LMFDB - Embedded newform 392.2.z.a.205.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, minimal)

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:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			205.14
Character	$\chi$	$=$	392.205
Dual form			392.2.z.a.109.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11505 + 0.869863i) q^{2} +(0.264046 - 1.75183i) q^{3} +(0.486677 - 1.93988i) q^{4} +(3.38580 - 1.32883i) q^{5} +(1.22943 + 2.18307i) q^{6} +(-0.357778 - 2.62145i) q^{7} +(1.14476 + 2.58641i) q^{8} +(-0.132482 - 0.0408653i) q^{9} +O(q^{10})$	\(q+(-1.11505 + 0.869863i) q^{2} +(0.264046 - 1.75183i) q^{3} +(0.486677 - 1.93988i) q^{4} +(3.38580 - 1.32883i) q^{5} +(1.22943 + 2.18307i) q^{6} +(-0.357778 - 2.62145i) q^{7} +(1.14476 + 2.58641i) q^{8} +(-0.132482 - 0.0408653i) q^{9} +(-2.61944 + 4.42689i) q^{10} +(0.946542 + 3.06861i) q^{11} +(-3.26985 - 1.36480i) q^{12} +(4.21081 + 0.961090i) q^{13} +(2.67924 + 2.61183i) q^{14} +(-1.43388 - 6.28223i) q^{15} +(-3.52629 - 1.88819i) q^{16} +(-3.19299 - 2.17694i) q^{17} +(0.183271 - 0.0696742i) q^{18} +(-2.19780 - 1.26890i) q^{19} +(-0.929978 - 7.21476i) q^{20} +(-4.68681 - 0.0654163i) q^{21} +(-3.72472 - 2.59830i) q^{22} +(-6.54375 + 4.46145i) q^{23} +(4.83323 - 1.32250i) q^{24} +(6.03258 - 5.59742i) q^{25} +(-5.53129 + 2.59116i) q^{26} +(2.19946 - 4.56723i) q^{27} +(-5.25943 - 0.581752i) q^{28} +(3.71732 + 7.71910i) q^{29} +(7.06352 + 5.75773i) q^{30} +(1.03774 + 1.79741i) q^{31} +(5.57446 - 0.961955i) q^{32} +(5.62563 - 0.847928i) q^{33} +(5.45399 - 0.350060i) q^{34} +(-4.69482 - 8.40027i) q^{35} +(-0.143750 + 0.237111i) q^{36} +(-9.23936 - 0.692394i) q^{37} +(3.55442 - 0.496895i) q^{38} +(2.79552 - 7.12287i) q^{39} +(7.31282 + 7.23587i) q^{40} +(5.03910 - 6.31884i) q^{41} +(5.28294 - 4.00394i) q^{42} +(0.212516 - 0.169476i) q^{43} +(6.41341 - 0.342755i) q^{44} +(-0.502860 + 0.0376841i) q^{45} +(3.41576 - 10.6669i) q^{46} +(2.62394 + 2.43466i) q^{47} +(-4.23891 + 5.67890i) q^{48} +(-6.74399 + 1.87579i) q^{49} +(-1.85765 + 11.4889i) q^{50} +(-4.65674 + 5.01878i) q^{51} +(3.91371 - 7.70074i) q^{52} +(2.67165 - 0.200213i) q^{53} +(1.52035 + 7.00593i) q^{54} +(7.28246 + 9.13191i) q^{55} +(6.37057 - 3.92630i) q^{56} +(-2.80322 + 3.51513i) q^{57} +(-10.8596 - 5.37363i) q^{58} +(-1.20757 - 0.473937i) q^{59} +(-12.8846 - 0.275865i) q^{60} +(-3.05785 - 0.229154i) q^{61} +(-2.72063 - 1.10152i) q^{62} +(-0.0597270 + 0.361915i) q^{63} +(-5.37904 + 5.92165i) q^{64} +(15.5341 - 2.34138i) q^{65} +(-5.53529 + 5.83901i) q^{66} +(-4.44977 + 2.56908i) q^{67} +(-5.77697 + 5.13456i) q^{68} +(6.08787 + 12.6416i) q^{69} +(12.5420 + 5.28288i) q^{70} +(-3.15445 - 1.51910i) q^{71} +(-0.0459659 - 0.389434i) q^{72} +(-4.56009 + 4.23114i) q^{73} +(10.9046 - 7.26492i) q^{74} +(-8.21286 - 12.0461i) q^{75} +(-3.53113 + 3.64592i) q^{76} +(7.70556 - 3.57920i) q^{77} +(3.07877 + 10.3741i) q^{78} +(-5.58625 + 9.67567i) q^{79} +(-14.4484 - 1.70721i) q^{80} +(-7.76392 - 5.29335i) q^{81} +(-0.122337 + 11.4292i) q^{82} +(8.47811 - 1.93507i) q^{83} +(-2.40787 + 9.06003i) q^{84} +(-13.7036 - 3.12776i) q^{85} +(-0.0895455 + 0.373834i) q^{86} +(14.5041 - 4.47393i) q^{87} +(-6.85313 + 5.96098i) q^{88} +(-3.08481 - 0.951537i) q^{89} +(0.527934 - 0.479439i) q^{90} +(1.01291 - 11.3823i) q^{91} +(5.47000 + 14.8654i) q^{92} +(3.42278 - 1.34334i) q^{93} +(-5.04364 - 0.432302i) q^{94} +(-9.12744 - 1.37574i) q^{95} +(-0.213268 - 10.0195i) q^{96} -7.26359 q^{97} +(5.88821 - 7.95795i) q^{98} -0.445217i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−1.11505	+	0.869863i	−0.788460	+	0.615086i
$2$	−1.11505	+	0.869863i	−0.788460	+	0.615086i
$3$	0.264046	−	1.75183i	0.152447	−	1.01142i	−0.773507	−	0.633787i	$-0.781500\pi$
$3$	0.264046	−	1.75183i	0.152447	−	1.01142i	0.925955	−	0.377634i	$-0.123262\pi$
$4$	0.486677	−	1.93988i	0.243339	−	0.969941i
$5$	3.38580	−	1.32883i	1.51417	−	0.594270i	0.544520	−	0.838748i	$-0.316712\pi$
$5$	3.38580	−	1.32883i	1.51417	−	0.594270i	0.969655	+	0.244478i	$0.0786167\pi$
$6$	1.22943	+	2.18307i	0.501913	+	0.891234i
$7$	−0.357778	−	2.62145i	−0.135227	−	0.990815i
$7$	−0.357778	−	2.62145i	−0.135227	−	0.990815i
$8$	1.14476	+	2.58641i	0.404734	+	0.914434i
$9$	−0.132482	−	0.0408653i	−0.0441606	−	0.0136218i
$10$	−2.61944	+	4.42689i	−0.828339	+	1.39991i
$11$	0.946542	+	3.06861i	0.285393	+	0.925222i	0.978825	+	0.204700i	$0.0656218\pi$
$11$	0.946542	+	3.06861i	0.285393	+	0.925222i	−0.693432	+	0.720522i	$0.743902\pi$
$12$	−3.26985	−	1.36480i	−0.943923	−	0.393983i
$13$	4.21081	+	0.961090i	1.16787	+	0.266558i	0.762126	−	0.647429i	$-0.224156\pi$
$13$	4.21081	+	0.961090i	1.16787	+	0.266558i	0.405743	+	0.913987i	$0.367013\pi$
$14$	2.67924	+	2.61183i	0.716058	+	0.698041i
$15$	−1.43388	−	6.28223i	−0.370225	−	1.62206i
$16$	−3.52629	−	1.88819i	−0.881573	−	0.472049i
$17$	−3.19299	−	2.17694i	−0.774414	−	0.527987i	0.110424	−	0.993885i	$-0.464779\pi$
$17$	−3.19299	−	2.17694i	−0.774414	−	0.527987i	−0.884838	+	0.465898i	$0.845731\pi$
$18$	0.183271	−	0.0696742i	0.0431974	−	0.0164224i
$19$	−2.19780	−	1.26890i	−0.504209	−	0.291105i	0.226241	−	0.974071i	$-0.427356\pi$
$19$	−2.19780	−	1.26890i	−0.504209	−	0.291105i	−0.730450	+	0.682966i	$0.760690\pi$
$20$	−0.929978	−	7.21476i	−0.207949	−	1.61327i
$21$	−4.68681	−	0.0654163i	−1.02275	−	0.0142750i
$22$	−3.72472	−	2.59830i	−0.794112	−	0.553959i
$23$	−6.54375	+	4.46145i	−1.36447	+	0.930277i	−1.00000		0.000940129i	$-0.999701\pi$
$23$	−6.54375	+	4.46145i	−1.36447	+	0.930277i	−0.364466	+	0.931217i	$0.618748\pi$
$24$	4.83323	−	1.32250i	0.986579	−	0.269954i
$25$	6.03258	−	5.59742i	1.20652	−	1.11948i
$26$	−5.53129	+	2.59116i	−1.08477	+	0.508169i
$27$	2.19946	−	4.56723i	0.423287	−	0.878964i
$28$	−5.25943	−	0.581752i	−0.993938	−	0.109941i
$29$	3.71732	+	7.71910i	0.690289	+	1.43340i	0.891117	+	0.453774i	$0.149923\pi$
$29$	3.71732	+	7.71910i	0.690289	+	1.43340i	−0.200828	+	0.979627i	$0.564363\pi$
$30$	7.06352	+	5.75773i	1.28962	+	1.05121i
$31$	1.03774	+	1.79741i	0.186383	+	0.322825i	0.944042	−	0.329826i	$-0.106990\pi$
$31$	1.03774	+	1.79741i	0.186383	+	0.322825i	−0.757659	+	0.652651i	$0.773657\pi$
$32$	5.57446	−	0.961955i	0.985435	−	0.170051i
$33$	5.62563	−	0.847928i	0.979297	−	0.147605i
$34$	5.45399	−	0.350060i	0.935352	−	0.0600348i
$35$	−4.69482	−	8.40027i	−0.793569	−	1.41990i
$36$	−0.143750	+	0.237111i	−0.0239583	+	0.0395185i
$37$	−9.23936	−	0.692394i	−1.51894	−	0.113829i	−0.711042	−	0.703149i	$-0.751777\pi$
$37$	−9.23936	−	0.692394i	−1.51894	−	0.113829i	−0.807899	+	0.589320i	$0.799396\pi$
$38$	3.55442	−	0.496895i	0.576604	−	0.0806070i
$39$	2.79552	−	7.12287i	0.447641	−	1.14057i
$40$	7.31282	+	7.23587i	1.15626	+	1.14409i
$41$	5.03910	−	6.31884i	0.786976	−	0.986837i	−0.212976	−	0.977057i	$-0.568316\pi$
$41$	5.03910	−	6.31884i	0.786976	−	0.986837i	0.999952	−	0.00977915i	$-0.00311285\pi$
$42$	5.28294	−	4.00394i	0.815175	−	0.617822i
$43$	0.212516	−	0.169476i	0.0324084	−	0.0258448i	−0.607152	−	0.794586i	$-0.707688\pi$
$43$	0.212516	−	0.169476i	0.0324084	−	0.0258448i	0.639560	+	0.768741i	$0.279117\pi$
$44$	6.41341	−	0.342755i	0.966858	−	0.0516723i
$45$	−0.502860	+	0.0376841i	−0.0749619	+	0.00561762i
$46$	3.41576	−	10.6669i	0.503626	−	1.57275i
$47$	2.62394	+	2.43466i	0.382740	+	0.355131i	0.847956	−	0.530066i	$-0.177833\pi$
$47$	2.62394	+	2.43466i	0.382740	+	0.355131i	−0.465216	+	0.885197i	$0.654023\pi$
$48$	−4.23891	+	5.67890i	−0.611834	+	0.819679i
$49$	−6.74399	+	1.87579i	−0.963427	+	0.267971i
$50$	−1.85765	+	11.4889i	−0.262711	+	1.62478i
$51$	−4.65674	+	5.01878i	−0.652074	+	0.702769i
$52$	3.91371	−	7.70074i	0.542734	−	1.06790i
$53$	2.67165	−	0.200213i	0.366980	−	0.0275013i	0.110036	−	0.993928i	$-0.464903\pi$
$53$	2.67165	−	0.200213i	0.366980	−	0.0275013i	0.256944	+	0.966426i	$0.417284\pi$
$54$	1.52035	+	7.00593i	0.206894	+	0.953386i
$55$	7.28246	+	9.13191i	0.981967	+	1.23135i
$56$	6.37057	−	3.92630i	0.851304	−	0.524673i
$57$	−2.80322	+	3.51513i	−0.371295	+	0.465590i
$58$	−10.8596	−	5.37363i	−1.42593	−	0.705592i
$59$	−1.20757	−	0.473937i	−0.157212	−	0.0617014i	0.285430	−	0.958400i	$-0.407864\pi$
$59$	−1.20757	−	0.473937i	−0.157212	−	0.0617014i	−0.442642	+	0.896698i	$0.645959\pi$
$60$	−12.8846	−	0.275865i	−1.66340	−	0.0356140i
$61$	−3.05785	−	0.229154i	−0.391518	−	0.0293402i	−0.122483	−	0.992471i	$-0.539086\pi$
$61$	−3.05785	−	0.229154i	−0.391518	−	0.0293402i	−0.269035	+	0.963130i	$0.586705\pi$
$62$	−2.72063	−	1.10152i	−0.345521	−	0.139893i
$63$	−0.0597270	+	0.361915i	−0.00752490	+	0.0455970i
$64$	−5.37904	+	5.92165i	−0.672380	+	0.740206i
$65$	15.5341	−	2.34138i	1.92676	−	0.290413i
$66$	−5.53529	+	5.83901i	−0.681347	+	0.718733i
$67$	−4.44977	+	2.56908i	−0.543626	+	0.313863i	−0.746547	−	0.665332i	$-0.768290\pi$
$67$	−4.44977	+	2.56908i	−0.543626	+	0.313863i	0.202921	+	0.979195i	$0.434956\pi$
$68$	−5.77697	+	5.13456i	−0.700561	+	0.622657i
$69$	6.08787	+	12.6416i	0.732893	+	1.52187i
$70$	12.5420	+	5.28288i	1.49906	+	0.631425i
$71$	−3.15445	−	1.51910i	−0.374364	−	0.180284i	0.237234	−	0.971452i	$-0.423759\pi$
$71$	−3.15445	−	1.51910i	−0.374364	−	0.180284i	−0.611599	+	0.791168i	$0.709473\pi$
$72$	−0.0459659	−	0.389434i	−0.00541713	−	0.0458952i
$73$	−4.56009	+	4.23114i	−0.533718	+	0.495218i	−0.900361	−	0.435144i	$-0.856698\pi$
$73$	−4.56009	+	4.23114i	−0.533718	+	0.495218i	0.366643	+	0.930362i	$0.380507\pi$
$74$	10.9046	−	7.26492i	1.26764	−	0.844530i
$75$	−8.21286	−	12.0461i	−0.948340	−	1.39096i
$76$	−3.53113	+	3.64592i	−0.405049	+	0.418216i
$77$	7.70556	−	3.57920i	0.878130	−	0.407887i
$78$	3.07877	+	10.3741i	0.348602	+	1.17463i
$79$	−5.58625	+	9.67567i	−0.628503	+	1.08860i	0.359350	+	0.933203i	$0.382999\pi$
$79$	−5.58625	+	9.67567i	−0.628503	+	1.08860i	−0.987852	+	0.155395i	$0.950335\pi$
$80$	−14.4484	−	1.70721i	−1.61538	−	0.190872i
$81$	−7.76392	−	5.29335i	−0.862658	−	0.588150i
$82$	−0.122337	+	11.4292i	−0.0135099	+	1.26214i
$83$	8.47811	−	1.93507i	0.930594	−	0.212402i	0.269754	−	0.962929i	$-0.413057\pi$
$83$	8.47811	−	1.93507i	0.930594	−	0.212402i	0.660840	+	0.750527i	$0.270200\pi$
$84$	−2.40787	+	9.06003i	−0.262720	+	0.988530i
$85$	−13.7036	−	3.12776i	−1.48636	−	0.339253i
$86$	−0.0895455	+	0.373834i	−0.00965594	+	0.0403116i
$87$	14.5041	−	4.47393i	1.55500	−	0.479655i
$88$	−6.85313	+	5.96098i	−0.730546	+	0.635442i
$89$	−3.08481	−	0.951537i	−0.326989	−	0.100863i	0.126914	−	0.991914i	$-0.459493\pi$
$89$	−3.08481	−	0.951537i	−0.326989	−	0.100863i	−0.453903	+	0.891051i	$0.649969\pi$
$90$	0.527934	−	0.479439i	0.0556492	−	0.0505373i
$91$	1.01291	−	11.3823i	0.106182	−	1.19319i
$92$	5.47000	+	14.8654i	0.570287	+	1.54982i
$93$	3.42278	−	1.34334i	0.354926	−	0.139298i
$94$	−5.04364	−	0.432302i	−0.520212	−	0.0445886i
$95$	−9.12744	−	1.37574i	−0.936456	−	0.141148i
$96$	−0.213268	−	10.0195i	−0.0217666	−	1.02261i
$97$	−7.26359			−0.737505			−0.368753	−	0.929528i	$-0.620215\pi$
$97$	−7.26359			−0.737505			−0.368753	+	0.929528i	$0.620215\pi$
$98$	5.88821	−	7.95795i	0.594799	−	0.803875i
$99$		−	0.445217i		−	0.0447459i
$100$	−7.92241	−	14.4266i	−0.792241	−	1.44266i
$101$	−1.37385	+	9.11491i	−0.136703	+	0.906967i	0.810363	+	0.585929i	$0.199270\pi$
$101$	−1.37385	+	9.11491i	−0.136703	+	0.906967i	−0.947066	+	0.321039i	$0.895968\pi$
$102$	0.826860	−	9.64692i	0.0818713	−	0.955187i
$103$	−5.24420	−	13.3620i	−0.516726	−	1.31660i	−0.916519	−	0.399991i	$-0.869013\pi$
$103$	−5.24420	−	13.3620i	−0.516726	−	1.31660i	0.399793	−	0.916606i	$-0.369082\pi$
$104$	2.33460	+	11.9911i	0.228926	+	1.17582i
$105$	−15.9555	+	6.00648i	−1.55710	+	0.586172i
$106$	−2.80487	+	2.54722i	−0.272433	+	0.247408i
$107$	3.22057	−	10.4408i	0.311344	−	1.00935i	−0.655760	−	0.754970i	$-0.727652\pi$
$107$	3.22057	−	10.4408i	0.311344	−	1.00935i	0.967104	−	0.254383i	$-0.0818723\pi$
$108$	−7.78946	−	6.48947i	−0.749541	−	0.624449i
$109$	5.91292	+	19.1692i	0.566355	+	1.83608i	0.548363	+	0.836240i	$0.315251\pi$
$109$	5.91292	+	19.1692i	0.566355	+	1.83608i	0.0179919	+	0.999838i	$0.494273\pi$
$110$	−16.0638	−	3.84781i	−1.53163	−	0.366874i
$111$	−3.65258	+	16.0030i	−0.346688	+	1.51894i
$112$	−3.68818	+	9.91954i	−0.348500	+	0.937309i
$113$	−0.591655	−	2.59221i	−0.0556582	−	0.243854i	0.939444	−	0.342701i	$-0.111342\pi$
$113$	−0.591655	−	2.59221i	−0.0556582	−	0.243854i	−0.995103	+	0.0988466i	$0.968485\pi$
$114$	0.0680554	−	6.35796i	0.00637397	−	0.595478i
$115$	−16.2273	+	23.8011i	−1.51320	+	2.21946i
$116$	16.7833	−	3.45446i	1.55829	−	0.320738i
$117$	−0.518581	−	0.299403i	−0.0479428	−	0.0276798i
$118$	1.75876	−	0.521958i	0.161907	−	0.0480501i
$119$	−4.56437	+	9.14913i	−0.418415	+	0.838699i
$120$	14.6070	−	10.9002i	1.33343	−	0.995052i
$121$	0.568174	−	0.387375i	0.0516522	−	0.0352159i
$122$	3.60899	−	2.40439i	0.326743	−	0.217683i
$123$	−9.73899	−	10.4961i	−0.878135	−	0.946405i
$124$	3.99181	−	1.13833i	0.358476	−	0.102225i
$125$	5.09643	−	10.5828i	0.455838	−	0.946558i
$126$	−0.248218	−	0.455508i	−0.0221130	−	0.0405799i
$127$	19.8102	−	9.54011i	1.75788	−	0.846548i	0.783575	−	0.621298i	$-0.213394\pi$
$127$	19.8102	−	9.54011i	1.75788	−	0.846548i	0.974301	−	0.225250i	$-0.0723200\pi$
$128$	0.846886	−	11.2820i	0.0748548	−	0.997194i
$129$	−0.240780	−	0.417042i	−0.0211995	−	0.0367185i
$130$	−15.2846	+	16.1233i	−1.34055	+	1.41410i
$131$	1.05153	+	6.97646i	0.0918728	+	0.609536i	0.986629	+	0.162982i	$0.0521111\pi$
$131$	1.05153	+	6.97646i	0.0918728	+	0.609536i	−0.894756	+	0.446555i	$0.852651\pi$
$132$	1.09299	−	11.3257i	0.0951324	−	0.985779i
$133$	−2.54003	+	6.21540i	−0.220248	+	0.538943i
$134$	2.72698	−	6.73534i	0.235575	−	0.581845i
$135$	1.37787	−	18.3864i	0.118588	−	1.58245i
$136$	1.97526	−	10.7505i	0.169377	−	0.921845i
$137$	−1.70991	+	4.35678i	−0.146087	+	0.372225i	−0.985123	−	0.171852i	$-0.945025\pi$
$137$	−1.70991	+	4.35678i	−0.146087	+	0.372225i	0.839035	+	0.544077i	$0.183120\pi$
$138$	−17.7847	−	8.80040i	−1.51394	−	0.749140i
$139$	12.0799	+	9.63339i	1.02460	+	0.817093i	0.983289	−	0.182053i	$-0.0582743\pi$
$139$	12.0799	+	9.63339i	1.02460	+	0.817093i	0.0413137	+	0.999146i	$0.486846\pi$
$140$	−18.5804	+	5.01917i	−1.57033	+	0.424198i
$141$	4.95795	−	3.95384i	0.417535	−	0.332973i
$142$	4.83878	−	1.05006i	0.406062	−	0.0881192i
$143$	1.03650	+	13.8311i	0.0866761	+	1.15661i
$144$	0.390008	+	0.394254i	0.0325007	+	0.0328545i
$145$	22.8434	+	21.1956i	1.89704	+	1.76020i
$146$	1.40422	−	8.68459i	0.116214	−	0.718742i
$147$	1.50535	+	12.3096i	0.124160	+	1.01528i
$148$	−5.83975	+	17.5863i	−0.480025	+	1.44559i
$149$	6.17324	−	6.65317i	0.505731	−	0.545049i	−0.427646	−	0.903946i	$-0.640657\pi$
$149$	6.17324	−	6.65317i	0.505731	−	0.545049i	0.933377	+	0.358898i	$0.116847\pi$
$150$	19.6362	+	6.28790i	1.60329	+	0.513405i
$151$	−0.552154	−	7.36799i	−0.0449337	−	0.599598i	−0.973538	−	0.228526i	$-0.926609\pi$
$151$	−0.552154	−	7.36799i	−0.0449337	−	0.599598i	0.928604	−	0.371072i	$-0.121010\pi$
$152$	0.765940	−	7.13699i	0.0621259	−	0.578886i
$153$	0.334052	+	0.418888i	0.0270065	+	0.0338651i
$154$	−5.47869	+	10.6938i	−0.441485	+	0.861728i
$155$	5.90202	+	4.70670i	0.474062	+	0.378052i
$156$	−12.4570	−	8.88952i	−0.997359	−	0.711731i
$157$	6.85651	+	2.69098i	0.547209	+	0.214764i	0.622808	−	0.782375i	$-0.285992\pi$
$157$	6.85651	+	2.69098i	0.547209	+	0.214764i	−0.0755991	+	0.997138i	$0.524087\pi$
$158$	−2.18755	−	15.6481i	−0.174032	−	1.24490i
$159$	0.354701	−	4.73316i	0.0281296	−	0.375364i
$160$	17.5957	−	10.6645i	1.39106	−	0.843102i
$161$	14.0367	+	15.5579i	1.10624	+	1.22613i
$162$	13.2617	−	0.851189i	1.04193	−	0.0668757i
$163$	0.0341261	+	0.226412i	0.00267296	+	0.0177339i	0.990128	−	0.140169i	$-0.0447647\pi$
$163$	0.0341261	+	0.226412i	0.00267296	+	0.0177339i	−0.987455	+	0.157903i	$0.949527\pi$
$164$	−9.80538	−	12.8505i	−0.765672	−	1.00346i
$165$	17.9205	−	10.3464i	1.39511	−	0.805467i
$166$	−7.77028	+	9.53250i	−0.603091	+	0.739866i
$167$	−3.66835	+	1.76659i	−0.283866	+	0.136703i	−0.570399	−	0.821368i	$-0.693211\pi$
$167$	−3.66835	+	1.76659i	−0.283866	+	0.136703i	0.286533	+	0.958070i	$0.407497\pi$
$168$	−5.19609	−	12.1969i	−0.400887	−	0.941012i
$169$	5.09464	+	2.45345i	0.391895	+	0.188727i
$170$	18.0009	−	8.43265i	1.38061	−	0.646754i
$171$	0.239314	+	0.257920i	0.0183008	+	0.0197236i
$172$	−0.225337	−	0.494737i	−0.0171818	−	0.0377233i
$173$	13.9151	+	20.4096i	1.05794	+	1.55172i	0.813075	+	0.582159i	$0.197792\pi$
$173$	13.9151	+	20.4096i	1.05794	+	1.55172i	0.244867	+	0.969557i	$0.421256\pi$
$174$	−12.2811	+	17.6053i	−0.931030	+	1.33465i
$175$	−16.8317	−	13.8115i	−1.27235	−	1.04405i
$176$	2.45636	−	12.6081i	0.185155	−	0.950370i
$177$	−1.14911	+	1.99032i	−0.0863727	+	0.149602i
$178$	4.26743	−	1.62235i	0.319857	−	0.121600i
$179$	1.42467	−	2.08961i	0.106485	−	0.156184i	−0.769298	−	0.638891i	$-0.779394\pi$
$179$	1.42467	−	2.08961i	0.106485	−	0.156184i	0.875782	+	0.482706i	$0.160346\pi$
$180$	−0.171628	+	0.993829i	−0.0127924	+	0.0740756i
$181$	−17.9397	+	4.09462i	−1.33345	+	0.304351i	−0.829077	−	0.559135i	$-0.811133\pi$
$181$	−17.9397	+	4.09462i	−1.33345	+	0.304351i	−0.504372	+	0.863486i	$0.668276\pi$
$182$	8.77158	+	13.5729i	0.650192	+	1.00609i
$183$	−1.20885	+	5.29634i	−0.0893611	+	0.391517i
$184$	−19.0302	−	11.8175i	−1.40292	−	0.871199i
$185$	−32.2027	+	9.93321i	−2.36759	+	0.730304i
$186$	−2.64805	+	4.47524i	−0.194164	+	0.328141i
$187$	3.65790	−	11.8586i	0.267492	−	0.867189i
$188$	5.99996	−	3.90523i	0.437592	−	0.284819i
$189$	−12.7597	−	4.13172i	−0.928130	−	0.300539i
$190$	11.3743	−	6.40560i	0.825176	−	0.464711i
$191$	9.66035	+	24.6142i	0.698998	+	1.78102i	0.620644	+	0.784092i	$0.286871\pi$
$191$	9.66035	+	24.6142i	0.698998	+	1.78102i	0.0783541	+	0.996926i	$0.475034\pi$
$192$	8.95342	+	10.9868i	0.646158	+	0.792902i
$193$	−3.83394	−	0.577874i	−0.275973	−	0.0415963i	0.00959736	−	0.999954i	$-0.496945\pi$
$193$	−3.83394	−	0.577874i	−0.275973	−	0.0415963i	−0.285571	+	0.958358i	$0.592183\pi$
$194$	8.09927	−	6.31832i	0.581494	−	0.453629i
$195$		−	27.8313i		−	1.99304i
$196$	0.356674	+	13.9955i	0.0254767	+	0.999675i
$197$		−	0.804222i		−	0.0572984i	−0.999590	−	0.0286492i	$-0.990879\pi$
$197$		−	0.804222i		−	0.0572984i	0.999590	−	0.0286492i	$-0.00912058\pi$
$198$	0.387277	+	0.496439i	0.0275226	+	0.0352804i
$199$	−2.18022	−	0.328616i	−0.154552	−	0.0232949i	0.0713105	−	0.997454i	$-0.477282\pi$
$199$	−2.18022	−	0.328616i	−0.154552	−	0.0232949i	−0.225862	+	0.974159i	$0.572520\pi$
$200$	21.3831	+	9.19502i	1.51201	+	0.650186i
$201$	3.32565	+	8.47361i	0.234573	+	0.597682i
$202$	−6.39680	−	11.3586i	−0.450078	−	0.799192i
$203$	18.9052	−	12.5065i	1.32689	−	0.877784i
$204$	7.46950	+	11.4761i	0.522970	+	0.803485i
$205$	8.66474	−	28.0904i	0.605172	−	1.96192i
$206$	17.4707	+	10.3376i	1.21724	+	0.720253i
$207$	1.04925	−	0.323650i	0.0729277	−	0.0224952i
$208$	−13.0338	−	11.3399i	−0.903732	−	0.786281i
$209$	1.81345	−	7.94526i	0.125439	−	0.549585i
$210$	12.5664	−	20.5766i	0.867165	−	1.41992i
$211$	−2.42509	+	0.553511i	−0.166950	+	0.0381053i	−0.305179	−	0.952295i	$-0.598716\pi$
$211$	−2.42509	+	0.553511i	−0.166950	+	0.0381053i	0.138229	+	0.990400i	$0.455859\pi$
$212$	0.911844	−	5.28013i	0.0626257	−	0.362641i
$213$	−3.49414	+	5.12496i	−0.239414	+	0.351156i
$214$	5.49099	+	14.4435i	0.375356	+	0.987338i
$215$	0.494332	−	0.856209i	0.0337132	−	0.0583929i
$216$	14.3306	+	0.460323i	0.975073	+	0.0313210i
$217$	4.34055	−	3.36345i	0.294656	−	0.228326i
$218$	−23.2678	−	16.2312i	−1.57589	−	1.09932i
$219$	6.20819	+	9.10574i	0.419510	+	0.615309i
$220$	21.2591	−	9.68282i	1.43329	−	0.652816i
$221$	−11.3528	−	12.2355i	−0.763675	−	0.823046i
$222$	−9.84760	−	21.0214i	−0.660928	−	1.41086i
$223$	−1.01766	−	0.490079i	−0.0681476	−	0.0328181i	0.399500	−	0.916733i	$-0.369184\pi$
$223$	−1.01766	−	0.490079i	−0.0681476	−	0.0328181i	−0.467647	+	0.883915i	$0.654898\pi$
$224$	−4.51614	−	14.2690i	−0.301747	−	0.953388i
$225$	−1.02795	+	0.495033i	−0.0685298	+	0.0330022i
$226$	2.91459	+	2.37579i	0.193876	+	0.158035i
$227$	9.08788	−	5.24689i	0.603184	−	0.348248i	−0.167109	−	0.985938i	$-0.553443\pi$
$227$	9.08788	−	5.24689i	0.603184	−	0.348248i	0.770293	+	0.637690i	$0.220110\pi$
$228$	5.45467	+	7.14865i	0.361244	+	0.473431i
$229$	−3.09602	−	20.5407i	−0.204591	−	1.35737i	−0.821443	−	0.570291i	$-0.806831\pi$
$229$	−3.09602	−	20.5407i	−0.204591	−	1.35737i	0.616852	−	0.787079i	$-0.288408\pi$
$230$	−2.60940	−	40.6549i	−0.172059	−	2.68071i
$231$	−4.23553	−	14.4439i	−0.278677	−	0.950341i
$232$	−15.7093	+	18.4510i	−1.03137	+	1.21137i
$233$	0.335166	−	4.47248i	0.0219575	−	0.293002i	−0.975405	−	0.220420i	$-0.929257\pi$
$233$	0.335166	−	4.47248i	0.0219575	−	0.293002i	0.997362	−	0.0725817i	$-0.0231238\pi$
$234$	0.838684	−	0.117245i	0.0548265	−	0.00766453i
$235$	12.1194	+	4.75649i	0.790579	+	0.310280i
$236$	−1.50708	+	2.11189i	−0.0981026	+	0.137473i
$237$	15.4751	+	12.3410i	1.00522	+	0.801635i
$238$	−2.86898	−	14.1721i	−0.185969	−	0.918642i
$239$	11.0455	+	13.8506i	0.714472	+	0.895919i	0.998011	−	0.0630416i	$-0.0200801\pi$
$239$	11.0455	+	13.8506i	0.714472	+	0.895919i	−0.283539	+	0.958961i	$0.591509\pi$
$240$	−6.80580	+	24.8604i	−0.439312	+	1.60473i
$241$	0.412255	+	5.50115i	0.0265556	+	0.354361i	0.994615	+	0.103639i	$0.0330487\pi$
$241$	0.412255	+	5.50115i	0.0265556	+	0.354361i	−0.968059	+	0.250721i	$0.919332\pi$
$242$	−0.296581	+	0.926176i	−0.0190649	+	0.0595369i
$243$	−0.979222	+	1.05535i	−0.0628171	+	0.0677008i
$244$	−1.93272	+	5.82035i	−0.123730	+	0.372610i
$245$	−20.3412	+	15.3127i	−1.29955	+	0.978290i
$246$	19.9897	+	3.23214i	1.27450	+	0.206074i
$247$	−8.03498	−	7.45537i	−0.511254	−	0.474374i
$248$	−3.46089	+	4.74162i	−0.219767	+	0.301093i
$249$	−1.15131	−	15.3632i	−0.0729615	−	0.973603i
$250$	3.52284	+	16.2336i	0.222804	+	1.02670i
$251$	−9.01330	+	7.18787i	−0.568915	+	0.453694i	−0.865215	−	0.501400i	$-0.832818\pi$
$251$	−9.01330	+	7.18787i	−0.568915	+	0.453694i	0.296301	+	0.955095i	$0.404247\pi$
$252$	0.673005	+	0.291999i	0.0423954	+	0.0183942i
$253$	−19.8844	−	15.8573i	−1.25012	−	0.996939i
$254$	−13.7908	+	27.8699i	−0.865315	+	1.74871i
$255$	−9.09770	+	23.1806i	−0.569720	+	1.45162i
$256$	8.86944	+	13.3166i	0.554340	+	0.832290i
$257$	0.783099	−	10.4497i	0.0488484	−	0.651836i	−0.918016	−	0.396544i	$-0.870209\pi$
$257$	0.783099	−	10.4497i	0.0488484	−	0.651836i	0.966864	−	0.255292i	$-0.0821716\pi$
$258$	0.631251	+	0.255578i	0.0393000	+	0.0159116i
$259$	1.49057	+	24.4682i	0.0926193	+	1.52038i
$260$	3.01807	−	31.2738i	0.187173	−	1.93952i
$261$	−0.177035	−	1.17455i	−0.0109582	−	0.0727028i
$262$	−7.24108	−	6.86442i	−0.447355	−	0.424085i
$263$	7.11895	+	12.3304i	0.438973	+	0.760324i	0.997611	−	0.0690878i	$-0.0220089\pi$
$263$	7.11895	+	12.3304i	0.438973	+	0.760324i	−0.558637	+	0.829412i	$0.688676\pi$
$264$	8.63310	+	13.5795i	0.531330	+	0.835762i
$265$	8.77963	−	4.22805i	0.539328	−	0.259727i
$266$	−2.57428	−	9.13996i	−0.157839	−	0.560407i
$267$	−2.48147	+	5.15282i	−0.151863	+	0.315348i
$268$	2.81810	+	9.88234i	0.172143	+	0.603660i
$269$	−8.69857	−	9.37482i	−0.530361	−	0.571593i	0.409864	−	0.912147i	$-0.365576\pi$
$269$	−8.69857	−	9.37482i	−0.530361	−	0.571593i	−0.940225	+	0.340553i	$0.889386\pi$
$270$	14.4573	+	21.7004i	0.879841	+	1.32064i
$271$	−7.66853	+	5.22831i	−0.465830	+	0.317597i	−0.773389	−	0.633932i	$-0.781440\pi$
$271$	−7.66853	+	5.22831i	−0.465830	+	0.317597i	0.307559	+	0.951529i	$0.400488\pi$
$272$	7.14892	+	13.7055i	0.433467	+	0.831020i
$273$	−19.6724	−	4.77990i	−1.19063	−	0.289293i
$274$	−1.88316	−	6.34542i	−0.113766	−	0.383341i
$275$	22.8864	+	13.2135i	1.38010	+	0.796802i
$276$	27.4860	−	5.65737i	1.65446	−	0.340534i
$277$	13.9795	−	20.5042i	0.839949	−	1.23198i	−0.130687	−	0.991424i	$-0.541718\pi$
$277$	13.9795	−	20.5042i	0.839949	−	1.23198i	0.970636	−	0.240555i	$-0.0773293\pi$
$278$	−21.8494	−	0.233875i	−1.31044	−	0.0140269i
$279$	−0.0640296	−	0.280532i	−0.00383335	−	0.0167950i
$280$	16.3521	−	21.7590i	0.977225	−	1.30035i
$281$	6.80717	−	29.8242i	0.406082	−	1.77916i	−0.195872	−	0.980629i	$-0.562754\pi$
$281$	6.80717	−	29.8242i	0.406082	−	1.77916i	0.601954	−	0.798531i	$-0.294389\pi$
$282$	−2.08908	+	8.72147i	−0.124403	+	0.519356i
$283$	1.14499	+	3.71197i	0.0680627	+	0.220654i	0.983214	−	0.182457i	$-0.0584051\pi$
$283$	1.14499	+	3.71197i	0.0680627	+	0.220654i	−0.915151	+	0.403111i	$0.867929\pi$
$284$	−4.48208	+	5.37995i	−0.265963	+	0.319241i
$285$	−4.82014	+	15.6265i	−0.285520	+	0.925634i
$286$	−13.1869	−	14.5207i	−0.779756	−	0.858629i
$287$	−18.3674	−	10.9490i	−1.08419	−	0.646300i
$288$	−0.777826	−	0.100360i	−0.0458338	−	0.00591378i
$289$	−0.754691	−	1.92292i	−0.0443936	−	0.113113i
$290$	−43.9089	−	3.76353i	−2.57842	−	0.221002i
$291$	−1.91792	+	12.7246i	−0.112431	+	0.745929i
$292$	5.98863	+	10.9052i	0.350458	+	0.638181i
$293$			9.27503i			0.541853i	0.962600	+	0.270927i	$0.0873301\pi$
$293$			9.27503i			0.541853i	−0.962600	+	0.270927i	$0.912670\pi$
$294$	−12.3862	−	12.4164i	−0.722381	−	0.724141i
$295$	−4.71837			−0.274714
$296$	−8.78605	−	24.6894i	−0.510679	−	1.43504i
$297$	16.0970	+	2.42623i	0.934040	+	0.140784i
$298$	−1.09613	+	12.7885i	−0.0634972	+	0.740817i
$299$	−31.8423	+	12.4972i	−1.84149	+	0.722731i
$300$	−27.3649	+	10.0694i	−1.57992	+	0.581360i
$301$	−0.520306	−	0.496465i	−0.0299900	−	0.0286158i
$302$	7.02482	+	7.73538i	0.404233	+	0.445121i
$303$	15.6050	+	4.81352i	0.896486	+	0.276529i
$304$	5.35414	+	8.62437i	0.307081	+	0.494642i
$305$	−10.6578	+	3.28749i	−0.610262	+	0.188241i
$306$	−0.736860	−	0.176502i	−0.0421235	−	0.0100900i
$307$	−15.4065	−	3.51644i	−0.879297	−	0.200694i	−0.241038	−	0.970516i	$-0.577488\pi$
$307$	−15.4065	−	3.51644i	−0.879297	−	0.200694i	−0.638259	+	0.769822i	$0.720345\pi$
$308$	−3.19310	−	16.6898i	−0.181943	−	0.950990i
$309$	−24.7927	+	5.65877i	−1.41041	+	0.321916i
$310$	−10.6752	−	0.114267i	−0.606313	−	0.00648995i
$311$	−15.9366	−	10.8654i	−0.903683	−	0.616121i	0.0197815	−	0.999804i	$-0.493703\pi$
$311$	−15.9366	−	10.8654i	−0.903683	−	0.616121i	−0.923465	+	0.383684i	$0.874655\pi$
$312$	21.6229	−	0.923623i	1.22415	−	0.0522899i
$313$	13.0037	−	22.5230i	0.735010	−	1.27307i	−0.219709	−	0.975565i	$-0.570511\pi$
$313$	13.0037	−	22.5230i	0.735010	−	1.27307i	0.954719	−	0.297509i	$-0.0961559\pi$
$314$	−9.98614	+	2.96364i	−0.563551	+	0.167248i
$315$	0.278699	+	1.30474i	0.0157029	+	0.0735137i
$316$	16.0510	+	15.5456i	0.902938	+	0.874509i
$317$	−5.69598	−	8.35446i	−0.319918	−	0.469233i	0.632269	−	0.774749i	$-0.282124\pi$
$317$	−5.69598	−	8.35446i	−0.319918	−	0.469233i	−0.952187	+	0.305515i	$0.901171\pi$
$318$	3.72169	+	5.58625i	0.208702	+	0.313261i
$319$	−20.1683	+	18.7135i	−1.12921	+	1.04775i
$320$	−10.3435	+	27.1973i	−0.578219	+	1.52038i
$321$	−17.4402	−	8.39876i	−0.973417	−	0.468773i
$322$	−29.1848	−	5.13786i	−1.62641	−	0.286321i
$323$	4.25522	+	8.83606i	0.236767	+	0.491652i
$324$	−14.0470	+	12.4849i	−0.780389	+	0.693608i
$325$	30.7817	−	17.7718i	1.70746	−	0.985803i
$326$	−0.234999	−	0.222776i	−0.0130154	−	0.0123384i
$327$	35.1426	−	5.29689i	1.94339	−	0.292919i
$328$	22.1117	+	5.79963i	1.22091	+	0.320231i
$329$	5.44354	−	7.74958i	0.300112	−	0.427248i
$330$	−10.9823	+	27.1251i	−0.604557	+	1.49319i
$331$	11.2263	+	0.841292i	0.617051	+	0.0462416i	0.379589	−	0.925155i	$-0.376065\pi$
$331$	11.2263	+	0.841292i	0.617051	+	0.0462416i	0.237462	+	0.971397i	$0.423684\pi$
$332$	0.372290	−	17.3883i	0.0204321	−	0.954307i
$333$	1.19575	+	0.469299i	0.0655269	+	0.0257174i
$334$	2.55371	−	5.16080i	0.139733	−	0.282386i
$335$	−11.6522	+	14.6113i	−0.636626	+	0.798303i
$336$	16.4035	+	9.08029i	0.894887	+	0.495370i
$337$	−14.7941	−	18.5513i	−0.805888	−	1.01055i	−0.999565	−	0.0294867i	$-0.990613\pi$
$337$	−14.7941	−	18.5513i	−0.805888	−	1.01055i	0.193677	−	0.981065i	$-0.437959\pi$
$338$	−7.81494	+	1.69592i	−0.425077	+	0.0922457i
$339$	−4.69734	+	0.352017i	−0.255125	+	0.0191189i
$340$	−12.7367	+	25.0612i	−0.690746	+	1.35913i
$341$	−4.53331	+	4.88574i	−0.245492	+	0.264578i
$342$	−0.491202	−	0.0794228i	−0.0265612	−	0.00429469i
$343$	7.33015	+	17.0079i	0.395791	+	0.918341i
$344$	0.681615	+	0.355644i	0.0367502	+	0.0191751i
$345$	37.4108	+	34.7121i	2.01413	+	1.86884i
$346$	−33.2696	−	10.6536i	−1.78858	−	0.572741i
$347$	−18.9892	+	1.42304i	−1.01939	+	0.0763928i	−0.573927	−	0.818907i	$-0.694581\pi$
$347$	−18.9892	+	1.42304i	−1.01939	+	0.0763928i	−0.445465	+	0.895300i	$0.646961\pi$
$348$	−1.62007	−	30.3137i	−0.0868448	−	1.62498i
$349$	−11.0108	+	8.78080i	−0.589393	+	0.470025i	−0.872199	−	0.489152i	$-0.837306\pi$
$349$	−11.0108	+	8.78080i	−0.589393	+	0.470025i	0.282805	+	0.959177i	$0.408735\pi$
$350$	30.7823	+	0.759249i	1.64538	+	0.0405836i
$351$	13.6510	−	17.1179i	0.728639	−	0.913684i
$352$	8.22833	+	16.1953i	0.438572	+	0.863215i
$353$	−7.23273	+	18.4287i	−0.384959	+	0.980860i	0.598725	+	0.800955i	$0.295674\pi$
$353$	−7.23273	+	18.4287i	−0.384959	+	0.980860i	−0.983684	+	0.179905i	$0.942421\pi$
$354$	−0.449988	−	3.21888i	−0.0239166	−	0.171082i
$355$	−12.6990	−	0.951655i	−0.673991	−	0.0505086i
$356$	−3.34718	+	5.52107i	−0.177400	+	0.292616i
$357$	14.8225	+	10.4118i	0.784492	+	0.551051i
$358$	0.229092	+	3.56928i	0.0121079	+	0.188642i
$359$	−2.03721	+	0.307060i	−0.107520	+	0.0162060i	−0.202582	−	0.979265i	$-0.564933\pi$
$359$	−2.03721	+	0.307060i	−0.107520	+	0.0162060i	0.0950619	+	0.995471i	$0.469695\pi$
$360$	−0.673121	−	1.25746i	−0.0354766	−	0.0662741i
$361$	−6.27979	−	10.8769i	−0.330515	−	0.572470i
$362$	16.4419	−	20.1708i	0.864169	−	1.06015i
$363$	−0.528592	−	1.09763i	−0.0277439	−	0.0576107i
$364$	−21.5873	−	7.50443i	−1.13148	−	0.393339i
$365$	−9.81708	+	20.3854i	−0.513849	+	1.06702i
$366$	−3.25915	−	6.95722i	−0.170359	−	0.363660i
$367$	14.9895	−	13.9082i	0.782444	−	0.726002i	−0.183987	−	0.982929i	$-0.558900\pi$
$367$	14.9895	−	13.9082i	0.782444	−	0.726002i	0.966431	+	0.256927i	$0.0827100\pi$
$368$	31.4992	−	3.37650i	1.64201	−	0.176012i
$369$	−0.925811	+	0.631207i	−0.0481958	+	0.0328593i
$370$	27.2671	−	39.0879i	1.41755	−	2.03209i
$371$	−1.48071	−	6.93197i	−0.0768745	−	0.359890i
$372$	−0.940136	−	7.29357i	−0.0487438	−	0.378154i
$373$	−26.2561	−	15.1590i	−1.35949	−	0.784901i	−0.369934	−	0.929058i	$-0.620620\pi$
$373$	−26.2561	−	15.1590i	−1.35949	−	0.784901i	−0.989555	+	0.144157i	$0.953953\pi$
$374$	6.23663	+	16.4049i	0.322489	+	0.848275i
$375$	−17.1937	−	11.7225i	−0.887878	−	0.605345i
$376$	−3.29324	+	9.57368i	−0.169836	+	0.493725i
$377$	8.23419	+	36.0763i	0.424082	+	1.85803i
$378$	17.8217	−	6.49209i	0.916651	−	0.333917i
$379$	17.1804	+	3.92132i	0.882500	+	0.201425i	0.639675	−	0.768645i	$-0.279069\pi$
$379$	17.1804	+	3.92132i	0.882500	+	0.201425i	0.242825	+	0.970070i	$0.421926\pi$
$380$	−7.11089	+	17.0366i	−0.364781	+	0.873960i
$381$	−11.4819	−	37.2233i	−0.588234	−	1.90701i
$382$	−32.1827	−	19.0429i	−1.64661	−	0.974318i
$383$	3.15728	+	0.973892i	0.161329	+	0.0497635i	0.374368	−	0.927280i	$-0.377860\pi$
$383$	3.15728	+	0.973892i	0.161329	+	0.0497635i	−0.213038	+	0.977044i	$0.568336\pi$
$384$	−19.5405	−	4.46257i	−0.997173	−	0.227729i
$385$	21.3333	−	22.3578i	1.08725	−	1.13946i
$386$	4.77771	−	2.69065i	0.243179	−	0.136950i
$387$	−0.0350802	+	0.0137680i	−0.00178323	+	0.000699865i
$388$	−3.53502	+	14.0905i	−0.179464	+	0.715337i
$389$	0.606130	−	4.02141i	0.0307320	−	0.203894i	−0.968196	−	0.250195i	$-0.919505\pi$
$389$	0.606130	−	4.02141i	0.0307320	−	0.203894i	0.998928	+	0.0463013i	$0.0147434\pi$
$390$	24.2095	+	31.0334i	1.22589	+	1.57144i
$391$	30.6065			1.54783
$392$	−12.5718	−	15.2954i	−0.634974	−	0.772534i
$393$	12.4993			0.630504
$394$	0.699563	+	0.896748i	0.0352435	+	0.0451775i
$395$	−6.05662	+	40.1830i	−0.304742	+	2.02183i
$396$	−0.863668	−	0.216677i	−0.0434009	−	0.0108884i
$397$	29.0058	−	11.3839i	1.45576	−	0.571343i	0.500138	−	0.865946i	$-0.333283\pi$
$397$	29.0058	−	11.3839i	1.45576	−	0.571343i	0.955620	+	0.294603i	$0.0951874\pi$
$398$	2.71691	−	1.53007i	0.136186	−	0.0766955i
$399$	10.2177	+	6.09086i	0.511522	+	0.304924i
$400$	−31.8416	+	8.34743i	−1.59208	+	0.417371i
$401$	−9.07807	−	2.80021i	−0.453337	−	0.139836i	0.0596741	−	0.998218i	$-0.480994\pi$
$401$	−9.07807	−	2.80021i	−0.453337	−	0.139836i	−0.513011	+	0.858382i	$0.671470\pi$
$402$	−11.0791	−	6.55565i	−0.552578	−	0.326966i
$403$	2.64224	+	8.56593i	0.131619	+	0.426699i
$404$	17.0132	+	7.10113i	0.846440	+	0.353294i
$405$	−33.3210	−	7.60530i	−1.65573	−	0.377911i
$406$	−10.2014	+	30.3903i	−0.506286	+	1.50825i
$407$	−6.62075	−	29.0074i	−0.328179	−	1.43784i
$408$	−18.3115	−	6.29895i	−0.906553	−	0.311844i
$409$	13.3207	+	9.08193i	0.658668	+	0.449073i	0.845970	−	0.533230i	$-0.179022\pi$
$409$	13.3207	+	9.08193i	0.658668	+	0.449073i	−0.187302	+	0.982302i	$0.559974\pi$
$410$	14.7732	+	38.8594i	0.729595	+	1.91913i
$411$	7.18085	+	4.14587i	0.354205	+	0.204501i
$412$	−28.4729	+	3.67014i	−1.40276	+	0.180815i
$413$	−0.810359	+	3.33515i	−0.0398752	+	0.164112i
$414$	−0.888432	+	1.27359i	−0.0436641	+	0.0625933i
$415$	26.1338	−	17.8177i	1.28286	−	0.874637i
$416$	24.3975	+	1.30695i	1.19619	+	0.0640785i
$417$	20.0657	−	18.6183i	0.982623	−	0.911741i
$418$	4.88919	+	10.4368i	0.239138	+	0.510482i
$419$	9.98104	−	20.7259i	0.487606	−	1.01252i	−0.501478	−	0.865170i	$-0.667210\pi$
$419$	9.98104	−	20.7259i	0.487606	−	1.01252i	0.989084	−	0.147354i	$-0.0470756\pi$
$420$	3.88667	+	33.8751i	0.189650	+	1.65293i
$421$	−4.99559	−	10.3734i	−0.243470	−	0.505571i	0.743045	−	0.669242i	$-0.233381\pi$
$421$	−4.99559	−	10.3734i	−0.243470	−	0.505571i	−0.986515	+	0.163671i	$0.947667\pi$
$422$	2.22262	−	2.72669i	0.108195	−	0.132733i
$423$	−0.248131	−	0.429776i	−0.0120645	−	0.0208964i
$424$	3.57624	+	6.68080i	0.173677	+	0.324448i
$425$	−31.4472	+	4.73991i	−1.52542	+	0.229919i
$426$	−0.561869	−	8.75401i	−0.0272226	−	0.424133i
$427$	0.493316	+	8.09798i	0.0238732	+	0.391889i
$428$	−18.6866	−	11.3288i	−0.903251	−	0.547600i
$429$	24.5034	+	1.83628i	1.18304	+	0.0886563i
$430$	0.193578	+	1.38472i	0.00933517	+	0.0667770i
$431$	5.58039	−	14.2186i	0.268798	−	0.684886i	−0.731198	−	0.682165i	$-0.761039\pi$
$431$	5.58039	−	14.2186i	0.268798	−	0.684886i	0.999996	−	0.00272110i	$-0.000866155\pi$
$432$	−16.3798	+	11.9524i	−0.788072	+	0.575059i
$433$	−18.9161	+	23.7201i	−0.909052	+	1.13991i	0.0806460	+	0.996743i	$0.474302\pi$
$433$	−18.9161	+	23.7201i	−0.909052	+	1.13991i	−0.989698	+	0.143172i	$0.954270\pi$
$434$	−1.91419	+	7.52610i	−0.0918841	+	0.361264i
$435$	43.1629	−	34.4213i	2.06950	−	1.65037i
$436$	40.0637	−	2.14115i	1.91870	−	0.102542i
$437$	20.0429	−	1.50201i	0.958784	−	0.0718509i
$438$	−14.8432	−	4.75309i	−0.709235	−	0.227111i
$439$	18.0529	+	16.7506i	0.861618	+	0.799465i	0.981126	−	0.193368i	$-0.0619413\pi$
$439$	18.0529	+	16.7506i	0.861618	+	0.799465i	−0.119508	+	0.992833i	$0.538132\pi$
$440$	−15.2822	+	29.2893i	−0.728550	+	1.39631i
$441$	0.970111	+	0.0270860i	0.0461958	+	0.00128981i
$442$	23.3022	+	3.76774i	1.10837	+	0.179213i
$443$	0.764006	−	0.823402i	0.0362990	−	0.0391210i	−0.714641	−	0.699491i	$-0.753410\pi$
$443$	0.764006	−	0.823402i	0.0362990	−	0.0391210i	0.750940	+	0.660370i	$0.229601\pi$
$444$	29.2663	+	14.8739i	1.38892	+	0.705883i
$445$	−11.7090	+	0.877466i	−0.555058	+	0.0415959i
$446$	1.56105	−	0.338761i	0.0739176	−	0.0160408i
$447$	−10.0252	−	12.5712i	−0.474177	−	0.594599i
$448$	17.4478	+	11.9822i	0.824331	+	0.566108i
$449$	−5.57504	+	6.99088i	−0.263103	+	0.329920i	−0.895782	−	0.444494i	$-0.853384\pi$
$449$	−5.57504	+	6.99088i	−0.263103	+	0.329920i	0.632679	+	0.774414i	$0.281955\pi$
$450$	0.715603	−	1.44616i	0.0337338	−	0.0681727i
$451$	24.1598	+	9.48202i	1.13764	+	0.446491i
$452$	−5.31653	−	0.113829i	−0.250068	−	0.00535406i
$453$	−13.0533	−	0.978208i	−0.613297	−	0.0459602i
$454$	−5.56938	+	13.7558i	−0.261384	+	0.645590i
$455$	−11.6956	−	39.8841i	−0.548297	−	1.86979i
$456$	−12.3006	−	3.22630i	−0.576027	−	0.151085i
$457$	−29.3335	+	4.42132i	−1.37216	+	0.206821i	−0.793413	−	0.608684i	$-0.791698\pi$
$457$	−29.3335	+	4.42132i	−1.37216	+	0.206821i	−0.578751	+	0.815504i	$0.696460\pi$
$458$	21.3198	+	20.2109i	0.996210	+	0.944391i
$459$	−16.9655	+	9.79502i	−0.791880	+	0.457192i
$460$	38.2738	+	43.0625i	1.78453	+	2.00780i
$461$	2.98132	+	6.19078i	0.138854	+	0.288333i	0.958787	−	0.284126i	$-0.0917036\pi$
$461$	2.98132	+	6.19078i	0.138854	+	0.288333i	−0.819933	+	0.572460i	$0.805989\pi$
$462$	17.2871	+	12.4214i	0.804268	+	0.577896i
$463$	−9.94250	−	4.78806i	−0.462067	−	0.222520i	0.188343	−	0.982103i	$-0.439688\pi$
$463$	−9.94250	−	4.78806i	−0.462067	−	0.222520i	−0.650410	+	0.759584i	$0.725403\pi$
$464$	1.46680	−	34.2388i	0.0680947	−	1.58950i
$465$	9.80377	−	9.09657i	0.454639	−	0.421843i
$466$	3.51672	+	5.27859i	0.162909	+	0.244526i
$467$	−9.30649	−	13.6501i	−0.430653	−	0.631652i	0.548168	−	0.836368i	$-0.315325\pi$
$467$	−9.30649	−	13.6501i	−0.430653	−	0.631652i	−0.978821	+	0.204716i	$0.934373\pi$
$468$	−0.833188	+	0.860274i	−0.0385141	+	0.0397662i
$469$	8.32673	+	10.7457i	0.384493	+	0.496190i
$470$	−17.6512	+	5.23844i	−0.814189	+	0.241631i
$471$	6.52459	−	11.3009i	0.300637	−	0.520719i
$472$	−0.156586	−	3.66582i	−0.00720745	−	0.168733i
$473$	0.721212	+	0.491714i	0.0331614	+	0.0226090i
$474$	−27.9906	−	0.299610i	−1.28565	−	0.0137615i
$475$	−20.3609	+	4.64725i	−0.934224	+	0.213231i
$476$	15.5269	+	13.3070i	0.711672	+	0.609926i
$477$	−0.362127	−	0.0826532i	−0.0165807	−	0.00378443i
$478$	−24.3643	−	5.83606i	−1.11440	−	0.266935i
$479$	−34.4069	+	10.6131i	−1.57209	+	0.484926i	−0.953653	−	0.300908i	$-0.902710\pi$
$479$	−34.4069	+	10.6131i	−1.57209	+	0.484926i	−0.618438	+	0.785834i	$0.712234\pi$
$480$	−14.0363	−	33.6407i	−0.640667	−	1.53548i
$481$	−38.2397	−	11.7954i	−1.74358	−	0.537824i
$482$	−5.24493	−	5.77546i	−0.238900	−	0.263065i
$483$	30.9612	−	20.4819i	1.40878	−	0.931959i
$484$	−0.474944	−	1.29072i	−0.0215884	−	0.0586690i
$485$	−24.5930	+	9.65205i	−1.11671	+	0.438277i
$486$	0.173873	−	2.02856i	0.00788702	−	0.0920173i
$487$	−7.09683	−	1.06968i	−0.321588	−	0.0484716i	−0.0137355	−	0.999906i	$-0.504372\pi$
$487$	−7.09683	−	1.06968i	−0.321588	−	0.0484716i	−0.307853	+	0.951434i	$0.599610\pi$
$488$	−2.90782	−	8.17118i	−0.131631	−	0.369892i
$489$	0.405646			0.0183440
$490$	9.36153	−	34.7684i	0.422911	−	1.57068i
$491$			19.5368i			0.881685i	0.897585	+	0.440842i	$0.145320\pi$
$491$			19.5368i			0.881685i	−0.897585	+	0.440842i	$0.854680\pi$
$492$	−25.1010	+	13.7843i	−1.13164	+	0.621443i
$493$	4.93467	−	32.7394i	0.222246	−	1.47451i
$494$	15.4446	+	1.32379i	0.694884	+	0.0595601i
$495$	−0.591616	−	1.50741i	−0.0265912	−	0.0677532i
$496$	−0.265496	−	8.29765i	−0.0119211	−	0.372575i
$497$	−2.85366	+	8.81273i	−0.128004	+	0.395305i
$498$	14.6476	+	16.1293i	0.656377	+	0.722770i
$499$	−1.98915	+	6.44867i	−0.0890466	+	0.288682i	−0.989132	−	0.147032i	$-0.953028\pi$
$499$	−1.98915	+	6.44867i	−0.0890466	+	0.288682i	0.900085	+	0.435714i	$0.143504\pi$
$500$	−18.0492	−	15.0369i	−0.807183	−	0.672471i
$501$	2.12615	+	6.89280i	0.0949893	+	0.307948i
$502$	3.79783	−	15.8552i	0.169506	−	0.707651i
$503$	5.00664	−	21.9355i	0.223235	−	0.978056i	−0.731790	−	0.681530i	$-0.761315\pi$
$503$	5.00664	−	21.9355i	0.223235	−	0.978056i	0.955025	−	0.296526i	$-0.0958281\pi$
$504$	−1.00443	+	0.259828i	−0.0447411	+	0.0115737i
$505$	7.46056	+	32.6868i	0.331990	+	1.45455i
$506$	35.9658	+	0.384976i	1.59887	+	0.0171143i
$507$	5.64325	−	8.27713i	0.250626	−	0.367600i
$508$	−8.86550	−	43.0725i	−0.393343	−	1.91103i
$509$	16.8230	+	9.71275i	0.745665	+	0.430510i	0.824126	−	0.566407i	$-0.191667\pi$
$509$	16.8230	+	9.71275i	0.745665	+	0.430510i	−0.0784602	+	0.996917i	$0.525000\pi$
$510$	−10.0195	−	33.7613i	−0.443671	−	1.49497i
$511$	12.7232	+	10.4402i	0.562843	+	0.461849i
$512$	−21.4735	−	7.13354i	−0.949005	−	0.315261i
$513$	−10.6293	+	7.24695i	−0.469296	+	0.319961i
$514$	8.21664	+	12.3332i	0.362420	+	0.543993i
$515$	−35.5116	−	38.2724i	−1.56483	−	1.68648i
$516$	−0.926195	+	0.264119i	−0.0407735	+	0.0116272i
$517$	−4.98736	+	10.3564i	−0.219344	+	0.455472i
$518$	−22.9461	−	25.9867i	−1.00819	−	1.14179i
$519$	39.4285	−	18.9878i	1.73072	−	0.833470i
$520$	23.8386	+	37.4972i	1.04539	+	1.64436i
$521$	−18.5252	−	32.0867i	−0.811606	−	1.40574i	−0.911740	−	0.410768i	$-0.865260\pi$
$521$	−18.5252	−	32.0867i	−0.811606	−	1.40574i	0.100134	−	0.994974i	$-0.468073\pi$
$522$	1.21910	+	1.15569i	0.0533586	+	0.0505831i
$523$	−3.38859	−	22.4818i	−0.148173	−	0.983060i	−0.932098	−	0.362206i	$-0.882024\pi$
$523$	−3.38859	−	22.4818i	−0.148173	−	0.983060i	0.783926	−	0.620855i	$-0.213214\pi$
$524$	14.0453	+	1.35544i	0.613571	+	0.0592126i
$525$	−28.6397	+	25.8394i	−1.24994	+	1.12772i
$526$	−18.6637	−	7.55650i	−0.813778	−	0.329479i
$527$	0.599384	−	7.99822i	0.0261096	−	0.348408i
$528$	−21.4387	−	7.63225i	−0.932998	−	0.332151i
$529$	14.5132	−	36.9791i	0.631010	−	1.60779i
$530$	−6.11191	+	12.3516i	−0.265484	+	0.536517i
$531$	0.140614	+	0.112136i	0.00610212	+	0.00486628i
$532$	10.8210	+	7.95225i	0.469148	+	0.344774i
$533$	27.2917	−	21.7644i	1.18213	−	0.942721i
$534$	−1.71528	−	7.90419i	−0.0742276	−	0.342048i
$535$	−2.96986	−	39.6301i	−0.128398	−	1.71336i
$536$	−11.7386	−	8.56795i	−0.507031	−	0.370079i
$537$	−3.28446	−	3.04754i	−0.141735	−	0.131511i
$538$	17.8542	+	2.88685i	0.769747	+	0.124461i
$539$	−12.1396	−	18.9192i	−0.522888	−	0.814907i
$540$	−34.9969	−	11.6212i	−1.50603	−	0.500095i
$541$	2.02749	−	2.18512i	0.0871687	−	0.0939455i	−0.687961	−	0.725748i	$-0.741494\pi$
$541$	2.02749	−	2.18512i	0.0871687	−	0.0939455i	0.775130	+	0.631802i	$0.217684\pi$
$542$	4.00288	−	12.5004i	0.171939	−	0.536938i
$543$	2.43618	+	32.5086i	0.104547	+	1.39508i
$544$	−19.8933	−	9.06378i	−0.852920	−	0.388607i
$545$	45.4925	+	57.0458i	1.94869	+	2.44358i
$546$	26.0936	−	11.7825i	1.11670	−	0.504243i
$547$	−7.50860	−	5.98791i	−0.321045	−	0.256025i	0.449685	−	0.893187i	$-0.351536\pi$
$547$	−7.50860	−	5.98791i	−0.321045	−	0.256025i	−0.770729	+	0.637163i	$0.780108\pi$
$548$	7.61946	+	5.43737i	0.325487	+	0.232273i
$549$	0.395745	+	0.155319i	0.0168900	+	0.00662884i
$550$	−37.0134	+	5.17434i	−1.57826	+	0.220634i
$551$	1.62483	−	21.6819i	0.0692203	−	0.923680i
$552$	−25.7272	+	30.2173i	−1.09502	+	1.28613i
$553$	27.3629	+	11.1823i	1.16359	+	0.475521i
$554$	2.24796	+	35.0235i	0.0955065	+	1.48801i
$555$	8.89833	+	59.0366i	0.377713	+	2.50596i
$556$	24.5666	−	18.7452i	1.04186	−	0.794974i
$557$	−22.1461	+	12.7860i	−0.938359	+	0.541762i	−0.889446	−	0.457041i	$-0.848909\pi$
$557$	−22.1461	+	12.7860i	−0.938359	+	0.541762i	−0.0489136	+	0.998803i	$0.515576\pi$
$558$	0.315421	+	0.257111i	0.0133528	+	0.0108844i
$559$	1.05775	−	0.509384i	0.0447379	−	0.0215447i
$560$	0.693948	+	38.4865i	0.0293247	+	1.62635i
$561$	−19.8085	−	9.53927i	−0.836315	−	0.402748i
$562$	18.3526	+	39.1768i	0.774157	+	1.65257i
$563$	−17.2352	−	18.5752i	−0.726378	−	0.782849i	0.256611	−	0.966515i	$-0.417394\pi$
$563$	−17.2352	−	18.5752i	−0.726378	−	0.782849i	−0.982989	+	0.183665i	$0.941204\pi$
$564$	−5.25705	−	11.5421i	−0.221362	−	0.486010i
$565$	−5.44782	−	7.99049i	−0.229192	−	0.336162i
$566$	−4.50563	−	3.14305i	−0.189386	−	0.132112i
$567$	−11.0985	+	22.2466i	−0.466093	+	0.934268i
$568$	0.317932	−	9.89772i	0.0133401	−	0.415299i
$569$	−3.52360	+	6.10305i	−0.147717	+	0.255853i	−0.930383	−	0.366588i	$-0.880526\pi$
$569$	−3.52360	+	6.10305i	−0.147717	+	0.255853i	0.782666	+	0.622441i	$0.213859\pi$
$570$	−8.21821	−	21.6172i	−0.344223	−	0.905445i
$571$	−18.6910	+	27.4147i	−0.782196	+	1.14727i	0.203556	+	0.979063i	$0.434750\pi$
$571$	−18.6910	+	27.4147i	−0.782196	+	1.14727i	−0.985752	+	0.168207i	$0.946202\pi$
$572$	27.3351	+	4.72059i	1.14294	+	0.197378i
$573$	45.6707	−	10.4240i	1.90792	−	0.435470i
$574$	30.0047	−	3.76840i	1.25237	−	0.157290i
$575$	−14.5031	+	63.5421i	−0.604820	+	2.64989i
$576$	0.954615	−	0.564695i	0.0397756	−	0.0235290i
$577$	9.97830	−	3.07790i	0.415402	−	0.128135i	−0.0800072	−	0.996794i	$-0.525494\pi$
$577$	9.97830	−	3.07790i	0.415402	−	0.128135i	0.495409	+	0.868660i	$0.335018\pi$
$578$	2.51420	+	1.48768i	0.104577	+	0.0618792i
$579$	−2.02468	+	6.56384i	−0.0841427	+	0.272784i
$580$	52.2344	−	33.9982i	2.16892	−	1.41170i
$581$	−8.10598	−	21.5326i	−0.336293	−	0.893323i
$582$	−8.93007	−	15.8569i	−0.370163	−	0.657290i
$583$	3.14321	+	8.00876i	0.130178	+	0.331689i
$584$	−16.1637	−	6.95061i	−0.668858	−	0.287618i
$585$	−2.15367	−	0.324613i	−0.0890431	−	0.0134211i
$586$	−8.06800	−	10.3421i	−0.333286	−	0.427230i
$587$			13.9435i			0.575509i	0.957704	+	0.287755i	$0.0929088\pi$
$587$			13.9435i			0.575509i	−0.957704	+	0.287755i	$0.907091\pi$
$588$	24.6119	+	3.07062i	1.01498	+	0.126630i
$589$		−	5.26713i		−	0.217028i
$590$	5.26123	−	4.10434i	0.216601	−	0.168973i
$591$	−1.40886	−	0.212352i	−0.0579529	−	0.00873499i
$592$	31.2733	+	19.8873i	1.28532	+	0.817363i
$593$	1.35191	+	3.44461i	0.0555162	+	0.141453i	0.955941	−	0.293558i	$-0.0948395\pi$
$593$	1.35191	+	3.44461i	0.0555162	+	0.141453i	−0.900425	+	0.435012i	$0.856744\pi$
$594$	−20.0594	+	11.2968i	−0.823047	+	0.463512i
$595$	−3.29641	+	37.0423i	−0.135140	+	1.51859i
$596$	−9.90199	−	15.2133i	−0.405601	−	0.623161i
$597$	−1.15136	+	3.73262i	−0.0471220	+	0.152766i
$598$	24.6350	−	41.6335i	1.00740	−	1.70252i
$599$	23.9626	−	7.39149i	0.979086	−	0.302008i	0.236406	−	0.971654i	$-0.424030\pi$
$599$	23.9626	−	7.39149i	0.979086	−	0.302008i	0.742680	+	0.669646i	$0.233554\pi$
$600$	21.7543	−	35.0317i	0.888115	−	1.43016i
$601$	2.93278	−	12.8493i	0.119630	−	0.524135i	−0.879229	−	0.476398i	$-0.841942\pi$
$601$	2.93278	−	12.8493i	0.119630	−	0.524135i	0.998860	−	0.0477368i	$-0.0152009\pi$
$602$	1.01202	+	0.100989i	0.0412471	+	0.00411601i
$603$	0.694500	−	0.158515i	0.0282822	−	0.00645523i
$604$	−14.5618	−	2.51472i	−0.592509	−	0.102322i
$605$	1.40897	−	2.06658i	0.0572827	−	0.0840184i
$606$	−21.5875	+	8.20693i	−0.876933	+	0.333384i
$607$	−22.7705	+	39.4397i	−0.924227	+	1.60081i	−0.131428	+	0.991326i	$0.541956\pi$
$607$	−22.7705	+	39.4397i	−0.924227	+	1.60081i	−0.792800	+	0.609482i	$0.791377\pi$
$608$	−13.4722	−	4.95925i	−0.546368	−	0.201124i
$609$	−16.9174	−	36.4211i	−0.685529	−	1.47586i
$610$	9.02429	−	12.9365i	0.365383	−	0.523784i
$611$	8.70897	+	12.7737i	0.352327	+	0.516769i
$612$	0.975170	−	0.444159i	0.0394189	−	0.0179540i
$613$	0.219006	+	0.236032i	0.00884557	+	0.00953325i	0.737459	−	0.675392i	$-0.236025\pi$
$613$	0.219006	+	0.236032i	0.00884557	+	0.00953325i	−0.728614	+	0.684925i	$0.759835\pi$
$614$	20.2379	−	9.48055i	0.816734	−	0.382604i
$615$	−46.9218	−	22.5964i	−1.89207	−	0.911173i
$616$	18.0783	+	15.8324i	0.728396	+	0.637907i
$617$	−8.44595	+	4.06736i	−0.340021	+	0.163746i	−0.596100	−	0.802910i	$-0.703284\pi$
$617$	−8.44595	+	4.06736i	−0.340021	+	0.163746i	0.256078	+	0.966656i	$0.417569\pi$
$618$	22.7228	−	27.8761i	0.914044	−	1.12134i
$619$	13.1127	−	7.57063i	0.527044	−	0.304289i	−0.212768	−	0.977103i	$-0.568248\pi$
$619$	13.1127	−	7.57063i	0.527044	−	0.304289i	0.739812	+	0.672814i	$0.234914\pi$
$620$	12.0028	−	9.15858i	0.482045	−	0.367817i
$621$	5.98375	+	39.6996i	0.240120	+	1.59309i
$622$	27.2216	−	1.74719i	1.09149	−	0.0700561i
$623$	−1.39073	+	8.42711i	−0.0557184	+	0.337625i
$624$	−23.3072	+	19.8388i	−0.933034	+	0.794188i
$625$	0.117780	−	1.57167i	0.00471122	−	0.0628668i
$626$	5.09217	+	36.4257i	0.203524	+	1.45586i
$627$	−13.4399	−	5.27478i	−0.536739	−	0.210655i
$628$	8.55710	−	11.9912i	0.341465	−	0.478500i
$629$	27.9939	+	22.3244i	1.11619	+	0.890132i
$630$	−1.44571	−	1.21242i	−0.0575984	−	0.0483040i
$631$	−12.1818	−	15.2755i	−0.484950	−	0.608108i	0.477811	−	0.878463i	$-0.341430\pi$
$631$	−12.1818	−	15.2755i	−0.484950	−	0.608108i	−0.962761	+	0.270355i	$0.912859\pi$
$632$	−31.4202	−	3.37201i	−1.24983	−	0.134131i
$633$	0.329323	+	4.39451i	0.0130894	+	0.174666i
$634$	13.6185	+	4.36094i	0.540861	+	0.173195i
$635$	54.3963	−	58.6253i	2.15865	−	2.32647i
$636$	−9.00914	−	2.99160i	−0.357236	−	0.118625i
$637$	−30.2005	+	1.41704i	−1.19659	+	0.0561450i
$638$	6.21056	−	38.4102i	0.245878	−	1.52067i
$639$	0.355829	+	0.330161i	0.0140764	+	0.0130610i
$640$	−12.1244	−	39.3238i	−0.479259	−	1.55441i
$641$	2.79878	+	37.3472i	0.110545	+	1.47513i	0.726404	+	0.687268i	$0.241190\pi$
$641$	2.79878	+	37.3472i	0.110545	+	1.47513i	−0.615858	+	0.787857i	$0.711191\pi$
$642$	26.7525	−	5.80554i	1.05584	−	0.229126i
$643$	22.1551	−	17.6681i	0.873712	−	0.696762i	−0.0802224	−	0.996777i	$-0.525563\pi$
$643$	22.1551	−	17.6681i	0.873712	−	0.696762i	0.953935	+	0.300015i	$0.0969916\pi$
$644$	37.0118	−	19.6578i	1.45847	−	0.774627i
$645$	−1.36941	−	1.09207i	−0.0539204	−	0.0430001i
$646$	−12.4310	−	6.15120i	−0.489089	−	0.242016i
$647$	3.96344	−	10.0987i	0.155819	−	0.397020i	−0.831552	−	0.555447i	$-0.812547\pi$
$647$	3.96344	−	10.0987i	0.155819	−	0.397020i	0.987371	+	0.158427i	$0.0506423\pi$
$648$	4.80294	−	26.1403i	0.188677	−	1.02689i
$649$	0.311312	−	4.15417i	0.0122201	−	0.163066i
$650$	−18.8641	+	46.5923i	−0.739911	+	1.82750i
$651$	−4.74610	−	8.49202i	−0.186014	−	0.332829i
$652$	0.455821	+	0.0439889i	0.0178513	+	0.00172274i
$653$	1.01603	+	6.74091i	0.0397603	+	0.263792i	0.999875	−	0.0158144i	$-0.00503410\pi$
$653$	1.01603	+	6.74091i	0.0397603	+	0.263792i	−0.960115	+	0.279606i	$0.909796\pi$
$654$	−34.5782	+	36.4755i	−1.35211	+	1.42631i
$655$	12.8308	+	22.2236i	0.501341	+	0.868347i
$656$	−29.7005	+	12.7672i	−1.15961	+	0.498477i
$657$	0.777036	−	0.374201i	0.0303151	−	0.0145990i
$658$	0.671246	+	13.3763i	0.0261679	+	0.521463i
$659$	6.50370	−	13.5051i	0.253348	−	0.526083i	−0.735042	−	0.678022i	$-0.762837\pi$
$659$	6.50370	−	13.5051i	0.253348	−	0.526083i	0.988390	+	0.151939i	$0.0485517\pi$
$660$	−11.3493	−	39.7990i	−0.441771	−	1.54918i
$661$	5.17611	+	5.57852i	0.201327	+	0.216979i	0.825643	−	0.564193i	$-0.190813\pi$
$661$	5.17611	+	5.57852i	0.201327	+	0.216979i	−0.624316	+	0.781172i	$0.714622\pi$
$662$	−13.2497	+	8.82722i	−0.514963	+	0.343080i
$663$	−24.4322	+	16.6576i	−0.948866	+	0.646926i
$664$	14.7103	+	19.7127i	0.570871	+	0.765001i
$665$	−0.340833	+	24.4193i	−0.0132169	+	0.946941i
$666$	−1.74155	+	0.516849i	−0.0674837	+	0.0200275i
$667$	−58.7636	−	33.9272i	−2.27533	−	1.31367i
$668$	1.64166	+	7.97593i	0.0635179	+	0.308598i
$669$	−1.12725	+	1.65337i	−0.0435819	+	0.0639229i
$670$	0.282886	−	26.4282i	0.0109289	−	1.02101i
$671$	−2.19120	−	9.60027i	−0.0845903	−	0.370614i
$672$	−26.1894	+	4.14384i	−1.01028	+	0.159852i
$673$	4.95154	−	21.6941i	0.190868	−	0.836247i	−0.785280	−	0.619141i	$-0.787481\pi$
$673$	4.95154	−	21.6941i	0.190868	−	0.836247i	0.976148	−	0.217107i	$-0.0696619\pi$
$674$	32.6333	+	7.81674i	1.25699	+	0.301089i
$675$	−12.2963	−	39.8635i	−0.473283	−	1.53435i
$676$	7.23885	−	8.68896i	0.278417	−	0.334191i
$677$	−0.615403	+	1.99509i	−0.0236519	+	0.0766774i	−0.966629	−	0.256179i	$-0.917536\pi$
$677$	−0.615403	+	1.99509i	−0.0236519	+	0.0766774i	0.942977	+	0.332857i	$0.108012\pi$
$678$	4.93157	−	4.47856i	0.189396	−	0.171998i
$679$	2.59875	+	19.0411i	0.0997310	+	0.730731i
$680$	−7.59769	−	39.0237i	−0.291358	−	1.49649i
$681$	−6.79206	−	17.3059i	−0.260272	−	0.663163i
$682$	0.804942	−	9.39121i	0.0308228	−	0.359608i
$683$	−5.81808	+	38.6004i	−0.222623	+	1.47700i	0.546260	+	0.837615i	$0.316051\pi$
$683$	−5.81808	+	38.6004i	−0.222623	+	1.47700i	−0.768883	+	0.639389i	$0.779187\pi$
$684$	0.616803	−	0.338718i	0.0235840	−	0.0129512i
$685$			17.0233i			0.650428i
$686$	−22.9680	−	12.5885i	−0.876924	−	0.480629i
$687$	−36.8014			−1.40406
$688$	−1.06940	+	0.196350i	−0.0407704	+	0.00748576i
$689$	11.4422	+	1.72464i	0.435915	+	0.0657036i
$690$	−71.9097	−	6.16355i	−2.73755	−	0.234642i
$691$	−3.20443	+	1.25765i	−0.121902	+	0.0478431i	−0.425508	−	0.904955i	$-0.639905\pi$
$691$	−3.20443	+	1.25765i	−0.121902	+	0.0478431i	0.303606	+	0.952798i	$0.401809\pi$
$692$	46.3644	−	17.0607i	1.76251	−	0.648549i
$693$	−1.16711	+	0.159289i	−0.0443349	+	0.00605088i
$694$	19.9360	−	18.1047i	0.756761	−	0.687246i
$695$	53.7011	+	16.5646i	2.03700	+	0.628331i
$696$	28.1752	+	32.3920i	1.06798	+	1.22782i
$697$	−29.8456	+	9.20614i	−1.13048	+	0.348707i
$698$	4.63948	−	19.3689i	0.175607	−	0.733124i
$699$	−7.74654	−	1.76810i	−0.293001	−	0.0668756i
$700$	−34.9842	+	25.9297i	−1.32228	+	0.980052i
$701$	−12.3550	+	2.81996i	−0.466643	+	0.106508i	−0.449376	−	0.893343i	$-0.648354\pi$
$701$	−12.3550	+	2.81996i	−0.466643	+	0.106508i	−0.0172671	+	0.999851i	$0.505497\pi$
$702$	−0.331414	+	30.9618i	−0.0125084	+	1.16858i
$703$	19.4277	+	13.2456i	0.732728	+	0.499565i
$704$	−23.2627	−	10.9011i	−0.876748	−	0.410851i
$705$	11.5327	−	19.9752i	0.434345	−	0.752308i
$706$	−7.96557	−	26.8404i	−0.299788	−	1.01015i
$707$	24.3858	+	0.340365i	0.917122	+	0.0128008i
$708$	3.30175	+	3.19779i	0.124087	+	0.120180i
$709$	8.97420	+	13.1627i	0.337033	+	0.494337i	0.956919	−	0.290355i	$-0.0937734\pi$
$709$	8.97420	+	13.1627i	0.337033	+	0.494337i	−0.619886	+	0.784692i	$0.712821\pi$
$710$	14.9878	−	9.98521i	0.562482	−	0.374738i
$711$	1.13548	−	1.05357i	0.0425837	−	0.0395119i
$712$	−1.07030	−	9.06787i	−0.0401113	−	0.339833i
$713$	−14.8098	−	7.13200i	−0.554630	−	0.267096i
$714$	−25.5847	+	1.28389i	−0.957485	+	0.0480482i
$715$	21.8885	+	45.4519i	0.818582	+	1.69980i
$716$	−3.36024	−	3.78065i	−0.125578	−	0.141290i
$717$	27.1804	−	15.6926i	1.01507	−	0.586052i
$718$	2.00449	−	2.11448i	0.0748070	−	0.0789117i
$719$	38.2978	−	5.77247i	1.42827	−	0.215277i	0.611043	−	0.791597i	$-0.290750\pi$
$719$	38.2978	−	5.77247i	1.42827	−	0.215277i	0.817224	+	0.576320i	$0.195512\pi$
$720$	1.84438	+	0.816612i	0.0687361	+	0.0304333i
$721$	−33.1515	+	18.5280i	−1.23463	+	0.690020i
$722$	16.4637	+	6.66576i	0.612716	+	0.248074i
$723$	9.74596	+	0.730359i	0.362456	+	0.0271623i
$724$	−0.787768	+	36.7937i	−0.0292772	+	1.36743i
$725$	65.6320	+	25.7587i	2.43751	+	0.956653i
$726$	1.54420	+	0.764113i	0.0573105	+	0.0283589i
$727$	−14.4073	+	18.0661i	−0.534336	+	0.670036i	−0.973584	−	0.228330i	$-0.926673\pi$
$727$	−14.4073	+	18.0661i	−0.534336	+	0.670036i	0.439248	+	0.898366i	$0.355245\pi$
$728$	30.5988	−	10.4102i	1.13407	−	0.385827i
$729$	−15.9860	−	20.0458i	−0.592074	−	0.742438i
$730$	−6.78593	−	31.2702i	−0.251159	−	1.15736i
$731$	−1.04750	+	0.0784994i	−0.0387433	+	0.00290341i
$732$	9.68595	+	4.92264i	0.358003	+	0.181946i
$733$	14.6003	−	15.7354i	0.539276	−	0.581202i	−0.403352	−	0.915045i	$-0.632155\pi$
$733$	14.6003	−	15.7354i	0.539276	−	0.581202i	0.942629	+	0.333843i	$0.108346\pi$
$734$	−4.61580	+	28.5471i	−0.170372	+	1.05369i
$735$	21.4542	+	39.6776i	0.791351	+	1.46353i
$736$	−32.1862	+	31.1650i	−1.18640	+	1.14876i
$737$	−12.0954	−	11.2229i	−0.445540	−	0.413400i
$738$	0.483263	−	1.50916i	0.0177891	−	0.0555528i
$739$	−7.00618	+	0.525040i	−0.257726	+	0.0193139i	−0.202967	−	0.979186i	$-0.565058\pi$
$739$	−7.00618	+	0.525040i	−0.257726	+	0.0193139i	−0.0547597	+	0.998500i	$0.517439\pi$
$740$	3.59694	+	67.3037i	0.132226	+	2.47413i
$741$	−15.1822	+	12.1074i	−0.557731	+	0.444776i
$742$	7.68093	+	6.44149i	0.281976	+	0.236474i
$743$	−27.4238	+	34.3884i	−1.00608	+	1.26159i	−0.0411337	+	0.999154i	$0.513097\pi$
$743$	−27.4238	+	34.3884i	−1.00608	+	1.26159i	−0.964950	+	0.262435i	$0.915474\pi$
$744$	7.39270	+	7.31491i	0.271030	+	0.268178i
$745$	12.0604	−	30.7294i	0.441859	−	1.12584i
$746$	42.4631	−	5.93618i	1.55468	−	0.217339i
$747$	−1.20227	−	0.0900980i	−0.0439889	−	0.00329651i
$748$	−21.2241	−	12.8672i	−0.776031	−	0.470473i
$749$	−28.5223	−	4.70705i	−1.04218	−	0.171992i
$750$	29.3688	−	1.88501i	1.07240	−	0.0688309i
$751$	−31.2795	+	4.71462i	−1.14140	+	0.172039i	−0.692416	−	0.721498i	$-0.743454\pi$
$751$	−31.2795	+	4.71462i	−1.14140	+	0.172039i	−0.448989	+	0.893538i	$0.648216\pi$
$752$	−4.65565	−	13.5398i	−0.169774	−	0.493746i
$753$	10.2120	+	17.6877i	0.372147	+	0.644577i
$754$	−40.5630	−	33.0643i	−1.47722	−	1.20413i
$755$	−11.6603	−	24.2128i	−0.424361	−	0.881194i
$756$	−14.2249	+	22.7415i	−0.517355	+	0.827099i
$757$	18.9545	−	39.3594i	0.688913	−	1.43054i	−0.203386	−	0.979099i	$-0.565195\pi$
$757$	18.9545	−	39.3594i	0.688913	−	1.43054i	0.892299	−	0.451445i	$-0.149091\pi$
$758$	−22.5681	+	10.5721i	−0.819710	+	0.383998i
$759$	−33.0297	+	30.6471i	−1.19890	+	1.11242i
$760$	−6.89051	−	25.1822i	−0.249945	−	0.913455i
$761$	41.9503	−	28.6012i	1.52070	−	1.03679i	0.539906	−	0.841725i	$-0.318460\pi$
$761$	41.9503	−	28.6012i	1.52070	−	1.03679i	0.980790	−	0.195067i	$-0.0624925\pi$
$762$	45.1820	+	31.5182i	1.63677	+	1.14178i
$763$	48.1356	−	22.3588i	1.74263	−	0.809441i
$764$	52.4501	−	6.76078i	1.89758	−	0.244596i
$765$	1.68766	+	0.974373i	0.0610176	+	0.0352285i
$766$	−4.36768	+	1.66046i	−0.157811	+	0.0599949i

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11505 + 0.869863i) q^{2} +(0.264046 - 1.75183i) q^{3} +(0.486677 - 1.93988i) q^{4} +(3.38580 - 1.32883i) q^{5} +(1.22943 + 2.18307i) q^{6} +(-0.357778 - 2.62145i) q^{7} +(1.14476 + 2.58641i) q^{8} +(-0.132482 - 0.0408653i) q^{9} +O(q^{10})\)	\(q+(-1.11505 + 0.869863i) q^{2} +(0.264046 - 1.75183i) q^{3} +(0.486677 - 1.93988i) q^{4} +(3.38580 - 1.32883i) q^{5} +(1.22943 + 2.18307i) q^{6} +(-0.357778 - 2.62145i) q^{7} +(1.14476 + 2.58641i) q^{8} +(-0.132482 - 0.0408653i) q^{9} +(-2.61944 + 4.42689i) q^{10} +(0.946542 + 3.06861i) q^{11} +(-3.26985 - 1.36480i) q^{12} +(4.21081 + 0.961090i) q^{13} +(2.67924 + 2.61183i) q^{14} +(-1.43388 - 6.28223i) q^{15} +(-3.52629 - 1.88819i) q^{16} +(-3.19299 - 2.17694i) q^{17} +(0.183271 - 0.0696742i) q^{18} +(-2.19780 - 1.26890i) q^{19} +(-0.929978 - 7.21476i) q^{20} +(-4.68681 - 0.0654163i) q^{21} +(-3.72472 - 2.59830i) q^{22} +(-6.54375 + 4.46145i) q^{23} +(4.83323 - 1.32250i) q^{24} +(6.03258 - 5.59742i) q^{25} +(-5.53129 + 2.59116i) q^{26} +(2.19946 - 4.56723i) q^{27} +(-5.25943 - 0.581752i) q^{28} +(3.71732 + 7.71910i) q^{29} +(7.06352 + 5.75773i) q^{30} +(1.03774 + 1.79741i) q^{31} +(5.57446 - 0.961955i) q^{32} +(5.62563 - 0.847928i) q^{33} +(5.45399 - 0.350060i) q^{34} +(-4.69482 - 8.40027i) q^{35} +(-0.143750 + 0.237111i) q^{36} +(-9.23936 - 0.692394i) q^{37} +(3.55442 - 0.496895i) q^{38} +(2.79552 - 7.12287i) q^{39} +(7.31282 + 7.23587i) q^{40} +(5.03910 - 6.31884i) q^{41} +(5.28294 - 4.00394i) q^{42} +(0.212516 - 0.169476i) q^{43} +(6.41341 - 0.342755i) q^{44} +(-0.502860 + 0.0376841i) q^{45} +(3.41576 - 10.6669i) q^{46} +(2.62394 + 2.43466i) q^{47} +(-4.23891 + 5.67890i) q^{48} +(-6.74399 + 1.87579i) q^{49} +(-1.85765 + 11.4889i) q^{50} +(-4.65674 + 5.01878i) q^{51} +(3.91371 - 7.70074i) q^{52} +(2.67165 - 0.200213i) q^{53} +(1.52035 + 7.00593i) q^{54} +(7.28246 + 9.13191i) q^{55} +(6.37057 - 3.92630i) q^{56} +(-2.80322 + 3.51513i) q^{57} +(-10.8596 - 5.37363i) q^{58} +(-1.20757 - 0.473937i) q^{59} +(-12.8846 - 0.275865i) q^{60} +(-3.05785 - 0.229154i) q^{61} +(-2.72063 - 1.10152i) q^{62} +(-0.0597270 + 0.361915i) q^{63} +(-5.37904 + 5.92165i) q^{64} +(15.5341 - 2.34138i) q^{65} +(-5.53529 + 5.83901i) q^{66} +(-4.44977 + 2.56908i) q^{67} +(-5.77697 + 5.13456i) q^{68} +(6.08787 + 12.6416i) q^{69} +(12.5420 + 5.28288i) q^{70} +(-3.15445 - 1.51910i) q^{71} +(-0.0459659 - 0.389434i) q^{72} +(-4.56009 + 4.23114i) q^{73} +(10.9046 - 7.26492i) q^{74} +(-8.21286 - 12.0461i) q^{75} +(-3.53113 + 3.64592i) q^{76} +(7.70556 - 3.57920i) q^{77} +(3.07877 + 10.3741i) q^{78} +(-5.58625 + 9.67567i) q^{79} +(-14.4484 - 1.70721i) q^{80} +(-7.76392 - 5.29335i) q^{81} +(-0.122337 + 11.4292i) q^{82} +(8.47811 - 1.93507i) q^{83} +(-2.40787 + 9.06003i) q^{84} +(-13.7036 - 3.12776i) q^{85} +(-0.0895455 + 0.373834i) q^{86} +(14.5041 - 4.47393i) q^{87} +(-6.85313 + 5.96098i) q^{88} +(-3.08481 - 0.951537i) q^{89} +(0.527934 - 0.479439i) q^{90} +(1.01291 - 11.3823i) q^{91} +(5.47000 + 14.8654i) q^{92} +(3.42278 - 1.34334i) q^{93} +(-5.04364 - 0.432302i) q^{94} +(-9.12744 - 1.37574i) q^{95} +(-0.213268 - 10.0195i) q^{96} -7.26359 q^{97} +(5.88821 - 7.95795i) q^{98} -0.445217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

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