LMFDB - Embedded newform 196.2.f.d.31.5

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			31.5
Root			$-1.33546 + 0.465333i$ of defining polynomial
Character	$\chi$	$=$	196.31
Dual form			196.2.f.d.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10799 - 0.878843i) q^{2} +(-1.07072 + 1.85455i) q^{3} +(0.455270 - 1.94749i) q^{4} +(2.26303 - 1.30656i) q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +(-0.792893 - 1.37333i) q^{9} +O(q^{10})$	\(q+(1.10799 - 0.878843i) q^{2} +(-1.07072 + 1.85455i) q^{3} +(0.455270 - 1.94749i) 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} +(1.35915 - 3.43651i) q^{10} +(3.42675 + 1.97844i) q^{11} +(3.12425 + 2.92954i) q^{12} +1.08239i q^{13} +5.59587i q^{15} +(-3.58546 - 1.77327i) q^{16} +(-0.274552 - 0.158513i) q^{17} +(-2.08546 - 0.824805i) 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} +(6.03623 + 0.500175i) q^{24} +(0.914214 - 1.58346i) q^{25} +(0.951253 + 1.19928i) q^{26} -3.02846 q^{27} -6.82843 q^{29} +(4.91789 + 6.20015i) q^{30} +(-3.02846 + 5.24545i) q^{31} +(-5.53107 + 1.18629i) 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} +(-6.79891 - 2.68899i) q^{38} +(-2.00735 - 1.15894i) q^{39} +(-6.07379 - 4.21147i) q^{40} -2.29610i q^{41} -7.23486i q^{43} +(5.41309 - 5.77286i) q^{44} +(-3.58869 - 2.07193i) q^{45} +(-1.20559 + 3.04823i) 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} +(2.10795 + 0.492781i) q^{52} +(-5.24264 + 9.08052i) q^{53} +(-3.35549 + 2.66154i) q^{54} +10.3398 q^{55} +11.0711 q^{57} +(-7.56581 + 6.00111i) q^{58} +(5.61341 - 9.72272i) q^{59} +(10.8979 + 2.54763i) 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} +(-4.40723 + 11.1434i) q^{66} +(-2.83882 - 1.63899i) q^{67} +(-0.433698 + 0.462522i) q^{68} -4.96362i q^{69} +(-2.55575 + 3.68591i) q^{72} +(12.1388 + 7.00835i) q^{73} +(5.26038 + 2.08049i) 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} +(-10.4309 + 0.671654i) q^{80} +(5.62132 - 9.73641i) q^{81} +(-2.01791 - 2.54405i) q^{82} -9.45280 q^{83} -0.828427 q^{85} +(-6.35830 - 8.01613i) q^{86} +(7.31135 - 12.6636i) q^{87} +(0.924203 - 11.1535i) 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} +(5.63240 + 2.22763i) q^{94} +(-11.6997 - 6.75481i) q^{95} +(3.72221 - 11.5278i) 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 $

$2$	1.10799	−	0.878843i	0.783465	−	0.621436i
$2$	1.10799	−	0.878843i	0.783465	−	0.621436i
$3$	−1.07072	+	1.85455i	−0.618182	+	1.07072i	0.371635	+	0.928379i	$0.378797\pi$
$3$	−1.07072	+	1.85455i	−0.618182	+	1.07072i	−0.989817	+	0.142344i	$0.954536\pi$
$4$	0.455270	−	1.94749i	0.227635	−	0.973746i
$5$	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
$10$	1.35915	−	3.43651i	0.429800	−	1.08672i
$11$	3.42675	+	1.97844i	1.03321	+	0.596521i	0.917901	−	0.396809i	$-0.129882\pi$
$11$	3.42675	+	1.97844i	1.03321	+	0.596521i	0.115304	+	0.993330i	$0.463216\pi$
$12$	3.12425	+	2.92954i	0.901892	+	0.845687i
$13$			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
$16$	−3.58546	−	1.77327i	−0.896364	−	0.443318i
$17$	−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	$0.678907\pi$
$18$	−2.08546	−	0.824805i	−0.491547	−	0.194408i
$19$	−2.58495	−	4.47727i	−0.593029	−	1.02716i	−0.993822	−	0.110987i	$-0.964599\pi$
$19$	−2.58495	−	4.47727i	−0.593029	−	1.02716i	0.400793	−	0.916169i	$-0.368735\pi$
$20$	−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	−0.694461	−	0.719530i	$-0.744357\pi$
$23$	−2.00735	+	1.15894i	−0.418561	+	0.241656i	0.275901	+	0.961186i	$0.411024\pi$
$24$	6.03623	+	0.500175i	1.23214	+	0.102098i
$25$	0.914214	−	1.58346i	0.182843	−	0.316693i
$26$	0.951253	+	1.19928i	0.186556	+	0.235197i
$27$	−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	$0.718590\pi$
$30$	4.91789	+	6.20015i	0.897879	+	1.13199i
$31$	−3.02846	+	5.24545i	−0.543928	+	0.942110i	0.454746	+	0.890621i	$0.349730\pi$
$31$	−3.02846	+	5.24545i	−0.543928	+	0.942110i	−0.998674	+	0.0514890i	$0.983603\pi$
$32$	−5.53107	+	1.18629i	−0.977764	+	0.209709i
$33$	−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	$0.726690\pi$
$38$	−6.79891	−	2.68899i	−1.10293	−	0.436212i
$39$	−2.00735	−	1.15894i	−0.321433	−	0.185579i
$40$	−6.07379	−	4.21147i	−0.960351	−	0.665892i
$41$		−	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	$-0.813997\pi$
$43$		−	7.23486i		−	1.10331i	0.834074	−	0.551653i	$-0.186003\pi$
$44$	5.41309	−	5.77286i	0.816054	−	0.870291i
$45$	−3.58869	−	2.07193i	−0.534970	−	0.308865i
$46$	−1.20559	+	3.04823i	−0.177754	+	0.449438i
$47$	2.14144	+	3.70909i	0.312362	+	0.541027i	0.978873	−	0.204468i	$-0.0655465\pi$
$47$	2.14144	+	3.70909i	0.312362	+	0.541027i	−0.666511	+	0.745495i	$0.732213\pi$
$48$	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
$52$	2.10795	+	0.492781i	0.292320	+	0.0683364i
$53$	−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	$0.910748\pi$
$54$	−3.35549	+	2.66154i	−0.456625	+	0.362190i
$55$	10.3398			1.39422
$56$		0			0
$57$	11.0711			1.46640
$58$	−7.56581	+	6.00111i	−0.993439	+	0.787985i
$59$	5.61341	−	9.72272i	0.730804	−	1.26579i	−0.225736	−	0.974189i	$-0.572479\pi$
$59$	5.61341	−	9.72272i	0.730804	−	1.26579i	0.956540	−	0.291601i	$-0.0941881\pi$
$60$	10.8979	+	2.54763i	1.40691	+	0.328898i
$61$	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
$66$	−4.40723	+	11.1434i	−0.542492	+	1.37165i
$67$	−2.83882	−	1.63899i	−0.346817	−	0.200235i	0.316466	−	0.948604i	$-0.397504\pi$
$67$	−2.83882	−	1.63899i	−0.346817	−	0.200235i	−0.663282	+	0.748369i	$0.730837\pi$
$68$	−0.433698	+	0.462522i	−0.0525936	+	0.0560890i
$69$		−	4.96362i		−	0.597550i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−2.55575	+	3.68591i	−0.301198	+	0.434388i
$73$	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	$0.360492\pi$
$74$	5.26038	+	2.08049i	0.611506	+	0.241852i
$75$	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	−0.0621799	−	0.998065i	$-0.519805\pi$
$79$	6.85351	−	3.95687i	0.771080	−	0.445183i	0.833260	+	0.552882i	$0.186472\pi$
$80$	−10.4309	+	0.671654i	−1.16621	+	0.0750932i
$81$	5.62132	−	9.73641i	0.624591	−	1.08182i
$82$	−2.01791	−	2.54405i	−0.222841	−	0.280943i
$83$	−9.45280			−1.03758			−0.518790	−	0.854902i	$-0.673617\pi$
$83$	−9.45280			−1.03758			−0.518790	+	0.854902i	$0.673617\pi$
$84$		0			0
$85$	−0.828427			−0.0898555
$86$	−6.35830	−	8.01613i	−0.685633	−	0.864401i
$87$	7.31135	−	12.6636i	0.783859	−	1.35768i
$88$	0.924203	−	11.1535i	0.0985203	−	1.18897i
$89$	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
$94$	5.63240	+	2.22763i	0.580938	+	0.229763i
$95$	−11.6997	−	6.75481i	−1.20036	−	0.693029i
$96$	3.72221	−	11.5278i	0.379896	−	1.17655i
$97$			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
$100$	−2.66757	−	2.50133i	−0.266757	−	0.250133i
$101$	−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	$0.940364\pi$
$102$	0.353108	−	0.892807i	0.0349629	−	0.0884011i
$103$	6.05692	+	10.4909i	0.596806	+	1.03370i	0.993289	+	0.115657i	$0.0368972\pi$
$103$	6.05692	+	10.4909i	0.596806	+	1.03370i	−0.396483	+	0.918042i	$0.629769\pi$
$104$	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	−0.593881	−	0.804553i	$-0.702405\pi$
$107$	−2.00735	+	1.15894i	−0.194057	+	0.112039i	0.399823	+	0.916592i	$0.369072\pi$
$108$	−1.37877	+	5.89791i	−0.132672	+	0.567526i
$109$	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	$0.0793407\pi$
$110$	11.4564	−	9.08707i	1.09232	−	0.866418i
$111$	−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	$0.563950\pi$
$114$	12.2666	−	9.72973i	1.14887	−	0.911273i
$115$	−3.02846	+	5.24545i	−0.282405	+	0.489140i
$116$	−3.10878	+	13.2983i	−0.288643	+	1.23472i
$117$	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
$122$	2.81489	−	7.11724i	0.254848	−	0.644364i
$123$	4.25822	+	2.45849i	0.383951	+	0.221674i
$124$	8.83670	+	8.28600i	0.793559	+	0.744105i
$125$			8.28772i			0.741276i
$126$		0			0
$127$		−	10.2316i		−	0.907911i	−0.891024	−	0.453955i	$-0.850013\pi$
$127$		−	10.2316i		−	0.907911i	0.891024	−	0.453955i	$-0.149987\pi$
$128$	−0.207835	+	11.3118i	−0.0183702	+	0.999831i
$129$	13.4174	+	7.74652i	1.18133	+	0.682043i
$130$	3.71965	+	1.47113i	0.326235	+	0.129027i
$131$	0.183707	+	0.318190i	0.0160505	+	0.0278004i	0.873939	−	0.486035i	$-0.161557\pi$
$131$	0.183707	+	0.318190i	0.0160505	+	0.0278004i	−0.857889	+	0.513836i	$0.828224\pi$
$132$	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
$136$	−0.0740472	+	0.893620i	−0.00634950	+	0.0766273i
$137$	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	$0.0521316\pi$
$138$	−4.36224	−	5.49963i	−0.371339	−	0.468159i
$139$	22.8211			1.93566			0.967829	−	0.251610i	$-0.0809599\pi$
$139$	22.8211			1.93566			0.967829	+	0.251610i	$0.0809599\pi$
$140$		0			0
$141$	−9.17157			−0.772386
$142$		0			0
$143$	−2.14144	+	3.70909i	−0.179077	+	0.310170i
$144$	0.407596	+	6.33004i	0.0339663	+	0.527503i
$145$	−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	$0.896707\pi$
$150$	5.14922	+	2.03653i	0.420432	+	0.166282i
$151$	18.5532	+	10.7117i	1.50984	+	0.871704i	0.999934	+	0.0114717i	$0.00365163\pi$
$151$	18.5532	+	10.7117i	1.50984	+	0.871704i	0.509902	+	0.860233i	$0.329682\pi$
$152$	−8.33213	+	12.0166i	−0.675825	+	0.974676i
$153$			0.502734i			0.0406437i
$154$		0			0
$155$			15.8275i			1.27130i
$156$	−3.17092	+	3.38166i	−0.253876	+	0.270749i
$157$	−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	$0.944277\pi$
$158$	4.11613	−	10.4073i	0.327461	−	0.827962i
$159$	−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	0.111279	−	0.993789i	$-0.464505\pi$
$163$	13.1191	−	7.57430i	1.02757	−	0.593265i	0.916286	+	0.400524i	$0.131172\pi$
$164$	−4.47164	−	1.04535i	−0.349176	−	0.0816278i
$165$	−11.0711	+	19.1757i	−0.861881	+	1.49282i
$166$	−10.4736	+	8.30752i	−0.812907	+	0.644789i
$167$	−7.83095			−0.605977			−0.302989	−	0.952994i	$-0.597984\pi$
$167$	−7.83095			−0.605977			−0.302989	+	0.952994i	$0.597984\pi$
$168$		0			0
$169$	11.8284			0.909879
$170$	−0.917886	+	0.728057i	−0.0703987	+	0.0558394i
$171$	−4.09918	+	7.09999i	−0.313472	+	0.542950i
$172$	−14.0898	−	3.29382i	−1.07434	−	0.251151i
$173$	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
$178$	3.11638	−	7.87954i	0.233583	−	0.590597i
$179$	−11.6997	−	6.75481i	−0.874474	−	0.504878i	−0.00564179	−	0.999984i	$-0.501796\pi$
$179$	−11.6997	−	6.75481i	−0.874474	−	0.504878i	−0.868833	+	0.495106i	$0.835129\pi$
$180$	−5.66889	+	6.04566i	−0.422534	+	0.450617i
$181$		−	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
$184$	5.38755	+	3.73564i	0.397175	+	0.275395i
$185$	9.05213	+	5.22625i	0.665526	+	0.384242i
$186$	−17.0575	−	6.74629i	−1.25072	−	0.494662i
$187$	−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	−0.691142	−	0.722719i	$-0.742892\pi$
$191$	−5.67763	+	3.27798i	−0.410819	+	0.237186i	0.280323	+	0.959906i	$0.409559\pi$
$192$	−6.00698	−	16.0439i	−0.433516	−	1.15787i
$193$	−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	$0.990749\pi$
$194$	8.11945	+	10.2365i	0.582943	+	0.734935i
$195$	−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	$0.477302\pi$
$198$	−5.51453	−	6.95235i	−0.391900	−	0.494082i
$199$	−8.56578	+	14.8364i	−0.607212	+	1.05172i	0.384486	+	0.923131i	$0.374379\pi$
$199$	−8.56578	+	14.8364i	−0.607212	+	1.05172i	−0.991698	+	0.128591i	$0.958955\pi$
$200$	−5.15391	−	0.427064i	−0.364436	−	0.0301980i
$201$	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
$206$	15.9308	+	6.30069i	1.10995	+	0.438990i
$207$	3.18322	+	1.83783i	0.221249	+	0.127738i
$208$	1.91938	−	3.88087i	0.133085	−	0.269090i
$209$		−	20.4567i		−	1.41502i
$210$		0			0
$211$			14.4697i			0.996136i	0.867138	+	0.498068i	$0.165957\pi$
$211$			14.4697i			0.996136i	−0.867138	+	0.498068i	$0.834043\pi$
$212$	15.2974	+	14.3441i	1.05063	+	0.985157i
$213$		0			0
$214$	−1.20559	+	3.04823i	−0.0824121	+	0.208373i
$215$	−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
$220$	4.70741	−	20.1367i	0.317373	−	1.35762i
$221$	0.171573	−	0.297173i	0.0115412	−	0.0199900i
$222$	−9.49077	+	7.52797i	−0.636979	+	0.505245i
$223$	−7.83095			−0.524399			−0.262200	−	0.965014i	$-0.584448\pi$
$223$	−7.83095			−0.524399			−0.262200	+	0.965014i	$0.584448\pi$
$224$		0			0
$225$	−2.89949			−0.193300
$226$	−4.70079	+	3.72861i	−0.312692	+	0.248024i
$227$	−4.98620	+	8.63635i	−0.330946	+	0.573215i	−0.982698	−	0.185218i	$-0.940701\pi$
$227$	−4.98620	+	8.63635i	−0.330946	+	0.573215i	0.651752	+	0.758432i	$0.274034\pi$
$228$	5.04033	−	21.5608i	0.333804	−	1.42790i
$229$	−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	$-0.345243\pi$
$234$	0.892762	−	2.25728i	0.0583617	−	0.147563i
$235$	9.69232	+	5.59587i	0.632257	+	0.365034i
$236$	−16.3793	−	15.3585i	−1.06620	−	0.999756i
$237$			16.9469i			1.10082i
$238$		0			0
$239$		−	10.2316i		−	0.661829i	−0.943661	−	0.330915i	$-0.892643\pi$
$239$		−	10.2316i		−	0.661829i	0.943661	−	0.330915i	$-0.107357\pi$
$240$	9.92299	−	20.0637i	0.640526	−	1.29511i
$241$	−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	$0.719138\pi$
$242$	6.12420	+	2.42214i	0.393678	+	0.155701i
$243$	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
$248$	17.0730	+	1.41471i	1.08414	+	0.0898341i
$249$	10.1213	−	17.5306i	0.641413	−	1.11096i
$250$	7.28360	+	9.18269i	0.460656	+	0.580764i
$251$	3.91548			0.247143			0.123571	−	0.992336i	$-0.460565\pi$
$251$	3.91548			0.247143			0.123571	+	0.992336i	$0.460565\pi$
$252$		0			0
$253$	−9.17157			−0.576612
$254$	−8.99200	−	11.3365i	−0.564208	−	0.711316i
$255$	0.887016	−	1.53636i	0.0555471	−	0.0962103i
$256$	9.71102	+	12.7160i	0.606939	+	0.794749i
$257$	−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
$262$	0.483184	+	0.191101i	0.0298512	+	0.0118062i
$263$	22.2235	+	12.8307i	1.37036	+	0.791176i	0.990973	−	0.134063i	$-0.0428024\pi$
$263$	22.2235	+	12.8307i	1.37036	+	0.791176i	0.379385	+	0.925239i	$0.376136\pi$
$264$	19.6951	+	13.6563i	1.21215	+	0.840486i
$265$			27.3994i			1.68313i
$266$		0			0
$267$			12.8307i			0.785227i
$268$	−4.48435	+	4.78239i	−0.273925	+	0.292131i
$269$	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	$0.617559\pi$
$270$	−4.11613	+	10.4073i	−0.250499	+	0.633369i
$271$	2.14144	+	3.70909i	0.130084	+	0.225311i	0.923709	−	0.383096i	$-0.125142\pi$
$271$	2.14144	+	3.70909i	0.130084	+	0.225311i	−0.793625	+	0.608407i	$0.791809\pi$
$272$	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
$276$	−9.66661	−	2.25979i	−0.581862	−	0.136023i
$277$	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	$0.126954\pi$
$278$	25.2854	−	20.0561i	1.51652	−	1.20289i
$279$	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	$0.399754\pi$
$282$	−10.1620	+	8.06037i	−0.605137	+	0.479988i
$283$	1.69794	−	2.94091i	0.100932	−	0.174819i	−0.811137	−	0.584856i	$-0.801151\pi$
$283$	1.69794	−	2.94091i	0.100932	−	0.174819i	0.912069	+	0.410037i	$0.134484\pi$
$284$		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
$290$	−9.28084	+	23.4659i	−0.544990	+	1.37797i
$291$	−17.1338	−	9.89219i	−1.00440	−	0.579890i
$292$	19.1752	−	20.4496i	1.12214	−	1.19672i
$293$			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
$296$	6.44664	−	9.29736i	0.374703	−	0.540398i
$297$	−10.3778	−	5.99162i	−0.602180	−	0.347669i
$298$	−6.34983	−	2.51138i	−0.367836	−	0.145480i
$299$	−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
$304$	1.32882	+	20.6369i	0.0762133	+	1.18361i
$305$	7.07107	−	12.2474i	0.404888	−	0.701287i
$306$	0.441825	+	0.557023i	0.0252574	+	0.0318429i
$307$	3.91548			0.223468			0.111734	−	0.993738i	$-0.464360\pi$
$307$	3.91548			0.223468			0.111734	+	0.993738i	$0.464360\pi$
$308$		0			0
$309$	−25.9411			−1.47574
$310$	13.9099	+	17.5367i	0.790028	+	0.996015i
$311$	10.3398	−	17.9091i	0.586317	−	1.01553i	−0.408393	−	0.912806i	$-0.633911\pi$
$311$	10.3398	−	17.9091i	0.586317	−	1.01553i	0.994710	−	0.102724i	$-0.0327560\pi$
$312$	−0.541385	+	6.53357i	−0.0306499	+	0.369891i
$313$	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	$0.783838\pi$
$318$	−29.5287	−	11.6787i	−1.65588	−	0.654907i
$319$	−23.3993	−	13.5096i	−1.31011	−	0.756393i
$320$	−3.44084	+	20.6199i	−0.192349	+	1.15269i
$321$		−	4.96362i		−	0.277042i
$322$		0			0
$323$			1.63899i			0.0911959i
$324$	−16.4024	−	15.3802i	−0.911243	−	0.854455i
$325$	1.71393	+	0.989538i	0.0950717	+	0.0548897i
$326$	7.87914	−	19.9218i	0.436385	−	1.10337i
$327$	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	−0.0940639	−	0.995566i	$-0.529986\pi$
$331$	13.1191	−	7.57430i	0.721090	−	0.416321i	0.815154	+	0.579245i	$0.196652\pi$
$332$	−4.30358	+	18.4093i	−0.236189	+	1.01034i
$333$	3.17157	−	5.49333i	0.173801	−	0.301032i
$334$	−8.67659	+	6.88218i	−0.474762	+	0.376576i
$335$	−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	$0.404703\pi$
$338$	13.1057	−	10.3953i	0.712858	−	0.565431i
$339$	4.54269	−	7.86817i	0.246725	−	0.427340i
$340$	−0.377158	+	1.61336i	−0.0204543	+	0.0874965i
$341$	−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
$346$	3.41787	−	8.64184i	0.183746	−	0.464588i
$347$	3.42675	+	1.97844i	0.183958	+	0.106208i	0.589151	−	0.808023i	$-0.299462\pi$
$347$	3.42675	+	1.97844i	0.183958	+	0.106208i	−0.405193	+	0.914231i	$0.632796\pi$
$348$	−21.3337	−	20.0042i	−1.14361	−	1.07234i
$349$		−	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
$352$	−21.3006	−	6.87774i	−1.13533	−	0.366585i
$353$	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	$0.580409\pi$
$354$	31.6170	+	12.5046i	1.68042	+	0.664613i
$355$		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	−0.997017	−	0.0771860i	$-0.975406\pi$
$359$	−27.0696	+	15.6287i	−1.42868	+	0.824849i	−0.431663	+	0.902035i	$0.642073\pi$
$360$	−0.967877	+	11.6806i	−0.0510116	+	0.615620i
$361$	−3.86396	+	6.69258i	−0.203366	+	0.352241i
$362$	−19.3235	−	24.3618i	−1.01562	−	1.28043i
$363$	−9.97240			−0.523415
$364$		0			0
$365$	36.6274			1.91717
$366$	10.1853	+	12.8409i	0.532393	+	0.671206i
$367$	6.42433	−	11.1273i	0.335348	−	0.580839i	−0.648204	−	0.761467i	$-0.724480\pi$
$367$	6.42433	−	11.1273i	0.335348	−	0.580839i	0.983552	+	0.180628i	$0.0578129\pi$
$368$	9.25237	−	0.595767i	0.482313	−	0.0310565i
$369$	−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	$0.658721\pi$
$374$	−1.64969	−	0.652458i	−0.0853036	−	0.0337378i
$375$	−15.3700	−	8.87385i	−0.793701	−	0.458244i
$376$	6.90256	−	9.95489i	0.355972	−	0.513384i
$377$		−	7.39104i		−	0.380658i
$378$		0			0
$379$		−	21.7046i		−	1.11489i	−0.830214	−	0.557444i	$-0.811782\pi$
$379$		−	21.7046i		−	1.11489i	0.830214	−	0.557444i	$-0.188218\pi$
$380$	−18.4815	+	19.7098i	−0.948078	+	1.01109i
$381$	18.9750	+	10.9552i	0.972120	+	0.561254i
$382$	−3.40991	+	8.62171i	−0.174466	+	0.441125i
$383$	15.5097	+	26.8636i	0.792509	+	1.37267i	0.924409	+	0.381404i	$0.124559\pi$
$383$	15.5097	+	26.8636i	0.792509	+	1.37267i	−0.131899	+	0.991263i	$0.542108\pi$
$384$	−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
$388$	17.9925	+	4.20615i	0.913430	+	0.213535i
$389$	−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	$0.283384\pi$
$390$	−6.71099	+	5.32308i	−0.339824	+	0.269545i
$391$	0.734828			0.0371618
$392$		0			0
$393$	−0.786797			−0.0396886
$394$	2.21597	−	1.75769i	0.111639	−	0.0885509i
$395$	10.3398	−	17.9091i	0.520252	−	0.901103i
$396$	−12.2200	−	2.85671i	−0.614080	−	0.143555i
$397$	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	$0.729546\pi$
$402$	3.65107	−	9.23146i	0.182099	−	0.460423i
$403$	−5.67763	−	3.27798i	−0.282823	−	0.163288i
$404$	−20.8355	+	22.2203i	−1.03661	+	1.10550i
$405$		−	29.3784i		−	1.45983i
$406$		0			0
$407$			15.8275i			0.784540i
$408$	−1.57798	−	1.09414i	−0.0781214	−	0.0541682i
$409$	−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	$0.777754\pi$
$410$	−7.89056	−	3.12074i	−0.389687	−	0.154122i
$411$	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
$416$	−1.28403	−	5.98678i	−0.0629549	−	0.293526i
$417$	−24.4350	+	42.3227i	−1.19659	+	2.07255i
$418$	−17.9782	−	22.6657i	−0.879342	−	1.10862i
$419$	17.2837			0.844366			0.422183	−	0.906511i	$-0.361264\pi$
$419$	17.2837			0.844366			0.422183	+	0.906511i	$0.361264\pi$
$420$		0			0
$421$	−10.4853			−0.511021			−0.255511	−	0.966806i	$-0.582244\pi$
$421$	−10.4853			−0.511021			−0.255511	+	0.966806i	$0.582244\pi$
$422$	12.7166	+	16.0323i	0.619035	+	0.780438i
$423$	3.39587	−	5.88183i	0.165113	−	0.285984i
$424$	29.5556	+	2.44904i	1.43534	+	0.118936i
$425$	−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
$430$	−24.8626	−	9.83324i	−1.19898	−	0.474201i
$431$	0.831470	+	0.480049i	0.0400505	+	0.0231232i	0.519892	−	0.854232i	$-0.325972\pi$
$431$	0.831470	+	0.480049i	0.0400505	+	0.0231232i	−0.479841	+	0.877355i	$0.659306\pi$
$432$	10.8584	+	5.37028i	0.522426	+	0.258378i
$433$		−	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
$436$	−8.25303	−	7.73870i	−0.395248	−	0.370617i
$437$	10.3778	+	5.99162i	0.496437	+	0.286618i
$438$	−15.6120	+	39.4739i	−0.745971	+	1.88613i
$439$	−11.2268	−	19.4454i	−0.535827	−	0.928080i	−0.999123	−	0.0418761i	$-0.986667\pi$
$439$	−11.2268	−	19.4454i	−0.535827	−	0.928080i	0.463296	−	0.886204i	$-0.346667\pi$
$440$	−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	0.214489	−	0.976726i	$-0.431191\pi$
$443$	24.5752	−	14.1885i	1.16760	−	0.674116i	0.953114	+	0.302610i	$0.0978580\pi$
$444$	−3.89975	+	16.6818i	−0.185074	+	0.791683i
$445$	7.82843	−	13.5592i	0.371103	−	0.642769i
$446$	−8.67659	+	6.88218i	−0.410849	+	0.325881i
$447$	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	$0.625540\pi$
$450$	−3.21260	+	2.54820i	−0.151444	+	0.120123i
$451$	4.54269	−	7.86817i	0.213907	−	0.370498i
$452$	−1.93155	+	8.26251i	−0.0908524	+	0.388636i
$453$	−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	$0.838753\pi$
$458$	−0.699579	+	1.76883i	−0.0326892	+	0.0826522i
$459$	0.831470	+	0.480049i	0.0388097	+	0.0224068i
$460$	8.83670	+	8.28600i	0.412013	+	0.386337i
$461$			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	$0.301477\pi$
$463$			34.9330i			1.62347i	−0.584024	+	0.811737i	$0.698523\pi$
$464$	24.4830	+	12.1087i	1.13660	+	0.562130i
$465$	−29.3528	−	16.9469i	−1.36120	−	0.785892i
$466$	−21.3606	−	8.44818i	−0.989510	−	0.391354i
$467$	−12.0377	−	20.8500i	−0.557041	−	0.964823i	−0.997742	−	0.0671686i	$-0.978603\pi$
$467$	−12.0377	−	20.8500i	−0.557041	−	0.964823i	0.440701	−	0.897654i	$-0.354730\pi$
$468$	−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
$472$	−31.6458	−	2.62224i	−1.45662	−	0.120698i
$473$	14.3137	−	24.7921i	0.658145	−	1.13994i
$474$	14.8936	+	18.7769i	0.684087	+	0.862451i
$475$	−9.45280			−0.433724
$476$		0			0
$477$	16.6274			0.761317
$478$	−8.99200	−	11.3365i	−0.411284	−	0.518520i
$479$	−16.3967	+	28.4000i	−0.749186	+	1.29763i	0.199028	+	0.979994i	$0.436222\pi$
$479$	−16.3967	+	28.4000i	−0.749186	+	1.29763i	−0.948213	+	0.317634i	$0.897112\pi$
$480$	−6.63833	−	30.9511i	−0.302997	−	1.41272i
$481$	−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
$486$	19.7134	+	7.79671i	0.894218	+	0.353666i
$487$	−16.8902	−	9.75158i	−0.765370	−	0.441886i	0.0658507	−	0.997829i	$-0.479024\pi$
$487$	−16.8902	−	9.75158i	−0.765370	−	0.441886i	−0.831220	+	0.555943i	$0.812357\pi$
$488$	−12.5792	−	8.72224i	−0.569435	−	0.394837i
$489$			32.4399i			1.46698i
$490$		0			0
$491$		−	14.4697i		−	0.653009i	−0.945196	−	0.326504i	$-0.894129\pi$
$491$		−	14.4697i		−	0.653009i	0.945196	−	0.326504i	$-0.105871\pi$
$492$	6.72653	−	7.17358i	0.303255	−	0.323410i
$493$	1.87476	+	1.08239i	0.0844349	+	0.0487485i
$494$	2.91054	−	7.35909i	0.130951	−	0.331101i
$495$	−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	−0.723133	−	0.690709i	$-0.757299\pi$
$499$	−10.8682	+	6.27476i	−0.486527	+	0.280897i	0.236605	+	0.971606i	$0.423965\pi$
$500$	16.1403	+	3.77315i	0.721815	+	0.168741i
$501$	8.38478	−	14.5229i	0.374604	−	0.648833i
$502$	4.33830	−	3.44109i	0.193628	−	0.153583i
$503$	7.83095			0.349165			0.174582	−	0.984643i	$-0.444142\pi$
$503$	7.83095			0.349165			0.174582	+	0.984643i	$0.444142\pi$
$504$		0			0
$505$	−39.7990			−1.77103
$506$	−10.1620	+	8.06037i	−0.451755	+	0.358327i
$507$	−12.6650	+	21.9364i	−0.562471	+	0.974228i
$508$	−19.9260	−	4.65816i	−0.884075	−	0.206672i
$509$	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
$514$	−9.91212	+	25.0621i	−0.437205	+	1.10544i
$515$	27.4140	+	15.8275i	1.20801	+	0.697443i
$516$	21.1948	−	22.6035i	0.933050	−	0.995063i
$517$			16.9469i			0.745322i
$518$		0			0
$519$			14.0720i			0.617693i
$520$	4.55846	−	6.57422i	0.199902	−	0.288299i
$521$	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	$0.581727\pi$
$522$	14.2404	+	5.63212i	0.623285	+	0.246511i
$523$	−3.73177	−	6.46361i	−0.163179	−	0.282634i	0.772828	−	0.634615i	$-0.218841\pi$
$523$	−3.73177	−	6.46361i	−0.163179	−	0.282634i	−0.936007	+	0.351981i	$0.885508\pi$
$524$	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
$528$	33.8237	−	2.17793i	1.47199	−	0.0947823i
$529$	−8.81371	+	15.2658i	−0.383205	+	0.663730i
$530$	24.0797	+	30.3581i	1.04596	+	1.31867i
$531$	−17.8033			−0.772600
$532$		0			0
$533$	2.48528			0.107649
$534$	11.2762	+	14.2163i	0.487968	+	0.615198i
$535$	−3.02846	+	5.24545i	−0.130932	+	0.226780i
$536$	−0.765634	+	9.23987i	−0.0330704	+	0.399101i
$537$	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	$-0.594055\pi$
$542$	5.63240	+	2.22763i	0.241932	+	0.0956850i
$543$	40.7766	+	23.5424i	1.74989	+	1.01030i
$544$	1.70661	+	0.551045i	0.0731702	+	0.0236259i
$545$		−	14.7821i		−	0.633194i
$546$		0			0
$547$			27.6981i			1.18429i	0.805833	+	0.592143i	$0.201718\pi$
$547$			27.6981i			1.18429i	−0.805833	+	0.592143i	$0.798282\pi$
$548$	−12.0255	−	11.2761i	−0.513706	−	0.481692i
$549$	−7.43242	−	4.29111i	−0.317208	−	0.183140i
$550$	3.76302	−	9.51451i	0.160456	−	0.405700i
$551$	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
$556$	10.3898	−	44.4439i	0.440624	−	1.88484i
$557$	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	$0.0299429\pi$
$558$	10.6422	−	8.44127i	0.450520	−	0.357348i
$559$	7.83095			0.331214
$560$		0			0
$561$	2.68629			0.113415
$562$	11.5062	−	9.12659i	0.485360	−	0.384982i
$563$	−10.5235	+	18.2273i	−0.443513	+	0.768188i	−0.997947	−	0.0640400i	$-0.979601\pi$
$563$	−10.5235	+	18.2273i	−0.443513	+	0.768188i	0.554434	+	0.832228i	$0.312935\pi$
$564$	−4.17554	+	17.8616i	−0.175822	+	0.752108i
$565$	−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	$0.962472\pi$
$570$	15.0472	−	38.0458i	0.630259	−	1.59356i
$571$	8.61732	+	4.97521i	0.360624	+	0.208206i	0.669354	−	0.742943i	$-0.266571\pi$
$571$	8.61732	+	4.97521i	0.360624	+	0.208206i	−0.308731	+	0.951150i	$0.599904\pi$
$572$	6.24849	+	5.85909i	0.261263	+	0.244981i
$573$		−	14.0392i		−	0.586497i
$574$		0			0
$575$			4.23808i			0.176740i
$576$	12.5133	+	2.08809i	0.521386	+	0.0870037i
$577$	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	$0.661086\pi$
$578$	−22.2244	−	8.78982i	−0.924414	−	0.365608i
$579$	−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
$584$	3.27387	−	39.5098i	0.135474	−	1.63493i
$585$	2.24264	−	3.88437i	0.0927218	−	0.160599i
$586$	10.3682	+	13.0715i	0.428305	+	0.539979i
$587$	−22.8211			−0.941926			−0.470963	−	0.882153i	$-0.656094\pi$
$587$	−22.8211			−0.941926			−0.470963	+	0.882153i	$0.656094\pi$
$588$		0			0
$589$	31.3137			1.29026
$590$	−25.7827	−	32.5051i	−1.06146	−	1.33822i
$591$	−2.14144	+	3.70909i	−0.0880873	+	0.152572i
$592$	−1.02812	−	15.9669i	−0.0422556	−	0.656237i
$593$	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
$598$	−3.29938	−	1.30492i	−0.134922	−	0.0533620i
$599$	−27.9011	−	16.1087i	−1.14001	−	0.658184i	−0.193575	−	0.981085i	$-0.562008\pi$
$599$	−27.9011	−	16.1087i	−1.14001	−	0.658184i	−0.946433	+	0.322902i	$0.895342\pi$
$600$	6.31042	−	9.10089i	0.257622	−	0.371542i
$601$			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
$604$	29.3076	−	31.2555i	1.19251	−	1.27177i
$605$	10.5386	+	6.08447i	0.428456	+	0.247369i
$606$	16.9639	−	42.8919i	0.689110	−	1.74236i
$607$	6.05692	+	10.4909i	0.245843	+	0.425812i	0.962368	−	0.271749i	$-0.0876020\pi$
$607$	6.05692	+	10.4909i	0.245843	+	0.425812i	−0.716525	+	0.697561i	$0.754269\pi$
$608$	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
$612$	0.979072	+	0.228880i	0.0395766	+	0.00925193i
$613$	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	$0.110539\pi$
$614$	4.33830	−	3.44109i	0.175079	−	0.138871i
$615$	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	$0.752982\pi$
$618$	−28.7424	+	22.7982i	−1.15619	+	0.917077i
$619$	6.76023	−	11.7091i	0.271717	−	0.470627i	−0.697585	−	0.716502i	$-0.745742\pi$
$619$	6.76023	−	11.7091i	0.271717	−	0.470627i	0.969301	+	0.245875i	$0.0790753\pi$
$620$	30.8239	+	7.20579i	1.23792	+	0.289391i
$621$	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
$626$	6.63085	−	16.7656i	0.265022	−	0.670089i
$627$	37.9378	+	21.9034i	1.51509	+	0.874738i
$628$	−26.2504	+	27.9950i	−1.04750	+	1.11712i
$629$		−	1.26810i		−	0.0505625i
$630$		0			0
$631$			20.4633i			0.814630i	0.913288	+	0.407315i	$0.133535\pi$
$631$			20.4633i			0.814630i	−0.913288	+	0.407315i	$0.866465\pi$
$632$	−18.3942	−	12.7543i	−0.731683	−	0.507338i
$633$	−26.8347	−	15.4930i	−1.06659	−	0.615793i
$634$	7.25237	+	2.86833i	0.288028	+	0.113916i
$635$	−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
$640$	14.3092	+	25.8705i	0.565622	+	1.02262i
$641$	−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	$0.735523\pi$
$642$	−4.36224	−	5.49963i	−0.172164	−	0.217053i
$643$	−41.7267			−1.64554			−0.822769	−	0.568375i	$-0.807572\pi$
$643$	−41.7267			−1.64554			−0.822769	+	0.568375i	$0.807572\pi$
$644$		0			0
$645$	40.4853			1.59411
$646$	1.44042	+	1.81598i	0.0566724	+	0.0714488i
$647$	−21.9341	+	37.9909i	−0.862317	+	1.49358i	0.00737070	+	0.999973i	$0.497654\pi$
$647$	−21.9341	+	37.9909i	−0.862317	+	1.49358i	−0.869687	+	0.493603i	$0.835680\pi$
$648$	−31.6904	−	2.62593i	−1.24492	−	0.103156i
$649$	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	$0.679149\pi$
$654$	15.9308	+	6.30069i	0.622945	+	0.246377i
$655$	0.831470	+	0.480049i	0.0324882	+	0.0187571i
$656$	−4.07161	+	8.23257i	−0.158970	+	0.321428i
$657$		−	22.2275i		−	0.867177i
$658$		0			0
$659$			13.2284i			0.515306i	0.966238	+	0.257653i	$0.0829491\pi$
$659$			13.2284i			0.515306i	−0.966238	+	0.257653i	$0.917051\pi$
$660$	32.3041	+	30.2909i	1.25744	+	1.17907i
$661$	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	$0.405010\pi$
$662$	7.87914	−	19.9218i	0.306232	−	0.774284i
$663$	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
$668$	−3.56520	+	15.2507i	−0.137942	+	0.590068i
$669$	8.38478	−	14.5229i	0.324174	−	0.561486i
$670$	−9.49077	+	7.52797i	−0.366661	+	0.290831i
$671$	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	$0.435856\pi$
$674$	11.9978	−	9.51649i	0.462136	−	0.366561i
$675$	−2.76866	+	4.79546i	−0.106566	+	0.184577i
$676$	5.38513	−	23.0358i	0.207120	−	0.885991i
$677$	−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
$682$	−12.4655	+	31.5182i	−0.477330	+	1.20689i
$683$	−27.9011	−	16.1087i	−1.06761	−	0.616382i	−0.140079	−	0.990140i	$-0.544736\pi$
$683$	−27.9011	−	16.1087i	−1.06761	−	0.616382i	−0.927526	+	0.373758i	$0.878069\pi$
$684$	11.9610	+	11.2155i	0.457338	+	0.428837i
$685$		−	21.5391i		−	0.822965i
$686$		0			0
$687$		−	2.88030i		−	0.109890i
$688$	−12.8294	+	25.9403i	−0.489115	+	0.988964i
$689$	−9.82868	−	5.67459i	−0.374443	−	0.216185i
$690$	−17.0575	−	6.74629i	−0.649368	−	0.256827i
$691$	4.09918	+	7.09999i	0.155940	+	0.270096i	0.933401	−	0.358835i	$-0.116826\pi$
$691$	4.09918	+	7.09999i	0.155940	+	0.270096i	−0.777461	+	0.628931i	$0.783493\pi$
$692$	−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
$696$	−41.2180	−	3.41541i	−1.56236	−	0.129461i
$697$	−0.363961	+	0.630399i	−0.0137860	+	0.0238781i
$698$	−7.44681	−	9.38845i	−0.281866	−	0.355358i
$699$	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	$0.402294\pi$
$702$	−2.88083	−	3.63196i	−0.108730	−	0.137080i
$703$	10.3398	−	17.9091i	0.389973	−	0.675454i
$704$	−29.6453	+	11.0994i	−1.11730	+	0.418326i
$705$	−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
$712$	−13.9266	−	9.65645i	−0.521920	−	0.361891i
$713$		−	14.0392i		−	0.525774i
$714$		0			0
$715$			11.1917i			0.418547i
$716$	−18.4815	+	19.7098i	−0.690684	+	0.736588i
$717$	18.9750	+	10.9552i	0.708635	+	0.409131i
$718$	−16.2577	+	41.1063i	−0.606730	+	1.53407i
$719$	−16.7641	−	29.0364i	−0.625197	−	1.08287i	−0.988503	−	0.151203i	$-0.951685\pi$
$719$	−16.7641	−	29.0364i	−0.625197	−	1.08287i	0.363306	−	0.931670i	$-0.381648\pi$
$720$	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
$724$	−42.8203	−	10.0102i	−1.59140	−	0.372027i
$725$	−6.24264	+	10.8126i	−0.231846	+	0.401569i
$726$	−11.0493	+	8.76417i	−0.410077	+	0.325269i
$727$	−29.9802			−1.11191			−0.555953	−	0.831214i	$-0.687646\pi$
$727$	−29.9802			−1.11191			−0.555953	+	0.831214i	$0.687646\pi$
$728$		0			0
$729$	1.62742			0.0602747
$730$	40.5827	−	32.1897i	1.50203	−	1.19140i
$731$	−1.14682	+	1.98634i	−0.0424165	+	0.0734676i
$732$	22.5703	+	5.27632i	0.834223	+	0.195018i
$733$	−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
$738$	−1.89383	+	4.78842i	−0.0697130	+	0.176264i
$739$	10.7673	+	6.21652i	0.396082	+	0.228678i	0.684792	−	0.728738i	$-0.259893\pi$
$739$	10.7673	+	6.21652i	0.396082	+	0.228678i	−0.288710	+	0.957417i	$0.593226\pi$
$740$	14.2993	−	15.2496i	0.525651	−	0.560587i
$741$			11.9832i			0.440215i
$742$		0			0
$743$		−	45.1646i		−	1.65693i	−0.560042	−	0.828464i	$-0.689215\pi$
$743$		−	45.1646i		−	1.65693i	0.560042	−	0.828464i	$-0.310785\pi$
$744$	−20.9041	+	30.1480i	−0.766383	+	1.10528i
$745$	−10.9269	−	6.30864i	−0.400330	−	0.231131i
$746$	26.4888	+	10.4764i	0.969824	+	0.383568i
$747$	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	−0.955363	−	0.295434i	$-0.904536\pi$
$751$	−32.2602	+	18.6254i	−1.17719	+	0.679652i	−0.221828	+	0.975086i	$0.571202\pi$
$752$	−1.10083	−	17.0962i	−0.0401433	−	0.623433i
$753$	−4.19239	+	7.26143i	−0.152779	+	0.264621i
$754$	−6.49556	−	8.18917i	−0.236554	−	0.298232i
$755$	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	$0.797711\pi$
$758$	−19.0749	−	24.0484i	−0.692832	−	0.873476i
$759$	9.82021	−	17.0091i	0.356451	−	0.617391i
$760$	−3.15542	+	38.0804i	−0.114459	+	1.38132i
$761$	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
$766$	40.7935	+	16.1339i	1.47393	+	0.582943i
$767$	10.5238	+	6.07591i	0.379992	+	0.219389i
$768$	−33.9802	+	4.39424i	−1.22615	+	0.158563i
$769$			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
$772$	21.2798	+	19.9537i	0.765878	+	0.718149i
$773$	−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	$-0.682710\pi$
$774$	−5.96734	+	15.0880i	−0.214492	+	0.542327i
$775$	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
$780$	−2.75754	+	11.7958i	−0.0987356	+	0.422358i
$781$		0			0
$782$	0.814180	−	0.645798i	0.0291150	−	0.0230937i
$783$	20.6796			0.739029
$784$		0			0
$785$	−50.1421			−1.78965
$786$	−0.871760	+	0.691471i	−0.0310947	+	0.0246639i
$787$	20.6035	−	35.6864i	0.734436	−	1.27208i	−0.220534	−	0.975379i	$-0.570780\pi$
$787$	20.6035	−	35.6864i	0.734436	−	1.27208i	0.954970	−	0.296702i	$-0.0958868\pi$
$788$	0.910541	−	3.89499i	0.0324367	−	0.138753i
$789$	−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
$794$	8.38808	−	21.2086i	0.297682	−	0.752667i
$795$	−50.8134	−	29.3371i	−1.80216	−	1.04048i
$796$	24.9940	+	23.4364i	0.885888	+	0.830680i
$797$			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
$800$	−3.17813	+	9.84277i	−0.112364	+	0.347995i
$801$	−8.22848	−	4.75071i	−0.290739	−	0.167858i
$802$	16.8706	+	6.67237i	0.595721	+	0.235609i
$803$	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
$808$	−3.55735	+	42.9310i	−0.125147	+	1.51031i
$809$	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	$0.166434\pi$
$810$	−25.8190	−	32.5509i	−0.907188	−	1.14372i
$811$	−39.4330			−1.38468			−0.692340	−	0.721571i	$-0.743420\pi$
$811$	−39.4330			−1.38468			−0.692340	+	0.721571i	$0.743420\pi$
$812$		0			0
$813$	−9.17157			−0.321661
$814$	13.9099	+	17.5367i	0.487541	+	0.614660i
$815$	19.7926	−	34.2818i	0.693305	−	1.20084i
$816$	−2.70996	+	0.174496i	−0.0948675	+	0.00610859i
$817$	−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	$0.731630\pi$
$822$	23.2129	+	9.18078i	0.809644	+	0.320217i
$823$	14.8829	+	8.59264i	0.518785	+	0.299521i	0.736437	−	0.676506i	$-0.236507\pi$
$823$	14.8829	+	8.59264i	0.518785	+	0.299521i	−0.217652	+	0.976026i	$0.569840\pi$
$824$	19.5234	−	28.1567i	0.680130	−	0.980884i
$825$			15.4930i			0.539399i
$826$		0			0
$827$		−	45.1646i		−	1.57053i	−0.619162	−	0.785264i	$-0.712527\pi$
$827$		−	45.1646i		−	1.57053i	0.619162	−	0.785264i	$-0.287473\pi$
$828$	5.02840	−	5.36259i	0.174749	−	0.186363i
$829$	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	$0.360616\pi$
$830$	−12.8477	+	32.4846i	−0.445952	+	1.12756i
$831$	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
$836$	−39.8392	−	9.31331i	−1.37787	−	0.322108i
$837$	9.17157	−	15.8856i	0.317016	−	0.549088i
$838$	19.1502	−	15.1897i	0.661532	−	0.524719i
$839$	−42.3984			−1.46376			−0.731878	−	0.681435i	$-0.761356\pi$
$839$	−42.3984			−1.46376			−0.731878	+	0.681435i	$0.761356\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	−11.6176	+	9.21492i	−0.400367	+	0.317567i
$843$	−11.1192	+	19.2590i	−0.382966	+	0.663317i
$844$	28.1797	+	6.58763i	0.969984	+	0.226756i
$845$	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
$850$	−0.301494	+	0.762304i	−0.0103411	+	0.0261468i
$851$	−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
$856$	5.38755	+	3.73564i	0.184143	+	0.127682i
$857$	−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	$0.685463\pi$
$858$	−12.0615	−	4.77035i	−0.411772	−	0.162857i
$859$	1.33052	+	2.30453i	0.0453969	+	0.0786297i	0.887831	−	0.460170i	$-0.152211\pi$
$859$	1.33052	+	2.30453i	0.0453969	+	0.0786297i	−0.842434	+	0.538799i	$0.818878\pi$
$860$	−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	−0.673440	−	0.739242i	$-0.735184\pi$
$863$	−10.8682	+	6.27476i	−0.369958	+	0.213595i	0.303482	+	0.952837i	$0.401851\pi$
$864$	16.7506	−	3.59264i	0.569868	−	0.122224i
$865$	8.58579	−	14.8710i	0.291925	−	0.505630i
$866$	−23.0131	−	29.0134i	−0.782016	−	0.985914i
$867$	36.1893			1.22905
$868$		0			0
$869$	31.3137			1.06224
$870$	−33.5814	−	42.3372i	−1.13852	−	1.43537i
$871$	1.77403	−	3.07271i	0.0601107	−	0.104115i
$872$	−15.9454	−	1.32126i	−0.539978	−	0.0447437i
$873$	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	$-0.338397\pi$
$878$	−29.5287	−	11.6787i	−0.996544	−	0.394136i
$879$	−21.8791	−	12.6319i	−0.737962	−	0.426063i
$880$	−37.0730	−	18.3353i	−1.24973	−	0.618083i
$881$		−	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	$0.136440\pi$
$883$			24.7013i			0.831266i	−0.909532	+	0.415633i	$0.863560\pi$
$884$	−0.500630	−	0.469431i	−0.0168380	−	0.0157887i
$885$	54.4070	+	31.4119i	1.82887	+	1.05590i
$886$	14.7595	−	37.3184i	0.495857	−	1.25374i
$887$	−11.2268	−	19.4454i	−0.376960	−	0.652914i	0.613658	−	0.789572i	$-0.289697\pi$
$887$	−11.2268	−	19.4454i	−0.376960	−	0.652914i	−0.990618	+	0.136658i	$0.956364\pi$
$888$	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
$892$	−3.56520	+	15.2507i	−0.119372	+	0.510632i
$893$	11.0711	−	19.1757i	0.370479	−	0.641689i
$894$	11.4564	−	9.08707i	0.383159	−	0.303917i
$895$	−35.3023			−1.18003
$896$		0			0
$897$	5.37258			0.179385
$898$	−18.0428	+	14.3113i	−0.602095	+	0.477575i
$899$	20.6796	−	35.8182i	0.689704	−	1.19460i
$900$	−1.32005	+	5.64675i	−0.0440018	+	0.188225i
$901$	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
$906$	−23.8617	+	60.3325i	−0.792751	+	2.00441i
$907$	−29.4214	−	16.9864i	−0.976921	−	0.564025i	−0.0755817	−	0.997140i	$-0.524081\pi$
$907$	−29.4214	−	16.9864i	−0.976921	−	0.564025i	−0.901339	+	0.433114i	$0.857415\pi$
$908$	14.5492	+	13.6425i	0.482831	+	0.452741i
$909$			24.1522i			0.801077i
$910$		0			0
$911$		−	18.7078i		−	0.619817i	−0.950766	−	0.309908i	$-0.899702\pi$
$911$		−	18.7078i		−	0.619817i	0.950766	−	0.309908i	$-0.100298\pi$
$912$	−39.6948	−	19.6320i	−1.31443	−	0.650081i
$913$	−32.3924	−	18.7018i	−1.07203	−	0.618938i
$914$	−0.957286	−	0.378609i	−0.0316642	−	0.0125233i
$915$	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	0.401357	−	0.915922i	$-0.368539\pi$
$919$	42.2969	−	24.4201i	1.39525	−	0.805546i	0.993890	+	0.110376i	$0.0352054\pi$
$920$	17.0730	+	1.41471i	0.562882	+	0.0466415i
$921$	−4.19239	+	7.26143i	−0.138144	+	0.239272i
$922$	26.1454	+	32.9625i	0.861054	+	1.08556i
$923$		0			0
$924$		0			0
$925$	7.31371			0.240473
$926$	30.7006	+	38.7053i	1.00888	+	1.27193i
$927$	9.60498	−	16.6363i	0.315469	−	0.546408i
$928$	37.7685	−	8.10051i	1.23981	−	0.265912i
$929$	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
$934$	−31.6615	−	12.5222i	−1.03600	−	0.409740i
$935$	−2.83882	−	1.63899i	−0.0928392	−	0.0536007i
$936$	−3.98960	−	2.76632i	−0.130404	−	0.0904201i
$937$		−	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
$940$	15.3105	−	16.3281i	0.499375	−	0.532564i
$941$	−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	$0.799049\pi$
$942$	21.3725	−	54.0389i	0.696354	−	1.76068i
$943$	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	−0.365616	−	0.930766i	$-0.619142\pi$
$947$	7.92851	−	4.57753i	0.257642	−	0.148750i	0.623258	+	0.782016i	$0.285808\pi$
$948$	33.0039	+	7.71540i	1.07192	+	0.250585i
$949$	−7.58579	+	13.1390i	−0.246245	+	0.426509i
$950$	−10.4736	+	8.30752i	−0.339808	+	0.269532i
$951$	−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	$0.359687\pi$
$954$	18.4230	−	14.6129i	0.596465	−	0.473110i
$955$	−8.56578	+	14.8364i	−0.277182	+	0.480094i
$956$	−19.9260	−	4.65816i	−0.644454	−	0.150656i
$957$	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
$962$	−2.25191	+	5.69379i	−0.0726045	+	0.183575i
$963$	3.18322	+	1.83783i	0.102578	+	0.0592234i
$964$	−6.96998	+	7.43322i	−0.224488	+	0.239408i
$965$			38.1145i			1.22695i
$966$		0			0
$967$		−	45.1646i		−	1.45240i	−0.687486	−	0.726198i	$-0.741286\pi$
$967$		−	45.1646i		−	1.45240i	0.687486	−	0.726198i	$-0.258714\pi$
$968$	7.50527	−	10.8241i	0.241228	−	0.347900i
$969$	−3.03958	−	1.75490i	−0.0976455	−	0.0563757i
$970$	31.7492	+	12.5569i	1.01940	+	0.403177i
$971$	−6.50043	−	11.2591i	−0.208609	−	0.361321i	0.742668	−	0.669660i	$-0.233560\pi$
$971$	−6.50043	−	11.2591i	−0.208609	−	0.361321i	−0.951276	+	0.308339i	$0.900227\pi$
$972$	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
$976$	−21.6031	+	1.39104i	−0.691499	+	0.0445261i
$977$	−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	$0.257592\pi$
$978$	28.5096	+	35.9430i	0.911636	+	1.14933i
$979$	23.7081			0.757714
$980$		0			0
$981$	−8.97056			−0.286408
$982$	−12.7166	−	16.0323i	−0.405803	−	0.511610i
$983$	4.80249	−	8.31816i	0.153176	−	0.265308i	−0.779218	−	0.626754i	$-0.784383\pi$
$983$	4.80249	−	8.31816i	0.153176	−	0.265308i	0.932393	+	0.361445i	$0.117717\pi$
$984$	1.14845	−	13.8598i	0.0366113	−	0.441834i
$985$	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
$990$	−21.5632	−	8.52832i	−0.685325	−	0.271048i
$991$	22.2235	+	12.8307i	0.705952	+	0.407581i	0.809560	−	0.587037i	$-0.199706\pi$
$991$	22.2235	+	12.8307i	0.705952	+	0.407581i	−0.103609	+	0.994618i	$0.533039\pi$
$992$	10.5280	−	32.6056i	0.334264	−	1.03523i
$993$			32.4399i			1.02945i
$994$		0			0
$995$			44.7669i			1.41921i
$996$	−29.5329	−	27.6924i	−0.935785	−	0.877467i
$997$	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	$0.503864\pi$
$998$	−6.52730	+	16.5038i	−0.206618	+	0.522418i
$999$	−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.31.5		16
4.3	odd	2	inner	196.2.f.d.31.2		16
7.2	even	3	inner	196.2.f.d.19.1		16
7.3	odd	6		196.2.d.c.195.7	yes	8
7.4	even	3		196.2.d.c.195.8	yes	8
7.5	odd	6	inner	196.2.f.d.19.2		16
7.6	odd	2	inner	196.2.f.d.31.6		16
21.11	odd	6		1764.2.b.k.1567.1		8
21.17	even	6		1764.2.b.k.1567.2		8
28.3	even	6		196.2.d.c.195.6	yes	8
28.11	odd	6		196.2.d.c.195.5	✓	8
28.19	even	6	inner	196.2.f.d.19.5		16
28.23	odd	6	inner	196.2.f.d.19.6		16
28.27	even	2	inner	196.2.f.d.31.1		16
56.3	even	6		3136.2.f.i.3135.4		8
56.11	odd	6		3136.2.f.i.3135.5		8
56.45	odd	6		3136.2.f.i.3135.6		8
56.53	even	6		3136.2.f.i.3135.3		8
84.11	even	6		1764.2.b.k.1567.3		8
84.59	odd	6		1764.2.b.k.1567.4		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.10799 - 0.878843i) q^{2} +(-1.07072 + 1.85455i) q^{3} +(0.455270 - 1.94749i) q^{4} +(2.26303 - 1.30656i) q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +(-0.792893 - 1.37333i) q^{9} +O(q^{10})\)	\(q+(1.10799 - 0.878843i) q^{2} +(-1.07072 + 1.85455i) q^{3} +(0.455270 - 1.94749i) 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} +(1.35915 - 3.43651i) q^{10} +(3.42675 + 1.97844i) q^{11} +(3.12425 + 2.92954i) q^{12} +1.08239i q^{13} +5.59587i q^{15} +(-3.58546 - 1.77327i) q^{16} +(-0.274552 - 0.158513i) q^{17} +(-2.08546 - 0.824805i) 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} +(6.03623 + 0.500175i) q^{24} +(0.914214 - 1.58346i) q^{25} +(0.951253 + 1.19928i) q^{26} -3.02846 q^{27} -6.82843 q^{29} +(4.91789 + 6.20015i) q^{30} +(-3.02846 + 5.24545i) q^{31} +(-5.53107 + 1.18629i) 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} +(-6.79891 - 2.68899i) q^{38} +(-2.00735 - 1.15894i) q^{39} +(-6.07379 - 4.21147i) q^{40} -2.29610i q^{41} -7.23486i q^{43} +(5.41309 - 5.77286i) q^{44} +(-3.58869 - 2.07193i) q^{45} +(-1.20559 + 3.04823i) 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} +(2.10795 + 0.492781i) q^{52} +(-5.24264 + 9.08052i) q^{53} +(-3.35549 + 2.66154i) q^{54} +10.3398 q^{55} +11.0711 q^{57} +(-7.56581 + 6.00111i) q^{58} +(5.61341 - 9.72272i) q^{59} +(10.8979 + 2.54763i) 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} +(-4.40723 + 11.1434i) q^{66} +(-2.83882 - 1.63899i) q^{67} +(-0.433698 + 0.462522i) q^{68} -4.96362i q^{69} +(-2.55575 + 3.68591i) q^{72} +(12.1388 + 7.00835i) q^{73} +(5.26038 + 2.08049i) 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} +(-10.4309 + 0.671654i) q^{80} +(5.62132 - 9.73641i) q^{81} +(-2.01791 - 2.54405i) q^{82} -9.45280 q^{83} -0.828427 q^{85} +(-6.35830 - 8.01613i) q^{86} +(7.31135 - 12.6636i) q^{87} +(0.924203 - 11.1535i) 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} +(5.63240 + 2.22763i) q^{94} +(-11.6997 - 6.75481i) q^{95} +(3.72221 - 11.5278i) 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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