LMFDB - Embedded newform 196.2.f.d.31.4

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			31.4
Root			$1.01214 - 0.987711i$ of defining polynomial
Character	$\chi$	$=$	196.31
Dual form			196.2.f.d.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0345453 + 1.41379i) q^{2} +(1.36145 - 2.35811i) q^{3} +(-1.99761 - 0.0976797i) q^{4} +(0.937379 - 0.541196i) q^{5} +(3.28684 + 2.00627i) q^{6} +(0.207107 - 2.82083i) q^{8} +(-2.20711 - 3.82282i) q^{9} +O(q^{10})$	\(q+(-0.0345453 + 1.41379i) q^{2} +(1.36145 - 2.35811i) q^{3} +(-1.99761 - 0.0976797i) 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} +(0.732756 + 1.34395i) q^{10} +(1.80482 + 1.04201i) q^{11} +(-2.94999 + 4.57760i) q^{12} -2.61313i q^{13} -2.94725i q^{15} +(3.98092 + 0.390252i) q^{16} +(3.86324 + 2.23044i) q^{17} +(5.48092 - 2.98833i) 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} +(-6.36986 - 4.32881i) q^{24} +(-1.91421 + 3.31552i) q^{25} +(3.69442 + 0.0902712i) q^{26} -3.85077 q^{27} -1.17157 q^{29} +(4.16680 + 0.101814i) q^{30} +(-3.85077 + 6.66973i) q^{31} +(-0.689257 + 5.61471i) 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} +(1.40042 - 0.763540i) q^{38} +(-6.16203 - 3.55765i) q^{39} +(-1.33249 - 2.75628i) q^{40} -5.54328i q^{41} +7.97852i q^{43} +(-3.50354 - 2.25783i) q^{44} +(-4.13779 - 2.38896i) q^{45} +(-4.81690 - 8.83472i) 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} +(-0.255249 + 5.22001i) q^{52} +(3.24264 - 5.61642i) q^{53} +(0.133026 - 5.44419i) q^{54} +2.25573 q^{55} -3.07107 q^{57} +(0.0404723 - 1.65636i) q^{58} +(4.41470 - 7.64649i) q^{59} +(-0.287887 + 5.88747i) 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} +(3.84158 + 7.04587i) q^{66} +(8.71442 + 5.03127i) q^{67} +(-7.49939 - 4.83292i) q^{68} +19.3743i q^{69} +(-11.2407 + 5.43415i) q^{72} +(-6.90282 - 3.98535i) q^{73} +(-4.96661 + 2.70791i) 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} +(3.94283 - 1.78864i) q^{80} +(1.37868 - 2.38794i) q^{81} +(7.83704 + 0.191494i) q^{82} +4.31795 q^{83} +4.82843 q^{85} +(-11.2800 - 0.275620i) q^{86} +(-1.59504 + 2.76269i) q^{87} +(3.31313 - 4.87528i) 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} +(6.76180 - 3.68670i) q^{94} +(-1.05724 - 0.610396i) q^{95} +(12.3017 + 9.26950i) 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 $

$2$	−0.0345453	+	1.41379i	−0.0244272	+	0.999702i
$2$	−0.0345453	+	1.41379i	−0.0244272	+	0.999702i
$3$	1.36145	−	2.35811i	0.786035	−	1.36145i	−0.142344	−	0.989817i	$-0.545464\pi$
$3$	1.36145	−	2.35811i	0.786035	−	1.36145i	0.928379	−	0.371635i	$-0.121203\pi$
$4$	−1.99761	−	0.0976797i	−0.998807	−	0.0488398i
$5$	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
$10$	0.732756	+	1.34395i	0.231718	+	0.424996i
$11$	1.80482	+	1.04201i	0.544172	+	0.314178i	0.746768	−	0.665084i	$-0.231604\pi$
$11$	1.80482	+	1.04201i	0.544172	+	0.314178i	−0.202596	+	0.979262i	$0.564938\pi$
$12$	−2.94999	+	4.57760i	−0.851590	+	1.32144i
$13$		−	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
$16$	3.98092	+	0.390252i	0.995229	+	0.0975631i
$17$	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	$0.484727\pi$
$18$	5.48092	−	2.98833i	1.29186	−	0.704356i
$19$	−0.563932	−	0.976759i	−0.129375	−	0.224084i	0.794060	−	0.607840i	$-0.207964\pi$
$19$	−0.563932	−	0.976759i	−0.129375	−	0.224084i	−0.923435	+	0.383756i	$0.874630\pi$
$20$	−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	−0.977735	−	0.209845i	$-0.932704\pi$
$23$	−6.16203	+	3.55765i	−1.28487	+	0.741821i	−0.307136	+	0.951665i	$0.599371\pi$
$24$	−6.36986	−	4.32881i	−1.30024	−	0.883615i
$25$	−1.91421	+	3.31552i	−0.382843	+	0.663103i
$26$	3.69442	+	0.0902712i	0.724534	+	0.0177036i
$27$	−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	$0.534694\pi$
$30$	4.16680	+	0.101814i	0.760750	+	0.0185885i
$31$	−3.85077	+	6.66973i	−0.691619	+	1.19792i	0.279689	+	0.960091i	$0.409769\pi$
$31$	−3.85077	+	6.66973i	−0.691619	+	1.19792i	−0.971307	+	0.237828i	$0.923565\pi$
$32$	−0.689257	+	5.61471i	−0.121845	+	0.992549i
$33$	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	$0.726690\pi$
$38$	1.40042	−	0.763540i	0.227177	−	0.123863i
$39$	−6.16203	−	3.55765i	−0.986714	−	0.569679i
$40$	−1.33249	−	2.75628i	−0.210685	−	0.435806i
$41$		−	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	$0.208171\pi$
$43$			7.97852i			1.21671i	−0.793664	+	0.608357i	$0.791829\pi$
$44$	−3.50354	−	2.25783i	−0.528179	−	0.340380i
$45$	−4.13779	−	2.38896i	−0.616826	−	0.356124i
$46$	−4.81690	−	8.83472i	−0.710214	−	1.30261i
$47$	−2.72291	−	4.71621i	−0.397177	−	0.687930i	0.596200	−	0.802836i	$-0.296677\pi$
$47$	−2.72291	−	4.71621i	−0.397177	−	0.687930i	−0.993376	+	0.114906i	$0.963343\pi$
$48$	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
$52$	−0.255249	+	5.22001i	−0.0353967	+	0.723886i
$53$	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	$0.0197243\pi$
$54$	0.133026	−	5.44419i	0.0181025	−	0.740860i
$55$	2.25573			0.304162
$56$		0			0
$57$	−3.07107			−0.406773
$58$	0.0404723	−	1.65636i	0.00531428	−	0.217491i
$59$	4.41470	−	7.64649i	0.574745	−	0.995488i	−0.421324	−	0.906910i	$-0.638434\pi$
$59$	4.41470	−	7.64649i	0.574745	−	0.995488i	0.996069	−	0.0885778i	$-0.0282322\pi$
$60$	−0.287887	+	5.88747i	−0.0371660	+	0.760069i
$61$	−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
$66$	3.84158	+	7.04587i	0.472866	+	0.867287i
$67$	8.71442	+	5.03127i	1.06464	+	0.614668i	0.926711	−	0.375775i	$-0.122623\pi$
$67$	8.71442	+	5.03127i	1.06464	+	0.614668i	0.137925	+	0.990443i	$0.455957\pi$
$68$	−7.49939	−	4.83292i	−0.909435	−	0.586078i
$69$			19.3743i			2.33239i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−11.2407	+	5.43415i	−1.32472	+	0.640421i
$73$	−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	$0.821134\pi$
$74$	−4.96661	+	2.70791i	−0.577356	+	0.314789i
$75$	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	−0.283004	−	0.959119i	$-0.591331\pi$
$79$	3.60963	−	2.08402i	0.406115	−	0.234471i	0.689119	+	0.724648i	$0.257998\pi$
$80$	3.94283	−	1.78864i	0.440822	−	0.199976i
$81$	1.37868	−	2.38794i	0.153187	−	0.265327i
$82$	7.83704	+	0.191494i	0.865456	+	0.0211470i
$83$	4.31795			0.473956			0.236978	−	0.971515i	$-0.423843\pi$
$83$	4.31795			0.473956			0.236978	+	0.971515i	$0.423843\pi$
$84$		0			0
$85$	4.82843			0.523716
$86$	−11.2800	−	0.275620i	−1.21635	−	0.0297209i
$87$	−1.59504	+	2.76269i	−0.171006	+	0.296192i
$88$	3.31313	−	4.87528i	0.353181	−	0.519706i
$89$	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
$94$	6.76180	−	3.68670i	0.697427	−	0.380254i
$95$	−1.05724	−	0.610396i	−0.108470	−	0.0626253i
$96$	12.3017	+	9.26950i	1.25553	+	0.946064i
$97$		−	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
$100$	4.14772	−	6.43614i	0.414772	−	0.643614i
$101$	−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	$0.669608\pi$
$102$	8.22297	+	15.0818i	0.814195	+	1.49332i
$103$	7.70154	+	13.3395i	0.758855	+	1.31438i	0.943435	+	0.331558i	$0.107574\pi$
$103$	7.70154	+	13.3395i	0.758855	+	1.31438i	−0.184580	+	0.982818i	$0.559092\pi$
$104$	−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	−0.767350	−	0.641228i	$-0.778425\pi$
$107$	−6.16203	+	3.55765i	−0.595706	+	0.343931i	0.171645	+	0.985159i	$0.445092\pi$
$108$	7.69235	+	0.376142i	0.740197	+	0.0361943i
$109$	−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	$0.253993\pi$
$110$	−0.0779248	+	3.18913i	−0.00742984	+	0.304072i
$111$	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	$0.436050\pi$
$114$	0.106091	−	4.34185i	0.00993632	−	0.406651i
$115$	−3.85077	+	6.66973i	−0.359086	+	0.621955i
$116$	2.34035	+	0.114439i	0.217296	+	0.0106254i
$117$	−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
$122$	−8.84515	−	16.2230i	−0.800803	−	1.46876i
$123$	−13.0716	−	7.54691i	−1.17863	−	0.680482i
$124$	8.34385	−	12.9474i	0.749299	−	1.16271i
$125$			9.55582i			0.854699i
$126$		0			0
$127$		−	11.2833i		−	1.00123i	−0.865669	−	0.500617i	$-0.833106\pi$
$127$		−	11.2833i		−	1.00123i	0.865669	−	0.500617i	$-0.166894\pi$
$128$	1.92531	−	11.1487i	0.170175	−	0.985414i
$129$	18.8142	+	10.8624i	1.65650	+	0.956380i
$130$	3.51192	−	1.91478i	0.308016	−	0.167938i
$131$	−7.93513	−	13.7440i	−0.693295	−	1.20082i	−0.970752	−	0.240085i	$-0.922825\pi$
$131$	−7.93513	−	13.7440i	−0.693295	−	1.20082i	0.277457	−	0.960738i	$-0.410509\pi$
$132$	−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
$136$	7.09181	−	10.4356i	0.608118	−	0.894847i
$137$	−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	$0.169966\pi$
$138$	−27.3912	−	0.669290i	−2.33169	−	0.0569737i
$139$	1.78855			0.151703			0.0758515	−	0.997119i	$-0.475833\pi$
$139$	1.78855			0.151703			0.0758515	+	0.997119i	$0.475833\pi$
$140$		0			0
$141$	−14.8284			−1.24878
$142$		0			0
$143$	2.72291	−	4.71621i	0.227701	−	0.394389i
$144$	−7.29444	−	16.0797i	−0.607870	−	1.33997i
$145$	−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	$0.822530\pi$
$150$	−12.9435	+	7.05713i	−1.05684	+	0.576212i
$151$	4.66687	+	2.69442i	0.379784	+	0.219269i	0.677724	−	0.735316i	$-0.262966\pi$
$151$	4.66687	+	2.69442i	0.379784	+	0.219269i	−0.297940	+	0.954585i	$0.596300\pi$
$152$	−2.87207	+	1.38847i	−0.232956	+	0.112619i
$153$		−	19.6913i		−	1.59195i
$154$		0			0
$155$			8.33609i			0.669571i
$156$	11.9618	+	7.70871i	0.957713	+	0.617191i
$157$	−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	$0.964947\pi$
$158$	2.82168	+	5.17526i	0.224481	+	0.411722i
$159$	−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	−0.623638	−	0.781713i	$-0.714346\pi$
$163$	−3.29997	+	1.90524i	−0.258474	+	0.149230i	0.365164	+	0.930943i	$0.381013\pi$
$164$	−0.541465	+	11.0733i	−0.0422813	+	0.864681i
$165$	3.07107	−	5.31925i	0.239082	−	0.414103i
$166$	−0.149165	+	6.10468i	−0.0115774	+	0.473815i
$167$	−20.8489			−1.61334			−0.806668	−	0.591005i	$-0.798731\pi$
$167$	−20.8489			−1.61334			−0.806668	+	0.591005i	$0.798731\pi$
$168$		0			0
$169$	6.17157			0.474736
$170$	−0.166799	+	6.82639i	−0.0127929	+	0.523560i
$171$	−2.48932	+	4.31162i	−0.190363	+	0.329718i
$172$	0.779340	−	15.9380i	0.0594241	−	1.21526i
$173$	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
$178$	2.71641	+	4.98218i	0.203603	+	0.373430i
$179$	−1.05724	−	0.610396i	−0.0790216	−	0.0456231i	0.459969	−	0.887935i	$-0.347861\pi$
$179$	−1.05724	−	0.610396i	−0.0790216	−	0.0456231i	−0.538990	+	0.842312i	$0.681194\pi$
$180$	8.03236	+	5.17639i	0.598696	+	0.385825i
$181$		−	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
$184$	8.75934	+	18.1189i	0.645747	+	1.33574i
$185$	3.74952	+	2.16478i	0.275670	+	0.159158i
$186$	−26.0381	+	14.1966i	−1.90921	+	1.04095i
$187$	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	0.287818	−	0.957685i	$-0.407070\pi$
$191$	17.4288	−	10.0625i	1.26111	−	0.728100i	0.973289	+	0.229585i	$0.0737368\pi$
$192$	−13.5301	+	17.0718i	−0.976451	+	1.23205i
$193$	−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	$0.951051\pi$
$194$	5.41035	+	0.132199i	0.388440	+	0.00949134i
$195$	−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	$0.477302\pi$
$198$	13.0059	+	0.317793i	0.924290	+	0.0225846i
$199$	10.8916	−	18.8648i	0.772087	−	1.33729i	−0.164331	−	0.986405i	$-0.552546\pi$
$199$	10.8916	−	18.8648i	0.772087	−	1.33729i	0.936417	−	0.350888i	$-0.114120\pi$
$200$	8.95607	+	6.08635i	0.633290	+	0.430370i
$201$	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
$206$	−19.1253	+	10.4276i	−1.33252	+	0.726522i
$207$	27.2005	+	15.7042i	1.89057	+	1.09152i
$208$	1.01978	−	10.4026i	0.0707089	−	0.721293i
$209$		−	2.35049i		−	0.162587i
$210$		0			0
$211$		−	15.9570i		−	1.09853i	−0.835649	−	0.549264i	$-0.814908\pi$
$211$		−	15.9570i		−	1.09853i	0.835649	−	0.549264i	$-0.185092\pi$
$212$	−7.02615	+	10.9027i	−0.482558	+	0.748800i
$213$		0			0
$214$	−4.81690	−	8.83472i	−0.329277	−	0.603929i
$215$	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
$220$	−4.50607	−	0.220339i	−0.303799	−	0.0148552i
$221$	5.82843	−	10.0951i	0.392062	−	0.679072i
$222$	−0.376254	+	15.3985i	−0.0252525	+	1.03348i
$223$	−20.8489			−1.39614			−0.698072	−	0.716027i	$-0.745959\pi$
$223$	−20.8489			−1.39614			−0.698072	+	0.716027i	$0.745959\pi$
$224$		0			0
$225$	16.8995			1.12663
$226$	−0.146563	+	5.99821i	−0.00974924	+	0.398995i
$227$	−9.06299	+	15.6976i	−0.601532	+	1.04188i	0.391057	+	0.920366i	$0.372109\pi$
$227$	−9.06299	+	15.6976i	−0.601532	+	1.04188i	−0.992589	+	0.121518i	$0.961224\pi$
$228$	6.13481	+	0.299981i	0.406287	+	0.0198667i
$229$	−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	$0.915113\pi$
$234$	−7.80888	−	14.3223i	−0.510482	−	0.936280i
$235$	−5.10479	−	2.94725i	−0.333000	−	0.192257i
$236$	−9.56577	+	14.8435i	−0.622679	+	0.966229i
$237$		−	11.3492i		−	0.737209i
$238$		0			0
$239$		−	11.2833i		−	0.729858i	−0.931035	−	0.364929i	$-0.881093\pi$
$239$		−	11.2833i		−	0.729858i	0.931035	−	0.364929i	$-0.118907\pi$
$240$	1.15017	−	11.7328i	0.0742433	−	0.757347i
$241$	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	$0.577280\pi$
$242$	8.26550	−	4.50655i	0.531326	−	0.289692i
$243$	−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
$248$	18.0167	+	12.2437i	1.14406	+	0.777478i
$249$	5.87868	−	10.1822i	0.372546	−	0.645269i
$250$	−13.5099	−	0.330109i	−0.854444	−	0.0208779i
$251$	10.4244			0.657985			0.328993	−	0.944333i	$-0.393291\pi$
$251$	10.4244			0.657985			0.328993	+	0.944333i	$0.393291\pi$
$252$		0			0
$253$	−14.8284			−0.932255
$254$	15.9523	+	0.389786i	1.00094	+	0.0244574i
$255$	6.57368	−	11.3859i	0.411659	−	0.713015i
$256$	15.6954	+	3.10712i	0.980963	+	0.194195i
$257$	−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
$262$	19.7053	−	10.7438i	1.21740	−	0.663756i
$263$	−18.9240	−	10.9258i	−1.16690	−	0.673712i	−0.213955	−	0.976844i	$-0.568635\pi$
$263$	−18.9240	−	10.9258i	−1.16690	−	0.673712i	−0.952949	+	0.303131i	$0.901968\pi$
$264$	−6.98575	−	14.4502i	−0.429943	−	0.889346i
$265$		−	7.01962i		−	0.431212i
$266$		0			0
$267$		−	10.9258i		−	0.668647i
$268$	−16.9166	−	10.9018i	−1.03335	−	0.665931i
$269$	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	$0.488745\pi$
$270$	−2.82168	−	5.17526i	−0.171722	−	0.314956i
$271$	−2.72291	−	4.71621i	−0.165405	−	0.286489i	0.771394	−	0.636358i	$-0.219560\pi$
$271$	−2.72291	−	4.71621i	−0.165405	−	0.286489i	−0.936799	+	0.349868i	$0.886226\pi$
$272$	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
$276$	1.89247	−	38.7023i	0.113913	−	2.32961i
$277$	−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	$0.908377\pi$
$278$	−0.0617860	+	2.52864i	−0.00370568	+	0.151658i
$279$	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	$0.788363\pi$
$282$	0.512252	−	20.9643i	0.0305042	−	1.24841i
$283$	−6.00974	+	10.4092i	−0.357242	+	0.618762i	−0.987499	−	0.157625i	$-0.949616\pi$
$283$	−6.00974	+	10.4092i	−0.357242	+	0.618762i	0.630257	+	0.776387i	$0.282950\pi$
$284$		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
$290$	−0.858478	−	1.57454i	−0.0504115	−	0.0924602i
$291$	−9.02408	−	5.21005i	−0.529001	−	0.305419i
$292$	13.3999	+	8.63545i	0.784169	+	0.505351i
$293$			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
$296$	10.1859	−	4.92423i	0.592042	−	0.286215i
$297$	−6.94993	−	4.01254i	−0.403276	−	0.232831i
$298$	−1.02862	+	0.560828i	−0.0595863	+	0.0324879i
$299$	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
$304$	−1.86378	−	4.10847i	−0.106895	−	0.235637i
$305$	−7.07107	+	12.2474i	−0.404888	+	0.701287i
$306$	27.8394	+	0.680241i	1.59147	+	0.0388868i
$307$	10.4244			0.594954			0.297477	−	0.954729i	$-0.403855\pi$
$307$	10.4244			0.594954			0.297477	+	0.954729i	$0.403855\pi$
$308$		0			0
$309$	41.9411			2.38595
$310$	−11.7855	−	0.287972i	−0.669371	−	0.0163557i
$311$	2.25573	−	3.90704i	0.127911	−	0.221548i	−0.794956	−	0.606667i	$-0.792506\pi$
$311$	2.25573	−	3.90704i	0.127911	−	0.221548i	0.922867	+	0.385119i	$0.125840\pi$
$312$	−11.3117	+	16.6452i	−0.640401	+	0.942351i
$313$	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	$0.615794\pi$
$318$	21.9261	−	11.9546i	1.22955	−	0.670383i
$319$	−2.11447	−	1.22079i	−0.118388	−	0.0683512i
$320$	−8.05097	+	3.18788i	−0.450063	+	0.178208i
$321$			19.3743i			1.08137i
$322$		0			0
$323$		−	5.03127i		−	0.279948i
$324$	−2.98732	+	4.63552i	−0.165962	+	0.257529i
$325$	8.66386	+	5.00208i	0.480584	+	0.277466i
$326$	−2.57961	−	4.73129i	−0.142872	−	0.262042i
$327$	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	−0.587942	−	0.808903i	$-0.700062\pi$
$331$	−3.29997	+	1.90524i	−0.181383	+	0.104722i	0.406559	+	0.913624i	$0.366728\pi$
$332$	−8.62559	−	0.421776i	−0.473391	−	0.0231479i
$333$	8.82843	−	15.2913i	0.483795	−	0.837957i
$334$	0.720231	−	29.4760i	0.0394093	−	1.61285i
$335$	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	$0.455014\pi$
$338$	−0.213199	+	8.72532i	−0.0115965	+	0.474595i
$339$	5.77615	−	10.0046i	0.313718	−	0.543375i
$340$	−9.64533	−	0.471639i	−0.523091	−	0.0255782i
$341$	−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
$346$	14.2780	+	26.1873i	0.767588	+	1.40784i
$347$	1.80482	+	1.04201i	0.0968876	+	0.0559381i	0.547661	−	0.836700i	$-0.315518\pi$
$347$	1.80482	+	1.04201i	0.0968876	+	0.0559381i	−0.450773	+	0.892638i	$0.648852\pi$
$348$	3.45613	−	5.36299i	0.185268	−	0.287486i
$349$			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
$352$	−7.09457	+	9.41530i	−0.378142	+	0.501837i
$353$	−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	$0.934020\pi$
$354$	29.8513	−	16.2757i	1.58658	−	0.865042i
$355$		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	0.188673	−	0.982040i	$-0.439581\pi$
$359$	21.4764	−	12.3994i	1.13348	−	0.654415i	0.944808	+	0.327625i	$0.106248\pi$
$360$	−7.59581	+	11.1773i	−0.400334	+	0.589093i
$361$	8.86396	−	15.3528i	0.466524	−	0.808044i
$362$	8.54780	+	0.208861i	0.449262	+	0.0109775i
$363$	−18.1260			−0.951367
$364$		0			0
$365$	−8.62742			−0.451580
$366$	−50.2977	−	1.22900i	−2.62910	−	0.0642408i
$367$	−8.16872	+	14.1486i	−0.426404	+	0.738553i	−0.996550	−	0.0829903i	$-0.973553\pi$
$367$	−8.16872	+	14.1486i	−0.426404	+	0.738553i	0.570147	+	0.821543i	$0.306886\pi$
$368$	−25.9189	+	11.7580i	−1.35112	+	0.612926i
$369$	−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	$0.900938\pi$
$374$	−11.5431	+	6.29359i	−0.596880	+	0.325434i
$375$	22.5336	+	13.0098i	1.16363	+	0.671823i
$376$	−13.8676	+	6.70411i	−0.715166	+	0.345738i
$377$			3.06147i			0.157674i
$378$		0			0
$379$			23.9356i			1.22949i	0.788727	+	0.614744i	$0.210741\pi$
$379$			23.9356i			1.22949i	−0.788727	+	0.614744i	$0.789259\pi$
$380$	2.05233	+	1.32261i	0.105282	+	0.0678482i
$381$	−26.6073	−	15.3617i	−1.36313	−	0.787005i
$382$	13.6243	+	24.9884i	0.697078	+	1.27852i
$383$	3.38359	+	5.86055i	0.172894	+	0.299460i	0.939430	−	0.342740i	$-0.111355\pi$
$383$	3.38359	+	5.86055i	0.172894	+	0.299460i	−0.766537	+	0.642200i	$0.778022\pi$
$384$	−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
$388$	−0.373804	+	7.64453i	−0.0189770	+	0.388092i
$389$	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	$0.0499491\pi$
$390$	0.266052	−	10.8884i	0.0134721	−	0.551354i
$391$	−31.7405			−1.60519
$392$		0			0
$393$	−43.2132			−2.17982
$394$	−0.0690906	+	2.82758i	−0.00348073	+	0.142452i
$395$	2.25573	−	3.90704i	0.113498	−	0.196584i
$396$	−0.898586	+	18.3767i	−0.0451556	+	0.923463i
$397$	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	$0.776026\pi$
$402$	18.5488	+	34.0205i	0.925129	+	1.69679i
$403$	17.4288	+	10.0625i	0.868192	+	0.501251i
$404$	0.312204	+	0.201197i	0.0155327	+	0.0100099i
$405$		−	2.98454i		−	0.148303i
$406$		0			0
$407$			8.33609i			0.413204i
$408$	−14.9531	−	30.9308i	−0.740290	−	1.53130i
$409$	−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	$0.724110\pi$
$410$	7.44991	−	4.06187i	0.367925	−	0.200602i
$411$	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
$416$	14.6719	+	1.80112i	0.719351	+	0.0883070i
$417$	2.43503	−	4.21759i	0.119244	−	0.206536i
$418$	3.32311	+	0.0811985i	0.162539	+	0.00397155i
$419$	16.5309			0.807589			0.403795	−	0.914850i	$-0.367691\pi$
$419$	16.5309			0.807589			0.403795	+	0.914850i	$0.367691\pi$
$420$		0			0
$421$	6.48528			0.316073			0.158037	−	0.987433i	$-0.449484\pi$
$421$	6.48528			0.316073			0.158037	+	0.987433i	$0.449484\pi$
$422$	22.5599	+	0.551241i	1.09820	+	0.0268340i
$423$	−12.0195	+	20.8184i	−0.584407	+	1.01222i
$424$	−15.1714	−	10.3102i	−0.736789	−	0.500705i
$425$	−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
$430$	−10.7228	+	5.84632i	−0.517098	+	0.281934i
$431$	−14.8764	−	8.58892i	−0.716573	−	0.413714i	0.0969169	−	0.995292i	$-0.469102\pi$
$431$	−14.8764	−	8.58892i	−0.716573	−	0.413714i	−0.813490	+	0.581579i	$0.802435\pi$
$432$	−15.3296	−	1.50277i	−0.737546	−	0.0723021i
$433$			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
$436$	6.12863	−	9.50999i	0.293508	−	0.455446i
$437$	6.94993	+	4.01254i	0.332460	+	0.191946i
$438$	−14.6928	−	26.9481i	−0.702048	−	1.28763i
$439$	−8.82940	−	15.2930i	−0.421404	−	0.729894i	0.574673	−	0.818383i	$-0.305129\pi$
$439$	−8.82940	−	15.2930i	−0.421404	−	0.729894i	−0.996077	+	0.0884894i	$0.971796\pi$
$440$	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	0.163801	−	0.986493i	$-0.447625\pi$
$443$	23.1529	−	13.3674i	1.10003	−	0.635102i	0.936229	+	0.351391i	$0.114291\pi$
$444$	−21.7572	−	1.06389i	−1.03255	−	0.0504900i
$445$	2.17157	−	3.76127i	0.102942	−	0.178302i
$446$	0.720231	−	29.4760i	0.0341039	−	1.39573i
$447$	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	$0.100504\pi$
$450$	−0.583798	+	23.8924i	−0.0275205	+	1.12630i
$451$	5.77615	−	10.0046i	0.271988	−	0.471098i
$452$	−8.47516	−	0.414420i	−0.398638	−	0.0194927i
$453$	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	$0.637026\pi$
$458$	−12.8125	−	23.4994i	−0.598687	−	1.09806i
$459$	−14.8764	−	8.58892i	−0.694373	−	0.400896i
$460$	8.34385	−	12.9474i	0.389034	−	0.603675i
$461$		−	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	$0.0490828\pi$
$463$			6.60963i			0.307175i	−0.988135	+	0.153588i	$0.950917\pi$
$464$	−4.66393	−	0.457209i	−0.216518	−	0.0212254i
$465$	19.6574	+	11.3492i	0.911589	+	0.526306i
$466$	9.63194	−	5.25157i	0.446191	−	0.243274i
$467$	3.75401	+	6.50214i	0.173715	+	0.300883i	0.939716	−	0.341956i	$-0.111089\pi$
$467$	3.75401	+	6.50214i	0.173715	+	0.300883i	−0.766001	+	0.642840i	$0.777756\pi$
$468$	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
$472$	−20.6552	−	14.0368i	−0.950731	−	0.646095i
$473$	−8.31371	+	14.3998i	−0.382265	+	0.662102i
$474$	16.0454	+	0.392061i	0.736989	+	0.0180080i
$475$	4.31795			0.198121
$476$		0			0
$477$	−28.6274			−1.31076
$478$	15.9523	+	0.389786i	0.729641	+	0.0178284i
$479$	−9.95727	+	17.2465i	−0.454959	+	0.788012i	−0.998686	−	0.0512499i	$-0.983679\pi$
$479$	−9.95727	+	17.2465i	−0.454959	+	0.788012i	0.543727	+	0.839262i	$0.317013\pi$
$480$	16.5480	+	2.03141i	0.755307	+	0.0927210i
$481$	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
$486$	23.6663	−	12.9034i	1.07353	−	0.585312i
$487$	−34.4198	−	19.8723i	−1.55971	−	0.900498i	−0.997284	−	0.0736490i	$-0.976536\pi$
$487$	−34.4198	−	19.8723i	−1.55971	−	0.900498i	−0.562424	−	0.826849i	$-0.690131\pi$
$488$	16.0845	+	33.2712i	0.728113	+	1.50612i
$489$			10.3756i			0.469200i
$490$		0			0
$491$			15.9570i			0.720132i	0.932927	+	0.360066i	$0.117246\pi$
$491$			15.9570i			0.720132i	−0.932927	+	0.360066i	$0.882754\pi$
$492$	25.3749	+	16.3526i	1.14399	+	0.737234i
$493$	−4.52607	−	2.61313i	−0.203844	−	0.117689i
$494$	−1.99523	−	3.65946i	−0.0897695	−	0.164647i
$495$	−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	−0.812278	−	0.583271i	$-0.801773\pi$
$499$	−15.9337	+	9.19932i	−0.713290	+	0.411818i	0.0989883	+	0.995089i	$0.468439\pi$
$500$	0.933409	−	19.0888i	0.0417433	−	0.853679i
$501$	−28.3848	+	49.1639i	−1.26814	+	2.19648i
$502$	−0.360115	+	14.7380i	−0.0160727	+	0.657789i
$503$	20.8489			0.929606			0.464803	−	0.885414i	$-0.346125\pi$
$503$	20.8489			0.929606			0.464803	+	0.885414i	$0.346125\pi$
$504$		0			0
$505$	−0.201010			−0.00894483
$506$	0.512252	−	20.9643i	0.0227724	−	0.931977i
$507$	8.40230	−	14.5532i	0.373159	−	0.646331i
$508$	−1.10215	+	22.5397i	−0.0489001	+	1.00004i
$509$	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
$514$	−6.38019	−	11.7020i	−0.281418	−	0.516151i
$515$	14.4385	+	8.33609i	0.636237	+	0.367332i
$516$	−36.5225	−	23.5366i	−1.60781	−	1.03614i
$517$		−	11.3492i		−	0.499137i
$518$		0			0
$519$		−	57.4280i		−	2.52081i
$520$	−7.20250	+	3.48196i	−0.315850	+	0.152694i
$521$	−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	$0.795488\pi$
$522$	−6.42129	+	3.50104i	−0.281052	+	0.153237i
$523$	−18.3596	−	31.7997i	−0.802808	−	1.39050i	−0.917761	−	0.397133i	$-0.870005\pi$
$523$	−18.3596	−	31.7997i	−0.802808	−	1.39050i	0.114953	−	0.993371i	$-0.463328\pi$
$524$	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
$528$	20.6709	−	9.37721i	0.899583	−	0.408091i
$529$	13.8137	−	23.9260i	0.600596	−	1.04026i
$530$	9.92428	+	0.242495i	0.431083	+	0.0105333i
$531$	−38.9749			−1.69137
$532$		0			0
$533$	−14.4853			−0.627427
$534$	15.4468	+	0.377434i	0.668447	+	0.0163332i
$535$	−3.85077	+	6.66973i	−0.166483	+	0.288358i
$536$	15.9972	−	23.5399i	0.690974	−	1.01677i
$537$	−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	$0.995490\pi$
$542$	6.76180	−	3.68670i	0.290444	−	0.158357i
$543$	−14.2571	−	8.23136i	−0.611832	−	0.353241i
$544$	−15.1860	+	20.1536i	−0.651096	+	0.864079i
$545$			6.12293i			0.262278i
$546$		0			0
$547$			14.5882i			0.623744i	0.950124	+	0.311872i	$0.100956\pi$
$547$			14.5882i			0.623744i	−0.950124	+	0.311872i	$0.899044\pi$
$548$	0.262877	−	0.407914i	0.0112295	−	0.0174252i
$549$	49.9476	+	28.8372i	2.13171	+	1.23074i
$550$	−5.40129	−	9.90655i	−0.230312	−	0.422417i
$551$	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
$556$	−3.57284	−	0.174705i	−0.151522	−	0.00740915i
$557$	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	$0.110107\pi$
$558$	−1.17441	+	48.0636i	−0.0497167	+	2.03469i
$559$	20.8489			0.881814
$560$		0			0
$561$	25.3137			1.06875
$562$	0.911469	−	37.3026i	0.0384480	−	1.57351i
$563$	5.67940	−	9.83701i	0.239358	−	0.414580i	−0.721172	−	0.692756i	$-0.756396\pi$
$563$	5.67940	−	9.83701i	0.239358	−	0.414580i	0.960530	+	0.278175i	$0.0897297\pi$
$564$	29.6215	+	1.44844i	1.24729	+	0.0609901i
$565$	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	$0.922372\pi$
$570$	−2.25034	−	4.12738i	−0.0942566	−	0.172877i
$571$	35.1673	+	20.3039i	1.47171	+	0.849691i	0.999494	−	0.0317939i	$-0.0101220\pi$
$571$	35.1673	+	20.3039i	1.47171	+	0.849691i	0.472213	+	0.881485i	$0.343455\pi$
$572$	−5.89999	+	9.15519i	−0.246691	+	0.382798i
$573$		−	54.7987i		−	2.28925i
$574$		0			0
$575$		−	27.2404i		−	1.13600i
$576$	13.0008	+	32.8335i	0.541701	+	1.36806i
$577$	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	$0.369460\pi$
$578$	−3.60016	+	1.96290i	−0.149747	+	0.0816457i
$579$	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
$584$	−12.6716	+	18.6463i	−0.524356	+	0.771591i
$585$	−6.24264	+	10.8126i	−0.258101	+	0.447045i
$586$	−32.8784	−	0.803368i	−1.35820	−	0.0331868i
$587$	−1.78855			−0.0738214			−0.0369107	−	0.999319i	$-0.511752\pi$
$587$	−1.78855			−0.0738214			−0.0369107	+	0.999319i	$0.511752\pi$
$588$		0			0
$589$	8.68629			0.357912
$590$	13.5114	+	0.330145i	0.556257	+	0.0135919i
$591$	2.72291	−	4.71621i	0.112005	−	0.193999i
$592$	6.60996	+	14.5708i	0.271668	+	0.598856i
$593$	−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
$598$	−23.0862	+	12.5872i	−0.944066	+	0.514728i
$599$	36.3528	+	20.9883i	1.48534	+	0.857560i	0.999861	−	0.0166904i	$-0.00531295\pi$
$599$	36.3528	+	20.9883i	1.48534	+	0.857560i	0.485476	+	0.874250i	$0.338646\pi$
$600$	26.5455	−	12.8331i	1.08372	−	0.523909i
$601$		−	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
$604$	−9.05941	−	5.83826i	−0.368622	−	0.237556i
$605$	−6.24000	−	3.60266i	−0.253692	−	0.146469i
$606$	−0.342327	−	0.627864i	−0.0139061	−	0.0255052i
$607$	7.70154	+	13.3395i	0.312596	+	0.541432i	0.978924	−	0.204227i	$-0.0654681\pi$
$607$	7.70154	+	13.3395i	0.312596	+	0.541432i	−0.666328	+	0.745659i	$0.732135\pi$
$608$	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
$612$	−1.92344	+	39.3356i	−0.0777504	+	1.59005i
$613$	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	$-0.0512529\pi$
$614$	−0.360115	+	14.7380i	−0.0145331	+	0.594777i
$615$	−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	$0.399298\pi$
$618$	−1.44887	+	59.2960i	−0.0582820	+	2.38524i
$619$	22.2103	−	38.4694i	0.892709	−	1.54622i	0.0560944	−	0.998425i	$-0.482135\pi$
$619$	22.2103	−	38.4694i	0.892709	−	1.54622i	0.836615	−	0.547792i	$-0.184531\pi$
$620$	0.814266	−	16.6523i	0.0327017	−	0.668772i
$621$	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
$626$	6.68371	+	12.2586i	0.267135	+	0.489954i
$627$	−5.54271	−	3.20009i	−0.221355	−	0.127799i
$628$	33.9491	+	21.8782i	1.35472	+	0.873036i
$629$			17.8435i			0.711469i
$630$		0			0
$631$			22.5667i			0.898365i	0.893440	+	0.449183i	$0.148285\pi$
$631$			22.5667i			0.898365i	−0.893440	+	0.449183i	$0.851715\pi$
$632$	−5.13110	−	10.6138i	−0.204104	−	0.422194i
$633$	−37.6284	−	21.7248i	−1.49559	−	0.863482i
$634$	−27.9189	+	15.2221i	−1.10880	+	0.604545i
$635$	−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
$640$	−4.22888	−	11.4925i	−0.167161	−	0.454282i
$641$	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	$0.157514\pi$
$642$	−27.3912	−	0.669290i	−1.08104	−	0.0264148i
$643$	6.84734			0.270033			0.135016	−	0.990843i	$-0.456891\pi$
$643$	6.84734			0.270033			0.135016	+	0.990843i	$0.456891\pi$
$644$		0			0
$645$	23.5147			0.925891
$646$	7.11317	+	0.173807i	0.279864	+	0.00683833i
$647$	4.78512	−	8.28808i	0.188123	−	0.325838i	−0.756502	−	0.653992i	$-0.773093\pi$
$647$	4.78512	−	8.28808i	0.188123	−	0.325838i	0.944624	+	0.328154i	$0.106426\pi$
$648$	−6.45046	−	4.38359i	−0.253398	−	0.172204i
$649$	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	$0.933372\pi$
$654$	−19.1253	+	10.4276i	−0.747857	+	0.407750i
$655$	−14.8764	−	8.58892i	−0.581271	−	0.335597i
$656$	2.16328	−	22.0673i	0.0844618	−	0.861584i
$657$			35.1843i			1.37267i
$658$		0			0
$659$			30.5452i			1.18987i	0.803773	+	0.594936i	$0.202823\pi$
$659$			30.5452i			1.18987i	−0.803773	+	0.594936i	$0.797177\pi$
$660$	−6.65439	+	10.3258i	−0.259022	+	0.401932i
$661$	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	$0.588246\pi$
$662$	−2.57961	−	4.73129i	−0.100260	−	0.183887i
$663$	−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
$668$	41.6480	+	2.03651i	1.61141	+	0.0787950i
$669$	−28.3848	+	49.1639i	−1.09742	+	1.90079i
$670$	−0.376254	+	15.3985i	−0.0145360	+	0.594895i
$671$	−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	$0.669811\pi$
$674$	−0.178653	+	7.31153i	−0.00688147	+	0.281629i
$675$	7.37120	−	12.7673i	0.283717	−	0.491413i
$676$	−12.3284	−	0.602837i	−0.474170	−	0.0231860i
$677$	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
$682$	−10.8656	−	19.9287i	−0.416066	−	0.763111i
$683$	36.3528	+	20.9883i	1.39100	+	0.803096i	0.993426	−	0.114473i	$-0.0365180\pi$
$683$	36.3528	+	20.9883i	1.39100	+	0.803096i	0.397576	+	0.917569i	$0.369851\pi$
$684$	5.39385	−	8.36980i	0.206239	−	0.320027i
$685$			0.262632i			0.0100347i
$686$		0			0
$687$			51.5335i			1.96613i
$688$	−3.11364	+	31.7618i	−0.118706	+	1.21091i
$689$	−14.6764	−	8.47343i	−0.559127	−	0.322812i
$690$	−26.0381	+	14.1966i	−0.991255	+	0.540456i
$691$	2.48932	+	4.31162i	0.0946981	+	0.164022i	0.909483	−	0.415742i	$-0.136478\pi$
$691$	2.48932	+	4.31162i	0.0946981	+	0.164022i	−0.814784	+	0.579764i	$0.803145\pi$
$692$	−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
$696$	7.46275	+	5.07152i	0.282875	+	0.192235i
$697$	12.3640	−	21.4150i	0.468318	−	0.811151i
$698$	−8.02269	−	0.196030i	−0.303663	−	0.00741986i
$699$	−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	$0.402294\pi$
$702$	−14.2263	−	0.347613i	−0.536939	−	0.0131198i
$703$	2.25573	−	3.90704i	0.0850764	−	0.147357i
$704$	−13.0662	−	10.3555i	−0.492450	−	0.390287i
$705$	−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
$712$	−4.93967	−	10.2178i	−0.185122	−	0.382929i
$713$		−	54.7987i		−	2.05223i
$714$		0			0
$715$		−	5.89450i		−	0.220442i
$716$	2.05233	+	1.32261i	0.0766990	+	0.0494281i
$717$	−26.6073	−	15.3617i	−0.993668	−	0.573694i
$718$	16.7883	+	30.7915i	0.626532	+	1.14913i
$719$	5.91299	+	10.2416i	0.220517	+	0.381947i	0.954965	−	0.296718i	$-0.0958921\pi$
$719$	5.91299	+	10.2416i	0.220517	+	0.381947i	−0.734448	+	0.678665i	$0.762559\pi$
$720$	−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
$724$	−0.590572	+	12.0776i	−0.0219484	+	0.448860i
$725$	2.24264	−	3.88437i	0.0832896	−	0.144262i
$726$	0.626167	−	25.6264i	0.0232392	−	0.951084i
$727$	38.1207			1.41382			0.706909	−	0.707305i	$-0.250089\pi$
$727$	38.1207			1.41382			0.706909	+	0.707305i	$0.250089\pi$
$728$		0			0
$729$	−43.6274			−1.61583
$730$	0.298037	−	12.1974i	0.0110308	−	0.451445i
$731$	−17.7956	+	30.8230i	−0.658196	+	1.14003i
$732$	3.47510	−	71.0680i	0.128443	−	2.62675i
$733$	−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
$738$	−16.5651	−	30.3822i	−0.609771	−	1.11839i
$739$	−45.3769	−	26.1984i	−1.66922	−	0.963723i	−0.968061	−	0.250715i	$-0.919334\pi$
$739$	−45.3769	−	26.1984i	−1.66922	−	0.963723i	−0.701156	−	0.713008i	$-0.747332\pi$
$740$	−7.27863	−	4.69065i	−0.267568	−	0.172432i
$741$			8.02509i			0.294809i
$742$		0			0
$743$		−	17.8930i		−	0.656429i	−0.944603	−	0.328215i	$-0.893553\pi$
$743$		−	17.8930i		−	0.656429i	0.944603	−	0.328215i	$-0.106447\pi$
$744$	53.4009	−	25.8160i	1.95777	−	0.946459i
$745$	0.776550	+	0.448342i	0.0284506	+	0.0164260i
$746$	10.1097	−	5.51205i	0.370142	−	0.201811i
$747$	−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	−0.700935	−	0.713225i	$-0.747234\pi$
$751$	−11.8861	+	6.86246i	−0.433731	+	0.250415i	0.267204	+	0.963640i	$0.413900\pi$
$752$	−8.99915	−	19.8375i	−0.328165	−	0.723398i
$753$	14.1924	−	24.5819i	0.517199	−	0.895816i
$754$	−4.32828	−	0.105759i	−0.157627	−	0.00385152i
$755$	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	$0.428337\pi$
$758$	−33.8399	−	0.826861i	−1.22912	−	0.0300329i
$759$	−20.1882	+	34.9670i	−0.732785	+	1.26922i
$760$	−1.94079	+	2.85587i	−0.0703997	+	0.103593i
$761$	−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
$766$	−8.40249	+	4.58124i	−0.303594	+	0.165527i
$767$	−19.9812	−	11.5362i	−0.721481	−	0.416547i
$768$	28.6955	−	32.7812i	1.03546	−	1.18289i
$769$			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
$772$	18.8666	−	29.2758i	0.679022	−	1.05366i
$773$	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	$0.264999\pi$
$774$	23.8425	+	43.7296i	0.856999	+	1.57183i
$775$	−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
$780$	15.3847	+	0.752284i	0.550861	+	0.0269361i
$781$		0			0
$782$	1.09648	−	44.8745i	0.0392102	−	1.60471i
$783$	4.51146			0.161226
$784$		0			0
$785$	−21.8579			−0.780141
$786$	1.49281	−	61.0945i	0.0532468	−	2.17917i
$787$	−14.6456	+	25.3670i	−0.522061	+	0.904235i	0.477610	+	0.878572i	$0.341503\pi$
$787$	−14.6456	+	25.3670i	−0.522061	+	0.904235i	−0.999671	+	0.0256635i	$0.991830\pi$
$788$	−3.99523	−	0.195359i	−0.142324	−	0.00695939i
$789$	−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
$794$	8.66736	+	15.8969i	0.307593	+	0.564159i
$795$	−16.5530	−	9.55688i	−0.587074	−	0.338948i
$796$	−23.6000	+	36.6208i	−0.836478	+	1.29799i
$797$		−	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
$800$	−17.2963	−	13.0330i	−0.611515	−	0.460786i
$801$	−15.3392	−	8.85611i	−0.541985	−	0.312915i
$802$	−8.90460	+	4.85500i	−0.314432	+	0.171436i
$803$	−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
$808$	−0.295236	+	0.434441i	−0.0103864	+	0.0152836i
$809$	−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	$0.846548\pi$
$810$	4.21952	+	0.103102i	0.148259	+	0.00362263i
$811$	42.4386			1.49022			0.745111	−	0.666941i	$-0.232397\pi$
$811$	42.4386			1.49022			0.745111	+	0.666941i	$0.232397\pi$
$812$		0			0
$813$	−14.8284			−0.520056
$814$	−11.7855	−	0.287972i	−0.413081	−	0.0100934i
$815$	−2.06222	+	3.57187i	−0.0722363	+	0.125117i
$816$	44.2463	−	20.0721i	1.54893	−	0.702664i
$817$	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	$0.731630\pi$
$822$	−0.820344	+	0.447271i	−0.0286128	+	0.0156004i
$823$	28.2577	+	16.3146i	0.985003	+	0.568692i	0.903777	−	0.428004i	$-0.140783\pi$
$823$	28.2577	+	16.3146i	0.985003	+	0.568692i	0.0812259	+	0.996696i	$0.474116\pi$
$824$	39.2234	−	18.9621i	1.36641	−	0.660575i
$825$			21.7248i			0.756359i
$826$		0			0
$827$		−	17.8930i		−	0.622199i	−0.950377	−	0.311100i	$-0.899303\pi$
$827$		−	17.8930i		−	0.622199i	0.950377	−	0.311100i	$-0.100697\pi$
$828$	−52.8021	−	34.0279i	−1.83500	−	1.18255i
$829$	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	$0.643138\pi$
$830$	3.16400	+	5.80312i	0.109824	+	0.201429i
$831$	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
$836$	−0.229595	+	4.69538i	−0.00794072	+	0.162393i
$837$	14.8284	−	25.6836i	0.512545	−	0.887755i
$838$	−0.571066	+	23.3713i	−0.0197271	+	0.807348i
$839$	−53.9108			−1.86121			−0.930603	−	0.366029i	$-0.880717\pi$
$839$	−53.9108			−1.86121			−0.930603	+	0.366029i	$0.880717\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$	−0.224036	+	9.16884i	−0.00772079	+	0.315979i
$843$	−35.9216	+	62.2181i	−1.23721	+	2.14290i
$844$	−1.55868	+	31.8760i	−0.0536519	+	1.09722i
$845$	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
$850$	−11.5616	−	21.2051i	−0.396558	−	0.727331i
$851$	−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
$856$	8.75934	+	18.1189i	0.299388	+	0.619290i
$857$	−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	$0.903844\pi$
$858$	18.4117	−	10.0385i	0.628567	−	0.342710i
$859$	9.86051	+	17.0789i	0.336436	+	0.582725i	0.983760	−	0.179491i	$-0.0574450\pi$
$859$	9.86051	+	17.0789i	0.336436	+	0.582725i	−0.647323	+	0.762216i	$0.724112\pi$
$860$	−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	−0.746047	−	0.665894i	$-0.768050\pi$
$863$	−15.9337	+	9.19932i	−0.542389	+	0.313148i	0.203658	+	0.979042i	$0.434717\pi$
$864$	2.65417	−	21.6209i	0.0902967	−	0.735559i
$865$	11.4142	−	19.7700i	0.388095	−	0.672200i
$866$	−21.4557	−	0.524260i	−0.729095	−	0.0178151i
$867$	7.89505			0.268130
$868$		0			0
$869$	8.68629			0.294662
$870$	−4.88171	−	0.119282i	−0.165505	−	0.00404404i
$871$	13.1474	−	22.7719i	0.445481	−	0.771596i
$872$	13.2334	+	8.99314i	0.448140	+	0.304546i
$873$	−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	$0.462392\pi$
$878$	21.9261	−	11.9546i	0.739970	−	0.403449i
$879$	54.8389	+	31.6613i	1.84967	+	1.06791i
$880$	8.97987	+	0.880303i	0.302711	+	0.0296750i
$881$			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	$-0.974942\pi$
$883$		−	4.67371i		−	0.157283i	0.996903	−	0.0786415i	$-0.0250582\pi$
$884$	−12.6290	+	19.5969i	−0.424760	+	0.659113i
$885$	−22.5361	−	13.0112i	−0.757543	−	0.437368i
$886$	18.0988	+	33.1952i	0.608042	+	1.11522i
$887$	−8.82940	−	15.2930i	−0.296462	−	0.513488i	0.678862	−	0.734266i	$-0.262474\pi$
$887$	−8.82940	−	15.2930i	−0.296462	−	0.513488i	−0.975324	+	0.220778i	$0.929140\pi$
$888$	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
$892$	41.6480	+	2.03651i	1.39448	+	0.0681875i
$893$	−3.07107	+	5.31925i	−0.102769	+	0.178002i
$894$	−0.0779248	+	3.18913i	−0.00260619	+	0.106660i
$895$	−1.32138			−0.0441687
$896$		0			0
$897$	50.6274			1.69040
$898$	−1.39163	+	56.9536i	−0.0464393	+	1.90057i
$899$	4.51146	−	7.81407i	0.150466	−	0.260614i
$900$	−33.7587	−	1.65074i	−1.12529	−	0.0550246i
$901$	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
$906$	9.93350	+	18.2191i	0.330019	+	0.605290i
$907$	−20.6006	−	11.8937i	−0.684030	−	0.394925i	0.117342	−	0.993092i	$-0.462563\pi$
$907$	−20.6006	−	11.8937i	−0.684030	−	0.394925i	−0.801372	+	0.598167i	$0.795896\pi$
$908$	19.6377	−	30.4724i	0.651699	−	1.01126i
$909$			0.819760i			0.0271897i
$910$		0			0
$911$			43.1974i			1.43119i	0.698513	+	0.715597i	$0.253845\pi$
$911$			43.1974i			1.43119i	−0.698513	+	0.715597i	$0.746155\pi$
$912$	−12.2257	−	1.19849i	−0.404832	−	0.0396860i
$913$	7.79310	+	4.49935i	0.257914	+	0.148907i
$914$	−30.7035	+	16.7403i	−1.01558	+	0.553719i
$915$	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	0.413184	−	0.910648i	$-0.364417\pi$
$919$	42.6963	−	24.6507i	1.40842	−	0.813151i	0.995236	+	0.0974962i	$0.0310834\pi$
$920$	18.0167	+	12.2437i	0.593992	+	0.403664i
$921$	14.1924	−	24.5819i	0.467655	−	0.810002i
$922$	38.8457	+	0.949176i	1.27932	+	0.0312594i
$923$		0			0
$924$		0			0
$925$	−15.3137			−0.503512
$926$	−9.34463	−	0.228331i	−0.307084	−	0.00750344i
$927$	33.9962	−	58.8832i	1.11658	−	1.93398i
$928$	0.807515	−	6.57804i	0.0265080	−	0.215935i
$929$	−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
$934$	−9.32236	+	5.08278i	−0.305037	+	0.166313i
$935$	8.71442	+	5.03127i	0.284992	+	0.164540i
$936$	14.2001	+	29.3732i	0.464145	+	0.960094i
$937$			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
$940$	9.90951	+	6.38610i	0.323213	+	0.208292i
$941$	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	$0.624508\pi$
$942$	−37.2246	−	68.2740i	−1.21284	−	2.22449i
$943$	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	−0.958617	−	0.284697i	$-0.908107\pi$
$947$	−36.6625	+	21.1671i	−1.19137	+	0.687838i	−0.232754	+	0.972536i	$0.574774\pi$
$948$	−1.10858	+	22.6713i	−0.0360052	+	0.736329i
$949$	−10.4142	+	18.0379i	−0.338060	+	0.585537i
$950$	−0.149165	+	6.10468i	−0.00483954	+	0.198062i
$951$	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	$0.291205\pi$
$954$	0.988942	−	40.4732i	0.0320182	−	1.31037i
$955$	10.8916	−	18.8648i	0.352445	−	0.610452i
$956$	−1.10215	+	22.5397i	−0.0356462	+	0.728987i
$957$	−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
$962$	7.07612	+	12.9784i	0.228143	+	0.418440i
$963$	27.2005	+	15.7042i	0.876524	+	0.506061i
$964$	−14.4658	−	9.32238i	−0.465913	−	0.300254i
$965$			18.8490i			0.606771i
$966$		0			0
$967$		−	17.8930i		−	0.575399i	−0.957721	−	0.287699i	$-0.907110\pi$
$967$		−	17.8930i		−	0.575399i	0.957721	−	0.287699i	$-0.0928904\pi$
$968$	−16.9515	+	8.19497i	−0.544841	+	0.263396i
$969$	−11.8643	−	6.84984i	−0.381135	−	0.220049i
$970$	5.14309	−	2.80414i	0.165135	−	0.0900354i
$971$	−10.9884	−	19.0324i	−0.352634	−	0.610780i	0.634076	−	0.773271i	$-0.281381\pi$
$971$	−10.9884	−	19.0324i	−0.352634	−	0.610780i	−0.986710	+	0.162491i	$0.948047\pi$
$972$	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
$976$	−47.5942	+	21.5908i	−1.52345	+	0.691105i
$977$	−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	$0.830810\pi$
$978$	−14.6689	−	0.358427i	−0.469060	−	0.0114612i
$979$	8.36223			0.267258
$980$		0			0
$981$	24.9706			0.797249
$982$	−22.5599	−	0.551241i	−0.719917	−	0.0175908i
$983$	16.9981	−	29.4416i	0.542156	−	0.939041i	−0.456624	−	0.889660i	$-0.650942\pi$
$983$	16.9981	−	29.4416i	0.542156	−	0.939041i	0.998780	−	0.0493817i	$-0.0157251\pi$
$984$	−23.9958	+	35.3099i	−0.764958	+	1.12564i
$985$	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
$990$	12.3635	−	6.74086i	0.392937	−	0.214239i
$991$	−18.9240	−	10.9258i	−0.601141	−	0.347069i	0.168350	−	0.985727i	$-0.446156\pi$
$991$	−18.9240	−	10.9258i	−0.601141	−	0.347069i	−0.769490	+	0.638659i	$0.779490\pi$
$992$	−34.7944	−	26.2181i	−1.10472	−	0.832425i
$993$			10.3756i			0.329259i
$994$		0			0
$995$		−	23.5780i		−	0.747473i
$996$	−12.7379	+	19.7658i	−0.403616	+	0.626304i
$997$	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	$0.632933\pi$
$998$	−12.4555	−	22.8447i	−0.394271	−	0.723136i
$999$	−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.31.4		16
4.3	odd	2	inner	196.2.f.d.31.7		16
7.2	even	3	inner	196.2.f.d.19.8		16
7.3	odd	6		196.2.d.c.195.2	yes	8
7.4	even	3		196.2.d.c.195.1	✓	8
7.5	odd	6	inner	196.2.f.d.19.7		16
7.6	odd	2	inner	196.2.f.d.31.3		16
21.11	odd	6		1764.2.b.k.1567.7		8
21.17	even	6		1764.2.b.k.1567.8		8
28.3	even	6		196.2.d.c.195.3	yes	8
28.11	odd	6		196.2.d.c.195.4	yes	8
28.19	even	6	inner	196.2.f.d.19.4		16
28.23	odd	6	inner	196.2.f.d.19.3		16
28.27	even	2	inner	196.2.f.d.31.8		16
56.3	even	6		3136.2.f.i.3135.8		8
56.11	odd	6		3136.2.f.i.3135.1		8
56.45	odd	6		3136.2.f.i.3135.2		8
56.53	even	6		3136.2.f.i.3135.7		8
84.11	even	6		1764.2.b.k.1567.5		8
84.59	odd	6		1764.2.b.k.1567.6		8

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

\(f(q)\)	\(=\)	\(q+(-0.0345453 + 1.41379i) q^{2} +(1.36145 - 2.35811i) q^{3} +(-1.99761 - 0.0976797i) q^{4} +(0.937379 - 0.541196i) q^{5} +(3.28684 + 2.00627i) q^{6} +(0.207107 - 2.82083i) q^{8} +(-2.20711 - 3.82282i) q^{9} +O(q^{10})\)	\(q+(-0.0345453 + 1.41379i) q^{2} +(1.36145 - 2.35811i) q^{3} +(-1.99761 - 0.0976797i) 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} +(0.732756 + 1.34395i) q^{10} +(1.80482 + 1.04201i) q^{11} +(-2.94999 + 4.57760i) q^{12} -2.61313i q^{13} -2.94725i q^{15} +(3.98092 + 0.390252i) q^{16} +(3.86324 + 2.23044i) q^{17} +(5.48092 - 2.98833i) 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} +(-6.36986 - 4.32881i) q^{24} +(-1.91421 + 3.31552i) q^{25} +(3.69442 + 0.0902712i) q^{26} -3.85077 q^{27} -1.17157 q^{29} +(4.16680 + 0.101814i) q^{30} +(-3.85077 + 6.66973i) q^{31} +(-0.689257 + 5.61471i) 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} +(1.40042 - 0.763540i) q^{38} +(-6.16203 - 3.55765i) q^{39} +(-1.33249 - 2.75628i) q^{40} -5.54328i q^{41} +7.97852i q^{43} +(-3.50354 - 2.25783i) q^{44} +(-4.13779 - 2.38896i) q^{45} +(-4.81690 - 8.83472i) 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} +(-0.255249 + 5.22001i) q^{52} +(3.24264 - 5.61642i) q^{53} +(0.133026 - 5.44419i) q^{54} +2.25573 q^{55} -3.07107 q^{57} +(0.0404723 - 1.65636i) q^{58} +(4.41470 - 7.64649i) q^{59} +(-0.287887 + 5.88747i) 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} +(3.84158 + 7.04587i) q^{66} +(8.71442 + 5.03127i) q^{67} +(-7.49939 - 4.83292i) q^{68} +19.3743i q^{69} +(-11.2407 + 5.43415i) q^{72} +(-6.90282 - 3.98535i) q^{73} +(-4.96661 + 2.70791i) 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} +(3.94283 - 1.78864i) q^{80} +(1.37868 - 2.38794i) q^{81} +(7.83704 + 0.191494i) q^{82} +4.31795 q^{83} +4.82843 q^{85} +(-11.2800 - 0.275620i) q^{86} +(-1.59504 + 2.76269i) q^{87} +(3.31313 - 4.87528i) 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} +(6.76180 - 3.68670i) q^{94} +(-1.05724 - 0.610396i) q^{95} +(12.3017 + 9.26950i) 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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