LMFDB - Embedded newform 9282.2.a.ce.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 23x^{5} + 70x^{4} + 115x^{3} - 422x^{2} + 118x + 208 $ x^7 - 3x^6 - 23x^5 + 70x^4 + 115x^3 - 422x^2 + 118x + 208
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.10233$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.10233 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.10233 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.10233 q^{10} -4.99240 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -3.10233 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -3.54327 q^{19} -3.10233 q^{20} -1.00000 q^{21} -4.99240 q^{22} +7.35108 q^{23} +1.00000 q^{24} +4.62448 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.98625 q^{29} -3.10233 q^{30} -4.66140 q^{31} +1.00000 q^{32} -4.99240 q^{33} +1.00000 q^{34} +3.10233 q^{35} +1.00000 q^{36} +6.36814 q^{37} -3.54327 q^{38} -1.00000 q^{39} -3.10233 q^{40} -0.0654124 q^{41} -1.00000 q^{42} +0.192192 q^{43} -4.99240 q^{44} -3.10233 q^{45} +7.35108 q^{46} -10.1599 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.62448 q^{50} +1.00000 q^{51} -1.00000 q^{52} +12.1770 q^{53} +1.00000 q^{54} +15.4881 q^{55} -1.00000 q^{56} -3.54327 q^{57} -1.98625 q^{58} -8.24241 q^{59} -3.10233 q^{60} +6.49723 q^{61} -4.66140 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.10233 q^{65} -4.99240 q^{66} +0.608207 q^{67} +1.00000 q^{68} +7.35108 q^{69} +3.10233 q^{70} -1.33610 q^{71} +1.00000 q^{72} +6.85900 q^{73} +6.36814 q^{74} +4.62448 q^{75} -3.54327 q^{76} +4.99240 q^{77} -1.00000 q^{78} +0.327645 q^{79} -3.10233 q^{80} +1.00000 q^{81} -0.0654124 q^{82} +4.36177 q^{83} -1.00000 q^{84} -3.10233 q^{85} +0.192192 q^{86} -1.98625 q^{87} -4.99240 q^{88} -7.33502 q^{89} -3.10233 q^{90} +1.00000 q^{91} +7.35108 q^{92} -4.66140 q^{93} -10.1599 q^{94} +10.9924 q^{95} +1.00000 q^{96} -1.90124 q^{97} +1.00000 q^{98} -4.99240 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 7 q^{13} - 7 q^{14} + 3 q^{15} + 7 q^{16} + 7 q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 7 q^{22} + 12 q^{23} + 7 q^{24} + 20 q^{25} - 7 q^{26} + 7 q^{27} - 7 q^{28} + 18 q^{29} + 3 q^{30} - 6 q^{31} + 7 q^{32} + 7 q^{33} + 7 q^{34} - 3 q^{35} + 7 q^{36} + 5 q^{37} - 2 q^{38} - 7 q^{39} + 3 q^{40} + 10 q^{41} - 7 q^{42} + 18 q^{43} + 7 q^{44} + 3 q^{45} + 12 q^{46} + 3 q^{47} + 7 q^{48} + 7 q^{49} + 20 q^{50} + 7 q^{51} - 7 q^{52} + 18 q^{53} + 7 q^{54} + 4 q^{55} - 7 q^{56} - 2 q^{57} + 18 q^{58} + 20 q^{59} + 3 q^{60} + 19 q^{61} - 6 q^{62} - 7 q^{63} + 7 q^{64} - 3 q^{65} + 7 q^{66} - 16 q^{67} + 7 q^{68} + 12 q^{69} - 3 q^{70} + 5 q^{71} + 7 q^{72} + 2 q^{73} + 5 q^{74} + 20 q^{75} - 2 q^{76} - 7 q^{77} - 7 q^{78} + 12 q^{79} + 3 q^{80} + 7 q^{81} + 10 q^{82} + 11 q^{83} - 7 q^{84} + 3 q^{85} + 18 q^{86} + 18 q^{87} + 7 q^{88} + 6 q^{89} + 3 q^{90} + 7 q^{91} + 12 q^{92} - 6 q^{93} + 3 q^{94} + 35 q^{95} + 7 q^{96} - 3 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 7 * q^13 - 7 * q^14 + 3 * q^15 + 7 * q^16 + 7 * q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 7 * q^22 + 12 * q^23 + 7 * q^24 + 20 * q^25 - 7 * q^26 + 7 * q^27 - 7 * q^28 + 18 * q^29 + 3 * q^30 - 6 * q^31 + 7 * q^32 + 7 * q^33 + 7 * q^34 - 3 * q^35 + 7 * q^36 + 5 * q^37 - 2 * q^38 - 7 * q^39 + 3 * q^40 + 10 * q^41 - 7 * q^42 + 18 * q^43 + 7 * q^44 + 3 * q^45 + 12 * q^46 + 3 * q^47 + 7 * q^48 + 7 * q^49 + 20 * q^50 + 7 * q^51 - 7 * q^52 + 18 * q^53 + 7 * q^54 + 4 * q^55 - 7 * q^56 - 2 * q^57 + 18 * q^58 + 20 * q^59 + 3 * q^60 + 19 * q^61 - 6 * q^62 - 7 * q^63 + 7 * q^64 - 3 * q^65 + 7 * q^66 - 16 * q^67 + 7 * q^68 + 12 * q^69 - 3 * q^70 + 5 * q^71 + 7 * q^72 + 2 * q^73 + 5 * q^74 + 20 * q^75 - 2 * q^76 - 7 * q^77 - 7 * q^78 + 12 * q^79 + 3 * q^80 + 7 * q^81 + 10 * q^82 + 11 * q^83 - 7 * q^84 + 3 * q^85 + 18 * q^86 + 18 * q^87 + 7 * q^88 + 6 * q^89 + 3 * q^90 + 7 * q^91 + 12 * q^92 - 6 * q^93 + 3 * q^94 + 35 * q^95 + 7 * q^96 - 3 * q^97 + 7 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.10233	−1.38741	−0.693703	−	0.720261i	$-0.744022\pi$
$5$	−3.10233	−1.38741	−0.693703	+	0.720261i	$0.744022\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.10233	−0.981044
$11$	−4.99240	−1.50527	−0.752633	−	0.658440i	$-0.771216\pi$
$11$	−4.99240	−1.50527	−0.752633	+	0.658440i	$0.771216\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	−3.10233	−0.801019
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−3.54327	−0.812881	−0.406441	−	0.913677i	$-0.633230\pi$
$19$	−3.54327	−0.812881	−0.406441	+	0.913677i	$0.633230\pi$
$20$	−3.10233	−0.693703
$21$	−1.00000	−0.218218
$22$	−4.99240	−1.06438
$23$	7.35108	1.53281	0.766403	−	0.642361i	$-0.222045\pi$
$23$	7.35108	1.53281	0.766403	+	0.642361i	$0.222045\pi$
$24$	1.00000	0.204124
$25$	4.62448	0.924896
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−1.98625	−0.368838	−0.184419	−	0.982848i	$-0.559040\pi$
$29$	−1.98625	−0.368838	−0.184419	+	0.982848i	$0.559040\pi$
$30$	−3.10233	−0.566406
$31$	−4.66140	−0.837212	−0.418606	−	0.908168i	$-0.637481\pi$
$31$	−4.66140	−0.837212	−0.418606	+	0.908168i	$0.637481\pi$
$32$	1.00000	0.176777
$33$	−4.99240	−0.869065
$34$	1.00000	0.171499
$35$	3.10233	0.524390
$36$	1.00000	0.166667
$37$	6.36814	1.04692	0.523458	−	0.852052i	$-0.324642\pi$
$37$	6.36814	1.04692	0.523458	+	0.852052i	$0.324642\pi$
$38$	−3.54327	−0.574794
$39$	−1.00000	−0.160128
$40$	−3.10233	−0.490522
$41$	−0.0654124	−0.0102157	−0.00510785	−	0.999987i	$-0.501626\pi$
$41$	−0.0654124	−0.0102157	−0.00510785	+	0.999987i	$0.501626\pi$
$42$	−1.00000	−0.154303
$43$	0.192192	0.0293090	0.0146545	−	0.999893i	$-0.495335\pi$
$43$	0.192192	0.0293090	0.0146545	+	0.999893i	$0.495335\pi$
$44$	−4.99240	−0.752633
$45$	−3.10233	−0.462469
$46$	7.35108	1.08386
$47$	−10.1599	−1.48197	−0.740986	−	0.671520i	$-0.765642\pi$
$47$	−10.1599	−1.48197	−0.740986	+	0.671520i	$0.765642\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.62448	0.654000
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	12.1770	1.67264	0.836319	−	0.548242i	$-0.184703\pi$
$53$	12.1770	1.67264	0.836319	+	0.548242i	$0.184703\pi$
$54$	1.00000	0.136083
$55$	15.4881	2.08841
$56$	−1.00000	−0.133631
$57$	−3.54327	−0.469317
$58$	−1.98625	−0.260808
$59$	−8.24241	−1.07307	−0.536535	−	0.843878i	$-0.680267\pi$
$59$	−8.24241	−1.07307	−0.536535	+	0.843878i	$0.680267\pi$
$60$	−3.10233	−0.400510
$61$	6.49723	0.831885	0.415942	−	0.909391i	$-0.363452\pi$
$61$	6.49723	0.831885	0.415942	+	0.909391i	$0.363452\pi$
$62$	−4.66140	−0.591999
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.10233	0.384797
$66$	−4.99240	−0.614522
$67$	0.608207	0.0743043	0.0371522	−	0.999310i	$-0.488171\pi$
$67$	0.608207	0.0743043	0.0371522	+	0.999310i	$0.488171\pi$
$68$	1.00000	0.121268
$69$	7.35108	0.884965
$70$	3.10233	0.370800
$71$	−1.33610	−0.158566	−0.0792830	−	0.996852i	$-0.525263\pi$
$71$	−1.33610	−0.158566	−0.0792830	+	0.996852i	$0.525263\pi$
$72$	1.00000	0.117851
$73$	6.85900	0.802785	0.401393	−	0.915906i	$-0.368526\pi$
$73$	6.85900	0.802785	0.401393	+	0.915906i	$0.368526\pi$
$74$	6.36814	0.740281
$75$	4.62448	0.533989
$76$	−3.54327	−0.406441
$77$	4.99240	0.568937
$78$	−1.00000	−0.113228
$79$	0.327645	0.0368630	0.0184315	−	0.999830i	$-0.494133\pi$
$79$	0.327645	0.0368630	0.0184315	+	0.999830i	$0.494133\pi$
$80$	−3.10233	−0.346852
$81$	1.00000	0.111111
$82$	−0.0654124	−0.00722359
$83$	4.36177	0.478767	0.239383	−	0.970925i	$-0.423055\pi$
$83$	4.36177	0.478767	0.239383	+	0.970925i	$0.423055\pi$
$84$	−1.00000	−0.109109
$85$	−3.10233	−0.336495
$86$	0.192192	0.0207246
$87$	−1.98625	−0.212949
$88$	−4.99240	−0.532192
$89$	−7.33502	−0.777511	−0.388755	−	0.921341i	$-0.627095\pi$
$89$	−7.33502	−0.777511	−0.388755	+	0.921341i	$0.627095\pi$
$90$	−3.10233	−0.327015
$91$	1.00000	0.104828
$92$	7.35108	0.766403
$93$	−4.66140	−0.483365
$94$	−10.1599	−1.04791
$95$	10.9924	1.12780
$96$	1.00000	0.102062
$97$	−1.90124	−0.193041	−0.0965207	−	0.995331i	$-0.530771\pi$
$97$	−1.90124	−0.193041	−0.0965207	+	0.995331i	$0.530771\pi$
$98$	1.00000	0.101015
$99$	−4.99240	−0.501755
$100$	4.62448	0.462448
$101$	12.8473	1.27835	0.639175	−	0.769061i	$-0.279276\pi$
$101$	12.8473	1.27835	0.639175	+	0.769061i	$0.279276\pi$
$102$	1.00000	0.0990148
$103$	2.03509	0.200523	0.100262	−	0.994961i	$-0.468032\pi$
$103$	2.03509	0.200523	0.100262	+	0.994961i	$0.468032\pi$
$104$	−1.00000	−0.0980581
$105$	3.10233	0.302757
$106$	12.1770	1.18273
$107$	4.44324	0.429544	0.214772	−	0.976664i	$-0.431099\pi$
$107$	4.44324	0.429544	0.214772	+	0.976664i	$0.431099\pi$
$108$	1.00000	0.0962250
$109$	18.8387	1.80442	0.902208	−	0.431302i	$-0.141946\pi$
$109$	18.8387	1.80442	0.902208	+	0.431302i	$0.141946\pi$
$110$	15.4881	1.47673
$111$	6.36814	0.604437
$112$	−1.00000	−0.0944911
$113$	−2.04049	−0.191954	−0.0959768	−	0.995384i	$-0.530597\pi$
$113$	−2.04049	−0.191954	−0.0959768	+	0.995384i	$0.530597\pi$
$114$	−3.54327	−0.331857
$115$	−22.8055	−2.12662
$116$	−1.98625	−0.184419
$117$	−1.00000	−0.0924500
$118$	−8.24241	−0.758775
$119$	−1.00000	−0.0916698
$120$	−3.10233	−0.283203
$121$	13.9241	1.26582
$122$	6.49723	0.588231
$123$	−0.0654124	−0.00589804
$124$	−4.66140	−0.418606
$125$	1.16499	0.104200
$126$	−1.00000	−0.0890871
$127$	1.88697	0.167441	0.0837206	−	0.996489i	$-0.473320\pi$
$127$	1.88697	0.167441	0.0837206	+	0.996489i	$0.473320\pi$
$128$	1.00000	0.0883883
$129$	0.192192	0.0169216
$130$	3.10233	0.272093
$131$	20.5793	1.79802	0.899009	−	0.437930i	$-0.144288\pi$
$131$	20.5793	1.79802	0.899009	+	0.437930i	$0.144288\pi$
$132$	−4.99240	−0.434533
$133$	3.54327	0.307240
$134$	0.608207	0.0525411
$135$	−3.10233	−0.267006
$136$	1.00000	0.0857493
$137$	4.42641	0.378174	0.189087	−	0.981960i	$-0.439447\pi$
$137$	4.42641	0.378174	0.189087	+	0.981960i	$0.439447\pi$
$138$	7.35108	0.625765
$139$	−2.19760	−0.186398	−0.0931989	−	0.995648i	$-0.529709\pi$
$139$	−2.19760	−0.186398	−0.0931989	+	0.995648i	$0.529709\pi$
$140$	3.10233	0.262195
$141$	−10.1599	−0.855617
$142$	−1.33610	−0.112123
$143$	4.99240	0.417486
$144$	1.00000	0.0833333
$145$	6.16202	0.511728
$146$	6.85900	0.567655
$147$	1.00000	0.0824786
$148$	6.36814	0.523458
$149$	−12.0978	−0.991093	−0.495547	−	0.868581i	$-0.665032\pi$
$149$	−12.0978	−0.991093	−0.495547	+	0.868581i	$0.665032\pi$
$150$	4.62448	0.377587
$151$	−6.32817	−0.514979	−0.257490	−	0.966281i	$-0.582895\pi$
$151$	−6.32817	−0.514979	−0.257490	+	0.966281i	$0.582895\pi$
$152$	−3.54327	−0.287397
$153$	1.00000	0.0808452
$154$	4.99240	0.402299
$155$	14.4612	1.16155
$156$	−1.00000	−0.0800641
$157$	−3.03770	−0.242435	−0.121217	−	0.992626i	$-0.538680\pi$
$157$	−3.03770	−0.242435	−0.121217	+	0.992626i	$0.538680\pi$
$158$	0.327645	0.0260661
$159$	12.1770	0.965698
$160$	−3.10233	−0.245261
$161$	−7.35108	−0.579346
$162$	1.00000	0.0785674
$163$	4.39891	0.344549	0.172275	−	0.985049i	$-0.444888\pi$
$163$	4.39891	0.344549	0.172275	+	0.985049i	$0.444888\pi$
$164$	−0.0654124	−0.00510785
$165$	15.4881	1.20575
$166$	4.36177	0.338539
$167$	7.34309	0.568226	0.284113	−	0.958791i	$-0.408301\pi$
$167$	7.34309	0.568226	0.284113	+	0.958791i	$0.408301\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	−3.10233	−0.237938
$171$	−3.54327	−0.270960
$172$	0.192192	0.0146545
$173$	−15.6520	−1.19000	−0.595000	−	0.803725i	$-0.702848\pi$
$173$	−15.6520	−1.19000	−0.595000	+	0.803725i	$0.702848\pi$
$174$	−1.98625	−0.150577
$175$	−4.62448	−0.349578
$176$	−4.99240	−0.376316
$177$	−8.24241	−0.619537
$178$	−7.33502	−0.549783
$179$	−1.80480	−0.134897	−0.0674484	−	0.997723i	$-0.521486\pi$
$179$	−1.80480	−0.134897	−0.0674484	+	0.997723i	$0.521486\pi$
$180$	−3.10233	−0.231234
$181$	23.1665	1.72195	0.860975	−	0.508647i	$-0.169854\pi$
$181$	23.1665	1.72195	0.860975	+	0.508647i	$0.169854\pi$
$182$	1.00000	0.0741249
$183$	6.49723	0.480289
$184$	7.35108	0.541928
$185$	−19.7561	−1.45250
$186$	−4.66140	−0.341791
$187$	−4.99240	−0.365081
$188$	−10.1599	−0.740986
$189$	−1.00000	−0.0727393
$190$	10.9924	0.797473
$191$	8.81138	0.637569	0.318785	−	0.947827i	$-0.396725\pi$
$191$	8.81138	0.637569	0.318785	+	0.947827i	$0.396725\pi$
$192$	1.00000	0.0721688
$193$	20.3976	1.46825	0.734127	−	0.679012i	$-0.237592\pi$
$193$	20.3976	1.46825	0.734127	+	0.679012i	$0.237592\pi$
$194$	−1.90124	−0.136501
$195$	3.10233	0.222163
$196$	1.00000	0.0714286
$197$	13.6105	0.969706	0.484853	−	0.874596i	$-0.338873\pi$
$197$	13.6105	0.969706	0.484853	+	0.874596i	$0.338873\pi$
$198$	−4.99240	−0.354795
$199$	−4.47978	−0.317563	−0.158782	−	0.987314i	$-0.550757\pi$
$199$	−4.47978	−0.317563	−0.158782	+	0.987314i	$0.550757\pi$
$200$	4.62448	0.327000
$201$	0.608207	0.0428996
$202$	12.8473	0.903930
$203$	1.98625	0.139408
$204$	1.00000	0.0700140
$205$	0.202931	0.0141733
$206$	2.03509	0.141791
$207$	7.35108	0.510935
$208$	−1.00000	−0.0693375
$209$	17.6894	1.22360
$210$	3.10233	0.214081
$211$	7.50132	0.516412	0.258206	−	0.966090i	$-0.416869\pi$
$211$	7.50132	0.516412	0.258206	+	0.966090i	$0.416869\pi$
$212$	12.1770	0.836319
$213$	−1.33610	−0.0915481
$214$	4.44324	0.303734
$215$	−0.596244	−0.0406635
$216$	1.00000	0.0680414
$217$	4.66140	0.316437
$218$	18.8387	1.27591
$219$	6.85900	0.463488
$220$	15.4881	1.04421
$221$	−1.00000	−0.0672673
$222$	6.36814	0.427402
$223$	−3.99822	−0.267740	−0.133870	−	0.990999i	$-0.542741\pi$
$223$	−3.99822	−0.267740	−0.133870	+	0.990999i	$0.542741\pi$
$224$	−1.00000	−0.0668153
$225$	4.62448	0.308299
$226$	−2.04049	−0.135732
$227$	−3.79856	−0.252120	−0.126060	−	0.992023i	$-0.540233\pi$
$227$	−3.79856	−0.252120	−0.126060	+	0.992023i	$0.540233\pi$
$228$	−3.54327	−0.234659
$229$	24.3283	1.60766	0.803829	−	0.594860i	$-0.202793\pi$
$229$	24.3283	1.60766	0.803829	+	0.594860i	$0.202793\pi$
$230$	−22.8055	−1.50375
$231$	4.99240	0.328476
$232$	−1.98625	−0.130404
$233$	−1.38293	−0.0905987	−0.0452994	−	0.998973i	$-0.514424\pi$
$233$	−1.38293	−0.0905987	−0.0452994	+	0.998973i	$0.514424\pi$
$234$	−1.00000	−0.0653720
$235$	31.5194	2.05610
$236$	−8.24241	−0.536535
$237$	0.327645	0.0212829
$238$	−1.00000	−0.0648204
$239$	−12.1798	−0.787843	−0.393921	−	0.919144i	$-0.628882\pi$
$239$	−12.1798	−0.787843	−0.393921	+	0.919144i	$0.628882\pi$
$240$	−3.10233	−0.200255
$241$	24.8042	1.59778	0.798890	−	0.601477i	$-0.205421\pi$
$241$	24.8042	1.59778	0.798890	+	0.601477i	$0.205421\pi$
$242$	13.9241	0.895073
$243$	1.00000	0.0641500
$244$	6.49723	0.415942
$245$	−3.10233	−0.198201
$246$	−0.0654124	−0.00417054
$247$	3.54327	0.225453
$248$	−4.66140	−0.295999
$249$	4.36177	0.276416
$250$	1.16499	0.0736805
$251$	−16.7069	−1.05453	−0.527264	−	0.849702i	$-0.676782\pi$
$251$	−16.7069	−1.05453	−0.527264	+	0.849702i	$0.676782\pi$
$252$	−1.00000	−0.0629941
$253$	−36.6995	−2.30728
$254$	1.88697	0.118399
$255$	−3.10233	−0.194276
$256$	1.00000	0.0625000
$257$	25.0352	1.56165	0.780827	−	0.624748i	$-0.214798\pi$
$257$	25.0352	1.56165	0.780827	+	0.624748i	$0.214798\pi$
$258$	0.192192	0.0119654
$259$	−6.36814	−0.395697
$260$	3.10233	0.192399
$261$	−1.98625	−0.122946
$262$	20.5793	1.27139
$263$	−20.7897	−1.28195	−0.640974	−	0.767563i	$-0.721469\pi$
$263$	−20.7897	−1.28195	−0.640974	+	0.767563i	$0.721469\pi$
$264$	−4.99240	−0.307261
$265$	−37.7771	−2.32063
$266$	3.54327	0.217252
$267$	−7.33502	−0.448896
$268$	0.608207	0.0371522
$269$	17.2748	1.05326	0.526632	−	0.850093i	$-0.323454\pi$
$269$	17.2748	1.05326	0.526632	+	0.850093i	$0.323454\pi$
$270$	−3.10233	−0.188802
$271$	20.4914	1.24476	0.622382	−	0.782713i	$-0.286165\pi$
$271$	20.4914	1.24476	0.622382	+	0.782713i	$0.286165\pi$
$272$	1.00000	0.0606339
$273$	1.00000	0.0605228
$274$	4.42641	0.267409
$275$	−23.0873	−1.39221
$276$	7.35108	0.442483
$277$	19.9899	1.20108	0.600538	−	0.799596i	$-0.294953\pi$
$277$	19.9899	1.20108	0.600538	+	0.799596i	$0.294953\pi$
$278$	−2.19760	−0.131803
$279$	−4.66140	−0.279071
$280$	3.10233	0.185400
$281$	4.03438	0.240671	0.120336	−	0.992733i	$-0.461603\pi$
$281$	4.03438	0.240671	0.120336	+	0.992733i	$0.461603\pi$
$282$	−10.1599	−0.605013
$283$	6.65342	0.395505	0.197752	−	0.980252i	$-0.436636\pi$
$283$	6.65342	0.395505	0.197752	+	0.980252i	$0.436636\pi$
$284$	−1.33610	−0.0792830
$285$	10.9924	0.651134
$286$	4.99240	0.295207
$287$	0.0654124	0.00386117
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	6.16202	0.361846
$291$	−1.90124	−0.111453
$292$	6.85900	0.401393
$293$	−33.3547	−1.94860	−0.974302	−	0.225247i	$-0.927681\pi$
$293$	−33.3547	−1.94860	−0.974302	+	0.225247i	$0.927681\pi$
$294$	1.00000	0.0583212
$295$	25.5707	1.48878
$296$	6.36814	0.370141
$297$	−4.99240	−0.289688
$298$	−12.0978	−0.700809
$299$	−7.35108	−0.425124
$300$	4.62448	0.266994
$301$	−0.192192	−0.0110778
$302$	−6.32817	−0.364145
$303$	12.8473	0.738056
$304$	−3.54327	−0.203220
$305$	−20.1566	−1.15416
$306$	1.00000	0.0571662
$307$	32.1460	1.83467	0.917335	−	0.398117i	$-0.130336\pi$
$307$	32.1460	1.83467	0.917335	+	0.398117i	$0.130336\pi$
$308$	4.99240	0.284468
$309$	2.03509	0.115772
$310$	14.4612	0.821342
$311$	−7.18630	−0.407498	−0.203749	−	0.979023i	$-0.565313\pi$
$311$	−7.18630	−0.407498	−0.203749	+	0.979023i	$0.565313\pi$
$312$	−1.00000	−0.0566139
$313$	−20.7269	−1.17155	−0.585776	−	0.810473i	$-0.699210\pi$
$313$	−20.7269	−1.17155	−0.585776	+	0.810473i	$0.699210\pi$
$314$	−3.03770	−0.171427
$315$	3.10233	0.174797
$316$	0.327645	0.0184315
$317$	1.84150	0.103429	0.0517145	−	0.998662i	$-0.483531\pi$
$317$	1.84150	0.103429	0.0517145	+	0.998662i	$0.483531\pi$
$318$	12.1770	0.682852
$319$	9.91617	0.555199
$320$	−3.10233	−0.173426
$321$	4.44324	0.247997
$322$	−7.35108	−0.409659
$323$	−3.54327	−0.197153
$324$	1.00000	0.0555556
$325$	−4.62448	−0.256520
$326$	4.39891	0.243633
$327$	18.8387	1.04178
$328$	−0.0654124	−0.00361180
$329$	10.1599	0.560133
$330$	15.4881	0.852592
$331$	5.50054	0.302337	0.151169	−	0.988508i	$-0.451696\pi$
$331$	5.50054	0.302337	0.151169	+	0.988508i	$0.451696\pi$
$332$	4.36177	0.239383
$333$	6.36814	0.348972
$334$	7.34309	0.401796
$335$	−1.88686	−0.103090
$336$	−1.00000	−0.0545545
$337$	−9.88988	−0.538736	−0.269368	−	0.963037i	$-0.586815\pi$
$337$	−9.88988	−0.538736	−0.269368	+	0.963037i	$0.586815\pi$
$338$	1.00000	0.0543928
$339$	−2.04049	−0.110824
$340$	−3.10233	−0.168248
$341$	23.2716	1.26023
$342$	−3.54327	−0.191598
$343$	−1.00000	−0.0539949
$344$	0.192192	0.0103623
$345$	−22.8055	−1.22781
$346$	−15.6520	−0.841458
$347$	−26.7411	−1.43554	−0.717769	−	0.696281i	$-0.754837\pi$
$347$	−26.7411	−1.43554	−0.717769	+	0.696281i	$0.754837\pi$
$348$	−1.98625	−0.106474
$349$	−7.68059	−0.411133	−0.205566	−	0.978643i	$-0.565904\pi$
$349$	−7.68059	−0.411133	−0.205566	+	0.978643i	$0.565904\pi$
$350$	−4.62448	−0.247189
$351$	−1.00000	−0.0533761
$352$	−4.99240	−0.266096
$353$	4.00999	0.213430	0.106715	−	0.994290i	$-0.465967\pi$
$353$	4.00999	0.213430	0.106715	+	0.994290i	$0.465967\pi$
$354$	−8.24241	−0.438079
$355$	4.14503	0.219996
$356$	−7.33502	−0.388755
$357$	−1.00000	−0.0529256
$358$	−1.80480	−0.0953865
$359$	−8.59624	−0.453692	−0.226846	−	0.973931i	$-0.572841\pi$
$359$	−8.59624	−0.453692	−0.226846	+	0.973931i	$0.572841\pi$
$360$	−3.10233	−0.163507
$361$	−6.44526	−0.339224
$362$	23.1665	1.21760
$363$	13.9241	0.730824
$364$	1.00000	0.0524142
$365$	−21.2789	−1.11379
$366$	6.49723	0.339615
$367$	−32.2942	−1.68574	−0.842871	−	0.538115i	$-0.819137\pi$
$367$	−32.2942	−1.68574	−0.842871	+	0.538115i	$0.819137\pi$
$368$	7.35108	0.383201
$369$	−0.0654124	−0.00340523
$370$	−19.7561	−1.02707
$371$	−12.1770	−0.632198
$372$	−4.66140	−0.241682
$373$	−17.5979	−0.911182	−0.455591	−	0.890189i	$-0.650572\pi$
$373$	−17.5979	−0.911182	−0.455591	+	0.890189i	$0.650572\pi$
$374$	−4.99240	−0.258151
$375$	1.16499	0.0601599
$376$	−10.1599	−0.523956
$377$	1.98625	0.102297
$378$	−1.00000	−0.0514344
$379$	15.4331	0.792747	0.396374	−	0.918089i	$-0.370268\pi$
$379$	15.4331	0.792747	0.396374	+	0.918089i	$0.370268\pi$
$380$	10.9924	0.563898
$381$	1.88697	0.0966723
$382$	8.81138	0.450829
$383$	8.35414	0.426876	0.213438	−	0.976957i	$-0.431534\pi$
$383$	8.35414	0.426876	0.213438	+	0.976957i	$0.431534\pi$
$384$	1.00000	0.0510310
$385$	−15.4881	−0.789347
$386$	20.3976	1.03821
$387$	0.192192	0.00976967
$388$	−1.90124	−0.0965207
$389$	−7.77599	−0.394258	−0.197129	−	0.980378i	$-0.563162\pi$
$389$	−7.77599	−0.394258	−0.197129	+	0.980378i	$0.563162\pi$
$390$	3.10233	0.157093
$391$	7.35108	0.371760
$392$	1.00000	0.0505076
$393$	20.5793	1.03809
$394$	13.6105	0.685686
$395$	−1.01647	−0.0511439
$396$	−4.99240	−0.250878
$397$	−9.21827	−0.462652	−0.231326	−	0.972876i	$-0.574306\pi$
$397$	−9.21827	−0.462652	−0.231326	+	0.972876i	$0.574306\pi$
$398$	−4.47978	−0.224551
$399$	3.54327	0.177385
$400$	4.62448	0.231224
$401$	−23.7393	−1.18548	−0.592741	−	0.805393i	$-0.701954\pi$
$401$	−23.7393	−1.18548	−0.592741	+	0.805393i	$0.701954\pi$
$402$	0.608207	0.0303346
$403$	4.66140	0.232201
$404$	12.8473	0.639175
$405$	−3.10233	−0.154156
$406$	1.98625	0.0985761
$407$	−31.7923	−1.57589
$408$	1.00000	0.0495074
$409$	22.2093	1.09818	0.549090	−	0.835763i	$-0.314974\pi$
$409$	22.2093	1.09818	0.549090	+	0.835763i	$0.314974\pi$
$410$	0.202931	0.0100221
$411$	4.42641	0.218339
$412$	2.03509	0.100262
$413$	8.24241	0.405582
$414$	7.35108	0.361286
$415$	−13.5317	−0.664244
$416$	−1.00000	−0.0490290
$417$	−2.19760	−0.107617
$418$	17.6894	0.865217
$419$	−24.3152	−1.18788	−0.593938	−	0.804511i	$-0.702427\pi$
$419$	−24.3152	−1.18788	−0.593938	+	0.804511i	$0.702427\pi$
$420$	3.10233	0.151378
$421$	7.41746	0.361505	0.180752	−	0.983529i	$-0.442147\pi$
$421$	7.41746	0.361505	0.180752	+	0.983529i	$0.442147\pi$
$422$	7.50132	0.365159
$423$	−10.1599	−0.493991
$424$	12.1770	0.591367
$425$	4.62448	0.224320
$426$	−1.33610	−0.0647343
$427$	−6.49723	−0.314423
$428$	4.44324	0.214772
$429$	4.99240	0.241035
$430$	−0.596244	−0.0287535
$431$	11.8963	0.573025	0.286513	−	0.958076i	$-0.407504\pi$
$431$	11.8963	0.573025	0.286513	+	0.958076i	$0.407504\pi$
$432$	1.00000	0.0481125
$433$	31.6396	1.52050	0.760251	−	0.649630i	$-0.225076\pi$
$433$	31.6396	1.52050	0.760251	+	0.649630i	$0.225076\pi$
$434$	4.66140	0.223754
$435$	6.16202	0.295446
$436$	18.8387	0.902208
$437$	−26.0468	−1.24599
$438$	6.85900	0.327736
$439$	−40.7763	−1.94615	−0.973073	−	0.230498i	$-0.925965\pi$
$439$	−40.7763	−1.94615	−0.973073	+	0.230498i	$0.925965\pi$
$440$	15.4881	0.738366
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	7.73519	0.367510	0.183755	−	0.982972i	$-0.441175\pi$
$443$	7.73519	0.367510	0.183755	+	0.982972i	$0.441175\pi$
$444$	6.36814	0.302219
$445$	22.7557	1.07872
$446$	−3.99822	−0.189321
$447$	−12.0978	−0.572208
$448$	−1.00000	−0.0472456
$449$	17.1940	0.811434	0.405717	−	0.913999i	$-0.367022\pi$
$449$	17.1940	0.811434	0.405717	+	0.913999i	$0.367022\pi$
$450$	4.62448	0.218000
$451$	0.326565	0.0153773
$452$	−2.04049	−0.0959768
$453$	−6.32817	−0.297323
$454$	−3.79856	−0.178275
$455$	−3.10233	−0.145440
$456$	−3.54327	−0.165929
$457$	−24.9067	−1.16509	−0.582543	−	0.812800i	$-0.697942\pi$
$457$	−24.9067	−1.16509	−0.582543	+	0.812800i	$0.697942\pi$
$458$	24.3283	1.13679
$459$	1.00000	0.0466760
$460$	−22.8055	−1.06331
$461$	10.1026	0.470524	0.235262	−	0.971932i	$-0.424405\pi$
$461$	10.1026	0.470524	0.235262	+	0.971932i	$0.424405\pi$
$462$	4.99240	0.232268
$463$	7.97736	0.370739	0.185370	−	0.982669i	$-0.440652\pi$
$463$	7.97736	0.370739	0.185370	+	0.982669i	$0.440652\pi$
$464$	−1.98625	−0.0922095
$465$	14.4612	0.670623
$466$	−1.38293	−0.0640630
$467$	−17.7930	−0.823360	−0.411680	−	0.911329i	$-0.635058\pi$
$467$	−17.7930	−0.823360	−0.411680	+	0.911329i	$0.635058\pi$
$468$	−1.00000	−0.0462250
$469$	−0.608207	−0.0280844
$470$	31.5194	1.45388
$471$	−3.03770	−0.139970
$472$	−8.24241	−0.379388
$473$	−0.959500	−0.0441179
$474$	0.327645	0.0150493
$475$	−16.3858	−0.751831
$476$	−1.00000	−0.0458349
$477$	12.1770	0.557546
$478$	−12.1798	−0.557089
$479$	−9.05685	−0.413818	−0.206909	−	0.978360i	$-0.566340\pi$
$479$	−9.05685	−0.413818	−0.206909	+	0.978360i	$0.566340\pi$
$480$	−3.10233	−0.141602
$481$	−6.36814	−0.290362
$482$	24.8042	1.12980
$483$	−7.35108	−0.334486
$484$	13.9241	0.632912
$485$	5.89828	0.267827
$486$	1.00000	0.0453609
$487$	30.5813	1.38577	0.692887	−	0.721047i	$-0.256339\pi$
$487$	30.5813	1.38577	0.692887	+	0.721047i	$0.256339\pi$
$488$	6.49723	0.294116
$489$	4.39891	0.198926
$490$	−3.10233	−0.140149
$491$	−4.66174	−0.210382	−0.105191	−	0.994452i	$-0.533545\pi$
$491$	−4.66174	−0.210382	−0.105191	+	0.994452i	$0.533545\pi$
$492$	−0.0654124	−0.00294902
$493$	−1.98625	−0.0894563
$494$	3.54327	0.159419
$495$	15.4881	0.696138
$496$	−4.66140	−0.209303
$497$	1.33610	0.0599323
$498$	4.36177	0.195456
$499$	19.5249	0.874056	0.437028	−	0.899448i	$-0.356031\pi$
$499$	19.5249	0.874056	0.437028	+	0.899448i	$0.356031\pi$
$500$	1.16499	0.0521000
$501$	7.34309	0.328065
$502$	−16.7069	−0.745663
$503$	−22.1887	−0.989345	−0.494672	−	0.869080i	$-0.664712\pi$
$503$	−22.1887	−0.989345	−0.494672	+	0.869080i	$0.664712\pi$
$504$	−1.00000	−0.0445435
$505$	−39.8565	−1.77359
$506$	−36.6995	−1.63149
$507$	1.00000	0.0444116
$508$	1.88697	0.0837206
$509$	−16.6412	−0.737606	−0.368803	−	0.929508i	$-0.620232\pi$
$509$	−16.6412	−0.737606	−0.368803	+	0.929508i	$0.620232\pi$
$510$	−3.10233	−0.137374
$511$	−6.85900	−0.303424
$512$	1.00000	0.0441942
$513$	−3.54327	−0.156439
$514$	25.0352	1.10426
$515$	−6.31352	−0.278207
$516$	0.192192	0.00846079
$517$	50.7223	2.23076
$518$	−6.36814	−0.279800
$519$	−15.6520	−0.687047
$520$	3.10233	0.136046
$521$	25.9858	1.13846	0.569229	−	0.822179i	$-0.307242\pi$
$521$	25.9858	1.13846	0.569229	+	0.822179i	$0.307242\pi$
$522$	−1.98625	−0.0869359
$523$	−31.8230	−1.39152	−0.695762	−	0.718272i	$-0.744933\pi$
$523$	−31.8230	−1.39152	−0.695762	+	0.718272i	$0.744933\pi$
$524$	20.5793	0.899009
$525$	−4.62448	−0.201829
$526$	−20.7897	−0.906474
$527$	−4.66140	−0.203054
$528$	−4.99240	−0.217266
$529$	31.0383	1.34949
$530$	−37.7771	−1.64093
$531$	−8.24241	−0.357690
$532$	3.54327	0.153620
$533$	0.0654124	0.00283333
$534$	−7.33502	−0.317417
$535$	−13.7844	−0.595952
$536$	0.608207	0.0262705
$537$	−1.80480	−0.0778827
$538$	17.2748	0.744771
$539$	−4.99240	−0.215038
$540$	−3.10233	−0.133503
$541$	9.44494	0.406070	0.203035	−	0.979172i	$-0.434920\pi$
$541$	9.44494	0.406070	0.203035	+	0.979172i	$0.434920\pi$
$542$	20.4914	0.880182
$543$	23.1665	0.994169
$544$	1.00000	0.0428746
$545$	−58.4438	−2.50346
$546$	1.00000	0.0427960
$547$	7.93674	0.339351	0.169675	−	0.985500i	$-0.445728\pi$
$547$	7.93674	0.339351	0.169675	+	0.985500i	$0.445728\pi$
$548$	4.42641	0.189087
$549$	6.49723	0.277295
$550$	−23.0873	−0.984444
$551$	7.03782	0.299821
$552$	7.35108	0.312883
$553$	−0.327645	−0.0139329
$554$	19.9899	0.849289
$555$	−19.7561	−0.838600
$556$	−2.19760	−0.0931989
$557$	−7.87900	−0.333844	−0.166922	−	0.985970i	$-0.553383\pi$
$557$	−7.87900	−0.333844	−0.166922	+	0.985970i	$0.553383\pi$
$558$	−4.66140	−0.197333
$559$	−0.192192	−0.00812886
$560$	3.10233	0.131098
$561$	−4.99240	−0.210779
$562$	4.03438	0.170180
$563$	35.2010	1.48355	0.741773	−	0.670652i	$-0.233985\pi$
$563$	35.2010	1.48355	0.741773	+	0.670652i	$0.233985\pi$
$564$	−10.1599	−0.427809
$565$	6.33030	0.266318
$566$	6.65342	0.279664
$567$	−1.00000	−0.0419961
$568$	−1.33610	−0.0560616
$569$	−10.6730	−0.447436	−0.223718	−	0.974654i	$-0.571820\pi$
$569$	−10.6730	−0.447436	−0.223718	+	0.974654i	$0.571820\pi$
$570$	10.9924	0.460421
$571$	−9.36648	−0.391975	−0.195988	−	0.980606i	$-0.562791\pi$
$571$	−9.36648	−0.391975	−0.195988	+	0.980606i	$0.562791\pi$
$572$	4.99240	0.208743
$573$	8.81138	0.368101
$574$	0.0654124	0.00273026
$575$	33.9949	1.41769
$576$	1.00000	0.0416667
$577$	−23.5547	−0.980595	−0.490297	−	0.871555i	$-0.663112\pi$
$577$	−23.5547	−0.980595	−0.490297	+	0.871555i	$0.663112\pi$
$578$	1.00000	0.0415945
$579$	20.3976	0.847697
$580$	6.16202	0.255864
$581$	−4.36177	−0.180957
$582$	−1.90124	−0.0788088
$583$	−60.7924	−2.51777
$584$	6.85900	0.283827
$585$	3.10233	0.128266
$586$	−33.3547	−1.37787
$587$	24.0906	0.994325	0.497162	−	0.867657i	$-0.334375\pi$
$587$	24.0906	0.994325	0.497162	+	0.867657i	$0.334375\pi$
$588$	1.00000	0.0412393
$589$	16.5166	0.680554
$590$	25.5707	1.05273
$591$	13.6105	0.559860
$592$	6.36814	0.261729
$593$	−41.9068	−1.72090	−0.860452	−	0.509531i	$-0.829819\pi$
$593$	−41.9068	−1.72090	−0.860452	+	0.509531i	$0.829819\pi$
$594$	−4.99240	−0.204841
$595$	3.10233	0.127183
$596$	−12.0978	−0.495547
$597$	−4.47978	−0.183345
$598$	−7.35108	−0.300608
$599$	22.6866	0.926950	0.463475	−	0.886110i	$-0.346602\pi$
$599$	22.6866	0.926950	0.463475	+	0.886110i	$0.346602\pi$
$600$	4.62448	0.188794
$601$	22.3938	0.913462	0.456731	−	0.889605i	$-0.349020\pi$
$601$	22.3938	0.913462	0.456731	+	0.889605i	$0.349020\pi$
$602$	−0.192192	−0.00783317
$603$	0.608207	0.0247681
$604$	−6.32817	−0.257490
$605$	−43.1971	−1.75621
$606$	12.8473	0.521884
$607$	−25.1531	−1.02093	−0.510466	−	0.859898i	$-0.670527\pi$
$607$	−25.1531	−1.02093	−0.510466	+	0.859898i	$0.670527\pi$
$608$	−3.54327	−0.143698
$609$	1.98625	0.0804870
$610$	−20.1566	−0.816116
$611$	10.1599	0.411025
$612$	1.00000	0.0404226
$613$	29.6815	1.19883	0.599413	−	0.800440i	$-0.295401\pi$
$613$	29.6815	1.19883	0.599413	+	0.800440i	$0.295401\pi$
$614$	32.1460	1.29731
$615$	0.202931	0.00818298
$616$	4.99240	0.201150
$617$	31.4202	1.26493	0.632466	−	0.774589i	$-0.282043\pi$
$617$	31.4202	1.26493	0.632466	+	0.774589i	$0.282043\pi$
$618$	2.03509	0.0818632
$619$	35.0922	1.41048	0.705238	−	0.708971i	$-0.250840\pi$
$619$	35.0922	1.41048	0.705238	+	0.708971i	$0.250840\pi$
$620$	14.4612	0.580777
$621$	7.35108	0.294988
$622$	−7.18630	−0.288144
$623$	7.33502	0.293871
$624$	−1.00000	−0.0400320
$625$	−26.7366	−1.06946
$626$	−20.7269	−0.828412
$627$	17.6894	0.706447
$628$	−3.03770	−0.121217
$629$	6.36814	0.253914
$630$	3.10233	0.123600
$631$	12.5091	0.497980	0.248990	−	0.968506i	$-0.419901\pi$
$631$	12.5091	0.497980	0.248990	+	0.968506i	$0.419901\pi$
$632$	0.327645	0.0130330
$633$	7.50132	0.298151
$634$	1.84150	0.0731353
$635$	−5.85400	−0.232309
$636$	12.1770	0.482849
$637$	−1.00000	−0.0396214
$638$	9.91617	0.392585
$639$	−1.33610	−0.0528553
$640$	−3.10233	−0.122631
$641$	17.9851	0.710369	0.355185	−	0.934796i	$-0.384418\pi$
$641$	17.9851	0.710369	0.355185	+	0.934796i	$0.384418\pi$
$642$	4.44324	0.175361
$643$	46.5773	1.83683	0.918415	−	0.395617i	$-0.129469\pi$
$643$	46.5773	1.83683	0.918415	+	0.395617i	$0.129469\pi$
$644$	−7.35108	−0.289673
$645$	−0.596244	−0.0234771
$646$	−3.54327	−0.139408
$647$	−19.6013	−0.770605	−0.385303	−	0.922790i	$-0.625903\pi$
$647$	−19.6013	−0.770605	−0.385303	+	0.922790i	$0.625903\pi$
$648$	1.00000	0.0392837
$649$	41.1494	1.61526
$650$	−4.62448	−0.181387
$651$	4.66140	0.182695
$652$	4.39891	0.172275
$653$	−23.0306	−0.901258	−0.450629	−	0.892711i	$-0.648800\pi$
$653$	−23.0306	−0.901258	−0.450629	+	0.892711i	$0.648800\pi$
$654$	18.8387	0.736650
$655$	−63.8438	−2.49458
$656$	−0.0654124	−0.00255393
$657$	6.85900	0.267595
$658$	10.1599	0.396074
$659$	42.8450	1.66900	0.834502	−	0.551005i	$-0.185755\pi$
$659$	42.8450	1.66900	0.834502	+	0.551005i	$0.185755\pi$
$660$	15.4881	0.602873
$661$	−29.1244	−1.13281	−0.566404	−	0.824128i	$-0.691666\pi$
$661$	−29.1244	−1.13281	−0.566404	+	0.824128i	$0.691666\pi$
$662$	5.50054	0.213785
$663$	−1.00000	−0.0388368
$664$	4.36177	0.169270
$665$	−10.9924	−0.426267
$666$	6.36814	0.246760
$667$	−14.6011	−0.565357
$668$	7.34309	0.284113
$669$	−3.99822	−0.154580
$670$	−1.88686	−0.0728958
$671$	−32.4368	−1.25221
$672$	−1.00000	−0.0385758
$673$	17.9784	0.693016	0.346508	−	0.938047i	$-0.387367\pi$
$673$	17.9784	0.693016	0.346508	+	0.938047i	$0.387367\pi$
$674$	−9.88988	−0.380944
$675$	4.62448	0.177996
$676$	1.00000	0.0384615
$677$	−25.0864	−0.964148	−0.482074	−	0.876130i	$-0.660116\pi$
$677$	−25.0864	−0.964148	−0.482074	+	0.876130i	$0.660116\pi$
$678$	−2.04049	−0.0783647
$679$	1.90124	0.0729628
$680$	−3.10233	−0.118969
$681$	−3.79856	−0.145561
$682$	23.2716	0.891115
$683$	14.0148	0.536260	0.268130	−	0.963383i	$-0.413594\pi$
$683$	14.0148	0.536260	0.268130	+	0.963383i	$0.413594\pi$
$684$	−3.54327	−0.135480
$685$	−13.7322	−0.524680
$686$	−1.00000	−0.0381802
$687$	24.3283	0.928182
$688$	0.192192	0.00732726
$689$	−12.1770	−0.463907
$690$	−22.8055	−0.868190
$691$	23.9421	0.910802	0.455401	−	0.890286i	$-0.349496\pi$
$691$	23.9421	0.910802	0.455401	+	0.890286i	$0.349496\pi$
$692$	−15.6520	−0.595000
$693$	4.99240	0.189646
$694$	−26.7411	−1.01508
$695$	6.81769	0.258610
$696$	−1.98625	−0.0752887
$697$	−0.0654124	−0.00247767
$698$	−7.68059	−0.290715
$699$	−1.38293	−0.0523072
$700$	−4.62448	−0.174789
$701$	−37.9353	−1.43280	−0.716398	−	0.697691i	$-0.754211\pi$
$701$	−37.9353	−1.43280	−0.716398	+	0.697691i	$0.754211\pi$
$702$	−1.00000	−0.0377426
$703$	−22.5640	−0.851018
$704$	−4.99240	−0.188158
$705$	31.5194	1.18709
$706$	4.00999	0.150918
$707$	−12.8473	−0.483171
$708$	−8.24241	−0.309769
$709$	24.6235	0.924756	0.462378	−	0.886683i	$-0.346996\pi$
$709$	24.6235	0.924756	0.462378	+	0.886683i	$0.346996\pi$
$710$	4.14503	0.155560
$711$	0.327645	0.0122877
$712$	−7.33502	−0.274892
$713$	−34.2663	−1.28328
$714$	−1.00000	−0.0374241
$715$	−15.4881	−0.579222
$716$	−1.80480	−0.0674484
$717$	−12.1798	−0.454861
$718$	−8.59624	−0.320809
$719$	−0.945509	−0.0352615	−0.0176308	−	0.999845i	$-0.505612\pi$
$719$	−0.945509	−0.0352615	−0.0176308	+	0.999845i	$0.505612\pi$
$720$	−3.10233	−0.115617
$721$	−2.03509	−0.0757906
$722$	−6.44526	−0.239868
$723$	24.8042	0.922479
$724$	23.1665	0.860975
$725$	−9.18538	−0.341137
$726$	13.9241	0.516771
$727$	12.4554	0.461944	0.230972	−	0.972960i	$-0.425809\pi$
$727$	12.4554	0.461944	0.230972	+	0.972960i	$0.425809\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	−21.2789	−0.787568
$731$	0.192192	0.00710848
$732$	6.49723	0.240144
$733$	−31.3642	−1.15846	−0.579231	−	0.815164i	$-0.696647\pi$
$733$	−31.3642	−1.15846	−0.579231	+	0.815164i	$0.696647\pi$
$734$	−32.2942	−1.19200
$735$	−3.10233	−0.114431
$736$	7.35108	0.270964
$737$	−3.03641	−0.111848
$738$	−0.0654124	−0.00240786
$739$	−14.0205	−0.515754	−0.257877	−	0.966178i	$-0.583023\pi$
$739$	−14.0205	−0.515754	−0.257877	+	0.966178i	$0.583023\pi$
$740$	−19.7561	−0.726249
$741$	3.54327	0.130165
$742$	−12.1770	−0.447032
$743$	37.0935	1.36083	0.680413	−	0.732828i	$-0.261800\pi$
$743$	37.0935	1.36083	0.680413	+	0.732828i	$0.261800\pi$
$744$	−4.66140	−0.170895
$745$	37.5315	1.37505
$746$	−17.5979	−0.644303
$747$	4.36177	0.159589
$748$	−4.99240	−0.182540
$749$	−4.44324	−0.162352
$750$	1.16499	0.0425394
$751$	10.0766	0.367700	0.183850	−	0.982954i	$-0.441144\pi$
$751$	10.0766	0.367700	0.183850	+	0.982954i	$0.441144\pi$
$752$	−10.1599	−0.370493
$753$	−16.7069	−0.608832
$754$	1.98625	0.0723351
$755$	19.6321	0.714485
$756$	−1.00000	−0.0363696
$757$	−3.73368	−0.135703	−0.0678514	−	0.997695i	$-0.521614\pi$
$757$	−3.73368	−0.135703	−0.0678514	+	0.997695i	$0.521614\pi$
$758$	15.4331	0.560557
$759$	−36.6995	−1.33211
$760$	10.9924	0.398736
$761$	−18.1296	−0.657196	−0.328598	−	0.944470i	$-0.606576\pi$
$761$	−18.1296	−0.657196	−0.328598	+	0.944470i	$0.606576\pi$
$762$	1.88697	0.0683576
$763$	−18.8387	−0.682005
$764$	8.81138	0.318785
$765$	−3.10233	−0.112165
$766$	8.35414	0.301847
$767$	8.24241	0.297616
$768$	1.00000	0.0360844
$769$	31.7640	1.14544	0.572719	−	0.819752i	$-0.305889\pi$
$769$	31.7640	1.14544	0.572719	+	0.819752i	$0.305889\pi$
$770$	−15.4881	−0.558152
$771$	25.0352	0.901621
$772$	20.3976	0.734127
$773$	−43.9067	−1.57921	−0.789607	−	0.613613i	$-0.789716\pi$
$773$	−43.9067	−1.57921	−0.789607	+	0.613613i	$0.789716\pi$
$774$	0.192192	0.00690820
$775$	−21.5566	−0.774334
$776$	−1.90124	−0.0682505
$777$	−6.36814	−0.228456
$778$	−7.77599	−0.278783
$779$	0.231774	0.00830415
$780$	3.10233	0.111081
$781$	6.67035	0.238684
$782$	7.35108	0.262874
$783$	−1.98625	−0.0709829
$784$	1.00000	0.0357143
$785$	9.42396	0.336356
$786$	20.5793	0.734038
$787$	−10.4642	−0.373010	−0.186505	−	0.982454i	$-0.559716\pi$
$787$	−10.4642	−0.373010	−0.186505	+	0.982454i	$0.559716\pi$
$788$	13.6105	0.484853
$789$	−20.7897	−0.740133
$790$	−1.01647	−0.0361642
$791$	2.04049	0.0725516
$792$	−4.99240	−0.177397
$793$	−6.49723	−0.230723
$794$	−9.21827	−0.327144
$795$	−37.7771	−1.33982
$796$	−4.47978	−0.158782
$797$	20.0021	0.708509	0.354255	−	0.935149i	$-0.384735\pi$
$797$	20.0021	0.708509	0.354255	+	0.935149i	$0.384735\pi$
$798$	3.54327	0.125430
$799$	−10.1599	−0.359431
$800$	4.62448	0.163500
$801$	−7.33502	−0.259170
$802$	−23.7393	−0.838262
$803$	−34.2429	−1.20840
$804$	0.608207	0.0214498
$805$	22.8055	0.803788
$806$	4.66140	0.164191
$807$	17.2748	0.608103
$808$	12.8473	0.451965
$809$	−19.6022	−0.689178	−0.344589	−	0.938754i	$-0.611982\pi$
$809$	−19.6022	−0.689178	−0.344589	+	0.938754i	$0.611982\pi$
$810$	−3.10233	−0.109005
$811$	−18.8509	−0.661945	−0.330973	−	0.943640i	$-0.607377\pi$
$811$	−18.8509	−0.661945	−0.330973	+	0.943640i	$0.607377\pi$
$812$	1.98625	0.0697038
$813$	20.4914	0.718665
$814$	−31.7923	−1.11432
$815$	−13.6469	−0.478030
$816$	1.00000	0.0350070
$817$	−0.680988	−0.0238248
$818$	22.2093	0.776531
$819$	1.00000	0.0349428
$820$	0.202931	0.00708666
$821$	−4.13515	−0.144318	−0.0721589	−	0.997393i	$-0.522989\pi$
$821$	−4.13515	−0.144318	−0.0721589	+	0.997393i	$0.522989\pi$
$822$	4.42641	0.154389
$823$	−29.6291	−1.03281	−0.516403	−	0.856345i	$-0.672729\pi$
$823$	−29.6291	−1.03281	−0.516403	+	0.856345i	$0.672729\pi$
$824$	2.03509	0.0708956
$825$	−23.0873	−0.803795
$826$	8.24241	0.286790
$827$	46.0844	1.60251	0.801255	−	0.598322i	$-0.204166\pi$
$827$	46.0844	1.60251	0.801255	+	0.598322i	$0.204166\pi$
$828$	7.35108	0.255468
$829$	−3.02319	−0.105000	−0.0524999	−	0.998621i	$-0.516719\pi$
$829$	−3.02319	−0.105000	−0.0524999	+	0.998621i	$0.516719\pi$
$830$	−13.5317	−0.469691
$831$	19.9899	0.693442
$832$	−1.00000	−0.0346688
$833$	1.00000	0.0346479
$834$	−2.19760	−0.0760966
$835$	−22.7807	−0.788360
$836$	17.6894	0.611801
$837$	−4.66140	−0.161122
$838$	−24.3152	−0.839955
$839$	−49.1379	−1.69643	−0.848215	−	0.529652i	$-0.822323\pi$
$839$	−49.1379	−1.69643	−0.848215	+	0.529652i	$0.822323\pi$
$840$	3.10233	0.107041
$841$	−25.0548	−0.863959
$842$	7.41746	0.255622
$843$	4.03438	0.138952
$844$	7.50132	0.258206
$845$	−3.10233	−0.106724
$846$	−10.1599	−0.349304
$847$	−13.9241	−0.478437
$848$	12.1770	0.418160
$849$	6.65342	0.228345
$850$	4.62448	0.158618
$851$	46.8127	1.60472
$852$	−1.33610	−0.0457741
$853$	−9.21949	−0.315669	−0.157835	−	0.987466i	$-0.550451\pi$
$853$	−9.21949	−0.315669	−0.157835	+	0.987466i	$0.550451\pi$
$854$	−6.49723	−0.222331
$855$	10.9924	0.375932
$856$	4.44324	0.151867
$857$	−40.0146	−1.36687	−0.683437	−	0.730010i	$-0.739515\pi$
$857$	−40.0146	−1.36687	−0.683437	+	0.730010i	$0.739515\pi$
$858$	4.99240	0.170438
$859$	13.0920	0.446693	0.223346	−	0.974739i	$-0.428302\pi$
$859$	13.0920	0.446693	0.223346	+	0.974739i	$0.428302\pi$
$860$	−0.596244	−0.0203318
$861$	0.0654124	0.00222925
$862$	11.8963	0.405190
$863$	−19.5878	−0.666775	−0.333388	−	0.942790i	$-0.608192\pi$
$863$	−19.5878	−0.666775	−0.333388	+	0.942790i	$0.608192\pi$
$864$	1.00000	0.0340207
$865$	48.5578	1.65101
$866$	31.6396	1.07516
$867$	1.00000	0.0339618
$868$	4.66140	0.158218
$869$	−1.63574	−0.0554886
$870$	6.16202	0.208912
$871$	−0.608207	−0.0206083
$872$	18.8387	0.637957
$873$	−1.90124	−0.0643471
$874$	−26.0468	−0.881047
$875$	−1.16499	−0.0393839
$876$	6.85900	0.231744
$877$	20.4677	0.691144	0.345572	−	0.938392i	$-0.387685\pi$
$877$	20.4677	0.691144	0.345572	+	0.938392i	$0.387685\pi$
$878$	−40.7763	−1.37613
$879$	−33.3547	−1.12503
$880$	15.4881	0.522104
$881$	39.0160	1.31448	0.657241	−	0.753680i	$-0.271723\pi$
$881$	39.0160	1.31448	0.657241	+	0.753680i	$0.271723\pi$
$882$	1.00000	0.0336718
$883$	−49.0996	−1.65233	−0.826167	−	0.563426i	$-0.809483\pi$
$883$	−49.0996	−1.65233	−0.826167	+	0.563426i	$0.809483\pi$
$884$	−1.00000	−0.0336336
$885$	25.5707	0.859550
$886$	7.73519	0.259869
$887$	−23.3415	−0.783732	−0.391866	−	0.920022i	$-0.628170\pi$
$887$	−23.3415	−0.783732	−0.391866	+	0.920022i	$0.628170\pi$
$888$	6.36814	0.213701
$889$	−1.88697	−0.0632869
$890$	22.7557	0.762772
$891$	−4.99240	−0.167252
$892$	−3.99822	−0.133870
$893$	35.9992	1.20467
$894$	−12.0978	−0.404612
$895$	5.59908	0.187157
$896$	−1.00000	−0.0334077
$897$	−7.35108	−0.245445
$898$	17.1940	0.573771
$899$	9.25872	0.308796
$900$	4.62448	0.154149
$901$	12.1770	0.405675
$902$	0.326565	0.0108734
$903$	−0.192192	−0.00639575
$904$	−2.04049	−0.0678658
$905$	−71.8702	−2.38904
$906$	−6.32817	−0.210239
$907$	38.0509	1.26346	0.631730	−	0.775189i	$-0.282345\pi$
$907$	38.0509	1.26346	0.631730	+	0.775189i	$0.282345\pi$
$908$	−3.79856	−0.126060
$909$	12.8473	0.426117
$910$	−3.10233	−0.102841
$911$	32.6697	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$911$	32.6697	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$912$	−3.54327	−0.117329
$913$	−21.7757	−0.720671
$914$	−24.9067	−0.823841
$915$	−20.1566	−0.666356
$916$	24.3283	0.803829
$917$	−20.5793	−0.679587
$918$	1.00000	0.0330049
$919$	18.0900	0.596735	0.298368	−	0.954451i	$-0.403558\pi$
$919$	18.0900	0.596735	0.298368	+	0.954451i	$0.403558\pi$
$920$	−22.8055	−0.751875
$921$	32.1460	1.05925
$922$	10.1026	0.332711
$923$	1.33610	0.0439783
$924$	4.99240	0.164238
$925$	29.4493	0.968288
$926$	7.97736	0.262152
$927$	2.03509	0.0668411
$928$	−1.98625	−0.0652019
$929$	−24.9239	−0.817726	−0.408863	−	0.912596i	$-0.634075\pi$
$929$	−24.9239	−0.817726	−0.408863	+	0.912596i	$0.634075\pi$
$930$	14.4612	0.474202
$931$	−3.54327	−0.116126
$932$	−1.38293	−0.0452994
$933$	−7.18630	−0.235269
$934$	−17.7930	−0.582203
$935$	15.4881	0.506515
$936$	−1.00000	−0.0326860
$937$	28.9145	0.944594	0.472297	−	0.881439i	$-0.343425\pi$
$937$	28.9145	0.944594	0.472297	+	0.881439i	$0.343425\pi$
$938$	−0.608207	−0.0198587
$939$	−20.7269	−0.676395
$940$	31.5194	1.02805
$941$	57.6158	1.87822	0.939110	−	0.343617i	$-0.111652\pi$
$941$	57.6158	1.87822	0.939110	+	0.343617i	$0.111652\pi$
$942$	−3.03770	−0.0989736
$943$	−0.480852	−0.0156587
$944$	−8.24241	−0.268267
$945$	3.10233	0.100919
$946$	−0.959500	−0.0311960
$947$	35.0789	1.13991	0.569955	−	0.821676i	$-0.306960\pi$
$947$	35.0789	1.13991	0.569955	+	0.821676i	$0.306960\pi$
$948$	0.327645	0.0106414
$949$	−6.85900	−0.222653
$950$	−16.3858	−0.531625
$951$	1.84150	0.0597148
$952$	−1.00000	−0.0324102
$953$	−7.57402	−0.245347	−0.122673	−	0.992447i	$-0.539147\pi$
$953$	−7.57402	−0.245347	−0.122673	+	0.992447i	$0.539147\pi$
$954$	12.1770	0.394245
$955$	−27.3358	−0.884567
$956$	−12.1798	−0.393921
$957$	9.91617	0.320544
$958$	−9.05685	−0.292614
$959$	−4.42641	−0.142936
$960$	−3.10233	−0.100127
$961$	−9.27134	−0.299075
$962$	−6.36814	−0.205317
$963$	4.44324	0.143181
$964$	24.8042	0.798890
$965$	−63.2803	−2.03707
$966$	−7.35108	−0.236517
$967$	−1.08004	−0.0347316	−0.0173658	−	0.999849i	$-0.505528\pi$
$967$	−1.08004	−0.0347316	−0.0173658	+	0.999849i	$0.505528\pi$
$968$	13.9241	0.447537
$969$	−3.54327	−0.113826
$970$	5.89828	0.189382
$971$	−56.8061	−1.82299	−0.911497	−	0.411306i	$-0.865073\pi$
$971$	−56.8061	−1.82299	−0.911497	+	0.411306i	$0.865073\pi$
$972$	1.00000	0.0320750
$973$	2.19760	0.0704518
$974$	30.5813	0.979890
$975$	−4.62448	−0.148102
$976$	6.49723	0.207971
$977$	37.9179	1.21310	0.606550	−	0.795045i	$-0.292553\pi$
$977$	37.9179	1.21310	0.606550	+	0.795045i	$0.292553\pi$
$978$	4.39891	0.140662
$979$	36.6194	1.17036
$980$	−3.10233	−0.0991004
$981$	18.8387	0.601472
$982$	−4.66174	−0.148762
$983$	−35.5787	−1.13478	−0.567392	−	0.823448i	$-0.692047\pi$
$983$	−35.5787	−1.13478	−0.567392	+	0.823448i	$0.692047\pi$
$984$	−0.0654124	−0.00208527
$985$	−42.2243	−1.34538
$986$	−1.98625	−0.0632552
$987$	10.1599	0.323393
$988$	3.54327	0.112726
$989$	1.41282	0.0449250
$990$	15.4881	0.492244
$991$	−1.12847	−0.0358469	−0.0179235	−	0.999839i	$-0.505706\pi$
$991$	−1.12847	−0.0358469	−0.0179235	+	0.999839i	$0.505706\pi$
$992$	−4.66140	−0.148000
$993$	5.50054	0.174554
$994$	1.33610	0.0423786
$995$	13.8978	0.440589
$996$	4.36177	0.138208
$997$	−39.4962	−1.25086	−0.625429	−	0.780281i	$-0.715076\pi$
$997$	−39.4962	−1.25086	−0.625429	+	0.780281i	$0.715076\pi$
$998$	19.5249	0.618051
$999$	6.36814	0.201479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.ce.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.ce.1.2	✓	7	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.10233 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.10233 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.10233 q^{10} -4.99240 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -3.10233 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -3.54327 q^{19} -3.10233 q^{20} -1.00000 q^{21} -4.99240 q^{22} +7.35108 q^{23} +1.00000 q^{24} +4.62448 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.98625 q^{29} -3.10233 q^{30} -4.66140 q^{31} +1.00000 q^{32} -4.99240 q^{33} +1.00000 q^{34} +3.10233 q^{35} +1.00000 q^{36} +6.36814 q^{37} -3.54327 q^{38} -1.00000 q^{39} -3.10233 q^{40} -0.0654124 q^{41} -1.00000 q^{42} +0.192192 q^{43} -4.99240 q^{44} -3.10233 q^{45} +7.35108 q^{46} -10.1599 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.62448 q^{50} +1.00000 q^{51} -1.00000 q^{52} +12.1770 q^{53} +1.00000 q^{54} +15.4881 q^{55} -1.00000 q^{56} -3.54327 q^{57} -1.98625 q^{58} -8.24241 q^{59} -3.10233 q^{60} +6.49723 q^{61} -4.66140 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.10233 q^{65} -4.99240 q^{66} +0.608207 q^{67} +1.00000 q^{68} +7.35108 q^{69} +3.10233 q^{70} -1.33610 q^{71} +1.00000 q^{72} +6.85900 q^{73} +6.36814 q^{74} +4.62448 q^{75} -3.54327 q^{76} +4.99240 q^{77} -1.00000 q^{78} +0.327645 q^{79} -3.10233 q^{80} +1.00000 q^{81} -0.0654124 q^{82} +4.36177 q^{83} -1.00000 q^{84} -3.10233 q^{85} +0.192192 q^{86} -1.98625 q^{87} -4.99240 q^{88} -7.33502 q^{89} -3.10233 q^{90} +1.00000 q^{91} +7.35108 q^{92} -4.66140 q^{93} -10.1599 q^{94} +10.9924 q^{95} +1.00000 q^{96} -1.90124 q^{97} +1.00000 q^{98} -4.99240 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 7 q^{13} - 7 q^{14} + 3 q^{15} + 7 q^{16} + 7 q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 7 q^{22} + 12 q^{23} + 7 q^{24} + 20 q^{25} - 7 q^{26} + 7 q^{27} - 7 q^{28} + 18 q^{29} + 3 q^{30} - 6 q^{31} + 7 q^{32} + 7 q^{33} + 7 q^{34} - 3 q^{35} + 7 q^{36} + 5 q^{37} - 2 q^{38} - 7 q^{39} + 3 q^{40} + 10 q^{41} - 7 q^{42} + 18 q^{43} + 7 q^{44} + 3 q^{45} + 12 q^{46} + 3 q^{47} + 7 q^{48} + 7 q^{49} + 20 q^{50} + 7 q^{51} - 7 q^{52} + 18 q^{53} + 7 q^{54} + 4 q^{55} - 7 q^{56} - 2 q^{57} + 18 q^{58} + 20 q^{59} + 3 q^{60} + 19 q^{61} - 6 q^{62} - 7 q^{63} + 7 q^{64} - 3 q^{65} + 7 q^{66} - 16 q^{67} + 7 q^{68} + 12 q^{69} - 3 q^{70} + 5 q^{71} + 7 q^{72} + 2 q^{73} + 5 q^{74} + 20 q^{75} - 2 q^{76} - 7 q^{77} - 7 q^{78} + 12 q^{79} + 3 q^{80} + 7 q^{81} + 10 q^{82} + 11 q^{83} - 7 q^{84} + 3 q^{85} + 18 q^{86} + 18 q^{87} + 7 q^{88} + 6 q^{89} + 3 q^{90} + 7 q^{91} + 12 q^{92} - 6 q^{93} + 3 q^{94} + 35 q^{95} + 7 q^{96} - 3 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 7 * q^13 - 7 * q^14 + 3 * q^15 + 7 * q^16 + 7 * q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 7 * q^22 + 12 * q^23 + 7 * q^24 + 20 * q^25 - 7 * q^26 + 7 * q^27 - 7 * q^28 + 18 * q^29 + 3 * q^30 - 6 * q^31 + 7 * q^32 + 7 * q^33 + 7 * q^34 - 3 * q^35 + 7 * q^36 + 5 * q^37 - 2 * q^38 - 7 * q^39 + 3 * q^40 + 10 * q^41 - 7 * q^42 + 18 * q^43 + 7 * q^44 + 3 * q^45 + 12 * q^46 + 3 * q^47 + 7 * q^48 + 7 * q^49 + 20 * q^50 + 7 * q^51 - 7 * q^52 + 18 * q^53 + 7 * q^54 + 4 * q^55 - 7 * q^56 - 2 * q^57 + 18 * q^58 + 20 * q^59 + 3 * q^60 + 19 * q^61 - 6 * q^62 - 7 * q^63 + 7 * q^64 - 3 * q^65 + 7 * q^66 - 16 * q^67 + 7 * q^68 + 12 * q^69 - 3 * q^70 + 5 * q^71 + 7 * q^72 + 2 * q^73 + 5 * q^74 + 20 * q^75 - 2 * q^76 - 7 * q^77 - 7 * q^78 + 12 * q^79 + 3 * q^80 + 7 * q^81 + 10 * q^82 + 11 * q^83 - 7 * q^84 + 3 * q^85 + 18 * q^86 + 18 * q^87 + 7 * q^88 + 6 * q^89 + 3 * q^90 + 7 * q^91 + 12 * q^92 - 6 * q^93 + 3 * q^94 + 35 * q^95 + 7 * q^96 - 3 * q^97 + 7 * q^98 + 7 * q^99

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