LMFDB - Embedded newform 756.2.bs.a.275.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(11,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13, 12]))

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

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

chi := DirichletCharacter("756.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bs (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			275.2
Character	$\chi$	$=$	756.275
Dual form			756.2.bs.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41382 - 0.0335363i) q^{2} +(-1.23240 + 1.21704i) q^{3} +(1.99775 + 0.0948283i) q^{4} +(-1.44666 - 0.255085i) q^{5} +(1.78320 - 1.67934i) q^{6} +(1.11827 + 2.39781i) q^{7} +(-2.82127 - 0.201067i) q^{8} +(0.0376115 - 2.99976i) q^{9} +O(q^{10})$	\(q+(-1.41382 - 0.0335363i) q^{2} +(-1.23240 + 1.21704i) q^{3} +(1.99775 + 0.0948283i) q^{4} +(-1.44666 - 0.255085i) q^{5} +(1.78320 - 1.67934i) q^{6} +(1.11827 + 2.39781i) q^{7} +(-2.82127 - 0.201067i) q^{8} +(0.0376115 - 2.99976i) q^{9} +(2.03676 + 0.409160i) q^{10} +(-0.00244493 - 0.0138659i) q^{11} +(-2.57743 + 2.31448i) q^{12} +(1.58092 + 1.32655i) q^{13} +(-1.50061 - 3.42756i) q^{14} +(2.09331 - 1.44628i) q^{15} +(3.98202 + 0.378887i) q^{16} +2.29523i q^{17} +(-0.153777 + 4.23985i) q^{18} +4.12101i q^{19} +(-2.86588 - 0.646782i) q^{20} +(-4.29639 - 1.59407i) q^{21} +(0.00299167 + 0.0196858i) q^{22} +(1.92989 + 1.61937i) q^{23} +(3.72164 - 3.18581i) q^{24} +(-2.67070 - 0.972056i) q^{25} +(-2.19064 - 1.92851i) q^{26} +(3.60449 + 3.74268i) q^{27} +(2.00664 + 4.89626i) q^{28} +(-2.29185 - 2.73132i) q^{29} +(-3.00806 + 1.97458i) q^{30} +(0.515894 + 1.41741i) q^{31} +(-5.61713 - 0.669218i) q^{32} +(0.0198885 + 0.0141127i) q^{33} +(0.0769734 - 3.24503i) q^{34} +(-1.00611 - 3.75407i) q^{35} +(0.359601 - 5.98921i) q^{36} +(-0.994595 - 1.72269i) q^{37} +(0.138203 - 5.82635i) q^{38} +(-3.56279 + 0.289210i) q^{39} +(4.03014 + 1.01054i) q^{40} +(-0.938622 + 1.11861i) q^{41} +(6.02084 + 2.39781i) q^{42} +(0.563883 - 1.54925i) q^{43} +(-0.00356948 - 0.0279324i) q^{44} +(-0.819607 + 4.33005i) q^{45} +(-2.67420 - 2.35422i) q^{46} +(4.42251 + 1.60966i) q^{47} +(-5.36855 + 4.37935i) q^{48} +(-4.49896 + 5.36278i) q^{49} +(3.74328 + 1.46387i) q^{50} +(-2.79339 - 2.82863i) q^{51} +(3.03249 + 2.80003i) q^{52} +(-9.83550 + 5.67853i) q^{53} +(-4.97057 - 5.41234i) q^{54} +0.0206829i q^{55} +(-2.67282 - 6.98971i) q^{56} +(-5.01544 - 5.07872i) q^{57} +(3.14865 + 3.93844i) q^{58} +(-4.91278 - 4.12231i) q^{59} +(4.31907 - 2.69081i) q^{60} +(-12.6903 - 4.61888i) q^{61} +(-0.681845 - 2.02125i) q^{62} +(7.23492 - 3.26435i) q^{63} +(7.91914 + 1.13453i) q^{64} +(-1.94867 - 2.32234i) q^{65} +(-0.0276454 - 0.0206198i) q^{66} +(-6.18343 - 1.09031i) q^{67} +(-0.217652 + 4.58529i) q^{68} +(-4.34924 + 0.353051i) q^{69} +(1.29655 + 5.34130i) q^{70} +(1.34225 - 2.32484i) q^{71} +(-0.709266 + 8.45559i) q^{72} +(0.541328 - 0.937608i) q^{73} +(1.34840 + 2.46892i) q^{74} +(4.47440 - 2.05240i) q^{75} +(-0.390788 + 8.23275i) q^{76} +(0.0305136 - 0.0213682i) q^{77} +(5.04683 - 0.289408i) q^{78} +(-15.0615 + 2.65575i) q^{79} +(-5.66398 - 1.56388i) q^{80} +(-8.99717 - 0.225651i) q^{81} +(1.36455 - 1.55002i) q^{82} +(-12.9130 + 10.8353i) q^{83} +(-8.43194 - 3.59198i) q^{84} +(0.585479 - 3.32041i) q^{85} +(-0.849182 + 2.17145i) q^{86} +(6.14861 + 0.576794i) q^{87} +(0.00410984 + 0.0396110i) q^{88} -6.30985i q^{89} +(1.30399 - 6.09441i) q^{90} +(-1.41292 + 5.27417i) q^{91} +(3.70188 + 3.41811i) q^{92} +(-2.36083 - 1.11895i) q^{93} +(-6.19864 - 2.42408i) q^{94} +(1.05121 - 5.96170i) q^{95} +(7.73701 - 6.01155i) q^{96} +(7.83670 + 2.85233i) q^{97} +(6.54055 - 7.43110i) q^{98} +(-0.0416863 + 0.00681270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.41382	−	0.0335363i	−0.999719	−	0.0237137i
$2$	−1.41382	−	0.0335363i	−0.999719	−	0.0237137i
$3$	−1.23240	+	1.21704i	−0.711526	+	0.702660i
$3$	−1.23240	+	1.21704i	−0.711526	+	0.702660i
$4$	1.99775	+	0.0948283i	0.998875	+	0.0474141i
$5$	−1.44666	−	0.255085i	−0.646967	−	0.114078i	−0.159470	−	0.987203i	$-0.550979\pi$
$5$	−1.44666	−	0.255085i	−0.646967	−	0.114078i	−0.487496	+	0.873125i	$0.662090\pi$
$6$	1.78320	−	1.67934i	0.727988	−	0.685590i
$7$	1.11827	+	2.39781i	0.422665	+	0.906286i
$7$	1.11827	+	2.39781i	0.422665	+	0.906286i
$8$	−2.82127	−	0.201067i	−0.997470	−	0.0710879i
$9$	0.0376115	−	2.99976i	0.0125372	−	0.999921i
$10$	2.03676	+	0.409160i	0.644080	+	0.129388i
$11$	−0.00244493	−	0.0138659i	−0.000737174	−	0.00418072i	0.984437	−	0.175738i	$-0.0562312\pi$
$11$	−0.00244493	−	0.0138659i	−0.000737174	−	0.00418072i	−0.985174	+	0.171557i	$0.945120\pi$
$12$	−2.57743	+	2.31448i	−0.744041	+	0.668134i
$13$	1.58092	+	1.32655i	0.438468	+	0.367918i	0.835136	−	0.550044i	$-0.185389\pi$
$13$	1.58092	+	1.32655i	0.438468	+	0.367918i	−0.396668	+	0.917962i	$0.629833\pi$
$14$	−1.50061	−	3.42756i	−0.401055	−	0.916054i
$15$	2.09331	−	1.44628i	0.540491	−	0.373429i
$16$	3.98202	+	0.378887i	0.995504	+	0.0947216i
$17$			2.29523i			0.556674i	0.960483	+	0.278337i	$0.0897832\pi$
$17$			2.29523i			0.556674i	−0.960483	+	0.278337i	$0.910217\pi$
$18$	−0.153777	+	4.23985i	−0.0362455	+	0.999343i
$19$			4.12101i			0.945424i	0.881217	+	0.472712i	$0.156725\pi$
$19$			4.12101i			0.945424i	−0.881217	+	0.472712i	$0.843275\pi$
$20$	−2.86588	−	0.646782i	−0.640830	−	0.144625i
$21$	−4.29639	−	1.59407i	−0.937548	−	0.347856i
$22$	0.00299167	+	0.0196858i	0.000637826	+	0.00419703i
$23$	1.92989	+	1.61937i	0.402410	+	0.337662i	0.821424	−	0.570317i	$-0.193180\pi$
$23$	1.92989	+	1.61937i	0.402410	+	0.337662i	−0.419014	+	0.907980i	$0.637624\pi$
$24$	3.72164	−	3.18581i	0.759676	−	0.650302i
$25$	−2.67070	−	0.972056i	−0.534140	−	0.194411i
$26$	−2.19064	−	1.92851i	−0.429620	−	0.378213i
$27$	3.60449	+	3.74268i	0.693685	+	0.720279i
$28$	2.00664	+	4.89626i	0.379219	+	0.925307i
$29$	−2.29185	−	2.73132i	−0.425586	−	0.507193i	0.510058	−	0.860140i	$-0.329624\pi$
$29$	−2.29185	−	2.73132i	−0.425586	−	0.507193i	−0.935643	+	0.352947i	$0.885180\pi$
$30$	−3.00806	+	1.97458i	−0.549195	+	0.360507i
$31$	0.515894	+	1.41741i	0.0926573	+	0.254574i	0.977360	−	0.211581i	$-0.0678612\pi$
$31$	0.515894	+	1.41741i	0.0926573	+	0.254574i	−0.884703	+	0.466155i	$0.845639\pi$
$32$	−5.61713	−	0.669218i	−0.992978	−	0.118302i
$33$	0.0198885	+	0.0141127i	0.00346214	+	0.00245671i
$34$	0.0769734	−	3.24503i	0.0132008	−	0.556517i
$35$	−1.00611	−	3.75407i	−0.170063	−	0.634554i
$36$	0.359601	−	5.98921i	0.0599335	−	0.998202i
$37$	−0.994595	−	1.72269i	−0.163510	−	0.283208i	0.772615	−	0.634875i	$-0.218948\pi$
$37$	−0.994595	−	1.72269i	−0.163510	−	0.283208i	−0.936125	+	0.351667i	$0.885615\pi$
$38$	0.138203	−	5.82635i	0.0224195	−	0.945158i
$39$	−3.56279	+	0.289210i	−0.570503	+	0.0463107i
$40$	4.03014	+	1.01054i	0.637220	+	0.159781i
$41$	−0.938622	+	1.11861i	−0.146588	+	0.174697i	−0.834342	−	0.551247i	$-0.814152\pi$
$41$	−0.938622	+	1.11861i	−0.146588	+	0.174697i	0.687754	+	0.725944i	$0.258597\pi$
$42$	6.02084	+	2.39781i	0.929036	+	0.369990i
$43$	0.563883	−	1.54925i	0.0859913	−	0.236259i	−0.889242	−	0.457436i	$-0.848768\pi$
$43$	0.563883	−	1.54925i	0.0859913	−	0.236259i	0.975234	+	0.221177i	$0.0709900\pi$
$44$	−0.00356948	−	0.0279324i	−0.000538120	−	0.00421097i
$45$	−0.819607	+	4.33005i	−0.122180	+	0.645486i
$46$	−2.67420	−	2.35422i	−0.394290	−	0.347110i
$47$	4.42251	+	1.60966i	0.645090	+	0.234794i	0.643786	−	0.765206i	$-0.277363\pi$
$47$	4.42251	+	1.60966i	0.645090	+	0.234794i	0.00130397	+	0.999999i	$0.499585\pi$
$48$	−5.36855	+	4.37935i	−0.774884	+	0.632104i
$49$	−4.49896	+	5.36278i	−0.642708	+	0.766111i
$50$	3.74328	+	1.46387i	0.529380	+	0.207023i
$51$	−2.79339	−	2.82863i	−0.391153	−	0.396088i
$52$	3.03249	+	2.80003i	0.420530	+	0.388294i
$53$	−9.83550	+	5.67853i	−1.35101	+	0.780006i	−0.988391	−	0.151932i	$-0.951451\pi$
$53$	−9.83550	+	5.67853i	−1.35101	+	0.780006i	−0.362619	+	0.931938i	$0.618117\pi$
$54$	−4.97057	−	5.41234i	−0.676409	−	0.736526i
$55$			0.0206829i			0.00278888i
$56$	−2.67282	−	6.98971i	−0.357170	−	0.934039i
$57$	−5.01544	−	5.07872i	−0.664312	−	0.672693i
$58$	3.14865	+	3.93844i	0.413439	+	0.517143i
$59$	−4.91278	−	4.12231i	−0.639589	−	0.536679i	0.264303	−	0.964440i	$-0.414858\pi$
$59$	−4.91278	−	4.12231i	−0.639589	−	0.536679i	−0.903892	+	0.427761i	$0.859303\pi$
$60$	4.31907	−	2.69081i	0.557589	−	0.347382i
$61$	−12.6903	−	4.61888i	−1.62482	−	0.591387i	−0.640529	−	0.767934i	$-0.721285\pi$
$61$	−12.6903	−	4.61888i	−1.62482	−	0.591387i	−0.984292	+	0.176547i	$0.943507\pi$
$62$	−0.681845	−	2.02125i	−0.0865944	−	0.256700i
$63$	7.23492	−	3.26435i	0.911514	−	0.411270i
$64$	7.91914	+	1.13453i	0.989893	+	0.141816i
$65$	−1.94867	−	2.32234i	−0.241703	−	0.288050i
$66$	−0.0276454	−	0.0206198i	−0.00340291	−	0.00253812i
$67$	−6.18343	−	1.09031i	−0.755426	−	0.133202i	−0.217345	−	0.976095i	$-0.569740\pi$
$67$	−6.18343	−	1.09031i	−0.755426	−	0.133202i	−0.538082	+	0.842893i	$0.680851\pi$
$68$	−0.217652	+	4.58529i	−0.0263942	+	0.556048i
$69$	−4.34924	+	0.353051i	−0.523587	+	0.0425024i
$70$	1.29655	+	5.34130i	0.154968	+	0.638408i
$71$	1.34225	−	2.32484i	0.159295	−	0.275908i	−0.775319	−	0.631569i	$-0.782411\pi$
$71$	1.34225	−	2.32484i	0.159295	−	0.275908i	0.934615	+	0.355662i	$0.115744\pi$
$72$	−0.709266	+	8.45559i	−0.0835878	+	0.996500i
$73$	0.541328	−	0.937608i	0.0633577	−	0.109739i	−0.832607	−	0.553865i	$-0.813152\pi$
$73$	0.541328	−	0.937608i	0.0633577	−	0.109739i	0.895964	+	0.444126i	$0.146486\pi$
$74$	1.34840	+	2.46892i	0.156749	+	0.287006i
$75$	4.47440	−	2.05240i	0.516659	−	0.236991i
$76$	−0.390788	+	8.23275i	−0.0448265	+	0.944361i
$77$	0.0305136	−	0.0213682i	0.00347735	−	0.00243514i
$78$	5.04683	−	0.289408i	0.571440	−	0.0327690i
$79$	−15.0615	+	2.65575i	−1.69455	+	0.298795i	−0.935785	−	0.352571i	$-0.885308\pi$
$79$	−15.0615	+	2.65575i	−1.69455	+	0.298795i	−0.758764	+	0.651366i	$0.774196\pi$
$80$	−5.66398	−	1.56388i	−0.633252	−	0.174847i
$81$	−8.99717	−	0.225651i	−0.999686	−	0.0250724i
$82$	1.36455	−	1.55002i	0.150690	−	0.171172i
$83$	−12.9130	+	10.8353i	−1.41739	+	1.18933i	−0.464664	+	0.885487i	$0.653825\pi$
$83$	−12.9130	+	10.8353i	−1.41739	+	1.18933i	−0.952722	+	0.303842i	$0.901731\pi$
$84$	−8.43194	−	3.59198i	−0.920000	−	0.391917i
$85$	0.585479	−	3.32041i	0.0635041	−	0.360150i
$86$	−0.849182	+	2.17145i	−0.0915697	+	0.234153i
$87$	6.14861	+	0.576794i	0.659200	+	0.0618388i
$88$	0.00410984	+	0.0396110i	0.000438110	+	0.00422255i
$89$		−	6.30985i		−	0.668842i	−0.942424	−	0.334421i	$-0.891459\pi$
$89$		−	6.30985i		−	0.668842i	0.942424	−	0.334421i	$-0.108541\pi$
$90$	1.30399	−	6.09441i	0.137452	−	0.642407i
$91$	−1.41292	+	5.27417i	−0.148114	+	0.552884i
$92$	3.70188	+	3.41811i	0.385948	+	0.356363i
$93$	−2.36083	−	1.11895i	−0.244807	−	0.116029i
$94$	−6.19864	−	2.42408i	−0.639341	−	0.250025i
$95$	1.05121	−	5.96170i	0.107852	−	0.611658i
$96$	7.73701	−	6.01155i	0.789655	−	0.613551i
$97$	7.83670	+	2.85233i	0.795697	+	0.289610i	0.707702	−	0.706511i	$-0.249732\pi$
$97$	7.83670	+	2.85233i	0.795697	+	0.289610i	0.0879947	+	0.996121i	$0.471954\pi$
$98$	6.54055	−	7.43110i	0.660695	−	0.750655i
$99$	−0.0416863	+	0.00681270i	−0.00418963	+	0.000684702i
$100$	−5.24322	−	2.19518i	−0.524322	−	0.219518i
$101$	−10.2370	−	12.2000i	−1.01862	−	1.21394i	−0.976652	−	0.214826i	$-0.931082\pi$
$101$	−10.2370	−	12.2000i	−1.01862	−	1.21394i	−0.0419681	−	0.999119i	$-0.513363\pi$
$102$	3.85448	+	4.09284i	0.381650	+	0.405252i
$103$	7.48532	+	1.31986i	0.737551	+	0.130050i	0.529789	−	0.848129i	$-0.322271\pi$
$103$	7.48532	+	1.31986i	0.737551	+	0.130050i	0.207762	+	0.978179i	$0.433382\pi$
$104$	−4.19348	−	4.06042i	−0.411204	−	0.398157i
$105$	5.80879	+	3.40203i	0.566880	+	0.332004i
$106$	14.0960	−	7.69855i	1.36913	−	0.747749i
$107$	−7.01422	+	12.1490i	−0.678090	+	1.17449i	0.297465	+	0.954733i	$0.403859\pi$
$107$	−7.01422	+	12.1490i	−0.678090	+	1.17449i	−0.975555	+	0.219754i	$0.929475\pi$
$108$	6.84596	+	7.81875i	0.658753	+	0.752359i
$109$	−3.13424	−	5.42866i	−0.300205	−	0.519971i	0.675977	−	0.736923i	$-0.263722\pi$
$109$	−3.13424	−	5.42866i	−0.300205	−	0.519971i	−0.976182	+	0.216952i	$0.930389\pi$
$110$	0.000693628	−	0.0292418i	6.61349e−5	−	0.00278810i
$111$	3.32232	+	0.912574i	0.315341	+	0.0866177i
$112$	3.54446	+	9.97180i	0.334920	+	0.942247i
$113$	3.14446	+	8.63934i	0.295806	+	0.812721i	0.995189	+	0.0979736i	$0.0312361\pi$
$113$	3.14446	+	8.63934i	0.295806	+	0.812721i	−0.699383	+	0.714747i	$0.746542\pi$
$114$	6.92059	+	7.34858i	0.648173	+	0.688257i
$115$	−2.37882	−	2.83497i	−0.221826	−	0.264362i
$116$	−4.31954	−	5.67383i	−0.401059	−	0.526802i
$117$	4.03879	−	4.69249i	0.373387	−	0.433821i
$118$	6.80751	+	5.99294i	0.626682	+	0.551695i
$119$	−5.50351	+	2.56667i	−0.504506	+	0.235287i
$120$	−6.19661	+	3.65946i	−0.565670	+	0.334062i
$121$	10.3364	−	3.76215i	0.939676	−	0.342014i
$122$	17.7868	+	6.95583i	1.61034	+	0.629751i
$123$	−0.204636	−	2.52091i	−0.0184514	−	0.227303i
$124$	0.896218	+	2.88055i	0.0804827	+	0.258681i
$125$	9.97651	+	5.75994i	0.892326	+	0.515185i
$126$	−10.3383	+	4.37256i	−0.921010	+	0.389539i
$127$	−1.57419	+	0.908861i	−0.139687	+	0.0806484i	−0.568215	−	0.822880i	$-0.692366\pi$
$127$	−1.57419	+	0.908861i	−0.139687	+	0.0806484i	0.428528	+	0.903529i	$0.359032\pi$
$128$	−11.1582	−	1.86959i	−0.986252	−	0.165250i
$129$	1.19058	+	2.59557i	0.104825	+	0.228527i
$130$	2.67718	+	3.34871i	0.234804	+	0.293701i
$131$	12.3069	+	10.3267i	1.07526	+	0.902251i	0.995519	−	0.0945644i	$-0.0301458\pi$
$131$	12.3069	+	10.3267i	1.07526	+	0.902251i	0.0797423	+	0.996816i	$0.474590\pi$
$132$	0.0383940	+	0.0300797i	0.00334177	+	0.00261810i
$133$	−9.88138	+	4.60839i	−0.856824	+	0.399598i
$134$	8.70567	+	1.74886i	0.752055	+	0.151079i
$135$	−4.25978	−	6.33384i	−0.366623	−	0.545131i
$136$	0.461494	−	6.47545i	0.0395728	−	0.555266i
$137$	2.85975	−	7.85711i	0.244325	−	0.671278i	−0.755544	−	0.655098i	$-0.772627\pi$
$137$	2.85975	−	7.85711i	0.244325	−	0.671278i	0.999869	−	0.0161801i	$-0.00515052\pi$
$138$	6.16087	−	0.353292i	0.524448	−	0.0300742i
$139$	8.27560	+	1.45921i	0.701927	+	0.123769i	0.513210	−	0.858263i	$-0.328456\pi$
$139$	8.27560	+	1.45921i	0.701927	+	0.123769i	0.188717	+	0.982032i	$0.439567\pi$
$140$	−1.65396	−	7.59510i	−0.139785	−	0.641903i
$141$	−7.40933	+	3.39864i	−0.623978	+	0.286217i
$142$	−1.97566	+	3.24188i	−0.165793	+	0.272053i
$143$	0.0145285	−	0.0251642i	0.00121494	−	0.00210433i
$144$	1.28634	−	11.9309i	0.107195	−	0.994238i
$145$	2.61881	+	4.53591i	0.217480	+	0.376687i
$146$	−0.796783	+	1.30745i	−0.0659422	+	0.108205i
$147$	−0.982224	−	12.0845i	−0.0810124	−	0.996713i
$148$	−1.82359	−	3.53582i	−0.149898	−	0.290643i
$149$	5.36195	+	14.7318i	0.439268	+	1.20688i	0.939970	+	0.341258i	$0.110853\pi$
$149$	5.36195	+	14.7318i	0.439268	+	1.20688i	−0.500702	+	0.865620i	$0.666925\pi$
$150$	−6.39481	+	2.75166i	−0.522134	+	0.224672i
$151$	−10.6170	+	1.87207i	−0.864001	+	0.152347i	−0.588050	−	0.808825i	$-0.700104\pi$
$151$	−10.6170	+	1.87207i	−0.864001	+	0.152347i	−0.275952	+	0.961172i	$0.588993\pi$
$152$	0.828598	−	11.6265i	0.0672082	−	0.943032i
$153$	6.88513	+	0.0863269i	0.556630	+	0.00697911i
$154$	−0.0438573	+	0.0291874i	−0.00353412	+	0.00235199i
$155$	−0.384764	−	2.18211i	−0.0309050	−	0.175271i
$156$	−7.14499	+	0.239917i	−0.572057	+	0.0192087i
$157$	12.5738	+	10.5507i	1.00350	+	0.842034i	0.987465	−	0.157838i	$-0.0504523\pi$
$157$	12.5738	+	10.5507i	1.00350	+	0.842034i	0.0160315	+	0.999871i	$0.494897\pi$
$158$	21.3832	−	3.24963i	1.70116	−	0.258527i
$159$	5.21024	−	18.9684i	0.413199	−	1.50429i
$160$	7.95538	+	2.40098i	0.628928	+	0.189814i
$161$	−1.72481	+	6.43840i	−0.135934	+	0.507417i
$162$	12.7128	+	0.620761i	0.998810	+	0.0487716i
$163$	−13.2329	−	7.64005i	−1.03648	−	0.598415i	−0.117649	−	0.993055i	$-0.537536\pi$
$163$	−13.2329	−	7.64005i	−1.03648	−	0.598415i	−0.918836	+	0.394641i	$0.870869\pi$
$164$	−1.98121	+	2.14569i	−0.154706	+	0.167550i
$165$	−0.0251720	−	0.0254896i	−0.00195964	−	0.00198436i
$166$	18.6200	−	14.8861i	1.44519	−	1.15538i
$167$	2.34744	−	0.854399i	0.181650	−	0.0661154i	−0.249594	−	0.968351i	$-0.580297\pi$
$167$	2.34744	−	0.854399i	0.181650	−	0.0661154i	0.431244	+	0.902235i	$0.358075\pi$
$168$	11.8008	+	5.36118i	0.910448	+	0.413624i
$169$	−1.51785	−	8.60817i	−0.116758	−	0.662167i
$170$	−0.939113	+	4.67482i	−0.0720267	+	0.358542i
$171$	12.3621	+	0.154997i	0.945350	+	0.0118529i
$172$	1.27341	−	3.04155i	0.0970966	−	0.231916i
$173$	−1.64020	−	1.95471i	−0.124702	−	0.148614i	0.700081	−	0.714063i	$-0.253147\pi$
$173$	−1.64020	−	1.95471i	−0.124702	−	0.148614i	−0.824783	+	0.565449i	$0.808703\pi$
$174$	−8.67365	−	1.02168i	−0.657548	−	0.0774535i
$175$	−0.655755	−	7.49084i	−0.0495704	−	0.566255i
$176$	−0.00448215	−	0.0561405i	−0.000337855	−	0.00423175i
$177$	11.0715	−	0.898734i	0.832187	−	0.0675530i
$178$	−0.211609	+	8.92096i	−0.0158608	+	0.668654i
$179$	−5.64831			−0.422174			−0.211087	−	0.977467i	$-0.567700\pi$
$179$	−5.64831			−0.422174			−0.211087	+	0.977467i	$0.567700\pi$
$180$	−2.04798	+	8.57264i	−0.152648	+	0.638967i
$181$	9.61726	+	16.6576i	0.714845	+	1.23815i	0.963019	+	0.269433i	$0.0868361\pi$
$181$	9.61726	+	16.6576i	0.714845	+	1.23815i	−0.248174	+	0.968715i	$0.579831\pi$
$182$	2.17448	−	7.40933i	0.161183	−	0.549216i
$183$	21.2608	−	9.75230i	1.57165	−	0.720911i
$184$	−5.11915	−	4.95673i	−0.377389	−	0.365415i
$185$	0.999410	+	2.74586i	0.0734781	+	0.201879i
$186$	3.30026	+	1.66116i	0.241987	+	0.121802i
$187$	0.0318253	−	0.00561166i	0.00232730	−	0.000410366i
$188$	8.68244	+	3.63509i	0.633232	+	0.265116i
$189$	−4.94344	+	12.8282i	−0.359582	+	0.933113i
$190$	−1.68615	+	8.39350i	−0.122326	+	0.608928i
$191$	2.76413	+	15.6762i	0.200006	+	1.13429i	0.905108	+	0.425183i	$0.139790\pi$
$191$	2.76413	+	15.6762i	0.200006	+	1.13429i	−0.705102	+	0.709106i	$0.749099\pi$
$192$	−11.1403	+	8.23975i	−0.803983	+	0.594653i
$193$	25.3777	−	9.23671i	1.82672	−	0.664873i	0.832965	−	0.553326i	$-0.186642\pi$
$193$	25.3777	−	9.23671i	1.82672	−	0.664873i	0.993759	−	0.111547i	$-0.0355806\pi$
$194$	−10.9840	−	4.29548i	−0.788605	−	0.308397i
$195$	5.22792	+	0.490426i	0.374379	+	0.0351201i
$196$	−9.49634	+	10.2869i	−0.678310	+	0.734776i
$197$	12.9337	−	7.46726i	0.921487	−	0.532021i	0.0373776	−	0.999301i	$-0.488100\pi$
$197$	12.9337	−	7.46726i	0.921487	−	0.532021i	0.884109	+	0.467281i	$0.154766\pi$
$198$	0.0591653	−	0.00823389i	0.00420469	−	0.000585157i
$199$			7.82906i			0.554987i	0.960727	+	0.277494i	$0.0895038\pi$
$199$			7.82906i			0.554987i	−0.960727	+	0.277494i	$0.910496\pi$
$200$	7.33933	+	3.27942i	0.518969	+	0.231890i
$201$	8.94740	−	6.18181i	0.631101	−	0.436031i
$202$	14.0641	+	17.5919i	0.989547	+	1.23776i
$203$	3.98628	−	8.54976i	0.279782	−	0.600075i
$204$	−5.31226	−	5.91579i	−0.371933	−	0.414188i
$205$	1.64321	−	1.37882i	0.114767	−	0.0963006i
$206$	−10.5386	−	2.11708i	−0.734259	−	0.147504i
$207$	4.93032	−	5.72832i	0.342681	−	0.398145i
$208$	5.79263	+	5.88132i	0.401647	+	0.407796i
$209$	0.0571414	−	0.0100756i	0.00395255	−	0.000696942i
$210$	−8.09847	−	5.00465i	−0.558847	−	0.345354i
$211$	−6.91309	−	18.9936i	−0.475917	−	1.30757i	−0.912930	−	0.408116i	$-0.866186\pi$
$211$	−6.91309	−	18.9936i	−0.475917	−	1.30757i	0.437013	−	0.899455i	$-0.356036\pi$
$212$	−20.1874	+	10.4116i	−1.38647	+	0.715071i
$213$	1.17525	+	4.49870i	0.0805266	+	0.308246i
$214$	10.3242	−	16.9412i	0.705751	−	1.15808i
$215$	−1.21094	+	2.09741i	−0.0825854	+	0.143042i
$216$	−9.41672	−	11.2839i	−0.640726	−	0.767769i
$217$	−2.82176	+	2.82206i	−0.191554	+	0.191574i
$218$	4.24918	+	7.78023i	0.287791	+	0.526944i
$219$	0.473978	+	1.81433i	0.0320284	+	0.122601i
$220$	−0.00196133	+	0.0413193i	−0.000132233	+	0.00278575i
$221$	−3.04473	+	3.62856i	−0.204811	+	0.244084i
$222$	−4.66655	−	1.40163i	−0.313198	−	0.0940713i
$223$	0.229080	−	0.0403929i	0.0153403	−	0.00270491i	−0.165973	−	0.986130i	$-0.553076\pi$
$223$	0.229080	−	0.0403929i	0.0153403	−	0.00270491i	0.181313	+	0.983425i	$0.441965\pi$
$224$	−4.67680	−	14.2172i	−0.312482	−	0.949924i
$225$	−3.01639	+	7.97491i	−0.201092	+	0.531661i
$226$	−4.15596	−	12.3199i	−0.276450	−	0.819507i
$227$	−1.77188	−	10.0488i	−0.117604	−	0.666963i	−0.985428	−	0.170092i	$-0.945593\pi$
$227$	−1.77188	−	10.0488i	−0.117604	−	0.666963i	0.867825	−	0.496871i	$-0.165518\pi$
$228$	−9.53800	−	10.6216i	−0.631669	−	0.703434i
$229$	−12.4047	+	4.51496i	−0.819728	+	0.298357i	−0.717636	−	0.696418i	$-0.754776\pi$
$229$	−12.4047	+	4.51496i	−0.819728	+	0.298357i	−0.102092	+	0.994775i	$0.532554\pi$
$230$	3.26814	+	4.08790i	0.215495	+	0.269548i
$231$	−0.0115989	+	0.0634706i	−0.000763151	+	0.00417606i
$232$	5.91675	+	8.16661i	0.388454	+	0.536164i
$233$	5.50550	−	3.17860i	0.360677	−	0.208237i	−0.308701	−	0.951159i	$-0.599894\pi$
$233$	5.50550	−	3.17860i	0.360677	−	0.208237i	0.669378	+	0.742922i	$0.266561\pi$
$234$	−5.86748	+	6.49887i	−0.383569	+	0.424844i
$235$	−5.98728	−	3.45676i	−0.390567	−	0.225494i
$236$	−9.42359	−	8.70121i	−0.613423	−	0.566401i
$237$	15.3296	−	21.6034i	0.995764	−	1.40329i
$238$	7.86702	−	3.44424i	0.509943	−	0.223257i
$239$	−0.808144	+	4.58321i	−0.0522745	+	0.296463i	−0.999725	−	0.0234382i	$-0.992539\pi$
$239$	−0.808144	+	4.58321i	−0.0522745	+	0.296463i	0.947451	+	0.319902i	$0.103650\pi$
$240$	8.88358	−	4.96599i	0.573433	−	0.320553i
$241$	−12.8996	−	4.69507i	−0.830935	−	0.302436i	−0.108693	−	0.994075i	$-0.534666\pi$
$241$	−12.8996	−	4.69507i	−0.830935	−	0.302436i	−0.722243	+	0.691640i	$0.756889\pi$
$242$	−14.7400	+	4.97235i	−0.947522	+	0.319635i
$243$	11.3627	−	10.6719i	0.728919	−	0.684600i
$244$	−24.9140	−	10.4308i	−1.59495	−	0.667761i
$245$	7.87644	−	6.61051i	0.503207	−	0.422330i
$246$	0.204775	+	3.57097i	0.0130560	+	0.227677i
$247$	−5.46672	+	6.51498i	−0.347839	+	0.414538i
$248$	−1.17048	−	4.10262i	−0.0743258	−	0.260517i
$249$	2.72694	−	29.0691i	0.172813	−	1.84218i
$250$	−13.9118	−	8.47807i	−0.879858	−	0.536200i
$251$	6.64458	+	11.5088i	0.419402	+	0.726426i	0.995879	−	0.0906871i	$-0.0289063\pi$
$251$	6.64458	+	11.5088i	0.419402	+	0.726426i	−0.576477	+	0.817113i	$0.695573\pi$
$252$	14.7631	−	5.83529i	0.929989	−	0.367589i
$253$	0.0177356	−	0.0307189i	0.00111503	−	0.00193128i
$254$	2.25610	−	1.23217i	0.141560	−	0.0773132i
$255$	3.31955	+	4.80463i	0.207878	+	0.300877i
$256$	15.7129	+	3.01746i	0.982056	+	0.188592i
$257$	7.95488	+	21.8559i	0.496212	+	1.36333i	0.894909	+	0.446248i	$0.147240\pi$
$257$	7.95488	+	21.8559i	0.496212	+	1.36333i	−0.398698	+	0.917082i	$0.630538\pi$
$258$	−1.59622	−	3.70958i	−0.0993762	−	0.230949i
$259$	3.01845	−	4.31127i	0.187558	−	0.267889i
$260$	−3.67274	−	4.82424i	−0.227773	−	0.299187i
$261$	−8.27952	+	6.77228i	−0.512489	+	0.419194i
$262$	−17.0534	−	15.0128i	−1.05356	−	0.927496i
$263$	−9.79687	+	8.22055i	−0.604101	+	0.506901i	−0.892761	−	0.450531i	$-0.851235\pi$
$263$	−9.79687	+	8.22055i	−0.604101	+	0.506901i	0.288660	+	0.957432i	$0.406790\pi$
$264$	−0.0532733	−	0.0438147i	−0.00327874	−	0.00269661i
$265$	15.6771	−	5.70602i	0.963040	−	0.350518i
$266$	14.1250	−	6.18403i	0.866059	−	0.379167i
$267$	7.67936	+	7.77625i	0.469969	+	0.475899i
$268$	−12.2496	−	2.76452i	−0.748261	−	0.168870i
$269$	2.17371	−	1.25499i	0.132534	−	0.0765183i	−0.432267	−	0.901746i	$-0.642286\pi$
$269$	2.17371	−	1.25499i	0.132534	−	0.0765183i	0.564801	+	0.825227i	$0.308953\pi$
$270$	5.81012	+	9.09775i	0.353593	+	0.553671i
$271$	1.18674	+	0.685162i	0.0720890	+	0.0416206i	0.535611	−	0.844465i	$-0.320081\pi$
$271$	1.18674	+	0.685162i	0.0720890	+	0.0416206i	−0.463522	+	0.886085i	$0.653415\pi$
$272$	−0.869630	+	9.13962i	−0.0527291	+	0.554171i
$273$	−4.67762	−	8.21946i	−0.283102	−	0.497465i
$274$	−4.30666	+	11.0126i	−0.260175	+	0.665296i
$275$	−0.00694874	+	0.0394082i	−0.000419025	+	0.00237641i
$276$	−8.72218	+	0.292877i	−0.525014	+	0.0176291i
$277$	−13.6432	+	11.4480i	−0.819740	+	0.687843i	−0.952911	−	0.303250i	$-0.901928\pi$
$277$	−13.6432	+	11.4480i	−0.819740	+	0.687843i	0.133171	+	0.991093i	$0.457484\pi$
$278$	−11.6512	−	2.34059i	−0.698794	−	0.140379i
$279$	4.27129	−	1.49425i	0.255716	−	0.0894584i
$280$	2.08369	+	10.7935i	0.124524	+	0.645038i
$281$	8.54606	−	23.4801i	0.509815	−	1.40071i	−0.371613	−	0.928388i	$-0.621195\pi$
$281$	8.54606	−	23.4801i	0.509815	−	1.40071i	0.881428	−	0.472318i	$-0.156582\pi$
$282$	10.5894	−	4.55658i	0.630590	−	0.271340i
$283$	−15.7834	−	2.78304i	−0.938227	−	0.165435i	−0.316432	−	0.948615i	$-0.602485\pi$
$283$	−15.7834	−	2.78304i	−0.938227	−	0.165435i	−0.621795	+	0.783180i	$0.713596\pi$
$284$	2.90194	−	4.51717i	0.172198	−	0.268045i
$285$	5.96014	+	8.62656i	0.353048	+	0.510993i
$286$	−0.0213846	+	0.0350902i	−0.00126450	+	0.00207493i
$287$	−3.73183	−	0.999734i	−0.220283	−	0.0590124i
$288$	−2.21876	+	16.8249i	−0.130742	+	0.991416i
$289$	11.7319			0.690114
$290$	−3.55040	−	6.50077i	−0.208487	−	0.381738i
$291$	−13.1293	+	6.02240i	−0.769656	+	0.353040i
$292$	1.17035	−	1.82177i	0.0684896	−	0.106611i
$293$	−12.4088	−	2.18801i	−0.724929	−	0.127825i	−0.201006	−	0.979590i	$-0.564421\pi$
$293$	−12.4088	−	2.18801i	−0.724929	−	0.127825i	−0.523923	+	0.851765i	$0.675532\pi$
$294$	0.983414	+	17.1182i	0.0573539	+	0.998354i
$295$	6.05558	+	7.21676i	0.352570	+	0.420176i
$296$	2.45965	+	5.06015i	0.142964	+	0.294115i
$297$	0.0430828	−	0.0591300i	0.00249992	−	0.00343107i
$298$	−7.08675	−	21.0079i	−0.410525	−	1.21696i
$299$	0.902828	+	5.12019i	0.0522119	+	0.296108i
$300$	9.13337	−	3.67588i	0.527315	−	0.212227i
$301$	4.34538	−	0.380399i	0.250464	−	0.0219258i
$302$	15.0733	−	2.29070i	0.867371	−	0.131815i
$303$	27.4640	+	2.57637i	1.57777	+	0.148008i
$304$	−1.56139	+	16.4099i	−0.0895521	+	0.941173i
$305$	17.1803	+	9.91906i	0.983742	+	0.567964i
$306$	−9.73142	−	0.352952i	−0.556308	−	0.0201769i
$307$	2.98225	+	1.72180i	0.170206	+	0.0982684i	0.582683	−	0.812700i	$-0.302003\pi$
$307$	2.98225	+	1.72180i	0.170206	+	0.0982684i	−0.412477	+	0.910968i	$0.635336\pi$
$308$	0.0629849	−	0.0397948i	0.00358890	−	0.00226752i
$309$	−10.8312	+	7.48336i	−0.616167	+	0.425714i
$310$	0.470806	+	3.09800i	0.0267400	+	0.175955i
$311$	−5.23157	+	29.6697i	−0.296655	+	1.68241i	0.363743	+	0.931499i	$0.381499\pi$
$311$	−5.23157	+	29.6697i	−0.296655	+	1.68241i	−0.660398	+	0.750915i	$0.729613\pi$
$312$	10.1097	−	0.0995823i	0.572351	−	0.00563774i
$313$	−18.5157	+	15.5365i	−1.04657	+	0.878175i	−0.992729	−	0.120375i	$-0.961590\pi$
$313$	−18.5157	+	15.5365i	−1.04657	+	0.878175i	−0.0538394	+	0.998550i	$0.517146\pi$
$314$	−17.4232	−	15.3384i	−0.983247	−	0.865593i
$315$	−11.2992	+	2.87689i	−0.636636	+	0.162094i
$316$	−30.3409	+	3.87726i	−1.70681	+	0.218113i
$317$	−6.10726	+	16.7796i	−0.343018	+	0.942435i	0.641495	+	0.767127i	$0.278314\pi$
$317$	−6.10726	+	16.7796i	−0.343018	+	0.942435i	−0.984514	+	0.175308i	$0.943908\pi$
$318$	−8.00245	+	26.6431i	−0.448755	+	1.49407i
$319$	−0.0322688	+	0.0384564i	−0.00180670	+	0.00215315i
$320$	−11.1669	−	3.66134i	−0.624250	−	0.204675i
$321$	−6.14152	−	23.5090i	−0.342786	−	1.31214i
$322$	2.65448	−	9.04487i	0.147928	−	0.504051i
$323$	−9.45864			−0.526293
$324$	−17.9527	−	1.30398i	−0.997373	−	0.0724434i
$325$	−2.93268	−	5.07956i	−0.162676	−	0.281763i
$326$	18.4527	+	11.2454i	1.02200	+	0.622825i
$327$	10.4695	+	2.87577i	0.578967	+	0.159030i
$328$	2.87302	−	2.96716i	0.158636	−	0.163834i
$329$	1.08589	+	12.4044i	0.0598670	+	0.683875i
$330$	0.0347337	+	0.0368818i	0.00191203	+	0.00203027i
$331$	−9.80826	+	26.9480i	−0.539111	+	1.48119i	0.308838	+	0.951115i	$0.400060\pi$
$331$	−9.80826	+	26.9480i	−0.539111	+	1.48119i	−0.847948	+	0.530079i	$0.822162\pi$
$332$	−26.8245	+	20.4217i	−1.47218	+	1.12079i
$333$	−5.20507	+	2.91876i	−0.285236	+	0.159947i
$334$	−3.34750	+	1.12924i	−0.183167	+	0.0617892i
$335$	8.66721	+	3.15461i	0.473540	+	0.172355i
$336$	−16.5043	−	7.97547i	−0.900383	−	0.435098i
$337$	−6.35241	−	5.33030i	−0.346038	−	0.290360i	0.453159	−	0.891430i	$-0.350297\pi$
$337$	−6.35241	−	5.33030i	−0.346038	−	0.290360i	−0.799197	+	0.601070i	$0.794741\pi$
$338$	1.85728	+	12.2213i	0.101023	+	0.664750i
$339$	−14.3897	−	6.82016i	−0.781540	−	0.370420i
$340$	1.48451	−	6.57784i	0.0805088	−	0.356733i
$341$	0.0183923	−	0.0106188i	0.000995998	−	0.000575040i
$342$	−17.4725	−	0.633715i	−0.944803	−	0.0342674i
$343$	−17.8899	−	4.79062i	−0.965966	−	0.258669i
$344$	−1.90237	+	4.25749i	−0.102569	+	0.229548i
$345$	6.38194	+	0.598683i	0.343592	+	0.0322320i
$346$	2.25338	+	2.81861i	0.121143	+	0.151529i
$347$	15.3166	−	5.57480i	0.822241	−	0.299271i	0.103570	−	0.994622i	$-0.466973\pi$
$347$	15.3166	−	5.57480i	0.822241	−	0.299271i	0.718670	+	0.695351i	$0.244751\pi$
$348$	12.2287	+	1.73535i	0.655526	+	0.0930247i
$349$	−25.0726	+	21.0384i	−1.34210	+	1.12616i	−0.361025	+	0.932556i	$0.617573\pi$
$349$	−25.0726	+	21.0384i	−1.34210	+	1.12616i	−0.981080	+	0.193604i	$0.937982\pi$
$350$	0.675902	+	10.6127i	0.0361285	+	0.567271i
$351$	0.733561	+	10.6984i	0.0391546	+	0.571038i
$352$	0.00445419	+	0.0795227i	0.000237409	+	0.00423857i
$353$	9.41981	−	25.8807i	0.501366	−	1.37749i	−0.388576	−	0.921417i	$-0.627033\pi$
$353$	9.41981	−	25.8807i	0.501366	−	1.37749i	0.889942	−	0.456074i	$-0.150745\pi$
$354$	−15.6832	+	0.899347i	−0.833555	+	0.0477998i
$355$	−2.53481	+	3.02087i	−0.134534	+	0.160331i
$356$	0.598352	−	12.6055i	0.0317126	−	0.668090i
$357$	3.65876	−	9.86117i	0.193642	−	0.521909i
$358$	7.98567	+	0.189423i	0.422056	+	0.0100113i
$359$	8.18813			0.432153			0.216077	−	0.976376i	$-0.430674\pi$
$359$	8.18813			0.432153			0.216077	+	0.976376i	$0.430674\pi$
$360$	3.18296	−	12.0515i	0.167757	−	0.635167i
$361$	2.01730			0.106174
$362$	−13.0384	−	23.8733i	−0.685283	−	1.25475i
$363$	−8.15990	+	17.2164i	−0.428284	+	0.903624i
$364$	−3.32280	+	10.4025i	−0.174162	+	0.545239i
$365$	−1.02229	+	1.21832i	−0.0535091	+	0.0637696i
$366$	−30.3860	+	13.0749i	−1.58830	+	0.683439i
$367$	17.5857	−	3.10084i	0.917968	−	0.161863i	0.305349	−	0.952241i	$-0.401227\pi$
$367$	17.5857	−	3.10084i	0.917968	−	0.161863i	0.612620	+	0.790378i	$0.290116\pi$
$368$	7.07130	+	7.17957i	0.368617	+	0.374261i
$369$	3.32025	+	2.85772i	0.172845	+	0.148767i
$370$	−1.32090	−	3.91565i	−0.0686701	−	0.203565i
$371$	−24.6147	−	17.2335i	−1.27793	−	0.894720i
$372$	−4.61025	−	2.45925i	−0.239030	−	0.127506i
$373$	0.529704	−	3.00410i	0.0274270	−	0.155547i	−0.968018	−	0.250879i	$-0.919280\pi$
$373$	0.529704	−	3.00410i	0.0274270	−	0.155547i	0.995445	+	0.0953326i	$0.0303915\pi$
$374$	−0.0451833	+	0.00686656i	−0.00233638	+	0.000355061i
$375$	−19.3051	+	5.04330i	−0.996913	+	0.260435i
$376$	−12.1535	−	5.43052i	−0.626767	−	0.280058i
$377$		−	7.35824i		−	0.378969i
$378$	7.41932	−	17.9709i	0.381609	−	0.924324i
$379$		−	29.6655i		−	1.52381i	−0.647687	−	0.761907i	$-0.724263\pi$
$379$		−	29.6655i		−	1.52381i	0.647687	−	0.761907i	$-0.275737\pi$
$380$	2.66539	−	11.8103i	0.136732	−	0.605856i
$381$	0.833911	−	3.03594i	0.0427225	−	0.155536i
$382$	−3.38225	−	22.2559i	−0.173051	−	1.13871i
$383$	−4.57086	+	25.9226i	−0.233560	+	1.32458i	0.612066	+	0.790807i	$0.290339\pi$
$383$	−4.57086	+	25.9226i	−0.233560	+	1.32458i	−0.845625	+	0.533777i	$0.820772\pi$
$384$	16.0267	−	11.2759i	0.817858	−	0.575420i
$385$	−0.0495936	+	0.0231290i	−0.00252753	+	0.00117876i
$386$	−36.1891	+	12.2079i	−1.84198	+	0.621368i
$387$	−4.62619	−	1.74978i	−0.235162	−	0.0889465i
$388$	15.3853	+	6.44138i	0.781070	+	0.327011i
$389$	29.3499	−	5.17518i	1.48810	−	0.262392i	0.630290	−	0.776360i	$-0.282936\pi$
$389$	29.3499	−	5.17518i	1.48810	−	0.262392i	0.857810	+	0.513968i	$0.171825\pi$
$390$	−7.37487	−	0.868697i	−0.373441	−	0.0439882i
$391$	−3.71682	+	4.42954i	−0.187968	+	0.224011i
$392$	13.7711	−	14.2253i	0.695543	−	0.718484i
$393$	−27.7351	+	2.25141i	−1.39905	+	0.113568i
$394$	−18.5363	+	10.1236i	−0.933844	+	0.510019i
$395$	22.4663			1.13040
$396$	−0.0839249	+	0.00965702i	−0.00421739	+	0.000485284i
$397$	−11.2167			−0.562951			−0.281476	−	0.959568i	$-0.590824\pi$
$397$	−11.2167			−0.562951			−0.281476	+	0.959568i	$0.590824\pi$
$398$	0.262558	−	11.0689i	0.0131608	−	0.554831i
$399$	6.56919	−	17.7054i	0.328871	−	0.886380i
$400$	−10.2665	−	4.88263i	−0.513324	−	0.244132i
$401$	−15.4507	+	18.4134i	−0.771569	+	0.919520i	−0.998520	−	0.0543860i	$-0.982680\pi$
$401$	−15.4507	+	18.4134i	−0.771569	+	0.919520i	0.226951	+	0.973906i	$0.427124\pi$
$402$	−12.8573	+	8.43988i	−0.641263	+	0.420943i
$403$	−1.06467	+	2.92516i	−0.0530351	+	0.145713i
$404$	−19.2941	−	25.3433i	−0.959917	−	1.26088i
$405$	12.9583	+	2.62149i	0.643903	+	0.130263i
$406$	−5.92259	+	11.9541i	−0.293933	+	0.593272i
$407$	−0.0214549	+	0.0180028i	−0.00106348	+	0.000892365i
$408$	7.31216	+	8.54200i	0.362006	+	0.422892i
$409$	33.1563	−	12.0679i	1.63947	−	0.596719i	0.652525	−	0.757767i	$-0.273710\pi$
$409$	33.1563	−	12.0679i	1.63947	−	0.596719i	0.986947	+	0.161048i	$0.0514875\pi$
$410$	−2.36943	+	1.89428i	−0.117018	+	0.0935520i
$411$	6.03809	+	13.1635i	0.297837	+	0.649309i
$412$	14.8286	+	3.34658i	0.730555	+	0.164874i
$413$	4.39070	−	16.3897i	0.216052	−	0.806486i
$414$	−7.16267	+	7.93344i	−0.352026	+	0.389907i
$415$	21.4447	−	12.3811i	1.05268	−	0.607764i
$416$	−7.99248	−	8.50937i	−0.391863	−	0.417206i
$417$	−11.9748	+	8.27343i	−0.586406	+	0.405152i
$418$	−0.0811253	+	0.0123287i	−0.00396797	+	0.000603016i
$419$	18.8532	+	15.8197i	0.921037	+	0.772842i	0.974186	−	0.225745i	$-0.0724816\pi$
$419$	18.8532	+	15.8197i	0.921037	+	0.772842i	−0.0531496	+	0.998587i	$0.516926\pi$
$420$	11.2819	+	7.34725i	0.550501	+	0.358509i
$421$	−1.18052	−	0.429673i	−0.0575349	−	0.0209410i	0.313092	−	0.949723i	$-0.398635\pi$
$421$	−1.18052	−	0.429673i	−0.0575349	−	0.0209410i	−0.370627	+	0.928782i	$0.620857\pi$
$422$	9.13686	+	27.0852i	0.444776	+	1.31849i
$423$	4.99495	−	13.2060i	0.242863	−	0.642096i
$424$	28.8904	−	14.0431i	1.40304	−	0.681992i
$425$	2.23109	−	6.12986i	0.108224	−	0.297342i
$426$	−1.51071	−	6.39975i	−0.0731943	−	0.310069i
$427$	−3.11592	−	35.5939i	−0.150790	−	1.72251i
$428$	−15.1647	+	23.6055i	−0.733015	+	1.14101i
$429$	0.0127209	+	0.0486941i	0.000614172	+	0.00235097i
$430$	1.78239	−	2.92474i	0.0859542	−	0.141043i
$431$	5.59958	+	9.69877i	0.269723	+	0.467173i	0.968790	−	0.247882i	$-0.0797347\pi$
$431$	5.59958	+	9.69877i	0.269723	+	0.467173i	−0.699068	+	0.715056i	$0.746401\pi$
$432$	12.9351	+	16.2691i	0.622340	+	0.782747i
$433$	−2.01067			−0.0966267			−0.0483133	−	0.998832i	$-0.515385\pi$
$433$	−2.01067			−0.0966267			−0.0483133	+	0.998832i	$0.515385\pi$
$434$	4.08409	−	3.89523i	0.196043	−	0.186977i
$435$	−8.74782	−	2.40285i	−0.419426	−	0.115208i
$436$	−5.74663	−	11.1423i	−0.275214	−	0.533620i
$437$	−6.67344	+	7.95310i	−0.319234	+	0.380448i
$438$	−0.609271	−	2.58102i	−0.0291121	−	0.123326i
$439$	−0.994634	+	2.73274i	−0.0474713	+	0.130426i	−0.961163	−	0.275982i	$-0.910997\pi$
$439$	−0.994634	+	2.73274i	−0.0474713	+	0.130426i	0.913691	+	0.406409i	$0.133219\pi$
$440$	0.00415865	−	0.0583521i	0.000198256	−	0.00278183i
$441$	15.9179	+	13.6975i	0.757993	+	0.652263i
$442$	4.42637	−	5.02801i	0.210541	−	0.239158i
$443$	26.5761	−	22.3000i	1.26267	−	1.05950i	0.267275	−	0.963620i	$-0.413877\pi$
$443$	26.5761	−	22.3000i	1.26267	−	1.05950i	0.995393	−	0.0958831i	$-0.0305675\pi$
$444$	6.55064	+	2.13815i	0.310880	+	0.101472i
$445$	−1.60955	+	9.12822i	−0.0763000	+	0.432719i
$446$	−0.325231	+	0.0494257i	−0.0154001	+	0.00234037i
$447$	−24.5373	−	11.6298i	−1.16058	−	0.550069i
$448$	6.13534	+	20.2573i	0.289867	+	0.957067i
$449$	3.34104	+	1.92895i	0.157673	+	0.0910327i	0.576761	−	0.816913i	$-0.304317\pi$
$449$	3.34104	+	1.92895i	0.157673	+	0.0910327i	−0.419087	+	0.907946i	$0.637650\pi$
$450$	4.53207	−	11.1739i	0.213644	−	0.526743i
$451$	0.0178053	+	0.0102799i	0.000838420	+	0.000484062i
$452$	5.46260	+	17.5574i	0.256939	+	0.825832i
$453$	10.8060	−	15.2285i	0.507711	−	0.715498i
$454$	2.16811	+	14.2666i	0.101754	+	0.669564i
$455$	3.38938	−	7.26953i	0.158897	−	0.340801i
$456$	13.1288	+	15.3369i	0.614811	+	0.718216i
$457$	1.64684	+	9.33971i	0.0770361	+	0.436893i	0.998793	+	0.0491244i	$0.0156431\pi$
$457$	1.64684	+	9.33971i	0.0770361	+	0.436893i	−0.921757	+	0.387769i	$0.873246\pi$
$458$	17.6894	−	5.96731i	0.826573	−	0.278834i
$459$	−8.59029	+	8.27312i	−0.400961	+	0.386156i
$460$	−4.48346	−	5.88915i	−0.209042	−	0.274583i
$461$	−13.2333	−	15.7709i	−0.616338	−	0.734523i	0.364098	−	0.931361i	$-0.381377\pi$
$461$	−13.2333	−	15.7709i	−0.616338	−	0.734523i	−0.980436	+	0.196838i	$0.936933\pi$
$462$	0.0185273	−	0.0893467i	0.000861966	−	0.00415679i
$463$	−33.1622	−	5.84739i	−1.54118	−	0.271751i	−0.662462	−	0.749095i	$-0.730489\pi$
$463$	−33.1622	−	5.84739i	−1.54118	−	0.271751i	−0.878717	+	0.477344i	$0.841600\pi$
$464$	−8.09132	−	11.7445i	−0.375630	−	0.545225i
$465$	3.12990	+	2.22095i	0.145146	+	0.102994i
$466$	−7.89036	+	4.30932i	−0.365514	+	0.199625i
$467$	17.7935			0.823385			0.411692	−	0.911323i	$-0.364938\pi$
$467$	17.7935			0.823385			0.411692	+	0.911323i	$0.364938\pi$
$468$	8.51348	−	8.99143i	0.393536	−	0.415629i
$469$	−4.30038	−	16.0459i	−0.198573	−	0.740932i
$470$	8.34898	+	5.08801i	0.385110	+	0.234692i
$471$	−28.3365	+	2.30022i	−1.30568	+	0.105989i
$472$	13.0314	+	12.6179i	0.599819	+	0.580788i
$473$	−0.0228604	−	0.00403091i	−0.00105112	−	0.000185342i
$474$	−22.3977	+	30.0291i	−1.02876	+	1.37928i
$475$	4.00585	−	11.0060i	0.183801	−	0.504989i
$476$	−11.2380	+	4.60569i	−0.515094	+	0.211101i
$477$	16.6643	+	29.7178i	0.763007	+	1.36068i
$478$	1.29627	−	6.45272i	0.0592900	−	0.295140i
$479$	−0.672399	+	0.564210i	−0.0307227	+	0.0257794i	−0.658020	−	0.753001i	$-0.728606\pi$
$479$	−0.672399	+	0.564210i	−0.0307227	+	0.0257794i	0.627297	+	0.778780i	$0.284161\pi$
$480$	−12.7263	+	6.72308i	−0.580873	+	0.306865i
$481$	0.712856	−	4.04281i	0.0325035	−	0.184336i
$482$	18.0802	+	7.07056i	0.823530	+	0.322055i
$483$	−5.71016	−	10.0338i	−0.259821	−	0.456555i
$484$	21.0064	−	6.53566i	0.954835	−	0.297075i
$485$	−10.6095	−	6.12538i	−0.481751	−	0.278139i
$486$	−16.4227	+	14.7070i	−0.744949	+	0.667122i
$487$	8.46367	−	4.88651i	0.383526	−	0.221429i	−0.295825	−	0.955242i	$-0.595595\pi$
$487$	8.46367	−	4.88651i	0.383526	−	0.221429i	0.679351	+	0.733813i	$0.262261\pi$
$488$	34.8740	+	15.5827i	1.57867	+	0.705396i
$489$	25.6065	−	6.68949i	1.15797	−	0.302509i
$490$	−11.3575	+	9.08189i	−0.513081	+	0.410278i
$491$	3.82043	−	1.39052i	0.172414	−	0.0627535i	−0.254371	−	0.967107i	$-0.581868\pi$
$491$	3.82043	−	1.39052i	0.172414	−	0.0627535i	0.426785	+	0.904353i	$0.359646\pi$
$492$	−0.169757	−	5.05556i	−0.00765326	−	0.227922i
$493$	6.26899	−	5.26031i	0.282341	−	0.236912i
$494$	7.94742	−	9.02764i	0.357571	−	0.406173i
$495$	0.0620439		0.000777915i	0.00278866		3.49647e-5i
$496$	1.51726	+	5.83960i	0.0681271	+	0.262206i
$497$	7.07551	+	0.618657i	0.317380	+	0.0277506i
$498$	−4.83026	+	41.0069i	−0.216449	+	1.83756i
$499$	−12.1489	−	33.3788i	−0.543859	−	1.49424i	−0.841872	−	0.539678i	$-0.818546\pi$
$499$	−12.1489	−	33.3788i	−0.543859	−	1.49424i	0.298013	−	0.954562i	$-0.403676\pi$
$500$	19.3844	+	12.4530i	0.866895	+	0.556914i
$501$	−1.85314	+	3.90990i	−0.0827923	+	0.174681i
$502$	−9.00826	−	16.4941i	−0.402058	−	0.736168i
$503$	0.978093	−	1.69411i	0.0436110	−	0.0755365i	−0.843396	−	0.537293i	$-0.819447\pi$
$503$	0.978093	−	1.69411i	0.0436110	−	0.0755365i	0.887007	+	0.461756i	$0.152780\pi$
$504$	−21.0680	+	7.75492i	−0.938444	+	0.345432i
$505$	11.6974	+	20.2606i	0.520530	+	0.901584i
$506$	−0.0261050	+	0.0428361i	−0.00116051	+	0.00190430i
$507$	12.3471	+	8.76140i	0.548355	+	0.389108i
$508$	−3.23103	+	1.66640i	−0.143354	+	0.0739345i
$509$	16.6573	−	19.8514i	0.738321	−	0.879896i	−0.257952	−	0.966158i	$-0.583048\pi$
$509$	16.6573	−	19.8514i	0.738321	−	0.879896i	0.996273	+	0.0862615i	$0.0274921\pi$
$510$	−4.53210	−	6.90418i	−0.200685	−	0.305722i
$511$	2.85355	+	0.249505i	0.126234	+	0.0110374i
$512$	−22.1139	−	4.79309i	−0.977307	−	0.211827i
$513$	−15.4236	+	14.8541i	−0.680969	+	0.655826i
$514$	−10.5138	−	31.1669i	−0.463743	−	1.37471i
$515$	−10.4921	−	3.81879i	−0.462335	−	0.168276i
$516$	2.13235	+	5.29820i	0.0938716	+	0.233240i
$517$	0.0115067	−	0.0652576i	0.000506063	−	0.00287002i
$518$	−4.41212	+	5.99412i	−0.193857	+	0.263366i
$519$	4.40034	+	0.412792i	0.193154	+	0.0181195i
$520$	5.03079	+	6.94375i	0.220615	+	0.304504i
$521$	−25.4075	−	14.6690i	−1.11312	−	0.642661i	−0.173485	−	0.984837i	$-0.555503\pi$
$521$	−25.4075	−	14.6690i	−1.11312	−	0.642661i	−0.939636	+	0.342176i	$0.888836\pi$
$522$	11.9328	−	9.29709i	0.522286	−	0.406923i
$523$	−17.1690	+	9.91255i	−0.750750	+	0.433446i	−0.825965	−	0.563722i	$-0.809369\pi$
$523$	−17.1690	+	9.91255i	−0.750750	+	0.433446i	0.0752150	+	0.997167i	$0.476036\pi$
$524$	23.6069	+	21.7973i	1.03127	+	0.952219i
$525$	9.92483	+	8.43362i	0.433155	+	0.368073i
$526$	14.1267	−	11.2938i	0.615951	−	0.492433i
$527$	−3.25327	+	1.18409i	−0.141715	+	0.0515799i
$528$	0.0738492	+	0.0637325i	0.00321387	+	0.00277360i
$529$	−2.89179	−	16.4002i	−0.125730	−	0.713050i
$530$	−22.3560	+	7.54150i	−0.971081	+	0.327582i
$531$	−12.5507	+	14.5821i	−0.544655	+	0.632810i
$532$	−20.1775	+	8.26937i	−0.874807	+	0.358523i
$533$	−2.96777	+	0.523298i	−0.128548	+	0.0226665i
$534$	−10.5964	−	11.2517i	−0.458552	−	0.486909i
$535$	13.2462	−	15.7862i	0.572684	−	0.682499i
$536$	17.2259	+	4.31933i	0.744046	+	0.186567i
$537$	6.96096	−	6.87423i	0.300388	−	0.296645i
$538$	−3.11532	+	1.70143i	−0.134311	+	0.0733539i
$539$	0.0853593	+	0.0492704i	0.00367668	+	0.00212223i
$540$	−7.90934	−	13.0574i	−0.340364	−	0.561901i
$541$	10.8950	−	18.8706i	0.468411	−	0.811311i	−0.530938	−	0.847411i	$-0.678160\pi$
$541$	10.8950	−	18.8706i	0.468411	−	0.811311i	0.999348	+	0.0360999i	$0.0114934\pi$
$542$	−1.65485	−	1.00849i	−0.0710818	−	0.0433184i
$543$	−32.1253	−	8.82415i	−1.37863	−	0.378681i
$544$	1.53601	−	12.8926i	0.0658557	−	0.552765i
$545$	3.14941	+	8.65293i	0.134906	+	0.370651i
$546$	6.33764	+	11.7777i	0.271226	+	0.504038i
$547$	27.4910	−	4.84741i	1.17543	−	0.207260i	0.448379	−	0.893843i	$-0.352001\pi$
$547$	27.4910	−	4.84741i	1.17543	−	0.207260i	0.727051	+	0.686583i	$0.240890\pi$
$548$	6.45815	−	15.4254i	0.275879	−	0.658939i
$549$	−14.3328	+	37.8941i	−0.611711	+	1.61728i
$550$	0.0111458	−	0.0554830i	0.000475260	−	0.00236580i
$551$	11.2558	−	9.44473i	0.479513	−	0.402359i
$552$	12.3414	−	0.121564i	0.525284	−	0.00517412i
$553$	−23.2107	−	33.1447i	−0.987020	−	1.40946i
$554$	19.6729	−	15.7278i	0.835820	−	0.668211i
$555$	−4.57350	−	2.16766i	−0.194134	−	0.0920122i
$556$	16.3942	+	3.69990i	0.695269	+	0.156911i
$557$			36.0423i			1.52716i	0.645712	+	0.763581i	$0.276561\pi$
$557$			36.0423i			1.52716i	−0.645712	+	0.763581i	$0.723439\pi$
$558$	−6.08893	+	1.96935i	−0.257765	+	0.0833693i
$559$	2.94661	−	1.70123i	0.124628	−	0.0719543i
$560$	−2.58397	−	15.3300i	−0.109193	−	0.647809i
$561$	−0.0323918	+	0.0456486i	−0.00136758	+	0.00192729i
$562$	−12.8700	+	32.9099i	−0.542888	+	1.38822i
$563$	−15.1265	+	5.50559i	−0.637505	+	0.232033i	−0.640495	−	0.767963i	$-0.721271\pi$
$563$	−15.1265	+	5.50559i	−0.637505	+	0.232033i	0.00298946	+	0.999996i	$0.499048\pi$
$564$	−15.1243	+	6.08703i	−0.636847	+	0.256310i
$565$	−2.34520	−	13.3003i	−0.0986635	−	0.559548i
$566$	22.2215	+	4.46403i	0.934040	+	0.187637i
$567$	−9.52017	−	21.8258i	−0.399810	−	0.916598i
$568$	−4.25429	+	6.28912i	−0.178506	+	0.263886i
$569$	−4.38145	+	0.772568i	−0.183680	+	0.0323877i	−0.264731	−	0.964322i	$-0.585283\pi$
$569$	−4.38145	+	0.772568i	−0.183680	+	0.0323877i	0.0810514	+	0.996710i	$0.474172\pi$
$570$	−8.13724	−	12.3963i	−0.340832	−	0.519222i
$571$	3.77568	+	10.3736i	0.158007	+	0.434122i	0.993283	−	0.115709i	$-0.0369142\pi$
$571$	3.77568	+	10.3736i	0.158007	+	0.434122i	−0.835276	+	0.549831i	$0.814692\pi$
$572$	0.0314107	−	0.0488940i	0.00131335	−	0.00204436i
$573$	−22.4851	−	15.9552i	−0.939329	−	0.666539i
$574$	5.24259	+	1.53859i	0.218822	+	0.0642196i
$575$	−3.58005	−	6.20082i	−0.149298	−	0.258592i
$576$	3.70117	−	23.7129i	0.154215	−	0.988037i
$577$	12.0318			0.500891			0.250445	−	0.968131i	$-0.419423\pi$
$577$	12.0318			0.500891			0.250445	+	0.968131i	$0.419423\pi$
$578$	−16.5868	−	0.393446i	−0.689920	−	0.0163652i
$579$	−20.0339	+	42.2690i	−0.832581	+	1.75664i
$580$	4.80160	+	9.30996i	0.199376	+	0.386575i
$581$	−40.4212	−	18.8461i	−1.67695	−	0.781870i
$582$	18.7644	−	8.07426i	0.777811	−	0.334689i
$583$	0.102785	+	0.122494i	0.00425692	+	0.00507319i
$584$	−1.71576	+	2.53640i	−0.0709985	+	0.104957i
$585$	−7.03975	+	5.75821i	−0.291058	+	0.238073i
$586$	17.4704	+	3.50958i	0.721694	+	0.144979i
$587$	−1.78020	−	10.0960i	−0.0734766	−	0.416707i	−0.999253	−	0.0386359i	$-0.987699\pi$
$587$	−1.78020	−	10.0960i	−0.0734766	−	0.416707i	0.925777	−	0.378071i	$-0.123412\pi$
$588$	−0.816285	−	24.2350i	−0.0336630	−	0.999433i
$589$	−5.84115	+	2.12600i	−0.240680	+	0.0876005i
$590$	−8.31946	−	10.4063i	−0.342507	−	0.428419i
$591$	−6.85146	+	24.9435i	−0.281832	+	1.02604i
$592$	−3.30779	−	7.23661i	−0.135949	−	0.297423i
$593$	4.49719	+	2.59645i	0.184677	+	0.106623i	0.589488	−	0.807777i	$-0.299329\pi$
$593$	4.49719	+	2.59645i	0.184677	+	0.106623i	−0.404811	+	0.914400i	$0.632663\pi$
$594$	−0.0628942	+	0.0821541i	−0.00258058	+	0.00337083i
$595$	8.61644	−	2.30925i	0.353239	−	0.0946698i
$596$	9.31484	+	29.9390i	0.381551	+	1.22635i
$597$	−9.52831	−	9.64852i	−0.389968	−	0.394888i
$598$	−1.10472	−	7.26928i	−0.0451754	−	0.297263i
$599$	−7.79658	−	6.54211i	−0.318560	−	0.267303i	0.469459	−	0.882954i	$-0.344449\pi$
$599$	−7.79658	−	6.54211i	−0.318560	−	0.267303i	−0.788019	+	0.615651i	$0.788893\pi$
$600$	−13.0362	+	4.89072i	−0.532200	+	0.199663i
$601$	2.98466	+	16.9268i	0.121747	+	0.690460i	0.983187	+	0.182601i	$0.0584517\pi$
$601$	2.98466	+	16.9268i	0.121747	+	0.690460i	−0.861440	+	0.507859i	$0.830437\pi$
$602$	−6.15633	+	0.392086i	−0.250913	+	0.0159802i
$603$	−3.50323	+	18.5078i	−0.142663	+	0.753697i
$604$	−21.3877	+	2.73313i	−0.870253	+	0.111210i
$605$	−15.9130	+	2.80589i	−0.646955	+	0.114076i
$606$	−38.7426	−	4.56355i	−1.57381	−	0.185382i
$607$	12.7355	+	34.9905i	0.516918	+	1.42022i	0.873898	+	0.486109i	$0.161584\pi$
$607$	12.7355	+	34.9905i	0.516918	+	1.42022i	−0.356980	+	0.934112i	$0.616194\pi$
$608$	2.75785	−	23.1482i	0.111846	−	0.938785i
$609$	5.49274	+	15.3882i	0.222577	+	0.623561i
$610$	−23.9571	−	14.5999i	−0.969996	−	0.591132i
$611$	4.85634	+	8.41142i	0.196466	+	0.340290i
$612$	13.7466	+	0.825365i	0.555673	+	0.0333634i
$613$	−12.2229	+	21.1707i	−0.493678	+	0.855075i	−0.999973	−	0.00728476i	$-0.997681\pi$
$613$	−12.2229	+	21.1707i	−0.493678	+	0.855075i	0.506296	+	0.862360i	$0.331015\pi$
$614$	−4.15861	−	2.53432i	−0.167828	−	0.102277i
$615$	−0.347009	+	3.69910i	−0.0139928	+	0.149162i
$616$	−0.0903837	+	0.0541503i	−0.00364166	+	0.00218178i
$617$	7.81316	+	1.37767i	0.314546	+	0.0554630i	0.328693	−	0.944437i	$-0.393392\pi$
$617$	7.81316	+	1.37767i	0.314546	+	0.0554630i	−0.0141465	+	0.999900i	$0.504503\pi$
$618$	15.5643	−	10.2169i	0.626089	−	0.410982i
$619$	10.8286	−	29.7514i	0.435240	−	1.19581i	−0.507315	−	0.861760i	$-0.669362\pi$
$619$	10.8286	−	29.7514i	0.435240	−	1.19581i	0.942555	−	0.334051i	$-0.108416\pi$
$620$	−0.561738	−	4.39579i	−0.0225599	−	0.176539i
$621$	0.895488	+	13.0600i	0.0359347	+	0.524079i
$622$	8.39149	−	41.7721i	0.336468	−	1.67491i
$623$	15.1298	−	7.05609i	0.606163	−	0.282696i
$624$	−14.2967	−	0.198252i	−0.572324	−	0.00793644i
$625$	−2.07748	−	1.74321i	−0.0830991	−	0.0697285i
$626$	26.6988	−	21.3448i	1.06710	−	0.853110i
$627$	−0.0581586	+	0.0819607i	−0.00232263	+	0.00327319i
$628$	24.1188	+	22.2699i	0.962444	+	0.888667i
$629$	3.95396	−	2.28282i	0.157655	−	0.0910220i
$630$	16.0714	−	3.68846i	0.640301	−	0.146952i
$631$	−0.620013	−	0.357965i	−0.0246823	−	0.0142504i	0.487608	−	0.873063i	$-0.337870\pi$
$631$	−0.620013	−	0.357965i	−0.0246823	−	0.0142504i	−0.512290	+	0.858812i	$0.671203\pi$
$632$	43.0265	−	4.46421i	1.71150	−	0.177577i
$633$	31.6357	+	14.9941i	1.25740	+	0.595962i
$634$	9.19727	−	23.5184i	0.365270	−	0.934035i
$635$	2.50916	−	0.913261i	0.0995731	−	0.0362416i
$636$	12.2075	−	37.4001i	0.484059	−	1.48301i
$637$	−14.2265	+	2.51003i	−0.563673	+	0.0994510i
$638$	0.0469118	−	0.0532881i	0.00185725	−	0.00210970i
$639$	−6.92349	−	4.11386i	−0.273889	−	0.162742i
$640$	15.6652	+	5.55096i	0.619221	+	0.219421i
$641$	12.5158	+	14.9157i	0.494343	+	0.589136i	0.954317	−	0.298797i	$-0.0965854\pi$
$641$	12.5158	+	14.9157i	0.494343	+	0.589136i	−0.459973	+	0.887933i	$0.652141\pi$
$642$	7.89458	+	33.4433i	0.311574	+	1.31990i
$643$	8.30696	+	22.8232i	0.327595	+	0.900059i	0.988719	+	0.149782i	$0.0478573\pi$
$643$	8.30696	+	22.8232i	0.327595	+	0.900059i	−0.661124	+	0.750276i	$0.729920\pi$
$644$	−4.05628	+	12.6988i	−0.159840	+	0.500401i
$645$	−1.06028	−	4.05861i	−0.0417484	−	0.159808i
$646$	13.3728	+	0.317208i	0.526145	+	0.0124804i
$647$	−2.58052	−	4.46959i	−0.101451	−	0.175718i	0.810832	−	0.585279i	$-0.199015\pi$
$647$	−2.58052	−	4.46959i	−0.101451	−	0.175718i	−0.912282	+	0.409562i	$0.865682\pi$
$648$	25.3381	+	2.44566i	0.995374	+	0.0960745i
$649$	−0.0451481	+	0.0781987i	−0.00177222	+	0.00306957i
$650$	3.97592	+	7.27991i	0.155949	+	0.285541i
$651$	0.0429727	−	6.91210i	0.00168423	−	0.270907i
$652$	−25.7116	−	16.5178i	−1.00695	−	0.646886i
$653$	−28.1983	−	4.97212i	−1.10349	−	0.194574i	−0.407906	−	0.913024i	$-0.633741\pi$
$653$	−28.1983	−	4.97212i	−1.10349	−	0.194574i	−0.695579	+	0.718450i	$0.744852\pi$
$654$	−14.7056	−	4.41691i	−0.575033	−	0.172715i
$655$	−15.1698	−	18.0786i	−0.592731	−	0.706390i
$656$	−4.16143	+	4.09867i	−0.162477	+	0.160026i
$657$	−2.79224	−	1.65912i	−0.108936	−	0.0647285i
$658$	−1.11925	−	17.5739i	−0.0436329	−	0.685102i
$659$	38.1436	+	13.8831i	1.48587	+	0.540811i	0.952357	−	0.304985i	$-0.0986513\pi$
$659$	38.1436	+	13.8831i	1.48587	+	0.540811i	0.533508	+	0.845795i	$0.320874\pi$
$660$	−0.0478702	−	0.0533089i	−0.00186335	−	0.00207504i
$661$	3.19929	−	18.1441i	0.124438	−	0.705724i	−0.857202	−	0.514981i	$-0.827799\pi$
$661$	3.19929	−	18.1441i	0.124438	−	0.705724i	0.981640	−	0.190743i	$-0.0610898\pi$
$662$	14.7708	−	37.7705i	0.574084	−	1.46799i
$663$	−0.663803	−	8.17740i	−0.0257800	−	0.317584i
$664$	38.6097	−	27.9729i	1.49835	−	1.08556i
$665$	15.4705	−	4.14618i	0.599922	−	0.160782i
$666$	7.45689	−	3.95203i	0.288949	−	0.153138i
$667$		−	8.98251i		−	0.347804i
$668$	4.77062	−	1.48427i	0.184581	−	0.0574282i
$669$	−0.233158	+	0.328580i	−0.00901439	+	0.0127036i
$670$	−12.1480	−	4.75070i	−0.469320	−	0.183536i
$671$	−0.0330180	+	0.187255i	−0.00127465	+	0.00722888i
$672$	23.0666	+	11.8293i	0.889812	+	0.456327i
$673$	−11.9624	+	10.0377i	−0.461118	+	0.386924i	−0.843542	−	0.537063i	$-0.819534\pi$
$673$	−11.9624	+	10.0377i	−0.461118	+	0.386924i	0.382424	+	0.923987i	$0.375089\pi$
$674$	8.80238	+	7.74911i	0.339055	+	0.298484i
$675$	−5.98842	−	13.4993i	−0.230495	−	0.519590i
$676$	−2.21599	−	17.3409i	−0.0852305	−	0.666958i
$677$	43.7772	−	7.71910i	1.68249	−	0.296669i	0.750966	−	0.660341i	$-0.229588\pi$
$677$	43.7772	−	7.71910i	1.68249	−	0.296669i	0.931527	+	0.363672i	$0.118477\pi$
$678$	20.1156	+	10.1250i	0.772536	+	0.388849i
$679$	1.92420	+	21.9806i	0.0738439	+	0.843537i
$680$	−2.31942	+	9.25007i	−0.0889457	+	0.354724i
$681$	14.4135	+	10.2277i	0.552326	+	0.391926i
$682$	−0.0263594	+	0.0143962i	−0.00100935	+	0.000551259i
$683$	−4.39140	+	7.60612i	−0.168032	+	0.291040i	−0.937728	−	0.347371i	$-0.887075\pi$
$683$	−4.39140	+	7.60612i	−0.168032	+	0.291040i	0.769696	+	0.638411i	$0.220408\pi$
$684$	24.6816	+	1.48192i	0.943724	+	0.0566626i
$685$	−6.14133	+	10.6371i	−0.234648	+	0.406423i
$686$	25.1324	+	7.37301i	0.959560	+	0.281503i
$687$	9.79268	−	20.6613i	0.373614	−	0.788279i
$688$	2.83238	−	5.95551i	0.107983	−	0.227052i
$689$	−23.0820	−	4.06997i	−0.879353	−	0.155054i
$690$	−9.00281	−	1.06045i	−0.342731	−	0.0403708i
$691$	14.3809	+	17.1385i	0.547077	+	0.651981i	0.966759	−	0.255690i	$-0.0823028\pi$
$691$	14.3809	+	17.1385i	0.547077	+	0.651981i	−0.419682	+	0.907671i	$0.637858\pi$
$692$	−3.09134	−	4.06056i	−0.117515	−	0.154359i
$693$	−0.0629520	−	0.0923374i	−0.00239135	−	0.00350761i
$694$	−21.8419	+	7.36808i	−0.829106	+	0.279689i
$695$	−11.5998	−	4.22197i	−0.440004	−	0.160148i
$696$	−17.2309	−	2.86357i	−0.653136	−	0.108544i
$697$	−2.56745	−	2.15435i	−0.0972492	−	0.0816018i
$698$	36.1536	−	28.9036i	1.36843	−	1.09402i
$699$	−2.91647	+	10.6177i	−0.110311	+	0.401599i
$700$	−0.599691	−	15.0270i	−0.0226662	−	0.567968i
$701$		−	19.8222i		−	0.748673i	−0.927293	−	0.374337i	$-0.877870\pi$
$701$		−	19.8222i		−	0.748673i	0.927293	−	0.374337i	$-0.122130\pi$
$702$	−0.678336	−	15.1502i	−0.0256021	−	0.571806i
$703$	7.09921	−	4.09873i	0.267752	−	0.154587i
$704$	−0.00363051	−	0.112580i	−0.000136830	−	0.00424301i
$705$	11.5857	−	3.02668i	0.436344	−	0.113991i
$706$	−14.1858	+	36.2746i	−0.533890	+	1.36521i
$707$	17.8055	−	38.1892i	0.669645	−	1.43625i
$708$	22.2034	−	0.745553i	0.834454	−	0.0280196i
$709$	34.8423	+	12.6816i	1.30853	+	0.476266i	0.899765	−	0.436374i	$-0.143738\pi$
$709$	34.8423	+	12.6816i	1.30853	+	0.476266i	0.408764	+	0.912640i	$0.365960\pi$
$710$	3.68506	−	4.18594i	0.138298	−	0.157096i
$711$	7.40013	+	45.2808i	0.277526	+	1.69816i
$712$	−1.26870	+	17.8018i	−0.0475466	+	0.667150i
$713$	−1.29969	+	3.57087i	−0.0486738	+	0.133730i
$714$	−5.50352	+	13.8192i	−0.205964	+	0.517170i
$715$	−0.0274369	+	0.0326980i	−0.00102608	+	0.00122284i
$716$	−11.2839	−	0.535619i	−0.421699	−	0.0200170i
$717$	−4.58201	−	6.63189i	−0.171118	−	0.247672i
$718$	−11.5765	−	0.274600i	−0.432031	−	0.0102480i
$719$	−19.8290	−	34.3449i	−0.739498	−	1.28085i	−0.952722	−	0.303845i	$-0.901730\pi$
$719$	−19.8290	−	34.3449i	−0.739498	−	1.28085i	0.213223	−	0.977003i	$-0.431604\pi$
$720$	−4.90429	+	16.9318i	−0.182772	+	0.631010i
$721$	5.20581	+	19.4243i	0.193874	+	0.723399i
$722$	−2.85209	−	0.0676527i	−0.106144	−	0.00251777i
$723$	21.6115	−	9.91316i	0.803741	−	0.368674i
$724$	17.6333	+	34.1897i	0.655335	+	1.27065i
$725$	3.46585	+	9.52235i	0.128718	+	0.353651i
$726$	12.1140	−	24.0671i	0.449591	−	0.893214i
$727$	23.5837	+	28.1060i	0.874672	+	1.04239i	0.998743	+	0.0501203i	$0.0159605\pi$
$727$	23.5837	+	28.1060i	0.874672	+	1.04239i	−0.124071	+	0.992273i	$0.539595\pi$
$728$	5.04669	−	14.5958i	0.187043	−	0.540956i
$729$	−1.01530	+	26.9809i	−0.0376036	+	0.999293i
$730$	1.48619	−	1.68819i	0.0550062	−	0.0624828i
$731$	3.55589	+	1.29424i	0.131519	+	0.0478691i
$732$	43.3986	−	17.4665i	1.60406	−	0.645582i
$733$	−29.9001	−	25.0892i	−1.10438	−	0.926689i	−0.106673	−	0.994294i	$-0.534020\pi$
$733$	−29.9001	−	25.0892i	−1.10438	−	0.926689i	−0.997712	+	0.0676052i	$0.978464\pi$
$734$	−24.9670	+	3.79426i	−0.921549	+	0.140049i
$735$	−1.66164	+	17.7327i	−0.0612904	+	0.654082i
$736$	−9.75674	−	10.3877i	−0.359638	−	0.382897i
$737$			0.0884045i			0.00325642i
$738$	−4.59839	−	4.15163i	−0.169269	−	0.152824i
$739$			43.5453i			1.60184i	0.598772	+	0.800920i	$0.295656\pi$
$739$			43.5453i			1.60184i	−0.598772	+	0.800920i	$0.704344\pi$
$740$	1.73619	+	5.58031i	0.0638235	+	0.205136i
$741$	−1.19184	−	14.6823i	−0.0437833	−	0.539367i
$742$	34.2227	+	25.1905i	1.25636	+	0.924773i
$743$	−37.9621	−	31.8540i	−1.39269	−	1.16861i	−0.964236	−	0.265046i	$-0.914613\pi$
$743$	−37.9621	−	31.8540i	−1.39269	−	1.16861i	−0.428457	−	0.903562i	$-0.640943\pi$
$744$	6.43557	+	3.63153i	0.235939	+	0.133138i
$745$	−3.99905	−	22.6797i	−0.146514	−	0.830921i
$746$	−0.849651	+	4.22948i	−0.0311079	+	0.154852i
$747$	32.0177	+	39.1435i	1.17147	+	1.43219i
$748$	0.0641112	−	0.00819276i	0.00234414	−	0.000299557i
$749$	−36.9747	−	3.23293i	−1.35103	−	0.118129i
$750$	27.4630	−	6.48288i	1.00281	−	0.236721i
$751$	37.9185	+	6.68605i	1.38366	+	0.243977i	0.815414	−	0.578878i	$-0.196509\pi$
$751$	37.9185	+	6.68605i	1.38366	+	0.243977i	0.568251	+	0.822855i	$0.307620\pi$
$752$	17.0006	+	8.08534i	0.619949	+	0.294842i
$753$	−22.1954	−	6.09663i	−0.808846	−	0.222173i
$754$	−0.246768	+	10.4032i	−0.00898677	+	0.378862i
$755$	15.8368			0.576360
$756$	−11.0922	+	25.1587i	−0.403421	+	0.915015i
$757$	46.5028			1.69017			0.845086	−	0.534631i	$-0.179549\pi$
$757$	46.5028			1.69017			0.845086	+	0.534631i	$0.179549\pi$
$758$	−0.994870	+	41.9415i	−0.0361353	+	1.52339i
$759$	0.0155290	+	0.0594429i	0.000563665	+	0.00215764i
$760$	−4.16445	+	16.6082i	−0.151060	+	0.602443i
$761$	23.6742	+	4.17440i	0.858189	+	0.151322i	0.585393	−	0.810750i	$-0.300940\pi$
$761$	23.6742	+	4.17440i	0.858189	+	0.151322i	0.272796	+	0.962072i	$0.412051\pi$
$762$	−1.28081	+	4.26430i	−0.0463989	+	0.154479i
$763$	9.51196	−	13.5860i	0.344356	−	0.491846i
$764$	4.03550	+	31.5792i	0.145999	+	1.14250i
$765$	−9.93844	−	1.88118i	−0.359325	−	0.0680143i
$766$	7.33170	−	36.4965i	0.264905	−	1.31867i
$767$	−2.29826	−	13.0341i	−0.0829853	−	0.470633i
$768$	−23.0369	+	15.4045i	−0.831273	+	0.555864i
$769$	10.1423	+	8.51041i	0.365741	+	0.306893i	0.807074	−	0.590450i	$-0.201050\pi$
$769$	10.1423	+	8.51041i	0.365741	+	0.306893i	−0.441333	+	0.897343i	$0.645494\pi$
$770$	0.0708919	−	0.0310370i	0.00255477	−	0.00111850i
$771$	−36.4031	−	17.2537i	−1.31103	−	0.621376i
$772$	51.5741	−	16.0461i	1.85619	−	0.577513i
$773$			45.5770i			1.63929i	0.572870	+	0.819646i	$0.305830\pi$
$773$			45.5770i			1.63929i	−0.572870	+	0.819646i	$0.694170\pi$
$774$	6.48190	+	2.62902i	0.232987	+	0.0944981i
$775$		−	4.28695i		−	0.153992i
$776$	−21.5360	−	9.62289i	−0.773096	−	0.345442i
$777$	1.52707	+	8.98679i	0.0547833	+	0.322399i
$778$	−41.6689	+	6.33247i	−1.49390	+	0.227030i
$779$	−4.60978	−	3.86807i	−0.165163	−	0.138588i
$780$	10.3976	+	1.47550i	0.372293	+	0.0528315i
$781$	−0.0355177	−	0.0129274i	−0.00127092	−	0.000462578i
$782$	5.40345	−	6.13790i	0.193227	−	0.219491i
$783$	1.96151	−	18.4227i	0.0700985	−	0.658373i
$784$	−19.9468	+	19.6501i	−0.712386	+	0.701788i
$785$	−15.4987	−	18.4706i	−0.553172	−	0.659244i
$786$	39.2879	−	2.25294i	1.40135	−	0.0803598i
$787$	13.4005	+	36.8175i	0.477675	+	1.31240i	0.911462	+	0.411385i	$0.134955\pi$
$787$	13.4005	+	36.8175i	0.477675	+	1.31240i	−0.433787	+	0.901016i	$0.642823\pi$
$788$	26.5464	−	13.6913i	0.945675	−	0.487731i
$789$	2.06888	−	22.0542i	0.0736541	−	0.785150i
$790$	−31.7632	−	0.753437i	−1.13008	−	0.0268061i
$791$	−17.1991	+	17.2009i	−0.611530	+	0.611594i
$792$	0.118978	−	0.0108387i	0.00422771	−	0.000385137i
$793$	−13.9351	−	24.1363i	−0.494850	−	0.857106i
$794$	15.8584	+	0.376167i	0.562793	+	0.0133497i
$795$	−12.3760	+	26.1119i	−0.438932	+	0.926092i
$796$	−0.742417	+	15.6405i	−0.0263143	+	0.554363i
$797$	−6.19881	+	7.38745i	−0.219573	+	0.261677i	−0.864575	−	0.502504i	$-0.832412\pi$
$797$	−6.19881	+	7.38745i	−0.219573	+	0.261677i	0.645002	+	0.764181i	$0.276857\pi$
$798$	−9.88140	+	24.8119i	−0.349798	+	0.878332i
$799$	−3.69454	+	10.1507i	−0.130703	+	0.359105i
$800$	14.3512	+	7.24745i	0.507390	+	0.256236i
$801$	−18.9281	−	0.237323i	−0.668790	−	0.00838539i
$802$	22.4619	−	25.5150i	0.793157	−	0.900965i
$803$	−0.0143243	−	0.00521361i	−0.000505493	−	0.000183984i
$804$	18.4609	−	11.5013i	0.651065	−	0.405618i
$805$	4.13755	−	8.87421i	0.145830	−	0.312775i
$806$	1.60335	−	4.09994i	0.0564756	−	0.144414i
$807$	−1.15150	+	4.19215i	−0.0405346	+	0.147571i
$808$	26.4284	+	36.4778i	0.929747	+	1.28329i
$809$	23.6941	−	13.6798i	0.833042	−	0.480957i	−0.0218513	−	0.999761i	$-0.506956\pi$
$809$	23.6941	−	13.6798i	0.833042	−	0.480957i	0.854893	+	0.518804i	$0.173623\pi$
$810$	−18.2327	−	4.14088i	−0.640633	−	0.145496i
$811$		−	15.0257i		−	0.527624i	−0.964574	−	0.263812i	$-0.915020\pi$
$811$		−	15.0257i		−	0.527624i	0.964574	−	0.263812i	$-0.0849798\pi$
$812$	8.77435	−	16.7023i	0.307919	−	0.586135i
$813$	−2.29640	+	0.599916i	−0.0805383	+	0.0210400i
$814$	0.0309370	−	0.0247331i	0.00108434	−	0.000866895i
$815$	17.1947	+	14.4281i	0.602305	+	0.505394i
$816$	−10.0516	−	12.3220i	−0.351876	−	0.431357i
$817$	6.38449	+	2.32376i	0.223365	+	0.0812982i
$818$	−47.2816	+	15.9498i	−1.65316	+	0.557673i
$819$	15.7681	+	4.43679i	0.550983	+	0.155034i
$820$	3.41347	−	2.59871i	0.119204	−	0.0907508i
$821$	−22.3948	−	26.6891i	−0.781585	−	0.931457i	0.217419	−	0.976078i	$-0.430236\pi$
$821$	−22.3948	−	26.6891i	−0.781585	−	0.931457i	−0.999004	+	0.0446217i	$0.985792\pi$
$822$	−8.09529	−	18.8133i	−0.282356	−	0.656190i
$823$	−15.5550	−	2.74277i	−0.542214	−	0.0956069i	−0.104168	−	0.994560i	$-0.533218\pi$
$823$	−15.5550	−	2.74277i	−0.542214	−	0.0956069i	−0.438046	+	0.898953i	$0.644329\pi$
$824$	−20.8527	−	5.22875i	−0.726440	−	0.182152i
$825$	−0.0393979	−	0.0570236i	−0.00137166	−	0.00198531i
$826$	−6.75730	+	23.0248i	−0.235117	+	0.801136i
$827$	7.28264	−	12.6139i	0.253242	−	0.438628i	−0.711174	−	0.703016i	$-0.751836\pi$
$827$	7.28264	−	12.6139i	0.253242	−	0.438628i	0.964417	+	0.264387i	$0.0851697\pi$
$828$	10.3928	−	10.9762i	0.361173	−	0.381450i
$829$	2.40540	−	4.16627i	0.0835430	−	0.144701i	−0.821226	−	0.570602i	$-0.806710\pi$
$829$	2.40540	−	4.16627i	0.0835430	−	0.144701i	0.904769	+	0.425902i	$0.140043\pi$
$830$	−30.7340	+	16.7854i	−1.06679	+	0.582630i
$831$	2.88114	−	30.7128i	0.0999456	−	1.06542i
$832$	11.0145	+	12.2987i	0.381860	+	0.426382i
$833$	−12.3088	−	10.3261i	−0.426474	−	0.357779i
$834$	17.2076	−	11.2955i	0.595849	−	0.391132i
$835$	−3.61390	+	0.637228i	−0.125064	+	0.0220522i
$836$	0.115110	−	0.0147099i	0.00398115	−	0.000508751i
$837$	−3.44537	+	7.03986i	−0.119089	+	0.243333i
$838$	−26.1244	−	22.9984i	−0.902451	−	0.794466i
$839$	−43.1031	+	36.1678i	−1.48808	+	1.24865i	−0.591089	+	0.806606i	$0.701302\pi$
$839$	−43.1031	+	36.1678i	−1.48808	+	1.24865i	−0.896994	+	0.442044i	$0.854254\pi$
$840$	−15.7041	−	10.7660i	−0.541844	−	0.371463i
$841$	2.82826	−	16.0399i	0.0975263	−	0.553099i
$842$	1.65462	+	0.647069i	0.0570221	+	0.0222995i
$843$	18.0441	+	39.3378i	0.621473	+	1.35486i
$844$	−12.0095	−	38.6000i	−0.413384	−	1.32867i
$845$			12.8403i			0.441720i
$846$	−7.50482	+	18.5033i	−0.258021	+	0.636156i
$847$	20.5798	+	20.5777i	0.707131	+	0.707057i
$848$	−41.3166	+	18.8854i	−1.41882	+	0.648529i
$849$	22.8385	−	15.7793i	0.783817	−	0.541544i
$850$	−3.35992	+	8.59167i	−0.115244	+	0.294692i
$851$	0.870213	−	4.93522i	0.0298305	−	0.169177i
$852$	1.92125	+	9.09873i	0.0658209	+	0.311717i
$853$	−20.0197	−	7.28657i	−0.685461	−	0.249487i	−0.0242703	−	0.999705i	$-0.507726\pi$
$853$	−20.0197	−	7.28657i	−0.685461	−	0.249487i	−0.661190	+	0.750218i	$0.729948\pi$
$854$	3.21165	+	50.4278i	0.109901	+	1.72560i
$855$	−17.8442	−	3.37761i	−0.610258	−	0.115512i
$856$	22.2318	−	32.8652i	0.759866	−	1.12331i
$857$	0.655859	+	0.781622i	0.0224037	+	0.0266997i	0.777130	−	0.629340i	$-0.216675\pi$
$857$	0.655859	+	0.781622i	0.0224037	+	0.0266997i	−0.754726	+	0.656040i	$0.772230\pi$
$858$	−0.0163520	−	0.0692711i	−0.000558249	−	0.00236488i
$859$	49.3914	+	8.70903i	1.68521	+	0.297148i	0.932491	−	0.361192i	$-0.117630\pi$
$859$	49.3914	+	8.70903i	1.68521	+	0.297148i	0.752720	+	0.658340i	$0.228741\pi$
$860$	−2.61805	+	4.07527i	−0.0892747	+	0.138966i
$861$	5.81582	−	3.30973i	0.198203	−	0.112795i
$862$	−7.59152	−	13.9001i	−0.258568	−	0.473438i
$863$	−7.58651	+	13.1402i	−0.258248	+	0.447299i	−0.965773	−	0.259390i	$-0.916478\pi$
$863$	−7.58651	+	13.1402i	−0.258248	+	0.447299i	0.707525	+	0.706689i	$0.249812\pi$
$864$	−17.7422	−	23.4353i	−0.603603	−	0.797285i
$865$	1.87419	+	3.24620i	0.0637245	+	0.110374i
$866$	2.84272	+	0.0674304i	0.0965995	+	0.00229138i
$867$	−14.4584	+	14.2783i	−0.491034	+	0.484916i
$868$	−5.90479	+	5.37018i	−0.200422	+	0.182276i
$869$	0.0736485	+	0.202348i	0.00249836	+	0.00686417i
$870$	12.2872	+	3.69055i	0.416576	+	0.125121i
$871$	−8.32916	−	9.92631i	−0.282223	−	0.336340i
$872$	7.75101	+	15.9459i	0.262482	+	0.539996i
$873$	8.85106	−	23.4010i	0.299563	−	0.792003i
$874$	9.70174	−	11.0204i	0.328166	−	0.372771i
$875$	−2.65482	+	30.3629i	−0.0897494	+	1.02645i
$876$	0.774839	+	3.66952i	0.0261794	+	0.123982i
$877$	−31.1148	+	11.3249i	−1.05067	+	0.382414i	−0.808917	−	0.587923i	$-0.799946\pi$
$877$	−31.1148	+	11.3249i	−1.05067	+	0.382414i	−0.241756	+	0.970337i	$0.577723\pi$
$878$	1.49788	−	3.83023i	0.0505509	−	0.129264i
$879$	17.9555	−	12.4055i	0.605623	−	0.418429i
$880$	−0.00783648	+	0.0823597i	−0.000264168	+	0.00277634i
$881$	−38.2056	−	22.0580i	−1.28718	−	0.743153i	−0.309029	−	0.951053i	$-0.600004\pi$
$881$	−38.2056	−	22.0580i	−1.28718	−	0.743153i	−0.978150	+	0.207899i	$0.933337\pi$
$882$	−22.0456	−	19.8996i	−0.742312	−	0.670054i
$883$	−2.71206	+	1.56581i	−0.0912680	+	0.0526936i	−0.544939	−	0.838475i	$-0.683447\pi$
$883$	−2.71206	+	1.56581i	−0.0912680	+	0.0526936i	0.453671	+	0.891169i	$0.350114\pi$
$884$	−6.42670	+	6.96024i	−0.216153	+	0.234098i
$885$	−16.2460	−	1.52402i	−0.546103	−	0.0512294i
$886$	−38.3215	+	30.6368i	−1.28744	+	1.02926i
$887$	−39.0991	−	32.8081i	−1.31282	−	1.10159i	−0.987775	−	0.155889i	$-0.950176\pi$
$887$	−39.0991	−	32.8081i	−1.31282	−	1.10159i	−0.325046	−	0.945698i	$-0.605380\pi$
$888$	−9.18969	−	3.24263i	−0.308386	−	0.108815i
$889$	−3.93964	−	2.75826i	−0.132131	−	0.0925092i
$890$	2.58173	−	12.8516i	0.0865399	−	0.430788i
$891$	0.0188686	+	0.125305i	0.000632122	+	0.00419789i
$892$	0.461475	−	0.0589718i	0.0154513	−	0.00197452i
$893$	−6.63343	+	18.2252i	−0.221979	+	0.609883i
$894$	34.3012	+	17.2652i	1.14721	+	0.577436i
$895$	8.17119	+	1.44080i	0.273133	+	0.0481607i
$896$	−7.99488	−	28.8458i	−0.267090	−	0.963672i
$897$	−7.34414	−	5.21133i	−0.245214	−	0.174001i
$898$	−4.65892	−	2.83922i	−0.155470	−	0.0947461i
$899$	2.68904	−	4.65756i	0.0896846	−	0.155338i
$900$	−6.78224	+	15.6459i	−0.226075	+	0.521528i
$901$	−13.0335	−	22.5747i	−0.434209	−	0.752072i
$902$	−0.0248287	−	0.0151310i	−0.000826705	−	0.000503808i
$903$	−4.89228	+	5.75732i	−0.162805	+	0.191592i
$904$	−7.13430	−	25.0062i	−0.237283	−	0.831693i
$905$	−9.66381	−	26.5511i	−0.321236	−	0.882588i
$906$	−15.7884	+	21.1679i	−0.524535	+	0.703257i
$907$	−48.1401	+	8.48839i	−1.59846	+	0.281852i	−0.900689	−	0.434464i	$-0.856938\pi$
$907$	−48.1401	+	8.48839i	−1.59846	+	0.281852i	−0.697775	+	0.716317i	$0.745827\pi$
$908$	−2.58685	−	20.2430i	−0.0858478	−	0.671789i
$909$	−36.9821	+	30.2498i	−1.22662	+	1.00332i
$910$	−5.03575	+	10.1641i	−0.166934	+	0.336937i
$911$	−7.15606	−	40.5840i	−0.237091	−	1.34461i	−0.838165	−	0.545416i	$-0.816372\pi$
$911$	−7.15606	−	40.5840i	−0.237091	−	1.34461i	0.601075	−	0.799193i	$-0.294739\pi$
$912$	−18.0473	−	22.1238i	−0.597606	−	0.732593i
$913$	0.181812	+	0.152559i	0.00601711	+	0.00504896i
$914$	−2.01511	−	13.2599i	−0.0666541	−	0.438597i
$915$	−33.2449	+	8.68495i	−1.09904	+	0.287116i
$916$	−25.2097	+	7.84344i	−0.832953	+	0.259154i
$917$	−10.9991	+	41.0577i	−0.363222	+	1.35584i
$918$	12.4225	−	11.4086i	0.410005	−	0.376539i
$919$	35.2666	+	20.3612i	1.16334	+	0.671654i	0.952102	−	0.305781i	$-0.0989174\pi$
$919$	35.2666	+	20.3612i	1.16334	+	0.671654i	0.211237	+	0.977435i	$0.432251\pi$
$920$	6.14129	+	8.47653i	0.202472	+	0.279463i
$921$	−5.77082	+	1.50758i	−0.190155	+	0.0496764i
$922$	18.1806	+	22.7409i	0.598746	+	0.748932i
$923$	5.20600	−	1.89483i	0.171357	−	0.0623690i
$924$	−0.0291905	+	0.125698i	−0.000960297	+	0.00413518i
$925$	0.981716	+	5.56759i	0.0322786	+	0.183061i
$926$	46.6892	+	9.37928i	1.53430	+	0.308222i
$927$	4.24082	−	22.4046i	0.139287	−	0.735862i
$928$	11.0458	+	16.8759i	0.362595	+	0.553979i
$929$	19.9871	+	23.8197i	0.655756	+	0.781500i	0.986770	−	0.162126i	$-0.0518352\pi$
$929$	19.9871	+	23.8197i	0.655756	+	0.781500i	−0.331014	+	0.943626i	$0.607391\pi$
$930$	−4.35062	−	3.24498i	−0.142662	−	0.106407i
$931$	−22.1000	−	18.5402i	−0.724300	−	0.607632i
$932$	11.3000	−	5.82797i	0.370145	−	0.190902i
$933$	−29.6619	−	42.9319i	−0.971088	−	1.40553i
$934$	−25.1567	−	0.596728i	−0.823153	−	0.0195255i
$935$	−0.0474719			−0.00155250
$936$	−12.3380	+	12.4267i	−0.403281	+	0.406180i
$937$	25.9262	+	44.9056i	0.846973	+	1.46700i	0.883896	+	0.467683i	$0.154911\pi$
$937$	25.9262	+	44.9056i	0.846973	+	1.46700i	−0.0369231	+	0.999318i	$0.511756\pi$
$938$	5.54183	+	22.8302i	0.180947	+	0.745433i
$939$	3.91010	−	41.6815i	0.127601	−	1.36023i
$940$	−11.6333	−	7.47350i	−0.379436	−	0.243759i
$941$	3.54033	+	9.72696i	0.115411	+	0.317090i	0.983927	−	0.178572i	$-0.0571477\pi$
$941$	3.54033	+	9.72696i	0.115411	+	0.317090i	−0.868516	+	0.495662i	$0.834926\pi$
$942$	40.1397	−	2.30179i	1.30782	−	0.0749964i
$943$	−3.62288	+	0.638811i	−0.117977	+	0.0208025i
$944$	−18.0009	−	18.2765i	−0.585878	−	0.594849i
$945$	10.4238	−	17.2970i	0.339085	−	0.562673i
$946$	0.0321853	+	0.00646562i	0.00104643	+	0.000210215i
$947$	−1.43914	−	8.16174i	−0.0467656	−	0.265221i	0.952456	−	0.304677i	$-0.0985486\pi$
$947$	−1.43914	−	8.16174i	−0.0467656	−	0.265221i	−0.999221	+	0.0394562i	$0.987437\pi$
$948$	32.6733	−	41.7046i	1.06118	−	1.35450i
$949$	2.09958	−	0.764184i	0.0681552	−	0.0248065i
$950$	−6.03263	+	15.4261i	−0.195724	+	0.500488i
$951$	−12.8949	−	28.1119i	−0.418145	−	0.911592i
$952$	16.0430	−	6.13471i	0.519955	−	0.198827i
$953$	10.9694	−	6.33316i	0.355332	−	0.205151i	−0.311699	−	0.950181i	$-0.600898\pi$
$953$	10.9694	−	6.33316i	0.355332	−	0.205151i	0.667031	+	0.745030i	$0.267565\pi$
$954$	−22.5636	−	42.5743i	−0.730525	−	1.37839i
$955$		−	23.3832i		−	0.756663i
$956$	−2.04909	+	9.07948i	−0.0662723	+	0.293651i
$957$	−0.00703515	−	0.0866661i	−0.000227414	−	0.00280152i
$958$	0.969570	−	0.775139i	0.0313254	−	0.0250436i
$959$	22.0378	−	1.92921i	0.711638	−	0.0622974i
$960$	18.2181	−	9.07840i	0.587987	−	0.293004i
$961$	22.0045	−	18.4640i	0.709822	−	0.595611i
$962$	−1.14343	+	5.69188i	−0.0368656	+	0.183514i
$963$	36.1803	+	21.4979i	1.16589	+	0.692761i
$964$	−25.3249	−	10.6028i	−0.815661	−	0.341494i
$965$	−39.0690	+	6.88893i	−1.25768	+	0.221762i
$966$	7.73662	+	14.3775i	0.248922	+	0.462588i
$967$	14.5638	+	40.0138i	0.468342	+	1.28676i	0.919069	+	0.394097i	$0.128943\pi$
$967$	14.5638	+	40.0138i	0.468342	+	1.28676i	−0.450727	+	0.892662i	$0.648835\pi$
$968$	−29.9183	+	8.53574i	−0.961611	+	0.274349i
$969$	11.6568	−	11.5116i	0.374471	−	0.369805i
$970$	14.7944	+	9.01596i	0.475020	+	0.289485i
$971$	25.6989	−	44.5118i	0.824716	−	1.42845i	−0.0774195	−	0.996999i	$-0.524668\pi$
$971$	25.6989	−	44.5118i	0.824716	−	1.42845i	0.902136	−	0.431452i	$-0.141999\pi$
$972$	23.7119	−	20.2422i	0.760559	−	0.649269i
$973$	5.75542	+	21.4751i	0.184510	+	0.688459i
$974$	−12.1300	+	6.62478i	−0.388669	+	0.212272i
$975$	9.79627	+	2.69083i	0.313732	+	0.0861757i
$976$	−48.7828	−	23.2006i	−1.56150	−	0.742634i
$977$	−13.7209	+	16.3519i	−0.438971	+	0.523145i	−0.939488	−	0.342581i	$-0.888699\pi$
$977$	−13.7209	+	16.3519i	−0.438971	+	0.523145i	0.500517	+	0.865727i	$0.333143\pi$
$978$	−36.4273	+	8.59896i	−1.16482	+	0.274964i
$979$	−0.0874916	+	0.0154271i	−0.00279624	+	0.000493053i
$980$	16.3620	−	12.4592i	0.522666	−	0.397996i
$981$	−16.4026	+	9.19779i	−0.523694	+	0.293663i
$982$	−5.44802	+	1.83782i	−0.173853	+	0.0586473i
$983$	−4.38028	−	24.8418i	−0.139709	−	0.792331i	−0.971464	−	0.237187i	$-0.923774\pi$
$983$	−4.38028	−	24.8418i	−0.139709	−	0.792331i	0.831755	−	0.555143i	$-0.187337\pi$
$984$	0.0704612	+	7.15332i	0.00224622	+	0.228039i
$985$	−20.6155	+	7.50341i	−0.656863	+	0.239079i
$986$	−9.03962	+	7.22687i	−0.287880	+	0.230150i
$987$	−16.4349	−	13.9655i	−0.523129	−	0.444528i
$988$	−11.5389	+	12.4969i	−0.367103	+	0.397579i
$989$	3.59705	−	2.07676i	0.114380	−	0.0660371i
$990$	−0.0876925	−	0.00318055i	−0.00278705	−	0.000101085i
$991$	9.66394	+	5.57948i	0.306985	+	0.177238i	0.645577	−	0.763696i	$-0.276617\pi$
$991$	9.66394	+	5.57948i	0.306985	+	0.177238i	−0.338591	+	0.940934i	$0.609950\pi$
$992$	−1.94929	−	8.30701i	−0.0618900	−	0.263748i
$993$	−20.7092	−	45.1477i	−0.657185	−	1.43272i
$994$	−9.98272	−	1.11195i	−0.316633	−	0.0352690i
$995$	1.99708	−	11.3260i	0.0633117	−	0.359058i
$996$	8.20432	−	57.8142i	0.259964	−	1.83191i
$997$	3.16212	+	1.15092i	0.100145	+	0.0364499i	0.391607	−	0.920133i	$-0.371919\pi$
$997$	3.16212	+	1.15092i	0.100145	+	0.0364499i	−0.291462	+	0.956583i	$0.594142\pi$
$998$	16.0569	+	47.5989i	0.508272	+	1.50672i
$999$	2.86246	−	9.93187i	0.0905644	−	0.314230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bs.a.275.2	yes	840
4.3	odd	2	inner	756.2.bs.a.275.16	yes	840
7.4	even	3		756.2.ci.a.599.94	yes	840
27.11	odd	18		756.2.ci.a.443.78	yes	840
28.11	odd	6		756.2.ci.a.599.78	yes	840
108.11	even	18		756.2.ci.a.443.94	yes	840
189.11	odd	18	inner	756.2.bs.a.11.16	yes	840
756.11	even	18	inner	756.2.bs.a.11.2	✓	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.11.2	✓	840	756.11	even	18	inner
756.2.bs.a.11.16	yes	840	189.11	odd	18	inner
756.2.bs.a.275.2	yes	840	1.1	even	1	trivial
756.2.bs.a.275.16	yes	840	4.3	odd	2	inner
756.2.ci.a.443.78	yes	840	27.11	odd	18
756.2.ci.a.443.94	yes	840	108.11	even	18
756.2.ci.a.599.78	yes	840	28.11	odd	6
756.2.ci.a.599.94	yes	840	7.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41382 - 0.0335363i) q^{2} +(-1.23240 + 1.21704i) q^{3} +(1.99775 + 0.0948283i) q^{4} +(-1.44666 - 0.255085i) q^{5} +(1.78320 - 1.67934i) q^{6} +(1.11827 + 2.39781i) q^{7} +(-2.82127 - 0.201067i) q^{8} +(0.0376115 - 2.99976i) q^{9} +O(q^{10})\)	\(q+(-1.41382 - 0.0335363i) q^{2} +(-1.23240 + 1.21704i) q^{3} +(1.99775 + 0.0948283i) q^{4} +(-1.44666 - 0.255085i) q^{5} +(1.78320 - 1.67934i) q^{6} +(1.11827 + 2.39781i) q^{7} +(-2.82127 - 0.201067i) q^{8} +(0.0376115 - 2.99976i) q^{9} +(2.03676 + 0.409160i) q^{10} +(-0.00244493 - 0.0138659i) q^{11} +(-2.57743 + 2.31448i) q^{12} +(1.58092 + 1.32655i) q^{13} +(-1.50061 - 3.42756i) q^{14} +(2.09331 - 1.44628i) q^{15} +(3.98202 + 0.378887i) q^{16} +2.29523i q^{17} +(-0.153777 + 4.23985i) q^{18} +4.12101i q^{19} +(-2.86588 - 0.646782i) q^{20} +(-4.29639 - 1.59407i) q^{21} +(0.00299167 + 0.0196858i) q^{22} +(1.92989 + 1.61937i) q^{23} +(3.72164 - 3.18581i) q^{24} +(-2.67070 - 0.972056i) q^{25} +(-2.19064 - 1.92851i) q^{26} +(3.60449 + 3.74268i) q^{27} +(2.00664 + 4.89626i) q^{28} +(-2.29185 - 2.73132i) q^{29} +(-3.00806 + 1.97458i) q^{30} +(0.515894 + 1.41741i) q^{31} +(-5.61713 - 0.669218i) q^{32} +(0.0198885 + 0.0141127i) q^{33} +(0.0769734 - 3.24503i) q^{34} +(-1.00611 - 3.75407i) q^{35} +(0.359601 - 5.98921i) q^{36} +(-0.994595 - 1.72269i) q^{37} +(0.138203 - 5.82635i) q^{38} +(-3.56279 + 0.289210i) q^{39} +(4.03014 + 1.01054i) q^{40} +(-0.938622 + 1.11861i) q^{41} +(6.02084 + 2.39781i) q^{42} +(0.563883 - 1.54925i) q^{43} +(-0.00356948 - 0.0279324i) q^{44} +(-0.819607 + 4.33005i) q^{45} +(-2.67420 - 2.35422i) q^{46} +(4.42251 + 1.60966i) q^{47} +(-5.36855 + 4.37935i) q^{48} +(-4.49896 + 5.36278i) q^{49} +(3.74328 + 1.46387i) q^{50} +(-2.79339 - 2.82863i) q^{51} +(3.03249 + 2.80003i) q^{52} +(-9.83550 + 5.67853i) q^{53} +(-4.97057 - 5.41234i) q^{54} +0.0206829i q^{55} +(-2.67282 - 6.98971i) q^{56} +(-5.01544 - 5.07872i) q^{57} +(3.14865 + 3.93844i) q^{58} +(-4.91278 - 4.12231i) q^{59} +(4.31907 - 2.69081i) q^{60} +(-12.6903 - 4.61888i) q^{61} +(-0.681845 - 2.02125i) q^{62} +(7.23492 - 3.26435i) q^{63} +(7.91914 + 1.13453i) q^{64} +(-1.94867 - 2.32234i) q^{65} +(-0.0276454 - 0.0206198i) q^{66} +(-6.18343 - 1.09031i) q^{67} +(-0.217652 + 4.58529i) q^{68} +(-4.34924 + 0.353051i) q^{69} +(1.29655 + 5.34130i) q^{70} +(1.34225 - 2.32484i) q^{71} +(-0.709266 + 8.45559i) q^{72} +(0.541328 - 0.937608i) q^{73} +(1.34840 + 2.46892i) q^{74} +(4.47440 - 2.05240i) q^{75} +(-0.390788 + 8.23275i) q^{76} +(0.0305136 - 0.0213682i) q^{77} +(5.04683 - 0.289408i) q^{78} +(-15.0615 + 2.65575i) q^{79} +(-5.66398 - 1.56388i) q^{80} +(-8.99717 - 0.225651i) q^{81} +(1.36455 - 1.55002i) q^{82} +(-12.9130 + 10.8353i) q^{83} +(-8.43194 - 3.59198i) q^{84} +(0.585479 - 3.32041i) q^{85} +(-0.849182 + 2.17145i) q^{86} +(6.14861 + 0.576794i) q^{87} +(0.00410984 + 0.0396110i) q^{88} -6.30985i q^{89} +(1.30399 - 6.09441i) q^{90} +(-1.41292 + 5.27417i) q^{91} +(3.70188 + 3.41811i) q^{92} +(-2.36083 - 1.11895i) q^{93} +(-6.19864 - 2.42408i) q^{94} +(1.05121 - 5.96170i) q^{95} +(7.73701 - 6.01155i) q^{96} +(7.83670 + 2.85233i) q^{97} +(6.54055 - 7.43110i) q^{98} +(-0.0416863 + 0.00681270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Introduction

L-functions

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