LMFDB - Embedded newform 4730.2.a.bc.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 24x^{9} - x^{8} + 200x^{7} + 14x^{6} - 653x^{5} - 26x^{4} + 620x^{3} - 177x^{2} - 90x + 32 $ x^11 - 24x^9 - x^8 + 200x^7 + 14x^6 - 653x^5 - 26x^4 + 620x^3 - 177x^2 - 90x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.60939$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.60939 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.60939 q^{6} +2.64901 q^{7} -1.00000 q^{8} +3.80893 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.60939 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.60939 q^{6} +2.64901 q^{7} -1.00000 q^{8} +3.80893 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.60939 q^{12} +6.18554 q^{13} -2.64901 q^{14} -2.60939 q^{15} +1.00000 q^{16} +5.19903 q^{17} -3.80893 q^{18} +7.41680 q^{19} -1.00000 q^{20} +6.91232 q^{21} -1.00000 q^{22} -2.86736 q^{23} -2.60939 q^{24} +1.00000 q^{25} -6.18554 q^{26} +2.11081 q^{27} +2.64901 q^{28} -0.143879 q^{29} +2.60939 q^{30} +2.25001 q^{31} -1.00000 q^{32} +2.60939 q^{33} -5.19903 q^{34} -2.64901 q^{35} +3.80893 q^{36} +3.19404 q^{37} -7.41680 q^{38} +16.1405 q^{39} +1.00000 q^{40} -4.28959 q^{41} -6.91232 q^{42} -1.00000 q^{43} +1.00000 q^{44} -3.80893 q^{45} +2.86736 q^{46} -11.1183 q^{47} +2.60939 q^{48} +0.0172767 q^{49} -1.00000 q^{50} +13.5663 q^{51} +6.18554 q^{52} +2.54902 q^{53} -2.11081 q^{54} -1.00000 q^{55} -2.64901 q^{56} +19.3533 q^{57} +0.143879 q^{58} -5.65535 q^{59} -2.60939 q^{60} -9.29768 q^{61} -2.25001 q^{62} +10.0899 q^{63} +1.00000 q^{64} -6.18554 q^{65} -2.60939 q^{66} +2.95118 q^{67} +5.19903 q^{68} -7.48207 q^{69} +2.64901 q^{70} +4.56445 q^{71} -3.80893 q^{72} -7.02527 q^{73} -3.19404 q^{74} +2.60939 q^{75} +7.41680 q^{76} +2.64901 q^{77} -16.1405 q^{78} -9.86319 q^{79} -1.00000 q^{80} -5.91885 q^{81} +4.28959 q^{82} -10.9794 q^{83} +6.91232 q^{84} -5.19903 q^{85} +1.00000 q^{86} -0.375436 q^{87} -1.00000 q^{88} -4.94364 q^{89} +3.80893 q^{90} +16.3856 q^{91} -2.86736 q^{92} +5.87116 q^{93} +11.1183 q^{94} -7.41680 q^{95} -2.60939 q^{96} -3.22351 q^{97} -0.0172767 q^{98} +3.80893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.60939	1.50653	0.753267	−	0.657715i	$-0.228477\pi$
$3$	2.60939	1.50653	0.753267	+	0.657715i	$0.228477\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.60939	−1.06528
$7$	2.64901	1.00123	0.500617	−	0.865669i	$-0.333107\pi$
$7$	2.64901	1.00123	0.500617	+	0.865669i	$0.333107\pi$
$8$	−1.00000	−0.353553
$9$	3.80893	1.26964
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.60939	0.753267
$13$	6.18554	1.71556	0.857780	−	0.514017i	$-0.171843\pi$
$13$	6.18554	1.71556	0.857780	+	0.514017i	$0.171843\pi$
$14$	−2.64901	−0.707979
$15$	−2.60939	−0.673742
$16$	1.00000	0.250000
$17$	5.19903	1.26095	0.630475	−	0.776210i	$-0.282860\pi$
$17$	5.19903	1.26095	0.630475	+	0.776210i	$0.282860\pi$
$18$	−3.80893	−0.897773
$19$	7.41680	1.70153	0.850765	−	0.525546i	$-0.176139\pi$
$19$	7.41680	1.70153	0.850765	+	0.525546i	$0.176139\pi$
$20$	−1.00000	−0.223607
$21$	6.91232	1.50839
$22$	−1.00000	−0.213201
$23$	−2.86736	−0.597886	−0.298943	−	0.954271i	$-0.596634\pi$
$23$	−2.86736	−0.597886	−0.298943	+	0.954271i	$0.596634\pi$
$24$	−2.60939	−0.532640
$25$	1.00000	0.200000
$26$	−6.18554	−1.21308
$27$	2.11081	0.406226
$28$	2.64901	0.500617
$29$	−0.143879	−0.0267176	−0.0133588	−	0.999911i	$-0.504252\pi$
$29$	−0.143879	−0.0267176	−0.0133588	+	0.999911i	$0.504252\pi$
$30$	2.60939	0.476408
$31$	2.25001	0.404114	0.202057	−	0.979374i	$-0.435237\pi$
$31$	2.25001	0.404114	0.202057	+	0.979374i	$0.435237\pi$
$32$	−1.00000	−0.176777
$33$	2.60939	0.454237
$34$	−5.19903	−0.891626
$35$	−2.64901	−0.447765
$36$	3.80893	0.634821
$37$	3.19404	0.525096	0.262548	−	0.964919i	$-0.415437\pi$
$37$	3.19404	0.525096	0.262548	+	0.964919i	$0.415437\pi$
$38$	−7.41680	−1.20316
$39$	16.1405	2.58455
$40$	1.00000	0.158114
$41$	−4.28959	−0.669922	−0.334961	−	0.942232i	$-0.608723\pi$
$41$	−4.28959	−0.669922	−0.334961	+	0.942232i	$0.608723\pi$
$42$	−6.91232	−1.06659
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−3.80893	−0.567801
$46$	2.86736	0.422770
$47$	−11.1183	−1.62177	−0.810887	−	0.585203i	$-0.801015\pi$
$47$	−11.1183	−1.62177	−0.810887	+	0.585203i	$0.801015\pi$
$48$	2.60939	0.376633
$49$	0.0172767	0.00246809
$50$	−1.00000	−0.141421
$51$	13.5663	1.89966
$52$	6.18554	0.857780
$53$	2.54902	0.350135	0.175068	−	0.984556i	$-0.443986\pi$
$53$	2.54902	0.350135	0.175068	+	0.984556i	$0.443986\pi$
$54$	−2.11081	−0.287245
$55$	−1.00000	−0.134840
$56$	−2.64901	−0.353989
$57$	19.3533	2.56341
$58$	0.143879	0.0188922
$59$	−5.65535	−0.736264	−0.368132	−	0.929773i	$-0.620003\pi$
$59$	−5.65535	−0.736264	−0.368132	+	0.929773i	$0.620003\pi$
$60$	−2.60939	−0.336871
$61$	−9.29768	−1.19045	−0.595223	−	0.803560i	$-0.702936\pi$
$61$	−9.29768	−1.19045	−0.595223	+	0.803560i	$0.702936\pi$
$62$	−2.25001	−0.285752
$63$	10.0899	1.27121
$64$	1.00000	0.125000
$65$	−6.18554	−0.767222
$66$	−2.60939	−0.321194
$67$	2.95118	0.360544	0.180272	−	0.983617i	$-0.442302\pi$
$67$	2.95118	0.360544	0.180272	+	0.983617i	$0.442302\pi$
$68$	5.19903	0.630475
$69$	−7.48207	−0.900736
$70$	2.64901	0.316618
$71$	4.56445	0.541701	0.270850	−	0.962621i	$-0.412695\pi$
$71$	4.56445	0.541701	0.270850	+	0.962621i	$0.412695\pi$
$72$	−3.80893	−0.448886
$73$	−7.02527	−0.822246	−0.411123	−	0.911580i	$-0.634863\pi$
$73$	−7.02527	−0.822246	−0.411123	+	0.911580i	$0.634863\pi$
$74$	−3.19404	−0.371299
$75$	2.60939	0.301307
$76$	7.41680	0.850765
$77$	2.64901	0.301883
$78$	−16.1405	−1.82755
$79$	−9.86319	−1.10970	−0.554848	−	0.831952i	$-0.687223\pi$
$79$	−9.86319	−1.10970	−0.554848	+	0.831952i	$0.687223\pi$
$80$	−1.00000	−0.111803
$81$	−5.91885	−0.657650
$82$	4.28959	0.473706
$83$	−10.9794	−1.20515	−0.602574	−	0.798063i	$-0.705858\pi$
$83$	−10.9794	−1.20515	−0.602574	+	0.798063i	$0.705858\pi$
$84$	6.91232	0.754196
$85$	−5.19903	−0.563914
$86$	1.00000	0.107833
$87$	−0.375436	−0.0402509
$88$	−1.00000	−0.106600
$89$	−4.94364	−0.524024	−0.262012	−	0.965065i	$-0.584386\pi$
$89$	−4.94364	−0.524024	−0.262012	+	0.965065i	$0.584386\pi$
$90$	3.80893	0.401496
$91$	16.3856	1.71768
$92$	−2.86736	−0.298943
$93$	5.87116	0.608811
$94$	11.1183	1.14677
$95$	−7.41680	−0.760947
$96$	−2.60939	−0.266320
$97$	−3.22351	−0.327297	−0.163649	−	0.986519i	$-0.552326\pi$
$97$	−3.22351	−0.327297	−0.163649	+	0.986519i	$0.552326\pi$
$98$	−0.0172767	−0.00174521
$99$	3.80893	0.382812
$100$	1.00000	0.100000
$101$	−4.33812	−0.431659	−0.215829	−	0.976431i	$-0.569246\pi$
$101$	−4.33812	−0.431659	−0.215829	+	0.976431i	$0.569246\pi$
$102$	−13.5663	−1.34326
$103$	6.52110	0.642544	0.321272	−	0.946987i	$-0.395890\pi$
$103$	6.52110	0.642544	0.321272	+	0.946987i	$0.395890\pi$
$104$	−6.18554	−0.606542
$105$	−6.91232	−0.674573
$106$	−2.54902	−0.247583
$107$	10.8717	1.05100	0.525502	−	0.850792i	$-0.323877\pi$
$107$	10.8717	1.05100	0.525502	+	0.850792i	$0.323877\pi$
$108$	2.11081	0.203113
$109$	−5.08256	−0.486821	−0.243410	−	0.969923i	$-0.578266\pi$
$109$	−5.08256	−0.486821	−0.243410	+	0.969923i	$0.578266\pi$
$110$	1.00000	0.0953463
$111$	8.33449	0.791075
$112$	2.64901	0.250308
$113$	0.573397	0.0539407	0.0269703	−	0.999636i	$-0.491414\pi$
$113$	0.573397	0.0539407	0.0269703	+	0.999636i	$0.491414\pi$
$114$	−19.3533	−1.81261
$115$	2.86736	0.267383
$116$	−0.143879	−0.0133588
$117$	23.5603	2.17815
$118$	5.65535	0.520617
$119$	13.7723	1.26250
$120$	2.60939	0.238204
$121$	1.00000	0.0909091
$122$	9.29768	0.841773
$123$	−11.1932	−1.00926
$124$	2.25001	0.202057
$125$	−1.00000	−0.0894427
$126$	−10.0899	−0.898880
$127$	19.9107	1.76679	0.883394	−	0.468630i	$-0.155252\pi$
$127$	19.9107	1.76679	0.883394	+	0.468630i	$0.155252\pi$
$128$	−1.00000	−0.0883883
$129$	−2.60939	−0.229744
$130$	6.18554	0.542508
$131$	−12.7769	−1.11633	−0.558163	−	0.829731i	$-0.688494\pi$
$131$	−12.7769	−1.11633	−0.558163	+	0.829731i	$0.688494\pi$
$132$	2.60939	0.227118
$133$	19.6472	1.70363
$134$	−2.95118	−0.254943
$135$	−2.11081	−0.181670
$136$	−5.19903	−0.445813
$137$	19.3904	1.65663	0.828316	−	0.560261i	$-0.189299\pi$
$137$	19.3904	1.65663	0.828316	+	0.560261i	$0.189299\pi$
$138$	7.48207	0.636916
$139$	5.98518	0.507657	0.253828	−	0.967249i	$-0.418310\pi$
$139$	5.98518	0.507657	0.253828	+	0.967249i	$0.418310\pi$
$140$	−2.64901	−0.223883
$141$	−29.0121	−2.44326
$142$	−4.56445	−0.383040
$143$	6.18554	0.517261
$144$	3.80893	0.317411
$145$	0.143879	0.0119485
$146$	7.02527	0.581415
$147$	0.0450816	0.00371827
$148$	3.19404	0.262548
$149$	−14.8106	−1.21333	−0.606665	−	0.794957i	$-0.707493\pi$
$149$	−14.8106	−1.21333	−0.606665	+	0.794957i	$0.707493\pi$
$150$	−2.60939	−0.213056
$151$	−1.29207	−0.105147	−0.0525737	−	0.998617i	$-0.516742\pi$
$151$	−1.29207	−0.105147	−0.0525737	+	0.998617i	$0.516742\pi$
$152$	−7.41680	−0.601582
$153$	19.8027	1.60096
$154$	−2.64901	−0.213464
$155$	−2.25001	−0.180725
$156$	16.1405	1.29227
$157$	−21.4895	−1.71505	−0.857526	−	0.514440i	$-0.828000\pi$
$157$	−21.4895	−1.71505	−0.857526	+	0.514440i	$0.828000\pi$
$158$	9.86319	0.784673
$159$	6.65140	0.527490
$160$	1.00000	0.0790569
$161$	−7.59568	−0.598624
$162$	5.91885	0.465029
$163$	3.50936	0.274875	0.137437	−	0.990510i	$-0.456113\pi$
$163$	3.50936	0.274875	0.137437	+	0.990510i	$0.456113\pi$
$164$	−4.28959	−0.334961
$165$	−2.60939	−0.203141
$166$	10.9794	0.852168
$167$	−18.6721	−1.44489	−0.722446	−	0.691427i	$-0.756982\pi$
$167$	−18.6721	−1.44489	−0.722446	+	0.691427i	$0.756982\pi$
$168$	−6.91232	−0.533297
$169$	25.2609	1.94315
$170$	5.19903	0.398747
$171$	28.2501	2.16034
$172$	−1.00000	−0.0762493
$173$	−8.76748	−0.666579	−0.333290	−	0.942825i	$-0.608159\pi$
$173$	−8.76748	−0.666579	−0.333290	+	0.942825i	$0.608159\pi$
$174$	0.375436	0.0284617
$175$	2.64901	0.200247
$176$	1.00000	0.0753778
$177$	−14.7570	−1.10921
$178$	4.94364	0.370541
$179$	8.31830	0.621739	0.310869	−	0.950453i	$-0.399380\pi$
$179$	8.31830	0.621739	0.310869	+	0.950453i	$0.399380\pi$
$180$	−3.80893	−0.283901
$181$	21.8248	1.62223	0.811113	−	0.584889i	$-0.198862\pi$
$181$	21.8248	1.62223	0.811113	+	0.584889i	$0.198862\pi$
$182$	−16.3856	−1.21458
$183$	−24.2613	−1.79345
$184$	2.86736	0.211385
$185$	−3.19404	−0.234830
$186$	−5.87116	−0.430494
$187$	5.19903	0.380191
$188$	−11.1183	−0.810887
$189$	5.59157	0.406727
$190$	7.41680	0.538071
$191$	7.19487	0.520603	0.260301	−	0.965527i	$-0.416178\pi$
$191$	7.19487	0.520603	0.260301	+	0.965527i	$0.416178\pi$
$192$	2.60939	0.188317
$193$	1.88220	0.135484	0.0677419	−	0.997703i	$-0.478421\pi$
$193$	1.88220	0.135484	0.0677419	+	0.997703i	$0.478421\pi$
$194$	3.22351	0.231434
$195$	−16.1405	−1.15585
$196$	0.0172767	0.00123405
$197$	16.5886	1.18189	0.590946	−	0.806711i	$-0.298755\pi$
$197$	16.5886	1.18189	0.590946	+	0.806711i	$0.298755\pi$
$198$	−3.80893	−0.270689
$199$	−18.3604	−1.30154	−0.650768	−	0.759277i	$-0.725553\pi$
$199$	−18.3604	−1.30154	−0.650768	+	0.759277i	$0.725553\pi$
$200$	−1.00000	−0.0707107
$201$	7.70078	0.543171
$202$	4.33812	0.305229
$203$	−0.381136	−0.0267505
$204$	13.5663	0.949831
$205$	4.28959	0.299598
$206$	−6.52110	−0.454347
$207$	−10.9216	−0.759102
$208$	6.18554	0.428890
$209$	7.41680	0.513031
$210$	6.91232	0.476995
$211$	−4.26735	−0.293777	−0.146888	−	0.989153i	$-0.546926\pi$
$211$	−4.26735	−0.293777	−0.146888	+	0.989153i	$0.546926\pi$
$212$	2.54902	0.175068
$213$	11.9104	0.816091
$214$	−10.8717	−0.743172
$215$	1.00000	0.0681994
$216$	−2.11081	−0.143622
$217$	5.96031	0.404612
$218$	5.08256	0.344234
$219$	−18.3317	−1.23874
$220$	−1.00000	−0.0674200
$221$	32.1588	2.16324
$222$	−8.33449	−0.559374
$223$	15.8038	1.05830	0.529151	−	0.848528i	$-0.322511\pi$
$223$	15.8038	1.05830	0.529151	+	0.848528i	$0.322511\pi$
$224$	−2.64901	−0.176995
$225$	3.80893	0.253929
$226$	−0.573397	−0.0381418
$227$	20.0050	1.32778	0.663888	−	0.747832i	$-0.268905\pi$
$227$	20.0050	1.32778	0.663888	+	0.747832i	$0.268905\pi$
$228$	19.3533	1.28171
$229$	−7.23644	−0.478197	−0.239099	−	0.970995i	$-0.576852\pi$
$229$	−7.23644	−0.478197	−0.239099	+	0.970995i	$0.576852\pi$
$230$	−2.86736	−0.189068
$231$	6.91232	0.454797
$232$	0.143879	0.00944609
$233$	6.30894	0.413312	0.206656	−	0.978414i	$-0.433742\pi$
$233$	6.30894	0.413312	0.206656	+	0.978414i	$0.433742\pi$
$234$	−23.5603	−1.54018
$235$	11.1183	0.725279
$236$	−5.65535	−0.368132
$237$	−25.7369	−1.67179
$238$	−13.7723	−0.892726
$239$	4.07861	0.263824	0.131912	−	0.991261i	$-0.457888\pi$
$239$	4.07861	0.263824	0.131912	+	0.991261i	$0.457888\pi$
$240$	−2.60939	−0.168436
$241$	4.14505	0.267006	0.133503	−	0.991048i	$-0.457377\pi$
$241$	4.14505	0.267006	0.133503	+	0.991048i	$0.457377\pi$
$242$	−1.00000	−0.0642824
$243$	−21.7770	−1.39700
$244$	−9.29768	−0.595223
$245$	−0.0172767	−0.00110377
$246$	11.1932	0.713654
$247$	45.8769	2.91908
$248$	−2.25001	−0.142876
$249$	−28.6496	−1.81559
$250$	1.00000	0.0632456
$251$	27.1303	1.71245	0.856226	−	0.516602i	$-0.172803\pi$
$251$	27.1303	1.71245	0.856226	+	0.516602i	$0.172803\pi$
$252$	10.0899	0.635604
$253$	−2.86736	−0.180270
$254$	−19.9107	−1.24931
$255$	−13.5663	−0.849555
$256$	1.00000	0.0625000
$257$	18.6975	1.16632	0.583160	−	0.812358i	$-0.301816\pi$
$257$	18.6975	1.16632	0.583160	+	0.812358i	$0.301816\pi$
$258$	2.60939	0.162454
$259$	8.46105	0.525744
$260$	−6.18554	−0.383611
$261$	−0.548023	−0.0339218
$262$	12.7769	0.789362
$263$	6.78734	0.418526	0.209263	−	0.977859i	$-0.432894\pi$
$263$	6.78734	0.418526	0.209263	+	0.977859i	$0.432894\pi$
$264$	−2.60939	−0.160597
$265$	−2.54902	−0.156585
$266$	−19.6472	−1.20465
$267$	−12.8999	−0.789460
$268$	2.95118	0.180272
$269$	−1.13357	−0.0691150	−0.0345575	−	0.999403i	$-0.511002\pi$
$269$	−1.13357	−0.0691150	−0.0345575	+	0.999403i	$0.511002\pi$
$270$	2.11081	0.128460
$271$	10.2541	0.622891	0.311446	−	0.950264i	$-0.399187\pi$
$271$	10.2541	0.622891	0.311446	+	0.950264i	$0.399187\pi$
$272$	5.19903	0.315237
$273$	42.7564	2.58774
$274$	−19.3904	−1.17142
$275$	1.00000	0.0603023
$276$	−7.48207	−0.450368
$277$	−18.5121	−1.11228	−0.556141	−	0.831088i	$-0.687719\pi$
$277$	−18.5121	−1.11228	−0.556141	+	0.831088i	$0.687719\pi$
$278$	−5.98518	−0.358967
$279$	8.57013	0.513080
$280$	2.64901	0.158309
$281$	10.5493	0.629316	0.314658	−	0.949205i	$-0.398110\pi$
$281$	10.5493	0.629316	0.314658	+	0.949205i	$0.398110\pi$
$282$	29.0121	1.72764
$283$	−14.3370	−0.852246	−0.426123	−	0.904665i	$-0.640121\pi$
$283$	−14.3370	−0.852246	−0.426123	+	0.904665i	$0.640121\pi$
$284$	4.56445	0.270850
$285$	−19.3533	−1.14639
$286$	−6.18554	−0.365759
$287$	−11.3632	−0.670748
$288$	−3.80893	−0.224443
$289$	10.0299	0.589994
$290$	−0.143879	−0.00844884
$291$	−8.41139	−0.493084
$292$	−7.02527	−0.411123
$293$	7.57129	0.442320	0.221160	−	0.975238i	$-0.429016\pi$
$293$	7.57129	0.442320	0.221160	+	0.975238i	$0.429016\pi$
$294$	−0.0450816	−0.00262921
$295$	5.65535	0.329267
$296$	−3.19404	−0.185650
$297$	2.11081	0.122482
$298$	14.8106	0.857954
$299$	−17.7362	−1.02571
$300$	2.60939	0.150653
$301$	−2.64901	−0.152687
$302$	1.29207	0.0743504
$303$	−11.3199	−0.650309
$304$	7.41680	0.425383
$305$	9.29768	0.532384
$306$	−19.8027	−1.13205
$307$	1.78256	0.101736	0.0508679	−	0.998705i	$-0.483801\pi$
$307$	1.78256	0.101736	0.0508679	+	0.998705i	$0.483801\pi$
$308$	2.64901	0.150942
$309$	17.0161	0.968013
$310$	2.25001	0.127792
$311$	−21.2791	−1.20663	−0.603314	−	0.797504i	$-0.706153\pi$
$311$	−21.2791	−1.20663	−0.603314	+	0.797504i	$0.706153\pi$
$312$	−16.1405	−0.913776
$313$	−23.4855	−1.32748	−0.663739	−	0.747965i	$-0.731031\pi$
$313$	−23.4855	−1.32748	−0.663739	+	0.747965i	$0.731031\pi$
$314$	21.4895	1.21273
$315$	−10.0899	−0.568502
$316$	−9.86319	−0.554848
$317$	−15.1256	−0.849537	−0.424769	−	0.905302i	$-0.639645\pi$
$317$	−15.1256	−0.849537	−0.424769	+	0.905302i	$0.639645\pi$
$318$	−6.65140	−0.372992
$319$	−0.143879	−0.00805565
$320$	−1.00000	−0.0559017
$321$	28.3685	1.58337
$322$	7.59568	0.423291
$323$	38.5601	2.14554
$324$	−5.91885	−0.328825
$325$	6.18554	0.343112
$326$	−3.50936	−0.194366
$327$	−13.2624	−0.733411
$328$	4.28959	0.236853
$329$	−29.4526	−1.62377
$330$	2.60939	0.143642
$331$	−6.18748	−0.340095	−0.170047	−	0.985436i	$-0.554392\pi$
$331$	−6.18748	−0.340095	−0.170047	+	0.985436i	$0.554392\pi$
$332$	−10.9794	−0.602574
$333$	12.1659	0.666685
$334$	18.6721	1.02169
$335$	−2.95118	−0.161240
$336$	6.91232	0.377098
$337$	−25.7768	−1.40415	−0.702075	−	0.712103i	$-0.747743\pi$
$337$	−25.7768	−1.40415	−0.702075	+	0.712103i	$0.747743\pi$
$338$	−25.2609	−1.37401
$339$	1.49622	0.0812634
$340$	−5.19903	−0.281957
$341$	2.25001	0.121845
$342$	−28.2501	−1.52759
$343$	−18.4973	−0.998762
$344$	1.00000	0.0539164
$345$	7.48207	0.402821
$346$	8.76748	0.471343
$347$	−33.9261	−1.82125	−0.910624	−	0.413236i	$-0.864398\pi$
$347$	−33.9261	−1.82125	−0.910624	+	0.413236i	$0.864398\pi$
$348$	−0.375436	−0.0201255
$349$	−34.6733	−1.85602	−0.928010	−	0.372555i	$-0.878482\pi$
$349$	−34.6733	−1.85602	−0.928010	+	0.372555i	$0.878482\pi$
$350$	−2.64901	−0.141596
$351$	13.0565	0.696905
$352$	−1.00000	−0.0533002
$353$	−28.1388	−1.49768	−0.748840	−	0.662751i	$-0.769389\pi$
$353$	−28.1388	−1.49768	−0.748840	+	0.662751i	$0.769389\pi$
$354$	14.7570	0.784328
$355$	−4.56445	−0.242256
$356$	−4.94364	−0.262012
$357$	35.9373	1.90201
$358$	−8.31830	−0.439636
$359$	−3.05343	−0.161154	−0.0805770	−	0.996748i	$-0.525676\pi$
$359$	−3.05343	−0.161154	−0.0805770	+	0.996748i	$0.525676\pi$
$360$	3.80893	0.200748
$361$	36.0089	1.89521
$362$	−21.8248	−1.14709
$363$	2.60939	0.136958
$364$	16.3856	0.858838
$365$	7.02527	0.367719
$366$	24.2613	1.26816
$367$	3.70225	0.193256	0.0966280	−	0.995321i	$-0.469194\pi$
$367$	3.70225	0.193256	0.0966280	+	0.995321i	$0.469194\pi$
$368$	−2.86736	−0.149472
$369$	−16.3388	−0.850561
$370$	3.19404	0.166050
$371$	6.75239	0.350567
$372$	5.87116	0.304406
$373$	12.4167	0.642914	0.321457	−	0.946924i	$-0.395827\pi$
$373$	12.4167	0.642914	0.321457	+	0.946924i	$0.395827\pi$
$374$	−5.19903	−0.268835
$375$	−2.60939	−0.134748
$376$	11.1183	0.573383
$377$	−0.889967	−0.0458356
$378$	−5.59157	−0.287599
$379$	−8.54844	−0.439104	−0.219552	−	0.975601i	$-0.570460\pi$
$379$	−8.54844	−0.439104	−0.219552	+	0.975601i	$0.570460\pi$
$380$	−7.41680	−0.380474
$381$	51.9548	2.66173
$382$	−7.19487	−0.368122
$383$	−11.9897	−0.612645	−0.306323	−	0.951928i	$-0.599099\pi$
$383$	−11.9897	−0.612645	−0.306323	+	0.951928i	$0.599099\pi$
$384$	−2.60939	−0.133160
$385$	−2.64901	−0.135006
$386$	−1.88220	−0.0958015
$387$	−3.80893	−0.193619
$388$	−3.22351	−0.163649
$389$	0.687575	0.0348614	0.0174307	−	0.999848i	$-0.494451\pi$
$389$	0.687575	0.0348614	0.0174307	+	0.999848i	$0.494451\pi$
$390$	16.1405	0.817306
$391$	−14.9075	−0.753905
$392$	−0.0172767	−0.000872603 0
$393$	−33.3400	−1.68178
$394$	−16.5886	−0.835724
$395$	9.86319	0.496271
$396$	3.80893	0.191406
$397$	−31.9492	−1.60348	−0.801742	−	0.597671i	$-0.796093\pi$
$397$	−31.9492	−1.60348	−0.801742	+	0.597671i	$0.796093\pi$
$398$	18.3604	0.920325
$399$	51.2673	2.56657
$400$	1.00000	0.0500000
$401$	23.2762	1.16236	0.581179	−	0.813776i	$-0.302592\pi$
$401$	23.2762	1.16236	0.581179	+	0.813776i	$0.302592\pi$
$402$	−7.70078	−0.384080
$403$	13.9175	0.693282
$404$	−4.33812	−0.215829
$405$	5.91885	0.294110
$406$	0.381136	0.0189155
$407$	3.19404	0.158322
$408$	−13.5663	−0.671632
$409$	28.9827	1.43310	0.716552	−	0.697534i	$-0.245719\pi$
$409$	28.9827	1.43310	0.716552	+	0.697534i	$0.245719\pi$
$410$	−4.28959	−0.211848
$411$	50.5971	2.49577
$412$	6.52110	0.321272
$413$	−14.9811	−0.737172
$414$	10.9216	0.536766
$415$	10.9794	0.538958
$416$	−6.18554	−0.303271
$417$	15.6177	0.764801
$418$	−7.41680	−0.362767
$419$	−25.5192	−1.24670	−0.623348	−	0.781944i	$-0.714228\pi$
$419$	−25.5192	−1.24670	−0.623348	+	0.781944i	$0.714228\pi$
$420$	−6.91232	−0.337287
$421$	12.5331	0.610827	0.305413	−	0.952220i	$-0.401205\pi$
$421$	12.5331	0.610827	0.305413	+	0.952220i	$0.401205\pi$
$422$	4.26735	0.207732
$423$	−42.3489	−2.05907
$424$	−2.54902	−0.123791
$425$	5.19903	0.252190
$426$	−11.9104	−0.577063
$427$	−24.6297	−1.19191
$428$	10.8717	0.525502
$429$	16.1405	0.779271
$430$	−1.00000	−0.0482243
$431$	−17.3498	−0.835710	−0.417855	−	0.908514i	$-0.637218\pi$
$431$	−17.3498	−0.835710	−0.417855	+	0.908514i	$0.637218\pi$
$432$	2.11081	0.101556
$433$	13.9699	0.671352	0.335676	−	0.941978i	$-0.391035\pi$
$433$	13.9699	0.671352	0.335676	+	0.941978i	$0.391035\pi$
$434$	−5.96031	−0.286104
$435$	0.375436	0.0180008
$436$	−5.08256	−0.243410
$437$	−21.2666	−1.01732
$438$	18.3317	0.875922
$439$	−16.3274	−0.779266	−0.389633	−	0.920970i	$-0.627398\pi$
$439$	−16.3274	−0.779266	−0.389633	+	0.920970i	$0.627398\pi$
$440$	1.00000	0.0476731
$441$	0.0658056	0.00313360
$442$	−32.1588	−1.52964
$443$	21.8397	1.03763	0.518817	−	0.854885i	$-0.326372\pi$
$443$	21.8397	1.03763	0.518817	+	0.854885i	$0.326372\pi$
$444$	8.33449	0.395537
$445$	4.94364	0.234351
$446$	−15.8038	−0.748332
$447$	−38.6466	−1.82792
$448$	2.64901	0.125154
$449$	17.5895	0.830101	0.415051	−	0.909798i	$-0.363764\pi$
$449$	17.5895	0.830101	0.415051	+	0.909798i	$0.363764\pi$
$450$	−3.80893	−0.179555
$451$	−4.28959	−0.201989
$452$	0.573397	0.0269703
$453$	−3.37152	−0.158408
$454$	−20.0050	−0.938880
$455$	−16.3856	−0.768168
$456$	−19.3533	−0.906303
$457$	12.9629	0.606378	0.303189	−	0.952931i	$-0.401949\pi$
$457$	12.9629	0.606378	0.303189	+	0.952931i	$0.401949\pi$
$458$	7.23644	0.338136
$459$	10.9742	0.512230
$460$	2.86736	0.133691
$461$	−3.50686	−0.163331	−0.0816653	−	0.996660i	$-0.526024\pi$
$461$	−3.50686	−0.163331	−0.0816653	+	0.996660i	$0.526024\pi$
$462$	−6.91232	−0.321590
$463$	19.2426	0.894281	0.447140	−	0.894464i	$-0.352442\pi$
$463$	19.2426	0.894281	0.447140	+	0.894464i	$0.352442\pi$
$464$	−0.143879	−0.00667939
$465$	−5.87116	−0.272269
$466$	−6.30894	−0.292256
$467$	−39.1915	−1.81356	−0.906782	−	0.421600i	$-0.861469\pi$
$467$	−39.1915	−1.81356	−0.906782	+	0.421600i	$0.861469\pi$
$468$	23.5603	1.08907
$469$	7.81771	0.360988
$470$	−11.1183	−0.512850
$471$	−56.0747	−2.58378
$472$	5.65535	0.260309
$473$	−1.00000	−0.0459800
$474$	25.7369	1.18214
$475$	7.41680	0.340306
$476$	13.7723	0.631252
$477$	9.70904	0.444546
$478$	−4.07861	−0.186551
$479$	−13.8705	−0.633760	−0.316880	−	0.948466i	$-0.602635\pi$
$479$	−13.8705	−0.633760	−0.316880	+	0.948466i	$0.602635\pi$
$480$	2.60939	0.119102
$481$	19.7568	0.900834
$482$	−4.14505	−0.188802
$483$	−19.8201	−0.901847
$484$	1.00000	0.0454545
$485$	3.22351	0.146372
$486$	21.7770	0.987826
$487$	−8.05651	−0.365075	−0.182538	−	0.983199i	$-0.558431\pi$
$487$	−8.05651	−0.365075	−0.182538	+	0.983199i	$0.558431\pi$
$488$	9.29768	0.420886
$489$	9.15731	0.414108
$490$	0.0172767	0.000780480 0
$491$	1.61871	0.0730514	0.0365257	−	0.999333i	$-0.488371\pi$
$491$	1.61871	0.0730514	0.0365257	+	0.999333i	$0.488371\pi$
$492$	−11.1932	−0.504630
$493$	−0.748029	−0.0336895
$494$	−45.8769	−2.06410
$495$	−3.80893	−0.171199
$496$	2.25001	0.101028
$497$	12.0913	0.542369
$498$	28.6496	1.28382
$499$	10.9959	0.492244	0.246122	−	0.969239i	$-0.420844\pi$
$499$	10.9959	0.492244	0.246122	+	0.969239i	$0.420844\pi$
$500$	−1.00000	−0.0447214
$501$	−48.7229	−2.17678
$502$	−27.1303	−1.21089
$503$	21.3606	0.952420	0.476210	−	0.879332i	$-0.342010\pi$
$503$	21.3606	0.952420	0.476210	+	0.879332i	$0.342010\pi$
$504$	−10.0899	−0.449440
$505$	4.33812	0.193044
$506$	2.86736	0.127470
$507$	65.9156	2.92742
$508$	19.9107	0.883394
$509$	−14.6295	−0.648441	−0.324220	−	0.945982i	$-0.605102\pi$
$509$	−14.6295	−0.648441	−0.324220	+	0.945982i	$0.605102\pi$
$510$	13.5663	0.600726
$511$	−18.6100	−0.823260
$512$	−1.00000	−0.0441942
$513$	15.6555	0.691205
$514$	−18.6975	−0.824712
$515$	−6.52110	−0.287354
$516$	−2.60939	−0.114872
$517$	−11.1183	−0.488983
$518$	−8.46105	−0.371757
$519$	−22.8778	−1.00422
$520$	6.18554	0.271254
$521$	8.41599	0.368711	0.184356	−	0.982860i	$-0.440980\pi$
$521$	8.41599	0.368711	0.184356	+	0.982860i	$0.440980\pi$
$522$	0.548023	0.0239863
$523$	10.1307	0.442986	0.221493	−	0.975162i	$-0.428907\pi$
$523$	10.1307	0.442986	0.221493	+	0.975162i	$0.428907\pi$
$524$	−12.7769	−0.558163
$525$	6.91232	0.301678
$526$	−6.78734	−0.295942
$527$	11.6979	0.509567
$528$	2.60939	0.113559
$529$	−14.7782	−0.642532
$530$	2.54902	0.110722
$531$	−21.5408	−0.934792
$532$	19.6472	0.851814
$533$	−26.5335	−1.14929
$534$	12.8999	0.558233
$535$	−10.8717	−0.470023
$536$	−2.95118	−0.127471
$537$	21.7057	0.936670
$538$	1.13357	0.0488717
$539$	0.0172767	0.000744158 0
$540$	−2.11081	−0.0908348
$541$	−2.17034	−0.0933100	−0.0466550	−	0.998911i	$-0.514856\pi$
$541$	−2.17034	−0.0933100	−0.0466550	+	0.998911i	$0.514856\pi$
$542$	−10.2541	−0.440450
$543$	56.9495	2.44394
$544$	−5.19903	−0.222906
$545$	5.08256	0.217713
$546$	−42.7564	−1.82981
$547$	−16.1830	−0.691937	−0.345968	−	0.938246i	$-0.612450\pi$
$547$	−16.1830	−0.691937	−0.345968	+	0.938246i	$0.612450\pi$
$548$	19.3904	0.828316
$549$	−35.4142	−1.51144
$550$	−1.00000	−0.0426401
$551$	−1.06712	−0.0454608
$552$	7.48207	0.318458
$553$	−26.1277	−1.11106
$554$	18.5121	0.786502
$555$	−8.33449	−0.353779
$556$	5.98518	0.253828
$557$	14.3336	0.607333	0.303666	−	0.952778i	$-0.401789\pi$
$557$	14.3336	0.607333	0.303666	+	0.952778i	$0.401789\pi$
$558$	−8.57013	−0.362803
$559$	−6.18554	−0.261621
$560$	−2.64901	−0.111941
$561$	13.5663	0.572770
$562$	−10.5493	−0.444994
$563$	−38.6619	−1.62940	−0.814702	−	0.579880i	$-0.803100\pi$
$563$	−38.6619	−1.62940	−0.814702	+	0.579880i	$0.803100\pi$
$564$	−29.0121	−1.22163
$565$	−0.573397	−0.0241230
$566$	14.3370	0.602629
$567$	−15.6791	−0.658461
$568$	−4.56445	−0.191520
$569$	33.7062	1.41304	0.706519	−	0.707694i	$-0.250265\pi$
$569$	33.7062	1.41304	0.706519	+	0.707694i	$0.250265\pi$
$570$	19.3533	0.810622
$571$	3.87030	0.161967	0.0809835	−	0.996715i	$-0.474194\pi$
$571$	3.87030	0.161967	0.0809835	+	0.996715i	$0.474194\pi$
$572$	6.18554	0.258630
$573$	18.7742	0.784305
$574$	11.3632	0.474291
$575$	−2.86736	−0.119577
$576$	3.80893	0.158705
$577$	13.8291	0.575711	0.287856	−	0.957674i	$-0.407058\pi$
$577$	13.8291	0.575711	0.287856	+	0.957674i	$0.407058\pi$
$578$	−10.0299	−0.417189
$579$	4.91140	0.204111
$580$	0.143879	0.00597423
$581$	−29.0846	−1.20663
$582$	8.41139	0.348663
$583$	2.54902	0.105570
$584$	7.02527	0.290708
$585$	−23.5603	−0.974098
$586$	−7.57129	−0.312767
$587$	8.50882	0.351197	0.175598	−	0.984462i	$-0.443814\pi$
$587$	8.50882	0.351197	0.175598	+	0.984462i	$0.443814\pi$
$588$	0.0450816	0.00185913
$589$	16.6879	0.687612
$590$	−5.65535	−0.232827
$591$	43.2863	1.78056
$592$	3.19404	0.131274
$593$	25.1842	1.03419	0.517095	−	0.855928i	$-0.327013\pi$
$593$	25.1842	1.03419	0.517095	+	0.855928i	$0.327013\pi$
$594$	−2.11081	−0.0866076
$595$	−13.7723	−0.564609
$596$	−14.8106	−0.606665
$597$	−47.9095	−1.96081
$598$	17.7362	0.725287
$599$	26.4397	1.08029	0.540147	−	0.841570i	$-0.318368\pi$
$599$	26.4397	1.08029	0.540147	+	0.841570i	$0.318368\pi$
$600$	−2.60939	−0.106528
$601$	42.4528	1.73169	0.865843	−	0.500316i	$-0.166783\pi$
$601$	42.4528	1.73169	0.865843	+	0.500316i	$0.166783\pi$
$602$	2.64901	0.107966
$603$	11.2408	0.457762
$604$	−1.29207	−0.0525737
$605$	−1.00000	−0.0406558
$606$	11.3199	0.459838
$607$	−12.7448	−0.517296	−0.258648	−	0.965972i	$-0.583277\pi$
$607$	−12.7448	−0.517296	−0.258648	+	0.965972i	$0.583277\pi$
$608$	−7.41680	−0.300791
$609$	−0.994534	−0.0403006
$610$	−9.29768	−0.376452
$611$	−68.7728	−2.78225
$612$	19.8027	0.800478
$613$	29.8069	1.20389	0.601944	−	0.798538i	$-0.294393\pi$
$613$	29.8069	1.20389	0.601944	+	0.798538i	$0.294393\pi$
$614$	−1.78256	−0.0719381
$615$	11.1932	0.451355
$616$	−2.64901	−0.106732
$617$	6.42871	0.258810	0.129405	−	0.991592i	$-0.458693\pi$
$617$	6.42871	0.258810	0.129405	+	0.991592i	$0.458693\pi$
$618$	−17.0161	−0.684489
$619$	−41.3906	−1.66363	−0.831814	−	0.555054i	$-0.812698\pi$
$619$	−41.3906	−1.66363	−0.831814	+	0.555054i	$0.812698\pi$
$620$	−2.25001	−0.0903626
$621$	−6.05246	−0.242877
$622$	21.2791	0.853215
$623$	−13.0958	−0.524671
$624$	16.1405	0.646137
$625$	1.00000	0.0400000
$626$	23.4855	0.938668
$627$	19.3533	0.772898
$628$	−21.4895	−0.857526
$629$	16.6059	0.662120
$630$	10.0899	0.401991
$631$	34.7952	1.38518	0.692588	−	0.721333i	$-0.256470\pi$
$631$	34.7952	1.38518	0.692588	+	0.721333i	$0.256470\pi$
$632$	9.86319	0.392337
$633$	−11.1352	−0.442584
$634$	15.1256	0.600714
$635$	−19.9107	−0.790132
$636$	6.65140	0.263745
$637$	0.106865	0.00423417
$638$	0.143879	0.00569621
$639$	17.3857	0.687767
$640$	1.00000	0.0395285
$641$	−43.0294	−1.69956	−0.849780	−	0.527137i	$-0.823266\pi$
$641$	−43.0294	−1.69956	−0.849780	+	0.527137i	$0.823266\pi$
$642$	−28.3685	−1.11961
$643$	2.45936	0.0969876	0.0484938	−	0.998823i	$-0.484558\pi$
$643$	2.45936	0.0969876	0.0484938	+	0.998823i	$0.484558\pi$
$644$	−7.59568	−0.299312
$645$	2.60939	0.102745
$646$	−38.5601	−1.51713
$647$	−30.0555	−1.18160	−0.590801	−	0.806817i	$-0.701188\pi$
$647$	−30.0555	−1.18160	−0.590801	+	0.806817i	$0.701188\pi$
$648$	5.91885	0.232514
$649$	−5.65535	−0.221992
$650$	−6.18554	−0.242617
$651$	15.5528	0.609562
$652$	3.50936	0.137437
$653$	42.0494	1.64552	0.822761	−	0.568387i	$-0.192433\pi$
$653$	42.0494	1.64552	0.822761	+	0.568387i	$0.192433\pi$
$654$	13.2624	0.518600
$655$	12.7769	0.499236
$656$	−4.28959	−0.167480
$657$	−26.7587	−1.04396
$658$	29.4526	1.14818
$659$	32.5481	1.26789	0.633947	−	0.773376i	$-0.281434\pi$
$659$	32.5481	1.26789	0.633947	+	0.773376i	$0.281434\pi$
$660$	−2.60939	−0.101570
$661$	38.0141	1.47858	0.739288	−	0.673389i	$-0.235162\pi$
$661$	38.0141	1.47858	0.739288	+	0.673389i	$0.235162\pi$
$662$	6.18748	0.240483
$663$	83.9149	3.25899
$664$	10.9794	0.426084
$665$	−19.6472	−0.761886
$666$	−12.1659	−0.471417
$667$	0.412552	0.0159741
$668$	−18.6721	−0.722446
$669$	41.2383	1.59437
$670$	2.95118	0.114014
$671$	−9.29768	−0.358933
$672$	−6.91232	−0.266648
$673$	−2.82196	−0.108779	−0.0543893	−	0.998520i	$-0.517321\pi$
$673$	−2.82196	−0.108779	−0.0543893	+	0.998520i	$0.517321\pi$
$674$	25.7768	0.992884
$675$	2.11081	0.0812451
$676$	25.2609	0.971574
$677$	−38.1507	−1.46625	−0.733124	−	0.680095i	$-0.761939\pi$
$677$	−38.1507	−1.46625	−0.733124	+	0.680095i	$0.761939\pi$
$678$	−1.49622	−0.0574619
$679$	−8.53911	−0.327701
$680$	5.19903	0.199374
$681$	52.2008	2.00034
$682$	−2.25001	−0.0861574
$683$	−17.4630	−0.668201	−0.334101	−	0.942537i	$-0.608433\pi$
$683$	−17.4630	−0.668201	−0.334101	+	0.942537i	$0.608433\pi$
$684$	28.2501	1.08017
$685$	−19.3904	−0.740868
$686$	18.4973	0.706231
$687$	−18.8827	−0.720420
$688$	−1.00000	−0.0381246
$689$	15.7671	0.600678
$690$	−7.48207	−0.284838
$691$	34.5438	1.31411	0.657055	−	0.753843i	$-0.271802\pi$
$691$	34.5438	1.31411	0.657055	+	0.753843i	$0.271802\pi$
$692$	−8.76748	−0.333290
$693$	10.0899	0.383284
$694$	33.9261	1.28782
$695$	−5.98518	−0.227031
$696$	0.375436	0.0142309
$697$	−22.3017	−0.844738
$698$	34.6733	1.31240
$699$	16.4625	0.622669
$700$	2.64901	0.100123
$701$	48.3995	1.82802	0.914012	−	0.405688i	$-0.132968\pi$
$701$	48.3995	1.82802	0.914012	+	0.405688i	$0.132968\pi$
$702$	−13.0565	−0.492786
$703$	23.6895	0.893467
$704$	1.00000	0.0376889
$705$	29.0121	1.09266
$706$	28.1388	1.05902
$707$	−11.4917	−0.432191
$708$	−14.7570	−0.554603
$709$	−2.50738	−0.0941666	−0.0470833	−	0.998891i	$-0.514993\pi$
$709$	−2.50738	−0.0941666	−0.0470833	+	0.998891i	$0.514993\pi$
$710$	4.56445	0.171301
$711$	−37.5682	−1.40892
$712$	4.94364	0.185271
$713$	−6.45160	−0.241614
$714$	−35.9373	−1.34492
$715$	−6.18554	−0.231326
$716$	8.31830	0.310869
$717$	10.6427	0.397459
$718$	3.05343	0.113953
$719$	29.7851	1.11080	0.555399	−	0.831584i	$-0.312566\pi$
$719$	29.7851	1.11080	0.555399	+	0.831584i	$0.312566\pi$
$720$	−3.80893	−0.141950
$721$	17.2745	0.643336
$722$	−36.0089	−1.34011
$723$	10.8161	0.402253
$724$	21.8248	0.811113
$725$	−0.143879	−0.00534352
$726$	−2.60939	−0.0968436
$727$	11.6767	0.433066	0.216533	−	0.976275i	$-0.430525\pi$
$727$	11.6767	0.433066	0.216533	+	0.976275i	$0.430525\pi$
$728$	−16.3856	−0.607290
$729$	−39.0683	−1.44697
$730$	−7.02527	−0.260017
$731$	−5.19903	−0.192293
$732$	−24.2613	−0.896724
$733$	12.8718	0.475430	0.237715	−	0.971335i	$-0.423602\pi$
$733$	12.8718	0.475430	0.237715	+	0.971335i	$0.423602\pi$
$734$	−3.70225	−0.136653
$735$	−0.0450816	−0.00166286
$736$	2.86736	0.105692
$737$	2.95118	0.108708
$738$	16.3388	0.601438
$739$	−7.30024	−0.268544	−0.134272	−	0.990945i	$-0.542870\pi$
$739$	−7.30024	−0.268544	−0.134272	+	0.990945i	$0.542870\pi$
$740$	−3.19404	−0.117415
$741$	119.711	4.39769
$742$	−6.75239	−0.247888
$743$	−9.86501	−0.361912	−0.180956	−	0.983491i	$-0.557919\pi$
$743$	−9.86501	−0.361912	−0.180956	+	0.983491i	$0.557919\pi$
$744$	−5.87116	−0.215247
$745$	14.8106	0.542618
$746$	−12.4167	−0.454609
$747$	−41.8198	−1.53011
$748$	5.19903	0.190095
$749$	28.7992	1.05230
$750$	2.60939	0.0952815
$751$	−10.0186	−0.365585	−0.182793	−	0.983151i	$-0.558514\pi$
$751$	−10.0186	−0.365585	−0.182793	+	0.983151i	$0.558514\pi$
$752$	−11.1183	−0.405443
$753$	70.7937	2.57987
$754$	0.889967	0.0324107
$755$	1.29207	0.0470233
$756$	5.59157	0.203363
$757$	−8.52533	−0.309858	−0.154929	−	0.987926i	$-0.549515\pi$
$757$	−8.52533	−0.309858	−0.154929	+	0.987926i	$0.549515\pi$
$758$	8.54844	0.310493
$759$	−7.48207	−0.271582
$760$	7.41680	0.269036
$761$	5.49471	0.199183	0.0995915	−	0.995028i	$-0.468246\pi$
$761$	5.49471	0.199183	0.0995915	+	0.995028i	$0.468246\pi$
$762$	−51.9548	−1.88212
$763$	−13.4638	−0.487421
$764$	7.19487	0.260301
$765$	−19.8027	−0.715969
$766$	11.9897	0.433206
$767$	−34.9814	−1.26311
$768$	2.60939	0.0941583
$769$	−7.58106	−0.273380	−0.136690	−	0.990614i	$-0.543646\pi$
$769$	−7.58106	−0.273380	−0.136690	+	0.990614i	$0.543646\pi$
$770$	2.64901	0.0954638
$771$	48.7892	1.75710
$772$	1.88220	0.0677419
$773$	−27.4957	−0.988952	−0.494476	−	0.869191i	$-0.664640\pi$
$773$	−27.4957	−0.988952	−0.494476	+	0.869191i	$0.664640\pi$
$774$	3.80893	0.136909
$775$	2.25001	0.0808228
$776$	3.22351	0.115717
$777$	22.0782	0.792051
$778$	−0.687575	−0.0246508
$779$	−31.8150	−1.13989
$780$	−16.1405	−0.577923
$781$	4.56445	0.163329
$782$	14.9075	0.533091
$783$	−0.303700	−0.0108534
$784$	0.0172767	0.000617024 0
$785$	21.4895	0.766995
$786$	33.3400	1.18920
$787$	31.3460	1.11737	0.558683	−	0.829381i	$-0.311307\pi$
$787$	31.3460	1.11737	0.558683	+	0.829381i	$0.311307\pi$
$788$	16.5886	0.590946
$789$	17.7108	0.630523
$790$	−9.86319	−0.350916
$791$	1.51894	0.0540072
$792$	−3.80893	−0.135344
$793$	−57.5112	−2.04228
$794$	31.9492	1.13383
$795$	−6.65140	−0.235901
$796$	−18.3604	−0.650768
$797$	44.2412	1.56710	0.783552	−	0.621326i	$-0.213406\pi$
$797$	44.2412	1.56710	0.783552	+	0.621326i	$0.213406\pi$
$798$	−51.2673	−1.81484
$799$	−57.8044	−2.04497
$800$	−1.00000	−0.0353553
$801$	−18.8300	−0.665324
$802$	−23.2762	−0.821911
$803$	−7.02527	−0.247916
$804$	7.70078	0.271586
$805$	7.59568	0.267713
$806$	−13.9175	−0.490224
$807$	−2.95793	−0.104124
$808$	4.33812	0.152614
$809$	−38.2660	−1.34536	−0.672680	−	0.739933i	$-0.734857\pi$
$809$	−38.2660	−1.34536	−0.672680	+	0.739933i	$0.734857\pi$
$810$	−5.91885	−0.207967
$811$	10.6487	0.373926	0.186963	−	0.982367i	$-0.440136\pi$
$811$	10.6487	0.373926	0.186963	+	0.982367i	$0.440136\pi$
$812$	−0.381136	−0.0133753
$813$	26.7569	0.938406
$814$	−3.19404	−0.111951
$815$	−3.50936	−0.122928
$816$	13.5663	0.474916
$817$	−7.41680	−0.259481
$818$	−28.9827	−1.01336
$819$	62.4115	2.18084
$820$	4.28959	0.149799
$821$	−30.9909	−1.08159	−0.540796	−	0.841154i	$-0.681877\pi$
$821$	−30.9909	−1.08159	−0.540796	+	0.841154i	$0.681877\pi$
$822$	−50.5971	−1.76478
$823$	−13.5542	−0.472471	−0.236235	−	0.971696i	$-0.575914\pi$
$823$	−13.5542	−0.472471	−0.236235	+	0.971696i	$0.575914\pi$
$824$	−6.52110	−0.227173
$825$	2.60939	0.0908474
$826$	14.9811	0.521259
$827$	7.36348	0.256053	0.128027	−	0.991771i	$-0.459136\pi$
$827$	7.36348	0.256053	0.128027	+	0.991771i	$0.459136\pi$
$828$	−10.9216	−0.379551
$829$	−44.9875	−1.56248	−0.781240	−	0.624231i	$-0.785412\pi$
$829$	−44.9875	−1.56248	−0.781240	+	0.624231i	$0.785412\pi$
$830$	−10.9794	−0.381101
$831$	−48.3052	−1.67569
$832$	6.18554	0.214445
$833$	0.0898218	0.00311214
$834$	−15.6177	−0.540796
$835$	18.6721	0.646175
$836$	7.41680	0.256515
$837$	4.74935	0.164161
$838$	25.5192	0.881547
$839$	5.60835	0.193622	0.0968109	−	0.995303i	$-0.469136\pi$
$839$	5.60835	0.193622	0.0968109	+	0.995303i	$0.469136\pi$
$840$	6.91232	0.238498
$841$	−28.9793	−0.999286
$842$	−12.5331	−0.431920
$843$	27.5272	0.948086
$844$	−4.26735	−0.146888
$845$	−25.2609	−0.869002
$846$	42.3489	1.45598
$847$	2.64901	0.0910212
$848$	2.54902	0.0875338
$849$	−37.4109	−1.28394
$850$	−5.19903	−0.178325
$851$	−9.15846	−0.313948
$852$	11.9104	0.408045
$853$	20.3061	0.695269	0.347634	−	0.937630i	$-0.386985\pi$
$853$	20.3061	0.695269	0.347634	+	0.937630i	$0.386985\pi$
$854$	24.6297	0.842811
$855$	−28.2501	−0.966131
$856$	−10.8717	−0.371586
$857$	−14.4001	−0.491897	−0.245948	−	0.969283i	$-0.579099\pi$
$857$	−14.4001	−0.491897	−0.245948	+	0.969283i	$0.579099\pi$
$858$	−16.1405	−0.551028
$859$	34.5446	1.17865	0.589324	−	0.807897i	$-0.299394\pi$
$859$	34.5446	1.17865	0.589324	+	0.807897i	$0.299394\pi$
$860$	1.00000	0.0340997
$861$	−29.6510	−1.01050
$862$	17.3498	0.590936
$863$	39.0842	1.33044	0.665221	−	0.746647i	$-0.268337\pi$
$863$	39.0842	1.33044	0.665221	+	0.746647i	$0.268337\pi$
$864$	−2.11081	−0.0718112
$865$	8.76748	0.298103
$866$	−13.9699	−0.474717
$867$	26.1719	0.888845
$868$	5.96031	0.202306
$869$	−9.86319	−0.334586
$870$	−0.375436	−0.0127285
$871$	18.2546	0.618535
$872$	5.08256	0.172117
$873$	−12.2781	−0.415551
$874$	21.2666	0.719355
$875$	−2.64901	−0.0895530
$876$	−18.3317	−0.619370
$877$	−50.8511	−1.71712	−0.858560	−	0.512714i	$-0.828640\pi$
$877$	−50.8511	−1.71712	−0.858560	+	0.512714i	$0.828640\pi$
$878$	16.3274	0.551024
$879$	19.7565	0.666369
$880$	−1.00000	−0.0337100
$881$	43.9656	1.48124	0.740620	−	0.671924i	$-0.234532\pi$
$881$	43.9656	1.48124	0.740620	+	0.671924i	$0.234532\pi$
$882$	−0.0658056	−0.00221579
$883$	−10.0700	−0.338882	−0.169441	−	0.985540i	$-0.554196\pi$
$883$	−10.0700	−0.338882	−0.169441	+	0.985540i	$0.554196\pi$
$884$	32.1588	1.08162
$885$	14.7570	0.496052
$886$	−21.8397	−0.733719
$887$	−2.11879	−0.0711419	−0.0355709	−	0.999367i	$-0.511325\pi$
$887$	−2.11879	−0.0711419	−0.0355709	+	0.999367i	$0.511325\pi$
$888$	−8.33449	−0.279687
$889$	52.7437	1.76897
$890$	−4.94364	−0.165711
$891$	−5.91885	−0.198289
$892$	15.8038	0.529151
$893$	−82.4623	−2.75950
$894$	38.6466	1.29254
$895$	−8.31830	−0.278050
$896$	−2.64901	−0.0884974
$897$	−46.2807	−1.54527
$898$	−17.5895	−0.586970
$899$	−0.323728	−0.0107969
$900$	3.80893	0.126964
$901$	13.2524	0.441503
$902$	4.28959	0.142828
$903$	−6.91232	−0.230028
$904$	−0.573397	−0.0190709
$905$	−21.8248	−0.725482
$906$	3.37152	0.112011
$907$	26.9426	0.894613	0.447306	−	0.894381i	$-0.352383\pi$
$907$	26.9426	0.894613	0.447306	+	0.894381i	$0.352383\pi$
$908$	20.0050	0.663888
$909$	−16.5236	−0.548053
$910$	16.3856	0.543177
$911$	55.1973	1.82877	0.914384	−	0.404848i	$-0.132675\pi$
$911$	55.1973	1.82877	0.914384	+	0.404848i	$0.132675\pi$
$912$	19.3533	0.640853
$913$	−10.9794	−0.363365
$914$	−12.9629	−0.428774
$915$	24.2613	0.802054
$916$	−7.23644	−0.239099
$917$	−33.8463	−1.11770
$918$	−10.9742	−0.362201
$919$	−13.8614	−0.457245	−0.228622	−	0.973515i	$-0.573422\pi$
$919$	−13.8614	−0.457245	−0.228622	+	0.973515i	$0.573422\pi$
$920$	−2.86736	−0.0945341
$921$	4.65139	0.153268
$922$	3.50686	0.115492
$923$	28.2336	0.929321
$924$	6.91232	0.227399
$925$	3.19404	0.105019
$926$	−19.2426	−0.632352
$927$	24.8384	0.815801
$928$	0.143879	0.00472305
$929$	26.8617	0.881303	0.440652	−	0.897678i	$-0.354747\pi$
$929$	26.8617	0.881303	0.440652	+	0.897678i	$0.354747\pi$
$930$	5.87116	0.192523
$931$	0.128138	0.00419954
$932$	6.30894	0.206656
$933$	−55.5256	−1.81783
$934$	39.1915	1.28238
$935$	−5.19903	−0.170026
$936$	−23.5603	−0.770092
$937$	−18.4841	−0.603849	−0.301924	−	0.953332i	$-0.597629\pi$
$937$	−18.4841	−0.603849	−0.301924	+	0.953332i	$0.597629\pi$
$938$	−7.81771	−0.255257
$939$	−61.2828	−1.99989
$940$	11.1183	0.362640
$941$	−24.7970	−0.808359	−0.404179	−	0.914680i	$-0.632443\pi$
$941$	−24.7970	−0.808359	−0.404179	+	0.914680i	$0.632443\pi$
$942$	56.0747	1.82701
$943$	12.2998	0.400537
$944$	−5.65535	−0.184066
$945$	−5.59157	−0.181894
$946$	1.00000	0.0325128
$947$	0.415506	0.0135021	0.00675106	−	0.999977i	$-0.497851\pi$
$947$	0.415506	0.0135021	0.00675106	+	0.999977i	$0.497851\pi$
$948$	−25.7369	−0.835896
$949$	−43.4551	−1.41061
$950$	−7.41680	−0.240633
$951$	−39.4686	−1.27986
$952$	−13.7723	−0.446363
$953$	28.6038	0.926569	0.463285	−	0.886210i	$-0.346671\pi$
$953$	28.6038	0.926569	0.463285	+	0.886210i	$0.346671\pi$
$954$	−9.70904	−0.314342
$955$	−7.19487	−0.232821
$956$	4.07861	0.131912
$957$	−0.375436	−0.0121361
$958$	13.8705	0.448136
$959$	51.3654	1.65868
$960$	−2.60939	−0.0842178
$961$	−25.9375	−0.836692
$962$	−19.7568	−0.636986
$963$	41.4094	1.33440
$964$	4.14505	0.133503
$965$	−1.88220	−0.0605902
$966$	19.8201	0.637702
$967$	−20.2688	−0.651800	−0.325900	−	0.945404i	$-0.605667\pi$
$967$	−20.2688	−0.651800	−0.325900	+	0.945404i	$0.605667\pi$
$968$	−1.00000	−0.0321412
$969$	100.619	3.23233
$970$	−3.22351	−0.103501
$971$	51.7175	1.65969	0.829846	−	0.557992i	$-0.188428\pi$
$971$	51.7175	1.65969	0.829846	+	0.557992i	$0.188428\pi$
$972$	−21.7770	−0.698499
$973$	15.8548	0.508283
$974$	8.05651	0.258147
$975$	16.1405	0.516910
$976$	−9.29768	−0.297612
$977$	−11.0379	−0.353135	−0.176567	−	0.984289i	$-0.556499\pi$
$977$	−11.0379	−0.353135	−0.176567	+	0.984289i	$0.556499\pi$
$978$	−9.15731	−0.292818
$979$	−4.94364	−0.157999
$980$	−0.0172767	−0.000551883 0
$981$	−19.3591	−0.618088
$982$	−1.61871	−0.0516552
$983$	−13.6118	−0.434150	−0.217075	−	0.976155i	$-0.569652\pi$
$983$	−13.6118	−0.434150	−0.217075	+	0.976155i	$0.569652\pi$
$984$	11.1932	0.356827
$985$	−16.5886	−0.528558
$986$	0.748029	0.0238221
$987$	−76.8533	−2.44627
$988$	45.8769	1.45954
$989$	2.86736	0.0911768
$990$	3.80893	0.121056
$991$	−50.0469	−1.58979	−0.794895	−	0.606747i	$-0.792474\pi$
$991$	−50.0469	−1.58979	−0.794895	+	0.606747i	$0.792474\pi$
$992$	−2.25001	−0.0714379
$993$	−16.1456	−0.512364
$994$	−12.0913	−0.383513
$995$	18.3604	0.582064
$996$	−28.6496	−0.907797
$997$	−37.5957	−1.19067	−0.595334	−	0.803478i	$-0.702980\pi$
$997$	−37.5957	−1.19067	−0.595334	+	0.803478i	$0.702980\pi$
$998$	−10.9959	−0.348069
$999$	6.74201	0.213308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bc.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bc.1.9	✓	11	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.60939 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.60939 q^{6} +2.64901 q^{7} -1.00000 q^{8} +3.80893 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.60939 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.60939 q^{6} +2.64901 q^{7} -1.00000 q^{8} +3.80893 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.60939 q^{12} +6.18554 q^{13} -2.64901 q^{14} -2.60939 q^{15} +1.00000 q^{16} +5.19903 q^{17} -3.80893 q^{18} +7.41680 q^{19} -1.00000 q^{20} +6.91232 q^{21} -1.00000 q^{22} -2.86736 q^{23} -2.60939 q^{24} +1.00000 q^{25} -6.18554 q^{26} +2.11081 q^{27} +2.64901 q^{28} -0.143879 q^{29} +2.60939 q^{30} +2.25001 q^{31} -1.00000 q^{32} +2.60939 q^{33} -5.19903 q^{34} -2.64901 q^{35} +3.80893 q^{36} +3.19404 q^{37} -7.41680 q^{38} +16.1405 q^{39} +1.00000 q^{40} -4.28959 q^{41} -6.91232 q^{42} -1.00000 q^{43} +1.00000 q^{44} -3.80893 q^{45} +2.86736 q^{46} -11.1183 q^{47} +2.60939 q^{48} +0.0172767 q^{49} -1.00000 q^{50} +13.5663 q^{51} +6.18554 q^{52} +2.54902 q^{53} -2.11081 q^{54} -1.00000 q^{55} -2.64901 q^{56} +19.3533 q^{57} +0.143879 q^{58} -5.65535 q^{59} -2.60939 q^{60} -9.29768 q^{61} -2.25001 q^{62} +10.0899 q^{63} +1.00000 q^{64} -6.18554 q^{65} -2.60939 q^{66} +2.95118 q^{67} +5.19903 q^{68} -7.48207 q^{69} +2.64901 q^{70} +4.56445 q^{71} -3.80893 q^{72} -7.02527 q^{73} -3.19404 q^{74} +2.60939 q^{75} +7.41680 q^{76} +2.64901 q^{77} -16.1405 q^{78} -9.86319 q^{79} -1.00000 q^{80} -5.91885 q^{81} +4.28959 q^{82} -10.9794 q^{83} +6.91232 q^{84} -5.19903 q^{85} +1.00000 q^{86} -0.375436 q^{87} -1.00000 q^{88} -4.94364 q^{89} +3.80893 q^{90} +16.3856 q^{91} -2.86736 q^{92} +5.87116 q^{93} +11.1183 q^{94} -7.41680 q^{95} -2.60939 q^{96} -3.22351 q^{97} -0.0172767 q^{98} +3.80893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * q^99

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