LMFDB - Embedded newform 6034.2.a.k.1.10

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:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.509862$ of defining polynomial
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.509862 q^{3} +1.00000 q^{4} +0.844791 q^{5} -0.509862 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.74004 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.509862 q^{3} +1.00000 q^{4} +0.844791 q^{5} -0.509862 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.74004 q^{9} -0.844791 q^{10} +4.76333 q^{11} +0.509862 q^{12} +1.82171 q^{13} -1.00000 q^{14} +0.430727 q^{15} +1.00000 q^{16} +2.72344 q^{17} +2.74004 q^{18} -5.56142 q^{19} +0.844791 q^{20} +0.509862 q^{21} -4.76333 q^{22} +6.28959 q^{23} -0.509862 q^{24} -4.28633 q^{25} -1.82171 q^{26} -2.92663 q^{27} +1.00000 q^{28} -4.07135 q^{29} -0.430727 q^{30} -9.57509 q^{31} -1.00000 q^{32} +2.42864 q^{33} -2.72344 q^{34} +0.844791 q^{35} -2.74004 q^{36} -9.14943 q^{37} +5.56142 q^{38} +0.928823 q^{39} -0.844791 q^{40} -8.14789 q^{41} -0.509862 q^{42} -5.56166 q^{43} +4.76333 q^{44} -2.31476 q^{45} -6.28959 q^{46} -10.6681 q^{47} +0.509862 q^{48} +1.00000 q^{49} +4.28633 q^{50} +1.38858 q^{51} +1.82171 q^{52} -11.6056 q^{53} +2.92663 q^{54} +4.02402 q^{55} -1.00000 q^{56} -2.83555 q^{57} +4.07135 q^{58} +4.29623 q^{59} +0.430727 q^{60} -0.930735 q^{61} +9.57509 q^{62} -2.74004 q^{63} +1.00000 q^{64} +1.53897 q^{65} -2.42864 q^{66} +3.97435 q^{67} +2.72344 q^{68} +3.20682 q^{69} -0.844791 q^{70} +0.673873 q^{71} +2.74004 q^{72} +0.583534 q^{73} +9.14943 q^{74} -2.18543 q^{75} -5.56142 q^{76} +4.76333 q^{77} -0.928823 q^{78} -4.38636 q^{79} +0.844791 q^{80} +6.72795 q^{81} +8.14789 q^{82} +3.40864 q^{83} +0.509862 q^{84} +2.30073 q^{85} +5.56166 q^{86} -2.07583 q^{87} -4.76333 q^{88} +9.12857 q^{89} +2.31476 q^{90} +1.82171 q^{91} +6.28959 q^{92} -4.88197 q^{93} +10.6681 q^{94} -4.69824 q^{95} -0.509862 q^{96} -7.24259 q^{97} -1.00000 q^{98} -13.0517 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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
$3$	0.509862	0.294369	0.147184	−	0.989109i	$-0.452979\pi$
$3$	0.509862	0.294369	0.147184	+	0.989109i	$0.452979\pi$
$4$	1.00000	0.500000
$5$	0.844791	0.377802	0.188901	−	0.981996i	$-0.439507\pi$
$5$	0.844791	0.377802	0.188901	+	0.981996i	$0.439507\pi$
$6$	−0.509862	−0.208150
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.74004	−0.913347
$10$	−0.844791	−0.267146
$11$	4.76333	1.43620	0.718099	−	0.695941i	$-0.245013\pi$
$11$	4.76333	1.43620	0.718099	+	0.695941i	$0.245013\pi$
$12$	0.509862	0.147184
$13$	1.82171	0.505253	0.252626	−	0.967564i	$-0.418706\pi$
$13$	1.82171	0.505253	0.252626	+	0.967564i	$0.418706\pi$
$14$	−1.00000	−0.267261
$15$	0.430727	0.111213
$16$	1.00000	0.250000
$17$	2.72344	0.660530	0.330265	−	0.943888i	$-0.392862\pi$
$17$	2.72344	0.660530	0.330265	+	0.943888i	$0.392862\pi$
$18$	2.74004	0.645834
$19$	−5.56142	−1.27588	−0.637938	−	0.770087i	$-0.720213\pi$
$19$	−5.56142	−1.27588	−0.637938	+	0.770087i	$0.720213\pi$
$20$	0.844791	0.188901
$21$	0.509862	0.111261
$22$	−4.76333	−1.01554
$23$	6.28959	1.31147	0.655735	−	0.754992i	$-0.272359\pi$
$23$	6.28959	1.31147	0.655735	+	0.754992i	$0.272359\pi$
$24$	−0.509862	−0.104075
$25$	−4.28633	−0.857266
$26$	−1.82171	−0.357268
$27$	−2.92663	−0.563230
$28$	1.00000	0.188982
$29$	−4.07135	−0.756032	−0.378016	−	0.925799i	$-0.623393\pi$
$29$	−4.07135	−0.756032	−0.378016	+	0.925799i	$0.623393\pi$
$30$	−0.430727	−0.0786396
$31$	−9.57509	−1.71974	−0.859869	−	0.510515i	$-0.829455\pi$
$31$	−9.57509	−1.71974	−0.859869	+	0.510515i	$0.829455\pi$
$32$	−1.00000	−0.176777
$33$	2.42864	0.422772
$34$	−2.72344	−0.467065
$35$	0.844791	0.142796
$36$	−2.74004	−0.456674
$37$	−9.14943	−1.50416	−0.752079	−	0.659073i	$-0.770949\pi$
$37$	−9.14943	−1.50416	−0.752079	+	0.659073i	$0.770949\pi$
$38$	5.56142	0.902181
$39$	0.928823	0.148731
$40$	−0.844791	−0.133573
$41$	−8.14789	−1.27249	−0.636244	−	0.771488i	$-0.719513\pi$
$41$	−8.14789	−1.27249	−0.636244	+	0.771488i	$0.719513\pi$
$42$	−0.509862	−0.0786734
$43$	−5.56166	−0.848145	−0.424072	−	0.905628i	$-0.639400\pi$
$43$	−5.56166	−0.848145	−0.424072	+	0.905628i	$0.639400\pi$
$44$	4.76333	0.718099
$45$	−2.31476	−0.345064
$46$	−6.28959	−0.927349
$47$	−10.6681	−1.55611	−0.778054	−	0.628198i	$-0.783793\pi$
$47$	−10.6681	−1.55611	−0.778054	+	0.628198i	$0.783793\pi$
$48$	0.509862	0.0735922
$49$	1.00000	0.142857
$50$	4.28633	0.606178
$51$	1.38858	0.194439
$52$	1.82171	0.252626
$53$	−11.6056	−1.59415	−0.797076	−	0.603879i	$-0.793621\pi$
$53$	−11.6056	−1.59415	−0.797076	+	0.603879i	$0.793621\pi$
$54$	2.92663	0.398264
$55$	4.02402	0.542598
$56$	−1.00000	−0.133631
$57$	−2.83555	−0.375578
$58$	4.07135	0.534595
$59$	4.29623	0.559321	0.279661	−	0.960099i	$-0.409778\pi$
$59$	4.29623	0.559321	0.279661	+	0.960099i	$0.409778\pi$
$60$	0.430727	0.0556066
$61$	−0.930735	−0.119168	−0.0595842	−	0.998223i	$-0.518977\pi$
$61$	−0.930735	−0.119168	−0.0595842	+	0.998223i	$0.518977\pi$
$62$	9.57509	1.21604
$63$	−2.74004	−0.345213
$64$	1.00000	0.125000
$65$	1.53897	0.190886
$66$	−2.42864	−0.298945
$67$	3.97435	0.485544	0.242772	−	0.970083i	$-0.421943\pi$
$67$	3.97435	0.485544	0.242772	+	0.970083i	$0.421943\pi$
$68$	2.72344	0.330265
$69$	3.20682	0.386056
$70$	−0.844791	−0.100972
$71$	0.673873	0.0799740	0.0399870	−	0.999200i	$-0.487268\pi$
$71$	0.673873	0.0799740	0.0399870	+	0.999200i	$0.487268\pi$
$72$	2.74004	0.322917
$73$	0.583534	0.0682975	0.0341488	−	0.999417i	$-0.489128\pi$
$73$	0.583534	0.0682975	0.0341488	+	0.999417i	$0.489128\pi$
$74$	9.14943	1.06360
$75$	−2.18543	−0.252352
$76$	−5.56142	−0.637938
$77$	4.76333	0.542832
$78$	−0.928823	−0.105168
$79$	−4.38636	−0.493504	−0.246752	−	0.969079i	$-0.579363\pi$
$79$	−4.38636	−0.493504	−0.246752	+	0.969079i	$0.579363\pi$
$80$	0.844791	0.0944505
$81$	6.72795	0.747550
$82$	8.14789	0.899784
$83$	3.40864	0.374147	0.187073	−	0.982346i	$-0.440100\pi$
$83$	3.40864	0.374147	0.187073	+	0.982346i	$0.440100\pi$
$84$	0.509862	0.0556305
$85$	2.30073	0.249550
$86$	5.56166	0.599729
$87$	−2.07583	−0.222552
$88$	−4.76333	−0.507772
$89$	9.12857	0.967626	0.483813	−	0.875171i	$-0.339251\pi$
$89$	9.12857	0.967626	0.483813	+	0.875171i	$0.339251\pi$
$90$	2.31476	0.243997
$91$	1.82171	0.190968
$92$	6.28959	0.655735
$93$	−4.88197	−0.506237
$94$	10.6681	1.10033
$95$	−4.69824	−0.482029
$96$	−0.509862	−0.0520375
$97$	−7.24259	−0.735374	−0.367687	−	0.929950i	$-0.619850\pi$
$97$	−7.24259	−0.735374	−0.367687	+	0.929950i	$0.619850\pi$
$98$	−1.00000	−0.101015
$99$	−13.0517	−1.31175
$100$	−4.28633	−0.428633
$101$	3.50803	0.349062	0.174531	−	0.984652i	$-0.444159\pi$
$101$	3.50803	0.349062	0.174531	+	0.984652i	$0.444159\pi$
$102$	−1.38858	−0.137489
$103$	5.49961	0.541893	0.270947	−	0.962594i	$-0.412663\pi$
$103$	5.49961	0.541893	0.270947	+	0.962594i	$0.412663\pi$
$104$	−1.82171	−0.178634
$105$	0.430727	0.0420346
$106$	11.6056	1.12724
$107$	4.23619	0.409528	0.204764	−	0.978811i	$-0.434357\pi$
$107$	4.23619	0.409528	0.204764	+	0.978811i	$0.434357\pi$
$108$	−2.92663	−0.281615
$109$	−6.52254	−0.624746	−0.312373	−	0.949960i	$-0.601124\pi$
$109$	−6.52254	−0.624746	−0.312373	+	0.949960i	$0.601124\pi$
$110$	−4.02402	−0.383675
$111$	−4.66494	−0.442777
$112$	1.00000	0.0944911
$113$	−8.51539	−0.801061	−0.400530	−	0.916284i	$-0.631174\pi$
$113$	−8.51539	−0.801061	−0.400530	+	0.916284i	$0.631174\pi$
$114$	2.83555	0.265574
$115$	5.31339	0.495476
$116$	−4.07135	−0.378016
$117$	−4.99157	−0.461471
$118$	−4.29623	−0.395500
$119$	2.72344	0.249657
$120$	−0.430727	−0.0393198
$121$	11.6893	1.06266
$122$	0.930735	0.0842648
$123$	−4.15430	−0.374581
$124$	−9.57509	−0.859869
$125$	−7.84501	−0.701679
$126$	2.74004	0.244102
$127$	−4.08450	−0.362440	−0.181220	−	0.983443i	$-0.558005\pi$
$127$	−4.08450	−0.362440	−0.181220	+	0.983443i	$0.558005\pi$
$128$	−1.00000	−0.0883883
$129$	−2.83568	−0.249667
$130$	−1.53897	−0.134976
$131$	13.4930	1.17889	0.589444	−	0.807809i	$-0.299347\pi$
$131$	13.4930	1.17889	0.589444	+	0.807809i	$0.299347\pi$
$132$	2.42864	0.211386
$133$	−5.56142	−0.482236
$134$	−3.97435	−0.343331
$135$	−2.47239	−0.212789
$136$	−2.72344	−0.233533
$137$	1.18864	0.101552	0.0507762	−	0.998710i	$-0.483830\pi$
$137$	1.18864	0.101552	0.0507762	+	0.998710i	$0.483830\pi$
$138$	−3.20682	−0.272983
$139$	−1.93542	−0.164161	−0.0820803	−	0.996626i	$-0.526156\pi$
$139$	−1.93542	−0.164161	−0.0820803	+	0.996626i	$0.526156\pi$
$140$	0.844791	0.0713979
$141$	−5.43927	−0.458069
$142$	−0.673873	−0.0565502
$143$	8.67742	0.725643
$144$	−2.74004	−0.228337
$145$	−3.43944	−0.285630
$146$	−0.583534	−0.0482936
$147$	0.509862	0.0420527
$148$	−9.14943	−0.752079
$149$	4.21157	0.345026	0.172513	−	0.985007i	$-0.444811\pi$
$149$	4.21157	0.345026	0.172513	+	0.985007i	$0.444811\pi$
$150$	2.18543	0.178440
$151$	1.95086	0.158759	0.0793794	−	0.996844i	$-0.474706\pi$
$151$	1.95086	0.158759	0.0793794	+	0.996844i	$0.474706\pi$
$152$	5.56142	0.451091
$153$	−7.46233	−0.603293
$154$	−4.76333	−0.383840
$155$	−8.08895	−0.649720
$156$	0.928823	0.0743653
$157$	9.40661	0.750729	0.375364	−	0.926877i	$-0.377518\pi$
$157$	9.40661	0.750729	0.375364	+	0.926877i	$0.377518\pi$
$158$	4.38636	0.348960
$159$	−5.91725	−0.469269
$160$	−0.844791	−0.0667866
$161$	6.28959	0.495689
$162$	−6.72795	−0.528598
$163$	−1.01479	−0.0794846	−0.0397423	−	0.999210i	$-0.512654\pi$
$163$	−1.01479	−0.0794846	−0.0397423	+	0.999210i	$0.512654\pi$
$164$	−8.14789	−0.636244
$165$	2.05169	0.159724
$166$	−3.40864	−0.264562
$167$	−1.13852	−0.0881017	−0.0440508	−	0.999029i	$-0.514026\pi$
$167$	−1.13852	−0.0881017	−0.0440508	+	0.999029i	$0.514026\pi$
$168$	−0.509862	−0.0393367
$169$	−9.68135	−0.744720
$170$	−2.30073	−0.176458
$171$	15.2385	1.16532
$172$	−5.56166	−0.424072
$173$	−14.3215	−1.08885	−0.544423	−	0.838811i	$-0.683251\pi$
$173$	−14.3215	−1.08885	−0.544423	+	0.838811i	$0.683251\pi$
$174$	2.07583	0.157368
$175$	−4.28633	−0.324016
$176$	4.76333	0.359049
$177$	2.19048	0.164647
$178$	−9.12857	−0.684215
$179$	−8.62551	−0.644701	−0.322350	−	0.946620i	$-0.604473\pi$
$179$	−8.62551	−0.644701	−0.322350	+	0.946620i	$0.604473\pi$
$180$	−2.31476	−0.172532
$181$	4.00491	0.297683	0.148841	−	0.988861i	$-0.452446\pi$
$181$	4.00491	0.297683	0.148841	+	0.988861i	$0.452446\pi$
$182$	−1.82171	−0.135034
$183$	−0.474546	−0.0350795
$184$	−6.28959	−0.463674
$185$	−7.72936	−0.568274
$186$	4.88197	0.357964
$187$	12.9726	0.948652
$188$	−10.6681	−0.778054
$189$	−2.92663	−0.212881
$190$	4.69824	0.340846
$191$	15.8793	1.14899	0.574493	−	0.818510i	$-0.305199\pi$
$191$	15.8793	1.14899	0.574493	+	0.818510i	$0.305199\pi$
$192$	0.509862	0.0367961
$193$	4.33214	0.311834	0.155917	−	0.987770i	$-0.450167\pi$
$193$	4.33214	0.311834	0.155917	+	0.987770i	$0.450167\pi$
$194$	7.24259	0.519988
$195$	0.784661	0.0561908
$196$	1.00000	0.0714286
$197$	1.47192	0.104870	0.0524348	−	0.998624i	$-0.483302\pi$
$197$	1.47192	0.104870	0.0524348	+	0.998624i	$0.483302\pi$
$198$	13.0517	0.927545
$199$	15.6370	1.10848	0.554239	−	0.832358i	$-0.313010\pi$
$199$	15.6370	1.10848	0.554239	+	0.832358i	$0.313010\pi$
$200$	4.28633	0.303089
$201$	2.02637	0.142929
$202$	−3.50803	−0.246824
$203$	−4.07135	−0.285753
$204$	1.38858	0.0972197
$205$	−6.88327	−0.480748
$206$	−5.49961	−0.383176
$207$	−17.2337	−1.19783
$208$	1.82171	0.126313
$209$	−26.4909	−1.83241
$210$	−0.430727	−0.0297230
$211$	3.18646	0.219365	0.109683	−	0.993967i	$-0.465017\pi$
$211$	3.18646	0.219365	0.109683	+	0.993967i	$0.465017\pi$
$212$	−11.6056	−0.797076
$213$	0.343582	0.0235419
$214$	−4.23619	−0.289580
$215$	−4.69844	−0.320431
$216$	2.92663	0.199132
$217$	−9.57509	−0.650000
$218$	6.52254	0.441762
$219$	0.297522	0.0201047
$220$	4.02402	0.271299
$221$	4.96132	0.333735
$222$	4.66494	0.313091
$223$	−18.0684	−1.20995	−0.604975	−	0.796245i	$-0.706817\pi$
$223$	−18.0684	−1.20995	−0.604975	+	0.796245i	$0.706817\pi$
$224$	−1.00000	−0.0668153
$225$	11.7447	0.782981
$226$	8.51539	0.566435
$227$	−14.3945	−0.955393	−0.477697	−	0.878525i	$-0.658528\pi$
$227$	−14.3945	−0.955393	−0.477697	+	0.878525i	$0.658528\pi$
$228$	−2.83555	−0.187789
$229$	0.956883	0.0632326	0.0316163	−	0.999500i	$-0.489935\pi$
$229$	0.956883	0.0632326	0.0316163	+	0.999500i	$0.489935\pi$
$230$	−5.31339	−0.350354
$231$	2.42864	0.159793
$232$	4.07135	0.267298
$233$	−3.09213	−0.202572	−0.101286	−	0.994857i	$-0.532296\pi$
$233$	−3.09213	−0.202572	−0.101286	+	0.994857i	$0.532296\pi$
$234$	4.99157	0.326309
$235$	−9.01234	−0.587901
$236$	4.29623	0.279661
$237$	−2.23644	−0.145272
$238$	−2.72344	−0.176534
$239$	−22.4412	−1.45160	−0.725800	−	0.687905i	$-0.758530\pi$
$239$	−22.4412	−1.45160	−0.725800	+	0.687905i	$0.758530\pi$
$240$	0.430727	0.0278033
$241$	−8.76202	−0.564411	−0.282206	−	0.959354i	$-0.591066\pi$
$241$	−8.76202	−0.564411	−0.282206	+	0.959354i	$0.591066\pi$
$242$	−11.6893	−0.751416
$243$	12.2102	0.783285
$244$	−0.930735	−0.0595842
$245$	0.844791	0.0539717
$246$	4.15430	0.264868
$247$	−10.1313	−0.644640
$248$	9.57509	0.608019
$249$	1.73794	0.110137
$250$	7.84501	0.496162
$251$	3.39738	0.214441	0.107220	−	0.994235i	$-0.465805\pi$
$251$	3.39738	0.214441	0.107220	+	0.994235i	$0.465805\pi$
$252$	−2.74004	−0.172606
$253$	29.9594	1.88353
$254$	4.08450	0.256284
$255$	1.17306	0.0734596
$256$	1.00000	0.0625000
$257$	0.0590538	0.00368368	0.00184184	−	0.999998i	$-0.499414\pi$
$257$	0.0590538	0.00368368	0.00184184	+	0.999998i	$0.499414\pi$
$258$	2.83568	0.176541
$259$	−9.14943	−0.568518
$260$	1.53897	0.0954428
$261$	11.1557	0.690519
$262$	−13.4930	−0.833600
$263$	−29.0333	−1.79027	−0.895134	−	0.445797i	$-0.852920\pi$
$263$	−29.0333	−1.79027	−0.895134	+	0.445797i	$0.852920\pi$
$264$	−2.42864	−0.149472
$265$	−9.80431	−0.602274
$266$	5.56142	0.340992
$267$	4.65431	0.284839
$268$	3.97435	0.242772
$269$	8.69114	0.529908	0.264954	−	0.964261i	$-0.414643\pi$
$269$	8.69114	0.529908	0.264954	+	0.964261i	$0.414643\pi$
$270$	2.47239	0.150465
$271$	3.62163	0.219998	0.109999	−	0.993932i	$-0.464915\pi$
$271$	3.62163	0.219998	0.109999	+	0.993932i	$0.464915\pi$
$272$	2.72344	0.165133
$273$	0.928823	0.0562149
$274$	−1.18864	−0.0718084
$275$	−20.4172	−1.23120
$276$	3.20682	0.193028
$277$	−8.99956	−0.540731	−0.270366	−	0.962758i	$-0.587145\pi$
$277$	−8.99956	−0.540731	−0.270366	+	0.962758i	$0.587145\pi$
$278$	1.93542	0.116079
$279$	26.2361	1.57072
$280$	−0.844791	−0.0504859
$281$	28.5860	1.70530	0.852648	−	0.522485i	$-0.174995\pi$
$281$	28.5860	1.70530	0.852648	+	0.522485i	$0.174995\pi$
$282$	5.43927	0.323904
$283$	6.54949	0.389327	0.194663	−	0.980870i	$-0.437639\pi$
$283$	6.54949	0.389327	0.194663	+	0.980870i	$0.437639\pi$
$284$	0.673873	0.0399870
$285$	−2.39545	−0.141894
$286$	−8.67742	−0.513107
$287$	−8.14789	−0.480955
$288$	2.74004	0.161458
$289$	−9.58290	−0.563700
$290$	3.43944	0.201971
$291$	−3.69272	−0.216471
$292$	0.583534	0.0341488
$293$	−15.2396	−0.890305	−0.445153	−	0.895455i	$-0.646851\pi$
$293$	−15.2396	−0.890305	−0.445153	+	0.895455i	$0.646851\pi$
$294$	−0.509862	−0.0297357
$295$	3.62941	0.211313
$296$	9.14943	0.531800
$297$	−13.9405	−0.808909
$298$	−4.21157	−0.243970
$299$	11.4578	0.662623
$300$	−2.18543	−0.126176
$301$	−5.56166	−0.320569
$302$	−1.95086	−0.112259
$303$	1.78861	0.102753
$304$	−5.56142	−0.318969
$305$	−0.786277	−0.0450221
$306$	7.46233	0.426593
$307$	−13.6900	−0.781328	−0.390664	−	0.920533i	$-0.627755\pi$
$307$	−13.6900	−0.781328	−0.390664	+	0.920533i	$0.627755\pi$
$308$	4.76333	0.271416
$309$	2.80404	0.159516
$310$	8.08895	0.459422
$311$	11.2425	0.637503	0.318751	−	0.947838i	$-0.396737\pi$
$311$	11.2425	0.637503	0.318751	+	0.947838i	$0.396737\pi$
$312$	−0.928823	−0.0525842
$313$	26.4443	1.49472	0.747361	−	0.664419i	$-0.231321\pi$
$313$	26.4443	1.49472	0.747361	+	0.664419i	$0.231321\pi$
$314$	−9.40661	−0.530846
$315$	−2.31476	−0.130422
$316$	−4.38636	−0.246752
$317$	−9.23092	−0.518460	−0.259230	−	0.965816i	$-0.583469\pi$
$317$	−9.23092	−0.518460	−0.259230	+	0.965816i	$0.583469\pi$
$318$	5.91725	0.331823
$319$	−19.3932	−1.08581
$320$	0.844791	0.0472253
$321$	2.15987	0.120552
$322$	−6.28959	−0.350505
$323$	−15.1462	−0.842755
$324$	6.72795	0.373775
$325$	−7.80847	−0.433136
$326$	1.01479	0.0562041
$327$	−3.32559	−0.183906
$328$	8.14789	0.449892
$329$	−10.6681	−0.588153
$330$	−2.05169	−0.112942
$331$	7.86056	0.432056	0.216028	−	0.976387i	$-0.430690\pi$
$331$	7.86056	0.432056	0.216028	+	0.976387i	$0.430690\pi$
$332$	3.40864	0.187073
$333$	25.0698	1.37382
$334$	1.13852	0.0622973
$335$	3.35749	0.183439
$336$	0.509862	0.0278152
$337$	10.3107	0.561662	0.280831	−	0.959757i	$-0.409390\pi$
$337$	10.3107	0.561662	0.280831	+	0.959757i	$0.409390\pi$
$338$	9.68135	0.526596
$339$	−4.34167	−0.235807
$340$	2.30073	0.124775
$341$	−45.6093	−2.46988
$342$	−15.2385	−0.824004
$343$	1.00000	0.0539949
$344$	5.56166	0.299864
$345$	2.70909	0.145853
$346$	14.3215	0.769931
$347$	4.60845	0.247395	0.123697	−	0.992320i	$-0.460525\pi$
$347$	4.60845	0.247395	0.123697	+	0.992320i	$0.460525\pi$
$348$	−2.07583	−0.111276
$349$	−18.7368	−1.00296	−0.501478	−	0.865170i	$-0.667210\pi$
$349$	−18.7368	−1.00296	−0.501478	+	0.865170i	$0.667210\pi$
$350$	4.28633	0.229114
$351$	−5.33148	−0.284573
$352$	−4.76333	−0.253886
$353$	−18.0940	−0.963044	−0.481522	−	0.876434i	$-0.659916\pi$
$353$	−18.0940	−0.963044	−0.481522	+	0.876434i	$0.659916\pi$
$354$	−2.19048	−0.116423
$355$	0.569282	0.0302144
$356$	9.12857	0.483813
$357$	1.38858	0.0734912
$358$	8.62551	0.455872
$359$	15.4762	0.816801	0.408400	−	0.912803i	$-0.366087\pi$
$359$	15.4762	0.816801	0.408400	+	0.912803i	$0.366087\pi$
$360$	2.31476	0.121999
$361$	11.9294	0.627861
$362$	−4.00491	−0.210494
$363$	5.95992	0.312815
$364$	1.82171	0.0954838
$365$	0.492964	0.0258029
$366$	0.474546	0.0248049
$367$	33.5130	1.74936	0.874682	−	0.484696i	$-0.161070\pi$
$367$	33.5130	1.74936	0.874682	+	0.484696i	$0.161070\pi$
$368$	6.28959	0.327867
$369$	22.3256	1.16222
$370$	7.72936	0.401830
$371$	−11.6056	−0.602533
$372$	−4.88197	−0.253119
$373$	28.8871	1.49572	0.747858	−	0.663858i	$-0.231082\pi$
$373$	28.8871	1.49572	0.747858	+	0.663858i	$0.231082\pi$
$374$	−12.9726	−0.670798
$375$	−3.99987	−0.206552
$376$	10.6681	0.550167
$377$	−7.41685	−0.381987
$378$	2.92663	0.150529
$379$	0.767444	0.0394209	0.0197105	−	0.999806i	$-0.493726\pi$
$379$	0.767444	0.0394209	0.0197105	+	0.999806i	$0.493726\pi$
$380$	−4.69824	−0.241014
$381$	−2.08253	−0.106691
$382$	−15.8793	−0.812455
$383$	7.86595	0.401931	0.200966	−	0.979598i	$-0.435592\pi$
$383$	7.86595	0.401931	0.200966	+	0.979598i	$0.435592\pi$
$384$	−0.509862	−0.0260188
$385$	4.02402	0.205083
$386$	−4.33214	−0.220500
$387$	15.2392	0.774650
$388$	−7.24259	−0.367687
$389$	−3.66686	−0.185917	−0.0929585	−	0.995670i	$-0.529632\pi$
$389$	−3.66686	−0.185917	−0.0929585	+	0.995670i	$0.529632\pi$
$390$	−0.784661	−0.0397329
$391$	17.1293	0.866265
$392$	−1.00000	−0.0505076
$393$	6.87956	0.347028
$394$	−1.47192	−0.0741540
$395$	−3.70556	−0.186447
$396$	−13.0517	−0.655873
$397$	12.5203	0.628374	0.314187	−	0.949361i	$-0.398268\pi$
$397$	12.5203	0.628374	0.314187	+	0.949361i	$0.398268\pi$
$398$	−15.6370	−0.783812
$399$	−2.83555	−0.141955
$400$	−4.28633	−0.214316
$401$	−19.9056	−0.994040	−0.497020	−	0.867739i	$-0.665572\pi$
$401$	−19.9056	−0.994040	−0.497020	+	0.867739i	$0.665572\pi$
$402$	−2.02637	−0.101066
$403$	−17.4431	−0.868902
$404$	3.50803	0.174531
$405$	5.68371	0.282426
$406$	4.07135	0.202058
$407$	−43.5817	−2.16027
$408$	−1.38858	−0.0687447
$409$	1.89688	0.0937949	0.0468974	−	0.998900i	$-0.485067\pi$
$409$	1.89688	0.0937949	0.0468974	+	0.998900i	$0.485067\pi$
$410$	6.88327	0.339940
$411$	0.606042	0.0298939
$412$	5.49961	0.270947
$413$	4.29623	0.211404
$414$	17.2337	0.846991
$415$	2.87959	0.141353
$416$	−1.82171	−0.0893169
$417$	−0.986798	−0.0483237
$418$	26.4909	1.29571
$419$	−17.4404	−0.852021	−0.426010	−	0.904718i	$-0.640081\pi$
$419$	−17.4404	−0.852021	−0.426010	+	0.904718i	$0.640081\pi$
$420$	0.430727	0.0210173
$421$	40.3392	1.96601	0.983006	−	0.183571i	$-0.0587658\pi$
$421$	40.3392	1.96601	0.983006	+	0.183571i	$0.0587658\pi$
$422$	−3.18646	−0.155115
$423$	29.2311	1.42127
$424$	11.6056	0.563618
$425$	−11.6735	−0.566250
$426$	−0.343582	−0.0166466
$427$	−0.930735	−0.0450414
$428$	4.23619	0.204764
$429$	4.42429	0.213607
$430$	4.69844	0.226579
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−2.92663	−0.140807
$433$	1.66097	0.0798210	0.0399105	−	0.999203i	$-0.487293\pi$
$433$	1.66097	0.0798210	0.0399105	+	0.999203i	$0.487293\pi$
$434$	9.57509	0.459619
$435$	−1.75364	−0.0840806
$436$	−6.52254	−0.312373
$437$	−34.9790	−1.67327
$438$	−0.297522	−0.0142161
$439$	−18.3080	−0.873792	−0.436896	−	0.899512i	$-0.643922\pi$
$439$	−18.3080	−0.873792	−0.436896	+	0.899512i	$0.643922\pi$
$440$	−4.02402	−0.191837
$441$	−2.74004	−0.130478
$442$	−4.96132	−0.235986
$443$	27.4509	1.30423	0.652117	−	0.758119i	$-0.273881\pi$
$443$	27.4509	1.30423	0.652117	+	0.758119i	$0.273881\pi$
$444$	−4.66494	−0.221388
$445$	7.71173	0.365571
$446$	18.0684	0.855563
$447$	2.14732	0.101565
$448$	1.00000	0.0472456
$449$	−21.7201	−1.02504	−0.512518	−	0.858677i	$-0.671287\pi$
$449$	−21.7201	−1.02504	−0.512518	+	0.858677i	$0.671287\pi$
$450$	−11.7447	−0.553651
$451$	−38.8111	−1.82754
$452$	−8.51539	−0.400530
$453$	0.994669	0.0467336
$454$	14.3945	0.675565
$455$	1.53897	0.0721480
$456$	2.83555	0.132787
$457$	−37.1412	−1.73739	−0.868696	−	0.495345i	$-0.835042\pi$
$457$	−37.1412	−1.73739	−0.868696	+	0.495345i	$0.835042\pi$
$458$	−0.956883	−0.0447122
$459$	−7.97048	−0.372030
$460$	5.31339	0.247738
$461$	−42.1070	−1.96112	−0.980559	−	0.196225i	$-0.937132\pi$
$461$	−42.1070	−1.96112	−0.980559	+	0.196225i	$0.937132\pi$
$462$	−2.42864	−0.112990
$463$	8.77726	0.407914	0.203957	−	0.978980i	$-0.434620\pi$
$463$	8.77726	0.407914	0.203957	+	0.978980i	$0.434620\pi$
$464$	−4.07135	−0.189008
$465$	−4.12425	−0.191257
$466$	3.09213	0.143240
$467$	9.05951	0.419224	0.209612	−	0.977785i	$-0.432780\pi$
$467$	9.05951	0.419224	0.209612	+	0.977785i	$0.432780\pi$
$468$	−4.99157	−0.230736
$469$	3.97435	0.183518
$470$	9.01234	0.415708
$471$	4.79607	0.220991
$472$	−4.29623	−0.197750
$473$	−26.4920	−1.21810
$474$	2.23644	0.102723
$475$	23.8381	1.09377
$476$	2.72344	0.124828
$477$	31.7998	1.45601
$478$	22.4412	1.02644
$479$	5.49880	0.251247	0.125623	−	0.992078i	$-0.459907\pi$
$479$	5.49880	0.251247	0.125623	+	0.992078i	$0.459907\pi$
$480$	−0.430727	−0.0196599
$481$	−16.6677	−0.759980
$482$	8.76202	0.399099
$483$	3.20682	0.145915
$484$	11.6893	0.531331
$485$	−6.11848	−0.277826
$486$	−12.2102	−0.553866
$487$	29.7626	1.34867	0.674335	−	0.738425i	$-0.264430\pi$
$487$	29.7626	1.34867	0.674335	+	0.738425i	$0.264430\pi$
$488$	0.930735	0.0421324
$489$	−0.517403	−0.0233978
$490$	−0.844791	−0.0381638
$491$	10.4222	0.470349	0.235175	−	0.971953i	$-0.424434\pi$
$491$	10.4222	0.470349	0.235175	+	0.971953i	$0.424434\pi$
$492$	−4.15430	−0.187290
$493$	−11.0881	−0.499382
$494$	10.1313	0.455830
$495$	−11.0260	−0.495581
$496$	−9.57509	−0.429934
$497$	0.673873	0.0302273
$498$	−1.73794	−0.0778788
$499$	−9.31862	−0.417159	−0.208579	−	0.978005i	$-0.566884\pi$
$499$	−9.31862	−0.417159	−0.208579	+	0.978005i	$0.566884\pi$
$500$	−7.84501	−0.350839
$501$	−0.580490	−0.0259344
$502$	−3.39738	−0.151633
$503$	13.8832	0.619020	0.309510	−	0.950896i	$-0.399835\pi$
$503$	13.8832	0.619020	0.309510	+	0.950896i	$0.399835\pi$
$504$	2.74004	0.122051
$505$	2.96355	0.131876
$506$	−29.9594	−1.33186
$507$	−4.93615	−0.219222
$508$	−4.08450	−0.181220
$509$	9.18311	0.407034	0.203517	−	0.979071i	$-0.434763\pi$
$509$	9.18311	0.407034	0.203517	+	0.979071i	$0.434763\pi$
$510$	−1.17306	−0.0519438
$511$	0.583534	0.0258140
$512$	−1.00000	−0.0441942
$513$	16.2762	0.718612
$514$	−0.0590538	−0.00260475
$515$	4.64603	0.204728
$516$	−2.83568	−0.124834
$517$	−50.8158	−2.23488
$518$	9.14943	0.402003
$519$	−7.30200	−0.320522
$520$	−1.53897	−0.0674882
$521$	−0.203672	−0.00892303	−0.00446151	−	0.999990i	$-0.501420\pi$
$521$	−0.203672	−0.00892303	−0.00446151	+	0.999990i	$0.501420\pi$
$522$	−11.1557	−0.488271
$523$	−16.4344	−0.718626	−0.359313	−	0.933217i	$-0.616989\pi$
$523$	−16.4344	−0.718626	−0.359313	+	0.933217i	$0.616989\pi$
$524$	13.4930	0.589444
$525$	−2.18543	−0.0953802
$526$	29.0333	1.26591
$527$	−26.0772	−1.13594
$528$	2.42864	0.105693
$529$	16.5589	0.719951
$530$	9.80431	0.425872
$531$	−11.7718	−0.510854
$532$	−5.56142	−0.241118
$533$	−14.8431	−0.642928
$534$	−4.65431	−0.201412
$535$	3.57870	0.154721
$536$	−3.97435	−0.171666
$537$	−4.39782	−0.189780
$538$	−8.69114	−0.374702
$539$	4.76333	0.205171
$540$	−2.47239	−0.106395
$541$	−13.1168	−0.563934	−0.281967	−	0.959424i	$-0.590987\pi$
$541$	−13.1168	−0.563934	−0.281967	+	0.959424i	$0.590987\pi$
$542$	−3.62163	−0.155562
$543$	2.04195	0.0876285
$544$	−2.72344	−0.116766
$545$	−5.51018	−0.236030
$546$	−0.928823	−0.0397499
$547$	−13.9078	−0.594655	−0.297328	−	0.954776i	$-0.596095\pi$
$547$	−13.9078	−0.594655	−0.297328	+	0.954776i	$0.596095\pi$
$548$	1.18864	0.0507762
$549$	2.55025	0.108842
$550$	20.4172	0.870592
$551$	22.6425	0.964603
$552$	−3.20682	−0.136491
$553$	−4.38636	−0.186527
$554$	8.99956	0.382355
$555$	−3.94090	−0.167282
$556$	−1.93542	−0.0820803
$557$	−42.9892	−1.82151	−0.910756	−	0.412946i	$-0.864500\pi$
$557$	−42.9892	−1.82151	−0.910756	+	0.412946i	$0.864500\pi$
$558$	−26.2361	−1.11066
$559$	−10.1318	−0.428527
$560$	0.844791	0.0356989
$561$	6.61424	0.279253
$562$	−28.5860	−1.20583
$563$	−22.2550	−0.937937	−0.468968	−	0.883215i	$-0.655374\pi$
$563$	−22.2550	−0.937937	−0.468968	+	0.883215i	$0.655374\pi$
$564$	−5.43927	−0.229035
$565$	−7.19373	−0.302642
$566$	−6.54949	−0.275296
$567$	6.72795	0.282547
$568$	−0.673873	−0.0282751
$569$	2.03218	0.0851935	0.0425968	−	0.999092i	$-0.486437\pi$
$569$	2.03218	0.0851935	0.0425968	+	0.999092i	$0.486437\pi$
$570$	2.39545	0.100334
$571$	2.13704	0.0894322	0.0447161	−	0.999000i	$-0.485762\pi$
$571$	2.13704	0.0894322	0.0447161	+	0.999000i	$0.485762\pi$
$572$	8.67742	0.362821
$573$	8.09624	0.338225
$574$	8.14789	0.340086
$575$	−26.9592	−1.12428
$576$	−2.74004	−0.114168
$577$	31.7645	1.32238	0.661188	−	0.750221i	$-0.270053\pi$
$577$	31.7645	1.32238	0.661188	+	0.750221i	$0.270053\pi$
$578$	9.58290	0.398596
$579$	2.20879	0.0917943
$580$	−3.43944	−0.142815
$581$	3.40864	0.141414
$582$	3.69272	0.153068
$583$	−55.2813	−2.28952
$584$	−0.583534	−0.0241468
$585$	−4.21684	−0.174345
$586$	15.2396	0.629541
$587$	−12.6713	−0.523003	−0.261501	−	0.965203i	$-0.584218\pi$
$587$	−12.6713	−0.523003	−0.261501	+	0.965203i	$0.584218\pi$
$588$	0.509862	0.0210263
$589$	53.2511	2.19417
$590$	−3.62941	−0.149421
$591$	0.750473	0.0308703
$592$	−9.14943	−0.376039
$593$	41.3519	1.69812	0.849060	−	0.528296i	$-0.177169\pi$
$593$	41.3519	1.69812	0.849060	+	0.528296i	$0.177169\pi$
$594$	13.9405	0.571985
$595$	2.30073	0.0943209
$596$	4.21157	0.172513
$597$	7.97271	0.326301
$598$	−11.4578	−0.468546
$599$	19.5918	0.800497	0.400249	−	0.916407i	$-0.368924\pi$
$599$	19.5918	0.800497	0.400249	+	0.916407i	$0.368924\pi$
$600$	2.18543	0.0892200
$601$	−6.91713	−0.282156	−0.141078	−	0.989999i	$-0.545057\pi$
$601$	−6.91713	−0.282156	−0.141078	+	0.989999i	$0.545057\pi$
$602$	5.56166	0.226676
$603$	−10.8899	−0.443470
$604$	1.95086	0.0793794
$605$	9.87501	0.401476
$606$	−1.78861	−0.0726573
$607$	12.5138	0.507917	0.253959	−	0.967215i	$-0.418267\pi$
$607$	12.5138	0.507917	0.253959	+	0.967215i	$0.418267\pi$
$608$	5.56142	0.225545
$609$	−2.07583	−0.0841168
$610$	0.786277	0.0318354
$611$	−19.4343	−0.786228
$612$	−7.46233	−0.301647
$613$	43.9152	1.77372	0.886859	−	0.462039i	$-0.152882\pi$
$613$	43.9152	1.77372	0.886859	+	0.462039i	$0.152882\pi$
$614$	13.6900	0.552482
$615$	−3.50951	−0.141517
$616$	−4.76333	−0.191920
$617$	−38.0894	−1.53342	−0.766710	−	0.641993i	$-0.778108\pi$
$617$	−38.0894	−1.53342	−0.766710	+	0.641993i	$0.778108\pi$
$618$	−2.80404	−0.112795
$619$	22.3578	0.898634	0.449317	−	0.893372i	$-0.351667\pi$
$619$	22.3578	0.898634	0.449317	+	0.893372i	$0.351667\pi$
$620$	−8.08895	−0.324860
$621$	−18.4073	−0.738658
$622$	−11.2425	−0.450782
$623$	9.12857	0.365728
$624$	0.928823	0.0371827
$625$	14.8042	0.592170
$626$	−26.4443	−1.05693
$627$	−13.5067	−0.539404
$628$	9.40661	0.375364
$629$	−24.9179	−0.993541
$630$	2.31476	0.0922223
$631$	12.9059	0.513774	0.256887	−	0.966441i	$-0.417303\pi$
$631$	12.9059	0.513774	0.256887	+	0.966441i	$0.417303\pi$
$632$	4.38636	0.174480
$633$	1.62466	0.0645743
$634$	9.23092	0.366607
$635$	−3.45055	−0.136931
$636$	−5.91725	−0.234634
$637$	1.82171	0.0721790
$638$	19.3932	0.767784
$639$	−1.84644	−0.0730440
$640$	−0.844791	−0.0333933
$641$	−25.8331	−1.02034	−0.510172	−	0.860072i	$-0.670418\pi$
$641$	−25.8331	−1.02034	−0.510172	+	0.860072i	$0.670418\pi$
$642$	−2.15987	−0.0852434
$643$	20.1656	0.795253	0.397627	−	0.917547i	$-0.369834\pi$
$643$	20.1656	0.795253	0.397627	+	0.917547i	$0.369834\pi$
$644$	6.28959	0.247844
$645$	−2.39555	−0.0943248
$646$	15.1462	0.595918
$647$	−31.8055	−1.25040	−0.625201	−	0.780464i	$-0.714983\pi$
$647$	−31.8055	−1.25040	−0.625201	+	0.780464i	$0.714983\pi$
$648$	−6.72795	−0.264299
$649$	20.4643	0.803296
$650$	7.80847	0.306273
$651$	−4.88197	−0.191340
$652$	−1.01479	−0.0397423
$653$	−2.94976	−0.115433	−0.0577165	−	0.998333i	$-0.518382\pi$
$653$	−2.94976	−0.115433	−0.0577165	+	0.998333i	$0.518382\pi$
$654$	3.32559	0.130041
$655$	11.3988	0.445386
$656$	−8.14789	−0.318122
$657$	−1.59891	−0.0623793
$658$	10.6681	0.415887
$659$	−2.37872	−0.0926620	−0.0463310	−	0.998926i	$-0.514753\pi$
$659$	−2.37872	−0.0926620	−0.0463310	+	0.998926i	$0.514753\pi$
$660$	2.05169	0.0798620
$661$	−10.6376	−0.413753	−0.206876	−	0.978367i	$-0.566330\pi$
$661$	−10.6376	−0.413753	−0.206876	+	0.978367i	$0.566330\pi$
$662$	−7.86056	−0.305509
$663$	2.52959	0.0982411
$664$	−3.40864	−0.132281
$665$	−4.69824	−0.182190
$666$	−25.0698	−0.971436
$667$	−25.6071	−0.991512
$668$	−1.13852	−0.0440508
$669$	−9.21238	−0.356171
$670$	−3.35749	−0.129711
$671$	−4.43340	−0.171149
$672$	−0.509862	−0.0196683
$673$	20.7954	0.801603	0.400802	−	0.916165i	$-0.368732\pi$
$673$	20.7954	0.801603	0.400802	+	0.916165i	$0.368732\pi$
$674$	−10.3107	−0.397155
$675$	12.5445	0.482837
$676$	−9.68135	−0.372360
$677$	−9.52574	−0.366104	−0.183052	−	0.983103i	$-0.558598\pi$
$677$	−9.52574	−0.366104	−0.183052	+	0.983103i	$0.558598\pi$
$678$	4.34167	0.166741
$679$	−7.24259	−0.277945
$680$	−2.30073	−0.0882291
$681$	−7.33918	−0.281238
$682$	45.6093	1.74647
$683$	−10.7412	−0.411001	−0.205500	−	0.978657i	$-0.565882\pi$
$683$	−10.7412	−0.411001	−0.205500	+	0.978657i	$0.565882\pi$
$684$	15.2385	0.582659
$685$	1.00415	0.0383667
$686$	−1.00000	−0.0381802
$687$	0.487878	0.0186137
$688$	−5.56166	−0.212036
$689$	−21.1421	−0.805450
$690$	−2.70909	−0.103133
$691$	−12.2773	−0.467052	−0.233526	−	0.972351i	$-0.575026\pi$
$691$	−12.2773	−0.467052	−0.233526	+	0.972351i	$0.575026\pi$
$692$	−14.3215	−0.544423
$693$	−13.0517	−0.495794
$694$	−4.60845	−0.174934
$695$	−1.63503	−0.0620202
$696$	2.07583	0.0786840
$697$	−22.1903	−0.840516
$698$	18.7368	0.709197
$699$	−1.57656	−0.0596308
$700$	−4.28633	−0.162008
$701$	47.6517	1.79978	0.899890	−	0.436116i	$-0.143646\pi$
$701$	47.6517	1.79978	0.899890	+	0.436116i	$0.143646\pi$
$702$	5.33148	0.201224
$703$	50.8838	1.91912
$704$	4.76333	0.179525
$705$	−4.59505	−0.173060
$706$	18.0940	0.680975
$707$	3.50803	0.131933
$708$	2.19048	0.0823234
$709$	−37.4633	−1.40696	−0.703481	−	0.710714i	$-0.748372\pi$
$709$	−37.4633	−1.40696	−0.703481	+	0.710714i	$0.748372\pi$
$710$	−0.569282	−0.0213648
$711$	12.0188	0.450741
$712$	−9.12857	−0.342107
$713$	−60.2234	−2.25538
$714$	−1.38858	−0.0519661
$715$	7.33061	0.274149
$716$	−8.62551	−0.322350
$717$	−11.4419	−0.427306
$718$	−15.4762	−0.577565
$719$	−40.4580	−1.50883	−0.754414	−	0.656399i	$-0.772079\pi$
$719$	−40.4580	−1.50883	−0.754414	+	0.656399i	$0.772079\pi$
$720$	−2.31476	−0.0862661
$721$	5.49961	0.204816
$722$	−11.9294	−0.443965
$723$	−4.46742	−0.166145
$724$	4.00491	0.148841
$725$	17.4512	0.648120
$726$	−5.95992	−0.221193
$727$	−8.95640	−0.332174	−0.166087	−	0.986111i	$-0.553113\pi$
$727$	−8.95640	−0.332174	−0.166087	+	0.986111i	$0.553113\pi$
$728$	−1.82171	−0.0675172
$729$	−13.9583	−0.516975
$730$	−0.492964	−0.0182454
$731$	−15.1468	−0.560225
$732$	−0.474546	−0.0175397
$733$	21.2783	0.785930	0.392965	−	0.919553i	$-0.371449\pi$
$733$	21.2783	0.785930	0.392965	+	0.919553i	$0.371449\pi$
$734$	−33.5130	−1.23699
$735$	0.430727	0.0158876
$736$	−6.28959	−0.231837
$737$	18.9311	0.697337
$738$	−22.3256	−0.821815
$739$	−21.2837	−0.782935	−0.391467	−	0.920192i	$-0.628032\pi$
$739$	−21.2837	−0.782935	−0.391467	+	0.920192i	$0.628032\pi$
$740$	−7.72936	−0.284137
$741$	−5.16557	−0.189762
$742$	11.6056	0.426055
$743$	22.9593	0.842297	0.421148	−	0.906992i	$-0.361627\pi$
$743$	22.9593	0.842297	0.421148	+	0.906992i	$0.361627\pi$
$744$	4.88197	0.178982
$745$	3.55790	0.130351
$746$	−28.8871	−1.05763
$747$	−9.33982	−0.341726
$748$	12.9726	0.474326
$749$	4.23619	0.154787
$750$	3.99987	0.146055
$751$	−29.2863	−1.06867	−0.534336	−	0.845272i	$-0.679438\pi$
$751$	−29.2863	−1.06867	−0.534336	+	0.845272i	$0.679438\pi$
$752$	−10.6681	−0.389027
$753$	1.73220	0.0631247
$754$	7.41685	0.270106
$755$	1.64807	0.0599794
$756$	−2.92663	−0.106440
$757$	−3.48570	−0.126690	−0.0633450	−	0.997992i	$-0.520177\pi$
$757$	−3.48570	−0.126690	−0.0633450	+	0.997992i	$0.520177\pi$
$758$	−0.767444	−0.0278748
$759$	15.2751	0.554452
$760$	4.69824	0.170423
$761$	−44.9736	−1.63029	−0.815145	−	0.579256i	$-0.803343\pi$
$761$	−44.9736	−1.63029	−0.815145	+	0.579256i	$0.803343\pi$
$762$	2.08253	0.0754420
$763$	−6.52254	−0.236132
$764$	15.8793	0.574493
$765$	−6.30411	−0.227925
$766$	−7.86595	−0.284208
$767$	7.82650	0.282599
$768$	0.509862	0.0183980
$769$	−13.4735	−0.485867	−0.242933	−	0.970043i	$-0.578110\pi$
$769$	−13.4735	−0.485867	−0.242933	+	0.970043i	$0.578110\pi$
$770$	−4.02402	−0.145015
$771$	0.0301093	0.00108436
$772$	4.33214	0.155917
$773$	2.26034	0.0812989	0.0406494	−	0.999173i	$-0.487057\pi$
$773$	2.26034	0.0812989	0.0406494	+	0.999173i	$0.487057\pi$
$774$	−15.2392	−0.547761
$775$	41.0420	1.47427
$776$	7.24259	0.259994
$777$	−4.66494	−0.167354
$778$	3.66686	0.131463
$779$	45.3138	1.62354
$780$	0.784661	0.0280954
$781$	3.20988	0.114858
$782$	−17.1293	−0.612542
$783$	11.9153	0.425819
$784$	1.00000	0.0357143
$785$	7.94662	0.283627
$786$	−6.87956	−0.245386
$787$	−22.2690	−0.793804	−0.396902	−	0.917861i	$-0.629915\pi$
$787$	−22.2690	−0.793804	−0.396902	+	0.917861i	$0.629915\pi$
$788$	1.47192	0.0524348
$789$	−14.8029	−0.526999
$790$	3.70556	0.131838
$791$	−8.51539	−0.302772
$792$	13.0517	0.463772
$793$	−1.69553	−0.0602102
$794$	−12.5203	−0.444327
$795$	−4.99884	−0.177291
$796$	15.6370	0.554239
$797$	45.1545	1.59945	0.799727	−	0.600364i	$-0.204978\pi$
$797$	45.1545	1.59945	0.799727	+	0.600364i	$0.204978\pi$
$798$	2.83555	0.100378
$799$	−29.0540	−1.02786
$800$	4.28633	0.151545
$801$	−25.0126	−0.883778
$802$	19.9056	0.702892
$803$	2.77956	0.0980887
$804$	2.02637	0.0714645
$805$	5.31339	0.187272
$806$	17.4431	0.614407
$807$	4.43128	0.155988
$808$	−3.50803	−0.123412
$809$	28.8364	1.01383	0.506916	−	0.861995i	$-0.330785\pi$
$809$	28.8364	1.01383	0.506916	+	0.861995i	$0.330785\pi$
$810$	−5.68371	−0.199705
$811$	−19.3323	−0.678848	−0.339424	−	0.940633i	$-0.610232\pi$
$811$	−19.3323	−0.678848	−0.339424	+	0.940633i	$0.610232\pi$
$812$	−4.07135	−0.142877
$813$	1.84653	0.0647606
$814$	43.5817	1.52754
$815$	−0.857287	−0.0300294
$816$	1.38858	0.0486099
$817$	30.9307	1.08213
$818$	−1.89688	−0.0663230
$819$	−4.99157	−0.174420
$820$	−6.88327	−0.240374
$821$	35.0852	1.22448	0.612241	−	0.790671i	$-0.290268\pi$
$821$	35.0852	1.22448	0.612241	+	0.790671i	$0.290268\pi$
$822$	−0.606042	−0.0211382
$823$	−37.2599	−1.29880	−0.649399	−	0.760448i	$-0.724979\pi$
$823$	−37.2599	−1.29880	−0.649399	+	0.760448i	$0.724979\pi$
$824$	−5.49961	−0.191588
$825$	−10.4099	−0.362428
$826$	−4.29623	−0.149485
$827$	−19.3139	−0.671609	−0.335805	−	0.941932i	$-0.609008\pi$
$827$	−19.3139	−0.671609	−0.335805	+	0.941932i	$0.609008\pi$
$828$	−17.2337	−0.598913
$829$	19.5854	0.680230	0.340115	−	0.940384i	$-0.389534\pi$
$829$	19.5854	0.680230	0.340115	+	0.940384i	$0.389534\pi$
$830$	−2.87959	−0.0999520
$831$	−4.58853	−0.159174
$832$	1.82171	0.0631566
$833$	2.72344	0.0943615
$834$	0.986798	0.0341700
$835$	−0.961815	−0.0332850
$836$	−26.4909	−0.916205
$837$	28.0227	0.968607
$838$	17.4404	0.602470
$839$	−51.2413	−1.76904	−0.884522	−	0.466498i	$-0.845516\pi$
$839$	−51.2413	−1.76904	−0.884522	+	0.466498i	$0.845516\pi$
$840$	−0.430727	−0.0148615
$841$	−12.4241	−0.428416
$842$	−40.3392	−1.39018
$843$	14.5749	0.501986
$844$	3.18646	0.109683
$845$	−8.17872	−0.281357
$846$	−29.2311	−1.00499
$847$	11.6893	0.401649
$848$	−11.6056	−0.398538
$849$	3.33934	0.114606
$850$	11.6735	0.400399
$851$	−57.5461	−1.97266
$852$	0.343582	0.0117709
$853$	30.1891	1.03366	0.516828	−	0.856089i	$-0.327113\pi$
$853$	30.1891	1.03366	0.516828	+	0.856089i	$0.327113\pi$
$854$	0.930735	0.0318491
$855$	12.8734	0.440260
$856$	−4.23619	−0.144790
$857$	0.129988	0.00444031	0.00222016	−	0.999998i	$-0.499293\pi$
$857$	0.129988	0.00444031	0.00222016	+	0.999998i	$0.499293\pi$
$858$	−4.42429	−0.151043
$859$	−41.6901	−1.42245	−0.711223	−	0.702966i	$-0.751859\pi$
$859$	−41.6901	−1.42245	−0.711223	+	0.702966i	$0.751859\pi$
$860$	−4.69844	−0.160215
$861$	−4.15430	−0.141578
$862$	−1.00000	−0.0340601
$863$	−28.5840	−0.973010	−0.486505	−	0.873678i	$-0.661729\pi$
$863$	−28.5840	−0.973010	−0.486505	+	0.873678i	$0.661729\pi$
$864$	2.92663	0.0995659
$865$	−12.0987	−0.411368
$866$	−1.66097	−0.0564419
$867$	−4.88595	−0.165936
$868$	−9.57509	−0.325000
$869$	−20.8937	−0.708770
$870$	1.75364	0.0594540
$871$	7.24013	0.245322
$872$	6.52254	0.220881
$873$	19.8450	0.671651
$874$	34.9790	1.18318
$875$	−7.84501	−0.265210
$876$	0.297522	0.0100523
$877$	−21.4417	−0.724035	−0.362018	−	0.932171i	$-0.617912\pi$
$877$	−21.4417	−0.724035	−0.362018	+	0.932171i	$0.617912\pi$
$878$	18.3080	0.617864
$879$	−7.77007	−0.262078
$880$	4.02402	0.135650
$881$	53.1402	1.79034	0.895169	−	0.445726i	$-0.147055\pi$
$881$	53.1402	1.79034	0.895169	+	0.445726i	$0.147055\pi$
$882$	2.74004	0.0922620
$883$	−6.45577	−0.217254	−0.108627	−	0.994083i	$-0.534645\pi$
$883$	−6.45577	−0.217254	−0.108627	+	0.994083i	$0.534645\pi$
$884$	4.96132	0.166867
$885$	1.85050	0.0622039
$886$	−27.4509	−0.922232
$887$	53.8792	1.80909	0.904543	−	0.426383i	$-0.140212\pi$
$887$	53.8792	1.80909	0.904543	+	0.426383i	$0.140212\pi$
$888$	4.66494	0.156545
$889$	−4.08450	−0.136990
$890$	−7.71173	−0.258498
$891$	32.0474	1.07363
$892$	−18.0684	−0.604975
$893$	59.3299	1.98540
$894$	−2.14732	−0.0718171
$895$	−7.28676	−0.243569
$896$	−1.00000	−0.0334077
$897$	5.84191	0.195056
$898$	21.7201	0.724809
$899$	38.9836	1.30018
$900$	11.7447	0.391490
$901$	−31.6071	−1.05299
$902$	38.8111	1.29227
$903$	−2.83568	−0.0943654
$904$	8.51539	0.283218
$905$	3.38331	0.112465
$906$	−0.994669	−0.0330457
$907$	−22.3230	−0.741223	−0.370611	−	0.928788i	$-0.620852\pi$
$907$	−22.3230	−0.741223	−0.370611	+	0.928788i	$0.620852\pi$
$908$	−14.3945	−0.477697
$909$	−9.61214	−0.318815
$910$	−1.53897	−0.0510163
$911$	−41.6024	−1.37835	−0.689174	−	0.724596i	$-0.742027\pi$
$911$	−41.6024	−1.37835	−0.689174	+	0.724596i	$0.742027\pi$
$912$	−2.83555	−0.0938946
$913$	16.2365	0.537349
$914$	37.1412	1.22852
$915$	−0.400892	−0.0132531
$916$	0.956883	0.0316163
$917$	13.4930	0.445578
$918$	7.97048	0.263065
$919$	0.150423	0.00496200	0.00248100	−	0.999997i	$-0.499210\pi$
$919$	0.150423	0.00496200	0.00248100	+	0.999997i	$0.499210\pi$
$920$	−5.31339	−0.175177
$921$	−6.97999	−0.229999
$922$	42.1070	1.38672
$923$	1.22760	0.0404071
$924$	2.42864	0.0798963
$925$	39.2175	1.28946
$926$	−8.77726	−0.288439
$927$	−15.0692	−0.494936
$928$	4.07135	0.133649
$929$	42.8406	1.40556	0.702778	−	0.711409i	$-0.251943\pi$
$929$	42.8406	1.40556	0.702778	+	0.711409i	$0.251943\pi$
$930$	4.12425	0.135239
$931$	−5.56142	−0.182268
$932$	−3.09213	−0.101286
$933$	5.73211	0.187661
$934$	−9.05951	−0.296436
$935$	10.9592	0.358403
$936$	4.99157	0.163155
$937$	36.7463	1.20045	0.600225	−	0.799831i	$-0.295078\pi$
$937$	36.7463	1.20045	0.600225	+	0.799831i	$0.295078\pi$
$938$	−3.97435	−0.129767
$939$	13.4829	0.439999
$940$	−9.01234	−0.293950
$941$	7.86865	0.256511	0.128255	−	0.991741i	$-0.459062\pi$
$941$	7.86865	0.256511	0.128255	+	0.991741i	$0.459062\pi$
$942$	−4.79607	−0.156264
$943$	−51.2469	−1.66883
$944$	4.29623	0.139830
$945$	−2.47239	−0.0804268
$946$	26.4920	0.861329
$947$	10.4075	0.338198	0.169099	−	0.985599i	$-0.445914\pi$
$947$	10.4075	0.338198	0.169099	+	0.985599i	$0.445914\pi$
$948$	−2.23644	−0.0726361
$949$	1.06303	0.0345075
$950$	−23.8381	−0.773409
$951$	−4.70649	−0.152618
$952$	−2.72344	−0.0882671
$953$	3.66933	0.118861	0.0594307	−	0.998232i	$-0.481071\pi$
$953$	3.66933	0.118861	0.0594307	+	0.998232i	$0.481071\pi$
$954$	−31.7998	−1.02956
$955$	13.4147	0.434089
$956$	−22.4412	−0.725800
$957$	−9.88785	−0.319629
$958$	−5.49880	−0.177658
$959$	1.18864	0.0383832
$960$	0.430727	0.0139016
$961$	60.6824	1.95750
$962$	16.6677	0.537387
$963$	−11.6073	−0.374041
$964$	−8.76202	−0.282206
$965$	3.65975	0.117812
$966$	−3.20682	−0.103178
$967$	−42.2477	−1.35860	−0.679298	−	0.733863i	$-0.737715\pi$
$967$	−42.2477	−1.35860	−0.679298	+	0.733863i	$0.737715\pi$
$968$	−11.6893	−0.375708
$969$	−7.72245	−0.248081
$970$	6.11848	0.196452
$971$	4.71978	0.151465	0.0757325	−	0.997128i	$-0.475870\pi$
$971$	4.71978	0.151465	0.0757325	+	0.997128i	$0.475870\pi$
$972$	12.2102	0.391642
$973$	−1.93542	−0.0620468
$974$	−29.7626	−0.953654
$975$	−3.98124	−0.127502
$976$	−0.930735	−0.0297921
$977$	−30.0166	−0.960317	−0.480158	−	0.877182i	$-0.659421\pi$
$977$	−30.0166	−0.960317	−0.480158	+	0.877182i	$0.659421\pi$
$978$	0.517403	0.0165447
$979$	43.4823	1.38970
$980$	0.844791	0.0269859
$981$	17.8720	0.570610
$982$	−10.4222	−0.332587
$983$	−5.41466	−0.172701	−0.0863505	−	0.996265i	$-0.527520\pi$
$983$	−5.41466	−0.172701	−0.0863505	+	0.996265i	$0.527520\pi$
$984$	4.15430	0.132434
$985$	1.24346	0.0396200
$986$	11.0881	0.353116
$987$	−5.43927	−0.173134
$988$	−10.1313	−0.322320
$989$	−34.9805	−1.11232
$990$	11.0260	0.350428
$991$	−18.5942	−0.590666	−0.295333	−	0.955394i	$-0.595431\pi$
$991$	−18.5942	−0.590666	−0.295333	+	0.955394i	$0.595431\pi$
$992$	9.57509	0.304010
$993$	4.00780	0.127184
$994$	−0.673873	−0.0213740
$995$	13.2100	0.418785
$996$	1.73794	0.0550686
$997$	−32.8535	−1.04048	−0.520240	−	0.854020i	$-0.674157\pi$
$997$	−32.8535	−1.04048	−0.520240	+	0.854020i	$0.674157\pi$
$998$	9.31862	0.294976
$999$	26.7770	0.847186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.10	✓	20	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.509862 q^{3} +1.00000 q^{4} +0.844791 q^{5} -0.509862 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.74004 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.509862 q^{3} +1.00000 q^{4} +0.844791 q^{5} -0.509862 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.74004 q^{9} -0.844791 q^{10} +4.76333 q^{11} +0.509862 q^{12} +1.82171 q^{13} -1.00000 q^{14} +0.430727 q^{15} +1.00000 q^{16} +2.72344 q^{17} +2.74004 q^{18} -5.56142 q^{19} +0.844791 q^{20} +0.509862 q^{21} -4.76333 q^{22} +6.28959 q^{23} -0.509862 q^{24} -4.28633 q^{25} -1.82171 q^{26} -2.92663 q^{27} +1.00000 q^{28} -4.07135 q^{29} -0.430727 q^{30} -9.57509 q^{31} -1.00000 q^{32} +2.42864 q^{33} -2.72344 q^{34} +0.844791 q^{35} -2.74004 q^{36} -9.14943 q^{37} +5.56142 q^{38} +0.928823 q^{39} -0.844791 q^{40} -8.14789 q^{41} -0.509862 q^{42} -5.56166 q^{43} +4.76333 q^{44} -2.31476 q^{45} -6.28959 q^{46} -10.6681 q^{47} +0.509862 q^{48} +1.00000 q^{49} +4.28633 q^{50} +1.38858 q^{51} +1.82171 q^{52} -11.6056 q^{53} +2.92663 q^{54} +4.02402 q^{55} -1.00000 q^{56} -2.83555 q^{57} +4.07135 q^{58} +4.29623 q^{59} +0.430727 q^{60} -0.930735 q^{61} +9.57509 q^{62} -2.74004 q^{63} +1.00000 q^{64} +1.53897 q^{65} -2.42864 q^{66} +3.97435 q^{67} +2.72344 q^{68} +3.20682 q^{69} -0.844791 q^{70} +0.673873 q^{71} +2.74004 q^{72} +0.583534 q^{73} +9.14943 q^{74} -2.18543 q^{75} -5.56142 q^{76} +4.76333 q^{77} -0.928823 q^{78} -4.38636 q^{79} +0.844791 q^{80} +6.72795 q^{81} +8.14789 q^{82} +3.40864 q^{83} +0.509862 q^{84} +2.30073 q^{85} +5.56166 q^{86} -2.07583 q^{87} -4.76333 q^{88} +9.12857 q^{89} +2.31476 q^{90} +1.82171 q^{91} +6.28959 q^{92} -4.88197 q^{93} +10.6681 q^{94} -4.69824 q^{95} -0.509862 q^{96} -7.24259 q^{97} -1.00000 q^{98} -13.0517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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