LMFDB - Embedded newform 273.2.cg.a.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.1
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.a.262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.639011 + 2.38482i) q^{2} +1.00000i q^{3} +(-3.54699 - 2.04786i) q^{4} +(-0.746344 - 2.78539i) q^{5} +(-2.38482 - 0.639011i) q^{6} +(-2.52355 - 0.794791i) q^{7} +(3.65872 - 3.65872i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.639011 + 2.38482i) q^{2} +1.00000i q^{3} +(-3.54699 - 2.04786i) q^{4} +(-0.746344 - 2.78539i) q^{5} +(-2.38482 - 0.639011i) q^{6} +(-2.52355 - 0.794791i) q^{7} +(3.65872 - 3.65872i) q^{8} -1.00000 q^{9} +7.11959 q^{10} +(0.990792 - 0.990792i) q^{11} +(2.04786 - 3.54699i) q^{12} +(-3.49837 - 0.872572i) q^{13} +(3.50801 - 5.51034i) q^{14} +(2.78539 - 0.746344i) q^{15} +(2.29172 + 3.96937i) q^{16} +(3.77833 - 6.54425i) q^{17} +(0.639011 - 2.38482i) q^{18} +(-4.88884 + 4.88884i) q^{19} +(-3.05681 + 11.4082i) q^{20} +(0.794791 - 2.52355i) q^{21} +(1.72974 + 2.99599i) q^{22} +(-1.97286 + 1.13903i) q^{23} +(3.65872 + 3.65872i) q^{24} +(-2.87125 + 1.65772i) q^{25} +(4.31643 - 7.78542i) q^{26} -1.00000i q^{27} +(7.32339 + 7.98699i) q^{28} +(-3.75108 + 6.49707i) q^{29} +7.11959i q^{30} +(-5.19745 - 1.39265i) q^{31} +(-0.934879 + 0.250500i) q^{32} +(0.990792 + 0.990792i) q^{33} +(13.1925 + 13.1925i) q^{34} +(-0.330370 + 7.62227i) q^{35} +(3.54699 + 2.04786i) q^{36} +(-2.20910 - 0.591926i) q^{37} +(-8.53499 - 14.7830i) q^{38} +(0.872572 - 3.49837i) q^{39} +(-12.9216 - 7.46031i) q^{40} +(-2.38652 - 8.90661i) q^{41} +(5.51034 + 3.50801i) q^{42} +(3.04772 - 1.75960i) q^{43} +(-5.54333 + 1.48533i) q^{44} +(0.746344 + 2.78539i) q^{45} +(-1.45571 - 5.43279i) q^{46} +(-0.833593 + 0.223361i) q^{47} +(-3.96937 + 2.29172i) q^{48} +(5.73661 + 4.01139i) q^{49} +(-2.11860 - 7.90673i) q^{50} +(6.54425 + 3.77833i) q^{51} +(10.6218 + 10.2592i) q^{52} +(-0.886338 - 1.53518i) q^{53} +(2.38482 + 0.639011i) q^{54} +(-3.49922 - 2.02027i) q^{55} +(-12.1409 + 6.32504i) q^{56} +(-4.88884 - 4.88884i) q^{57} +(-13.0974 - 13.0974i) q^{58} +(5.19948 - 1.39320i) q^{59} +(-11.4082 - 3.05681i) q^{60} -4.18771i q^{61} +(6.64246 - 11.5051i) q^{62} +(2.52355 + 0.794791i) q^{63} +6.77728i q^{64} +(0.180534 + 10.3956i) q^{65} +(-2.99599 + 1.72974i) q^{66} +(-3.93850 - 3.93850i) q^{67} +(-26.8034 + 15.4749i) q^{68} +(-1.13903 - 1.97286i) q^{69} +(-17.9666 - 5.65859i) q^{70} +(-1.75325 + 6.54321i) q^{71} +(-3.65872 + 3.65872i) q^{72} +(2.17041 - 8.10009i) q^{73} +(2.82328 - 4.89006i) q^{74} +(-1.65772 - 2.87125i) q^{75} +(27.3523 - 7.32903i) q^{76} +(-3.28779 + 1.71284i) q^{77} +(7.78542 + 4.31643i) q^{78} +(0.411935 - 0.713493i) q^{79} +(9.34585 - 9.34585i) q^{80} +1.00000 q^{81} +22.7657 q^{82} +(-2.15380 + 2.15380i) q^{83} +(-7.98699 + 7.32339i) q^{84} +(-21.0482 - 5.63986i) q^{85} +(2.24881 + 8.39268i) q^{86} +(-6.49707 - 3.75108i) q^{87} -7.25006i q^{88} +(-0.666102 + 2.48593i) q^{89} -7.11959 q^{90} +(8.13481 + 4.98246i) q^{91} +9.33031 q^{92} +(1.39265 - 5.19745i) q^{93} -2.13070i q^{94} +(17.2661 + 9.96859i) q^{95} +(-0.250500 - 0.934879i) q^{96} +(-8.79336 - 2.35617i) q^{97} +(-13.2322 + 11.1175i) q^{98} +(-0.990792 + 0.990792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.639011	+	2.38482i	−0.451849	+	1.68632i	0.245340	+	0.969437i	$0.421100\pi$
$2$	−0.639011	+	2.38482i	−0.451849	+	1.68632i	−0.697189	+	0.716887i	$0.745566\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−3.54699	−	2.04786i	−1.77350	−	1.02393i
$5$	−0.746344	−	2.78539i	−0.333775	−	1.24567i	−0.905191	−	0.425005i	$-0.860272\pi$
$5$	−0.746344	−	2.78539i	−0.333775	−	1.24567i	0.571416	−	0.820661i	$-0.306394\pi$
$6$	−2.38482	−	0.639011i	−0.973600	−	0.260875i
$7$	−2.52355	−	0.794791i	−0.953812	−	0.300403i
$7$	−2.52355	−	0.794791i	−0.953812	−	0.300403i
$8$	3.65872	−	3.65872i	1.29355	−	1.29355i
$9$	−1.00000			−0.333333
$10$	7.11959			2.25141
$11$	0.990792	−	0.990792i	0.298735	−	0.298735i	−0.541783	−	0.840518i	$-0.682251\pi$
$11$	0.990792	−	0.990792i	0.298735	−	0.298735i	0.840518	+	0.541783i	$0.182251\pi$
$12$	2.04786	−	3.54699i	0.591165	−	1.02393i
$13$	−3.49837	−	0.872572i	−0.970274	−	0.242008i
$13$	−3.49837	−	0.872572i	−0.970274	−	0.242008i
$14$	3.50801	−	5.51034i	0.937556	−	1.47270i
$15$	2.78539	−	0.746344i	0.719185	−	0.192705i
$16$	2.29172	+	3.96937i	0.572930	+	0.992343i
$17$	3.77833	−	6.54425i	0.916379	−	1.58721i	0.111509	−	0.993763i	$-0.464432\pi$
$17$	3.77833	−	6.54425i	0.916379	−	1.58721i	0.804870	−	0.593451i	$-0.202235\pi$
$18$	0.639011	−	2.38482i	0.150616	−	0.562108i
$19$	−4.88884	+	4.88884i	−1.12158	+	1.12158i	−0.130073	+	0.991504i	$0.541521\pi$
$19$	−4.88884	+	4.88884i	−1.12158	+	1.12158i	−0.991504	+	0.130073i	$0.958479\pi$
$20$	−3.05681	+	11.4082i	−0.683523	+	2.55094i
$21$	0.794791	−	2.52355i	0.173438	−	0.550684i
$22$	1.72974	+	2.99599i	0.368781	+	0.638747i
$23$	−1.97286	+	1.13903i	−0.411371	+	0.237505i	−0.691378	−	0.722493i	$-0.742996\pi$
$23$	−1.97286	+	1.13903i	−0.411371	+	0.237505i	0.280008	+	0.959998i	$0.409663\pi$
$24$	3.65872	+	3.65872i	0.746833	+	0.746833i
$25$	−2.87125	+	1.65772i	−0.574251	+	0.331544i
$26$	4.31643	−	7.78542i	0.846521	−	1.52685i
$27$		−	1.00000i		−	0.192450i
$28$	7.32339	+	7.98699i	1.38399	+	1.50940i
$29$	−3.75108	+	6.49707i	−0.696559	+	1.20647i	0.273094	+	0.961987i	$0.411953\pi$
$29$	−3.75108	+	6.49707i	−0.696559	+	1.20647i	−0.969652	+	0.244487i	$0.921380\pi$
$30$			7.11959i			1.29985i
$31$	−5.19745	−	1.39265i	−0.933490	−	0.250128i	−0.240148	−	0.970736i	$-0.577196\pi$
$31$	−5.19745	−	1.39265i	−0.933490	−	0.250128i	−0.693342	+	0.720608i	$0.743863\pi$
$32$	−0.934879	+	0.250500i	−0.165265	+	0.0442826i
$33$	0.990792	+	0.990792i	0.172475	+	0.172475i
$34$	13.1925	+	13.1925i	2.26249	+	2.26249i
$35$	−0.330370	+	7.62227i	−0.0558426	+	1.28840i
$36$	3.54699	+	2.04786i	0.591165	+	0.341309i
$37$	−2.20910	−	0.591926i	−0.363174	−	0.0973121i	0.0726176	−	0.997360i	$-0.476865\pi$
$37$	−2.20910	−	0.591926i	−0.363174	−	0.0973121i	−0.435791	+	0.900048i	$0.643531\pi$
$38$	−8.53499	−	14.7830i	−1.38456	−	2.39813i
$39$	0.872572	−	3.49837i	0.139723	−	0.560188i
$40$	−12.9216	−	7.46031i	−2.04309	−	1.17958i
$41$	−2.38652	−	8.90661i	−0.372712	−	1.39098i	−0.856659	−	0.515882i	$-0.827464\pi$
$41$	−2.38652	−	8.90661i	−0.372712	−	1.39098i	0.483948	−	0.875097i	$-0.339203\pi$
$42$	5.51034	+	3.50801i	0.850264	+	0.541298i
$43$	3.04772	−	1.75960i	0.464773	−	0.268337i	−0.249276	−	0.968432i	$-0.580193\pi$
$43$	3.04772	−	1.75960i	0.464773	−	0.268337i	0.714049	+	0.700096i	$0.246859\pi$
$44$	−5.54333	+	1.48533i	−0.835689	+	0.223922i
$45$	0.746344	+	2.78539i	0.111258	+	0.415222i
$46$	−1.45571	−	5.43279i	−0.214633	−	0.801021i
$47$	−0.833593	+	0.223361i	−0.121592	+	0.0325805i	−0.319102	−	0.947720i	$-0.603381\pi$
$47$	−0.833593	+	0.223361i	−0.121592	+	0.0325805i	0.197510	+	0.980301i	$0.436715\pi$
$48$	−3.96937	+	2.29172i	−0.572930	+	0.330781i
$49$	5.73661	+	4.01139i	0.819516	+	0.573056i
$50$	−2.11860	−	7.90673i	−0.299616	−	1.11818i
$51$	6.54425	+	3.77833i	0.916379	+	0.529072i
$52$	10.6218	+	10.2592i	1.47298	+	1.42269i
$53$	−0.886338	−	1.53518i	−0.121748	−	0.210873i	0.798709	−	0.601717i	$-0.205517\pi$
$53$	−0.886338	−	1.53518i	−0.121748	−	0.210873i	−0.920457	+	0.390844i	$0.872183\pi$
$54$	2.38482	+	0.639011i	0.324533	+	0.0869584i
$55$	−3.49922	−	2.02027i	−0.471834	−	0.272414i
$56$	−12.1409	+	6.32504i	−1.62239	+	0.845220i
$57$	−4.88884	−	4.88884i	−0.647543	−	0.647543i
$58$	−13.0974	−	13.0974i	−1.71977	−	1.71977i
$59$	5.19948	−	1.39320i	0.676915	−	0.181379i	0.0960471	−	0.995377i	$-0.469380\pi$
$59$	5.19948	−	1.39320i	0.676915	−	0.181379i	0.580868	+	0.813998i	$0.302713\pi$
$60$	−11.4082	−	3.05681i	−1.47279	−	0.394632i
$61$		−	4.18771i		−	0.536182i	−0.963394	−	0.268091i	$-0.913607\pi$
$61$		−	4.18771i		−	0.536182i	0.963394	−	0.268091i	$-0.0863927\pi$
$62$	6.64246	−	11.5051i	0.843594	−	1.46115i
$63$	2.52355	+	0.794791i	0.317937	+	0.100134i
$64$			6.77728i			0.847160i
$65$	0.180534	+	10.3956i	0.0223925	+	1.28941i
$66$	−2.99599	+	1.72974i	−0.368781	+	0.212916i
$67$	−3.93850	−	3.93850i	−0.481165	−	0.481165i	0.424339	−	0.905504i	$-0.360507\pi$
$67$	−3.93850	−	3.93850i	−0.481165	−	0.481165i	−0.905504	+	0.424339i	$0.860507\pi$
$68$	−26.8034	+	15.4749i	−3.25039	+	1.87661i
$69$	−1.13903	−	1.97286i	−0.137124	−	0.237505i
$70$	−17.9666	−	5.65859i	−2.14742	−	0.676330i
$71$	−1.75325	+	6.54321i	−0.208072	+	0.776536i	0.780419	+	0.625257i	$0.215006\pi$
$71$	−1.75325	+	6.54321i	−0.208072	+	0.776536i	−0.988491	+	0.151279i	$0.951661\pi$
$72$	−3.65872	+	3.65872i	−0.431184	+	0.431184i
$73$	2.17041	−	8.10009i	0.254027	−	0.948043i	−0.714601	−	0.699532i	$-0.753392\pi$
$73$	2.17041	−	8.10009i	0.254027	−	0.948043i	0.968629	−	0.248512i	$-0.0799414\pi$
$74$	2.82328	−	4.89006i	0.328199	−	0.568458i
$75$	−1.65772	−	2.87125i	−0.191417	−	0.331544i
$76$	27.3523	−	7.32903i	3.13753	−	0.840698i
$77$	−3.28779	+	1.71284i	−0.374678	+	0.195196i
$78$	7.78542	+	4.31643i	0.881525	+	0.488739i
$79$	0.411935	−	0.713493i	0.0463463	−	0.0802742i	−0.841922	−	0.539600i	$-0.818576\pi$
$79$	0.411935	−	0.713493i	0.0463463	−	0.0802742i	0.888268	+	0.459326i	$0.151909\pi$
$80$	9.34585	−	9.34585i	1.04490	−	1.04490i
$81$	1.00000			0.111111
$82$	22.7657			2.51405
$83$	−2.15380	+	2.15380i	−0.236410	+	0.236410i	−0.815362	−	0.578952i	$-0.803462\pi$
$83$	−2.15380	+	2.15380i	−0.236410	+	0.236410i	0.578952	+	0.815362i	$0.303462\pi$
$84$	−7.98699	+	7.32339i	−0.871452	+	0.799048i
$85$	−21.0482	−	5.63986i	−2.28300	−	0.611729i
$86$	2.24881	+	8.39268i	0.242496	+	0.905006i
$87$	−6.49707	−	3.75108i	−0.696559	−	0.402158i
$88$		−	7.25006i		−	0.772859i
$89$	−0.666102	+	2.48593i	−0.0706067	+	0.263508i	−0.992201	−	0.124646i	$-0.960220\pi$
$89$	−0.666102	+	2.48593i	−0.0706067	+	0.263508i	0.921595	+	0.388154i	$0.126887\pi$
$90$	−7.11959			−0.750470
$91$	8.13481	+	4.98246i	0.852760	+	0.522303i
$92$	9.33031			0.972752
$93$	1.39265	−	5.19745i	0.144411	−	0.538951i
$94$		−	2.13070i		−	0.219765i
$95$	17.2661	+	9.96859i	1.77146	+	1.02276i
$96$	−0.250500	−	0.934879i	−0.0255666	−	0.0954157i
$97$	−8.79336	−	2.35617i	−0.892830	−	0.239233i	−0.216896	−	0.976195i	$-0.569593\pi$
$97$	−8.79336	−	2.35617i	−0.892830	−	0.239233i	−0.675934	+	0.736962i	$0.736260\pi$
$98$	−13.2322	+	11.1175i	−1.33666	+	1.12304i
$99$	−0.990792	+	0.990792i	−0.0995784	+	0.0995784i
$100$	13.5791			1.35791
$101$	17.9528			1.78637			0.893187	−	0.449686i	$-0.148464\pi$
$101$	17.9528			1.78637			0.893187	+	0.449686i	$0.148464\pi$
$102$	−13.1925	+	13.1925i	−1.30625	+	1.30625i
$103$	−3.06226	+	5.30399i	−0.301734	+	0.522618i	−0.976529	−	0.215387i	$-0.930899\pi$
$103$	−3.06226	+	5.30399i	−0.301734	+	0.522618i	0.674795	+	0.738005i	$0.264232\pi$
$104$	−15.9921	+	9.60707i	−1.56815	+	0.942051i
$105$	−7.62227	−	0.330370i	−0.743857	−	0.0322408i
$106$	4.22752	−	1.13276i	0.410613	−	0.110023i
$107$	2.36698	+	4.09974i	0.228825	+	0.396336i	0.957460	−	0.288566i	$-0.0931783\pi$
$107$	2.36698	+	4.09974i	0.228825	+	0.396336i	−0.728635	+	0.684902i	$0.759845\pi$
$108$	−2.04786	+	3.54699i	−0.197055	+	0.341309i
$109$	−4.56224	+	17.0265i	−0.436983	+	1.63084i	0.299291	+	0.954162i	$0.403250\pi$
$109$	−4.56224	+	17.0265i	−0.436983	+	1.63084i	−0.736275	+	0.676683i	$0.763417\pi$
$110$	7.05403	−	7.05403i	0.672576	−	0.672576i
$111$	0.591926	−	2.20910i	0.0561832	−	0.209678i
$112$	−2.62844	−	11.8384i	−0.248365	−	1.11862i
$113$	−6.86440	−	11.8895i	−0.645748	−	1.11847i	−0.984128	−	0.177459i	$-0.943212\pi$
$113$	−6.86440	−	11.8895i	−0.645748	−	1.11847i	0.338380	−	0.941010i	$-0.390121\pi$
$114$	14.7830	−	8.53499i	1.38456	−	0.799376i
$115$	4.64509	+	4.64509i	0.433157	+	0.433157i
$116$	26.6101	−	15.3634i	2.47069	−	1.42645i
$117$	3.49837	+	0.872572i	0.323425	+	0.0806693i
$118$			13.2901i			1.22345i
$119$	−14.7361	+	13.5118i	−1.35086	+	1.23862i
$120$	7.46031	−	12.9216i	0.681030	−	1.17958i
$121$			9.03666i			0.821515i
$122$	9.98695	+	2.67600i	0.904176	+	0.242273i
$123$	8.90661	−	2.38652i	0.803082	−	0.215185i
$124$	15.5834	+	15.5834i	1.39943	+	1.39943i
$125$	−3.43490	−	3.43490i	−0.307227	−	0.307227i
$126$	−3.50801	+	5.51034i	−0.312519	+	0.490900i
$127$	−9.36268	−	5.40554i	−0.830803	−	0.479665i	0.0233243	−	0.999728i	$-0.492575\pi$
$127$	−9.36268	−	5.40554i	−0.830803	−	0.479665i	−0.854128	+	0.520063i	$0.825908\pi$
$128$	−18.0324	−	4.83176i	−1.59385	−	0.427071i
$129$	1.75960	+	3.04772i	0.154924	+	0.268337i
$130$	−24.9070	−	6.21235i	−2.18449	−	0.544859i
$131$	15.7531	+	9.09505i	1.37635	+	0.794638i	0.991719	−	0.128431i	$-0.0409939\pi$
$131$	15.7531	+	9.09505i	1.37635	+	0.794638i	0.384635	+	0.923069i	$0.374327\pi$
$132$	−1.48533	−	5.54333i	−0.129282	−	0.482485i
$133$	16.2228	−	8.45163i	1.40670	−	0.732849i
$134$	11.9094	−	6.87588i	1.02881	−	0.593986i
$135$	−2.78539	+	0.746344i	−0.239728	+	0.0642350i
$136$	−10.1197	−	37.7674i	−0.867761	−	3.23853i
$137$	−2.52073	−	9.40750i	−0.215361	−	0.803737i	−0.986039	−	0.166513i	$-0.946749\pi$
$137$	−2.52073	−	9.40750i	−0.215361	−	0.803737i	0.770679	−	0.637224i	$-0.219917\pi$
$138$	5.43279	−	1.45571i	0.462469	−	0.123918i
$139$	13.6153	−	7.86079i	1.15483	−	0.666744i	0.204773	−	0.978809i	$-0.434354\pi$
$139$	13.6153	−	7.86079i	1.15483	−	0.666744i	0.950060	+	0.312066i	$0.101021\pi$
$140$	16.7811	−	26.3596i	1.41826	−	2.22779i
$141$	−0.223361	−	0.833593i	−0.0188104	−	0.0702012i
$142$	−14.4840	−	8.36236i	−1.21547	−	0.701754i
$143$	−4.33070	+	2.60162i	−0.362151	+	0.217559i
$144$	−2.29172	−	3.96937i	−0.190977	−	0.330781i
$145$	20.8965	+	5.59919i	1.73536	+	0.464988i
$146$	17.9303	+	10.3521i	1.48393	+	0.856745i
$147$	−4.01139	+	5.73661i	−0.330854	+	0.473148i
$148$	6.62347	+	6.62347i	0.544446	+	0.544446i
$149$	−9.10487	−	9.10487i	−0.745900	−	0.745900i	0.227807	−	0.973706i	$-0.426845\pi$
$149$	−9.10487	−	9.10487i	−0.745900	−	0.745900i	−0.973706	+	0.227807i	$0.926845\pi$
$150$	7.90673	−	2.11860i	0.645582	−	0.172983i
$151$	−3.37382	−	0.904012i	−0.274557	−	0.0735674i	0.118913	−	0.992905i	$-0.462059\pi$
$151$	−3.37382	−	0.904012i	−0.274557	−	0.0735674i	−0.393471	+	0.919337i	$0.628726\pi$
$152$			35.7738i			2.90164i
$153$	−3.77833	+	6.54425i	−0.305460	+	0.529072i
$154$	−1.98389	−	8.93531i	−0.159866	−	0.720028i
$155$			15.5163i			1.24630i
$156$	−10.2592	+	10.6218i	−0.821391	+	0.850425i
$157$	0.246511	−	0.142323i	0.0196737	−	0.0113586i	−0.490131	−	0.871649i	$-0.663051\pi$
$157$	0.246511	−	0.142323i	0.0196737	−	0.0113586i	0.509805	+	0.860290i	$0.329718\pi$
$158$	1.43832	+	1.43832i	0.114427	+	0.114427i
$159$	1.53518	−	0.886338i	0.121748	−	0.0702911i
$160$	1.39548	+	2.41705i	0.110323	+	0.191084i
$161$	5.88392	−	1.30639i	0.463718	−	0.102958i
$162$	−0.639011	+	2.38482i	−0.0502055	+	0.187369i
$163$	9.69311	−	9.69311i	0.759223	−	0.759223i	−0.216958	−	0.976181i	$-0.569614\pi$
$163$	9.69311	−	9.69311i	0.759223	−	0.759223i	0.976181	+	0.216958i	$0.0696135\pi$
$164$	−9.77450	+	36.4789i	−0.763260	+	2.84853i
$165$	2.02027	−	3.49922i	0.157278	−	0.272414i
$166$	−3.76012	−	6.51273i	−0.291842	−	0.505486i
$167$	8.45838	−	2.26642i	0.654529	−	0.175381i	0.0837535	−	0.996487i	$-0.473309\pi$
$167$	8.45838	−	2.26642i	0.654529	−	0.175381i	0.570776	+	0.821106i	$0.306642\pi$
$168$	−6.32504	−	12.1409i	−0.487988	−	0.936689i
$169$	11.4772	+	6.10516i	0.882864	+	0.469628i
$170$	26.9001	−	46.5924i	2.06315	−	3.57347i
$171$	4.88884	−	4.88884i	0.373859	−	0.373859i
$172$	−14.4137			−1.09903
$173$	−10.8426			−0.824344			−0.412172	−	0.911106i	$-0.635230\pi$
$173$	−10.8426			−0.824344			−0.412172	+	0.911106i	$0.635230\pi$
$174$	13.0974	−	13.0974i	0.992909	−	0.992909i
$175$	8.56330	−	1.90129i	0.647324	−	0.143724i
$176$	6.20344	+	1.66221i	0.467602	+	0.125294i
$177$	1.39320	+	5.19948i	0.104719	+	0.390817i
$178$	−5.50285	−	3.17707i	−0.412456	−	0.238131i
$179$		−	8.17300i		−	0.610879i	−0.952212	−	0.305439i	$-0.901197\pi$
$179$		−	8.17300i		−	0.610879i	0.952212	−	0.305439i	$-0.0988033\pi$
$180$	3.05681	−	11.4082i	0.227841	−	0.850315i
$181$	−4.10394			−0.305043			−0.152522	−	0.988300i	$-0.548739\pi$
$181$	−4.10394			−0.305043			−0.152522	+	0.988300i	$0.548739\pi$
$182$	−17.0805	+	16.2162i	−1.26609	+	1.20203i
$183$	4.18771			0.309565
$184$	−3.05075	+	11.3856i	−0.224904	+	0.839355i
$185$			6.59499i			0.484873i
$186$	11.5051	+	6.64246i	0.843594	+	0.487049i
$187$	−2.74046	−	10.2275i	−0.200402	−	0.747911i
$188$	3.41416	+	0.914821i	0.249003	+	0.0667201i
$189$	−0.794791	+	2.52355i	−0.0578126	+	0.183561i
$190$	−34.8065	+	34.8065i	−2.52513	+	2.52513i
$191$	−4.41878			−0.319732			−0.159866	−	0.987139i	$-0.551106\pi$
$191$	−4.41878			−0.319732			−0.159866	+	0.987139i	$0.551106\pi$
$192$	−6.77728			−0.489108
$193$	−7.97873	+	7.97873i	−0.574322	+	0.574322i	−0.933333	−	0.359011i	$-0.883114\pi$
$193$	−7.97873	+	7.97873i	−0.574322	+	0.574322i	0.359011	+	0.933333i	$0.383114\pi$
$194$	11.2381	−	19.4650i	0.806849	−	1.39750i
$195$	−10.3956	+	0.180534i	−0.744443	+	0.0129283i
$196$	−12.1330	−	25.9761i	−0.866640	−	1.85544i
$197$	4.66242	−	1.24929i	0.332183	−	0.0890083i	−0.0888723	−	0.996043i	$-0.528326\pi$
$197$	4.66242	−	1.24929i	0.332183	−	0.0890083i	0.421056	+	0.907035i	$0.361660\pi$
$198$	−1.72974	−	2.99599i	−0.122927	−	0.212916i
$199$	−5.75542	+	9.96867i	−0.407991	+	0.706660i	−0.994664	−	0.103163i	$-0.967104\pi$
$199$	−5.75542	+	9.96867i	−0.407991	+	0.706660i	0.586674	+	0.809823i	$0.300437\pi$
$200$	−4.43998	+	16.5702i	−0.313954	+	1.17169i
$201$	3.93850	−	3.93850i	0.277801	−	0.277801i
$202$	−11.4721	+	42.8143i	−0.807171	+	3.01240i
$203$	14.6299	−	13.4143i	1.02681	−	0.941503i
$204$	−15.4749	−	26.8034i	−1.08346	−	1.87661i
$205$	−23.0273	+	13.2948i	−1.60829	+	0.928548i
$206$	−10.6923	−	10.6923i	−0.744965	−	0.744965i
$207$	1.97286	−	1.13903i	0.137124	−	0.0791683i
$208$	−4.55373	−	15.8860i	−0.315744	−	1.10150i
$209$			9.68766i			0.670109i
$210$	5.65859	−	17.9666i	0.390480	−	1.23982i
$211$	−1.96759	+	3.40797i	−0.135454	+	0.234614i	−0.925771	−	0.378085i	$-0.876583\pi$
$211$	−1.96759	+	3.40797i	−0.135454	+	0.234614i	0.790317	+	0.612699i	$0.209916\pi$
$212$			7.26037i			0.498644i
$213$	−6.54321	−	1.75325i	−0.448333	−	0.120130i
$214$	−11.2897	+	3.02506i	−0.771746	+	0.206789i
$215$	−7.17583	−	7.17583i	−0.489388	−	0.489388i
$216$	−3.65872	−	3.65872i	−0.248944	−	0.248944i
$217$	12.0092	+	7.64532i	0.815236	+	0.518998i
$218$	−37.6899	−	21.7603i	−2.55268	−	1.47379i
$219$	8.10009	+	2.17041i	0.547353	+	0.146663i
$220$	8.27446	+	14.3318i	0.557864	+	0.966249i
$221$	−18.9283	+	19.5974i	−1.27326	+	1.31826i
$222$	4.89006	+	2.82328i	0.328199	+	0.189486i
$223$	−2.38797	−	8.91203i	−0.159910	−	0.596794i	−0.998635	−	0.0522375i	$-0.983365\pi$
$223$	−2.38797	−	8.91203i	−0.159910	−	0.596794i	0.838724	−	0.544556i	$-0.183302\pi$
$224$	2.55831	+	0.110884i	0.170934	+	0.00740875i
$225$	2.87125	−	1.65772i	0.191417	−	0.110515i
$226$	32.7408	−	8.77286i	2.17788	−	0.583562i
$227$	−1.52167	−	5.67894i	−0.100997	−	0.376924i	0.896864	−	0.442307i	$-0.145840\pi$
$227$	−1.52167	−	5.67894i	−0.100997	−	0.376924i	−0.997860	+	0.0653827i	$0.979173\pi$
$228$	7.32903	+	27.3523i	0.485377	+	1.81145i
$229$	2.10769	−	0.564755i	0.139280	−	0.0373201i	−0.188505	−	0.982072i	$-0.560364\pi$
$229$	2.10769	−	0.564755i	0.139280	−	0.0373201i	0.327786	+	0.944752i	$0.393698\pi$
$230$	−14.0460	+	8.10945i	−0.926164	+	0.534721i
$231$	−1.71284	−	3.28779i	−0.112697	−	0.216321i
$232$	10.0468	+	37.4951i	0.659603	+	2.46167i
$233$	10.5892	+	6.11367i	0.693720	+	0.400520i	0.805004	−	0.593269i	$-0.202163\pi$
$233$	10.5892	+	6.11367i	0.693720	+	0.400520i	−0.111284	+	0.993789i	$0.535496\pi$
$234$	−4.31643	+	7.78542i	−0.282174	+	0.508949i
$235$	1.24429	+	2.15518i	0.0811688	+	0.140588i
$236$	−21.2956	−	5.70613i	−1.38622	−	0.371438i
$237$	0.713493	+	0.411935i	0.0463463	+	0.0267581i
$238$	−22.8066	−	43.7772i	−1.47833	−	2.83765i
$239$	7.97620	+	7.97620i	0.515938	+	0.515938i	0.916340	−	0.400402i	$-0.131130\pi$
$239$	7.97620	+	7.97620i	0.515938	+	0.515938i	−0.400402	+	0.916340i	$0.631130\pi$
$240$	9.34585	+	9.34585i	0.603272	+	0.603272i
$241$	−12.4172	+	3.32719i	−0.799865	+	0.214323i	−0.635525	−	0.772081i	$-0.719216\pi$
$241$	−12.4172	+	3.32719i	−0.799865	+	0.214323i	−0.164340	+	0.986404i	$0.552550\pi$
$242$	−21.5508	−	5.77453i	−1.38534	−	0.371201i
$243$			1.00000i			0.0641500i
$244$	−8.57584	+	14.8538i	−0.549012	+	0.950916i
$245$	6.89181	−	18.9726i	0.440302	−	1.21211i
$246$			22.7657i			1.45149i
$247$	21.3689	−	12.8371i	1.35967	−	0.816807i
$248$	−24.1114	+	13.9207i	−1.53107	+	0.883965i
$249$	−2.15380	−	2.15380i	−0.136491	−	0.136491i
$250$	10.3866	−	5.99669i	0.656904	−	0.379264i
$251$	−13.1084	−	22.7045i	−0.827397	−	1.43309i	−0.900073	−	0.435739i	$-0.856487\pi$
$251$	−13.1084	−	22.7045i	−0.827397	−	1.43309i	0.0726757	−	0.997356i	$-0.476846\pi$
$252$	−7.32339	−	7.98699i	−0.461330	−	0.503133i
$253$	−0.826153	+	3.08324i	−0.0519398	+	0.193842i
$254$	18.8741	−	18.8741i	1.18427	−	1.18427i
$255$	5.63986	−	21.0482i	0.353182	−	1.31809i
$256$	16.2685	−	28.1779i	1.01678	−	1.76112i
$257$	3.21682	+	5.57169i	0.200660	+	0.347553i	0.948741	−	0.316054i	$-0.102358\pi$
$257$	3.21682	+	5.57169i	0.200660	+	0.347553i	−0.748081	+	0.663607i	$0.769025\pi$
$258$	−8.39268	+	2.24881i	−0.522505	+	0.140005i
$259$	5.10431	+	3.24953i	0.317167	+	0.201916i
$260$	20.6483	−	37.2427i	1.28055	−	2.30970i
$261$	3.75108	−	6.49707i	0.232186	−	0.402158i
$262$	−31.7565	+	31.7565i	−1.96192	+	1.96192i
$263$	15.0122			0.925692			0.462846	−	0.886439i	$-0.346828\pi$
$263$	15.0122			0.925692			0.462846	+	0.886439i	$0.346828\pi$
$264$	7.25006			0.446210
$265$	−3.61457	+	3.61457i	−0.222041	+	0.222041i
$266$	9.78906	+	44.0893i	0.600206	+	2.70329i
$267$	−2.48593	−	0.666102i	−0.152136	−	0.0407648i
$268$	5.90435	+	22.0353i	0.360665	+	1.34602i
$269$	−19.1989	−	11.0845i	−1.17058	−	0.675834i	−0.216763	−	0.976224i	$-0.569550\pi$
$269$	−19.1989	−	11.0845i	−1.17058	−	0.675834i	−0.953816	+	0.300390i	$0.902883\pi$
$270$		−	7.11959i		−	0.433284i
$271$	5.45440	−	20.3561i	0.331331	−	1.23655i	−0.576461	−	0.817125i	$-0.695567\pi$
$271$	5.45440	−	20.3561i	0.331331	−	1.23655i	0.907792	−	0.419420i	$-0.137767\pi$
$272$	34.6354			2.10008
$273$	−4.98246	+	8.13481i	−0.301552	+	0.492341i
$274$	24.0460			1.45267
$275$	−1.20236	+	4.48727i	−0.0725051	+	0.270593i
$276$			9.33031i			0.561619i
$277$	8.54607	+	4.93407i	0.513483	+	0.296460i	0.734264	−	0.678864i	$-0.237527\pi$
$277$	8.54607	+	4.93407i	0.513483	+	0.296460i	−0.220781	+	0.975323i	$0.570861\pi$
$278$	10.0463	+	37.4932i	0.602535	+	2.24869i
$279$	5.19745	+	1.39265i	0.311163	+	0.0833760i
$280$	26.6790	+	29.0965i	1.59437	+	1.73885i
$281$	21.3933	−	21.3933i	1.27622	−	1.27622i	0.333449	−	0.942768i	$-0.391788\pi$
$281$	21.3933	−	21.3933i	1.27622	−	1.27622i	0.942768	−	0.333449i	$-0.108212\pi$
$282$	2.13070			0.126881
$283$	21.4880			1.27733			0.638666	−	0.769484i	$-0.279487\pi$
$283$	21.4880			1.27733			0.638666	+	0.769484i	$0.279487\pi$
$284$	19.6183	−	19.6183i	1.16413	−	1.16413i
$285$	−9.96859	+	17.2661i	−0.590488	+	1.02276i
$286$	−3.43705	−	11.9904i	−0.203237	−	0.709008i
$287$	−1.05639	+	24.3731i	−0.0623570	+	1.43870i
$288$	0.934879	−	0.250500i	0.0550883	−	0.0147609i
$289$	−20.0515	−	34.7302i	−1.17950	−	2.04295i
$290$	−26.7062	+	46.2564i	−1.56824	+	2.71627i
$291$	2.35617	−	8.79336i	0.138121	−	0.515476i
$292$	−24.2862	+	24.2862i	−1.42124	+	1.42124i
$293$	0.259901	−	0.969962i	0.0151836	−	0.0566658i	−0.957918	−	0.287041i	$-0.907329\pi$
$293$	0.259901	−	0.969962i	0.0151836	−	0.0566658i	0.973102	+	0.230375i	$0.0739952\pi$
$294$	−11.1175	−	13.2322i	−0.648385	−	0.771719i
$295$	−7.76120	−	13.4428i	−0.451874	−	0.782670i
$296$	−10.2482	+	5.91678i	−0.595662	+	0.343906i
$297$	−0.990792	−	0.990792i	−0.0574916	−	0.0574916i
$298$	27.5316	−	15.8954i	1.59486	−	0.920795i
$299$	7.89571	−	2.26330i	0.456620	−	0.130890i
$300$			13.5791i			0.783989i
$301$	−9.08960	+	2.01814i	−0.523916	+	0.116324i
$302$	4.31182	−	7.46828i	0.248117	−	0.429751i
$303$			17.9528i			1.03136i
$304$	−30.6095	−	8.20179i	−1.75557	−	0.470405i
$305$	−11.6644	+	3.12547i	−0.667903	+	0.178964i
$306$	−13.1925	−	13.1925i	−0.754164	−	0.754164i
$307$	4.86151	+	4.86151i	0.277461	+	0.277461i	0.832095	−	0.554634i	$-0.187142\pi$
$307$	4.86151	+	4.86151i	0.277461	+	0.277461i	−0.554634	+	0.832095i	$0.687142\pi$
$308$	15.1694	+	0.657483i	0.864357	+	0.0374636i
$309$	−5.30399	−	3.06226i	−0.301734	−	0.174206i
$310$	−37.0037	−	9.91512i	−2.10167	−	0.563141i
$311$	−6.85636	−	11.8756i	−0.388789	−	0.673402i	0.603498	−	0.797364i	$-0.293773\pi$
$311$	−6.85636	−	11.8756i	−0.388789	−	0.673402i	−0.992287	+	0.123963i	$0.960440\pi$
$312$	−9.60707	−	15.9921i	−0.543893	−	0.905372i
$313$	−29.5010	−	17.0324i	−1.66750	−	0.962730i	−0.968981	−	0.247137i	$-0.920510\pi$
$313$	−29.5010	−	17.0324i	−1.66750	−	0.962730i	−0.698517	−	0.715593i	$-0.746156\pi$
$314$	0.181892	+	0.678830i	0.0102648	+	0.0383086i
$315$	0.330370	−	7.62227i	0.0186142	−	0.429466i
$316$	−2.92226	+	1.68717i	−0.164390	+	0.0949106i
$317$	9.41539	−	2.52285i	0.528821	−	0.141697i	0.0154772	−	0.999880i	$-0.495073\pi$
$317$	9.41539	−	2.52285i	0.528821	−	0.141697i	0.513344	+	0.858183i	$0.328407\pi$
$318$	1.13276	+	4.22752i	0.0635220	+	0.237067i
$319$	2.72070	+	10.1538i	0.152330	+	0.568503i
$320$	18.8774	−	5.05818i	1.05528	−	0.282761i
$321$	−4.09974	+	2.36698i	−0.228825	+	0.132112i
$322$	−0.644371	+	14.8669i	−0.0359094	+	0.828500i
$323$	13.5222	+	50.4655i	0.752394	+	2.80797i
$324$	−3.54699	−	2.04786i	−0.197055	−	0.113770i
$325$	11.4912	−	3.29395i	0.637417	−	0.182715i
$326$	16.9223	+	29.3103i	0.937241	+	1.62335i
$327$	−17.0265	−	4.56224i	−0.941569	−	0.252293i
$328$	−41.3184	−	23.8552i	−2.28143	−	1.31718i
$329$	2.28114	+	0.0988707i	0.125763	+	0.00545092i
$330$	7.05403	+	7.05403i	0.388312	+	0.388312i
$331$	14.6501	+	14.6501i	0.805241	+	0.805241i	0.983909	−	0.178669i	$-0.0571790\pi$
$331$	14.6501	+	14.6501i	0.805241	+	0.805241i	−0.178669	+	0.983909i	$0.557179\pi$
$332$	12.0502	−	3.22883i	0.661339	−	0.177205i
$333$	2.20910	+	0.591926i	0.121058	+	0.0324374i
$334$			21.6200i			1.18299i
$335$	−8.03080	+	13.9098i	−0.438769	+	0.759971i
$336$	11.8384	−	2.62844i	0.645835	−	0.143393i
$337$		−	26.8744i		−	1.46394i	−0.681336	−	0.731971i	$-0.738601\pi$
$337$		−	26.8744i		−	1.46394i	0.681336	−	0.731971i	$-0.261399\pi$
$338$	−21.8938	+	23.4699i	−1.19087	+	1.27659i
$339$	11.8895	−	6.86440i	0.645748	−	0.372823i
$340$	63.1083	+	63.1083i	3.42253	+	3.42253i
$341$	−6.52943	+	3.76977i	−0.353588	+	0.204144i
$342$	8.53499	+	14.7830i	0.461520	+	0.799376i
$343$	−11.2884	−	14.6824i	−0.609517	−	0.792773i
$344$	4.71286	−	17.5886i	0.254101	−	0.948316i
$345$	−4.64509	+	4.64509i	−0.250083	+	0.250083i
$346$	6.92851	−	25.8576i	0.372479	−	1.39011i
$347$	3.08435	−	5.34226i	0.165577	−	0.286787i	−0.771283	−	0.636492i	$-0.780385\pi$
$347$	3.08435	−	5.34226i	0.165577	−	0.286787i	0.936860	+	0.349705i	$0.113718\pi$
$348$	15.3634	+	26.6101i	0.823562	+	1.42645i
$349$	20.8536	−	5.58771i	1.11627	−	0.299103i	0.346896	−	0.937904i	$-0.387236\pi$
$349$	20.8536	−	5.58771i	1.11627	−	0.299103i	0.769372	+	0.638801i	$0.220569\pi$
$350$	−0.937801	+	21.6369i	−0.0501276	+	1.15654i
$351$	−0.872572	+	3.49837i	−0.0465744	+	0.186729i
$352$	−0.678077	+	1.17446i	−0.0361416	+	0.0625992i
$353$	9.36561	−	9.36561i	0.498481	−	0.498481i	−0.412484	−	0.910965i	$-0.635339\pi$
$353$	9.36561	−	9.36561i	0.498481	−	0.498481i	0.910965	+	0.412484i	$0.135339\pi$
$354$	−13.2901			−0.706361
$355$	19.5339			1.03675
$356$	7.45348	−	7.45348i	0.395034	−	0.395034i
$357$	−13.5118	−	14.7361i	−0.715119	−	0.779918i
$358$	19.4911	+	5.22264i	1.03014	+	0.276025i
$359$	−1.27796	−	4.76941i	−0.0674482	−	0.251720i	0.923967	−	0.382473i	$-0.124927\pi$
$359$	−1.27796	−	4.76941i	−0.0674482	−	0.251720i	−0.991415	+	0.130753i	$0.958261\pi$
$360$	12.9216	+	7.46031i	0.681030	+	0.393193i
$361$		−	28.8016i		−	1.51587i
$362$	2.62246	−	9.78717i	0.137834	−	0.514402i
$363$	−9.03666			−0.474302
$364$	−18.6507	−	34.3316i	−0.977565	−	1.79947i
$365$	−24.1818			−1.26573
$366$	−2.67600	+	9.98695i	−0.139877	+	0.522026i
$367$		−	20.4939i		−	1.06978i	−0.844923	−	0.534888i	$-0.820354\pi$
$367$		−	20.4939i		−	1.06978i	0.844923	−	0.534888i	$-0.179646\pi$
$368$	−9.04250	−	5.22069i	−0.471373	−	0.272147i
$369$	2.38652	+	8.90661i	0.124237	+	0.463660i
$370$	−15.7279	−	4.21427i	−0.817653	−	0.219090i
$371$	1.01657	+	4.57856i	0.0527776	+	0.237707i
$372$	−15.5834	+	15.5834i	−0.807960	+	0.807960i
$373$	23.2429			1.20347			0.601735	−	0.798696i	$-0.294476\pi$
$373$	23.2429			1.20347			0.601735	+	0.798696i	$0.294476\pi$
$374$	26.1420			1.35177
$375$	3.43490	−	3.43490i	0.177378	−	0.177378i
$376$	−2.23267	+	3.86710i	−0.115141	+	0.199430i
$377$	18.7918	−	19.4561i	0.967829	−	1.00204i
$378$	−5.51034	−	3.50801i	−0.283421	−	0.180433i
$379$	−20.6487	+	5.53282i	−1.06066	+	0.284202i	−0.746648	−	0.665219i	$-0.768338\pi$
$379$	−20.6487	+	5.53282i	−1.06066	+	0.284202i	−0.314007	+	0.949421i	$0.601671\pi$
$380$	−40.8285	−	70.7170i	−2.09446	−	3.62770i
$381$	5.40554	−	9.36268i	0.276934	−	0.479665i
$382$	2.82365	−	10.5380i	0.144471	−	0.539171i
$383$	−7.50873	+	7.50873i	−0.383678	+	0.383678i	−0.872425	−	0.488747i	$-0.837454\pi$
$383$	−7.50873	+	7.50873i	−0.383678	+	0.383678i	0.488747	+	0.872425i	$0.337454\pi$
$384$	4.83176	−	18.0324i	0.246570	−	0.920211i
$385$	7.22476	+	7.87941i	0.368208	+	0.401572i
$386$	−13.9294	−	24.1264i	−0.708986	−	1.22800i
$387$	−3.04772	+	1.75960i	−0.154924	+	0.0894456i
$388$	26.3649	+	26.3649i	1.33847	+	1.33847i
$389$	−14.3360	+	8.27689i	−0.726864	+	0.419655i	−0.817274	−	0.576250i	$-0.804516\pi$
$389$	−14.3360	+	8.27689i	−0.726864	+	0.419655i	0.0904098	+	0.995905i	$0.471182\pi$
$390$	6.21235	−	24.9070i	0.314575	−	1.26121i
$391$			17.2146i			0.870578i
$392$	35.6652	−	6.31210i	1.80137	−	0.318809i
$393$	−9.09505	+	15.7531i	−0.458785	+	0.794638i
$394$			11.9173i			0.600387i
$395$	−2.29480	−	0.614890i	−0.115464	−	0.0309385i
$396$	5.54333	−	1.48533i	0.278563	−	0.0746407i
$397$	−20.9177	−	20.9177i	−1.04983	−	1.04983i	−0.998692	−	0.0511377i	$-0.983715\pi$
$397$	−20.9177	−	20.9177i	−1.04983	−	1.04983i	−0.0511377	−	0.998692i	$-0.516285\pi$
$398$	−20.0957	−	20.0957i	−1.00731	−	1.00731i
$399$	8.45163	+	16.2228i	0.423111	+	0.812158i
$400$	−13.1602	−	7.59805i	−0.658011	−	0.379903i
$401$	−9.79088	−	2.62346i	−0.488933	−	0.131009i	0.00592592	−	0.999982i	$-0.498114\pi$
$401$	−9.79088	−	2.62346i	−0.488933	−	0.131009i	−0.494859	+	0.868973i	$0.664780\pi$
$402$	6.87588	+	11.9094i	0.342938	+	0.593986i
$403$	16.9674	+	9.40718i	0.845209	+	0.468605i
$404$	−63.6785	−	36.7648i	−3.16813	−	1.82912i
$405$	−0.746344	−	2.78539i	−0.0370861	−	0.138407i
$406$	22.6422	+	43.4615i	1.12371	+	2.15696i
$407$	−2.77523	+	1.60228i	−0.137563	+	0.0794222i
$408$	37.7674	−	10.1197i	1.86977	−	0.501002i
$409$	0.754787	+	2.81690i	0.0373218	+	0.139287i	0.982073	−	0.188502i	$-0.0603632\pi$
$409$	0.754787	+	2.81690i	0.0373218	+	0.139287i	−0.944751	+	0.327789i	$0.893697\pi$
$410$	−16.9910	−	63.4114i	−0.839128	−	3.13167i
$411$	9.40750	−	2.52073i	0.464038	−	0.124338i
$412$	21.7236	−	12.5421i	1.07025	−	0.617907i
$413$	−14.2285	−	0.616700i	−0.700136	−	0.0303458i
$414$	1.45571	+	5.43279i	0.0715443	+	0.267007i
$415$	7.60664	+	4.39170i	0.373395	+	0.215580i
$416$	3.48913	−	0.0605938i	0.171069	−	0.00297086i
$417$	7.86079	+	13.6153i	0.384945	+	0.666744i
$418$	−23.1033	−	6.19052i	−1.13002	−	0.302788i
$419$	−8.98142	−	5.18542i	−0.438771	−	0.253325i	0.264305	−	0.964439i	$-0.414857\pi$
$419$	−8.98142	−	5.18542i	−0.438771	−	0.253325i	−0.703076	+	0.711115i	$0.748191\pi$
$420$	26.3596	+	16.7811i	1.28621	+	0.818835i
$421$	26.7368	+	26.7368i	1.30307	+	1.30307i	0.926310	+	0.376762i	$0.122962\pi$
$421$	26.7368	+	26.7368i	1.30307	+	1.30307i	0.376762	+	0.926310i	$0.377038\pi$
$422$	−6.87008	−	6.87008i	−0.334430	−	0.334430i
$423$	0.833593	−	0.223361i	0.0405307	−	0.0108602i
$424$	−8.85966	−	2.37394i	−0.430263	−	0.115289i
$425$			25.0536i			1.21528i
$426$	8.36236	−	14.4840i	0.405158	−	0.701754i
$427$	−3.32836	+	10.5679i	−0.161071	+	0.511417i
$428$		−	19.3890i		−	0.937201i
$429$	−2.60162	−	4.33070i	−0.125608	−	0.209088i
$430$	21.6985	−	12.5276i	1.04640	−	0.604137i
$431$	−17.2979	−	17.2979i	−0.833209	−	0.833209i	0.154746	−	0.987954i	$-0.450544\pi$
$431$	−17.2979	−	17.2979i	−0.833209	−	0.833209i	−0.987954	+	0.154746i	$0.950544\pi$
$432$	3.96937	−	2.29172i	0.190977	−	0.110260i
$433$	−8.76052	−	15.1737i	−0.421004	−	0.729200i	0.575034	−	0.818129i	$-0.304989\pi$
$433$	−8.76052	−	15.1737i	−0.421004	−	0.729200i	−0.996038	+	0.0889293i	$0.971655\pi$
$434$	−25.9067	+	23.7543i	−1.24356	+	1.14024i
$435$	−5.59919	+	20.8965i	−0.268461	+	1.00191i
$436$	51.0501	−	51.0501i	2.44486	−	2.44486i
$437$	4.07647	−	15.2136i	0.195004	−	0.727764i
$438$	−10.3521	+	17.9303i	−0.494642	+	0.856745i
$439$	9.94646	+	17.2278i	0.474719	+	0.822237i	0.999581	−	0.0289504i	$-0.00921649\pi$
$439$	9.94646	+	17.2278i	0.474719	+	0.822237i	−0.524862	+	0.851187i	$0.675883\pi$
$440$	−20.1943	+	5.41104i	−0.962724	+	0.257961i
$441$	−5.73661	−	4.01139i	−0.273172	−	0.191019i
$442$	−34.6409	−	57.6636i	−1.64770	−	2.74278i
$443$	7.68921	−	13.3181i	0.365325	−	0.632762i	−0.623503	−	0.781821i	$-0.714291\pi$
$443$	7.68921	−	13.3181i	0.365325	−	0.632762i	0.988828	+	0.149059i	$0.0476245\pi$
$444$	−6.62347	+	6.62347i	−0.314336	+	0.314336i
$445$	7.42142			0.351809
$446$	22.7796			1.07864
$447$	9.10487	−	9.10487i	0.430645	−	0.430645i
$448$	5.38652	−	17.1028i	0.254489	−	0.808032i
$449$	−3.38883	−	0.908034i	−0.159929	−	0.0428528i	0.177966	−	0.984037i	$-0.443048\pi$
$449$	−3.38883	−	0.908034i	−0.159929	−	0.0428528i	−0.337895	+	0.941184i	$0.609715\pi$
$450$	2.11860	+	7.90673i	0.0998719	+	0.372727i
$451$	−11.1892	−	6.46006i	−0.526877	−	0.304192i
$452$			56.2292i			2.64480i
$453$	0.904012	−	3.37382i	0.0424742	−	0.158516i
$454$	14.5156			0.681252
$455$	7.80673	−	26.3773i	0.365985	−	1.23659i
$456$	−35.7738			−1.67526
$457$	−7.89373	+	29.4598i	−0.369253	+	1.37807i	0.492310	+	0.870420i	$0.336153\pi$
$457$	−7.89373	+	29.4598i	−0.369253	+	1.37807i	−0.861563	+	0.507651i	$0.830514\pi$
$458$			5.38736i			0.251735i
$459$	−6.54425	−	3.77833i	−0.305460	−	0.176357i
$460$	−6.96362	−	25.9886i	−0.324680	−	1.21172i
$461$	19.6958	+	5.27746i	0.917323	+	0.245796i	0.686441	−	0.727186i	$-0.259172\pi$
$461$	19.6958	+	5.27746i	0.917323	+	0.245796i	0.230882	+	0.972982i	$0.425839\pi$
$462$	8.93531	−	1.98389i	0.415708	−	0.0922989i
$463$	7.72370	−	7.72370i	0.358951	−	0.358951i	−0.504475	−	0.863426i	$-0.668314\pi$
$463$	7.72370	−	7.72370i	0.358951	−	0.358951i	0.863426	+	0.504475i	$0.168314\pi$
$464$	−34.3857			−1.59632
$465$	−15.5163			−0.719553
$466$	−21.3466	+	21.3466i	−0.988863	+	0.988863i
$467$	−17.0696	+	29.5655i	−0.789888	+	1.36813i	0.136147	+	0.990689i	$0.456528\pi$
$467$	−17.0696	+	29.5655i	−0.789888	+	1.36813i	−0.926035	+	0.377438i	$0.876805\pi$
$468$	−10.6218	−	10.2592i	−0.490993	−	0.474230i
$469$	6.80872	+	13.0693i	0.314398	+	0.603484i
$470$	−5.93484	+	1.59023i	−0.273754	+	0.0733521i
$471$	0.142323	+	0.246511i	0.00655789	+	0.0113586i
$472$	13.9261	−	24.1208i	0.641002	−	1.11025i
$473$	1.27626	−	4.76306i	0.0586824	−	0.219006i
$474$	−1.43832	+	1.43832i	−0.0660643	+	0.0660643i
$475$	5.93278	−	22.1414i	0.272215	−	1.01592i
$476$	79.9390	−	17.7487i	3.66400	−	0.813510i
$477$	0.886338	+	1.53518i	0.0405826	+	0.0702911i
$478$	−24.1187	+	13.9249i	−1.10316	+	0.636912i
$479$	−12.2833	−	12.2833i	−0.561240	−	0.561240i	0.368420	−	0.929659i	$-0.379899\pi$
$479$	−12.2833	−	12.2833i	−0.561240	−	0.561240i	−0.929659	+	0.368420i	$0.879899\pi$
$480$	−2.41705	+	1.39548i	−0.110323	+	0.0636947i
$481$	7.21176	+	3.99838i	0.328828	+	0.182310i
$482$		−	31.7390i		−	1.44567i
$483$	1.30639	+	5.88392i	0.0594430	+	0.267727i
$484$	18.5058	−	32.0530i	0.841172	−	1.45695i
$485$			26.2515i			1.19202i
$486$	−2.38482	−	0.639011i	−0.108178	−	0.0289861i
$487$	−12.3178	+	3.30054i	−0.558171	+	0.149562i	−0.526866	−	0.849948i	$-0.676633\pi$
$487$	−12.3178	+	3.30054i	−0.558171	+	0.149562i	−0.0313053	+	0.999510i	$0.509966\pi$
$488$	−15.3217	−	15.3217i	−0.693579	−	0.693579i
$489$	9.69311	+	9.69311i	0.438337	+	0.438337i
$490$	40.8423	+	28.5595i	1.84507	+	1.29018i
$491$	−16.0173	−	9.24760i	−0.722851	−	0.417339i	0.0929498	−	0.995671i	$-0.470370\pi$
$491$	−16.0173	−	9.24760i	−0.722851	−	0.417339i	−0.815801	+	0.578332i	$0.803704\pi$
$492$	−36.4789	−	9.77450i	−1.64460	−	0.440669i
$493$	28.3456	+	49.0961i	1.27662	+	2.21118i
$494$	16.9593	+	59.1640i	0.763037	+	2.66191i
$495$	3.49922	+	2.02027i	0.157278	+	0.0908046i
$496$	−6.38314	−	23.8222i	−0.286612	−	1.06965i
$497$	9.62489	−	15.1186i	0.431735	−	0.678164i
$498$	6.51273	−	3.76012i	0.291842	−	0.168495i
$499$	−36.0336	+	9.65516i	−1.61308	+	0.432224i	−0.948960	−	0.315398i	$-0.897862\pi$
$499$	−36.0336	+	9.65516i	−1.61308	+	0.432224i	−0.664124	+	0.747622i	$0.731195\pi$
$500$	5.14938	+	19.2178i	0.230287	+	0.859444i
$501$	2.26642	+	8.45838i	0.101256	+	0.377893i
$502$	62.5226	−	16.7529i	2.79052	−	0.747718i
$503$	−12.6061	+	7.27816i	−0.562080	+	0.324517i	−0.753980	−	0.656897i	$-0.771868\pi$
$503$	−12.6061	+	7.27816i	−0.562080	+	0.324517i	0.191900	+	0.981415i	$0.438535\pi$
$504$	12.1409	−	6.32504i	0.540798	−	0.281740i
$505$	−13.3990	−	50.0057i	−0.596247	−	2.22522i
$506$	−6.82507	−	3.94046i	−0.303411	−	0.175175i
$507$	−6.10516	+	11.4772i	−0.271140	+	0.509722i
$508$	22.1396	+	38.3468i	0.982284	+	1.70137i
$509$	0.521178	+	0.139649i	0.0231008	+	0.00618984i	0.270351	−	0.962762i	$-0.412860\pi$
$509$	0.521178	+	0.139649i	0.0231008	+	0.00618984i	−0.247250	+	0.968952i	$0.579527\pi$
$510$	46.5924	+	26.9001i	2.06315	+	1.19116i
$511$	−11.9150	+	18.7160i	−0.527089	+	0.827945i
$512$	30.4022	+	30.4022i	1.34360	+	1.34360i
$513$	4.88884	+	4.88884i	0.215848	+	0.215848i
$514$	−15.3431	+	4.11117i	−0.676755	+	0.181336i
$515$	17.0592	+	4.57100i	0.751718	+	0.201422i
$516$		−	14.4137i		−	0.634526i
$517$	−0.604614	+	1.04722i	−0.0265909	+	0.0460567i
$518$	−11.0113	+	10.0964i	−0.483807	+	0.443610i
$519$		−	10.8426i		−	0.475935i
$520$	38.6950	+	37.3740i	1.69689	+	1.63896i
$521$	−30.2442	+	17.4615i	−1.32502	+	0.765003i	−0.984525	−	0.175242i	$-0.943929\pi$
$521$	−30.2442	+	17.4615i	−1.32502	+	0.765003i	−0.340499	+	0.940245i	$0.610596\pi$
$522$	13.0974	+	13.0974i	0.573256	+	0.573256i
$523$	−18.2352	+	10.5281i	−0.797371	+	0.460362i	−0.842551	−	0.538616i	$-0.818947\pi$
$523$	−18.2352	+	10.5281i	−0.797371	+	0.460362i	0.0451800	+	0.998979i	$0.485614\pi$
$524$	−37.2507	−	64.5201i	−1.62730	−	2.81857i
$525$	1.90129	+	8.56330i	0.0829791	+	0.373733i
$526$	−9.59297	+	35.8014i	−0.418273	+	1.56102i
$527$	−28.7516	+	28.7516i	−1.25244	+	1.25244i
$528$	−1.66221	+	6.20344i	−0.0723383	+	0.269970i
$529$	−8.90520	+	15.4243i	−0.387183	+	0.670620i
$530$	−6.31036	−	10.9299i	−0.274104	−	0.474763i
$531$	−5.19948	+	1.39320i	−0.225638	+	0.0604596i
$532$	−74.8500	−	3.24420i	−3.24516	−	0.140654i
$533$	0.577279	+	33.2411i	0.0250047	+	1.43983i
$534$	3.17707	−	5.50285i	0.137485	−	0.238131i
$535$	9.65279	−	9.65279i	0.417326	−	0.417326i
$536$	−28.8198			−1.24482
$537$	8.17300			0.352691
$538$	38.7029	−	38.7029i	1.66860	−	1.66860i
$539$	9.65825	−	1.70934i	0.416010	−	0.0736264i
$540$	11.4082	+	3.05681i	0.490929	+	0.131544i
$541$	8.30427	+	30.9919i	0.357028	+	1.33245i	0.877913	+	0.478821i	$0.158936\pi$
$541$	8.30427	+	30.9919i	0.357028	+	1.33245i	−0.520884	+	0.853627i	$0.674398\pi$
$542$	45.0603	+	26.0156i	1.93550	+	1.11746i
$543$		−	4.10394i		−	0.176117i
$544$	−1.89294	+	7.06456i	−0.0811592	+	0.302890i
$545$	50.8305			2.17734
$546$	−16.2162	−	17.0805i	−0.693991	−	0.730978i
$547$	12.5039			0.534630			0.267315	−	0.963609i	$-0.413864\pi$
$547$	12.5039			0.534630			0.267315	+	0.963609i	$0.413864\pi$
$548$	−10.3242	+	38.5304i	−0.441027	+	1.64594i
$549$			4.18771i			0.178727i
$550$	−9.93303	−	5.73484i	−0.423546	−	0.244534i
$551$	−13.4247	−	50.1016i	−0.571911	−	2.13440i
$552$	−11.3856	−	3.05075i	−0.484602	−	0.129849i
$553$	−1.60662	+	1.47313i	−0.0683203	+	0.0626439i
$554$	−17.2279	+	17.2279i	−0.731944	+	0.731944i
$555$	−6.59499			−0.279942
$556$	−64.3911			−2.73079
$557$	22.2599	−	22.2599i	0.943183	−	0.943183i	−0.0552879	−	0.998470i	$-0.517608\pi$
$557$	22.2599	−	22.2599i	0.943183	−	0.943183i	0.998470	+	0.0552879i	$0.0176077\pi$
$558$	−6.64246	+	11.5051i	−0.281198	+	0.487049i
$559$	−12.1974	+	3.49639i	−0.515897	+	0.147882i
$560$	−31.0127	+	16.1567i	−1.31053	+	0.682746i
$561$	10.2275	−	2.74046i	0.431807	−	0.115702i
$562$	37.3487	+	64.6898i	1.57546	+	2.72877i
$563$	1.85725	−	3.21684i	0.0782736	−	0.135574i	−0.824232	−	0.566253i	$-0.808393\pi$
$563$	1.85725	−	3.21684i	0.0782736	−	0.135574i	0.902505	+	0.430679i	$0.141726\pi$
$564$	−0.914821	+	3.41416i	−0.0385209	+	0.143762i
$565$	−27.9937	+	27.9937i	−1.17770	+	1.17770i
$566$	−13.7311	+	51.2452i	−0.577161	+	2.15399i
$567$	−2.52355	−	0.794791i	−0.105979	−	0.0333781i
$568$	17.5251	+	30.3544i	0.735337	+	1.27364i
$569$	24.9147	−	14.3845i	1.04448	−	0.603030i	0.123381	−	0.992359i	$-0.460626\pi$
$569$	24.9147	−	14.3845i	1.04448	−	0.603030i	0.921099	+	0.389329i	$0.127293\pi$
$570$	−34.8065	−	34.8065i	−1.45789	−	1.45789i
$571$	−38.1385	+	22.0193i	−1.59605	+	0.921478i	−0.603808	+	0.797130i	$0.706351\pi$
$571$	−38.1385	+	22.0193i	−1.59605	+	0.921478i	−0.992239	+	0.124348i	$0.960316\pi$
$572$	20.6887	−	0.359289i	0.865038	−	0.0150226i
$573$		−	4.41878i		−	0.184597i
$574$	−57.4504	−	18.0940i	−2.39793	−	0.755228i
$575$	3.77640	−	6.54091i	0.157487	−	0.272775i
$576$		−	6.77728i		−	0.282387i
$577$	20.0715	+	5.37814i	0.835587	+	0.223895i	0.651149	−	0.758950i	$-0.274287\pi$
$577$	20.0715	+	5.37814i	0.835587	+	0.223895i	0.184437	+	0.982844i	$0.440954\pi$
$578$	95.6385	−	25.6263i	3.97804	−	1.06591i
$579$	−7.97873	−	7.97873i	−0.331585	−	0.331585i
$580$	−62.6533	−	62.6533i	−2.60154	−	2.60154i
$581$	7.14704	−	3.72340i	0.296509	−	0.154473i
$582$	19.4650	+	11.2381i	0.806849	+	0.465835i
$583$	−2.39922	−	0.642870i	−0.0993657	−	0.0266250i
$584$	−21.6950	−	37.5769i	−0.897746	−	1.55494i
$585$	−0.180534	−	10.3956i	−0.00746417	−	0.429804i
$586$	2.14711	+	1.23963i	0.0886962	+	0.0512088i
$587$	11.1326	+	41.5473i	0.459491	+	1.71484i	0.674540	+	0.738239i	$0.264342\pi$
$587$	11.1326	+	41.5473i	0.459491	+	1.71484i	−0.215049	+	0.976603i	$0.568991\pi$
$588$	25.9761	−	12.1330i	1.07124	−	0.500355i
$589$	32.2180	−	18.6011i	1.32752	−	0.766444i
$590$	37.0182	−	9.91899i	1.52401	−	0.408358i
$591$	1.24929	+	4.66242i	0.0513890	+	0.191786i
$592$	−2.71306	−	10.1253i	−0.111506	−	0.416146i
$593$	−1.71884	+	0.460561i	−0.0705842	+	0.0189130i	−0.293938	−	0.955824i	$-0.594966\pi$
$593$	−1.71884	+	0.460561i	−0.0705842	+	0.0189130i	0.223354	+	0.974737i	$0.428299\pi$
$594$	2.99599	−	1.72974i	0.122927	−	0.0709719i
$595$	48.6338	+	30.9614i	1.99379	+	1.26929i
$596$	13.6494	+	50.9403i	0.559102	+	2.08660i
$597$	−9.96867	−	5.75542i	−0.407991	−	0.235553i
$598$	0.352124	+	20.2761i	0.0143994	+	0.829153i
$599$	8.48260	+	14.6923i	0.346590	+	0.600311i	0.985641	−	0.168853i	$-0.0540063\pi$
$599$	8.48260	+	14.6923i	0.346590	+	0.600311i	−0.639052	+	0.769164i	$0.720673\pi$
$600$	−16.5702	−	4.43998i	−0.676477	−	0.181262i
$601$	−30.5871	−	17.6595i	−1.24767	−	0.720345i	−0.277029	−	0.960862i	$-0.589350\pi$
$601$	−30.5871	−	17.6595i	−1.24767	−	0.720345i	−0.970645	+	0.240517i	$0.922683\pi$
$602$	0.995438	−	22.9667i	0.0405710	−	0.936052i
$603$	3.93850	+	3.93850i	0.160388	+	0.160388i
$604$	10.1156	+	10.1156i	0.411599	+	0.411599i
$605$	25.1706	−	6.74445i	1.02333	−	0.274201i
$606$	−42.8143	−	11.4721i	−1.73921	−	0.466021i
$607$		−	20.2834i		−	0.823279i	−0.911347	−	0.411639i	$-0.864956\pi$
$607$		−	20.2834i		−	0.823279i	0.911347	−	0.411639i	$-0.135044\pi$
$608$	3.34582	−	5.79513i	0.135691	−	0.235024i
$609$	13.4143	+	14.6299i	0.543577	+	0.592832i
$610$		−	29.8148i		−	1.20717i
$611$	3.11112	−	0.0540290i	0.125862	−	0.00218578i
$612$	26.8034	−	15.4749i	1.08346	−	0.625537i
$613$	−17.5571	−	17.5571i	−0.709123	−	0.709123i	0.257228	−	0.966351i	$-0.417191\pi$
$613$	−17.5571	−	17.5571i	−0.709123	−	0.709123i	−0.966351	+	0.257228i	$0.917191\pi$
$614$	−14.7004	+	8.48727i	−0.593259	+	0.342518i
$615$	−13.2948	−	23.0273i	−0.536098	−	0.928548i
$616$	−5.76228	+	18.2959i	−0.232169	+	0.737163i
$617$	7.80877	−	29.1427i	0.314369	−	1.17324i	−0.610206	−	0.792243i	$-0.708913\pi$
$617$	7.80877	−	29.1427i	0.314369	−	1.17324i	0.924575	−	0.380999i	$-0.124420\pi$
$618$	10.6923	−	10.6923i	0.430106	−	0.430106i
$619$	−10.4480	+	38.9926i	−0.419942	+	1.56724i	0.354785	+	0.934948i	$0.384554\pi$
$619$	−10.4480	+	38.9926i	−0.419942	+	1.56724i	−0.774727	+	0.632296i	$0.782113\pi$
$620$	31.7753	−	55.0364i	1.27612	−	2.21031i
$621$	1.13903	+	1.97286i	0.0457078	+	0.0791683i
$622$	32.7024	−	8.76259i	1.31125	−	0.351348i
$623$	3.65674	−	5.74395i	0.146504	−	0.230127i
$624$	15.8860	−	4.55373i	0.635951	−	0.182295i
$625$	−15.2925	+	26.4874i	−0.611701	+	1.05950i
$626$	59.4708	−	59.4708i	2.37693	−	2.37693i
$627$	−9.68766			−0.386888
$628$	−1.16583			−0.0465216
$629$	−12.2204	+	12.2204i	−0.487260	+	0.487260i
$630$	17.9666	+	5.65859i	0.715808	+	0.225443i
$631$	11.8790	+	3.18298i	0.472897	+	0.126712i	0.487393	−	0.873183i	$-0.337948\pi$
$631$	11.8790	+	3.18298i	0.472897	+	0.126712i	−0.0144963	+	0.999895i	$0.504614\pi$
$632$	−1.10331	−	4.11762i	−0.0438875	−	0.163790i
$633$	−3.40797	−	1.96759i	−0.135454	−	0.0782047i
$634$			24.0662i			0.955789i
$635$	−8.06879	+	30.1131i	−0.320200	+	1.19500i
$636$	−7.26037			−0.287892
$637$	−16.5686	−	19.0390i	−0.656472	−	0.754351i
$638$	−25.9535			−1.02751
$639$	1.75325	−	6.54321i	0.0693574	−	0.258845i
$640$			53.8334i			2.12795i
$641$	−9.51493	−	5.49345i	−0.375817	−	0.216978i	0.300180	−	0.953883i	$-0.402953\pi$
$641$	−9.51493	−	5.49345i	−0.375817	−	0.216978i	−0.675997	+	0.736905i	$0.736287\pi$
$642$	−3.02506	−	11.2897i	−0.119389	−	0.445568i
$643$	5.20127	+	1.39368i	0.205118	+	0.0549612i	0.359915	−	0.932985i	$-0.382806\pi$
$643$	5.20127	+	1.39368i	0.205118	+	0.0549612i	−0.154797	+	0.987946i	$0.549472\pi$
$644$	−23.5455	−	7.41565i	−0.927823	−	0.292217i
$645$	7.17583	−	7.17583i	0.282548	−	0.282548i
$646$	−128.992			−5.07512
$647$	−38.3238			−1.50667			−0.753333	−	0.657639i	$-0.771555\pi$
$647$	−38.3238			−1.50667			−0.753333	+	0.657639i	$0.771555\pi$
$648$	3.65872	−	3.65872i	0.143728	−	0.143728i
$649$	3.77124	−	6.53198i	0.148034	−	0.256402i
$650$	0.512472	+	29.5093i	0.0201008	+	1.15745i
$651$	−7.64532	+	12.0092i	−0.299644	+	0.470677i
$652$	−54.2315	+	14.5313i	−2.12387	+	0.569089i
$653$	−3.87397	−	6.70991i	−0.151600	−	0.262579i	0.780216	−	0.625511i	$-0.215109\pi$
$653$	−3.87397	−	6.70991i	−0.151600	−	0.262579i	−0.931816	+	0.362931i	$0.881776\pi$
$654$	21.7603	−	37.6899i	0.850894	−	1.47379i
$655$	13.5761	−	50.6666i	0.530461	−	1.97971i
$656$	29.8844	−	29.8844i	1.16679	−	1.16679i
$657$	−2.17041	+	8.10009i	−0.0846758	+	0.316014i
$658$	−1.69346	+	5.37693i	−0.0660180	+	0.209615i
$659$	1.59593	+	2.76423i	0.0621686	+	0.107679i	0.895435	−	0.445193i	$-0.146865\pi$
$659$	1.59593	+	2.76423i	0.0621686	+	0.107679i	−0.833266	+	0.552872i	$0.813532\pi$
$660$	−14.3318	+	8.27446i	−0.557864	+	0.322083i
$661$	−3.03520	−	3.03520i	−0.118055	−	0.118055i	0.645611	−	0.763666i	$-0.276603\pi$
$661$	−3.03520	−	3.03520i	−0.118055	−	0.118055i	−0.763666	+	0.645611i	$0.776603\pi$
$662$	−44.2994	+	25.5763i	−1.72174	+	0.994049i
$663$	−19.5974	−	18.9283i	−0.761099	−	0.735115i
$664$			15.7603i			0.611617i
$665$	−35.6489	−	38.8792i	−1.38241	−	1.50767i
$666$	−2.82328	+	4.89006i	−0.109400	+	0.189486i
$667$		−	17.0904i		−	0.661744i
$668$	−34.6431	−	9.28259i	−1.34038	−	0.359154i
$669$	8.91203	−	2.38797i	0.344559	−	0.0923243i
$670$	−28.0405	−	28.0405i	−1.08330	−	1.08330i
$671$	−4.14915	−	4.14915i	−0.160176	−	0.160176i
$672$	−0.110884	+	2.55831i	−0.00427744	+	0.0986889i
$673$	11.6256	+	6.71205i	0.448134	+	0.258731i	0.707042	−	0.707172i	$-0.250029\pi$
$673$	11.6256	+	6.71205i	0.448134	+	0.258731i	−0.258908	+	0.965902i	$0.583362\pi$
$674$	64.0907	+	17.1730i	2.46868	+	0.661481i
$675$	1.65772	+	2.87125i	0.0638057	+	0.110515i
$676$	−28.2072	−	45.1587i	−1.08489	−	1.73687i
$677$	−19.3278	−	11.1589i	−0.742830	−	0.428873i	0.0802677	−	0.996773i	$-0.474422\pi$
$677$	−19.3278	−	11.1589i	−0.742830	−	0.428873i	−0.823097	+	0.567901i	$0.807756\pi$
$678$	8.77286	+	32.7408i	0.336920	+	1.25740i
$679$	20.3178	+	12.9348i	0.779726	+	0.496392i
$680$	−97.6443	+	56.3749i	−3.74449	+	2.16188i
$681$	5.67894	−	1.52167i	0.217617	−	0.0583104i
$682$	−4.81785	−	17.9805i	−0.184485	−	0.688507i
$683$	−1.88738	−	7.04378i	−0.0722184	−	0.269523i	0.920370	−	0.391049i	$-0.127888\pi$
$683$	−1.88738	−	7.04378i	−0.0722184	−	0.269523i	−0.992588	+	0.121526i	$0.961221\pi$
$684$	−27.3523	+	7.32903i	−1.04584	+	0.280233i
$685$	−24.3222	+	14.0424i	−0.929305	+	0.536534i
$686$	42.2282	−	17.5387i	1.61228	−	0.669630i
$687$	0.564755	+	2.10769i	0.0215467	+	0.0804136i
$688$	13.9690	+	8.06503i	0.532565	+	0.307476i
$689$	1.76118	+	6.14403i	0.0670958	+	0.234069i
$690$	−8.10945	−	14.0460i	−0.308721	−	0.534721i
$691$	10.9128	+	2.92407i	0.415142	+	0.111237i	0.460343	−	0.887741i	$-0.347726\pi$
$691$	10.9128	+	2.92407i	0.415142	+	0.111237i	−0.0452016	+	0.998978i	$0.514393\pi$
$692$	38.4584	+	22.2040i	1.46197	+	0.844069i
$693$	3.28779	−	1.71284i	0.124893	−	0.0650655i
$694$	10.7694	+	10.7694i	0.408801	+	0.408801i
$695$	−32.0571	−	32.0571i	−1.21599	−	1.21599i
$696$	−37.4951	+	10.0468i	−1.42125	+	0.380822i
$697$	−67.3042	−	18.0341i	−2.54933	−	0.683090i
$698$			53.3028i			2.01754i
$699$	−6.11367	+	10.5892i	−0.231240	+	0.400520i
$700$	−34.2675	−	10.7925i	−1.29519	−	0.407920i
$701$			0.777837i			0.0293785i	0.999892	+	0.0146892i	$0.00467590\pi$
$701$			0.777837i			0.0293785i	−0.999892	+	0.0146892i	$0.995324\pi$
$702$	−7.78542	−	4.31643i	−0.293842	−	0.162913i
$703$	13.6938	−	7.90610i	0.516470	−	0.298184i
$704$	6.71488	+	6.71488i	0.253077	+	0.253077i
$705$	−2.15518	+	1.24429i	−0.0811688	+	0.0468628i
$706$	16.3506	+	28.3200i	0.615362	+	1.06584i
$707$	−45.3049	−	14.2688i	−1.70387	−	0.536632i
$708$	5.70613	−	21.2956i	0.214450	−	0.800337i
$709$	1.56235	−	1.56235i	0.0586752	−	0.0586752i	−0.677160	−	0.735836i	$-0.736790\pi$
$709$	1.56235	−	1.56235i	0.0586752	−	0.0586752i	0.735836	+	0.677160i	$0.236790\pi$
$710$	−12.4824	+	46.5849i	−0.468456	+	1.74830i
$711$	−0.411935	+	0.713493i	−0.0154488	+	0.0267581i
$712$	6.65823	+	11.5324i	0.249528	+	0.432194i
$713$	11.8402	−	3.17256i	0.443417	−	0.118813i
$714$	43.7772	−	22.8066i	1.63832	−	0.853517i
$715$	10.4787	+	10.1210i	0.391882	+	0.378504i
$716$	−16.7371	+	28.9896i	−0.625496	+	1.08339i
$717$	−7.97620	+	7.97620i	−0.297877	+	0.297877i
$718$	12.1908			0.454958
$719$	−12.3064			−0.458951			−0.229476	−	0.973314i	$-0.573701\pi$
$719$	−12.3064			−0.458951			−0.229476	+	0.973314i	$0.573701\pi$
$720$	−9.34585	+	9.34585i	−0.348299	+	0.348299i
$721$	11.9433	−	10.9510i	0.444793	−	0.407838i
$722$	68.6866	+	18.4045i	2.55625	+	0.684945i
$723$	−3.32719	−	12.4172i	−0.123740	−	0.461802i
$724$	14.5566	+	8.40428i	0.540993	+	0.312343i
$725$		−	24.8730i		−	0.923759i
$726$	5.77453	−	21.5508i	0.214313	−	0.799826i
$727$	−46.3414			−1.71871			−0.859353	−	0.511383i	$-0.829133\pi$
$727$	−46.3414			−1.71871			−0.859353	+	0.511383i	$0.829133\pi$
$728$	47.9924	−	11.5336i	1.77872	−	0.427463i
$729$	−1.00000			−0.0370370
$730$	15.4524	−	57.6693i	0.571920	−	2.13444i
$731$		−	26.5934i		−	0.983593i
$732$	−14.8538	−	8.57584i	−0.549012	−	0.316972i
$733$	4.29994	+	16.0476i	0.158822	+	0.592731i	0.998748	+	0.0500300i	$0.0159317\pi$
$733$	4.29994	+	16.0476i	0.158822	+	0.592731i	−0.839926	+	0.542701i	$0.817402\pi$
$734$	48.8744	+	13.0959i	1.80399	+	0.483377i
$735$	18.9726	+	6.89181i	0.699815	+	0.254208i
$736$	1.55906	−	1.55906i	0.0574678	−	0.0574678i
$737$	−7.80448			−0.287482
$738$	−22.7657			−0.838017
$739$	2.49614	−	2.49614i	0.0918219	−	0.0918219i	−0.659704	−	0.751526i	$-0.729318\pi$
$739$	2.49614	−	2.49614i	0.0918219	−	0.0918219i	0.751526	+	0.659704i	$0.229318\pi$
$740$	13.5056	−	23.3924i	0.496475	−	0.859920i
$741$	12.8371	+	21.3689i	0.471584	+	0.785005i
$742$	−11.5687	−	0.501417i	−0.424699	−	0.0184076i
$743$	42.9886	−	11.5188i	1.57710	−	0.422583i	0.639073	−	0.769146i	$-0.279318\pi$
$743$	42.9886	−	11.5188i	1.57710	−	0.422583i	0.938027	+	0.346563i	$0.112651\pi$
$744$	−13.9207	−	24.1114i	−0.510357	−	0.883965i
$745$	−18.5653	+	32.1560i	−0.680179	+	1.17810i
$746$	−14.8525	+	55.4301i	−0.543787	+	2.02944i
$747$	2.15380	−	2.15380i	0.0788033	−	0.0788033i
$748$	−11.2241	+	41.8890i	−0.410395	+	1.53161i
$749$	−2.71477	−	12.2271i	−0.0991955	−	0.446770i
$750$	5.99669	+	10.3866i	0.218968	+	0.379264i
$751$	45.1124	−	26.0457i	1.64618	−	0.950420i	0.667603	−	0.744518i	$-0.267321\pi$
$751$	45.1124	−	26.0457i	1.64618	−	0.950420i	0.978573	−	0.205902i	$-0.0660128\pi$
$752$	−2.79696	−	2.79696i	−0.101995	−	0.101995i
$753$	22.7045	−	13.1084i	0.827397	−	0.477698i
$754$	34.3911	+	57.2479i	1.25245	+	2.08484i
$755$			10.0721i			0.366562i
$756$	7.98699	−	7.32339i	0.290484	−	0.266349i
$757$	23.5702	−	40.8248i	0.856674	−	1.48380i	−0.0184085	−	0.999831i	$-0.505860\pi$
$757$	23.5702	−	40.8248i	0.856674	−	1.48380i	0.875083	−	0.483973i	$-0.160807\pi$
$758$		−	52.7791i		−	1.91702i
$759$	−3.08324	−	0.826153i	−0.111915	−	0.0299875i
$760$	99.6441	−	26.6995i	3.61447	−	0.968494i
$761$	21.3753	+	21.3753i	0.774854	+	0.774854i	0.978951	−	0.204096i	$-0.0654256\pi$
$761$	21.3753	+	21.3753i	0.774854	+	0.774854i	−0.204096	+	0.978951i	$0.565426\pi$
$762$	18.8741	+	18.8741i	0.683737	+	0.683737i
$763$	25.0456	−	39.3412i	0.906711	−	1.42425i
$764$	15.6734	+	9.04903i	0.567043	+	0.327382i
$765$	21.0482	+	5.63986i	0.761001	+	0.203910i
$766$	−13.1088	−	22.7052i	−0.473641	−	0.820371i
$767$	−19.4054	+	0.337002i	−0.700688	+	0.0121685i
$768$	28.1779	+	16.2685i	1.01678	+	0.587039i
$769$	−1.17278	−	4.37689i	−0.0422916	−	0.157835i	0.941551	−	0.336871i	$-0.109369\pi$
$769$	−1.17278	−	4.37689i	−0.0422916	−	0.157835i	−0.983842	+	0.179037i	$0.942702\pi$
$770$	−23.4077	+	12.1947i	−0.843555	+	0.439467i
$771$	−5.57169	+	3.21682i	−0.200660	+	0.115851i
$772$	44.6398	−	11.9612i	1.60662	−	0.430493i
$773$	0.578937	+	2.16062i	0.0208229	+	0.0777122i	0.975555	−	0.219753i	$-0.0705253\pi$
$773$	0.578937	+	2.16062i	0.0208229	+	0.0777122i	−0.954733	+	0.297466i	$0.903859\pi$
$774$	−2.24881	−	8.39268i	−0.0808319	−	0.301669i
$775$	17.2318	−	4.61726i	0.618986	−	0.165857i
$776$	−40.7930	+	23.5518i	−1.46438	+	0.845462i
$777$	−3.24953	+	5.10431i	−0.116576	+	0.183116i
$778$	−10.5781	−	39.4778i	−0.379242	−	1.41535i
$779$	55.2104	+	31.8757i	1.97812	+	1.14207i
$780$	37.2427	+	20.6483i	1.33350	+	0.739328i
$781$	4.74586	+	8.22006i	0.169820	+	0.294137i
$782$	−41.0537	−	11.0003i	−1.46808	−	0.393370i
$783$	6.49707	+	3.75108i	0.232186	+	0.134053i
$784$	−2.77600	+	31.9637i	−0.0991430	+	1.14156i
$785$	−0.580407	−	0.580407i	−0.0207156	−	0.0207156i
$786$	−31.7565	−	31.7565i	−1.13272	−	1.13272i
$787$	−38.0262	+	10.1891i	−1.35549	+	0.363202i	−0.862158	−	0.506640i	$-0.830887\pi$
$787$	−38.0262	+	10.1891i	−1.35549	+	0.363202i	−0.493330	+	0.869842i	$0.664221\pi$
$788$	−19.0959	−	5.11674i	−0.680264	−	0.182276i
$789$			15.0122i			0.534449i
$790$	2.93281	−	5.07977i	0.104345	−	0.180730i
$791$	7.87300	+	35.4595i	0.279932	+	1.26079i
$792$			7.25006i			0.257620i
$793$	−3.65408	+	14.6502i	−0.129760	+	0.520243i
$794$	63.2516	−	36.5184i	2.24472	−	1.29599i
$795$	−3.61457	−	3.61457i	−0.128196	−	0.128196i
$796$	40.8288	−	23.5725i	1.44714	−	0.835506i
$797$	8.77705	+	15.2023i	0.310899	+	0.538493i	0.978557	−	0.205975i	$-0.0660366\pi$
$797$	8.77705	+	15.2023i	0.310899	+	0.538493i	−0.667658	+	0.744468i	$0.732703\pi$
$798$	−44.0893	+	9.78906i	−1.56074	+	0.346529i
$799$	−1.68786	+	6.29917i	−0.0597121	+	0.222849i
$800$	2.26902	−	2.26902i	0.0802218	−	0.0802218i
$801$	0.666102	−	2.48593i	0.0235356	−	0.0878359i
$802$	12.5130	−	21.6731i	0.441848	−	0.765304i
$803$	−5.87508	−	10.1759i	−0.207327	−	0.359101i
$804$	−22.0353	+	5.90435i	−0.777126	+	0.208230i
$805$	−8.03024	−	15.4140i	−0.283029	−	0.543272i
$806$	−33.2768	+	34.4531i	−1.17213	+	1.21356i
$807$	11.0845	−	19.1989i	0.390193	−	0.675834i
$808$	65.6844	−	65.6844i	2.31077	−	2.31077i
$809$	7.52320			0.264502			0.132251	−	0.991216i	$-0.457780\pi$
$809$	7.52320			0.264502			0.132251	+	0.991216i	$0.457780\pi$
$810$	7.11959			0.250157
$811$	−39.4597	+	39.4597i	−1.38562	+	1.38562i	−0.551327	+	0.834289i	$0.685878\pi$
$811$	−39.4597	+	39.4597i	−1.38562	+	1.38562i	−0.834289	+	0.551327i	$0.814122\pi$
$812$	−79.3626	+	17.6207i	−2.78508	+	0.618366i
$813$	20.3561	+	5.45440i	0.713920	+	0.191294i
$814$	−2.04775	−	7.64232i	−0.0717737	−	0.267863i
$815$	−34.2335	−	19.7647i	−1.19915	−	0.692328i
$816$			34.6354i			1.21248i
$817$	−6.29741	+	23.5023i	−0.220318	+	0.822240i
$818$	−7.20013			−0.251747
$819$	−8.13481	−	4.98246i	−0.284253	−	0.174101i
$820$	108.903			3.80307
$821$	3.78554	−	14.1278i	0.132116	−	0.493064i	−0.867877	−	0.496779i	$-0.834516\pi$
$821$	3.78554	−	14.1278i	0.132116	−	0.493064i	0.999993	+	0.00371513i	$0.00118256\pi$
$822$			24.0460i			0.838700i
$823$	5.36076	+	3.09504i	0.186864	+	0.107886i	0.590514	−	0.807027i	$-0.298925\pi$
$823$	5.36076	+	3.09504i	0.186864	+	0.107886i	−0.403649	+	0.914914i	$0.632258\pi$
$824$	8.20186	+	30.6098i	0.285725	+	1.06634i
$825$	−4.48727	−	1.20236i	−0.156227	−	0.0418608i
$826$	10.5629	−	33.5383i	0.367529	−	1.16695i
$827$	−17.1035	+	17.1035i	−0.594748	+	0.594748i	−0.938910	−	0.344162i	$-0.888163\pi$
$827$	−17.1035	+	17.1035i	−0.594748	+	0.594748i	0.344162	+	0.938910i	$0.388163\pi$
$828$	−9.33031			−0.324251
$829$	29.6970			1.03142			0.515710	−	0.856763i	$-0.327528\pi$
$829$	29.6970			1.03142			0.515710	+	0.856763i	$0.327528\pi$
$830$	−15.3342	+	15.3342i	−0.532256	+	0.532256i
$831$	−4.93407	+	8.54607i	−0.171161	+	0.296460i
$832$	5.91367	−	23.7095i	0.205019	−	0.821978i
$833$	47.9264	−	22.3855i	1.66055	−	0.775612i
$834$	−37.4932	+	10.0463i	−1.29828	+	0.347874i
$835$	−12.6257	−	21.8684i	−0.436931	−	0.756787i
$836$	19.8389	−	34.3620i	0.686144	−	1.18844i
$837$	−1.39265	+	5.19745i	−0.0481372	+	0.179650i
$838$	18.1055	−	18.1055i	0.625446	−	0.625446i
$839$	10.2057	−	38.0883i	0.352341	−	1.31496i	−0.531456	−	0.847086i	$-0.678355\pi$
$839$	10.2057	−	38.0883i	0.352341	−	1.31496i	0.883797	−	0.467870i	$-0.154978\pi$
$840$	−29.0965	+	26.6790i	−1.00392	+	0.920513i
$841$	−13.6412	−	23.6273i	−0.470388	−	0.814735i
$842$	−80.8476	+	46.6774i	−2.78619	+	1.60861i
$843$	21.3933	+	21.3933i	0.736824	+	0.736824i
$844$	13.9580	−	8.05868i	0.480456	−	0.277391i
$845$	8.43932	−	36.5252i	0.290321	−	1.25650i
$846$			2.13070i			0.0732550i
$847$	7.18226	−	22.8045i	0.246785	−	0.783571i
$848$	4.06247	−	7.03641i	0.139506	−	0.241631i
$849$			21.4880i			0.737468i
$850$	−59.7484	−	16.0095i	−2.04935	−	0.549123i
$851$	5.03248	−	1.34845i	0.172511	−	0.0462242i
$852$	19.6183	+	19.6183i	0.672112	+	0.672112i
$853$	14.6711	+	14.6711i	0.502329	+	0.502329i	0.912161	−	0.409832i	$-0.134413\pi$
$853$	14.6711	+	14.6711i	0.502329	+	0.502329i	−0.409832	+	0.912161i	$0.634413\pi$
$854$	−23.0757	−	14.6906i	−0.789635	−	0.502700i
$855$	−17.2661	−	9.96859i	−0.590488	−	0.340918i
$856$	23.6599	+	6.33965i	0.808679	+	0.216685i
$857$	−4.44642	−	7.70143i	−0.151887	−	0.263076i	0.780034	−	0.625737i	$-0.215202\pi$
$857$	−4.44642	−	7.70143i	−0.151887	−	0.263076i	−0.931921	+	0.362661i	$0.881868\pi$
$858$	11.9904	−	3.43705i	0.409346	−	0.117339i
$859$	−17.8913	−	10.3296i	−0.610445	−	0.352440i	0.162695	−	0.986676i	$-0.447981\pi$
$859$	−17.8913	−	10.3296i	−0.610445	−	0.352440i	−0.773139	+	0.634236i	$0.781315\pi$
$860$	10.7575	+	40.1477i	0.366829	+	1.36902i
$861$	−24.3731	−	1.05639i	−0.830632	−	0.0360018i
$862$	52.3059	−	30.1988i	1.78154	−	1.02858i
$863$	−11.7025	+	3.13567i	−0.398358	+	0.106740i	−0.452435	−	0.891797i	$-0.649445\pi$
$863$	−11.7025	+	3.13567i	−0.398358	+	0.106740i	0.0540779	+	0.998537i	$0.482778\pi$
$864$	0.250500	+	0.934879i	0.00852218	+	0.0318052i
$865$	8.09227	+	30.2008i	0.275145	+	1.02686i
$866$	41.7846	−	11.1961i	1.41990	−	0.380461i
$867$	34.7302	−	20.0515i	1.17950	−	0.680985i
$868$	−26.9399	−	51.7110i	−0.914400	−	1.75518i
$869$	−0.298781	−	1.11507i	−0.0101354	−	0.0378260i
$870$	−46.2564	−	26.7062i	−1.56824	−	0.905424i
$871$	10.3417	+	17.2150i	0.350416	+	0.583307i
$872$	45.6033	+	78.9872i	1.54432	+	2.67484i
$873$	8.79336	+	2.35617i	0.297610	+	0.0797444i
$874$	33.6768	+	19.4433i	1.13913	+	0.657679i
$875$	5.93812	+	11.3982i	0.200745	+	0.385329i
$876$	−24.2862	−	24.2862i	−0.820556	−	0.820556i
$877$	2.72331	+	2.72331i	0.0919597	+	0.0919597i	0.751590	−	0.659630i	$-0.229287\pi$
$877$	2.72331	+	2.72331i	0.0919597	+	0.0919597i	−0.659630	+	0.751590i	$0.729287\pi$
$878$	−47.4411	+	12.7118i	−1.60106	+	0.429002i
$879$	0.969962	+	0.259901i	0.0327160	+	0.00876623i
$880$		−	18.5196i		−	0.624296i
$881$	11.7705	−	20.3872i	0.396559	−	0.686861i	−0.596739	−	0.802435i	$-0.703537\pi$
$881$	11.7705	−	20.3872i	0.396559	−	0.686861i	0.993299	+	0.115574i	$0.0368707\pi$
$882$	13.2322	−	11.1175i	0.445552	−	0.374345i
$883$		−	27.7063i		−	0.932390i	−0.884682	−	0.466195i	$-0.845625\pi$
$883$		−	27.7063i		−	0.932390i	0.884682	−	0.466195i	$-0.154375\pi$
$884$	107.271	−	30.7492i	3.60792	−	1.03421i
$885$	13.4428	−	7.76120i	0.451874	−	0.260890i
$886$	26.8478	+	26.8478i	0.901970	+	0.901970i
$887$	23.9756	−	13.8423i	0.805023	−	0.464780i	−0.0402013	−	0.999192i	$-0.512800\pi$
$887$	23.9756	−	13.8423i	0.805023	−	0.464780i	0.845225	+	0.534411i	$0.179467\pi$
$888$	−5.91678	−	10.2482i	−0.198554	−	0.343906i
$889$	19.3309	+	21.0825i	0.648338	+	0.707086i
$890$	−4.74237	+	17.6988i	−0.158965	+	0.593264i
$891$	0.990792	−	0.990792i	0.0331928	−	0.0331928i
$892$	−9.78045	+	36.5011i	−0.327474	+	1.22215i
$893$	2.98333	−	5.16728i	0.0998333	−	0.172916i
$894$	15.8954	+	27.5316i	0.531621	+	0.920795i
$895$	−22.7650	+	6.09987i	−0.760950	+	0.203896i
$896$	41.6654	+	26.5252i	1.39194	+	0.886143i
$897$	2.26330	+	7.89571i	0.0755694	+	0.263630i
$898$	4.33100	−	7.50151i	0.144527	−	0.250329i
$899$	28.5442	−	28.5442i	0.952004	−	0.952004i
$900$	−13.5791			−0.452636
$901$	−13.3955			−0.446269
$902$	22.5561	−	22.5561i	0.751036	−	0.751036i
$903$	−2.01814	−	9.08960i	−0.0671596	−	0.302483i
$904$	−68.6152	−	18.3854i	−2.28211	−	0.611489i
$905$	3.06295	+	11.4311i	0.101816	+	0.379982i
$906$	7.46828	+	4.31182i	0.248117	+	0.143250i
$907$			12.2311i			0.406127i	0.979166	+	0.203063i	$0.0650897\pi$
$907$			12.2311i			0.406127i	−0.979166	+	0.203063i	$0.934910\pi$
$908$	−6.23231	+	23.2593i	−0.206827	+	0.771887i
$909$	−17.9528			−0.595458
$910$	57.9165	+	35.4730i	1.91991	+	1.17592i
$911$	1.08514			0.0359525			0.0179762	−	0.999838i	$-0.494278\pi$
$911$	1.08514			0.0359525			0.0179762	+	0.999838i	$0.494278\pi$
$912$	8.20179	−	30.6095i	0.271588	−	1.01358i
$913$			4.26793i			0.141248i
$914$	−65.2122	−	37.6503i	−2.15703	−	1.24536i
$915$	−3.12547	−	11.6644i	−0.103325	−	0.385614i
$916$	−8.63251	−	2.31307i	−0.285226	−	0.0764261i
$917$	−32.5250	−	35.4722i	−1.07407	−	1.17140i
$918$	13.1925	−	13.1925i	0.435417	−	0.435417i
$919$	−44.7066			−1.47474			−0.737368	−	0.675491i	$-0.763932\pi$
$919$	−44.7066			−1.47474			−0.737368	+	0.675491i	$0.763932\pi$
$920$	33.9902			1.12062
$921$	−4.86151	+	4.86151i	−0.160192	+	0.160192i
$922$	−25.1716	+	43.5985i	−0.828983	+	1.43584i
$923$	11.8429	−	21.3607i	0.389815	−	0.703098i
$924$	−0.657483	+	15.1694i	−0.0216296	+	0.499037i
$925$	7.32413	−	1.96250i	0.240816	−	0.0645265i
$926$	13.4841	+	23.3552i	0.443116	+	0.767499i
$927$	3.06226	−	5.30399i	0.100578	−	0.174206i
$928$	1.87929	−	7.01362i	0.0616908	−	0.230233i
$929$	−12.9874	+	12.9874i	−0.426102	+	0.426102i	−0.887298	−	0.461196i	$-0.847420\pi$
$929$	−12.9874	+	12.9874i	−0.426102	+	0.426102i	0.461196	+	0.887298i	$0.347420\pi$
$930$	9.91512	−	37.0037i	0.325130	−	1.21340i
$931$	−47.6565	+	8.43434i	−1.56188	+	0.276424i
$932$	−25.0398	−	43.3703i	−0.820207	−	1.42064i
$933$	11.8756	−	6.85636i	0.388789	−	0.224467i
$934$	−59.6007	−	59.6007i	−1.95019	−	1.95019i
$935$	−26.4424	+	15.2665i	−0.864758	+	0.499268i
$936$	15.9921	−	9.60707i	0.522717	−	0.314017i
$937$			36.6713i			1.19800i	0.800749	+	0.598999i	$0.204435\pi$
$937$			36.6713i			1.19800i	−0.800749	+	0.598999i	$0.795565\pi$
$938$	−35.5188	+	7.88617i	−1.15973	+	0.257493i
$939$	17.0324	−	29.5010i	0.555833	−	0.962730i
$940$		−	10.1925i		−	0.332444i
$941$	−2.10032	−	0.562780i	−0.0684686	−	0.0183461i	0.224422	−	0.974492i	$-0.427951\pi$
$941$	−2.10032	−	0.562780i	−0.0684686	−	0.0183461i	−0.292891	+	0.956146i	$0.594617\pi$
$942$	−0.678830	+	0.181892i	−0.0221175	+	0.00592636i
$943$	14.8532	+	14.8532i	0.483687	+	0.483687i
$944$	17.4459	+	17.4459i	0.567815	+	0.567815i
$945$	7.62227	+	0.330370i	0.247952	+	0.0107469i
$946$	10.5435	+	6.08730i	0.342799	+	0.197915i
$947$	−32.3492	−	8.66795i	−1.05121	−	0.281671i	−0.308458	−	0.951238i	$-0.599813\pi$
$947$	−32.3492	−	8.66795i	−1.05121	−	0.281671i	−0.742751	+	0.669567i	$0.766480\pi$
$948$	−1.68717	−	2.92226i	−0.0547967	−	0.0949106i
$949$	−14.6608	+	26.4433i	−0.475910	+	0.858385i
$950$	49.0123	+	28.2973i	1.59017	+	0.918084i
$951$	2.52285	+	9.41539i	0.0818089	+	0.305315i
$952$	−4.47951	+	103.351i	−0.145182	+	3.34963i
$953$	−23.8594	+	13.7752i	−0.772881	+	0.446223i	−0.833901	−	0.551914i	$-0.813898\pi$
$953$	−23.8594	+	13.7752i	−0.772881	+	0.446223i	0.0610206	+	0.998137i	$0.480564\pi$
$954$	−4.22752	+	1.13276i	−0.136871	+	0.0366744i
$955$	3.29793	+	12.3080i	0.106718	+	0.398279i
$956$	−11.9574	−	44.6256i	−0.386730	−	1.44330i
$957$	−10.1538	+	2.72070i	−0.328225	+	0.0879477i
$958$	37.1427	−	21.4444i	1.20003	−	0.692836i
$959$	−1.11580	+	25.7437i	−0.0360312	+	0.831309i
$960$	5.05818	+	18.8774i	0.163252	+	0.609265i
$961$	−1.77273	−	1.02349i	−0.0571850	−	0.0330158i
$962$	−14.1438	+	14.6437i	−0.456015	+	0.472133i
$963$	−2.36698	−	4.09974i	−0.0762750	−	0.132112i
$964$	50.8575	+	13.6272i	1.63801	+	0.438903i
$965$	28.1788	+	16.2690i	0.907107	+	0.523718i
$966$	−14.8669	−	0.644371i	−0.478335	−	0.0207323i
$967$	−15.7669	−	15.7669i	−0.507030	−	0.507030i	0.406584	−	0.913613i	$-0.366720\pi$
$967$	−15.7669	−	15.7669i	−0.507030	−	0.507030i	−0.913613	+	0.406584i	$0.866720\pi$
$968$	33.0626	+	33.0626i	1.06267	+	1.06267i
$969$	−50.4655	+	13.5222i	−1.62118	+	0.434395i
$970$	−62.6051	−	16.7750i	−2.01013	−	0.538612i
$971$		−	16.4342i		−	0.527399i	−0.964605	−	0.263700i	$-0.915057\pi$
$971$		−	16.4342i		−	0.527399i	0.964605	−	0.263700i	$-0.0849427\pi$
$972$	2.04786	−	3.54699i	0.0656850	−	0.113770i
$973$	−40.6066	+	9.01579i	−1.30179	+	0.289033i
$974$		−	31.4848i		−	1.00884i
$975$	3.29395	+	11.4912i	0.105491	+	0.368013i
$976$	16.6226	−	9.59706i	0.532076	−	0.307194i
$977$	26.5750	+	26.5750i	0.850210	+	0.850210i	0.990159	−	0.139948i	$-0.0446937\pi$
$977$	26.5750	+	26.5750i	0.850210	+	0.850210i	−0.139948	+	0.990159i	$0.544694\pi$
$978$	−29.3103	+	16.9223i	−0.937241	+	0.541117i
$979$	1.80307	+	3.12301i	0.0576263	+	0.0998117i
$980$	−63.2984	+	53.1822i	−2.02199	+	1.69884i
$981$	4.56224	−	17.0265i	0.145661	−	0.543615i
$982$	32.2891	−	32.2891i	1.03039	−	1.03039i
$983$	−10.7875	+	40.2595i	−0.344068	+	1.28408i	0.549629	+	0.835409i	$0.314769\pi$
$983$	−10.7875	+	40.2595i	−0.344068	+	1.28408i	−0.893697	+	0.448671i	$0.851898\pi$
$984$	23.8552	−	41.3184i	0.760476	−	1.31718i
$985$	−6.95953	−	12.0543i	−0.221749	−	0.384081i
$986$	−135.199	+	36.2264i	−4.30560	+	1.15368i
$987$	−0.0988707	+	2.28114i	−0.00314709	+	0.0726094i
$988$	−102.084	+	1.77283i	−3.24772	+	0.0564013i
$989$	−4.00849	+	6.94292i	−0.127463	+	0.220772i
$990$	−7.05403	+	7.05403i	−0.224192	+	0.224192i
$991$	15.8259			0.502726			0.251363	−	0.967893i	$-0.419121\pi$
$991$	15.8259			0.502726			0.251363	+	0.967893i	$0.419121\pi$
$992$	5.20785			0.165349
$993$	−14.6501	+	14.6501i	−0.464906	+	0.464906i
$994$	29.9049	+	32.6146i	0.948525	+	1.03447i
$995$	32.0622	+	8.59104i	1.01644	+	0.272354i
$996$	3.22883	+	12.0502i	0.102309	+	0.381824i
$997$	−9.53745	−	5.50645i	−0.302054	−	0.174391i	0.341311	−	0.939950i	$-0.389129\pi$
$997$	−9.53745	−	5.50645i	−0.302054	−	0.174391i	−0.643365	+	0.765559i	$0.722462\pi$
$998$		−	92.1034i		−	2.91548i
$999$	−0.591926	+	2.20910i	−0.0187277	+	0.0698928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.124.1	yes	36
3.2	odd	2		819.2.gh.c.397.9		36
7.3	odd	6		273.2.bt.a.241.1	yes	36
13.2	odd	12		273.2.bt.a.145.1	✓	36
21.17	even	6		819.2.et.c.514.9		36
39.2	even	12		819.2.et.c.145.9		36
91.80	even	12	inner	273.2.cg.a.262.1	yes	36
273.80	odd	12		819.2.gh.c.262.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.1	✓	36	13.2	odd	12
273.2.bt.a.241.1	yes	36	7.3	odd	6
273.2.cg.a.124.1	yes	36	1.1	even	1	trivial
273.2.cg.a.262.1	yes	36	91.80	even	12	inner
819.2.et.c.145.9		36	39.2	even	12
819.2.et.c.514.9		36	21.17	even	6
819.2.gh.c.262.9		36	273.80	odd	12
819.2.gh.c.397.9		36	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.639011 + 2.38482i) q^{2} +1.00000i q^{3} +(-3.54699 - 2.04786i) q^{4} +(-0.746344 - 2.78539i) q^{5} +(-2.38482 - 0.639011i) q^{6} +(-2.52355 - 0.794791i) q^{7} +(3.65872 - 3.65872i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.639011 + 2.38482i) q^{2} +1.00000i q^{3} +(-3.54699 - 2.04786i) q^{4} +(-0.746344 - 2.78539i) q^{5} +(-2.38482 - 0.639011i) q^{6} +(-2.52355 - 0.794791i) q^{7} +(3.65872 - 3.65872i) q^{8} -1.00000 q^{9} +7.11959 q^{10} +(0.990792 - 0.990792i) q^{11} +(2.04786 - 3.54699i) q^{12} +(-3.49837 - 0.872572i) q^{13} +(3.50801 - 5.51034i) q^{14} +(2.78539 - 0.746344i) q^{15} +(2.29172 + 3.96937i) q^{16} +(3.77833 - 6.54425i) q^{17} +(0.639011 - 2.38482i) q^{18} +(-4.88884 + 4.88884i) q^{19} +(-3.05681 + 11.4082i) q^{20} +(0.794791 - 2.52355i) q^{21} +(1.72974 + 2.99599i) q^{22} +(-1.97286 + 1.13903i) q^{23} +(3.65872 + 3.65872i) q^{24} +(-2.87125 + 1.65772i) q^{25} +(4.31643 - 7.78542i) q^{26} -1.00000i q^{27} +(7.32339 + 7.98699i) q^{28} +(-3.75108 + 6.49707i) q^{29} +7.11959i q^{30} +(-5.19745 - 1.39265i) q^{31} +(-0.934879 + 0.250500i) q^{32} +(0.990792 + 0.990792i) q^{33} +(13.1925 + 13.1925i) q^{34} +(-0.330370 + 7.62227i) q^{35} +(3.54699 + 2.04786i) q^{36} +(-2.20910 - 0.591926i) q^{37} +(-8.53499 - 14.7830i) q^{38} +(0.872572 - 3.49837i) q^{39} +(-12.9216 - 7.46031i) q^{40} +(-2.38652 - 8.90661i) q^{41} +(5.51034 + 3.50801i) q^{42} +(3.04772 - 1.75960i) q^{43} +(-5.54333 + 1.48533i) q^{44} +(0.746344 + 2.78539i) q^{45} +(-1.45571 - 5.43279i) q^{46} +(-0.833593 + 0.223361i) q^{47} +(-3.96937 + 2.29172i) q^{48} +(5.73661 + 4.01139i) q^{49} +(-2.11860 - 7.90673i) q^{50} +(6.54425 + 3.77833i) q^{51} +(10.6218 + 10.2592i) q^{52} +(-0.886338 - 1.53518i) q^{53} +(2.38482 + 0.639011i) q^{54} +(-3.49922 - 2.02027i) q^{55} +(-12.1409 + 6.32504i) q^{56} +(-4.88884 - 4.88884i) q^{57} +(-13.0974 - 13.0974i) q^{58} +(5.19948 - 1.39320i) q^{59} +(-11.4082 - 3.05681i) q^{60} -4.18771i q^{61} +(6.64246 - 11.5051i) q^{62} +(2.52355 + 0.794791i) q^{63} +6.77728i q^{64} +(0.180534 + 10.3956i) q^{65} +(-2.99599 + 1.72974i) q^{66} +(-3.93850 - 3.93850i) q^{67} +(-26.8034 + 15.4749i) q^{68} +(-1.13903 - 1.97286i) q^{69} +(-17.9666 - 5.65859i) q^{70} +(-1.75325 + 6.54321i) q^{71} +(-3.65872 + 3.65872i) q^{72} +(2.17041 - 8.10009i) q^{73} +(2.82328 - 4.89006i) q^{74} +(-1.65772 - 2.87125i) q^{75} +(27.3523 - 7.32903i) q^{76} +(-3.28779 + 1.71284i) q^{77} +(7.78542 + 4.31643i) q^{78} +(0.411935 - 0.713493i) q^{79} +(9.34585 - 9.34585i) q^{80} +1.00000 q^{81} +22.7657 q^{82} +(-2.15380 + 2.15380i) q^{83} +(-7.98699 + 7.32339i) q^{84} +(-21.0482 - 5.63986i) q^{85} +(2.24881 + 8.39268i) q^{86} +(-6.49707 - 3.75108i) q^{87} -7.25006i q^{88} +(-0.666102 + 2.48593i) q^{89} -7.11959 q^{90} +(8.13481 + 4.98246i) q^{91} +9.33031 q^{92} +(1.39265 - 5.19745i) q^{93} -2.13070i q^{94} +(17.2661 + 9.96859i) q^{95} +(-0.250500 - 0.934879i) q^{96} +(-8.79336 - 2.35617i) q^{97} +(-13.2322 + 11.1175i) q^{98} +(-0.990792 + 0.990792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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