LMFDB - Embedded newform 6034.2.a.r.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.239534 q^{3} +1.00000 q^{4} -1.50535 q^{5} +0.239534 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.94262 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.239534 q^{3} +1.00000 q^{4} -1.50535 q^{5} +0.239534 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.94262 q^{9} -1.50535 q^{10} +2.73499 q^{11} +0.239534 q^{12} +1.04707 q^{13} -1.00000 q^{14} -0.360583 q^{15} +1.00000 q^{16} +3.39761 q^{17} -2.94262 q^{18} -0.333561 q^{19} -1.50535 q^{20} -0.239534 q^{21} +2.73499 q^{22} +4.21071 q^{23} +0.239534 q^{24} -2.73392 q^{25} +1.04707 q^{26} -1.42346 q^{27} -1.00000 q^{28} -8.38551 q^{29} -0.360583 q^{30} -1.25117 q^{31} +1.00000 q^{32} +0.655122 q^{33} +3.39761 q^{34} +1.50535 q^{35} -2.94262 q^{36} +9.51957 q^{37} -0.333561 q^{38} +0.250809 q^{39} -1.50535 q^{40} -0.332418 q^{41} -0.239534 q^{42} -4.45003 q^{43} +2.73499 q^{44} +4.42968 q^{45} +4.21071 q^{46} +6.78246 q^{47} +0.239534 q^{48} +1.00000 q^{49} -2.73392 q^{50} +0.813843 q^{51} +1.04707 q^{52} +3.54718 q^{53} -1.42346 q^{54} -4.11712 q^{55} -1.00000 q^{56} -0.0798990 q^{57} -8.38551 q^{58} +5.27058 q^{59} -0.360583 q^{60} -0.525085 q^{61} -1.25117 q^{62} +2.94262 q^{63} +1.00000 q^{64} -1.57621 q^{65} +0.655122 q^{66} +2.06059 q^{67} +3.39761 q^{68} +1.00861 q^{69} +1.50535 q^{70} +6.28891 q^{71} -2.94262 q^{72} +11.8184 q^{73} +9.51957 q^{74} -0.654866 q^{75} -0.333561 q^{76} -2.73499 q^{77} +0.250809 q^{78} -0.276173 q^{79} -1.50535 q^{80} +8.48690 q^{81} -0.332418 q^{82} -4.38801 q^{83} -0.239534 q^{84} -5.11460 q^{85} -4.45003 q^{86} -2.00861 q^{87} +2.73499 q^{88} -12.2789 q^{89} +4.42968 q^{90} -1.04707 q^{91} +4.21071 q^{92} -0.299698 q^{93} +6.78246 q^{94} +0.502126 q^{95} +0.239534 q^{96} +10.1737 q^{97} +1.00000 q^{98} -8.04803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * 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
$3$	0.239534	0.138295	0.0691475	−	0.997606i	$-0.477972\pi$
$3$	0.239534	0.138295	0.0691475	+	0.997606i	$0.477972\pi$
$4$	1.00000	0.500000
$5$	−1.50535	−0.673214	−0.336607	−	0.941645i	$-0.609279\pi$
$5$	−1.50535	−0.673214	−0.336607	+	0.941645i	$0.609279\pi$
$6$	0.239534	0.0977893
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.94262	−0.980875
$10$	−1.50535	−0.476034
$11$	2.73499	0.824629	0.412315	−	0.911041i	$-0.364720\pi$
$11$	2.73499	0.824629	0.412315	+	0.911041i	$0.364720\pi$
$12$	0.239534	0.0691475
$13$	1.04707	0.290406	0.145203	−	0.989402i	$-0.453617\pi$
$13$	1.04707	0.290406	0.145203	+	0.989402i	$0.453617\pi$
$14$	−1.00000	−0.267261
$15$	−0.360583	−0.0931020
$16$	1.00000	0.250000
$17$	3.39761	0.824042	0.412021	−	0.911174i	$-0.364823\pi$
$17$	3.39761	0.824042	0.412021	+	0.911174i	$0.364823\pi$
$18$	−2.94262	−0.693583
$19$	−0.333561	−0.0765240	−0.0382620	−	0.999268i	$-0.512182\pi$
$19$	−0.333561	−0.0765240	−0.0382620	+	0.999268i	$0.512182\pi$
$20$	−1.50535	−0.336607
$21$	−0.239534	−0.0522706
$22$	2.73499	0.583101
$23$	4.21071	0.877994	0.438997	−	0.898489i	$-0.355334\pi$
$23$	4.21071	0.877994	0.438997	+	0.898489i	$0.355334\pi$
$24$	0.239534	0.0488946
$25$	−2.73392	−0.546783
$26$	1.04707	0.205348
$27$	−1.42346	−0.273945
$28$	−1.00000	−0.188982
$29$	−8.38551	−1.55715	−0.778575	−	0.627551i	$-0.784057\pi$
$29$	−8.38551	−1.55715	−0.778575	+	0.627551i	$0.784057\pi$
$30$	−0.360583	−0.0658331
$31$	−1.25117	−0.224717	−0.112358	−	0.993668i	$-0.535840\pi$
$31$	−1.25117	−0.224717	−0.112358	+	0.993668i	$0.535840\pi$
$32$	1.00000	0.176777
$33$	0.655122	0.114042
$34$	3.39761	0.582685
$35$	1.50535	0.254451
$36$	−2.94262	−0.490437
$37$	9.51957	1.56501	0.782504	−	0.622645i	$-0.213942\pi$
$37$	9.51957	1.56501	0.782504	+	0.622645i	$0.213942\pi$
$38$	−0.333561	−0.0541107
$39$	0.250809	0.0401616
$40$	−1.50535	−0.238017
$41$	−0.332418	−0.0519150	−0.0259575	−	0.999663i	$-0.508263\pi$
$41$	−0.332418	−0.0519150	−0.0259575	+	0.999663i	$0.508263\pi$
$42$	−0.239534	−0.0369609
$43$	−4.45003	−0.678624	−0.339312	−	0.940674i	$-0.610194\pi$
$43$	−4.45003	−0.678624	−0.339312	+	0.940674i	$0.610194\pi$
$44$	2.73499	0.412315
$45$	4.42968	0.660338
$46$	4.21071	0.620835
$47$	6.78246	0.989323	0.494662	−	0.869086i	$-0.335292\pi$
$47$	6.78246	0.989323	0.494662	+	0.869086i	$0.335292\pi$
$48$	0.239534	0.0345737
$49$	1.00000	0.142857
$50$	−2.73392	−0.386634
$51$	0.813843	0.113961
$52$	1.04707	0.145203
$53$	3.54718	0.487242	0.243621	−	0.969871i	$-0.421665\pi$
$53$	3.54718	0.487242	0.243621	+	0.969871i	$0.421665\pi$
$54$	−1.42346	−0.193708
$55$	−4.11712	−0.555152
$56$	−1.00000	−0.133631
$57$	−0.0798990	−0.0105829
$58$	−8.38551	−1.10107
$59$	5.27058	0.686171	0.343085	−	0.939304i	$-0.388528\pi$
$59$	5.27058	0.686171	0.343085	+	0.939304i	$0.388528\pi$
$60$	−0.360583	−0.0465510
$61$	−0.525085	−0.0672302	−0.0336151	−	0.999435i	$-0.510702\pi$
$61$	−0.525085	−0.0672302	−0.0336151	+	0.999435i	$0.510702\pi$
$62$	−1.25117	−0.158899
$63$	2.94262	0.370736
$64$	1.00000	0.125000
$65$	−1.57621	−0.195505
$66$	0.655122	0.0806399
$67$	2.06059	0.251741	0.125870	−	0.992047i	$-0.459828\pi$
$67$	2.06059	0.251741	0.125870	+	0.992047i	$0.459828\pi$
$68$	3.39761	0.412021
$69$	1.00861	0.121422
$70$	1.50535	0.179924
$71$	6.28891	0.746356	0.373178	−	0.927760i	$-0.378268\pi$
$71$	6.28891	0.746356	0.373178	+	0.927760i	$0.378268\pi$
$72$	−2.94262	−0.346792
$73$	11.8184	1.38324	0.691620	−	0.722261i	$-0.256897\pi$
$73$	11.8184	1.38324	0.691620	+	0.722261i	$0.256897\pi$
$74$	9.51957	1.10663
$75$	−0.654866	−0.0756174
$76$	−0.333561	−0.0382620
$77$	−2.73499	−0.311681
$78$	0.250809	0.0283986
$79$	−0.276173	−0.0310719	−0.0155360	−	0.999879i	$-0.504945\pi$
$79$	−0.276173	−0.0310719	−0.0155360	+	0.999879i	$0.504945\pi$
$80$	−1.50535	−0.168303
$81$	8.48690	0.942989
$82$	−0.332418	−0.0367094
$83$	−4.38801	−0.481646	−0.240823	−	0.970569i	$-0.577417\pi$
$83$	−4.38801	−0.481646	−0.240823	+	0.970569i	$0.577417\pi$
$84$	−0.239534	−0.0261353
$85$	−5.11460	−0.554756
$86$	−4.45003	−0.479859
$87$	−2.00861	−0.215346
$88$	2.73499	0.291551
$89$	−12.2789	−1.30156	−0.650779	−	0.759267i	$-0.725558\pi$
$89$	−12.2789	−1.30156	−0.650779	+	0.759267i	$0.725558\pi$
$90$	4.42968	0.466930
$91$	−1.04707	−0.109763
$92$	4.21071	0.438997
$93$	−0.299698	−0.0310772
$94$	6.78246	0.699557
$95$	0.502126	0.0515170
$96$	0.239534	0.0244473
$97$	10.1737	1.03298	0.516492	−	0.856292i	$-0.327238\pi$
$97$	10.1737	1.03298	0.516492	+	0.856292i	$0.327238\pi$
$98$	1.00000	0.101015
$99$	−8.04803	−0.808858
$100$	−2.73392	−0.273392
$101$	−15.1650	−1.50897	−0.754487	−	0.656315i	$-0.772114\pi$
$101$	−15.1650	−1.50897	−0.754487	+	0.656315i	$0.772114\pi$
$102$	0.813843	0.0805824
$103$	10.4816	1.03279	0.516393	−	0.856352i	$-0.327274\pi$
$103$	10.4816	1.03279	0.516393	+	0.856352i	$0.327274\pi$
$104$	1.04707	0.102674
$105$	0.360583	0.0351893
$106$	3.54718	0.344532
$107$	9.81664	0.949010	0.474505	−	0.880253i	$-0.342627\pi$
$107$	9.81664	0.949010	0.474505	+	0.880253i	$0.342627\pi$
$108$	−1.42346	−0.136972
$109$	11.7069	1.12132	0.560660	−	0.828046i	$-0.310548\pi$
$109$	11.7069	1.12132	0.560660	+	0.828046i	$0.310548\pi$
$110$	−4.11712	−0.392552
$111$	2.28026	0.216433
$112$	−1.00000	−0.0944911
$113$	15.0886	1.41942	0.709710	−	0.704494i	$-0.248826\pi$
$113$	15.0886	1.41942	0.709710	+	0.704494i	$0.248826\pi$
$114$	−0.0798990	−0.00748323
$115$	−6.33860	−0.591077
$116$	−8.38551	−0.778575
$117$	−3.08114	−0.284851
$118$	5.27058	0.485196
$119$	−3.39761	−0.311458
$120$	−0.360583	−0.0329165
$121$	−3.51985	−0.319986
$122$	−0.525085	−0.0475389
$123$	−0.0796254	−0.00717958
$124$	−1.25117	−0.112358
$125$	11.6423	1.04132
$126$	2.94262	0.262150
$127$	−1.68633	−0.149637	−0.0748187	−	0.997197i	$-0.523838\pi$
$127$	−1.68633	−0.149637	−0.0748187	+	0.997197i	$0.523838\pi$
$128$	1.00000	0.0883883
$129$	−1.06593	−0.0938502
$130$	−1.57621	−0.138243
$131$	11.1784	0.976661	0.488331	−	0.872659i	$-0.337606\pi$
$131$	11.1784	0.976661	0.488331	+	0.872659i	$0.337606\pi$
$132$	0.655122	0.0570210
$133$	0.333561	0.0289234
$134$	2.06059	0.178008
$135$	2.14281	0.184423
$136$	3.39761	0.291343
$137$	−20.2342	−1.72873	−0.864363	−	0.502868i	$-0.832278\pi$
$137$	−20.2342	−1.72873	−0.864363	+	0.502868i	$0.832278\pi$
$138$	1.00861	0.0858584
$139$	11.2613	0.955174	0.477587	−	0.878585i	$-0.341512\pi$
$139$	11.2613	0.955174	0.477587	+	0.878585i	$0.341512\pi$
$140$	1.50535	0.127225
$141$	1.62463	0.136818
$142$	6.28891	0.527753
$143$	2.86373	0.239477
$144$	−2.94262	−0.245219
$145$	12.6231	1.04829
$146$	11.8184	0.978099
$147$	0.239534	0.0197564
$148$	9.51957	0.782504
$149$	−15.5674	−1.27533	−0.637666	−	0.770313i	$-0.720100\pi$
$149$	−15.5674	−1.27533	−0.637666	+	0.770313i	$0.720100\pi$
$150$	−0.654866	−0.0534696
$151$	−5.66472	−0.460988	−0.230494	−	0.973074i	$-0.574034\pi$
$151$	−5.66472	−0.460988	−0.230494	+	0.973074i	$0.574034\pi$
$152$	−0.333561	−0.0270553
$153$	−9.99789	−0.808281
$154$	−2.73499	−0.220391
$155$	1.88345	0.151282
$156$	0.250809	0.0200808
$157$	19.2922	1.53968	0.769841	−	0.638236i	$-0.220335\pi$
$157$	19.2922	1.53968	0.769841	+	0.638236i	$0.220335\pi$
$158$	−0.276173	−0.0219712
$159$	0.849669	0.0673831
$160$	−1.50535	−0.119008
$161$	−4.21071	−0.331851
$162$	8.48690	0.666794
$163$	16.2800	1.27515	0.637573	−	0.770390i	$-0.279938\pi$
$163$	16.2800	1.27515	0.637573	+	0.770390i	$0.279938\pi$
$164$	−0.332418	−0.0259575
$165$	−0.986188	−0.0767747
$166$	−4.38801	−0.340575
$167$	16.4389	1.27208	0.636040	−	0.771656i	$-0.280571\pi$
$167$	16.4389	1.27208	0.636040	+	0.771656i	$0.280571\pi$
$168$	−0.239534	−0.0184804
$169$	−11.9036	−0.915665
$170$	−5.11460	−0.392272
$171$	0.981543	0.0750605
$172$	−4.45003	−0.339312
$173$	6.92763	0.526698	0.263349	−	0.964701i	$-0.415173\pi$
$173$	6.92763	0.526698	0.263349	+	0.964701i	$0.415173\pi$
$174$	−2.00861	−0.152273
$175$	2.73392	0.206665
$176$	2.73499	0.206157
$177$	1.26248	0.0948939
$178$	−12.2789	−0.920341
$179$	14.5286	1.08592	0.542961	−	0.839758i	$-0.317303\pi$
$179$	14.5286	1.08592	0.542961	+	0.839758i	$0.317303\pi$
$180$	4.42968	0.330169
$181$	5.90565	0.438963	0.219482	−	0.975617i	$-0.429563\pi$
$181$	5.90565	0.438963	0.219482	+	0.975617i	$0.429563\pi$
$182$	−1.04707	−0.0776142
$183$	−0.125776	−0.00929760
$184$	4.21071	0.310418
$185$	−14.3303	−1.05358
$186$	−0.299698	−0.0219749
$187$	9.29242	0.679529
$188$	6.78246	0.494662
$189$	1.42346	0.103541
$190$	0.502126	0.0364280
$191$	23.5793	1.70614	0.853069	−	0.521799i	$-0.174739\pi$
$191$	23.5793	1.70614	0.853069	+	0.521799i	$0.174739\pi$
$192$	0.239534	0.0172869
$193$	−6.55196	−0.471620	−0.235810	−	0.971799i	$-0.575774\pi$
$193$	−6.55196	−0.471620	−0.235810	+	0.971799i	$0.575774\pi$
$194$	10.1737	0.730430
$195$	−0.377556	−0.0270374
$196$	1.00000	0.0714286
$197$	11.7534	0.837394	0.418697	−	0.908126i	$-0.362487\pi$
$197$	11.7534	0.837394	0.418697	+	0.908126i	$0.362487\pi$
$198$	−8.04803	−0.571949
$199$	−17.9786	−1.27447	−0.637236	−	0.770669i	$-0.719922\pi$
$199$	−17.9786	−1.27447	−0.637236	+	0.770669i	$0.719922\pi$
$200$	−2.73392	−0.193317
$201$	0.493581	0.0348145
$202$	−15.1650	−1.06701
$203$	8.38551	0.588548
$204$	0.813843	0.0569804
$205$	0.500406	0.0349499
$206$	10.4816	0.730290
$207$	−12.3905	−0.861202
$208$	1.04707	0.0726014
$209$	−0.912283	−0.0631040
$210$	0.360583	0.0248826
$211$	16.5647	1.14036	0.570180	−	0.821520i	$-0.306873\pi$
$211$	16.5647	1.14036	0.570180	+	0.821520i	$0.306873\pi$
$212$	3.54718	0.243621
$213$	1.50641	0.103217
$214$	9.81664	0.671051
$215$	6.69886	0.456859
$216$	−1.42346	−0.0968542
$217$	1.25117	0.0849349
$218$	11.7069	0.792893
$219$	2.83091	0.191295
$220$	−4.11712	−0.277576
$221$	3.55754	0.239306
$222$	2.28026	0.153041
$223$	16.0145	1.07241	0.536206	−	0.844087i	$-0.319857\pi$
$223$	16.0145	1.07241	0.536206	+	0.844087i	$0.319857\pi$
$224$	−1.00000	−0.0668153
$225$	8.04489	0.536326
$226$	15.0886	1.00368
$227$	16.4935	1.09471	0.547357	−	0.836899i	$-0.315634\pi$
$227$	16.4935	1.09471	0.547357	+	0.836899i	$0.315634\pi$
$228$	−0.0798990	−0.00529144
$229$	5.51799	0.364639	0.182319	−	0.983239i	$-0.441640\pi$
$229$	5.51799	0.364639	0.182319	+	0.983239i	$0.441640\pi$
$230$	−6.33860	−0.417955
$231$	−0.655122	−0.0431039
$232$	−8.38551	−0.550536
$233$	0.332467	0.0217806	0.0108903	−	0.999941i	$-0.496533\pi$
$233$	0.332467	0.0217806	0.0108903	+	0.999941i	$0.496533\pi$
$234$	−3.08114	−0.201420
$235$	−10.2100	−0.666026
$236$	5.27058	0.343085
$237$	−0.0661529	−0.00429709
$238$	−3.39761	−0.220234
$239$	−27.0921	−1.75244	−0.876220	−	0.481912i	$-0.839942\pi$
$239$	−27.0921	−1.75244	−0.876220	+	0.481912i	$0.839942\pi$
$240$	−0.360583	−0.0232755
$241$	9.87082	0.635836	0.317918	−	0.948118i	$-0.397016\pi$
$241$	9.87082	0.635836	0.317918	+	0.948118i	$0.397016\pi$
$242$	−3.51985	−0.226265
$243$	6.30328	0.404356
$244$	−0.525085	−0.0336151
$245$	−1.50535	−0.0961734
$246$	−0.0796254	−0.00507673
$247$	−0.349262	−0.0222230
$248$	−1.25117	−0.0794494
$249$	−1.05108	−0.0666092
$250$	11.6423	0.736321
$251$	−9.67145	−0.610456	−0.305228	−	0.952279i	$-0.598733\pi$
$251$	−9.67145	−0.610456	−0.305228	+	0.952279i	$0.598733\pi$
$252$	2.94262	0.185368
$253$	11.5162	0.724020
$254$	−1.68633	−0.105810
$255$	−1.22512	−0.0767199
$256$	1.00000	0.0625000
$257$	16.7830	1.04690	0.523448	−	0.852058i	$-0.324646\pi$
$257$	16.7830	1.04690	0.523448	+	0.852058i	$0.324646\pi$
$258$	−1.06593	−0.0663621
$259$	−9.51957	−0.591517
$260$	−1.57621	−0.0977525
$261$	24.6754	1.52737
$262$	11.1784	0.690604
$263$	−12.7046	−0.783400	−0.391700	−	0.920093i	$-0.628113\pi$
$263$	−12.7046	−0.783400	−0.391700	+	0.920093i	$0.628113\pi$
$264$	0.655122	0.0403200
$265$	−5.33975	−0.328018
$266$	0.333561	0.0204519
$267$	−2.94121	−0.179999
$268$	2.06059	0.125870
$269$	26.6568	1.62530	0.812648	−	0.582755i	$-0.198025\pi$
$269$	26.6568	1.62530	0.812648	+	0.582755i	$0.198025\pi$
$270$	2.14281	0.130407
$271$	3.76674	0.228813	0.114407	−	0.993434i	$-0.463503\pi$
$271$	3.76674	0.228813	0.114407	+	0.993434i	$0.463503\pi$
$272$	3.39761	0.206010
$273$	−0.250809	−0.0151797
$274$	−20.2342	−1.22239
$275$	−7.47723	−0.450894
$276$	1.00861	0.0607111
$277$	−18.0403	−1.08393	−0.541967	−	0.840400i	$-0.682320\pi$
$277$	−18.0403	−1.08393	−0.541967	+	0.840400i	$0.682320\pi$
$278$	11.2613	0.675410
$279$	3.68172	0.220419
$280$	1.50535	0.0899619
$281$	−6.01162	−0.358623	−0.179312	−	0.983792i	$-0.557387\pi$
$281$	−6.01162	−0.358623	−0.179312	+	0.983792i	$0.557387\pi$
$282$	1.62463	0.0967452
$283$	−7.05844	−0.419581	−0.209790	−	0.977746i	$-0.567278\pi$
$283$	−7.05844	−0.419581	−0.209790	+	0.977746i	$0.567278\pi$
$284$	6.28891	0.373178
$285$	0.120276	0.00712454
$286$	2.86373	0.169336
$287$	0.332418	0.0196220
$288$	−2.94262	−0.173396
$289$	−5.45624	−0.320956
$290$	12.6231	0.741256
$291$	2.43695	0.142857
$292$	11.8184	0.691620
$293$	−20.0866	−1.17347	−0.586736	−	0.809778i	$-0.699588\pi$
$293$	−20.0866	−1.17347	−0.586736	+	0.809778i	$0.699588\pi$
$294$	0.239534	0.0139699
$295$	−7.93407	−0.461939
$296$	9.51957	0.553314
$297$	−3.89314	−0.225903
$298$	−15.5674	−0.901795
$299$	4.40892	0.254974
$300$	−0.654866	−0.0378087
$301$	4.45003	0.256496
$302$	−5.66472	−0.325968
$303$	−3.63253	−0.208683
$304$	−0.333561	−0.0191310
$305$	0.790437	0.0452603
$306$	−9.99789	−0.571541
$307$	−10.8695	−0.620358	−0.310179	−	0.950678i	$-0.600389\pi$
$307$	−10.8695	−0.620358	−0.310179	+	0.950678i	$0.600389\pi$
$308$	−2.73499	−0.155840
$309$	2.51070	0.142829
$310$	1.88345	0.106973
$311$	−11.4894	−0.651506	−0.325753	−	0.945455i	$-0.605618\pi$
$311$	−11.4894	−0.651506	−0.325753	+	0.945455i	$0.605618\pi$
$312$	0.250809	0.0141993
$313$	20.4729	1.15719	0.578597	−	0.815613i	$-0.303600\pi$
$313$	20.4729	1.15719	0.578597	+	0.815613i	$0.303600\pi$
$314$	19.2922	1.08872
$315$	−4.42968	−0.249584
$316$	−0.276173	−0.0155360
$317$	−25.6042	−1.43807	−0.719037	−	0.694972i	$-0.755417\pi$
$317$	−25.6042	−1.43807	−0.719037	+	0.694972i	$0.755417\pi$
$318$	0.849669	0.0476471
$319$	−22.9343	−1.28407
$320$	−1.50535	−0.0841517
$321$	2.35142	0.131243
$322$	−4.21071	−0.234654
$323$	−1.13331	−0.0630590
$324$	8.48690	0.471495
$325$	−2.86261	−0.158789
$326$	16.2800	0.901664
$327$	2.80420	0.155073
$328$	−0.332418	−0.0183547
$329$	−6.78246	−0.373929
$330$	−0.986188	−0.0542879
$331$	−16.7052	−0.918200	−0.459100	−	0.888385i	$-0.651828\pi$
$331$	−16.7052	−0.918200	−0.459100	+	0.888385i	$0.651828\pi$
$332$	−4.38801	−0.240823
$333$	−28.0125	−1.53508
$334$	16.4389	0.899497
$335$	−3.10191	−0.169475
$336$	−0.239534	−0.0130676
$337$	13.6187	0.741858	0.370929	−	0.928661i	$-0.379039\pi$
$337$	13.6187	0.741858	0.370929	+	0.928661i	$0.379039\pi$
$338$	−11.9036	−0.647473
$339$	3.61424	0.196299
$340$	−5.11460	−0.277378
$341$	−3.42193	−0.185308
$342$	0.981543	0.0530758
$343$	−1.00000	−0.0539949
$344$	−4.45003	−0.239930
$345$	−1.51831	−0.0817430
$346$	6.92763	0.372432
$347$	7.45949	0.400446	0.200223	−	0.979750i	$-0.435833\pi$
$347$	7.45949	0.400446	0.200223	+	0.979750i	$0.435833\pi$
$348$	−2.00861	−0.107673
$349$	−9.66074	−0.517128	−0.258564	−	0.965994i	$-0.583249\pi$
$349$	−9.66074	−0.517128	−0.258564	+	0.965994i	$0.583249\pi$
$350$	2.73392	0.146134
$351$	−1.49047	−0.0795552
$352$	2.73499	0.145775
$353$	−11.9968	−0.638525	−0.319263	−	0.947666i	$-0.603435\pi$
$353$	−11.9968	−0.638525	−0.319263	+	0.947666i	$0.603435\pi$
$354$	1.26248	0.0671001
$355$	−9.46702	−0.502457
$356$	−12.2789	−0.650779
$357$	−0.813843	−0.0430731
$358$	14.5286	0.767862
$359$	10.1447	0.535419	0.267710	−	0.963500i	$-0.413733\pi$
$359$	10.1447	0.535419	0.267710	+	0.963500i	$0.413733\pi$
$360$	4.42968	0.233465
$361$	−18.8887	−0.994144
$362$	5.90565	0.310394
$363$	−0.843123	−0.0442525
$364$	−1.04707	−0.0548815
$365$	−17.7909	−0.931217
$366$	−0.125776	−0.00657439
$367$	1.33048	0.0694504	0.0347252	−	0.999397i	$-0.488944\pi$
$367$	1.33048	0.0694504	0.0347252	+	0.999397i	$0.488944\pi$
$368$	4.21071	0.219498
$369$	0.978181	0.0509221
$370$	−14.3303	−0.744997
$371$	−3.54718	−0.184160
$372$	−0.299698	−0.0155386
$373$	−24.0102	−1.24320	−0.621601	−	0.783334i	$-0.713517\pi$
$373$	−24.0102	−1.24320	−0.621601	+	0.783334i	$0.713517\pi$
$374$	9.29242	0.480499
$375$	2.78872	0.144009
$376$	6.78246	0.349779
$377$	−8.78024	−0.452205
$378$	1.42346	0.0732149
$379$	3.52759	0.181200	0.0906000	−	0.995887i	$-0.471122\pi$
$379$	3.52759	0.181200	0.0906000	+	0.995887i	$0.471122\pi$
$380$	0.502126	0.0257585
$381$	−0.403933	−0.0206941
$382$	23.5793	1.20642
$383$	23.6248	1.20717	0.603585	−	0.797299i	$-0.293738\pi$
$383$	23.6248	1.20717	0.603585	+	0.797299i	$0.293738\pi$
$384$	0.239534	0.0122237
$385$	4.11712	0.209828
$386$	−6.55196	−0.333486
$387$	13.0948	0.665645
$388$	10.1737	0.516492
$389$	−7.05231	−0.357567	−0.178783	−	0.983888i	$-0.557216\pi$
$389$	−7.05231	−0.357567	−0.178783	+	0.983888i	$0.557216\pi$
$390$	−0.377556	−0.0191183
$391$	14.3064	0.723503
$392$	1.00000	0.0505076
$393$	2.67761	0.135067
$394$	11.7534	0.592127
$395$	0.415738	0.0209181
$396$	−8.04803	−0.404429
$397$	31.6559	1.58876	0.794382	−	0.607419i	$-0.207795\pi$
$397$	31.6559	1.58876	0.794382	+	0.607419i	$0.207795\pi$
$398$	−17.9786	−0.901188
$399$	0.0798990	0.00399996
$400$	−2.73392	−0.136696
$401$	21.7143	1.08436	0.542181	−	0.840262i	$-0.317599\pi$
$401$	21.7143	1.08436	0.542181	+	0.840262i	$0.317599\pi$
$402$	0.493581	0.0246176
$403$	−1.31007	−0.0652590
$404$	−15.1650	−0.754487
$405$	−12.7758	−0.634833
$406$	8.38551	0.416166
$407$	26.0359	1.29055
$408$	0.813843	0.0402912
$409$	−15.2243	−0.752793	−0.376396	−	0.926459i	$-0.622837\pi$
$409$	−15.2243	−0.752793	−0.376396	+	0.926459i	$0.622837\pi$
$410$	0.500406	0.0247133
$411$	−4.84678	−0.239074
$412$	10.4816	0.516393
$413$	−5.27058	−0.259348
$414$	−12.3905	−0.608962
$415$	6.60549	0.324251
$416$	1.04707	0.0513370
$417$	2.69747	0.132096
$418$	−0.912283	−0.0446212
$419$	−12.5217	−0.611725	−0.305862	−	0.952076i	$-0.598945\pi$
$419$	−12.5217	−0.611725	−0.305862	+	0.952076i	$0.598945\pi$
$420$	0.360583	0.0175946
$421$	2.37394	0.115699	0.0578495	−	0.998325i	$-0.481576\pi$
$421$	2.37394	0.115699	0.0578495	+	0.998325i	$0.481576\pi$
$422$	16.5647	0.806356
$423$	−19.9582	−0.970402
$424$	3.54718	0.172266
$425$	−9.28879	−0.450572
$426$	1.50641	0.0729856
$427$	0.525085	0.0254106
$428$	9.81664	0.474505
$429$	0.685960	0.0331185
$430$	6.69886	0.323048
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−1.42346	−0.0684862
$433$	24.6418	1.18421	0.592105	−	0.805861i	$-0.298297\pi$
$433$	24.6418	1.18421	0.592105	+	0.805861i	$0.298297\pi$
$434$	1.25117	0.0600581
$435$	3.02367	0.144974
$436$	11.7069	0.560660
$437$	−1.40453	−0.0671876
$438$	2.83091	0.135266
$439$	−33.9408	−1.61991	−0.809954	−	0.586494i	$-0.800508\pi$
$439$	−33.9408	−1.61991	−0.809954	+	0.586494i	$0.800508\pi$
$440$	−4.11712	−0.196276
$441$	−2.94262	−0.140125
$442$	3.55754	0.169215
$443$	5.62528	0.267265	0.133633	−	0.991031i	$-0.457336\pi$
$443$	5.62528	0.267265	0.133633	+	0.991031i	$0.457336\pi$
$444$	2.28026	0.108216
$445$	18.4840	0.876227
$446$	16.0145	0.758310
$447$	−3.72892	−0.176372
$448$	−1.00000	−0.0472456
$449$	−23.7516	−1.12091	−0.560454	−	0.828186i	$-0.689373\pi$
$449$	−23.7516	−1.12091	−0.560454	+	0.828186i	$0.689373\pi$
$450$	8.04489	0.379240
$451$	−0.909159	−0.0428106
$452$	15.0886	0.709710
$453$	−1.35689	−0.0637523
$454$	16.4935	0.774079
$455$	1.57621	0.0738940
$456$	−0.0798990	−0.00374162
$457$	−19.3352	−0.904464	−0.452232	−	0.891900i	$-0.649372\pi$
$457$	−19.3352	−0.904464	−0.452232	+	0.891900i	$0.649372\pi$
$458$	5.51799	0.257839
$459$	−4.83636	−0.225742
$460$	−6.33860	−0.295539
$461$	12.8955	0.600605	0.300303	−	0.953844i	$-0.402912\pi$
$461$	12.8955	0.600605	0.300303	+	0.953844i	$0.402912\pi$
$462$	−0.655122	−0.0304790
$463$	18.9017	0.878438	0.439219	−	0.898380i	$-0.355255\pi$
$463$	18.9017	0.878438	0.439219	+	0.898380i	$0.355255\pi$
$464$	−8.38551	−0.389288
$465$	0.451150	0.0209216
$466$	0.332467	0.0154012
$467$	−6.16318	−0.285198	−0.142599	−	0.989781i	$-0.545546\pi$
$467$	−6.16318	−0.285198	−0.142599	+	0.989781i	$0.545546\pi$
$468$	−3.08114	−0.142426
$469$	−2.06059	−0.0951491
$470$	−10.2100	−0.470951
$471$	4.62113	0.212930
$472$	5.27058	0.242598
$473$	−12.1708	−0.559613
$474$	−0.0661529	−0.00303850
$475$	0.911927	0.0418421
$476$	−3.39761	−0.155729
$477$	−10.4380	−0.477923
$478$	−27.0921	−1.23916
$479$	−19.6428	−0.897501	−0.448750	−	0.893657i	$-0.648131\pi$
$479$	−19.6428	−0.897501	−0.448750	+	0.893657i	$0.648131\pi$
$480$	−0.360583	−0.0164583
$481$	9.96768	0.454487
$482$	9.87082	0.449604
$483$	−1.00861	−0.0458932
$484$	−3.51985	−0.159993
$485$	−15.3150	−0.695419
$486$	6.30328	0.285923
$487$	13.4703	0.610400	0.305200	−	0.952288i	$-0.401277\pi$
$487$	13.4703	0.610400	0.305200	+	0.952288i	$0.401277\pi$
$488$	−0.525085	−0.0237695
$489$	3.89960	0.176346
$490$	−1.50535	−0.0680048
$491$	−12.0184	−0.542382	−0.271191	−	0.962526i	$-0.587418\pi$
$491$	−12.0184	−0.542382	−0.271191	+	0.962526i	$0.587418\pi$
$492$	−0.0796254	−0.00358979
$493$	−28.4907	−1.28316
$494$	−0.349262	−0.0157140
$495$	12.1151	0.544534
$496$	−1.25117	−0.0561792
$497$	−6.28891	−0.282096
$498$	−1.05108	−0.0470998
$499$	−20.1975	−0.904164	−0.452082	−	0.891976i	$-0.649319\pi$
$499$	−20.1975	−0.904164	−0.452082	+	0.891976i	$0.649319\pi$
$500$	11.6423	0.520658
$501$	3.93767	0.175922
$502$	−9.67145	−0.431658
$503$	−2.49788	−0.111375	−0.0556875	−	0.998448i	$-0.517735\pi$
$503$	−2.49788	−0.111375	−0.0556875	+	0.998448i	$0.517735\pi$
$504$	2.94262	0.131075
$505$	22.8287	1.01586
$506$	11.5162	0.511959
$507$	−2.85132	−0.126632
$508$	−1.68633	−0.0748187
$509$	−10.7841	−0.477999	−0.238999	−	0.971020i	$-0.576819\pi$
$509$	−10.7841	−0.477999	−0.238999	+	0.971020i	$0.576819\pi$
$510$	−1.22512	−0.0542492
$511$	−11.8184	−0.522816
$512$	1.00000	0.0441942
$513$	0.474810	0.0209634
$514$	16.7830	0.740267
$515$	−15.7785	−0.695285
$516$	−1.06593	−0.0469251
$517$	18.5499	0.815825
$518$	−9.51957	−0.418266
$519$	1.65940	0.0728396
$520$	−1.57621	−0.0691215
$521$	6.30182	0.276088	0.138044	−	0.990426i	$-0.455919\pi$
$521$	6.30182	0.276088	0.138044	+	0.990426i	$0.455919\pi$
$522$	24.6754	1.08001
$523$	−34.1350	−1.49262	−0.746310	−	0.665598i	$-0.768177\pi$
$523$	−34.1350	−1.49262	−0.746310	+	0.665598i	$0.768177\pi$
$524$	11.1784	0.488331
$525$	0.654866	0.0285807
$526$	−12.7046	−0.553947
$527$	−4.25099	−0.185176
$528$	0.655122	0.0285105
$529$	−5.26991	−0.229127
$530$	−5.33975	−0.231944
$531$	−15.5093	−0.673047
$532$	0.333561	0.0144617
$533$	−0.348066	−0.0150764
$534$	−2.94121	−0.127279
$535$	−14.7775	−0.638886
$536$	2.06059	0.0890039
$537$	3.48010	0.150177
$538$	26.6568	1.14926
$539$	2.73499	0.117804
$540$	2.14281	0.0922117
$541$	−13.1575	−0.565684	−0.282842	−	0.959167i	$-0.591277\pi$
$541$	−13.1575	−0.565684	−0.282842	+	0.959167i	$0.591277\pi$
$542$	3.76674	0.161795
$543$	1.41460	0.0607064
$544$	3.39761	0.145671
$545$	−17.6230	−0.754887
$546$	−0.250809	−0.0107336
$547$	−33.4182	−1.42886	−0.714430	−	0.699707i	$-0.753314\pi$
$547$	−33.4182	−1.42886	−0.714430	+	0.699707i	$0.753314\pi$
$548$	−20.2342	−0.864363
$549$	1.54513	0.0659444
$550$	−7.47723	−0.318830
$551$	2.79708	0.119159
$552$	1.00861	0.0429292
$553$	0.276173	0.0117441
$554$	−18.0403	−0.766458
$555$	−3.43259	−0.145705
$556$	11.2613	0.477587
$557$	−34.8065	−1.47480	−0.737399	−	0.675458i	$-0.763946\pi$
$557$	−34.8065	−1.47480	−0.737399	+	0.675458i	$0.763946\pi$
$558$	3.68172	0.155860
$559$	−4.65951	−0.197076
$560$	1.50535	0.0636127
$561$	2.22585	0.0939754
$562$	−6.01162	−0.253585
$563$	−29.5898	−1.24706	−0.623531	−	0.781799i	$-0.714302\pi$
$563$	−29.5898	−1.24706	−0.623531	+	0.781799i	$0.714302\pi$
$564$	1.62463	0.0684092
$565$	−22.7137	−0.955573
$566$	−7.05844	−0.296688
$567$	−8.48690	−0.356416
$568$	6.28891	0.263877
$569$	20.3722	0.854046	0.427023	−	0.904241i	$-0.359562\pi$
$569$	20.3722	0.854046	0.427023	+	0.904241i	$0.359562\pi$
$570$	0.120276	0.00503781
$571$	−7.95613	−0.332954	−0.166477	−	0.986045i	$-0.553239\pi$
$571$	−7.95613	−0.332954	−0.166477	+	0.986045i	$0.553239\pi$
$572$	2.86373	0.119739
$573$	5.64804	0.235950
$574$	0.332418	0.0138749
$575$	−11.5117	−0.480073
$576$	−2.94262	−0.122609
$577$	32.0133	1.33273	0.666365	−	0.745626i	$-0.267849\pi$
$577$	32.0133	1.33273	0.666365	+	0.745626i	$0.267849\pi$
$578$	−5.45624	−0.226950
$579$	−1.56942	−0.0652227
$580$	12.6231	0.524147
$581$	4.38801	0.182045
$582$	2.43695	0.101015
$583$	9.70148	0.401794
$584$	11.8184	0.489050
$585$	4.63820	0.191766
$586$	−20.0866	−0.829771
$587$	46.2278	1.90802	0.954012	−	0.299767i	$-0.0969091\pi$
$587$	46.2278	1.90802	0.954012	+	0.299767i	$0.0969091\pi$
$588$	0.239534	0.00987821
$589$	0.417341	0.0171962
$590$	−7.93407	−0.326640
$591$	2.81534	0.115807
$592$	9.51957	0.391252
$593$	28.1554	1.15620	0.578102	−	0.815964i	$-0.303794\pi$
$593$	28.1554	1.15620	0.578102	+	0.815964i	$0.303794\pi$
$594$	−3.89314	−0.159738
$595$	5.11460	0.209678
$596$	−15.5674	−0.637666
$597$	−4.30649	−0.176253
$598$	4.40892	0.180294
$599$	7.58882	0.310071	0.155035	−	0.987909i	$-0.450451\pi$
$599$	7.58882	0.310071	0.155035	+	0.987909i	$0.450451\pi$
$600$	−0.654866	−0.0267348
$601$	35.8750	1.46337	0.731686	−	0.681642i	$-0.238734\pi$
$601$	35.8750	1.46337	0.731686	+	0.681642i	$0.238734\pi$
$602$	4.45003	0.181370
$603$	−6.06354	−0.246926
$604$	−5.66472	−0.230494
$605$	5.29861	0.215419
$606$	−3.63253	−0.147561
$607$	−13.6034	−0.552144	−0.276072	−	0.961137i	$-0.589033\pi$
$607$	−13.6034	−0.552144	−0.276072	+	0.961137i	$0.589033\pi$
$608$	−0.333561	−0.0135277
$609$	2.00861	0.0813931
$610$	0.790437	0.0320039
$611$	7.10173	0.287305
$612$	−9.99789	−0.404141
$613$	1.07199	0.0432974	0.0216487	−	0.999766i	$-0.493108\pi$
$613$	1.07199	0.0432974	0.0216487	+	0.999766i	$0.493108\pi$
$614$	−10.8695	−0.438659
$615$	0.119864	0.00483339
$616$	−2.73499	−0.110196
$617$	38.7410	1.55965	0.779827	−	0.625995i	$-0.215307\pi$
$617$	38.7410	1.55965	0.779827	+	0.625995i	$0.215307\pi$
$618$	2.51070	0.100995
$619$	−14.3828	−0.578095	−0.289048	−	0.957315i	$-0.593339\pi$
$619$	−14.3828	−0.578095	−0.289048	+	0.957315i	$0.593339\pi$
$620$	1.88345	0.0756412
$621$	−5.99378	−0.240522
$622$	−11.4894	−0.460685
$623$	12.2789	0.491943
$624$	0.250809	0.0100404
$625$	−3.85611	−0.154244
$626$	20.4729	0.818260
$627$	−0.218523	−0.00872696
$628$	19.2922	0.769841
$629$	32.3438	1.28963
$630$	−4.42968	−0.176483
$631$	7.33068	0.291830	0.145915	−	0.989297i	$-0.453387\pi$
$631$	7.33068	0.291830	0.145915	+	0.989297i	$0.453387\pi$
$632$	−0.276173	−0.0109856
$633$	3.96780	0.157706
$634$	−25.6042	−1.01687
$635$	2.53852	0.100738
$636$	0.849669	0.0336916
$637$	1.04707	0.0414865
$638$	−22.9343	−0.907976
$639$	−18.5059	−0.732082
$640$	−1.50535	−0.0595042
$641$	−42.7138	−1.68709	−0.843547	−	0.537055i	$-0.819537\pi$
$641$	−42.7138	−1.68709	−0.843547	+	0.537055i	$0.819537\pi$
$642$	2.35142	0.0928030
$643$	32.3410	1.27541	0.637703	−	0.770282i	$-0.279885\pi$
$643$	32.3410	1.27541	0.637703	+	0.770282i	$0.279885\pi$
$644$	−4.21071	−0.165925
$645$	1.60460	0.0631813
$646$	−1.13331	−0.0445894
$647$	33.1866	1.30470	0.652350	−	0.757918i	$-0.273783\pi$
$647$	33.1866	1.30470	0.652350	+	0.757918i	$0.273783\pi$
$648$	8.48690	0.333397
$649$	14.4150	0.565836
$650$	−2.86261	−0.112281
$651$	0.299698	0.0117461
$652$	16.2800	0.637573
$653$	28.3466	1.10929	0.554645	−	0.832087i	$-0.312854\pi$
$653$	28.3466	1.10929	0.554645	+	0.832087i	$0.312854\pi$
$654$	2.80420	0.109653
$655$	−16.8274	−0.657502
$656$	−0.332418	−0.0129787
$657$	−34.7771	−1.35679
$658$	−6.78246	−0.264408
$659$	2.35732	0.0918280	0.0459140	−	0.998945i	$-0.485380\pi$
$659$	2.35732	0.0918280	0.0459140	+	0.998945i	$0.485380\pi$
$660$	−0.986188	−0.0383873
$661$	−39.6656	−1.54281	−0.771407	−	0.636343i	$-0.780446\pi$
$661$	−39.6656	−1.54281	−0.771407	+	0.636343i	$0.780446\pi$
$662$	−16.7052	−0.649265
$663$	0.852152	0.0330949
$664$	−4.38801	−0.170288
$665$	−0.502126	−0.0194716
$666$	−28.0125	−1.08546
$667$	−35.3090	−1.36717
$668$	16.4389	0.636040
$669$	3.83602	0.148309
$670$	−3.10191	−0.119837
$671$	−1.43610	−0.0554400
$672$	−0.239534	−0.00924022
$673$	−21.2069	−0.817465	−0.408732	−	0.912654i	$-0.634029\pi$
$673$	−21.2069	−0.817465	−0.408732	+	0.912654i	$0.634029\pi$
$674$	13.6187	0.524573
$675$	3.89162	0.149789
$676$	−11.9036	−0.457832
$677$	−12.9917	−0.499313	−0.249656	−	0.968334i	$-0.580318\pi$
$677$	−12.9917	−0.499313	−0.249656	+	0.968334i	$0.580318\pi$
$678$	3.61424	0.138804
$679$	−10.1737	−0.390431
$680$	−5.11460	−0.196136
$681$	3.95076	0.151393
$682$	−3.42193	−0.131033
$683$	4.21522	0.161291	0.0806454	−	0.996743i	$-0.474302\pi$
$683$	4.21522	0.161291	0.0806454	+	0.996743i	$0.474302\pi$
$684$	0.981543	0.0375302
$685$	30.4596	1.16380
$686$	−1.00000	−0.0381802
$687$	1.32174	0.0504277
$688$	−4.45003	−0.169656
$689$	3.71415	0.141498
$690$	−1.51831	−0.0578010
$691$	−18.8317	−0.716393	−0.358197	−	0.933646i	$-0.616608\pi$
$691$	−18.8317	−0.716393	−0.358197	+	0.933646i	$0.616608\pi$
$692$	6.92763	0.263349
$693$	8.04803	0.305720
$694$	7.45949	0.283158
$695$	−16.9523	−0.643036
$696$	−2.00861	−0.0761363
$697$	−1.12943	−0.0427801
$698$	−9.66074	−0.365664
$699$	0.0796371	0.00301215
$700$	2.73392	0.103332
$701$	18.7154	0.706872	0.353436	−	0.935459i	$-0.385013\pi$
$701$	18.7154	0.706872	0.353436	+	0.935459i	$0.385013\pi$
$702$	−1.49047	−0.0562540
$703$	−3.17535	−0.119761
$704$	2.73499	0.103079
$705$	−2.44564	−0.0921080
$706$	−11.9968	−0.451506
$707$	15.1650	0.570339
$708$	1.26248	0.0474470
$709$	9.99447	0.375350	0.187675	−	0.982231i	$-0.439905\pi$
$709$	9.99447	0.375350	0.187675	+	0.982231i	$0.439905\pi$
$710$	−9.46702	−0.355291
$711$	0.812675	0.0304777
$712$	−12.2789	−0.460170
$713$	−5.26831	−0.197300
$714$	−0.813843	−0.0304573
$715$	−4.31092	−0.161219
$716$	14.5286	0.542961
$717$	−6.48946	−0.242353
$718$	10.1447	0.378599
$719$	26.0749	0.972429	0.486214	−	0.873840i	$-0.338377\pi$
$719$	26.0749	0.972429	0.486214	+	0.873840i	$0.338377\pi$
$720$	4.42968	0.165085
$721$	−10.4816	−0.390356
$722$	−18.8887	−0.702966
$723$	2.36440	0.0879329
$724$	5.90565	0.219482
$725$	22.9253	0.851424
$726$	−0.843123	−0.0312912
$727$	44.7452	1.65951	0.829753	−	0.558131i	$-0.188481\pi$
$727$	44.7452	1.65951	0.829753	+	0.558131i	$0.188481\pi$
$728$	−1.04707	−0.0388071
$729$	−23.9509	−0.887069
$730$	−17.7909	−0.658470
$731$	−15.1195	−0.559214
$732$	−0.125776	−0.00464880
$733$	−37.2736	−1.37673	−0.688366	−	0.725364i	$-0.741672\pi$
$733$	−37.2736	−1.37673	−0.688366	+	0.725364i	$0.741672\pi$
$734$	1.33048	0.0491089
$735$	−0.360583	−0.0133003
$736$	4.21071	0.155209
$737$	5.63568	0.207593
$738$	0.978181	0.0360074
$739$	34.8090	1.28047	0.640235	−	0.768179i	$-0.278837\pi$
$739$	34.8090	1.28047	0.640235	+	0.768179i	$0.278837\pi$
$740$	−14.3303	−0.526792
$741$	−0.0836601	−0.00307333
$742$	−3.54718	−0.130221
$743$	−33.8689	−1.24253	−0.621265	−	0.783600i	$-0.713381\pi$
$743$	−33.8689	−1.24253	−0.621265	+	0.783600i	$0.713381\pi$
$744$	−0.299698	−0.0109874
$745$	23.4344	0.858570
$746$	−24.0102	−0.879076
$747$	12.9123	0.472435
$748$	9.29242	0.339764
$749$	−9.81664	−0.358692
$750$	2.78872	0.101830
$751$	−49.7284	−1.81462	−0.907308	−	0.420467i	$-0.861866\pi$
$751$	−49.7284	−1.81462	−0.907308	+	0.420467i	$0.861866\pi$
$752$	6.78246	0.247331
$753$	−2.31664	−0.0844230
$754$	−8.78024	−0.319757
$755$	8.52739	0.310343
$756$	1.42346	0.0517707
$757$	−37.3429	−1.35725	−0.678625	−	0.734485i	$-0.737424\pi$
$757$	−37.3429	−1.35725	−0.678625	+	0.734485i	$0.737424\pi$
$758$	3.52759	0.128128
$759$	2.75853	0.100128
$760$	0.502126	0.0182140
$761$	27.6778	1.00332	0.501661	−	0.865065i	$-0.332723\pi$
$761$	27.6778	1.00332	0.501661	+	0.865065i	$0.332723\pi$
$762$	−0.403933	−0.0146329
$763$	−11.7069	−0.423819
$764$	23.5793	0.853069
$765$	15.0503	0.544146
$766$	23.6248	0.853598
$767$	5.51868	0.199268
$768$	0.239534	0.00864343
$769$	−22.2301	−0.801638	−0.400819	−	0.916157i	$-0.631274\pi$
$769$	−22.2301	−0.801638	−0.400819	+	0.916157i	$0.631274\pi$
$770$	4.11712	0.148371
$771$	4.02010	0.144780
$772$	−6.55196	−0.235810
$773$	−21.5579	−0.775385	−0.387693	−	0.921789i	$-0.626728\pi$
$773$	−21.5579	−0.775385	−0.387693	+	0.921789i	$0.626728\pi$
$774$	13.0948	0.470682
$775$	3.42059	0.122871
$776$	10.1737	0.365215
$777$	−2.28026	−0.0818039
$778$	−7.05231	−0.252838
$779$	0.110882	0.00397274
$780$	−0.377556	−0.0135187
$781$	17.2001	0.615467
$782$	14.3064	0.511594
$783$	11.9364	0.426573
$784$	1.00000	0.0357143
$785$	−29.0415	−1.03653
$786$	2.67761	0.0955070
$787$	−37.7090	−1.34418	−0.672091	−	0.740469i	$-0.734603\pi$
$787$	−37.7090	−1.34418	−0.672091	+	0.740469i	$0.734603\pi$
$788$	11.7534	0.418697
$789$	−3.04318	−0.108340
$790$	0.415738	0.0147913
$791$	−15.0886	−0.536490
$792$	−8.04803	−0.285974
$793$	−0.549802	−0.0195240
$794$	31.6559	1.12343
$795$	−1.27905	−0.0453632
$796$	−17.9786	−0.637236
$797$	32.1906	1.14025	0.570125	−	0.821558i	$-0.306895\pi$
$797$	32.1906	1.14025	0.570125	+	0.821558i	$0.306895\pi$
$798$	0.0798990	0.00282840
$799$	23.0442	0.815244
$800$	−2.73392	−0.0966586
$801$	36.1321	1.27667
$802$	21.7143	0.766759
$803$	32.3232	1.14066
$804$	0.493581	0.0174073
$805$	6.33860	0.223406
$806$	−1.31007	−0.0461451
$807$	6.38521	0.224770
$808$	−15.1650	−0.533503
$809$	6.07891	0.213723	0.106862	−	0.994274i	$-0.465920\pi$
$809$	6.07891	0.213723	0.106862	+	0.994274i	$0.465920\pi$
$810$	−12.7758	−0.448895
$811$	−15.4857	−0.543775	−0.271887	−	0.962329i	$-0.587648\pi$
$811$	−15.4857	−0.543775	−0.271887	+	0.962329i	$0.587648\pi$
$812$	8.38551	0.294274
$813$	0.902262	0.0316437
$814$	26.0359	0.912558
$815$	−24.5071	−0.858445
$816$	0.813843	0.0284902
$817$	1.48436	0.0519310
$818$	−15.2243	−0.532305
$819$	3.08114	0.107664
$820$	0.500406	0.0174749
$821$	−27.8223	−0.971003	−0.485502	−	0.874236i	$-0.661363\pi$
$821$	−27.8223	−0.971003	−0.485502	+	0.874236i	$0.661363\pi$
$822$	−4.84678	−0.169051
$823$	18.0197	0.628129	0.314064	−	0.949402i	$-0.398309\pi$
$823$	18.0197	0.628129	0.314064	+	0.949402i	$0.398309\pi$
$824$	10.4816	0.365145
$825$	−1.79105	−0.0623563
$826$	−5.27058	−0.183387
$827$	−29.5487	−1.02751	−0.513754	−	0.857938i	$-0.671746\pi$
$827$	−29.5487	−1.02751	−0.513754	+	0.857938i	$0.671746\pi$
$828$	−12.3905	−0.430601
$829$	−34.6851	−1.20466	−0.602332	−	0.798246i	$-0.705762\pi$
$829$	−34.6851	−1.20466	−0.602332	+	0.798246i	$0.705762\pi$
$830$	6.60549	0.229280
$831$	−4.32126	−0.149903
$832$	1.04707	0.0363007
$833$	3.39761	0.117720
$834$	2.69747	0.0934058
$835$	−24.7463	−0.856382
$836$	−0.912283	−0.0315520
$837$	1.78099	0.0615600
$838$	−12.5217	−0.432555
$839$	−51.0575	−1.76270	−0.881351	−	0.472463i	$-0.843365\pi$
$839$	−51.0575	−1.76270	−0.881351	+	0.472463i	$0.843365\pi$
$840$	0.360583	0.0124413
$841$	41.3168	1.42472
$842$	2.37394	0.0818115
$843$	−1.43999	−0.0495958
$844$	16.5647	0.570180
$845$	17.9192	0.616438
$846$	−19.9582	−0.686178
$847$	3.51985	0.120944
$848$	3.54718	0.121811
$849$	−1.69074	−0.0580259
$850$	−9.28879	−0.318603
$851$	40.0842	1.37407
$852$	1.50641	0.0516086
$853$	−17.4739	−0.598294	−0.299147	−	0.954207i	$-0.596702\pi$
$853$	−17.4739	−0.598294	−0.299147	+	0.954207i	$0.596702\pi$
$854$	0.525085	0.0179680
$855$	−1.47757	−0.0505317
$856$	9.81664	0.335526
$857$	−6.19138	−0.211494	−0.105747	−	0.994393i	$-0.533723\pi$
$857$	−6.19138	−0.211494	−0.105747	+	0.994393i	$0.533723\pi$
$858$	0.685960	0.0234183
$859$	32.9742	1.12506	0.562532	−	0.826775i	$-0.309827\pi$
$859$	32.9742	1.12506	0.562532	+	0.826775i	$0.309827\pi$
$860$	6.69886	0.228429
$861$	0.0796254	0.00271363
$862$	−1.00000	−0.0340601
$863$	−18.7668	−0.638830	−0.319415	−	0.947615i	$-0.603486\pi$
$863$	−18.7668	−0.638830	−0.319415	+	0.947615i	$0.603486\pi$
$864$	−1.42346	−0.0484271
$865$	−10.4285	−0.354580
$866$	24.6418	0.837362
$867$	−1.30696	−0.0443865
$868$	1.25117	0.0424675
$869$	−0.755331	−0.0256228
$870$	3.02367	0.102512
$871$	2.15759	0.0731070
$872$	11.7069	0.396446
$873$	−29.9374	−1.01323
$874$	−1.40453	−0.0475088
$875$	−11.6423	−0.393580
$876$	2.83091	0.0956476
$877$	1.90756	0.0644137	0.0322068	−	0.999481i	$-0.489746\pi$
$877$	1.90756	0.0644137	0.0322068	+	0.999481i	$0.489746\pi$
$878$	−33.9408	−1.14545
$879$	−4.81143	−0.162285
$880$	−4.11712	−0.138788
$881$	28.6522	0.965317	0.482658	−	0.875809i	$-0.339671\pi$
$881$	28.6522	0.965317	0.482658	+	0.875809i	$0.339671\pi$
$882$	−2.94262	−0.0990833
$883$	52.9262	1.78111	0.890554	−	0.454877i	$-0.150317\pi$
$883$	52.9262	1.78111	0.890554	+	0.454877i	$0.150317\pi$
$884$	3.55754	0.119653
$885$	−1.90048	−0.0638839
$886$	5.62528	0.188985
$887$	36.6505	1.23060	0.615302	−	0.788292i	$-0.289034\pi$
$887$	36.6505	1.23060	0.615302	+	0.788292i	$0.289034\pi$
$888$	2.28026	0.0765205
$889$	1.68633	0.0565577
$890$	18.4840	0.619586
$891$	23.2116	0.777617
$892$	16.0145	0.536206
$893$	−2.26236	−0.0757070
$894$	−3.72892	−0.124714
$895$	−21.8707	−0.731057
$896$	−1.00000	−0.0334077
$897$	1.05609	0.0352617
$898$	−23.7516	−0.792601
$899$	10.4917	0.349918
$900$	8.04489	0.268163
$901$	12.0519	0.401508
$902$	−0.909159	−0.0302717
$903$	1.06593	0.0354721
$904$	15.0886	0.501841
$905$	−8.89007	−0.295516
$906$	−1.35689	−0.0450797
$907$	22.6643	0.752557	0.376279	−	0.926507i	$-0.377204\pi$
$907$	22.6643	0.752557	0.376279	+	0.926507i	$0.377204\pi$
$908$	16.4935	0.547357
$909$	44.6249	1.48011
$910$	1.57621	0.0522509
$911$	−14.5942	−0.483527	−0.241763	−	0.970335i	$-0.577726\pi$
$911$	−14.5942	−0.483527	−0.241763	+	0.970335i	$0.577726\pi$
$912$	−0.0798990	−0.00264572
$913$	−12.0011	−0.397180
$914$	−19.3352	−0.639553
$915$	0.189336	0.00625927
$916$	5.51799	0.182319
$917$	−11.1784	−0.369143
$918$	−4.83636	−0.159624
$919$	−53.6923	−1.77115	−0.885573	−	0.464500i	$-0.846234\pi$
$919$	−53.6923	−1.77115	−0.885573	+	0.464500i	$0.846234\pi$
$920$	−6.33860	−0.208977
$921$	−2.60362	−0.0857923
$922$	12.8955	0.424692
$923$	6.58494	0.216746
$924$	−0.655122	−0.0215519
$925$	−26.0257	−0.855721
$926$	18.9017	0.621150
$927$	−30.8435	−1.01303
$928$	−8.38551	−0.275268
$929$	48.3154	1.58518	0.792588	−	0.609758i	$-0.208733\pi$
$929$	48.3154	1.58518	0.792588	+	0.609758i	$0.208733\pi$
$930$	0.451150	0.0147938
$931$	−0.333561	−0.0109320
$932$	0.332467	0.0108903
$933$	−2.75211	−0.0901001
$934$	−6.16318	−0.201666
$935$	−13.9884	−0.457468
$936$	−3.08114	−0.100710
$937$	−2.83478	−0.0926083	−0.0463041	−	0.998927i	$-0.514744\pi$
$937$	−2.83478	−0.0926083	−0.0463041	+	0.998927i	$0.514744\pi$
$938$	−2.06059	−0.0672806
$939$	4.90394	0.160034
$940$	−10.2100	−0.333013
$941$	−10.0197	−0.326634	−0.163317	−	0.986574i	$-0.552219\pi$
$941$	−10.0197	−0.326634	−0.163317	+	0.986574i	$0.552219\pi$
$942$	4.62113	0.150564
$943$	−1.39972	−0.0455810
$944$	5.27058	0.171543
$945$	−2.14281	−0.0697055
$946$	−12.1708	−0.395706
$947$	−16.2800	−0.529030	−0.264515	−	0.964382i	$-0.585212\pi$
$947$	−16.2800	−0.529030	−0.264515	+	0.964382i	$0.585212\pi$
$948$	−0.0661529	−0.00214855
$949$	12.3747	0.401701
$950$	0.911927	0.0295868
$951$	−6.13307	−0.198878
$952$	−3.39761	−0.110117
$953$	14.6881	0.475794	0.237897	−	0.971290i	$-0.423542\pi$
$953$	14.6881	0.475794	0.237897	+	0.971290i	$0.423542\pi$
$954$	−10.4380	−0.337943
$955$	−35.4951	−1.14859
$956$	−27.0921	−0.876220
$957$	−5.49353	−0.177581
$958$	−19.6428	−0.634629
$959$	20.2342	0.653397
$960$	−0.360583	−0.0116378
$961$	−29.4346	−0.949502
$962$	9.96768	0.321371
$963$	−28.8867	−0.930860
$964$	9.87082	0.317918
$965$	9.86300	0.317501
$966$	−1.00861	−0.0324514
$967$	47.2477	1.51938	0.759691	−	0.650284i	$-0.225350\pi$
$967$	47.2477	1.51938	0.759691	+	0.650284i	$0.225350\pi$
$968$	−3.51985	−0.113132
$969$	−0.271466	−0.00872074
$970$	−15.3150	−0.491736
$971$	2.85097	0.0914921	0.0457461	−	0.998953i	$-0.485433\pi$
$971$	2.85097	0.0914921	0.0457461	+	0.998953i	$0.485433\pi$
$972$	6.30328	0.202178
$973$	−11.2613	−0.361022
$974$	13.4703	0.431618
$975$	−0.685692	−0.0219597
$976$	−0.525085	−0.0168076
$977$	44.5493	1.42526	0.712629	−	0.701541i	$-0.247504\pi$
$977$	44.5493	1.42526	0.712629	+	0.701541i	$0.247504\pi$
$978$	3.89960	0.124696
$979$	−33.5826	−1.07330
$980$	−1.50535	−0.0480867
$981$	−34.4491	−1.09987
$982$	−12.0184	−0.383522
$983$	−33.9678	−1.08340	−0.541702	−	0.840570i	$-0.682220\pi$
$983$	−33.9678	−1.08340	−0.541702	+	0.840570i	$0.682220\pi$
$984$	−0.0796254	−0.00253836
$985$	−17.6930	−0.563745
$986$	−28.4907	−0.907329
$987$	−1.62463	−0.0517125
$988$	−0.349262	−0.0111115
$989$	−18.7378	−0.595828
$990$	12.1151	0.385044
$991$	−34.8946	−1.10846	−0.554231	−	0.832363i	$-0.686988\pi$
$991$	−34.8946	−1.10846	−0.554231	+	0.832363i	$0.686988\pi$
$992$	−1.25117	−0.0397247
$993$	−4.00146	−0.126982
$994$	−6.28891	−0.199472
$995$	27.0642	0.857992
$996$	−1.05108	−0.0333046
$997$	−24.5595	−0.777809	−0.388904	−	0.921278i	$-0.627146\pi$
$997$	−24.5595	−0.777809	−0.388904	+	0.921278i	$0.627146\pi$
$998$	−20.1975	−0.639340
$999$	−13.5507	−0.428726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.16	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.16	✓	31	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.239534 q^{3} +1.00000 q^{4} -1.50535 q^{5} +0.239534 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.94262 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.239534 q^{3} +1.00000 q^{4} -1.50535 q^{5} +0.239534 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.94262 q^{9} -1.50535 q^{10} +2.73499 q^{11} +0.239534 q^{12} +1.04707 q^{13} -1.00000 q^{14} -0.360583 q^{15} +1.00000 q^{16} +3.39761 q^{17} -2.94262 q^{18} -0.333561 q^{19} -1.50535 q^{20} -0.239534 q^{21} +2.73499 q^{22} +4.21071 q^{23} +0.239534 q^{24} -2.73392 q^{25} +1.04707 q^{26} -1.42346 q^{27} -1.00000 q^{28} -8.38551 q^{29} -0.360583 q^{30} -1.25117 q^{31} +1.00000 q^{32} +0.655122 q^{33} +3.39761 q^{34} +1.50535 q^{35} -2.94262 q^{36} +9.51957 q^{37} -0.333561 q^{38} +0.250809 q^{39} -1.50535 q^{40} -0.332418 q^{41} -0.239534 q^{42} -4.45003 q^{43} +2.73499 q^{44} +4.42968 q^{45} +4.21071 q^{46} +6.78246 q^{47} +0.239534 q^{48} +1.00000 q^{49} -2.73392 q^{50} +0.813843 q^{51} +1.04707 q^{52} +3.54718 q^{53} -1.42346 q^{54} -4.11712 q^{55} -1.00000 q^{56} -0.0798990 q^{57} -8.38551 q^{58} +5.27058 q^{59} -0.360583 q^{60} -0.525085 q^{61} -1.25117 q^{62} +2.94262 q^{63} +1.00000 q^{64} -1.57621 q^{65} +0.655122 q^{66} +2.06059 q^{67} +3.39761 q^{68} +1.00861 q^{69} +1.50535 q^{70} +6.28891 q^{71} -2.94262 q^{72} +11.8184 q^{73} +9.51957 q^{74} -0.654866 q^{75} -0.333561 q^{76} -2.73499 q^{77} +0.250809 q^{78} -0.276173 q^{79} -1.50535 q^{80} +8.48690 q^{81} -0.332418 q^{82} -4.38801 q^{83} -0.239534 q^{84} -5.11460 q^{85} -4.45003 q^{86} -2.00861 q^{87} +2.73499 q^{88} -12.2789 q^{89} +4.42968 q^{90} -1.04707 q^{91} +4.21071 q^{92} -0.299698 q^{93} +6.78246 q^{94} +0.502126 q^{95} +0.239534 q^{96} +10.1737 q^{97} +1.00000 q^{98} -8.04803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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