LMFDB - Embedded newform 8034.2.a.bc.1.5

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			1.5
Root			$2.05101$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05101 q^{5} -1.00000 q^{6} -1.63593 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05101 q^{5} -1.00000 q^{6} -1.63593 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.05101 q^{10} -1.96737 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.63593 q^{14} +2.05101 q^{15} +1.00000 q^{16} -4.75332 q^{17} +1.00000 q^{18} -7.72431 q^{19} -2.05101 q^{20} +1.63593 q^{21} -1.96737 q^{22} -0.952745 q^{23} -1.00000 q^{24} -0.793369 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.63593 q^{28} -2.09348 q^{29} +2.05101 q^{30} +9.14308 q^{31} +1.00000 q^{32} +1.96737 q^{33} -4.75332 q^{34} +3.35531 q^{35} +1.00000 q^{36} +2.77305 q^{37} -7.72431 q^{38} +1.00000 q^{39} -2.05101 q^{40} -9.56781 q^{41} +1.63593 q^{42} +3.74993 q^{43} -1.96737 q^{44} -2.05101 q^{45} -0.952745 q^{46} +5.58312 q^{47} -1.00000 q^{48} -4.32373 q^{49} -0.793369 q^{50} +4.75332 q^{51} -1.00000 q^{52} -1.37438 q^{53} -1.00000 q^{54} +4.03509 q^{55} -1.63593 q^{56} +7.72431 q^{57} -2.09348 q^{58} -9.37885 q^{59} +2.05101 q^{60} +2.60018 q^{61} +9.14308 q^{62} -1.63593 q^{63} +1.00000 q^{64} +2.05101 q^{65} +1.96737 q^{66} +5.60782 q^{67} -4.75332 q^{68} +0.952745 q^{69} +3.35531 q^{70} -0.768551 q^{71} +1.00000 q^{72} +9.15376 q^{73} +2.77305 q^{74} +0.793369 q^{75} -7.72431 q^{76} +3.21848 q^{77} +1.00000 q^{78} +3.23726 q^{79} -2.05101 q^{80} +1.00000 q^{81} -9.56781 q^{82} +12.4302 q^{83} +1.63593 q^{84} +9.74909 q^{85} +3.74993 q^{86} +2.09348 q^{87} -1.96737 q^{88} -6.28143 q^{89} -2.05101 q^{90} +1.63593 q^{91} -0.952745 q^{92} -9.14308 q^{93} +5.58312 q^{94} +15.8426 q^{95} -1.00000 q^{96} -7.59891 q^{97} -4.32373 q^{98} -1.96737 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.05101	−0.917238	−0.458619	−	0.888633i	$-0.651656\pi$
$5$	−2.05101	−0.917238	−0.458619	+	0.888633i	$0.651656\pi$
$6$	−1.00000	−0.408248
$7$	−1.63593	−0.618324	−0.309162	−	0.951009i	$-0.600049\pi$
$7$	−1.63593	−0.618324	−0.309162	+	0.951009i	$0.600049\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.05101	−0.648585
$11$	−1.96737	−0.593185	−0.296592	−	0.955004i	$-0.595850\pi$
$11$	−1.96737	−0.593185	−0.296592	+	0.955004i	$0.595850\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.63593	−0.437221
$15$	2.05101	0.529568
$16$	1.00000	0.250000
$17$	−4.75332	−1.15285	−0.576424	−	0.817151i	$-0.695552\pi$
$17$	−4.75332	−1.15285	−0.576424	+	0.817151i	$0.695552\pi$
$18$	1.00000	0.235702
$19$	−7.72431	−1.77208	−0.886039	−	0.463611i	$-0.846553\pi$
$19$	−7.72431	−1.77208	−0.886039	+	0.463611i	$0.846553\pi$
$20$	−2.05101	−0.458619
$21$	1.63593	0.356990
$22$	−1.96737	−0.419445
$23$	−0.952745	−0.198661	−0.0993306	−	0.995054i	$-0.531670\pi$
$23$	−0.952745	−0.198661	−0.0993306	+	0.995054i	$0.531670\pi$
$24$	−1.00000	−0.204124
$25$	−0.793369	−0.158674
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−1.63593	−0.309162
$29$	−2.09348	−0.388749	−0.194374	−	0.980927i	$-0.562268\pi$
$29$	−2.09348	−0.388749	−0.194374	+	0.980927i	$0.562268\pi$
$30$	2.05101	0.374461
$31$	9.14308	1.64215	0.821073	−	0.570823i	$-0.193376\pi$
$31$	9.14308	1.64215	0.821073	+	0.570823i	$0.193376\pi$
$32$	1.00000	0.176777
$33$	1.96737	0.342475
$34$	−4.75332	−0.815187
$35$	3.35531	0.567151
$36$	1.00000	0.166667
$37$	2.77305	0.455887	0.227943	−	0.973674i	$-0.426800\pi$
$37$	2.77305	0.455887	0.227943	+	0.973674i	$0.426800\pi$
$38$	−7.72431	−1.25305
$39$	1.00000	0.160128
$40$	−2.05101	−0.324293
$41$	−9.56781	−1.49424	−0.747121	−	0.664689i	$-0.768564\pi$
$41$	−9.56781	−1.49424	−0.747121	+	0.664689i	$0.768564\pi$
$42$	1.63593	0.252430
$43$	3.74993	0.571859	0.285929	−	0.958251i	$-0.407698\pi$
$43$	3.74993	0.571859	0.285929	+	0.958251i	$0.407698\pi$
$44$	−1.96737	−0.296592
$45$	−2.05101	−0.305746
$46$	−0.952745	−0.140475
$47$	5.58312	0.814382	0.407191	−	0.913343i	$-0.366508\pi$
$47$	5.58312	0.814382	0.407191	+	0.913343i	$0.366508\pi$
$48$	−1.00000	−0.144338
$49$	−4.32373	−0.617675
$50$	−0.793369	−0.112199
$51$	4.75332	0.665597
$52$	−1.00000	−0.138675
$53$	−1.37438	−0.188785	−0.0943926	−	0.995535i	$-0.530091\pi$
$53$	−1.37438	−0.188785	−0.0943926	+	0.995535i	$0.530091\pi$
$54$	−1.00000	−0.136083
$55$	4.03509	0.544092
$56$	−1.63593	−0.218611
$57$	7.72431	1.02311
$58$	−2.09348	−0.274887
$59$	−9.37885	−1.22102	−0.610511	−	0.792008i	$-0.709036\pi$
$59$	−9.37885	−1.22102	−0.610511	+	0.792008i	$0.709036\pi$
$60$	2.05101	0.264784
$61$	2.60018	0.332919	0.166459	−	0.986048i	$-0.446767\pi$
$61$	2.60018	0.332919	0.166459	+	0.986048i	$0.446767\pi$
$62$	9.14308	1.16117
$63$	−1.63593	−0.206108
$64$	1.00000	0.125000
$65$	2.05101	0.254396
$66$	1.96737	0.242167
$67$	5.60782	0.685104	0.342552	−	0.939499i	$-0.388709\pi$
$67$	5.60782	0.685104	0.342552	+	0.939499i	$0.388709\pi$
$68$	−4.75332	−0.576424
$69$	0.952745	0.114697
$70$	3.35531	0.401036
$71$	−0.768551	−0.0912102	−0.0456051	−	0.998960i	$-0.514522\pi$
$71$	−0.768551	−0.0912102	−0.0456051	+	0.998960i	$0.514522\pi$
$72$	1.00000	0.117851
$73$	9.15376	1.07137	0.535683	−	0.844419i	$-0.320054\pi$
$73$	9.15376	1.07137	0.535683	+	0.844419i	$0.320054\pi$
$74$	2.77305	0.322360
$75$	0.793369	0.0916103
$76$	−7.72431	−0.886039
$77$	3.21848	0.366780
$78$	1.00000	0.113228
$79$	3.23726	0.364220	0.182110	−	0.983278i	$-0.441707\pi$
$79$	3.23726	0.364220	0.182110	+	0.983278i	$0.441707\pi$
$80$	−2.05101	−0.229310
$81$	1.00000	0.111111
$82$	−9.56781	−1.05659
$83$	12.4302	1.36439	0.682193	−	0.731172i	$-0.261026\pi$
$83$	12.4302	1.36439	0.682193	+	0.731172i	$0.261026\pi$
$84$	1.63593	0.178495
$85$	9.74909	1.05744
$86$	3.74993	0.404365
$87$	2.09348	0.224444
$88$	−1.96737	−0.209722
$89$	−6.28143	−0.665830	−0.332915	−	0.942957i	$-0.608032\pi$
$89$	−6.28143	−0.665830	−0.332915	+	0.942957i	$0.608032\pi$
$90$	−2.05101	−0.216195
$91$	1.63593	0.171492
$92$	−0.952745	−0.0993306
$93$	−9.14308	−0.948093
$94$	5.58312	0.575855
$95$	15.8426	1.62542
$96$	−1.00000	−0.102062
$97$	−7.59891	−0.771552	−0.385776	−	0.922592i	$-0.626066\pi$
$97$	−7.59891	−0.771552	−0.385776	+	0.922592i	$0.626066\pi$
$98$	−4.32373	−0.436762
$99$	−1.96737	−0.197728
$100$	−0.793369	−0.0793369
$101$	16.7085	1.66256	0.831280	−	0.555854i	$-0.187609\pi$
$101$	16.7085	1.66256	0.831280	+	0.555854i	$0.187609\pi$
$102$	4.75332	0.470648
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−3.35531	−0.327445
$106$	−1.37438	−0.133491
$107$	−15.8026	−1.52769	−0.763847	−	0.645397i	$-0.776692\pi$
$107$	−15.8026	−1.52769	−0.763847	+	0.645397i	$0.776692\pi$
$108$	−1.00000	−0.0962250
$109$	−7.02817	−0.673176	−0.336588	−	0.941652i	$-0.609273\pi$
$109$	−7.02817	−0.673176	−0.336588	+	0.941652i	$0.609273\pi$
$110$	4.03509	0.384731
$111$	−2.77305	−0.263206
$112$	−1.63593	−0.154581
$113$	−4.15073	−0.390468	−0.195234	−	0.980757i	$-0.562547\pi$
$113$	−4.15073	−0.390468	−0.195234	+	0.980757i	$0.562547\pi$
$114$	7.72431	0.723448
$115$	1.95409	0.182220
$116$	−2.09348	−0.194374
$117$	−1.00000	−0.0924500
$118$	−9.37885	−0.863393
$119$	7.77610	0.712834
$120$	2.05101	0.187230
$121$	−7.12945	−0.648132
$122$	2.60018	0.235409
$123$	9.56781	0.862701
$124$	9.14308	0.821073
$125$	11.8822	1.06278
$126$	−1.63593	−0.145740
$127$	2.15288	0.191037	0.0955184	−	0.995428i	$-0.469549\pi$
$127$	2.15288	0.191037	0.0955184	+	0.995428i	$0.469549\pi$
$128$	1.00000	0.0883883
$129$	−3.74993	−0.330163
$130$	2.05101	0.179885
$131$	6.40579	0.559676	0.279838	−	0.960047i	$-0.409719\pi$
$131$	6.40579	0.559676	0.279838	+	0.960047i	$0.409719\pi$
$132$	1.96737	0.171238
$133$	12.6364	1.09572
$134$	5.60782	0.484442
$135$	2.05101	0.176523
$136$	−4.75332	−0.407594
$137$	3.49417	0.298527	0.149264	−	0.988797i	$-0.452310\pi$
$137$	3.49417	0.298527	0.149264	+	0.988797i	$0.452310\pi$
$138$	0.952745	0.0811031
$139$	−8.19183	−0.694822	−0.347411	−	0.937713i	$-0.612939\pi$
$139$	−8.19183	−0.694822	−0.347411	+	0.937713i	$0.612939\pi$
$140$	3.35531	0.283575
$141$	−5.58312	−0.470184
$142$	−0.768551	−0.0644954
$143$	1.96737	0.164520
$144$	1.00000	0.0833333
$145$	4.29373	0.356575
$146$	9.15376	0.757570
$147$	4.32373	0.356615
$148$	2.77305	0.227943
$149$	15.2604	1.25018	0.625090	−	0.780553i	$-0.285062\pi$
$149$	15.2604	1.25018	0.625090	+	0.780553i	$0.285062\pi$
$150$	0.793369	0.0647783
$151$	3.51375	0.285945	0.142973	−	0.989727i	$-0.454334\pi$
$151$	3.51375	0.285945	0.142973	+	0.989727i	$0.454334\pi$
$152$	−7.72431	−0.626524
$153$	−4.75332	−0.384283
$154$	3.21848	0.259353
$155$	−18.7525	−1.50624
$156$	1.00000	0.0800641
$157$	13.6112	1.08629	0.543146	−	0.839638i	$-0.317233\pi$
$157$	13.6112	1.08629	0.543146	+	0.839638i	$0.317233\pi$
$158$	3.23726	0.257542
$159$	1.37438	0.108995
$160$	−2.05101	−0.162146
$161$	1.55863	0.122837
$162$	1.00000	0.0785674
$163$	−2.48927	−0.194975	−0.0974875	−	0.995237i	$-0.531081\pi$
$163$	−2.48927	−0.194975	−0.0974875	+	0.995237i	$0.531081\pi$
$164$	−9.56781	−0.747121
$165$	−4.03509	−0.314131
$166$	12.4302	0.964767
$167$	5.51732	0.426943	0.213471	−	0.976949i	$-0.431523\pi$
$167$	5.51732	0.426943	0.213471	+	0.976949i	$0.431523\pi$
$168$	1.63593	0.126215
$169$	1.00000	0.0769231
$170$	9.74909	0.747721
$171$	−7.72431	−0.590692
$172$	3.74993	0.285929
$173$	−3.49076	−0.265398	−0.132699	−	0.991156i	$-0.542364\pi$
$173$	−3.49076	−0.265398	−0.132699	+	0.991156i	$0.542364\pi$
$174$	2.09348	0.158706
$175$	1.29790	0.0981118
$176$	−1.96737	−0.148296
$177$	9.37885	0.704957
$178$	−6.28143	−0.470813
$179$	0.869690	0.0650037	0.0325018	−	0.999472i	$-0.489653\pi$
$179$	0.869690	0.0650037	0.0325018	+	0.999472i	$0.489653\pi$
$180$	−2.05101	−0.152873
$181$	14.1847	1.05434	0.527171	−	0.849759i	$-0.323253\pi$
$181$	14.1847	1.05434	0.527171	+	0.849759i	$0.323253\pi$
$182$	1.63593	0.121263
$183$	−2.60018	−0.192211
$184$	−0.952745	−0.0702373
$185$	−5.68754	−0.418157
$186$	−9.14308	−0.670403
$187$	9.35154	0.683852
$188$	5.58312	0.407191
$189$	1.63593	0.118997
$190$	15.8426	1.14934
$191$	5.68390	0.411272	0.205636	−	0.978628i	$-0.434074\pi$
$191$	5.68390	0.411272	0.205636	+	0.978628i	$0.434074\pi$
$192$	−1.00000	−0.0721688
$193$	13.5512	0.975439	0.487719	−	0.873000i	$-0.337829\pi$
$193$	13.5512	0.975439	0.487719	+	0.873000i	$0.337829\pi$
$194$	−7.59891	−0.545570
$195$	−2.05101	−0.146876
$196$	−4.32373	−0.308838
$197$	0.197262	0.0140543	0.00702716	−	0.999975i	$-0.497763\pi$
$197$	0.197262	0.0140543	0.00702716	+	0.999975i	$0.497763\pi$
$198$	−1.96737	−0.139815
$199$	−4.70360	−0.333430	−0.166715	−	0.986005i	$-0.553316\pi$
$199$	−4.70360	−0.333430	−0.166715	+	0.986005i	$0.553316\pi$
$200$	−0.793369	−0.0560997
$201$	−5.60782	−0.395545
$202$	16.7085	1.17561
$203$	3.42478	0.240373
$204$	4.75332	0.332799
$205$	19.6237	1.37058
$206$	−1.00000	−0.0696733
$207$	−0.952745	−0.0662204
$208$	−1.00000	−0.0693375
$209$	15.1966	1.05117
$210$	−3.35531	−0.231538
$211$	9.02680	0.621430	0.310715	−	0.950503i	$-0.399431\pi$
$211$	9.02680	0.621430	0.310715	+	0.950503i	$0.399431\pi$
$212$	−1.37438	−0.0943926
$213$	0.768551	0.0526602
$214$	−15.8026	−1.08024
$215$	−7.69113	−0.524531
$216$	−1.00000	−0.0680414
$217$	−14.9575	−1.01538
$218$	−7.02817	−0.476008
$219$	−9.15376	−0.618554
$220$	4.03509	0.272046
$221$	4.75332	0.319743
$222$	−2.77305	−0.186115
$223$	−27.5351	−1.84389	−0.921944	−	0.387324i	$-0.873399\pi$
$223$	−27.5351	−1.84389	−0.921944	+	0.387324i	$0.873399\pi$
$224$	−1.63593	−0.109305
$225$	−0.793369	−0.0528913
$226$	−4.15073	−0.276103
$227$	8.37920	0.556147	0.278073	−	0.960560i	$-0.410304\pi$
$227$	8.37920	0.556147	0.278073	+	0.960560i	$0.410304\pi$
$228$	7.72431	0.511555
$229$	7.16726	0.473626	0.236813	−	0.971555i	$-0.423897\pi$
$229$	7.16726	0.473626	0.236813	+	0.971555i	$0.423897\pi$
$230$	1.95409	0.128849
$231$	−3.21848	−0.211761
$232$	−2.09348	−0.137443
$233$	16.8531	1.10408	0.552042	−	0.833816i	$-0.313849\pi$
$233$	16.8531	1.10408	0.552042	+	0.833816i	$0.313849\pi$
$234$	−1.00000	−0.0653720
$235$	−11.4510	−0.746983
$236$	−9.37885	−0.610511
$237$	−3.23726	−0.210282
$238$	7.77610	0.504050
$239$	−23.4242	−1.51519	−0.757593	−	0.652727i	$-0.773625\pi$
$239$	−23.4242	−1.51519	−0.757593	+	0.652727i	$0.773625\pi$
$240$	2.05101	0.132392
$241$	1.65066	0.106328	0.0531641	−	0.998586i	$-0.483069\pi$
$241$	1.65066	0.106328	0.0531641	+	0.998586i	$0.483069\pi$
$242$	−7.12945	−0.458299
$243$	−1.00000	−0.0641500
$244$	2.60018	0.166459
$245$	8.86800	0.566556
$246$	9.56781	0.610021
$247$	7.72431	0.491486
$248$	9.14308	0.580586
$249$	−12.4302	−0.787729
$250$	11.8822	0.751499
$251$	−11.1260	−0.702270	−0.351135	−	0.936325i	$-0.614204\pi$
$251$	−11.1260	−0.702270	−0.351135	+	0.936325i	$0.614204\pi$
$252$	−1.63593	−0.103054
$253$	1.87440	0.117843
$254$	2.15288	0.135083
$255$	−9.74909	−0.610512
$256$	1.00000	0.0625000
$257$	−17.3102	−1.07978	−0.539890	−	0.841735i	$-0.681534\pi$
$257$	−17.3102	−1.07978	−0.539890	+	0.841735i	$0.681534\pi$
$258$	−3.74993	−0.233460
$259$	−4.53652	−0.281886
$260$	2.05101	0.127198
$261$	−2.09348	−0.129583
$262$	6.40579	0.395751
$263$	−7.79407	−0.480603	−0.240301	−	0.970698i	$-0.577246\pi$
$263$	−7.79407	−0.480603	−0.240301	+	0.970698i	$0.577246\pi$
$264$	1.96737	0.121083
$265$	2.81886	0.173161
$266$	12.6364	0.774790
$267$	6.28143	0.384417
$268$	5.60782	0.342552
$269$	−10.1302	−0.617652	−0.308826	−	0.951119i	$-0.599936\pi$
$269$	−10.1302	−0.617652	−0.308826	+	0.951119i	$0.599936\pi$
$270$	2.05101	0.124820
$271$	13.4818	0.818961	0.409480	−	0.912319i	$-0.365710\pi$
$271$	13.4818	0.818961	0.409480	+	0.912319i	$0.365710\pi$
$272$	−4.75332	−0.288212
$273$	−1.63593	−0.0990111
$274$	3.49417	0.211091
$275$	1.56085	0.0941228
$276$	0.952745	0.0573485
$277$	26.0301	1.56400	0.781998	−	0.623281i	$-0.214201\pi$
$277$	26.0301	1.56400	0.781998	+	0.623281i	$0.214201\pi$
$278$	−8.19183	−0.491313
$279$	9.14308	0.547382
$280$	3.35531	0.200518
$281$	3.54102	0.211240	0.105620	−	0.994407i	$-0.466317\pi$
$281$	3.54102	0.211240	0.105620	+	0.994407i	$0.466317\pi$
$282$	−5.58312	−0.332470
$283$	−18.7384	−1.11388	−0.556941	−	0.830552i	$-0.688025\pi$
$283$	−18.7384	−1.11388	−0.556941	+	0.830552i	$0.688025\pi$
$284$	−0.768551	−0.0456051
$285$	−15.8426	−0.938435
$286$	1.96737	0.116333
$287$	15.6523	0.923925
$288$	1.00000	0.0589256
$289$	5.59402	0.329060
$290$	4.29373	0.252137
$291$	7.59891	0.445456
$292$	9.15376	0.535683
$293$	−14.0709	−0.822033	−0.411016	−	0.911628i	$-0.634826\pi$
$293$	−14.0709	−0.822033	−0.411016	+	0.911628i	$0.634826\pi$
$294$	4.32373	0.252165
$295$	19.2361	1.11997
$296$	2.77305	0.161180
$297$	1.96737	0.114158
$298$	15.2604	0.884010
$299$	0.952745	0.0550987
$300$	0.793369	0.0458052
$301$	−6.13463	−0.353594
$302$	3.51375	0.202194
$303$	−16.7085	−0.959879
$304$	−7.72431	−0.443019
$305$	−5.33299	−0.305366
$306$	−4.75332	−0.271729
$307$	8.85911	0.505616	0.252808	−	0.967516i	$-0.418646\pi$
$307$	8.85911	0.505616	0.252808	+	0.967516i	$0.418646\pi$
$308$	3.21848	0.183390
$309$	1.00000	0.0568880
$310$	−18.7525	−1.06507
$311$	34.3848	1.94978	0.974892	−	0.222678i	$-0.0714797\pi$
$311$	34.3848	1.94978	0.974892	+	0.222678i	$0.0714797\pi$
$312$	1.00000	0.0566139
$313$	−22.8294	−1.29039	−0.645197	−	0.764016i	$-0.723225\pi$
$313$	−22.8294	−1.29039	−0.645197	+	0.764016i	$0.723225\pi$
$314$	13.6112	0.768125
$315$	3.35531	0.189050
$316$	3.23726	0.182110
$317$	26.9585	1.51414	0.757071	−	0.653332i	$-0.226630\pi$
$317$	26.9585	1.51414	0.757071	+	0.653332i	$0.226630\pi$
$318$	1.37438	0.0770712
$319$	4.11864	0.230600
$320$	−2.05101	−0.114655
$321$	15.8026	0.882015
$322$	1.55863	0.0868588
$323$	36.7161	2.04294
$324$	1.00000	0.0555556
$325$	0.793369	0.0440082
$326$	−2.48927	−0.137868
$327$	7.02817	0.388659
$328$	−9.56781	−0.528294
$329$	−9.13361	−0.503552
$330$	−4.03509	−0.222124
$331$	−14.0868	−0.774280	−0.387140	−	0.922021i	$-0.626537\pi$
$331$	−14.0868	−0.774280	−0.387140	+	0.922021i	$0.626537\pi$
$332$	12.4302	0.682193
$333$	2.77305	0.151962
$334$	5.51732	0.301894
$335$	−11.5017	−0.628404
$336$	1.63593	0.0892474
$337$	24.1632	1.31625	0.658126	−	0.752908i	$-0.271349\pi$
$337$	24.1632	1.31625	0.658126	+	0.752908i	$0.271349\pi$
$338$	1.00000	0.0543928
$339$	4.15073	0.225437
$340$	9.74909	0.528719
$341$	−17.9878	−0.974096
$342$	−7.72431	−0.417683
$343$	18.5248	1.00025
$344$	3.74993	0.202183
$345$	−1.95409	−0.105205
$346$	−3.49076	−0.187664
$347$	22.5146	1.20865	0.604324	−	0.796739i	$-0.293443\pi$
$347$	22.5146	1.20865	0.604324	+	0.796739i	$0.293443\pi$
$348$	2.09348	0.112222
$349$	−9.14497	−0.489519	−0.244760	−	0.969584i	$-0.578709\pi$
$349$	−9.14497	−0.489519	−0.244760	+	0.969584i	$0.578709\pi$
$350$	1.29790	0.0693755
$351$	1.00000	0.0533761
$352$	−1.96737	−0.104861
$353$	−29.2329	−1.55591	−0.777954	−	0.628321i	$-0.783742\pi$
$353$	−29.2329	−1.55591	−0.777954	+	0.628321i	$0.783742\pi$
$354$	9.37885	0.498480
$355$	1.57630	0.0836615
$356$	−6.28143	−0.332915
$357$	−7.77610	−0.411555
$358$	0.869690	0.0459645
$359$	−14.2120	−0.750083	−0.375041	−	0.927008i	$-0.622372\pi$
$359$	−14.2120	−0.750083	−0.375041	+	0.927008i	$0.622372\pi$
$360$	−2.05101	−0.108098
$361$	40.6649	2.14026
$362$	14.1847	0.745532
$363$	7.12945	0.374199
$364$	1.63593	0.0857461
$365$	−18.7744	−0.982698
$366$	−2.60018	−0.135914
$367$	−33.2324	−1.73472	−0.867358	−	0.497685i	$-0.834184\pi$
$367$	−33.2324	−1.73472	−0.867358	+	0.497685i	$0.834184\pi$
$368$	−0.952745	−0.0496653
$369$	−9.56781	−0.498080
$370$	−5.68754	−0.295681
$371$	2.24839	0.116730
$372$	−9.14308	−0.474047
$373$	28.9657	1.49979	0.749893	−	0.661559i	$-0.230105\pi$
$373$	28.9657	1.49979	0.749893	+	0.661559i	$0.230105\pi$
$374$	9.35154	0.483556
$375$	−11.8822	−0.613596
$376$	5.58312	0.287928
$377$	2.09348	0.107820
$378$	1.63593	0.0841432
$379$	9.51928	0.488973	0.244486	−	0.969653i	$-0.421381\pi$
$379$	9.51928	0.488973	0.244486	+	0.969653i	$0.421381\pi$
$380$	15.8426	0.812709
$381$	−2.15288	−0.110295
$382$	5.68390	0.290814
$383$	4.91506	0.251148	0.125574	−	0.992084i	$-0.459923\pi$
$383$	4.91506	0.251148	0.125574	+	0.992084i	$0.459923\pi$
$384$	−1.00000	−0.0510310
$385$	−6.60113	−0.336425
$386$	13.5512	0.689739
$387$	3.74993	0.190620
$388$	−7.59891	−0.385776
$389$	13.5847	0.688772	0.344386	−	0.938828i	$-0.388087\pi$
$389$	13.5847	0.688772	0.344386	+	0.938828i	$0.388087\pi$
$390$	−2.05101	−0.103857
$391$	4.52870	0.229026
$392$	−4.32373	−0.218381
$393$	−6.40579	−0.323129
$394$	0.197262	0.00993790
$395$	−6.63964	−0.334076
$396$	−1.96737	−0.0988641
$397$	26.5233	1.33117	0.665583	−	0.746324i	$-0.268183\pi$
$397$	26.5233	1.33117	0.665583	+	0.746324i	$0.268183\pi$
$398$	−4.70360	−0.235770
$399$	−12.6364	−0.632613
$400$	−0.793369	−0.0396684
$401$	11.4425	0.571413	0.285706	−	0.958317i	$-0.407772\pi$
$401$	11.4425	0.571413	0.285706	+	0.958317i	$0.407772\pi$
$402$	−5.60782	−0.279692
$403$	−9.14308	−0.455449
$404$	16.7085	0.831280
$405$	−2.05101	−0.101915
$406$	3.42478	0.169969
$407$	−5.45562	−0.270425
$408$	4.75332	0.235324
$409$	30.8632	1.52609	0.763043	−	0.646348i	$-0.223705\pi$
$409$	30.8632	1.52609	0.763043	+	0.646348i	$0.223705\pi$
$410$	19.6237	0.969143
$411$	−3.49417	−0.172355
$412$	−1.00000	−0.0492665
$413$	15.3432	0.754987
$414$	−0.952745	−0.0468249
$415$	−25.4943	−1.25147
$416$	−1.00000	−0.0490290
$417$	8.19183	0.401155
$418$	15.1966	0.743289
$419$	−9.88812	−0.483066	−0.241533	−	0.970393i	$-0.577650\pi$
$419$	−9.88812	−0.483066	−0.241533	+	0.970393i	$0.577650\pi$
$420$	−3.35531	−0.163722
$421$	37.1616	1.81115	0.905573	−	0.424191i	$-0.139441\pi$
$421$	37.1616	1.81115	0.905573	+	0.424191i	$0.139441\pi$
$422$	9.02680	0.439418
$423$	5.58312	0.271461
$424$	−1.37438	−0.0667457
$425$	3.77113	0.182927
$426$	0.768551	0.0372364
$427$	−4.25372	−0.205852
$428$	−15.8026	−0.763847
$429$	−1.96737	−0.0949855
$430$	−7.69113	−0.370899
$431$	−26.6743	−1.28486	−0.642428	−	0.766346i	$-0.722073\pi$
$431$	−26.6743	−1.28486	−0.642428	+	0.766346i	$0.722073\pi$
$432$	−1.00000	−0.0481125
$433$	31.0568	1.49249	0.746247	−	0.665669i	$-0.231854\pi$
$433$	31.0568	1.49249	0.746247	+	0.665669i	$0.231854\pi$
$434$	−14.9575	−0.717981
$435$	−4.29373	−0.205869
$436$	−7.02817	−0.336588
$437$	7.35930	0.352043
$438$	−9.15376	−0.437384
$439$	19.0081	0.907208	0.453604	−	0.891203i	$-0.350138\pi$
$439$	19.0081	0.907208	0.453604	+	0.891203i	$0.350138\pi$
$440$	4.03509	0.192365
$441$	−4.32373	−0.205892
$442$	4.75332	0.226092
$443$	27.5936	1.31101	0.655507	−	0.755189i	$-0.272455\pi$
$443$	27.5936	1.31101	0.655507	+	0.755189i	$0.272455\pi$
$444$	−2.77305	−0.131603
$445$	12.8833	0.610725
$446$	−27.5351	−1.30383
$447$	−15.2604	−0.721791
$448$	−1.63593	−0.0772905
$449$	32.0669	1.51333	0.756664	−	0.653804i	$-0.226828\pi$
$449$	32.0669	1.51333	0.756664	+	0.653804i	$0.226828\pi$
$450$	−0.793369	−0.0373998
$451$	18.8234	0.886361
$452$	−4.15073	−0.195234
$453$	−3.51375	−0.165091
$454$	8.37920	0.393255
$455$	−3.35531	−0.157299
$456$	7.72431	0.361724
$457$	13.9628	0.653151	0.326576	−	0.945171i	$-0.394105\pi$
$457$	13.9628	0.653151	0.326576	+	0.945171i	$0.394105\pi$
$458$	7.16726	0.334904
$459$	4.75332	0.221866
$460$	1.95409	0.0911098
$461$	21.1741	0.986178	0.493089	−	0.869979i	$-0.335868\pi$
$461$	21.1741	0.986178	0.493089	+	0.869979i	$0.335868\pi$
$462$	−3.21848	−0.149737
$463$	−3.10076	−0.144105	−0.0720523	−	0.997401i	$-0.522955\pi$
$463$	−3.10076	−0.144105	−0.0720523	+	0.997401i	$0.522955\pi$
$464$	−2.09348	−0.0971872
$465$	18.7525	0.869628
$466$	16.8531	0.780705
$467$	−11.1953	−0.518057	−0.259028	−	0.965870i	$-0.583402\pi$
$467$	−11.1953	−0.518057	−0.259028	+	0.965870i	$0.583402\pi$
$468$	−1.00000	−0.0462250
$469$	−9.17401	−0.423616
$470$	−11.4510	−0.528197
$471$	−13.6112	−0.627171
$472$	−9.37885	−0.431696
$473$	−7.37750	−0.339218
$474$	−3.23726	−0.148692
$475$	6.12822	0.281182
$476$	7.77610	0.356417
$477$	−1.37438	−0.0629284
$478$	−23.4242	−1.07140
$479$	−20.8766	−0.953876	−0.476938	−	0.878937i	$-0.658253\pi$
$479$	−20.8766	−0.953876	−0.476938	+	0.878937i	$0.658253\pi$
$480$	2.05101	0.0936152
$481$	−2.77305	−0.126440
$482$	1.65066	0.0751854
$483$	−1.55863	−0.0709199
$484$	−7.12945	−0.324066
$485$	15.5854	0.707697
$486$	−1.00000	−0.0453609
$487$	37.8999	1.71741	0.858703	−	0.512473i	$-0.171271\pi$
$487$	37.8999	1.71741	0.858703	+	0.512473i	$0.171271\pi$
$488$	2.60018	0.117705
$489$	2.48927	0.112569
$490$	8.86800	0.400615
$491$	15.4924	0.699160	0.349580	−	0.936906i	$-0.386324\pi$
$491$	15.4924	0.699160	0.349580	+	0.936906i	$0.386324\pi$
$492$	9.56781	0.431350
$493$	9.95096	0.448168
$494$	7.72431	0.347533
$495$	4.03509	0.181364
$496$	9.14308	0.410536
$497$	1.25730	0.0563975
$498$	−12.4302	−0.557008
$499$	−33.2335	−1.48774	−0.743868	−	0.668326i	$-0.767011\pi$
$499$	−33.2335	−1.48774	−0.743868	+	0.668326i	$0.767011\pi$
$500$	11.8822	0.531390
$501$	−5.51732	−0.246496
$502$	−11.1260	−0.496580
$503$	−20.5650	−0.916947	−0.458474	−	0.888708i	$-0.651604\pi$
$503$	−20.5650	−0.916947	−0.458474	+	0.888708i	$0.651604\pi$
$504$	−1.63593	−0.0728702
$505$	−34.2693	−1.52496
$506$	1.87440	0.0833274
$507$	−1.00000	−0.0444116
$508$	2.15288	0.0955184
$509$	−30.1255	−1.33529	−0.667645	−	0.744480i	$-0.732697\pi$
$509$	−30.1255	−1.33529	−0.667645	+	0.744480i	$0.732697\pi$
$510$	−9.74909	−0.431697
$511$	−14.9749	−0.662452
$512$	1.00000	0.0441942
$513$	7.72431	0.341036
$514$	−17.3102	−0.763520
$515$	2.05101	0.0903782
$516$	−3.74993	−0.165081
$517$	−10.9841	−0.483079
$518$	−4.53652	−0.199323
$519$	3.49076	0.153227
$520$	2.05101	0.0899426
$521$	−42.4093	−1.85799	−0.928993	−	0.370097i	$-0.879324\pi$
$521$	−42.4093	−1.85799	−0.928993	+	0.370097i	$0.879324\pi$
$522$	−2.09348	−0.0916290
$523$	−0.665979	−0.0291212	−0.0145606	−	0.999894i	$-0.504635\pi$
$523$	−0.665979	−0.0291212	−0.0145606	+	0.999894i	$0.504635\pi$
$524$	6.40579	0.279838
$525$	−1.29790	−0.0566449
$526$	−7.79407	−0.339837
$527$	−43.4600	−1.89315
$528$	1.96737	0.0856188
$529$	−22.0923	−0.960534
$530$	2.81886	0.122443
$531$	−9.37885	−0.407007
$532$	12.6364	0.547859
$533$	9.56781	0.414428
$534$	6.28143	0.271824
$535$	32.4112	1.40126
$536$	5.60782	0.242221
$537$	−0.869690	−0.0375299
$538$	−10.1302	−0.436746
$539$	8.50637	0.366395
$540$	2.05101	0.0882613
$541$	26.9992	1.16079	0.580393	−	0.814336i	$-0.302899\pi$
$541$	26.9992	1.16079	0.580393	+	0.814336i	$0.302899\pi$
$542$	13.4818	0.579093
$543$	−14.1847	−0.608724
$544$	−4.75332	−0.203797
$545$	14.4148	0.617463
$546$	−1.63593	−0.0700114
$547$	−7.96155	−0.340411	−0.170206	−	0.985409i	$-0.554443\pi$
$547$	−7.96155	−0.340411	−0.170206	+	0.985409i	$0.554443\pi$
$548$	3.49417	0.149264
$549$	2.60018	0.110973
$550$	1.56085	0.0665549
$551$	16.1706	0.688893
$552$	0.952745	0.0405515
$553$	−5.29593	−0.225206
$554$	26.0301	1.10591
$555$	5.68754	0.241423
$556$	−8.19183	−0.347411
$557$	15.3251	0.649347	0.324674	−	0.945826i	$-0.394746\pi$
$557$	15.3251	0.649347	0.324674	+	0.945826i	$0.394746\pi$
$558$	9.14308	0.387057
$559$	−3.74993	−0.158605
$560$	3.35531	0.141788
$561$	−9.35154	−0.394822
$562$	3.54102	0.149369
$563$	−41.2756	−1.73956	−0.869779	−	0.493441i	$-0.835739\pi$
$563$	−41.2756	−1.73956	−0.869779	+	0.493441i	$0.835739\pi$
$564$	−5.58312	−0.235092
$565$	8.51318	0.358152
$566$	−18.7384	−0.787633
$567$	−1.63593	−0.0687027
$568$	−0.768551	−0.0322477
$569$	27.1026	1.13620	0.568099	−	0.822960i	$-0.307679\pi$
$569$	27.1026	1.13620	0.568099	+	0.822960i	$0.307679\pi$
$570$	−15.8426	−0.663574
$571$	7.89439	0.330370	0.165185	−	0.986263i	$-0.447178\pi$
$571$	7.89439	0.330370	0.165185	+	0.986263i	$0.447178\pi$
$572$	1.96737	0.0822599
$573$	−5.68390	−0.237448
$574$	15.6523	0.653314
$575$	0.755878	0.0315223
$576$	1.00000	0.0416667
$577$	−21.9953	−0.915678	−0.457839	−	0.889035i	$-0.651376\pi$
$577$	−21.9953	−0.915678	−0.457839	+	0.889035i	$0.651376\pi$
$578$	5.59402	0.232681
$579$	−13.5512	−0.563170
$580$	4.29373	0.178288
$581$	−20.3349	−0.843633
$582$	7.59891	0.314985
$583$	2.70391	0.111984
$584$	9.15376	0.378785
$585$	2.05101	0.0847987
$586$	−14.0709	−0.581265
$587$	−10.1600	−0.419346	−0.209673	−	0.977772i	$-0.567240\pi$
$587$	−10.1600	−0.419346	−0.209673	+	0.977772i	$0.567240\pi$
$588$	4.32373	0.178308
$589$	−70.6240	−2.91001
$590$	19.2361	0.791937
$591$	−0.197262	−0.00811426
$592$	2.77305	0.113972
$593$	−36.2785	−1.48978	−0.744891	−	0.667187i	$-0.767498\pi$
$593$	−36.2785	−1.48978	−0.744891	+	0.667187i	$0.767498\pi$
$594$	1.96737	0.0807222
$595$	−15.9488	−0.653839
$596$	15.2604	0.625090
$597$	4.70360	0.192506
$598$	0.952745	0.0389606
$599$	37.9189	1.54932	0.774662	−	0.632376i	$-0.217920\pi$
$599$	37.9189	1.54932	0.774662	+	0.632376i	$0.217920\pi$
$600$	0.793369	0.0323891
$601$	−28.5638	−1.16514	−0.582571	−	0.812780i	$-0.697953\pi$
$601$	−28.5638	−1.16514	−0.582571	+	0.812780i	$0.697953\pi$
$602$	−6.13463	−0.250029
$603$	5.60782	0.228368
$604$	3.51375	0.142973
$605$	14.6226	0.594492
$606$	−16.7085	−0.678737
$607$	27.2317	1.10530	0.552651	−	0.833413i	$-0.313616\pi$
$607$	27.2317	1.10530	0.552651	+	0.833413i	$0.313616\pi$
$608$	−7.72431	−0.313262
$609$	−3.42478	−0.138779
$610$	−5.33299	−0.215926
$611$	−5.58312	−0.225869
$612$	−4.75332	−0.192141
$613$	15.1951	0.613724	0.306862	−	0.951754i	$-0.400721\pi$
$613$	15.1951	0.613724	0.306862	+	0.951754i	$0.400721\pi$
$614$	8.85911	0.357524
$615$	−19.6237	−0.791302
$616$	3.21848	0.129676
$617$	0.124161	0.00499852	0.00249926	−	0.999997i	$-0.499204\pi$
$617$	0.124161	0.00499852	0.00249926	+	0.999997i	$0.499204\pi$
$618$	1.00000	0.0402259
$619$	−4.35831	−0.175175	−0.0875876	−	0.996157i	$-0.527916\pi$
$619$	−4.35831	−0.175175	−0.0875876	+	0.996157i	$0.527916\pi$
$620$	−18.7525	−0.753120
$621$	0.952745	0.0382323
$622$	34.3848	1.37871
$623$	10.2760	0.411699
$624$	1.00000	0.0400320
$625$	−20.4037	−0.816149
$626$	−22.8294	−0.912447
$627$	−15.1966	−0.606893
$628$	13.6112	0.543146
$629$	−13.1812	−0.525568
$630$	3.35531	0.133679
$631$	−11.7231	−0.466690	−0.233345	−	0.972394i	$-0.574967\pi$
$631$	−11.7231	−0.466690	−0.233345	+	0.972394i	$0.574967\pi$
$632$	3.23726	0.128771
$633$	−9.02680	−0.358783
$634$	26.9585	1.07066
$635$	−4.41556	−0.175226
$636$	1.37438	0.0544976
$637$	4.32373	0.171312
$638$	4.11864	0.163059
$639$	−0.768551	−0.0304034
$640$	−2.05101	−0.0810732
$641$	−34.1541	−1.34901	−0.674503	−	0.738272i	$-0.735642\pi$
$641$	−34.1541	−1.34901	−0.674503	+	0.738272i	$0.735642\pi$
$642$	15.8026	0.623679
$643$	−5.89952	−0.232654	−0.116327	−	0.993211i	$-0.537112\pi$
$643$	−5.89952	−0.232654	−0.116327	+	0.993211i	$0.537112\pi$
$644$	1.55863	0.0614185
$645$	7.69113	0.302838
$646$	36.7161	1.44457
$647$	−4.52293	−0.177815	−0.0889075	−	0.996040i	$-0.528338\pi$
$647$	−4.52293	−0.177815	−0.0889075	+	0.996040i	$0.528338\pi$
$648$	1.00000	0.0392837
$649$	18.4517	0.724291
$650$	0.793369	0.0311185
$651$	14.9575	0.586229
$652$	−2.48927	−0.0974875
$653$	−1.04118	−0.0407446	−0.0203723	−	0.999792i	$-0.506485\pi$
$653$	−1.04118	−0.0407446	−0.0203723	+	0.999792i	$0.506485\pi$
$654$	7.02817	0.274823
$655$	−13.1383	−0.513357
$656$	−9.56781	−0.373560
$657$	9.15376	0.357122
$658$	−9.13361	−0.356065
$659$	12.7324	0.495983	0.247991	−	0.968762i	$-0.420230\pi$
$659$	12.7324	0.495983	0.247991	+	0.968762i	$0.420230\pi$
$660$	−4.03509	−0.157066
$661$	14.5700	0.566709	0.283354	−	0.959015i	$-0.408553\pi$
$661$	14.5700	0.566709	0.283354	+	0.959015i	$0.408553\pi$
$662$	−14.0868	−0.547499
$663$	−4.75332	−0.184604
$664$	12.4302	0.482383
$665$	−25.9174	−1.00503
$666$	2.77305	0.107453
$667$	1.99455	0.0772293
$668$	5.51732	0.213471
$669$	27.5351	1.06457
$670$	−11.5017	−0.444348
$671$	−5.11552	−0.197482
$672$	1.63593	0.0631074
$673$	−0.563354	−0.0217157	−0.0108579	−	0.999941i	$-0.503456\pi$
$673$	−0.563354	−0.0217157	−0.0108579	+	0.999941i	$0.503456\pi$
$674$	24.1632	0.930731
$675$	0.793369	0.0305368
$676$	1.00000	0.0384615
$677$	−50.4341	−1.93834	−0.969169	−	0.246395i	$-0.920754\pi$
$677$	−50.4341	−1.93834	−0.969169	+	0.246395i	$0.920754\pi$
$678$	4.15073	0.159408
$679$	12.4313	0.477069
$680$	9.74909	0.373860
$681$	−8.37920	−0.321092
$682$	−17.9878	−0.688790
$683$	3.47283	0.132884	0.0664420	−	0.997790i	$-0.478835\pi$
$683$	3.47283	0.132884	0.0664420	+	0.997790i	$0.478835\pi$
$684$	−7.72431	−0.295346
$685$	−7.16658	−0.273821
$686$	18.5248	0.707282
$687$	−7.16726	−0.273448
$688$	3.74993	0.142965
$689$	1.37438	0.0523596
$690$	−1.95409	−0.0743908
$691$	33.3395	1.26829	0.634147	−	0.773213i	$-0.281351\pi$
$691$	33.3395	1.26829	0.634147	+	0.773213i	$0.281351\pi$
$692$	−3.49076	−0.132699
$693$	3.21848	0.122260
$694$	22.5146	0.854643
$695$	16.8015	0.637317
$696$	2.09348	0.0793530
$697$	45.4788	1.72263
$698$	−9.14497	−0.346142
$699$	−16.8531	−0.637443
$700$	1.29790	0.0490559
$701$	−15.9443	−0.602207	−0.301103	−	0.953592i	$-0.597355\pi$
$701$	−15.9443	−0.602207	−0.301103	+	0.953592i	$0.597355\pi$
$702$	1.00000	0.0377426
$703$	−21.4199	−0.807866
$704$	−1.96737	−0.0741481
$705$	11.4510	0.431271
$706$	−29.2329	−1.10019
$707$	−27.3340	−1.02800
$708$	9.37885	0.352479
$709$	24.4755	0.919196	0.459598	−	0.888127i	$-0.347993\pi$
$709$	24.4755	0.919196	0.459598	+	0.888127i	$0.347993\pi$
$710$	1.57630	0.0591576
$711$	3.23726	0.121407
$712$	−6.28143	−0.235407
$713$	−8.71103	−0.326231
$714$	−7.77610	−0.291013
$715$	−4.03509	−0.150904
$716$	0.869690	0.0325018
$717$	23.4242	0.874793
$718$	−14.2120	−0.530389
$719$	8.89640	0.331780	0.165890	−	0.986144i	$-0.446950\pi$
$719$	8.89640	0.331780	0.165890	+	0.986144i	$0.446950\pi$
$720$	−2.05101	−0.0764365
$721$	1.63593	0.0609253
$722$	40.6649	1.51339
$723$	−1.65066	−0.0613886
$724$	14.1847	0.527171
$725$	1.66090	0.0616842
$726$	7.12945	0.264599
$727$	−48.6352	−1.80378	−0.901890	−	0.431967i	$-0.857820\pi$
$727$	−48.6352	−1.80378	−0.901890	+	0.431967i	$0.857820\pi$
$728$	1.63593	0.0606317
$729$	1.00000	0.0370370
$730$	−18.7744	−0.694873
$731$	−17.8246	−0.659267
$732$	−2.60018	−0.0961054
$733$	−25.3578	−0.936611	−0.468305	−	0.883567i	$-0.655135\pi$
$733$	−25.3578	−0.936611	−0.468305	+	0.883567i	$0.655135\pi$
$734$	−33.2324	−1.22663
$735$	−8.86800	−0.327101
$736$	−0.952745	−0.0351187
$737$	−11.0327	−0.406393
$738$	−9.56781	−0.352196
$739$	4.13060	0.151947	0.0759733	−	0.997110i	$-0.475794\pi$
$739$	4.13060	0.151947	0.0759733	+	0.997110i	$0.475794\pi$
$740$	−5.68754	−0.209078
$741$	−7.72431	−0.283759
$742$	2.24839	0.0825409
$743$	−4.36600	−0.160173	−0.0800864	−	0.996788i	$-0.525520\pi$
$743$	−4.36600	−0.160173	−0.0800864	+	0.996788i	$0.525520\pi$
$744$	−9.14308	−0.335202
$745$	−31.2992	−1.14671
$746$	28.9657	1.06051
$747$	12.4302	0.454796
$748$	9.35154	0.341926
$749$	25.8520	0.944611
$750$	−11.8822	−0.433878
$751$	−7.68384	−0.280387	−0.140194	−	0.990124i	$-0.544773\pi$
$751$	−7.68384	−0.280387	−0.140194	+	0.990124i	$0.544773\pi$
$752$	5.58312	0.203596
$753$	11.1260	0.405456
$754$	2.09348	0.0762399
$755$	−7.20673	−0.262280
$756$	1.63593	0.0594983
$757$	37.6196	1.36731	0.683654	−	0.729807i	$-0.260390\pi$
$757$	37.6196	1.36731	0.683654	+	0.729807i	$0.260390\pi$
$758$	9.51928	0.345756
$759$	−1.87440	−0.0680365
$760$	15.8426	0.574672
$761$	−2.30144	−0.0834272	−0.0417136	−	0.999130i	$-0.513282\pi$
$761$	−2.30144	−0.0834272	−0.0417136	+	0.999130i	$0.513282\pi$
$762$	−2.15288	−0.0779905
$763$	11.4976	0.416241
$764$	5.68390	0.205636
$765$	9.74909	0.352479
$766$	4.91506	0.177588
$767$	9.37885	0.338650
$768$	−1.00000	−0.0360844
$769$	9.62219	0.346985	0.173493	−	0.984835i	$-0.444495\pi$
$769$	9.62219	0.346985	0.173493	+	0.984835i	$0.444495\pi$
$770$	−6.60113	−0.237888
$771$	17.3102	0.623412
$772$	13.5512	0.487719
$773$	−21.4875	−0.772852	−0.386426	−	0.922320i	$-0.626291\pi$
$773$	−21.4875	−0.772852	−0.386426	+	0.922320i	$0.626291\pi$
$774$	3.74993	0.134788
$775$	−7.25384	−0.260565
$776$	−7.59891	−0.272785
$777$	4.53652	0.162747
$778$	13.5847	0.487035
$779$	73.9047	2.64791
$780$	−2.05101	−0.0734378
$781$	1.51202	0.0541045
$782$	4.52870	0.161946
$783$	2.09348	0.0748147
$784$	−4.32373	−0.154419
$785$	−27.9167	−0.996389
$786$	−6.40579	−0.228487
$787$	−52.2357	−1.86200	−0.931002	−	0.365015i	$-0.881064\pi$
$787$	−52.2357	−1.86200	−0.931002	+	0.365015i	$0.881064\pi$
$788$	0.197262	0.00702716
$789$	7.79407	0.277476
$790$	−6.63964	−0.236228
$791$	6.79032	0.241436
$792$	−1.96737	−0.0699075
$793$	−2.60018	−0.0923351
$794$	26.5233	0.941276
$795$	−2.81886	−0.0999746
$796$	−4.70360	−0.166715
$797$	−38.1373	−1.35089	−0.675446	−	0.737410i	$-0.736049\pi$
$797$	−38.1373	−1.35089	−0.675446	+	0.737410i	$0.736049\pi$
$798$	−12.6364	−0.447325
$799$	−26.5384	−0.938860
$800$	−0.793369	−0.0280498
$801$	−6.28143	−0.221943
$802$	11.4425	0.404050
$803$	−18.0088	−0.635518
$804$	−5.60782	−0.197772
$805$	−3.19675	−0.112671
$806$	−9.14308	−0.322051
$807$	10.1302	0.356602
$808$	16.7085	0.587804
$809$	5.60400	0.197026	0.0985130	−	0.995136i	$-0.468591\pi$
$809$	5.60400	0.197026	0.0985130	+	0.995136i	$0.468591\pi$
$810$	−2.05101	−0.0720651
$811$	25.2858	0.887906	0.443953	−	0.896050i	$-0.353576\pi$
$811$	25.2858	0.887906	0.443953	+	0.896050i	$0.353576\pi$
$812$	3.42478	0.120186
$813$	−13.4818	−0.472827
$814$	−5.45562	−0.191219
$815$	5.10552	0.178839
$816$	4.75332	0.166399
$817$	−28.9656	−1.01338
$818$	30.8632	1.07911
$819$	1.63593	0.0571641
$820$	19.6237	0.685288
$821$	4.00401	0.139741	0.0698705	−	0.997556i	$-0.477741\pi$
$821$	4.00401	0.139741	0.0698705	+	0.997556i	$0.477741\pi$
$822$	−3.49417	−0.121873
$823$	−52.2745	−1.82217	−0.911087	−	0.412214i	$-0.864756\pi$
$823$	−52.2745	−1.82217	−0.911087	+	0.412214i	$0.864756\pi$
$824$	−1.00000	−0.0348367
$825$	−1.56085	−0.0543418
$826$	15.3432	0.533857
$827$	−27.6416	−0.961193	−0.480597	−	0.876942i	$-0.659580\pi$
$827$	−27.6416	−0.961193	−0.480597	+	0.876942i	$0.659580\pi$
$828$	−0.952745	−0.0331102
$829$	5.56663	0.193337	0.0966685	−	0.995317i	$-0.469181\pi$
$829$	5.56663	0.193337	0.0966685	+	0.995317i	$0.469181\pi$
$830$	−25.4943	−0.884921
$831$	−26.0301	−0.902973
$832$	−1.00000	−0.0346688
$833$	20.5520	0.712086
$834$	8.19183	0.283660
$835$	−11.3161	−0.391608
$836$	15.1966	0.525584
$837$	−9.14308	−0.316031
$838$	−9.88812	−0.341579
$839$	28.6618	0.989516	0.494758	−	0.869031i	$-0.335257\pi$
$839$	28.6618	0.989516	0.494758	+	0.869031i	$0.335257\pi$
$840$	−3.35531	−0.115769
$841$	−24.6174	−0.848874
$842$	37.1616	1.28067
$843$	−3.54102	−0.121959
$844$	9.02680	0.310715
$845$	−2.05101	−0.0705568
$846$	5.58312	0.191952
$847$	11.6633	0.400756
$848$	−1.37438	−0.0471963
$849$	18.7384	0.643100
$850$	3.77113	0.129349
$851$	−2.64201	−0.0905669
$852$	0.768551	0.0263301
$853$	53.0347	1.81587	0.907937	−	0.419106i	$-0.137656\pi$
$853$	53.0347	1.81587	0.907937	+	0.419106i	$0.137656\pi$
$854$	−4.25372	−0.145559
$855$	15.8426	0.541806
$856$	−15.8026	−0.540122
$857$	−47.8208	−1.63353	−0.816764	−	0.576973i	$-0.804234\pi$
$857$	−47.8208	−1.63353	−0.816764	+	0.576973i	$0.804234\pi$
$858$	−1.96737	−0.0671649
$859$	−6.92360	−0.236230	−0.118115	−	0.993000i	$-0.537685\pi$
$859$	−6.92360	−0.236230	−0.118115	+	0.993000i	$0.537685\pi$
$860$	−7.69113	−0.262265
$861$	−15.6523	−0.533429
$862$	−26.6743	−0.908530
$863$	29.7291	1.01199	0.505996	−	0.862536i	$-0.331125\pi$
$863$	29.7291	1.01199	0.505996	+	0.862536i	$0.331125\pi$
$864$	−1.00000	−0.0340207
$865$	7.15957	0.243433
$866$	31.0568	1.05535
$867$	−5.59402	−0.189983
$868$	−14.9575	−0.507689
$869$	−6.36888	−0.216050
$870$	−4.29373	−0.145571
$871$	−5.60782	−0.190014
$872$	−7.02817	−0.238004
$873$	−7.59891	−0.257184
$874$	7.35930	0.248932
$875$	−19.4385	−0.657142
$876$	−9.15376	−0.309277
$877$	30.3693	1.02550	0.512750	−	0.858538i	$-0.328627\pi$
$877$	30.3693	1.02550	0.512750	+	0.858538i	$0.328627\pi$
$878$	19.0081	0.641493
$879$	14.0709	0.474601
$880$	4.03509	0.136023
$881$	42.2381	1.42304	0.711519	−	0.702667i	$-0.248008\pi$
$881$	42.2381	1.42304	0.711519	+	0.702667i	$0.248008\pi$
$882$	−4.32373	−0.145587
$883$	6.78836	0.228447	0.114223	−	0.993455i	$-0.463562\pi$
$883$	6.78836	0.228447	0.114223	+	0.993455i	$0.463562\pi$
$884$	4.75332	0.159871
$885$	−19.2361	−0.646614
$886$	27.5936	0.927027
$887$	−48.8961	−1.64177	−0.820884	−	0.571094i	$-0.806519\pi$
$887$	−48.8961	−1.64177	−0.820884	+	0.571094i	$0.806519\pi$
$888$	−2.77305	−0.0930574
$889$	−3.52196	−0.118123
$890$	12.8833	0.431848
$891$	−1.96737	−0.0659094
$892$	−27.5351	−0.921944
$893$	−43.1258	−1.44315
$894$	−15.2604	−0.510384
$895$	−1.78374	−0.0596239
$896$	−1.63593	−0.0546526
$897$	−0.952745	−0.0318112
$898$	32.0669	1.07008
$899$	−19.1408	−0.638382
$900$	−0.793369	−0.0264456
$901$	6.53285	0.217641
$902$	18.8234	0.626752
$903$	6.13463	0.204148
$904$	−4.15073	−0.138051
$905$	−29.0929	−0.967082
$906$	−3.51375	−0.116737
$907$	41.9144	1.39175	0.695873	−	0.718165i	$-0.255018\pi$
$907$	41.9144	1.39175	0.695873	+	0.718165i	$0.255018\pi$
$908$	8.37920	0.278073
$909$	16.7085	0.554186
$910$	−3.35531	−0.111227
$911$	5.97789	0.198056	0.0990282	−	0.995085i	$-0.468427\pi$
$911$	5.97789	0.198056	0.0990282	+	0.995085i	$0.468427\pi$
$912$	7.72431	0.255777
$913$	−24.4547	−0.809333
$914$	13.9628	0.461848
$915$	5.33299	0.176303
$916$	7.16726	0.236813
$917$	−10.4794	−0.346061
$918$	4.75332	0.156883
$919$	14.0890	0.464754	0.232377	−	0.972626i	$-0.425350\pi$
$919$	14.0890	0.464754	0.232377	+	0.972626i	$0.425350\pi$
$920$	1.95409	0.0644244
$921$	−8.85911	−0.291918
$922$	21.1741	0.697333
$923$	0.768551	0.0252972
$924$	−3.21848	−0.105880
$925$	−2.20005	−0.0723372
$926$	−3.10076	−0.101897
$927$	−1.00000	−0.0328443
$928$	−2.09348	−0.0687217
$929$	33.7949	1.10878	0.554388	−	0.832259i	$-0.312953\pi$
$929$	33.7949	1.10878	0.554388	+	0.832259i	$0.312953\pi$
$930$	18.7525	0.614920
$931$	33.3978	1.09457
$932$	16.8531	0.552042
$933$	−34.3848	−1.12571
$934$	−11.1953	−0.366322
$935$	−19.1801	−0.627255
$936$	−1.00000	−0.0326860
$937$	−55.7089	−1.81993	−0.909965	−	0.414684i	$-0.863892\pi$
$937$	−55.7089	−1.81993	−0.909965	+	0.414684i	$0.863892\pi$
$938$	−9.17401	−0.299542
$939$	22.8294	0.745010
$940$	−11.4510	−0.373491
$941$	−28.6326	−0.933396	−0.466698	−	0.884417i	$-0.654556\pi$
$941$	−28.6326	−0.933396	−0.466698	+	0.884417i	$0.654556\pi$
$942$	−13.6112	−0.443477
$943$	9.11569	0.296848
$944$	−9.37885	−0.305255
$945$	−3.35531	−0.109148
$946$	−7.37750	−0.239863
$947$	−38.6602	−1.25629	−0.628143	−	0.778098i	$-0.716185\pi$
$947$	−38.6602	−1.25629	−0.628143	+	0.778098i	$0.716185\pi$
$948$	−3.23726	−0.105141
$949$	−9.15376	−0.297144
$950$	6.12822	0.198826
$951$	−26.9585	−0.874191
$952$	7.77610	0.252025
$953$	−39.3523	−1.27475	−0.637373	−	0.770556i	$-0.719979\pi$
$953$	−39.3523	−1.27475	−0.637373	+	0.770556i	$0.719979\pi$
$954$	−1.37438	−0.0444971
$955$	−11.6577	−0.377235
$956$	−23.4242	−0.757593
$957$	−4.11864	−0.133137
$958$	−20.8766	−0.674492
$959$	−5.71623	−0.184587
$960$	2.05101	0.0661960
$961$	52.5959	1.69664
$962$	−2.77305	−0.0894067
$963$	−15.8026	−0.509232
$964$	1.65066	0.0531641
$965$	−27.7937	−0.894710
$966$	−1.55863	−0.0501480
$967$	7.76103	0.249578	0.124789	−	0.992183i	$-0.460175\pi$
$967$	7.76103	0.249578	0.124789	+	0.992183i	$0.460175\pi$
$968$	−7.12945	−0.229149
$969$	−36.7161	−1.17949
$970$	15.5854	0.500417
$971$	−37.9637	−1.21831	−0.609156	−	0.793050i	$-0.708492\pi$
$971$	−37.9637	−1.21831	−0.609156	+	0.793050i	$0.708492\pi$
$972$	−1.00000	−0.0320750
$973$	13.4013	0.429625
$974$	37.8999	1.21439
$975$	−0.793369	−0.0254081
$976$	2.60018	0.0832297
$977$	−44.3722	−1.41959	−0.709797	−	0.704406i	$-0.751213\pi$
$977$	−44.3722	−1.41959	−0.709797	+	0.704406i	$0.751213\pi$
$978$	2.48927	0.0795982
$979$	12.3579	0.394960
$980$	8.86800	0.283278
$981$	−7.02817	−0.224392
$982$	15.4924	0.494381
$983$	47.9513	1.52941	0.764704	−	0.644382i	$-0.222885\pi$
$983$	47.9513	1.52941	0.764704	+	0.644382i	$0.222885\pi$
$984$	9.56781	0.305011
$985$	−0.404585	−0.0128912
$986$	9.95096	0.316903
$987$	9.13361	0.290726
$988$	7.72431	0.245743
$989$	−3.57273	−0.113606
$990$	4.03509	0.128244
$991$	10.1341	0.321920	0.160960	−	0.986961i	$-0.448541\pi$
$991$	10.1341	0.321920	0.160960	+	0.986961i	$0.448541\pi$
$992$	9.14308	0.290293
$993$	14.0868	0.447031
$994$	1.25730	0.0398790
$995$	9.64713	0.305834
$996$	−12.4302	−0.393864
$997$	−23.4023	−0.741157	−0.370578	−	0.928801i	$-0.620841\pi$
$997$	−23.4023	−0.741157	−0.370578	+	0.928801i	$0.620841\pi$
$998$	−33.2335	−1.05199
$999$	−2.77305	−0.0877354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bc.1.5	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bc.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05101 q^{5} -1.00000 q^{6} -1.63593 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05101 q^{5} -1.00000 q^{6} -1.63593 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.05101 q^{10} -1.96737 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.63593 q^{14} +2.05101 q^{15} +1.00000 q^{16} -4.75332 q^{17} +1.00000 q^{18} -7.72431 q^{19} -2.05101 q^{20} +1.63593 q^{21} -1.96737 q^{22} -0.952745 q^{23} -1.00000 q^{24} -0.793369 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.63593 q^{28} -2.09348 q^{29} +2.05101 q^{30} +9.14308 q^{31} +1.00000 q^{32} +1.96737 q^{33} -4.75332 q^{34} +3.35531 q^{35} +1.00000 q^{36} +2.77305 q^{37} -7.72431 q^{38} +1.00000 q^{39} -2.05101 q^{40} -9.56781 q^{41} +1.63593 q^{42} +3.74993 q^{43} -1.96737 q^{44} -2.05101 q^{45} -0.952745 q^{46} +5.58312 q^{47} -1.00000 q^{48} -4.32373 q^{49} -0.793369 q^{50} +4.75332 q^{51} -1.00000 q^{52} -1.37438 q^{53} -1.00000 q^{54} +4.03509 q^{55} -1.63593 q^{56} +7.72431 q^{57} -2.09348 q^{58} -9.37885 q^{59} +2.05101 q^{60} +2.60018 q^{61} +9.14308 q^{62} -1.63593 q^{63} +1.00000 q^{64} +2.05101 q^{65} +1.96737 q^{66} +5.60782 q^{67} -4.75332 q^{68} +0.952745 q^{69} +3.35531 q^{70} -0.768551 q^{71} +1.00000 q^{72} +9.15376 q^{73} +2.77305 q^{74} +0.793369 q^{75} -7.72431 q^{76} +3.21848 q^{77} +1.00000 q^{78} +3.23726 q^{79} -2.05101 q^{80} +1.00000 q^{81} -9.56781 q^{82} +12.4302 q^{83} +1.63593 q^{84} +9.74909 q^{85} +3.74993 q^{86} +2.09348 q^{87} -1.96737 q^{88} -6.28143 q^{89} -2.05101 q^{90} +1.63593 q^{91} -0.952745 q^{92} -9.14308 q^{93} +5.58312 q^{94} +15.8426 q^{95} -1.00000 q^{96} -7.59891 q^{97} -4.32373 q^{98} -1.96737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) \) 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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