LMFDB - Embedded newform 8034.2.a.bc.1.10

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 $ x^15 - x^14 - 48x^13 + 44x^12 + 872x^11 - 707x^10 - 7580x^9 + 5112x^8 + 33191x^7 - 16428x^6 - 71361x^5 + 21747x^4 + 65434x^3 - 11840x^2 - 17600*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.34829$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.34829 q^{5} -1.00000 q^{6} -1.25683 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.34829 q^{5} -1.00000 q^{6} -1.25683 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.34829 q^{10} +6.18039 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.25683 q^{14} -1.34829 q^{15} +1.00000 q^{16} +0.669960 q^{17} +1.00000 q^{18} +5.57232 q^{19} +1.34829 q^{20} +1.25683 q^{21} +6.18039 q^{22} -6.51348 q^{23} -1.00000 q^{24} -3.18210 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.25683 q^{28} +7.00067 q^{29} -1.34829 q^{30} +9.94843 q^{31} +1.00000 q^{32} -6.18039 q^{33} +0.669960 q^{34} -1.69458 q^{35} +1.00000 q^{36} -6.41537 q^{37} +5.57232 q^{38} +1.00000 q^{39} +1.34829 q^{40} +3.07063 q^{41} +1.25683 q^{42} +5.34321 q^{43} +6.18039 q^{44} +1.34829 q^{45} -6.51348 q^{46} +6.23707 q^{47} -1.00000 q^{48} -5.42038 q^{49} -3.18210 q^{50} -0.669960 q^{51} -1.00000 q^{52} -8.03980 q^{53} -1.00000 q^{54} +8.33299 q^{55} -1.25683 q^{56} -5.57232 q^{57} +7.00067 q^{58} -3.12465 q^{59} -1.34829 q^{60} +1.33683 q^{61} +9.94843 q^{62} -1.25683 q^{63} +1.00000 q^{64} -1.34829 q^{65} -6.18039 q^{66} +8.66119 q^{67} +0.669960 q^{68} +6.51348 q^{69} -1.69458 q^{70} +6.62891 q^{71} +1.00000 q^{72} -2.20900 q^{73} -6.41537 q^{74} +3.18210 q^{75} +5.57232 q^{76} -7.76770 q^{77} +1.00000 q^{78} -12.7247 q^{79} +1.34829 q^{80} +1.00000 q^{81} +3.07063 q^{82} -0.863190 q^{83} +1.25683 q^{84} +0.903303 q^{85} +5.34321 q^{86} -7.00067 q^{87} +6.18039 q^{88} +4.65035 q^{89} +1.34829 q^{90} +1.25683 q^{91} -6.51348 q^{92} -9.94843 q^{93} +6.23707 q^{94} +7.51313 q^{95} -1.00000 q^{96} -11.6073 q^{97} -5.42038 q^{98} +6.18039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * 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
$5$	1.34829	0.602975	0.301488	−	0.953470i	$-0.402517\pi$
$5$	1.34829	0.602975	0.301488	+	0.953470i	$0.402517\pi$
$6$	−1.00000	−0.408248
$7$	−1.25683	−0.475037	−0.237518	−	0.971383i	$-0.576334\pi$
$7$	−1.25683	−0.475037	−0.237518	+	0.971383i	$0.576334\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.34829	0.426368
$11$	6.18039	1.86346	0.931729	−	0.363154i	$-0.118300\pi$
$11$	6.18039	1.86346	0.931729	+	0.363154i	$0.118300\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.25683	−0.335902
$15$	−1.34829	−0.348128
$16$	1.00000	0.250000
$17$	0.669960	0.162489	0.0812445	−	0.996694i	$-0.474111\pi$
$17$	0.669960	0.162489	0.0812445	+	0.996694i	$0.474111\pi$
$18$	1.00000	0.235702
$19$	5.57232	1.27838	0.639189	−	0.769050i	$-0.279270\pi$
$19$	5.57232	1.27838	0.639189	+	0.769050i	$0.279270\pi$
$20$	1.34829	0.301488
$21$	1.25683	0.274263
$22$	6.18039	1.31766
$23$	−6.51348	−1.35815	−0.679077	−	0.734067i	$-0.737620\pi$
$23$	−6.51348	−1.35815	−0.679077	+	0.734067i	$0.737620\pi$
$24$	−1.00000	−0.204124
$25$	−3.18210	−0.636421
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−1.25683	−0.237518
$29$	7.00067	1.29999	0.649996	−	0.759938i	$-0.274771\pi$
$29$	7.00067	1.29999	0.649996	+	0.759938i	$0.274771\pi$
$30$	−1.34829	−0.246164
$31$	9.94843	1.78679	0.893396	−	0.449270i	$-0.148316\pi$
$31$	9.94843	1.78679	0.893396	+	0.449270i	$0.148316\pi$
$32$	1.00000	0.176777
$33$	−6.18039	−1.07587
$34$	0.669960	0.114897
$35$	−1.69458	−0.286436
$36$	1.00000	0.166667
$37$	−6.41537	−1.05468	−0.527341	−	0.849654i	$-0.676811\pi$
$37$	−6.41537	−1.05468	−0.527341	+	0.849654i	$0.676811\pi$
$38$	5.57232	0.903949
$39$	1.00000	0.160128
$40$	1.34829	0.213184
$41$	3.07063	0.479552	0.239776	−	0.970828i	$-0.422926\pi$
$41$	3.07063	0.479552	0.239776	+	0.970828i	$0.422926\pi$
$42$	1.25683	0.193933
$43$	5.34321	0.814832	0.407416	−	0.913243i	$-0.366430\pi$
$43$	5.34321	0.814832	0.407416	+	0.913243i	$0.366430\pi$
$44$	6.18039	0.931729
$45$	1.34829	0.200992
$46$	−6.51348	−0.960360
$47$	6.23707	0.909770	0.454885	−	0.890550i	$-0.349680\pi$
$47$	6.23707	0.909770	0.454885	+	0.890550i	$0.349680\pi$
$48$	−1.00000	−0.144338
$49$	−5.42038	−0.774340
$50$	−3.18210	−0.450017
$51$	−0.669960	−0.0938131
$52$	−1.00000	−0.138675
$53$	−8.03980	−1.10435	−0.552176	−	0.833728i	$-0.686202\pi$
$53$	−8.03980	−1.10435	−0.552176	+	0.833728i	$0.686202\pi$
$54$	−1.00000	−0.136083
$55$	8.33299	1.12362
$56$	−1.25683	−0.167951
$57$	−5.57232	−0.738072
$58$	7.00067	0.919233
$59$	−3.12465	−0.406795	−0.203398	−	0.979096i	$-0.565198\pi$
$59$	−3.12465	−0.406795	−0.203398	+	0.979096i	$0.565198\pi$
$60$	−1.34829	−0.174064
$61$	1.33683	0.171163	0.0855815	−	0.996331i	$-0.472725\pi$
$61$	1.33683	0.171163	0.0855815	+	0.996331i	$0.472725\pi$
$62$	9.94843	1.26345
$63$	−1.25683	−0.158346
$64$	1.00000	0.125000
$65$	−1.34829	−0.167235
$66$	−6.18039	−0.760754
$67$	8.66119	1.05813	0.529067	−	0.848580i	$-0.322542\pi$
$67$	8.66119	1.05813	0.529067	+	0.848580i	$0.322542\pi$
$68$	0.669960	0.0812445
$69$	6.51348	0.784131
$70$	−1.69458	−0.202541
$71$	6.62891	0.786707	0.393353	−	0.919387i	$-0.371315\pi$
$71$	6.62891	0.786707	0.393353	+	0.919387i	$0.371315\pi$
$72$	1.00000	0.117851
$73$	−2.20900	−0.258544	−0.129272	−	0.991609i	$-0.541264\pi$
$73$	−2.20900	−0.258544	−0.129272	+	0.991609i	$0.541264\pi$
$74$	−6.41537	−0.745772
$75$	3.18210	0.367438
$76$	5.57232	0.639189
$77$	−7.76770	−0.885211
$78$	1.00000	0.113228
$79$	−12.7247	−1.43164	−0.715822	−	0.698283i	$-0.753948\pi$
$79$	−12.7247	−1.43164	−0.715822	+	0.698283i	$0.753948\pi$
$80$	1.34829	0.150744
$81$	1.00000	0.111111
$82$	3.07063	0.339094
$83$	−0.863190	−0.0947474	−0.0473737	−	0.998877i	$-0.515085\pi$
$83$	−0.863190	−0.0947474	−0.0473737	+	0.998877i	$0.515085\pi$
$84$	1.25683	0.137131
$85$	0.903303	0.0979769
$86$	5.34321	0.576173
$87$	−7.00067	−0.750551
$88$	6.18039	0.658832
$89$	4.65035	0.492936	0.246468	−	0.969151i	$-0.420730\pi$
$89$	4.65035	0.492936	0.246468	+	0.969151i	$0.420730\pi$
$90$	1.34829	0.142123
$91$	1.25683	0.131752
$92$	−6.51348	−0.679077
$93$	−9.94843	−1.03160
$94$	6.23707	0.643305
$95$	7.51313	0.770830
$96$	−1.00000	−0.102062
$97$	−11.6073	−1.17855	−0.589273	−	0.807934i	$-0.700586\pi$
$97$	−11.6073	−1.17855	−0.589273	+	0.807934i	$0.700586\pi$
$98$	−5.42038	−0.547541
$99$	6.18039	0.621153
$100$	−3.18210	−0.318210
$101$	7.53357	0.749618	0.374809	−	0.927102i	$-0.377708\pi$
$101$	7.53357	0.749618	0.374809	+	0.927102i	$0.377708\pi$
$102$	−0.669960	−0.0663359
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	1.69458	0.165374
$106$	−8.03980	−0.780895
$107$	10.7444	1.03870	0.519352	−	0.854560i	$-0.326173\pi$
$107$	10.7444	1.03870	0.519352	+	0.854560i	$0.326173\pi$
$108$	−1.00000	−0.0962250
$109$	0.0532230	0.00509784	0.00254892	−	0.999997i	$-0.499189\pi$
$109$	0.0532230	0.00509784	0.00254892	+	0.999997i	$0.499189\pi$
$110$	8.33299	0.794519
$111$	6.41537	0.608920
$112$	−1.25683	−0.118759
$113$	13.8205	1.30012	0.650060	−	0.759883i	$-0.274744\pi$
$113$	13.8205	1.30012	0.650060	+	0.759883i	$0.274744\pi$
$114$	−5.57232	−0.521895
$115$	−8.78209	−0.818934
$116$	7.00067	0.649996
$117$	−1.00000	−0.0924500
$118$	−3.12465	−0.287648
$119$	−0.842025	−0.0771883
$120$	−1.34829	−0.123082
$121$	27.1972	2.47248
$122$	1.33683	0.121031
$123$	−3.07063	−0.276869
$124$	9.94843	0.893396
$125$	−11.0319	−0.986721
$126$	−1.25683	−0.111967
$127$	−3.53406	−0.313597	−0.156799	−	0.987631i	$-0.550117\pi$
$127$	−3.53406	−0.313597	−0.156799	+	0.987631i	$0.550117\pi$
$128$	1.00000	0.0883883
$129$	−5.34321	−0.470443
$130$	−1.34829	−0.118253
$131$	1.91302	0.167142	0.0835708	−	0.996502i	$-0.473368\pi$
$131$	1.91302	0.167142	0.0835708	+	0.996502i	$0.473368\pi$
$132$	−6.18039	−0.537934
$133$	−7.00345	−0.607276
$134$	8.66119	0.748213
$135$	−1.34829	−0.116043
$136$	0.669960	0.0574486
$137$	−5.22718	−0.446588	−0.223294	−	0.974751i	$-0.571681\pi$
$137$	−5.22718	−0.446588	−0.223294	+	0.974751i	$0.571681\pi$
$138$	6.51348	0.554464
$139$	−9.43083	−0.799913	−0.399956	−	0.916534i	$-0.630975\pi$
$139$	−9.43083	−0.799913	−0.399956	+	0.916534i	$0.630975\pi$
$140$	−1.69458	−0.143218
$141$	−6.23707	−0.525256
$142$	6.62891	0.556286
$143$	−6.18039	−0.516830
$144$	1.00000	0.0833333
$145$	9.43896	0.783863
$146$	−2.20900	−0.182818
$147$	5.42038	0.447065
$148$	−6.41537	−0.527341
$149$	−7.36592	−0.603439	−0.301720	−	0.953397i	$-0.597561\pi$
$149$	−7.36592	−0.603439	−0.301720	+	0.953397i	$0.597561\pi$
$150$	3.18210	0.259818
$151$	8.10419	0.659509	0.329755	−	0.944067i	$-0.393034\pi$
$151$	8.10419	0.659509	0.329755	+	0.944067i	$0.393034\pi$
$152$	5.57232	0.451975
$153$	0.669960	0.0541630
$154$	−7.76770	−0.625939
$155$	13.4134	1.07739
$156$	1.00000	0.0800641
$157$	−7.16921	−0.572165	−0.286083	−	0.958205i	$-0.592353\pi$
$157$	−7.16921	−0.572165	−0.286083	+	0.958205i	$0.592353\pi$
$158$	−12.7247	−1.01232
$159$	8.03980	0.637598
$160$	1.34829	0.106592
$161$	8.18633	0.645173
$162$	1.00000	0.0785674
$163$	−14.4487	−1.13171	−0.565855	−	0.824505i	$-0.691454\pi$
$163$	−14.4487	−1.13171	−0.565855	+	0.824505i	$0.691454\pi$
$164$	3.07063	0.239776
$165$	−8.33299	−0.648722
$166$	−0.863190	−0.0669965
$167$	−19.0982	−1.47786	−0.738932	−	0.673780i	$-0.764670\pi$
$167$	−19.0982	−1.47786	−0.738932	+	0.673780i	$0.764670\pi$
$168$	1.25683	0.0969665
$169$	1.00000	0.0769231
$170$	0.903303	0.0692801
$171$	5.57232	0.426126
$172$	5.34321	0.407416
$173$	22.9671	1.74616	0.873079	−	0.487579i	$-0.162120\pi$
$173$	22.9671	1.74616	0.873079	+	0.487579i	$0.162120\pi$
$174$	−7.00067	−0.530719
$175$	3.99936	0.302323
$176$	6.18039	0.465865
$177$	3.12465	0.234863
$178$	4.65035	0.348559
$179$	2.88656	0.215752	0.107876	−	0.994164i	$-0.465595\pi$
$179$	2.88656	0.215752	0.107876	+	0.994164i	$0.465595\pi$
$180$	1.34829	0.100496
$181$	16.8058	1.24917	0.624584	−	0.780958i	$-0.285269\pi$
$181$	16.8058	1.24917	0.624584	+	0.780958i	$0.285269\pi$
$182$	1.25683	0.0931624
$183$	−1.33683	−0.0988210
$184$	−6.51348	−0.480180
$185$	−8.64981	−0.635947
$186$	−9.94843	−0.729455
$187$	4.14061	0.302792
$188$	6.23707	0.454885
$189$	1.25683	0.0914209
$190$	7.51313	0.545059
$191$	−4.98127	−0.360432	−0.180216	−	0.983627i	$-0.557680\pi$
$191$	−4.98127	−0.360432	−0.180216	+	0.983627i	$0.557680\pi$
$192$	−1.00000	−0.0721688
$193$	7.47451	0.538027	0.269014	−	0.963136i	$-0.413302\pi$
$193$	7.47451	0.538027	0.269014	+	0.963136i	$0.413302\pi$
$194$	−11.6073	−0.833358
$195$	1.34829	0.0965534
$196$	−5.42038	−0.387170
$197$	16.2736	1.15945	0.579725	−	0.814812i	$-0.303160\pi$
$197$	16.2736	1.15945	0.579725	+	0.814812i	$0.303160\pi$
$198$	6.18039	0.439221
$199$	−10.9796	−0.778320	−0.389160	−	0.921170i	$-0.627235\pi$
$199$	−10.9796	−0.778320	−0.389160	+	0.921170i	$0.627235\pi$
$200$	−3.18210	−0.225009
$201$	−8.66119	−0.610913
$202$	7.53357	0.530060
$203$	−8.79865	−0.617544
$204$	−0.669960	−0.0469066
$205$	4.14011	0.289158
$206$	−1.00000	−0.0696733
$207$	−6.51348	−0.452718
$208$	−1.00000	−0.0693375
$209$	34.4391	2.38220
$210$	1.69458	0.116937
$211$	−20.4841	−1.41018	−0.705091	−	0.709117i	$-0.749094\pi$
$211$	−20.4841	−1.41018	−0.705091	+	0.709117i	$0.749094\pi$
$212$	−8.03980	−0.552176
$213$	−6.62891	−0.454205
$214$	10.7444	0.734475
$215$	7.20422	0.491324
$216$	−1.00000	−0.0680414
$217$	−12.5035	−0.848792
$218$	0.0532230	0.00360472
$219$	2.20900	0.149270
$220$	8.33299	0.561810
$221$	−0.669960	−0.0450664
$222$	6.41537	0.430572
$223$	3.21166	0.215068	0.107534	−	0.994201i	$-0.465704\pi$
$223$	3.21166	0.215068	0.107534	+	0.994201i	$0.465704\pi$
$224$	−1.25683	−0.0839754
$225$	−3.18210	−0.212140
$226$	13.8205	0.919324
$227$	−28.6424	−1.90106	−0.950530	−	0.310633i	$-0.899459\pi$
$227$	−28.6424	−1.90106	−0.950530	+	0.310633i	$0.899459\pi$
$228$	−5.57232	−0.369036
$229$	10.9174	0.721444	0.360722	−	0.932673i	$-0.382530\pi$
$229$	10.9174	0.721444	0.360722	+	0.932673i	$0.382530\pi$
$230$	−8.78209	−0.579074
$231$	7.76770	0.511077
$232$	7.00067	0.459617
$233$	22.8998	1.50022	0.750108	−	0.661316i	$-0.230002\pi$
$233$	22.8998	1.50022	0.750108	+	0.661316i	$0.230002\pi$
$234$	−1.00000	−0.0653720
$235$	8.40941	0.548569
$236$	−3.12465	−0.203398
$237$	12.7247	0.826560
$238$	−0.842025	−0.0545804
$239$	2.97784	0.192621	0.0963103	−	0.995351i	$-0.469296\pi$
$239$	2.97784	0.192621	0.0963103	+	0.995351i	$0.469296\pi$
$240$	−1.34829	−0.0870320
$241$	13.4226	0.864626	0.432313	−	0.901724i	$-0.357698\pi$
$241$	13.4226	0.864626	0.432313	+	0.901724i	$0.357698\pi$
$242$	27.1972	1.74831
$243$	−1.00000	−0.0641500
$244$	1.33683	0.0855815
$245$	−7.30827	−0.466908
$246$	−3.07063	−0.195776
$247$	−5.57232	−0.354558
$248$	9.94843	0.631726
$249$	0.863190	0.0547024
$250$	−11.0319	−0.697717
$251$	−11.9131	−0.751947	−0.375973	−	0.926631i	$-0.622692\pi$
$251$	−11.9131	−0.751947	−0.375973	+	0.926631i	$0.622692\pi$
$252$	−1.25683	−0.0791728
$253$	−40.2559	−2.53086
$254$	−3.53406	−0.221747
$255$	−0.903303	−0.0565670
$256$	1.00000	0.0625000
$257$	22.7340	1.41811	0.709054	−	0.705154i	$-0.249122\pi$
$257$	22.7340	1.41811	0.709054	+	0.705154i	$0.249122\pi$
$258$	−5.34321	−0.332654
$259$	8.06303	0.501012
$260$	−1.34829	−0.0836177
$261$	7.00067	0.433331
$262$	1.91302	0.118187
$263$	15.9585	0.984046	0.492023	−	0.870582i	$-0.336258\pi$
$263$	15.9585	0.984046	0.492023	+	0.870582i	$0.336258\pi$
$264$	−6.18039	−0.380377
$265$	−10.8400	−0.665897
$266$	−7.00345	−0.429409
$267$	−4.65035	−0.284597
$268$	8.66119	0.529067
$269$	16.0982	0.981526	0.490763	−	0.871293i	$-0.336718\pi$
$269$	16.0982	0.981526	0.490763	+	0.871293i	$0.336718\pi$
$270$	−1.34829	−0.0820546
$271$	2.40939	0.146360	0.0731801	−	0.997319i	$-0.476685\pi$
$271$	2.40939	0.146360	0.0731801	+	0.997319i	$0.476685\pi$
$272$	0.669960	0.0406223
$273$	−1.25683	−0.0760668
$274$	−5.22718	−0.315785
$275$	−19.6666	−1.18594
$276$	6.51348	0.392065
$277$	1.30583	0.0784598	0.0392299	−	0.999230i	$-0.487510\pi$
$277$	1.30583	0.0784598	0.0392299	+	0.999230i	$0.487510\pi$
$278$	−9.43083	−0.565624
$279$	9.94843	0.595597
$280$	−1.69458	−0.101270
$281$	12.3979	0.739596	0.369798	−	0.929112i	$-0.379427\pi$
$281$	12.3979	0.739596	0.369798	+	0.929112i	$0.379427\pi$
$282$	−6.23707	−0.371412
$283$	23.0980	1.37303	0.686516	−	0.727115i	$-0.259139\pi$
$283$	23.0980	1.37303	0.686516	+	0.727115i	$0.259139\pi$
$284$	6.62891	0.393353
$285$	−7.51313	−0.445039
$286$	−6.18039	−0.365454
$287$	−3.85926	−0.227805
$288$	1.00000	0.0589256
$289$	−16.5512	−0.973597
$290$	9.43896	0.554275
$291$	11.6073	0.680434
$292$	−2.20900	−0.129272
$293$	4.86440	0.284181	0.142091	−	0.989854i	$-0.454618\pi$
$293$	4.86440	0.284181	0.142091	+	0.989854i	$0.454618\pi$
$294$	5.42038	0.316123
$295$	−4.21295	−0.245288
$296$	−6.41537	−0.372886
$297$	−6.18039	−0.358623
$298$	−7.36592	−0.426696
$299$	6.51348	0.376684
$300$	3.18210	0.183719
$301$	−6.71550	−0.387075
$302$	8.10419	0.466344
$303$	−7.53357	−0.432792
$304$	5.57232	0.319594
$305$	1.80243	0.103207
$306$	0.669960	0.0382990
$307$	−28.0036	−1.59825	−0.799124	−	0.601167i	$-0.794703\pi$
$307$	−28.0036	−1.59825	−0.799124	+	0.601167i	$0.794703\pi$
$308$	−7.76770	−0.442606
$309$	1.00000	0.0568880
$310$	13.4134	0.761831
$311$	25.6298	1.45333	0.726666	−	0.686991i	$-0.241069\pi$
$311$	25.6298	1.45333	0.726666	+	0.686991i	$0.241069\pi$
$312$	1.00000	0.0566139
$313$	0.830172	0.0469241	0.0234621	−	0.999725i	$-0.492531\pi$
$313$	0.830172	0.0469241	0.0234621	+	0.999725i	$0.492531\pi$
$314$	−7.16921	−0.404582
$315$	−1.69458	−0.0954785
$316$	−12.7247	−0.715822
$317$	15.6607	0.879593	0.439796	−	0.898098i	$-0.355051\pi$
$317$	15.6607	0.879593	0.439796	+	0.898098i	$0.355051\pi$
$318$	8.03980	0.450850
$319$	43.2669	2.42248
$320$	1.34829	0.0753719
$321$	−10.7444	−0.599696
$322$	8.18633	0.456206
$323$	3.73323	0.207722
$324$	1.00000	0.0555556
$325$	3.18210	0.176511
$326$	−14.4487	−0.800240
$327$	−0.0532230	−0.00294324
$328$	3.07063	0.169547
$329$	−7.83893	−0.432174
$330$	−8.33299	−0.458716
$331$	33.8850	1.86249	0.931244	−	0.364396i	$-0.118725\pi$
$331$	33.8850	1.86249	0.931244	+	0.364396i	$0.118725\pi$
$332$	−0.863190	−0.0473737
$333$	−6.41537	−0.351560
$334$	−19.0982	−1.04501
$335$	11.6778	0.638028
$336$	1.25683	0.0685657
$337$	4.89288	0.266532	0.133266	−	0.991080i	$-0.457454\pi$
$337$	4.89288	0.266532	0.133266	+	0.991080i	$0.457454\pi$
$338$	1.00000	0.0543928
$339$	−13.8205	−0.750625
$340$	0.903303	0.0489885
$341$	61.4852	3.32961
$342$	5.57232	0.301316
$343$	15.6103	0.842877
$344$	5.34321	0.288086
$345$	8.78209	0.472812
$346$	22.9671	1.23472
$347$	−15.6931	−0.842449	−0.421225	−	0.906956i	$-0.638400\pi$
$347$	−15.6931	−0.842449	−0.421225	+	0.906956i	$0.638400\pi$
$348$	−7.00067	−0.375275
$349$	−17.0990	−0.915290	−0.457645	−	0.889135i	$-0.651307\pi$
$349$	−17.0990	−0.915290	−0.457645	+	0.889135i	$0.651307\pi$
$350$	3.99936	0.213775
$351$	1.00000	0.0533761
$352$	6.18039	0.329416
$353$	21.2245	1.12967	0.564833	−	0.825205i	$-0.308940\pi$
$353$	21.2245	1.12967	0.564833	+	0.825205i	$0.308940\pi$
$354$	3.12465	0.166074
$355$	8.93772	0.474365
$356$	4.65035	0.246468
$357$	0.842025	0.0445647
$358$	2.88656	0.152560
$359$	−14.9473	−0.788888	−0.394444	−	0.918920i	$-0.629063\pi$
$359$	−14.9473	−0.788888	−0.394444	+	0.918920i	$0.629063\pi$
$360$	1.34829	0.0710613
$361$	12.0507	0.634249
$362$	16.8058	0.883295
$363$	−27.1972	−1.42749
$364$	1.25683	0.0658758
$365$	−2.97838	−0.155896
$366$	−1.33683	−0.0698770
$367$	−12.1126	−0.632272	−0.316136	−	0.948714i	$-0.602386\pi$
$367$	−12.1126	−0.632272	−0.316136	+	0.948714i	$0.602386\pi$
$368$	−6.51348	−0.339539
$369$	3.07063	0.159851
$370$	−8.64981	−0.449682
$371$	10.1047	0.524608
$372$	−9.94843	−0.515802
$373$	−6.77801	−0.350952	−0.175476	−	0.984484i	$-0.556146\pi$
$373$	−6.77801	−0.350952	−0.175476	+	0.984484i	$0.556146\pi$
$374$	4.14061	0.214106
$375$	11.0319	0.569684
$376$	6.23707	0.321652
$377$	−7.00067	−0.360553
$378$	1.25683	0.0646443
$379$	−4.76965	−0.245001	−0.122500	−	0.992468i	$-0.539091\pi$
$379$	−4.76965	−0.245001	−0.122500	+	0.992468i	$0.539091\pi$
$380$	7.51313	0.385415
$381$	3.53406	0.181055
$382$	−4.98127	−0.254864
$383$	−12.0847	−0.617499	−0.308749	−	0.951143i	$-0.599910\pi$
$383$	−12.0847	−0.617499	−0.308749	+	0.951143i	$0.599910\pi$
$384$	−1.00000	−0.0510310
$385$	−10.4731	−0.533761
$386$	7.47451	0.380443
$387$	5.34321	0.271611
$388$	−11.6073	−0.589273
$389$	26.8990	1.36383	0.681916	−	0.731431i	$-0.261147\pi$
$389$	26.8990	1.36383	0.681916	+	0.731431i	$0.261147\pi$
$390$	1.34829	0.0682735
$391$	−4.36377	−0.220685
$392$	−5.42038	−0.273771
$393$	−1.91302	−0.0964993
$394$	16.2736	0.819854
$395$	−17.1567	−0.863246
$396$	6.18039	0.310576
$397$	9.11191	0.457314	0.228657	−	0.973507i	$-0.426567\pi$
$397$	9.11191	0.457314	0.228657	+	0.973507i	$0.426567\pi$
$398$	−10.9796	−0.550356
$399$	7.00345	0.350611
$400$	−3.18210	−0.159105
$401$	5.41938	0.270631	0.135315	−	0.990803i	$-0.456795\pi$
$401$	5.41938	0.270631	0.135315	+	0.990803i	$0.456795\pi$
$402$	−8.66119	−0.431981
$403$	−9.94843	−0.495567
$404$	7.53357	0.374809
$405$	1.34829	0.0669973
$406$	−8.79865	−0.436670
$407$	−39.6495	−1.96535
$408$	−0.669960	−0.0331679
$409$	23.0164	1.13809	0.569043	−	0.822308i	$-0.307314\pi$
$409$	23.0164	1.13809	0.569043	+	0.822308i	$0.307314\pi$
$410$	4.14011	0.204466
$411$	5.22718	0.257838
$412$	−1.00000	−0.0492665
$413$	3.92716	0.193243
$414$	−6.51348	−0.320120
$415$	−1.16383	−0.0571303
$416$	−1.00000	−0.0490290
$417$	9.43083	0.461830
$418$	34.4391	1.68447
$419$	12.9522	0.632758	0.316379	−	0.948633i	$-0.397533\pi$
$419$	12.9522	0.632758	0.316379	+	0.948633i	$0.397533\pi$
$420$	1.69458	0.0826868
$421$	−30.0337	−1.46375	−0.731877	−	0.681437i	$-0.761355\pi$
$421$	−30.0337	−1.46375	−0.731877	+	0.681437i	$0.761355\pi$
$422$	−20.4841	−0.997149
$423$	6.23707	0.303257
$424$	−8.03980	−0.390447
$425$	−2.13188	−0.103411
$426$	−6.62891	−0.321172
$427$	−1.68016	−0.0813087
$428$	10.7444	0.519352
$429$	6.18039	0.298392
$430$	7.20422	0.347418
$431$	−27.0278	−1.30188	−0.650942	−	0.759127i	$-0.725626\pi$
$431$	−27.0278	−1.30188	−0.650942	+	0.759127i	$0.725626\pi$
$432$	−1.00000	−0.0481125
$433$	38.4811	1.84928	0.924641	−	0.380841i	$-0.124365\pi$
$433$	38.4811	1.84928	0.924641	+	0.380841i	$0.124365\pi$
$434$	−12.5035	−0.600186
$435$	−9.43896	−0.452564
$436$	0.0532230	0.00254892
$437$	−36.2952	−1.73623
$438$	2.20900	0.105550
$439$	−28.9181	−1.38018	−0.690092	−	0.723722i	$-0.742430\pi$
$439$	−28.9181	−1.38018	−0.690092	+	0.723722i	$0.742430\pi$
$440$	8.33299	0.397260
$441$	−5.42038	−0.258113
$442$	−0.669960	−0.0318667
$443$	5.38288	0.255748	0.127874	−	0.991790i	$-0.459185\pi$
$443$	5.38288	0.255748	0.127874	+	0.991790i	$0.459185\pi$
$444$	6.41537	0.304460
$445$	6.27004	0.297229
$446$	3.21166	0.152076
$447$	7.36592	0.348396
$448$	−1.25683	−0.0593796
$449$	−14.8713	−0.701821	−0.350910	−	0.936409i	$-0.614128\pi$
$449$	−14.8713	−0.701821	−0.350910	+	0.936409i	$0.614128\pi$
$450$	−3.18210	−0.150006
$451$	18.9777	0.893625
$452$	13.8205	0.650060
$453$	−8.10419	−0.380768
$454$	−28.6424	−1.34425
$455$	1.69458	0.0794429
$456$	−5.57232	−0.260948
$457$	4.72695	0.221118	0.110559	−	0.993870i	$-0.464736\pi$
$457$	4.72695	0.221118	0.110559	+	0.993870i	$0.464736\pi$
$458$	10.9174	0.510138
$459$	−0.669960	−0.0312710
$460$	−8.78209	−0.409467
$461$	−9.95374	−0.463592	−0.231796	−	0.972764i	$-0.574460\pi$
$461$	−9.95374	−0.463592	−0.231796	+	0.972764i	$0.574460\pi$
$462$	7.76770	0.361386
$463$	29.5029	1.37112	0.685559	−	0.728018i	$-0.259558\pi$
$463$	29.5029	1.37112	0.685559	+	0.728018i	$0.259558\pi$
$464$	7.00067	0.324998
$465$	−13.4134	−0.622032
$466$	22.8998	1.06081
$467$	−34.5248	−1.59762	−0.798810	−	0.601584i	$-0.794537\pi$
$467$	−34.5248	−1.59762	−0.798810	+	0.601584i	$0.794537\pi$
$468$	−1.00000	−0.0462250
$469$	−10.8856	−0.502652
$470$	8.40941	0.387897
$471$	7.16921	0.330340
$472$	−3.12465	−0.143824
$473$	33.0231	1.51840
$474$	12.7247	0.584466
$475$	−17.7317	−0.813586
$476$	−0.842025	−0.0385941
$477$	−8.03980	−0.368117
$478$	2.97784	0.136203
$479$	−14.2751	−0.652248	−0.326124	−	0.945327i	$-0.605743\pi$
$479$	−14.2751	−0.652248	−0.326124	+	0.945327i	$0.605743\pi$
$480$	−1.34829	−0.0615409
$481$	6.41537	0.292516
$482$	13.4226	0.611383
$483$	−8.18633	−0.372491
$484$	27.1972	1.23624
$485$	−15.6501	−0.710635
$486$	−1.00000	−0.0453609
$487$	11.3377	0.513762	0.256881	−	0.966443i	$-0.417305\pi$
$487$	11.3377	0.513762	0.256881	+	0.966443i	$0.417305\pi$
$488$	1.33683	0.0605153
$489$	14.4487	0.653393
$490$	−7.30827	−0.330154
$491$	−26.6950	−1.20473	−0.602363	−	0.798222i	$-0.705774\pi$
$491$	−26.6950	−1.20473	−0.602363	+	0.798222i	$0.705774\pi$
$492$	−3.07063	−0.138435
$493$	4.69017	0.211234
$494$	−5.57232	−0.250710
$495$	8.33299	0.374540
$496$	9.94843	0.446698
$497$	−8.33141	−0.373715
$498$	0.863190	0.0386804
$499$	7.46541	0.334197	0.167099	−	0.985940i	$-0.446560\pi$
$499$	7.46541	0.334197	0.167099	+	0.985940i	$0.446560\pi$
$500$	−11.0319	−0.493361
$501$	19.0982	0.853245
$502$	−11.9131	−0.531707
$503$	17.5149	0.780950	0.390475	−	0.920614i	$-0.372311\pi$
$503$	17.5149	0.780950	0.390475	+	0.920614i	$0.372311\pi$
$504$	−1.25683	−0.0559836
$505$	10.1575	0.452001
$506$	−40.2559	−1.78959
$507$	−1.00000	−0.0444116
$508$	−3.53406	−0.156799
$509$	−5.39952	−0.239330	−0.119665	−	0.992814i	$-0.538182\pi$
$509$	−5.39952	−0.239330	−0.119665	+	0.992814i	$0.538182\pi$
$510$	−0.903303	−0.0399989
$511$	2.77634	0.122818
$512$	1.00000	0.0441942
$513$	−5.57232	−0.246024
$514$	22.7340	1.00275
$515$	−1.34829	−0.0594129
$516$	−5.34321	−0.235222
$517$	38.5475	1.69532
$518$	8.06303	0.354269
$519$	−22.9671	−1.00814
$520$	−1.34829	−0.0591266
$521$	−1.82746	−0.0800624	−0.0400312	−	0.999198i	$-0.512746\pi$
$521$	−1.82746	−0.0800624	−0.0400312	+	0.999198i	$0.512746\pi$
$522$	7.00067	0.306411
$523$	−4.67744	−0.204530	−0.102265	−	0.994757i	$-0.532609\pi$
$523$	−4.67744	−0.204530	−0.102265	+	0.994757i	$0.532609\pi$
$524$	1.91302	0.0835708
$525$	−3.99936	−0.174546
$526$	15.9585	0.695825
$527$	6.66505	0.290334
$528$	−6.18039	−0.268967
$529$	19.4254	0.844583
$530$	−10.8400	−0.470860
$531$	−3.12465	−0.135598
$532$	−7.00345	−0.303638
$533$	−3.07063	−0.133004
$534$	−4.65035	−0.201240
$535$	14.4867	0.626313
$536$	8.66119	0.374107
$537$	−2.88656	−0.124564
$538$	16.0982	0.694044
$539$	−33.5001	−1.44295
$540$	−1.34829	−0.0580213
$541$	7.49168	0.322092	0.161046	−	0.986947i	$-0.448513\pi$
$541$	7.49168	0.322092	0.161046	+	0.986947i	$0.448513\pi$
$542$	2.40939	0.103492
$543$	−16.8058	−0.721207
$544$	0.669960	0.0287243
$545$	0.0717602	0.00307387
$546$	−1.25683	−0.0537873
$547$	33.3140	1.42440	0.712202	−	0.701975i	$-0.247698\pi$
$547$	33.3140	1.42440	0.712202	+	0.701975i	$0.247698\pi$
$548$	−5.22718	−0.223294
$549$	1.33683	0.0570543
$550$	−19.6666	−0.838588
$551$	39.0100	1.66188
$552$	6.51348	0.277232
$553$	15.9928	0.680083
$554$	1.30583	0.0554794
$555$	8.64981	0.367164
$556$	−9.43083	−0.399956
$557$	−20.5170	−0.869331	−0.434666	−	0.900592i	$-0.643133\pi$
$557$	−20.5170	−0.869331	−0.434666	+	0.900592i	$0.643133\pi$
$558$	9.94843	0.421151
$559$	−5.34321	−0.225994
$560$	−1.69458	−0.0716089
$561$	−4.14061	−0.174817
$562$	12.3979	0.522973
$563$	−10.1882	−0.429383	−0.214691	−	0.976682i	$-0.568875\pi$
$563$	−10.1882	−0.429383	−0.214691	+	0.976682i	$0.568875\pi$
$564$	−6.23707	−0.262628
$565$	18.6341	0.783941
$566$	23.0980	0.970880
$567$	−1.25683	−0.0527819
$568$	6.62891	0.278143
$569$	−31.7117	−1.32943	−0.664713	−	0.747099i	$-0.731446\pi$
$569$	−31.7117	−1.32943	−0.664713	+	0.747099i	$0.731446\pi$
$570$	−7.51313	−0.314690
$571$	42.4864	1.77800	0.889000	−	0.457906i	$-0.151401\pi$
$571$	42.4864	1.77800	0.889000	+	0.457906i	$0.151401\pi$
$572$	−6.18039	−0.258415
$573$	4.98127	0.208095
$574$	−3.85926	−0.161082
$575$	20.7266	0.864357
$576$	1.00000	0.0416667
$577$	−20.5607	−0.855951	−0.427976	−	0.903790i	$-0.640773\pi$
$577$	−20.5607	−0.855951	−0.427976	+	0.903790i	$0.640773\pi$
$578$	−16.5512	−0.688437
$579$	−7.47451	−0.310630
$580$	9.43896	0.391932
$581$	1.08488	0.0450085
$582$	11.6073	0.481140
$583$	−49.6891	−2.05791
$584$	−2.20900	−0.0914091
$585$	−1.34829	−0.0557451
$586$	4.86440	0.200946
$587$	−13.9190	−0.574498	−0.287249	−	0.957856i	$-0.592741\pi$
$587$	−13.9190	−0.574498	−0.287249	+	0.957856i	$0.592741\pi$
$588$	5.42038	0.223533
$589$	55.4358	2.28419
$590$	−4.21295	−0.173445
$591$	−16.2736	−0.669408
$592$	−6.41537	−0.263670
$593$	−29.1791	−1.19824	−0.599121	−	0.800658i	$-0.704483\pi$
$593$	−29.1791	−1.19824	−0.599121	+	0.800658i	$0.704483\pi$
$594$	−6.18039	−0.253585
$595$	−1.13530	−0.0465426
$596$	−7.36592	−0.301720
$597$	10.9796	0.449363
$598$	6.51348	0.266356
$599$	1.96570	0.0803162	0.0401581	−	0.999193i	$-0.487214\pi$
$599$	1.96570	0.0803162	0.0401581	+	0.999193i	$0.487214\pi$
$600$	3.18210	0.129909
$601$	12.3062	0.501981	0.250991	−	0.967990i	$-0.419244\pi$
$601$	12.3062	0.501981	0.250991	+	0.967990i	$0.419244\pi$
$602$	−6.71550	−0.273703
$603$	8.66119	0.352711
$604$	8.10419	0.329755
$605$	36.6699	1.49084
$606$	−7.53357	−0.306030
$607$	14.1524	0.574426	0.287213	−	0.957867i	$-0.407271\pi$
$607$	14.1524	0.574426	0.287213	+	0.957867i	$0.407271\pi$
$608$	5.57232	0.225987
$609$	8.79865	0.356539
$610$	1.80243	0.0729784
$611$	−6.23707	−0.252325
$612$	0.669960	0.0270815
$613$	−20.7064	−0.836322	−0.418161	−	0.908373i	$-0.637325\pi$
$613$	−20.7064	−0.836322	−0.418161	+	0.908373i	$0.637325\pi$
$614$	−28.0036	−1.13013
$615$	−4.14011	−0.166945
$616$	−7.76770	−0.312969
$617$	−9.87894	−0.397711	−0.198856	−	0.980029i	$-0.563722\pi$
$617$	−9.87894	−0.397711	−0.198856	+	0.980029i	$0.563722\pi$
$618$	1.00000	0.0402259
$619$	39.0760	1.57060	0.785298	−	0.619118i	$-0.212510\pi$
$619$	39.0760	1.57060	0.785298	+	0.619118i	$0.212510\pi$
$620$	13.4134	0.538696
$621$	6.51348	0.261377
$622$	25.6298	1.02766
$623$	−5.84470	−0.234163
$624$	1.00000	0.0400320
$625$	1.03629	0.0414517
$626$	0.830172	0.0331804
$627$	−34.4391	−1.37537
$628$	−7.16921	−0.286083
$629$	−4.29804	−0.171374
$630$	−1.69458	−0.0675135
$631$	42.4635	1.69044	0.845222	−	0.534415i	$-0.179468\pi$
$631$	42.4635	1.69044	0.845222	+	0.534415i	$0.179468\pi$
$632$	−12.7247	−0.506162
$633$	20.4841	0.814169
$634$	15.6607	0.621966
$635$	−4.76496	−0.189091
$636$	8.03980	0.318799
$637$	5.42038	0.214763
$638$	43.2669	1.71295
$639$	6.62891	0.262236
$640$	1.34829	0.0532960
$641$	−41.5522	−1.64121	−0.820606	−	0.571494i	$-0.806364\pi$
$641$	−41.5522	−1.64121	−0.820606	+	0.571494i	$0.806364\pi$
$642$	−10.7444	−0.424049
$643$	−24.4953	−0.966000	−0.483000	−	0.875620i	$-0.660453\pi$
$643$	−24.4953	−0.966000	−0.483000	+	0.875620i	$0.660453\pi$
$644$	8.18633	0.322587
$645$	−7.20422	−0.283666
$646$	3.73323	0.146882
$647$	23.2463	0.913907	0.456954	−	0.889491i	$-0.348941\pi$
$647$	23.2463	0.913907	0.456954	+	0.889491i	$0.348941\pi$
$648$	1.00000	0.0392837
$649$	−19.3116	−0.758046
$650$	3.18210	0.124812
$651$	12.5035	0.490050
$652$	−14.4487	−0.565855
$653$	5.51615	0.215864	0.107932	−	0.994158i	$-0.465577\pi$
$653$	5.51615	0.215864	0.107932	+	0.994158i	$0.465577\pi$
$654$	−0.0532230	−0.00208118
$655$	2.57932	0.100782
$656$	3.07063	0.119888
$657$	−2.20900	−0.0861813
$658$	−7.83893	−0.305593
$659$	31.6062	1.23120	0.615600	−	0.788058i	$-0.288914\pi$
$659$	31.6062	1.23120	0.615600	+	0.788058i	$0.288914\pi$
$660$	−8.33299	−0.324361
$661$	−40.1139	−1.56025	−0.780124	−	0.625624i	$-0.784844\pi$
$661$	−40.1139	−1.56025	−0.780124	+	0.625624i	$0.784844\pi$
$662$	33.8850	1.31698
$663$	0.669960	0.0260191
$664$	−0.863190	−0.0334983
$665$	−9.44272	−0.366173
$666$	−6.41537	−0.248591
$667$	−45.5987	−1.76559
$668$	−19.0982	−0.738932
$669$	−3.21166	−0.124170
$670$	11.6778	0.451154
$671$	8.26211	0.318955
$672$	1.25683	0.0484832
$673$	−21.7284	−0.837569	−0.418785	−	0.908086i	$-0.637544\pi$
$673$	−21.7284	−0.837569	−0.418785	+	0.908086i	$0.637544\pi$
$674$	4.89288	0.188467
$675$	3.18210	0.122479
$676$	1.00000	0.0384615
$677$	−40.5339	−1.55785	−0.778923	−	0.627120i	$-0.784234\pi$
$677$	−40.5339	−1.55785	−0.778923	+	0.627120i	$0.784234\pi$
$678$	−13.8205	−0.530772
$679$	14.5884	0.559853
$680$	0.903303	0.0346401
$681$	28.6424	1.09758
$682$	61.4852	2.35439
$683$	33.7817	1.29262	0.646311	−	0.763074i	$-0.276311\pi$
$683$	33.7817	1.29262	0.646311	+	0.763074i	$0.276311\pi$
$684$	5.57232	0.213063
$685$	−7.04778	−0.269282
$686$	15.6103	0.596004
$687$	−10.9174	−0.416526
$688$	5.34321	0.203708
$689$	8.03980	0.306292
$690$	8.78209	0.334328
$691$	−14.7146	−0.559771	−0.279885	−	0.960033i	$-0.590296\pi$
$691$	−14.7146	−0.559771	−0.279885	+	0.960033i	$0.590296\pi$
$692$	22.9671	0.873079
$693$	−7.76770	−0.295070
$694$	−15.6931	−0.595702
$695$	−12.7155	−0.482328
$696$	−7.00067	−0.265360
$697$	2.05720	0.0779219
$698$	−17.0990	−0.647208
$699$	−22.8998	−0.866150
$700$	3.99936	0.151162
$701$	−47.0866	−1.77844	−0.889218	−	0.457483i	$-0.848751\pi$
$701$	−47.0866	−1.77844	−0.889218	+	0.457483i	$0.848751\pi$
$702$	1.00000	0.0377426
$703$	−35.7485	−1.34828
$704$	6.18039	0.232932
$705$	−8.40941	−0.316717
$706$	21.2245	0.798795
$707$	−9.46841	−0.356096
$708$	3.12465	0.117432
$709$	−6.68250	−0.250966	−0.125483	−	0.992096i	$-0.540048\pi$
$709$	−6.68250	−0.250966	−0.125483	+	0.992096i	$0.540048\pi$
$710$	8.93772	0.335427
$711$	−12.7247	−0.477215
$712$	4.65035	0.174279
$713$	−64.7989	−2.42674
$714$	0.842025	0.0315120
$715$	−8.33299	−0.311636
$716$	2.88656	0.107876
$717$	−2.97784	−0.111210
$718$	−14.9473	−0.557828
$719$	3.95188	0.147380	0.0736902	−	0.997281i	$-0.476522\pi$
$719$	3.95188	0.147380	0.0736902	+	0.997281i	$0.476522\pi$
$720$	1.34829	0.0502480
$721$	1.25683	0.0468068
$722$	12.0507	0.448482
$723$	−13.4226	−0.499192
$724$	16.8058	0.624584
$725$	−22.2769	−0.827342
$726$	−27.1972	−1.00938
$727$	29.7334	1.10275	0.551375	−	0.834257i	$-0.314103\pi$
$727$	29.7334	1.10275	0.551375	+	0.834257i	$0.314103\pi$
$728$	1.25683	0.0465812
$729$	1.00000	0.0370370
$730$	−2.97838	−0.110235
$731$	3.57973	0.132401
$732$	−1.33683	−0.0494105
$733$	−7.34755	−0.271388	−0.135694	−	0.990751i	$-0.543326\pi$
$733$	−7.34755	−0.271388	−0.135694	+	0.990751i	$0.543326\pi$
$734$	−12.1126	−0.447084
$735$	7.30827	0.269569
$736$	−6.51348	−0.240090
$737$	53.5296	1.97179
$738$	3.07063	0.113031
$739$	−8.11466	−0.298503	−0.149251	−	0.988799i	$-0.547686\pi$
$739$	−8.11466	−0.298503	−0.149251	+	0.988799i	$0.547686\pi$
$740$	−8.64981	−0.317973
$741$	5.57232	0.204704
$742$	10.1047	0.370954
$743$	−26.4538	−0.970497	−0.485248	−	0.874376i	$-0.661271\pi$
$743$	−26.4538	−0.970497	−0.485248	+	0.874376i	$0.661271\pi$
$744$	−9.94843	−0.364727
$745$	−9.93142	−0.363859
$746$	−6.77801	−0.248161
$747$	−0.863190	−0.0315825
$748$	4.14061	0.151396
$749$	−13.5039	−0.493423
$750$	11.0319	0.402827
$751$	4.89738	0.178708	0.0893539	−	0.996000i	$-0.471520\pi$
$751$	4.89738	0.178708	0.0893539	+	0.996000i	$0.471520\pi$
$752$	6.23707	0.227443
$753$	11.9131	0.434137
$754$	−7.00067	−0.254949
$755$	10.9268	0.397668
$756$	1.25683	0.0457104
$757$	−31.6179	−1.14917	−0.574586	−	0.818444i	$-0.694837\pi$
$757$	−31.6179	−1.14917	−0.574586	+	0.818444i	$0.694837\pi$
$758$	−4.76965	−0.173242
$759$	40.2559	1.46119
$760$	7.51313	0.272530
$761$	35.5981	1.29043	0.645214	−	0.764002i	$-0.276768\pi$
$761$	35.5981	1.29043	0.645214	+	0.764002i	$0.276768\pi$
$762$	3.53406	0.128026
$763$	−0.0668922	−0.00242166
$764$	−4.98127	−0.180216
$765$	0.903303	0.0326590
$766$	−12.0847	−0.436638
$767$	3.12465	0.112825
$768$	−1.00000	−0.0360844
$769$	39.1829	1.41297	0.706486	−	0.707727i	$-0.250279\pi$
$769$	39.1829	1.41297	0.706486	+	0.707727i	$0.250279\pi$
$770$	−10.4731	−0.377426
$771$	−22.7340	−0.818745
$772$	7.47451	0.269014
$773$	−22.3613	−0.804280	−0.402140	−	0.915578i	$-0.631733\pi$
$773$	−22.3613	−0.804280	−0.402140	+	0.915578i	$0.631733\pi$
$774$	5.34321	0.192058
$775$	−31.6569	−1.13715
$776$	−11.6073	−0.416679
$777$	−8.06303	−0.289260
$778$	26.8990	0.964374
$779$	17.1105	0.613048
$780$	1.34829	0.0482767
$781$	40.9693	1.46600
$782$	−4.36377	−0.156048
$783$	−7.00067	−0.250184
$784$	−5.42038	−0.193585
$785$	−9.66620	−0.345002
$786$	−1.91302	−0.0682353
$787$	−54.0364	−1.92619	−0.963094	−	0.269164i	$-0.913253\pi$
$787$	−54.0364	−1.92619	−0.963094	+	0.269164i	$0.913253\pi$
$788$	16.2736	0.579725
$789$	−15.9585	−0.568139
$790$	−17.1567	−0.610407
$791$	−17.3700	−0.617605
$792$	6.18039	0.219611
$793$	−1.33683	−0.0474721
$794$	9.11191	0.323370
$795$	10.8400	0.384456
$796$	−10.9796	−0.389160
$797$	−5.35792	−0.189787	−0.0948937	−	0.995487i	$-0.530251\pi$
$797$	−5.35792	−0.189787	−0.0948937	+	0.995487i	$0.530251\pi$
$798$	7.00345	0.247920
$799$	4.17858	0.147828
$800$	−3.18210	−0.112504
$801$	4.65035	0.164312
$802$	5.41938	0.191365
$803$	−13.6525	−0.481786
$804$	−8.66119	−0.305457
$805$	11.0376	0.389024
$806$	−9.94843	−0.350419
$807$	−16.0982	−0.566684
$808$	7.53357	0.265030
$809$	47.7356	1.67829	0.839147	−	0.543904i	$-0.183055\pi$
$809$	47.7356	1.67829	0.839147	+	0.543904i	$0.183055\pi$
$810$	1.34829	0.0473742
$811$	−14.6324	−0.513815	−0.256907	−	0.966436i	$-0.582704\pi$
$811$	−14.6324	−0.513815	−0.256907	+	0.966436i	$0.582704\pi$
$812$	−8.79865	−0.308772
$813$	−2.40939	−0.0845012
$814$	−39.6495	−1.38972
$815$	−19.4811	−0.682394
$816$	−0.669960	−0.0234533
$817$	29.7741	1.04166
$818$	23.0164	0.804749
$819$	1.25683	0.0439172
$820$	4.14011	0.144579
$821$	−14.8031	−0.516631	−0.258316	−	0.966061i	$-0.583167\pi$
$821$	−14.8031	−0.516631	−0.258316	+	0.966061i	$0.583167\pi$
$822$	5.22718	0.182319
$823$	−30.8013	−1.07367	−0.536833	−	0.843688i	$-0.680380\pi$
$823$	−30.8013	−1.07367	−0.536833	+	0.843688i	$0.680380\pi$
$824$	−1.00000	−0.0348367
$825$	19.6666	0.684705
$826$	3.92716	0.136643
$827$	−52.7224	−1.83334	−0.916668	−	0.399649i	$-0.869132\pi$
$827$	−52.7224	−1.83334	−0.916668	+	0.399649i	$0.869132\pi$
$828$	−6.51348	−0.226359
$829$	9.03526	0.313807	0.156904	−	0.987614i	$-0.449849\pi$
$829$	9.03526	0.313807	0.156904	+	0.987614i	$0.449849\pi$
$830$	−1.16383	−0.0403972
$831$	−1.30583	−0.0452988
$832$	−1.00000	−0.0346688
$833$	−3.63144	−0.125822
$834$	9.43083	0.326563
$835$	−25.7500	−0.891116
$836$	34.4391	1.19110
$837$	−9.94843	−0.343868
$838$	12.9522	0.447427
$839$	−42.8789	−1.48034	−0.740172	−	0.672418i	$-0.765256\pi$
$839$	−42.8789	−1.48034	−0.740172	+	0.672418i	$0.765256\pi$
$840$	1.69458	0.0584684
$841$	20.0094	0.689979
$842$	−30.0337	−1.03503
$843$	−12.3979	−0.427006
$844$	−20.4841	−0.705091
$845$	1.34829	0.0463827
$846$	6.23707	0.214435
$847$	−34.1823	−1.17452
$848$	−8.03980	−0.276088
$849$	−23.0980	−0.792720
$850$	−2.13188	−0.0731229
$851$	41.7864	1.43242
$852$	−6.62891	−0.227103
$853$	−40.6980	−1.39347	−0.696737	−	0.717327i	$-0.745365\pi$
$853$	−40.6980	−1.39347	−0.696737	+	0.717327i	$0.745365\pi$
$854$	−1.68016	−0.0574940
$855$	7.51313	0.256943
$856$	10.7444	0.367237
$857$	−8.67792	−0.296432	−0.148216	−	0.988955i	$-0.547353\pi$
$857$	−8.67792	−0.296432	−0.148216	+	0.988955i	$0.547353\pi$
$858$	6.18039	0.210995
$859$	16.7189	0.570441	0.285221	−	0.958462i	$-0.407933\pi$
$859$	16.7189	0.570441	0.285221	+	0.958462i	$0.407933\pi$
$860$	7.20422	0.245662
$861$	3.85926	0.131523
$862$	−27.0278	−0.920571
$863$	−41.7091	−1.41979	−0.709896	−	0.704306i	$-0.751258\pi$
$863$	−41.7091	−1.41979	−0.709896	+	0.704306i	$0.751258\pi$
$864$	−1.00000	−0.0340207
$865$	30.9664	1.05289
$866$	38.4811	1.30764
$867$	16.5512	0.562107
$868$	−12.5035	−0.424396
$869$	−78.6438	−2.66781
$870$	−9.43896	−0.320011
$871$	−8.66119	−0.293473
$872$	0.0532230	0.00180236
$873$	−11.6073	−0.392849
$874$	−36.2952	−1.22770
$875$	13.8652	0.468729
$876$	2.20900	0.0746352
$877$	31.6801	1.06976	0.534880	−	0.844928i	$-0.320357\pi$
$877$	31.6801	1.06976	0.534880	+	0.844928i	$0.320357\pi$
$878$	−28.9181	−0.975937
$879$	−4.86440	−0.164072
$880$	8.33299	0.280905
$881$	39.7532	1.33932	0.669660	−	0.742668i	$-0.266440\pi$
$881$	39.7532	1.33932	0.669660	+	0.742668i	$0.266440\pi$
$882$	−5.42038	−0.182514
$883$	18.7507	0.631011	0.315506	−	0.948924i	$-0.397826\pi$
$883$	18.7507	0.631011	0.315506	+	0.948924i	$0.397826\pi$
$884$	−0.669960	−0.0225332
$885$	4.21295	0.141617
$886$	5.38288	0.180841
$887$	−39.1134	−1.31330	−0.656649	−	0.754196i	$-0.728027\pi$
$887$	−39.1134	−1.31330	−0.656649	+	0.754196i	$0.728027\pi$
$888$	6.41537	0.215286
$889$	4.44171	0.148970
$890$	6.27004	0.210172
$891$	6.18039	0.207051
$892$	3.21166	0.107534
$893$	34.7549	1.16303
$894$	7.36592	0.246353
$895$	3.89194	0.130093
$896$	−1.25683	−0.0419877
$897$	−6.51348	−0.217479
$898$	−14.8713	−0.496262
$899$	69.6457	2.32281
$900$	−3.18210	−0.106070
$901$	−5.38634	−0.179445
$902$	18.9777	0.631888
$903$	6.71550	0.223478
$904$	13.8205	0.459662
$905$	22.6592	0.753217
$906$	−8.10419	−0.269244
$907$	−0.204614	−0.00679409	−0.00339704	−	0.999994i	$-0.501081\pi$
$907$	−0.204614	−0.00679409	−0.00339704	+	0.999994i	$0.501081\pi$
$908$	−28.6424	−0.950530
$909$	7.53357	0.249873
$910$	1.69458	0.0561746
$911$	−34.0664	−1.12867	−0.564334	−	0.825546i	$-0.690867\pi$
$911$	−34.0664	−1.12867	−0.564334	+	0.825546i	$0.690867\pi$
$912$	−5.57232	−0.184518
$913$	−5.33485	−0.176558
$914$	4.72695	0.156354
$915$	−1.80243	−0.0595866
$916$	10.9174	0.360722
$917$	−2.40434	−0.0793984
$918$	−0.669960	−0.0221120
$919$	−18.2922	−0.603405	−0.301703	−	0.953402i	$-0.597555\pi$
$919$	−18.2922	−0.603405	−0.301703	+	0.953402i	$0.597555\pi$
$920$	−8.78209	−0.289537
$921$	28.0036	0.922749
$922$	−9.95374	−0.327809
$923$	−6.62891	−0.218193
$924$	7.76770	0.255539
$925$	20.4144	0.671221
$926$	29.5029	0.969526
$927$	−1.00000	−0.0328443
$928$	7.00067	0.229808
$929$	1.22656	0.0402420	0.0201210	−	0.999798i	$-0.493595\pi$
$929$	1.22656	0.0402420	0.0201210	+	0.999798i	$0.493595\pi$
$930$	−13.4134	−0.439843
$931$	−30.2041	−0.989899
$932$	22.8998	0.750108
$933$	−25.6298	−0.839082
$934$	−34.5248	−1.12969
$935$	5.58276	0.182576
$936$	−1.00000	−0.0326860
$937$	2.86560	0.0936152	0.0468076	−	0.998904i	$-0.485095\pi$
$937$	2.86560	0.0936152	0.0468076	+	0.998904i	$0.485095\pi$
$938$	−10.8856	−0.355429
$939$	−0.830172	−0.0270916
$940$	8.40941	0.274285
$941$	31.6790	1.03271	0.516353	−	0.856376i	$-0.327289\pi$
$941$	31.6790	1.03271	0.516353	+	0.856376i	$0.327289\pi$
$942$	7.16921	0.233585
$943$	−20.0005	−0.651305
$944$	−3.12465	−0.101699
$945$	1.69458	0.0551246
$946$	33.0231	1.07367
$947$	36.8970	1.19899	0.599495	−	0.800378i	$-0.295368\pi$
$947$	36.8970	1.19899	0.599495	+	0.800378i	$0.295368\pi$
$948$	12.7247	0.413280
$949$	2.20900	0.0717072
$950$	−17.7317	−0.575292
$951$	−15.6607	−0.507833
$952$	−0.842025	−0.0272902
$953$	−11.3224	−0.366768	−0.183384	−	0.983041i	$-0.558705\pi$
$953$	−11.3224	−0.366768	−0.183384	+	0.983041i	$0.558705\pi$
$954$	−8.03980	−0.260298
$955$	−6.71621	−0.217331
$956$	2.97784	0.0963103
$957$	−43.2669	−1.39862
$958$	−14.2751	−0.461209
$959$	6.56967	0.212146
$960$	−1.34829	−0.0435160
$961$	67.9713	2.19262
$962$	6.41537	0.206840
$963$	10.7444	0.346235
$964$	13.4226	0.432313
$965$	10.0778	0.324417
$966$	−8.18633	−0.263391
$967$	14.0860	0.452975	0.226487	−	0.974014i	$-0.427276\pi$
$967$	14.0860	0.452975	0.226487	+	0.974014i	$0.427276\pi$
$968$	27.1972	0.874153
$969$	−3.73323	−0.119929
$970$	−15.6501	−0.502495
$971$	−9.68061	−0.310666	−0.155333	−	0.987862i	$-0.549645\pi$
$971$	−9.68061	−0.310666	−0.155333	+	0.987862i	$0.549645\pi$
$972$	−1.00000	−0.0320750
$973$	11.8529	0.379988
$974$	11.3377	0.363284
$975$	−3.18210	−0.101909
$976$	1.33683	0.0427908
$977$	−14.3093	−0.457794	−0.228897	−	0.973451i	$-0.573512\pi$
$977$	−14.3093	−0.457794	−0.228897	+	0.973451i	$0.573512\pi$
$978$	14.4487	0.462019
$979$	28.7410	0.918567
$980$	−7.30827	−0.233454
$981$	0.0532230	0.00169928
$982$	−26.6950	−0.851870
$983$	27.6668	0.882433	0.441216	−	0.897401i	$-0.354547\pi$
$983$	27.6668	0.882433	0.441216	+	0.897401i	$0.354547\pi$
$984$	−3.07063	−0.0978881
$985$	21.9417	0.699120
$986$	4.69017	0.149365
$987$	7.83893	0.249516
$988$	−5.57232	−0.177279
$989$	−34.8029	−1.10667
$990$	8.33299	0.264840
$991$	−7.77320	−0.246924	−0.123462	−	0.992349i	$-0.539400\pi$
$991$	−7.77320	−0.246924	−0.123462	+	0.992349i	$0.539400\pi$
$992$	9.94843	0.315863
$993$	−33.8850	−1.07531
$994$	−8.33141	−0.264256
$995$	−14.8037	−0.469308
$996$	0.863190	0.0273512
$997$	3.58907	0.113667	0.0568336	−	0.998384i	$-0.481900\pi$
$997$	3.58907	0.113667	0.0568336	+	0.998384i	$0.481900\pi$
$998$	7.46541	0.236313
$999$	6.41537	0.202973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bc.1.10	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bc.1.10	✓	15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.34829 q^{5} -1.00000 q^{6} -1.25683 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.34829 q^{5} -1.00000 q^{6} -1.25683 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.34829 q^{10} +6.18039 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.25683 q^{14} -1.34829 q^{15} +1.00000 q^{16} +0.669960 q^{17} +1.00000 q^{18} +5.57232 q^{19} +1.34829 q^{20} +1.25683 q^{21} +6.18039 q^{22} -6.51348 q^{23} -1.00000 q^{24} -3.18210 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.25683 q^{28} +7.00067 q^{29} -1.34829 q^{30} +9.94843 q^{31} +1.00000 q^{32} -6.18039 q^{33} +0.669960 q^{34} -1.69458 q^{35} +1.00000 q^{36} -6.41537 q^{37} +5.57232 q^{38} +1.00000 q^{39} +1.34829 q^{40} +3.07063 q^{41} +1.25683 q^{42} +5.34321 q^{43} +6.18039 q^{44} +1.34829 q^{45} -6.51348 q^{46} +6.23707 q^{47} -1.00000 q^{48} -5.42038 q^{49} -3.18210 q^{50} -0.669960 q^{51} -1.00000 q^{52} -8.03980 q^{53} -1.00000 q^{54} +8.33299 q^{55} -1.25683 q^{56} -5.57232 q^{57} +7.00067 q^{58} -3.12465 q^{59} -1.34829 q^{60} +1.33683 q^{61} +9.94843 q^{62} -1.25683 q^{63} +1.00000 q^{64} -1.34829 q^{65} -6.18039 q^{66} +8.66119 q^{67} +0.669960 q^{68} +6.51348 q^{69} -1.69458 q^{70} +6.62891 q^{71} +1.00000 q^{72} -2.20900 q^{73} -6.41537 q^{74} +3.18210 q^{75} +5.57232 q^{76} -7.76770 q^{77} +1.00000 q^{78} -12.7247 q^{79} +1.34829 q^{80} +1.00000 q^{81} +3.07063 q^{82} -0.863190 q^{83} +1.25683 q^{84} +0.903303 q^{85} +5.34321 q^{86} -7.00067 q^{87} +6.18039 q^{88} +4.65035 q^{89} +1.34829 q^{90} +1.25683 q^{91} -6.51348 q^{92} -9.94843 q^{93} +6.23707 q^{94} +7.51313 q^{95} -1.00000 q^{96} -11.6073 q^{97} -5.42038 q^{98} +6.18039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * q^99

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