LMFDB - Embedded newform 378.2.z.a.41.16

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			41.16
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(-1.33409 - 1.10463i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.22837 - 1.03073i) q^{5} +(-1.50564 - 0.856190i) q^{6} +(-2.38077 - 1.15409i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.559569 + 2.94735i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(-1.33409 - 1.10463i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.22837 - 1.03073i) q^{5} +(-1.50564 - 0.856190i) q^{6} +(-2.38077 - 1.15409i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.559569 + 2.94735i) q^{9} +(-1.38870 - 0.801764i) q^{10} +(-1.11807 - 1.33247i) q^{11} +(-1.63144 - 0.581732i) q^{12} +(-5.29296 - 0.933292i) q^{13} +(-2.54501 - 0.723144i) q^{14} +(0.500179 + 2.73198i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.60003 + 2.77133i) q^{17} +(1.06287 + 2.80541i) q^{18} +(5.32168 - 3.07247i) q^{19} +(-1.50682 - 0.548439i) q^{20} +(1.90130 + 4.16954i) q^{21} +(-1.33247 - 1.11807i) q^{22} +(-0.619562 - 1.70223i) q^{23} +(-1.70767 - 0.289598i) q^{24} +(-0.421739 - 2.39180i) q^{25} -5.37462 q^{26} +(2.50923 - 4.55014i) q^{27} +(-2.63192 - 0.270222i) q^{28} +(-8.43923 + 1.48806i) q^{29} +(0.966984 + 2.60362i) q^{30} +(0.708408 + 1.94633i) q^{31} +(0.642788 - 0.766044i) q^{32} +(0.0197165 + 3.01269i) q^{33} +(-1.09448 + 3.00707i) q^{34} +(1.73492 + 3.87158i) q^{35} +(1.53388 + 2.57822i) q^{36} +(4.14213 - 7.17438i) q^{37} +(4.70730 - 3.94989i) q^{38} +(6.03032 + 7.09188i) q^{39} +(-1.57917 - 0.278450i) q^{40} +(0.912715 - 5.17626i) q^{41} +(2.59645 + 3.77604i) q^{42} +(6.21667 - 5.21641i) q^{43} +(-1.50638 - 0.869708i) q^{44} +(2.35056 - 4.19721i) q^{45} +(-0.905739 - 1.56879i) q^{46} +(4.67097 + 1.70009i) q^{47} +(-1.73201 + 0.0113352i) q^{48} +(4.33614 + 5.49526i) q^{49} +(-0.830664 - 2.28223i) q^{50} +(5.19588 - 1.92975i) q^{51} +(-5.29296 + 0.933292i) q^{52} +2.98316i q^{53} +(1.68099 - 4.91673i) q^{54} +2.78920i q^{55} +(-2.63885 + 0.190911i) q^{56} +(-10.4935 - 1.77956i) q^{57} +(-8.05262 + 2.93091i) q^{58} +(2.37450 + 1.99244i) q^{59} +(1.40441 + 2.39615i) q^{60} +(-1.98669 + 5.45838i) q^{61} +(1.03562 + 1.79375i) q^{62} +(2.06931 - 7.66276i) q^{63} +(0.500000 - 0.866025i) q^{64} +(5.53977 + 6.60204i) q^{65} +(0.542565 + 2.96350i) q^{66} +(1.59914 - 9.06919i) q^{67} +(-0.555684 + 3.15144i) q^{68} +(-1.05380 + 2.95531i) q^{69} +(2.38086 + 3.51150i) q^{70} +(-5.78309 - 3.33887i) q^{71} +(1.95828 + 2.27270i) q^{72} +(10.2097 - 5.89460i) q^{73} +(2.83338 - 7.78466i) q^{74} +(-2.07943 + 3.65673i) q^{75} +(3.94989 - 4.70730i) q^{76} +(1.12409 + 4.46267i) q^{77} +(7.17020 + 5.93698i) q^{78} +(1.51573 + 8.59615i) q^{79} -1.60353 q^{80} +(-8.37377 + 3.29849i) q^{81} -5.25611i q^{82} +(-2.15397 - 12.2158i) q^{83} +(3.21270 + 3.26780i) q^{84} +(4.82192 - 1.75503i) q^{85} +(5.21641 - 6.21667i) q^{86} +(12.9024 + 7.33706i) q^{87} +(-1.63452 - 0.594915i) q^{88} +(5.87485 + 10.1755i) q^{89} +(1.58601 - 4.54162i) q^{90} +(11.5242 + 8.33053i) q^{91} +(-1.16440 - 1.38767i) q^{92} +(1.20491 - 3.37911i) q^{93} +(4.89523 + 0.863161i) q^{94} +(-9.70389 - 1.71106i) q^{95} +(-1.70373 + 0.311924i) q^{96} +(-10.4532 - 12.4576i) q^{97} +(5.22450 + 4.65882i) q^{98} +(3.30162 - 4.04097i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−1.33409	−	1.10463i	−0.770235	−	0.637761i
$3$	−1.33409	−	1.10463i	−0.770235	−	0.637761i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−1.22837	−	1.03073i	−0.549345	−	0.460956i	0.325374	−	0.945585i	$-0.394510\pi$
$5$	−1.22837	−	1.03073i	−0.549345	−	0.460956i	−0.874719	+	0.484630i	$0.838954\pi$
$6$	−1.50564	−	0.856190i	−0.614673	−	0.349538i
$7$	−2.38077	−	1.15409i	−0.899847	−	0.436206i
$7$	−2.38077	−	1.15409i	−0.899847	−	0.436206i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	0.559569	+	2.94735i	0.186523	+	0.982451i
$10$	−1.38870	−	0.801764i	−0.439144	−	0.253540i
$11$	−1.11807	−	1.33247i	−0.337112	−	0.401755i	0.570682	−	0.821171i	$-0.306679\pi$
$11$	−1.11807	−	1.33247i	−0.337112	−	0.401755i	−0.907794	+	0.419417i	$0.862235\pi$
$12$	−1.63144	−	0.581732i	−0.470955	−	0.167932i
$13$	−5.29296	−	0.933292i	−1.46800	−	0.258849i	−0.618230	−	0.785997i	$-0.712150\pi$
$13$	−5.29296	−	0.933292i	−1.46800	−	0.258849i	−0.849773	+	0.527148i	$0.823261\pi$
$14$	−2.54501	−	0.723144i	−0.680182	−	0.193268i
$15$	0.500179	+	2.73198i	0.129146	+	0.705395i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.60003	+	2.77133i	−0.388064	+	0.672146i	−0.992189	−	0.124743i	$-0.960189\pi$
$17$	−1.60003	+	2.77133i	−0.388064	+	0.672146i	0.604125	+	0.796889i	$0.293523\pi$
$18$	1.06287	+	2.80541i	0.250521	+	0.661241i
$19$	5.32168	−	3.07247i	1.22088	−	0.704873i	0.255771	−	0.966737i	$-0.417671\pi$
$19$	5.32168	−	3.07247i	1.22088	−	0.704873i	0.965105	+	0.261864i	$0.0843372\pi$
$20$	−1.50682	−	0.548439i	−0.336936	−	0.122635i
$21$	1.90130	+	4.16954i	0.414898	+	0.909868i
$22$	−1.33247	−	1.11807i	−0.284084	−	0.238374i
$23$	−0.619562	−	1.70223i	−0.129188	−	0.354940i	0.858188	−	0.513335i	$-0.171590\pi$
$23$	−0.619562	−	1.70223i	−0.129188	−	0.354940i	−0.987376	+	0.158395i	$0.949368\pi$
$24$	−1.70767	−	0.289598i	−0.348576	−	0.0591140i
$25$	−0.421739	−	2.39180i	−0.0843478	−	0.478360i
$26$	−5.37462			−1.05405
$27$	2.50923	−	4.55014i	0.482902	−	0.875674i
$28$	−2.63192	−	0.270222i	−0.497385	−	0.0510671i
$29$	−8.43923	+	1.48806i	−1.56713	+	0.276327i	−0.888751	−	0.458389i	$-0.848426\pi$
$29$	−8.43923	+	1.48806i	−1.56713	+	0.276327i	−0.678375	+	0.734716i	$0.737315\pi$
$30$	0.966984	+	2.60362i	0.176546	+	0.475354i
$31$	0.708408	+	1.94633i	0.127234	+	0.349572i	0.986911	−	0.161266i	$-0.0515576\pi$
$31$	0.708408	+	1.94633i	0.127234	+	0.349572i	−0.859677	+	0.510838i	$0.829335\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	0.0197165	+	3.01269i	0.00343221	+	0.524442i
$34$	−1.09448	+	3.00707i	−0.187702	+	0.515708i
$35$	1.73492	+	3.87158i	0.293255	+	0.654417i
$36$	1.53388	+	2.57822i	0.255646	+	0.429704i
$37$	4.14213	−	7.17438i	0.680962	−	1.17946i	−0.293726	−	0.955890i	$-0.594895\pi$
$37$	4.14213	−	7.17438i	0.680962	−	1.17946i	0.974688	−	0.223571i	$-0.0717715\pi$
$38$	4.70730	−	3.94989i	0.763625	−	0.640757i
$39$	6.03032	+	7.09188i	0.965624	+	1.13561i
$40$	−1.57917	−	0.278450i	−0.249688	−	0.0440268i
$41$	0.912715	−	5.17626i	0.142542	−	0.808396i	−0.826766	−	0.562546i	$-0.809822\pi$
$41$	0.912715	−	5.17626i	0.142542	−	0.808396i	0.969308	−	0.245850i	$-0.0790671\pi$
$42$	2.59645	+	3.77604i	0.400641	+	0.582655i
$43$	6.21667	−	5.21641i	0.948034	−	0.795495i	−0.0309317	−	0.999522i	$-0.509847\pi$
$43$	6.21667	−	5.21641i	0.948034	−	0.795495i	0.978965	+	0.204027i	$0.0654030\pi$
$44$	−1.50638	−	0.869708i	−0.227095	−	0.131113i
$45$	2.35056	−	4.19721i	0.350401	−	0.625684i
$46$	−0.905739	−	1.56879i	−0.133544	−	0.231305i
$47$	4.67097	+	1.70009i	0.681331	+	0.247984i	0.659419	−	0.751776i	$-0.270802\pi$
$47$	4.67097	+	1.70009i	0.681331	+	0.247984i	0.0219122	+	0.999760i	$0.493025\pi$
$48$	−1.73201	+	0.0113352i	−0.249995	+	0.00163609i
$49$	4.33614	+	5.49526i	0.619448	+	0.785038i
$50$	−0.830664	−	2.28223i	−0.117474	−	0.322756i
$51$	5.19588	−	1.92975i	0.727568	−	0.270218i
$52$	−5.29296	+	0.933292i	−0.734002	+	0.129424i
$53$			2.98316i			0.409768i	0.978786	+	0.204884i	$0.0656817\pi$
$53$			2.98316i			0.409768i	−0.978786	+	0.204884i	$0.934318\pi$
$54$	1.68099	−	4.91673i	0.228753	−	0.669083i
$55$			2.78920i			0.376096i
$56$	−2.63885	+	0.190911i	−0.352632	+	0.0255116i
$57$	−10.4935	−	1.77956i	−1.38990	−	0.235709i
$58$	−8.05262	+	2.93091i	−1.05736	+	0.384848i
$59$	2.37450	+	1.99244i	0.309133	+	0.259394i	0.784134	−	0.620592i	$-0.213108\pi$
$59$	2.37450	+	1.99244i	0.309133	+	0.259394i	−0.475000	+	0.879986i	$0.657552\pi$
$60$	1.40441	+	2.39615i	0.181308	+	0.309342i
$61$	−1.98669	+	5.45838i	−0.254369	+	0.698873i	0.745121	+	0.666930i	$0.232392\pi$
$61$	−1.98669	+	5.45838i	−0.254369	+	0.698873i	−0.999490	+	0.0319436i	$0.989830\pi$
$62$	1.03562	+	1.79375i	0.131524	+	0.227807i
$63$	2.06931	−	7.66276i	0.260709	−	0.965417i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	5.53977	+	6.60204i	0.687123	+	0.818882i
$66$	0.542565	+	2.96350i	0.0667852	+	0.364781i
$67$	1.59914	−	9.06919i	0.195366	−	1.10798i	−0.716530	−	0.697556i	$-0.754271\pi$
$67$	1.59914	−	9.06919i	0.195366	−	1.10798i	0.911896	−	0.410421i	$-0.134618\pi$
$68$	−0.555684	+	3.15144i	−0.0673866	+	0.382168i
$69$	−1.05380	+	2.95531i	−0.126862	+	0.355778i
$70$	2.38086	+	3.51150i	0.284567	+	0.419705i
$71$	−5.78309	−	3.33887i	−0.686327	−	0.396251i	0.115908	−	0.993260i	$-0.463022\pi$
$71$	−5.78309	−	3.33887i	−0.686327	−	0.396251i	−0.802235	+	0.597009i	$0.796356\pi$
$72$	1.95828	+	2.27270i	0.230785	+	0.267840i
$73$	10.2097	−	5.89460i	1.19496	−	0.689911i	0.235533	−	0.971866i	$-0.424316\pi$
$73$	10.2097	−	5.89460i	1.19496	−	0.689911i	0.959427	+	0.281956i	$0.0909831\pi$
$74$	2.83338	−	7.78466i	0.329374	−	0.904948i
$75$	−2.07943	+	3.65673i	−0.240112	+	0.422243i
$76$	3.94989	−	4.70730i	0.453084	−	0.539964i
$77$	1.12409	+	4.46267i	0.128101	+	0.508568i
$78$	7.17020	+	5.93698i	0.811865	+	0.672231i
$79$	1.51573	+	8.59615i	0.170533	+	0.967143i	0.943174	+	0.332299i	$0.107824\pi$
$79$	1.51573	+	8.59615i	0.170533	+	0.967143i	−0.772641	+	0.634844i	$0.781065\pi$
$80$	−1.60353			−0.179280
$81$	−8.37377	+	3.29849i	−0.930418	+	0.366499i
$82$		−	5.25611i		−	0.580441i
$83$	−2.15397	−	12.2158i	−0.236429	−	1.34085i	−0.839584	−	0.543230i	$-0.817201\pi$
$83$	−2.15397	−	12.2158i	−0.236429	−	1.34085i	0.603156	−	0.797624i	$-0.293910\pi$
$84$	3.21270	+	3.26780i	0.350535	+	0.356546i
$85$	4.82192	−	1.75503i	0.523011	−	0.190360i
$86$	5.21641	−	6.21667i	0.562500	−	0.670361i
$87$	12.9024	+	7.33706i	1.38329	+	0.786615i
$88$	−1.63452	−	0.594915i	−0.174240	−	0.0634182i
$89$	5.87485	+	10.1755i	0.622732	+	1.07860i	0.988975	+	0.148085i	$0.0473108\pi$
$89$	5.87485	+	10.1755i	0.622732	+	1.07860i	−0.366242	+	0.930520i	$0.619356\pi$
$90$	1.58601	−	4.54162i	0.167180	−	0.478729i
$91$	11.5242	+	8.33053i	1.20807	+	0.873277i
$92$	−1.16440	−	1.38767i	−0.121397	−	0.144675i
$93$	1.20491	−	3.37911i	0.124943	−	0.350397i
$94$	4.89523	+	0.863161i	0.504904	+	0.0890282i
$95$	−9.70389	−	1.71106i	−0.995598	−	0.175551i
$96$	−1.70373	+	0.311924i	−0.173886	+	0.0318356i
$97$	−10.4532	−	12.4576i	−1.06136	−	1.26488i	−0.962934	−	0.269737i	$-0.913063\pi$
$97$	−10.4532	−	12.4576i	−1.06136	−	1.26488i	−0.0984275	−	0.995144i	$-0.531381\pi$
$98$	5.22450	+	4.65882i	0.527755	+	0.470611i
$99$	3.30162	−	4.04097i	0.331825	−	0.406133i
$100$	−1.21435	−	2.10331i	−0.121435	−	0.210331i
$101$	−3.21758	−	1.17110i	−0.320162	−	0.116529i	0.176940	−	0.984222i	$-0.443380\pi$
$101$	−3.21758	−	1.17110i	−0.320162	−	0.116529i	−0.497102	+	0.867692i	$0.665602\pi$
$102$	4.78184	−	2.80268i	0.473473	−	0.277507i
$103$	−2.82956	+	3.37214i	−0.278805	+	0.332267i	−0.887215	−	0.461356i	$-0.847363\pi$
$103$	−2.82956	+	3.37214i	−0.278805	+	0.332267i	0.608410	+	0.793623i	$0.291808\pi$
$104$	−5.05049	+	1.83823i	−0.495241	+	0.180253i
$105$	1.96215	−	7.08148i	0.191486	−	0.691081i
$106$	0.518020	+	2.93784i	0.0503145	+	0.285348i
$107$			1.33167i			0.128738i	0.997926	+	0.0643688i	$0.0205034\pi$
$107$			1.33167i			0.128738i	−0.997926	+	0.0643688i	$0.979497\pi$
$108$	0.801668	−	5.13394i	0.0771405	−	0.494014i
$109$	10.1589			0.973049			0.486525	−	0.873667i	$-0.338264\pi$
$109$	10.1589			0.973049			0.486525	+	0.873667i	$0.338264\pi$
$110$	0.484340	+	2.74683i	0.0461800	+	0.261900i
$111$	−13.4510	+	4.99570i	−1.27671	+	0.474171i
$112$	−2.56561	+	0.646243i	−0.242428	+	0.0610642i
$113$	−12.6657	+	15.0944i	−1.19149	+	1.41996i	−0.308075	+	0.951362i	$0.599685\pi$
$113$	−12.6657	+	15.0944i	−1.19149	+	1.41996i	−0.883412	+	0.468597i	$0.844760\pi$
$114$	−10.6431	+	0.0696538i	−0.996820	+	0.00652368i
$115$	−0.993485	+	2.72958i	−0.0926430	+	0.254535i
$116$	−7.42134	+	4.28471i	−0.689054	+	0.397825i
$117$	−0.211036	−	16.1225i	−0.0195103	−	1.49052i
$118$	2.68441	+	1.54984i	0.247120	+	0.142675i
$119$	7.00767	−	4.75132i	0.642392	−	0.435553i
$120$	1.79916	+	2.11588i	0.164240	+	0.193152i
$121$	1.38475	−	7.85328i	0.125886	−	0.713935i
$122$	−1.00867	+	5.72044i	−0.0913204	+	0.517904i
$123$	−6.93551	+	5.89736i	−0.625354	+	0.531747i
$124$	1.33137	+	1.58667i	0.119561	+	0.142487i
$125$	−5.95606	+	10.3162i	−0.532726	+	0.922709i
$126$	0.707252	−	7.90568i	0.0630071	−	0.704294i
$127$	5.05821	+	8.76108i	0.448844	+	0.777420i	0.998311	−	0.0580951i	$-0.0185027\pi$
$127$	5.05821	+	8.76108i	0.448844	+	0.777420i	−0.549467	+	0.835515i	$0.685169\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−14.0558	+	0.0919880i	−1.23754	+	0.00809909i
$130$	6.60204	+	5.53977i	0.579037	+	0.485870i
$131$	5.94083	−	2.16229i	0.519053	−	0.188920i	−0.0691909	−	0.997603i	$-0.522042\pi$
$131$	5.94083	−	2.16229i	0.519053	−	0.188920i	0.588244	+	0.808684i	$0.299820\pi$
$132$	1.04893	+	2.82426i	0.0912975	+	0.245820i
$133$	−16.2156	+	1.17314i	−1.40607	+	0.101724i
$134$		−	9.20909i		−	0.795544i
$135$	−7.77223	+	3.00293i	−0.668927	+	0.258451i
$136$			3.20006i			0.274403i
$137$	−13.4336	+	2.36870i	−1.14771	+	0.202372i	−0.714975	−	0.699150i	$-0.753562\pi$
$137$	−13.4336	+	2.36870i	−1.14771	+	0.202372i	−0.432733	+	0.901522i	$0.642451\pi$
$138$	−0.524601	+	3.09341i	−0.0446570	+	0.263328i
$139$	−5.44079	−	14.9484i	−0.461482	−	1.26791i	−0.924371	−	0.381495i	$-0.875409\pi$
$139$	−5.44079	−	14.9484i	−0.461482	−	1.26791i	0.462889	−	0.886416i	$-0.346813\pi$
$140$	2.95445	+	3.04472i	0.249697	+	0.257326i
$141$	−4.35349	−	7.42778i	−0.366630	−	0.625532i
$142$	−6.27502	−	2.28392i	−0.526588	−	0.191662i
$143$	4.67435	+	8.09620i	0.390888	+	0.677039i
$144$	2.32318	+	1.89812i	0.193598	+	0.158177i
$145$	11.9003	+	6.87065i	0.988268	+	0.570577i
$146$	9.03105	−	7.57795i	0.747415	−	0.627156i
$147$	0.285476	−	12.1210i	0.0235456	−	0.999723i
$148$	1.43855	−	8.15840i	0.118248	−	0.670617i
$149$	7.31949	+	1.29062i	0.599636	+	0.105732i	0.465223	−	0.885193i	$-0.345974\pi$
$149$	7.31949	+	1.29062i	0.599636	+	0.105732i	0.134413	+	0.990925i	$0.457085\pi$
$150$	−1.41285	+	3.96227i	−0.115359	+	0.323518i
$151$	2.73491	−	2.29487i	0.222564	−	0.186754i	−0.524687	−	0.851295i	$-0.675818\pi$
$151$	2.73491	−	2.29487i	0.222564	−	0.186754i	0.747251	+	0.664542i	$0.231373\pi$
$152$	3.07247	−	5.32168i	0.249210	−	0.431645i
$153$	−9.06341	−	3.16510i	−0.732733	−	0.255883i
$154$	1.88194	+	4.19967i	0.151651	+	0.338419i
$155$	1.13595	−	3.12100i	0.0912418	−	0.250685i
$156$	8.09221	+	4.60169i	0.647895	+	0.368430i
$157$	0.928447	−	1.10648i	0.0740981	−	0.0883067i	−0.727722	−	0.685872i	$-0.759421\pi$
$157$	0.928447	−	1.10648i	0.0740981	−	0.0883067i	0.801820	+	0.597566i	$0.203865\pi$
$158$	2.98541	+	8.20235i	0.237507	+	0.652544i
$159$	3.29530	−	3.97979i	0.261334	−	0.315618i
$160$	−1.57917	+	0.278450i	−0.124844	+	0.0220134i
$161$	−0.489501	+	4.76766i	−0.0385781	+	0.375744i
$162$	−7.67377	+	4.70247i	−0.602909	+	0.369461i
$163$	−19.2613			−1.50866			−0.754332	−	0.656493i	$-0.772039\pi$
$163$	−19.2613			−1.50866			−0.754332	+	0.656493i	$0.772039\pi$
$164$	−0.912715	−	5.17626i	−0.0712710	−	0.404198i
$165$	3.08105	−	3.72103i	0.239859	−	0.289682i
$166$	−4.24249	−	11.6561i	−0.329281	−	0.904692i
$167$	−19.7152	−	16.5431i	−1.52561	−	1.28014i	−0.821850	−	0.569704i	$-0.807058\pi$
$167$	−19.7152	−	16.5431i	−1.52561	−	1.28014i	−0.703762	−	0.710436i	$-0.748498\pi$
$168$	3.73134	+	2.66028i	0.287879	+	0.205245i
$169$	14.9284	+	5.43350i	1.14834	+	0.417961i
$170$	4.44390	−	2.56569i	0.340832	−	0.196779i
$171$	12.0335	+	13.9656i	0.920224	+	1.06798i
$172$	4.05764	−	7.02805i	0.309392	−	0.535884i
$173$	−6.13189	+	5.14527i	−0.466199	+	0.391187i	−0.845406	−	0.534124i	$-0.820641\pi$
$173$	−6.13189	+	5.14527i	−0.466199	+	0.391187i	0.379207	+	0.925312i	$0.376197\pi$
$174$	13.9805	+	4.98511i	1.05986	+	0.377920i
$175$	−1.75630	+	6.18105i	−0.132764	+	0.467244i
$176$	−1.71299	−	0.302046i	−0.129121	−	0.0227676i
$177$	−0.966867	−	5.28104i	−0.0726742	−	0.396947i
$178$	7.55256	+	9.00079i	0.566088	+	0.674637i
$179$	−3.14472	−	1.81561i	−0.235048	−	0.135705i	0.377851	−	0.925866i	$-0.376663\pi$
$179$	−3.14472	−	1.81561i	−0.235048	−	0.135705i	−0.612898	+	0.790162i	$0.709997\pi$
$180$	0.773271	−	4.74803i	0.0576362	−	0.353897i
$181$	−2.16569	+	1.25036i	−0.160974	+	0.0929386i	−0.578323	−	0.815808i	$-0.696293\pi$
$181$	−2.16569	+	1.25036i	−0.160974	+	0.0929386i	0.417349	+	0.908746i	$0.362959\pi$
$182$	12.7957	+	6.20281i	0.948482	+	0.459783i
$183$	8.67992	−	5.08738i	0.641638	−	0.376070i
$184$	−1.38767	−	1.16440i	−0.102301	−	0.0858404i
$185$	−12.4829	+	4.54341i	−0.917762	+	0.334038i
$186$	0.599829	−	3.53700i	0.0439816	−	0.259346i
$187$	5.48166	−	0.966565i	0.400859	−	0.0706822i
$188$	4.97074			0.362529
$189$	−11.2252	+	7.93695i	−0.816512	+	0.577328i
$190$	−9.85359			−0.714854
$191$	13.1908	−	2.32589i	0.954451	−	0.168296i	0.325328	−	0.945601i	$-0.394525\pi$
$191$	13.1908	−	2.32589i	0.954451	−	0.168296i	0.629123	+	0.777306i	$0.283414\pi$
$192$	−1.62368	+	0.603035i	−0.117179	+	0.0435203i
$193$	−7.49502	+	2.72796i	−0.539503	+	0.196363i	−0.597377	−	0.801961i	$-0.703790\pi$
$193$	−7.49502	+	2.72796i	−0.539503	+	0.196363i	0.0578734	+	0.998324i	$0.481568\pi$
$194$	−12.4576	−	10.4532i	−0.894406	−	0.750496i
$195$	−0.0976903	−	14.9271i	−0.00699574	−	1.06895i
$196$	5.95413	+	3.68081i	0.425295	+	0.262915i
$197$	5.83373	−	3.36811i	0.415636	−	0.239968i	−0.277572	−	0.960705i	$-0.589530\pi$
$197$	5.83373	−	3.36811i	0.415636	−	0.239968i	0.693209	+	0.720737i	$0.256196\pi$
$198$	2.54975	−	4.55290i	0.181203	−	0.323560i
$199$	−1.71387	−	0.989503i	−0.121493	−	0.0701440i	0.438022	−	0.898964i	$-0.355679\pi$
$199$	−1.71387	−	0.989503i	−0.121493	−	0.0701440i	−0.559515	+	0.828820i	$0.689013\pi$
$200$	−1.56114	−	1.86049i	−0.110389	−	0.131557i
$201$	−12.1515	+	10.3326i	−0.857102	+	0.728806i
$202$	−3.37206	−	0.594586i	−0.237257	−	0.0418349i
$203$	21.8092	+	6.19692i	1.53071	+	0.434939i
$204$	4.22252	−	3.59046i	0.295635	−	0.251383i
$205$	−6.45647	+	5.41762i	−0.450940	+	0.378383i
$206$	−2.20101	+	3.81226i	−0.153352	+	0.265613i
$207$	4.67039	−	2.77858i	0.324615	−	0.193125i
$208$	−4.65455	+	2.68731i	−0.322735	+	0.186331i
$209$	−10.0440	−	3.65572i	−0.694759	−	0.252871i
$210$	0.702657	−	7.31462i	0.0484879	−	0.504757i
$211$	14.1109	+	11.8405i	0.971436	+	0.815131i	0.982775	−	0.184804i	$-0.0591651\pi$
$211$	14.1109	+	11.8405i	0.971436	+	0.815131i	−0.0113396	+	0.999936i	$0.503610\pi$
$212$	1.02030	+	2.80325i	0.0700745	+	0.192528i
$213$	4.02691	+	10.8425i	0.275919	+	0.742918i
$214$	0.231242	+	1.31144i	0.0158074	+	0.0896482i
$215$	−13.0131			−0.887486
$216$	−0.102011	−	5.19515i	−0.00694094	−	0.353485i
$217$	0.559695	−	5.45134i	0.0379946	−	0.370061i
$218$	10.0046	−	1.76408i	0.677597	−	0.119479i
$219$	−20.1321	−	3.41413i	−1.36040	−	0.230706i
$220$	0.953963	+	2.62099i	0.0643162	+	0.176707i
$221$	11.0553	−	13.1753i	0.743663	−	0.886263i
$222$	−12.3792	+	7.25555i	−0.830836	+	0.486961i
$223$	−3.35466	+	9.21684i	−0.224644	+	0.617205i	−0.999896	−	0.0144477i	$-0.995401\pi$
$223$	−3.35466	+	9.21684i	−0.224644	+	0.617205i	0.775251	+	0.631653i	$0.217623\pi$
$224$	−2.41442	+	1.08194i	−0.161320	+	0.0722901i
$225$	6.81349	−	2.58139i	0.454232	−	0.172093i
$226$	−9.85215	+	17.0644i	−0.655355	+	1.13511i
$227$	16.4371	−	13.7924i	1.09097	−	0.915432i	0.0941848	−	0.995555i	$-0.469976\pi$
$227$	16.4371	−	13.7924i	1.09097	−	0.915432i	0.996785	+	0.0801223i	$0.0255311\pi$
$228$	−10.4693	+	1.91675i	−0.693349	+	0.126940i
$229$	−21.1385	−	3.72728i	−1.39687	−	0.246306i	−0.576013	−	0.817441i	$-0.695392\pi$
$229$	−21.1385	−	3.72728i	−1.39687	−	0.246306i	−0.820856	+	0.571135i	$0.806503\pi$
$230$	−0.504406	+	2.86063i	−0.0332595	+	0.188624i
$231$	3.42999	−	7.19528i	0.225677	−	0.473415i
$232$	−6.56456	+	5.50832i	−0.430984	+	0.361639i
$233$	13.5669	+	7.83287i	0.888799	+	0.513149i	0.873550	−	0.486735i	$-0.161812\pi$
$233$	13.5669	+	7.83287i	0.888799	+	0.513149i	0.0152499	+	0.999884i	$0.495146\pi$
$234$	−3.00747	−	15.8409i	−0.196604	−	1.03555i
$235$	−3.98536	−	6.90285i	−0.259976	−	0.450292i
$236$	2.91275	+	1.06016i	0.189604	+	0.0690103i
$237$	7.47348	−	13.1423i	0.485455	−	0.853686i
$238$	6.07615	−	5.89600i	0.393858	−	0.382181i
$239$	−3.12366	−	8.58218i	−0.202053	−	0.555135i	0.796737	−	0.604326i	$-0.206558\pi$
$239$	−3.12366	−	8.58218i	−0.202053	−	0.555135i	−0.998789	+	0.0491916i	$0.984336\pi$
$240$	2.13924	+	1.77131i	0.138088	+	0.114338i
$241$	−9.06995	+	1.59928i	−0.584247	+	0.103018i	−0.457956	−	0.888975i	$-0.651418\pi$
$241$	−9.06995	+	1.59928i	−0.584247	+	0.103018i	−0.126291	+	0.991993i	$0.540307\pi$
$242$		−	7.97443i		−	0.512616i
$243$	14.8149	+	4.84947i	0.950379	+	0.311094i
$244$			5.80868i			0.371863i
$245$	0.337725	−	11.2196i	0.0215764	−	0.716795i
$246$	−5.80608	+	7.01211i	−0.370182	+	0.447076i
$247$	−31.0349	+	11.2958i	−1.97471	+	0.718734i
$248$	1.58667	+	1.33137i	0.100753	+	0.0845421i
$249$	−10.6204	+	18.6762i	−0.673038	+	1.18356i
$250$	−4.07419	+	11.1937i	−0.257674	+	0.707954i
$251$	10.9768	+	19.0123i	0.692847	+	1.20005i	0.970901	+	0.239481i	$0.0769771\pi$
$251$	10.9768	+	19.0123i	0.692847	+	1.20005i	−0.278054	+	0.960565i	$0.589690\pi$
$252$	−0.676299	−	7.90839i	−0.0426029	−	0.498182i
$253$	−1.57546	+	2.72877i	−0.0990482	+	0.171556i
$254$	6.50271	+	7.74963i	0.408016	+	0.486255i
$255$	−8.37152	−	2.98509i	−0.524245	−	0.186933i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	5.48114	−	31.0851i	0.341904	−	1.93904i	−0.00190994	−	0.999998i	$-0.500608\pi$
$257$	5.48114	−	31.0851i	0.341904	−	1.93904i	0.343814	−	0.939038i	$-0.388281\pi$
$258$	−13.8263	+	2.53135i	−0.860787	+	0.157595i
$259$	−18.1414	+	12.3001i	−1.12725	+	0.764294i
$260$	7.46371	+	4.30917i	0.462879	+	0.267244i
$261$	−9.10818	−	24.0407i	−0.563782	−	1.48808i
$262$	5.47510	−	3.16105i	0.338253	−	0.195290i
$263$	2.50148	−	6.87277i	0.154248	−	0.423793i	−0.838366	−	0.545108i	$-0.816489\pi$
$263$	2.50148	−	6.87277i	0.154248	−	0.423793i	0.992614	+	0.121315i	$0.0387110\pi$
$264$	1.52342	+	2.59921i	0.0937601	+	0.159970i
$265$	3.07482	−	3.66443i	0.188885	−	0.225104i
$266$	−15.7655	+	3.97113i	−0.966647	+	0.243485i
$267$	3.40269	−	20.0646i	0.208241	−	1.22793i
$268$	−1.59914	−	9.06919i	−0.0976831	−	0.553989i
$269$	14.2394			0.868190			0.434095	−	0.900867i	$-0.357068\pi$
$269$	14.2394			0.868190			0.434095	+	0.900867i	$0.357068\pi$
$270$	−7.13270	+	4.30695i	−0.434082	+	0.262112i
$271$		−	12.6413i		−	0.767903i	−0.923353	−	0.383951i	$-0.874563\pi$
$271$		−	12.6413i		−	0.767903i	0.923353	−	0.383951i	$-0.125437\pi$
$272$	0.555684	+	3.15144i	0.0336933	+	0.191084i
$273$	−6.17212	−	23.8437i	−0.373554	−	1.44309i
$274$	−12.8182	+	4.66543i	−0.774374	+	0.281849i
$275$	−2.71547	+	3.23617i	−0.163749	+	0.195148i
$276$	0.0205334	+	3.13751i	0.00123596	+	0.188856i
$277$	0.920051	+	0.334871i	0.0552805	+	0.0201205i	0.369512	−	0.929226i	$-0.379525\pi$
$277$	0.920051	+	0.334871i	0.0552805	+	0.0201205i	−0.314232	+	0.949346i	$0.601747\pi$
$278$	−7.95390	−	13.7766i	−0.477043	−	0.826263i
$279$	−5.34013	+	3.17703i	−0.319705	+	0.190204i
$280$	3.43828	+	2.48543i	0.205476	+	0.148533i
$281$	16.5364	+	19.7074i	0.986481	+	1.17564i	0.984454	+	0.175644i	$0.0562008\pi$
$281$	16.5364	+	19.7074i	0.986481	+	1.17564i	0.00202711	+	0.999998i	$0.499355\pi$
$282$	−5.57718	−	6.55896i	−0.332116	−	0.390581i
$283$	0.657693	+	0.115969i	0.0390958	+	0.00689364i	0.193162	−	0.981167i	$-0.438126\pi$
$283$	0.657693	+	0.115969i	0.0390958	+	0.00689364i	−0.154066	+	0.988061i	$0.549237\pi$
$284$	−6.57629	−	1.15958i	−0.390231	−	0.0688083i
$285$	11.0557	+	13.0019i	0.654885	+	0.770168i
$286$	6.00922	+	7.16151i	0.355333	+	0.423469i
$287$	−8.14685	+	11.2701i	−0.480894	+	0.665255i
$288$	2.61749	+	1.46587i	0.154237	+	0.0863770i
$289$	3.37982	+	5.85402i	0.198813	+	0.344354i
$290$	12.9126	+	4.69980i	0.758254	+	0.275982i
$291$	0.184336	+	28.1665i	0.0108059	+	1.65115i
$292$	7.57795	−	9.03105i	0.443466	−	0.528502i
$293$	−3.25175	+	1.18354i	−0.189969	+	0.0691431i	−0.435253	−	0.900308i	$-0.643341\pi$
$293$	−3.25175	+	1.18354i	−0.189969	+	0.0691431i	0.245284	+	0.969451i	$0.421119\pi$
$294$	−1.82365	−	11.9864i	−0.106357	−	0.699062i
$295$	−0.863107	−	4.89493i	−0.0502521	−	0.284994i
$296$		−	8.28426i		−	0.481513i
$297$	−8.86843	+	1.74392i	−0.514599	+	0.101192i
$298$	7.43241			0.430548
$299$	1.69064	+	9.58809i	0.0977722	+	0.554494i
$300$	−0.703346	+	4.14741i	−0.0406077	+	0.239451i
$301$	−20.8207	+	5.24445i	−1.20008	+	0.302285i
$302$	2.29487	−	2.73491i	0.132055	−	0.157377i
$303$	2.99889	+	5.11661i	0.172282	+	0.293941i
$304$	2.10169	−	5.77436i	0.120540	−	0.331182i
$305$	8.06649	−	4.65719i	0.461886	−	0.266670i
$306$	−9.47533	−	1.54317i	−0.541668	−	0.0882170i
$307$	11.6130	+	6.70477i	0.662789	+	0.382662i	0.793339	−	0.608780i	$-0.208341\pi$
$307$	11.6130	+	6.70477i	0.662789	+	0.382662i	−0.130550	+	0.991442i	$0.541674\pi$
$308$	2.58262	+	3.80908i	0.147158	+	0.217042i
$309$	7.49986	−	1.37309i	0.426652	−	0.0781126i
$310$	0.576738	−	3.27084i	0.0327565	−	0.185771i
$311$	−0.883926	+	5.01299i	−0.0501228	+	0.284261i	−0.999559	−	0.0296998i	$-0.990545\pi$
$311$	−0.883926	+	5.01299i	−0.0501228	+	0.284261i	0.949436	+	0.313961i	$0.101656\pi$
$312$	8.76835	+	3.12659i	0.496410	+	0.177008i
$313$	9.10627	+	10.8524i	0.514717	+	0.613416i	0.959323	−	0.282311i	$-0.0911009\pi$
$313$	9.10627	+	10.8524i	0.514717	+	0.613416i	−0.444606	+	0.895726i	$0.646656\pi$
$314$	0.722203	−	1.25089i	0.0407563	−	0.0705920i
$315$	−10.4401	+	7.27984i	−0.588234	+	0.410172i
$316$	4.36438	+	7.55933i	0.245516	+	0.425246i
$317$	6.24042	−	17.1454i	0.350497	−	0.962982i	−0.631714	−	0.775201i	$-0.717648\pi$
$317$	6.24042	−	17.1454i	0.350497	−	0.962982i	0.982211	−	0.187780i	$-0.0601293\pi$
$318$	2.55415	−	4.49155i	0.143230	−	0.251873i
$319$	11.4185	+	9.58126i	0.639313	+	0.536447i
$320$	−1.50682	+	0.548439i	−0.0842340	+	0.0306587i
$321$	1.47101	−	1.77656i	0.0821037	−	0.0991581i
$322$	0.345831	+	4.78023i	0.0192724	+	0.266392i
$323$			19.6642i			1.09414i
$324$	−6.74062	+	5.96356i	−0.374479	+	0.331309i
$325$			13.0533i			0.724068i
$326$	−18.9687	+	3.34470i	−1.05058	+	0.185246i
$327$	−13.5529	−	11.2219i	−0.749476	−	0.620572i
$328$	−1.79770	−	4.93913i	−0.0992612	−	0.272718i
$329$	−9.15844	−	9.43827i	−0.504921	−	0.520349i
$330$	2.38809	−	4.19952i	0.131460	−	0.231176i
$331$	−16.2498	−	5.91444i	−0.893169	−	0.325087i	−0.145657	−	0.989335i	$-0.546530\pi$
$331$	−16.2498	−	5.91444i	−0.893169	−	0.325087i	−0.747512	+	0.664248i	$0.768752\pi$
$332$	−6.20210	−	10.7424i	−0.340385	−	0.589563i
$333$	23.4632	+	8.19376i	1.28578	+	0.449015i
$334$	−22.2884	−	12.8682i	−1.21957	−	0.704117i
$335$	−11.3122	+	9.49207i	−0.618052	+	0.518607i
$336$	4.13661	+	1.97192i	0.225671	+	0.107577i
$337$	3.88611	−	22.0392i	0.211690	−	1.20055i	−0.674869	−	0.737938i	$-0.735800\pi$
$337$	3.88611	−	22.0392i	0.211690	−	1.20055i	0.886559	−	0.462616i	$-0.153089\pi$
$338$	15.6451	+	2.75866i	0.850983	+	0.150051i
$339$	33.5709	−	6.14625i	1.82332	−	0.333818i
$340$	3.93086	−	3.29839i	0.213181	−	0.178880i
$341$	1.80138	−	3.12008i	0.0975501	−	0.168962i
$342$	14.2758	+	11.6638i	0.771946	+	0.630708i
$343$	−3.98130	−	18.0873i	−0.214970	−	0.976621i
$344$	2.77559	−	7.62588i	0.149650	−	0.411160i
$345$	4.34058	−	2.54405i	0.233689	−	0.136967i
$346$	−5.14527	+	6.13189i	−0.276611	+	0.329653i
$347$	−4.31557	−	11.8569i	−0.231672	−	0.636513i	0.768322	−	0.640064i	$-0.221092\pi$
$347$	−4.31557	−	11.8569i	−0.231672	−	0.636513i	−0.999994	+	0.00355038i	$0.998870\pi$
$348$	14.6337	+	2.48169i	0.784450	+	0.133032i
$349$	32.5133	−	5.73298i	1.74040	−	0.306879i	0.788898	−	0.614524i	$-0.210652\pi$
$349$	32.5133	−	5.73298i	1.74040	−	0.306879i	0.951501	+	0.307644i	$0.0995407\pi$
$350$	−0.656287	+	6.39213i	−0.0350800	+	0.341674i
$351$	−17.5279	+	21.7419i	−0.935569	+	1.16049i
$352$	−1.73942			−0.0927112
$353$	4.61908	+	26.1961i	0.245849	+	1.39428i	0.818513	+	0.574488i	$0.194799\pi$
$353$	4.61908	+	26.1961i	0.245849	+	1.39428i	−0.572664	+	0.819790i	$0.694090\pi$
$354$	−1.86922	−	5.03291i	−0.0993480	−	0.267496i
$355$	3.66233	+	10.0622i	0.194376	+	0.534045i
$356$	9.00079	+	7.55256i	0.477041	+	0.400285i
$357$	−14.5973	−	1.40225i	−0.772571	−	0.0742147i
$358$	−3.41222	−	1.24195i	−0.180342	−	0.0656390i
$359$	24.4201	−	14.0989i	1.28884	−	0.744113i	0.310394	−	0.950608i	$-0.399539\pi$
$359$	24.4201	−	14.0989i	1.28884	−	0.744113i	0.978448	+	0.206494i	$0.0662055\pi$
$360$	−0.0629630	−	4.81017i	−0.00331844	−	0.253518i
$361$	9.38016	−	16.2469i	0.493692	−	0.855100i
$362$	−1.91566	+	1.60743i	−0.100685	+	0.0844848i
$363$	−10.5224	+	8.94732i	−0.552281	+	0.469612i
$364$	13.6784	+	3.88662i	0.716945	+	0.203714i
$365$	−18.6171	−	3.28270i	−0.974464	−	0.171824i
$366$	7.66463	−	6.51734i	0.400637	−	0.340667i
$367$	2.45598	+	2.92692i	0.128201	+	0.152784i	0.826326	−	0.563191i	$-0.190427\pi$
$367$	2.45598	+	2.92692i	0.128201	+	0.152784i	−0.698125	+	0.715976i	$0.745982\pi$
$368$	−1.56879	−	0.905739i	−0.0817787	−	0.0472149i
$369$	15.7670	−	0.206383i	0.820797	−	0.0107439i
$370$	−11.5043	+	6.64202i	−0.598081	+	0.345302i
$371$	3.44284	−	7.10221i	0.178743	−	0.368728i
$372$	−0.0234779	−	3.58743i	−0.00121727	−	0.185999i
$373$	15.1183	+	12.6858i	0.782798	+	0.656846i	0.943952	−	0.330084i	$-0.107077\pi$
$373$	15.1183	+	12.6858i	0.782798	+	0.656846i	−0.161154	+	0.986929i	$0.551521\pi$
$374$	5.23054	−	1.90376i	0.270465	−	0.0984412i
$375$	19.3415	−	7.18343i	0.998792	−	0.370951i
$376$	4.89523	−	0.863161i	0.252452	−	0.0445141i
$377$	46.0573			2.37207
$378$	−9.67642	+	9.76560i	−0.497701	+	0.502288i
$379$	0.150694			0.00774063			0.00387031	−	0.999993i	$-0.498768\pi$
$379$	0.150694			0.00774063			0.00387031	+	0.999993i	$0.498768\pi$
$380$	−9.70389	+	1.71106i	−0.497799	+	0.0877754i
$381$	2.92970	−	17.2755i	0.150093	−	0.885051i
$382$	12.5865	−	4.58111i	0.643981	−	0.234390i
$383$	27.4731	+	23.0527i	1.40381	+	1.17794i	0.959378	+	0.282124i	$0.0910389\pi$
$383$	27.4731	+	23.0527i	1.40381	+	1.17794i	0.444432	+	0.895813i	$0.353406\pi$
$384$	−1.49430	+	0.875823i	−0.0762557	+	0.0446942i
$385$	3.21900	−	6.64045i	0.164055	−	0.338429i
$386$	−6.90745	+	3.98802i	−0.351580	+	0.202985i
$387$	18.8532	+	15.4038i	0.958364	+	0.783018i
$388$	−14.0836	−	8.13114i	−0.714984	−	0.412796i
$389$	−9.44854	−	11.2603i	−0.479060	−	0.570922i	0.471340	−	0.881952i	$-0.343771\pi$
$389$	−9.44854	−	11.2603i	−0.479060	−	0.570922i	−0.950400	+	0.311030i	$0.899326\pi$
$390$	−2.68827	−	14.6834i	−0.136126	−	0.743521i
$391$	5.70877	+	1.00661i	0.288705	+	0.0509064i
$392$	6.50284	+	2.59097i	0.328443	+	0.130864i
$393$	−10.3141	−	3.67777i	−0.520278	−	0.185519i
$394$	5.16024	−	4.32995i	0.259969	−	0.218140i
$395$	6.99841	−	12.1216i	0.352128	−	0.609904i
$396$	1.72041	−	4.92649i	0.0864540	−	0.247565i
$397$	20.0560	−	11.5793i	1.00658	−	0.581149i	0.0963916	−	0.995343i	$-0.469270\pi$
$397$	20.0560	−	11.5793i	1.00658	−	0.581149i	0.910189	+	0.414194i	$0.135937\pi$
$398$	−1.85966	−	0.676860i	−0.0932162	−	0.0339279i
$399$	22.9289	+	16.3472i	1.14788	+	0.818386i
$400$	−1.86049	−	1.56114i	−0.0930245	−	0.0780568i
$401$	8.16730	+	22.4395i	0.407856	+	1.12057i	0.958315	+	0.285713i	$0.0922303\pi$
$401$	8.16730	+	22.4395i	0.407856	+	1.12057i	−0.550460	+	0.834862i	$0.685548\pi$
$402$	−10.1727	+	12.2857i	−0.507367	+	0.612756i
$403$	−1.93308	−	10.9630i	−0.0962934	−	0.546107i
$404$	−3.42408			−0.170354
$405$	13.6860	+	4.57929i	0.680061	+	0.227547i
$406$	22.5540	+	2.31564i	1.11934	+	0.114923i
$407$	−14.1909	+	2.50223i	−0.703415	+	0.124031i
$408$	3.53489	−	4.26915i	0.175003	−	0.211354i
$409$	4.78525	+	13.1474i	0.236615	+	0.650096i	0.999991	+	0.00414126i	$0.00131821\pi$
$409$	4.78525	+	13.1474i	0.236615	+	0.650096i	−0.763376	+	0.645954i	$0.776460\pi$
$410$	−5.41762	+	6.45647i	−0.267557	+	0.318862i
$411$	20.5381	+	11.6791i	1.01307	+	0.576089i
$412$	−1.50558	+	4.13654i	−0.0741745	+	0.203793i
$413$	−3.35367	−	7.48394i	−0.165024	−	0.368261i
$414$	4.11694	−	3.54738i	0.202337	−	0.174344i
$415$	−9.94524	+	17.2257i	−0.488193	+	0.845575i
$416$	−4.11719	+	3.45474i	−0.201862	+	0.169382i
$417$	−9.25408	+	25.9526i	−0.453174	+	1.27090i
$418$	−10.5262	−	1.85606i	−0.514855	−	0.0907827i
$419$	0.0954356	−	0.541242i	0.00466233	−	0.0264414i	−0.982388	−	0.186853i	$-0.940171\pi$
$419$	0.0954356	−	0.541242i	0.00466233	−	0.0264414i	0.987050	+	0.160412i	$0.0512822\pi$
$420$	−0.578188	−	7.32551i	−0.0282127	−	0.357448i
$421$	−1.82662	+	1.53272i	−0.0890240	+	0.0747000i	−0.686214	−	0.727400i	$-0.740728\pi$
$421$	−1.82662	+	1.53272i	−0.0890240	+	0.0747000i	0.597190	+	0.802100i	$0.296284\pi$
$422$	15.9526	+	9.21025i	0.776561	+	0.448348i
$423$	−2.39705	+	14.7183i	−0.116548	+	0.715629i
$424$	1.49158	+	2.58349i	0.0724374	+	0.125465i
$425$	7.30326	+	2.65817i	0.354260	+	0.128940i
$426$	5.84852	+	9.97855i	0.283362	+	0.483462i
$427$	11.0293	−	10.7023i	0.533746	−	0.517921i
$428$	0.455458	+	1.25136i	0.0220154	+	0.0604869i
$429$	2.70736	−	15.9645i	0.130713	−	0.770772i
$430$	−12.8154	+	2.25970i	−0.618013	+	0.108972i
$431$		−	15.8551i		−	0.763715i	−0.924221	−	0.381857i	$-0.875285\pi$
$431$		−	15.8551i		−	0.763715i	0.924221	−	0.381857i	$-0.124715\pi$
$432$	−1.00259	−	5.09851i	−0.0482371	−	0.245302i
$433$			36.7588i			1.76651i	0.468889	+	0.883257i	$0.344654\pi$
$433$			36.7588i			1.76651i	−0.468889	+	0.883257i	$0.655346\pi$
$434$	−0.395424	−	5.46572i	−0.0189809	−	0.262363i
$435$	−8.28649	−	22.3115i	−0.397307	−	1.06976i
$436$	9.54627	−	3.47456i	0.457184	−	0.166401i
$437$	−8.52717	−	7.15515i	−0.407910	−	0.342277i
$438$	−20.4191	+	0.133632i	−0.975660	+	0.00638520i
$439$	1.10729	−	3.04226i	0.0528483	−	0.145199i	−0.910460	−	0.413598i	$-0.864272\pi$
$439$	1.10729	−	3.04226i	0.0528483	−	0.145199i	0.963308	+	0.268398i	$0.0864943\pi$
$440$	1.39460	+	2.41552i	0.0664850	+	0.115155i
$441$	−13.7701	+	15.8551i	−0.655719	+	0.755005i
$442$	8.59953	−	14.8948i	0.409038	−	0.708475i
$443$	−4.05781	−	4.83591i	−0.192792	−	0.229761i	0.660985	−	0.750399i	$-0.270139\pi$
$443$	−4.05781	−	4.83591i	−0.192792	−	0.229761i	−0.853778	+	0.520638i	$0.825694\pi$
$444$	−10.9312	+	9.29494i	−0.518772	+	0.441118i
$445$	3.27170	−	18.5547i	0.155093	−	0.879578i
$446$	−1.70320	+	9.65935i	−0.0806490	+	0.457383i
$447$	−8.33917	−	9.80716i	−0.394429	−	0.463863i
$448$	−2.18986	+	1.48476i	−0.103461	+	0.0701484i
$449$	−30.9116	−	17.8468i	−1.45881	−	0.842244i	−0.459856	−	0.887994i	$-0.652099\pi$
$449$	−30.9116	−	17.8468i	−1.45881	−	0.842244i	−0.998953	+	0.0457500i	$0.985432\pi$
$450$	6.26172	−	3.72532i	0.295180	−	0.175613i
$451$	−7.91770	+	4.57128i	−0.372830	+	0.215253i
$452$	−6.73927	+	18.5160i	−0.316989	+	0.870919i
$453$	−6.18360	+	0.0404685i	−0.290531	+	0.00190138i
$454$	13.7924	−	16.4371i	0.647308	−	0.771432i
$455$	−5.56955	−	22.1113i	−0.261104	−	1.03660i
$456$	−9.97744	+	3.70562i	−0.467237	+	0.173531i
$457$	0.345111	+	1.95722i	0.0161436	+	0.0915549i	0.991815	−	0.127683i	$-0.0407540\pi$
$457$	0.345111	+	1.95722i	0.0161436	+	0.0915549i	−0.975671	+	0.219238i	$0.929643\pi$
$458$	−21.4646			−1.00297
$459$	8.59509	+	14.2343i	0.401184	+	0.664398i
$460$			2.90476i			0.135435i
$461$	3.21451	+	18.2304i	0.149715	+	0.849075i	0.963460	+	0.267853i	$0.0863141\pi$
$461$	3.21451	+	18.2304i	0.149715	+	0.849075i	−0.813745	+	0.581222i	$0.802575\pi$
$462$	2.12843	−	7.68158i	0.0990235	−	0.357380i
$463$	−27.5487	+	10.0269i	−1.28029	+	0.465989i	−0.890530	−	0.454925i	$-0.849666\pi$
$463$	−27.5487	+	10.0269i	−1.28029	+	0.465989i	−0.389765	+	0.920914i	$0.627444\pi$
$464$	−5.50832	+	6.56456i	−0.255717	+	0.304752i
$465$	−4.96302	+	2.90887i	−0.230155	+	0.134896i
$466$	14.7210	+	5.35800i	0.681937	+	0.248205i
$467$	−18.1270	−	31.3969i	−0.838817	−	1.45287i	−0.890884	−	0.454230i	$-0.849914\pi$
$467$	−18.1270	−	31.3969i	−0.838817	−	1.45287i	0.0520675	−	0.998644i	$-0.483419\pi$
$468$	−5.71252	−	15.0780i	−0.264061	−	0.696980i
$469$	−14.2739	+	19.7461i	−0.659106	+	0.911790i
$470$	−5.12348	−	6.10593i	−0.236329	−	0.281646i
$471$	−2.46088	+	0.450545i	−0.113391	+	0.0207600i
$472$	3.05260	+	0.538255i	0.140507	+	0.0247752i
$473$	−13.9014	−	2.45119i	−0.639188	−	0.112706i
$474$	5.07780	−	14.2404i	0.233231	−	0.654085i
$475$	−9.59310	−	11.4326i	−0.440161	−	0.524564i
$476$	4.96001	−	6.86154i	0.227342	−	0.314498i
$477$	−8.79241	+	1.66928i	−0.402577	+	0.0764311i
$478$	−4.56648	−	7.90938i	−0.208866	−	0.361766i
$479$	−26.1409	−	9.51451i	−1.19441	−	0.434729i	−0.333139	−	0.942878i	$-0.608108\pi$
$479$	−26.1409	−	9.51451i	−1.19441	−	0.434729i	−0.861269	+	0.508149i	$0.830330\pi$
$480$	2.41433	+	1.37293i	0.110199	+	0.0626652i
$481$	−28.6199	+	34.1079i	−1.30496	+	1.55519i
$482$	−8.65445	+	3.14996i	−0.394199	+	0.143477i
$483$	5.91955	−	5.81975i	0.269349	−	0.264808i
$484$	−1.38475	−	7.85328i	−0.0629430	−	0.356967i
$485$			26.0770i			1.18410i
$486$	15.4320	+	2.20321i	0.700009	+	0.0999397i
$487$	10.8334			0.490910			0.245455	−	0.969408i	$-0.421063\pi$
$487$	10.8334			0.490910			0.245455	+	0.969408i	$0.421063\pi$
$488$	1.00867	+	5.72044i	0.0456602	+	0.258952i
$489$	25.6963	+	21.2767i	1.16203	+	0.962167i
$490$	−1.61567	−	11.1078i	−0.0729886	−	0.501800i
$491$	17.2429	−	20.5492i	0.778159	−	0.927374i	−0.220689	−	0.975344i	$-0.570831\pi$
$491$	17.2429	−	20.5492i	0.778159	−	0.927374i	0.998849	+	0.0479700i	$0.0152752\pi$
$492$	−4.50023	+	7.91379i	−0.202886	+	0.356781i
$493$	9.37909	−	25.7688i	0.422413	−	1.16057i
$494$	−28.6020	+	16.5133i	−1.28686	+	0.742971i
$495$	−8.22076	+	1.56075i	−0.369496	+	0.0701505i
$496$	1.79375	+	1.03562i	0.0805418	+	0.0465008i
$497$	9.91485	+	14.6233i	0.444742	+	0.655945i
$498$	−7.21592	+	20.2367i	−0.323353	+	0.906827i
$499$	2.01165	−	11.4086i	0.0900537	−	0.510720i	−0.906098	−	0.423069i	$-0.860953\pi$
$499$	2.01165	−	11.4086i	0.0900537	−	0.510720i	0.996151	−	0.0876511i	$-0.0279361\pi$
$500$	−2.06852	+	11.7312i	−0.0925070	+	0.524633i
$501$	8.02781	+	43.8480i	0.358656	+	1.95898i
$502$	14.1114	+	16.8174i	0.629825	+	0.750596i
$503$	2.49206	−	4.31637i	0.111115	−	0.192457i	−0.805105	−	0.593132i	$-0.797891\pi$
$503$	2.49206	−	4.31637i	0.111115	−	0.192457i	0.916220	+	0.400675i	$0.131224\pi$
$504$	−2.03930	−	7.67080i	−0.0908377	−	0.341685i
$505$	2.74531	+	4.75501i	0.122164	+	0.211595i
$506$	−1.07768	+	2.96089i	−0.0479086	+	0.131628i
$507$	−13.9138	−	23.7392i	−0.617932	−	1.05429i
$508$	7.74963	+	6.50271i	0.343834	+	0.288511i
$509$	31.3602	−	11.4142i	1.39002	−	0.505925i	0.464819	−	0.885406i	$-0.346119\pi$
$509$	31.3602	−	11.4142i	1.39002	−	0.505925i	0.925200	+	0.379480i	$0.123897\pi$
$510$	−8.76270	−	1.48604i	−0.388019	−	0.0658028i
$511$	−31.1100	+	2.25069i	−1.37622	+	0.0995646i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.626849	−	31.9239i	−0.0276761	−	1.40947i
$514$		−	31.5646i		−	1.39226i
$515$	6.95152	−	1.22574i	0.306320	−	0.0540126i
$516$	−13.1767	+	4.89380i	−0.580070	+	0.215438i
$517$	−2.95717	−	8.12476i	−0.130056	−	0.357327i
$518$	−15.7299	+	15.2635i	−0.691130	+	0.670640i
$519$	13.8641	−	0.0907335i	0.608567	−	0.00398276i
$520$	8.09860	+	2.94765i	0.355147	+	0.129263i
$521$	−17.6096	−	30.5007i	−0.771491	−	1.33626i	−0.936746	−	0.350011i	$-0.886178\pi$
$521$	−17.6096	−	30.5007i	−0.771491	−	1.33626i	0.165255	−	0.986251i	$-0.447155\pi$
$522$	−13.1444	−	22.0939i	−0.575316	−	0.967022i
$523$	−30.3929	−	17.5474i	−1.32899	−	0.767293i	−0.343847	−	0.939026i	$-0.611730\pi$
$523$	−30.3929	−	17.5474i	−1.32899	−	0.767293i	−0.985144	+	0.171733i	$0.945063\pi$
$524$	4.84301	−	4.06377i	0.211568	−	0.177527i
$525$	9.17085	−	6.30599i	0.400249	−	0.275216i
$526$	1.27004	−	7.20273i	0.0553762	−	0.314054i
$527$	−6.52741	−	1.15096i	−0.284338	−	0.0501365i
$528$	1.95162	+	2.29518i	0.0849336	+	0.0998850i
$529$	15.1053	−	12.6748i	0.656751	−	0.551080i
$530$	2.39179	−	4.14270i	0.103893	−	0.179947i
$531$	−4.54373	+	8.11339i	−0.197181	+	0.352091i
$532$	−14.8365	+	6.64845i	−0.643242	+	0.288247i
$533$	−9.66193	+	26.5459i	−0.418505	+	1.14983i
$534$	−0.133185	−	20.3506i	−0.00576346	−	0.880658i
$535$	1.37259	−	1.63579i	0.0593423	−	0.0707214i
$536$	−3.14970	−	8.65372i	−0.136046	−	0.373784i
$537$	2.18975	+	5.89594i	0.0944946	+	0.254429i
$538$	14.0231	−	2.47264i	0.604577	−	0.106603i
$539$	2.47415	−	11.9219i	0.106569	−	0.513512i
$540$	−6.27644	+	5.48009i	−0.270095	+	0.235826i
$541$	19.8606			0.853875			0.426937	−	0.904281i	$-0.359592\pi$
$541$	19.8606			0.853875			0.426937	+	0.904281i	$0.359592\pi$
$542$	−2.19513	−	12.4492i	−0.0942891	−	0.534740i
$543$	4.27041	+	0.724205i	0.183261	+	0.0310786i
$544$	1.09448	+	3.00707i	0.0469256	+	0.128927i
$545$	−12.4790	−	10.4711i	−0.534540	−	0.448532i
$546$	−10.2188	−	22.4097i	−0.437323	−	0.959045i
$547$	15.7946	+	5.74878i	0.675330	+	0.245800i	0.656841	−	0.754029i	$-0.271892\pi$
$547$	15.7946	+	5.74878i	0.675330	+	0.245800i	0.0184889	+	0.999829i	$0.494114\pi$
$548$	−11.8133	+	6.82041i	−0.504639	+	0.291353i
$549$	−17.1994	−	2.80113i	−0.734054	−	0.119549i
$550$	−2.11226	+	3.65854i	−0.0900670	+	0.156001i
$551$	−40.3388	+	33.8483i	−1.71849	+	1.44199i
$552$	0.565044	+	3.08627i	0.0240499	+	0.131361i
$553$	6.31215	−	22.2148i	0.268420	−	0.944668i
$554$	0.964223	+	0.170019i	0.0409659	+	0.00722340i
$555$	21.6721	+	7.72775i	0.919929	+	0.328025i
$556$	−10.2253	−	12.1861i	−0.433651	−	0.516805i
$557$	−27.8434	−	16.0754i	−1.17976	−	0.681136i	−0.223803	−	0.974634i	$-0.571847\pi$
$557$	−27.8434	−	16.0754i	−1.17976	−	0.681136i	−0.955960	+	0.293498i	$0.905181\pi$
$558$	−4.70731	+	4.05607i	−0.199277	+	0.171707i
$559$	−37.7730	+	21.8083i	−1.59763	+	0.922392i
$560$	3.81763	+	1.85062i	0.161324	+	0.0782030i
$561$	−8.38071	−	4.76575i	−0.353834	−	0.201210i
$562$	19.7074	+	16.5364i	0.831304	+	0.697547i
$563$	3.65909	−	1.33180i	0.154212	−	0.0561287i	−0.263761	−	0.964588i	$-0.584963\pi$
$563$	3.65909	−	1.33180i	0.154212	−	0.0561287i	0.417973	+	0.908459i	$0.362741\pi$
$564$	−6.63140	−	5.49085i	−0.279232	−	0.231207i
$565$	31.1164	−	5.48666i	1.30908	−	0.230825i
$566$	0.667839			0.0280714
$567$	23.7428	+	1.81116i	0.997103	+	0.0760614i
$568$	−6.67774			−0.280192
$569$	−11.7033	+	2.06361i	−0.490627	+	0.0865108i	−0.413488	−	0.910509i	$-0.635690\pi$
$569$	−11.7033	+	2.06361i	−0.490627	+	0.0865108i	−0.0771392	+	0.997020i	$0.524579\pi$
$570$	13.1455	+	10.8846i	0.550606	+	0.455906i
$571$	6.19644	−	2.25532i	0.259313	−	0.0943822i	−0.209092	−	0.977896i	$-0.567051\pi$
$571$	6.19644	−	2.25532i	0.259313	−	0.0943822i	0.468405	+	0.883514i	$0.344829\pi$
$572$	7.16151	+	6.00922i	0.299438	+	0.251258i
$573$	−20.1669	−	11.4680i	−0.842484	−	0.479084i
$574$	−6.06605	+	12.5136i	−0.253192	+	0.522308i
$575$	−3.81011	+	2.19977i	−0.158893	+	0.0917366i
$576$	2.83227	+	0.989075i	0.118011	+	0.0412115i
$577$	−10.7996	−	6.23516i	−0.449594	−	0.259573i	0.258065	−	0.966128i	$-0.416915\pi$
$577$	−10.7996	−	6.23516i	−0.449594	−	0.259573i	−0.707659	+	0.706555i	$0.750248\pi$
$578$	4.34502	+	5.17819i	0.180729	+	0.215384i
$579$	13.0124	+	4.63991i	0.540777	+	0.192828i
$580$	13.5325	+	2.38615i	0.561908	+	0.0990796i
$581$	−8.97002	+	31.5688i	−0.372139	+	1.30969i
$582$	5.07260	+	27.7066i	0.210266	+	1.14847i
$583$	3.97497	−	3.33539i	0.164626	−	0.138138i
$584$	5.89460	−	10.2097i	0.243920	−	0.422482i
$585$	−16.3586	+	20.0219i	−0.676347	+	0.827805i
$586$	−2.99683	+	1.73022i	−0.123798	+	0.0714747i
$587$	−7.02298	−	2.55616i	−0.289869	−	0.105504i	0.192993	−	0.981200i	$-0.438181\pi$
$587$	−7.02298	−	2.55616i	−0.289869	−	0.105504i	−0.482862	+	0.875696i	$0.660403\pi$
$588$	−3.87736	−	11.4876i	−0.159900	−	0.473743i
$589$	9.74997	+	8.18120i	0.401741	+	0.337100i
$590$	−1.69999	−	4.67068i	−0.0699875	−	0.192289i
$591$	−11.5032	−	1.95079i	−0.473179	−	0.0802450i
$592$	−1.43855	−	8.15840i	−0.0591239	−	0.335308i
$593$	4.71184			0.193492			0.0967461	−	0.995309i	$-0.469157\pi$
$593$	4.71184			0.193492			0.0967461	+	0.995309i	$0.469157\pi$
$594$	−8.43087	+	3.25741i	−0.345923	+	0.133653i
$595$	−13.5054	−	1.38661i	−0.553666	−	0.0568454i
$596$	7.31949	−	1.29062i	0.299818	−	0.0528660i
$597$	1.19341	+	3.21328i	0.0488430	+	0.131511i
$598$	3.32991	+	9.14885i	0.136170	+	0.374124i
$599$	−5.10528	+	6.08423i	−0.208596	+	0.248595i	−0.860191	−	0.509972i	$-0.829656\pi$
$599$	−5.10528	+	6.08423i	−0.208596	+	0.248595i	0.651595	+	0.758567i	$0.274100\pi$
$600$	0.0275297	+	4.20654i	0.00112389	+	0.171731i
$601$	8.27886	−	22.7460i	0.337702	−	0.927828i	−0.648343	−	0.761348i	$-0.724538\pi$
$601$	8.27886	−	22.7460i	0.337702	−	0.927828i	0.986045	−	0.166480i	$-0.0532401\pi$
$602$	−19.5937	+	8.78025i	−0.798579	+	0.357856i
$603$	27.6249	−	0.361598i	1.12497	−	0.0147254i
$604$	1.78509	−	3.09186i	0.0726342	−	0.125806i
$605$	−9.79558	+	8.21947i	−0.398247	+	0.334169i
$606$	3.84182	+	4.51812i	0.156063	+	0.183536i
$607$	3.08287	+	0.543592i	0.125130	+	0.0220637i	0.235862	−	0.971787i	$-0.424209\pi$
$607$	3.08287	+	0.543592i	0.125130	+	0.0220637i	−0.110733	+	0.993850i	$0.535320\pi$
$608$	1.06706	−	6.05159i	0.0432749	−	0.245424i
$609$	−22.2501	−	32.3584i	−0.901618	−	1.31123i
$610$	7.13523	−	5.98717i	0.288897	−	0.242413i
$611$	−23.1366	−	13.3579i	−0.936006	−	0.540403i
$612$	−9.59934	+	0.125651i	−0.388031	+	0.00507914i
$613$	−17.6416	−	30.5562i	−0.712538	−	1.23415i	−0.963901	−	0.266260i	$-0.914212\pi$
$613$	−17.6416	−	30.5562i	−0.712538	−	1.23415i	0.251363	−	0.967893i	$-0.419121\pi$
$614$	12.6009	+	4.58633i	0.508529	+	0.185089i
$615$	14.5980	−	0.0955363i	0.588647	−	0.00385240i
$616$	3.20482	+	3.30274i	0.129126	+	0.133071i
$617$	11.3252	+	31.1158i	0.455937	+	1.25268i	0.928484	+	0.371371i	$0.121112\pi$
$617$	11.3252	+	31.1158i	0.455937	+	1.25268i	−0.472547	+	0.881305i	$0.656665\pi$
$618$	7.14748	−	2.65457i	0.287514	−	0.106782i
$619$	24.5649	−	4.33145i	0.987346	−	0.174096i	0.343419	−	0.939182i	$-0.388415\pi$
$619$	24.5649	−	4.33145i	0.987346	−	0.174096i	0.643927	+	0.765087i	$0.277304\pi$
$620$		−	3.32130i		−	0.133387i
$621$	−9.30002	−	1.45220i	−0.373197	−	0.0582749i
$622$			5.09033i			0.204103i
$623$	−2.24315	−	31.0057i	−0.0898698	−	1.24222i
$624$	9.17806	+	1.55648i	0.367417	+	0.0623090i
$625$	6.53832	−	2.37975i	0.261533	−	0.0951902i
$626$	10.8524	+	9.10627i	0.433750	+	0.363960i
$627$	9.36133	+	15.9720i	0.373856	+	0.637860i
$628$	0.494016	−	1.35730i	0.0197134	−	0.0541621i
$629$	13.2550	+	22.9584i	0.528513	+	0.915412i
$630$	−9.01738	+	8.98215i	−0.359261	+	0.357857i
$631$	17.2586	−	29.8928i	0.687056	−	1.19002i	−0.285730	−	0.958310i	$-0.592236\pi$
$631$	17.2586	−	29.8928i	0.687056	−	1.19002i	0.972786	−	0.231705i	$-0.0744305\pi$
$632$	5.61074	+	6.68662i	0.223183	+	0.265979i
$633$	−5.74579	−	31.3836i	−0.228375	−	1.24739i
$634$	3.16834	−	17.9686i	0.125831	−	0.713623i
$635$	2.81692	−	15.9755i	0.111786	−	0.633969i
$636$	1.73540	−	4.86683i	0.0688130	−	0.192982i
$637$	−17.8223	−	33.1331i	−0.706146	−	1.31278i
$638$	12.9088	+	7.45289i	0.511064	+	0.295063i
$639$	6.60479	−	18.9131i	0.261281	−	0.748192i
$640$	−1.38870	+	0.801764i	−0.0548930	+	0.0316925i
$641$	9.50637	−	26.1185i	0.375479	−	1.03162i	−0.597730	−	0.801698i	$-0.703930\pi$
$641$	9.50637	−	26.1185i	0.375479	−	1.03162i	0.973209	−	0.229923i	$-0.0738474\pi$
$642$	1.14016	−	2.00501i	0.0449987	−	0.0791315i
$643$	3.29387	−	3.92549i	0.129898	−	0.154806i	−0.697175	−	0.716901i	$-0.745560\pi$
$643$	3.29387	−	3.92549i	0.129898	−	0.154806i	0.827073	+	0.562095i	$0.190004\pi$
$644$	1.17066	+	4.64755i	0.0461303	+	0.183139i
$645$	17.3606	+	14.3747i	0.683572	+	0.566003i
$646$	3.41465	+	19.3654i	0.134347	+	0.761922i
$647$	−23.6758			−0.930793			−0.465396	−	0.885102i	$-0.654088\pi$
$647$	−23.6758			−0.930793			−0.465396	+	0.885102i	$0.654088\pi$
$648$	−5.60265	+	7.04346i	−0.220093	+	0.276693i
$649$		−	5.39165i		−	0.211641i
$650$	2.26668	+	12.8550i	0.0889067	+	0.504215i
$651$	−6.76842	+	6.65430i	−0.265275	+	0.260803i
$652$	−18.0997	+	6.58777i	−0.708841	+	0.257997i
$653$	−5.11269	+	6.09307i	−0.200075	+	0.238440i	−0.856748	−	0.515735i	$-0.827519\pi$
$653$	−5.11269	+	6.09307i	−0.200075	+	0.238440i	0.656673	+	0.754176i	$0.271963\pi$
$654$	−15.2956	−	8.69798i	−0.598107	−	0.340118i
$655$	−9.52629	−	3.46729i	−0.372223	−	0.135478i
$656$	−2.62806	−	4.55193i	−0.102608	−	0.177723i
$657$	23.0865	+	26.7933i	0.900691	+	1.04531i
$658$	−10.6582	−	7.70454i	−0.415502	−	0.300354i
$659$	−15.7090	−	18.7213i	−0.611936	−	0.729277i	0.367726	−	0.929934i	$-0.380137\pi$
$659$	−15.7090	−	18.7213i	−0.611936	−	0.729277i	−0.979661	+	0.200658i	$0.935692\pi$
$660$	1.62257	−	4.55041i	0.0631584	−	0.177124i
$661$	−26.3966	−	4.65443i	−1.02671	−	0.181036i	−0.365165	−	0.930943i	$-0.618987\pi$
$661$	−26.3966	−	4.65443i	−1.02671	−	0.181036i	−0.661544	+	0.749907i	$0.730098\pi$
$662$	−17.0300	−	3.00284i	−0.661888	−	0.116709i
$663$	−29.3026	+	5.36480i	−1.13802	+	0.208352i
$664$	−7.97327	−	9.50217i	−0.309423	−	0.368756i
$665$	21.1280	+	15.2728i	0.819309	+	0.592255i
$666$	24.5296	+	3.99493i	0.950503	+	0.154800i
$667$	7.76166	+	13.4436i	0.300533	+	0.520538i
$668$	−24.1843	−	8.80238i	−0.935720	−	0.340574i
$669$	14.6566	−	8.59039i	0.566658	−	0.332124i
$670$	−9.49207	+	11.3122i	−0.366711	+	0.437029i
$671$	9.49438	−	3.45567i	0.366527	−	0.133405i
$672$	4.41618	+	1.22365i	0.170358	+	0.0472032i
$673$	0.328912	+	1.86535i	0.0126786	+	0.0719041i	0.990491	−	0.137580i	$-0.0439325\pi$
$673$	0.328912	+	1.86535i	0.0126786	+	0.0719041i	−0.977812	+	0.209484i	$0.932821\pi$
$674$		−	22.3792i		−	0.862016i
$675$	−11.9413	−	4.08261i	−0.459619	−	0.157140i
$676$	15.8865			0.611019
$677$	1.95245	+	11.0729i	0.0750387	+	0.425566i	0.999065	+	0.0432364i	$0.0137669\pi$
$677$	1.95245	+	11.0729i	0.0750387	+	0.425566i	−0.924026	+	0.382329i	$0.875122\pi$
$678$	31.9936	−	11.8824i	1.22871	−	0.456340i
$679$	10.5094	+	41.7227i	0.403313	+	1.60117i
$680$	3.29839	−	3.93086i	0.126487	−	0.150742i
$681$	−37.1640	+	0.243220i	−1.42413	+	0.00932021i
$682$	1.23222	−	3.38548i	0.0471840	−	0.129637i
$683$	−9.64029	+	5.56582i	−0.368875	+	0.212970i	−0.672967	−	0.739672i	$-0.734980\pi$
$683$	−9.64029	+	5.56582i	−0.368875	+	0.212970i	0.304092	+	0.952643i	$0.401647\pi$
$684$	16.0843	+	9.00767i	0.614999	+	0.344417i
$685$	18.9429	+	10.9367i	0.723773	+	0.417870i
$686$	−7.06164	−	17.1211i	−0.269615	−	0.653688i
$687$	24.0832	+	28.3228i	0.918833	+	1.08058i
$688$	1.40921	−	7.99200i	0.0537254	−	0.304692i
$689$	2.78416	−	15.7897i	0.106068	−	0.601541i
$690$	3.83287	−	3.25914i	0.145915	−	0.124073i
$691$	14.0944	+	16.7970i	0.536176	+	0.638989i	0.964326	−	0.264718i	$-0.0852790\pi$
$691$	14.0944	+	16.7970i	0.536176	+	0.638989i	−0.428150	+	0.903708i	$0.640835\pi$
$692$	−4.00231	+	6.93220i	−0.152145	+	0.263523i
$693$	−12.5240	+	5.81024i	−0.475749	+	0.220713i
$694$	−6.30894	−	10.9274i	−0.239484	−	0.414799i
$695$	−8.72446	+	23.9703i	−0.330938	+	0.909244i
$696$	14.8424	−	0.0971357i	0.562598	−	0.00368192i
$697$	12.8848	+	10.8116i	0.488045	+	0.409518i
$698$	31.0239	−	11.2918i	1.17427	−	0.427400i
$699$	−9.44700	−	25.4362i	−0.357318	−	0.962086i
$700$	0.463665	+	6.40898i	0.0175249	+	0.242237i
$701$		−	15.5108i		−	0.585834i	−0.956138	−	0.292917i	$-0.905374\pi$
$701$		−	15.5108i		−	0.585834i	0.956138	−	0.292917i	$-0.0946260\pi$
$702$	−13.4862	+	24.4552i	−0.509002	+	0.923004i
$703$		−	50.9063i		−	1.91997i
$704$	−1.71299	+	0.302046i	−0.0645607	+	0.0113838i
$705$	−2.30831	+	13.6114i	−0.0869359	+	0.512634i
$706$	9.09782	+	24.9960i	0.342401	+	0.940738i
$707$	6.30877	+	6.50153i	0.237266	+	0.244515i
$708$	−2.71478	−	4.63187i	−0.102028	−	0.174076i
$709$	−16.5983	−	6.04129i	−0.623362	−	0.226885i	0.0109773	−	0.999940i	$-0.496506\pi$
$709$	−16.5983	−	6.04129i	−0.623362	−	0.226885i	−0.634340	+	0.773054i	$0.718728\pi$
$710$	5.35397	+	9.27335i	0.200931	+	0.348023i
$711$	−24.4877	+	9.27754i	−0.918362	+	0.347935i
$712$	10.1755	+	5.87485i	0.381344	+	0.220169i
$713$	2.87421	−	2.41175i	0.107640	−	0.0903208i
$714$	−14.6190	+	1.15385i	−0.547104	+	0.0431818i
$715$	2.60314	−	14.7631i	0.0973519	−	0.552110i
$716$	−3.57605	−	0.630553i	−0.133643	−	0.0235649i
$717$	−5.31294	+	14.8999i	−0.198415	+	0.556445i
$718$	21.6008	−	18.1252i	0.806136	−	0.676428i
$719$	−23.5227	+	40.7425i	−0.877247	+	1.51944i	−0.0228981	+	0.999738i	$0.507289\pi$
$719$	−23.5227	+	40.7425i	−0.877247	+	1.51944i	−0.854349	+	0.519699i	$0.826044\pi$
$720$	−0.897284	−	4.72616i	−0.0334398	−	0.176134i
$721$	10.6283	−	4.76271i	0.395819	−	0.177373i
$722$	6.41641	−	17.6289i	0.238794	−	0.656081i
$723$	13.8667	+	7.88540i	0.515708	+	0.293261i
$724$	−1.60743	+	1.91566i	−0.0597398	+	0.0711951i
$725$	7.11831	+	19.5574i	0.264367	+	0.726343i
$726$	−8.80883	+	10.6386i	−0.326926	+	0.394835i
$727$	−38.6709	+	6.81873i	−1.43423	+	0.252893i	−0.836130	−	0.548532i	$-0.815187\pi$
$727$	−38.6709	+	6.81873i	−1.43423	+	0.252893i	−0.598096	+	0.801424i	$0.704076\pi$
$728$	14.1455	+	1.45234i	0.524268	+	0.0538272i
$729$	−14.4075	−	22.8347i	−0.533612	−	0.845730i
$730$	−18.9043			−0.699680
$731$	4.50953	+	25.5748i	0.166791	+	0.945920i
$732$	6.41647	−	7.74928i	0.237159	−	0.286422i
$733$	5.69843	+	15.6563i	0.210476	+	0.578279i	0.999341	−	0.0362876i	$-0.0115532\pi$
$733$	5.69843	+	15.6563i	0.210476	+	0.578279i	−0.788865	+	0.614566i	$0.789331\pi$
$734$	2.92692	+	2.45598i	0.108035	+	0.0906519i
$735$	−12.8441	+	14.5949i	−0.473762	+	0.538340i
$736$	−1.70223	−	0.619562i	−0.0627452	−	0.0228374i
$737$	−13.8724	+	8.00922i	−0.510996	+	0.295023i
$738$	15.4916	−	2.94116i	0.570254	−	0.108265i
$739$	−22.0028	+	38.1099i	−0.809384	+	1.40189i	0.103907	+	0.994587i	$0.466866\pi$
$739$	−22.0028	+	38.1099i	−0.809384	+	1.40189i	−0.913291	+	0.407308i	$0.866468\pi$
$740$	−10.1762	+	8.53882i	−0.374083	+	0.313893i
$741$	53.8810	+	19.2127i	1.97937	+	0.705796i
$742$	2.15725	−	7.59216i	0.0791952	−	0.278717i
$743$	5.04480	+	0.889535i	0.185076	+	0.0326339i	0.265418	−	0.964133i	$-0.414490\pi$
$743$	5.04480	+	0.889535i	0.185076	+	0.0326339i	−0.0803419	+	0.996767i	$0.525601\pi$
$744$	−0.646071	−	3.52885i	−0.0236861	−	0.129374i
$745$	−7.66079	−	9.12978i	−0.280670	−	0.334489i
$746$	17.0915	+	9.86780i	0.625765	+	0.361286i
$747$	34.7988	−	13.1841i	1.27322	−	0.482379i
$748$	4.82049	−	2.78311i	0.176255	−	0.101761i
$749$	1.53687	−	3.17040i	0.0561561	−	0.115844i
$750$	17.8003	−	10.4329i	0.649975	−	0.380956i
$751$	−16.3130	−	13.6882i	−0.595268	−	0.499490i	0.294652	−	0.955605i	$-0.404796\pi$
$751$	−16.3130	−	13.6882i	−0.595268	−	0.499490i	−0.889921	+	0.456115i	$0.849241\pi$
$752$	4.67097	−	1.70009i	0.170333	−	0.0619961i
$753$	6.35770	−	37.4893i	0.231687	−	1.36619i
$754$	45.3576	−	7.99777i	1.65183	−	0.291262i
$755$	−5.72488			−0.208350
$756$	−7.83363	+	11.2975i	−0.284906	+	0.410887i
$757$	−17.3360			−0.630089			−0.315045	−	0.949077i	$-0.602020\pi$
$757$	−17.3360			−0.630089			−0.315045	+	0.949077i	$0.602020\pi$
$758$	0.148405	−	0.0261677i	0.00539030	−	0.000950455i
$759$	5.11609	−	1.90011i	0.185702	−	0.0689697i
$760$	−9.25934	+	3.37013i	−0.335872	+	0.122247i
$761$	23.0654	+	19.3541i	0.836119	+	0.701587i	0.956687	−	0.291118i	$-0.0940273\pi$
$761$	23.0654	+	19.3541i	0.836119	+	0.701587i	−0.120568	+	0.992705i	$0.538472\pi$
$762$	−0.114671	−	17.5218i	−0.00415410	−	0.634747i
$763$	−24.1861	−	11.7244i	−0.875595	−	0.424450i
$764$	11.5998	−	6.69714i	0.419665	−	0.242294i
$765$	7.87090	+	13.2298i	0.284573	+	0.478325i
$766$	31.0588	+	17.9318i	1.12220	+	0.647902i
$767$	−10.7086	−	12.7620i	−0.386665	−	0.460810i
$768$	−1.31951	+	1.12200i	−0.0476138	+	0.0404867i
$769$	26.5452	+	4.68063i	0.957243	+	0.168788i	0.630382	−	0.776285i	$-0.282898\pi$
$769$	26.5452	+	4.68063i	0.957243	+	0.168788i	0.326861	+	0.945073i	$0.394009\pi$
$770$	2.01699	−	7.09854i	0.0726874	−	0.255814i
$771$	−41.6500	+	35.4155i	−1.49999	+	1.27546i
$772$	−6.10999	+	5.12689i	−0.219904	+	0.184521i
$773$	16.0948	−	27.8770i	0.578890	−	1.00267i	−0.416717	−	0.909036i	$-0.636819\pi$
$773$	16.0948	−	27.8770i	0.578890	−	1.00267i	0.995607	−	0.0936304i	$-0.0298472\pi$
$774$	21.2417	+	11.8959i	0.763516	+	0.427590i
$775$	4.35648	−	2.51522i	0.156489	−	0.0903492i
$776$	−15.2816	−	5.56203i	−0.548576	−	0.199665i
$777$	37.7893	+	3.63012i	1.35568	+	0.130230i
$778$	−11.2603	−	9.44854i	−0.403703	−	0.338747i
$779$	−11.0467	−	30.3507i	−0.395791	−	1.08743i
$780$	−5.19717	−	13.9935i	−0.186088	−	0.501047i
$781$	2.01699	+	11.4389i	0.0721735	+	0.409316i
$782$	5.79683			0.207294
$783$	−14.4051	+	42.1336i	−0.514796	+	1.50573i
$784$	6.85396	+	1.42240i	0.244784	+	0.0508000i
$785$	−2.28096	+	0.402195i	−0.0814109	+	0.0143549i
$786$	−10.7961	−	1.83087i	−0.385083	−	0.0653049i
$787$	5.62574	+	15.4566i	0.200536	+	0.550968i	0.998673	−	0.0515084i	$-0.0164029\pi$
$787$	5.62574	+	15.4566i	0.200536	+	0.550968i	−0.798137	+	0.602477i	$0.794181\pi$
$788$	4.32995	−	5.16024i	0.154248	−	0.183826i
$789$	−10.9291	+	6.40564i	−0.389086	+	0.228047i
$790$	4.78719	−	13.1527i	0.170321	−	0.467952i
$791$	47.5744	−	21.3189i	1.69155	−	0.758011i
$792$	0.838800	−	5.15039i	0.0298055	−	0.183011i
$793$	15.6097	−	27.0368i	0.554317	−	0.960106i
$794$	17.7405	−	14.8861i	0.629588	−	0.528287i
$795$	−8.14993	+	1.49211i	−0.289048	+	0.0529198i
$796$	−1.94894	−	0.343651i	−0.0690783	−	0.0121804i
$797$	−3.08077	+	17.4719i	−0.109127	+	0.618888i	0.880365	+	0.474297i	$0.157298\pi$
$797$	−3.08077	+	17.4719i	−0.109127	+	0.618888i	−0.989492	+	0.144591i	$0.953813\pi$
$798$	25.4192	+	12.1173i	0.899831	+	0.428949i
$799$	−12.1852	+	10.2246i	−0.431082	+	0.361720i
$800$	−2.10331	−	1.21435i	−0.0743634	−	0.0429337i
$801$	−26.7035	+	23.0091i	−0.943522	+	0.812988i
$802$	11.9398	+	20.6803i	0.421609	+	0.730248i
$803$	−19.2696	−	7.01358i	−0.680011	−	0.247504i
$804$	−7.88474	+	13.8655i	−0.278073	+	0.489000i
$805$	5.51545	−	5.35193i	0.194394	−	0.188631i
$806$	−3.80742	−	10.4608i	−0.134111	−	0.368466i
$807$	−18.9966	−	15.7293i	−0.668710	−	0.553698i
$808$	−3.37206	+	0.594586i	−0.118629	+	0.0209174i
$809$			30.6625i			1.07804i	0.842294	+	0.539018i	$0.181204\pi$
$809$			30.6625i			1.07804i	−0.842294	+	0.539018i	$0.818796\pi$
$810$	14.2732	+	2.13318i	0.501510	+	0.0749524i
$811$			3.02277i			0.106144i	0.998591	+	0.0530720i	$0.0169013\pi$
$811$			3.02277i			0.106144i	−0.998591	+	0.0530720i	$0.983099\pi$
$812$	22.6135	−	1.63600i	0.793577	−	0.0574123i
$813$	−13.9640	+	16.8645i	−0.489738	+	0.591465i
$814$	−13.5408	+	4.92843i	−0.474603	+	0.172741i
$815$	23.6601	+	19.8532i	0.828778	+	0.695427i
$816$	2.73986	−	4.81812i	0.0959142	−	0.168668i
$817$	17.0559	−	46.8606i	0.596709	−	1.63944i
$818$	6.99557	+	12.1167i	0.244594	+	0.423650i
$819$	−18.1044	+	38.6274i	−0.632619	+	1.34975i
$820$	−4.21416	+	7.29914i	−0.147165	+	0.254897i
$821$	−6.41109	−	7.64043i	−0.223748	−	0.266653i	0.642479	−	0.766304i	$-0.277906\pi$
$821$	−6.41109	−	7.64043i	−0.223748	−	0.266653i	−0.866227	+	0.499651i	$0.833462\pi$
$822$	22.2541	+	7.93530i	0.776202	+	0.276775i
$823$	4.16374	−	23.6137i	0.145139	−	0.823123i	−0.822117	−	0.569319i	$-0.807207\pi$
$823$	4.16374	−	23.6137i	0.145139	−	0.823123i	0.967256	−	0.253804i	$-0.0816819\pi$
$824$	−0.764402	+	4.33514i	−0.0266292	+	0.151022i
$825$	7.19744	−	1.31773i	0.250583	−	0.0458774i
$826$	−4.60230	−	6.78788i	−0.160134	−	0.236181i
$827$	8.51498	+	4.91613i	0.296095	+	0.170951i	0.640687	−	0.767802i	$-0.278650\pi$
$827$	8.51498	+	4.91613i	0.296095	+	0.170951i	−0.344592	+	0.938752i	$0.611983\pi$
$828$	3.43840	−	4.20838i	0.119493	−	0.146251i
$829$	−35.9405	+	20.7503i	−1.24827	+	0.720687i	−0.970764	−	0.240038i	$-0.922840\pi$
$829$	−35.9405	+	20.7503i	−1.24827	+	0.720687i	−0.277503	+	0.960725i	$0.589507\pi$
$830$	−6.80295	+	18.6909i	−0.236134	+	0.648772i
$831$	−0.857517	−	1.46307i	−0.0297469	−	0.0507532i
$832$	−3.45474	+	4.11719i	−0.119771	+	0.142738i
$833$	−22.1671	+	3.22429i	−0.768045	+	0.111715i
$834$	−4.60687	+	27.1653i	−0.159523	+	0.940656i
$835$	7.16630	+	40.6421i	0.248000	+	1.40648i
$836$	−10.6886			−0.369673
$837$	10.6336	+	1.66045i	0.367553	+	0.0573936i
$838$		−	0.549592i		−	0.0189853i
$839$	−9.88562	−	56.0642i	−0.341290	−	1.93555i	−0.353013	−	0.935618i	$-0.614843\pi$
$839$	−9.88562	−	56.0642i	−0.341290	−	1.93555i	0.0117233	−	0.999931i	$-0.496268\pi$
$840$	−1.84146	−	7.11381i	−0.0635366	−	0.245450i
$841$	41.7552	−	15.1977i	1.43984	−	0.524057i
$842$	−1.53272	+	1.82662i	−0.0528209	+	0.0629495i
$843$	−0.291609	−	44.5580i	−0.0100436	−	1.53466i
$844$	17.3096	+	6.30018i	0.595821	+	0.216861i
$845$	−12.7372	−	22.0615i	−0.438173	−	0.758939i
$846$	0.195178	+	14.9110i	0.00671034	+	0.512649i
$847$	−12.3602	+	17.0987i	−0.424701	+	0.587520i
$848$	1.91754	+	2.28523i	0.0658485	+	0.0784751i
$849$	−0.749315	−	0.881222i	−0.0257164	−	0.0302435i
$850$	7.65389	+	1.34959i	0.262526	+	0.0462905i
$851$	−14.7788	−	2.60590i	−0.506610	−	0.0893290i
$852$	7.49243	+	8.81137i	0.256686	+	0.301872i
$853$	18.9804	+	22.6200i	0.649878	+	0.774494i	0.985896	−	0.167361i	$-0.0535247\pi$
$853$	18.9804	+	22.6200i	0.649878	+	0.774494i	−0.336018	+	0.941856i	$0.609080\pi$
$854$	9.00332	−	12.4549i	0.308087	−	0.426200i
$855$	−0.386904	−	29.5582i	−0.0132318	−	1.01087i
$856$	0.665836	+	1.15326i	0.0227578	+	0.0394177i
$857$	17.5089	+	6.37272i	0.598092	+	0.217688i	0.623285	−	0.781995i	$-0.285798\pi$
$857$	17.5089	+	6.37272i	0.598092	+	0.217688i	−0.0251925	+	0.999683i	$0.508020\pi$
$858$	−0.105969	−	16.1921i	−0.00361772	−	0.552788i
$859$	−8.61091	+	10.2621i	−0.293800	+	0.350138i	−0.892672	−	0.450708i	$-0.851172\pi$
$859$	−8.61091	+	10.2621i	−0.293800	+	0.350138i	0.598871	+	0.800845i	$0.295616\pi$
$860$	−12.2283	+	4.45074i	−0.416982	+	0.151769i
$861$	23.3180	−	6.03603i	0.794674	−	0.205707i
$862$	−2.75321	−	15.6143i	−0.0937748	−	0.531824i
$863$			18.5034i			0.629863i	0.949114	+	0.314932i	$0.101982\pi$
$863$			18.5034i			0.629863i	−0.949114	+	0.314932i	$0.898018\pi$
$864$	−1.87270	−	4.84696i	−0.0637107	−	0.164897i
$865$	12.8356			0.436424
$866$	6.38309	+	36.2003i	0.216906	+	1.23014i
$867$	1.95758	−	11.5432i	0.0664829	−	0.392029i
$868$	−1.33853	−	5.31401i	−0.0454326	−	0.180369i
$869$	9.75941	−	11.6308i	0.331065	−	0.394548i
$870$	−12.0350	−	20.5336i	−0.408023	−	0.696156i
$871$	−16.9284	+	46.5104i	−0.573597	+	1.57594i
$872$	8.79789	−	5.07947i	0.297934	−	0.172012i
$873$	30.8678	−	37.7802i	1.04472	−	1.27866i
$874$	−9.64010	−	5.56572i	−0.326081	−	0.188263i
$875$	26.0859	−	17.6867i	0.881864	−	0.597918i
$876$	−20.0856	+	3.67733i	−0.678631	+	0.124246i
$877$	−4.02447	+	22.8239i	−0.135897	+	0.770709i	0.838334	+	0.545157i	$0.183530\pi$
$877$	−4.02447	+	22.8239i	−0.135897	+	0.770709i	−0.974231	+	0.225553i	$0.927581\pi$
$878$	0.562188	−	3.18833i	0.0189729	−	0.107601i
$879$	5.64549	+	2.01305i	0.190418	+	0.0678984i
$880$	1.79286	+	2.13665i	0.0604374	+	0.0720265i
$881$	20.2972	−	35.1558i	0.683829	−	1.18443i	−0.289974	−	0.957035i	$-0.593647\pi$
$881$	20.2972	−	35.1558i	0.683829	−	1.18443i	0.973803	−	0.227393i	$-0.0730201\pi$
$882$	−10.8077	+	18.0054i	−0.363914	+	0.606273i
$883$	13.1801	+	22.8285i	0.443545	+	0.768242i	0.997950	−	0.0640052i	$-0.0203874\pi$
$883$	13.1801	+	22.8285i	0.443545	+	0.768242i	−0.554405	+	0.832247i	$0.687054\pi$
$884$	5.88243	−	16.1618i	0.197847	−	0.543581i
$885$	−4.25564	+	7.48367i	−0.143052	+	0.251561i
$886$	−4.83591	−	4.05781i	−0.162466	−	0.136325i
$887$	28.0677	−	10.2158i	0.942422	−	0.343013i	0.175300	−	0.984515i	$-0.443910\pi$
$887$	28.0677	−	10.2158i	0.942422	−	0.343013i	0.767122	+	0.641502i	$0.221688\pi$
$888$	−9.15107	+	11.0519i	−0.307090	+	0.370878i
$889$	−1.93134	−	26.6958i	−0.0647750	−	0.895347i
$890$		−	18.8410i		−	0.631550i
$891$	13.7576	+	7.46983i	0.460898	+	0.250249i
$892$			9.80836i			0.328408i
$893$	30.0809	−	5.30407i	1.00662	−	0.177494i
$894$	−9.91547	−	8.21009i	−0.331623	−	0.274586i
$895$	1.99150	+	5.47159i	0.0665684	+	0.182895i
$896$	−1.89876	+	1.84247i	−0.0634333	+	0.0615526i
$897$	8.33587	−	14.6589i	0.278327	−	0.489445i
$898$	−33.5411	−	12.2079i	−1.11928	−	0.407384i
$899$	−8.87469	−	15.3714i	−0.295987	−	0.512665i
$900$	5.51970	−	4.75606i	0.183990	−	0.158535i
$901$	−8.26731	−	4.77313i	−0.275424	−	0.159016i
$902$	−7.00361	+	5.87673i	−0.233195	+	0.195674i
$903$	33.5698	+	16.0027i	1.11713	+	0.532536i
$904$	−3.42162	+	19.4050i	−0.113801	+	0.645399i
$905$	3.94906	+	0.696326i	0.131271	+	0.0231466i
$906$	−6.08263	+	1.11362i	−0.202082	+	0.0369977i
$907$	−9.72332	+	8.15883i	−0.322858	+	0.270910i	−0.789782	−	0.613388i	$-0.789806\pi$
$907$	−9.72332	+	8.15883i	−0.322858	+	0.270910i	0.466925	+	0.884297i	$0.345362\pi$
$908$	10.7286	−	18.5824i	0.356040	−	0.616679i
$909$	1.65120	−	10.1387i	0.0547668	−	0.336278i
$910$	−9.32453	−	20.8083i	−0.309105	−	0.689788i
$911$	0.736361	−	2.02314i	0.0243967	−	0.0670295i	−0.926896	−	0.375317i	$-0.877534\pi$
$911$	0.736361	−	2.02314i	0.0243967	−	0.0670295i	0.951293	+	0.308288i	$0.0997560\pi$
$912$	−9.18239	+	5.38188i	−0.304059	+	0.178212i
$913$	−13.8688	+	16.5282i	−0.458991	+	0.547004i
$914$	0.679735	+	1.86756i	0.0224836	+	0.0617733i
$915$	−15.9059	−	2.69743i	−0.525832	−	0.0891742i
$916$	−21.1385	+	3.72728i	−0.698434	+	0.123153i
$917$	−16.6392	−	1.70837i	−0.549476	−	0.0564153i
$918$	10.9363	+	12.5255i	0.360951	+	0.413403i
$919$	10.4011			0.343099			0.171550	−	0.985175i	$-0.445123\pi$
$919$	10.4011			0.343099			0.171550	+	0.985175i	$0.445123\pi$
$920$	0.504406	+	2.86063i	0.0166298	+	0.0943121i
$921$	−8.08643	−	21.7729i	−0.266457	−	0.717440i
$922$	6.33135	+	17.3953i	0.208512	+	0.572882i
$923$	27.4936	+	23.0698i	0.904961	+	0.759353i
$924$	0.762202	−	7.93448i	0.0250746	−	0.261025i
$925$	−18.9066	−	6.88143i	−0.621645	−	0.226260i
$926$	−25.3890	+	14.6583i	−0.834334	+	0.481703i
$927$	−11.5222	−	6.45277i	−0.378439	−	0.211937i
$928$	−4.28471	+	7.42134i	−0.140653	+	0.243617i
$929$	−32.0041	+	26.8546i	−1.05002	+	0.881072i	−0.993096	−	0.117306i	$-0.962574\pi$
$929$	−32.0041	+	26.8546i	−1.05002	+	0.881072i	−0.0569252	+	0.998378i	$0.518130\pi$
$930$	−4.38250	+	3.72650i	−0.143708	+	0.122197i
$931$	39.9596	+	15.9214i	1.30962	+	0.521801i
$932$	15.4277	+	2.72033i	0.505353	+	0.0891073i
$933$	6.71675	−	5.71135i	0.219897	−	0.186981i
$934$	−23.3036	−	27.7722i	−0.762517	−	0.908733i
$935$	−7.72980	−	4.46280i	−0.252791	−	0.145949i
$936$	−8.24399	−	13.8569i	−0.269463	−	0.452928i
$937$	−1.86448	+	1.07646i	−0.0609101	+	0.0351664i	−0.530146	−	0.847907i	$-0.677863\pi$
$937$	−1.86448	+	1.07646i	−0.0609101	+	0.0351664i	0.469236	+	0.883073i	$0.344529\pi$
$938$	−10.6282	+	21.9247i	−0.347021	+	0.715868i
$939$	−0.160583	−	24.5372i	−0.00524044	−	0.800740i
$940$	−6.10593	−	5.12348i	−0.199154	−	0.167110i
$941$	18.6275	−	6.77984i	0.607238	−	0.221016i	−0.0200564	−	0.999799i	$-0.506385\pi$
$941$	18.6275	−	6.77984i	0.607238	−	0.221016i	0.627294	+	0.778782i	$0.284162\pi$
$942$	−2.34526	+	0.871028i	−0.0764127	+	0.0283796i
$943$	−9.37669	+	1.65336i	−0.305347	+	0.0538409i
$944$	3.09969			0.100886
$945$	21.9696	+	1.82058i	0.714670	+	0.0592235i
$946$	−14.1159			−0.458946
$947$	30.4714	−	5.37294i	0.990189	−	0.174597i	0.344985	−	0.938608i	$-0.387884\pi$
$947$	30.4714	−	5.37294i	0.990189	−	0.174597i	0.645203	+	0.764011i	$0.276773\pi$
$948$	2.52783	−	14.9058i	0.0821002	−	0.484119i
$949$	−59.5412	+	21.6712i	−1.93279	+	0.703478i
$950$	−11.4326	−	9.59310i	−0.370923	−	0.311241i
$951$	−27.2646	+	15.9801i	−0.884116	+	0.518189i
$952$	3.69316	−	7.61860i	0.119696	−	0.246920i
$953$	9.22287	−	5.32482i	0.298758	−	0.172488i	−0.343127	−	0.939289i	$-0.611486\pi$
$953$	9.22287	−	5.32482i	0.298758	−	0.172488i	0.641885	+	0.766801i	$0.278153\pi$
$954$	−8.36897	+	3.17071i	−0.270955	+	0.102655i
$955$	−18.6006	−	10.7390i	−0.601900	−	0.347507i
$956$	−5.87055	−	6.99625i	−0.189867	−	0.226275i
$957$	−4.64947	−	25.3955i	−0.150296	−	0.820919i
$958$	−27.3959	−	4.83064i	−0.885123	−	0.156071i
$959$	34.7160	+	9.86427i	1.12104	+	0.318534i
$960$	2.61606	+	0.932824i	0.0844328	+	0.0301068i
$961$	20.4610	−	17.1688i	0.660032	−	0.553833i
$962$	−22.2624	+	38.5595i	−0.717767	+	1.24321i
$963$	−3.92490	+	0.745162i	−0.126478	+	0.0240125i
$964$	−7.97598	+	4.60494i	−0.256889	+	0.148315i
$965$	12.0185	+	4.37437i	0.386888	+	0.140816i
$966$	4.81903	−	6.75925i	0.155050	−	0.217475i
$967$	35.7404	+	29.9897i	1.14933	+	0.964404i	0.999704	−	0.0243381i	$-0.00774782\pi$
$967$	35.7404	+	29.9897i	1.14933	+	0.964404i	0.149628	+	0.988742i	$0.452192\pi$
$968$	−2.72742	−	7.49352i	−0.0876625	−	0.240851i
$969$	21.7217	−	26.2337i	0.697801	−	0.842747i
$970$	4.52823	+	25.6809i	0.145393	+	0.824563i
$971$	−44.5663			−1.43020			−0.715100	−	0.699022i	$-0.753619\pi$
$971$	−44.5663			−1.43020			−0.715100	+	0.699022i	$0.753619\pi$
$972$	15.5801	−	0.509994i	0.499732	−	0.0163581i
$973$	−4.29863	+	41.8680i	−0.137808	+	1.34223i
$974$	10.6688	−	1.88121i	0.341852	−	0.0602777i
$975$	14.4191	−	17.4142i	0.461782	−	0.557702i
$976$	1.98669	+	5.45838i	0.0635923	+	0.174718i
$977$	39.0686	−	46.5602i	1.24992	−	1.48959i	0.445784	−	0.895141i	$-0.352925\pi$
$977$	39.0686	−	46.5602i	1.24992	−	1.48959i	0.804132	−	0.594451i	$-0.202631\pi$
$978$	29.0006	+	16.4914i	0.927336	+	0.527336i
$979$	6.99007	−	19.2051i	0.223404	−	0.613796i
$980$	−3.51998	−	10.6585i	−0.112442	−	0.340473i
$981$	5.68462	+	29.9419i	0.181496	+	0.955973i
$982$	13.4126	−	23.2312i	0.428012	−	0.741339i
$983$	8.15192	−	6.84028i	0.260006	−	0.218171i	−0.503461	−	0.864018i	$-0.667940\pi$
$983$	8.15192	−	6.84028i	0.260006	−	0.218171i	0.763467	+	0.645847i	$0.223496\pi$
$984$	−3.05765	+	8.57502i	−0.0974743	+	0.273362i
$985$	−10.6376	−	1.87570i	−0.338942	−	0.0597647i
$986$	4.76189	−	27.0060i	0.151649	−	0.860047i
$987$	1.79231	+	22.7082i	0.0570499	+	0.722810i
$988$	−25.2999	+	21.2292i	−0.804898	+	0.675389i
$989$	−12.7312	−	7.35034i	−0.404827	−	0.233727i
$990$	−7.82485	+	2.96456i	−0.248690	+	0.0942199i
$991$	−10.8448	−	18.7837i	−0.344495	−	0.596683i	0.640767	−	0.767736i	$-0.278617\pi$
$991$	−10.8448	−	18.7837i	−0.344495	−	0.596683i	−0.985262	+	0.171053i	$0.945283\pi$
$992$	1.94633	+	0.708408i	0.0617962	+	0.0224920i
$993$	15.1453	+	25.8404i	0.480622	+	0.820021i
$994$	12.3035	+	12.6795i	0.390244	+	0.402168i
$995$	1.08536	+	2.98201i	0.0344083	+	0.0945361i
$996$	−3.59223	+	21.1823i	−0.113824	+	0.671186i
$997$	19.8076	−	3.49262i	0.627314	−	0.110612i	0.149052	−	0.988829i	$-0.452378\pi$
$997$	19.8076	−	3.49262i	0.627314	−	0.110612i	0.478263	+	0.878217i	$0.341267\pi$
$998$		−	11.5846i		−	0.366705i
$999$	−22.2509	−	36.8495i	−0.703986	−	1.16587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.16	✓	144
7.6	odd	2	inner	378.2.z.a.41.21	yes	144
27.2	odd	18	inner	378.2.z.a.83.21	yes	144
189.83	even	18	inner	378.2.z.a.83.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.16	✓	144	1.1	even	1	trivial
378.2.z.a.41.21	yes	144	7.6	odd	2	inner
378.2.z.a.83.16	yes	144	189.83	even	18	inner
378.2.z.a.83.21	yes	144	27.2	odd	18	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)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.33409 - 1.10463i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.22837 - 1.03073i) q^{5} +(-1.50564 - 0.856190i) q^{6} +(-2.38077 - 1.15409i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.559569 + 2.94735i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.33409 - 1.10463i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.22837 - 1.03073i) q^{5} +(-1.50564 - 0.856190i) q^{6} +(-2.38077 - 1.15409i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.559569 + 2.94735i) q^{9} +(-1.38870 - 0.801764i) q^{10} +(-1.11807 - 1.33247i) q^{11} +(-1.63144 - 0.581732i) q^{12} +(-5.29296 - 0.933292i) q^{13} +(-2.54501 - 0.723144i) q^{14} +(0.500179 + 2.73198i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.60003 + 2.77133i) q^{17} +(1.06287 + 2.80541i) q^{18} +(5.32168 - 3.07247i) q^{19} +(-1.50682 - 0.548439i) q^{20} +(1.90130 + 4.16954i) q^{21} +(-1.33247 - 1.11807i) q^{22} +(-0.619562 - 1.70223i) q^{23} +(-1.70767 - 0.289598i) q^{24} +(-0.421739 - 2.39180i) q^{25} -5.37462 q^{26} +(2.50923 - 4.55014i) q^{27} +(-2.63192 - 0.270222i) q^{28} +(-8.43923 + 1.48806i) q^{29} +(0.966984 + 2.60362i) q^{30} +(0.708408 + 1.94633i) q^{31} +(0.642788 - 0.766044i) q^{32} +(0.0197165 + 3.01269i) q^{33} +(-1.09448 + 3.00707i) q^{34} +(1.73492 + 3.87158i) q^{35} +(1.53388 + 2.57822i) q^{36} +(4.14213 - 7.17438i) q^{37} +(4.70730 - 3.94989i) q^{38} +(6.03032 + 7.09188i) q^{39} +(-1.57917 - 0.278450i) q^{40} +(0.912715 - 5.17626i) q^{41} +(2.59645 + 3.77604i) q^{42} +(6.21667 - 5.21641i) q^{43} +(-1.50638 - 0.869708i) q^{44} +(2.35056 - 4.19721i) q^{45} +(-0.905739 - 1.56879i) q^{46} +(4.67097 + 1.70009i) q^{47} +(-1.73201 + 0.0113352i) q^{48} +(4.33614 + 5.49526i) q^{49} +(-0.830664 - 2.28223i) q^{50} +(5.19588 - 1.92975i) q^{51} +(-5.29296 + 0.933292i) q^{52} +2.98316i q^{53} +(1.68099 - 4.91673i) q^{54} +2.78920i q^{55} +(-2.63885 + 0.190911i) q^{56} +(-10.4935 - 1.77956i) q^{57} +(-8.05262 + 2.93091i) q^{58} +(2.37450 + 1.99244i) q^{59} +(1.40441 + 2.39615i) q^{60} +(-1.98669 + 5.45838i) q^{61} +(1.03562 + 1.79375i) q^{62} +(2.06931 - 7.66276i) q^{63} +(0.500000 - 0.866025i) q^{64} +(5.53977 + 6.60204i) q^{65} +(0.542565 + 2.96350i) q^{66} +(1.59914 - 9.06919i) q^{67} +(-0.555684 + 3.15144i) q^{68} +(-1.05380 + 2.95531i) q^{69} +(2.38086 + 3.51150i) q^{70} +(-5.78309 - 3.33887i) q^{71} +(1.95828 + 2.27270i) q^{72} +(10.2097 - 5.89460i) q^{73} +(2.83338 - 7.78466i) q^{74} +(-2.07943 + 3.65673i) q^{75} +(3.94989 - 4.70730i) q^{76} +(1.12409 + 4.46267i) q^{77} +(7.17020 + 5.93698i) q^{78} +(1.51573 + 8.59615i) q^{79} -1.60353 q^{80} +(-8.37377 + 3.29849i) q^{81} -5.25611i q^{82} +(-2.15397 - 12.2158i) q^{83} +(3.21270 + 3.26780i) q^{84} +(4.82192 - 1.75503i) q^{85} +(5.21641 - 6.21667i) q^{86} +(12.9024 + 7.33706i) q^{87} +(-1.63452 - 0.594915i) q^{88} +(5.87485 + 10.1755i) q^{89} +(1.58601 - 4.54162i) q^{90} +(11.5242 + 8.33053i) q^{91} +(-1.16440 - 1.38767i) q^{92} +(1.20491 - 3.37911i) q^{93} +(4.89523 + 0.863161i) q^{94} +(-9.70389 - 1.71106i) q^{95} +(-1.70373 + 0.311924i) q^{96} +(-10.4532 - 12.4576i) q^{97} +(5.22450 + 4.65882i) q^{98} +(3.30162 - 4.04097i) 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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