LMFDB - Embedded newform 8034.2.a.bb.1.12

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:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-2.36221$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.36221 q^{5} -1.00000 q^{6} -4.26027 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.36221 q^{5} -1.00000 q^{6} -4.26027 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.36221 q^{10} -1.66695 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.26027 q^{14} +2.36221 q^{15} +1.00000 q^{16} +1.26660 q^{17} -1.00000 q^{18} -4.50257 q^{19} +2.36221 q^{20} -4.26027 q^{21} +1.66695 q^{22} +8.71852 q^{23} -1.00000 q^{24} +0.580037 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.26027 q^{28} +7.70479 q^{29} -2.36221 q^{30} -7.02642 q^{31} -1.00000 q^{32} -1.66695 q^{33} -1.26660 q^{34} -10.0637 q^{35} +1.00000 q^{36} +1.42734 q^{37} +4.50257 q^{38} -1.00000 q^{39} -2.36221 q^{40} -2.88901 q^{41} +4.26027 q^{42} -2.87221 q^{43} -1.66695 q^{44} +2.36221 q^{45} -8.71852 q^{46} +2.32318 q^{47} +1.00000 q^{48} +11.1499 q^{49} -0.580037 q^{50} +1.26660 q^{51} -1.00000 q^{52} -3.14222 q^{53} -1.00000 q^{54} -3.93768 q^{55} +4.26027 q^{56} -4.50257 q^{57} -7.70479 q^{58} +13.9271 q^{59} +2.36221 q^{60} -4.27701 q^{61} +7.02642 q^{62} -4.26027 q^{63} +1.00000 q^{64} -2.36221 q^{65} +1.66695 q^{66} -9.62761 q^{67} +1.26660 q^{68} +8.71852 q^{69} +10.0637 q^{70} -7.37836 q^{71} -1.00000 q^{72} -5.92878 q^{73} -1.42734 q^{74} +0.580037 q^{75} -4.50257 q^{76} +7.10165 q^{77} +1.00000 q^{78} +5.42560 q^{79} +2.36221 q^{80} +1.00000 q^{81} +2.88901 q^{82} -13.7743 q^{83} -4.26027 q^{84} +2.99198 q^{85} +2.87221 q^{86} +7.70479 q^{87} +1.66695 q^{88} -11.4042 q^{89} -2.36221 q^{90} +4.26027 q^{91} +8.71852 q^{92} -7.02642 q^{93} -2.32318 q^{94} -10.6360 q^{95} -1.00000 q^{96} +8.92335 q^{97} -11.1499 q^{98} -1.66695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * 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
$5$	2.36221	1.05641	0.528206	−	0.849116i	$-0.322865\pi$
$5$	2.36221	1.05641	0.528206	+	0.849116i	$0.322865\pi$
$6$	−1.00000	−0.408248
$7$	−4.26027	−1.61023	−0.805115	−	0.593118i	$-0.797897\pi$
$7$	−4.26027	−1.61023	−0.805115	+	0.593118i	$0.797897\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.36221	−0.746996
$11$	−1.66695	−0.502604	−0.251302	−	0.967909i	$-0.580859\pi$
$11$	−1.66695	−0.502604	−0.251302	+	0.967909i	$0.580859\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.26027	1.13860
$15$	2.36221	0.609920
$16$	1.00000	0.250000
$17$	1.26660	0.307197	0.153598	−	0.988133i	$-0.450914\pi$
$17$	1.26660	0.307197	0.153598	+	0.988133i	$0.450914\pi$
$18$	−1.00000	−0.235702
$19$	−4.50257	−1.03296	−0.516480	−	0.856299i	$-0.672758\pi$
$19$	−4.50257	−1.03296	−0.516480	+	0.856299i	$0.672758\pi$
$20$	2.36221	0.528206
$21$	−4.26027	−0.929667
$22$	1.66695	0.355395
$23$	8.71852	1.81794	0.908968	−	0.416865i	$-0.136871\pi$
$23$	8.71852	1.81794	0.908968	+	0.416865i	$0.136871\pi$
$24$	−1.00000	−0.204124
$25$	0.580037	0.116007
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−4.26027	−0.805115
$29$	7.70479	1.43074	0.715372	−	0.698744i	$-0.246257\pi$
$29$	7.70479	1.43074	0.715372	+	0.698744i	$0.246257\pi$
$30$	−2.36221	−0.431279
$31$	−7.02642	−1.26198	−0.630991	−	0.775790i	$-0.717351\pi$
$31$	−7.02642	−1.26198	−0.630991	+	0.775790i	$0.717351\pi$
$32$	−1.00000	−0.176777
$33$	−1.66695	−0.290179
$34$	−1.26660	−0.217221
$35$	−10.0637	−1.70107
$36$	1.00000	0.166667
$37$	1.42734	0.234653	0.117327	−	0.993093i	$-0.462568\pi$
$37$	1.42734	0.234653	0.117327	+	0.993093i	$0.462568\pi$
$38$	4.50257	0.730414
$39$	−1.00000	−0.160128
$40$	−2.36221	−0.373498
$41$	−2.88901	−0.451187	−0.225594	−	0.974222i	$-0.572432\pi$
$41$	−2.88901	−0.451187	−0.225594	+	0.974222i	$0.572432\pi$
$42$	4.26027	0.657374
$43$	−2.87221	−0.438007	−0.219004	−	0.975724i	$-0.570281\pi$
$43$	−2.87221	−0.438007	−0.219004	+	0.975724i	$0.570281\pi$
$44$	−1.66695	−0.251302
$45$	2.36221	0.352137
$46$	−8.71852	−1.28548
$47$	2.32318	0.338871	0.169435	−	0.985541i	$-0.445806\pi$
$47$	2.32318	0.338871	0.169435	+	0.985541i	$0.445806\pi$
$48$	1.00000	0.144338
$49$	11.1499	1.59284
$50$	−0.580037	−0.0820296
$51$	1.26660	0.177360
$52$	−1.00000	−0.138675
$53$	−3.14222	−0.431617	−0.215809	−	0.976436i	$-0.569239\pi$
$53$	−3.14222	−0.431617	−0.215809	+	0.976436i	$0.569239\pi$
$54$	−1.00000	−0.136083
$55$	−3.93768	−0.530957
$56$	4.26027	0.569302
$57$	−4.50257	−0.596380
$58$	−7.70479	−1.01169
$59$	13.9271	1.81315	0.906575	−	0.422046i	$-0.138688\pi$
$59$	13.9271	1.81315	0.906575	+	0.422046i	$0.138688\pi$
$60$	2.36221	0.304960
$61$	−4.27701	−0.547615	−0.273807	−	0.961785i	$-0.588283\pi$
$61$	−4.27701	−0.547615	−0.273807	+	0.961785i	$0.588283\pi$
$62$	7.02642	0.892356
$63$	−4.26027	−0.536743
$64$	1.00000	0.125000
$65$	−2.36221	−0.292996
$66$	1.66695	0.205187
$67$	−9.62761	−1.17620	−0.588100	−	0.808788i	$-0.700124\pi$
$67$	−9.62761	−1.17620	−0.588100	+	0.808788i	$0.700124\pi$
$68$	1.26660	0.153598
$69$	8.71852	1.04959
$70$	10.0637	1.20284
$71$	−7.37836	−0.875650	−0.437825	−	0.899060i	$-0.644251\pi$
$71$	−7.37836	−0.875650	−0.437825	+	0.899060i	$0.644251\pi$
$72$	−1.00000	−0.117851
$73$	−5.92878	−0.693912	−0.346956	−	0.937881i	$-0.612785\pi$
$73$	−5.92878	−0.693912	−0.346956	+	0.937881i	$0.612785\pi$
$74$	−1.42734	−0.165925
$75$	0.580037	0.0669769
$76$	−4.50257	−0.516480
$77$	7.10165	0.809309
$78$	1.00000	0.113228
$79$	5.42560	0.610427	0.305214	−	0.952284i	$-0.401272\pi$
$79$	5.42560	0.610427	0.305214	+	0.952284i	$0.401272\pi$
$80$	2.36221	0.264103
$81$	1.00000	0.111111
$82$	2.88901	0.319037
$83$	−13.7743	−1.51192	−0.755962	−	0.654616i	$-0.772830\pi$
$83$	−13.7743	−1.51192	−0.755962	+	0.654616i	$0.772830\pi$
$84$	−4.26027	−0.464833
$85$	2.99198	0.324526
$86$	2.87221	0.309718
$87$	7.70479	0.826040
$88$	1.66695	0.177697
$89$	−11.4042	−1.20884	−0.604420	−	0.796666i	$-0.706595\pi$
$89$	−11.4042	−1.20884	−0.604420	+	0.796666i	$0.706595\pi$
$90$	−2.36221	−0.248999
$91$	4.26027	0.446598
$92$	8.71852	0.908968
$93$	−7.02642	−0.728605
$94$	−2.32318	−0.239618
$95$	−10.6360	−1.09123
$96$	−1.00000	−0.102062
$97$	8.92335	0.906029	0.453014	−	0.891503i	$-0.350349\pi$
$97$	8.92335	0.906029	0.453014	+	0.891503i	$0.350349\pi$
$98$	−11.1499	−1.12631
$99$	−1.66695	−0.167535
$100$	0.580037	0.0580037
$101$	8.26469	0.822367	0.411184	−	0.911553i	$-0.365116\pi$
$101$	8.26469	0.822367	0.411184	+	0.911553i	$0.365116\pi$
$102$	−1.26660	−0.125412
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−10.0637	−0.982112
$106$	3.14222	0.305199
$107$	1.47218	0.142321	0.0711606	−	0.997465i	$-0.477330\pi$
$107$	1.47218	0.142321	0.0711606	+	0.997465i	$0.477330\pi$
$108$	1.00000	0.0962250
$109$	−12.0292	−1.15218	−0.576092	−	0.817385i	$-0.695423\pi$
$109$	−12.0292	−1.15218	−0.576092	+	0.817385i	$0.695423\pi$
$110$	3.93768	0.375444
$111$	1.42734	0.135477
$112$	−4.26027	−0.402558
$113$	15.0560	1.41635	0.708175	−	0.706037i	$-0.249519\pi$
$113$	15.0560	1.41635	0.708175	+	0.706037i	$0.249519\pi$
$114$	4.50257	0.421704
$115$	20.5950	1.92049
$116$	7.70479	0.715372
$117$	−1.00000	−0.0924500
$118$	−13.9271	−1.28209
$119$	−5.39607	−0.494657
$120$	−2.36221	−0.215639
$121$	−8.22128	−0.747389
$122$	4.27701	0.387222
$123$	−2.88901	−0.260493
$124$	−7.02642	−0.630991
$125$	−10.4409	−0.933861
$126$	4.26027	0.379535
$127$	−5.21000	−0.462313	−0.231157	−	0.972917i	$-0.574251\pi$
$127$	−5.21000	−0.462313	−0.231157	+	0.972917i	$0.574251\pi$
$128$	−1.00000	−0.0883883
$129$	−2.87221	−0.252884
$130$	2.36221	0.207180
$131$	1.34822	0.117795	0.0588974	−	0.998264i	$-0.481242\pi$
$131$	1.34822	0.117795	0.0588974	+	0.998264i	$0.481242\pi$
$132$	−1.66695	−0.145089
$133$	19.1822	1.66330
$134$	9.62761	0.831699
$135$	2.36221	0.203307
$136$	−1.26660	−0.108610
$137$	9.34712	0.798579	0.399289	−	0.916825i	$-0.369257\pi$
$137$	9.34712	0.798579	0.399289	+	0.916825i	$0.369257\pi$
$138$	−8.71852	−0.742170
$139$	−19.8168	−1.68084	−0.840420	−	0.541935i	$-0.817692\pi$
$139$	−19.8168	−1.68084	−0.840420	+	0.541935i	$0.817692\pi$
$140$	−10.0637	−0.850534
$141$	2.32318	0.195647
$142$	7.37836	0.619178
$143$	1.66695	0.139397
$144$	1.00000	0.0833333
$145$	18.2003	1.51146
$146$	5.92878	0.490670
$147$	11.1499	0.919628
$148$	1.42734	0.117327
$149$	22.6402	1.85476	0.927379	−	0.374123i	$-0.122056\pi$
$149$	22.6402	1.85476	0.927379	+	0.374123i	$0.122056\pi$
$150$	−0.580037	−0.0473598
$151$	5.85954	0.476843	0.238421	−	0.971162i	$-0.423370\pi$
$151$	5.85954	0.476843	0.238421	+	0.971162i	$0.423370\pi$
$152$	4.50257	0.365207
$153$	1.26660	0.102399
$154$	−7.10165	−0.572268
$155$	−16.5979	−1.33317
$156$	−1.00000	−0.0800641
$157$	−17.7129	−1.41365	−0.706823	−	0.707390i	$-0.749872\pi$
$157$	−17.7129	−1.41365	−0.706823	+	0.707390i	$0.749872\pi$
$158$	−5.42560	−0.431637
$159$	−3.14222	−0.249194
$160$	−2.36221	−0.186749
$161$	−37.1432	−2.92730
$162$	−1.00000	−0.0785674
$163$	−18.1900	−1.42475	−0.712375	−	0.701799i	$-0.752380\pi$
$163$	−18.1900	−1.42475	−0.712375	+	0.701799i	$0.752380\pi$
$164$	−2.88901	−0.225594
$165$	−3.93768	−0.306548
$166$	13.7743	1.06909
$167$	−13.9975	−1.08316	−0.541580	−	0.840649i	$-0.682174\pi$
$167$	−13.9975	−1.08316	−0.541580	+	0.840649i	$0.682174\pi$
$168$	4.26027	0.328687
$169$	1.00000	0.0769231
$170$	−2.99198	−0.229475
$171$	−4.50257	−0.344320
$172$	−2.87221	−0.219004
$173$	−12.2515	−0.931465	−0.465733	−	0.884925i	$-0.654209\pi$
$173$	−12.2515	−0.931465	−0.465733	+	0.884925i	$0.654209\pi$
$174$	−7.70479	−0.584099
$175$	−2.47111	−0.186799
$176$	−1.66695	−0.125651
$177$	13.9271	1.04682
$178$	11.4042	0.854778
$179$	−13.6911	−1.02332	−0.511661	−	0.859188i	$-0.670970\pi$
$179$	−13.6911	−1.02332	−0.511661	+	0.859188i	$0.670970\pi$
$180$	2.36221	0.176069
$181$	0.681068	0.0506234	0.0253117	−	0.999680i	$-0.491942\pi$
$181$	0.681068	0.0506234	0.0253117	+	0.999680i	$0.491942\pi$
$182$	−4.26027	−0.315792
$183$	−4.27701	−0.316165
$184$	−8.71852	−0.642738
$185$	3.37168	0.247891
$186$	7.02642	0.515202
$187$	−2.11136	−0.154398
$188$	2.32318	0.169435
$189$	−4.26027	−0.309889
$190$	10.6360	0.771618
$191$	−24.7389	−1.79004	−0.895022	−	0.446021i	$-0.852840\pi$
$191$	−24.7389	−1.79004	−0.895022	+	0.446021i	$0.852840\pi$
$192$	1.00000	0.0721688
$193$	−16.3916	−1.17989	−0.589947	−	0.807442i	$-0.700851\pi$
$193$	−16.3916	−1.17989	−0.589947	+	0.807442i	$0.700851\pi$
$194$	−8.92335	−0.640659
$195$	−2.36221	−0.169161
$196$	11.1499	0.796421
$197$	3.50420	0.249664	0.124832	−	0.992178i	$-0.460161\pi$
$197$	3.50420	0.249664	0.124832	+	0.992178i	$0.460161\pi$
$198$	1.66695	0.118465
$199$	0.914258	0.0648100	0.0324050	−	0.999475i	$-0.489683\pi$
$199$	0.914258	0.0648100	0.0324050	+	0.999475i	$0.489683\pi$
$200$	−0.580037	−0.0410148
$201$	−9.62761	−0.679079
$202$	−8.26469	−0.581501
$203$	−32.8245	−2.30383
$204$	1.26660	0.0886800
$205$	−6.82444	−0.476640
$206$	−1.00000	−0.0696733
$207$	8.71852	0.605979
$208$	−1.00000	−0.0693375
$209$	7.50556	0.519170
$210$	10.0637	0.694458
$211$	8.56299	0.589501	0.294750	−	0.955574i	$-0.404763\pi$
$211$	8.56299	0.589501	0.294750	+	0.955574i	$0.404763\pi$
$212$	−3.14222	−0.215809
$213$	−7.37836	−0.505557
$214$	−1.47218	−0.100636
$215$	−6.78475	−0.462716
$216$	−1.00000	−0.0680414
$217$	29.9344	2.03208
$218$	12.0292	0.814717
$219$	−5.92878	−0.400630
$220$	−3.93768	−0.265479
$221$	−1.26660	−0.0852010
$222$	−1.42734	−0.0957968
$223$	2.60556	0.174481	0.0872407	−	0.996187i	$-0.472195\pi$
$223$	2.60556	0.174481	0.0872407	+	0.996187i	$0.472195\pi$
$224$	4.26027	0.284651
$225$	0.580037	0.0386691
$226$	−15.0560	−1.00151
$227$	−3.21031	−0.213076	−0.106538	−	0.994309i	$-0.533977\pi$
$227$	−3.21031	−0.213076	−0.106538	+	0.994309i	$0.533977\pi$
$228$	−4.50257	−0.298190
$229$	−14.5877	−0.963985	−0.481992	−	0.876175i	$-0.660087\pi$
$229$	−14.5877	−0.963985	−0.481992	+	0.876175i	$0.660087\pi$
$230$	−20.5950	−1.35799
$231$	7.10165	0.467254
$232$	−7.70479	−0.505844
$233$	−17.0098	−1.11435	−0.557175	−	0.830395i	$-0.688115\pi$
$233$	−17.0098	−1.11435	−0.557175	+	0.830395i	$0.688115\pi$
$234$	1.00000	0.0653720
$235$	5.48784	0.357987
$236$	13.9271	0.906575
$237$	5.42560	0.352430
$238$	5.39607	0.349775
$239$	−8.89537	−0.575393	−0.287697	−	0.957722i	$-0.592890\pi$
$239$	−8.89537	−0.575393	−0.287697	+	0.957722i	$0.592890\pi$
$240$	2.36221	0.152480
$241$	−15.3927	−0.991529	−0.495765	−	0.868457i	$-0.665112\pi$
$241$	−15.3927	−0.991529	−0.495765	+	0.868457i	$0.665112\pi$
$242$	8.22128	0.528484
$243$	1.00000	0.0641500
$244$	−4.27701	−0.273807
$245$	26.3384	1.68270
$246$	2.88901	0.184196
$247$	4.50257	0.286492
$248$	7.02642	0.446178
$249$	−13.7743	−0.872909
$250$	10.4409	0.660339
$251$	−6.09295	−0.384584	−0.192292	−	0.981338i	$-0.561592\pi$
$251$	−6.09295	−0.384584	−0.192292	+	0.981338i	$0.561592\pi$
$252$	−4.26027	−0.268372
$253$	−14.5333	−0.913703
$254$	5.21000	0.326905
$255$	2.99198	0.187365
$256$	1.00000	0.0625000
$257$	1.88357	0.117494	0.0587469	−	0.998273i	$-0.481290\pi$
$257$	1.88357	0.117494	0.0587469	+	0.998273i	$0.481290\pi$
$258$	2.87221	0.178816
$259$	−6.08085	−0.377846
$260$	−2.36221	−0.146498
$261$	7.70479	0.476915
$262$	−1.34822	−0.0832935
$263$	−8.86701	−0.546763	−0.273382	−	0.961906i	$-0.588142\pi$
$263$	−8.86701	−0.546763	−0.273382	+	0.961906i	$0.588142\pi$
$264$	1.66695	0.102594
$265$	−7.42259	−0.455966
$266$	−19.1822	−1.17613
$267$	−11.4042	−0.697924
$268$	−9.62761	−0.588100
$269$	4.60253	0.280621	0.140311	−	0.990108i	$-0.455190\pi$
$269$	4.60253	0.280621	0.140311	+	0.990108i	$0.455190\pi$
$270$	−2.36221	−0.143760
$271$	−6.60696	−0.401344	−0.200672	−	0.979658i	$-0.564313\pi$
$271$	−6.60696	−0.401344	−0.200672	+	0.979658i	$0.564313\pi$
$272$	1.26660	0.0767991
$273$	4.26027	0.257843
$274$	−9.34712	−0.564680
$275$	−0.966892	−0.0583058
$276$	8.71852	0.524793
$277$	−8.44048	−0.507140	−0.253570	−	0.967317i	$-0.581605\pi$
$277$	−8.44048	−0.507140	−0.253570	+	0.967317i	$0.581605\pi$
$278$	19.8168	1.18853
$279$	−7.02642	−0.420660
$280$	10.0637	0.601418
$281$	−1.72109	−0.102672	−0.0513359	−	0.998681i	$-0.516348\pi$
$281$	−1.72109	−0.102672	−0.0513359	+	0.998681i	$0.516348\pi$
$282$	−2.32318	−0.138343
$283$	5.31556	0.315977	0.157988	−	0.987441i	$-0.449499\pi$
$283$	5.31556	0.315977	0.157988	+	0.987441i	$0.449499\pi$
$284$	−7.37836	−0.437825
$285$	−10.6360	−0.630023
$286$	−1.66695	−0.0985688
$287$	12.3079	0.726515
$288$	−1.00000	−0.0589256
$289$	−15.3957	−0.905630
$290$	−18.2003	−1.06876
$291$	8.92335	0.523096
$292$	−5.92878	−0.346956
$293$	−0.477341	−0.0278866	−0.0139433	−	0.999903i	$-0.504438\pi$
$293$	−0.477341	−0.0278866	−0.0139433	+	0.999903i	$0.504438\pi$
$294$	−11.1499	−0.650275
$295$	32.8987	1.91543
$296$	−1.42734	−0.0829624
$297$	−1.66695	−0.0967262
$298$	−22.6402	−1.31151
$299$	−8.71852	−0.504205
$300$	0.580037	0.0334884
$301$	12.2364	0.705293
$302$	−5.85954	−0.337179
$303$	8.26469	0.474794
$304$	−4.50257	−0.258240
$305$	−10.1032	−0.578507
$306$	−1.26660	−0.0724069
$307$	10.0577	0.574020	0.287010	−	0.957928i	$-0.407339\pi$
$307$	10.0577	0.574020	0.287010	+	0.957928i	$0.407339\pi$
$308$	7.10165	0.404654
$309$	1.00000	0.0568880
$310$	16.5979	0.942696
$311$	−14.0208	−0.795044	−0.397522	−	0.917593i	$-0.630130\pi$
$311$	−14.0208	−0.795044	−0.397522	+	0.917593i	$0.630130\pi$
$312$	1.00000	0.0566139
$313$	−1.47426	−0.0833301	−0.0416651	−	0.999132i	$-0.513266\pi$
$313$	−1.47426	−0.0833301	−0.0416651	+	0.999132i	$0.513266\pi$
$314$	17.7129	0.999599
$315$	−10.0637	−0.567022
$316$	5.42560	0.305214
$317$	13.3249	0.748401	0.374201	−	0.927348i	$-0.377917\pi$
$317$	13.3249	0.748401	0.374201	+	0.927348i	$0.377917\pi$
$318$	3.14222	0.176207
$319$	−12.8435	−0.719098
$320$	2.36221	0.132052
$321$	1.47218	0.0821692
$322$	37.1432	2.06991
$323$	−5.70297	−0.317322
$324$	1.00000	0.0555556
$325$	−0.580037	−0.0321746
$326$	18.1900	1.00745
$327$	−12.0292	−0.665214
$328$	2.88901	0.159519
$329$	−9.89738	−0.545660
$330$	3.93768	0.216762
$331$	11.1195	0.611182	0.305591	−	0.952163i	$-0.401146\pi$
$331$	11.1195	0.611182	0.305591	+	0.952163i	$0.401146\pi$
$332$	−13.7743	−0.755962
$333$	1.42734	0.0782177
$334$	13.9975	0.765910
$335$	−22.7424	−1.24255
$336$	−4.26027	−0.232417
$337$	13.0367	0.710152	0.355076	−	0.934837i	$-0.384455\pi$
$337$	13.0367	0.710152	0.355076	+	0.934837i	$0.384455\pi$
$338$	−1.00000	−0.0543928
$339$	15.0560	0.817730
$340$	2.99198	0.162263
$341$	11.7127	0.634277
$342$	4.50257	0.243471
$343$	−17.6797	−0.954612
$344$	2.87221	0.154859
$345$	20.5950	1.10880
$346$	12.2515	0.658645
$347$	0.928402	0.0498392	0.0249196	−	0.999689i	$-0.492067\pi$
$347$	0.928402	0.0498392	0.0249196	+	0.999689i	$0.492067\pi$
$348$	7.70479	0.413020
$349$	−9.85850	−0.527713	−0.263857	−	0.964562i	$-0.584995\pi$
$349$	−9.85850	−0.527713	−0.263857	+	0.964562i	$0.584995\pi$
$350$	2.47111	0.132087
$351$	−1.00000	−0.0533761
$352$	1.66695	0.0888487
$353$	−0.710646	−0.0378239	−0.0189119	−	0.999821i	$-0.506020\pi$
$353$	−0.710646	−0.0378239	−0.0189119	+	0.999821i	$0.506020\pi$
$354$	−13.9271	−0.740215
$355$	−17.4292	−0.925048
$356$	−11.4042	−0.604420
$357$	−5.39607	−0.285590
$358$	13.6911	0.723598
$359$	−7.75035	−0.409048	−0.204524	−	0.978862i	$-0.565565\pi$
$359$	−7.75035	−0.409048	−0.204524	+	0.978862i	$0.565565\pi$
$360$	−2.36221	−0.124499
$361$	1.27315	0.0670080
$362$	−0.681068	−0.0357961
$363$	−8.22128	−0.431505
$364$	4.26027	0.223299
$365$	−14.0050	−0.733057
$366$	4.27701	0.223563
$367$	4.64274	0.242349	0.121175	−	0.992631i	$-0.461334\pi$
$367$	4.64274	0.242349	0.121175	+	0.992631i	$0.461334\pi$
$368$	8.71852	0.454484
$369$	−2.88901	−0.150396
$370$	−3.37168	−0.175285
$371$	13.3867	0.695003
$372$	−7.02642	−0.364303
$373$	10.6033	0.549020	0.274510	−	0.961584i	$-0.411484\pi$
$373$	10.6033	0.549020	0.274510	+	0.961584i	$0.411484\pi$
$374$	2.11136	0.109176
$375$	−10.4409	−0.539165
$376$	−2.32318	−0.119809
$377$	−7.70479	−0.396817
$378$	4.26027	0.219125
$379$	14.6685	0.753468	0.376734	−	0.926322i	$-0.377047\pi$
$379$	14.6685	0.753468	0.376734	+	0.926322i	$0.377047\pi$
$380$	−10.6360	−0.545616
$381$	−5.21000	−0.266917
$382$	24.7389	1.26575
$383$	−12.9463	−0.661525	−0.330762	−	0.943714i	$-0.607306\pi$
$383$	−12.9463	−0.661525	−0.330762	+	0.943714i	$0.607306\pi$
$384$	−1.00000	−0.0510310
$385$	16.7756	0.854964
$386$	16.3916	0.834311
$387$	−2.87221	−0.146002
$388$	8.92335	0.453014
$389$	6.44531	0.326790	0.163395	−	0.986561i	$-0.447755\pi$
$389$	6.44531	0.326790	0.163395	+	0.986561i	$0.447755\pi$
$390$	2.36221	0.119615
$391$	11.0429	0.558464
$392$	−11.1499	−0.563155
$393$	1.34822	0.0680089
$394$	−3.50420	−0.176539
$395$	12.8164	0.644863
$396$	−1.66695	−0.0837674
$397$	15.9602	0.801019	0.400510	−	0.916293i	$-0.368833\pi$
$397$	15.9602	0.801019	0.400510	+	0.916293i	$0.368833\pi$
$398$	−0.914258	−0.0458276
$399$	19.1822	0.960309
$400$	0.580037	0.0290018
$401$	−15.7998	−0.789003	−0.394502	−	0.918895i	$-0.629083\pi$
$401$	−15.7998	−0.789003	−0.394502	+	0.918895i	$0.629083\pi$
$402$	9.62761	0.480182
$403$	7.02642	0.350011
$404$	8.26469	0.411184
$405$	2.36221	0.117379
$406$	32.8245	1.62905
$407$	−2.37930	−0.117938
$408$	−1.26660	−0.0627062
$409$	33.5454	1.65871	0.829357	−	0.558718i	$-0.188707\pi$
$409$	33.5454	1.65871	0.829357	+	0.558718i	$0.188707\pi$
$410$	6.82444	0.337035
$411$	9.34712	0.461060
$412$	1.00000	0.0492665
$413$	−59.3330	−2.91959
$414$	−8.71852	−0.428492
$415$	−32.5377	−1.59721
$416$	1.00000	0.0490290
$417$	−19.8168	−0.970434
$418$	−7.50556	−0.367109
$419$	−2.61430	−0.127717	−0.0638585	−	0.997959i	$-0.520341\pi$
$419$	−2.61430	−0.127717	−0.0638585	+	0.997959i	$0.520341\pi$
$420$	−10.0637	−0.491056
$421$	−2.75049	−0.134050	−0.0670252	−	0.997751i	$-0.521351\pi$
$421$	−2.75049	−0.134050	−0.0670252	+	0.997751i	$0.521351\pi$
$422$	−8.56299	−0.416840
$423$	2.32318	0.112957
$424$	3.14222	0.152600
$425$	0.734677	0.0356371
$426$	7.37836	0.357483
$427$	18.2212	0.881786
$428$	1.47218	0.0711606
$429$	1.66695	0.0804811
$430$	6.78475	0.327190
$431$	29.1265	1.40297	0.701486	−	0.712683i	$-0.252520\pi$
$431$	29.1265	1.40297	0.701486	+	0.712683i	$0.252520\pi$
$432$	1.00000	0.0481125
$433$	0.469219	0.0225492	0.0112746	−	0.999936i	$-0.496411\pi$
$433$	0.469219	0.0225492	0.0112746	+	0.999936i	$0.496411\pi$
$434$	−29.9344	−1.43690
$435$	18.2003	0.872639
$436$	−12.0292	−0.576092
$437$	−39.2558	−1.87786
$438$	5.92878	0.283288
$439$	−36.5321	−1.74358	−0.871792	−	0.489876i	$-0.837042\pi$
$439$	−36.5321	−1.74358	−0.871792	+	0.489876i	$0.837042\pi$
$440$	3.93768	0.187722
$441$	11.1499	0.530947
$442$	1.26660	0.0602462
$443$	−35.0074	−1.66325	−0.831626	−	0.555336i	$-0.812590\pi$
$443$	−35.0074	−1.66325	−0.831626	+	0.555336i	$0.812590\pi$
$444$	1.42734	0.0677385
$445$	−26.9390	−1.27703
$446$	−2.60556	−0.123377
$447$	22.6402	1.07085
$448$	−4.26027	−0.201279
$449$	−13.6421	−0.643812	−0.321906	−	0.946772i	$-0.604323\pi$
$449$	−13.6421	−0.643812	−0.321906	+	0.946772i	$0.604323\pi$
$450$	−0.580037	−0.0273432
$451$	4.81583	0.226769
$452$	15.0560	0.708175
$453$	5.85954	0.275305
$454$	3.21031	0.150667
$455$	10.0637	0.471791
$456$	4.50257	0.210852
$457$	−2.07818	−0.0972134	−0.0486067	−	0.998818i	$-0.515478\pi$
$457$	−2.07818	−0.0972134	−0.0486067	+	0.998818i	$0.515478\pi$
$458$	14.5877	0.681640
$459$	1.26660	0.0591200
$460$	20.5950	0.960246
$461$	35.1380	1.63654	0.818270	−	0.574834i	$-0.194933\pi$
$461$	35.1380	1.63654	0.818270	+	0.574834i	$0.194933\pi$
$462$	−7.10165	−0.330399
$463$	38.1923	1.77495	0.887473	−	0.460861i	$-0.152459\pi$
$463$	38.1923	1.77495	0.887473	+	0.460861i	$0.152459\pi$
$464$	7.70479	0.357686
$465$	−16.5979	−0.769708
$466$	17.0098	0.787965
$467$	4.09872	0.189666	0.0948331	−	0.995493i	$-0.469768\pi$
$467$	4.09872	0.189666	0.0948331	+	0.995493i	$0.469768\pi$
$468$	−1.00000	−0.0462250
$469$	41.0162	1.89395
$470$	−5.48784	−0.253135
$471$	−17.7129	−0.816169
$472$	−13.9271	−0.641045
$473$	4.78782	0.220144
$474$	−5.42560	−0.249206
$475$	−2.61166	−0.119831
$476$	−5.39607	−0.247329
$477$	−3.14222	−0.143872
$478$	8.89537	0.406865
$479$	−25.1514	−1.14920	−0.574598	−	0.818436i	$-0.694842\pi$
$479$	−25.1514	−1.14920	−0.574598	+	0.818436i	$0.694842\pi$
$480$	−2.36221	−0.107820
$481$	−1.42734	−0.0650811
$482$	15.3927	0.701117
$483$	−37.1432	−1.69008
$484$	−8.22128	−0.373695
$485$	21.0788	0.957140
$486$	−1.00000	−0.0453609
$487$	−36.4381	−1.65117	−0.825584	−	0.564280i	$-0.809154\pi$
$487$	−36.4381	−1.65117	−0.825584	+	0.564280i	$0.809154\pi$
$488$	4.27701	0.193611
$489$	−18.1900	−0.822579
$490$	−26.3384	−1.18985
$491$	−1.60528	−0.0724451	−0.0362226	−	0.999344i	$-0.511533\pi$
$491$	−1.60528	−0.0724451	−0.0362226	+	0.999344i	$0.511533\pi$
$492$	−2.88901	−0.130247
$493$	9.75892	0.439520
$494$	−4.50257	−0.202580
$495$	−3.93768	−0.176986
$496$	−7.02642	−0.315495
$497$	31.4338	1.41000
$498$	13.7743	0.617240
$499$	1.43114	0.0640667	0.0320333	−	0.999487i	$-0.489802\pi$
$499$	1.43114	0.0640667	0.0320333	+	0.999487i	$0.489802\pi$
$500$	−10.4409	−0.466930
$501$	−13.9975	−0.625363
$502$	6.09295	0.271942
$503$	39.5014	1.76128	0.880641	−	0.473785i	$-0.157113\pi$
$503$	39.5014	1.76128	0.880641	+	0.473785i	$0.157113\pi$
$504$	4.26027	0.189767
$505$	19.5229	0.868759
$506$	14.5333	0.646085
$507$	1.00000	0.0444116
$508$	−5.21000	−0.231157
$509$	31.2303	1.38426	0.692130	−	0.721773i	$-0.256672\pi$
$509$	31.2303	1.38426	0.692130	+	0.721773i	$0.256672\pi$
$510$	−2.99198	−0.132487
$511$	25.2582	1.11736
$512$	−1.00000	−0.0441942
$513$	−4.50257	−0.198793
$514$	−1.88357	−0.0830806
$515$	2.36221	0.104091
$516$	−2.87221	−0.126442
$517$	−3.87263	−0.170318
$518$	6.08085	0.267177
$519$	−12.2515	−0.537782
$520$	2.36221	0.103590
$521$	42.5234	1.86298	0.931492	−	0.363761i	$-0.118508\pi$
$521$	42.5234	1.86298	0.931492	+	0.363761i	$0.118508\pi$
$522$	−7.70479	−0.337230
$523$	−27.2989	−1.19370	−0.596850	−	0.802353i	$-0.703581\pi$
$523$	−27.2989	−1.19370	−0.596850	+	0.802353i	$0.703581\pi$
$524$	1.34822	0.0588974
$525$	−2.47111	−0.107848
$526$	8.86701	0.386620
$527$	−8.89969	−0.387676
$528$	−1.66695	−0.0725447
$529$	53.0126	2.30489
$530$	7.42259	0.322417
$531$	13.9271	0.604383
$532$	19.1822	0.831652
$533$	2.88901	0.125137
$534$	11.4042	0.493507
$535$	3.47761	0.150350
$536$	9.62761	0.415849
$537$	−13.6911	−0.590815
$538$	−4.60253	−0.198429
$539$	−18.5863	−0.800569
$540$	2.36221	0.101653
$541$	−40.3793	−1.73604	−0.868021	−	0.496527i	$-0.834608\pi$
$541$	−40.3793	−1.73604	−0.868021	+	0.496527i	$0.834608\pi$
$542$	6.60696	0.283793
$543$	0.681068	0.0292274
$544$	−1.26660	−0.0543052
$545$	−28.4154	−1.21718
$546$	−4.26027	−0.182323
$547$	−23.7025	−1.01344	−0.506722	−	0.862109i	$-0.669143\pi$
$547$	−23.7025	−1.01344	−0.506722	+	0.862109i	$0.669143\pi$
$548$	9.34712	0.399289
$549$	−4.27701	−0.182538
$550$	0.966892	0.0412284
$551$	−34.6914	−1.47790
$552$	−8.71852	−0.371085
$553$	−23.1145	−0.982929
$554$	8.44048	0.358602
$555$	3.37168	0.143120
$556$	−19.8168	−0.840420
$557$	1.20823	0.0511942	0.0255971	−	0.999672i	$-0.491851\pi$
$557$	1.20823	0.0511942	0.0255971	+	0.999672i	$0.491851\pi$
$558$	7.02642	0.297452
$559$	2.87221	0.121481
$560$	−10.0637	−0.425267
$561$	−2.11136	−0.0891419
$562$	1.72109	0.0726000
$563$	−44.5681	−1.87832	−0.939160	−	0.343480i	$-0.888394\pi$
$563$	−44.5681	−1.87832	−0.939160	+	0.343480i	$0.888394\pi$
$564$	2.32318	0.0978236
$565$	35.5654	1.49625
$566$	−5.31556	−0.223429
$567$	−4.26027	−0.178914
$568$	7.37836	0.309589
$569$	−8.12797	−0.340742	−0.170371	−	0.985380i	$-0.554497\pi$
$569$	−8.12797	−0.340742	−0.170371	+	0.985380i	$0.554497\pi$
$570$	10.6360	0.445494
$571$	−41.1313	−1.72129	−0.860645	−	0.509205i	$-0.829939\pi$
$571$	−41.1313	−1.72129	−0.860645	+	0.509205i	$0.829939\pi$
$572$	1.66695	0.0696987
$573$	−24.7389	−1.03348
$574$	−12.3079	−0.513724
$575$	5.05706	0.210894
$576$	1.00000	0.0416667
$577$	0.0968216	0.00403074	0.00201537	−	0.999998i	$-0.499358\pi$
$577$	0.0968216	0.00403074	0.00201537	+	0.999998i	$0.499358\pi$
$578$	15.3957	0.640377
$579$	−16.3916	−0.681212
$580$	18.2003	0.755728
$581$	58.6821	2.43454
$582$	−8.92335	−0.369885
$583$	5.23792	0.216933
$584$	5.92878	0.245335
$585$	−2.36221	−0.0976654
$586$	0.477341	0.0197188
$587$	16.4362	0.678394	0.339197	−	0.940715i	$-0.389845\pi$
$587$	16.4362	0.678394	0.339197	+	0.940715i	$0.389845\pi$
$588$	11.1499	0.459814
$589$	31.6369	1.30358
$590$	−32.8987	−1.35442
$591$	3.50420	0.144143
$592$	1.42734	0.0586633
$593$	−15.3817	−0.631652	−0.315826	−	0.948817i	$-0.602282\pi$
$593$	−15.3817	−0.631652	−0.315826	+	0.948817i	$0.602282\pi$
$594$	1.66695	0.0683958
$595$	−12.7467	−0.522562
$596$	22.6402	0.927379
$597$	0.914258	0.0374181
$598$	8.71852	0.356527
$599$	0.343825	0.0140483	0.00702416	−	0.999975i	$-0.497764\pi$
$599$	0.343825	0.0140483	0.00702416	+	0.999975i	$0.497764\pi$
$600$	−0.580037	−0.0236799
$601$	5.46049	0.222738	0.111369	−	0.993779i	$-0.464476\pi$
$601$	5.46049	0.222738	0.111369	+	0.993779i	$0.464476\pi$
$602$	−12.2364	−0.498717
$603$	−9.62761	−0.392067
$604$	5.85954	0.238421
$605$	−19.4204	−0.789551
$606$	−8.26469	−0.335730
$607$	23.3753	0.948772	0.474386	−	0.880317i	$-0.342670\pi$
$607$	23.3753	0.948772	0.474386	+	0.880317i	$0.342670\pi$
$608$	4.50257	0.182603
$609$	−32.8245	−1.33012
$610$	10.1032	0.409066
$611$	−2.32318	−0.0939859
$612$	1.26660	0.0511994
$613$	27.5513	1.11278	0.556392	−	0.830920i	$-0.312185\pi$
$613$	27.5513	1.11278	0.556392	+	0.830920i	$0.312185\pi$
$614$	−10.0577	−0.405894
$615$	−6.82444	−0.275188
$616$	−7.10165	−0.286134
$617$	35.9168	1.44596	0.722978	−	0.690871i	$-0.242773\pi$
$617$	35.9168	1.44596	0.722978	+	0.690871i	$0.242773\pi$
$618$	−1.00000	−0.0402259
$619$	10.0906	0.405577	0.202788	−	0.979223i	$-0.435000\pi$
$619$	10.0906	0.405577	0.202788	+	0.979223i	$0.435000\pi$
$620$	−16.5979	−0.666586
$621$	8.71852	0.349862
$622$	14.0208	0.562181
$623$	48.5848	1.94651
$624$	−1.00000	−0.0400320
$625$	−27.5637	−1.10255
$626$	1.47426	0.0589233
$627$	7.50556	0.299743
$628$	−17.7129	−0.706823
$629$	1.80787	0.0720847
$630$	10.0637	0.400945
$631$	−12.1634	−0.484217	−0.242108	−	0.970249i	$-0.577839\pi$
$631$	−12.1634	−0.484217	−0.242108	+	0.970249i	$0.577839\pi$
$632$	−5.42560	−0.215819
$633$	8.56299	0.340348
$634$	−13.3249	−0.529199
$635$	−12.3071	−0.488393
$636$	−3.14222	−0.124597
$637$	−11.1499	−0.441775
$638$	12.8435	0.508479
$639$	−7.37836	−0.291883
$640$	−2.36221	−0.0933746
$641$	29.9449	1.18275	0.591376	−	0.806396i	$-0.298585\pi$
$641$	29.9449	1.18275	0.591376	+	0.806396i	$0.298585\pi$
$642$	−1.47218	−0.0581024
$643$	43.7484	1.72527	0.862634	−	0.505829i	$-0.168813\pi$
$643$	43.7484	1.72527	0.862634	+	0.505829i	$0.168813\pi$
$644$	−37.1432	−1.46365
$645$	−6.78475	−0.267149
$646$	5.70297	0.224381
$647$	−7.60258	−0.298888	−0.149444	−	0.988770i	$-0.547748\pi$
$647$	−7.60258	−0.298888	−0.149444	+	0.988770i	$0.547748\pi$
$648$	−1.00000	−0.0392837
$649$	−23.2157	−0.911296
$650$	0.580037	0.0227509
$651$	29.9344	1.17322
$652$	−18.1900	−0.712375
$653$	44.9286	1.75819	0.879095	−	0.476646i	$-0.158148\pi$
$653$	44.9286	1.75819	0.879095	+	0.476646i	$0.158148\pi$
$654$	12.0292	0.470377
$655$	3.18479	0.124440
$656$	−2.88901	−0.112797
$657$	−5.92878	−0.231304
$658$	9.89738	0.385840
$659$	−26.8676	−1.04661	−0.523306	−	0.852145i	$-0.675302\pi$
$659$	−26.8676	−1.04661	−0.523306	+	0.852145i	$0.675302\pi$
$660$	−3.93768	−0.153274
$661$	29.9859	1.16632	0.583159	−	0.812358i	$-0.301816\pi$
$661$	29.9859	1.16632	0.583159	+	0.812358i	$0.301816\pi$
$662$	−11.1195	−0.432171
$663$	−1.26660	−0.0491908
$664$	13.7743	0.534546
$665$	45.3123	1.75714
$666$	−1.42734	−0.0553083
$667$	67.1744	2.60100
$668$	−13.9975	−0.541580
$669$	2.60556	0.100737
$670$	22.7424	0.878617
$671$	7.12956	0.275233
$672$	4.26027	0.164343
$673$	−16.9433	−0.653116	−0.326558	−	0.945177i	$-0.605889\pi$
$673$	−16.9433	−0.653116	−0.326558	+	0.945177i	$0.605889\pi$
$674$	−13.0367	−0.502153
$675$	0.580037	0.0223256
$676$	1.00000	0.0384615
$677$	33.3594	1.28211	0.641053	−	0.767496i	$-0.278498\pi$
$677$	33.3594	1.28211	0.641053	+	0.767496i	$0.278498\pi$
$678$	−15.0560	−0.578222
$679$	−38.0159	−1.45891
$680$	−2.99198	−0.114737
$681$	−3.21031	−0.123019
$682$	−11.7127	−0.448502
$683$	27.1261	1.03795	0.518975	−	0.854789i	$-0.326314\pi$
$683$	27.1261	1.03795	0.518975	+	0.854789i	$0.326314\pi$
$684$	−4.50257	−0.172160
$685$	22.0799	0.843629
$686$	17.6797	0.675013
$687$	−14.5877	−0.556557
$688$	−2.87221	−0.109502
$689$	3.14222	0.119709
$690$	−20.5950	−0.784037
$691$	−16.5747	−0.630530	−0.315265	−	0.949004i	$-0.602093\pi$
$691$	−16.5747	−0.630530	−0.315265	+	0.949004i	$0.602093\pi$
$692$	−12.2515	−0.465733
$693$	7.10165	0.269770
$694$	−0.928402	−0.0352417
$695$	−46.8115	−1.77566
$696$	−7.70479	−0.292049
$697$	−3.65923	−0.138603
$698$	9.85850	0.373150
$699$	−17.0098	−0.643370
$700$	−2.47111	−0.0933993
$701$	8.50111	0.321082	0.160541	−	0.987029i	$-0.448676\pi$
$701$	8.50111	0.321082	0.160541	+	0.987029i	$0.448676\pi$
$702$	1.00000	0.0377426
$703$	−6.42670	−0.242388
$704$	−1.66695	−0.0628255
$705$	5.48784	0.206684
$706$	0.710646	0.0267455
$707$	−35.2098	−1.32420
$708$	13.9271	0.523411
$709$	30.6892	1.15256	0.576279	−	0.817253i	$-0.304504\pi$
$709$	30.6892	1.15256	0.576279	+	0.817253i	$0.304504\pi$
$710$	17.4292	0.654108
$711$	5.42560	0.203476
$712$	11.4042	0.427389
$713$	−61.2599	−2.29420
$714$	5.39607	0.201943
$715$	3.93768	0.147261
$716$	−13.6911	−0.511661
$717$	−8.89537	−0.332204
$718$	7.75035	0.289241
$719$	1.03188	0.0384825	0.0192412	−	0.999815i	$-0.493875\pi$
$719$	1.03188	0.0384825	0.0192412	+	0.999815i	$0.493875\pi$
$720$	2.36221	0.0880344
$721$	−4.26027	−0.158661
$722$	−1.27315	−0.0473818
$723$	−15.3927	−0.572460
$724$	0.681068	0.0253117
$725$	4.46906	0.165977
$726$	8.22128	0.305120
$727$	8.03359	0.297949	0.148975	−	0.988841i	$-0.452403\pi$
$727$	8.03359	0.297949	0.148975	+	0.988841i	$0.452403\pi$
$728$	−4.26027	−0.157896
$729$	1.00000	0.0370370
$730$	14.0050	0.518349
$731$	−3.63795	−0.134554
$732$	−4.27701	−0.158083
$733$	2.09541	0.0773957	0.0386979	−	0.999251i	$-0.487679\pi$
$733$	2.09541	0.0773957	0.0386979	+	0.999251i	$0.487679\pi$
$734$	−4.64274	−0.171367
$735$	26.3384	0.971506
$736$	−8.71852	−0.321369
$737$	16.0487	0.591163
$738$	2.88901	0.106346
$739$	7.01750	0.258143	0.129071	−	0.991635i	$-0.458800\pi$
$739$	7.01750	0.258143	0.129071	+	0.991635i	$0.458800\pi$
$740$	3.37168	0.123945
$741$	4.50257	0.165406
$742$	−13.3867	−0.491441
$743$	15.9286	0.584365	0.292182	−	0.956363i	$-0.405619\pi$
$743$	15.9286	0.584365	0.292182	+	0.956363i	$0.405619\pi$
$744$	7.02642	0.257601
$745$	53.4809	1.95939
$746$	−10.6033	−0.388216
$747$	−13.7743	−0.503974
$748$	−2.11136	−0.0771991
$749$	−6.27190	−0.229170
$750$	10.4409	0.381247
$751$	−35.9437	−1.31161	−0.655803	−	0.754932i	$-0.727670\pi$
$751$	−35.9437	−1.31161	−0.655803	+	0.754932i	$0.727670\pi$
$752$	2.32318	0.0847177
$753$	−6.09295	−0.222039
$754$	7.70479	0.280592
$755$	13.8415	0.503742
$756$	−4.26027	−0.154944
$757$	−35.6824	−1.29690	−0.648449	−	0.761258i	$-0.724582\pi$
$757$	−35.6824	−1.29690	−0.648449	+	0.761258i	$0.724582\pi$
$758$	−14.6685	−0.532782
$759$	−14.5333	−0.527526
$760$	10.6360	0.385809
$761$	−49.2518	−1.78538	−0.892688	−	0.450675i	$-0.851184\pi$
$761$	−49.2518	−1.78538	−0.892688	+	0.450675i	$0.851184\pi$
$762$	5.21000	0.188739
$763$	51.2474	1.85528
$764$	−24.7389	−0.895022
$765$	2.99198	0.108175
$766$	12.9463	0.467769
$767$	−13.9271	−0.502877
$768$	1.00000	0.0360844
$769$	−31.7831	−1.14613	−0.573065	−	0.819510i	$-0.694246\pi$
$769$	−31.7831	−1.14613	−0.573065	+	0.819510i	$0.694246\pi$
$770$	−16.7756	−0.604551
$771$	1.88357	0.0678351
$772$	−16.3916	−0.589947
$773$	26.1389	0.940152	0.470076	−	0.882626i	$-0.344226\pi$
$773$	26.1389	0.940152	0.470076	+	0.882626i	$0.344226\pi$
$774$	2.87221	0.103239
$775$	−4.07558	−0.146399
$776$	−8.92335	−0.320329
$777$	−6.08085	−0.218149
$778$	−6.44531	−0.231076
$779$	13.0080	0.466059
$780$	−2.36221	−0.0845807
$781$	12.2994	0.440105
$782$	−11.0429	−0.394894
$783$	7.70479	0.275347
$784$	11.1499	0.398210
$785$	−41.8417	−1.49339
$786$	−1.34822	−0.0480895
$787$	18.5019	0.659520	0.329760	−	0.944065i	$-0.393032\pi$
$787$	18.5019	0.659520	0.329760	+	0.944065i	$0.393032\pi$
$788$	3.50420	0.124832
$789$	−8.86701	−0.315674
$790$	−12.8164	−0.455987
$791$	−64.1426	−2.28065
$792$	1.66695	0.0592325
$793$	4.27701	0.151881
$794$	−15.9602	−0.566406
$795$	−7.42259	−0.263252
$796$	0.914258	0.0324050
$797$	−48.7167	−1.72563	−0.862816	−	0.505517i	$-0.831302\pi$
$797$	−48.7167	−1.72563	−0.862816	+	0.505517i	$0.831302\pi$
$798$	−19.1822	−0.679041
$799$	2.94255	0.104100
$800$	−0.580037	−0.0205074
$801$	−11.4042	−0.402946
$802$	15.7998	0.557910
$803$	9.88298	0.348763
$804$	−9.62761	−0.339540
$805$	−87.7401	−3.09243
$806$	−7.02642	−0.247495
$807$	4.60253	0.162017
$808$	−8.26469	−0.290751
$809$	−42.0086	−1.47694	−0.738472	−	0.674285i	$-0.764452\pi$
$809$	−42.0086	−1.47694	−0.738472	+	0.674285i	$0.764452\pi$
$810$	−2.36221	−0.0829996
$811$	34.5480	1.21315	0.606573	−	0.795028i	$-0.292544\pi$
$811$	34.5480	1.21315	0.606573	+	0.795028i	$0.292544\pi$
$812$	−32.8245	−1.15191
$813$	−6.60696	−0.231716
$814$	2.37930	0.0833945
$815$	−42.9686	−1.50512
$816$	1.26660	0.0443400
$817$	12.9323	0.452444
$818$	−33.5454	−1.17289
$819$	4.26027	0.148866
$820$	−6.82444	−0.238320
$821$	−15.3923	−0.537195	−0.268598	−	0.963252i	$-0.586560\pi$
$821$	−15.3923	−0.537195	−0.268598	+	0.963252i	$0.586560\pi$
$822$	−9.34712	−0.326018
$823$	−29.9132	−1.04271	−0.521355	−	0.853340i	$-0.674573\pi$
$823$	−29.9132	−1.04271	−0.521355	+	0.853340i	$0.674573\pi$
$824$	−1.00000	−0.0348367
$825$	−0.966892	−0.0336629
$826$	59.3330	2.06446
$827$	−45.1536	−1.57015	−0.785073	−	0.619404i	$-0.787374\pi$
$827$	−45.1536	−1.57015	−0.785073	+	0.619404i	$0.787374\pi$
$828$	8.71852	0.302989
$829$	40.4980	1.40655	0.703276	−	0.710917i	$-0.251720\pi$
$829$	40.4980	1.40655	0.703276	+	0.710917i	$0.251720\pi$
$830$	32.5377	1.12940
$831$	−8.44048	−0.292797
$832$	−1.00000	−0.0346688
$833$	14.1225	0.489316
$834$	19.8168	0.686200
$835$	−33.0651	−1.14426
$836$	7.50556	0.259585
$837$	−7.02642	−0.242868
$838$	2.61430	0.0903096
$839$	41.1163	1.41949	0.709746	−	0.704457i	$-0.248810\pi$
$839$	41.1163	1.41949	0.709746	+	0.704457i	$0.248810\pi$
$840$	10.0637	0.347229
$841$	30.3638	1.04703
$842$	2.75049	0.0947880
$843$	−1.72109	−0.0592776
$844$	8.56299	0.294750
$845$	2.36221	0.0812625
$846$	−2.32318	−0.0798726
$847$	35.0249	1.20347
$848$	−3.14222	−0.107904
$849$	5.31556	0.182429
$850$	−0.734677	−0.0251992
$851$	12.4443	0.426585
$852$	−7.37836	−0.252778
$853$	22.8673	0.782963	0.391481	−	0.920186i	$-0.371963\pi$
$853$	22.8673	0.782963	0.391481	+	0.920186i	$0.371963\pi$
$854$	−18.2212	−0.623517
$855$	−10.6360	−0.363744
$856$	−1.47218	−0.0503182
$857$	4.48293	0.153134	0.0765671	−	0.997064i	$-0.475604\pi$
$857$	4.48293	0.153134	0.0765671	+	0.997064i	$0.475604\pi$
$858$	−1.66695	−0.0569087
$859$	−9.76511	−0.333181	−0.166591	−	0.986026i	$-0.553276\pi$
$859$	−9.76511	−0.333181	−0.166591	+	0.986026i	$0.553276\pi$
$860$	−6.78475	−0.231358
$861$	12.3079	0.419454
$862$	−29.1265	−0.992051
$863$	−41.9300	−1.42732	−0.713658	−	0.700495i	$-0.752963\pi$
$863$	−41.9300	−1.42732	−0.713658	+	0.700495i	$0.752963\pi$
$864$	−1.00000	−0.0340207
$865$	−28.9406	−0.984012
$866$	−0.469219	−0.0159447
$867$	−15.3957	−0.522866
$868$	29.9344	1.01604
$869$	−9.04420	−0.306803
$870$	−18.2003	−0.617049
$871$	9.62761	0.326219
$872$	12.0292	0.407359
$873$	8.92335	0.302010
$874$	39.2558	1.32785
$875$	44.4810	1.50373
$876$	−5.92878	−0.200315
$877$	2.02273	0.0683027	0.0341513	−	0.999417i	$-0.489127\pi$
$877$	2.02273	0.0683027	0.0341513	+	0.999417i	$0.489127\pi$
$878$	36.5321	1.23290
$879$	−0.477341	−0.0161003
$880$	−3.93768	−0.132739
$881$	−26.0273	−0.876881	−0.438440	−	0.898760i	$-0.644469\pi$
$881$	−26.0273	−0.876881	−0.438440	+	0.898760i	$0.644469\pi$
$882$	−11.1499	−0.375436
$883$	9.85073	0.331503	0.165752	−	0.986168i	$-0.446995\pi$
$883$	9.85073	0.331503	0.165752	+	0.986168i	$0.446995\pi$
$884$	−1.26660	−0.0426005
$885$	32.8987	1.10588
$886$	35.0074	1.17610
$887$	−5.47297	−0.183764	−0.0918822	−	0.995770i	$-0.529288\pi$
$887$	−5.47297	−0.183764	−0.0918822	+	0.995770i	$0.529288\pi$
$888$	−1.42734	−0.0478984
$889$	22.1960	0.744431
$890$	26.9390	0.902999
$891$	−1.66695	−0.0558449
$892$	2.60556	0.0872407
$893$	−10.4603	−0.350040
$894$	−22.6402	−0.757202
$895$	−32.3413	−1.08105
$896$	4.26027	0.142326
$897$	−8.71852	−0.291103
$898$	13.6421	0.455244
$899$	−54.1371	−1.80557
$900$	0.580037	0.0193346
$901$	−3.97995	−0.132591
$902$	−4.81583	−0.160350
$903$	12.2364	0.407201
$904$	−15.0560	−0.500755
$905$	1.60883	0.0534792
$906$	−5.85954	−0.194670
$907$	−3.72175	−0.123579	−0.0617893	−	0.998089i	$-0.519681\pi$
$907$	−3.72175	−0.123579	−0.0617893	+	0.998089i	$0.519681\pi$
$908$	−3.21031	−0.106538
$909$	8.26469	0.274122
$910$	−10.0637	−0.333607
$911$	−37.9160	−1.25621	−0.628106	−	0.778127i	$-0.716170\pi$
$911$	−37.9160	−1.25621	−0.628106	+	0.778127i	$0.716170\pi$
$912$	−4.50257	−0.149095
$913$	22.9610	0.759899
$914$	2.07818	0.0687402
$915$	−10.1032	−0.334001
$916$	−14.5877	−0.481992
$917$	−5.74380	−0.189677
$918$	−1.26660	−0.0418042
$919$	−55.1846	−1.82037	−0.910186	−	0.414199i	$-0.864062\pi$
$919$	−55.1846	−1.82037	−0.910186	+	0.414199i	$0.864062\pi$
$920$	−20.5950	−0.678996
$921$	10.0577	0.331411
$922$	−35.1380	−1.15721
$923$	7.37836	0.242862
$924$	7.10165	0.233627
$925$	0.827909	0.0272215
$926$	−38.1923	−1.25508
$927$	1.00000	0.0328443
$928$	−7.70479	−0.252922
$929$	15.0471	0.493681	0.246840	−	0.969056i	$-0.420608\pi$
$929$	15.0471	0.493681	0.246840	+	0.969056i	$0.420608\pi$
$930$	16.5979	0.544266
$931$	−50.2032	−1.64534
$932$	−17.0098	−0.557175
$933$	−14.0208	−0.459019
$934$	−4.09872	−0.134114
$935$	−4.98749	−0.163108
$936$	1.00000	0.0326860
$937$	40.2496	1.31490	0.657448	−	0.753500i	$-0.271636\pi$
$937$	40.2496	1.31490	0.657448	+	0.753500i	$0.271636\pi$
$938$	−41.0162	−1.33923
$939$	−1.47426	−0.0481107
$940$	5.48784	0.178994
$941$	−47.4710	−1.54751	−0.773756	−	0.633484i	$-0.781624\pi$
$941$	−47.4710	−1.54751	−0.773756	+	0.633484i	$0.781624\pi$
$942$	17.7129	0.577119
$943$	−25.1879	−0.820230
$944$	13.9271	0.453287
$945$	−10.0637	−0.327371
$946$	−4.78782	−0.155666
$947$	−47.7648	−1.55215	−0.776074	−	0.630642i	$-0.782792\pi$
$947$	−47.7648	−1.55215	−0.776074	+	0.630642i	$0.782792\pi$
$948$	5.42560	0.176215
$949$	5.92878	0.192456
$950$	2.61166	0.0847333
$951$	13.3249	0.432090
$952$	5.39607	0.174888
$953$	−16.4522	−0.532939	−0.266469	−	0.963843i	$-0.585857\pi$
$953$	−16.4522	−0.532939	−0.266469	+	0.963843i	$0.585857\pi$
$954$	3.14222	0.101733
$955$	−58.4385	−1.89103
$956$	−8.89537	−0.287697
$957$	−12.8435	−0.415171
$958$	25.1514	0.812604
$959$	−39.8213	−1.28590
$960$	2.36221	0.0762400
$961$	18.3705	0.592597
$962$	1.42734	0.0460193
$963$	1.47218	0.0474404
$964$	−15.3927	−0.495765
$965$	−38.7204	−1.24645
$966$	37.1432	1.19506
$967$	−5.40543	−0.173827	−0.0869134	−	0.996216i	$-0.527700\pi$
$967$	−5.40543	−0.173827	−0.0869134	+	0.996216i	$0.527700\pi$
$968$	8.22128	0.264242
$969$	−5.70297	−0.183206
$970$	−21.0788	−0.676800
$971$	34.3399	1.10202	0.551009	−	0.834499i	$-0.314243\pi$
$971$	34.3399	1.10202	0.551009	+	0.834499i	$0.314243\pi$
$972$	1.00000	0.0320750
$973$	84.4250	2.70654
$974$	36.4381	1.16755
$975$	−0.580037	−0.0185760
$976$	−4.27701	−0.136904
$977$	−6.98418	−0.223444	−0.111722	−	0.993740i	$-0.535637\pi$
$977$	−6.98418	−0.223444	−0.111722	+	0.993740i	$0.535637\pi$
$978$	18.1900	0.581651
$979$	19.0102	0.607568
$980$	26.3384	0.841349
$981$	−12.0292	−0.384061
$982$	1.60528	0.0512264
$983$	11.9398	0.380822	0.190411	−	0.981705i	$-0.439018\pi$
$983$	11.9398	0.380822	0.190411	+	0.981705i	$0.439018\pi$
$984$	2.88901	0.0920982
$985$	8.27765	0.263748
$986$	−9.75892	−0.310787
$987$	−9.89738	−0.315037
$988$	4.50257	0.143246
$989$	−25.0414	−0.796269
$990$	3.93768	0.125148
$991$	−25.6204	−0.813859	−0.406929	−	0.913460i	$-0.633401\pi$
$991$	−25.6204	−0.813859	−0.406929	+	0.913460i	$0.633401\pi$
$992$	7.02642	0.223089
$993$	11.1195	0.352866
$994$	−31.4338	−0.997020
$995$	2.15967	0.0684661
$996$	−13.7743	−0.436455
$997$	−23.1463	−0.733051	−0.366525	−	0.930408i	$-0.619453\pi$
$997$	−23.1463	−0.733051	−0.366525	+	0.930408i	$0.619453\pi$
$998$	−1.43114	−0.0453020
$999$	1.42734	0.0451590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.12	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.36221 q^{5} -1.00000 q^{6} -4.26027 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.36221 q^{5} -1.00000 q^{6} -4.26027 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.36221 q^{10} -1.66695 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.26027 q^{14} +2.36221 q^{15} +1.00000 q^{16} +1.26660 q^{17} -1.00000 q^{18} -4.50257 q^{19} +2.36221 q^{20} -4.26027 q^{21} +1.66695 q^{22} +8.71852 q^{23} -1.00000 q^{24} +0.580037 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.26027 q^{28} +7.70479 q^{29} -2.36221 q^{30} -7.02642 q^{31} -1.00000 q^{32} -1.66695 q^{33} -1.26660 q^{34} -10.0637 q^{35} +1.00000 q^{36} +1.42734 q^{37} +4.50257 q^{38} -1.00000 q^{39} -2.36221 q^{40} -2.88901 q^{41} +4.26027 q^{42} -2.87221 q^{43} -1.66695 q^{44} +2.36221 q^{45} -8.71852 q^{46} +2.32318 q^{47} +1.00000 q^{48} +11.1499 q^{49} -0.580037 q^{50} +1.26660 q^{51} -1.00000 q^{52} -3.14222 q^{53} -1.00000 q^{54} -3.93768 q^{55} +4.26027 q^{56} -4.50257 q^{57} -7.70479 q^{58} +13.9271 q^{59} +2.36221 q^{60} -4.27701 q^{61} +7.02642 q^{62} -4.26027 q^{63} +1.00000 q^{64} -2.36221 q^{65} +1.66695 q^{66} -9.62761 q^{67} +1.26660 q^{68} +8.71852 q^{69} +10.0637 q^{70} -7.37836 q^{71} -1.00000 q^{72} -5.92878 q^{73} -1.42734 q^{74} +0.580037 q^{75} -4.50257 q^{76} +7.10165 q^{77} +1.00000 q^{78} +5.42560 q^{79} +2.36221 q^{80} +1.00000 q^{81} +2.88901 q^{82} -13.7743 q^{83} -4.26027 q^{84} +2.99198 q^{85} +2.87221 q^{86} +7.70479 q^{87} +1.66695 q^{88} -11.4042 q^{89} -2.36221 q^{90} +4.26027 q^{91} +8.71852 q^{92} -7.02642 q^{93} -2.32318 q^{94} -10.6360 q^{95} -1.00000 q^{96} +8.92335 q^{97} -11.1499 q^{98} -1.66695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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