
$626$	10.0467	0.401547
$627$	−19.1504	−0.764795
$628$	−18.1555	−0.724483
$629$	−27.5660	−1.09913
$630$	9.15675	0.364814
$631$	−45.4147	−1.80793	−0.903965	−	0.427606i	$-0.859357\pi$
$631$	−45.4147	−1.80793	−0.903965	+	0.427606i	$0.859357\pi$
$632$	3.26874	0.130023
$633$	−10.3608	−0.411806
$634$	30.5597	1.21368
$635$	−71.0516	−2.81960
$636$	13.6836	0.542592
$637$	−2.41703	−0.0957663
$638$	−36.3018	−1.43720
$639$	3.83076	0.151543
$640$	−4.27728	−0.169074
$641$	−35.9298	−1.41914	−0.709571	−	0.704634i	$-0.751111\pi$
$641$	−35.9298	−1.41914	−0.709571	+	0.704634i	$0.751111\pi$
$642$	1.42869	0.0563857
$643$	29.3300	1.15666	0.578332	−	0.815802i	$-0.303704\pi$
$643$	29.3300	1.15666	0.578332	+	0.815802i	$0.303704\pi$
$644$	18.2218	0.718038
$645$	−11.3636	−0.447440
$646$	−20.6089	−0.810848
$647$	−25.7212	−1.01121	−0.505603	−	0.862766i	$-0.668730\pi$
$647$	−25.7212	−1.01121	−0.505603	+	0.862766i	$0.668730\pi$
$648$	1.00000	0.0392837
$649$	0.568570	0.0223183
$650$	13.2951	0.521478
$651$	7.26116	0.284587
$652$	7.54505	0.295487
$653$	46.1946	1.80773	0.903867	−	0.427813i	$-0.140716\pi$
$653$	46.1946	1.80773	0.903867	+	0.427813i	$0.140716\pi$
$654$	−9.69578	−0.379135
$655$	−23.8084	−0.930270
$656$	4.61293	0.180105
$657$	3.15864	0.123230
$658$	12.8438	0.500702
$659$	−2.35332	−0.0916722	−0.0458361	−	0.998949i	$-0.514595\pi$
$659$	−2.35332	−0.0916722	−0.0458361	+	0.998949i	$0.514595\pi$
$660$	24.1498	0.940031
$661$	27.7452	1.07916	0.539582	−	0.841933i	$-0.318582\pi$
$661$	27.7452	1.07916	0.539582	+	0.841933i	$0.318582\pi$
$662$	3.61802	0.140618
$663$	6.07608	0.235975
$664$	15.6894	0.608868
$665$	31.0580	1.20438
$666$	4.53681	0.175798
$667$	54.7266	2.11902
$668$	8.92695	0.345394
$669$	16.0141	0.619140
$670$	33.6020	1.29816
$671$	−11.2243	−0.433308
$672$	2.14079	0.0825827
$673$	−19.1824	−0.739426	−0.369713	−	0.929146i	$-0.620544\pi$
$673$	−19.1824	−0.739426	−0.369713	+	0.929146i	$0.620544\pi$
$674$	18.7014	0.720351
$675$	−13.2951	−0.511730
$676$	1.00000	0.0384615
$677$	−35.0163	−1.34579	−0.672893	−	0.739740i	$-0.734948\pi$
$677$	−35.0163	−1.34579	−0.672893	+	0.739740i	$0.734948\pi$
$678$	−8.55748	−0.328648
$679$	13.9647	0.535915
$680$	25.9891	0.996636
$681$	−12.4891	−0.478582
$682$	19.1504	0.733308
$683$	27.3097	1.04498	0.522489	−	0.852646i	$-0.325004\pi$
$683$	27.3097	1.04498	0.522489	+	0.852646i	$0.325004\pi$
$684$	3.39182	0.129689
$685$	−77.8909	−2.97606
$686$	20.1599	0.769707
$687$	1.97084	0.0751922
$688$	−2.65673	−0.101287
$689$	−13.6836	−0.521305
$690$	−36.4070	−1.38599
$691$	26.9898	1.02674	0.513369	−	0.858168i	$-0.328397\pi$
$691$	26.9898	1.02674	0.513369	+	0.858168i	$0.328397\pi$
$692$	16.2335	0.617105
$693$	−12.0870	−0.459149
$694$	17.4950	0.664100
$695$	3.71418	0.140887
$696$	6.42956	0.243712
$697$	−28.0285	−1.06166
$698$	−20.4362	−0.773523
$699$	24.0527	0.909756
$700$	−28.4620	−1.07576
$701$	26.0528	0.984003	0.492001	−	0.870594i	$-0.336266\pi$
$701$	26.0528	0.984003	0.492001	+	0.870594i	$0.336266\pi$
$702$	−1.00000	−0.0377426
$703$	15.3880	0.580371
$704$	5.64607	0.212794
$705$	−25.6618	−0.966479
$706$	−0.541050	−0.0203627
$707$	32.5911	1.22571
$708$	−0.100702	−0.00378461
$709$	−49.7919	−1.86998	−0.934988	−	0.354680i	$-0.884590\pi$
$709$	−49.7919	−1.86998	−0.934988	+	0.354680i	$0.884590\pi$
$710$	−16.3852	−0.614927
$711$	3.26874	0.122587
$712$	−7.32723	−0.274600
$713$	−28.8702	−1.08120
$714$	−13.0076	−0.486797
$715$	−24.1498	−0.903152
$716$	−3.61131	−0.134961
$717$	4.27172	0.159530
$718$	−16.4361	−0.613390
$719$	−41.9626	−1.56494	−0.782470	−	0.622689i	$-0.786040\pi$
$719$	−41.9626	−1.56494	−0.782470	+	0.622689i	$0.786040\pi$
$720$	−4.27728	−0.159405
$721$	−2.14079	−0.0797271
$722$	−7.49558	−0.278956
$723$	7.49584	0.278773
$724$	4.01150	0.149086
$725$	−85.4819	−3.17472
$726$	−20.8781	−0.774860
$727$	−22.5563	−0.836567	−0.418283	−	0.908317i	$-0.637368\pi$
$727$	−22.5563	−0.836567	−0.418283	+	0.908317i	$0.637368\pi$
$728$	−2.14079	−0.0793428
$729$	1.00000	0.0370370
$730$	−13.5104	−0.500042
$731$	16.1425	0.597051
$732$	1.98798	0.0734778
$733$	−1.83749	−0.0678693	−0.0339346	−	0.999424i	$-0.510804\pi$
$733$	−1.83749	−0.0678693	−0.0339346	+	0.999424i	$0.510804\pi$
$734$	14.3975	0.531420
$735$	−10.3383	−0.381335
$736$	−8.51171	−0.313746
$737$	−44.3551	−1.63384
$738$	4.61293	0.169804
$739$	−14.1912	−0.522033	−0.261017	−	0.965334i	$-0.584058\pi$
$739$	−14.1912	−0.522033	−0.261017	+	0.965334i	$0.584058\pi$
$740$	−19.4052	−0.713350
$741$	−3.39182	−0.124602
$742$	29.2938	1.07541
$743$	−38.2464	−1.40312	−0.701562	−	0.712609i	$-0.747513\pi$
$743$	−38.2464	−1.40312	−0.701562	+	0.712609i	$0.747513\pi$
$744$	−3.39182	−0.124350
$745$	−40.1934	−1.47257
$746$	11.0628	0.405036
$747$	15.6894	0.574047
$748$	−34.3060	−1.25435
$749$	3.05851	0.111756
$750$	35.4806	1.29557
$751$	0.869679	0.0317350	0.0158675	−	0.999874i	$-0.494949\pi$
$751$	0.869679	0.0317350	0.0158675	+	0.999874i	$0.494949\pi$
$752$	−5.99956	−0.218781
$753$	−18.8336	−0.686334
$754$	−6.42956	−0.234151
$755$	−29.2312	−1.06383
$756$	2.14079	0.0778597
$757$	−44.0394	−1.60064	−0.800320	−	0.599573i	$-0.795337\pi$
$757$	−44.0394	−1.60064	−0.800320	+	0.599573i	$0.795337\pi$
$758$	27.1919	0.987654
$759$	48.0577	1.74439
$760$	−14.5078	−0.526252
$761$	15.1960	0.550854	0.275427	−	0.961322i	$-0.411181\pi$
$761$	15.1960	0.550854	0.275427	+	0.961322i	$0.411181\pi$
$762$	−16.6114	−0.601767
$763$	−20.7566	−0.751439
$764$	22.0004	0.795945
$765$	25.9891	0.939638
$766$	−10.2183	−0.369203
$767$	0.100702	0.00363613
$768$	−1.00000	−0.0360844
$769$	−10.8093	−0.389792	−0.194896	−	0.980824i	$-0.562437\pi$
$769$	−10.8093	−0.389792	−0.194896	+	0.980824i	$0.562437\pi$
$770$	51.6996	1.86313
$771$	−3.11482	−0.112178
$772$	12.5347	0.451135
$773$	19.6308	0.706069	0.353035	−	0.935610i	$-0.385150\pi$
$773$	19.6308	0.706069	0.353035	+	0.935610i	$0.385150\pi$
$774$	−2.65673	−0.0954940
$775$	45.0946	1.61985
$776$	−6.52315	−0.234168
$777$	9.71235	0.348429
$778$	20.7818	0.745063
$779$	15.6462	0.560584
$780$	4.27728	0.153151
$781$	21.6288	0.773938
$782$	51.7178	1.84943
$783$	6.42956	0.229774
$784$	−2.41703	−0.0863225
$785$	77.6561	2.77167
$786$	−5.56624	−0.198541
$787$	11.1470	0.397347	0.198674	−	0.980066i	$-0.436337\pi$
$787$	11.1470	0.397347	0.198674	+	0.980066i	$0.436337\pi$
$788$	−1.47488	−0.0525406
$789$	−23.0982	−0.822317
$790$	−13.9813	−0.497433
$791$	−18.3197	−0.651375
$792$	5.64607	0.200624
$793$	−1.98798	−0.0705952
$794$	−23.1114	−0.820192
$795$	−58.5288	−2.07580
$796$	−5.86202	−0.207774
$797$	48.5317	1.71908	0.859541	−	0.511067i	$-0.170750\pi$
$797$	48.5317	1.71908	0.859541	+	0.511067i	$0.170750\pi$
$798$	7.26116	0.257042
$799$	36.4538	1.28964
$800$	13.2951	0.470054
$801$	−7.32723	−0.258895
$802$	18.7174	0.660935
$803$	17.8339	0.629346
$804$	7.85593	0.277057
$805$	−77.9396	−2.74701
$806$	3.39182	0.119472
$807$	24.8798	0.875809
$808$	−15.2239	−0.535575
$809$	−48.5770	−1.70788	−0.853938	−	0.520375i	$-0.825792\pi$
$809$	−48.5770	−1.70788	−0.853938	+	0.520375i	$0.825792\pi$
$810$	−4.27728	−0.150288
$811$	−13.7951	−0.484411	−0.242205	−	0.970225i	$-0.577871\pi$
$811$	−13.7951	−0.484411	−0.242205	+	0.970225i	$0.577871\pi$
$812$	13.7643	0.483033
$813$	−20.5256	−0.719863
$814$	25.6152	0.897811
$815$	−32.2723	−1.13045
$816$	6.07608	0.212705
$817$	−9.01113	−0.315259
$818$	16.7184	0.584545
$819$	−2.14079	−0.0748052
$820$	−19.7308	−0.689030
$821$	49.0103	1.71047	0.855235	−	0.518240i	$-0.173413\pi$
$821$	49.0103	1.71047	0.855235	+	0.518240i	$0.173413\pi$
$822$	−18.2104	−0.635160
$823$	10.5338	0.367185	0.183592	−	0.983002i	$-0.441227\pi$
$823$	10.5338	0.367185	0.183592	+	0.983002i	$0.441227\pi$
$824$	1.00000	0.0348367
$825$	−75.0652	−2.61344
$826$	−0.215581	−0.00750103
$827$	−43.1958	−1.50207	−0.751033	−	0.660264i	$-0.770444\pi$
$827$	−43.1958	−1.50207	−0.751033	+	0.660264i	$0.770444\pi$
$828$	−8.51171	−0.295802
$829$	51.3208	1.78244	0.891222	−	0.453568i	$-0.149849\pi$
$829$	51.3208	1.78244	0.891222	+	0.453568i	$0.149849\pi$
$830$	−67.1081	−2.32936
$831$	−27.5111	−0.954348
$832$	1.00000	0.0346688
$833$	14.6861	0.508842
$834$	0.868351	0.0300685
$835$	−38.1831	−1.32138
$836$	19.1504	0.662332
$837$	−3.39182	−0.117238
$838$	−0.375740	−0.0129797
$839$	11.3755	0.392726	0.196363	−	0.980531i	$-0.437087\pi$
$839$	11.3755	0.392726	0.196363	+	0.980531i	$0.437087\pi$
$840$	−9.15675	−0.315938
$841$	12.3393	0.425492
$842$	−17.6135	−0.607001
$843$	7.60620	0.261972
$844$	10.3608	0.356635
$845$	−4.27728	−0.147143
$846$	−5.99956	−0.206269
$847$	−44.6956	−1.53576
$848$	−13.6836	−0.469898
$849$	9.07187	0.311346
$850$	−80.7823	−2.77081
$851$	−38.6160	−1.32374
$852$	−3.83076	−0.131240
$853$	8.22375	0.281576	0.140788	−	0.990040i	$-0.455036\pi$
$853$	8.22375	0.281576	0.140788	+	0.990040i	$0.455036\pi$
$854$	4.25584	0.145632
$855$	−14.5078	−0.496155
$856$	−1.42869	−0.0488315
$857$	−46.8967	−1.60196	−0.800980	−	0.598690i	$-0.795688\pi$
$857$	−46.8967	−1.60196	−0.800980	+	0.598690i	$0.795688\pi$
$858$	−5.64607	−0.192754
$859$	45.3249	1.54646	0.773232	−	0.634123i	$-0.218639\pi$
$859$	45.3249	1.54646	0.773232	+	0.634123i	$0.218639\pi$
$860$	11.3636	0.387494
$861$	9.87531	0.336550
$862$	38.1357	1.29891
$863$	−11.6352	−0.396067	−0.198033	−	0.980195i	$-0.563455\pi$
$863$	−11.6352	−0.396067	−0.198033	+	0.980195i	$0.563455\pi$
$864$	−1.00000	−0.0340207
$865$	−69.4352	−2.36087
$866$	−33.1341	−1.12594
$867$	−19.9187	−0.676476
$868$	−7.26116	−0.246460
$869$	18.4555	0.626061
$870$	−27.5010	−0.932373
$871$	−7.85593	−0.266188
$872$	9.69578	0.328341
$873$	−6.52315	−0.220775
$874$	−28.8702	−0.976548
$875$	75.9564	2.56779
$876$	−3.15864	−0.106721
$877$	48.7039	1.64462	0.822308	−	0.569043i	$-0.192686\pi$
$877$	48.7039	1.64462	0.822308	+	0.569043i	$0.192686\pi$
$878$	38.5264	1.30020
$879$	21.2646	0.717237
$880$	−24.1498	−0.814091
$881$	−46.3292	−1.56087	−0.780434	−	0.625238i	$-0.785002\pi$
$881$	−46.3292	−1.56087	−0.780434	+	0.625238i	$0.785002\pi$
$882$	−2.41703	−0.0813857
$883$	−4.59076	−0.154491	−0.0772457	−	0.997012i	$-0.524613\pi$
$883$	−4.59076	−0.154491	−0.0772457	+	0.997012i	$0.524613\pi$
$884$	−6.07608	−0.204361
$885$	0.430730	0.0144788
$886$	−36.6885	−1.23258
$887$	−0.245659	−0.00824842	−0.00412421	−	0.999991i	$-0.501313\pi$
$887$	−0.245659	−0.00824842	−0.00412421	+	0.999991i	$0.501313\pi$
$888$	−4.53681	−0.152245
$889$	−35.5615	−1.19269
$890$	31.3406	1.05054
$891$	5.64607	0.189151
$892$	−16.0141	−0.536191
$893$	−20.3494	−0.680967
$894$	−9.39696	−0.314281
$895$	15.4466	0.516322
$896$	−2.14079	−0.0715187
$897$	8.51171	0.284198
$898$	15.8187	0.527877
$899$	−21.8079	−0.727334
$900$	13.2951	0.443171
$901$	83.1429	2.76989
$902$	26.0450	0.867202
$903$	−5.68748	−0.189268
$904$	8.55748	0.284617
$905$	−17.1583	−0.570362
$906$	−6.83407	−0.227047
$907$	51.7311	1.71770	0.858851	−	0.512225i	$-0.171179\pi$
$907$	51.7311	1.71770	0.858851	+	0.512225i	$0.171179\pi$
$908$	12.4891	0.414465
$909$	−15.2239	−0.504945
$910$	9.15675	0.303543
$911$	31.7403	1.05160	0.525801	−	0.850608i	$-0.323766\pi$
$911$	31.7403	1.05160	0.525801	+	0.850608i	$0.323766\pi$
$912$	−3.39182	−0.112314
$913$	88.5837	2.93169
$914$	−8.59896	−0.284428
$915$	−8.50315	−0.281105
$916$	−1.97084	−0.0651183
$917$	−11.9161	−0.393506
$918$	6.07608	0.200540
$919$	−34.3967	−1.13464	−0.567322	−	0.823496i	$-0.692021\pi$
$919$	−34.3967	−1.13464	−0.567322	+	0.823496i	$0.692021\pi$
$920$	36.4070	1.20030
$921$	10.2841	0.338872
$922$	5.80201	0.191079
$923$	3.83076	0.126091
$924$	12.0870	0.397634
$925$	60.3175	1.98323
$926$	−9.29261	−0.305374
$927$	1.00000	0.0328443
$928$	−6.42956	−0.211061
$929$	−51.9657	−1.70494	−0.852470	−	0.522776i	$-0.824897\pi$
$929$	−51.9657	−1.70494	−0.852470	+	0.522776i	$0.824897\pi$
$930$	14.5078	0.475728
$931$	−8.19813	−0.268683
$932$	−24.0527	−0.787872
$933$	−11.8628	−0.388372
$934$	30.9688	1.01333
$935$	146.736	4.79879
$936$	1.00000	0.0326860
$937$	−47.6147	−1.55550	−0.777752	−	0.628571i	$-0.783640\pi$
$937$	−47.6147	−1.55550	−0.777752	+	0.628571i	$0.783640\pi$
$938$	16.8179	0.549123
$939$	−10.0467	−0.327862
$940$	25.6618	0.836995
$941$	−25.6255	−0.835368	−0.417684	−	0.908592i	$-0.637158\pi$
$941$	−25.6255	−0.835368	−0.417684	+	0.908592i	$0.637158\pi$
$942$	18.1555	0.591538
$943$	−39.2640	−1.27861
$944$	0.100702	0.00327757
$945$	−9.15675	−0.297869
$946$	−15.0001	−0.487694
$947$	58.5334	1.90208	0.951040	−	0.309068i	$-0.100017\pi$
$947$	58.5334	1.90208	0.951040	+	0.309068i	$0.100017\pi$
$948$	−3.26874	−0.106164
$949$	3.15864	0.102534
$950$	45.0946	1.46306
$951$	−30.5597	−0.990967
$952$	13.0076	0.421578
$953$	22.0255	0.713476	0.356738	−	0.934204i	$-0.383889\pi$
$953$	22.0255	0.713476	0.356738	+	0.934204i	$0.383889\pi$
$954$	−13.6836	−0.443024
$955$	−94.1017	−3.04506
$956$	−4.27172	−0.138157
$957$	36.3018	1.17347
$958$	0.294271	0.00950745
$959$	−38.9845	−1.25888
$960$	4.27728	0.138049
$961$	−19.4956	−0.628890
$962$	4.53681	0.146273
$963$	−1.42869	−0.0460387
$964$	−7.49584	−0.241425
$965$	−53.6146	−1.72591
$966$	−18.2218	−0.586276
$967$	1.05476	0.0339189	0.0169594	−	0.999856i	$-0.494601\pi$
$967$	1.05476	0.0339189	0.0169594	+	0.999856i	$0.494601\pi$
$968$	20.8781	0.671048
$969$	20.6089	0.662055
$970$	27.9014	0.895859
$971$	30.0391	0.964001	0.482000	−	0.876171i	$-0.339910\pi$
$971$	30.0391	0.964001	0.482000	+	0.876171i	$0.339910\pi$
$972$	−1.00000	−0.0320750
$973$	1.85895	0.0595953
$974$	5.79774	0.185772
$975$	−13.2951	−0.425785
$976$	−1.98798	−0.0636337
$977$	18.0775	0.578349	0.289175	−	0.957276i	$-0.406619\pi$
$977$	18.0775	0.578349	0.289175	+	0.957276i	$0.406619\pi$
$978$	−7.54505	−0.241264
$979$	−41.3701	−1.32219
$980$	10.3383	0.330246
$981$	9.69578	0.309562
$982$	−27.9075	−0.890565
$983$	23.0040	0.733712	0.366856	−	0.930278i	$-0.380434\pi$
$983$	23.0040	0.733712	0.366856	+	0.930278i	$0.380434\pi$
$984$	−4.61293	−0.147055
$985$	6.30850	0.201005
$986$	39.0665	1.24413
$987$	−12.8438	−0.408822
$988$	3.39182	0.107908
$989$	22.6133	0.719061
$990$	−24.1498	−0.767532
$991$	28.1236	0.893375	0.446687	−	0.894690i	$-0.352604\pi$
$991$	28.1236	0.893375	0.446687	+	0.894690i	$0.352604\pi$
$992$	3.39182	0.107690
$993$	−3.61802	−0.114814
$994$	−8.20085	−0.260115
$995$	25.0735	0.794884
$996$	−15.6894	−0.497139
$997$	59.9006	1.89707	0.948536	−	0.316670i	$-0.102565\pi$
$997$	59.9006	1.89707	0.948536	+	0.316670i	$0.102565\pi$
$998$	12.6617	0.400799
$999$	−4.53681	−0.143538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.1	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.1	✓	13	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.27728 q^{5} -1.00000 q^{6} -2.14079 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.27728 q^{5} -1.00000 q^{6} -2.14079 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.27728 q^{10} +5.64607 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.14079 q^{14} +4.27728 q^{15} +1.00000 q^{16} -6.07608 q^{17} +1.00000 q^{18} +3.39182 q^{19} -4.27728 q^{20} +2.14079 q^{21} +5.64607 q^{22} -8.51171 q^{23} -1.00000 q^{24} +13.2951 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.14079 q^{28} -6.42956 q^{29} +4.27728 q^{30} +3.39182 q^{31} +1.00000 q^{32} -5.64607 q^{33} -6.07608 q^{34} +9.15675 q^{35} +1.00000 q^{36} +4.53681 q^{37} +3.39182 q^{38} -1.00000 q^{39} -4.27728 q^{40} +4.61293 q^{41} +2.14079 q^{42} -2.65673 q^{43} +5.64607 q^{44} -4.27728 q^{45} -8.51171 q^{46} -5.99956 q^{47} -1.00000 q^{48} -2.41703 q^{49} +13.2951 q^{50} +6.07608 q^{51} +1.00000 q^{52} -13.6836 q^{53} -1.00000 q^{54} -24.1498 q^{55} -2.14079 q^{56} -3.39182 q^{57} -6.42956 q^{58} +0.100702 q^{59} +4.27728 q^{60} -1.98798 q^{61} +3.39182 q^{62} -2.14079 q^{63} +1.00000 q^{64} -4.27728 q^{65} -5.64607 q^{66} -7.85593 q^{67} -6.07608 q^{68} +8.51171 q^{69} +9.15675 q^{70} +3.83076 q^{71} +1.00000 q^{72} +3.15864 q^{73} +4.53681 q^{74} -13.2951 q^{75} +3.39182 q^{76} -12.0870 q^{77} -1.00000 q^{78} +3.26874 q^{79} -4.27728 q^{80} +1.00000 q^{81} +4.61293 q^{82} +15.6894 q^{83} +2.14079 q^{84} +25.9891 q^{85} -2.65673 q^{86} +6.42956 q^{87} +5.64607 q^{88} -7.32723 q^{89} -4.27728 q^{90} -2.14079 q^{91} -8.51171 q^{92} -3.39182 q^{93} -5.99956 q^{94} -14.5078 q^{95} -1.00000 q^{96} -6.52315 q^{97} -2.41703 q^{98} +5.64607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

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