LMFDB - Embedded newform 8034.2.a.y.1.5

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			1.5
Root			$1.94320$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.714571 q^{5} -1.00000 q^{6} +1.94320 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.714571 q^{5} -1.00000 q^{6} +1.94320 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.714571 q^{10} -2.05273 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.94320 q^{14} +0.714571 q^{15} +1.00000 q^{16} -7.24316 q^{17} +1.00000 q^{18} +3.15532 q^{19} -0.714571 q^{20} -1.94320 q^{21} -2.05273 q^{22} +2.78843 q^{23} -1.00000 q^{24} -4.48939 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.94320 q^{28} +3.55081 q^{29} +0.714571 q^{30} +3.15532 q^{31} +1.00000 q^{32} +2.05273 q^{33} -7.24316 q^{34} -1.38855 q^{35} +1.00000 q^{36} -6.57100 q^{37} +3.15532 q^{38} -1.00000 q^{39} -0.714571 q^{40} -1.66403 q^{41} -1.94320 q^{42} +5.71368 q^{43} -2.05273 q^{44} -0.714571 q^{45} +2.78843 q^{46} +12.8467 q^{47} -1.00000 q^{48} -3.22398 q^{49} -4.48939 q^{50} +7.24316 q^{51} +1.00000 q^{52} -9.25022 q^{53} -1.00000 q^{54} +1.46682 q^{55} +1.94320 q^{56} -3.15532 q^{57} +3.55081 q^{58} +12.3150 q^{59} +0.714571 q^{60} +11.2133 q^{61} +3.15532 q^{62} +1.94320 q^{63} +1.00000 q^{64} -0.714571 q^{65} +2.05273 q^{66} +3.69525 q^{67} -7.24316 q^{68} -2.78843 q^{69} -1.38855 q^{70} +9.88886 q^{71} +1.00000 q^{72} +0.674630 q^{73} -6.57100 q^{74} +4.48939 q^{75} +3.15532 q^{76} -3.98886 q^{77} -1.00000 q^{78} -2.88763 q^{79} -0.714571 q^{80} +1.00000 q^{81} -1.66403 q^{82} +7.36282 q^{83} -1.94320 q^{84} +5.17575 q^{85} +5.71368 q^{86} -3.55081 q^{87} -2.05273 q^{88} +2.45175 q^{89} -0.714571 q^{90} +1.94320 q^{91} +2.78843 q^{92} -3.15532 q^{93} +12.8467 q^{94} -2.25470 q^{95} -1.00000 q^{96} +12.8591 q^{97} -3.22398 q^{98} -2.05273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.714571	−0.319566	−0.159783	−	0.987152i	$-0.551079\pi$
$5$	−0.714571	−0.319566	−0.159783	+	0.987152i	$0.551079\pi$
$6$	−1.00000	−0.408248
$7$	1.94320	0.734460	0.367230	−	0.930130i	$-0.380306\pi$
$7$	1.94320	0.734460	0.367230	+	0.930130i	$0.380306\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.714571	−0.225967
$11$	−2.05273	−0.618920	−0.309460	−	0.950912i	$-0.600148\pi$
$11$	−2.05273	−0.618920	−0.309460	+	0.950912i	$0.600148\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.94320	0.519342
$15$	0.714571	0.184501
$16$	1.00000	0.250000
$17$	−7.24316	−1.75672	−0.878362	−	0.477995i	$-0.841364\pi$
$17$	−7.24316	−1.75672	−0.878362	+	0.477995i	$0.841364\pi$
$18$	1.00000	0.235702
$19$	3.15532	0.723881	0.361940	−	0.932201i	$-0.382114\pi$
$19$	3.15532	0.723881	0.361940	+	0.932201i	$0.382114\pi$
$20$	−0.714571	−0.159783
$21$	−1.94320	−0.424041
$22$	−2.05273	−0.437643
$23$	2.78843	0.581428	0.290714	−	0.956810i	$-0.406107\pi$
$23$	2.78843	0.581428	0.290714	+	0.956810i	$0.406107\pi$
$24$	−1.00000	−0.204124
$25$	−4.48939	−0.897878
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.94320	0.367230
$29$	3.55081	0.659369	0.329684	−	0.944091i	$-0.393058\pi$
$29$	3.55081	0.659369	0.329684	+	0.944091i	$0.393058\pi$
$30$	0.714571	0.130462
$31$	3.15532	0.566713	0.283356	−	0.959015i	$-0.408552\pi$
$31$	3.15532	0.566713	0.283356	+	0.959015i	$0.408552\pi$
$32$	1.00000	0.176777
$33$	2.05273	0.357334
$34$	−7.24316	−1.24219
$35$	−1.38855	−0.234708
$36$	1.00000	0.166667
$37$	−6.57100	−1.08026	−0.540132	−	0.841580i	$-0.681626\pi$
$37$	−6.57100	−1.08026	−0.540132	+	0.841580i	$0.681626\pi$
$38$	3.15532	0.511861
$39$	−1.00000	−0.160128
$40$	−0.714571	−0.112984
$41$	−1.66403	−0.259877	−0.129939	−	0.991522i	$-0.541478\pi$
$41$	−1.66403	−0.259877	−0.129939	+	0.991522i	$0.541478\pi$
$42$	−1.94320	−0.299842
$43$	5.71368	0.871329	0.435664	−	0.900109i	$-0.356513\pi$
$43$	5.71368	0.871329	0.435664	+	0.900109i	$0.356513\pi$
$44$	−2.05273	−0.309460
$45$	−0.714571	−0.106522
$46$	2.78843	0.411132
$47$	12.8467	1.87388	0.936942	−	0.349485i	$-0.113644\pi$
$47$	12.8467	1.87388	0.936942	+	0.349485i	$0.113644\pi$
$48$	−1.00000	−0.144338
$49$	−3.22398	−0.460568
$50$	−4.48939	−0.634895
$51$	7.24316	1.01425
$52$	1.00000	0.138675
$53$	−9.25022	−1.27062	−0.635308	−	0.772259i	$-0.719127\pi$
$53$	−9.25022	−1.27062	−0.635308	+	0.772259i	$0.719127\pi$
$54$	−1.00000	−0.136083
$55$	1.46682	0.197786
$56$	1.94320	0.259671
$57$	−3.15532	−0.417933
$58$	3.55081	0.466244
$59$	12.3150	1.60328	0.801640	−	0.597808i	$-0.203961\pi$
$59$	12.3150	1.60328	0.801640	+	0.597808i	$0.203961\pi$
$60$	0.714571	0.0922507
$61$	11.2133	1.43571	0.717857	−	0.696190i	$-0.245123\pi$
$61$	11.2133	1.43571	0.717857	+	0.696190i	$0.245123\pi$
$62$	3.15532	0.400726
$63$	1.94320	0.244820
$64$	1.00000	0.125000
$65$	−0.714571	−0.0886316
$66$	2.05273	0.252673
$67$	3.69525	0.451446	0.225723	−	0.974192i	$-0.427526\pi$
$67$	3.69525	0.451446	0.225723	+	0.974192i	$0.427526\pi$
$68$	−7.24316	−0.878362
$69$	−2.78843	−0.335688
$70$	−1.38855	−0.165964
$71$	9.88886	1.17359	0.586796	−	0.809735i	$-0.300389\pi$
$71$	9.88886	1.17359	0.586796	+	0.809735i	$0.300389\pi$
$72$	1.00000	0.117851
$73$	0.674630	0.0789594	0.0394797	−	0.999220i	$-0.487430\pi$
$73$	0.674630	0.0789594	0.0394797	+	0.999220i	$0.487430\pi$
$74$	−6.57100	−0.763863
$75$	4.48939	0.518390
$76$	3.15532	0.361940
$77$	−3.98886	−0.454572
$78$	−1.00000	−0.113228
$79$	−2.88763	−0.324884	−0.162442	−	0.986718i	$-0.551937\pi$
$79$	−2.88763	−0.324884	−0.162442	+	0.986718i	$0.551937\pi$
$80$	−0.714571	−0.0798914
$81$	1.00000	0.111111
$82$	−1.66403	−0.183761
$83$	7.36282	0.808174	0.404087	−	0.914720i	$-0.367589\pi$
$83$	7.36282	0.808174	0.404087	+	0.914720i	$0.367589\pi$
$84$	−1.94320	−0.212020
$85$	5.17575	0.561389
$86$	5.71368	0.616122
$87$	−3.55081	−0.380687
$88$	−2.05273	−0.218821
$89$	2.45175	0.259885	0.129942	−	0.991522i	$-0.458521\pi$
$89$	2.45175	0.259885	0.129942	+	0.991522i	$0.458521\pi$
$90$	−0.714571	−0.0753224
$91$	1.94320	0.203703
$92$	2.78843	0.290714
$93$	−3.15532	−0.327192
$94$	12.8467	1.32504
$95$	−2.25470	−0.231327
$96$	−1.00000	−0.102062
$97$	12.8591	1.30564	0.652822	−	0.757511i	$-0.273585\pi$
$97$	12.8591	1.30564	0.652822	+	0.757511i	$0.273585\pi$
$98$	−3.22398	−0.325671
$99$	−2.05273	−0.206307
$100$	−4.48939	−0.448939
$101$	−16.3980	−1.63167	−0.815833	−	0.578287i	$-0.803721\pi$
$101$	−16.3980	−1.63167	−0.815833	+	0.578287i	$0.803721\pi$
$102$	7.24316	0.717180
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	1.38855	0.135509
$106$	−9.25022	−0.898461
$107$	−3.83793	−0.371026	−0.185513	−	0.982642i	$-0.559395\pi$
$107$	−3.83793	−0.371026	−0.185513	+	0.982642i	$0.559395\pi$
$108$	−1.00000	−0.0962250
$109$	9.66094	0.925351	0.462675	−	0.886528i	$-0.346890\pi$
$109$	9.66094	0.925351	0.462675	+	0.886528i	$0.346890\pi$
$110$	1.46682	0.139856
$111$	6.57100	0.623691
$112$	1.94320	0.183615
$113$	−16.0724	−1.51196	−0.755980	−	0.654595i	$-0.772839\pi$
$113$	−16.0724	−1.51196	−0.755980	+	0.654595i	$0.772839\pi$
$114$	−3.15532	−0.295523
$115$	−1.99253	−0.185805
$116$	3.55081	0.329684
$117$	1.00000	0.0924500
$118$	12.3150	1.13369
$119$	−14.0749	−1.29024
$120$	0.714571	0.0652311
$121$	−6.78631	−0.616938
$122$	11.2133	1.01520
$123$	1.66403	0.150040
$124$	3.15532	0.283356
$125$	6.78084	0.606497
$126$	1.94320	0.173114
$127$	5.59677	0.496633	0.248316	−	0.968679i	$-0.420123\pi$
$127$	5.59677	0.496633	0.248316	+	0.968679i	$0.420123\pi$
$128$	1.00000	0.0883883
$129$	−5.71368	−0.503062
$130$	−0.714571	−0.0626720
$131$	−8.55830	−0.747742	−0.373871	−	0.927481i	$-0.621970\pi$
$131$	−8.55830	−0.747742	−0.373871	+	0.927481i	$0.621970\pi$
$132$	2.05273	0.178667
$133$	6.13142	0.531662
$134$	3.69525	0.319221
$135$	0.714571	0.0615004
$136$	−7.24316	−0.621096
$137$	8.31911	0.710750	0.355375	−	0.934724i	$-0.384353\pi$
$137$	8.31911	0.710750	0.355375	+	0.934724i	$0.384353\pi$
$138$	−2.78843	−0.237367
$139$	−0.00440462	−0.000373595 0	−0.000186798	−	1.00000i	$-0.500059\pi$
$139$	−0.00440462	−0.000373595 0	−0.000186798		1.00000i	$0.500059\pi$
$140$	−1.38855	−0.117354
$141$	−12.8467	−1.08189
$142$	9.88886	0.829855
$143$	−2.05273	−0.171658
$144$	1.00000	0.0833333
$145$	−2.53730	−0.210712
$146$	0.674630	0.0558328
$147$	3.22398	0.265909
$148$	−6.57100	−0.540132
$149$	−7.55634	−0.619039	−0.309520	−	0.950893i	$-0.600168\pi$
$149$	−7.55634	−0.619039	−0.309520	+	0.950893i	$0.600168\pi$
$150$	4.48939	0.366557
$151$	17.8855	1.45550	0.727750	−	0.685843i	$-0.240566\pi$
$151$	17.8855	1.45550	0.727750	+	0.685843i	$0.240566\pi$
$152$	3.15532	0.255931
$153$	−7.24316	−0.585575
$154$	−3.98886	−0.321431
$155$	−2.25470	−0.181102
$156$	−1.00000	−0.0800641
$157$	23.2499	1.85554	0.927771	−	0.373150i	$-0.121722\pi$
$157$	23.2499	1.85554	0.927771	+	0.373150i	$0.121722\pi$
$158$	−2.88763	−0.229727
$159$	9.25022	0.733590
$160$	−0.714571	−0.0564918
$161$	5.41848	0.427036
$162$	1.00000	0.0785674
$163$	−13.2352	−1.03666	−0.518329	−	0.855181i	$-0.673446\pi$
$163$	−13.2352	−1.03666	−0.518329	+	0.855181i	$0.673446\pi$
$164$	−1.66403	−0.129939
$165$	−1.46682	−0.114192
$166$	7.36282	0.571466
$167$	−7.03944	−0.544728	−0.272364	−	0.962194i	$-0.587805\pi$
$167$	−7.03944	−0.544728	−0.272364	+	0.962194i	$0.587805\pi$
$168$	−1.94320	−0.149921
$169$	1.00000	0.0769231
$170$	5.17575	0.396962
$171$	3.15532	0.241294
$172$	5.71368	0.435664
$173$	14.8519	1.12917	0.564583	−	0.825376i	$-0.309037\pi$
$173$	14.8519	1.12917	0.564583	+	0.825376i	$0.309037\pi$
$174$	−3.55081	−0.269186
$175$	−8.72377	−0.659455
$176$	−2.05273	−0.154730
$177$	−12.3150	−0.925654
$178$	2.45175	0.183766
$179$	−13.3652	−0.998966	−0.499483	−	0.866324i	$-0.666477\pi$
$179$	−13.3652	−0.998966	−0.499483	+	0.866324i	$0.666477\pi$
$180$	−0.714571	−0.0532609
$181$	−5.80679	−0.431616	−0.215808	−	0.976436i	$-0.569238\pi$
$181$	−5.80679	−0.431616	−0.215808	+	0.976436i	$0.569238\pi$
$182$	1.94320	0.144039
$183$	−11.2133	−0.828910
$184$	2.78843	0.205566
$185$	4.69544	0.345216
$186$	−3.15532	−0.231360
$187$	14.8682	1.08727
$188$	12.8467	0.936942
$189$	−1.94320	−0.141347
$190$	−2.25470	−0.163573
$191$	−3.41345	−0.246989	−0.123494	−	0.992345i	$-0.539410\pi$
$191$	−3.41345	−0.246989	−0.123494	+	0.992345i	$0.539410\pi$
$192$	−1.00000	−0.0721688
$193$	23.6875	1.70506	0.852531	−	0.522677i	$-0.175067\pi$
$193$	23.6875	1.70506	0.852531	+	0.522677i	$0.175067\pi$
$194$	12.8591	0.923230
$195$	0.714571	0.0511715
$196$	−3.22398	−0.230284
$197$	17.8203	1.26965	0.634824	−	0.772657i	$-0.281073\pi$
$197$	17.8203	1.26965	0.634824	+	0.772657i	$0.281073\pi$
$198$	−2.05273	−0.145881
$199$	16.0499	1.13775	0.568873	−	0.822426i	$-0.307380\pi$
$199$	16.0499	1.13775	0.568873	+	0.822426i	$0.307380\pi$
$200$	−4.48939	−0.317448
$201$	−3.69525	−0.260643
$202$	−16.3980	−1.15376
$203$	6.89993	0.484280
$204$	7.24316	0.507123
$205$	1.18907	0.0830479
$206$	1.00000	0.0696733
$207$	2.78843	0.193809
$208$	1.00000	0.0693375
$209$	−6.47702	−0.448025
$210$	1.38855	0.0958192
$211$	19.3542	1.33240	0.666199	−	0.745774i	$-0.267920\pi$
$211$	19.3542	1.33240	0.666199	+	0.745774i	$0.267920\pi$
$212$	−9.25022	−0.635308
$213$	−9.88886	−0.677573
$214$	−3.83793	−0.262355
$215$	−4.08283	−0.278447
$216$	−1.00000	−0.0680414
$217$	6.13142	0.416228
$218$	9.66094	0.654322
$219$	−0.674630	−0.0455873
$220$	1.46682	0.0988929
$221$	−7.24316	−0.487228
$222$	6.57100	0.441016
$223$	9.16474	0.613716	0.306858	−	0.951755i	$-0.400722\pi$
$223$	9.16474	0.613716	0.306858	+	0.951755i	$0.400722\pi$
$224$	1.94320	0.129835
$225$	−4.48939	−0.299293
$226$	−16.0724	−1.06912
$227$	−24.8758	−1.65107	−0.825534	−	0.564353i	$-0.809126\pi$
$227$	−24.8758	−1.65107	−0.825534	+	0.564353i	$0.809126\pi$
$228$	−3.15532	−0.208966
$229$	1.91634	0.126635	0.0633176	−	0.997993i	$-0.479832\pi$
$229$	1.91634	0.126635	0.0633176	+	0.997993i	$0.479832\pi$
$230$	−1.99253	−0.131384
$231$	3.98886	0.262447
$232$	3.55081	0.233122
$233$	3.45081	0.226070	0.113035	−	0.993591i	$-0.463943\pi$
$233$	3.45081	0.226070	0.113035	+	0.993591i	$0.463943\pi$
$234$	1.00000	0.0653720
$235$	−9.17987	−0.598829
$236$	12.3150	0.801640
$237$	2.88763	0.187572
$238$	−14.0749	−0.912340
$239$	11.0788	0.716625	0.358313	−	0.933602i	$-0.383352\pi$
$239$	11.0788	0.716625	0.358313	+	0.933602i	$0.383352\pi$
$240$	0.714571	0.0461253
$241$	14.7466	0.949913	0.474957	−	0.880009i	$-0.342464\pi$
$241$	14.7466	0.949913	0.474957	+	0.880009i	$0.342464\pi$
$242$	−6.78631	−0.436241
$243$	−1.00000	−0.0641500
$244$	11.2133	0.717857
$245$	2.30376	0.147182
$246$	1.66403	0.106095
$247$	3.15532	0.200768
$248$	3.15532	0.200363
$249$	−7.36282	−0.466600
$250$	6.78084	0.428858
$251$	8.43392	0.532344	0.266172	−	0.963926i	$-0.414241\pi$
$251$	8.43392	0.532344	0.266172	+	0.963926i	$0.414241\pi$
$252$	1.94320	0.122410
$253$	−5.72389	−0.359858
$254$	5.59677	0.351172
$255$	−5.17575	−0.324118
$256$	1.00000	0.0625000
$257$	−14.3619	−0.895868	−0.447934	−	0.894067i	$-0.647840\pi$
$257$	−14.3619	−0.895868	−0.447934	+	0.894067i	$0.647840\pi$
$258$	−5.71368	−0.355718
$259$	−12.7688	−0.793412
$260$	−0.714571	−0.0443158
$261$	3.55081	0.219790
$262$	−8.55830	−0.528734
$263$	5.96407	0.367760	0.183880	−	0.982949i	$-0.441134\pi$
$263$	5.96407	0.367760	0.183880	+	0.982949i	$0.441134\pi$
$264$	2.05273	0.126337
$265$	6.60994	0.406045
$266$	6.13142	0.375942
$267$	−2.45175	−0.150045
$268$	3.69525	0.225723
$269$	10.8798	0.663356	0.331678	−	0.943393i	$-0.392385\pi$
$269$	10.8798	0.663356	0.331678	+	0.943393i	$0.392385\pi$
$270$	0.714571	0.0434874
$271$	−4.14209	−0.251614	−0.125807	−	0.992055i	$-0.540152\pi$
$271$	−4.14209	−0.251614	−0.125807	+	0.992055i	$0.540152\pi$
$272$	−7.24316	−0.439181
$273$	−1.94320	−0.117608
$274$	8.31911	0.502576
$275$	9.21549	0.555715
$276$	−2.78843	−0.167844
$277$	−8.16157	−0.490381	−0.245191	−	0.969475i	$-0.578851\pi$
$277$	−8.16157	−0.490381	−0.245191	+	0.969475i	$0.578851\pi$
$278$	−0.00440462	−0.000264172 0
$279$	3.15532	0.188904
$280$	−1.38855	−0.0829819
$281$	25.3865	1.51443	0.757217	−	0.653164i	$-0.226559\pi$
$281$	25.3865	1.51443	0.757217	+	0.653164i	$0.226559\pi$
$282$	−12.8467	−0.765010
$283$	−27.4546	−1.63201	−0.816003	−	0.578047i	$-0.803815\pi$
$283$	−27.4546	−1.63201	−0.816003	+	0.578047i	$0.803815\pi$
$284$	9.88886	0.586796
$285$	2.25470	0.133557
$286$	−2.05273	−0.121380
$287$	−3.23354	−0.190870
$288$	1.00000	0.0589256
$289$	35.4634	2.08608
$290$	−2.53730	−0.148996
$291$	−12.8591	−0.753814
$292$	0.674630	0.0394797
$293$	−7.86878	−0.459699	−0.229850	−	0.973226i	$-0.573823\pi$
$293$	−7.86878	−0.459699	−0.229850	+	0.973226i	$0.573823\pi$
$294$	3.22398	0.188026
$295$	−8.79995	−0.512353
$296$	−6.57100	−0.381931
$297$	2.05273	0.119111
$298$	−7.55634	−0.437727
$299$	2.78843	0.161259
$300$	4.48939	0.259195
$301$	11.1028	0.639956
$302$	17.8855	1.02919
$303$	16.3980	0.942043
$304$	3.15532	0.180970
$305$	−8.01269	−0.458805
$306$	−7.24316	−0.414064
$307$	−30.7275	−1.75371	−0.876854	−	0.480756i	$-0.840362\pi$
$307$	−30.7275	−1.75371	−0.876854	+	0.480756i	$0.840362\pi$
$308$	−3.98886	−0.227286
$309$	−1.00000	−0.0568880
$310$	−2.25470	−0.128058
$311$	−14.2786	−0.809665	−0.404832	−	0.914391i	$-0.632670\pi$
$311$	−14.2786	−0.809665	−0.404832	+	0.914391i	$0.632670\pi$
$312$	−1.00000	−0.0566139
$313$	27.5810	1.55897	0.779484	−	0.626422i	$-0.215481\pi$
$313$	27.5810	1.55897	0.779484	+	0.626422i	$0.215481\pi$
$314$	23.2499	1.31207
$315$	−1.38855	−0.0782361
$316$	−2.88763	−0.162442
$317$	−0.915024	−0.0513929	−0.0256964	−	0.999670i	$-0.508180\pi$
$317$	−0.915024	−0.0513929	−0.0256964	+	0.999670i	$0.508180\pi$
$318$	9.25022	0.518727
$319$	−7.28884	−0.408097
$320$	−0.714571	−0.0399457
$321$	3.83793	0.214212
$322$	5.41848	0.301960
$323$	−22.8545	−1.27166
$324$	1.00000	0.0555556
$325$	−4.48939	−0.249026
$326$	−13.2352	−0.733028
$327$	−9.66094	−0.534251
$328$	−1.66403	−0.0918806
$329$	24.9637	1.37629
$330$	−1.46682	−0.0807457
$331$	28.8518	1.58584	0.792919	−	0.609328i	$-0.208561\pi$
$331$	28.8518	1.58584	0.792919	+	0.609328i	$0.208561\pi$
$332$	7.36282	0.404087
$333$	−6.57100	−0.360088
$334$	−7.03944	−0.385181
$335$	−2.64051	−0.144267
$336$	−1.94320	−0.106010
$337$	0.862810	0.0470003	0.0235001	−	0.999724i	$-0.492519\pi$
$337$	0.862810	0.0470003	0.0235001	+	0.999724i	$0.492519\pi$
$338$	1.00000	0.0543928
$339$	16.0724	0.872931
$340$	5.17575	0.280694
$341$	−6.47702	−0.350750
$342$	3.15532	0.170620
$343$	−19.8672	−1.07273
$344$	5.71368	0.308061
$345$	1.99253	0.107274
$346$	14.8519	0.798442
$347$	21.2936	1.14310	0.571550	−	0.820567i	$-0.306342\pi$
$347$	21.2936	1.14310	0.571550	+	0.820567i	$0.306342\pi$
$348$	−3.55081	−0.190343
$349$	34.6954	1.85720	0.928602	−	0.371078i	$-0.121012\pi$
$349$	34.6954	1.85720	0.928602	+	0.371078i	$0.121012\pi$
$350$	−8.72377	−0.466305
$351$	−1.00000	−0.0533761
$352$	−2.05273	−0.109411
$353$	−28.4224	−1.51277	−0.756386	−	0.654125i	$-0.773037\pi$
$353$	−28.4224	−1.51277	−0.756386	+	0.654125i	$0.773037\pi$
$354$	−12.3150	−0.654536
$355$	−7.06629	−0.375040
$356$	2.45175	0.129942
$357$	14.0749	0.744923
$358$	−13.3652	−0.706375
$359$	0.128772	0.00679630	0.00339815	−	0.999994i	$-0.498918\pi$
$359$	0.128772	0.00679630	0.00339815	+	0.999994i	$0.498918\pi$
$360$	−0.714571	−0.0376612
$361$	−9.04393	−0.475997
$362$	−5.80679	−0.305198
$363$	6.78631	0.356189
$364$	1.94320	0.101851
$365$	−0.482071	−0.0252327
$366$	−11.2133	−0.586128
$367$	−0.565222	−0.0295043	−0.0147522	−	0.999891i	$-0.504696\pi$
$367$	−0.565222	−0.0295043	−0.0147522	+	0.999891i	$0.504696\pi$
$368$	2.78843	0.145357
$369$	−1.66403	−0.0866258
$370$	4.69544	0.244104
$371$	−17.9750	−0.933216
$372$	−3.15532	−0.163596
$373$	−1.66702	−0.0863150	−0.0431575	−	0.999068i	$-0.513742\pi$
$373$	−1.66702	−0.0863150	−0.0431575	+	0.999068i	$0.513742\pi$
$374$	14.8682	0.768818
$375$	−6.78084	−0.350161
$376$	12.8467	0.662518
$377$	3.55081	0.182876
$378$	−1.94320	−0.0999474
$379$	16.4501	0.844987	0.422494	−	0.906366i	$-0.361155\pi$
$379$	16.4501	0.844987	0.422494	+	0.906366i	$0.361155\pi$
$380$	−2.25470	−0.115664
$381$	−5.59677	−0.286731
$382$	−3.41345	−0.174647
$383$	0.266649	0.0136251	0.00681256	−	0.999977i	$-0.497831\pi$
$383$	0.266649	0.0136251	0.00681256	+	0.999977i	$0.497831\pi$
$384$	−1.00000	−0.0510310
$385$	2.85032	0.145266
$386$	23.6875	1.20566
$387$	5.71368	0.290443
$388$	12.8591	0.652822
$389$	37.5288	1.90279	0.951394	−	0.307978i	$-0.0996523\pi$
$389$	37.5288	1.90279	0.951394	+	0.307978i	$0.0996523\pi$
$390$	0.714571	0.0361837
$391$	−20.1971	−1.02141
$392$	−3.22398	−0.162836
$393$	8.55830	0.431709
$394$	17.8203	0.897776
$395$	2.06342	0.103822
$396$	−2.05273	−0.103153
$397$	2.13003	0.106903	0.0534515	−	0.998570i	$-0.482978\pi$
$397$	2.13003	0.106903	0.0534515	+	0.998570i	$0.482978\pi$
$398$	16.0499	0.804508
$399$	−6.13142	−0.306955
$400$	−4.48939	−0.224469
$401$	−34.9649	−1.74606	−0.873031	−	0.487664i	$-0.837849\pi$
$401$	−34.9649	−1.74606	−0.873031	+	0.487664i	$0.837849\pi$
$402$	−3.69525	−0.184302
$403$	3.15532	0.157178
$404$	−16.3980	−0.815833
$405$	−0.714571	−0.0355073
$406$	6.89993	0.342438
$407$	13.4885	0.668598
$408$	7.24316	0.358590
$409$	−18.3631	−0.907999	−0.453999	−	0.891002i	$-0.650003\pi$
$409$	−18.3631	−0.907999	−0.453999	+	0.891002i	$0.650003\pi$
$410$	1.18907	0.0587237
$411$	−8.31911	−0.410351
$412$	1.00000	0.0492665
$413$	23.9305	1.17754
$414$	2.78843	0.137044
$415$	−5.26125	−0.258265
$416$	1.00000	0.0490290
$417$	0.00440462	0.000215695 0
$418$	−6.47702	−0.316801
$419$	28.8460	1.40922	0.704609	−	0.709596i	$-0.251122\pi$
$419$	28.8460	1.40922	0.704609	+	0.709596i	$0.251122\pi$
$420$	1.38855	0.0677544
$421$	−9.28103	−0.452330	−0.226165	−	0.974089i	$-0.572619\pi$
$421$	−9.28103	−0.452330	−0.226165	+	0.974089i	$0.572619\pi$
$422$	19.3542	0.942147
$423$	12.8467	0.624628
$424$	−9.25022	−0.449230
$425$	32.5174	1.57732
$426$	−9.88886	−0.479117
$427$	21.7897	1.05448
$428$	−3.83793	−0.185513
$429$	2.05273	0.0991066
$430$	−4.08283	−0.196892
$431$	20.0651	0.966504	0.483252	−	0.875481i	$-0.339456\pi$
$431$	20.0651	0.966504	0.483252	+	0.875481i	$0.339456\pi$
$432$	−1.00000	−0.0481125
$433$	−33.9816	−1.63305	−0.816525	−	0.577311i	$-0.804102\pi$
$433$	−33.9816	−1.63305	−0.816525	+	0.577311i	$0.804102\pi$
$434$	6.13142	0.294318
$435$	2.53730	0.121654
$436$	9.66094	0.462675
$437$	8.79841	0.420885
$438$	−0.674630	−0.0322351
$439$	30.5291	1.45708	0.728538	−	0.685005i	$-0.240200\pi$
$439$	30.5291	1.45708	0.728538	+	0.685005i	$0.240200\pi$
$440$	1.46682	0.0699278
$441$	−3.22398	−0.153523
$442$	−7.24316	−0.344522
$443$	14.3022	0.679517	0.339759	−	0.940513i	$-0.389655\pi$
$443$	14.3022	0.679517	0.339759	+	0.940513i	$0.389655\pi$
$444$	6.57100	0.311846
$445$	−1.75195	−0.0830502
$446$	9.16474	0.433963
$447$	7.55634	0.357402
$448$	1.94320	0.0918075
$449$	25.0443	1.18191	0.590956	−	0.806704i	$-0.298751\pi$
$449$	25.0443	1.18191	0.590956	+	0.806704i	$0.298751\pi$
$450$	−4.48939	−0.211632
$451$	3.41579	0.160843
$452$	−16.0724	−0.755980
$453$	−17.8855	−0.840333
$454$	−24.8758	−1.16748
$455$	−1.38855	−0.0650964
$456$	−3.15532	−0.147762
$457$	4.22994	0.197868	0.0989340	−	0.995094i	$-0.468457\pi$
$457$	4.22994	0.197868	0.0989340	+	0.995094i	$0.468457\pi$
$458$	1.91634	0.0895446
$459$	7.24316	0.338082
$460$	−1.99253	−0.0929023
$461$	17.1105	0.796917	0.398458	−	0.917186i	$-0.369545\pi$
$461$	17.1105	0.796917	0.398458	+	0.917186i	$0.369545\pi$
$462$	3.98886	0.185578
$463$	14.2257	0.661124	0.330562	−	0.943784i	$-0.392762\pi$
$463$	14.2257	0.661124	0.330562	+	0.943784i	$0.392762\pi$
$464$	3.55081	0.164842
$465$	2.25470	0.104559
$466$	3.45081	0.159856
$467$	−20.7976	−0.962400	−0.481200	−	0.876611i	$-0.659799\pi$
$467$	−20.7976	−0.962400	−0.481200	+	0.876611i	$0.659799\pi$
$468$	1.00000	0.0462250
$469$	7.18060	0.331569
$470$	−9.17987	−0.423436
$471$	−23.2499	−1.07130
$472$	12.3150	0.566845
$473$	−11.7286	−0.539283
$474$	2.88763	0.132633
$475$	−14.1655	−0.649957
$476$	−14.0749	−0.645122
$477$	−9.25022	−0.423538
$478$	11.0788	0.506731
$479$	−37.6611	−1.72078	−0.860391	−	0.509635i	$-0.829781\pi$
$479$	−37.6611	−1.72078	−0.860391	+	0.509635i	$0.829781\pi$
$480$	0.714571	0.0326155
$481$	−6.57100	−0.299612
$482$	14.7466	0.671690
$483$	−5.41848	−0.246549
$484$	−6.78631	−0.308469
$485$	−9.18874	−0.417239
$486$	−1.00000	−0.0453609
$487$	41.8641	1.89704	0.948522	−	0.316710i	$-0.102578\pi$
$487$	41.8641	1.89704	0.948522	+	0.316710i	$0.102578\pi$
$488$	11.2133	0.507602
$489$	13.2352	0.598515
$490$	2.30376	0.104073
$491$	−14.4677	−0.652918	−0.326459	−	0.945211i	$-0.605856\pi$
$491$	−14.4677	−0.652918	−0.326459	+	0.945211i	$0.605856\pi$
$492$	1.66403	0.0750202
$493$	−25.7191	−1.15833
$494$	3.15532	0.141965
$495$	1.46682	0.0659286
$496$	3.15532	0.141678
$497$	19.2160	0.861956
$498$	−7.36282	−0.329936
$499$	36.1054	1.61630	0.808150	−	0.588977i	$-0.200469\pi$
$499$	36.1054	1.61630	0.808150	+	0.588977i	$0.200469\pi$
$500$	6.78084	0.303248
$501$	7.03944	0.314499
$502$	8.43392	0.376424
$503$	1.56039	0.0695742	0.0347871	−	0.999395i	$-0.488925\pi$
$503$	1.56039	0.0695742	0.0347871	+	0.999395i	$0.488925\pi$
$504$	1.94320	0.0865570
$505$	11.7176	0.521425
$506$	−5.72389	−0.254458
$507$	−1.00000	−0.0444116
$508$	5.59677	0.248316
$509$	26.9060	1.19259	0.596295	−	0.802766i	$-0.296639\pi$
$509$	26.9060	1.19259	0.596295	+	0.802766i	$0.296639\pi$
$510$	−5.17575	−0.229186
$511$	1.31094	0.0579926
$512$	1.00000	0.0441942
$513$	−3.15532	−0.139311
$514$	−14.3619	−0.633474
$515$	−0.714571	−0.0314877
$516$	−5.71368	−0.251531
$517$	−26.3708	−1.15978
$518$	−12.7688	−0.561027
$519$	−14.8519	−0.651925
$520$	−0.714571	−0.0313360
$521$	−30.8035	−1.34952	−0.674762	−	0.738035i	$-0.735754\pi$
$521$	−30.8035	−1.34952	−0.674762	+	0.738035i	$0.735754\pi$
$522$	3.55081	0.155415
$523$	−36.8392	−1.61087	−0.805433	−	0.592687i	$-0.798067\pi$
$523$	−36.8392	−1.61087	−0.805433	+	0.592687i	$0.798067\pi$
$524$	−8.55830	−0.373871
$525$	8.72377	0.380737
$526$	5.96407	0.260046
$527$	−22.8545	−0.995558
$528$	2.05273	0.0893335
$529$	−15.2246	−0.661941
$530$	6.60994	0.287117
$531$	12.3150	0.534426
$532$	6.13142	0.265831
$533$	−1.66403	−0.0720770
$534$	−2.45175	−0.106097
$535$	2.74247	0.118567
$536$	3.69525	0.159610
$537$	13.3652	0.576753
$538$	10.8798	0.469064
$539$	6.61795	0.285055
$540$	0.714571	0.0307502
$541$	22.5904	0.971235	0.485618	−	0.874171i	$-0.338595\pi$
$541$	22.5904	0.971235	0.485618	+	0.874171i	$0.338595\pi$
$542$	−4.14209	−0.177918
$543$	5.80679	0.249193
$544$	−7.24316	−0.310548
$545$	−6.90343	−0.295710
$546$	−1.94320	−0.0831612
$547$	22.5287	0.963256	0.481628	−	0.876376i	$-0.340046\pi$
$547$	22.5287	0.963256	0.481628	+	0.876376i	$0.340046\pi$
$548$	8.31911	0.355375
$549$	11.2133	0.478572
$550$	9.21549	0.392950
$551$	11.2040	0.477305
$552$	−2.78843	−0.118684
$553$	−5.61124	−0.238614
$554$	−8.16157	−0.346752
$555$	−4.69544	−0.199310
$556$	−0.00440462	−0.000186798 0
$557$	11.4611	0.485622	0.242811	−	0.970074i	$-0.421931\pi$
$557$	11.4611	0.485622	0.242811	+	0.970074i	$0.421931\pi$
$558$	3.15532	0.133575
$559$	5.71368	0.241663
$560$	−1.38855	−0.0586771
$561$	−14.8682	−0.627737
$562$	25.3865	1.07087
$563$	−13.7290	−0.578608	−0.289304	−	0.957237i	$-0.593424\pi$
$563$	−13.7290	−0.578608	−0.289304	+	0.957237i	$0.593424\pi$
$564$	−12.8467	−0.540944
$565$	11.4848	0.483171
$566$	−27.4546	−1.15400
$567$	1.94320	0.0816067
$568$	9.88886	0.414927
$569$	25.4382	1.06642	0.533212	−	0.845982i	$-0.320985\pi$
$569$	25.4382	1.06642	0.533212	+	0.845982i	$0.320985\pi$
$570$	2.25470	0.0944390
$571$	−29.0995	−1.21778	−0.608888	−	0.793256i	$-0.708384\pi$
$571$	−29.0995	−1.21778	−0.608888	+	0.793256i	$0.708384\pi$
$572$	−2.05273	−0.0858288
$573$	3.41345	0.142599
$574$	−3.23354	−0.134965
$575$	−12.5184	−0.522052
$576$	1.00000	0.0416667
$577$	−39.7480	−1.65473	−0.827366	−	0.561663i	$-0.810162\pi$
$577$	−39.7480	−1.65473	−0.827366	+	0.561663i	$0.810162\pi$
$578$	35.4634	1.47508
$579$	−23.6875	−0.984418
$580$	−2.53730	−0.105356
$581$	14.3074	0.593572
$582$	−12.8591	−0.533027
$583$	18.9882	0.786410
$584$	0.674630	0.0279164
$585$	−0.714571	−0.0295439
$586$	−7.86878	−0.325056
$587$	−7.37841	−0.304540	−0.152270	−	0.988339i	$-0.548658\pi$
$587$	−7.37841	−0.304540	−0.152270	+	0.988339i	$0.548658\pi$
$588$	3.22398	0.132955
$589$	9.95607	0.410233
$590$	−8.79995	−0.362288
$591$	−17.8203	−0.733031
$592$	−6.57100	−0.270066
$593$	17.4627	0.717107	0.358554	−	0.933509i	$-0.383270\pi$
$593$	17.4627	0.717107	0.358554	+	0.933509i	$0.383270\pi$
$594$	2.05273	0.0842244
$595$	10.0575	0.412318
$596$	−7.55634	−0.309520
$597$	−16.0499	−0.656878
$598$	2.78843	0.114028
$599$	−24.2927	−0.992571	−0.496286	−	0.868159i	$-0.665303\pi$
$599$	−24.2927	−0.992571	−0.496286	+	0.868159i	$0.665303\pi$
$600$	4.48939	0.183279
$601$	6.59187	0.268888	0.134444	−	0.990921i	$-0.457075\pi$
$601$	6.59187	0.268888	0.134444	+	0.990921i	$0.457075\pi$
$602$	11.1028	0.452517
$603$	3.69525	0.150482
$604$	17.8855	0.727750
$605$	4.84930	0.197152
$606$	16.3980	0.666125
$607$	7.23711	0.293745	0.146873	−	0.989155i	$-0.453079\pi$
$607$	7.23711	0.293745	0.146873	+	0.989155i	$0.453079\pi$
$608$	3.15532	0.127965
$609$	−6.89993	−0.279599
$610$	−8.01269	−0.324424
$611$	12.8467	0.519722
$612$	−7.24316	−0.292787
$613$	15.9942	0.646000	0.323000	−	0.946399i	$-0.395309\pi$
$613$	15.9942	0.646000	0.323000	+	0.946399i	$0.395309\pi$
$614$	−30.7275	−1.24006
$615$	−1.18907	−0.0479477
$616$	−3.98886	−0.160716
$617$	−23.1419	−0.931659	−0.465829	−	0.884875i	$-0.654244\pi$
$617$	−23.1419	−0.931659	−0.465829	+	0.884875i	$0.654244\pi$
$618$	−1.00000	−0.0402259
$619$	−34.4236	−1.38360	−0.691802	−	0.722088i	$-0.743183\pi$
$619$	−34.4236	−1.38360	−0.691802	+	0.722088i	$0.743183\pi$
$620$	−2.25470	−0.0905510
$621$	−2.78843	−0.111896
$622$	−14.2786	−0.572519
$623$	4.76423	0.190875
$624$	−1.00000	−0.0400320
$625$	17.6016	0.704062
$626$	27.5810	1.10236
$627$	6.47702	0.258667
$628$	23.2499	0.927771
$629$	47.5948	1.89773
$630$	−1.38855	−0.0553213
$631$	11.3605	0.452255	0.226128	−	0.974098i	$-0.427393\pi$
$631$	11.3605	0.452255	0.226128	+	0.974098i	$0.427393\pi$
$632$	−2.88763	−0.114864
$633$	−19.3542	−0.769260
$634$	−0.915024	−0.0363402
$635$	−3.99928	−0.158707
$636$	9.25022	0.366795
$637$	−3.22398	−0.127739
$638$	−7.28884	−0.288568
$639$	9.88886	0.391197
$640$	−0.714571	−0.0282459
$641$	−17.1444	−0.677165	−0.338582	−	0.940937i	$-0.609947\pi$
$641$	−17.1444	−0.677165	−0.338582	+	0.940937i	$0.609947\pi$
$642$	3.83793	0.151471
$643$	22.9598	0.905446	0.452723	−	0.891651i	$-0.350453\pi$
$643$	22.9598	0.905446	0.452723	+	0.891651i	$0.350453\pi$
$644$	5.41848	0.213518
$645$	4.08283	0.160761
$646$	−22.8545	−0.899199
$647$	−44.0854	−1.73318	−0.866588	−	0.499024i	$-0.833692\pi$
$647$	−44.0854	−1.73318	−0.866588	+	0.499024i	$0.833692\pi$
$648$	1.00000	0.0392837
$649$	−25.2794	−0.992302
$650$	−4.48939	−0.176088
$651$	−6.13142	−0.240309
$652$	−13.2352	−0.518329
$653$	−4.92709	−0.192812	−0.0964060	−	0.995342i	$-0.530735\pi$
$653$	−4.92709	−0.192812	−0.0964060	+	0.995342i	$0.530735\pi$
$654$	−9.66094	−0.377773
$655$	6.11551	0.238953
$656$	−1.66403	−0.0649694
$657$	0.674630	0.0263198
$658$	24.9637	0.973186
$659$	−38.3313	−1.49318	−0.746588	−	0.665287i	$-0.768309\pi$
$659$	−38.3313	−1.49318	−0.746588	+	0.665287i	$0.768309\pi$
$660$	−1.46682	−0.0570958
$661$	22.0008	0.855732	0.427866	−	0.903842i	$-0.359265\pi$
$661$	22.0008	0.855732	0.427866	+	0.903842i	$0.359265\pi$
$662$	28.8518	1.12136
$663$	7.24316	0.281301
$664$	7.36282	0.285733
$665$	−4.38133	−0.169901
$666$	−6.57100	−0.254621
$667$	9.90120	0.383376
$668$	−7.03944	−0.272364
$669$	−9.16474	−0.354329
$670$	−2.64051	−0.102012
$671$	−23.0178	−0.888593
$672$	−1.94320	−0.0749605
$673$	1.77096	0.0682654	0.0341327	−	0.999417i	$-0.489133\pi$
$673$	1.77096	0.0682654	0.0341327	+	0.999417i	$0.489133\pi$
$674$	0.862810	0.0332342
$675$	4.48939	0.172797
$676$	1.00000	0.0384615
$677$	−3.06111	−0.117648	−0.0588240	−	0.998268i	$-0.518735\pi$
$677$	−3.06111	−0.117648	−0.0588240	+	0.998268i	$0.518735\pi$
$678$	16.0724	0.617255
$679$	24.9878	0.958944
$680$	5.17575	0.198481
$681$	24.8758	0.953244
$682$	−6.47702	−0.248018
$683$	38.9316	1.48967	0.744837	−	0.667246i	$-0.232527\pi$
$683$	38.9316	1.48967	0.744837	+	0.667246i	$0.232527\pi$
$684$	3.15532	0.120647
$685$	−5.94459	−0.227131
$686$	−19.8672	−0.758534
$687$	−1.91634	−0.0731129
$688$	5.71368	0.217832
$689$	−9.25022	−0.352405
$690$	1.99253	0.0758544
$691$	25.8289	0.982576	0.491288	−	0.870997i	$-0.336526\pi$
$691$	25.8289	0.982576	0.491288	+	0.870997i	$0.336526\pi$
$692$	14.8519	0.564583
$693$	−3.98886	−0.151524
$694$	21.2936	0.808294
$695$	0.00314741	0.000119388 0
$696$	−3.55081	−0.134593
$697$	12.0528	0.456533
$698$	34.6954	1.31324
$699$	−3.45081	−0.130521
$700$	−8.72377	−0.329728
$701$	6.63706	0.250678	0.125339	−	0.992114i	$-0.459998\pi$
$701$	6.63706	0.250678	0.125339	+	0.992114i	$0.459998\pi$
$702$	−1.00000	−0.0377426
$703$	−20.7336	−0.781983
$704$	−2.05273	−0.0773650
$705$	9.17987	0.345734
$706$	−28.4224	−1.06969
$707$	−31.8647	−1.19839
$708$	−12.3150	−0.462827
$709$	−11.4800	−0.431141	−0.215571	−	0.976488i	$-0.569161\pi$
$709$	−11.4800	−0.431141	−0.215571	+	0.976488i	$0.569161\pi$
$710$	−7.06629	−0.265193
$711$	−2.88763	−0.108295
$712$	2.45175	0.0918831
$713$	8.79841	0.329503
$714$	14.0749	0.526740
$715$	1.46682	0.0548559
$716$	−13.3652	−0.499483
$717$	−11.0788	−0.413744
$718$	0.128772	0.00480571
$719$	29.7515	1.10954	0.554772	−	0.832002i	$-0.312806\pi$
$719$	29.7515	1.10954	0.554772	+	0.832002i	$0.312806\pi$
$720$	−0.714571	−0.0266305
$721$	1.94320	0.0723685
$722$	−9.04393	−0.336580
$723$	−14.7466	−0.548433
$724$	−5.80679	−0.215808
$725$	−15.9410	−0.592033
$726$	6.78631	0.251864
$727$	50.0124	1.85486	0.927428	−	0.374001i	$-0.122014\pi$
$727$	50.0124	1.85486	0.927428	+	0.374001i	$0.122014\pi$
$728$	1.94320	0.0720197
$729$	1.00000	0.0370370
$730$	−0.482071	−0.0178422
$731$	−41.3851	−1.53068
$732$	−11.2133	−0.414455
$733$	50.4977	1.86517	0.932587	−	0.360945i	$-0.117546\pi$
$733$	50.4977	1.86517	0.932587	+	0.360945i	$0.117546\pi$
$734$	−0.565222	−0.0208627
$735$	−2.30376	−0.0849755
$736$	2.78843	0.102783
$737$	−7.58533	−0.279409
$738$	−1.66403	−0.0612537
$739$	18.1659	0.668243	0.334122	−	0.942530i	$-0.391560\pi$
$739$	18.1659	0.668243	0.334122	+	0.942530i	$0.391560\pi$
$740$	4.69544	0.172608
$741$	−3.15532	−0.115914
$742$	−17.9750	−0.659884
$743$	5.86830	0.215287	0.107644	−	0.994190i	$-0.465669\pi$
$743$	5.86830	0.215287	0.107644	+	0.994190i	$0.465669\pi$
$744$	−3.15532	−0.115680
$745$	5.39954	0.197824
$746$	−1.66702	−0.0610339
$747$	7.36282	0.269391
$748$	14.8682	0.543636
$749$	−7.45785	−0.272504
$750$	−6.78084	−0.247601
$751$	18.3543	0.669757	0.334879	−	0.942261i	$-0.391305\pi$
$751$	18.3543	0.669757	0.334879	+	0.942261i	$0.391305\pi$
$752$	12.8467	0.468471
$753$	−8.43392	−0.307349
$754$	3.55081	0.129313
$755$	−12.7804	−0.465128
$756$	−1.94320	−0.0706735
$757$	5.71362	0.207665	0.103833	−	0.994595i	$-0.466889\pi$
$757$	5.71362	0.207665	0.103833	+	0.994595i	$0.466889\pi$
$758$	16.4501	0.597496
$759$	5.72389	0.207764
$760$	−2.25470	−0.0817866
$761$	−42.3538	−1.53532	−0.767662	−	0.640855i	$-0.778580\pi$
$761$	−42.3538	−1.53532	−0.767662	+	0.640855i	$0.778580\pi$
$762$	−5.59677	−0.202749
$763$	18.7731	0.679633
$764$	−3.41345	−0.123494
$765$	5.17575	0.187130
$766$	0.266649	0.00963441
$767$	12.3150	0.444670
$768$	−1.00000	−0.0360844
$769$	−52.6970	−1.90030	−0.950151	−	0.311789i	$-0.899072\pi$
$769$	−52.6970	−1.90030	−0.950151	+	0.311789i	$0.899072\pi$
$770$	2.85032	0.102718
$771$	14.3619	0.517230
$772$	23.6875	0.852531
$773$	−41.2274	−1.48285	−0.741423	−	0.671038i	$-0.765849\pi$
$773$	−41.2274	−1.48285	−0.741423	+	0.671038i	$0.765849\pi$
$774$	5.71368	0.205374
$775$	−14.1655	−0.508839
$776$	12.8591	0.461615
$777$	12.7688	0.458076
$778$	37.5288	1.34547
$779$	−5.25055	−0.188120
$780$	0.714571	0.0255857
$781$	−20.2991	−0.726360
$782$	−20.1971	−0.722246
$783$	−3.55081	−0.126896
$784$	−3.22398	−0.115142
$785$	−16.6137	−0.592968
$786$	8.55830	0.305265
$787$	−51.2073	−1.82534	−0.912672	−	0.408694i	$-0.865984\pi$
$787$	−51.2073	−1.82534	−0.912672	+	0.408694i	$0.865984\pi$
$788$	17.8203	0.634824
$789$	−5.96407	−0.212327
$790$	2.06342	0.0734130
$791$	−31.2318	−1.11047
$792$	−2.05273	−0.0729405
$793$	11.2133	0.398196
$794$	2.13003	0.0755918
$795$	−6.60994	−0.234430
$796$	16.0499	0.568873
$797$	48.5652	1.72027	0.860134	−	0.510069i	$-0.170380\pi$
$797$	48.5652	1.72027	0.860134	+	0.510069i	$0.170380\pi$
$798$	−6.13142	−0.217050
$799$	−93.0507	−3.29190
$800$	−4.48939	−0.158724
$801$	2.45175	0.0866282
$802$	−34.9649	−1.23465
$803$	−1.38483	−0.0488696
$804$	−3.69525	−0.130321
$805$	−3.87189	−0.136466
$806$	3.15532	0.111142
$807$	−10.8798	−0.382989
$808$	−16.3980	−0.576881
$809$	−42.3543	−1.48910	−0.744549	−	0.667568i	$-0.767335\pi$
$809$	−42.3543	−1.48910	−0.744549	+	0.667568i	$0.767335\pi$
$810$	−0.714571	−0.0251075
$811$	−22.0368	−0.773818	−0.386909	−	0.922118i	$-0.626457\pi$
$811$	−22.0368	−0.773818	−0.386909	+	0.922118i	$0.626457\pi$
$812$	6.89993	0.242140
$813$	4.14209	0.145269
$814$	13.4885	0.472770
$815$	9.45746	0.331280
$816$	7.24316	0.253561
$817$	18.0285	0.630738
$818$	−18.3631	−0.642052
$819$	1.94320	0.0679009
$820$	1.18907	0.0415240
$821$	23.5916	0.823354	0.411677	−	0.911330i	$-0.364943\pi$
$821$	23.5916	0.823354	0.411677	+	0.911330i	$0.364943\pi$
$822$	−8.31911	−0.290162
$823$	26.7734	0.933261	0.466630	−	0.884452i	$-0.345468\pi$
$823$	26.7734	0.933261	0.466630	+	0.884452i	$0.345468\pi$
$824$	1.00000	0.0348367
$825$	−9.21549	−0.320842
$826$	23.9305	0.832650
$827$	38.7610	1.34785	0.673925	−	0.738800i	$-0.264607\pi$
$827$	38.7610	1.34785	0.673925	+	0.738800i	$0.264607\pi$
$828$	2.78843	0.0969047
$829$	−15.6931	−0.545044	−0.272522	−	0.962150i	$-0.587858\pi$
$829$	−15.6931	−0.545044	−0.272522	+	0.962150i	$0.587858\pi$
$830$	−5.26125	−0.182621
$831$	8.16157	0.283122
$832$	1.00000	0.0346688
$833$	23.3518	0.809092
$834$	0.00440462	0.000152520 0
$835$	5.03017	0.174076
$836$	−6.47702	−0.224012
$837$	−3.15532	−0.109064
$838$	28.8460	0.996468
$839$	12.6167	0.435576	0.217788	−	0.975996i	$-0.430116\pi$
$839$	12.6167	0.435576	0.217788	+	0.975996i	$0.430116\pi$
$840$	1.38855	0.0479096
$841$	−16.3917	−0.565233
$842$	−9.28103	−0.319845
$843$	−25.3865	−0.874358
$844$	19.3542	0.666199
$845$	−0.714571	−0.0245820
$846$	12.8467	0.441679
$847$	−13.1872	−0.453116
$848$	−9.25022	−0.317654
$849$	27.4546	0.942240
$850$	32.5174	1.11534
$851$	−18.3228	−0.628097
$852$	−9.88886	−0.338787
$853$	−24.8218	−0.849883	−0.424941	−	0.905221i	$-0.639705\pi$
$853$	−24.8218	−0.849883	−0.424941	+	0.905221i	$0.639705\pi$
$854$	21.7897	0.745627
$855$	−2.25470	−0.0771092
$856$	−3.83793	−0.131178
$857$	−39.5879	−1.35230	−0.676148	−	0.736765i	$-0.736352\pi$
$857$	−39.5879	−1.35230	−0.676148	+	0.736765i	$0.736352\pi$
$858$	2.05273	0.0700789
$859$	−45.9060	−1.56629	−0.783147	−	0.621837i	$-0.786387\pi$
$859$	−45.9060	−1.56629	−0.783147	+	0.621837i	$0.786387\pi$
$860$	−4.08283	−0.139223
$861$	3.23354	0.110199
$862$	20.0651	0.683421
$863$	−7.58578	−0.258223	−0.129112	−	0.991630i	$-0.541213\pi$
$863$	−7.58578	−0.258223	−0.129112	+	0.991630i	$0.541213\pi$
$864$	−1.00000	−0.0340207
$865$	−10.6127	−0.360843
$866$	−33.9816	−1.15474
$867$	−35.4634	−1.20440
$868$	6.13142	0.208114
$869$	5.92751	0.201077
$870$	2.53730	0.0860227
$871$	3.69525	0.125209
$872$	9.66094	0.327161
$873$	12.8591	0.435215
$874$	8.79841	0.297611
$875$	13.1765	0.445448
$876$	−0.674630	−0.0227936
$877$	−45.0858	−1.52244	−0.761220	−	0.648494i	$-0.775399\pi$
$877$	−45.0858	−1.52244	−0.761220	+	0.648494i	$0.775399\pi$
$878$	30.5291	1.03031
$879$	7.86878	0.265407
$880$	1.46682	0.0494464
$881$	−41.3264	−1.39232	−0.696161	−	0.717886i	$-0.745110\pi$
$881$	−41.3264	−1.39232	−0.696161	+	0.717886i	$0.745110\pi$
$882$	−3.22398	−0.108557
$883$	57.4286	1.93263	0.966313	−	0.257369i	$-0.0828554\pi$
$883$	57.4286	1.93263	0.966313	+	0.257369i	$0.0828554\pi$
$884$	−7.24316	−0.243614
$885$	8.79995	0.295807
$886$	14.3022	0.480491
$887$	1.51393	0.0508326	0.0254163	−	0.999677i	$-0.491909\pi$
$887$	1.51393	0.0508326	0.0254163	+	0.999677i	$0.491909\pi$
$888$	6.57100	0.220508
$889$	10.8756	0.364757
$890$	−1.75195	−0.0587254
$891$	−2.05273	−0.0687689
$892$	9.16474	0.306858
$893$	40.5355	1.35647
$894$	7.55634	0.252722
$895$	9.55041	0.319235
$896$	1.94320	0.0649177
$897$	−2.78843	−0.0931031
$898$	25.0443	0.835738
$899$	11.2040	0.373673
$900$	−4.48939	−0.149646
$901$	67.0008	2.23212
$902$	3.41579	0.113733
$903$	−11.1028	−0.369479
$904$	−16.0724	−0.534559
$905$	4.14936	0.137930
$906$	−17.8855	−0.594205
$907$	−53.8865	−1.78927	−0.894636	−	0.446795i	$-0.852565\pi$
$907$	−53.8865	−1.78927	−0.894636	+	0.446795i	$0.852565\pi$
$908$	−24.8758	−0.825534
$909$	−16.3980	−0.543889
$910$	−1.38855	−0.0460301
$911$	56.3464	1.86684	0.933419	−	0.358787i	$-0.116810\pi$
$911$	56.3464	1.86684	0.933419	+	0.358787i	$0.116810\pi$
$912$	−3.15532	−0.104483
$913$	−15.1139	−0.500196
$914$	4.22994	0.139914
$915$	8.01269	0.264891
$916$	1.91634	0.0633176
$917$	−16.6305	−0.549187
$918$	7.24316	0.239060
$919$	13.2836	0.438187	0.219093	−	0.975704i	$-0.429690\pi$
$919$	13.2836	0.438187	0.219093	+	0.975704i	$0.429690\pi$
$920$	−1.99253	−0.0656918
$921$	30.7275	1.01250
$922$	17.1105	0.563505
$923$	9.88886	0.325496
$924$	3.98886	0.131224
$925$	29.4998	0.969946
$926$	14.2257	0.467485
$927$	1.00000	0.0328443
$928$	3.55081	0.116561
$929$	7.07725	0.232197	0.116099	−	0.993238i	$-0.462961\pi$
$929$	7.07725	0.232197	0.116099	+	0.993238i	$0.462961\pi$
$930$	2.25470	0.0739346
$931$	−10.1727	−0.333397
$932$	3.45081	0.113035
$933$	14.2786	0.467460
$934$	−20.7976	−0.680520
$935$	−10.6244	−0.347455
$936$	1.00000	0.0326860
$937$	23.2421	0.759287	0.379644	−	0.925133i	$-0.376047\pi$
$937$	23.2421	0.759287	0.379644	+	0.925133i	$0.376047\pi$
$938$	7.18060	0.234455
$939$	−27.5810	−0.900070
$940$	−9.17987	−0.299414
$941$	−2.99536	−0.0976459	−0.0488230	−	0.998807i	$-0.515547\pi$
$941$	−2.99536	−0.0976459	−0.0488230	+	0.998807i	$0.515547\pi$
$942$	−23.2499	−0.757522
$943$	−4.64003	−0.151100
$944$	12.3150	0.400820
$945$	1.38855	0.0451696
$946$	−11.7286	−0.381331
$947$	−5.09041	−0.165416	−0.0827080	−	0.996574i	$-0.526357\pi$
$947$	−5.09041	−0.165416	−0.0827080	+	0.996574i	$0.526357\pi$
$948$	2.88763	0.0937859
$949$	0.674630	0.0218994
$950$	−14.1655	−0.459589
$951$	0.915024	0.0296717
$952$	−14.0749	−0.456170
$953$	40.6931	1.31818	0.659090	−	0.752064i	$-0.270942\pi$
$953$	40.6931	1.31818	0.659090	+	0.752064i	$0.270942\pi$
$954$	−9.25022	−0.299487
$955$	2.43915	0.0789292
$956$	11.0788	0.358313
$957$	7.28884	0.235615
$958$	−37.6611	−1.21678
$959$	16.1657	0.522017
$960$	0.714571	0.0230627
$961$	−21.0439	−0.678837
$962$	−6.57100	−0.211857
$963$	−3.83793	−0.123675
$964$	14.7466	0.474957
$965$	−16.9264	−0.544879
$966$	−5.41848	−0.174337
$967$	−30.1714	−0.970248	−0.485124	−	0.874445i	$-0.661225\pi$
$967$	−30.1714	−0.970248	−0.485124	+	0.874445i	$0.661225\pi$
$968$	−6.78631	−0.218120
$969$	22.8545	0.734193
$970$	−9.18874	−0.295033
$971$	2.70265	0.0867323	0.0433661	−	0.999059i	$-0.486192\pi$
$971$	2.70265	0.0867323	0.0433661	+	0.999059i	$0.486192\pi$
$972$	−1.00000	−0.0320750
$973$	−0.00855906	−0.000274391 0
$974$	41.8641	1.34141
$975$	4.48939	0.143776
$976$	11.2133	0.358929
$977$	−27.5965	−0.882889	−0.441444	−	0.897289i	$-0.645534\pi$
$977$	−27.5965	−0.882889	−0.441444	+	0.897289i	$0.645534\pi$
$978$	13.2352	0.423214
$979$	−5.03277	−0.160848
$980$	2.30376	0.0735909
$981$	9.66094	0.308450
$982$	−14.4677	−0.461683
$983$	−9.72528	−0.310188	−0.155094	−	0.987900i	$-0.549568\pi$
$983$	−9.72528	−0.310188	−0.155094	+	0.987900i	$0.549568\pi$
$984$	1.66403	0.0530473
$985$	−12.7339	−0.405736
$986$	−25.7191	−0.819063
$987$	−24.9637	−0.794603
$988$	3.15532	0.100384
$989$	15.9322	0.506615
$990$	1.46682	0.0466185
$991$	−51.6963	−1.64219	−0.821093	−	0.570794i	$-0.806635\pi$
$991$	−51.6963	−1.64219	−0.821093	+	0.570794i	$0.806635\pi$
$992$	3.15532	0.100182
$993$	−28.8518	−0.915584
$994$	19.2160	0.609495
$995$	−11.4688	−0.363584
$996$	−7.36282	−0.233300
$997$	−4.44717	−0.140843	−0.0704216	−	0.997517i	$-0.522434\pi$
$997$	−4.44717	−0.140843	−0.0704216	+	0.997517i	$0.522434\pi$
$998$	36.1054	1.14290
$999$	6.57100	0.207897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.5	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.714571 q^{5} -1.00000 q^{6} +1.94320 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.714571 q^{5} -1.00000 q^{6} +1.94320 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.714571 q^{10} -2.05273 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.94320 q^{14} +0.714571 q^{15} +1.00000 q^{16} -7.24316 q^{17} +1.00000 q^{18} +3.15532 q^{19} -0.714571 q^{20} -1.94320 q^{21} -2.05273 q^{22} +2.78843 q^{23} -1.00000 q^{24} -4.48939 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.94320 q^{28} +3.55081 q^{29} +0.714571 q^{30} +3.15532 q^{31} +1.00000 q^{32} +2.05273 q^{33} -7.24316 q^{34} -1.38855 q^{35} +1.00000 q^{36} -6.57100 q^{37} +3.15532 q^{38} -1.00000 q^{39} -0.714571 q^{40} -1.66403 q^{41} -1.94320 q^{42} +5.71368 q^{43} -2.05273 q^{44} -0.714571 q^{45} +2.78843 q^{46} +12.8467 q^{47} -1.00000 q^{48} -3.22398 q^{49} -4.48939 q^{50} +7.24316 q^{51} +1.00000 q^{52} -9.25022 q^{53} -1.00000 q^{54} +1.46682 q^{55} +1.94320 q^{56} -3.15532 q^{57} +3.55081 q^{58} +12.3150 q^{59} +0.714571 q^{60} +11.2133 q^{61} +3.15532 q^{62} +1.94320 q^{63} +1.00000 q^{64} -0.714571 q^{65} +2.05273 q^{66} +3.69525 q^{67} -7.24316 q^{68} -2.78843 q^{69} -1.38855 q^{70} +9.88886 q^{71} +1.00000 q^{72} +0.674630 q^{73} -6.57100 q^{74} +4.48939 q^{75} +3.15532 q^{76} -3.98886 q^{77} -1.00000 q^{78} -2.88763 q^{79} -0.714571 q^{80} +1.00000 q^{81} -1.66403 q^{82} +7.36282 q^{83} -1.94320 q^{84} +5.17575 q^{85} +5.71368 q^{86} -3.55081 q^{87} -2.05273 q^{88} +2.45175 q^{89} -0.714571 q^{90} +1.94320 q^{91} +2.78843 q^{92} -3.15532 q^{93} +12.8467 q^{94} -2.25470 q^{95} -1.00000 q^{96} +12.8591 q^{97} -3.22398 q^{98} -2.05273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 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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