LMFDB - Embedded newform 8034.2.a.x.1.11

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} - x^{12} - 40 x^{11} + 34 x^{10} + 604 x^{9} - 381 x^{8} - 4352 x^{7} + 1474 x^{6} + 15809 x^{5} + \cdots + 8832 $ x^13 - x^12 - 40x^11 + 34x^10 + 604x^9 - 381x^8 - 4352x^7 + 1474x^6 + 15809x^5 - 368x^4 - 27369x^3 - 7621x^2 + 17300*x + 8832
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$3.21537$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.21537 q^{5} -1.00000 q^{6} -0.928130 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.21537 q^{5} -1.00000 q^{6} -0.928130 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.21537 q^{10} -0.454630 q^{11} +1.00000 q^{12} +1.00000 q^{13} +0.928130 q^{14} +3.21537 q^{15} +1.00000 q^{16} +3.97222 q^{17} -1.00000 q^{18} +1.03342 q^{19} +3.21537 q^{20} -0.928130 q^{21} +0.454630 q^{22} -8.01149 q^{23} -1.00000 q^{24} +5.33861 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.928130 q^{28} +4.75525 q^{29} -3.21537 q^{30} +3.55794 q^{31} -1.00000 q^{32} -0.454630 q^{33} -3.97222 q^{34} -2.98428 q^{35} +1.00000 q^{36} -6.52036 q^{37} -1.03342 q^{38} +1.00000 q^{39} -3.21537 q^{40} -3.35845 q^{41} +0.928130 q^{42} +8.82693 q^{43} -0.454630 q^{44} +3.21537 q^{45} +8.01149 q^{46} +10.3975 q^{47} +1.00000 q^{48} -6.13858 q^{49} -5.33861 q^{50} +3.97222 q^{51} +1.00000 q^{52} +0.418935 q^{53} -1.00000 q^{54} -1.46180 q^{55} +0.928130 q^{56} +1.03342 q^{57} -4.75525 q^{58} +11.2912 q^{59} +3.21537 q^{60} +0.360950 q^{61} -3.55794 q^{62} -0.928130 q^{63} +1.00000 q^{64} +3.21537 q^{65} +0.454630 q^{66} +4.15666 q^{67} +3.97222 q^{68} -8.01149 q^{69} +2.98428 q^{70} +4.04024 q^{71} -1.00000 q^{72} +3.48725 q^{73} +6.52036 q^{74} +5.33861 q^{75} +1.03342 q^{76} +0.421955 q^{77} -1.00000 q^{78} +0.976844 q^{79} +3.21537 q^{80} +1.00000 q^{81} +3.35845 q^{82} -7.97939 q^{83} -0.928130 q^{84} +12.7722 q^{85} -8.82693 q^{86} +4.75525 q^{87} +0.454630 q^{88} -5.87631 q^{89} -3.21537 q^{90} -0.928130 q^{91} -8.01149 q^{92} +3.55794 q^{93} -10.3975 q^{94} +3.32281 q^{95} -1.00000 q^{96} +6.80598 q^{97} +6.13858 q^{98} -0.454630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * 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
$5$	3.21537	1.43796	0.718979	−	0.695032i	$-0.244610\pi$
$5$	3.21537	1.43796	0.718979	+	0.695032i	$0.244610\pi$
$6$	−1.00000	−0.408248
$7$	−0.928130	−0.350800	−0.175400	−	0.984497i	$-0.556122\pi$
$7$	−0.928130	−0.350800	−0.175400	+	0.984497i	$0.556122\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.21537	−1.01679
$11$	−0.454630	−0.137076	−0.0685380	−	0.997649i	$-0.521833\pi$
$11$	−0.454630	−0.137076	−0.0685380	+	0.997649i	$0.521833\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.928130	0.248053
$15$	3.21537	0.830205
$16$	1.00000	0.250000
$17$	3.97222	0.963405	0.481702	−	0.876335i	$-0.340019\pi$
$17$	3.97222	0.963405	0.481702	+	0.876335i	$0.340019\pi$
$18$	−1.00000	−0.235702
$19$	1.03342	0.237082	0.118541	−	0.992949i	$-0.462178\pi$
$19$	1.03342	0.237082	0.118541	+	0.992949i	$0.462178\pi$
$20$	3.21537	0.718979
$21$	−0.928130	−0.202535
$22$	0.454630	0.0969274
$23$	−8.01149	−1.67051	−0.835256	−	0.549862i	$-0.814680\pi$
$23$	−8.01149	−1.67051	−0.835256	+	0.549862i	$0.814680\pi$
$24$	−1.00000	−0.204124
$25$	5.33861	1.06772
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−0.928130	−0.175400
$29$	4.75525	0.883027	0.441514	−	0.897255i	$-0.354442\pi$
$29$	4.75525	0.883027	0.441514	+	0.897255i	$0.354442\pi$
$30$	−3.21537	−0.587044
$31$	3.55794	0.639024	0.319512	−	0.947582i	$-0.396481\pi$
$31$	3.55794	0.639024	0.319512	+	0.947582i	$0.396481\pi$
$32$	−1.00000	−0.176777
$33$	−0.454630	−0.0791409
$34$	−3.97222	−0.681230
$35$	−2.98428	−0.504436
$36$	1.00000	0.166667
$37$	−6.52036	−1.07194	−0.535970	−	0.844237i	$-0.680054\pi$
$37$	−6.52036	−1.07194	−0.535970	+	0.844237i	$0.680054\pi$
$38$	−1.03342	−0.167642
$39$	1.00000	0.160128
$40$	−3.21537	−0.508395
$41$	−3.35845	−0.524502	−0.262251	−	0.965000i	$-0.584465\pi$
$41$	−3.35845	−0.524502	−0.262251	+	0.965000i	$0.584465\pi$
$42$	0.928130	0.143214
$43$	8.82693	1.34609	0.673047	−	0.739599i	$-0.264985\pi$
$43$	8.82693	1.34609	0.673047	+	0.739599i	$0.264985\pi$
$44$	−0.454630	−0.0685380
$45$	3.21537	0.479319
$46$	8.01149	1.18123
$47$	10.3975	1.51663	0.758317	−	0.651886i	$-0.226022\pi$
$47$	10.3975	1.51663	0.758317	+	0.651886i	$0.226022\pi$
$48$	1.00000	0.144338
$49$	−6.13858	−0.876939
$50$	−5.33861	−0.754993
$51$	3.97222	0.556222
$52$	1.00000	0.138675
$53$	0.418935	0.0575451	0.0287725	−	0.999586i	$-0.490840\pi$
$53$	0.418935	0.0575451	0.0287725	+	0.999586i	$0.490840\pi$
$54$	−1.00000	−0.136083
$55$	−1.46180	−0.197110
$56$	0.928130	0.124027
$57$	1.03342	0.136879
$58$	−4.75525	−0.624395
$59$	11.2912	1.46999	0.734996	−	0.678072i	$-0.237184\pi$
$59$	11.2912	1.46999	0.734996	+	0.678072i	$0.237184\pi$
$60$	3.21537	0.415103
$61$	0.360950	0.0462149	0.0231074	−	0.999733i	$-0.492644\pi$
$61$	0.360950	0.0462149	0.0231074	+	0.999733i	$0.492644\pi$
$62$	−3.55794	−0.451858
$63$	−0.928130	−0.116933
$64$	1.00000	0.125000
$65$	3.21537	0.398818
$66$	0.454630	0.0559611
$67$	4.15666	0.507817	0.253909	−	0.967228i	$-0.418284\pi$
$67$	4.15666	0.507817	0.253909	+	0.967228i	$0.418284\pi$
$68$	3.97222	0.481702
$69$	−8.01149	−0.964470
$70$	2.98428	0.356690
$71$	4.04024	0.479488	0.239744	−	0.970836i	$-0.422936\pi$
$71$	4.04024	0.479488	0.239744	+	0.970836i	$0.422936\pi$
$72$	−1.00000	−0.117851
$73$	3.48725	0.408151	0.204076	−	0.978955i	$-0.434581\pi$
$73$	3.48725	0.408151	0.204076	+	0.978955i	$0.434581\pi$
$74$	6.52036	0.757977
$75$	5.33861	0.616449
$76$	1.03342	0.118541
$77$	0.421955	0.0480863
$78$	−1.00000	−0.113228
$79$	0.976844	0.109904	0.0549518	−	0.998489i	$-0.482499\pi$
$79$	0.976844	0.109904	0.0549518	+	0.998489i	$0.482499\pi$
$80$	3.21537	0.359489
$81$	1.00000	0.111111
$82$	3.35845	0.370879
$83$	−7.97939	−0.875852	−0.437926	−	0.899011i	$-0.644287\pi$
$83$	−7.97939	−0.875852	−0.437926	+	0.899011i	$0.644287\pi$
$84$	−0.928130	−0.101267
$85$	12.7722	1.38533
$86$	−8.82693	−0.951833
$87$	4.75525	0.509816
$88$	0.454630	0.0484637
$89$	−5.87631	−0.622888	−0.311444	−	0.950265i	$-0.600813\pi$
$89$	−5.87631	−0.622888	−0.311444	+	0.950265i	$0.600813\pi$
$90$	−3.21537	−0.338930
$91$	−0.928130	−0.0972944
$92$	−8.01149	−0.835256
$93$	3.55794	0.368941
$94$	−10.3975	−1.07242
$95$	3.32281	0.340913
$96$	−1.00000	−0.102062
$97$	6.80598	0.691043	0.345521	−	0.938411i	$-0.387702\pi$
$97$	6.80598	0.691043	0.345521	+	0.938411i	$0.387702\pi$
$98$	6.13858	0.620090
$99$	−0.454630	−0.0456920
$100$	5.33861	0.533861
$101$	−4.34998	−0.432839	−0.216419	−	0.976300i	$-0.569438\pi$
$101$	−4.34998	−0.432839	−0.216419	+	0.976300i	$0.569438\pi$
$102$	−3.97222	−0.393308
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−2.98428	−0.291236
$106$	−0.418935	−0.0406905
$107$	−7.64705	−0.739268	−0.369634	−	0.929177i	$-0.620517\pi$
$107$	−7.64705	−0.739268	−0.369634	+	0.929177i	$0.620517\pi$
$108$	1.00000	0.0962250
$109$	4.38493	0.420000	0.210000	−	0.977701i	$-0.432654\pi$
$109$	4.38493	0.420000	0.210000	+	0.977701i	$0.432654\pi$
$110$	1.46180	0.139377
$111$	−6.52036	−0.618885
$112$	−0.928130	−0.0877000
$113$	12.8168	1.20570	0.602852	−	0.797853i	$-0.294031\pi$
$113$	12.8168	1.20570	0.602852	+	0.797853i	$0.294031\pi$
$114$	−1.03342	−0.0967882
$115$	−25.7599	−2.40212
$116$	4.75525	0.441514
$117$	1.00000	0.0924500
$118$	−11.2912	−1.03944
$119$	−3.68673	−0.337962
$120$	−3.21537	−0.293522
$121$	−10.7933	−0.981210
$122$	−0.360950	−0.0326789
$123$	−3.35845	−0.302821
$124$	3.55794	0.319512
$125$	1.08875	0.0973807
$126$	0.928130	0.0826844
$127$	5.17329	0.459055	0.229528	−	0.973302i	$-0.426282\pi$
$127$	5.17329	0.459055	0.229528	+	0.973302i	$0.426282\pi$
$128$	−1.00000	−0.0883883
$129$	8.82693	0.777168
$130$	−3.21537	−0.282007
$131$	16.5660	1.44737	0.723687	−	0.690128i	$-0.242446\pi$
$131$	16.5660	1.44737	0.723687	+	0.690128i	$0.242446\pi$
$132$	−0.454630	−0.0395704
$133$	−0.959144	−0.0831683
$134$	−4.15666	−0.359081
$135$	3.21537	0.276735
$136$	−3.97222	−0.340615
$137$	−6.00607	−0.513133	−0.256567	−	0.966527i	$-0.582591\pi$
$137$	−6.00607	−0.513133	−0.256567	+	0.966527i	$0.582591\pi$
$138$	8.01149	0.681984
$139$	7.60984	0.645458	0.322729	−	0.946491i	$-0.395400\pi$
$139$	7.60984	0.645458	0.322729	+	0.946491i	$0.395400\pi$
$140$	−2.98428	−0.252218
$141$	10.3975	0.875629
$142$	−4.04024	−0.339049
$143$	−0.454630	−0.0380181
$144$	1.00000	0.0833333
$145$	15.2899	1.26976
$146$	−3.48725	−0.288606
$147$	−6.13858	−0.506301
$148$	−6.52036	−0.535970
$149$	−10.4058	−0.852476	−0.426238	−	0.904611i	$-0.640161\pi$
$149$	−10.4058	−0.852476	−0.426238	+	0.904611i	$0.640161\pi$
$150$	−5.33861	−0.435895
$151$	14.9499	1.21661	0.608303	−	0.793705i	$-0.291851\pi$
$151$	14.9499	1.21661	0.608303	+	0.793705i	$0.291851\pi$
$152$	−1.03342	−0.0838211
$153$	3.97222	0.321135
$154$	−0.421955	−0.0340021
$155$	11.4401	0.918890
$156$	1.00000	0.0800641
$157$	11.1944	0.893414	0.446707	−	0.894680i	$-0.352597\pi$
$157$	11.1944	0.893414	0.446707	+	0.894680i	$0.352597\pi$
$158$	−0.976844	−0.0777135
$159$	0.418935	0.0332237
$160$	−3.21537	−0.254197
$161$	7.43570	0.586016
$162$	−1.00000	−0.0785674
$163$	10.4526	0.818709	0.409354	−	0.912375i	$-0.365754\pi$
$163$	10.4526	0.818709	0.409354	+	0.912375i	$0.365754\pi$
$164$	−3.35845	−0.262251
$165$	−1.46180	−0.113801
$166$	7.97939	0.619321
$167$	−9.62381	−0.744712	−0.372356	−	0.928090i	$-0.621450\pi$
$167$	−9.62381	−0.744712	−0.372356	+	0.928090i	$0.621450\pi$
$168$	0.928130	0.0716068
$169$	1.00000	0.0769231
$170$	−12.7722	−0.979580
$171$	1.03342	0.0790273
$172$	8.82693	0.673047
$173$	0.875860	0.0665904	0.0332952	−	0.999446i	$-0.489400\pi$
$173$	0.875860	0.0665904	0.0332952	+	0.999446i	$0.489400\pi$
$174$	−4.75525	−0.360494
$175$	−4.95492	−0.374557
$176$	−0.454630	−0.0342690
$177$	11.2912	0.848700
$178$	5.87631	0.440448
$179$	22.9694	1.71681	0.858406	−	0.512971i	$-0.171455\pi$
$179$	22.9694	1.71681	0.858406	+	0.512971i	$0.171455\pi$
$180$	3.21537	0.239660
$181$	−10.9708	−0.815456	−0.407728	−	0.913103i	$-0.633679\pi$
$181$	−10.9708	−0.815456	−0.407728	+	0.913103i	$0.633679\pi$
$182$	0.928130	0.0687976
$183$	0.360950	0.0266822
$184$	8.01149	0.590615
$185$	−20.9654	−1.54141
$186$	−3.55794	−0.260881
$187$	−1.80589	−0.132060
$188$	10.3975	0.758317
$189$	−0.928130	−0.0675115
$190$	−3.32281	−0.241062
$191$	13.6477	0.987515	0.493757	−	0.869600i	$-0.335623\pi$
$191$	13.6477	0.987515	0.493757	+	0.869600i	$0.335623\pi$
$192$	1.00000	0.0721688
$193$	−11.8171	−0.850613	−0.425307	−	0.905049i	$-0.639834\pi$
$193$	−11.8171	−0.850613	−0.425307	+	0.905049i	$0.639834\pi$
$194$	−6.80598	−0.488641
$195$	3.21537	0.230257
$196$	−6.13858	−0.438470
$197$	18.7302	1.33447	0.667236	−	0.744847i	$-0.267477\pi$
$197$	18.7302	1.33447	0.667236	+	0.744847i	$0.267477\pi$
$198$	0.454630	0.0323091
$199$	7.58245	0.537506	0.268753	−	0.963209i	$-0.413388\pi$
$199$	7.58245	0.537506	0.268753	+	0.963209i	$0.413388\pi$
$200$	−5.33861	−0.377497
$201$	4.15666	0.293188
$202$	4.34998	0.306063
$203$	−4.41349	−0.309766
$204$	3.97222	0.278111
$205$	−10.7987	−0.754211
$206$	−1.00000	−0.0696733
$207$	−8.01149	−0.556837
$208$	1.00000	0.0693375
$209$	−0.469821	−0.0324982
$210$	2.98428	0.205935
$211$	15.9587	1.09864	0.549320	−	0.835612i	$-0.314887\pi$
$211$	15.9587	1.09864	0.549320	+	0.835612i	$0.314887\pi$
$212$	0.418935	0.0287725
$213$	4.04024	0.276833
$214$	7.64705	0.522742
$215$	28.3819	1.93563
$216$	−1.00000	−0.0680414
$217$	−3.30223	−0.224170
$218$	−4.38493	−0.296985
$219$	3.48725	0.235646
$220$	−1.46180	−0.0985548
$221$	3.97222	0.267200
$222$	6.52036	0.437618
$223$	15.8704	1.06276	0.531380	−	0.847133i	$-0.321673\pi$
$223$	15.8704	1.06276	0.531380	+	0.847133i	$0.321673\pi$
$224$	0.928130	0.0620133
$225$	5.33861	0.355907
$226$	−12.8168	−0.852562
$227$	−11.0757	−0.735118	−0.367559	−	0.930000i	$-0.619806\pi$
$227$	−11.0757	−0.735118	−0.367559	+	0.930000i	$0.619806\pi$
$228$	1.03342	0.0684396
$229$	−26.1162	−1.72580	−0.862902	−	0.505371i	$-0.831356\pi$
$229$	−26.1162	−1.72580	−0.862902	+	0.505371i	$0.831356\pi$
$230$	25.7599	1.69856
$231$	0.421955	0.0277626
$232$	−4.75525	−0.312197
$233$	−23.1879	−1.51909	−0.759546	−	0.650453i	$-0.774579\pi$
$233$	−23.1879	−1.51909	−0.759546	+	0.650453i	$0.774579\pi$
$234$	−1.00000	−0.0653720
$235$	33.4319	2.18085
$236$	11.2912	0.734996
$237$	0.976844	0.0634528
$238$	3.68673	0.238976
$239$	−5.93568	−0.383947	−0.191974	−	0.981400i	$-0.561489\pi$
$239$	−5.93568	−0.383947	−0.191974	+	0.981400i	$0.561489\pi$
$240$	3.21537	0.207551
$241$	−26.3372	−1.69653	−0.848263	−	0.529576i	$-0.822351\pi$
$241$	−26.3372	−1.69653	−0.848263	+	0.529576i	$0.822351\pi$
$242$	10.7933	0.693820
$243$	1.00000	0.0641500
$244$	0.360950	0.0231074
$245$	−19.7378	−1.26100
$246$	3.35845	0.214127
$247$	1.03342	0.0657547
$248$	−3.55794	−0.225929
$249$	−7.97939	−0.505673
$250$	−1.08875	−0.0688586
$251$	−1.87145	−0.118125	−0.0590626	−	0.998254i	$-0.518811\pi$
$251$	−1.87145	−0.118125	−0.0590626	+	0.998254i	$0.518811\pi$
$252$	−0.928130	−0.0584667
$253$	3.64226	0.228987
$254$	−5.17329	−0.324601
$255$	12.7722	0.799823
$256$	1.00000	0.0625000
$257$	−2.63343	−0.164269	−0.0821345	−	0.996621i	$-0.526174\pi$
$257$	−2.63343	−0.164269	−0.0821345	+	0.996621i	$0.526174\pi$
$258$	−8.82693	−0.549541
$259$	6.05174	0.376037
$260$	3.21537	0.199409
$261$	4.75525	0.294342
$262$	−16.5660	−1.02345
$263$	12.0830	0.745072	0.372536	−	0.928018i	$-0.378488\pi$
$263$	12.0830	0.745072	0.372536	+	0.928018i	$0.378488\pi$
$264$	0.454630	0.0279805
$265$	1.34703	0.0827474
$266$	0.959144	0.0588089
$267$	−5.87631	−0.359624
$268$	4.15666	0.253909
$269$	15.4356	0.941125	0.470563	−	0.882367i	$-0.344051\pi$
$269$	15.4356	0.941125	0.470563	+	0.882367i	$0.344051\pi$
$270$	−3.21537	−0.195681
$271$	26.1731	1.58990	0.794952	−	0.606672i	$-0.207496\pi$
$271$	26.1731	1.58990	0.794952	+	0.606672i	$0.207496\pi$
$272$	3.97222	0.240851
$273$	−0.928130	−0.0561730
$274$	6.00607	0.362840
$275$	−2.42709	−0.146359
$276$	−8.01149	−0.482235
$277$	20.8506	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$277$	20.8506	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$278$	−7.60984	−0.456408
$279$	3.55794	0.213008
$280$	2.98428	0.178345
$281$	14.7016	0.877024	0.438512	−	0.898725i	$-0.355506\pi$
$281$	14.7016	0.877024	0.438512	+	0.898725i	$0.355506\pi$
$282$	−10.3975	−0.619163
$283$	−4.06899	−0.241876	−0.120938	−	0.992660i	$-0.538590\pi$
$283$	−4.06899	−0.241876	−0.120938	+	0.992660i	$0.538590\pi$
$284$	4.04024	0.239744
$285$	3.32281	0.196826
$286$	0.454630	0.0268828
$287$	3.11708	0.183995
$288$	−1.00000	−0.0589256
$289$	−1.22148	−0.0718516
$290$	−15.2899	−0.897853
$291$	6.80598	0.398974
$292$	3.48725	0.204076
$293$	26.8024	1.56581	0.782905	−	0.622141i	$-0.213737\pi$
$293$	26.8024	1.56581	0.782905	+	0.622141i	$0.213737\pi$
$294$	6.13858	0.358009
$295$	36.3055	2.11379
$296$	6.52036	0.378988
$297$	−0.454630	−0.0263803
$298$	10.4058	0.602792
$299$	−8.01149	−0.463317
$300$	5.33861	0.308225
$301$	−8.19254	−0.472210
$302$	−14.9499	−0.860270
$303$	−4.34998	−0.249900
$304$	1.03342	0.0592704
$305$	1.16059	0.0664551
$306$	−3.97222	−0.227077
$307$	−5.33949	−0.304741	−0.152370	−	0.988323i	$-0.548691\pi$
$307$	−5.33949	−0.304741	−0.152370	+	0.988323i	$0.548691\pi$
$308$	0.421955	0.0240431
$309$	1.00000	0.0568880
$310$	−11.4401	−0.649753
$311$	17.3577	0.984265	0.492133	−	0.870520i	$-0.336217\pi$
$311$	17.3577	0.984265	0.492133	+	0.870520i	$0.336217\pi$
$312$	−1.00000	−0.0566139
$313$	−30.4068	−1.71870	−0.859348	−	0.511391i	$-0.829130\pi$
$313$	−30.4068	−1.71870	−0.859348	+	0.511391i	$0.829130\pi$
$314$	−11.1944	−0.631739
$315$	−2.98428	−0.168145
$316$	0.976844	0.0549518
$317$	−20.1471	−1.13157	−0.565786	−	0.824552i	$-0.691427\pi$
$317$	−20.1471	−1.13157	−0.565786	+	0.824552i	$0.691427\pi$
$318$	−0.418935	−0.0234927
$319$	−2.16188	−0.121042
$320$	3.21537	0.179745
$321$	−7.64705	−0.426817
$322$	−7.43570	−0.414376
$323$	4.10495	0.228406
$324$	1.00000	0.0555556
$325$	5.33861	0.296133
$326$	−10.4526	−0.578914
$327$	4.38493	0.242487
$328$	3.35845	0.185439
$329$	−9.65024	−0.532035
$330$	1.46180	0.0804696
$331$	−7.94080	−0.436466	−0.218233	−	0.975897i	$-0.570029\pi$
$331$	−7.94080	−0.436466	−0.218233	+	0.975897i	$0.570029\pi$
$332$	−7.97939	−0.437926
$333$	−6.52036	−0.357314
$334$	9.62381	0.526591
$335$	13.3652	0.730219
$336$	−0.928130	−0.0506336
$337$	−26.5895	−1.44842	−0.724210	−	0.689580i	$-0.757795\pi$
$337$	−26.5895	−1.44842	−0.724210	+	0.689580i	$0.757795\pi$
$338$	−1.00000	−0.0543928
$339$	12.8168	0.696114
$340$	12.7722	0.692667
$341$	−1.61754	−0.0875949
$342$	−1.03342	−0.0558807
$343$	12.1943	0.658430
$344$	−8.82693	−0.475916
$345$	−25.7599	−1.38687
$346$	−0.875860	−0.0470865
$347$	−3.83838	−0.206055	−0.103028	−	0.994678i	$-0.532853\pi$
$347$	−3.83838	−0.206055	−0.103028	+	0.994678i	$0.532853\pi$
$348$	4.75525	0.254908
$349$	−26.7509	−1.43194	−0.715971	−	0.698130i	$-0.754016\pi$
$349$	−26.7509	−1.43194	−0.715971	+	0.698130i	$0.754016\pi$
$350$	4.95492	0.264852
$351$	1.00000	0.0533761
$352$	0.454630	0.0242318
$353$	29.5372	1.57211	0.786053	−	0.618159i	$-0.212121\pi$
$353$	29.5372	1.57211	0.786053	+	0.618159i	$0.212121\pi$
$354$	−11.2912	−0.600122
$355$	12.9909	0.689483
$356$	−5.87631	−0.311444
$357$	−3.68673	−0.195123
$358$	−22.9694	−1.21397
$359$	−14.6850	−0.775047	−0.387523	−	0.921860i	$-0.626669\pi$
$359$	−14.6850	−0.775047	−0.387523	+	0.921860i	$0.626669\pi$
$360$	−3.21537	−0.169465
$361$	−17.9321	−0.943792
$362$	10.9708	0.576615
$363$	−10.7933	−0.566502
$364$	−0.928130	−0.0486472
$365$	11.2128	0.586904
$366$	−0.360950	−0.0188672
$367$	9.77067	0.510025	0.255013	−	0.966938i	$-0.417920\pi$
$367$	9.77067	0.510025	0.255013	+	0.966938i	$0.417920\pi$
$368$	−8.01149	−0.417628
$369$	−3.35845	−0.174834
$370$	20.9654	1.08994
$371$	−0.388826	−0.0201868
$372$	3.55794	0.184470
$373$	−11.3539	−0.587884	−0.293942	−	0.955823i	$-0.594967\pi$
$373$	−11.3539	−0.587884	−0.293942	+	0.955823i	$0.594967\pi$
$374$	1.80589	0.0933803
$375$	1.08875	0.0562228
$376$	−10.3975	−0.536211
$377$	4.75525	0.244908
$378$	0.928130	0.0477378
$379$	5.37748	0.276223	0.138111	−	0.990417i	$-0.455897\pi$
$379$	5.37748	0.276223	0.138111	+	0.990417i	$0.455897\pi$
$380$	3.32281	0.170457
$381$	5.17329	0.265036
$382$	−13.6477	−0.698278
$383$	−33.6517	−1.71952	−0.859762	−	0.510696i	$-0.829388\pi$
$383$	−33.6517	−1.71952	−0.859762	+	0.510696i	$0.829388\pi$
$384$	−1.00000	−0.0510310
$385$	1.35674	0.0691460
$386$	11.8171	0.601474
$387$	8.82693	0.448698
$388$	6.80598	0.345521
$389$	10.5910	0.536983	0.268492	−	0.963282i	$-0.413475\pi$
$389$	10.5910	0.536983	0.268492	+	0.963282i	$0.413475\pi$
$390$	−3.21537	−0.162817
$391$	−31.8234	−1.60938
$392$	6.13858	0.310045
$393$	16.5660	0.835642
$394$	−18.7302	−0.943614
$395$	3.14092	0.158037
$396$	−0.454630	−0.0228460
$397$	−13.2699	−0.665998	−0.332999	−	0.942927i	$-0.608061\pi$
$397$	−13.2699	−0.665998	−0.332999	+	0.942927i	$0.608061\pi$
$398$	−7.58245	−0.380074
$399$	−0.959144	−0.0480172
$400$	5.33861	0.266930
$401$	36.7892	1.83717	0.918583	−	0.395229i	$-0.129335\pi$
$401$	36.7892	1.83717	0.918583	+	0.395229i	$0.129335\pi$
$402$	−4.15666	−0.207315
$403$	3.55794	0.177233
$404$	−4.34998	−0.216419
$405$	3.21537	0.159773
$406$	4.41349	0.219038
$407$	2.96435	0.146937
$408$	−3.97222	−0.196654
$409$	−6.24859	−0.308973	−0.154486	−	0.987995i	$-0.549372\pi$
$409$	−6.24859	−0.308973	−0.154486	+	0.987995i	$0.549372\pi$
$410$	10.7987	0.533308
$411$	−6.00607	−0.296258
$412$	1.00000	0.0492665
$413$	−10.4797	−0.515673
$414$	8.01149	0.393743
$415$	−25.6567	−1.25944
$416$	−1.00000	−0.0490290
$417$	7.60984	0.372655
$418$	0.469821	0.0229797
$419$	21.2858	1.03988	0.519938	−	0.854204i	$-0.325955\pi$
$419$	21.2858	1.03988	0.519938	+	0.854204i	$0.325955\pi$
$420$	−2.98428	−0.145618
$421$	−9.61556	−0.468634	−0.234317	−	0.972160i	$-0.575285\pi$
$421$	−9.61556	−0.468634	−0.234317	+	0.972160i	$0.575285\pi$
$422$	−15.9587	−0.776855
$423$	10.3975	0.505545
$424$	−0.418935	−0.0203453
$425$	21.2061	1.02865
$426$	−4.04024	−0.195750
$427$	−0.335008	−0.0162122
$428$	−7.64705	−0.369634
$429$	−0.454630	−0.0219497
$430$	−28.3819	−1.36870
$431$	22.2724	1.07282	0.536411	−	0.843957i	$-0.319780\pi$
$431$	22.2724	1.07282	0.536411	+	0.843957i	$0.319780\pi$
$432$	1.00000	0.0481125
$433$	−36.2772	−1.74337	−0.871686	−	0.490064i	$-0.836973\pi$
$433$	−36.2772	−1.74337	−0.871686	+	0.490064i	$0.836973\pi$
$434$	3.30223	0.158512
$435$	15.2899	0.733094
$436$	4.38493	0.210000
$437$	−8.27920	−0.396048
$438$	−3.48725	−0.166627
$439$	−21.2268	−1.01310	−0.506549	−	0.862211i	$-0.669079\pi$
$439$	−21.2268	−1.01310	−0.506549	+	0.862211i	$0.669079\pi$
$440$	1.46180	0.0696887
$441$	−6.13858	−0.292313
$442$	−3.97222	−0.188939
$443$	−9.95010	−0.472743	−0.236372	−	0.971663i	$-0.575958\pi$
$443$	−9.95010	−0.472743	−0.236372	+	0.971663i	$0.575958\pi$
$444$	−6.52036	−0.309443
$445$	−18.8945	−0.895686
$446$	−15.8704	−0.751485
$447$	−10.4058	−0.492177
$448$	−0.928130	−0.0438500
$449$	−0.934908	−0.0441210	−0.0220605	−	0.999757i	$-0.507023\pi$
$449$	−0.934908	−0.0441210	−0.0220605	+	0.999757i	$0.507023\pi$
$450$	−5.33861	−0.251664
$451$	1.52685	0.0718966
$452$	12.8168	0.602852
$453$	14.9499	0.702408
$454$	11.0757	0.519807
$455$	−2.98428	−0.139905
$456$	−1.03342	−0.0483941
$457$	−20.8130	−0.973592	−0.486796	−	0.873516i	$-0.661835\pi$
$457$	−20.8130	−0.973592	−0.486796	+	0.873516i	$0.661835\pi$
$458$	26.1162	1.22033
$459$	3.97222	0.185407
$460$	−25.7599	−1.20106
$461$	23.4451	1.09195	0.545975	−	0.837802i	$-0.316159\pi$
$461$	23.4451	1.09195	0.545975	+	0.837802i	$0.316159\pi$
$462$	−0.421955	−0.0196311
$463$	−34.2457	−1.59153	−0.795767	−	0.605603i	$-0.792932\pi$
$463$	−34.2457	−1.59153	−0.795767	+	0.605603i	$0.792932\pi$
$464$	4.75525	0.220757
$465$	11.4401	0.530521
$466$	23.1879	1.07416
$467$	0.585770	0.0271062	0.0135531	−	0.999908i	$-0.495686\pi$
$467$	0.585770	0.0271062	0.0135531	+	0.999908i	$0.495686\pi$
$468$	1.00000	0.0462250
$469$	−3.85792	−0.178142
$470$	−33.4319	−1.54210
$471$	11.1944	0.515813
$472$	−11.2912	−0.519721
$473$	−4.01299	−0.184517
$474$	−0.976844	−0.0448679
$475$	5.51700	0.253137
$476$	−3.68673	−0.168981
$477$	0.418935	0.0191817
$478$	5.93568	0.271492
$479$	−13.2026	−0.603244	−0.301622	−	0.953428i	$-0.597528\pi$
$479$	−13.2026	−0.603244	−0.301622	+	0.953428i	$0.597528\pi$
$480$	−3.21537	−0.146761
$481$	−6.52036	−0.297303
$482$	26.3372	1.19962
$483$	7.43570	0.338336
$484$	−10.7933	−0.490605
$485$	21.8837	0.993690
$486$	−1.00000	−0.0453609
$487$	−36.2570	−1.64296	−0.821481	−	0.570236i	$-0.806852\pi$
$487$	−36.2570	−1.64296	−0.821481	+	0.570236i	$0.806852\pi$
$488$	−0.360950	−0.0163394
$489$	10.4526	0.472682
$490$	19.7378	0.891663
$491$	−30.1626	−1.36122	−0.680609	−	0.732647i	$-0.738285\pi$
$491$	−30.1626	−1.36122	−0.680609	+	0.732647i	$0.738285\pi$
$492$	−3.35845	−0.151411
$493$	18.8889	0.850713
$494$	−1.03342	−0.0464956
$495$	−1.46180	−0.0657032
$496$	3.55794	0.159756
$497$	−3.74987	−0.168204
$498$	7.97939	0.357565
$499$	21.5782	0.965974	0.482987	−	0.875627i	$-0.339552\pi$
$499$	21.5782	0.965974	0.482987	+	0.875627i	$0.339552\pi$
$500$	1.08875	0.0486903
$501$	−9.62381	−0.429960
$502$	1.87145	0.0835271
$503$	34.8132	1.55225	0.776123	−	0.630582i	$-0.217184\pi$
$503$	34.8132	1.55225	0.776123	+	0.630582i	$0.217184\pi$
$504$	0.928130	0.0413422
$505$	−13.9868	−0.622404
$506$	−3.64226	−0.161918
$507$	1.00000	0.0444116
$508$	5.17329	0.229528
$509$	−19.4386	−0.861602	−0.430801	−	0.902447i	$-0.641769\pi$
$509$	−19.4386	−0.861602	−0.430801	+	0.902447i	$0.641769\pi$
$510$	−12.7722	−0.565561
$511$	−3.23662	−0.143179
$512$	−1.00000	−0.0441942
$513$	1.03342	0.0456264
$514$	2.63343	0.116156
$515$	3.21537	0.141686
$516$	8.82693	0.388584
$517$	−4.72702	−0.207894
$518$	−6.05174	−0.265898
$519$	0.875860	0.0384460
$520$	−3.21537	−0.141003
$521$	35.7733	1.56726	0.783629	−	0.621229i	$-0.213366\pi$
$521$	35.7733	1.56726	0.783629	+	0.621229i	$0.213366\pi$
$522$	−4.75525	−0.208132
$523$	−25.9084	−1.13290	−0.566448	−	0.824097i	$-0.691683\pi$
$523$	−25.9084	−1.13290	−0.566448	+	0.824097i	$0.691683\pi$
$524$	16.5660	0.723687
$525$	−4.95492	−0.216250
$526$	−12.0830	−0.526846
$527$	14.1329	0.615639
$528$	−0.454630	−0.0197852
$529$	41.1840	1.79061
$530$	−1.34703	−0.0585112
$531$	11.2912	0.489997
$532$	−0.959144	−0.0415842
$533$	−3.35845	−0.145471
$534$	5.87631	0.254293
$535$	−24.5881	−1.06304
$536$	−4.15666	−0.179540
$537$	22.9694	0.991202
$538$	−15.4356	−0.665476
$539$	2.79078	0.120207
$540$	3.21537	0.138368
$541$	4.97643	0.213953	0.106977	−	0.994262i	$-0.465883\pi$
$541$	4.97643	0.213953	0.106977	+	0.994262i	$0.465883\pi$
$542$	−26.1731	−1.12423
$543$	−10.9708	−0.470804
$544$	−3.97222	−0.170307
$545$	14.0992	0.603942
$546$	0.928130	0.0397203
$547$	0.583242	0.0249376	0.0124688	−	0.999922i	$-0.496031\pi$
$547$	0.583242	0.0249376	0.0124688	+	0.999922i	$0.496031\pi$
$548$	−6.00607	−0.256567
$549$	0.360950	0.0154050
$550$	2.42709	0.103491
$551$	4.91415	0.209350
$552$	8.01149	0.340992
$553$	−0.906638	−0.0385542
$554$	−20.8506	−0.885856
$555$	−20.9654	−0.889931
$556$	7.60984	0.322729
$557$	−6.72376	−0.284895	−0.142447	−	0.989802i	$-0.545497\pi$
$557$	−6.72376	−0.284895	−0.142447	+	0.989802i	$0.545497\pi$
$558$	−3.55794	−0.150619
$559$	8.82693	0.373340
$560$	−2.98428	−0.126109
$561$	−1.80589	−0.0762447
$562$	−14.7016	−0.620149
$563$	30.0243	1.26537	0.632687	−	0.774407i	$-0.281952\pi$
$563$	30.0243	1.26537	0.632687	+	0.774407i	$0.281952\pi$
$564$	10.3975	0.437814
$565$	41.2108	1.73375
$566$	4.06899	0.171032
$567$	−0.928130	−0.0389778
$568$	−4.04024	−0.169525
$569$	−12.1010	−0.507299	−0.253650	−	0.967296i	$-0.581631\pi$
$569$	−12.1010	−0.507299	−0.253650	+	0.967296i	$0.581631\pi$
$570$	−3.32281	−0.139177
$571$	−8.14516	−0.340864	−0.170432	−	0.985369i	$-0.554516\pi$
$571$	−8.14516	−0.340864	−0.170432	+	0.985369i	$0.554516\pi$
$572$	−0.454630	−0.0190090
$573$	13.6477	0.570142
$574$	−3.11708	−0.130104
$575$	−42.7702	−1.78364
$576$	1.00000	0.0416667
$577$	22.1557	0.922355	0.461177	−	0.887308i	$-0.347427\pi$
$577$	22.1557	0.922355	0.461177	+	0.887308i	$0.347427\pi$
$578$	1.22148	0.0508067
$579$	−11.8171	−0.491102
$580$	15.2899	0.634878
$581$	7.40591	0.307249
$582$	−6.80598	−0.282117
$583$	−0.190460	−0.00788805
$584$	−3.48725	−0.144303
$585$	3.21537	0.132939
$586$	−26.8024	−1.10719
$587$	−11.9293	−0.492377	−0.246188	−	0.969222i	$-0.579178\pi$
$587$	−11.9293	−0.492377	−0.246188	+	0.969222i	$0.579178\pi$
$588$	−6.13858	−0.253151
$589$	3.67683	0.151501
$590$	−36.3055	−1.49467
$591$	18.7302	0.770458
$592$	−6.52036	−0.267985
$593$	17.5781	0.721844	0.360922	−	0.932596i	$-0.382462\pi$
$593$	17.5781	0.721844	0.360922	+	0.932596i	$0.382462\pi$
$594$	0.454630	0.0186537
$595$	−11.8542	−0.485976
$596$	−10.4058	−0.426238
$597$	7.58245	0.310329
$598$	8.01149	0.327614
$599$	5.88807	0.240580	0.120290	−	0.992739i	$-0.461618\pi$
$599$	5.88807	0.240580	0.120290	+	0.992739i	$0.461618\pi$
$600$	−5.33861	−0.217948
$601$	−12.2748	−0.500700	−0.250350	−	0.968155i	$-0.580546\pi$
$601$	−12.2748	−0.500700	−0.250350	+	0.968155i	$0.580546\pi$
$602$	8.19254	0.333903
$603$	4.15666	0.169272
$604$	14.9499	0.608303
$605$	−34.7045	−1.41094
$606$	4.34998	0.176706
$607$	29.2767	1.18830	0.594152	−	0.804353i	$-0.297488\pi$
$607$	29.2767	1.18830	0.594152	+	0.804353i	$0.297488\pi$
$608$	−1.03342	−0.0419105
$609$	−4.41349	−0.178844
$610$	−1.16059	−0.0469908
$611$	10.3975	0.420638
$612$	3.97222	0.160567
$613$	7.29613	0.294688	0.147344	−	0.989085i	$-0.452928\pi$
$613$	7.29613	0.294688	0.147344	+	0.989085i	$0.452928\pi$
$614$	5.33949	0.215484
$615$	−10.7987	−0.435444
$616$	−0.421955	−0.0170011
$617$	−14.5956	−0.587597	−0.293798	−	0.955867i	$-0.594919\pi$
$617$	−14.5956	−0.587597	−0.293798	+	0.955867i	$0.594919\pi$
$618$	−1.00000	−0.0402259
$619$	15.1164	0.607581	0.303790	−	0.952739i	$-0.401748\pi$
$619$	15.1164	0.607581	0.303790	+	0.952739i	$0.401748\pi$
$620$	11.4401	0.459445
$621$	−8.01149	−0.321490
$622$	−17.3577	−0.695981
$623$	5.45398	0.218509
$624$	1.00000	0.0400320
$625$	−23.1923	−0.927692
$626$	30.4068	1.21530
$627$	−0.469821	−0.0187629
$628$	11.1944	0.446707
$629$	−25.9003	−1.03271
$630$	2.98428	0.118897
$631$	−1.53073	−0.0609376	−0.0304688	−	0.999536i	$-0.509700\pi$
$631$	−1.53073	−0.0609376	−0.0304688	+	0.999536i	$0.509700\pi$
$632$	−0.976844	−0.0388568
$633$	15.9587	0.634300
$634$	20.1471	0.800142
$635$	16.6340	0.660102
$636$	0.418935	0.0166118
$637$	−6.13858	−0.243219
$638$	2.16188	0.0855896
$639$	4.04024	0.159829
$640$	−3.21537	−0.127099
$641$	−5.90045	−0.233054	−0.116527	−	0.993188i	$-0.537176\pi$
$641$	−5.90045	−0.233054	−0.116527	+	0.993188i	$0.537176\pi$
$642$	7.64705	0.301805
$643$	−18.6475	−0.735384	−0.367692	−	0.929948i	$-0.619852\pi$
$643$	−18.6475	−0.735384	−0.367692	+	0.929948i	$0.619852\pi$
$644$	7.43570	0.293008
$645$	28.3819	1.11753
$646$	−4.10495	−0.161507
$647$	−1.14273	−0.0449252	−0.0224626	−	0.999748i	$-0.507151\pi$
$647$	−1.14273	−0.0449252	−0.0224626	+	0.999748i	$0.507151\pi$
$648$	−1.00000	−0.0392837
$649$	−5.13333	−0.201501
$650$	−5.33861	−0.209397
$651$	−3.30223	−0.129424
$652$	10.4526	0.409354
$653$	29.8398	1.16772	0.583860	−	0.811854i	$-0.301542\pi$
$653$	29.8398	1.16772	0.583860	+	0.811854i	$0.301542\pi$
$654$	−4.38493	−0.171464
$655$	53.2657	2.08126
$656$	−3.35845	−0.131125
$657$	3.48725	0.136050
$658$	9.65024	0.376206
$659$	−3.21386	−0.125194	−0.0625970	−	0.998039i	$-0.519938\pi$
$659$	−3.21386	−0.125194	−0.0625970	+	0.998039i	$0.519938\pi$
$660$	−1.46180	−0.0569006
$661$	−33.8003	−1.31468	−0.657340	−	0.753594i	$-0.728318\pi$
$661$	−33.8003	−1.31468	−0.657340	+	0.753594i	$0.728318\pi$
$662$	7.94080	0.308628
$663$	3.97222	0.154268
$664$	7.97939	0.309660
$665$	−3.08400	−0.119592
$666$	6.52036	0.252659
$667$	−38.0966	−1.47511
$668$	−9.62381	−0.372356
$669$	15.8704	0.613585
$670$	−13.3652	−0.516343
$671$	−0.164099	−0.00633496
$672$	0.928130	0.0358034
$673$	2.15635	0.0831212	0.0415606	−	0.999136i	$-0.486767\pi$
$673$	2.15635	0.0831212	0.0415606	+	0.999136i	$0.486767\pi$
$674$	26.5895	1.02419
$675$	5.33861	0.205483
$676$	1.00000	0.0384615
$677$	−6.34560	−0.243881	−0.121941	−	0.992537i	$-0.538912\pi$
$677$	−6.34560	−0.243881	−0.121941	+	0.992537i	$0.538912\pi$
$678$	−12.8168	−0.492227
$679$	−6.31683	−0.242418
$680$	−12.7722	−0.489790
$681$	−11.0757	−0.424420
$682$	1.61754	0.0619390
$683$	−49.3922	−1.88994	−0.944970	−	0.327157i	$-0.893909\pi$
$683$	−49.3922	−1.88994	−0.944970	+	0.327157i	$0.893909\pi$
$684$	1.03342	0.0395136
$685$	−19.3117	−0.737864
$686$	−12.1943	−0.465581
$687$	−26.1162	−0.996394
$688$	8.82693	0.336524
$689$	0.418935	0.0159601
$690$	25.7599	0.980663
$691$	9.88923	0.376204	0.188102	−	0.982150i	$-0.439766\pi$
$691$	9.88923	0.376204	0.188102	+	0.982150i	$0.439766\pi$
$692$	0.875860	0.0332952
$693$	0.421955	0.0160288
$694$	3.83838	0.145703
$695$	24.4684	0.928141
$696$	−4.75525	−0.180247
$697$	−13.3405	−0.505307
$698$	26.7509	1.01254
$699$	−23.1879	−0.877049
$700$	−4.95492	−0.187278
$701$	43.1657	1.63035	0.815173	−	0.579217i	$-0.196642\pi$
$701$	43.1657	1.63035	0.815173	+	0.579217i	$0.196642\pi$
$702$	−1.00000	−0.0377426
$703$	−6.73824	−0.254138
$704$	−0.454630	−0.0171345
$705$	33.4319	1.25912
$706$	−29.5372	−1.11165
$707$	4.03734	0.151840
$708$	11.2912	0.424350
$709$	−23.8051	−0.894019	−0.447009	−	0.894529i	$-0.647511\pi$
$709$	−23.8051	−0.894019	−0.447009	+	0.894529i	$0.647511\pi$
$710$	−12.9909	−0.487538
$711$	0.976844	0.0366345
$712$	5.87631	0.220224
$713$	−28.5044	−1.06750
$714$	3.68673	0.137973
$715$	−1.46180	−0.0546683
$716$	22.9694	0.858406
$717$	−5.93568	−0.221672
$718$	14.6850	0.548041
$719$	−16.3891	−0.611210	−0.305605	−	0.952158i	$-0.598859\pi$
$719$	−16.3891	−0.611210	−0.305605	+	0.952158i	$0.598859\pi$
$720$	3.21537	0.119830
$721$	−0.928130	−0.0345654
$722$	17.9321	0.667362
$723$	−26.3372	−0.979489
$724$	−10.9708	−0.407728
$725$	25.3864	0.942827
$726$	10.7933	0.400577
$727$	−43.1543	−1.60050	−0.800252	−	0.599664i	$-0.795301\pi$
$727$	−43.1543	−1.60050	−0.800252	+	0.599664i	$0.795301\pi$
$728$	0.928130	0.0343988
$729$	1.00000	0.0370370
$730$	−11.2128	−0.415004
$731$	35.0625	1.29683
$732$	0.360950	0.0133411
$733$	−5.25388	−0.194057	−0.0970283	−	0.995282i	$-0.530934\pi$
$733$	−5.25388	−0.194057	−0.0970283	+	0.995282i	$0.530934\pi$
$734$	−9.77067	−0.360642
$735$	−19.7378	−0.728039
$736$	8.01149	0.295308
$737$	−1.88974	−0.0696096
$738$	3.35845	0.123626
$739$	38.3054	1.40909	0.704544	−	0.709660i	$-0.251152\pi$
$739$	38.3054	1.40909	0.704544	+	0.709660i	$0.251152\pi$
$740$	−20.9654	−0.770703
$741$	1.03342	0.0379635
$742$	0.388826	0.0142742
$743$	34.1283	1.25205	0.626023	−	0.779805i	$-0.284682\pi$
$743$	34.1283	1.25205	0.626023	+	0.779805i	$0.284682\pi$
$744$	−3.55794	−0.130440
$745$	−33.4585	−1.22582
$746$	11.3539	0.415697
$747$	−7.97939	−0.291951
$748$	−1.80589	−0.0660298
$749$	7.09745	0.259335
$750$	−1.08875	−0.0397555
$751$	3.25356	0.118724	0.0593620	−	0.998237i	$-0.481093\pi$
$751$	3.25356	0.118724	0.0593620	+	0.998237i	$0.481093\pi$
$752$	10.3975	0.379158
$753$	−1.87145	−0.0681996
$754$	−4.75525	−0.173176
$755$	48.0695	1.74943
$756$	−0.928130	−0.0337558
$757$	24.7742	0.900432	0.450216	−	0.892920i	$-0.351347\pi$
$757$	24.7742	0.900432	0.450216	+	0.892920i	$0.351347\pi$
$758$	−5.37748	−0.195319
$759$	3.64226	0.132206
$760$	−3.32281	−0.120531
$761$	16.3443	0.592482	0.296241	−	0.955113i	$-0.404267\pi$
$761$	16.3443	0.592482	0.296241	+	0.955113i	$0.404267\pi$
$762$	−5.17329	−0.187409
$763$	−4.06978	−0.147336
$764$	13.6477	0.493757
$765$	12.7722	0.461778
$766$	33.6517	1.21589
$767$	11.2912	0.407702
$768$	1.00000	0.0360844
$769$	29.6620	1.06964	0.534820	−	0.844966i	$-0.320379\pi$
$769$	29.6620	1.06964	0.534820	+	0.844966i	$0.320379\pi$
$770$	−1.35674	−0.0488936
$771$	−2.63343	−0.0948407
$772$	−11.8171	−0.425307
$773$	3.81462	0.137202	0.0686011	−	0.997644i	$-0.478146\pi$
$773$	3.81462	0.137202	0.0686011	+	0.997644i	$0.478146\pi$
$774$	−8.82693	−0.317278
$775$	18.9944	0.682300
$776$	−6.80598	−0.244320
$777$	6.05174	0.217105
$778$	−10.5910	−0.379705
$779$	−3.47067	−0.124350
$780$	3.21537	0.115129
$781$	−1.83681	−0.0657263
$782$	31.8234	1.13800
$783$	4.75525	0.169939
$784$	−6.13858	−0.219235
$785$	35.9943	1.28469
$786$	−16.5660	−0.590888
$787$	12.0595	0.429875	0.214938	−	0.976628i	$-0.431045\pi$
$787$	12.0595	0.429875	0.214938	+	0.976628i	$0.431045\pi$
$788$	18.7302	0.667236
$789$	12.0830	0.430168
$790$	−3.14092	−0.111749
$791$	−11.8957	−0.422961
$792$	0.454630	0.0161546
$793$	0.360950	0.0128177
$794$	13.2699	0.470931
$795$	1.34703	0.0477742
$796$	7.58245	0.268753
$797$	49.1364	1.74050	0.870251	−	0.492609i	$-0.163957\pi$
$797$	49.1364	1.74050	0.870251	+	0.492609i	$0.163957\pi$
$798$	0.959144	0.0339533
$799$	41.3012	1.46113
$800$	−5.33861	−0.188748
$801$	−5.87631	−0.207629
$802$	−36.7892	−1.29907
$803$	−1.58541	−0.0559477
$804$	4.15666	0.146594
$805$	23.9085	0.842665
$806$	−3.55794	−0.125323
$807$	15.4356	0.543359
$808$	4.34998	0.153032
$809$	−16.3155	−0.573623	−0.286812	−	0.957987i	$-0.592595\pi$
$809$	−16.3155	−0.573623	−0.286812	+	0.957987i	$0.592595\pi$
$810$	−3.21537	−0.112977
$811$	−30.6671	−1.07687	−0.538433	−	0.842668i	$-0.680984\pi$
$811$	−30.6671	−1.07687	−0.538433	+	0.842668i	$0.680984\pi$
$812$	−4.41349	−0.154883
$813$	26.1731	0.917932
$814$	−2.96435	−0.103900
$815$	33.6089	1.17727
$816$	3.97222	0.139055
$817$	9.12189	0.319135
$818$	6.24859	0.218477
$819$	−0.928130	−0.0324315
$820$	−10.7987	−0.377105
$821$	38.2230	1.33399	0.666996	−	0.745062i	$-0.267580\pi$
$821$	38.2230	1.33399	0.666996	+	0.745062i	$0.267580\pi$
$822$	6.00607	0.209486
$823$	37.3886	1.30328	0.651642	−	0.758526i	$-0.274080\pi$
$823$	37.3886	1.30328	0.651642	+	0.758526i	$0.274080\pi$
$824$	−1.00000	−0.0348367
$825$	−2.42709	−0.0845004
$826$	10.4797	0.364636
$827$	21.2201	0.737896	0.368948	−	0.929450i	$-0.379718\pi$
$827$	21.2201	0.737896	0.368948	+	0.929450i	$0.379718\pi$
$828$	−8.01149	−0.278419
$829$	12.7689	0.443484	0.221742	−	0.975105i	$-0.428826\pi$
$829$	12.7689	0.443484	0.221742	+	0.975105i	$0.428826\pi$
$830$	25.6567	0.890557
$831$	20.8506	0.723299
$832$	1.00000	0.0346688
$833$	−24.3838	−0.844847
$834$	−7.60984	−0.263507
$835$	−30.9441	−1.07086
$836$	−0.469821	−0.0162491
$837$	3.55794	0.122980
$838$	−21.2858	−0.735304
$839$	5.84676	0.201853	0.100926	−	0.994894i	$-0.467819\pi$
$839$	5.84676	0.201853	0.100926	+	0.994894i	$0.467819\pi$
$840$	2.98428	0.102967
$841$	−6.38761	−0.220263
$842$	9.61556	0.331374
$843$	14.7016	0.506350
$844$	15.9587	0.549320
$845$	3.21537	0.110612
$846$	−10.3975	−0.357474
$847$	10.0176	0.344209
$848$	0.418935	0.0143863
$849$	−4.06899	−0.139647
$850$	−21.2061	−0.727364
$851$	52.2378	1.79069
$852$	4.04024	0.138416
$853$	6.24014	0.213658	0.106829	−	0.994277i	$-0.465930\pi$
$853$	6.24014	0.213658	0.106829	+	0.994277i	$0.465930\pi$
$854$	0.335008	0.0114637
$855$	3.32281	0.113638
$856$	7.64705	0.261371
$857$	8.40585	0.287138	0.143569	−	0.989640i	$-0.454142\pi$
$857$	8.40585	0.287138	0.143569	+	0.989640i	$0.454142\pi$
$858$	0.454630	0.0155208
$859$	25.5009	0.870079	0.435039	−	0.900411i	$-0.356734\pi$
$859$	25.5009	0.870079	0.435039	+	0.900411i	$0.356734\pi$
$860$	28.3819	0.967814
$861$	3.11708	0.106230
$862$	−22.2724	−0.758600
$863$	−19.0822	−0.649566	−0.324783	−	0.945789i	$-0.605291\pi$
$863$	−19.0822	−0.649566	−0.324783	+	0.945789i	$0.605291\pi$
$864$	−1.00000	−0.0340207
$865$	2.81621	0.0957541
$866$	36.2772	1.23275
$867$	−1.22148	−0.0414835
$868$	−3.30223	−0.112085
$869$	−0.444102	−0.0150651
$870$	−15.2899	−0.518376
$871$	4.15666	0.140843
$872$	−4.38493	−0.148492
$873$	6.80598	0.230348
$874$	8.27920	0.280048
$875$	−1.01050	−0.0341612
$876$	3.48725	0.117823
$877$	24.7563	0.835960	0.417980	−	0.908456i	$-0.362738\pi$
$877$	24.7563	0.835960	0.417980	+	0.908456i	$0.362738\pi$
$878$	21.2268	0.716368
$879$	26.8024	0.904021
$880$	−1.46180	−0.0492774
$881$	−49.5414	−1.66909	−0.834547	−	0.550937i	$-0.814270\pi$
$881$	−49.5414	−1.66909	−0.834547	+	0.550937i	$0.814270\pi$
$882$	6.13858	0.206697
$883$	−24.2005	−0.814411	−0.407205	−	0.913337i	$-0.633497\pi$
$883$	−24.2005	−0.814411	−0.407205	+	0.913337i	$0.633497\pi$
$884$	3.97222	0.133600
$885$	36.3055	1.22039
$886$	9.95010	0.334280
$887$	−8.48042	−0.284745	−0.142372	−	0.989813i	$-0.545473\pi$
$887$	−8.48042	−0.284745	−0.142372	+	0.989813i	$0.545473\pi$
$888$	6.52036	0.218809
$889$	−4.80148	−0.161037
$890$	18.8945	0.633346
$891$	−0.454630	−0.0152307
$892$	15.8704	0.531380
$893$	10.7450	0.359566
$894$	10.4058	0.348022
$895$	73.8550	2.46870
$896$	0.928130	0.0310066
$897$	−8.01149	−0.267496
$898$	0.934908	0.0311983
$899$	16.9189	0.564276
$900$	5.33861	0.177954
$901$	1.66410	0.0554392
$902$	−1.52685	−0.0508386
$903$	−8.19254	−0.272631
$904$	−12.8168	−0.426281
$905$	−35.2753	−1.17259
$906$	−14.9499	−0.496677
$907$	−16.3440	−0.542695	−0.271348	−	0.962481i	$-0.587469\pi$
$907$	−16.3440	−0.542695	−0.271348	+	0.962481i	$0.587469\pi$
$908$	−11.0757	−0.367559
$909$	−4.34998	−0.144280
$910$	2.98428	0.0989280
$911$	−19.4241	−0.643550	−0.321775	−	0.946816i	$-0.604279\pi$
$911$	−19.4241	−0.643550	−0.321775	+	0.946816i	$0.604279\pi$
$912$	1.03342	0.0342198
$913$	3.62767	0.120058
$914$	20.8130	0.688434
$915$	1.16059	0.0383678
$916$	−26.1162	−0.862902
$917$	−15.3754	−0.507739
$918$	−3.97222	−0.131103
$919$	−25.9270	−0.855254	−0.427627	−	0.903955i	$-0.640650\pi$
$919$	−25.9270	−0.855254	−0.427627	+	0.903955i	$0.640650\pi$
$920$	25.7599	0.849279
$921$	−5.33949	−0.175942
$922$	−23.4451	−0.772125
$923$	4.04024	0.132986
$924$	0.421955	0.0138813
$925$	−34.8097	−1.14453
$926$	34.2457	1.12538
$927$	1.00000	0.0328443
$928$	−4.75525	−0.156099
$929$	40.3701	1.32450	0.662251	−	0.749282i	$-0.269601\pi$
$929$	40.3701	1.32450	0.662251	+	0.749282i	$0.269601\pi$
$930$	−11.4401	−0.375135
$931$	−6.34370	−0.207906
$932$	−23.1879	−0.759546
$933$	17.3577	0.568266
$934$	−0.585770	−0.0191670
$935$	−5.80660	−0.189896
$936$	−1.00000	−0.0326860
$937$	9.85152	0.321835	0.160918	−	0.986968i	$-0.448555\pi$
$937$	9.85152	0.321835	0.160918	+	0.986968i	$0.448555\pi$
$938$	3.85792	0.125966
$939$	−30.4068	−0.992290
$940$	33.4319	1.09043
$941$	−28.8034	−0.938965	−0.469482	−	0.882942i	$-0.655559\pi$
$941$	−28.8034	−0.938965	−0.469482	+	0.882942i	$0.655559\pi$
$942$	−11.1944	−0.364735
$943$	26.9062	0.876186
$944$	11.2912	0.367498
$945$	−2.98428	−0.0970787
$946$	4.01299	0.130473
$947$	9.80525	0.318628	0.159314	−	0.987228i	$-0.449072\pi$
$947$	9.80525	0.318628	0.159314	+	0.987228i	$0.449072\pi$
$948$	0.976844	0.0317264
$949$	3.48725	0.113201
$950$	−5.51700	−0.178995
$951$	−20.1471	−0.653313
$952$	3.68673	0.119488
$953$	22.6136	0.732528	0.366264	−	0.930511i	$-0.380637\pi$
$953$	22.6136	0.732528	0.366264	+	0.930511i	$0.380637\pi$
$954$	−0.418935	−0.0135635
$955$	43.8825	1.42000
$956$	−5.93568	−0.191974
$957$	−2.16188	−0.0698836
$958$	13.2026	0.426558
$959$	5.57441	0.180007
$960$	3.21537	0.103776
$961$	−18.3411	−0.591648
$962$	6.52036	0.210225
$963$	−7.64705	−0.246423
$964$	−26.3372	−0.848263
$965$	−37.9963	−1.22315
$966$	−7.43570	−0.239240
$967$	19.6188	0.630899	0.315449	−	0.948942i	$-0.397845\pi$
$967$	19.6188	0.630899	0.315449	+	0.948942i	$0.397845\pi$
$968$	10.7933	0.346910
$969$	4.10495	0.131870
$970$	−21.8837	−0.702645
$971$	10.4056	0.333930	0.166965	−	0.985963i	$-0.446603\pi$
$971$	10.4056	0.333930	0.166965	+	0.985963i	$0.446603\pi$
$972$	1.00000	0.0320750
$973$	−7.06292	−0.226427
$974$	36.2570	1.16175
$975$	5.33861	0.170972
$976$	0.360950	0.0115537
$977$	−35.3318	−1.13036	−0.565182	−	0.824966i	$-0.691194\pi$
$977$	−35.3318	−1.13036	−0.565182	+	0.824966i	$0.691194\pi$
$978$	−10.4526	−0.334236
$979$	2.67155	0.0853830
$980$	−19.7378	−0.630501
$981$	4.38493	0.140000
$982$	30.1626	0.962526
$983$	−53.1627	−1.69563	−0.847814	−	0.530294i	$-0.822082\pi$
$983$	−53.1627	−1.69563	−0.847814	+	0.530294i	$0.822082\pi$
$984$	3.35845	0.107063
$985$	60.2245	1.91891
$986$	−18.8889	−0.601545
$987$	−9.65024	−0.307171
$988$	1.03342	0.0328773
$989$	−70.7169	−2.24867
$990$	1.46180	0.0464592
$991$	−48.7179	−1.54758	−0.773788	−	0.633445i	$-0.781640\pi$
$991$	−48.7179	−1.54758	−0.773788	+	0.633445i	$0.781640\pi$
$992$	−3.55794	−0.112965
$993$	−7.94080	−0.251994
$994$	3.74987	0.118939
$995$	24.3804	0.772910
$996$	−7.97939	−0.252837
$997$	−5.35761	−0.169677	−0.0848385	−	0.996395i	$-0.527037\pi$
$997$	−5.35761	−0.169677	−0.0848385	+	0.996395i	$0.527037\pi$
$998$	−21.5782	−0.683047
$999$	−6.52036	−0.206295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.x.1.11	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.x.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.21537 q^{5} -1.00000 q^{6} -0.928130 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.21537 q^{5} -1.00000 q^{6} -0.928130 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.21537 q^{10} -0.454630 q^{11} +1.00000 q^{12} +1.00000 q^{13} +0.928130 q^{14} +3.21537 q^{15} +1.00000 q^{16} +3.97222 q^{17} -1.00000 q^{18} +1.03342 q^{19} +3.21537 q^{20} -0.928130 q^{21} +0.454630 q^{22} -8.01149 q^{23} -1.00000 q^{24} +5.33861 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.928130 q^{28} +4.75525 q^{29} -3.21537 q^{30} +3.55794 q^{31} -1.00000 q^{32} -0.454630 q^{33} -3.97222 q^{34} -2.98428 q^{35} +1.00000 q^{36} -6.52036 q^{37} -1.03342 q^{38} +1.00000 q^{39} -3.21537 q^{40} -3.35845 q^{41} +0.928130 q^{42} +8.82693 q^{43} -0.454630 q^{44} +3.21537 q^{45} +8.01149 q^{46} +10.3975 q^{47} +1.00000 q^{48} -6.13858 q^{49} -5.33861 q^{50} +3.97222 q^{51} +1.00000 q^{52} +0.418935 q^{53} -1.00000 q^{54} -1.46180 q^{55} +0.928130 q^{56} +1.03342 q^{57} -4.75525 q^{58} +11.2912 q^{59} +3.21537 q^{60} +0.360950 q^{61} -3.55794 q^{62} -0.928130 q^{63} +1.00000 q^{64} +3.21537 q^{65} +0.454630 q^{66} +4.15666 q^{67} +3.97222 q^{68} -8.01149 q^{69} +2.98428 q^{70} +4.04024 q^{71} -1.00000 q^{72} +3.48725 q^{73} +6.52036 q^{74} +5.33861 q^{75} +1.03342 q^{76} +0.421955 q^{77} -1.00000 q^{78} +0.976844 q^{79} +3.21537 q^{80} +1.00000 q^{81} +3.35845 q^{82} -7.97939 q^{83} -0.928130 q^{84} +12.7722 q^{85} -8.82693 q^{86} +4.75525 q^{87} +0.454630 q^{88} -5.87631 q^{89} -3.21537 q^{90} -0.928130 q^{91} -8.01149 q^{92} +3.55794 q^{93} -10.3975 q^{94} +3.32281 q^{95} -1.00000 q^{96} +6.80598 q^{97} +6.13858 q^{98} -0.454630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * q^99

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