LMFDB - Embedded newform 650.2.t.h.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(7,650)]

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([3, 11]))

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

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

chi := DirichletCharacter("650.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.2
Root			$1.05387i$ of defining polynomial
Character	$\chi$	$=$	650.7
Dual form			650.2.t.h.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.272763 - 1.01796i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.272763 + 1.01796i) q^{6} +(-0.303090 - 0.524968i) q^{7} -1.00000i q^{8} +(1.63622 - 0.944675i) q^{9} +(1.67250 + 6.24184i) q^{11} +(0.745202 - 0.745202i) q^{12} +(-0.572444 + 3.55982i) q^{13} +0.606181i q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.996913 + 0.267122i) q^{17} -1.88935 q^{18} +(-0.896383 - 0.240185i) q^{19} +(-0.451727 + 0.451727i) q^{21} +(1.67250 - 6.24184i) q^{22} +(4.90919 - 1.31541i) q^{23} +(-1.01796 + 0.272763i) q^{24} +(2.27566 - 2.79667i) q^{26} +(-3.64355 - 3.64355i) q^{27} +(0.303090 - 0.524968i) q^{28} +(-2.65606 - 1.53348i) q^{29} +(7.06078 + 7.06078i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.89778 - 3.40508i) q^{33} +(-0.729791 - 0.729791i) q^{34} +(1.63622 + 0.944675i) q^{36} +(0.0214890 - 0.0372201i) q^{37} +(0.656198 + 0.656198i) q^{38} +(3.77991 - 0.388258i) q^{39} +(1.75959 - 0.471482i) q^{41} +(0.617070 - 0.165343i) q^{42} +(-1.81693 + 6.78086i) q^{43} +(-4.56935 + 4.56935i) q^{44} +(-4.90919 - 1.31541i) q^{46} +7.31779 q^{47} +(1.01796 + 0.272763i) q^{48} +(3.31627 - 5.74395i) q^{49} -1.08768i q^{51} +(-3.36912 + 1.28416i) q^{52} +(3.80438 - 3.80438i) q^{53} +(1.33363 + 4.97718i) q^{54} +(-0.524968 + 0.303090i) q^{56} +0.977999i q^{57} +(1.53348 + 2.65606i) q^{58} +(1.52251 - 5.68207i) q^{59} +(-1.28063 - 2.21812i) q^{61} +(-2.58442 - 9.64520i) q^{62} +(-0.991848 - 0.572643i) q^{63} -1.00000 q^{64} -6.81017 q^{66} +(5.69428 + 3.28759i) q^{67} +(0.267122 + 0.996913i) q^{68} +(-2.67809 - 4.63859i) q^{69} +(2.71447 - 10.1305i) q^{71} +(-0.944675 - 1.63622i) q^{72} +2.04350i q^{73} +(-0.0372201 + 0.0214890i) q^{74} +(-0.240185 - 0.896383i) q^{76} +(2.76985 - 2.76985i) q^{77} +(-3.46763 - 1.55371i) q^{78} +4.09352i q^{79} +(0.118845 - 0.205845i) q^{81} +(-1.75959 - 0.471482i) q^{82} -7.40916 q^{83} +(-0.617070 - 0.165343i) q^{84} +(4.96394 - 4.96394i) q^{86} +(-0.836550 + 3.12205i) q^{87} +(6.24184 - 1.67250i) q^{88} +(14.6031 - 3.91289i) q^{89} +(2.04229 - 0.778432i) q^{91} +(3.59378 + 3.59378i) q^{92} +(5.26170 - 9.11354i) q^{93} +(-6.33739 - 3.65890i) q^{94} +(-0.745202 - 0.745202i) q^{96} +(-15.2570 + 8.80863i) q^{97} +(-5.74395 + 3.31627i) q^{98} +(8.63309 + 8.63309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33}+ \cdots + 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.272763	−	1.01796i	−0.157480	−	0.587722i	−0.998880	−	0.0473101i	$-0.984935\pi$
$3$	−0.272763	−	1.01796i	−0.157480	−	0.587722i	0.841401	−	0.540412i	$-0.181732\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.272763	+	1.01796i	−0.111355	+	0.415582i
$7$	−0.303090	−	0.524968i	−0.114557	−	0.198419i	0.803045	−	0.595918i	$-0.203212\pi$
$7$	−0.303090	−	0.524968i	−0.114557	−	0.198419i	−0.917603	+	0.397499i	$0.869878\pi$
$8$		−	1.00000i		−	0.353553i
$9$	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
$13$	−0.572444	+	3.55982i	−0.158767	+	0.987316i
$13$	−0.572444	+	3.55982i	−0.158767	+	0.987316i
$14$			0.606181i			0.162009i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.996913	+	0.267122i	0.241787	+	0.0647866i	0.377677	−	0.925937i	$-0.376723\pi$
$17$	0.996913	+	0.267122i	0.241787	+	0.0647866i	−0.135890	+	0.990724i	$0.543390\pi$
$18$	−1.88935			−0.445324
$19$	−0.896383	−	0.240185i	−0.205644	−	0.0551022i	0.154526	−	0.987989i	$-0.450615\pi$
$19$	−0.896383	−	0.240185i	−0.205644	−	0.0551022i	−0.360171	+	0.932886i	$0.617282\pi$
$20$		0			0
$21$	−0.451727	+	0.451727i	−0.0985748	+	0.0985748i
$22$	1.67250	−	6.24184i	0.356577	−	1.33077i
$23$	4.90919	−	1.31541i	1.02364	−	0.274283i	0.292320	−	0.956320i	$-0.405573\pi$
$23$	4.90919	−	1.31541i	1.02364	−	0.274283i	0.731317	+	0.682038i	$0.238906\pi$
$24$	−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
$28$	0.303090	−	0.524968i	0.0572787	−	0.0992096i
$29$	−2.65606	−	1.53348i	−0.493218	−	0.284759i	0.232691	−	0.972551i	$-0.425247\pi$
$29$	−2.65606	−	1.53348i	−0.493218	−	0.284759i	−0.725908	+	0.687791i	$0.758580\pi$
$30$		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	$0.395943\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	5.89778	−	3.40508i	1.02667	−	0.592749i
$34$	−0.729791	−	0.729791i	−0.125158	−	0.125158i
$35$		0			0
$36$	1.63622	+	0.944675i	0.272704	+	0.157446i
$37$	0.0214890	−	0.0372201i	0.00353278	−	0.00611895i	−0.864254	−	0.503056i	$-0.832209\pi$
$37$	0.0214890	−	0.0372201i	0.00353278	−	0.00611895i	0.867786	+	0.496937i	$0.165542\pi$
$38$	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	$0.371234\pi$
$42$	0.617070	−	0.165343i	0.0952160	−	0.0255130i
$43$	−1.81693	+	6.78086i	−0.277079	+	1.03407i	0.677357	+	0.735655i	$0.263125\pi$
$43$	−1.81693	+	6.78086i	−0.277079	+	1.03407i	−0.954436	+	0.298417i	$0.903541\pi$
$44$	−4.56935	+	4.56935i	−0.688855	+	0.688855i
$45$		0			0
$46$	−4.90919	−	1.31541i	−0.723821	−	0.193947i
$47$	7.31779			1.06741			0.533705	−	0.845671i	$-0.320799\pi$
$47$	7.31779			1.06741			0.533705	+	0.845671i	$0.320799\pi$
$48$	1.01796	+	0.272763i	0.146930	+	0.0393699i
$49$	3.31627	−	5.74395i	0.473753	−	0.820565i
$50$		0			0
$51$		−	1.08768i		−	0.152306i
$52$	−3.36912	+	1.28416i	−0.467212	+	0.178081i
$53$	3.80438	−	3.80438i	0.522572	−	0.522572i	−0.395775	−	0.918347i	$-0.629524\pi$
$53$	3.80438	−	3.80438i	0.522572	−	0.522572i	0.918347	+	0.395775i	$0.129524\pi$
$54$	1.33363	+	4.97718i	0.181484	+	0.677309i
$55$		0			0
$56$	−0.524968	+	0.303090i	−0.0701518	+	0.0405021i
$57$			0.977999i			0.129539i
$58$	1.53348	+	2.65606i	0.201355	+	0.348757i
$59$	1.52251	−	5.68207i	0.198213	−	0.739742i	−0.793198	−	0.608963i	$-0.791586\pi$
$59$	1.52251	−	5.68207i	0.198213	−	0.739742i	0.991412	−	0.130779i	$-0.0417477\pi$
$60$		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	$0.885763\pi$
$62$	−2.58442	−	9.64520i	−0.328222	−	1.22494i
$63$	−0.991848	−	0.572643i	−0.124961	−	0.0721463i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.81017			−0.838274
$67$	5.69428	+	3.28759i	0.695667	+	0.401643i	0.805731	−	0.592281i	$-0.201773\pi$
$67$	5.69428	+	3.28759i	0.695667	+	0.401643i	−0.110065	+	0.993924i	$0.535106\pi$
$68$	0.267122	+	0.996913i	0.0323933	+	0.120893i
$69$	−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	$-0.130486\pi$
$72$	−0.944675	−	1.63622i	−0.111331	−	0.192831i
$73$			2.04350i			0.239173i	0.992824	+	0.119587i	$0.0381569\pi$
$73$			2.04350i			0.239173i	−0.992824	+	0.119587i	$0.961843\pi$
$74$	−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
$78$	−3.46763	−	1.55371i	−0.392631	−	0.175923i
$79$			4.09352i			0.460556i	0.973125	+	0.230278i	$0.0739636\pi$
$79$			4.09352i			0.460556i	−0.973125	+	0.230278i	$0.926036\pi$
$80$		0			0
$81$	0.118845	−	0.205845i	0.0132050	−	0.0228717i
$82$	−1.75959	−	0.471482i	−0.194315	−	0.0520664i
$83$	−7.40916			−0.813260			−0.406630	−	0.913593i	$-0.633296\pi$
$83$	−7.40916			−0.813260			−0.406630	+	0.913593i	$0.633296\pi$
$84$	−0.617070	−	0.165343i	−0.0673279	−	0.0180404i
$85$		0			0
$86$	4.96394	−	4.96394i	0.535275	−	0.535275i
$87$	−0.836550	+	3.12205i	−0.0896876	+	0.334719i
$88$	6.24184	−	1.67250i	0.665383	−	0.178289i
$89$	14.6031	−	3.91289i	1.54792	−	0.414765i	0.619108	−	0.785306i	$-0.287494\pi$
$89$	14.6031	−	3.91289i	1.54792	−	0.414765i	0.928816	+	0.370541i	$0.120828\pi$
$90$		0			0
$91$	2.04229	−	0.778432i	0.214090	−	0.0816018i
$92$	3.59378	+	3.59378i	0.374677	+	0.374677i
$93$	5.26170	−	9.11354i	0.545613	−	0.945030i
$94$	−6.33739	−	3.65890i	−0.653652	−	0.377386i
$95$		0			0
$96$	−0.745202	−	0.745202i	−0.0760568	−	0.0760568i
$97$	−15.2570	+	8.80863i	−1.54911	+	0.894380i	−0.550903	+	0.834569i	$0.685716\pi$
$97$	−15.2570	+	8.80863i	−1.54911	+	0.894380i	−0.998210	+	0.0598111i	$0.980950\pi$
$98$	−5.74395	+	3.31627i	−0.580227	+	0.334994i
$99$	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	$0.783200\pi$
$102$	−0.543841	+	0.941961i	−0.0538483	+	0.0932680i
$103$	9.96404	+	9.96404i	0.981787	+	0.981787i	0.999837	−	0.0180506i	$-0.00574599\pi$
$103$	9.96404	+	9.96404i	0.981787	+	0.981787i	−0.0180506	+	0.999837i	$0.505746\pi$
$104$	3.55982	+	0.572444i	0.349069	+	0.0561327i
$105$		0			0
$106$	−5.19688	+	1.39250i	−0.504766	+	0.135252i
$107$	−2.92733	+	0.784375i	−0.282995	+	0.0758284i	−0.397525	−	0.917591i	$-0.630131\pi$
$107$	−2.92733	+	0.784375i	−0.282995	+	0.0758284i	0.114529	+	0.993420i	$0.463464\pi$
$108$	1.33363	−	4.97718i	0.128329	−	0.478930i
$109$	−6.48284	+	6.48284i	−0.620943	+	0.620943i	−0.945773	−	0.324830i	$-0.894693\pi$
$109$	−6.48284	+	6.48284i	−0.620943	+	0.620943i	0.324830	+	0.945773i	$0.394693\pi$
$110$		0			0
$111$	−0.0437502	−	0.0117228i	−0.00415258	−	0.00111268i
$112$	0.606181			0.0572787
$113$	−16.6037	−	4.44894i	−1.56194	−	0.418521i	−0.628664	−	0.777677i	$-0.716398\pi$
$113$	−16.6037	−	4.44894i	−1.56194	−	0.418521i	−0.933277	+	0.359156i	$0.883065\pi$
$114$	0.489000	−	0.846972i	0.0457990	−	0.0793262i
$115$		0			0
$116$		−	3.06695i		−	0.284759i
$117$	2.42622	+	6.36544i	0.224304	+	0.588485i
$118$	−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
$122$			2.56127i			0.231886i
$123$	−0.959903	−	1.66260i	−0.0865515	−	0.149912i
$124$	−2.58442	+	9.64520i	−0.232088	+	0.866165i
$125$		0			0
$126$	0.572643	+	0.991848i	0.0510151	+	0.0883608i
$127$	3.36158	+	12.5456i	0.298292	+	1.11324i	0.938568	+	0.345096i	$0.112154\pi$
$127$	3.36158	+	12.5456i	0.298292	+	1.11324i	−0.640275	+	0.768145i	$0.721180\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	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	$0.413627\pi$
$132$	5.89778	+	3.40508i	0.513336	+	0.296374i
$133$	0.145596	+	0.543370i	0.0126247	+	0.0471161i
$134$	−3.28759	−	5.69428i	−0.284005	−	0.491911i
$135$		0			0
$136$	0.267122	−	0.996913i	0.0229055	−	0.0854846i
$137$	6.95440	+	12.0454i	0.594154	+	1.02911i	0.993666	+	0.112377i	$0.0358464\pi$
$137$	6.95440	+	12.0454i	0.594154	+	1.02911i	−0.399511	+	0.916728i	$0.630820\pi$
$138$			5.35618i			0.455948i
$139$	−2.27272	+	1.31215i	−0.192769	+	0.111296i	−0.593278	−	0.804997i	$-0.702167\pi$
$139$	−2.27272	+	1.31215i	−0.192769	+	0.111296i	0.400509	+	0.916293i	$0.368833\pi$
$140$		0			0
$141$	−1.99602	−	7.44925i	−0.168095	−	0.627340i
$142$	−7.41607	+	7.41607i	−0.622342	+	0.622342i
$143$	−23.1772	+	2.38068i	−1.93818	+	0.199082i
$144$			1.88935i			0.157446i
$145$		0			0
$146$	1.02175	−	1.76972i	0.0845605	−	0.146463i
$147$	−6.75169	−	1.80911i	−0.556870	−	0.149213i
$148$	0.0429781			0.00353278
$149$	−15.1622	−	4.06270i	−1.24214	−	0.332829i	−0.422842	−	0.906204i	$-0.638967\pi$
$149$	−15.1622	−	4.06270i	−1.24214	−	0.332829i	−0.819293	+	0.573374i	$0.805634\pi$
$150$		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	$0.00749285\pi$
$152$	−0.240185	+	0.896383i	−0.0194816	+	0.0727063i
$153$	1.88352	−	0.504687i	0.152273	−	0.0408015i
$154$	−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	$-0.401491\pi$
$157$	−8.11859	−	8.11859i	−0.647934	−	0.647934i	−0.952493	+	0.304559i	$0.901491\pi$
$158$	2.04676	−	3.54509i	0.162831	−	0.282032i
$159$	−4.91042	−	2.83503i	−0.389422	−	0.224833i
$160$		0			0
$161$	−2.17848	−	2.17848i	−0.171688	−	0.171688i
$162$	−0.205845	+	0.118845i	−0.0161727	+	0.00933732i
$163$	−7.28290	+	4.20479i	−0.570441	+	0.329344i	−0.757325	−	0.653038i	$-0.773494\pi$
$163$	−7.28290	+	4.20479i	−0.570441	+	0.329344i	0.186885	+	0.982382i	$0.440161\pi$
$164$	1.28811	+	1.28811i	0.100585	+	0.100585i
$165$		0			0
$166$	6.41652	+	3.70458i	0.498018	+	0.287531i
$167$	1.27667	−	2.21126i	0.0987919	−	0.171113i	−0.812393	−	0.583110i	$-0.801836\pi$
$167$	1.27667	−	2.21126i	0.0987919	−	0.171113i	0.911185	+	0.411998i	$0.135169\pi$
$168$	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
$172$	−6.78086	+	1.81693i	−0.517036	+	0.138539i
$173$	5.98108	−	22.3217i	0.454733	−	1.69709i	−0.234137	−	0.972204i	$-0.575226\pi$
$173$	5.98108	−	22.3217i	0.454733	−	1.69709i	0.688870	−	0.724885i	$-0.258107\pi$
$174$	2.28550	−	2.28550i	0.173263	−	0.173263i
$175$		0			0
$176$	−6.24184	−	1.67250i	−0.470497	−	0.126069i
$177$	−6.19942			−0.465977
$178$	−14.6031	−	3.91289i	−1.09455	−	0.293283i
$179$	−11.2286	+	19.4485i	−0.839266	+	1.45365i	0.0512437	+	0.998686i	$0.483681\pi$
$179$	−11.2286	+	19.4485i	−0.839266	+	1.45365i	−0.890509	+	0.454965i	$0.849652\pi$
$180$		0			0
$181$		−	14.4224i		−	1.07201i	−0.844215	−	0.536005i	$-0.819933\pi$
$181$		−	14.4224i		−	1.07201i	0.844215	−	0.536005i	$-0.180067\pi$
$182$	−2.15789	−	0.347004i	−0.159954	−	0.0257217i
$183$	−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
$187$			6.66934i			0.487710i
$188$	3.65890	+	6.33739i	0.266852	+	0.462202i
$189$	−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	$0.631855\pi$
$192$	0.272763	+	1.01796i	0.0196850	+	0.0734652i
$193$	10.8714	+	6.27661i	0.782541	+	0.451800i	0.837330	−	0.546698i	$-0.184115\pi$
$193$	10.8714	+	6.27661i	0.782541	+	0.451800i	−0.0547891	+	0.998498i	$0.517449\pi$
$194$	17.6173			1.26485
$195$		0			0
$196$	6.63255			0.473753
$197$	9.90468	+	5.71847i	0.705679	+	0.407424i	0.809459	−	0.587176i	$-0.199760\pi$
$197$	9.90468	+	5.71847i	0.705679	+	0.407424i	−0.103780	+	0.994600i	$0.533094\pi$
$198$	−3.15993	−	11.7930i	−0.224566	−	0.838094i
$199$	−8.02327	−	13.8967i	−0.568755	−	0.985112i	−0.996689	−	0.0813024i	$-0.974092\pi$
$199$	−8.02327	−	13.8967i	−0.568755	−	0.985112i	0.427935	−	0.903810i	$-0.359241\pi$
$200$		0			0
$201$	1.79346	−	6.69330i	0.126501	−	0.472109i
$202$	3.59761	+	6.23125i	0.253127	+	0.438429i
$203$			1.85913i			0.130485i
$204$	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
$208$	−2.79667	−	2.27566i	−0.193914	−	0.157789i
$209$		−	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	$0.227986\pi$
$212$	5.19688	+	1.39250i	0.356923	+	0.0956373i
$213$	−11.0529			−0.757334
$214$	2.92733	+	0.784375i	0.200108	+	0.0536188i
$215$		0			0
$216$	−3.64355	+	3.64355i	−0.247912	+	0.247912i
$217$	1.56663	−	5.84673i	0.106350	−	0.396902i
$218$	8.85572	−	2.37288i	0.599785	−	0.160712i
$219$	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
$223$	−1.66273	+	2.87993i	−0.111344	+	0.192854i	−0.916313	−	0.400464i	$-0.868849\pi$
$223$	−1.66273	+	2.87993i	−0.111344	+	0.192854i	0.804968	+	0.593318i	$0.202182\pi$
$224$	−0.524968	−	0.303090i	−0.0350759	−	0.0202511i
$225$		0			0
$226$	12.1547	+	12.1547i	0.808520	+	0.808520i
$227$	4.55857	−	2.63189i	0.302563	−	0.174685i	−0.341031	−	0.940052i	$-0.610776\pi$
$227$	4.55857	−	2.63189i	0.302563	−	0.174685i	0.643594	+	0.765367i	$0.277443\pi$
$228$	−0.846972	+	0.489000i	−0.0560921	+	0.0323848i
$229$	12.8566	+	12.8566i	0.849585	+	0.849585i	0.990081	−	0.140496i	$-0.0448698\pi$
$229$	12.8566	+	12.8566i	0.849585	+	0.849585i	−0.140496	+	0.990081i	$0.544870\pi$
$230$		0			0
$231$	−3.57512	−	2.06410i	−0.235226	−	0.135808i
$232$	−1.53348	+	2.65606i	−0.100678	+	0.174379i
$233$	5.38182	+	5.38182i	0.352575	+	0.352575i	0.861067	−	0.508492i	$-0.169797\pi$
$233$	5.38182	+	5.38182i	0.352575	+	0.352575i	−0.508492	+	0.861067i	$0.669797\pi$
$234$	1.08155	−	6.72574i	0.0707029	−	0.439675i
$235$		0			0
$236$	5.68207	−	1.52251i	0.369871	−	0.0991066i
$237$	4.16705	−	1.11656i	0.270679	−	0.0725282i
$238$	−0.161924	+	0.604310i	−0.0104960	+	0.0391716i
$239$	−18.9666	+	18.9666i	−1.22685	+	1.22685i	−0.261697	+	0.965150i	$0.584282\pi$
$239$	−18.9666	+	18.9666i	−1.22685	+	1.22685i	−0.965150	+	0.261697i	$0.915718\pi$
$240$		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	$0.760487\pi$
$242$	30.7578			1.97719
$243$	−15.1735	−	4.06573i	−0.973381	−	0.260817i
$244$	1.28063	−	2.21812i	0.0819843	−	0.142001i
$245$		0			0
$246$			1.91981i			0.122402i
$247$	1.36814	−	3.05347i	0.0870529	−	0.194288i
$248$	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	$0.475368\pi$
$252$		−	1.14529i		−	0.0721463i
$253$	16.4212	+	28.4424i	1.03239	+	1.78816i
$254$	3.36158	−	12.5456i	0.210924	−	0.787180i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.09097	−	22.7318i	−0.379944	−	1.41797i	−0.845984	−	0.533208i	$-0.820986\pi$
$257$	−6.09097	−	22.7318i	−0.379944	−	1.41797i	0.466040	−	0.884764i	$-0.345680\pi$
$258$	−6.40709	−	3.69913i	−0.398888	−	0.230298i
$259$	−0.0260525			−0.00161882
$260$		0			0
$261$	−5.79454			−0.358673
$262$	−5.31349	−	3.06775i	−0.328269	−	0.189526i
$263$	−1.77496	−	6.62424i	−0.109449	−	0.408468i	0.889363	−	0.457202i	$-0.151148\pi$
$263$	−1.77496	−	6.62424i	−0.109449	−	0.408468i	−0.998812	+	0.0487334i	$0.984482\pi$
$264$	−3.40508	−	5.89778i	−0.209568	−	0.362983i
$265$		0			0
$266$	0.145596	−	0.543370i	0.00892703	−	0.0333161i
$267$	−7.96636	−	13.7981i	−0.487533	−	0.844432i
$268$			6.57518i			0.401643i
$269$	13.9856	−	8.07459i	0.852717	−	0.492317i	−0.00884947	−	0.999961i	$-0.502817\pi$
$269$	13.9856	−	8.07459i	0.852717	−	0.492317i	0.861567	+	0.507644i	$0.169484\pi$
$270$		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
$273$	−1.34948	−	1.86665i	−0.0816741	−	0.112975i
$274$		−	13.9088i		−	0.840261i
$275$		0			0
$276$	2.67809	−	4.63859i	0.161202	−	0.279210i
$277$	−17.9593	−	4.81219i	−1.07907	−	0.289136i	−0.324856	−	0.945764i	$-0.605316\pi$
$277$	−17.9593	−	4.81219i	−1.07907	−	0.289136i	−0.754215	+	0.656627i	$0.771982\pi$
$278$	2.62431			0.157396
$279$	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	$-0.0705432\pi$
$282$	−1.99602	+	7.44925i	−0.118861	+	0.443596i
$283$	16.8211	−	4.50721i	0.999913	−	0.267926i	0.278504	−	0.960435i	$-0.410161\pi$
$283$	16.8211	−	4.50721i	0.999913	−	0.267926i	0.721409	+	0.692509i	$0.243495\pi$
$284$	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
$288$	0.944675	−	1.63622i	0.0556655	−	0.0964155i
$289$	−13.7999	−	7.96740i	−0.811762	−	0.468671i
$290$		0			0
$291$	13.1284	+	13.1284i	0.769601	+	0.769601i
$292$	−1.76972	+	1.02175i	−0.103565	+	0.0597933i
$293$	24.9588	−	14.4099i	1.45811	−	0.841838i	0.459188	−	0.888339i	$-0.348141\pi$
$293$	24.9588	−	14.4099i	1.45811	−	0.841838i	0.998918	+	0.0465015i	$0.0148072\pi$
$294$	4.94258	+	4.94258i	0.288257	+	0.288257i
$295$		0			0
$296$	−0.0372201	−	0.0214890i	−0.00216338	−	0.00124903i
$297$	16.6486	−	28.8363i	0.966052	−	1.67325i
$298$	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
$302$	−16.3863	+	4.39068i	−0.942923	+	0.252655i
$303$	−1.96259	+	7.32448i	−0.112748	+	0.420781i
$304$	0.656198	−	0.656198i	0.0376355	−	0.0376355i
$305$		0			0
$306$	−1.88352	−	0.504687i	−0.107674	−	0.0288510i
$307$	−33.2780			−1.89928			−0.949638	−	0.313348i	$-0.898549\pi$
$307$	−33.2780			−1.89928			−0.949638	+	0.313348i	$0.898549\pi$
$308$	3.78368	+	1.01384i	0.215595	+	0.0577686i
$309$	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	$-0.111385\pi$
$312$	−0.388258	−	3.77991i	−0.0219808	−	0.213995i
$313$	−0.198788	+	0.198788i	−0.0112361	+	0.0112361i	−0.712703	−	0.701466i	$-0.752529\pi$
$313$	−0.198788	+	0.198788i	−0.0112361	+	0.0112361i	0.701466	+	0.712703i	$0.252529\pi$
$314$	2.97161	+	11.0902i	0.167698	+	0.625856i
$315$		0			0
$316$	−3.54509	+	2.04676i	−0.199427	+	0.115139i
$317$			11.0668i			0.621576i	0.950479	+	0.310788i	$0.100593\pi$
$317$			11.0668i			0.621576i	−0.950479	+	0.310788i	$0.899407\pi$
$318$	2.83503	+	4.91042i	0.158981	+	0.275363i
$319$	5.12947	−	19.1434i	0.287195	−	1.07183i
$320$		0			0
$321$	1.59693	+	2.76597i	0.0891320	+	0.154381i
$322$	0.797378	+	2.97586i	0.0444362	+	0.165838i
$323$	−0.829457	−	0.478887i	−0.0461522	−	0.0266460i
$324$	0.237689			0.0132050
$325$		0			0
$326$	8.40957			0.465763
$327$	8.36757	+	4.83102i	0.462728	+	0.267156i
$328$	−0.471482	−	1.75959i	−0.0260332	−	0.0971573i
$329$	−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	$-0.0600168\pi$
$332$	−3.70458	−	6.41652i	−0.203315	−	0.352152i
$333$		−	0.0812006i		−	0.00444977i
$334$	−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	0.0395494	−	0.999218i	$-0.487408\pi$
$337$	19.0692	−	19.0692i	1.03877	−	1.03877i	0.999218	−	0.0395494i	$-0.0125922\pi$
$338$	8.65295	+	9.70187i	0.470659	+	0.527712i
$339$			18.1154i			0.983896i
$340$		0			0
$341$	−32.2631	+	55.8814i	−1.74715	+	3.02615i
$342$	1.69358	+	0.453794i	0.0915783	+	0.0245383i
$343$	−8.26378			−0.446202
$344$	6.78086	+	1.81693i	0.365600	+	0.0979621i
$345$		0			0
$346$	−16.3406	+	16.3406i	−0.878478	+	0.878478i
$347$	5.13148	−	19.1509i	0.275472	−	1.02808i	−0.680052	−	0.733164i	$-0.738043\pi$
$347$	5.13148	−	19.1509i	0.275472	−	1.02808i	0.955524	−	0.294912i	$-0.0952904\pi$
$348$	−3.12205	+	0.836550i	−0.167359	+	0.0448438i
$349$	−12.7939	+	3.42812i	−0.684842	+	0.183503i	−0.584431	−	0.811443i	$-0.698682\pi$
$349$	−12.7939	+	3.42812i	−0.684842	+	0.183503i	−0.100411	+	0.994946i	$0.532016\pi$
$350$		0			0
$351$	15.0561	−	10.8847i	0.803636	−	0.580980i
$352$	4.56935	+	4.56935i	0.243547	+	0.243547i
$353$	6.04628	−	10.4725i	0.321811	−	0.557393i	−0.659051	−	0.752098i	$-0.729042\pi$
$353$	6.04628	−	10.4725i	0.321811	−	0.557393i	0.980862	+	0.194706i	$0.0623751\pi$
$354$	5.36886	+	3.09971i	0.285352	+	0.164748i
$355$		0			0
$356$	10.6902	+	10.6902i	0.566580	+	0.566580i
$357$	−0.570999	+	0.329666i	−0.0302204	+	0.0174478i
$358$	19.4485	−	11.2286i	1.02789	−	0.593451i
$359$	−9.24091	−	9.24091i	−0.487717	−	0.487717i	0.419868	−	0.907585i	$-0.362076\pi$
$359$	−9.24091	−	9.24091i	−0.487717	−	0.487717i	−0.907585	+	0.419868i	$0.862076\pi$
$360$		0			0
$361$	−15.7087	−	9.06940i	−0.826772	−	0.477337i
$362$	−7.21122	+	12.4902i	−0.379013	+	0.656470i
$363$	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
$367$	9.95527	−	2.66751i	0.519661	−	0.139243i	0.0105510	−	0.999944i	$-0.496641\pi$
$367$	9.95527	−	2.66751i	0.519661	−	0.139243i	0.509110	+	0.860702i	$0.329975\pi$
$368$	−1.31541	+	4.90919i	−0.0685707	+	0.255909i
$369$	2.43369	−	2.43369i	0.126693	−	0.126693i
$370$		0			0
$371$	−3.15025	−	0.844107i	−0.163553	−	0.0438238i
$372$	10.5234			0.545613
$373$	27.4979	+	7.36803i	1.42379	+	0.381502i	0.886825	−	0.462105i	$-0.152906\pi$
$373$	27.4979	+	7.36803i	1.42379	+	0.381502i	0.536960	+	0.843608i	$0.319572\pi$
$374$	3.33467	−	5.77582i	0.172432	−	0.298660i
$375$		0			0
$376$		−	7.31779i		−	0.377386i
$377$	6.97934	−	8.57726i	0.359454	−	0.441751i
$378$	2.20865	−	2.20865i	0.113601	−	0.113601i
$379$	5.36719	+	20.0306i	0.275694	+	1.02890i	0.955375	+	0.295396i	$0.0954515\pi$
$379$	5.36719	+	20.0306i	0.275694	+	1.02890i	−0.679681	+	0.733508i	$0.737882\pi$
$380$		0			0
$381$	11.8540	−	6.84394i	0.607301	−	0.350626i
$382$		−	16.3504i		−	0.836560i
$383$	−5.73449	−	9.93243i	−0.293019	−	0.507523i	0.681503	−	0.731815i	$-0.261327\pi$
$383$	−5.73449	−	9.93243i	−0.293019	−	0.507523i	−0.974522	+	0.224292i	$0.927993\pi$
$384$	0.272763	−	1.01796i	0.0139194	−	0.0519478i
$385$		0			0
$386$	−6.27661	−	10.8714i	−0.319471	−	0.553340i
$387$	3.43281	+	12.8114i	0.174499	+	0.651241i
$388$	−15.2570	−	8.80863i	−0.774556	−	0.447190i
$389$	14.4854			0.734439			0.367219	−	0.930134i	$-0.380310\pi$
$389$	14.4854			0.734439			0.367219	+	0.930134i	$0.380310\pi$
$390$		0			0
$391$	5.24541			0.265272
$392$	−5.74395	−	3.31627i	−0.290113	−	0.167497i
$393$	−1.67353	−	6.24571i	−0.0844186	−	0.315055i
$394$	−5.71847	−	9.90468i	−0.288092	−	0.498990i
$395$		0			0
$396$	−3.15993	+	11.7930i	−0.158792	+	0.592622i
$397$	−10.4664	−	18.1283i	−0.525293	−	0.909835i	−0.999566	−	0.0294568i	$-0.990622\pi$
$397$	−10.4664	−	18.1283i	−0.525293	−	0.909835i	0.474273	−	0.880378i	$-0.342711\pi$
$398$			16.0465i			0.804341i
$399$	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
$403$	−29.1770	+	21.0932i	−1.45341	+	1.05073i
$404$		−	7.19523i		−	0.357976i
$405$		0			0
$406$	0.929563	−	1.61005i	0.0461334	−	0.0799055i
$407$	0.268262	+	0.0718807i	0.0132973	+	0.00356299i
$408$	−1.08768			−0.0538483
$409$	−27.7285	−	7.42982i	−1.37108	−	0.367381i	−0.503209	−	0.864164i	$-0.667848\pi$
$409$	−27.7285	−	7.42982i	−1.37108	−	0.367381i	−0.867874	+	0.496784i	$0.834514\pi$
$410$		0			0
$411$	10.3649	−	10.3649i	0.511261	−	0.511261i
$412$	−3.64709	+	13.6111i	−0.179679	+	0.670573i
$413$	−3.44436	+	0.922913i	−0.169486	+	0.0454136i
$414$	−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
$418$	−2.99839	+	5.19337i	−0.146656	+	0.254016i
$419$	10.0023	+	5.77483i	0.488645	+	0.282119i	0.724012	−	0.689787i	$-0.242296\pi$
$419$	10.0023	+	5.77483i	0.488645	+	0.282119i	−0.235367	+	0.971906i	$0.575629\pi$
$420$		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	$0.549263\pi$
$422$	4.81682	−	2.78099i	0.234479	−	0.135377i
$423$	11.9735	−	6.91293i	0.582174	−	0.336118i
$424$	−3.80438	−	3.80438i	−0.184757	−	0.184757i
$425$		0			0
$426$	9.57212	+	5.52646i	0.463771	+	0.267758i
$427$	−0.776296	+	1.34458i	−0.0375676	+	0.0650690i
$428$	−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	$0.362174\pi$
$432$	4.97718	−	1.33363i	0.239465	−	0.0641644i
$433$	6.98295	−	26.0607i	0.335579	−	1.25240i	−0.567661	−	0.823262i	$-0.692152\pi$
$433$	6.98295	−	26.0607i	0.335579	−	1.25240i	0.903240	−	0.429135i	$-0.141182\pi$
$434$	−4.28011	+	4.28011i	−0.205452	+	0.205452i
$435$		0			0
$436$	−8.85572	−	2.37288i	−0.424112	−	0.113640i
$437$	−4.71646			−0.225619
$438$	−2.08021	−	0.557390i	−0.0993961	−	0.0266331i
$439$	8.56872	−	14.8415i	0.408963	−	0.708345i	−0.585811	−	0.810448i	$-0.699224\pi$
$439$	8.56872	−	14.8415i	0.408963	−	0.708345i	0.994774	+	0.102103i	$0.0325572\pi$
$440$		0			0
$441$		−	12.5312i		−	0.596724i
$442$	3.01569	−	2.18016i	0.143442	−	0.103700i
$443$	−2.44587	+	2.44587i	−0.116207	+	0.116207i	−0.762819	−	0.646612i	$-0.776185\pi$
$443$	−2.44587	+	2.44587i	−0.116207	+	0.116207i	0.646612	+	0.762819i	$0.276185\pi$
$444$	−0.0117228	−	0.0437502i	−0.000556340	−	0.00207629i
$445$		0			0
$446$	2.87993	−	1.66273i	0.136368	−	0.0787324i
$447$			16.5427i			0.782444i
$448$	0.303090	+	0.524968i	0.0143197	+	0.0248024i
$449$	3.61806	−	13.5028i	0.170747	−	0.637236i	−0.826490	−	0.562951i	$-0.809666\pi$
$449$	3.61806	−	13.5028i	0.170747	−	0.637236i	0.997237	−	0.0742848i	$-0.0236674\pi$
$450$		0			0
$451$	5.88583	+	10.1946i	0.277153	+	0.480043i
$452$	−4.44894	−	16.6037i	−0.209260	−	0.780971i
$453$	−15.4830	−	8.93912i	−0.727455	−	0.419996i
$454$	−5.26379			−0.247042
$455$		0			0
$456$	0.977999			0.0457990
$457$	−22.2746	−	12.8602i	−1.04196	−	0.601576i	−0.121572	−	0.992583i	$-0.538794\pi$
$457$	−22.2746	−	12.8602i	−1.04196	−	0.601576i	−0.920388	+	0.391007i	$0.872127\pi$
$458$	−4.70583	−	17.5624i	−0.219889	−	0.820636i
$459$	−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	$0.0984106\pi$
$462$	2.06410	+	3.57512i	0.0960304	+	0.166330i
$463$		−	0.620968i		−	0.0288588i	−0.999896	−	0.0144294i	$-0.995407\pi$
$463$		−	0.620968i		−	0.0288588i	0.999896	−	0.0144294i	$-0.00459318\pi$
$464$	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	−0.715613	−	0.698497i	$-0.753853\pi$
$467$	−0.369896	+	0.369896i	−0.0171167	+	0.0171167i	0.698497	+	0.715613i	$0.253853\pi$
$468$	−4.29952	+	5.28389i	−0.198745	+	0.244248i
$469$		−	3.98575i		−	0.184045i
$470$		0			0
$471$	−6.04999	+	10.4789i	−0.278769	+	0.482841i
$472$	−5.68207	−	1.52251i	−0.261538	−	0.0700790i
$473$	−45.3639			−2.08583
$474$	−4.16705	−	1.11656i	−0.191399	−	0.0512852i
$475$		0			0
$476$	0.442385	−	0.442385i	0.0202767	−	0.0202767i
$477$	2.63092	−	9.81873i	0.120462	−	0.449569i
$478$	25.9089	−	6.94226i	1.18504	−	0.317531i
$479$	−5.22504	+	1.40005i	−0.238738	+	0.0639697i	−0.376204	−	0.926537i	$-0.622771\pi$
$479$	−5.22504	+	1.40005i	−0.238738	+	0.0639697i	0.137466	+	0.990506i	$0.456104\pi$
$480$		0			0
$481$	0.120196	+	0.0978035i	0.00548045	+	0.00445946i
$482$	11.5976	+	11.5976i	0.528255	+	0.528255i
$483$	−1.62341	+	2.81182i	−0.0738675	+	0.127942i
$484$	−26.6371	−	15.3789i	−1.21078	−	0.699042i
$485$		0			0
$486$	11.1078	+	11.1078i	0.503859	+	0.503859i
$487$	22.9978	−	13.2778i	1.04213	−	0.601675i	0.121695	−	0.992568i	$-0.461167\pi$
$487$	22.9978	−	13.2778i	1.04213	−	0.601675i	0.920436	+	0.390893i	$0.127834\pi$
$488$	−2.21812	+	1.28063i	−0.100410	+	0.0579716i
$489$	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	$0.916957\pi$
$492$	0.959903	−	1.66260i	0.0432758	−	0.0749558i
$493$	−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
$497$	−6.14093	+	1.64546i	−0.275459	+	0.0738089i
$498$	2.02094	−	7.54226i	0.0905605	−	0.337977i
$499$	−12.6591	+	12.6591i	−0.566698	+	0.566698i	−0.931202	−	0.364504i	$-0.881239\pi$
$499$	−12.6591	+	12.6591i	−0.566698	+	0.566698i	0.364504	+	0.931202i	$0.381239\pi$
$500$		0			0
$501$	−2.59921	−	0.696457i	−0.116124	−	0.0311154i
$502$	13.6742			0.610311
$503$	−24.9713	−	6.69103i	−1.11341	−	0.298338i	−0.345198	−	0.938530i	$-0.612188\pi$
$503$	−24.9713	−	6.69103i	−1.11341	−	0.298338i	−0.768215	+	0.640192i	$0.778855\pi$
$504$	−0.572643	+	0.991848i	−0.0255076	+	0.0441804i
$505$		0			0
$506$		−	32.8424i		−	1.46002i
$507$	−0.781657	+	13.6780i	−0.0347146	+	0.607463i
$508$	−9.18401	+	9.18401i	−0.407475	+	0.407475i
$509$	−3.62983	−	13.5467i	−0.160889	−	0.600447i	−0.998529	−	0.0542239i	$-0.982732\pi$
$509$	−3.62983	−	13.5467i	−0.160889	−	0.600447i	0.837639	−	0.546224i	$-0.183935\pi$
$510$		0			0
$511$	1.07277	−	0.619364i	0.0474566	−	0.0273991i
$512$			1.00000i			0.0441942i
$513$	2.39089	+	4.14114i	0.105560	+	0.182836i
$514$	−6.09097	+	22.7318i	−0.268661	+	1.00266i
$515$		0			0
$516$	3.69913	+	6.40709i	0.162845	+	0.282056i
$517$	12.2390	+	45.6765i	0.538270	+	2.00885i
$518$	0.0225621	+	0.0130262i	0.000991322	+	0.000572340i
$519$	−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	$0.584260\pi$
$522$	5.01822	+	2.89727i	0.219642	+	0.126810i
$523$	−2.28726	−	8.53615i	−0.100015	−	0.373260i	0.897717	−	0.440572i	$-0.145224\pi$
$523$	−2.28726	−	8.53615i	−0.100015	−	0.373260i	−0.997732	+	0.0673121i	$0.978558\pi$
$524$	3.06775	+	5.31349i	0.134015	+	0.232121i
$525$		0			0
$526$	−1.77496	+	6.62424i	−0.0773919	+	0.288831i
$527$	5.15289	+	8.92507i	0.224464	+	0.388782i
$528$			6.81017i			0.296374i
$529$	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
$533$	0.671121	+	6.53373i	0.0290695	+	0.283007i
$534$			15.9327i			0.689476i
$535$		0			0
$536$	3.28759	−	5.69428i	0.142002	−	0.245955i
$537$	22.8606	+	6.12549i	0.986510	+	0.264334i
$538$	−16.1492			−0.696241
$539$	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	$0.205495\pi$
$542$	2.53695	−	9.46802i	0.108971	−	0.406686i
$543$	−14.6815	+	3.93390i	−0.630044	+	0.168820i
$544$	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	$-0.116194\pi$
$547$	13.4979	+	13.4979i	0.577128	+	0.577128i	−0.356983	+	0.934111i	$0.616194\pi$
$548$	−6.95440	+	12.0454i	−0.297077	+	0.514553i
$549$	−4.19081	−	2.41957i	−0.178860	−	0.103265i
$550$		0			0
$551$	2.01253	+	2.01253i	0.0857365	+	0.0857365i
$552$	−4.63859	+	2.67809i	−0.197431	+	0.113987i
$553$	2.14896	−	1.24070i	0.0913832	−	0.0527601i
$554$	13.1471	+	13.1471i	0.558568	+	0.558568i
$555$		0			0
$556$	−2.27272	−	1.31215i	−0.0963847	−	0.0556478i
$557$	−12.6509	+	21.9120i	−0.536036	+	0.928441i	0.463077	+	0.886318i	$0.346745\pi$
$557$	−12.6509	+	21.9120i	−0.536036	+	0.928441i	−0.999112	+	0.0421230i	$0.986588\pi$
$558$	−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
$562$	−27.3721	+	7.33432i	−1.15462	+	0.309380i
$563$	7.83537	−	29.2420i	0.330222	−	1.23240i	−0.578736	−	0.815515i	$-0.696454\pi$
$563$	7.83537	−	29.2420i	0.330222	−	1.23240i	0.908957	−	0.416889i	$-0.136880\pi$
$564$	5.45323	−	5.45323i	0.229622	−	0.229622i
$565$		0			0
$566$	−16.8211	−	4.50721i	−0.707045	−	0.189452i
$567$	−0.144083			−0.00605091
$568$	−10.1305	−	2.71447i	−0.425068	−	0.113897i
$569$	−6.47393	+	11.2132i	−0.271401	+	0.470081i	−0.969221	−	0.246193i	$-0.920820\pi$
$569$	−6.47393	+	11.2132i	−0.271401	+	0.470081i	0.697820	+	0.716273i	$0.254154\pi$
$570$		0			0
$571$		−	12.4096i		−	0.519324i	−0.965700	−	0.259662i	$-0.916389\pi$
$571$		−	12.4096i		−	0.519324i	0.965700	−	0.259662i	$-0.0836111\pi$
$572$	−13.6503	−	18.8817i	−0.570750	−	0.789485i
$573$	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
$577$			22.8030i			0.949301i	0.880174	+	0.474650i	$0.157425\pi$
$577$			22.8030i			0.949301i	−0.880174	+	0.474650i	$0.842575\pi$
$578$	7.96740	+	13.7999i	0.331400	+	0.574002i
$579$	3.42405	−	12.7787i	0.142299	−	0.531066i
$580$		0			0
$581$	2.24564	+	3.88957i	0.0931650	+	0.161366i
$582$	−4.80533	−	17.9337i	−0.199187	−	0.743377i
$583$	30.1092	+	17.3835i	1.24699	+	0.719953i
$584$	2.04350			0.0845605
$585$		0			0
$586$	−28.8199			−1.19054
$587$	−32.6525	−	18.8519i	−1.34771	−	0.778102i	−0.359787	−	0.933034i	$-0.617151\pi$
$587$	−32.6525	−	18.8519i	−1.34771	−	0.778102i	−0.987925	+	0.154933i	$0.950484\pi$
$588$	−1.80911	−	6.75169i	−0.0746065	−	0.278435i
$589$	−4.63327	−	8.02505i	−0.190910	−	0.330667i
$590$		0			0
$591$	3.11957	−	11.6424i	0.128322	−	0.478904i
$592$	0.0214890	+	0.0372201i	0.000883194	+	0.00152974i
$593$			6.88681i			0.282807i	0.989952	+	0.141404i	$0.0451616\pi$
$593$			6.88681i			0.282807i	−0.989952	+	0.141404i	$0.954838\pi$
$594$	−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
$598$	7.49287	−	16.7228i	0.306406	−	0.683847i
$599$		−	39.1133i		−	1.59813i	−0.601246	−	0.799064i	$-0.705329\pi$
$599$		−	39.1133i		−	1.59813i	0.601246	−	0.799064i	$-0.294671\pi$
$600$		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	$0.0504989\pi$
$602$	−4.11043	−	1.10139i	−0.167529	−	0.0448891i
$603$	12.4228			0.505896
$604$	16.3863	+	4.39068i	0.666747	+	0.178654i
$605$		0			0
$606$	5.36189	−	5.36189i	0.217812	−	0.217812i
$607$	−10.4684	+	39.0688i	−0.424901	+	1.58575i	0.339238	+	0.940701i	$0.389831\pi$
$607$	−10.4684	+	39.0688i	−0.424901	+	1.58575i	−0.764139	+	0.645052i	$0.776836\pi$
$608$	−0.896383	+	0.240185i	−0.0363531	+	0.00974079i
$609$	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
$613$	−13.4145	+	23.2346i	−0.541806	+	0.938436i	0.456994	+	0.889470i	$0.348926\pi$
$613$	−13.4145	+	23.2346i	−0.541806	+	0.938436i	−0.998800	+	0.0489665i	$0.984407\pi$
$614$	28.8196	+	16.6390i	1.16306	+	0.671496i
$615$		0			0
$616$	−2.76985	−	2.76985i	−0.111600	−	0.111600i
$617$	−28.1287	+	16.2401i	−1.13242	+	0.653803i	−0.944542	−	0.328390i	$-0.893494\pi$
$617$	−28.1287	+	16.2401i	−1.13242	+	0.653803i	−0.187877	+	0.982192i	$0.560161\pi$
$618$	−12.8609	+	7.42522i	−0.517340	+	0.298686i
$619$	8.37271	+	8.37271i	0.336528	+	0.336528i	0.855059	−	0.518531i	$-0.173521\pi$
$619$	8.37271	+	8.37271i	0.336528	+	0.336528i	−0.518531	+	0.855059i	$0.673521\pi$
$620$		0			0
$621$	−22.6797	−	13.0941i	−0.910104	−	0.525449i
$622$	−6.04583	+	10.4717i	−0.242416	+	0.419876i
$623$	−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
$627$	−6.10452	+	1.63570i	−0.243791	+	0.0653236i
$628$	2.97161	−	11.0902i	0.118580	−	0.442547i
$629$	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	$0.389344\pi$
$632$	4.09352			0.162831
$633$	5.66190	+	1.51710i	0.225040	+	0.0602994i
$634$	5.53342	−	9.58416i	0.219760	−	0.380636i
$635$		0			0
$636$		−	5.67006i		−	0.224833i
$637$	18.5490	+	15.0934i	0.734940	+	0.598023i
$638$	−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	$0.509136\pi$
$642$		−	3.19386i		−	0.126052i
$643$	1.13518	+	1.96619i	0.0447671	+	0.0775389i	0.887541	−	0.460729i	$-0.152412\pi$
$643$	1.13518	+	1.96619i	0.0447671	+	0.0775389i	−0.842774	+	0.538268i	$0.819079\pi$
$644$	0.797378	−	2.97586i	0.0314211	−	0.117265i
$645$		0			0
$646$	0.478887	+	0.829457i	0.0188416	+	0.0326346i
$647$	8.35147	+	31.1681i	0.328330	+	1.22534i	0.910922	+	0.412580i	$0.135372\pi$
$647$	8.35147	+	31.1681i	0.328330	+	1.22534i	−0.582591	+	0.812765i	$0.697961\pi$
$648$	−0.205845	−	0.118845i	−0.00808636	−	0.00466866i
$649$	38.0130			1.49214
$650$		0			0
$651$	−6.37908			−0.250016
$652$	−7.28290	−	4.20479i	−0.285220	−	0.164672i
$653$	7.02367	+	26.2127i	0.274858	+	1.02578i	0.955937	+	0.293573i	$0.0948442\pi$
$653$	7.02367	+	26.2127i	0.274858	+	1.02578i	−0.681079	+	0.732210i	$0.738489\pi$
$654$	−4.83102	−	8.36757i	−0.188908	−	0.327198i
$655$		0			0
$656$	−0.471482	+	1.75959i	−0.0184083	+	0.0687006i
$657$	1.93044	+	3.34362i	0.0753136	+	0.130447i
$658$			4.43590i			0.172930i
$659$	−29.1194	+	16.8121i	−1.13433	+	0.654905i	−0.945020	−	0.327012i	$-0.893958\pi$
$659$	−29.1194	+	16.8121i	−1.13433	+	0.654905i	−0.189309	+	0.981918i	$0.560625\pi$
$660$		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
$663$	3.87195	+	0.622638i	0.150374	+	0.0241812i
$664$			7.40916i			0.287531i
$665$		0			0
$666$	−0.0406003	+	0.0703218i	−0.00157323	+	0.00272491i
$667$	−15.0563	−	4.03431i	−0.582980	−	0.156209i
$668$	2.55335			0.0987919
$669$	3.38519	+	0.907060i	0.130879	+	0.0350689i
$670$		0			0
$671$	11.7033	−	11.7033i	0.451802	−	0.451802i
$672$	−0.165343	+	0.617070i	−0.00637826	+	0.0238040i
$673$	−31.6023	+	8.46780i	−1.21818	+	0.326410i	−0.809965	−	0.586478i	$-0.800514\pi$
$673$	−31.6023	+	8.46780i	−1.21818	+	0.326410i	−0.408212	+	0.912887i	$0.633848\pi$
$674$	−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	$-0.341098\pi$
$677$	−10.3878	−	10.3878i	−0.399237	−	0.399237i	−0.877964	+	0.478727i	$0.841098\pi$
$678$	9.05772	−	15.6884i	0.347860	−	0.602511i
$679$	9.24849	+	5.33962i	0.354924	+	0.204916i
$680$		0			0
$681$	−3.92258	−	3.92258i	−0.150314	−	0.150314i
$682$	55.8814	−	32.2631i	2.13981	−	1.23542i
$683$	−4.50264	+	2.59960i	−0.172289	+	0.0994710i	−0.583665	−	0.811995i	$-0.698382\pi$
$683$	−4.50264	+	2.59960i	−0.172289	+	0.0994710i	0.411376	+	0.911466i	$0.365048\pi$
$684$	−1.23979	−	1.23979i	−0.0474044	−	0.0474044i
$685$		0			0
$686$	7.15665	+	4.13189i	0.273242	+	0.157756i
$687$	9.58072	−	16.5943i	0.365527	−	0.633112i
$688$	−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	$0.730342\pi$
$692$	22.3217	−	5.98108i	0.848544	−	0.227367i
$693$	1.91549	−	7.14870i	0.0727634	−	0.271557i
$694$	−14.0195	+	14.0195i	−0.532171	+	0.532171i
$695$		0			0
$696$	3.12205	+	0.836550i	0.118341	+	0.0317093i
$697$	1.88011			0.0712141
$698$	12.7939	+	3.42812i	0.484256	+	0.129756i
$699$	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	$-0.121423\pi$
$702$	−18.4813	+	1.89833i	−0.697532	+	0.0716479i
$703$	−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
$707$			4.36161i			0.164035i
$708$	−3.09971	−	5.36886i	−0.116494	−	0.201774i
$709$	−2.68781	+	10.0310i	−0.100943	+	0.376724i	−0.997853	−	0.0654883i	$-0.979140\pi$
$709$	−2.68781	+	10.0310i	−0.100943	+	0.376724i	0.896910	+	0.442212i	$0.145806\pi$
$710$		0			0
$711$	3.86704	+	6.69791i	0.145025	+	0.251191i
$712$	−3.91289	−	14.6031i	−0.146642	−	0.547274i
$713$	43.9506	+	25.3749i	1.64596	+	0.950296i
$714$	0.659332			0.0246749
$715$		0			0
$716$	−22.4572			−0.839266
$717$	24.4807	+	14.1339i	0.914248	+	0.527842i
$718$	3.38241	+	12.6233i	0.126230	+	0.471098i
$719$	−7.17711	−	12.4311i	−0.267661	−	0.463603i	0.700596	−	0.713558i	$-0.252917\pi$
$719$	−7.17711	−	12.4311i	−0.267661	−	0.463603i	−0.968257	+	0.249955i	$0.919584\pi$
$720$		0			0
$721$	2.21080	−	8.25081i	0.0823344	−	0.307276i
$722$	9.06940	+	15.7087i	0.337528	+	0.584616i
$723$			17.2850i			0.642838i
$724$	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	−0.644753	−	0.764391i	$-0.723040\pi$
$727$	3.22577	−	3.22577i	0.119637	−	0.119637i	0.764391	+	0.644753i	$0.223040\pi$
$728$	−0.778432	−	2.04229i	−0.0288506	−	0.0756924i
$729$			15.8420i			0.586741i
$730$		0			0
$731$	−3.62264	+	6.27459i	−0.133988	+	0.232074i
$732$	−2.60728	−	0.698619i	−0.0963679	−	0.0258217i
$733$	−30.7847			−1.13706			−0.568530	−	0.822662i	$-0.692488\pi$
$733$	−30.7847			−1.13706			−0.568530	+	0.822662i	$0.692488\pi$
$734$	−9.95527	−	2.66751i	−0.367456	−	0.0984594i
$735$		0			0
$736$	3.59378	−	3.59378i	0.132468	−	0.132468i
$737$	−10.9970	+	41.0413i	−0.405079	+	1.51177i
$738$	−3.32449	+	0.890794i	−0.122376	+	0.0327906i
$739$	38.3464	−	10.2749i	1.41059	−	0.377968i	0.528457	−	0.848960i	$-0.322771\pi$
$739$	38.3464	−	10.2749i	1.41059	−	0.377968i	0.882137	+	0.470992i	$0.156104\pi$
$740$		0			0
$741$	−3.48150	−	0.559850i	−0.127896	−	0.0205666i
$742$	2.30614	+	2.30614i	0.0846612	+	0.0846612i
$743$	21.8058	−	37.7688i	0.799979	−	1.38560i	−0.119650	−	0.992816i	$-0.538177\pi$
$743$	21.8058	−	37.7688i	0.799979	−	1.38560i	0.919629	−	0.392788i	$-0.128489\pi$
$744$	−9.11354	−	5.26170i	−0.334118	−	0.192903i
$745$		0			0
$746$	−20.1298	−	20.1298i	−0.737006	−	0.737006i
$747$	−12.1230	+	6.99924i	−0.443559	+	0.256089i
$748$	−5.77582	+	3.33467i	−0.211185	+	0.121928i
$749$	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	$0.842519\pi$
$752$	−3.65890	+	6.33739i	−0.133426	+	0.231101i
$753$	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
$757$	38.2740	−	10.2555i	1.39109	−	0.372742i	0.515954	−	0.856616i	$-0.327438\pi$
$757$	38.2740	−	10.2555i	1.39109	−	0.372742i	0.875137	+	0.483875i	$0.160771\pi$
$758$	5.36719	−	20.0306i	0.194945	−	0.727545i
$759$	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	$0.302392\pi$
$762$	−13.6879			−0.495859
$763$	5.36816	+	1.43840i	0.194341	+	0.0520734i
$764$	−8.17521	+	14.1599i	−0.295769	+	0.512286i
$765$		0			0
$766$			11.4690i			0.414391i
$767$	19.3556	+	8.67251i	0.698889	+	0.313146i
$768$	−0.745202	+	0.745202i	−0.0268901	+	0.0268901i
$769$	−4.20166	−	15.6808i	−0.151516	−	0.565464i	−0.999379	−	0.0352485i	$-0.988778\pi$
$769$	−4.20166	−	15.6808i	−0.151516	−	0.565464i	0.847863	−	0.530215i	$-0.177889\pi$
$770$		0			0
$771$	−21.4788	+	12.4008i	−0.773540	+	0.446603i
$772$			12.5532i			0.451800i
$773$	−17.6239	−	30.5255i	−0.633889	−	1.09793i	−0.986749	−	0.162252i	$-0.948124\pi$
$773$	−17.6239	−	30.5255i	−0.633889	−	1.09793i	0.352861	−	0.935676i	$-0.385209\pi$
$774$	3.43281	−	12.8114i	0.123390	−	0.460497i
$775$		0			0
$776$	8.80863	+	15.2570i	0.316211	+	0.547694i
$777$	0.00710614	+	0.0265205i	0.000254932	+	0.000951417i
$778$	−12.5447	−	7.24270i	−0.449750	−	0.259663i
$779$	−1.69051			−0.0605689
$780$		0			0
$781$	67.7731			2.42511
$782$	−4.54266	−	2.62271i	−0.162445	−	0.0937878i
$783$	4.09018	+	15.2648i	0.146171	+	0.545519i
$784$	3.31627	+	5.74395i	0.118438	+	0.205141i
$785$		0			0
$786$	−1.67353	+	6.24571i	−0.0596930	+	0.222777i
$787$	−24.5889	−	42.5892i	−0.876499	−	1.51814i	−0.855157	−	0.518369i	$-0.826539\pi$
$787$	−24.5889	−	42.5892i	−0.876499	−	1.51814i	−0.0213419	−	0.999772i	$-0.506794\pi$
$788$			11.4369i			0.407424i
$789$	−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
$793$	8.62921	−	3.28908i	0.306432	−	0.116799i
$794$			20.9328i			0.742877i
$795$		0			0
$796$	8.02327	−	13.8967i	0.284377	−	0.492556i
$797$	−25.2737	−	6.77206i	−0.895240	−	0.239879i	−0.218269	−	0.975889i	$-0.570041\pi$
$797$	−25.2737	−	6.77206i	−0.895240	−	0.239879i	−0.676971	+	0.736010i	$0.736708\pi$
$798$	−0.592844			−0.0209865
$799$	7.29520	+	1.95474i	0.258086	+	0.0691539i
$800$		0			0
$801$	20.1975	−	20.1975i	0.713645	−	0.713645i
$802$	6.71066	−	25.0445i	0.236962	−	0.884353i
$803$	−12.7552	+	3.41774i	−0.450121	+	0.120609i
$804$	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
$808$	−3.59761	+	6.23125i	−0.126564	+	0.219215i
$809$	7.12231	+	4.11207i	0.250407	+	0.144573i	0.619951	−	0.784641i	$-0.287153\pi$
$809$	7.12231	+	4.11207i	0.250407	+	0.144573i	−0.369544	+	0.929213i	$0.620486\pi$
$810$		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	$0.793960\pi$
$812$	−1.61005	+	0.929563i	−0.0565017	+	0.0326213i
$813$	8.94612	−	5.16505i	0.313754	−	0.181146i
$814$	−0.196382	−	0.196382i	−0.00688318	−	0.00688318i
$815$		0			0
$816$	0.941961	+	0.543841i	0.0329752	+	0.0190383i
$817$	3.25732	−	5.64185i	0.113959	−	0.197383i
$818$	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	$0.354946\pi$
$822$	−14.1587	+	3.79380i	−0.493840	+	0.132324i
$823$	12.9700	−	48.4047i	0.452106	−	1.68728i	−0.244353	−	0.969686i	$-0.578576\pi$
$823$	12.9700	−	48.4047i	0.452106	−	1.68728i	0.696459	−	0.717596i	$-0.254758\pi$
$824$	9.96404	−	9.96404i	0.347114	−	0.347114i
$825$		0			0
$826$	3.44436	+	0.922913i	0.119845	+	0.0321123i
$827$	−4.23112			−0.147130			−0.0735652	−	0.997290i	$-0.523438\pi$
$827$	−4.23112			−0.147130			−0.0735652	+	0.997290i	$0.523438\pi$
$828$	9.27518	+	2.48528i	0.322335	+	0.0863693i
$829$	5.50337	−	9.53212i	0.191140	−	0.331064i	−0.754488	−	0.656313i	$-0.772115\pi$
$829$	5.50337	−	9.53212i	0.191140	−	0.331064i	0.945628	+	0.325249i	$0.105448\pi$
$830$		0			0
$831$			19.5945i			0.679727i
$832$	0.572444	−	3.55982i	0.0198459	−	0.123415i
$833$	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
$837$		−	51.4526i		−	1.77846i
$838$	−5.77483	−	10.0023i	−0.199488	−	0.345524i
$839$	−5.94322	+	22.1804i	−0.205183	+	0.765752i	0.784211	+	0.620494i	$0.213068\pi$
$839$	−5.94322	+	22.1804i	−0.205183	+	0.765752i	−0.989394	+	0.145258i	$0.953599\pi$
$840$		0			0
$841$	−9.79690	−	16.9687i	−0.337824	−	0.585129i
$842$	−6.26276	−	23.3729i	−0.215829	−	0.805485i
$843$	−25.8633	−	14.9322i	−0.890778	−	0.514291i
$844$	−5.56198			−0.191451
$845$		0			0
$846$	−13.8259			−0.475343
$847$	16.1469	+	9.32240i	0.554813	+	0.320322i
$848$	1.39250	+	5.19688i	0.0478187	+	0.178462i
$849$	−9.17636	−	15.8939i	−0.314932	−	0.545478i
$850$		0			0
$851$	0.0565340	−	0.210988i	0.00193796	−	0.00723256i
$852$	−5.52646	−	9.57212i	−0.189334	−	0.327935i
$853$			11.1600i			0.382112i	0.981579	+	0.191056i	$0.0611912\pi$
$853$			11.1600i			0.382112i	−0.981579	+	0.191056i	$0.938809\pi$
$854$	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	−0.790408	−	0.612581i	$-0.790131\pi$
$857$	−5.20581	+	5.20581i	−0.177827	+	0.177827i	0.612581	+	0.790408i	$0.290131\pi$
$858$	3.89844	−	24.2430i	0.133090	−	0.827641i
$859$		−	24.5758i		−	0.838514i	−0.907868	−	0.419257i	$-0.862291\pi$
$859$		−	24.5758i		−	0.838514i	0.907868	−	0.419257i	$-0.137709\pi$
$860$		0			0
$861$	−0.581874	+	1.00784i	−0.0198302	+	0.0343470i
$862$	−6.83242	−	1.83074i	−0.232713	−	0.0623553i
$863$	21.2881			0.724655			0.362328	−	0.932051i	$-0.381982\pi$
$863$	21.2881			0.724655			0.362328	+	0.932051i	$0.381982\pi$
$864$	−4.97718	−	1.33363i	−0.169327	−	0.0453711i
$865$		0			0
$866$	−19.0778	+	19.0778i	−0.648289	+	0.648289i
$867$	−4.34642	+	16.2211i	−0.147612	+	0.550896i
$868$	5.84673	−	1.56663i	0.198451	−	0.0531748i
$869$	−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
$873$	−16.6426	+	28.8258i	−0.563266	+	0.975605i
$874$	4.08457	+	2.35823i	0.138163	+	0.0797683i
$875$		0			0
$876$	1.52282	+	1.52282i	0.0514512	+	0.0514512i
$877$	18.8205	−	10.8660i	0.635524	−	0.366920i	−0.147364	−	0.989082i	$-0.547079\pi$
$877$	18.8205	−	10.8660i	0.635524	−	0.366920i	0.782888	+	0.622162i	$0.213746\pi$
$878$	−14.8415	+	8.56872i	−0.500875	+	0.289180i
$879$	−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	$0.577654\pi$
$882$	−6.26560	+	10.8523i	−0.210974	+	0.365417i
$883$	14.4246	+	14.4246i	0.485427	+	0.485427i	0.906860	−	0.421433i	$-0.138473\pi$
$883$	14.4246	+	14.4246i	0.485427	+	0.485427i	−0.421433	+	0.906860i	$0.638473\pi$
$884$	−3.70174	+	0.380229i	−0.124503	+	0.0127885i
$885$		0			0
$886$	3.34113	−	0.895252i	0.112247	−	0.0300766i
$887$	37.1305	−	9.94910i	1.24672	−	0.334058i	0.425652	−	0.904887i	$-0.360045\pi$
$887$	37.1305	−	9.94910i	1.24672	−	0.334058i	0.821069	+	0.570829i	$0.193378\pi$
$888$	−0.0117228	+	0.0437502i	−0.000393392	+	0.00146816i
$889$	5.56717	−	5.56717i	0.186717	−	0.186717i
$890$		0			0
$891$	1.48362	+	0.397535i	0.0497031	+	0.0133179i
$892$	−3.32545			−0.111344
$893$	−6.55954	−	1.75762i	−0.219507	−	0.0588167i
$894$	8.27136	−	14.3264i	0.276636	−	0.479147i
$895$		0			0
$896$		−	0.606181i		−	0.0202511i
$897$	18.0456	−	6.87818i	0.602524	−	0.229656i
$898$	−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
$902$		−	11.7717i		−	0.391953i
$903$	−2.24234	−	3.88385i	−0.0746205	−	0.129246i
$904$	−4.44894	+	16.6037i	−0.147969	+	0.552230i
$905$		0			0
$906$	8.93912	+	15.4830i	0.296982	+	0.514388i
$907$	−3.87478	−	14.4609i	−0.128660	−	0.480166i	0.871284	−	0.490780i	$-0.163288\pi$
$907$	−3.87478	−	14.4609i	−0.128660	−	0.480166i	−0.999944	+	0.0106141i	$0.996621\pi$
$908$	4.55857	+	2.63189i	0.151282	+	0.0873425i
$909$	−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	$0.494435\pi$
$912$	−0.846972	−	0.489000i	−0.0280461	−	0.0161924i
$913$	−12.3918	−	46.2468i	−0.410108	−	1.53055i
$914$	12.8602	+	22.2746i	0.425378	+	0.736777i
$915$		0			0
$916$	−4.70583	+	17.5624i	−0.155485	+	0.580277i
$917$	−1.85961	−	3.22094i	−0.0614097	−	0.106365i
$918$			5.31806i			0.175522i
$919$	−25.9016	+	14.9543i	−0.854414	+	0.493296i	−0.862138	−	0.506674i	$-0.830875\pi$
$919$	−25.9016	+	14.9543i	−0.854414	+	0.493296i	0.00772358	+	0.999970i	$0.497541\pi$
$920$		0			0
$921$	9.07700	+	33.8758i	0.299097	+	1.11625i
$922$	1.43772	−	1.43772i	0.0473489	−	0.0473489i
$923$	34.5090	+	15.4622i	1.13588	+	0.508944i
$924$		−	4.12819i		−	0.135808i
$925$		0			0
$926$	−0.310484	+	0.537774i	−0.0102031	+	0.0176723i
$927$	25.7162	+	6.89063i	0.844631	+	0.226318i
$928$	−3.06695			−0.100678
$929$	14.3249	+	3.83833i	0.469983	+	0.125932i	0.486035	−	0.873940i	$-0.338443\pi$
$929$	14.3249	+	3.83833i	0.469983	+	0.125932i	−0.0160515	+	0.999871i	$0.505110\pi$
$930$		0			0
$931$	−4.35226	+	4.35226i	−0.142640	+	0.142640i
$932$	−1.96988	+	7.35170i	−0.0645256	+	0.240813i
$933$	−12.3089	+	3.29815i	−0.402975	+	0.107977i
$934$	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	$-0.0241752\pi$
$937$	28.1996	+	28.1996i	0.921242	+	0.921242i	−0.0758757	+	0.997117i	$0.524175\pi$
$938$	−1.99287	+	3.45176i	−0.0650697	+	0.112704i
$939$	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	$0.632608\pi$
$942$	10.4789	−	6.04999i	0.341420	−	0.197119i
$943$	8.01799	−	4.62919i	0.261102	−	0.150747i
$944$	4.15956	+	4.15956i	0.135382	+	0.135382i
$945$		0			0
$946$	39.2863	+	22.6819i	1.27731	+	0.737453i
$947$	18.4380	−	31.9355i	0.599153	−	1.03776i	−0.393793	−	0.919199i	$-0.628837\pi$
$947$	18.4380	−	31.9355i	0.599153	−	1.03776i	0.992946	−	0.118565i	$-0.0378293\pi$
$948$	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
$952$	−0.604310	+	0.161924i	−0.0195858	+	0.00524799i
$953$	−11.9005	+	44.4134i	−0.385496	+	1.43869i	0.451888	+	0.892075i	$0.350751\pi$
$953$	−11.9005	+	44.4134i	−0.385496	+	1.43869i	−0.837384	+	0.546616i	$0.815916\pi$
$954$	−7.18781	+	7.18781i	−0.232714	+	0.232714i
$955$		0			0
$956$	−25.9089	−	6.94226i	−0.837952	−	0.224529i
$957$	−20.8865			−0.675163
$958$	5.22504	+	1.40005i	0.168813	+	0.0452334i
$959$	4.21562	−	7.30167i	0.136129	−	0.235783i
$960$		0			0
$961$			68.7092i			2.21642i
$962$	−0.0551907	−	0.144798i	−0.00177942	−	0.00466848i
$963$	−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
$967$		−	27.7061i		−	0.890968i	−0.895290	−	0.445484i	$-0.853032\pi$
$967$		−	27.7061i		−	0.890968i	0.895290	−	0.445484i	$-0.146968\pi$
$968$	15.3789	+	26.6371i	0.494297	+	0.856148i
$969$	−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	$0.729705\pi$
$972$	−4.06573	−	15.1735i	−0.130408	−	0.486690i
$973$	1.37768	+	0.795403i	0.0441663	+	0.0254994i
$974$	−26.5556			−0.850897
$975$		0			0
$976$	2.56127			0.0819843
$977$	−29.1362	−	16.8218i	−0.932148	−	0.538176i	−0.0446580	−	0.999002i	$-0.514220\pi$
$977$	−29.1362	−	16.8218i	−0.932148	−	0.538176i	−0.887490	+	0.460826i	$0.847553\pi$
$978$	−2.29382	−	8.56064i	−0.0733482	−	0.273739i
$979$	48.8472	+	84.6059i	1.56116	+	2.70402i
$980$		0			0
$981$	−4.48320	+	16.7315i	−0.143138	+	0.534197i
$982$	15.6827	+	27.1633i	0.500456	+	0.866816i
$983$		−	8.53839i		−	0.272332i	−0.990686	−	0.136166i	$-0.956522\pi$
$983$		−	8.53839i		−	0.272332i	0.990686	−	0.136166i	$-0.0434781\pi$
$984$	−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
$988$	3.32845	−	0.341886i	0.105892	−	0.0108769i
$989$			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	$0.135248\pi$
$992$	9.64520	+	2.58442i	0.306235	+	0.0820555i
$993$	−16.6917			−0.529694
$994$	6.14093	+	1.64546i	0.194779	+	0.0521908i
$995$		0			0
$996$	−5.52131	+	5.52131i	−0.174950	+	0.174950i
$997$	11.0834	−	41.3639i	0.351016	−	1.31001i	−0.534409	−	0.845226i	$-0.679466\pi$
$997$	11.0834	−	41.3639i	0.351016	−	1.31001i	0.885425	−	0.464783i	$-0.153868\pi$
$998$	17.2926	−	4.63354i	0.547388	−	0.146672i
$999$	−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.t.h.7.2	yes	16
5.2	odd	4		650.2.w.h.293.2	yes	16
5.3	odd	4		650.2.w.f.293.3	yes	16
5.4	even	2		650.2.t.f.7.3	✓	16
13.2	odd	12		650.2.w.f.457.3	yes	16
65.2	even	12		650.2.t.f.93.3	yes	16
65.28	even	12	inner	650.2.t.h.93.2	yes	16
65.54	odd	12		650.2.w.h.457.2	yes	16

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

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.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.272763 - 1.01796i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.272763 + 1.01796i) q^{6} +(-0.303090 - 0.524968i) q^{7} -1.00000i q^{8} +(1.63622 - 0.944675i) q^{9} +(1.67250 + 6.24184i) q^{11} +(0.745202 - 0.745202i) q^{12} +(-0.572444 + 3.55982i) q^{13} +0.606181i q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.996913 + 0.267122i) q^{17} -1.88935 q^{18} +(-0.896383 - 0.240185i) q^{19} +(-0.451727 + 0.451727i) q^{21} +(1.67250 - 6.24184i) q^{22} +(4.90919 - 1.31541i) q^{23} +(-1.01796 + 0.272763i) q^{24} +(2.27566 - 2.79667i) q^{26} +(-3.64355 - 3.64355i) q^{27} +(0.303090 - 0.524968i) q^{28} +(-2.65606 - 1.53348i) q^{29} +(7.06078 + 7.06078i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.89778 - 3.40508i) q^{33} +(-0.729791 - 0.729791i) q^{34} +(1.63622 + 0.944675i) q^{36} +(0.0214890 - 0.0372201i) q^{37} +(0.656198 + 0.656198i) q^{38} +(3.77991 - 0.388258i) q^{39} +(1.75959 - 0.471482i) q^{41} +(0.617070 - 0.165343i) q^{42} +(-1.81693 + 6.78086i) q^{43} +(-4.56935 + 4.56935i) q^{44} +(-4.90919 - 1.31541i) q^{46} +7.31779 q^{47} +(1.01796 + 0.272763i) q^{48} +(3.31627 - 5.74395i) q^{49} -1.08768i q^{51} +(-3.36912 + 1.28416i) q^{52} +(3.80438 - 3.80438i) q^{53} +(1.33363 + 4.97718i) q^{54} +(-0.524968 + 0.303090i) q^{56} +0.977999i q^{57} +(1.53348 + 2.65606i) q^{58} +(1.52251 - 5.68207i) q^{59} +(-1.28063 - 2.21812i) q^{61} +(-2.58442 - 9.64520i) q^{62} +(-0.991848 - 0.572643i) q^{63} -1.00000 q^{64} -6.81017 q^{66} +(5.69428 + 3.28759i) q^{67} +(0.267122 + 0.996913i) q^{68} +(-2.67809 - 4.63859i) q^{69} +(2.71447 - 10.1305i) q^{71} +(-0.944675 - 1.63622i) q^{72} +2.04350i q^{73} +(-0.0372201 + 0.0214890i) q^{74} +(-0.240185 - 0.896383i) q^{76} +(2.76985 - 2.76985i) q^{77} +(-3.46763 - 1.55371i) q^{78} +4.09352i q^{79} +(0.118845 - 0.205845i) q^{81} +(-1.75959 - 0.471482i) q^{82} -7.40916 q^{83} +(-0.617070 - 0.165343i) q^{84} +(4.96394 - 4.96394i) q^{86} +(-0.836550 + 3.12205i) q^{87} +(6.24184 - 1.67250i) q^{88} +(14.6031 - 3.91289i) q^{89} +(2.04229 - 0.778432i) q^{91} +(3.59378 + 3.59378i) q^{92} +(5.26170 - 9.11354i) q^{93} +(-6.33739 - 3.65890i) q^{94} +(-0.745202 - 0.745202i) q^{96} +(-15.2570 + 8.80863i) q^{97} +(-5.74395 + 3.31627i) q^{98} +(8.63309 + 8.63309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33}+ \cdots + 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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