LMFDB - Embedded newform 6034.2.a.k.1.1

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			1.1
Root			$-3.26119$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.26119 q^{3} +1.00000 q^{4} -1.57113 q^{5} +3.26119 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.63538 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.26119 q^{3} +1.00000 q^{4} -1.57113 q^{5} +3.26119 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.63538 q^{9} +1.57113 q^{10} +3.36723 q^{11} -3.26119 q^{12} +4.38488 q^{13} -1.00000 q^{14} +5.12375 q^{15} +1.00000 q^{16} +6.97133 q^{17} -7.63538 q^{18} +1.24277 q^{19} -1.57113 q^{20} -3.26119 q^{21} -3.36723 q^{22} -5.34535 q^{23} +3.26119 q^{24} -2.53156 q^{25} -4.38488 q^{26} -15.1169 q^{27} +1.00000 q^{28} +0.714285 q^{29} -5.12375 q^{30} -8.61163 q^{31} -1.00000 q^{32} -10.9812 q^{33} -6.97133 q^{34} -1.57113 q^{35} +7.63538 q^{36} +3.84539 q^{37} -1.24277 q^{38} -14.2999 q^{39} +1.57113 q^{40} -2.93275 q^{41} +3.26119 q^{42} -9.05346 q^{43} +3.36723 q^{44} -11.9962 q^{45} +5.34535 q^{46} +5.79002 q^{47} -3.26119 q^{48} +1.00000 q^{49} +2.53156 q^{50} -22.7349 q^{51} +4.38488 q^{52} -10.6069 q^{53} +15.1169 q^{54} -5.29034 q^{55} -1.00000 q^{56} -4.05293 q^{57} -0.714285 q^{58} -11.6527 q^{59} +5.12375 q^{60} +9.51910 q^{61} +8.61163 q^{62} +7.63538 q^{63} +1.00000 q^{64} -6.88921 q^{65} +10.9812 q^{66} +9.67742 q^{67} +6.97133 q^{68} +17.4322 q^{69} +1.57113 q^{70} -8.28126 q^{71} -7.63538 q^{72} +7.58502 q^{73} -3.84539 q^{74} +8.25589 q^{75} +1.24277 q^{76} +3.36723 q^{77} +14.2999 q^{78} -11.6261 q^{79} -1.57113 q^{80} +26.3929 q^{81} +2.93275 q^{82} +15.1640 q^{83} -3.26119 q^{84} -10.9529 q^{85} +9.05346 q^{86} -2.32942 q^{87} -3.36723 q^{88} -3.09589 q^{89} +11.9962 q^{90} +4.38488 q^{91} -5.34535 q^{92} +28.0842 q^{93} -5.79002 q^{94} -1.95256 q^{95} +3.26119 q^{96} +12.5883 q^{97} -1.00000 q^{98} +25.7100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.26119	−1.88285	−0.941425	−	0.337221i	$-0.890513\pi$
$3$	−3.26119	−1.88285	−0.941425	+	0.337221i	$0.890513\pi$
$4$	1.00000	0.500000
$5$	−1.57113	−0.702630	−0.351315	−	0.936257i	$-0.614265\pi$
$5$	−1.57113	−0.702630	−0.351315	+	0.936257i	$0.614265\pi$
$6$	3.26119	1.33138
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	7.63538	2.54513
$10$	1.57113	0.496834
$11$	3.36723	1.01526	0.507628	−	0.861576i	$-0.330522\pi$
$11$	3.36723	1.01526	0.507628	+	0.861576i	$0.330522\pi$
$12$	−3.26119	−0.941425
$13$	4.38488	1.21615	0.608073	−	0.793881i	$-0.291943\pi$
$13$	4.38488	1.21615	0.608073	+	0.793881i	$0.291943\pi$
$14$	−1.00000	−0.267261
$15$	5.12375	1.32295
$16$	1.00000	0.250000
$17$	6.97133	1.69080	0.845398	−	0.534137i	$-0.179363\pi$
$17$	6.97133	1.69080	0.845398	+	0.534137i	$0.179363\pi$
$18$	−7.63538	−1.79968
$19$	1.24277	0.285112	0.142556	−	0.989787i	$-0.454468\pi$
$19$	1.24277	0.285112	0.142556	+	0.989787i	$0.454468\pi$
$20$	−1.57113	−0.351315
$21$	−3.26119	−0.711651
$22$	−3.36723	−0.717895
$23$	−5.34535	−1.11458	−0.557291	−	0.830317i	$-0.688159\pi$
$23$	−5.34535	−1.11458	−0.557291	+	0.830317i	$0.688159\pi$
$24$	3.26119	0.665688
$25$	−2.53156	−0.506311
$26$	−4.38488	−0.859946
$27$	−15.1169	−2.90924
$28$	1.00000	0.188982
$29$	0.714285	0.132639	0.0663197	−	0.997798i	$-0.478874\pi$
$29$	0.714285	0.132639	0.0663197	+	0.997798i	$0.478874\pi$
$30$	−5.12375	−0.935465
$31$	−8.61163	−1.54669	−0.773347	−	0.633982i	$-0.781419\pi$
$31$	−8.61163	−1.54669	−0.773347	+	0.633982i	$0.781419\pi$
$32$	−1.00000	−0.176777
$33$	−10.9812	−1.91158
$34$	−6.97133	−1.19557
$35$	−1.57113	−0.265569
$36$	7.63538	1.27256
$37$	3.84539	0.632179	0.316089	−	0.948729i	$-0.397630\pi$
$37$	3.84539	0.632179	0.316089	+	0.948729i	$0.397630\pi$
$38$	−1.24277	−0.201605
$39$	−14.2999	−2.28982
$40$	1.57113	0.248417
$41$	−2.93275	−0.458019	−0.229009	−	0.973424i	$-0.573549\pi$
$41$	−2.93275	−0.458019	−0.229009	+	0.973424i	$0.573549\pi$
$42$	3.26119	0.503213
$43$	−9.05346	−1.38064	−0.690319	−	0.723505i	$-0.742530\pi$
$43$	−9.05346	−1.38064	−0.690319	+	0.723505i	$0.742530\pi$
$44$	3.36723	0.507628
$45$	−11.9962	−1.78828
$46$	5.34535	0.788128
$47$	5.79002	0.844561	0.422280	−	0.906465i	$-0.361230\pi$
$47$	5.79002	0.844561	0.422280	+	0.906465i	$0.361230\pi$
$48$	−3.26119	−0.470713
$49$	1.00000	0.142857
$50$	2.53156	0.358016
$51$	−22.7349	−3.18352
$52$	4.38488	0.608073
$53$	−10.6069	−1.45696	−0.728482	−	0.685065i	$-0.759774\pi$
$53$	−10.6069	−1.45696	−0.728482	+	0.685065i	$0.759774\pi$
$54$	15.1169	2.05715
$55$	−5.29034	−0.713350
$56$	−1.00000	−0.133631
$57$	−4.05293	−0.536823
$58$	−0.714285	−0.0937902
$59$	−11.6527	−1.51705	−0.758523	−	0.651646i	$-0.774079\pi$
$59$	−11.6527	−1.51705	−0.758523	+	0.651646i	$0.774079\pi$
$60$	5.12375	0.661474
$61$	9.51910	1.21880	0.609398	−	0.792865i	$-0.291411\pi$
$61$	9.51910	1.21880	0.609398	+	0.792865i	$0.291411\pi$
$62$	8.61163	1.09368
$63$	7.63538	0.961968
$64$	1.00000	0.125000
$65$	−6.88921	−0.854501
$66$	10.9812	1.35169
$67$	9.67742	1.18229	0.591143	−	0.806567i	$-0.298677\pi$
$67$	9.67742	1.18229	0.591143	+	0.806567i	$0.298677\pi$
$68$	6.97133	0.845398
$69$	17.4322	2.09859
$70$	1.57113	0.187786
$71$	−8.28126	−0.982805	−0.491402	−	0.870933i	$-0.663516\pi$
$71$	−8.28126	−0.982805	−0.491402	+	0.870933i	$0.663516\pi$
$72$	−7.63538	−0.899838
$73$	7.58502	0.887759	0.443880	−	0.896086i	$-0.353602\pi$
$73$	7.58502	0.887759	0.443880	+	0.896086i	$0.353602\pi$
$74$	−3.84539	−0.447018
$75$	8.25589	0.953309
$76$	1.24277	0.142556
$77$	3.36723	0.383731
$78$	14.2999	1.61915
$79$	−11.6261	−1.30803	−0.654017	−	0.756479i	$-0.726918\pi$
$79$	−11.6261	−1.30803	−0.654017	+	0.756479i	$0.726918\pi$
$80$	−1.57113	−0.175657
$81$	26.3929	2.93254
$82$	2.93275	0.323868
$83$	15.1640	1.66446	0.832231	−	0.554430i	$-0.187064\pi$
$83$	15.1640	1.66446	0.832231	+	0.554430i	$0.187064\pi$
$84$	−3.26119	−0.355825
$85$	−10.9529	−1.18800
$86$	9.05346	0.976259
$87$	−2.32942	−0.249740
$88$	−3.36723	−0.358947
$89$	−3.09589	−0.328164	−0.164082	−	0.986447i	$-0.552466\pi$
$89$	−3.09589	−0.328164	−0.164082	+	0.986447i	$0.552466\pi$
$90$	11.9962	1.26451
$91$	4.38488	0.459660
$92$	−5.34535	−0.557291
$93$	28.0842	2.91220
$94$	−5.79002	−0.597195
$95$	−1.95256	−0.200328
$96$	3.26119	0.332844
$97$	12.5883	1.27815	0.639076	−	0.769144i	$-0.279317\pi$
$97$	12.5883	1.27815	0.639076	+	0.769144i	$0.279317\pi$
$98$	−1.00000	−0.101015
$99$	25.7100	2.58396
$100$	−2.53156	−0.253156
$101$	−14.2268	−1.41562	−0.707808	−	0.706405i	$-0.750316\pi$
$101$	−14.2268	−1.41562	−0.707808	+	0.706405i	$0.750316\pi$
$102$	22.7349	2.25109
$103$	−13.2806	−1.30858	−0.654290	−	0.756244i	$-0.727032\pi$
$103$	−13.2806	−1.30858	−0.654290	+	0.756244i	$0.727032\pi$
$104$	−4.38488	−0.429973
$105$	5.12375	0.500027
$106$	10.6069	1.03023
$107$	−2.18528	−0.211259	−0.105630	−	0.994406i	$-0.533686\pi$
$107$	−2.18528	−0.211259	−0.105630	+	0.994406i	$0.533686\pi$
$108$	−15.1169	−1.45462
$109$	−4.48445	−0.429532	−0.214766	−	0.976666i	$-0.568899\pi$
$109$	−4.48445	−0.429532	−0.214766	+	0.976666i	$0.568899\pi$
$110$	5.29034	0.504414
$111$	−12.5406	−1.19030
$112$	1.00000	0.0944911
$113$	−13.9140	−1.30892	−0.654459	−	0.756097i	$-0.727104\pi$
$113$	−13.9140	−1.30892	−0.654459	+	0.756097i	$0.727104\pi$
$114$	4.05293	0.379591
$115$	8.39823	0.783139
$116$	0.714285	0.0663197
$117$	33.4802	3.09525
$118$	11.6527	1.07271
$119$	6.97133	0.639061
$120$	−5.12375	−0.467732
$121$	0.338206	0.0307460
$122$	−9.51910	−0.861819
$123$	9.56427	0.862381
$124$	−8.61163	−0.773347
$125$	11.8330	1.05838
$126$	−7.63538	−0.680214
$127$	−7.03075	−0.623878	−0.311939	−	0.950102i	$-0.600979\pi$
$127$	−7.03075	−0.623878	−0.311939	+	0.950102i	$0.600979\pi$
$128$	−1.00000	−0.0883883
$129$	29.5251	2.59954
$130$	6.88921	0.604223
$131$	4.17590	0.364850	0.182425	−	0.983220i	$-0.441605\pi$
$131$	4.17590	0.364850	0.182425	+	0.983220i	$0.441605\pi$
$132$	−10.9812	−0.955788
$133$	1.24277	0.107762
$134$	−9.67742	−0.836002
$135$	23.7505	2.04412
$136$	−6.97133	−0.597787
$137$	−3.71306	−0.317228	−0.158614	−	0.987341i	$-0.550703\pi$
$137$	−3.71306	−0.317228	−0.158614	+	0.987341i	$0.550703\pi$
$138$	−17.4322	−1.48393
$139$	3.63187	0.308052	0.154026	−	0.988067i	$-0.450776\pi$
$139$	3.63187	0.308052	0.154026	+	0.988067i	$0.450776\pi$
$140$	−1.57113	−0.132785
$141$	−18.8824	−1.59018
$142$	8.28126	0.694948
$143$	14.7649	1.23470
$144$	7.63538	0.636282
$145$	−1.12223	−0.0931964
$146$	−7.58502	−0.627741
$147$	−3.26119	−0.268979
$148$	3.84539	0.316089
$149$	−19.7410	−1.61725	−0.808623	−	0.588327i	$-0.799787\pi$
$149$	−19.7410	−1.61725	−0.808623	+	0.588327i	$0.799787\pi$
$150$	−8.25589	−0.674091
$151$	−6.27958	−0.511025	−0.255512	−	0.966806i	$-0.582244\pi$
$151$	−6.27958	−0.511025	−0.255512	+	0.966806i	$0.582244\pi$
$152$	−1.24277	−0.100802
$153$	53.2288	4.30329
$154$	−3.36723	−0.271339
$155$	13.5300	1.08675
$156$	−14.2999	−1.14491
$157$	−11.6640	−0.930885	−0.465442	−	0.885078i	$-0.654105\pi$
$157$	−11.6640	−0.930885	−0.465442	+	0.885078i	$0.654105\pi$
$158$	11.6261	0.924920
$159$	34.5910	2.74325
$160$	1.57113	0.124209
$161$	−5.34535	−0.421272
$162$	−26.3929	−2.07362
$163$	7.11424	0.557230	0.278615	−	0.960403i	$-0.410125\pi$
$163$	7.11424	0.557230	0.278615	+	0.960403i	$0.410125\pi$
$164$	−2.93275	−0.229009
$165$	17.2528	1.34313
$166$	−15.1640	−1.17695
$167$	14.9273	1.15511	0.577553	−	0.816353i	$-0.304008\pi$
$167$	14.9273	1.15511	0.577553	+	0.816353i	$0.304008\pi$
$168$	3.26119	0.251607
$169$	6.22716	0.479013
$170$	10.9529	0.840045
$171$	9.48906	0.725646
$172$	−9.05346	−0.690319
$173$	2.92196	0.222153	0.111076	−	0.993812i	$-0.464570\pi$
$173$	2.92196	0.222153	0.111076	+	0.993812i	$0.464570\pi$
$174$	2.32942	0.176593
$175$	−2.53156	−0.191368
$176$	3.36723	0.253814
$177$	38.0016	2.85637
$178$	3.09589	0.232047
$179$	−19.3029	−1.44276	−0.721381	−	0.692538i	$-0.756493\pi$
$179$	−19.3029	−1.44276	−0.721381	+	0.692538i	$0.756493\pi$
$180$	−11.9962	−0.894141
$181$	−21.4000	−1.59065	−0.795324	−	0.606184i	$-0.792699\pi$
$181$	−21.4000	−1.59065	−0.795324	+	0.606184i	$0.792699\pi$
$182$	−4.38488	−0.325029
$183$	−31.0436	−2.29481
$184$	5.34535	0.394064
$185$	−6.04161	−0.444188
$186$	−28.0842	−2.05923
$187$	23.4740	1.71659
$188$	5.79002	0.422280
$189$	−15.1169	−1.09959
$190$	1.95256	0.141653
$191$	−0.683469	−0.0494541	−0.0247270	−	0.999694i	$-0.507872\pi$
$191$	−0.683469	−0.0494541	−0.0247270	+	0.999694i	$0.507872\pi$
$192$	−3.26119	−0.235356
$193$	−8.49410	−0.611419	−0.305709	−	0.952125i	$-0.598894\pi$
$193$	−8.49410	−0.611419	−0.305709	+	0.952125i	$0.598894\pi$
$194$	−12.5883	−0.903789
$195$	22.4670	1.60890
$196$	1.00000	0.0714286
$197$	−3.62907	−0.258560	−0.129280	−	0.991608i	$-0.541267\pi$
$197$	−3.62907	−0.258560	−0.129280	+	0.991608i	$0.541267\pi$
$198$	−25.7100	−1.82713
$199$	4.16886	0.295522	0.147761	−	0.989023i	$-0.452793\pi$
$199$	4.16886	0.295522	0.147761	+	0.989023i	$0.452793\pi$
$200$	2.53156	0.179008
$201$	−31.5599	−2.22607
$202$	14.2268	1.00099
$203$	0.714285	0.0501330
$204$	−22.7349	−1.59176
$205$	4.60773	0.321818
$206$	13.2806	0.925305
$207$	−40.8138	−2.83675
$208$	4.38488	0.304037
$209$	4.18470	0.289462
$210$	−5.12375	−0.353573
$211$	1.29992	0.0894904	0.0447452	−	0.998998i	$-0.485752\pi$
$211$	1.29992	0.0894904	0.0447452	+	0.998998i	$0.485752\pi$
$212$	−10.6069	−0.728482
$213$	27.0068	1.85048
$214$	2.18528	0.149383
$215$	14.2241	0.970078
$216$	15.1169	1.02857
$217$	−8.61163	−0.584596
$218$	4.48445	0.303725
$219$	−24.7362	−1.67152
$220$	−5.29034	−0.356675
$221$	30.5684	2.05626
$222$	12.5406	0.841668
$223$	−1.72546	−0.115545	−0.0577726	−	0.998330i	$-0.518400\pi$
$223$	−1.72546	−0.115545	−0.0577726	+	0.998330i	$0.518400\pi$
$224$	−1.00000	−0.0668153
$225$	−19.3294	−1.28863
$226$	13.9140	0.925545
$227$	−6.83743	−0.453816	−0.226908	−	0.973916i	$-0.572862\pi$
$227$	−6.83743	−0.453816	−0.226908	+	0.973916i	$0.572862\pi$
$228$	−4.05293	−0.268412
$229$	13.3205	0.880246	0.440123	−	0.897937i	$-0.354935\pi$
$229$	13.3205	0.880246	0.440123	+	0.897937i	$0.354935\pi$
$230$	−8.39823	−0.553763
$231$	−10.9812	−0.722508
$232$	−0.714285	−0.0468951
$233$	−10.5460	−0.690890	−0.345445	−	0.938439i	$-0.612272\pi$
$233$	−10.5460	−0.690890	−0.345445	+	0.938439i	$0.612272\pi$
$234$	−33.4802	−2.18867
$235$	−9.09686	−0.593414
$236$	−11.6527	−0.758523
$237$	37.9149	2.46283
$238$	−6.97133	−0.451884
$239$	22.1887	1.43527	0.717634	−	0.696421i	$-0.245225\pi$
$239$	22.1887	1.43527	0.717634	+	0.696421i	$0.245225\pi$
$240$	5.12375	0.330737
$241$	0.311904	0.0200915	0.0100458	−	0.999950i	$-0.496802\pi$
$241$	0.311904	0.0200915	0.0100458	+	0.999950i	$0.496802\pi$
$242$	−0.338206	−0.0217407
$243$	−40.7217	−2.61230
$244$	9.51910	0.609398
$245$	−1.57113	−0.100376
$246$	−9.56427	−0.609796
$247$	5.44942	0.346738
$248$	8.61163	0.546839
$249$	−49.4526	−3.13393
$250$	−11.8330	−0.748387
$251$	−15.1712	−0.957599	−0.478800	−	0.877924i	$-0.658928\pi$
$251$	−15.1712	−0.957599	−0.478800	+	0.877924i	$0.658928\pi$
$252$	7.63538	0.480984
$253$	−17.9990	−1.13159
$254$	7.03075	0.441149
$255$	35.7194	2.23683
$256$	1.00000	0.0625000
$257$	−21.6673	−1.35157	−0.675783	−	0.737101i	$-0.736194\pi$
$257$	−21.6673	−1.35157	−0.675783	+	0.737101i	$0.736194\pi$
$258$	−29.5251	−1.83815
$259$	3.84539	0.238941
$260$	−6.88921	−0.427250
$261$	5.45384	0.337584
$262$	−4.17590	−0.257988
$263$	−23.4746	−1.44750	−0.723751	−	0.690061i	$-0.757584\pi$
$263$	−23.4746	−1.44750	−0.723751	+	0.690061i	$0.757584\pi$
$264$	10.9812	0.675844
$265$	16.6647	1.02371
$266$	−1.24277	−0.0761994
$267$	10.0963	0.617884
$268$	9.67742	0.591143
$269$	−11.9068	−0.725970	−0.362985	−	0.931795i	$-0.618242\pi$
$269$	−11.9068	−0.725970	−0.362985	+	0.931795i	$0.618242\pi$
$270$	−23.7505	−1.44541
$271$	6.70377	0.407225	0.203613	−	0.979052i	$-0.434732\pi$
$271$	6.70377	0.407225	0.203613	+	0.979052i	$0.434732\pi$
$272$	6.97133	0.422699
$273$	−14.2999	−0.865472
$274$	3.71306	0.224314
$275$	−8.52432	−0.514036
$276$	17.4322	1.04930
$277$	24.7887	1.48941	0.744705	−	0.667394i	$-0.232590\pi$
$277$	24.7887	1.48941	0.744705	+	0.667394i	$0.232590\pi$
$278$	−3.63187	−0.217825
$279$	−65.7531	−3.93654
$280$	1.57113	0.0938929
$281$	−1.12004	−0.0668159	−0.0334080	−	0.999442i	$-0.510636\pi$
$281$	−1.12004	−0.0668159	−0.0334080	+	0.999442i	$0.510636\pi$
$282$	18.8824	1.12443
$283$	−15.1845	−0.902625	−0.451313	−	0.892366i	$-0.649044\pi$
$283$	−15.1845	−0.902625	−0.451313	+	0.892366i	$0.649044\pi$
$284$	−8.28126	−0.491402
$285$	6.36767	0.377188
$286$	−14.7649	−0.873065
$287$	−2.93275	−0.173115
$288$	−7.63538	−0.449919
$289$	31.5994	1.85879
$290$	1.12223	0.0658998
$291$	−41.0530	−2.40657
$292$	7.58502	0.443880
$293$	2.36549	0.138194	0.0690968	−	0.997610i	$-0.477988\pi$
$293$	2.36549	0.138194	0.0690968	+	0.997610i	$0.477988\pi$
$294$	3.26119	0.190197
$295$	18.3078	1.06592
$296$	−3.84539	−0.223509
$297$	−50.9019	−2.95363
$298$	19.7410	1.14357
$299$	−23.4387	−1.35550
$300$	8.25589	0.476654
$301$	−9.05346	−0.521832
$302$	6.27958	0.361349
$303$	46.3962	2.66539
$304$	1.24277	0.0712780
$305$	−14.9557	−0.856362
$306$	−53.2288	−3.04289
$307$	31.5770	1.80220	0.901098	−	0.433616i	$-0.142763\pi$
$307$	31.5770	1.80220	0.901098	+	0.433616i	$0.142763\pi$
$308$	3.36723	0.191865
$309$	43.3107	2.46386
$310$	−13.5300	−0.768451
$311$	−31.4236	−1.78187	−0.890935	−	0.454130i	$-0.849950\pi$
$311$	−31.4236	−1.78187	−0.890935	+	0.454130i	$0.849950\pi$
$312$	14.2999	0.809575
$313$	14.6221	0.826490	0.413245	−	0.910620i	$-0.364395\pi$
$313$	14.6221	0.826490	0.413245	+	0.910620i	$0.364395\pi$
$314$	11.6640	0.658235
$315$	−11.9962	−0.675907
$316$	−11.6261	−0.654017
$317$	18.6590	1.04800	0.523998	−	0.851719i	$-0.324440\pi$
$317$	18.6590	1.04800	0.523998	+	0.851719i	$0.324440\pi$
$318$	−34.5910	−1.93977
$319$	2.40516	0.134663
$320$	−1.57113	−0.0878287
$321$	7.12663	0.397770
$322$	5.34535	0.297885
$323$	8.66379	0.482066
$324$	26.3929	1.46627
$325$	−11.1006	−0.615749
$326$	−7.11424	−0.394021
$327$	14.6246	0.808745
$328$	2.93275	0.161934
$329$	5.79002	0.319214
$330$	−17.2528	−0.949737
$331$	16.6382	0.914520	0.457260	−	0.889333i	$-0.348831\pi$
$331$	16.6382	0.914520	0.457260	+	0.889333i	$0.348831\pi$
$332$	15.1640	0.832231
$333$	29.3611	1.60898
$334$	−14.9273	−0.816783
$335$	−15.2045	−0.830709
$336$	−3.26119	−0.177913
$337$	34.5642	1.88283	0.941417	−	0.337244i	$-0.109495\pi$
$337$	34.5642	1.88283	0.941417	+	0.337244i	$0.109495\pi$
$338$	−6.22716	−0.338713
$339$	45.3762	2.46450
$340$	−10.9529	−0.594002
$341$	−28.9973	−1.57029
$342$	−9.48906	−0.513109
$343$	1.00000	0.0539949
$344$	9.05346	0.488130
$345$	−27.3882	−1.47453
$346$	−2.92196	−0.157086
$347$	2.49822	0.134112	0.0670558	−	0.997749i	$-0.478639\pi$
$347$	2.49822	0.134112	0.0670558	+	0.997749i	$0.478639\pi$
$348$	−2.32942	−0.124870
$349$	3.46239	0.185337	0.0926686	−	0.995697i	$-0.470460\pi$
$349$	3.46239	0.185337	0.0926686	+	0.995697i	$0.470460\pi$
$350$	2.53156	0.135317
$351$	−66.2857	−3.53807
$352$	−3.36723	−0.179474
$353$	6.79546	0.361686	0.180843	−	0.983512i	$-0.442117\pi$
$353$	6.79546	0.361686	0.180843	+	0.983512i	$0.442117\pi$
$354$	−38.0016	−2.01976
$355$	13.0109	0.690548
$356$	−3.09589	−0.164082
$357$	−22.7349	−1.20326
$358$	19.3029	1.02019
$359$	30.4002	1.60446	0.802231	−	0.597013i	$-0.203646\pi$
$359$	30.4002	1.60446	0.802231	+	0.597013i	$0.203646\pi$
$360$	11.9962	0.632253
$361$	−17.4555	−0.918711
$362$	21.4000	1.12476
$363$	−1.10295	−0.0578901
$364$	4.38488	0.229830
$365$	−11.9170	−0.623766
$366$	31.0436	1.62268
$367$	−2.07915	−0.108531	−0.0542654	−	0.998527i	$-0.517282\pi$
$367$	−2.07915	−0.108531	−0.0542654	+	0.998527i	$0.517282\pi$
$368$	−5.34535	−0.278645
$369$	−22.3927	−1.16572
$370$	6.04161	0.314088
$371$	−10.6069	−0.550681
$372$	28.0842	1.45610
$373$	5.48030	0.283759	0.141880	−	0.989884i	$-0.454685\pi$
$373$	5.48030	0.283759	0.141880	+	0.989884i	$0.454685\pi$
$374$	−23.4740	−1.21381
$375$	−38.5898	−1.99277
$376$	−5.79002	−0.298597
$377$	3.13205	0.161309
$378$	15.1169	0.777528
$379$	−1.62719	−0.0835829	−0.0417914	−	0.999126i	$-0.513307\pi$
$379$	−1.62719	−0.0835829	−0.0417914	+	0.999126i	$0.513307\pi$
$380$	−1.95256	−0.100164
$381$	22.9286	1.17467
$382$	0.683469	0.0349693
$383$	−13.2210	−0.675559	−0.337780	−	0.941225i	$-0.609676\pi$
$383$	−13.2210	−0.675559	−0.337780	+	0.941225i	$0.609676\pi$
$384$	3.26119	0.166422
$385$	−5.29034	−0.269621
$386$	8.49410	0.432338
$387$	−69.1266	−3.51390
$388$	12.5883	0.639076
$389$	−3.02357	−0.153301	−0.0766505	−	0.997058i	$-0.524423\pi$
$389$	−3.02357	−0.153301	−0.0766505	+	0.997058i	$0.524423\pi$
$390$	−22.4670	−1.13766
$391$	−37.2642	−1.88453
$392$	−1.00000	−0.0505076
$393$	−13.6184	−0.686959
$394$	3.62907	0.182830
$395$	18.2660	0.919064
$396$	25.7100	1.29198
$397$	−13.4729	−0.676186	−0.338093	−	0.941113i	$-0.609782\pi$
$397$	−13.4729	−0.676186	−0.338093	+	0.941113i	$0.609782\pi$
$398$	−4.16886	−0.208966
$399$	−4.05293	−0.202900
$400$	−2.53156	−0.126578
$401$	−19.2938	−0.963489	−0.481744	−	0.876312i	$-0.659997\pi$
$401$	−19.2938	−0.963489	−0.481744	+	0.876312i	$0.659997\pi$
$402$	31.5599	1.57407
$403$	−37.7610	−1.88101
$404$	−14.2268	−0.707808
$405$	−41.4666	−2.06049
$406$	−0.714285	−0.0354494
$407$	12.9483	0.641824
$408$	22.7349	1.12554
$409$	10.3677	0.512649	0.256324	−	0.966591i	$-0.417488\pi$
$409$	10.3677	0.512649	0.256324	+	0.966591i	$0.417488\pi$
$410$	−4.60773	−0.227560
$411$	12.1090	0.597294
$412$	−13.2806	−0.654290
$413$	−11.6527	−0.573390
$414$	40.8138	2.00589
$415$	−23.8245	−1.16950
$416$	−4.38488	−0.214986
$417$	−11.8442	−0.580015
$418$	−4.18470	−0.204680
$419$	23.9351	1.16931	0.584653	−	0.811283i	$-0.301231\pi$
$419$	23.9351	1.16931	0.584653	+	0.811283i	$0.301231\pi$
$420$	5.12375	0.250014
$421$	32.5135	1.58461	0.792305	−	0.610125i	$-0.208881\pi$
$421$	32.5135	1.58461	0.792305	+	0.610125i	$0.208881\pi$
$422$	−1.29992	−0.0632793
$423$	44.2090	2.14951
$424$	10.6069	0.515114
$425$	−17.6483	−0.856069
$426$	−27.0068	−1.30848
$427$	9.51910	0.460662
$428$	−2.18528	−0.105630
$429$	−48.1511	−2.32476
$430$	−14.2241	−0.685949
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−15.1169	−0.727311
$433$	21.3318	1.02514	0.512570	−	0.858645i	$-0.328693\pi$
$433$	21.3318	1.02514	0.512570	+	0.858645i	$0.328693\pi$
$434$	8.61163	0.413372
$435$	3.65982	0.175475
$436$	−4.48445	−0.214766
$437$	−6.64306	−0.317781
$438$	24.7362	1.18194
$439$	−30.9592	−1.47760	−0.738801	−	0.673924i	$-0.764608\pi$
$439$	−30.9592	−1.47760	−0.738801	+	0.673924i	$0.764608\pi$
$440$	5.29034	0.252207
$441$	7.63538	0.363590
$442$	−30.5684	−1.45399
$443$	−18.0899	−0.859478	−0.429739	−	0.902953i	$-0.641394\pi$
$443$	−18.0899	−0.859478	−0.429739	+	0.902953i	$0.641394\pi$
$444$	−12.5406	−0.595149
$445$	4.86404	0.230578
$446$	1.72546	0.0817027
$447$	64.3792	3.04503
$448$	1.00000	0.0472456
$449$	−24.9108	−1.17561	−0.587807	−	0.809001i	$-0.700009\pi$
$449$	−24.9108	−1.17561	−0.587807	+	0.809001i	$0.700009\pi$
$450$	19.3294	0.911197
$451$	−9.87524	−0.465007
$452$	−13.9140	−0.654459
$453$	20.4789	0.962183
$454$	6.83743	0.320897
$455$	−6.88921	−0.322971
$456$	4.05293	0.189796
$457$	4.95753	0.231904	0.115952	−	0.993255i	$-0.463008\pi$
$457$	4.95753	0.231904	0.115952	+	0.993255i	$0.463008\pi$
$458$	−13.3205	−0.622428
$459$	−105.385	−4.91894
$460$	8.39823	0.391569
$461$	26.9228	1.25392	0.626960	−	0.779052i	$-0.284299\pi$
$461$	26.9228	1.25392	0.626960	+	0.779052i	$0.284299\pi$
$462$	10.9812	0.510890
$463$	−7.07952	−0.329013	−0.164506	−	0.986376i	$-0.552603\pi$
$463$	−7.07952	−0.329013	−0.164506	+	0.986376i	$0.552603\pi$
$464$	0.714285	0.0331598
$465$	−44.1239	−2.04620
$466$	10.5460	0.488533
$467$	2.70233	0.125049	0.0625246	−	0.998043i	$-0.480085\pi$
$467$	2.70233	0.125049	0.0625246	+	0.998043i	$0.480085\pi$
$468$	33.4802	1.54762
$469$	9.67742	0.446862
$470$	9.09686	0.419607
$471$	38.0384	1.75272
$472$	11.6527	0.536357
$473$	−30.4850	−1.40170
$474$	−37.9149	−1.74149
$475$	−3.14615	−0.144355
$476$	6.97133	0.319530
$477$	−80.9874	−3.70816
$478$	−22.1887	−1.01489
$479$	−18.1714	−0.830274	−0.415137	−	0.909759i	$-0.636266\pi$
$479$	−18.1714	−0.830274	−0.415137	+	0.909759i	$0.636266\pi$
$480$	−5.12375	−0.233866
$481$	16.8616	0.768822
$482$	−0.311904	−0.0142068
$483$	17.4322	0.793193
$484$	0.338206	0.0153730
$485$	−19.7779	−0.898067
$486$	40.7217	1.84718
$487$	−16.1307	−0.730953	−0.365476	−	0.930821i	$-0.619094\pi$
$487$	−16.1307	−0.730953	−0.365476	+	0.930821i	$0.619094\pi$
$488$	−9.51910	−0.430909
$489$	−23.2009	−1.04918
$490$	1.57113	0.0709763
$491$	−18.1349	−0.818417	−0.409208	−	0.912441i	$-0.634195\pi$
$491$	−18.1349	−0.818417	−0.409208	+	0.912441i	$0.634195\pi$
$492$	9.56427	0.431191
$493$	4.97951	0.224266
$494$	−5.44942	−0.245181
$495$	−40.3938	−1.81557
$496$	−8.61163	−0.386674
$497$	−8.28126	−0.371465
$498$	49.4526	2.21602
$499$	−32.7814	−1.46750	−0.733748	−	0.679422i	$-0.762231\pi$
$499$	−32.7814	−1.46750	−0.733748	+	0.679422i	$0.762231\pi$
$500$	11.8330	0.529190
$501$	−48.6807	−2.17489
$502$	15.1712	0.677125
$503$	−34.4754	−1.53718	−0.768592	−	0.639739i	$-0.779042\pi$
$503$	−34.4754	−1.53718	−0.768592	+	0.639739i	$0.779042\pi$
$504$	−7.63538	−0.340107
$505$	22.3521	0.994654
$506$	17.9990	0.800153
$507$	−20.3080	−0.901909
$508$	−7.03075	−0.311939
$509$	12.2201	0.541646	0.270823	−	0.962629i	$-0.412704\pi$
$509$	12.2201	0.541646	0.270823	+	0.962629i	$0.412704\pi$
$510$	−35.7194	−1.58168
$511$	7.58502	0.335542
$512$	−1.00000	−0.0441942
$513$	−18.7869	−0.829460
$514$	21.6673	0.955702
$515$	20.8656	0.919447
$516$	29.5251	1.29977
$517$	19.4963	0.857446
$518$	−3.84539	−0.168957
$519$	−9.52908	−0.418280
$520$	6.88921	0.302112
$521$	−36.7535	−1.61020	−0.805101	−	0.593138i	$-0.797889\pi$
$521$	−36.7535	−1.61020	−0.805101	+	0.593138i	$0.797889\pi$
$522$	−5.45384	−0.238708
$523$	−37.4162	−1.63610	−0.818049	−	0.575149i	$-0.804944\pi$
$523$	−37.4162	−1.63610	−0.818049	+	0.575149i	$0.804944\pi$
$524$	4.17590	0.182425
$525$	8.25589	0.360317
$526$	23.4746	1.02354
$527$	−60.0345	−2.61515
$528$	−10.9812	−0.477894
$529$	5.57273	0.242293
$530$	−16.6647	−0.723870
$531$	−88.9725	−3.86108
$532$	1.24277	0.0538811
$533$	−12.8598	−0.557018
$534$	−10.0963	−0.436910
$535$	3.43336	0.148437
$536$	−9.67742	−0.418001
$537$	62.9503	2.71651
$538$	11.9068	0.513339
$539$	3.36723	0.145037
$540$	23.7505	1.02206
$541$	3.29851	0.141814	0.0709071	−	0.997483i	$-0.477411\pi$
$541$	3.29851	0.141814	0.0709071	+	0.997483i	$0.477411\pi$
$542$	−6.70377	−0.287952
$543$	69.7895	2.99495
$544$	−6.97133	−0.298893
$545$	7.04564	0.301802
$546$	14.2999	0.611981
$547$	44.4439	1.90028	0.950141	−	0.311819i	$-0.100938\pi$
$547$	44.4439	1.90028	0.950141	+	0.311819i	$0.100938\pi$
$548$	−3.71306	−0.158614
$549$	72.6820	3.10199
$550$	8.52432	0.363478
$551$	0.887695	0.0378171
$552$	−17.4322	−0.741964
$553$	−11.6261	−0.494391
$554$	−24.7887	−1.05317
$555$	19.7028	0.836339
$556$	3.63187	0.154026
$557$	26.6439	1.12894	0.564470	−	0.825454i	$-0.309081\pi$
$557$	26.6439	1.12894	0.564470	+	0.825454i	$0.309081\pi$
$558$	65.7531	2.78355
$559$	−39.6983	−1.67906
$560$	−1.57113	−0.0663923
$561$	−76.5534	−3.23209
$562$	1.12004	0.0472460
$563$	19.9398	0.840360	0.420180	−	0.907441i	$-0.361967\pi$
$563$	19.9398	0.840360	0.420180	+	0.907441i	$0.361967\pi$
$564$	−18.8824	−0.795091
$565$	21.8607	0.919685
$566$	15.1845	0.638253
$567$	26.3929	1.10840
$568$	8.28126	0.347474
$569$	1.28540	0.0538868	0.0269434	−	0.999637i	$-0.491423\pi$
$569$	1.28540	0.0538868	0.0269434	+	0.999637i	$0.491423\pi$
$570$	−6.36767	−0.266712
$571$	32.1980	1.34745	0.673723	−	0.738984i	$-0.264694\pi$
$571$	32.1980	1.34745	0.673723	+	0.738984i	$0.264694\pi$
$572$	14.7649	0.617350
$573$	2.22893	0.0931147
$574$	2.93275	0.122411
$575$	13.5320	0.564325
$576$	7.63538	0.318141
$577$	−13.4500	−0.559931	−0.279966	−	0.960010i	$-0.590323\pi$
$577$	−13.4500	−0.559931	−0.279966	+	0.960010i	$0.590323\pi$
$578$	−31.5994	−1.31436
$579$	27.7009	1.15121
$580$	−1.12223	−0.0465982
$581$	15.1640	0.629107
$582$	41.0530	1.70170
$583$	−35.7157	−1.47919
$584$	−7.58502	−0.313870
$585$	−52.6017	−2.17481
$586$	−2.36549	−0.0977176
$587$	14.3519	0.592368	0.296184	−	0.955131i	$-0.404286\pi$
$587$	14.3519	0.592368	0.296184	+	0.955131i	$0.404286\pi$
$588$	−3.26119	−0.134489
$589$	−10.7023	−0.440981
$590$	−18.3078	−0.753721
$591$	11.8351	0.486830
$592$	3.84539	0.158045
$593$	−34.3015	−1.40859	−0.704296	−	0.709906i	$-0.748737\pi$
$593$	−34.3015	−1.40859	−0.704296	+	0.709906i	$0.748737\pi$
$594$	50.9019	2.08853
$595$	−10.9529	−0.449023
$596$	−19.7410	−0.808623
$597$	−13.5954	−0.556424
$598$	23.4387	0.958480
$599$	−46.2196	−1.88848	−0.944240	−	0.329258i	$-0.893201\pi$
$599$	−46.2196	−1.88848	−0.944240	+	0.329258i	$0.893201\pi$
$600$	−8.25589	−0.337045
$601$	31.6371	1.29051	0.645253	−	0.763969i	$-0.276752\pi$
$601$	31.6371	1.29051	0.645253	+	0.763969i	$0.276752\pi$
$602$	9.05346	0.368991
$603$	73.8908	3.00907
$604$	−6.27958	−0.255512
$605$	−0.531365	−0.0216031
$606$	−46.3962	−1.88472
$607$	−6.66317	−0.270450	−0.135225	−	0.990815i	$-0.543176\pi$
$607$	−6.66317	−0.270450	−0.135225	+	0.990815i	$0.543176\pi$
$608$	−1.24277	−0.0504012
$609$	−2.32942	−0.0943929
$610$	14.9557	0.605540
$611$	25.3885	1.02711
$612$	53.2288	2.15165
$613$	−20.7301	−0.837281	−0.418641	−	0.908152i	$-0.637493\pi$
$613$	−20.7301	−0.837281	−0.418641	+	0.908152i	$0.637493\pi$
$614$	−31.5770	−1.27434
$615$	−15.0267	−0.605935
$616$	−3.36723	−0.135669
$617$	24.1935	0.973993	0.486996	−	0.873404i	$-0.338092\pi$
$617$	24.1935	0.973993	0.486996	+	0.873404i	$0.338092\pi$
$618$	−43.3107	−1.74221
$619$	−4.78915	−0.192492	−0.0962461	−	0.995358i	$-0.530684\pi$
$619$	−4.78915	−0.192492	−0.0962461	+	0.995358i	$0.530684\pi$
$620$	13.5300	0.543377
$621$	80.8049	3.24259
$622$	31.4236	1.25997
$623$	−3.09589	−0.124034
$624$	−14.2999	−0.572456
$625$	−5.93344	−0.237338
$626$	−14.6221	−0.584416
$627$	−13.6471	−0.545014
$628$	−11.6640	−0.465442
$629$	26.8075	1.06889
$630$	11.9962	0.477939
$631$	−24.7116	−0.983752	−0.491876	−	0.870665i	$-0.663689\pi$
$631$	−24.7116	−0.983752	−0.491876	+	0.870665i	$0.663689\pi$
$632$	11.6261	0.462460
$633$	−4.23930	−0.168497
$634$	−18.6590	−0.741045
$635$	11.0462	0.438356
$636$	34.5910	1.37162
$637$	4.38488	0.173735
$638$	−2.40516	−0.0952211
$639$	−63.2306	−2.50136
$640$	1.57113	0.0621043
$641$	−33.2427	−1.31301	−0.656505	−	0.754322i	$-0.727966\pi$
$641$	−33.2427	−1.31301	−0.656505	+	0.754322i	$0.727966\pi$
$642$	−7.12663	−0.281266
$643$	17.2791	0.681422	0.340711	−	0.940168i	$-0.389332\pi$
$643$	17.2791	0.681422	0.340711	+	0.940168i	$0.389332\pi$
$644$	−5.34535	−0.210636
$645$	−46.3877	−1.82651
$646$	−8.66379	−0.340872
$647$	−47.6101	−1.87175	−0.935873	−	0.352336i	$-0.885387\pi$
$647$	−47.6101	−1.87175	−0.935873	+	0.352336i	$0.885387\pi$
$648$	−26.3929	−1.03681
$649$	−39.2371	−1.54019
$650$	11.1006	0.435400
$651$	28.0842	1.10071
$652$	7.11424	0.278615
$653$	1.35550	0.0530447	0.0265223	−	0.999648i	$-0.491557\pi$
$653$	1.35550	0.0530447	0.0265223	+	0.999648i	$0.491557\pi$
$654$	−14.6246	−0.571869
$655$	−6.56088	−0.256355
$656$	−2.93275	−0.114505
$657$	57.9145	2.25946
$658$	−5.79002	−0.225718
$659$	−20.8063	−0.810499	−0.405250	−	0.914206i	$-0.632815\pi$
$659$	−20.8063	−0.810499	−0.405250	+	0.914206i	$0.632815\pi$
$660$	17.2528	0.671565
$661$	40.5697	1.57798	0.788989	−	0.614407i	$-0.210605\pi$
$661$	40.5697	1.57798	0.788989	+	0.614407i	$0.210605\pi$
$662$	−16.6382	−0.646663
$663$	−99.6896	−3.87162
$664$	−15.1640	−0.588476
$665$	−1.95256	−0.0757170
$666$	−29.3611	−1.13772
$667$	−3.81810	−0.147837
$668$	14.9273	0.577553
$669$	5.62705	0.217554
$670$	15.2045	0.587400
$671$	32.0530	1.23739
$672$	3.26119	0.125803
$673$	−14.7209	−0.567450	−0.283725	−	0.958906i	$-0.591570\pi$
$673$	−14.7209	−0.567450	−0.283725	+	0.958906i	$0.591570\pi$
$674$	−34.5642	−1.33137
$675$	38.2692	1.47298
$676$	6.22716	0.239506
$677$	15.6906	0.603038	0.301519	−	0.953460i	$-0.402506\pi$
$677$	15.6906	0.603038	0.301519	+	0.953460i	$0.402506\pi$
$678$	−45.3762	−1.74266
$679$	12.5883	0.483096
$680$	10.9529	0.420023
$681$	22.2982	0.854468
$682$	28.9973	1.11036
$683$	36.9372	1.41336	0.706681	−	0.707532i	$-0.250191\pi$
$683$	36.9372	1.41336	0.706681	+	0.707532i	$0.250191\pi$
$684$	9.48906	0.362823
$685$	5.83370	0.222894
$686$	−1.00000	−0.0381802
$687$	−43.4409	−1.65737
$688$	−9.05346	−0.345160
$689$	−46.5098	−1.77188
$690$	27.3882	1.04265
$691$	16.1687	0.615088	0.307544	−	0.951534i	$-0.400493\pi$
$691$	16.1687	0.615088	0.307544	+	0.951534i	$0.400493\pi$
$692$	2.92196	0.111076
$693$	25.7100	0.976644
$694$	−2.49822	−0.0948313
$695$	−5.70614	−0.216446
$696$	2.32942	0.0882965
$697$	−20.4452	−0.774417
$698$	−3.46239	−0.131053
$699$	34.3925	1.30084
$700$	−2.53156	−0.0956838
$701$	42.3903	1.60106	0.800530	−	0.599292i	$-0.204551\pi$
$701$	42.3903	1.60106	0.800530	+	0.599292i	$0.204551\pi$
$702$	66.2857	2.50179
$703$	4.77896	0.180242
$704$	3.36723	0.126907
$705$	29.6666	1.11731
$706$	−6.79546	−0.255751
$707$	−14.2268	−0.535052
$708$	38.0016	1.42819
$709$	13.8289	0.519356	0.259678	−	0.965695i	$-0.416384\pi$
$709$	13.8289	0.519356	0.259678	+	0.965695i	$0.416384\pi$
$710$	−13.0109	−0.488291
$711$	−88.7695	−3.32911
$712$	3.09589	0.116023
$713$	46.0322	1.72392
$714$	22.7349	0.850831
$715$	−23.1975	−0.867538
$716$	−19.3029	−0.721381
$717$	−72.3616	−2.70240
$718$	−30.4002	−1.13453
$719$	0.806829	0.0300896	0.0150448	−	0.999887i	$-0.495211\pi$
$719$	0.806829	0.0300896	0.0150448	+	0.999887i	$0.495211\pi$
$720$	−11.9962	−0.447071
$721$	−13.2806	−0.494596
$722$	17.4555	0.649627
$723$	−1.01718	−0.0378293
$724$	−21.4000	−0.795324
$725$	−1.80825	−0.0671568
$726$	1.10295	0.0409345
$727$	−24.9063	−0.923725	−0.461863	−	0.886952i	$-0.652819\pi$
$727$	−24.9063	−0.923725	−0.461863	+	0.886952i	$0.652819\pi$
$728$	−4.38488	−0.162514
$729$	53.6227	1.98603
$730$	11.9170	0.441069
$731$	−63.1146	−2.33438
$732$	−31.0436	−1.14741
$733$	−16.3177	−0.602708	−0.301354	−	0.953512i	$-0.597439\pi$
$733$	−16.3177	−0.602708	−0.301354	+	0.953512i	$0.597439\pi$
$734$	2.07915	0.0767429
$735$	5.12375	0.188992
$736$	5.34535	0.197032
$737$	32.5861	1.20032
$738$	22.3927	0.824286
$739$	−8.66294	−0.318671	−0.159336	−	0.987224i	$-0.550935\pi$
$739$	−8.66294	−0.318671	−0.159336	+	0.987224i	$0.550935\pi$
$740$	−6.04161	−0.222094
$741$	−17.7716	−0.652856
$742$	10.6069	0.389390
$743$	−45.8861	−1.68340	−0.841699	−	0.539947i	$-0.818444\pi$
$743$	−45.8861	−1.68340	−0.841699	+	0.539947i	$0.818444\pi$
$744$	−28.0842	−1.02962
$745$	31.0156	1.13633
$746$	−5.48030	−0.200648
$747$	115.783	4.23627
$748$	23.4740	0.858296
$749$	−2.18528	−0.0798485
$750$	38.5898	1.40910
$751$	−25.1720	−0.918538	−0.459269	−	0.888297i	$-0.651889\pi$
$751$	−25.1720	−0.918538	−0.459269	+	0.888297i	$0.651889\pi$
$752$	5.79002	0.211140
$753$	49.4763	1.80302
$754$	−3.13205	−0.114063
$755$	9.86602	0.359061
$756$	−15.1169	−0.549795
$757$	−53.6092	−1.94846	−0.974230	−	0.225557i	$-0.927580\pi$
$757$	−53.6092	−1.94846	−0.974230	+	0.225557i	$0.927580\pi$
$758$	1.62719	0.0591020
$759$	58.6982	2.13061
$760$	1.95256	0.0708267
$761$	−3.15020	−0.114195	−0.0570973	−	0.998369i	$-0.518185\pi$
$761$	−3.15020	−0.114195	−0.0570973	+	0.998369i	$0.518185\pi$
$762$	−22.9286	−0.830617
$763$	−4.48445	−0.162348
$764$	−0.683469	−0.0247270
$765$	−83.6292	−3.02362
$766$	13.2210	0.477693
$767$	−51.0955	−1.84495
$768$	−3.26119	−0.117678
$769$	16.1388	0.581981	0.290991	−	0.956726i	$-0.406015\pi$
$769$	16.1388	0.581981	0.290991	+	0.956726i	$0.406015\pi$
$770$	5.29034	0.190651
$771$	70.6611	2.54480
$772$	−8.49410	−0.305709
$773$	−4.95524	−0.178228	−0.0891139	−	0.996021i	$-0.528403\pi$
$773$	−4.95524	−0.178228	−0.0891139	+	0.996021i	$0.528403\pi$
$774$	69.1266	2.48470
$775$	21.8008	0.783109
$776$	−12.5883	−0.451895
$777$	−12.5406	−0.449891
$778$	3.02357	0.108400
$779$	−3.64475	−0.130587
$780$	22.4670	0.804449
$781$	−27.8849	−0.997799
$782$	37.2642	1.33256
$783$	−10.7978	−0.385880
$784$	1.00000	0.0357143
$785$	18.3256	0.654068
$786$	13.6184	0.485753
$787$	46.0584	1.64180	0.820901	−	0.571070i	$-0.193471\pi$
$787$	46.0584	1.64180	0.820901	+	0.571070i	$0.193471\pi$
$788$	−3.62907	−0.129280
$789$	76.5550	2.72543
$790$	−18.2660	−0.649877
$791$	−13.9140	−0.494725
$792$	−25.7100	−0.913567
$793$	41.7401	1.48223
$794$	13.4729	0.478136
$795$	−54.3469	−1.92749
$796$	4.16886	0.147761
$797$	−3.72891	−0.132085	−0.0660423	−	0.997817i	$-0.521037\pi$
$797$	−3.72891	−0.132085	−0.0660423	+	0.997817i	$0.521037\pi$
$798$	4.05293	0.143472
$799$	40.3641	1.42798
$800$	2.53156	0.0895040
$801$	−23.6383	−0.835219
$802$	19.2938	0.681289
$803$	25.5405	0.901304
$804$	−31.5599	−1.11303
$805$	8.39823	0.295999
$806$	37.7610	1.33007
$807$	38.8304	1.36689
$808$	14.2268	0.500496
$809$	−8.85209	−0.311223	−0.155611	−	0.987818i	$-0.549735\pi$
$809$	−8.85209	−0.311223	−0.155611	+	0.987818i	$0.549735\pi$
$810$	41.4666	1.45699
$811$	−4.67052	−0.164004	−0.0820020	−	0.996632i	$-0.526131\pi$
$811$	−4.67052	−0.164004	−0.0820020	+	0.996632i	$0.526131\pi$
$812$	0.714285	0.0250665
$813$	−21.8623	−0.766744
$814$	−12.9483	−0.453838
$815$	−11.1774	−0.391527
$816$	−22.7349	−0.795879
$817$	−11.2514	−0.393637
$818$	−10.3677	−0.362497
$819$	33.4802	1.16989
$820$	4.60773	0.160909
$821$	32.7449	1.14280	0.571402	−	0.820670i	$-0.306400\pi$
$821$	32.7449	1.14280	0.571402	+	0.820670i	$0.306400\pi$
$822$	−12.1090	−0.422351
$823$	0.628101	0.0218942	0.0109471	−	0.999940i	$-0.496515\pi$
$823$	0.628101	0.0218942	0.0109471	+	0.999940i	$0.496515\pi$
$824$	13.2806	0.462653
$825$	27.7995	0.967853
$826$	11.6527	0.405448
$827$	−24.2206	−0.842231	−0.421116	−	0.907007i	$-0.638361\pi$
$827$	−24.2206	−0.842231	−0.421116	+	0.907007i	$0.638361\pi$
$828$	−40.8138	−1.41838
$829$	−30.1071	−1.04566	−0.522831	−	0.852436i	$-0.675124\pi$
$829$	−30.1071	−1.04566	−0.522831	+	0.852436i	$0.675124\pi$
$830$	23.8245	0.826961
$831$	−80.8408	−2.80434
$832$	4.38488	0.152018
$833$	6.97133	0.241542
$834$	11.8442	0.410133
$835$	−23.4526	−0.811612
$836$	4.18470	0.144731
$837$	130.181	4.49971
$838$	−23.9351	−0.826824
$839$	−30.9338	−1.06795	−0.533977	−	0.845499i	$-0.679303\pi$
$839$	−30.9338	−1.06795	−0.533977	+	0.845499i	$0.679303\pi$
$840$	−5.12375	−0.176786
$841$	−28.4898	−0.982407
$842$	−32.5135	−1.12049
$843$	3.65266	0.125804
$844$	1.29992	0.0447452
$845$	−9.78367	−0.336569
$846$	−44.2090	−1.51994
$847$	0.338206	0.0116209
$848$	−10.6069	−0.364241
$849$	49.5196	1.69951
$850$	17.6483	0.605332
$851$	−20.5550	−0.704615
$852$	27.0068	0.925238
$853$	−27.0888	−0.927504	−0.463752	−	0.885965i	$-0.653497\pi$
$853$	−27.0888	−0.927504	−0.463752	+	0.885965i	$0.653497\pi$
$854$	−9.51910	−0.325737
$855$	−14.9085	−0.509861
$856$	2.18528	0.0746914
$857$	−32.3127	−1.10378	−0.551890	−	0.833917i	$-0.686093\pi$
$857$	−32.3127	−1.10378	−0.551890	+	0.833917i	$0.686093\pi$
$858$	48.1511	1.64385
$859$	45.4196	1.54970	0.774849	−	0.632146i	$-0.217826\pi$
$859$	45.4196	1.54970	0.774849	+	0.632146i	$0.217826\pi$
$860$	14.2241	0.485039
$861$	9.56427	0.325949
$862$	−1.00000	−0.0340601
$863$	4.68965	0.159638	0.0798188	−	0.996809i	$-0.474566\pi$
$863$	4.68965	0.159638	0.0798188	+	0.996809i	$0.474566\pi$
$864$	15.1169	0.514287
$865$	−4.59078	−0.156091
$866$	−21.3318	−0.724884
$867$	−103.052	−3.49983
$868$	−8.61163	−0.292298
$869$	−39.1476	−1.32799
$870$	−3.65982	−0.124079
$871$	42.4343	1.43783
$872$	4.48445	0.151863
$873$	96.1167	3.25306
$874$	6.64306	0.224705
$875$	11.8330	0.400030
$876$	−24.7362	−0.835759
$877$	−33.1684	−1.12002	−0.560008	−	0.828487i	$-0.689202\pi$
$877$	−33.1684	−1.12002	−0.560008	+	0.828487i	$0.689202\pi$
$878$	30.9592	1.04482
$879$	−7.71433	−0.260198
$880$	−5.29034	−0.178337
$881$	4.10609	0.138338	0.0691689	−	0.997605i	$-0.477965\pi$
$881$	4.10609	0.138338	0.0691689	+	0.997605i	$0.477965\pi$
$882$	−7.63538	−0.257097
$883$	−13.8065	−0.464624	−0.232312	−	0.972641i	$-0.574629\pi$
$883$	−13.8065	−0.464624	−0.232312	+	0.972641i	$0.574629\pi$
$884$	30.5684	1.02813
$885$	−59.7053	−2.00697
$886$	18.0899	0.607743
$887$	54.3458	1.82475	0.912377	−	0.409350i	$-0.134244\pi$
$887$	54.3458	1.82475	0.912377	+	0.409350i	$0.134244\pi$
$888$	12.5406	0.420834
$889$	−7.03075	−0.235804
$890$	−4.86404	−0.163043
$891$	88.8709	2.97729
$892$	−1.72546	−0.0577726
$893$	7.19569	0.240794
$894$	−64.3792	−2.15316
$895$	30.3273	1.01373
$896$	−1.00000	−0.0334077
$897$	76.4381	2.55219
$898$	24.9108	0.831285
$899$	−6.15116	−0.205153
$900$	−19.3294	−0.644313
$901$	−73.9439	−2.46343
$902$	9.87524	0.328809
$903$	29.5251	0.982533
$904$	13.9140	0.462772
$905$	33.6221	1.11764
$906$	−20.4789	−0.680366
$907$	8.36601	0.277789	0.138894	−	0.990307i	$-0.455645\pi$
$907$	8.36601	0.277789	0.138894	+	0.990307i	$0.455645\pi$
$908$	−6.83743	−0.226908
$909$	−108.627	−3.60292
$910$	6.88921	0.228375
$911$	57.2065	1.89534	0.947668	−	0.319257i	$-0.103433\pi$
$911$	57.2065	1.89534	0.947668	+	0.319257i	$0.103433\pi$
$912$	−4.05293	−0.134206
$913$	51.0605	1.68986
$914$	−4.95753	−0.163981
$915$	48.7735	1.61240
$916$	13.3205	0.440123
$917$	4.17590	0.137901
$918$	105.385	3.47821
$919$	−37.3857	−1.23324	−0.616619	−	0.787261i	$-0.711498\pi$
$919$	−37.3857	−1.23324	−0.616619	+	0.787261i	$0.711498\pi$
$920$	−8.39823	−0.276881
$921$	−102.979	−3.39327
$922$	−26.9228	−0.886655
$923$	−36.3123	−1.19523
$924$	−10.9812	−0.361254
$925$	−9.73483	−0.320079
$926$	7.07952	0.232647
$927$	−101.403	−3.33050
$928$	−0.714285	−0.0234475
$929$	3.18317	0.104437	0.0522183	−	0.998636i	$-0.483371\pi$
$929$	3.18317	0.104437	0.0522183	+	0.998636i	$0.483371\pi$
$930$	44.1239	1.44688
$931$	1.24277	0.0407303
$932$	−10.5460	−0.345445
$933$	102.479	3.35500
$934$	−2.70233	−0.0884231
$935$	−36.8807	−1.20613
$936$	−33.4802	−1.09434
$937$	−6.52518	−0.213168	−0.106584	−	0.994304i	$-0.533991\pi$
$937$	−6.52518	−0.213168	−0.106584	+	0.994304i	$0.533991\pi$
$938$	−9.67742	−0.315979
$939$	−47.6855	−1.55616
$940$	−9.09686	−0.296707
$941$	−10.2289	−0.333452	−0.166726	−	0.986003i	$-0.553320\pi$
$941$	−10.2289	−0.333452	−0.166726	+	0.986003i	$0.553320\pi$
$942$	−38.0384	−1.23936
$943$	15.6766	0.510500
$944$	−11.6527	−0.379262
$945$	23.7505	0.772605
$946$	30.4850	0.991154
$947$	38.0021	1.23490	0.617451	−	0.786610i	$-0.288165\pi$
$947$	38.0021	1.23490	0.617451	+	0.786610i	$0.288165\pi$
$948$	37.9149	1.23142
$949$	33.2594	1.07965
$950$	3.14615	0.102075
$951$	−60.8508	−1.97322
$952$	−6.97133	−0.225942
$953$	3.63754	0.117831	0.0589157	−	0.998263i	$-0.481236\pi$
$953$	3.63754	0.117831	0.0589157	+	0.998263i	$0.481236\pi$
$954$	80.9874	2.62206
$955$	1.07382	0.0347479
$956$	22.1887	0.717634
$957$	−7.84368	−0.253550
$958$	18.1714	0.587092
$959$	−3.71306	−0.119901
$960$	5.12375	0.165368
$961$	43.1602	1.39227
$962$	−16.8616	−0.543639
$963$	−16.6855	−0.537682
$964$	0.311904	0.0100458
$965$	13.3453	0.429601
$966$	−17.4322	−0.560872
$967$	40.4191	1.29979	0.649896	−	0.760023i	$-0.274813\pi$
$967$	40.4191	1.29979	0.649896	+	0.760023i	$0.274813\pi$
$968$	−0.338206	−0.0108703
$969$	−28.2543	−0.907659
$970$	19.7779	0.635029
$971$	36.7845	1.18047	0.590236	−	0.807231i	$-0.299035\pi$
$971$	36.7845	1.18047	0.590236	+	0.807231i	$0.299035\pi$
$972$	−40.7217	−1.30615
$973$	3.63187	0.116433
$974$	16.1307	0.516862
$975$	36.2011	1.15936
$976$	9.51910	0.304699
$977$	31.0061	0.991972	0.495986	−	0.868331i	$-0.334807\pi$
$977$	31.0061	0.991972	0.495986	+	0.868331i	$0.334807\pi$
$978$	23.2009	0.741884
$979$	−10.4246	−0.333171
$980$	−1.57113	−0.0501878
$981$	−34.2405	−1.09321
$982$	18.1349	0.578708
$983$	21.8076	0.695554	0.347777	−	0.937577i	$-0.386937\pi$
$983$	21.8076	0.695554	0.347777	+	0.937577i	$0.386937\pi$
$984$	−9.56427	−0.304898
$985$	5.70173	0.181672
$986$	−4.97951	−0.158580
$987$	−18.8824	−0.601032
$988$	5.44942	0.173369
$989$	48.3939	1.53884
$990$	40.3938	1.28380
$991$	−2.79087	−0.0886548	−0.0443274	−	0.999017i	$-0.514114\pi$
$991$	−2.79087	−0.0886548	−0.0443274	+	0.999017i	$0.514114\pi$
$992$	8.61163	0.273420
$993$	−54.2605	−1.72190
$994$	8.28126	0.262666
$995$	−6.54981	−0.207643
$996$	−49.4526	−1.56697
$997$	8.17537	0.258916	0.129458	−	0.991585i	$-0.458676\pi$
$997$	8.17537	0.258916	0.129458	+	0.991585i	$0.458676\pi$
$998$	32.7814	1.03768
$999$	−58.1303	−1.83916

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.26119 q^{3} +1.00000 q^{4} -1.57113 q^{5} +3.26119 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.63538 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.26119 q^{3} +1.00000 q^{4} -1.57113 q^{5} +3.26119 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.63538 q^{9} +1.57113 q^{10} +3.36723 q^{11} -3.26119 q^{12} +4.38488 q^{13} -1.00000 q^{14} +5.12375 q^{15} +1.00000 q^{16} +6.97133 q^{17} -7.63538 q^{18} +1.24277 q^{19} -1.57113 q^{20} -3.26119 q^{21} -3.36723 q^{22} -5.34535 q^{23} +3.26119 q^{24} -2.53156 q^{25} -4.38488 q^{26} -15.1169 q^{27} +1.00000 q^{28} +0.714285 q^{29} -5.12375 q^{30} -8.61163 q^{31} -1.00000 q^{32} -10.9812 q^{33} -6.97133 q^{34} -1.57113 q^{35} +7.63538 q^{36} +3.84539 q^{37} -1.24277 q^{38} -14.2999 q^{39} +1.57113 q^{40} -2.93275 q^{41} +3.26119 q^{42} -9.05346 q^{43} +3.36723 q^{44} -11.9962 q^{45} +5.34535 q^{46} +5.79002 q^{47} -3.26119 q^{48} +1.00000 q^{49} +2.53156 q^{50} -22.7349 q^{51} +4.38488 q^{52} -10.6069 q^{53} +15.1169 q^{54} -5.29034 q^{55} -1.00000 q^{56} -4.05293 q^{57} -0.714285 q^{58} -11.6527 q^{59} +5.12375 q^{60} +9.51910 q^{61} +8.61163 q^{62} +7.63538 q^{63} +1.00000 q^{64} -6.88921 q^{65} +10.9812 q^{66} +9.67742 q^{67} +6.97133 q^{68} +17.4322 q^{69} +1.57113 q^{70} -8.28126 q^{71} -7.63538 q^{72} +7.58502 q^{73} -3.84539 q^{74} +8.25589 q^{75} +1.24277 q^{76} +3.36723 q^{77} +14.2999 q^{78} -11.6261 q^{79} -1.57113 q^{80} +26.3929 q^{81} +2.93275 q^{82} +15.1640 q^{83} -3.26119 q^{84} -10.9529 q^{85} +9.05346 q^{86} -2.32942 q^{87} -3.36723 q^{88} -3.09589 q^{89} +11.9962 q^{90} +4.38488 q^{91} -5.34535 q^{92} +28.0842 q^{93} -5.79002 q^{94} -1.95256 q^{95} +3.26119 q^{96} +12.5883 q^{97} -1.00000 q^{98} +25.7100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 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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