LMFDB - Embedded newform 8034.2.a.bc.1.3

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			1.3
Root			$2.75355$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.75355 q^{5} -1.00000 q^{6} +0.824838 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.75355 q^{5} -1.00000 q^{6} +0.824838 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.75355 q^{10} -4.01662 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.824838 q^{14} +2.75355 q^{15} +1.00000 q^{16} -4.88498 q^{17} +1.00000 q^{18} +5.85873 q^{19} -2.75355 q^{20} -0.824838 q^{21} -4.01662 q^{22} +6.04631 q^{23} -1.00000 q^{24} +2.58202 q^{25} -1.00000 q^{26} -1.00000 q^{27} +0.824838 q^{28} -6.86586 q^{29} +2.75355 q^{30} +0.898245 q^{31} +1.00000 q^{32} +4.01662 q^{33} -4.88498 q^{34} -2.27123 q^{35} +1.00000 q^{36} +4.98543 q^{37} +5.85873 q^{38} +1.00000 q^{39} -2.75355 q^{40} -8.56990 q^{41} -0.824838 q^{42} +12.5165 q^{43} -4.01662 q^{44} -2.75355 q^{45} +6.04631 q^{46} -11.9912 q^{47} -1.00000 q^{48} -6.31964 q^{49} +2.58202 q^{50} +4.88498 q^{51} -1.00000 q^{52} -6.44142 q^{53} -1.00000 q^{54} +11.0599 q^{55} +0.824838 q^{56} -5.85873 q^{57} -6.86586 q^{58} -2.07171 q^{59} +2.75355 q^{60} -12.3179 q^{61} +0.898245 q^{62} +0.824838 q^{63} +1.00000 q^{64} +2.75355 q^{65} +4.01662 q^{66} +9.95884 q^{67} -4.88498 q^{68} -6.04631 q^{69} -2.27123 q^{70} +5.23569 q^{71} +1.00000 q^{72} -2.85779 q^{73} +4.98543 q^{74} -2.58202 q^{75} +5.85873 q^{76} -3.31306 q^{77} +1.00000 q^{78} +8.39757 q^{79} -2.75355 q^{80} +1.00000 q^{81} -8.56990 q^{82} -5.21802 q^{83} -0.824838 q^{84} +13.4510 q^{85} +12.5165 q^{86} +6.86586 q^{87} -4.01662 q^{88} +15.1576 q^{89} -2.75355 q^{90} -0.824838 q^{91} +6.04631 q^{92} -0.898245 q^{93} -11.9912 q^{94} -16.1323 q^{95} -1.00000 q^{96} +6.12659 q^{97} -6.31964 q^{98} -4.01662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.75355	−1.23142	−0.615712	−	0.787971i	$-0.711131\pi$
$5$	−2.75355	−1.23142	−0.615712	+	0.787971i	$0.711131\pi$
$6$	−1.00000	−0.408248
$7$	0.824838	0.311760	0.155880	−	0.987776i	$-0.450179\pi$
$7$	0.824838	0.311760	0.155880	+	0.987776i	$0.450179\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.75355	−0.870748
$11$	−4.01662	−1.21106	−0.605528	−	0.795824i	$-0.707038\pi$
$11$	−4.01662	−1.21106	−0.605528	+	0.795824i	$0.707038\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.824838	0.220447
$15$	2.75355	0.710963
$16$	1.00000	0.250000
$17$	−4.88498	−1.18478	−0.592391	−	0.805650i	$-0.701816\pi$
$17$	−4.88498	−1.18478	−0.592391	+	0.805650i	$0.701816\pi$
$18$	1.00000	0.235702
$19$	5.85873	1.34408	0.672042	−	0.740513i	$-0.265417\pi$
$19$	5.85873	1.34408	0.672042	+	0.740513i	$0.265417\pi$
$20$	−2.75355	−0.615712
$21$	−0.824838	−0.179994
$22$	−4.01662	−0.856346
$23$	6.04631	1.26074	0.630372	−	0.776294i	$-0.282903\pi$
$23$	6.04631	1.26074	0.630372	+	0.776294i	$0.282903\pi$
$24$	−1.00000	−0.204124
$25$	2.58202	0.516404
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0.824838	0.155880
$29$	−6.86586	−1.27496	−0.637479	−	0.770468i	$-0.720023\pi$
$29$	−6.86586	−1.27496	−0.637479	+	0.770468i	$0.720023\pi$
$30$	2.75355	0.502727
$31$	0.898245	0.161330	0.0806648	−	0.996741i	$-0.474296\pi$
$31$	0.898245	0.161330	0.0806648	+	0.996741i	$0.474296\pi$
$32$	1.00000	0.176777
$33$	4.01662	0.699204
$34$	−4.88498	−0.837768
$35$	−2.27123	−0.383908
$36$	1.00000	0.166667
$37$	4.98543	0.819599	0.409800	−	0.912176i	$-0.365599\pi$
$37$	4.98543	0.819599	0.409800	+	0.912176i	$0.365599\pi$
$38$	5.85873	0.950411
$39$	1.00000	0.160128
$40$	−2.75355	−0.435374
$41$	−8.56990	−1.33839	−0.669197	−	0.743085i	$-0.733362\pi$
$41$	−8.56990	−1.33839	−0.669197	+	0.743085i	$0.733362\pi$
$42$	−0.824838	−0.127275
$43$	12.5165	1.90875	0.954373	−	0.298617i	$-0.0965252\pi$
$43$	12.5165	1.90875	0.954373	+	0.298617i	$0.0965252\pi$
$44$	−4.01662	−0.605528
$45$	−2.75355	−0.410474
$46$	6.04631	0.891480
$47$	−11.9912	−1.74910	−0.874549	−	0.484938i	$-0.838842\pi$
$47$	−11.9912	−1.74910	−0.874549	+	0.484938i	$0.838842\pi$
$48$	−1.00000	−0.144338
$49$	−6.31964	−0.902806
$50$	2.58202	0.365153
$51$	4.88498	0.684035
$52$	−1.00000	−0.138675
$53$	−6.44142	−0.884797	−0.442399	−	0.896818i	$-0.645872\pi$
$53$	−6.44142	−0.884797	−0.442399	+	0.896818i	$0.645872\pi$
$54$	−1.00000	−0.136083
$55$	11.0599	1.49132
$56$	0.824838	0.110224
$57$	−5.85873	−0.776008
$58$	−6.86586	−0.901532
$59$	−2.07171	−0.269713	−0.134857	−	0.990865i	$-0.543057\pi$
$59$	−2.07171	−0.269713	−0.134857	+	0.990865i	$0.543057\pi$
$60$	2.75355	0.355481
$61$	−12.3179	−1.57714	−0.788570	−	0.614945i	$-0.789178\pi$
$61$	−12.3179	−1.57714	−0.788570	+	0.614945i	$0.789178\pi$
$62$	0.898245	0.114077
$63$	0.824838	0.103920
$64$	1.00000	0.125000
$65$	2.75355	0.341535
$66$	4.01662	0.494412
$67$	9.95884	1.21667	0.608333	−	0.793682i	$-0.291838\pi$
$67$	9.95884	1.21667	0.608333	+	0.793682i	$0.291838\pi$
$68$	−4.88498	−0.592391
$69$	−6.04631	−0.727890
$70$	−2.27123	−0.271464
$71$	5.23569	0.621363	0.310681	−	0.950514i	$-0.399443\pi$
$71$	5.23569	0.621363	0.310681	+	0.950514i	$0.399443\pi$
$72$	1.00000	0.117851
$73$	−2.85779	−0.334479	−0.167240	−	0.985916i	$-0.553485\pi$
$73$	−2.85779	−0.334479	−0.167240	+	0.985916i	$0.553485\pi$
$74$	4.98543	0.579544
$75$	−2.58202	−0.298146
$76$	5.85873	0.672042
$77$	−3.31306	−0.377559
$78$	1.00000	0.113228
$79$	8.39757	0.944800	0.472400	−	0.881384i	$-0.343388\pi$
$79$	8.39757	0.944800	0.472400	+	0.881384i	$0.343388\pi$
$80$	−2.75355	−0.307856
$81$	1.00000	0.111111
$82$	−8.56990	−0.946388
$83$	−5.21802	−0.572752	−0.286376	−	0.958117i	$-0.592451\pi$
$83$	−5.21802	−0.572752	−0.286376	+	0.958117i	$0.592451\pi$
$84$	−0.824838	−0.0899972
$85$	13.4510	1.45897
$86$	12.5165	1.34969
$87$	6.86586	0.736097
$88$	−4.01662	−0.428173
$89$	15.1576	1.60670	0.803349	−	0.595508i	$-0.203049\pi$
$89$	15.1576	1.60670	0.803349	+	0.595508i	$0.203049\pi$
$90$	−2.75355	−0.290249
$91$	−0.824838	−0.0864666
$92$	6.04631	0.630372
$93$	−0.898245	−0.0931437
$94$	−11.9912	−1.23680
$95$	−16.1323	−1.65514
$96$	−1.00000	−0.102062
$97$	6.12659	0.622061	0.311030	−	0.950400i	$-0.399326\pi$
$97$	6.12659	0.622061	0.311030	+	0.950400i	$0.399326\pi$
$98$	−6.31964	−0.638380
$99$	−4.01662	−0.403685
$100$	2.58202	0.258202
$101$	−17.5626	−1.74754	−0.873771	−	0.486338i	$-0.838332\pi$
$101$	−17.5626	−1.74754	−0.873771	+	0.486338i	$0.838332\pi$
$102$	4.88498	0.483685
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	2.27123	0.221649
$106$	−6.44142	−0.625646
$107$	20.3015	1.96262	0.981310	−	0.192434i	$-0.0616381\pi$
$107$	20.3015	1.96262	0.981310	+	0.192434i	$0.0616381\pi$
$108$	−1.00000	−0.0962250
$109$	−3.09481	−0.296429	−0.148215	−	0.988955i	$-0.547353\pi$
$109$	−3.09481	−0.296429	−0.148215	+	0.988955i	$0.547353\pi$
$110$	11.0599	1.05452
$111$	−4.98543	−0.473196
$112$	0.824838	0.0779399
$113$	14.6484	1.37801	0.689004	−	0.724758i	$-0.258048\pi$
$113$	14.6484	1.37801	0.689004	+	0.724758i	$0.258048\pi$
$114$	−5.85873	−0.548720
$115$	−16.6488	−1.55251
$116$	−6.86586	−0.637479
$117$	−1.00000	−0.0924500
$118$	−2.07171	−0.190716
$119$	−4.02932	−0.369367
$120$	2.75355	0.251363
$121$	5.13324	0.466658
$122$	−12.3179	−1.11521
$123$	8.56990	0.772722
$124$	0.898245	0.0806648
$125$	6.65802	0.595512
$126$	0.824838	0.0734824
$127$	14.5076	1.28735	0.643673	−	0.765301i	$-0.277410\pi$
$127$	14.5076	1.28735	0.643673	+	0.765301i	$0.277410\pi$
$128$	1.00000	0.0883883
$129$	−12.5165	−1.10202
$130$	2.75355	0.241502
$131$	13.3775	1.16880	0.584399	−	0.811467i	$-0.301330\pi$
$131$	13.3775	1.16880	0.584399	+	0.811467i	$0.301330\pi$
$132$	4.01662	0.349602
$133$	4.83251	0.419031
$134$	9.95884	0.860313
$135$	2.75355	0.236988
$136$	−4.88498	−0.418884
$137$	−3.65086	−0.311914	−0.155957	−	0.987764i	$-0.549846\pi$
$137$	−3.65086	−0.311914	−0.155957	+	0.987764i	$0.549846\pi$
$138$	−6.04631	−0.514696
$139$	14.9078	1.26446	0.632232	−	0.774779i	$-0.282139\pi$
$139$	14.9078	1.26446	0.632232	+	0.774779i	$0.282139\pi$
$140$	−2.27123	−0.191954
$141$	11.9912	1.00984
$142$	5.23569	0.439370
$143$	4.01662	0.335887
$144$	1.00000	0.0833333
$145$	18.9055	1.57001
$146$	−2.85779	−0.236513
$147$	6.31964	0.521235
$148$	4.98543	0.409800
$149$	2.99240	0.245147	0.122573	−	0.992459i	$-0.460885\pi$
$149$	2.99240	0.245147	0.122573	+	0.992459i	$0.460885\pi$
$150$	−2.58202	−0.210821
$151$	−19.8765	−1.61753	−0.808765	−	0.588132i	$-0.799863\pi$
$151$	−19.8765	−1.61753	−0.808765	+	0.588132i	$0.799863\pi$
$152$	5.85873	0.475206
$153$	−4.88498	−0.394928
$154$	−3.31306	−0.266974
$155$	−2.47336	−0.198665
$156$	1.00000	0.0800641
$157$	−5.48855	−0.438034	−0.219017	−	0.975721i	$-0.570285\pi$
$157$	−5.48855	−0.438034	−0.219017	+	0.975721i	$0.570285\pi$
$158$	8.39757	0.668075
$159$	6.44142	0.510838
$160$	−2.75355	−0.217687
$161$	4.98723	0.393049
$162$	1.00000	0.0785674
$163$	7.06211	0.553147	0.276574	−	0.960993i	$-0.410801\pi$
$163$	7.06211	0.553147	0.276574	+	0.960993i	$0.410801\pi$
$164$	−8.56990	−0.669197
$165$	−11.0599	−0.861016
$166$	−5.21802	−0.404997
$167$	16.9953	1.31513	0.657567	−	0.753396i	$-0.271586\pi$
$167$	16.9953	1.31513	0.657567	+	0.753396i	$0.271586\pi$
$168$	−0.824838	−0.0636377
$169$	1.00000	0.0769231
$170$	13.4510	1.03165
$171$	5.85873	0.448028
$172$	12.5165	0.954373
$173$	4.34169	0.330093	0.165046	−	0.986286i	$-0.447223\pi$
$173$	4.34169	0.330093	0.165046	+	0.986286i	$0.447223\pi$
$174$	6.86586	0.520499
$175$	2.12975	0.160994
$176$	−4.01662	−0.302764
$177$	2.07171	0.155719
$178$	15.1576	1.13611
$179$	17.0414	1.27373	0.636865	−	0.770975i	$-0.280231\pi$
$179$	17.0414	1.27373	0.636865	+	0.770975i	$0.280231\pi$
$180$	−2.75355	−0.205237
$181$	17.2522	1.28234	0.641172	−	0.767397i	$-0.278448\pi$
$181$	17.2522	1.28234	0.641172	+	0.767397i	$0.278448\pi$
$182$	−0.824838	−0.0611411
$183$	12.3179	0.910562
$184$	6.04631	0.445740
$185$	−13.7276	−1.00927
$186$	−0.898245	−0.0658626
$187$	19.6211	1.43484
$188$	−11.9912	−0.874549
$189$	−0.824838	−0.0599982
$190$	−16.1323	−1.17036
$191$	−16.2534	−1.17606	−0.588029	−	0.808840i	$-0.700096\pi$
$191$	−16.2534	−1.17606	−0.588029	+	0.808840i	$0.700096\pi$
$192$	−1.00000	−0.0721688
$193$	−14.9122	−1.07341	−0.536703	−	0.843771i	$-0.680330\pi$
$193$	−14.9122	−1.07341	−0.536703	+	0.843771i	$0.680330\pi$
$194$	6.12659	0.439863
$195$	−2.75355	−0.197186
$196$	−6.31964	−0.451403
$197$	17.5228	1.24845	0.624224	−	0.781245i	$-0.285415\pi$
$197$	17.5228	1.24845	0.624224	+	0.781245i	$0.285415\pi$
$198$	−4.01662	−0.285449
$199$	−8.66641	−0.614346	−0.307173	−	0.951654i	$-0.599383\pi$
$199$	−8.66641	−0.614346	−0.307173	+	0.951654i	$0.599383\pi$
$200$	2.58202	0.182576
$201$	−9.95884	−0.702443
$202$	−17.5626	−1.23570
$203$	−5.66322	−0.397480
$204$	4.88498	0.342017
$205$	23.5976	1.64813
$206$	−1.00000	−0.0696733
$207$	6.04631	0.420248
$208$	−1.00000	−0.0693375
$209$	−23.5323	−1.62776
$210$	2.27123	0.156730
$211$	−7.82353	−0.538594	−0.269297	−	0.963057i	$-0.586791\pi$
$211$	−7.82353	−0.538594	−0.269297	+	0.963057i	$0.586791\pi$
$212$	−6.44142	−0.442399
$213$	−5.23569	−0.358744
$214$	20.3015	1.38778
$215$	−34.4647	−2.35047
$216$	−1.00000	−0.0680414
$217$	0.740907	0.0502961
$218$	−3.09481	−0.209607
$219$	2.85779	0.193112
$220$	11.0599	0.745662
$221$	4.88498	0.328600
$222$	−4.98543	−0.334600
$223$	−0.973709	−0.0652044	−0.0326022	−	0.999468i	$-0.510379\pi$
$223$	−0.973709	−0.0652044	−0.0326022	+	0.999468i	$0.510379\pi$
$224$	0.824838	0.0551118
$225$	2.58202	0.172135
$226$	14.6484	0.974398
$227$	25.0223	1.66079	0.830395	−	0.557175i	$-0.188115\pi$
$227$	25.0223	1.66079	0.830395	+	0.557175i	$0.188115\pi$
$228$	−5.85873	−0.388004
$229$	20.2628	1.33900	0.669500	−	0.742812i	$-0.266508\pi$
$229$	20.2628	1.33900	0.669500	+	0.742812i	$0.266508\pi$
$230$	−16.6488	−1.09779
$231$	3.31306	0.217984
$232$	−6.86586	−0.450766
$233$	−10.4040	−0.681589	−0.340795	−	0.940138i	$-0.610696\pi$
$233$	−10.4040	−0.681589	−0.340795	+	0.940138i	$0.610696\pi$
$234$	−1.00000	−0.0653720
$235$	33.0183	2.15388
$236$	−2.07171	−0.134857
$237$	−8.39757	−0.545481
$238$	−4.02932	−0.261182
$239$	26.4940	1.71375	0.856876	−	0.515523i	$-0.172402\pi$
$239$	26.4940	1.71375	0.856876	+	0.515523i	$0.172402\pi$
$240$	2.75355	0.177741
$241$	1.31680	0.0848228	0.0424114	−	0.999100i	$-0.486496\pi$
$241$	1.31680	0.0848228	0.0424114	+	0.999100i	$0.486496\pi$
$242$	5.13324	0.329977
$243$	−1.00000	−0.0641500
$244$	−12.3179	−0.788570
$245$	17.4014	1.11174
$246$	8.56990	0.546397
$247$	−5.85873	−0.372782
$248$	0.898245	0.0570386
$249$	5.21802	0.330679
$250$	6.65802	0.421090
$251$	−13.8996	−0.877337	−0.438669	−	0.898649i	$-0.644550\pi$
$251$	−13.8996	−0.877337	−0.438669	+	0.898649i	$0.644550\pi$
$252$	0.824838	0.0519599
$253$	−24.2857	−1.52683
$254$	14.5076	0.910291
$255$	−13.4510	−0.842336
$256$	1.00000	0.0625000
$257$	22.3217	1.39239	0.696193	−	0.717854i	$-0.254876\pi$
$257$	22.3217	1.39239	0.696193	+	0.717854i	$0.254876\pi$
$258$	−12.5165	−0.779242
$259$	4.11217	0.255518
$260$	2.75355	0.170768
$261$	−6.86586	−0.424986
$262$	13.3775	0.826465
$263$	−16.1592	−0.996420	−0.498210	−	0.867056i	$-0.666009\pi$
$263$	−16.1592	−0.996420	−0.498210	+	0.867056i	$0.666009\pi$
$264$	4.01662	0.247206
$265$	17.7368	1.08956
$266$	4.83251	0.296300
$267$	−15.1576	−0.927628
$268$	9.95884	0.608333
$269$	6.48600	0.395459	0.197729	−	0.980257i	$-0.436643\pi$
$269$	6.48600	0.395459	0.197729	+	0.980257i	$0.436643\pi$
$270$	2.75355	0.167576
$271$	−25.7060	−1.56153	−0.780763	−	0.624827i	$-0.785170\pi$
$271$	−25.7060	−1.56153	−0.780763	+	0.624827i	$0.785170\pi$
$272$	−4.88498	−0.296196
$273$	0.824838	0.0499215
$274$	−3.65086	−0.220556
$275$	−10.3710	−0.625394
$276$	−6.04631	−0.363945
$277$	−16.0917	−0.966856	−0.483428	−	0.875384i	$-0.660608\pi$
$277$	−16.0917	−0.966856	−0.483428	+	0.875384i	$0.660608\pi$
$278$	14.9078	0.894111
$279$	0.898245	0.0537765
$280$	−2.27123	−0.135732
$281$	0.0961083	0.00573334	0.00286667	−	0.999996i	$-0.499088\pi$
$281$	0.0961083	0.00573334	0.00286667	+	0.999996i	$0.499088\pi$
$282$	11.9912	0.714066
$283$	5.39853	0.320909	0.160455	−	0.987043i	$-0.448704\pi$
$283$	5.39853	0.320909	0.160455	+	0.987043i	$0.448704\pi$
$284$	5.23569	0.310681
$285$	16.1323	0.955594
$286$	4.01662	0.237508
$287$	−7.06879	−0.417257
$288$	1.00000	0.0589256
$289$	6.86306	0.403710
$290$	18.9055	1.11017
$291$	−6.12659	−0.359147
$292$	−2.85779	−0.167240
$293$	22.2615	1.30053	0.650266	−	0.759706i	$-0.274657\pi$
$293$	22.2615	1.30053	0.650266	+	0.759706i	$0.274657\pi$
$294$	6.31964	0.368569
$295$	5.70455	0.332131
$296$	4.98543	0.289772
$297$	4.01662	0.233068
$298$	2.99240	0.173345
$299$	−6.04631	−0.349667
$300$	−2.58202	−0.149073
$301$	10.3241	0.595070
$302$	−19.8765	−1.14377
$303$	17.5626	1.00894
$304$	5.85873	0.336021
$305$	33.9178	1.94213
$306$	−4.88498	−0.279256
$307$	−2.18512	−0.124711	−0.0623557	−	0.998054i	$-0.519861\pi$
$307$	−2.18512	−0.124711	−0.0623557	+	0.998054i	$0.519861\pi$
$308$	−3.31306	−0.188779
$309$	1.00000	0.0568880
$310$	−2.47336	−0.140477
$311$	−0.0801534	−0.00454508	−0.00227254	−	0.999997i	$-0.500723\pi$
$311$	−0.0801534	−0.00454508	−0.00227254	+	0.999997i	$0.500723\pi$
$312$	1.00000	0.0566139
$313$	9.05156	0.511624	0.255812	−	0.966726i	$-0.417657\pi$
$313$	9.05156	0.511624	0.255812	+	0.966726i	$0.417657\pi$
$314$	−5.48855	−0.309737
$315$	−2.27123	−0.127969
$316$	8.39757	0.472400
$317$	4.18981	0.235323	0.117662	−	0.993054i	$-0.462460\pi$
$317$	4.18981	0.235323	0.117662	+	0.993054i	$0.462460\pi$
$318$	6.44142	0.361217
$319$	27.5775	1.54405
$320$	−2.75355	−0.153928
$321$	−20.3015	−1.13312
$322$	4.98723	0.277927
$323$	−28.6198	−1.59245
$324$	1.00000	0.0555556
$325$	−2.58202	−0.143225
$326$	7.06211	0.391134
$327$	3.09481	0.171144
$328$	−8.56990	−0.473194
$329$	−9.89081	−0.545298
$330$	−11.0599	−0.608830
$331$	18.0911	0.994377	0.497188	−	0.867643i	$-0.334366\pi$
$331$	18.0911	0.994377	0.497188	+	0.867643i	$0.334366\pi$
$332$	−5.21802	−0.286376
$333$	4.98543	0.273200
$334$	16.9953	0.929940
$335$	−27.4221	−1.49823
$336$	−0.824838	−0.0449986
$337$	−2.00641	−0.109296	−0.0546480	−	0.998506i	$-0.517404\pi$
$337$	−2.00641	−0.109296	−0.0546480	+	0.998506i	$0.517404\pi$
$338$	1.00000	0.0543928
$339$	−14.6484	−0.795593
$340$	13.4510	0.729484
$341$	−3.60791	−0.195379
$342$	5.85873	0.316804
$343$	−10.9866	−0.593218
$344$	12.5165	0.674844
$345$	16.6488	0.896341
$346$	4.34169	0.233411
$347$	−3.06551	−0.164565	−0.0822826	−	0.996609i	$-0.526221\pi$
$347$	−3.06551	−0.164565	−0.0822826	+	0.996609i	$0.526221\pi$
$348$	6.86586	0.368049
$349$	11.4089	0.610703	0.305351	−	0.952240i	$-0.401226\pi$
$349$	11.4089	0.610703	0.305351	+	0.952240i	$0.401226\pi$
$350$	2.12975	0.113840
$351$	1.00000	0.0533761
$352$	−4.01662	−0.214087
$353$	−27.4910	−1.46320	−0.731599	−	0.681735i	$-0.761226\pi$
$353$	−27.4910	−1.46320	−0.731599	+	0.681735i	$0.761226\pi$
$354$	2.07171	0.110110
$355$	−14.4167	−0.765160
$356$	15.1576	0.803349
$357$	4.02932	0.213254
$358$	17.0414	0.900664
$359$	−12.5262	−0.661106	−0.330553	−	0.943787i	$-0.607235\pi$
$359$	−12.5262	−0.661106	−0.330553	+	0.943787i	$0.607235\pi$
$360$	−2.75355	−0.145125
$361$	15.3247	0.806564
$362$	17.2522	0.906754
$363$	−5.13324	−0.269425
$364$	−0.824838	−0.0432333
$365$	7.86906	0.411886
$366$	12.3179	0.643865
$367$	21.5573	1.12528	0.562642	−	0.826701i	$-0.309785\pi$
$367$	21.5573	1.12528	0.562642	+	0.826701i	$0.309785\pi$
$368$	6.04631	0.315186
$369$	−8.56990	−0.446131
$370$	−13.7276	−0.713664
$371$	−5.31313	−0.275844
$372$	−0.898245	−0.0465719
$373$	34.6777	1.79554	0.897772	−	0.440460i	$-0.145185\pi$
$373$	34.6777	1.79554	0.897772	+	0.440460i	$0.145185\pi$
$374$	19.6211	1.01458
$375$	−6.65802	−0.343819
$376$	−11.9912	−0.618399
$377$	6.86586	0.353610
$378$	−0.824838	−0.0424251
$379$	−10.8080	−0.555172	−0.277586	−	0.960701i	$-0.589534\pi$
$379$	−10.8080	−0.555172	−0.277586	+	0.960701i	$0.589534\pi$
$380$	−16.1323	−0.827569
$381$	−14.5076	−0.743249
$382$	−16.2534	−0.831598
$383$	2.54440	0.130013	0.0650063	−	0.997885i	$-0.479293\pi$
$383$	2.54440	0.130013	0.0650063	+	0.997885i	$0.479293\pi$
$384$	−1.00000	−0.0510310
$385$	9.12267	0.464934
$386$	−14.9122	−0.759013
$387$	12.5165	0.636249
$388$	6.12659	0.311030
$389$	18.6438	0.945277	0.472639	−	0.881256i	$-0.343302\pi$
$389$	18.6438	0.945277	0.472639	+	0.881256i	$0.343302\pi$
$390$	−2.75355	−0.139431
$391$	−29.5361	−1.49371
$392$	−6.31964	−0.319190
$393$	−13.3775	−0.674806
$394$	17.5228	0.882787
$395$	−23.1231	−1.16345
$396$	−4.01662	−0.201843
$397$	−12.1568	−0.610133	−0.305067	−	0.952331i	$-0.598679\pi$
$397$	−12.1568	−0.610133	−0.305067	+	0.952331i	$0.598679\pi$
$398$	−8.66641	−0.434408
$399$	−4.83251	−0.241928
$400$	2.58202	0.129101
$401$	17.1721	0.857536	0.428768	−	0.903415i	$-0.358948\pi$
$401$	17.1721	0.857536	0.428768	+	0.903415i	$0.358948\pi$
$402$	−9.95884	−0.496702
$403$	−0.898245	−0.0447448
$404$	−17.5626	−0.873771
$405$	−2.75355	−0.136825
$406$	−5.66322	−0.281061
$407$	−20.0246	−0.992581
$408$	4.88498	0.241843
$409$	−2.80065	−0.138483	−0.0692415	−	0.997600i	$-0.522058\pi$
$409$	−2.80065	−0.138483	−0.0692415	+	0.997600i	$0.522058\pi$
$410$	23.5976	1.16540
$411$	3.65086	0.180084
$412$	−1.00000	−0.0492665
$413$	−1.70882	−0.0840858
$414$	6.04631	0.297160
$415$	14.3681	0.705300
$416$	−1.00000	−0.0490290
$417$	−14.9078	−0.730038
$418$	−23.5323	−1.15100
$419$	40.3556	1.97150	0.985751	−	0.168210i	$-0.0537988\pi$
$419$	40.3556	1.97150	0.985751	+	0.168210i	$0.0537988\pi$
$420$	2.27123	0.110825
$421$	−15.1113	−0.736481	−0.368240	−	0.929731i	$-0.620040\pi$
$421$	−15.1113	−0.736481	−0.368240	+	0.929731i	$0.620040\pi$
$422$	−7.82353	−0.380843
$423$	−11.9912	−0.583032
$424$	−6.44142	−0.312823
$425$	−12.6131	−0.611826
$426$	−5.23569	−0.253670
$427$	−10.1602	−0.491689
$428$	20.3015	0.981310
$429$	−4.01662	−0.193924
$430$	−34.4647	−1.66204
$431$	23.8797	1.15024	0.575122	−	0.818068i	$-0.304955\pi$
$431$	23.8797	1.15024	0.575122	+	0.818068i	$0.304955\pi$
$432$	−1.00000	−0.0481125
$433$	−22.2116	−1.06742	−0.533712	−	0.845667i	$-0.679203\pi$
$433$	−22.2116	−1.06742	−0.533712	+	0.845667i	$0.679203\pi$
$434$	0.740907	0.0355647
$435$	−18.9055	−0.906448
$436$	−3.09481	−0.148215
$437$	35.4237	1.69455
$438$	2.85779	0.136551
$439$	13.5722	0.647765	0.323882	−	0.946097i	$-0.395012\pi$
$439$	13.5722	0.647765	0.323882	+	0.946097i	$0.395012\pi$
$440$	11.0599	0.527262
$441$	−6.31964	−0.300935
$442$	4.88498	0.232355
$443$	3.04113	0.144488	0.0722441	−	0.997387i	$-0.476984\pi$
$443$	3.04113	0.144488	0.0722441	+	0.997387i	$0.476984\pi$
$444$	−4.98543	−0.236598
$445$	−41.7370	−1.97853
$446$	−0.973709	−0.0461064
$447$	−2.99240	−0.141536
$448$	0.824838	0.0389700
$449$	−14.6556	−0.691641	−0.345821	−	0.938301i	$-0.612399\pi$
$449$	−14.6556	−0.691641	−0.345821	+	0.938301i	$0.612399\pi$
$450$	2.58202	0.121718
$451$	34.4220	1.62087
$452$	14.6484	0.689004
$453$	19.8765	0.933881
$454$	25.0223	1.17436
$455$	2.27123	0.106477
$456$	−5.85873	−0.274360
$457$	19.5597	0.914966	0.457483	−	0.889218i	$-0.348751\pi$
$457$	19.5597	0.914966	0.457483	+	0.889218i	$0.348751\pi$
$458$	20.2628	0.946817
$459$	4.88498	0.228012
$460$	−16.6488	−0.776254
$461$	6.48694	0.302127	0.151063	−	0.988524i	$-0.451730\pi$
$461$	6.48694	0.302127	0.151063	+	0.988524i	$0.451730\pi$
$462$	3.31306	0.154138
$463$	30.7177	1.42757	0.713787	−	0.700362i	$-0.246978\pi$
$463$	30.7177	1.42757	0.713787	+	0.700362i	$0.246978\pi$
$464$	−6.86586	−0.318740
$465$	2.47336	0.114699
$466$	−10.4040	−0.481956
$467$	22.1129	1.02327	0.511633	−	0.859204i	$-0.329041\pi$
$467$	22.1129	1.02327	0.511633	+	0.859204i	$0.329041\pi$
$468$	−1.00000	−0.0462250
$469$	8.21444	0.379307
$470$	33.0183	1.52302
$471$	5.48855	0.252899
$472$	−2.07171	−0.0953581
$473$	−50.2740	−2.31160
$474$	−8.39757	−0.385713
$475$	15.1273	0.694090
$476$	−4.02932	−0.184684
$477$	−6.44142	−0.294932
$478$	26.4940	1.21181
$479$	28.0901	1.28347	0.641734	−	0.766927i	$-0.278215\pi$
$479$	28.0901	1.28347	0.641734	+	0.766927i	$0.278215\pi$
$480$	2.75355	0.125682
$481$	−4.98543	−0.227316
$482$	1.31680	0.0599788
$483$	−4.98723	−0.226927
$484$	5.13324	0.233329
$485$	−16.8698	−0.766020
$486$	−1.00000	−0.0453609
$487$	−43.1659	−1.95603	−0.978016	−	0.208529i	$-0.933133\pi$
$487$	−43.1659	−1.95603	−0.978016	+	0.208529i	$0.933133\pi$
$488$	−12.3179	−0.557603
$489$	−7.06211	−0.319360
$490$	17.4014	0.786116
$491$	4.59882	0.207542	0.103771	−	0.994601i	$-0.466909\pi$
$491$	4.59882	0.207542	0.103771	+	0.994601i	$0.466909\pi$
$492$	8.56990	0.386361
$493$	33.5396	1.51055
$494$	−5.85873	−0.263597
$495$	11.0599	0.497108
$496$	0.898245	0.0403324
$497$	4.31860	0.193716
$498$	5.21802	0.233825
$499$	14.7370	0.659717	0.329858	−	0.944030i	$-0.392999\pi$
$499$	14.7370	0.659717	0.329858	+	0.944030i	$0.392999\pi$
$500$	6.65802	0.297756
$501$	−16.9953	−0.759293
$502$	−13.8996	−0.620371
$503$	34.2400	1.52669	0.763343	−	0.645994i	$-0.223557\pi$
$503$	34.2400	1.52669	0.763343	+	0.645994i	$0.223557\pi$
$504$	0.824838	0.0367412
$505$	48.3594	2.15196
$506$	−24.2857	−1.07963
$507$	−1.00000	−0.0444116
$508$	14.5076	0.643673
$509$	−13.8444	−0.613640	−0.306820	−	0.951767i	$-0.599265\pi$
$509$	−13.8444	−0.613640	−0.306820	+	0.951767i	$0.599265\pi$
$510$	−13.4510	−0.595622
$511$	−2.35722	−0.104277
$512$	1.00000	0.0441942
$513$	−5.85873	−0.258669
$514$	22.3217	0.984566
$515$	2.75355	0.121336
$516$	−12.5165	−0.551008
$517$	48.1641	2.11826
$518$	4.11217	0.180679
$519$	−4.34169	−0.190579
$520$	2.75355	0.120751
$521$	−37.9825	−1.66404	−0.832021	−	0.554744i	$-0.812816\pi$
$521$	−37.9825	−1.66404	−0.832021	+	0.554744i	$0.812816\pi$
$522$	−6.86586	−0.300511
$523$	−44.5784	−1.94928	−0.974639	−	0.223784i	$-0.928159\pi$
$523$	−44.5784	−1.94928	−0.974639	+	0.223784i	$0.928159\pi$
$524$	13.3775	0.584399
$525$	−2.12975	−0.0929498
$526$	−16.1592	−0.704576
$527$	−4.38791	−0.191141
$528$	4.01662	0.174801
$529$	13.5579	0.589473
$530$	17.7368	0.770435
$531$	−2.07171	−0.0899045
$532$	4.83251	0.209516
$533$	8.56990	0.371204
$534$	−15.1576	−0.655932
$535$	−55.9011	−2.41682
$536$	9.95884	0.430156
$537$	−17.0414	−0.735389
$538$	6.48600	0.279631
$539$	25.3836	1.09335
$540$	2.75355	0.118494
$541$	31.0027	1.33291	0.666455	−	0.745545i	$-0.267811\pi$
$541$	31.0027	1.33291	0.666455	+	0.745545i	$0.267811\pi$
$542$	−25.7060	−1.10417
$543$	−17.2522	−0.740362
$544$	−4.88498	−0.209442
$545$	8.52171	0.365030
$546$	0.824838	0.0352998
$547$	−40.7446	−1.74211	−0.871056	−	0.491184i	$-0.836564\pi$
$547$	−40.7446	−1.74211	−0.871056	+	0.491184i	$0.836564\pi$
$548$	−3.65086	−0.155957
$549$	−12.3179	−0.525713
$550$	−10.3710	−0.442220
$551$	−40.2252	−1.71365
$552$	−6.04631	−0.257348
$553$	6.92664	0.294551
$554$	−16.0917	−0.683670
$555$	13.7276	0.582705
$556$	14.9078	0.632232
$557$	−13.2768	−0.562555	−0.281277	−	0.959627i	$-0.590758\pi$
$557$	−13.2768	−0.562555	−0.281277	+	0.959627i	$0.590758\pi$
$558$	0.898245	0.0380258
$559$	−12.5165	−0.529391
$560$	−2.27123	−0.0959770
$561$	−19.6211	−0.828404
$562$	0.0961083	0.00405408
$563$	−16.6142	−0.700207	−0.350103	−	0.936711i	$-0.613854\pi$
$563$	−16.6142	−0.700207	−0.350103	+	0.936711i	$0.613854\pi$
$564$	11.9912	0.504921
$565$	−40.3351	−1.69691
$566$	5.39853	0.226917
$567$	0.824838	0.0346400
$568$	5.23569	0.219685
$569$	−12.6190	−0.529018	−0.264509	−	0.964383i	$-0.585210\pi$
$569$	−12.6190	−0.529018	−0.264509	+	0.964383i	$0.585210\pi$
$570$	16.1323	0.675707
$571$	1.19760	0.0501178	0.0250589	−	0.999686i	$-0.492023\pi$
$571$	1.19760	0.0501178	0.0250589	+	0.999686i	$0.492023\pi$
$572$	4.01662	0.167943
$573$	16.2534	0.678997
$574$	−7.06879	−0.295045
$575$	15.6117	0.651052
$576$	1.00000	0.0416667
$577$	−0.301179	−0.0125382	−0.00626912	−	0.999980i	$-0.501996\pi$
$577$	−0.301179	−0.0125382	−0.00626912	+	0.999980i	$0.501996\pi$
$578$	6.86306	0.285466
$579$	14.9122	0.619731
$580$	18.9055	0.785007
$581$	−4.30402	−0.178561
$582$	−6.12659	−0.253955
$583$	25.8727	1.07154
$584$	−2.85779	−0.118256
$585$	2.75355	0.113845
$586$	22.2615	0.919616
$587$	21.8124	0.900294	0.450147	−	0.892954i	$-0.351372\pi$
$587$	21.8124	0.900294	0.450147	+	0.892954i	$0.351372\pi$
$588$	6.31964	0.260618
$589$	5.26258	0.216841
$590$	5.70455	0.234852
$591$	−17.5228	−0.720792
$592$	4.98543	0.204900
$593$	−5.08535	−0.208830	−0.104415	−	0.994534i	$-0.533297\pi$
$593$	−5.08535	−0.208830	−0.104415	+	0.994534i	$0.533297\pi$
$594$	4.01662	0.164804
$595$	11.0949	0.454848
$596$	2.99240	0.122573
$597$	8.66641	0.354693
$598$	−6.04631	−0.247252
$599$	37.2656	1.52263	0.761315	−	0.648382i	$-0.224554\pi$
$599$	37.2656	1.52263	0.761315	+	0.648382i	$0.224554\pi$
$600$	−2.58202	−0.105410
$601$	39.5448	1.61306	0.806532	−	0.591190i	$-0.201342\pi$
$601$	39.5448	1.61306	0.806532	+	0.591190i	$0.201342\pi$
$602$	10.3241	0.420778
$603$	9.95884	0.405555
$604$	−19.8765	−0.808765
$605$	−14.1346	−0.574653
$606$	17.5626	0.713431
$607$	2.47845	0.100597	0.0502986	−	0.998734i	$-0.483983\pi$
$607$	2.47845	0.100597	0.0502986	+	0.998734i	$0.483983\pi$
$608$	5.85873	0.237603
$609$	5.66322	0.229485
$610$	33.9178	1.37329
$611$	11.9912	0.485112
$612$	−4.88498	−0.197464
$613$	17.3008	0.698774	0.349387	−	0.936978i	$-0.386390\pi$
$613$	17.3008	0.698774	0.349387	+	0.936978i	$0.386390\pi$
$614$	−2.18512	−0.0881842
$615$	−23.5976	−0.951548
$616$	−3.31306	−0.133487
$617$	26.0657	1.04937	0.524683	−	0.851298i	$-0.324184\pi$
$617$	26.0657	1.04937	0.524683	+	0.851298i	$0.324184\pi$
$618$	1.00000	0.0402259
$619$	−20.0939	−0.807641	−0.403821	−	0.914838i	$-0.632318\pi$
$619$	−20.0939	−0.807641	−0.403821	+	0.914838i	$0.632318\pi$
$620$	−2.47336	−0.0993326
$621$	−6.04631	−0.242630
$622$	−0.0801534	−0.00321386
$623$	12.5025	0.500904
$624$	1.00000	0.0400320
$625$	−31.2433	−1.24973
$626$	9.05156	0.361773
$627$	23.5323	0.939789
$628$	−5.48855	−0.219017
$629$	−24.3537	−0.971047
$630$	−2.27123	−0.0904880
$631$	45.0779	1.79452	0.897261	−	0.441501i	$-0.145554\pi$
$631$	45.0779	1.79452	0.897261	+	0.441501i	$0.145554\pi$
$632$	8.39757	0.334037
$633$	7.82353	0.310957
$634$	4.18981	0.166399
$635$	−39.9475	−1.58527
$636$	6.44142	0.255419
$637$	6.31964	0.250393
$638$	27.5775	1.09181
$639$	5.23569	0.207121
$640$	−2.75355	−0.108843
$641$	5.02160	0.198341	0.0991707	−	0.995070i	$-0.468381\pi$
$641$	5.02160	0.198341	0.0991707	+	0.995070i	$0.468381\pi$
$642$	−20.3015	−0.801236
$643$	25.4848	1.00502	0.502511	−	0.864571i	$-0.332410\pi$
$643$	25.4848	1.00502	0.502511	+	0.864571i	$0.332410\pi$
$644$	4.98723	0.196524
$645$	34.4647	1.35705
$646$	−28.6198	−1.12603
$647$	15.6812	0.616492	0.308246	−	0.951307i	$-0.400258\pi$
$647$	15.6812	0.616492	0.308246	+	0.951307i	$0.400258\pi$
$648$	1.00000	0.0392837
$649$	8.32127	0.326638
$650$	−2.58202	−0.101275
$651$	−0.740907	−0.0290384
$652$	7.06211	0.276574
$653$	−19.0441	−0.745255	−0.372627	−	0.927981i	$-0.621543\pi$
$653$	−19.0441	−0.745255	−0.372627	+	0.927981i	$0.621543\pi$
$654$	3.09481	0.121017
$655$	−36.8356	−1.43928
$656$	−8.56990	−0.334599
$657$	−2.85779	−0.111493
$658$	−9.89081	−0.385584
$659$	28.4790	1.10938	0.554692	−	0.832056i	$-0.312836\pi$
$659$	28.4790	1.10938	0.554692	+	0.832056i	$0.312836\pi$
$660$	−11.0599	−0.430508
$661$	−36.2555	−1.41017	−0.705087	−	0.709121i	$-0.749092\pi$
$661$	−36.2555	−1.41017	−0.705087	+	0.709121i	$0.749092\pi$
$662$	18.0911	0.703131
$663$	−4.88498	−0.189717
$664$	−5.21802	−0.202498
$665$	−13.3065	−0.516005
$666$	4.98543	0.193181
$667$	−41.5131	−1.60739
$668$	16.9953	0.657567
$669$	0.973709	0.0376458
$670$	−27.4221	−1.05941
$671$	49.4761	1.91001
$672$	−0.824838	−0.0318188
$673$	19.2441	0.741804	0.370902	−	0.928672i	$-0.379049\pi$
$673$	19.2441	0.741804	0.370902	+	0.928672i	$0.379049\pi$
$674$	−2.00641	−0.0772839
$675$	−2.58202	−0.0993819
$676$	1.00000	0.0384615
$677$	−19.9685	−0.767453	−0.383726	−	0.923447i	$-0.625359\pi$
$677$	−19.9685	−0.767453	−0.383726	+	0.923447i	$0.625359\pi$
$678$	−14.6484	−0.562569
$679$	5.05345	0.193933
$680$	13.4510	0.515823
$681$	−25.0223	−0.958858
$682$	−3.60791	−0.138154
$683$	−34.1733	−1.30761	−0.653803	−	0.756665i	$-0.726828\pi$
$683$	−34.1733	−1.30761	−0.653803	+	0.756665i	$0.726828\pi$
$684$	5.85873	0.224014
$685$	10.0528	0.384098
$686$	−10.9866	−0.419469
$687$	−20.2628	−0.773072
$688$	12.5165	0.477187
$689$	6.44142	0.245399
$690$	16.6488	0.633809
$691$	−1.84750	−0.0702824	−0.0351412	−	0.999382i	$-0.511188\pi$
$691$	−1.84750	−0.0702824	−0.0351412	+	0.999382i	$0.511188\pi$
$692$	4.34169	0.165046
$693$	−3.31306	−0.125853
$694$	−3.06551	−0.116365
$695$	−41.0493	−1.55709
$696$	6.86586	0.260250
$697$	41.8638	1.58571
$698$	11.4089	0.431832
$699$	10.4040	0.393516
$700$	2.12975	0.0804969
$701$	10.1157	0.382065	0.191033	−	0.981584i	$-0.438816\pi$
$701$	10.1157	0.382065	0.191033	+	0.981584i	$0.438816\pi$
$702$	1.00000	0.0377426
$703$	29.2083	1.10161
$704$	−4.01662	−0.151382
$705$	−33.0183	−1.24354
$706$	−27.4910	−1.03464
$707$	−14.4863	−0.544813
$708$	2.07171	0.0778596
$709$	−10.8613	−0.407906	−0.203953	−	0.978981i	$-0.565379\pi$
$709$	−10.8613	−0.407906	−0.203953	+	0.978981i	$0.565379\pi$
$710$	−14.4167	−0.541050
$711$	8.39757	0.314933
$712$	15.1576	0.568054
$713$	5.43107	0.203395
$714$	4.02932	0.150794
$715$	−11.0599	−0.413619
$716$	17.0414	0.636865
$717$	−26.4940	−0.989435
$718$	−12.5262	−0.467473
$719$	−3.69888	−0.137945	−0.0689725	−	0.997619i	$-0.521972\pi$
$719$	−3.69888	−0.137945	−0.0689725	+	0.997619i	$0.521972\pi$
$720$	−2.75355	−0.102619
$721$	−0.824838	−0.0307186
$722$	15.3247	0.570327
$723$	−1.31680	−0.0489725
$724$	17.2522	0.641172
$725$	−17.7278	−0.658393
$726$	−5.13324	−0.190512
$727$	47.4382	1.75938	0.879692	−	0.475543i	$-0.157749\pi$
$727$	47.4382	1.75938	0.879692	+	0.475543i	$0.157749\pi$
$728$	−0.824838	−0.0305705
$729$	1.00000	0.0370370
$730$	7.86906	0.291247
$731$	−61.1428	−2.26145
$732$	12.3179	0.455281
$733$	42.9033	1.58467	0.792335	−	0.610086i	$-0.208865\pi$
$733$	42.9033	1.58467	0.792335	+	0.610086i	$0.208865\pi$
$734$	21.5573	0.795696
$735$	−17.4014	−0.641861
$736$	6.04631	0.222870
$737$	−40.0009	−1.47345
$738$	−8.56990	−0.315463
$739$	−18.5493	−0.682348	−0.341174	−	0.940000i	$-0.610825\pi$
$739$	−18.5493	−0.682348	−0.341174	+	0.940000i	$0.610825\pi$
$740$	−13.7276	−0.504637
$741$	5.85873	0.215226
$742$	−5.31313	−0.195051
$743$	1.24993	0.0458556	0.0229278	−	0.999737i	$-0.492701\pi$
$743$	1.24993	0.0458556	0.0229278	+	0.999737i	$0.492701\pi$
$744$	−0.898245	−0.0329313
$745$	−8.23971	−0.301879
$746$	34.6777	1.26964
$747$	−5.21802	−0.190917
$748$	19.6211	0.717419
$749$	16.7455	0.611866
$750$	−6.65802	−0.243117
$751$	6.97426	0.254494	0.127247	−	0.991871i	$-0.459386\pi$
$751$	6.97426	0.254494	0.127247	+	0.991871i	$0.459386\pi$
$752$	−11.9912	−0.437274
$753$	13.8996	0.506531
$754$	6.86586	0.250040
$755$	54.7310	1.99186
$756$	−0.824838	−0.0299991
$757$	2.68607	0.0976270	0.0488135	−	0.998808i	$-0.484456\pi$
$757$	2.68607	0.0976270	0.0488135	+	0.998808i	$0.484456\pi$
$758$	−10.8080	−0.392566
$759$	24.2857	0.881516
$760$	−16.1323	−0.585179
$761$	−31.4888	−1.14147	−0.570734	−	0.821135i	$-0.693341\pi$
$761$	−31.4888	−1.14147	−0.570734	+	0.821135i	$0.693341\pi$
$762$	−14.5076	−0.525557
$763$	−2.55272	−0.0924147
$764$	−16.2534	−0.588029
$765$	13.4510	0.486323
$766$	2.54440	0.0919327
$767$	2.07171	0.0748051
$768$	−1.00000	−0.0360844
$769$	−39.1019	−1.41005	−0.705025	−	0.709182i	$-0.749064\pi$
$769$	−39.1019	−1.41005	−0.705025	+	0.709182i	$0.749064\pi$
$770$	9.12267	0.328758
$771$	−22.3217	−0.803895
$772$	−14.9122	−0.536703
$773$	29.1520	1.04852	0.524262	−	0.851557i	$-0.324341\pi$
$773$	29.1520	1.04852	0.524262	+	0.851557i	$0.324341\pi$
$774$	12.5165	0.449896
$775$	2.31929	0.0833112
$776$	6.12659	0.219932
$777$	−4.11217	−0.147523
$778$	18.6438	0.668412
$779$	−50.2088	−1.79892
$780$	−2.75355	−0.0985928
$781$	−21.0298	−0.752505
$782$	−29.5361	−1.05621
$783$	6.86586	0.245366
$784$	−6.31964	−0.225701
$785$	15.1130	0.539405
$786$	−13.3775	−0.477160
$787$	37.0525	1.32078	0.660389	−	0.750924i	$-0.270391\pi$
$787$	37.0525	1.32078	0.660389	+	0.750924i	$0.270391\pi$
$788$	17.5228	0.624224
$789$	16.1592	0.575284
$790$	−23.1231	−0.822683
$791$	12.0826	0.429607
$792$	−4.01662	−0.142724
$793$	12.3179	0.437420
$794$	−12.1568	−0.431429
$795$	−17.7368	−0.629058
$796$	−8.66641	−0.307173
$797$	−28.2779	−1.00166	−0.500828	−	0.865547i	$-0.666971\pi$
$797$	−28.2779	−1.00166	−0.500828	+	0.865547i	$0.666971\pi$
$798$	−4.83251	−0.171069
$799$	58.5768	2.07230
$800$	2.58202	0.0912881
$801$	15.1576	0.535566
$802$	17.1721	0.606370
$803$	11.4787	0.405073
$804$	−9.95884	−0.351221
$805$	−13.7326	−0.484009
$806$	−0.898245	−0.0316393
$807$	−6.48600	−0.228318
$808$	−17.5626	−0.617849
$809$	15.9799	0.561822	0.280911	−	0.959734i	$-0.409363\pi$
$809$	15.9799	0.561822	0.280911	+	0.959734i	$0.409363\pi$
$810$	−2.75355	−0.0967498
$811$	−37.0996	−1.30274	−0.651372	−	0.758758i	$-0.725806\pi$
$811$	−37.0996	−1.30274	−0.651372	+	0.758758i	$0.725806\pi$
$812$	−5.66322	−0.198740
$813$	25.7060	0.901548
$814$	−20.0246	−0.701861
$815$	−19.4459	−0.681158
$816$	4.88498	0.171009
$817$	73.3307	2.56552
$818$	−2.80065	−0.0979223
$819$	−0.824838	−0.0288222
$820$	23.5976	0.824065
$821$	−3.11002	−0.108541	−0.0542703	−	0.998526i	$-0.517283\pi$
$821$	−3.11002	−0.108541	−0.0542703	+	0.998526i	$0.517283\pi$
$822$	3.65086	0.127338
$823$	−26.3115	−0.917162	−0.458581	−	0.888653i	$-0.651642\pi$
$823$	−26.3115	−0.917162	−0.458581	+	0.888653i	$0.651642\pi$
$824$	−1.00000	−0.0348367
$825$	10.3710	0.361071
$826$	−1.70882	−0.0594576
$827$	−36.0829	−1.25472	−0.627362	−	0.778727i	$-0.715865\pi$
$827$	−36.0829	−1.25472	−0.627362	+	0.778727i	$0.715865\pi$
$828$	6.04631	0.210124
$829$	−0.0737644	−0.00256194	−0.00128097	−	0.999999i	$-0.500408\pi$
$829$	−0.0737644	−0.00256194	−0.00128097	+	0.999999i	$0.500408\pi$
$830$	14.3681	0.498723
$831$	16.0917	0.558214
$832$	−1.00000	−0.0346688
$833$	30.8713	1.06963
$834$	−14.9078	−0.516215
$835$	−46.7973	−1.61949
$836$	−23.5323	−0.813881
$837$	−0.898245	−0.0310479
$838$	40.3556	1.39406
$839$	−15.1825	−0.524160	−0.262080	−	0.965046i	$-0.584408\pi$
$839$	−15.1825	−0.524160	−0.262080	+	0.965046i	$0.584408\pi$
$840$	2.27123	0.0783649
$841$	18.1400	0.625518
$842$	−15.1113	−0.520771
$843$	−0.0961083	−0.00331014
$844$	−7.82353	−0.269297
$845$	−2.75355	−0.0947249
$846$	−11.9912	−0.412266
$847$	4.23409	0.145485
$848$	−6.44142	−0.221199
$849$	−5.39853	−0.185277
$850$	−12.6131	−0.432626
$851$	30.1435	1.03330
$852$	−5.23569	−0.179372
$853$	−44.9003	−1.53736	−0.768679	−	0.639634i	$-0.779086\pi$
$853$	−44.9003	−1.53736	−0.768679	+	0.639634i	$0.779086\pi$
$854$	−10.1602	−0.347676
$855$	−16.1323	−0.551712
$856$	20.3015	0.693891
$857$	27.5661	0.941641	0.470821	−	0.882229i	$-0.343958\pi$
$857$	27.5661	0.941641	0.470821	+	0.882229i	$0.343958\pi$
$858$	−4.01662	−0.137125
$859$	−17.7050	−0.604087	−0.302044	−	0.953294i	$-0.597669\pi$
$859$	−17.7050	−0.604087	−0.302044	+	0.953294i	$0.597669\pi$
$860$	−34.4647	−1.17524
$861$	7.06879	0.240904
$862$	23.8797	0.813345
$863$	−28.7685	−0.979291	−0.489645	−	0.871922i	$-0.662874\pi$
$863$	−28.7685	−0.979291	−0.489645	+	0.871922i	$0.662874\pi$
$864$	−1.00000	−0.0340207
$865$	−11.9551	−0.406484
$866$	−22.2116	−0.754782
$867$	−6.86306	−0.233082
$868$	0.740907	0.0251480
$869$	−33.7298	−1.14421
$870$	−18.9055	−0.640955
$871$	−9.95884	−0.337443
$872$	−3.09481	−0.104804
$873$	6.12659	0.207354
$874$	35.4237	1.19822
$875$	5.49179	0.185657
$876$	2.85779	0.0965558
$877$	0.0975824	0.00329512	0.00164756	−	0.999999i	$-0.499476\pi$
$877$	0.0975824	0.00329512	0.00164756	+	0.999999i	$0.499476\pi$
$878$	13.5722	0.458039
$879$	−22.2615	−0.750863
$880$	11.0599	0.372831
$881$	27.4355	0.924325	0.462163	−	0.886795i	$-0.347074\pi$
$881$	27.4355	0.924325	0.462163	+	0.886795i	$0.347074\pi$
$882$	−6.31964	−0.212793
$883$	6.74837	0.227101	0.113550	−	0.993532i	$-0.463778\pi$
$883$	6.74837	0.227101	0.113550	+	0.993532i	$0.463778\pi$
$884$	4.88498	0.164300
$885$	−5.70455	−0.191756
$886$	3.04113	0.102169
$887$	−53.6082	−1.79999	−0.899993	−	0.435904i	$-0.856429\pi$
$887$	−53.6082	−1.79999	−0.899993	+	0.435904i	$0.856429\pi$
$888$	−4.98543	−0.167300
$889$	11.9665	0.401342
$890$	−41.7370	−1.39903
$891$	−4.01662	−0.134562
$892$	−0.973709	−0.0326022
$893$	−70.2532	−2.35094
$894$	−2.99240	−0.100081
$895$	−46.9242	−1.56850
$896$	0.824838	0.0275559
$897$	6.04631	0.201880
$898$	−14.6556	−0.489064
$899$	−6.16723	−0.205689
$900$	2.58202	0.0860673
$901$	31.4662	1.04829
$902$	34.4220	1.14613
$903$	−10.3241	−0.343564
$904$	14.6484	0.487199
$905$	−47.5047	−1.57911
$906$	19.8765	0.660354
$907$	14.6663	0.486987	0.243494	−	0.969903i	$-0.421707\pi$
$907$	14.6663	0.486987	0.243494	+	0.969903i	$0.421707\pi$
$908$	25.0223	0.830395
$909$	−17.5626	−0.582514
$910$	2.27123	0.0752906
$911$	−15.7552	−0.521992	−0.260996	−	0.965340i	$-0.584051\pi$
$911$	−15.7552	−0.521992	−0.260996	+	0.965340i	$0.584051\pi$
$912$	−5.85873	−0.194002
$913$	20.9588	0.693635
$914$	19.5597	0.646979
$915$	−33.9178	−1.12129
$916$	20.2628	0.669500
$917$	11.0343	0.364384
$918$	4.88498	0.161228
$919$	−12.0221	−0.396574	−0.198287	−	0.980144i	$-0.563538\pi$
$919$	−12.0221	−0.396574	−0.198287	+	0.980144i	$0.563538\pi$
$920$	−16.6488	−0.548895
$921$	2.18512	0.0720021
$922$	6.48694	0.213636
$923$	−5.23569	−0.172335
$924$	3.31306	0.108992
$925$	12.8725	0.423244
$926$	30.7177	1.00945
$927$	−1.00000	−0.0328443
$928$	−6.86586	−0.225383
$929$	23.3913	0.767444	0.383722	−	0.923449i	$-0.374642\pi$
$929$	23.3913	0.767444	0.383722	+	0.923449i	$0.374642\pi$
$930$	2.47336	0.0811047
$931$	−37.0251	−1.21345
$932$	−10.4040	−0.340795
$933$	0.0801534	0.00262411
$934$	22.1129	0.723558
$935$	−54.0277	−1.76689
$936$	−1.00000	−0.0326860
$937$	−56.1198	−1.83336	−0.916678	−	0.399627i	$-0.869140\pi$
$937$	−56.1198	−1.83336	−0.916678	+	0.399627i	$0.869140\pi$
$938$	8.21444	0.268211
$939$	−9.05156	−0.295387
$940$	33.0183	1.07694
$941$	3.75419	0.122383	0.0611915	−	0.998126i	$-0.480510\pi$
$941$	3.75419	0.122383	0.0611915	+	0.998126i	$0.480510\pi$
$942$	5.48855	0.178827
$943$	−51.8163	−1.68737
$944$	−2.07171	−0.0674284
$945$	2.27123	0.0738831
$946$	−50.2740	−1.63455
$947$	48.9388	1.59030	0.795149	−	0.606414i	$-0.207392\pi$
$947$	48.9388	1.59030	0.795149	+	0.606414i	$0.207392\pi$
$948$	−8.39757	−0.272740
$949$	2.85779	0.0927678
$950$	15.1273	0.490796
$951$	−4.18981	−0.135864
$952$	−4.02932	−0.130591
$953$	−56.1519	−1.81894	−0.909469	−	0.415772i	$-0.863512\pi$
$953$	−56.1519	−1.81894	−0.909469	+	0.415772i	$0.863512\pi$
$954$	−6.44142	−0.208549
$955$	44.7546	1.44823
$956$	26.4940	0.856876
$957$	−27.5775	−0.891456
$958$	28.0901	0.907549
$959$	−3.01137	−0.0972421
$960$	2.75355	0.0888703
$961$	−30.1932	−0.973973
$962$	−4.98543	−0.160737
$963$	20.3015	0.654207
$964$	1.31680	0.0424114
$965$	41.0615	1.32182
$966$	−4.98723	−0.160461
$967$	−26.4792	−0.851514	−0.425757	−	0.904837i	$-0.639992\pi$
$967$	−26.4792	−0.851514	−0.425757	+	0.904837i	$0.639992\pi$
$968$	5.13324	0.164988
$969$	28.6198	0.919400
$970$	−16.8698	−0.541658
$971$	−32.1713	−1.03243	−0.516213	−	0.856460i	$-0.672659\pi$
$971$	−32.1713	−1.03243	−0.516213	+	0.856460i	$0.672659\pi$
$972$	−1.00000	−0.0320750
$973$	12.2965	0.394209
$974$	−43.1659	−1.38312
$975$	2.58202	0.0826908
$976$	−12.3179	−0.394285
$977$	−27.8028	−0.889490	−0.444745	−	0.895657i	$-0.646706\pi$
$977$	−27.8028	−0.889490	−0.444745	+	0.895657i	$0.646706\pi$
$978$	−7.06211	−0.225821
$979$	−60.8822	−1.94580
$980$	17.4014	0.555868
$981$	−3.09481	−0.0988098
$982$	4.59882	0.146754
$983$	−13.9383	−0.444561	−0.222281	−	0.974983i	$-0.571350\pi$
$983$	−13.9383	−0.444561	−0.222281	+	0.974983i	$0.571350\pi$
$984$	8.56990	0.273199
$985$	−48.2499	−1.53737
$986$	33.5396	1.06812
$987$	9.89081	0.314828
$988$	−5.85873	−0.186391
$989$	75.6786	2.40644
$990$	11.0599	0.351508
$991$	−16.6732	−0.529642	−0.264821	−	0.964298i	$-0.585313\pi$
$991$	−16.6732	−0.529642	−0.264821	+	0.964298i	$0.585313\pi$
$992$	0.898245	0.0285193
$993$	−18.0911	−0.574104
$994$	4.31860	0.136978
$995$	23.8634	0.756520
$996$	5.21802	0.165339
$997$	−30.0597	−0.952000	−0.476000	−	0.879445i	$-0.657914\pi$
$997$	−30.0597	−0.952000	−0.476000	+	0.879445i	$0.657914\pi$
$998$	14.7370	0.466490
$999$	−4.98543	−0.157732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bc.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bc.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.75355 q^{5} -1.00000 q^{6} +0.824838 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.75355 q^{5} -1.00000 q^{6} +0.824838 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.75355 q^{10} -4.01662 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.824838 q^{14} +2.75355 q^{15} +1.00000 q^{16} -4.88498 q^{17} +1.00000 q^{18} +5.85873 q^{19} -2.75355 q^{20} -0.824838 q^{21} -4.01662 q^{22} +6.04631 q^{23} -1.00000 q^{24} +2.58202 q^{25} -1.00000 q^{26} -1.00000 q^{27} +0.824838 q^{28} -6.86586 q^{29} +2.75355 q^{30} +0.898245 q^{31} +1.00000 q^{32} +4.01662 q^{33} -4.88498 q^{34} -2.27123 q^{35} +1.00000 q^{36} +4.98543 q^{37} +5.85873 q^{38} +1.00000 q^{39} -2.75355 q^{40} -8.56990 q^{41} -0.824838 q^{42} +12.5165 q^{43} -4.01662 q^{44} -2.75355 q^{45} +6.04631 q^{46} -11.9912 q^{47} -1.00000 q^{48} -6.31964 q^{49} +2.58202 q^{50} +4.88498 q^{51} -1.00000 q^{52} -6.44142 q^{53} -1.00000 q^{54} +11.0599 q^{55} +0.824838 q^{56} -5.85873 q^{57} -6.86586 q^{58} -2.07171 q^{59} +2.75355 q^{60} -12.3179 q^{61} +0.898245 q^{62} +0.824838 q^{63} +1.00000 q^{64} +2.75355 q^{65} +4.01662 q^{66} +9.95884 q^{67} -4.88498 q^{68} -6.04631 q^{69} -2.27123 q^{70} +5.23569 q^{71} +1.00000 q^{72} -2.85779 q^{73} +4.98543 q^{74} -2.58202 q^{75} +5.85873 q^{76} -3.31306 q^{77} +1.00000 q^{78} +8.39757 q^{79} -2.75355 q^{80} +1.00000 q^{81} -8.56990 q^{82} -5.21802 q^{83} -0.824838 q^{84} +13.4510 q^{85} +12.5165 q^{86} +6.86586 q^{87} -4.01662 q^{88} +15.1576 q^{89} -2.75355 q^{90} -0.824838 q^{91} +6.04631 q^{92} -0.898245 q^{93} -11.9912 q^{94} -16.1323 q^{95} -1.00000 q^{96} +6.12659 q^{97} -6.31964 q^{98} -4.01662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) \) 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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