LMFDB - Embedded newform 6034.2.a.k.1.8

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			1.8
Root			$-0.141161$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.141161 q^{3} +1.00000 q^{4} -1.57700 q^{5} +0.141161 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.98007 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.141161 q^{3} +1.00000 q^{4} -1.57700 q^{5} +0.141161 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.98007 q^{9} +1.57700 q^{10} -0.868545 q^{11} -0.141161 q^{12} -4.18869 q^{13} -1.00000 q^{14} +0.222611 q^{15} +1.00000 q^{16} +5.52327 q^{17} +2.98007 q^{18} +0.527471 q^{19} -1.57700 q^{20} -0.141161 q^{21} +0.868545 q^{22} +2.36080 q^{23} +0.141161 q^{24} -2.51306 q^{25} +4.18869 q^{26} +0.844151 q^{27} +1.00000 q^{28} +6.24643 q^{29} -0.222611 q^{30} +4.35182 q^{31} -1.00000 q^{32} +0.122604 q^{33} -5.52327 q^{34} -1.57700 q^{35} -2.98007 q^{36} -8.73325 q^{37} -0.527471 q^{38} +0.591277 q^{39} +1.57700 q^{40} -10.6400 q^{41} +0.141161 q^{42} +8.28956 q^{43} -0.868545 q^{44} +4.69959 q^{45} -2.36080 q^{46} +9.80223 q^{47} -0.141161 q^{48} +1.00000 q^{49} +2.51306 q^{50} -0.779668 q^{51} -4.18869 q^{52} -0.274214 q^{53} -0.844151 q^{54} +1.36970 q^{55} -1.00000 q^{56} -0.0744581 q^{57} -6.24643 q^{58} -4.14179 q^{59} +0.222611 q^{60} +11.0753 q^{61} -4.35182 q^{62} -2.98007 q^{63} +1.00000 q^{64} +6.60558 q^{65} -0.122604 q^{66} +4.92691 q^{67} +5.52327 q^{68} -0.333252 q^{69} +1.57700 q^{70} +3.02190 q^{71} +2.98007 q^{72} -1.36759 q^{73} +8.73325 q^{74} +0.354745 q^{75} +0.527471 q^{76} -0.868545 q^{77} -0.591277 q^{78} +5.42830 q^{79} -1.57700 q^{80} +8.82106 q^{81} +10.6400 q^{82} -1.60235 q^{83} -0.141161 q^{84} -8.71023 q^{85} -8.28956 q^{86} -0.881749 q^{87} +0.868545 q^{88} -13.8326 q^{89} -4.69959 q^{90} -4.18869 q^{91} +2.36080 q^{92} -0.614306 q^{93} -9.80223 q^{94} -0.831824 q^{95} +0.141161 q^{96} -8.09710 q^{97} -1.00000 q^{98} +2.58833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.141161	−0.0814991	−0.0407495	−	0.999169i	$-0.512975\pi$
$3$	−0.141161	−0.0814991	−0.0407495	+	0.999169i	$0.512975\pi$
$4$	1.00000	0.500000
$5$	−1.57700	−0.705258	−0.352629	−	0.935763i	$-0.614712\pi$
$5$	−1.57700	−0.705258	−0.352629	+	0.935763i	$0.614712\pi$
$6$	0.141161	0.0576286
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.98007	−0.993358
$10$	1.57700	0.498692
$11$	−0.868545	−0.261876	−0.130938	−	0.991391i	$-0.541799\pi$
$11$	−0.868545	−0.261876	−0.130938	+	0.991391i	$0.541799\pi$
$12$	−0.141161	−0.0407495
$13$	−4.18869	−1.16173	−0.580866	−	0.813999i	$-0.697286\pi$
$13$	−4.18869	−1.16173	−0.580866	+	0.813999i	$0.697286\pi$
$14$	−1.00000	−0.267261
$15$	0.222611	0.0574779
$16$	1.00000	0.250000
$17$	5.52327	1.33959	0.669795	−	0.742546i	$-0.266382\pi$
$17$	5.52327	1.33959	0.669795	+	0.742546i	$0.266382\pi$
$18$	2.98007	0.702410
$19$	0.527471	0.121010	0.0605051	−	0.998168i	$-0.480729\pi$
$19$	0.527471	0.121010	0.0605051	+	0.998168i	$0.480729\pi$
$20$	−1.57700	−0.352629
$21$	−0.141161	−0.0308038
$22$	0.868545	0.185174
$23$	2.36080	0.492261	0.246130	−	0.969237i	$-0.420841\pi$
$23$	2.36080	0.492261	0.246130	+	0.969237i	$0.420841\pi$
$24$	0.141161	0.0288143
$25$	−2.51306	−0.502612
$26$	4.18869	0.821469
$27$	0.844151	0.162457
$28$	1.00000	0.188982
$29$	6.24643	1.15993	0.579966	−	0.814641i	$-0.303066\pi$
$29$	6.24643	1.15993	0.579966	+	0.814641i	$0.303066\pi$
$30$	−0.222611	−0.0406430
$31$	4.35182	0.781610	0.390805	−	0.920473i	$-0.372197\pi$
$31$	4.35182	0.781610	0.390805	+	0.920473i	$0.372197\pi$
$32$	−1.00000	−0.176777
$33$	0.122604	0.0213427
$34$	−5.52327	−0.947234
$35$	−1.57700	−0.266562
$36$	−2.98007	−0.496679
$37$	−8.73325	−1.43574	−0.717869	−	0.696178i	$-0.754882\pi$
$37$	−8.73325	−1.43574	−0.717869	+	0.696178i	$0.754882\pi$
$38$	−0.527471	−0.0855671
$39$	0.591277	0.0946802
$40$	1.57700	0.249346
$41$	−10.6400	−1.66169	−0.830845	−	0.556504i	$-0.812142\pi$
$41$	−10.6400	−1.66169	−0.830845	+	0.556504i	$0.812142\pi$
$42$	0.141161	0.0217815
$43$	8.28956	1.26415	0.632073	−	0.774909i	$-0.282204\pi$
$43$	8.28956	1.26415	0.632073	+	0.774909i	$0.282204\pi$
$44$	−0.868545	−0.130938
$45$	4.69959	0.700573
$46$	−2.36080	−0.348081
$47$	9.80223	1.42980	0.714901	−	0.699225i	$-0.246472\pi$
$47$	9.80223	1.42980	0.714901	+	0.699225i	$0.246472\pi$
$48$	−0.141161	−0.0203748
$49$	1.00000	0.142857
$50$	2.51306	0.355400
$51$	−0.779668	−0.109175
$52$	−4.18869	−0.580866
$53$	−0.274214	−0.0376662	−0.0188331	−	0.999823i	$-0.505995\pi$
$53$	−0.274214	−0.0376662	−0.0188331	+	0.999823i	$0.505995\pi$
$54$	−0.844151	−0.114874
$55$	1.36970	0.184690
$56$	−1.00000	−0.133631
$57$	−0.0744581	−0.00986222
$58$	−6.24643	−0.820196
$59$	−4.14179	−0.539215	−0.269607	−	0.962970i	$-0.586894\pi$
$59$	−4.14179	−0.539215	−0.269607	+	0.962970i	$0.586894\pi$
$60$	0.222611	0.0287389
$61$	11.0753	1.41804	0.709022	−	0.705186i	$-0.249137\pi$
$61$	11.0753	1.41804	0.709022	+	0.705186i	$0.249137\pi$
$62$	−4.35182	−0.552682
$63$	−2.98007	−0.375454
$64$	1.00000	0.125000
$65$	6.60558	0.819321
$66$	−0.122604	−0.0150915
$67$	4.92691	0.601918	0.300959	−	0.953637i	$-0.402693\pi$
$67$	4.92691	0.601918	0.300959	+	0.953637i	$0.402693\pi$
$68$	5.52327	0.669795
$69$	−0.333252	−0.0401188
$70$	1.57700	0.188488
$71$	3.02190	0.358633	0.179317	−	0.983791i	$-0.442611\pi$
$71$	3.02190	0.358633	0.179317	+	0.983791i	$0.442611\pi$
$72$	2.98007	0.351205
$73$	−1.36759	−0.160065	−0.0800323	−	0.996792i	$-0.525502\pi$
$73$	−1.36759	−0.160065	−0.0800323	+	0.996792i	$0.525502\pi$
$74$	8.73325	1.01522
$75$	0.354745	0.0409624
$76$	0.527471	0.0605051
$77$	−0.868545	−0.0989799
$78$	−0.591277	−0.0669490
$79$	5.42830	0.610732	0.305366	−	0.952235i	$-0.401221\pi$
$79$	5.42830	0.610732	0.305366	+	0.952235i	$0.401221\pi$
$80$	−1.57700	−0.176314
$81$	8.82106	0.980118
$82$	10.6400	1.17499
$83$	−1.60235	−0.175880	−0.0879401	−	0.996126i	$-0.528028\pi$
$83$	−1.60235	−0.175880	−0.0879401	+	0.996126i	$0.528028\pi$
$84$	−0.141161	−0.0154019
$85$	−8.71023	−0.944757
$86$	−8.28956	−0.893886
$87$	−0.881749	−0.0945334
$88$	0.868545	0.0925872
$89$	−13.8326	−1.46625	−0.733126	−	0.680093i	$-0.761939\pi$
$89$	−13.8326	−1.46625	−0.733126	+	0.680093i	$0.761939\pi$
$90$	−4.69959	−0.495380
$91$	−4.18869	−0.439094
$92$	2.36080	0.246130
$93$	−0.614306	−0.0637005
$94$	−9.80223	−1.01102
$95$	−0.831824	−0.0853434
$96$	0.141161	0.0144071
$97$	−8.09710	−0.822136	−0.411068	−	0.911605i	$-0.634844\pi$
$97$	−8.09710	−0.822136	−0.411068	+	0.911605i	$0.634844\pi$
$98$	−1.00000	−0.101015
$99$	2.58833	0.260137
$100$	−2.51306	−0.251306
$101$	−0.210142	−0.0209099	−0.0104550	−	0.999945i	$-0.503328\pi$
$101$	−0.210142	−0.0209099	−0.0104550	+	0.999945i	$0.503328\pi$
$102$	0.779668	0.0771987
$103$	13.4657	1.32682	0.663410	−	0.748256i	$-0.269109\pi$
$103$	13.4657	1.32682	0.663410	+	0.748256i	$0.269109\pi$
$104$	4.18869	0.410735
$105$	0.222611	0.0217246
$106$	0.274214	0.0266340
$107$	−6.31071	−0.610079	−0.305040	−	0.952340i	$-0.598670\pi$
$107$	−6.31071	−0.610079	−0.305040	+	0.952340i	$0.598670\pi$
$108$	0.844151	0.0812284
$109$	2.25488	0.215978	0.107989	−	0.994152i	$-0.465559\pi$
$109$	2.25488	0.215978	0.107989	+	0.994152i	$0.465559\pi$
$110$	−1.36970	−0.130596
$111$	1.23279	0.117011
$112$	1.00000	0.0944911
$113$	−17.5793	−1.65372	−0.826861	−	0.562406i	$-0.809876\pi$
$113$	−17.5793	−1.65372	−0.826861	+	0.562406i	$0.809876\pi$
$114$	0.0744581	0.00697364
$115$	−3.72299	−0.347171
$116$	6.24643	0.579966
$117$	12.4826	1.15402
$118$	4.14179	0.381283
$119$	5.52327	0.506318
$120$	−0.222611	−0.0203215
$121$	−10.2456	−0.931421
$122$	−11.0753	−1.00271
$123$	1.50195	0.135426
$124$	4.35182	0.390805
$125$	11.8481	1.05973
$126$	2.98007	0.265486
$127$	−10.7257	−0.951753	−0.475876	−	0.879512i	$-0.657869\pi$
$127$	−10.7257	−0.951753	−0.475876	+	0.879512i	$0.657869\pi$
$128$	−1.00000	−0.0883883
$129$	−1.17016	−0.103027
$130$	−6.60558	−0.579347
$131$	−17.6331	−1.54061	−0.770305	−	0.637676i	$-0.779896\pi$
$131$	−17.6331	−1.54061	−0.770305	+	0.637676i	$0.779896\pi$
$132$	0.122604	0.0106713
$133$	0.527471	0.0457375
$134$	−4.92691	−0.425620
$135$	−1.33123	−0.114574
$136$	−5.52327	−0.473617
$137$	−9.33095	−0.797197	−0.398599	−	0.917125i	$-0.630503\pi$
$137$	−9.33095	−0.797197	−0.398599	+	0.917125i	$0.630503\pi$
$138$	0.333252	0.0283683
$139$	−6.07116	−0.514949	−0.257475	−	0.966285i	$-0.582890\pi$
$139$	−6.07116	−0.514949	−0.257475	+	0.966285i	$0.582890\pi$
$140$	−1.57700	−0.133281
$141$	−1.38369	−0.116528
$142$	−3.02190	−0.253592
$143$	3.63806	0.304230
$144$	−2.98007	−0.248339
$145$	−9.85064	−0.818051
$146$	1.36759	0.113183
$147$	−0.141161	−0.0116427
$148$	−8.73325	−0.717869
$149$	13.1945	1.08094	0.540470	−	0.841363i	$-0.318247\pi$
$149$	13.1945	1.08094	0.540470	+	0.841363i	$0.318247\pi$
$150$	−0.354745	−0.0289648
$151$	3.15973	0.257135	0.128568	−	0.991701i	$-0.458962\pi$
$151$	3.15973	0.257135	0.128568	+	0.991701i	$0.458962\pi$
$152$	−0.527471	−0.0427836
$153$	−16.4598	−1.33069
$154$	0.868545	0.0699894
$155$	−6.86284	−0.551237
$156$	0.591277	0.0473401
$157$	−18.6982	−1.49228	−0.746141	−	0.665788i	$-0.768096\pi$
$157$	−18.6982	−1.49228	−0.746141	+	0.665788i	$0.768096\pi$
$158$	−5.42830	−0.431852
$159$	0.0387082	0.00306976
$160$	1.57700	0.124673
$161$	2.36080	0.186057
$162$	−8.82106	−0.693048
$163$	−1.74870	−0.136969	−0.0684843	−	0.997652i	$-0.521816\pi$
$163$	−1.74870	−0.136969	−0.0684843	+	0.997652i	$0.521816\pi$
$164$	−10.6400	−0.830845
$165$	−0.193347	−0.0150521
$166$	1.60235	0.124366
$167$	−24.7736	−1.91704	−0.958518	−	0.285032i	$-0.907996\pi$
$167$	−24.7736	−1.91704	−0.958518	+	0.285032i	$0.907996\pi$
$168$	0.141161	0.0108908
$169$	4.54510	0.349623
$170$	8.71023	0.668044
$171$	−1.57190	−0.120206
$172$	8.28956	0.632073
$173$	4.15589	0.315967	0.157983	−	0.987442i	$-0.449501\pi$
$173$	4.15589	0.315967	0.157983	+	0.987442i	$0.449501\pi$
$174$	0.881749	0.0668452
$175$	−2.51306	−0.189969
$176$	−0.868545	−0.0654691
$177$	0.584657	0.0439455
$178$	13.8326	1.03680
$179$	−1.65603	−0.123777	−0.0618887	−	0.998083i	$-0.519712\pi$
$179$	−1.65603	−0.123777	−0.0618887	+	0.998083i	$0.519712\pi$
$180$	4.69959	0.350287
$181$	−10.0989	−0.750644	−0.375322	−	0.926894i	$-0.622468\pi$
$181$	−10.0989	−0.750644	−0.375322	+	0.926894i	$0.622468\pi$
$182$	4.18869	0.310486
$183$	−1.56339	−0.115569
$184$	−2.36080	−0.174040
$185$	13.7724	1.01257
$186$	0.614306	0.0450431
$187$	−4.79721	−0.350807
$188$	9.80223	0.714901
$189$	0.844151	0.0614029
$190$	0.831824	0.0603469
$191$	20.8623	1.50954	0.754770	−	0.655989i	$-0.227748\pi$
$191$	20.8623	1.50954	0.754770	+	0.655989i	$0.227748\pi$
$192$	−0.141161	−0.0101874
$193$	−14.2126	−1.02305	−0.511524	−	0.859269i	$-0.670919\pi$
$193$	−14.2126	−1.02305	−0.511524	+	0.859269i	$0.670919\pi$
$194$	8.09710	0.581338
$195$	−0.932447	−0.0667739
$196$	1.00000	0.0714286
$197$	4.10246	0.292289	0.146144	−	0.989263i	$-0.453314\pi$
$197$	4.10246	0.292289	0.146144	+	0.989263i	$0.453314\pi$
$198$	−2.58833	−0.183944
$199$	22.0627	1.56399	0.781993	−	0.623288i	$-0.214203\pi$
$199$	22.0627	1.56399	0.781993	+	0.623288i	$0.214203\pi$
$200$	2.51306	0.177700
$201$	−0.695486	−0.0490558
$202$	0.210142	0.0147855
$203$	6.24643	0.438413
$204$	−0.779668	−0.0545877
$205$	16.7793	1.17192
$206$	−13.4657	−0.938203
$207$	−7.03536	−0.488991
$208$	−4.18869	−0.290433
$209$	−0.458132	−0.0316897
$210$	−0.222611	−0.0153616
$211$	11.7749	0.810615	0.405308	−	0.914180i	$-0.367164\pi$
$211$	11.7749	0.810615	0.405308	+	0.914180i	$0.367164\pi$
$212$	−0.274214	−0.0188331
$213$	−0.426573	−0.0292283
$214$	6.31071	0.431391
$215$	−13.0727	−0.891549
$216$	−0.844151	−0.0574372
$217$	4.35182	0.295421
$218$	−2.25488	−0.152720
$219$	0.193050	0.0130451
$220$	1.36970	0.0923451
$221$	−23.1353	−1.55625
$222$	−1.23279	−0.0827395
$223$	−6.62290	−0.443502	−0.221751	−	0.975103i	$-0.571177\pi$
$223$	−6.62290	−0.443502	−0.221751	+	0.975103i	$0.571177\pi$
$224$	−1.00000	−0.0668153
$225$	7.48910	0.499273
$226$	17.5793	1.16936
$227$	15.5456	1.03180	0.515898	−	0.856650i	$-0.327459\pi$
$227$	15.5456	1.03180	0.515898	+	0.856650i	$0.327459\pi$
$228$	−0.0744581	−0.00493111
$229$	4.14511	0.273916	0.136958	−	0.990577i	$-0.456267\pi$
$229$	4.14511	0.273916	0.136958	+	0.990577i	$0.456267\pi$
$230$	3.72299	0.245487
$231$	0.122604	0.00806677
$232$	−6.24643	−0.410098
$233$	8.19461	0.536847	0.268424	−	0.963301i	$-0.413497\pi$
$233$	8.19461	0.536847	0.268424	+	0.963301i	$0.413497\pi$
$234$	−12.4826	−0.816013
$235$	−15.4582	−1.00838
$236$	−4.14179	−0.269607
$237$	−0.766262	−0.0497741
$238$	−5.52327	−0.358021
$239$	−27.6999	−1.79175	−0.895877	−	0.444301i	$-0.853452\pi$
$239$	−27.6999	−1.79175	−0.895877	+	0.444301i	$0.853452\pi$
$240$	0.222611	0.0143695
$241$	−13.4044	−0.863456	−0.431728	−	0.902004i	$-0.642096\pi$
$241$	−13.4044	−0.863456	−0.431728	+	0.902004i	$0.642096\pi$
$242$	10.2456	0.658614
$243$	−3.77764	−0.242336
$244$	11.0753	0.709022
$245$	−1.57700	−0.100751
$246$	−1.50195	−0.0957608
$247$	−2.20941	−0.140582
$248$	−4.35182	−0.276341
$249$	0.226188	0.0143341
$250$	−11.8481	−0.749341
$251$	20.4793	1.29264	0.646321	−	0.763066i	$-0.276307\pi$
$251$	20.4793	1.29264	0.646321	+	0.763066i	$0.276307\pi$
$252$	−2.98007	−0.187727
$253$	−2.05046	−0.128911
$254$	10.7257	0.672991
$255$	1.22954	0.0769968
$256$	1.00000	0.0625000
$257$	7.05421	0.440030	0.220015	−	0.975497i	$-0.429389\pi$
$257$	7.05421	0.440030	0.220015	+	0.975497i	$0.429389\pi$
$258$	1.17016	0.0728509
$259$	−8.73325	−0.542658
$260$	6.60558	0.409660
$261$	−18.6148	−1.15223
$262$	17.6331	1.08938
$263$	−24.2304	−1.49411	−0.747056	−	0.664761i	$-0.768533\pi$
$263$	−24.2304	−1.49411	−0.747056	+	0.664761i	$0.768533\pi$
$264$	−0.122604	−0.00754577
$265$	0.432437	0.0265644
$266$	−0.527471	−0.0323413
$267$	1.95262	0.119498
$268$	4.92691	0.300959
$269$	−15.5164	−0.946053	−0.473027	−	0.881048i	$-0.656839\pi$
$269$	−15.5164	−0.946053	−0.473027	+	0.881048i	$0.656839\pi$
$270$	1.33123	0.0810160
$271$	18.4691	1.12192	0.560959	−	0.827844i	$-0.310433\pi$
$271$	18.4691	1.12192	0.560959	+	0.827844i	$0.310433\pi$
$272$	5.52327	0.334898
$273$	0.591277	0.0357857
$274$	9.33095	0.563704
$275$	2.18270	0.131622
$276$	−0.333252	−0.0200594
$277$	31.3486	1.88355	0.941776	−	0.336241i	$-0.109156\pi$
$277$	31.3486	1.88355	0.941776	+	0.336241i	$0.109156\pi$
$278$	6.07116	0.364124
$279$	−12.9687	−0.776419
$280$	1.57700	0.0942440
$281$	−21.5074	−1.28302	−0.641511	−	0.767114i	$-0.721692\pi$
$281$	−21.5074	−1.28302	−0.641511	+	0.767114i	$0.721692\pi$
$282$	1.38369	0.0823974
$283$	27.7311	1.64844	0.824222	−	0.566267i	$-0.191613\pi$
$283$	27.7311	1.64844	0.824222	+	0.566267i	$0.191613\pi$
$284$	3.02190	0.179317
$285$	0.117421	0.00695540
$286$	−3.63806	−0.215123
$287$	−10.6400	−0.628060
$288$	2.98007	0.175603
$289$	13.5066	0.794503
$290$	9.85064	0.578449
$291$	1.14299	0.0670034
$292$	−1.36759	−0.0800323
$293$	−26.1884	−1.52994	−0.764972	−	0.644064i	$-0.777247\pi$
$293$	−26.1884	−1.52994	−0.764972	+	0.644064i	$0.777247\pi$
$294$	0.141161	0.00823265
$295$	6.53162	0.380285
$296$	8.73325	0.507610
$297$	−0.733183	−0.0425436
$298$	−13.1945	−0.764340
$299$	−9.88865	−0.571876
$300$	0.354745	0.0204812
$301$	8.28956	0.477802
$302$	−3.15973	−0.181822
$303$	0.0296638	0.00170414
$304$	0.527471	0.0302525
$305$	−17.4658	−1.00009
$306$	16.4598	0.940942
$307$	24.6924	1.40927	0.704635	−	0.709570i	$-0.251111\pi$
$307$	24.6924	1.40927	0.704635	+	0.709570i	$0.251111\pi$
$308$	−0.868545	−0.0494900
$309$	−1.90083	−0.108135
$310$	6.86284	0.389783
$311$	−35.1702	−1.99432	−0.997159	−	0.0753239i	$-0.976001\pi$
$311$	−35.1702	−1.99432	−0.997159	+	0.0753239i	$0.976001\pi$
$312$	−0.591277	−0.0334745
$313$	5.43134	0.306998	0.153499	−	0.988149i	$-0.450946\pi$
$313$	5.43134	0.306998	0.153499	+	0.988149i	$0.450946\pi$
$314$	18.6982	1.05520
$315$	4.69959	0.264792
$316$	5.42830	0.305366
$317$	−34.0146	−1.91045	−0.955226	−	0.295877i	$-0.904388\pi$
$317$	−34.0146	−1.91045	−0.955226	+	0.295877i	$0.904388\pi$
$318$	−0.0387082	−0.00217065
$319$	−5.42530	−0.303759
$320$	−1.57700	−0.0881572
$321$	0.890823	0.0497209
$322$	−2.36080	−0.131562
$323$	2.91337	0.162104
$324$	8.82106	0.490059
$325$	10.5264	0.583901
$326$	1.74870	0.0968515
$327$	−0.318300	−0.0176020
$328$	10.6400	0.587496
$329$	9.80223	0.540415
$330$	0.193347	0.0106434
$331$	−11.1237	−0.611415	−0.305708	−	0.952125i	$-0.598893\pi$
$331$	−11.1237	−0.611415	−0.305708	+	0.952125i	$0.598893\pi$
$332$	−1.60235	−0.0879401
$333$	26.0257	1.42620
$334$	24.7736	1.35555
$335$	−7.76976	−0.424507
$336$	−0.141161	−0.00770094
$337$	−15.1533	−0.825454	−0.412727	−	0.910855i	$-0.635424\pi$
$337$	−15.1533	−0.825454	−0.412727	+	0.910855i	$0.635424\pi$
$338$	−4.54510	−0.247221
$339$	2.48151	0.134777
$340$	−8.71023	−0.472378
$341$	−3.77975	−0.204685
$342$	1.57190	0.0849988
$343$	1.00000	0.0539949
$344$	−8.28956	−0.446943
$345$	0.525539	0.0282941
$346$	−4.15589	−0.223422
$347$	−15.2360	−0.817913	−0.408957	−	0.912554i	$-0.634107\pi$
$347$	−15.2360	−0.817913	−0.408957	+	0.912554i	$0.634107\pi$
$348$	−0.881749	−0.0472667
$349$	−13.1301	−0.702837	−0.351418	−	0.936219i	$-0.614300\pi$
$349$	−13.1301	−0.702837	−0.351418	+	0.936219i	$0.614300\pi$
$350$	2.51306	0.134329
$351$	−3.53588	−0.188731
$352$	0.868545	0.0462936
$353$	28.0672	1.49387	0.746933	−	0.664899i	$-0.231526\pi$
$353$	28.0672	1.49387	0.746933	+	0.664899i	$0.231526\pi$
$354$	−0.584657	−0.0310742
$355$	−4.76554	−0.252929
$356$	−13.8326	−0.733126
$357$	−0.779668	−0.0412644
$358$	1.65603	0.0875238
$359$	−3.93133	−0.207488	−0.103744	−	0.994604i	$-0.533082\pi$
$359$	−3.93133	−0.207488	−0.103744	+	0.994604i	$0.533082\pi$
$360$	−4.69959	−0.247690
$361$	−18.7218	−0.985357
$362$	10.0989	0.530786
$363$	1.44628	0.0759099
$364$	−4.18869	−0.219547
$365$	2.15670	0.112887
$366$	1.56339	0.0817199
$367$	−3.00038	−0.156619	−0.0783093	−	0.996929i	$-0.524952\pi$
$367$	−3.00038	−0.156619	−0.0783093	+	0.996929i	$0.524952\pi$
$368$	2.36080	0.123065
$369$	31.7080	1.65065
$370$	−13.7724	−0.715992
$371$	−0.274214	−0.0142365
$372$	−0.614306	−0.0318503
$373$	−9.79193	−0.507007	−0.253503	−	0.967335i	$-0.581583\pi$
$373$	−9.79193	−0.507007	−0.253503	+	0.967335i	$0.581583\pi$
$374$	4.79721	0.248058
$375$	−1.67249	−0.0863669
$376$	−9.80223	−0.505512
$377$	−26.1643	−1.34753
$378$	−0.844151	−0.0434184
$379$	21.2933	1.09376	0.546882	−	0.837210i	$-0.315815\pi$
$379$	21.2933	1.09376	0.546882	+	0.837210i	$0.315815\pi$
$380$	−0.831824	−0.0426717
$381$	1.51405	0.0775670
$382$	−20.8623	−1.06741
$383$	−33.1536	−1.69407	−0.847036	−	0.531536i	$-0.821615\pi$
$383$	−33.1536	−1.69407	−0.847036	+	0.531536i	$0.821615\pi$
$384$	0.141161	0.00720357
$385$	1.36970	0.0698063
$386$	14.2126	0.723404
$387$	−24.7035	−1.25575
$388$	−8.09710	−0.411068
$389$	−2.86053	−0.145035	−0.0725173	−	0.997367i	$-0.523103\pi$
$389$	−2.86053	−0.145035	−0.0725173	+	0.997367i	$0.523103\pi$
$390$	0.932447	0.0472163
$391$	13.0393	0.659428
$392$	−1.00000	−0.0505076
$393$	2.48909	0.125558
$394$	−4.10246	−0.206679
$395$	−8.56045	−0.430723
$396$	2.58833	0.130068
$397$	−9.01205	−0.452302	−0.226151	−	0.974092i	$-0.572614\pi$
$397$	−9.01205	−0.452302	−0.226151	+	0.974092i	$0.572614\pi$
$398$	−22.0627	−1.10590
$399$	−0.0744581	−0.00372757
$400$	−2.51306	−0.125653
$401$	11.7924	0.588886	0.294443	−	0.955669i	$-0.404866\pi$
$401$	11.7924	0.588886	0.294443	+	0.955669i	$0.404866\pi$
$402$	0.695486	0.0346877
$403$	−18.2284	−0.908022
$404$	−0.210142	−0.0104550
$405$	−13.9108	−0.691236
$406$	−6.24643	−0.310005
$407$	7.58523	0.375986
$408$	0.779668	0.0385993
$409$	−18.8841	−0.933761	−0.466881	−	0.884320i	$-0.654622\pi$
$409$	−18.8841	−0.933761	−0.466881	+	0.884320i	$0.654622\pi$
$410$	−16.7793	−0.828672
$411$	1.31716	0.0649708
$412$	13.4657	0.663410
$413$	−4.14179	−0.203804
$414$	7.03536	0.345769
$415$	2.52690	0.124041
$416$	4.18869	0.205367
$417$	0.857008	0.0419679
$418$	0.458132	0.0224080
$419$	6.06646	0.296366	0.148183	−	0.988960i	$-0.452658\pi$
$419$	6.06646	0.296366	0.148183	+	0.988960i	$0.452658\pi$
$420$	0.222611	0.0108623
$421$	−35.7976	−1.74467	−0.872334	−	0.488910i	$-0.837395\pi$
$421$	−35.7976	−1.74467	−0.872334	+	0.488910i	$0.837395\pi$
$422$	−11.7749	−0.573192
$423$	−29.2114	−1.42031
$424$	0.274214	0.0133170
$425$	−13.8803	−0.673294
$426$	0.426573	0.0206675
$427$	11.0753	0.535971
$428$	−6.31071	−0.305040
$429$	−0.513551	−0.0247945
$430$	13.0727	0.630420
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	0.844151	0.0406142
$433$	24.8339	1.19344	0.596720	−	0.802449i	$-0.296470\pi$
$433$	24.8339	1.19344	0.596720	+	0.802449i	$0.296470\pi$
$434$	−4.35182	−0.208894
$435$	1.39052	0.0666704
$436$	2.25488	0.107989
$437$	1.24525	0.0595686
$438$	−0.193050	−0.00922429
$439$	−7.49325	−0.357633	−0.178817	−	0.983882i	$-0.557227\pi$
$439$	−7.49325	−0.357633	−0.178817	+	0.983882i	$0.557227\pi$
$440$	−1.36970	−0.0652978
$441$	−2.98007	−0.141908
$442$	23.1353	1.10043
$443$	−4.01998	−0.190995	−0.0954975	−	0.995430i	$-0.530444\pi$
$443$	−4.01998	−0.190995	−0.0954975	+	0.995430i	$0.530444\pi$
$444$	1.23279	0.0585057
$445$	21.8140	1.03408
$446$	6.62290	0.313604
$447$	−1.86255	−0.0880956
$448$	1.00000	0.0472456
$449$	−9.26816	−0.437392	−0.218696	−	0.975793i	$-0.570180\pi$
$449$	−9.26816	−0.437392	−0.218696	+	0.975793i	$0.570180\pi$
$450$	−7.48910	−0.353040
$451$	9.24132	0.435157
$452$	−17.5793	−0.826861
$453$	−0.446030	−0.0209563
$454$	−15.5456	−0.729589
$455$	6.60558	0.309674
$456$	0.0744581	0.00348682
$457$	12.4899	0.584251	0.292125	−	0.956380i	$-0.405638\pi$
$457$	12.4899	0.584251	0.292125	+	0.956380i	$0.405638\pi$
$458$	−4.14511	−0.193688
$459$	4.66247	0.217626
$460$	−3.72299	−0.173585
$461$	−35.6558	−1.66066	−0.830328	−	0.557275i	$-0.811847\pi$
$461$	−35.6558	−1.66066	−0.830328	+	0.557275i	$0.811847\pi$
$462$	−0.122604	−0.00570407
$463$	10.0550	0.467298	0.233649	−	0.972321i	$-0.424933\pi$
$463$	10.0550	0.467298	0.233649	+	0.972321i	$0.424933\pi$
$464$	6.24643	0.289983
$465$	0.968762	0.0449253
$466$	−8.19461	−0.379608
$467$	6.76218	0.312916	0.156458	−	0.987685i	$-0.449992\pi$
$467$	6.76218	0.312916	0.156458	+	0.987685i	$0.449992\pi$
$468$	12.4826	0.577008
$469$	4.92691	0.227504
$470$	15.4582	0.713032
$471$	2.63945	0.121620
$472$	4.14179	0.190641
$473$	−7.19986	−0.331050
$474$	0.766262	0.0351956
$475$	−1.32557	−0.0608211
$476$	5.52327	0.253159
$477$	0.817178	0.0374160
$478$	27.6999	1.26696
$479$	−30.5005	−1.39360	−0.696802	−	0.717264i	$-0.745394\pi$
$479$	−30.5005	−1.39360	−0.696802	+	0.717264i	$0.745394\pi$
$480$	−0.222611	−0.0101607
$481$	36.5809	1.66794
$482$	13.4044	0.610556
$483$	−0.333252	−0.0151635
$484$	−10.2456	−0.465710
$485$	12.7692	0.579818
$486$	3.77764	0.171357
$487$	−27.8626	−1.26258	−0.631288	−	0.775548i	$-0.717474\pi$
$487$	−27.8626	−1.26258	−0.631288	+	0.775548i	$0.717474\pi$
$488$	−11.0753	−0.501355
$489$	0.246847	0.0111628
$490$	1.57700	0.0712418
$491$	−8.32377	−0.375646	−0.187823	−	0.982203i	$-0.560143\pi$
$491$	−8.32377	−0.375646	−0.187823	+	0.982203i	$0.560143\pi$
$492$	1.50195	0.0677131
$493$	34.5007	1.55383
$494$	2.20941	0.0994061
$495$	−4.08180	−0.183463
$496$	4.35182	0.195403
$497$	3.02190	0.135551
$498$	−0.226188	−0.0101357
$499$	23.5460	1.05406	0.527031	−	0.849846i	$-0.323305\pi$
$499$	23.5460	1.05406	0.527031	+	0.849846i	$0.323305\pi$
$500$	11.8481	0.529864
$501$	3.49705	0.156237
$502$	−20.4793	−0.914036
$503$	27.3842	1.22100	0.610501	−	0.792016i	$-0.290968\pi$
$503$	27.3842	1.22100	0.610501	+	0.792016i	$0.290968\pi$
$504$	2.98007	0.132743
$505$	0.331395	0.0147469
$506$	2.05046	0.0911541
$507$	−0.641589	−0.0284940
$508$	−10.7257	−0.475876
$509$	18.1739	0.805542	0.402771	−	0.915301i	$-0.368047\pi$
$509$	18.1739	0.805542	0.402771	+	0.915301i	$0.368047\pi$
$510$	−1.22954	−0.0544450
$511$	−1.36759	−0.0604987
$512$	−1.00000	−0.0441942
$513$	0.445265	0.0196589
$514$	−7.05421	−0.311148
$515$	−21.2355	−0.935750
$516$	−1.17016	−0.0515134
$517$	−8.51368	−0.374431
$518$	8.73325	0.383717
$519$	−0.586648	−0.0257510
$520$	−6.60558	−0.289674
$521$	−30.9390	−1.35546	−0.677731	−	0.735310i	$-0.737037\pi$
$521$	−30.9390	−1.35546	−0.677731	+	0.735310i	$0.737037\pi$
$522$	18.6148	0.814748
$523$	−1.16223	−0.0508206	−0.0254103	−	0.999677i	$-0.508089\pi$
$523$	−1.16223	−0.0508206	−0.0254103	+	0.999677i	$0.508089\pi$
$524$	−17.6331	−0.770305
$525$	0.354745	0.0154823
$526$	24.2304	1.05650
$527$	24.0363	1.04704
$528$	0.122604	0.00533567
$529$	−17.4266	−0.757679
$530$	−0.432437	−0.0187838
$531$	12.3428	0.535633
$532$	0.527471	0.0228688
$533$	44.5677	1.93044
$534$	−1.95262	−0.0844979
$535$	9.95201	0.430263
$536$	−4.92691	−0.212810
$537$	0.233766	0.0100877
$538$	15.5164	0.668961
$539$	−0.868545	−0.0374109
$540$	−1.33123	−0.0572870
$541$	−27.0852	−1.16448	−0.582241	−	0.813016i	$-0.697824\pi$
$541$	−27.0852	−1.16448	−0.582241	+	0.813016i	$0.697824\pi$
$542$	−18.4691	−0.793315
$543$	1.42556	0.0611768
$544$	−5.52327	−0.236808
$545$	−3.55596	−0.152320
$546$	−0.591277	−0.0253043
$547$	39.9132	1.70657	0.853283	−	0.521448i	$-0.174608\pi$
$547$	39.9132	1.70657	0.853283	+	0.521448i	$0.174608\pi$
$548$	−9.33095	−0.398599
$549$	−33.0052	−1.40863
$550$	−2.18270	−0.0930708
$551$	3.29481	0.140364
$552$	0.333252	0.0141841
$553$	5.42830	0.230835
$554$	−31.3486	−1.33187
$555$	−1.94412	−0.0825231
$556$	−6.07116	−0.257475
$557$	−13.4199	−0.568620	−0.284310	−	0.958732i	$-0.591765\pi$
$557$	−13.4199	−0.568620	−0.284310	+	0.958732i	$0.591765\pi$
$558$	12.9687	0.549011
$559$	−34.7224	−1.46860
$560$	−1.57700	−0.0666406
$561$	0.677177	0.0285904
$562$	21.5074	0.907234
$563$	−34.4342	−1.45123	−0.725615	−	0.688101i	$-0.758445\pi$
$563$	−34.4342	−1.45123	−0.725615	+	0.688101i	$0.758445\pi$
$564$	−1.38369	−0.0582638
$565$	27.7226	1.16630
$566$	−27.7311	−1.16563
$567$	8.82106	0.370450
$568$	−3.02190	−0.126796
$569$	−9.80976	−0.411247	−0.205623	−	0.978631i	$-0.565922\pi$
$569$	−9.80976	−0.411247	−0.205623	+	0.978631i	$0.565922\pi$
$570$	−0.117421	−0.00491821
$571$	−2.46956	−0.103348	−0.0516739	−	0.998664i	$-0.516456\pi$
$571$	−2.46956	−0.103348	−0.0516739	+	0.998664i	$0.516456\pi$
$572$	3.63806	0.152115
$573$	−2.94493	−0.123026
$574$	10.6400	0.444105
$575$	−5.93283	−0.247416
$576$	−2.98007	−0.124170
$577$	−40.4298	−1.68311	−0.841557	−	0.540168i	$-0.818361\pi$
$577$	−40.4298	−1.68311	−0.841557	+	0.540168i	$0.818361\pi$
$578$	−13.5066	−0.561799
$579$	2.00626	0.0833775
$580$	−9.85064	−0.409025
$581$	−1.60235	−0.0664765
$582$	−1.14299	−0.0473785
$583$	0.238167	0.00986388
$584$	1.36759	0.0565914
$585$	−19.6851	−0.813879
$586$	26.1884	1.08183
$587$	7.68374	0.317142	0.158571	−	0.987348i	$-0.449311\pi$
$587$	7.68374	0.317142	0.158571	+	0.987348i	$0.449311\pi$
$588$	−0.141161	−0.00582136
$589$	2.29546	0.0945828
$590$	−6.53162	−0.268902
$591$	−0.579106	−0.0238212
$592$	−8.73325	−0.358935
$593$	−2.13055	−0.0874911	−0.0437456	−	0.999043i	$-0.513929\pi$
$593$	−2.13055	−0.0874911	−0.0437456	+	0.999043i	$0.513929\pi$
$594$	0.733183	0.0300829
$595$	−8.71023	−0.357084
$596$	13.1945	0.540470
$597$	−3.11439	−0.127463
$598$	9.88865	0.404377
$599$	−16.0042	−0.653914	−0.326957	−	0.945039i	$-0.606023\pi$
$599$	−16.0042	−0.653914	−0.326957	+	0.945039i	$0.606023\pi$
$600$	−0.354745	−0.0144824
$601$	−23.8467	−0.972726	−0.486363	−	0.873757i	$-0.661677\pi$
$601$	−23.8467	−0.972726	−0.486363	+	0.873757i	$0.661677\pi$
$602$	−8.28956	−0.337857
$603$	−14.6826	−0.597920
$604$	3.15973	0.128568
$605$	16.1574	0.656892
$606$	−0.0296638	−0.00120501
$607$	−19.8112	−0.804111	−0.402055	−	0.915615i	$-0.631704\pi$
$607$	−19.8112	−0.804111	−0.402055	+	0.915615i	$0.631704\pi$
$608$	−0.527471	−0.0213918
$609$	−0.881749	−0.0357303
$610$	17.4658	0.707168
$611$	−41.0585	−1.66105
$612$	−16.4598	−0.665347
$613$	−22.9794	−0.928130	−0.464065	−	0.885801i	$-0.653610\pi$
$613$	−22.9794	−0.928130	−0.464065	+	0.885801i	$0.653610\pi$
$614$	−24.6924	−0.996505
$615$	−2.36858	−0.0955103
$616$	0.868545	0.0349947
$617$	−18.2663	−0.735373	−0.367686	−	0.929950i	$-0.619850\pi$
$617$	−18.2663	−0.735373	−0.367686	+	0.929950i	$0.619850\pi$
$618$	1.90083	0.0764627
$619$	−3.77971	−0.151919	−0.0759596	−	0.997111i	$-0.524202\pi$
$619$	−3.77971	−0.151919	−0.0759596	+	0.997111i	$0.524202\pi$
$620$	−6.86284	−0.275618
$621$	1.99287	0.0799711
$622$	35.1702	1.41020
$623$	−13.8326	−0.554191
$624$	0.591277	0.0236700
$625$	−6.11925	−0.244770
$626$	−5.43134	−0.217080
$627$	0.0646702	0.00258268
$628$	−18.6982	−0.746141
$629$	−48.2362	−1.92330
$630$	−4.69959	−0.187236
$631$	−17.4563	−0.694925	−0.347463	−	0.937694i	$-0.612957\pi$
$631$	−17.4563	−0.694925	−0.347463	+	0.937694i	$0.612957\pi$
$632$	−5.42830	−0.215926
$633$	−1.66215	−0.0660644
$634$	34.0146	1.35089
$635$	16.9145	0.671231
$636$	0.0387082	0.00153488
$637$	−4.18869	−0.165962
$638$	5.42530	0.214790
$639$	−9.00548	−0.356251
$640$	1.57700	0.0623366
$641$	16.6005	0.655680	0.327840	−	0.944733i	$-0.393679\pi$
$641$	16.6005	0.655680	0.327840	+	0.944733i	$0.393679\pi$
$642$	−0.890823	−0.0351580
$643$	37.5811	1.48205	0.741027	−	0.671476i	$-0.234339\pi$
$643$	37.5811	1.48205	0.741027	+	0.671476i	$0.234339\pi$
$644$	2.36080	0.0930285
$645$	1.84535	0.0726604
$646$	−2.91337	−0.114625
$647$	44.0675	1.73247	0.866236	−	0.499635i	$-0.166532\pi$
$647$	44.0675	1.73247	0.866236	+	0.499635i	$0.166532\pi$
$648$	−8.82106	−0.346524
$649$	3.59733	0.141208
$650$	−10.5264	−0.412880
$651$	−0.614306	−0.0240765
$652$	−1.74870	−0.0684843
$653$	−22.4983	−0.880428	−0.440214	−	0.897893i	$-0.645097\pi$
$653$	−22.4983	−0.880428	−0.440214	+	0.897893i	$0.645097\pi$
$654$	0.318300	0.0124465
$655$	27.8074	1.08653
$656$	−10.6400	−0.415422
$657$	4.07553	0.159001
$658$	−9.80223	−0.382131
$659$	−7.12543	−0.277567	−0.138784	−	0.990323i	$-0.544319\pi$
$659$	−7.12543	−0.277567	−0.138784	+	0.990323i	$0.544319\pi$
$660$	−0.193347	−0.00752604
$661$	−3.54628	−0.137934	−0.0689672	−	0.997619i	$-0.521970\pi$
$661$	−3.54628	−0.137934	−0.0689672	+	0.997619i	$0.521970\pi$
$662$	11.1237	0.432336
$663$	3.26579	0.126833
$664$	1.60235	0.0621831
$665$	−0.831824	−0.0322568
$666$	−26.0257	−1.00848
$667$	14.7466	0.570989
$668$	−24.7736	−0.958518
$669$	0.934893	0.0361450
$670$	7.76976	0.300172
$671$	−9.61938	−0.371352
$672$	0.141161	0.00544539
$673$	36.1875	1.39492	0.697462	−	0.716621i	$-0.254312\pi$
$673$	36.1875	1.39492	0.697462	+	0.716621i	$0.254312\pi$
$674$	15.1533	0.583684
$675$	−2.12140	−0.0816527
$676$	4.54510	0.174812
$677$	30.1140	1.15738	0.578688	−	0.815549i	$-0.303565\pi$
$677$	30.1140	1.15738	0.578688	+	0.815549i	$0.303565\pi$
$678$	−2.48151	−0.0953016
$679$	−8.09710	−0.310738
$680$	8.71023	0.334022
$681$	−2.19442	−0.0840904
$682$	3.77975	0.144734
$683$	−24.5897	−0.940898	−0.470449	−	0.882427i	$-0.655908\pi$
$683$	−24.5897	−0.940898	−0.470449	+	0.882427i	$0.655908\pi$
$684$	−1.57190	−0.0601032
$685$	14.7150	0.562229
$686$	−1.00000	−0.0381802
$687$	−0.585126	−0.0223239
$688$	8.28956	0.316036
$689$	1.14860	0.0437581
$690$	−0.525539	−0.0200069
$691$	−16.4228	−0.624753	−0.312377	−	0.949958i	$-0.601125\pi$
$691$	−16.4228	−0.624753	−0.312377	+	0.949958i	$0.601125\pi$
$692$	4.15589	0.157983
$693$	2.58833	0.0983225
$694$	15.2360	0.578352
$695$	9.57424	0.363172
$696$	0.881749	0.0334226
$697$	−58.7677	−2.22598
$698$	13.1301	0.496980
$699$	−1.15676	−0.0437525
$700$	−2.51306	−0.0949847
$701$	−4.78492	−0.180724	−0.0903619	−	0.995909i	$-0.528802\pi$
$701$	−4.78492	−0.180724	−0.0903619	+	0.995909i	$0.528802\pi$
$702$	3.53588	0.133453
$703$	−4.60654	−0.173739
$704$	−0.868545	−0.0327345
$705$	2.18208	0.0821820
$706$	−28.0672	−1.05632
$707$	−0.210142	−0.00790320
$708$	0.584657	0.0219728
$709$	22.3865	0.840744	0.420372	−	0.907352i	$-0.361900\pi$
$709$	22.3865	0.840744	0.420372	+	0.907352i	$0.361900\pi$
$710$	4.76554	0.178848
$711$	−16.1767	−0.606675
$712$	13.8326	0.518398
$713$	10.2738	0.384756
$714$	0.779668	0.0291784
$715$	−5.73724	−0.214561
$716$	−1.65603	−0.0618887
$717$	3.91013	0.146026
$718$	3.93133	0.146716
$719$	41.4410	1.54549	0.772744	−	0.634718i	$-0.218884\pi$
$719$	41.4410	1.54549	0.772744	+	0.634718i	$0.218884\pi$
$720$	4.69959	0.175143
$721$	13.4657	0.501491
$722$	18.7218	0.696752
$723$	1.89218	0.0703709
$724$	−10.0989	−0.375322
$725$	−15.6976	−0.582995
$726$	−1.44628	−0.0536764
$727$	−23.8481	−0.884478	−0.442239	−	0.896897i	$-0.645816\pi$
$727$	−23.8481	−0.884478	−0.442239	+	0.896897i	$0.645816\pi$
$728$	4.18869	0.155243
$729$	−25.9299	−0.960368
$730$	−2.15670	−0.0798230
$731$	45.7855	1.69344
$732$	−1.56339	−0.0577847
$733$	34.7720	1.28433	0.642167	−	0.766565i	$-0.278035\pi$
$733$	34.7720	1.28433	0.642167	+	0.766565i	$0.278035\pi$
$734$	3.00038	0.110746
$735$	0.222611	0.00821112
$736$	−2.36080	−0.0870202
$737$	−4.27924	−0.157628
$738$	−31.7080	−1.16719
$739$	28.7723	1.05841	0.529203	−	0.848496i	$-0.322491\pi$
$739$	28.7723	1.05841	0.529203	+	0.848496i	$0.322491\pi$
$740$	13.7724	0.506283
$741$	0.311882	0.0114573
$742$	0.274214	0.0100667
$743$	−30.3932	−1.11502	−0.557510	−	0.830170i	$-0.688243\pi$
$743$	−30.3932	−1.11502	−0.557510	+	0.830170i	$0.688243\pi$
$744$	0.614306	0.0225215
$745$	−20.8079	−0.762341
$746$	9.79193	0.358508
$747$	4.77511	0.174712
$748$	−4.79721	−0.175403
$749$	−6.31071	−0.230588
$750$	1.67249	0.0610706
$751$	14.5504	0.530951	0.265476	−	0.964118i	$-0.414471\pi$
$751$	14.5504	0.530951	0.265476	+	0.964118i	$0.414471\pi$
$752$	9.80223	0.357451
$753$	−2.89087	−0.105349
$754$	26.1643	0.952848
$755$	−4.98291	−0.181347
$756$	0.844151	0.0307015
$757$	−31.3045	−1.13778	−0.568891	−	0.822413i	$-0.692627\pi$
$757$	−31.3045	−1.13778	−0.568891	+	0.822413i	$0.692627\pi$
$758$	−21.2933	−0.773408
$759$	0.289444	0.0105062
$760$	0.831824	0.0301734
$761$	−5.33440	−0.193372	−0.0966860	−	0.995315i	$-0.530824\pi$
$761$	−5.33440	−0.193372	−0.0966860	+	0.995315i	$0.530824\pi$
$762$	−1.51405	−0.0548481
$763$	2.25488	0.0816322
$764$	20.8623	0.754770
$765$	25.9571	0.938481
$766$	33.1536	1.19789
$767$	17.3487	0.626424
$768$	−0.141161	−0.00509369
$769$	38.6713	1.39452	0.697262	−	0.716816i	$-0.254401\pi$
$769$	38.6713	1.39452	0.697262	+	0.716816i	$0.254401\pi$
$770$	−1.36970	−0.0493605
$771$	−0.995776	−0.0358620
$772$	−14.2126	−0.511524
$773$	50.1232	1.80281	0.901404	−	0.432979i	$-0.142538\pi$
$773$	50.1232	1.80281	0.901404	+	0.432979i	$0.142538\pi$
$774$	24.7035	0.887949
$775$	−10.9364	−0.392846
$776$	8.09710	0.290669
$777$	1.23279	0.0442261
$778$	2.86053	0.102555
$779$	−5.61230	−0.201081
$780$	−0.932447	−0.0333870
$781$	−2.62465	−0.0939175
$782$	−13.0393	−0.466286
$783$	5.27292	0.188439
$784$	1.00000	0.0357143
$785$	29.4872	1.05244
$786$	−2.48909	−0.0887831
$787$	1.67505	0.0597090	0.0298545	−	0.999554i	$-0.490496\pi$
$787$	1.67505	0.0597090	0.0298545	+	0.999554i	$0.490496\pi$
$788$	4.10246	0.146144
$789$	3.42038	0.121769
$790$	8.56045	0.304567
$791$	−17.5793	−0.625048
$792$	−2.58833	−0.0919722
$793$	−46.3909	−1.64739
$794$	9.01205	0.319826
$795$	−0.0610430	−0.00216497
$796$	22.0627	0.781993
$797$	24.8194	0.879147	0.439573	−	0.898207i	$-0.355130\pi$
$797$	24.8194	0.879147	0.439573	+	0.898207i	$0.355130\pi$
$798$	0.0744581	0.00263579
$799$	54.1404	1.91535
$800$	2.51306	0.0888500
$801$	41.2221	1.45651
$802$	−11.7924	−0.416405
$803$	1.18782	0.0419171
$804$	−0.695486	−0.0245279
$805$	−3.72299	−0.131218
$806$	18.2284	0.642069
$807$	2.19031	0.0771025
$808$	0.210142	0.00739277
$809$	−56.5867	−1.98948	−0.994742	−	0.102414i	$-0.967343\pi$
$809$	−56.5867	−1.98948	−0.994742	+	0.102414i	$0.967343\pi$
$810$	13.9108	0.488777
$811$	3.24824	0.114061	0.0570306	−	0.998372i	$-0.481837\pi$
$811$	3.24824	0.114061	0.0570306	+	0.998372i	$0.481837\pi$
$812$	6.24643	0.219207
$813$	−2.60711	−0.0914352
$814$	−7.58523	−0.265862
$815$	2.75770	0.0965982
$816$	−0.779668	−0.0272939
$817$	4.37250	0.152975
$818$	18.8841	0.660269
$819$	12.4826	0.436177
$820$	16.7793	0.585960
$821$	−40.2205	−1.40371	−0.701853	−	0.712322i	$-0.747644\pi$
$821$	−40.2205	−1.40371	−0.701853	+	0.712322i	$0.747644\pi$
$822$	−1.31716	−0.0459413
$823$	13.6406	0.475480	0.237740	−	0.971329i	$-0.423593\pi$
$823$	13.6406	0.475480	0.237740	+	0.971329i	$0.423593\pi$
$824$	−13.4657	−0.469102
$825$	−0.308112	−0.0107271
$826$	4.14179	0.144111
$827$	−40.6090	−1.41211	−0.706057	−	0.708155i	$-0.749528\pi$
$827$	−40.6090	−1.41211	−0.706057	+	0.708155i	$0.749528\pi$
$828$	−7.03536	−0.244496
$829$	3.49895	0.121523	0.0607617	−	0.998152i	$-0.480647\pi$
$829$	3.49895	0.121523	0.0607617	+	0.998152i	$0.480647\pi$
$830$	−2.52690	−0.0877102
$831$	−4.42518	−0.153508
$832$	−4.18869	−0.145217
$833$	5.52327	0.191370
$834$	−0.857008	−0.0296758
$835$	39.0680	1.35200
$836$	−0.458132	−0.0158448
$837$	3.67359	0.126978
$838$	−6.06646	−0.209562
$839$	52.5155	1.81304	0.906518	−	0.422167i	$-0.138730\pi$
$839$	52.5155	1.81304	0.906518	+	0.422167i	$0.138730\pi$
$840$	−0.222611	−0.00768080
$841$	10.0178	0.345442
$842$	35.7976	1.23367
$843$	3.03599	0.104565
$844$	11.7749	0.405308
$845$	−7.16765	−0.246575
$846$	29.2114	1.00431
$847$	−10.2456	−0.352044
$848$	−0.274214	−0.00941655
$849$	−3.91454	−0.134347
$850$	13.8803	0.476091
$851$	−20.6175	−0.706758
$852$	−0.426573	−0.0146141
$853$	10.3063	0.352882	0.176441	−	0.984311i	$-0.443542\pi$
$853$	10.3063	0.352882	0.176441	+	0.984311i	$0.443542\pi$
$854$	−11.0753	−0.378988
$855$	2.47890	0.0847765
$856$	6.31071	0.215696
$857$	−45.0448	−1.53870	−0.769351	−	0.638827i	$-0.779420\pi$
$857$	−45.0448	−1.53870	−0.769351	+	0.638827i	$0.779420\pi$
$858$	0.513551	0.0175323
$859$	16.7284	0.570767	0.285384	−	0.958413i	$-0.407879\pi$
$859$	16.7284	0.570767	0.285384	+	0.958413i	$0.407879\pi$
$860$	−13.0727	−0.445774
$861$	1.50195	0.0511863
$862$	−1.00000	−0.0340601
$863$	−16.4258	−0.559141	−0.279570	−	0.960125i	$-0.590192\pi$
$863$	−16.4258	−0.559141	−0.279570	+	0.960125i	$0.590192\pi$
$864$	−0.844151	−0.0287186
$865$	−6.55386	−0.222838
$866$	−24.8339	−0.843890
$867$	−1.90659	−0.0647513
$868$	4.35182	0.147710
$869$	−4.71472	−0.159936
$870$	−1.39052	−0.0471431
$871$	−20.6373	−0.699268
$872$	−2.25488	−0.0763599
$873$	24.1300	0.816676
$874$	−1.24525	−0.0421213
$875$	11.8481	0.400540
$876$	0.193050	0.00652256
$877$	41.3602	1.39663	0.698317	−	0.715789i	$-0.253933\pi$
$877$	41.3602	1.39663	0.698317	+	0.715789i	$0.253933\pi$
$878$	7.49325	0.252885
$879$	3.69677	0.124689
$880$	1.36970	0.0461725
$881$	18.0902	0.609475	0.304738	−	0.952436i	$-0.401431\pi$
$881$	18.0902	0.609475	0.304738	+	0.952436i	$0.401431\pi$
$882$	2.98007	0.100344
$883$	−18.8219	−0.633406	−0.316703	−	0.948525i	$-0.602576\pi$
$883$	−18.8219	−0.633406	−0.316703	+	0.948525i	$0.602576\pi$
$884$	−23.1353	−0.778123
$885$	−0.922007	−0.0309929
$886$	4.01998	0.135054
$887$	−46.5776	−1.56392	−0.781961	−	0.623327i	$-0.785781\pi$
$887$	−46.5776	−1.56392	−0.781961	+	0.623327i	$0.785781\pi$
$888$	−1.23279	−0.0413698
$889$	−10.7257	−0.359729
$890$	−21.8140	−0.731208
$891$	−7.66149	−0.256670
$892$	−6.62290	−0.221751
$893$	5.17039	0.173021
$894$	1.86255	0.0622930
$895$	2.61156	0.0872949
$896$	−1.00000	−0.0334077
$897$	1.39589	0.0466073
$898$	9.26816	0.309283
$899$	27.1833	0.906615
$900$	7.48910	0.249637
$901$	−1.51456	−0.0504573
$902$	−9.24132	−0.307702
$903$	−1.17016	−0.0389404
$904$	17.5793	0.584679
$905$	15.9260	0.529398
$906$	0.446030	0.0148183
$907$	4.65401	0.154534	0.0772670	−	0.997010i	$-0.475381\pi$
$907$	4.65401	0.154534	0.0772670	+	0.997010i	$0.475381\pi$
$908$	15.5456	0.515898
$909$	0.626239	0.0207710
$910$	−6.60558	−0.218973
$911$	−46.2354	−1.53185	−0.765924	−	0.642931i	$-0.777718\pi$
$911$	−46.2354	−1.53185	−0.765924	+	0.642931i	$0.777718\pi$
$912$	−0.0744581	−0.00246555
$913$	1.39171	0.0460589
$914$	−12.4899	−0.413128
$915$	2.46548	0.0815062
$916$	4.14511	0.136958
$917$	−17.6331	−0.582295
$918$	−4.66247	−0.153885
$919$	52.0360	1.71651	0.858255	−	0.513223i	$-0.171549\pi$
$919$	52.0360	1.71651	0.858255	+	0.513223i	$0.171549\pi$
$920$	3.72299	0.122743
$921$	−3.48559	−0.114854
$922$	35.6558	1.17426
$923$	−12.6578	−0.416636
$924$	0.122604	0.00403339
$925$	21.9472	0.721619
$926$	−10.0550	−0.330429
$927$	−40.1289	−1.31801
$928$	−6.24643	−0.205049
$929$	29.5018	0.967924	0.483962	−	0.875089i	$-0.339197\pi$
$929$	29.5018	0.967924	0.483962	+	0.875089i	$0.339197\pi$
$930$	−0.968762	−0.0317670
$931$	0.527471	0.0172872
$932$	8.19461	0.268424
$933$	4.96464	0.162535
$934$	−6.76218	−0.221265
$935$	7.56522	0.247409
$936$	−12.4826	−0.408006
$937$	21.9349	0.716581	0.358291	−	0.933610i	$-0.383360\pi$
$937$	21.9349	0.716581	0.358291	+	0.933610i	$0.383360\pi$
$938$	−4.92691	−0.160869
$939$	−0.766691	−0.0250200
$940$	−15.4582	−0.504190
$941$	−34.8182	−1.13504	−0.567521	−	0.823359i	$-0.692097\pi$
$941$	−34.8182	−1.13504	−0.567521	+	0.823359i	$0.692097\pi$
$942$	−2.63945	−0.0859981
$943$	−25.1189	−0.817985
$944$	−4.14179	−0.134804
$945$	−1.33123	−0.0433049
$946$	7.19986	0.234088
$947$	−31.0438	−1.00879	−0.504394	−	0.863474i	$-0.668284\pi$
$947$	−31.0438	−1.00879	−0.504394	+	0.863474i	$0.668284\pi$
$948$	−0.766262	−0.0248870
$949$	5.72842	0.185952
$950$	1.32557	0.0430070
$951$	4.80152	0.155700
$952$	−5.52327	−0.179010
$953$	8.68919	0.281470	0.140735	−	0.990047i	$-0.455053\pi$
$953$	8.68919	0.281470	0.140735	+	0.990047i	$0.455053\pi$
$954$	−0.817178	−0.0264571
$955$	−32.8999	−1.06462
$956$	−27.6999	−0.895877
$957$	0.765839	0.0247560
$958$	30.5005	0.985426
$959$	−9.33095	−0.301312
$960$	0.222611	0.00718473
$961$	−12.0617	−0.389085
$962$	−36.5809	−1.17941
$963$	18.8064	0.606027
$964$	−13.4044	−0.431728
$965$	22.4134	0.721512
$966$	0.333252	0.0107222
$967$	−36.8401	−1.18470	−0.592349	−	0.805681i	$-0.701799\pi$
$967$	−36.8401	−1.18470	−0.592349	+	0.805681i	$0.701799\pi$
$968$	10.2456	0.329307
$969$	−0.411253	−0.0132113
$970$	−12.7692	−0.409993
$971$	−56.8493	−1.82438	−0.912190	−	0.409768i	$-0.865610\pi$
$971$	−56.8493	−1.82438	−0.912190	+	0.409768i	$0.865610\pi$
$972$	−3.77764	−0.121168
$973$	−6.07116	−0.194632
$974$	27.8626	0.892777
$975$	−1.48591	−0.0475874
$976$	11.0753	0.354511
$977$	11.6867	0.373892	0.186946	−	0.982370i	$-0.440141\pi$
$977$	11.6867	0.373892	0.186946	+	0.982370i	$0.440141\pi$
$978$	−0.246847	−0.00789331
$979$	12.0142	0.383976
$980$	−1.57700	−0.0503755
$981$	−6.71971	−0.214544
$982$	8.32377	0.265622
$983$	55.6562	1.77516	0.887579	−	0.460655i	$-0.152386\pi$
$983$	55.6562	1.77516	0.887579	+	0.460655i	$0.152386\pi$
$984$	−1.50195	−0.0478804
$985$	−6.46960	−0.206139
$986$	−34.5007	−1.09873
$987$	−1.38369	−0.0440433
$988$	−2.20941	−0.0702908
$989$	19.5700	0.622290
$990$	4.08180	0.129728
$991$	−24.4865	−0.777838	−0.388919	−	0.921272i	$-0.627151\pi$
$991$	−24.4865	−0.777838	−0.388919	+	0.921272i	$0.627151\pi$
$992$	−4.35182	−0.138170
$993$	1.57023	0.0498298
$994$	−3.02190	−0.0958488
$995$	−34.7930	−1.10301
$996$	0.226188	0.00716704
$997$	−10.5355	−0.333662	−0.166831	−	0.985986i	$-0.553353\pi$
$997$	−10.5355	−0.333662	−0.166831	+	0.985986i	$0.553353\pi$
$998$	−23.5460	−0.745335
$999$	−7.37218	−0.233245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.141161 q^{3} +1.00000 q^{4} -1.57700 q^{5} +0.141161 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.98007 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.141161 q^{3} +1.00000 q^{4} -1.57700 q^{5} +0.141161 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.98007 q^{9} +1.57700 q^{10} -0.868545 q^{11} -0.141161 q^{12} -4.18869 q^{13} -1.00000 q^{14} +0.222611 q^{15} +1.00000 q^{16} +5.52327 q^{17} +2.98007 q^{18} +0.527471 q^{19} -1.57700 q^{20} -0.141161 q^{21} +0.868545 q^{22} +2.36080 q^{23} +0.141161 q^{24} -2.51306 q^{25} +4.18869 q^{26} +0.844151 q^{27} +1.00000 q^{28} +6.24643 q^{29} -0.222611 q^{30} +4.35182 q^{31} -1.00000 q^{32} +0.122604 q^{33} -5.52327 q^{34} -1.57700 q^{35} -2.98007 q^{36} -8.73325 q^{37} -0.527471 q^{38} +0.591277 q^{39} +1.57700 q^{40} -10.6400 q^{41} +0.141161 q^{42} +8.28956 q^{43} -0.868545 q^{44} +4.69959 q^{45} -2.36080 q^{46} +9.80223 q^{47} -0.141161 q^{48} +1.00000 q^{49} +2.51306 q^{50} -0.779668 q^{51} -4.18869 q^{52} -0.274214 q^{53} -0.844151 q^{54} +1.36970 q^{55} -1.00000 q^{56} -0.0744581 q^{57} -6.24643 q^{58} -4.14179 q^{59} +0.222611 q^{60} +11.0753 q^{61} -4.35182 q^{62} -2.98007 q^{63} +1.00000 q^{64} +6.60558 q^{65} -0.122604 q^{66} +4.92691 q^{67} +5.52327 q^{68} -0.333252 q^{69} +1.57700 q^{70} +3.02190 q^{71} +2.98007 q^{72} -1.36759 q^{73} +8.73325 q^{74} +0.354745 q^{75} +0.527471 q^{76} -0.868545 q^{77} -0.591277 q^{78} +5.42830 q^{79} -1.57700 q^{80} +8.82106 q^{81} +10.6400 q^{82} -1.60235 q^{83} -0.141161 q^{84} -8.71023 q^{85} -8.28956 q^{86} -0.881749 q^{87} +0.868545 q^{88} -13.8326 q^{89} -4.69959 q^{90} -4.18869 q^{91} +2.36080 q^{92} -0.614306 q^{93} -9.80223 q^{94} -0.831824 q^{95} +0.141161 q^{96} -8.09710 q^{97} -1.00000 q^{98} +2.58833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 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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