LMFDB - Embedded newform 288.2.bc.a.61.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			61.41
Character	$\chi$	$=$	288.61
Dual form			288.2.bc.a.85.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33488 + 0.466998i) q^{2} +(-0.104067 + 1.72892i) q^{3} +(1.56383 + 1.24678i) q^{4} +(-0.809510 + 1.05497i) q^{5} +(-0.946320 + 2.25931i) q^{6} +(-0.106824 - 0.398671i) q^{7} +(1.50528 + 2.39460i) q^{8} +(-2.97834 - 0.359847i) q^{9} +O(q^{10})$	\(q+(1.33488 + 0.466998i) q^{2} +(-0.104067 + 1.72892i) q^{3} +(1.56383 + 1.24678i) q^{4} +(-0.809510 + 1.05497i) q^{5} +(-0.946320 + 2.25931i) q^{6} +(-0.106824 - 0.398671i) q^{7} +(1.50528 + 2.39460i) q^{8} +(-2.97834 - 0.359847i) q^{9} +(-1.57327 + 1.03023i) q^{10} +(0.236676 - 1.79774i) q^{11} +(-2.31832 + 2.57398i) q^{12} +(1.12453 - 0.148047i) q^{13} +(0.0435816 - 0.582065i) q^{14} +(-1.73972 - 1.50937i) q^{15} +(0.891101 + 3.89948i) q^{16} +1.83494i q^{17} +(-3.80769 - 1.87123i) q^{18} +(3.15166 - 7.60878i) q^{19} +(-2.58125 + 0.640518i) q^{20} +(0.700387 - 0.143201i) q^{21} +(1.15547 - 2.28924i) q^{22} +(-1.15598 + 4.31416i) q^{23} +(-4.29673 + 2.35332i) q^{24} +(0.836431 + 3.12160i) q^{25} +(1.57026 + 0.327528i) q^{26} +(0.932094 - 5.11187i) q^{27} +(0.330000 - 0.756637i) q^{28} +(4.50296 - 3.45524i) q^{29} +(-1.61746 - 2.82728i) q^{30} +(-1.20515 - 2.08738i) q^{31} +(-0.631535 + 5.62149i) q^{32} +(3.08352 + 0.596280i) q^{33} +(-0.856911 + 2.44942i) q^{34} +(0.507062 + 0.210032i) q^{35} +(-4.20896 - 4.27606i) q^{36} +(2.01433 + 4.86303i) q^{37} +(7.76039 - 8.68502i) q^{38} +(0.138936 + 1.95963i) q^{39} +(-3.74479 - 0.350422i) q^{40} +(0.00469380 - 0.0175175i) q^{41} +(1.00181 + 0.135923i) q^{42} +(1.13921 - 8.65317i) q^{43} +(2.61149 - 2.51626i) q^{44} +(2.79063 - 2.85077i) q^{45} +(-3.55780 + 5.21906i) q^{46} +(-2.27428 - 1.31306i) q^{47} +(-6.83463 + 1.13484i) q^{48} +(5.91465 - 3.41483i) q^{49} +(-0.341245 + 4.55759i) q^{50} +(-3.17246 - 0.190956i) q^{51} +(1.94315 + 1.17052i) q^{52} +(-11.3924 + 4.71890i) q^{53} +(3.63147 - 6.38846i) q^{54} +(1.70497 + 1.70497i) q^{55} +(0.793859 - 0.855912i) q^{56} +(12.8270 + 6.24080i) q^{57} +(7.62451 - 2.50947i) q^{58} +(3.58165 - 4.66770i) q^{59} +(-0.838783 - 4.52943i) q^{60} +(4.05953 - 3.11499i) q^{61} +(-0.633930 - 3.34921i) q^{62} +(0.174696 + 1.22582i) q^{63} +(-3.46825 + 7.20911i) q^{64} +(-0.754133 + 1.30620i) q^{65} +(3.83767 + 2.23596i) q^{66} +(-0.523374 - 3.97542i) q^{67} +(-2.28775 + 2.86952i) q^{68} +(-7.33855 - 2.44755i) q^{69} +(0.578784 + 0.517165i) q^{70} +(-4.17197 + 4.17197i) q^{71} +(-3.62155 - 7.67361i) q^{72} +(-7.49687 - 7.49687i) q^{73} +(0.417873 + 7.43226i) q^{74} +(-5.48406 + 1.12127i) q^{75} +(14.4151 - 7.96939i) q^{76} +(-0.741988 + 0.0976845i) q^{77} +(-0.729682 + 2.68076i) q^{78} +(-11.0415 - 6.37483i) q^{79} +(-4.83520 - 2.21658i) q^{80} +(8.74102 + 2.14349i) q^{81} +(0.0144463 - 0.0211918i) q^{82} +(2.34186 + 3.05198i) q^{83} +(1.27382 + 0.649285i) q^{84} +(-1.93581 - 1.48540i) q^{85} +(5.56173 - 11.0190i) q^{86} +(5.50523 + 8.14483i) q^{87} +(4.66113 - 2.13935i) q^{88} +(-2.97192 + 2.97192i) q^{89} +(5.05646 - 2.50223i) q^{90} +(-0.179149 - 0.432503i) q^{91} +(-7.18654 + 5.30535i) q^{92} +(3.73433 - 1.86638i) q^{93} +(-2.42270 - 2.81486i) q^{94} +(5.47577 + 9.48431i) q^{95} +(-9.65340 - 1.67688i) q^{96} +(2.46473 - 4.26904i) q^{97} +(9.49008 - 1.79626i) q^{98} +(-1.35181 + 5.26910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.33488	+	0.466998i	0.943905	+	0.330218i
$2$	1.33488	+	0.466998i	0.943905	+	0.330218i
$3$	−0.104067	+	1.72892i	−0.0600830	+	0.998193i
$3$	−0.104067	+	1.72892i	−0.0600830	+	0.998193i
$4$	1.56383	+	1.24678i	0.781913	+	0.623388i
$5$	−0.809510	+	1.05497i	−0.362024	+	0.471799i	−0.938482	−	0.345328i	$-0.887768\pi$
$5$	−0.809510	+	1.05497i	−0.362024	+	0.471799i	0.576458	+	0.817127i	$0.304434\pi$
$6$	−0.946320	+	2.25931i	−0.386334	+	0.922359i
$7$	−0.106824	−	0.398671i	−0.0403755	−	0.150683i	0.942795	−	0.333372i	$-0.108187\pi$
$7$	−0.106824	−	0.398671i	−0.0403755	−	0.150683i	−0.983171	+	0.182689i	$0.941520\pi$
$8$	1.50528	+	2.39460i	0.532198	+	0.846620i
$9$	−2.97834	−	0.359847i	−0.992780	−	0.119949i
$10$	−1.57327	+	1.03023i	−0.497512	+	0.325786i
$11$	0.236676	−	1.79774i	0.0713606	−	0.542038i	−0.918003	−	0.396574i	$-0.870199\pi$
$11$	0.236676	−	1.79774i	0.0713606	−	0.542038i	0.989364	−	0.145464i	$-0.0464676\pi$
$12$	−2.31832	+	2.57398i	−0.669241	+	0.743045i
$13$	1.12453	−	0.148047i	0.311889	−	0.0410610i	0.0270430	−	0.999634i	$-0.491391\pi$
$13$	1.12453	−	0.148047i	0.311889	−	0.0410610i	0.284846	+	0.958573i	$0.408058\pi$
$14$	0.0435816	−	0.582065i	0.0116477	−	0.155564i
$15$	−1.73972	−	1.50937i	−0.449195	−	0.389717i
$16$	0.891101	+	3.89948i	0.222775	+	0.974870i
$17$			1.83494i			0.445037i	0.974928	+	0.222519i	$0.0714278\pi$
$17$			1.83494i			0.445037i	−0.974928	+	0.222519i	$0.928572\pi$
$18$	−3.80769	−	1.87123i	−0.897481	−	0.441054i
$19$	3.15166	−	7.60878i	0.723041	−	1.74557i	0.0585421	−	0.998285i	$-0.481355\pi$
$19$	3.15166	−	7.60878i	0.723041	−	1.74557i	0.664499	−	0.747290i	$-0.268645\pi$
$20$	−2.58125	+	0.640518i	−0.577185	+	0.143224i
$21$	0.700387	−	0.143201i	0.152837	−	0.0312490i
$22$	1.15547	−	2.28924i	0.246348	−	0.488068i
$23$	−1.15598	+	4.31416i	−0.241038	+	0.899565i	0.734296	+	0.678829i	$0.237512\pi$
$23$	−1.15598	+	4.31416i	−0.241038	+	0.899565i	−0.975334	+	0.220736i	$0.929154\pi$
$24$	−4.29673	+	2.35332i	−0.877067	+	0.480369i
$25$	0.836431	+	3.12160i	0.167286	+	0.624321i
$26$	1.57026	+	0.327528i	0.307952	+	0.0642335i
$27$	0.932094	−	5.11187i	0.179382	−	0.983780i
$28$	0.330000	−	0.756637i	0.0623641	−	0.142991i
$29$	4.50296	−	3.45524i	0.836178	−	0.641622i	−0.0992803	−	0.995060i	$-0.531654\pi$
$29$	4.50296	−	3.45524i	0.836178	−	0.641622i	0.935458	+	0.353438i	$0.114987\pi$
$30$	−1.61746	−	2.82728i	−0.295306	−	0.516188i
$31$	−1.20515	−	2.08738i	−0.216451	−	0.374904i	0.737269	−	0.675599i	$-0.236115\pi$
$31$	−1.20515	−	2.08738i	−0.216451	−	0.374904i	−0.953720	+	0.300695i	$0.902782\pi$
$32$	−0.631535	+	5.62149i	−0.111641	+	0.993749i
$33$	3.08352	+	0.596280i	0.536771	+	0.103799i
$34$	−0.856911	+	2.44942i	−0.146959	+	0.420073i
$35$	0.507062	+	0.210032i	0.0857091	+	0.0355019i
$36$	−4.20896	−	4.27606i	−0.701493	−	0.712677i
$37$	2.01433	+	4.86303i	0.331154	+	0.799477i	0.998501	+	0.0547300i	$0.0174298\pi$
$37$	2.01433	+	4.86303i	0.331154	+	0.799477i	−0.667347	+	0.744747i	$0.732570\pi$
$38$	7.76039	−	8.68502i	1.25890	−	1.40890i
$39$	0.138936	+	1.95963i	0.0222475	+	0.313792i
$40$	−3.74479	−	0.350422i	−0.592103	−	0.0554066i
$41$	0.00469380	−	0.0175175i	0.000733048	−	0.00273577i	−0.965558	−	0.260187i	$-0.916216\pi$
$41$	0.00469380	−	0.0175175i	0.000733048	−	0.00273577i	0.966291	+	0.257451i	$0.0828826\pi$
$42$	1.00181	+	0.135923i	0.154583	+	0.0209734i
$43$	1.13921	−	8.65317i	0.173728	−	1.31960i	−0.653156	−	0.757223i	$-0.726555\pi$
$43$	1.13921	−	8.65317i	0.173728	−	1.31960i	0.826884	−	0.562372i	$-0.190111\pi$
$44$	2.61149	−	2.51626i	0.393698	−	0.379341i
$45$	2.79063	−	2.85077i	0.416002	−	0.424968i
$46$	−3.55780	+	5.21906i	−0.524569	+	0.769509i
$47$	−2.27428	−	1.31306i	−0.331738	−	0.191529i	0.324875	−	0.945757i	$-0.394678\pi$
$47$	−2.27428	−	1.31306i	−0.331738	−	0.191529i	−0.656612	+	0.754228i	$0.728011\pi$
$48$	−6.83463	+	1.13484i	−0.986494	+	0.163800i
$49$	5.91465	−	3.41483i	0.844950	−	0.487832i
$50$	−0.341245	+	4.55759i	−0.0482594	+	0.644540i
$51$	−3.17246	−	0.190956i	−0.444233	−	0.0267392i
$52$	1.94315	+	1.17052i	0.269467	+	0.162322i
$53$	−11.3924	+	4.71890i	−1.56487	+	0.648191i	−0.985927	−	0.167177i	$-0.946535\pi$
$53$	−11.3924	+	4.71890i	−1.56487	+	0.648191i	−0.578944	+	0.815368i	$0.696535\pi$
$54$	3.63147	−	6.38846i	0.494180	−	0.869359i
$55$	1.70497	+	1.70497i	0.229899	+	0.229899i
$56$	0.793859	−	0.855912i	0.106084	−	0.114376i
$57$	12.8270	+	6.24080i	1.69898	+	0.826614i
$58$	7.62451	−	2.50947i	1.00115	−	0.329509i
$59$	3.58165	−	4.66770i	0.466291	−	0.607683i	−0.499719	−	0.866188i	$-0.666563\pi$
$59$	3.58165	−	4.66770i	0.466291	−	0.607683i	0.966010	+	0.258505i	$0.0832299\pi$
$60$	−0.838783	−	4.52943i	−0.108286	−	0.584747i
$61$	4.05953	−	3.11499i	0.519770	−	0.398833i	−0.315288	−	0.948996i	$-0.602101\pi$
$61$	4.05953	−	3.11499i	0.519770	−	0.398833i	0.835057	+	0.550163i	$0.185434\pi$
$62$	−0.633930	−	3.34921i	−0.0805093	−	0.425350i
$63$	0.174696	+	1.22582i	0.0220097	+	0.154438i
$64$	−3.46825	+	7.20911i	−0.433531	+	0.901138i
$65$	−0.754133	+	1.30620i	−0.0935387	+	0.162014i
$66$	3.83767	+	2.23596i	0.472385	+	0.275228i
$67$	−0.523374	−	3.97542i	−0.0639403	−	0.485674i	−0.993216	−	0.116287i	$-0.962901\pi$
$67$	−0.523374	−	3.97542i	−0.0639403	−	0.485674i	0.929275	−	0.369388i	$-0.120433\pi$
$68$	−2.28775	+	2.86952i	−0.277431	+	0.347980i
$69$	−7.33855	−	2.44755i	−0.883458	−	0.294651i
$70$	0.578784	+	0.517165i	0.0691779	+	0.0618131i
$71$	−4.17197	+	4.17197i	−0.495122	+	0.495122i	−0.909915	−	0.414794i	$-0.863854\pi$
$71$	−4.17197	+	4.17197i	−0.495122	+	0.495122i	0.414794	+	0.909915i	$0.363854\pi$
$72$	−3.62155	−	7.67361i	−0.426804	−	0.904344i
$73$	−7.49687	−	7.49687i	−0.877442	−	0.877442i	0.115828	−	0.993269i	$-0.463048\pi$
$73$	−7.49687	−	7.49687i	−0.877442	−	0.877442i	−0.993269	+	0.115828i	$0.963048\pi$
$74$	0.417873	+	7.43226i	0.0485767	+	0.863983i
$75$	−5.48406	+	1.12127i	−0.633244	+	0.129473i
$76$	14.4151	−	7.96939i	1.65352	−	0.914152i
$77$	−0.741988	+	0.0976845i	−0.0845573	+	0.0111322i
$78$	−0.729682	+	2.68076i	−0.0826202	+	0.303537i
$79$	−11.0415	−	6.37483i	−1.24227	−	0.717225i	−0.272714	−	0.962095i	$-0.587921\pi$
$79$	−11.0415	−	6.37483i	−1.24227	−	0.717225i	−0.969556	+	0.244871i	$0.921254\pi$
$80$	−4.83520	−	2.21658i	−0.540592	−	0.247821i
$81$	8.74102	+	2.14349i	0.971224	+	0.238166i
$82$	0.0144463	−	0.0211918i	0.00159533	−	0.00234024i
$83$	2.34186	+	3.05198i	0.257053	+	0.334998i	0.903996	−	0.427540i	$-0.140620\pi$
$83$	2.34186	+	3.05198i	0.257053	+	0.334998i	−0.646944	+	0.762538i	$0.723953\pi$
$84$	1.27382	+	0.649285i	0.138986	+	0.0708428i
$85$	−1.93581	−	1.48540i	−0.209968	−	0.161114i
$86$	5.56173	−	11.0190i	0.599736	−	1.18820i
$87$	5.50523	+	8.14483i	0.590223	+	0.873218i
$88$	4.66113	−	2.13935i	0.496878	−	0.228056i
$89$	−2.97192	+	2.97192i	−0.315023	+	0.315023i	−0.846852	−	0.531829i	$-0.821505\pi$
$89$	−2.97192	+	2.97192i	−0.315023	+	0.315023i	0.531829	+	0.846852i	$0.321505\pi$
$90$	5.05646	−	2.50223i	0.532998	−	0.263758i
$91$	−0.179149	−	0.432503i	−0.0187799	−	0.0453386i
$92$	−7.18654	+	5.30535i	−0.749248	+	0.553121i
$93$	3.73433	−	1.86638i	0.387232	−	0.193535i
$94$	−2.42270	−	2.81486i	−0.249883	−	0.290330i
$95$	5.47577	+	9.48431i	0.561802	+	0.973069i
$96$	−9.65340	−	1.67688i	−0.985246	−	0.171146i
$97$	2.46473	−	4.26904i	0.250255	−	0.433455i	−0.713341	−	0.700817i	$-0.752819\pi$
$97$	2.46473	−	4.26904i	0.250255	−	0.433455i	0.963596	+	0.267362i	$0.0861521\pi$
$98$	9.49008	−	1.79626i	0.958643	−	0.181450i
$99$	−1.35181	+	5.26910i	−0.135862	+	0.529565i
$100$	−2.58391	+	5.92449i	−0.258391	+	0.592449i
$101$	8.22532	+	1.08288i	0.818450	+	0.107751i	0.528114	−	0.849174i	$-0.322899\pi$
$101$	8.22532	+	1.08288i	0.818450	+	0.107751i	0.290336	+	0.956925i	$0.406233\pi$
$102$	−4.14569	−	1.73644i	−0.410484	−	0.171933i
$103$	−13.5984	−	3.64369i	−1.33989	−	0.359023i	−0.483498	−	0.875345i	$-0.660634\pi$
$103$	−13.5984	−	3.64369i	−1.33989	−	0.359023i	−0.856395	+	0.516322i	$0.827301\pi$
$104$	2.04725	+	2.46995i	0.200750	+	0.242199i
$105$	−0.415897	+	0.854813i	−0.0405874	+	0.0834212i
$106$	−17.4113	+	0.978935i	−1.69113	+	0.0950826i
$107$	−13.2296	+	5.47989i	−1.27896	+	0.529761i	−0.915676	−	0.401918i	$-0.868344\pi$
$107$	−13.2296	+	5.47989i	−1.27896	+	0.529761i	−0.363281	+	0.931680i	$0.618344\pi$
$108$	7.83099	−	6.83196i	0.753537	−	0.657406i
$109$	−4.97212	+	12.0038i	−0.476243	+	1.14975i	0.485115	+	0.874450i	$0.338778\pi$
$109$	−4.97212	+	12.0038i	−0.476243	+	1.14975i	−0.961358	+	0.275302i	$0.911222\pi$
$110$	1.47972	+	3.07216i	0.141086	+	0.292919i
$111$	−8.61742	+	2.97654i	−0.817929	+	0.282521i
$112$	1.45942	−	0.771812i	0.137902	−	0.0729294i
$113$	−12.2792	+	7.08941i	−1.15513	+	0.666915i	−0.950132	−	0.311847i	$-0.899052\pi$
$113$	−12.2792	+	7.08941i	−1.15513	+	0.666915i	−0.204999	+	0.978762i	$0.565719\pi$
$114$	14.2081	+	14.3209i	1.33071	+	1.34128i
$115$	−3.61555	−	4.71188i	−0.337152	−	0.439385i
$116$	11.3497	+	0.210784i	1.05380	+	0.0195708i
$117$	−3.40251	+	0.0362762i	−0.314562	+	0.00335374i
$118$	6.96089	−	4.55821i	0.640802	−	0.419617i
$119$	0.731535	−	0.196014i	0.0670597	−	0.0179686i
$120$	0.995560	−	6.43797i	0.0908818	−	0.587704i
$121$	7.44934	+	1.99605i	0.677213	+	0.181459i
$122$	6.87369	−	2.26235i	0.622315	−	0.204824i
$123$	0.0297979	+	0.00993820i	0.00268679	+	0.000896097i
$124$	0.717851	−	4.76685i	0.0644649	−	0.428075i
$125$	−10.1130	−	4.18895i	−0.904537	−	0.374671i
$126$	−0.339255	+	1.71791i	−0.0302233	+	0.153043i
$127$	13.5480			1.20219			0.601097	−	0.799176i	$-0.294730\pi$
$127$	13.5480			1.20219			0.601097	+	0.799176i	$0.294730\pi$
$128$	−7.99635	+	8.00365i	−0.706784	+	0.707429i
$129$	14.8421	+	2.87011i	1.30677	+	0.252700i
$130$	−1.61667	+	1.39144i	−0.141791	+	0.122038i
$131$	−0.621886	−	4.72369i	−0.0543344	−	0.412711i	−0.996899	−	0.0786879i	$-0.974927\pi$
$131$	−0.621886	−	4.72369i	−0.0543344	−	0.412711i	0.942565	−	0.334023i	$-0.108406\pi$
$132$	4.07865	+	4.77693i	0.355001	+	0.415778i
$133$	−3.37007	−	0.443678i	−0.292222	−	0.0384718i
$134$	1.15787	−	5.55113i	0.100025	−	0.479545i
$135$	4.63835	+	5.12144i	0.399206	+	0.440784i
$136$	−4.39394	+	2.76210i	−0.376777	+	0.236848i
$137$	1.71932	−	0.460689i	0.146891	−	0.0393593i	−0.184624	−	0.982809i	$-0.559107\pi$
$137$	1.71932	−	0.460689i	0.146891	−	0.0393593i	0.331515	+	0.943450i	$0.392440\pi$
$138$	−8.65310	−	6.69429i	−0.736601	−	0.569856i
$139$	0.255663	+	0.196177i	0.0216851	+	0.0166395i	0.619547	−	0.784959i	$-0.287316\pi$
$139$	0.255663	+	0.196177i	0.0216851	+	0.0166395i	−0.597862	+	0.801599i	$0.703983\pi$
$140$	0.531094	+	0.960646i	0.0448856	+	0.0811894i
$141$	2.50685	−	3.79540i	0.211115	−	0.319631i
$142$	−7.51739	+	3.62079i	−0.630846	+	0.303850i
$143$		−	2.05665i		−	0.171986i
$144$	−1.25078	−	11.9346i	−0.104232	−	0.994553i
$145$			7.54755i			0.626790i
$146$	−6.50642	−	13.5085i	−0.538475	−	1.11797i
$147$	5.28845	+	10.5813i	0.436184	+	0.872734i
$148$	−2.91304	+	10.1163i	−0.239451	+	0.831559i
$149$	−5.73686	−	4.40205i	−0.469982	−	0.360630i	0.346453	−	0.938067i	$-0.387386\pi$
$149$	−5.73686	−	4.40205i	−0.469982	−	0.360630i	−0.816435	+	0.577438i	$0.804053\pi$
$150$	−7.84420	−	1.06428i	−0.640476	−	0.0868981i
$151$	−3.50994	+	0.940485i	−0.285635	+	0.0765356i	−0.398792	−	0.917042i	$-0.630570\pi$
$151$	−3.50994	+	0.940485i	−0.285635	+	0.0765356i	0.113157	+	0.993577i	$0.463904\pi$
$152$	22.9642	−	3.90639i	1.86264	−	0.316850i
$153$	0.660296	−	5.46506i	0.0533818	−	0.441824i
$154$	−1.03609	−	0.216109i	−0.0834901	−	0.0174146i
$155$	3.17771	+	0.418353i	0.255240	+	0.0336030i
$156$	−2.22595	+	3.23775i	−0.178219	+	0.259227i
$157$	1.11456	+	8.46591i	0.0889515	+	0.675653i	0.976589	+	0.215112i	$0.0690115\pi$
$157$	1.11456	+	8.46591i	0.0889515	+	0.675653i	−0.887638	+	0.460542i	$0.847655\pi$
$158$	−11.7621	−	13.6660i	−0.935744	−	1.08721i
$159$	−6.97303	−	20.1877i	−0.552997	−	1.60099i
$160$	−5.41929	−	5.21691i	−0.428433	−	0.412433i
$161$	1.84342			0.145282
$162$	10.6672	+	6.94335i	0.838097	+	0.545521i
$163$	16.8189	+	6.96661i	1.31736	+	0.545667i	0.927022	−	0.375007i	$-0.122360\pi$
$163$	16.8189	+	6.96661i	1.31736	+	0.545667i	0.390334	+	0.920673i	$0.372360\pi$
$164$	0.0291807	−	0.0215422i	0.00227863	−	0.00168216i
$165$	−3.12520	+	2.77033i	−0.243296	+	0.215670i
$166$	1.70085	+	5.16768i	0.132011	+	0.401089i
$167$	21.2533	+	5.69481i	1.64463	+	0.440678i	0.958103	−	0.286425i	$-0.0924670\pi$
$167$	21.2533	+	5.69481i	1.64463	+	0.440678i	0.686529	+	0.727103i	$0.259134\pi$
$168$	1.39719	+	1.46159i	0.107796	+	0.112764i
$169$	−11.3144	+	3.03168i	−0.870337	+	0.233206i
$170$	−1.89040	−	2.88685i	−0.144987	−	0.221411i
$171$	−12.1247	+	21.5274i	−0.927200	+	1.64624i
$172$	12.5701	−	12.1117i	0.958460	−	0.923509i
$173$	−13.2922	−	17.3227i	−1.01059	−	1.31702i	−0.947756	−	0.318996i	$-0.896654\pi$
$173$	−13.2922	−	17.3227i	−1.01059	−	1.31702i	−0.0628289	−	0.998024i	$-0.520012\pi$
$174$	3.54522	+	13.4433i	0.268762	+	1.01914i
$175$	1.15514	−	0.666922i	0.0873205	−	0.0504145i
$176$	7.22114	−	0.679049i	0.544314	−	0.0511852i
$177$	7.69735	+	6.67815i	0.578569	+	0.501960i
$178$	−5.35505	+	2.57928i	−0.401378	+	0.193326i
$179$	1.98495	−	4.79209i	0.148362	−	0.358177i	−0.832175	−	0.554513i	$-0.812904\pi$
$179$	1.98495	−	4.79209i	0.148362	−	0.358177i	0.980537	+	0.196336i	$0.0629044\pi$
$180$	7.91832	−	0.978826i	0.590197	−	0.0729574i
$181$	−16.7677	+	6.94540i	−1.24633	+	0.516247i	−0.905688	−	0.423945i	$-0.860645\pi$
$181$	−16.7677	+	6.94540i	−1.24633	+	0.516247i	−0.340643	+	0.940193i	$0.610645\pi$
$182$	−0.0371643	−	0.661003i	−0.00275480	−	0.0489968i
$183$	4.96311	+	7.34278i	0.366883	+	0.542794i
$184$	−12.0708	+	3.72593i	−0.889870	+	0.274679i
$185$	−6.76099	−	1.81160i	−0.497078	−	0.133192i
$186$	5.85649	−	0.747475i	0.429419	−	0.0548075i
$187$	3.29873	+	0.434286i	0.241227	+	0.0317581i
$188$	−1.91949	−	4.88890i	−0.139993	−	0.356560i
$189$	−2.13752	+	0.174469i	−0.155482	+	0.0126908i
$190$	2.88036	+	15.2176i	0.208963	+	1.10400i
$191$	−8.48268	+	14.6924i	−0.613785	+	1.06311i	0.376811	+	0.926290i	$0.377021\pi$
$191$	−8.48268	+	14.6924i	−0.613785	+	1.06311i	−0.990596	+	0.136817i	$0.956313\pi$
$192$	−12.1031	−	6.74656i	−0.873463	−	0.486891i
$193$	7.81252	+	13.5317i	0.562357	+	0.974031i	0.997290	+	0.0735685i	$0.0234388\pi$
$193$	7.81252	+	13.5317i	0.562357	+	0.974031i	−0.434933	+	0.900463i	$0.643228\pi$
$194$	5.28376	−	4.54764i	0.379352	−	0.326502i
$195$	−2.17983	−	1.43977i	−0.156101	−	0.103104i
$196$	13.5070	+	2.03405i	0.964786	+	0.145289i
$197$	2.20509	+	5.32355i	0.157106	+	0.379287i	0.982759	−	0.184891i	$-0.0591931\pi$
$197$	2.20509	+	5.32355i	0.157106	+	0.379287i	−0.825653	+	0.564178i	$0.809193\pi$
$198$	−4.26517	+	6.40234i	−0.303113	+	0.454995i
$199$	−15.6096	+	15.6096i	−1.10654	+	1.10654i	−0.112934	+	0.993602i	$0.536025\pi$
$199$	−15.6096	+	15.6096i	−1.10654	+	1.10654i	−0.993602	+	0.112934i	$0.963975\pi$
$200$	−6.21594	+	6.70182i	−0.439533	+	0.473890i
$201$	6.92765	−	0.491163i	0.488639	−	0.0346439i
$202$	10.4741	+	5.28673i	0.736958	+	0.371973i
$203$	−1.85852	−	1.42610i	−0.130443	−	0.100092i
$204$	−4.72309	−	4.25397i	−0.330683	−	0.297837i
$205$	0.0146808	+	0.0191324i	0.00102535	+	0.00133627i
$206$	−16.4507	−	11.2143i	−1.14618	−	0.781340i
$207$	4.99533	−	12.4331i	0.347199	−	0.864158i
$208$	1.57938	+	4.25316i	0.109510	+	0.294904i
$209$	−12.9327	−	7.46668i	−0.894571	−	0.516481i
$210$	−0.954370	+	0.946853i	−0.0658578	+	0.0653390i
$211$	13.6309	−	1.79454i	0.938387	−	0.123541i	0.354209	−	0.935166i	$-0.384750\pi$
$211$	13.6309	−	1.79454i	0.938387	−	0.123541i	0.584178	+	0.811625i	$0.301417\pi$
$212$	−23.6992	−	6.82427i	−1.62767	−	0.468693i
$213$	−6.77885	−	7.64717i	−0.464479	−	0.523976i
$214$	−20.2191	+	1.13680i	−1.38215	+	0.0777103i
$215$	8.20666	+	8.20666i	0.559690	+	0.559690i
$216$	13.6440	−	5.46281i	0.928354	−	0.371697i
$217$	−0.703439	+	0.703439i	−0.0477525	+	0.0477525i
$218$	−12.2429	+	13.7016i	−0.829196	+	0.927993i
$219$	13.7417	−	12.1813i	0.928576	−	0.823137i
$220$	0.540561	+	4.79200i	0.0364446	+	0.323077i
$221$	0.271657	+	2.06344i	0.0182736	+	0.138802i
$222$	−12.8933	−	0.0509828i	−0.865341	−	0.00342174i
$223$	−5.72721	+	9.91981i	−0.383522	+	0.664280i	−0.991563	−	0.129626i	$-0.958622\pi$
$223$	−5.72721	+	9.91981i	−0.383522	+	0.664280i	0.608041	+	0.793906i	$0.291956\pi$
$224$	2.30859	−	0.348733i	0.154249	−	0.0233007i
$225$	−1.36788	−	9.59819i	−0.0911918	−	0.639879i
$226$	−19.7020	+	3.72916i	−1.31056	+	0.248060i
$227$	18.5612	−	14.2425i	1.23195	−	0.945309i	0.232324	−	0.972638i	$-0.425367\pi$
$227$	18.5612	−	14.2425i	1.23195	−	0.945309i	0.999626	+	0.0273297i	$0.00870039\pi$
$228$	12.2783	+	25.7519i	0.813152	+	1.70546i
$229$	−1.11158	+	1.44864i	−0.0734552	+	0.0957287i	−0.828636	−	0.559788i	$-0.810883\pi$
$229$	−1.11158	+	1.44864i	−0.0734552	+	0.0957287i	0.755181	+	0.655517i	$0.227549\pi$
$230$	−2.62590	−	7.97827i	−0.173147	−	0.526072i
$231$	−0.0916726	−	1.29300i	−0.00603161	−	0.0850734i
$232$	15.0521	+	5.58168i	0.988222	+	0.366455i
$233$	1.23941	+	1.23941i	0.0811965	+	0.0811965i	0.746539	−	0.665342i	$-0.231714\pi$
$233$	1.23941	+	1.23941i	0.0811965	+	0.0811965i	−0.665342	+	0.746539i	$0.731714\pi$
$234$	−4.55890	−	1.54054i	−0.298024	−	0.100708i
$235$	3.22629	−	1.33637i	0.210460	−	0.0871754i
$236$	11.4207	−	2.83395i	0.743421	−	0.184474i
$237$	12.1706	−	18.4265i	0.790568	−	1.19693i
$238$	1.06805	+	0.0799694i	0.0692315	+	0.00518365i
$239$	20.6410	−	11.9171i	1.33516	−	0.770853i	0.349071	−	0.937096i	$-0.386497\pi$
$239$	20.6410	−	11.9171i	1.33516	−	0.770853i	0.986085	+	0.166244i	$0.0531638\pi$
$240$	4.33548	−	8.12902i	0.279854	−	0.524726i
$241$	−2.09278	−	1.20827i	−0.134808	−	0.0778313i	0.431079	−	0.902314i	$-0.358133\pi$
$241$	−2.09278	−	1.20827i	−0.134808	−	0.0778313i	−0.565887	+	0.824483i	$0.691466\pi$
$242$	9.01185	+	6.14332i	0.579304	+	0.394907i
$243$	−4.61558	+	14.8895i	−0.296090	+	0.955160i
$244$	10.2321	+	0.190028i	0.655042	+	0.0121653i
$245$	−1.18542	+	9.00414i	−0.0757335	+	0.575253i
$246$	0.0351356	+	0.0271819i	0.00224016	+	0.00173305i
$247$	2.41768	−	9.02291i	0.153833	−	0.574114i
$248$	3.18435	−	6.02795i	0.202207	−	0.382775i
$249$	−5.52034	+	3.73129i	−0.349837	+	0.236461i
$250$	−11.5435	−	10.3145i	−0.730074	−	0.652348i
$251$	−10.8739	−	26.2519i	−0.686353	−	1.65700i	−0.752003	−	0.659159i	$-0.770912\pi$
$251$	−10.8739	−	26.2519i	−0.686353	−	1.65700i	0.0656504	−	0.997843i	$-0.479088\pi$
$252$	−1.25512	+	2.13477i	−0.0790654	+	0.134478i
$253$	7.48213	+	3.09920i	0.470398	+	0.194845i
$254$	18.0851	+	6.32691i	1.13476	+	0.396986i
$255$	2.76959	−	3.19228i	0.173439	−	0.199908i
$256$	−14.4119	+	6.94966i	−0.900742	+	0.434354i
$257$	4.08599	+	7.07715i	0.254877	+	0.441461i	0.964862	−	0.262756i	$-0.0846316\pi$
$257$	4.08599	+	7.07715i	0.254877	+	0.441461i	−0.709985	+	0.704217i	$0.751298\pi$
$258$	18.4721	+	10.7625i	1.15002	+	0.670044i
$259$	1.72357	−	1.32254i	0.107097	−	0.0821787i
$260$	−2.80787	+	1.10243i	−0.174137	+	0.0683698i
$261$	−14.6547	+	8.67050i	−0.907103	+	0.536691i
$262$	1.37581	−	6.59600i	0.0849979	−	0.407502i
$263$	−2.39635	−	8.94331i	−0.147765	−	0.551468i	−0.999617	−	0.0276843i	$-0.991187\pi$
$263$	−2.39635	−	8.94331i	−0.147765	−	0.551468i	0.851851	−	0.523784i	$-0.175480\pi$
$264$	3.21371	+	8.28137i	0.197790	+	0.509683i
$265$	4.24397	−	15.8387i	0.260705	−	0.972965i
$266$	−4.29145	−	2.16608i	−0.263126	−	0.132811i
$267$	−4.82894	−	5.44749i	−0.295526	−	0.333381i
$268$	4.13799	−	6.86939i	0.252768	−	0.419615i
$269$	9.15897	−	22.1117i	0.558432	−	1.34817i	−0.352575	−	0.935784i	$-0.614694\pi$
$269$	9.15897	−	22.1117i	0.558432	−	1.34817i	0.911007	−	0.412391i	$-0.135306\pi$
$270$	3.79995	+	9.00263i	0.231258	+	0.547883i
$271$		−	24.3306i		−	1.47798i	−0.673717	−	0.738990i	$-0.735303\pi$
$271$		−	24.3306i		−	1.47798i	0.673717	−	0.738990i	$-0.264697\pi$
$272$	−7.15529	+	1.63511i	−0.433853	+	0.0991432i
$273$	0.766407	−	0.264725i	0.0463851	−	0.0160219i
$274$	2.51023	+	0.187951i	0.151648	+	0.0113545i
$275$	5.80979	−	0.764873i	0.350343	−	0.0461236i
$276$	−8.42466	−	12.9771i	−0.507105	−	0.781128i
$277$	1.08779	−	8.26258i	0.0653589	−	0.496450i	−0.927189	−	0.374594i	$-0.877782\pi$
$277$	1.08779	−	8.26258i	0.0653589	−	0.496450i	0.992548	−	0.121856i	$-0.0388846\pi$
$278$	0.249666	+	0.381268i	0.0149740	+	0.0228669i
$279$	2.83821	+	6.65059i	0.169919	+	0.398161i
$280$	0.260328	+	1.53037i	0.0155576	+	0.0914571i
$281$	−8.00039	−	29.8579i	−0.477263	−	1.78117i	−0.612625	−	0.790374i	$-0.709886\pi$
$281$	−8.00039	−	29.8579i	−0.477263	−	1.78117i	0.135362	−	0.990796i	$-0.456780\pi$
$282$	5.11879	−	3.89573i	0.304820	−	0.231987i
$283$	−16.0225	+	20.8810i	−0.952440	+	1.24124i	0.0179837	+	0.999838i	$0.494275\pi$
$283$	−16.0225	+	20.8810i	−0.952440	+	1.24124i	−0.970424	+	0.241406i	$0.922391\pi$
$284$	−11.7257	+	1.32272i	−0.695795	+	0.0784891i
$285$	−16.9675	+	8.48017i	−1.00507	+	0.502322i
$286$	0.960452	−	2.74539i	0.0567927	−	0.162338i
$287$	−0.00748512			−0.000441833
$288$	3.90380	−	16.5155i	0.230034	−	0.973183i
$289$	13.6330			0.801942
$290$	−3.52469	+	10.0751i	−0.206977	+	0.591630i
$291$	7.12433	+	4.70559i	0.417636	+	0.275847i
$292$	−2.37688	−	21.0707i	−0.139096	−	1.23307i
$293$	13.6142	−	17.7424i	0.795351	−	1.03652i	−0.203003	−	0.979178i	$-0.565070\pi$
$293$	13.6142	−	17.7424i	0.795351	−	1.03652i	0.998354	−	0.0573438i	$-0.0182631\pi$
$294$	2.11799	+	16.5945i	0.123524	+	0.967813i
$295$	2.02492	+	7.55710i	0.117895	+	0.439991i
$296$	−8.61288	+	12.1438i	−0.500614	+	0.705842i
$297$	−8.96919	−	2.88552i	−0.520445	−	0.167435i
$298$	−5.60229	−	8.55532i	−0.324532	−	0.495596i
$299$	−0.661231	+	5.02255i	−0.0382400	+	0.290462i
$300$	−9.97408	−	5.08392i	−0.575854	−	0.293520i
$301$	−3.57146	+	0.470192i	−0.205856	+	0.0271014i
$302$	−5.12456	−	0.383697i	−0.294885	−	0.0220793i
$303$	−2.72821	+	14.1082i	−0.156731	+	0.810497i
$304$	32.4787	+	5.50965i	1.86278	+	0.316000i
$305$			6.80431i			0.389614i
$306$	3.43359	−	6.98686i	0.196285	−	0.399412i
$307$	7.93499	−	19.1568i	0.452874	−	1.09333i	−0.518351	−	0.855168i	$-0.673454\pi$
$307$	7.93499	−	19.1568i	0.452874	−	1.09333i	0.971224	−	0.238166i	$-0.0765462\pi$
$308$	−1.28213	−	0.772331i	−0.0730561	−	0.0440076i
$309$	7.71480	−	23.1314i	0.438879	−	1.31590i
$310$	4.04650	+	2.04244i	0.229826	+	0.116003i
$311$	−2.28659	+	8.53367i	−0.129661	+	0.483900i	−0.999963	−	0.00861804i	$-0.997257\pi$
$311$	−2.28659	+	8.53367i	−0.129661	+	0.483900i	0.870302	+	0.492518i	$0.163923\pi$
$312$	−4.48341	+	3.28250i	−0.253823	+	0.185835i
$313$	−0.461911	−	1.72387i	−0.0261087	−	0.0974391i	0.951642	−	0.307209i	$-0.0993951\pi$
$313$	−0.461911	−	1.72387i	−0.0261087	−	0.0974391i	−0.977751	+	0.209770i	$0.932728\pi$
$314$	−2.46576	+	11.8215i	−0.139151	+	0.667126i
$315$	−1.43462	−	0.808012i	−0.0808319	−	0.0455263i
$316$	−9.31904	−	23.7354i	−0.524237	−	1.33522i
$317$	23.2554	−	17.8445i	1.30615	−	1.00225i	0.307438	−	0.951568i	$-0.400528\pi$
$317$	23.2554	−	17.8445i	1.30615	−	1.00225i	0.998715	−	0.0506787i	$-0.0161384\pi$
$318$	0.119436	−	30.2046i	0.00669761	−	1.69379i
$319$	−5.14587	−	8.91290i	−0.288113	−	0.499027i
$320$	−4.79784	−	9.49476i	−0.268207	−	0.530773i
$321$	−8.09754	−	23.4433i	−0.451961	−	1.30848i
$322$	2.46075	+	0.860872i	0.137132	+	0.0479745i
$323$	13.9616	+	5.78309i	0.776846	+	0.321780i
$324$	10.9970	+	14.2501i	0.610943	+	0.791675i
$325$	1.40274	+	3.38651i	0.0778100	+	0.187850i
$326$	19.1978	+	17.1540i	1.06327	+	0.950072i
$327$	−20.2361	−	9.84560i	−1.11906	−	0.544463i
$328$	0.0490129	−	0.0151290i	0.00270629	−	0.000835359i
$329$	−0.280530	+	1.04695i	−0.0154661	+	0.0577204i
$330$	−5.46551	+	2.23861i	−0.300867	+	0.123231i
$331$	−2.79715	+	21.2464i	−0.153745	+	1.16781i	0.724388	+	0.689393i	$0.242123\pi$
$331$	−2.79715	+	21.2464i	−0.153745	+	1.16781i	−0.878133	+	0.478417i	$0.841211\pi$
$332$	−0.142864	+	7.69254i	−0.00784066	+	0.422183i
$333$	−4.24942	−	15.2086i	−0.232867	−	0.833426i
$334$	25.7112	+	17.5272i	1.40686	+	0.959044i
$335$	4.61764	+	2.66599i	0.252289	+	0.145659i
$336$	1.18253	+	2.60354i	0.0645120	+	0.142035i
$337$	3.14467	−	1.81558i	0.171301	−	0.0989007i	−0.411898	−	0.911230i	$-0.635134\pi$
$337$	3.14467	−	1.81558i	0.171301	−	0.0989007i	0.583199	+	0.812329i	$0.301801\pi$
$338$	−16.5192	−	1.23686i	−0.898524	−	0.0672762i
$339$	−10.9792	−	21.9676i	−0.596307	−	1.19311i
$340$	−1.17531	−	4.73642i	−0.0637401	−	0.256869i
$341$	−4.03779	+	1.67251i	−0.218658	+	0.0905713i
$342$	−26.2383	+	23.0744i	−1.41881	+	1.24772i
$343$	−4.03615	−	4.03615i	−0.217931	−	0.217931i
$344$	22.4357	−	10.2975i	1.20965	−	0.555204i
$345$	8.52274	−	5.76066i	0.458849	−	0.310144i
$346$	−9.65383	−	29.3312i	−0.518993	−	1.57685i
$347$	−19.5990	+	25.5420i	−1.05213	+	1.37116i	−0.126834	+	0.991924i	$0.540482\pi$
$347$	−19.5990	+	25.5420i	−1.05213	+	1.37116i	−0.925298	+	0.379241i	$0.876185\pi$
$348$	−1.54556	+	19.6009i	−0.0828508	+	1.05072i
$349$	−10.5928	+	8.12816i	−0.567021	+	0.435090i	−0.852074	−	0.523421i	$-0.824655\pi$
$349$	−10.5928	+	8.12816i	−0.567021	+	0.435090i	0.285053	+	0.958512i	$0.407989\pi$
$350$	1.85343	−	0.350813i	0.0990701	−	0.0187518i
$351$	0.291370	−	5.88645i	0.0155522	−	0.314196i
$352$	9.95649	+	2.46581i	0.530683	+	0.131428i
$353$	−16.2127	+	28.0813i	−0.862916	+	1.49461i	0.00618506	+	0.999981i	$0.498031\pi$
$353$	−16.2127	+	28.0813i	−0.862916	+	1.49461i	−0.869101	+	0.494634i	$0.835302\pi$
$354$	7.15639	+	12.5092i	0.380358	+	0.664856i
$355$	−1.02407	−	7.77857i	−0.0543519	−	0.412844i
$356$	−8.35288	+	0.942246i	−0.442702	+	0.0499390i
$357$	0.262765	+	1.28517i	0.0139070	+	0.0680182i
$358$	4.88757	−	5.46991i	0.258316	−	0.289094i
$359$	1.28177	−	1.28177i	0.0676490	−	0.0676490i	−0.672473	−	0.740122i	$-0.734768\pi$
$359$	1.28177	−	1.28177i	0.0676490	−	0.0676490i	0.740122	+	0.672473i	$0.234768\pi$
$360$	11.0271	+	2.39123i	0.581182	+	0.126029i
$361$	−34.5256	−	34.5256i	−1.81714	−	1.81714i
$362$	−25.6264	+	1.44082i	−1.34689	+	0.0757279i
$363$	−4.22624	+	12.6716i	−0.221820	+	0.665087i
$364$	0.259077	−	0.899717i	0.0135793	−	0.0471580i
$365$	13.9778	−	1.84021i	0.731631	−	0.0963210i
$366$	3.19610	+	12.1195i	0.167063	+	0.633497i
$367$	27.3193	+	15.7728i	1.42606	+	0.823333i	0.996807	−	0.0798532i	$-0.0254452\pi$
$367$	27.3193	+	15.7728i	1.42606	+	0.823333i	0.429248	+	0.903186i	$0.358778\pi$
$368$	−17.8531	−	0.663354i	−0.930656	−	0.0345797i
$369$	−0.0202833	+	0.0504840i	−0.00105591	+	0.00262809i
$370$	−8.17912	−	5.57565i	−0.425212	−	0.289864i
$371$	3.09827	+	4.03774i	0.160854	+	0.209629i
$372$	8.16680	+	1.73718i	0.423429	+	0.0900685i
$373$	27.7169	+	21.2679i	1.43513	+	1.10121i	0.977224	+	0.212209i	$0.0680659\pi$
$373$	27.7169	+	21.2679i	1.43513	+	1.10121i	0.457903	+	0.889002i	$0.348601\pi$
$374$	4.20061	+	2.12022i	0.217208	+	0.109634i
$375$	8.29480	−	17.0487i	0.428342	−	0.880391i
$376$	−0.279184	−	7.42251i	−0.0143978	−	0.382787i
$377$	4.55218	−	4.55218i	0.234449	−	0.234449i
$378$	−2.93482	−	0.765323i	−0.150951	−	0.0393640i
$379$	3.30143	+	7.97035i	0.169583	+	0.409409i	0.985707	−	0.168467i	$-0.0538816\pi$
$379$	3.30143	+	7.97035i	0.169583	+	0.409409i	−0.816124	+	0.577876i	$0.803882\pi$
$380$	−3.26166	+	21.6589i	−0.167320	+	1.11108i
$381$	−1.40990	+	23.4235i	−0.0722315	+	1.20002i
$382$	−18.1847	+	15.6513i	−0.930411	+	0.800789i
$383$	8.46693	+	14.6652i	0.432640	+	0.749355i	0.997100	−	0.0761061i	$-0.0242488\pi$
$383$	8.46693	+	14.6652i	0.432640	+	0.749355i	−0.564460	+	0.825461i	$0.690915\pi$
$384$	−13.0055	−	14.6580i	−0.663686	−	0.748012i
$385$	0.497592	−	0.861854i	0.0253596	−	0.0439242i
$386$	4.10953	+	21.7116i	0.209170	+	1.10509i
$387$	−6.50677	+	25.3621i	−0.330758	+	1.28923i
$388$	9.17694	−	3.60306i	0.465889	−	0.182918i
$389$	19.7826	+	2.60443i	1.00302	+	0.132050i	0.614106	−	0.789224i	$-0.289517\pi$
$389$	19.7826	+	2.60443i	1.00302	+	0.132050i	0.388914	+	0.921274i	$0.372850\pi$
$390$	−2.23745	−	2.93990i	−0.113298	−	0.148868i
$391$	−7.91621	−	2.12114i	−0.400340	−	0.107271i
$392$	17.0804	+	9.02297i	0.862689	+	0.455729i
$393$	8.23161	−	0.583612i	0.415230	−	0.0294393i
$394$	0.457445	+	8.13609i	0.0230458	+	0.409890i
$395$	15.6635	−	6.48804i	0.788117	−	0.326449i
$396$	−8.68339	+	6.55455i	−0.436357	+	0.329379i
$397$	−10.2369	+	24.7141i	−0.513777	+	1.24037i	0.427893	+	0.903829i	$0.359256\pi$
$397$	−10.2369	+	24.7141i	−0.513777	+	1.24037i	−0.941670	+	0.336538i	$0.890744\pi$
$398$	−28.1267	+	13.5474i	−1.40986	+	0.679068i
$399$	1.11780	−	5.78042i	0.0559599	−	0.289383i
$400$	−11.4273	+	6.04331i	−0.571364	+	0.302166i
$401$	−2.39963	+	1.38543i	−0.119832	+	0.0691850i	−0.558718	−	0.829358i	$-0.688707\pi$
$401$	−2.39963	+	1.38543i	−0.119832	+	0.0691850i	0.438886	+	0.898543i	$0.355373\pi$
$402$	9.47697	+	2.57955i	0.472669	+	0.128657i
$403$	−1.66426	−	2.16890i	−0.0829026	−	0.108041i
$404$	11.5129	+	11.9486i	0.572786	+	0.594464i
$405$	−9.33727	+	7.48637i	−0.463973	+	0.372001i
$406$	−1.81493	−	2.77160i	−0.0900734	−	0.137552i
$407$	9.21919	−	2.47027i	0.456978	−	0.122447i
$408$	−4.31818	−	7.88422i	−0.213782	−	0.390327i
$409$	−14.0856	−	3.77422i	−0.696488	−	0.186623i	−0.106831	−	0.994277i	$-0.534070\pi$
$409$	−14.0856	−	3.77422i	−0.696488	−	0.186623i	−0.589657	+	0.807654i	$0.700737\pi$
$410$	0.0106624	+	0.0323955i	0.000526577	+	0.00159990i
$411$	0.617572	+	3.02051i	0.0304626	+	0.148991i
$412$	−16.7227	−	22.6523i	−0.823869	−	1.11600i
$413$	−2.24348	−	0.929280i	−0.110394	−	0.0457269i
$414$	12.4744	−	14.2639i	0.613083	−	0.701032i
$415$	−5.11552			−0.251111
$416$	0.122066	+	6.41504i	0.00598480	+	0.314523i
$417$	−0.365781	+	0.421606i	−0.0179124	+	0.0206461i
$418$	−13.7767	−	16.0067i	−0.673839	−	0.782912i
$419$	−0.472127	−	3.58616i	−0.0230649	−	0.175195i	0.976035	−	0.217613i	$-0.0698272\pi$
$419$	−0.472127	−	3.58616i	−0.0230649	−	0.175195i	−0.999100	+	0.0424180i	$0.986494\pi$
$420$	−1.71615	+	0.818248i	−0.0837396	+	0.0399264i
$421$	30.0600	+	3.95748i	1.46504	+	0.192876i	0.820477	−	0.571679i	$-0.193708\pi$
$421$	30.0600	+	3.95748i	1.46504	+	0.192876i	0.644559	+	0.764555i	$0.277041\pi$
$422$	19.0337	+	3.97009i	0.926544	+	0.193261i
$423$	6.30107	+	4.72912i	0.306369	+	0.229938i
$424$	−28.4487	−	20.1771i	−1.38159	−	0.979885i
$425$	−5.72794	+	1.53480i	−0.277846	+	0.0744486i
$426$	−5.47775	−	13.3738i	−0.265398	−	0.647962i
$427$	−1.67551	−	1.28566i	−0.0810835	−	0.0622176i
$428$	−27.5210	−	7.92479i	−1.33028	−	0.383059i
$429$	3.55579	+	0.214029i	0.171675	+	0.0103334i
$430$	7.12244	+	14.7874i	0.343475	+	0.713113i
$431$			11.4530i			0.551669i	0.961205	+	0.275835i	$0.0889542\pi$
$431$			11.4530i			0.551669i	−0.961205	+	0.275835i	$0.911046\pi$
$432$	20.7642	−	0.920508i	0.999019	−	0.0442880i
$433$			2.47297i			0.118843i	0.998233	+	0.0594216i	$0.0189256\pi$
$433$			2.47297i			0.118843i	−0.998233	+	0.0594216i	$0.981074\pi$
$434$	−1.26751	+	0.610504i	−0.0608426	+	0.0293051i
$435$	−13.0491	−	0.785450i	−0.625658	−	0.0376595i
$436$	−22.7415	+	12.5727i	−1.08912	+	0.602122i
$437$	29.1823	+	22.3924i	1.39598	+	1.07117i
$438$	24.0322	−	9.84330i	1.14830	−	0.470331i
$439$	−7.61083	+	2.03931i	−0.363245	+	0.0973312i	−0.435825	−	0.900031i	$-0.643543\pi$
$439$	−7.61083	+	2.03931i	−0.363245	+	0.0973312i	0.0725801	+	0.997363i	$0.476877\pi$
$440$	−1.51627	+	6.64920i	−0.0722853	+	0.316988i
$441$	−18.8447	+	8.04214i	−0.897365	+	0.382959i
$442$	−0.600993	+	2.88132i	−0.0285863	+	0.137050i
$443$	−23.9934	−	3.15879i	−1.13996	−	0.150079i	−0.463181	−	0.886264i	$-0.653292\pi$
$443$	−23.9934	−	3.15879i	−1.13996	−	0.150079i	−0.676780	+	0.736185i	$0.736625\pi$
$444$	−17.1872	−	6.08920i	−0.815669	−	0.288981i
$445$	−0.729499	−	5.54110i	−0.0345816	−	0.262673i
$446$	−12.2777	+	10.5672i	−0.581365	+	0.500371i
$447$	8.20781	−	9.46047i	0.388216	−	0.447465i
$448$	3.24455	+	0.612588i	0.153291	+	0.0289421i
$449$	1.32247			0.0624113			0.0312056	−	0.999513i	$-0.490065\pi$
$449$	1.32247			0.0624113			0.0312056	+	0.999513i	$0.490065\pi$
$450$	2.65638	−	13.4513i	0.125223	−	0.634098i
$451$	−0.0303809	−	0.0125842i	−0.00143058	−	0.000592566i
$452$	−28.0414	−	4.22283i	−1.31896	−	0.198625i
$453$	−1.26076	−	6.16628i	−0.0592355	−	0.289717i
$454$	31.4283	−	10.3440i	1.47500	−	0.485470i
$455$	0.601302	+	0.161118i	0.0281895	+	0.00755335i
$456$	4.36403	+	40.1098i	0.204364	+	1.87831i
$457$	16.3307	−	4.37579i	0.763916	−	0.204691i	0.144234	−	0.989544i	$-0.453928\pi$
$457$	16.3307	−	4.37579i	0.763916	−	0.204691i	0.619682	+	0.784853i	$0.287262\pi$
$458$	−2.16034	+	1.41466i	−0.100946	+	0.0661026i
$459$	9.37995	+	1.71033i	0.437818	+	0.0798314i
$460$	0.220564	−	11.8763i	0.0102839	−	0.553738i
$461$	−2.27025	−	2.95864i	−0.105736	−	0.137798i	0.737488	−	0.675360i	$-0.236012\pi$
$461$	−2.27025	−	2.95864i	−0.105736	−	0.137798i	−0.843224	+	0.537563i	$0.819345\pi$
$462$	0.481458	−	1.76882i	0.0223995	−	0.0822930i
$463$	−0.00983874	+	0.00568040i	−0.000457245	+	0.000263990i	−0.500229	−	0.865893i	$-0.666751\pi$
$463$	−0.00983874	+	0.00568040i	−0.000457245	+	0.000263990i	0.499771	+	0.866157i	$0.333417\pi$
$464$	17.4862	+	14.4802i	0.811777	+	0.672227i
$465$	−1.05399	+	5.45047i	−0.0488778	+	0.252760i
$466$	1.07567	+	2.23327i	0.0498293	+	0.103454i
$467$	−7.68930	+	18.5636i	−0.355819	+	0.859022i	0.640060	+	0.768325i	$0.278909\pi$
$467$	−7.68930	+	18.5636i	−0.355819	+	0.859022i	−0.995879	+	0.0906970i	$0.971091\pi$
$468$	−5.36616	−	4.18544i	−0.248051	−	0.193472i
$469$	−1.52897	+	0.633322i	−0.0706015	+	0.0292441i
$470$	4.93080	−	0.277230i	0.227441	−	0.0127877i
$471$	−14.7529	+	1.04596i	−0.679777	+	0.0481954i
$472$	16.5687	+	1.55043i	0.762635	+	0.0713643i
$473$	−15.2865	−	4.09600i	−0.702874	−	0.188334i
$474$	24.8515	−	18.9136i	1.14147	−	0.868731i
$475$	26.3878	+	3.47401i	1.21075	+	0.159399i
$476$	1.38838	+	0.605528i	0.0636363	+	0.0277543i
$477$	35.6286	−	9.95496i	1.63132	−	0.455806i
$478$	33.1186	−	6.26861i	1.51481	−	0.286720i
$479$	−11.5695	+	20.0390i	−0.528624	+	0.915604i	0.470819	+	0.882230i	$0.343959\pi$
$479$	−11.5695	+	20.0390i	−0.528624	+	0.915604i	−0.999443	+	0.0333741i	$0.989375\pi$
$480$	9.58359	−	8.82663i	0.437429	−	0.402879i
$481$	2.98514	+	5.17041i	0.136111	+	0.235750i
$482$	−2.22936	−	2.59022i	−0.101544	−	0.117981i
$483$	−0.191839	+	3.18712i	−0.00872896	+	0.145019i
$484$	9.16085	+	12.4091i	0.416402	+	0.564051i
$485$	2.50850	+	6.05605i	0.113905	+	0.274991i
$486$	−13.1146	+	17.7202i	−0.594891	+	0.803806i
$487$	−19.7651	+	19.7651i	−0.895642	+	0.895642i	−0.995047	−	0.0994048i	$-0.968306\pi$
$487$	−19.7651	+	19.7651i	−0.895642	+	0.895642i	0.0994048	+	0.995047i	$0.468306\pi$
$488$	13.5699	+	5.03203i	0.614281	+	0.227789i
$489$	−13.7950	+	28.3535i	−0.623832	+	1.28219i
$490$	−5.78731	+	11.4659i	−0.261444	+	0.517976i
$491$	−23.1775	−	17.7847i	−1.04598	−	0.802612i	−0.0652327	−	0.997870i	$-0.520779\pi$
$491$	−23.1775	−	17.7847i	−1.04598	−	0.802612i	−0.980752	+	0.195258i	$0.937446\pi$
$492$	0.0342080	+	0.0526929i	0.00154222	+	0.00237558i
$493$	6.34014	+	8.26263i	0.285546	+	0.372130i
$494$	7.44100	−	10.9155i	0.334787	−	0.491111i
$495$	−4.46446	−	5.69152i	−0.200663	−	0.255815i
$496$	7.06578	−	6.55952i	0.317263	−	0.294531i
$497$	2.10891	+	1.21758i	0.0945974	+	0.0546159i
$498$	−9.11151	+	2.40285i	−0.408296	+	0.107674i
$499$	−7.92615	+	1.04350i	−0.354823	+	0.0467133i	−0.305831	−	0.952086i	$-0.598934\pi$
$499$	−7.92615	+	1.04350i	−0.354823	+	0.0467133i	−0.0489921	+	0.998799i	$0.515601\pi$
$500$	−10.5923	−	19.1595i	−0.473703	−	0.856838i
$501$	−12.0576	+	36.1527i	−0.538696	+	1.61518i
$502$	−2.25578	−	40.1212i	−0.100681	−	1.79070i
$503$	1.73937	+	1.73937i	0.0775547	+	0.0775547i	0.744820	−	0.667265i	$-0.232535\pi$
$503$	1.73937	+	1.73937i	0.0775547	+	0.0775547i	−0.667265	+	0.744820i	$0.732535\pi$
$504$	−2.67238	+	2.26353i	−0.119037	+	0.100826i
$505$	−7.80090	+	7.80090i	−0.347135	+	0.347135i
$506$	8.54045	+	7.63121i	0.379669	+	0.339249i
$507$	−4.06408	−	19.8772i	−0.180492	−	0.882777i
$508$	21.1868	+	16.8914i	0.940011	+	0.749433i
$509$	4.85591	+	36.8843i	0.215234	+	1.63487i	0.668656	+	0.743572i	$0.266870\pi$
$509$	4.85591	+	36.8843i	0.215234	+	1.63487i	−0.453422	+	0.891296i	$0.649797\pi$
$510$	5.18787	−	2.96793i	0.229723	−	0.131422i
$511$	−2.18794	+	3.78962i	−0.0967888	+	0.167643i
$512$	−22.4837	+	2.54666i	−0.993646	+	0.112547i
$513$	−35.9575	−	23.2030i	−1.58756	−	1.02444i
$514$	2.14931	+	11.3553i	0.0948020	+	0.500862i
$515$	14.8521	−	11.3964i	0.654460	−	0.502185i
$516$	19.6321	+	22.9931i	0.864253	+	1.01222i
$517$	−2.89880	+	3.77778i	−0.127489	+	0.166147i
$518$	2.91839	−	0.960534i	0.128227	−	0.0422035i
$519$	31.3329	−	21.1784i	1.37536	−	0.929629i
$520$	−4.26301	+	0.160345i	−0.186945	+	0.00703161i
$521$	22.8734	+	22.8734i	1.00210	+	1.00210i	0.999998	+	0.00210331i	$0.000669506\pi$
$521$	22.8734	+	22.8734i	1.00210	+	1.00210i	0.00210331	+	0.999998i	$0.499330\pi$
$522$	−23.6114	+	4.73039i	−1.03344	+	0.207044i
$523$	30.1005	−	12.4680i	1.31620	−	0.545190i	0.389516	−	0.921020i	$-0.372642\pi$
$523$	30.1005	−	12.4680i	1.31620	−	0.545190i	0.926689	+	0.375830i	$0.122642\pi$
$524$	4.91687	−	8.16239i	0.214794	−	0.356575i
$525$	1.03284	+	2.06655i	0.0450770	+	0.0901918i
$526$	0.977658	−	13.0574i	0.0426279	−	0.569328i
$527$	3.83020	−	2.21137i	0.166846	−	0.0963288i
$528$	0.422541	+	12.5554i	0.0183887	+	0.546406i
$529$	2.64287	+	1.52586i	0.114907	+	0.0663418i
$530$	13.0619	−	19.1609i	0.567371	−	0.832297i
$531$	−12.3470	+	12.6131i	−0.535816	+	0.547364i
$532$	−4.71704	−	4.89556i	−0.204509	−	0.212249i
$533$	0.00268490	−	0.0203939i	0.000116296	−	0.000883357i
$534$	−3.90210	−	9.52687i	−0.168860	−	0.412268i
$535$	4.92838	−	18.3929i	0.213072	−	0.795196i
$536$	8.73172	−	7.23740i	0.377153	−	0.312608i
$537$	8.07857	+	3.93051i	0.348616	+	0.169614i
$538$	22.5523	−	25.2393i	0.972298	−	1.08814i
$539$	−4.73910	−	11.4412i	−0.204127	−	0.492807i
$540$	0.868277	+	13.7920i	0.0373647	+	0.593514i
$541$	12.4925	+	5.17456i	0.537094	+	0.222472i	0.634707	−	0.772753i	$-0.281121\pi$
$541$	12.4925	+	5.17456i	0.537094	+	0.222472i	−0.0976129	+	0.995224i	$0.531121\pi$
$542$	11.3623	−	32.4785i	0.488055	−	1.39507i
$543$	−10.2631	−	29.7128i	−0.440431	−	1.27510i
$544$	−10.3151	−	1.15883i	−0.442255	−	0.0496842i
$545$	−8.63868	−	14.9626i	−0.370040	−	0.640928i
$546$	1.14669	+	0.00453426i	0.0490738	+	0.000194048i
$547$	−25.4990	+	19.5661i	−1.09026	+	0.836584i	−0.987421	−	0.158114i	$-0.949459\pi$
$547$	−25.4990	+	19.5661i	−1.09026	+	0.836584i	−0.102837	+	0.994698i	$0.532792\pi$
$548$	3.26309	+	1.42316i	0.139392	+	0.0607945i
$549$	−13.2116	+	7.81668i	−0.563857	+	0.333608i
$550$	8.11258	+	1.69214i	0.345922	+	0.0721532i
$551$	−12.0984	−	45.1518i	−0.515408	−	1.92353i
$552$	−5.18567	−	21.2572i	−0.220717	−	0.904765i
$553$	−1.36196	+	5.08292i	−0.0579166	+	0.216148i
$554$	5.31068	−	10.5216i	0.225629	−	0.447019i
$555$	3.83571	−	11.5007i	0.162817	−	0.488177i
$556$	0.155224	+	0.625542i	0.00658295	+	0.0265289i
$557$	−4.75658	+	11.4834i	−0.201543	+	0.486567i	−0.992044	−	0.125893i	$-0.959820\pi$
$557$	−4.75658	+	11.4834i	−0.201543	+	0.486567i	0.790501	+	0.612461i	$0.209820\pi$
$558$	0.682858	+	10.2032i	0.0289077	+	0.431936i
$559$		−	9.89942i		−	0.418701i
$560$	−0.367172	+	2.16444i	−0.0155159	+	0.0914642i
$561$	−1.09414	+	5.65805i	−0.0461944	+	0.238883i
$562$	3.26398	−	43.5929i	0.137683	−	1.83886i
$563$	−22.6525	+	2.98226i	−0.954690	+	0.125687i	−0.591747	−	0.806124i	$-0.701562\pi$
$563$	−22.6525	+	2.98226i	−0.954690	+	0.125687i	−0.362943	+	0.931811i	$0.618228\pi$
$564$	8.65229	−	2.80987i	0.364327	−	0.118317i
$565$	2.46101	−	18.6932i	0.103535	−	0.786429i
$566$	−31.1396	+	20.3912i	−1.30889	+	0.857104i
$567$	−0.0791984	−	3.71377i	−0.00332602	−	0.155963i
$568$	−16.2702	−	3.71022i	−0.682683	−	0.155677i
$569$	6.70960	+	25.0406i	0.281281	+	1.04976i	0.951514	+	0.307605i	$0.0995274\pi$
$569$	6.70960	+	25.0406i	0.281281	+	1.04976i	−0.670233	+	0.742151i	$0.733806\pi$
$570$	−26.6098	+	3.39626i	−1.11456	+	0.142254i
$571$	−5.26729	+	6.86446i	−0.220429	+	0.287269i	−0.890457	−	0.455067i	$-0.849615\pi$
$571$	−5.26729	+	6.86446i	−0.220429	+	0.287269i	0.670028	+	0.742336i	$0.266282\pi$
$572$	2.56418	−	3.21624i	0.107214	−	0.134478i
$573$	−24.5193	−	16.1949i	−1.02431	−	0.676551i
$574$	−0.00999176	−	0.00349554i	−0.000417048	−	0.000145901i
$575$	−14.4340			−0.601940
$576$	12.9238	−	20.2231i	0.538492	−	0.842631i
$577$	−6.42642			−0.267535			−0.133768	−	0.991013i	$-0.542708\pi$
$577$	−6.42642			−0.267535			−0.133768	+	0.991013i	$0.542708\pi$
$578$	18.1985	+	6.36659i	0.756957	+	0.264815i
$579$	−24.2082	+	12.0990i	−1.00606	+	0.502819i
$580$	−9.41010	+	11.8031i	−0.390733	+	0.490095i
$581$	0.966568	−	1.25966i	0.0401000	−	0.0522593i
$582$	7.31265	+	9.60846i	0.303119	+	0.398284i
$583$	5.78702	+	21.5974i	0.239674	+	0.894475i
$584$	6.66712	−	29.2369i	0.275887	−	1.20983i
$585$	2.71610	−	3.61893i	0.112297	−	0.149624i
$586$	26.4591	−	17.3262i	1.09301	−	0.715739i
$587$	1.76453	−	13.4029i	0.0728299	−	0.553198i	−0.915665	−	0.401943i	$-0.868335\pi$
$587$	1.76453	−	13.4029i	0.0728299	−	0.553198i	0.988495	−	0.151255i	$-0.0483315\pi$
$588$	−4.92235	+	23.1409i	−0.202994	+	0.954313i
$589$	−19.6806	+	2.59100i	−0.810926	+	0.106760i
$590$	−0.826121	+	11.0335i	−0.0340109	+	0.454241i
$591$	−9.43348	+	3.25842i	−0.388042	+	0.134033i
$592$	−17.1683	+	12.1883i	−0.705613	+	0.500936i
$593$		−	1.59774i		−	0.0656112i	−0.999462	−	0.0328056i	$-0.989556\pi$
$593$		−	1.59774i		−	0.0656112i	0.999462	−	0.0328056i	$-0.0104442\pi$
$594$	−10.6253	−	8.04042i	−0.435961	−	0.329903i
$595$	−0.385395	+	0.930426i	−0.0157997	+	0.0381438i
$596$	−3.48308	−	14.0366i	−0.142673	−	0.574962i
$597$	−25.3634	−	28.6123i	−1.03805	−	1.17102i
$598$	−3.22819	+	6.39572i	−0.132010	+	0.261541i
$599$	5.98072	−	22.3203i	0.244366	−	0.911985i	−0.729336	−	0.684156i	$-0.760171\pi$
$599$	5.98072	−	22.3203i	0.244366	−	0.911985i	0.973701	−	0.227829i	$-0.0731626\pi$
$600$	−10.9400	−	11.4443i	−0.446625	−	0.467212i
$601$	−2.19988	−	8.21005i	−0.0897349	−	0.334895i	0.906434	−	0.422348i	$-0.138794\pi$
$601$	−2.19988	−	8.21005i	−0.0897349	−	0.334895i	−0.996169	+	0.0874528i	$0.972127\pi$
$602$	−4.98706	−	1.04021i	−0.203257	−	0.0423960i
$603$	0.128243	+	12.0285i	0.00522245	+	0.489837i
$604$	−6.66150	−	2.90535i	−0.271053	−	0.118217i
$605$	−8.13610	+	6.24305i	−0.330779	+	0.253816i
$606$	−10.2304	+	17.5588i	−0.415580	+	0.713277i
$607$	−3.68932	−	6.39009i	−0.149745	−	0.259366i	0.781388	−	0.624045i	$-0.214512\pi$
$607$	−3.68932	−	6.39009i	−0.149745	−	0.259366i	−0.931133	+	0.364679i	$0.881179\pi$
$608$	40.7823	+	22.5222i	1.65394	+	0.913398i
$609$	2.65902	−	3.06483i	0.107749	−	0.124193i
$610$	−3.17760	+	9.08296i	−0.128657	+	0.367758i
$611$	−2.75189	−	1.13987i	−0.111330	−	0.0461142i
$612$	7.84629	−	7.72316i	0.317168	−	0.312190i
$613$	−16.2856	−	39.3168i	−0.657768	−	1.58799i	−0.801244	−	0.598338i	$-0.795828\pi$
$613$	−16.2856	−	39.3168i	−0.657768	−	1.58799i	0.143476	−	0.989654i	$-0.454172\pi$
$614$	19.5385	−	21.8664i	0.788508	−	0.882457i
$615$	−0.0346062	+	0.0233909i	−0.00139546	+	0.000943214i
$616$	−1.35082	−	1.62972i	−0.0544260	−	0.0656634i
$617$	5.49884	−	20.5219i	0.221375	−	0.826182i	−0.762450	−	0.647048i	$-0.776004\pi$
$617$	5.49884	−	20.5219i	0.221375	−	0.826182i	0.983825	−	0.179135i	$-0.0573298\pi$
$618$	21.1007	−	27.2750i	0.848794	−	1.09716i
$619$	−1.31239	+	9.96857i	−0.0527493	+	0.400671i	0.944619	+	0.328169i	$0.106432\pi$
$619$	−1.31239	+	9.96857i	−0.0527493	+	0.400671i	−0.997368	+	0.0725017i	$0.976902\pi$
$620$	4.44779	+	4.61612i	0.178628	+	0.185388i
$621$	20.9760	+	9.93040i	0.841736	+	0.398493i
$622$	−7.03754	+	10.3236i	−0.282180	+	0.413939i
$623$	1.50229	+	0.867347i	0.0601879	+	0.0347495i
$624$	−7.51774	+	2.28801i	−0.300951	+	0.0915936i
$625$	−1.38794	+	0.801325i	−0.0555174	+	0.0320530i
$626$	0.188449	−	2.51688i	0.00753195	−	0.100595i
$627$	14.2552	−	21.5825i	0.569296	−	0.861923i
$628$	−8.81212	+	14.6288i	−0.351642	+	0.583753i
$629$	−8.92334	+	3.69617i	−0.355797	+	0.147376i
$630$	−1.53772	−	1.74857i	−0.0612641	−	0.0696646i
$631$	−17.2814	−	17.2814i	−0.687961	−	0.687961i	0.273820	−	0.961781i	$-0.411713\pi$
$631$	−17.2814	−	17.2814i	−0.687961	−	0.687961i	−0.961781	+	0.273820i	$0.911713\pi$
$632$	−1.35543	−	36.0360i	−0.0539161	−	1.43344i
$633$	1.68409	+	23.7535i	0.0669367	+	0.944115i
$634$	39.3766	−	12.9601i	1.56384	−	0.514711i
$635$	−10.9673	+	14.2928i	−0.435223	+	0.567194i
$636$	14.2649	−	40.2638i	0.565641	−	1.59657i
$637$	6.14565	−	4.71573i	0.243500	−	0.186844i
$638$	−2.70682	−	14.3008i	−0.107164	−	0.566174i
$639$	13.9268	−	10.9243i	0.550936	−	0.432158i
$640$	−1.97052	−	14.9150i	−0.0778916	−	0.589566i
$641$	1.67402	−	2.89949i	0.0661198	−	0.114523i	−0.831070	−	0.556167i	$-0.812271\pi$
$641$	1.67402	−	2.89949i	0.0661198	−	0.114523i	0.897190	+	0.441644i	$0.145605\pi$
$642$	0.138696	−	35.0756i	0.00547391	−	1.38432i
$643$	0.170903	+	1.29814i	0.00673977	+	0.0511937i	0.994484	−	0.104886i	$-0.0334477\pi$
$643$	0.170903	+	1.29814i	0.00673977	+	0.0511937i	−0.987744	+	0.156080i	$0.950114\pi$
$644$	2.88278	+	2.29833i	0.113597	+	0.0905668i
$645$	−15.0427	+	13.3346i	−0.592307	+	0.525051i
$646$	15.9364	+	14.2398i	0.627011	+	0.560258i
$647$	10.4033	−	10.4033i	0.408998	−	0.408998i	−0.472391	−	0.881389i	$-0.656609\pi$
$647$	10.4033	−	10.4033i	0.408998	−	0.408998i	0.881389	+	0.472391i	$0.156609\pi$
$648$	8.02489	+	24.1578i	0.315247	+	0.949010i
$649$	−7.54360	−	7.54360i	−0.296112	−	0.296112i
$650$	0.290998	+	5.17567i	0.0114139	+	0.203007i
$651$	−1.14299	−	1.28939i	−0.0447971	−	0.0505354i
$652$	17.6160	+	31.8639i	0.689895	+	1.24789i
$653$	30.0462	−	3.95565i	1.17580	−	0.154797i	0.482796	−	0.875733i	$-0.339621\pi$
$653$	30.0462	−	3.95565i	1.17580	−	0.154797i	0.693002	+	0.720936i	$0.256288\pi$
$654$	−22.4150	−	22.5930i	−0.876496	−	0.883455i
$655$	5.48680	+	3.16780i	0.214387	+	0.123776i
$656$	0.0724917	+	0.00269352i	0.00283033	+	0.000105164i
$657$	19.6305	+	25.0259i	0.765858	+	0.976355i
$658$	−0.863401	+	1.26655i	−0.0336589	+	0.0493754i
$659$	8.14235	+	10.6113i	0.317181	+	0.413358i	0.924550	−	0.381062i	$-0.124441\pi$
$659$	8.14235	+	10.6113i	0.317181	+	0.413358i	−0.607368	+	0.794420i	$0.707775\pi$
$660$	−8.34125	+	0.435900i	−0.324683	+	0.0169674i
$661$	30.8767	+	23.6925i	1.20096	+	0.921532i	0.998333	−	0.0577225i	$-0.0183839\pi$
$661$	30.8767	+	23.6925i	1.20096	+	0.921532i	0.202632	+	0.979255i	$0.435051\pi$
$662$	−13.6559	+	27.0553i	−0.530752	+	1.05153i
$663$	−3.59580	+	0.254938i	−0.139649	+	0.00990098i
$664$	−3.78311	+	10.2019i	−0.146813	+	0.395911i
$665$	3.19618	−	3.19618i	0.123942	−	0.123942i
$666$	1.42991	−	22.2862i	0.0554079	−	0.863572i
$667$	9.70115	+	23.4207i	0.375630	+	0.906851i
$668$	26.1363	+	35.4038i	1.01125	+	1.36981i
$669$	−16.5546	−	10.9342i	−0.640037	−	0.422741i
$670$	4.91899	+	5.71522i	0.190037	+	0.220798i
$671$	−4.63913	−	8.03521i	−0.179092	−	0.310196i
$672$	0.362685	+	4.02766i	0.0139909	+	0.155370i
$673$	11.6979	−	20.2614i	0.450922	−	0.781020i	−0.547521	−	0.836792i	$-0.684429\pi$
$673$	11.6979	−	20.2614i	0.450922	−	0.781020i	0.998444	+	0.0557716i	$0.0177619\pi$
$674$	5.04564	−	0.955027i	0.194351	−	0.0367863i
$675$	16.7369	−	1.36610i	0.644202	−	0.0525812i
$676$	−21.4735	−	9.36548i	−0.825906	−	0.360211i
$677$	27.9690	+	3.68219i	1.07494	+	0.141518i	0.647151	−	0.762362i	$-0.275960\pi$
$677$	27.9690	+	3.68219i	1.07494	+	0.141518i	0.427786	+	0.903880i	$0.359294\pi$
$678$	−4.39709	−	34.4514i	−0.168869	−	1.32310i
$679$	−1.96523	−	0.526582i	−0.0754187	−	0.0202084i
$680$	0.643001	−	6.87144i	0.0246580	−	0.263508i
$681$	22.6926	+	33.5730i	0.869582	+	1.28652i
$682$	−6.17103	+	0.346961i	−0.236301	+	0.0132858i
$683$	−6.58710	+	2.72846i	−0.252048	+	0.104402i	−0.505131	−	0.863043i	$-0.668556\pi$
$683$	−6.58710	+	2.72846i	−0.252048	+	0.104402i	0.253082	+	0.967445i	$0.418556\pi$
$684$	−45.8008	+	18.5483i	−1.75124	+	0.709213i
$685$	−0.905788	+	2.18677i	−0.0346084	+	0.0835521i
$686$	−3.50291	−	7.27266i	−0.133742	−	0.277671i
$687$	−2.38890	−	2.07259i	−0.0911424	−	0.0790742i
$688$	34.7580	−	3.26851i	1.32514	−	0.124611i
$689$	−12.1125	+	6.99317i	−0.461450	+	0.266419i
$690$	14.0671	−	3.70971i	0.535524	−	0.141226i
$691$	0.0839718	+	0.109434i	0.00319444	+	0.00416307i	0.794948	−	0.606678i	$-0.207498\pi$
$691$	0.0839718	+	0.109434i	0.00319444	+	0.00416307i	−0.791753	+	0.610841i	$0.790832\pi$
$692$	0.810879	−	43.6620i	0.0308250	−	1.65978i
$693$	2.24504	−	0.0239358i	0.0852821	−	0.000909244i
$694$	−38.0905	+	24.9428i	−1.44590	+	0.946817i
$695$	−0.413924	+	0.110911i	−0.0157010	+	0.00420708i
$696$	−11.2167	+	25.4431i	−0.425169	+	0.964419i
$697$	0.0321435	+	0.00861282i	0.00121752	+	0.000326234i
$698$	−17.9360	+	5.90331i	−0.678888	+	0.223444i
$699$	−2.27183	+	2.01386i	−0.0859284	+	0.0761713i
$700$	2.63794	+	0.397254i	0.0997049	+	0.0150148i
$701$	−34.9437	−	14.4741i	−1.31980	−	0.546681i	−0.392074	−	0.919934i	$-0.628242\pi$
$701$	−34.9437	−	14.4741i	−1.31980	−	0.546681i	−0.927730	+	0.373253i	$0.878242\pi$
$702$	3.13791	−	7.72165i	0.118433	−	0.291435i
$703$	43.3502			1.63498
$704$	12.1392	+	7.94123i	0.457514	+	0.299296i
$705$	1.97473	+	5.71707i	0.0743728	+	0.215318i
$706$	−34.7560	+	29.9139i	−1.30806	+	1.12582i
$707$	−0.446944	−	3.39487i	−0.0168090	−	0.127677i
$708$	3.71117	+	20.0403i	0.139474	+	0.753162i
$709$	−30.3373	−	3.99399i	−1.13934	−	0.149997i	−0.462843	−	0.886440i	$-0.653171\pi$
$709$	−30.3373	−	3.99399i	−1.13934	−	0.149997i	−0.676500	+	0.736443i	$0.736504\pi$
$710$	2.26557	−	10.8617i	0.0850252	−	0.407633i
$711$	30.5915	+	22.9597i	1.14727	+	0.861055i
$712$	−11.5901	−	2.64299i	−0.434359	−	0.0990503i
$713$	10.3984	−	2.78625i	0.389424	−	0.104346i
$714$	−0.249410	+	1.83826i	−0.00933393	+	0.0687950i
$715$	2.16971	+	1.66488i	0.0811427	+	0.0622630i
$716$	9.07877	−	5.01920i	0.339289	−	0.187576i
$717$	18.4557	+	36.9269i	0.689240	+	1.37906i
$718$	2.30959	−	1.11242i	0.0861931	−	0.0415153i
$719$		−	7.65848i		−	0.285613i	−0.989751	−	0.142807i	$-0.954387\pi$
$719$		−	7.65848i		−	0.285613i	0.989751	−	0.142807i	$-0.0456127\pi$
$720$	13.6033	+	8.34166i	0.506963	+	0.310875i
$721$			5.81053i			0.216395i
$722$	−29.9642	−	62.2110i	−1.11515	−	2.31525i
$723$	2.30679	−	3.49251i	0.0857904	−	0.129888i
$724$	−34.8811	−	10.0441i	−1.29634	−	0.373287i
$725$	14.5523	+	11.1664i	0.540459	+	0.414709i
$726$	−11.5591	+	14.9415i	−0.429000	+	0.554530i
$727$	0.553366	−	0.148274i	0.0205232	−	0.00549918i	−0.248543	−	0.968621i	$-0.579952\pi$
$727$	0.553366	−	0.148274i	0.0205232	−	0.00549918i	0.269066	+	0.963122i	$0.413285\pi$
$728$	0.766004	−	1.08003i	0.0283900	−	0.0400285i
$729$	−25.2624	−	9.52948i	−0.935645	−	0.352944i
$730$	19.5181	+	4.07113i	0.722397	+	0.150679i
$731$	15.8780	+	2.09038i	0.587269	+	0.0773154i
$732$	−1.39336	+	17.6707i	−0.0515002	+	0.653128i
$733$	−2.09359	−	15.9024i	−0.0773284	−	0.587368i	−0.985613	−	0.169016i	$-0.945941\pi$
$733$	−2.09359	−	15.9024i	−0.0773284	−	0.587368i	0.908285	−	0.418352i	$-0.137392\pi$
$734$	29.1022	+	33.8129i	1.07418	+	1.24806i
$735$	−15.4441	−	2.98653i	−0.569664	−	0.110160i
$736$	−23.5220	−	9.22285i	−0.867032	−	0.339959i
$737$	−7.27062			−0.267817
$738$	−0.0506518	+	0.0579180i	−0.00186452	+	0.00213199i
$739$	−13.2659	−	5.49490i	−0.487993	−	0.202133i	0.125100	−	0.992144i	$-0.460075\pi$
$739$	−13.2659	−	5.49490i	−0.487993	−	0.202133i	−0.613093	+	0.790011i	$0.710075\pi$
$740$	−8.31435	−	11.2625i	−0.305642	−	0.414017i
$741$	15.3483	+	5.11897i	0.563834	+	0.188050i
$742$	2.25021	+	6.83680i	0.0826077	+	0.250987i
$743$	−19.3394	−	5.18198i	−0.709494	−	0.190108i	−0.114015	−	0.993479i	$-0.536371\pi$
$743$	−19.3394	−	5.18198i	−0.709494	−	0.190108i	−0.595479	+	0.803371i	$0.703038\pi$
$744$	10.0905	+	6.13281i	0.369934	+	0.224840i
$745$	9.28809	−	2.48874i	0.340289	−	0.0911802i
$746$	27.0667	+	41.3339i	0.990984	+	1.51334i
$747$	−5.87662	−	9.93253i	−0.215014	−	0.363412i
$748$	4.61718	+	4.79192i	0.168821	+	0.175210i
$749$	3.59791	+	4.68889i	0.131465	+	0.171328i
$750$	19.0343	−	18.8844i	0.695035	−	0.689560i
$751$	−34.9739	+	20.1922i	−1.27622	+	0.736824i	−0.976151	−	0.217095i	$-0.930342\pi$
$751$	−34.9739	+	20.1922i	−1.27622	+	0.736824i	−0.300066	+	0.953919i	$0.597009\pi$
$752$	3.09362	−	10.0386i	0.112813	−	0.366069i
$753$	46.5190	−	16.0681i	1.69525	−	0.585555i
$754$	8.20248	−	3.95076i	0.298717	−	0.143878i
$755$	1.84914	−	4.46422i	0.0672972	−	0.162470i
$756$	−3.56024	−	2.39217i	−0.129485	−	0.0870024i
$757$	28.8377	−	11.9450i	1.04812	−	0.434147i	0.208902	−	0.977937i	$-0.433011\pi$
$757$	28.8377	−	11.9450i	1.04812	−	0.434147i	0.839222	+	0.543790i	$0.183011\pi$
$758$	0.684880	+	12.1812i	0.0248760	+	0.442443i
$759$	−6.13692	+	12.6135i	−0.222756	+	0.457841i
$760$	−14.4686	+	27.3889i	−0.524831	+	0.993498i
$761$	25.5538	+	6.84711i	0.926324	+	0.248208i	0.690286	−	0.723536i	$-0.257485\pi$
$761$	25.5538	+	6.84711i	0.926324	+	0.248208i	0.236037	+	0.971744i	$0.424151\pi$
$762$	−12.8208	+	30.6092i	−0.464448	+	1.10885i
$763$	5.31669	+	0.699955i	0.192477	+	0.0253401i
$764$	−31.5836	+	12.4004i	−1.14265	+	0.448631i
$765$	5.23098	+	5.12062i	0.189127	+	0.185136i
$766$	4.45376	+	23.5303i	0.160921	+	0.850185i
$767$	3.33664	−	5.77923i	0.120479	−	0.208676i
$768$	−10.5156	−	25.6402i	−0.379449	−	0.925212i
$769$	3.38991	+	5.87149i	0.122243	+	0.211731i	0.920652	−	0.390384i	$-0.127658\pi$
$769$	3.38991	+	5.87149i	0.122243	+	0.211731i	−0.798409	+	0.602116i	$0.794325\pi$
$770$	1.06671	−	0.918100i	0.0384416	−	0.0330860i
$771$	−12.6611	+	6.32787i	−0.455977	+	0.227893i
$772$	−4.65355	+	30.9016i	−0.167485	+	1.11217i
$773$	−13.1686	−	31.7919i	−0.473642	−	1.14347i	−0.962542	−	0.271134i	$-0.912601\pi$
$773$	−13.1686	−	31.7919i	−0.473642	−	1.14347i	0.488899	−	0.872340i	$-0.337399\pi$
$774$	−20.5299	+	30.8168i	−0.737930	+	1.10769i
$775$	5.50795	−	5.50795i	0.197851	−	0.197851i
$776$	13.9328	−	0.524056i	0.500157	−	0.0188125i
$777$	2.10720	+	3.11755i	0.0755955	+	0.111841i
$778$	25.1913	+	12.7151i	0.903150	+	0.455857i
$779$	−0.118494	−	0.0909233i	−0.00424547	−	0.00325766i
$780$	−1.61381	−	4.96931i	−0.0577836	−	0.177930i
$781$	6.51270	+	8.48751i	0.233043	+	0.303707i
$782$	−9.57664	−	6.52833i	−0.342460	−	0.233453i
$783$	−13.4656	−	26.2391i	−0.481220	−	0.937710i
$784$	18.5866	+	20.0211i	0.663807	+	0.715040i
$785$	−9.83356	−	5.67741i	−0.350975	−	0.202635i
$786$	11.2608	+	3.06509i	0.401659	+	0.109328i
$787$	5.00824	−	0.659347i	0.178525	−	0.0235032i	−0.0407339	−	0.999170i	$-0.512970\pi$
$787$	5.00824	−	0.659347i	0.178525	−	0.0235032i	0.219258	+	0.975667i	$0.429636\pi$
$788$	−3.18890	+	11.0744i	−0.113600	+	0.394508i
$789$	15.7117	−	3.21240i	0.559350	−	0.114365i
$790$	23.9389	−	1.34594i	0.851706	−	0.0478865i
$791$	4.13805	+	4.13805i	0.147132	+	0.147132i
$792$	−14.6523	+	4.69443i	−0.520646	+	0.166809i
$793$	4.10390	−	4.10390i	0.145734	−	0.145734i
$794$	−25.2066	+	28.2099i	−0.894548	+	1.00113i
$795$	26.9422	+	8.98578i	0.955543	+	0.318693i
$796$	−43.8724	+	4.94903i	−1.55502	+	0.175414i
$797$	−3.60528	−	27.3849i	−0.127706	−	0.970021i	−0.928565	−	0.371169i	$-0.878957\pi$
$797$	−3.60528	−	27.3849i	−0.127706	−	0.970021i	0.800860	−	0.598852i	$-0.204376\pi$
$798$	4.19157	−	7.19417i	0.148380	−	0.254671i
$799$	2.40937	−	4.17315i	0.0852374	−	0.147636i
$800$	−18.0763	+	2.73059i	−0.639094	+	0.0965410i
$801$	9.92082	−	7.78195i	0.350535	−	0.274962i
$802$	−3.85022	+	0.728761i	−0.135956	+	0.0257334i
$803$	−15.2517	+	11.7031i	−0.538222	+	0.412992i
$804$	11.4460	+	7.86913i	0.403669	+	0.277523i
$805$	−1.49226	+	1.94476i	−0.0525954	+	0.0685437i
$806$	−1.20872	−	3.67244i	−0.0425752	−	0.129356i
$807$	37.2763	+	18.1362i	1.31219	+	0.638426i
$808$	9.78835	+	21.3264i	0.344353	+	0.750261i
$809$	21.9542	+	21.9542i	0.771870	+	0.771870i	0.978433	−	0.206563i	$-0.0662278\pi$
$809$	21.9542	+	21.9542i	0.771870	+	0.771870i	−0.206563	+	0.978433i	$0.566228\pi$
$810$	−15.9603	+	5.63294i	−0.560787	+	0.197921i
$811$	−15.9799	+	6.61907i	−0.561129	+	0.232427i	−0.645175	−	0.764035i	$-0.723216\pi$
$811$	−15.9799	+	6.61907i	−0.561129	+	0.232427i	0.0840465	+	0.996462i	$0.473216\pi$
$812$	−1.12839	−	4.54733i	−0.0395986	−	0.159580i
$813$	42.0657	+	2.53201i	1.47531	+	0.0888015i
$814$	13.4602	+	1.00782i	0.471778	+	0.0353240i
$815$	−20.9646	+	12.1039i	−0.734359	+	0.423983i
$816$	−2.08235	−	12.5411i	−0.0728969	−	0.439026i
$817$	−62.2497	−	35.9399i	−2.17784	−	1.25738i
$818$	−17.0401	−	11.6161i	−0.595792	−	0.406147i
$819$	0.377931	+	1.35261i	0.0132060	+	0.0472639i
$820$	−0.000895593		0.0482235i	−3.12755e−5		0.00168404i
$821$	−1.55156	+	11.7853i	−0.0541500	+	0.411310i	0.942806	+	0.333342i	$0.108176\pi$
$821$	−1.55156	+	11.7853i	−0.0541500	+	0.411310i	−0.996956	+	0.0779676i	$0.975157\pi$
$822$	−0.586184	+	4.32043i	−0.0204455	+	0.150692i
$823$	−5.52304	+	20.6123i	−0.192521	+	0.718498i	0.800374	+	0.599501i	$0.204634\pi$
$823$	−5.52304	+	20.6123i	−0.192521	+	0.718498i	−0.992895	+	0.118997i	$0.962032\pi$
$824$	−11.7443	−	38.0476i	−0.409132	−	1.32545i
$825$	0.717799	+	10.1243i	0.0249906	+	0.352482i
$826$	−2.56081	−	2.28818i	−0.0891020	−	0.0796160i
$827$	−4.36063	−	10.5275i	−0.151634	−	0.366076i	0.829749	−	0.558136i	$-0.188483\pi$
$827$	−4.36063	−	10.5275i	−0.151634	−	0.366076i	−0.981383	+	0.192060i	$0.938483\pi$
$828$	23.3131	−	13.2151i	0.810185	−	0.459256i
$829$	19.2024	+	7.95389i	0.666926	+	0.276250i	0.690350	−	0.723476i	$-0.257457\pi$
$829$	19.2024	+	7.95389i	0.666926	+	0.276250i	−0.0234236	+	0.999726i	$0.507457\pi$
$830$	−6.82862	−	2.38894i	−0.237025	−	0.0829212i
$831$	14.1721	+	2.74056i	0.491626	+	0.0950690i
$832$	−2.83287	+	8.62033i	−0.0982120	+	0.298856i
$833$	6.26598	+	10.8530i	0.217103	+	0.376034i
$834$	−0.685164	+	0.391976i	−0.0237253	+	0.0135730i
$835$	−23.2127	+	17.8117i	−0.803307	+	0.616399i
$836$	−10.9152	−	27.8007i	−0.377509	−	0.961508i
$837$	−11.7937	+	4.21493i	−0.407650	+	0.145689i
$838$	1.04450	−	5.00759i	0.0360815	−	0.172984i
$839$	−7.16513	−	26.7406i	−0.247368	−	0.923189i	−0.972179	−	0.234241i	$-0.924740\pi$
$839$	−7.16513	−	26.7406i	−0.247368	−	0.923189i	0.724811	−	0.688948i	$-0.241927\pi$
$840$	−2.67298	+	0.290826i	−0.0922266	+	0.0100345i
$841$	0.832176	−	3.10572i	0.0286957	−	0.107094i
$842$	38.2785	+	19.3208i	1.31916	+	0.665837i
$843$	52.4545	−	10.7248i	1.80663	−	0.369383i
$844$	23.5537	+	14.1883i	0.810751	+	0.488381i
$845$	5.96076	−	14.3906i	0.205056	−	0.495050i
$846$	6.20271	+	9.25541i	0.213254	+	0.318207i
$847$		−	3.18306i		−	0.109371i
$848$	−28.5531	−	40.2195i	−0.980516	−	1.38114i
$849$	−34.4341	−	29.8747i	−1.18178	−	1.02530i
$850$	−8.36288	−	0.626163i	−0.286844	−	0.0214772i
$851$	−23.3084	+	3.06861i	−0.799002	+	0.105191i
$852$	−1.06662	−	20.4105i	−0.0365419	−	0.699254i
$853$	7.36092	−	55.9117i	0.252033	−	1.91438i	−0.132342	−	0.991204i	$-0.542250\pi$
$853$	7.36092	−	55.9117i	0.252033	−	1.91438i	0.384375	−	0.923177i	$-0.374417\pi$
$854$	−1.63621	−	2.49867i	−0.0559898	−	0.0855027i
$855$	−12.8958	−	30.2179i	−0.441027	−	1.03343i
$856$	−33.0365	−	23.4309i	−1.12916	−	0.800853i
$857$	2.86351	+	10.6868i	0.0978155	+	0.365053i	0.997431	−	0.0716298i	$-0.0228200\pi$
$857$	2.86351	+	10.6868i	0.0978155	+	0.365053i	−0.899616	+	0.436682i	$0.856153\pi$
$858$	4.64661	+	1.94625i	0.158633	+	0.0664439i
$859$	−16.2491	+	21.1762i	−0.554411	+	0.722522i	−0.983534	−	0.180724i	$-0.942156\pi$
$859$	−16.2491	+	21.1762i	−0.554411	+	0.722522i	0.429123	+	0.903246i	$0.358823\pi$
$860$	2.60192	+	23.0657i	0.0887248	+	0.786533i
$861$	0.000778953	−	0.0129412i	2.65467e−5	−	0.000441035i
$862$	−5.34851	+	15.2884i	−0.182171	+	0.520723i
$863$	−47.4962			−1.61679			−0.808395	−	0.588641i	$-0.799663\pi$
$863$	−47.4962			−1.61679			−0.808395	+	0.588641i	$0.799663\pi$
$864$	28.1477	+	8.46808i	0.957603	+	0.288090i
$865$	29.0351			0.987224
$866$	−1.15487	+	3.30112i	−0.0392441	+	0.112177i
$867$	−1.41875	+	23.5704i	−0.0481831	+	0.800493i
$868$	−1.97709	+	0.223025i	−0.0671067	+	0.00756996i
$869$	−14.0735	+	18.3410i	−0.477412	+	0.622176i
$870$	−17.0523	−	7.14240i	−0.578126	−	0.242150i
$871$	−1.17710	−	4.39300i	−0.0398845	−	0.148851i
$872$	−36.2287	+	6.16279i	−1.22686	+	0.208698i
$873$	−8.87700	+	11.8277i	−0.300441	+	0.400308i
$874$	28.4977	+	43.5192i	0.963951	+	1.47206i
$875$	−0.589704	+	4.47925i	−0.0199356	+	0.151426i
$876$	36.6769	−	1.91668i	1.23920	−	0.0647585i
$877$	−43.4516	+	5.72051i	−1.46725	+	0.193168i	−0.821426	−	0.570315i	$-0.806821\pi$
$877$	−43.4516	+	5.72051i	−1.46725	+	0.193168i	−0.645829	+	0.763482i	$0.723488\pi$
$878$	−11.1119	−	0.831995i	−0.375009	−	0.0280785i
$879$	29.2584	+	25.3843i	0.986862	+	0.856192i
$880$	−5.12921	+	8.16781i	−0.172905	+	0.275337i
$881$		−	37.4678i		−	1.26232i	−0.775651	−	0.631162i	$-0.782578\pi$
$881$		−	37.4678i		−	1.26232i	0.775651	−	0.631162i	$-0.217422\pi$
$882$	−28.9111	+	1.93490i	−0.973487	+	0.0651515i
$883$	0.0453961	−	0.109596i	0.00152770	−	0.00368820i	−0.923114	−	0.384527i	$-0.874365\pi$
$883$	0.0453961	−	0.109596i	0.00152770	−	0.00368820i	0.924642	+	0.380839i	$0.124365\pi$
$884$	−2.14783	+	3.56556i	−0.0722392	+	0.119923i
$885$	−13.2764	+	2.71448i	−0.446280	+	0.0912463i
$886$	−30.5533	−	15.4215i	−1.02646	−	0.518095i
$887$	6.70250	−	25.0141i	0.225048	−	0.839891i	−0.757337	−	0.653024i	$-0.773500\pi$
$887$	6.70250	−	25.0141i	0.225048	−	0.839891i	0.982385	−	0.186867i	$-0.0598332\pi$
$888$	−20.0993	−	16.1548i	−0.674488	−	0.542118i
$889$	−1.44725	−	5.40121i	−0.0485392	−	0.181151i
$890$	1.61389	−	7.73739i	0.0540976	−	0.259358i
$891$	5.92223	−	15.2067i	0.198402	−	0.509445i
$892$	−21.3241	+	8.37232i	−0.713985	+	0.280326i
$893$	−17.1585	+	13.1662i	−0.574187	+	0.440590i
$894$	15.3745	−	8.79559i	0.514200	−	0.294169i
$895$	3.44869	+	5.97331i	0.115277	+	0.199666i
$896$	4.04502	+	2.33293i	0.135135	+	0.0779378i
$897$	−8.61478	−	1.66590i	−0.287639	−	0.0556227i
$898$	1.76534	+	0.617591i	0.0589103	+	0.0206093i
$899$	−12.6391	−	5.23530i	−0.421538	−	0.174607i
$900$	9.82767	−	16.7153i	0.327589	−	0.557178i
$901$	−8.65887	−	20.9044i	−0.288469	−	0.696426i
$902$	−0.0346782	−	0.0309863i	−0.00115466	−	0.00103173i
$903$	−0.441254	−	6.22371i	−0.0146840	−	0.207112i
$904$	−35.4600	−	18.7323i	−1.17938	−	0.623026i
$905$	6.24639	−	23.3118i	0.207637	−	0.774911i
$906$	1.19668	−	8.82003i	0.0397570	−	0.293026i
$907$	5.47686	−	41.6009i	0.181856	−	1.38133i	−0.620368	−	0.784311i	$-0.713017\pi$
$907$	5.47686	−	41.6009i	0.181856	−	1.38133i	0.802224	−	0.597023i	$-0.203650\pi$
$908$	46.7837	+	0.868854i	1.55257	+	0.0288339i
$909$	−24.1081	−	6.18505i	−0.799616	−	0.205145i
$910$	0.727426	+	0.495881i	0.0241139	+	0.0164383i
$911$	−31.6743	−	18.2872i	−1.04942	−	0.605881i	−0.126931	−	0.991912i	$-0.540513\pi$
$911$	−31.6743	−	18.2872i	−1.04942	−	0.605881i	−0.922486	+	0.386030i	$0.873846\pi$
$912$	−12.9057	+	55.5798i	−0.427351	+	1.84043i
$913$	6.04091	−	3.48772i	0.199925	−	0.115427i
$914$	23.8430	+	1.78522i	0.788656	+	0.0590499i
$915$	−11.7641	−	0.708104i	−0.388910	−	0.0234092i
$916$	−3.54444	+	0.879528i	−0.117112	+	0.0290604i
$917$	−1.81677	+	0.752530i	−0.0599949	+	0.0248507i
$918$	11.7224	+	6.66351i	0.386897	+	0.219929i
$919$	9.41883	+	9.41883i	0.310699	+	0.310699i	0.845180	−	0.534482i	$-0.179493\pi$
$919$	9.41883	+	9.41883i	0.310699	+	0.310699i	−0.534482	+	0.845180i	$0.679493\pi$
$920$	5.84066	−	15.7505i	0.192561	−	0.519280i
$921$	32.2948	+	15.7126i	1.06415	+	0.517747i
$922$	−1.64883	−	5.00964i	−0.0543014	−	0.164984i
$923$	−4.07386	+	5.30916i	−0.134093	+	0.174753i
$924$	1.46873	−	2.13633i	0.0483176	−	0.0702800i
$925$	−13.4956	+	10.3555i	−0.443733	+	0.340488i
$926$	−0.0157863	+	0.00298799i	−0.000518770	+	9.81916e-5i
$927$	39.1896	+	15.7455i	1.28715	+	0.517150i
$928$	16.5798	+	27.4954i	0.544259	+	0.902582i
$929$	−26.9603	+	46.6966i	−0.884538	+	1.53207i	−0.0382963	+	0.999266i	$0.512193\pi$
$929$	−26.9603	+	46.6966i	−0.884538	+	1.53207i	−0.846242	+	0.532799i	$0.821140\pi$
$930$	−3.95232	+	6.78353i	−0.129602	+	0.222441i
$931$	−7.34169	−	55.7657i	−0.240614	−	1.82765i
$932$	0.392955	+	3.48349i	0.0128717	+	0.114106i
$933$	−14.5161	−	4.84141i	−0.475235	−	0.158501i
$934$	−18.9335	+	21.1894i	−0.619523	+	0.693337i
$935$	−3.12852	+	3.12852i	−0.102313	+	0.102313i
$936$	−5.20861	−	8.09306i	−0.170249	−	0.264530i
$937$	5.95337	+	5.95337i	0.194488	+	0.194488i	0.797632	−	0.603144i	$-0.206086\pi$
$937$	5.95337	+	5.95337i	0.194488	+	0.194488i	−0.603144	+	0.797632i	$0.706086\pi$
$938$	−2.33676	+	0.131383i	−0.0762980	+	0.00428979i
$939$	3.02851	−	0.619209i	0.0988318	−	0.0202071i
$940$	6.71151	+	1.93261i	0.218905	+	0.0630347i
$941$	−57.6832	+	7.59413i	−1.88042	+	0.247562i	−0.981626	−	0.190815i	$-0.938887\pi$
$941$	−57.6832	+	7.59413i	−1.88042	+	0.247562i	−0.898791	+	0.438377i	$0.855554\pi$
$942$	−20.1818	−	5.49333i	−0.657560	−	0.178982i
$943$	0.0701474	+	0.0404996i	0.00228431	+	0.00131885i
$944$	21.3932	+	9.80719i	0.696290	+	0.319197i
$945$	1.54629	−	2.39627i	0.0503007	−	0.0779505i
$946$	−18.4929	−	12.6064i	−0.601254	−	0.409871i
$947$	33.6882	+	43.9033i	1.09472	+	1.42666i	0.894586	+	0.446895i	$0.147470\pi$
$947$	33.6882	+	43.9033i	1.09472	+	1.42666i	0.200132	+	0.979769i	$0.435863\pi$
$948$	42.0065	−	13.6418i	1.36431	−	0.443066i
$949$	−9.54035	−	7.32057i	−0.309693	−	0.237636i
$950$	33.6022	+	16.9604i	1.09020	+	0.550269i
$951$	28.4316	+	42.0638i	0.921958	+	1.36401i
$952$	1.57054	+	1.45668i	0.0509016	+	0.0472113i
$953$	15.6406	−	15.6406i	0.506647	−	0.506647i	−0.406848	−	0.913496i	$-0.633372\pi$
$953$	15.6406	−	15.6406i	0.506647	−	0.506647i	0.913496	+	0.406848i	$0.133372\pi$
$954$	52.2090	+	3.34979i	1.69033	+	0.108454i
$955$	−8.63332	−	20.8427i	−0.279368	−	0.674453i
$956$	47.1369	+	7.09846i	1.52452	+	0.229580i
$957$	15.9452	−	7.96926i	0.515436	−	0.257610i
$958$	−24.8021	+	21.3468i	−0.801320	+	0.689682i
$959$	−0.367327	−	0.636229i	−0.0118616	−	0.0205449i
$960$	16.9150	−	7.30700i	0.545929	−	0.235832i
$961$	12.5952	−	21.8156i	0.406298	−	0.703729i
$962$	1.57024	+	8.29595i	0.0506265	+	0.267472i
$963$	41.3743	−	11.5603i	1.33327	−	0.372527i
$964$	−1.76630	−	4.49875i	−0.0568888	−	0.144895i
$965$	−20.5999	−	2.71203i	−0.663134	−	0.0873032i
$966$	−1.74446	+	4.16485i	−0.0561271	+	0.134002i
$967$	22.6684	+	6.07397i	0.728966	+	0.195326i	0.604169	−	0.796856i	$-0.293505\pi$
$967$	22.6684	+	6.07397i	0.728966	+	0.195326i	0.124797	+	0.992182i	$0.460172\pi$
$968$	6.43363	+	20.8428i	0.206785	+	0.669914i
$969$	−11.4515	+	23.5367i	−0.367874	+	0.756109i
$970$	0.520388	+	9.25559i	0.0167087	+	0.297179i
$971$	22.6343	−	9.37545i	0.726370	−	0.300872i	0.0113108	−	0.999936i	$-0.496400\pi$
$971$	22.6343	−	9.37545i	0.726370	−	0.300872i	0.715059	+	0.699064i	$0.246400\pi$
$972$	−25.7818	+	17.5299i	−0.826952	+	0.562273i
$973$	0.0508993	−	0.122882i	0.00163176	−	0.00393941i
$974$	−35.6144	+	17.1538i	−1.14116	+	0.549644i
$975$	−6.00099	+	2.07280i	−0.192186	+	0.0663828i
$976$	15.7643	+	13.0543i	0.504602	+	0.417858i
$977$	41.2246	−	23.8010i	1.31889	−	0.761462i	0.335341	−	0.942097i	$-0.391148\pi$
$977$	41.2246	−	23.8010i	1.31889	−	0.761462i	0.983550	+	0.180635i	$0.0578151\pi$
$978$	−31.6558	+	31.4064i	−1.01224	+	1.00427i
$979$	4.63934	+	6.04611i	0.148274	+	0.193235i
$980$	−13.0799	+	12.6030i	−0.417823	+	0.402587i
$981$	19.1282	−	33.9621i	0.610716	−	1.08433i
$982$	−22.6338	−	34.5643i	−0.722273	−	1.10299i
$983$	−31.4335	+	8.42257i	−1.00257	+	0.268638i	−0.722523	−	0.691347i	$-0.757018\pi$
$983$	−31.4335	+	8.42257i	−1.00257	+	0.268638i	−0.280049	+	0.959986i	$0.590351\pi$
$984$	0.0210562	+	0.0863140i	0.000671247	+	0.00275159i
$985$	−7.40125	−	1.98316i	−0.235823	−	0.0631887i
$986$	4.60471	+	13.9905i	0.146644	+	0.445548i
$987$	−1.78091	−	0.593968i	−0.0566869	−	0.0189062i
$988$	15.0304	−	11.0960i	0.478180	−	0.353009i
$989$	36.0143	+	14.9176i	1.14519	+	0.474352i
$990$	−3.30160	−	9.68241i	−0.104932	−	0.307727i
$991$	12.6996			0.403416			0.201708	−	0.979446i	$-0.435351\pi$
$991$	12.6996			0.403416			0.201708	+	0.979446i	$0.435351\pi$
$992$	12.4953	−	5.45648i	0.396725	−	0.173243i
$993$	−36.4423	−	7.04710i	−1.15646	−	0.223633i
$994$	2.24654	+	2.61018i	0.0712559	+	0.0827899i
$995$	−3.83160	−	29.1039i	−0.121470	−	0.922655i
$996$	−13.2849	−	1.04754i	−0.420949	−	0.0331925i
$997$	−10.1938	−	1.34204i	−0.322842	−	0.0425029i	−0.0326364	−	0.999467i	$-0.510390\pi$
$997$	−10.1938	−	1.34204i	−0.322842	−	0.0425029i	−0.290206	+	0.956964i	$0.593724\pi$
$998$	−11.0678	−	2.30855i	−0.350345	−	0.0730758i
$999$	26.7367	−	5.76420i	0.845912	−	0.182371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.61.41	✓	368
3.2	odd	2		864.2.bk.a.829.6		368
9.4	even	3	inner	288.2.bc.a.157.10	yes	368
9.5	odd	6		864.2.bk.a.253.37		368
32.21	even	8	inner	288.2.bc.a.277.10	yes	368
96.53	odd	8		864.2.bk.a.181.37		368
288.85	even	24	inner	288.2.bc.a.85.41	yes	368
288.149	odd	24		864.2.bk.a.469.6		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.61.41	✓	368	1.1	even	1	trivial
288.2.bc.a.85.41	yes	368	288.85	even	24	inner
288.2.bc.a.157.10	yes	368	9.4	even	3	inner
288.2.bc.a.277.10	yes	368	32.21	even	8	inner
864.2.bk.a.181.37		368	96.53	odd	8
864.2.bk.a.253.37		368	9.5	odd	6
864.2.bk.a.469.6		368	288.149	odd	24
864.2.bk.a.829.6		368	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33488 + 0.466998i) q^{2} +(-0.104067 + 1.72892i) q^{3} +(1.56383 + 1.24678i) q^{4} +(-0.809510 + 1.05497i) q^{5} +(-0.946320 + 2.25931i) q^{6} +(-0.106824 - 0.398671i) q^{7} +(1.50528 + 2.39460i) q^{8} +(-2.97834 - 0.359847i) q^{9} +O(q^{10})\)	\(q+(1.33488 + 0.466998i) q^{2} +(-0.104067 + 1.72892i) q^{3} +(1.56383 + 1.24678i) q^{4} +(-0.809510 + 1.05497i) q^{5} +(-0.946320 + 2.25931i) q^{6} +(-0.106824 - 0.398671i) q^{7} +(1.50528 + 2.39460i) q^{8} +(-2.97834 - 0.359847i) q^{9} +(-1.57327 + 1.03023i) q^{10} +(0.236676 - 1.79774i) q^{11} +(-2.31832 + 2.57398i) q^{12} +(1.12453 - 0.148047i) q^{13} +(0.0435816 - 0.582065i) q^{14} +(-1.73972 - 1.50937i) q^{15} +(0.891101 + 3.89948i) q^{16} +1.83494i q^{17} +(-3.80769 - 1.87123i) q^{18} +(3.15166 - 7.60878i) q^{19} +(-2.58125 + 0.640518i) q^{20} +(0.700387 - 0.143201i) q^{21} +(1.15547 - 2.28924i) q^{22} +(-1.15598 + 4.31416i) q^{23} +(-4.29673 + 2.35332i) q^{24} +(0.836431 + 3.12160i) q^{25} +(1.57026 + 0.327528i) q^{26} +(0.932094 - 5.11187i) q^{27} +(0.330000 - 0.756637i) q^{28} +(4.50296 - 3.45524i) q^{29} +(-1.61746 - 2.82728i) q^{30} +(-1.20515 - 2.08738i) q^{31} +(-0.631535 + 5.62149i) q^{32} +(3.08352 + 0.596280i) q^{33} +(-0.856911 + 2.44942i) q^{34} +(0.507062 + 0.210032i) q^{35} +(-4.20896 - 4.27606i) q^{36} +(2.01433 + 4.86303i) q^{37} +(7.76039 - 8.68502i) q^{38} +(0.138936 + 1.95963i) q^{39} +(-3.74479 - 0.350422i) q^{40} +(0.00469380 - 0.0175175i) q^{41} +(1.00181 + 0.135923i) q^{42} +(1.13921 - 8.65317i) q^{43} +(2.61149 - 2.51626i) q^{44} +(2.79063 - 2.85077i) q^{45} +(-3.55780 + 5.21906i) q^{46} +(-2.27428 - 1.31306i) q^{47} +(-6.83463 + 1.13484i) q^{48} +(5.91465 - 3.41483i) q^{49} +(-0.341245 + 4.55759i) q^{50} +(-3.17246 - 0.190956i) q^{51} +(1.94315 + 1.17052i) q^{52} +(-11.3924 + 4.71890i) q^{53} +(3.63147 - 6.38846i) q^{54} +(1.70497 + 1.70497i) q^{55} +(0.793859 - 0.855912i) q^{56} +(12.8270 + 6.24080i) q^{57} +(7.62451 - 2.50947i) q^{58} +(3.58165 - 4.66770i) q^{59} +(-0.838783 - 4.52943i) q^{60} +(4.05953 - 3.11499i) q^{61} +(-0.633930 - 3.34921i) q^{62} +(0.174696 + 1.22582i) q^{63} +(-3.46825 + 7.20911i) q^{64} +(-0.754133 + 1.30620i) q^{65} +(3.83767 + 2.23596i) q^{66} +(-0.523374 - 3.97542i) q^{67} +(-2.28775 + 2.86952i) q^{68} +(-7.33855 - 2.44755i) q^{69} +(0.578784 + 0.517165i) q^{70} +(-4.17197 + 4.17197i) q^{71} +(-3.62155 - 7.67361i) q^{72} +(-7.49687 - 7.49687i) q^{73} +(0.417873 + 7.43226i) q^{74} +(-5.48406 + 1.12127i) q^{75} +(14.4151 - 7.96939i) q^{76} +(-0.741988 + 0.0976845i) q^{77} +(-0.729682 + 2.68076i) q^{78} +(-11.0415 - 6.37483i) q^{79} +(-4.83520 - 2.21658i) q^{80} +(8.74102 + 2.14349i) q^{81} +(0.0144463 - 0.0211918i) q^{82} +(2.34186 + 3.05198i) q^{83} +(1.27382 + 0.649285i) q^{84} +(-1.93581 - 1.48540i) q^{85} +(5.56173 - 11.0190i) q^{86} +(5.50523 + 8.14483i) q^{87} +(4.66113 - 2.13935i) q^{88} +(-2.97192 + 2.97192i) q^{89} +(5.05646 - 2.50223i) q^{90} +(-0.179149 - 0.432503i) q^{91} +(-7.18654 + 5.30535i) q^{92} +(3.73433 - 1.86638i) q^{93} +(-2.42270 - 2.81486i) q^{94} +(5.47577 + 9.48431i) q^{95} +(-9.65340 - 1.67688i) q^{96} +(2.46473 - 4.26904i) q^{97} +(9.49008 - 1.79626i) q^{98} +(-1.35181 + 5.26910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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