LMFDB - Embedded newform 8034.2.a.ba.1.7

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
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			1.7
Root			$0.503883$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.503883 q^{5} +1.00000 q^{6} +2.75905 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.503883 q^{5} +1.00000 q^{6} +2.75905 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.503883 q^{10} +6.03100 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.75905 q^{14} +0.503883 q^{15} +1.00000 q^{16} -6.29407 q^{17} -1.00000 q^{18} -6.31941 q^{19} -0.503883 q^{20} -2.75905 q^{21} -6.03100 q^{22} -7.22879 q^{23} +1.00000 q^{24} -4.74610 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.75905 q^{28} +9.35117 q^{29} -0.503883 q^{30} +2.92979 q^{31} -1.00000 q^{32} -6.03100 q^{33} +6.29407 q^{34} -1.39024 q^{35} +1.00000 q^{36} -2.31736 q^{37} +6.31941 q^{38} +1.00000 q^{39} +0.503883 q^{40} -3.89839 q^{41} +2.75905 q^{42} +4.29142 q^{43} +6.03100 q^{44} -0.503883 q^{45} +7.22879 q^{46} -6.99841 q^{47} -1.00000 q^{48} +0.612353 q^{49} +4.74610 q^{50} +6.29407 q^{51} -1.00000 q^{52} +3.51811 q^{53} +1.00000 q^{54} -3.03892 q^{55} -2.75905 q^{56} +6.31941 q^{57} -9.35117 q^{58} -9.24734 q^{59} +0.503883 q^{60} -0.178206 q^{61} -2.92979 q^{62} +2.75905 q^{63} +1.00000 q^{64} +0.503883 q^{65} +6.03100 q^{66} +9.08548 q^{67} -6.29407 q^{68} +7.22879 q^{69} +1.39024 q^{70} +12.4784 q^{71} -1.00000 q^{72} +4.54685 q^{73} +2.31736 q^{74} +4.74610 q^{75} -6.31941 q^{76} +16.6398 q^{77} -1.00000 q^{78} +10.0968 q^{79} -0.503883 q^{80} +1.00000 q^{81} +3.89839 q^{82} -0.865830 q^{83} -2.75905 q^{84} +3.17148 q^{85} -4.29142 q^{86} -9.35117 q^{87} -6.03100 q^{88} +0.262117 q^{89} +0.503883 q^{90} -2.75905 q^{91} -7.22879 q^{92} -2.92979 q^{93} +6.99841 q^{94} +3.18424 q^{95} +1.00000 q^{96} +18.9602 q^{97} -0.612353 q^{98} +6.03100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$5$	−0.503883	−0.225344	−0.112672	−	0.993632i	$-0.535941\pi$
$5$	−0.503883	−0.225344	−0.112672	+	0.993632i	$0.535941\pi$
$6$	1.00000	0.408248
$7$	2.75905	1.04282	0.521411	−	0.853305i	$-0.325406\pi$
$7$	2.75905	1.04282	0.521411	+	0.853305i	$0.325406\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.503883	0.159342
$11$	6.03100	1.81841	0.909207	−	0.416344i	$-0.136689\pi$
$11$	6.03100	1.81841	0.909207	+	0.416344i	$0.136689\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.75905	−0.737387
$15$	0.503883	0.130102
$16$	1.00000	0.250000
$17$	−6.29407	−1.52654	−0.763269	−	0.646081i	$-0.776407\pi$
$17$	−6.29407	−1.52654	−0.763269	+	0.646081i	$0.776407\pi$
$18$	−1.00000	−0.235702
$19$	−6.31941	−1.44977	−0.724886	−	0.688869i	$-0.758107\pi$
$19$	−6.31941	−1.44977	−0.724886	+	0.688869i	$0.758107\pi$
$20$	−0.503883	−0.112672
$21$	−2.75905	−0.602074
$22$	−6.03100	−1.28581
$23$	−7.22879	−1.50731	−0.753653	−	0.657272i	$-0.771710\pi$
$23$	−7.22879	−1.50731	−0.753653	+	0.657272i	$0.771710\pi$
$24$	1.00000	0.204124
$25$	−4.74610	−0.949220
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	2.75905	0.521411
$29$	9.35117	1.73647	0.868234	−	0.496155i	$-0.165255\pi$
$29$	9.35117	1.73647	0.868234	+	0.496155i	$0.165255\pi$
$30$	−0.503883	−0.0919961
$31$	2.92979	0.526206	0.263103	−	0.964768i	$-0.415254\pi$
$31$	2.92979	0.526206	0.263103	+	0.964768i	$0.415254\pi$
$32$	−1.00000	−0.176777
$33$	−6.03100	−1.04986
$34$	6.29407	1.07942
$35$	−1.39024	−0.234993
$36$	1.00000	0.166667
$37$	−2.31736	−0.380972	−0.190486	−	0.981690i	$-0.561006\pi$
$37$	−2.31736	−0.380972	−0.190486	+	0.981690i	$0.561006\pi$
$38$	6.31941	1.02514
$39$	1.00000	0.160128
$40$	0.503883	0.0796710
$41$	−3.89839	−0.608827	−0.304413	−	0.952540i	$-0.598460\pi$
$41$	−3.89839	−0.608827	−0.304413	+	0.952540i	$0.598460\pi$
$42$	2.75905	0.425731
$43$	4.29142	0.654435	0.327217	−	0.944949i	$-0.393889\pi$
$43$	4.29142	0.654435	0.327217	+	0.944949i	$0.393889\pi$
$44$	6.03100	0.909207
$45$	−0.503883	−0.0751145
$46$	7.22879	1.06583
$47$	−6.99841	−1.02082	−0.510411	−	0.859930i	$-0.670507\pi$
$47$	−6.99841	−1.02082	−0.510411	+	0.859930i	$0.670507\pi$
$48$	−1.00000	−0.144338
$49$	0.612353	0.0874790
$50$	4.74610	0.671200
$51$	6.29407	0.881347
$52$	−1.00000	−0.138675
$53$	3.51811	0.483249	0.241625	−	0.970370i	$-0.422320\pi$
$53$	3.51811	0.483249	0.241625	+	0.970370i	$0.422320\pi$
$54$	1.00000	0.136083
$55$	−3.03892	−0.409768
$56$	−2.75905	−0.368693
$57$	6.31941	0.837026
$58$	−9.35117	−1.22787
$59$	−9.24734	−1.20390	−0.601951	−	0.798533i	$-0.705610\pi$
$59$	−9.24734	−1.20390	−0.601951	+	0.798533i	$0.705610\pi$
$60$	0.503883	0.0650511
$61$	−0.178206	−0.0228169	−0.0114085	−	0.999935i	$-0.503632\pi$
$61$	−0.178206	−0.0228169	−0.0114085	+	0.999935i	$0.503632\pi$
$62$	−2.92979	−0.372084
$63$	2.75905	0.347608
$64$	1.00000	0.125000
$65$	0.503883	0.0624990
$66$	6.03100	0.742365
$67$	9.08548	1.10997	0.554984	−	0.831861i	$-0.312724\pi$
$67$	9.08548	1.10997	0.554984	+	0.831861i	$0.312724\pi$
$68$	−6.29407	−0.763269
$69$	7.22879	0.870244
$70$	1.39024	0.166165
$71$	12.4784	1.48091	0.740454	−	0.672107i	$-0.234611\pi$
$71$	12.4784	1.48091	0.740454	+	0.672107i	$0.234611\pi$
$72$	−1.00000	−0.117851
$73$	4.54685	0.532168	0.266084	−	0.963950i	$-0.414270\pi$
$73$	4.54685	0.532168	0.266084	+	0.963950i	$0.414270\pi$
$74$	2.31736	0.269388
$75$	4.74610	0.548033
$76$	−6.31941	−0.724886
$77$	16.6398	1.89628
$78$	−1.00000	−0.113228
$79$	10.0968	1.13598	0.567992	−	0.823034i	$-0.307720\pi$
$79$	10.0968	1.13598	0.567992	+	0.823034i	$0.307720\pi$
$80$	−0.503883	−0.0563359
$81$	1.00000	0.111111
$82$	3.89839	0.430506
$83$	−0.865830	−0.0950372	−0.0475186	−	0.998870i	$-0.515131\pi$
$83$	−0.865830	−0.0950372	−0.0475186	+	0.998870i	$0.515131\pi$
$84$	−2.75905	−0.301037
$85$	3.17148	0.343995
$86$	−4.29142	−0.462755
$87$	−9.35117	−1.00255
$88$	−6.03100	−0.642907
$89$	0.262117	0.0277843	0.0138922	−	0.999903i	$-0.495578\pi$
$89$	0.262117	0.0277843	0.0138922	+	0.999903i	$0.495578\pi$
$90$	0.503883	0.0531140
$91$	−2.75905	−0.289227
$92$	−7.22879	−0.753653
$93$	−2.92979	−0.303805
$94$	6.99841	0.721830
$95$	3.18424	0.326697
$96$	1.00000	0.102062
$97$	18.9602	1.92512	0.962561	−	0.271066i	$-0.0873761\pi$
$97$	18.9602	1.92512	0.962561	+	0.271066i	$0.0873761\pi$
$98$	−0.612353	−0.0618570
$99$	6.03100	0.606138
$100$	−4.74610	−0.474610
$101$	10.3574	1.03060	0.515298	−	0.857011i	$-0.327681\pi$
$101$	10.3574	1.03060	0.515298	+	0.857011i	$0.327681\pi$
$102$	−6.29407	−0.623206
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	1.39024	0.135673
$106$	−3.51811	−0.341709
$107$	2.12190	0.205132	0.102566	−	0.994726i	$-0.467295\pi$
$107$	2.12190	0.205132	0.102566	+	0.994726i	$0.467295\pi$
$108$	−1.00000	−0.0962250
$109$	10.6953	1.02443	0.512213	−	0.858859i	$-0.328826\pi$
$109$	10.6953	1.02443	0.512213	+	0.858859i	$0.328826\pi$
$110$	3.03892	0.289750
$111$	2.31736	0.219954
$112$	2.75905	0.260706
$113$	−12.7474	−1.19917	−0.599585	−	0.800311i	$-0.704668\pi$
$113$	−12.7474	−1.19917	−0.599585	+	0.800311i	$0.704668\pi$
$114$	−6.31941	−0.591867
$115$	3.64247	0.339662
$116$	9.35117	0.868234
$117$	−1.00000	−0.0924500
$118$	9.24734	0.851287
$119$	−17.3657	−1.59191
$120$	−0.503883	−0.0459981
$121$	25.3729	2.30663
$122$	0.178206	0.0161340
$123$	3.89839	0.351506
$124$	2.92979	0.263103
$125$	4.91090	0.439244
$126$	−2.75905	−0.245796
$127$	−8.59083	−0.762313	−0.381157	−	0.924510i	$-0.624474\pi$
$127$	−8.59083	−0.762313	−0.381157	+	0.924510i	$0.624474\pi$
$128$	−1.00000	−0.0883883
$129$	−4.29142	−0.377838
$130$	−0.503883	−0.0441935
$131$	19.8384	1.73329	0.866645	−	0.498925i	$-0.166272\pi$
$131$	19.8384	1.73329	0.866645	+	0.498925i	$0.166272\pi$
$132$	−6.03100	−0.524931
$133$	−17.4356	−1.51185
$134$	−9.08548	−0.784866
$135$	0.503883	0.0433674
$136$	6.29407	0.539712
$137$	−1.81911	−0.155417	−0.0777084	−	0.996976i	$-0.524760\pi$
$137$	−1.81911	−0.155417	−0.0777084	+	0.996976i	$0.524760\pi$
$138$	−7.22879	−0.615355
$139$	13.6876	1.16097	0.580485	−	0.814271i	$-0.302863\pi$
$139$	13.6876	1.16097	0.580485	+	0.814271i	$0.302863\pi$
$140$	−1.39024	−0.117497
$141$	6.99841	0.589372
$142$	−12.4784	−1.04716
$143$	−6.03100	−0.504337
$144$	1.00000	0.0833333
$145$	−4.71190	−0.391302
$146$	−4.54685	−0.376300
$147$	−0.612353	−0.0505060
$148$	−2.31736	−0.190486
$149$	7.98738	0.654352	0.327176	−	0.944963i	$-0.393903\pi$
$149$	7.98738	0.654352	0.327176	+	0.944963i	$0.393903\pi$
$150$	−4.74610	−0.387518
$151$	−14.5122	−1.18098	−0.590492	−	0.807043i	$-0.701066\pi$
$151$	−14.5122	−1.18098	−0.590492	+	0.807043i	$0.701066\pi$
$152$	6.31941	0.512572
$153$	−6.29407	−0.508846
$154$	−16.6398	−1.34088
$155$	−1.47627	−0.118577
$156$	1.00000	0.0800641
$157$	23.3549	1.86393	0.931963	−	0.362553i	$-0.118095\pi$
$157$	23.3549	1.86393	0.931963	+	0.362553i	$0.118095\pi$
$158$	−10.0968	−0.803262
$159$	−3.51811	−0.279004
$160$	0.503883	0.0398355
$161$	−19.9446	−1.57185
$162$	−1.00000	−0.0785674
$163$	10.9941	0.861126	0.430563	−	0.902561i	$-0.358315\pi$
$163$	10.9941	0.861126	0.430563	+	0.902561i	$0.358315\pi$
$164$	−3.89839	−0.304413
$165$	3.03892	0.236580
$166$	0.865830	0.0672015
$167$	−16.8168	−1.30132	−0.650662	−	0.759367i	$-0.725509\pi$
$167$	−16.8168	−1.30132	−0.650662	+	0.759367i	$0.725509\pi$
$168$	2.75905	0.212865
$169$	1.00000	0.0769231
$170$	−3.17148	−0.243241
$171$	−6.31941	−0.483257
$172$	4.29142	0.327217
$173$	−3.12094	−0.237281	−0.118640	−	0.992937i	$-0.537854\pi$
$173$	−3.12094	−0.237281	−0.118640	+	0.992937i	$0.537854\pi$
$174$	9.35117	0.708910
$175$	−13.0947	−0.989868
$176$	6.03100	0.454604
$177$	9.24734	0.695073
$178$	−0.262117	−0.0196465
$179$	−7.23510	−0.540777	−0.270388	−	0.962751i	$-0.587152\pi$
$179$	−7.23510	−0.540777	−0.270388	+	0.962751i	$0.587152\pi$
$180$	−0.503883	−0.0375573
$181$	−7.50319	−0.557707	−0.278854	−	0.960334i	$-0.589954\pi$
$181$	−7.50319	−0.557707	−0.278854	+	0.960334i	$0.589954\pi$
$182$	2.75905	0.204514
$183$	0.178206	0.0131733
$184$	7.22879	0.532913
$185$	1.16768	0.0858496
$186$	2.92979	0.214823
$187$	−37.9596	−2.77588
$188$	−6.99841	−0.510411
$189$	−2.75905	−0.200691
$190$	−3.18424	−0.231009
$191$	−2.89259	−0.209300	−0.104650	−	0.994509i	$-0.533372\pi$
$191$	−2.89259	−0.209300	−0.104650	+	0.994509i	$0.533372\pi$
$192$	−1.00000	−0.0721688
$193$	20.2076	1.45458	0.727288	−	0.686333i	$-0.240781\pi$
$193$	20.2076	1.45458	0.727288	+	0.686333i	$0.240781\pi$
$194$	−18.9602	−1.36127
$195$	−0.503883	−0.0360838
$196$	0.612353	0.0437395
$197$	−16.8072	−1.19746	−0.598732	−	0.800950i	$-0.704328\pi$
$197$	−16.8072	−1.19746	−0.598732	+	0.800950i	$0.704328\pi$
$198$	−6.03100	−0.428604
$199$	1.86963	0.132535	0.0662674	−	0.997802i	$-0.478891\pi$
$199$	1.86963	0.132535	0.0662674	+	0.997802i	$0.478891\pi$
$200$	4.74610	0.335600
$201$	−9.08548	−0.640841
$202$	−10.3574	−0.728741
$203$	25.8003	1.81083
$204$	6.29407	0.440673
$205$	1.96434	0.137195
$206$	−1.00000	−0.0696733
$207$	−7.22879	−0.502435
$208$	−1.00000	−0.0693375
$209$	−38.1123	−2.63629
$210$	−1.39024	−0.0959356
$211$	3.95736	0.272436	0.136218	−	0.990679i	$-0.456505\pi$
$211$	3.95736	0.272436	0.136218	+	0.990679i	$0.456505\pi$
$212$	3.51811	0.241625
$213$	−12.4784	−0.855003
$214$	−2.12190	−0.145050
$215$	−2.16237	−0.147473
$216$	1.00000	0.0680414
$217$	8.08344	0.548740
$218$	−10.6953	−0.724378
$219$	−4.54685	−0.307248
$220$	−3.03892	−0.204884
$221$	6.29407	0.423385
$222$	−2.31736	−0.155531
$223$	−11.4512	−0.766830	−0.383415	−	0.923576i	$-0.625252\pi$
$223$	−11.4512	−0.766830	−0.383415	+	0.923576i	$0.625252\pi$
$224$	−2.75905	−0.184347
$225$	−4.74610	−0.316407
$226$	12.7474	0.847941
$227$	−9.36186	−0.621369	−0.310684	−	0.950513i	$-0.600558\pi$
$227$	−9.36186	−0.621369	−0.310684	+	0.950513i	$0.600558\pi$
$228$	6.31941	0.418513
$229$	13.4812	0.890861	0.445431	−	0.895317i	$-0.353051\pi$
$229$	13.4812	0.890861	0.445431	+	0.895317i	$0.353051\pi$
$230$	−3.64247	−0.240177
$231$	−16.6398	−1.09482
$232$	−9.35117	−0.613934
$233$	−23.5946	−1.54574	−0.772868	−	0.634566i	$-0.781179\pi$
$233$	−23.5946	−1.54574	−0.772868	+	0.634566i	$0.781179\pi$
$234$	1.00000	0.0653720
$235$	3.52638	0.230036
$236$	−9.24734	−0.601951
$237$	−10.0968	−0.655861
$238$	17.3657	1.12565
$239$	28.9815	1.87466	0.937329	−	0.348445i	$-0.113290\pi$
$239$	28.9815	1.87466	0.937329	+	0.348445i	$0.113290\pi$
$240$	0.503883	0.0325255
$241$	13.8376	0.891361	0.445681	−	0.895192i	$-0.352962\pi$
$241$	13.8376	0.891361	0.445681	+	0.895192i	$0.352962\pi$
$242$	−25.3729	−1.63103
$243$	−1.00000	−0.0641500
$244$	−0.178206	−0.0114085
$245$	−0.308554	−0.0197128
$246$	−3.89839	−0.248553
$247$	6.31941	0.402094
$248$	−2.92979	−0.186042
$249$	0.865830	0.0548698
$250$	−4.91090	−0.310593
$251$	−2.15987	−0.136330	−0.0681650	−	0.997674i	$-0.521714\pi$
$251$	−2.15987	−0.136330	−0.0681650	+	0.997674i	$0.521714\pi$
$252$	2.75905	0.173804
$253$	−43.5968	−2.74091
$254$	8.59083	0.539037
$255$	−3.17148	−0.198606
$256$	1.00000	0.0625000
$257$	16.0148	0.998978	0.499489	−	0.866320i	$-0.333521\pi$
$257$	16.0148	0.998978	0.499489	+	0.866320i	$0.333521\pi$
$258$	4.29142	0.267172
$259$	−6.39372	−0.397286
$260$	0.503883	0.0312495
$261$	9.35117	0.578823
$262$	−19.8384	−1.22562
$263$	4.66348	0.287563	0.143781	−	0.989609i	$-0.454074\pi$
$263$	4.66348	0.287563	0.143781	+	0.989609i	$0.454074\pi$
$264$	6.03100	0.371182
$265$	−1.77272	−0.108897
$266$	17.4356	1.06904
$267$	−0.262117	−0.0160413
$268$	9.08548	0.554984
$269$	−4.05727	−0.247376	−0.123688	−	0.992321i	$-0.539472\pi$
$269$	−4.05727	−0.247376	−0.123688	+	0.992321i	$0.539472\pi$
$270$	−0.503883	−0.0306654
$271$	−15.6485	−0.950581	−0.475291	−	0.879829i	$-0.657657\pi$
$271$	−15.6485	−0.950581	−0.475291	+	0.879829i	$0.657657\pi$
$272$	−6.29407	−0.381634
$273$	2.75905	0.166985
$274$	1.81911	0.109896
$275$	−28.6237	−1.72608
$276$	7.22879	0.435122
$277$	19.1029	1.14778	0.573892	−	0.818931i	$-0.305433\pi$
$277$	19.1029	1.14778	0.573892	+	0.818931i	$0.305433\pi$
$278$	−13.6876	−0.820930
$279$	2.92979	0.175402
$280$	1.39024	0.0830827
$281$	−3.80257	−0.226842	−0.113421	−	0.993547i	$-0.536181\pi$
$281$	−3.80257	−0.226842	−0.113421	+	0.993547i	$0.536181\pi$
$282$	−6.99841	−0.416749
$283$	4.96282	0.295009	0.147505	−	0.989061i	$-0.452876\pi$
$283$	4.96282	0.295009	0.147505	+	0.989061i	$0.452876\pi$
$284$	12.4784	0.740454
$285$	−3.18424	−0.188618
$286$	6.03100	0.356620
$287$	−10.7559	−0.634898
$288$	−1.00000	−0.0589256
$289$	22.6154	1.33032
$290$	4.71190	0.276692
$291$	−18.9602	−1.11147
$292$	4.54685	0.266084
$293$	4.80936	0.280966	0.140483	−	0.990083i	$-0.455135\pi$
$293$	4.80936	0.280966	0.140483	+	0.990083i	$0.455135\pi$
$294$	0.612353	0.0357132
$295$	4.65958	0.271291
$296$	2.31736	0.134694
$297$	−6.03100	−0.349954
$298$	−7.98738	−0.462697
$299$	7.22879	0.418052
$300$	4.74610	0.274016
$301$	11.8402	0.682460
$302$	14.5122	0.835082
$303$	−10.3574	−0.595015
$304$	−6.31941	−0.362443
$305$	0.0897949	0.00514164
$306$	6.29407	0.359808
$307$	−4.41310	−0.251869	−0.125935	−	0.992039i	$-0.540193\pi$
$307$	−4.41310	−0.251869	−0.125935	+	0.992039i	$0.540193\pi$
$308$	16.6398	0.948142
$309$	−1.00000	−0.0568880
$310$	1.47627	0.0838467
$311$	12.0144	0.681275	0.340638	−	0.940195i	$-0.389357\pi$
$311$	12.0144	0.681275	0.340638	+	0.940195i	$0.389357\pi$
$312$	−1.00000	−0.0566139
$313$	24.5115	1.38547	0.692735	−	0.721192i	$-0.256405\pi$
$313$	24.5115	1.38547	0.692735	+	0.721192i	$0.256405\pi$
$314$	−23.3549	−1.31799
$315$	−1.39024	−0.0783311
$316$	10.0968	0.567992
$317$	−10.1665	−0.571008	−0.285504	−	0.958378i	$-0.592161\pi$
$317$	−10.1665	−0.571008	−0.285504	+	0.958378i	$0.592161\pi$
$318$	3.51811	0.197286
$319$	56.3969	3.15762
$320$	−0.503883	−0.0281679
$321$	−2.12190	−0.118433
$322$	19.9446	1.11147
$323$	39.7748	2.21313
$324$	1.00000	0.0555556
$325$	4.74610	0.263266
$326$	−10.9941	−0.608908
$327$	−10.6953	−0.591452
$328$	3.89839	0.215253
$329$	−19.3089	−1.06454
$330$	−3.03892	−0.167287
$331$	14.2271	0.781991	0.390995	−	0.920393i	$-0.372131\pi$
$331$	14.2271	0.781991	0.390995	+	0.920393i	$0.372131\pi$
$332$	−0.865830	−0.0475186
$333$	−2.31736	−0.126991
$334$	16.8168	0.920175
$335$	−4.57802	−0.250124
$336$	−2.75905	−0.150518
$337$	33.4153	1.82025	0.910124	−	0.414337i	$-0.135986\pi$
$337$	33.4153	1.82025	0.910124	+	0.414337i	$0.135986\pi$
$338$	−1.00000	−0.0543928
$339$	12.7474	0.692341
$340$	3.17148	0.171998
$341$	17.6696	0.956861
$342$	6.31941	0.341714
$343$	−17.6238	−0.951598
$344$	−4.29142	−0.231378
$345$	−3.64247	−0.196104
$346$	3.12094	0.167783
$347$	2.61928	0.140610	0.0703051	−	0.997526i	$-0.477603\pi$
$347$	2.61928	0.140610	0.0703051	+	0.997526i	$0.477603\pi$
$348$	−9.35117	−0.501275
$349$	−11.5718	−0.619426	−0.309713	−	0.950830i	$-0.600233\pi$
$349$	−11.5718	−0.619426	−0.309713	+	0.950830i	$0.600233\pi$
$350$	13.0947	0.699943
$351$	1.00000	0.0533761
$352$	−6.03100	−0.321453
$353$	34.9353	1.85942	0.929709	−	0.368294i	$-0.120058\pi$
$353$	34.9353	1.85942	0.929709	+	0.368294i	$0.120058\pi$
$354$	−9.24734	−0.491491
$355$	−6.28764	−0.333713
$356$	0.262117	0.0138922
$357$	17.3657	0.919088
$358$	7.23510	0.382387
$359$	3.37328	0.178035	0.0890175	−	0.996030i	$-0.471627\pi$
$359$	3.37328	0.178035	0.0890175	+	0.996030i	$0.471627\pi$
$360$	0.503883	0.0265570
$361$	20.9349	1.10184
$362$	7.50319	0.394359
$363$	−25.3729	−1.33173
$364$	−2.75905	−0.144613
$365$	−2.29108	−0.119921
$366$	−0.178206	−0.00931496
$367$	34.0021	1.77490	0.887448	−	0.460907i	$-0.152476\pi$
$367$	34.0021	1.77490	0.887448	+	0.460907i	$0.152476\pi$
$368$	−7.22879	−0.376827
$369$	−3.89839	−0.202942
$370$	−1.16768	−0.0607048
$371$	9.70663	0.503943
$372$	−2.92979	−0.151903
$373$	−0.141490	−0.00732607	−0.00366303	−	0.999993i	$-0.501166\pi$
$373$	−0.141490	−0.00732607	−0.00366303	+	0.999993i	$0.501166\pi$
$374$	37.9596	1.96284
$375$	−4.91090	−0.253598
$376$	6.99841	0.360915
$377$	−9.35117	−0.481610
$378$	2.75905	0.141910
$379$	30.8204	1.58314	0.791569	−	0.611080i	$-0.209264\pi$
$379$	30.8204	1.58314	0.791569	+	0.611080i	$0.209264\pi$
$380$	3.18424	0.163348
$381$	8.59083	0.440122
$382$	2.89259	0.147998
$383$	−21.3338	−1.09011	−0.545054	−	0.838401i	$-0.683491\pi$
$383$	−21.3338	−1.09011	−0.545054	+	0.838401i	$0.683491\pi$
$384$	1.00000	0.0510310
$385$	−8.38453	−0.427315
$386$	−20.2076	−1.02854
$387$	4.29142	0.218145
$388$	18.9602	0.962561
$389$	22.0340	1.11717	0.558585	−	0.829447i	$-0.311344\pi$
$389$	22.0340	1.11717	0.558585	+	0.829447i	$0.311344\pi$
$390$	0.503883	0.0255151
$391$	45.4985	2.30096
$392$	−0.612353	−0.0309285
$393$	−19.8384	−1.00072
$394$	16.8072	0.846734
$395$	−5.08763	−0.255987
$396$	6.03100	0.303069
$397$	−29.2872	−1.46988	−0.734942	−	0.678130i	$-0.762790\pi$
$397$	−29.2872	−1.46988	−0.734942	+	0.678130i	$0.762790\pi$
$398$	−1.86963	−0.0937162
$399$	17.4356	0.872870
$400$	−4.74610	−0.237305
$401$	−11.9102	−0.594767	−0.297383	−	0.954758i	$-0.596114\pi$
$401$	−11.9102	−0.594767	−0.297383	+	0.954758i	$0.596114\pi$
$402$	9.08548	0.453143
$403$	−2.92979	−0.145943
$404$	10.3574	0.515298
$405$	−0.503883	−0.0250382
$406$	−25.8003	−1.28045
$407$	−13.9760	−0.692765
$408$	−6.29407	−0.311603
$409$	−29.6075	−1.46400	−0.732000	−	0.681305i	$-0.761413\pi$
$409$	−29.6075	−1.46400	−0.732000	+	0.681305i	$0.761413\pi$
$410$	−1.96434	−0.0970116
$411$	1.81911	0.0897299
$412$	1.00000	0.0492665
$413$	−25.5139	−1.25546
$414$	7.22879	0.355276
$415$	0.436277	0.0214160
$416$	1.00000	0.0490290
$417$	−13.6876	−0.670287
$418$	38.1123	1.86414
$419$	3.51354	0.171648	0.0858239	−	0.996310i	$-0.472648\pi$
$419$	3.51354	0.171648	0.0858239	+	0.996310i	$0.472648\pi$
$420$	1.39024	0.0678367
$421$	−23.4775	−1.14422	−0.572112	−	0.820175i	$-0.693876\pi$
$421$	−23.4775	−1.14422	−0.572112	+	0.820175i	$0.693876\pi$
$422$	−3.95736	−0.192641
$423$	−6.99841	−0.340274
$424$	−3.51811	−0.170854
$425$	29.8723	1.44902
$426$	12.4784	0.604578
$427$	−0.491678	−0.0237940
$428$	2.12190	0.102566
$429$	6.03100	0.291179
$430$	2.16237	0.104279
$431$	−3.68034	−0.177276	−0.0886379	−	0.996064i	$-0.528251\pi$
$431$	−3.68034	−0.177276	−0.0886379	+	0.996064i	$0.528251\pi$
$432$	−1.00000	−0.0481125
$433$	−22.3102	−1.07216	−0.536080	−	0.844167i	$-0.680095\pi$
$433$	−22.3102	−1.07216	−0.536080	+	0.844167i	$0.680095\pi$
$434$	−8.08344	−0.388018
$435$	4.71190	0.225918
$436$	10.6953	0.512213
$437$	45.6817	2.18525
$438$	4.54685	0.217257
$439$	−19.5096	−0.931142	−0.465571	−	0.885010i	$-0.654151\pi$
$439$	−19.5096	−0.931142	−0.465571	+	0.885010i	$0.654151\pi$
$440$	3.03892	0.144875
$441$	0.612353	0.0291597
$442$	−6.29407	−0.299379
$443$	−31.9728	−1.51907	−0.759536	−	0.650466i	$-0.774574\pi$
$443$	−31.9728	−1.51907	−0.759536	+	0.650466i	$0.774574\pi$
$444$	2.31736	0.109977
$445$	−0.132076	−0.00626102
$446$	11.4512	0.542231
$447$	−7.98738	−0.377790
$448$	2.75905	0.130353
$449$	25.0632	1.18281	0.591403	−	0.806376i	$-0.298574\pi$
$449$	25.0632	1.18281	0.591403	+	0.806376i	$0.298574\pi$
$450$	4.74610	0.223733
$451$	−23.5112	−1.10710
$452$	−12.7474	−0.599585
$453$	14.5122	0.681842
$454$	9.36186	0.439374
$455$	1.39024	0.0651754
$456$	−6.31941	−0.295933
$457$	41.1417	1.92453	0.962264	−	0.272116i	$-0.0877235\pi$
$457$	41.1417	1.92453	0.962264	+	0.272116i	$0.0877235\pi$
$458$	−13.4812	−0.629934
$459$	6.29407	0.293782
$460$	3.64247	0.169831
$461$	−21.6234	−1.00710	−0.503551	−	0.863965i	$-0.667974\pi$
$461$	−21.6234	−1.00710	−0.503551	+	0.863965i	$0.667974\pi$
$462$	16.6398	0.774155
$463$	−37.9222	−1.76239	−0.881196	−	0.472750i	$-0.843261\pi$
$463$	−37.9222	−1.76239	−0.881196	+	0.472750i	$0.843261\pi$
$464$	9.35117	0.434117
$465$	1.47627	0.0684606
$466$	23.5946	1.09300
$467$	28.5116	1.31936	0.659680	−	0.751546i	$-0.270692\pi$
$467$	28.5116	1.31936	0.659680	+	0.751546i	$0.270692\pi$
$468$	−1.00000	−0.0462250
$469$	25.0673	1.15750
$470$	−3.52638	−0.162660
$471$	−23.3549	−1.07614
$472$	9.24734	0.425643
$473$	25.8815	1.19003
$474$	10.0968	0.463764
$475$	29.9926	1.37615
$476$	−17.3657	−0.795954
$477$	3.51811	0.161083
$478$	−28.9815	−1.32558
$479$	−6.33889	−0.289632	−0.144816	−	0.989459i	$-0.546259\pi$
$479$	−6.33889	−0.289632	−0.144816	+	0.989459i	$0.546259\pi$
$480$	−0.503883	−0.0229990
$481$	2.31736	0.105663
$482$	−13.8376	−0.630288
$483$	19.9446	0.907510
$484$	25.3729	1.15332
$485$	−9.55376	−0.433814
$486$	1.00000	0.0453609
$487$	7.00106	0.317248	0.158624	−	0.987339i	$-0.449294\pi$
$487$	7.00106	0.317248	0.158624	+	0.987339i	$0.449294\pi$
$488$	0.178206	0.00806699
$489$	−10.9941	−0.497171
$490$	0.308554	0.0139391
$491$	−12.4695	−0.562739	−0.281369	−	0.959600i	$-0.590789\pi$
$491$	−12.4695	−0.562739	−0.281369	+	0.959600i	$0.590789\pi$
$492$	3.89839	0.175753
$493$	−58.8569	−2.65078
$494$	−6.31941	−0.284324
$495$	−3.03892	−0.136589
$496$	2.92979	0.131552
$497$	34.4284	1.54432
$498$	−0.865830	−0.0387988
$499$	27.5059	1.23133	0.615666	−	0.788007i	$-0.288887\pi$
$499$	27.5059	1.23133	0.615666	+	0.788007i	$0.288887\pi$
$500$	4.91090	0.219622
$501$	16.8168	0.751320
$502$	2.15987	0.0963998
$503$	15.9920	0.713048	0.356524	−	0.934286i	$-0.383962\pi$
$503$	15.9920	0.713048	0.356524	+	0.934286i	$0.383962\pi$
$504$	−2.75905	−0.122898
$505$	−5.21890	−0.232238
$506$	43.5968	1.93811
$507$	−1.00000	−0.0444116
$508$	−8.59083	−0.381157
$509$	−22.1900	−0.983554	−0.491777	−	0.870721i	$-0.663653\pi$
$509$	−22.1900	−0.983554	−0.491777	+	0.870721i	$0.663653\pi$
$510$	3.17148	0.140435
$511$	12.5450	0.554957
$512$	−1.00000	−0.0441942
$513$	6.31941	0.279009
$514$	−16.0148	−0.706384
$515$	−0.503883	−0.0222038
$516$	−4.29142	−0.188919
$517$	−42.2074	−1.85628
$518$	6.39372	0.280924
$519$	3.12094	0.136994
$520$	−0.503883	−0.0220967
$521$	19.7796	0.866559	0.433279	−	0.901260i	$-0.357356\pi$
$521$	19.7796	0.866559	0.433279	+	0.901260i	$0.357356\pi$
$522$	−9.35117	−0.409289
$523$	26.0735	1.14011	0.570057	−	0.821605i	$-0.306921\pi$
$523$	26.0735	1.14011	0.570057	+	0.821605i	$0.306921\pi$
$524$	19.8384	0.866645
$525$	13.0947	0.571501
$526$	−4.66348	−0.203337
$527$	−18.4403	−0.803274
$528$	−6.03100	−0.262466
$529$	29.2554	1.27197
$530$	1.77272	0.0770019
$531$	−9.24734	−0.401301
$532$	−17.4356	−0.755927
$533$	3.89839	0.168858
$534$	0.262117	0.0113429
$535$	−1.06919	−0.0462252
$536$	−9.08548	−0.392433
$537$	7.23510	0.312218
$538$	4.05727	0.174921
$539$	3.69310	0.159073
$540$	0.503883	0.0216837
$541$	−13.4090	−0.576499	−0.288249	−	0.957555i	$-0.593073\pi$
$541$	−13.4090	−0.576499	−0.288249	+	0.957555i	$0.593073\pi$
$542$	15.6485	0.672163
$543$	7.50319	0.321993
$544$	6.29407	0.269856
$545$	−5.38919	−0.230848
$546$	−2.75905	−0.118076
$547$	12.3792	0.529298	0.264649	−	0.964345i	$-0.414744\pi$
$547$	12.3792	0.529298	0.264649	+	0.964345i	$0.414744\pi$
$548$	−1.81911	−0.0777084
$549$	−0.178206	−0.00760563
$550$	28.6237	1.22052
$551$	−59.0938	−2.51748
$552$	−7.22879	−0.307678
$553$	27.8577	1.18463
$554$	−19.1029	−0.811606
$555$	−1.16768	−0.0495653
$556$	13.6876	0.580485
$557$	9.07673	0.384593	0.192297	−	0.981337i	$-0.438406\pi$
$557$	9.07673	0.384593	0.192297	+	0.981337i	$0.438406\pi$
$558$	−2.92979	−0.124028
$559$	−4.29142	−0.181508
$560$	−1.39024	−0.0587483
$561$	37.9596	1.60265
$562$	3.80257	0.160402
$563$	−11.8934	−0.501247	−0.250623	−	0.968085i	$-0.580636\pi$
$563$	−11.8934	−0.501247	−0.250623	+	0.968085i	$0.580636\pi$
$564$	6.99841	0.294686
$565$	6.42318	0.270225
$566$	−4.96282	−0.208603
$567$	2.75905	0.115869
$568$	−12.4784	−0.523580
$569$	−15.3651	−0.644137	−0.322068	−	0.946716i	$-0.604378\pi$
$569$	−15.3651	−0.644137	−0.322068	+	0.946716i	$0.604378\pi$
$570$	3.18424	0.133373
$571$	11.4601	0.479592	0.239796	−	0.970823i	$-0.422919\pi$
$571$	11.4601	0.479592	0.239796	+	0.970823i	$0.422919\pi$
$572$	−6.03100	−0.252169
$573$	2.89259	0.120840
$574$	10.7559	0.448941
$575$	34.3086	1.43077
$576$	1.00000	0.0416667
$577$	4.06515	0.169234	0.0846172	−	0.996414i	$-0.473033\pi$
$577$	4.06515	0.169234	0.0846172	+	0.996414i	$0.473033\pi$
$578$	−22.6154	−0.940676
$579$	−20.2076	−0.839800
$580$	−4.71190	−0.195651
$581$	−2.38887	−0.0991070
$582$	18.9602	0.785928
$583$	21.2177	0.878748
$584$	−4.54685	−0.188150
$585$	0.503883	0.0208330
$586$	−4.80936	−0.198673
$587$	23.9173	0.987173	0.493586	−	0.869697i	$-0.335686\pi$
$587$	23.9173	0.987173	0.493586	+	0.869697i	$0.335686\pi$
$588$	−0.612353	−0.0252530
$589$	−18.5146	−0.762879
$590$	−4.65958	−0.191832
$591$	16.8072	0.691356
$592$	−2.31736	−0.0952430
$593$	−25.2899	−1.03853	−0.519266	−	0.854613i	$-0.673795\pi$
$593$	−25.2899	−1.03853	−0.519266	+	0.854613i	$0.673795\pi$
$594$	6.03100	0.247455
$595$	8.75027	0.358726
$596$	7.98738	0.327176
$597$	−1.86963	−0.0765190
$598$	−7.22879	−0.295607
$599$	25.4212	1.03868	0.519342	−	0.854566i	$-0.326177\pi$
$599$	25.4212	1.03868	0.519342	+	0.854566i	$0.326177\pi$
$600$	−4.74610	−0.193759
$601$	−18.3380	−0.748025	−0.374012	−	0.927424i	$-0.622018\pi$
$601$	−18.3380	−0.748025	−0.374012	+	0.927424i	$0.622018\pi$
$602$	−11.8402	−0.482572
$603$	9.08548	0.369989
$604$	−14.5122	−0.590492
$605$	−12.7850	−0.519784
$606$	10.3574	0.420739
$607$	−6.87350	−0.278987	−0.139493	−	0.990223i	$-0.544547\pi$
$607$	−6.87350	−0.278987	−0.139493	+	0.990223i	$0.544547\pi$
$608$	6.31941	0.256286
$609$	−25.8003	−1.04548
$610$	−0.0897949	−0.00363569
$611$	6.99841	0.283125
$612$	−6.29407	−0.254423
$613$	10.2451	0.413794	0.206897	−	0.978363i	$-0.433664\pi$
$613$	10.2451	0.413794	0.206897	+	0.978363i	$0.433664\pi$
$614$	4.41310	0.178098
$615$	−1.96434	−0.0792097
$616$	−16.6398	−0.670438
$617$	−27.7863	−1.11863	−0.559317	−	0.828954i	$-0.688937\pi$
$617$	−27.7863	−1.11863	−0.559317	+	0.828954i	$0.688937\pi$
$618$	1.00000	0.0402259
$619$	−38.1871	−1.53487	−0.767435	−	0.641127i	$-0.778467\pi$
$619$	−38.1871	−1.53487	−0.767435	+	0.641127i	$0.778467\pi$
$620$	−1.47627	−0.0592886
$621$	7.22879	0.290081
$622$	−12.0144	−0.481734
$623$	0.723194	0.0289741
$624$	1.00000	0.0400320
$625$	21.2560	0.850239
$626$	−24.5115	−0.979676
$627$	38.1123	1.52206
$628$	23.3549	0.931963
$629$	14.5856	0.581568
$630$	1.39024	0.0553885
$631$	3.13563	0.124828	0.0624138	−	0.998050i	$-0.480120\pi$
$631$	3.13563	0.124828	0.0624138	+	0.998050i	$0.480120\pi$
$632$	−10.0968	−0.401631
$633$	−3.95736	−0.157291
$634$	10.1665	0.403764
$635$	4.32878	0.171782
$636$	−3.51811	−0.139502
$637$	−0.612353	−0.0242623
$638$	−56.3969	−2.23277
$639$	12.4784	0.493636
$640$	0.503883	0.0199177
$641$	11.2172	0.443053	0.221526	−	0.975154i	$-0.428896\pi$
$641$	11.2172	0.443053	0.221526	+	0.975154i	$0.428896\pi$
$642$	2.12190	0.0837448
$643$	−2.65135	−0.104559	−0.0522794	−	0.998632i	$-0.516649\pi$
$643$	−2.65135	−0.104559	−0.0522794	+	0.998632i	$0.516649\pi$
$644$	−19.9446	−0.785927
$645$	2.16237	0.0851434
$646$	−39.7748	−1.56492
$647$	29.2799	1.15111	0.575557	−	0.817762i	$-0.304785\pi$
$647$	29.2799	1.15111	0.575557	+	0.817762i	$0.304785\pi$
$648$	−1.00000	−0.0392837
$649$	−55.7707	−2.18919
$650$	−4.74610	−0.186157
$651$	−8.08344	−0.316815
$652$	10.9941	0.430563
$653$	−10.6861	−0.418180	−0.209090	−	0.977896i	$-0.567050\pi$
$653$	−10.6861	−0.418180	−0.209090	+	0.977896i	$0.567050\pi$
$654$	10.6953	0.418220
$655$	−9.99625	−0.390586
$656$	−3.89839	−0.152207
$657$	4.54685	0.177389
$658$	19.3089	0.752741
$659$	−31.4957	−1.22690	−0.613449	−	0.789734i	$-0.710218\pi$
$659$	−31.4957	−1.22690	−0.613449	+	0.789734i	$0.710218\pi$
$660$	3.03892	0.118290
$661$	35.2958	1.37285	0.686424	−	0.727201i	$-0.259179\pi$
$661$	35.2958	1.37285	0.686424	+	0.727201i	$0.259179\pi$
$662$	−14.2271	−0.552951
$663$	−6.29407	−0.244442
$664$	0.865830	0.0336007
$665$	8.78549	0.340687
$666$	2.31736	0.0897959
$667$	−67.5976	−2.61739
$668$	−16.8168	−0.650662
$669$	11.4512	0.442730
$670$	4.57802	0.176865
$671$	−1.07476	−0.0414906
$672$	2.75905	0.106433
$673$	−30.2560	−1.16628	−0.583141	−	0.812371i	$-0.698176\pi$
$673$	−30.2560	−1.16628	−0.583141	+	0.812371i	$0.698176\pi$
$674$	−33.4153	−1.28711
$675$	4.74610	0.182678
$676$	1.00000	0.0384615
$677$	8.31515	0.319577	0.159789	−	0.987151i	$-0.448919\pi$
$677$	8.31515	0.319577	0.159789	+	0.987151i	$0.448919\pi$
$678$	−12.7474	−0.489559
$679$	52.3123	2.00756
$680$	−3.17148	−0.121621
$681$	9.36186	0.358747
$682$	−17.6696	−0.676603
$683$	−3.33370	−0.127561	−0.0637803	−	0.997964i	$-0.520316\pi$
$683$	−3.33370	−0.127561	−0.0637803	+	0.997964i	$0.520316\pi$
$684$	−6.31941	−0.241629
$685$	0.916618	0.0350222
$686$	17.6238	0.672881
$687$	−13.4812	−0.514339
$688$	4.29142	0.163609
$689$	−3.51811	−0.134029
$690$	3.64247	0.138666
$691$	37.5626	1.42895	0.714474	−	0.699662i	$-0.246666\pi$
$691$	37.5626	1.42895	0.714474	+	0.699662i	$0.246666\pi$
$692$	−3.12094	−0.118640
$693$	16.6398	0.632095
$694$	−2.61928	−0.0994264
$695$	−6.89698	−0.261617
$696$	9.35117	0.354455
$697$	24.5368	0.929397
$698$	11.5718	0.438001
$699$	23.5946	0.892432
$700$	−13.0947	−0.494934
$701$	25.7722	0.973404	0.486702	−	0.873568i	$-0.338200\pi$
$701$	25.7722	0.973404	0.486702	+	0.873568i	$0.338200\pi$
$702$	−1.00000	−0.0377426
$703$	14.6444	0.552322
$704$	6.03100	0.227302
$705$	−3.52638	−0.132811
$706$	−34.9353	−1.31481
$707$	28.5765	1.07473
$708$	9.24734	0.347536
$709$	15.6569	0.588007	0.294004	−	0.955804i	$-0.405012\pi$
$709$	15.6569	0.588007	0.294004	+	0.955804i	$0.405012\pi$
$710$	6.28764	0.235971
$711$	10.0968	0.378661
$712$	−0.262117	−0.00982325
$713$	−21.1788	−0.793154
$714$	−17.3657	−0.649894
$715$	3.03892	0.113649
$716$	−7.23510	−0.270388
$717$	−28.9815	−1.08233
$718$	−3.37328	−0.125890
$719$	5.85120	0.218213	0.109106	−	0.994030i	$-0.465201\pi$
$719$	5.85120	0.218213	0.109106	+	0.994030i	$0.465201\pi$
$720$	−0.503883	−0.0187786
$721$	2.75905	0.102752
$722$	−20.9349	−0.779117
$723$	−13.8376	−0.514628
$724$	−7.50319	−0.278854
$725$	−44.3816	−1.64829
$726$	25.3729	0.941678
$727$	−10.2008	−0.378326	−0.189163	−	0.981946i	$-0.560577\pi$
$727$	−10.2008	−0.378326	−0.189163	+	0.981946i	$0.560577\pi$
$728$	2.75905	0.102257
$729$	1.00000	0.0370370
$730$	2.29108	0.0847967
$731$	−27.0105	−0.999019
$732$	0.178206	0.00658667
$733$	−27.2842	−1.00777	−0.503883	−	0.863772i	$-0.668096\pi$
$733$	−27.2842	−1.00777	−0.503883	+	0.863772i	$0.668096\pi$
$734$	−34.0021	−1.25504
$735$	0.308554	0.0113812
$736$	7.22879	0.266457
$737$	54.7945	2.01838
$738$	3.89839	0.143502
$739$	−5.82201	−0.214166	−0.107083	−	0.994250i	$-0.534151\pi$
$739$	−5.82201	−0.214166	−0.107083	+	0.994250i	$0.534151\pi$
$740$	1.16768	0.0429248
$741$	−6.31941	−0.232149
$742$	−9.70663	−0.356342
$743$	11.3652	0.416949	0.208474	−	0.978028i	$-0.433150\pi$
$743$	11.3652	0.416949	0.208474	+	0.978028i	$0.433150\pi$
$744$	2.92979	0.107411
$745$	−4.02471	−0.147454
$746$	0.141490	0.00518031
$747$	−0.865830	−0.0316791
$748$	−37.9596	−1.38794
$749$	5.85443	0.213916
$750$	4.91090	0.179321
$751$	28.3200	1.03341	0.516706	−	0.856163i	$-0.327158\pi$
$751$	28.3200	1.03341	0.516706	+	0.856163i	$0.327158\pi$
$752$	−6.99841	−0.255206
$753$	2.15987	0.0787101
$754$	9.35117	0.340549
$755$	7.31245	0.266127
$756$	−2.75905	−0.100346
$757$	25.4858	0.926296	0.463148	−	0.886281i	$-0.346720\pi$
$757$	25.4858	0.926296	0.463148	+	0.886281i	$0.346720\pi$
$758$	−30.8204	−1.11945
$759$	43.5968	1.58246
$760$	−3.18424	−0.115505
$761$	29.3339	1.06335	0.531676	−	0.846948i	$-0.321562\pi$
$761$	29.3339	1.06335	0.531676	+	0.846948i	$0.321562\pi$
$762$	−8.59083	−0.311213
$763$	29.5089	1.06829
$764$	−2.89259	−0.104650
$765$	3.17148	0.114665
$766$	21.3338	0.770823
$767$	9.24734	0.333902
$768$	−1.00000	−0.0360844
$769$	−25.1097	−0.905479	−0.452740	−	0.891643i	$-0.649553\pi$
$769$	−25.1097	−0.905479	−0.452740	+	0.891643i	$0.649553\pi$
$770$	8.38453	0.302157
$771$	−16.0148	−0.576760
$772$	20.2076	0.727288
$773$	31.2150	1.12273	0.561363	−	0.827570i	$-0.310277\pi$
$773$	31.2150	1.12273	0.561363	+	0.827570i	$0.310277\pi$
$774$	−4.29142	−0.154252
$775$	−13.9051	−0.499486
$776$	−18.9602	−0.680633
$777$	6.39372	0.229373
$778$	−22.0340	−0.789959
$779$	24.6355	0.882660
$780$	−0.503883	−0.0180419
$781$	75.2569	2.69290
$782$	−45.4985	−1.62702
$783$	−9.35117	−0.334183
$784$	0.612353	0.0218697
$785$	−11.7682	−0.420024
$786$	19.8384	0.707613
$787$	26.8139	0.955814	0.477907	−	0.878410i	$-0.341396\pi$
$787$	26.8139	0.955814	0.477907	+	0.878410i	$0.341396\pi$
$788$	−16.8072	−0.598732
$789$	−4.66348	−0.166024
$790$	5.08763	0.181010
$791$	−35.1706	−1.25052
$792$	−6.03100	−0.214302
$793$	0.178206	0.00632827
$794$	29.2872	1.03936
$795$	1.77272	0.0628718
$796$	1.86963	0.0662674
$797$	9.27410	0.328505	0.164253	−	0.986418i	$-0.447479\pi$
$797$	9.27410	0.328505	0.164253	+	0.986418i	$0.447479\pi$
$798$	−17.4356	−0.617212
$799$	44.0485	1.55832
$800$	4.74610	0.167800
$801$	0.262117	0.00926145
$802$	11.9102	0.420563
$803$	27.4220	0.967703
$804$	−9.08548	−0.320420
$805$	10.0497	0.354207
$806$	2.92979	0.103198
$807$	4.05727	0.142823
$808$	−10.3574	−0.364371
$809$	−0.168548	−0.00592582	−0.00296291	−	0.999996i	$-0.500943\pi$
$809$	−0.168548	−0.00592582	−0.00296291	+	0.999996i	$0.500943\pi$
$810$	0.503883	0.0177047
$811$	30.9742	1.08765	0.543826	−	0.839198i	$-0.316975\pi$
$811$	30.9742	1.08765	0.543826	+	0.839198i	$0.316975\pi$
$812$	25.8003	0.905414
$813$	15.6485	0.548818
$814$	13.9760	0.489859
$815$	−5.53975	−0.194049
$816$	6.29407	0.220337
$817$	−27.1192	−0.948781
$818$	29.6075	1.03520
$819$	−2.75905	−0.0964090
$820$	1.96434	0.0685976
$821$	38.8853	1.35711	0.678553	−	0.734551i	$-0.262607\pi$
$821$	38.8853	1.35711	0.678553	+	0.734551i	$0.262607\pi$
$822$	−1.81911	−0.0634487
$823$	−12.3747	−0.431356	−0.215678	−	0.976465i	$-0.569196\pi$
$823$	−12.3747	−0.431356	−0.215678	+	0.976465i	$0.569196\pi$
$824$	−1.00000	−0.0348367
$825$	28.6237	0.996550
$826$	25.5139	0.887741
$827$	3.84890	0.133839	0.0669196	−	0.997758i	$-0.478683\pi$
$827$	3.84890	0.133839	0.0669196	+	0.997758i	$0.478683\pi$
$828$	−7.22879	−0.251218
$829$	−5.45892	−0.189596	−0.0947981	−	0.995497i	$-0.530221\pi$
$829$	−5.45892	−0.189596	−0.0947981	+	0.995497i	$0.530221\pi$
$830$	−0.436277	−0.0151434
$831$	−19.1029	−0.662674
$832$	−1.00000	−0.0346688
$833$	−3.85420	−0.133540
$834$	13.6876	0.473964
$835$	8.47372	0.293245
$836$	−38.1123	−1.31814
$837$	−2.92979	−0.101268
$838$	−3.51354	−0.121373
$839$	26.3422	0.909432	0.454716	−	0.890636i	$-0.349741\pi$
$839$	26.3422	0.909432	0.454716	+	0.890636i	$0.349741\pi$
$840$	−1.39024	−0.0479678
$841$	58.4443	2.01532
$842$	23.4775	0.809089
$843$	3.80257	0.130968
$844$	3.95736	0.136218
$845$	−0.503883	−0.0173341
$846$	6.99841	0.240610
$847$	70.0052	2.40541
$848$	3.51811	0.120812
$849$	−4.96282	−0.170324
$850$	−29.8723	−1.02461
$851$	16.7517	0.574241
$852$	−12.4784	−0.427501
$853$	25.8598	0.885423	0.442712	−	0.896664i	$-0.354017\pi$
$853$	25.8598	0.885423	0.442712	+	0.896664i	$0.354017\pi$
$854$	0.491678	0.0168249
$855$	3.18424	0.108899
$856$	−2.12190	−0.0725251
$857$	−21.8546	−0.746539	−0.373269	−	0.927723i	$-0.621763\pi$
$857$	−21.8546	−0.746539	−0.373269	+	0.927723i	$0.621763\pi$
$858$	−6.03100	−0.205895
$859$	4.92636	0.168085	0.0840427	−	0.996462i	$-0.473217\pi$
$859$	4.92636	0.168085	0.0840427	+	0.996462i	$0.473217\pi$
$860$	−2.16237	−0.0737363
$861$	10.7559	0.366559
$862$	3.68034	0.125353
$863$	−38.5056	−1.31075	−0.655374	−	0.755305i	$-0.727489\pi$
$863$	−38.5056	−1.31075	−0.655374	+	0.755305i	$0.727489\pi$
$864$	1.00000	0.0340207
$865$	1.57259	0.0534697
$866$	22.3102	0.758131
$867$	−22.6154	−0.768058
$868$	8.08344	0.274370
$869$	60.8941	2.06569
$870$	−4.71190	−0.159748
$871$	−9.08548	−0.307850
$872$	−10.6953	−0.362189
$873$	18.9602	0.641707
$874$	−45.6817	−1.54521
$875$	13.5494	0.458054
$876$	−4.54685	−0.153624
$877$	−0.00168568	−5.69213e−5 0	−2.84607e−5	−	1.00000i	$-0.500009\pi$
$877$	−0.00168568	−5.69213e−5 0	−2.84607e−5		1.00000i	$0.500009\pi$
$878$	19.5096	0.658417
$879$	−4.80936	−0.162216
$880$	−3.03892	−0.102442
$881$	1.68023	0.0566084	0.0283042	−	0.999599i	$-0.490989\pi$
$881$	1.68023	0.0566084	0.0283042	+	0.999599i	$0.490989\pi$
$882$	−0.612353	−0.0206190
$883$	−14.5958	−0.491188	−0.245594	−	0.969373i	$-0.578983\pi$
$883$	−14.5958	−0.491188	−0.245594	+	0.969373i	$0.578983\pi$
$884$	6.29407	0.211693
$885$	−4.65958	−0.156630
$886$	31.9728	1.07415
$887$	−44.9844	−1.51043	−0.755214	−	0.655478i	$-0.772467\pi$
$887$	−44.9844	−1.51043	−0.755214	+	0.655478i	$0.772467\pi$
$888$	−2.31736	−0.0777656
$889$	−23.7025	−0.794957
$890$	0.132076	0.00442721
$891$	6.03100	0.202046
$892$	−11.4512	−0.383415
$893$	44.2258	1.47996
$894$	7.98738	0.267138
$895$	3.64565	0.121861
$896$	−2.75905	−0.0921734
$897$	−7.22879	−0.241362
$898$	−25.0632	−0.836370
$899$	27.3970	0.913740
$900$	−4.74610	−0.158203
$901$	−22.1432	−0.737698
$902$	23.5112	0.782838
$903$	−11.8402	−0.394018
$904$	12.7474	0.423971
$905$	3.78073	0.125676
$906$	−14.5122	−0.482135
$907$	7.34618	0.243926	0.121963	−	0.992535i	$-0.461081\pi$
$907$	7.34618	0.243926	0.121963	+	0.992535i	$0.461081\pi$
$908$	−9.36186	−0.310684
$909$	10.3574	0.343532
$910$	−1.39024	−0.0460860
$911$	34.0544	1.12827	0.564136	−	0.825682i	$-0.309209\pi$
$911$	34.0544	1.12827	0.564136	+	0.825682i	$0.309209\pi$
$912$	6.31941	0.209256
$913$	−5.22182	−0.172817
$914$	−41.1417	−1.36085
$915$	−0.0897949	−0.00296853
$916$	13.4812	0.445431
$917$	54.7352	1.80751
$918$	−6.29407	−0.207735
$919$	−23.4227	−0.772642	−0.386321	−	0.922364i	$-0.626254\pi$
$919$	−23.4227	−0.772642	−0.386321	+	0.922364i	$0.626254\pi$
$920$	−3.64247	−0.120089
$921$	4.41310	0.145417
$922$	21.6234	0.712129
$923$	−12.4784	−0.410730
$924$	−16.6398	−0.547410
$925$	10.9984	0.361626
$926$	37.9222	1.24620
$927$	1.00000	0.0328443
$928$	−9.35117	−0.306967
$929$	−54.3395	−1.78282	−0.891411	−	0.453195i	$-0.850284\pi$
$929$	−54.3395	−1.78282	−0.891411	+	0.453195i	$0.850284\pi$
$930$	−1.47627	−0.0484089
$931$	−3.86971	−0.126825
$932$	−23.5946	−0.772868
$933$	−12.0144	−0.393335
$934$	−28.5116	−0.932929
$935$	19.1272	0.625526
$936$	1.00000	0.0326860
$937$	−35.0824	−1.14609	−0.573045	−	0.819524i	$-0.694238\pi$
$937$	−35.0824	−1.14609	−0.573045	+	0.819524i	$0.694238\pi$
$938$	−25.0673	−0.818476
$939$	−24.5115	−0.799902
$940$	3.52638	0.115018
$941$	−10.1397	−0.330543	−0.165272	−	0.986248i	$-0.552850\pi$
$941$	−10.1397	−0.330543	−0.165272	+	0.986248i	$0.552850\pi$
$942$	23.3549	0.760945
$943$	28.1807	0.917689
$944$	−9.24734	−0.300975
$945$	1.39024	0.0452245
$946$	−25.8815	−0.841481
$947$	45.2354	1.46995	0.734976	−	0.678093i	$-0.237193\pi$
$947$	45.2354	1.46995	0.734976	+	0.678093i	$0.237193\pi$
$948$	−10.0968	−0.327930
$949$	−4.54685	−0.147597
$950$	−29.9926	−0.973087
$951$	10.1665	0.329672
$952$	17.3657	0.562824
$953$	−26.9631	−0.873419	−0.436710	−	0.899603i	$-0.643856\pi$
$953$	−26.9631	−0.873419	−0.436710	+	0.899603i	$0.643856\pi$
$954$	−3.51811	−0.113903
$955$	1.45753	0.0471645
$956$	28.9815	0.937329
$957$	−56.3969	−1.82305
$958$	6.33889	0.204800
$959$	−5.01901	−0.162072
$960$	0.503883	0.0162628
$961$	−22.4163	−0.723107
$962$	−2.31736	−0.0747147
$963$	2.12190	0.0683774
$964$	13.8376	0.445681
$965$	−10.1823	−0.327779
$966$	−19.9446	−0.641706
$967$	40.6646	1.30769	0.653843	−	0.756630i	$-0.273156\pi$
$967$	40.6646	1.30769	0.653843	+	0.756630i	$0.273156\pi$
$968$	−25.3729	−0.815517
$969$	−39.7748	−1.27775
$970$	9.55376	0.306753
$971$	−11.7350	−0.376595	−0.188297	−	0.982112i	$-0.560297\pi$
$971$	−11.7350	−0.376595	−0.188297	+	0.982112i	$0.560297\pi$
$972$	−1.00000	−0.0320750
$973$	37.7649	1.21069
$974$	−7.00106	−0.224328
$975$	−4.74610	−0.151997
$976$	−0.178206	−0.00570423
$977$	47.2456	1.51152	0.755761	−	0.654848i	$-0.227267\pi$
$977$	47.2456	1.51152	0.755761	+	0.654848i	$0.227267\pi$
$978$	10.9941	0.351553
$979$	1.58083	0.0505234
$980$	−0.308554	−0.00985641
$981$	10.6953	0.341475
$982$	12.4695	0.397917
$983$	3.11285	0.0992843	0.0496422	−	0.998767i	$-0.484192\pi$
$983$	3.11285	0.0992843	0.0496422	+	0.998767i	$0.484192\pi$
$984$	−3.89839	−0.124276
$985$	8.46887	0.269841
$986$	58.8569	1.87439
$987$	19.3089	0.614611
$988$	6.31941	0.201047
$989$	−31.0217	−0.986434
$990$	3.03892	0.0965832
$991$	4.85277	0.154153	0.0770767	−	0.997025i	$-0.475441\pi$
$991$	4.85277	0.154153	0.0770767	+	0.997025i	$0.475441\pi$
$992$	−2.92979	−0.0930210
$993$	−14.2271	−0.451482
$994$	−34.4284	−1.09200
$995$	−0.942077	−0.0298658
$996$	0.865830	0.0274349
$997$	−55.7601	−1.76594	−0.882970	−	0.469430i	$-0.844460\pi$
$997$	−55.7601	−1.76594	−0.882970	+	0.469430i	$0.844460\pi$
$998$	−27.5059	−0.870684
$999$	2.31736	0.0733181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.7	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.503883 q^{5} +1.00000 q^{6} +2.75905 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.503883 q^{5} +1.00000 q^{6} +2.75905 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.503883 q^{10} +6.03100 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.75905 q^{14} +0.503883 q^{15} +1.00000 q^{16} -6.29407 q^{17} -1.00000 q^{18} -6.31941 q^{19} -0.503883 q^{20} -2.75905 q^{21} -6.03100 q^{22} -7.22879 q^{23} +1.00000 q^{24} -4.74610 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.75905 q^{28} +9.35117 q^{29} -0.503883 q^{30} +2.92979 q^{31} -1.00000 q^{32} -6.03100 q^{33} +6.29407 q^{34} -1.39024 q^{35} +1.00000 q^{36} -2.31736 q^{37} +6.31941 q^{38} +1.00000 q^{39} +0.503883 q^{40} -3.89839 q^{41} +2.75905 q^{42} +4.29142 q^{43} +6.03100 q^{44} -0.503883 q^{45} +7.22879 q^{46} -6.99841 q^{47} -1.00000 q^{48} +0.612353 q^{49} +4.74610 q^{50} +6.29407 q^{51} -1.00000 q^{52} +3.51811 q^{53} +1.00000 q^{54} -3.03892 q^{55} -2.75905 q^{56} +6.31941 q^{57} -9.35117 q^{58} -9.24734 q^{59} +0.503883 q^{60} -0.178206 q^{61} -2.92979 q^{62} +2.75905 q^{63} +1.00000 q^{64} +0.503883 q^{65} +6.03100 q^{66} +9.08548 q^{67} -6.29407 q^{68} +7.22879 q^{69} +1.39024 q^{70} +12.4784 q^{71} -1.00000 q^{72} +4.54685 q^{73} +2.31736 q^{74} +4.74610 q^{75} -6.31941 q^{76} +16.6398 q^{77} -1.00000 q^{78} +10.0968 q^{79} -0.503883 q^{80} +1.00000 q^{81} +3.89839 q^{82} -0.865830 q^{83} -2.75905 q^{84} +3.17148 q^{85} -4.29142 q^{86} -9.35117 q^{87} -6.03100 q^{88} +0.262117 q^{89} +0.503883 q^{90} -2.75905 q^{91} -7.22879 q^{92} -2.92979 q^{93} +6.99841 q^{94} +3.18424 q^{95} +1.00000 q^{96} +18.9602 q^{97} -0.612353 q^{98} +6.03100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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