LMFDB - Embedded newform 650.2.w.h.293.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(193,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("650.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} + 28x^{14} + 294x^{12} + 1516x^{10} + 4147x^{8} + 6012x^{6} + 4338x^{4} + 1296x^{2} + 81 $ x^16 + 28x^14 + 294x^12 + 1516x^10 + 4147x^8 + 6012x^6 + 4338x^4 + 1296*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.2
Root			$-1.05387i$ of defining polynomial
Character	$\chi$	$=$	650.293
Dual form			650.2.w.h.457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.01796 + 0.272763i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.272763 + 1.01796i) q^{6} +(0.524968 - 0.303090i) q^{7} -1.00000 q^{8} +(-1.63622 + 0.944675i) q^{9} +(1.67250 + 6.24184i) q^{11} +(0.745202 + 0.745202i) q^{12} +(3.55982 + 0.572444i) q^{13} -0.606181i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.267122 + 0.996913i) q^{17} +1.88935i q^{18} +(0.896383 + 0.240185i) q^{19} +(-0.451727 + 0.451727i) q^{21} +(6.24184 + 1.67250i) q^{22} +(-1.31541 - 4.90919i) q^{23} +(1.01796 - 0.272763i) q^{24} +(2.27566 - 2.79667i) q^{26} +(3.64355 - 3.64355i) q^{27} +(-0.524968 - 0.303090i) q^{28} +(2.65606 + 1.53348i) q^{29} +(7.06078 + 7.06078i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.40508 - 5.89778i) q^{33} +(0.729791 + 0.729791i) q^{34} +(1.63622 + 0.944675i) q^{36} +(0.0372201 + 0.0214890i) q^{37} +(0.656198 - 0.656198i) q^{38} +(-3.77991 + 0.388258i) q^{39} +(1.75959 - 0.471482i) q^{41} +(0.165343 + 0.617070i) q^{42} +(6.78086 + 1.81693i) q^{43} +(4.56935 - 4.56935i) q^{44} +(-4.90919 - 1.31541i) q^{46} +7.31779i q^{47} +(0.272763 - 1.01796i) q^{48} +(-3.31627 + 5.74395i) q^{49} -1.08768i q^{51} +(-1.28416 - 3.36912i) q^{52} +(-3.80438 - 3.80438i) q^{53} +(-1.33363 - 4.97718i) q^{54} +(-0.524968 + 0.303090i) q^{56} -0.977999 q^{57} +(2.65606 - 1.53348i) q^{58} +(-1.52251 + 5.68207i) q^{59} +(-1.28063 - 2.21812i) q^{61} +(9.64520 - 2.58442i) q^{62} +(-0.572643 + 0.991848i) q^{63} +1.00000 q^{64} -6.81017 q^{66} +(-3.28759 + 5.69428i) q^{67} +(0.996913 - 0.267122i) q^{68} +(2.67809 + 4.63859i) q^{69} +(2.71447 - 10.1305i) q^{71} +(1.63622 - 0.944675i) q^{72} +2.04350 q^{73} +(0.0372201 - 0.0214890i) q^{74} +(-0.240185 - 0.896383i) q^{76} +(2.76985 + 2.76985i) q^{77} +(-1.55371 + 3.46763i) q^{78} -4.09352i q^{79} +(0.118845 - 0.205845i) q^{81} +(0.471482 - 1.75959i) q^{82} +7.40916i q^{83} +(0.617070 + 0.165343i) q^{84} +(4.96394 - 4.96394i) q^{86} +(-3.12205 - 0.836550i) q^{87} +(-1.67250 - 6.24184i) q^{88} +(-14.6031 + 3.91289i) q^{89} +(2.04229 - 0.778432i) q^{91} +(-3.59378 + 3.59378i) q^{92} +(-9.11354 - 5.26170i) q^{93} +(6.33739 + 3.65890i) q^{94} +(-0.745202 - 0.745202i) q^{96} +(-8.80863 - 15.2570i) q^{97} +(3.31627 + 5.74395i) q^{98} +(-8.63309 - 8.63309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.01796	+	0.272763i	−0.587722	+	0.157480i	−0.540412	−	0.841401i	$-0.681732\pi$
$3$	−1.01796	+	0.272763i	−0.587722	+	0.157480i	−0.0473101	+	0.998880i	$0.515065\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.272763	+	1.01796i	−0.111355	+	0.415582i
$7$	0.524968	−	0.303090i	0.198419	−	0.114557i	−0.397499	−	0.917603i	$-0.630122\pi$
$7$	0.524968	−	0.303090i	0.198419	−	0.114557i	0.595918	+	0.803045i	$0.296788\pi$
$8$	−1.00000			−0.353553
$9$	−1.63622	+	0.944675i	−0.545408	+	0.314892i
$10$		0			0
$11$	1.67250	+	6.24184i	0.504277	+	1.88199i	0.470186	+	0.882568i	$0.344187\pi$
$11$	1.67250	+	6.24184i	0.504277	+	1.88199i	0.0340912	+	0.999419i	$0.489146\pi$
$12$	0.745202	+	0.745202i	0.215121	+	0.215121i
$13$	3.55982	+	0.572444i	0.987316	+	0.158767i
$13$	3.55982	+	0.572444i	0.987316	+	0.158767i
$14$		−	0.606181i		−	0.162009i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.267122	+	0.996913i	−0.0647866	+	0.241787i	−0.990724	−	0.135890i	$-0.956610\pi$
$17$	−0.267122	+	0.996913i	−0.0647866	+	0.241787i	0.925937	+	0.377677i	$0.123277\pi$
$18$			1.88935i			0.445324i
$19$	0.896383	+	0.240185i	0.205644	+	0.0551022i	0.360171	−	0.932886i	$-0.382718\pi$
$19$	0.896383	+	0.240185i	0.205644	+	0.0551022i	−0.154526	+	0.987989i	$0.549385\pi$
$20$		0			0
$21$	−0.451727	+	0.451727i	−0.0985748	+	0.0985748i
$22$	6.24184	+	1.67250i	1.33077	+	0.356577i
$23$	−1.31541	−	4.90919i	−0.274283	−	1.02364i	−0.956320	−	0.292320i	$-0.905573\pi$
$23$	−1.31541	−	4.90919i	−0.274283	−	1.02364i	0.682038	−	0.731317i	$-0.261094\pi$
$24$	1.01796	−	0.272763i	0.207791	−	0.0556774i
$25$		0			0
$26$	2.27566	−	2.79667i	0.446294	−	0.548472i
$27$	3.64355	−	3.64355i	0.701202	−	0.701202i
$28$	−0.524968	−	0.303090i	−0.0992096	−	0.0572787i
$29$	2.65606	+	1.53348i	0.493218	+	0.284759i	0.725908	−	0.687791i	$-0.241420\pi$
$29$	2.65606	+	1.53348i	0.493218	+	0.284759i	−0.232691	+	0.972551i	$0.574753\pi$
$30$		0			0
$31$	7.06078	+	7.06078i	1.26815	+	1.26815i	0.947041	+	0.321112i	$0.104057\pi$
$31$	7.06078	+	7.06078i	1.26815	+	1.26815i	0.321112	+	0.947041i	$0.395943\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.40508	−	5.89778i	−0.592749	−	1.02667i
$34$	0.729791	+	0.729791i	0.125158	+	0.125158i
$35$		0			0
$36$	1.63622	+	0.944675i	0.272704	+	0.157446i
$37$	0.0372201	+	0.0214890i	0.00611895	+	0.00353278i	0.503056	−	0.864254i	$-0.332209\pi$
$37$	0.0372201	+	0.0214890i	0.00611895	+	0.00353278i	−0.496937	+	0.867786i	$0.665542\pi$
$38$	0.656198	−	0.656198i	0.106449	−	0.106449i
$39$	−3.77991	+	0.388258i	−0.605270	+	0.0621711i
$40$		0			0
$41$	1.75959	−	0.471482i	0.274802	−	0.0736331i	−0.118786	−	0.992920i	$-0.537900\pi$
$41$	1.75959	−	0.471482i	0.274802	−	0.0736331i	0.393588	+	0.919287i	$0.371234\pi$
$42$	0.165343	+	0.617070i	0.0255130	+	0.0952160i
$43$	6.78086	+	1.81693i	1.03407	+	0.277079i	0.735655	−	0.677357i	$-0.236875\pi$
$43$	6.78086	+	1.81693i	1.03407	+	0.277079i	0.298417	+	0.954436i	$0.403541\pi$
$44$	4.56935	−	4.56935i	0.688855	−	0.688855i
$45$		0			0
$46$	−4.90919	−	1.31541i	−0.723821	−	0.193947i
$47$			7.31779i			1.06741i	0.845671	+	0.533705i	$0.179201\pi$
$47$			7.31779i			1.06741i	−0.845671	+	0.533705i	$0.820799\pi$
$48$	0.272763	−	1.01796i	0.0393699	−	0.146930i
$49$	−3.31627	+	5.74395i	−0.473753	+	0.820565i
$50$		0			0
$51$		−	1.08768i		−	0.152306i
$52$	−1.28416	−	3.36912i	−0.178081	−	0.467212i
$53$	−3.80438	−	3.80438i	−0.522572	−	0.522572i	0.395775	−	0.918347i	$-0.370476\pi$
$53$	−3.80438	−	3.80438i	−0.522572	−	0.522572i	−0.918347	+	0.395775i	$0.870476\pi$
$54$	−1.33363	−	4.97718i	−0.181484	−	0.677309i
$55$		0			0
$56$	−0.524968	+	0.303090i	−0.0701518	+	0.0405021i
$57$	−0.977999			−0.129539
$58$	2.65606	−	1.53348i	0.348757	−	0.201355i
$59$	−1.52251	+	5.68207i	−0.198213	+	0.739742i	0.793198	+	0.608963i	$0.208414\pi$
$59$	−1.52251	+	5.68207i	−0.198213	+	0.739742i	−0.991412	+	0.130779i	$0.958252\pi$
$60$		0			0
$61$	−1.28063	−	2.21812i	−0.163969	−	0.284002i	0.772320	−	0.635234i	$-0.219096\pi$
$61$	−1.28063	−	2.21812i	−0.163969	−	0.284002i	−0.936289	+	0.351232i	$0.885763\pi$
$62$	9.64520	−	2.58442i	1.22494	−	0.328222i
$63$	−0.572643	+	0.991848i	−0.0721463	+	0.124961i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.81017			−0.838274
$67$	−3.28759	+	5.69428i	−0.401643	+	0.695667i	−0.993924	−	0.110065i	$-0.964894\pi$
$67$	−3.28759	+	5.69428i	−0.401643	+	0.695667i	0.592281	+	0.805731i	$0.298227\pi$
$68$	0.996913	−	0.267122i	0.120893	−	0.0323933i
$69$	2.67809	+	4.63859i	0.322404	+	0.558420i
$70$		0			0
$71$	2.71447	−	10.1305i	0.322148	−	1.20227i	−0.595000	−	0.803726i	$-0.702848\pi$
$71$	2.71447	−	10.1305i	0.322148	−	1.20227i	0.917148	−	0.398547i	$-0.130486\pi$
$72$	1.63622	−	0.944675i	0.192831	−	0.111331i
$73$	2.04350			0.239173			0.119587	−	0.992824i	$-0.461843\pi$
$73$	2.04350			0.239173			0.119587	+	0.992824i	$0.461843\pi$
$74$	0.0372201	−	0.0214890i	0.00432675	−	0.00249805i
$75$		0			0
$76$	−0.240185	−	0.896383i	−0.0275511	−	0.102822i
$77$	2.76985	+	2.76985i	0.315654	+	0.315654i
$78$	−1.55371	+	3.46763i	−0.175923	+	0.392631i
$79$		−	4.09352i		−	0.460556i	−0.973125	−	0.230278i	$-0.926036\pi$
$79$		−	4.09352i		−	0.460556i	0.973125	−	0.230278i	$-0.0739636\pi$
$80$		0			0
$81$	0.118845	−	0.205845i	0.0132050	−	0.0228717i
$82$	0.471482	−	1.75959i	0.0520664	−	0.194315i
$83$			7.40916i			0.813260i	0.913593	+	0.406630i	$0.133296\pi$
$83$			7.40916i			0.813260i	−0.913593	+	0.406630i	$0.866704\pi$
$84$	0.617070	+	0.165343i	0.0673279	+	0.0180404i
$85$		0			0
$86$	4.96394	−	4.96394i	0.535275	−	0.535275i
$87$	−3.12205	−	0.836550i	−0.334719	−	0.0896876i
$88$	−1.67250	−	6.24184i	−0.178289	−	0.665383i
$89$	−14.6031	+	3.91289i	−1.54792	+	0.414765i	−0.928816	−	0.370541i	$-0.879172\pi$
$89$	−14.6031	+	3.91289i	−1.54792	+	0.414765i	−0.619108	+	0.785306i	$0.712506\pi$
$90$		0			0
$91$	2.04229	−	0.778432i	0.214090	−	0.0816018i
$92$	−3.59378	+	3.59378i	−0.374677	+	0.374677i
$93$	−9.11354	−	5.26170i	−0.945030	−	0.545613i
$94$	6.33739	+	3.65890i	0.653652	+	0.377386i
$95$		0			0
$96$	−0.745202	−	0.745202i	−0.0760568	−	0.0760568i
$97$	−8.80863	−	15.2570i	−0.894380	−	1.54911i	−0.834569	−	0.550903i	$-0.814284\pi$
$97$	−8.80863	−	15.2570i	−0.894380	−	1.54911i	−0.0598111	−	0.998210i	$-0.519050\pi$
$98$	3.31627	+	5.74395i	0.334994	+	0.580227i
$99$	−8.63309	−	8.63309i	−0.867658	−	0.867658i
$100$		0			0
$101$	−6.23125	−	3.59761i	−0.620033	−	0.357976i	0.156849	−	0.987623i	$-0.449866\pi$
$101$	−6.23125	−	3.59761i	−0.620033	−	0.357976i	−0.776882	+	0.629647i	$0.783200\pi$
$102$	−0.941961	−	0.543841i	−0.0932680	−	0.0538483i
$103$	9.96404	−	9.96404i	0.981787	−	0.981787i	−0.0180506	−	0.999837i	$-0.505746\pi$
$103$	9.96404	−	9.96404i	0.981787	−	0.981787i	0.999837	+	0.0180506i	$0.00574599\pi$
$104$	−3.55982	−	0.572444i	−0.349069	−	0.0561327i
$105$		0			0
$106$	−5.19688	+	1.39250i	−0.504766	+	0.135252i
$107$	−0.784375	−	2.92733i	−0.0758284	−	0.282995i	0.917591	−	0.397525i	$-0.130131\pi$
$107$	−0.784375	−	2.92733i	−0.0758284	−	0.282995i	−0.993420	+	0.114529i	$0.963464\pi$
$108$	−4.97718	−	1.33363i	−0.478930	−	0.128329i
$109$	6.48284	−	6.48284i	0.620943	−	0.620943i	−0.324830	−	0.945773i	$-0.605307\pi$
$109$	6.48284	−	6.48284i	0.620943	−	0.620943i	0.945773	+	0.324830i	$0.105307\pi$
$110$		0			0
$111$	−0.0437502	−	0.0117228i	−0.00415258	−	0.00111268i
$112$			0.606181i			0.0572787i
$113$	−4.44894	+	16.6037i	−0.418521	+	1.56194i	0.359156	+	0.933277i	$0.383065\pi$
$113$	−4.44894	+	16.6037i	−0.418521	+	1.56194i	−0.777677	+	0.628664i	$0.783602\pi$
$114$	−0.489000	+	0.846972i	−0.0457990	+	0.0793262i
$115$		0			0
$116$		−	3.06695i		−	0.284759i
$117$	−6.36544	+	2.42622i	−0.588485	+	0.224304i
$118$	4.15956	+	4.15956i	0.382919	+	0.382919i
$119$	0.161924	+	0.604310i	0.0148436	+	0.0553970i
$120$		0			0
$121$	−26.6371	+	15.3789i	−2.42155	+	1.39808i
$122$	−2.56127			−0.231886
$123$	−1.66260	+	0.959903i	−0.149912	+	0.0865515i
$124$	2.58442	−	9.64520i	0.232088	−	0.866165i
$125$		0			0
$126$	0.572643	+	0.991848i	0.0510151	+	0.0883608i
$127$	−12.5456	+	3.36158i	−1.11324	+	0.298292i	−0.768145	−	0.640275i	$-0.778820\pi$
$127$	−12.5456	+	3.36158i	−1.11324	+	0.298292i	−0.345096	+	0.938568i	$0.612154\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−7.39826			−0.651381
$130$		0			0
$131$	6.13550			0.536061			0.268030	−	0.963410i	$-0.413627\pi$
$131$	6.13550			0.536061			0.268030	+	0.963410i	$0.413627\pi$
$132$	−3.40508	+	5.89778i	−0.296374	+	0.513336i
$133$	0.543370	−	0.145596i	0.0471161	−	0.0126247i
$134$	3.28759	+	5.69428i	0.284005	+	0.491911i
$135$		0			0
$136$	0.267122	−	0.996913i	0.0229055	−	0.0854846i
$137$	−12.0454	+	6.95440i	−1.02911	+	0.594154i	−0.916728	−	0.399511i	$-0.869180\pi$
$137$	−12.0454	+	6.95440i	−1.02911	+	0.594154i	−0.112377	+	0.993666i	$0.535846\pi$
$138$	5.35618			0.455948
$139$	2.27272	−	1.31215i	0.192769	−	0.111296i	−0.400509	−	0.916293i	$-0.631167\pi$
$139$	2.27272	−	1.31215i	0.192769	−	0.111296i	0.593278	+	0.804997i	$0.297833\pi$
$140$		0			0
$141$	−1.99602	−	7.44925i	−0.168095	−	0.627340i
$142$	−7.41607	−	7.41607i	−0.622342	−	0.622342i
$143$	2.38068	+	23.1772i	0.199082	+	1.93818i
$144$		−	1.88935i		−	0.157446i
$145$		0			0
$146$	1.02175	−	1.76972i	0.0845605	−	0.146463i
$147$	1.80911	−	6.75169i	0.149213	−	0.556870i
$148$		−	0.0429781i		−	0.00353278i
$149$	15.1622	+	4.06270i	1.24214	+	0.332829i	0.819293	−	0.573374i	$-0.194366\pi$
$149$	15.1622	+	4.06270i	1.24214	+	0.332829i	0.422842	+	0.906204i	$0.361033\pi$
$150$		0			0
$151$	11.9956	−	11.9956i	0.976186	−	0.976186i	−0.0235373	−	0.999723i	$-0.507493\pi$
$151$	11.9956	−	11.9956i	0.976186	−	0.976186i	0.999723	+	0.0235373i	$0.00749285\pi$
$152$	−0.896383	−	0.240185i	−0.0727063	−	0.0194816i
$153$	−0.504687	−	1.88352i	−0.0408015	−	0.152273i
$154$	3.78368	−	1.01384i	0.304898	−	0.0816972i
$155$		0			0
$156$	2.22620	+	3.07937i	0.178238	+	0.246547i
$157$	8.11859	−	8.11859i	0.647934	−	0.647934i	−0.304559	−	0.952493i	$-0.598509\pi$
$157$	8.11859	−	8.11859i	0.647934	−	0.647934i	0.952493	+	0.304559i	$0.0985092\pi$
$158$	−3.54509	−	2.04676i	−0.282032	−	0.162831i
$159$	4.91042	+	2.83503i	0.389422	+	0.224833i
$160$		0			0
$161$	−2.17848	−	2.17848i	−0.171688	−	0.171688i
$162$	−0.118845	−	0.205845i	−0.00933732	−	0.0161727i
$163$	4.20479	+	7.28290i	0.329344	+	0.570441i	0.982382	−	0.186885i	$-0.0598390\pi$
$163$	4.20479	+	7.28290i	0.329344	+	0.570441i	−0.653038	+	0.757325i	$0.726506\pi$
$164$	−1.28811	−	1.28811i	−0.100585	−	0.100585i
$165$		0			0
$166$	6.41652	+	3.70458i	0.498018	+	0.287531i
$167$	2.21126	+	1.27667i	0.171113	+	0.0987919i	0.583110	−	0.812393i	$-0.301836\pi$
$167$	2.21126	+	1.27667i	0.171113	+	0.0987919i	−0.411998	+	0.911185i	$0.635169\pi$
$168$	0.451727	−	0.451727i	0.0348515	−	0.0348515i
$169$	12.3446	+	4.07559i	0.949586	+	0.313507i
$170$		0			0
$171$	−1.69358	+	0.453794i	−0.129511	+	0.0347025i
$172$	−1.81693	−	6.78086i	−0.138539	−	0.517036i
$173$	−22.3217	−	5.98108i	−1.69709	−	0.454733i	−0.724885	−	0.688870i	$-0.758107\pi$
$173$	−22.3217	−	5.98108i	−1.69709	−	0.454733i	−0.972204	+	0.234137i	$0.924774\pi$
$174$	−2.28550	+	2.28550i	−0.173263	+	0.173263i
$175$		0			0
$176$	−6.24184	−	1.67250i	−0.470497	−	0.126069i
$177$		−	6.19942i		−	0.465977i
$178$	−3.91289	+	14.6031i	−0.293283	+	1.09455i
$179$	11.2286	−	19.4485i	0.839266	−	1.45365i	−0.0512437	−	0.998686i	$-0.516319\pi$
$179$	11.2286	−	19.4485i	0.839266	−	1.45365i	0.890509	−	0.454965i	$-0.150348\pi$
$180$		0			0
$181$		−	14.4224i		−	1.07201i	−0.844215	−	0.536005i	$-0.819933\pi$
$181$		−	14.4224i		−	1.07201i	0.844215	−	0.536005i	$-0.180067\pi$
$182$	0.347004	−	2.15789i	0.0257217	−	0.159954i
$183$	1.90866	+	1.90866i	0.141092	+	0.141092i
$184$	1.31541	+	4.90919i	0.0969736	+	0.361910i
$185$		0			0
$186$	−9.11354	+	5.26170i	−0.668237	+	0.385807i
$187$	−6.66934			−0.487710
$188$	6.33739	−	3.65890i	0.462202	−	0.266852i
$189$	0.808422	−	3.01707i	0.0588040	−	0.219460i
$190$		0			0
$191$	8.17521	+	14.1599i	0.591537	+	1.02457i	0.994026	+	0.109147i	$0.0348120\pi$
$191$	8.17521	+	14.1599i	0.591537	+	1.02457i	−0.402488	+	0.915425i	$0.631855\pi$
$192$	−1.01796	+	0.272763i	−0.0734652	+	0.0196850i
$193$	6.27661	−	10.8714i	0.451800	−	0.782541i	−0.546698	−	0.837330i	$-0.684115\pi$
$193$	6.27661	−	10.8714i	0.451800	−	0.782541i	0.998498	+	0.0547891i	$0.0174486\pi$
$194$	−17.6173			−1.26485
$195$		0			0
$196$	6.63255			0.473753
$197$	−5.71847	+	9.90468i	−0.407424	+	0.705679i	−0.994600	−	0.103780i	$-0.966906\pi$
$197$	−5.71847	+	9.90468i	−0.407424	+	0.705679i	0.587176	+	0.809459i	$0.300240\pi$
$198$	−11.7930	+	3.15993i	−0.838094	+	0.224566i
$199$	8.02327	+	13.8967i	0.568755	+	0.985112i	0.996689	+	0.0813024i	$0.0259080\pi$
$199$	8.02327	+	13.8967i	0.568755	+	0.985112i	−0.427935	+	0.903810i	$0.640759\pi$
$200$		0			0
$201$	1.79346	−	6.69330i	0.126501	−	0.472109i
$202$	−6.23125	+	3.59761i	−0.438429	+	0.253127i
$203$	1.85913			0.130485
$204$	−0.941961	+	0.543841i	−0.0659505	+	0.0380765i
$205$		0			0
$206$	−3.64709	−	13.6111i	−0.254105	−	0.948333i
$207$	6.78990	+	6.78990i	0.471931	+	0.471931i
$208$	−2.27566	+	2.79667i	−0.157789	+	0.193914i
$209$			5.99679i			0.414807i
$210$		0			0
$211$	−2.78099	+	4.81682i	−0.191451	+	0.331603i	−0.945731	−	0.324949i	$-0.894653\pi$
$211$	−2.78099	+	4.81682i	−0.191451	+	0.331603i	0.754280	+	0.656553i	$0.227986\pi$
$212$	−1.39250	+	5.19688i	−0.0956373	+	0.356923i
$213$			11.0529i			0.757334i
$214$	−2.92733	−	0.784375i	−0.200108	−	0.0536188i
$215$		0			0
$216$	−3.64355	+	3.64355i	−0.247912	+	0.247912i
$217$	5.84673	+	1.56663i	0.396902	+	0.106350i
$218$	−2.37288	−	8.85572i	−0.160712	−	0.599785i
$219$	−2.08021	+	0.557390i	−0.140567	+	0.0376649i
$220$		0			0
$221$	−1.52158	+	3.39592i	−0.102353	+	0.228434i
$222$	−0.0320273	+	0.0320273i	−0.00214953	+	0.00214953i
$223$	2.87993	+	1.66273i	0.192854	+	0.111344i	0.593318	−	0.804968i	$-0.297818\pi$
$223$	2.87993	+	1.66273i	0.192854	+	0.111344i	−0.400464	+	0.916313i	$0.631151\pi$
$224$	0.524968	+	0.303090i	0.0350759	+	0.0202511i
$225$		0			0
$226$	12.1547	+	12.1547i	0.808520	+	0.808520i
$227$	2.63189	+	4.55857i	0.174685	+	0.302563i	0.940052	−	0.341031i	$-0.110776\pi$
$227$	2.63189	+	4.55857i	0.174685	+	0.302563i	−0.765367	+	0.643594i	$0.777443\pi$
$228$	0.489000	+	0.846972i	0.0323848	+	0.0560921i
$229$	−12.8566	−	12.8566i	−0.849585	−	0.849585i	0.140496	−	0.990081i	$-0.455130\pi$
$229$	−12.8566	−	12.8566i	−0.849585	−	0.849585i	−0.990081	+	0.140496i	$0.955130\pi$
$230$		0			0
$231$	−3.57512	−	2.06410i	−0.235226	−	0.135808i
$232$	−2.65606	−	1.53348i	−0.174379	−	0.100678i
$233$	5.38182	−	5.38182i	0.352575	−	0.352575i	−0.508492	−	0.861067i	$-0.669797\pi$
$233$	5.38182	−	5.38182i	0.352575	−	0.352575i	0.861067	+	0.508492i	$0.169797\pi$
$234$	−1.08155	+	6.72574i	−0.0707029	+	0.439675i
$235$		0			0
$236$	5.68207	−	1.52251i	0.369871	−	0.0991066i
$237$	1.11656	+	4.16705i	0.0725282	+	0.270679i
$238$	0.604310	+	0.161924i	0.0391716	+	0.0104960i
$239$	18.9666	−	18.9666i	1.22685	−	1.22685i	0.261697	−	0.965150i	$-0.415718\pi$
$239$	18.9666	−	18.9666i	1.22685	−	1.22685i	0.965150	−	0.261697i	$-0.0842822\pi$
$240$		0			0
$241$	−15.8426	−	4.24500i	−1.02051	−	0.273445i	−0.290495	−	0.956876i	$-0.593820\pi$
$241$	−15.8426	−	4.24500i	−1.02051	−	0.273445i	−0.730014	+	0.683432i	$0.760487\pi$
$242$			30.7578i			1.97719i
$243$	−4.06573	+	15.1735i	−0.260817	+	0.973381i
$244$	−1.28063	+	2.21812i	−0.0819843	+	0.142001i
$245$		0			0
$246$			1.91981i			0.122402i
$247$	3.05347	+	1.36814i	0.194288	+	0.0870529i
$248$	−7.06078	−	7.06078i	−0.448360	−	0.448360i
$249$	−2.02094	−	7.54226i	−0.128072	−	0.477971i
$250$		0			0
$251$	−11.8422	+	6.83711i	−0.747475	+	0.431555i	−0.824781	−	0.565453i	$-0.808702\pi$
$251$	−11.8422	+	6.83711i	−0.747475	+	0.431555i	0.0773059	+	0.997007i	$0.475368\pi$
$252$	1.14529			0.0721463
$253$	28.4424	−	16.4212i	1.78816	−	1.03239i
$254$	−3.36158	+	12.5456i	−0.210924	+	0.787180i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	22.7318	−	6.09097i	1.41797	−	0.379944i	0.533208	−	0.845984i	$-0.320986\pi$
$257$	22.7318	−	6.09097i	1.41797	−	0.379944i	0.884764	+	0.466040i	$0.154320\pi$
$258$	−3.69913	+	6.40709i	−0.230298	+	0.398888i
$259$	0.0260525			0.00161882
$260$		0			0
$261$	−5.79454			−0.358673
$262$	3.06775	−	5.31349i	0.189526	−	0.328269i
$263$	−6.62424	+	1.77496i	−0.408468	+	0.109449i	−0.457202	−	0.889363i	$-0.651148\pi$
$263$	−6.62424	+	1.77496i	−0.408468	+	0.109449i	0.0487334	+	0.998812i	$0.484482\pi$
$264$	3.40508	+	5.89778i	0.209568	+	0.362983i
$265$		0			0
$266$	0.145596	−	0.543370i	0.00892703	−	0.0333161i
$267$	13.7981	−	7.96636i	0.844432	−	0.487533i
$268$	6.57518			0.401643
$269$	−13.9856	+	8.07459i	−0.852717	+	0.492317i	−0.861567	−	0.507644i	$-0.830516\pi$
$269$	−13.9856	+	8.07459i	−0.852717	+	0.492317i	0.00884947	+	0.999961i	$0.497183\pi$
$270$		0			0
$271$	2.53695	+	9.46802i	0.154109	+	0.575141i	0.999180	+	0.0404878i	$0.0128912\pi$
$271$	2.53695	+	9.46802i	0.154109	+	0.575141i	−0.845071	+	0.534653i	$0.820442\pi$
$272$	−0.729791	−	0.729791i	−0.0442501	−	0.0442501i
$273$	−1.86665	+	1.34948i	−0.112975	+	0.0816741i
$274$			13.9088i			0.840261i
$275$		0			0
$276$	2.67809	−	4.63859i	0.161202	−	0.279210i
$277$	4.81219	−	17.9593i	0.289136	−	1.07907i	−0.656627	−	0.754215i	$-0.728018\pi$
$277$	4.81219	−	17.9593i	0.289136	−	1.07907i	0.945764	−	0.324856i	$-0.105316\pi$
$278$		−	2.62431i		−	0.157396i
$279$	−18.2232	−	4.88288i	−1.09099	−	0.292330i
$280$		0			0
$281$	20.0377	−	20.0377i	1.19535	−	1.19535i	0.219808	−	0.975543i	$-0.429457\pi$
$281$	20.0377	−	20.0377i	1.19535	−	1.19535i	0.975543	−	0.219808i	$-0.0705432\pi$
$282$	−7.44925	−	1.99602i	−0.443596	−	0.118861i
$283$	−4.50721	−	16.8211i	−0.267926	−	0.999913i	−0.960435	−	0.278504i	$-0.910161\pi$
$283$	−4.50721	−	16.8211i	−0.267926	−	0.999913i	0.692509	−	0.721409i	$-0.256505\pi$
$284$	−10.1305	+	2.71447i	−0.601137	+	0.161074i
$285$		0			0
$286$	21.2624	+	9.52689i	1.25727	+	0.563337i
$287$	0.780828	−	0.780828i	0.0460908	−	0.0460908i
$288$	−1.63622	−	0.944675i	−0.0964155	−	0.0556655i
$289$	13.7999	+	7.96740i	0.811762	+	0.468671i
$290$		0			0
$291$	13.1284	+	13.1284i	0.769601	+	0.769601i
$292$	−1.02175	−	1.76972i	−0.0597933	−	0.103565i
$293$	−14.4099	−	24.9588i	−0.841838	−	1.45811i	−0.888339	−	0.459188i	$-0.848141\pi$
$293$	−14.4099	−	24.9588i	−0.841838	−	1.45811i	0.0465015	−	0.998918i	$-0.485193\pi$
$294$	−4.94258	−	4.94258i	−0.288257	−	0.288257i
$295$		0			0
$296$	−0.0372201	−	0.0214890i	−0.00216338	−	0.00124903i
$297$	28.8363	+	16.6486i	1.67325	+	0.966052i
$298$	11.0995	−	11.0995i	0.642976	−	0.642976i
$299$	−1.87240	−	18.2288i	−0.108284	−	1.05420i
$300$		0			0
$301$	4.11043	−	1.10139i	0.236921	−	0.0634828i
$302$	−4.39068	−	16.3863i	−0.252655	−	0.942923i
$303$	7.32448	+	1.96259i	0.420781	+	0.112748i
$304$	−0.656198	+	0.656198i	−0.0376355	+	0.0376355i
$305$		0			0
$306$	−1.88352	−	0.504687i	−0.107674	−	0.0288510i
$307$		−	33.2780i		−	1.89928i	−0.313348	−	0.949638i	$-0.601451\pi$
$307$		−	33.2780i		−	1.89928i	0.313348	−	0.949638i	$-0.398549\pi$
$308$	1.01384	−	3.78368i	0.0577686	−	0.215595i
$309$	−7.42522	+	12.8609i	−0.422406	+	0.731629i
$310$		0			0
$311$		−	12.0917i		−	0.685655i	−0.939398	−	0.342828i	$-0.888615\pi$
$311$		−	12.0917i		−	0.685655i	0.939398	−	0.342828i	$-0.111385\pi$
$312$	3.77991	−	0.388258i	0.213995	−	0.0219808i
$313$	0.198788	+	0.198788i	0.0112361	+	0.0112361i	0.712703	−	0.701466i	$-0.247471\pi$
$313$	0.198788	+	0.198788i	0.0112361	+	0.0112361i	−0.701466	+	0.712703i	$0.747471\pi$
$314$	−2.97161	−	11.0902i	−0.167698	−	0.625856i
$315$		0			0
$316$	−3.54509	+	2.04676i	−0.199427	+	0.115139i
$317$	−11.0668			−0.621576			−0.310788	−	0.950479i	$-0.600593\pi$
$317$	−11.0668			−0.621576			−0.310788	+	0.950479i	$0.600593\pi$
$318$	4.91042	−	2.83503i	0.275363	−	0.158981i
$319$	−5.12947	+	19.1434i	−0.287195	+	1.07183i
$320$		0			0
$321$	1.59693	+	2.76597i	0.0891320	+	0.154381i
$322$	−2.97586	+	0.797378i	−0.165838	+	0.0444362i
$323$	−0.478887	+	0.829457i	−0.0266460	+	0.0461522i
$324$	−0.237689			−0.0132050
$325$		0			0
$326$	8.40957			0.465763
$327$	−4.83102	+	8.36757i	−0.267156	+	0.462728i
$328$	−1.75959	+	0.471482i	−0.0971573	+	0.0260332i
$329$	2.21795	+	3.84160i	0.122280	+	0.211795i
$330$		0			0
$331$	4.09928	−	15.2987i	0.225317	−	0.840894i	−0.756961	−	0.653461i	$-0.773317\pi$
$331$	4.09928	−	15.2987i	0.225317	−	0.840894i	0.982277	−	0.187433i	$-0.0600168\pi$
$332$	6.41652	−	3.70458i	0.352152	−	0.203315i
$333$	−0.0812006			−0.00444977
$334$	2.21126	−	1.27667i	0.120995	−	0.0698564i
$335$		0			0
$336$	−0.165343	−	0.617070i	−0.00902022	−	0.0336639i
$337$	19.0692	+	19.0692i	1.03877	+	1.03877i	0.999218	+	0.0395494i	$0.0125922\pi$
$337$	19.0692	+	19.0692i	1.03877	+	1.03877i	0.0395494	+	0.999218i	$0.487408\pi$
$338$	9.70187	−	8.65295i	0.527712	−	0.470659i
$339$		−	18.1154i		−	0.983896i
$340$		0			0
$341$	−32.2631	+	55.8814i	−1.74715	+	3.02615i
$342$	−0.453794	+	1.69358i	−0.0245383	+	0.0915783i
$343$			8.26378i			0.446202i
$344$	−6.78086	−	1.81693i	−0.365600	−	0.0979621i
$345$		0			0
$346$	−16.3406	+	16.3406i	−0.878478	+	0.878478i
$347$	19.1509	+	5.13148i	1.02808	+	0.275472i	0.733164	−	0.680052i	$-0.238043\pi$
$347$	19.1509	+	5.13148i	1.02808	+	0.275472i	0.294912	+	0.955524i	$0.404710\pi$
$348$	0.836550	+	3.12205i	0.0448438	+	0.167359i
$349$	12.7939	−	3.42812i	0.684842	−	0.183503i	0.100411	−	0.994946i	$-0.467984\pi$
$349$	12.7939	−	3.42812i	0.684842	−	0.183503i	0.584431	+	0.811443i	$0.301318\pi$
$350$		0			0
$351$	15.0561	−	10.8847i	0.803636	−	0.580980i
$352$	−4.56935	+	4.56935i	−0.243547	+	0.243547i
$353$	−10.4725	−	6.04628i	−0.557393	−	0.321811i	0.194706	−	0.980862i	$-0.437625\pi$
$353$	−10.4725	−	6.04628i	−0.557393	−	0.321811i	−0.752098	+	0.659051i	$0.770958\pi$
$354$	−5.36886	−	3.09971i	−0.285352	−	0.164748i
$355$		0			0
$356$	10.6902	+	10.6902i	0.566580	+	0.566580i
$357$	−0.329666	−	0.570999i	−0.0174478	−	0.0302204i
$358$	−11.2286	−	19.4485i	−0.593451	−	1.02789i
$359$	9.24091	+	9.24091i	0.487717	+	0.487717i	0.907585	−	0.419868i	$-0.137924\pi$
$359$	9.24091	+	9.24091i	0.487717	+	0.487717i	−0.419868	+	0.907585i	$0.637924\pi$
$360$		0			0
$361$	−15.7087	−	9.06940i	−0.826772	−	0.477337i
$362$	−12.4902	−	7.21122i	−0.656470	−	0.379013i
$363$	22.9208	−	22.9208i	1.20303	−	1.20303i
$364$	−1.69529	−	1.37946i	−0.0888572	−	0.0723034i
$365$		0			0
$366$	2.60728	−	0.698619i	0.136285	−	0.0365174i
$367$	2.66751	+	9.95527i	0.139243	+	0.519661i	0.999944	+	0.0105510i	$0.00335857\pi$
$367$	2.66751	+	9.95527i	0.139243	+	0.519661i	−0.860702	+	0.509110i	$0.829975\pi$
$368$	4.90919	+	1.31541i	0.255909	+	0.0685707i
$369$	−2.43369	+	2.43369i	−0.126693	+	0.126693i
$370$		0			0
$371$	−3.15025	−	0.844107i	−0.163553	−	0.0438238i
$372$			10.5234i			0.545613i
$373$	7.36803	−	27.4979i	0.381502	−	1.42379i	−0.462105	−	0.886825i	$-0.652906\pi$
$373$	7.36803	−	27.4979i	0.381502	−	1.42379i	0.843608	−	0.536960i	$-0.180428\pi$
$374$	−3.33467	+	5.77582i	−0.172432	+	0.298660i
$375$		0			0
$376$		−	7.31779i		−	0.377386i
$377$	8.57726	+	6.97934i	0.441751	+	0.359454i
$378$	−2.20865	−	2.20865i	−0.113601	−	0.113601i
$379$	−5.36719	−	20.0306i	−0.275694	−	1.02890i	−0.955375	−	0.295396i	$-0.904548\pi$
$379$	−5.36719	−	20.0306i	−0.275694	−	1.02890i	0.679681	−	0.733508i	$-0.262118\pi$
$380$		0			0
$381$	11.8540	−	6.84394i	0.607301	−	0.350626i
$382$	16.3504			0.836560
$383$	−9.93243	+	5.73449i	−0.507523	+	0.293019i	−0.731815	−	0.681503i	$-0.761327\pi$
$383$	−9.93243	+	5.73449i	−0.507523	+	0.293019i	0.224292	+	0.974522i	$0.427993\pi$
$384$	−0.272763	+	1.01796i	−0.0139194	+	0.0519478i
$385$		0			0
$386$	−6.27661	−	10.8714i	−0.319471	−	0.553340i
$387$	−12.8114	+	3.43281i	−0.651241	+	0.174499i
$388$	−8.80863	+	15.2570i	−0.447190	+	0.774556i
$389$	−14.4854			−0.734439			−0.367219	−	0.930134i	$-0.619690\pi$
$389$	−14.4854			−0.734439			−0.367219	+	0.930134i	$0.619690\pi$
$390$		0			0
$391$	5.24541			0.265272
$392$	3.31627	−	5.74395i	0.167497	−	0.290113i
$393$	−6.24571	+	1.67353i	−0.315055	+	0.0844186i
$394$	5.71847	+	9.90468i	0.288092	+	0.498990i
$395$		0			0
$396$	−3.15993	+	11.7930i	−0.158792	+	0.592622i
$397$	18.1283	−	10.4664i	0.909835	−	0.525293i	0.0294568	−	0.999566i	$-0.490622\pi$
$397$	18.1283	−	10.4664i	0.909835	−	0.525293i	0.880378	+	0.474273i	$0.157289\pi$
$398$	16.0465			0.804341
$399$	−0.513418	+	0.296422i	−0.0257031	+	0.0148397i
$400$		0			0
$401$	6.71066	+	25.0445i	0.335114	+	1.25066i	0.903745	+	0.428071i	$0.140807\pi$
$401$	6.71066	+	25.0445i	0.335114	+	1.25066i	−0.568631	+	0.822593i	$0.692527\pi$
$402$	−4.89984	−	4.89984i	−0.244382	−	0.244382i
$403$	21.0932	+	29.1770i	1.05073	+	1.45341i
$404$			7.19523i			0.357976i
$405$		0			0
$406$	0.929563	−	1.61005i	0.0461334	−	0.0799055i
$407$	−0.0718807	+	0.268262i	−0.00356299	+	0.0132973i
$408$			1.08768i			0.0538483i
$409$	27.7285	+	7.42982i	1.37108	+	0.367381i	0.867874	−	0.496784i	$-0.165486\pi$
$409$	27.7285	+	7.42982i	1.37108	+	0.367381i	0.503209	+	0.864164i	$0.332152\pi$
$410$		0			0
$411$	10.3649	−	10.3649i	0.511261	−	0.511261i
$412$	−13.6111	−	3.64709i	−0.670573	−	0.179679i
$413$	0.922913	+	3.44436i	0.0454136	+	0.169486i
$414$	9.27518	−	2.48528i	0.455850	−	0.122145i
$415$		0			0
$416$	1.28416	+	3.36912i	0.0629610	+	0.165184i
$417$	−1.95564	+	1.95564i	−0.0957681	+	0.0957681i
$418$	5.19337	+	2.99839i	0.254016	+	0.146656i
$419$	−10.0023	−	5.77483i	−0.488645	−	0.282119i	0.235367	−	0.971906i	$-0.424371\pi$
$419$	−10.0023	−	5.77483i	−0.488645	−	0.282119i	−0.724012	+	0.689787i	$0.757704\pi$
$420$		0			0
$421$	17.1102	+	17.1102i	0.833899	+	0.833899i	0.988048	−	0.154148i	$-0.0492634\pi$
$421$	17.1102	+	17.1102i	0.833899	+	0.833899i	−0.154148	+	0.988048i	$0.549263\pi$
$422$	2.78099	+	4.81682i	0.135377	+	0.234479i
$423$	−6.91293	−	11.9735i	−0.336118	−	0.582174i
$424$	3.80438	+	3.80438i	0.184757	+	0.184757i
$425$		0			0
$426$	9.57212	+	5.52646i	0.463771	+	0.267758i
$427$	−1.34458	−	0.776296i	−0.0650690	−	0.0375676i
$428$	−2.14295	+	2.14295i	−0.103584	+	0.103584i
$429$	−8.74533	−	22.9442i	−0.422229	−	1.10776i
$430$		0			0
$431$	6.83242	−	1.83074i	0.329106	−	0.0881837i	−0.0904826	−	0.995898i	$-0.528841\pi$
$431$	6.83242	−	1.83074i	0.329106	−	0.0881837i	0.419589	+	0.907714i	$0.362174\pi$
$432$	1.33363	+	4.97718i	0.0641644	+	0.239465i
$433$	−26.0607	−	6.98295i	−1.25240	−	0.335579i	−0.429135	−	0.903240i	$-0.641182\pi$
$433$	−26.0607	−	6.98295i	−1.25240	−	0.335579i	−0.823262	+	0.567661i	$0.807848\pi$
$434$	4.28011	−	4.28011i	0.205452	−	0.205452i
$435$		0			0
$436$	−8.85572	−	2.37288i	−0.424112	−	0.113640i
$437$		−	4.71646i		−	0.225619i
$438$	−0.557390	+	2.08021i	−0.0266331	+	0.0993961i
$439$	−8.56872	+	14.8415i	−0.408963	+	0.708345i	−0.994774	−	0.102103i	$-0.967443\pi$
$439$	−8.56872	+	14.8415i	−0.408963	+	0.708345i	0.585811	+	0.810448i	$0.300776\pi$
$440$		0			0
$441$		−	12.5312i		−	0.596724i
$442$	2.18016	+	3.01569i	0.103700	+	0.143442i
$443$	2.44587	+	2.44587i	0.116207	+	0.116207i	0.762819	−	0.646612i	$-0.223815\pi$
$443$	2.44587	+	2.44587i	0.116207	+	0.116207i	−0.646612	+	0.762819i	$0.723815\pi$
$444$	0.0117228	+	0.0437502i	0.000556340	+	0.00207629i
$445$		0			0
$446$	2.87993	−	1.66273i	0.136368	−	0.0787324i
$447$	−16.5427			−0.782444
$448$	0.524968	−	0.303090i	0.0248024	−	0.0143197i
$449$	−3.61806	+	13.5028i	−0.170747	+	0.637236i	0.826490	+	0.562951i	$0.190334\pi$
$449$	−3.61806	+	13.5028i	−0.170747	+	0.637236i	−0.997237	+	0.0742848i	$0.976333\pi$
$450$		0			0
$451$	5.88583	+	10.1946i	0.277153	+	0.480043i
$452$	16.6037	−	4.44894i	0.780971	−	0.209260i
$453$	−8.93912	+	15.4830i	−0.419996	+	0.727455i
$454$	5.26379			0.247042
$455$		0			0
$456$	0.977999			0.0457990
$457$	12.8602	−	22.2746i	0.601576	−	1.04196i	−0.391007	−	0.920388i	$-0.627873\pi$
$457$	12.8602	−	22.2746i	0.601576	−	1.04196i	0.992583	−	0.121572i	$-0.0387935\pi$
$458$	−17.5624	+	4.70583i	−0.820636	+	0.219889i
$459$	2.65903	+	4.60558i	0.124113	+	0.214970i
$460$		0			0
$461$	−0.526243	+	1.96397i	−0.0245096	+	0.0914710i	−0.977097	−	0.212793i	$-0.931744\pi$
$461$	−0.526243	+	1.96397i	−0.0245096	+	0.0914710i	0.952588	+	0.304264i	$0.0984106\pi$
$462$	−3.57512	+	2.06410i	−0.166330	+	0.0960304i
$463$	−0.620968			−0.0288588			−0.0144294	−	0.999896i	$-0.504593\pi$
$463$	−0.620968			−0.0288588			−0.0144294	+	0.999896i	$0.504593\pi$
$464$	−2.65606	+	1.53348i	−0.123304	+	0.0711898i
$465$		0			0
$466$	−1.96988	−	7.35170i	−0.0912530	−	0.340561i
$467$	−0.369896	−	0.369896i	−0.0171167	−	0.0171167i	0.698497	−	0.715613i	$-0.253853\pi$
$467$	−0.369896	−	0.369896i	−0.0171167	−	0.0171167i	−0.715613	+	0.698497i	$0.753853\pi$
$468$	5.28389	+	4.29952i	0.244248	+	0.198745i
$469$			3.98575i			0.184045i
$470$		0			0
$471$	−6.04999	+	10.4789i	−0.278769	+	0.482841i
$472$	1.52251	−	5.68207i	0.0700790	−	0.261538i
$473$			45.3639i			2.08583i
$474$	4.16705	+	1.11656i	0.191399	+	0.0512852i
$475$		0			0
$476$	0.442385	−	0.442385i	0.0202767	−	0.0202767i
$477$	9.81873	+	2.63092i	0.449569	+	0.120462i
$478$	−6.94226	−	25.9089i	−0.317531	−	1.18504i
$479$	5.22504	−	1.40005i	0.238738	−	0.0639697i	−0.137466	−	0.990506i	$-0.543896\pi$
$479$	5.22504	−	1.40005i	0.238738	−	0.0639697i	0.376204	+	0.926537i	$0.377229\pi$
$480$		0			0
$481$	0.120196	+	0.0978035i	0.00548045	+	0.00445946i
$482$	−11.5976	+	11.5976i	−0.528255	+	0.528255i
$483$	2.81182	+	1.62341i	0.127942	+	0.0738675i
$484$	26.6371	+	15.3789i	1.21078	+	0.699042i
$485$		0			0
$486$	11.1078	+	11.1078i	0.503859	+	0.503859i
$487$	13.2778	+	22.9978i	0.601675	+	1.04213i	0.992568	+	0.121695i	$0.0388330\pi$
$487$	13.2778	+	22.9978i	0.601675	+	1.04213i	−0.390893	+	0.920436i	$0.627834\pi$
$488$	1.28063	+	2.21812i	0.0579716	+	0.100410i
$489$	−6.26682	−	6.26682i	−0.283396	−	0.283396i
$490$		0			0
$491$	−27.1633	−	15.6827i	−1.22586	−	0.707752i	−0.259701	−	0.965689i	$-0.583624\pi$
$491$	−27.1633	−	15.6827i	−1.22586	−	0.707752i	−0.966162	+	0.257937i	$0.916957\pi$
$492$	1.66260	+	0.959903i	0.0749558	+	0.0432758i
$493$	−2.23823	+	2.23823i	−0.100805	+	0.100805i
$494$	2.71158	−	1.96031i	0.122000	−	0.0881985i
$495$		0			0
$496$	−9.64520	+	2.58442i	−0.433082	+	0.116044i
$497$	−1.64546	−	6.14093i	−0.0738089	−	0.275459i
$498$	−7.54226	−	2.02094i	−0.337977	−	0.0905605i
$499$	12.6591	−	12.6591i	0.566698	−	0.566698i	−0.364504	−	0.931202i	$-0.618761\pi$
$499$	12.6591	−	12.6591i	0.566698	−	0.566698i	0.931202	+	0.364504i	$0.118761\pi$
$500$		0			0
$501$	−2.59921	−	0.696457i	−0.116124	−	0.0311154i
$502$			13.6742i			0.610311i
$503$	−6.69103	+	24.9713i	−0.298338	+	1.11341i	0.640192	+	0.768215i	$0.278855\pi$
$503$	−6.69103	+	24.9713i	−0.298338	+	1.11341i	−0.938530	+	0.345198i	$0.887812\pi$
$504$	0.572643	−	0.991848i	0.0255076	−	0.0441804i
$505$		0			0
$506$		−	32.8424i		−	1.46002i
$507$	−13.6780	−	0.781657i	−0.607463	−	0.0347146i
$508$	9.18401	+	9.18401i	0.407475	+	0.407475i
$509$	3.62983	+	13.5467i	0.160889	+	0.600447i	0.998529	+	0.0542239i	$0.0172685\pi$
$509$	3.62983	+	13.5467i	0.160889	+	0.600447i	−0.837639	+	0.546224i	$0.816065\pi$
$510$		0			0
$511$	1.07277	−	0.619364i	0.0474566	−	0.0273991i
$512$	−1.00000			−0.0441942
$513$	4.14114	−	2.39089i	0.182836	−	0.105560i
$514$	6.09097	−	22.7318i	0.268661	−	1.00266i
$515$		0			0
$516$	3.69913	+	6.40709i	0.162845	+	0.282056i
$517$	−45.6765	+	12.2390i	−2.00885	+	0.538270i
$518$	0.0130262	−	0.0225621i	0.000572340	−	0.000991322i
$519$	24.3541			1.06903
$520$		0			0
$521$	−11.9436			−0.523260			−0.261630	−	0.965168i	$-0.584260\pi$
$521$	−11.9436			−0.523260			−0.261630	+	0.965168i	$0.584260\pi$
$522$	−2.89727	+	5.01822i	−0.126810	+	0.219642i
$523$	−8.53615	+	2.28726i	−0.373260	+	0.100015i	−0.440572	−	0.897717i	$-0.645224\pi$
$523$	−8.53615	+	2.28726i	−0.373260	+	0.100015i	0.0673121	+	0.997732i	$0.478558\pi$
$524$	−3.06775	−	5.31349i	−0.134015	−	0.232121i
$525$		0			0
$526$	−1.77496	+	6.62424i	−0.0773919	+	0.288831i
$527$	−8.92507	+	5.15289i	−0.388782	+	0.224464i
$528$	6.81017			0.296374
$529$	−2.45126	+	1.41524i	−0.106577	+	0.0615321i
$530$		0			0
$531$	−2.87654	−	10.7354i	−0.124831	−	0.465877i
$532$	−0.397774	−	0.397774i	−0.0172457	−	0.0172457i
$533$	6.53373	−	0.671121i	0.283007	−	0.0290695i
$534$		−	15.9327i		−	0.689476i
$535$		0			0
$536$	3.28759	−	5.69428i	0.142002	−	0.245955i
$537$	−6.12549	+	22.8606i	−0.264334	+	0.986510i
$538$			16.1492i			0.696241i
$539$	−41.3993	−	11.0929i	−1.78319	−	0.477805i
$540$		0			0
$541$	4.58410	−	4.58410i	0.197086	−	0.197086i	−0.601664	−	0.798749i	$-0.705495\pi$
$541$	4.58410	−	4.58410i	0.197086	−	0.197086i	0.798749	+	0.601664i	$0.205495\pi$
$542$	9.46802	+	2.53695i	0.406686	+	0.108971i
$543$	3.93390	+	14.6815i	0.168820	+	0.630044i
$544$	−0.996913	+	0.267122i	−0.0427423	+	0.0114528i
$545$		0			0
$546$	0.235355	+	2.29131i	0.0100722	+	0.0980589i
$547$	−13.4979	+	13.4979i	−0.577128	+	0.577128i	−0.934111	−	0.356983i	$-0.883806\pi$
$547$	−13.4979	+	13.4979i	−0.577128	+	0.577128i	0.356983	+	0.934111i	$0.383806\pi$
$548$	12.0454	+	6.95440i	0.514553	+	0.297077i
$549$	4.19081	+	2.41957i	0.178860	+	0.103265i
$550$		0			0
$551$	2.01253	+	2.01253i	0.0857365	+	0.0857365i
$552$	−2.67809	−	4.63859i	−0.113987	−	0.197431i
$553$	−1.24070	−	2.14896i	−0.0527601	−	0.0913832i
$554$	−13.1471	−	13.1471i	−0.558568	−	0.558568i
$555$		0			0
$556$	−2.27272	−	1.31215i	−0.0963847	−	0.0556478i
$557$	−21.9120	−	12.6509i	−0.928441	−	0.536036i	−0.0421230	−	0.999112i	$-0.513412\pi$
$557$	−21.9120	−	12.6509i	−0.928441	−	0.536036i	−0.886318	+	0.463077i	$0.846745\pi$
$558$	−13.3403	+	13.3403i	−0.564739	+	0.564739i
$559$	23.0986	+	10.3496i	0.976965	+	0.437741i
$560$		0			0
$561$	6.78915	−	1.81915i	0.286638	−	0.0768044i
$562$	−7.33432	−	27.3721i	−0.309380	−	1.15462i
$563$	−29.2420	−	7.83537i	−1.23240	−	0.330222i	−0.416889	−	0.908957i	$-0.636880\pi$
$563$	−29.2420	−	7.83537i	−1.23240	−	0.330222i	−0.815515	+	0.578736i	$0.803546\pi$
$564$	−5.45323	+	5.45323i	−0.229622	+	0.229622i
$565$		0			0
$566$	−16.8211	−	4.50721i	−0.707045	−	0.189452i
$567$		−	0.144083i		−	0.00605091i
$568$	−2.71447	+	10.1305i	−0.113897	+	0.425068i
$569$	6.47393	−	11.2132i	0.271401	−	0.470081i	−0.697820	−	0.716273i	$-0.745846\pi$
$569$	6.47393	−	11.2132i	0.271401	−	0.470081i	0.969221	+	0.246193i	$0.0791796\pi$
$570$		0			0
$571$		−	12.4096i		−	0.519324i	−0.965700	−	0.259662i	$-0.916389\pi$
$571$		−	12.4096i		−	0.519324i	0.965700	−	0.259662i	$-0.0836111\pi$
$572$	18.8817	−	13.6503i	0.789485	−	0.570750i
$573$	−12.1844	−	12.1844i	−0.509009	−	0.509009i
$574$	−0.285803	−	1.06663i	−0.0119292	−	0.0445203i
$575$		0			0
$576$	−1.63622	+	0.944675i	−0.0681760	+	0.0393614i
$577$	−22.8030			−0.949301			−0.474650	−	0.880174i	$-0.657425\pi$
$577$	−22.8030			−0.949301			−0.474650	+	0.880174i	$0.657425\pi$
$578$	13.7999	−	7.96740i	0.574002	−	0.331400i
$579$	−3.42405	+	12.7787i	−0.142299	+	0.531066i
$580$		0			0
$581$	2.24564	+	3.88957i	0.0931650	+	0.161366i
$582$	17.9337	−	4.80533i	0.743377	−	0.199187i
$583$	17.3835	−	30.1092i	0.719953	−	1.24699i
$584$	−2.04350			−0.0845605
$585$		0			0
$586$	−28.8199			−1.19054
$587$	18.8519	−	32.6525i	0.778102	−	1.34771i	−0.154933	−	0.987925i	$-0.549516\pi$
$587$	18.8519	−	32.6525i	0.778102	−	1.34771i	0.933034	−	0.359787i	$-0.117151\pi$
$588$	−6.75169	+	1.80911i	−0.278435	+	0.0746065i
$589$	4.63327	+	8.02505i	0.190910	+	0.330667i
$590$		0			0
$591$	3.11957	−	11.6424i	0.128322	−	0.478904i
$592$	−0.0372201	+	0.0214890i	−0.00152974	+	0.000883194i
$593$	6.88681			0.282807			0.141404	−	0.989952i	$-0.454838\pi$
$593$	6.88681			0.282807			0.141404	+	0.989952i	$0.454838\pi$
$594$	28.8363	−	16.6486i	1.18317	−	0.683102i
$595$		0			0
$596$	−4.06270	−	15.1622i	−0.166415	−	0.621068i
$597$	−11.9579	−	11.9579i	−0.489405	−	0.489405i
$598$	−16.7228	−	7.49287i	−0.683847	−	0.306406i
$599$			39.1133i			1.59813i	0.601246	+	0.799064i	$0.294671\pi$
$599$			39.1133i			1.59813i	−0.601246	+	0.799064i	$0.705329\pi$
$600$		0			0
$601$	8.74962	−	15.1548i	0.356904	−	0.618176i	−0.630538	−	0.776159i	$-0.717166\pi$
$601$	8.74962	−	15.1548i	0.356904	−	0.618176i	0.987442	+	0.157982i	$0.0504989\pi$
$602$	1.10139	−	4.11043i	0.0448891	−	0.167529i
$603$		−	12.4228i		−	0.505896i
$604$	−16.3863	−	4.39068i	−0.666747	−	0.178654i
$605$		0			0
$606$	5.36189	−	5.36189i	0.217812	−	0.217812i
$607$	−39.0688	−	10.4684i	−1.58575	−	0.424901i	−0.645052	−	0.764139i	$-0.723164\pi$
$607$	−39.0688	−	10.4684i	−1.58575	−	0.424901i	−0.940701	+	0.339238i	$0.889831\pi$
$608$	0.240185	+	0.896383i	0.00974079	+	0.0363531i
$609$	−1.89252	+	0.507100i	−0.0766889	+	0.0205487i
$610$		0			0
$611$	−4.18903	+	26.0500i	−0.169470	+	1.05387i
$612$	−1.37883	+	1.37883i	−0.0557359	+	0.0557359i
$613$	23.2346	+	13.4145i	0.938436	+	0.541806i	0.889470	−	0.456994i	$-0.151074\pi$
$613$	23.2346	+	13.4145i	0.938436	+	0.541806i	0.0489665	+	0.998800i	$0.484407\pi$
$614$	−28.8196	−	16.6390i	−1.16306	−	0.671496i
$615$		0			0
$616$	−2.76985	−	2.76985i	−0.111600	−	0.111600i
$617$	−16.2401	−	28.1287i	−0.653803	−	1.13242i	−0.982192	−	0.187877i	$-0.939839\pi$
$617$	−16.2401	−	28.1287i	−0.653803	−	1.13242i	0.328390	−	0.944542i	$-0.393494\pi$
$618$	7.42522	+	12.8609i	0.298686	+	0.517340i
$619$	−8.37271	−	8.37271i	−0.336528	−	0.336528i	0.518531	−	0.855059i	$-0.326479\pi$
$619$	−8.37271	−	8.37271i	−0.336528	−	0.336528i	−0.855059	+	0.518531i	$0.826479\pi$
$620$		0			0
$621$	−22.6797	−	13.0941i	−0.910104	−	0.525449i
$622$	−10.4717	−	6.04583i	−0.419876	−	0.242416i
$623$	−6.48019	+	6.48019i	−0.259623	+	0.259623i
$624$	1.55371	−	3.46763i	0.0621983	−	0.138816i
$625$		0			0
$626$	0.271549	−	0.0727613i	0.0108533	−	0.00290813i
$627$	−1.63570	−	6.10452i	−0.0653236	−	0.243791i
$628$	−11.0902	−	2.97161i	−0.442547	−	0.118580i
$629$	−0.0313650	+	0.0313650i	−0.00125061	+	0.00125061i
$630$		0			0
$631$	27.7774	+	7.44294i	1.10580	+	0.296299i	0.765125	−	0.643882i	$-0.222677\pi$
$631$	27.7774	+	7.44294i	1.10580	+	0.296299i	0.340677	+	0.940180i	$0.389344\pi$
$632$			4.09352i			0.162831i
$633$	1.51710	−	5.66190i	0.0602994	−	0.225040i
$634$	−5.53342	+	9.58416i	−0.219760	+	0.380636i
$635$		0			0
$636$		−	5.67006i		−	0.224833i
$637$	−15.0934	+	18.5490i	−0.598023	+	0.734940i
$638$	14.0140	+	14.0140i	0.554818	+	0.554818i
$639$	5.12858	+	19.1401i	0.202883	+	0.757171i
$640$		0			0
$641$	−23.0068	+	13.2830i	−0.908715	+	0.524647i	−0.880017	−	0.474942i	$-0.842469\pi$
$641$	−23.0068	+	13.2830i	−0.908715	+	0.524647i	−0.0286972	+	0.999588i	$0.509136\pi$
$642$	3.19386			0.126052
$643$	1.96619	−	1.13518i	0.0775389	−	0.0447671i	−0.460729	−	0.887541i	$-0.652412\pi$
$643$	1.96619	−	1.13518i	0.0775389	−	0.0447671i	0.538268	+	0.842774i	$0.319079\pi$
$644$	−0.797378	+	2.97586i	−0.0314211	+	0.117265i
$645$		0			0
$646$	0.478887	+	0.829457i	0.0188416	+	0.0326346i
$647$	−31.1681	+	8.35147i	−1.22534	+	0.328330i	−0.812765	−	0.582591i	$-0.802039\pi$
$647$	−31.1681	+	8.35147i	−1.22534	+	0.328330i	−0.412580	+	0.910922i	$0.635372\pi$
$648$	−0.118845	+	0.205845i	−0.00466866	+	0.00808636i
$649$	−38.0130			−1.49214
$650$		0			0
$651$	−6.37908			−0.250016
$652$	4.20479	−	7.28290i	0.164672	−	0.285220i
$653$	26.2127	−	7.02367i	1.02578	−	0.274858i	0.293573	−	0.955937i	$-0.405156\pi$
$653$	26.2127	−	7.02367i	1.02578	−	0.274858i	0.732210	+	0.681079i	$0.238489\pi$
$654$	4.83102	+	8.36757i	0.188908	+	0.327198i
$655$		0			0
$656$	−0.471482	+	1.75959i	−0.0184083	+	0.0687006i
$657$	−3.34362	+	1.93044i	−0.130447	+	0.0753136i
$658$	4.43590			0.172930
$659$	29.1194	−	16.8121i	1.13433	−	0.654905i	0.189309	−	0.981918i	$-0.439375\pi$
$659$	29.1194	−	16.8121i	1.13433	−	0.654905i	0.945020	+	0.327012i	$0.106042\pi$
$660$		0			0
$661$	−6.61555	−	24.6896i	−0.257315	−	0.960313i	−0.966788	−	0.255580i	$-0.917733\pi$
$661$	−6.61555	−	24.6896i	−0.257315	−	0.960313i	0.709473	−	0.704733i	$-0.248933\pi$
$662$	−11.1994	−	11.1994i	−0.435279	−	0.435279i
$663$	0.622638	−	3.87195i	0.0241812	−	0.150374i
$664$		−	7.40916i		−	0.287531i
$665$		0			0
$666$	−0.0406003	+	0.0703218i	−0.00157323	+	0.00272491i
$667$	4.03431	−	15.0563i	0.156209	−	0.582980i
$668$		−	2.55335i		−	0.0987919i
$669$	−3.38519	−	0.907060i	−0.130879	−	0.0350689i
$670$		0			0
$671$	11.7033	−	11.7033i	0.451802	−	0.451802i
$672$	−0.617070	−	0.165343i	−0.0238040	−	0.00637826i
$673$	8.46780	+	31.6023i	0.326410	+	1.21818i	0.912887	+	0.408212i	$0.133848\pi$
$673$	8.46780	+	31.6023i	0.326410	+	1.21818i	−0.586478	+	0.809965i	$0.699486\pi$
$674$	26.0490	−	6.97982i	1.00337	−	0.268853i
$675$		0			0
$676$	−2.64274	−	12.7285i	−0.101644	−	0.489560i
$677$	10.3878	−	10.3878i	0.399237	−	0.399237i	−0.478727	−	0.877964i	$-0.658902\pi$
$677$	10.3878	−	10.3878i	0.399237	−	0.399237i	0.877964	+	0.478727i	$0.158902\pi$
$678$	−15.6884	−	9.05772i	−0.602511	−	0.347860i
$679$	−9.24849	−	5.33962i	−0.354924	−	0.204916i
$680$		0			0
$681$	−3.92258	−	3.92258i	−0.150314	−	0.150314i
$682$	32.2631	+	55.8814i	1.23542	+	2.13981i
$683$	2.59960	+	4.50264i	0.0994710	+	0.172289i	0.911466	−	0.411376i	$-0.134952\pi$
$683$	2.59960	+	4.50264i	0.0994710	+	0.172289i	−0.811995	+	0.583665i	$0.801618\pi$
$684$	1.23979	+	1.23979i	0.0474044	+	0.0474044i
$685$		0			0
$686$	7.15665	+	4.13189i	0.273242	+	0.157756i
$687$	16.5943	+	9.58072i	0.633112	+	0.365527i
$688$	−4.96394	+	4.96394i	−0.189248	+	0.189248i
$689$	−11.3651	−	15.7207i	−0.432976	−	0.598911i
$690$		0			0
$691$	−42.3278	+	11.3417i	−1.61023	+	0.431459i	−0.948110	−	0.317942i	$-0.897008\pi$
$691$	−42.3278	+	11.3417i	−1.61023	+	0.431459i	−0.662117	+	0.749401i	$0.730342\pi$
$692$	5.98108	+	22.3217i	0.227367	+	0.848544i
$693$	−7.14870	−	1.91549i	−0.271557	−	0.0727634i
$694$	14.0195	−	14.0195i	0.532171	−	0.532171i
$695$		0			0
$696$	3.12205	+	0.836550i	0.118341	+	0.0317093i
$697$			1.88011i			0.0712141i
$698$	3.42812	−	12.7939i	0.129756	−	0.484256i
$699$	−4.01054	+	6.94646i	−0.151693	+	0.262739i
$700$		0			0
$701$		−	19.7131i		−	0.744552i	−0.928122	−	0.372276i	$-0.878577\pi$
$701$		−	19.7131i		−	0.744552i	0.928122	−	0.372276i	$-0.121423\pi$
$702$	−1.89833	−	18.4813i	−0.0716479	−	0.697532i
$703$	0.0282021	+	0.0282021i	0.00106366	+	0.00106366i
$704$	1.67250	+	6.24184i	0.0630346	+	0.235248i
$705$		0			0
$706$	−10.4725	+	6.04628i	−0.394136	+	0.227555i
$707$	−4.36161			−0.164035
$708$	−5.36886	+	3.09971i	−0.201774	+	0.116494i
$709$	2.68781	−	10.0310i	0.100943	−	0.376724i	−0.896910	−	0.442212i	$-0.854194\pi$
$709$	2.68781	−	10.0310i	0.100943	−	0.376724i	0.997853	+	0.0654883i	$0.0208605\pi$
$710$		0			0
$711$	3.86704	+	6.69791i	0.145025	+	0.251191i
$712$	14.6031	−	3.91289i	0.547274	−	0.146642i
$713$	25.3749	−	43.9506i	0.950296	−	1.64596i
$714$	−0.659332			−0.0246749
$715$		0			0
$716$	−22.4572			−0.839266
$717$	−14.1339	+	24.4807i	−0.527842	+	0.914248i
$718$	12.6233	−	3.38241i	0.471098	−	0.126230i
$719$	7.17711	+	12.4311i	0.267661	+	0.463603i	0.968257	−	0.249955i	$-0.0804159\pi$
$719$	7.17711	+	12.4311i	0.267661	+	0.463603i	−0.700596	+	0.713558i	$0.747083\pi$
$720$		0			0
$721$	2.21080	−	8.25081i	0.0823344	−	0.307276i
$722$	−15.7087	+	9.06940i	−0.584616	+	0.337528i
$723$	17.2850			0.642838
$724$	−12.4902	+	7.21122i	−0.464194	+	0.268003i
$725$		0			0
$726$	−8.38959	−	31.3104i	−0.311367	−	1.16204i
$727$	3.22577	+	3.22577i	0.119637	+	0.119637i	0.764391	−	0.644753i	$-0.223040\pi$
$727$	3.22577	+	3.22577i	0.119637	+	0.119637i	−0.644753	+	0.764391i	$0.723040\pi$
$728$	−2.04229	+	0.778432i	−0.0756924	+	0.0288506i
$729$		−	15.8420i		−	0.586741i
$730$		0			0
$731$	−3.62264	+	6.27459i	−0.133988	+	0.232074i
$732$	0.698619	−	2.60728i	0.0258217	−	0.0963679i
$733$			30.7847i			1.13706i	0.822662	+	0.568530i	$0.192488\pi$
$733$			30.7847i			1.13706i	−0.822662	+	0.568530i	$0.807512\pi$
$734$	9.95527	+	2.66751i	0.367456	+	0.0984594i
$735$		0			0
$736$	3.59378	−	3.59378i	0.132468	−	0.132468i
$737$	−41.0413	−	10.9970i	−1.51177	−	0.405079i
$738$	0.890794	+	3.32449i	0.0327906	+	0.122376i
$739$	−38.3464	+	10.2749i	−1.41059	+	0.377968i	−0.882137	−	0.470992i	$-0.843896\pi$
$739$	−38.3464	+	10.2749i	−1.41059	+	0.377968i	−0.528457	+	0.848960i	$0.677229\pi$
$740$		0			0
$741$	−3.48150	−	0.559850i	−0.127896	−	0.0205666i
$742$	−2.30614	+	2.30614i	−0.0846612	+	0.0846612i
$743$	−37.7688	−	21.8058i	−1.38560	−	0.799979i	−0.392788	−	0.919629i	$-0.628489\pi$
$743$	−37.7688	−	21.8058i	−1.38560	−	0.799979i	−0.992816	+	0.119650i	$0.961823\pi$
$744$	9.11354	+	5.26170i	0.334118	+	0.192903i
$745$		0			0
$746$	−20.1298	−	20.1298i	−0.737006	−	0.737006i
$747$	−6.99924	−	12.1230i	−0.256089	−	0.443559i
$748$	3.33467	+	5.77582i	0.121928	+	0.211185i
$749$	−1.29902	−	1.29902i	−0.0474650	−	0.0474650i
$750$		0			0
$751$	−24.9091	−	14.3813i	−0.908945	−	0.524780i	−0.0288538	−	0.999584i	$-0.509186\pi$
$751$	−24.9091	−	14.3813i	−0.908945	−	0.524780i	−0.880092	+	0.474804i	$0.842519\pi$
$752$	−6.33739	−	3.65890i	−0.231101	−	0.133426i
$753$	10.1901	−	10.1901i	0.371346	−	0.371346i
$754$	10.3329	−	3.93845i	0.376302	−	0.143430i
$755$		0			0
$756$	−3.01707	+	0.808422i	−0.109730	+	0.0294020i
$757$	10.2555	+	38.2740i	0.372742	+	1.39109i	0.856616	+	0.515954i	$0.172562\pi$
$757$	10.2555	+	38.2740i	0.372742	+	1.39109i	−0.483875	+	0.875137i	$0.660771\pi$
$758$	−20.0306	−	5.36719i	−0.727545	−	0.194945i
$759$	−24.4742	+	24.4742i	−0.888358	+	0.888358i
$760$		0			0
$761$	41.1629	+	11.0296i	1.49215	+	0.399821i	0.910463	−	0.413590i	$-0.135725\pi$
$761$	41.1629	+	11.0296i	1.49215	+	0.399821i	0.581689	+	0.813411i	$0.302392\pi$
$762$		−	13.6879i		−	0.495859i
$763$	1.43840	−	5.36816i	0.0520734	−	0.194341i
$764$	8.17521	−	14.1599i	0.295769	−	0.512286i
$765$		0			0
$766$			11.4690i			0.414391i
$767$	−8.67251	+	19.3556i	−0.313146	+	0.698889i
$768$	0.745202	+	0.745202i	0.0268901	+	0.0268901i
$769$	4.20166	+	15.6808i	0.151516	+	0.565464i	0.999379	+	0.0352485i	$0.0112223\pi$
$769$	4.20166	+	15.6808i	0.151516	+	0.565464i	−0.847863	+	0.530215i	$0.822111\pi$
$770$		0			0
$771$	−21.4788	+	12.4008i	−0.773540	+	0.446603i
$772$	−12.5532			−0.451800
$773$	−30.5255	+	17.6239i	−1.09793	+	0.633889i	−0.935676	−	0.352861i	$-0.885209\pi$
$773$	−30.5255	+	17.6239i	−1.09793	+	0.633889i	−0.162252	+	0.986749i	$0.551876\pi$
$774$	−3.43281	+	12.8114i	−0.123390	+	0.460497i
$775$		0			0
$776$	8.80863	+	15.2570i	0.316211	+	0.547694i
$777$	−0.0265205	+	0.00710614i	−0.000951417	+	0.000254932i
$778$	−7.24270	+	12.5447i	−0.259663	+	0.449750i
$779$	1.69051			0.0605689
$780$		0			0
$781$	67.7731			2.42511
$782$	2.62271	−	4.54266i	0.0937878	−	0.162445i
$783$	15.2648	−	4.09018i	0.545519	−	0.146171i
$784$	−3.31627	−	5.74395i	−0.118438	−	0.205141i
$785$		0			0
$786$	−1.67353	+	6.24571i	−0.0596930	+	0.222777i
$787$	42.5892	−	24.5889i	1.51814	−	0.876499i	0.518369	−	0.855157i	$-0.326539\pi$
$787$	42.5892	−	24.5889i	1.51814	−	0.876499i	0.999772	−	0.0213419i	$-0.00679384\pi$
$788$	11.4369			0.407424
$789$	6.25910	−	3.61369i	0.222830	−	0.128651i
$790$		0			0
$791$	2.69686	+	10.0648i	0.0958893	+	0.357864i
$792$	8.63309	+	8.63309i	0.306764	+	0.306764i
$793$	−3.28908	−	8.62921i	−0.116799	−	0.306432i
$794$		−	20.9328i		−	0.742877i
$795$		0			0
$796$	8.02327	−	13.8967i	0.284377	−	0.492556i
$797$	6.77206	−	25.2737i	0.239879	−	0.895240i	−0.736010	−	0.676971i	$-0.763292\pi$
$797$	6.77206	−	25.2737i	0.239879	−	0.895240i	0.975889	−	0.218269i	$-0.0700410\pi$
$798$			0.592844i			0.0209865i
$799$	−7.29520	−	1.95474i	−0.258086	−	0.0691539i
$800$		0			0
$801$	20.1975	−	20.1975i	0.713645	−	0.713645i
$802$	25.0445	+	6.71066i	0.884353	+	0.236962i
$803$	3.41774	+	12.7552i	0.120609	+	0.450121i
$804$	−6.69330	+	1.79346i	−0.236055	+	0.0632506i
$805$		0			0
$806$	35.8146	−	3.67874i	1.26152	−	0.129578i
$807$	12.0344	−	12.0344i	0.423631	−	0.423631i
$808$	6.23125	+	3.59761i	0.219215	+	0.126564i
$809$	−7.12231	−	4.11207i	−0.250407	−	0.144573i	0.369544	−	0.929213i	$-0.379514\pi$
$809$	−7.12231	−	4.11207i	−0.250407	−	0.144573i	−0.619951	+	0.784641i	$0.712847\pi$
$810$		0			0
$811$	−5.54440	−	5.54440i	−0.194690	−	0.194690i	0.603029	−	0.797719i	$-0.293960\pi$
$811$	−5.54440	−	5.54440i	−0.194690	−	0.194690i	−0.797719	+	0.603029i	$0.793960\pi$
$812$	−0.929563	−	1.61005i	−0.0326213	−	0.0565017i
$813$	−5.16505	−	8.94612i	−0.181146	−	0.313754i
$814$	0.196382	+	0.196382i	0.00688318	+	0.00688318i
$815$		0			0
$816$	0.941961	+	0.543841i	0.0329752	+	0.0190383i
$817$	5.64185	+	3.25732i	0.197383	+	0.113959i
$818$	20.2986	−	20.2986i	0.709725	−	0.709725i
$819$	−2.60628	+	3.20299i	−0.0910709	+	0.111922i
$820$		0			0
$821$	10.6659	−	2.85793i	0.372243	−	0.0997423i	−0.0678472	−	0.997696i	$-0.521613\pi$
$821$	10.6659	−	2.85793i	0.372243	−	0.0997423i	0.440090	+	0.897953i	$0.354946\pi$
$822$	−3.79380	−	14.1587i	−0.132324	−	0.493840i
$823$	−48.4047	−	12.9700i	−1.68728	−	0.452106i	−0.717596	−	0.696459i	$-0.754758\pi$
$823$	−48.4047	−	12.9700i	−1.68728	−	0.452106i	−0.969686	+	0.244353i	$0.921424\pi$
$824$	−9.96404	+	9.96404i	−0.347114	+	0.347114i
$825$		0			0
$826$	3.44436	+	0.922913i	0.119845	+	0.0321123i
$827$		−	4.23112i		−	0.147130i	−0.997290	−	0.0735652i	$-0.976562\pi$
$827$		−	4.23112i		−	0.147130i	0.997290	−	0.0735652i	$-0.0234377\pi$
$828$	2.48528	−	9.27518i	0.0863693	−	0.322335i
$829$	−5.50337	+	9.53212i	−0.191140	+	0.331064i	−0.945628	−	0.325249i	$-0.894552\pi$
$829$	−5.50337	+	9.53212i	−0.191140	+	0.331064i	0.754488	+	0.656313i	$0.227885\pi$
$830$		0			0
$831$			19.5945i			0.679727i
$832$	3.55982	+	0.572444i	0.123415	+	0.0198459i
$833$	−4.84037	−	4.84037i	−0.167709	−	0.167709i
$834$	0.715814	+	2.67145i	0.0247866	+	0.0925049i
$835$		0			0
$836$	5.19337	−	2.99839i	0.179617	−	0.103702i
$837$	51.4526			1.77846
$838$	−10.0023	+	5.77483i	−0.345524	+	0.199488i
$839$	5.94322	−	22.1804i	0.205183	−	0.765752i	−0.784211	−	0.620494i	$-0.786932\pi$
$839$	5.94322	−	22.1804i	0.205183	−	0.765752i	0.989394	−	0.145258i	$-0.0464012\pi$
$840$		0			0
$841$	−9.79690	−	16.9687i	−0.337824	−	0.585129i
$842$	23.3729	−	6.26276i	0.805485	−	0.215829i
$843$	−14.9322	+	25.8633i	−0.514291	+	0.890778i
$844$	5.56198			0.191451
$845$		0			0
$846$	−13.8259			−0.475343
$847$	−9.32240	+	16.1469i	−0.320322	+	0.554813i
$848$	5.19688	−	1.39250i	0.178462	−	0.0478187i
$849$	9.17636	+	15.8939i	0.314932	+	0.545478i
$850$		0			0
$851$	0.0565340	−	0.210988i	0.00193796	−	0.00723256i
$852$	9.57212	−	5.52646i	0.327935	−	0.189334i
$853$	11.1600			0.382112			0.191056	−	0.981579i	$-0.438809\pi$
$853$	11.1600			0.382112			0.191056	+	0.981579i	$0.438809\pi$
$854$	−1.34458	+	0.776296i	−0.0460107	+	0.0265643i
$855$		0			0
$856$	0.784375	+	2.92733i	0.0268094	+	0.100054i
$857$	−5.20581	−	5.20581i	−0.177827	−	0.177827i	0.612581	−	0.790408i	$-0.290131\pi$
$857$	−5.20581	−	5.20581i	−0.177827	−	0.177827i	−0.790408	+	0.612581i	$0.790131\pi$
$858$	−24.2430	−	3.89844i	−0.827641	−	0.133090i
$859$			24.5758i			0.838514i	0.907868	+	0.419257i	$0.137709\pi$
$859$			24.5758i			0.838514i	−0.907868	+	0.419257i	$0.862291\pi$
$860$		0			0
$861$	−0.581874	+	1.00784i	−0.0198302	+	0.0343470i
$862$	1.83074	−	6.83242i	0.0623553	−	0.232713i
$863$		−	21.2881i		−	0.724655i	−0.932051	−	0.362328i	$-0.881982\pi$
$863$		−	21.2881i		−	0.724655i	0.932051	−	0.362328i	$-0.118018\pi$
$864$	4.97718	+	1.33363i	0.169327	+	0.0453711i
$865$		0			0
$866$	−19.0778	+	19.0778i	−0.648289	+	0.648289i
$867$	−16.2211	−	4.34642i	−0.550896	−	0.147612i
$868$	−1.56663	−	5.84673i	−0.0531748	−	0.198451i
$869$	25.5511	−	6.84639i	0.866761	−	0.232248i
$870$		0			0
$871$	−14.9629	+	18.3886i	−0.506998	+	0.623075i
$872$	−6.48284	+	6.48284i	−0.219537	+	0.219537i
$873$	28.8258	+	16.6426i	0.975605	+	0.563266i
$874$	−4.08457	−	2.35823i	−0.138163	−	0.0797683i
$875$		0			0
$876$	1.52282	+	1.52282i	0.0514512	+	0.0514512i
$877$	10.8660	+	18.8205i	0.366920	+	0.635524i	0.989082	−	0.147364i	$-0.0470789\pi$
$877$	10.8660	+	18.8205i	0.366920	+	0.635524i	−0.622162	+	0.782888i	$0.713746\pi$
$878$	8.56872	+	14.8415i	0.289180	+	0.500875i
$879$	21.4766	+	21.4766i	0.724388	+	0.724388i
$880$		0			0
$881$	14.1897	+	8.19243i	0.478063	+	0.276010i	0.719609	−	0.694380i	$-0.244321\pi$
$881$	14.1897	+	8.19243i	0.478063	+	0.276010i	−0.241546	+	0.970389i	$0.577654\pi$
$882$	−10.8523	−	6.26560i	−0.365417	−	0.210974i
$883$	14.4246	−	14.4246i	0.485427	−	0.485427i	−0.421433	−	0.906860i	$-0.638473\pi$
$883$	14.4246	−	14.4246i	0.485427	−	0.485427i	0.906860	+	0.421433i	$0.138473\pi$
$884$	3.70174	−	0.380229i	0.124503	−	0.0127885i
$885$		0			0
$886$	3.34113	−	0.895252i	0.112247	−	0.0300766i
$887$	9.94910	+	37.1305i	0.334058	+	1.24672i	0.904887	+	0.425652i	$0.139955\pi$
$887$	9.94910	+	37.1305i	0.334058	+	1.24672i	−0.570829	+	0.821069i	$0.693378\pi$
$888$	0.0437502	+	0.0117228i	0.00146816	+	0.000393392i
$889$	−5.56717	+	5.56717i	−0.186717	+	0.186717i
$890$		0			0
$891$	1.48362	+	0.397535i	0.0497031	+	0.0133179i
$892$		−	3.32545i		−	0.111344i
$893$	−1.75762	+	6.55954i	−0.0588167	+	0.219507i
$894$	−8.27136	+	14.3264i	−0.276636	+	0.479147i
$895$		0			0
$896$		−	0.606181i		−	0.0202511i
$897$	6.87818	+	18.0456i	0.229656	+	0.602524i
$898$	9.88472	+	9.88472i	0.329858	+	0.329858i
$899$	7.92630	+	29.5814i	0.264357	+	0.986594i
$900$		0			0
$901$	4.80887	−	2.77640i	0.160207	−	0.0924955i
$902$	11.7717			0.391953
$903$	−3.88385	+	2.24234i	−0.129246	+	0.0746205i
$904$	4.44894	−	16.6037i	0.147969	−	0.552230i
$905$		0			0
$906$	8.93912	+	15.4830i	0.296982	+	0.514388i
$907$	14.4609	−	3.87478i	0.480166	−	0.128660i	−0.0106141	−	0.999944i	$-0.503379\pi$
$907$	14.4609	−	3.87478i	0.480166	−	0.128660i	0.490780	+	0.871284i	$0.336712\pi$
$908$	2.63189	−	4.55857i	0.0873425	−	0.151282i
$909$	13.5943			0.450894
$910$		0			0
$911$	1.05531			0.0349639			0.0174820	−	0.999847i	$-0.494435\pi$
$911$	1.05531			0.0349639			0.0174820	+	0.999847i	$0.494435\pi$
$912$	0.489000	−	0.846972i	0.0161924	−	0.0280461i
$913$	−46.2468	+	12.3918i	−1.53055	+	0.410108i
$914$	−12.8602	−	22.2746i	−0.425378	−	0.736777i
$915$		0			0
$916$	−4.70583	+	17.5624i	−0.155485	+	0.580277i
$917$	3.22094	−	1.85961i	0.106365	−	0.0614097i
$918$	5.31806			0.175522
$919$	25.9016	−	14.9543i	0.854414	−	0.493296i	−0.00772358	−	0.999970i	$-0.502459\pi$
$919$	25.9016	−	14.9543i	0.854414	−	0.493296i	0.862138	+	0.506674i	$0.169125\pi$
$920$		0			0
$921$	9.07700	+	33.8758i	0.299097	+	1.11625i
$922$	1.43772	+	1.43772i	0.0473489	+	0.0473489i
$923$	15.4622	−	34.5090i	0.508944	−	1.13588i
$924$			4.12819i			0.135808i
$925$		0			0
$926$	−0.310484	+	0.537774i	−0.0102031	+	0.0176723i
$927$	−6.89063	+	25.7162i	−0.226318	+	0.844631i
$928$			3.06695i			0.100678i
$929$	−14.3249	−	3.83833i	−0.469983	−	0.125932i	0.0160515	−	0.999871i	$-0.494890\pi$
$929$	−14.3249	−	3.83833i	−0.469983	−	0.125932i	−0.486035	+	0.873940i	$0.661557\pi$
$930$		0			0
$931$	−4.35226	+	4.35226i	−0.142640	+	0.142640i
$932$	−7.35170	−	1.96988i	−0.240813	−	0.0645256i
$933$	3.29815	+	12.3089i	0.107977	+	0.402975i
$934$	−0.505287	+	0.135391i	−0.0165335	+	0.00443014i
$935$		0			0
$936$	6.36544	−	2.42622i	0.208061	−	0.0793036i
$937$	−28.1996	+	28.1996i	−0.921242	+	0.921242i	−0.997117	−	0.0758757i	$-0.975825\pi$
$937$	−28.1996	+	28.1996i	−0.921242	+	0.921242i	0.0758757	+	0.997117i	$0.475825\pi$
$938$	3.45176	+	1.99287i	0.112704	+	0.0650697i
$939$	−0.256581	−	0.148137i	−0.00837319	−	0.00483426i
$940$		0			0
$941$	15.6390	+	15.6390i	0.509816	+	0.509816i	0.914470	−	0.404654i	$-0.132608\pi$
$941$	15.6390	+	15.6390i	0.509816	+	0.509816i	−0.404654	+	0.914470i	$0.632608\pi$
$942$	6.04999	+	10.4789i	0.197119	+	0.341420i
$943$	−4.62919	−	8.01799i	−0.150747	−	0.261102i
$944$	−4.15956	−	4.15956i	−0.135382	−	0.135382i
$945$		0			0
$946$	39.2863	+	22.6819i	1.27731	+	0.737453i
$947$	31.9355	+	18.4380i	1.03776	+	0.599153i	0.919199	−	0.393793i	$-0.128837\pi$
$947$	31.9355	+	18.4380i	1.03776	+	0.599153i	0.118565	+	0.992946i	$0.462171\pi$
$948$	3.05049	−	3.05049i	0.0990754	−	0.0990754i
$949$	7.27448	+	1.16979i	0.236140	+	0.0379729i
$950$		0			0
$951$	11.2656	−	3.01862i	0.365314	−	0.0978855i
$952$	−0.161924	−	0.604310i	−0.00524799	−	0.0195858i
$953$	44.4134	+	11.9005i	1.43869	+	0.385496i	0.892075	−	0.451888i	$-0.149249\pi$
$953$	44.4134	+	11.9005i	1.43869	+	0.385496i	0.546616	+	0.837384i	$0.315916\pi$
$954$	7.18781	−	7.18781i	0.232714	−	0.232714i
$955$		0			0
$956$	−25.9089	−	6.94226i	−0.837952	−	0.224529i
$957$		−	20.8865i		−	0.675163i
$958$	1.40005	−	5.22504i	0.0452334	−	0.168813i
$959$	−4.21562	+	7.30167i	−0.136129	+	0.235783i
$960$		0			0
$961$			68.7092i			2.21642i
$962$	0.144798	−	0.0551907i	0.00466848	−	0.00177942i
$963$	4.04879	+	4.04879i	0.130470	+	0.130470i
$964$	4.24500	+	15.8426i	0.136722	+	0.510255i
$965$		0			0
$966$	2.81182	−	1.62341i	0.0904688	−	0.0522322i
$967$	27.7061			0.890968			0.445484	−	0.895290i	$-0.353032\pi$
$967$	27.7061			0.890968			0.445484	+	0.895290i	$0.353032\pi$
$968$	26.6371	−	15.3789i	0.856148	−	0.494297i
$969$	0.261245	−	0.974980i	0.00839241	−	0.0313209i
$970$		0			0
$971$	9.96646	+	17.2624i	0.319839	+	0.553977i	0.980454	−	0.196747i	$-0.0630379\pi$
$971$	9.96646	+	17.2624i	0.319839	+	0.553977i	−0.660615	+	0.750725i	$0.729705\pi$
$972$	15.1735	−	4.06573i	0.486690	−	0.130408i
$973$	0.795403	−	1.37768i	0.0254994	−	0.0441663i
$974$	26.5556			0.850897
$975$		0			0
$976$	2.56127			0.0819843
$977$	16.8218	−	29.1362i	0.538176	−	0.932148i	−0.460826	−	0.887490i	$-0.652447\pi$
$977$	16.8218	−	29.1362i	0.538176	−	0.932148i	0.999002	−	0.0446580i	$-0.0142198\pi$
$978$	−8.56064	+	2.29382i	−0.273739	+	0.0733482i
$979$	−48.8472	−	84.6059i	−1.56116	−	2.70402i
$980$		0			0
$981$	−4.48320	+	16.7315i	−0.143138	+	0.534197i
$982$	−27.1633	+	15.6827i	−0.866816	+	0.500456i
$983$	−8.53839			−0.272332			−0.136166	−	0.990686i	$-0.543478\pi$
$983$	−8.53839			−0.272332			−0.136166	+	0.990686i	$0.543478\pi$
$984$	1.66260	−	0.959903i	0.0530018	−	0.0306006i
$985$		0			0
$986$	0.819251	+	3.05748i	0.0260903	+	0.0973702i
$987$	−3.30564	−	3.30564i	−0.105220	−	0.105220i
$988$	−0.341886	−	3.32845i	−0.0108769	−	0.105892i
$989$		−	35.6786i		−	1.13451i
$990$		0			0
$991$	3.10218	−	5.37313i	0.0985438	−	0.170683i	−0.812538	−	0.582908i	$-0.801915\pi$
$991$	3.10218	−	5.37313i	0.0985438	−	0.170683i	0.911082	+	0.412225i	$0.135248\pi$
$992$	−2.58442	+	9.64520i	−0.0820555	+	0.306235i
$993$			16.6917i			0.529694i
$994$	−6.14093	−	1.64546i	−0.194779	−	0.0521908i
$995$		0			0
$996$	−5.52131	+	5.52131i	−0.174950	+	0.174950i
$997$	41.3639	+	11.0834i	1.31001	+	0.351016i	0.845226	−	0.534409i	$-0.179466\pi$
$997$	41.3639	+	11.0834i	1.31001	+	0.351016i	0.464783	+	0.885425i	$0.346132\pi$
$998$	−4.63354	−	17.2926i	−0.146672	−	0.547388i
$999$	0.213910	−	0.0573170i	0.00676781	−	0.00181343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.h.293.2	yes	16
5.2	odd	4		650.2.t.f.7.3	✓	16
5.3	odd	4		650.2.t.h.7.2	yes	16
5.4	even	2		650.2.w.f.293.3	yes	16
13.2	odd	12		650.2.t.f.93.3	yes	16
65.2	even	12	inner	650.2.w.h.457.2	yes	16
65.28	even	12		650.2.w.f.457.3	yes	16
65.54	odd	12		650.2.t.h.93.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.7.3	✓	16	5.2	odd	4
650.2.t.f.93.3	yes	16	13.2	odd	12
650.2.t.h.7.2	yes	16	5.3	odd	4
650.2.t.h.93.2	yes	16	65.54	odd	12
650.2.w.f.293.3	yes	16	5.4	even	2
650.2.w.f.457.3	yes	16	65.28	even	12
650.2.w.h.293.2	yes	16	1.1	even	1	trivial
650.2.w.h.457.2	yes	16	65.2	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.01796 + 0.272763i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.272763 + 1.01796i) q^{6} +(0.524968 - 0.303090i) q^{7} -1.00000 q^{8} +(-1.63622 + 0.944675i) q^{9} +(1.67250 + 6.24184i) q^{11} +(0.745202 + 0.745202i) q^{12} +(3.55982 + 0.572444i) q^{13} -0.606181i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.267122 + 0.996913i) q^{17} +1.88935i q^{18} +(0.896383 + 0.240185i) q^{19} +(-0.451727 + 0.451727i) q^{21} +(6.24184 + 1.67250i) q^{22} +(-1.31541 - 4.90919i) q^{23} +(1.01796 - 0.272763i) q^{24} +(2.27566 - 2.79667i) q^{26} +(3.64355 - 3.64355i) q^{27} +(-0.524968 - 0.303090i) q^{28} +(2.65606 + 1.53348i) q^{29} +(7.06078 + 7.06078i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.40508 - 5.89778i) q^{33} +(0.729791 + 0.729791i) q^{34} +(1.63622 + 0.944675i) q^{36} +(0.0372201 + 0.0214890i) q^{37} +(0.656198 - 0.656198i) q^{38} +(-3.77991 + 0.388258i) q^{39} +(1.75959 - 0.471482i) q^{41} +(0.165343 + 0.617070i) q^{42} +(6.78086 + 1.81693i) q^{43} +(4.56935 - 4.56935i) q^{44} +(-4.90919 - 1.31541i) q^{46} +7.31779i q^{47} +(0.272763 - 1.01796i) q^{48} +(-3.31627 + 5.74395i) q^{49} -1.08768i q^{51} +(-1.28416 - 3.36912i) q^{52} +(-3.80438 - 3.80438i) q^{53} +(-1.33363 - 4.97718i) q^{54} +(-0.524968 + 0.303090i) q^{56} -0.977999 q^{57} +(2.65606 - 1.53348i) q^{58} +(-1.52251 + 5.68207i) q^{59} +(-1.28063 - 2.21812i) q^{61} +(9.64520 - 2.58442i) q^{62} +(-0.572643 + 0.991848i) q^{63} +1.00000 q^{64} -6.81017 q^{66} +(-3.28759 + 5.69428i) q^{67} +(0.996913 - 0.267122i) q^{68} +(2.67809 + 4.63859i) q^{69} +(2.71447 - 10.1305i) q^{71} +(1.63622 - 0.944675i) q^{72} +2.04350 q^{73} +(0.0372201 - 0.0214890i) q^{74} +(-0.240185 - 0.896383i) q^{76} +(2.76985 + 2.76985i) q^{77} +(-1.55371 + 3.46763i) q^{78} -4.09352i q^{79} +(0.118845 - 0.205845i) q^{81} +(0.471482 - 1.75959i) q^{82} +7.40916i q^{83} +(0.617070 + 0.165343i) q^{84} +(4.96394 - 4.96394i) q^{86} +(-3.12205 - 0.836550i) q^{87} +(-1.67250 - 6.24184i) q^{88} +(-14.6031 + 3.91289i) q^{89} +(2.04229 - 0.778432i) q^{91} +(-3.59378 + 3.59378i) q^{92} +(-9.11354 - 5.26170i) q^{93} +(6.33739 + 3.65890i) q^{94} +(-0.745202 - 0.745202i) q^{96} +(-8.80863 - 15.2570i) q^{97} +(3.31627 + 5.74395i) q^{98} +(-8.63309 - 8.63309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Introduction

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