LMFDB - Embedded newform 378.2.z.a.293.18

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			293.18
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(-0.591720 + 1.62784i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.0649147 + 0.368150i) q^{5} +(1.32729 + 1.11279i) q^{6} +(-0.330590 + 2.62502i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.29974 - 1.92645i) q^{9} +O(q^{10})$	\(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} +(-0.330590 + 2.62502i) 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} +(2.35364 + 1.20846i) 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} +(-4.07749 - 2.09142i) 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} +(-0.944939 - 0.292109i) 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} +(-3.35988 + 3.11628i) 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} +(-6.78142 - 1.73561i) 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} +(-1.02621 - 2.43863i) 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} +(5.81724 - 5.39998i) 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} +(-0.597681 + 0.788045i) 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} +(-0.276706 - 5.61338i) 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} +(1.77920 + 4.22308i) 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} +(-6.77168 + 1.54123i) 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} +(-3.95032 + 5.77884i) 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	−0.995876	−	0.0907197i	$-0.971083\pi$
$5$	−0.0649147	+	0.368150i	−0.0290307	+	0.164642i	0.966846	+	0.255361i	$0.0821944\pi$
$6$	1.32729	+	1.11279i	0.541864	+	0.454294i
$7$	−0.330590	+	2.62502i	−0.124951	+	0.992163i
$7$	−0.330590	+	2.62502i	−0.124951	+	0.992163i
$8$	−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	$0.00748129\pi$
$13$	0.897772	+	2.46661i	0.248997	+	0.684114i	−0.750727	+	0.660613i	$0.770296\pi$
$14$	2.35364	+	1.20846i	0.629037	+	0.322975i
$15$	−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	−0.998572	−	0.0534191i	$-0.982988\pi$
$17$	−1.86786	+	3.23524i	−0.453024	+	0.784660i	0.545548	+	0.838079i	$0.316321\pi$
$18$	−2.59683	+	1.50216i	−0.612078	+	0.354062i
$19$	−3.92673	+	2.26710i	−0.900854	+	0.520109i	−0.877477	−	0.479618i	$-0.840775\pi$
$19$	−3.92673	+	2.26710i	−0.900854	+	0.520109i	−0.0233771	+	0.999727i	$0.507442\pi$
$20$	0.286370	−	0.240293i	0.0640342	−	0.0537311i
$21$	−4.07749	−	2.09142i	−0.889782	−	0.456386i
$22$	−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	−0.989359	−	0.145496i	$-0.953522\pi$
$31$	−3.75419	+	4.47407i	−0.674273	+	0.803567i	0.315086	+	0.949063i	$0.397967\pi$
$32$	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
$35$	−0.944939	−	0.292109i	−0.159724	−	0.0493754i
$36$	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	0.0922099	−	0.995740i	$-0.470607\pi$
$41$	5.14104	−	1.87119i	0.802896	−	0.292230i	0.710686	+	0.703509i	$0.248385\pi$
$42$	−3.35988	+	3.11628i	−0.518441	+	0.480853i
$43$	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	−0.632221	−	0.774788i	$-0.717857\pi$
$47$	0.144049	−	0.120872i	0.0210117	−	0.0176309i	0.653233	+	0.757157i	$0.273412\pi$
$48$	−1.70586	−	0.300058i	−0.246220	−	0.0433097i
$49$	−6.78142	−	1.73561i	−0.968774	−	0.247944i
$50$	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
$56$	−1.02621	−	2.43863i	−0.137133	−	0.325875i
$57$	−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	$-0.728654\pi$
$59$	1.67308	−	9.48853i	0.217817	−	1.23530i	0.875951	−	0.482400i	$-0.160235\pi$
$60$	0.221708	+	0.608350i	0.0286224	+	0.0785377i
$61$	4.15155	+	4.94762i	0.531551	+	0.633478i	0.963271	−	0.268530i	$-0.0865377\pi$
$61$	4.15155	+	4.94762i	0.531551	+	0.633478i	−0.431720	+	0.902008i	$0.642093\pi$
$62$	2.92024	+	5.05801i	0.370871	+	0.642368i
$63$	5.81724	−	5.39998i	0.732903	−	0.680333i
$64$	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
$70$	−0.597681	+	0.788045i	−0.0714365	+	0.0941893i
$71$	−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	−0.907627	−	0.419777i	$-0.862108\pi$
$73$	−8.52609	+	4.92254i	−0.997903	+	0.576140i	−0.0902761	+	0.995917i	$0.528775\pi$
$74$	−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
$77$	−0.276706	−	5.61338i	−0.0315335	−	0.639704i
$78$	−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	0.910935	−	0.412549i	$-0.135362\pi$
$83$	12.2405	+	4.45518i	1.34357	+	0.489020i	0.432635	+	0.901569i	$0.357584\pi$
$84$	1.77920	+	4.22308i	0.194127	+	0.460776i
$85$	−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	$-0.952334\pi$
$89$	−5.88308	−	10.1898i	−0.623606	−	1.08012i	0.365203	−	0.930928i	$-0.381000\pi$
$90$	−0.384447	−	1.05353i	−0.0405243	−	0.111052i
$91$	−6.77168	+	1.54123i	−0.709865	+	0.161565i
$92$	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	0.185846	−	0.982579i	$-0.440498\pi$
$97$	6.86017	−	1.20963i	0.696545	−	0.122820i	0.510699	+	0.859759i	$0.329386\pi$
$98$	−3.95032	+	5.77884i	−0.399043	+	0.583751i
$99$	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	−0.949467	−	0.313867i	$-0.898375\pi$
$101$	−8.09258	+	6.79048i	−0.805242	+	0.675678i	0.144225	+	0.989545i	$0.453931\pi$
$102$	−6.07934	+	2.21556i	−0.601944	+	0.219373i
$103$	−5.69305	−	1.00384i	−0.560953	−	0.0989111i	−0.114020	−	0.993479i	$-0.536373\pi$
$103$	−5.69305	−	1.00384i	−0.560953	−	0.0989111i	−0.446933	+	0.894567i	$0.647484\pi$
$104$	−2.01080	−	1.68726i	−0.197175	−	0.165449i
$105$	1.03465	−	1.36536i	0.100971	−	0.133246i
$106$	−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
$112$	−2.64254	+	0.130261i	−0.249697	+	0.0123085i
$113$	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
$119$	−7.87505	−	5.97271i	−0.721905	−	0.547518i
$120$	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
$126$	−3.08471	−	7.31332i	−0.274808	−	0.651522i
$127$	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	0.966005	−	0.258524i	$-0.0832360\pi$
$131$	10.0624	+	8.44334i	0.879154	+	0.737698i	−0.0868510	+	0.996221i	$0.527680\pi$
$132$	−2.81751	+	2.36617i	−0.245233	+	0.205949i
$133$	−4.65304	−	11.0572i	−0.403469	−	0.958783i
$134$		−	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	−0.778815	−	0.627254i	$-0.784179\pi$
$139$	−0.304778	+	0.363221i	−0.0258510	+	0.0308080i	0.752964	+	0.658062i	$0.228623\pi$
$140$	0.536101	+	0.831163i	0.0453088	+	0.0702461i
$141$	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
$147$	6.83800	−	10.0121i	0.563989	−	0.825783i
$148$	−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
$154$	−5.36949	−	1.65987i	−0.432686	−	0.133756i
$155$	−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	0.0689243	−	0.997622i	$-0.478043\pi$
$157$	−2.60015	−	0.458477i	−0.207515	−	0.0365905i	−0.276439	+	0.961031i	$0.589154\pi$
$158$	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	−0.958838	−	0.283953i	$-0.908354\pi$
$167$	0.507771	−	2.87971i	0.0392925	−	0.222839i	0.998131	+	0.0611138i	$0.0194653\pi$
$168$	4.57692	−	0.227522i	0.353117	−	0.0175537i
$169$	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	$0.125892\pi$
$173$	2.46516	+	13.9806i	0.187422	+	1.06292i	−0.735381	+	0.677654i	$0.762997\pi$
$174$	1.83573	−	1.06087i	0.139166	−	0.0804247i
$175$	−5.87343	+	11.4393i	−0.443989	+	0.864728i
$176$	−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	0.0368273	−	0.999322i	$-0.488275\pi$
$181$	12.3865	−	7.15133i	0.920679	−	0.531554i	0.883852	+	0.467767i	$0.154942\pi$
$182$	−0.867770	+	6.89043i	−0.0643234	+	0.510753i
$183$	−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
$189$	5.34813	+	12.6648i	0.389020	+	0.921229i
$190$	−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
$196$	4.07924	+	5.68857i	0.291374	+	0.406326i
$197$	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	0.808248	−	0.588843i	$-0.200416\pi$
$199$	9.90883	+	5.72087i	0.702419	+	0.405542i	−0.105829	+	0.994384i	$0.533750\pi$
$200$	−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
$203$	2.88112	+	1.47929i	0.202215	+	0.103826i
$204$	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
$210$	−0.929152	−	1.43923i	−0.0641176	−	0.0993164i
$211$	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	$0.0451754\pi$
$223$	14.2962	+	17.0375i	0.957341	+	1.14091i	−0.0326045	+	0.999468i	$0.510380\pi$
$224$	−0.781397	+	2.52773i	−0.0522093	+	0.168891i
$225$	−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	0.974993	−	0.222237i	$-0.0713359\pi$
$227$	−0.259300	−	1.47056i	−0.0172103	−	0.0976046i	−0.992203	+	0.124633i	$0.960225\pi$
$228$	−3.92391	+	6.80293i	−0.259867	+	0.450535i
$229$	2.83038	+	7.77640i	0.187037	+	0.513879i	0.997401	−	0.0720471i	$-0.0229532\pi$
$229$	2.83038	+	7.77640i	0.187037	+	0.513879i	−0.810365	+	0.585926i	$0.800731\pi$
$230$	−0.518656	+	0.188775i	−0.0341991	+	0.0124475i
$231$	9.30143	+	2.87112i	0.611989	+	0.188906i
$232$	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
$238$	−8.30594	+	5.35734i	−0.538394	+	0.347265i
$239$	−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	$-0.555103\pi$
$241$	9.20400	−	25.2878i	0.592882	−	1.62893i	0.765130	−	0.643876i	$-0.222675\pi$
$242$			6.48762i			0.417040i
$243$	−15.3572	−	2.67499i	−0.985167	−	0.171601i
$244$		−	6.45866i		−	0.413473i
$245$	1.07918	−	2.38391i	0.0689462	−	0.152302i
$246$	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	$-0.836433\pi$
$251$	−13.6426	−	23.6298i	−0.861116	−	1.49150i	0.00973638	−	0.999953i	$-0.496901\pi$
$252$	−7.92730	+	0.397375i	−0.499373	+	0.0250323i
$253$	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	−0.750297	−	0.661101i	$-0.770090\pi$
$257$	−14.4299	+	5.25204i	−0.900111	+	0.327614i	−0.149814	+	0.988714i	$0.547867\pi$
$258$	−11.0202	+	19.1059i	−0.686088	+	1.18948i
$259$	14.5665	+	11.0478i	0.905121	+	0.686475i
$260$	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
$266$	−11.9818	+	0.590631i	−0.734653	+	0.0362139i
$267$	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	$-0.687934\pi$
$269$	−18.2612			−1.11340			−0.556702	+	0.830712i	$0.687934\pi$
$270$	1.94247	−	0.00242267i	0.118215	−	0.000147439i
$271$			20.0809i			1.21983i	0.792469	+	0.609913i	$0.208795\pi$
$271$			20.0809i			1.21983i	−0.792469	+	0.609913i	$0.791205\pi$
$272$	−3.51044	−	1.27769i	−0.212852	−	0.0774716i
$273$	1.49806	−	11.9352i	0.0906667	−	0.722351i
$274$	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
$280$	0.964395	−	0.219496i	0.0576336	−	0.0131174i
$281$	−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	$-0.968015\pi$
$283$	−5.00062	−	13.7391i	−0.297256	−	0.816703i	0.697700	−	0.716390i	$-0.254207\pi$
$284$	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
$287$	3.21231	+	14.1139i	0.189617	+	0.833118i
$288$	−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	0.412038	−	0.911167i	$-0.364817\pi$
$293$	−7.08202	−	5.94252i	−0.413736	−	0.347166i	−0.825774	+	0.564001i	$0.809261\pi$
$294$	−7.06955	−	9.84995i	−0.412304	−	0.574461i
$295$	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
$301$	−33.6507	+	1.65877i	−1.93959	+	0.0956101i
$302$	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	−0.470340	−	0.882485i	$-0.655869\pi$
$307$	−25.7524	−	14.8681i	−1.46976	−	0.848569i	−0.999425	+	0.0339159i	$0.989202\pi$
$308$	−3.39624	+	4.47796i	−0.193519	+	0.255156i
$309$	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	−0.146661	−	0.989187i	$-0.546853\pi$
$311$	6.64542	−	2.41873i	0.376827	−	0.137154i	0.523488	+	0.852033i	$0.324630\pi$
$312$	3.93642	−	2.27487i	0.222856	−	0.128789i
$313$	−28.8767	+	5.09175i	−1.63221	+	0.287803i	−0.913296	−	0.407297i	$-0.866472\pi$
$313$	−28.8767	+	5.09175i	−1.63221	+	0.287803i	−0.718914	+	0.695099i	$0.755360\pi$
$314$	−1.32013	+	2.28654i	−0.0744994	+	0.129037i
$315$	1.61038	+	2.49215i	0.0907344	+	0.140417i
$316$	−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
$322$	−3.60052	+	1.51515i	−0.200649	+	0.0844361i
$323$		−	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
$329$	0.269669	+	0.418091i	0.0148673	+	0.0230501i
$330$	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
$336$	1.35160	−	4.37872i	0.0737358	−	0.238879i
$337$	−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
$343$	6.79788	−	17.2276i	0.367051	−	0.930201i
$344$	−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	$-0.768758\pi$
$349$	4.70912	−	12.9382i	0.252073	−	0.692566i	0.999599	−	0.0283324i	$-0.00901969\pi$
$350$	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	0.330863	−	0.943679i	$-0.392660\pi$
$353$	−0.418345	−	0.152265i	−0.0222662	−	0.00810425i	−0.353129	+	0.935575i	$0.614882\pi$
$354$	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
$357$	14.3825	−	9.28516i	0.761200	−	0.491423i
$358$	−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
$364$	6.17809	+	3.17210i	0.323820	+	0.166263i
$365$	−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	−0.268200	−	0.963363i	$-0.586429\pi$
$367$	−3.65398	+	0.644296i	−0.190736	+	0.0336320i	0.0774638	+	0.996995i	$0.475318\pi$
$368$	−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
$371$	32.1047	+	4.04322i	1.66679	+	0.209913i
$372$	−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
$378$	13.7302	−	0.693982i	0.706205	−	0.0356946i
$379$	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	$0.282701\pi$
$383$	−4.44885	+	25.2307i	−0.227326	+	1.28923i	−0.858189	+	0.513334i	$0.828410\pi$
$384$	1.62735	−	0.593073i	0.0830453	−	0.0302651i
$385$	2.08453	+	0.262522i	0.106237	+	0.0133794i
$386$	−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
$392$	6.74069	−	1.88763i	0.340456	−	0.0953396i
$393$	−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	0.222917	−	0.974837i	$-0.428442\pi$
$397$	23.4836	−	13.5583i	1.17861	−	0.680471i	0.955693	+	0.294367i	$0.0951087\pi$
$398$	8.76488	−	7.35461i	0.439344	−	0.368653i
$399$	20.7527	−	1.03163i	1.03893	−	0.0516461i
$400$	−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	−0.708033	−	0.706179i	$-0.750417\pi$
$409$	2.23201	−	2.66000i	0.110366	−	0.131529i	0.818399	+	0.574650i	$0.194862\pi$
$410$	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
$413$	24.3544	+	7.52869i	1.19840	+	0.370463i
$414$	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	$0.799407\pi$
$419$	−36.9600	+	13.4523i	−1.80561	+	0.657189i	−0.997692	+	0.0678982i	$0.978371\pi$
$420$	−1.67022	+	0.380872i	−0.0814986	+	0.0185846i
$421$	−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
$427$	−14.3600	+	9.26224i	−0.694931	+	0.448231i
$428$	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	$-0.841693\pi$
$433$		−	19.8551i		−	0.954174i	0.878856	−	0.477087i	$-0.158307\pi$
$434$	−14.2428	+	5.99355i	−0.683674	+	0.287700i
$435$	−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	0.560873	−	0.827902i	$-0.310466\pi$
$439$	−7.37199	−	8.78559i	−0.351846	−	0.419313i	−0.912719	+	0.408588i	$0.866021\pi$
$440$	0.397050	+	0.687711i	0.0189286	+	0.0327854i
$441$	12.2519	+	17.0555i	0.583424	+	0.812168i
$442$	−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
$448$	2.10804	+	1.59881i	0.0995953	+	0.0755366i
$449$	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
$455$	−0.127821	−	2.59304i	−0.00599234	−	0.121564i
$456$	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	0.959944	−	0.280190i	$-0.0903976\pi$
$461$	32.5328	+	11.8410i	1.51520	+	0.551488i	0.555257	+	0.831679i	$0.312620\pi$
$462$	5.87924	−	7.75851i	0.273527	−	0.360958i
$463$	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	$-0.774651\pi$
$467$	−20.3785	−	35.2967i	−0.943006	−	1.63334i	−0.183312	−	0.983055i	$-0.558682\pi$
$468$	−6.81644	+	3.94303i	−0.315090	+	0.182267i
$469$	6.31770	+	27.7580i	0.291724	+	1.28175i
$470$	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
$476$	2.19345	+	9.63735i	0.100537	+	0.441727i
$477$	−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	−0.394860	−	0.918741i	$-0.629207\pi$
$479$	9.65957	−	8.10534i	0.441357	−	0.370342i	0.836217	+	0.548399i	$0.184762\pi$
$480$	−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
$483$	6.23520	−	2.62691i	0.283711	−	0.119529i
$484$	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
$490$	−1.87104	−	1.82944i	−0.0845251	−	0.0826457i
$491$	−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
$497$	4.31223	−	5.68570i	0.193430	−	0.255038i
$498$	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	−0.972858	−	0.231405i	$-0.925668\pi$
$503$	−6.41491	+	11.1109i	−0.286026	+	0.495412i	0.686831	+	0.726817i	$0.259001\pi$
$504$	−2.33789	+	7.58514i	−0.104138	+	0.337869i
$505$	−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	$0.0996321\pi$
$509$	32.0336	+	26.8794i	1.41986	+	1.19141i	0.468451	+	0.883490i	$0.344812\pi$
$510$	−0.421019	−	2.38193i	−0.0186430	−	0.105474i
$511$	−10.1031	−	24.0085i	−0.446935	−	1.06207i
$512$			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
$518$	15.3636	−	9.90951i	0.675036	−	0.435399i
$519$	−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	$0.186446\pi$
$521$	20.4380	+	35.3996i	0.895403	+	1.55088i	0.0620990	+	0.998070i	$0.480221\pi$
$522$	0.640701	+	3.61601i	0.0280427	+	0.158269i
$523$	10.6613	+	6.15532i	0.466187	+	0.269153i	0.714642	−	0.699490i	$-0.246590\pi$
$523$	10.6613	+	6.15532i	0.466187	+	0.269153i	−0.248455	+	0.968643i	$0.579923\pi$
$524$	−2.28096	−	12.9359i	−0.0996440	−	0.565109i
$525$	−15.1459	−	16.3299i	−0.661022	−	0.712693i
$526$	−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
$532$	−3.54301	+	11.4612i	−0.153609	+	0.496908i
$533$	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
$546$	−10.7030	−	5.48979i	−0.458048	−	0.234941i
$547$	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
$553$	−2.32913	+	4.53628i	−0.0990446	+	0.192902i
$554$	−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
$560$	0.123584	−	0.981307i	0.00522239	−	0.0414678i
$561$	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	$0.0502879\pi$
$563$	31.1774	+	26.1609i	1.31397	+	1.10255i	0.326423	+	0.945224i	$0.394157\pi$
$564$	0.111269	−	0.306104i	0.00468526	−	0.0128893i
$565$	−0.253591	+	0.696734i	−0.0106686	+	0.0293118i
$566$	−14.6208			−0.614559
$567$	−23.7809	+	1.21190i	−0.998704	+	0.0508950i
$568$	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
$574$	14.3614	+	1.80865i	0.599434	+	0.0754918i
$575$	−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	0.969788	−	0.243948i	$-0.0784425\pi$
$577$	29.8679	+	17.2443i	1.24342	+	0.717888i	0.273629	+	0.961835i	$0.411776\pi$
$578$	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
$581$	−15.7415	+	30.6587i	−0.653068	+	1.27194i
$582$	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	−0.0412791	−	0.999148i	$-0.513143\pi$
$587$	22.6659	−	19.0189i	0.935521	−	0.784996i	0.976800	+	0.214152i	$0.0686988\pi$
$588$	−11.6739	+	3.27432i	−0.481422	+	0.135031i
$589$	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	$-0.267538\pi$
$593$	32.4896			1.33419			0.667094	+	0.744974i	$0.267538\pi$
$594$	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	0.994750	−	0.102334i	$-0.0326309\pi$
$601$	17.6813	+	21.0717i	0.721235	+	0.859534i	−0.273515	+	0.961868i	$0.588186\pi$
$602$	−9.95048	+	32.1886i	−0.405551	+	1.31191i
$603$	−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	$-0.884053\pi$
$607$	−11.0278	−	30.2985i	−0.447603	−	1.22978i	0.486785	−	0.873522i	$-0.338169\pi$
$608$	−4.26076	+	1.55079i	−0.172796	+	0.0628928i
$609$	−4.11287	+	3.81468i	−0.166662	+	0.154579i
$610$	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
$616$	3.04633	+	4.72298i	0.122740	+	0.190294i
$617$	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	−0.911660	−	0.410946i	$-0.865198\pi$
$619$	1.26546	−	3.47683i	0.0508632	−	0.139745i	0.962523	+	0.271201i	$0.0874207\pi$
$620$			2.18334i			0.0876851i
$621$	−1.32279	+	7.55699i	−0.0530816	+	0.303252i
$622$		−	7.07190i		−	0.283558i
$623$	28.6933	−	12.0745i	1.14957	−	0.483756i
$624$	−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
$630$	2.89264	−	0.660892i	0.115245	−	0.0263306i
$631$	−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
$637$	−1.80710	−	18.2853i	−0.0715998	−	0.724489i
$638$	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	−0.179235	−	0.983806i	$-0.557362\pi$
$643$	−17.3481	−	3.05894i	−0.684142	−	0.120633i	−0.504907	+	0.863174i	$0.668473\pi$
$644$	0.192325	+	3.90160i	0.00757866	+	0.153744i
$645$	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	$-0.339271\pi$
$647$	24.6099			0.967517			0.483758	+	0.875202i	$0.339271\pi$
$648$	−5.79655	−	6.88477i	−0.227710	−	0.270459i
$649$			20.4668i			0.803393i
$650$	11.9883	+	4.36340i	0.470221	+	0.171147i
$651$	24.6649	−	10.3914i	0.966692	−	0.407271i
$652$	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
$658$	0.485109	−	0.110410i	0.0189115	−	0.00430424i
$659$	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	0.944107	−	0.329638i	$-0.106927\pi$
$661$	0.231184	+	0.635172i	0.00899201	+	0.0247053i	−0.935115	+	0.354343i	$0.884704\pi$
$662$	−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
$665$	4.37276	−	0.995237i	0.169568	−	0.0385936i
$666$	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
$672$	−3.65238	−	2.76770i	−0.140893	−	0.106766i
$673$	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	−0.370676	−	0.928762i	$-0.620874\pi$
$677$	−32.5664	−	11.8532i	−1.25163	−	0.455555i	−0.880951	+	0.473207i	$0.843096\pi$
$678$	2.20928	+	2.63070i	0.0848471	+	0.101031i
$679$	0.907400	+	18.4080i	0.0348228	+	0.706433i
$680$	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
$686$	−13.8636	−	12.2801i	−0.529315	−	0.468856i
$687$	−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	−0.961965	−	0.273174i	$-0.911926\pi$
$691$	−46.5931	+	8.21562i	−1.77248	+	0.312537i	−0.810520	+	0.585711i	$0.800815\pi$
$692$	7.09813	−	12.2943i	0.269831	−	0.467360i
$693$	−10.1776	+	13.4424i	−0.386614	+	0.510633i
$694$	−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
$700$	11.8523	−	4.98763i	0.447976	−	0.188515i
$701$			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
$707$	−15.1498	−	23.4880i	−0.569767	−	0.883358i
$708$	−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
$714$	−3.80611	−	16.6908i	−0.142440	−	0.624637i
$715$	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	$-0.619645\pi$
$719$	16.6790	−	28.8889i	0.622021	−	1.07737i	0.989109	−	0.147186i	$-0.0470216\pi$
$720$	0.859708	+	0.720163i	0.0320394	+	0.0268389i
$721$	4.51716	−	14.6125i	0.168228	−	0.544197i
$722$	−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	−0.988438	−	0.151628i	$-0.951548\pi$
$727$	−3.60726	+	9.91086i	−0.133786	+	0.367573i	0.854652	+	0.519201i	$0.173771\pi$
$728$	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	$-0.484740\pi$
$733$	27.7041	−	33.0165i	1.02328	−	1.21949i	0.975355	−	0.220642i	$-0.0708152\pi$
$734$	−0.644296	+	3.65398i	−0.0237814	+	0.134871i
$735$	3.24206	+	3.16734i	0.119585	+	0.116829i
$736$	−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
$742$	14.7798	−	28.7857i	0.542585	−	1.05676i
$743$	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
$749$	−1.49576	−	0.188374i	−0.0546539	−	0.00688303i
$750$	−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
$756$	4.04388	−	13.1395i	0.147074	−	0.477880i
$757$	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	−0.957863	−	0.287226i	$-0.907267\pi$
$761$	1.11644	−	6.33162i	0.0404707	−	0.229521i	0.998334	+	0.0577046i	$0.0183782\pi$
$762$	−0.487663	+	2.77242i	−0.0176662	+	0.100434i
$763$	−2.74412	+	21.7894i	−0.0993439	+	0.788829i
$764$	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	0.915033	−	0.403379i	$-0.132164\pi$
$769$	−1.25372	−	3.44456i	−0.0452102	−	0.124214i	−0.960243	+	0.279165i	$0.909942\pi$
$770$	0.959640	−	1.86903i	0.0345830	−	0.0673551i
$771$	−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	−0.911939	−	0.410327i	$-0.865415\pi$
$773$	−2.79742	+	4.84527i	−0.100616	+	0.174272i	0.811323	+	0.584599i	$0.198748\pi$
$774$	−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
$777$	−26.6033	+	17.1748i	−0.954389	+	0.616144i
$778$	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	$-0.444949\pi$
$787$	31.2045	−	37.1880i	1.11232	−	1.32561i	0.940234	−	0.340529i	$-0.110606\pi$
$788$	−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
$791$	−1.54982	+	5.01348i	−0.0551052	+	0.178259i
$792$	−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	$0.804403\pi$
$797$	−51.1994	+	18.6350i	−1.81357	+	0.660087i	−0.996504	+	0.0835492i	$0.973374\pi$
$798$	6.12842	−	19.8540i	0.216944	−	0.702824i
$799$	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
$805$	1.22718	−	0.791529i	0.0432523	−	0.0278977i
$806$	−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	$-0.838131\pi$
$811$		−	27.7315i		−	0.973784i	0.873462	−	0.486892i	$-0.161869\pi$
$812$	−1.25619	−	2.98515i	−0.0440837	−	0.104758i
$813$	−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
$819$	18.5422	+	9.50089i	0.647916	+	0.331988i
$820$	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
$826$	15.4044	−	20.3107i	0.535986	−	0.706700i
$827$	−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	−0.599470	−	0.800397i	$-0.704622\pi$
$829$	−5.93242	+	3.42508i	−0.206041	+	0.118958i	0.393429	+	0.919355i	$0.371289\pi$
$830$	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
$833$	18.2819	−	18.6976i	0.633430	−	0.647834i
$834$	−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	−0.196267	−	0.980550i	$-0.562882\pi$
$839$	−28.2964	−	10.2991i	−0.976902	−	0.355563i	−0.780635	+	0.624987i	$0.785104\pi$
$840$	−0.213348	+	1.69976i	−0.00736119	+	0.0586474i
$841$	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
$847$	−3.80924	−	16.7366i	−0.130887	−	0.575077i
$848$	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	0.0499726	−	0.998751i	$-0.484087\pi$
$853$	12.8076	−	2.25833i	0.438524	−	0.0773237i	0.388552	+	0.921427i	$0.372975\pi$
$854$	3.79224	+	16.6619i	0.129768	+	0.570159i
$855$	−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	−0.999999	−	0.00115767i	$-0.999632\pi$
$857$	−34.3246	+	28.8018i	−1.17251	+	0.983850i	−0.172508	+	0.985008i	$0.555187\pi$
$858$	1.67310	−	9.51176i	0.0571188	−	0.324726i
$859$	49.1261	+	8.66226i	1.67616	+	0.295552i	0.929272	−	0.369396i	$-0.120435\pi$
$859$	49.1261	+	8.66226i	1.67616	+	0.295552i	0.746889	+	0.664948i	$0.231546\pi$
$860$	3.64669	+	3.05994i	0.124351	+	0.104343i
$861$	−24.8760	−	3.12234i	−0.847772	−	0.106409i
$862$	−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
$868$	0.760789	+	15.4337i	0.0258229	+	0.523855i
$869$	−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
$875$	−7.77032	−	5.89328i	−0.262685	−	0.199229i
$876$	−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	−0.743137	−	0.669139i	$-0.766663\pi$
$881$	6.17149	−	10.6893i	0.207923	−	0.360133i	0.951060	+	0.309006i	$0.0999964\pi$
$882$	20.2173	−	5.67969i	0.680753	−	0.191245i
$883$	−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	0.710408	−	0.703790i	$-0.248510\pi$
$887$	4.18954	+	3.51545i	0.140671	+	0.118037i	−0.569737	+	0.821827i	$0.692955\pi$
$888$	−11.2484	−	4.08879i	−0.377471	−	0.137211i
$889$	−3.96333	+	1.66782i	−0.132926	+	0.0559370i
$890$		−	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
$896$	2.22338	−	1.43408i	0.0742779	−	0.0479093i
$897$	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
$903$	17.2115	−	55.7595i	0.572765	−	1.85556i
$904$	−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
$910$	−2.48038	−	0.766759i	−0.0822237	−	0.0254178i
$911$	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
$924$	−5.27979	−	8.17825i	−0.173692	−	0.269045i
$925$	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	$-0.994018\pi$
$929$	−2.03372	−	11.5338i	−0.0667242	−	0.378412i	0.933099	−	0.359619i	$-0.117093\pi$
$930$	−0.00157218	−	3.78166i	−5.15537e−5	−	0.124005i
$931$	30.5636	−	8.55888i	1.00168	−	0.280506i
$932$	−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	−0.534395	−	0.845235i	$-0.679461\pi$
$937$	−2.13044	+	1.23001i	−0.0695985	+	0.0401827i	0.464797	+	0.885417i	$0.346127\pi$
$938$	28.2448	+	3.55711i	0.922225	+	0.116144i
$939$	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	0.122213	−	0.992504i	$-0.461001\pi$
$941$	−25.5832	−	21.4669i	−0.833990	−	0.699801i	−0.956203	+	0.292703i	$0.905445\pi$
$942$	−2.94097	−	3.50196i	−0.0958221	−	0.114100i
$943$	−2.76272	+	7.59052i	−0.0899667	+	0.247181i
$944$	9.63491			0.313589
$945$	−5.00972	+	1.14678i	−0.162966	+	0.0373048i
$946$	−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
$952$	9.80635	+	1.23500i	0.317826	+	0.0400265i
$953$	−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
$959$	−5.24669	−	2.69388i	−0.169425	−	0.0869900i
$960$	−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
$966$	−0.335926	−	6.75763i	−0.0108082	−	0.217423i
$967$	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	$-0.840632\pi$
$971$	−54.6725			−1.75452			−0.877261	+	0.480013i	$0.840632\pi$
$972$	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
$980$	−2.35905	+	1.13250i	−0.0753570	+	0.0361764i
$981$	−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	0.987461	−	0.157861i	$-0.0504599\pi$
$983$	0.174305	+	0.988531i	0.00555945	+	0.0315292i	−0.981902	+	0.189391i	$0.939349\pi$
$984$	−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
$987$	−0.840153	+	0.191586i	−0.0267424	+	0.00609824i
$988$	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
$994$	−3.86794	−	5.99680i	−0.122684	−	0.190207i
$995$	−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	−0.999978	−	0.00668886i	$-0.997871\pi$
$997$	−7.25129	+	19.9228i	−0.229651	+	0.630960i	0.770327	+	0.637649i	$0.220093\pi$
$998$		−	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.293.18	yes	144
7.6	odd	2	inner	378.2.z.a.293.19	yes	144
27.20	odd	18	inner	378.2.z.a.209.19	yes	144
189.20	even	18	inner	378.2.z.a.209.18	✓	144

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

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)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.591720 + 1.62784i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.0649147 + 0.368150i) q^{5} +(1.32729 + 1.11279i) q^{6} +(-0.330590 + 2.62502i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.29974 - 1.92645i) q^{9} +O(q^{10})\)	\(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} +(-0.330590 + 2.62502i) 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} +(2.35364 + 1.20846i) 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} +(-4.07749 - 2.09142i) 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} +(-0.944939 - 0.292109i) 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} +(-3.35988 + 3.11628i) 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} +(-6.78142 - 1.73561i) 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} +(-1.02621 - 2.43863i) 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} +(5.81724 - 5.39998i) 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} +(-0.597681 + 0.788045i) 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} +(-0.276706 - 5.61338i) 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} +(1.77920 + 4.22308i) 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} +(-6.77168 + 1.54123i) 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} +(-3.95032 + 5.77884i) 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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