LMFDB - Embedded newform 6034.2.a.l.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-1.01642$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.01642 q^{3} +1.00000 q^{4} +1.24888 q^{5} +1.01642 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.96689 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.01642 q^{3} +1.00000 q^{4} +1.24888 q^{5} +1.01642 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.96689 q^{9} +1.24888 q^{10} -5.56916 q^{11} +1.01642 q^{12} -0.887869 q^{13} -1.00000 q^{14} +1.26939 q^{15} +1.00000 q^{16} +5.38855 q^{17} -1.96689 q^{18} -3.39392 q^{19} +1.24888 q^{20} -1.01642 q^{21} -5.56916 q^{22} +9.12541 q^{23} +1.01642 q^{24} -3.44030 q^{25} -0.887869 q^{26} -5.04844 q^{27} -1.00000 q^{28} -6.61923 q^{29} +1.26939 q^{30} -6.71686 q^{31} +1.00000 q^{32} -5.66060 q^{33} +5.38855 q^{34} -1.24888 q^{35} -1.96689 q^{36} -8.86453 q^{37} -3.39392 q^{38} -0.902447 q^{39} +1.24888 q^{40} -3.04186 q^{41} -1.01642 q^{42} -0.183147 q^{43} -5.56916 q^{44} -2.45641 q^{45} +9.12541 q^{46} +9.52407 q^{47} +1.01642 q^{48} +1.00000 q^{49} -3.44030 q^{50} +5.47702 q^{51} -0.887869 q^{52} -0.256833 q^{53} -5.04844 q^{54} -6.95522 q^{55} -1.00000 q^{56} -3.44964 q^{57} -6.61923 q^{58} +0.643755 q^{59} +1.26939 q^{60} +2.06300 q^{61} -6.71686 q^{62} +1.96689 q^{63} +1.00000 q^{64} -1.10884 q^{65} -5.66060 q^{66} -15.2851 q^{67} +5.38855 q^{68} +9.27524 q^{69} -1.24888 q^{70} -3.02723 q^{71} -1.96689 q^{72} +0.462173 q^{73} -8.86453 q^{74} -3.49678 q^{75} -3.39392 q^{76} +5.56916 q^{77} -0.902447 q^{78} -13.5743 q^{79} +1.24888 q^{80} +0.769343 q^{81} -3.04186 q^{82} +7.90135 q^{83} -1.01642 q^{84} +6.72965 q^{85} -0.183147 q^{86} -6.72791 q^{87} -5.56916 q^{88} +4.67259 q^{89} -2.45641 q^{90} +0.887869 q^{91} +9.12541 q^{92} -6.82714 q^{93} +9.52407 q^{94} -4.23860 q^{95} +1.01642 q^{96} -11.5116 q^{97} +1.00000 q^{98} +10.9539 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.01642	0.586830	0.293415	−	0.955985i	$-0.405208\pi$
$3$	1.01642	0.586830	0.293415	+	0.955985i	$0.405208\pi$
$4$	1.00000	0.500000
$5$	1.24888	0.558516	0.279258	−	0.960216i	$-0.409911\pi$
$5$	1.24888	0.558516	0.279258	+	0.960216i	$0.409911\pi$
$6$	1.01642	0.414951
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.96689	−0.655631
$10$	1.24888	0.394931
$11$	−5.56916	−1.67917	−0.839583	−	0.543232i	$-0.817200\pi$
$11$	−5.56916	−1.67917	−0.839583	+	0.543232i	$0.817200\pi$
$12$	1.01642	0.293415
$13$	−0.887869	−0.246250	−0.123125	−	0.992391i	$-0.539292\pi$
$13$	−0.887869	−0.246250	−0.123125	+	0.992391i	$0.539292\pi$
$14$	−1.00000	−0.267261
$15$	1.26939	0.327754
$16$	1.00000	0.250000
$17$	5.38855	1.30692	0.653458	−	0.756963i	$-0.273318\pi$
$17$	5.38855	1.30692	0.653458	+	0.756963i	$0.273318\pi$
$18$	−1.96689	−0.463601
$19$	−3.39392	−0.778619	−0.389309	−	0.921107i	$-0.627286\pi$
$19$	−3.39392	−0.778619	−0.389309	+	0.921107i	$0.627286\pi$
$20$	1.24888	0.279258
$21$	−1.01642	−0.221801
$22$	−5.56916	−1.18735
$23$	9.12541	1.90278	0.951390	−	0.307988i	$-0.0996558\pi$
$23$	9.12541	1.90278	0.951390	+	0.307988i	$0.0996558\pi$
$24$	1.01642	0.207476
$25$	−3.44030	−0.688060
$26$	−0.887869	−0.174125
$27$	−5.04844	−0.971573
$28$	−1.00000	−0.188982
$29$	−6.61923	−1.22916	−0.614580	−	0.788854i	$-0.710675\pi$
$29$	−6.61923	−1.22916	−0.614580	+	0.788854i	$0.710675\pi$
$30$	1.26939	0.231757
$31$	−6.71686	−1.20638	−0.603191	−	0.797596i	$-0.706105\pi$
$31$	−6.71686	−1.20638	−0.603191	+	0.797596i	$0.706105\pi$
$32$	1.00000	0.176777
$33$	−5.66060	−0.985384
$34$	5.38855	0.924129
$35$	−1.24888	−0.211099
$36$	−1.96689	−0.327815
$37$	−8.86453	−1.45732	−0.728659	−	0.684876i	$-0.759856\pi$
$37$	−8.86453	−1.45732	−0.728659	+	0.684876i	$0.759856\pi$
$38$	−3.39392	−0.550567
$39$	−0.902447	−0.144507
$40$	1.24888	0.197465
$41$	−3.04186	−0.475058	−0.237529	−	0.971380i	$-0.576337\pi$
$41$	−3.04186	−0.475058	−0.237529	+	0.971380i	$0.576337\pi$
$42$	−1.01642	−0.156837
$43$	−0.183147	−0.0279296	−0.0139648	−	0.999902i	$-0.504445\pi$
$43$	−0.183147	−0.0279296	−0.0139648	+	0.999902i	$0.504445\pi$
$44$	−5.56916	−0.839583
$45$	−2.45641	−0.366180
$46$	9.12541	1.34547
$47$	9.52407	1.38923	0.694614	−	0.719383i	$-0.255575\pi$
$47$	9.52407	1.38923	0.694614	+	0.719383i	$0.255575\pi$
$48$	1.01642	0.146707
$49$	1.00000	0.142857
$50$	−3.44030	−0.486532
$51$	5.47702	0.766937
$52$	−0.887869	−0.123125
$53$	−0.256833	−0.0352788	−0.0176394	−	0.999844i	$-0.505615\pi$
$53$	−0.256833	−0.0352788	−0.0176394	+	0.999844i	$0.505615\pi$
$54$	−5.04844	−0.687006
$55$	−6.95522	−0.937841
$56$	−1.00000	−0.133631
$57$	−3.44964	−0.456917
$58$	−6.61923	−0.869148
$59$	0.643755	0.0838098	0.0419049	−	0.999122i	$-0.486657\pi$
$59$	0.643755	0.0838098	0.0419049	+	0.999122i	$0.486657\pi$
$60$	1.26939	0.163877
$61$	2.06300	0.264140	0.132070	−	0.991240i	$-0.457838\pi$
$61$	2.06300	0.264140	0.132070	+	0.991240i	$0.457838\pi$
$62$	−6.71686	−0.853042
$63$	1.96689	0.247805
$64$	1.00000	0.125000
$65$	−1.10884	−0.137535
$66$	−5.66060	−0.696772
$67$	−15.2851	−1.86738	−0.933688	−	0.358088i	$-0.883429\pi$
$67$	−15.2851	−1.86738	−0.933688	+	0.358088i	$0.883429\pi$
$68$	5.38855	0.653458
$69$	9.27524	1.11661
$70$	−1.24888	−0.149270
$71$	−3.02723	−0.359266	−0.179633	−	0.983734i	$-0.557491\pi$
$71$	−3.02723	−0.359266	−0.179633	+	0.983734i	$0.557491\pi$
$72$	−1.96689	−0.231800
$73$	0.462173	0.0540932	0.0270466	−	0.999634i	$-0.491390\pi$
$73$	0.462173	0.0540932	0.0270466	+	0.999634i	$0.491390\pi$
$74$	−8.86453	−1.03048
$75$	−3.49678	−0.403774
$76$	−3.39392	−0.389309
$77$	5.56916	0.634665
$78$	−0.902447	−0.102182
$79$	−13.5743	−1.52723	−0.763616	−	0.645670i	$-0.776578\pi$
$79$	−13.5743	−1.52723	−0.763616	+	0.645670i	$0.776578\pi$
$80$	1.24888	0.139629
$81$	0.769343	0.0854826
$82$	−3.04186	−0.335917
$83$	7.90135	0.867286	0.433643	−	0.901085i	$-0.357228\pi$
$83$	7.90135	0.867286	0.433643	+	0.901085i	$0.357228\pi$
$84$	−1.01642	−0.110900
$85$	6.72965	0.729933
$86$	−0.183147	−0.0197492
$87$	−6.72791	−0.721308
$88$	−5.56916	−0.593675
$89$	4.67259	0.495294	0.247647	−	0.968850i	$-0.420343\pi$
$89$	4.67259	0.495294	0.247647	+	0.968850i	$0.420343\pi$
$90$	−2.45641	−0.258929
$91$	0.887869	0.0930739
$92$	9.12541	0.951390
$93$	−6.82714	−0.707941
$94$	9.52407	0.982333
$95$	−4.23860	−0.434871
$96$	1.01642	0.103738
$97$	−11.5116	−1.16882	−0.584411	−	0.811458i	$-0.698674\pi$
$97$	−11.5116	−1.16882	−0.584411	+	0.811458i	$0.698674\pi$
$98$	1.00000	0.101015
$99$	10.9539	1.10091
$100$	−3.44030	−0.344030
$101$	−1.64589	−0.163772	−0.0818862	−	0.996642i	$-0.526094\pi$
$101$	−1.64589	−0.163772	−0.0818862	+	0.996642i	$0.526094\pi$
$102$	5.47702	0.542306
$103$	0.581102	0.0572576	0.0286288	−	0.999590i	$-0.490886\pi$
$103$	0.581102	0.0572576	0.0286288	+	0.999590i	$0.490886\pi$
$104$	−0.887869	−0.0870627
$105$	−1.26939	−0.123879
$106$	−0.256833	−0.0249459
$107$	−1.12849	−0.109096	−0.0545478	−	0.998511i	$-0.517372\pi$
$107$	−1.12849	−0.109096	−0.0545478	+	0.998511i	$0.517372\pi$
$108$	−5.04844	−0.485787
$109$	−19.3209	−1.85060	−0.925302	−	0.379231i	$-0.876189\pi$
$109$	−19.3209	−1.85060	−0.925302	+	0.379231i	$0.876189\pi$
$110$	−6.95522	−0.663154
$111$	−9.01007	−0.855198
$112$	−1.00000	−0.0944911
$113$	10.8406	1.01979	0.509897	−	0.860235i	$-0.329683\pi$
$113$	10.8406	1.01979	0.509897	+	0.860235i	$0.329683\pi$
$114$	−3.44964	−0.323089
$115$	11.3965	1.06273
$116$	−6.61923	−0.614580
$117$	1.74634	0.161449
$118$	0.643755	0.0592625
$119$	−5.38855	−0.493967
$120$	1.26939	0.115879
$121$	20.0156	1.81960
$122$	2.06300	0.186775
$123$	−3.09180	−0.278778
$124$	−6.71686	−0.603191
$125$	−10.5409	−0.942809
$126$	1.96689	0.175225
$127$	−5.72680	−0.508171	−0.254086	−	0.967182i	$-0.581774\pi$
$127$	−5.72680	−0.508171	−0.254086	+	0.967182i	$0.581774\pi$
$128$	1.00000	0.0883883
$129$	−0.186154	−0.0163899
$130$	−1.10884	−0.0972518
$131$	2.27551	0.198812	0.0994060	−	0.995047i	$-0.468306\pi$
$131$	2.27551	0.198812	0.0994060	+	0.995047i	$0.468306\pi$
$132$	−5.66060	−0.492692
$133$	3.39392	0.294290
$134$	−15.2851	−1.32043
$135$	−6.30490	−0.542639
$136$	5.38855	0.462064
$137$	−5.90771	−0.504729	−0.252365	−	0.967632i	$-0.581208\pi$
$137$	−5.90771	−0.504729	−0.252365	+	0.967632i	$0.581208\pi$
$138$	9.27524	0.789561
$139$	−12.9053	−1.09462	−0.547308	−	0.836931i	$-0.684347\pi$
$139$	−12.9053	−1.09462	−0.547308	+	0.836931i	$0.684347\pi$
$140$	−1.24888	−0.105550
$141$	9.68044	0.815240
$142$	−3.02723	−0.254039
$143$	4.94468	0.413495
$144$	−1.96689	−0.163908
$145$	−8.26663	−0.686506
$146$	0.462173	0.0382497
$147$	1.01642	0.0838328
$148$	−8.86453	−0.728659
$149$	17.2303	1.41156	0.705779	−	0.708432i	$-0.250597\pi$
$149$	17.2303	1.41156	0.705779	+	0.708432i	$0.250597\pi$
$150$	−3.49678	−0.285511
$151$	13.1733	1.07203	0.536015	−	0.844209i	$-0.319929\pi$
$151$	13.1733	1.07203	0.536015	+	0.844209i	$0.319929\pi$
$152$	−3.39392	−0.275283
$153$	−10.5987	−0.856854
$154$	5.56916	0.448776
$155$	−8.38855	−0.673784
$156$	−0.902447	−0.0722535
$157$	−3.53453	−0.282086	−0.141043	−	0.990003i	$-0.545046\pi$
$157$	−3.53453	−0.282086	−0.141043	+	0.990003i	$0.545046\pi$
$158$	−13.5743	−1.07992
$159$	−0.261050	−0.0207026
$160$	1.24888	0.0987326
$161$	−9.12541	−0.719183
$162$	0.769343	0.0604453
$163$	1.62071	0.126943	0.0634717	−	0.997984i	$-0.479783\pi$
$163$	1.62071	0.126943	0.0634717	+	0.997984i	$0.479783\pi$
$164$	−3.04186	−0.237529
$165$	−7.06941	−0.550353
$166$	7.90135	0.613264
$167$	0.265569	0.0205504	0.0102752	−	0.999947i	$-0.496729\pi$
$167$	0.265569	0.0205504	0.0102752	+	0.999947i	$0.496729\pi$
$168$	−1.01642	−0.0784184
$169$	−12.2117	−0.939361
$170$	6.72965	0.516141
$171$	6.67548	0.510486
$172$	−0.183147	−0.0139648
$173$	−13.6500	−1.03779	−0.518894	−	0.854839i	$-0.673656\pi$
$173$	−13.6500	−1.03779	−0.518894	+	0.854839i	$0.673656\pi$
$174$	−6.72791	−0.510042
$175$	3.44030	0.260062
$176$	−5.56916	−0.419791
$177$	0.654325	0.0491821
$178$	4.67259	0.350226
$179$	−4.74476	−0.354640	−0.177320	−	0.984153i	$-0.556743\pi$
$179$	−4.74476	−0.354640	−0.177320	+	0.984153i	$0.556743\pi$
$180$	−2.45641	−0.183090
$181$	−3.67189	−0.272930	−0.136465	−	0.990645i	$-0.543574\pi$
$181$	−3.67189	−0.272930	−0.136465	+	0.990645i	$0.543574\pi$
$182$	0.887869	0.0658132
$183$	2.09687	0.155005
$184$	9.12541	0.672734
$185$	−11.0707	−0.813936
$186$	−6.82714	−0.500590
$187$	−30.0097	−2.19453
$188$	9.52407	0.694614
$189$	5.04844	0.367220
$190$	−4.23860	−0.307500
$191$	−20.7777	−1.50342	−0.751712	−	0.659492i	$-0.770772\pi$
$191$	−20.7777	−1.50342	−0.751712	+	0.659492i	$0.770772\pi$
$192$	1.01642	0.0733537
$193$	−20.2996	−1.46120	−0.730598	−	0.682808i	$-0.760759\pi$
$193$	−20.2996	−1.46120	−0.730598	+	0.682808i	$0.760759\pi$
$194$	−11.5116	−0.826482
$195$	−1.12705	−0.0807095
$196$	1.00000	0.0714286
$197$	−0.0193130	−0.00137600	−0.000687999	−	1.00000i	$-0.500219\pi$
$197$	−0.0193130	−0.00137600	−0.000687999		1.00000i	$0.500219\pi$
$198$	10.9539	0.778463
$199$	16.1957	1.14808	0.574040	−	0.818827i	$-0.305376\pi$
$199$	16.1957	1.14808	0.574040	+	0.818827i	$0.305376\pi$
$200$	−3.44030	−0.243266
$201$	−15.5361	−1.09583
$202$	−1.64589	−0.115805
$203$	6.61923	0.464579
$204$	5.47702	0.383468
$205$	−3.79891	−0.265328
$206$	0.581102	0.0404873
$207$	−17.9487	−1.24752
$208$	−0.887869	−0.0615626
$209$	18.9013	1.30743
$210$	−1.26939	−0.0875959
$211$	−1.10737	−0.0762342	−0.0381171	−	0.999273i	$-0.512136\pi$
$211$	−1.10737	−0.0762342	−0.0381171	+	0.999273i	$0.512136\pi$
$212$	−0.256833	−0.0176394
$213$	−3.07693	−0.210828
$214$	−1.12849	−0.0771423
$215$	−0.228729	−0.0155992
$216$	−5.04844	−0.343503
$217$	6.71686	0.455970
$218$	−19.3209	−1.30857
$219$	0.469761	0.0317435
$220$	−6.95522	−0.468921
$221$	−4.78432	−0.321828
$222$	−9.01007	−0.604716
$223$	26.6539	1.78488	0.892439	−	0.451169i	$-0.148993\pi$
$223$	26.6539	1.78488	0.892439	+	0.451169i	$0.148993\pi$
$224$	−1.00000	−0.0668153
$225$	6.76670	0.451113
$226$	10.8406	0.721103
$227$	4.04787	0.268666	0.134333	−	0.990936i	$-0.457111\pi$
$227$	4.04787	0.268666	0.134333	+	0.990936i	$0.457111\pi$
$228$	−3.44964	−0.228458
$229$	−11.4424	−0.756134	−0.378067	−	0.925778i	$-0.623411\pi$
$229$	−11.4424	−0.756134	−0.378067	+	0.925778i	$0.623411\pi$
$230$	11.3965	0.751466
$231$	5.66060	0.372440
$232$	−6.61923	−0.434574
$233$	−2.70235	−0.177037	−0.0885184	−	0.996075i	$-0.528213\pi$
$233$	−2.70235	−0.177037	−0.0885184	+	0.996075i	$0.528213\pi$
$234$	1.74634	0.114162
$235$	11.8944	0.775906
$236$	0.643755	0.0419049
$237$	−13.7972	−0.896226
$238$	−5.38855	−0.349288
$239$	24.2668	1.56969	0.784845	−	0.619693i	$-0.212743\pi$
$239$	24.2668	1.56969	0.784845	+	0.619693i	$0.212743\pi$
$240$	1.26939	0.0819385
$241$	21.2645	1.36976	0.684882	−	0.728654i	$-0.259854\pi$
$241$	21.2645	1.36976	0.684882	+	0.728654i	$0.259854\pi$
$242$	20.0156	1.28665
$243$	15.9273	1.02174
$244$	2.06300	0.132070
$245$	1.24888	0.0797880
$246$	−3.09180	−0.197126
$247$	3.01336	0.191735
$248$	−6.71686	−0.426521
$249$	8.03108	0.508949
$250$	−10.5409	−0.666666
$251$	−3.88635	−0.245304	−0.122652	−	0.992450i	$-0.539140\pi$
$251$	−3.88635	−0.245304	−0.122652	+	0.992450i	$0.539140\pi$
$252$	1.96689	0.123903
$253$	−50.8209	−3.19508
$254$	−5.72680	−0.359331
$255$	6.84015	0.428347
$256$	1.00000	0.0625000
$257$	22.9701	1.43283	0.716417	−	0.697673i	$-0.245781\pi$
$257$	22.9701	1.43283	0.716417	+	0.697673i	$0.245781\pi$
$258$	−0.186154	−0.0115894
$259$	8.86453	0.550815
$260$	−1.10884	−0.0687674
$261$	13.0193	0.805876
$262$	2.27551	0.140581
$263$	13.8320	0.852916	0.426458	−	0.904507i	$-0.359761\pi$
$263$	13.8320	0.852916	0.426458	+	0.904507i	$0.359761\pi$
$264$	−5.66060	−0.348386
$265$	−0.320754	−0.0197038
$266$	3.39392	0.208095
$267$	4.74931	0.290653
$268$	−15.2851	−0.933688
$269$	11.3952	0.694779	0.347389	−	0.937721i	$-0.387068\pi$
$269$	11.3952	0.694779	0.347389	+	0.937721i	$0.387068\pi$
$270$	−6.30490	−0.383704
$271$	15.0139	0.912032	0.456016	−	0.889971i	$-0.349276\pi$
$271$	15.0139	0.912032	0.456016	+	0.889971i	$0.349276\pi$
$272$	5.38855	0.326729
$273$	0.902447	0.0546185
$274$	−5.90771	−0.356898
$275$	19.1596	1.15537
$276$	9.27524	0.558304
$277$	1.99314	0.119756	0.0598782	−	0.998206i	$-0.480929\pi$
$277$	1.99314	0.119756	0.0598782	+	0.998206i	$0.480929\pi$
$278$	−12.9053	−0.774010
$279$	13.2113	0.790942
$280$	−1.24888	−0.0746349
$281$	−6.61157	−0.394413	−0.197207	−	0.980362i	$-0.563187\pi$
$281$	−6.61157	−0.394413	−0.197207	+	0.980362i	$0.563187\pi$
$282$	9.68044	0.576462
$283$	25.2836	1.50295	0.751476	−	0.659761i	$-0.229342\pi$
$283$	25.2836	1.50295	0.751476	+	0.659761i	$0.229342\pi$
$284$	−3.02723	−0.179633
$285$	−4.30819	−0.255195
$286$	4.94468	0.292385
$287$	3.04186	0.179555
$288$	−1.96689	−0.115900
$289$	12.0365	0.708027
$290$	−8.26663	−0.485433
$291$	−11.7006	−0.685900
$292$	0.462173	0.0270466
$293$	−22.7815	−1.33091	−0.665455	−	0.746438i	$-0.731763\pi$
$293$	−22.7815	−1.33091	−0.665455	+	0.746438i	$0.731763\pi$
$294$	1.01642	0.0592788
$295$	0.803973	0.0468091
$296$	−8.86453	−0.515240
$297$	28.1156	1.63143
$298$	17.2303	0.998123
$299$	−8.10217	−0.468561
$300$	−3.49678	−0.201887
$301$	0.183147	0.0105564
$302$	13.1733	0.758039
$303$	−1.67292	−0.0961065
$304$	−3.39392	−0.194655
$305$	2.57644	0.147526
$306$	−10.5987	−0.605887
$307$	15.9422	0.909867	0.454933	−	0.890525i	$-0.349663\pi$
$307$	15.9422	0.909867	0.454933	+	0.890525i	$0.349663\pi$
$308$	5.56916	0.317332
$309$	0.590643	0.0336005
$310$	−8.38855	−0.476437
$311$	18.2932	1.03731	0.518655	−	0.854984i	$-0.326433\pi$
$311$	18.2932	1.03731	0.518655	+	0.854984i	$0.326433\pi$
$312$	−0.902447	−0.0510910
$313$	10.8912	0.615605	0.307802	−	0.951450i	$-0.400406\pi$
$313$	10.8912	0.615605	0.307802	+	0.951450i	$0.400406\pi$
$314$	−3.53453	−0.199465
$315$	2.45641	0.138403
$316$	−13.5743	−0.763616
$317$	5.04936	0.283600	0.141800	−	0.989895i	$-0.454711\pi$
$317$	5.04936	0.283600	0.141800	+	0.989895i	$0.454711\pi$
$318$	−0.261050	−0.0146390
$319$	36.8636	2.06396
$320$	1.24888	0.0698145
$321$	−1.14702	−0.0640206
$322$	−9.12541	−0.508539
$323$	−18.2883	−1.01759
$324$	0.769343	0.0427413
$325$	3.05453	0.169435
$326$	1.62071	0.0897626
$327$	−19.6381	−1.08599
$328$	−3.04186	−0.167958
$329$	−9.52407	−0.525079
$330$	−7.06941	−0.389158
$331$	−16.6898	−0.917354	−0.458677	−	0.888603i	$-0.651677\pi$
$331$	−16.6898	−0.917354	−0.458677	+	0.888603i	$0.651677\pi$
$332$	7.90135	0.433643
$333$	17.4356	0.955463
$334$	0.265569	0.0145313
$335$	−19.0893	−1.04296
$336$	−1.01642	−0.0554502
$337$	−0.352135	−0.0191820	−0.00959101	−	0.999954i	$-0.503053\pi$
$337$	−0.352135	−0.0191820	−0.00959101	+	0.999954i	$0.503053\pi$
$338$	−12.2117	−0.664228
$339$	11.0186	0.598446
$340$	6.72965	0.364967
$341$	37.4073	2.02572
$342$	6.67548	0.360968
$343$	−1.00000	−0.0539949
$344$	−0.183147	−0.00987462
$345$	11.5837	0.623644
$346$	−13.6500	−0.733826
$347$	18.1594	0.974849	0.487425	−	0.873165i	$-0.337936\pi$
$347$	18.1594	0.974849	0.487425	+	0.873165i	$0.337936\pi$
$348$	−6.72791	−0.360654
$349$	−17.4642	−0.934836	−0.467418	−	0.884037i	$-0.654816\pi$
$349$	−17.4642	−0.934836	−0.467418	+	0.884037i	$0.654816\pi$
$350$	3.44030	0.183892
$351$	4.48235	0.239250
$352$	−5.56916	−0.296837
$353$	2.97583	0.158388	0.0791938	−	0.996859i	$-0.474765\pi$
$353$	2.97583	0.158388	0.0791938	+	0.996859i	$0.474765\pi$
$354$	0.654325	0.0347770
$355$	−3.78064	−0.200656
$356$	4.67259	0.247647
$357$	−5.47702	−0.289875
$358$	−4.74476	−0.250768
$359$	−5.98194	−0.315715	−0.157857	−	0.987462i	$-0.550459\pi$
$359$	−5.98194	−0.315715	−0.157857	+	0.987462i	$0.550459\pi$
$360$	−2.45641	−0.129464
$361$	−7.48131	−0.393753
$362$	−3.67189	−0.192990
$363$	20.3442	1.06779
$364$	0.887869	0.0465370
$365$	0.577198	0.0302119
$366$	2.09687	0.109605
$367$	2.26109	0.118028	0.0590140	−	0.998257i	$-0.481204\pi$
$367$	2.26109	0.118028	0.0590140	+	0.998257i	$0.481204\pi$
$368$	9.12541	0.475695
$369$	5.98300	0.311463
$370$	−11.0707	−0.575540
$371$	0.256833	0.0133341
$372$	−6.82714	−0.353971
$373$	−18.5304	−0.959466	−0.479733	−	0.877415i	$-0.659266\pi$
$373$	−18.5304	−0.959466	−0.479733	+	0.877415i	$0.659266\pi$
$374$	−30.0097	−1.55176
$375$	−10.7140	−0.553268
$376$	9.52407	0.491166
$377$	5.87701	0.302681
$378$	5.04844	0.259664
$379$	2.06645	0.106146	0.0530731	−	0.998591i	$-0.483098\pi$
$379$	2.06645	0.106146	0.0530731	+	0.998591i	$0.483098\pi$
$380$	−4.23860	−0.217436
$381$	−5.82082	−0.298210
$382$	−20.7777	−1.06308
$383$	−3.48529	−0.178090	−0.0890451	−	0.996028i	$-0.528382\pi$
$383$	−3.48529	−0.178090	−0.0890451	+	0.996028i	$0.528382\pi$
$384$	1.01642	0.0518689
$385$	6.95522	0.354471
$386$	−20.2996	−1.03322
$387$	0.360230	0.0183115
$388$	−11.5116	−0.584411
$389$	−22.5703	−1.14436	−0.572179	−	0.820129i	$-0.693902\pi$
$389$	−22.5703	−1.14436	−0.572179	+	0.820129i	$0.693902\pi$
$390$	−1.12705	−0.0570703
$391$	49.1727	2.48677
$392$	1.00000	0.0505076
$393$	2.31287	0.116669
$394$	−0.0193130	−0.000972977 0
$395$	−16.9527	−0.852984
$396$	10.9539	0.550456
$397$	−23.8515	−1.19707	−0.598537	−	0.801095i	$-0.704251\pi$
$397$	−23.8515	−1.19707	−0.598537	+	0.801095i	$0.704251\pi$
$398$	16.1957	0.811815
$399$	3.44964	0.172698
$400$	−3.44030	−0.172015
$401$	17.6981	0.883800	0.441900	−	0.897064i	$-0.354305\pi$
$401$	17.6981	0.883800	0.441900	+	0.897064i	$0.354305\pi$
$402$	−15.5361	−0.774870
$403$	5.96369	0.297072
$404$	−1.64589	−0.0818862
$405$	0.960818	0.0477434
$406$	6.61923	0.328507
$407$	49.3680	2.44708
$408$	5.47702	0.271153
$409$	−18.5012	−0.914824	−0.457412	−	0.889255i	$-0.651223\pi$
$409$	−18.5012	−0.914824	−0.457412	+	0.889255i	$0.651223\pi$
$410$	−3.79891	−0.187615
$411$	−6.00470	−0.296190
$412$	0.581102	0.0286288
$413$	−0.643755	−0.0316771
$414$	−17.9487	−0.882131
$415$	9.86784	0.484393
$416$	−0.887869	−0.0435313
$417$	−13.1172	−0.642353
$418$	18.9013	0.924492
$419$	36.4843	1.78237	0.891186	−	0.453637i	$-0.149874\pi$
$419$	36.4843	1.78237	0.891186	+	0.453637i	$0.149874\pi$
$420$	−1.26939	−0.0619397
$421$	9.16299	0.446577	0.223288	−	0.974752i	$-0.428321\pi$
$421$	9.16299	0.446577	0.223288	+	0.974752i	$0.428321\pi$
$422$	−1.10737	−0.0539057
$423$	−18.7328	−0.910821
$424$	−0.256833	−0.0124729
$425$	−18.5382	−0.899236
$426$	−3.07693	−0.149078
$427$	−2.06300	−0.0998355
$428$	−1.12849	−0.0545478
$429$	5.02587	0.242651
$430$	−0.228729	−0.0110303
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.04844	−0.242893
$433$	−16.2592	−0.781367	−0.390683	−	0.920525i	$-0.627761\pi$
$433$	−16.2592	−0.781367	−0.390683	+	0.920525i	$0.627761\pi$
$434$	6.71686	0.322419
$435$	−8.40236	−0.402862
$436$	−19.3209	−0.925302
$437$	−30.9709	−1.48154
$438$	0.469761	0.0224461
$439$	−4.88080	−0.232948	−0.116474	−	0.993194i	$-0.537159\pi$
$439$	−4.88080	−0.232948	−0.116474	+	0.993194i	$0.537159\pi$
$440$	−6.95522	−0.331577
$441$	−1.96689	−0.0936615
$442$	−4.78432	−0.227567
$443$	10.2830	0.488562	0.244281	−	0.969705i	$-0.421448\pi$
$443$	10.2830	0.488562	0.244281	+	0.969705i	$0.421448\pi$
$444$	−9.01007	−0.427599
$445$	5.83551	0.276630
$446$	26.6539	1.26210
$447$	17.5132	0.828345
$448$	−1.00000	−0.0472456
$449$	31.0749	1.46652	0.733259	−	0.679950i	$-0.237998\pi$
$449$	31.0749	1.46652	0.733259	+	0.679950i	$0.237998\pi$
$450$	6.76670	0.318985
$451$	16.9406	0.797701
$452$	10.8406	0.509897
$453$	13.3896	0.629099
$454$	4.04787	0.189976
$455$	1.10884	0.0519833
$456$	−3.44964	−0.161544
$457$	25.4357	1.18983	0.594915	−	0.803789i	$-0.297186\pi$
$457$	25.4357	1.18983	0.594915	+	0.803789i	$0.297186\pi$
$458$	−11.4424	−0.534667
$459$	−27.2038	−1.26976
$460$	11.3965	0.531367
$461$	−34.6678	−1.61464	−0.807320	−	0.590114i	$-0.799083\pi$
$461$	−34.6678	−1.61464	−0.807320	+	0.590114i	$0.799083\pi$
$462$	5.66060	0.263355
$463$	−30.1846	−1.40280	−0.701399	−	0.712768i	$-0.747441\pi$
$463$	−30.1846	−1.40280	−0.701399	+	0.712768i	$0.747441\pi$
$464$	−6.61923	−0.307290
$465$	−8.52628	−0.395397
$466$	−2.70235	−0.125184
$467$	−39.4335	−1.82476	−0.912382	−	0.409339i	$-0.865759\pi$
$467$	−39.4335	−1.82476	−0.912382	+	0.409339i	$0.865759\pi$
$468$	1.74634	0.0807247
$469$	15.2851	0.705802
$470$	11.8944	0.548649
$471$	−3.59256	−0.165537
$472$	0.643755	0.0296312
$473$	1.01997	0.0468985
$474$	−13.7972	−0.633727
$475$	11.6761	0.535736
$476$	−5.38855	−0.246984
$477$	0.505163	0.0231298
$478$	24.2668	1.10994
$479$	−24.3234	−1.11137	−0.555683	−	0.831394i	$-0.687543\pi$
$479$	−24.3234	−1.11137	−0.555683	+	0.831394i	$0.687543\pi$
$480$	1.26939	0.0579393
$481$	7.87053	0.358865
$482$	21.2645	0.968569
$483$	−9.27524	−0.422038
$484$	20.0156	0.909798
$485$	−14.3766	−0.652806
$486$	15.9273	0.722477
$487$	31.4432	1.42483	0.712414	−	0.701760i	$-0.247602\pi$
$487$	31.4432	1.42483	0.712414	+	0.701760i	$0.247602\pi$
$488$	2.06300	0.0933876
$489$	1.64732	0.0744942
$490$	1.24888	0.0564187
$491$	−18.0644	−0.815234	−0.407617	−	0.913153i	$-0.633640\pi$
$491$	−18.0644	−0.815234	−0.407617	+	0.913153i	$0.633640\pi$
$492$	−3.09180	−0.139389
$493$	−35.6681	−1.60641
$494$	3.01336	0.135577
$495$	13.6802	0.614877
$496$	−6.71686	−0.301596
$497$	3.02723	0.135790
$498$	8.03108	0.359881
$499$	14.3924	0.644292	0.322146	−	0.946690i	$-0.395596\pi$
$499$	14.3924	0.644292	0.322146	+	0.946690i	$0.395596\pi$
$500$	−10.5409	−0.471404
$501$	0.269930	0.0120596
$502$	−3.88635	−0.173456
$503$	−14.2814	−0.636778	−0.318389	−	0.947960i	$-0.603142\pi$
$503$	−14.2814	−0.636778	−0.318389	+	0.947960i	$0.603142\pi$
$504$	1.96689	0.0876124
$505$	−2.05552	−0.0914695
$506$	−50.8209	−2.25926
$507$	−12.4122	−0.551245
$508$	−5.72680	−0.254086
$509$	−26.9799	−1.19586	−0.597932	−	0.801547i	$-0.704011\pi$
$509$	−26.9799	−1.19586	−0.597932	+	0.801547i	$0.704011\pi$
$510$	6.84015	0.302887
$511$	−0.462173	−0.0204453
$512$	1.00000	0.0441942
$513$	17.1340	0.756485
$514$	22.9701	1.01317
$515$	0.725726	0.0319793
$516$	−0.186154	−0.00819497
$517$	−53.0411	−2.33274
$518$	8.86453	0.389485
$519$	−13.8741	−0.609005
$520$	−1.10884	−0.0486259
$521$	39.0847	1.71233	0.856166	−	0.516700i	$-0.172840\pi$
$521$	39.0847	1.71233	0.856166	+	0.516700i	$0.172840\pi$
$522$	13.0193	0.569840
$523$	17.0284	0.744599	0.372300	−	0.928113i	$-0.378569\pi$
$523$	17.0284	0.744599	0.372300	+	0.928113i	$0.378569\pi$
$524$	2.27551	0.0994060
$525$	3.49678	0.152612
$526$	13.8320	0.603103
$527$	−36.1941	−1.57664
$528$	−5.66060	−0.246346
$529$	60.2732	2.62057
$530$	−0.320754	−0.0139327
$531$	−1.26620	−0.0549483
$532$	3.39392	0.147145
$533$	2.70077	0.116983
$534$	4.74931	0.205523
$535$	−1.40935	−0.0609317
$536$	−15.2851	−0.660217
$537$	−4.82266	−0.208113
$538$	11.3952	0.491283
$539$	−5.56916	−0.239881
$540$	−6.30490	−0.271320
$541$	32.8802	1.41363	0.706815	−	0.707398i	$-0.250131\pi$
$541$	32.8802	1.41363	0.706815	+	0.707398i	$0.250131\pi$
$542$	15.0139	0.644904
$543$	−3.73218	−0.160163
$544$	5.38855	0.231032
$545$	−24.1295	−1.03359
$546$	0.902447	0.0386211
$547$	−14.4602	−0.618275	−0.309138	−	0.951017i	$-0.600040\pi$
$547$	−14.4602	−0.618275	−0.309138	+	0.951017i	$0.600040\pi$
$548$	−5.90771	−0.252365
$549$	−4.05770	−0.173178
$550$	19.1596	0.816967
$551$	22.4651	0.957047
$552$	9.27524	0.394781
$553$	13.5743	0.577240
$554$	1.99314	0.0846806
$555$	−11.2525	−0.477642
$556$	−12.9053	−0.547308
$557$	4.57466	0.193834	0.0969172	−	0.995292i	$-0.469102\pi$
$557$	4.57466	0.193834	0.0969172	+	0.995292i	$0.469102\pi$
$558$	13.2113	0.559280
$559$	0.162610	0.00687769
$560$	−1.24888	−0.0527748
$561$	−30.5024	−1.28781
$562$	−6.61157	−0.278892
$563$	−32.4939	−1.36945	−0.684727	−	0.728799i	$-0.740079\pi$
$563$	−32.4939	−1.36945	−0.684727	+	0.728799i	$0.740079\pi$
$564$	9.68044	0.407620
$565$	13.5386	0.569572
$566$	25.2836	1.06275
$567$	−0.769343	−0.0323094
$568$	−3.02723	−0.127020
$569$	2.24248	0.0940096	0.0470048	−	0.998895i	$-0.485032\pi$
$569$	2.24248	0.0940096	0.0470048	+	0.998895i	$0.485032\pi$
$570$	−4.30819	−0.180450
$571$	3.62349	0.151638	0.0758192	−	0.997122i	$-0.475843\pi$
$571$	3.62349	0.151638	0.0758192	+	0.997122i	$0.475843\pi$
$572$	4.94468	0.206748
$573$	−21.1189	−0.882254
$574$	3.04186	0.126965
$575$	−31.3941	−1.30923
$576$	−1.96689	−0.0819539
$577$	−36.3522	−1.51336	−0.756681	−	0.653785i	$-0.773180\pi$
$577$	−36.3522	−1.51336	−0.756681	+	0.653785i	$0.773180\pi$
$578$	12.0365	0.500651
$579$	−20.6329	−0.857473
$580$	−8.26663	−0.343253
$581$	−7.90135	−0.327803
$582$	−11.7006	−0.485004
$583$	1.43035	0.0592389
$584$	0.462173	0.0191248
$585$	2.18097	0.0901721
$586$	−22.7815	−0.941096
$587$	−15.1779	−0.626460	−0.313230	−	0.949677i	$-0.601411\pi$
$587$	−15.1779	−0.626460	−0.313230	+	0.949677i	$0.601411\pi$
$588$	1.01642	0.0419164
$589$	22.7965	0.939312
$590$	0.803973	0.0330990
$591$	−0.0196301	−0.000807476 0
$592$	−8.86453	−0.364330
$593$	−10.5911	−0.434923	−0.217462	−	0.976069i	$-0.569778\pi$
$593$	−10.5911	−0.434923	−0.217462	+	0.976069i	$0.569778\pi$
$594$	28.1156	1.15360
$595$	−6.72965	−0.275889
$596$	17.2303	0.705779
$597$	16.4616	0.673727
$598$	−8.10217	−0.331322
$599$	−18.4395	−0.753417	−0.376709	−	0.926332i	$-0.622944\pi$
$599$	−18.4395	−0.753417	−0.376709	+	0.926332i	$0.622944\pi$
$600$	−3.49678	−0.142756
$601$	45.7862	1.86766	0.933830	−	0.357718i	$-0.116445\pi$
$601$	45.7862	1.86766	0.933830	+	0.357718i	$0.116445\pi$
$602$	0.183147	0.00746451
$603$	30.0642	1.22431
$604$	13.1733	0.536015
$605$	24.9970	1.01627
$606$	−1.67292	−0.0679576
$607$	−20.1046	−0.816021	−0.408010	−	0.912977i	$-0.633777\pi$
$607$	−20.1046	−0.816021	−0.408010	+	0.912977i	$0.633777\pi$
$608$	−3.39392	−0.137642
$609$	6.72791	0.272629
$610$	2.57644	0.104317
$611$	−8.45612	−0.342098
$612$	−10.5987	−0.428427
$613$	22.9667	0.927615	0.463807	−	0.885936i	$-0.346483\pi$
$613$	22.9667	0.927615	0.463807	+	0.885936i	$0.346483\pi$
$614$	15.9422	0.643373
$615$	−3.86129	−0.155702
$616$	5.56916	0.224388
$617$	7.54111	0.303594	0.151797	−	0.988412i	$-0.451494\pi$
$617$	7.54111	0.303594	0.151797	+	0.988412i	$0.451494\pi$
$618$	0.590643	0.0237591
$619$	−12.3636	−0.496935	−0.248468	−	0.968640i	$-0.579927\pi$
$619$	−12.3636	−0.496935	−0.248468	+	0.968640i	$0.579927\pi$
$620$	−8.38855	−0.336892
$621$	−46.0691	−1.84869
$622$	18.2932	0.733489
$623$	−4.67259	−0.187203
$624$	−0.902447	−0.0361268
$625$	4.03714	0.161486
$626$	10.8912	0.435298
$627$	19.2116	0.767239
$628$	−3.53453	−0.141043
$629$	−47.7669	−1.90459
$630$	2.45641	0.0978658
$631$	−24.7458	−0.985115	−0.492557	−	0.870280i	$-0.663938\pi$
$631$	−24.7458	−0.985115	−0.492557	+	0.870280i	$0.663938\pi$
$632$	−13.5743	−0.539958
$633$	−1.12555	−0.0447365
$634$	5.04936	0.200536
$635$	−7.15208	−0.283822
$636$	−0.261050	−0.0103513
$637$	−0.887869	−0.0351786
$638$	36.8636	1.45944
$639$	5.95423	0.235546
$640$	1.24888	0.0493663
$641$	11.8324	0.467353	0.233677	−	0.972314i	$-0.424924\pi$
$641$	11.8324	0.467353	0.233677	+	0.972314i	$0.424924\pi$
$642$	−1.14702	−0.0452694
$643$	1.25864	0.0496358	0.0248179	−	0.999692i	$-0.492099\pi$
$643$	1.25864	0.0496358	0.0248179	+	0.999692i	$0.492099\pi$
$644$	−9.12541	−0.359592
$645$	−0.232484	−0.00915405
$646$	−18.2883	−0.719544
$647$	−20.3737	−0.800974	−0.400487	−	0.916302i	$-0.631159\pi$
$647$	−20.3737	−0.800974	−0.400487	+	0.916302i	$0.631159\pi$
$648$	0.769343	0.0302227
$649$	−3.58518	−0.140730
$650$	3.05453	0.119809
$651$	6.82714	0.267577
$652$	1.62071	0.0634717
$653$	26.1474	1.02323	0.511613	−	0.859216i	$-0.329048\pi$
$653$	26.1474	1.02323	0.511613	+	0.859216i	$0.329048\pi$
$654$	−19.6381	−0.767911
$655$	2.84184	0.111040
$656$	−3.04186	−0.118764
$657$	−0.909044	−0.0354652
$658$	−9.52407	−0.371287
$659$	12.9529	0.504572	0.252286	−	0.967653i	$-0.418818\pi$
$659$	12.9529	0.504572	0.252286	+	0.967653i	$0.418818\pi$
$660$	−7.06941	−0.275177
$661$	34.2801	1.33334	0.666671	−	0.745352i	$-0.267719\pi$
$661$	34.2801	1.33334	0.666671	+	0.745352i	$0.267719\pi$
$662$	−16.6898	−0.648668
$663$	−4.86288	−0.188859
$664$	7.90135	0.306632
$665$	4.23860	0.164366
$666$	17.4356	0.675615
$667$	−60.4032	−2.33882
$668$	0.265569	0.0102752
$669$	27.0915	1.04742
$670$	−19.0893	−0.737484
$671$	−11.4892	−0.443535
$672$	−1.01642	−0.0392092
$673$	−22.3946	−0.863247	−0.431624	−	0.902054i	$-0.642059\pi$
$673$	−22.3946	−0.863247	−0.431624	+	0.902054i	$0.642059\pi$
$674$	−0.352135	−0.0135637
$675$	17.3682	0.668501
$676$	−12.2117	−0.469680
$677$	−46.8602	−1.80098	−0.900492	−	0.434873i	$-0.856793\pi$
$677$	−46.8602	−1.80098	−0.900492	+	0.434873i	$0.856793\pi$
$678$	11.0186	0.423165
$679$	11.5116	0.441773
$680$	6.72965	0.258070
$681$	4.11433	0.157661
$682$	37.4073	1.43240
$683$	−16.3320	−0.624925	−0.312463	−	0.949930i	$-0.601154\pi$
$683$	−16.3320	−0.624925	−0.312463	+	0.949930i	$0.601154\pi$
$684$	6.67548	0.255243
$685$	−7.37802	−0.281900
$686$	−1.00000	−0.0381802
$687$	−11.6303	−0.443722
$688$	−0.183147	−0.00698241
$689$	0.228034	0.00868741
$690$	11.5837	0.440983
$691$	−18.9392	−0.720480	−0.360240	−	0.932860i	$-0.617305\pi$
$691$	−18.9392	−0.720480	−0.360240	+	0.932860i	$0.617305\pi$
$692$	−13.6500	−0.518894
$693$	−10.9539	−0.416106
$694$	18.1594	0.689322
$695$	−16.1172	−0.611361
$696$	−6.72791	−0.255021
$697$	−16.3912	−0.620860
$698$	−17.4642	−0.661029
$699$	−2.74672	−0.103890
$700$	3.44030	0.130031
$701$	−3.29919	−0.124609	−0.0623043	−	0.998057i	$-0.519845\pi$
$701$	−3.29919	−0.124609	−0.0623043	+	0.998057i	$0.519845\pi$
$702$	4.48235	0.169176
$703$	30.0855	1.13470
$704$	−5.56916	−0.209896
$705$	12.0897	0.455325
$706$	2.97583	0.111997
$707$	1.64589	0.0619001
$708$	0.654325	0.0245910
$709$	4.08622	0.153461	0.0767306	−	0.997052i	$-0.475552\pi$
$709$	4.08622	0.153461	0.0767306	+	0.997052i	$0.475552\pi$
$710$	−3.78064	−0.141885
$711$	26.6993	1.00130
$712$	4.67259	0.175113
$713$	−61.2941	−2.29548
$714$	−5.47702	−0.204972
$715$	6.17532	0.230944
$716$	−4.74476	−0.177320
$717$	24.6652	0.921140
$718$	−5.98194	−0.223244
$719$	41.4168	1.54458	0.772292	−	0.635267i	$-0.219110\pi$
$719$	41.4168	1.54458	0.772292	+	0.635267i	$0.219110\pi$
$720$	−2.45641	−0.0915451
$721$	−0.581102	−0.0216414
$722$	−7.48131	−0.278425
$723$	21.6136	0.803818
$724$	−3.67189	−0.136465
$725$	22.7721	0.845736
$726$	20.3442	0.755044
$727$	−48.8083	−1.81020	−0.905099	−	0.425200i	$-0.860204\pi$
$727$	−48.8083	−1.81020	−0.905099	+	0.425200i	$0.860204\pi$
$728$	0.887869	0.0329066
$729$	13.8808	0.514103
$730$	0.577198	0.0213631
$731$	−0.986896	−0.0365017
$732$	2.09687	0.0775026
$733$	11.0072	0.406559	0.203280	−	0.979121i	$-0.434840\pi$
$733$	11.0072	0.406559	0.203280	+	0.979121i	$0.434840\pi$
$734$	2.26109	0.0834584
$735$	1.26939	0.0468220
$736$	9.12541	0.336367
$737$	85.1253	3.13563
$738$	5.98300	0.220237
$739$	44.2929	1.62934	0.814671	−	0.579924i	$-0.196918\pi$
$739$	44.2929	1.62934	0.814671	+	0.579924i	$0.196918\pi$
$740$	−11.0707	−0.406968
$741$	3.06283	0.112516
$742$	0.256833	0.00942865
$743$	31.2342	1.14587	0.572935	−	0.819601i	$-0.305805\pi$
$743$	31.2342	1.14587	0.572935	+	0.819601i	$0.305805\pi$
$744$	−6.82714	−0.250295
$745$	21.5185	0.788378
$746$	−18.5304	−0.678445
$747$	−15.5411	−0.568619
$748$	−30.0097	−1.09726
$749$	1.12849	0.0412343
$750$	−10.7140	−0.391220
$751$	−20.0662	−0.732227	−0.366114	−	0.930570i	$-0.619312\pi$
$751$	−20.0662	−0.732227	−0.366114	+	0.930570i	$0.619312\pi$
$752$	9.52407	0.347307
$753$	−3.95016	−0.143952
$754$	5.87701	0.214028
$755$	16.4519	0.598746
$756$	5.04844	0.183610
$757$	−26.3824	−0.958883	−0.479442	−	0.877574i	$-0.659161\pi$
$757$	−26.3824	−0.958883	−0.479442	+	0.877574i	$0.659161\pi$
$758$	2.06645	0.0750567
$759$	−51.6553	−1.87497
$760$	−4.23860	−0.153750
$761$	45.4072	1.64601	0.823005	−	0.568034i	$-0.192296\pi$
$761$	45.4072	1.64601	0.823005	+	0.568034i	$0.192296\pi$
$762$	−5.82082	−0.210866
$763$	19.3209	0.699463
$764$	−20.7777	−0.751712
$765$	−13.2365	−0.478567
$766$	−3.48529	−0.125929
$767$	−0.571570	−0.0206382
$768$	1.01642	0.0366769
$769$	−15.1576	−0.546597	−0.273298	−	0.961929i	$-0.588115\pi$
$769$	−15.1576	−0.546597	−0.273298	+	0.961929i	$0.588115\pi$
$770$	6.95522	0.250649
$771$	23.3472	0.840829
$772$	−20.2996	−0.730598
$773$	−46.6468	−1.67777	−0.838884	−	0.544311i	$-0.816791\pi$
$773$	−46.6468	−1.67777	−0.838884	+	0.544311i	$0.816791\pi$
$774$	0.360230	0.0129482
$775$	23.1080	0.830063
$776$	−11.5116	−0.413241
$777$	9.01007	0.323235
$778$	−22.5703	−0.809183
$779$	10.3238	0.369889
$780$	−1.12705	−0.0403548
$781$	16.8591	0.603266
$782$	49.1727	1.75841
$783$	33.4168	1.19422
$784$	1.00000	0.0357143
$785$	−4.41420	−0.157550
$786$	2.31287	0.0824973
$787$	12.9118	0.460256	0.230128	−	0.973160i	$-0.426085\pi$
$787$	12.9118	0.460256	0.230128	+	0.973160i	$0.426085\pi$
$788$	−0.0193130	−0.000687999 0
$789$	14.0591	0.500517
$790$	−16.9527	−0.603151
$791$	−10.8406	−0.385446
$792$	10.9539	0.389231
$793$	−1.83167	−0.0650446
$794$	−23.8515	−0.846459
$795$	−0.326020	−0.0115628
$796$	16.1957	0.574040
$797$	49.2420	1.74424	0.872120	−	0.489292i	$-0.162745\pi$
$797$	49.2420	1.74424	0.872120	+	0.489292i	$0.162745\pi$
$798$	3.44964	0.122116
$799$	51.3209	1.81560
$800$	−3.44030	−0.121633
$801$	−9.19049	−0.324730
$802$	17.6981	0.624941
$803$	−2.57391	−0.0908315
$804$	−15.5361	−0.547916
$805$	−11.3965	−0.401676
$806$	5.96369	0.210062
$807$	11.5823	0.407717
$808$	−1.64589	−0.0579023
$809$	−31.4226	−1.10476	−0.552380	−	0.833593i	$-0.686280\pi$
$809$	−31.4226	−1.10476	−0.552380	+	0.833593i	$0.686280\pi$
$810$	0.960818	0.0337597
$811$	37.5290	1.31782	0.658911	−	0.752221i	$-0.271017\pi$
$811$	37.5290	1.31782	0.658911	+	0.752221i	$0.271017\pi$
$812$	6.61923	0.232290
$813$	15.2605	0.535208
$814$	49.3680	1.73035
$815$	2.02407	0.0709000
$816$	5.47702	0.191734
$817$	0.621586	0.0217465
$818$	−18.5012	−0.646878
$819$	−1.74634	−0.0610221
$820$	−3.79891	−0.132664
$821$	−4.25760	−0.148591	−0.0742956	−	0.997236i	$-0.523671\pi$
$821$	−4.25760	−0.148591	−0.0742956	+	0.997236i	$0.523671\pi$
$822$	−6.00470	−0.209438
$823$	2.19107	0.0763760	0.0381880	−	0.999271i	$-0.487841\pi$
$823$	2.19107	0.0763760	0.0381880	+	0.999271i	$0.487841\pi$
$824$	0.581102	0.0202436
$825$	19.4742	0.678003
$826$	−0.643755	−0.0223991
$827$	13.6557	0.474854	0.237427	−	0.971405i	$-0.423696\pi$
$827$	13.6557	0.474854	0.237427	+	0.971405i	$0.423696\pi$
$828$	−17.9487	−0.623761
$829$	12.3040	0.427335	0.213668	−	0.976906i	$-0.431459\pi$
$829$	12.3040	0.427335	0.213668	+	0.976906i	$0.431459\pi$
$830$	9.86784	0.342518
$831$	2.02587	0.0702767
$832$	−0.887869	−0.0307813
$833$	5.38855	0.186702
$834$	−13.1172	−0.454212
$835$	0.331664	0.0114777
$836$	18.9013	0.653715
$837$	33.9097	1.17209
$838$	36.4843	1.26033
$839$	−7.53984	−0.260304	−0.130152	−	0.991494i	$-0.541547\pi$
$839$	−7.53984	−0.260304	−0.130152	+	0.991494i	$0.541547\pi$
$840$	−1.26939	−0.0437980
$841$	14.8142	0.510836
$842$	9.16299	0.315777
$843$	−6.72012	−0.231453
$844$	−1.10737	−0.0381171
$845$	−15.2509	−0.524648
$846$	−18.7328	−0.644048
$847$	−20.0156	−0.687743
$848$	−0.256833	−0.00881969
$849$	25.6987	0.881977
$850$	−18.5382	−0.635856
$851$	−80.8925	−2.77296
$852$	−3.07693	−0.105414
$853$	27.9112	0.955661	0.477831	−	0.878452i	$-0.341423\pi$
$853$	27.9112	0.955661	0.477831	+	0.878452i	$0.341423\pi$
$854$	−2.06300	−0.0705944
$855$	8.33687	0.285115
$856$	−1.12849	−0.0385711
$857$	−1.12202	−0.0383273	−0.0191637	−	0.999816i	$-0.506100\pi$
$857$	−1.12202	−0.0383273	−0.0191637	+	0.999816i	$0.506100\pi$
$858$	5.02587	0.171580
$859$	−32.7413	−1.11712	−0.558559	−	0.829464i	$-0.688646\pi$
$859$	−32.7413	−1.11712	−0.558559	+	0.829464i	$0.688646\pi$
$860$	−0.228729	−0.00779958
$861$	3.09180	0.105368
$862$	1.00000	0.0340601
$863$	−31.5585	−1.07426	−0.537132	−	0.843498i	$-0.680492\pi$
$863$	−31.5585	−1.07426	−0.537132	+	0.843498i	$0.680492\pi$
$864$	−5.04844	−0.171752
$865$	−17.0472	−0.579621
$866$	−16.2592	−0.552510
$867$	12.2341	0.415491
$868$	6.71686	0.227985
$869$	75.5977	2.56448
$870$	−8.40236	−0.284867
$871$	13.5712	0.459842
$872$	−19.3209	−0.654287
$873$	22.6420	0.766316
$874$	−30.9709	−1.04761
$875$	10.5409	0.356348
$876$	0.469761	0.0158718
$877$	−12.7921	−0.431957	−0.215979	−	0.976398i	$-0.569294\pi$
$877$	−12.7921	−0.431957	−0.215979	+	0.976398i	$0.569294\pi$
$878$	−4.88080	−0.164719
$879$	−23.1556	−0.781018
$880$	−6.95522	−0.234460
$881$	−18.7516	−0.631757	−0.315878	−	0.948800i	$-0.602299\pi$
$881$	−18.7516	−0.631757	−0.315878	+	0.948800i	$0.602299\pi$
$882$	−1.96689	−0.0662287
$883$	−37.5607	−1.26402	−0.632010	−	0.774961i	$-0.717770\pi$
$883$	−37.5607	−1.26402	−0.632010	+	0.774961i	$0.717770\pi$
$884$	−4.78432	−0.160914
$885$	0.817173	0.0274690
$886$	10.2830	0.345465
$887$	9.03509	0.303369	0.151684	−	0.988429i	$-0.451530\pi$
$887$	9.03509	0.303369	0.151684	+	0.988429i	$0.451530\pi$
$888$	−9.01007	−0.302358
$889$	5.72680	0.192071
$890$	5.83551	0.195607
$891$	−4.28460	−0.143539
$892$	26.6539	0.892439
$893$	−32.3239	−1.08168
$894$	17.5132	0.585728
$895$	−5.92564	−0.198072
$896$	−1.00000	−0.0334077
$897$	−8.23520	−0.274965
$898$	31.0749	1.03698
$899$	44.4604	1.48284
$900$	6.76670	0.225557
$901$	−1.38396	−0.0461064
$902$	16.9406	0.564060
$903$	0.186154	0.00619482
$904$	10.8406	0.360552
$905$	−4.58575	−0.152436
$906$	13.3896	0.444840
$907$	8.11552	0.269471	0.134736	−	0.990882i	$-0.456981\pi$
$907$	8.11552	0.269471	0.134736	+	0.990882i	$0.456981\pi$
$908$	4.04787	0.134333
$909$	3.23729	0.107374
$910$	1.10884	0.0367577
$911$	18.8816	0.625574	0.312787	−	0.949823i	$-0.398737\pi$
$911$	18.8816	0.625574	0.312787	+	0.949823i	$0.398737\pi$
$912$	−3.44964	−0.114229
$913$	−44.0039	−1.45632
$914$	25.4357	0.841337
$915$	2.61874	0.0865729
$916$	−11.4424	−0.378067
$917$	−2.27551	−0.0751439
$918$	−27.2038	−0.897859
$919$	−6.73833	−0.222277	−0.111138	−	0.993805i	$-0.535450\pi$
$919$	−6.73833	−0.222277	−0.111138	+	0.993805i	$0.535450\pi$
$920$	11.3965	0.375733
$921$	16.2039	0.533937
$922$	−34.6678	−1.14172
$923$	2.68778	0.0884693
$924$	5.66060	0.186220
$925$	30.4966	1.00272
$926$	−30.1846	−0.991929
$927$	−1.14296	−0.0375399
$928$	−6.61923	−0.217287
$929$	−20.9274	−0.686606	−0.343303	−	0.939225i	$-0.611546\pi$
$929$	−20.9274	−0.686606	−0.343303	+	0.939225i	$0.611546\pi$
$930$	−8.52628	−0.279588
$931$	−3.39392	−0.111231
$932$	−2.70235	−0.0885184
$933$	18.5935	0.608724
$934$	−39.4335	−1.29030
$935$	−37.4785	−1.22568
$936$	1.74634	0.0570810
$937$	−7.49627	−0.244892	−0.122446	−	0.992475i	$-0.539074\pi$
$937$	−7.49627	−0.244892	−0.122446	+	0.992475i	$0.539074\pi$
$938$	15.2851	0.499077
$939$	11.0700	0.361255
$940$	11.8944	0.387953
$941$	−23.0742	−0.752199	−0.376099	−	0.926579i	$-0.622735\pi$
$941$	−23.0742	−0.752199	−0.376099	+	0.926579i	$0.622735\pi$
$942$	−3.59256	−0.117052
$943$	−27.7582	−0.903931
$944$	0.643755	0.0209524
$945$	6.30490	0.205098
$946$	1.01997	0.0331622
$947$	54.9579	1.78589	0.892946	−	0.450164i	$-0.148635\pi$
$947$	54.9579	1.78589	0.892946	+	0.450164i	$0.148635\pi$
$948$	−13.7972	−0.448113
$949$	−0.410349	−0.0133205
$950$	11.6761	0.378823
$951$	5.13227	0.166425
$952$	−5.38855	−0.174644
$953$	−43.3853	−1.40539	−0.702695	−	0.711492i	$-0.748020\pi$
$953$	−43.3853	−1.40539	−0.702695	+	0.711492i	$0.748020\pi$
$954$	0.505163	0.0163553
$955$	−25.9489	−0.839686
$956$	24.2668	0.784845
$957$	37.4688	1.21120
$958$	−24.3234	−0.785855
$959$	5.90771	0.190770
$960$	1.26939	0.0409692
$961$	14.1162	0.455360
$962$	7.87053	0.253756
$963$	2.21963	0.0715265
$964$	21.2645	0.684882
$965$	−25.3517	−0.816101
$966$	−9.27524	−0.298426
$967$	−16.9791	−0.546010	−0.273005	−	0.962013i	$-0.588018\pi$
$967$	−16.9791	−0.546010	−0.273005	+	0.962013i	$0.588018\pi$
$968$	20.0156	0.643325
$969$	−18.5886	−0.597151
$970$	−14.3766	−0.461604
$971$	−17.0168	−0.546095	−0.273047	−	0.962001i	$-0.588032\pi$
$971$	−17.0168	−0.546095	−0.273047	+	0.962001i	$0.588032\pi$
$972$	15.9273	0.510869
$973$	12.9053	0.413726
$974$	31.4432	1.00750
$975$	3.10469	0.0994295
$976$	2.06300	0.0660350
$977$	−12.0934	−0.386901	−0.193451	−	0.981110i	$-0.561968\pi$
$977$	−12.0934	−0.386901	−0.193451	+	0.981110i	$0.561968\pi$
$978$	1.64732	0.0526754
$979$	−26.0224	−0.831680
$980$	1.24888	0.0398940
$981$	38.0021	1.21331
$982$	−18.0644	−0.576458
$983$	59.4576	1.89640	0.948201	−	0.317671i	$-0.102901\pi$
$983$	59.4576	1.89640	0.948201	+	0.317671i	$0.102901\pi$
$984$	−3.09180	−0.0985630
$985$	−0.0241197	−0.000768517 0
$986$	−35.6681	−1.13590
$987$	−9.68044	−0.308132
$988$	3.01336	0.0958676
$989$	−1.67129	−0.0531440
$990$	13.6802	0.434784
$991$	23.6508	0.751291	0.375646	−	0.926763i	$-0.377421\pi$
$991$	23.6508	0.751291	0.375646	+	0.926763i	$0.377421\pi$
$992$	−6.71686	−0.213260
$993$	−16.9638	−0.538331
$994$	3.02723	0.0960178
$995$	20.2264	0.641221
$996$	8.03108	0.254475
$997$	−1.60908	−0.0509601	−0.0254800	−	0.999675i	$-0.508111\pi$
$997$	−1.60908	−0.0509601	−0.0254800	+	0.999675i	$0.508111\pi$
$998$	14.3924	0.455583
$999$	44.7521	1.41589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.01642 q^{3} +1.00000 q^{4} +1.24888 q^{5} +1.01642 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.96689 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.01642 q^{3} +1.00000 q^{4} +1.24888 q^{5} +1.01642 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.96689 q^{9} +1.24888 q^{10} -5.56916 q^{11} +1.01642 q^{12} -0.887869 q^{13} -1.00000 q^{14} +1.26939 q^{15} +1.00000 q^{16} +5.38855 q^{17} -1.96689 q^{18} -3.39392 q^{19} +1.24888 q^{20} -1.01642 q^{21} -5.56916 q^{22} +9.12541 q^{23} +1.01642 q^{24} -3.44030 q^{25} -0.887869 q^{26} -5.04844 q^{27} -1.00000 q^{28} -6.61923 q^{29} +1.26939 q^{30} -6.71686 q^{31} +1.00000 q^{32} -5.66060 q^{33} +5.38855 q^{34} -1.24888 q^{35} -1.96689 q^{36} -8.86453 q^{37} -3.39392 q^{38} -0.902447 q^{39} +1.24888 q^{40} -3.04186 q^{41} -1.01642 q^{42} -0.183147 q^{43} -5.56916 q^{44} -2.45641 q^{45} +9.12541 q^{46} +9.52407 q^{47} +1.01642 q^{48} +1.00000 q^{49} -3.44030 q^{50} +5.47702 q^{51} -0.887869 q^{52} -0.256833 q^{53} -5.04844 q^{54} -6.95522 q^{55} -1.00000 q^{56} -3.44964 q^{57} -6.61923 q^{58} +0.643755 q^{59} +1.26939 q^{60} +2.06300 q^{61} -6.71686 q^{62} +1.96689 q^{63} +1.00000 q^{64} -1.10884 q^{65} -5.66060 q^{66} -15.2851 q^{67} +5.38855 q^{68} +9.27524 q^{69} -1.24888 q^{70} -3.02723 q^{71} -1.96689 q^{72} +0.462173 q^{73} -8.86453 q^{74} -3.49678 q^{75} -3.39392 q^{76} +5.56916 q^{77} -0.902447 q^{78} -13.5743 q^{79} +1.24888 q^{80} +0.769343 q^{81} -3.04186 q^{82} +7.90135 q^{83} -1.01642 q^{84} +6.72965 q^{85} -0.183147 q^{86} -6.72791 q^{87} -5.56916 q^{88} +4.67259 q^{89} -2.45641 q^{90} +0.887869 q^{91} +9.12541 q^{92} -6.82714 q^{93} +9.52407 q^{94} -4.23860 q^{95} +1.01642 q^{96} -11.5116 q^{97} +1.00000 q^{98} +10.9539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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