LMFDB - Embedded newform 378.2.z.a.293.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			293.19
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(0.591720 - 1.62784i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.0649147 - 0.368150i) q^{5} +(-1.32729 - 1.11279i) q^{6} +(-2.64254 - 0.130261i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.29974 - 1.92645i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(0.591720 - 1.62784i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.0649147 - 0.368150i) q^{5} +(-1.32729 - 1.11279i) q^{6} +(-2.64254 - 0.130261i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.29974 - 1.92645i) q^{9} +(-0.323745 - 0.186914i) q^{10} +(-2.09196 + 0.368870i) q^{11} +(-1.49964 + 0.866649i) q^{12} +(-0.897772 - 2.46661i) q^{13} +(-1.02621 + 2.43863i) q^{14} +(-0.560878 - 0.323512i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.86786 - 3.23524i) q^{17} +(-2.59683 + 1.50216i) q^{18} +(3.92673 - 2.26710i) q^{19} +(-0.286370 + 0.240293i) q^{20} +(-1.77569 + 4.22456i) q^{21} +(-0.368870 + 2.09196i) q^{22} +(-0.949048 + 1.13103i) q^{23} +(0.301477 + 1.70561i) q^{24} +(4.56714 + 1.66230i) q^{25} -2.62491 q^{26} +(-4.49676 + 2.60369i) q^{27} +(1.94057 + 1.79838i) q^{28} +(0.418671 - 1.15029i) q^{29} +(-0.495834 + 0.416405i) q^{30} +(3.75419 - 4.47407i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-0.637395 + 3.62365i) q^{33} +(-2.40128 - 2.86174i) q^{34} +(-0.219496 + 0.964395i) q^{35} +(0.523401 + 2.95399i) q^{36} +(3.45500 - 5.98424i) q^{37} +(-0.787356 - 4.46532i) q^{38} +(-4.54648 + 0.00189014i) q^{39} +(0.127857 + 0.351284i) q^{40} +(-5.14104 + 1.87119i) q^{41} +(3.36247 + 3.11349i) q^{42} +(2.21127 + 12.5407i) q^{43} +(1.83964 + 1.06212i) q^{44} +(-0.858509 + 0.721592i) q^{45} +(0.738228 + 1.27865i) q^{46} +(-0.144049 + 0.120872i) q^{47} +(1.70586 + 0.300058i) q^{48} +(6.96606 + 0.688442i) q^{49} +(3.12411 - 3.72317i) q^{50} +(-4.16120 - 4.95494i) q^{51} +(-0.897772 + 2.46661i) q^{52} -12.2303i q^{53} +(0.908684 + 5.11608i) q^{54} +0.794101i q^{55} +(2.35364 - 1.20846i) q^{56} +(-1.36696 - 7.73359i) q^{57} +(-0.937724 - 0.786844i) q^{58} +(-1.67308 + 9.48853i) q^{59} +(0.221708 + 0.608350i) q^{60} +(-4.15155 - 4.94762i) q^{61} +(-2.92024 - 5.05801i) q^{62} +(5.82621 + 5.39030i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.966359 + 0.170395i) q^{65} +(3.18712 + 1.83832i) q^{66} +(10.1110 - 3.68009i) q^{67} +(-3.51044 + 1.27769i) q^{68} +(1.27957 + 2.21415i) q^{69} +(0.831163 + 0.536101i) q^{70} +(-2.33580 - 1.34858i) q^{71} +(2.95486 + 0.518488i) q^{72} +(8.52609 - 4.92254i) q^{73} +(-4.44167 - 5.29337i) q^{74} +(5.40844 - 6.45097i) q^{75} +(-4.46532 - 0.787356i) q^{76} +(5.57615 - 0.702252i) q^{77} +(-1.55321 + 4.27294i) q^{78} +(1.81112 + 0.659192i) q^{79} +0.373829 q^{80} +(1.57757 + 8.86066i) q^{81} +5.47098i q^{82} +(-12.2405 - 4.45518i) q^{83} +(4.07575 - 2.09481i) q^{84} +(-1.06980 - 0.897668i) q^{85} +(12.5407 + 2.21127i) q^{86} +(-1.62475 - 1.36218i) q^{87} +(1.62726 - 1.36543i) q^{88} +(5.88308 + 10.1898i) q^{89} +(0.384447 + 1.05353i) q^{90} +(2.05110 + 6.63506i) q^{91} +(1.45403 - 0.256384i) q^{92} +(-5.06165 - 8.75862i) q^{93} +(0.0643145 + 0.176703i) q^{94} +(-0.579729 - 1.59279i) q^{95} +(0.865402 - 1.50036i) q^{96} +(-6.86017 + 1.20963i) q^{97} +(3.02946 - 6.31050i) q^{98} +(5.52157 + 3.18176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	0.591720	−	1.62784i	0.341629	−	0.939835i
$3$	0.591720	−	1.62784i	0.341629	−	0.939835i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.0649147	−	0.368150i	0.0290307	−	0.164642i	−0.966846	−	0.255361i	$-0.917806\pi$
$5$	0.0649147	−	0.368150i	0.0290307	−	0.164642i	0.995876	+	0.0907197i	$0.0289167\pi$
$6$	−1.32729	−	1.11279i	−0.541864	−	0.454294i
$7$	−2.64254	−	0.130261i	−0.998787	−	0.0492341i
$7$	−2.64254	−	0.130261i	−0.998787	−	0.0492341i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.29974	−	1.92645i	−0.766579	−	0.642150i
$10$	−0.323745	−	0.186914i	−0.102377	−	0.0591075i
$11$	−2.09196	+	0.368870i	−0.630751	+	0.111218i	−0.479879	−	0.877335i	$-0.659319\pi$
$11$	−2.09196	+	0.368870i	−0.630751	+	0.111218i	−0.150872	+	0.988553i	$0.548208\pi$
$12$	−1.49964	+	0.866649i	−0.432909	+	0.250180i
$13$	−0.897772	−	2.46661i	−0.248997	−	0.684114i	−0.999724	−	0.0235010i	$-0.992519\pi$
$13$	−0.897772	−	2.46661i	−0.248997	−	0.684114i	0.750727	−	0.660613i	$-0.229704\pi$
$14$	−1.02621	+	2.43863i	−0.274266	+	0.651750i
$15$	−0.560878	−	0.323512i	−0.144818	−	0.0835305i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.86786	−	3.23524i	0.453024	−	0.784660i	−0.545548	−	0.838079i	$-0.683679\pi$
$17$	1.86786	−	3.23524i	0.453024	−	0.784660i	0.998572	+	0.0534191i	$0.0170119\pi$
$18$	−2.59683	+	1.50216i	−0.612078	+	0.354062i
$19$	3.92673	−	2.26710i	0.900854	−	0.520109i	0.0233771	−	0.999727i	$-0.492558\pi$
$19$	3.92673	−	2.26710i	0.900854	−	0.520109i	0.877477	+	0.479618i	$0.159225\pi$
$20$	−0.286370	+	0.240293i	−0.0640342	+	0.0537311i
$21$	−1.77569	+	4.22456i	−0.387487	+	0.921875i
$22$	−0.368870	+	2.09196i	−0.0786433	+	0.446008i
$23$	−0.949048	+	1.13103i	−0.197890	+	0.235836i	−0.855859	−	0.517208i	$-0.826971\pi$
$23$	−0.949048	+	1.13103i	−0.197890	+	0.235836i	0.657969	+	0.753045i	$0.271416\pi$
$24$	0.301477	+	1.70561i	0.0615386	+	0.348157i
$25$	4.56714	+	1.66230i	0.913429	+	0.332461i
$26$	−2.62491			−0.514787
$27$	−4.49676	+	2.60369i	−0.865401	+	0.501080i
$28$	1.94057	+	1.79838i	0.366734	+	0.339862i
$29$	0.418671	−	1.15029i	0.0777452	−	0.213603i	−0.894731	−	0.446606i	$-0.852633\pi$
$29$	0.418671	−	1.15029i	0.0777452	−	0.213603i	0.972476	+	0.233002i	$0.0748550\pi$
$30$	−0.495834	+	0.416405i	−0.0905264	+	0.0760248i
$31$	3.75419	−	4.47407i	0.674273	−	0.803567i	−0.315086	−	0.949063i	$-0.602033\pi$
$31$	3.75419	−	4.47407i	0.674273	−	0.803567i	0.989359	+	0.145496i	$0.0464779\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−0.637395	+	3.62365i	−0.110956	+	0.630797i
$34$	−2.40128	−	2.86174i	−0.411816	−	0.490784i
$35$	−0.219496	+	0.964395i	−0.0371015	+	0.163013i
$36$	0.523401	+	2.95399i	0.0872335	+	0.492332i
$37$	3.45500	−	5.98424i	0.567999	−	0.983803i	−0.428765	−	0.903416i	$-0.641051\pi$
$37$	3.45500	−	5.98424i	0.567999	−	0.983803i	0.996764	−	0.0803870i	$-0.0256156\pi$
$38$	−0.787356	−	4.46532i	−0.127726	−	0.724370i
$39$	−4.54648	+	0.00189014i	−0.728019	+	0.000302664i
$40$	0.127857	+	0.351284i	0.0202160	+	0.0555429i
$41$	−5.14104	+	1.87119i	−0.802896	+	0.292230i	−0.710686	−	0.703509i	$-0.751615\pi$
$41$	−5.14104	+	1.87119i	−0.802896	+	0.292230i	−0.0922099	+	0.995740i	$0.529393\pi$
$42$	3.36247	+	3.11349i	0.518840	+	0.480422i
$43$	2.21127	+	12.5407i	0.337216	+	1.91245i	0.404158	+	0.914689i	$0.367564\pi$
$43$	2.21127	+	12.5407i	0.337216	+	1.91245i	−0.0669425	+	0.997757i	$0.521324\pi$
$44$	1.83964	+	1.06212i	0.277336	+	0.160120i
$45$	−0.858509	+	0.721592i	−0.127979	+	0.107569i
$46$	0.738228	+	1.27865i	0.108846	+	0.188526i
$47$	−0.144049	+	0.120872i	−0.0210117	+	0.0176309i	−0.653233	−	0.757157i	$-0.726588\pi$
$47$	−0.144049	+	0.120872i	−0.0210117	+	0.0176309i	0.632221	+	0.774788i	$0.282143\pi$
$48$	1.70586	+	0.300058i	0.246220	+	0.0433097i
$49$	6.96606	+	0.688442i	0.995152	+	0.0983488i
$50$	3.12411	−	3.72317i	0.441816	−	0.526536i
$51$	−4.16120	−	4.95494i	−0.582685	−	0.693831i
$52$	−0.897772	+	2.46661i	−0.124499	+	0.342057i
$53$		−	12.2303i		−	1.67996i	−0.542618	−	0.839979i	$-0.682567\pi$
$53$		−	12.2303i		−	1.67996i	0.542618	−	0.839979i	$-0.317433\pi$
$54$	0.908684	+	5.11608i	0.123656	+	0.696211i
$55$			0.794101i			0.107077i
$56$	2.35364	−	1.20846i	0.314518	−	0.161488i
$57$	−1.36696	−	7.73359i	−0.181058	−	1.02434i
$58$	−0.937724	−	0.786844i	−0.123129	−	0.103318i
$59$	−1.67308	+	9.48853i	−0.217817	+	1.23530i	0.658134	+	0.752901i	$0.271346\pi$
$59$	−1.67308	+	9.48853i	−0.217817	+	1.23530i	−0.875951	+	0.482400i	$0.839765\pi$
$60$	0.221708	+	0.608350i	0.0286224	+	0.0785377i
$61$	−4.15155	−	4.94762i	−0.531551	−	0.633478i	0.431720	−	0.902008i	$-0.357907\pi$
$61$	−4.15155	−	4.94762i	−0.531551	−	0.633478i	−0.963271	+	0.268530i	$0.913462\pi$
$62$	−2.92024	−	5.05801i	−0.370871	−	0.642368i
$63$	5.82621	+	5.39030i	0.734033	+	0.679114i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−0.966359	+	0.170395i	−0.119862	+	0.0211349i
$66$	3.18712	+	1.83832i	0.392307	+	0.226281i
$67$	10.1110	−	3.68009i	1.23525	−	0.449594i	0.359858	−	0.933007i	$-0.382825\pi$
$67$	10.1110	−	3.68009i	1.23525	−	0.449594i	0.875392	+	0.483413i	$0.160603\pi$
$68$	−3.51044	+	1.27769i	−0.425703	+	0.154943i
$69$	1.27957	+	2.21415i	0.154042	+	0.266553i
$70$	0.831163	+	0.536101i	0.0993430	+	0.0640763i
$71$	−2.33580	−	1.34858i	−0.277209	−	0.160047i	0.354950	−	0.934885i	$-0.384498\pi$
$71$	−2.33580	−	1.34858i	−0.277209	−	0.160047i	−0.632159	+	0.774839i	$0.717831\pi$
$72$	2.95486	+	0.518488i	0.348233	+	0.0611044i
$73$	8.52609	−	4.92254i	0.997903	−	0.576140i	0.0902761	−	0.995917i	$-0.471225\pi$
$73$	8.52609	−	4.92254i	0.997903	−	0.576140i	0.907627	+	0.419777i	$0.137892\pi$
$74$	−4.44167	−	5.29337i	−0.516333	−	0.615342i
$75$	5.40844	−	6.45097i	0.624512	−	0.744893i
$76$	−4.46532	−	0.787356i	−0.512207	−	0.0903159i
$77$	5.57615	−	0.702252i	0.635462	−	0.0800290i
$78$	−1.55321	+	4.27294i	−0.175866	+	0.483815i
$79$	1.81112	+	0.659192i	0.203766	+	0.0741649i	0.441887	−	0.897071i	$-0.354309\pi$
$79$	1.81112	+	0.659192i	0.203766	+	0.0741649i	−0.238121	+	0.971236i	$0.576531\pi$
$80$	0.373829			0.0417953
$81$	1.57757	+	8.86066i	0.175286	+	0.984518i
$82$			5.47098i			0.604169i
$83$	−12.2405	−	4.45518i	−1.34357	−	0.489020i	−0.432635	−	0.901569i	$-0.642416\pi$
$83$	−12.2405	−	4.45518i	−1.34357	−	0.489020i	−0.910935	+	0.412549i	$0.864638\pi$
$84$	4.07575	−	2.09481i	0.444701	−	0.228563i
$85$	−1.06980	−	0.897668i	−0.116036	−	0.0973658i
$86$	12.5407	+	2.21127i	1.35230	+	0.238448i
$87$	−1.62475	−	1.36218i	−0.174192	−	0.146041i
$88$	1.62726	−	1.36543i	0.173466	−	0.145556i
$89$	5.88308	+	10.1898i	0.623606	+	1.08012i	0.988809	+	0.149189i	$0.0476662\pi$
$89$	5.88308	+	10.1898i	0.623606	+	1.08012i	−0.365203	+	0.930928i	$0.619000\pi$
$90$	0.384447	+	1.05353i	0.0405243	+	0.111052i
$91$	2.05110	+	6.63506i	0.215013	+	0.695543i
$92$	1.45403	−	0.256384i	0.151593	−	0.0267299i
$93$	−5.06165	−	8.75862i	−0.524869	−	0.908227i
$94$	0.0643145	+	0.176703i	0.00663353	+	0.0182255i
$95$	−0.579729	−	1.59279i	−0.0594790	−	0.163417i
$96$	0.865402	−	1.50036i	0.0883247	−	0.153130i
$97$	−6.86017	+	1.20963i	−0.696545	+	0.122820i	−0.510699	−	0.859759i	$-0.670614\pi$
$97$	−6.86017	+	1.20963i	−0.696545	+	0.122820i	−0.185846	+	0.982579i	$0.559502\pi$
$98$	3.02946	−	6.31050i	0.306021	−	0.637457i
$99$	5.52157	+	3.18176i	0.554939	+	0.319779i
$100$	−2.43013	−	4.20910i	−0.243013	−	0.420910i
$101$	8.09258	−	6.79048i	0.805242	−	0.675678i	−0.144225	−	0.989545i	$-0.546069\pi$
$101$	8.09258	−	6.79048i	0.805242	−	0.675678i	0.949467	+	0.313867i	$0.101625\pi$
$102$	−6.07934	+	2.21556i	−0.601944	+	0.219373i
$103$	5.69305	+	1.00384i	0.560953	+	0.0989111i	0.446933	−	0.894567i	$-0.352516\pi$
$103$	5.69305	+	1.00384i	0.560953	+	0.0989111i	0.114020	+	0.993479i	$0.463627\pi$
$104$	2.01080	+	1.68726i	0.197175	+	0.165449i
$105$	1.44000	+	0.927955i	0.140530	+	0.0905592i
$106$	−11.4927	−	4.18300i	−1.11627	−	0.406289i
$107$			0.569810i			0.0550856i	0.999621	+	0.0275428i	$0.00876826\pi$
$107$			0.569810i			0.0550856i	−0.999621	+	0.0275428i	$0.991232\pi$
$108$	5.11833	+	0.895919i	0.492512	+	0.0862099i
$109$	8.30067			0.795060			0.397530	−	0.917589i	$-0.369867\pi$
$109$	8.30067			0.795060			0.397530	+	0.917589i	$0.369867\pi$
$110$	0.746211	+	0.271598i	0.0711484	+	0.0258959i
$111$	−7.69700	−	9.16519i	−0.730567	−	0.869921i
$112$	−0.330590	−	2.62502i	−0.0312379	−	0.248041i
$113$	1.95326	+	0.344412i	0.183747	+	0.0323996i	0.264764	−	0.964313i	$-0.414706\pi$
$113$	1.95326	+	0.344412i	0.183747	+	0.0323996i	−0.0810173	+	0.996713i	$0.525817\pi$
$114$	−7.73472	−	1.36052i	−0.724423	−	0.127425i
$115$	0.354781	+	0.422812i	0.0330835	+	0.0394274i
$116$	−1.06011	+	0.612056i	−0.0984289	+	0.0568280i
$117$	−2.68716	+	7.40206i	−0.248428	+	0.684321i
$118$	8.34407	+	4.81745i	0.768134	+	0.443482i
$119$	−5.35734	+	8.30594i	−0.491106	+	0.761404i
$120$	0.647491		0.000269186i	0.0591075		2.45732e-5i
$121$	−6.09637	+	2.21890i	−0.554216	+	0.201718i
$122$	−6.06916	+	2.20899i	−0.549476	+	0.199993i
$123$	0.00393953	+	9.47602i	0.000355216	+	0.854424i
$124$	−5.75175	+	1.01419i	−0.516523	+	0.0910769i
$125$	1.84302	−	3.19221i	0.164845	−	0.285520i
$126$	7.05790	−	3.63126i	0.628768	−	0.323498i
$127$	0.812614	+	1.40749i	0.0721079	+	0.124894i	0.899825	−	0.436251i	$-0.143694\pi$
$127$	0.812614	+	1.40749i	0.0721079	+	0.124894i	−0.827717	+	0.561146i	$0.810361\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	21.7228	+	3.82100i	1.91259	+	0.336421i
$130$	−0.170395	+	0.966359i	−0.0149446	+	0.0847553i
$131$	−10.0624	−	8.44334i	−0.879154	−	0.737698i	0.0868510	−	0.996221i	$-0.472320\pi$
$131$	−10.0624	−	8.44334i	−0.879154	−	0.737698i	−0.966005	+	0.258524i	$0.916764\pi$
$132$	2.81751	−	2.36617i	0.245233	−	0.205949i
$133$	−10.6719	+	5.47941i	−0.925369	+	0.475125i
$134$		−	10.7599i		−	0.929510i
$135$	0.666641	+	1.82450i	0.0573753	+	0.157028i
$136$			3.73573i			0.320336i
$137$	−0.762426	+	2.09475i	−0.0651384	+	0.178966i	−0.967992	−	0.250983i	$-0.919246\pi$
$137$	−0.762426	+	2.09475i	−0.0651384	+	0.178966i	0.902853	+	0.429949i	$0.141468\pi$
$138$	2.51826	−	0.445117i	0.214369	−	0.0378909i
$139$	0.304778	−	0.363221i	0.0258510	−	0.0308080i	−0.752964	−	0.658062i	$-0.771377\pi$
$139$	0.304778	−	0.363221i	0.0258510	−	0.0308080i	0.778815	+	0.627254i	$0.215821\pi$
$140$	0.788045	−	0.597681i	0.0666019	−	0.0505132i
$141$	0.111523	+	0.306011i	0.00939194	+	0.0257708i
$142$	−2.06614	+	1.73370i	−0.173387	+	0.145489i
$143$	2.78796	+	4.82889i	0.233141	+	0.403812i
$144$	1.49784	−	2.59932i	0.124820	−	0.216610i
$145$	−0.396300	−	0.228804i	−0.0329110	−	0.0190012i
$146$	−1.70958	−	9.69551i	−0.141486	−	0.802406i
$147$	5.24263	−	10.9323i	0.432405	−	0.901680i
$148$	−6.49328	+	2.36336i	−0.533745	+	0.194267i
$149$	8.13560	+	22.3524i	0.666495	+	1.83118i	0.544714	+	0.838622i	$0.316638\pi$
$149$	8.13560	+	22.3524i	0.666495	+	1.83118i	0.121780	+	0.992557i	$0.461140\pi$
$150$	−4.21213	−	7.28863i	−0.343919	−	0.595114i
$151$	2.58184	+	14.6423i	0.210107	+	1.19158i	0.889198	+	0.457522i	$0.151263\pi$
$151$	2.58184	+	14.6423i	0.210107	+	1.19158i	−0.679091	+	0.734054i	$0.737626\pi$
$152$	−2.26710	+	3.92673i	−0.183886	+	0.318500i
$153$	−10.5281	+	3.84184i	−0.851148	+	0.310594i
$154$	1.24726	−	5.48005i	0.100507	−	0.441595i
$155$	−1.40343	−	1.67254i	−0.112726	−	0.134341i
$156$	3.48402	+	2.92097i	0.278945	+	0.233865i
$157$	2.60015	+	0.458477i	0.207515	+	0.0365905i	0.276439	−	0.961031i	$-0.410846\pi$
$157$	2.60015	+	0.458477i	0.207515	+	0.0365905i	−0.0689243	+	0.997622i	$0.521957\pi$
$158$	1.23888	−	1.47643i	0.0985597	−	0.117459i
$159$	−19.9090	−	7.23690i	−1.57888	−	0.573923i
$160$	0.127857	−	0.351284i	0.0101080	−	0.0277715i
$161$	2.65523	−	2.86517i	0.209261	−	0.225807i
$162$	8.86586	+	1.54809i	0.696567	+	0.121630i
$163$	−4.95914			−0.388430			−0.194215	−	0.980959i	$-0.562216\pi$
$163$	−4.95914			−0.388430			−0.194215	+	0.980959i	$0.562216\pi$
$164$	5.14104	+	1.87119i	0.401448	+	0.146115i
$165$	1.29267	+	0.469885i	0.100634	+	0.0365805i
$166$	−8.37300	+	9.97856i	−0.649871	+	0.774486i
$167$	−0.507771	+	2.87971i	−0.0392925	+	0.222839i	−0.998131	−	0.0611138i	$-0.980535\pi$
$167$	−0.507771	+	2.87971i	−0.0392925	+	0.222839i	0.958838	+	0.283953i	$0.0916459\pi$
$168$	−0.574490	−	4.54642i	−0.0443228	−	0.350764i
$169$	4.68042	−	3.92734i	0.360032	−	0.302103i
$170$	−1.20943	+	0.698262i	−0.0927587	+	0.0535542i
$171$	−13.3979	−	2.35093i	−1.02456	−	0.179780i
$172$	6.36710	−	11.0281i	0.485487	−	0.840888i
$173$	−2.46516	−	13.9806i	−0.187422	−	1.06292i	−0.922803	−	0.385271i	$-0.874108\pi$
$173$	−2.46516	−	13.9806i	−0.187422	−	1.06292i	0.735381	−	0.677654i	$-0.237003\pi$
$174$	−1.83573	+	1.06087i	−0.139166	+	0.0804247i
$175$	−11.8523	−	4.98763i	−0.895952	−	0.377029i
$176$	−0.726531	−	1.99613i	−0.0547644	−	0.150464i
$177$	14.4558	+	8.33806i	1.08657	+	0.626727i
$178$	11.5874	−	2.04317i	0.868513	−	0.153142i
$179$	−3.19849	−	1.84665i	−0.239066	−	0.138025i	0.375681	−	0.926749i	$-0.377409\pi$
$179$	−3.19849	−	1.84665i	−0.239066	−	0.138025i	−0.614747	+	0.788724i	$0.710742\pi$
$180$	1.12149		0.000932487i	0.0835907		6.95035e-5i
$181$	−12.3865	+	7.15133i	−0.920679	+	0.531554i	−0.883852	−	0.467767i	$-0.845058\pi$
$181$	−12.3865	+	7.15133i	−0.920679	+	0.531554i	−0.0368273	+	0.999322i	$0.511725\pi$
$182$	6.93643	+	0.341924i	0.514163	+	0.0253451i
$183$	−10.5105	+	3.83046i	−0.776958	+	0.283156i
$184$	0.256384	−	1.45403i	0.0189009	−	0.107192i
$185$	−1.97882	−	1.66042i	−0.145485	−	0.122077i
$186$	−9.96160	+	1.76077i	−0.730420	+	0.129106i
$187$	−2.71412	+	7.45700i	−0.198476	+	0.545310i
$188$	0.188043			0.0137144
$189$	12.2220	−	6.29460i	0.889022	−	0.457865i
$190$	−1.69502			−0.122969
$191$	−8.11668	+	22.3004i	−0.587302	+	1.61360i	0.188112	+	0.982148i	$0.439763\pi$
$191$	−8.11668	+	22.3004i	−0.587302	+	1.61360i	−0.775415	+	0.631452i	$0.782459\pi$
$192$	−1.11389	−	1.32636i	−0.0803883	−	0.0957221i
$193$	−6.65508	−	5.58427i	−0.479043	−	0.401965i	0.371037	−	0.928618i	$-0.379002\pi$
$193$	−6.65508	−	5.58427i	−0.479043	−	0.401965i	−0.850080	+	0.526653i	$0.823447\pi$
$194$	−1.20963	+	6.86017i	−0.0868466	+	0.492532i
$195$	−0.294437	+	1.67391i	−0.0210851	+	0.119871i
$196$	−4.89379	−	5.00508i	−0.349557	−	0.357505i
$197$	2.89632	−	1.67219i	0.206354	−	0.119139i	−0.393262	−	0.919427i	$-0.628653\pi$
$197$	2.89632	−	1.67219i	0.206354	−	0.119139i	0.599616	+	0.800288i	$0.295320\pi$
$198$	4.87837	−	4.10035i	0.346691	−	0.291400i
$199$	−9.90883	−	5.72087i	−0.702419	−	0.405542i	0.105829	−	0.994384i	$-0.466250\pi$
$199$	−9.90883	−	5.72087i	−0.702419	−	0.405542i	−0.808248	+	0.588843i	$0.799584\pi$
$200$	−4.78641	+	0.843974i	−0.338451	+	0.0596780i
$201$	−0.00774793	−	18.6366i	−0.000546497	−	1.31453i
$202$	−3.61314	−	9.92702i	−0.254220	−	0.698463i
$203$	−1.25619	+	2.98515i	−0.0881675	+	0.209516i
$204$	0.00269002	+	6.47047i	0.000188339	+	0.453024i
$205$	0.355147	+	2.01414i	0.0248046	+	0.140674i
$206$	2.89044	−	5.00638i	0.201386	−	0.348811i
$207$	4.36143	−	0.772778i	0.303141	−	0.0537118i
$208$	2.27324	−	1.31245i	0.157621	−	0.0910023i
$209$	−7.37832	+	6.19114i	−0.510369	+	0.428250i
$210$	1.36450	−	1.03578i	0.0941596	−	0.0714756i
$211$	1.56877	−	8.89692i	0.107998	−	0.612489i	−0.881982	−	0.471283i	$-0.843791\pi$
$211$	1.56877	−	8.89692i	0.107998	−	0.612489i	0.989980	−	0.141206i	$-0.0450980\pi$
$212$	−7.86147	+	9.36894i	−0.539928	+	0.643461i
$213$	−3.57741	+	3.00434i	−0.245120	+	0.205854i
$214$	0.535446	+	0.194887i	0.0366024	+	0.0133222i
$215$	4.76041			0.324658
$216$	2.59246	−	4.50324i	0.176395	−	0.306406i
$217$	−10.5034	+	11.3339i	−0.713018	+	0.769395i
$218$	2.83900	−	7.80008i	0.192281	−	0.528288i
$219$	−2.96806	−	16.7919i	−0.200563	−	1.13469i
$220$	0.510438	−	0.608316i	0.0344137	−	0.0410127i
$221$	−9.65698	−	1.70279i	−0.649599	−	0.114542i
$222$	−11.2450	+	4.09814i	−0.754714	+	0.275049i
$223$	−14.2962	−	17.0375i	−0.957341	−	1.14091i	−0.989946	−	0.141447i	$-0.954825\pi$
$223$	−14.2962	−	17.0375i	−0.957341	−	1.14091i	0.0326045	−	0.999468i	$-0.489620\pi$
$224$	−2.57978	−	0.587155i	−0.172369	−	0.0392309i
$225$	−7.30087	−	12.6212i	−0.486725	−	0.841416i
$226$	0.991696	−	1.71767i	0.0659666	−	0.114258i
$227$	0.259300	+	1.47056i	0.0172103	+	0.0976046i	0.992203	−	0.124633i	$-0.0397752\pi$
$227$	0.259300	+	1.47056i	0.0172103	+	0.0976046i	−0.974993	+	0.222237i	$0.928664\pi$
$228$	−3.92391	+	6.80293i	−0.259867	+	0.450535i
$229$	−2.83038	−	7.77640i	−0.187037	−	0.513879i	0.810365	−	0.585926i	$-0.199269\pi$
$229$	−2.83038	−	7.77640i	−0.187037	−	0.513879i	−0.997401	+	0.0720471i	$0.977047\pi$
$230$	0.518656	−	0.188775i	0.0341991	−	0.0124475i
$231$	2.15636	−	9.49263i	0.141878	−	0.624569i
$232$	0.212565	+	1.20551i	0.0139556	+	0.0791459i
$233$	17.6553	+	10.1933i	1.15664	+	0.667786i	0.950496	−	0.310736i	$-0.100575\pi$
$233$	17.6553	+	10.1933i	1.15664	+	0.667786i	0.206143	+	0.978522i	$0.433909\pi$
$234$	6.03660	+	5.05676i	0.394625	+	0.330571i
$235$	0.0351479	+	0.0608780i	0.00229280	+	0.00397124i
$236$	7.38077	−	6.19320i	0.480447	−	0.403143i
$237$	2.14473	−	2.55815i	0.139315	−	0.166170i
$238$	5.97271	+	7.87505i	0.387154	+	0.510464i
$239$	−11.0204	+	13.1335i	−0.712847	+	0.849538i	−0.993915	−	0.110150i	$-0.964867\pi$
$239$	−11.0204	+	13.1335i	−0.712847	+	0.849538i	0.281068	+	0.959688i	$0.409311\pi$
$240$	0.221202	−	0.608534i	0.0142785	−	0.0392807i
$241$	−9.20400	+	25.2878i	−0.592882	+	1.62893i	0.172249	+	0.985054i	$0.444897\pi$
$241$	−9.20400	+	25.2878i	−0.592882	+	1.62893i	−0.765130	+	0.643876i	$0.777325\pi$
$242$			6.48762i			0.417040i
$243$	15.3572	+	2.67499i	0.985167	+	0.171601i
$244$			6.45866i			0.413473i
$245$	0.705650	−	2.51986i	0.0450823	−	0.160988i
$246$	8.90589	+	3.23729i	0.567819	+	0.206402i
$247$	−9.11736	−	7.65037i	−0.580124	−	0.486782i
$248$	−1.01419	+	5.75175i	−0.0644011	+	0.365237i
$249$	−14.4953	+	17.2894i	−0.918601	+	1.09567i
$250$	−2.36935	−	2.82368i	−0.149851	−	0.178585i
$251$	13.6426	+	23.6298i	0.861116	+	1.49150i	0.870853	+	0.491544i	$0.163567\pi$
$251$	13.6426	+	23.6298i	0.861116	+	1.49150i	−0.00973638	+	0.999953i	$0.503099\pi$
$252$	−0.998319	−	7.87422i	−0.0628882	−	0.496029i
$253$	1.56817	−	2.71615i	0.0985900	−	0.170763i
$254$	1.60054	−	0.282218i	0.100427	−	0.0177079i
$255$	−2.09428	+	1.21030i	−0.131149	+	0.0757917i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	14.4299	−	5.25204i	0.900111	−	0.327614i	0.149814	−	0.988714i	$-0.452133\pi$
$257$	14.4299	−	5.25204i	0.900111	−	0.327614i	0.750297	+	0.661101i	$0.229910\pi$
$258$	11.0202	−	19.1059i	0.686088	−	1.18948i
$259$	−9.90951	+	15.3636i	−0.615747	+	0.954645i
$260$	0.849802	+	0.490633i	0.0527025	+	0.0304278i
$261$	−3.17881	+	1.83881i	−0.196763	+	0.113820i
$262$	−11.3757	+	6.56775i	−0.702792	+	0.405757i
$263$	−12.4495	−	14.8368i	−0.767670	−	0.914874i	0.230637	−	0.973040i	$-0.425919\pi$
$263$	−12.4495	−	14.8368i	−0.767670	−	0.914874i	−0.998307	+	0.0581663i	$0.981475\pi$
$264$	−1.25983	−	3.45687i	−0.0775370	−	0.212756i
$265$	−4.50257	−	0.793925i	−0.276591	−	0.0487704i
$266$	1.49896	+	11.9024i	0.0919074	+	0.729780i
$267$	20.0685	−	3.54722i	1.22817	−	0.217087i
$268$	−10.1110	−	3.68009i	−0.617625	−	0.224797i
$269$	18.2612			1.11340			0.556702	−	0.830712i	$-0.312066\pi$
$269$	18.2612			1.11340			0.556702	+	0.830712i	$0.312066\pi$
$270$	1.94247	−	0.00242267i	0.118215	−	0.000147439i
$271$		−	20.0809i		−	1.21983i	−0.792469	−	0.609913i	$-0.791205\pi$
$271$		−	20.0809i		−	1.21983i	0.792469	−	0.609913i	$-0.208795\pi$
$272$	3.51044	+	1.27769i	0.212852	+	0.0774716i
$273$	12.0145	+	0.587235i	0.727151	+	0.0355411i
$274$	1.70765	+	1.43289i	0.103163	+	0.0865641i
$275$	−10.1675	−	1.79280i	−0.613122	−	0.108110i
$276$	0.443023	−	2.51863i	0.0266668	−	0.151604i
$277$	20.7202	−	17.3863i	1.24496	−	1.04464i	0.247839	−	0.968801i	$-0.420280\pi$
$277$	20.7202	−	17.3863i	1.24496	−	1.04464i	0.997120	−	0.0758431i	$-0.0241648\pi$
$278$	−0.237075	−	0.410627i	−0.0142188	−	0.0246278i
$279$	−17.2527	+	3.05691i	−1.03289	+	0.183013i
$280$	−0.292109	−	0.944939i	−0.0174568	−	0.0564709i
$281$	−18.7567	+	3.30732i	−1.11893	+	0.197298i	−0.702372	−	0.711810i	$-0.747876\pi$
$281$	−18.7567	+	3.30732i	−1.11893	+	0.197298i	−0.416561	+	0.909108i	$0.636765\pi$
$282$	0.325700		0.000135405i	0.0193951		8.06328e-6i
$283$	5.00062	+	13.7391i	0.297256	+	0.816703i	0.994956	+	0.100313i	$0.0319846\pi$
$283$	5.00062	+	13.7391i	0.297256	+	0.816703i	−0.697700	+	0.716390i	$0.745793\pi$
$284$	0.922481	+	2.53450i	0.0547392	+	0.150395i
$285$	−2.93585	+	0.00122054i	−0.173905	+	7.22987e-5i
$286$	5.49121	−	0.968249i	0.324702	−	0.0572538i
$287$	13.8292	−	4.27501i	0.816310	−	0.252346i
$288$	−1.93027	−	2.29653i	−0.113742	−	0.135324i
$289$	1.52216	+	2.63646i	0.0895389	+	0.155086i
$290$	−0.350548	+	0.294145i	−0.0205849	+	0.0172728i
$291$	−2.09021	+	11.8830i	−0.122530	+	0.696596i
$292$	−9.69551	−	1.70958i	−0.567387	−	0.100046i
$293$	7.08202	+	5.94252i	0.413736	+	0.347166i	0.825774	−	0.564001i	$-0.190739\pi$
$293$	7.08202	+	5.94252i	0.413736	+	0.347166i	−0.412038	+	0.911167i	$0.635183\pi$
$294$	−8.47990	−	8.66552i	−0.494558	−	0.505384i
$295$	3.38459	+	1.23189i	0.197059	+	0.0717234i
$296$			6.91001i			0.401636i
$297$	8.44663	−	7.10553i	0.490123	−	0.412305i
$298$	23.7869			1.37794
$299$	3.64184	+	1.32552i	0.210613	+	0.0766568i
$300$	−8.28970	+	1.46525i	−0.478606	+	0.0845964i
$301$	−4.20981	−	33.4275i	−0.242649	−	1.92673i
$302$	14.6423	+	2.58184i	0.842572	+	0.148568i
$303$	−6.26529	−	17.1915i	−0.359931	−	0.987626i
$304$	2.91453	+	3.47340i	0.167160	+	0.199213i
$305$	−2.09096	+	1.20722i	−0.119728	+	0.0691251i
$306$	0.00931849	+	11.2072i	0.000532702	+	0.640672i
$307$	25.7524	+	14.8681i	1.46976	+	0.848569i	0.999425	−	0.0339159i	$-0.0107978\pi$
$307$	25.7524	+	14.8681i	1.46976	+	0.848569i	0.470340	+	0.882485i	$0.344131\pi$
$308$	−4.72298	−	3.04633i	−0.269117	−	0.173581i
$309$	5.00278	−	8.67339i	0.284598	−	0.493412i
$310$	−2.05167	+	0.746747i	−0.116527	+	0.0424124i
$311$	−6.64542	+	2.41873i	−0.376827	+	0.137154i	−0.523488	−	0.852033i	$-0.675370\pi$
$311$	−6.64542	+	2.41873i	−0.376827	+	0.137154i	0.146661	+	0.989187i	$0.453147\pi$
$312$	3.93642	−	2.27487i	0.222856	−	0.128789i
$313$	28.8767	−	5.09175i	1.63221	−	0.287803i	0.718914	−	0.695099i	$-0.244640\pi$
$313$	28.8767	−	5.09175i	1.63221	−	0.287803i	0.913296	+	0.407297i	$0.133528\pi$
$314$	1.32013	−	2.28654i	0.0744994	−	0.129037i
$315$	2.36264	−	1.79501i	0.133120	−	0.101137i
$316$	−0.963674	−	1.66913i	−0.0542109	−	0.0938961i
$317$	17.3532	+	20.6808i	0.974656	+	1.16155i	0.986852	+	0.161624i	$0.0516730\pi$
$317$	17.3532	+	20.6808i	0.974656	+	1.16155i	−0.0121970	+	0.999926i	$0.503883\pi$
$318$	−13.6097	+	16.2331i	−0.763196	+	0.910309i
$319$	−0.451538	+	2.56080i	−0.0252813	+	0.143377i
$320$	−0.286370	−	0.240293i	−0.0160085	−	0.0134328i
$321$	0.927561	+	0.337168i	0.0517714	+	0.0188189i
$322$	−1.78424	−	3.47505i	−0.0994318	−	0.193657i
$323$		−	16.9386i		−	0.942486i
$324$	4.48703	−	7.80170i	0.249280	−	0.433428i
$325$		−	12.7577i		−	0.707671i
$326$	−1.69613	+	4.66007i	−0.0939397	+	0.258097i
$327$	4.91167	−	13.5122i	0.271616	−	0.747225i
$328$	3.51668	−	4.19102i	0.194176	−	0.231410i
$329$	0.396401	−	0.300644i	0.0218543	−	0.0165751i
$330$	0.883667	−	1.05400i	0.0486442	−	0.0580209i
$331$	6.59257	−	5.53182i	0.362360	−	0.304057i	−0.443370	−	0.896339i	$-0.646217\pi$
$331$	6.59257	−	5.53182i	0.362360	−	0.304057i	0.805731	+	0.592282i	$0.201773\pi$
$332$	6.51304	+	11.2809i	0.357449	+	0.619121i
$333$	−19.4739	+	7.10628i	−1.06717	+	0.389422i
$334$	2.53238	+	1.46207i	0.138565	+	0.0800008i
$335$	−0.698473	−	3.96124i	−0.0381617	−	0.216426i
$336$	−4.46873	−	1.01512i	−0.243789	−	0.0553796i
$337$	−1.53883	+	0.560089i	−0.0838255	+	0.0305100i	−0.383593	−	0.923502i	$-0.625313\pi$
$337$	−1.53883	+	0.560089i	−0.0838255	+	0.0305100i	0.299767	+	0.954012i	$0.403091\pi$
$338$	−2.08969	−	5.74138i	−0.113664	−	0.312290i
$339$	1.71643	−	2.97580i	0.0932237	−	0.161623i
$340$	0.242504	+	1.37531i	0.0131516	+	0.0745865i
$341$	−6.20328	+	10.7444i	−0.335927	+	0.581842i
$342$	−6.79150	+	11.7859i	−0.367243	+	0.637306i
$343$	−18.3184	−	2.72664i	−0.989103	−	0.147225i
$344$	−8.18539	−	9.75497i	−0.441327	−	0.525953i
$345$	0.898202	−	0.327342i	0.0483576	−	0.0176235i
$346$	−13.9806	−	2.46516i	−0.751601	−	0.132528i
$347$	13.5918	−	16.1980i	0.729644	−	0.869556i	−0.265886	−	0.964005i	$-0.585664\pi$
$347$	13.5918	−	16.1980i	0.729644	−	0.869556i	0.995530	+	0.0944489i	$0.0301089\pi$
$348$	0.369041	+	2.08786i	0.0197827	+	0.111921i
$349$	−4.70912	+	12.9382i	−0.252073	+	0.692566i	0.747525	+	0.664233i	$0.231242\pi$
$349$	−4.70912	+	12.9382i	−0.252073	+	0.692566i	−0.999599	+	0.0283324i	$0.990980\pi$
$350$	−8.74058	+	9.43168i	−0.467204	+	0.504145i
$351$	10.4593	+	8.75422i	0.558278	+	0.467266i
$352$	−2.12424			−0.113222
$353$	0.418345	+	0.152265i	0.0222662	+	0.00810425i	0.353129	−	0.935575i	$-0.385118\pi$
$353$	0.418345	+	0.152265i	0.0222662	+	0.00810425i	−0.330863	+	0.943679i	$0.607340\pi$
$354$	12.7794	−	10.7322i	0.679218	−	0.570413i
$355$	−0.648106	+	0.772383i	−0.0343979	+	0.0409938i
$356$	2.04317	−	11.5874i	0.108288	−	0.614132i
$357$	10.3507	+	13.6357i	0.547818	+	0.721677i
$358$	−2.82923	+	2.37400i	−0.149529	+	0.125470i
$359$	−3.97193	+	2.29320i	−0.209631	+	0.121030i	−0.601140	−	0.799144i	$-0.705286\pi$
$359$	−3.97193	+	2.29320i	−0.209631	+	0.121030i	0.391509	+	0.920174i	$0.371953\pi$
$360$	0.382695	−	1.05417i	0.0201698	−	0.0555597i
$361$	0.779490	−	1.35012i	0.0410258	−	0.0710588i
$362$	2.48363	+	14.0854i	0.130537	+	0.740311i
$363$	0.00467159	+	11.2369i	0.000245195	+	0.589784i
$364$	2.69370	−	6.40117i	0.141188	−	0.335513i
$365$	−1.25876	−	3.45842i	−0.0658867	−	0.181022i
$366$	0.00465074	+	11.1867i	0.000243098	+	0.584740i
$367$	3.65398	−	0.644296i	0.190736	−	0.0336320i	−0.0774638	−	0.996995i	$-0.524682\pi$
$367$	3.65398	−	0.644296i	0.190736	−	0.0336320i	0.268200	+	0.963363i	$0.413571\pi$
$368$	−1.27865	−	0.738228i	−0.0666542	−	0.0384828i
$369$	15.4278	+	5.60073i	0.803139	+	0.291563i
$370$	−2.23708	+	1.29158i	−0.116300	+	0.0671461i
$371$	−1.59313	+	32.3190i	−0.0827113	+	1.67792i
$372$	−1.75249	+	9.96306i	−0.0908622	+	0.516561i
$373$	3.30156	−	18.7241i	0.170949	−	0.969497i	−0.771768	−	0.635904i	$-0.780628\pi$
$373$	3.30156	−	18.7241i	0.170949	−	0.969497i	0.942717	−	0.333594i	$-0.108261\pi$
$374$	6.07900	+	5.10089i	0.314338	+	0.263761i
$375$	−4.10586	−	4.88904i	−0.212026	−	0.252469i
$376$	0.0643145	−	0.176703i	0.00331677	−	0.00911274i
$377$	−3.21318			−0.165487
$378$	−1.73481	−	13.6378i	−0.0892290	−	0.701454i
$379$	18.4396			0.947179			0.473589	−	0.880746i	$-0.342958\pi$
$379$	18.4396			0.947179			0.473589	+	0.880746i	$0.342958\pi$
$380$	−0.579729	+	1.59279i	−0.0297395	+	0.0817086i
$381$	2.77201	−	0.489968i	0.142014	−	0.0251018i
$382$	18.1794	+	15.2544i	0.930141	+	0.780481i
$383$	4.44885	−	25.2307i	0.227326	−	1.28923i	−0.630863	−	0.775894i	$-0.717299\pi$
$383$	4.44885	−	25.2307i	0.227326	−	1.28923i	0.858189	−	0.513334i	$-0.171590\pi$
$384$	−1.62735	+	0.593073i	−0.0830453	+	0.0302651i
$385$	0.103441	−	2.09844i	0.00527182	−	0.106947i
$386$	−7.52367	+	4.34379i	−0.382945	+	0.221093i
$387$	19.0738	−	33.1003i	0.969576	−	1.68258i
$388$	6.03273	+	3.48300i	0.306266	+	0.176823i
$389$	20.6257	−	3.63687i	1.04576	−	0.184396i	0.375732	−	0.926728i	$-0.377391\pi$
$389$	20.6257	−	3.63687i	1.04576	−	0.184396i	0.670032	+	0.742332i	$0.266280\pi$
$390$	1.47225	+	0.849190i	0.0745505	+	0.0430004i
$391$	1.88646	+	5.18301i	0.0954024	+	0.262116i
$392$	−6.37701	+	2.88682i	−0.322088	+	0.145807i
$393$	−19.6985	+	11.3839i	−0.993659	+	0.574240i
$394$	−0.580746	−	3.29357i	−0.0292576	−	0.165928i
$395$	0.360249	−	0.623970i	0.0181261	−	0.0313953i
$396$	−2.18457	−	5.98657i	−0.109779	−	0.300837i
$397$	−23.4836	+	13.5583i	−1.17861	+	0.680471i	−0.955693	−	0.294367i	$-0.904891\pi$
$397$	−23.4836	+	13.5583i	−1.17861	+	0.680471i	−0.222917	+	0.974837i	$0.571558\pi$
$398$	−8.76488	+	7.35461i	−0.439344	+	0.368653i
$399$	2.60485	+	20.6144i	0.130406	+	1.03201i
$400$	−0.843974	+	4.78641i	−0.0421987	+	0.239321i
$401$	7.92564	−	9.44541i	0.395787	−	0.471681i	−0.530943	−	0.847407i	$-0.678162\pi$
$401$	7.92564	−	9.44541i	0.395787	−	0.471681i	0.926731	+	0.375726i	$0.122607\pi$
$402$	−17.5153	−	6.36682i	−0.873586	−	0.317548i
$403$	−14.4062	−	5.24342i	−0.717623	−	0.261193i
$404$	−10.5641			−0.525584
$405$	3.36446	−	0.00559492i	0.167181	−	0.000278014i
$406$	2.37548	+	2.20142i	0.117893	+	0.109255i
$407$	−5.02034	+	13.7933i	−0.248849	+	0.683707i
$408$	6.08118	+	2.21050i	0.301063	+	0.109436i
$409$	−2.23201	+	2.66000i	−0.110366	+	0.131529i	−0.818399	−	0.574650i	$-0.805138\pi$
$409$	−2.23201	+	2.66000i	−0.110366	+	0.131529i	0.708033	+	0.706179i	$0.249583\pi$
$410$	2.01414	+	0.355147i	0.0994713	+	0.0175395i
$411$	2.95877	+	2.48061i	0.145946	+	0.122360i
$412$	−3.71587	−	4.42840i	−0.183068	−	0.218172i
$413$	5.65718	−	24.8559i	0.278372	−	1.22308i
$414$	0.765524	−	4.36271i	0.0376235	−	0.214416i
$415$	−2.43476	+	4.21713i	−0.119518	+	0.207011i
$416$	−0.455811	−	2.58503i	−0.0223480	−	0.126742i
$417$	−0.410922	−	0.711056i	−0.0201230	−	0.0348205i
$418$	3.29424	+	9.05085i	0.161127	+	0.442691i
$419$	36.9600	−	13.4523i	1.80561	−	0.657189i	0.807921	−	0.589291i	$-0.200593\pi$
$419$	36.9600	−	13.4523i	1.80561	−	0.657189i	0.997692	−	0.0678982i	$-0.0216293\pi$
$420$	−0.506628	−	1.63647i	−0.0247209	−	0.0798516i
$421$	−0.515471	−	2.92338i	−0.0251225	−	0.142477i	0.969667	−	0.244432i	$-0.0786014\pi$
$421$	−0.515471	−	2.92338i	−0.0251225	−	0.142477i	−0.994789	+	0.101955i	$0.967490\pi$
$422$	−7.82382	−	4.51709i	−0.380858	−	0.219888i
$423$	0.564129		0.000469058i	0.0274289		2.28064e-5i
$424$	6.11514	+	10.5917i	0.296978	+	0.514380i
$425$	13.9088	−	11.6708i	0.674674	−	0.566118i
$426$	1.59961	+	4.38921i	0.0775013	+	0.212658i
$427$	10.3262	+	13.6151i	0.499718	+	0.658880i
$428$	0.366267	−	0.436500i	0.0177042	−	0.0210990i
$429$	9.51036	−	1.68101i	0.459165	−	0.0811600i
$430$	1.62816	−	4.47333i	0.0785167	−	0.215723i
$431$		−	31.3892i		−	1.51196i	−0.654592	−	0.755982i	$-0.727160\pi$
$431$		−	31.3892i		−	1.51196i	0.654592	−	0.755982i	$-0.272840\pi$
$432$	−3.34498	−	3.97631i	−0.160936	−	0.191311i
$433$			19.8551i			0.954174i	0.878856	+	0.477087i	$0.158307\pi$
$433$			19.8551i			0.954174i	−0.878856	+	0.477087i	$0.841693\pi$
$434$	7.05800	+	13.7464i	0.338795	+	0.659848i
$435$	−0.606956	+	0.509726i	−0.0291013	+	0.0244395i
$436$	−6.35868	−	5.33557i	−0.304526	−	0.255527i
$437$	−1.16250	+	6.59284i	−0.0556097	+	0.315378i
$438$	−16.7943	−	2.95410i	−0.802465	−	0.141152i
$439$	7.37199	+	8.78559i	0.351846	+	0.419313i	0.912719	−	0.408588i	$-0.133979\pi$
$439$	7.37199	+	8.78559i	0.351846	+	0.419313i	−0.560873	+	0.827902i	$0.689534\pi$
$440$	−0.397050	−	0.687711i	−0.0189286	−	0.0327854i
$441$	−14.6939	−	15.0030i	−0.699708	−	0.714429i
$442$	−4.90298	+	8.49220i	−0.233211	+	0.403933i
$443$	8.46588	−	1.49276i	0.402226	−	0.0709233i	0.0311243	−	0.999516i	$-0.490091\pi$
$443$	8.46588	−	1.49276i	0.402226	−	0.0709233i	0.371102	+	0.928592i	$0.378980\pi$
$444$	0.00497574	+	11.9685i	0.000236138	+	0.567999i
$445$	4.13327	−	1.50439i	0.195936	−	0.0713148i
$446$	−20.8996	+	7.60683i	−0.989624	+	0.360194i
$447$	41.2001	−	0.0171284i	1.94870	−	0.000810147i
$448$	−1.43408	+	2.22338i	−0.0677540	+	0.105045i
$449$	1.73651	+	1.00258i	0.0819511	+	0.0473145i	0.540416	−	0.841398i	$-0.318267\pi$
$449$	1.73651	+	1.00258i	0.0819511	+	0.0473145i	−0.458464	+	0.888713i	$0.651600\pi$
$450$	−14.3571	+	2.54386i	−0.676802	+	0.119919i
$451$	10.0646	−	5.81083i	0.473926	−	0.273621i
$452$	−1.27490	−	1.51937i	−0.0599662	−	0.0714650i
$453$	25.3631	+	4.46133i	1.19166	+	0.209612i
$454$	1.47056	+	0.259300i	0.0690168	+	0.0121695i
$455$	2.57584	−	0.324397i	0.120757	−	0.0152080i
$456$	5.05061	+	6.01401i	0.236517	+	0.281632i
$457$	−29.2881	−	10.6600i	−1.37004	−	0.498654i	−0.450897	−	0.892576i	$-0.648896\pi$
$457$	−29.2881	−	10.6600i	−1.37004	−	0.498654i	−0.919144	+	0.393922i	$0.871118\pi$
$458$	−8.27547			−0.386687
$459$	0.0242101	+	19.4114i	0.00113003	+	0.906047i
$460$		−	0.551942i		−	0.0257344i
$461$	−32.5328	−	11.8410i	−1.51520	−	0.551488i	−0.555257	−	0.831679i	$-0.687380\pi$
$461$	−32.5328	−	11.8410i	−1.51520	−	0.551488i	−0.959944	+	0.280190i	$0.909602\pi$
$462$	−8.18263	−	5.27299i	−0.380691	−	0.245322i
$463$	27.6725	+	23.2200i	1.28605	+	1.07913i	0.992379	+	0.123220i	$0.0393220\pi$
$463$	27.6725	+	23.2200i	1.28605	+	1.07913i	0.293673	+	0.955906i	$0.405122\pi$
$464$	1.20551	+	0.212565i	0.0559646	+	0.00986807i
$465$	−3.55306	+	1.29488i	−0.164769	+	0.0600487i
$466$	15.6171	−	13.1043i	0.723446	−	0.607044i
$467$	20.3785	+	35.2967i	0.943006	+	1.63334i	0.759694	+	0.650280i	$0.225349\pi$
$467$	20.3785	+	35.2967i	0.943006	+	1.63334i	0.183312	+	0.983055i	$0.441318\pi$
$468$	6.81644	−	3.94303i	0.315090	−	0.182267i
$469$	−27.1980	+	8.40772i	−1.25589	+	0.388233i
$470$	0.0692279	−	0.0122068i	0.00319325	−	0.000563055i
$471$	2.28489	−	3.96135i	0.105282	−	0.182529i
$472$	−3.29533	−	9.05385i	−0.151680	−	0.416737i
$473$	−9.25180	−	25.4191i	−0.425398	−	1.16877i
$474$	−1.67033	−	2.89033i	−0.0767210	−	0.132757i
$475$	21.7026	−	3.82675i	0.995782	−	0.175583i
$476$	9.44292	−	2.91909i	0.432815	−	0.133796i
$477$	−23.5610	+	28.1264i	−1.07879	+	1.28782i
$478$	8.57231	+	14.8477i	0.392088	+	0.679117i
$479$	−9.65957	+	8.10534i	−0.441357	+	0.370342i	−0.836217	−	0.548399i	$-0.815238\pi$
$479$	−9.65957	+	8.10534i	−0.441357	+	0.370342i	0.394860	+	0.918741i	$0.370793\pi$
$480$	−0.496180	−	0.415993i	−0.0226474	−	0.0189874i
$481$	−17.8626	−	3.14965i	−0.814464	−	0.143612i
$482$	20.6148	+	17.2979i	0.938978	+	0.787896i
$483$	−3.09290	−	6.01767i	−0.140732	−	0.273813i
$484$	6.09637	+	2.21890i	0.277108	+	0.100859i
$485$			2.60409i			0.118246i
$486$	7.76615	−	13.5162i	0.352280	−	0.613106i
$487$	−19.9114			−0.902273			−0.451136	−	0.892455i	$-0.648981\pi$
$487$	−19.9114			−0.902273			−0.451136	+	0.892455i	$0.648981\pi$
$488$	6.06916	+	2.20899i	0.274738	+	0.0999964i
$489$	−2.93442	+	8.07269i	−0.132699	+	0.365060i
$490$	−2.12655	−	1.52494i	−0.0960678	−	0.0688897i
$491$	−25.5358	−	4.50265i	−1.15241	−	0.203202i	−0.435384	−	0.900245i	$-0.643388\pi$
$491$	−25.5358	−	4.50265i	−1.15241	−	0.203202i	−0.717029	+	0.697043i	$0.754499\pi$
$492$	6.08805	−	7.26158i	0.274471	−	0.327378i
$493$	−2.93944	−	3.50308i	−0.132386	−	0.157771i
$494$	−10.3073	+	5.95093i	−0.463748	+	0.267745i
$495$	1.52980	−	1.82622i	0.0687592	−	0.0820826i
$496$	5.05801	+	2.92024i	0.227111	+	0.131123i
$497$	5.99680	+	3.86794i	0.268993	+	0.173501i
$498$	11.2890	+	19.5344i	0.505874	+	0.875359i
$499$	1.45434	−	0.529336i	0.0651052	−	0.0236963i	−0.309262	−	0.950977i	$-0.600082\pi$
$499$	1.45434	−	0.529336i	0.0651052	−	0.0236963i	0.374367	+	0.927280i	$0.377860\pi$
$500$	−3.46375	+	1.26070i	−0.154904	+	0.0563803i
$501$	4.38726	+	2.53055i	0.196008	+	0.113057i
$502$	26.8708	−	4.73804i	1.19930	−	0.211469i
$503$	6.41491	−	11.1109i	0.286026	−	0.495412i	−0.686831	−	0.726817i	$-0.740999\pi$
$503$	6.41491	−	11.1109i	0.286026	−	0.495412i	0.972858	+	0.231405i	$0.0743321\pi$
$504$	−7.74079	−	1.75503i	−0.344802	−	0.0781752i
$505$	−1.97459	−	3.42008i	−0.0878679	−	0.152192i
$506$	−2.01600	−	2.40258i	−0.0896222	−	0.106808i
$507$	−3.62359	−	9.94286i	−0.160929	−	0.441578i
$508$	0.282218	−	1.60054i	0.0125214	−	0.0710124i
$509$	−32.0336	−	26.8794i	−1.41986	−	1.19141i	−0.951413	−	0.307917i	$-0.900368\pi$
$509$	−32.0336	−	26.8794i	−1.41986	−	1.19141i	−0.468451	−	0.883490i	$-0.655188\pi$
$510$	0.421019	+	2.38193i	0.0186430	+	0.105474i
$511$	−23.1718	+	11.8974i	−1.02506	+	0.526310i
$512$			1.00000i			0.0441942i
$513$	−11.7547	+	20.4186i	−0.518985	+	0.901502i
$514$		−	15.3560i		−	0.677322i
$515$	0.739125	−	2.03073i	0.0325697	−	0.0894846i
$516$	−14.1845	−	16.8902i	−0.624439	−	0.743550i
$517$	0.256760	−	0.305995i	0.0112923	−	0.0134576i
$518$	11.0478	+	14.5665i	0.485411	+	0.640017i
$519$	−24.2169	−	4.25971i	−1.06300	−	0.186980i
$520$	0.751694	−	0.630746i	0.0329640	−	0.0276601i
$521$	−20.4380	−	35.3996i	−0.895403	−	1.55088i	−0.833304	−	0.552814i	$-0.813554\pi$
$521$	−20.4380	−	35.3996i	−0.895403	−	1.55088i	−0.0620990	−	0.998070i	$-0.519779\pi$
$522$	0.640701	+	3.61601i	0.0280427	+	0.158269i
$523$	−10.6613	−	6.15532i	−0.466187	−	0.269153i	0.248455	−	0.968643i	$-0.420077\pi$
$523$	−10.6613	−	6.15532i	−0.466187	−	0.269153i	−0.714642	+	0.699490i	$0.753410\pi$
$524$	2.28096	+	12.9359i	0.0996440	+	0.565109i
$525$	−15.1323	+	16.3424i	−0.660429	+	0.713243i
$526$	−18.2000	+	6.62425i	−0.793557	+	0.288831i
$527$	−7.46236	−	20.5027i	−0.325065	−	0.893110i
$528$	−3.67928	+	0.00152961i	−0.160120	+	6.65679e-5i
$529$	3.61537	+	20.5038i	0.157190	+	0.891468i
$530$	−2.28602	+	3.95950i	−0.0992982	+	0.171990i
$531$	22.1268	−	18.5980i	0.960223	−	0.807084i
$532$	11.6972	+	2.66228i	0.507139	+	0.115424i
$533$	9.23097	+	11.0010i	0.399837	+	0.476508i
$534$	3.53054	−	20.0715i	0.152781	−	0.868577i
$535$	0.209775	+	0.0369891i	0.00906938	+	0.00159918i
$536$	−6.91630	+	8.24253i	−0.298739	+	0.356023i
$537$	−4.89866	+	4.11393i	−0.211393	+	0.177529i
$538$	6.24570	−	17.1599i	0.269271	−	0.739816i
$539$	−14.8267	+	1.12937i	−0.638631	+	0.0486456i
$540$	0.662087	−	1.82615i	0.0284917	−	0.0785851i
$541$	−32.1069			−1.38038			−0.690191	−	0.723628i	$-0.742473\pi$
$541$	−32.1069			−1.38038			−0.690191	+	0.723628i	$0.742473\pi$
$542$	−18.8698	−	6.86806i	−0.810529	−	0.295008i
$543$	4.31192	+	24.3948i	0.185042	+	1.04688i
$544$	2.40128	−	2.86174i	0.102954	−	0.122696i
$545$	0.538836	−	3.05589i	0.0230812	−	0.130900i
$546$	4.66102	−	11.0891i	0.199473	−	0.474569i
$547$	20.8745	−	17.5158i	0.892530	−	0.748921i	−0.0761862	−	0.997094i	$-0.524274\pi$
$547$	20.8745	−	17.5158i	0.892530	−	0.748921i	0.968716	+	0.248172i	$0.0798299\pi$
$548$	1.93053	−	1.11459i	0.0824681	−	0.0476130i
$549$	0.0161106	+	19.3760i	0.000687585	+	0.826947i
$550$	−5.16216	+	8.94112i	−0.220115	+	0.381251i
$551$	−0.963811	−	5.46605i	−0.0410597	−	0.232861i
$552$	−2.21522	−	1.27773i	−0.0942858	−	0.0543837i
$553$	−4.70008	−	1.97786i	−0.199868	−	0.0841072i
$554$	−9.25108	−	25.4171i	−0.393041	−	1.07987i
$555$	−3.87381	+	2.23869i	−0.164434	+	0.0950272i
$556$	−0.466948	+	0.0823355i	−0.0198030	+	0.00349180i
$557$	−4.03655	−	2.33050i	−0.171034	−	0.0987467i	0.412039	−	0.911166i	$-0.364817\pi$
$557$	−4.03655	−	2.33050i	−0.171034	−	0.0987467i	−0.583073	+	0.812419i	$0.698150\pi$
$558$	−3.02822	+	17.2578i	−0.128195	+	0.730580i
$559$	28.9479	−	16.7131i	1.22437	−	0.706887i
$560$	−0.987859	−	0.0486954i	−0.0417447	−	0.00205776i
$561$	10.5328	+	8.83062i	0.444696	+	0.372829i
$562$	−3.30732	+	18.7567i	−0.139511	+	0.791205i
$563$	−31.1774	−	26.1609i	−1.31397	−	1.10255i	−0.987546	−	0.157328i	$-0.949712\pi$
$563$	−31.1774	−	26.1609i	−1.31397	−	1.10255i	−0.326423	−	0.945224i	$-0.605843\pi$
$564$	0.111269	−	0.306104i	0.00468526	−	0.0128893i
$565$	0.253591	−	0.696734i	0.0106686	−	0.0293118i
$566$	14.6208			0.614559
$567$	−3.01460	−	23.6202i	−0.126601	−	0.991954i
$568$	2.69715			0.113170
$569$	10.5209	−	28.9060i	0.441059	−	1.21180i	−0.497737	−	0.867328i	$-0.665835\pi$
$569$	10.5209	−	28.9060i	0.441059	−	1.21180i	0.938796	−	0.344473i	$-0.111942\pi$
$570$	−1.00297	+	2.75922i	−0.0420100	+	0.115571i
$571$	−1.07319	−	0.900516i	−0.0449118	−	0.0376854i	0.620055	−	0.784558i	$-0.287110\pi$
$571$	−1.07319	−	0.900516i	−0.0449118	−	0.0376854i	−0.664967	+	0.746873i	$0.731555\pi$
$572$	0.968249	−	5.49121i	0.0404845	−	0.229599i
$573$	31.4987	+	26.4082i	1.31588	+	1.10322i
$574$	0.712657	−	14.4573i	0.0297457	−	0.603436i
$575$	−6.21455	+	3.58797i	−0.259165	+	0.149629i
$576$	−2.81822	+	1.02840i	−0.117426	+	0.0428502i
$577$	−29.8679	−	17.2443i	−1.24342	−	0.717888i	−0.273629	−	0.961835i	$-0.588224\pi$
$577$	−29.8679	−	17.2443i	−1.24342	−	0.717888i	−0.969788	+	0.243948i	$0.921557\pi$
$578$	2.99807	−	0.528641i	0.124703	−	0.0219886i
$579$	−13.0283	+	7.52909i	−0.541436	+	0.312898i
$580$	0.156511	+	0.430011i	0.00649878	+	0.0178552i
$581$	31.7657	+	13.3675i	1.31786	+	0.554576i
$582$	10.4515	+	6.02839i	0.433229	+	0.249885i
$583$	4.51138	+	25.5853i	0.186842	+	1.05964i
$584$	−4.92254	+	8.52609i	−0.203696	+	0.352812i
$585$	2.55063	+	1.46978i	0.105456	+	0.0607679i
$586$	8.00634	−	4.62246i	0.330739	−	0.190952i
$587$	−22.6659	+	19.0189i	−0.935521	+	0.784996i	−0.976800	−	0.214152i	$-0.931301\pi$
$587$	−22.6659	+	19.0189i	−0.935521	+	0.784996i	0.0412791	+	0.999148i	$0.486857\pi$
$588$	−11.0432	+	5.00472i	−0.455415	+	0.206391i
$589$	4.59854	−	26.0796i	0.189480	−	1.07459i
$590$	2.31520	−	2.75914i	0.0953151	−	0.113592i
$591$	−1.00825	−	5.70422i	−0.0414740	−	0.234640i
$592$	6.49328	+	2.36336i	0.266872	+	0.0971336i
$593$	−32.4896			−1.33419			−0.667094	−	0.744974i	$-0.732462\pi$
$593$	−32.4896			−1.33419			−0.667094	+	0.744974i	$0.732462\pi$
$594$	−3.78810	−	10.3675i	−0.155428	−	0.425383i
$595$	2.71006	+	2.51148i	0.111102	+	0.102961i
$596$	8.13560	−	22.3524i	0.333247	−	0.915589i
$597$	−15.1759	+	12.7449i	−0.621109	+	0.521612i
$598$	2.49116	−	2.96885i	0.101871	−	0.121405i
$599$	−26.2017	−	4.62006i	−1.07057	−	0.188771i	−0.389528	−	0.921014i	$-0.627362\pi$
$599$	−26.2017	−	4.62006i	−1.07057	−	0.188771i	−0.681042	+	0.732244i	$0.738473\pi$
$600$	−1.45836	+	8.29092i	−0.0595373	+	0.338475i
$601$	−17.6813	−	21.0717i	−0.721235	−	0.859534i	0.273515	−	0.961868i	$-0.411814\pi$
$601$	−17.6813	−	21.0717i	−0.721235	−	0.859534i	−0.994750	+	0.102334i	$0.967369\pi$
$602$	−32.8514	−	7.47695i	−1.33892	−	0.304738i
$603$	−30.3420	−	11.0150i	−1.23562	−	0.448567i
$604$	7.43411	−	12.8763i	0.302490	−	0.523927i
$605$	0.421142	+	2.38842i	0.0171219	+	0.0971029i
$606$	−18.2976	+	0.00760698i	−0.743288	+	0.000309012i
$607$	11.0278	+	30.2985i	0.447603	+	1.22978i	0.934388	+	0.356257i	$0.115947\pi$
$607$	11.0278	+	30.2985i	0.447603	+	1.22978i	−0.486785	+	0.873522i	$0.661831\pi$
$608$	4.26076	−	1.55079i	0.172796	−	0.0628928i
$609$	4.11604	+	3.81126i	0.166790	+	0.154440i
$610$	0.419262	+	2.37775i	0.0169754	+	0.0962724i
$611$	0.427466	+	0.246798i	0.0172934	+	0.00998437i
$612$	10.5345	+	3.82433i	0.425832	+	0.154589i
$613$	13.9965	+	24.2426i	0.565311	+	0.979148i	0.997021	+	0.0771353i	$0.0245774\pi$
$613$	13.9965	+	24.2426i	0.565311	+	0.979148i	−0.431709	+	0.902013i	$0.642089\pi$
$614$	22.7793	−	19.1141i	0.919298	−	0.771382i
$615$	3.48885	+	0.613683i	0.140684	+	0.0247461i
$616$	−4.47796	+	3.39624i	−0.180422	+	0.136839i
$617$	13.2618	−	15.8049i	0.533902	−	0.636279i	−0.429907	−	0.902873i	$-0.641454\pi$
$617$	13.2618	−	15.8049i	0.533902	−	0.636279i	0.963809	+	0.266594i	$0.0858982\pi$
$618$	−6.43927	−	7.66754i	−0.259025	−	0.308434i
$619$	−1.26546	+	3.47683i	−0.0508632	+	0.139745i	−0.962523	−	0.271201i	$-0.912579\pi$
$619$	−1.26546	+	3.47683i	−0.0508632	+	0.139745i	0.911660	+	0.410946i	$0.134802\pi$
$620$			2.18334i			0.0876851i
$621$	1.32279	−	7.55699i	0.0530816	−	0.303252i
$622$			7.07190i			0.283558i
$623$	−14.2190	−	27.6933i	−0.569671	−	1.10951i
$624$	−0.791349	−	4.47708i	−0.0316793	−	0.179226i
$625$	17.5603	+	14.7348i	0.702411	+	0.589393i
$626$	5.09175	−	28.8767i	0.203507	−	1.15415i
$627$	5.71231	+	15.6742i	0.228128	+	0.625965i
$628$	−1.69713	−	2.02256i	−0.0677229	−	0.0807090i
$629$	−12.9070	−	22.3555i	−0.514634	−	0.891373i
$630$	−0.878684	−	2.83409i	−0.0350076	−	0.112913i
$631$	−4.65223	+	8.05789i	−0.185202	+	0.320780i	−0.943645	−	0.330960i	$-0.892627\pi$
$631$	−4.65223	+	8.05789i	−0.185202	+	0.320780i	0.758442	+	0.651740i	$0.225961\pi$
$632$	−1.89807	+	0.334681i	−0.0755011	+	0.0133129i
$633$	−13.5545	−	7.81819i	−0.538743	−	0.310745i
$634$	25.3688	−	9.23347i	1.00752	−	0.366708i
$635$	0.570917	−	0.207797i	0.0226562	−	0.00824617i
$636$	10.5994	+	18.3410i	0.420292	+	0.727269i
$637$	−4.55582	−	17.8006i	−0.180508	−	0.705286i
$638$	2.25193	+	1.30015i	0.0891546	+	0.0514735i
$639$	2.77376	+	7.60118i	0.109728	+	0.300698i
$640$	−0.323745	+	0.186914i	−0.0127972	+	0.00738844i
$641$	−22.6713	−	27.0186i	−0.895462	−	1.06717i	−0.997377	−	0.0723769i	$-0.976942\pi$
$641$	−22.6713	−	27.0186i	−0.895462	−	1.06717i	0.101915	−	0.994793i	$-0.467503\pi$
$642$	0.634079	−	0.756304i	0.0250251	−	0.0298489i
$643$	17.3481	+	3.05894i	0.684142	+	0.120633i	0.504907	−	0.863174i	$-0.331527\pi$
$643$	17.3481	+	3.05894i	0.684142	+	0.120633i	0.179235	+	0.983806i	$0.442638\pi$
$644$	−3.87572	+	0.488102i	−0.152725	+	0.0192339i
$645$	2.81683	−	7.74920i	0.110913	−	0.305124i
$646$	−15.9170	−	5.79333i	−0.626247	−	0.227935i
$647$	−24.6099			−0.967517			−0.483758	−	0.875202i	$-0.660729\pi$
$647$	−24.6099			−0.967517			−0.483758	+	0.875202i	$0.660729\pi$
$648$	−5.79655	−	6.88477i	−0.227710	−	0.270459i
$649$		−	20.4668i		−	0.803393i
$650$	−11.9883	−	4.36340i	−0.470221	−	0.171147i
$651$	12.2347	+	23.8044i	0.479516	+	0.932967i
$652$	3.79892	+	3.18767i	0.148777	+	0.124839i
$653$	19.6337	+	3.46195i	0.768326	+	0.135477i	0.544054	−	0.839050i	$-0.316889\pi$
$653$	19.6337	+	3.46195i	0.768326	+	0.135477i	0.224272	+	0.974527i	$0.428000\pi$
$654$	−11.0174	−	9.23690i	−0.430815	−	0.361191i
$655$	−3.76161	+	3.15636i	−0.146978	+	0.123329i
$656$	−2.73549	−	4.73801i	−0.106803	−	0.184988i
$657$	−29.0908	−	5.10455i	−1.13494	−	0.199148i
$658$	−0.146936	−	0.475322i	−0.00572817	−	0.0185300i
$659$	35.7817	−	6.30928i	1.39386	−	0.245775i	0.574240	−	0.818687i	$-0.305298\pi$
$659$	35.7817	−	6.30928i	1.39386	−	0.245775i	0.819617	+	0.572912i	$0.194186\pi$
$660$	−0.688207	−	1.19087i	−0.0267884	−	0.0463544i
$661$	−0.231184	−	0.635172i	−0.00899201	−	0.0247053i	0.935115	−	0.354343i	$-0.115296\pi$
$661$	−0.231184	−	0.635172i	−0.00899201	−	0.0247053i	−0.944107	+	0.329638i	$0.893073\pi$
$662$	−2.94342	−	8.08699i	−0.114399	−	0.314310i
$663$	−8.48609	+	14.7125i	−0.329572	+	0.571384i
$664$	12.8282	−	2.26195i	0.497830	−	0.0877809i
$665$	1.32448	+	4.28454i	0.0513612	+	0.166147i
$666$	0.0172365	+	20.7300i	0.000667900	+	0.803272i
$667$	0.903673	+	1.56521i	0.0349904	+	0.0606051i
$668$	2.24002	−	1.87960i	0.0866689	−	0.0727239i
$669$	−36.1937	+	13.1905i	−1.39933	+	0.509972i
$670$	−3.96124	−	0.698473i	−0.153036	−	0.0269844i
$671$	10.5099	+	8.81886i	0.405731	+	0.340448i
$672$	−2.48230	+	3.85204i	−0.0957568	+	0.148596i
$673$	9.36788	+	3.40963i	0.361105	+	0.131432i	0.516200	−	0.856468i	$-0.327346\pi$
$673$	9.36788	+	3.40963i	0.361105	+	0.131432i	−0.155095	+	0.987900i	$0.549568\pi$
$674$			1.63759i			0.0630776i
$675$	−24.8654	+	4.41643i	−0.957071	+	0.169989i
$676$	−6.10985			−0.234994
$677$	32.5664	+	11.8532i	1.25163	+	0.455555i	0.880951	−	0.473207i	$-0.156904\pi$
$677$	32.5664	+	11.8532i	1.25163	+	0.455555i	0.370676	+	0.928762i	$0.379126\pi$
$678$	−2.20928	−	2.63070i	−0.0848471	−	0.101031i
$679$	18.2859	−	2.30289i	0.701747	−	0.0883770i
$680$	1.37531	+	0.242504i	0.0527406	+	0.00929960i
$681$	2.54727	+	0.448061i	0.0976117	+	0.0171697i
$682$	7.97479	+	9.50398i	0.305370	+	0.363926i
$683$	33.4886	−	19.3347i	1.28141	−	0.739820i	0.304300	−	0.952576i	$-0.401577\pi$
$683$	33.4886	−	19.3347i	1.28141	−	0.739820i	0.977105	+	0.212756i	$0.0682441\pi$
$684$	8.75225	+	10.4129i	0.334650	+	0.398148i
$685$	0.721688	+	0.416667i	0.0275743	+	0.0159200i
$686$	−8.82748	+	16.2811i	−0.337035	+	0.621617i
$687$	−14.3335	+	0.00595898i	−0.546858	+	0.000227349i
$688$	−11.9662	+	4.35536i	−0.456209	+	0.166046i
$689$	−30.1673	+	10.9800i	−1.14928	+	0.418305i
$690$	−0.000397441	−	0.955991i	−1.51303e−5	−	0.0363940i
$691$	46.5931	−	8.21562i	1.77248	−	0.312537i	0.810520	−	0.585711i	$-0.199185\pi$
$691$	46.5931	−	8.21562i	1.77248	−	0.312537i	0.961965	+	0.273174i	$0.0880735\pi$
$692$	−7.09813	+	12.2943i	−0.269831	+	0.467360i
$693$	−14.1765	−	9.12719i	−0.538522	−	0.346713i
$694$	−10.5725	−	18.3121i	−0.401327	−	0.695119i
$695$	−0.113935	−	0.135782i	−0.00432180	−	0.00515052i
$696$	2.08817	+	0.367305i	0.0791517	+	0.0139227i
$697$	−3.54904	+	20.1276i	−0.134430	+	0.762388i
$698$	10.5473	+	8.85025i	0.399222	+	0.334987i
$699$	27.0401	−	22.7085i	1.02275	−	0.858915i
$700$	5.87343	+	11.4393i	0.221995	+	0.432364i
$701$			51.5429i			1.94675i	0.229220	+	0.973375i	$0.426382\pi$
$701$			51.5429i			1.94675i	−0.229220	+	0.973375i	$0.573618\pi$
$702$	11.8036	−	6.83444i	0.445497	−	0.257949i
$703$		−	31.3314i		−	1.18168i
$704$	−0.726531	+	1.99613i	−0.0273822	+	0.0752319i
$705$	0.119897	−	0.0211926i	0.00451560	−	0.000798158i
$706$	0.286165	−	0.341038i	0.0107699	−	0.0128351i
$707$	−22.2695	+	16.8900i	−0.837532	+	0.635213i
$708$	−5.71420	−	15.6794i	−0.214753	−	0.589266i
$709$	17.2750	−	14.4955i	0.648777	−	0.544389i	−0.257922	−	0.966166i	$-0.583038\pi$
$709$	17.2750	−	14.4955i	0.648777	−	0.544389i	0.906700	+	0.421777i	$0.138593\pi$
$710$	0.504137	+	0.873191i	0.0189199	+	0.0327703i
$711$	−2.89519	−	5.00499i	−0.108578	−	0.187702i
$712$	−10.1898	−	5.88308i	−0.381879	−	0.220478i
$713$	1.49741	+	8.49221i	0.0560783	+	0.318036i
$714$	16.3535	−	5.06281i	0.612015	−	0.189471i
$715$	1.95873	−	0.712921i	0.0732525	−	0.0266617i
$716$	1.26318	+	3.47056i	0.0472073	+	0.129701i
$717$	14.8584	+	25.7108i	0.554896	+	0.960186i
$718$	0.796418	+	4.51671i	0.0297221	+	0.168562i
$719$	−16.6790	+	28.8889i	−0.622021	+	1.07737i	0.367088	+	0.930186i	$0.380355\pi$
$719$	−16.6790	+	28.8889i	−0.622021	+	1.07737i	−0.989109	+	0.147186i	$0.952978\pi$
$720$	−0.859708	−	0.720163i	−0.0320394	−	0.0268389i
$721$	−14.9134	−	3.39427i	−0.555402	−	0.126409i
$722$	−1.00209	−	1.19425i	−0.0372941	−	0.0444453i
$723$	35.7183	+	29.9459i	1.32838	+	1.11370i
$724$	14.0854	+	2.48363i	0.523479	+	0.0923034i
$725$	3.82426	−	4.55757i	0.142029	−	0.169264i
$726$	10.5608	+	3.83885i	0.391949	+	0.142473i
$727$	3.60726	−	9.91086i	0.133786	−	0.367573i	−0.854652	−	0.519201i	$-0.826229\pi$
$727$	3.60726	−	9.91086i	0.133786	−	0.367573i	0.988438	+	0.151628i	$0.0484516\pi$
$728$	−5.09383	−	4.72058i	−0.188790	−	0.174956i
$729$	13.4416	−	23.4163i	0.497838	−	0.867270i
$730$	−3.68038			−0.136217
$731$	44.7026	+	16.2704i	1.65339	+	0.601784i
$732$	10.5137	+	3.82172i	0.388597	+	0.141255i
$733$	−27.7041	+	33.0165i	−1.02328	+	1.21949i	−0.0479211	+	0.998851i	$0.515260\pi$
$733$	−27.7041	+	33.0165i	−1.02328	+	1.21949i	−0.975355	+	0.220642i	$0.929185\pi$
$734$	0.644296	−	3.65398i	0.0237814	−	0.134871i
$735$	−3.68439	−	2.63974i	−0.135901	−	0.0973682i
$736$	−1.13103	+	0.949048i	−0.0416904	+	0.0349824i
$737$	−19.7943	+	11.4282i	−0.729132	+	0.420964i
$738$	10.5396	−	12.5818i	0.387967	−	0.463143i
$739$	1.31171	−	2.27195i	0.0482520	−	0.0835750i	−0.840891	−	0.541205i	$-0.817968\pi$
$739$	1.31171	−	2.27195i	0.0482520	−	0.0835750i	0.889143	+	0.457630i	$0.151302\pi$
$740$	0.448561	+	2.54392i	0.0164894	+	0.0935162i
$741$	−17.8485	+	10.3147i	−0.655681	+	0.378921i
$742$	29.8251	+	12.5508i	1.09491	+	0.460755i
$743$	7.39907	+	20.3288i	0.271446	+	0.745791i	0.998261	+	0.0589572i	$0.0187776\pi$
$743$	7.39907	+	20.3288i	0.271446	+	0.745791i	−0.726815	+	0.686833i	$0.759000\pi$
$744$	8.76283	+	5.05437i	0.321261	+	0.185302i
$745$	8.75714	−	1.54412i	0.320837	−	0.0565722i
$746$	−16.4657	−	9.50648i	−0.602852	−	0.348057i
$747$	19.5673	+	33.8265i	0.715928	+	1.23765i
$748$	6.87241	−	3.96779i	0.251280	−	0.145077i
$749$	0.0742242	−	1.50575i	0.00271209	−	0.0550188i
$750$	−5.99849	+	2.18609i	−0.219034	+	0.0798249i
$751$	−1.42229	+	8.06620i	−0.0519000	+	0.294340i	−0.999699	−	0.0245284i	$-0.992192\pi$
$751$	−1.42229	+	8.06620i	−0.0519000	+	0.294340i	0.947799	+	0.318868i	$0.103303\pi$
$752$	−0.144049	−	0.120872i	−0.00525294	−	0.00440774i
$753$	46.5381	−	8.22588i	1.69594	−	0.299768i
$754$	−1.09897	+	3.01940i	−0.0400222	+	0.109960i
$755$	5.55817			0.202283
$756$	−13.4087	−	3.03423i	−0.487670	−	0.110354i
$757$	15.6393			0.568419			0.284210	−	0.958762i	$-0.408269\pi$
$757$	15.6393			0.568419			0.284210	+	0.958762i	$0.408269\pi$
$758$	6.30671	−	17.3276i	0.229070	−	0.629365i
$759$	−3.49355	−	4.15993i	−0.126808	−	0.150996i
$760$	1.29846	+	1.08953i	0.0471000	+	0.0395216i
$761$	−1.11644	+	6.33162i	−0.0404707	+	0.229521i	−0.998334	−	0.0577046i	$-0.981622\pi$
$761$	−1.11644	+	6.33162i	−0.0404707	+	0.229521i	0.957863	+	0.287226i	$0.0927329\pi$
$762$	0.487663	−	2.77242i	0.0176662	−	0.100434i
$763$	−21.9349	−	1.08126i	−0.794096	−	0.0391441i
$764$	20.5522	−	11.8658i	0.743551	−	0.429289i
$765$	0.730942	+	4.12532i	0.0264273	+	0.149151i
$766$	−22.1875	−	12.8100i	−0.801667	−	0.462842i
$767$	24.9065	−	4.39169i	0.899323	−	0.158575i
$768$	0.000720078		1.73205i	2.59836e−5		0.0625000i
$769$	1.25372	+	3.44456i	0.0452102	+	0.124214i	0.960243	−	0.279165i	$-0.0900577\pi$
$769$	1.25372	+	3.44456i	0.0452102	+	0.124214i	−0.915033	+	0.403379i	$0.867836\pi$
$770$	−1.93651	−	0.814913i	−0.0697871	−	0.0293674i
$771$	−0.0110575	−	26.5973i	−0.000398225	−	0.957878i
$772$	1.50858	+	8.55560i	0.0542951	+	0.307923i
$773$	2.79742	−	4.84527i	0.100616	−	0.174272i	−0.811323	−	0.584599i	$-0.801252\pi$
$773$	2.79742	−	4.84527i	0.100616	−	0.174272i	0.911939	+	0.410327i	$0.134585\pi$
$774$	−24.5805	−	29.2445i	−0.883528	−	1.05117i
$775$	24.5832	−	14.1931i	0.883054	−	0.509832i
$776$	5.33627	−	4.47766i	0.191561	−	0.160739i
$777$	19.1458	+	25.2220i	0.686851	+	0.904835i
$778$	3.63687	−	20.6257i	0.130388	−	0.739467i
$779$	−15.9453	+	19.0029i	−0.571301	+	0.680850i
$780$	1.30152	−	1.09303i	0.0466018	−	0.0391366i
$781$	5.38387	+	1.95957i	0.192650	+	0.0701188i
$782$	5.51564			0.197239
$783$	1.11233	+	6.26265i	0.0397514	+	0.223809i
$784$	0.531662	+	6.97978i	0.0189879	+	0.249278i
$785$	0.337577	−	0.927484i	0.0120486	−	0.0331033i
$786$	3.96005	+	22.4041i	0.141250	+	0.799126i
$787$	−31.2045	+	37.1880i	−1.11232	+	1.32561i	−0.172085	+	0.985082i	$0.555051\pi$
$787$	−31.2045	+	37.1880i	−1.11232	+	1.32561i	−0.940234	+	0.340529i	$0.889394\pi$
$788$	−3.29357	−	0.580746i	−0.117329	−	0.0206882i
$789$	−31.5185	+	11.4866i	−1.12209	+	0.408935i
$790$	−0.463128	−	0.551934i	−0.0164773	−	0.0196369i
$791$	−5.11671	−	1.16456i	−0.181929	−	0.0414069i
$792$	−6.37270	+	0.00529874i	−0.226444	+	0.000188282i
$793$	−8.47670	+	14.6821i	−0.301016	+	0.521376i
$794$	4.70874	+	26.7046i	0.167107	+	0.947711i
$795$	−3.95665	+	6.85970i	−0.140328	+	0.243288i
$796$	3.91330	+	10.7517i	0.138703	+	0.381084i
$797$	51.1994	−	18.6350i	1.81357	−	0.660087i	0.817070	−	0.576538i	$-0.195597\pi$
$797$	51.1994	−	18.6350i	1.81357	−	0.660087i	0.996504	−	0.0835492i	$-0.0266256\pi$
$798$	20.2621	+	4.60278i	0.717271	+	0.162937i
$799$	0.121984	+	0.691805i	0.00431548	+	0.0244743i
$800$	4.20910	+	2.43013i	0.148814	+	0.0859179i
$801$	6.10062	−	34.7673i	0.215555	−	1.22844i
$802$	−6.16505	−	10.6782i	−0.217696	−	0.377060i
$803$	−16.0205	+	13.4428i	−0.565351	+	0.474386i
$804$	−11.9735	+	14.2815i	−0.422271	+	0.503668i
$805$	−0.882449	−	1.16351i	−0.0311022	−	0.0410085i
$806$	−9.85441	+	11.7440i	−0.347107	+	0.413666i
$807$	10.8055	−	29.7263i	0.380372	−	1.04642i
$808$	−3.61314	+	9.92702i	−0.127110	+	0.349231i
$809$			44.7188i			1.57223i	0.618081	+	0.786115i	$0.287910\pi$
$809$			44.7188i			1.57223i	−0.618081	+	0.786115i	$0.712090\pi$
$810$	1.14545	−	3.16347i	0.0402472	−	0.111153i
$811$			27.7315i			0.973784i	0.873462	+	0.486892i	$0.161869\pi$
$811$			27.7315i			0.973784i	−0.873462	+	0.486892i	$0.838131\pi$
$812$	2.88112	−	1.47929i	0.101107	−	0.0519130i
$813$	−32.6885	−	11.8822i	−1.14643	−	0.416728i
$814$	11.2444	+	9.43515i	0.394115	+	0.330702i
$815$	−0.321921	+	1.82571i	−0.0112764	+	0.0639517i
$816$	4.15708	−	4.95840i	0.145527	−	0.173579i
$817$	37.1142	+	44.2310i	1.29846	+	1.54745i
$818$	1.73619	+	3.00718i	0.0607046	+	0.105143i
$819$	8.06514	−	19.2102i	0.281819	−	0.671260i
$820$	1.02261	−	1.77121i	0.0357109	−	0.0618532i
$821$	−24.6126	+	4.33986i	−0.858985	+	0.151462i	−0.585757	−	0.810487i	$-0.699203\pi$
$821$	−24.6126	+	4.33986i	−0.858985	+	0.151462i	−0.273228	+	0.961949i	$0.588092\pi$
$822$	3.34297	−	1.93192i	0.116600	−	0.0673834i
$823$	32.1922	−	11.7170i	1.12215	−	0.408429i	0.286714	−	0.958016i	$-0.407437\pi$
$823$	32.1922	−	11.7170i	1.12215	−	0.408429i	0.835437	+	0.549587i	$0.185215\pi$
$824$	−5.43224	+	1.97717i	−0.189241	+	0.0688781i
$825$	−8.93468	+	15.4902i	−0.311066	+	0.539299i
$826$	−21.4220	−	13.8172i	−0.745368	−	0.480763i
$827$	−9.91501	−	5.72443i	−0.344779	−	0.199058i	0.317604	−	0.948223i	$-0.397122\pi$
$827$	−9.91501	−	5.72443i	−0.344779	−	0.199058i	−0.662383	+	0.749165i	$0.730455\pi$
$828$	−3.83779	−	2.21149i	−0.133372	−	0.0768547i
$829$	5.93242	−	3.42508i	0.206041	−	0.118958i	−0.393429	−	0.919355i	$-0.628711\pi$
$829$	5.93242	−	3.42508i	0.206041	−	0.118958i	0.599470	+	0.800397i	$0.295378\pi$
$830$	3.13007	+	3.73027i	0.108646	+	0.129480i
$831$	−16.0416	−	44.0171i	−0.556479	−	1.52694i
$832$	−2.58503	−	0.455811i	−0.0896198	−	0.0158024i
$833$	15.2389	−	21.2510i	0.527998	−	0.736302i
$834$	−0.808718	+	0.142945i	−0.0280036	+	0.00494979i
$835$	1.02720	+	0.373871i	0.0355478	+	0.0129384i
$836$	9.63171			0.333120
$837$	−5.23260	+	29.8935i	−0.180865	+	1.03327i
$838$		−	39.3320i		−	1.35870i
$839$	28.2964	+	10.2991i	0.976902	+	0.355563i	0.780635	−	0.624987i	$-0.214896\pi$
$839$	28.2964	+	10.2991i	0.976902	+	0.355563i	0.196267	+	0.980550i	$0.437118\pi$
$840$	−1.71106	−	0.0836316i	−0.0590371	−	0.00288556i
$841$	21.0674	+	17.6777i	0.726462	+	0.609574i
$842$	−2.92338	−	0.515471i	−0.100746	−	0.0177643i
$843$	−5.71494	+	32.4900i	−0.196833	+	1.11901i
$844$	−6.92058	+	5.80705i	−0.238216	+	0.199887i
$845$	−1.14202	−	1.97804i	−0.0392867	−	0.0680465i
$846$	0.192503	−	0.530268i	0.00661837	−	0.0182310i
$847$	16.3990	−	5.06941i	0.563475	−	0.174187i
$848$	12.0445	−	2.12377i	0.413609	−	0.0729304i
$849$	25.3240	−	0.0105281i	0.869118	−	0.000361324i
$850$	−6.20992	−	17.0616i	−0.212998	−	0.585208i
$851$	3.48940	+	9.58705i	0.119615	+	0.328640i
$852$	4.67161	−	0.00194216i	0.160047	−	6.65373e-5i
$853$	−12.8076	+	2.25833i	−0.438524	+	0.0773237i	−0.388552	−	0.921427i	$-0.627025\pi$
$853$	−12.8076	+	2.25833i	−0.438524	+	0.0773237i	−0.0499726	+	0.998751i	$0.515913\pi$
$854$	16.3258	−	5.04678i	0.558656	−	0.172697i
$855$	−1.73521	+	4.77983i	−0.0593431	+	0.163467i
$856$	−0.284905	−	0.493470i	−0.00973786	−	0.0168665i
$857$	34.3246	−	28.8018i	1.17251	−	0.983850i	0.172508	−	0.985008i	$-0.444813\pi$
$857$	34.3246	−	28.8018i	1.17251	−	0.983850i	0.999999	+	0.00115767i	$0.000368497\pi$
$858$	1.67310	−	9.51176i	0.0571188	−	0.324726i
$859$	−49.1261	−	8.66226i	−1.67616	−	0.295552i	−0.746889	−	0.664948i	$-0.768454\pi$
$859$	−49.1261	−	8.66226i	−1.67616	−	0.295552i	−0.929272	+	0.369396i	$0.879565\pi$
$860$	−3.64669	−	3.05994i	−0.124351	−	0.104343i
$861$	1.22395	−	25.0413i	0.0417120	−	0.853405i
$862$	−29.4962	−	10.7357i	−1.00464	−	0.365661i
$863$			3.97221i			0.135216i	0.997712	+	0.0676078i	$0.0215366\pi$
$863$			3.97221i			0.135216i	−0.997712	+	0.0676078i	$0.978463\pi$
$864$	−4.88057	+	1.78328i	−0.166040	+	0.0606683i
$865$	−5.30697			−0.180443
$866$	18.6577	+	6.79084i	0.634013	+	0.230762i
$867$	5.19243	−	0.917792i	0.176344	−	0.0311698i
$868$	15.3314	−	1.93081i	0.520381	−	0.0655359i
$869$	−4.03194	−	0.710940i	−0.136774	−	0.0241170i
$870$	0.271395	+	0.744688i	0.00920115	+	0.0252473i
$871$	−18.1547	−	21.6359i	−0.615147	−	0.733104i
$872$	−7.18859	+	4.15034i	−0.243436	+	0.140548i
$873$	18.1069	+	10.4340i	0.612825	+	0.353136i
$874$	5.79765	+	3.34727i	0.196108	+	0.113223i
$875$	−5.28609	+	8.19548i	−0.178702	+	0.277058i
$876$	−8.51995	+	14.7712i	−0.287862	+	0.499071i
$877$	−28.2072	+	10.2666i	−0.952490	+	0.346678i	−0.771086	−	0.636731i	$-0.780286\pi$
$877$	−28.2072	+	10.2666i	−0.952490	+	0.346678i	−0.181404	+	0.983409i	$0.558064\pi$
$878$	10.7771	−	3.92255i	0.363710	−	0.132380i
$879$	13.8641	−	8.01210i	0.467623	−	0.270241i
$880$	−0.782037	+	0.137894i	−0.0263624	+	0.00464841i
$881$	−6.17149	+	10.6893i	−0.207923	+	0.360133i	−0.951060	−	0.309006i	$-0.900004\pi$
$881$	−6.17149	+	10.6893i	−0.207923	+	0.360133i	0.743137	+	0.669139i	$0.233337\pi$
$882$	−19.1238	+	8.67638i	−0.643933	+	0.292149i
$883$	−3.02490	−	5.23928i	−0.101796	−	0.176316i	0.810629	−	0.585561i	$-0.199126\pi$
$883$	−3.02490	−	5.23928i	−0.101796	−	0.176316i	−0.912425	+	0.409245i	$0.865792\pi$
$884$	6.30314	+	7.51179i	0.211998	+	0.252649i
$885$	4.00805	−	4.78064i	0.134729	−	0.160700i
$886$	1.49276	−	8.46588i	0.0501503	−	0.284417i
$887$	−4.18954	−	3.51545i	−0.140671	−	0.118037i	0.569737	−	0.821827i	$-0.307045\pi$
$887$	−4.18954	−	3.51545i	−0.140671	−	0.118037i	−0.710408	+	0.703790i	$0.751490\pi$
$888$	11.2484	+	4.08879i	0.377471	+	0.137211i
$889$	−1.96403	−	3.82520i	−0.0658713	−	0.128293i
$890$		−	4.39853i		−	0.147439i
$891$	−6.56865	−	17.9543i	−0.220058	−	0.601490i
$892$			22.2409i			0.744679i
$893$	−0.291615	+	0.801205i	−0.00975852	+	0.0268113i
$894$	14.0752	−	38.7213i	0.470744	−	1.29503i
$895$	−0.887471	+	1.05765i	−0.0296649	+	0.0353533i
$896$	1.59881	+	2.10804i	0.0534124	+	0.0704245i
$897$	4.31268	−	5.14400i	0.143996	−	0.171753i
$898$	1.53604	−	1.28889i	0.0512582	−	0.0430107i
$899$	−3.57470	−	6.19157i	−0.119223	−	0.206500i
$900$	−2.51998	+	14.3613i	−0.0839994	+	0.478711i
$901$	−39.5679	−	22.8445i	−1.31820	−	0.761061i
$902$	−2.01808	−	11.4451i	−0.0671947	−	0.381080i
$903$	−56.9057	−	12.9268i	−1.89370	−	0.430177i
$904$	−1.86378	+	0.678360i	−0.0619884	+	0.0225619i
$905$	1.82870	+	5.02430i	0.0607879	+	0.167013i
$906$	12.8670	−	22.3077i	0.427477	−	0.741123i
$907$	−7.45378	−	42.2725i	−0.247499	−	1.40364i	−0.814617	−	0.579999i	$-0.803053\pi$
$907$	−7.45378	−	42.2725i	−0.247499	−	1.40364i	0.567118	−	0.823636i	$-0.308058\pi$
$908$	0.746623	−	1.29319i	0.0247776	−	0.0429160i
$909$	−31.6923	+	0.0263514i	−1.05117	+	0.000874019i
$910$	0.576156	−	2.53145i	0.0190994	−	0.0839167i
$911$	6.00081	+	7.15149i	0.198816	+	0.236939i	0.856236	−	0.516585i	$-0.172797\pi$
$911$	6.00081	+	7.15149i	0.198816	+	0.236939i	−0.657420	+	0.753524i	$0.728352\pi$
$912$	7.37873	−	2.68911i	0.244334	−	0.0890454i
$913$	27.2501	+	4.80492i	0.901846	+	0.159020i
$914$	−20.0343	+	23.8759i	−0.662674	+	0.789745i
$915$	0.727895	+	4.11809i	0.0240635	+	0.136140i
$916$	−2.83038	+	7.77640i	−0.0935183	+	0.256939i
$917$	25.4904	+	23.6226i	0.841768	+	0.780087i
$918$	18.2490	+	6.61634i	0.602308	+	0.218372i
$919$	−10.3225			−0.340509			−0.170254	−	0.985400i	$-0.554459\pi$
$919$	−10.3225			−0.340509			−0.170254	+	0.985400i	$0.554459\pi$
$920$	−0.518656	−	0.188775i	−0.0170996	−	0.00622374i
$921$	39.4411	−	33.1230i	1.29963	−	1.09144i
$922$	−22.2537	+	26.5209i	−0.732887	+	0.873421i
$923$	−1.22939	+	6.97223i	−0.0404659	+	0.229494i
$924$	−7.75361	+	5.88569i	−0.255075	+	0.193625i
$925$	25.7271	−	21.5876i	0.845903	−	0.709797i
$926$	31.2842	−	18.0620i	1.02806	−	0.593553i
$927$	−11.1587	−	13.2759i	−0.366498	−	0.436039i
$928$	0.612056	−	1.06011i	0.0200917	−	0.0347999i
$929$	2.03372	+	11.5338i	0.0667242	+	0.378412i	0.999823	+	0.0187926i	$0.00598221\pi$
$929$	2.03372	+	11.5338i	0.0667242	+	0.378412i	−0.933099	+	0.359619i	$0.882907\pi$
$930$	0.00157218	+	3.78166i	5.15537e−5	+	0.124005i
$931$	28.9146	−	13.0894i	0.947639	−	0.428989i
$932$	−6.97264	−	19.1572i	−0.228396	−	0.627514i
$933$	0.00509232	+	12.2489i	0.000166715	+	0.401011i
$934$	40.1379	−	7.07739i	1.31335	−	0.231579i
$935$	2.56910	+	1.48327i	0.0840187	+	0.0485082i
$936$	−1.37388	−	7.75395i	−0.0449067	−	0.253446i
$937$	2.13044	−	1.23001i	0.0695985	−	0.0401827i	−0.464797	−	0.885417i	$-0.653873\pi$
$937$	2.13044	−	1.23001i	0.0695985	−	0.0401827i	0.534395	+	0.845235i	$0.320539\pi$
$938$	−1.40159	+	28.4334i	−0.0457636	+	0.928383i
$939$	8.79837	−	50.0196i	0.287124	−	1.63233i
$940$	0.0122068	−	0.0692279i	0.000398140	−	0.00225797i
$941$	25.5832	+	21.4669i	0.833990	+	0.699801i	0.956203	−	0.292703i	$-0.0945548\pi$
$941$	25.5832	+	21.4669i	0.833990	+	0.699801i	−0.122213	+	0.992504i	$0.538999\pi$
$942$	−2.94097	−	3.50196i	−0.0958221	−	0.114100i
$943$	2.76272	−	7.59052i	0.0899667	−	0.247181i
$944$	−9.63491			−0.313589
$945$	−1.52397	−	4.90815i	−0.0495746	−	0.159662i
$946$	−27.0505			−0.879486
$947$	4.01306	−	11.0258i	0.130407	−	0.358290i	−0.857255	−	0.514892i	$-0.827832\pi$
$947$	4.01306	−	11.0258i	0.130407	−	0.358290i	0.987662	+	0.156602i	$0.0500541\pi$
$948$	−3.28731	+	0.581051i	−0.106767	+	0.0188716i
$949$	−19.7965	−	16.6112i	−0.642620	−	0.539222i
$950$	3.82675	−	21.7026i	0.124156	−	0.704124i
$951$	43.9333	−	16.0111i	1.42464	−	0.519196i
$952$	0.486621	−	9.87183i	0.0157715	−	0.319948i
$953$	−20.1327	+	11.6236i	−0.652161	+	0.376525i	−0.789284	−	0.614029i	$-0.789548\pi$
$953$	−20.1327	+	11.6236i	−0.652161	+	0.376525i	0.137123	+	0.990554i	$0.456215\pi$
$954$	18.3718	+	31.7599i	0.594810	+	1.02827i
$955$	7.68299	+	4.43578i	0.248616	+	0.143538i
$956$	16.8842	−	2.97713i	0.546073	−	0.0962874i
$957$	3.90139	+	2.25031i	0.126114	+	0.0727420i
$958$	4.31276	+	11.8492i	0.139339	+	0.382831i
$959$	2.28761	−	5.43614i	0.0738707	−	0.175542i
$960$	−0.560609	+	0.323978i	−0.0180936	+	0.0104564i
$961$	−0.540265	−	3.06400i	−0.0174279	−	0.0988386i
$962$	−9.06907	+	15.7081i	−0.292399	+	0.506449i
$963$	1.09771	−	1.31041i	0.0353733	−	0.0422275i
$964$	23.3053	−	13.4553i	0.750615	−	0.433368i
$965$	−2.48786	+	2.08756i	−0.0800871	+	0.0672010i
$966$	−6.71259	+	0.848209i	−0.215974	+	0.0272907i
$967$	5.67274	−	32.1717i	0.182423	−	1.03457i	−0.746799	−	0.665050i	$-0.768410\pi$
$967$	5.67274	−	32.1717i	0.182423	−	1.03457i	0.929222	−	0.369523i	$-0.120479\pi$
$968$	4.17016	−	4.96981i	0.134034	−	0.159736i
$969$	−27.5733	−	10.0229i	−0.885781	−	0.321981i
$970$	2.44705	+	0.890652i	0.0785699	+	0.0285971i
$971$	54.6725			1.75452			0.877261	−	0.480013i	$-0.159368\pi$
$971$	54.6725			1.75452			0.877261	+	0.480013i	$0.159368\pi$
$972$	−10.0449	−	11.9206i	−0.322189	−	0.382353i
$973$	−0.852703	+	0.920125i	−0.0273364	+	0.0294979i
$974$	−6.81011	+	18.7106i	−0.218210	+	0.599527i
$975$	−20.7675	−	7.54899i	−0.665094	−	0.241761i
$976$	4.15155	−	4.94762i	0.132888	−	0.158370i
$977$	12.6834	+	2.23643i	0.405778	+	0.0715496i	0.372812	−	0.927907i	$-0.378394\pi$
$977$	12.6834	+	2.23643i	0.405778	+	0.0715496i	0.0329660	+	0.999456i	$0.489505\pi$
$978$	6.58222	+	5.51848i	0.210476	+	0.176461i
$979$	−16.0659	−	19.1466i	−0.513469	−	0.611928i
$980$	−2.16030	+	1.47674i	−0.0690081	+	0.0471729i
$981$	−19.0894	−	15.9908i	−0.609476	−	0.510548i
$982$	−12.9649	+	22.4558i	−0.413725	+	0.716593i
$983$	−0.174305	−	0.988531i	−0.00555945	−	0.0315292i	0.981902	−	0.189391i	$-0.0606512\pi$
$983$	−0.174305	−	0.988531i	−0.00555945	−	0.0315292i	−0.987461	+	0.157861i	$0.949540\pi$
$984$	−4.74142	−	8.20450i	−0.151151	−	0.261550i
$985$	−0.427603	−	1.17483i	−0.0136246	−	0.0374332i
$986$	−4.29717	+	1.56404i	−0.136850	+	0.0498092i
$987$	−0.254843	−	0.823175i	−0.00811175	−	0.0262020i
$988$	2.06674	+	11.7210i	0.0657517	+	0.372896i
$989$	−16.2826	−	9.40075i	−0.517756	−	0.298926i
$990$	−1.19287	−	2.06214i	−0.0379118	−	0.0655392i
$991$	−15.5456	−	26.9257i	−0.493822	−	0.855325i	0.506153	−	0.862444i	$-0.331067\pi$
$991$	−15.5456	−	26.9257i	−0.493822	−	0.855325i	−0.999975	+	0.00711926i	$0.997734\pi$
$992$	4.47407	−	3.75419i	0.142052	−	0.119196i
$993$	−5.10398	−	14.0049i	−0.161970	−	0.444434i
$994$	5.68570	−	4.31223i	0.180339	−	0.136776i
$995$	−2.74936	+	3.27656i	−0.0871607	+	0.103874i
$996$	22.2174	−	3.92706i	0.703986	−	0.124434i
$997$	7.25129	−	19.9228i	0.229651	−	0.630960i	−0.770327	−	0.637649i	$-0.779907\pi$
$997$	7.25129	−	19.9228i	0.229651	−	0.630960i	0.999978	+	0.00668886i	$0.00212914\pi$
$998$		−	1.54768i		−	0.0489908i
$999$	0.0447817	+	35.9054i	0.00141683	+	1.13600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.293.19	yes	144
7.6	odd	2	inner	378.2.z.a.293.18	yes	144
27.20	odd	18	inner	378.2.z.a.209.18	✓	144
189.20	even	18	inner	378.2.z.a.209.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.18	✓	144	27.20	odd	18	inner
378.2.z.a.209.19	yes	144	189.20	even	18	inner
378.2.z.a.293.18	yes	144	7.6	odd	2	inner
378.2.z.a.293.19	yes	144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(0.591720 - 1.62784i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.0649147 - 0.368150i) q^{5} +(-1.32729 - 1.11279i) q^{6} +(-2.64254 - 0.130261i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.29974 - 1.92645i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(0.591720 - 1.62784i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.0649147 - 0.368150i) q^{5} +(-1.32729 - 1.11279i) q^{6} +(-2.64254 - 0.130261i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.29974 - 1.92645i) q^{9} +(-0.323745 - 0.186914i) q^{10} +(-2.09196 + 0.368870i) q^{11} +(-1.49964 + 0.866649i) q^{12} +(-0.897772 - 2.46661i) q^{13} +(-1.02621 + 2.43863i) q^{14} +(-0.560878 - 0.323512i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.86786 - 3.23524i) q^{17} +(-2.59683 + 1.50216i) q^{18} +(3.92673 - 2.26710i) q^{19} +(-0.286370 + 0.240293i) q^{20} +(-1.77569 + 4.22456i) q^{21} +(-0.368870 + 2.09196i) q^{22} +(-0.949048 + 1.13103i) q^{23} +(0.301477 + 1.70561i) q^{24} +(4.56714 + 1.66230i) q^{25} -2.62491 q^{26} +(-4.49676 + 2.60369i) q^{27} +(1.94057 + 1.79838i) q^{28} +(0.418671 - 1.15029i) q^{29} +(-0.495834 + 0.416405i) q^{30} +(3.75419 - 4.47407i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-0.637395 + 3.62365i) q^{33} +(-2.40128 - 2.86174i) q^{34} +(-0.219496 + 0.964395i) q^{35} +(0.523401 + 2.95399i) q^{36} +(3.45500 - 5.98424i) q^{37} +(-0.787356 - 4.46532i) q^{38} +(-4.54648 + 0.00189014i) q^{39} +(0.127857 + 0.351284i) q^{40} +(-5.14104 + 1.87119i) q^{41} +(3.36247 + 3.11349i) q^{42} +(2.21127 + 12.5407i) q^{43} +(1.83964 + 1.06212i) q^{44} +(-0.858509 + 0.721592i) q^{45} +(0.738228 + 1.27865i) q^{46} +(-0.144049 + 0.120872i) q^{47} +(1.70586 + 0.300058i) q^{48} +(6.96606 + 0.688442i) q^{49} +(3.12411 - 3.72317i) q^{50} +(-4.16120 - 4.95494i) q^{51} +(-0.897772 + 2.46661i) q^{52} -12.2303i q^{53} +(0.908684 + 5.11608i) q^{54} +0.794101i q^{55} +(2.35364 - 1.20846i) q^{56} +(-1.36696 - 7.73359i) q^{57} +(-0.937724 - 0.786844i) q^{58} +(-1.67308 + 9.48853i) q^{59} +(0.221708 + 0.608350i) q^{60} +(-4.15155 - 4.94762i) q^{61} +(-2.92024 - 5.05801i) q^{62} +(5.82621 + 5.39030i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.966359 + 0.170395i) q^{65} +(3.18712 + 1.83832i) q^{66} +(10.1110 - 3.68009i) q^{67} +(-3.51044 + 1.27769i) q^{68} +(1.27957 + 2.21415i) q^{69} +(0.831163 + 0.536101i) q^{70} +(-2.33580 - 1.34858i) q^{71} +(2.95486 + 0.518488i) q^{72} +(8.52609 - 4.92254i) q^{73} +(-4.44167 - 5.29337i) q^{74} +(5.40844 - 6.45097i) q^{75} +(-4.46532 - 0.787356i) q^{76} +(5.57615 - 0.702252i) q^{77} +(-1.55321 + 4.27294i) q^{78} +(1.81112 + 0.659192i) q^{79} +0.373829 q^{80} +(1.57757 + 8.86066i) q^{81} +5.47098i q^{82} +(-12.2405 - 4.45518i) q^{83} +(4.07575 - 2.09481i) q^{84} +(-1.06980 - 0.897668i) q^{85} +(12.5407 + 2.21127i) q^{86} +(-1.62475 - 1.36218i) q^{87} +(1.62726 - 1.36543i) q^{88} +(5.88308 + 10.1898i) q^{89} +(0.384447 + 1.05353i) q^{90} +(2.05110 + 6.63506i) q^{91} +(1.45403 - 0.256384i) q^{92} +(-5.06165 - 8.75862i) q^{93} +(0.0643145 + 0.176703i) q^{94} +(-0.579729 - 1.59279i) q^{95} +(0.865402 - 1.50036i) q^{96} +(-6.86017 + 1.20963i) q^{97} +(3.02946 - 6.31050i) q^{98} +(5.52157 + 3.18176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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