LMFDB - Embedded newform 6034.2.a.l.1.20

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} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Root			$-2.96642$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.96642 q^{3} +1.00000 q^{4} -3.00590 q^{5} +2.96642 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.79966 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.96642 q^{3} +1.00000 q^{4} -3.00590 q^{5} +2.96642 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.79966 q^{9} -3.00590 q^{10} -1.37377 q^{11} +2.96642 q^{12} +0.937766 q^{13} -1.00000 q^{14} -8.91676 q^{15} +1.00000 q^{16} -3.48021 q^{17} +5.79966 q^{18} -6.44664 q^{19} -3.00590 q^{20} -2.96642 q^{21} -1.37377 q^{22} -4.32532 q^{23} +2.96642 q^{24} +4.03543 q^{25} +0.937766 q^{26} +8.30496 q^{27} -1.00000 q^{28} +0.0370281 q^{29} -8.91676 q^{30} -10.7635 q^{31} +1.00000 q^{32} -4.07517 q^{33} -3.48021 q^{34} +3.00590 q^{35} +5.79966 q^{36} -5.90313 q^{37} -6.44664 q^{38} +2.78181 q^{39} -3.00590 q^{40} -3.70284 q^{41} -2.96642 q^{42} +0.915912 q^{43} -1.37377 q^{44} -17.4332 q^{45} -4.32532 q^{46} -8.61848 q^{47} +2.96642 q^{48} +1.00000 q^{49} +4.03543 q^{50} -10.3238 q^{51} +0.937766 q^{52} +11.6509 q^{53} +8.30496 q^{54} +4.12940 q^{55} -1.00000 q^{56} -19.1235 q^{57} +0.0370281 q^{58} +2.05026 q^{59} -8.91676 q^{60} +12.9923 q^{61} -10.7635 q^{62} -5.79966 q^{63} +1.00000 q^{64} -2.81883 q^{65} -4.07517 q^{66} -0.176395 q^{67} -3.48021 q^{68} -12.8307 q^{69} +3.00590 q^{70} +12.2520 q^{71} +5.79966 q^{72} -0.855500 q^{73} -5.90313 q^{74} +11.9708 q^{75} -6.44664 q^{76} +1.37377 q^{77} +2.78181 q^{78} +8.20852 q^{79} -3.00590 q^{80} +7.23705 q^{81} -3.70284 q^{82} -14.3193 q^{83} -2.96642 q^{84} +10.4612 q^{85} +0.915912 q^{86} +0.109841 q^{87} -1.37377 q^{88} -13.9544 q^{89} -17.4332 q^{90} -0.937766 q^{91} -4.32532 q^{92} -31.9290 q^{93} -8.61848 q^{94} +19.3779 q^{95} +2.96642 q^{96} -1.23383 q^{97} +1.00000 q^{98} -7.96737 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	2.96642	1.71266	0.856332	−	0.516425i	$-0.172738\pi$
$3$	2.96642	1.71266	0.856332	+	0.516425i	$0.172738\pi$
$4$	1.00000	0.500000
$5$	−3.00590	−1.34428	−0.672139	−	0.740425i	$-0.734624\pi$
$5$	−3.00590	−1.34428	−0.672139	+	0.740425i	$0.734624\pi$
$6$	2.96642	1.21104
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	5.79966	1.93322
$10$	−3.00590	−0.950549
$11$	−1.37377	−0.414206	−0.207103	−	0.978319i	$-0.566404\pi$
$11$	−1.37377	−0.414206	−0.207103	+	0.978319i	$0.566404\pi$
$12$	2.96642	0.856332
$13$	0.937766	0.260089	0.130045	−	0.991508i	$-0.458488\pi$
$13$	0.937766	0.260089	0.130045	+	0.991508i	$0.458488\pi$
$14$	−1.00000	−0.267261
$15$	−8.91676	−2.30230
$16$	1.00000	0.250000
$17$	−3.48021	−0.844075	−0.422038	−	0.906578i	$-0.638685\pi$
$17$	−3.48021	−0.844075	−0.422038	+	0.906578i	$0.638685\pi$
$18$	5.79966	1.36699
$19$	−6.44664	−1.47896	−0.739480	−	0.673178i	$-0.764929\pi$
$19$	−6.44664	−1.47896	−0.739480	+	0.673178i	$0.764929\pi$
$20$	−3.00590	−0.672139
$21$	−2.96642	−0.647326
$22$	−1.37377	−0.292888
$23$	−4.32532	−0.901891	−0.450945	−	0.892552i	$-0.648913\pi$
$23$	−4.32532	−0.901891	−0.450945	+	0.892552i	$0.648913\pi$
$24$	2.96642	0.605518
$25$	4.03543	0.807085
$26$	0.937766	0.183911
$27$	8.30496	1.59829
$28$	−1.00000	−0.188982
$29$	0.0370281	0.00687594	0.00343797	−	0.999994i	$-0.498906\pi$
$29$	0.0370281	0.00687594	0.00343797	+	0.999994i	$0.498906\pi$
$30$	−8.91676	−1.62797
$31$	−10.7635	−1.93318	−0.966589	−	0.256332i	$-0.917486\pi$
$31$	−10.7635	−1.93318	−0.966589	+	0.256332i	$0.917486\pi$
$32$	1.00000	0.176777
$33$	−4.07517	−0.709396
$34$	−3.48021	−0.596851
$35$	3.00590	0.508090
$36$	5.79966	0.966610
$37$	−5.90313	−0.970468	−0.485234	−	0.874384i	$-0.661266\pi$
$37$	−5.90313	−0.970468	−0.485234	+	0.874384i	$0.661266\pi$
$38$	−6.44664	−1.04578
$39$	2.78181	0.445446
$40$	−3.00590	−0.475274
$41$	−3.70284	−0.578287	−0.289143	−	0.957286i	$-0.593370\pi$
$41$	−3.70284	−0.578287	−0.289143	+	0.957286i	$0.593370\pi$
$42$	−2.96642	−0.457729
$43$	0.915912	0.139675	0.0698376	−	0.997558i	$-0.477752\pi$
$43$	0.915912	0.139675	0.0698376	+	0.997558i	$0.477752\pi$
$44$	−1.37377	−0.207103
$45$	−17.4332	−2.59879
$46$	−4.32532	−0.637733
$47$	−8.61848	−1.25713	−0.628567	−	0.777755i	$-0.716358\pi$
$47$	−8.61848	−1.25713	−0.628567	+	0.777755i	$0.716358\pi$
$48$	2.96642	0.428166
$49$	1.00000	0.142857
$50$	4.03543	0.570695
$51$	−10.3238	−1.44562
$52$	0.937766	0.130045
$53$	11.6509	1.60037	0.800186	−	0.599752i	$-0.204734\pi$
$53$	11.6509	1.60037	0.800186	+	0.599752i	$0.204734\pi$
$54$	8.30496	1.13016
$55$	4.12940	0.556808
$56$	−1.00000	−0.133631
$57$	−19.1235	−2.53296
$58$	0.0370281	0.00486202
$59$	2.05026	0.266921	0.133461	−	0.991054i	$-0.457391\pi$
$59$	2.05026	0.266921	0.133461	+	0.991054i	$0.457391\pi$
$60$	−8.91676	−1.15115
$61$	12.9923	1.66350	0.831749	−	0.555152i	$-0.187340\pi$
$61$	12.9923	1.66350	0.831749	+	0.555152i	$0.187340\pi$
$62$	−10.7635	−1.36696
$63$	−5.79966	−0.730688
$64$	1.00000	0.125000
$65$	−2.81883	−0.349633
$66$	−4.07517	−0.501619
$67$	−0.176395	−0.0215501	−0.0107750	−	0.999942i	$-0.503430\pi$
$67$	−0.176395	−0.0215501	−0.0107750	+	0.999942i	$0.503430\pi$
$68$	−3.48021	−0.422038
$69$	−12.8307	−1.54464
$70$	3.00590	0.359274
$71$	12.2520	1.45405	0.727025	−	0.686611i	$-0.240902\pi$
$71$	12.2520	1.45405	0.727025	+	0.686611i	$0.240902\pi$
$72$	5.79966	0.683496
$73$	−0.855500	−0.100129	−0.0500643	−	0.998746i	$-0.515943\pi$
$73$	−0.855500	−0.100129	−0.0500643	+	0.998746i	$0.515943\pi$
$74$	−5.90313	−0.686224
$75$	11.9708	1.38227
$76$	−6.44664	−0.739480
$77$	1.37377	0.156555
$78$	2.78181	0.314978
$79$	8.20852	0.923531	0.461765	−	0.887002i	$-0.347216\pi$
$79$	8.20852	0.923531	0.461765	+	0.887002i	$0.347216\pi$
$80$	−3.00590	−0.336070
$81$	7.23705	0.804117
$82$	−3.70284	−0.408911
$83$	−14.3193	−1.57175	−0.785875	−	0.618386i	$-0.787787\pi$
$83$	−14.3193	−1.57175	−0.785875	+	0.618386i	$0.787787\pi$
$84$	−2.96642	−0.323663
$85$	10.4612	1.13467
$86$	0.915912	0.0987653
$87$	0.109841	0.0117762
$88$	−1.37377	−0.146444
$89$	−13.9544	−1.47916	−0.739579	−	0.673070i	$-0.764975\pi$
$89$	−13.9544	−1.47916	−0.739579	+	0.673070i	$0.764975\pi$
$90$	−17.4332	−1.83762
$91$	−0.937766	−0.0983046
$92$	−4.32532	−0.450945
$93$	−31.9290	−3.31088
$94$	−8.61848	−0.888928
$95$	19.3779	1.98814
$96$	2.96642	0.302759
$97$	−1.23383	−0.125277	−0.0626383	−	0.998036i	$-0.519951\pi$
$97$	−1.23383	−0.125277	−0.0626383	+	0.998036i	$0.519951\pi$
$98$	1.00000	0.101015
$99$	−7.96737	−0.800751
$100$	4.03543	0.403543
$101$	9.92744	0.987817	0.493909	−	0.869514i	$-0.335568\pi$
$101$	9.92744	0.987817	0.493909	+	0.869514i	$0.335568\pi$
$102$	−10.3238	−1.02221
$103$	16.0479	1.58125	0.790626	−	0.612300i	$-0.209755\pi$
$103$	16.0479	1.58125	0.790626	+	0.612300i	$0.209755\pi$
$104$	0.937766	0.0919555
$105$	8.91676	0.870187
$106$	11.6509	1.13163
$107$	−17.4730	−1.68918	−0.844589	−	0.535415i	$-0.820155\pi$
$107$	−17.4730	−1.68918	−0.844589	+	0.535415i	$0.820155\pi$
$108$	8.30496	0.799146
$109$	−8.49212	−0.813398	−0.406699	−	0.913562i	$-0.633320\pi$
$109$	−8.49212	−0.813398	−0.406699	+	0.913562i	$0.633320\pi$
$110$	4.12940	0.393723
$111$	−17.5112	−1.66209
$112$	−1.00000	−0.0944911
$113$	6.61603	0.622383	0.311192	−	0.950347i	$-0.399272\pi$
$113$	6.61603	0.622383	0.311192	+	0.950347i	$0.399272\pi$
$114$	−19.1235	−1.79108
$115$	13.0015	1.21239
$116$	0.0370281	0.00343797
$117$	5.43872	0.502810
$118$	2.05026	0.188742
$119$	3.48021	0.319030
$120$	−8.91676	−0.813985
$121$	−9.11277	−0.828433
$122$	12.9923	1.17627
$123$	−10.9842	−0.990411
$124$	−10.7635	−0.966589
$125$	2.89941	0.259331
$126$	−5.79966	−0.516675
$127$	13.2357	1.17448	0.587241	−	0.809412i	$-0.300214\pi$
$127$	13.2357	1.17448	0.587241	+	0.809412i	$0.300214\pi$
$128$	1.00000	0.0883883
$129$	2.71698	0.239217
$130$	−2.81883	−0.247228
$131$	1.04367	0.0911862	0.0455931	−	0.998960i	$-0.485482\pi$
$131$	1.04367	0.0911862	0.0455931	+	0.998960i	$0.485482\pi$
$132$	−4.07517	−0.354698
$133$	6.44664	0.558995
$134$	−0.176395	−0.0152382
$135$	−24.9639	−2.14855
$136$	−3.48021	−0.298426
$137$	−5.76411	−0.492461	−0.246231	−	0.969211i	$-0.579192\pi$
$137$	−5.76411	−0.492461	−0.246231	+	0.969211i	$0.579192\pi$
$138$	−12.8307	−1.09222
$139$	−21.2810	−1.80503	−0.902514	−	0.430660i	$-0.858281\pi$
$139$	−21.2810	−1.80503	−0.902514	+	0.430660i	$0.858281\pi$
$140$	3.00590	0.254045
$141$	−25.5660	−2.15305
$142$	12.2520	1.02817
$143$	−1.28827	−0.107731
$144$	5.79966	0.483305
$145$	−0.111303	−0.00924318
$146$	−0.855500	−0.0708016
$147$	2.96642	0.244666
$148$	−5.90313	−0.485234
$149$	−3.73734	−0.306174	−0.153087	−	0.988213i	$-0.548922\pi$
$149$	−3.73734	−0.306174	−0.153087	+	0.988213i	$0.548922\pi$
$150$	11.9708	0.977409
$151$	8.40533	0.684016	0.342008	−	0.939697i	$-0.388893\pi$
$151$	8.40533	0.684016	0.342008	+	0.939697i	$0.388893\pi$
$152$	−6.44664	−0.522892
$153$	−20.1840	−1.63178
$154$	1.37377	0.110701
$155$	32.3539	2.59873
$156$	2.78181	0.222723
$157$	−21.5879	−1.72290	−0.861449	−	0.507843i	$-0.830443\pi$
$157$	−21.5879	−1.72290	−0.861449	+	0.507843i	$0.830443\pi$
$158$	8.20852	0.653035
$159$	34.5614	2.74090
$160$	−3.00590	−0.237637
$161$	4.32532	0.340883
$162$	7.23705	0.568597
$163$	21.1360	1.65550	0.827749	−	0.561099i	$-0.189621\pi$
$163$	21.1360	1.65550	0.827749	+	0.561099i	$0.189621\pi$
$164$	−3.70284	−0.289143
$165$	12.2495	0.953626
$166$	−14.3193	−1.11139
$167$	21.1278	1.63492	0.817459	−	0.575987i	$-0.195382\pi$
$167$	21.1278	1.63492	0.817459	+	0.575987i	$0.195382\pi$
$168$	−2.96642	−0.228864
$169$	−12.1206	−0.932354
$170$	10.4612	0.802334
$171$	−37.3883	−2.85916
$172$	0.915912	0.0698376
$173$	−11.2725	−0.857030	−0.428515	−	0.903535i	$-0.640963\pi$
$173$	−11.2725	−0.857030	−0.428515	+	0.903535i	$0.640963\pi$
$174$	0.109841	0.00832701
$175$	−4.03543	−0.305049
$176$	−1.37377	−0.103552
$177$	6.08194	0.457147
$178$	−13.9544	−1.04592
$179$	−5.26281	−0.393361	−0.196680	−	0.980468i	$-0.563016\pi$
$179$	−5.26281	−0.393361	−0.196680	+	0.980468i	$0.563016\pi$
$180$	−17.4332	−1.29939
$181$	14.0991	1.04798	0.523990	−	0.851724i	$-0.324443\pi$
$181$	14.0991	1.04798	0.523990	+	0.851724i	$0.324443\pi$
$182$	−0.937766	−0.0695118
$183$	38.5407	2.84901
$184$	−4.32532	−0.318867
$185$	17.7442	1.30458
$186$	−31.9290	−2.34115
$187$	4.78100	0.349621
$188$	−8.61848	−0.628567
$189$	−8.30496	−0.604097
$190$	19.3779	1.40582
$191$	0.718916	0.0520189	0.0260095	−	0.999662i	$-0.491720\pi$
$191$	0.718916	0.0520189	0.0260095	+	0.999662i	$0.491720\pi$
$192$	2.96642	0.214083
$193$	−19.5383	−1.40639	−0.703197	−	0.710995i	$-0.748245\pi$
$193$	−19.5383	−1.40639	−0.703197	+	0.710995i	$0.748245\pi$
$194$	−1.23383	−0.0885840
$195$	−8.36183	−0.598803
$196$	1.00000	0.0714286
$197$	12.8357	0.914505	0.457253	−	0.889337i	$-0.348833\pi$
$197$	12.8357	0.914505	0.457253	+	0.889337i	$0.348833\pi$
$198$	−7.96737	−0.566217
$199$	−19.9007	−1.41072	−0.705361	−	0.708848i	$-0.749215\pi$
$199$	−19.9007	−1.41072	−0.705361	+	0.708848i	$0.749215\pi$
$200$	4.03543	0.285348
$201$	−0.523261	−0.0369080
$202$	9.92744	0.698492
$203$	−0.0370281	−0.00259886
$204$	−10.3238	−0.722809
$205$	11.1304	0.777379
$206$	16.0479	1.11811
$207$	−25.0854	−1.74355
$208$	0.937766	0.0650224
$209$	8.85618	0.612595
$210$	8.91676	0.615315
$211$	13.5039	0.929644	0.464822	−	0.885404i	$-0.346118\pi$
$211$	13.5039	0.929644	0.464822	+	0.885404i	$0.346118\pi$
$212$	11.6509	0.800186
$213$	36.3447	2.49030
$214$	−17.4730	−1.19443
$215$	−2.75314	−0.187762
$216$	8.30496	0.565081
$217$	10.7635	0.730673
$218$	−8.49212	−0.575159
$219$	−2.53777	−0.171487
$220$	4.12940	0.278404
$221$	−3.26362	−0.219535
$222$	−17.5112	−1.17527
$223$	3.12125	0.209014	0.104507	−	0.994524i	$-0.466673\pi$
$223$	3.12125	0.209014	0.104507	+	0.994524i	$0.466673\pi$
$224$	−1.00000	−0.0668153
$225$	23.4041	1.56027
$226$	6.61603	0.440092
$227$	−4.67463	−0.310266	−0.155133	−	0.987894i	$-0.549581\pi$
$227$	−4.67463	−0.310266	−0.155133	+	0.987894i	$0.549581\pi$
$228$	−19.1235	−1.26648
$229$	−2.24151	−0.148123	−0.0740616	−	0.997254i	$-0.523596\pi$
$229$	−2.24151	−0.148123	−0.0740616	+	0.997254i	$0.523596\pi$
$230$	13.0015	0.857291
$231$	4.07517	0.268127
$232$	0.0370281	0.00243101
$233$	−2.81106	−0.184159	−0.0920793	−	0.995752i	$-0.529351\pi$
$233$	−2.81106	−0.184159	−0.0920793	+	0.995752i	$0.529351\pi$
$234$	5.43872	0.355540
$235$	25.9063	1.68994
$236$	2.05026	0.133461
$237$	24.3499	1.58170
$238$	3.48021	0.225589
$239$	−19.6110	−1.26853	−0.634264	−	0.773117i	$-0.718697\pi$
$239$	−19.6110	−1.26853	−0.634264	+	0.773117i	$0.718697\pi$
$240$	−8.91676	−0.575575
$241$	10.6059	0.683183	0.341592	−	0.939848i	$-0.389034\pi$
$241$	10.6059	0.683183	0.341592	+	0.939848i	$0.389034\pi$
$242$	−9.11277	−0.585791
$243$	−3.44674	−0.221108
$244$	12.9923	0.831749
$245$	−3.00590	−0.192040
$246$	−10.9842	−0.700326
$247$	−6.04544	−0.384662
$248$	−10.7635	−0.683482
$249$	−42.4771	−2.69188
$250$	2.89941	0.183375
$251$	21.8129	1.37682	0.688409	−	0.725322i	$-0.258309\pi$
$251$	21.8129	1.37682	0.688409	+	0.725322i	$0.258309\pi$
$252$	−5.79966	−0.365344
$253$	5.94197	0.373569
$254$	13.2357	0.830484
$255$	31.0322	1.94331
$256$	1.00000	0.0625000
$257$	−1.29504	−0.0807826	−0.0403913	−	0.999184i	$-0.512860\pi$
$257$	−1.29504	−0.0807826	−0.0403913	+	0.999184i	$0.512860\pi$
$258$	2.71698	0.169152
$259$	5.90313	0.366802
$260$	−2.81883	−0.174816
$261$	0.214750	0.0132927
$262$	1.04367	0.0644784
$263$	−8.70897	−0.537018	−0.268509	−	0.963277i	$-0.586531\pi$
$263$	−8.70897	−0.537018	−0.268509	+	0.963277i	$0.586531\pi$
$264$	−4.07517	−0.250809
$265$	−35.0214	−2.15135
$266$	6.44664	0.395269
$267$	−41.3945	−2.53330
$268$	−0.176395	−0.0107750
$269$	−22.4265	−1.36737	−0.683685	−	0.729777i	$-0.739624\pi$
$269$	−22.4265	−1.36737	−0.683685	+	0.729777i	$0.739624\pi$
$270$	−24.9639	−1.51925
$271$	28.6844	1.74245	0.871226	−	0.490882i	$-0.163325\pi$
$271$	28.6844	1.74245	0.871226	+	0.490882i	$0.163325\pi$
$272$	−3.48021	−0.211019
$273$	−2.78181	−0.168363
$274$	−5.76411	−0.348223
$275$	−5.54373	−0.334300
$276$	−12.8307	−0.772318
$277$	14.4946	0.870897	0.435448	−	0.900214i	$-0.356590\pi$
$277$	14.4946	0.870897	0.435448	+	0.900214i	$0.356590\pi$
$278$	−21.2810	−1.27635
$279$	−62.4245	−3.73726
$280$	3.00590	0.179637
$281$	−25.1528	−1.50049	−0.750246	−	0.661159i	$-0.770065\pi$
$281$	−25.1528	−1.50049	−0.750246	+	0.661159i	$0.770065\pi$
$282$	−25.5660	−1.52244
$283$	17.9157	1.06498	0.532490	−	0.846436i	$-0.321256\pi$
$283$	17.9157	1.06498	0.532490	+	0.846436i	$0.321256\pi$
$284$	12.2520	0.727025
$285$	57.4832	3.40501
$286$	−1.28827	−0.0761771
$287$	3.70284	0.218572
$288$	5.79966	0.341748
$289$	−4.88813	−0.287537
$290$	−0.111303	−0.00653591
$291$	−3.66007	−0.214557
$292$	−0.855500	−0.0500643
$293$	−25.6817	−1.50034	−0.750172	−	0.661243i	$-0.770029\pi$
$293$	−25.6817	−1.50034	−0.750172	+	0.661243i	$0.770029\pi$
$294$	2.96642	0.173005
$295$	−6.16288	−0.358817
$296$	−5.90313	−0.343112
$297$	−11.4091	−0.662022
$298$	−3.73734	−0.216498
$299$	−4.05613	−0.234572
$300$	11.9708	0.691133
$301$	−0.915912	−0.0527923
$302$	8.40533	0.483673
$303$	29.4490	1.69180
$304$	−6.44664	−0.369740
$305$	−39.0536	−2.23620
$306$	−20.1840	−1.15384
$307$	12.4749	0.711981	0.355990	−	0.934490i	$-0.384144\pi$
$307$	12.4749	0.711981	0.355990	+	0.934490i	$0.384144\pi$
$308$	1.37377	0.0782776
$309$	47.6050	2.70815
$310$	32.3539	1.83758
$311$	14.5160	0.823126	0.411563	−	0.911381i	$-0.364983\pi$
$311$	14.5160	0.823126	0.411563	+	0.911381i	$0.364983\pi$
$312$	2.78181	0.157489
$313$	−15.4656	−0.874168	−0.437084	−	0.899421i	$-0.643989\pi$
$313$	−15.4656	−0.874168	−0.437084	+	0.899421i	$0.643989\pi$
$314$	−21.5879	−1.21827
$315$	17.4332	0.982248
$316$	8.20852	0.461765
$317$	−6.26073	−0.351638	−0.175819	−	0.984423i	$-0.556257\pi$
$317$	−6.26073	−0.351638	−0.175819	+	0.984423i	$0.556257\pi$
$318$	34.5614	1.93811
$319$	−0.0508679	−0.00284806
$320$	−3.00590	−0.168035
$321$	−51.8323	−2.89299
$322$	4.32532	0.241040
$323$	22.4357	1.24835
$324$	7.23705	0.402059
$325$	3.78428	0.209914
$326$	21.1360	1.17061
$327$	−25.1912	−1.39308
$328$	−3.70284	−0.204455
$329$	8.61848	0.475152
$330$	12.2495	0.674315
$331$	−4.56838	−0.251101	−0.125551	−	0.992087i	$-0.540070\pi$
$331$	−4.56838	−0.251101	−0.125551	+	0.992087i	$0.540070\pi$
$332$	−14.3193	−0.785875
$333$	−34.2361	−1.87613
$334$	21.1278	1.15606
$335$	0.530225	0.0289693
$336$	−2.96642	−0.161832
$337$	9.33280	0.508390	0.254195	−	0.967153i	$-0.418189\pi$
$337$	9.33280	0.508390	0.254195	+	0.967153i	$0.418189\pi$
$338$	−12.1206	−0.659273
$339$	19.6259	1.06593
$340$	10.4612	0.567336
$341$	14.7865	0.800734
$342$	−37.3883	−2.02173
$343$	−1.00000	−0.0539949
$344$	0.915912	0.0493826
$345$	38.5678	2.07642
$346$	−11.2725	−0.606012
$347$	−3.05837	−0.164182	−0.0820910	−	0.996625i	$-0.526160\pi$
$347$	−3.05837	−0.164182	−0.0820910	+	0.996625i	$0.526160\pi$
$348$	0.109841	0.00588809
$349$	−24.9104	−1.33342	−0.666711	−	0.745317i	$-0.732298\pi$
$349$	−24.9104	−1.33342	−0.666711	+	0.745317i	$0.732298\pi$
$350$	−4.03543	−0.215703
$351$	7.78811	0.415699
$352$	−1.37377	−0.0732220
$353$	−21.8752	−1.16430	−0.582149	−	0.813082i	$-0.697788\pi$
$353$	−21.8752	−1.16430	−0.582149	+	0.813082i	$0.697788\pi$
$354$	6.08194	0.323251
$355$	−36.8284	−1.95465
$356$	−13.9544	−0.739579
$357$	10.3238	0.546392
$358$	−5.26281	−0.278148
$359$	−23.0808	−1.21816	−0.609079	−	0.793109i	$-0.708461\pi$
$359$	−23.0808	−1.21816	−0.609079	+	0.793109i	$0.708461\pi$
$360$	−17.4332	−0.918809
$361$	22.5592	1.18733
$362$	14.0991	0.741034
$363$	−27.0323	−1.41883
$364$	−0.937766	−0.0491523
$365$	2.57154	0.134601
$366$	38.5407	2.01456
$367$	−22.2115	−1.15943	−0.579717	−	0.814818i	$-0.696837\pi$
$367$	−22.2115	−1.15943	−0.579717	+	0.814818i	$0.696837\pi$
$368$	−4.32532	−0.225473
$369$	−21.4752	−1.11796
$370$	17.7442	0.922477
$371$	−11.6509	−0.604884
$372$	−31.9290	−1.65544
$373$	0.803450	0.0416010	0.0208005	−	0.999784i	$-0.493379\pi$
$373$	0.803450	0.0416010	0.0208005	+	0.999784i	$0.493379\pi$
$374$	4.78100	0.247219
$375$	8.60088	0.444148
$376$	−8.61848	−0.444464
$377$	0.0347236	0.00178836
$378$	−8.30496	−0.427161
$379$	−1.82536	−0.0937622	−0.0468811	−	0.998900i	$-0.514928\pi$
$379$	−1.82536	−0.0937622	−0.0468811	+	0.998900i	$0.514928\pi$
$380$	19.3779	0.994068
$381$	39.2628	2.01149
$382$	0.718916	0.0367829
$383$	−25.7165	−1.31405	−0.657025	−	0.753868i	$-0.728186\pi$
$383$	−25.7165	−1.31405	−0.657025	+	0.753868i	$0.728186\pi$
$384$	2.96642	0.151380
$385$	−4.12940	−0.210454
$386$	−19.5383	−0.994471
$387$	5.31197	0.270023
$388$	−1.23383	−0.0626383
$389$	25.5339	1.29462	0.647310	−	0.762227i	$-0.275894\pi$
$389$	25.5339	1.29462	0.647310	+	0.762227i	$0.275894\pi$
$390$	−8.36183	−0.423418
$391$	15.0530	0.761263
$392$	1.00000	0.0505076
$393$	3.09598	0.156171
$394$	12.8357	0.646653
$395$	−24.6740	−1.24148
$396$	−7.96737	−0.400376
$397$	5.67122	0.284630	0.142315	−	0.989821i	$-0.454545\pi$
$397$	5.67122	0.284630	0.142315	+	0.989821i	$0.454545\pi$
$398$	−19.9007	−0.997531
$399$	19.1235	0.957370
$400$	4.03543	0.201771
$401$	−31.3277	−1.56443	−0.782215	−	0.623008i	$-0.785910\pi$
$401$	−31.3277	−1.56443	−0.782215	+	0.623008i	$0.785910\pi$
$402$	−0.523261	−0.0260979
$403$	−10.0936	−0.502799
$404$	9.92744	0.493909
$405$	−21.7538	−1.08096
$406$	−0.0370281	−0.00183767
$407$	8.10952	0.401974
$408$	−10.3238	−0.511103
$409$	4.06830	0.201165	0.100582	−	0.994929i	$-0.467929\pi$
$409$	4.06830	0.201165	0.100582	+	0.994929i	$0.467929\pi$
$410$	11.1304	0.549690
$411$	−17.0988	−0.843421
$412$	16.0479	0.790626
$413$	−2.05026	−0.100887
$414$	−25.0854	−1.23288
$415$	43.0424	2.11287
$416$	0.937766	0.0459777
$417$	−63.1283	−3.09141
$418$	8.85618	0.433170
$419$	3.10913	0.151891	0.0759454	−	0.997112i	$-0.475803\pi$
$419$	3.10913	0.151891	0.0759454	+	0.997112i	$0.475803\pi$
$420$	8.91676	0.435093
$421$	−3.23947	−0.157882	−0.0789411	−	0.996879i	$-0.525154\pi$
$421$	−3.23947	−0.157882	−0.0789411	+	0.996879i	$0.525154\pi$
$422$	13.5039	0.657357
$423$	−49.9842	−2.43032
$424$	11.6509	0.565817
$425$	−14.0441	−0.681240
$426$	36.3447	1.76091
$427$	−12.9923	−0.628743
$428$	−17.4730	−0.844589
$429$	−3.82155	−0.184506
$430$	−2.75314	−0.132768
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	8.30496	0.399573
$433$	14.7918	0.710848	0.355424	−	0.934705i	$-0.384336\pi$
$433$	14.7918	0.710848	0.355424	+	0.934705i	$0.384336\pi$
$434$	10.7635	0.516664
$435$	−0.330170	−0.0158305
$436$	−8.49212	−0.406699
$437$	27.8838	1.33386
$438$	−2.53777	−0.121259
$439$	−11.4528	−0.546613	−0.273306	−	0.961927i	$-0.588117\pi$
$439$	−11.4528	−0.546613	−0.273306	+	0.961927i	$0.588117\pi$
$440$	4.12940	0.196862
$441$	5.79966	0.276174
$442$	−3.26362	−0.155235
$443$	13.1124	0.622989	0.311494	−	0.950248i	$-0.399171\pi$
$443$	13.1124	0.622989	0.311494	+	0.950248i	$0.399171\pi$
$444$	−17.5112	−0.831043
$445$	41.9454	1.98840
$446$	3.12125	0.147796
$447$	−11.0865	−0.524374
$448$	−1.00000	−0.0472456
$449$	40.7329	1.92230	0.961151	−	0.276022i	$-0.0890163\pi$
$449$	40.7329	1.92230	0.961151	+	0.276022i	$0.0890163\pi$
$450$	23.4041	1.10328
$451$	5.08684	0.239530
$452$	6.61603	0.311192
$453$	24.9338	1.17149
$454$	−4.67463	−0.219391
$455$	2.81883	0.132149
$456$	−19.1235	−0.895538
$457$	−7.19538	−0.336586	−0.168293	−	0.985737i	$-0.553825\pi$
$457$	−7.19538	−0.336586	−0.168293	+	0.985737i	$0.553825\pi$
$458$	−2.24151	−0.104739
$459$	−28.9030	−1.34908
$460$	13.0015	0.606196
$461$	16.7898	0.781977	0.390988	−	0.920396i	$-0.372133\pi$
$461$	16.7898	0.781977	0.390988	+	0.920396i	$0.372133\pi$
$462$	4.07517	0.189594
$463$	32.7932	1.52403	0.762015	−	0.647560i	$-0.224210\pi$
$463$	32.7932	1.52403	0.762015	+	0.647560i	$0.224210\pi$
$464$	0.0370281	0.00171898
$465$	95.9754	4.45075
$466$	−2.81106	−0.130220
$467$	4.47941	0.207283	0.103641	−	0.994615i	$-0.466951\pi$
$467$	4.47941	0.207283	0.103641	+	0.994615i	$0.466951\pi$
$468$	5.43872	0.251405
$469$	0.176395	0.00814516
$470$	25.9063	1.19497
$471$	−64.0387	−2.95075
$472$	2.05026	0.0943709
$473$	−1.25825	−0.0578543
$474$	24.3499	1.11843
$475$	−26.0149	−1.19365
$476$	3.48021	0.159515
$477$	67.5711	3.09387
$478$	−19.6110	−0.896985
$479$	32.2647	1.47421	0.737106	−	0.675777i	$-0.236192\pi$
$479$	32.2647	1.47421	0.737106	+	0.675777i	$0.236192\pi$
$480$	−8.91676	−0.406993
$481$	−5.53575	−0.252408
$482$	10.6059	0.483084
$483$	12.8307	0.583818
$484$	−9.11277	−0.414217
$485$	3.70877	0.168407
$486$	−3.44674	−0.156347
$487$	28.0469	1.27093	0.635464	−	0.772130i	$-0.280809\pi$
$487$	28.0469	1.27093	0.635464	+	0.772130i	$0.280809\pi$
$488$	12.9923	0.588135
$489$	62.6982	2.83531
$490$	−3.00590	−0.135793
$491$	6.40585	0.289092	0.144546	−	0.989498i	$-0.453828\pi$
$491$	6.40585	0.289092	0.144546	+	0.989498i	$0.453828\pi$
$492$	−10.9842	−0.495206
$493$	−0.128865	−0.00580381
$494$	−6.04544	−0.271997
$495$	23.9491	1.07643
$496$	−10.7635	−0.483294
$497$	−12.2520	−0.549579
$498$	−42.4771	−1.90345
$499$	27.1875	1.21708	0.608539	−	0.793524i	$-0.291756\pi$
$499$	27.1875	1.21708	0.608539	+	0.793524i	$0.291756\pi$
$500$	2.89941	0.129666
$501$	62.6739	2.80007
$502$	21.8129	0.973558
$503$	−17.0838	−0.761728	−0.380864	−	0.924631i	$-0.624373\pi$
$503$	−17.0838	−0.761728	−0.380864	+	0.924631i	$0.624373\pi$
$504$	−5.79966	−0.258337
$505$	−29.8409	−1.32790
$506$	5.94197	0.264153
$507$	−35.9548	−1.59681
$508$	13.2357	0.587241
$509$	−2.19887	−0.0974630	−0.0487315	−	0.998812i	$-0.515518\pi$
$509$	−2.19887	−0.0974630	−0.0487315	+	0.998812i	$0.515518\pi$
$510$	31.0322	1.37413
$511$	0.855500	0.0378451
$512$	1.00000	0.0441942
$513$	−53.5391	−2.36381
$514$	−1.29504	−0.0571219
$515$	−48.2385	−2.12564
$516$	2.71698	0.119608
$517$	11.8398	0.520713
$518$	5.90313	0.259368
$519$	−33.4389	−1.46780
$520$	−2.81883	−0.123614
$521$	30.9060	1.35402	0.677009	−	0.735975i	$-0.263276\pi$
$521$	30.9060	1.35402	0.677009	+	0.735975i	$0.263276\pi$
$522$	0.214750	0.00939935
$523$	3.94114	0.172334	0.0861669	−	0.996281i	$-0.472538\pi$
$523$	3.94114	0.172334	0.0861669	+	0.996281i	$0.472538\pi$
$524$	1.04367	0.0455931
$525$	−11.9708	−0.522447
$526$	−8.70897	−0.379729
$527$	37.4592	1.63175
$528$	−4.07517	−0.177349
$529$	−4.29164	−0.186593
$530$	−35.0214	−1.52123
$531$	11.8908	0.516017
$532$	6.44664	0.279497
$533$	−3.47240	−0.150406
$534$	−41.3945	−1.79131
$535$	52.5220	2.27073
$536$	−0.176395	−0.00761910
$537$	−15.6117	−0.673695
$538$	−22.4265	−0.966876
$539$	−1.37377	−0.0591723
$540$	−24.9639	−1.07427
$541$	−37.2842	−1.60297	−0.801487	−	0.598013i	$-0.795957\pi$
$541$	−37.2842	−1.60297	−0.801487	+	0.598013i	$0.795957\pi$
$542$	28.6844	1.23210
$543$	41.8240	1.79484
$544$	−3.48021	−0.149213
$545$	25.5265	1.09343
$546$	−2.78181	−0.119050
$547$	42.7929	1.82969	0.914845	−	0.403805i	$-0.132313\pi$
$547$	42.7929	1.82969	0.914845	+	0.403805i	$0.132313\pi$
$548$	−5.76411	−0.246231
$549$	75.3511	3.21591
$550$	−5.54373	−0.236385
$551$	−0.238707	−0.0101692
$552$	−12.8307	−0.546111
$553$	−8.20852	−0.349062
$554$	14.4946	0.615817
$555$	52.6368	2.23431
$556$	−21.2810	−0.902514
$557$	−9.33823	−0.395673	−0.197837	−	0.980235i	$-0.563392\pi$
$557$	−9.33823	−0.395673	−0.197837	+	0.980235i	$0.563392\pi$
$558$	−62.4245	−2.64264
$559$	0.858910	0.0363280
$560$	3.00590	0.127022
$561$	14.1824	0.598783
$562$	−25.1528	−1.06101
$563$	−12.4035	−0.522744	−0.261372	−	0.965238i	$-0.584175\pi$
$563$	−12.4035	−0.522744	−0.261372	+	0.965238i	$0.584175\pi$
$564$	−25.5660	−1.07652
$565$	−19.8871	−0.836657
$566$	17.9157	0.753055
$567$	−7.23705	−0.303928
$568$	12.2520	0.514084
$569$	−8.34402	−0.349799	−0.174900	−	0.984586i	$-0.555960\pi$
$569$	−8.34402	−0.349799	−0.174900	+	0.984586i	$0.555960\pi$
$570$	57.4832	2.40770
$571$	36.3113	1.51958	0.759790	−	0.650168i	$-0.225302\pi$
$571$	36.3113	1.51958	0.759790	+	0.650168i	$0.225302\pi$
$572$	−1.28827	−0.0538653
$573$	2.13261	0.0890910
$574$	3.70284	0.154554
$575$	−17.4545	−0.727903
$576$	5.79966	0.241652
$577$	29.4664	1.22670	0.613352	−	0.789810i	$-0.289821\pi$
$577$	29.4664	1.22670	0.613352	+	0.789810i	$0.289821\pi$
$578$	−4.88813	−0.203320
$579$	−57.9587	−2.40868
$580$	−0.111303	−0.00462159
$581$	14.3193	0.594065
$582$	−3.66007	−0.151715
$583$	−16.0056	−0.662884
$584$	−0.855500	−0.0354008
$585$	−16.3482	−0.675916
$586$	−25.6817	−1.06090
$587$	−34.3985	−1.41978	−0.709889	−	0.704314i	$-0.751255\pi$
$587$	−34.3985	−1.41978	−0.709889	+	0.704314i	$0.751255\pi$
$588$	2.96642	0.122333
$589$	69.3883	2.85909
$590$	−6.16288	−0.253722
$591$	38.0761	1.56624
$592$	−5.90313	−0.242617
$593$	3.85993	0.158508	0.0792542	−	0.996854i	$-0.474746\pi$
$593$	3.85993	0.158508	0.0792542	+	0.996854i	$0.474746\pi$
$594$	−11.4091	−0.468120
$595$	−10.4612	−0.428866
$596$	−3.73734	−0.153087
$597$	−59.0338	−2.41609
$598$	−4.05613	−0.165868
$599$	−2.29302	−0.0936903	−0.0468452	−	0.998902i	$-0.514917\pi$
$599$	−2.29302	−0.0936903	−0.0468452	+	0.998902i	$0.514917\pi$
$600$	11.9708	0.488705
$601$	21.4503	0.874978	0.437489	−	0.899224i	$-0.355868\pi$
$601$	21.4503	0.874978	0.437489	+	0.899224i	$0.355868\pi$
$602$	−0.915912	−0.0373298
$603$	−1.02303	−0.0416610
$604$	8.40533	0.342008
$605$	27.3920	1.11365
$606$	29.4490	1.19628
$607$	16.7552	0.680073	0.340036	−	0.940412i	$-0.389561\pi$
$607$	16.7552	0.680073	0.340036	+	0.940412i	$0.389561\pi$
$608$	−6.44664	−0.261446
$609$	−0.109841	−0.00445097
$610$	−39.0536	−1.58124
$611$	−8.08211	−0.326967
$612$	−20.1840	−0.815891
$613$	25.2545	1.02002	0.510010	−	0.860168i	$-0.329642\pi$
$613$	25.2545	1.02002	0.510010	+	0.860168i	$0.329642\pi$
$614$	12.4749	0.503447
$615$	33.0174	1.33139
$616$	1.37377	0.0553506
$617$	22.8729	0.920826	0.460413	−	0.887705i	$-0.347701\pi$
$617$	22.8729	0.920826	0.460413	+	0.887705i	$0.347701\pi$
$618$	47.6050	1.91495
$619$	−32.3072	−1.29854	−0.649268	−	0.760560i	$-0.724925\pi$
$619$	−32.3072	−1.29854	−0.649268	+	0.760560i	$0.724925\pi$
$620$	32.3539	1.29936
$621$	−35.9216	−1.44148
$622$	14.5160	0.582038
$623$	13.9544	0.559069
$624$	2.78181	0.111361
$625$	−28.8925	−1.15570
$626$	−15.4656	−0.618130
$627$	26.2712	1.04917
$628$	−21.5879	−0.861449
$629$	20.5441	0.819148
$630$	17.4332	0.694555
$631$	0.705786	0.0280969	0.0140484	−	0.999901i	$-0.495528\pi$
$631$	0.705786	0.0280969	0.0140484	+	0.999901i	$0.495528\pi$
$632$	8.20852	0.326518
$633$	40.0581	1.59217
$634$	−6.26073	−0.248645
$635$	−39.7853	−1.57883
$636$	34.5614	1.37045
$637$	0.937766	0.0371556
$638$	−0.0508679	−0.00201388
$639$	71.0576	2.81100
$640$	−3.00590	−0.118819
$641$	−22.3288	−0.881936	−0.440968	−	0.897523i	$-0.645365\pi$
$641$	−22.3288	−0.881936	−0.440968	+	0.897523i	$0.645365\pi$
$642$	−51.8323	−2.04566
$643$	−41.2884	−1.62826	−0.814128	−	0.580686i	$-0.802784\pi$
$643$	−41.2884	−1.62826	−0.814128	+	0.580686i	$0.802784\pi$
$644$	4.32532	0.170441
$645$	−8.16697	−0.321574
$646$	22.4357	0.882719
$647$	−7.11364	−0.279666	−0.139833	−	0.990175i	$-0.544657\pi$
$647$	−7.11364	−0.279666	−0.139833	+	0.990175i	$0.544657\pi$
$648$	7.23705	0.284298
$649$	−2.81658	−0.110560
$650$	3.78428	0.148432
$651$	31.9290	1.25140
$652$	21.1360	0.827749
$653$	−25.5178	−0.998590	−0.499295	−	0.866432i	$-0.666408\pi$
$653$	−25.5178	−0.998590	−0.499295	+	0.866432i	$0.666408\pi$
$654$	−25.1912	−0.985055
$655$	−3.13718	−0.122580
$656$	−3.70284	−0.144572
$657$	−4.96160	−0.193571
$658$	8.61848	0.335983
$659$	−39.5584	−1.54098	−0.770488	−	0.637454i	$-0.779987\pi$
$659$	−39.5584	−1.54098	−0.770488	+	0.637454i	$0.779987\pi$
$660$	12.2495	0.476813
$661$	15.4648	0.601510	0.300755	−	0.953701i	$-0.402761\pi$
$661$	15.4648	0.601510	0.300755	+	0.953701i	$0.402761\pi$
$662$	−4.56838	−0.177555
$663$	−9.68128	−0.375990
$664$	−14.3193	−0.555697
$665$	−19.3779	−0.751445
$666$	−34.2361	−1.32662
$667$	−0.160158	−0.00620134
$668$	21.1278	0.817459
$669$	9.25895	0.357972
$670$	0.530225	0.0204844
$671$	−17.8484	−0.689031
$672$	−2.96642	−0.114432
$673$	−14.9594	−0.576644	−0.288322	−	0.957533i	$-0.593097\pi$
$673$	−14.9594	−0.576644	−0.288322	+	0.957533i	$0.593097\pi$
$674$	9.33280	0.359486
$675$	33.5141	1.28996
$676$	−12.1206	−0.466177
$677$	−19.6776	−0.756273	−0.378137	−	0.925750i	$-0.623435\pi$
$677$	−19.6776	−0.756273	−0.378137	+	0.925750i	$0.623435\pi$
$678$	19.6259	0.753729
$679$	1.23383	0.0473501
$680$	10.4612	0.401167
$681$	−13.8669	−0.531382
$682$	14.7865	0.566205
$683$	17.8825	0.684256	0.342128	−	0.939653i	$-0.388852\pi$
$683$	17.8825	0.684256	0.342128	+	0.939653i	$0.388852\pi$
$684$	−37.3883	−1.42958
$685$	17.3263	0.662005
$686$	−1.00000	−0.0381802
$687$	−6.64927	−0.253685
$688$	0.915912	0.0349188
$689$	10.9258	0.416240
$690$	38.5678	1.46825
$691$	35.4320	1.34790	0.673948	−	0.738779i	$-0.264597\pi$
$691$	35.4320	1.34790	0.673948	+	0.738779i	$0.264597\pi$
$692$	−11.2725	−0.428515
$693$	7.96737	0.302656
$694$	−3.05837	−0.116094
$695$	63.9684	2.42646
$696$	0.109841	0.00416351
$697$	12.8867	0.488117
$698$	−24.9104	−0.942871
$699$	−8.33879	−0.315402
$700$	−4.03543	−0.152525
$701$	23.7083	0.895452	0.447726	−	0.894171i	$-0.352234\pi$
$701$	23.7083	0.895452	0.447726	+	0.894171i	$0.352234\pi$
$702$	7.78811	0.293943
$703$	38.0553	1.43528
$704$	−1.37377	−0.0517758
$705$	76.8489	2.89430
$706$	−21.8752	−0.823283
$707$	−9.92744	−0.373360
$708$	6.08194	0.228573
$709$	21.8777	0.821633	0.410816	−	0.911718i	$-0.365244\pi$
$709$	21.8777	0.821633	0.410816	+	0.911718i	$0.365244\pi$
$710$	−36.8284	−1.38214
$711$	47.6066	1.78539
$712$	−13.9544	−0.522961
$713$	46.5554	1.74352
$714$	10.3238	0.386357
$715$	3.87241	0.144820
$716$	−5.26281	−0.196680
$717$	−58.1744	−2.17256
$718$	−23.0808	−0.861368
$719$	−34.7601	−1.29633	−0.648166	−	0.761499i	$-0.724464\pi$
$719$	−34.7601	−1.29633	−0.648166	+	0.761499i	$0.724464\pi$
$720$	−17.4332	−0.649696
$721$	−16.0479	−0.597657
$722$	22.5592	0.839566
$723$	31.4614	1.17006
$724$	14.0991	0.523990
$725$	0.149424	0.00554947
$726$	−27.0323	−1.00326
$727$	37.6886	1.39779	0.698896	−	0.715223i	$-0.253675\pi$
$727$	37.6886	1.39779	0.698896	+	0.715223i	$0.253675\pi$
$728$	−0.937766	−0.0347559
$729$	−31.9356	−1.18280
$730$	2.57154	0.0951771
$731$	−3.18756	−0.117896
$732$	38.5407	1.42451
$733$	−23.2839	−0.860009	−0.430005	−	0.902827i	$-0.641488\pi$
$733$	−23.2839	−0.860009	−0.430005	+	0.902827i	$0.641488\pi$
$734$	−22.2115	−0.819843
$735$	−8.91676	−0.328900
$736$	−4.32532	−0.159433
$737$	0.242325	0.00892616
$738$	−21.4752	−0.790514
$739$	24.9815	0.918958	0.459479	−	0.888189i	$-0.348036\pi$
$739$	24.9815	0.918958	0.459479	+	0.888189i	$0.348036\pi$
$740$	17.7442	0.652290
$741$	−17.9333	−0.658797
$742$	−11.6509	−0.427717
$743$	−27.7849	−1.01933	−0.509665	−	0.860373i	$-0.670231\pi$
$743$	−27.7849	−1.01933	−0.509665	+	0.860373i	$0.670231\pi$
$744$	−31.9290	−1.17057
$745$	11.2341	0.411584
$746$	0.803450	0.0294164
$747$	−83.0471	−3.03854
$748$	4.78100	0.174811
$749$	17.4730	0.638449
$750$	8.60088	0.314060
$751$	−26.7482	−0.976057	−0.488028	−	0.872828i	$-0.662284\pi$
$751$	−26.7482	−0.976057	−0.488028	+	0.872828i	$0.662284\pi$
$752$	−8.61848	−0.314283
$753$	64.7063	2.35803
$754$	0.0347236	0.00126456
$755$	−25.2656	−0.919508
$756$	−8.30496	−0.302049
$757$	−2.28693	−0.0831198	−0.0415599	−	0.999136i	$-0.513233\pi$
$757$	−2.28693	−0.0831198	−0.0415599	+	0.999136i	$0.513233\pi$
$758$	−1.82536	−0.0662999
$759$	17.6264	0.639798
$760$	19.3779	0.702912
$761$	45.0721	1.63386	0.816932	−	0.576735i	$-0.195673\pi$
$761$	45.0721	1.63386	0.816932	+	0.576735i	$0.195673\pi$
$762$	39.2628	1.42234
$763$	8.49212	0.307435
$764$	0.718916	0.0260095
$765$	60.6711	2.19357
$766$	−25.7165	−0.929174
$767$	1.92266	0.0694234
$768$	2.96642	0.107042
$769$	−25.7462	−0.928432	−0.464216	−	0.885722i	$-0.653664\pi$
$769$	−25.7462	−0.928432	−0.464216	+	0.885722i	$0.653664\pi$
$770$	−4.12940	−0.148813
$771$	−3.84165	−0.138354
$772$	−19.5383	−0.703197
$773$	17.7050	0.636805	0.318403	−	0.947956i	$-0.396854\pi$
$773$	17.7050	0.636805	0.318403	+	0.947956i	$0.396854\pi$
$774$	5.31197	0.190935
$775$	−43.4352	−1.56024
$776$	−1.23383	−0.0442920
$777$	17.5112	0.628209
$778$	25.5339	0.915435
$779$	23.8709	0.855263
$780$	−8.36183	−0.299402
$781$	−16.8314	−0.602276
$782$	15.0530	0.538295
$783$	0.307517	0.0109897
$784$	1.00000	0.0357143
$785$	64.8909	2.31606
$786$	3.09598	0.110430
$787$	5.67061	0.202135	0.101068	−	0.994880i	$-0.467774\pi$
$787$	5.67061	0.202135	0.101068	+	0.994880i	$0.467774\pi$
$788$	12.8357	0.457253
$789$	−25.8345	−0.919732
$790$	−24.6740	−0.877861
$791$	−6.61603	−0.235239
$792$	−7.96737	−0.283108
$793$	12.1838	0.432658
$794$	5.67122	0.201264
$795$	−103.888	−3.68453
$796$	−19.9007	−0.705361
$797$	12.2509	0.433949	0.216974	−	0.976177i	$-0.430381\pi$
$797$	12.2509	0.433949	0.216974	+	0.976177i	$0.430381\pi$
$798$	19.1235	0.676963
$799$	29.9941	1.06112
$800$	4.03543	0.142674
$801$	−80.9305	−2.85954
$802$	−31.3277	−1.10622
$803$	1.17526	0.0414739
$804$	−0.523261	−0.0184540
$805$	−13.0015	−0.458241
$806$	−10.0936	−0.355533
$807$	−66.5265	−2.34185
$808$	9.92744	0.349246
$809$	−54.8140	−1.92716	−0.963579	−	0.267423i	$-0.913828\pi$
$809$	−54.8140	−1.92716	−0.963579	+	0.267423i	$0.913828\pi$
$810$	−21.7538	−0.764352
$811$	11.7310	0.411933	0.205966	−	0.978559i	$-0.433966\pi$
$811$	11.7310	0.411933	0.205966	+	0.978559i	$0.433966\pi$
$812$	−0.0370281	−0.00129943
$813$	85.0900	2.98424
$814$	8.10952	0.284238
$815$	−63.5326	−2.22545
$816$	−10.3238	−0.361404
$817$	−5.90455	−0.206574
$818$	4.06830	0.142245
$819$	−5.43872	−0.190044
$820$	11.1304	0.388689
$821$	−42.5494	−1.48498	−0.742492	−	0.669855i	$-0.766356\pi$
$821$	−42.5494	−1.48498	−0.742492	+	0.669855i	$0.766356\pi$
$822$	−17.0988	−0.596388
$823$	−30.8817	−1.07647	−0.538235	−	0.842795i	$-0.680909\pi$
$823$	−30.8817	−1.07647	−0.538235	+	0.842795i	$0.680909\pi$
$824$	16.0479	0.559057
$825$	−16.4450	−0.572543
$826$	−2.05026	−0.0713377
$827$	−2.97663	−0.103508	−0.0517539	−	0.998660i	$-0.516481\pi$
$827$	−2.97663	−0.103508	−0.0517539	+	0.998660i	$0.516481\pi$
$828$	−25.0854	−0.871776
$829$	47.8925	1.66338	0.831688	−	0.555243i	$-0.187375\pi$
$829$	47.8925	1.66338	0.831688	+	0.555243i	$0.187375\pi$
$830$	43.0424	1.49402
$831$	42.9971	1.49155
$832$	0.937766	0.0325112
$833$	−3.48021	−0.120582
$834$	−63.1283	−2.18596
$835$	−63.5080	−2.19778
$836$	8.85618	0.306297
$837$	−89.3903	−3.08978
$838$	3.10913	0.107403
$839$	−23.9922	−0.828302	−0.414151	−	0.910208i	$-0.635921\pi$
$839$	−23.9922	−0.828302	−0.414151	+	0.910208i	$0.635921\pi$
$840$	8.91676	0.307658
$841$	−28.9986	−0.999953
$842$	−3.23947	−0.111640
$843$	−74.6139	−2.56984
$844$	13.5039	0.464822
$845$	36.4333	1.25334
$846$	−49.9842	−1.71849
$847$	9.11277	0.313118
$848$	11.6509	0.400093
$849$	53.1456	1.82395
$850$	−14.0441	−0.481710
$851$	25.5329	0.875256
$852$	36.3447	1.24515
$853$	51.1841	1.75251	0.876256	−	0.481847i	$-0.160034\pi$
$853$	51.1841	1.75251	0.876256	+	0.481847i	$0.160034\pi$
$854$	−12.9923	−0.444589
$855$	112.385	3.84350
$856$	−17.4730	−0.597215
$857$	−39.3677	−1.34478	−0.672388	−	0.740199i	$-0.734731\pi$
$857$	−39.3677	−1.34478	−0.672388	+	0.740199i	$0.734731\pi$
$858$	−3.82155	−0.130466
$859$	−16.9264	−0.577522	−0.288761	−	0.957401i	$-0.593243\pi$
$859$	−16.9264	−0.577522	−0.288761	+	0.957401i	$0.593243\pi$
$860$	−2.75314	−0.0938812
$861$	10.9842	0.374340
$862$	1.00000	0.0340601
$863$	−14.7284	−0.501362	−0.250681	−	0.968070i	$-0.580655\pi$
$863$	−14.7284	−0.501362	−0.250681	+	0.968070i	$0.580655\pi$
$864$	8.30496	0.282541
$865$	33.8839	1.15209
$866$	14.7918	0.502645
$867$	−14.5003	−0.492455
$868$	10.7635	0.365336
$869$	−11.2766	−0.382532
$870$	−0.330170	−0.0111938
$871$	−0.165417	−0.00560494
$872$	−8.49212	−0.287580
$873$	−7.15580	−0.242187
$874$	27.8838	0.943182
$875$	−2.89941	−0.0980181
$876$	−2.53777	−0.0857434
$877$	−0.532952	−0.0179965	−0.00899826	−	0.999960i	$-0.502864\pi$
$877$	−0.532952	−0.0179965	−0.00899826	+	0.999960i	$0.502864\pi$
$878$	−11.4528	−0.386513
$879$	−76.1829	−2.56958
$880$	4.12940	0.139202
$881$	38.4403	1.29509	0.647543	−	0.762029i	$-0.275796\pi$
$881$	38.4403	1.29509	0.647543	+	0.762029i	$0.275796\pi$
$882$	5.79966	0.195285
$883$	−34.1674	−1.14982	−0.574912	−	0.818215i	$-0.694964\pi$
$883$	−34.1674	−1.14982	−0.574912	+	0.818215i	$0.694964\pi$
$884$	−3.26362	−0.109767
$885$	−18.2817	−0.614532
$886$	13.1124	0.440519
$887$	1.25877	0.0422653	0.0211326	−	0.999777i	$-0.493273\pi$
$887$	1.25877	0.0422653	0.0211326	+	0.999777i	$0.493273\pi$
$888$	−17.5112	−0.587636
$889$	−13.2357	−0.443912
$890$	41.9454	1.40601
$891$	−9.94202	−0.333070
$892$	3.12125	0.104507
$893$	55.5602	1.85925
$894$	−11.0865	−0.370788
$895$	15.8195	0.528786
$896$	−1.00000	−0.0334077
$897$	−12.0322	−0.401743
$898$	40.7329	1.35927
$899$	−0.398551	−0.0132924
$900$	23.4041	0.780136
$901$	−40.5475	−1.35083
$902$	5.08684	0.169373
$903$	−2.71698	−0.0904154
$904$	6.61603	0.220046
$905$	−42.3806	−1.40878
$906$	24.9338	0.828369
$907$	27.2497	0.904812	0.452406	−	0.891812i	$-0.350566\pi$
$907$	27.2497	0.904812	0.452406	+	0.891812i	$0.350566\pi$
$908$	−4.67463	−0.155133
$909$	57.5758	1.90967
$910$	2.81883	0.0934432
$911$	−24.8941	−0.824779	−0.412389	−	0.911008i	$-0.635306\pi$
$911$	−24.8941	−0.824779	−0.412389	+	0.911008i	$0.635306\pi$
$912$	−19.1235	−0.633241
$913$	19.6714	0.651028
$914$	−7.19538	−0.238002
$915$	−115.850	−3.82987
$916$	−2.24151	−0.0740616
$917$	−1.04367	−0.0344651
$918$	−28.9030	−0.953942
$919$	−40.8439	−1.34731	−0.673657	−	0.739044i	$-0.735278\pi$
$919$	−40.8439	−1.34731	−0.673657	+	0.739044i	$0.735278\pi$
$920$	13.0015	0.428645
$921$	37.0059	1.21938
$922$	16.7898	0.552941
$923$	11.4895	0.378183
$924$	4.07517	0.134063
$925$	−23.8216	−0.783250
$926$	32.7932	1.07765
$927$	93.0726	3.05691
$928$	0.0370281	0.00121551
$929$	12.4382	0.408085	0.204043	−	0.978962i	$-0.434592\pi$
$929$	12.4382	0.408085	0.204043	+	0.978962i	$0.434592\pi$
$930$	95.9754	3.14716
$931$	−6.44664	−0.211280
$932$	−2.81106	−0.0920793
$933$	43.0605	1.40974
$934$	4.47941	0.146571
$935$	−14.3712	−0.469988
$936$	5.43872	0.177770
$937$	−55.0862	−1.79959	−0.899794	−	0.436316i	$-0.856283\pi$
$937$	−55.0862	−1.79959	−0.899794	+	0.436316i	$0.856283\pi$
$938$	0.176395	0.00575949
$939$	−45.8775	−1.49716
$940$	25.9063	0.844969
$941$	31.7018	1.03345	0.516724	−	0.856152i	$-0.327151\pi$
$941$	31.7018	1.03345	0.516724	+	0.856152i	$0.327151\pi$
$942$	−64.0387	−2.08649
$943$	16.0160	0.521552
$944$	2.05026	0.0667303
$945$	24.9639	0.812075
$946$	−1.25825	−0.0409092
$947$	15.3141	0.497641	0.248821	−	0.968550i	$-0.419957\pi$
$947$	15.3141	0.497641	0.248821	+	0.968550i	$0.419957\pi$
$948$	24.3499	0.790849
$949$	−0.802258	−0.0260424
$950$	−26.0149	−0.844036
$951$	−18.5720	−0.602237
$952$	3.48021	0.112794
$953$	57.9519	1.87725	0.938624	−	0.344943i	$-0.112102\pi$
$953$	57.9519	1.87725	0.938624	+	0.344943i	$0.112102\pi$
$954$	67.5711	2.18770
$955$	−2.16099	−0.0699279
$956$	−19.6110	−0.634264
$957$	−0.150896	−0.00487776
$958$	32.2647	1.04243
$959$	5.76411	0.186133
$960$	−8.91676	−0.287787
$961$	84.8525	2.73718
$962$	−5.53575	−0.178480
$963$	−101.337	−3.26555
$964$	10.6059	0.341592
$965$	58.7300	1.89059
$966$	12.8307	0.412821
$967$	25.5371	0.821217	0.410608	−	0.911812i	$-0.365316\pi$
$967$	25.5371	0.821217	0.410608	+	0.911812i	$0.365316\pi$
$968$	−9.11277	−0.292895
$969$	66.5536	2.13801
$970$	3.70877	0.119082
$971$	−41.2352	−1.32330	−0.661649	−	0.749813i	$-0.730143\pi$
$971$	−41.2352	−1.32330	−0.661649	+	0.749813i	$0.730143\pi$
$972$	−3.44674	−0.110554
$973$	21.2810	0.682237
$974$	28.0469	0.898682
$975$	11.2258	0.359513
$976$	12.9923	0.415875
$977$	−45.9068	−1.46869	−0.734344	−	0.678777i	$-0.762510\pi$
$977$	−45.9068	−1.46869	−0.734344	+	0.678777i	$0.762510\pi$
$978$	62.6982	2.00487
$979$	19.1700	0.612676
$980$	−3.00590	−0.0960199
$981$	−49.2514	−1.57248
$982$	6.40585	0.204419
$983$	49.7930	1.58815	0.794075	−	0.607820i	$-0.207956\pi$
$983$	49.7930	1.58815	0.794075	+	0.607820i	$0.207956\pi$
$984$	−10.9842	−0.350163
$985$	−38.5828	−1.22935
$986$	−0.128865	−0.00410391
$987$	25.5660	0.813776
$988$	−6.04544	−0.192331
$989$	−3.96161	−0.125972
$990$	23.9491	0.761153
$991$	43.5072	1.38205	0.691026	−	0.722830i	$-0.257159\pi$
$991$	43.5072	1.38205	0.691026	+	0.722830i	$0.257159\pi$
$992$	−10.7635	−0.341741
$993$	−13.5518	−0.430052
$994$	−12.2520	−0.388611
$995$	59.8194	1.89640
$996$	−42.4771	−1.34594
$997$	−42.7707	−1.35456	−0.677281	−	0.735725i	$-0.736842\pi$
$997$	−42.7707	−1.35456	−0.677281	+	0.735725i	$0.736842\pi$
$998$	27.1875	0.860605
$999$	−49.0253	−1.55109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.20	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.96642 q^{3} +1.00000 q^{4} -3.00590 q^{5} +2.96642 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.79966 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.96642 q^{3} +1.00000 q^{4} -3.00590 q^{5} +2.96642 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.79966 q^{9} -3.00590 q^{10} -1.37377 q^{11} +2.96642 q^{12} +0.937766 q^{13} -1.00000 q^{14} -8.91676 q^{15} +1.00000 q^{16} -3.48021 q^{17} +5.79966 q^{18} -6.44664 q^{19} -3.00590 q^{20} -2.96642 q^{21} -1.37377 q^{22} -4.32532 q^{23} +2.96642 q^{24} +4.03543 q^{25} +0.937766 q^{26} +8.30496 q^{27} -1.00000 q^{28} +0.0370281 q^{29} -8.91676 q^{30} -10.7635 q^{31} +1.00000 q^{32} -4.07517 q^{33} -3.48021 q^{34} +3.00590 q^{35} +5.79966 q^{36} -5.90313 q^{37} -6.44664 q^{38} +2.78181 q^{39} -3.00590 q^{40} -3.70284 q^{41} -2.96642 q^{42} +0.915912 q^{43} -1.37377 q^{44} -17.4332 q^{45} -4.32532 q^{46} -8.61848 q^{47} +2.96642 q^{48} +1.00000 q^{49} +4.03543 q^{50} -10.3238 q^{51} +0.937766 q^{52} +11.6509 q^{53} +8.30496 q^{54} +4.12940 q^{55} -1.00000 q^{56} -19.1235 q^{57} +0.0370281 q^{58} +2.05026 q^{59} -8.91676 q^{60} +12.9923 q^{61} -10.7635 q^{62} -5.79966 q^{63} +1.00000 q^{64} -2.81883 q^{65} -4.07517 q^{66} -0.176395 q^{67} -3.48021 q^{68} -12.8307 q^{69} +3.00590 q^{70} +12.2520 q^{71} +5.79966 q^{72} -0.855500 q^{73} -5.90313 q^{74} +11.9708 q^{75} -6.44664 q^{76} +1.37377 q^{77} +2.78181 q^{78} +8.20852 q^{79} -3.00590 q^{80} +7.23705 q^{81} -3.70284 q^{82} -14.3193 q^{83} -2.96642 q^{84} +10.4612 q^{85} +0.915912 q^{86} +0.109841 q^{87} -1.37377 q^{88} -13.9544 q^{89} -17.4332 q^{90} -0.937766 q^{91} -4.32532 q^{92} -31.9290 q^{93} -8.61848 q^{94} +19.3779 q^{95} +2.96642 q^{96} -1.23383 q^{97} +1.00000 q^{98} -7.96737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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