LMFDB - Embedded newform 8034.2.a.v.1.11

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} + \cdots + 576 $ x^11 - 5x^10 - 31x^9 + 168x^8 + 300x^7 - 1928x^6 - 736x^5 + 8532x^4 - 2065x^3 - 10494x^2 + 4024x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$4.22313$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.22313 q^{5} +1.00000 q^{6} -0.979791 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.22313 q^{5} +1.00000 q^{6} -0.979791 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.22313 q^{10} +1.72364 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.979791 q^{14} +4.22313 q^{15} +1.00000 q^{16} -2.27139 q^{17} +1.00000 q^{18} -1.97979 q^{19} +4.22313 q^{20} -0.979791 q^{21} +1.72364 q^{22} +1.31153 q^{23} +1.00000 q^{24} +12.8348 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.979791 q^{28} +9.39422 q^{29} +4.22313 q^{30} +1.97979 q^{31} +1.00000 q^{32} +1.72364 q^{33} -2.27139 q^{34} -4.13778 q^{35} +1.00000 q^{36} +11.5499 q^{37} -1.97979 q^{38} +1.00000 q^{39} +4.22313 q^{40} +4.25364 q^{41} -0.979791 q^{42} -11.5427 q^{43} +1.72364 q^{44} +4.22313 q^{45} +1.31153 q^{46} -4.84646 q^{47} +1.00000 q^{48} -6.04001 q^{49} +12.8348 q^{50} -2.27139 q^{51} +1.00000 q^{52} -12.6032 q^{53} +1.00000 q^{54} +7.27914 q^{55} -0.979791 q^{56} -1.97979 q^{57} +9.39422 q^{58} +1.57384 q^{59} +4.22313 q^{60} -8.99104 q^{61} +1.97979 q^{62} -0.979791 q^{63} +1.00000 q^{64} +4.22313 q^{65} +1.72364 q^{66} -13.7166 q^{67} -2.27139 q^{68} +1.31153 q^{69} -4.13778 q^{70} -10.0286 q^{71} +1.00000 q^{72} +5.91922 q^{73} +11.5499 q^{74} +12.8348 q^{75} -1.97979 q^{76} -1.68880 q^{77} +1.00000 q^{78} -8.55846 q^{79} +4.22313 q^{80} +1.00000 q^{81} +4.25364 q^{82} +7.40636 q^{83} -0.979791 q^{84} -9.59239 q^{85} -11.5427 q^{86} +9.39422 q^{87} +1.72364 q^{88} +10.5963 q^{89} +4.22313 q^{90} -0.979791 q^{91} +1.31153 q^{92} +1.97979 q^{93} -4.84646 q^{94} -8.36091 q^{95} +1.00000 q^{96} +13.8253 q^{97} -6.04001 q^{98} +1.72364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * 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
$5$	4.22313	1.88864	0.944320	−	0.329027i	$-0.106721\pi$
$5$	4.22313	1.88864	0.944320	+	0.329027i	$0.106721\pi$
$6$	1.00000	0.408248
$7$	−0.979791	−0.370326	−0.185163	−	0.982708i	$-0.559281\pi$
$7$	−0.979791	−0.370326	−0.185163	+	0.982708i	$0.559281\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.22313	1.33547
$11$	1.72364	0.519696	0.259848	−	0.965650i	$-0.416328\pi$
$11$	1.72364	0.519696	0.259848	+	0.965650i	$0.416328\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.979791	−0.261860
$15$	4.22313	1.09041
$16$	1.00000	0.250000
$17$	−2.27139	−0.550894	−0.275447	−	0.961316i	$-0.588826\pi$
$17$	−2.27139	−0.550894	−0.275447	+	0.961316i	$0.588826\pi$
$18$	1.00000	0.235702
$19$	−1.97979	−0.454195	−0.227098	−	0.973872i	$-0.572924\pi$
$19$	−1.97979	−0.454195	−0.227098	+	0.973872i	$0.572924\pi$
$20$	4.22313	0.944320
$21$	−0.979791	−0.213808
$22$	1.72364	0.367480
$23$	1.31153	0.273473	0.136737	−	0.990607i	$-0.456339\pi$
$23$	1.31153	0.273473	0.136737	+	0.990607i	$0.456339\pi$
$24$	1.00000	0.204124
$25$	12.8348	2.56696
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−0.979791	−0.185163
$29$	9.39422	1.74446	0.872231	−	0.489094i	$-0.162672\pi$
$29$	9.39422	1.74446	0.872231	+	0.489094i	$0.162672\pi$
$30$	4.22313	0.771034
$31$	1.97979	0.355581	0.177790	−	0.984068i	$-0.443105\pi$
$31$	1.97979	0.355581	0.177790	+	0.984068i	$0.443105\pi$
$32$	1.00000	0.176777
$33$	1.72364	0.300047
$34$	−2.27139	−0.389541
$35$	−4.13778	−0.699413
$36$	1.00000	0.166667
$37$	11.5499	1.89879	0.949395	−	0.314085i	$-0.101698\pi$
$37$	11.5499	1.89879	0.949395	+	0.314085i	$0.101698\pi$
$38$	−1.97979	−0.321164
$39$	1.00000	0.160128
$40$	4.22313	0.667735
$41$	4.25364	0.664307	0.332154	−	0.943225i	$-0.392225\pi$
$41$	4.25364	0.664307	0.332154	+	0.943225i	$0.392225\pi$
$42$	−0.979791	−0.151185
$43$	−11.5427	−1.76024	−0.880121	−	0.474750i	$-0.842538\pi$
$43$	−11.5427	−1.76024	−0.880121	+	0.474750i	$0.842538\pi$
$44$	1.72364	0.259848
$45$	4.22313	0.629547
$46$	1.31153	0.193375
$47$	−4.84646	−0.706929	−0.353464	−	0.935448i	$-0.614996\pi$
$47$	−4.84646	−0.706929	−0.353464	+	0.935448i	$0.614996\pi$
$48$	1.00000	0.144338
$49$	−6.04001	−0.862859
$50$	12.8348	1.81512
$51$	−2.27139	−0.318059
$52$	1.00000	0.138675
$53$	−12.6032	−1.73118	−0.865589	−	0.500756i	$-0.833056\pi$
$53$	−12.6032	−1.73118	−0.865589	+	0.500756i	$0.833056\pi$
$54$	1.00000	0.136083
$55$	7.27914	0.981519
$56$	−0.979791	−0.130930
$57$	−1.97979	−0.262230
$58$	9.39422	1.23352
$59$	1.57384	0.204897	0.102448	−	0.994738i	$-0.467332\pi$
$59$	1.57384	0.204897	0.102448	+	0.994738i	$0.467332\pi$
$60$	4.22313	0.545204
$61$	−8.99104	−1.15118	−0.575592	−	0.817737i	$-0.695228\pi$
$61$	−8.99104	−1.15118	−0.575592	+	0.817737i	$0.695228\pi$
$62$	1.97979	0.251434
$63$	−0.979791	−0.123442
$64$	1.00000	0.125000
$65$	4.22313	0.523815
$66$	1.72364	0.212165
$67$	−13.7166	−1.67575	−0.837875	−	0.545862i	$-0.816202\pi$
$67$	−13.7166	−1.67575	−0.837875	+	0.545862i	$0.816202\pi$
$68$	−2.27139	−0.275447
$69$	1.31153	0.157890
$70$	−4.13778	−0.494560
$71$	−10.0286	−1.19017	−0.595087	−	0.803662i	$-0.702882\pi$
$71$	−10.0286	−1.19017	−0.595087	+	0.803662i	$0.702882\pi$
$72$	1.00000	0.117851
$73$	5.91922	0.692793	0.346396	−	0.938088i	$-0.387405\pi$
$73$	5.91922	0.692793	0.346396	+	0.938088i	$0.387405\pi$
$74$	11.5499	1.34265
$75$	12.8348	1.48204
$76$	−1.97979	−0.227098
$77$	−1.68880	−0.192457
$78$	1.00000	0.113228
$79$	−8.55846	−0.962901	−0.481451	−	0.876473i	$-0.659890\pi$
$79$	−8.55846	−0.962901	−0.481451	+	0.876473i	$0.659890\pi$
$80$	4.22313	0.472160
$81$	1.00000	0.111111
$82$	4.25364	0.469736
$83$	7.40636	0.812954	0.406477	−	0.913661i	$-0.366757\pi$
$83$	7.40636	0.812954	0.406477	+	0.913661i	$0.366757\pi$
$84$	−0.979791	−0.106904
$85$	−9.59239	−1.04044
$86$	−11.5427	−1.24468
$87$	9.39422	1.00717
$88$	1.72364	0.183740
$89$	10.5963	1.12321	0.561605	−	0.827405i	$-0.310184\pi$
$89$	10.5963	1.12321	0.561605	+	0.827405i	$0.310184\pi$
$90$	4.22313	0.445157
$91$	−0.979791	−0.102710
$92$	1.31153	0.136737
$93$	1.97979	0.205295
$94$	−4.84646	−0.499874
$95$	−8.36091	−0.857811
$96$	1.00000	0.102062
$97$	13.8253	1.40375	0.701875	−	0.712300i	$-0.252347\pi$
$97$	13.8253	1.40375	0.701875	+	0.712300i	$0.252347\pi$
$98$	−6.04001	−0.610133
$99$	1.72364	0.173232
$100$	12.8348	1.28348
$101$	16.8970	1.68131	0.840657	−	0.541568i	$-0.182169\pi$
$101$	16.8970	1.68131	0.840657	+	0.541568i	$0.182169\pi$
$102$	−2.27139	−0.224901
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−4.13778	−0.403806
$106$	−12.6032	−1.22413
$107$	−17.0183	−1.64522	−0.822612	−	0.568604i	$-0.807484\pi$
$107$	−17.0183	−1.64522	−0.822612	+	0.568604i	$0.807484\pi$
$108$	1.00000	0.0962250
$109$	13.5496	1.29782	0.648911	−	0.760865i	$-0.275225\pi$
$109$	13.5496	1.29782	0.648911	+	0.760865i	$0.275225\pi$
$110$	7.27914	0.694039
$111$	11.5499	1.09627
$112$	−0.979791	−0.0925815
$113$	−10.0415	−0.944626	−0.472313	−	0.881431i	$-0.656581\pi$
$113$	−10.0415	−0.944626	−0.472313	+	0.881431i	$0.656581\pi$
$114$	−1.97979	−0.185424
$115$	5.53876	0.516492
$116$	9.39422	0.872231
$117$	1.00000	0.0924500
$118$	1.57384	0.144884
$119$	2.22549	0.204010
$120$	4.22313	0.385517
$121$	−8.02908	−0.729916
$122$	−8.99104	−0.814010
$123$	4.25364	0.383538
$124$	1.97979	0.177790
$125$	33.0875	2.95943
$126$	−0.979791	−0.0872867
$127$	14.4615	1.28325	0.641625	−	0.767019i	$-0.278261\pi$
$127$	14.4615	1.28325	0.641625	+	0.767019i	$0.278261\pi$
$128$	1.00000	0.0883883
$129$	−11.5427	−1.01628
$130$	4.22313	0.370393
$131$	12.7661	1.11538	0.557688	−	0.830050i	$-0.311688\pi$
$131$	12.7661	1.11538	0.557688	+	0.830050i	$0.311688\pi$
$132$	1.72364	0.150023
$133$	1.93978	0.168200
$134$	−13.7166	−1.18493
$135$	4.22313	0.363469
$136$	−2.27139	−0.194770
$137$	−10.6843	−0.912823	−0.456411	−	0.889769i	$-0.650865\pi$
$137$	−10.6843	−0.912823	−0.456411	+	0.889769i	$0.650865\pi$
$138$	1.31153	0.111645
$139$	6.74315	0.571947	0.285973	−	0.958238i	$-0.407683\pi$
$139$	6.74315	0.571947	0.285973	+	0.958238i	$0.407683\pi$
$140$	−4.13778	−0.349706
$141$	−4.84646	−0.408146
$142$	−10.0286	−0.841579
$143$	1.72364	0.144138
$144$	1.00000	0.0833333
$145$	39.6730	3.29466
$146$	5.91922	0.489878
$147$	−6.04001	−0.498172
$148$	11.5499	0.949395
$149$	−14.5286	−1.19023	−0.595113	−	0.803642i	$-0.702893\pi$
$149$	−14.5286	−1.19023	−0.595113	+	0.803642i	$0.702893\pi$
$150$	12.8348	1.04796
$151$	3.01358	0.245242	0.122621	−	0.992454i	$-0.460870\pi$
$151$	3.01358	0.245242	0.122621	+	0.992454i	$0.460870\pi$
$152$	−1.97979	−0.160582
$153$	−2.27139	−0.183631
$154$	−1.68880	−0.136088
$155$	8.36091	0.671565
$156$	1.00000	0.0800641
$157$	−4.72873	−0.377394	−0.188697	−	0.982035i	$-0.560426\pi$
$157$	−4.72873	−0.377394	−0.188697	+	0.982035i	$0.560426\pi$
$158$	−8.55846	−0.680874
$159$	−12.6032	−0.999496
$160$	4.22313	0.333868
$161$	−1.28503	−0.101274
$162$	1.00000	0.0785674
$163$	14.3082	1.12071	0.560353	−	0.828254i	$-0.310665\pi$
$163$	14.3082	1.12071	0.560353	+	0.828254i	$0.310665\pi$
$164$	4.25364	0.332154
$165$	7.27914	0.566680
$166$	7.40636	0.574845
$167$	−8.68367	−0.671962	−0.335981	−	0.941869i	$-0.609068\pi$
$167$	−8.68367	−0.671962	−0.335981	+	0.941869i	$0.609068\pi$
$168$	−0.979791	−0.0755925
$169$	1.00000	0.0769231
$170$	−9.59239	−0.735702
$171$	−1.97979	−0.151398
$172$	−11.5427	−0.880121
$173$	7.28778	0.554080	0.277040	−	0.960858i	$-0.410647\pi$
$173$	7.28778	0.554080	0.277040	+	0.960858i	$0.410647\pi$
$174$	9.39422	0.712174
$175$	−12.5754	−0.950614
$176$	1.72364	0.129924
$177$	1.57384	0.118297
$178$	10.5963	0.794229
$179$	−9.43916	−0.705516	−0.352758	−	0.935715i	$-0.614756\pi$
$179$	−9.43916	−0.705516	−0.352758	+	0.935715i	$0.614756\pi$
$180$	4.22313	0.314773
$181$	−5.97443	−0.444076	−0.222038	−	0.975038i	$-0.571271\pi$
$181$	−5.97443	−0.444076	−0.222038	+	0.975038i	$0.571271\pi$
$182$	−0.979791	−0.0726269
$183$	−8.99104	−0.664637
$184$	1.31153	0.0966873
$185$	48.7767	3.58613
$186$	1.97979	0.145165
$187$	−3.91505	−0.286297
$188$	−4.84646	−0.353464
$189$	−0.979791	−0.0712693
$190$	−8.36091	−0.606564
$191$	0.232586	0.0168293	0.00841465	−	0.999965i	$-0.497322\pi$
$191$	0.232586	0.0168293	0.00841465	+	0.999965i	$0.497322\pi$
$192$	1.00000	0.0721688
$193$	−5.42993	−0.390855	−0.195427	−	0.980718i	$-0.562609\pi$
$193$	−5.42993	−0.390855	−0.195427	+	0.980718i	$0.562609\pi$
$194$	13.8253	0.992601
$195$	4.22313	0.302425
$196$	−6.04001	−0.431429
$197$	−8.24532	−0.587454	−0.293727	−	0.955889i	$-0.594896\pi$
$197$	−8.24532	−0.587454	−0.293727	+	0.955889i	$0.594896\pi$
$198$	1.72364	0.122493
$199$	−6.67633	−0.473273	−0.236636	−	0.971598i	$-0.576045\pi$
$199$	−6.67633	−0.473273	−0.236636	+	0.971598i	$0.576045\pi$
$200$	12.8348	0.907559
$201$	−13.7166	−0.967495
$202$	16.8970	1.18887
$203$	−9.20437	−0.646020
$204$	−2.27139	−0.159029
$205$	17.9637	1.25464
$206$	−1.00000	−0.0696733
$207$	1.31153	0.0911577
$208$	1.00000	0.0693375
$209$	−3.41244	−0.236043
$210$	−4.13778	−0.285534
$211$	17.8872	1.23140	0.615702	−	0.787979i	$-0.288873\pi$
$211$	17.8872	1.23140	0.615702	+	0.787979i	$0.288873\pi$
$212$	−12.6032	−0.865589
$213$	−10.0286	−0.687147
$214$	−17.0183	−1.16335
$215$	−48.7462	−3.32446
$216$	1.00000	0.0680414
$217$	−1.93978	−0.131681
$218$	13.5496	0.917698
$219$	5.91922	0.399984
$220$	7.27914	0.490759
$221$	−2.27139	−0.152790
$222$	11.5499	0.775178
$223$	9.10790	0.609910	0.304955	−	0.952367i	$-0.401359\pi$
$223$	9.10790	0.609910	0.304955	+	0.952367i	$0.401359\pi$
$224$	−0.979791	−0.0654650
$225$	12.8348	0.855655
$226$	−10.0415	−0.667951
$227$	−1.51161	−0.100329	−0.0501644	−	0.998741i	$-0.515975\pi$
$227$	−1.51161	−0.100329	−0.0501644	+	0.998741i	$0.515975\pi$
$228$	−1.97979	−0.131115
$229$	21.5512	1.42414	0.712072	−	0.702107i	$-0.247757\pi$
$229$	21.5512	1.42414	0.712072	+	0.702107i	$0.247757\pi$
$230$	5.53876	0.365215
$231$	−1.68880	−0.111115
$232$	9.39422	0.616761
$233$	6.03691	0.395491	0.197746	−	0.980253i	$-0.436638\pi$
$233$	6.03691	0.395491	0.197746	+	0.980253i	$0.436638\pi$
$234$	1.00000	0.0653720
$235$	−20.4672	−1.33513
$236$	1.57384	0.102448
$237$	−8.55846	−0.555931
$238$	2.22549	0.144257
$239$	−23.1947	−1.50034	−0.750172	−	0.661243i	$-0.770029\pi$
$239$	−23.1947	−1.50034	−0.750172	+	0.661243i	$0.770029\pi$
$240$	4.22313	0.272602
$241$	−11.1732	−0.719732	−0.359866	−	0.933004i	$-0.617178\pi$
$241$	−11.1732	−0.719732	−0.359866	+	0.933004i	$0.617178\pi$
$242$	−8.02908	−0.516129
$243$	1.00000	0.0641500
$244$	−8.99104	−0.575592
$245$	−25.5077	−1.62963
$246$	4.25364	0.271202
$247$	−1.97979	−0.125971
$248$	1.97979	0.125717
$249$	7.40636	0.469359
$250$	33.0875	2.09263
$251$	−20.7756	−1.31135	−0.655673	−	0.755045i	$-0.727615\pi$
$251$	−20.7756	−1.31135	−0.655673	+	0.755045i	$0.727615\pi$
$252$	−0.979791	−0.0617210
$253$	2.26060	0.142123
$254$	14.4615	0.907394
$255$	−9.59239	−0.600698
$256$	1.00000	0.0625000
$257$	−12.4711	−0.777924	−0.388962	−	0.921254i	$-0.627166\pi$
$257$	−12.4711	−0.777924	−0.388962	+	0.921254i	$0.627166\pi$
$258$	−11.5427	−0.718616
$259$	−11.3165	−0.703171
$260$	4.22313	0.261907
$261$	9.39422	0.581487
$262$	12.7661	0.788691
$263$	−4.09568	−0.252550	−0.126275	−	0.991995i	$-0.540302\pi$
$263$	−4.09568	−0.252550	−0.126275	+	0.991995i	$0.540302\pi$
$264$	1.72364	0.106082
$265$	−53.2248	−3.26957
$266$	1.93978	0.118936
$267$	10.5963	0.648486
$268$	−13.7166	−0.837875
$269$	18.4427	1.12447	0.562237	−	0.826976i	$-0.309941\pi$
$269$	18.4427	1.12447	0.562237	+	0.826976i	$0.309941\pi$
$270$	4.22313	0.257011
$271$	19.6440	1.19329	0.596644	−	0.802506i	$-0.296501\pi$
$271$	19.6440	1.19329	0.596644	+	0.802506i	$0.296501\pi$
$272$	−2.27139	−0.137723
$273$	−0.979791	−0.0592996
$274$	−10.6843	−0.645463
$275$	22.1226	1.33404
$276$	1.31153	0.0789449
$277$	−19.8954	−1.19540	−0.597699	−	0.801720i	$-0.703918\pi$
$277$	−19.8954	−1.19540	−0.597699	+	0.801720i	$0.703918\pi$
$278$	6.74315	0.404427
$279$	1.97979	0.118527
$280$	−4.13778	−0.247280
$281$	−14.5316	−0.866882	−0.433441	−	0.901182i	$-0.642701\pi$
$281$	−14.5316	−0.866882	−0.433441	+	0.901182i	$0.642701\pi$
$282$	−4.84646	−0.288603
$283$	9.29044	0.552260	0.276130	−	0.961120i	$-0.410948\pi$
$283$	9.29044	0.552260	0.276130	+	0.961120i	$0.410948\pi$
$284$	−10.0286	−0.595087
$285$	−8.36091	−0.495258
$286$	1.72364	0.101921
$287$	−4.16768	−0.246010
$288$	1.00000	0.0589256
$289$	−11.8408	−0.696516
$290$	39.6730	2.32968
$291$	13.8253	0.810455
$292$	5.91922	0.346396
$293$	3.08643	0.180311	0.0901555	−	0.995928i	$-0.471264\pi$
$293$	3.08643	0.180311	0.0901555	+	0.995928i	$0.471264\pi$
$294$	−6.04001	−0.352261
$295$	6.64654	0.386976
$296$	11.5499	0.671324
$297$	1.72364	0.100016
$298$	−14.5286	−0.841617
$299$	1.31153	0.0758478
$300$	12.8348	0.741019
$301$	11.3094	0.651863
$302$	3.01358	0.173412
$303$	16.8970	0.970707
$304$	−1.97979	−0.113549
$305$	−37.9703	−2.17417
$306$	−2.27139	−0.129847
$307$	−15.1713	−0.865874	−0.432937	−	0.901424i	$-0.642523\pi$
$307$	−15.1713	−0.865874	−0.432937	+	0.901424i	$0.642523\pi$
$308$	−1.68880	−0.0962285
$309$	−1.00000	−0.0568880
$310$	8.36091	0.474868
$311$	29.8676	1.69364	0.846819	−	0.531881i	$-0.178515\pi$
$311$	29.8676	1.69364	0.846819	+	0.531881i	$0.178515\pi$
$312$	1.00000	0.0566139
$313$	−28.2380	−1.59611	−0.798053	−	0.602588i	$-0.794136\pi$
$313$	−28.2380	−1.59611	−0.798053	+	0.602588i	$0.794136\pi$
$314$	−4.72873	−0.266858
$315$	−4.13778	−0.233138
$316$	−8.55846	−0.481451
$317$	−17.2809	−0.970593	−0.485297	−	0.874350i	$-0.661288\pi$
$317$	−17.2809	−0.970593	−0.485297	+	0.874350i	$0.661288\pi$
$318$	−12.6032	−0.706750
$319$	16.1922	0.906590
$320$	4.22313	0.236080
$321$	−17.0183	−0.949870
$322$	−1.28503	−0.0716117
$323$	4.49688	0.250213
$324$	1.00000	0.0555556
$325$	12.8348	0.711948
$326$	14.3082	0.792459
$327$	13.5496	0.749297
$328$	4.25364	0.234868
$329$	4.74852	0.261794
$330$	7.27914	0.400703
$331$	17.3972	0.956239	0.478119	−	0.878295i	$-0.341319\pi$
$331$	17.3972	0.956239	0.478119	+	0.878295i	$0.341319\pi$
$332$	7.40636	0.406477
$333$	11.5499	0.632930
$334$	−8.68367	−0.475149
$335$	−57.9270	−3.16489
$336$	−0.979791	−0.0534520
$337$	4.41462	0.240479	0.120240	−	0.992745i	$-0.461634\pi$
$337$	4.41462	0.240479	0.120240	+	0.992745i	$0.461634\pi$
$338$	1.00000	0.0543928
$339$	−10.0415	−0.545380
$340$	−9.59239	−0.520220
$341$	3.41244	0.184794
$342$	−1.97979	−0.107055
$343$	12.7765	0.689865
$344$	−11.5427	−0.622339
$345$	5.53876	0.298197
$346$	7.28778	0.391794
$347$	−0.980828	−0.0526536	−0.0263268	−	0.999653i	$-0.508381\pi$
$347$	−0.980828	−0.0526536	−0.0263268	+	0.999653i	$0.508381\pi$
$348$	9.39422	0.503583
$349$	−12.8334	−0.686955	−0.343478	−	0.939161i	$-0.611605\pi$
$349$	−12.8334	−0.686955	−0.343478	+	0.939161i	$0.611605\pi$
$350$	−12.5754	−0.672185
$351$	1.00000	0.0533761
$352$	1.72364	0.0918701
$353$	−16.3378	−0.869576	−0.434788	−	0.900533i	$-0.643177\pi$
$353$	−16.3378	−0.869576	−0.434788	+	0.900533i	$0.643177\pi$
$354$	1.57384	0.0836488
$355$	−42.3520	−2.24781
$356$	10.5963	0.561605
$357$	2.22549	0.117785
$358$	−9.43916	−0.498875
$359$	32.5665	1.71879	0.859397	−	0.511309i	$-0.170839\pi$
$359$	32.5665	1.71879	0.859397	+	0.511309i	$0.170839\pi$
$360$	4.22313	0.222578
$361$	−15.0804	−0.793707
$362$	−5.97443	−0.314009
$363$	−8.02908	−0.421417
$364$	−0.979791	−0.0513550
$365$	24.9976	1.30844
$366$	−8.99104	−0.469969
$367$	15.7318	0.821193	0.410596	−	0.911817i	$-0.365321\pi$
$367$	15.7318	0.821193	0.410596	+	0.911817i	$0.365321\pi$
$368$	1.31153	0.0683683
$369$	4.25364	0.221436
$370$	48.7767	2.53578
$371$	12.3485	0.641100
$372$	1.97979	0.102647
$373$	22.9941	1.19059	0.595294	−	0.803508i	$-0.297035\pi$
$373$	22.9941	1.19059	0.595294	+	0.803508i	$0.297035\pi$
$374$	−3.91505	−0.202443
$375$	33.0875	1.70863
$376$	−4.84646	−0.249937
$377$	9.39422	0.483827
$378$	−0.979791	−0.0503950
$379$	−19.5531	−1.00437	−0.502187	−	0.864759i	$-0.667471\pi$
$379$	−19.5531	−1.00437	−0.502187	+	0.864759i	$0.667471\pi$
$380$	−8.36091	−0.428906
$381$	14.4615	0.740884
$382$	0.232586	0.0119001
$383$	−31.1535	−1.59187	−0.795934	−	0.605384i	$-0.793020\pi$
$383$	−31.1535	−1.59187	−0.795934	+	0.605384i	$0.793020\pi$
$384$	1.00000	0.0510310
$385$	−7.13203	−0.363482
$386$	−5.42993	−0.276376
$387$	−11.5427	−0.586747
$388$	13.8253	0.701875
$389$	0.744166	0.0377307	0.0188653	−	0.999822i	$-0.493995\pi$
$389$	0.744166	0.0377307	0.0188653	+	0.999822i	$0.493995\pi$
$390$	4.22313	0.213846
$391$	−2.97900	−0.150655
$392$	−6.04001	−0.305067
$393$	12.7661	0.643963
$394$	−8.24532	−0.415393
$395$	−36.1435	−1.81857
$396$	1.72364	0.0866160
$397$	23.7357	1.19126	0.595631	−	0.803258i	$-0.296902\pi$
$397$	23.7357	1.19126	0.595631	+	0.803258i	$0.296902\pi$
$398$	−6.67633	−0.334654
$399$	1.93978	0.0971105
$400$	12.8348	0.641741
$401$	−25.3216	−1.26450	−0.632251	−	0.774763i	$-0.717869\pi$
$401$	−25.3216	−1.26450	−0.632251	+	0.774763i	$0.717869\pi$
$402$	−13.7166	−0.684122
$403$	1.97979	0.0986204
$404$	16.8970	0.840657
$405$	4.22313	0.209849
$406$	−9.20437	−0.456805
$407$	19.9078	0.986793
$408$	−2.27139	−0.112451
$409$	38.7264	1.91490	0.957450	−	0.288600i	$-0.0931898\pi$
$409$	38.7264	1.91490	0.957450	+	0.288600i	$0.0931898\pi$
$410$	17.9637	0.887163
$411$	−10.6843	−0.527018
$412$	−1.00000	−0.0492665
$413$	−1.54204	−0.0758786
$414$	1.31153	0.0644582
$415$	31.2780	1.53538
$416$	1.00000	0.0490290
$417$	6.74315	0.330214
$418$	−3.41244	−0.166908
$419$	−9.73133	−0.475407	−0.237703	−	0.971338i	$-0.576395\pi$
$419$	−9.73133	−0.475407	−0.237703	+	0.971338i	$0.576395\pi$
$420$	−4.13778	−0.201903
$421$	−16.5366	−0.805945	−0.402972	−	0.915212i	$-0.632023\pi$
$421$	−16.5366	−0.805945	−0.402972	+	0.915212i	$0.632023\pi$
$422$	17.8872	0.870734
$423$	−4.84646	−0.235643
$424$	−12.6032	−0.612064
$425$	−29.1529	−1.41412
$426$	−10.0286	−0.485886
$427$	8.80934	0.426314
$428$	−17.0183	−0.822612
$429$	1.72364	0.0832179
$430$	−48.7462	−2.35075
$431$	37.1907	1.79141	0.895705	−	0.444648i	$-0.146671\pi$
$431$	37.1907	1.79141	0.895705	+	0.444648i	$0.146671\pi$
$432$	1.00000	0.0481125
$433$	−12.5636	−0.603766	−0.301883	−	0.953345i	$-0.597615\pi$
$433$	−12.5636	−0.603766	−0.301883	+	0.953345i	$0.597615\pi$
$434$	−1.93978	−0.0931124
$435$	39.6730	1.90217
$436$	13.5496	0.648911
$437$	−2.59656	−0.124210
$438$	5.91922	0.282831
$439$	−10.7977	−0.515346	−0.257673	−	0.966232i	$-0.582956\pi$
$439$	−10.7977	−0.515346	−0.257673	+	0.966232i	$0.582956\pi$
$440$	7.27914	0.347019
$441$	−6.04001	−0.287620
$442$	−2.27139	−0.108039
$443$	−1.44328	−0.0685724	−0.0342862	−	0.999412i	$-0.510916\pi$
$443$	−1.44328	−0.0685724	−0.0342862	+	0.999412i	$0.510916\pi$
$444$	11.5499	0.548133
$445$	44.7497	2.12134
$446$	9.10790	0.431272
$447$	−14.5286	−0.687178
$448$	−0.979791	−0.0462908
$449$	11.1342	0.525457	0.262728	−	0.964870i	$-0.415378\pi$
$449$	11.1342	0.525457	0.262728	+	0.964870i	$0.415378\pi$
$450$	12.8348	0.605039
$451$	7.33173	0.345238
$452$	−10.0415	−0.472313
$453$	3.01358	0.141591
$454$	−1.51161	−0.0709431
$455$	−4.13778	−0.193982
$456$	−1.97979	−0.0927122
$457$	−2.91013	−0.136130	−0.0680650	−	0.997681i	$-0.521683\pi$
$457$	−2.91013	−0.136130	−0.0680650	+	0.997681i	$0.521683\pi$
$458$	21.5512	1.00702
$459$	−2.27139	−0.106020
$460$	5.53876	0.258246
$461$	7.90418	0.368135	0.184067	−	0.982914i	$-0.441074\pi$
$461$	7.90418	0.368135	0.184067	+	0.982914i	$0.441074\pi$
$462$	−1.68880	−0.0785702
$463$	14.7612	0.686011	0.343005	−	0.939333i	$-0.388555\pi$
$463$	14.7612	0.686011	0.343005	+	0.939333i	$0.388555\pi$
$464$	9.39422	0.436116
$465$	8.36091	0.387728
$466$	6.03691	0.279655
$467$	−17.7336	−0.820613	−0.410306	−	0.911948i	$-0.634578\pi$
$467$	−17.7336	−0.820613	−0.410306	+	0.911948i	$0.634578\pi$
$468$	1.00000	0.0462250
$469$	13.4394	0.620574
$470$	−20.4672	−0.944083
$471$	−4.72873	−0.217888
$472$	1.57384	0.0724420
$473$	−19.8954	−0.914790
$474$	−8.55846	−0.393103
$475$	−25.4103	−1.16590
$476$	2.22549	0.102005
$477$	−12.6032	−0.577059
$478$	−23.1947	−1.06090
$479$	−7.54827	−0.344889	−0.172445	−	0.985019i	$-0.555167\pi$
$479$	−7.54827	−0.344889	−0.172445	+	0.985019i	$0.555167\pi$
$480$	4.22313	0.192759
$481$	11.5499	0.526630
$482$	−11.1732	−0.508928
$483$	−1.28503	−0.0584707
$484$	−8.02908	−0.364958
$485$	58.3861	2.65118
$486$	1.00000	0.0453609
$487$	8.33445	0.377670	0.188835	−	0.982009i	$-0.439529\pi$
$487$	8.33445	0.377670	0.188835	+	0.982009i	$0.439529\pi$
$488$	−8.99104	−0.407005
$489$	14.3082	0.647040
$490$	−25.5077	−1.15232
$491$	14.6852	0.662734	0.331367	−	0.943502i	$-0.392490\pi$
$491$	14.6852	0.662734	0.331367	+	0.943502i	$0.392490\pi$
$492$	4.25364	0.191769
$493$	−21.3380	−0.961013
$494$	−1.97979	−0.0890750
$495$	7.27914	0.327173
$496$	1.97979	0.0888952
$497$	9.82591	0.440752
$498$	7.40636	0.331887
$499$	−2.72075	−0.121798	−0.0608988	−	0.998144i	$-0.519397\pi$
$499$	−2.72075	−0.121798	−0.0608988	+	0.998144i	$0.519397\pi$
$500$	33.0875	1.47972
$501$	−8.68367	−0.387958
$502$	−20.7756	−0.927261
$503$	22.2206	0.990766	0.495383	−	0.868675i	$-0.335028\pi$
$503$	22.2206	0.990766	0.495383	+	0.868675i	$0.335028\pi$
$504$	−0.979791	−0.0436433
$505$	71.3582	3.17540
$506$	2.26060	0.100496
$507$	1.00000	0.0444116
$508$	14.4615	0.641625
$509$	8.77332	0.388871	0.194435	−	0.980915i	$-0.437713\pi$
$509$	8.77332	0.388871	0.194435	+	0.980915i	$0.437713\pi$
$510$	−9.59239	−0.424758
$511$	−5.79960	−0.256559
$512$	1.00000	0.0441942
$513$	−1.97979	−0.0874099
$514$	−12.4711	−0.550075
$515$	−4.22313	−0.186093
$516$	−11.5427	−0.508138
$517$	−8.35354	−0.367388
$518$	−11.3165	−0.497217
$519$	7.28778	0.319898
$520$	4.22313	0.185196
$521$	−19.8580	−0.869997	−0.434998	−	0.900431i	$-0.643251\pi$
$521$	−19.8580	−0.869997	−0.434998	+	0.900431i	$0.643251\pi$
$522$	9.39422	0.411174
$523$	−5.76413	−0.252048	−0.126024	−	0.992027i	$-0.540222\pi$
$523$	−5.76413	−0.252048	−0.126024	+	0.992027i	$0.540222\pi$
$524$	12.7661	0.557688
$525$	−12.5754	−0.548837
$526$	−4.09568	−0.178580
$527$	−4.49688	−0.195887
$528$	1.72364	0.0750116
$529$	−21.2799	−0.925212
$530$	−53.2248	−2.31194
$531$	1.57384	0.0682989
$532$	1.93978	0.0841002
$533$	4.25364	0.184246
$534$	10.5963	0.458549
$535$	−71.8706	−3.10724
$536$	−13.7166	−0.592467
$537$	−9.43916	−0.407330
$538$	18.4427	0.795123
$539$	−10.4108	−0.448424
$540$	4.22313	0.181735
$541$	−39.9753	−1.71867	−0.859337	−	0.511410i	$-0.829123\pi$
$541$	−39.9753	−1.71867	−0.859337	+	0.511410i	$0.829123\pi$
$542$	19.6440	0.843782
$543$	−5.97443	−0.256387
$544$	−2.27139	−0.0973852
$545$	57.2219	2.45112
$546$	−0.979791	−0.0419312
$547$	24.9131	1.06521	0.532603	−	0.846365i	$-0.321214\pi$
$547$	24.9131	1.06521	0.532603	+	0.846365i	$0.321214\pi$
$548$	−10.6843	−0.456411
$549$	−8.99104	−0.383728
$550$	22.1226	0.943309
$551$	−18.5986	−0.792326
$552$	1.31153	0.0558225
$553$	8.38550	0.356588
$554$	−19.8954	−0.845275
$555$	48.7767	2.07045
$556$	6.74315	0.285973
$557$	36.1515	1.53179	0.765894	−	0.642967i	$-0.222297\pi$
$557$	36.1515	1.53179	0.765894	+	0.642967i	$0.222297\pi$
$558$	1.97979	0.0838112
$559$	−11.5427	−0.488203
$560$	−4.13778	−0.174853
$561$	−3.91505	−0.165294
$562$	−14.5316	−0.612978
$563$	−34.9378	−1.47245	−0.736226	−	0.676736i	$-0.763394\pi$
$563$	−34.9378	−1.47245	−0.736226	+	0.676736i	$0.763394\pi$
$564$	−4.84646	−0.204073
$565$	−42.4066	−1.78406
$566$	9.29044	0.390506
$567$	−0.979791	−0.0411473
$568$	−10.0286	−0.420790
$569$	−24.7172	−1.03620	−0.518100	−	0.855320i	$-0.673361\pi$
$569$	−24.7172	−1.03620	−0.518100	+	0.855320i	$0.673361\pi$
$570$	−8.36091	−0.350200
$571$	−10.5324	−0.440766	−0.220383	−	0.975413i	$-0.570731\pi$
$571$	−10.5324	−0.440766	−0.220383	+	0.975413i	$0.570731\pi$
$572$	1.72364	0.0720688
$573$	0.232586	0.00971640
$574$	−4.16768	−0.173956
$575$	16.8333	0.701996
$576$	1.00000	0.0416667
$577$	−27.9575	−1.16389	−0.581943	−	0.813230i	$-0.697707\pi$
$577$	−27.9575	−1.16389	−0.581943	+	0.813230i	$0.697707\pi$
$578$	−11.8408	−0.492511
$579$	−5.42993	−0.225660
$580$	39.6730	1.64733
$581$	−7.25668	−0.301058
$582$	13.8253	0.573078
$583$	−21.7233	−0.899686
$584$	5.91922	0.244939
$585$	4.22313	0.174605
$586$	3.08643	0.127499
$587$	10.2746	0.424080	0.212040	−	0.977261i	$-0.431989\pi$
$587$	10.2746	0.424080	0.212040	+	0.977261i	$0.431989\pi$
$588$	−6.04001	−0.249086
$589$	−3.91957	−0.161503
$590$	6.64654	0.273634
$591$	−8.24532	−0.339167
$592$	11.5499	0.474697
$593$	12.9012	0.529787	0.264893	−	0.964278i	$-0.414663\pi$
$593$	12.9012	0.529787	0.264893	+	0.964278i	$0.414663\pi$
$594$	1.72364	0.0707216
$595$	9.39853	0.385302
$596$	−14.5286	−0.595113
$597$	−6.67633	−0.273244
$598$	1.31153	0.0536325
$599$	11.1161	0.454193	0.227096	−	0.973872i	$-0.427077\pi$
$599$	11.1161	0.454193	0.227096	+	0.973872i	$0.427077\pi$
$600$	12.8348	0.523979
$601$	22.6981	0.925876	0.462938	−	0.886391i	$-0.346795\pi$
$601$	22.6981	0.925876	0.462938	+	0.886391i	$0.346795\pi$
$602$	11.3094	0.460937
$603$	−13.7166	−0.558583
$604$	3.01358	0.122621
$605$	−33.9078	−1.37855
$606$	16.8970	0.686394
$607$	22.7801	0.924615	0.462307	−	0.886720i	$-0.347022\pi$
$607$	22.7801	0.924615	0.462307	+	0.886720i	$0.347022\pi$
$608$	−1.97979	−0.0802911
$609$	−9.20437	−0.372980
$610$	−37.9703	−1.53737
$611$	−4.84646	−0.196067
$612$	−2.27139	−0.0918156
$613$	−42.2873	−1.70797	−0.853985	−	0.520298i	$-0.825821\pi$
$613$	−42.2873	−1.70797	−0.853985	+	0.520298i	$0.825821\pi$
$614$	−15.1713	−0.612265
$615$	17.9637	0.724366
$616$	−1.68880	−0.0680438
$617$	−28.7006	−1.15544	−0.577722	−	0.816234i	$-0.696058\pi$
$617$	−28.7006	−1.15544	−0.577722	+	0.816234i	$0.696058\pi$
$618$	−1.00000	−0.0402259
$619$	28.9360	1.16304	0.581518	−	0.813534i	$-0.302459\pi$
$619$	28.9360	1.16304	0.581518	+	0.813534i	$0.302459\pi$
$620$	8.36091	0.335782
$621$	1.31153	0.0526299
$622$	29.8676	1.19758
$623$	−10.3822	−0.415954
$624$	1.00000	0.0400320
$625$	75.5585	3.02234
$626$	−28.2380	−1.12862
$627$	−3.41244	−0.136280
$628$	−4.72873	−0.188697
$629$	−26.2343	−1.04603
$630$	−4.13778	−0.164853
$631$	−11.6202	−0.462592	−0.231296	−	0.972883i	$-0.574297\pi$
$631$	−11.6202	−0.462592	−0.231296	+	0.972883i	$0.574297\pi$
$632$	−8.55846	−0.340437
$633$	17.8872	0.710951
$634$	−17.2809	−0.686313
$635$	61.0727	2.42360
$636$	−12.6032	−0.499748
$637$	−6.04001	−0.239314
$638$	16.1922	0.641056
$639$	−10.0286	−0.396724
$640$	4.22313	0.166934
$641$	−6.42136	−0.253629	−0.126814	−	0.991926i	$-0.540475\pi$
$641$	−6.42136	−0.253629	−0.126814	+	0.991926i	$0.540475\pi$
$642$	−17.0183	−0.671660
$643$	−31.6857	−1.24956	−0.624781	−	0.780800i	$-0.714812\pi$
$643$	−31.6857	−1.24956	−0.624781	+	0.780800i	$0.714812\pi$
$644$	−1.28503	−0.0506371
$645$	−48.7462	−1.91938
$646$	4.49688	0.176927
$647$	−43.9599	−1.72824	−0.864120	−	0.503285i	$-0.832125\pi$
$647$	−43.9599	−1.72824	−0.864120	+	0.503285i	$0.832125\pi$
$648$	1.00000	0.0392837
$649$	2.71273	0.106484
$650$	12.8348	0.503423
$651$	−1.93978	−0.0760260
$652$	14.3082	0.560353
$653$	−17.0695	−0.667983	−0.333991	−	0.942576i	$-0.608396\pi$
$653$	−17.0695	−0.667983	−0.333991	+	0.942576i	$0.608396\pi$
$654$	13.5496	0.529833
$655$	53.9128	2.10655
$656$	4.25364	0.166077
$657$	5.91922	0.230931
$658$	4.74852	0.185116
$659$	−35.8826	−1.39779	−0.698894	−	0.715225i	$-0.746324\pi$
$659$	−35.8826	−1.39779	−0.698894	+	0.715225i	$0.746324\pi$
$660$	7.27914	0.283340
$661$	−43.7631	−1.70219	−0.851094	−	0.525014i	$-0.824060\pi$
$661$	−43.7631	−1.70219	−0.851094	+	0.525014i	$0.824060\pi$
$662$	17.3972	0.676163
$663$	−2.27139	−0.0882136
$664$	7.40636	0.287422
$665$	8.19194	0.317670
$666$	11.5499	0.447549
$667$	12.3208	0.477064
$668$	−8.68367	−0.335981
$669$	9.10790	0.352132
$670$	−57.9270	−2.23792
$671$	−15.4973	−0.598266
$672$	−0.979791	−0.0377962
$673$	11.0569	0.426214	0.213107	−	0.977029i	$-0.431642\pi$
$673$	11.0569	0.426214	0.213107	+	0.977029i	$0.431642\pi$
$674$	4.41462	0.170045
$675$	12.8348	0.494012
$676$	1.00000	0.0384615
$677$	18.1873	0.698994	0.349497	−	0.936937i	$-0.386352\pi$
$677$	18.1873	0.698994	0.349497	+	0.936937i	$0.386352\pi$
$678$	−10.0415	−0.385642
$679$	−13.5459	−0.519845
$680$	−9.59239	−0.367851
$681$	−1.51161	−0.0579248
$682$	3.41244	0.130669
$683$	36.3342	1.39029	0.695145	−	0.718869i	$-0.255340\pi$
$683$	36.3342	1.39029	0.695145	+	0.718869i	$0.255340\pi$
$684$	−1.97979	−0.0756992
$685$	−45.1212	−1.72399
$686$	12.7765	0.487808
$687$	21.5512	0.822230
$688$	−11.5427	−0.440060
$689$	−12.6032	−0.480142
$690$	5.53876	0.210857
$691$	−8.18253	−0.311278	−0.155639	−	0.987814i	$-0.549744\pi$
$691$	−8.18253	−0.311278	−0.155639	+	0.987814i	$0.549744\pi$
$692$	7.28778	0.277040
$693$	−1.68880	−0.0641523
$694$	−0.980828	−0.0372317
$695$	28.4772	1.08020
$696$	9.39422	0.356087
$697$	−9.66170	−0.365963
$698$	−12.8334	−0.485751
$699$	6.03691	0.228337
$700$	−12.5754	−0.475307
$701$	36.8162	1.39053	0.695264	−	0.718754i	$-0.255287\pi$
$701$	36.8162	1.39053	0.695264	+	0.718754i	$0.255287\pi$
$702$	1.00000	0.0377426
$703$	−22.8664	−0.862421
$704$	1.72364	0.0649620
$705$	−20.4672	−0.770840
$706$	−16.3378	−0.614883
$707$	−16.5555	−0.622634
$708$	1.57384	0.0591486
$709$	34.4829	1.29503	0.647517	−	0.762051i	$-0.275808\pi$
$709$	34.4829	1.29503	0.647517	+	0.762051i	$0.275808\pi$
$710$	−42.3520	−1.58944
$711$	−8.55846	−0.320967
$712$	10.5963	0.397115
$713$	2.59656	0.0972418
$714$	2.22549	0.0832869
$715$	7.27914	0.272224
$716$	−9.43916	−0.352758
$717$	−23.1947	−0.866224
$718$	32.5665	1.21537
$719$	−39.2336	−1.46317	−0.731584	−	0.681752i	$-0.761219\pi$
$719$	−39.2336	−1.46317	−0.731584	+	0.681752i	$0.761219\pi$
$720$	4.22313	0.157387
$721$	0.979791	0.0364893
$722$	−15.0804	−0.561235
$723$	−11.1732	−0.415538
$724$	−5.97443	−0.222038
$725$	120.573	4.47797
$726$	−8.02908	−0.297987
$727$	−27.3712	−1.01514	−0.507570	−	0.861610i	$-0.669456\pi$
$727$	−27.3712	−1.01514	−0.507570	+	0.861610i	$0.669456\pi$
$728$	−0.979791	−0.0363135
$729$	1.00000	0.0370370
$730$	24.9976	0.925204
$731$	26.2180	0.969706
$732$	−8.99104	−0.332318
$733$	−25.3518	−0.936391	−0.468195	−	0.883625i	$-0.655096\pi$
$733$	−25.3518	−0.936391	−0.468195	+	0.883625i	$0.655096\pi$
$734$	15.7318	0.580671
$735$	−25.5077	−0.940867
$736$	1.31153	0.0483437
$737$	−23.6424	−0.870880
$738$	4.25364	0.156579
$739$	46.7592	1.72007	0.860033	−	0.510239i	$-0.170443\pi$
$739$	46.7592	1.72007	0.860033	+	0.510239i	$0.170443\pi$
$740$	48.7767	1.79307
$741$	−1.97979	−0.0727294
$742$	12.3485	0.453326
$743$	−10.6687	−0.391396	−0.195698	−	0.980664i	$-0.562697\pi$
$743$	−10.6687	−0.391396	−0.195698	+	0.980664i	$0.562697\pi$
$744$	1.97979	0.0725826
$745$	−61.3560	−2.24791
$746$	22.9941	0.841873
$747$	7.40636	0.270985
$748$	−3.91505	−0.143149
$749$	16.6744	0.609269
$750$	33.0875	1.20818
$751$	−28.6024	−1.04372	−0.521858	−	0.853032i	$-0.674761\pi$
$751$	−28.6024	−1.04372	−0.521858	+	0.853032i	$0.674761\pi$
$752$	−4.84646	−0.176732
$753$	−20.7756	−0.757106
$754$	9.39422	0.342117
$755$	12.7268	0.463174
$756$	−0.979791	−0.0356346
$757$	8.22922	0.299096	0.149548	−	0.988754i	$-0.452218\pi$
$757$	8.22922	0.299096	0.149548	+	0.988754i	$0.452218\pi$
$758$	−19.5531	−0.710200
$759$	2.26060	0.0820547
$760$	−8.36091	−0.303282
$761$	35.8390	1.29916	0.649581	−	0.760292i	$-0.274944\pi$
$761$	35.8390	1.29916	0.649581	+	0.760292i	$0.274944\pi$
$762$	14.4615	0.523884
$763$	−13.2758	−0.480617
$764$	0.232586	0.00841465
$765$	−9.59239	−0.346813
$766$	−31.1535	−1.12562
$767$	1.57384	0.0568282
$768$	1.00000	0.0360844
$769$	49.1905	1.77386	0.886928	−	0.461908i	$-0.152835\pi$
$769$	49.1905	1.77386	0.886928	+	0.461908i	$0.152835\pi$
$770$	−7.13203	−0.257021
$771$	−12.4711	−0.449135
$772$	−5.42993	−0.195427
$773$	−43.3278	−1.55839	−0.779196	−	0.626781i	$-0.784372\pi$
$773$	−43.3278	−1.55839	−0.779196	+	0.626781i	$0.784372\pi$
$774$	−11.5427	−0.414893
$775$	25.4103	0.912763
$776$	13.8253	0.496300
$777$	−11.3165	−0.405976
$778$	0.744166	0.0266796
$779$	−8.42132	−0.301725
$780$	4.22313	0.151212
$781$	−17.2856	−0.618528
$782$	−2.97900	−0.106529
$783$	9.39422	0.335722
$784$	−6.04001	−0.215715
$785$	−19.9700	−0.712761
$786$	12.7661	0.455351
$787$	−29.0354	−1.03500	−0.517501	−	0.855683i	$-0.673138\pi$
$787$	−29.0354	−1.03500	−0.517501	+	0.855683i	$0.673138\pi$
$788$	−8.24532	−0.293727
$789$	−4.09568	−0.145810
$790$	−36.1435	−1.28593
$791$	9.83858	0.349820
$792$	1.72364	0.0612467
$793$	−8.99104	−0.319281
$794$	23.7357	0.842350
$795$	−53.2248	−1.88769
$796$	−6.67633	−0.236636
$797$	49.8143	1.76451	0.882257	−	0.470767i	$-0.156023\pi$
$797$	49.8143	1.76451	0.882257	+	0.470767i	$0.156023\pi$
$798$	1.93978	0.0686675
$799$	11.0082	0.389443
$800$	12.8348	0.453779
$801$	10.5963	0.374403
$802$	−25.3216	−0.894138
$803$	10.2026	0.360041
$804$	−13.7166	−0.483747
$805$	−5.42683	−0.191271
$806$	1.97979	0.0697352
$807$	18.4427	0.649215
$808$	16.8970	0.594434
$809$	−14.3198	−0.503457	−0.251729	−	0.967798i	$-0.580999\pi$
$809$	−14.3198	−0.503457	−0.251729	+	0.967798i	$0.580999\pi$
$810$	4.22313	0.148386
$811$	−30.9736	−1.08763	−0.543815	−	0.839205i	$-0.683021\pi$
$811$	−30.9736	−1.08763	−0.543815	+	0.839205i	$0.683021\pi$
$812$	−9.20437	−0.323010
$813$	19.6440	0.688945
$814$	19.9078	0.697768
$815$	60.4255	2.11661
$816$	−2.27139	−0.0795147
$817$	22.8521	0.799493
$818$	38.7264	1.35404
$819$	−0.979791	−0.0342367
$820$	17.9637	0.627319
$821$	28.3625	0.989860	0.494930	−	0.868933i	$-0.335194\pi$
$821$	28.3625	0.989860	0.494930	+	0.868933i	$0.335194\pi$
$822$	−10.6843	−0.372658
$823$	−27.6974	−0.965470	−0.482735	−	0.875766i	$-0.660357\pi$
$823$	−27.6974	−0.965470	−0.482735	+	0.875766i	$0.660357\pi$
$824$	−1.00000	−0.0348367
$825$	22.1226	0.770209
$826$	−1.54204	−0.0536543
$827$	−35.1184	−1.22118	−0.610592	−	0.791945i	$-0.709069\pi$
$827$	−35.1184	−1.22118	−0.610592	+	0.791945i	$0.709069\pi$
$828$	1.31153	0.0455789
$829$	−36.7381	−1.27597	−0.637984	−	0.770049i	$-0.720232\pi$
$829$	−36.7381	−1.27597	−0.637984	+	0.770049i	$0.720232\pi$
$830$	31.2780	1.08568
$831$	−19.8954	−0.690164
$832$	1.00000	0.0346688
$833$	13.7192	0.475343
$834$	6.74315	0.233496
$835$	−36.6722	−1.26910
$836$	−3.41244	−0.118022
$837$	1.97979	0.0684316
$838$	−9.73133	−0.336163
$839$	25.7728	0.889775	0.444887	−	0.895587i	$-0.353244\pi$
$839$	25.7728	0.889775	0.444887	+	0.895587i	$0.353244\pi$
$840$	−4.13778	−0.142767
$841$	59.2513	2.04315
$842$	−16.5366	−0.569889
$843$	−14.5316	−0.500495
$844$	17.8872	0.615702
$845$	4.22313	0.145280
$846$	−4.84646	−0.166625
$847$	7.86682	0.270307
$848$	−12.6032	−0.432794
$849$	9.29044	0.318847
$850$	−29.1529	−0.999937
$851$	15.1480	0.519268
$852$	−10.0286	−0.343573
$853$	−33.3050	−1.14034	−0.570171	−	0.821526i	$-0.693123\pi$
$853$	−33.3050	−1.14034	−0.570171	+	0.821526i	$0.693123\pi$
$854$	8.80934	0.301449
$855$	−8.36091	−0.285937
$856$	−17.0183	−0.581674
$857$	48.2587	1.64849	0.824244	−	0.566235i	$-0.191601\pi$
$857$	48.2587	1.64849	0.824244	+	0.566235i	$0.191601\pi$
$858$	1.72364	0.0588440
$859$	2.12071	0.0723577	0.0361789	−	0.999345i	$-0.488481\pi$
$859$	2.12071	0.0723577	0.0361789	+	0.999345i	$0.488481\pi$
$860$	−48.7462	−1.66223
$861$	−4.16768	−0.142034
$862$	37.1907	1.26672
$863$	−41.0654	−1.39788	−0.698941	−	0.715180i	$-0.746345\pi$
$863$	−41.0654	−1.39788	−0.698941	+	0.715180i	$0.746345\pi$
$864$	1.00000	0.0340207
$865$	30.7772	1.04646
$866$	−12.5636	−0.426927
$867$	−11.8408	−0.402134
$868$	−1.93978	−0.0658404
$869$	−14.7517	−0.500416
$870$	39.6730	1.34504
$871$	−13.7166	−0.464770
$872$	13.5496	0.458849
$873$	13.8253	0.467916
$874$	−2.59656	−0.0878298
$875$	−32.4188	−1.09595
$876$	5.91922	0.199992
$877$	20.2948	0.685307	0.342653	−	0.939462i	$-0.388674\pi$
$877$	20.2948	0.685307	0.342653	+	0.939462i	$0.388674\pi$
$878$	−10.7977	−0.364405
$879$	3.08643	0.104103
$880$	7.27914	0.245380
$881$	−26.5141	−0.893283	−0.446641	−	0.894713i	$-0.647380\pi$
$881$	−26.5141	−0.893283	−0.446641	+	0.894713i	$0.647380\pi$
$882$	−6.04001	−0.203378
$883$	−54.7958	−1.84403	−0.922013	−	0.387160i	$-0.873456\pi$
$883$	−54.7958	−1.84403	−0.922013	+	0.387160i	$0.873456\pi$
$884$	−2.27139	−0.0763952
$885$	6.64654	0.223421
$886$	−1.44328	−0.0484880
$887$	−26.9948	−0.906397	−0.453199	−	0.891410i	$-0.649717\pi$
$887$	−26.9948	−0.906397	−0.453199	+	0.891410i	$0.649717\pi$
$888$	11.5499	0.387589
$889$	−14.1692	−0.475221
$890$	44.7497	1.50001
$891$	1.72364	0.0577440
$892$	9.10790	0.304955
$893$	9.59498	0.321084
$894$	−14.5286	−0.485908
$895$	−39.8628	−1.33247
$896$	−0.979791	−0.0327325
$897$	1.31153	0.0437907
$898$	11.1342	0.371554
$899$	18.5986	0.620298
$900$	12.8348	0.427827
$901$	28.6267	0.953695
$902$	7.33173	0.244120
$903$	11.3094	0.376353
$904$	−10.0415	−0.333976
$905$	−25.2308	−0.838700
$906$	3.01358	0.100120
$907$	12.0022	0.398525	0.199263	−	0.979946i	$-0.436145\pi$
$907$	12.0022	0.398525	0.199263	+	0.979946i	$0.436145\pi$
$908$	−1.51161	−0.0501644
$909$	16.8970	0.560438
$910$	−4.13778	−0.137166
$911$	−23.6834	−0.784667	−0.392333	−	0.919823i	$-0.628332\pi$
$911$	−23.6834	−0.784667	−0.392333	+	0.919823i	$0.628332\pi$
$912$	−1.97979	−0.0655574
$913$	12.7659	0.422489
$914$	−2.91013	−0.0962584
$915$	−37.9703	−1.25526
$916$	21.5512	0.712072
$917$	−12.5081	−0.413053
$918$	−2.27139	−0.0749671
$919$	−17.0119	−0.561171	−0.280585	−	0.959829i	$-0.590529\pi$
$919$	−17.0119	−0.561171	−0.280585	+	0.959829i	$0.590529\pi$
$920$	5.53876	0.182608
$921$	−15.1713	−0.499913
$922$	7.90418	0.260310
$923$	−10.0286	−0.330095
$924$	−1.68880	−0.0555575
$925$	148.241	4.87412
$926$	14.7612	0.485083
$927$	−1.00000	−0.0328443
$928$	9.39422	0.308380
$929$	33.9977	1.11543	0.557714	−	0.830033i	$-0.311679\pi$
$929$	33.9977	1.11543	0.557714	+	0.830033i	$0.311679\pi$
$930$	8.36091	0.274165
$931$	11.9580	0.391906
$932$	6.03691	0.197746
$933$	29.8676	0.977823
$934$	−17.7336	−0.580261
$935$	−16.5338	−0.540712
$936$	1.00000	0.0326860
$937$	25.3762	0.829003	0.414501	−	0.910049i	$-0.363956\pi$
$937$	25.3762	0.829003	0.414501	+	0.910049i	$0.363956\pi$
$938$	13.4394	0.438812
$939$	−28.2380	−0.921512
$940$	−20.4672	−0.667567
$941$	59.4827	1.93908	0.969541	−	0.244930i	$-0.0787651\pi$
$941$	59.4827	1.93908	0.969541	+	0.244930i	$0.0787651\pi$
$942$	−4.72873	−0.154070
$943$	5.57879	0.181670
$944$	1.57384	0.0512242
$945$	−4.13778	−0.134602
$946$	−19.8954	−0.646854
$947$	32.8978	1.06903	0.534517	−	0.845157i	$-0.320493\pi$
$947$	32.8978	1.06903	0.534517	+	0.845157i	$0.320493\pi$
$948$	−8.55846	−0.277966
$949$	5.91922	0.192146
$950$	−25.4103	−0.824418
$951$	−17.2809	−0.560372
$952$	2.22549	0.0721285
$953$	34.0512	1.10303	0.551513	−	0.834166i	$-0.314051\pi$
$953$	34.0512	1.10303	0.551513	+	0.834166i	$0.314051\pi$
$954$	−12.6032	−0.408042
$955$	0.982239	0.0317845
$956$	−23.1947	−0.750172
$957$	16.1922	0.523420
$958$	−7.54827	−0.243874
$959$	10.4684	0.338042
$960$	4.22313	0.136301
$961$	−27.0804	−0.873562
$962$	11.5499	0.372383
$963$	−17.0183	−0.548408
$964$	−11.1732	−0.359866
$965$	−22.9313	−0.738184
$966$	−1.28503	−0.0413450
$967$	42.7564	1.37495	0.687477	−	0.726206i	$-0.258718\pi$
$967$	42.7564	1.37495	0.687477	+	0.726206i	$0.258718\pi$
$968$	−8.02908	−0.258064
$969$	4.49688	0.144461
$970$	58.3861	1.87467
$971$	−13.3266	−0.427672	−0.213836	−	0.976870i	$-0.568596\pi$
$971$	−13.3266	−0.427672	−0.213836	+	0.976870i	$0.568596\pi$
$972$	1.00000	0.0320750
$973$	−6.60688	−0.211807
$974$	8.33445	0.267053
$975$	12.8348	0.411043
$976$	−8.99104	−0.287796
$977$	18.0026	0.575954	0.287977	−	0.957637i	$-0.407017\pi$
$977$	18.0026	0.575954	0.287977	+	0.957637i	$0.407017\pi$
$978$	14.3082	0.457527
$979$	18.2642	0.583728
$980$	−25.5077	−0.814815
$981$	13.5496	0.432607
$982$	14.6852	0.468624
$983$	−19.4049	−0.618919	−0.309459	−	0.950913i	$-0.600148\pi$
$983$	−19.4049	−0.618919	−0.309459	+	0.950913i	$0.600148\pi$
$984$	4.25364	0.135601
$985$	−34.8210	−1.10949
$986$	−21.3380	−0.679539
$987$	4.74852	0.151147
$988$	−1.97979	−0.0629855
$989$	−15.1386	−0.481379
$990$	7.27914	0.231346
$991$	24.4267	0.775939	0.387970	−	0.921672i	$-0.373177\pi$
$991$	24.4267	0.775939	0.387970	+	0.921672i	$0.373177\pi$
$992$	1.97979	0.0628584
$993$	17.3972	0.552085
$994$	9.82591	0.311659
$995$	−28.1950	−0.893842
$996$	7.40636	0.234679
$997$	13.8560	0.438823	0.219412	−	0.975632i	$-0.429586\pi$
$997$	13.8560	0.438823	0.219412	+	0.975632i	$0.429586\pi$
$998$	−2.72075	−0.0861239
$999$	11.5499	0.365422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.v.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.v.1.11	✓	11	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.22313 q^{5} +1.00000 q^{6} -0.979791 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.22313 q^{5} +1.00000 q^{6} -0.979791 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.22313 q^{10} +1.72364 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.979791 q^{14} +4.22313 q^{15} +1.00000 q^{16} -2.27139 q^{17} +1.00000 q^{18} -1.97979 q^{19} +4.22313 q^{20} -0.979791 q^{21} +1.72364 q^{22} +1.31153 q^{23} +1.00000 q^{24} +12.8348 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.979791 q^{28} +9.39422 q^{29} +4.22313 q^{30} +1.97979 q^{31} +1.00000 q^{32} +1.72364 q^{33} -2.27139 q^{34} -4.13778 q^{35} +1.00000 q^{36} +11.5499 q^{37} -1.97979 q^{38} +1.00000 q^{39} +4.22313 q^{40} +4.25364 q^{41} -0.979791 q^{42} -11.5427 q^{43} +1.72364 q^{44} +4.22313 q^{45} +1.31153 q^{46} -4.84646 q^{47} +1.00000 q^{48} -6.04001 q^{49} +12.8348 q^{50} -2.27139 q^{51} +1.00000 q^{52} -12.6032 q^{53} +1.00000 q^{54} +7.27914 q^{55} -0.979791 q^{56} -1.97979 q^{57} +9.39422 q^{58} +1.57384 q^{59} +4.22313 q^{60} -8.99104 q^{61} +1.97979 q^{62} -0.979791 q^{63} +1.00000 q^{64} +4.22313 q^{65} +1.72364 q^{66} -13.7166 q^{67} -2.27139 q^{68} +1.31153 q^{69} -4.13778 q^{70} -10.0286 q^{71} +1.00000 q^{72} +5.91922 q^{73} +11.5499 q^{74} +12.8348 q^{75} -1.97979 q^{76} -1.68880 q^{77} +1.00000 q^{78} -8.55846 q^{79} +4.22313 q^{80} +1.00000 q^{81} +4.25364 q^{82} +7.40636 q^{83} -0.979791 q^{84} -9.59239 q^{85} -11.5427 q^{86} +9.39422 q^{87} +1.72364 q^{88} +10.5963 q^{89} +4.22313 q^{90} -0.979791 q^{91} +1.31153 q^{92} +1.97979 q^{93} -4.84646 q^{94} -8.36091 q^{95} +1.00000 q^{96} +13.8253 q^{97} -6.04001 q^{98} +1.72364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * q^99

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