LMFDB - Embedded newform 8034.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.43788$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.43788 q^{5} +1.00000 q^{6} -0.875663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.43788 q^{5} +1.00000 q^{6} -0.875663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.43788 q^{10} -4.12894 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.875663 q^{14} +3.43788 q^{15} +1.00000 q^{16} +2.91275 q^{17} -1.00000 q^{18} +6.27054 q^{19} -3.43788 q^{20} +0.875663 q^{21} +4.12894 q^{22} -2.22770 q^{23} +1.00000 q^{24} +6.81900 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.875663 q^{28} -3.54973 q^{29} -3.43788 q^{30} +4.78943 q^{31} -1.00000 q^{32} +4.12894 q^{33} -2.91275 q^{34} +3.01042 q^{35} +1.00000 q^{36} +1.66087 q^{37} -6.27054 q^{38} +1.00000 q^{39} +3.43788 q^{40} -2.47869 q^{41} -0.875663 q^{42} -7.01489 q^{43} -4.12894 q^{44} -3.43788 q^{45} +2.22770 q^{46} +7.14668 q^{47} -1.00000 q^{48} -6.23321 q^{49} -6.81900 q^{50} -2.91275 q^{51} -1.00000 q^{52} -10.0017 q^{53} +1.00000 q^{54} +14.1948 q^{55} +0.875663 q^{56} -6.27054 q^{57} +3.54973 q^{58} -7.72440 q^{59} +3.43788 q^{60} -2.25787 q^{61} -4.78943 q^{62} -0.875663 q^{63} +1.00000 q^{64} +3.43788 q^{65} -4.12894 q^{66} -5.69363 q^{67} +2.91275 q^{68} +2.22770 q^{69} -3.01042 q^{70} -0.740352 q^{71} -1.00000 q^{72} +5.84278 q^{73} -1.66087 q^{74} -6.81900 q^{75} +6.27054 q^{76} +3.61556 q^{77} -1.00000 q^{78} -15.8644 q^{79} -3.43788 q^{80} +1.00000 q^{81} +2.47869 q^{82} -15.7650 q^{83} +0.875663 q^{84} -10.0137 q^{85} +7.01489 q^{86} +3.54973 q^{87} +4.12894 q^{88} +3.84817 q^{89} +3.43788 q^{90} +0.875663 q^{91} -2.22770 q^{92} -4.78943 q^{93} -7.14668 q^{94} -21.5574 q^{95} +1.00000 q^{96} +10.5202 q^{97} +6.23321 q^{98} -4.12894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.43788	−1.53747	−0.768733	−	0.639570i	$-0.779112\pi$
$5$	−3.43788	−1.53747	−0.768733	+	0.639570i	$0.779112\pi$
$6$	1.00000	0.408248
$7$	−0.875663	−0.330969	−0.165485	−	0.986212i	$-0.552919\pi$
$7$	−0.875663	−0.330969	−0.165485	+	0.986212i	$0.552919\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.43788	1.08715
$11$	−4.12894	−1.24492	−0.622462	−	0.782650i	$-0.713867\pi$
$11$	−4.12894	−1.24492	−0.622462	+	0.782650i	$0.713867\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.875663	0.234031
$15$	3.43788	0.887656
$16$	1.00000	0.250000
$17$	2.91275	0.706446	0.353223	−	0.935539i	$-0.385086\pi$
$17$	2.91275	0.706446	0.353223	+	0.935539i	$0.385086\pi$
$18$	−1.00000	−0.235702
$19$	6.27054	1.43856	0.719281	−	0.694719i	$-0.244471\pi$
$19$	6.27054	1.43856	0.719281	+	0.694719i	$0.244471\pi$
$20$	−3.43788	−0.768733
$21$	0.875663	0.191085
$22$	4.12894	0.880294
$23$	−2.22770	−0.464508	−0.232254	−	0.972655i	$-0.574610\pi$
$23$	−2.22770	−0.464508	−0.232254	+	0.972655i	$0.574610\pi$
$24$	1.00000	0.204124
$25$	6.81900	1.36380
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−0.875663	−0.165485
$29$	−3.54973	−0.659168	−0.329584	−	0.944126i	$-0.606909\pi$
$29$	−3.54973	−0.659168	−0.329584	+	0.944126i	$0.606909\pi$
$30$	−3.43788	−0.627668
$31$	4.78943	0.860206	0.430103	−	0.902780i	$-0.358477\pi$
$31$	4.78943	0.860206	0.430103	+	0.902780i	$0.358477\pi$
$32$	−1.00000	−0.176777
$33$	4.12894	0.718757
$34$	−2.91275	−0.499533
$35$	3.01042	0.508854
$36$	1.00000	0.166667
$37$	1.66087	0.273045	0.136522	−	0.990637i	$-0.456407\pi$
$37$	1.66087	0.273045	0.136522	+	0.990637i	$0.456407\pi$
$38$	−6.27054	−1.01722
$39$	1.00000	0.160128
$40$	3.43788	0.543576
$41$	−2.47869	−0.387107	−0.193553	−	0.981090i	$-0.562001\pi$
$41$	−2.47869	−0.387107	−0.193553	+	0.981090i	$0.562001\pi$
$42$	−0.875663	−0.135118
$43$	−7.01489	−1.06976	−0.534880	−	0.844928i	$-0.679643\pi$
$43$	−7.01489	−1.06976	−0.534880	+	0.844928i	$0.679643\pi$
$44$	−4.12894	−0.622462
$45$	−3.43788	−0.512488
$46$	2.22770	0.328457
$47$	7.14668	1.04245	0.521225	−	0.853419i	$-0.325475\pi$
$47$	7.14668	1.04245	0.521225	+	0.853419i	$0.325475\pi$
$48$	−1.00000	−0.144338
$49$	−6.23321	−0.890459
$50$	−6.81900	−0.964352
$51$	−2.91275	−0.407867
$52$	−1.00000	−0.138675
$53$	−10.0017	−1.37383	−0.686917	−	0.726736i	$-0.741036\pi$
$53$	−10.0017	−1.37383	−0.686917	+	0.726736i	$0.741036\pi$
$54$	1.00000	0.136083
$55$	14.1948	1.91403
$56$	0.875663	0.117015
$57$	−6.27054	−0.830554
$58$	3.54973	0.466102
$59$	−7.72440	−1.00563	−0.502816	−	0.864394i	$-0.667703\pi$
$59$	−7.72440	−1.00563	−0.502816	+	0.864394i	$0.667703\pi$
$60$	3.43788	0.443828
$61$	−2.25787	−0.289091	−0.144545	−	0.989498i	$-0.546172\pi$
$61$	−2.25787	−0.289091	−0.144545	+	0.989498i	$0.546172\pi$
$62$	−4.78943	−0.608258
$63$	−0.875663	−0.110323
$64$	1.00000	0.125000
$65$	3.43788	0.426416
$66$	−4.12894	−0.508238
$67$	−5.69363	−0.695588	−0.347794	−	0.937571i	$-0.613069\pi$
$67$	−5.69363	−0.695588	−0.347794	+	0.937571i	$0.613069\pi$
$68$	2.91275	0.353223
$69$	2.22770	0.268184
$70$	−3.01042	−0.359814
$71$	−0.740352	−0.0878636	−0.0439318	−	0.999035i	$-0.513988\pi$
$71$	−0.740352	−0.0878636	−0.0439318	+	0.999035i	$0.513988\pi$
$72$	−1.00000	−0.117851
$73$	5.84278	0.683845	0.341923	−	0.939728i	$-0.388922\pi$
$73$	5.84278	0.683845	0.341923	+	0.939728i	$0.388922\pi$
$74$	−1.66087	−0.193072
$75$	−6.81900	−0.787390
$76$	6.27054	0.719281
$77$	3.61556	0.412032
$78$	−1.00000	−0.113228
$79$	−15.8644	−1.78488	−0.892442	−	0.451162i	$-0.851010\pi$
$79$	−15.8644	−1.78488	−0.892442	+	0.451162i	$0.851010\pi$
$80$	−3.43788	−0.384366
$81$	1.00000	0.111111
$82$	2.47869	0.273726
$83$	−15.7650	−1.73044	−0.865219	−	0.501395i	$-0.832820\pi$
$83$	−15.7650	−1.73044	−0.865219	+	0.501395i	$0.832820\pi$
$84$	0.875663	0.0955426
$85$	−10.0137	−1.08614
$86$	7.01489	0.756435
$87$	3.54973	0.380571
$88$	4.12894	0.440147
$89$	3.84817	0.407905	0.203952	−	0.978981i	$-0.434621\pi$
$89$	3.84817	0.407905	0.203952	+	0.978981i	$0.434621\pi$
$90$	3.43788	0.362384
$91$	0.875663	0.0917944
$92$	−2.22770	−0.232254
$93$	−4.78943	−0.496640
$94$	−7.14668	−0.737124
$95$	−21.5574	−2.21174
$96$	1.00000	0.102062
$97$	10.5202	1.06817	0.534083	−	0.845432i	$-0.320657\pi$
$97$	10.5202	1.06817	0.534083	+	0.845432i	$0.320657\pi$
$98$	6.23321	0.629650
$99$	−4.12894	−0.414975
$100$	6.81900	0.681900
$101$	−2.19696	−0.218606	−0.109303	−	0.994008i	$-0.534862\pi$
$101$	−2.19696	−0.218606	−0.109303	+	0.994008i	$0.534862\pi$
$102$	2.91275	0.288405
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−3.01042	−0.293787
$106$	10.0017	0.971447
$107$	−5.52530	−0.534151	−0.267076	−	0.963676i	$-0.586057\pi$
$107$	−5.52530	−0.534151	−0.267076	+	0.963676i	$0.586057\pi$
$108$	−1.00000	−0.0962250
$109$	−11.0915	−1.06238	−0.531188	−	0.847254i	$-0.678254\pi$
$109$	−11.0915	−1.06238	−0.531188	+	0.847254i	$0.678254\pi$
$110$	−14.1948	−1.35342
$111$	−1.66087	−0.157642
$112$	−0.875663	−0.0827424
$113$	−15.7340	−1.48013	−0.740064	−	0.672536i	$-0.765205\pi$
$113$	−15.7340	−1.48013	−0.740064	+	0.672536i	$0.765205\pi$
$114$	6.27054	0.587290
$115$	7.65856	0.714165
$116$	−3.54973	−0.329584
$117$	−1.00000	−0.0924500
$118$	7.72440	0.711089
$119$	−2.55059	−0.233812
$120$	−3.43788	−0.313834
$121$	6.04818	0.549835
$122$	2.25787	0.204418
$123$	2.47869	0.223496
$124$	4.78943	0.430103
$125$	−6.25349	−0.559329
$126$	0.875663	0.0780102
$127$	−3.96860	−0.352156	−0.176078	−	0.984376i	$-0.556341\pi$
$127$	−3.96860	−0.352156	−0.176078	+	0.984376i	$0.556341\pi$
$128$	−1.00000	−0.0883883
$129$	7.01489	0.617627
$130$	−3.43788	−0.301522
$131$	9.42019	0.823046	0.411523	−	0.911399i	$-0.364997\pi$
$131$	9.42019	0.823046	0.411523	+	0.911399i	$0.364997\pi$
$132$	4.12894	0.359378
$133$	−5.49088	−0.476120
$134$	5.69363	0.491855
$135$	3.43788	0.295885
$136$	−2.91275	−0.249766
$137$	−11.3092	−0.966209	−0.483104	−	0.875563i	$-0.660491\pi$
$137$	−11.3092	−0.966209	−0.483104	+	0.875563i	$0.660491\pi$
$138$	−2.22770	−0.189635
$139$	2.37115	0.201118	0.100559	−	0.994931i	$-0.467937\pi$
$139$	2.37115	0.201118	0.100559	+	0.994931i	$0.467937\pi$
$140$	3.01042	0.254427
$141$	−7.14668	−0.601859
$142$	0.740352	0.0621290
$143$	4.12894	0.345280
$144$	1.00000	0.0833333
$145$	12.2035	1.01345
$146$	−5.84278	−0.483552
$147$	6.23321	0.514107
$148$	1.66087	0.136522
$149$	4.79584	0.392890	0.196445	−	0.980515i	$-0.437060\pi$
$149$	4.79584	0.392890	0.196445	+	0.980515i	$0.437060\pi$
$150$	6.81900	0.556769
$151$	7.33233	0.596697	0.298348	−	0.954457i	$-0.403564\pi$
$151$	7.33233	0.596697	0.298348	+	0.954457i	$0.403564\pi$
$152$	−6.27054	−0.508608
$153$	2.91275	0.235482
$154$	−3.61556	−0.291350
$155$	−16.4655	−1.32254
$156$	1.00000	0.0800641
$157$	−8.80210	−0.702484	−0.351242	−	0.936285i	$-0.614241\pi$
$157$	−8.80210	−0.702484	−0.351242	+	0.936285i	$0.614241\pi$
$158$	15.8644	1.26210
$159$	10.0017	0.793183
$160$	3.43788	0.271788
$161$	1.95072	0.153738
$162$	−1.00000	−0.0785674
$163$	−5.78137	−0.452832	−0.226416	−	0.974031i	$-0.572701\pi$
$163$	−5.78137	−0.452832	−0.226416	+	0.974031i	$0.572701\pi$
$164$	−2.47869	−0.193553
$165$	−14.1948	−1.10506
$166$	15.7650	1.22360
$167$	11.7593	0.909962	0.454981	−	0.890501i	$-0.349646\pi$
$167$	11.7593	0.909962	0.454981	+	0.890501i	$0.349646\pi$
$168$	−0.875663	−0.0675588
$169$	1.00000	0.0769231
$170$	10.0137	0.768014
$171$	6.27054	0.479521
$172$	−7.01489	−0.534880
$173$	4.87706	0.370796	0.185398	−	0.982664i	$-0.440643\pi$
$173$	4.87706	0.370796	0.185398	+	0.982664i	$0.440643\pi$
$174$	−3.54973	−0.269104
$175$	−5.97114	−0.451376
$176$	−4.12894	−0.311231
$177$	7.72440	0.580601
$178$	−3.84817	−0.288432
$179$	−1.99720	−0.149278	−0.0746389	−	0.997211i	$-0.523780\pi$
$179$	−1.99720	−0.149278	−0.0746389	+	0.997211i	$0.523780\pi$
$180$	−3.43788	−0.256244
$181$	10.2805	0.764146	0.382073	−	0.924132i	$-0.375210\pi$
$181$	10.2805	0.764146	0.382073	+	0.924132i	$0.375210\pi$
$182$	−0.875663	−0.0649084
$183$	2.25787	0.166907
$184$	2.22770	0.164228
$185$	−5.70985	−0.419797
$186$	4.78943	0.351178
$187$	−12.0266	−0.879471
$188$	7.14668	0.521225
$189$	0.875663	0.0636951
$190$	21.5574	1.56394
$191$	21.0062	1.51995	0.759976	−	0.649951i	$-0.225211\pi$
$191$	21.0062	1.51995	0.759976	+	0.649951i	$0.225211\pi$
$192$	−1.00000	−0.0721688
$193$	3.91167	0.281568	0.140784	−	0.990040i	$-0.455038\pi$
$193$	3.91167	0.281568	0.140784	+	0.990040i	$0.455038\pi$
$194$	−10.5202	−0.755308
$195$	−3.43788	−0.246191
$196$	−6.23321	−0.445230
$197$	22.7100	1.61802	0.809012	−	0.587793i	$-0.200003\pi$
$197$	22.7100	1.61802	0.809012	+	0.587793i	$0.200003\pi$
$198$	4.12894	0.293431
$199$	−5.93474	−0.420702	−0.210351	−	0.977626i	$-0.567461\pi$
$199$	−5.93474	−0.420702	−0.210351	+	0.977626i	$0.567461\pi$
$200$	−6.81900	−0.482176
$201$	5.69363	0.401598
$202$	2.19696	0.154578
$203$	3.10837	0.218165
$204$	−2.91275	−0.203933
$205$	8.52144	0.595163
$206$	−1.00000	−0.0696733
$207$	−2.22770	−0.154836
$208$	−1.00000	−0.0693375
$209$	−25.8907	−1.79090
$210$	3.01042	0.207739
$211$	3.86201	0.265871	0.132936	−	0.991125i	$-0.457560\pi$
$211$	3.86201	0.265871	0.132936	+	0.991125i	$0.457560\pi$
$212$	−10.0017	−0.686917
$213$	0.740352	0.0507281
$214$	5.52530	0.377702
$215$	24.1163	1.64472
$216$	1.00000	0.0680414
$217$	−4.19392	−0.284702
$218$	11.0915	0.751214
$219$	−5.84278	−0.394818
$220$	14.1948	0.957013
$221$	−2.91275	−0.195933
$222$	1.66087	0.111470
$223$	2.77489	0.185820	0.0929102	−	0.995674i	$-0.470383\pi$
$223$	2.77489	0.185820	0.0929102	+	0.995674i	$0.470383\pi$
$224$	0.875663	0.0585077
$225$	6.81900	0.454600
$226$	15.7340	1.04661
$227$	−26.0660	−1.73006	−0.865031	−	0.501719i	$-0.832701\pi$
$227$	−26.0660	−1.73006	−0.865031	+	0.501719i	$0.832701\pi$
$228$	−6.27054	−0.415277
$229$	−18.3397	−1.21192	−0.605960	−	0.795495i	$-0.707211\pi$
$229$	−18.3397	−1.21192	−0.605960	+	0.795495i	$0.707211\pi$
$230$	−7.65856	−0.504991
$231$	−3.61556	−0.237887
$232$	3.54973	0.233051
$233$	−8.09808	−0.530523	−0.265261	−	0.964177i	$-0.585458\pi$
$233$	−8.09808	−0.530523	−0.265261	+	0.964177i	$0.585458\pi$
$234$	1.00000	0.0653720
$235$	−24.5694	−1.60273
$236$	−7.72440	−0.502816
$237$	15.8644	1.03050
$238$	2.55059	0.165330
$239$	21.0662	1.36266	0.681330	−	0.731977i	$-0.261402\pi$
$239$	21.0662	1.36266	0.681330	+	0.731977i	$0.261402\pi$
$240$	3.43788	0.221914
$241$	8.02129	0.516696	0.258348	−	0.966052i	$-0.416822\pi$
$241$	8.02129	0.516696	0.258348	+	0.966052i	$0.416822\pi$
$242$	−6.04818	−0.388792
$243$	−1.00000	−0.0641500
$244$	−2.25787	−0.144545
$245$	21.4290	1.36905
$246$	−2.47869	−0.158036
$247$	−6.27054	−0.398985
$248$	−4.78943	−0.304129
$249$	15.7650	0.999068
$250$	6.25349	0.395505
$251$	18.0515	1.13940	0.569699	−	0.821853i	$-0.307060\pi$
$251$	18.0515	1.13940	0.569699	+	0.821853i	$0.307060\pi$
$252$	−0.875663	−0.0551616
$253$	9.19806	0.578277
$254$	3.96860	0.249012
$255$	10.0137	0.627081
$256$	1.00000	0.0625000
$257$	−2.46728	−0.153905	−0.0769524	−	0.997035i	$-0.524519\pi$
$257$	−2.46728	−0.153905	−0.0769524	+	0.997035i	$0.524519\pi$
$258$	−7.01489	−0.436728
$259$	−1.45436	−0.0903694
$260$	3.43788	0.213208
$261$	−3.54973	−0.219723
$262$	−9.42019	−0.581981
$263$	−11.8755	−0.732274	−0.366137	−	0.930561i	$-0.619320\pi$
$263$	−11.8755	−0.732274	−0.366137	+	0.930561i	$0.619320\pi$
$264$	−4.12894	−0.254119
$265$	34.3845	2.11222
$266$	5.49088	0.336668
$267$	−3.84817	−0.235504
$268$	−5.69363	−0.347794
$269$	4.75452	0.289888	0.144944	−	0.989440i	$-0.453700\pi$
$269$	4.75452	0.289888	0.144944	+	0.989440i	$0.453700\pi$
$270$	−3.43788	−0.209223
$271$	−1.68670	−0.102460	−0.0512299	−	0.998687i	$-0.516314\pi$
$271$	−1.68670	−0.102460	−0.0512299	+	0.998687i	$0.516314\pi$
$272$	2.91275	0.176611
$273$	−0.875663	−0.0529975
$274$	11.3092	0.683213
$275$	−28.1553	−1.69783
$276$	2.22770	0.134092
$277$	−17.6902	−1.06290	−0.531450	−	0.847089i	$-0.678353\pi$
$277$	−17.6902	−1.06290	−0.531450	+	0.847089i	$0.678353\pi$
$278$	−2.37115	−0.142212
$279$	4.78943	0.286735
$280$	−3.01042	−0.179907
$281$	−31.3662	−1.87115	−0.935574	−	0.353130i	$-0.885117\pi$
$281$	−31.3662	−1.87115	−0.935574	+	0.353130i	$0.885117\pi$
$282$	7.14668	0.425579
$283$	6.42432	0.381886	0.190943	−	0.981601i	$-0.438845\pi$
$283$	6.42432	0.381886	0.190943	+	0.981601i	$0.438845\pi$
$284$	−0.740352	−0.0439318
$285$	21.5574	1.27695
$286$	−4.12894	−0.244150
$287$	2.17050	0.128120
$288$	−1.00000	−0.0589256
$289$	−8.51589	−0.500935
$290$	−12.2035	−0.716616
$291$	−10.5202	−0.616706
$292$	5.84278	0.341923
$293$	13.7022	0.800492	0.400246	−	0.916408i	$-0.368925\pi$
$293$	13.7022	0.800492	0.400246	+	0.916408i	$0.368925\pi$
$294$	−6.23321	−0.363528
$295$	26.5555	1.54612
$296$	−1.66087	−0.0965359
$297$	4.12894	0.239586
$298$	−4.79584	−0.277815
$299$	2.22770	0.128831
$300$	−6.81900	−0.393695
$301$	6.14268	0.354058
$302$	−7.33233	−0.421928
$303$	2.19696	0.126212
$304$	6.27054	0.359640
$305$	7.76229	0.444467
$306$	−2.91275	−0.166511
$307$	10.4205	0.594728	0.297364	−	0.954764i	$-0.403892\pi$
$307$	10.4205	0.594728	0.297364	+	0.954764i	$0.403892\pi$
$308$	3.61556	0.206016
$309$	−1.00000	−0.0568880
$310$	16.4655	0.935175
$311$	−2.65273	−0.150423	−0.0752113	−	0.997168i	$-0.523963\pi$
$311$	−2.65273	−0.150423	−0.0752113	+	0.997168i	$0.523963\pi$
$312$	−1.00000	−0.0566139
$313$	0.504119	0.0284945	0.0142472	−	0.999899i	$-0.495465\pi$
$313$	0.504119	0.0284945	0.0142472	+	0.999899i	$0.495465\pi$
$314$	8.80210	0.496732
$315$	3.01042	0.169618
$316$	−15.8644	−0.892442
$317$	−31.0342	−1.74305	−0.871527	−	0.490347i	$-0.836870\pi$
$317$	−31.0342	−1.74305	−0.871527	+	0.490347i	$0.836870\pi$
$318$	−10.0017	−0.560865
$319$	14.6566	0.820614
$320$	−3.43788	−0.192183
$321$	5.52530	0.308392
$322$	−1.95072	−0.108709
$323$	18.2645	1.01627
$324$	1.00000	0.0555556
$325$	−6.81900	−0.378250
$326$	5.78137	0.320200
$327$	11.0915	0.613363
$328$	2.47869	0.136863
$329$	−6.25808	−0.345019
$330$	14.1948	0.781398
$331$	24.6859	1.35686	0.678430	−	0.734665i	$-0.262660\pi$
$331$	24.6859	1.35686	0.678430	+	0.734665i	$0.262660\pi$
$332$	−15.7650	−0.865219
$333$	1.66087	0.0910149
$334$	−11.7593	−0.643440
$335$	19.5740	1.06944
$336$	0.875663	0.0477713
$337$	28.0255	1.52665	0.763323	−	0.646018i	$-0.223567\pi$
$337$	28.0255	1.52665	0.763323	+	0.646018i	$0.223567\pi$
$338$	−1.00000	−0.0543928
$339$	15.7340	0.854552
$340$	−10.0137	−0.543068
$341$	−19.7753	−1.07089
$342$	−6.27054	−0.339072
$343$	11.5878	0.625684
$344$	7.01489	0.378217
$345$	−7.65856	−0.412323
$346$	−4.87706	−0.262192
$347$	2.12054	0.113837	0.0569183	−	0.998379i	$-0.481873\pi$
$347$	2.12054	0.113837	0.0569183	+	0.998379i	$0.481873\pi$
$348$	3.54973	0.190285
$349$	−36.3447	−1.94549	−0.972744	−	0.231883i	$-0.925511\pi$
$349$	−36.3447	−1.94549	−0.972744	+	0.231883i	$0.925511\pi$
$350$	5.97114	0.319171
$351$	1.00000	0.0533761
$352$	4.12894	0.220073
$353$	25.4726	1.35577	0.677884	−	0.735169i	$-0.262897\pi$
$353$	25.4726	1.35577	0.677884	+	0.735169i	$0.262897\pi$
$354$	−7.72440	−0.410547
$355$	2.54524	0.135087
$356$	3.84817	0.203952
$357$	2.55059	0.134991
$358$	1.99720	0.105555
$359$	−28.2455	−1.49074	−0.745369	−	0.666652i	$-0.767727\pi$
$359$	−28.2455	−1.49074	−0.745369	+	0.666652i	$0.767727\pi$
$360$	3.43788	0.181192
$361$	20.3197	1.06946
$362$	−10.2805	−0.540333
$363$	−6.04818	−0.317447
$364$	0.875663	0.0458972
$365$	−20.0868	−1.05139
$366$	−2.25787	−0.118021
$367$	8.99275	0.469418	0.234709	−	0.972066i	$-0.424586\pi$
$367$	8.99275	0.469418	0.234709	+	0.972066i	$0.424586\pi$
$368$	−2.22770	−0.116127
$369$	−2.47869	−0.129036
$370$	5.70985	0.296841
$371$	8.75808	0.454697
$372$	−4.78943	−0.248320
$373$	−5.98913	−0.310105	−0.155053	−	0.987906i	$-0.549555\pi$
$373$	−5.98913	−0.310105	−0.155053	+	0.987906i	$0.549555\pi$
$374$	12.0266	0.621880
$375$	6.25349	0.322929
$376$	−7.14668	−0.368562
$377$	3.54973	0.182820
$378$	−0.875663	−0.0450392
$379$	34.3213	1.76296	0.881482	−	0.472217i	$-0.156546\pi$
$379$	34.3213	1.76296	0.881482	+	0.472217i	$0.156546\pi$
$380$	−21.5574	−1.10587
$381$	3.96860	0.203317
$382$	−21.0062	−1.07477
$383$	1.97543	0.100940	0.0504699	−	0.998726i	$-0.483928\pi$
$383$	1.97543	0.100940	0.0504699	+	0.998726i	$0.483928\pi$
$384$	1.00000	0.0510310
$385$	−12.4299	−0.633484
$386$	−3.91167	−0.199099
$387$	−7.01489	−0.356587
$388$	10.5202	0.534083
$389$	14.2832	0.724188	0.362094	−	0.932142i	$-0.382062\pi$
$389$	14.2832	0.724188	0.362094	+	0.932142i	$0.382062\pi$
$390$	3.43788	0.174084
$391$	−6.48874	−0.328150
$392$	6.23321	0.314825
$393$	−9.42019	−0.475186
$394$	−22.7100	−1.14412
$395$	54.5399	2.74420
$396$	−4.12894	−0.207487
$397$	28.1499	1.41280	0.706401	−	0.707812i	$-0.250318\pi$
$397$	28.1499	1.41280	0.706401	+	0.707812i	$0.250318\pi$
$398$	5.93474	0.297482
$399$	5.49088	0.274888
$400$	6.81900	0.340950
$401$	−33.3899	−1.66741	−0.833707	−	0.552207i	$-0.813786\pi$
$401$	−33.3899	−1.66741	−0.833707	+	0.552207i	$0.813786\pi$
$402$	−5.69363	−0.283972
$403$	−4.78943	−0.238578
$404$	−2.19696	−0.109303
$405$	−3.43788	−0.170829
$406$	−3.10837	−0.154266
$407$	−6.85762	−0.339920
$408$	2.91275	0.144203
$409$	−14.4536	−0.714684	−0.357342	−	0.933974i	$-0.616317\pi$
$409$	−14.4536	−0.714684	−0.357342	+	0.933974i	$0.616317\pi$
$410$	−8.52144	−0.420844
$411$	11.3092	0.557841
$412$	1.00000	0.0492665
$413$	6.76397	0.332833
$414$	2.22770	0.109486
$415$	54.1982	2.66049
$416$	1.00000	0.0490290
$417$	−2.37115	−0.116116
$418$	25.8907	1.26636
$419$	−20.8682	−1.01948	−0.509739	−	0.860329i	$-0.670258\pi$
$419$	−20.8682	−1.01948	−0.509739	+	0.860329i	$0.670258\pi$
$420$	−3.01042	−0.146893
$421$	−4.12536	−0.201058	−0.100529	−	0.994934i	$-0.532053\pi$
$421$	−4.12536	−0.201058	−0.100529	+	0.994934i	$0.532053\pi$
$422$	−3.86201	−0.188000
$423$	7.14668	0.347484
$424$	10.0017	0.485724
$425$	19.8620	0.963450
$426$	−0.740352	−0.0358702
$427$	1.97713	0.0956803
$428$	−5.52530	−0.267076
$429$	−4.12894	−0.199347
$430$	−24.1163	−1.16299
$431$	29.8416	1.43742	0.718709	−	0.695311i	$-0.244734\pi$
$431$	29.8416	1.43742	0.718709	+	0.695311i	$0.244734\pi$
$432$	−1.00000	−0.0481125
$433$	−33.2387	−1.59735	−0.798675	−	0.601763i	$-0.794465\pi$
$433$	−33.2387	−1.59735	−0.798675	+	0.601763i	$0.794465\pi$
$434$	4.19392	0.201315
$435$	−12.2035	−0.585115
$436$	−11.0915	−0.531188
$437$	−13.9689	−0.668223
$438$	5.84278	0.279179
$439$	21.2514	1.01427	0.507137	−	0.861866i	$-0.330704\pi$
$439$	21.2514	1.01427	0.507137	+	0.861866i	$0.330704\pi$
$440$	−14.1948	−0.676711
$441$	−6.23321	−0.296820
$442$	2.91275	0.138545
$443$	−5.44412	−0.258658	−0.129329	−	0.991602i	$-0.541282\pi$
$443$	−5.44412	−0.258658	−0.129329	+	0.991602i	$0.541282\pi$
$444$	−1.66087	−0.0788212
$445$	−13.2295	−0.627140
$446$	−2.77489	−0.131395
$447$	−4.79584	−0.226835
$448$	−0.875663	−0.0413712
$449$	37.7400	1.78106	0.890530	−	0.454924i	$-0.150333\pi$
$449$	37.7400	1.78106	0.890530	+	0.454924i	$0.150333\pi$
$450$	−6.81900	−0.321451
$451$	10.2344	0.481918
$452$	−15.7340	−0.740064
$453$	−7.33233	−0.344503
$454$	26.0660	1.22334
$455$	−3.01042	−0.141131
$456$	6.27054	0.293645
$457$	11.0662	0.517657	0.258829	−	0.965923i	$-0.416664\pi$
$457$	11.0662	0.517657	0.258829	+	0.965923i	$0.416664\pi$
$458$	18.3397	0.856957
$459$	−2.91275	−0.135956
$460$	7.65856	0.357082
$461$	39.3826	1.83423	0.917115	−	0.398624i	$-0.130512\pi$
$461$	39.3826	1.83423	0.917115	+	0.398624i	$0.130512\pi$
$462$	3.61556	0.168211
$463$	−24.5365	−1.14031	−0.570154	−	0.821538i	$-0.693117\pi$
$463$	−24.5365	−1.14031	−0.570154	+	0.821538i	$0.693117\pi$
$464$	−3.54973	−0.164792
$465$	16.4655	0.763567
$466$	8.09808	0.375136
$467$	−37.4980	−1.73520	−0.867601	−	0.497261i	$-0.834339\pi$
$467$	−37.4980	−1.73520	−0.867601	+	0.497261i	$0.834339\pi$
$468$	−1.00000	−0.0462250
$469$	4.98570	0.230218
$470$	24.5694	1.13330
$471$	8.80210	0.405580
$472$	7.72440	0.355544
$473$	28.9641	1.33177
$474$	−15.8644	−0.728676
$475$	42.7588	1.96191
$476$	−2.55059	−0.116906
$477$	−10.0017	−0.457945
$478$	−21.0662	−0.963545
$479$	15.1467	0.692073	0.346036	−	0.938221i	$-0.387527\pi$
$479$	15.1467	0.692073	0.346036	+	0.938221i	$0.387527\pi$
$480$	−3.43788	−0.156917
$481$	−1.66087	−0.0757290
$482$	−8.02129	−0.365360
$483$	−1.95072	−0.0887606
$484$	6.04818	0.274917
$485$	−36.1672	−1.64227
$486$	1.00000	0.0453609
$487$	11.9348	0.540819	0.270410	−	0.962745i	$-0.412841\pi$
$487$	11.9348	0.540819	0.270410	+	0.962745i	$0.412841\pi$
$488$	2.25787	0.102209
$489$	5.78137	0.261442
$490$	−21.4290	−0.968065
$491$	−20.5208	−0.926090	−0.463045	−	0.886335i	$-0.653243\pi$
$491$	−20.5208	−0.926090	−0.463045	+	0.886335i	$0.653243\pi$
$492$	2.47869	0.111748
$493$	−10.3395	−0.465667
$494$	6.27054	0.282125
$495$	14.1948	0.638009
$496$	4.78943	0.215052
$497$	0.648299	0.0290802
$498$	−15.7650	−0.706448
$499$	−27.9203	−1.24988	−0.624942	−	0.780671i	$-0.714877\pi$
$499$	−27.9203	−1.24988	−0.624942	+	0.780671i	$0.714877\pi$
$500$	−6.25349	−0.279664
$501$	−11.7593	−0.525367
$502$	−18.0515	−0.805677
$503$	−12.8948	−0.574950	−0.287475	−	0.957788i	$-0.592816\pi$
$503$	−12.8948	−0.574950	−0.287475	+	0.957788i	$0.592816\pi$
$504$	0.875663	0.0390051
$505$	7.55289	0.336099
$506$	−9.19806	−0.408903
$507$	−1.00000	−0.0444116
$508$	−3.96860	−0.176078
$509$	2.25904	0.100130	0.0500650	−	0.998746i	$-0.484057\pi$
$509$	2.25904	0.100130	0.0500650	+	0.998746i	$0.484057\pi$
$510$	−10.0137	−0.443413
$511$	−5.11630	−0.226332
$512$	−1.00000	−0.0441942
$513$	−6.27054	−0.276851
$514$	2.46728	0.108827
$515$	−3.43788	−0.151491
$516$	7.01489	0.308813
$517$	−29.5083	−1.29777
$518$	1.45436	0.0639008
$519$	−4.87706	−0.214079
$520$	−3.43788	−0.150761
$521$	19.9571	0.874336	0.437168	−	0.899380i	$-0.355982\pi$
$521$	19.9571	0.874336	0.437168	+	0.899380i	$0.355982\pi$
$522$	3.54973	0.155367
$523$	15.6375	0.683780	0.341890	−	0.939740i	$-0.388933\pi$
$523$	15.6375	0.683780	0.341890	+	0.939740i	$0.388933\pi$
$524$	9.42019	0.411523
$525$	5.97114	0.260602
$526$	11.8755	0.517796
$527$	13.9504	0.607689
$528$	4.12894	0.179689
$529$	−18.0373	−0.784232
$530$	−34.3845	−1.49357
$531$	−7.72440	−0.335210
$532$	−5.49088	−0.238060
$533$	2.47869	0.107364
$534$	3.84817	0.166526
$535$	18.9953	0.821239
$536$	5.69363	0.245927
$537$	1.99720	0.0861856
$538$	−4.75452	−0.204982
$539$	25.7366	1.10855
$540$	3.43788	0.147943
$541$	30.9568	1.33094	0.665468	−	0.746426i	$-0.268232\pi$
$541$	30.9568	1.33094	0.665468	+	0.746426i	$0.268232\pi$
$542$	1.68670	0.0724500
$543$	−10.2805	−0.441180
$544$	−2.91275	−0.124883
$545$	38.1313	1.63337
$546$	0.875663	0.0374749
$547$	−33.0068	−1.41127	−0.705634	−	0.708576i	$-0.749338\pi$
$547$	−33.0068	−1.41127	−0.705634	+	0.708576i	$0.749338\pi$
$548$	−11.3092	−0.483104
$549$	−2.25787	−0.0963637
$550$	28.1553	1.20054
$551$	−22.2587	−0.948254
$552$	−2.22770	−0.0948173
$553$	13.8919	0.590742
$554$	17.6902	0.751584
$555$	5.70985	0.242370
$556$	2.37115	0.100559
$557$	21.6305	0.916512	0.458256	−	0.888820i	$-0.348474\pi$
$557$	21.6305	0.916512	0.458256	+	0.888820i	$0.348474\pi$
$558$	−4.78943	−0.202753
$559$	7.01489	0.296698
$560$	3.01042	0.127213
$561$	12.0266	0.507763
$562$	31.3662	1.32310
$563$	−19.9428	−0.840489	−0.420245	−	0.907411i	$-0.638056\pi$
$563$	−19.9428	−0.840489	−0.420245	+	0.907411i	$0.638056\pi$
$564$	−7.14668	−0.300930
$565$	54.0915	2.27565
$566$	−6.42432	−0.270034
$567$	−0.875663	−0.0367744
$568$	0.740352	0.0310645
$569$	−41.1857	−1.72659	−0.863296	−	0.504697i	$-0.831604\pi$
$569$	−41.1857	−1.72659	−0.863296	+	0.504697i	$0.831604\pi$
$570$	−21.5574	−0.902938
$571$	32.1447	1.34522	0.672608	−	0.739999i	$-0.265174\pi$
$571$	32.1447	1.34522	0.672608	+	0.739999i	$0.265174\pi$
$572$	4.12894	0.172640
$573$	−21.0062	−0.877545
$574$	−2.17050	−0.0905949
$575$	−15.1907	−0.633496
$576$	1.00000	0.0416667
$577$	−13.0790	−0.544487	−0.272244	−	0.962228i	$-0.587766\pi$
$577$	−13.0790	−0.544487	−0.272244	+	0.962228i	$0.587766\pi$
$578$	8.51589	0.354214
$579$	−3.91167	−0.162564
$580$	12.2035	0.506724
$581$	13.8049	0.572722
$582$	10.5202	0.436077
$583$	41.2963	1.71032
$584$	−5.84278	−0.241776
$585$	3.43788	0.142139
$586$	−13.7022	−0.566033
$587$	1.01916	0.0420651	0.0210326	−	0.999779i	$-0.493305\pi$
$587$	1.01916	0.0420651	0.0210326	+	0.999779i	$0.493305\pi$
$588$	6.23321	0.257053
$589$	30.0323	1.23746
$590$	−26.5555	−1.09327
$591$	−22.7100	−0.934166
$592$	1.66087	0.0682612
$593$	8.55788	0.351430	0.175715	−	0.984441i	$-0.443776\pi$
$593$	8.55788	0.351430	0.175715	+	0.984441i	$0.443776\pi$
$594$	−4.12894	−0.169413
$595$	8.76860	0.359478
$596$	4.79584	0.196445
$597$	5.93474	0.242893
$598$	−2.22770	−0.0910975
$599$	30.6520	1.25241	0.626203	−	0.779660i	$-0.284608\pi$
$599$	30.6520	1.25241	0.626203	+	0.779660i	$0.284608\pi$
$600$	6.81900	0.278384
$601$	33.7400	1.37628	0.688141	−	0.725577i	$-0.258427\pi$
$601$	33.7400	1.37628	0.688141	+	0.725577i	$0.258427\pi$
$602$	−6.14268	−0.250357
$603$	−5.69363	−0.231863
$604$	7.33233	0.298348
$605$	−20.7929	−0.845352
$606$	−2.19696	−0.0892456
$607$	0.587676	0.0238530	0.0119265	−	0.999929i	$-0.496204\pi$
$607$	0.587676	0.0238530	0.0119265	+	0.999929i	$0.496204\pi$
$608$	−6.27054	−0.254304
$609$	−3.10837	−0.125957
$610$	−7.76229	−0.314286
$611$	−7.14668	−0.289124
$612$	2.91275	0.117741
$613$	36.0967	1.45793	0.728967	−	0.684549i	$-0.240001\pi$
$613$	36.0967	1.45793	0.728967	+	0.684549i	$0.240001\pi$
$614$	−10.4205	−0.420536
$615$	−8.52144	−0.343618
$616$	−3.61556	−0.145675
$617$	−21.3445	−0.859296	−0.429648	−	0.902996i	$-0.641362\pi$
$617$	−21.3445	−0.859296	−0.429648	+	0.902996i	$0.641362\pi$
$618$	1.00000	0.0402259
$619$	−6.44665	−0.259113	−0.129556	−	0.991572i	$-0.541355\pi$
$619$	−6.44665	−0.259113	−0.129556	+	0.991572i	$0.541355\pi$
$620$	−16.4655	−0.661269
$621$	2.22770	0.0893946
$622$	2.65273	0.106365
$623$	−3.36970	−0.135004
$624$	1.00000	0.0400320
$625$	−12.5963	−0.503851
$626$	−0.504119	−0.0201486
$627$	25.8907	1.03398
$628$	−8.80210	−0.351242
$629$	4.83769	0.192891
$630$	−3.01042	−0.119938
$631$	−19.0214	−0.757231	−0.378616	−	0.925554i	$-0.623600\pi$
$631$	−19.0214	−0.757231	−0.378616	+	0.925554i	$0.623600\pi$
$632$	15.8644	0.631052
$633$	−3.86201	−0.153501
$634$	31.0342	1.23253
$635$	13.6436	0.541428
$636$	10.0017	0.396592
$637$	6.23321	0.246969
$638$	−14.6566	−0.580262
$639$	−0.740352	−0.0292879
$640$	3.43788	0.135894
$641$	46.6464	1.84242	0.921211	−	0.389062i	$-0.127201\pi$
$641$	46.6464	1.84242	0.921211	+	0.389062i	$0.127201\pi$
$642$	−5.52530	−0.218066
$643$	−23.0133	−0.907555	−0.453777	−	0.891115i	$-0.649924\pi$
$643$	−23.0133	−0.907555	−0.453777	+	0.891115i	$0.649924\pi$
$644$	1.95072	0.0768690
$645$	−24.1163	−0.949579
$646$	−18.2645	−0.718608
$647$	4.69070	0.184411	0.0922053	−	0.995740i	$-0.470608\pi$
$647$	4.69070	0.184411	0.0922053	+	0.995740i	$0.470608\pi$
$648$	−1.00000	−0.0392837
$649$	31.8936	1.25193
$650$	6.81900	0.267463
$651$	4.19392	0.164373
$652$	−5.78137	−0.226416
$653$	2.14583	0.0839730	0.0419865	−	0.999118i	$-0.486631\pi$
$653$	2.14583	0.0839730	0.0419865	+	0.999118i	$0.486631\pi$
$654$	−11.0915	−0.433713
$655$	−32.3854	−1.26540
$656$	−2.47869	−0.0967767
$657$	5.84278	0.227948
$658$	6.25808	0.243966
$659$	38.9252	1.51631	0.758155	−	0.652074i	$-0.226101\pi$
$659$	38.9252	1.51631	0.758155	+	0.652074i	$0.226101\pi$
$660$	−14.1948	−0.552532
$661$	29.4704	1.14627	0.573133	−	0.819462i	$-0.305728\pi$
$661$	29.4704	1.14627	0.573133	+	0.819462i	$0.305728\pi$
$662$	−24.6859	−0.959446
$663$	2.91275	0.113122
$664$	15.7650	0.611802
$665$	18.8770	0.732018
$666$	−1.66087	−0.0643572
$667$	7.90774	0.306189
$668$	11.7593	0.454981
$669$	−2.77489	−0.107284
$670$	−19.5740	−0.756209
$671$	9.32263	0.359896
$672$	−0.875663	−0.0337794
$673$	8.78181	0.338514	0.169257	−	0.985572i	$-0.445863\pi$
$673$	8.78181	0.338514	0.169257	+	0.985572i	$0.445863\pi$
$674$	−28.0255	−1.07950
$675$	−6.81900	−0.262463
$676$	1.00000	0.0384615
$677$	−23.2590	−0.893917	−0.446958	−	0.894555i	$-0.647493\pi$
$677$	−23.2590	−0.893917	−0.446958	+	0.894555i	$0.647493\pi$
$678$	−15.7340	−0.604260
$679$	−9.21217	−0.353531
$680$	10.0137	0.384007
$681$	26.0660	0.998852
$682$	19.7753	0.757234
$683$	34.6559	1.32607	0.663036	−	0.748588i	$-0.269268\pi$
$683$	34.6559	1.32607	0.663036	+	0.748588i	$0.269268\pi$
$684$	6.27054	0.239760
$685$	38.8796	1.48551
$686$	−11.5878	−0.442426
$687$	18.3397	0.699702
$688$	−7.01489	−0.267440
$689$	10.0017	0.381033
$690$	7.65856	0.291557
$691$	6.75173	0.256848	0.128424	−	0.991719i	$-0.459008\pi$
$691$	6.75173	0.256848	0.128424	+	0.991719i	$0.459008\pi$
$692$	4.87706	0.185398
$693$	3.61556	0.137344
$694$	−2.12054	−0.0804947
$695$	−8.15172	−0.309212
$696$	−3.54973	−0.134552
$697$	−7.21981	−0.273470
$698$	36.3447	1.37567
$699$	8.09808	0.306297
$700$	−5.97114	−0.225688
$701$	−41.2012	−1.55615	−0.778074	−	0.628173i	$-0.783803\pi$
$701$	−41.2012	−1.55615	−0.778074	+	0.628173i	$0.783803\pi$
$702$	−1.00000	−0.0377426
$703$	10.4145	0.392791
$704$	−4.12894	−0.155615
$705$	24.5694	0.925338
$706$	−25.4726	−0.958672
$707$	1.92380	0.0723519
$708$	7.72440	0.290301
$709$	20.8885	0.784485	0.392243	−	0.919862i	$-0.371699\pi$
$709$	20.8885	0.784485	0.392243	+	0.919862i	$0.371699\pi$
$710$	−2.54524	−0.0955211
$711$	−15.8644	−0.594961
$712$	−3.84817	−0.144216
$713$	−10.6694	−0.399573
$714$	−2.55059	−0.0954533
$715$	−14.1948	−0.530855
$716$	−1.99720	−0.0746389
$717$	−21.0662	−0.786732
$718$	28.2455	1.05411
$719$	24.7262	0.922131	0.461066	−	0.887366i	$-0.347467\pi$
$719$	24.7262	0.922131	0.461066	+	0.887366i	$0.347467\pi$
$720$	−3.43788	−0.128122
$721$	−0.875663	−0.0326114
$722$	−20.3197	−0.756222
$723$	−8.02129	−0.298315
$724$	10.2805	0.382073
$725$	−24.2056	−0.898973
$726$	6.04818	0.224469
$727$	−37.6271	−1.39551	−0.697757	−	0.716335i	$-0.745818\pi$
$727$	−37.6271	−1.39551	−0.697757	+	0.716335i	$0.745818\pi$
$728$	−0.875663	−0.0324542
$729$	1.00000	0.0370370
$730$	20.0868	0.743444
$731$	−20.4326	−0.755728
$732$	2.25787	0.0834534
$733$	35.7815	1.32162	0.660809	−	0.750554i	$-0.270213\pi$
$733$	35.7815	1.32162	0.660809	+	0.750554i	$0.270213\pi$
$734$	−8.99275	−0.331929
$735$	−21.4290	−0.790421
$736$	2.22770	0.0821142
$737$	23.5087	0.865953
$738$	2.47869	0.0912419
$739$	25.6956	0.945228	0.472614	−	0.881269i	$-0.343310\pi$
$739$	25.6956	0.945228	0.472614	+	0.881269i	$0.343310\pi$
$740$	−5.70985	−0.209898
$741$	6.27054	0.230354
$742$	−8.75808	−0.321519
$743$	−23.2477	−0.852875	−0.426437	−	0.904517i	$-0.640232\pi$
$743$	−23.2477	−0.852875	−0.426437	+	0.904517i	$0.640232\pi$
$744$	4.78943	0.175589
$745$	−16.4875	−0.604055
$746$	5.98913	0.219278
$747$	−15.7650	−0.576812
$748$	−12.0266	−0.439735
$749$	4.83830	0.176788
$750$	−6.25349	−0.228345
$751$	23.7486	0.866597	0.433299	−	0.901250i	$-0.357350\pi$
$751$	23.7486	0.866597	0.433299	+	0.901250i	$0.357350\pi$
$752$	7.14668	0.260613
$753$	−18.0515	−0.657832
$754$	−3.54973	−0.129274
$755$	−25.2076	−0.917400
$756$	0.875663	0.0318475
$757$	−33.9998	−1.23574	−0.617871	−	0.786279i	$-0.712005\pi$
$757$	−33.9998	−1.23574	−0.617871	+	0.786279i	$0.712005\pi$
$758$	−34.3213	−1.24660
$759$	−9.19806	−0.333868
$760$	21.5574	0.781968
$761$	45.5259	1.65031	0.825157	−	0.564904i	$-0.191087\pi$
$761$	45.5259	1.65031	0.825157	+	0.564904i	$0.191087\pi$
$762$	−3.96860	−0.143767
$763$	9.71245	0.351614
$764$	21.0062	0.759976
$765$	−10.0137	−0.362045
$766$	−1.97543	−0.0713752
$767$	7.72440	0.278912
$768$	−1.00000	−0.0360844
$769$	−6.84969	−0.247006	−0.123503	−	0.992344i	$-0.539413\pi$
$769$	−6.84969	−0.247006	−0.123503	+	0.992344i	$0.539413\pi$
$770$	12.4299	0.447941
$771$	2.46728	0.0888570
$772$	3.91167	0.140784
$773$	23.3368	0.839367	0.419684	−	0.907671i	$-0.362141\pi$
$773$	23.3368	0.839367	0.419684	+	0.907671i	$0.362141\pi$
$774$	7.01489	0.252145
$775$	32.6591	1.17315
$776$	−10.5202	−0.377654
$777$	1.45436	0.0521748
$778$	−14.2832	−0.512078
$779$	−15.5427	−0.556877
$780$	−3.43788	−0.123096
$781$	3.05687	0.109383
$782$	6.48874	0.232037
$783$	3.54973	0.126857
$784$	−6.23321	−0.222615
$785$	30.2606	1.08005
$786$	9.42019	0.336007
$787$	−33.8268	−1.20579	−0.602897	−	0.797819i	$-0.705987\pi$
$787$	−33.8268	−1.20579	−0.602897	+	0.797819i	$0.705987\pi$
$788$	22.7100	0.809012
$789$	11.8755	0.422779
$790$	−54.5399	−1.94044
$791$	13.7777	0.489877
$792$	4.12894	0.146716
$793$	2.25787	0.0801794
$794$	−28.1499	−0.999001
$795$	−34.3845	−1.21949
$796$	−5.93474	−0.210351
$797$	0.440113	0.0155896	0.00779480	−	0.999970i	$-0.497519\pi$
$797$	0.440113	0.0155896	0.00779480	+	0.999970i	$0.497519\pi$
$798$	−5.49088	−0.194375
$799$	20.8165	0.736435
$800$	−6.81900	−0.241088
$801$	3.84817	0.135968
$802$	33.3899	1.17904
$803$	−24.1245	−0.851335
$804$	5.69363	0.200799
$805$	−6.70632	−0.236367
$806$	4.78943	0.168700
$807$	−4.75452	−0.167367
$808$	2.19696	0.0772889
$809$	−8.41166	−0.295738	−0.147869	−	0.989007i	$-0.547241\pi$
$809$	−8.41166	−0.295738	−0.147869	+	0.989007i	$0.547241\pi$
$810$	3.43788	0.120795
$811$	−4.01487	−0.140981	−0.0704906	−	0.997512i	$-0.522456\pi$
$811$	−4.01487	−0.140981	−0.0704906	+	0.997512i	$0.522456\pi$
$812$	3.10837	0.109082
$813$	1.68670	0.0591552
$814$	6.85762	0.240360
$815$	19.8756	0.696213
$816$	−2.91275	−0.101967
$817$	−43.9872	−1.53892
$818$	14.4536	0.505358
$819$	0.875663	0.0305981
$820$	8.52144	0.297582
$821$	−17.0208	−0.594029	−0.297015	−	0.954873i	$-0.595991\pi$
$821$	−17.0208	−0.594029	−0.297015	+	0.954873i	$0.595991\pi$
$822$	−11.3092	−0.394453
$823$	−3.76801	−0.131345	−0.0656723	−	0.997841i	$-0.520919\pi$
$823$	−3.76801	−0.131345	−0.0656723	+	0.997841i	$0.520919\pi$
$824$	−1.00000	−0.0348367
$825$	28.1553	0.980240
$826$	−6.76397	−0.235349
$827$	27.3459	0.950909	0.475455	−	0.879740i	$-0.342284\pi$
$827$	27.3459	0.950909	0.475455	+	0.879740i	$0.342284\pi$
$828$	−2.22770	−0.0774180
$829$	−26.5720	−0.922884	−0.461442	−	0.887170i	$-0.652668\pi$
$829$	−26.5720	−0.922884	−0.461442	+	0.887170i	$0.652668\pi$
$830$	−54.1982	−1.88125
$831$	17.6902	0.613666
$832$	−1.00000	−0.0346688
$833$	−18.1558	−0.629061
$834$	2.37115	0.0821062
$835$	−40.4270	−1.39903
$836$	−25.8907	−0.895450
$837$	−4.78943	−0.165547
$838$	20.8682	0.720879
$839$	8.05851	0.278211	0.139105	−	0.990278i	$-0.455577\pi$
$839$	8.05851	0.278211	0.139105	+	0.990278i	$0.455577\pi$
$840$	3.01042	0.103869
$841$	−16.3994	−0.565497
$842$	4.12536	0.142169
$843$	31.3662	1.08031
$844$	3.86201	0.132936
$845$	−3.43788	−0.118267
$846$	−7.14668	−0.245708
$847$	−5.29617	−0.181978
$848$	−10.0017	−0.343458
$849$	−6.42432	−0.220482
$850$	−19.8620	−0.681262
$851$	−3.69991	−0.126831
$852$	0.740352	0.0253640
$853$	−15.1334	−0.518158	−0.259079	−	0.965856i	$-0.583419\pi$
$853$	−15.1334	−0.518158	−0.259079	+	0.965856i	$0.583419\pi$
$854$	−1.97713	−0.0676562
$855$	−21.5574	−0.737246
$856$	5.52530	0.188851
$857$	12.5579	0.428971	0.214485	−	0.976727i	$-0.431193\pi$
$857$	12.5579	0.428971	0.214485	+	0.976727i	$0.431193\pi$
$858$	4.12894	0.140960
$859$	−11.0310	−0.376374	−0.188187	−	0.982133i	$-0.560261\pi$
$859$	−11.0310	−0.376374	−0.188187	+	0.982133i	$0.560261\pi$
$860$	24.1163	0.822360
$861$	−2.17050	−0.0739704
$862$	−29.8416	−1.01641
$863$	−16.8235	−0.572680	−0.286340	−	0.958128i	$-0.592439\pi$
$863$	−16.8235	−0.572680	−0.286340	+	0.958128i	$0.592439\pi$
$864$	1.00000	0.0340207
$865$	−16.7667	−0.570085
$866$	33.2387	1.12950
$867$	8.51589	0.289215
$868$	−4.19392	−0.142351
$869$	65.5032	2.22204
$870$	12.2035	0.413739
$871$	5.69363	0.192921
$872$	11.0915	0.375607
$873$	10.5202	0.356056
$874$	13.9689	0.472505
$875$	5.47595	0.185121
$876$	−5.84278	−0.197409
$877$	57.9498	1.95683	0.978413	−	0.206659i	$-0.0662591\pi$
$877$	57.9498	1.95683	0.978413	+	0.206659i	$0.0662591\pi$
$878$	−21.2514	−0.717200
$879$	−13.7022	−0.462164
$880$	14.1948	0.478507
$881$	21.0322	0.708591	0.354296	−	0.935133i	$-0.384721\pi$
$881$	21.0322	0.708591	0.354296	+	0.935133i	$0.384721\pi$
$882$	6.23321	0.209883
$883$	48.3885	1.62840	0.814201	−	0.580584i	$-0.197176\pi$
$883$	48.3885	1.62840	0.814201	+	0.580584i	$0.197176\pi$
$884$	−2.91275	−0.0979664
$885$	−26.5555	−0.892655
$886$	5.44412	0.182899
$887$	−3.38532	−0.113668	−0.0568339	−	0.998384i	$-0.518101\pi$
$887$	−3.38532	−0.113668	−0.0568339	+	0.998384i	$0.518101\pi$
$888$	1.66087	0.0557350
$889$	3.47515	0.116553
$890$	13.2295	0.443455
$891$	−4.12894	−0.138325
$892$	2.77489	0.0929102
$893$	44.8136	1.49963
$894$	4.79584	0.160397
$895$	6.86613	0.229509
$896$	0.875663	0.0292538
$897$	−2.22770	−0.0743808
$898$	−37.7400	−1.25940
$899$	−17.0012	−0.567021
$900$	6.81900	0.227300
$901$	−29.1323	−0.970539
$902$	−10.2344	−0.340768
$903$	−6.14268	−0.204416
$904$	15.7340	0.523304
$905$	−35.3432	−1.17485
$906$	7.33233	0.243600
$907$	−14.3909	−0.477841	−0.238921	−	0.971039i	$-0.576794\pi$
$907$	−14.3909	−0.477841	−0.238921	+	0.971039i	$0.576794\pi$
$908$	−26.0660	−0.865031
$909$	−2.19696	−0.0728687
$910$	3.01042	0.0997945
$911$	−3.49541	−0.115808	−0.0579040	−	0.998322i	$-0.518442\pi$
$911$	−3.49541	−0.115808	−0.0579040	+	0.998322i	$0.518442\pi$
$912$	−6.27054	−0.207638
$913$	65.0929	2.15426
$914$	−11.0662	−0.366039
$915$	−7.76229	−0.256613
$916$	−18.3397	−0.605960
$917$	−8.24891	−0.272403
$918$	2.91275	0.0961351
$919$	14.9357	0.492684	0.246342	−	0.969183i	$-0.420771\pi$
$919$	14.9357	0.492684	0.246342	+	0.969183i	$0.420771\pi$
$920$	−7.65856	−0.252495
$921$	−10.4205	−0.343367
$922$	−39.3826	−1.29700
$923$	0.740352	0.0243690
$924$	−3.61556	−0.118943
$925$	11.3254	0.372378
$926$	24.5365	0.806320
$927$	1.00000	0.0328443
$928$	3.54973	0.116526
$929$	32.3954	1.06286	0.531430	−	0.847103i	$-0.321655\pi$
$929$	32.3954	1.06286	0.531430	+	0.847103i	$0.321655\pi$
$930$	−16.4655	−0.539924
$931$	−39.0856	−1.28098
$932$	−8.09808	−0.265261
$933$	2.65273	0.0868465
$934$	37.4980	1.22697
$935$	41.3459	1.35216
$936$	1.00000	0.0326860
$937$	−20.9785	−0.685336	−0.342668	−	0.939456i	$-0.611331\pi$
$937$	−20.9785	−0.685336	−0.342668	+	0.939456i	$0.611331\pi$
$938$	−4.98570	−0.162789
$939$	−0.504119	−0.0164513
$940$	−24.5694	−0.801366
$941$	−36.2449	−1.18155	−0.590775	−	0.806837i	$-0.701178\pi$
$941$	−36.2449	−1.18155	−0.590775	+	0.806837i	$0.701178\pi$
$942$	−8.80210	−0.286788
$943$	5.52179	0.179814
$944$	−7.72440	−0.251408
$945$	−3.01042	−0.0979290
$946$	−28.9641	−0.941704
$947$	40.0744	1.30224	0.651122	−	0.758973i	$-0.274299\pi$
$947$	40.0744	1.30224	0.651122	+	0.758973i	$0.274299\pi$
$948$	15.8644	0.515252
$949$	−5.84278	−0.189665
$950$	−42.7588	−1.38728
$951$	31.0342	1.00635
$952$	2.55059	0.0826650
$953$	−28.7014	−0.929730	−0.464865	−	0.885381i	$-0.653897\pi$
$953$	−28.7014	−0.929730	−0.464865	+	0.885381i	$0.653897\pi$
$954$	10.0017	0.323816
$955$	−72.2166	−2.33687
$956$	21.0662	0.681330
$957$	−14.6566	−0.473782
$958$	−15.1467	−0.489369
$959$	9.90303	0.319786
$960$	3.43788	0.110957
$961$	−8.06140	−0.260045
$962$	1.66087	0.0535485
$963$	−5.52530	−0.178050
$964$	8.02129	0.258348
$965$	−13.4478	−0.432902
$966$	1.95072	0.0627632
$967$	−13.8179	−0.444353	−0.222177	−	0.975006i	$-0.571316\pi$
$967$	−13.8179	−0.444353	−0.222177	+	0.975006i	$0.571316\pi$
$968$	−6.04818	−0.194396
$969$	−18.2645	−0.586741
$970$	36.1672	1.16126
$971$	−30.1735	−0.968314	−0.484157	−	0.874981i	$-0.660874\pi$
$971$	−30.1735	−0.968314	−0.484157	+	0.874981i	$0.660874\pi$
$972$	−1.00000	−0.0320750
$973$	−2.07633	−0.0665640
$974$	−11.9348	−0.382417
$975$	6.81900	0.218383
$976$	−2.25787	−0.0722727
$977$	−6.27177	−0.200652	−0.100326	−	0.994955i	$-0.531989\pi$
$977$	−6.27177	−0.200652	−0.100326	+	0.994955i	$0.531989\pi$
$978$	−5.78137	−0.184868
$979$	−15.8889	−0.507810
$980$	21.4290	0.684525
$981$	−11.0915	−0.354126
$982$	20.5208	0.654845
$983$	26.0909	0.832171	0.416086	−	0.909325i	$-0.363402\pi$
$983$	26.0909	0.832171	0.416086	+	0.909325i	$0.363402\pi$
$984$	−2.47869	−0.0790178
$985$	−78.0743	−2.48765
$986$	10.3395	0.329276
$987$	6.25808	0.199197
$988$	−6.27054	−0.199493
$989$	15.6271	0.496912
$990$	−14.1948	−0.451140
$991$	17.8943	0.568431	0.284216	−	0.958760i	$-0.408267\pi$
$991$	17.8943	0.568431	0.284216	+	0.958760i	$0.408267\pi$
$992$	−4.78943	−0.152064
$993$	−24.6859	−0.783384
$994$	−0.648299	−0.0205628
$995$	20.4029	0.646815
$996$	15.7650	0.499534
$997$	44.3111	1.40335	0.701673	−	0.712499i	$-0.252437\pi$
$997$	44.3111	1.40335	0.701673	+	0.712499i	$0.252437\pi$
$998$	27.9203	0.883802
$999$	−1.66087	−0.0525475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.43788 q^{5} +1.00000 q^{6} -0.875663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.43788 q^{5} +1.00000 q^{6} -0.875663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.43788 q^{10} -4.12894 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.875663 q^{14} +3.43788 q^{15} +1.00000 q^{16} +2.91275 q^{17} -1.00000 q^{18} +6.27054 q^{19} -3.43788 q^{20} +0.875663 q^{21} +4.12894 q^{22} -2.22770 q^{23} +1.00000 q^{24} +6.81900 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.875663 q^{28} -3.54973 q^{29} -3.43788 q^{30} +4.78943 q^{31} -1.00000 q^{32} +4.12894 q^{33} -2.91275 q^{34} +3.01042 q^{35} +1.00000 q^{36} +1.66087 q^{37} -6.27054 q^{38} +1.00000 q^{39} +3.43788 q^{40} -2.47869 q^{41} -0.875663 q^{42} -7.01489 q^{43} -4.12894 q^{44} -3.43788 q^{45} +2.22770 q^{46} +7.14668 q^{47} -1.00000 q^{48} -6.23321 q^{49} -6.81900 q^{50} -2.91275 q^{51} -1.00000 q^{52} -10.0017 q^{53} +1.00000 q^{54} +14.1948 q^{55} +0.875663 q^{56} -6.27054 q^{57} +3.54973 q^{58} -7.72440 q^{59} +3.43788 q^{60} -2.25787 q^{61} -4.78943 q^{62} -0.875663 q^{63} +1.00000 q^{64} +3.43788 q^{65} -4.12894 q^{66} -5.69363 q^{67} +2.91275 q^{68} +2.22770 q^{69} -3.01042 q^{70} -0.740352 q^{71} -1.00000 q^{72} +5.84278 q^{73} -1.66087 q^{74} -6.81900 q^{75} +6.27054 q^{76} +3.61556 q^{77} -1.00000 q^{78} -15.8644 q^{79} -3.43788 q^{80} +1.00000 q^{81} +2.47869 q^{82} -15.7650 q^{83} +0.875663 q^{84} -10.0137 q^{85} +7.01489 q^{86} +3.54973 q^{87} +4.12894 q^{88} +3.84817 q^{89} +3.43788 q^{90} +0.875663 q^{91} -2.22770 q^{92} -4.78943 q^{93} -7.14668 q^{94} -21.5574 q^{95} +1.00000 q^{96} +10.5202 q^{97} +6.23321 q^{98} -4.12894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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