LMFDB - Embedded newform 196.2.f.d.31.2

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			31.2
Root			$-0.264742 - 1.38921i$ of defining polynomial
Character	$\chi$	$=$	196.31
Dual form			196.2.f.d.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31509 + 0.520123i) q^{2} +(1.07072 - 1.85455i) q^{3} +(1.45894 - 1.36802i) q^{4} +(2.26303 - 1.30656i) q^{5} +(-0.443508 + 2.99581i) q^{6} +(-1.20711 + 2.55791i) q^{8} +(-0.792893 - 1.37333i) q^{9} +O(q^{10})$	\(q+(-1.31509 + 0.520123i) q^{2} +(1.07072 - 1.85455i) q^{3} +(1.45894 - 1.36802i) q^{4} +(2.26303 - 1.30656i) q^{5} +(-0.443508 + 2.99581i) q^{6} +(-1.20711 + 2.55791i) q^{8} +(-0.792893 - 1.37333i) q^{9} +(-2.29653 + 2.89531i) q^{10} +(-3.42675 - 1.97844i) q^{11} +(-0.974936 - 4.17045i) q^{12} +1.08239i q^{13} -5.59587i q^{15} +(0.257031 - 3.99173i) q^{16} +(-0.274552 - 0.158513i) q^{17} +(1.75703 + 1.39366i) q^{18} +(2.58495 + 4.47727i) q^{19} +(1.51423 - 5.00208i) q^{20} +(5.53553 + 0.819496i) q^{22} +(2.00735 - 1.15894i) q^{23} +(3.45128 + 4.97744i) q^{24} +(0.914214 - 1.58346i) q^{25} +(-0.562978 - 1.42345i) q^{26} +3.02846 q^{27} -6.82843 q^{29} +(2.91054 + 7.35909i) q^{30} +(3.02846 - 5.24545i) q^{31} +(1.73817 + 5.38319i) q^{32} +(-7.33820 + 4.23671i) q^{33} +(0.443508 + 0.0656581i) q^{34} +(-3.03553 - 0.918917i) q^{36} +(2.00000 + 3.46410i) q^{37} +(-5.72819 - 4.54353i) q^{38} +(2.00735 + 1.15894i) q^{39} +(0.610345 + 7.36579i) q^{40} -2.29610i q^{41} +7.23486i q^{43} +(-7.70598 + 1.80145i) q^{44} +(-3.58869 - 2.07193i) q^{45} +(-2.03706 + 2.56818i) q^{46} +(-2.14144 - 3.70909i) q^{47} +(-7.12764 - 4.75071i) q^{48} +(-0.378680 + 2.55791i) q^{50} +(-0.587938 + 0.339446i) q^{51} +(1.48074 + 1.57915i) q^{52} +(-5.24264 + 9.08052i) q^{53} +(-3.98271 + 1.57517i) q^{54} -10.3398 q^{55} +11.0711 q^{57} +(8.98002 - 3.55162i) q^{58} +(-5.61341 + 9.72272i) q^{59} +(-7.65527 - 8.16405i) q^{60} +(4.68690 - 2.70598i) q^{61} +(-1.25443 + 8.47343i) q^{62} +(-5.08579 - 6.17534i) q^{64} +(1.41421 + 2.44949i) q^{65} +(7.44681 - 9.38845i) q^{66} +(2.83882 + 1.63899i) q^{67} +(-0.617405 + 0.144332i) q^{68} -4.96362i q^{69} +(4.46996 - 0.370390i) q^{72} +(12.1388 + 7.00835i) q^{73} +(-4.43195 - 3.51537i) q^{74} +(-1.95774 - 3.39090i) q^{75} +(9.89630 + 2.99581i) q^{76} +(-3.24264 - 0.480049i) q^{78} +(-6.85351 + 3.95687i) q^{79} +(-4.63378 - 9.36925i) q^{80} +(5.62132 - 9.73641i) q^{81} +(1.19426 + 3.01959i) q^{82} +9.45280 q^{83} -0.828427 q^{85} +(-3.76302 - 9.51451i) q^{86} +(-7.31135 + 12.6636i) q^{87} +(9.19712 - 6.37714i) q^{88} +(5.18889 - 2.99581i) q^{89} +(5.79712 + 0.858221i) q^{90} +(1.34315 - 4.43692i) q^{92} +(-6.48528 - 11.2328i) q^{93} +(4.74539 + 3.76399i) q^{94} +(11.6997 + 6.75481i) q^{95} +(11.8445 + 2.54038i) q^{96} +9.23880i q^{97} +6.27476i 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 $

$2$	−1.31509	+	0.520123i	−0.929912	+	0.367783i
$2$	−1.31509	+	0.520123i	−0.929912	+	0.367783i
$3$	1.07072	−	1.85455i	0.618182	−	1.07072i	−0.371635	−	0.928379i	$-0.621203\pi$
$3$	1.07072	−	1.85455i	0.618182	−	1.07072i	0.989817	−	0.142344i	$-0.0454638\pi$
$4$	1.45894	−	1.36802i	0.729472	−	0.684011i
$5$	2.26303	−	1.30656i	1.01206	−	0.584313i	0.100265	−	0.994961i	$-0.468031\pi$
$5$	2.26303	−	1.30656i	1.01206	−	0.584313i	0.911794	+	0.410648i	$0.134697\pi$
$6$	−0.443508	+	2.99581i	−0.181061	+	1.22303i
$7$		0			0
$7$		0			0
$8$	−1.20711	+	2.55791i	−0.426777	+	0.904357i
$9$	−0.792893	−	1.37333i	−0.264298	−	0.457777i
$10$	−2.29653	+	2.89531i	−0.726226	+	0.915577i
$11$	−3.42675	−	1.97844i	−1.03321	−	0.596521i	−0.115304	−	0.993330i	$-0.536784\pi$
$11$	−3.42675	−	1.97844i	−1.03321	−	0.596521i	−0.917901	+	0.396809i	$0.870118\pi$
$12$	−0.974936	−	4.17045i	−0.281440	−	1.20390i
$13$			1.08239i			0.300202i	0.988671	+	0.150101i	$0.0479598\pi$
$13$			1.08239i			0.300202i	−0.988671	+	0.150101i	$0.952040\pi$
$14$		0			0
$15$		−	5.59587i		−	1.44485i
$16$	0.257031	−	3.99173i	0.0642577	−	0.997933i
$17$	−0.274552	−	0.158513i	−0.0665886	−	0.0384450i	0.466336	−	0.884608i	$-0.345574\pi$
$17$	−0.274552	−	0.158513i	−0.0665886	−	0.0384450i	−0.532925	+	0.846163i	$0.678907\pi$
$18$	1.75703	+	1.39366i	0.414136	+	0.328488i
$19$	2.58495	+	4.47727i	0.593029	+	1.02716i	0.993822	+	0.110987i	$0.0354013\pi$
$19$	2.58495	+	4.47727i	0.593029	+	1.02716i	−0.400793	+	0.916169i	$0.631265\pi$
$20$	1.51423	−	5.00208i	0.338592	−	1.11850i
$21$		0			0
$22$	5.53553	+	0.819496i	1.18018	+	0.174717i
$23$	2.00735	−	1.15894i	0.418561	−	0.241656i	−0.275901	−	0.961186i	$-0.588976\pi$
$23$	2.00735	−	1.15894i	0.418561	−	0.241656i	0.694461	+	0.719530i	$0.255643\pi$
$24$	3.45128	+	4.97744i	0.704490	+	1.01602i
$25$	0.914214	−	1.58346i	0.182843	−	0.316693i
$26$	−0.562978	−	1.42345i	−0.110409	−	0.279161i
$27$	3.02846			0.582827
$28$		0			0
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$	2.91054	+	7.35909i	0.531390	+	1.34358i
$31$	3.02846	−	5.24545i	0.543928	−	0.942110i	−0.454746	−	0.890621i	$-0.650270\pi$
$31$	3.02846	−	5.24545i	0.543928	−	0.942110i	0.998674	−	0.0514890i	$-0.0163967\pi$
$32$	1.73817	+	5.38319i	0.307269	+	0.951623i
$33$	−7.33820	+	4.23671i	−1.27742	+	0.737517i
$34$	0.443508	+	0.0656581i	0.0760610	+	0.0112603i
$35$		0			0
$36$	−3.03553	−	0.918917i	−0.505922	−	0.153153i
$37$	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	$0.726690\pi$
$38$	−5.72819	−	4.54353i	−0.929235	−	0.737059i
$39$	2.00735	+	1.15894i	0.321433	+	0.185579i
$40$	0.610345	+	7.36579i	0.0965040	+	1.16463i
$41$		−	2.29610i		−	0.358591i	−0.983795	−	0.179295i	$-0.942618\pi$
$41$		−	2.29610i		−	0.358591i	0.983795	−	0.179295i	$-0.0573818\pi$
$42$		0			0
$43$			7.23486i			1.10331i	0.834074	+	0.551653i	$0.186003\pi$
$43$			7.23486i			1.10331i	−0.834074	+	0.551653i	$0.813997\pi$
$44$	−7.70598	+	1.80145i	−1.16172	+	0.271578i
$45$	−3.58869	−	2.07193i	−0.534970	−	0.308865i
$46$	−2.03706	+	2.56818i	−0.300347	+	0.378658i
$47$	−2.14144	−	3.70909i	−0.312362	−	0.541027i	0.666511	−	0.745495i	$-0.267787\pi$
$47$	−2.14144	−	3.70909i	−0.312362	−	0.541027i	−0.978873	+	0.204468i	$0.934453\pi$
$48$	−7.12764	−	4.75071i	−1.02879	−	0.685706i
$49$		0			0
$50$	−0.378680	+	2.55791i	−0.0535534	+	0.361743i
$51$	−0.587938	+	0.339446i	−0.0823278	+	0.0475320i
$52$	1.48074	+	1.57915i	0.205341	+	0.218989i
$53$	−5.24264	+	9.08052i	−0.720132	+	1.24731i	0.240814	+	0.970571i	$0.422585\pi$
$53$	−5.24264	+	9.08052i	−0.720132	+	1.24731i	−0.960947	+	0.276734i	$0.910748\pi$
$54$	−3.98271	+	1.57517i	−0.541978	+	0.214354i
$55$	−10.3398			−1.39422
$56$		0			0
$57$	11.0711			1.46640
$58$	8.98002	−	3.55162i	1.17913	−	0.466351i
$59$	−5.61341	+	9.72272i	−0.730804	+	1.26579i	0.225736	+	0.974189i	$0.427521\pi$
$59$	−5.61341	+	9.72272i	−0.730804	+	1.26579i	−0.956540	+	0.291601i	$0.905812\pi$
$60$	−7.65527	−	8.16405i	−0.988291	−	1.05397i
$61$	4.68690	−	2.70598i	0.600096	−	0.346465i	−0.168984	−	0.985619i	$-0.554049\pi$
$61$	4.68690	−	2.70598i	0.600096	−	0.346465i	0.769079	+	0.639154i	$0.220715\pi$
$62$	−1.25443	+	8.47343i	−0.159313	+	1.07613i
$63$		0			0
$64$	−5.08579	−	6.17534i	−0.635723	−	0.771917i
$65$	1.41421	+	2.44949i	0.175412	+	0.303822i
$66$	7.44681	−	9.38845i	0.916639	−	1.15564i
$67$	2.83882	+	1.63899i	0.346817	+	0.200235i	0.663282	−	0.748369i	$-0.269163\pi$
$67$	2.83882	+	1.63899i	0.346817	+	0.200235i	−0.316466	+	0.948604i	$0.602496\pi$
$68$	−0.617405	+	0.144332i	−0.0748713	+	0.0175029i
$69$		−	4.96362i		−	0.597550i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	4.46996	−	0.370390i	0.526790	−	0.0436509i
$73$	12.1388	+	7.00835i	1.42074	+	0.820266i	0.996362	−	0.0852188i	$-0.0271589\pi$
$73$	12.1388	+	7.00835i	1.42074	+	0.820266i	0.424380	+	0.905484i	$0.360492\pi$
$74$	−4.43195	−	3.51537i	−0.515203	−	0.408654i
$75$	−1.95774	−	3.39090i	−0.226060	−	0.391548i
$76$	9.89630	+	2.99581i	1.13518	+	0.343643i
$77$		0			0
$78$	−3.24264	−	0.480049i	−0.367157	−	0.0543549i
$79$	−6.85351	+	3.95687i	−0.771080	+	0.445183i	−0.833260	−	0.552882i	$-0.813528\pi$
$79$	−6.85351	+	3.95687i	−0.771080	+	0.445183i	0.0621799	+	0.998065i	$0.480195\pi$
$80$	−4.63378	−	9.36925i	−0.518073	−	1.04751i
$81$	5.62132	−	9.73641i	0.624591	−	1.08182i
$82$	1.19426	+	3.01959i	0.131883	+	0.333458i
$83$	9.45280			1.03758			0.518790	−	0.854902i	$-0.326383\pi$
$83$	9.45280			1.03758			0.518790	+	0.854902i	$0.326383\pi$
$84$		0			0
$85$	−0.828427			−0.0898555
$86$	−3.76302	−	9.51451i	−0.405777	−	1.02598i
$87$	−7.31135	+	12.6636i	−0.783859	+	1.35768i
$88$	9.19712	−	6.37714i	0.980416	−	0.679805i
$89$	5.18889	−	2.99581i	0.550022	−	0.317555i	−0.199109	−	0.979977i	$-0.563805\pi$
$89$	5.18889	−	2.99581i	0.550022	−	0.317555i	0.749131	+	0.662422i	$0.230471\pi$
$90$	5.79712	+	0.858221i	0.611070	+	0.0904645i
$91$		0			0
$92$	1.34315	−	4.43692i	0.140033	−	0.462581i
$93$	−6.48528	−	11.2328i	−0.672492	−	1.16479i
$94$	4.74539	+	3.76399i	0.489449	+	0.388226i
$95$	11.6997	+	6.75481i	1.20036	+	0.693029i
$96$	11.8445	+	2.54038i	1.20887	+	0.259276i
$97$			9.23880i			0.938058i	0.883183	+	0.469029i	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		0			0
$99$			6.27476i			0.630637i
$100$	−0.832429	−	3.56085i	−0.0832429	−	0.356085i
$101$	−13.1899	−	7.61521i	−1.31245	−	0.757741i	−0.329946	−	0.944000i	$-0.607030\pi$
$101$	−13.1899	−	7.61521i	−1.31245	−	0.757741i	−0.982501	+	0.186258i	$0.940364\pi$
$102$	0.596640	−	0.752204i	0.0590761	−	0.0744793i
$103$	−6.05692	−	10.4909i	−0.596806	−	1.03370i	−0.993289	−	0.115657i	$-0.963103\pi$
$103$	−6.05692	−	10.4909i	−0.596806	−	1.03370i	0.396483	−	0.918042i	$-0.370231\pi$
$104$	−2.76866	−	1.30656i	−0.271489	−	0.128119i
$105$		0			0
$106$	2.17157	−	14.6686i	0.210922	−	1.42474i
$107$	2.00735	−	1.15894i	0.194057	−	0.112039i	−0.399823	−	0.916592i	$-0.630928\pi$
$107$	2.00735	−	1.15894i	0.194057	−	0.112039i	0.593881	+	0.804553i	$0.297595\pi$
$108$	4.41835	−	4.14300i	0.425156	−	0.398660i
$109$	2.82843	−	4.89898i	0.270914	−	0.469237i	−0.698182	−	0.715920i	$-0.746007\pi$
$109$	2.82843	−	4.89898i	0.270914	−	0.469237i	0.969096	+	0.246683i	$0.0793407\pi$
$110$	13.5978	−	5.37798i	1.29650	−	0.512770i
$111$	8.56578			0.813028
$112$		0			0
$113$	−4.24264			−0.399114			−0.199557	−	0.979886i	$-0.563950\pi$
$113$	−4.24264			−0.399114			−0.199557	+	0.979886i	$0.563950\pi$
$114$	−14.5595	+	5.75832i	−1.36362	+	0.539316i
$115$	3.02846	−	5.24545i	0.282405	−	0.489140i
$116$	−9.96229	+	9.34144i	−0.924975	+	0.867331i
$117$	1.48648	−	0.858221i	0.137425	−	0.0793426i
$118$	2.32515	−	15.7060i	0.214048	−	1.44585i
$119$		0			0
$120$	14.3137	+	6.75481i	1.30666	+	0.616627i
$121$	2.32843	+	4.03295i	0.211675	+	0.366632i
$122$	−4.75626	+	5.99638i	−0.430612	+	0.542887i
$123$	−4.25822	−	2.45849i	−0.383951	−	0.221674i
$124$	−2.75754	−	11.7958i	−0.247634	−	1.05930i
$125$			8.28772i			0.741276i
$126$		0			0
$127$			10.2316i			0.907911i	0.891024	+	0.453955i	$0.149987\pi$
$127$			10.2316i			0.907911i	−0.891024	+	0.453955i	$0.850013\pi$
$128$	9.90022	+	5.47591i	0.875064	+	0.484007i
$129$	13.4174	+	7.74652i	1.18133	+	0.682043i
$130$	−3.13386	−	2.48574i	−0.274858	−	0.218014i
$131$	−0.183707	−	0.318190i	−0.0160505	−	0.0278004i	0.857889	−	0.513836i	$-0.171776\pi$
$131$	−0.183707	−	0.318190i	−0.0160505	−	0.0278004i	−0.873939	+	0.486035i	$0.838443\pi$
$132$	−4.91010	+	16.2200i	−0.427370	+	1.41177i
$133$		0			0
$134$	−4.58579	−	0.678892i	−0.396152	−	0.0586474i
$135$	6.85351	−	3.95687i	0.589856	−	0.340554i
$136$	0.736874	−	0.510937i	0.0631865	−	0.0438125i
$137$	4.12132	−	7.13834i	0.352108	−	0.609869i	−0.634510	−	0.772914i	$-0.718798\pi$
$137$	4.12132	−	7.13834i	0.352108	−	0.609869i	0.986619	+	0.163045i	$0.0521316\pi$
$138$	2.58169	+	6.52763i	0.219768	+	0.555668i
$139$	−22.8211			−1.93566			−0.967829	−	0.251610i	$-0.919040\pi$
$139$	−22.8211			−1.93566			−0.967829	+	0.251610i	$0.919040\pi$
$140$		0			0
$141$	−9.17157			−0.772386
$142$		0			0
$143$	2.14144	−	3.70909i	0.179077	−	0.310170i
$144$	−5.68577	+	2.81203i	−0.473814	+	0.234336i
$145$	−15.4530	+	8.92177i	−1.28330	+	0.740913i
$146$	−19.6089	−	2.90295i	−1.62284	−	0.240250i
$147$		0			0
$148$	7.65685	+	2.31788i	0.629390	+	0.190529i
$149$	−2.41421	−	4.18154i	−0.197780	−	0.342565i	0.750028	−	0.661406i	$-0.230040\pi$
$149$	−2.41421	−	4.18154i	−0.197780	−	0.342565i	−0.947808	+	0.318841i	$0.896707\pi$
$150$	4.33830	+	3.44109i	0.354220	+	0.280964i
$151$	−18.5532	−	10.7117i	−1.50984	−	0.871704i	−0.999934	−	0.0114717i	$-0.996348\pi$
$151$	−18.5532	−	10.7117i	−1.50984	−	0.871704i	−0.509902	−	0.860233i	$-0.670318\pi$
$152$	−14.5728	+	1.20753i	−1.18201	+	0.0979435i
$153$			0.502734i			0.0406437i
$154$		0			0
$155$		−	15.8275i		−	1.27130i
$156$	4.51406	−	1.05526i	0.361414	−	0.0844887i
$157$	−16.6178	−	9.59428i	−1.32624	−	0.765707i	−0.341527	−	0.939872i	$-0.610944\pi$
$157$	−16.6178	−	9.59428i	−1.32624	−	0.765707i	−0.984717	+	0.174165i	$0.944277\pi$
$158$	6.95494	−	8.76833i	0.553305	−	0.697571i
$159$	11.2268	+	19.4454i	0.890345	+	1.54212i
$160$	10.9670	+	9.91131i	0.867019	+	0.783558i
$161$		0			0
$162$	−2.32843	+	15.7281i	−0.182939	+	1.23571i
$163$	−13.1191	+	7.57430i	−1.02757	+	0.593265i	−0.916286	−	0.400524i	$-0.868828\pi$
$163$	−13.1191	+	7.57430i	−1.02757	+	0.593265i	−0.111279	+	0.993789i	$0.535495\pi$
$164$	−3.14112	−	3.34988i	−0.245280	−	0.261582i
$165$	−11.0711	+	19.1757i	−0.861881	+	1.49282i
$166$	−12.4313	+	4.91662i	−0.964857	+	0.381604i
$167$	7.83095			0.605977			0.302989	−	0.952994i	$-0.402016\pi$
$167$	7.83095			0.605977			0.302989	+	0.952994i	$0.402016\pi$
$168$		0			0
$169$	11.8284			0.909879
$170$	1.08946	−	0.430884i	0.0835577	−	0.0330473i
$171$	4.09918	−	7.09999i	0.313472	−	0.542950i
$172$	9.89744	+	10.5552i	0.754673	+	0.804830i
$173$	5.69089	−	3.28564i	0.432671	−	0.249802i	−0.267813	−	0.963471i	$-0.586301\pi$
$173$	5.69089	−	3.28564i	0.432671	−	0.249802i	0.700484	+	0.713668i	$0.252968\pi$
$174$	3.02846	−	20.4567i	0.229587	−	1.55082i
$175$		0			0
$176$	−8.77817	+	13.1702i	−0.661680	+	0.992739i
$177$	12.0208	+	20.8207i	0.903540	+	1.56498i
$178$	−5.26569	+	6.63864i	−0.394680	+	0.497587i
$179$	11.6997	+	6.75481i	0.874474	+	0.504878i	0.868833	−	0.495106i	$-0.164871\pi$
$179$	11.6997	+	6.75481i	0.874474	+	0.504878i	0.00564179	+	0.999984i	$0.498204\pi$
$180$	−8.07014	+	1.88658i	−0.601513	+	0.140617i
$181$		−	21.9874i		−	1.63431i	−0.576418	−	0.817155i	$-0.695550\pi$
$181$		−	21.9874i		−	1.63431i	0.576418	−	0.817155i	$-0.304450\pi$
$182$		0			0
$183$		−	11.5894i		−	0.856714i
$184$	0.541385	+	6.53357i	0.0399115	+	0.481661i
$185$	9.05213	+	5.22625i	0.665526	+	0.384242i
$186$	14.3712	+	11.3991i	1.05375	+	0.835822i
$187$	0.627215	+	1.08637i	0.0458665	+	0.0794431i
$188$	−8.19837	−	2.48181i	−0.597927	−	0.181005i
$189$		0			0
$190$	−18.8995	−	2.79793i	−1.37111	−	0.202983i
$191$	5.67763	−	3.27798i	0.410819	−	0.237186i	−0.280323	−	0.959906i	$-0.590441\pi$
$191$	5.67763	−	3.27798i	0.410819	−	0.237186i	0.691142	+	0.722719i	$0.257108\pi$
$192$	−16.8979	+	2.81975i	−1.21950	+	0.203498i
$193$	−7.29289	+	12.6317i	−0.524954	+	0.909247i	0.474624	+	0.880189i	$0.342584\pi$
$193$	−7.29289	+	12.6317i	−0.524954	+	0.909247i	−0.999578	+	0.0290581i	$0.990749\pi$
$194$	−4.80531	−	12.1499i	−0.345001	−	0.872311i
$195$	6.05692			0.433745
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−3.26365	−	8.25189i	−0.231937	−	0.586437i
$199$	8.56578	−	14.8364i	0.607212	−	1.05172i	−0.384486	−	0.923131i	$-0.625621\pi$
$199$	8.56578	−	14.8364i	0.607212	−	1.05172i	0.991698	−	0.128591i	$-0.0410455\pi$
$200$	2.94680	+	4.24988i	0.208370	+	0.300512i
$201$	6.07917	−	3.50981i	0.428791	−	0.247563i
$202$	21.3068	+	3.15432i	1.49914	+	0.221937i
$203$		0			0
$204$	−0.393398	+	1.29954i	−0.0275434	+	0.0909863i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	13.4220	+	10.6462i	0.935154	+	0.741753i
$207$	−3.18322	−	1.83783i	−0.221249	−	0.127738i
$208$	4.32062	+	0.278208i	0.299581	+	0.0192903i
$209$		−	20.4567i		−	1.41502i
$210$		0			0
$211$		−	14.4697i		−	0.996136i	−0.867138	−	0.498068i	$-0.834043\pi$
$211$		−	14.4697i		−	0.996136i	0.867138	−	0.498068i	$-0.165957\pi$
$212$	4.77364	+	20.4200i	0.327855	+	1.40245i
$213$		0			0
$214$	−2.03706	+	2.56818i	−0.139250	+	0.175557i
$215$	9.45280	+	16.3727i	0.644675	+	1.11661i
$216$	−3.65568	+	7.74652i	−0.248737	+	0.527084i
$217$		0			0
$218$	−1.17157	+	7.91375i	−0.0793489	+	0.535987i
$219$	25.9946	−	15.0080i	1.75655	−	1.01415i
$220$	−15.0852	+	14.1451i	−1.01704	+	0.953662i
$221$	0.171573	−	0.297173i	0.0115412	−	0.0199900i
$222$	−11.2648	+	4.45526i	−0.756044	+	0.299018i
$223$	7.83095			0.524399			0.262200	−	0.965014i	$-0.415552\pi$
$223$	7.83095			0.524399			0.262200	+	0.965014i	$0.415552\pi$
$224$		0			0
$225$	−2.89949			−0.193300
$226$	5.57947	−	2.20670i	0.371141	−	0.146787i
$227$	4.98620	−	8.63635i	0.330946	−	0.573215i	−0.651752	−	0.758432i	$-0.725966\pi$
$227$	4.98620	−	8.63635i	0.330946	−	0.573215i	0.982698	+	0.185218i	$0.0592990\pi$
$228$	16.1521	−	15.1455i	1.06970	−	1.00303i
$229$	−1.16483	+	0.672512i	−0.0769738	+	0.0444409i	−0.537993	−	0.842949i	$-0.680817\pi$
$229$	−1.16483	+	0.672512i	−0.0769738	+	0.0444409i	0.461019	+	0.887390i	$0.347484\pi$
$230$	−1.25443	+	8.47343i	−0.0827146	+	0.558721i
$231$		0			0
$232$	8.24264	−	17.4665i	0.541156	−	1.14673i
$233$	−8.12132	−	14.0665i	−0.532045	−	0.921530i	−0.999300	−	0.0374069i	$-0.988090\pi$
$233$	−8.12132	−	14.0665i	−0.532045	−	0.921530i	0.467255	−	0.884123i	$-0.345243\pi$
$234$	−1.50848	+	1.90180i	−0.0986127	+	0.124324i
$235$	−9.69232	−	5.59587i	−0.632257	−	0.365034i
$236$	5.11124	+	21.8642i	0.332713	+	1.42324i
$237$			16.9469i			1.10082i
$238$		0			0
$239$			10.2316i			0.661829i	0.943661	+	0.330915i	$0.107357\pi$
$239$			10.2316i			0.661829i	−0.943661	+	0.330915i	$0.892643\pi$
$240$	−22.3372	−	1.43831i	−1.44186	−	0.0928425i
$241$	−4.41234	−	2.54747i	−0.284224	−	0.164097i	0.351110	−	0.936334i	$-0.385804\pi$
$241$	−4.41234	−	2.54747i	−0.284224	−	0.164097i	−0.635334	+	0.772237i	$0.719138\pi$
$242$	−5.15973	−	4.09264i	−0.331680	−	0.263085i
$243$	−7.49506	−	12.9818i	−0.480808	−	0.832784i
$244$	3.13607	−	10.3596i	0.200767	−	0.663209i
$245$		0			0
$246$	6.87868	+	1.01834i	0.438569	+	0.0649269i
$247$	−4.84616	+	2.79793i	−0.308354	+	0.178028i
$248$	9.76170	+	14.0783i	0.619868	+	0.893975i
$249$	10.1213	−	17.5306i	0.641413	−	1.11096i
$250$	−4.31064	−	10.8991i	−0.272629	−	0.689321i
$251$	−3.91548			−0.247143			−0.123571	−	0.992336i	$-0.539435\pi$
$251$	−3.91548			−0.247143			−0.123571	+	0.992336i	$0.539435\pi$
$252$		0			0
$253$	−9.17157			−0.576612
$254$	−5.32171	−	13.4556i	−0.333914	−	0.844277i
$255$	−0.887016	+	1.53636i	−0.0555471	+	0.0962103i
$256$	−15.8679	−	2.05200i	−0.991742	−	0.128250i
$257$	−16.5041	+	9.52862i	−1.02950	+	0.594379i	−0.916840	−	0.399255i	$-0.869269\pi$
$257$	−16.5041	+	9.52862i	−1.02950	+	0.594379i	−0.112655	+	0.993634i	$0.535936\pi$
$258$	−21.6743	−	3.20871i	−1.34938	−	0.199766i
$259$		0			0
$260$	5.41421	+	1.63899i	0.335775	+	0.101646i
$261$	5.41421	+	9.37769i	0.335131	+	0.580465i
$262$	0.407090	+	0.322899i	0.0251501	+	0.0199488i
$263$	−22.2235	−	12.8307i	−1.37036	−	0.791176i	−0.379385	−	0.925239i	$-0.623864\pi$
$263$	−22.2235	−	12.8307i	−1.37036	−	0.791176i	−0.990973	+	0.134063i	$0.957198\pi$
$264$	−1.97913	−	23.8846i	−0.121807	−	1.47000i
$265$			27.3994i			1.68313i
$266$		0			0
$267$		−	12.8307i		−	0.785227i
$268$	6.38385	−	1.49237i	0.389956	−	0.0911609i
$269$	4.36524	+	2.52027i	0.266153	+	0.153664i	0.627138	−	0.778908i	$-0.284226\pi$
$269$	4.36524	+	2.52027i	0.266153	+	0.153664i	−0.360985	+	0.932572i	$0.617559\pi$
$270$	−6.95494	+	8.76833i	−0.423264	+	0.533624i
$271$	−2.14144	−	3.70909i	−0.130084	−	0.225311i	0.793625	−	0.608407i	$-0.208191\pi$
$271$	−2.14144	−	3.70909i	−0.130084	−	0.225311i	−0.923709	+	0.383096i	$0.874858\pi$
$272$	−0.703309	+	1.05520i	−0.0426443	+	0.0639806i
$273$		0			0
$274$	−1.70711	+	11.5312i	−0.103130	+	0.696624i
$275$	−6.26557	+	3.61743i	−0.377828	+	0.218139i
$276$	−6.79034	−	7.24164i	−0.408731	−	0.435895i
$277$	2.07107	−	3.58719i	0.124438	−	0.215534i	−0.797075	−	0.603880i	$-0.793620\pi$
$277$	2.07107	−	3.58719i	0.124438	−	0.215534i	0.921513	+	0.388347i	$0.126954\pi$
$278$	30.0118	−	11.8698i	1.79999	−	0.711902i
$279$	−9.60498			−0.575035
$280$		0			0
$281$	10.3848			0.619504			0.309752	−	0.950817i	$-0.399754\pi$
$281$	10.3848			0.619504			0.309752	+	0.950817i	$0.399754\pi$
$282$	12.0615	−	4.77035i	0.718251	−	0.284070i
$283$	−1.69794	+	2.94091i	−0.100932	+	0.174819i	−0.912069	−	0.410037i	$-0.865516\pi$
$283$	−1.69794	+	2.94091i	−0.100932	+	0.174819i	0.811137	+	0.584856i	$0.198849\pi$
$284$		0			0
$285$	25.0542	−	14.4650i	1.48408	−	0.856835i
$286$	−0.887016	+	5.99162i	−0.0524503	+	0.354292i
$287$		0			0
$288$	6.01472	−	6.65539i	0.354421	−	0.392172i
$289$	−8.44975	−	14.6354i	−0.497044	−	0.860905i
$290$	15.6817	−	19.7704i	0.920859	−	1.16096i
$291$	17.1338	+	9.89219i	1.00440	+	0.579890i
$292$	27.2974	−	6.38139i	1.59746	−	0.373443i
$293$			11.7975i			0.689219i	0.938746	+	0.344609i	$0.111989\pi$
$293$			11.7975i			0.689219i	−0.938746	+	0.344609i	$0.888011\pi$
$294$		0			0
$295$			29.3371i			1.70807i
$296$	−11.2751	+	0.934275i	−0.655350	+	0.0543037i
$297$	−10.3778	−	5.99162i	−0.602180	−	0.347669i
$298$	5.34983	+	4.24343i	0.309908	+	0.245815i
$299$	1.25443	+	2.17274i	0.0725455	+	0.125653i
$300$	−7.49506	−	2.26890i	−0.432727	−	0.130995i
$301$		0			0
$302$	29.9706	+	4.43692i	1.72461	+	0.255316i
$303$	−28.2455	+	16.3075i	−1.62266	+	0.936844i
$304$	18.5365	−	9.16765i	1.06314	−	0.525801i
$305$	7.07107	−	12.2474i	0.404888	−	0.701287i
$306$	−0.261484	−	0.661143i	−0.0149480	−	0.0377950i
$307$	−3.91548			−0.223468			−0.111734	−	0.993738i	$-0.535640\pi$
$307$	−3.91548			−0.223468			−0.111734	+	0.993738i	$0.535640\pi$
$308$		0			0
$309$	−25.9411			−1.47574
$310$	8.23225	+	20.8146i	0.467561	+	1.18219i
$311$	−10.3398	+	17.9091i	−0.586317	+	1.01553i	0.408393	+	0.912806i	$0.366089\pi$
$311$	−10.3398	+	17.9091i	−0.586317	+	1.01553i	−0.994710	+	0.102724i	$0.967244\pi$
$312$	−5.38755	+	3.73564i	−0.305010	+	0.211489i
$313$	11.0406	−	6.37430i	0.624052	−	0.360297i	−0.154393	−	0.988010i	$-0.549342\pi$
$313$	11.0406	−	6.37430i	0.624052	−	0.360297i	0.778445	+	0.627713i	$0.216009\pi$
$314$	26.8442	+	3.97408i	1.51490	+	0.224270i
$315$		0			0
$316$	−4.58579	+	15.1486i	−0.257971	+	0.852176i
$317$	2.75736	+	4.77589i	0.154869	+	0.268241i	0.933011	−	0.359847i	$-0.117171\pi$
$317$	2.75736	+	4.77589i	0.154869	+	0.268241i	−0.778142	+	0.628088i	$0.783838\pi$
$318$	−24.8784	−	19.7332i	−1.39511	−	1.10658i
$319$	23.3993	+	13.5096i	1.31011	+	0.756393i
$320$	−19.5778	−	7.33009i	−1.09443	−	0.409765i
$321$		−	4.96362i		−	0.277042i
$322$		0			0
$323$		−	1.63899i		−	0.0911959i
$324$	−5.11844	−	21.8950i	−0.284358	−	1.21639i
$325$	1.71393	+	0.989538i	0.0950717	+	0.0548897i
$326$	13.3132	−	16.7845i	0.737352	−	0.929605i
$327$	−6.05692	−	10.4909i	−0.334948	−	0.580148i
$328$	5.87321	+	2.77164i	0.324294	+	0.153038i
$329$		0			0
$330$	4.58579	−	30.9761i	0.252439	−	1.70518i
$331$	−13.1191	+	7.57430i	−0.721090	+	0.416321i	−0.815154	−	0.579245i	$-0.803348\pi$
$331$	−13.1191	+	7.57430i	−0.721090	+	0.416321i	0.0940639	+	0.995566i	$0.470014\pi$
$332$	13.7911	−	12.9316i	0.756884	−	0.709716i
$333$	3.17157	−	5.49333i	0.173801	−	0.301032i
$334$	−10.2984	+	4.07306i	−0.563505	+	0.222868i
$335$	8.56578			0.467999
$336$		0			0
$337$	10.8284			0.589862			0.294931	−	0.955519i	$-0.404703\pi$
$337$	10.8284			0.589862			0.294931	+	0.955519i	$0.404703\pi$
$338$	−15.5555	+	6.15224i	−0.846107	+	0.334638i
$339$	−4.54269	+	7.86817i	−0.246725	+	0.427340i
$340$	−1.20863	+	1.13331i	−0.0655471	+	0.0614622i
$341$	−20.7556	+	11.9832i	−1.12398	+	0.648929i
$342$	−1.69794	+	11.4692i	−0.0918139	+	0.620185i
$343$		0			0
$344$	−18.5061	−	8.73324i	−0.997782	−	0.470865i
$345$	−6.48528	−	11.2328i	−0.349156	−	0.604756i
$346$	−5.77512	+	7.28089i	−0.310472	+	0.391423i
$347$	−3.42675	−	1.97844i	−0.183958	−	0.106208i	0.405193	−	0.914231i	$-0.367204\pi$
$347$	−3.42675	−	1.97844i	−0.183958	−	0.106208i	−0.589151	+	0.808023i	$0.700538\pi$
$348$	6.65728	+	28.4776i	0.356868	+	1.52656i
$349$		−	8.47343i		−	0.453572i	−0.973945	−	0.226786i	$-0.927178\pi$
$349$		−	8.47343i		−	0.453572i	0.973945	−	0.226786i	$-0.0728218\pi$
$350$		0			0
$351$			3.27798i			0.174966i
$352$	4.69401	−	21.8857i	0.250192	−	1.16651i
$353$	8.71096	+	5.02928i	0.463638	+	0.267681i	0.713573	−	0.700581i	$-0.247076\pi$
$353$	8.71096	+	5.02928i	0.463638	+	0.267681i	−0.249935	+	0.968263i	$0.580409\pi$
$354$	−26.6378	−	21.1288i	−1.41578	−	1.12298i
$355$		0			0
$356$	3.47197	−	11.4692i	0.184014	−	0.607868i
$357$		0			0
$358$	−18.8995	−	2.79793i	−0.998869	−	0.147875i
$359$	27.0696	−	15.6287i	1.42868	−	0.824849i	0.431663	−	0.902035i	$-0.357927\pi$
$359$	27.0696	−	15.6287i	1.42868	−	0.824849i	0.997017	+	0.0771860i	$0.0245935\pi$
$360$	9.63174	−	6.67849i	0.507637	−	0.351987i
$361$	−3.86396	+	6.69258i	−0.203366	+	0.352241i
$362$	11.4362	+	28.9155i	0.601071	+	1.51976i
$363$	9.97240			0.523415
$364$		0			0
$365$	36.6274			1.91717
$366$	6.02793	+	15.2412i	0.315085	+	0.796669i
$367$	−6.42433	+	11.1273i	−0.335348	+	0.580839i	−0.983552	−	0.180628i	$-0.942187\pi$
$367$	−6.42433	+	11.1273i	−0.335348	+	0.580839i	0.648204	+	0.761467i	$0.275520\pi$
$368$	−4.11024	−	8.31067i	−0.214261	−	0.433224i
$369$	−3.15331	+	1.82056i	−0.164155	+	0.0947747i
$370$	−14.6227	−	2.16478i	−0.760198	−	0.112542i
$371$		0			0
$372$	−24.8284	−	7.51606i	−1.28729	−	0.389690i
$373$	10.0711	+	17.4436i	0.521460	+	0.903195i	0.999688	+	0.0249599i	$0.00794580\pi$
$373$	10.0711	+	17.4436i	0.521460	+	0.903195i	−0.478228	+	0.878236i	$0.658721\pi$
$374$	−1.38989	−	1.10245i	−0.0718696	−	0.0570061i
$375$	15.3700	+	8.87385i	0.793701	+	0.458244i
$376$	12.0725	−	1.00035i	0.622590	−	0.0515891i
$377$		−	7.39104i		−	0.380658i
$378$		0			0
$379$			21.7046i			1.11489i	0.830214	+	0.557444i	$0.188218\pi$
$379$			21.7046i			1.11489i	−0.830214	+	0.557444i	$0.811782\pi$
$380$	26.3099	−	6.15053i	1.34967	−	0.315515i
$381$	18.9750	+	10.9552i	0.972120	+	0.561254i
$382$	−5.76166	+	7.26392i	−0.294792	+	0.371655i
$383$	−15.5097	−	26.8636i	−0.792509	−	1.37267i	−0.924409	−	0.381404i	$-0.875441\pi$
$383$	−15.5097	−	26.8636i	−0.792509	−	1.37267i	0.131899	−	0.991263i	$-0.457892\pi$
$384$	20.7557	−	12.4972i	1.05919	−	0.637747i
$385$		0			0
$386$	3.02082	−	20.4050i	0.153755	−	1.03859i
$387$	9.93585	−	5.73647i	0.505068	−	0.291601i
$388$	12.6389	+	13.4789i	0.641642	+	0.684286i
$389$	−7.07107	+	12.2474i	−0.358517	+	0.620970i	−0.987713	−	0.156276i	$-0.950051\pi$
$389$	−7.07107	+	12.2474i	−0.358517	+	0.620970i	0.629196	+	0.777247i	$0.283384\pi$
$390$	−7.96542	+	3.15035i	−0.403345	+	0.159524i
$391$	−0.734828			−0.0371618
$392$		0			0
$393$	−0.786797			−0.0396886
$394$	−2.63019	+	1.04025i	−0.132507	+	0.0524069i
$395$	−10.3398	+	17.9091i	−0.520252	+	0.901103i
$396$	8.58401	+	9.15452i	0.431363	+	0.460032i
$397$	13.9665	−	8.06355i	0.700957	−	0.404698i	−0.106747	−	0.994286i	$-0.534043\pi$
$397$	13.9665	−	8.06355i	0.700957	−	0.404698i	0.807704	+	0.589588i	$0.200710\pi$
$398$	−3.54806	+	23.9665i	−0.177848	+	1.20133i
$399$		0			0
$400$	−6.08579	−	4.05630i	−0.304289	−	0.202815i
$401$	6.41421	+	11.1097i	0.320311	+	0.554794i	0.980552	−	0.196259i	$-0.0628794\pi$
$401$	6.41421	+	11.1097i	0.320311	+	0.554794i	−0.660242	+	0.751053i	$0.729546\pi$
$402$	−6.16914	+	7.77765i	−0.307689	+	0.387914i
$403$	5.67763	+	3.27798i	0.282823	+	0.163288i
$404$	−29.6611	+	6.93396i	−1.47570	+	0.344977i
$405$		−	29.3784i		−	1.45983i
$406$		0			0
$407$		−	15.8275i		−	0.784540i
$408$	−0.158568	−	1.91364i	−0.00785029	−	0.0947392i
$409$	−11.9780	−	6.91550i	−0.592274	−	0.341949i	0.173722	−	0.984795i	$-0.444420\pi$
$409$	−11.9780	−	6.91550i	−0.592274	−	0.341949i	−0.765996	+	0.642845i	$0.777754\pi$
$410$	6.64792	+	5.27306i	0.328317	+	0.260418i
$411$	−8.82558	−	15.2864i	−0.435334	−	0.754020i
$412$	−23.1885	−	7.01962i	−1.14241	−	0.345832i
$413$		0			0
$414$	5.14214	+	0.761256i	0.252722	+	0.0374137i
$415$	21.3920	−	12.3507i	1.05009	−	0.606271i
$416$	−5.82672	+	1.88139i	−0.285679	+	0.0922426i
$417$	−24.4350	+	42.3227i	−1.19659	+	2.07255i
$418$	10.6400	+	26.9024i	0.520419	+	1.31584i
$419$	−17.2837			−0.844366			−0.422183	−	0.906511i	$-0.638736\pi$
$419$	−17.2837			−0.844366			−0.422183	+	0.906511i	$0.638736\pi$
$420$		0			0
$421$	−10.4853			−0.511021			−0.255511	−	0.966806i	$-0.582244\pi$
$421$	−10.4853			−0.511021			−0.255511	+	0.966806i	$0.582244\pi$
$422$	7.52604	+	19.0290i	0.366362	+	0.926319i
$423$	−3.39587	+	5.88183i	−0.165113	+	0.285984i
$424$	−16.8987	−	24.3713i	−0.820674	−	1.18358i
$425$	−0.501998	+	0.289829i	−0.0243505	+	0.0140588i
$426$		0			0
$427$		0			0
$428$	1.34315	−	4.43692i	0.0649234	−	0.214467i
$429$	−4.58579	−	7.94282i	−0.221404	−	0.383483i
$430$	−20.9471	−	16.6150i	−1.01016	−	0.801249i
$431$	−0.831470	−	0.480049i	−0.0400505	−	0.0231232i	0.479841	−	0.877355i	$-0.340694\pi$
$431$	−0.831470	−	0.480049i	−0.0400505	−	0.0231232i	−0.519892	+	0.854232i	$0.674028\pi$
$432$	0.778407	−	12.0888i	0.0374511	−	0.581623i
$433$		−	26.1857i		−	1.25840i	−0.777243	−	0.629201i	$-0.783382\pi$
$433$		−	26.1857i		−	1.25840i	0.777243	−	0.629201i	$-0.216618\pi$
$434$		0			0
$435$			38.2110i			1.83208i
$436$	−2.57540	−	11.0167i	−0.123339	−	0.527603i
$437$	10.3778	+	5.99162i	0.496437	+	0.286618i
$438$	−26.3794	+	33.2573i	−1.26045	+	1.58910i
$439$	11.2268	+	19.4454i	0.535827	+	0.928080i	0.999123	+	0.0418761i	$0.0133335\pi$
$439$	11.2268	+	19.4454i	0.535827	+	0.928080i	−0.463296	+	0.886204i	$0.653333\pi$
$440$	12.4813	−	26.4483i	0.595021	−	1.26087i
$441$		0			0
$442$	−0.0710678	+	0.480049i	−0.00338035	+	0.0228336i
$443$	−24.5752	+	14.1885i	−1.16760	+	0.674116i	−0.953114	−	0.302610i	$-0.902142\pi$
$443$	−24.5752	+	14.1885i	−1.16760	+	0.674116i	−0.214489	+	0.976726i	$0.568809\pi$
$444$	12.4970	−	11.7182i	0.593081	−	0.556120i
$445$	7.82843	−	13.5592i	0.371103	−	0.642769i
$446$	−10.2984	+	4.07306i	−0.487645	+	0.192865i
$447$	−10.3398			−0.489056
$448$		0			0
$449$	−16.2843			−0.768502			−0.384251	−	0.923229i	$-0.625540\pi$
$449$	−16.2843			−0.768502			−0.384251	+	0.923229i	$0.625540\pi$
$450$	3.81311	−	1.50810i	0.179752	−	0.0710923i
$451$	−4.54269	+	7.86817i	−0.213907	+	0.370498i
$452$	−6.18977	+	5.80403i	−0.291142	+	0.272998i
$453$	−39.7306	+	22.9385i	−1.86671	+	1.07774i
$454$	−2.06535	+	13.9510i	−0.0969317	+	0.654755i
$455$		0			0
$456$	−13.3640	+	28.3188i	−0.625825	+	1.32615i
$457$	−0.363961	−	0.630399i	−0.0170254	−	0.0294888i	0.857387	−	0.514672i	$-0.172086\pi$
$457$	−0.363961	−	0.630399i	−0.0170254	−	0.0294888i	−0.874413	+	0.485183i	$0.838753\pi$
$458$	1.18207	−	1.49027i	0.0552343	−	0.0696357i
$459$	−0.831470	−	0.480049i	−0.0388097	−	0.0224068i
$460$	−2.75754	−	11.7958i	−0.128571	−	0.549983i
$461$			29.7499i			1.38559i	0.721135	+	0.692794i	$0.243621\pi$
$461$			29.7499i			1.38559i	−0.721135	+	0.692794i	$0.756379\pi$
$462$		0			0
$463$		−	34.9330i		−	1.62347i	−0.584024	−	0.811737i	$-0.698523\pi$
$463$		−	34.9330i		−	1.62347i	0.584024	−	0.811737i	$-0.301477\pi$
$464$	−1.75512	+	27.2573i	−0.0814792	+	1.26539i
$465$	−29.3528	−	16.9469i	−1.36120	−	0.785892i
$466$	17.9966	+	14.2747i	0.833678	+	0.661264i
$467$	12.0377	+	20.8500i	0.557041	+	0.964823i	0.997742	+	0.0671686i	$0.0213965\pi$
$467$	12.0377	+	20.8500i	0.557041	+	0.964823i	−0.440701	+	0.897654i	$0.645270\pi$
$468$	0.994629	−	3.28564i	0.0459767	−	0.151879i
$469$		0			0
$470$	15.6569	+	2.31788i	0.722197	+	0.106916i
$471$	−35.5861	+	20.5456i	−1.63972	+	0.946693i
$472$	−18.0938	−	26.0950i	−0.832836	−	1.20112i
$473$	14.3137	−	24.7921i	0.658145	−	1.13994i
$474$	−8.81446	−	22.2867i	−0.404861	−	1.02366i
$475$	9.45280			0.433724
$476$		0			0
$477$	16.6274			0.761317
$478$	−5.32171	−	13.4556i	−0.243409	−	0.615443i
$479$	16.3967	−	28.4000i	0.749186	−	1.29763i	−0.199028	−	0.979994i	$-0.563778\pi$
$479$	16.3967	−	28.4000i	0.749186	−	1.29763i	0.948213	−	0.317634i	$-0.102888\pi$
$480$	30.1236	−	9.72659i	1.37495	−	0.443956i
$481$	−3.74952	+	2.16478i	−0.170963	+	0.0987057i
$482$	7.12764	+	1.05520i	0.324655	+	0.0480628i
$483$		0			0
$484$	8.91421	+	2.69851i	0.405192	+	0.122660i
$485$	12.0711	+	20.9077i	0.548119	+	0.949370i
$486$	16.6089	+	13.1740i	0.753393	+	0.597583i
$487$	16.8902	+	9.75158i	0.765370	+	0.441886i	0.831220	−	0.555943i	$-0.187643\pi$
$487$	16.8902	+	9.75158i	0.765370	+	0.441886i	−0.0658507	+	0.997829i	$0.520976\pi$
$488$	1.26407	+	15.2551i	0.0572216	+	0.690564i
$489$			32.4399i			1.46698i
$490$		0			0
$491$			14.4697i			0.653009i	0.945196	+	0.326504i	$0.105871\pi$
$491$			14.4697i			0.653009i	−0.945196	+	0.326504i	$0.894129\pi$
$492$	−9.57577	+	2.23855i	−0.431709	+	0.100922i
$493$	1.87476	+	1.08239i	0.0844349	+	0.0487485i
$494$	4.91789	−	6.20015i	0.221266	−	0.278958i
$495$	8.19837	+	14.2000i	0.368489	+	0.638242i
$496$	−20.1600	−	13.4370i	−0.905212	−	0.603341i
$497$		0			0
$498$	−4.19239	+	28.3188i	−0.187865	+	1.26899i
$499$	10.8682	−	6.27476i	0.486527	−	0.280897i	−0.236605	−	0.971606i	$-0.576035\pi$
$499$	10.8682	−	6.27476i	0.486527	−	0.280897i	0.723133	+	0.690709i	$0.242701\pi$
$500$	11.3378	+	12.0913i	0.507041	+	0.540740i
$501$	8.38478	−	14.5229i	0.374604	−	0.648833i
$502$	5.14922	−	2.03653i	0.229821	−	0.0908948i
$503$	−7.83095			−0.349165			−0.174582	−	0.984643i	$-0.555858\pi$
$503$	−7.83095			−0.349165			−0.174582	+	0.984643i	$0.555858\pi$
$504$		0			0
$505$	−39.7990			−1.77103
$506$	12.0615	−	4.77035i	0.536198	−	0.212068i
$507$	12.6650	−	21.9364i	0.562471	−	0.974228i
$508$	13.9971	+	14.9274i	0.621021	+	0.662295i
$509$	5.69089	−	3.28564i	0.252244	−	0.145633i	−0.368547	−	0.929609i	$-0.620145\pi$
$509$	5.69089	−	3.28564i	0.252244	−	0.145633i	0.620791	+	0.783976i	$0.286811\pi$
$510$	0.367414	−	2.48181i	0.0162694	−	0.109896i
$511$		0			0
$512$	21.9350	−	5.55468i	0.969400	−	0.245485i
$513$	7.82843	+	13.5592i	0.345634	+	0.598655i
$514$	16.7483	−	21.1152i	0.738737	−	0.931351i
$515$	−27.4140	−	15.8275i	−1.20801	−	0.697443i
$516$	30.1726	−	7.05352i	1.32827	−	0.310514i
$517$			16.9469i			0.745322i
$518$		0			0
$519$		−	14.0720i		−	0.617693i
$520$	−7.97268	+	0.660632i	−0.349625	+	0.0289707i
$521$	10.4249	+	6.01882i	0.456723	+	0.263689i	0.710665	−	0.703530i	$-0.248394\pi$
$521$	10.4249	+	6.01882i	0.456723	+	0.263689i	−0.253942	+	0.967219i	$0.581727\pi$
$522$	−11.9978	−	9.51649i	−0.525128	−	0.416525i
$523$	3.73177	+	6.46361i	0.163179	+	0.282634i	0.936007	−	0.351981i	$-0.114492\pi$
$523$	3.73177	+	6.46361i	0.163179	+	0.282634i	−0.772828	+	0.634615i	$0.781159\pi$
$524$	−0.703309	−	0.212906i	−0.0307242	−	0.00930083i
$525$		0			0
$526$	35.8995	+	5.31466i	1.56529	+	0.231730i
$527$	−1.66294	+	0.960099i	−0.0724388	+	0.0418226i
$528$	15.0257	+	30.3811i	0.653909	+	1.32217i
$529$	−8.81371	+	15.2658i	−0.383205	+	0.663730i
$530$	−14.2510	−	36.0327i	−0.619026	−	1.56516i
$531$	17.8033			0.772600
$532$		0			0
$533$	2.48528			0.107649
$534$	6.67356	+	16.8736i	0.288793	+	0.730192i
$535$	3.02846	−	5.24545i	0.130932	−	0.226780i
$536$	−7.61914	+	5.28299i	−0.329097	+	0.228191i
$537$	25.0542	−	14.4650i	1.08117	−	0.624213i
$538$	−7.05155	−	1.04393i	−0.304014	−	0.0450070i
$539$		0			0
$540$	4.58579	−	15.1486i	0.197341	−	0.651892i
$541$	−22.6569	−	39.2428i	−0.974094	−	1.68718i	−0.682892	−	0.730519i	$-0.739278\pi$
$541$	−22.6569	−	39.2428i	−0.974094	−	1.68718i	−0.291202	−	0.956662i	$-0.594055\pi$
$542$	4.74539	+	3.76399i	0.203832	+	0.161677i
$543$	−40.7766	−	23.5424i	−1.74989	−	1.01030i
$544$	0.376085	−	1.75349i	0.0161245	−	0.0751802i
$545$		−	14.7821i		−	0.633194i
$546$		0			0
$547$		−	27.6981i		−	1.18429i	−0.805833	−	0.592143i	$-0.798282\pi$
$547$		−	27.6981i		−	1.18429i	0.805833	−	0.592143i	$-0.201718\pi$
$548$	−3.75263	−	16.0525i	−0.160304	−	0.685728i
$549$	−7.43242	−	4.29111i	−0.317208	−	0.183140i
$550$	6.35830	−	8.01613i	0.271119	−	0.341809i
$551$	−17.6512	−	30.5727i	−0.751965	−	1.30244i
$552$	12.6965	+	5.99162i	0.540398	+	0.255020i
$553$		0			0
$554$	−0.857864	+	5.79471i	−0.0364472	+	0.246194i
$555$	19.3846	−	11.1917i	0.822832	−	0.475063i
$556$	−33.2946	+	31.2197i	−1.41201	+	1.32401i
$557$	9.82843	−	17.0233i	0.416444	−	0.721302i	−0.579135	−	0.815232i	$-0.696610\pi$
$557$	9.82843	−	17.0233i	0.416444	−	0.721302i	0.995579	+	0.0939298i	$0.0299429\pi$
$558$	12.6315	−	4.99578i	0.534732	−	0.211488i
$559$	−7.83095			−0.331214
$560$		0			0
$561$	2.68629			0.113415
$562$	−13.6570	+	5.40137i	−0.576084	+	0.227843i
$563$	10.5235	−	18.2273i	0.443513	−	0.768188i	−0.554434	−	0.832228i	$-0.687065\pi$
$563$	10.5235	−	18.2273i	0.443513	−	0.768188i	0.997947	+	0.0640400i	$0.0203985\pi$
$564$	−13.3808	+	12.5469i	−0.563433	+	0.528320i
$565$	−9.60124	+	5.54328i	−0.403927	+	0.233207i
$566$	0.703309	−	4.75071i	0.0295623	−	0.199687i
$567$		0			0
$568$		0			0
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	0.598394	−	0.801202i	$-0.295806\pi$
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	−0.993058	+	0.117623i	$0.962472\pi$
$570$	−25.4250	+	32.0542i	−1.06494	+	1.34260i
$571$	−8.61732	−	4.97521i	−0.360624	−	0.208206i	0.308731	−	0.951150i	$-0.400096\pi$
$571$	−8.61732	−	4.97521i	−0.360624	−	0.208206i	−0.669354	+	0.742943i	$0.733429\pi$
$572$	−1.94987	−	8.34090i	−0.0815283	−	0.348750i
$573$		−	14.0392i		−	0.586497i
$574$		0			0
$575$		−	4.23808i		−	0.176740i
$576$	−4.44830	+	11.8809i	−0.185346	+	0.495036i
$577$	0.729445	+	0.421145i	0.0303672	+	0.0175325i	0.515107	−	0.857126i	$-0.327752\pi$
$577$	0.729445	+	0.421145i	0.0303672	+	0.0175325i	−0.484740	+	0.874659i	$0.661086\pi$
$578$	18.7244	+	14.8520i	0.778833	+	0.617762i
$579$	15.6173	+	27.0500i	0.649034	+	1.12416i
$580$	−10.3398	+	34.1563i	−0.429337	+	1.41827i
$581$		0			0
$582$	−27.6777	−	4.09748i	−1.14728	−	0.169846i
$583$	35.9305	−	20.7445i	1.48809	−	0.859148i
$584$	−32.5796	+	22.5902i	−1.34815	+	0.934788i
$585$	2.24264	−	3.88437i	0.0927218	−	0.160599i
$586$	−6.13617	−	15.5149i	−0.253483	−	0.640913i
$587$	22.8211			0.941926			0.470963	−	0.882153i	$-0.343906\pi$
$587$	22.8211			0.941926			0.470963	+	0.882153i	$0.343906\pi$
$588$		0			0
$589$	31.3137			1.29026
$590$	−15.2589	−	38.5811i	−0.628200	−	1.58836i
$591$	2.14144	−	3.70909i	0.0880873	−	0.152572i
$592$	14.3418	−	7.09309i	0.589446	−	0.291524i
$593$	32.4395	−	18.7290i	1.33213	−	0.769106i	0.346505	−	0.938048i	$-0.387368\pi$
$593$	32.4395	−	18.7290i	1.33213	−	0.769106i	0.985626	+	0.168942i	$0.0540351\pi$
$594$	16.7641	+	2.48181i	0.687841	+	0.101830i
$595$		0			0
$596$	−9.24264	−	2.79793i	−0.378593	−	0.114608i
$597$	−18.3431	−	31.7713i	−0.750735	−	1.30031i
$598$	−2.77978	−	2.20489i	−0.113674	−	0.0901648i
$599$	27.9011	+	16.1087i	1.14001	+	0.658184i	0.946433	−	0.322902i	$-0.104658\pi$
$599$	27.9011	+	16.1087i	1.14001	+	0.658184i	0.193575	+	0.981085i	$0.437992\pi$
$600$	11.0368	−	0.914533i	0.450576	−	0.0373357i
$601$			25.5516i			1.04227i	0.853474	+	0.521136i	$0.174491\pi$
$601$			25.5516i			1.04227i	−0.853474	+	0.521136i	$0.825509\pi$
$602$		0			0
$603$		−	5.19818i		−	0.211686i
$604$	−41.7218	+	9.75342i	−1.69764	+	0.396861i
$605$	10.5386	+	6.08447i	0.428456	+	0.247369i
$606$	28.6635	−	36.1371i	1.16438	−	1.46797i
$607$	−6.05692	−	10.4909i	−0.245843	−	0.425812i	0.716525	−	0.697561i	$-0.245731\pi$
$607$	−6.05692	−	10.4909i	−0.245843	−	0.425812i	−0.962368	+	0.271749i	$0.912398\pi$
$608$	−19.6089	+	21.6976i	−0.795246	+	0.879953i
$609$		0			0
$610$	−2.92893	+	19.7844i	−0.118589	+	0.801046i
$611$	4.01469	−	2.31788i	0.162417	−	0.0937715i
$612$	0.687752	+	0.733461i	0.0278007	+	0.0296484i
$613$	4.34315	−	7.52255i	0.175418	−	0.303833i	−0.764888	−	0.644163i	$-0.777206\pi$
$613$	4.34315	−	7.52255i	0.175418	−	0.303833i	0.940306	+	0.340331i	$0.110539\pi$
$614$	5.14922	−	2.03653i	0.207806	−	0.0821877i
$615$	−12.8487			−0.518108
$616$		0			0
$617$	−35.4558			−1.42740			−0.713699	−	0.700452i	$-0.752982\pi$
$617$	−35.4558			−1.42740			−0.713699	+	0.700452i	$0.752982\pi$
$618$	34.1150	−	13.4926i	1.37231	−	0.542751i
$619$	−6.76023	+	11.7091i	−0.271717	+	0.470627i	−0.969301	−	0.245875i	$-0.920925\pi$
$619$	−6.76023	+	11.7091i	−0.271717	+	0.470627i	0.697585	+	0.716502i	$0.254258\pi$
$620$	−21.6524	−	23.0914i	−0.869580	−	0.927374i
$621$	6.07917	−	3.50981i	0.243949	−	0.140844i
$622$	4.28289	−	28.9301i	0.171728	−	1.15999i
$623$		0			0
$624$	5.14214	−	7.71491i	0.205850	−	0.308843i
$625$	15.3995	+	26.6727i	0.615980	+	1.06691i
$626$	−11.2040	+	14.1253i	−0.447803	+	0.564560i
$627$	−37.9378	−	21.9034i	−1.51509	−	0.874738i
$628$	−37.3696	+	8.73598i	−1.49121	+	0.348604i
$629$		−	1.26810i		−	0.0505625i
$630$		0			0
$631$		−	20.4633i		−	0.814630i	−0.913288	−	0.407315i	$-0.866465\pi$
$631$		−	20.4633i		−	0.814630i	0.913288	−	0.407315i	$-0.133535\pi$
$632$	−1.84841	−	22.3070i	−0.0735256	−	0.887325i
$633$	−26.8347	−	15.4930i	−1.06659	−	0.615793i
$634$	−6.11024	−	4.84657i	−0.242668	−	0.192482i
$635$	13.3683	+	23.1545i	0.530504	+	0.918859i
$636$	42.9811	+	13.0112i	1.70431	+	0.515929i
$637$		0			0
$638$	−37.7990	−	5.59587i	−1.49648	−	0.221542i
$639$		0			0
$640$	29.5592	−	0.543099i	1.16843	−	0.0214679i
$641$	−24.7279	+	42.8300i	−0.976694	+	1.69168i	−0.302467	+	0.953160i	$0.597810\pi$
$641$	−24.7279	+	42.8300i	−0.976694	+	1.69168i	−0.674227	+	0.738524i	$0.735523\pi$
$642$	2.58169	+	6.52763i	0.101891	+	0.257625i
$643$	41.7267			1.64554			0.822769	−	0.568375i	$-0.192428\pi$
$643$	41.7267			1.64554			0.822769	+	0.568375i	$0.192428\pi$
$644$		0			0
$645$	40.4853			1.59411
$646$	0.852478	+	2.15543i	0.0335403	+	0.0848041i
$647$	21.9341	−	37.9909i	0.862317	−	1.49358i	−0.00737070	−	0.999973i	$-0.502346\pi$
$647$	21.9341	−	37.9909i	0.862317	−	1.49358i	0.869687	−	0.493603i	$-0.164320\pi$
$648$	18.1193	+	26.1317i	0.711794	+	1.02655i
$649$	38.4716	−	22.2116i	1.51014	−	0.871880i
$650$	−2.76866	−	0.409880i	−0.108596	−	0.0160768i
$651$		0			0
$652$	−8.77817	+	28.9977i	−0.343780	+	1.13564i
$653$	11.8995	+	20.6105i	0.465663	+	0.806552i	0.999231	−	0.0392048i	$-0.0124825\pi$
$653$	11.8995	+	20.6105i	0.465663	+	0.806552i	−0.533568	+	0.845757i	$0.679149\pi$
$654$	13.4220	+	10.6462i	0.524841	+	0.416298i
$655$	−0.831470	−	0.480049i	−0.0324882	−	0.0187571i
$656$	−9.16542	−	0.590168i	−0.357850	−	0.0230422i
$657$		−	22.2275i		−	0.867177i
$658$		0			0
$659$		−	13.2284i		−	0.515306i	−0.966238	−	0.257653i	$-0.917051\pi$
$659$		−	13.2284i		−	0.515306i	0.966238	−	0.257653i	$-0.0829491\pi$
$660$	10.0807	+	43.1217i	0.392389	+	1.67851i
$661$	32.6198	+	18.8331i	1.26877	+	0.732522i	0.974754	−	0.223280i	$-0.0716765\pi$
$661$	32.6198	+	18.8331i	1.26877	+	0.732522i	0.294011	+	0.955802i	$0.405010\pi$
$662$	13.3132	−	16.7845i	0.517434	−	0.652346i
$663$	−0.367414	−	0.636379i	−0.0142692	−	0.0247149i
$664$	−11.4105	+	24.1794i	−0.442815	+	0.938342i
$665$		0			0
$666$	−1.31371	+	8.87385i	−0.0509052	+	0.343855i
$667$	−13.7070	+	7.91375i	−0.530738	+	0.306422i
$668$	11.4249	−	10.7129i	0.442043	−	0.414495i
$669$	8.38478	−	14.5229i	0.324174	−	0.561486i
$670$	−11.2648	+	4.45526i	−0.435197	+	0.172122i
$671$	−21.4144			−0.826696
$672$		0			0
$673$	10.3848			0.400304			0.200152	−	0.979765i	$-0.435856\pi$
$673$	10.3848			0.400304			0.200152	+	0.979765i	$0.435856\pi$
$674$	−14.2404	+	5.63212i	−0.548520	+	0.216941i
$675$	2.76866	−	4.79546i	0.106566	−	0.184577i
$676$	17.2570	−	16.1816i	0.663731	−	0.622367i
$677$	−24.9876	+	14.4266i	−0.960351	+	0.554459i	−0.896281	−	0.443487i	$-0.853741\pi$
$677$	−24.9876	+	14.4266i	−0.960351	+	0.554459i	−0.0640697	+	0.997945i	$0.520408\pi$
$678$	1.88164	−	12.7101i	0.0722641	−	0.488130i
$679$		0			0
$680$	1.00000	−	2.11904i	0.0383482	−	0.0812615i
$681$	−10.6777	−	18.4943i	−0.409169	−	0.708702i
$682$	21.0628	−	26.5545i	0.806535	−	1.01683i
$683$	27.9011	+	16.1087i	1.06761	+	0.616382i	0.927526	−	0.373758i	$-0.121931\pi$
$683$	27.9011	+	16.1087i	1.06761	+	0.616382i	0.140079	+	0.990140i	$0.455264\pi$
$684$	−3.73247	−	15.9663i	−0.142715	−	0.610485i
$685$		−	21.5391i		−	0.822965i
$686$		0			0
$687$			2.88030i			0.109890i
$688$	28.8796	+	1.85958i	1.10103	+	0.0708958i
$689$	−9.82868	−	5.67459i	−0.374443	−	0.216185i
$690$	14.3712	+	11.3991i	0.547103	+	0.433956i
$691$	−4.09918	−	7.09999i	−0.155940	−	0.270096i	0.777461	−	0.628931i	$-0.216507\pi$
$691$	−4.09918	−	7.09999i	−0.155940	−	0.270096i	−0.933401	+	0.358835i	$0.883174\pi$
$692$	3.80786	−	12.5788i	0.144753	−	0.478175i
$693$		0			0
$694$	5.53553	+	0.819496i	0.210126	+	0.0311076i
$695$	−51.6448	+	29.8172i	−1.95900	+	1.13103i
$696$	−23.5668	−	33.9881i	−0.893298	−	1.28832i
$697$	−0.363961	+	0.630399i	−0.0137860	+	0.0238781i
$698$	4.40723	+	11.1434i	0.166816	+	0.421782i
$699$	−34.7827			−1.31560
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$	−1.70496	−	4.31085i	−0.0643494	−	0.162703i
$703$	−10.3398	+	17.9091i	−0.389973	+	0.675454i
$704$	5.21022	+	31.2233i	0.196368	+	1.17677i
$705$	−20.7556	+	11.9832i	−0.781700	+	0.451315i
$706$	−14.0716	−	2.08319i	−0.529591	−	0.0784021i
$707$		0			0
$708$	46.0208	+	13.9314i	1.72957	+	0.523575i
$709$	23.3137	+	40.3805i	0.875565	+	1.51652i	0.856160	+	0.516711i	$0.172844\pi$
$709$	23.3137	+	40.3805i	0.875565	+	1.51652i	0.0194047	+	0.999812i	$0.493823\pi$
$710$		0			0
$711$	10.8682	+	6.27476i	0.407589	+	0.235322i
$712$	1.39946	+	16.8890i	0.0524468	+	0.632941i
$713$		−	14.0392i		−	0.525774i
$714$		0			0
$715$		−	11.1917i		−	0.418547i
$716$	26.3099	−	6.15053i	0.983246	−	0.229856i
$717$	18.9750	+	10.9552i	0.708635	+	0.409131i
$718$	−27.4703	+	34.6327i	−1.02518	+	1.29248i
$719$	16.7641	+	29.0364i	0.625197	+	1.08287i	0.988503	+	0.151203i	$0.0483148\pi$
$719$	16.7641	+	29.0364i	0.625197	+	1.08287i	−0.363306	+	0.931670i	$0.618352\pi$
$720$	−9.19299	+	13.7925i	−0.342603	+	0.514017i
$721$		0			0
$722$	1.60051	−	10.8111i	0.0595646	−	0.402348i
$723$	−9.44879	+	5.45526i	−0.351404	+	0.202883i
$724$	−30.0792	−	32.0784i	−1.11789	−	1.19218i
$725$	−6.24264	+	10.8126i	−0.231846	+	0.401569i
$726$	−13.1146	+	5.18688i	−0.486730	+	0.192503i
$727$	29.9802			1.11191			0.555953	−	0.831214i	$-0.312354\pi$
$727$	29.9802			1.11191			0.555953	+	0.831214i	$0.312354\pi$
$728$		0			0
$729$	1.62742			0.0602747
$730$	−48.1685	+	19.0508i	−1.78280	+	0.705101i
$731$	1.14682	−	1.98634i	0.0424165	−	0.0734676i
$732$	−15.8546	−	16.9083i	−0.586002	−	0.624949i
$733$	−17.7160	+	10.2283i	−0.654355	+	0.377792i	−0.790123	−	0.612949i	$-0.789983\pi$
$733$	−17.7160	+	10.2283i	−0.654355	+	0.377792i	0.135768	+	0.990741i	$0.456650\pi$
$734$	2.66105	−	17.9749i	0.0982210	−	0.663464i
$735$		0			0
$736$	9.72792	+	8.79148i	0.358576	+	0.324058i
$737$	−6.48528	−	11.2328i	−0.238888	−	0.413767i
$738$	3.19998	−	4.03432i	0.117793	−	0.148505i
$739$	−10.7673	−	6.21652i	−0.396082	−	0.228678i	0.288710	−	0.957417i	$-0.406774\pi$
$739$	−10.7673	−	6.21652i	−0.396082	−	0.228678i	−0.684792	+	0.728738i	$0.740107\pi$
$740$	20.3562	−	4.75871i	0.748308	−	0.174934i
$741$			11.9832i			0.440215i
$742$		0			0
$743$			45.1646i			1.65693i	0.560042	+	0.828464i	$0.310785\pi$
$743$			45.1646i			1.65693i	−0.560042	+	0.828464i	$0.689215\pi$
$744$	36.5610	−	3.02952i	1.34039	−	0.111068i
$745$	−10.9269	−	6.30864i	−0.400330	−	0.231131i
$746$	−22.3172	−	17.7018i	−0.817092	−	0.648108i
$747$	−7.49506	−	12.9818i	−0.274230	−	0.474980i
$748$	2.40125	+	0.726905i	0.0877982	+	0.0265783i
$749$		0			0
$750$	−24.8284	−	3.67567i	−0.906606	−	0.134216i
$751$	32.2602	−	18.6254i	1.17719	−	0.679652i	0.221828	−	0.975086i	$-0.428798\pi$
$751$	32.2602	−	18.6254i	1.17719	−	0.679652i	0.955363	+	0.295434i	$0.0954643\pi$
$752$	−15.3561	+	7.59473i	−0.559980	+	0.276951i
$753$	−4.19239	+	7.26143i	−0.152779	+	0.264621i
$754$	3.84425	+	9.71991i	0.139999	+	0.353978i
$755$	−55.9819			−2.03739
$756$		0			0
$757$	−44.2843			−1.60954			−0.804770	−	0.593587i	$-0.797711\pi$
$757$	−44.2843			−1.60954			−0.804770	+	0.593587i	$0.797711\pi$
$758$	−11.2891	−	28.5435i	−0.410037	−	1.03675i
$759$	−9.82021	+	17.0091i	−0.356451	+	0.617391i
$760$	−31.4009	+	21.7729i	−1.13903	+	0.789786i
$761$	0.0471057	−	0.0271965i	0.00170758	−	0.000985871i	−0.499146	−	0.866518i	$-0.666353\pi$
$761$	0.0471057	−	0.0271965i	0.00170758	−	0.000985871i	0.500854	+	0.865532i	$0.333020\pi$
$762$	−30.6520	−	4.53781i	−1.11041	−	0.164387i
$763$		0			0
$764$	3.79899	−	12.5495i	0.137443	−	0.454026i
$765$	0.656854	+	1.13770i	0.0237486	+	0.0411338i
$766$	34.3691	+	27.2612i	1.24181	+	0.984987i
$767$	−10.5238	−	6.07591i	−0.379992	−	0.219389i
$768$	−20.7956	+	27.2306i	−0.750397	+	0.982599i
$769$			19.1342i			0.689996i	0.938603	+	0.344998i	$0.112120\pi$
$769$			19.1342i			0.689996i	−0.938603	+	0.344998i	$0.887880\pi$
$770$		0			0
$771$			40.8100i			1.46974i
$772$	6.64048	+	28.4057i	0.238996	+	1.02234i
$773$	−42.8644	−	24.7478i	−1.54173	−	0.890116i	−0.998730	−	0.0503797i	$-0.983957\pi$
$773$	−42.8644	−	24.7478i	−1.54173	−	0.890116i	−0.542995	−	0.839736i	$-0.682710\pi$
$774$	−10.0829	+	12.7119i	−0.362423	+	0.456919i
$775$	−5.53732	−	9.59092i	−0.198906	−	0.344516i
$776$	−23.6320	−	11.1522i	−0.848339	−	0.400341i
$777$		0			0
$778$	2.92893	−	19.7844i	0.105007	−	0.709304i
$779$	10.2803	−	5.93531i	0.368329	−	0.212655i
$780$	8.83670	−	8.28600i	0.316405	−	0.296686i
$781$		0			0
$782$	0.966367	−	0.382201i	0.0345572	−	0.0136675i
$783$	−20.6796			−0.739029
$784$		0			0
$785$	−50.1421			−1.78965
$786$	1.03471	−	0.409231i	0.0369069	−	0.0145968i
$787$	−20.6035	+	35.6864i	−0.734436	+	1.27208i	0.220534	+	0.975379i	$0.429220\pi$
$787$	−20.6035	+	35.6864i	−0.734436	+	1.27208i	−0.954970	+	0.296702i	$0.904113\pi$
$788$	2.91789	−	2.73604i	0.103945	−	0.0974675i
$789$	−47.5903	+	27.4763i	−1.69426	+	0.978182i
$790$	4.28289	−	28.9301i	0.152378	−	1.02929i
$791$		0			0
$792$	−16.0503	−	7.57430i	−0.570321	−	0.269141i
$793$	2.92893	+	5.07306i	0.104009	+	0.180150i
$794$	−14.1732	+	17.8686i	−0.502988	+	0.634133i
$795$	50.8134	+	29.3371i	1.80216	+	1.04048i
$796$	−7.79949	−	33.3636i	−0.276446	−	1.18254i
$797$			20.1940i			0.715309i	0.933854	+	0.357655i	$0.116424\pi$
$797$			20.1940i			0.715309i	−0.933854	+	0.357655i	$0.883576\pi$
$798$		0			0
$799$			1.35778i			0.0480350i
$800$	10.1132	+	2.16905i	0.357554	+	0.0766875i
$801$	−8.22848	−	4.75071i	−0.290739	−	0.167858i
$802$	−14.2137	−	11.2742i	−0.501904	−	0.398105i
$803$	−27.7312	−	48.0318i	−0.978612	−	1.69501i
$804$	4.06766	−	13.4370i	0.143455	−	0.473888i
$805$		0			0
$806$	−9.17157	−	1.35778i	−0.323055	−	0.0478259i
$807$	9.34792	−	5.39702i	0.329062	−	0.189984i
$808$	35.4006	−	24.5462i	1.24539	−	0.863534i
$809$	0.0208153	−	0.0360531i	0.000731826	−	0.00126756i	−0.865659	−	0.500634i	$-0.833100\pi$
$809$	0.0208153	−	0.0360531i	0.000731826	−	0.00126756i	0.866391	+	0.499366i	$0.166434\pi$
$810$	15.2804	+	38.6354i	0.536899	+	1.35751i
$811$	39.4330			1.38468			0.692340	−	0.721571i	$-0.256580\pi$
$811$	39.4330			1.38468			0.692340	+	0.721571i	$0.256580\pi$
$812$		0			0
$813$	−9.17157			−0.321661
$814$	8.23225	+	20.8146i	0.288540	+	0.729553i
$815$	−19.7926	+	34.2818i	−0.693305	+	1.20084i
$816$	1.20386	+	2.43414i	0.0421435	+	0.0852119i
$817$	−32.3924	+	18.7018i	−1.13327	+	0.654292i
$818$	19.3491	+	2.86449i	0.676525	+	0.100155i
$819$		0			0
$820$	−11.4853	−	3.47682i	−0.401083	−	0.121416i
$821$	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	$0.731630\pi$
$822$	19.5573	+	15.5126i	0.682138	+	0.541064i
$823$	−14.8829	−	8.59264i	−0.518785	−	0.299521i	0.217652	−	0.976026i	$-0.430160\pi$
$823$	−14.8829	−	8.59264i	−0.518785	−	0.299521i	−0.736437	+	0.676506i	$0.763493\pi$
$824$	34.1461	−	2.82942i	1.18954	−	0.0985674i
$825$			15.4930i			0.539399i
$826$		0			0
$827$			45.1646i			1.57053i	0.619162	+	0.785264i	$0.287473\pi$
$827$			45.1646i			1.57053i	−0.619162	+	0.785264i	$0.712527\pi$
$828$	−7.15834	+	1.67342i	−0.248769	+	0.0581555i
$829$	40.8954	+	23.6110i	1.42036	+	0.820044i	0.996329	−	0.0856056i	$-0.0272825\pi$
$829$	40.8954	+	23.6110i	1.42036	+	0.820044i	0.424028	+	0.905649i	$0.360616\pi$
$830$	−21.7086	+	27.3688i	−0.753517	+	0.949984i
$831$	−4.43508	−	7.68178i	−0.153851	−	0.266478i
$832$	6.68414	−	5.50482i	0.231731	−	0.190845i
$833$		0			0
$834$	10.1213	−	68.3676i	0.350473	−	2.36738i
$835$	17.7217	−	10.2316i	0.613285	−	0.354080i
$836$	−27.9852	−	29.8451i	−0.967887	−	1.03221i
$837$	9.17157	−	15.8856i	0.317016	−	0.549088i
$838$	22.7297	−	8.98968i	0.785186	−	0.310543i
$839$	42.3984			1.46376			0.731878	−	0.681435i	$-0.238644\pi$
$839$	42.3984			1.46376			0.731878	+	0.681435i	$0.238644\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	13.7891	−	5.45364i	0.475205	−	0.187945i
$843$	11.1192	−	19.2590i	0.382966	−	0.663317i
$844$	−19.7949	−	21.1105i	−0.681368	−	0.726653i
$845$	26.7681	−	15.4546i	0.920852	−	0.531654i
$846$	1.40662	−	9.50143i	0.0483605	−	0.326666i
$847$		0			0
$848$	34.8995	+	23.2612i	1.19845	+	0.798793i
$849$	3.63604	+	6.29780i	0.124789	+	0.216140i
$850$	0.509428	−	0.642253i	0.0174732	−	0.0220291i
$851$	8.02938	+	4.63577i	0.275244	+	0.158912i
$852$		0			0
$853$		−	38.3002i		−	1.31137i	−0.755033	−	0.655687i	$-0.772379\pi$
$853$		−	38.3002i		−	1.31137i	0.755033	−	0.655687i	$-0.227621\pi$
$854$		0			0
$855$		−	21.4234i		−	0.732664i
$856$	0.541385	+	6.53357i	0.0185042	+	0.223313i
$857$	−2.99248	−	1.72771i	−0.102221	−	0.0590174i	0.448018	−	0.894025i	$-0.352130\pi$
$857$	−2.99248	−	1.72771i	−0.102221	−	0.0590174i	−0.550239	+	0.835007i	$0.685463\pi$
$858$	10.1620	+	8.06037i	0.346924	+	0.275177i
$859$	−1.33052	−	2.30453i	−0.0453969	−	0.0786297i	0.842434	−	0.538799i	$-0.181122\pi$
$859$	−1.33052	−	2.30453i	−0.0453969	−	0.0786297i	−0.887831	+	0.460170i	$0.847789\pi$
$860$	36.1893	+	10.9552i	1.23405	+	0.373571i
$861$		0			0
$862$	1.34315	+	0.198843i	0.0457477	+	0.00677262i
$863$	10.8682	−	6.27476i	0.369958	−	0.213595i	−0.303482	−	0.952837i	$-0.598149\pi$
$863$	10.8682	−	6.27476i	0.369958	−	0.213595i	0.673440	+	0.739242i	$0.264816\pi$
$864$	5.26399	+	16.3028i	0.179085	+	0.554632i
$865$	8.58579	−	14.8710i	0.291925	−	0.505630i
$866$	13.6198	+	34.4366i	0.462819	+	1.17020i
$867$	−36.1893			−1.22905
$868$		0			0
$869$	31.3137			1.06224
$870$	−19.8744	−	50.2510i	−0.673806	−	1.70367i
$871$	−1.77403	+	3.07271i	−0.0601107	+	0.104115i
$872$	9.11693	+	13.1484i	0.308738	+	0.445263i
$873$	12.6879	−	7.32538i	0.429421	−	0.247926i
$874$	−16.7641	−	2.48181i	−0.567056	−	0.0839485i
$875$		0			0
$876$	17.3934	−	57.4570i	0.587668	−	1.94129i
$877$	−15.2132	−	26.3500i	−0.513713	−	0.889778i	−0.999873	−	0.0159079i	$-0.994936\pi$
$877$	−15.2132	−	26.3500i	−0.513713	−	0.889778i	0.486160	−	0.873870i	$-0.338397\pi$
$878$	−24.8784	−	19.7332i	−0.839604	−	0.665964i
$879$	21.8791	+	12.6319i	0.737962	+	0.426063i
$880$	−2.65765	+	41.2738i	−0.0895893	+	1.39134i
$881$		−	26.1857i		−	0.882217i	−0.897454	−	0.441109i	$-0.854585\pi$
$881$		−	26.1857i		−	0.882217i	0.897454	−	0.441109i	$-0.145415\pi$
$882$		0			0
$883$		−	24.7013i		−	0.831266i	−0.909532	−	0.415633i	$-0.863560\pi$
$883$		−	24.7013i		−	0.831266i	0.909532	−	0.415633i	$-0.136440\pi$
$884$	−0.156224	−	0.668274i	−0.00525438	−	0.0224765i
$885$	54.4070	+	31.4119i	1.82887	+	1.05590i
$886$	24.9389	−	31.4414i	0.837840	−	1.05629i
$887$	11.2268	+	19.4454i	0.376960	+	0.652914i	0.990618	−	0.136658i	$-0.0436361\pi$
$887$	11.2268	+	19.4454i	0.376960	+	0.652914i	−0.613658	+	0.789572i	$0.710303\pi$
$888$	−10.3398	+	21.9105i	−0.346981	+	0.735267i
$889$		0			0
$890$	−3.24264	+	21.9034i	−0.108694	+	0.734204i
$891$	−38.5258	+	22.2429i	−1.29066	+	0.745164i
$892$	11.4249	−	10.7129i	0.382534	−	0.358695i
$893$	11.0711	−	19.1757i	0.370479	−	0.641689i
$894$	13.5978	−	5.37798i	0.454779	−	0.179866i
$895$	35.3023			1.18003
$896$		0			0
$897$	5.37258			0.179385
$898$	21.4153	−	8.46983i	0.714639	−	0.282642i
$899$	−20.6796	+	35.8182i	−0.689704	+	1.19460i
$900$	−4.23020	+	3.96657i	−0.141007	+	0.132219i
$901$	2.87875	−	1.66205i	0.0959052	−	0.0553709i
$902$	1.88164	−	12.7101i	0.0626519	−	0.423201i
$903$		0			0
$904$	5.12132	−	10.8523i	0.170333	−	0.360942i
$905$	−28.7279	−	49.7582i	−0.954948	−	1.65402i
$906$	40.3186	−	50.8311i	1.33950	−	1.68875i
$907$	29.4214	+	16.9864i	0.976921	+	0.564025i	0.901339	−	0.433114i	$-0.142585\pi$
$907$	29.4214	+	16.9864i	0.976921	+	0.564025i	0.0755817	+	0.997140i	$0.475919\pi$
$908$	−4.54014	−	19.4212i	−0.150670	−	0.644514i
$909$			24.1522i			0.801077i
$910$		0			0
$911$			18.7078i			0.619817i	0.950766	+	0.309908i	$0.100298\pi$
$911$			18.7078i			0.619817i	−0.950766	+	0.309908i	$0.899702\pi$
$912$	2.84560	−	44.1928i	0.0942274	−	1.46337i
$913$	−32.3924	−	18.7018i	−1.07203	−	0.618938i
$914$	0.806528	+	0.639729i	0.0266776	+	0.0211604i
$915$	−15.1423	−	26.2272i	−0.500589	−	0.867046i
$916$	−0.779403	+	2.57466i	−0.0257522	+	0.0850693i
$917$		0			0
$918$	1.34315	+	0.198843i	0.0443304	+	0.00656280i
$919$	−42.2969	+	24.4201i	−1.39525	+	0.805546i	−0.993890	−	0.110376i	$-0.964795\pi$
$919$	−42.2969	+	24.4201i	−1.39525	+	0.805546i	−0.401357	+	0.915922i	$0.631461\pi$
$920$	9.76170	+	14.0783i	0.321834	+	0.464149i
$921$	−4.19239	+	7.26143i	−0.138144	+	0.239272i
$922$	−15.4736	−	39.1238i	−0.509596	−	1.28848i
$923$		0			0
$924$		0			0
$925$	7.31371			0.240473
$926$	18.1695	+	45.9401i	0.597085	+	1.50969i
$927$	−9.60498	+	16.6363i	−0.315469	+	0.546408i
$928$	−11.8690	−	36.7587i	−0.389619	−	1.20666i
$929$	25.8779	−	14.9406i	0.849025	−	0.490185i	−0.0112969	−	0.999936i	$-0.503596\pi$
$929$	25.8779	−	14.9406i	0.849025	−	0.490185i	0.860322	+	0.509751i	$0.170263\pi$
$930$	47.4162	+	7.01962i	1.55484	+	0.230182i
$931$		0			0
$932$	−31.0919	−	9.41214i	−1.01845	−	0.308305i
$933$	22.1421	+	38.3513i	0.724901	+	1.25557i
$934$	−26.6753	−	21.1586i	−0.872844	−	0.692330i
$935$	2.83882	+	1.63899i	0.0928392	+	0.0536007i
$936$	0.400908	+	4.83825i	0.0131041	+	0.158143i
$937$		−	29.8042i		−	0.973662i	−0.873496	−	0.486831i	$-0.838153\pi$
$937$		−	29.8042i		−	0.973662i	0.873496	−	0.486831i	$-0.161847\pi$
$938$		0			0
$939$		−	27.3004i		−	0.890916i
$940$	−21.7958	+	5.09526i	−0.710901	+	0.166189i
$941$	−21.4655	−	12.3931i	−0.699756	−	0.404004i	0.107501	−	0.994205i	$-0.465715\pi$
$941$	−21.4655	−	12.3931i	−0.699756	−	0.404004i	−0.807256	+	0.590201i	$0.799049\pi$
$942$	36.1128	−	45.5286i	1.17662	−	1.48340i
$943$	−2.66105	−	4.60907i	−0.0866556	−	0.150092i
$944$	37.3677	+	24.9063i	1.21621	+	0.810631i
$945$		0			0
$946$	−5.92893	+	40.0488i	−0.192766	+	1.30210i
$947$	−7.92851	+	4.57753i	−0.257642	+	0.148750i	−0.623258	−	0.782016i	$-0.714192\pi$
$947$	−7.92851	+	4.57753i	−0.257642	+	0.148750i	0.365616	+	0.930766i	$0.380858\pi$
$948$	23.1837	+	24.7245i	0.752971	+	0.803015i
$949$	−7.58579	+	13.1390i	−0.246245	+	0.426509i
$950$	−12.4313	+	4.91662i	−0.403325	+	0.159516i
$951$	11.8095			0.382948
$952$		0			0
$953$	26.3431			0.853338			0.426669	−	0.904408i	$-0.359687\pi$
$953$	26.3431			0.853338			0.426669	+	0.904408i	$0.359687\pi$
$954$	−21.8666	+	8.64831i	−0.707958	+	0.279999i
$955$	8.56578	−	14.8364i	0.277182	−	0.480094i
$956$	13.9971	+	14.9274i	0.452699	+	0.482786i
$957$	50.1084	−	28.9301i	1.61977	−	0.935177i
$958$	−6.79175	+	45.8770i	−0.219431	+	1.48222i
$959$		0			0
$960$	−34.5563	+	28.4594i	−1.11530	+	0.918522i
$961$	−2.84315	−	4.92447i	−0.0917144	−	0.158854i
$962$	3.80501	−	4.79711i	0.122678	−	0.154665i
$963$	−3.18322	−	1.83783i	−0.102578	−	0.0592234i
$964$	−9.92235	+	2.31957i	−0.319577	+	0.0747084i
$965$			38.1145i			1.22695i
$966$		0			0
$967$			45.1646i			1.45240i	0.687486	+	0.726198i	$0.258714\pi$
$967$			45.1646i			1.45240i	−0.687486	+	0.726198i	$0.741286\pi$
$968$	−13.1266	+	1.08770i	−0.421904	+	0.0349599i
$969$	−3.03958	−	1.75490i	−0.0976455	−	0.0563757i
$970$	−26.7492	−	21.2171i	−0.858864	−	0.681241i
$971$	6.50043	+	11.2591i	0.208609	+	0.361321i	0.951276	−	0.308339i	$-0.0997732\pi$
$971$	6.50043	+	11.2591i	0.208609	+	0.361321i	−0.742668	+	0.669660i	$0.766440\pi$
$972$	−28.6943	−	8.68633i	−0.920369	−	0.278614i
$973$		0			0
$974$	−27.2843	−	4.03924i	−0.874244	−	0.129426i
$975$	3.67029	−	2.11904i	0.117543	−	0.0678636i
$976$	−9.59688	−	19.4044i	−0.307189	−	0.621118i
$977$	−8.80761	+	15.2552i	−0.281780	+	0.488058i	−0.971823	−	0.235710i	$-0.924258\pi$
$977$	−8.80761	+	15.2552i	−0.281780	+	0.488058i	0.690043	+	0.723768i	$0.257592\pi$
$978$	−16.8728	−	42.6615i	−0.539531	−	1.36416i
$979$	−23.7081			−0.757714
$980$		0			0
$981$	−8.97056			−0.286408
$982$	−7.52604	−	19.0290i	−0.240165	−	0.607241i
$983$	−4.80249	+	8.31816i	−0.153176	+	0.265308i	−0.932393	−	0.361445i	$-0.882283\pi$
$983$	−4.80249	+	8.31816i	−0.153176	+	0.265308i	0.779218	+	0.626754i	$0.215617\pi$
$984$	11.4287	−	7.92449i	0.364334	−	0.252623i
$985$	4.52607	−	2.61313i	0.144212	−	0.0832611i
$986$	−3.02846	−	0.448342i	−0.0964458	−	0.0142781i
$987$		0			0
$988$	−3.24264	+	10.7117i	−0.103162	+	0.340784i
$989$	8.38478	+	14.5229i	0.266620	+	0.461800i
$990$	−18.1674	−	14.4102i	−0.577397	−	0.457985i
$991$	−22.2235	−	12.8307i	−0.705952	−	0.407581i	0.103609	−	0.994618i	$-0.466961\pi$
$991$	−22.2235	−	12.8307i	−0.705952	−	0.407581i	−0.809560	+	0.587037i	$0.800294\pi$
$992$	33.5012	+	7.18528i	1.06367	+	0.228133i
$993$			32.4399i			1.02945i
$994$		0			0
$995$		−	44.7669i		−	1.41921i
$996$	−9.21587	−	39.4224i	−0.292016	−	1.24915i
$997$	26.7681	+	15.4546i	0.847755	+	0.489452i	0.859893	−	0.510475i	$-0.170530\pi$
$997$	26.7681	+	15.4546i	0.847755	+	0.489452i	−0.0121377	+	0.999926i	$0.503864\pi$
$998$	−11.0291	+	13.9047i	−0.349119	+	0.440146i
$999$	6.05692	+	10.4909i	0.191632	+	0.331917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.f.d.31.2		16
4.3	odd	2	inner	196.2.f.d.31.5		16
7.2	even	3	inner	196.2.f.d.19.6		16
7.3	odd	6		196.2.d.c.195.6	yes	8
7.4	even	3		196.2.d.c.195.5	✓	8
7.5	odd	6	inner	196.2.f.d.19.5		16
7.6	odd	2	inner	196.2.f.d.31.1		16
21.11	odd	6		1764.2.b.k.1567.3		8
21.17	even	6		1764.2.b.k.1567.4		8
28.3	even	6		196.2.d.c.195.7	yes	8
28.11	odd	6		196.2.d.c.195.8	yes	8
28.19	even	6	inner	196.2.f.d.19.2		16
28.23	odd	6	inner	196.2.f.d.19.1		16
28.27	even	2	inner	196.2.f.d.31.6		16
56.3	even	6		3136.2.f.i.3135.6		8
56.11	odd	6		3136.2.f.i.3135.3		8
56.45	odd	6		3136.2.f.i.3135.4		8
56.53	even	6		3136.2.f.i.3135.5		8
84.11	even	6		1764.2.b.k.1567.1		8
84.59	odd	6		1764.2.b.k.1567.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.c.195.5	✓	8	7.4	even	3
196.2.d.c.195.6	yes	8	7.3	odd	6
196.2.d.c.195.7	yes	8	28.3	even	6
196.2.d.c.195.8	yes	8	28.11	odd	6
196.2.f.d.19.1		16	28.23	odd	6	inner
196.2.f.d.19.2		16	28.19	even	6	inner
196.2.f.d.19.5		16	7.5	odd	6	inner
196.2.f.d.19.6		16	7.2	even	3	inner
196.2.f.d.31.1		16	7.6	odd	2	inner
196.2.f.d.31.2		16	1.1	even	1	trivial
196.2.f.d.31.5		16	4.3	odd	2	inner
196.2.f.d.31.6		16	28.27	even	2	inner
1764.2.b.k.1567.1		8	84.11	even	6
1764.2.b.k.1567.2		8	84.59	odd	6
1764.2.b.k.1567.3		8	21.11	odd	6
1764.2.b.k.1567.4		8	21.17	even	6
3136.2.f.i.3135.3		8	56.11	odd	6
3136.2.f.i.3135.4		8	56.45	odd	6
3136.2.f.i.3135.5		8	56.53	even	6
3136.2.f.i.3135.6		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)

\(f(q)\)	\(=\)	\(q+(-1.31509 + 0.520123i) q^{2} +(1.07072 - 1.85455i) q^{3} +(1.45894 - 1.36802i) q^{4} +(2.26303 - 1.30656i) q^{5} +(-0.443508 + 2.99581i) q^{6} +(-1.20711 + 2.55791i) q^{8} +(-0.792893 - 1.37333i) q^{9} +O(q^{10})\)	\(q+(-1.31509 + 0.520123i) q^{2} +(1.07072 - 1.85455i) q^{3} +(1.45894 - 1.36802i) q^{4} +(2.26303 - 1.30656i) q^{5} +(-0.443508 + 2.99581i) q^{6} +(-1.20711 + 2.55791i) q^{8} +(-0.792893 - 1.37333i) q^{9} +(-2.29653 + 2.89531i) q^{10} +(-3.42675 - 1.97844i) q^{11} +(-0.974936 - 4.17045i) q^{12} +1.08239i q^{13} -5.59587i q^{15} +(0.257031 - 3.99173i) q^{16} +(-0.274552 - 0.158513i) q^{17} +(1.75703 + 1.39366i) q^{18} +(2.58495 + 4.47727i) q^{19} +(1.51423 - 5.00208i) q^{20} +(5.53553 + 0.819496i) q^{22} +(2.00735 - 1.15894i) q^{23} +(3.45128 + 4.97744i) q^{24} +(0.914214 - 1.58346i) q^{25} +(-0.562978 - 1.42345i) q^{26} +3.02846 q^{27} -6.82843 q^{29} +(2.91054 + 7.35909i) q^{30} +(3.02846 - 5.24545i) q^{31} +(1.73817 + 5.38319i) q^{32} +(-7.33820 + 4.23671i) q^{33} +(0.443508 + 0.0656581i) q^{34} +(-3.03553 - 0.918917i) q^{36} +(2.00000 + 3.46410i) q^{37} +(-5.72819 - 4.54353i) q^{38} +(2.00735 + 1.15894i) q^{39} +(0.610345 + 7.36579i) q^{40} -2.29610i q^{41} +7.23486i q^{43} +(-7.70598 + 1.80145i) q^{44} +(-3.58869 - 2.07193i) q^{45} +(-2.03706 + 2.56818i) q^{46} +(-2.14144 - 3.70909i) q^{47} +(-7.12764 - 4.75071i) q^{48} +(-0.378680 + 2.55791i) q^{50} +(-0.587938 + 0.339446i) q^{51} +(1.48074 + 1.57915i) q^{52} +(-5.24264 + 9.08052i) q^{53} +(-3.98271 + 1.57517i) q^{54} -10.3398 q^{55} +11.0711 q^{57} +(8.98002 - 3.55162i) q^{58} +(-5.61341 + 9.72272i) q^{59} +(-7.65527 - 8.16405i) q^{60} +(4.68690 - 2.70598i) q^{61} +(-1.25443 + 8.47343i) q^{62} +(-5.08579 - 6.17534i) q^{64} +(1.41421 + 2.44949i) q^{65} +(7.44681 - 9.38845i) q^{66} +(2.83882 + 1.63899i) q^{67} +(-0.617405 + 0.144332i) q^{68} -4.96362i q^{69} +(4.46996 - 0.370390i) q^{72} +(12.1388 + 7.00835i) q^{73} +(-4.43195 - 3.51537i) q^{74} +(-1.95774 - 3.39090i) q^{75} +(9.89630 + 2.99581i) q^{76} +(-3.24264 - 0.480049i) q^{78} +(-6.85351 + 3.95687i) q^{79} +(-4.63378 - 9.36925i) q^{80} +(5.62132 - 9.73641i) q^{81} +(1.19426 + 3.01959i) q^{82} +9.45280 q^{83} -0.828427 q^{85} +(-3.76302 - 9.51451i) q^{86} +(-7.31135 + 12.6636i) q^{87} +(9.19712 - 6.37714i) q^{88} +(5.18889 - 2.99581i) q^{89} +(5.79712 + 0.858221i) q^{90} +(1.34315 - 4.43692i) q^{92} +(-6.48528 - 11.2328i) q^{93} +(4.74539 + 3.76399i) q^{94} +(11.6997 + 6.75481i) q^{95} +(11.8445 + 2.54038i) q^{96} +9.23880i q^{97} +6.27476i 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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