LMFDB - Embedded newform 8034.2.a.t.1.6

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			1.6
Root			$-0.203778$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.203778 q^{5} -1.00000 q^{6} +0.561930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.203778 q^{5} -1.00000 q^{6} +0.561930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.203778 q^{10} -2.27691 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.561930 q^{14} -0.203778 q^{15} +1.00000 q^{16} -3.49451 q^{17} -1.00000 q^{18} -2.88016 q^{19} -0.203778 q^{20} +0.561930 q^{21} +2.27691 q^{22} +1.20754 q^{23} -1.00000 q^{24} -4.95847 q^{25} +1.00000 q^{26} +1.00000 q^{27} +0.561930 q^{28} +4.71617 q^{29} +0.203778 q^{30} +3.74458 q^{31} -1.00000 q^{32} -2.27691 q^{33} +3.49451 q^{34} -0.114509 q^{35} +1.00000 q^{36} -2.70363 q^{37} +2.88016 q^{38} -1.00000 q^{39} +0.203778 q^{40} +0.285084 q^{41} -0.561930 q^{42} +4.78817 q^{43} -2.27691 q^{44} -0.203778 q^{45} -1.20754 q^{46} -0.764630 q^{47} +1.00000 q^{48} -6.68423 q^{49} +4.95847 q^{50} -3.49451 q^{51} -1.00000 q^{52} +12.3687 q^{53} -1.00000 q^{54} +0.463985 q^{55} -0.561930 q^{56} -2.88016 q^{57} -4.71617 q^{58} +5.47596 q^{59} -0.203778 q^{60} -12.0023 q^{61} -3.74458 q^{62} +0.561930 q^{63} +1.00000 q^{64} +0.203778 q^{65} +2.27691 q^{66} -0.176387 q^{67} -3.49451 q^{68} +1.20754 q^{69} +0.114509 q^{70} -4.55986 q^{71} -1.00000 q^{72} +8.20440 q^{73} +2.70363 q^{74} -4.95847 q^{75} -2.88016 q^{76} -1.27946 q^{77} +1.00000 q^{78} -7.70730 q^{79} -0.203778 q^{80} +1.00000 q^{81} -0.285084 q^{82} +15.6737 q^{83} +0.561930 q^{84} +0.712107 q^{85} -4.78817 q^{86} +4.71617 q^{87} +2.27691 q^{88} +18.2876 q^{89} +0.203778 q^{90} -0.561930 q^{91} +1.20754 q^{92} +3.74458 q^{93} +0.764630 q^{94} +0.586915 q^{95} -1.00000 q^{96} +7.19245 q^{97} +6.68423 q^{98} -2.27691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.203778	−0.0911325	−0.0455663	−	0.998961i	$-0.514509\pi$
$5$	−0.203778	−0.0911325	−0.0455663	+	0.998961i	$0.514509\pi$
$6$	−1.00000	−0.408248
$7$	0.561930	0.212390	0.106195	−	0.994345i	$-0.466133\pi$
$7$	0.561930	0.212390	0.106195	+	0.994345i	$0.466133\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.203778	0.0644404
$11$	−2.27691	−0.686513	−0.343257	−	0.939242i	$-0.611530\pi$
$11$	−2.27691	−0.686513	−0.343257	+	0.939242i	$0.611530\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.561930	−0.150182
$15$	−0.203778	−0.0526154
$16$	1.00000	0.250000
$17$	−3.49451	−0.847544	−0.423772	−	0.905769i	$-0.639294\pi$
$17$	−3.49451	−0.847544	−0.423772	+	0.905769i	$0.639294\pi$
$18$	−1.00000	−0.235702
$19$	−2.88016	−0.660754	−0.330377	−	0.943849i	$-0.607176\pi$
$19$	−2.88016	−0.660754	−0.330377	+	0.943849i	$0.607176\pi$
$20$	−0.203778	−0.0455663
$21$	0.561930	0.122623
$22$	2.27691	0.485438
$23$	1.20754	0.251789	0.125894	−	0.992044i	$-0.459820\pi$
$23$	1.20754	0.251789	0.125894	+	0.992044i	$0.459820\pi$
$24$	−1.00000	−0.204124
$25$	−4.95847	−0.991695
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0.561930	0.106195
$29$	4.71617	0.875770	0.437885	−	0.899031i	$-0.355728\pi$
$29$	4.71617	0.875770	0.437885	+	0.899031i	$0.355728\pi$
$30$	0.203778	0.0372047
$31$	3.74458	0.672547	0.336273	−	0.941764i	$-0.390833\pi$
$31$	3.74458	0.672547	0.336273	+	0.941764i	$0.390833\pi$
$32$	−1.00000	−0.176777
$33$	−2.27691	−0.396359
$34$	3.49451	0.599304
$35$	−0.114509	−0.0193556
$36$	1.00000	0.166667
$37$	−2.70363	−0.444474	−0.222237	−	0.974993i	$-0.571336\pi$
$37$	−2.70363	−0.444474	−0.222237	+	0.974993i	$0.571336\pi$
$38$	2.88016	0.467224
$39$	−1.00000	−0.160128
$40$	0.203778	0.0322202
$41$	0.285084	0.0445227	0.0222613	−	0.999752i	$-0.492913\pi$
$41$	0.285084	0.0445227	0.0222613	+	0.999752i	$0.492913\pi$
$42$	−0.561930	−0.0867077
$43$	4.78817	0.730189	0.365094	−	0.930970i	$-0.381037\pi$
$43$	4.78817	0.730189	0.365094	+	0.930970i	$0.381037\pi$
$44$	−2.27691	−0.343257
$45$	−0.203778	−0.0303775
$46$	−1.20754	−0.178041
$47$	−0.764630	−0.111533	−0.0557664	−	0.998444i	$-0.517760\pi$
$47$	−0.764630	−0.111533	−0.0557664	+	0.998444i	$0.517760\pi$
$48$	1.00000	0.144338
$49$	−6.68423	−0.954891
$50$	4.95847	0.701234
$51$	−3.49451	−0.489330
$52$	−1.00000	−0.138675
$53$	12.3687	1.69897	0.849485	−	0.527613i	$-0.176913\pi$
$53$	12.3687	1.69897	0.849485	+	0.527613i	$0.176913\pi$
$54$	−1.00000	−0.136083
$55$	0.463985	0.0625637
$56$	−0.561930	−0.0750911
$57$	−2.88016	−0.381487
$58$	−4.71617	−0.619263
$59$	5.47596	0.712909	0.356455	−	0.934313i	$-0.383985\pi$
$59$	5.47596	0.712909	0.356455	+	0.934313i	$0.383985\pi$
$60$	−0.203778	−0.0263077
$61$	−12.0023	−1.53674	−0.768369	−	0.640008i	$-0.778931\pi$
$61$	−12.0023	−1.53674	−0.768369	+	0.640008i	$0.778931\pi$
$62$	−3.74458	−0.475562
$63$	0.561930	0.0707966
$64$	1.00000	0.125000
$65$	0.203778	0.0252756
$66$	2.27691	0.280268
$67$	−0.176387	−0.0215491	−0.0107745	−	0.999942i	$-0.503430\pi$
$67$	−0.176387	−0.0215491	−0.0107745	+	0.999942i	$0.503430\pi$
$68$	−3.49451	−0.423772
$69$	1.20754	0.145370
$70$	0.114509	0.0136865
$71$	−4.55986	−0.541156	−0.270578	−	0.962698i	$-0.587215\pi$
$71$	−4.55986	−0.541156	−0.270578	+	0.962698i	$0.587215\pi$
$72$	−1.00000	−0.117851
$73$	8.20440	0.960252	0.480126	−	0.877200i	$-0.340591\pi$
$73$	8.20440	0.960252	0.480126	+	0.877200i	$0.340591\pi$
$74$	2.70363	0.314291
$75$	−4.95847	−0.572555
$76$	−2.88016	−0.330377
$77$	−1.27946	−0.145808
$78$	1.00000	0.113228
$79$	−7.70730	−0.867138	−0.433569	−	0.901120i	$-0.642746\pi$
$79$	−7.70730	−0.867138	−0.433569	+	0.901120i	$0.642746\pi$
$80$	−0.203778	−0.0227831
$81$	1.00000	0.111111
$82$	−0.285084	−0.0314823
$83$	15.6737	1.72041	0.860206	−	0.509946i	$-0.170335\pi$
$83$	15.6737	1.72041	0.860206	+	0.509946i	$0.170335\pi$
$84$	0.561930	0.0613116
$85$	0.712107	0.0772388
$86$	−4.78817	−0.516322
$87$	4.71617	0.505626
$88$	2.27691	0.242719
$89$	18.2876	1.93848	0.969241	−	0.246114i	$-0.0791539\pi$
$89$	18.2876	1.93848	0.969241	+	0.246114i	$0.0791539\pi$
$90$	0.203778	0.0214801
$91$	−0.561930	−0.0589063
$92$	1.20754	0.125894
$93$	3.74458	0.388295
$94$	0.764630	0.0788655
$95$	0.586915	0.0602162
$96$	−1.00000	−0.102062
$97$	7.19245	0.730282	0.365141	−	0.930952i	$-0.381021\pi$
$97$	7.19245	0.730282	0.365141	+	0.930952i	$0.381021\pi$
$98$	6.68423	0.675210
$99$	−2.27691	−0.228838
$100$	−4.95847	−0.495847
$101$	17.2540	1.71684	0.858420	−	0.512948i	$-0.171447\pi$
$101$	17.2540	1.71684	0.858420	+	0.512948i	$0.171447\pi$
$102$	3.49451	0.346008
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−0.114509	−0.0111750
$106$	−12.3687	−1.20135
$107$	−16.7999	−1.62411	−0.812056	−	0.583580i	$-0.801652\pi$
$107$	−16.7999	−1.62411	−0.812056	+	0.583580i	$0.801652\pi$
$108$	1.00000	0.0962250
$109$	0.840747	0.0805290	0.0402645	−	0.999189i	$-0.487180\pi$
$109$	0.840747	0.0805290	0.0402645	+	0.999189i	$0.487180\pi$
$110$	−0.463985	−0.0442392
$111$	−2.70363	−0.256617
$112$	0.561930	0.0530974
$113$	7.04978	0.663188	0.331594	−	0.943422i	$-0.392414\pi$
$113$	7.04978	0.663188	0.331594	+	0.943422i	$0.392414\pi$
$114$	2.88016	0.269752
$115$	−0.246070	−0.0229461
$116$	4.71617	0.437885
$117$	−1.00000	−0.0924500
$118$	−5.47596	−0.504103
$119$	−1.96367	−0.180010
$120$	0.203778	0.0186023
$121$	−5.81569	−0.528699
$122$	12.0023	1.08664
$123$	0.285084	0.0257052
$124$	3.74458	0.336273
$125$	2.02932	0.181508
$126$	−0.561930	−0.0500607
$127$	15.5433	1.37925	0.689623	−	0.724169i	$-0.257776\pi$
$127$	15.5433	1.37925	0.689623	+	0.724169i	$0.257776\pi$
$128$	−1.00000	−0.0883883
$129$	4.78817	0.421575
$130$	−0.203778	−0.0178726
$131$	−7.48808	−0.654237	−0.327118	−	0.944983i	$-0.606078\pi$
$131$	−7.48808	−0.654237	−0.327118	+	0.944983i	$0.606078\pi$
$132$	−2.27691	−0.198179
$133$	−1.61845	−0.140337
$134$	0.176387	0.0152375
$135$	−0.203778	−0.0175385
$136$	3.49451	0.299652
$137$	18.1952	1.55452	0.777262	−	0.629177i	$-0.216608\pi$
$137$	18.1952	1.55452	0.777262	+	0.629177i	$0.216608\pi$
$138$	−1.20754	−0.102792
$139$	10.1316	0.859347	0.429674	−	0.902984i	$-0.358629\pi$
$139$	10.1316	0.859347	0.429674	+	0.902984i	$0.358629\pi$
$140$	−0.114509	−0.00967780
$141$	−0.764630	−0.0643934
$142$	4.55986	0.382655
$143$	2.27691	0.190405
$144$	1.00000	0.0833333
$145$	−0.961053	−0.0798111
$146$	−8.20440	−0.679001
$147$	−6.68423	−0.551306
$148$	−2.70363	−0.222237
$149$	3.54128	0.290113	0.145057	−	0.989423i	$-0.453664\pi$
$149$	3.54128	0.290113	0.145057	+	0.989423i	$0.453664\pi$
$150$	4.95847	0.404858
$151$	16.8036	1.36746	0.683729	−	0.729736i	$-0.260357\pi$
$151$	16.8036	1.36746	0.683729	+	0.729736i	$0.260357\pi$
$152$	2.88016	0.233612
$153$	−3.49451	−0.282515
$154$	1.27946	0.103102
$155$	−0.763065	−0.0612909
$156$	−1.00000	−0.0800641
$157$	−1.71818	−0.137126	−0.0685630	−	0.997647i	$-0.521841\pi$
$157$	−1.71818	−0.137126	−0.0685630	+	0.997647i	$0.521841\pi$
$158$	7.70730	0.613159
$159$	12.3687	0.980901
$160$	0.203778	0.0161101
$161$	0.678551	0.0534773
$162$	−1.00000	−0.0785674
$163$	6.36940	0.498890	0.249445	−	0.968389i	$-0.419752\pi$
$163$	6.36940	0.498890	0.249445	+	0.968389i	$0.419752\pi$
$164$	0.285084	0.0222613
$165$	0.463985	0.0361212
$166$	−15.6737	−1.21652
$167$	13.2366	1.02428	0.512141	−	0.858901i	$-0.328852\pi$
$167$	13.2366	1.02428	0.512141	+	0.858901i	$0.328852\pi$
$168$	−0.561930	−0.0433539
$169$	1.00000	0.0769231
$170$	−0.712107	−0.0546161
$171$	−2.88016	−0.220251
$172$	4.78817	0.365094
$173$	−0.656119	−0.0498838	−0.0249419	−	0.999689i	$-0.507940\pi$
$173$	−0.656119	−0.0498838	−0.0249419	+	0.999689i	$0.507940\pi$
$174$	−4.71617	−0.357532
$175$	−2.78632	−0.210626
$176$	−2.27691	−0.171628
$177$	5.47596	0.411598
$178$	−18.2876	−1.37071
$179$	5.96982	0.446205	0.223102	−	0.974795i	$-0.428382\pi$
$179$	5.96982	0.446205	0.223102	+	0.974795i	$0.428382\pi$
$180$	−0.203778	−0.0151888
$181$	4.07297	0.302742	0.151371	−	0.988477i	$-0.451631\pi$
$181$	4.07297	0.302742	0.151371	+	0.988477i	$0.451631\pi$
$182$	0.561930	0.0416530
$183$	−12.0023	−0.887236
$184$	−1.20754	−0.0890207
$185$	0.550942	0.0405061
$186$	−3.74458	−0.274566
$187$	7.95668	0.581850
$188$	−0.764630	−0.0557664
$189$	0.561930	0.0408744
$190$	−0.586915	−0.0425793
$191$	−15.8400	−1.14614	−0.573072	−	0.819505i	$-0.694248\pi$
$191$	−15.8400	−1.14614	−0.573072	+	0.819505i	$0.694248\pi$
$192$	1.00000	0.0721688
$193$	11.5319	0.830087	0.415044	−	0.909802i	$-0.363766\pi$
$193$	11.5319	0.830087	0.415044	+	0.909802i	$0.363766\pi$
$194$	−7.19245	−0.516388
$195$	0.203778	0.0145929
$196$	−6.68423	−0.477445
$197$	−15.8945	−1.13243	−0.566217	−	0.824256i	$-0.691594\pi$
$197$	−15.8945	−1.13243	−0.566217	+	0.824256i	$0.691594\pi$
$198$	2.27691	0.161813
$199$	−12.2060	−0.865258	−0.432629	−	0.901572i	$-0.642414\pi$
$199$	−12.2060	−0.865258	−0.432629	+	0.901572i	$0.642414\pi$
$200$	4.95847	0.350617
$201$	−0.176387	−0.0124414
$202$	−17.2540	−1.21399
$203$	2.65016	0.186005
$204$	−3.49451	−0.244665
$205$	−0.0580941	−0.00405747
$206$	1.00000	0.0696733
$207$	1.20754	0.0839295
$208$	−1.00000	−0.0693375
$209$	6.55786	0.453616
$210$	0.114509	0.00790189
$211$	−2.88268	−0.198452	−0.0992259	−	0.995065i	$-0.531637\pi$
$211$	−2.88268	−0.198452	−0.0992259	+	0.995065i	$0.531637\pi$
$212$	12.3687	0.849485
$213$	−4.55986	−0.312436
$214$	16.7999	1.14842
$215$	−0.975726	−0.0665440
$216$	−1.00000	−0.0680414
$217$	2.10419	0.142842
$218$	−0.840747	−0.0569426
$219$	8.20440	0.554402
$220$	0.463985	0.0312818
$221$	3.49451	0.235066
$222$	2.70363	0.181456
$223$	−27.7940	−1.86123	−0.930613	−	0.366006i	$-0.880725\pi$
$223$	−27.7940	−1.86123	−0.930613	+	0.366006i	$0.880725\pi$
$224$	−0.561930	−0.0375455
$225$	−4.95847	−0.330565
$226$	−7.04978	−0.468945
$227$	1.35962	0.0902413	0.0451206	−	0.998982i	$-0.485633\pi$
$227$	1.35962	0.0902413	0.0451206	+	0.998982i	$0.485633\pi$
$228$	−2.88016	−0.190743
$229$	1.47067	0.0971844	0.0485922	−	0.998819i	$-0.484527\pi$
$229$	1.47067	0.0971844	0.0485922	+	0.998819i	$0.484527\pi$
$230$	0.246070	0.0162254
$231$	−1.27946	−0.0841825
$232$	−4.71617	−0.309632
$233$	6.14500	0.402572	0.201286	−	0.979533i	$-0.435488\pi$
$233$	6.14500	0.402572	0.201286	+	0.979533i	$0.435488\pi$
$234$	1.00000	0.0653720
$235$	0.155815	0.0101643
$236$	5.47596	0.356455
$237$	−7.70730	−0.500643
$238$	1.96367	0.127286
$239$	19.9945	1.29333	0.646667	−	0.762772i	$-0.276162\pi$
$239$	19.9945	1.29333	0.646667	+	0.762772i	$0.276162\pi$
$240$	−0.203778	−0.0131538
$241$	−3.45147	−0.222329	−0.111164	−	0.993802i	$-0.535458\pi$
$241$	−3.45147	−0.222329	−0.111164	+	0.993802i	$0.535458\pi$
$242$	5.81569	0.373847
$243$	1.00000	0.0641500
$244$	−12.0023	−0.768369
$245$	1.36210	0.0870216
$246$	−0.285084	−0.0181763
$247$	2.88016	0.183260
$248$	−3.74458	−0.237781
$249$	15.6737	0.993281
$250$	−2.02932	−0.128346
$251$	10.7546	0.678822	0.339411	−	0.940638i	$-0.389772\pi$
$251$	10.7546	0.678822	0.339411	+	0.940638i	$0.389772\pi$
$252$	0.561930	0.0353983
$253$	−2.74945	−0.172856
$254$	−15.5433	−0.975274
$255$	0.712107	0.0445939
$256$	1.00000	0.0625000
$257$	−12.4561	−0.776989	−0.388494	−	0.921451i	$-0.627005\pi$
$257$	−12.4561	−0.776989	−0.388494	+	0.921451i	$0.627005\pi$
$258$	−4.78817	−0.298098
$259$	−1.51925	−0.0944018
$260$	0.203778	0.0126378
$261$	4.71617	0.291923
$262$	7.48808	0.462615
$263$	−6.73210	−0.415119	−0.207559	−	0.978222i	$-0.566552\pi$
$263$	−6.73210	−0.415119	−0.207559	+	0.978222i	$0.566552\pi$
$264$	2.27691	0.140134
$265$	−2.52047	−0.154831
$266$	1.61845	0.0992335
$267$	18.2876	1.11918
$268$	−0.176387	−0.0107745
$269$	27.2803	1.66331	0.831656	−	0.555291i	$-0.187393\pi$
$269$	27.2803	1.66331	0.831656	+	0.555291i	$0.187393\pi$
$270$	0.203778	0.0124016
$271$	11.5759	0.703183	0.351592	−	0.936153i	$-0.385641\pi$
$271$	11.5759	0.703183	0.351592	+	0.936153i	$0.385641\pi$
$272$	−3.49451	−0.211886
$273$	−0.561930	−0.0340096
$274$	−18.1952	−1.09921
$275$	11.2900	0.680812
$276$	1.20754	0.0726851
$277$	−4.16517	−0.250261	−0.125131	−	0.992140i	$-0.539935\pi$
$277$	−4.16517	−0.250261	−0.125131	+	0.992140i	$0.539935\pi$
$278$	−10.1316	−0.607650
$279$	3.74458	0.224182
$280$	0.114509	0.00684324
$281$	18.5897	1.10897	0.554483	−	0.832195i	$-0.312916\pi$
$281$	18.5897	1.10897	0.554483	+	0.832195i	$0.312916\pi$
$282$	0.764630	0.0455330
$283$	20.3557	1.21002	0.605009	−	0.796218i	$-0.293169\pi$
$283$	20.3557	1.21002	0.605009	+	0.796218i	$0.293169\pi$
$284$	−4.55986	−0.270578
$285$	0.586915	0.0347658
$286$	−2.27691	−0.134636
$287$	0.160198	0.00945616
$288$	−1.00000	−0.0589256
$289$	−4.78837	−0.281669
$290$	0.961053	0.0564350
$291$	7.19245	0.421629
$292$	8.20440	0.480126
$293$	−8.38036	−0.489586	−0.244793	−	0.969575i	$-0.578720\pi$
$293$	−8.38036	−0.489586	−0.244793	+	0.969575i	$0.578720\pi$
$294$	6.68423	0.389832
$295$	−1.11588	−0.0649692
$296$	2.70363	0.157145
$297$	−2.27691	−0.132120
$298$	−3.54128	−0.205141
$299$	−1.20754	−0.0698336
$300$	−4.95847	−0.286278
$301$	2.69062	0.155085
$302$	−16.8036	−0.966938
$303$	17.2540	0.991218
$304$	−2.88016	−0.165189
$305$	2.44581	0.140047
$306$	3.49451	0.199768
$307$	19.1620	1.09363	0.546816	−	0.837253i	$-0.315840\pi$
$307$	19.1620	1.09363	0.546816	+	0.837253i	$0.315840\pi$
$308$	−1.27946	−0.0729042
$309$	−1.00000	−0.0568880
$310$	0.763065	0.0433392
$311$	3.38483	0.191936	0.0959680	−	0.995384i	$-0.469405\pi$
$311$	3.38483	0.191936	0.0959680	+	0.995384i	$0.469405\pi$
$312$	1.00000	0.0566139
$313$	0.769485	0.0434939	0.0217469	−	0.999764i	$-0.493077\pi$
$313$	0.769485	0.0434939	0.0217469	+	0.999764i	$0.493077\pi$
$314$	1.71818	0.0969627
$315$	−0.114509	−0.00645187
$316$	−7.70730	−0.433569
$317$	−27.0929	−1.52169	−0.760846	−	0.648933i	$-0.775216\pi$
$317$	−27.0929	−1.52169	−0.760846	+	0.648933i	$0.775216\pi$
$318$	−12.3687	−0.693601
$319$	−10.7383	−0.601228
$320$	−0.203778	−0.0113916
$321$	−16.7999	−0.937681
$322$	−0.678551	−0.0378142
$323$	10.0648	0.560018
$324$	1.00000	0.0555556
$325$	4.95847	0.275047
$326$	−6.36940	−0.352769
$327$	0.840747	0.0464934
$328$	−0.285084	−0.0157411
$329$	−0.429669	−0.0236884
$330$	−0.463985	−0.0255415
$331$	−10.1247	−0.556507	−0.278253	−	0.960508i	$-0.589755\pi$
$331$	−10.1247	−0.556507	−0.278253	+	0.960508i	$0.589755\pi$
$332$	15.6737	0.860206
$333$	−2.70363	−0.148158
$334$	−13.2366	−0.724277
$335$	0.0359438	0.00196382
$336$	0.561930	0.0306558
$337$	−17.9559	−0.978118	−0.489059	−	0.872251i	$-0.662660\pi$
$337$	−17.9559	−0.978118	−0.489059	+	0.872251i	$0.662660\pi$
$338$	−1.00000	−0.0543928
$339$	7.04978	0.382892
$340$	0.712107	0.0386194
$341$	−8.52607	−0.461712
$342$	2.88016	0.155741
$343$	−7.68959	−0.415199
$344$	−4.78817	−0.258161
$345$	−0.246070	−0.0132480
$346$	0.656119	0.0352732
$347$	23.8329	1.27942	0.639708	−	0.768618i	$-0.279055\pi$
$347$	23.8329	1.27942	0.639708	+	0.768618i	$0.279055\pi$
$348$	4.71617	0.252813
$349$	19.3454	1.03553	0.517767	−	0.855521i	$-0.326763\pi$
$349$	19.3454	1.03553	0.517767	+	0.855521i	$0.326763\pi$
$350$	2.78632	0.148935
$351$	−1.00000	−0.0533761
$352$	2.27691	0.121360
$353$	9.56854	0.509282	0.254641	−	0.967036i	$-0.418043\pi$
$353$	9.56854	0.509282	0.254641	+	0.967036i	$0.418043\pi$
$354$	−5.47596	−0.291044
$355$	0.929201	0.0493169
$356$	18.2876	0.969241
$357$	−1.96367	−0.103929
$358$	−5.96982	−0.315515
$359$	−19.8864	−1.04956	−0.524782	−	0.851236i	$-0.675853\pi$
$359$	−19.8864	−1.04956	−0.524782	+	0.851236i	$0.675853\pi$
$360$	0.203778	0.0107401
$361$	−10.7047	−0.563404
$362$	−4.07297	−0.214071
$363$	−5.81569	−0.305245
$364$	−0.561930	−0.0294532
$365$	−1.67188	−0.0875102
$366$	12.0023	0.627370
$367$	−9.37289	−0.489261	−0.244630	−	0.969616i	$-0.578667\pi$
$367$	−9.37289	−0.489261	−0.244630	+	0.969616i	$0.578667\pi$
$368$	1.20754	0.0629472
$369$	0.285084	0.0148409
$370$	−0.550942	−0.0286421
$371$	6.95034	0.360844
$372$	3.74458	0.194148
$373$	7.76688	0.402154	0.201077	−	0.979575i	$-0.435556\pi$
$373$	7.76688	0.402154	0.201077	+	0.979575i	$0.435556\pi$
$374$	−7.95668	−0.411430
$375$	2.02932	0.104794
$376$	0.764630	0.0394328
$377$	−4.71617	−0.242895
$378$	−0.561930	−0.0289026
$379$	−16.5270	−0.848937	−0.424469	−	0.905443i	$-0.639539\pi$
$379$	−16.5270	−0.848937	−0.424469	+	0.905443i	$0.639539\pi$
$380$	0.586915	0.0301081
$381$	15.5433	0.796308
$382$	15.8400	0.810446
$383$	−10.6099	−0.542138	−0.271069	−	0.962560i	$-0.587377\pi$
$383$	−10.6099	−0.542138	−0.271069	+	0.962560i	$0.587377\pi$
$384$	−1.00000	−0.0510310
$385$	0.260727	0.0132879
$386$	−11.5319	−0.586960
$387$	4.78817	0.243396
$388$	7.19245	0.365141
$389$	−18.7657	−0.951456	−0.475728	−	0.879592i	$-0.657815\pi$
$389$	−18.7657	−0.951456	−0.475728	+	0.879592i	$0.657815\pi$
$390$	−0.203778	−0.0103187
$391$	−4.21975	−0.213402
$392$	6.68423	0.337605
$393$	−7.48808	−0.377724
$394$	15.8945	0.800752
$395$	1.57058	0.0790245
$396$	−2.27691	−0.114419
$397$	13.7486	0.690021	0.345010	−	0.938599i	$-0.387875\pi$
$397$	13.7486	0.690021	0.345010	+	0.938599i	$0.387875\pi$
$398$	12.2060	0.611830
$399$	−1.61845	−0.0810238
$400$	−4.95847	−0.247924
$401$	−3.17162	−0.158383	−0.0791916	−	0.996859i	$-0.525234\pi$
$401$	−3.17162	−0.158383	−0.0791916	+	0.996859i	$0.525234\pi$
$402$	0.176387	0.00879737
$403$	−3.74458	−0.186531
$404$	17.2540	0.858420
$405$	−0.203778	−0.0101258
$406$	−2.65016	−0.131525
$407$	6.15592	0.305138
$408$	3.49451	0.173004
$409$	8.79584	0.434926	0.217463	−	0.976069i	$-0.430222\pi$
$409$	8.79584	0.434926	0.217463	+	0.976069i	$0.430222\pi$
$410$	0.0580941	0.00286906
$411$	18.1952	0.897505
$412$	−1.00000	−0.0492665
$413$	3.07711	0.151415
$414$	−1.20754	−0.0593472
$415$	−3.19396	−0.156786
$416$	1.00000	0.0490290
$417$	10.1316	0.496144
$418$	−6.55786	−0.320755
$419$	35.9763	1.75756	0.878780	−	0.477227i	$-0.158358\pi$
$419$	35.9763	1.75756	0.878780	+	0.477227i	$0.158358\pi$
$420$	−0.114509	−0.00558748
$421$	−3.02382	−0.147372	−0.0736859	−	0.997281i	$-0.523476\pi$
$421$	−3.02382	−0.147372	−0.0736859	+	0.997281i	$0.523476\pi$
$422$	2.88268	0.140327
$423$	−0.764630	−0.0371776
$424$	−12.3687	−0.600676
$425$	17.3275	0.840505
$426$	4.55986	0.220926
$427$	−6.74446	−0.326387
$428$	−16.7999	−0.812056
$429$	2.27691	0.109930
$430$	0.975726	0.0470537
$431$	30.4450	1.46648	0.733242	−	0.679968i	$-0.238006\pi$
$431$	30.4450	1.46648	0.733242	+	0.679968i	$0.238006\pi$
$432$	1.00000	0.0481125
$433$	−28.8658	−1.38720	−0.693602	−	0.720359i	$-0.743977\pi$
$433$	−28.8658	−1.38720	−0.693602	+	0.720359i	$0.743977\pi$
$434$	−2.10419	−0.101005
$435$	−0.961053	−0.0460790
$436$	0.840747	0.0402645
$437$	−3.47790	−0.166370
$438$	−8.20440	−0.392021
$439$	26.1161	1.24645	0.623226	−	0.782041i	$-0.285821\pi$
$439$	26.1161	1.24645	0.623226	+	0.782041i	$0.285821\pi$
$440$	−0.463985	−0.0221196
$441$	−6.68423	−0.318297
$442$	−3.49451	−0.166217
$443$	13.5145	0.642092	0.321046	−	0.947064i	$-0.395966\pi$
$443$	13.5145	0.642092	0.321046	+	0.947064i	$0.395966\pi$
$444$	−2.70363	−0.128309
$445$	−3.72662	−0.176659
$446$	27.7940	1.31608
$447$	3.54128	0.167497
$448$	0.561930	0.0265487
$449$	−23.1077	−1.09052	−0.545261	−	0.838266i	$-0.683569\pi$
$449$	−23.1077	−1.09052	−0.545261	+	0.838266i	$0.683569\pi$
$450$	4.95847	0.233745
$451$	−0.649111	−0.0305654
$452$	7.04978	0.331594
$453$	16.8036	0.789502
$454$	−1.35962	−0.0638102
$455$	0.114509	0.00536828
$456$	2.88016	0.134876
$457$	6.20279	0.290154	0.145077	−	0.989420i	$-0.453657\pi$
$457$	6.20279	0.290154	0.145077	+	0.989420i	$0.453657\pi$
$458$	−1.47067	−0.0687198
$459$	−3.49451	−0.163110
$460$	−0.246070	−0.0114731
$461$	−0.965703	−0.0449773	−0.0224886	−	0.999747i	$-0.507159\pi$
$461$	−0.965703	−0.0449773	−0.0224886	+	0.999747i	$0.507159\pi$
$462$	1.27946	0.0595260
$463$	3.01015	0.139893	0.0699467	−	0.997551i	$-0.477717\pi$
$463$	3.01015	0.139893	0.0699467	+	0.997551i	$0.477717\pi$
$464$	4.71617	0.218943
$465$	−0.763065	−0.0353863
$466$	−6.14500	−0.284661
$467$	−24.9167	−1.15301	−0.576503	−	0.817095i	$-0.695583\pi$
$467$	−24.9167	−1.15301	−0.576503	+	0.817095i	$0.695583\pi$
$468$	−1.00000	−0.0462250
$469$	−0.0991170	−0.00457680
$470$	−0.155815	−0.00718721
$471$	−1.71818	−0.0791697
$472$	−5.47596	−0.252051
$473$	−10.9022	−0.501284
$474$	7.70730	0.354008
$475$	14.2812	0.655266
$476$	−1.96367	−0.0900048
$477$	12.3687	0.566323
$478$	−19.9945	−0.914526
$479$	−16.8721	−0.770908	−0.385454	−	0.922727i	$-0.625955\pi$
$479$	−16.8721	−0.770908	−0.385454	+	0.922727i	$0.625955\pi$
$480$	0.203778	0.00930117
$481$	2.70363	0.123275
$482$	3.45147	0.157210
$483$	0.678551	0.0308751
$484$	−5.81569	−0.264350
$485$	−1.46567	−0.0665525
$486$	−1.00000	−0.0453609
$487$	4.30773	0.195202	0.0976010	−	0.995226i	$-0.468883\pi$
$487$	4.30773	0.195202	0.0976010	+	0.995226i	$0.468883\pi$
$488$	12.0023	0.543319
$489$	6.36940	0.288034
$490$	−1.36210	−0.0615336
$491$	−12.4639	−0.562486	−0.281243	−	0.959637i	$-0.590747\pi$
$491$	−12.4639	−0.562486	−0.281243	+	0.959637i	$0.590747\pi$
$492$	0.285084	0.0128526
$493$	−16.4807	−0.742254
$494$	−2.88016	−0.129585
$495$	0.463985	0.0208546
$496$	3.74458	0.168137
$497$	−2.56232	−0.114936
$498$	−15.6737	−0.702355
$499$	38.3085	1.71492	0.857461	−	0.514548i	$-0.172040\pi$
$499$	38.3085	1.71492	0.857461	+	0.514548i	$0.172040\pi$
$500$	2.02932	0.0907541
$501$	13.2366	0.591370
$502$	−10.7546	−0.480000
$503$	34.3758	1.53274	0.766370	−	0.642399i	$-0.222061\pi$
$503$	34.3758	1.53274	0.766370	+	0.642399i	$0.222061\pi$
$504$	−0.561930	−0.0250304
$505$	−3.51600	−0.156460
$506$	2.74945	0.122228
$507$	1.00000	0.0444116
$508$	15.5433	0.689623
$509$	32.3171	1.43243	0.716215	−	0.697880i	$-0.245873\pi$
$509$	32.3171	1.43243	0.716215	+	0.697880i	$0.245873\pi$
$510$	−0.712107	−0.0315326
$511$	4.61030	0.203948
$512$	−1.00000	−0.0441942
$513$	−2.88016	−0.127162
$514$	12.4561	0.549414
$515$	0.203778	0.00897955
$516$	4.78817	0.210787
$517$	1.74099	0.0765687
$518$	1.51925	0.0667521
$519$	−0.656119	−0.0288004
$520$	−0.203778	−0.00893628
$521$	−1.35405	−0.0593220	−0.0296610	−	0.999560i	$-0.509443\pi$
$521$	−1.35405	−0.0593220	−0.0296610	+	0.999560i	$0.509443\pi$
$522$	−4.71617	−0.206421
$523$	−14.3991	−0.629631	−0.314815	−	0.949153i	$-0.601943\pi$
$523$	−14.3991	−0.629631	−0.314815	+	0.949153i	$0.601943\pi$
$524$	−7.48808	−0.327118
$525$	−2.78632	−0.121605
$526$	6.73210	0.293533
$527$	−13.0855	−0.570013
$528$	−2.27691	−0.0990897
$529$	−21.5419	−0.936602
$530$	2.52047	0.109482
$531$	5.47596	0.237636
$532$	−1.61845	−0.0701687
$533$	−0.285084	−0.0123484
$534$	−18.2876	−0.791382
$535$	3.42347	0.148009
$536$	0.176387	0.00761874
$537$	5.96982	0.257617
$538$	−27.2803	−1.17614
$539$	15.2194	0.655545
$540$	−0.203778	−0.00876923
$541$	−10.4889	−0.450954	−0.225477	−	0.974248i	$-0.572394\pi$
$541$	−10.4889	−0.450954	−0.225477	+	0.974248i	$0.572394\pi$
$542$	−11.5759	−0.497226
$543$	4.07297	0.174788
$544$	3.49451	0.149826
$545$	−0.171326	−0.00733881
$546$	0.561930	0.0240484
$547$	−11.0058	−0.470573	−0.235287	−	0.971926i	$-0.575603\pi$
$547$	−11.0058	−0.470573	−0.235287	+	0.971926i	$0.575603\pi$
$548$	18.1952	0.777262
$549$	−12.0023	−0.512246
$550$	−11.2900	−0.481407
$551$	−13.5833	−0.578669
$552$	−1.20754	−0.0513961
$553$	−4.33096	−0.184171
$554$	4.16517	0.176961
$555$	0.550942	0.0233862
$556$	10.1316	0.429674
$557$	−24.1847	−1.02474	−0.512369	−	0.858765i	$-0.671232\pi$
$557$	−24.1847	−1.02474	−0.512369	+	0.858765i	$0.671232\pi$
$558$	−3.74458	−0.158521
$559$	−4.78817	−0.202518
$560$	−0.114509	−0.00483890
$561$	7.95668	0.335931
$562$	−18.5897	−0.784158
$563$	−9.64066	−0.406305	−0.203153	−	0.979147i	$-0.565119\pi$
$563$	−9.64066	−0.406305	−0.203153	+	0.979147i	$0.565119\pi$
$564$	−0.764630	−0.0321967
$565$	−1.43659	−0.0604380
$566$	−20.3557	−0.855612
$567$	0.561930	0.0235989
$568$	4.55986	0.191327
$569$	25.1470	1.05422	0.527110	−	0.849797i	$-0.323276\pi$
$569$	25.1470	1.05422	0.527110	+	0.849797i	$0.323276\pi$
$570$	−0.586915	−0.0245832
$571$	3.33887	0.139728	0.0698638	−	0.997557i	$-0.477744\pi$
$571$	3.33887	0.139728	0.0698638	+	0.997557i	$0.477744\pi$
$572$	2.27691	0.0952023
$573$	−15.8400	−0.661727
$574$	−0.160198	−0.00668652
$575$	−5.98754	−0.249697
$576$	1.00000	0.0416667
$577$	−5.25162	−0.218628	−0.109314	−	0.994007i	$-0.534865\pi$
$577$	−5.25162	−0.218628	−0.109314	+	0.994007i	$0.534865\pi$
$578$	4.78837	0.199170
$579$	11.5319	0.479251
$580$	−0.961053	−0.0399056
$581$	8.80753	0.365398
$582$	−7.19245	−0.298137
$583$	−28.1623	−1.16637
$584$	−8.20440	−0.339500
$585$	0.203778	0.00842520
$586$	8.38036	0.346190
$587$	−16.0008	−0.660426	−0.330213	−	0.943907i	$-0.607121\pi$
$587$	−16.0008	−0.660426	−0.330213	+	0.943907i	$0.607121\pi$
$588$	−6.68423	−0.275653
$589$	−10.7850	−0.444388
$590$	1.11588	0.0459402
$591$	−15.8945	−0.653811
$592$	−2.70363	−0.111119
$593$	30.8396	1.26643	0.633216	−	0.773975i	$-0.281735\pi$
$593$	30.8396	1.26643	0.633216	+	0.773975i	$0.281735\pi$
$594$	2.27691	0.0934226
$595$	0.400154	0.0164047
$596$	3.54128	0.145057
$597$	−12.2060	−0.499557
$598$	1.20754	0.0493798
$599$	3.66545	0.149766	0.0748831	−	0.997192i	$-0.476142\pi$
$599$	3.66545	0.149766	0.0748831	+	0.997192i	$0.476142\pi$
$600$	4.95847	0.202429
$601$	45.8768	1.87136	0.935678	−	0.352856i	$-0.114789\pi$
$601$	45.8768	1.87136	0.935678	+	0.352856i	$0.114789\pi$
$602$	−2.69062	−0.109661
$603$	−0.176387	−0.00718302
$604$	16.8036	0.683729
$605$	1.18511	0.0481817
$606$	−17.2540	−0.700897
$607$	−20.3044	−0.824132	−0.412066	−	0.911154i	$-0.635193\pi$
$607$	−20.3044	−0.824132	−0.412066	+	0.911154i	$0.635193\pi$
$608$	2.88016	0.116806
$609$	2.65016	0.107390
$610$	−2.44581	−0.0990280
$611$	0.764630	0.0309336
$612$	−3.49451	−0.141257
$613$	31.5308	1.27352	0.636758	−	0.771064i	$-0.280275\pi$
$613$	31.5308	1.27352	0.636758	+	0.771064i	$0.280275\pi$
$614$	−19.1620	−0.773314
$615$	−0.0580941	−0.00234258
$616$	1.27946	0.0515510
$617$	−31.4965	−1.26800	−0.634001	−	0.773332i	$-0.718589\pi$
$617$	−31.4965	−1.26800	−0.634001	+	0.773332i	$0.718589\pi$
$618$	1.00000	0.0402259
$619$	−37.7519	−1.51738	−0.758689	−	0.651453i	$-0.774160\pi$
$619$	−37.7519	−1.51738	−0.758689	+	0.651453i	$0.774160\pi$
$620$	−0.763065	−0.0306454
$621$	1.20754	0.0484567
$622$	−3.38483	−0.135719
$623$	10.2764	0.411714
$624$	−1.00000	−0.0400320
$625$	24.3788	0.975154
$626$	−0.769485	−0.0307548
$627$	6.55786	0.261896
$628$	−1.71818	−0.0685630
$629$	9.44788	0.376712
$630$	0.114509	0.00456216
$631$	10.2761	0.409083	0.204542	−	0.978858i	$-0.434430\pi$
$631$	10.2761	0.409083	0.204542	+	0.978858i	$0.434430\pi$
$632$	7.70730	0.306580
$633$	−2.88268	−0.114576
$634$	27.0929	1.07600
$635$	−3.16739	−0.125694
$636$	12.3687	0.490450
$637$	6.68423	0.264839
$638$	10.7383	0.425132
$639$	−4.55986	−0.180385
$640$	0.203778	0.00805505
$641$	39.6268	1.56517	0.782583	−	0.622547i	$-0.213902\pi$
$641$	39.6268	1.56517	0.782583	+	0.622547i	$0.213902\pi$
$642$	16.7999	0.663041
$643$	−5.98951	−0.236203	−0.118102	−	0.993002i	$-0.537681\pi$
$643$	−5.98951	−0.236203	−0.118102	+	0.993002i	$0.537681\pi$
$644$	0.678551	0.0267387
$645$	−0.975726	−0.0384192
$646$	−10.0648	−0.395993
$647$	−28.6105	−1.12479	−0.562397	−	0.826868i	$-0.690121\pi$
$647$	−28.6105	−1.12479	−0.562397	+	0.826868i	$0.690121\pi$
$648$	−1.00000	−0.0392837
$649$	−12.4683	−0.489422
$650$	−4.95847	−0.194487
$651$	2.10419	0.0824699
$652$	6.36940	0.249445
$653$	34.7916	1.36150	0.680750	−	0.732516i	$-0.261654\pi$
$653$	34.7916	1.36150	0.680750	+	0.732516i	$0.261654\pi$
$654$	−0.840747	−0.0328758
$655$	1.52591	0.0596222
$656$	0.285084	0.0111307
$657$	8.20440	0.320084
$658$	0.429669	0.0167502
$659$	−40.7102	−1.58584	−0.792922	−	0.609323i	$-0.791441\pi$
$659$	−40.7102	−1.58584	−0.792922	+	0.609323i	$0.791441\pi$
$660$	0.463985	0.0180606
$661$	38.2859	1.48915	0.744575	−	0.667539i	$-0.232652\pi$
$661$	38.2859	1.48915	0.744575	+	0.667539i	$0.232652\pi$
$662$	10.1247	0.393510
$663$	3.49451	0.135716
$664$	−15.6737	−0.608258
$665$	0.329805	0.0127893
$666$	2.70363	0.104764
$667$	5.69494	0.220509
$668$	13.2366	0.512141
$669$	−27.7940	−1.07458
$670$	−0.0359438	−0.00138863
$671$	27.3281	1.05499
$672$	−0.561930	−0.0216769
$673$	−9.81644	−0.378396	−0.189198	−	0.981939i	$-0.560589\pi$
$673$	−9.81644	−0.378396	−0.189198	+	0.981939i	$0.560589\pi$
$674$	17.9559	0.691634
$675$	−4.95847	−0.190852
$676$	1.00000	0.0384615
$677$	−32.9477	−1.26628	−0.633142	−	0.774036i	$-0.718235\pi$
$677$	−32.9477	−1.26628	−0.633142	+	0.774036i	$0.718235\pi$
$678$	−7.04978	−0.270745
$679$	4.04165	0.155104
$680$	−0.712107	−0.0273080
$681$	1.35962	0.0521008
$682$	8.52607	0.326480
$683$	13.9623	0.534254	0.267127	−	0.963661i	$-0.413926\pi$
$683$	13.9623	0.534254	0.267127	+	0.963661i	$0.413926\pi$
$684$	−2.88016	−0.110126
$685$	−3.70780	−0.141668
$686$	7.68959	0.293590
$687$	1.47067	0.0561095
$688$	4.78817	0.182547
$689$	−12.3687	−0.471209
$690$	0.246070	0.00936772
$691$	−15.1692	−0.577062	−0.288531	−	0.957470i	$-0.593167\pi$
$691$	−15.1692	−0.577062	−0.288531	+	0.957470i	$0.593167\pi$
$692$	−0.656119	−0.0249419
$693$	−1.27946	−0.0486028
$694$	−23.8329	−0.904684
$695$	−2.06459	−0.0783145
$696$	−4.71617	−0.178766
$697$	−0.996231	−0.0377349
$698$	−19.3454	−0.732234
$699$	6.14500	0.232425
$700$	−2.78632	−0.105313
$701$	18.4472	0.696742	0.348371	−	0.937357i	$-0.386735\pi$
$701$	18.4472	0.696742	0.348371	+	0.937357i	$0.386735\pi$
$702$	1.00000	0.0377426
$703$	7.78689	0.293688
$704$	−2.27691	−0.0858142
$705$	0.155815	0.00586834
$706$	−9.56854	−0.360117
$707$	9.69556	0.364639
$708$	5.47596	0.205799
$709$	−6.08373	−0.228479	−0.114240	−	0.993453i	$-0.536443\pi$
$709$	−6.08373	−0.228479	−0.114240	+	0.993453i	$0.536443\pi$
$710$	−0.929201	−0.0348723
$711$	−7.70730	−0.289046
$712$	−18.2876	−0.685357
$713$	4.52172	0.169340
$714$	1.96367	0.0734886
$715$	−0.463985	−0.0173520
$716$	5.96982	0.223102
$717$	19.9945	0.746707
$718$	19.8864	0.742155
$719$	14.2389	0.531021	0.265510	−	0.964108i	$-0.414460\pi$
$719$	14.2389	0.531021	0.265510	+	0.964108i	$0.414460\pi$
$720$	−0.203778	−0.00759438
$721$	−0.561930	−0.0209274
$722$	10.7047	0.398387
$723$	−3.45147	−0.128361
$724$	4.07297	0.151371
$725$	−23.3850	−0.868497
$726$	5.81569	0.215841
$727$	12.2539	0.454472	0.227236	−	0.973840i	$-0.427031\pi$
$727$	12.2539	0.454472	0.227236	+	0.973840i	$0.427031\pi$
$728$	0.561930	0.0208265
$729$	1.00000	0.0370370
$730$	1.67188	0.0618790
$731$	−16.7323	−0.618867
$732$	−12.0023	−0.443618
$733$	30.2814	1.11847	0.559234	−	0.829010i	$-0.311095\pi$
$733$	30.2814	1.11847	0.559234	+	0.829010i	$0.311095\pi$
$734$	9.37289	0.345960
$735$	1.36210	0.0502419
$736$	−1.20754	−0.0445104
$737$	0.401616	0.0147937
$738$	−0.285084	−0.0104941
$739$	31.8582	1.17192	0.585962	−	0.810338i	$-0.300717\pi$
$739$	31.8582	1.17192	0.585962	+	0.810338i	$0.300717\pi$
$740$	0.550942	0.0202530
$741$	2.88016	0.105805
$742$	−6.95034	−0.255155
$743$	−22.5123	−0.825894	−0.412947	−	0.910755i	$-0.635501\pi$
$743$	−22.5123	−0.825894	−0.412947	+	0.910755i	$0.635501\pi$
$744$	−3.74458	−0.137283
$745$	−0.721637	−0.0264388
$746$	−7.76688	−0.284366
$747$	15.6737	0.573471
$748$	7.95668	0.290925
$749$	−9.44040	−0.344945
$750$	−2.02932	−0.0741004
$751$	−26.9271	−0.982585	−0.491293	−	0.870995i	$-0.663475\pi$
$751$	−26.9271	−0.982585	−0.491293	+	0.870995i	$0.663475\pi$
$752$	−0.764630	−0.0278832
$753$	10.7546	0.391918
$754$	4.71617	0.171753
$755$	−3.42421	−0.124620
$756$	0.561930	0.0204372
$757$	13.8822	0.504558	0.252279	−	0.967655i	$-0.418820\pi$
$757$	13.8822	0.504558	0.252279	+	0.967655i	$0.418820\pi$
$758$	16.5270	0.600289
$759$	−2.74945	−0.0997986
$760$	−0.586915	−0.0212896
$761$	2.54723	0.0923370	0.0461685	−	0.998934i	$-0.485299\pi$
$761$	2.54723	0.0923370	0.0461685	+	0.998934i	$0.485299\pi$
$762$	−15.5433	−0.563075
$763$	0.472441	0.0171035
$764$	−15.8400	−0.573072
$765$	0.712107	0.0257463
$766$	10.6099	0.383350
$767$	−5.47596	−0.197725
$768$	1.00000	0.0360844
$769$	−31.8616	−1.14896	−0.574479	−	0.818519i	$-0.694795\pi$
$769$	−31.8616	−1.14896	−0.574479	+	0.818519i	$0.694795\pi$
$770$	−0.260727	−0.00939595
$771$	−12.4561	−0.448595
$772$	11.5319	0.415044
$773$	−29.5880	−1.06421	−0.532104	−	0.846679i	$-0.678598\pi$
$773$	−29.5880	−1.06421	−0.532104	+	0.846679i	$0.678598\pi$
$774$	−4.78817	−0.172107
$775$	−18.5674	−0.666961
$776$	−7.19245	−0.258194
$777$	−1.51925	−0.0545029
$778$	18.7657	0.672781
$779$	−0.821089	−0.0294186
$780$	0.203778	0.00729644
$781$	10.3824	0.371510
$782$	4.21975	0.150898
$783$	4.71617	0.168542
$784$	−6.68423	−0.238723
$785$	0.350129	0.0124966
$786$	7.48808	0.267091
$787$	3.17761	0.113270	0.0566349	−	0.998395i	$-0.481963\pi$
$787$	3.17761	0.113270	0.0566349	+	0.998395i	$0.481963\pi$
$788$	−15.8945	−0.566217
$789$	−6.73210	−0.239669
$790$	−1.57058	−0.0558788
$791$	3.96149	0.140854
$792$	2.27691	0.0809064
$793$	12.0023	0.426214
$794$	−13.7486	−0.487918
$795$	−2.52047	−0.0893919
$796$	−12.2060	−0.432629
$797$	−21.5903	−0.764769	−0.382384	−	0.924003i	$-0.624897\pi$
$797$	−21.5903	−0.764769	−0.382384	+	0.924003i	$0.624897\pi$
$798$	1.61845	0.0572925
$799$	2.67201	0.0945289
$800$	4.95847	0.175309
$801$	18.2876	0.646161
$802$	3.17162	0.111994
$803$	−18.6806	−0.659226
$804$	−0.176387	−0.00622068
$805$	−0.138274	−0.00487352
$806$	3.74458	0.131897
$807$	27.2803	0.960313
$808$	−17.2540	−0.606995
$809$	43.3570	1.52435	0.762175	−	0.647371i	$-0.224131\pi$
$809$	43.3570	1.52435	0.762175	+	0.647371i	$0.224131\pi$
$810$	0.203778	0.00716005
$811$	27.7756	0.975332	0.487666	−	0.873030i	$-0.337848\pi$
$811$	27.7756	0.975332	0.487666	+	0.873030i	$0.337848\pi$
$812$	2.65016	0.0930023
$813$	11.5759	0.405983
$814$	−6.15592	−0.215765
$815$	−1.29795	−0.0454651
$816$	−3.49451	−0.122332
$817$	−13.7907	−0.482475
$818$	−8.79584	−0.307539
$819$	−0.561930	−0.0196354
$820$	−0.0580941	−0.00202873
$821$	−26.0536	−0.909278	−0.454639	−	0.890676i	$-0.650232\pi$
$821$	−26.0536	−0.909278	−0.454639	+	0.890676i	$0.650232\pi$
$822$	−18.1952	−0.634632
$823$	38.5222	1.34280	0.671400	−	0.741096i	$-0.265693\pi$
$823$	38.5222	1.34280	0.671400	+	0.741096i	$0.265693\pi$
$824$	1.00000	0.0348367
$825$	11.2900	0.393067
$826$	−3.07711	−0.107066
$827$	35.8312	1.24597	0.622986	−	0.782233i	$-0.285919\pi$
$827$	35.8312	1.24597	0.622986	+	0.782233i	$0.285919\pi$
$828$	1.20754	0.0419648
$829$	−42.6206	−1.48027	−0.740137	−	0.672456i	$-0.765239\pi$
$829$	−42.6206	−1.48027	−0.740137	+	0.672456i	$0.765239\pi$
$830$	3.19396	0.110864
$831$	−4.16517	−0.144488
$832$	−1.00000	−0.0346688
$833$	23.3581	0.809312
$834$	−10.1316	−0.350827
$835$	−2.69734	−0.0933454
$836$	6.55786	0.226808
$837$	3.74458	0.129432
$838$	−35.9763	−1.24278
$839$	37.6568	1.30006	0.650029	−	0.759909i	$-0.274757\pi$
$839$	37.6568	1.30006	0.650029	+	0.759909i	$0.274757\pi$
$840$	0.114509	0.00395095
$841$	−6.75777	−0.233027
$842$	3.02382	0.104208
$843$	18.5897	0.640262
$844$	−2.88268	−0.0992259
$845$	−0.203778	−0.00701019
$846$	0.764630	0.0262885
$847$	−3.26801	−0.112290
$848$	12.3687	0.424742
$849$	20.3557	0.698605
$850$	−17.3275	−0.594327
$851$	−3.26473	−0.111914
$852$	−4.55986	−0.156218
$853$	−45.6410	−1.56272	−0.781359	−	0.624082i	$-0.785473\pi$
$853$	−45.6410	−1.56272	−0.781359	+	0.624082i	$0.785473\pi$
$854$	6.74446	0.230791
$855$	0.586915	0.0200721
$856$	16.7999	0.574210
$857$	18.8297	0.643210	0.321605	−	0.946874i	$-0.395778\pi$
$857$	18.8297	0.643210	0.321605	+	0.946874i	$0.395778\pi$
$858$	−2.27691	−0.0777323
$859$	−17.3002	−0.590276	−0.295138	−	0.955455i	$-0.595366\pi$
$859$	−17.3002	−0.590276	−0.295138	+	0.955455i	$0.595366\pi$
$860$	−0.975726	−0.0332720
$861$	0.160198	0.00545952
$862$	−30.4450	−1.03696
$863$	49.4833	1.68443	0.842216	−	0.539140i	$-0.181251\pi$
$863$	49.4833	1.68443	0.842216	+	0.539140i	$0.181251\pi$
$864$	−1.00000	−0.0340207
$865$	0.133703	0.00454604
$866$	28.8658	0.980901
$867$	−4.78837	−0.162622
$868$	2.10419	0.0714210
$869$	17.5488	0.595302
$870$	0.961053	0.0325828
$871$	0.176387	0.00597663
$872$	−0.840747	−0.0284713
$873$	7.19245	0.243427
$874$	3.47790	0.117642
$875$	1.14034	0.0385505
$876$	8.20440	0.277201
$877$	7.53387	0.254401	0.127200	−	0.991877i	$-0.459401\pi$
$877$	7.53387	0.254401	0.127200	+	0.991877i	$0.459401\pi$
$878$	−26.1161	−0.881375
$879$	−8.38036	−0.282663
$880$	0.463985	0.0156409
$881$	1.91588	0.0645477	0.0322739	−	0.999479i	$-0.489725\pi$
$881$	1.91588	0.0645477	0.0322739	+	0.999479i	$0.489725\pi$
$882$	6.68423	0.225070
$883$	33.6433	1.13219	0.566093	−	0.824341i	$-0.308454\pi$
$883$	33.6433	1.13219	0.566093	+	0.824341i	$0.308454\pi$
$884$	3.49451	0.117533
$885$	−1.11588	−0.0375100
$886$	−13.5145	−0.454028
$887$	56.7337	1.90493	0.952466	−	0.304646i	$-0.0985380\pi$
$887$	56.7337	1.90493	0.952466	+	0.304646i	$0.0985380\pi$
$888$	2.70363	0.0907280
$889$	8.73425	0.292937
$890$	3.72662	0.124917
$891$	−2.27691	−0.0762793
$892$	−27.7940	−0.930613
$893$	2.20226	0.0736957
$894$	−3.54128	−0.118438
$895$	−1.21652	−0.0406638
$896$	−0.561930	−0.0187728
$897$	−1.20754	−0.0403184
$898$	23.1077	0.771115
$899$	17.6601	0.588997
$900$	−4.95847	−0.165282
$901$	−43.2225	−1.43995
$902$	0.649111	0.0216130
$903$	2.69062	0.0895381
$904$	−7.04978	−0.234472
$905$	−0.829985	−0.0275896
$906$	−16.8036	−0.558262
$907$	−12.4463	−0.413273	−0.206637	−	0.978418i	$-0.566252\pi$
$907$	−12.4463	−0.413273	−0.206637	+	0.978418i	$0.566252\pi$
$908$	1.35962	0.0451206
$909$	17.2540	0.572280
$910$	−0.114509	−0.00379595
$911$	26.9579	0.893154	0.446577	−	0.894745i	$-0.352643\pi$
$911$	26.9579	0.893154	0.446577	+	0.894745i	$0.352643\pi$
$912$	−2.88016	−0.0953716
$913$	−35.6876	−1.18109
$914$	−6.20279	−0.205170
$915$	2.44581	0.0808560
$916$	1.47067	0.0485922
$917$	−4.20778	−0.138953
$918$	3.49451	0.115336
$919$	−31.5669	−1.04129	−0.520647	−	0.853772i	$-0.674309\pi$
$919$	−31.5669	−1.04129	−0.520647	+	0.853772i	$0.674309\pi$
$920$	0.246070	0.00811268
$921$	19.1620	0.631408
$922$	0.965703	0.0318037
$923$	4.55986	0.150090
$924$	−1.27946	−0.0420912
$925$	13.4059	0.440783
$926$	−3.01015	−0.0989195
$927$	−1.00000	−0.0328443
$928$	−4.71617	−0.154816
$929$	22.5751	0.740664	0.370332	−	0.928900i	$-0.379244\pi$
$929$	22.5751	0.740664	0.370332	+	0.928900i	$0.379244\pi$
$930$	0.763065	0.0250219
$931$	19.2517	0.630948
$932$	6.14500	0.201286
$933$	3.38483	0.110814
$934$	24.9167	0.815298
$935$	−1.62140	−0.0530255
$936$	1.00000	0.0326860
$937$	24.6874	0.806503	0.403252	−	0.915089i	$-0.367880\pi$
$937$	24.6874	0.806503	0.403252	+	0.915089i	$0.367880\pi$
$938$	0.0991170	0.00323629
$939$	0.769485	0.0251112
$940$	0.155815	0.00508213
$941$	−44.3476	−1.44569	−0.722845	−	0.691010i	$-0.757166\pi$
$941$	−44.3476	−1.44569	−0.722845	+	0.691010i	$0.757166\pi$
$942$	1.71818	0.0559814
$943$	0.344250	0.0112103
$944$	5.47596	0.178227
$945$	−0.114509	−0.00372499
$946$	10.9022	0.354462
$947$	45.9687	1.49378	0.746891	−	0.664946i	$-0.231546\pi$
$947$	45.9687	1.49378	0.746891	+	0.664946i	$0.231546\pi$
$948$	−7.70730	−0.250321
$949$	−8.20440	−0.266326
$950$	−14.2812	−0.463343
$951$	−27.0929	−0.878549
$952$	1.96367	0.0636430
$953$	−13.1912	−0.427306	−0.213653	−	0.976910i	$-0.568536\pi$
$953$	−13.1912	−0.427306	−0.213653	+	0.976910i	$0.568536\pi$
$954$	−12.3687	−0.400451
$955$	3.22786	0.104451
$956$	19.9945	0.646667
$957$	−10.7383	−0.347119
$958$	16.8721	0.545114
$959$	10.2245	0.330165
$960$	−0.203778	−0.00657692
$961$	−16.9781	−0.547681
$962$	−2.70363	−0.0871686
$963$	−16.7999	−0.541371
$964$	−3.45147	−0.111164
$965$	−2.34996	−0.0756479
$966$	−0.678551	−0.0218320
$967$	10.7969	0.347204	0.173602	−	0.984816i	$-0.444459\pi$
$967$	10.7969	0.347204	0.173602	+	0.984816i	$0.444459\pi$
$968$	5.81569	0.186923
$969$	10.0648	0.323327
$970$	1.46567	0.0470597
$971$	38.5922	1.23848	0.619241	−	0.785201i	$-0.287440\pi$
$971$	38.5922	1.23848	0.619241	+	0.785201i	$0.287440\pi$
$972$	1.00000	0.0320750
$973$	5.69323	0.182516
$974$	−4.30773	−0.138029
$975$	4.95847	0.158798
$976$	−12.0023	−0.384184
$977$	5.24043	0.167656	0.0838282	−	0.996480i	$-0.473285\pi$
$977$	5.24043	0.167656	0.0838282	+	0.996480i	$0.473285\pi$
$978$	−6.36940	−0.203671
$979$	−41.6392	−1.33079
$980$	1.36210	0.0435108
$981$	0.840747	0.0268430
$982$	12.4639	0.397738
$983$	−24.9829	−0.796830	−0.398415	−	0.917205i	$-0.630440\pi$
$983$	−24.9829	−0.796830	−0.398415	+	0.917205i	$0.630440\pi$
$984$	−0.285084	−0.00908816
$985$	3.23895	0.103202
$986$	16.4807	0.524853
$987$	−0.429669	−0.0136765
$988$	2.88016	0.0916301
$989$	5.78189	0.183853
$990$	−0.463985	−0.0147464
$991$	−8.68342	−0.275838	−0.137919	−	0.990444i	$-0.544041\pi$
$991$	−8.68342	−0.275838	−0.137919	+	0.990444i	$0.544041\pi$
$992$	−3.74458	−0.118891
$993$	−10.1247	−0.321299
$994$	2.56232	0.0812719
$995$	2.48731	0.0788531
$996$	15.6737	0.496640
$997$	−0.161129	−0.00510301	−0.00255150	−	0.999997i	$-0.500812\pi$
$997$	−0.161129	−0.00510301	−0.00255150	+	0.999997i	$0.500812\pi$
$998$	−38.3085	−1.21263
$999$	−2.70363	−0.0855391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.t.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.t.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.203778 q^{5} -1.00000 q^{6} +0.561930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.203778 q^{5} -1.00000 q^{6} +0.561930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.203778 q^{10} -2.27691 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.561930 q^{14} -0.203778 q^{15} +1.00000 q^{16} -3.49451 q^{17} -1.00000 q^{18} -2.88016 q^{19} -0.203778 q^{20} +0.561930 q^{21} +2.27691 q^{22} +1.20754 q^{23} -1.00000 q^{24} -4.95847 q^{25} +1.00000 q^{26} +1.00000 q^{27} +0.561930 q^{28} +4.71617 q^{29} +0.203778 q^{30} +3.74458 q^{31} -1.00000 q^{32} -2.27691 q^{33} +3.49451 q^{34} -0.114509 q^{35} +1.00000 q^{36} -2.70363 q^{37} +2.88016 q^{38} -1.00000 q^{39} +0.203778 q^{40} +0.285084 q^{41} -0.561930 q^{42} +4.78817 q^{43} -2.27691 q^{44} -0.203778 q^{45} -1.20754 q^{46} -0.764630 q^{47} +1.00000 q^{48} -6.68423 q^{49} +4.95847 q^{50} -3.49451 q^{51} -1.00000 q^{52} +12.3687 q^{53} -1.00000 q^{54} +0.463985 q^{55} -0.561930 q^{56} -2.88016 q^{57} -4.71617 q^{58} +5.47596 q^{59} -0.203778 q^{60} -12.0023 q^{61} -3.74458 q^{62} +0.561930 q^{63} +1.00000 q^{64} +0.203778 q^{65} +2.27691 q^{66} -0.176387 q^{67} -3.49451 q^{68} +1.20754 q^{69} +0.114509 q^{70} -4.55986 q^{71} -1.00000 q^{72} +8.20440 q^{73} +2.70363 q^{74} -4.95847 q^{75} -2.88016 q^{76} -1.27946 q^{77} +1.00000 q^{78} -7.70730 q^{79} -0.203778 q^{80} +1.00000 q^{81} -0.285084 q^{82} +15.6737 q^{83} +0.561930 q^{84} +0.712107 q^{85} -4.78817 q^{86} +4.71617 q^{87} +2.27691 q^{88} +18.2876 q^{89} +0.203778 q^{90} -0.561930 q^{91} +1.20754 q^{92} +3.74458 q^{93} +0.764630 q^{94} +0.586915 q^{95} -1.00000 q^{96} +7.19245 q^{97} +6.68423 q^{98} -2.27691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 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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