LMFDB - Embedded newform 6034.2.a.r.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.718722 q^{3} +1.00000 q^{4} +3.07705 q^{5} +0.718722 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.48344 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.718722 q^{3} +1.00000 q^{4} +3.07705 q^{5} +0.718722 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.48344 q^{9} +3.07705 q^{10} +5.70212 q^{11} +0.718722 q^{12} -5.09419 q^{13} -1.00000 q^{14} +2.21154 q^{15} +1.00000 q^{16} +0.718085 q^{17} -2.48344 q^{18} -5.60157 q^{19} +3.07705 q^{20} -0.718722 q^{21} +5.70212 q^{22} +6.84741 q^{23} +0.718722 q^{24} +4.46822 q^{25} -5.09419 q^{26} -3.94107 q^{27} -1.00000 q^{28} -1.61552 q^{29} +2.21154 q^{30} +8.84864 q^{31} +1.00000 q^{32} +4.09824 q^{33} +0.718085 q^{34} -3.07705 q^{35} -2.48344 q^{36} +7.02715 q^{37} -5.60157 q^{38} -3.66130 q^{39} +3.07705 q^{40} +9.54762 q^{41} -0.718722 q^{42} -2.94933 q^{43} +5.70212 q^{44} -7.64166 q^{45} +6.84741 q^{46} +8.41052 q^{47} +0.718722 q^{48} +1.00000 q^{49} +4.46822 q^{50} +0.516103 q^{51} -5.09419 q^{52} -12.2287 q^{53} -3.94107 q^{54} +17.5457 q^{55} -1.00000 q^{56} -4.02597 q^{57} -1.61552 q^{58} +12.4210 q^{59} +2.21154 q^{60} -1.32428 q^{61} +8.84864 q^{62} +2.48344 q^{63} +1.00000 q^{64} -15.6751 q^{65} +4.09824 q^{66} +1.89696 q^{67} +0.718085 q^{68} +4.92138 q^{69} -3.07705 q^{70} +10.4179 q^{71} -2.48344 q^{72} -5.09389 q^{73} +7.02715 q^{74} +3.21141 q^{75} -5.60157 q^{76} -5.70212 q^{77} -3.66130 q^{78} +4.77803 q^{79} +3.07705 q^{80} +4.61779 q^{81} +9.54762 q^{82} +9.55400 q^{83} -0.718722 q^{84} +2.20958 q^{85} -2.94933 q^{86} -1.16111 q^{87} +5.70212 q^{88} +13.6962 q^{89} -7.64166 q^{90} +5.09419 q^{91} +6.84741 q^{92} +6.35971 q^{93} +8.41052 q^{94} -17.2363 q^{95} +0.718722 q^{96} -10.3975 q^{97} +1.00000 q^{98} -14.1609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.718722	0.414954	0.207477	−	0.978240i	$-0.433475\pi$
$3$	0.718722	0.414954	0.207477	+	0.978240i	$0.433475\pi$
$4$	1.00000	0.500000
$5$	3.07705	1.37610	0.688049	−	0.725665i	$-0.258468\pi$
$5$	3.07705	1.37610	0.688049	+	0.725665i	$0.258468\pi$
$6$	0.718722	0.293417
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.48344	−0.827813
$10$	3.07705	0.973048
$11$	5.70212	1.71925	0.859627	−	0.510922i	$-0.170696\pi$
$11$	5.70212	1.71925	0.859627	+	0.510922i	$0.170696\pi$
$12$	0.718722	0.207477
$13$	−5.09419	−1.41287	−0.706437	−	0.707776i	$-0.749698\pi$
$13$	−5.09419	−1.41287	−0.706437	+	0.707776i	$0.749698\pi$
$14$	−1.00000	−0.267261
$15$	2.21154	0.571017
$16$	1.00000	0.250000
$17$	0.718085	0.174161	0.0870805	−	0.996201i	$-0.472246\pi$
$17$	0.718085	0.174161	0.0870805	+	0.996201i	$0.472246\pi$
$18$	−2.48344	−0.585352
$19$	−5.60157	−1.28509	−0.642544	−	0.766249i	$-0.722121\pi$
$19$	−5.60157	−1.28509	−0.642544	+	0.766249i	$0.722121\pi$
$20$	3.07705	0.688049
$21$	−0.718722	−0.156838
$22$	5.70212	1.21570
$23$	6.84741	1.42778	0.713892	−	0.700256i	$-0.246931\pi$
$23$	6.84741	1.42778	0.713892	+	0.700256i	$0.246931\pi$
$24$	0.718722	0.146708
$25$	4.46822	0.893644
$26$	−5.09419	−0.999052
$27$	−3.94107	−0.758459
$28$	−1.00000	−0.188982
$29$	−1.61552	−0.299994	−0.149997	−	0.988686i	$-0.547926\pi$
$29$	−1.61552	−0.299994	−0.149997	+	0.988686i	$0.547926\pi$
$30$	2.21154	0.403770
$31$	8.84864	1.58926	0.794631	−	0.607093i	$-0.207664\pi$
$31$	8.84864	1.58926	0.794631	+	0.607093i	$0.207664\pi$
$32$	1.00000	0.176777
$33$	4.09824	0.713412
$34$	0.718085	0.123150
$35$	−3.07705	−0.520116
$36$	−2.48344	−0.413906
$37$	7.02715	1.15526	0.577628	−	0.816300i	$-0.303978\pi$
$37$	7.02715	1.15526	0.577628	+	0.816300i	$0.303978\pi$
$38$	−5.60157	−0.908694
$39$	−3.66130	−0.586278
$40$	3.07705	0.486524
$41$	9.54762	1.49109	0.745544	−	0.666456i	$-0.232190\pi$
$41$	9.54762	1.49109	0.745544	+	0.666456i	$0.232190\pi$
$42$	−0.718722	−0.110901
$43$	−2.94933	−0.449768	−0.224884	−	0.974386i	$-0.572200\pi$
$43$	−2.94933	−0.449768	−0.224884	+	0.974386i	$0.572200\pi$
$44$	5.70212	0.859627
$45$	−7.64166	−1.13915
$46$	6.84741	1.00960
$47$	8.41052	1.22680	0.613400	−	0.789772i	$-0.289801\pi$
$47$	8.41052	1.22680	0.613400	+	0.789772i	$0.289801\pi$
$48$	0.718722	0.103739
$49$	1.00000	0.142857
$50$	4.46822	0.631901
$51$	0.516103	0.0722689
$52$	−5.09419	−0.706437
$53$	−12.2287	−1.67974	−0.839870	−	0.542787i	$-0.817369\pi$
$53$	−12.2287	−1.67974	−0.839870	+	0.542787i	$0.817369\pi$
$54$	−3.94107	−0.536311
$55$	17.5457	2.36586
$56$	−1.00000	−0.133631
$57$	−4.02597	−0.533253
$58$	−1.61552	−0.212128
$59$	12.4210	1.61707	0.808536	−	0.588446i	$-0.200260\pi$
$59$	12.4210	1.61707	0.808536	+	0.588446i	$0.200260\pi$
$60$	2.21154	0.285509
$61$	−1.32428	−0.169557	−0.0847783	−	0.996400i	$-0.527018\pi$
$61$	−1.32428	−0.169557	−0.0847783	+	0.996400i	$0.527018\pi$
$62$	8.84864	1.12378
$63$	2.48344	0.312884
$64$	1.00000	0.125000
$65$	−15.6751	−1.94425
$66$	4.09824	0.504458
$67$	1.89696	0.231751	0.115875	−	0.993264i	$-0.463033\pi$
$67$	1.89696	0.231751	0.115875	+	0.993264i	$0.463033\pi$
$68$	0.718085	0.0870805
$69$	4.92138	0.592465
$70$	−3.07705	−0.367777
$71$	10.4179	1.23637	0.618186	−	0.786032i	$-0.287868\pi$
$71$	10.4179	1.23637	0.618186	+	0.786032i	$0.287868\pi$
$72$	−2.48344	−0.292676
$73$	−5.09389	−0.596194	−0.298097	−	0.954536i	$-0.596352\pi$
$73$	−5.09389	−0.596194	−0.298097	+	0.954536i	$0.596352\pi$
$74$	7.02715	0.816890
$75$	3.21141	0.370821
$76$	−5.60157	−0.642544
$77$	−5.70212	−0.649817
$78$	−3.66130	−0.414561
$79$	4.77803	0.537570	0.268785	−	0.963200i	$-0.413378\pi$
$79$	4.77803	0.537570	0.268785	+	0.963200i	$0.413378\pi$
$80$	3.07705	0.344024
$81$	4.61779	0.513087
$82$	9.54762	1.05436
$83$	9.55400	1.04869	0.524344	−	0.851507i	$-0.324311\pi$
$83$	9.55400	1.04869	0.524344	+	0.851507i	$0.324311\pi$
$84$	−0.718722	−0.0784190
$85$	2.20958	0.239663
$86$	−2.94933	−0.318034
$87$	−1.16111	−0.124484
$88$	5.70212	0.607848
$89$	13.6962	1.45179	0.725896	−	0.687804i	$-0.241425\pi$
$89$	13.6962	1.45179	0.725896	+	0.687804i	$0.241425\pi$
$90$	−7.64166	−0.805502
$91$	5.09419	0.534016
$92$	6.84741	0.713892
$93$	6.35971	0.659471
$94$	8.41052	0.867479
$95$	−17.2363	−1.76841
$96$	0.718722	0.0733542
$97$	−10.3975	−1.05570	−0.527851	−	0.849337i	$-0.677002\pi$
$97$	−10.3975	−1.05570	−0.527851	+	0.849337i	$0.677002\pi$
$98$	1.00000	0.101015
$99$	−14.1609	−1.42322
$100$	4.46822	0.446822
$101$	9.85702	0.980810	0.490405	−	0.871495i	$-0.336849\pi$
$101$	9.85702	0.980810	0.490405	+	0.871495i	$0.336849\pi$
$102$	0.516103	0.0511018
$103$	8.57857	0.845271	0.422636	−	0.906300i	$-0.361105\pi$
$103$	8.57857	0.845271	0.422636	+	0.906300i	$0.361105\pi$
$104$	−5.09419	−0.499526
$105$	−2.21154	−0.215824
$106$	−12.2287	−1.18776
$107$	−15.2940	−1.47852	−0.739261	−	0.673419i	$-0.764825\pi$
$107$	−15.2940	−1.47852	−0.739261	+	0.673419i	$0.764825\pi$
$108$	−3.94107	−0.379229
$109$	18.0379	1.72772	0.863858	−	0.503735i	$-0.168041\pi$
$109$	18.0379	1.72772	0.863858	+	0.503735i	$0.168041\pi$
$110$	17.5457	1.67292
$111$	5.05057	0.479379
$112$	−1.00000	−0.0944911
$113$	−20.4930	−1.92782	−0.963909	−	0.266233i	$-0.914221\pi$
$113$	−20.4930	−1.92782	−0.963909	+	0.266233i	$0.914221\pi$
$114$	−4.02597	−0.377067
$115$	21.0698	1.96477
$116$	−1.61552	−0.149997
$117$	12.6511	1.16959
$118$	12.4210	1.14344
$119$	−0.718085	−0.0658267
$120$	2.21154	0.201885
$121$	21.5142	1.95584
$122$	−1.32428	−0.119895
$123$	6.86208	0.618733
$124$	8.84864	0.794631
$125$	−1.63632	−0.146357
$126$	2.48344	0.221242
$127$	−19.4719	−1.72785	−0.863925	−	0.503620i	$-0.832001\pi$
$127$	−19.4719	−1.72785	−0.863925	+	0.503620i	$0.832001\pi$
$128$	1.00000	0.0883883
$129$	−2.11975	−0.186633
$130$	−15.6751	−1.37479
$131$	12.7508	1.11404	0.557020	−	0.830499i	$-0.311945\pi$
$131$	12.7508	1.11404	0.557020	+	0.830499i	$0.311945\pi$
$132$	4.09824	0.356706
$133$	5.60157	0.485718
$134$	1.89696	0.163872
$135$	−12.1268	−1.04371
$136$	0.718085	0.0615752
$137$	−0.593065	−0.0506690	−0.0253345	−	0.999679i	$-0.508065\pi$
$137$	−0.593065	−0.0506690	−0.0253345	+	0.999679i	$0.508065\pi$
$138$	4.92138	0.418936
$139$	−18.0068	−1.52732	−0.763660	−	0.645618i	$-0.776600\pi$
$139$	−18.0068	−1.52732	−0.763660	+	0.645618i	$0.776600\pi$
$140$	−3.07705	−0.260058
$141$	6.04482	0.509066
$142$	10.4179	0.874247
$143$	−29.0477	−2.42909
$144$	−2.48344	−0.206953
$145$	−4.97102	−0.412820
$146$	−5.09389	−0.421573
$147$	0.718722	0.0592792
$148$	7.02715	0.577628
$149$	−9.38816	−0.769108	−0.384554	−	0.923102i	$-0.625645\pi$
$149$	−9.38816	−0.769108	−0.384554	+	0.923102i	$0.625645\pi$
$150$	3.21141	0.262210
$151$	13.0851	1.06485	0.532427	−	0.846476i	$-0.321280\pi$
$151$	13.0851	1.06485	0.532427	+	0.846476i	$0.321280\pi$
$152$	−5.60157	−0.454347
$153$	−1.78332	−0.144173
$154$	−5.70212	−0.459490
$155$	27.2277	2.18698
$156$	−3.66130	−0.293139
$157$	−6.56392	−0.523858	−0.261929	−	0.965087i	$-0.584359\pi$
$157$	−6.56392	−0.523858	−0.261929	+	0.965087i	$0.584359\pi$
$158$	4.77803	0.380120
$159$	−8.78903	−0.697015
$160$	3.07705	0.243262
$161$	−6.84741	−0.539651
$162$	4.61779	0.362808
$163$	−18.9292	−1.48265	−0.741325	−	0.671146i	$-0.765802\pi$
$163$	−18.9292	−1.48265	−0.741325	+	0.671146i	$0.765802\pi$
$164$	9.54762	0.745544
$165$	12.6105	0.981724
$166$	9.55400	0.741534
$167$	−8.24406	−0.637944	−0.318972	−	0.947764i	$-0.603338\pi$
$167$	−8.24406	−0.637944	−0.318972	+	0.947764i	$0.603338\pi$
$168$	−0.718722	−0.0554506
$169$	12.9507	0.996210
$170$	2.20958	0.169467
$171$	13.9112	1.06381
$172$	−2.94933	−0.224884
$173$	−6.97818	−0.530541	−0.265271	−	0.964174i	$-0.585461\pi$
$173$	−6.97818	−0.530541	−0.265271	+	0.964174i	$0.585461\pi$
$174$	−1.16111	−0.0880232
$175$	−4.46822	−0.337766
$176$	5.70212	0.429814
$177$	8.92722	0.671011
$178$	13.6962	1.02657
$179$	7.98797	0.597049	0.298525	−	0.954402i	$-0.403506\pi$
$179$	7.98797	0.597049	0.298525	+	0.954402i	$0.403506\pi$
$180$	−7.64166	−0.569576
$181$	−1.18551	−0.0881179	−0.0440590	−	0.999029i	$-0.514029\pi$
$181$	−1.18551	−0.0881179	−0.0440590	+	0.999029i	$0.514029\pi$
$182$	5.09419	0.377606
$183$	−0.951788	−0.0703582
$184$	6.84741	0.504798
$185$	21.6229	1.58975
$186$	6.35971	0.466316
$187$	4.09461	0.299427
$188$	8.41052	0.613400
$189$	3.94107	0.286670
$190$	−17.2363	−1.25045
$191$	−17.3136	−1.25277	−0.626384	−	0.779515i	$-0.715466\pi$
$191$	−17.3136	−1.25277	−0.626384	+	0.779515i	$0.715466\pi$
$192$	0.718722	0.0518693
$193$	−11.2090	−0.806843	−0.403421	−	0.915014i	$-0.632179\pi$
$193$	−11.2090	−0.806843	−0.403421	+	0.915014i	$0.632179\pi$
$194$	−10.3975	−0.746495
$195$	−11.2660	−0.806775
$196$	1.00000	0.0714286
$197$	−5.88784	−0.419491	−0.209746	−	0.977756i	$-0.567264\pi$
$197$	−5.88784	−0.419491	−0.209746	+	0.977756i	$0.567264\pi$
$198$	−14.1609	−1.00637
$199$	−6.03880	−0.428079	−0.214040	−	0.976825i	$-0.568662\pi$
$199$	−6.03880	−0.428079	−0.214040	+	0.976825i	$0.568662\pi$
$200$	4.46822	0.315951
$201$	1.36339	0.0961659
$202$	9.85702	0.693538
$203$	1.61552	0.113387
$204$	0.516103	0.0361344
$205$	29.3785	2.05188
$206$	8.57857	0.597697
$207$	−17.0051	−1.18194
$208$	−5.09419	−0.353218
$209$	−31.9408	−2.20939
$210$	−2.21154	−0.152611
$211$	−13.1967	−0.908495	−0.454248	−	0.890876i	$-0.650092\pi$
$211$	−13.1967	−0.908495	−0.454248	+	0.890876i	$0.650092\pi$
$212$	−12.2287	−0.839870
$213$	7.48754	0.513038
$214$	−15.2940	−1.04547
$215$	−9.07522	−0.618925
$216$	−3.94107	−0.268156
$217$	−8.84864	−0.600685
$218$	18.0379	1.22168
$219$	−3.66109	−0.247393
$220$	17.5457	1.18293
$221$	−3.65806	−0.246068
$222$	5.05057	0.338972
$223$	−21.9048	−1.46685	−0.733426	−	0.679770i	$-0.762080\pi$
$223$	−21.9048	−1.46685	−0.733426	+	0.679770i	$0.762080\pi$
$224$	−1.00000	−0.0668153
$225$	−11.0965	−0.739770
$226$	−20.4930	−1.36317
$227$	2.36284	0.156827	0.0784137	−	0.996921i	$-0.475015\pi$
$227$	2.36284	0.156827	0.0784137	+	0.996921i	$0.475015\pi$
$228$	−4.02597	−0.266626
$229$	18.1301	1.19807	0.599037	−	0.800721i	$-0.295550\pi$
$229$	18.1301	1.19807	0.599037	+	0.800721i	$0.295550\pi$
$230$	21.0698	1.38930
$231$	−4.09824	−0.269644
$232$	−1.61552	−0.106064
$233$	−23.4169	−1.53409	−0.767045	−	0.641593i	$-0.778274\pi$
$233$	−23.4169	−1.53409	−0.767045	+	0.641593i	$0.778274\pi$
$234$	12.6511	0.827028
$235$	25.8796	1.68820
$236$	12.4210	0.808536
$237$	3.43407	0.223067
$238$	−0.718085	−0.0465465
$239$	−8.21163	−0.531166	−0.265583	−	0.964088i	$-0.585564\pi$
$239$	−8.21163	−0.531166	−0.265583	+	0.964088i	$0.585564\pi$
$240$	2.21154	0.142754
$241$	−11.4375	−0.736751	−0.368376	−	0.929677i	$-0.620086\pi$
$241$	−11.4375	−0.736751	−0.368376	+	0.929677i	$0.620086\pi$
$242$	21.5142	1.38299
$243$	15.1421	0.971366
$244$	−1.32428	−0.0847783
$245$	3.07705	0.196585
$246$	6.86208	0.437510
$247$	28.5354	1.81567
$248$	8.84864	0.561889
$249$	6.86667	0.435157
$250$	−1.63632	−0.103490
$251$	−3.51904	−0.222120	−0.111060	−	0.993814i	$-0.535425\pi$
$251$	−3.51904	−0.222120	−0.111060	+	0.993814i	$0.535425\pi$
$252$	2.48344	0.156442
$253$	39.0448	2.45472
$254$	−19.4719	−1.22177
$255$	1.58807	0.0994490
$256$	1.00000	0.0625000
$257$	13.9466	0.869962	0.434981	−	0.900440i	$-0.356755\pi$
$257$	13.9466	0.869962	0.434981	+	0.900440i	$0.356755\pi$
$258$	−2.11975	−0.131970
$259$	−7.02715	−0.436646
$260$	−15.6751	−0.972125
$261$	4.01203	0.248339
$262$	12.7508	0.787745
$263$	−1.45597	−0.0897790	−0.0448895	−	0.998992i	$-0.514294\pi$
$263$	−1.45597	−0.0897790	−0.0448895	+	0.998992i	$0.514294\pi$
$264$	4.09824	0.252229
$265$	−37.6283	−2.31149
$266$	5.60157	0.343454
$267$	9.84375	0.602427
$268$	1.89696	0.115875
$269$	−28.6253	−1.74531	−0.872657	−	0.488334i	$-0.837605\pi$
$269$	−28.6253	−1.74531	−0.872657	+	0.488334i	$0.837605\pi$
$270$	−12.1268	−0.738016
$271$	22.2686	1.35272	0.676359	−	0.736572i	$-0.263557\pi$
$271$	22.2686	1.35272	0.676359	+	0.736572i	$0.263557\pi$
$272$	0.718085	0.0435403
$273$	3.66130	0.221592
$274$	−0.593065	−0.0358284
$275$	25.4783	1.53640
$276$	4.92138	0.296232
$277$	24.9999	1.50210	0.751049	−	0.660247i	$-0.229548\pi$
$277$	24.9999	1.50210	0.751049	+	0.660247i	$0.229548\pi$
$278$	−18.0068	−1.07998
$279$	−21.9751	−1.31561
$280$	−3.07705	−0.183889
$281$	−11.2746	−0.672588	−0.336294	−	0.941757i	$-0.609174\pi$
$281$	−11.2746	−0.672588	−0.336294	+	0.941757i	$0.609174\pi$
$282$	6.04482	0.359964
$283$	1.18886	0.0706706	0.0353353	−	0.999376i	$-0.488750\pi$
$283$	1.18886	0.0706706	0.0353353	+	0.999376i	$0.488750\pi$
$284$	10.4179	0.618186
$285$	−12.3881	−0.733808
$286$	−29.0477	−1.71763
$287$	−9.54762	−0.563578
$288$	−2.48344	−0.146338
$289$	−16.4844	−0.969668
$290$	−4.97102	−0.291908
$291$	−7.47289	−0.438068
$292$	−5.09389	−0.298097
$293$	−13.1745	−0.769664	−0.384832	−	0.922987i	$-0.625741\pi$
$293$	−13.1745	−0.769664	−0.384832	+	0.922987i	$0.625741\pi$
$294$	0.718722	0.0419167
$295$	38.2199	2.22525
$296$	7.02715	0.408445
$297$	−22.4724	−1.30398
$298$	−9.38816	−0.543842
$299$	−34.8820	−2.01728
$300$	3.21141	0.185411
$301$	2.94933	0.169996
$302$	13.0851	0.752965
$303$	7.08446	0.406991
$304$	−5.60157	−0.321272
$305$	−4.07487	−0.233326
$306$	−1.78332	−0.101946
$307$	−10.3457	−0.590458	−0.295229	−	0.955427i	$-0.595396\pi$
$307$	−10.3457	−0.590458	−0.295229	+	0.955427i	$0.595396\pi$
$308$	−5.70212	−0.324909
$309$	6.16560	0.350749
$310$	27.2277	1.54643
$311$	7.32706	0.415479	0.207740	−	0.978184i	$-0.433389\pi$
$311$	7.32706	0.415479	0.207740	+	0.978184i	$0.433389\pi$
$312$	−3.66130	−0.207280
$313$	7.29624	0.412408	0.206204	−	0.978509i	$-0.433889\pi$
$313$	7.29624	0.412408	0.206204	+	0.978509i	$0.433889\pi$
$314$	−6.56392	−0.370423
$315$	7.64166	0.430559
$316$	4.77803	0.268785
$317$	15.6404	0.878453	0.439226	−	0.898376i	$-0.355253\pi$
$317$	15.6404	0.878453	0.439226	+	0.898376i	$0.355253\pi$
$318$	−8.78903	−0.492864
$319$	−9.21186	−0.515765
$320$	3.07705	0.172012
$321$	−10.9921	−0.613519
$322$	−6.84741	−0.381591
$323$	−4.02240	−0.223812
$324$	4.61779	0.256544
$325$	−22.7619	−1.26260
$326$	−18.9292	−1.04839
$327$	12.9642	0.716923
$328$	9.54762	0.527179
$329$	−8.41052	−0.463687
$330$	12.6105	0.694184
$331$	1.56111	0.0858064	0.0429032	−	0.999079i	$-0.486339\pi$
$331$	1.56111	0.0858064	0.0429032	+	0.999079i	$0.486339\pi$
$332$	9.55400	0.524344
$333$	−17.4515	−0.956336
$334$	−8.24406	−0.451095
$335$	5.83703	0.318911
$336$	−0.718722	−0.0392095
$337$	−23.2897	−1.26867	−0.634334	−	0.773059i	$-0.718726\pi$
$337$	−23.2897	−1.26867	−0.634334	+	0.773059i	$0.718726\pi$
$338$	12.9507	0.704427
$339$	−14.7288	−0.799956
$340$	2.20958	0.119831
$341$	50.4560	2.73235
$342$	13.9112	0.752229
$343$	−1.00000	−0.0539949
$344$	−2.94933	−0.159017
$345$	15.1433	0.815289
$346$	−6.97818	−0.375149
$347$	−16.5736	−0.889718	−0.444859	−	0.895601i	$-0.646746\pi$
$347$	−16.5736	−0.889718	−0.444859	+	0.895601i	$0.646746\pi$
$348$	−1.16111	−0.0622418
$349$	9.68580	0.518469	0.259234	−	0.965814i	$-0.416530\pi$
$349$	9.68580	0.518469	0.259234	+	0.965814i	$0.416530\pi$
$350$	−4.46822	−0.238836
$351$	20.0765	1.07161
$352$	5.70212	0.303924
$353$	26.1261	1.39055	0.695277	−	0.718742i	$-0.255282\pi$
$353$	26.1261	1.39055	0.695277	+	0.718742i	$0.255282\pi$
$354$	8.92722	0.474476
$355$	32.0562	1.70137
$356$	13.6962	0.725896
$357$	−0.516103	−0.0273151
$358$	7.98797	0.422178
$359$	−9.06291	−0.478322	−0.239161	−	0.970980i	$-0.576872\pi$
$359$	−9.06291	−0.478322	−0.239161	+	0.970980i	$0.576872\pi$
$360$	−7.64166	−0.402751
$361$	12.3776	0.651451
$362$	−1.18551	−0.0623088
$363$	15.4627	0.811583
$364$	5.09419	0.267008
$365$	−15.6741	−0.820421
$366$	−0.951788	−0.0497508
$367$	−2.68221	−0.140010	−0.0700052	−	0.997547i	$-0.522302\pi$
$367$	−2.68221	−0.140010	−0.0700052	+	0.997547i	$0.522302\pi$
$368$	6.84741	0.356946
$369$	−23.7109	−1.23434
$370$	21.6229	1.12412
$371$	12.2287	0.634882
$372$	6.35971	0.329736
$373$	12.4727	0.645810	0.322905	−	0.946431i	$-0.395341\pi$
$373$	12.4727	0.645810	0.322905	+	0.946431i	$0.395341\pi$
$374$	4.09461	0.211727
$375$	−1.17606	−0.0607314
$376$	8.41052	0.433739
$377$	8.22973	0.423853
$378$	3.94107	0.202707
$379$	34.1914	1.75629	0.878147	−	0.478390i	$-0.158780\pi$
$379$	34.1914	1.75629	0.878147	+	0.478390i	$0.158780\pi$
$380$	−17.2363	−0.884203
$381$	−13.9949	−0.716979
$382$	−17.3136	−0.885840
$383$	−25.1376	−1.28447	−0.642236	−	0.766507i	$-0.721993\pi$
$383$	−25.1376	−1.28447	−0.642236	+	0.766507i	$0.721993\pi$
$384$	0.718722	0.0366771
$385$	−17.5457	−0.894212
$386$	−11.2090	−0.570524
$387$	7.32447	0.372324
$388$	−10.3975	−0.527851
$389$	−11.1545	−0.565556	−0.282778	−	0.959185i	$-0.591256\pi$
$389$	−11.1545	−0.565556	−0.282778	+	0.959185i	$0.591256\pi$
$390$	−11.2660	−0.570476
$391$	4.91702	0.248664
$392$	1.00000	0.0505076
$393$	9.16425	0.462275
$394$	−5.88784	−0.296625
$395$	14.7022	0.739749
$396$	−14.1609	−0.711611
$397$	23.3206	1.17043	0.585214	−	0.810879i	$-0.301010\pi$
$397$	23.3206	1.17043	0.585214	+	0.810879i	$0.301010\pi$
$398$	−6.03880	−0.302698
$399$	4.02597	0.201551
$400$	4.46822	0.223411
$401$	−34.9485	−1.74525	−0.872623	−	0.488394i	$-0.837583\pi$
$401$	−34.9485	−1.74525	−0.872623	+	0.488394i	$0.837583\pi$
$402$	1.36339	0.0679995
$403$	−45.0766	−2.24543
$404$	9.85702	0.490405
$405$	14.2091	0.706058
$406$	1.61552	0.0801767
$407$	40.0697	1.98618
$408$	0.516103	0.0255509
$409$	11.9857	0.592652	0.296326	−	0.955087i	$-0.404238\pi$
$409$	11.9857	0.592652	0.296326	+	0.955087i	$0.404238\pi$
$410$	29.3785	1.45090
$411$	−0.426249	−0.0210253
$412$	8.57857	0.422636
$413$	−12.4210	−0.611196
$414$	−17.0051	−0.835756
$415$	29.3981	1.44310
$416$	−5.09419	−0.249763
$417$	−12.9419	−0.633768
$418$	−31.9408	−1.56228
$419$	−22.2461	−1.08679	−0.543396	−	0.839477i	$-0.682862\pi$
$419$	−22.2461	−1.08679	−0.543396	+	0.839477i	$0.682862\pi$
$420$	−2.21154	−0.107912
$421$	4.36876	0.212921	0.106460	−	0.994317i	$-0.466048\pi$
$421$	4.36876	0.212921	0.106460	+	0.994317i	$0.466048\pi$
$422$	−13.1967	−0.642403
$423$	−20.8870	−1.01556
$424$	−12.2287	−0.593878
$425$	3.20856	0.155638
$426$	7.48754	0.362773
$427$	1.32428	0.0640863
$428$	−15.2940	−0.739261
$429$	−20.8772	−1.00796
$430$	−9.07522	−0.437646
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−3.94107	−0.189615
$433$	33.2489	1.59784	0.798921	−	0.601436i	$-0.205405\pi$
$433$	33.2489	1.59784	0.798921	+	0.601436i	$0.205405\pi$
$434$	−8.84864	−0.424748
$435$	−3.57278	−0.171302
$436$	18.0379	0.863858
$437$	−38.3562	−1.83483
$438$	−3.66109	−0.174934
$439$	1.79752	0.0857910	0.0428955	−	0.999080i	$-0.486342\pi$
$439$	1.79752	0.0857910	0.0428955	+	0.999080i	$0.486342\pi$
$440$	17.5457	0.836458
$441$	−2.48344	−0.118259
$442$	−3.65806	−0.173996
$443$	6.79267	0.322729	0.161365	−	0.986895i	$-0.448410\pi$
$443$	6.79267	0.322729	0.161365	+	0.986895i	$0.448410\pi$
$444$	5.05057	0.239689
$445$	42.1438	1.99781
$446$	−21.9048	−1.03722
$447$	−6.74748	−0.319145
$448$	−1.00000	−0.0472456
$449$	−26.4556	−1.24852	−0.624258	−	0.781218i	$-0.714599\pi$
$449$	−26.4556	−1.24852	−0.624258	+	0.781218i	$0.714599\pi$
$450$	−11.0965	−0.523096
$451$	54.4417	2.56356
$452$	−20.4930	−0.963909
$453$	9.40458	0.441866
$454$	2.36284	0.110894
$455$	15.6751	0.734858
$456$	−4.02597	−0.188533
$457$	−14.1709	−0.662888	−0.331444	−	0.943475i	$-0.607536\pi$
$457$	−14.1709	−0.662888	−0.331444	+	0.943475i	$0.607536\pi$
$458$	18.1301	0.847166
$459$	−2.83002	−0.132094
$460$	21.0698	0.982384
$461$	−37.7411	−1.75778	−0.878888	−	0.477028i	$-0.841714\pi$
$461$	−37.7411	−1.75778	−0.878888	+	0.477028i	$0.841714\pi$
$462$	−4.09824	−0.190667
$463$	2.35034	0.109229	0.0546147	−	0.998508i	$-0.482607\pi$
$463$	2.35034	0.109229	0.0546147	+	0.998508i	$0.482607\pi$
$464$	−1.61552	−0.0749984
$465$	19.5691	0.907496
$466$	−23.4169	−1.08477
$467$	−13.7104	−0.634439	−0.317220	−	0.948352i	$-0.602749\pi$
$467$	−13.7104	−0.634439	−0.317220	+	0.948352i	$0.602749\pi$
$468$	12.6511	0.584797
$469$	−1.89696	−0.0875935
$470$	25.8796	1.19374
$471$	−4.71763	−0.217377
$472$	12.4210	0.571721
$473$	−16.8174	−0.773266
$474$	3.43407	0.157732
$475$	−25.0290	−1.14841
$476$	−0.718085	−0.0329134
$477$	30.3692	1.39051
$478$	−8.21163	−0.375591
$479$	−8.48690	−0.387776	−0.193888	−	0.981024i	$-0.562110\pi$
$479$	−8.48690	−0.387776	−0.193888	+	0.981024i	$0.562110\pi$
$480$	2.21154	0.100943
$481$	−35.7976	−1.63223
$482$	−11.4375	−0.520962
$483$	−4.92138	−0.223931
$484$	21.5142	0.977918
$485$	−31.9935	−1.45275
$486$	15.1421	0.686860
$487$	−0.0977135	−0.00442782	−0.00221391	−	0.999998i	$-0.500705\pi$
$487$	−0.0977135	−0.00442782	−0.00221391	+	0.999998i	$0.500705\pi$
$488$	−1.32428	−0.0599473
$489$	−13.6048	−0.615232
$490$	3.07705	0.139007
$491$	10.7493	0.485109	0.242555	−	0.970138i	$-0.422015\pi$
$491$	10.7493	0.485109	0.242555	+	0.970138i	$0.422015\pi$
$492$	6.86208	0.309367
$493$	−1.16008	−0.0522472
$494$	28.5354	1.28387
$495$	−43.5737	−1.95849
$496$	8.84864	0.397316
$497$	−10.4179	−0.467305
$498$	6.86667	0.307703
$499$	−13.0640	−0.584824	−0.292412	−	0.956292i	$-0.594458\pi$
$499$	−13.0640	−0.584824	−0.292412	+	0.956292i	$0.594458\pi$
$500$	−1.63632	−0.0731784
$501$	−5.92518	−0.264718
$502$	−3.51904	−0.157062
$503$	−33.5239	−1.49476	−0.747379	−	0.664398i	$-0.768688\pi$
$503$	−33.5239	−1.49476	−0.747379	+	0.664398i	$0.768688\pi$
$504$	2.48344	0.110621
$505$	30.3305	1.34969
$506$	39.0448	1.73575
$507$	9.30797	0.413382
$508$	−19.4719	−0.863925
$509$	−13.5163	−0.599099	−0.299550	−	0.954081i	$-0.596836\pi$
$509$	−13.5163	−0.599099	−0.299550	+	0.954081i	$0.596836\pi$
$510$	1.58807	0.0703211
$511$	5.09389	0.225340
$512$	1.00000	0.0441942
$513$	22.0762	0.974686
$514$	13.9466	0.615156
$515$	26.3967	1.16318
$516$	−2.11975	−0.0933166
$517$	47.9578	2.10918
$518$	−7.02715	−0.308755
$519$	−5.01537	−0.220150
$520$	−15.6751	−0.687396
$521$	0.967053	0.0423673	0.0211837	−	0.999776i	$-0.493257\pi$
$521$	0.967053	0.0423673	0.0211837	+	0.999776i	$0.493257\pi$
$522$	4.01203	0.175602
$523$	−5.70733	−0.249564	−0.124782	−	0.992184i	$-0.539823\pi$
$523$	−5.70733	−0.249564	−0.124782	+	0.992184i	$0.539823\pi$
$524$	12.7508	0.557020
$525$	−3.21141	−0.140157
$526$	−1.45597	−0.0634833
$527$	6.35407	0.276788
$528$	4.09824	0.178353
$529$	23.8870	1.03857
$530$	−37.6283	−1.63447
$531$	−30.8467	−1.33863
$532$	5.60157	0.242859
$533$	−48.6374	−2.10672
$534$	9.84375	0.425981
$535$	−47.0602	−2.03459
$536$	1.89696	0.0819362
$537$	5.74113	0.247748
$538$	−28.6253	−1.23412
$539$	5.70212	0.245608
$540$	−12.1268	−0.521856
$541$	17.6418	0.758482	0.379241	−	0.925298i	$-0.376185\pi$
$541$	17.6418	0.758482	0.379241	+	0.925298i	$0.376185\pi$
$542$	22.2686	0.956516
$543$	−0.852049	−0.0365649
$544$	0.718085	0.0307876
$545$	55.5034	2.37751
$546$	3.66130	0.156689
$547$	31.3322	1.33967	0.669833	−	0.742511i	$-0.266365\pi$
$547$	31.3322	1.33967	0.669833	+	0.742511i	$0.266365\pi$
$548$	−0.593065	−0.0253345
$549$	3.28877	0.140361
$550$	25.4783	1.08640
$551$	9.04942	0.385518
$552$	4.92138	0.209468
$553$	−4.77803	−0.203183
$554$	24.9999	1.06214
$555$	15.5408	0.659672
$556$	−18.0068	−0.763660
$557$	−20.8610	−0.883908	−0.441954	−	0.897038i	$-0.645715\pi$
$557$	−20.8610	−0.883908	−0.441954	+	0.897038i	$0.645715\pi$
$558$	−21.9751	−0.930278
$559$	15.0244	0.635465
$560$	−3.07705	−0.130029
$561$	2.94288	0.124249
$562$	−11.2746	−0.475591
$563$	31.8999	1.34442	0.672211	−	0.740360i	$-0.265345\pi$
$563$	31.8999	1.34442	0.672211	+	0.740360i	$0.265345\pi$
$564$	6.04482	0.254533
$565$	−63.0579	−2.65286
$566$	1.18886	0.0499716
$567$	−4.61779	−0.193929
$568$	10.4179	0.437124
$569$	15.0073	0.629140	0.314570	−	0.949234i	$-0.398140\pi$
$569$	15.0073	0.629140	0.314570	+	0.949234i	$0.398140\pi$
$570$	−12.3881	−0.518880
$571$	41.0978	1.71989	0.859945	−	0.510387i	$-0.170498\pi$
$571$	41.0978	1.71989	0.859945	+	0.510387i	$0.170498\pi$
$572$	−29.0477	−1.21454
$573$	−12.4437	−0.519841
$574$	−9.54762	−0.398510
$575$	30.5957	1.27593
$576$	−2.48344	−0.103477
$577$	−18.3041	−0.762008	−0.381004	−	0.924573i	$-0.624422\pi$
$577$	−18.3041	−0.762008	−0.381004	+	0.924573i	$0.624422\pi$
$578$	−16.4844	−0.685659
$579$	−8.05617	−0.334803
$580$	−4.97102	−0.206410
$581$	−9.55400	−0.396367
$582$	−7.47289	−0.309761
$583$	−69.7295	−2.88790
$584$	−5.09389	−0.210787
$585$	38.9280	1.60948
$586$	−13.1745	−0.544235
$587$	3.91144	0.161442	0.0807212	−	0.996737i	$-0.474278\pi$
$587$	3.91144	0.161442	0.0807212	+	0.996737i	$0.474278\pi$
$588$	0.718722	0.0296396
$589$	−49.5663	−2.04234
$590$	38.2199	1.57349
$591$	−4.23172	−0.174070
$592$	7.02715	0.288814
$593$	0.687861	0.0282471	0.0141235	−	0.999900i	$-0.495504\pi$
$593$	0.687861	0.0282471	0.0141235	+	0.999900i	$0.495504\pi$
$594$	−22.4724	−0.922056
$595$	−2.20958	−0.0905839
$596$	−9.38816	−0.384554
$597$	−4.34022	−0.177633
$598$	−34.8820	−1.42643
$599$	−45.0900	−1.84233	−0.921164	−	0.389174i	$-0.872760\pi$
$599$	−45.0900	−1.84233	−0.921164	+	0.389174i	$0.872760\pi$
$600$	3.21141	0.131105
$601$	19.0054	0.775246	0.387623	−	0.921818i	$-0.373296\pi$
$601$	19.0054	0.775246	0.387623	+	0.921818i	$0.373296\pi$
$602$	2.94933	0.120206
$603$	−4.71098	−0.191846
$604$	13.0851	0.532427
$605$	66.2002	2.69142
$606$	7.08446	0.287786
$607$	−22.2454	−0.902913	−0.451457	−	0.892293i	$-0.649095\pi$
$607$	−22.2454	−0.902913	−0.451457	+	0.892293i	$0.649095\pi$
$608$	−5.60157	−0.227174
$609$	1.16111	0.0470504
$610$	−4.07487	−0.164987
$611$	−42.8447	−1.73331
$612$	−1.78332	−0.0720864
$613$	36.9079	1.49070	0.745348	−	0.666676i	$-0.232284\pi$
$613$	36.9079	1.49070	0.745348	+	0.666676i	$0.232284\pi$
$614$	−10.3457	−0.417517
$615$	21.1150	0.851437
$616$	−5.70212	−0.229745
$617$	32.3117	1.30082	0.650409	−	0.759584i	$-0.274597\pi$
$617$	32.3117	1.30082	0.650409	+	0.759584i	$0.274597\pi$
$618$	6.16560	0.248017
$619$	−41.0267	−1.64900	−0.824502	−	0.565859i	$-0.808545\pi$
$619$	−41.0267	−1.64900	−0.824502	+	0.565859i	$0.808545\pi$
$620$	27.2277	1.09349
$621$	−26.9861	−1.08291
$622$	7.32706	0.293788
$623$	−13.6962	−0.548726
$624$	−3.66130	−0.146569
$625$	−27.3761	−1.09504
$626$	7.29624	0.291616
$627$	−22.9566	−0.916797
$628$	−6.56392	−0.261929
$629$	5.04609	0.201201
$630$	7.64166	0.304451
$631$	−17.9537	−0.714725	−0.357363	−	0.933966i	$-0.616324\pi$
$631$	−17.9537	−0.714725	−0.357363	+	0.933966i	$0.616324\pi$
$632$	4.77803	0.190060
$633$	−9.48472	−0.376984
$634$	15.6404	0.621160
$635$	−59.9159	−2.37769
$636$	−8.78903	−0.348508
$637$	−5.09419	−0.201839
$638$	−9.21186	−0.364701
$639$	−25.8721	−1.02348
$640$	3.07705	0.121631
$641$	41.3867	1.63468	0.817338	−	0.576158i	$-0.195449\pi$
$641$	41.3867	1.63468	0.817338	+	0.576158i	$0.195449\pi$
$642$	−10.9921	−0.433824
$643$	−14.8044	−0.583829	−0.291915	−	0.956444i	$-0.594292\pi$
$643$	−14.8044	−0.583829	−0.291915	+	0.956444i	$0.594292\pi$
$644$	−6.84741	−0.269826
$645$	−6.52256	−0.256825
$646$	−4.02240	−0.158259
$647$	16.4292	0.645899	0.322949	−	0.946416i	$-0.395326\pi$
$647$	16.4292	0.645899	0.322949	+	0.946416i	$0.395326\pi$
$648$	4.61779	0.181404
$649$	70.8259	2.78016
$650$	−22.7619	−0.892796
$651$	−6.35971	−0.249257
$652$	−18.9292	−0.741325
$653$	17.0577	0.667521	0.333760	−	0.942658i	$-0.391682\pi$
$653$	17.0577	0.667521	0.333760	+	0.942658i	$0.391682\pi$
$654$	12.9642	0.506941
$655$	39.2347	1.53303
$656$	9.54762	0.372772
$657$	12.6504	0.493537
$658$	−8.41052	−0.327876
$659$	34.2651	1.33478	0.667390	−	0.744709i	$-0.267412\pi$
$659$	34.2651	1.33478	0.667390	+	0.744709i	$0.267412\pi$
$660$	12.6105	0.490862
$661$	−25.8301	−1.00467	−0.502337	−	0.864672i	$-0.667526\pi$
$661$	−25.8301	−1.00467	−0.502337	+	0.864672i	$0.667526\pi$
$662$	1.56111	0.0606743
$663$	−2.62913	−0.102107
$664$	9.55400	0.370767
$665$	17.2363	0.668395
$666$	−17.4515	−0.676232
$667$	−11.0621	−0.428326
$668$	−8.24406	−0.318972
$669$	−15.7434	−0.608676
$670$	5.83703	0.225504
$671$	−7.55120	−0.291511
$672$	−0.718722	−0.0277253
$673$	9.33638	0.359891	0.179945	−	0.983677i	$-0.442408\pi$
$673$	9.33638	0.359891	0.179945	+	0.983677i	$0.442408\pi$
$674$	−23.2897	−0.897084
$675$	−17.6095	−0.677792
$676$	12.9507	0.498105
$677$	45.3033	1.74115	0.870573	−	0.492039i	$-0.163748\pi$
$677$	45.3033	1.74115	0.870573	+	0.492039i	$0.163748\pi$
$678$	−14.7288	−0.565654
$679$	10.3975	0.399018
$680$	2.20958	0.0847335
$681$	1.69823	0.0650762
$682$	50.4560	1.93206
$683$	17.9919	0.688442	0.344221	−	0.938889i	$-0.388143\pi$
$683$	17.9919	0.688442	0.344221	+	0.938889i	$0.388143\pi$
$684$	13.9112	0.531906
$685$	−1.82489	−0.0697254
$686$	−1.00000	−0.0381802
$687$	13.0305	0.497146
$688$	−2.94933	−0.112442
$689$	62.2952	2.37326
$690$	15.1433	0.576497
$691$	10.6845	0.406457	0.203228	−	0.979131i	$-0.434857\pi$
$691$	10.6845	0.406457	0.203228	+	0.979131i	$0.434857\pi$
$692$	−6.97818	−0.265271
$693$	14.1609	0.537927
$694$	−16.5736	−0.629126
$695$	−55.4079	−2.10174
$696$	−1.16111	−0.0440116
$697$	6.85600	0.259690
$698$	9.68580	0.366613
$699$	−16.8302	−0.636577
$700$	−4.46822	−0.168883
$701$	−17.1978	−0.649551	−0.324776	−	0.945791i	$-0.605289\pi$
$701$	−17.1978	−0.649551	−0.324776	+	0.945791i	$0.605289\pi$
$702$	20.0765	0.757740
$703$	−39.3631	−1.48461
$704$	5.70212	0.214907
$705$	18.6002	0.700524
$706$	26.1261	0.983270
$707$	−9.85702	−0.370711
$708$	8.92722	0.335505
$709$	−39.4439	−1.48134	−0.740672	−	0.671866i	$-0.765493\pi$
$709$	−39.4439	−1.48134	−0.740672	+	0.671866i	$0.765493\pi$
$710$	32.0562	1.20305
$711$	−11.8659	−0.445008
$712$	13.6962	0.513286
$713$	60.5902	2.26912
$714$	−0.516103	−0.0193147
$715$	−89.3811	−3.34266
$716$	7.98797	0.298525
$717$	−5.90188	−0.220410
$718$	−9.06291	−0.338225
$719$	38.2340	1.42589	0.712944	−	0.701221i	$-0.247361\pi$
$719$	38.2340	1.42589	0.712944	+	0.701221i	$0.247361\pi$
$720$	−7.64166	−0.284788
$721$	−8.57857	−0.319483
$722$	12.3776	0.460646
$723$	−8.22035	−0.305718
$724$	−1.18551	−0.0440590
$725$	−7.21847	−0.268087
$726$	15.4627	0.573876
$727$	41.9638	1.55635	0.778175	−	0.628047i	$-0.216145\pi$
$727$	41.9638	1.55635	0.778175	+	0.628047i	$0.216145\pi$
$728$	5.09419	0.188803
$729$	−2.97040	−0.110015
$730$	−15.6741	−0.580126
$731$	−2.11787	−0.0783321
$732$	−0.951788	−0.0351791
$733$	50.6019	1.86903	0.934513	−	0.355930i	$-0.115836\pi$
$733$	50.6019	1.86903	0.934513	+	0.355930i	$0.115836\pi$
$734$	−2.68221	−0.0990023
$735$	2.21154	0.0815739
$736$	6.84741	0.252399
$737$	10.8167	0.398438
$738$	−23.7109	−0.872812
$739$	−34.3759	−1.26454	−0.632269	−	0.774749i	$-0.717876\pi$
$739$	−34.3759	−1.26454	−0.632269	+	0.774749i	$0.717876\pi$
$740$	21.6229	0.794873
$741$	20.5090	0.753418
$742$	12.2287	0.448929
$743$	−10.3079	−0.378160	−0.189080	−	0.981962i	$-0.560551\pi$
$743$	−10.3079	−0.378160	−0.189080	+	0.981962i	$0.560551\pi$
$744$	6.35971	0.233158
$745$	−28.8878	−1.05837
$746$	12.4727	0.456656
$747$	−23.7268	−0.868117
$748$	4.09461	0.149714
$749$	15.2940	0.558829
$750$	−1.17606	−0.0429436
$751$	0.253486	0.00924983	0.00462491	−	0.999989i	$-0.498528\pi$
$751$	0.253486	0.00924983	0.00462491	+	0.999989i	$0.498528\pi$
$752$	8.41052	0.306700
$753$	−2.52921	−0.0921695
$754$	8.22973	0.299709
$755$	40.2636	1.46534
$756$	3.94107	0.143335
$757$	53.1929	1.93333	0.966665	−	0.256044i	$-0.0824190\pi$
$757$	53.1929	1.93333	0.966665	+	0.256044i	$0.0824190\pi$
$758$	34.1914	1.24189
$759$	28.0623	1.01860
$760$	−17.2363	−0.625226
$761$	−7.96530	−0.288742	−0.144371	−	0.989524i	$-0.546116\pi$
$761$	−7.96530	−0.288742	−0.144371	+	0.989524i	$0.546116\pi$
$762$	−13.9949	−0.506981
$763$	−18.0379	−0.653015
$764$	−17.3136	−0.626384
$765$	−5.48736	−0.198396
$766$	−25.1376	−0.908259
$767$	−63.2747	−2.28472
$768$	0.718722	0.0259346
$769$	19.6441	0.708384	0.354192	−	0.935173i	$-0.384756\pi$
$769$	19.6441	0.708384	0.354192	+	0.935173i	$0.384756\pi$
$770$	−17.5457	−0.632303
$771$	10.0237	0.360995
$772$	−11.2090	−0.403421
$773$	44.5339	1.60177	0.800887	−	0.598815i	$-0.204362\pi$
$773$	44.5339	1.60177	0.800887	+	0.598815i	$0.204362\pi$
$774$	7.32447	0.263273
$775$	39.5376	1.42023
$776$	−10.3975	−0.373247
$777$	−5.05057	−0.181188
$778$	−11.1545	−0.399909
$779$	−53.4817	−1.91618
$780$	−11.2660	−0.403388
$781$	59.4039	2.12564
$782$	4.91702	0.175832
$783$	6.36685	0.227533
$784$	1.00000	0.0357143
$785$	−20.1975	−0.720879
$786$	9.16425	0.326878
$787$	27.4623	0.978925	0.489463	−	0.872024i	$-0.337193\pi$
$787$	27.4623	0.978925	0.489463	+	0.872024i	$0.337193\pi$
$788$	−5.88784	−0.209746
$789$	−1.04644	−0.0372542
$790$	14.7022	0.523082
$791$	20.4930	0.728647
$792$	−14.1609	−0.503185
$793$	6.74612	0.239562
$794$	23.3206	0.827618
$795$	−27.0443	−0.959161
$796$	−6.03880	−0.214040
$797$	41.9728	1.48675	0.743377	−	0.668873i	$-0.233223\pi$
$797$	41.9728	1.48675	0.743377	+	0.668873i	$0.233223\pi$
$798$	4.02597	0.142518
$799$	6.03946	0.213661
$800$	4.46822	0.157975
$801$	−34.0136	−1.20181
$802$	−34.9485	−1.23408
$803$	−29.0460	−1.02501
$804$	1.36339	0.0480829
$805$	−21.0698	−0.742613
$806$	−45.0766	−1.58776
$807$	−20.5736	−0.724225
$808$	9.85702	0.346769
$809$	−15.2565	−0.536389	−0.268195	−	0.963365i	$-0.586427\pi$
$809$	−15.2565	−0.536389	−0.268195	+	0.963365i	$0.586427\pi$
$810$	14.2091	0.499258
$811$	−23.4166	−0.822269	−0.411134	−	0.911575i	$-0.634867\pi$
$811$	−23.4166	−0.822269	−0.411134	+	0.911575i	$0.634867\pi$
$812$	1.61552	0.0566935
$813$	16.0049	0.561316
$814$	40.0697	1.40444
$815$	−58.2461	−2.04027
$816$	0.516103	0.0180672
$817$	16.5209	0.577992
$818$	11.9857	0.419068
$819$	−12.6511	−0.442065
$820$	29.3785	1.02594
$821$	19.2936	0.673350	0.336675	−	0.941621i	$-0.390698\pi$
$821$	19.2936	0.673350	0.336675	+	0.941621i	$0.390698\pi$
$822$	−0.426249	−0.0148671
$823$	−48.5091	−1.69092	−0.845460	−	0.534039i	$-0.820674\pi$
$823$	−48.5091	−1.69092	−0.845460	+	0.534039i	$0.820674\pi$
$824$	8.57857	0.298849
$825$	18.3118	0.637536
$826$	−12.4210	−0.432181
$827$	28.3056	0.984281	0.492141	−	0.870516i	$-0.336215\pi$
$827$	28.3056	0.984281	0.492141	+	0.870516i	$0.336215\pi$
$828$	−17.0051	−0.590969
$829$	37.9979	1.31972	0.659860	−	0.751388i	$-0.270615\pi$
$829$	37.9979	1.31972	0.659860	+	0.751388i	$0.270615\pi$
$830$	29.3981	1.02042
$831$	17.9680	0.623301
$832$	−5.09419	−0.176609
$833$	0.718085	0.0248802
$834$	−12.9419	−0.448142
$835$	−25.3674	−0.877874
$836$	−31.9408	−1.10470
$837$	−34.8731	−1.20539
$838$	−22.2461	−0.768477
$839$	3.31713	0.114520	0.0572601	−	0.998359i	$-0.481764\pi$
$839$	3.31713	0.114520	0.0572601	+	0.998359i	$0.481764\pi$
$840$	−2.21154	−0.0763054
$841$	−26.3901	−0.910004
$842$	4.36876	0.150558
$843$	−8.10332	−0.279093
$844$	−13.1967	−0.454248
$845$	39.8500	1.37088
$846$	−20.8870	−0.718110
$847$	−21.5142	−0.739237
$848$	−12.2287	−0.419935
$849$	0.854462	0.0293251
$850$	3.20856	0.110053
$851$	48.1178	1.64946
$852$	7.48754	0.256519
$853$	−39.9200	−1.36684	−0.683418	−	0.730028i	$-0.739507\pi$
$853$	−39.9200	−1.36684	−0.683418	+	0.730028i	$0.739507\pi$
$854$	1.32428	0.0453159
$855$	42.8053	1.46391
$856$	−15.2940	−0.522737
$857$	−5.45193	−0.186234	−0.0931172	−	0.995655i	$-0.529683\pi$
$857$	−5.45193	−0.186234	−0.0931172	+	0.995655i	$0.529683\pi$
$858$	−20.8772	−0.712736
$859$	8.04717	0.274566	0.137283	−	0.990532i	$-0.456163\pi$
$859$	8.04717	0.274566	0.137283	+	0.990532i	$0.456163\pi$
$860$	−9.07522	−0.309462
$861$	−6.86208	−0.233859
$862$	−1.00000	−0.0340601
$863$	31.7600	1.08112	0.540561	−	0.841305i	$-0.318212\pi$
$863$	31.7600	1.08112	0.540561	+	0.841305i	$0.318212\pi$
$864$	−3.94107	−0.134078
$865$	−21.4722	−0.730077
$866$	33.2489	1.12984
$867$	−11.8477	−0.402368
$868$	−8.84864	−0.300342
$869$	27.2449	0.924220
$870$	−3.57278	−0.121128
$871$	−9.66347	−0.327434
$872$	18.0379	0.610840
$873$	25.8215	0.873925
$874$	−38.3562	−1.29742
$875$	1.63632	0.0553177
$876$	−3.66109	−0.123697
$877$	−44.4484	−1.50092	−0.750458	−	0.660918i	$-0.770167\pi$
$877$	−44.4484	−1.50092	−0.750458	+	0.660918i	$0.770167\pi$
$878$	1.79752	0.0606634
$879$	−9.46882	−0.319375
$880$	17.5457	0.591465
$881$	30.4941	1.02737	0.513686	−	0.857978i	$-0.328280\pi$
$881$	30.4941	1.02737	0.513686	+	0.857978i	$0.328280\pi$
$882$	−2.48344	−0.0836217
$883$	29.6731	0.998580	0.499290	−	0.866435i	$-0.333594\pi$
$883$	29.6731	0.998580	0.499290	+	0.866435i	$0.333594\pi$
$884$	−3.65806	−0.123034
$885$	27.4695	0.923376
$886$	6.79267	0.228204
$887$	26.3231	0.883844	0.441922	−	0.897053i	$-0.354297\pi$
$887$	26.3231	0.883844	0.441922	+	0.897053i	$0.354297\pi$
$888$	5.05057	0.169486
$889$	19.4719	0.653066
$890$	42.1438	1.41266
$891$	26.3312	0.882128
$892$	−21.9048	−0.733426
$893$	−47.1121	−1.57655
$894$	−6.74748	−0.225669
$895$	24.5794	0.821598
$896$	−1.00000	−0.0334077
$897$	−25.0704	−0.837078
$898$	−26.4556	−0.882834
$899$	−14.2951	−0.476769
$900$	−11.0965	−0.369885
$901$	−8.78124	−0.292545
$902$	54.4417	1.81271
$903$	2.11975	0.0705407
$904$	−20.4930	−0.681586
$905$	−3.64786	−0.121259
$906$	9.40458	0.312446
$907$	55.1827	1.83231	0.916156	−	0.400822i	$-0.131275\pi$
$907$	55.1827	1.83231	0.916156	+	0.400822i	$0.131275\pi$
$908$	2.36284	0.0784137
$909$	−24.4793	−0.811928
$910$	15.6751	0.519623
$911$	11.9424	0.395670	0.197835	−	0.980235i	$-0.436609\pi$
$911$	11.9424	0.395670	0.197835	+	0.980235i	$0.436609\pi$
$912$	−4.02597	−0.133313
$913$	54.4781	1.80296
$914$	−14.1709	−0.468733
$915$	−2.92870	−0.0968197
$916$	18.1301	0.599037
$917$	−12.7508	−0.421067
$918$	−2.83002	−0.0934046
$919$	−52.4397	−1.72982	−0.864912	−	0.501923i	$-0.832626\pi$
$919$	−52.4397	−1.72982	−0.864912	+	0.501923i	$0.832626\pi$
$920$	21.0698	0.694651
$921$	−7.43565	−0.245013
$922$	−37.7411	−1.24294
$923$	−53.0705	−1.74684
$924$	−4.09824	−0.134822
$925$	31.3988	1.03239
$926$	2.35034	0.0772369
$927$	−21.3043	−0.699727
$928$	−1.61552	−0.0530319
$929$	26.0425	0.854427	0.427214	−	0.904151i	$-0.359495\pi$
$929$	26.0425	0.854427	0.427214	+	0.904151i	$0.359495\pi$
$930$	19.5691	0.641697
$931$	−5.60157	−0.183584
$932$	−23.4169	−0.767045
$933$	5.26612	0.172405
$934$	−13.7104	−0.448616
$935$	12.5993	0.412041
$936$	12.6511	0.413514
$937$	38.0554	1.24322	0.621608	−	0.783329i	$-0.286480\pi$
$937$	38.0554	1.24322	0.621608	+	0.783329i	$0.286480\pi$
$938$	−1.89696	−0.0619379
$939$	5.24397	0.171130
$940$	25.8796	0.844098
$941$	−38.5475	−1.25661	−0.628306	−	0.777966i	$-0.716251\pi$
$941$	−38.5475	−1.25661	−0.628306	+	0.777966i	$0.716251\pi$
$942$	−4.71763	−0.153709
$943$	65.3765	2.12895
$944$	12.4210	0.404268
$945$	12.1268	0.394486
$946$	−16.8174	−0.546782
$947$	−28.4499	−0.924496	−0.462248	−	0.886751i	$-0.652957\pi$
$947$	−28.4499	−0.924496	−0.462248	+	0.886751i	$0.652957\pi$
$948$	3.43407	0.111534
$949$	25.9492	0.842347
$950$	−25.0290	−0.812049
$951$	11.2411	0.364518
$952$	−0.718085	−0.0232733
$953$	−1.98105	−0.0641723	−0.0320862	−	0.999485i	$-0.510215\pi$
$953$	−1.98105	−0.0641723	−0.0320862	+	0.999485i	$0.510215\pi$
$954$	30.3692	0.983240
$955$	−53.2747	−1.72393
$956$	−8.21163	−0.265583
$957$	−6.62077	−0.214019
$958$	−8.48690	−0.274199
$959$	0.593065	0.0191511
$960$	2.21154	0.0713772
$961$	47.2984	1.52575
$962$	−35.7976	−1.15416
$963$	37.9816	1.22394
$964$	−11.4375	−0.368376
$965$	−34.4907	−1.11029
$966$	−4.92138	−0.158343
$967$	−46.1310	−1.48347	−0.741737	−	0.670691i	$-0.765998\pi$
$967$	−46.1310	−1.48347	−0.741737	+	0.670691i	$0.765998\pi$
$968$	21.5142	0.691493
$969$	−2.89099	−0.0928719
$970$	−31.9935	−1.02725
$971$	−25.3084	−0.812184	−0.406092	−	0.913832i	$-0.633109\pi$
$971$	−25.3084	−0.812184	−0.406092	+	0.913832i	$0.633109\pi$
$972$	15.1421	0.485683
$973$	18.0068	0.577273
$974$	−0.0977135	−0.00313094
$975$	−16.3595	−0.523923
$976$	−1.32428	−0.0423891
$977$	−1.08288	−0.0346443	−0.0173222	−	0.999850i	$-0.505514\pi$
$977$	−1.08288	−0.0346443	−0.0173222	+	0.999850i	$0.505514\pi$
$978$	−13.6048	−0.435035
$979$	78.0973	2.49600
$980$	3.07705	0.0982927
$981$	−44.7960	−1.43023
$982$	10.7493	0.343024
$983$	8.34618	0.266202	0.133101	−	0.991102i	$-0.457507\pi$
$983$	8.34618	0.266202	0.133101	+	0.991102i	$0.457507\pi$
$984$	6.86208	0.218755
$985$	−18.1172	−0.577261
$986$	−1.16008	−0.0369444
$987$	−6.04482	−0.192409
$988$	28.5354	0.907833
$989$	−20.1952	−0.642171
$990$	−43.5737	−1.38486
$991$	−33.0784	−1.05077	−0.525384	−	0.850865i	$-0.676078\pi$
$991$	−33.0784	−1.05077	−0.525384	+	0.850865i	$0.676078\pi$
$992$	8.84864	0.280945
$993$	1.12200	0.0356057
$994$	−10.4179	−0.330434
$995$	−18.5817	−0.589078
$996$	6.86667	0.217579
$997$	−52.1245	−1.65080	−0.825400	−	0.564548i	$-0.809051\pi$
$997$	−52.1245	−1.65080	−0.825400	+	0.564548i	$0.809051\pi$
$998$	−13.0640	−0.413533
$999$	−27.6945	−0.876214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.18	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.718722 q^{3} +1.00000 q^{4} +3.07705 q^{5} +0.718722 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.48344 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.718722 q^{3} +1.00000 q^{4} +3.07705 q^{5} +0.718722 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.48344 q^{9} +3.07705 q^{10} +5.70212 q^{11} +0.718722 q^{12} -5.09419 q^{13} -1.00000 q^{14} +2.21154 q^{15} +1.00000 q^{16} +0.718085 q^{17} -2.48344 q^{18} -5.60157 q^{19} +3.07705 q^{20} -0.718722 q^{21} +5.70212 q^{22} +6.84741 q^{23} +0.718722 q^{24} +4.46822 q^{25} -5.09419 q^{26} -3.94107 q^{27} -1.00000 q^{28} -1.61552 q^{29} +2.21154 q^{30} +8.84864 q^{31} +1.00000 q^{32} +4.09824 q^{33} +0.718085 q^{34} -3.07705 q^{35} -2.48344 q^{36} +7.02715 q^{37} -5.60157 q^{38} -3.66130 q^{39} +3.07705 q^{40} +9.54762 q^{41} -0.718722 q^{42} -2.94933 q^{43} +5.70212 q^{44} -7.64166 q^{45} +6.84741 q^{46} +8.41052 q^{47} +0.718722 q^{48} +1.00000 q^{49} +4.46822 q^{50} +0.516103 q^{51} -5.09419 q^{52} -12.2287 q^{53} -3.94107 q^{54} +17.5457 q^{55} -1.00000 q^{56} -4.02597 q^{57} -1.61552 q^{58} +12.4210 q^{59} +2.21154 q^{60} -1.32428 q^{61} +8.84864 q^{62} +2.48344 q^{63} +1.00000 q^{64} -15.6751 q^{65} +4.09824 q^{66} +1.89696 q^{67} +0.718085 q^{68} +4.92138 q^{69} -3.07705 q^{70} +10.4179 q^{71} -2.48344 q^{72} -5.09389 q^{73} +7.02715 q^{74} +3.21141 q^{75} -5.60157 q^{76} -5.70212 q^{77} -3.66130 q^{78} +4.77803 q^{79} +3.07705 q^{80} +4.61779 q^{81} +9.54762 q^{82} +9.55400 q^{83} -0.718722 q^{84} +2.20958 q^{85} -2.94933 q^{86} -1.16111 q^{87} +5.70212 q^{88} +13.6962 q^{89} -7.64166 q^{90} +5.09419 q^{91} +6.84741 q^{92} +6.35971 q^{93} +8.41052 q^{94} -17.2363 q^{95} +0.718722 q^{96} -10.3975 q^{97} +1.00000 q^{98} -14.1609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 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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