LMFDB - Embedded newform 5290.2.a.bk.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.763450$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.763450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.763450 q^{6} -4.04396 q^{7} +1.00000 q^{8} -2.41714 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.763450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.763450 q^{6} -4.04396 q^{7} +1.00000 q^{8} -2.41714 q^{9} -1.00000 q^{10} +0.263186 q^{11} +0.763450 q^{12} +3.03780 q^{13} -4.04396 q^{14} -0.763450 q^{15} +1.00000 q^{16} -0.160435 q^{17} -2.41714 q^{18} +1.01862 q^{19} -1.00000 q^{20} -3.08736 q^{21} +0.263186 q^{22} +0.763450 q^{24} +1.00000 q^{25} +3.03780 q^{26} -4.13572 q^{27} -4.04396 q^{28} +5.02313 q^{29} -0.763450 q^{30} -2.89990 q^{31} +1.00000 q^{32} +0.200929 q^{33} -0.160435 q^{34} +4.04396 q^{35} -2.41714 q^{36} +3.70669 q^{37} +1.01862 q^{38} +2.31921 q^{39} -1.00000 q^{40} +4.05754 q^{41} -3.08736 q^{42} -0.864573 q^{43} +0.263186 q^{44} +2.41714 q^{45} +13.0224 q^{47} +0.763450 q^{48} +9.35363 q^{49} +1.00000 q^{50} -0.122484 q^{51} +3.03780 q^{52} -10.4009 q^{53} -4.13572 q^{54} -0.263186 q^{55} -4.04396 q^{56} +0.777666 q^{57} +5.02313 q^{58} -1.97740 q^{59} -0.763450 q^{60} +4.65658 q^{61} -2.89990 q^{62} +9.77484 q^{63} +1.00000 q^{64} -3.03780 q^{65} +0.200929 q^{66} -3.68328 q^{67} -0.160435 q^{68} +4.04396 q^{70} -3.70176 q^{71} -2.41714 q^{72} +15.1829 q^{73} +3.70669 q^{74} +0.763450 q^{75} +1.01862 q^{76} -1.06431 q^{77} +2.31921 q^{78} -1.31107 q^{79} -1.00000 q^{80} +4.09402 q^{81} +4.05754 q^{82} +16.3350 q^{83} -3.08736 q^{84} +0.160435 q^{85} -0.864573 q^{86} +3.83491 q^{87} +0.263186 q^{88} +7.07268 q^{89} +2.41714 q^{90} -12.2847 q^{91} -2.21393 q^{93} +13.0224 q^{94} -1.01862 q^{95} +0.763450 q^{96} +11.0101 q^{97} +9.35363 q^{98} -0.636158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.763450	0.440778	0.220389	−	0.975412i	$-0.429267\pi$
$3$	0.763450	0.440778	0.220389	+	0.975412i	$0.429267\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.763450	0.311677
$7$	−4.04396	−1.52847	−0.764237	−	0.644936i	$-0.776884\pi$
$7$	−4.04396	−1.52847	−0.764237	+	0.644936i	$0.776884\pi$
$8$	1.00000	0.353553
$9$	−2.41714	−0.805715
$10$	−1.00000	−0.316228
$11$	0.263186	0.0793535	0.0396767	−	0.999213i	$-0.487367\pi$
$11$	0.263186	0.0793535	0.0396767	+	0.999213i	$0.487367\pi$
$12$	0.763450	0.220389
$13$	3.03780	0.842534	0.421267	−	0.906937i	$-0.361586\pi$
$13$	3.03780	0.842534	0.421267	+	0.906937i	$0.361586\pi$
$14$	−4.04396	−1.08079
$15$	−0.763450	−0.197122
$16$	1.00000	0.250000
$17$	−0.160435	−0.0389112	−0.0194556	−	0.999811i	$-0.506193\pi$
$17$	−0.160435	−0.0389112	−0.0194556	+	0.999811i	$0.506193\pi$
$18$	−2.41714	−0.569726
$19$	1.01862	0.233688	0.116844	−	0.993150i	$-0.462722\pi$
$19$	1.01862	0.233688	0.116844	+	0.993150i	$0.462722\pi$
$20$	−1.00000	−0.223607
$21$	−3.08736	−0.673718
$22$	0.263186	0.0561114
$23$	0	0
$23$	0	0
$24$	0.763450	0.155839
$25$	1.00000	0.200000
$26$	3.03780	0.595761
$27$	−4.13572	−0.795919
$28$	−4.04396	−0.764237
$29$	5.02313	0.932773	0.466386	−	0.884581i	$-0.345556\pi$
$29$	5.02313	0.932773	0.466386	+	0.884581i	$0.345556\pi$
$30$	−0.763450	−0.139386
$31$	−2.89990	−0.520837	−0.260418	−	0.965496i	$-0.583861\pi$
$31$	−2.89990	−0.520837	−0.260418	+	0.965496i	$0.583861\pi$
$32$	1.00000	0.176777
$33$	0.200929	0.0349773
$34$	−0.160435	−0.0275144
$35$	4.04396	0.683554
$36$	−2.41714	−0.402857
$37$	3.70669	0.609377	0.304688	−	0.952452i	$-0.401448\pi$
$37$	3.70669	0.609377	0.304688	+	0.952452i	$0.401448\pi$
$38$	1.01862	0.165242
$39$	2.31921	0.371370
$40$	−1.00000	−0.158114
$41$	4.05754	0.633682	0.316841	−	0.948479i	$-0.397378\pi$
$41$	4.05754	0.633682	0.316841	+	0.948479i	$0.397378\pi$
$42$	−3.08736	−0.476390
$43$	−0.864573	−0.131846	−0.0659231	−	0.997825i	$-0.520999\pi$
$43$	−0.864573	−0.131846	−0.0659231	+	0.997825i	$0.520999\pi$
$44$	0.263186	0.0396767
$45$	2.41714	0.360327
$46$	0	0
$47$	13.0224	1.89952	0.949758	−	0.312984i	$-0.101329\pi$
$47$	13.0224	1.89952	0.949758	+	0.312984i	$0.101329\pi$
$48$	0.763450	0.110195
$49$	9.35363	1.33623
$50$	1.00000	0.141421
$51$	−0.122484	−0.0171512
$52$	3.03780	0.421267
$53$	−10.4009	−1.42867	−0.714337	−	0.699801i	$-0.753272\pi$
$53$	−10.4009	−1.42867	−0.714337	+	0.699801i	$0.753272\pi$
$54$	−4.13572	−0.562800
$55$	−0.263186	−0.0354880
$56$	−4.04396	−0.540397
$57$	0.777666	0.103004
$58$	5.02313	0.659570
$59$	−1.97740	−0.257436	−0.128718	−	0.991681i	$-0.541086\pi$
$59$	−1.97740	−0.257436	−0.128718	+	0.991681i	$0.541086\pi$
$60$	−0.763450	−0.0985610
$61$	4.65658	0.596214	0.298107	−	0.954532i	$-0.403645\pi$
$61$	4.65658	0.596214	0.298107	+	0.954532i	$0.403645\pi$
$62$	−2.89990	−0.368287
$63$	9.77484	1.23151
$64$	1.00000	0.125000
$65$	−3.03780	−0.376793
$66$	0.200929	0.0247327
$67$	−3.68328	−0.449984	−0.224992	−	0.974361i	$-0.572236\pi$
$67$	−3.68328	−0.449984	−0.224992	+	0.974361i	$0.572236\pi$
$68$	−0.160435	−0.0194556
$69$	0	0
$70$	4.04396	0.483346
$71$	−3.70176	−0.439318	−0.219659	−	0.975577i	$-0.570495\pi$
$71$	−3.70176	−0.439318	−0.219659	+	0.975577i	$0.570495\pi$
$72$	−2.41714	−0.284863
$73$	15.1829	1.77703	0.888513	−	0.458852i	$-0.151739\pi$
$73$	15.1829	1.77703	0.888513	+	0.458852i	$0.151739\pi$
$74$	3.70669	0.430894
$75$	0.763450	0.0881556
$76$	1.01862	0.116844
$77$	−1.06431	−0.121290
$78$	2.31921	0.262599
$79$	−1.31107	−0.147507	−0.0737533	−	0.997277i	$-0.523498\pi$
$79$	−1.31107	−0.147507	−0.0737533	+	0.997277i	$0.523498\pi$
$80$	−1.00000	−0.111803
$81$	4.09402	0.454891
$82$	4.05754	0.448081
$83$	16.3350	1.79300	0.896501	−	0.443042i	$-0.146101\pi$
$83$	16.3350	1.79300	0.896501	+	0.443042i	$0.146101\pi$
$84$	−3.08736	−0.336859
$85$	0.160435	0.0174016
$86$	−0.864573	−0.0932293
$87$	3.83491	0.411146
$88$	0.263186	0.0280557
$89$	7.07268	0.749702	0.374851	−	0.927085i	$-0.377694\pi$
$89$	7.07268	0.749702	0.374851	+	0.927085i	$0.377694\pi$
$90$	2.41714	0.254789
$91$	−12.2847	−1.28779
$92$	0	0
$93$	−2.21393	−0.229573
$94$	13.0224	1.34316
$95$	−1.01862	−0.104508
$96$	0.763450	0.0779193
$97$	11.0101	1.11791	0.558955	−	0.829198i	$-0.311202\pi$
$97$	11.0101	1.11791	0.558955	+	0.829198i	$0.311202\pi$
$98$	9.35363	0.944859
$99$	−0.636158	−0.0639363
$100$	1.00000	0.100000
$101$	2.95966	0.294497	0.147249	−	0.989100i	$-0.452958\pi$
$101$	2.95966	0.294497	0.147249	+	0.989100i	$0.452958\pi$
$102$	−0.122484	−0.0121277
$103$	−12.8902	−1.27011	−0.635055	−	0.772467i	$-0.719022\pi$
$103$	−12.8902	−1.27011	−0.635055	+	0.772467i	$0.719022\pi$
$104$	3.03780	0.297881
$105$	3.08736	0.301296
$106$	−10.4009	−1.01023
$107$	11.7636	1.13723	0.568616	−	0.822603i	$-0.307479\pi$
$107$	11.7636	1.13723	0.568616	+	0.822603i	$0.307479\pi$
$108$	−4.13572	−0.397960
$109$	20.2232	1.93703	0.968515	−	0.248956i	$-0.0800875\pi$
$109$	20.2232	1.93703	0.968515	+	0.248956i	$0.0800875\pi$
$110$	−0.263186	−0.0250938
$111$	2.82987	0.268600
$112$	−4.04396	−0.382118
$113$	−3.75557	−0.353294	−0.176647	−	0.984274i	$-0.556525\pi$
$113$	−3.75557	−0.353294	−0.176647	+	0.984274i	$0.556525\pi$
$114$	0.777666	0.0728351
$115$	0	0
$116$	5.02313	0.466386
$117$	−7.34280	−0.678842
$118$	−1.97740	−0.182035
$119$	0.648793	0.0594748
$120$	−0.763450	−0.0696931
$121$	−10.9307	−0.993703
$122$	4.65658	0.421587
$123$	3.09773	0.279313
$124$	−2.89990	−0.260418
$125$	−1.00000	−0.0894427
$126$	9.77484	0.870812
$127$	7.92760	0.703461	0.351731	−	0.936101i	$-0.385593\pi$
$127$	7.92760	0.703461	0.351731	+	0.936101i	$0.385593\pi$
$128$	1.00000	0.0883883
$129$	−0.660058	−0.0581149
$130$	−3.03780	−0.266433
$131$	−21.5900	−1.88633	−0.943165	−	0.332326i	$-0.892167\pi$
$131$	−21.5900	−1.88633	−0.943165	+	0.332326i	$0.892167\pi$
$132$	0.200929	0.0174886
$133$	−4.11926	−0.357185
$134$	−3.68328	−0.318187
$135$	4.13572	0.355946
$136$	−0.160435	−0.0137572
$137$	−22.1080	−1.88881	−0.944405	−	0.328783i	$-0.893361\pi$
$137$	−22.1080	−1.88881	−0.944405	+	0.328783i	$0.893361\pi$
$138$	0	0
$139$	11.0960	0.941153	0.470576	−	0.882359i	$-0.344046\pi$
$139$	11.0960	0.941153	0.470576	+	0.882359i	$0.344046\pi$
$140$	4.04396	0.341777
$141$	9.94197	0.837265
$142$	−3.70176	−0.310645
$143$	0.799505	0.0668580
$144$	−2.41714	−0.201429
$145$	−5.02313	−0.417149
$146$	15.1829	1.25655
$147$	7.14103	0.588982
$148$	3.70669	0.304688
$149$	13.3212	1.09132	0.545658	−	0.838008i	$-0.316280\pi$
$149$	13.3212	1.09132	0.545658	+	0.838008i	$0.316280\pi$
$150$	0.763450	0.0623354
$151$	13.9154	1.13242	0.566208	−	0.824262i	$-0.308410\pi$
$151$	13.9154	1.13242	0.566208	+	0.824262i	$0.308410\pi$
$152$	1.01862	0.0826210
$153$	0.387795	0.0313513
$154$	−1.06431	−0.0857648
$155$	2.89990	0.232925
$156$	2.31921	0.185685
$157$	12.3195	0.983200	0.491600	−	0.870821i	$-0.336412\pi$
$157$	12.3195	0.983200	0.491600	+	0.870821i	$0.336412\pi$
$158$	−1.31107	−0.104303
$159$	−7.94058	−0.629729
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	4.09402	0.321656
$163$	16.8918	1.32307	0.661534	−	0.749915i	$-0.269906\pi$
$163$	16.8918	1.32307	0.661534	+	0.749915i	$0.269906\pi$
$164$	4.05754	0.316841
$165$	−0.200929	−0.0156423
$166$	16.3350	1.26784
$167$	−8.15918	−0.631376	−0.315688	−	0.948863i	$-0.602235\pi$
$167$	−8.15918	−0.631376	−0.315688	+	0.948863i	$0.602235\pi$
$168$	−3.08736	−0.238195
$169$	−3.77178	−0.290137
$170$	0.160435	0.0123048
$171$	−2.46215	−0.188286
$172$	−0.864573	−0.0659231
$173$	23.0755	1.75439	0.877197	−	0.480130i	$-0.159411\pi$
$173$	23.0755	1.75439	0.877197	+	0.480130i	$0.159411\pi$
$174$	3.83491	0.290724
$175$	−4.04396	−0.305695
$176$	0.263186	0.0198384
$177$	−1.50965	−0.113472
$178$	7.07268	0.530120
$179$	10.2075	0.762948	0.381474	−	0.924380i	$-0.375417\pi$
$179$	10.2075	0.762948	0.381474	+	0.924380i	$0.375417\pi$
$180$	2.41714	0.180163
$181$	−16.5373	−1.22921	−0.614603	−	0.788836i	$-0.710684\pi$
$181$	−16.5373	−1.22921	−0.614603	+	0.788836i	$0.710684\pi$
$182$	−12.2847	−0.910606
$183$	3.55506	0.262798
$184$	0	0
$185$	−3.70669	−0.272521
$186$	−2.21393	−0.162333
$187$	−0.0422242	−0.00308774
$188$	13.0224	0.949758
$189$	16.7247	1.21654
$190$	−1.01862	−0.0738985
$191$	17.0092	1.23075	0.615373	−	0.788236i	$-0.289006\pi$
$191$	17.0092	1.23075	0.615373	+	0.788236i	$0.289006\pi$
$192$	0.763450	0.0550973
$193$	9.67497	0.696420	0.348210	−	0.937417i	$-0.386790\pi$
$193$	9.67497	0.696420	0.348210	+	0.937417i	$0.386790\pi$
$194$	11.0101	0.790482
$195$	−2.31921	−0.166082
$196$	9.35363	0.668116
$197$	−15.3333	−1.09245	−0.546226	−	0.837638i	$-0.683936\pi$
$197$	−15.3333	−1.09245	−0.546226	+	0.837638i	$0.683936\pi$
$198$	−0.636158	−0.0452098
$199$	12.9687	0.919326	0.459663	−	0.888094i	$-0.347970\pi$
$199$	12.9687	0.919326	0.459663	+	0.888094i	$0.347970\pi$
$200$	1.00000	0.0707107
$201$	−2.81200	−0.198343
$202$	2.95966	0.208241
$203$	−20.3134	−1.42572
$204$	−0.122484	−0.00857560
$205$	−4.05754	−0.283391
$206$	−12.8902	−0.898103
$207$	0	0
$208$	3.03780	0.210633
$209$	0.268086	0.0185439
$210$	3.08736	0.213048
$211$	−26.8205	−1.84640	−0.923200	−	0.384320i	$-0.874436\pi$
$211$	−26.8205	−1.84640	−0.923200	+	0.384320i	$0.874436\pi$
$212$	−10.4009	−0.714337
$213$	−2.82611	−0.193642
$214$	11.7636	0.804145
$215$	0.864573	0.0589634
$216$	−4.13572	−0.281400
$217$	11.7271	0.796086
$218$	20.2232	1.36969
$219$	11.5914	0.783274
$220$	−0.263186	−0.0177440
$221$	−0.487369	−0.0327840
$222$	2.82987	0.189929
$223$	−12.7120	−0.851255	−0.425628	−	0.904898i	$-0.639947\pi$
$223$	−12.7120	−0.851255	−0.425628	+	0.904898i	$0.639947\pi$
$224$	−4.04396	−0.270199
$225$	−2.41714	−0.161143
$226$	−3.75557	−0.249817
$227$	3.82927	0.254158	0.127079	−	0.991893i	$-0.459440\pi$
$227$	3.82927	0.254158	0.127079	+	0.991893i	$0.459440\pi$
$228$	0.777666	0.0515022
$229$	12.2061	0.806603	0.403301	−	0.915067i	$-0.367863\pi$
$229$	12.2061	0.806603	0.403301	+	0.915067i	$0.367863\pi$
$230$	0	0
$231$	−0.812550	−0.0534619
$232$	5.02313	0.329785
$233$	−4.04669	−0.265107	−0.132554	−	0.991176i	$-0.542318\pi$
$233$	−4.04669	−0.265107	−0.132554	+	0.991176i	$0.542318\pi$
$234$	−7.34280	−0.480014
$235$	−13.0224	−0.849490
$236$	−1.97740	−0.128718
$237$	−1.00093	−0.0650176
$238$	0.648793	0.0420550
$239$	18.0922	1.17029	0.585144	−	0.810929i	$-0.301038\pi$
$239$	18.0922	1.17029	0.585144	+	0.810929i	$0.301038\pi$
$240$	−0.763450	−0.0492805
$241$	21.4065	1.37891	0.689456	−	0.724327i	$-0.257850\pi$
$241$	21.4065	1.37891	0.689456	+	0.724327i	$0.257850\pi$
$242$	−10.9307	−0.702654
$243$	15.5327	0.996425
$244$	4.65658	0.298107
$245$	−9.35363	−0.597581
$246$	3.09773	0.197504
$247$	3.09436	0.196890
$248$	−2.89990	−0.184144
$249$	12.4710	0.790316
$250$	−1.00000	−0.0632456
$251$	−12.9299	−0.816127	−0.408063	−	0.912954i	$-0.633796\pi$
$251$	−12.9299	−0.816127	−0.408063	+	0.912954i	$0.633796\pi$
$252$	9.77484	0.615757
$253$	0	0
$254$	7.92760	0.497422
$255$	0.122484	0.00767025
$256$	1.00000	0.0625000
$257$	29.8049	1.85918	0.929588	−	0.368600i	$-0.120163\pi$
$257$	29.8049	1.85918	0.929588	+	0.368600i	$0.120163\pi$
$258$	−0.660058	−0.0410934
$259$	−14.9897	−0.931416
$260$	−3.03780	−0.188396
$261$	−12.1416	−0.751549
$262$	−21.5900	−1.33384
$263$	−14.2899	−0.881152	−0.440576	−	0.897715i	$-0.645226\pi$
$263$	−14.2899	−0.881152	−0.440576	+	0.897715i	$0.645226\pi$
$264$	0.200929	0.0123663
$265$	10.4009	0.638923
$266$	−4.11926	−0.252568
$267$	5.39963	0.330452
$268$	−3.68328	−0.224992
$269$	−4.23028	−0.257925	−0.128962	−	0.991649i	$-0.541165\pi$
$269$	−4.23028	−0.257925	−0.128962	+	0.991649i	$0.541165\pi$
$270$	4.13572	0.251692
$271$	−29.0173	−1.76267	−0.881336	−	0.472490i	$-0.843355\pi$
$271$	−29.0173	−1.76267	−0.881336	+	0.472490i	$0.843355\pi$
$272$	−0.160435	−0.00972780
$273$	−9.37879	−0.567630
$274$	−22.1080	−1.33559
$275$	0.263186	0.0158707
$276$	0	0
$277$	4.71166	0.283096	0.141548	−	0.989931i	$-0.454792\pi$
$277$	4.71166	0.283096	0.141548	+	0.989931i	$0.454792\pi$
$278$	11.0960	0.665496
$279$	7.00947	0.419646
$280$	4.04396	0.241673
$281$	0.554821	0.0330978	0.0165489	−	0.999863i	$-0.494732\pi$
$281$	0.554821	0.0330978	0.0165489	+	0.999863i	$0.494732\pi$
$282$	9.94197	0.592036
$283$	−23.4019	−1.39110	−0.695550	−	0.718477i	$-0.744839\pi$
$283$	−23.4019	−1.39110	−0.695550	+	0.718477i	$0.744839\pi$
$284$	−3.70176	−0.219659
$285$	−0.777666	−0.0460650
$286$	0.799505	0.0472757
$287$	−16.4085	−0.968566
$288$	−2.41714	−0.142432
$289$	−16.9743	−0.998486
$290$	−5.02313	−0.294969
$291$	8.40570	0.492751
$292$	15.1829	0.888513
$293$	7.97196	0.465727	0.232863	−	0.972509i	$-0.425190\pi$
$293$	7.97196	0.465727	0.232863	+	0.972509i	$0.425190\pi$
$294$	7.14103	0.416473
$295$	1.97740	0.115129
$296$	3.70669	0.215447
$297$	−1.08846	−0.0631590
$298$	13.3212	0.771677
$299$	0	0
$300$	0.763450	0.0440778
$301$	3.49630	0.201523
$302$	13.9154	0.800739
$303$	2.25955	0.129808
$304$	1.01862	0.0584219
$305$	−4.65658	−0.266635
$306$	0.387795	0.0221687
$307$	−1.64712	−0.0940062	−0.0470031	−	0.998895i	$-0.514967\pi$
$307$	−1.64712	−0.0940062	−0.0470031	+	0.998895i	$0.514967\pi$
$308$	−1.06431	−0.0606449
$309$	−9.84103	−0.559836
$310$	2.89990	0.164703
$311$	−1.81687	−0.103025	−0.0515126	−	0.998672i	$-0.516404\pi$
$311$	−1.81687	−0.103025	−0.0515126	+	0.998672i	$0.516404\pi$
$312$	2.31921	0.131299
$313$	−9.70498	−0.548558	−0.274279	−	0.961650i	$-0.588439\pi$
$313$	−9.70498	−0.548558	−0.274279	+	0.961650i	$0.588439\pi$
$314$	12.3195	0.695228
$315$	−9.77484	−0.550750
$316$	−1.31107	−0.0737533
$317$	−12.5327	−0.703905	−0.351953	−	0.936018i	$-0.614482\pi$
$317$	−12.5327	−0.703905	−0.351953	+	0.936018i	$0.614482\pi$
$318$	−7.94058	−0.445285
$319$	1.32202	0.0740188
$320$	−1.00000	−0.0559017
$321$	8.98094	0.501267
$322$	0	0
$323$	−0.163422	−0.00909307
$324$	4.09402	0.227445
$325$	3.03780	0.168507
$326$	16.8918	0.935550
$327$	15.4394	0.853800
$328$	4.05754	0.224040
$329$	−52.6622	−2.90336
$330$	−0.200929	−0.0110608
$331$	−11.8808	−0.653030	−0.326515	−	0.945192i	$-0.605874\pi$
$331$	−11.8808	−0.653030	−0.326515	+	0.945192i	$0.605874\pi$
$332$	16.3350	0.896501
$333$	−8.95961	−0.490984
$334$	−8.15918	−0.446450
$335$	3.68328	0.201239
$336$	−3.08736	−0.168429
$337$	29.7753	1.62196	0.810981	−	0.585072i	$-0.198934\pi$
$337$	29.7753	1.62196	0.810981	+	0.585072i	$0.198934\pi$
$338$	−3.77178	−0.205158
$339$	−2.86719	−0.155724
$340$	0.160435	0.00870081
$341$	−0.763212	−0.0413302
$342$	−2.46215	−0.133138
$343$	−9.51799	−0.513923
$344$	−0.864573	−0.0466146
$345$	0	0
$346$	23.0755	1.24054
$347$	−7.62078	−0.409105	−0.204552	−	0.978856i	$-0.565574\pi$
$347$	−7.62078	−0.409105	−0.204552	+	0.978856i	$0.565574\pi$
$348$	3.83491	0.205573
$349$	−25.6224	−1.37153	−0.685767	−	0.727821i	$-0.740533\pi$
$349$	−25.6224	−1.37153	−0.685767	+	0.727821i	$0.740533\pi$
$350$	−4.04396	−0.216159
$351$	−12.5635	−0.670589
$352$	0.263186	0.0140278
$353$	−2.67221	−0.142227	−0.0711137	−	0.997468i	$-0.522655\pi$
$353$	−2.67221	−0.142227	−0.0711137	+	0.997468i	$0.522655\pi$
$354$	−1.50965	−0.0802369
$355$	3.70176	0.196469
$356$	7.07268	0.374851
$357$	0.495321	0.0262152
$358$	10.2075	0.539485
$359$	20.3146	1.07217	0.536083	−	0.844165i	$-0.319903\pi$
$359$	20.3146	1.07217	0.536083	+	0.844165i	$0.319903\pi$
$360$	2.41714	0.127395
$361$	−17.9624	−0.945390
$362$	−16.5373	−0.869180
$363$	−8.34507	−0.438002
$364$	−12.2847	−0.643896
$365$	−15.1829	−0.794710
$366$	3.55506	0.185826
$367$	4.23616	0.221126	0.110563	−	0.993869i	$-0.464735\pi$
$367$	4.23616	0.221126	0.110563	+	0.993869i	$0.464735\pi$
$368$	0	0
$369$	−9.80767	−0.510567
$370$	−3.70669	−0.192702
$371$	42.0609	2.18369
$372$	−2.21393	−0.114787
$373$	−13.0935	−0.677958	−0.338979	−	0.940794i	$-0.610081\pi$
$373$	−13.0935	−0.677958	−0.338979	+	0.940794i	$0.610081\pi$
$374$	−0.0422242	−0.00218336
$375$	−0.763450	−0.0394244
$376$	13.0224	0.671581
$377$	15.2593	0.785893
$378$	16.7247	0.860225
$379$	−21.2771	−1.09293	−0.546467	−	0.837481i	$-0.684028\pi$
$379$	−21.2771	−1.09293	−0.546467	+	0.837481i	$0.684028\pi$
$380$	−1.01862	−0.0522541
$381$	6.05233	0.310070
$382$	17.0092	0.870268
$383$	21.0749	1.07688	0.538440	−	0.842664i	$-0.319014\pi$
$383$	21.0749	1.07688	0.538440	+	0.842664i	$0.319014\pi$
$384$	0.763450	0.0389596
$385$	1.06431	0.0542424
$386$	9.67497	0.492443
$387$	2.08980	0.106230
$388$	11.0101	0.558955
$389$	1.00195	0.0508008	0.0254004	−	0.999677i	$-0.491914\pi$
$389$	1.00195	0.0508008	0.0254004	+	0.999677i	$0.491914\pi$
$390$	−2.31921	−0.117438
$391$	0	0
$392$	9.35363	0.472430
$393$	−16.4829	−0.831453
$394$	−15.3333	−0.772480
$395$	1.31107	0.0659669
$396$	−0.636158	−0.0319681
$397$	4.36494	0.219070	0.109535	−	0.993983i	$-0.465064\pi$
$397$	4.36494	0.219070	0.109535	+	0.993983i	$0.465064\pi$
$398$	12.9687	0.650061
$399$	−3.14485	−0.157439
$400$	1.00000	0.0500000
$401$	−15.3889	−0.768484	−0.384242	−	0.923232i	$-0.625537\pi$
$401$	−15.3889	−0.768484	−0.384242	+	0.923232i	$0.625537\pi$
$402$	−2.81200	−0.140250
$403$	−8.80931	−0.438823
$404$	2.95966	0.147249
$405$	−4.09402	−0.203433
$406$	−20.3134	−1.00814
$407$	0.975549	0.0483562
$408$	−0.122484	−0.00606387
$409$	−26.0589	−1.28853	−0.644264	−	0.764803i	$-0.722836\pi$
$409$	−26.0589	−1.28853	−0.644264	+	0.764803i	$0.722836\pi$
$410$	−4.05754	−0.200388
$411$	−16.8783	−0.832546
$412$	−12.8902	−0.635055
$413$	7.99655	0.393484
$414$	0	0
$415$	−16.3350	−0.801855
$416$	3.03780	0.148940
$417$	8.47126	0.414840
$418$	0.268086	0.0131125
$419$	−7.49818	−0.366310	−0.183155	−	0.983084i	$-0.558631\pi$
$419$	−7.49818	−0.366310	−0.183155	+	0.983084i	$0.558631\pi$
$420$	3.08736	0.150648
$421$	12.8968	0.628549	0.314275	−	0.949332i	$-0.398239\pi$
$421$	12.8968	0.628549	0.314275	+	0.949332i	$0.398239\pi$
$422$	−26.8205	−1.30560
$423$	−31.4771	−1.53047
$424$	−10.4009	−0.505113
$425$	−0.160435	−0.00778224
$426$	−2.82611	−0.136925
$427$	−18.8310	−0.911297
$428$	11.7636	0.568616
$429$	0.610382	0.0294695
$430$	0.864573	0.0416934
$431$	−14.6113	−0.703800	−0.351900	−	0.936038i	$-0.614464\pi$
$431$	−14.6113	−0.703800	−0.351900	+	0.936038i	$0.614464\pi$
$432$	−4.13572	−0.198980
$433$	−17.8665	−0.858608	−0.429304	−	0.903160i	$-0.641241\pi$
$433$	−17.8665	−0.858608	−0.429304	+	0.903160i	$0.641241\pi$
$434$	11.7271	0.562918
$435$	−3.83491	−0.183870
$436$	20.2232	0.968515
$437$	0	0
$438$	11.5914	0.553858
$439$	11.7567	0.561118	0.280559	−	0.959837i	$-0.409480\pi$
$439$	11.7567	0.561118	0.280559	+	0.959837i	$0.409480\pi$
$440$	−0.263186	−0.0125469
$441$	−22.6091	−1.07662
$442$	−0.487369	−0.0231818
$443$	12.4787	0.592882	0.296441	−	0.955051i	$-0.404200\pi$
$443$	12.4787	0.592882	0.296441	+	0.955051i	$0.404200\pi$
$444$	2.82987	0.134300
$445$	−7.07268	−0.335277
$446$	−12.7120	−0.601928
$447$	10.1701	0.481028
$448$	−4.04396	−0.191059
$449$	−26.5510	−1.25302	−0.626509	−	0.779415i	$-0.715517\pi$
$449$	−26.5510	−1.25302	−0.626509	+	0.779415i	$0.715517\pi$
$450$	−2.41714	−0.113945
$451$	1.06789	0.0502849
$452$	−3.75557	−0.176647
$453$	10.6237	0.499144
$454$	3.82927	0.179717
$455$	12.2847	0.575918
$456$	0.777666	0.0364175
$457$	−28.1662	−1.31756	−0.658779	−	0.752336i	$-0.728927\pi$
$457$	−28.1662	−1.31756	−0.658779	+	0.752336i	$0.728927\pi$
$458$	12.2061	0.570354
$459$	0.663514	0.0309702
$460$	0	0
$461$	−15.4429	−0.719246	−0.359623	−	0.933098i	$-0.617095\pi$
$461$	−15.4429	−0.719246	−0.359623	+	0.933098i	$0.617095\pi$
$462$	−0.812550	−0.0378032
$463$	−22.9706	−1.06753	−0.533766	−	0.845632i	$-0.679224\pi$
$463$	−22.9706	−1.06753	−0.533766	+	0.845632i	$0.679224\pi$
$464$	5.02313	0.233193
$465$	2.21393	0.102668
$466$	−4.04669	−0.187459
$467$	−10.1615	−0.470216	−0.235108	−	0.971969i	$-0.575544\pi$
$467$	−10.1615	−0.470216	−0.235108	+	0.971969i	$0.575544\pi$
$468$	−7.34280	−0.339421
$469$	14.8951	0.687790
$470$	−13.0224	−0.600680
$471$	9.40530	0.433373
$472$	−1.97740	−0.0910174
$473$	−0.227543	−0.0104624
$474$	−1.00093	−0.0459744
$475$	1.01862	0.0467375
$476$	0.648793	0.0297374
$477$	25.1405	1.15110
$478$	18.0922	0.827519
$479$	−17.0280	−0.778029	−0.389015	−	0.921232i	$-0.627184\pi$
$479$	−17.0280	−0.778029	−0.389015	+	0.921232i	$0.627184\pi$
$480$	−0.763450	−0.0348466
$481$	11.2602	0.513420
$482$	21.4065	0.975038
$483$	0	0
$484$	−10.9307	−0.496852
$485$	−11.0101	−0.499945
$486$	15.5327	0.704579
$487$	−12.9903	−0.588648	−0.294324	−	0.955706i	$-0.595095\pi$
$487$	−12.9903	−0.588648	−0.294324	+	0.955706i	$0.595095\pi$
$488$	4.65658	0.210793
$489$	12.8960	0.583179
$490$	−9.35363	−0.422554
$491$	37.7731	1.70468	0.852338	−	0.522991i	$-0.175184\pi$
$491$	37.7731	1.70468	0.852338	+	0.522991i	$0.175184\pi$
$492$	3.09773	0.139656
$493$	−0.805887	−0.0362953
$494$	3.09436	0.139222
$495$	0.636158	0.0285932
$496$	−2.89990	−0.130209
$497$	14.9698	0.671486
$498$	12.4710	0.558838
$499$	4.70969	0.210835	0.105417	−	0.994428i	$-0.466382\pi$
$499$	4.70969	0.210835	0.105417	+	0.994428i	$0.466382\pi$
$500$	−1.00000	−0.0447214
$501$	−6.22912	−0.278297
$502$	−12.9299	−0.577089
$503$	−21.7328	−0.969018	−0.484509	−	0.874786i	$-0.661002\pi$
$503$	−21.7328	−0.969018	−0.484509	+	0.874786i	$0.661002\pi$
$504$	9.77484	0.435406
$505$	−2.95966	−0.131703
$506$	0	0
$507$	−2.87956	−0.127886
$508$	7.92760	0.351731
$509$	14.4318	0.639677	0.319838	−	0.947472i	$-0.396371\pi$
$509$	14.4318	0.639677	0.319838	+	0.947472i	$0.396371\pi$
$510$	0.122484	0.00542369
$511$	−61.3991	−2.71614
$512$	1.00000	0.0441942
$513$	−4.21273	−0.185996
$514$	29.8049	1.31464
$515$	12.8902	0.568010
$516$	−0.660058	−0.0290574
$517$	3.42732	0.150733
$518$	−14.9897	−0.658611
$519$	17.6170	0.773299
$520$	−3.03780	−0.133216
$521$	−30.8008	−1.34941	−0.674703	−	0.738089i	$-0.735728\pi$
$521$	−30.8008	−1.34941	−0.674703	+	0.738089i	$0.735728\pi$
$522$	−12.1416	−0.531425
$523$	29.7962	1.30290	0.651448	−	0.758693i	$-0.274162\pi$
$523$	29.7962	1.30290	0.651448	+	0.758693i	$0.274162\pi$
$524$	−21.5900	−0.943165
$525$	−3.08736	−0.134744
$526$	−14.2899	−0.623069
$527$	0.465245	0.0202664
$528$	0.200929	0.00874432
$529$	0	0
$530$	10.4009	0.451787
$531$	4.77967	0.207420
$532$	−4.11926	−0.178593
$533$	12.3260	0.533898
$534$	5.39963	0.233665
$535$	−11.7636	−0.508586
$536$	−3.68328	−0.159094
$537$	7.79295	0.336291
$538$	−4.23028	−0.182380
$539$	2.46174	0.106035
$540$	4.13572	0.177973
$541$	43.1049	1.85323	0.926613	−	0.376017i	$-0.122707\pi$
$541$	43.1049	1.85323	0.926613	+	0.376017i	$0.122707\pi$
$542$	−29.0173	−1.24640
$543$	−12.6254	−0.541807
$544$	−0.160435	−0.00687859
$545$	−20.2232	−0.866266
$546$	−9.37879	−0.401375
$547$	30.9775	1.32450	0.662251	−	0.749282i	$-0.269601\pi$
$547$	30.9775	1.32450	0.662251	+	0.749282i	$0.269601\pi$
$548$	−22.1080	−0.944405
$549$	−11.2556	−0.480378
$550$	0.263186	0.0112223
$551$	5.11667	0.217977
$552$	0	0
$553$	5.30190	0.225460
$554$	4.71166	0.200179
$555$	−2.82987	−0.120121
$556$	11.0960	0.470576
$557$	13.4295	0.569026	0.284513	−	0.958672i	$-0.408168\pi$
$557$	13.4295	0.569026	0.284513	+	0.958672i	$0.408168\pi$
$558$	7.00947	0.296735
$559$	−2.62640	−0.111085
$560$	4.04396	0.170889
$561$	−0.0322361	−0.00136101
$562$	0.554821	0.0234037
$563$	−3.17253	−0.133706	−0.0668530	−	0.997763i	$-0.521296\pi$
$563$	−3.17253	−0.133706	−0.0668530	+	0.997763i	$0.521296\pi$
$564$	9.94197	0.418633
$565$	3.75557	0.157998
$566$	−23.4019	−0.983657
$567$	−16.5561	−0.695289
$568$	−3.70176	−0.155322
$569$	−1.92177	−0.0805649	−0.0402824	−	0.999188i	$-0.512826\pi$
$569$	−1.92177	−0.0805649	−0.0402824	+	0.999188i	$0.512826\pi$
$570$	−0.777666	−0.0325728
$571$	23.9224	1.00112	0.500560	−	0.865702i	$-0.333128\pi$
$571$	23.9224	1.00112	0.500560	+	0.865702i	$0.333128\pi$
$572$	0.799505	0.0334290
$573$	12.9857	0.542486
$574$	−16.4085	−0.684880
$575$	0	0
$576$	−2.41714	−0.100714
$577$	13.1121	0.545865	0.272933	−	0.962033i	$-0.412006\pi$
$577$	13.1121	0.545865	0.272933	+	0.962033i	$0.412006\pi$
$578$	−16.9743	−0.706036
$579$	7.38636	0.306967
$580$	−5.02313	−0.208574
$581$	−66.0582	−2.74056
$582$	8.40570	0.348427
$583$	−2.73737	−0.113370
$584$	15.1829	0.628273
$585$	7.34280	0.303587
$586$	7.97196	0.329319
$587$	9.59970	0.396222	0.198111	−	0.980180i	$-0.436519\pi$
$587$	9.59970	0.396222	0.198111	+	0.980180i	$0.436519\pi$
$588$	7.14103	0.294491
$589$	−2.95390	−0.121713
$590$	1.97740	0.0814084
$591$	−11.7062	−0.481529
$592$	3.70669	0.152344
$593$	36.5019	1.49895	0.749476	−	0.662032i	$-0.230306\pi$
$593$	36.5019	1.49895	0.749476	+	0.662032i	$0.230306\pi$
$594$	−1.08846	−0.0446601
$595$	−0.648793	−0.0265979
$596$	13.3212	0.545658
$597$	9.90094	0.405219
$598$	0	0
$599$	−36.1230	−1.47595	−0.737974	−	0.674829i	$-0.764217\pi$
$599$	−36.1230	−1.47595	−0.737974	+	0.674829i	$0.764217\pi$
$600$	0.763450	0.0311677
$601$	−4.76078	−0.194196	−0.0970982	−	0.995275i	$-0.530956\pi$
$601$	−4.76078	−0.194196	−0.0970982	+	0.995275i	$0.530956\pi$
$602$	3.49630	0.142499
$603$	8.90302	0.362559
$604$	13.9154	0.566208
$605$	10.9307	0.444398
$606$	2.25955	0.0917881
$607$	26.5399	1.07722	0.538611	−	0.842554i	$-0.318949\pi$
$607$	26.5399	1.07722	0.538611	+	0.842554i	$0.318949\pi$
$608$	1.01862	0.0413105
$609$	−15.5082	−0.628426
$610$	−4.65658	−0.188539
$611$	39.5595	1.60041
$612$	0.387795	0.0156757
$613$	42.5217	1.71744	0.858718	−	0.512448i	$-0.171261\pi$
$613$	42.5217	1.71744	0.858718	+	0.512448i	$0.171261\pi$
$614$	−1.64712	−0.0664724
$615$	−3.09773	−0.124913
$616$	−1.06431	−0.0428824
$617$	9.95930	0.400946	0.200473	−	0.979699i	$-0.435752\pi$
$617$	9.95930	0.400946	0.200473	+	0.979699i	$0.435752\pi$
$618$	−9.84103	−0.395864
$619$	0.0115130	0.000462746 0	0.000231373	−	1.00000i	$-0.499926\pi$
$619$	0.0115130	0.000462746 0	0.000231373		1.00000i	$0.499926\pi$
$620$	2.89990	0.116463
$621$	0	0
$622$	−1.81687	−0.0728498
$623$	−28.6016	−1.14590
$624$	2.31921	0.0928426
$625$	1.00000	0.0400000
$626$	−9.70498	−0.387889
$627$	0.204671	0.00817376
$628$	12.3195	0.491600
$629$	−0.594683	−0.0237116
$630$	−9.77484	−0.389439
$631$	15.4296	0.614242	0.307121	−	0.951671i	$-0.400634\pi$
$631$	15.4296	0.614242	0.307121	+	0.951671i	$0.400634\pi$
$632$	−1.31107	−0.0521514
$633$	−20.4761	−0.813852
$634$	−12.5327	−0.497736
$635$	−7.92760	−0.314597
$636$	−7.94058	−0.314864
$637$	28.4144	1.12582
$638$	1.32202	0.0523392
$639$	8.94769	0.353965
$640$	−1.00000	−0.0395285
$641$	35.3857	1.39765	0.698826	−	0.715292i	$-0.253706\pi$
$641$	35.3857	1.39765	0.698826	+	0.715292i	$0.253706\pi$
$642$	8.98094	0.354449
$643$	−12.0042	−0.473399	−0.236699	−	0.971583i	$-0.576066\pi$
$643$	−12.0042	−0.473399	−0.236699	+	0.971583i	$0.576066\pi$
$644$	0	0
$645$	0.660058	0.0259898
$646$	−0.163422	−0.00642977
$647$	−39.7487	−1.56268	−0.781341	−	0.624104i	$-0.785464\pi$
$647$	−39.7487	−1.56268	−0.781341	+	0.624104i	$0.785464\pi$
$648$	4.09402	0.160828
$649$	−0.520425	−0.0204284
$650$	3.03780	0.119152
$651$	8.95304	0.350897
$652$	16.8918	0.661534
$653$	14.4284	0.564626	0.282313	−	0.959322i	$-0.408898\pi$
$653$	14.4284	0.564626	0.282313	+	0.959322i	$0.408898\pi$
$654$	15.4394	0.603728
$655$	21.5900	0.843592
$656$	4.05754	0.158420
$657$	−36.6993	−1.43178
$658$	−52.6622	−2.05299
$659$	17.7542	0.691604	0.345802	−	0.938308i	$-0.387607\pi$
$659$	17.7542	0.691604	0.345802	+	0.938308i	$0.387607\pi$
$660$	−0.200929	−0.00782116
$661$	−12.5406	−0.487772	−0.243886	−	0.969804i	$-0.578422\pi$
$661$	−12.5406	−0.487772	−0.243886	+	0.969804i	$0.578422\pi$
$662$	−11.8808	−0.461762
$663$	−0.372082	−0.0144505
$664$	16.3350	0.633922
$665$	4.11926	0.159738
$666$	−8.95961	−0.347178
$667$	0	0
$668$	−8.15918	−0.315688
$669$	−9.70494	−0.375215
$670$	3.68328	0.142298
$671$	1.22555	0.0473116
$672$	−3.08736	−0.119098
$673$	−1.78711	−0.0688881	−0.0344441	−	0.999407i	$-0.510966\pi$
$673$	−1.78711	−0.0688881	−0.0344441	+	0.999407i	$0.510966\pi$
$674$	29.7753	1.14690
$675$	−4.13572	−0.159184
$676$	−3.77178	−0.145068
$677$	13.3070	0.511428	0.255714	−	0.966752i	$-0.417689\pi$
$677$	13.3070	0.511428	0.255714	+	0.966752i	$0.417689\pi$
$678$	−2.86719	−0.110114
$679$	−44.5246	−1.70870
$680$	0.160435	0.00615240
$681$	2.92346	0.112027
$682$	−0.763212	−0.0292249
$683$	4.48662	0.171676	0.0858379	−	0.996309i	$-0.472643\pi$
$683$	4.48662	0.171676	0.0858379	+	0.996309i	$0.472643\pi$
$684$	−2.46215	−0.0941428
$685$	22.1080	0.844702
$686$	−9.51799	−0.363398
$687$	9.31876	0.355533
$688$	−0.864573	−0.0329615
$689$	−31.5959	−1.20371
$690$	0	0
$691$	−14.4586	−0.550031	−0.275015	−	0.961440i	$-0.588683\pi$
$691$	−14.4586	−0.550031	−0.275015	+	0.961440i	$0.588683\pi$
$692$	23.0755	0.877197
$693$	2.57260	0.0977249
$694$	−7.62078	−0.289281
$695$	−11.0960	−0.420896
$696$	3.83491	0.145362
$697$	−0.650972	−0.0246573
$698$	−25.6224	−0.969821
$699$	−3.08944	−0.116853
$700$	−4.04396	−0.152847
$701$	−6.75245	−0.255037	−0.127518	−	0.991836i	$-0.540701\pi$
$701$	−6.75245	−0.255037	−0.127518	+	0.991836i	$0.540701\pi$
$702$	−12.5635	−0.474178
$703$	3.77571	0.142404
$704$	0.263186	0.00991919
$705$	−9.94197	−0.374436
$706$	−2.67221	−0.100570
$707$	−11.9688	−0.450131
$708$	−1.50965	−0.0567361
$709$	10.2002	0.383077	0.191538	−	0.981485i	$-0.438652\pi$
$709$	10.2002	0.383077	0.191538	+	0.981485i	$0.438652\pi$
$710$	3.70176	0.138925
$711$	3.16904	0.118848
$712$	7.07268	0.265060
$713$	0	0
$714$	0.495321	0.0185369
$715$	−0.799505	−0.0298998
$716$	10.2075	0.381474
$717$	13.8125	0.515837
$718$	20.3146	0.758136
$719$	−14.8189	−0.552653	−0.276326	−	0.961064i	$-0.589117\pi$
$719$	−14.8189	−0.552653	−0.276326	+	0.961064i	$0.589117\pi$
$720$	2.41714	0.0900816
$721$	52.1275	1.94133
$722$	−17.9624	−0.668492
$723$	16.3428	0.607794
$724$	−16.5373	−0.614603
$725$	5.02313	0.186555
$726$	−8.34507	−0.309715
$727$	44.4512	1.64860	0.824302	−	0.566151i	$-0.191568\pi$
$727$	44.4512	1.64860	0.824302	+	0.566151i	$0.191568\pi$
$728$	−12.2847	−0.455303
$729$	−0.423589	−0.0156885
$730$	−15.1829	−0.561945
$731$	0.138708	0.00513029
$732$	3.55506	0.131399
$733$	35.8089	1.32263	0.661315	−	0.750108i	$-0.269999\pi$
$733$	35.8089	1.32263	0.661315	+	0.750108i	$0.269999\pi$
$734$	4.23616	0.156360
$735$	−7.14103	−0.263401
$736$	0	0
$737$	−0.969387	−0.0357078
$738$	−9.80767	−0.361025
$739$	−9.56109	−0.351710	−0.175855	−	0.984416i	$-0.556269\pi$
$739$	−9.56109	−0.351710	−0.175855	+	0.984416i	$0.556269\pi$
$740$	−3.70669	−0.136261
$741$	2.36239	0.0867847
$742$	42.0609	1.54410
$743$	10.1938	0.373974	0.186987	−	0.982362i	$-0.440128\pi$
$743$	10.1938	0.373974	0.186987	+	0.982362i	$0.440128\pi$
$744$	−2.21393	−0.0811665
$745$	−13.3212	−0.488051
$746$	−13.0935	−0.479388
$747$	−39.4841	−1.44465
$748$	−0.0422242	−0.00154387
$749$	−47.5717	−1.73823
$750$	−0.763450	−0.0278773
$751$	−29.4088	−1.07314	−0.536571	−	0.843855i	$-0.680281\pi$
$751$	−29.4088	−1.07314	−0.536571	+	0.843855i	$0.680281\pi$
$752$	13.0224	0.474879
$753$	−9.87132	−0.359731
$754$	15.2593	0.555710
$755$	−13.9154	−0.506432
$756$	16.7247	0.608271
$757$	50.6071	1.83935	0.919673	−	0.392685i	$-0.128454\pi$
$757$	50.6071	1.83935	0.919673	+	0.392685i	$0.128454\pi$
$758$	−21.2771	−0.772821
$759$	0	0
$760$	−1.01862	−0.0369493
$761$	−1.59533	−0.0578305	−0.0289153	−	0.999582i	$-0.509205\pi$
$761$	−1.59533	−0.0578305	−0.0289153	+	0.999582i	$0.509205\pi$
$762$	6.05233	0.219253
$763$	−81.7818	−2.96070
$764$	17.0092	0.615373
$765$	−0.387795	−0.0140207
$766$	21.0749	0.761469
$767$	−6.00696	−0.216899
$768$	0.763450	0.0275486
$769$	38.5200	1.38907	0.694533	−	0.719461i	$-0.255611\pi$
$769$	38.5200	1.38907	0.694533	+	0.719461i	$0.255611\pi$
$770$	1.06431	0.0383552
$771$	22.7545	0.819484
$772$	9.67497	0.348210
$773$	−50.2153	−1.80612	−0.903059	−	0.429517i	$-0.858684\pi$
$773$	−50.2153	−1.80612	−0.903059	+	0.429517i	$0.858684\pi$
$774$	2.08980	0.0751162
$775$	−2.89990	−0.104167
$776$	11.0101	0.395241
$777$	−11.4439	−0.410548
$778$	1.00195	0.0359216
$779$	4.13310	0.148084
$780$	−2.31921	−0.0830410
$781$	−0.974251	−0.0348614
$782$	0	0
$783$	−20.7743	−0.742412
$784$	9.35363	0.334058
$785$	−12.3195	−0.439701
$786$	−16.4829	−0.587926
$787$	39.3478	1.40260	0.701299	−	0.712867i	$-0.252604\pi$
$787$	39.3478	1.40260	0.701299	+	0.712867i	$0.252604\pi$
$788$	−15.3333	−0.546226
$789$	−10.9096	−0.388393
$790$	1.31107	0.0466457
$791$	15.1874	0.540001
$792$	−0.636158	−0.0226049
$793$	14.1457	0.502330
$794$	4.36494	0.154906
$795$	7.94058	0.281623
$796$	12.9687	0.459663
$797$	52.5634	1.86189	0.930945	−	0.365159i	$-0.118986\pi$
$797$	52.5634	1.86189	0.930945	+	0.365159i	$0.118986\pi$
$798$	−3.14485	−0.111327
$799$	−2.08925	−0.0739125
$800$	1.00000	0.0353553
$801$	−17.0957	−0.604046
$802$	−15.3889	−0.543401
$803$	3.99593	0.141013
$804$	−2.81200	−0.0991716
$805$	0	0
$806$	−8.80931	−0.310295
$807$	−3.22961	−0.113688
$808$	2.95966	0.104121
$809$	39.5259	1.38966	0.694829	−	0.719175i	$-0.255480\pi$
$809$	39.5259	1.38966	0.694829	+	0.719175i	$0.255480\pi$
$810$	−4.09402	−0.143849
$811$	−18.6310	−0.654222	−0.327111	−	0.944986i	$-0.606075\pi$
$811$	−18.6310	−0.654222	−0.327111	+	0.944986i	$0.606075\pi$
$812$	−20.3134	−0.712859
$813$	−22.1532	−0.776947
$814$	0.975549	0.0341930
$815$	−16.8918	−0.591694
$816$	−0.122484	−0.00428780
$817$	−0.880672	−0.0308108
$818$	−26.0589	−0.911127
$819$	29.6940	1.03759
$820$	−4.05754	−0.141696
$821$	47.5135	1.65823	0.829116	−	0.559076i	$-0.188844\pi$
$821$	47.5135	1.65823	0.829116	+	0.559076i	$0.188844\pi$
$822$	−16.8783	−0.588699
$823$	16.1075	0.561473	0.280737	−	0.959785i	$-0.409421\pi$
$823$	16.1075	0.561473	0.280737	+	0.959785i	$0.409421\pi$
$824$	−12.8902	−0.449052
$825$	0.200929	0.00699546
$826$	7.99655	0.278235
$827$	10.7728	0.374606	0.187303	−	0.982302i	$-0.440025\pi$
$827$	10.7728	0.374606	0.187303	+	0.982302i	$0.440025\pi$
$828$	0	0
$829$	48.2185	1.67470	0.837349	−	0.546668i	$-0.184104\pi$
$829$	48.2185	1.67470	0.837349	+	0.546668i	$0.184104\pi$
$830$	−16.3350	−0.566997
$831$	3.59711	0.124782
$832$	3.03780	0.105317
$833$	−1.50065	−0.0519944
$834$	8.47126	0.293336
$835$	8.15918	0.282360
$836$	0.268086	0.00927196
$837$	11.9932	0.414544
$838$	−7.49818	−0.259020
$839$	19.4817	0.672584	0.336292	−	0.941758i	$-0.390827\pi$
$839$	19.4817	0.672584	0.336292	+	0.941758i	$0.390827\pi$
$840$	3.08736	0.106524
$841$	−3.76812	−0.129935
$842$	12.8968	0.444451
$843$	0.423578	0.0145888
$844$	−26.8205	−0.923200
$845$	3.77178	0.129753
$846$	−31.4771	−1.08220
$847$	44.2035	1.51885
$848$	−10.4009	−0.357169
$849$	−17.8662	−0.613167
$850$	−0.160435	−0.00550288
$851$	0	0
$852$	−2.82611	−0.0968209
$853$	−16.8339	−0.576381	−0.288191	−	0.957573i	$-0.593054\pi$
$853$	−16.8339	−0.576381	−0.288191	+	0.957573i	$0.593054\pi$
$854$	−18.8310	−0.644384
$855$	2.46215	0.0842039
$856$	11.7636	0.402072
$857$	5.62945	0.192298	0.0961492	−	0.995367i	$-0.469347\pi$
$857$	5.62945	0.192298	0.0961492	+	0.995367i	$0.469347\pi$
$858$	0.610382	0.0208381
$859$	−25.2359	−0.861038	−0.430519	−	0.902581i	$-0.641670\pi$
$859$	−25.2359	−0.861038	−0.430519	+	0.902581i	$0.641670\pi$
$860$	0.864573	0.0294817
$861$	−12.5271	−0.426923
$862$	−14.6113	−0.497662
$863$	−36.4519	−1.24084	−0.620418	−	0.784271i	$-0.713037\pi$
$863$	−36.4519	−1.24084	−0.620418	+	0.784271i	$0.713037\pi$
$864$	−4.13572	−0.140700
$865$	−23.0755	−0.784589
$866$	−17.8665	−0.607128
$867$	−12.9590	−0.440111
$868$	11.7271	0.398043
$869$	−0.345054	−0.0117052
$870$	−3.83491	−0.130016
$871$	−11.1891	−0.379127
$872$	20.2232	0.684843
$873$	−26.6131	−0.900717
$874$	0	0
$875$	4.04396	0.136711
$876$	11.5914	0.391637
$877$	−39.4294	−1.33144	−0.665718	−	0.746203i	$-0.731875\pi$
$877$	−39.4294	−1.33144	−0.665718	+	0.746203i	$0.731875\pi$
$878$	11.7567	0.396770
$879$	6.08619	0.205282
$880$	−0.263186	−0.00887199
$881$	−10.6013	−0.357167	−0.178583	−	0.983925i	$-0.557151\pi$
$881$	−10.6013	−0.357167	−0.178583	+	0.983925i	$0.557151\pi$
$882$	−22.6091	−0.761287
$883$	2.44823	0.0823894	0.0411947	−	0.999151i	$-0.486884\pi$
$883$	2.44823	0.0823894	0.0411947	+	0.999151i	$0.486884\pi$
$884$	−0.487369	−0.0163920
$885$	1.50965	0.0507463
$886$	12.4787	0.419231
$887$	−28.7720	−0.966070	−0.483035	−	0.875601i	$-0.660466\pi$
$887$	−28.7720	−0.966070	−0.483035	+	0.875601i	$0.660466\pi$
$888$	2.82987	0.0949644
$889$	−32.0589	−1.07522
$890$	−7.07268	−0.237077
$891$	1.07749	0.0360972
$892$	−12.7120	−0.425628
$893$	13.2649	0.443893
$894$	10.1701	0.340138
$895$	−10.2075	−0.341201
$896$	−4.04396	−0.135099
$897$	0	0
$898$	−26.5510	−0.886017
$899$	−14.5666	−0.485823
$900$	−2.41714	−0.0805715
$901$	1.66867	0.0555915
$902$	1.06789	0.0355568
$903$	2.66925	0.0888271
$904$	−3.75557	−0.124908
$905$	16.5373	0.549718
$906$	10.6237	0.352948
$907$	42.7353	1.41900	0.709501	−	0.704704i	$-0.248920\pi$
$907$	42.7353	1.41900	0.709501	+	0.704704i	$0.248920\pi$
$908$	3.82927	0.127079
$909$	−7.15393	−0.237281
$910$	12.2847	0.407235
$911$	20.1030	0.666043	0.333021	−	0.942919i	$-0.391932\pi$
$911$	20.1030	0.666043	0.333021	+	0.942919i	$0.391932\pi$
$912$	0.777666	0.0257511
$913$	4.29914	0.142281
$914$	−28.1662	−0.931655
$915$	−3.55506	−0.117527
$916$	12.2061	0.403301
$917$	87.3092	2.88321
$918$	0.663514	0.0218992
$919$	44.1667	1.45692	0.728462	−	0.685086i	$-0.240236\pi$
$919$	44.1667	1.45692	0.728462	+	0.685086i	$0.240236\pi$
$920$	0	0
$921$	−1.25749	−0.0414358
$922$	−15.4429	−0.508584
$923$	−11.2452	−0.370140
$924$	−0.812550	−0.0267309
$925$	3.70669	0.121875
$926$	−22.9706	−0.754860
$927$	31.1575	1.02335
$928$	5.02313	0.164892
$929$	−23.8478	−0.782422	−0.391211	−	0.920301i	$-0.627944\pi$
$929$	−23.8478	−0.782422	−0.391211	+	0.920301i	$0.627944\pi$
$930$	2.21393	0.0725975
$931$	9.52780	0.312261
$932$	−4.04669	−0.132554
$933$	−1.38709	−0.0454112
$934$	−10.1615	−0.332493
$935$	0.0422242	0.00138088
$936$	−7.34280	−0.240007
$937$	−31.2438	−1.02069	−0.510346	−	0.859969i	$-0.670483\pi$
$937$	−31.2438	−1.02069	−0.510346	+	0.859969i	$0.670483\pi$
$938$	14.8951	0.486341
$939$	−7.40927	−0.241792
$940$	−13.0224	−0.424745
$941$	34.7524	1.13290	0.566449	−	0.824097i	$-0.308317\pi$
$941$	34.7524	1.13290	0.566449	+	0.824097i	$0.308317\pi$
$942$	9.40530	0.306441
$943$	0	0
$944$	−1.97740	−0.0643590
$945$	−16.7247	−0.544054
$946$	−0.227543	−0.00739807
$947$	−9.78097	−0.317839	−0.158919	−	0.987292i	$-0.550801\pi$
$947$	−9.78097	−0.317839	−0.158919	+	0.987292i	$0.550801\pi$
$948$	−1.00093	−0.0325088
$949$	46.1226	1.49720
$950$	1.01862	0.0330484
$951$	−9.56807	−0.310266
$952$	0.648793	0.0210275
$953$	−58.8291	−1.90566	−0.952831	−	0.303502i	$-0.901844\pi$
$953$	−58.8291	−1.90566	−0.952831	+	0.303502i	$0.901844\pi$
$954$	25.1405	0.813954
$955$	−17.0092	−0.550406
$956$	18.0922	0.585144
$957$	1.00929	0.0326259
$958$	−17.0280	−0.550150
$959$	89.4038	2.88700
$960$	−0.763450	−0.0246402
$961$	−22.5906	−0.728729
$962$	11.2602	0.363043
$963$	−28.4344	−0.916285
$964$	21.4065	0.689456
$965$	−9.67497	−0.311448
$966$	0	0
$967$	−59.0770	−1.89979	−0.949894	−	0.312572i	$-0.898810\pi$
$967$	−59.0770	−1.89979	−0.949894	+	0.312572i	$0.898810\pi$
$968$	−10.9307	−0.351327
$969$	−0.124765	−0.00400802
$970$	−11.0101	−0.353514
$971$	−39.0388	−1.25281	−0.626407	−	0.779496i	$-0.715475\pi$
$971$	−39.0388	−1.25281	−0.626407	+	0.779496i	$0.715475\pi$
$972$	15.5327	0.498213
$973$	−44.8719	−1.43853
$974$	−12.9903	−0.416237
$975$	2.31921	0.0742741
$976$	4.65658	0.149053
$977$	−41.9880	−1.34331	−0.671657	−	0.740862i	$-0.734417\pi$
$977$	−41.9880	−1.34331	−0.671657	+	0.740862i	$0.734417\pi$
$978$	12.8960	0.412370
$979$	1.86143	0.0594915
$980$	−9.35363	−0.298791
$981$	−48.8823	−1.56069
$982$	37.7731	1.20539
$983$	−0.323090	−0.0103050	−0.00515248	−	0.999987i	$-0.501640\pi$
$983$	−0.323090	−0.0103050	−0.00515248	+	0.999987i	$0.501640\pi$
$984$	3.09773	0.0987521
$985$	15.3333	0.488559
$986$	−0.805887	−0.0256647
$987$	−40.2050	−1.27974
$988$	3.09436	0.0984449
$989$	0	0
$990$	0.636158	0.0202184
$991$	−36.6088	−1.16292	−0.581458	−	0.813576i	$-0.697518\pi$
$991$	−36.6088	−1.16292	−0.581458	+	0.813576i	$0.697518\pi$
$992$	−2.89990	−0.0920718
$993$	−9.07042	−0.287841
$994$	14.9698	0.474813
$995$	−12.9687	−0.411135
$996$	12.4710	0.395158
$997$	10.5207	0.333194	0.166597	−	0.986025i	$-0.446722\pi$
$997$	10.5207	0.333194	0.166597	+	0.986025i	$0.446722\pi$
$998$	4.70969	0.149083
$999$	−15.3298	−0.485015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bk.1.9		15
23.2	even	11		230.2.g.d.211.2	yes	30
23.12	even	11		230.2.g.d.121.2	✓	30
23.22	odd	2		5290.2.a.bl.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.121.2	✓	30	23.12	even	11
230.2.g.d.211.2	yes	30	23.2	even	11
5290.2.a.bk.1.9		15	1.1	even	1	trivial
5290.2.a.bl.1.9		15	23.22	odd	2

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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.763450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.763450 q^{6} -4.04396 q^{7} +1.00000 q^{8} -2.41714 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.763450 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.763450 q^{6} -4.04396 q^{7} +1.00000 q^{8} -2.41714 q^{9} -1.00000 q^{10} +0.263186 q^{11} +0.763450 q^{12} +3.03780 q^{13} -4.04396 q^{14} -0.763450 q^{15} +1.00000 q^{16} -0.160435 q^{17} -2.41714 q^{18} +1.01862 q^{19} -1.00000 q^{20} -3.08736 q^{21} +0.263186 q^{22} +0.763450 q^{24} +1.00000 q^{25} +3.03780 q^{26} -4.13572 q^{27} -4.04396 q^{28} +5.02313 q^{29} -0.763450 q^{30} -2.89990 q^{31} +1.00000 q^{32} +0.200929 q^{33} -0.160435 q^{34} +4.04396 q^{35} -2.41714 q^{36} +3.70669 q^{37} +1.01862 q^{38} +2.31921 q^{39} -1.00000 q^{40} +4.05754 q^{41} -3.08736 q^{42} -0.864573 q^{43} +0.263186 q^{44} +2.41714 q^{45} +13.0224 q^{47} +0.763450 q^{48} +9.35363 q^{49} +1.00000 q^{50} -0.122484 q^{51} +3.03780 q^{52} -10.4009 q^{53} -4.13572 q^{54} -0.263186 q^{55} -4.04396 q^{56} +0.777666 q^{57} +5.02313 q^{58} -1.97740 q^{59} -0.763450 q^{60} +4.65658 q^{61} -2.89990 q^{62} +9.77484 q^{63} +1.00000 q^{64} -3.03780 q^{65} +0.200929 q^{66} -3.68328 q^{67} -0.160435 q^{68} +4.04396 q^{70} -3.70176 q^{71} -2.41714 q^{72} +15.1829 q^{73} +3.70669 q^{74} +0.763450 q^{75} +1.01862 q^{76} -1.06431 q^{77} +2.31921 q^{78} -1.31107 q^{79} -1.00000 q^{80} +4.09402 q^{81} +4.05754 q^{82} +16.3350 q^{83} -3.08736 q^{84} +0.160435 q^{85} -0.864573 q^{86} +3.83491 q^{87} +0.263186 q^{88} +7.07268 q^{89} +2.41714 q^{90} -12.2847 q^{91} -2.21393 q^{93} +13.0224 q^{94} -1.01862 q^{95} +0.763450 q^{96} +11.0101 q^{97} +9.35363 q^{98} -0.636158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * q^99

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