LMFDB - Embedded newform 8034.2.a.t.1.2

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 24 x^{9} + 88 x^{8} + 220 x^{7} - 637 x^{6} - 977 x^{5} + 1739 x^{4} + 1872 x^{3} + \cdots - 162 $ x^11 - 4x^10 - 24x^9 + 88x^8 + 220x^7 - 637x^6 - 977x^5 + 1739x^4 + 1872x^3 - 1494x^2 - 1161x - 162
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			1.2
Root			$-2.18067$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.18067 q^{5} -1.00000 q^{6} -1.20699 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.18067 q^{5} -1.00000 q^{6} -1.20699 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.18067 q^{10} +4.76899 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.20699 q^{14} -2.18067 q^{15} +1.00000 q^{16} -4.43925 q^{17} -1.00000 q^{18} +1.23929 q^{19} -2.18067 q^{20} -1.20699 q^{21} -4.76899 q^{22} +4.79786 q^{23} -1.00000 q^{24} -0.244682 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.20699 q^{28} +3.70915 q^{29} +2.18067 q^{30} +2.65005 q^{31} -1.00000 q^{32} +4.76899 q^{33} +4.43925 q^{34} +2.63204 q^{35} +1.00000 q^{36} +7.15997 q^{37} -1.23929 q^{38} -1.00000 q^{39} +2.18067 q^{40} -0.244733 q^{41} +1.20699 q^{42} -2.09525 q^{43} +4.76899 q^{44} -2.18067 q^{45} -4.79786 q^{46} -6.43236 q^{47} +1.00000 q^{48} -5.54319 q^{49} +0.244682 q^{50} -4.43925 q^{51} -1.00000 q^{52} +2.47300 q^{53} -1.00000 q^{54} -10.3996 q^{55} +1.20699 q^{56} +1.23929 q^{57} -3.70915 q^{58} +6.52813 q^{59} -2.18067 q^{60} -5.67731 q^{61} -2.65005 q^{62} -1.20699 q^{63} +1.00000 q^{64} +2.18067 q^{65} -4.76899 q^{66} -1.11498 q^{67} -4.43925 q^{68} +4.79786 q^{69} -2.63204 q^{70} -10.2330 q^{71} -1.00000 q^{72} +0.890570 q^{73} -7.15997 q^{74} -0.244682 q^{75} +1.23929 q^{76} -5.75610 q^{77} +1.00000 q^{78} +4.05473 q^{79} -2.18067 q^{80} +1.00000 q^{81} +0.244733 q^{82} +7.35838 q^{83} -1.20699 q^{84} +9.68054 q^{85} +2.09525 q^{86} +3.70915 q^{87} -4.76899 q^{88} -9.13321 q^{89} +2.18067 q^{90} +1.20699 q^{91} +4.79786 q^{92} +2.65005 q^{93} +6.43236 q^{94} -2.70247 q^{95} -1.00000 q^{96} -9.93605 q^{97} +5.54319 q^{98} +4.76899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * 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
$5$	−2.18067	−0.975225	−0.487612	−	0.873060i	$-0.662132\pi$
$5$	−2.18067	−0.975225	−0.487612	+	0.873060i	$0.662132\pi$
$6$	−1.00000	−0.408248
$7$	−1.20699	−0.456198	−0.228099	−	0.973638i	$-0.573251\pi$
$7$	−1.20699	−0.456198	−0.228099	+	0.973638i	$0.573251\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.18067	0.689588
$11$	4.76899	1.43790	0.718952	−	0.695059i	$-0.244622\pi$
$11$	4.76899	1.43790	0.718952	+	0.695059i	$0.244622\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.20699	0.322581
$15$	−2.18067	−0.563046
$16$	1.00000	0.250000
$17$	−4.43925	−1.07668	−0.538338	−	0.842729i	$-0.680948\pi$
$17$	−4.43925	−1.07668	−0.538338	+	0.842729i	$0.680948\pi$
$18$	−1.00000	−0.235702
$19$	1.23929	0.284312	0.142156	−	0.989844i	$-0.454597\pi$
$19$	1.23929	0.284312	0.142156	+	0.989844i	$0.454597\pi$
$20$	−2.18067	−0.487612
$21$	−1.20699	−0.263386
$22$	−4.76899	−1.01675
$23$	4.79786	1.00042	0.500212	−	0.865903i	$-0.333256\pi$
$23$	4.79786	1.00042	0.500212	+	0.865903i	$0.333256\pi$
$24$	−1.00000	−0.204124
$25$	−0.244682	−0.0489364
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−1.20699	−0.228099
$29$	3.70915	0.688771	0.344386	−	0.938828i	$-0.388087\pi$
$29$	3.70915	0.688771	0.344386	+	0.938828i	$0.388087\pi$
$30$	2.18067	0.398134
$31$	2.65005	0.475962	0.237981	−	0.971270i	$-0.423514\pi$
$31$	2.65005	0.475962	0.237981	+	0.971270i	$0.423514\pi$
$32$	−1.00000	−0.176777
$33$	4.76899	0.830175
$34$	4.43925	0.761325
$35$	2.63204	0.444895
$36$	1.00000	0.166667
$37$	7.15997	1.17709	0.588546	−	0.808464i	$-0.299701\pi$
$37$	7.15997	1.17709	0.588546	+	0.808464i	$0.299701\pi$
$38$	−1.23929	−0.201039
$39$	−1.00000	−0.160128
$40$	2.18067	0.344794
$41$	−0.244733	−0.0382208	−0.0191104	−	0.999817i	$-0.506083\pi$
$41$	−0.244733	−0.0382208	−0.0191104	+	0.999817i	$0.506083\pi$
$42$	1.20699	0.186242
$43$	−2.09525	−0.319522	−0.159761	−	0.987156i	$-0.551072\pi$
$43$	−2.09525	−0.319522	−0.159761	+	0.987156i	$0.551072\pi$
$44$	4.76899	0.718952
$45$	−2.18067	−0.325075
$46$	−4.79786	−0.707406
$47$	−6.43236	−0.938256	−0.469128	−	0.883130i	$-0.655432\pi$
$47$	−6.43236	−0.938256	−0.469128	+	0.883130i	$0.655432\pi$
$48$	1.00000	0.144338
$49$	−5.54319	−0.791884
$50$	0.244682	0.0346033
$51$	−4.43925	−0.621619
$52$	−1.00000	−0.138675
$53$	2.47300	0.339693	0.169847	−	0.985471i	$-0.445673\pi$
$53$	2.47300	0.339693	0.169847	+	0.985471i	$0.445673\pi$
$54$	−1.00000	−0.136083
$55$	−10.3996	−1.40228
$56$	1.20699	0.161290
$57$	1.23929	0.164147
$58$	−3.70915	−0.487035
$59$	6.52813	0.849890	0.424945	−	0.905219i	$-0.360293\pi$
$59$	6.52813	0.849890	0.424945	+	0.905219i	$0.360293\pi$
$60$	−2.18067	−0.281523
$61$	−5.67731	−0.726905	−0.363452	−	0.931613i	$-0.618402\pi$
$61$	−5.67731	−0.726905	−0.363452	+	0.931613i	$0.618402\pi$
$62$	−2.65005	−0.336556
$63$	−1.20699	−0.152066
$64$	1.00000	0.125000
$65$	2.18067	0.270479
$66$	−4.76899	−0.587022
$67$	−1.11498	−0.136216	−0.0681079	−	0.997678i	$-0.521696\pi$
$67$	−1.11498	−0.136216	−0.0681079	+	0.997678i	$0.521696\pi$
$68$	−4.43925	−0.538338
$69$	4.79786	0.577595
$70$	−2.63204	−0.314589
$71$	−10.2330	−1.21444	−0.607219	−	0.794535i	$-0.707715\pi$
$71$	−10.2330	−1.21444	−0.607219	+	0.794535i	$0.707715\pi$
$72$	−1.00000	−0.117851
$73$	0.890570	0.104233	0.0521167	−	0.998641i	$-0.483403\pi$
$73$	0.890570	0.104233	0.0521167	+	0.998641i	$0.483403\pi$
$74$	−7.15997	−0.832329
$75$	−0.244682	−0.0282535
$76$	1.23929	0.142156
$77$	−5.75610	−0.655969
$78$	1.00000	0.113228
$79$	4.05473	0.456192	0.228096	−	0.973639i	$-0.426750\pi$
$79$	4.05473	0.456192	0.228096	+	0.973639i	$0.426750\pi$
$80$	−2.18067	−0.243806
$81$	1.00000	0.111111
$82$	0.244733	0.0270262
$83$	7.35838	0.807688	0.403844	−	0.914828i	$-0.367674\pi$
$83$	7.35838	0.807688	0.403844	+	0.914828i	$0.367674\pi$
$84$	−1.20699	−0.131693
$85$	9.68054	1.05000
$86$	2.09525	0.225936
$87$	3.70915	0.397662
$88$	−4.76899	−0.508376
$89$	−9.13321	−0.968118	−0.484059	−	0.875035i	$-0.660838\pi$
$89$	−9.13321	−0.968118	−0.484059	+	0.875035i	$0.660838\pi$
$90$	2.18067	0.229863
$91$	1.20699	0.126526
$92$	4.79786	0.500212
$93$	2.65005	0.274797
$94$	6.43236	0.663447
$95$	−2.70247	−0.277268
$96$	−1.00000	−0.102062
$97$	−9.93605	−1.00885	−0.504427	−	0.863454i	$-0.668296\pi$
$97$	−9.93605	−1.00885	−0.504427	+	0.863454i	$0.668296\pi$
$98$	5.54319	0.559946
$99$	4.76899	0.479301
$100$	−0.244682	−0.0244682
$101$	−4.79136	−0.476758	−0.238379	−	0.971172i	$-0.576616\pi$
$101$	−4.79136	−0.476758	−0.238379	+	0.971172i	$0.576616\pi$
$102$	4.43925	0.439551
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	2.63204	0.256860
$106$	−2.47300	−0.240199
$107$	9.66722	0.934566	0.467283	−	0.884108i	$-0.345233\pi$
$107$	9.66722	0.934566	0.467283	+	0.884108i	$0.345233\pi$
$108$	1.00000	0.0962250
$109$	17.2155	1.64895	0.824475	−	0.565898i	$-0.191471\pi$
$109$	17.2155	1.64895	0.824475	+	0.565898i	$0.191471\pi$
$110$	10.3996	0.991562
$111$	7.15997	0.679594
$112$	−1.20699	−0.114049
$113$	15.7734	1.48384	0.741920	−	0.670488i	$-0.233915\pi$
$113$	15.7734	1.48384	0.741920	+	0.670488i	$0.233915\pi$
$114$	−1.23929	−0.116070
$115$	−10.4625	−0.975638
$116$	3.70915	0.344386
$117$	−1.00000	−0.0924500
$118$	−6.52813	−0.600963
$119$	5.35811	0.491177
$120$	2.18067	0.199067
$121$	11.7433	1.06757
$122$	5.67731	0.513999
$123$	−0.244733	−0.0220668
$124$	2.65005	0.237981
$125$	11.4369	1.02295
$126$	1.20699	0.107527
$127$	−18.0746	−1.60386	−0.801931	−	0.597417i	$-0.796194\pi$
$127$	−18.0746	−1.60386	−0.801931	+	0.597417i	$0.796194\pi$
$128$	−1.00000	−0.0883883
$129$	−2.09525	−0.184476
$130$	−2.18067	−0.191257
$131$	9.18228	0.802260	0.401130	−	0.916021i	$-0.368618\pi$
$131$	9.18228	0.802260	0.401130	+	0.916021i	$0.368618\pi$
$132$	4.76899	0.415087
$133$	−1.49580	−0.129702
$134$	1.11498	0.0963192
$135$	−2.18067	−0.187682
$136$	4.43925	0.380663
$137$	1.79447	0.153312	0.0766559	−	0.997058i	$-0.475576\pi$
$137$	1.79447	0.153312	0.0766559	+	0.997058i	$0.475576\pi$
$138$	−4.79786	−0.408421
$139$	−5.77421	−0.489762	−0.244881	−	0.969553i	$-0.578749\pi$
$139$	−5.77421	−0.489762	−0.244881	+	0.969553i	$0.578749\pi$
$140$	2.63204	0.222448
$141$	−6.43236	−0.541702
$142$	10.2330	0.858737
$143$	−4.76899	−0.398803
$144$	1.00000	0.0833333
$145$	−8.08842	−0.671707
$146$	−0.890570	−0.0737041
$147$	−5.54319	−0.457194
$148$	7.15997	0.588546
$149$	6.80315	0.557336	0.278668	−	0.960388i	$-0.410107\pi$
$149$	6.80315	0.557336	0.278668	+	0.960388i	$0.410107\pi$
$150$	0.244682	0.0199782
$151$	−5.47003	−0.445145	−0.222573	−	0.974916i	$-0.571445\pi$
$151$	−5.47003	−0.445145	−0.222573	+	0.974916i	$0.571445\pi$
$152$	−1.23929	−0.100519
$153$	−4.43925	−0.358892
$154$	5.75610	0.463840
$155$	−5.77887	−0.464170
$156$	−1.00000	−0.0800641
$157$	5.38698	0.429928	0.214964	−	0.976622i	$-0.431037\pi$
$157$	5.38698	0.429928	0.214964	+	0.976622i	$0.431037\pi$
$158$	−4.05473	−0.322577
$159$	2.47300	0.196122
$160$	2.18067	0.172397
$161$	−5.79095	−0.456391
$162$	−1.00000	−0.0785674
$163$	3.69835	0.289677	0.144839	−	0.989455i	$-0.453734\pi$
$163$	3.69835	0.289677	0.144839	+	0.989455i	$0.453734\pi$
$164$	−0.244733	−0.0191104
$165$	−10.3996	−0.809607
$166$	−7.35838	−0.571121
$167$	2.05965	0.159380	0.0796902	−	0.996820i	$-0.474607\pi$
$167$	2.05965	0.159380	0.0796902	+	0.996820i	$0.474607\pi$
$168$	1.20699	0.0931210
$169$	1.00000	0.0769231
$170$	−9.68054	−0.742463
$171$	1.23929	0.0947705
$172$	−2.09525	−0.159761
$173$	15.0455	1.14389	0.571943	−	0.820293i	$-0.306190\pi$
$173$	15.0455	1.14389	0.571943	+	0.820293i	$0.306190\pi$
$174$	−3.70915	−0.281190
$175$	0.295328	0.0223247
$176$	4.76899	0.359476
$177$	6.52813	0.490684
$178$	9.13321	0.684563
$179$	7.18201	0.536808	0.268404	−	0.963306i	$-0.413504\pi$
$179$	7.18201	0.536808	0.268404	+	0.963306i	$0.413504\pi$
$180$	−2.18067	−0.162537
$181$	5.26696	0.391490	0.195745	−	0.980655i	$-0.437287\pi$
$181$	5.26696	0.391490	0.195745	+	0.980655i	$0.437287\pi$
$182$	−1.20699	−0.0894677
$183$	−5.67731	−0.419679
$184$	−4.79786	−0.353703
$185$	−15.6135	−1.14793
$186$	−2.65005	−0.194311
$187$	−21.1707	−1.54816
$188$	−6.43236	−0.469128
$189$	−1.20699	−0.0877953
$190$	2.70247	0.196058
$191$	10.0199	0.725016	0.362508	−	0.931981i	$-0.381921\pi$
$191$	10.0199	0.725016	0.362508	+	0.931981i	$0.381921\pi$
$192$	1.00000	0.0721688
$193$	−22.2445	−1.60119	−0.800597	−	0.599203i	$-0.795484\pi$
$193$	−22.2445	−1.60119	−0.800597	+	0.599203i	$0.795484\pi$
$194$	9.93605	0.713367
$195$	2.18067	0.156161
$196$	−5.54319	−0.395942
$197$	15.8282	1.12771	0.563856	−	0.825873i	$-0.309317\pi$
$197$	15.8282	1.12771	0.563856	+	0.825873i	$0.309317\pi$
$198$	−4.76899	−0.338917
$199$	−12.8502	−0.910924	−0.455462	−	0.890255i	$-0.650526\pi$
$199$	−12.8502	−0.910924	−0.455462	+	0.890255i	$0.650526\pi$
$200$	0.244682	0.0173016
$201$	−1.11498	−0.0786443
$202$	4.79136	0.337119
$203$	−4.47689	−0.314216
$204$	−4.43925	−0.310810
$205$	0.533681	0.0372739
$206$	1.00000	0.0696733
$207$	4.79786	0.333474
$208$	−1.00000	−0.0693375
$209$	5.91014	0.408813
$210$	−2.63204	−0.181628
$211$	−5.83687	−0.401826	−0.200913	−	0.979609i	$-0.564391\pi$
$211$	−5.83687	−0.401826	−0.200913	+	0.979609i	$0.564391\pi$
$212$	2.47300	0.169847
$213$	−10.2330	−0.701156
$214$	−9.66722	−0.660838
$215$	4.56904	0.311606
$216$	−1.00000	−0.0680414
$217$	−3.19857	−0.217133
$218$	−17.2155	−1.16598
$219$	0.890570	0.0601791
$220$	−10.3996	−0.701140
$221$	4.43925	0.298616
$222$	−7.15997	−0.480545
$223$	10.5947	0.709473	0.354736	−	0.934966i	$-0.384571\pi$
$223$	10.5947	0.709473	0.354736	+	0.934966i	$0.384571\pi$
$224$	1.20699	0.0806451
$225$	−0.244682	−0.0163121
$226$	−15.7734	−1.04923
$227$	−11.0723	−0.734893	−0.367447	−	0.930045i	$-0.619768\pi$
$227$	−11.0723	−0.734893	−0.367447	+	0.930045i	$0.619768\pi$
$228$	1.23929	0.0820737
$229$	15.3150	1.01204	0.506021	−	0.862521i	$-0.331116\pi$
$229$	15.3150	1.01204	0.506021	+	0.862521i	$0.331116\pi$
$230$	10.4625	0.689880
$231$	−5.75610	−0.378724
$232$	−3.70915	−0.243517
$233$	6.74014	0.441561	0.220781	−	0.975323i	$-0.429140\pi$
$233$	6.74014	0.441561	0.220781	+	0.975323i	$0.429140\pi$
$234$	1.00000	0.0653720
$235$	14.0268	0.915011
$236$	6.52813	0.424945
$237$	4.05473	0.263383
$238$	−5.35811	−0.347315
$239$	11.9733	0.774488	0.387244	−	0.921977i	$-0.373427\pi$
$239$	11.9733	0.774488	0.387244	+	0.921977i	$0.373427\pi$
$240$	−2.18067	−0.140762
$241$	20.9956	1.35244	0.676222	−	0.736698i	$-0.263616\pi$
$241$	20.9956	1.35244	0.676222	+	0.736698i	$0.263616\pi$
$242$	−11.7433	−0.754885
$243$	1.00000	0.0641500
$244$	−5.67731	−0.363452
$245$	12.0879	0.772265
$246$	0.244733	0.0156036
$247$	−1.23929	−0.0788539
$248$	−2.65005	−0.168278
$249$	7.35838	0.466319
$250$	−11.4369	−0.723334
$251$	−8.63514	−0.545045	−0.272523	−	0.962149i	$-0.587858\pi$
$251$	−8.63514	−0.545045	−0.272523	+	0.962149i	$0.587858\pi$
$252$	−1.20699	−0.0760330
$253$	22.8810	1.43851
$254$	18.0746	1.13410
$255$	9.68054	0.606219
$256$	1.00000	0.0625000
$257$	−30.7029	−1.91520	−0.957598	−	0.288108i	$-0.906974\pi$
$257$	−30.7029	−1.91520	−0.957598	+	0.288108i	$0.906974\pi$
$258$	2.09525	0.130444
$259$	−8.64198	−0.536986
$260$	2.18067	0.135239
$261$	3.70915	0.229590
$262$	−9.18228	−0.567283
$263$	11.7757	0.726119	0.363059	−	0.931766i	$-0.381732\pi$
$263$	11.7757	0.726119	0.363059	+	0.931766i	$0.381732\pi$
$264$	−4.76899	−0.293511
$265$	−5.39280	−0.331277
$266$	1.49580	0.0917134
$267$	−9.13321	−0.558943
$268$	−1.11498	−0.0681079
$269$	11.8327	0.721452	0.360726	−	0.932672i	$-0.382529\pi$
$269$	11.8327	0.721452	0.360726	+	0.932672i	$0.382529\pi$
$270$	2.18067	0.132711
$271$	6.67606	0.405542	0.202771	−	0.979226i	$-0.435005\pi$
$271$	6.67606	0.405542	0.202771	+	0.979226i	$0.435005\pi$
$272$	−4.43925	−0.269169
$273$	1.20699	0.0730501
$274$	−1.79447	−0.108408
$275$	−1.16689	−0.0703659
$276$	4.79786	0.288797
$277$	3.98922	0.239689	0.119844	−	0.992793i	$-0.461760\pi$
$277$	3.98922	0.239689	0.119844	+	0.992793i	$0.461760\pi$
$278$	5.77421	0.346314
$279$	2.65005	0.158654
$280$	−2.63204	−0.157294
$281$	−5.44270	−0.324684	−0.162342	−	0.986735i	$-0.551905\pi$
$281$	−5.44270	−0.324684	−0.162342	+	0.986735i	$0.551905\pi$
$282$	6.43236	0.383041
$283$	−22.5155	−1.33841	−0.669203	−	0.743080i	$-0.733364\pi$
$283$	−22.5155	−1.33841	−0.669203	+	0.743080i	$0.733364\pi$
$284$	−10.2330	−0.607219
$285$	−2.70247	−0.160081
$286$	4.76899	0.281996
$287$	0.295389	0.0174362
$288$	−1.00000	−0.0589256
$289$	2.70694	0.159232
$290$	8.08842	0.474969
$291$	−9.93605	−0.582462
$292$	0.890570	0.0521167
$293$	20.0880	1.17355	0.586776	−	0.809749i	$-0.300397\pi$
$293$	20.0880	1.17355	0.586776	+	0.809749i	$0.300397\pi$
$294$	5.54319	0.323285
$295$	−14.2357	−0.828834
$296$	−7.15997	−0.416165
$297$	4.76899	0.276725
$298$	−6.80315	−0.394096
$299$	−4.79786	−0.277468
$300$	−0.244682	−0.0141267
$301$	2.52893	0.145765
$302$	5.47003	0.314765
$303$	−4.79136	−0.275257
$304$	1.23929	0.0710779
$305$	12.3803	0.708895
$306$	4.43925	0.253775
$307$	25.6708	1.46511	0.732556	−	0.680707i	$-0.238327\pi$
$307$	25.6708	1.46511	0.732556	+	0.680707i	$0.238327\pi$
$308$	−5.75610	−0.327984
$309$	−1.00000	−0.0568880
$310$	5.77887	0.328218
$311$	−8.80266	−0.499153	−0.249577	−	0.968355i	$-0.580291\pi$
$311$	−8.80266	−0.499153	−0.249577	+	0.968355i	$0.580291\pi$
$312$	1.00000	0.0566139
$313$	6.78055	0.383259	0.191630	−	0.981467i	$-0.438623\pi$
$313$	6.78055	0.383259	0.191630	+	0.981467i	$0.438623\pi$
$314$	−5.38698	−0.304005
$315$	2.63204	0.148298
$316$	4.05473	0.228096
$317$	16.6288	0.933967	0.466983	−	0.884266i	$-0.345341\pi$
$317$	16.6288	0.933967	0.466983	+	0.884266i	$0.345341\pi$
$318$	−2.47300	−0.138679
$319$	17.6889	0.990387
$320$	−2.18067	−0.121903
$321$	9.66722	0.539572
$322$	5.79095	0.322717
$323$	−5.50150	−0.306112
$324$	1.00000	0.0555556
$325$	0.244682	0.0135725
$326$	−3.69835	−0.204833
$327$	17.2155	0.952022
$328$	0.244733	0.0135131
$329$	7.76377	0.428030
$330$	10.3996	0.572479
$331$	14.4701	0.795350	0.397675	−	0.917526i	$-0.369817\pi$
$331$	14.4701	0.795350	0.397675	+	0.917526i	$0.369817\pi$
$332$	7.35838	0.403844
$333$	7.15997	0.392364
$334$	−2.05965	−0.112699
$335$	2.43139	0.132841
$336$	−1.20699	−0.0658465
$337$	27.2443	1.48409	0.742045	−	0.670351i	$-0.233856\pi$
$337$	27.2443	1.48409	0.742045	+	0.670351i	$0.233856\pi$
$338$	−1.00000	−0.0543928
$339$	15.7734	0.856695
$340$	9.68054	0.525001
$341$	12.6380	0.684388
$342$	−1.23929	−0.0670129
$343$	15.1394	0.817453
$344$	2.09525	0.112968
$345$	−10.4625	−0.563285
$346$	−15.0455	−0.808850
$347$	17.7272	0.951644	0.475822	−	0.879541i	$-0.342151\pi$
$347$	17.7272	0.951644	0.475822	+	0.879541i	$0.342151\pi$
$348$	3.70915	0.198831
$349$	14.2484	0.762701	0.381351	−	0.924430i	$-0.375459\pi$
$349$	14.2484	0.762701	0.381351	+	0.924430i	$0.375459\pi$
$350$	−0.295328	−0.0157859
$351$	−1.00000	−0.0533761
$352$	−4.76899	−0.254188
$353$	33.2954	1.77213	0.886067	−	0.463558i	$-0.153427\pi$
$353$	33.2954	1.77213	0.886067	+	0.463558i	$0.153427\pi$
$354$	−6.52813	−0.346966
$355$	22.3148	1.18435
$356$	−9.13321	−0.484059
$357$	5.35811	0.283581
$358$	−7.18201	−0.379581
$359$	34.5101	1.82138	0.910688	−	0.413095i	$-0.135552\pi$
$359$	34.5101	1.82138	0.910688	+	0.413095i	$0.135552\pi$
$360$	2.18067	0.114931
$361$	−17.4642	−0.919167
$362$	−5.26696	−0.276825
$363$	11.7433	0.616361
$364$	1.20699	0.0632632
$365$	−1.94204	−0.101651
$366$	5.67731	0.296758
$367$	−29.2238	−1.52547	−0.762734	−	0.646712i	$-0.776144\pi$
$367$	−29.2238	−1.52547	−0.762734	+	0.646712i	$0.776144\pi$
$368$	4.79786	0.250106
$369$	−0.244733	−0.0127403
$370$	15.6135	0.811708
$371$	−2.98488	−0.154967
$372$	2.65005	0.137398
$373$	−16.2108	−0.839362	−0.419681	−	0.907672i	$-0.637858\pi$
$373$	−16.2108	−0.839362	−0.419681	+	0.907672i	$0.637858\pi$
$374$	21.1707	1.09471
$375$	11.4369	0.590600
$376$	6.43236	0.331724
$377$	−3.70915	−0.191031
$378$	1.20699	0.0620806
$379$	4.59751	0.236158	0.118079	−	0.993004i	$-0.462326\pi$
$379$	4.59751	0.236158	0.118079	+	0.993004i	$0.462326\pi$
$380$	−2.70247	−0.138634
$381$	−18.0746	−0.925990
$382$	−10.0199	−0.512664
$383$	11.4891	0.587067	0.293533	−	0.955949i	$-0.405169\pi$
$383$	11.4891	0.587067	0.293533	+	0.955949i	$0.405169\pi$
$384$	−1.00000	−0.0510310
$385$	12.5522	0.639717
$386$	22.2445	1.13222
$387$	−2.09525	−0.106507
$388$	−9.93605	−0.504427
$389$	26.7725	1.35742	0.678710	−	0.734406i	$-0.262539\pi$
$389$	26.7725	1.35742	0.678710	+	0.734406i	$0.262539\pi$
$390$	−2.18067	−0.110422
$391$	−21.2989	−1.07713
$392$	5.54319	0.279973
$393$	9.18228	0.463185
$394$	−15.8282	−0.797412
$395$	−8.84202	−0.444890
$396$	4.76899	0.239651
$397$	−14.1814	−0.711745	−0.355873	−	0.934534i	$-0.615816\pi$
$397$	−14.1814	−0.711745	−0.355873	+	0.934534i	$0.615816\pi$
$398$	12.8502	0.644121
$399$	−1.49580	−0.0748837
$400$	−0.244682	−0.0122341
$401$	−3.54837	−0.177197	−0.0885985	−	0.996067i	$-0.528239\pi$
$401$	−3.54837	−0.177197	−0.0885985	+	0.996067i	$0.528239\pi$
$402$	1.11498	0.0556099
$403$	−2.65005	−0.132008
$404$	−4.79136	−0.238379
$405$	−2.18067	−0.108358
$406$	4.47689	0.222184
$407$	34.1458	1.69254
$408$	4.43925	0.219776
$409$	1.14741	0.0567357	0.0283679	−	0.999598i	$-0.490969\pi$
$409$	1.14741	0.0567357	0.0283679	+	0.999598i	$0.490969\pi$
$410$	−0.533681	−0.0263566
$411$	1.79447	0.0885146
$412$	−1.00000	−0.0492665
$413$	−7.87936	−0.387718
$414$	−4.79786	−0.235802
$415$	−16.0462	−0.787677
$416$	1.00000	0.0490290
$417$	−5.77421	−0.282764
$418$	−5.91014	−0.289074
$419$	1.41029	0.0688973	0.0344487	−	0.999406i	$-0.489032\pi$
$419$	1.41029	0.0688973	0.0344487	+	0.999406i	$0.489032\pi$
$420$	2.63204	0.128430
$421$	17.0161	0.829313	0.414656	−	0.909978i	$-0.363902\pi$
$421$	17.0161	0.829313	0.414656	+	0.909978i	$0.363902\pi$
$422$	5.83687	0.284134
$423$	−6.43236	−0.312752
$424$	−2.47300	−0.120100
$425$	1.08621	0.0526887
$426$	10.2330	0.495792
$427$	6.85243	0.331612
$428$	9.66722	0.467283
$429$	−4.76899	−0.230249
$430$	−4.56904	−0.220339
$431$	26.4122	1.27223	0.636115	−	0.771595i	$-0.280541\pi$
$431$	26.4122	1.27223	0.636115	+	0.771595i	$0.280541\pi$
$432$	1.00000	0.0481125
$433$	5.74669	0.276168	0.138084	−	0.990420i	$-0.455906\pi$
$433$	5.74669	0.276168	0.138084	+	0.990420i	$0.455906\pi$
$434$	3.19857	0.153536
$435$	−8.08842	−0.387810
$436$	17.2155	0.824475
$437$	5.94592	0.284432
$438$	−0.890570	−0.0425531
$439$	−37.3888	−1.78447	−0.892235	−	0.451572i	$-0.850864\pi$
$439$	−37.3888	−1.78447	−0.892235	+	0.451572i	$0.850864\pi$
$440$	10.3996	0.495781
$441$	−5.54319	−0.263961
$442$	−4.43925	−0.211154
$443$	6.83064	0.324534	0.162267	−	0.986747i	$-0.448119\pi$
$443$	6.83064	0.324534	0.162267	+	0.986747i	$0.448119\pi$
$444$	7.15997	0.339797
$445$	19.9165	0.944133
$446$	−10.5947	−0.501673
$447$	6.80315	0.321778
$448$	−1.20699	−0.0570247
$449$	0.908216	0.0428613	0.0214307	−	0.999770i	$-0.493178\pi$
$449$	0.908216	0.0428613	0.0214307	+	0.999770i	$0.493178\pi$
$450$	0.244682	0.0115344
$451$	−1.16713	−0.0549579
$452$	15.7734	0.741920
$453$	−5.47003	−0.257005
$454$	11.0723	0.519648
$455$	−2.63204	−0.123392
$456$	−1.23929	−0.0580349
$457$	−0.789790	−0.0369448	−0.0184724	−	0.999829i	$-0.505880\pi$
$457$	−0.789790	−0.0369448	−0.0184724	+	0.999829i	$0.505880\pi$
$458$	−15.3150	−0.715622
$459$	−4.43925	−0.207206
$460$	−10.4625	−0.487819
$461$	20.4657	0.953183	0.476592	−	0.879125i	$-0.341872\pi$
$461$	20.4657	0.953183	0.476592	+	0.879125i	$0.341872\pi$
$462$	5.75610	0.267798
$463$	−27.4442	−1.27544	−0.637720	−	0.770269i	$-0.720122\pi$
$463$	−27.4442	−1.27544	−0.637720	+	0.770269i	$0.720122\pi$
$464$	3.70915	0.172193
$465$	−5.77887	−0.267989
$466$	−6.74014	−0.312231
$467$	5.49376	0.254221	0.127110	−	0.991889i	$-0.459430\pi$
$467$	5.49376	0.254221	0.127110	+	0.991889i	$0.459430\pi$
$468$	−1.00000	−0.0462250
$469$	1.34576	0.0621414
$470$	−14.0268	−0.647010
$471$	5.38698	0.248219
$472$	−6.52813	−0.300481
$473$	−9.99221	−0.459442
$474$	−4.05473	−0.186240
$475$	−0.303231	−0.0139132
$476$	5.35811	0.245589
$477$	2.47300	0.113231
$478$	−11.9733	−0.547646
$479$	32.1520	1.46906	0.734531	−	0.678575i	$-0.237402\pi$
$479$	32.1520	1.46906	0.734531	+	0.678575i	$0.237402\pi$
$480$	2.18067	0.0995335
$481$	−7.15997	−0.326466
$482$	−20.9956	−0.956322
$483$	−5.79095	−0.263497
$484$	11.7433	0.533785
$485$	21.6672	0.983859
$486$	−1.00000	−0.0453609
$487$	−20.0677	−0.909357	−0.454678	−	0.890656i	$-0.650246\pi$
$487$	−20.0677	−0.909357	−0.454678	+	0.890656i	$0.650246\pi$
$488$	5.67731	0.257000
$489$	3.69835	0.167245
$490$	−12.0879	−0.546074
$491$	−0.758502	−0.0342307	−0.0171153	−	0.999854i	$-0.505448\pi$
$491$	−0.758502	−0.0342307	−0.0171153	+	0.999854i	$0.505448\pi$
$492$	−0.244733	−0.0110334
$493$	−16.4658	−0.741584
$494$	1.23929	0.0557581
$495$	−10.3996	−0.467427
$496$	2.65005	0.118991
$497$	12.3511	0.554023
$498$	−7.35838	−0.329737
$499$	10.8459	0.485527	0.242764	−	0.970085i	$-0.421946\pi$
$499$	10.8459	0.485527	0.242764	+	0.970085i	$0.421946\pi$
$500$	11.4369	0.511474
$501$	2.05965	0.0920183
$502$	8.63514	0.385405
$503$	−23.3749	−1.04223	−0.521117	−	0.853485i	$-0.674485\pi$
$503$	−23.3749	−1.04223	−0.521117	+	0.853485i	$0.674485\pi$
$504$	1.20699	0.0537634
$505$	10.4484	0.464947
$506$	−22.8810	−1.01718
$507$	1.00000	0.0444116
$508$	−18.0746	−0.801931
$509$	12.2511	0.543019	0.271510	−	0.962436i	$-0.412477\pi$
$509$	12.2511	0.543019	0.271510	+	0.962436i	$0.412477\pi$
$510$	−9.68054	−0.428661
$511$	−1.07491	−0.0475510
$512$	−1.00000	−0.0441942
$513$	1.23929	0.0547158
$514$	30.7029	1.35425
$515$	2.18067	0.0960918
$516$	−2.09525	−0.0922381
$517$	−30.6759	−1.34912
$518$	8.64198	0.379707
$519$	15.0455	0.660423
$520$	−2.18067	−0.0956287
$521$	26.4098	1.15704	0.578518	−	0.815670i	$-0.303631\pi$
$521$	26.4098	1.15704	0.578518	+	0.815670i	$0.303631\pi$
$522$	−3.70915	−0.162345
$523$	−27.5569	−1.20498	−0.602489	−	0.798128i	$-0.705824\pi$
$523$	−27.5569	−1.20498	−0.602489	+	0.798128i	$0.705824\pi$
$524$	9.18228	0.401130
$525$	0.295328	0.0128892
$526$	−11.7757	−0.513443
$527$	−11.7642	−0.512457
$528$	4.76899	0.207544
$529$	0.0194780	0.000846871 0
$530$	5.39280	0.234248
$531$	6.52813	0.283297
$532$	−1.49580	−0.0648512
$533$	0.244733	0.0106005
$534$	9.13321	0.395233
$535$	−21.0810	−0.911412
$536$	1.11498	0.0481596
$537$	7.18201	0.309926
$538$	−11.8327	−0.510144
$539$	−26.4354	−1.13865
$540$	−2.18067	−0.0938411
$541$	34.5928	1.48726	0.743630	−	0.668592i	$-0.233103\pi$
$541$	34.5928	1.48726	0.743630	+	0.668592i	$0.233103\pi$
$542$	−6.67606	−0.286761
$543$	5.26696	0.226027
$544$	4.43925	0.190331
$545$	−37.5414	−1.60810
$546$	−1.20699	−0.0516542
$547$	0.221341	0.00946385	0.00473193	−	0.999989i	$-0.498494\pi$
$547$	0.221341	0.00946385	0.00473193	+	0.999989i	$0.498494\pi$
$548$	1.79447	0.0766559
$549$	−5.67731	−0.242302
$550$	1.16689	0.0497562
$551$	4.59669	0.195826
$552$	−4.79786	−0.204211
$553$	−4.89400	−0.208114
$554$	−3.98922	−0.169486
$555$	−15.6135	−0.662757
$556$	−5.77421	−0.244881
$557$	−23.3385	−0.988884	−0.494442	−	0.869211i	$-0.664628\pi$
$557$	−23.3385	−0.988884	−0.494442	+	0.869211i	$0.664628\pi$
$558$	−2.65005	−0.112185
$559$	2.09525	0.0886195
$560$	2.63204	0.111224
$561$	−21.1707	−0.893829
$562$	5.44270	0.229586
$563$	−27.9969	−1.17993	−0.589965	−	0.807429i	$-0.700859\pi$
$563$	−27.9969	−1.17993	−0.589965	+	0.807429i	$0.700859\pi$
$564$	−6.43236	−0.270851
$565$	−34.3966	−1.44708
$566$	22.5155	0.946396
$567$	−1.20699	−0.0506886
$568$	10.2330	0.429368
$569$	7.20583	0.302084	0.151042	−	0.988527i	$-0.451737\pi$
$569$	7.20583	0.302084	0.151042	+	0.988527i	$0.451737\pi$
$570$	2.70247	0.113194
$571$	23.1256	0.967778	0.483889	−	0.875129i	$-0.339224\pi$
$571$	23.1256	0.967778	0.483889	+	0.875129i	$0.339224\pi$
$572$	−4.76899	−0.199401
$573$	10.0199	0.418588
$574$	−0.295389	−0.0123293
$575$	−1.17395	−0.0489571
$576$	1.00000	0.0416667
$577$	13.8837	0.577984	0.288992	−	0.957331i	$-0.406680\pi$
$577$	13.8837	0.577984	0.288992	+	0.957331i	$0.406680\pi$
$578$	−2.70694	−0.112594
$579$	−22.2445	−0.924450
$580$	−8.08842	−0.335853
$581$	−8.88146	−0.368465
$582$	9.93605	0.411863
$583$	11.7937	0.488446
$584$	−0.890570	−0.0368520
$585$	2.18067	0.0901596
$586$	−20.0880	−0.829827
$587$	−19.9761	−0.824502	−0.412251	−	0.911070i	$-0.635257\pi$
$587$	−19.9761	−0.824502	−0.412251	+	0.911070i	$0.635257\pi$
$588$	−5.54319	−0.228597
$589$	3.28416	0.135322
$590$	14.2357	0.586074
$591$	15.8282	0.651084
$592$	7.15997	0.294273
$593$	−25.9648	−1.06625	−0.533123	−	0.846038i	$-0.678982\pi$
$593$	−25.9648	−1.06625	−0.533123	+	0.846038i	$0.678982\pi$
$594$	−4.76899	−0.195674
$595$	−11.6843	−0.479008
$596$	6.80315	0.278668
$597$	−12.8502	−0.525922
$598$	4.79786	0.196199
$599$	21.7180	0.887374	0.443687	−	0.896182i	$-0.353670\pi$
$599$	21.7180	0.887374	0.443687	+	0.896182i	$0.353670\pi$
$600$	0.244682	0.00998911
$601$	43.7936	1.78638	0.893189	−	0.449682i	$-0.148463\pi$
$601$	43.7936	1.78638	0.893189	+	0.449682i	$0.148463\pi$
$602$	−2.52893	−0.103072
$603$	−1.11498	−0.0454053
$604$	−5.47003	−0.222573
$605$	−25.6082	−1.04112
$606$	4.79136	0.194636
$607$	−0.441837	−0.0179336	−0.00896681	−	0.999960i	$-0.502854\pi$
$607$	−0.441837	−0.0179336	−0.00896681	+	0.999960i	$0.502854\pi$
$608$	−1.23929	−0.0502597
$609$	−4.47689	−0.181413
$610$	−12.3803	−0.501265
$611$	6.43236	0.260225
$612$	−4.43925	−0.179446
$613$	−35.5268	−1.43491	−0.717456	−	0.696604i	$-0.754694\pi$
$613$	−35.5268	−1.43491	−0.717456	+	0.696604i	$0.754694\pi$
$614$	−25.6708	−1.03599
$615$	0.533681	0.0215201
$616$	5.75610	0.231920
$617$	−14.5485	−0.585701	−0.292850	−	0.956158i	$-0.594604\pi$
$617$	−14.5485	−0.585701	−0.292850	+	0.956158i	$0.594604\pi$
$618$	1.00000	0.0402259
$619$	20.1783	0.811035	0.405517	−	0.914087i	$-0.367091\pi$
$619$	20.1783	0.811035	0.405517	+	0.914087i	$0.367091\pi$
$620$	−5.77887	−0.232085
$621$	4.79786	0.192532
$622$	8.80266	0.352955
$623$	11.0237	0.441653
$624$	−1.00000	−0.0400320
$625$	−23.7167	−0.948669
$626$	−6.78055	−0.271005
$627$	5.91014	0.236028
$628$	5.38698	0.214964
$629$	−31.7849	−1.26735
$630$	−2.63204	−0.104863
$631$	43.1796	1.71895	0.859476	−	0.511176i	$-0.170790\pi$
$631$	43.1796	1.71895	0.859476	+	0.511176i	$0.170790\pi$
$632$	−4.05473	−0.161288
$633$	−5.83687	−0.231995
$634$	−16.6288	−0.660414
$635$	39.4147	1.56413
$636$	2.47300	0.0980609
$637$	5.54319	0.219629
$638$	−17.6889	−0.700310
$639$	−10.2330	−0.404812
$640$	2.18067	0.0861985
$641$	−26.5517	−1.04873	−0.524364	−	0.851494i	$-0.675697\pi$
$641$	−26.5517	−1.04873	−0.524364	+	0.851494i	$0.675697\pi$
$642$	−9.66722	−0.381535
$643$	15.1726	0.598351	0.299175	−	0.954198i	$-0.403288\pi$
$643$	15.1726	0.598351	0.299175	+	0.954198i	$0.403288\pi$
$644$	−5.79095	−0.228195
$645$	4.56904	0.179906
$646$	5.50150	0.216454
$647$	−1.40916	−0.0553998	−0.0276999	−	0.999616i	$-0.508818\pi$
$647$	−1.40916	−0.0553998	−0.0276999	+	0.999616i	$0.508818\pi$
$648$	−1.00000	−0.0392837
$649$	31.1326	1.22206
$650$	−0.244682	−0.00959722
$651$	−3.19857	−0.125362
$652$	3.69835	0.144839
$653$	−48.7380	−1.90726	−0.953632	−	0.300976i	$-0.902688\pi$
$653$	−48.7380	−1.90726	−0.953632	+	0.300976i	$0.902688\pi$
$654$	−17.2155	−0.673181
$655$	−20.0235	−0.782384
$656$	−0.244733	−0.00955520
$657$	0.890570	0.0347444
$658$	−7.76377	−0.302663
$659$	45.7998	1.78411	0.892053	−	0.451930i	$-0.149264\pi$
$659$	45.7998	1.78411	0.892053	+	0.451930i	$0.149264\pi$
$660$	−10.3996	−0.404803
$661$	36.3121	1.41238	0.706189	−	0.708023i	$-0.250413\pi$
$661$	36.3121	1.41238	0.706189	+	0.708023i	$0.250413\pi$
$662$	−14.4701	−0.562397
$663$	4.43925	0.172406
$664$	−7.35838	−0.285561
$665$	3.26185	0.126489
$666$	−7.15997	−0.277443
$667$	17.7960	0.689063
$668$	2.05965	0.0796902
$669$	10.5947	0.409614
$670$	−2.43139	−0.0939329
$671$	−27.0750	−1.04522
$672$	1.20699	0.0465605
$673$	−3.92488	−0.151293	−0.0756465	−	0.997135i	$-0.524102\pi$
$673$	−3.92488	−0.151293	−0.0756465	+	0.997135i	$0.524102\pi$
$674$	−27.2443	−1.04941
$675$	−0.244682	−0.00941782
$676$	1.00000	0.0384615
$677$	14.7595	0.567256	0.283628	−	0.958934i	$-0.408462\pi$
$677$	14.7595	0.567256	0.283628	+	0.958934i	$0.408462\pi$
$678$	−15.7734	−0.605775
$679$	11.9927	0.460237
$680$	−9.68054	−0.371232
$681$	−11.0723	−0.424291
$682$	−12.6380	−0.483936
$683$	24.6452	0.943022	0.471511	−	0.881860i	$-0.343709\pi$
$683$	24.6452	0.943022	0.471511	+	0.881860i	$0.343709\pi$
$684$	1.23929	0.0473853
$685$	−3.91314	−0.149513
$686$	−15.1394	−0.578027
$687$	15.3150	0.584303
$688$	−2.09525	−0.0798806
$689$	−2.47300	−0.0942139
$690$	10.4625	0.398302
$691$	11.1997	0.426055	0.213027	−	0.977046i	$-0.431668\pi$
$691$	11.1997	0.426055	0.213027	+	0.977046i	$0.431668\pi$
$692$	15.0455	0.571943
$693$	−5.75610	−0.218656
$694$	−17.7272	−0.672914
$695$	12.5916	0.477628
$696$	−3.70915	−0.140595
$697$	1.08643	0.0411514
$698$	−14.2484	−0.539311
$699$	6.74014	0.254936
$700$	0.295328	0.0111623
$701$	−6.25397	−0.236209	−0.118105	−	0.993001i	$-0.537682\pi$
$701$	−6.25397	−0.236209	−0.118105	+	0.993001i	$0.537682\pi$
$702$	1.00000	0.0377426
$703$	8.87324	0.334661
$704$	4.76899	0.179738
$705$	14.0268	0.528282
$706$	−33.2954	−1.25309
$707$	5.78311	0.217496
$708$	6.52813	0.245342
$709$	3.64780	0.136996	0.0684981	−	0.997651i	$-0.478179\pi$
$709$	3.64780	0.136996	0.0684981	+	0.997651i	$0.478179\pi$
$710$	−22.3148	−0.837461
$711$	4.05473	0.152064
$712$	9.13321	0.342281
$713$	12.7146	0.476164
$714$	−5.35811	−0.200522
$715$	10.3996	0.388923
$716$	7.18201	0.268404
$717$	11.9733	0.447151
$718$	−34.5101	−1.28791
$719$	23.2040	0.865363	0.432681	−	0.901547i	$-0.357567\pi$
$719$	23.2040	0.865363	0.432681	+	0.901547i	$0.357567\pi$
$720$	−2.18067	−0.0812687
$721$	1.20699	0.0449505
$722$	17.4642	0.649949
$723$	20.9956	0.780833
$724$	5.26696	0.195745
$725$	−0.907562	−0.0337060
$726$	−11.7433	−0.435833
$727$	−28.8608	−1.07039	−0.535194	−	0.844729i	$-0.679761\pi$
$727$	−28.8608	−1.07039	−0.535194	+	0.844729i	$0.679761\pi$
$728$	−1.20699	−0.0447339
$729$	1.00000	0.0370370
$730$	1.94204	0.0718781
$731$	9.30133	0.344022
$732$	−5.67731	−0.209839
$733$	10.1926	0.376474	0.188237	−	0.982124i	$-0.439723\pi$
$733$	10.1926	0.376474	0.188237	+	0.982124i	$0.439723\pi$
$734$	29.2238	1.07867
$735$	12.0879	0.445867
$736$	−4.79786	−0.176852
$737$	−5.31730	−0.195865
$738$	0.244733	0.00900873
$739$	−39.9627	−1.47005	−0.735026	−	0.678039i	$-0.762830\pi$
$739$	−39.9627	−1.47005	−0.735026	+	0.678039i	$0.762830\pi$
$740$	−15.6135	−0.573964
$741$	−1.23929	−0.0455263
$742$	2.98488	0.109578
$743$	18.2283	0.668731	0.334365	−	0.942443i	$-0.391478\pi$
$743$	18.2283	0.668731	0.334365	+	0.942443i	$0.391478\pi$
$744$	−2.65005	−0.0971554
$745$	−14.8354	−0.543528
$746$	16.2108	0.593518
$747$	7.35838	0.269229
$748$	−21.1707	−0.774079
$749$	−11.6682	−0.426347
$750$	−11.4369	−0.417617
$751$	10.9088	0.398069	0.199035	−	0.979992i	$-0.436219\pi$
$751$	10.9088	0.398069	0.199035	+	0.979992i	$0.436219\pi$
$752$	−6.43236	−0.234564
$753$	−8.63514	−0.314682
$754$	3.70915	0.135079
$755$	11.9283	0.434116
$756$	−1.20699	−0.0438976
$757$	21.0608	0.765467	0.382733	−	0.923859i	$-0.374983\pi$
$757$	21.0608	0.765467	0.382733	+	0.923859i	$0.374983\pi$
$758$	−4.59751	−0.166989
$759$	22.8810	0.830526
$760$	2.70247	0.0980290
$761$	26.5933	0.964006	0.482003	−	0.876169i	$-0.339909\pi$
$761$	26.5933	0.964006	0.482003	+	0.876169i	$0.339909\pi$
$762$	18.0746	0.654774
$763$	−20.7789	−0.752247
$764$	10.0199	0.362508
$765$	9.68054	0.350001
$766$	−11.4891	−0.415119
$767$	−6.52813	−0.235717
$768$	1.00000	0.0360844
$769$	1.84275	0.0664512	0.0332256	−	0.999448i	$-0.489422\pi$
$769$	1.84275	0.0664512	0.0332256	+	0.999448i	$0.489422\pi$
$770$	−12.5522	−0.452348
$771$	−30.7029	−1.10574
$772$	−22.2445	−0.800597
$773$	8.15200	0.293207	0.146603	−	0.989195i	$-0.453166\pi$
$773$	8.15200	0.293207	0.146603	+	0.989195i	$0.453166\pi$
$774$	2.09525	0.0753121
$775$	−0.648419	−0.0232919
$776$	9.93605	0.356684
$777$	−8.64198	−0.310029
$778$	−26.7725	−0.959842
$779$	−0.303294	−0.0108666
$780$	2.18067	0.0780805
$781$	−48.8012	−1.74624
$782$	21.2989	0.761647
$783$	3.70915	0.132554
$784$	−5.54319	−0.197971
$785$	−11.7472	−0.419276
$786$	−9.18228	−0.327521
$787$	−13.8116	−0.492329	−0.246164	−	0.969228i	$-0.579170\pi$
$787$	−13.8116	−0.492329	−0.246164	+	0.969228i	$0.579170\pi$
$788$	15.8282	0.563856
$789$	11.7757	0.419225
$790$	8.84202	0.314585
$791$	−19.0383	−0.676924
$792$	−4.76899	−0.169459
$793$	5.67731	0.201607
$794$	14.1814	0.503280
$795$	−5.39280	−0.191263
$796$	−12.8502	−0.455462
$797$	−20.1683	−0.714396	−0.357198	−	0.934029i	$-0.616268\pi$
$797$	−20.1683	−0.714396	−0.357198	+	0.934029i	$0.616268\pi$
$798$	1.49580	0.0529508
$799$	28.5548	1.01020
$800$	0.244682	0.00865082
$801$	−9.13321	−0.322706
$802$	3.54837	0.125297
$803$	4.24712	0.149878
$804$	−1.11498	−0.0393221
$805$	12.6281	0.445084
$806$	2.65005	0.0933439
$807$	11.8327	0.416530
$808$	4.79136	0.168560
$809$	−10.7649	−0.378473	−0.189236	−	0.981932i	$-0.560601\pi$
$809$	−10.7649	−0.378473	−0.189236	+	0.981932i	$0.560601\pi$
$810$	2.18067	0.0766209
$811$	12.9432	0.454499	0.227249	−	0.973837i	$-0.427027\pi$
$811$	12.9432	0.454499	0.227249	+	0.973837i	$0.427027\pi$
$812$	−4.47689	−0.157108
$813$	6.67606	0.234140
$814$	−34.1458	−1.19681
$815$	−8.06488	−0.282501
$816$	−4.43925	−0.155405
$817$	−2.59661	−0.0908439
$818$	−1.14741	−0.0401182
$819$	1.20699	0.0421755
$820$	0.533681	0.0186369
$821$	−4.11902	−0.143755	−0.0718774	−	0.997413i	$-0.522899\pi$
$821$	−4.11902	−0.143755	−0.0718774	+	0.997413i	$0.522899\pi$
$822$	−1.79447	−0.0625893
$823$	−38.2228	−1.33236	−0.666182	−	0.745789i	$-0.732073\pi$
$823$	−38.2228	−1.33236	−0.666182	+	0.745789i	$0.732073\pi$
$824$	1.00000	0.0348367
$825$	−1.16689	−0.0406258
$826$	7.87936	0.274158
$827$	−4.45032	−0.154753	−0.0773765	−	0.997002i	$-0.524654\pi$
$827$	−4.45032	−0.154753	−0.0773765	+	0.997002i	$0.524654\pi$
$828$	4.79786	0.166737
$829$	−29.5987	−1.02801	−0.514003	−	0.857789i	$-0.671838\pi$
$829$	−29.5987	−1.02801	−0.514003	+	0.857789i	$0.671838\pi$
$830$	16.0462	0.556972
$831$	3.98922	0.138384
$832$	−1.00000	−0.0346688
$833$	24.6076	0.852602
$834$	5.77421	0.199945
$835$	−4.49141	−0.155432
$836$	5.91014	0.204406
$837$	2.65005	0.0915990
$838$	−1.41029	−0.0487177
$839$	38.6936	1.33585	0.667926	−	0.744228i	$-0.267182\pi$
$839$	38.6936	1.33585	0.667926	+	0.744228i	$0.267182\pi$
$840$	−2.63204	−0.0908139
$841$	−15.2422	−0.525594
$842$	−17.0161	−0.586413
$843$	−5.44270	−0.187456
$844$	−5.83687	−0.200913
$845$	−2.18067	−0.0750173
$846$	6.43236	0.221149
$847$	−14.1739	−0.487023
$848$	2.47300	0.0849233
$849$	−22.5155	−0.772729
$850$	−1.08621	−0.0372565
$851$	34.3525	1.17759
$852$	−10.2330	−0.350578
$853$	23.6645	0.810257	0.405129	−	0.914260i	$-0.367227\pi$
$853$	23.6645	0.810257	0.405129	+	0.914260i	$0.367227\pi$
$854$	−6.85243	−0.234485
$855$	−2.70247	−0.0924226
$856$	−9.66722	−0.330419
$857$	−27.4712	−0.938398	−0.469199	−	0.883093i	$-0.655457\pi$
$857$	−27.4712	−0.938398	−0.469199	+	0.883093i	$0.655457\pi$
$858$	4.76899	0.162811
$859$	−11.7498	−0.400899	−0.200449	−	0.979704i	$-0.564240\pi$
$859$	−11.7498	−0.400899	−0.200449	+	0.979704i	$0.564240\pi$
$860$	4.56904	0.155803
$861$	0.295389	0.0100668
$862$	−26.4122	−0.899602
$863$	−32.5904	−1.10939	−0.554694	−	0.832054i	$-0.687165\pi$
$863$	−32.5904	−1.10939	−0.554694	+	0.832054i	$0.687165\pi$
$864$	−1.00000	−0.0340207
$865$	−32.8092	−1.11555
$866$	−5.74669	−0.195281
$867$	2.70694	0.0919325
$868$	−3.19857	−0.108566
$869$	19.3369	0.655961
$870$	8.08842	0.274223
$871$	1.11498	0.0377795
$872$	−17.2155	−0.582992
$873$	−9.93605	−0.336284
$874$	−5.94592	−0.201124
$875$	−13.8042	−0.466667
$876$	0.890570	0.0300896
$877$	41.7839	1.41094	0.705471	−	0.708738i	$-0.250735\pi$
$877$	41.7839	1.41094	0.705471	+	0.708738i	$0.250735\pi$
$878$	37.3888	1.26181
$879$	20.0880	0.677551
$880$	−10.3996	−0.350570
$881$	−34.0028	−1.14558	−0.572792	−	0.819701i	$-0.694140\pi$
$881$	−34.0028	−1.14558	−0.572792	+	0.819701i	$0.694140\pi$
$882$	5.54319	0.186649
$883$	29.4486	0.991023	0.495511	−	0.868601i	$-0.334981\pi$
$883$	29.4486	0.991023	0.495511	+	0.868601i	$0.334981\pi$
$884$	4.43925	0.149308
$885$	−14.2357	−0.478527
$886$	−6.83064	−0.229480
$887$	4.83377	0.162302	0.0811511	−	0.996702i	$-0.474140\pi$
$887$	4.83377	0.162302	0.0811511	+	0.996702i	$0.474140\pi$
$888$	−7.15997	−0.240273
$889$	21.8158	0.731678
$890$	−19.9165	−0.667603
$891$	4.76899	0.159767
$892$	10.5947	0.354736
$893$	−7.97153	−0.266757
$894$	−6.80315	−0.227531
$895$	−15.6616	−0.523509
$896$	1.20699	0.0403226
$897$	−4.79786	−0.160196
$898$	−0.908216	−0.0303075
$899$	9.82941	0.327829
$900$	−0.244682	−0.00815607
$901$	−10.9783	−0.365739
$902$	1.16713	0.0388611
$903$	2.52893	0.0841576
$904$	−15.7734	−0.524617
$905$	−11.4855	−0.381791
$906$	5.47003	0.181730
$907$	8.22525	0.273115	0.136557	−	0.990632i	$-0.456396\pi$
$907$	8.22525	0.273115	0.136557	+	0.990632i	$0.456396\pi$
$908$	−11.0723	−0.367447
$909$	−4.79136	−0.158919
$910$	2.63204	0.0872512
$911$	−21.3082	−0.705972	−0.352986	−	0.935629i	$-0.614834\pi$
$911$	−21.3082	−0.705972	−0.352986	+	0.935629i	$0.614834\pi$
$912$	1.23929	0.0410368
$913$	35.0921	1.16138
$914$	0.789790	0.0261239
$915$	12.3803	0.409281
$916$	15.3150	0.506021
$917$	−11.0829	−0.365989
$918$	4.43925	0.146517
$919$	45.1784	1.49030	0.745149	−	0.666898i	$-0.232378\pi$
$919$	45.1784	1.49030	0.745149	+	0.666898i	$0.232378\pi$
$920$	10.4625	0.344940
$921$	25.6708	0.845883
$922$	−20.4657	−0.674002
$923$	10.2330	0.336824
$924$	−5.75610	−0.189362
$925$	−1.75192	−0.0576026
$926$	27.4442	0.901872
$927$	−1.00000	−0.0328443
$928$	−3.70915	−0.121759
$929$	−34.5106	−1.13226	−0.566128	−	0.824317i	$-0.691559\pi$
$929$	−34.5106	−1.13226	−0.566128	+	0.824317i	$0.691559\pi$
$930$	5.77887	0.189497
$931$	−6.86959	−0.225142
$932$	6.74014	0.220781
$933$	−8.80266	−0.288186
$934$	−5.49376	−0.179761
$935$	46.1664	1.50980
$936$	1.00000	0.0326860
$937$	47.7799	1.56090	0.780451	−	0.625217i	$-0.214990\pi$
$937$	47.7799	1.56090	0.780451	+	0.625217i	$0.214990\pi$
$938$	−1.34576	−0.0439406
$939$	6.78055	0.221275
$940$	14.0268	0.457505
$941$	0.993801	0.0323970	0.0161985	−	0.999869i	$-0.494844\pi$
$941$	0.993801	0.0323970	0.0161985	+	0.999869i	$0.494844\pi$
$942$	−5.38698	−0.175517
$943$	−1.17419	−0.0382370
$944$	6.52813	0.212473
$945$	2.63204	0.0856202
$946$	9.99221	0.324875
$947$	−12.7239	−0.413471	−0.206736	−	0.978397i	$-0.566284\pi$
$947$	−12.7239	−0.413471	−0.206736	+	0.978397i	$0.566284\pi$
$948$	4.05473	0.131691
$949$	−0.890570	−0.0289091
$950$	0.303231	0.00983811
$951$	16.6288	0.539226
$952$	−5.35811	−0.173657
$953$	11.8389	0.383498	0.191749	−	0.981444i	$-0.438584\pi$
$953$	11.8389	0.383498	0.191749	+	0.981444i	$0.438584\pi$
$954$	−2.47300	−0.0800664
$955$	−21.8501	−0.707053
$956$	11.9733	0.387244
$957$	17.6889	0.571800
$958$	−32.1520	−1.03878
$959$	−2.16590	−0.0699405
$960$	−2.18067	−0.0703808
$961$	−23.9773	−0.773460
$962$	7.15997	0.230847
$963$	9.66722	0.311522
$964$	20.9956	0.676222
$965$	48.5079	1.56152
$966$	5.79095	0.186321
$967$	28.9487	0.930929	0.465464	−	0.885067i	$-0.345887\pi$
$967$	28.9487	0.930929	0.465464	+	0.885067i	$0.345887\pi$
$968$	−11.7433	−0.377443
$969$	−5.50150	−0.176734
$970$	−21.6672	−0.695693
$971$	−26.9072	−0.863494	−0.431747	−	0.901995i	$-0.642103\pi$
$971$	−26.9072	−0.863494	−0.431747	+	0.901995i	$0.642103\pi$
$972$	1.00000	0.0320750
$973$	6.96939	0.223428
$974$	20.0677	0.643012
$975$	0.244682	0.00783610
$976$	−5.67731	−0.181726
$977$	42.5858	1.36244	0.681221	−	0.732078i	$-0.261449\pi$
$977$	42.5858	1.36244	0.681221	+	0.732078i	$0.261449\pi$
$978$	−3.69835	−0.118260
$979$	−43.5562	−1.39206
$980$	12.0879	0.386132
$981$	17.2155	0.549650
$982$	0.758502	0.0242048
$983$	−28.7782	−0.917882	−0.458941	−	0.888467i	$-0.651771\pi$
$983$	−28.7782	−0.917882	−0.458941	+	0.888467i	$0.651771\pi$
$984$	0.244733	0.00780179
$985$	−34.5160	−1.09977
$986$	16.4658	0.524379
$987$	7.76377	0.247123
$988$	−1.23929	−0.0394269
$989$	−10.0527	−0.319657
$990$	10.3996	0.330521
$991$	17.7164	0.562782	0.281391	−	0.959593i	$-0.409204\pi$
$991$	17.7164	0.562782	0.281391	+	0.959593i	$0.409204\pi$
$992$	−2.65005	−0.0841390
$993$	14.4701	0.459195
$994$	−12.3511	−0.391754
$995$	28.0220	0.888356
$996$	7.35838	0.233159
$997$	45.3186	1.43525	0.717627	−	0.696427i	$-0.245228\pi$
$997$	45.3186	1.43525	0.717627	+	0.696427i	$0.245228\pi$
$998$	−10.8459	−0.343320
$999$	7.15997	0.226531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.t.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.t.1.2	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.18067 q^{5} -1.00000 q^{6} -1.20699 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.18067 q^{5} -1.00000 q^{6} -1.20699 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.18067 q^{10} +4.76899 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.20699 q^{14} -2.18067 q^{15} +1.00000 q^{16} -4.43925 q^{17} -1.00000 q^{18} +1.23929 q^{19} -2.18067 q^{20} -1.20699 q^{21} -4.76899 q^{22} +4.79786 q^{23} -1.00000 q^{24} -0.244682 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.20699 q^{28} +3.70915 q^{29} +2.18067 q^{30} +2.65005 q^{31} -1.00000 q^{32} +4.76899 q^{33} +4.43925 q^{34} +2.63204 q^{35} +1.00000 q^{36} +7.15997 q^{37} -1.23929 q^{38} -1.00000 q^{39} +2.18067 q^{40} -0.244733 q^{41} +1.20699 q^{42} -2.09525 q^{43} +4.76899 q^{44} -2.18067 q^{45} -4.79786 q^{46} -6.43236 q^{47} +1.00000 q^{48} -5.54319 q^{49} +0.244682 q^{50} -4.43925 q^{51} -1.00000 q^{52} +2.47300 q^{53} -1.00000 q^{54} -10.3996 q^{55} +1.20699 q^{56} +1.23929 q^{57} -3.70915 q^{58} +6.52813 q^{59} -2.18067 q^{60} -5.67731 q^{61} -2.65005 q^{62} -1.20699 q^{63} +1.00000 q^{64} +2.18067 q^{65} -4.76899 q^{66} -1.11498 q^{67} -4.43925 q^{68} +4.79786 q^{69} -2.63204 q^{70} -10.2330 q^{71} -1.00000 q^{72} +0.890570 q^{73} -7.15997 q^{74} -0.244682 q^{75} +1.23929 q^{76} -5.75610 q^{77} +1.00000 q^{78} +4.05473 q^{79} -2.18067 q^{80} +1.00000 q^{81} +0.244733 q^{82} +7.35838 q^{83} -1.20699 q^{84} +9.68054 q^{85} +2.09525 q^{86} +3.70915 q^{87} -4.76899 q^{88} -9.13321 q^{89} +2.18067 q^{90} +1.20699 q^{91} +4.79786 q^{92} +2.65005 q^{93} +6.43236 q^{94} -2.70247 q^{95} -1.00000 q^{96} -9.93605 q^{97} +5.54319 q^{98} +4.76899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * q^99

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