LMFDB - Embedded newform 6014.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.34015 q^{3} +1.00000 q^{4} +0.146848 q^{5} +1.34015 q^{6} +4.48511 q^{7} -1.00000 q^{8} -1.20399 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.34015 q^{3} +1.00000 q^{4} +0.146848 q^{5} +1.34015 q^{6} +4.48511 q^{7} -1.00000 q^{8} -1.20399 q^{9} -0.146848 q^{10} -2.99195 q^{11} -1.34015 q^{12} -1.07630 q^{13} -4.48511 q^{14} -0.196799 q^{15} +1.00000 q^{16} +1.15865 q^{17} +1.20399 q^{18} -2.82538 q^{19} +0.146848 q^{20} -6.01073 q^{21} +2.99195 q^{22} +2.39860 q^{23} +1.34015 q^{24} -4.97844 q^{25} +1.07630 q^{26} +5.63399 q^{27} +4.48511 q^{28} +5.88696 q^{29} +0.196799 q^{30} +1.00000 q^{31} -1.00000 q^{32} +4.00967 q^{33} -1.15865 q^{34} +0.658628 q^{35} -1.20399 q^{36} -1.04411 q^{37} +2.82538 q^{38} +1.44241 q^{39} -0.146848 q^{40} -1.52787 q^{41} +6.01073 q^{42} -5.98268 q^{43} -2.99195 q^{44} -0.176803 q^{45} -2.39860 q^{46} -0.101142 q^{47} -1.34015 q^{48} +13.1162 q^{49} +4.97844 q^{50} -1.55277 q^{51} -1.07630 q^{52} +4.19310 q^{53} -5.63399 q^{54} -0.439360 q^{55} -4.48511 q^{56} +3.78645 q^{57} -5.88696 q^{58} +1.40207 q^{59} -0.196799 q^{60} +5.97341 q^{61} -1.00000 q^{62} -5.40002 q^{63} +1.00000 q^{64} -0.158052 q^{65} -4.00967 q^{66} -12.7619 q^{67} +1.15865 q^{68} -3.21450 q^{69} -0.658628 q^{70} +2.50946 q^{71} +1.20399 q^{72} -9.57088 q^{73} +1.04411 q^{74} +6.67187 q^{75} -2.82538 q^{76} -13.4192 q^{77} -1.44241 q^{78} -11.9579 q^{79} +0.146848 q^{80} -3.93845 q^{81} +1.52787 q^{82} +6.83383 q^{83} -6.01073 q^{84} +0.170145 q^{85} +5.98268 q^{86} -7.88943 q^{87} +2.99195 q^{88} -13.0241 q^{89} +0.176803 q^{90} -4.82732 q^{91} +2.39860 q^{92} -1.34015 q^{93} +0.101142 q^{94} -0.414901 q^{95} +1.34015 q^{96} +1.00000 q^{97} -13.1162 q^{98} +3.60227 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * 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
$3$	−1.34015	−0.773738	−0.386869	−	0.922135i	$-0.626443\pi$
$3$	−1.34015	−0.773738	−0.386869	+	0.922135i	$0.626443\pi$
$4$	1.00000	0.500000
$5$	0.146848	0.0656723	0.0328362	−	0.999461i	$-0.489546\pi$
$5$	0.146848	0.0656723	0.0328362	+	0.999461i	$0.489546\pi$
$6$	1.34015	0.547115
$7$	4.48511	1.69521	0.847606	−	0.530627i	$-0.178043\pi$
$7$	4.48511	1.69521	0.847606	+	0.530627i	$0.178043\pi$
$8$	−1.00000	−0.353553
$9$	−1.20399	−0.401329
$10$	−0.146848	−0.0464373
$11$	−2.99195	−0.902106	−0.451053	−	0.892497i	$-0.648951\pi$
$11$	−2.99195	−0.902106	−0.451053	+	0.892497i	$0.648951\pi$
$12$	−1.34015	−0.386869
$13$	−1.07630	−0.298512	−0.149256	−	0.988799i	$-0.547688\pi$
$13$	−1.07630	−0.298512	−0.149256	+	0.988799i	$0.547688\pi$
$14$	−4.48511	−1.19870
$15$	−0.196799	−0.0508132
$16$	1.00000	0.250000
$17$	1.15865	0.281013	0.140507	−	0.990080i	$-0.455127\pi$
$17$	1.15865	0.281013	0.140507	+	0.990080i	$0.455127\pi$
$18$	1.20399	0.283783
$19$	−2.82538	−0.648187	−0.324094	−	0.946025i	$-0.605059\pi$
$19$	−2.82538	−0.648187	−0.324094	+	0.946025i	$0.605059\pi$
$20$	0.146848	0.0328362
$21$	−6.01073	−1.31165
$22$	2.99195	0.637885
$23$	2.39860	0.500144	0.250072	−	0.968227i	$-0.419546\pi$
$23$	2.39860	0.500144	0.250072	+	0.968227i	$0.419546\pi$
$24$	1.34015	0.273558
$25$	−4.97844	−0.995687
$26$	1.07630	0.211080
$27$	5.63399	1.08426
$28$	4.48511	0.847606
$29$	5.88696	1.09318	0.546591	−	0.837400i	$-0.315925\pi$
$29$	5.88696	1.09318	0.546591	+	0.837400i	$0.315925\pi$
$30$	0.196799	0.0359303
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	4.00967	0.697993
$34$	−1.15865	−0.198707
$35$	0.658628	0.111328
$36$	−1.20399	−0.200665
$37$	−1.04411	−0.171650	−0.0858250	−	0.996310i	$-0.527353\pi$
$37$	−1.04411	−0.171650	−0.0858250	+	0.996310i	$0.527353\pi$
$38$	2.82538	0.458338
$39$	1.44241	0.230970
$40$	−0.146848	−0.0232187
$41$	−1.52787	−0.238614	−0.119307	−	0.992857i	$-0.538067\pi$
$41$	−1.52787	−0.238614	−0.119307	+	0.992857i	$0.538067\pi$
$42$	6.01073	0.927476
$43$	−5.98268	−0.912350	−0.456175	−	0.889890i	$-0.650781\pi$
$43$	−5.98268	−0.912350	−0.456175	+	0.889890i	$0.650781\pi$
$44$	−2.99195	−0.451053
$45$	−0.176803	−0.0263562
$46$	−2.39860	−0.353655
$47$	−0.101142	−0.0147530	−0.00737652	−	0.999973i	$-0.502348\pi$
$47$	−0.101142	−0.0147530	−0.00737652	+	0.999973i	$0.502348\pi$
$48$	−1.34015	−0.193435
$49$	13.1162	1.87374
$50$	4.97844	0.704057
$51$	−1.55277	−0.217431
$52$	−1.07630	−0.149256
$53$	4.19310	0.575967	0.287984	−	0.957635i	$-0.407015\pi$
$53$	4.19310	0.575967	0.287984	+	0.957635i	$0.407015\pi$
$54$	−5.63399	−0.766689
$55$	−0.439360	−0.0592434
$56$	−4.48511	−0.599348
$57$	3.78645	0.501527
$58$	−5.88696	−0.772996
$59$	1.40207	0.182535	0.0912673	−	0.995826i	$-0.470908\pi$
$59$	1.40207	0.182535	0.0912673	+	0.995826i	$0.470908\pi$
$60$	−0.196799	−0.0254066
$61$	5.97341	0.764817	0.382408	−	0.923993i	$-0.375095\pi$
$61$	5.97341	0.764817	0.382408	+	0.923993i	$0.375095\pi$
$62$	−1.00000	−0.127000
$63$	−5.40002	−0.680338
$64$	1.00000	0.125000
$65$	−0.158052	−0.0196040
$66$	−4.00967	−0.493556
$67$	−12.7619	−1.55911	−0.779555	−	0.626334i	$-0.784554\pi$
$67$	−12.7619	−1.55911	−0.779555	+	0.626334i	$0.784554\pi$
$68$	1.15865	0.140507
$69$	−3.21450	−0.386980
$70$	−0.658628	−0.0787211
$71$	2.50946	0.297818	0.148909	−	0.988851i	$-0.452424\pi$
$71$	2.50946	0.297818	0.148909	+	0.988851i	$0.452424\pi$
$72$	1.20399	0.141891
$73$	−9.57088	−1.12019	−0.560094	−	0.828429i	$-0.689235\pi$
$73$	−9.57088	−1.12019	−0.560094	+	0.828429i	$0.689235\pi$
$74$	1.04411	0.121375
$75$	6.67187	0.770401
$76$	−2.82538	−0.324094
$77$	−13.4192	−1.52926
$78$	−1.44241	−0.163321
$79$	−11.9579	−1.34537	−0.672683	−	0.739931i	$-0.734858\pi$
$79$	−11.9579	−1.34537	−0.672683	+	0.739931i	$0.734858\pi$
$80$	0.146848	0.0164181
$81$	−3.93845	−0.437605
$82$	1.52787	0.168725
$83$	6.83383	0.750110	0.375055	−	0.927003i	$-0.377624\pi$
$83$	6.83383	0.750110	0.375055	+	0.927003i	$0.377624\pi$
$84$	−6.01073	−0.655825
$85$	0.170145	0.0184548
$86$	5.98268	0.645129
$87$	−7.88943	−0.845836
$88$	2.99195	0.318943
$89$	−13.0241	−1.38055	−0.690274	−	0.723548i	$-0.742510\pi$
$89$	−13.0241	−1.38055	−0.690274	+	0.723548i	$0.742510\pi$
$90$	0.176803	0.0186367
$91$	−4.82732	−0.506041
$92$	2.39860	0.250072
$93$	−1.34015	−0.138967
$94$	0.101142	0.0104320
$95$	−0.414901	−0.0425680
$96$	1.34015	0.136779
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−13.1162	−1.32494
$99$	3.60227	0.362041
$100$	−4.97844	−0.497844
$101$	−2.96651	−0.295179	−0.147590	−	0.989049i	$-0.547151\pi$
$101$	−2.96651	−0.295179	−0.147590	+	0.989049i	$0.547151\pi$
$102$	1.55277	0.153747
$103$	4.33478	0.427119	0.213560	−	0.976930i	$-0.431494\pi$
$103$	4.33478	0.427119	0.213560	+	0.976930i	$0.431494\pi$
$104$	1.07630	0.105540
$105$	−0.882663	−0.0861391
$106$	−4.19310	−0.407270
$107$	14.7954	1.43032	0.715160	−	0.698960i	$-0.246354\pi$
$107$	14.7954	1.43032	0.715160	+	0.698960i	$0.246354\pi$
$108$	5.63399	0.542131
$109$	6.76662	0.648125	0.324062	−	0.946036i	$-0.394951\pi$
$109$	6.76662	0.648125	0.324062	+	0.946036i	$0.394951\pi$
$110$	0.439360	0.0418914
$111$	1.39926	0.132812
$112$	4.48511	0.423803
$113$	−13.5882	−1.27827	−0.639137	−	0.769093i	$-0.720708\pi$
$113$	−13.5882	−1.27827	−0.639137	+	0.769093i	$0.720708\pi$
$114$	−3.78645	−0.354633
$115$	0.352230	0.0328456
$116$	5.88696	0.546591
$117$	1.29585	0.119802
$118$	−1.40207	−0.129071
$119$	5.19666	0.476377
$120$	0.196799	0.0179652
$121$	−2.04826	−0.186205
$122$	−5.97341	−0.540807
$123$	2.04758	0.184624
$124$	1.00000	0.0898027
$125$	−1.46531	−0.131061
$126$	5.40002	0.481072
$127$	−11.9956	−1.06443	−0.532217	−	0.846608i	$-0.678641\pi$
$127$	−11.9956	−1.06443	−0.532217	+	0.846608i	$0.678641\pi$
$128$	−1.00000	−0.0883883
$129$	8.01771	0.705920
$130$	0.158052	0.0138621
$131$	1.32626	0.115876	0.0579378	−	0.998320i	$-0.481547\pi$
$131$	1.32626	0.115876	0.0579378	+	0.998320i	$0.481547\pi$
$132$	4.00967	0.348997
$133$	−12.6722	−1.09881
$134$	12.7619	1.10246
$135$	0.827339	0.0712060
$136$	−1.15865	−0.0993533
$137$	−3.14932	−0.269064	−0.134532	−	0.990909i	$-0.542953\pi$
$137$	−3.14932	−0.269064	−0.134532	+	0.990909i	$0.542953\pi$
$138$	3.21450	0.273636
$139$	−10.5165	−0.891996	−0.445998	−	0.895034i	$-0.647151\pi$
$139$	−10.5165	−0.891996	−0.445998	+	0.895034i	$0.647151\pi$
$140$	0.658628	0.0556642
$141$	0.135545	0.0114150
$142$	−2.50946	−0.210589
$143$	3.22023	0.269289
$144$	−1.20399	−0.100332
$145$	0.864487	0.0717917
$146$	9.57088	0.792092
$147$	−17.5777	−1.44979
$148$	−1.04411	−0.0858250
$149$	10.5659	0.865594	0.432797	−	0.901491i	$-0.357527\pi$
$149$	10.5659	0.865594	0.432797	+	0.901491i	$0.357527\pi$
$150$	−6.67187	−0.544756
$151$	2.37226	0.193052	0.0965260	−	0.995330i	$-0.469227\pi$
$151$	2.37226	0.193052	0.0965260	+	0.995330i	$0.469227\pi$
$152$	2.82538	0.229169
$153$	−1.39500	−0.112779
$154$	13.4192	1.08135
$155$	0.146848	0.0117951
$156$	1.44241	0.115485
$157$	5.30325	0.423245	0.211623	−	0.977351i	$-0.432125\pi$
$157$	5.30325	0.423245	0.211623	+	0.977351i	$0.432125\pi$
$158$	11.9579	0.951318
$159$	−5.61940	−0.445648
$160$	−0.146848	−0.0116093
$161$	10.7580	0.847849
$162$	3.93845	0.309434
$163$	−11.2080	−0.877875	−0.438937	−	0.898518i	$-0.644645\pi$
$163$	−11.2080	−0.877875	−0.438937	+	0.898518i	$0.644645\pi$
$164$	−1.52787	−0.119307
$165$	0.588811	0.0458388
$166$	−6.83383	−0.530408
$167$	−10.2237	−0.791131	−0.395565	−	0.918438i	$-0.629451\pi$
$167$	−10.2237	−0.791131	−0.395565	+	0.918438i	$0.629451\pi$
$168$	6.01073	0.463738
$169$	−11.8416	−0.910891
$170$	−0.170145	−0.0130495
$171$	3.40173	0.260137
$172$	−5.98268	−0.456175
$173$	−18.5330	−1.40904	−0.704518	−	0.709686i	$-0.748837\pi$
$173$	−18.5330	−1.40904	−0.704518	+	0.709686i	$0.748837\pi$
$174$	7.88943	0.598096
$175$	−22.3288	−1.68790
$176$	−2.99195	−0.225526
$177$	−1.87900	−0.141234
$178$	13.0241	0.976195
$179$	21.9729	1.64233	0.821164	−	0.570692i	$-0.193325\pi$
$179$	21.9729	1.64233	0.821164	+	0.570692i	$0.193325\pi$
$180$	−0.176803	−0.0131781
$181$	12.0120	0.892848	0.446424	−	0.894822i	$-0.352697\pi$
$181$	12.0120	0.892848	0.446424	+	0.894822i	$0.352697\pi$
$182$	4.82732	0.357825
$183$	−8.00529	−0.591768
$184$	−2.39860	−0.176828
$185$	−0.153325	−0.0112726
$186$	1.34015	0.0982648
$187$	−3.46661	−0.253504
$188$	−0.101142	−0.00737652
$189$	25.2691	1.83805
$190$	0.414901	0.0301001
$191$	7.09505	0.513380	0.256690	−	0.966494i	$-0.417368\pi$
$191$	7.09505	0.513380	0.256690	+	0.966494i	$0.417368\pi$
$192$	−1.34015	−0.0967173
$193$	15.9071	1.14502	0.572509	−	0.819898i	$-0.305970\pi$
$193$	15.9071	1.14502	0.572509	+	0.819898i	$0.305970\pi$
$194$	−1.00000	−0.0717958
$195$	0.211814	0.0151683
$196$	13.1162	0.936871
$197$	−8.07825	−0.575552	−0.287776	−	0.957698i	$-0.592916\pi$
$197$	−8.07825	−0.575552	−0.287776	+	0.957698i	$0.592916\pi$
$198$	−3.60227	−0.256002
$199$	12.8330	0.909710	0.454855	−	0.890565i	$-0.349691\pi$
$199$	12.8330	0.909710	0.454855	+	0.890565i	$0.349691\pi$
$200$	4.97844	0.352029
$201$	17.1029	1.20634
$202$	2.96651	0.208723
$203$	26.4037	1.85317
$204$	−1.55277	−0.108715
$205$	−0.224365	−0.0156703
$206$	−4.33478	−0.302019
$207$	−2.88789	−0.200722
$208$	−1.07630	−0.0746280
$209$	8.45340	0.584734
$210$	0.882663	0.0609095
$211$	−27.1374	−1.86822	−0.934109	−	0.356987i	$-0.883804\pi$
$211$	−27.1374	−1.86822	−0.934109	+	0.356987i	$0.883804\pi$
$212$	4.19310	0.287984
$213$	−3.36306	−0.230433
$214$	−14.7954	−1.01139
$215$	−0.878543	−0.0599161
$216$	−5.63399	−0.383344
$217$	4.48511	0.304469
$218$	−6.76662	−0.458293
$219$	12.8265	0.866732
$220$	−0.439360	−0.0296217
$221$	−1.24705	−0.0838859
$222$	−1.39926	−0.0939124
$223$	−17.4952	−1.17157	−0.585783	−	0.810468i	$-0.699213\pi$
$223$	−17.4952	−1.17157	−0.585783	+	0.810468i	$0.699213\pi$
$224$	−4.48511	−0.299674
$225$	5.99398	0.399598
$226$	13.5882	0.903876
$227$	24.3837	1.61840	0.809202	−	0.587531i	$-0.199900\pi$
$227$	24.3837	1.61840	0.809202	+	0.587531i	$0.199900\pi$
$228$	3.78645	0.250764
$229$	14.0174	0.926294	0.463147	−	0.886282i	$-0.346720\pi$
$229$	14.0174	0.926294	0.463147	+	0.886282i	$0.346720\pi$
$230$	−0.352230	−0.0232253
$231$	17.9838	1.18325
$232$	−5.88696	−0.386498
$233$	−3.57899	−0.234468	−0.117234	−	0.993104i	$-0.537403\pi$
$233$	−3.57899	−0.234468	−0.117234	+	0.993104i	$0.537403\pi$
$234$	−1.29585	−0.0847125
$235$	−0.0148524	−0.000968866 0
$236$	1.40207	0.0912673
$237$	16.0254	1.04096
$238$	−5.19666	−0.336850
$239$	−8.16959	−0.528447	−0.264224	−	0.964461i	$-0.585116\pi$
$239$	−8.16959	−0.528447	−0.264224	+	0.964461i	$0.585116\pi$
$240$	−0.196799	−0.0127033
$241$	9.41949	0.606763	0.303381	−	0.952869i	$-0.401884\pi$
$241$	9.41949	0.606763	0.303381	+	0.952869i	$0.401884\pi$
$242$	2.04826	0.131667
$243$	−11.6238	−0.745670
$244$	5.97341	0.382408
$245$	1.92608	0.123053
$246$	−2.04758	−0.130549
$247$	3.04096	0.193492
$248$	−1.00000	−0.0635001
$249$	−9.15838	−0.580389
$250$	1.46531	0.0926744
$251$	−7.41695	−0.468154	−0.234077	−	0.972218i	$-0.575207\pi$
$251$	−7.41695	−0.468154	−0.234077	+	0.972218i	$0.575207\pi$
$252$	−5.40002	−0.340169
$253$	−7.17650	−0.451182
$254$	11.9956	0.752669
$255$	−0.228020	−0.0142792
$256$	1.00000	0.0625000
$257$	1.07333	0.0669524	0.0334762	−	0.999440i	$-0.489342\pi$
$257$	1.07333	0.0669524	0.0334762	+	0.999440i	$0.489342\pi$
$258$	−8.01771	−0.499161
$259$	−4.68293	−0.290983
$260$	−0.158052	−0.00980198
$261$	−7.08783	−0.438726
$262$	−1.32626	−0.0819364
$263$	−23.1932	−1.43015	−0.715077	−	0.699046i	$-0.753608\pi$
$263$	−23.1932	−1.43015	−0.715077	+	0.699046i	$0.753608\pi$
$264$	−4.00967	−0.246778
$265$	0.615748	0.0378251
$266$	12.6722	0.776979
$267$	17.4543	1.06818
$268$	−12.7619	−0.779555
$269$	12.4005	0.756071	0.378035	−	0.925791i	$-0.376600\pi$
$269$	12.4005	0.756071	0.378035	+	0.925791i	$0.376600\pi$
$270$	−0.827339	−0.0503502
$271$	9.01640	0.547707	0.273854	−	0.961771i	$-0.411702\pi$
$271$	9.01640	0.547707	0.273854	+	0.961771i	$0.411702\pi$
$272$	1.15865	0.0702534
$273$	6.46935	0.391543
$274$	3.14932	0.190257
$275$	14.8952	0.898215
$276$	−3.21450	−0.193490
$277$	23.6807	1.42283	0.711417	−	0.702770i	$-0.248054\pi$
$277$	23.6807	1.42283	0.711417	+	0.702770i	$0.248054\pi$
$278$	10.5165	0.630737
$279$	−1.20399	−0.0720809
$280$	−0.658628	−0.0393605
$281$	7.14421	0.426188	0.213094	−	0.977032i	$-0.431646\pi$
$281$	7.14421	0.426188	0.213094	+	0.977032i	$0.431646\pi$
$282$	−0.135545	−0.00807161
$283$	−3.65870	−0.217487	−0.108744	−	0.994070i	$-0.534683\pi$
$283$	−3.65870	−0.217487	−0.108744	+	0.994070i	$0.534683\pi$
$284$	2.50946	0.148909
$285$	0.556031	0.0329365
$286$	−3.22023	−0.190416
$287$	−6.85267	−0.404501
$288$	1.20399	0.0709457
$289$	−15.6575	−0.921031
$290$	−0.864487	−0.0507644
$291$	−1.34015	−0.0785612
$292$	−9.57088	−0.560094
$293$	1.85544	0.108396	0.0541979	−	0.998530i	$-0.482740\pi$
$293$	1.85544	0.108396	0.0541979	+	0.998530i	$0.482740\pi$
$294$	17.5777	1.02515
$295$	0.205891	0.0119875
$296$	1.04411	0.0606874
$297$	−16.8566	−0.978119
$298$	−10.5659	−0.612068
$299$	−2.58162	−0.149299
$300$	6.67187	0.385201
$301$	−26.8330	−1.54663
$302$	−2.37226	−0.136508
$303$	3.97558	0.228391
$304$	−2.82538	−0.162047
$305$	0.877182	0.0502273
$306$	1.39500	0.0797468
$307$	−29.2078	−1.66698	−0.833489	−	0.552536i	$-0.813660\pi$
$307$	−29.2078	−1.66698	−0.833489	+	0.552536i	$0.813660\pi$
$308$	−13.4192	−0.764630
$309$	−5.80928	−0.330478
$310$	−0.146848	−0.00834039
$311$	−12.7806	−0.724720	−0.362360	−	0.932038i	$-0.618029\pi$
$311$	−12.7806	−0.724720	−0.362360	+	0.932038i	$0.618029\pi$
$312$	−1.44241	−0.0816603
$313$	−24.2974	−1.37337	−0.686685	−	0.726955i	$-0.740935\pi$
$313$	−24.2974	−1.37337	−0.686685	+	0.726955i	$0.740935\pi$
$314$	−5.30325	−0.299280
$315$	−0.792980	−0.0446794
$316$	−11.9579	−0.672683
$317$	7.82041	0.439238	0.219619	−	0.975586i	$-0.429519\pi$
$317$	7.82041	0.439238	0.219619	+	0.975586i	$0.429519\pi$
$318$	5.61940	0.315121
$319$	−17.6135	−0.986165
$320$	0.146848	0.00820904
$321$	−19.8280	−1.10669
$322$	−10.7580	−0.599520
$323$	−3.27363	−0.182149
$324$	−3.93845	−0.218803
$325$	5.35829	0.297225
$326$	11.2080	0.620751
$327$	−9.06831	−0.501479
$328$	1.52787	0.0843627
$329$	−0.453632	−0.0250095
$330$	−0.588811	−0.0324130
$331$	−30.4112	−1.67155	−0.835776	−	0.549071i	$-0.814982\pi$
$331$	−30.4112	−1.67155	−0.835776	+	0.549071i	$0.814982\pi$
$332$	6.83383	0.375055
$333$	1.25709	0.0688882
$334$	10.2237	0.559414
$335$	−1.87405	−0.102390
$336$	−6.01073	−0.327912
$337$	−0.441470	−0.0240484	−0.0120242	−	0.999928i	$-0.503828\pi$
$337$	−0.441470	−0.0240484	−0.0120242	+	0.999928i	$0.503828\pi$
$338$	11.8416	0.644097
$339$	18.2103	0.989049
$340$	0.170145	0.00922740
$341$	−2.99195	−0.162023
$342$	−3.40173	−0.183944
$343$	27.4318	1.48118
$344$	5.98268	0.322564
$345$	−0.472042	−0.0254139
$346$	18.5330	0.996339
$347$	32.4233	1.74057	0.870286	−	0.492547i	$-0.163934\pi$
$347$	32.4233	1.74057	0.870286	+	0.492547i	$0.163934\pi$
$348$	−7.88943	−0.422918
$349$	−2.68314	−0.143625	−0.0718125	−	0.997418i	$-0.522878\pi$
$349$	−2.68314	−0.143625	−0.0718125	+	0.997418i	$0.522878\pi$
$350$	22.3288	1.19353
$351$	−6.06386	−0.323665
$352$	2.99195	0.159471
$353$	15.8025	0.841082	0.420541	−	0.907274i	$-0.361840\pi$
$353$	15.8025	0.841082	0.420541	+	0.907274i	$0.361840\pi$
$354$	1.87900	0.0998675
$355$	0.368509	0.0195584
$356$	−13.0241	−0.690274
$357$	−6.96433	−0.368591
$358$	−21.9729	−1.16130
$359$	−13.3423	−0.704178	−0.352089	−	0.935967i	$-0.614529\pi$
$359$	−13.3423	−0.704178	−0.352089	+	0.935967i	$0.614529\pi$
$360$	0.176803	0.00931833
$361$	−11.0172	−0.579853
$362$	−12.0120	−0.631339
$363$	2.74498	0.144074
$364$	−4.82732	−0.253020
$365$	−1.40546	−0.0735653
$366$	8.00529	0.418443
$367$	−21.4463	−1.11949	−0.559745	−	0.828665i	$-0.689101\pi$
$367$	−21.4463	−1.11949	−0.559745	+	0.828665i	$0.689101\pi$
$368$	2.39860	0.125036
$369$	1.83954	0.0957627
$370$	0.153325	0.00797097
$371$	18.8065	0.976386
$372$	−1.34015	−0.0694837
$373$	−21.2229	−1.09888	−0.549439	−	0.835534i	$-0.685159\pi$
$373$	−21.2229	−1.09888	−0.549439	+	0.835534i	$0.685159\pi$
$374$	3.46661	0.179254
$375$	1.96374	0.101407
$376$	0.101142	0.00521599
$377$	−6.33614	−0.326328
$378$	−25.2691	−1.29970
$379$	−7.13701	−0.366604	−0.183302	−	0.983057i	$-0.558679\pi$
$379$	−7.13701	−0.366604	−0.183302	+	0.983057i	$0.558679\pi$
$380$	−0.414901	−0.0212840
$381$	16.0759	0.823594
$382$	−7.09505	−0.363014
$383$	−31.8545	−1.62769	−0.813845	−	0.581082i	$-0.802630\pi$
$383$	−31.8545	−1.62769	−0.813845	+	0.581082i	$0.802630\pi$
$384$	1.34015	0.0683894
$385$	−1.97058	−0.100430
$386$	−15.9071	−0.809650
$387$	7.20307	0.366153
$388$	1.00000	0.0507673
$389$	2.64003	0.133855	0.0669275	−	0.997758i	$-0.478680\pi$
$389$	2.64003	0.133855	0.0669275	+	0.997758i	$0.478680\pi$
$390$	−0.211814	−0.0107256
$391$	2.77914	0.140547
$392$	−13.1162	−0.662468
$393$	−1.77739	−0.0896574
$394$	8.07825	0.406976
$395$	−1.75599	−0.0883533
$396$	3.60227	0.181021
$397$	−36.3026	−1.82198	−0.910989	−	0.412431i	$-0.864680\pi$
$397$	−36.3026	−1.82198	−0.910989	+	0.412431i	$0.864680\pi$
$398$	−12.8330	−0.643262
$399$	16.9826	0.850195
$400$	−4.97844	−0.248922
$401$	−17.3212	−0.864978	−0.432489	−	0.901639i	$-0.642365\pi$
$401$	−17.3212	−0.864978	−0.432489	+	0.901639i	$0.642365\pi$
$402$	−17.1029	−0.853013
$403$	−1.07630	−0.0536143
$404$	−2.96651	−0.147590
$405$	−0.578352	−0.0287386
$406$	−26.4037	−1.31039
$407$	3.12391	0.154846
$408$	1.55277	0.0768734
$409$	−23.9393	−1.18372	−0.591860	−	0.806041i	$-0.701606\pi$
$409$	−23.9393	−1.18372	−0.591860	+	0.806041i	$0.701606\pi$
$410$	0.224365	0.0110806
$411$	4.22057	0.208185
$412$	4.33478	0.213560
$413$	6.28846	0.309435
$414$	2.88789	0.141932
$415$	1.00353	0.0492615
$416$	1.07630	0.0527700
$417$	14.0937	0.690172
$418$	−8.45340	−0.413469
$419$	32.3963	1.58266	0.791330	−	0.611389i	$-0.209389\pi$
$419$	32.3963	1.58266	0.791330	+	0.611389i	$0.209389\pi$
$420$	−0.882663	−0.0430695
$421$	−14.8157	−0.722074	−0.361037	−	0.932551i	$-0.617577\pi$
$421$	−14.8157	−0.722074	−0.361037	+	0.932551i	$0.617577\pi$
$422$	27.1374	1.32103
$423$	0.121773	0.00592083
$424$	−4.19310	−0.203635
$425$	−5.76826	−0.279801
$426$	3.36306	0.162941
$427$	26.7914	1.29653
$428$	14.7954	0.715160
$429$	−4.31561	−0.208359
$430$	0.878543	0.0423671
$431$	−17.9410	−0.864188	−0.432094	−	0.901829i	$-0.642225\pi$
$431$	−17.9410	−0.864188	−0.432094	+	0.901829i	$0.642225\pi$
$432$	5.63399	0.271065
$433$	−0.00155027	−7.45014e−5 0	−3.72507e−5	−	1.00000i	$-0.500012\pi$
$433$	−0.00155027	−7.45014e−5 0	−3.72507e−5		1.00000i	$0.500012\pi$
$434$	−4.48511	−0.215292
$435$	−1.15855	−0.0555480
$436$	6.76662	0.324062
$437$	−6.77698	−0.324187
$438$	−12.8265	−0.612872
$439$	23.3214	1.11307	0.556536	−	0.830824i	$-0.312130\pi$
$439$	23.3214	1.11307	0.556536	+	0.830824i	$0.312130\pi$
$440$	0.439360	0.0209457
$441$	−15.7917	−0.751988
$442$	1.24705	0.0593163
$443$	27.0887	1.28702	0.643512	−	0.765436i	$-0.277477\pi$
$443$	27.0887	1.28702	0.643512	+	0.765436i	$0.277477\pi$
$444$	1.39926	0.0664061
$445$	−1.91256	−0.0906638
$446$	17.4952	0.828423
$447$	−14.1600	−0.669743
$448$	4.48511	0.211901
$449$	−27.3286	−1.28972	−0.644858	−	0.764302i	$-0.723084\pi$
$449$	−27.3286	−1.28972	−0.644858	+	0.764302i	$0.723084\pi$
$450$	−5.99398	−0.282559
$451$	4.57131	0.215255
$452$	−13.5882	−0.639137
$453$	−3.17920	−0.149372
$454$	−24.3837	−1.14438
$455$	−0.708881	−0.0332329
$456$	−3.78645	−0.177317
$457$	−23.6778	−1.10760	−0.553799	−	0.832650i	$-0.686823\pi$
$457$	−23.6778	−1.10760	−0.553799	+	0.832650i	$0.686823\pi$
$458$	−14.0174	−0.654988
$459$	6.52781	0.304692
$460$	0.352230	0.0164228
$461$	−18.6428	−0.868281	−0.434140	−	0.900845i	$-0.642948\pi$
$461$	−18.6428	−0.868281	−0.434140	+	0.900845i	$0.642948\pi$
$462$	−17.9838	−0.836682
$463$	23.0551	1.07146	0.535730	−	0.844390i	$-0.320037\pi$
$463$	23.0551	1.07146	0.535730	+	0.844390i	$0.320037\pi$
$464$	5.88696	0.273295
$465$	−0.196799	−0.00912631
$466$	3.57899	0.165794
$467$	−25.2124	−1.16669	−0.583345	−	0.812225i	$-0.698256\pi$
$467$	−25.2124	−1.16669	−0.583345	+	0.812225i	$0.698256\pi$
$468$	1.29585	0.0599008
$469$	−57.2383	−2.64302
$470$	0.0148524	0.000685092 0
$471$	−7.10717	−0.327481
$472$	−1.40207	−0.0645357
$473$	17.8999	0.823036
$474$	−16.0254	−0.736071
$475$	14.0660	0.645392
$476$	5.19666	0.238189
$477$	−5.04845	−0.231153
$478$	8.16959	0.373669
$479$	13.4981	0.616744	0.308372	−	0.951266i	$-0.400216\pi$
$479$	13.4981	0.616744	0.308372	+	0.951266i	$0.400216\pi$
$480$	0.196799	0.00898258
$481$	1.12377	0.0512396
$482$	−9.41949	−0.429046
$483$	−14.4174	−0.656013
$484$	−2.04826	−0.0931027
$485$	0.146848	0.00666801
$486$	11.6238	0.527268
$487$	8.79030	0.398326	0.199163	−	0.979966i	$-0.436178\pi$
$487$	8.79030	0.398326	0.199163	+	0.979966i	$0.436178\pi$
$488$	−5.97341	−0.270404
$489$	15.0204	0.679245
$490$	−1.92608	−0.0870116
$491$	−27.4223	−1.23755	−0.618775	−	0.785569i	$-0.712371\pi$
$491$	−27.4223	−1.23755	−0.618775	+	0.785569i	$0.712371\pi$
$492$	2.04758	0.0923122
$493$	6.82092	0.307199
$494$	−3.04096	−0.136819
$495$	0.528985	0.0237761
$496$	1.00000	0.0449013
$497$	11.2552	0.504865
$498$	9.15838	0.410397
$499$	21.0745	0.943424	0.471712	−	0.881753i	$-0.343636\pi$
$499$	21.0745	0.943424	0.471712	+	0.881753i	$0.343636\pi$
$500$	−1.46531	−0.0655307
$501$	13.7013	0.612128
$502$	7.41695	0.331035
$503$	−12.1158	−0.540216	−0.270108	−	0.962830i	$-0.587059\pi$
$503$	−12.1158	−0.540216	−0.270108	+	0.962830i	$0.587059\pi$
$504$	5.40002	0.240536
$505$	−0.435626	−0.0193851
$506$	7.17650	0.319034
$507$	15.8695	0.704791
$508$	−11.9956	−0.532217
$509$	−21.0757	−0.934163	−0.467082	−	0.884214i	$-0.654695\pi$
$509$	−21.0757	−0.934163	−0.467082	+	0.884214i	$0.654695\pi$
$510$	0.228020	0.0100969
$511$	−42.9265	−1.89895
$512$	−1.00000	−0.0441942
$513$	−15.9182	−0.702805
$514$	−1.07333	−0.0473425
$515$	0.636553	0.0280499
$516$	8.01771	0.352960
$517$	0.302611	0.0133088
$518$	4.68293	0.205756
$519$	24.8370	1.09022
$520$	0.158052	0.00693105
$521$	−3.48680	−0.152759	−0.0763797	−	0.997079i	$-0.524336\pi$
$521$	−3.48680	−0.152759	−0.0763797	+	0.997079i	$0.524336\pi$
$522$	7.08783	0.310226
$523$	35.1540	1.53718	0.768590	−	0.639742i	$-0.220959\pi$
$523$	35.1540	1.53718	0.768590	+	0.639742i	$0.220959\pi$
$524$	1.32626	0.0579378
$525$	29.9241	1.30599
$526$	23.1932	1.01127
$527$	1.15865	0.0504715
$528$	4.00967	0.174498
$529$	−17.2467	−0.749856
$530$	−0.615748	−0.0267464
$531$	−1.68808	−0.0732565
$532$	−12.6722	−0.549407
$533$	1.64445	0.0712290
$534$	−17.4543	−0.755320
$535$	2.17266	0.0939325
$536$	12.7619	0.551228
$537$	−29.4470	−1.27073
$538$	−12.4005	−0.534623
$539$	−39.2429	−1.69031
$540$	0.827339	0.0356030
$541$	−27.7920	−1.19487	−0.597435	−	0.801917i	$-0.703813\pi$
$541$	−27.7920	−1.19487	−0.597435	+	0.801917i	$0.703813\pi$
$542$	−9.01640	−0.387287
$543$	−16.0980	−0.690831
$544$	−1.15865	−0.0496766
$545$	0.993663	0.0425639
$546$	−6.46935	−0.276863
$547$	−3.46159	−0.148007	−0.0740034	−	0.997258i	$-0.523578\pi$
$547$	−3.46159	−0.148007	−0.0740034	+	0.997258i	$0.523578\pi$
$548$	−3.14932	−0.134532
$549$	−7.19191	−0.306943
$550$	−14.8952	−0.635134
$551$	−16.6329	−0.708586
$552$	3.21450	0.136818
$553$	−53.6324	−2.28068
$554$	−23.6807	−1.00610
$555$	0.205479	0.00872208
$556$	−10.5165	−0.445998
$557$	−14.0837	−0.596747	−0.298373	−	0.954449i	$-0.596444\pi$
$557$	−14.0837	−0.596747	−0.298373	+	0.954449i	$0.596444\pi$
$558$	1.20399	0.0509689
$559$	6.43916	0.272347
$560$	0.658628	0.0278321
$561$	4.64579	0.196146
$562$	−7.14421	−0.301360
$563$	−4.81367	−0.202872	−0.101436	−	0.994842i	$-0.532344\pi$
$563$	−4.81367	−0.202872	−0.101436	+	0.994842i	$0.532344\pi$
$564$	0.135545	0.00570749
$565$	−1.99540	−0.0839472
$566$	3.65870	0.153787
$567$	−17.6644	−0.741834
$568$	−2.50946	−0.105295
$569$	7.50634	0.314682	0.157341	−	0.987544i	$-0.449708\pi$
$569$	7.50634	0.314682	0.157341	+	0.987544i	$0.449708\pi$
$570$	−0.556031	−0.0232896
$571$	−38.3944	−1.60675	−0.803377	−	0.595470i	$-0.796966\pi$
$571$	−38.3944	−1.60675	−0.803377	+	0.595470i	$0.796966\pi$
$572$	3.22023	0.134645
$573$	−9.50846	−0.397222
$574$	6.85267	0.286025
$575$	−11.9413	−0.497987
$576$	−1.20399	−0.0501662
$577$	−36.6173	−1.52440	−0.762199	−	0.647343i	$-0.775880\pi$
$577$	−36.6173	−1.52440	−0.762199	+	0.647343i	$0.775880\pi$
$578$	15.6575	0.651268
$579$	−21.3180	−0.885945
$580$	0.864487	0.0358959
$581$	30.6505	1.27160
$582$	1.34015	0.0555512
$583$	−12.5455	−0.519583
$584$	9.57088	0.396046
$585$	0.190293	0.00786765
$586$	−1.85544	−0.0766474
$587$	32.5405	1.34309	0.671544	−	0.740964i	$-0.265631\pi$
$587$	32.5405	1.34309	0.671544	+	0.740964i	$0.265631\pi$
$588$	−17.5777	−0.724893
$589$	−2.82538	−0.116418
$590$	−0.205891	−0.00847642
$591$	10.8261	0.445326
$592$	−1.04411	−0.0429125
$593$	−23.8164	−0.978023	−0.489012	−	0.872277i	$-0.662642\pi$
$593$	−23.8164	−0.978023	−0.489012	+	0.872277i	$0.662642\pi$
$594$	16.8566	0.691634
$595$	0.763118	0.0312848
$596$	10.5659	0.432797
$597$	−17.1982	−0.703877
$598$	2.58162	0.105570
$599$	−34.3917	−1.40521	−0.702604	−	0.711581i	$-0.747980\pi$
$599$	−34.3917	−1.40521	−0.702604	+	0.711581i	$0.747980\pi$
$600$	−6.67187	−0.272378
$601$	3.19879	0.130481	0.0652406	−	0.997870i	$-0.479218\pi$
$601$	3.19879	0.130481	0.0652406	+	0.997870i	$0.479218\pi$
$602$	26.8330	1.09363
$603$	15.3651	0.625716
$604$	2.37226	0.0965260
$605$	−0.300782	−0.0122285
$606$	−3.97558	−0.161497
$607$	1.93514	0.0785449	0.0392724	−	0.999229i	$-0.487496\pi$
$607$	1.93514	0.0785449	0.0392724	+	0.999229i	$0.487496\pi$
$608$	2.82538	0.114584
$609$	−35.3850	−1.43387
$610$	−0.877182	−0.0355160
$611$	0.108859	0.00440396
$612$	−1.39500	−0.0563895
$613$	−11.3735	−0.459373	−0.229687	−	0.973265i	$-0.573770\pi$
$613$	−11.3735	−0.459373	−0.229687	+	0.973265i	$0.573770\pi$
$614$	29.2078	1.17873
$615$	0.300683	0.0121247
$616$	13.4192	0.540675
$617$	−28.0968	−1.13113	−0.565567	−	0.824702i	$-0.691343\pi$
$617$	−28.0968	−1.13113	−0.565567	+	0.824702i	$0.691343\pi$
$618$	5.80928	0.233683
$619$	−3.34371	−0.134395	−0.0671975	−	0.997740i	$-0.521406\pi$
$619$	−3.34371	−0.134395	−0.0671975	+	0.997740i	$0.521406\pi$
$620$	0.146848	0.00589755
$621$	13.5137	0.542287
$622$	12.7806	0.512454
$623$	−58.4144	−2.34032
$624$	1.44241	0.0577425
$625$	24.6770	0.987080
$626$	24.2974	0.971119
$627$	−11.3288	−0.452431
$628$	5.30325	0.211623
$629$	−1.20975	−0.0482359
$630$	0.792980	0.0315931
$631$	−14.6718	−0.584076	−0.292038	−	0.956407i	$-0.594333\pi$
$631$	−14.6718	−0.584076	−0.292038	+	0.956407i	$0.594333\pi$
$632$	11.9579	0.475659
$633$	36.3683	1.44551
$634$	−7.82041	−0.310588
$635$	−1.76152	−0.0699039
$636$	−5.61940	−0.222824
$637$	−14.1170	−0.559334
$638$	17.6135	0.697324
$639$	−3.02136	−0.119523
$640$	−0.146848	−0.00580467
$641$	−31.2214	−1.23317	−0.616585	−	0.787288i	$-0.711484\pi$
$641$	−31.2214	−1.23317	−0.616585	+	0.787288i	$0.711484\pi$
$642$	19.8280	0.782551
$643$	33.0987	1.30529	0.652643	−	0.757666i	$-0.273660\pi$
$643$	33.0987	1.30529	0.652643	+	0.757666i	$0.273660\pi$
$644$	10.7580	0.423925
$645$	1.17738	0.0463594
$646$	3.27363	0.128799
$647$	32.0989	1.26194	0.630970	−	0.775807i	$-0.282657\pi$
$647$	32.0989	1.26194	0.630970	+	0.775807i	$0.282657\pi$
$648$	3.93845	0.154717
$649$	−4.19493	−0.164665
$650$	−5.35829	−0.210169
$651$	−6.01073	−0.235579
$652$	−11.2080	−0.438937
$653$	13.7170	0.536788	0.268394	−	0.963309i	$-0.413507\pi$
$653$	13.7170	0.536788	0.268394	+	0.963309i	$0.413507\pi$
$654$	9.06831	0.354599
$655$	0.194758	0.00760982
$656$	−1.52787	−0.0596534
$657$	11.5232	0.449564
$658$	0.453632	0.0176844
$659$	48.7908	1.90062	0.950310	−	0.311306i	$-0.100766\pi$
$659$	48.7908	1.90062	0.950310	+	0.311306i	$0.100766\pi$
$660$	0.588811	0.0229194
$661$	−1.95888	−0.0761915	−0.0380958	−	0.999274i	$-0.512129\pi$
$661$	−1.95888	−0.0761915	−0.0380958	+	0.999274i	$0.512129\pi$
$662$	30.4112	1.18197
$663$	1.67124	0.0649057
$664$	−6.83383	−0.265204
$665$	−1.86088	−0.0721617
$666$	−1.25709	−0.0487113
$667$	14.1205	0.546748
$668$	−10.2237	−0.395565
$669$	23.4463	0.906486
$670$	1.87405	0.0724009
$671$	−17.8721	−0.689945
$672$	6.01073	0.231869
$673$	−1.83855	−0.0708709	−0.0354354	−	0.999372i	$-0.511282\pi$
$673$	−1.83855	−0.0708709	−0.0354354	+	0.999372i	$0.511282\pi$
$674$	0.441470	0.0170048
$675$	−28.0485	−1.07959
$676$	−11.8416	−0.455445
$677$	−4.34107	−0.166841	−0.0834204	−	0.996514i	$-0.526584\pi$
$677$	−4.34107	−0.166841	−0.0834204	+	0.996514i	$0.526584\pi$
$678$	−18.2103	−0.699363
$679$	4.48511	0.172123
$680$	−0.170145	−0.00652476
$681$	−32.6779	−1.25222
$682$	2.99195	0.114568
$683$	−5.18603	−0.198438	−0.0992189	−	0.995066i	$-0.531634\pi$
$683$	−5.18603	−0.198438	−0.0992189	+	0.995066i	$0.531634\pi$
$684$	3.40173	0.130068
$685$	−0.462470	−0.0176701
$686$	−27.4318	−1.04735
$687$	−18.7854	−0.716709
$688$	−5.98268	−0.228088
$689$	−4.51304	−0.171933
$690$	0.472042	0.0179703
$691$	15.4031	0.585960	0.292980	−	0.956119i	$-0.405353\pi$
$691$	15.4031	0.585960	0.292980	+	0.956119i	$0.405353\pi$
$692$	−18.5330	−0.704518
$693$	16.1566	0.613737
$694$	−32.4233	−1.23077
$695$	−1.54432	−0.0585795
$696$	7.88943	0.299048
$697$	−1.77027	−0.0670536
$698$	2.68314	0.101558
$699$	4.79640	0.181417
$700$	−22.3288	−0.843950
$701$	−25.5560	−0.965238	−0.482619	−	0.875830i	$-0.660314\pi$
$701$	−25.5560	−0.965238	−0.482619	+	0.875830i	$0.660314\pi$
$702$	6.06386	0.228866
$703$	2.95000	0.111261
$704$	−2.99195	−0.112763
$705$	0.0199045	0.000749648 0
$706$	−15.8025	−0.594735
$707$	−13.3051	−0.500391
$708$	−1.87900	−0.0706170
$709$	−17.9408	−0.673780	−0.336890	−	0.941544i	$-0.609375\pi$
$709$	−17.9408	−0.673780	−0.336890	+	0.941544i	$0.609375\pi$
$710$	−0.368509	−0.0138299
$711$	14.3971	0.539935
$712$	13.0241	0.488098
$713$	2.39860	0.0898285
$714$	6.96433	0.260633
$715$	0.472884	0.0176849
$716$	21.9729	0.821164
$717$	10.9485	0.408880
$718$	13.3423	0.497929
$719$	7.02925	0.262147	0.131073	−	0.991373i	$-0.458158\pi$
$719$	7.02925	0.262147	0.131073	+	0.991373i	$0.458158\pi$
$720$	−0.176803	−0.00658906
$721$	19.4420	0.724057
$722$	11.0172	0.410018
$723$	−12.6236	−0.469475
$724$	12.0120	0.446424
$725$	−29.3079	−1.08847
$726$	−2.74498	−0.101876
$727$	−25.0600	−0.929423	−0.464711	−	0.885462i	$-0.653842\pi$
$727$	−25.0600	−0.929423	−0.464711	+	0.885462i	$0.653842\pi$
$728$	4.82732	0.178912
$729$	27.3931	1.01456
$730$	1.40546	0.0520185
$731$	−6.93182	−0.256383
$732$	−8.00529	−0.295884
$733$	−12.2857	−0.453783	−0.226892	−	0.973920i	$-0.572856\pi$
$733$	−12.2857	−0.453783	−0.226892	+	0.973920i	$0.572856\pi$
$734$	21.4463	0.791599
$735$	−2.58125	−0.0952108
$736$	−2.39860	−0.0884138
$737$	38.1828	1.40648
$738$	−1.83954	−0.0677144
$739$	3.67504	0.135188	0.0675942	−	0.997713i	$-0.478468\pi$
$739$	3.67504	0.135188	0.0675942	+	0.997713i	$0.478468\pi$
$740$	−0.153325	−0.00563632
$741$	−4.07536	−0.149712
$742$	−18.8065	−0.690409
$743$	44.3183	1.62588	0.812940	−	0.582348i	$-0.197866\pi$
$743$	44.3183	1.62588	0.812940	+	0.582348i	$0.197866\pi$
$744$	1.34015	0.0491324
$745$	1.55158	0.0568456
$746$	21.2229	0.777024
$747$	−8.22785	−0.301041
$748$	−3.46661	−0.126752
$749$	66.3588	2.42470
$750$	−1.96374	−0.0717057
$751$	2.36276	0.0862184	0.0431092	−	0.999070i	$-0.486274\pi$
$751$	2.36276	0.0862184	0.0431092	+	0.999070i	$0.486274\pi$
$752$	−0.101142	−0.00368826
$753$	9.93985	0.362228
$754$	6.33614	0.230748
$755$	0.348361	0.0126782
$756$	25.2691	0.919027
$757$	4.48289	0.162933	0.0814667	−	0.996676i	$-0.474040\pi$
$757$	4.48289	0.162933	0.0814667	+	0.996676i	$0.474040\pi$
$758$	7.13701	0.259228
$759$	9.61761	0.349097
$760$	0.414901	0.0150500
$761$	20.3149	0.736413	0.368207	−	0.929744i	$-0.379972\pi$
$761$	20.3149	0.736413	0.368207	+	0.929744i	$0.379972\pi$
$762$	−16.0759	−0.582369
$763$	30.3490	1.09871
$764$	7.09505	0.256690
$765$	−0.204852	−0.00740645
$766$	31.8545	1.15095
$767$	−1.50905	−0.0544887
$768$	−1.34015	−0.0483586
$769$	−2.49170	−0.0898531	−0.0449265	−	0.998990i	$-0.514305\pi$
$769$	−2.49170	−0.0898531	−0.0449265	+	0.998990i	$0.514305\pi$
$770$	1.97058	0.0710147
$771$	−1.43843	−0.0518036
$772$	15.9071	0.572509
$773$	22.0788	0.794118	0.397059	−	0.917793i	$-0.370031\pi$
$773$	22.0788	0.794118	0.397059	+	0.917793i	$0.370031\pi$
$774$	−7.20307	−0.258909
$775$	−4.97844	−0.178831
$776$	−1.00000	−0.0358979
$777$	6.27584	0.225145
$778$	−2.64003	−0.0946497
$779$	4.31683	0.154666
$780$	0.211814	0.00758417
$781$	−7.50817	−0.268663
$782$	−2.77914	−0.0993818
$783$	33.1671	1.18529
$784$	13.1162	0.468435
$785$	0.778770	0.0277955
$786$	1.77739	0.0633973
$787$	5.39212	0.192208	0.0961042	−	0.995371i	$-0.469362\pi$
$787$	5.39212	0.192208	0.0961042	+	0.995371i	$0.469362\pi$
$788$	−8.07825	−0.287776
$789$	31.0825	1.10656
$790$	1.75599	0.0624752
$791$	−60.9447	−2.16694
$792$	−3.60227	−0.128001
$793$	−6.42918	−0.228307
$794$	36.3026	1.28833
$795$	−0.825197	−0.0292667
$796$	12.8330	0.454855
$797$	−43.2738	−1.53284	−0.766419	−	0.642341i	$-0.777963\pi$
$797$	−43.2738	−1.53284	−0.766419	+	0.642341i	$0.777963\pi$
$798$	−16.9826	−0.601179
$799$	−0.117188	−0.00414580
$800$	4.97844	0.176014
$801$	15.6808	0.554055
$802$	17.3212	0.611632
$803$	28.6356	1.01053
$804$	17.1029	0.603171
$805$	1.57979	0.0556802
$806$	1.07630	0.0379111
$807$	−16.6185	−0.585001
$808$	2.96651	0.104362
$809$	48.8867	1.71876	0.859382	−	0.511334i	$-0.170848\pi$
$809$	48.8867	1.71876	0.859382	+	0.511334i	$0.170848\pi$
$810$	0.578352	0.0203212
$811$	−24.1878	−0.849348	−0.424674	−	0.905346i	$-0.639611\pi$
$811$	−24.1878	−0.849348	−0.424674	+	0.905346i	$0.639611\pi$
$812$	26.4037	0.926587
$813$	−12.0834	−0.423782
$814$	−3.12391	−0.109493
$815$	−1.64586	−0.0576520
$816$	−1.55277	−0.0543577
$817$	16.9034	0.591374
$818$	23.9393	0.837016
$819$	5.81204	0.203089
$820$	−0.224365	−0.00783515
$821$	−42.1625	−1.47148	−0.735741	−	0.677263i	$-0.763166\pi$
$821$	−42.1625	−1.47148	−0.735741	+	0.677263i	$0.763166\pi$
$822$	−4.22057	−0.147209
$823$	23.3936	0.815451	0.407726	−	0.913104i	$-0.366322\pi$
$823$	23.3936	0.815451	0.407726	+	0.913104i	$0.366322\pi$
$824$	−4.33478	−0.151009
$825$	−19.9619	−0.694983
$826$	−6.28846	−0.218803
$827$	3.04643	0.105935	0.0529673	−	0.998596i	$-0.483132\pi$
$827$	3.04643	0.105935	0.0529673	+	0.998596i	$0.483132\pi$
$828$	−2.88789	−0.100361
$829$	54.3618	1.88806	0.944032	−	0.329854i	$-0.107000\pi$
$829$	54.3618	1.88806	0.944032	+	0.329854i	$0.107000\pi$
$830$	−1.00353	−0.0348331
$831$	−31.7357	−1.10090
$832$	−1.07630	−0.0373140
$833$	15.1971	0.526547
$834$	−14.0937	−0.488025
$835$	−1.50132	−0.0519554
$836$	8.45340	0.292367
$837$	5.63399	0.194739
$838$	−32.3963	−1.11911
$839$	4.61678	0.159389	0.0796946	−	0.996819i	$-0.474606\pi$
$839$	4.61678	0.159389	0.0796946	+	0.996819i	$0.474606\pi$
$840$	0.882663	0.0304548
$841$	5.65630	0.195045
$842$	14.8157	0.510583
$843$	−9.57434	−0.329758
$844$	−27.1374	−0.934109
$845$	−1.73891	−0.0598203
$846$	−0.121773	−0.00418666
$847$	−9.18667	−0.315658
$848$	4.19310	0.143992
$849$	4.90322	0.168278
$850$	5.76826	0.197850
$851$	−2.50440	−0.0858497
$852$	−3.36306	−0.115217
$853$	9.22691	0.315923	0.157962	−	0.987445i	$-0.449508\pi$
$853$	9.22691	0.315923	0.157962	+	0.987445i	$0.449508\pi$
$854$	−26.7914	−0.916782
$855$	0.499536	0.0170838
$856$	−14.7954	−0.505695
$857$	−40.7660	−1.39254	−0.696271	−	0.717779i	$-0.745159\pi$
$857$	−40.7660	−1.39254	−0.696271	+	0.717779i	$0.745159\pi$
$858$	4.31561	0.147332
$859$	19.3457	0.660068	0.330034	−	0.943969i	$-0.392940\pi$
$859$	19.3457	0.660068	0.330034	+	0.943969i	$0.392940\pi$
$860$	−0.878543	−0.0299581
$861$	9.18364	0.312978
$862$	17.9410	0.611073
$863$	0.965053	0.0328508	0.0164254	−	0.999865i	$-0.494771\pi$
$863$	0.965053	0.0328508	0.0164254	+	0.999865i	$0.494771\pi$
$864$	−5.63399	−0.191672
$865$	−2.72153	−0.0925346
$866$	0.00155027	5.26804e−5 0
$867$	20.9835	0.712637
$868$	4.48511	0.152234
$869$	35.7773	1.21366
$870$	1.15855	0.0392784
$871$	13.7356	0.465413
$872$	−6.76662	−0.229147
$873$	−1.20399	−0.0407488
$874$	6.77698	0.229235
$875$	−6.57208	−0.222177
$876$	12.8265	0.433366
$877$	−25.7798	−0.870521	−0.435260	−	0.900305i	$-0.643344\pi$
$877$	−25.7798	−0.870521	−0.435260	+	0.900305i	$0.643344\pi$
$878$	−23.3214	−0.787061
$879$	−2.48657	−0.0838700
$880$	−0.439360	−0.0148108
$881$	30.5707	1.02995	0.514976	−	0.857205i	$-0.327801\pi$
$881$	30.5707	1.02995	0.514976	+	0.857205i	$0.327801\pi$
$882$	15.7917	0.531736
$883$	35.2770	1.18717	0.593583	−	0.804773i	$-0.297713\pi$
$883$	35.2770	1.18717	0.593583	+	0.804773i	$0.297713\pi$
$884$	−1.24705	−0.0419429
$885$	−0.275926	−0.00927516
$886$	−27.0887	−0.910064
$887$	31.2442	1.04908	0.524538	−	0.851387i	$-0.324238\pi$
$887$	31.2442	1.04908	0.524538	+	0.851387i	$0.324238\pi$
$888$	−1.39926	−0.0469562
$889$	−53.8014	−1.80444
$890$	1.91256	0.0641090
$891$	11.7836	0.394766
$892$	−17.4952	−0.585783
$893$	0.285764	0.00956273
$894$	14.1600	0.473580
$895$	3.22666	0.107856
$896$	−4.48511	−0.149837
$897$	3.45977	0.115518
$898$	27.3286	0.911968
$899$	5.88696	0.196341
$900$	5.99398	0.199799
$901$	4.85833	0.161855
$902$	−4.57131	−0.152208
$903$	35.9603	1.19668
$904$	13.5882	0.451938
$905$	1.76394	0.0586354
$906$	3.17920	0.105622
$907$	47.5481	1.57881	0.789405	−	0.613873i	$-0.210389\pi$
$907$	47.5481	1.57881	0.789405	+	0.613873i	$0.210389\pi$
$908$	24.3837	0.809202
$909$	3.57165	0.118464
$910$	0.708881	0.0234992
$911$	5.97819	0.198066	0.0990331	−	0.995084i	$-0.468425\pi$
$911$	5.97819	0.198066	0.0990331	+	0.995084i	$0.468425\pi$
$912$	3.78645	0.125382
$913$	−20.4464	−0.676679
$914$	23.6778	0.783191
$915$	−1.17556	−0.0388628
$916$	14.0174	0.463147
$917$	5.94841	0.196434
$918$	−6.52781	−0.215450
$919$	−33.0612	−1.09059	−0.545294	−	0.838245i	$-0.683582\pi$
$919$	−33.0612	−1.09059	−0.545294	+	0.838245i	$0.683582\pi$
$920$	−0.352230	−0.0116127
$921$	39.1430	1.28980
$922$	18.6428	0.613967
$923$	−2.70093	−0.0889023
$924$	17.9838	0.591623
$925$	5.19801	0.170910
$926$	−23.0551	−0.757636
$927$	−5.21903	−0.171415
$928$	−5.88696	−0.193249
$929$	−7.85732	−0.257790	−0.128895	−	0.991658i	$-0.541143\pi$
$929$	−7.85732	−0.257790	−0.128895	+	0.991658i	$0.541143\pi$
$930$	0.196799	0.00645328
$931$	−37.0583	−1.21454
$932$	−3.57899	−0.117234
$933$	17.1279	0.560743
$934$	25.2124	0.824974
$935$	−0.509064	−0.0166482
$936$	−1.29585	−0.0423563
$937$	−20.1903	−0.659588	−0.329794	−	0.944053i	$-0.606979\pi$
$937$	−20.1903	−0.659588	−0.329794	+	0.944053i	$0.606979\pi$
$938$	57.2383	1.86890
$939$	32.5622	1.06263
$940$	−0.0148524	−0.000484433 0
$941$	−2.99674	−0.0976910	−0.0488455	−	0.998806i	$-0.515554\pi$
$941$	−2.99674	−0.0976910	−0.0488455	+	0.998806i	$0.515554\pi$
$942$	7.10717	0.231564
$943$	−3.66476	−0.119341
$944$	1.40207	0.0456336
$945$	3.71070	0.120709
$946$	−17.8999	−0.581974
$947$	−37.6713	−1.22415	−0.612076	−	0.790799i	$-0.709666\pi$
$947$	−37.6713	−1.22415	−0.612076	+	0.790799i	$0.709666\pi$
$948$	16.0254	0.520481
$949$	10.3011	0.334389
$950$	−14.0660	−0.456361
$951$	−10.4806	−0.339855
$952$	−5.19666	−0.168425
$953$	2.60590	0.0844133	0.0422067	−	0.999109i	$-0.486561\pi$
$953$	2.60590	0.0844133	0.0422067	+	0.999109i	$0.486561\pi$
$954$	5.04845	0.163450
$955$	1.04189	0.0337148
$956$	−8.16959	−0.264224
$957$	23.6048	0.763033
$958$	−13.4981	−0.436104
$959$	−14.1250	−0.456121
$960$	−0.196799	−0.00635165
$961$	1.00000	0.0322581
$962$	−1.12377	−0.0362318
$963$	−17.8134	−0.574030
$964$	9.41949	0.303381
$965$	2.33592	0.0751960
$966$	14.4174	0.463871
$967$	39.5989	1.27342	0.636708	−	0.771105i	$-0.280296\pi$
$967$	39.5989	1.27342	0.636708	+	0.771105i	$0.280296\pi$
$968$	2.04826	0.0658336
$969$	4.38716	0.140936
$970$	−0.146848	−0.00471500
$971$	7.01466	0.225111	0.112556	−	0.993645i	$-0.464096\pi$
$971$	7.01466	0.225111	0.112556	+	0.993645i	$0.464096\pi$
$972$	−11.6238	−0.372835
$973$	−47.1676	−1.51212
$974$	−8.79030	−0.281659
$975$	−7.18093	−0.229974
$976$	5.97341	0.191204
$977$	−29.7055	−0.950363	−0.475182	−	0.879888i	$-0.657618\pi$
$977$	−29.7055	−0.950363	−0.475182	+	0.879888i	$0.657618\pi$
$978$	−15.0204	−0.480299
$979$	38.9673	1.24540
$980$	1.92608	0.0615265
$981$	−8.14693	−0.260112
$982$	27.4223	0.875079
$983$	−26.1333	−0.833523	−0.416762	−	0.909016i	$-0.636835\pi$
$983$	−26.1333	−0.833523	−0.416762	+	0.909016i	$0.636835\pi$
$984$	−2.04758	−0.0652746
$985$	−1.18627	−0.0377978
$986$	−6.82092	−0.217222
$987$	0.607936	0.0193508
$988$	3.04096	0.0967459
$989$	−14.3501	−0.456306
$990$	−0.528985	−0.0168122
$991$	22.1234	0.702774	0.351387	−	0.936230i	$-0.385710\pi$
$991$	22.1234	0.702774	0.351387	+	0.936230i	$0.385710\pi$
$992$	−1.00000	−0.0317500
$993$	40.7557	1.29334
$994$	−11.2552	−0.356993
$995$	1.88450	0.0597428
$996$	−9.15838	−0.290194
$997$	−24.0946	−0.763084	−0.381542	−	0.924352i	$-0.624607\pi$
$997$	−24.0946	−0.763084	−0.381542	+	0.924352i	$0.624607\pi$
$998$	−21.0745	−0.667101
$999$	−5.88248	−0.186114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.7	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.34015 q^{3} +1.00000 q^{4} +0.146848 q^{5} +1.34015 q^{6} +4.48511 q^{7} -1.00000 q^{8} -1.20399 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.34015 q^{3} +1.00000 q^{4} +0.146848 q^{5} +1.34015 q^{6} +4.48511 q^{7} -1.00000 q^{8} -1.20399 q^{9} -0.146848 q^{10} -2.99195 q^{11} -1.34015 q^{12} -1.07630 q^{13} -4.48511 q^{14} -0.196799 q^{15} +1.00000 q^{16} +1.15865 q^{17} +1.20399 q^{18} -2.82538 q^{19} +0.146848 q^{20} -6.01073 q^{21} +2.99195 q^{22} +2.39860 q^{23} +1.34015 q^{24} -4.97844 q^{25} +1.07630 q^{26} +5.63399 q^{27} +4.48511 q^{28} +5.88696 q^{29} +0.196799 q^{30} +1.00000 q^{31} -1.00000 q^{32} +4.00967 q^{33} -1.15865 q^{34} +0.658628 q^{35} -1.20399 q^{36} -1.04411 q^{37} +2.82538 q^{38} +1.44241 q^{39} -0.146848 q^{40} -1.52787 q^{41} +6.01073 q^{42} -5.98268 q^{43} -2.99195 q^{44} -0.176803 q^{45} -2.39860 q^{46} -0.101142 q^{47} -1.34015 q^{48} +13.1162 q^{49} +4.97844 q^{50} -1.55277 q^{51} -1.07630 q^{52} +4.19310 q^{53} -5.63399 q^{54} -0.439360 q^{55} -4.48511 q^{56} +3.78645 q^{57} -5.88696 q^{58} +1.40207 q^{59} -0.196799 q^{60} +5.97341 q^{61} -1.00000 q^{62} -5.40002 q^{63} +1.00000 q^{64} -0.158052 q^{65} -4.00967 q^{66} -12.7619 q^{67} +1.15865 q^{68} -3.21450 q^{69} -0.658628 q^{70} +2.50946 q^{71} +1.20399 q^{72} -9.57088 q^{73} +1.04411 q^{74} +6.67187 q^{75} -2.82538 q^{76} -13.4192 q^{77} -1.44241 q^{78} -11.9579 q^{79} +0.146848 q^{80} -3.93845 q^{81} +1.52787 q^{82} +6.83383 q^{83} -6.01073 q^{84} +0.170145 q^{85} +5.98268 q^{86} -7.88943 q^{87} +2.99195 q^{88} -13.0241 q^{89} +0.176803 q^{90} -4.82732 q^{91} +2.39860 q^{92} -1.34015 q^{93} +0.101142 q^{94} -0.414901 q^{95} +1.34015 q^{96} +1.00000 q^{97} -13.1162 q^{98} +3.60227 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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