LMFDB - Embedded newform 196.2.f.d.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(19,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("196.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.f (of order $6$, degree $2$, not 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Root			$-0.349313 + 1.37039i$ of defining polynomial
Character	$\chi$	$=$	196.31
Dual form			196.2.f.d.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24165 + 0.676979i) q^{2} +(-1.36145 + 2.35811i) q^{3} +(1.08340 + 1.68114i) q^{4} +(0.937379 - 0.541196i) q^{5} +(-3.28684 + 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +(-2.20711 - 3.82282i) q^{9} +O(q^{10})$	\(q+(1.24165 + 0.676979i) q^{2} +(-1.36145 + 2.35811i) q^{3} +(1.08340 + 1.68114i) q^{4} +(0.937379 - 0.541196i) q^{5} +(-3.28684 + 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +(-2.20711 - 3.82282i) q^{9} +(1.53028 - 0.0373915i) q^{10} +(-1.80482 - 1.04201i) q^{11} +(-5.43931 + 0.265972i) q^{12} -2.61313i q^{13} +2.94725i q^{15} +(-1.65249 + 3.64270i) q^{16} +(3.86324 + 2.23044i) q^{17} +(-0.152490 - 6.24078i) q^{18} +(0.563932 + 0.976759i) q^{19} +(1.92538 + 0.989538i) q^{20} +(-1.53553 - 2.51564i) q^{22} +(6.16203 - 3.55765i) q^{23} +(-6.93379 - 3.35205i) q^{24} +(-1.91421 + 3.31552i) q^{25} +(1.76903 - 3.24459i) q^{26} +3.85077 q^{27} -1.17157 q^{29} +(-1.99523 + 3.65946i) q^{30} +(3.85077 - 6.66973i) q^{31} +(-4.51785 + 3.40427i) q^{32} +(4.91434 - 2.83730i) q^{33} +(3.28684 + 5.38476i) q^{34} +(4.03553 - 7.85211i) q^{36} +(2.00000 + 3.46410i) q^{37} +(0.0389624 + 1.59457i) q^{38} +(6.16203 + 3.55765i) q^{39} +(1.72076 + 2.53211i) q^{40} -5.54328i q^{41} -7.97852i q^{43} +(-0.203567 - 4.16307i) q^{44} +(-4.13779 - 2.38896i) q^{45} +(10.0595 - 0.245800i) q^{46} +(2.72291 + 4.71621i) q^{47} +(-6.34009 - 8.85611i) q^{48} +(-4.62132 + 2.82083i) q^{50} +(-10.5192 + 6.07328i) q^{51} +(4.39304 - 2.83106i) q^{52} +(3.24264 - 5.61642i) q^{53} +(4.78132 + 2.60689i) q^{54} -2.25573 q^{55} -3.07107 q^{57} +(-1.45469 - 0.793130i) q^{58} +(-4.41470 + 7.64649i) q^{59} +(-4.95475 + 3.19305i) q^{60} +(-11.3152 + 6.53281i) q^{61} +(9.29658 - 5.67459i) q^{62} +(-7.91421 + 1.16843i) q^{64} +(-1.41421 - 2.44949i) q^{65} +(8.02269 - 0.196030i) q^{66} +(-8.71442 - 5.03127i) q^{67} +(0.435738 + 8.91112i) q^{68} +19.3743i q^{69} +(10.3264 - 7.01761i) q^{72} +(-6.90282 - 3.98535i) q^{73} +(0.138181 + 5.65517i) q^{74} +(-5.21222 - 9.02783i) q^{75} +(-1.03111 + 2.00627i) q^{76} +(5.24264 + 8.58892i) q^{78} +(-3.60963 + 2.08402i) q^{79} +(0.422406 + 4.30891i) q^{80} +(1.37868 - 2.38794i) q^{81} +(3.75268 - 6.88282i) q^{82} -4.31795 q^{83} +4.82843 q^{85} +(5.40129 - 9.90655i) q^{86} +(1.59504 - 2.76269i) q^{87} +(2.56555 - 5.30689i) q^{88} +(3.47496 - 2.00627i) q^{89} +(-3.52043 - 5.76745i) q^{90} +(12.6569 + 6.50490i) q^{92} +(10.4853 + 18.1610i) q^{93} +(0.188127 + 7.69924i) q^{94} +(1.05724 + 0.610396i) q^{95} +(-1.87678 - 15.2883i) q^{96} -3.82683i q^{97} +9.19932i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 4 * q^4 - 8 * q^8 - 24 * q^9	$ 16 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 24 q^{9} - 4 q^{16} + 20 q^{18} + 32 q^{22} - 8 q^{25} - 64 q^{29} + 40 q^{30} - 36 q^{32} + 8 q^{36} + 32 q^{37} - 24 q^{44} + 8 q^{46} - 40 q^{50} - 16 q^{53} + 64 q^{57} - 8 q^{60} - 104 q^{64} + 4 q^{72} - 16 q^{74} + 16 q^{78} + 56 q^{81} + 32 q^{85} - 64 q^{86} + 64 q^{88} + 112 q^{92} + 32 q^{93}+O(q^{100}) $ 16 * q + 4 * q^2 + 4 * q^4 - 8 * q^8 - 24 * q^9 - 4 * q^16 + 20 * q^18 + 32 * q^22 - 8 * q^25 - 64 * q^29 + 40 * q^30 - 36 * q^32 + 8 * q^36 + 32 * q^37 - 24 * q^44 + 8 * q^46 - 40 * q^50 - 16 * q^53 + 64 * q^57 - 8 * q^60 - 104 * q^64 + 4 * q^72 - 16 * q^74 + 16 * q^78 + 56 * q^81 + 32 * q^85 - 64 * q^86 + 64 * q^88 + 112 * q^92 + 32 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.24165	+	0.676979i	0.877981	+	0.478696i
$2$	1.24165	+	0.676979i	0.877981	+	0.478696i
$3$	−1.36145	+	2.35811i	−0.786035	+	1.36145i	0.142344	+	0.989817i	$0.454536\pi$
$3$	−1.36145	+	2.35811i	−0.786035	+	1.36145i	−0.928379	+	0.371635i	$0.878797\pi$
$4$	1.08340	+	1.68114i	0.541700	+	0.840572i
$5$	0.937379	−	0.541196i	0.419209	−	0.242030i	−0.275530	−	0.961292i	$-0.588853\pi$
$5$	0.937379	−	0.541196i	0.419209	−	0.242030i	0.694739	+	0.719262i	$0.255520\pi$
$6$	−3.28684	+	2.00627i	−1.34185	+	0.819057i
$7$		0			0
$7$		0			0
$8$	0.207107	+	2.82083i	0.0732233	+	0.997316i
$9$	−2.20711	−	3.82282i	−0.735702	−	1.27427i
$10$	1.53028	−	0.0373915i	0.483916	−	0.0118242i
$11$	−1.80482	−	1.04201i	−0.544172	−	0.314178i	0.202596	−	0.979262i	$-0.435062\pi$
$11$	−1.80482	−	1.04201i	−0.544172	−	0.314178i	−0.746768	+	0.665084i	$0.768396\pi$
$12$	−5.43931	+	0.265972i	−1.57019	+	0.0767796i
$13$		−	2.61313i		−	0.724751i	−0.932032	−	0.362375i	$-0.881966\pi$
$13$		−	2.61313i		−	0.724751i	0.932032	−	0.362375i	$-0.118034\pi$
$14$		0			0
$15$			2.94725i			0.760977i
$16$	−1.65249	+	3.64270i	−0.413123	+	0.910675i
$17$	3.86324	+	2.23044i	0.936973	+	0.540962i	0.889010	−	0.457887i	$-0.151394\pi$
$17$	3.86324	+	2.23044i	0.936973	+	0.540962i	0.0479630	+	0.998849i	$0.484727\pi$
$18$	−0.152490	−	6.24078i	−0.0359423	−	1.47097i
$19$	0.563932	+	0.976759i	0.129375	+	0.224084i	0.923435	−	0.383756i	$-0.125370\pi$
$19$	0.563932	+	0.976759i	0.129375	+	0.224084i	−0.794060	+	0.607840i	$0.792036\pi$
$20$	1.92538	+	0.989538i	0.430529	+	0.221267i
$21$		0			0
$22$	−1.53553	−	2.51564i	−0.327377	−	0.536336i
$23$	6.16203	−	3.55765i	1.28487	−	0.741821i	0.307136	−	0.951665i	$-0.400629\pi$
$23$	6.16203	−	3.55765i	1.28487	−	0.741821i	0.977735	+	0.209845i	$0.0672959\pi$
$24$	−6.93379	−	3.35205i	−1.41535	−	0.684235i
$25$	−1.91421	+	3.31552i	−0.382843	+	0.663103i
$26$	1.76903	−	3.24459i	0.346935	−	0.636317i
$27$	3.85077			0.741081
$28$		0			0
$29$	−1.17157			−0.217556			−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157			−0.217556			−0.108778	+	0.994066i	$0.534694\pi$
$30$	−1.99523	+	3.65946i	−0.364277	+	0.668123i
$31$	3.85077	−	6.66973i	0.691619	−	1.19792i	−0.279689	−	0.960091i	$-0.590231\pi$
$31$	3.85077	−	6.66973i	0.691619	−	1.19792i	0.971307	−	0.237828i	$-0.0764354\pi$
$32$	−4.51785	+	3.40427i	−0.798650	+	0.601795i
$33$	4.91434	−	2.83730i	0.855477	−	0.493910i
$34$	3.28684	+	5.38476i	0.563688	+	0.923479i
$35$		0			0
$36$	4.03553	−	7.85211i	0.672589	−	1.30868i
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	0.0389624	+	1.59457i	0.00632053	+	0.258673i
$39$	6.16203	+	3.55765i	0.986714	+	0.569679i
$40$	1.72076	+	2.53211i	0.272076	+	0.400361i
$41$		−	5.54328i		−	0.865714i	−0.901462	−	0.432857i	$-0.857505\pi$
$41$		−	5.54328i		−	0.865714i	0.901462	−	0.432857i	$-0.142495\pi$
$42$		0			0
$43$		−	7.97852i		−	1.21671i	−0.793664	−	0.608357i	$-0.791829\pi$
$43$		−	7.97852i		−	1.21671i	0.793664	−	0.608357i	$-0.208171\pi$
$44$	−0.203567	−	4.16307i	−0.0306888	−	0.627606i
$45$	−4.13779	−	2.38896i	−0.616826	−	0.356124i
$46$	10.0595	−	0.245800i	1.48320	−	0.0362412i
$47$	2.72291	+	4.71621i	0.397177	+	0.687930i	0.993376	−	0.114906i	$-0.0366567\pi$
$47$	2.72291	+	4.71621i	0.397177	+	0.687930i	−0.596200	+	0.802836i	$0.703323\pi$
$48$	−6.34009	−	8.85611i	−0.915113	−	1.27827i
$49$		0			0
$50$	−4.62132	+	2.82083i	−0.653553	+	0.398926i
$51$	−10.5192	+	6.07328i	−1.47299	+	0.850430i
$52$	4.39304	−	2.83106i	0.609205	−	0.392597i
$53$	3.24264	−	5.61642i	0.445411	−	0.771474i	−0.552670	−	0.833400i	$-0.686391\pi$
$53$	3.24264	−	5.61642i	0.445411	−	0.771474i	0.998081	+	0.0619259i	$0.0197243\pi$
$54$	4.78132	+	2.60689i	0.650655	+	0.354753i
$55$	−2.25573			−0.304162
$56$		0			0
$57$	−3.07107			−0.406773
$58$	−1.45469	−	0.793130i	−0.191010	−	0.104143i
$59$	−4.41470	+	7.64649i	−0.574745	+	0.995488i	0.421324	+	0.906910i	$0.361566\pi$
$59$	−4.41470	+	7.64649i	−0.574745	+	0.995488i	−0.996069	+	0.0885778i	$0.971768\pi$
$60$	−4.95475	+	3.19305i	−0.639656	+	0.412221i
$61$	−11.3152	+	6.53281i	−1.44876	+	0.836441i	−0.998408	−	0.0564104i	$-0.982034\pi$
$61$	−11.3152	+	6.53281i	−1.44876	+	0.836441i	−0.450351	+	0.892852i	$0.648701\pi$
$62$	9.29658	−	5.67459i	1.18067	−	0.720674i
$63$		0			0
$64$	−7.91421	+	1.16843i	−0.989277	+	0.146053i
$65$	−1.41421	−	2.44949i	−0.175412	−	0.303822i
$66$	8.02269	−	0.196030i	0.987525	−	0.0241297i
$67$	−8.71442	−	5.03127i	−1.06464	−	0.614668i	−0.137925	−	0.990443i	$-0.544043\pi$
$67$	−8.71442	−	5.03127i	−1.06464	−	0.614668i	−0.926711	+	0.375775i	$0.877377\pi$
$68$	0.435738	+	8.91112i	0.0528410	+	1.08063i
$69$			19.3743i			2.33239i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	10.3264	−	7.01761i	1.21698	−	0.827034i
$73$	−6.90282	−	3.98535i	−0.807914	−	0.466450i	0.0383167	−	0.999266i	$-0.487800\pi$
$73$	−6.90282	−	3.98535i	−0.807914	−	0.466450i	−0.846231	+	0.532816i	$0.821134\pi$
$74$	0.138181	+	5.65517i	0.0160632	+	0.657400i
$75$	−5.21222	−	9.02783i	−0.601856	−	1.04244i
$76$	−1.03111	+	2.00627i	−0.118276	+	0.230135i
$77$		0			0
$78$	5.24264	+	8.58892i	0.593612	+	0.972504i
$79$	−3.60963	+	2.08402i	−0.406115	+	0.234471i	−0.689119	−	0.724648i	$-0.742002\pi$
$79$	−3.60963	+	2.08402i	−0.406115	+	0.234471i	0.283004	+	0.959119i	$0.408669\pi$
$80$	0.422406	+	4.30891i	0.0472264	+	0.481751i
$81$	1.37868	−	2.38794i	0.153187	−	0.265327i
$82$	3.75268	−	6.88282i	0.414414	−	0.760080i
$83$	−4.31795			−0.473956			−0.236978	−	0.971515i	$-0.576157\pi$
$83$	−4.31795			−0.473956			−0.236978	+	0.971515i	$0.576157\pi$
$84$		0			0
$85$	4.82843			0.523716
$86$	5.40129	−	9.90655i	0.582436	−	1.06825i
$87$	1.59504	−	2.76269i	0.171006	−	0.296192i
$88$	2.56555	−	5.30689i	0.273489	−	0.565717i
$89$	3.47496	−	2.00627i	0.368346	−	0.212664i	−0.304390	−	0.952548i	$-0.598453\pi$
$89$	3.47496	−	2.00627i	0.368346	−	0.212664i	0.672735	+	0.739883i	$0.265119\pi$
$90$	−3.52043	−	5.76745i	−0.371085	−	0.607942i
$91$		0			0
$92$	12.6569	+	6.50490i	1.31957	+	0.678183i
$93$	10.4853	+	18.1610i	1.08727	+	1.88321i
$94$	0.188127	+	7.69924i	0.0194038	+	0.794116i
$95$	1.05724	+	0.610396i	0.108470	+	0.0626253i
$96$	−1.87678	−	15.2883i	−0.191548	−	1.56036i
$97$		−	3.82683i		−	0.388556i	−0.980946	−	0.194278i	$-0.937764\pi$
$97$		−	3.82683i		−	0.388556i	0.980946	−	0.194278i	$-0.0622364\pi$
$98$		0			0
$99$			9.19932i			0.924566i
$100$	−7.64772	+	0.373959i	−0.764772	+	0.0373959i
$101$	−0.160829	−	0.0928546i	−0.0160031	−	0.00923938i	0.491977	−	0.870608i	$-0.336274\pi$
$101$	−0.160829	−	0.0928546i	−0.0160031	−	0.00923938i	−0.507980	+	0.861369i	$0.669608\pi$
$102$	−17.1727	+	0.419607i	−1.70035	+	0.0415472i
$103$	−7.70154	−	13.3395i	−0.758855	−	1.31438i	−0.943435	−	0.331558i	$-0.892426\pi$
$103$	−7.70154	−	13.3395i	−0.758855	−	1.31438i	0.184580	−	0.982818i	$-0.440908\pi$
$104$	7.37120	−	0.541196i	0.722805	−	0.0530686i
$105$		0			0
$106$	7.82843	−	4.77844i	0.760364	−	0.464123i
$107$	6.16203	−	3.55765i	0.595706	−	0.343931i	−0.171645	−	0.985159i	$-0.554908\pi$
$107$	6.16203	−	3.55765i	0.595706	−	0.343931i	0.767350	+	0.641228i	$0.221575\pi$
$108$	4.17192	+	6.47370i	0.401443	+	0.622932i
$109$	−2.82843	+	4.89898i	−0.270914	+	0.469237i	−0.969096	−	0.246683i	$-0.920659\pi$
$109$	−2.82843	+	4.89898i	−0.270914	+	0.469237i	0.698182	+	0.715920i	$0.253993\pi$
$110$	−2.80083	−	1.52708i	−0.267049	−	0.145601i
$111$	−10.8916			−1.03379
$112$		0			0
$113$	4.24264			0.399114			0.199557	−	0.979886i	$-0.436050\pi$
$113$	4.24264			0.399114			0.199557	+	0.979886i	$0.436050\pi$
$114$	−3.81320	−	2.07905i	−0.357139	−	0.194721i
$115$	3.85077	−	6.66973i	0.359086	−	0.621955i
$116$	−1.26928	−	1.96958i	−0.117850	−	0.182871i
$117$	−9.98951	+	5.76745i	−0.923531	+	0.533201i
$118$	−10.6580	+	6.50562i	−0.981151	+	0.598891i
$119$		0			0
$120$	−8.31371	+	0.610396i	−0.758934	+	0.0557213i
$121$	−3.32843	−	5.76500i	−0.302584	−	0.524091i
$122$	−18.4721	+	0.451356i	−1.67238	+	0.0408638i
$123$	13.0716	+	7.54691i	1.17863	+	0.680482i
$124$	15.3847	−	0.752284i	1.38159	−	0.0675571i
$125$			9.55582i			0.854699i
$126$		0			0
$127$			11.2833i			1.00123i	0.865669	+	0.500617i	$0.166894\pi$
$127$			11.2833i			1.00123i	−0.865669	+	0.500617i	$0.833106\pi$
$128$	−10.6177	−	3.90697i	−0.938481	−	0.345331i
$129$	18.8142	+	10.8624i	1.65650	+	0.956380i
$130$	−0.0977088	−	3.99881i	−0.00856963	−	0.350719i
$131$	7.93513	+	13.7440i	0.693295	+	1.20082i	0.970752	+	0.240085i	$0.0771752\pi$
$131$	7.93513	+	13.7440i	0.693295	+	1.20082i	−0.277457	+	0.960738i	$0.589491\pi$
$132$	10.0941	+	5.18779i	0.878579	+	0.451539i
$133$		0			0
$134$	−7.41421	−	12.1466i	−0.640490	−	1.04930i
$135$	3.60963	−	2.08402i	0.310668	−	0.179364i
$136$	−5.49161	+	11.3595i	−0.470901	+	0.974069i
$137$	−0.121320	+	0.210133i	−0.0103651	+	0.0179529i	−0.871161	−	0.490997i	$-0.836633\pi$
$137$	−0.121320	+	0.210133i	−0.0103651	+	0.0179529i	0.860796	+	0.508950i	$0.169966\pi$
$138$	−13.1160	+	24.0561i	−1.11651	+	2.04779i
$139$	−1.78855			−0.151703			−0.0758515	−	0.997119i	$-0.524167\pi$
$139$	−1.78855			−0.151703			−0.0758515	+	0.997119i	$0.524167\pi$
$140$		0			0
$141$	−14.8284			−1.24878
$142$		0			0
$143$	−2.72291	+	4.71621i	−0.227701	+	0.394389i
$144$	17.5726	−	1.72266i	1.46438	−	0.143555i
$145$	−1.09821	+	0.634051i	−0.0912012	+	0.0526550i
$146$	−5.87291	−	9.62148i	−0.486045	−	0.796279i
$147$		0			0
$148$	−3.65685	+	7.11529i	−0.300592	+	0.584874i
$149$	0.414214	+	0.717439i	0.0339337	+	0.0587749i	0.882493	−	0.470325i	$-0.155863\pi$
$149$	0.414214	+	0.717439i	0.0339337	+	0.0587749i	−0.848560	+	0.529099i	$0.822530\pi$
$150$	−0.360115	−	14.7380i	−0.0294033	−	1.20335i
$151$	−4.66687	−	2.69442i	−0.379784	−	0.219269i	0.297940	−	0.954585i	$-0.403700\pi$
$151$	−4.66687	−	2.69442i	−0.379784	−	0.219269i	−0.677724	+	0.735316i	$0.737034\pi$
$152$	−2.63848	+	1.79305i	−0.214009	+	0.145436i
$153$		−	19.6913i		−	1.59195i
$154$		0			0
$155$		−	8.33609i		−	0.669571i
$156$	0.695020	+	14.2136i	0.0556461	+	1.13800i
$157$	−17.4885	−	10.0970i	−1.39574	−	0.805830i	−0.401795	−	0.915730i	$-0.631614\pi$
$157$	−17.4885	−	10.0970i	−1.39574	−	0.805830i	−0.993943	+	0.109900i	$0.964947\pi$
$158$	−5.89274	+	0.143986i	−0.468802	+	0.0114549i
$159$	8.82940	+	15.2930i	0.700217	+	1.21281i
$160$	−2.39256	+	5.63613i	−0.189149	+	0.445575i
$161$		0			0
$162$	3.32843	−	2.03166i	0.261506	−	0.159622i
$163$	3.29997	−	1.90524i	0.258474	−	0.149230i	−0.365164	−	0.930943i	$-0.618987\pi$
$163$	3.29997	−	1.90524i	0.258474	−	0.149230i	0.623638	+	0.781713i	$0.285654\pi$
$164$	9.31905	−	6.00558i	0.727695	−	0.468957i
$165$	3.07107	−	5.31925i	0.239082	−	0.414103i
$166$	−5.36139	−	2.92316i	−0.416124	−	0.226881i
$167$	20.8489			1.61334			0.806668	−	0.591005i	$-0.201269\pi$
$167$	20.8489			1.61334			0.806668	+	0.591005i	$0.201269\pi$
$168$		0			0
$169$	6.17157			0.474736
$170$	5.99523	+	3.26874i	0.459813	+	0.250701i
$171$	2.48932	−	4.31162i	0.190363	−	0.329718i
$172$	13.4130	−	8.64393i	1.02274	−	0.659094i
$173$	18.2651	−	10.5454i	1.38867	−	0.801749i	0.395504	−	0.918464i	$-0.370570\pi$
$173$	18.2651	−	10.5454i	1.38867	−	0.801749i	0.993165	+	0.116715i	$0.0372365\pi$
$174$	3.85077	−	2.35049i	0.291926	−	0.178190i
$175$		0			0
$176$	6.77817	−	4.85249i	0.510924	−	0.365770i
$177$	−12.0208	−	20.8207i	−0.903540	−	1.56498i
$178$	5.67290	−	0.138614i	0.425202	−	0.0103896i
$179$	1.05724	+	0.610396i	0.0790216	+	0.0456231i	0.538990	−	0.842312i	$-0.318806\pi$
$179$	1.05724	+	0.610396i	0.0790216	+	0.0456231i	−0.459969	+	0.887935i	$0.652139\pi$
$180$	−0.466705	−	9.54442i	−0.0347861	−	0.711399i
$181$		−	6.04601i		−	0.449397i	−0.974428	−	0.224698i	$-0.927860\pi$
$181$		−	6.04601i		−	0.449397i	0.974428	−	0.224698i	$-0.0721396\pi$
$182$		0			0
$183$		−	35.5765i		−	2.62989i
$184$	11.3117	+	16.6452i	0.833912	+	1.22710i
$185$	3.74952	+	2.16478i	0.275670	+	0.159158i
$186$	0.724434	+	29.6480i	0.0531181	+	2.17390i
$187$	−4.64829	−	8.05107i	−0.339917	−	0.588753i
$188$	−4.97863	+	9.68714i	−0.363104	+	0.706507i
$189$		0			0
$190$	0.899495	+	1.47363i	0.0652562	+	0.106908i
$191$	−17.4288	+	10.0625i	−1.26111	+	0.728100i	−0.973289	−	0.229585i	$-0.926263\pi$
$191$	−17.4288	+	10.0625i	−1.26111	+	0.728100i	−0.287818	+	0.957685i	$0.592930\pi$
$192$	8.01955	−	20.2533i	0.578761	−	1.46166i
$193$	−8.70711	+	15.0812i	−0.626751	+	1.08557i	0.361448	+	0.932392i	$0.382282\pi$
$193$	−8.70711	+	15.0812i	−0.626751	+	1.08557i	−0.988199	+	0.153173i	$0.951051\pi$
$194$	2.59069	−	4.75160i	0.186000	−	0.341145i
$195$	7.70154			0.551519
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−6.22774	+	11.4223i	−0.442586	+	0.811751i
$199$	−10.8916	+	18.8648i	−0.772087	+	1.33729i	0.164331	+	0.986405i	$0.447454\pi$
$199$	−10.8916	+	18.8648i	−0.772087	+	1.33729i	−0.936417	+	0.350888i	$0.885880\pi$
$200$	−9.74897	−	4.71301i	−0.689356	−	0.333260i
$201$	23.7285	−	13.6997i	1.67368	−	0.966301i
$202$	−0.136833	−	0.224171i	−0.00962753	−	0.0157726i
$203$		0			0
$204$	−21.6066	−	11.1046i	−1.51276	−	0.777474i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	−0.532104	−	21.7767i	−0.0370734	−	1.51726i
$207$	−27.2005	−	15.7042i	−1.89057	−	1.09152i
$208$	9.51884	+	4.31817i	0.660013	+	0.299411i
$209$		−	2.35049i		−	0.162587i
$210$		0			0
$211$			15.9570i			1.09853i	0.835649	+	0.549264i	$0.185092\pi$
$211$			15.9570i			1.09853i	−0.835649	+	0.549264i	$0.814908\pi$
$212$	12.9551	−	0.633480i	0.889759	−	0.0435076i
$213$		0			0
$214$	10.0595	−	0.245800i	0.687656	−	0.0168025i
$215$	−4.31795	−	7.47890i	−0.294481	−	0.510057i
$216$	0.797521	+	10.8624i	0.0542644	+	0.739092i
$217$		0			0
$218$	−6.82843	+	4.16804i	−0.462479	+	0.282295i
$219$	18.7957	−	10.8517i	1.27010	−	0.733291i
$220$	−2.44386	−	3.79220i	−0.164765	−	0.255670i
$221$	5.82843	−	10.0951i	0.392062	−	0.679072i
$222$	−13.5236	−	7.37340i	−0.907645	−	0.494870i
$223$	20.8489			1.39614			0.698072	−	0.716027i	$-0.254041\pi$
$223$	20.8489			1.39614			0.698072	+	0.716027i	$0.254041\pi$
$224$		0			0
$225$	16.8995			1.12663
$226$	5.26788	+	2.87218i	0.350414	+	0.191054i
$227$	9.06299	−	15.6976i	0.601532	−	1.04188i	−0.391057	−	0.920366i	$-0.627891\pi$
$227$	9.06299	−	15.6976i	0.601532	−	1.04188i	0.992589	−	0.121518i	$-0.0387761\pi$
$228$	−3.32719	−	5.16291i	−0.220349	−	0.341922i
$229$	−16.3903	+	9.46297i	−1.08310	+	0.625330i	−0.931732	−	0.363146i	$-0.881702\pi$
$229$	−16.3903	+	9.46297i	−1.08310	+	0.625330i	−0.151372	+	0.988477i	$0.548369\pi$
$230$	9.29658	−	5.67459i	0.612998	−	0.374172i
$231$		0			0
$232$	−0.242641	−	3.30481i	−0.0159301	−	0.216972i
$233$	−3.87868	−	6.71807i	−0.254101	−	0.440115i	0.710550	−	0.703647i	$-0.248446\pi$
$233$	−3.87868	−	6.71807i	−0.254101	−	0.440115i	−0.964651	+	0.263531i	$0.915113\pi$
$234$	−16.3079	+	0.398476i	−1.06608	+	0.0260492i
$235$	5.10479	+	2.94725i	0.333000	+	0.192257i
$236$	−17.6377	+	0.862453i	−1.14812	+	0.0561409i
$237$		−	11.3492i		−	0.737209i
$238$		0			0
$239$			11.2833i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$239$			11.2833i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$240$	−10.7360	−	4.87030i	−0.693003	−	0.314377i
$241$	7.45193	+	4.30237i	0.480021	+	0.277140i	0.720425	−	0.693533i	$-0.243947\pi$
$241$	7.45193	+	4.30237i	0.480021	+	0.277140i	−0.240404	+	0.970673i	$0.577280\pi$
$242$	−0.229963	−	9.41140i	−0.0147826	−	0.604988i
$243$	9.53017	+	16.5067i	0.611361	+	1.05891i
$244$	−23.2415	−	11.9448i	−1.48788	−	0.764686i
$245$		0			0
$246$	11.1213	+	18.2199i	0.709069	+	1.16166i
$247$	2.55239	−	1.47363i	0.162405	−	0.0937646i
$248$	19.6117	+	9.48104i	1.24535	+	0.602046i
$249$	5.87868	−	10.1822i	0.372546	−	0.645269i
$250$	−6.46909	+	11.8650i	−0.409141	+	0.750409i
$251$	−10.4244			−0.657985			−0.328993	−	0.944333i	$-0.606709\pi$
$251$	−10.4244			−0.657985			−0.328993	+	0.944333i	$0.606709\pi$
$252$		0			0
$253$	−14.8284			−0.932255
$254$	−7.63858	+	14.0100i	−0.479287	+	0.879064i
$255$	−6.57368	+	11.3859i	−0.411659	+	0.713015i
$256$	−10.5386	−	12.0391i	−0.658659	−	0.752441i
$257$	−8.16186	+	4.71225i	−0.509123	+	0.293942i	−0.732473	−	0.680796i	$-0.761634\pi$
$257$	−8.16186	+	4.71225i	−0.509123	+	0.293942i	0.223350	+	0.974738i	$0.428301\pi$
$258$	16.0071	+	26.2241i	0.996558	+	1.63264i
$259$		0			0
$260$	2.58579	−	5.03127i	0.160364	−	0.312026i
$261$	2.58579	+	4.47871i	0.160056	+	0.277225i
$262$	0.548242	+	22.4372i	0.0338705	+	1.38618i
$263$	18.9240	+	10.9258i	1.16690	+	0.673712i	0.952949	−	0.303131i	$-0.0980321\pi$
$263$	18.9240	+	10.9258i	1.16690	+	0.673712i	0.213955	+	0.976844i	$0.431365\pi$
$264$	9.02134	+	13.2749i	0.555225	+	0.817015i
$265$		−	7.01962i		−	0.431212i
$266$		0			0
$267$			10.9258i			0.668647i
$268$	−0.982906	−	20.1011i	−0.0600405	−	1.22787i
$269$	15.0647	+	8.69760i	0.918510	+	0.530302i	0.883159	−	0.469073i	$-0.155412\pi$
$269$	15.0647	+	8.69760i	0.918510	+	0.530302i	0.0353506	+	0.999375i	$0.488745\pi$
$270$	5.89274	−	0.143986i	0.358621	−	0.00876272i
$271$	2.72291	+	4.71621i	0.165405	+	0.286489i	0.936799	−	0.349868i	$-0.113774\pi$
$271$	2.72291	+	4.71621i	0.165405	+	0.286489i	−0.771394	+	0.636358i	$0.780440\pi$
$272$	−14.5088	+	10.3868i	−0.879725	+	0.629795i
$273$		0			0
$274$	−0.292893	+	0.178781i	−0.0176943	+	0.0108005i
$275$	6.90960	−	3.98926i	0.416665	−	0.240562i
$276$	−32.5709	+	20.9901i	−1.96054	+	1.26345i
$277$	−12.0711	+	20.9077i	−0.725280	+	1.25622i	0.233578	+	0.972338i	$0.424956\pi$
$277$	−12.0711	+	20.9077i	−0.725280	+	1.25622i	−0.958859	+	0.283884i	$0.908377\pi$
$278$	−2.22076	−	1.21081i	−0.133192	−	0.0726197i
$279$	−33.9962			−2.03530
$280$		0			0
$281$	−26.3848			−1.57398			−0.786992	−	0.616963i	$-0.788363\pi$
$281$	−26.3848			−1.57398			−0.786992	+	0.616963i	$0.788363\pi$
$282$	−18.4117	−	10.0385i	−1.09640	−	0.597786i
$283$	6.00974	−	10.4092i	0.357242	−	0.618762i	−0.630257	−	0.776387i	$-0.717050\pi$
$283$	6.00974	−	10.4092i	0.357242	−	0.618762i	0.987499	+	0.157625i	$0.0503838\pi$
$284$		0			0
$285$	−2.87875	+	1.66205i	−0.170523	+	0.0984513i
$286$	−6.57368	+	4.01254i	−0.388710	+	0.237267i
$287$		0			0
$288$	22.9853	+	9.75735i	1.35442	+	0.574957i
$289$	1.44975	+	2.51104i	0.0852793	+	0.147708i
$290$	−1.79283	+	0.0438069i	−0.105279	+	0.00257243i
$291$	9.02408	+	5.21005i	0.529001	+	0.305419i
$292$	−0.778575	−	15.9224i	−0.0455626	−	0.931786i
$293$			23.2555i			1.35860i	0.733860	+	0.679300i	$0.237717\pi$
$293$			23.2555i			1.35860i	−0.733860	+	0.679300i	$0.762283\pi$
$294$		0			0
$295$			9.55688i			0.556423i
$296$	−9.35744	+	6.35911i	−0.543890	+	0.369616i
$297$	−6.94993	−	4.01254i	−0.403276	−	0.232831i
$298$	0.0286182	+	1.17122i	0.00165781	+	0.0678471i
$299$	−9.29658	−	16.1021i	−0.537635	−	0.931211i
$300$	9.53017	−	18.5432i	0.550225	−	1.07059i
$301$		0			0
$302$	−3.97056	−	6.50490i	−0.228480	−	0.374315i
$303$	0.437922	−	0.252834i	0.0251579	−	0.0145249i
$304$	−4.48993	+	0.440152i	−0.257515	+	0.0252444i
$305$	−7.07107	+	12.2474i	−0.404888	+	0.701287i
$306$	13.3306	−	24.4497i	0.762059	−	1.39770i
$307$	−10.4244			−0.594954			−0.297477	−	0.954729i	$-0.596145\pi$
$307$	−10.4244			−0.594954			−0.297477	+	0.954729i	$0.596145\pi$
$308$		0			0
$309$	41.9411			2.38595
$310$	5.64335	−	10.3505i	0.320521	−	0.587870i
$311$	−2.25573	+	3.90704i	−0.127911	+	0.221548i	−0.922867	−	0.385119i	$-0.874160\pi$
$311$	−2.25573	+	3.90704i	−0.127911	+	0.221548i	0.794956	+	0.606667i	$0.207494\pi$
$312$	−8.75934	+	18.1189i	−0.495900	+	1.02578i
$313$	8.55014	−	4.93642i	0.483282	−	0.279023i	−0.238501	−	0.971142i	$-0.576656\pi$
$313$	8.55014	−	4.93642i	0.483282	−	0.279023i	0.721783	+	0.692119i	$0.243323\pi$
$314$	−14.8792	−	24.3764i	−0.839683	−	1.37564i
$315$		0			0
$316$	−7.41421	−	3.81048i	−0.417082	−	0.214356i
$317$	11.2426	+	19.4728i	0.631450	+	1.09370i	0.987256	+	0.159143i	$0.0508731\pi$
$317$	11.2426	+	19.4728i	0.631450	+	1.09370i	−0.355806	+	0.934560i	$0.615794\pi$
$318$	0.610028	+	24.9659i	0.0342087	+	1.40002i
$319$	2.11447	+	1.22079i	0.118388	+	0.0683512i
$320$	−6.78627	+	5.37840i	−0.379364	+	0.300662i
$321$			19.3743i			1.08137i
$322$		0			0
$323$			5.03127i			0.279948i
$324$	5.50814	−	0.269338i	0.306008	−	0.0149632i
$325$	8.66386	+	5.00208i	0.480584	+	0.277466i
$326$	5.38723	−	0.131634i	0.298371	−	0.00729054i
$327$	−7.70154	−	13.3395i	−0.425896	−	0.737674i
$328$	15.6367	−	1.14805i	0.863391	−	0.0633905i
$329$		0			0
$330$	7.41421	−	4.52560i	0.408139	−	0.249126i
$331$	3.29997	−	1.90524i	0.181383	−	0.104722i	−0.406559	−	0.913624i	$-0.633272\pi$
$331$	3.29997	−	1.90524i	0.181383	−	0.104722i	0.587942	+	0.808903i	$0.299938\pi$
$332$	−4.67806	−	7.25909i	−0.256742	−	0.398394i
$333$	8.82843	−	15.2913i	0.483795	−	0.837957i
$334$	25.8871	+	14.1143i	1.41648	+	0.772298i
$335$	−10.8916			−0.595073
$336$		0			0
$337$	5.17157			0.281714			0.140857	−	0.990030i	$-0.455014\pi$
$337$	5.17157			0.281714			0.140857	+	0.990030i	$0.455014\pi$
$338$	7.66295	+	4.17802i	0.416809	+	0.227255i
$339$	−5.77615	+	10.0046i	−0.313718	+	0.543375i
$340$	5.23112	+	8.11728i	0.283697	+	0.440221i
$341$	−13.8999	+	8.02509i	−0.752720	+	0.434583i
$342$	6.00974	−	3.66832i	0.324970	−	0.198360i
$343$		0			0
$344$	22.5061	−	1.65241i	1.21345	−	0.0890918i
$345$	10.4853	+	18.1610i	0.564509	+	0.977758i
$346$	29.8179	−	0.728585i	1.60302	−	0.0391690i
$347$	−1.80482	−	1.04201i	−0.0968876	−	0.0559381i	0.450773	−	0.892638i	$-0.351148\pi$
$347$	−1.80482	−	1.04201i	−0.0968876	−	0.0559381i	−0.547661	+	0.836700i	$0.684482\pi$
$348$	6.37255	−	0.311606i	0.341605	−	0.0167038i
$349$			5.67459i			0.303754i	0.988399	+	0.151877i	$0.0485318\pi$
$349$			5.67459i			0.303754i	−0.988399	+	0.151877i	$0.951468\pi$
$350$		0			0
$351$		−	10.0625i		−	0.537099i
$352$	11.7012	−	1.43643i	0.623674	−	0.0765618i
$353$	−24.2305	−	13.9895i	−1.28966	−	0.744586i	−0.311068	−	0.950388i	$-0.600687\pi$
$353$	−24.2305	−	13.9895i	−1.28966	−	0.744586i	−0.978594	+	0.205801i	$0.934020\pi$
$354$	−0.830525	−	33.9899i	−0.0441419	−	1.80654i
$355$		0			0
$356$	7.13761	+	3.66832i	0.378292	+	0.194421i
$357$		0			0
$358$	0.899495	+	1.47363i	0.0475398	+	0.0778835i
$359$	−21.4764	+	12.3994i	−1.13348	+	0.654415i	−0.944808	−	0.327625i	$-0.893752\pi$
$359$	−21.4764	+	12.3994i	−1.13348	+	0.654415i	−0.188673	+	0.982040i	$0.560419\pi$
$360$	5.88188	−	12.1668i	0.310002	−	0.641246i
$361$	8.86396	−	15.3528i	0.466524	−	0.808044i
$362$	4.09302	−	7.50704i	0.215124	−	0.394561i
$363$	18.1260			0.951367
$364$		0			0
$365$	−8.62742			−0.451580
$366$	24.0845	−	44.1736i	1.25892	−	2.30899i
$367$	8.16872	−	14.1486i	0.426404	−	0.738553i	−0.570147	−	0.821543i	$-0.693114\pi$
$367$	8.16872	−	14.1486i	0.426404	−	0.738553i	0.996550	+	0.0829903i	$0.0264470\pi$
$368$	2.77676	+	28.3254i	0.144749	+	1.47656i
$369$	−21.1910	+	12.2346i	−1.10316	+	0.636908i
$370$	3.19008	+	5.22625i	0.165844	+	0.271700i
$371$		0			0
$372$	−19.1716	+	37.3029i	−0.994000	+	1.93407i
$373$	−4.07107	−	7.05130i	−0.210792	−	0.365102i	0.741171	−	0.671317i	$-0.234271\pi$
$373$	−4.07107	−	7.05130i	−0.210792	−	0.365102i	−0.951963	+	0.306214i	$0.900938\pi$
$374$	−0.321153	−	13.1434i	−0.0166064	−	0.679630i
$375$	−22.5336	−	13.0098i	−1.16363	−	0.671823i
$376$	−12.7397	+	8.65762i	−0.657001	+	0.446483i
$377$			3.06147i			0.157674i
$378$		0			0
$379$		−	23.9356i		−	1.22949i	−0.788727	−	0.614744i	$-0.789259\pi$
$379$		−	23.9356i		−	1.22949i	0.788727	−	0.614744i	$-0.210741\pi$
$380$	0.119246	+	2.43867i	0.00611722	+	0.125101i
$381$	−26.6073	−	15.3617i	−1.36313	−	0.787005i
$382$	−28.4527	+	0.695227i	−1.45577	+	0.0355709i
$383$	−3.38359	−	5.86055i	−0.172894	−	0.299460i	0.766537	−	0.642200i	$-0.221978\pi$
$383$	−3.38359	−	5.86055i	−0.172894	−	0.299460i	−0.939430	+	0.342740i	$0.888645\pi$
$384$	23.6686	−	19.7185i	1.20783	−	1.00626i
$385$		0			0
$386$	−21.0208	+	12.8310i	−1.06993	+	0.653082i
$387$	−30.5005	+	17.6095i	−1.55043	+	0.895139i
$388$	6.43346	−	4.14599i	0.326609	−	0.210481i
$389$	7.07107	−	12.2474i	0.358517	−	0.620970i	−0.629196	−	0.777247i	$-0.716616\pi$
$389$	7.07107	−	12.2474i	0.358517	−	0.620970i	0.987713	+	0.156276i	$0.0499491\pi$
$390$	9.56263	+	5.21378i	0.484223	+	0.264010i
$391$	31.7405			1.60519
$392$		0			0
$393$	−43.2132			−2.17982
$394$	2.48330	+	1.35396i	0.125107	+	0.0682114i
$395$	−2.25573	+	3.90704i	−0.113498	+	0.196584i
$396$	−15.4654	+	9.96654i	−0.777164	+	0.500837i
$397$	11.0877	−	6.40150i	0.556477	−	0.321282i	−0.195253	−	0.980753i	$-0.562553\pi$
$397$	11.0877	−	6.40150i	0.556477	−	0.321282i	0.751730	+	0.659471i	$0.229220\pi$
$398$	−26.2947	+	16.0502i	−1.31803	+	0.804523i
$399$		0			0
$400$	−8.91421	−	12.4518i	−0.445711	−	0.622588i
$401$	3.58579	+	6.21076i	0.179066	+	0.310151i	0.941561	−	0.336843i	$-0.109359\pi$
$401$	3.58579	+	6.21076i	0.179066	+	0.310151i	−0.762495	+	0.646994i	$0.776026\pi$
$402$	38.7370	−	0.946519i	1.93203	−	0.0472081i
$403$	−17.4288	−	10.0625i	−0.868192	−	0.501251i
$404$	−0.0181400	−	0.370975i	−0.000902499	−	0.0184567i
$405$		−	2.98454i		−	0.148303i
$406$		0			0
$407$		−	8.33609i		−	0.413204i
$408$	−19.3103	−	28.4152i	−0.956004	−	1.40676i
$409$	−6.28710	−	3.62986i	−0.310877	−	0.179485i	0.336442	−	0.941704i	$-0.390776\pi$
$409$	−6.28710	−	3.62986i	−0.310877	−	0.179485i	−0.647319	+	0.762219i	$0.724110\pi$
$410$	−0.207272	−	8.48275i	−0.0102364	−	0.418933i
$411$	−0.330344	−	0.572172i	−0.0162947	−	0.0282232i
$412$	14.0817	−	27.3994i	0.693756	−	1.34987i
$413$		0			0
$414$	−23.1421	−	37.9133i	−1.13737	−	1.86334i
$415$	−4.04755	+	2.33686i	−0.198687	+	0.114712i
$416$	8.89578	+	11.8057i	0.436151	+	0.578823i
$417$	2.43503	−	4.21759i	0.119244	−	0.206536i
$418$	1.59123	−	2.91850i	0.0778298	−	0.142748i
$419$	−16.5309			−0.807589			−0.403795	−	0.914850i	$-0.632309\pi$
$419$	−16.5309			−0.807589			−0.403795	+	0.914850i	$0.632309\pi$
$420$		0			0
$421$	6.48528			0.316073			0.158037	−	0.987433i	$-0.449484\pi$
$421$	6.48528			0.316073			0.158037	+	0.987433i	$0.449484\pi$
$422$	−10.8026	+	19.8131i	−0.525861	+	0.964487i
$423$	12.0195	−	20.8184i	0.584407	−	1.01222i
$424$	16.5146	+	7.98375i	0.802018	+	0.387725i
$425$	−14.7901	+	8.53909i	−0.717427	+	0.414207i
$426$		0			0
$427$		0			0
$428$	12.6569	+	6.50490i	0.611792	+	0.314426i
$429$	−7.41421	−	12.8418i	−0.357962	−	0.620008i
$430$	−0.298329	−	12.2094i	−0.0143867	−	0.588787i
$431$	14.8764	+	8.58892i	0.716573	+	0.413714i	0.813490	−	0.581579i	$-0.197565\pi$
$431$	14.8764	+	8.58892i	0.716573	+	0.413714i	−0.0969169	+	0.995292i	$0.530898\pi$
$432$	−6.36336	+	14.0272i	−0.306157	+	0.674884i
$433$			15.1760i			0.729313i	0.931142	+	0.364657i	$0.118814\pi$
$433$			15.1760i			0.729313i	−0.931142	+	0.364657i	$0.881186\pi$
$434$		0			0
$435$		−	3.45292i		−	0.165555i
$436$	−11.3002	+	0.552560i	−0.541182	+	0.0264628i
$437$	6.94993	+	4.01254i	0.332460	+	0.191946i
$438$	30.6841	−	0.749752i	1.46615	−	0.0358245i
$439$	8.82940	+	15.2930i	0.421404	+	0.729894i	0.996077	−	0.0884894i	$-0.0282040\pi$
$439$	8.82940	+	15.2930i	0.421404	+	0.729894i	−0.574673	+	0.818383i	$0.694871\pi$
$440$	−0.467177	−	6.36304i	−0.0222718	−	0.303346i
$441$		0			0
$442$	14.0711	−	8.58892i	0.669292	−	0.408533i
$443$	−23.1529	+	13.3674i	−1.10003	+	0.635102i	−0.936229	−	0.351391i	$-0.885709\pi$
$443$	−23.1529	+	13.3674i	−1.10003	+	0.635102i	−0.163801	+	0.986493i	$0.552375\pi$
$444$	−11.8000	−	18.3104i	−0.560002	−	0.868972i
$445$	2.17157	−	3.76127i	0.102942	−	0.178302i
$446$	25.8871	+	14.1143i	1.22579	+	0.668329i
$447$	−2.25573			−0.106692
$448$		0			0
$449$	40.2843			1.90113			0.950566	−	0.310522i	$-0.100504\pi$
$449$	40.2843			1.90113			0.950566	+	0.310522i	$0.100504\pi$
$450$	20.9833	+	11.4406i	0.989162	+	0.539315i
$451$	−5.77615	+	10.0046i	−0.271988	+	0.471098i
$452$	4.59648	+	7.13249i	0.216200	+	0.335484i
$453$	12.7074	−	7.33664i	0.597048	−	0.344706i
$454$	21.8800	−	13.3555i	1.02688	−	0.626803i
$455$		0			0
$456$	−0.636039	−	8.66297i	−0.0297853	−	0.405681i
$457$	12.3640	+	21.4150i	0.578362	+	1.00175i	0.995667	+	0.0929857i	$0.0296411\pi$
$457$	12.3640	+	21.4150i	0.578362	+	1.00175i	−0.417306	+	0.908766i	$0.637026\pi$
$458$	−26.7573	+	0.653802i	−1.25029	+	0.0305501i
$459$	14.8764	+	8.58892i	0.694373	+	0.400896i
$460$	15.3847	−	0.752284i	0.717315	−	0.0350754i
$461$		−	27.4763i		−	1.27970i	−0.768501	−	0.639849i	$-0.778997\pi$
$461$		−	27.4763i		−	1.27970i	0.768501	−	0.639849i	$-0.221003\pi$
$462$		0			0
$463$		−	6.60963i		−	0.307175i	−0.988135	−	0.153588i	$-0.950917\pi$
$463$		−	6.60963i		−	0.307175i	0.988135	−	0.153588i	$-0.0490828\pi$
$464$	1.93601	−	4.26769i	0.0898771	−	0.198123i
$465$	19.6574	+	11.3492i	0.911589	+	0.526306i
$466$	−0.267980	−	10.9673i	−0.0124139	−	0.508050i
$467$	−3.75401	−	6.50214i	−0.173715	−	0.300883i	0.766001	−	0.642840i	$-0.222244\pi$
$467$	−3.75401	−	6.50214i	−0.173715	−	0.300883i	−0.939716	+	0.341956i	$0.888911\pi$
$468$	−20.5185	−	10.5454i	−0.948470	−	0.487459i
$469$		0			0
$470$	4.34315	+	7.11529i	0.200334	+	0.328204i
$471$	47.6197	−	27.4932i	2.19420	−	1.26682i
$472$	−22.4838	−	10.8695i	−1.03490	−	0.500309i
$473$	−8.31371	+	14.3998i	−0.382265	+	0.662102i
$474$	7.68316	−	14.0917i	0.352899	−	0.647255i
$475$	−4.31795			−0.198121
$476$		0			0
$477$	−28.6274			−1.31076
$478$	−7.63858	+	14.0100i	−0.349380	+	0.640802i
$479$	9.95727	−	17.2465i	0.454959	−	0.788012i	−0.543727	−	0.839262i	$-0.682987\pi$
$479$	9.95727	−	17.2465i	0.454959	−	0.788012i	0.998686	+	0.0512499i	$0.0163205\pi$
$480$	−10.0332	−	13.3152i	−0.457952	−	0.607755i
$481$	9.05213	−	5.22625i	0.412742	−	0.238297i
$482$	6.34009	+	10.3868i	0.288783	+	0.473108i
$483$		0			0
$484$	6.08579	−	11.8414i	0.276627	−	0.538244i
$485$	−2.07107	−	3.58719i	−0.0940423	−	0.162886i
$486$	0.658445	+	26.9473i	0.0298677	+	1.22236i
$487$	34.4198	+	19.8723i	1.55971	+	0.900498i	0.997284	+	0.0736490i	$0.0234644\pi$
$487$	34.4198	+	19.8723i	1.55971	+	0.900498i	0.562424	+	0.826849i	$0.309869\pi$
$488$	−20.7714	−	30.5652i	−0.940279	−	1.38362i
$489$			10.3756i			0.469200i
$490$		0			0
$491$		−	15.9570i		−	0.720132i	−0.932927	−	0.360066i	$-0.882754\pi$
$491$		−	15.9570i		−	0.720132i	0.932927	−	0.360066i	$-0.117246\pi$
$492$	1.47436	+	30.1516i	0.0664692	+	1.35934i
$493$	−4.52607	−	2.61313i	−0.203844	−	0.117689i
$494$	4.16680	−	0.101814i	0.187473	−	0.00458081i
$495$	4.97863	+	8.62325i	0.223773	+	0.387586i
$496$	17.9325	+	25.0489i	0.805192	+	1.12473i
$497$		0			0
$498$	14.1924	−	8.66297i	0.635976	−	0.388197i
$499$	15.9337	−	9.19932i	0.713290	−	0.411818i	−0.0989883	−	0.995089i	$-0.531561\pi$
$499$	15.9337	−	9.19932i	0.713290	−	0.411818i	0.812278	+	0.583271i	$0.198227\pi$
$500$	−16.0647	+	10.3528i	−0.718436	+	0.462990i
$501$	−28.3848	+	49.1639i	−1.26814	+	2.19648i
$502$	−12.9435	−	7.05713i	−0.577698	−	0.314975i
$503$	−20.8489			−0.929606			−0.464803	−	0.885414i	$-0.653875\pi$
$503$	−20.8489			−0.929606			−0.464803	+	0.885414i	$0.653875\pi$
$504$		0			0
$505$	−0.201010			−0.00894483
$506$	−18.4117	−	10.0385i	−0.818502	−	0.446267i
$507$	−8.40230	+	14.5532i	−0.373159	+	0.646331i
$508$	−18.9689	+	12.2244i	−0.841610	+	0.542368i
$509$	18.2651	−	10.5454i	0.809586	−	0.467415i	−0.0372260	−	0.999307i	$-0.511852\pi$
$509$	18.2651	−	10.5454i	0.809586	−	0.467415i	0.846812	+	0.531892i	$0.178519\pi$
$510$	−15.8703	+	9.68714i	−0.702747	+	0.428954i
$511$		0			0
$512$	−4.93503	−	22.0827i	−0.218100	−	0.975927i
$513$	2.17157	+	3.76127i	0.0958773	+	0.166064i
$514$	−13.3243	+	0.325572i	−0.587709	+	0.0143604i
$515$	−14.4385	−	8.33609i	−0.636237	−	0.367332i
$516$	2.12207	+	43.3977i	0.0934188	+	1.91048i
$517$		−	11.3492i		−	0.499137i
$518$		0			0
$519$			57.4280i			2.52081i
$520$	6.61671	−	4.49657i	0.290162	−	0.197188i
$521$	−15.5667	−	8.98743i	−0.681989	−	0.393746i	0.118615	−	0.992940i	$-0.462155\pi$
$521$	−15.5667	−	8.98743i	−0.681989	−	0.393746i	−0.800604	+	0.599194i	$0.795488\pi$
$522$	0.178653	+	7.31153i	0.00781945	+	0.320017i
$523$	18.3596	+	31.7997i	0.802808	+	1.39050i	0.917761	+	0.397133i	$0.129995\pi$
$523$	18.3596	+	31.7997i	0.802808	+	1.39050i	−0.114953	+	0.993371i	$0.536672\pi$
$524$	−14.5088	+	28.2304i	−0.633820	+	1.23325i
$525$		0			0
$526$	16.1005	+	26.3772i	0.702015	+	1.15010i
$527$	29.7529	−	17.1778i	1.29606	−	0.748278i
$528$	2.21452	+	22.5901i	0.0963748	+	0.983107i
$529$	13.8137	−	23.9260i	0.600596	−	1.04026i
$530$	4.75213	−	8.71592i	0.206419	−	0.378596i
$531$	38.9749			1.69137
$532$		0			0
$533$	−14.4853			−0.627427
$534$	−7.39652	+	13.5660i	−0.320079	+	0.587059i
$535$	3.85077	−	6.66973i	0.166483	−	0.288358i
$536$	12.3876	−	25.6239i	0.535062	−	1.10679i
$537$	−2.87875	+	1.66205i	−0.124227	+	0.0717227i
$538$	12.8170	+	20.9979i	0.552580	+	0.905282i
$539$		0			0
$540$	7.41421	+	3.81048i	0.319057	+	0.163977i
$541$	−11.3431	−	19.6469i	−0.487680	−	0.844686i	0.512220	−	0.858854i	$-0.328823\pi$
$541$	−11.3431	−	19.6469i	−0.487680	−	0.844686i	−0.999900	+	0.0141680i	$0.995490\pi$
$542$	0.188127	+	7.69924i	0.00808075	+	0.330711i
$543$	14.2571	+	8.23136i	0.611832	+	0.353241i
$544$	−25.0466	+	3.07470i	−1.07386	+	0.131827i
$545$			6.12293i			0.262278i
$546$		0			0
$547$		−	14.5882i		−	0.623744i	−0.950124	−	0.311872i	$-0.899044\pi$
$547$		−	14.5882i		−	0.623744i	0.950124	−	0.311872i	$-0.100956\pi$
$548$	−0.484702	+	0.0237011i	−0.0207055	+	0.00101246i
$549$	49.9476	+	28.8372i	2.13171	+	1.23074i
$550$	11.2800	−	0.275620i	0.480980	−	0.0117525i
$551$	−0.660688	−	1.14434i	−0.0281462	−	0.0487507i
$552$	−54.6516	+	4.01254i	−2.32613	+	0.170785i
$553$		0			0
$554$	−29.1421	+	17.7882i	−1.23813	+	0.755750i
$555$	−10.2096	+	5.89450i	−0.433372	+	0.250208i
$556$	−1.93772	−	3.00681i	−0.0821775	−	0.127517i
$557$	4.17157	−	7.22538i	0.176755	−	0.306149i	−0.764012	−	0.645202i	$-0.776773\pi$
$557$	4.17157	−	7.22538i	0.176755	−	0.306149i	0.940767	+	0.339053i	$0.110107\pi$
$558$	−42.2115	−	23.0147i	−1.78696	−	0.974291i
$559$	−20.8489			−0.881814
$560$		0			0
$561$	25.3137			1.06875
$562$	−32.7607	−	17.8619i	−1.38193	−	0.753460i
$563$	−5.67940	+	9.83701i	−0.239358	+	0.414580i	−0.960530	−	0.278175i	$-0.910270\pi$
$563$	−5.67940	+	9.83701i	−0.239358	+	0.414580i	0.721172	+	0.692756i	$0.243604\pi$
$564$	−16.0651	−	24.9287i	−0.676463	−	1.04969i
$565$	3.97696	−	2.29610i	0.167312	−	0.0965977i
$566$	14.5088	−	8.85611i	0.609850	−	0.372250i
$567$		0			0
$568$		0			0
$569$	−6.58579	−	11.4069i	−0.276091	−	0.478203i	0.694319	−	0.719667i	$-0.255706\pi$
$569$	−6.58579	−	11.4069i	−0.276091	−	0.478203i	−0.970410	+	0.241464i	$0.922372\pi$
$570$	−4.69958	+	0.114832i	−0.196844	+	0.00480978i
$571$	−35.1673	−	20.3039i	−1.47171	−	0.849691i	−0.472213	−	0.881485i	$-0.656545\pi$
$571$	−35.1673	−	20.3039i	−1.47171	−	0.849691i	−0.999494	+	0.0317939i	$0.989878\pi$
$572$	−10.8786	+	0.531945i	−0.454858	+	0.0222417i
$573$		−	54.7987i		−	2.28925i
$574$		0			0
$575$			27.2404i			1.13600i
$576$	21.9342	+	27.6758i	0.913925	+	1.15316i
$577$	33.4435	+	19.3086i	1.39227	+	0.803828i	0.993566	−	0.113251i	$-0.0361265\pi$
$577$	33.4435	+	19.3086i	1.39227	+	0.803828i	0.398705	+	0.917079i	$0.369460\pi$
$578$	0.100164	+	4.09928i	0.00416627	+	0.170508i
$579$	−23.7086	−	41.0645i	−0.985297	−	1.70658i
$580$	−2.25573	−	1.15932i	−0.0936640	−	0.0481380i
$581$		0			0
$582$	7.67767	+	12.5782i	0.318250	+	0.521382i
$583$	−11.7047	+	6.75773i	−0.484761	+	0.279877i
$584$	9.81238	−	20.2971i	0.406039	−	0.839901i
$585$	−6.24264	+	10.8126i	−0.258101	+	0.447045i
$586$	−15.7435	+	28.8752i	−0.650357	+	1.19283i
$587$	1.78855			0.0738214			0.0369107	−	0.999319i	$-0.488248\pi$
$587$	1.78855			0.0738214			0.0369107	+	0.999319i	$0.488248\pi$
$588$		0			0
$589$	8.68629			0.357912
$590$	−6.46980	+	11.8663i	−0.266358	+	0.488529i
$591$	−2.72291	+	4.71621i	−0.112005	+	0.193999i
$592$	−15.9237	+	1.56101i	−0.654459	+	0.0641571i
$593$	−30.3097	+	17.4993i	−1.24467	+	0.718611i	−0.970041	−	0.242939i	$-0.921888\pi$
$593$	−30.3097	+	17.4993i	−1.24467	+	0.718611i	−0.274629	+	0.961550i	$0.588555\pi$
$594$	−5.91299	−	9.68714i	−0.242613	−	0.397468i
$595$		0			0
$596$	−0.757359	+	1.47363i	−0.0310226	+	0.0603621i
$597$	−29.6569	−	51.3672i	−1.21377	−	2.10232i
$598$	−0.642306	−	26.2869i	−0.0262658	−	1.07495i
$599$	−36.3528	−	20.9883i	−1.48534	−	0.857560i	−0.485476	−	0.874250i	$-0.661354\pi$
$599$	−36.3528	−	20.9883i	−1.48534	−	0.857560i	−0.999861	+	0.0166904i	$0.994687\pi$
$600$	24.3865	−	16.5725i	0.995576	−	0.676571i
$601$		−	6.25425i		−	0.255116i	−0.991831	−	0.127558i	$-0.959286\pi$
$601$		−	6.25425i		−	0.255116i	0.991831	−	0.127558i	$-0.0407139\pi$
$602$		0			0
$603$			44.4182i			1.80885i
$604$	−0.526379	−	10.7648i	−0.0214181	−	0.438014i
$605$	−6.24000	−	3.60266i	−0.253692	−	0.146469i
$606$	0.714910	−	0.0174685i	0.0290412	−	0.000709608i
$607$	−7.70154	−	13.3395i	−0.312596	−	0.541432i	0.666328	−	0.745659i	$-0.267865\pi$
$607$	−7.70154	−	13.3395i	−0.312596	−	0.541432i	−0.978924	+	0.204227i	$0.934532\pi$
$608$	−5.87291	−	2.49307i	−0.238178	−	0.101108i
$609$		0			0
$610$	−17.0711	+	10.4201i	−0.691187	+	0.421898i
$611$	12.3241	−	7.11529i	0.498578	−	0.287854i
$612$	33.1039	−	21.3335i	1.33815	−	0.862358i
$613$	15.6569	−	27.1185i	0.632374	−	1.09530i	−0.354691	−	0.934984i	$-0.615414\pi$
$613$	15.6569	−	27.1185i	0.632374	−	1.09530i	0.987065	−	0.160321i	$-0.0512529\pi$
$614$	−12.9435	−	7.05713i	−0.522358	−	0.284802i
$615$	16.3374			0.658789
$616$		0			0
$617$	15.4558			0.622229			0.311114	−	0.950372i	$-0.399298\pi$
$617$	15.4558			0.622229			0.311114	+	0.950372i	$0.399298\pi$
$618$	52.0763	+	28.3932i	2.09482	+	1.14214i
$619$	−22.2103	+	38.4694i	−0.892709	+	1.54622i	−0.0560944	+	0.998425i	$0.517865\pi$
$619$	−22.2103	+	38.4694i	−0.892709	+	1.54622i	−0.836615	+	0.547792i	$0.815469\pi$
$620$	14.0142	−	9.03131i	0.562822	−	0.362706i
$621$	23.7285	−	13.6997i	0.952194	−	0.549749i
$622$	−5.44581	+	3.32410i	−0.218357	+	0.133284i
$623$		0			0
$624$	−23.1421	+	16.5674i	−0.926427	+	0.663229i
$625$	−4.39949	−	7.62015i	−0.175980	−	0.304806i
$626$	13.9581	−	0.341060i	0.557880	−	0.0136315i
$627$	5.54271	+	3.20009i	0.221355	+	0.127799i
$628$	−1.97255	−	40.3399i	−0.0787132	−	1.60974i
$629$			17.8435i			0.711469i
$630$		0			0
$631$		−	22.5667i		−	0.898365i	−0.893440	−	0.449183i	$-0.851715\pi$
$631$		−	22.5667i		−	0.898365i	0.893440	−	0.449183i	$-0.148285\pi$
$632$	−6.62626	−	9.75056i	−0.263578	−	0.387856i
$633$	−37.6284	−	21.7248i	−1.49559	−	0.863482i
$634$	0.776760	+	31.7895i	0.0308491	+	1.26252i
$635$	6.10650	+	10.5768i	0.242329	+	0.419726i
$636$	−16.1439	+	31.4119i	−0.640148	+	1.24556i
$637$		0			0
$638$	1.79899	+	2.94725i	0.0712227	+	0.116683i
$639$		0			0
$640$	−12.0672	+	2.08394i	−0.477000	+	0.0823751i
$641$	0.727922	−	1.26080i	0.0287512	−	0.0497985i	−0.851292	−	0.524693i	$-0.824180\pi$
$641$	0.727922	−	1.26080i	0.0287512	−	0.0497985i	0.880043	+	0.474894i	$0.157514\pi$
$642$	−13.1160	+	24.0561i	−0.517646	+	0.949419i
$643$	−6.84734			−0.270033			−0.135016	−	0.990843i	$-0.543109\pi$
$643$	−6.84734			−0.270033			−0.135016	+	0.990843i	$0.543109\pi$
$644$		0			0
$645$	23.5147			0.925891
$646$	−3.40606	+	6.24709i	−0.134010	+	0.245788i
$647$	−4.78512	+	8.28808i	−0.188123	+	0.325838i	−0.944624	−	0.328154i	$-0.893574\pi$
$647$	−4.78512	+	8.28808i	−0.188123	+	0.325838i	0.756502	+	0.653992i	$0.226907\pi$
$648$	7.02153	+	3.39447i	0.275832	+	0.133347i
$649$	15.9354	−	9.20033i	0.625521	−	0.361145i
$650$	7.37120	+	12.0761i	0.289122	+	0.473663i
$651$		0			0
$652$	6.77817	+	3.48359i	0.265454	+	0.136428i
$653$	−7.89949	−	13.6823i	−0.309131	−	0.535431i	0.669041	−	0.743225i	$-0.266705\pi$
$653$	−7.89949	−	13.6823i	−0.309131	−	0.535431i	−0.978173	+	0.207794i	$0.933372\pi$
$654$	−0.532104	−	21.7767i	−0.0208069	−	0.851538i
$655$	14.8764	+	8.58892i	0.581271	+	0.335597i
$656$	20.1925	+	9.16021i	0.788385	+	0.357646i
$657$			35.1843i			1.37267i
$658$		0			0
$659$		−	30.5452i		−	1.18987i	−0.803773	−	0.594936i	$-0.797177\pi$
$659$		−	30.5452i		−	1.18987i	0.803773	−	0.594936i	$-0.202823\pi$
$660$	12.2696	−	0.599962i	0.477594	−	0.0233535i
$661$	10.8603	+	6.27018i	0.422416	+	0.243882i	0.696110	−	0.717935i	$-0.254912\pi$
$661$	10.8603	+	6.27018i	0.422416	+	0.243882i	−0.273695	+	0.961817i	$0.588246\pi$
$662$	5.38723	−	0.131634i	0.209381	−	0.00511611i
$663$	15.8703	+	27.4881i	0.616350	+	1.06755i
$664$	−0.894276	−	12.1802i	−0.0347046	−	0.472684i
$665$		0			0
$666$	21.3137	−	13.0098i	0.825889	−	0.504119i
$667$	−7.21926	+	4.16804i	−0.279531	+	0.161387i
$668$	22.5877	+	35.0500i	0.873944	+	1.35612i
$669$	−28.3848	+	49.1639i	−1.09742	+	1.90079i
$670$	−13.5236	−	7.37340i	−0.522462	−	0.284859i
$671$	27.2291			1.05117
$672$		0			0
$673$	−26.3848			−1.01706			−0.508529	−	0.861045i	$-0.669811\pi$
$673$	−26.3848			−1.01706			−0.508529	+	0.861045i	$0.669811\pi$
$674$	6.42129	+	3.50104i	0.247339	+	0.134855i
$675$	−7.37120	+	12.7673i	−0.283717	+	0.491413i
$676$	6.68628	+	10.3753i	0.257165	+	0.399050i
$677$	34.7221	−	20.0468i	1.33448	−	0.770461i	0.348495	−	0.937311i	$-0.386693\pi$
$677$	34.7221	−	20.0468i	1.33448	−	0.770461i	0.985982	+	0.166850i	$0.0533596\pi$
$678$	−13.9449	+	8.51189i	−0.535550	+	0.326897i
$679$		0			0
$680$	1.00000	+	13.6202i	0.0383482	+	0.522311i
$681$	24.6777	+	42.7430i	0.945650	+	1.63791i
$682$	−22.6916	+	0.554458i	−0.868906	+	0.0212313i
$683$	−36.3528	−	20.9883i	−1.39100	−	0.803096i	−0.397576	−	0.917569i	$-0.630149\pi$
$683$	−36.3528	−	20.9883i	−1.39100	−	0.803096i	−0.993426	+	0.114473i	$0.963482\pi$
$684$	9.94539	−	0.486311i	0.380271	−	0.0185946i
$685$			0.262632i			0.0100347i
$686$		0			0
$687$		−	51.5335i		−	1.96613i
$688$	29.0634	+	13.1844i	1.10803	+	0.502652i
$689$	−14.6764	−	8.47343i	−0.559127	−	0.322812i
$690$	0.724434	+	29.6480i	0.0275787	+	1.12868i
$691$	−2.48932	−	4.31162i	−0.0946981	−	0.164022i	0.814784	−	0.579764i	$-0.196855\pi$
$691$	−2.48932	−	4.31162i	−0.0946981	−	0.164022i	−0.909483	+	0.415742i	$0.863522\pi$
$692$	37.5167	+	19.2814i	1.42617	+	0.732970i
$693$		0			0
$694$	−1.53553	−	2.51564i	−0.0582881	−	0.0954923i
$695$	−1.67655	+	0.967957i	−0.0635952	+	0.0367167i
$696$	8.12344	+	3.92717i	0.307918	+	0.148859i
$697$	12.3640	−	21.4150i	0.468318	−	0.811151i
$698$	−3.84158	+	7.04587i	−0.145406	+	0.266690i
$699$	21.1226			0.798928
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$	6.81213	−	12.4942i	0.257107	−	0.471562i
$703$	−2.25573	+	3.90704i	−0.0850764	+	0.147357i
$704$	15.5012	+	6.13790i	0.584224	+	0.231331i
$705$	−13.8999	+	8.02509i	−0.523499	+	0.302242i
$706$	−20.6153	−	33.7737i	−0.775867	−	1.27109i
$707$		0			0
$708$	21.9792	−	42.7658i	0.826028	−	1.60724i
$709$	0.686292	+	1.18869i	0.0257742	+	0.0446423i	0.878625	−	0.477513i	$-0.158462\pi$
$709$	0.686292	+	1.18869i	0.0257742	+	0.0446423i	−0.852851	+	0.522155i	$0.825128\pi$
$710$		0			0
$711$	15.9337	+	9.19932i	0.597560	+	0.345001i
$712$	6.37905	+	9.38679i	0.239065	+	0.351785i
$713$		−	54.7987i		−	2.05223i
$714$		0			0
$715$			5.89450i			0.220442i
$716$	0.119246	+	2.43867i	0.00445645	+	0.0911374i
$717$	−26.6073	−	15.3617i	−0.993668	−	0.573694i
$718$	−35.0603	+	0.856682i	−1.30844	+	0.0319711i
$719$	−5.91299	−	10.2416i	−0.220517	−	0.381947i	0.734448	−	0.678665i	$-0.237441\pi$
$719$	−5.91299	−	10.2416i	−0.220517	−	0.381947i	−0.954965	+	0.296718i	$0.904108\pi$
$720$	15.5399	−	11.1250i	0.579138	−	0.414605i
$721$		0			0
$722$	21.3995	−	13.0622i	0.796407	−	0.486123i
$723$	−20.2909	+	11.7150i	−0.754626	+	0.435684i
$724$	10.1642	−	6.55025i	0.377750	−	0.243438i
$725$	2.24264	−	3.88437i	0.0832896	−	0.144262i
$726$	22.5062	+	12.2709i	0.835282	+	0.455416i
$727$	−38.1207			−1.41382			−0.706909	−	0.707305i	$-0.749911\pi$
$727$	−38.1207			−1.41382			−0.706909	+	0.707305i	$0.749911\pi$
$728$		0			0
$729$	−43.6274			−1.61583
$730$	−10.7123	−	5.84058i	−0.396478	−	0.216169i
$731$	17.7956	−	30.8230i	0.658196	−	1.14003i
$732$	59.8092	−	38.5435i	2.21061	−	1.42461i
$733$	−2.03559	+	1.17525i	−0.0751861	+	0.0434087i	−0.537122	−	0.843505i	$-0.680488\pi$
$733$	−2.03559	+	1.17525i	−0.0751861	+	0.0434087i	0.461936	+	0.886913i	$0.347155\pi$
$734$	19.7210	−	12.0376i	0.727916	−	0.444317i
$735$		0			0
$736$	−15.7279	+	37.0501i	−0.579739	+	1.36568i
$737$	10.4853	+	18.1610i	0.386230	+	0.668971i
$738$	−34.5944	+	0.845296i	−1.27344	+	0.0311158i
$739$	45.3769	+	26.1984i	1.66922	+	0.963723i	0.968061	+	0.250715i	$0.0806657\pi$
$739$	45.3769	+	26.1984i	1.66922	+	0.963723i	0.701156	+	0.713008i	$0.252668\pi$
$740$	0.422911	+	8.64880i	0.0155465	+	0.317936i
$741$			8.02509i			0.294809i
$742$		0			0
$743$			17.8930i			0.656429i	0.944603	+	0.328215i	$0.106447\pi$
$743$			17.8930i			0.656429i	−0.944603	+	0.328215i	$0.893553\pi$
$744$	−49.0577	+	33.3385i	−1.79854	+	1.22225i
$745$	0.776550	+	0.448342i	0.0284506	+	0.0164260i
$746$	−0.281272	−	11.5113i	−0.0102981	−	0.421458i
$747$	9.53017	+	16.5067i	0.348691	+	0.603950i
$748$	8.49906	−	16.5370i	0.310756	−	0.604652i
$749$		0			0
$750$	−19.1716	−	31.4084i	−0.700047	−	1.14687i
$751$	11.8861	−	6.86246i	0.433731	−	0.250415i	−0.267204	−	0.963640i	$-0.586100\pi$
$751$	11.8861	−	6.86246i	0.433731	−	0.250415i	0.700935	+	0.713225i	$0.252766\pi$
$752$	−21.6793	+	2.12524i	−0.790564	+	0.0774995i
$753$	14.1924	−	24.5819i	0.517199	−	0.895816i
$754$	−2.07255	+	3.80128i	−0.0754778	+	0.138434i
$755$	−5.83283			−0.212279
$756$		0			0
$757$	12.2843			0.446479			0.223240	−	0.974764i	$-0.428337\pi$
$757$	12.2843			0.446479			0.223240	+	0.974764i	$0.428337\pi$
$758$	16.2039	−	29.7197i	0.588551	−	1.07947i
$759$	20.1882	−	34.9670i	0.732785	−	1.26922i
$760$	−1.50286	+	3.10871i	−0.0545146	+	0.112765i
$761$	−22.5166	+	13.0000i	−0.816227	+	0.471249i	−0.849113	−	0.528210i	$-0.822863\pi$
$761$	−22.5166	+	13.0000i	−0.816227	+	0.471249i	0.0328870	+	0.999459i	$0.489530\pi$
$762$	−22.6374	−	37.0865i	−0.820068	−	1.34350i
$763$		0			0
$764$	−35.7990	−	18.3986i	−1.29516	−	0.665639i
$765$	−10.6569	−	18.4582i	−0.385299	−	0.667358i
$766$	−0.233774	−	9.56739i	−0.00844661	−	0.345684i
$767$	19.9812	+	11.5362i	0.721481	+	0.416547i
$768$	42.7371	−	8.46041i	1.54214	−	0.305289i
$769$			46.1940i			1.66580i	0.553425	+	0.832899i	$0.313320\pi$
$769$			46.1940i			1.66580i	−0.553425	+	0.832899i	$0.686680\pi$
$770$		0			0
$771$		−	25.6620i		−	0.924196i
$772$	−34.7869	+	1.70101i	−1.25201	+	0.0612208i
$773$	45.8764	+	26.4867i	1.65006	+	0.952662i	0.977045	+	0.213032i	$0.0683339\pi$
$773$	45.8764	+	26.4867i	1.65006	+	0.952662i	0.673014	+	0.739630i	$0.264999\pi$
$774$	−49.7922	+	1.21665i	−1.78974	+	0.0437315i
$775$	14.7424	+	25.5346i	0.529562	+	0.917229i
$776$	10.7949	−	0.792563i	0.387513	−	0.0284514i
$777$		0			0
$778$	17.0711	−	10.4201i	0.612027	−	0.373579i
$779$	5.41445	−	3.12603i	0.193993	−	0.112002i
$780$	8.34385	+	12.9474i	0.298758	+	0.463591i
$781$		0			0
$782$	39.4107	+	21.4876i	1.40932	+	0.768397i
$783$	−4.51146			−0.161226
$784$		0			0
$785$	−21.8579			−0.780141
$786$	−53.6558	−	29.2544i	−1.91384	−	1.04347i
$787$	14.6456	−	25.3670i	0.522061	−	0.904235i	−0.477610	−	0.878572i	$-0.658497\pi$
$787$	14.6456	−	25.3670i	0.522061	−	0.904235i	0.999671	−	0.0256635i	$-0.00816983\pi$
$788$	2.16680	+	3.36229i	0.0771890	+	0.119777i
$789$	−51.5283	+	29.7499i	−1.83445	+	1.05912i
$790$	−5.44581	+	3.32410i	−0.193753	+	0.118266i
$791$		0			0
$792$	−25.9497	+	1.90524i	−0.922084	+	0.0676998i
$793$	17.0711	+	29.5680i	0.606211	+	1.04999i
$794$	18.1008	−	0.442283i	0.642372	−	0.0156960i
$795$	16.5530	+	9.55688i	0.587074	+	0.338948i
$796$	−43.5145	+	2.12778i	−1.54233	+	0.0754171i
$797$		−	19.1886i		−	0.679694i	−0.940481	−	0.339847i	$-0.889625\pi$
$797$		−	19.1886i		−	0.679694i	0.940481	−	0.339847i	$-0.110375\pi$
$798$		0			0
$799$			24.2931i			0.859429i
$800$	−2.63877	−	21.4955i	−0.0932947	−	0.759980i
$801$	−15.3392	−	8.85611i	−0.541985	−	0.312915i
$802$	0.247744	+	10.1391i	0.00874814	+	0.358024i
$803$	8.30555	+	14.3856i	0.293096	+	0.507658i
$804$	48.7386	+	25.0489i	1.71888	+	0.883405i
$805$		0			0
$806$	−14.8284	−	24.2931i	−0.522309	−	0.855689i
$807$	−41.0197	+	23.6827i	−1.44396	+	0.833672i
$808$	0.228619	−	0.472902i	0.00804278	−	0.0166366i
$809$	−24.0208	+	41.6053i	−0.844527	+	1.46276i	0.0415045	+	0.999138i	$0.486785\pi$
$809$	−24.0208	+	41.6053i	−0.844527	+	1.46276i	−0.886031	+	0.463625i	$0.846548\pi$
$810$	2.02047	−	3.70577i	0.0709922	−	0.130207i
$811$	−42.4386			−1.49022			−0.745111	−	0.666941i	$-0.767603\pi$
$811$	−42.4386			−1.49022			−0.745111	+	0.666941i	$0.767603\pi$
$812$		0			0
$813$	−14.8284			−0.520056
$814$	5.64335	−	10.3505i	0.197799	−	0.362785i
$815$	2.06222	−	3.57187i	0.0722363	−	0.125117i
$816$	−4.74023	−	48.3545i	−0.165941	−	1.69275i
$817$	7.79310	−	4.49935i	0.272646	−	0.157412i
$818$	−5.34906	−	8.76326i	−0.187025	−	0.306400i
$819$		0			0
$820$	5.48528	−	10.6729i	0.191554	−	0.372715i
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	−0.0228236	−	0.934075i	−0.000796066	−	0.0325796i
$823$	−28.2577	−	16.3146i	−0.985003	−	0.568692i	−0.0812259	−	0.996696i	$-0.525884\pi$
$823$	−28.2577	−	16.3146i	−0.985003	−	0.568692i	−0.903777	+	0.428004i	$0.859217\pi$
$824$	36.0334	−	24.4875i	1.25528	−	0.853061i
$825$			21.7248i			0.756359i
$826$		0			0
$827$			17.8930i			0.622199i	0.950377	+	0.311100i	$0.100697\pi$
$827$			17.8930i			0.622199i	−0.950377	+	0.311100i	$0.899303\pi$
$828$	−3.06796	−	62.7419i	−0.106619	−	2.18043i
$829$	3.68290	+	2.12632i	0.127912	+	0.0738502i	0.562591	−	0.826735i	$-0.309805\pi$
$829$	3.68290	+	2.12632i	0.127912	+	0.0738502i	−0.434678	+	0.900586i	$0.643138\pi$
$830$	−6.60765	+	0.161455i	−0.229355	+	0.00560417i
$831$	−32.8684	−	56.9297i	−1.14019	−	1.97487i
$832$	3.05325	+	20.6808i	0.105852	+	0.716979i
$833$		0			0
$834$	5.87868	−	3.58832i	0.203562	−	0.124253i
$835$	19.5433	−	11.2833i	0.676324	−	0.390476i
$836$	3.95152	−	2.54652i	0.136666	−	0.0880734i
$837$	14.8284	−	25.6836i	0.512545	−	0.887755i
$838$	−20.5257	−	11.1911i	−0.709048	−	0.386590i
$839$	53.9108			1.86121			0.930603	−	0.366029i	$-0.119283\pi$
$839$	53.9108			1.86121			0.930603	+	0.366029i	$0.119283\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$	8.05246	+	4.39040i	0.277506	+	0.151303i
$843$	35.9216	−	62.2181i	1.23721	−	2.14290i
$844$	−26.8261	+	17.2879i	−0.923392	+	0.595073i
$845$	5.78510	−	3.34003i	0.199014	−	0.114901i
$846$	29.0176	−	17.7122i	0.997646	−	0.608959i
$847$		0			0
$848$	15.1005	+	21.0930i	0.518553	+	0.724338i
$849$	16.3640	+	28.3432i	0.561610	+	0.972737i
$850$	−24.1450	+	0.589970i	−0.828166	+	0.0202358i
$851$	24.6481	+	14.2306i	0.844926	+	0.487818i
$852$		0			0
$853$		−	3.61859i		−	0.123898i	−0.998079	−	0.0619492i	$-0.980268\pi$
$853$		−	3.61859i		−	0.123898i	0.998079	−	0.0619492i	$-0.0197317\pi$
$854$		0			0
$855$		−	5.38883i		−	0.184294i
$856$	11.3117	+	16.6452i	0.386627	+	0.568923i
$857$	−34.3809	−	19.8498i	−1.17443	−	0.678057i	−0.219709	−	0.975565i	$-0.570511\pi$
$857$	−34.3809	−	19.8498i	−1.17443	−	0.678057i	−0.954719	+	0.297509i	$0.903844\pi$
$858$	−0.512252	−	20.9643i	−0.0174880	−	0.715710i
$859$	−9.86051	−	17.0789i	−0.336436	−	0.582725i	0.647323	−	0.762216i	$-0.275888\pi$
$859$	−9.86051	−	17.0789i	−0.336436	−	0.582725i	−0.983760	+	0.179491i	$0.942555\pi$
$860$	7.89505	−	15.3617i	0.269219	−	0.523831i
$861$		0			0
$862$	12.6569	+	20.7355i	0.431094	+	0.706254i
$863$	15.9337	−	9.19932i	0.542389	−	0.313148i	−0.203658	−	0.979042i	$-0.565283\pi$
$863$	15.9337	−	9.19932i	0.542389	−	0.313148i	0.746047	+	0.665894i	$0.231950\pi$
$864$	−17.3972	+	13.1090i	−0.591865	+	0.445979i
$865$	11.4142	−	19.7700i	0.388095	−	0.672200i
$866$	−10.2738	+	18.8433i	−0.349119	+	0.640323i
$867$	−7.89505			−0.268130
$868$		0			0
$869$	8.68629			0.294662
$870$	2.33755	−	4.28733i	0.0792505	−	0.145354i
$871$	−13.1474	+	22.7719i	−0.445481	+	0.771596i
$872$	−14.4050	−	6.96391i	−0.487815	−	0.235828i
$873$	−14.6293	+	8.44623i	−0.495127	+	0.285862i
$874$	5.91299	+	9.68714i	0.200010	+	0.327672i
$875$		0			0
$876$	38.6066	+	19.8416i	1.30440	+	0.670385i
$877$	27.2132	+	47.1347i	0.918925	+	1.59162i	0.801052	+	0.598595i	$0.204274\pi$
$877$	27.2132	+	47.1347i	0.918925	+	1.59162i	0.117873	+	0.993029i	$0.462392\pi$
$878$	0.610028	+	24.9659i	0.0205875	+	0.842557i
$879$	−54.8389	−	31.6613i	−1.84967	−	1.06791i
$880$	3.72757	−	8.21695i	0.125656	−	0.276993i
$881$			15.1760i			0.511293i	0.966770	+	0.255647i	$0.0822883\pi$
$881$			15.1760i			0.511293i	−0.966770	+	0.255647i	$0.917712\pi$
$882$		0			0
$883$			4.67371i			0.157283i	0.996903	+	0.0786415i	$0.0250582\pi$
$883$			4.67371i			0.157283i	−0.996903	+	0.0786415i	$0.974942\pi$
$884$	23.2859	−	1.13864i	0.783189	−	0.0382965i
$885$	−22.5361	−	13.0112i	−0.757543	−	0.437368i
$886$	−37.7973	+	0.923558i	−1.26983	+	0.0310275i
$887$	8.82940	+	15.2930i	0.296462	+	0.513488i	0.975324	−	0.220778i	$-0.0708597\pi$
$887$	8.82940	+	15.2930i	0.296462	+	0.513488i	−0.678862	+	0.734266i	$0.737526\pi$
$888$	−2.25573	−	30.7235i	−0.0756973	−	1.03101i
$889$		0			0
$890$	5.24264	−	3.20009i	0.175734	−	0.107267i
$891$	−4.97653	+	2.87320i	−0.166720	+	0.0962558i
$892$	22.5877	+	35.0500i	0.756291	+	1.17356i
$893$	−3.07107	+	5.31925i	−0.102769	+	0.178002i
$894$	−2.80083	−	1.52708i	−0.0936738	−	0.0510732i
$895$	1.32138			0.0441687
$896$		0			0
$897$	50.6274			1.69040
$898$	50.0190	+	27.2716i	1.66916	+	0.910065i
$899$	−4.51146	+	7.81407i	−0.150466	+	0.260614i
$900$	18.3089	+	28.4105i	0.610297	+	0.947016i
$901$	25.0542	−	14.4650i	0.834676	−	0.481901i
$902$	−13.9449	+	8.51189i	−0.464313	+	0.283415i
$903$		0			0
$904$	0.878680	+	11.9678i	0.0292245	+	0.398043i
$905$	−3.27208	−	5.66741i	−0.108768	−	0.188391i
$906$	20.7450	−	0.506893i	0.689205	−	0.0168404i
$907$	20.6006	+	11.8937i	0.684030	+	0.394925i	0.801372	−	0.598167i	$-0.204104\pi$
$907$	20.6006	+	11.8937i	0.684030	+	0.394925i	−0.117342	+	0.993092i	$0.537437\pi$
$908$	36.2087	−	1.77054i	1.20163	−	0.0587574i
$909$			0.819760i			0.0271897i
$910$		0			0
$911$		−	43.1974i		−	1.43119i	−0.698513	−	0.715597i	$-0.746155\pi$
$911$		−	43.1974i		−	1.43119i	0.698513	−	0.715597i	$-0.253845\pi$
$912$	5.07491	−	11.1870i	0.168047	−	0.370438i
$913$	7.79310	+	4.49935i	0.257914	+	0.148907i
$914$	0.854233	+	34.9601i	0.0282555	+	1.15638i
$915$	−19.2538	−	33.3486i	−0.636513	−	1.10247i
$916$	−33.6659	−	17.3023i	−1.11235	−	0.571686i
$917$		0			0
$918$	12.6569	+	20.7355i	0.417738	+	0.684373i
$919$	−42.6963	+	24.6507i	−1.40842	+	0.813151i	−0.995236	−	0.0974962i	$-0.968917\pi$
$919$	−42.6963	+	24.6507i	−1.40842	+	0.813151i	−0.413184	+	0.910648i	$0.635583\pi$
$920$	19.6117	+	9.48104i	0.646579	+	0.312581i
$921$	14.1924	−	24.5819i	0.467655	−	0.810002i
$922$	18.6009	−	34.1160i	0.612587	−	1.12355i
$923$		0			0
$924$		0			0
$925$	−15.3137			−0.503512
$926$	4.47458	−	8.20686i	0.147044	−	0.269694i
$927$	−33.9962	+	58.8832i	−1.11658	+	1.93398i
$928$	5.29299	−	3.98835i	0.173751	−	0.130924i
$929$	−14.4685	+	8.35338i	−0.474695	+	0.274065i	−0.718203	−	0.695833i	$-0.755035\pi$
$929$	−14.4685	+	8.35338i	−0.474695	+	0.274065i	0.243508	+	0.969899i	$0.421702\pi$
$930$	16.7245	+	27.3994i	0.548416	+	0.898460i
$931$		0			0
$932$	7.09188	−	13.7990i	0.232302	−	0.452000i
$933$	−6.14214	−	10.6385i	−0.201084	−	0.348289i
$934$	−0.259367	−	10.6148i	−0.00848675	−	0.347326i
$935$	−8.71442	−	5.03127i	−0.284992	−	0.164540i
$936$	−18.3379	−	26.9843i	−0.599393	−	0.882009i
$937$			53.4762i			1.74699i	0.486831	+	0.873496i	$0.338153\pi$
$937$			53.4762i			1.74699i	−0.486831	+	0.873496i	$0.661847\pi$
$938$		0			0
$939$			26.8828i			0.877288i
$940$	0.575773	+	11.7749i	0.0187796	+	0.384056i
$941$	7.01655	+	4.05101i	0.228733	+	0.132059i	0.609987	−	0.792411i	$-0.291175\pi$
$941$	7.01655	+	4.05101i	0.228733	+	0.132059i	−0.381254	+	0.924470i	$0.624508\pi$
$942$	77.7394	−	1.89952i	2.53289	−	0.0618898i
$943$	−19.7210	−	34.1578i	−0.642205	−	1.11233i
$944$	−20.5586	−	28.7172i	−0.669126	−	0.934665i
$945$		0			0
$946$	−20.0711	+	12.2513i	−0.652567	+	0.398324i
$947$	36.6625	−	21.1671i	1.19137	−	0.687838i	0.232754	−	0.972536i	$-0.425226\pi$
$947$	36.6625	−	21.1671i	1.19137	−	0.687838i	0.958617	+	0.284697i	$0.0918931\pi$
$948$	19.0796	−	12.2957i	0.619677	−	0.399346i
$949$	−10.4142	+	18.0379i	−0.338060	+	0.585537i
$950$	−5.36139	−	2.92316i	−0.173946	−	0.0948398i
$951$	−61.2253			−1.98537
$952$		0			0
$953$	37.6569			1.21983			0.609913	−	0.792469i	$-0.291205\pi$
$953$	37.6569			1.21983			0.609913	+	0.792469i	$0.291205\pi$
$954$	−35.5453	−	19.3802i	−1.15082	−	0.627456i
$955$	−10.8916	+	18.8648i	−0.352445	+	0.610452i
$956$	−18.9689	+	12.2244i	−0.613499	+	0.395364i
$957$	−5.75751	+	3.32410i	−0.186114	+	0.107453i
$958$	24.0390	−	14.6733i	0.776664	−	0.474072i
$959$		0			0
$960$	−3.44365	−	23.3252i	−0.111143	−	0.752817i
$961$	−14.1569	−	24.5204i	−0.456673	−	0.790980i
$962$	14.7777	−	0.361085i	0.476451	−	0.0116418i
$963$	−27.2005	−	15.7042i	−0.876524	−	0.506061i
$964$	0.840508	+	17.1890i	0.0270710	+	0.553619i
$965$			18.8490i			0.606771i
$966$		0			0
$967$			17.8930i			0.575399i	0.957721	+	0.287699i	$0.0928904\pi$
$967$			17.8930i			0.575399i	−0.957721	+	0.287699i	$0.907110\pi$
$968$	15.5728	−	10.5829i	0.500528	−	0.340148i
$969$	−11.8643	−	6.84984i	−0.381135	−	0.220049i
$970$	−0.143091	−	5.85612i	−0.00459438	−	0.188029i
$971$	10.9884	+	19.0324i	0.352634	+	0.610780i	0.986710	−	0.162491i	$-0.0519528\pi$
$971$	10.9884	+	19.0324i	0.352634	+	0.610780i	−0.634076	+	0.773271i	$0.718619\pi$
$972$	−17.4252	+	33.9050i	−0.558914	+	1.08750i
$973$		0			0
$974$	29.2843	+	47.9759i	0.938329	+	1.53725i
$975$	−23.5909	+	13.6202i	−0.755512	+	0.436195i
$976$	−5.09889	−	52.0132i	−0.163212	−	1.66490i
$977$	−27.1924	+	47.0986i	−0.869962	+	1.50682i	−0.00792675	+	0.999969i	$0.502523\pi$
$977$	−27.1924	+	47.0986i	−0.869962	+	1.50682i	−0.862035	+	0.506849i	$0.830810\pi$
$978$	−7.02405	+	12.8829i	−0.224604	+	0.411948i
$979$	−8.36223			−0.267258
$980$		0			0
$981$	24.9706			0.797249
$982$	10.8026	−	19.8131i	0.344724	−	0.632262i
$983$	−16.9981	+	29.4416i	−0.542156	+	0.939041i	0.456624	+	0.889660i	$0.349058\pi$
$983$	−16.9981	+	29.4416i	−0.542156	+	0.939041i	−0.998780	+	0.0493817i	$0.984275\pi$
$984$	−18.5814	+	38.4359i	−0.592352	+	1.22529i
$985$	1.87476	−	1.08239i	0.0597348	−	0.0344879i
$986$	−3.85077	−	6.30864i	−0.122633	−	0.200908i
$987$		0			0
$988$	5.24264	+	2.69442i	0.166791	+	0.0857208i
$989$	−28.3848	−	49.1639i	−0.902583	−	1.56332i
$990$	0.343977	+	14.0775i	0.0109323	+	0.447412i
$991$	18.9240	+	10.9258i	0.601141	+	0.347069i	0.769490	−	0.638659i	$-0.220510\pi$
$991$	18.9240	+	10.9258i	0.601141	+	0.347069i	−0.168350	+	0.985727i	$0.553844\pi$
$992$	5.30834	+	43.2419i	0.168540	+	1.37293i
$993$			10.3756i			0.329259i
$994$		0			0
$995$			23.5780i			0.747473i
$996$	23.4867	−	1.14845i	0.744203	−	0.0363902i
$997$	5.78510	+	3.34003i	0.183216	+	0.105780i	0.588803	−	0.808277i	$-0.299599\pi$
$997$	5.78510	+	3.34003i	0.183216	+	0.105780i	−0.405587	+	0.914057i	$0.632933\pi$
$998$	26.0118	−	0.635586i	0.823390	−	0.0201191i
$999$	7.70154	+	13.3395i	0.243666	+	0.422042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.f.d.31.7		16
4.3	odd	2	inner	196.2.f.d.31.4		16
7.2	even	3	inner	196.2.f.d.19.3		16
7.3	odd	6		196.2.d.c.195.3	yes	8
7.4	even	3		196.2.d.c.195.4	yes	8
7.5	odd	6	inner	196.2.f.d.19.4		16
7.6	odd	2	inner	196.2.f.d.31.8		16
21.11	odd	6		1764.2.b.k.1567.5		8
21.17	even	6		1764.2.b.k.1567.6		8
28.3	even	6		196.2.d.c.195.2	yes	8
28.11	odd	6		196.2.d.c.195.1	✓	8
28.19	even	6	inner	196.2.f.d.19.7		16
28.23	odd	6	inner	196.2.f.d.19.8		16
28.27	even	2	inner	196.2.f.d.31.3		16
56.3	even	6		3136.2.f.i.3135.2		8
56.11	odd	6		3136.2.f.i.3135.7		8
56.45	odd	6		3136.2.f.i.3135.8		8
56.53	even	6		3136.2.f.i.3135.1		8
84.11	even	6		1764.2.b.k.1567.7		8
84.59	odd	6		1764.2.b.k.1567.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.c.195.1	✓	8	28.11	odd	6
196.2.d.c.195.2	yes	8	28.3	even	6
196.2.d.c.195.3	yes	8	7.3	odd	6
196.2.d.c.195.4	yes	8	7.4	even	3
196.2.f.d.19.3		16	7.2	even	3	inner
196.2.f.d.19.4		16	7.5	odd	6	inner
196.2.f.d.19.7		16	28.19	even	6	inner
196.2.f.d.19.8		16	28.23	odd	6	inner
196.2.f.d.31.3		16	28.27	even	2	inner
196.2.f.d.31.4		16	4.3	odd	2	inner
196.2.f.d.31.7		16	1.1	even	1	trivial
196.2.f.d.31.8		16	7.6	odd	2	inner
1764.2.b.k.1567.5		8	21.11	odd	6
1764.2.b.k.1567.6		8	21.17	even	6
1764.2.b.k.1567.7		8	84.11	even	6
1764.2.b.k.1567.8		8	84.59	odd	6
3136.2.f.i.3135.1		8	56.53	even	6
3136.2.f.i.3135.2		8	56.3	even	6
3136.2.f.i.3135.7		8	56.11	odd	6
3136.2.f.i.3135.8		8	56.45	odd	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24165 + 0.676979i) q^{2} +(-1.36145 + 2.35811i) q^{3} +(1.08340 + 1.68114i) q^{4} +(0.937379 - 0.541196i) q^{5} +(-3.28684 + 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +(-2.20711 - 3.82282i) q^{9} +O(q^{10})\)	\(q+(1.24165 + 0.676979i) q^{2} +(-1.36145 + 2.35811i) q^{3} +(1.08340 + 1.68114i) q^{4} +(0.937379 - 0.541196i) q^{5} +(-3.28684 + 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +(-2.20711 - 3.82282i) q^{9} +(1.53028 - 0.0373915i) q^{10} +(-1.80482 - 1.04201i) q^{11} +(-5.43931 + 0.265972i) q^{12} -2.61313i q^{13} +2.94725i q^{15} +(-1.65249 + 3.64270i) q^{16} +(3.86324 + 2.23044i) q^{17} +(-0.152490 - 6.24078i) q^{18} +(0.563932 + 0.976759i) q^{19} +(1.92538 + 0.989538i) q^{20} +(-1.53553 - 2.51564i) q^{22} +(6.16203 - 3.55765i) q^{23} +(-6.93379 - 3.35205i) q^{24} +(-1.91421 + 3.31552i) q^{25} +(1.76903 - 3.24459i) q^{26} +3.85077 q^{27} -1.17157 q^{29} +(-1.99523 + 3.65946i) q^{30} +(3.85077 - 6.66973i) q^{31} +(-4.51785 + 3.40427i) q^{32} +(4.91434 - 2.83730i) q^{33} +(3.28684 + 5.38476i) q^{34} +(4.03553 - 7.85211i) q^{36} +(2.00000 + 3.46410i) q^{37} +(0.0389624 + 1.59457i) q^{38} +(6.16203 + 3.55765i) q^{39} +(1.72076 + 2.53211i) q^{40} -5.54328i q^{41} -7.97852i q^{43} +(-0.203567 - 4.16307i) q^{44} +(-4.13779 - 2.38896i) q^{45} +(10.0595 - 0.245800i) q^{46} +(2.72291 + 4.71621i) q^{47} +(-6.34009 - 8.85611i) q^{48} +(-4.62132 + 2.82083i) q^{50} +(-10.5192 + 6.07328i) q^{51} +(4.39304 - 2.83106i) q^{52} +(3.24264 - 5.61642i) q^{53} +(4.78132 + 2.60689i) q^{54} -2.25573 q^{55} -3.07107 q^{57} +(-1.45469 - 0.793130i) q^{58} +(-4.41470 + 7.64649i) q^{59} +(-4.95475 + 3.19305i) q^{60} +(-11.3152 + 6.53281i) q^{61} +(9.29658 - 5.67459i) q^{62} +(-7.91421 + 1.16843i) q^{64} +(-1.41421 - 2.44949i) q^{65} +(8.02269 - 0.196030i) q^{66} +(-8.71442 - 5.03127i) q^{67} +(0.435738 + 8.91112i) q^{68} +19.3743i q^{69} +(10.3264 - 7.01761i) q^{72} +(-6.90282 - 3.98535i) q^{73} +(0.138181 + 5.65517i) q^{74} +(-5.21222 - 9.02783i) q^{75} +(-1.03111 + 2.00627i) q^{76} +(5.24264 + 8.58892i) q^{78} +(-3.60963 + 2.08402i) q^{79} +(0.422406 + 4.30891i) q^{80} +(1.37868 - 2.38794i) q^{81} +(3.75268 - 6.88282i) q^{82} -4.31795 q^{83} +4.82843 q^{85} +(5.40129 - 9.90655i) q^{86} +(1.59504 - 2.76269i) q^{87} +(2.56555 - 5.30689i) q^{88} +(3.47496 - 2.00627i) q^{89} +(-3.52043 - 5.76745i) q^{90} +(12.6569 + 6.50490i) q^{92} +(10.4853 + 18.1610i) q^{93} +(0.188127 + 7.69924i) q^{94} +(1.05724 + 0.610396i) q^{95} +(-1.87678 - 15.2883i) q^{96} -3.82683i q^{97} +9.19932i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 4 * q^4 - 8 * q^8 - 24 * q^9	\( 16 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 24 q^{9} - 4 q^{16} + 20 q^{18} + 32 q^{22} - 8 q^{25} - 64 q^{29} + 40 q^{30} - 36 q^{32} + 8 q^{36} + 32 q^{37} - 24 q^{44} + 8 q^{46} - 40 q^{50} - 16 q^{53} + 64 q^{57} - 8 q^{60} - 104 q^{64} + 4 q^{72} - 16 q^{74} + 16 q^{78} + 56 q^{81} + 32 q^{85} - 64 q^{86} + 64 q^{88} + 112 q^{92} + 32 q^{93}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^4 - 8 * q^8 - 24 * q^9 - 4 * q^16 + 20 * q^18 + 32 * q^22 - 8 * q^25 - 64 * q^29 + 40 * q^30 - 36 * q^32 + 8 * q^36 + 32 * q^37 - 24 * q^44 + 8 * q^46 - 40 * q^50 - 16 * q^53 + 64 * q^57 - 8 * q^60 - 104 * q^64 + 4 * q^72 - 16 * q^74 + 16 * q^78 + 56 * q^81 + 32 * q^85 - 64 * q^86 + 64 * q^88 + 112 * q^92 + 32 * q^93

Introduction

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