LMFDB - Embedded newform 287.2.r.c.9.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(9,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("287.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.r (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			9.11
Character	$\chi$	$=$	287.9
Dual form			287.2.r.c.32.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.194567 - 0.112333i) q^{2} +(-0.270068 + 1.00791i) q^{3} +(-0.974763 - 1.68834i) q^{4} +(-0.875130 - 0.505256i) q^{5} +(0.165768 - 0.165768i) q^{6} +(-2.25178 + 1.38907i) q^{7} +0.887324i q^{8} +(1.65513 + 0.955593i) q^{9} +O(q^{10})$	\(q+(-0.194567 - 0.112333i) q^{2} +(-0.270068 + 1.00791i) q^{3} +(-0.974763 - 1.68834i) q^{4} +(-0.875130 - 0.505256i) q^{5} +(0.165768 - 0.165768i) q^{6} +(-2.25178 + 1.38907i) q^{7} +0.887324i q^{8} +(1.65513 + 0.955593i) q^{9} +(0.113514 + 0.196612i) q^{10} +(-1.53944 + 5.74527i) q^{11} +(1.96494 - 0.526505i) q^{12} +(2.81588 + 2.81588i) q^{13} +(0.594158 - 0.0173167i) q^{14} +(0.745597 - 0.745597i) q^{15} +(-1.84985 + 3.20403i) q^{16} +(-2.72388 - 0.729861i) q^{17} +(-0.214689 - 0.371853i) q^{18} +(0.588267 + 2.19544i) q^{19} +1.97002i q^{20} +(-0.791917 - 2.64473i) q^{21} +(0.944908 - 0.944908i) q^{22} +(1.15466 - 1.99992i) q^{23} +(-0.894341 - 0.239638i) q^{24} +(-1.98943 - 3.44580i) q^{25} +(-0.231560 - 0.864192i) q^{26} +(-3.62367 + 3.62367i) q^{27} +(4.54016 + 2.44775i) q^{28} +(-6.45897 - 6.45897i) q^{29} +(-0.228823 + 0.0613130i) q^{30} +(3.16024 + 5.47370i) q^{31} +(2.25673 - 1.30292i) q^{32} +(-5.37495 - 3.10323i) q^{33} +(0.447988 + 0.447988i) q^{34} +(2.67243 - 0.0778880i) q^{35} -3.72590i q^{36} +(-1.23031 + 2.13095i) q^{37} +(0.132164 - 0.493241i) q^{38} +(-3.59863 + 2.07767i) q^{39} +(0.448326 - 0.776524i) q^{40} +(-0.915918 + 6.33728i) q^{41} +(-0.143009 + 0.603533i) q^{42} -10.7195i q^{43} +(11.2006 - 3.00118i) q^{44} +(-0.965639 - 1.67254i) q^{45} +(-0.449314 + 0.259412i) q^{46} +(2.94386 + 10.9866i) q^{47} +(-2.72978 - 2.72978i) q^{48} +(3.14099 - 6.25573i) q^{49} +0.893916i q^{50} +(1.47127 - 2.54831i) q^{51} +(2.00934 - 7.49897i) q^{52} +(-0.523042 + 1.95202i) q^{53} +(1.11210 - 0.297987i) q^{54} +(4.25005 - 4.25005i) q^{55} +(-1.23255 - 1.99806i) q^{56} -2.37167 q^{57} +(0.531144 + 1.98226i) q^{58} +(-0.789913 - 1.36817i) q^{59} +(-1.98560 - 0.532040i) q^{60} +(6.64778 + 3.83810i) q^{61} -1.42000i q^{62} +(-5.05437 + 0.147310i) q^{63} +6.81395 q^{64} +(-1.04152 - 3.88700i) q^{65} +(0.697190 + 1.20757i) q^{66} +(-9.71822 - 2.60399i) q^{67} +(1.42288 + 5.31027i) q^{68} +(1.70390 + 1.70390i) q^{69} +(-0.528715 - 0.285048i) q^{70} +(5.48294 + 5.48294i) q^{71} +(-0.847921 + 1.46864i) q^{72} +(5.49080 - 3.17012i) q^{73} +(0.478753 - 0.276408i) q^{74} +(4.01033 - 1.07456i) q^{75} +(3.13323 - 3.13323i) q^{76} +(-4.51408 - 15.0755i) q^{77} +0.933563 q^{78} +(6.69120 - 1.79290i) q^{79} +(3.23772 - 1.86930i) q^{80} +(0.193092 + 0.334445i) q^{81} +(0.890093 - 1.13013i) q^{82} -18.1551 q^{83} +(-3.69326 + 3.91500i) q^{84} +(2.01498 + 2.01498i) q^{85} +(-1.20415 + 2.08565i) q^{86} +(8.25441 - 4.76568i) q^{87} +(-5.09792 - 1.36598i) q^{88} +(0.595128 - 0.159464i) q^{89} +0.433893i q^{90} +(-10.2522 - 2.42929i) q^{91} -4.50206 q^{92} +(-6.37046 + 1.70696i) q^{93} +(0.661385 - 2.46832i) q^{94} +(0.594451 - 2.21852i) q^{95} +(0.703756 + 2.62645i) q^{96} +(5.98800 - 5.98800i) q^{97} +(-1.31386 + 0.864318i) q^{98} +(-8.03812 + 8.03812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7}+O(q^{10}) $ 96 * q - 4 * q^3 + 48 * q^4 - 28 * q^6 - 14 * q^7	$ 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7} - 28 q^{10} + 12 q^{12} - 8 q^{13} + 8 q^{14} - 20 q^{15} - 40 q^{16} - 20 q^{17} - 16 q^{18} - 8 q^{19} - 12 q^{22} + 12 q^{23} - 30 q^{24} + 40 q^{25} + 8 q^{26} - 4 q^{27} - 20 q^{28} - 72 q^{29} + 14 q^{30} + 24 q^{31} + 40 q^{34} + 20 q^{35} + 16 q^{37} - 18 q^{38} + 80 q^{40} - 88 q^{41} - 76 q^{42} + 4 q^{44} - 16 q^{45} + 14 q^{47} - 24 q^{48} - 8 q^{51} + 10 q^{52} - 4 q^{53} + 16 q^{54} - 60 q^{55} + 36 q^{56} + 128 q^{57} - 16 q^{58} - 8 q^{59} + 54 q^{60} + 30 q^{63} - 16 q^{64} + 48 q^{66} + 14 q^{67} - 30 q^{68} + 56 q^{69} - 34 q^{70} - 68 q^{71} + 112 q^{72} - 62 q^{75} - 84 q^{76} - 96 q^{78} - 26 q^{79} - 32 q^{81} + 14 q^{82} + 56 q^{83} - 92 q^{85} + 36 q^{86} + 6 q^{88} + 40 q^{89} - 160 q^{92} - 78 q^{93} + 96 q^{94} + 72 q^{95} + 24 q^{96} + 60 q^{97} - 116 q^{98} - 128 q^{99}+O(q^{100}) $ 96 * q - 4 * q^3 + 48 * q^4 - 28 * q^6 - 14 * q^7 - 28 * q^10 + 12 * q^12 - 8 * q^13 + 8 * q^14 - 20 * q^15 - 40 * q^16 - 20 * q^17 - 16 * q^18 - 8 * q^19 - 12 * q^22 + 12 * q^23 - 30 * q^24 + 40 * q^25 + 8 * q^26 - 4 * q^27 - 20 * q^28 - 72 * q^29 + 14 * q^30 + 24 * q^31 + 40 * q^34 + 20 * q^35 + 16 * q^37 - 18 * q^38 + 80 * q^40 - 88 * q^41 - 76 * q^42 + 4 * q^44 - 16 * q^45 + 14 * q^47 - 24 * q^48 - 8 * q^51 + 10 * q^52 - 4 * q^53 + 16 * q^54 - 60 * q^55 + 36 * q^56 + 128 * q^57 - 16 * q^58 - 8 * q^59 + 54 * q^60 + 30 * q^63 - 16 * q^64 + 48 * q^66 + 14 * q^67 - 30 * q^68 + 56 * q^69 - 34 * q^70 - 68 * q^71 + 112 * q^72 - 62 * q^75 - 84 * q^76 - 96 * q^78 - 26 * q^79 - 32 * q^81 + 14 * q^82 + 56 * q^83 - 92 * q^85 + 36 * q^86 + 6 * q^88 + 40 * q^89 - 160 * q^92 - 78 * q^93 + 96 * q^94 + 72 * q^95 + 24 * q^96 + 60 * q^97 - 116 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.194567	−	0.112333i	−0.137579	−	0.0794315i	0.429631	−	0.903005i	$-0.358644\pi$
$2$	−0.194567	−	0.112333i	−0.137579	−	0.0794315i	−0.567210	+	0.823573i	$0.691977\pi$
$3$	−0.270068	+	1.00791i	−0.155924	+	0.581916i	0.843101	+	0.537756i	$0.180728\pi$
$3$	−0.270068	+	1.00791i	−0.155924	+	0.581916i	−0.999024	+	0.0441599i	$0.985939\pi$
$4$	−0.974763	−	1.68834i	−0.487381	−	0.844169i
$5$	−0.875130	−	0.505256i	−0.391370	−	0.225958i	0.291384	−	0.956606i	$-0.405884\pi$
$5$	−0.875130	−	0.505256i	−0.391370	−	0.225958i	−0.682754	+	0.730649i	$0.739218\pi$
$6$	0.165768	−	0.165768i	0.0676743	−	0.0676743i
$7$	−2.25178	+	1.38907i	−0.851092	+	0.525017i
$7$	−2.25178	+	1.38907i	−0.851092	+	0.525017i
$8$			0.887324i			0.313717i
$9$	1.65513	+	0.955593i	0.551712	+	0.318531i
$10$	0.113514	+	0.196612i	0.0358963	+	0.0621742i
$11$	−1.53944	+	5.74527i	−0.464159	+	1.73226i	0.195504	+	0.980703i	$0.437366\pi$
$11$	−1.53944	+	5.74527i	−0.464159	+	1.73226i	−0.659663	+	0.751562i	$0.729301\pi$
$12$	1.96494	−	0.526505i	0.567230	−	0.151989i
$13$	2.81588	+	2.81588i	0.780985	+	0.780985i	0.979997	−	0.199012i	$-0.0637734\pi$
$13$	2.81588	+	2.81588i	0.780985	+	0.780985i	−0.199012	+	0.979997i	$0.563773\pi$
$14$	0.594158	−	0.0173167i	0.158795	−	0.00462809i
$15$	0.745597	−	0.745597i	0.192512	−	0.192512i
$16$	−1.84985	+	3.20403i	−0.462462	+	0.801008i
$17$	−2.72388	−	0.729861i	−0.660638	−	0.177017i	−0.0871038	−	0.996199i	$-0.527761\pi$
$17$	−2.72388	−	0.729861i	−0.660638	−	0.177017i	−0.573534	+	0.819182i	$0.694428\pi$
$18$	−0.214689	−	0.371853i	−0.0506027	−	0.0876465i
$19$	0.588267	+	2.19544i	0.134958	+	0.503669i	0.999998	+	0.00196651i	$0.000625960\pi$
$19$	0.588267	+	2.19544i	0.134958	+	0.503669i	−0.865040	+	0.501702i	$0.832707\pi$
$20$			1.97002i			0.440510i
$21$	−0.791917	−	2.64473i	−0.172810	−	0.577126i
$22$	0.944908	−	0.944908i	0.201455	−	0.201455i
$23$	1.15466	−	1.99992i	0.240762	−	0.417012i	−0.720169	−	0.693798i	$-0.755936\pi$
$23$	1.15466	−	1.99992i	0.240762	−	0.417012i	0.960932	+	0.276786i	$0.0892693\pi$
$24$	−0.894341	−	0.239638i	−0.182557	−	0.0489159i
$25$	−1.98943	−	3.44580i	−0.397886	−	0.689159i
$26$	−0.231560	−	0.864192i	−0.0454126	−	0.169482i
$27$	−3.62367	+	3.62367i	−0.697375	+	0.697375i
$28$	4.54016	+	2.44775i	0.858010	+	0.462582i
$29$	−6.45897	−	6.45897i	−1.19940	−	1.19940i	−0.974346	−	0.225055i	$-0.927744\pi$
$29$	−6.45897	−	6.45897i	−1.19940	−	1.19940i	−0.225055	−	0.974346i	$-0.572256\pi$
$30$	−0.228823	+	0.0613130i	−0.0417772	+	0.0111942i
$31$	3.16024	+	5.47370i	0.567596	+	0.983105i	0.996803	+	0.0798990i	$0.0254598\pi$
$31$	3.16024	+	5.47370i	0.567596	+	0.983105i	−0.429207	+	0.903206i	$0.641207\pi$
$32$	2.25673	−	1.30292i	0.398937	−	0.230326i
$33$	−5.37495	−	3.10323i	−0.935659	−	0.540203i
$34$	0.447988	+	0.447988i	0.0768293	+	0.0768293i
$35$	2.67243	−	0.0778880i	0.451723	−	0.0131655i
$36$		−	3.72590i		−	0.620984i
$37$	−1.23031	+	2.13095i	−0.202261	+	0.350326i	−0.949257	−	0.314503i	$-0.898162\pi$
$37$	−1.23031	+	2.13095i	−0.202261	+	0.350326i	0.746996	+	0.664829i	$0.231496\pi$
$38$	0.132164	−	0.493241i	0.0214398	−	0.0800143i
$39$	−3.59863	+	2.07767i	−0.576242	+	0.332693i
$40$	0.448326	−	0.776524i	0.0708866	−	0.122779i
$41$	−0.915918	+	6.33728i	−0.143042	+	0.989717i
$41$	−0.915918	+	6.33728i	−0.143042	+	0.989717i
$42$	−0.143009	+	0.603533i	−0.0220668	+	0.0931272i
$43$		−	10.7195i		−	1.63470i	−0.576140	−	0.817351i	$-0.695442\pi$
$43$		−	10.7195i		−	1.63470i	0.576140	−	0.817351i	$-0.304558\pi$
$44$	11.2006	−	3.00118i	1.68855	−	0.452445i
$45$	−0.965639	−	1.67254i	−0.143949	−	0.249327i
$46$	−0.449314	+	0.259412i	−0.0662478	+	0.0382482i
$47$	2.94386	+	10.9866i	0.429406	+	1.60256i	0.754110	+	0.656748i	$0.228069\pi$
$47$	2.94386	+	10.9866i	0.429406	+	1.60256i	−0.324704	+	0.945816i	$0.605265\pi$
$48$	−2.72978	−	2.72978i	−0.394010	−	0.394010i
$49$	3.14099	−	6.25573i	0.448714	−	0.893676i
$50$			0.893916i			0.126419i
$51$	1.47127	−	2.54831i	0.206018	−	0.356834i
$52$	2.00934	−	7.49897i	0.278646	−	1.03992i
$53$	−0.523042	+	1.95202i	−0.0718453	+	0.268130i	−0.992499	−	0.122249i	$-0.960989\pi$
$53$	−0.523042	+	1.95202i	−0.0718453	+	0.268130i	0.920654	+	0.390379i	$0.127656\pi$
$54$	1.11210	−	0.297987i	0.151338	−	0.0405509i
$55$	4.25005	−	4.25005i	0.573076	−	0.573076i
$56$	−1.23255	−	1.99806i	−0.164707	−	0.267001i
$57$	−2.37167			−0.314136
$58$	0.531144	+	1.98226i	0.0697426	+	0.260283i
$59$	−0.789913	−	1.36817i	−0.102838	−	0.178121i	0.810015	−	0.586409i	$-0.199459\pi$
$59$	−0.789913	−	1.36817i	−0.102838	−	0.178121i	−0.912853	+	0.408289i	$0.866126\pi$
$60$	−1.98560	−	0.532040i	−0.256340	−	0.0686860i
$61$	6.64778	+	3.83810i	0.851162	+	0.491418i	0.861043	−	0.508533i	$-0.169812\pi$
$61$	6.64778	+	3.83810i	0.851162	+	0.491418i	−0.00988107	+	0.999951i	$0.503145\pi$
$62$		−	1.42000i		−	0.180340i
$63$	−5.05437	+	0.147310i	−0.636791	+	0.0185593i
$64$	6.81395			0.851744
$65$	−1.04152	−	3.88700i	−0.129185	−	0.482123i
$66$	0.697190	+	1.20757i	0.0858182	+	0.148641i
$67$	−9.71822	−	2.60399i	−1.18727	−	0.318128i	−0.389463	−	0.921042i	$-0.627339\pi$
$67$	−9.71822	−	2.60399i	−1.18727	−	0.318128i	−0.797806	+	0.602914i	$0.794006\pi$
$68$	1.42288	+	5.31027i	0.172550	+	0.643965i
$69$	1.70390	+	1.70390i	0.205126	+	0.205126i
$70$	−0.528715	−	0.285048i	−0.0631935	−	0.0340697i
$71$	5.48294	+	5.48294i	0.650705	+	0.650705i	0.953163	−	0.302458i	$-0.0978071\pi$
$71$	5.48294	+	5.48294i	0.650705	+	0.650705i	−0.302458	+	0.953163i	$0.597807\pi$
$72$	−0.847921	+	1.46864i	−0.0999284	+	0.173081i
$73$	5.49080	−	3.17012i	0.642650	−	0.371034i	−0.142985	−	0.989725i	$-0.545670\pi$
$73$	5.49080	−	3.17012i	0.642650	−	0.371034i	0.785635	+	0.618691i	$0.212337\pi$
$74$	0.478753	−	0.276408i	0.0556539	−	0.0321318i
$75$	4.01033	−	1.07456i	0.463073	−	0.124080i
$76$	3.13323	−	3.13323i	0.359406	−	0.359406i
$77$	−4.51408	−	15.0755i	−0.514427	−	1.71801i
$78$	0.933563			0.105705
$79$	6.69120	−	1.79290i	0.752819	−	0.201717i	0.138051	−	0.990425i	$-0.455916\pi$
$79$	6.69120	−	1.79290i	0.752819	−	0.201717i	0.614768	+	0.788708i	$0.289250\pi$
$80$	3.23772	−	1.86930i	0.361988	−	0.208994i
$81$	0.193092	+	0.334445i	0.0214547	+	0.0371606i
$82$	0.890093	−	1.13013i	0.0982943	−	0.124802i
$83$	−18.1551			−1.99278			−0.996389	−	0.0849031i	$-0.972942\pi$
$83$	−18.1551			−1.99278			−0.996389	+	0.0849031i	$0.972942\pi$
$84$	−3.69326	+	3.91500i	−0.402968	+	0.427162i
$85$	2.01498	+	2.01498i	0.218555	+	0.218555i
$86$	−1.20415	+	2.08565i	−0.129847	+	0.224901i
$87$	8.25441	−	4.76568i	0.884965	−	0.510935i
$88$	−5.09792	−	1.36598i	−0.543440	−	0.145614i
$89$	0.595128	−	0.159464i	0.0630835	−	0.0169032i	−0.227139	−	0.973862i	$-0.572937\pi$
$89$	0.595128	−	0.159464i	0.0630835	−	0.0169032i	0.290223	+	0.956959i	$0.406271\pi$
$90$			0.433893i			0.0457363i
$91$	−10.2522	−	2.42929i	−1.07472	−	0.254659i
$92$	−4.50206			−0.469372
$93$	−6.37046	+	1.70696i	−0.660586	+	0.177004i
$94$	0.661385	−	2.46832i	0.0682166	−	0.254588i
$95$	0.594451	−	2.21852i	0.0609894	−	0.227615i
$96$	0.703756	+	2.62645i	0.0718268	+	0.268061i
$97$	5.98800	−	5.98800i	0.607989	−	0.607989i	−0.334431	−	0.942420i	$-0.608544\pi$
$97$	5.98800	−	5.98800i	0.607989	−	0.607989i	0.942420	+	0.334431i	$0.108544\pi$
$98$	−1.31386	+	0.864318i	−0.132720	+	0.0873093i
$99$	−8.03812	+	8.03812i	−0.807862	+	0.807862i
$100$	−3.87845	+	6.71767i	−0.387845	+	0.671767i
$101$	−5.72061	−	1.53283i	−0.569222	−	0.152523i	−0.0372824	−	0.999305i	$-0.511870\pi$
$101$	−5.72061	−	1.53283i	−0.569222	−	0.152523i	−0.531940	+	0.846782i	$0.678537\pi$
$102$	−0.572518	+	0.330543i	−0.0566877	+	0.0327287i
$103$	−2.57650	−	1.48754i	−0.253870	−	0.146572i	0.367665	−	0.929958i	$-0.380157\pi$
$103$	−2.57650	−	1.48754i	−0.253870	−	0.146572i	−0.621535	+	0.783386i	$0.713491\pi$
$104$	−2.49860	+	2.49860i	−0.245008	+	0.245008i
$105$	−0.643234	+	2.71460i	−0.0627733	+	0.264918i
$106$	0.321043	−	0.321043i	0.0311824	−	0.0311824i
$107$	−0.193470	+	0.335100i	−0.0187035	+	0.0323953i	−0.875226	−	0.483715i	$-0.839287\pi$
$107$	−0.193470	+	0.335100i	−0.0187035	+	0.0323953i	0.856522	+	0.516110i	$0.172621\pi$
$108$	9.65019	+	2.58576i	0.928590	+	0.248815i
$109$	10.5004	+	2.81357i	1.00576	+	0.269491i	0.723855	−	0.689952i	$-0.242369\pi$
$109$	10.5004	+	2.81357i	1.00576	+	0.269491i	0.281900	+	0.959444i	$0.409035\pi$
$110$	−1.30434	+	0.349496i	−0.124364	+	0.0333232i
$111$	−1.81554	−	1.81554i	−0.172323	−	0.172323i
$112$	−0.285164	−	9.78433i	−0.0269455	−	0.924532i
$113$	5.27736			0.496453			0.248226	−	0.968702i	$-0.420152\pi$
$113$	5.27736			0.496453			0.248226	+	0.968702i	$0.420152\pi$
$114$	0.461448	+	0.266417i	0.0432186	+	0.0249523i
$115$	−2.02095	+	1.16679i	−0.188454	+	0.108804i
$116$	−4.60896	+	17.2009i	−0.427932	+	1.59706i
$117$	1.96983	+	7.35150i	0.182111	+	0.679646i
$118$			0.354933i			0.0326743i
$119$	7.14739	−	2.14016i	0.655200	−	0.196188i
$120$	0.661586	+	0.661586i	0.0603943	+	0.0603943i
$121$	−21.1120	−	12.1890i	−1.91927	−	1.10809i
$122$	−0.862291	−	1.49353i	−0.0780681	−	0.135218i
$123$	−6.14003	−	2.63466i	−0.553628	−	0.237559i
$124$	6.16097	−	10.6711i	0.553271	−	0.958294i
$125$			9.07326i			0.811537i
$126$	0.999960	+	0.539112i	0.0890835	+	0.0480279i
$127$	16.5900			1.47213			0.736064	−	0.676912i	$-0.236682\pi$
$127$	16.5900			1.47213			0.736064	+	0.676912i	$0.236682\pi$
$128$	−5.83922	−	3.37128i	−0.516119	−	0.297982i
$129$	10.8042	+	2.89498i	0.951259	+	0.254889i
$130$	−0.233994	+	0.873278i	−0.0205226	+	0.0765915i
$131$	16.5753	+	9.56974i	1.44819	+	0.836112i	0.998374	−	0.0570090i	$-0.0181564\pi$
$131$	16.5753	+	9.56974i	1.44819	+	0.836112i	0.449816	+	0.893121i	$0.351490\pi$
$132$			12.0996i			1.05314i
$133$	−4.37426	−	4.12650i	−0.379296	−	0.357813i
$134$	1.59833	+	1.59833i	0.138074	+	0.138074i
$135$	5.00206	−	1.34030i	0.430509	−	0.115355i
$136$	0.647623	−	2.41696i	0.0555333	−	0.207253i
$137$	−7.82507	−	2.09672i	−0.668541	−	0.179135i	−0.0914435	−	0.995810i	$-0.529148\pi$
$137$	−7.82507	−	2.09672i	−0.668541	−	0.179135i	−0.577098	+	0.816675i	$0.695815\pi$
$138$	−0.140118	−	0.522926i	−0.0119276	−	0.0445144i
$139$	22.0414			1.86952			0.934762	−	0.355274i	$-0.115613\pi$
$139$	22.0414			1.86952			0.934762	+	0.355274i	$0.115613\pi$
$140$	−2.73649	−	4.43605i	−0.231275	−	0.374914i
$141$	−11.8685			−0.999512
$142$	−0.450881	−	1.68271i	−0.0378371	−	0.141210i
$143$	−20.5129	+	11.8431i	−1.71537	+	0.990371i
$144$	−6.12350	+	3.53540i	−0.510292	+	0.294617i
$145$	2.38900	+	8.91587i	0.198396	+	0.740423i
$146$	−1.42444			−0.117887
$147$	5.45692	+	4.85531i	0.450079	+	0.400459i
$148$	4.79703			0.394313
$149$	3.38118	+	12.6187i	0.276997	+	1.03377i	0.954491	+	0.298238i	$0.0963990\pi$
$149$	3.38118	+	12.6187i	0.276997	+	1.03377i	−0.677495	+	0.735528i	$0.736934\pi$
$150$	−0.900985	−	0.241418i	−0.0735651	−	0.0197117i
$151$	−3.52098	+	13.1405i	−0.286533	+	1.06936i	0.661178	+	0.750229i	$0.270057\pi$
$151$	−3.52098	+	13.1405i	−0.286533	+	1.06936i	−0.947712	+	0.319128i	$0.896610\pi$
$152$	−1.94807	+	0.521983i	−0.158009	+	0.0423384i
$153$	−3.81094	−	3.81094i	−0.308096	−	0.308096i
$154$	−0.815182	+	3.44026i	−0.0656893	+	0.277224i
$155$		−	6.38693i		−	0.513011i
$156$	7.01561	+	4.05047i	0.561699	+	0.324297i
$157$	−3.43433	+	12.8171i	−0.274089	+	1.02292i	0.682360	+	0.731016i	$0.260954\pi$
$157$	−3.43433	+	12.8171i	−0.274089	+	1.02292i	−0.956449	+	0.291899i	$0.905713\pi$
$158$	−1.50329	−	0.402804i	−0.119595	−	0.0320454i
$159$	−1.82620	−	1.05436i	−0.144827	−	0.0836158i
$160$	−2.63324			−0.208176
$161$	0.177996	+	6.10727i	0.0140281	+	0.481320i
$162$		−	0.0867625i		−	0.00681670i
$163$	−0.0468081	+	0.0810741i	−0.00366630	+	0.00635021i	−0.867853	−	0.496822i	$-0.834500\pi$
$163$	−0.0468081	+	0.0810741i	−0.00366630	+	0.00635021i	0.864186	+	0.503172i	$0.167834\pi$
$164$	11.5923	−	4.63096i	0.905204	−	0.361617i
$165$	3.13585	+	5.43146i	0.244126	+	0.422838i
$166$	3.53237	+	2.03941i	0.274165	+	0.158289i
$167$	−0.935928	−	0.935928i	−0.0724243	−	0.0724243i	0.669967	−	0.742391i	$-0.266308\pi$
$167$	−0.935928	−	0.935928i	−0.0724243	−	0.0724243i	−0.742391	+	0.669967i	$0.766308\pi$
$168$	2.34673	−	0.702687i	0.181054	−	0.0542135i
$169$			2.85837i			0.219874i
$170$	−0.165699	−	0.618397i	−0.0127085	−	0.0474289i
$171$	−1.12429	+	4.19589i	−0.0859763	+	0.320868i
$172$	−18.0981	+	10.4489i	−1.37997	+	0.796723i
$173$	−8.65272	−	4.99565i	−0.657854	−	0.379812i	0.133605	−	0.991035i	$-0.457345\pi$
$173$	−8.65272	−	4.99565i	−0.657854	−	0.379812i	−0.791459	+	0.611222i	$0.790678\pi$
$174$	−2.14138			−0.162337
$175$	9.26619	+	4.99571i	0.700458	+	0.377640i
$176$	−15.5603	−	15.5603i	−1.17290	−	1.17290i
$177$	1.59232	−	0.426661i	0.119686	−	0.0320698i
$178$	−0.133705	−	0.0358262i	−0.0100216	−	0.00268529i
$179$	2.96776	+	0.795209i	0.221821	+	0.0594367i	0.368018	−	0.929819i	$-0.380037\pi$
$179$	2.96776	+	0.795209i	0.221821	+	0.0594367i	−0.146197	+	0.989256i	$0.546703\pi$
$180$	−1.88254	+	3.26065i	−0.140316	+	0.243034i
$181$	−4.16558	+	4.16558i	−0.309625	+	0.309625i	−0.844764	−	0.535139i	$-0.820259\pi$
$181$	−4.16558	+	4.16558i	−0.309625	+	0.309625i	0.535139	+	0.844764i	$0.320259\pi$
$182$	1.72184	+	1.62432i	0.127631	+	0.120402i
$183$	−5.66380	+	5.66380i	−0.418681	+	0.418681i
$184$	1.77458	+	1.02455i	0.130824	+	0.0755311i
$185$	2.15336	−	1.24324i	0.158318	−	0.0914048i
$186$	1.43123	+	0.383496i	0.104943	+	0.0281193i
$187$	8.38650	−	14.5258i	0.613282	−	1.06224i
$188$	15.6796	−	15.6796i	1.14355	−	1.14355i
$189$	3.12618	−	13.1932i	0.227396	−	0.959664i
$190$	−0.364873	+	0.364873i	−0.0264707	+	0.0264707i
$191$	0.574245	+	2.14311i	0.0415509	+	0.155070i	0.983584	−	0.180449i	$-0.0577550\pi$
$191$	0.574245	+	2.14311i	0.0415509	+	0.155070i	−0.942033	+	0.335519i	$0.891088\pi$
$192$	−1.84023	+	6.86784i	−0.132807	+	0.495643i
$193$	4.23130	−	15.7914i	0.304576	−	1.13669i	−0.628734	−	0.777621i	$-0.716426\pi$
$193$	4.23130	−	15.7914i	0.304576	−	1.13669i	0.933310	−	0.359072i	$-0.116907\pi$
$194$	−1.83771	+	0.492414i	−0.131940	+	0.0353533i
$195$	4.19902			0.300698
$196$	−13.6235	+	0.794790i	−0.973108	+	0.0567707i
$197$		−	1.39955i		−	0.0997140i	−0.998756	−	0.0498570i	$-0.984123\pi$
$197$		−	1.39955i		−	0.0997140i	0.998756	−	0.0498570i	$-0.0158766\pi$
$198$	2.46690	−	0.661003i	0.175315	−	0.0469754i
$199$	−6.84687	−	1.83461i	−0.485362	−	0.130052i	0.00783637	−	0.999969i	$-0.497506\pi$
$199$	−6.84687	−	1.83461i	−0.485362	−	0.130052i	−0.493198	+	0.869917i	$0.664172\pi$
$200$	3.05754	−	1.76527i	0.216201	−	0.124824i
$201$	5.24916	−	9.09181i	0.370247	−	0.641287i
$202$	0.940852	+	0.940852i	0.0661981	+	0.0661981i
$203$	23.5161	+	5.57223i	1.65051	+	0.391094i
$204$	−5.73654			−0.401638
$205$	4.00350	−	5.08317i	0.279616	−	0.355024i
$206$	0.334201	+	0.578853i	0.0232849	+	0.0403306i
$207$	3.82222	−	2.20676i	0.265663	−	0.153380i
$208$	−14.2311	+	3.81322i	−0.986751	+	0.264399i
$209$	−13.5190			−0.935129
$210$	0.430091	−	0.455914i	0.0296791	−	0.0314610i
$211$	8.15456	−	8.15456i	0.561383	−	0.561383i	−0.368317	−	0.929700i	$-0.620066\pi$
$211$	8.15456	−	8.15456i	0.561383	−	0.561383i	0.929700	+	0.368317i	$0.120066\pi$
$212$	3.80551	−	1.01968i	0.261363	−	0.0700321i
$213$	−7.00706	+	4.04553i	−0.480116	+	0.277195i
$214$	0.0752856	−	0.0434662i	0.00514642	−	0.00297129i
$215$	−5.41608	+	9.38092i	−0.369373	+	0.639773i
$216$	−3.21537	−	3.21537i	−0.218778	−	0.218778i
$217$	−14.7195	−	7.93576i	−0.999224	−	0.538715i
$218$	−1.72697	−	1.72697i	−0.116965	−	0.116965i
$219$	1.71229	+	6.39037i	0.115706	+	0.431821i
$220$	−11.3183	−	3.03273i	−0.763080	−	0.204467i
$221$	−5.61492	−	9.72532i	−0.377700	−	0.654196i
$222$	0.149298	+	0.557188i	0.0100202	+	0.0373960i
$223$	−25.1036			−1.68106			−0.840530	−	0.541765i	$-0.817756\pi$
$223$	−25.1036			−1.68106			−0.840530	+	0.541765i	$0.817756\pi$
$224$	−3.27180	+	6.06863i	−0.218607	+	0.405478i
$225$		−	7.60434i		−	0.506956i
$226$	−1.02680	−	0.592822i	−0.0683016	−	0.0394340i
$227$	6.01784	+	1.61248i	0.399418	+	0.107024i	0.452936	−	0.891543i	$-0.350377\pi$
$227$	6.01784	+	1.61248i	0.399418	+	0.107024i	−0.0535177	+	0.998567i	$0.517043\pi$
$228$	2.31182	+	4.00419i	0.153104	+	0.265184i
$229$	−0.723952	−	2.70182i	−0.0478401	−	0.178542i	0.937872	−	0.346982i	$-0.112794\pi$
$229$	−0.723952	−	2.70182i	−0.0478401	−	0.178542i	−0.985712	+	0.168441i	$0.946127\pi$
$230$	0.524278			0.0345699
$231$	16.4138	−	0.478380i	1.07995	−	0.0314751i
$232$	5.73120	−	5.73120i	0.376272	−	0.376272i
$233$	−3.65304	+	0.978828i	−0.239318	+	0.0641252i	−0.376485	−	0.926423i	$-0.622867\pi$
$233$	−3.65304	+	0.978828i	−0.239318	+	0.0641252i	0.137166	+	0.990548i	$0.456201\pi$
$234$	0.442553	−	1.65163i	0.0289306	−	0.107971i
$235$	2.97481	−	11.1021i	0.194055	−	0.724223i
$236$	−1.53996	+	2.66728i	−0.100243	+	0.173625i
$237$			7.22832i			0.469530i
$238$	−1.63105	−	0.386484i	−0.105726	−	0.0250521i
$239$	6.62216	+	6.62216i	0.428352	+	0.428352i	0.888067	−	0.459715i	$-0.152048\pi$
$239$	6.62216	+	6.62216i	0.428352	+	0.428352i	−0.459715	+	0.888067i	$0.652048\pi$
$240$	1.00967	+	3.76816i	0.0651742	+	0.243234i
$241$	18.7980	−	10.8530i	1.21088	−	0.699104i	0.247931	−	0.968778i	$-0.420249\pi$
$241$	18.7980	−	10.8530i	1.21088	−	0.699104i	0.962952	+	0.269674i	$0.0869160\pi$
$242$	2.73846	+	4.74315i	0.176035	+	0.304901i
$243$	−15.2393	+	4.08336i	−0.977602	+	0.261948i
$244$		−	14.9649i		−	0.958032i
$245$	−5.90953	+	3.88757i	−0.377546	+	0.248368i
$246$	0.898686	+	1.20234i	0.0572981	+	0.0766587i
$247$	−4.52561	+	7.83859i	−0.287958	+	0.498757i
$248$	−4.85695	+	2.80416i	−0.308416	+	0.178064i
$249$	4.90311	−	18.2986i	0.310722	−	1.15963i
$250$	1.01923	−	1.76535i	0.0644616	−	0.111651i
$251$			14.4612i			0.912786i	0.889778	+	0.456393i	$0.150859\pi$
$251$			14.4612i			0.912786i	−0.889778	+	0.456393i	$0.849141\pi$
$252$	5.17552	+	8.38990i	0.326027	+	0.528514i
$253$	9.71257	+	9.71257i	0.610624	+	0.610624i
$254$	−3.22787	−	1.86361i	−0.202534	−	0.116933i
$255$	−2.57510	+	1.48673i	−0.161259	+	0.0931028i
$256$	−6.05654	−	10.4902i	−0.378534	−	0.655640i
$257$	15.4700	−	4.14516i	0.964990	−	0.258568i	0.258279	−	0.966070i	$-0.416845\pi$
$257$	15.4700	−	4.14516i	0.964990	−	0.258568i	0.706711	+	0.707502i	$0.250178\pi$
$258$	−1.77694	−	1.77694i	−0.110627	−	0.110627i
$259$	−0.189658	−	6.50740i	−0.0117848	−	0.404350i
$260$	−5.54734	+	5.54734i	−0.344032	+	0.344032i
$261$	−4.51832	−	16.8626i	−0.279677	−	1.04377i
$262$	−2.15000	−	3.72390i	−0.132827	−	0.230064i
$263$	7.23581	+	1.93883i	0.446179	+	0.119553i	0.474911	−	0.880034i	$-0.342480\pi$
$263$	7.23581	+	1.93883i	0.446179	+	0.119553i	−0.0287317	+	0.999587i	$0.509147\pi$
$264$	2.75357	−	4.76932i	0.169471	−	0.293532i
$265$	1.44400	−	1.44400i	0.0887042	−	0.0887042i
$266$	0.387541	+	1.29425i	0.0237617	+	0.0793557i
$267$			0.642901i			0.0393449i
$268$	5.07654	+	18.9459i	0.310099	+	1.15731i
$269$	−3.54672	−	6.14311i	−0.216248	−	0.374552i	0.737410	−	0.675445i	$-0.236049\pi$
$269$	−3.54672	−	6.14311i	−0.216248	−	0.374552i	−0.953658	+	0.300893i	$0.902715\pi$
$270$	−1.12379	−	0.301120i	−0.0683919	−	0.0183256i
$271$	13.3970	−	23.2043i	0.813811	−	1.40956i	−0.0963668	−	0.995346i	$-0.530722\pi$
$271$	13.3970	−	23.2043i	0.813811	−	1.40956i	0.910178	−	0.414217i	$-0.135944\pi$
$272$	7.37726	−	7.37726i	0.447312	−	0.447312i
$273$	5.21729	−	9.67717i	0.315765	−	0.585689i
$274$	1.28697	+	1.28697i	0.0777485	+	0.0777485i
$275$	22.8597	−	6.12523i	1.37849	−	0.369365i
$276$	1.21586	−	4.53766i	0.0731863	−	0.273135i
$277$	14.6983	+	25.4582i	0.883135	+	1.52964i	0.847836	+	0.530259i	$0.177905\pi$
$277$	14.6983	+	25.4582i	0.883135	+	1.52964i	0.0352994	+	0.999377i	$0.488762\pi$
$278$	−4.28851	−	2.47597i	−0.257208	−	0.148499i
$279$			12.0796i			0.723187i
$280$	0.0691119	+	2.37131i	0.00413023	+	0.141713i
$281$	−4.77450	+	4.77450i	−0.284823	+	0.284823i	−0.835029	−	0.550206i	$-0.814549\pi$
$281$	−4.77450	+	4.77450i	−0.284823	+	0.284823i	0.550206	+	0.835029i	$0.314549\pi$
$282$	2.30922	+	1.33323i	0.137512	+	0.0793927i
$283$	4.98000	+	8.62562i	0.296030	+	0.512740i	0.975224	−	0.221219i	$-0.0710037\pi$
$283$	4.98000	+	8.62562i	0.296030	+	0.512740i	−0.679194	+	0.733959i	$0.737670\pi$
$284$	3.91249	−	14.6016i	0.232164	−	0.866447i
$285$	2.07552	+	1.19830i	0.122943	+	0.0709814i
$286$	5.32149			0.314667
$287$	−6.74045	−	15.5424i	−0.397876	−	0.917439i
$288$	4.98025			0.293464
$289$	−7.83561	−	4.52389i	−0.460918	−	0.266111i
$290$	0.536728	−	2.00309i	0.0315177	−	0.117626i
$291$	4.41818	+	7.65252i	0.258999	+	0.448599i
$292$	−10.7045	−	6.18022i	−0.626431	−	0.361670i
$293$	18.7884	−	18.7884i	1.09763	−	1.09763i	0.102942	−	0.994687i	$-0.467174\pi$
$293$	18.7884	−	18.7884i	1.09763	−	1.09763i	0.994687	−	0.102942i	$-0.0328257\pi$
$294$	−0.516322	−	1.55767i	−0.0301125	−	0.0908453i
$295$			1.59643i			0.0929480i
$296$	−1.89085	−	1.09168i	−0.109903	−	0.0634526i
$297$	−15.2405	−	26.3974i	−0.884346	−	1.53173i
$298$	0.759636	−	2.83500i	0.0440045	−	0.164227i
$299$	8.88291	−	2.38017i	0.513712	−	0.137649i
$300$	−5.72334	−	5.72334i	−0.330437	−	0.330437i
$301$	14.8900	+	24.1378i	0.858247	+	1.39128i
$302$	2.16118	−	2.16118i	0.124362	−	0.124362i
$303$	3.08991	−	5.35188i	0.177511	−	0.307458i
$304$	−8.12247	−	2.17641i	−0.465856	−	0.124826i
$305$	−3.87845	−	6.71767i	−0.222079	−	0.384653i
$306$	0.313387	+	1.16957i	0.0179151	+	0.0668601i
$307$			25.4638i			1.45330i	0.687010	+	0.726648i	$0.258923\pi$
$307$			25.4638i			1.45330i	−0.687010	+	0.726648i	$0.741077\pi$
$308$	−21.0523	+	22.3163i	−1.19957	+	1.27159i
$309$	2.19514	−	2.19514i	0.124877	−	0.124877i
$310$	−0.717463	+	1.24268i	−0.0407492	+	0.0705796i
$311$	0.413938	+	0.110914i	0.0234722	+	0.00628937i	0.270536	−	0.962710i	$-0.412799\pi$
$311$	0.413938	+	0.110914i	0.0234722	+	0.00628937i	−0.247064	+	0.968999i	$0.579466\pi$
$312$	−1.84357	−	3.19315i	−0.104371	−	0.180776i
$313$	3.11671	+	11.6317i	0.176167	+	0.657465i	0.996350	+	0.0853631i	$0.0272050\pi$
$313$	3.11671	+	11.6317i	0.176167	+	0.657465i	−0.820183	+	0.572102i	$0.806128\pi$
$314$	2.10799	−	2.10799i	0.118961	−	0.118961i
$315$	4.49766	+	2.42484i	0.253415	+	0.136624i
$316$	−9.54935	−	9.54935i	−0.537193	−	0.537193i
$317$	−7.58953	+	2.03361i	−0.426271	+	0.114219i	−0.465575	−	0.885008i	$-0.654152\pi$
$317$	−7.58953	+	2.03361i	−0.426271	+	0.114219i	0.0393045	+	0.999227i	$0.487486\pi$
$318$	0.236878	+	0.410285i	0.0132835	+	0.0230076i
$319$	47.0518	−	27.1653i	2.63439	−	1.52097i
$320$	−5.96309	−	3.44279i	−0.333347	−	0.192458i
$321$	−0.285500	−	0.285500i	−0.0159350	−	0.0159350i
$322$	0.651416	−	1.20826i	0.0363020	−	0.0673339i
$323$		−	6.40947i		−	0.356632i
$324$	0.376438	−	0.652010i	0.0209132	−	0.0362228i
$325$	4.10095	−	15.3050i	0.227480	−	0.848966i
$326$	0.0182146	−	0.0105162i	0.00100881	−	0.000582439i
$327$	−5.67164	+	9.82357i	−0.313643	+	0.543245i
$328$	−5.62322	−	0.812716i	−0.310490	−	0.0448747i
$329$	−21.8900	−	20.6502i	−1.20684	−	1.13848i
$330$		−	1.40904i		−	0.0775651i
$331$	−24.1020	+	6.45812i	−1.32477	+	0.354971i	−0.850762	−	0.525551i	$-0.823859\pi$
$331$	−24.1020	+	6.45812i	−1.32477	+	0.354971i	−0.474006	+	0.880522i	$0.657193\pi$
$332$	17.6969	+	30.6519i	0.971243	+	1.68224i
$333$	−4.07264	+	2.35134i	−0.223180	+	0.128853i
$334$	0.0769646	+	0.287236i	0.00421132	+	0.0157168i
$335$	7.18902	+	7.18902i	0.392778	+	0.392778i
$336$	9.93871	+	2.35502i	0.542201	+	0.128477i
$337$			6.98653i			0.380581i	0.981728	+	0.190290i	$0.0609430\pi$
$337$			6.98653i			0.380581i	−0.981728	+	0.190290i	$0.939057\pi$
$338$	0.321089	−	0.556142i	0.0174649	−	0.0302502i
$339$	−1.42525	+	5.31910i	−0.0774088	+	0.288894i
$340$	1.43784	−	5.36610i	0.0779779	−	0.291017i
$341$	−36.3129	+	9.73001i	−1.96645	+	0.526910i
$342$	0.690086	−	0.690086i	0.0373156	−	0.0373156i
$343$	1.61680	+	18.4496i	0.0872990	+	0.996182i
$344$	9.51164			0.512833
$345$	−0.630228	−	2.35204i	−0.0339303	−	0.126630i
$346$	1.12235	+	1.94397i	0.0603381	+	0.104509i
$347$	−13.8765	−	3.71820i	−0.744930	−	0.199603i	−0.133662	−	0.991027i	$-0.542674\pi$
$347$	−13.8765	−	3.71820i	−0.744930	−	0.199603i	−0.611268	+	0.791424i	$0.709340\pi$
$348$	−16.0922	−	9.29082i	−0.862631	−	0.498040i
$349$			17.9068i			0.958527i	0.877671	+	0.479264i	$0.159096\pi$
$349$			17.9068i			0.958527i	−0.877671	+	0.479264i	$0.840904\pi$
$350$	−1.24171	−	2.01290i	−0.0663720	−	0.107594i
$351$	−20.4076			−1.08928
$352$	4.01155	+	14.9713i	0.213816	+	0.797973i
$353$	−2.44582	−	4.23628i	−0.130178	−	0.225474i	0.793567	−	0.608483i	$-0.208221\pi$
$353$	−2.44582	−	4.23628i	−0.130178	−	0.225474i	−0.923745	+	0.383008i	$0.874888\pi$
$354$	−0.357740	−	0.0958562i	−0.0190137	−	0.00509470i
$355$	−2.02799	−	7.56858i	−0.107635	−	0.401698i
$356$	−0.849338	−	0.849338i	−0.0450148	−	0.0450148i
$357$	0.226803	+	7.78190i	0.0120037	+	0.411862i
$358$	−0.488099	−	0.488099i	−0.0257968	−	0.0257968i
$359$	10.0324	−	17.3766i	0.529489	−	0.917103i	−0.469919	−	0.882710i	$-0.655717\pi$
$359$	10.0324	−	17.3766i	0.529489	−	0.917103i	0.999408	−	0.0343931i	$-0.0109498\pi$
$360$	1.48408	−	0.856835i	0.0782179	−	0.0451592i
$361$	11.9806	−	6.91699i	0.630557	−	0.364052i
$362$	1.27841	−	0.342550i	0.0671920	−	0.0180040i
$363$	17.9871	−	17.9871i	0.944077	−	0.944077i
$364$	5.89197	+	19.6771i	0.308823	+	1.03136i
$365$	−6.40689			−0.335352
$366$	1.73822	−	0.465754i	0.0908582	−	0.0243454i
$367$	−2.05213	+	1.18480i	−0.107120	+	0.0618458i	−0.552603	−	0.833445i	$-0.686365\pi$
$367$	−2.05213	+	1.18480i	−0.107120	+	0.0618458i	0.445483	+	0.895290i	$0.353032\pi$
$368$	4.27188	+	7.39911i	0.222687	+	0.385705i
$369$	−7.57182	+	9.61381i	−0.394173	+	0.500475i
$370$	−0.558628			−0.0290417
$371$	−1.53371	−	5.12205i	−0.0796262	−	0.265923i
$372$	9.09162	+	9.09162i	0.471378	+	0.471378i
$373$	−9.03542	+	15.6498i	−0.467836	+	0.810317i	−0.999325	−	0.0367492i	$-0.988300\pi$
$373$	−9.03542	+	15.6498i	−0.467836	+	0.810317i	0.531488	+	0.847066i	$0.321633\pi$
$374$	−3.26347	+	1.88416i	−0.168750	+	0.0974277i
$375$	−9.14501	−	2.45040i	−0.472246	−	0.126538i
$376$	−9.74870	+	2.61216i	−0.502751	+	0.134712i
$377$		−	36.3754i		−	1.87343i
$378$	−2.09028	+	2.21578i	−0.107512	+	0.113968i
$379$	−4.97927			−0.255768			−0.127884	−	0.991789i	$-0.540819\pi$
$379$	−4.97927			−0.255768			−0.127884	+	0.991789i	$0.540819\pi$
$380$	−4.32506	+	1.15890i	−0.221871	+	0.0594502i
$381$	−4.48044	+	16.7212i	−0.229540	+	0.856654i
$382$	0.129013	−	0.481485i	0.00660090	−	0.0246349i
$383$	−8.62054	−	32.1723i	−0.440489	−	1.64393i	−0.727579	−	0.686024i	$-0.759354\pi$
$383$	−8.62054	−	32.1723i	−0.440489	−	1.64393i	0.287089	−	0.957904i	$-0.407312\pi$
$384$	4.97492	−	4.97492i	0.253876	−	0.253876i
$385$	−3.66656	+	15.4738i	−0.186865	+	0.788615i
$386$	−2.59717	+	2.59717i	−0.132193	+	0.132193i
$387$	10.2434	−	17.7421i	0.520703	−	0.901884i
$388$	−15.9466	−	4.27289i	−0.809568	−	0.216923i
$389$	−7.71899	+	4.45656i	−0.391368	+	0.225957i	−0.682753	−	0.730649i	$-0.739217\pi$
$389$	−7.71899	+	4.45656i	−0.391368	+	0.225957i	0.291385	+	0.956606i	$0.405884\pi$
$390$	−0.816989	−	0.471689i	−0.0413698	−	0.0238849i
$391$	−4.60480	+	4.60480i	−0.232875	+	0.232875i
$392$	5.55086	+	2.78708i	0.280361	+	0.140769i
$393$	−14.1219	+	14.1219i	−0.712354	+	0.712354i
$394$	−0.157216	+	0.272306i	−0.00792043	+	0.0137186i
$395$	−6.76154	−	1.81175i	−0.340210	−	0.0911590i
$396$	21.4063	+	5.73581i	1.07571	+	0.288235i
$397$	5.17905	−	1.38772i	0.259929	−	0.0696477i	−0.126501	−	0.991966i	$-0.540375\pi$
$397$	5.17905	−	1.38772i	0.259929	−	0.0696477i	0.386430	+	0.922319i	$0.373708\pi$
$398$	1.12608	+	1.12608i	0.0564455	+	0.0564455i
$399$	5.34048	−	3.29441i	0.267358	−	0.164927i
$400$	14.7206			0.736030
$401$	11.5591	+	6.67365i	0.577234	+	0.333266i	0.760033	−	0.649884i	$-0.225183\pi$
$401$	11.5591	+	6.67365i	0.577234	+	0.333266i	−0.182799	+	0.983150i	$0.558516\pi$
$402$	−2.04262	+	1.17931i	−0.101877	+	0.0588186i
$403$	−6.51442	+	24.3121i	−0.324506	+	1.21107i
$404$	2.98830	+	11.1525i	0.148673	+	0.554857i
$405$		−	0.390244i		−	0.0193914i
$406$	−3.94950	−	3.72580i	−0.196010	−	0.184908i
$407$	−10.3489	−	10.3489i	−0.512977	−	0.512977i
$408$	2.26117	+	1.30549i	0.111945	+	0.0646314i
$409$	−2.19561	−	3.80291i	−0.108566	−	0.188042i	0.806624	−	0.591066i	$-0.201293\pi$
$409$	−2.19561	−	3.80291i	−0.108566	−	0.188042i	−0.915190	+	0.403024i	$0.867959\pi$
$410$	−1.34995	+	0.539289i	−0.0666695	+	0.0266336i
$411$	4.22660	−	7.32069i	0.208483	−	0.361103i
$412$			5.80001i			0.285746i
$413$	3.67918	+	1.98357i	0.181041	+	0.0976052i
$414$	−0.991568			−0.0487329
$415$	15.8880	+	9.17297i	0.779914	+	0.450283i
$416$	10.0236	+	2.68580i	0.491445	+	0.131682i
$417$	−5.95267	+	22.2157i	−0.291503	+	1.08791i
$418$	2.63035	+	1.51863i	0.128654	+	0.0742787i
$419$			31.4721i			1.53751i	0.639542	+	0.768756i	$0.279124\pi$
$419$			31.4721i			1.53751i	−0.639542	+	0.768756i	$0.720876\pi$
$420$	5.21016	−	1.56009i	0.254230	−	0.0761247i
$421$	4.93580	+	4.93580i	0.240556	+	0.240556i	0.817080	−	0.576524i	$-0.195591\pi$
$421$	4.93580	+	4.93580i	0.240556	+	0.240556i	−0.576524	+	0.817080i	$0.695591\pi$
$422$	−2.50263	+	0.670578i	−0.121826	+	0.0326432i
$423$	−5.62626	+	20.9975i	−0.273558	+	1.02093i
$424$	−1.73207	−	0.464108i	−0.0841169	−	0.0225391i
$425$	2.90402	+	10.8379i	0.140866	+	0.525717i
$426$	1.81779			0.0880721
$427$	−20.3007	+	0.591664i	−0.982420	+	0.0286326i
$428$	0.754350			0.0364629
$429$	−6.39690	−	23.8735i	−0.308845	−	1.15263i
$430$	2.10757	−	1.21681i	0.101636	−	0.0586797i
$431$	6.73722	−	3.88973i	0.324520	−	0.187362i	−0.328885	−	0.944370i	$-0.606673\pi$
$431$	6.73722	−	3.88973i	0.324520	−	0.187362i	0.653406	+	0.757008i	$0.273340\pi$
$432$	−4.90711	−	18.3136i	−0.236094	−	0.881113i
$433$	2.63391			0.126578			0.0632888	−	0.997995i	$-0.479841\pi$
$433$	2.63391			0.126578			0.0632888	+	0.997995i	$0.479841\pi$
$434$	1.97247	+	3.19752i	0.0946816	+	0.153486i
$435$	−9.63157			−0.461799
$436$	−5.48513	−	20.4708i	−0.262690	−	0.980373i
$437$	5.06995	+	1.35849i	0.242529	+	0.0649854i
$438$	0.384694	−	1.43570i	0.0183814	−	0.0686004i
$439$	−0.472906	+	0.126715i	−0.0225706	+	0.00604777i	−0.270087	−	0.962836i	$-0.587052\pi$
$439$	−0.472906	+	0.126715i	−0.0225706	+	0.00604777i	0.247516	+	0.968884i	$0.420386\pi$
$440$	3.77117	+	3.77117i	0.179783	+	0.179783i
$441$	11.1767	−	7.35257i	0.532224	−	0.350122i
$442$			2.52296i			0.120005i
$443$	−15.6439	−	9.03204i	−0.743266	−	0.429125i	0.0799894	−	0.996796i	$-0.474511\pi$
$443$	−15.6439	−	9.03204i	−0.743266	−	0.429125i	−0.823256	+	0.567671i	$0.807845\pi$
$444$	−1.29552	+	4.83496i	−0.0614828	+	0.229457i
$445$	−0.601385	−	0.161141i	−0.0285084	−	0.00763880i
$446$	4.88432	+	2.81996i	0.231279	+	0.133529i
$447$	−13.6317			−0.644755
$448$	−15.3435	+	9.46503i	−0.724912	+	0.447180i
$449$			29.7355i			1.40331i	0.712518	+	0.701654i	$0.247555\pi$
$449$			29.7355i			1.40331i	−0.712518	+	0.701654i	$0.752445\pi$
$450$	−0.854219	+	1.47955i	−0.0402683	+	0.0697467i
$451$	−34.9994	−	15.0181i	−1.64806	−	0.707173i
$452$	−5.14418	−	8.90998i	−0.241962	−	0.419090i
$453$	−12.2935	−	7.09765i	−0.577598	−	0.333477i
$454$	−0.989736	−	0.989736i	−0.0464506	−	0.0464506i
$455$	7.74457	+	7.30592i	0.363071	+	0.342507i
$456$		−	2.10444i		−	0.0985496i
$457$	1.25373	+	4.67898i	0.0586470	+	0.218874i	0.989030	−	0.147716i	$-0.0471921\pi$
$457$	1.25373	+	4.67898i	0.0586470	+	0.218874i	−0.930383	+	0.366589i	$0.880525\pi$
$458$	−0.162647	+	0.607008i	−0.00760001	+	0.0283636i
$459$	12.5152	−	7.22566i	0.584160	−	0.337265i
$460$	3.93989	+	2.27469i	0.183698	+	0.106058i
$461$	34.0627			1.58646			0.793229	−	0.608924i	$-0.208398\pi$
$461$	34.0627			1.58646			0.793229	+	0.608924i	$0.208398\pi$
$462$	−3.24731	−	1.75073i	−0.151079	−	0.0814515i
$463$	23.0040	+	23.0040i	1.06908	+	1.06908i	0.997429	+	0.0716550i	$0.0228281\pi$
$463$	23.0040	+	23.0040i	1.06908	+	1.06908i	0.0716550	+	0.997429i	$0.477172\pi$
$464$	32.6429	−	8.74663i	1.51541	−	0.406052i
$465$	6.43744	+	1.72491i	0.298529	+	0.0799906i
$466$	0.820713	+	0.219909i	0.0380188	+	0.0101871i
$467$	−8.04231	+	13.9297i	−0.372154	+	0.644589i	−0.989897	−	0.141791i	$-0.954714\pi$
$467$	−8.04231	+	13.9297i	−0.372154	+	0.644589i	0.617743	+	0.786380i	$0.288047\pi$
$468$	10.4917	−	10.4917i	0.484979	−	0.484979i
$469$	25.5004	−	7.63564i	1.17750	−	0.352581i
$470$	−1.82593	+	1.82593i	−0.0842240	+	0.0842240i
$471$	−11.9909	−	6.92297i	−0.552514	−	0.318994i
$472$	1.21401	−	0.700909i	0.0558793	−	0.0322620i
$473$	61.5862	+	16.5020i	2.83174	+	0.758762i
$474$	0.811979	−	1.40639i	0.0372954	−	0.0645975i
$475$	6.39473	−	6.39473i	0.293410	−	0.293410i
$476$	−10.5803	−	9.98106i	−0.484948	−	0.457481i
$477$	−2.73104	+	2.73104i	−0.125046	+	0.125046i
$478$	−0.544563	−	2.03234i	−0.0249077	−	0.0929569i
$479$	−8.43136	+	31.4663i	−0.385239	+	1.43773i	0.452552	+	0.891738i	$0.350514\pi$
$479$	−8.43136	+	31.4663i	−0.385239	+	1.43773i	−0.837790	+	0.545992i	$0.816153\pi$
$480$	0.711154	−	2.65406i	0.0324596	−	0.121141i
$481$	−9.46490	+	2.53611i	−0.431562	+	0.115637i
$482$	−4.87660			−0.222123
$483$	−6.20363	−	1.46997i	−0.282275	−	0.0668861i
$484$			47.5256i			2.16025i
$485$	−8.26575	+	2.21480i	−0.375329	+	0.100569i
$486$	3.42375	+	0.917392i	0.155305	+	0.0416138i
$487$	14.5784	−	8.41684i	0.660610	−	0.381404i	−0.131899	−	0.991263i	$-0.542107\pi$
$487$	14.5784	−	8.41684i	0.660610	−	0.381404i	0.792510	+	0.609860i	$0.208774\pi$
$488$	−3.40564	+	5.89874i	−0.154166	+	0.267023i
$489$	−0.0690738	−	0.0690738i	−0.00312363	−	0.00312363i
$490$	1.58650	−	0.0925556i	0.0716707	−	0.00418124i
$491$	14.6583			0.661522			0.330761	−	0.943715i	$-0.392695\pi$
$491$	14.6583			0.661522			0.330761	+	0.943715i	$0.392695\pi$
$492$	1.53688	+	12.9346i	0.0692879	+	0.583138i
$493$	12.8793	+	22.3076i	0.580055	+	1.00468i
$494$	1.76106	−	1.01675i	0.0792340	−	0.0457458i
$495$	11.0957	−	2.97309i	0.498715	−	0.133630i
$496$	−23.3839			−1.04997
$497$	−19.9625	−	4.73019i	−0.895441	−	0.212178i
$498$	−3.00952	+	3.00952i	−0.134860	+	0.134860i
$499$	−21.6480	+	5.80056i	−0.969096	+	0.259669i	−0.708446	−	0.705765i	$-0.750604\pi$
$499$	−21.6480	+	5.80056i	−0.969096	+	0.259669i	−0.260650	+	0.965433i	$0.583937\pi$
$500$	15.3187	−	8.84427i	0.685074	−	0.395528i
$501$	1.19609	−	0.690565i	0.0534375	−	0.0308522i
$502$	1.62448	−	2.81367i	0.0725039	−	0.125580i
$503$	−7.49230	−	7.49230i	−0.334065	−	0.334065i	0.520063	−	0.854128i	$-0.325909\pi$
$503$	−7.49230	−	7.49230i	−0.334065	−	0.334065i	−0.854128	+	0.520063i	$0.825909\pi$
$504$	−0.130712	−	4.48487i	−0.00582235	−	0.199772i
$505$	4.23181	+	4.23181i	0.188313	+	0.188313i
$506$	−0.798698	−	2.98078i	−0.0355065	−	0.132512i
$507$	−2.88097	−	0.771953i	−0.127948	−	0.0342837i
$508$	−16.1713	−	28.0096i	−0.717487	−	1.24272i
$509$	−4.19581	−	15.6590i	−0.185976	−	0.694072i	−0.994419	−	0.105498i	$-0.966356\pi$
$509$	−4.19581	−	15.6590i	−0.185976	−	0.694072i	0.808443	−	0.588574i	$-0.200310\pi$
$510$	0.668037			0.0295812
$511$	−7.96056	+	14.7655i	−0.352154	+	0.653186i
$512$			16.2065i			0.716233i
$513$	−10.0872	−	5.82386i	−0.445362	−	0.257130i
$514$	−3.47558	−	0.931278i	−0.153301	−	0.0410769i
$515$	1.50318	+	2.60359i	0.0662382	+	0.114728i
$516$	−5.64384	−	21.0631i	−0.248456	−	0.927252i
$517$	−67.6530			−2.97538
$518$	−0.694095	+	1.28743i	−0.0304968	+	0.0565663i
$519$	7.37198	−	7.37198i	0.323594	−	0.323594i
$520$	3.44903	−	0.924165i	0.151250	−	0.0405273i
$521$	10.2702	−	38.3289i	0.449945	−	1.67922i	−0.252592	−	0.967573i	$-0.581283\pi$
$521$	10.2702	−	38.3289i	0.449945	−	1.67922i	0.702538	−	0.711646i	$-0.252050\pi$
$522$	−1.01511	+	3.78846i	−0.0444303	+	0.165816i
$523$	−14.7194	+	25.4948i	−0.643635	+	1.11481i	0.340980	+	0.940071i	$0.389241\pi$
$523$	−14.7194	+	25.4948i	−0.643635	+	1.11481i	−0.984615	+	0.174738i	$0.944092\pi$
$524$		−	37.3129i		−	1.63002i
$525$	−7.53772	+	7.99029i	−0.328973	+	0.348725i
$526$	−1.19005	−	1.19005i	−0.0518888	−	0.0518888i
$527$	−4.61307	−	17.2162i	−0.200949	−	0.749951i
$528$	19.8857	−	11.4810i	0.865414	−	0.499647i
$529$	8.83354	+	15.3001i	0.384067	+	0.665224i
$530$	−0.443163	+	0.118745i	−0.0192498	+	0.00515796i
$531$		−	3.01934i		−	0.131028i
$532$	−2.70307	+	11.4076i	−0.117193	+	0.494581i
$533$	−20.4241	+	15.2659i	−0.884667	+	0.661240i
$534$	0.0722190	−	0.125087i	0.00312522	−	0.00541304i
$535$	0.338623	−	0.195504i	0.0146399	−	0.00845238i
$536$	2.31058	−	8.62321i	0.0998020	−	0.372466i
$537$	−1.60300	+	2.77647i	−0.0691744	+	0.119814i
$538$			1.59366i			0.0687074i
$539$	31.1055	+	27.6762i	1.33981	+	1.19210i
$540$	−7.13870	−	7.13870i	−0.307201	−	0.307201i
$541$	−16.8888	−	9.75075i	−0.726106	−	0.419218i	0.0908899	−	0.995861i	$-0.471029\pi$
$541$	−16.8888	−	9.75075i	−0.726106	−	0.419218i	−0.816996	+	0.576643i	$0.804362\pi$
$542$	−5.21323	+	3.00986i	−0.223927	+	0.129284i
$543$	−3.07353	−	5.32351i	−0.131898	−	0.228454i
$544$	−7.09801	+	1.90191i	−0.304325	+	0.0815435i
$545$	−7.76763	−	7.76763i	−0.332729	−	0.332729i
$546$	−2.10218	+	1.29678i	−0.0899648	+	0.0554971i
$547$	12.2705	−	12.2705i	0.524650	−	0.524650i	−0.394322	−	0.918972i	$-0.629021\pi$
$547$	12.2705	−	12.2705i	0.524650	−	0.524650i	0.918972	+	0.394322i	$0.129021\pi$
$548$	4.08761	+	15.2552i	0.174614	+	0.651669i
$549$	7.33532	+	12.7051i	0.313064	+	0.542242i
$550$	−5.13579	−	1.37613i	−0.218991	−	0.0586784i
$551$	10.3807	−	17.9799i	0.442232	−	0.765969i
$552$	−1.51191	+	1.51191i	−0.0643513	+	0.0643513i
$553$	−12.5766	+	13.3317i	−0.534812	+	0.566923i
$554$		−	6.60442i		−	0.280595i
$555$	0.671519	+	2.50614i	0.0285044	+	0.106380i
$556$	−21.4851	−	37.2133i	−0.911171	−	1.57819i
$557$	−5.79823	−	1.55363i	−0.245679	−	0.0658295i	0.133878	−	0.990998i	$-0.457257\pi$
$557$	−5.79823	−	1.55363i	−0.245679	−	0.0658295i	−0.379557	+	0.925168i	$0.623924\pi$
$558$	1.35694	−	2.35029i	0.0574438	−	0.0994956i
$559$	30.1847	−	30.1847i	1.27668	−	1.27668i
$560$	−4.69404	+	8.70664i	−0.198359	+	0.367923i
$561$	12.3758	+	12.3758i	0.522506	+	0.522506i
$562$	1.46529	−	0.392624i	0.0618096	−	0.0165618i
$563$	5.82425	−	21.7364i	0.245463	−	0.916080i	−0.727687	−	0.685909i	$-0.759405\pi$
$563$	5.82425	−	21.7364i	0.245463	−	0.916080i	0.973150	−	0.230171i	$-0.0739286\pi$
$564$	11.5690	+	20.0381i	0.487143	+	0.843757i
$565$	−4.61838	−	2.66642i	−0.194297	−	0.112177i
$566$		−	2.23768i		−	0.0940565i
$567$	−0.899367	−	0.484879i	−0.0377698	−	0.0203630i
$568$	−4.86515	+	4.86515i	−0.204137	+	0.204137i
$569$	−14.5469	−	8.39867i	−0.609839	−	0.352091i	0.163063	−	0.986616i	$-0.447862\pi$
$569$	−14.5469	−	8.39867i	−0.609839	−	0.352091i	−0.772902	+	0.634525i	$0.781196\pi$
$570$	−0.269218	−	0.466299i	−0.0112763	−	0.0195311i
$571$	3.49094	−	13.0284i	0.146091	−	0.545220i	−0.853613	−	0.520908i	$-0.825594\pi$
$571$	3.49094	−	13.0284i	0.146091	−	0.545220i	0.999704	−	0.0243126i	$-0.00773969\pi$
$572$	39.9904	+	23.0885i	1.67208	+	0.965377i
$573$	−2.31514			−0.0967166
$574$	−0.434459	+	3.78121i	−0.0181340	+	0.157825i
$575$	−9.18843			−0.383184
$576$	11.2780	+	6.51136i	0.469917	+	0.271307i
$577$	8.19011	−	30.5659i	0.340959	−	1.27248i	−0.556304	−	0.830979i	$-0.687781\pi$
$577$	8.19011	−	30.5659i	0.340959	−	1.27248i	0.897263	−	0.441497i	$-0.145552\pi$
$578$	1.01637	+	1.76040i	0.0422752	+	0.0732228i
$579$	14.7736	+	8.52953i	0.613969	+	0.354475i
$580$	12.7243	−	12.7243i	0.528348	−	0.528348i
$581$	40.8812	−	25.2186i	1.69604	−	1.04624i
$582$		−	1.98523i		−	0.0822905i
$583$	−10.4097	−	6.01003i	−0.431125	−	0.248910i
$584$	2.81292	+	4.87212i	0.116400	+	0.201610i
$585$	1.99054	−	7.42878i	0.0822985	−	0.307142i
$586$	−5.76615	+	1.54504i	−0.238197	+	0.0638248i
$587$	2.90128	+	2.90128i	0.119748	+	0.119748i	0.764442	−	0.644693i	$-0.223015\pi$
$587$	2.90128	+	2.90128i	0.119748	+	0.119748i	−0.644693	+	0.764442i	$0.723015\pi$
$588$	2.87820	−	13.9459i	0.118695	−	0.575119i
$589$	−10.1581	+	10.1581i	−0.418558	+	0.418558i
$590$	0.179332	−	0.310613i	0.00738300	−	0.0127877i
$591$	1.41062	+	0.377974i	0.0580251	+	0.0155478i
$592$	−4.55176	−	7.88388i	−0.187076	−	0.324026i
$593$	−7.91448	−	29.5372i	−0.325009	−	1.21295i	−0.914303	−	0.405030i	$-0.867261\pi$
$593$	−7.91448	−	29.5372i	−0.325009	−	1.21295i	0.589295	−	0.807918i	$-0.299406\pi$
$594$			6.84806i			0.280979i
$595$	−7.33623	−	1.73835i	−0.300756	−	0.0712652i
$596$	18.0088	−	18.0088i	0.737670	−	0.737670i
$597$	3.69824	−	6.40554i	0.151359	−	0.262161i
$598$	−1.99569	−	0.534743i	−0.0816098	−	0.0218673i
$599$	−5.29014	−	9.16278i	−0.216149	−	0.374381i	0.737478	−	0.675371i	$-0.236016\pi$
$599$	−5.29014	−	9.16278i	−0.216149	−	0.374381i	−0.953627	+	0.300990i	$0.902683\pi$
$600$	0.953487	+	3.55846i	0.0389259	+	0.145274i
$601$	−3.32738	+	3.32738i	−0.135727	+	0.135727i	−0.771706	−	0.635979i	$-0.780596\pi$
$601$	−3.32738	+	3.32738i	−0.135727	+	0.135727i	0.635979	+	0.771706i	$0.280596\pi$
$602$	−0.185626	−	6.36905i	−0.00756556	−	0.259583i
$603$	−13.5966	−	13.5966i	−0.553697	−	0.553697i
$604$	25.6177	−	6.86424i	1.04237	−	0.279302i
$605$	12.3172	+	21.3340i	0.500764	+	0.867348i
$606$	−1.20239	+	0.694198i	−0.0488436	+	0.0281999i
$607$	4.43333	+	2.55958i	0.179943	+	0.103890i	0.587266	−	0.809394i	$-0.300204\pi$
$607$	4.43333	+	2.55958i	0.179943	+	0.103890i	−0.407323	+	0.913284i	$0.633538\pi$
$608$	4.18805	+	4.18805i	0.169848	+	0.169848i
$609$	−11.9672	+	22.1972i	−0.484937	+	0.899475i
$610$			1.74271i			0.0705604i
$611$	−22.6475	+	39.2266i	−0.916218	+	1.58694i
$612$	−2.71939	+	10.1489i	−0.109925	+	0.410245i
$613$	−24.6522	+	14.2330i	−0.995693	+	0.574863i	−0.906971	−	0.421193i	$-0.861612\pi$
$613$	−24.6522	+	14.2330i	−0.995693	+	0.574863i	−0.0887217	+	0.996056i	$0.528278\pi$
$614$	2.86043	−	4.95440i	0.115437	−	0.199943i
$615$	4.04215	+	5.40796i	0.162995	+	0.218070i
$616$	13.3768	−	4.00545i	0.538967	−	0.161384i
$617$		−	10.8915i		−	0.438476i	−0.975671	−	0.219238i	$-0.929643\pi$
$617$		−	10.8915i		−	0.438476i	0.975671	−	0.219238i	$-0.0703571\pi$
$618$	−0.673687	+	0.180514i	−0.0270997	+	0.00726134i
$619$	−9.81574	−	17.0014i	−0.394528	−	0.683342i	0.598513	−	0.801113i	$-0.295759\pi$
$619$	−9.81574	−	17.0014i	−0.394528	−	0.683342i	−0.993041	+	0.117771i	$0.962425\pi$
$620$	−10.7833	+	6.22574i	−0.433068	+	0.250032i
$621$	3.06296	+	11.4311i	0.122912	+	0.458716i
$622$	−0.0680791	−	0.0680791i	−0.00272972	−	0.00272972i
$623$	−1.11859	+	1.18575i	−0.0448153	+	0.0475061i
$624$		−	15.3735i		−	0.615432i
$625$	−5.36284	+	9.28870i	−0.214513	+	0.371548i
$626$	0.700220	−	2.61326i	0.0279864	−	0.104447i
$627$	3.65105	−	13.6259i	0.145809	−	0.544167i
$628$	24.9872	−	6.69531i	0.997100	−	0.267172i
$629$	4.90650	−	4.90650i	0.195635	−	0.195635i
$630$	−0.602705	−	0.977029i	−0.0240123	−	0.0389258i
$631$	−31.8567			−1.26819			−0.634097	−	0.773254i	$-0.718628\pi$
$631$	−31.8567			−1.26819			−0.634097	+	0.773254i	$0.718628\pi$
$632$	1.59088	+	5.93726i	0.0632820	+	0.236172i
$633$	6.01676	+	10.4213i	0.239145	+	0.414211i
$634$	1.70511	+	0.456883i	0.0677186	+	0.0181451i
$635$	−14.5184	−	8.38222i	−0.576147	−	0.332638i
$636$			4.11099i			0.163011i
$637$	26.4601	−	8.77072i	1.04839	−	0.347509i
$638$	−12.2063			−0.483251
$639$	3.83555	+	14.3145i	0.151732	+	0.566271i
$640$	3.40672	+	5.90061i	0.134662	+	0.233242i
$641$	14.1038	+	3.77910i	0.557066	+	0.149265i	0.526358	−	0.850263i	$-0.323557\pi$
$641$	14.1038	+	3.77910i	0.557066	+	0.149265i	0.0307081	+	0.999528i	$0.490224\pi$
$642$	0.0234777	+	0.0876198i	0.000926589	+	0.00345808i
$643$	−15.0627	−	15.0627i	−0.594013	−	0.594013i	0.344700	−	0.938713i	$-0.387981\pi$
$643$	−15.0627	−	15.0627i	−0.594013	−	0.594013i	−0.938713	+	0.344700i	$0.887981\pi$
$644$	10.1376	−	6.25365i	0.399479	−	0.246428i
$645$	−7.99239	−	7.99239i	−0.314700	−	0.314700i
$646$	−0.719995	+	1.24707i	−0.0283278	+	0.0490652i
$647$	−13.8814	+	8.01444i	−0.545735	+	0.315080i	−0.747400	−	0.664374i	$-0.768698\pi$
$647$	−13.8814	+	8.01444i	−0.545735	+	0.315080i	0.201665	+	0.979455i	$0.435365\pi$
$648$	−0.296761	+	0.171335i	−0.0116579	+	0.00673069i
$649$	9.07653	−	2.43205i	0.356285	−	0.0954663i
$650$	−2.51716	+	2.51716i	−0.0987311	+	0.0987311i
$651$	11.9738	−	12.6927i	0.469289	−	0.497466i
$652$	0.182507			0.00714754
$653$	3.26589	−	0.875094i	0.127804	−	0.0342451i	−0.194350	−	0.980932i	$-0.562260\pi$
$653$	3.26589	−	0.875094i	0.127804	−	0.0342451i	0.322154	+	0.946687i	$0.395593\pi$
$654$	2.20702	−	1.27423i	0.0863014	−	0.0498262i
$655$	−9.67035	−	16.7495i	−0.377852	−	0.654459i
$656$	−18.6105	−	14.6576i	−0.726619	−	0.572285i
$657$	12.1174			0.472743
$658$	1.93937	+	6.47681i	0.0756045	+	0.252493i
$659$	−18.8339	−	18.8339i	−0.733663	−	0.733663i	0.237680	−	0.971343i	$-0.423613\pi$
$659$	−18.8339	−	18.8339i	−0.733663	−	0.733663i	−0.971343	+	0.237680i	$0.923613\pi$
$660$	6.11343	−	10.5888i	0.237965	−	0.412167i
$661$	−25.2353	+	14.5696i	−0.981541	+	0.566693i	−0.902735	−	0.430197i	$-0.858444\pi$
$661$	−25.2353	+	14.5696i	−0.981541	+	0.566693i	−0.0788057	+	0.996890i	$0.525111\pi$
$662$	5.41491	+	1.45092i	0.210457	+	0.0563917i
$663$	11.3186	−	3.03282i	0.439579	−	0.117785i
$664$		−	16.1094i		−	0.625167i
$665$	1.74310	+	5.82134i	0.0675945	+	0.225742i
$666$	1.05653			0.0409399
$667$	−20.3753	+	5.45955i	−0.788935	+	0.211395i
$668$	−0.667856	+	2.49247i	−0.0258401	+	0.0964366i
$669$	6.77967	−	25.3021i	0.262117	−	0.978235i
$670$	−0.591178	−	2.20631i	−0.0228392	−	0.0852371i
$671$	−32.2848	+	32.2848i	−1.24634	+	1.24634i
$672$	−5.23301	−	4.93662i	−0.201868	−	0.190434i
$673$	10.9653	−	10.9653i	0.422680	−	0.422680i	−0.463446	−	0.886125i	$-0.653387\pi$
$673$	10.9653	−	10.9653i	0.422680	−	0.422680i	0.886125	+	0.463446i	$0.153387\pi$
$674$	0.784819	−	1.35935i	0.0302301	−	0.0523600i
$675$	19.6955	+	5.27738i	0.758079	+	0.203127i
$676$	4.82589	−	2.78623i	0.185611	−	0.107163i
$677$	−0.720005	−	0.415695i	−0.0276720	−	0.0159765i	0.486100	−	0.873903i	$-0.338419\pi$
$677$	−0.720005	−	0.415695i	−0.0276720	−	0.0159765i	−0.513772	+	0.857927i	$0.671752\pi$
$678$	0.874816	−	0.874816i	0.0335971	−	0.0335971i
$679$	−5.16591	+	21.8014i	−0.198250	+	0.836660i
$680$	−1.78794	+	1.78794i	−0.0685644	+	0.0685644i
$681$	−3.25045	+	5.62995i	−0.124558	+	0.215740i
$682$	8.15828	+	2.18600i	0.312397	+	0.0837064i
$683$	−10.8019	−	2.89437i	−0.413325	−	0.110750i	0.0461633	−	0.998934i	$-0.485301\pi$
$683$	−10.8019	−	2.89437i	−0.413325	−	0.110750i	−0.459488	+	0.888184i	$0.651967\pi$
$684$	8.18000	−	2.19182i	0.312770	−	0.0838065i
$685$	5.78857	+	5.78857i	0.221170	+	0.221170i
$686$	1.75792	−	3.77129i	0.0671177	−	0.143988i
$687$	2.91871			0.111356
$688$	34.3455	+	19.8294i	1.30941	+	0.755988i
$689$	−6.96947	+	4.02383i	−0.265516	+	0.153296i
$690$	−0.141591	+	0.528424i	−0.00539027	+	0.0201168i
$691$	2.63629	+	9.83877i	0.100289	+	0.374284i	0.997768	−	0.0667728i	$-0.0212703\pi$
$691$	2.63629	+	9.83877i	0.100289	+	0.374284i	−0.897479	+	0.441057i	$0.854604\pi$
$692$			19.4783i			0.740454i
$693$	6.93458	−	29.2655i	0.263423	−	1.11171i
$694$	2.28223	+	2.28223i	0.0866322	+	0.0866322i
$695$	−19.2891	−	11.1365i	−0.731676	−	0.422433i
$696$	4.22871	+	7.32434i	0.160289	+	0.277628i
$697$	7.12018	−	16.5935i	0.269696	−	0.628523i
$698$	2.01152	−	3.48406i	0.0761372	−	0.131874i
$699$		−	3.94627i		−	0.149262i
$700$	−0.597884	−	20.5141i	−0.0225979	−	0.775360i
$701$	28.8558			1.08987			0.544934	−	0.838479i	$-0.316555\pi$
$701$	28.8558			1.08987			0.544934	+	0.838479i	$0.316555\pi$
$702$	3.97064	+	2.29245i	0.149862	+	0.0865230i
$703$	−5.40213	−	1.44750i	−0.203745	−	0.0545933i
$704$	−10.4897	+	39.1480i	−0.395345	+	1.47545i
$705$	10.3865	+	5.99666i	0.391179	+	0.225847i
$706$			1.09898i			0.0413608i
$707$	15.0107	−	4.49471i	0.564537	−	0.169041i
$708$	−2.27248	−	2.27248i	−0.0854050	−	0.0854050i
$709$	41.6299	−	11.1547i	1.56344	−	0.418923i	0.629692	−	0.776845i	$-0.283181\pi$
$709$	41.6299	−	11.1547i	1.56344	−	0.418923i	0.933752	+	0.357922i	$0.116514\pi$
$710$	−0.455621	+	1.70040i	−0.0170992	+	0.0638150i
$711$	12.7881	+	3.42657i	0.479592	+	0.128506i
$712$	0.141496	+	0.528072i	0.00530280	+	0.0197903i
$713$	14.5960			0.546623
$714$	0.830036	−	1.53957i	0.0310633	−	0.0576171i
$715$	23.9353			0.895128
$716$	−1.55028	−	5.78573i	−0.0579367	−	0.216223i
$717$	−8.46296	+	4.88609i	−0.316055	+	0.182474i
$718$	−3.90394	+	2.25394i	−0.145694	+	0.0841162i
$719$	−4.39771	−	16.4125i	−0.164007	−	0.612082i	−0.998165	−	0.0605564i	$-0.980713\pi$
$719$	−4.39771	−	16.4125i	−0.164007	−	0.612082i	0.834158	−	0.551526i	$-0.185954\pi$
$720$	7.14514			0.266284
$721$	7.86801	−	0.229313i	0.293020	−	0.00854007i
$722$	−3.10803			−0.115669
$723$	5.86210	+	21.8777i	0.218014	+	0.813639i
$724$	11.0934	+	2.97246i	0.412281	+	0.110470i
$725$	−9.40662	+	35.1060i	−0.349353	+	1.30380i
$726$	−5.52023	+	1.47914i	−0.204875	+	0.0548961i
$727$	−4.41199	−	4.41199i	−0.163632	−	0.163632i	0.620542	−	0.784173i	$-0.286913\pi$
$727$	−4.41199	−	4.41199i	−0.163632	−	0.163632i	−0.784173	+	0.620542i	$0.786913\pi$
$728$	2.15557	−	9.09700i	0.0798907	−	0.337157i
$729$		−	15.3040i		−	0.566816i
$730$	1.24657	+	0.719705i	0.0461375	+	0.0266375i
$731$	−7.82372	+	29.1985i	−0.289371	+	1.07995i
$732$	15.0833	+	4.04155i	0.557494	+	0.149380i
$733$	−2.43976	−	1.40860i	−0.0901146	−	0.0520277i	0.454266	−	0.890866i	$-0.349902\pi$
$733$	−2.43976	−	1.40860i	−0.0901146	−	0.0520277i	−0.544380	+	0.838839i	$0.683235\pi$
$734$	0.532367			0.0196500
$735$	−2.32234	−	7.00617i	−0.0856606	−	0.258426i
$736$		−	6.01770i		−	0.221816i
$737$	29.9213	−	51.8251i	1.10216	−	1.90900i
$738$	2.55317	−	1.01996i	0.0939835	−	0.0375452i
$739$	−1.31775	−	2.28241i	−0.0484742	−	0.0839598i	0.840770	−	0.541392i	$-0.182103\pi$
$739$	−1.31775	−	2.28241i	−0.0484742	−	0.0839598i	−0.889244	+	0.457432i	$0.848769\pi$
$740$	−4.19802	−	2.42373i	−0.154322	−	0.0890980i
$741$	−6.67835	−	6.67835i	−0.245335	−	0.245335i
$742$	−0.276967	+	1.16887i	−0.0101678	+	0.0429104i
$743$		−	31.3037i		−	1.14842i	−0.818707	−	0.574211i	$-0.805309\pi$
$743$		−	31.3037i		−	1.14842i	0.818707	−	0.574211i	$-0.194691\pi$
$744$	−1.51463	−	5.65267i	−0.0555289	−	0.207237i
$745$	3.41672	−	12.7514i	0.125179	−	0.467175i
$746$	3.51598	−	2.02995i	0.128729	−	0.0743219i
$747$	−30.0491	−	17.3489i	−1.09944	−	0.634761i
$748$	−32.6994			−1.19561
$749$	−0.0298245	−	1.02331i	−0.00108976	−	0.0373910i
$750$	1.50405	+	1.50405i	0.0549202	+	0.0549202i
$751$	−0.162757	+	0.0436106i	−0.00593908	+	0.00159137i	−0.261787	−	0.965126i	$-0.584312\pi$
$751$	−0.162757	+	0.0436106i	−0.00593908	+	0.00159137i	0.255848	+	0.966717i	$0.417645\pi$
$752$	−40.6472	−	10.8914i	−1.48225	−	0.397168i
$753$	−14.5756	−	3.90552i	−0.531165	−	0.142325i
$754$	−4.08616	+	7.07743i	−0.148809	+	0.257745i
$755$	9.72063	−	9.72063i	0.353770	−	0.353770i
$756$	−25.3219	+	7.58219i	−0.920947	+	0.275762i
$757$	2.85940	−	2.85940i	0.103927	−	0.103927i	−0.653232	−	0.757158i	$-0.726587\pi$
$757$	2.85940	−	2.85940i	0.103927	−	0.103927i	0.757158	+	0.653232i	$0.226587\pi$
$758$	0.968800	+	0.559337i	0.0351884	+	0.0203160i
$759$	−12.4124	+	7.16632i	−0.450543	+	0.260121i
$760$	1.96855	+	0.527471i	0.0714067	+	0.0191334i
$761$	−21.9875	+	38.0834i	−0.797045	+	1.38052i	0.124488	+	0.992221i	$0.460271\pi$
$761$	−21.9875	+	38.0834i	−0.797045	+	1.38052i	−0.921533	+	0.388301i	$0.873062\pi$
$762$	2.75009	−	2.75009i	0.0996252	−	0.0996252i
$763$	−27.5528	+	8.25020i	−0.997477	+	0.298677i
$764$	3.05855	−	3.05855i	0.110654	−	0.110654i
$765$	1.40956	+	5.26057i	0.0509629	+	0.190196i
$766$	−1.93674	+	7.22803i	−0.0699774	+	0.261159i
$767$	1.62830	−	6.07690i	0.0587945	−	0.219424i
$768$	12.2089	−	3.27136i	0.440550	−	0.118045i
$769$	−21.3574			−0.770169			−0.385084	−	0.922881i	$-0.625828\pi$
$769$	−21.3574			−0.770169			−0.385084	+	0.922881i	$0.625828\pi$
$770$	2.45160	−	2.59880i	0.0883497	−	0.0936542i
$771$			16.7118i			0.601860i
$772$	−30.7858	+	8.24903i	−1.10801	+	0.296889i
$773$	12.8947	+	3.45512i	0.463789	+	0.124272i	0.483144	−	0.875541i	$-0.339495\pi$
$773$	12.8947	+	3.45512i	0.463789	+	0.124272i	−0.0193551	+	0.999813i	$0.506161\pi$
$774$	−3.98606	+	2.30135i	−0.143276	+	0.0827204i
$775$	12.5742	−	21.7791i	0.451677	−	0.782328i
$776$	5.31330	+	5.31330i	0.190736	+	0.190736i
$777$	6.61008	+	1.56628i	0.237135	+	0.0561901i
$778$	2.00248			0.0717922
$779$	−14.4519	+	1.71717i	−0.517794	+	0.0615238i
$780$	−4.09305	−	7.08937i	−0.146555	−	0.253840i
$781$	−39.9416	+	23.0603i	−1.42922	+	0.825163i
$782$	1.41321	−	0.378669i	0.0505364	−	0.0135412i
$783$	46.8103			1.67286
$784$	14.2332	+	21.6360i	0.508328	+	0.772715i
$785$	9.48140	−	9.48140i	0.338406	−	0.338406i
$786$	4.33400	−	1.16129i	0.154589	−	0.0414219i
$787$	−10.4728	+	6.04649i	−0.373316	+	0.215534i	−0.674906	−	0.737904i	$-0.735816\pi$
$787$	−10.4728	+	6.04649i	−0.373316	+	0.215534i	0.301590	+	0.953438i	$0.402483\pi$
$788$	−2.36292	+	1.36423i	−0.0841755	+	0.0485987i
$789$	−3.90832	+	6.76942i	−0.139140	+	0.240998i
$790$	1.11205	+	1.11205i	0.0395650	+	0.0395650i
$791$	−11.8834	+	7.33061i	−0.422527	+	0.260646i
$792$	−7.13242	−	7.13242i	−0.253440	−	0.253440i
$793$	7.91173	+	29.5270i	0.280954	+	1.04853i
$794$	−1.16356	−	0.311774i	−0.0412931	−	0.0110644i
$795$	1.06544	+	1.84540i	0.0377873	+	0.0654495i
$796$	3.57663	+	13.3481i	0.126770	+	0.473113i
$797$	−0.0997593			−0.00353365			−0.00176683	−	0.999998i	$-0.500562\pi$
$797$	−0.0997593			−0.00353365			−0.00176683	+	0.999998i	$0.500562\pi$
$798$	−1.40915	+	0.0410697i	−0.0498833	+	0.00145385i
$799$		−	32.0748i		−	1.13473i
$800$	−8.97921	−	5.18415i	−0.317463	−	0.183287i
$801$	1.13740	+	0.304765i	0.0401881	+	0.0107684i
$802$	−1.49934	−	2.59694i	−0.0529437	−	0.0917011i
$803$	9.76042	+	36.4264i	0.344438	+	1.28546i
$804$	−20.4667			−0.721806
$805$	2.92997	−	5.43459i	0.103268	−	0.191544i
$806$	3.99854	−	3.99854i	0.140843	−	0.140843i
$807$	7.14954	−	1.91571i	0.251676	−	0.0674363i
$808$	1.36012	−	5.07604i	0.0478489	−	0.178574i
$809$	5.76015	−	21.4972i	0.202516	−	0.755800i	−0.787676	−	0.616089i	$-0.788716\pi$
$809$	5.76015	−	21.4972i	0.202516	−	0.755800i	0.990192	−	0.139711i	$-0.0446173\pi$
$810$	−0.0438373	+	0.0759284i	−0.00154029	+	0.00266785i
$811$			24.9862i			0.877385i	0.898637	+	0.438692i	$0.144558\pi$
$811$			24.9862i			0.877385i	−0.898637	+	0.438692i	$0.855442\pi$
$812$	−13.5148	−	45.1347i	−0.474277	−	1.58392i
$813$	19.7697	+	19.7697i	0.693354	+	0.693354i
$814$	0.851028	+	3.17608i	0.0298285	+	0.111322i
$815$	0.0819264	−	0.0473002i	0.00286976	−	0.00165686i
$816$	5.44324	+	9.42797i	0.190551	+	0.330045i
$817$	23.5339	−	6.30590i	0.823348	−	0.220615i
$818$			0.986559i			0.0344942i
$819$	−14.6473	−	13.8177i	−0.511819	−	0.482830i
$820$	−12.4846	−	1.80438i	−0.435980	−	0.0630116i
$821$	11.2406	−	19.4694i	0.392301	−	0.679486i	−0.600451	−	0.799661i	$-0.705012\pi$
$821$	11.2406	−	19.4694i	0.392301	−	0.679486i	0.992753	+	0.120175i	$0.0383457\pi$
$822$	−1.64471	+	0.949575i	−0.0573659	+	0.0331202i
$823$	−11.3054	+	42.1923i	−0.394081	+	1.47073i	0.429259	+	0.903181i	$0.358775\pi$
$823$	−11.3054	+	42.1923i	−0.394081	+	1.47073i	−0.823340	+	0.567549i	$0.807892\pi$
$824$	1.31993	−	2.28619i	0.0459821	−	0.0796433i
$825$			24.6947i			0.859757i
$826$	−0.493026	−	0.799230i	−0.0171546	−	0.0278088i
$827$	−9.91870	−	9.91870i	−0.344907	−	0.344907i	0.513301	−	0.858208i	$-0.328422\pi$
$827$	−9.91870	−	9.91870i	−0.344907	−	0.344907i	−0.858208	+	0.513301i	$0.828422\pi$
$828$	−7.45151	−	4.30213i	−0.258958	−	0.149509i
$829$	−22.9172	+	13.2312i	−0.795946	+	0.459540i	−0.842052	−	0.539397i	$-0.818652\pi$
$829$	−22.9172	+	13.2312i	−0.795946	+	0.459540i	0.0461056	+	0.998937i	$0.485319\pi$
$830$	−2.06086	−	3.56951i	−0.0715333	−	0.123899i
$831$	−29.6291	+	7.93908i	−1.02782	+	0.275404i
$832$	19.1873	+	19.1873i	0.665199	+	0.665199i
$833$	−13.1215	+	14.7474i	−0.454633	+	0.510966i
$834$	3.65374	−	3.65374i	0.126519	−	0.126519i
$835$	0.346175	+	1.29194i	0.0119799	+	0.0447095i
$836$	13.1778	+	22.8247i	0.455764	+	0.789407i
$837$	−31.2865	−	8.38320i	−1.08142	−	0.289766i
$838$	3.53535	−	6.12341i	0.122127	−	0.211530i
$839$	−24.9781	+	24.9781i	−0.862340	+	0.862340i	−0.991609	−	0.129270i	$-0.958737\pi$
$839$	−24.9781	+	24.9781i	−0.862340	+	0.862340i	0.129270	+	0.991609i	$0.458737\pi$
$840$	−2.40873	−	0.570758i	−0.0831091	−	0.0196930i
$841$			54.4366i			1.87712i
$842$	−0.405888	−	1.51479i	−0.0139878	−	0.0522032i
$843$	−3.52281	−	6.10169i	−0.121332	−	0.210153i
$844$	−21.7164	−	5.81890i	−0.747510	−	0.200295i
$845$	1.44421	−	2.50144i	0.0496823	−	0.0860522i
$846$	3.45339	−	3.45339i	0.118730	−	0.118730i
$847$	64.4709	−	1.87900i	2.21524	−	0.0645633i
$848$	−5.28678	−	5.28678i	−0.181549	−	0.181549i
$849$	−10.0388	+	2.68988i	−0.344530	+	0.0923164i
$850$	0.652434	−	2.43492i	0.0223783	−	0.0835170i
$851$	2.84116	+	4.92103i	0.0973936	+	0.168691i
$852$	13.6604	+	7.88686i	0.467999	+	0.270200i
$853$		−	8.48975i		−	0.290683i	−0.989382	−	0.145342i	$-0.953572\pi$
$853$		−	8.48975i		−	0.290683i	0.989382	−	0.145342i	$-0.0464282\pi$
$854$	4.01630	+	2.16532i	0.137435	+	0.0740958i
$855$	3.10390	−	3.10390i	0.106151	−	0.106151i
$856$	−0.297342	−	0.171671i	−0.0101630	−	0.00586759i
$857$	15.0844	+	26.1270i	0.515275	+	0.892482i	0.999843	+	0.0177283i	$0.00564338\pi$
$857$	15.0844	+	26.1270i	0.515275	+	0.892482i	−0.484568	+	0.874753i	$0.661023\pi$
$858$	−1.43717	+	5.36358i	−0.0490640	+	0.183109i
$859$	−26.0423	−	15.0355i	−0.888553	−	0.513006i	−0.0150839	−	0.999886i	$-0.504802\pi$
$859$	−26.0423	−	15.0355i	−0.888553	−	0.513006i	−0.873469	+	0.486880i	$0.838135\pi$
$860$	21.1176			0.720103
$861$	17.4857	−	2.59625i	0.595911	−	0.0884798i
$862$	−1.74778			−0.0595297
$863$	27.2687	+	15.7436i	0.928237	+	0.535918i	0.886254	−	0.463200i	$-0.153299\pi$
$863$	27.2687	+	15.7436i	0.928237	+	0.535918i	0.0419837	+	0.999118i	$0.486632\pi$
$864$	−3.45627	+	12.8990i	−0.117585	+	0.438833i
$865$	5.04817	+	8.74369i	0.171643	+	0.297294i
$866$	−0.512471	−	0.295875i	−0.0174145	−	0.0100542i
$867$	6.67582	−	6.67582i	0.226723	−	0.226723i
$868$	0.949747	+	32.5870i	0.0322365	+	1.10607i
$869$			41.2028i			1.39771i
$870$	1.87398	+	1.08194i	0.0635339	+	0.0366813i
$871$	−20.0328	−	34.6979i	−0.678786	−	1.17569i
$872$	−2.49655	+	9.31725i	−0.0845439	+	0.315522i
$873$	15.6330	−	4.18886i	0.529098	−	0.141771i
$874$	−0.833840	−	0.833840i	−0.0282051	−	0.0282051i
$875$	−12.6033	−	20.4309i	−0.426071	−	0.690692i
$876$	9.12003	−	9.12003i	0.308137	−	0.308137i
$877$	−5.50956	+	9.54283i	−0.186045	+	0.322239i	−0.943928	−	0.330151i	$-0.892900\pi$
$877$	−5.50956	+	9.54283i	−0.186045	+	0.322239i	0.757883	+	0.652390i	$0.226234\pi$
$878$	0.106246	+	0.0284685i	0.00358563	+	0.000960766i
$879$	13.8628	+	24.0111i	0.467581	+	0.809875i
$880$	5.75535	+	21.4792i	0.194013	+	0.724065i
$881$			27.3791i			0.922424i	0.887290	+	0.461212i	$0.152585\pi$
$881$			27.3791i			0.922424i	−0.887290	+	0.461212i	$0.847415\pi$
$882$	−3.00055	+	0.175051i	−0.101034	+	0.00589426i
$883$	28.8476	−	28.8476i	0.970799	−	0.970799i	−0.0287863	−	0.999586i	$-0.509164\pi$
$883$	28.8476	−	28.8476i	0.970799	−	0.970799i	0.999586	+	0.0287863i	$0.00916424\pi$
$884$	−10.9464	+	18.9598i	−0.368168	+	0.637685i
$885$	−1.60906	−	0.431146i	−0.0540879	−	0.0144928i
$886$	2.02919	+	3.51466i	0.0681720	+	0.118077i
$887$	8.49572	+	31.7065i	0.285258	+	1.06460i	0.948650	+	0.316327i	$0.102450\pi$
$887$	8.49572	+	31.7065i	0.285258	+	1.06460i	−0.663392	+	0.748272i	$0.730884\pi$
$888$	1.61097	−	1.61097i	0.0540606	−	0.0540606i
$889$	−37.3571	+	23.0446i	−1.25292	+	0.772893i
$890$	0.0989079	+	0.0989079i	0.00331540	+	0.00331540i
$891$	−2.21873	+	0.594508i	−0.0743304	+	0.0199168i
$892$	24.4700	+	42.3833i	0.819317	+	1.41910i
$893$	−22.3887	+	12.9261i	−0.749209	+	0.432556i
$894$	2.65226	+	1.53129i	0.0887050	+	0.0512138i
$895$	−2.19539	−	2.19539i	−0.0733839	−	0.0733839i
$896$	17.8316	−	0.519701i	0.595710	−	0.0173620i
$897$			9.59596i			0.320400i
$898$	3.34028	−	5.78554i	0.111467	−	0.193066i
$899$	14.9426	−	55.7664i	0.498362	−	1.85991i
$900$	−12.8387	+	7.41243i	−0.427957	+	0.247081i
$901$	2.84940	−	4.93531i	0.0949274	−	0.164419i
$902$	5.12268	+	6.85360i	0.170567	+	0.228200i
$903$	−28.3500	+	8.48892i	−0.943430	+	0.282494i
$904$			4.68273i			0.155745i
$905$	5.75011	−	1.54074i	0.191140	−	0.0512158i
$906$	1.59460	+	2.76193i	0.0529771	+	0.0917590i
$907$	12.4465	−	7.18596i	0.413278	−	0.238606i	−0.278919	−	0.960315i	$-0.589976\pi$
$907$	12.4465	−	7.18596i	0.413278	−	0.238606i	0.692197	+	0.721709i	$0.256643\pi$
$908$	−3.14356	−	11.7319i	−0.104323	−	0.389338i
$909$	−8.00362	−	8.00362i	−0.265463	−	0.265463i
$910$	−0.686138	−	2.29146i	−0.0227452	−	0.0759611i
$911$			8.82993i			0.292549i	0.989244	+	0.146274i	$0.0467282\pi$
$911$			8.82993i			0.292549i	−0.989244	+	0.146274i	$0.953272\pi$
$912$	4.38724	−	7.59892i	0.145276	−	0.251625i
$913$	27.9487	−	104.306i	0.924966	−	3.45202i
$914$	0.281670	−	1.05121i	0.00931683	−	0.0347709i
$915$	7.81824	−	2.09489i	0.258463	−	0.0692550i
$916$	−3.85591	+	3.85591i	−0.127403	+	0.127403i
$917$	−50.6168	+	1.47523i	−1.67152	+	0.0487163i
$918$	−3.24672			−0.107158
$919$	−0.124020	−	0.462851i	−0.00409106	−	0.0152680i	0.963850	−	0.266445i	$-0.0858491\pi$
$919$	−0.124020	−	0.462851i	−0.00409106	−	0.0152680i	−0.967941	+	0.251177i	$0.919182\pi$
$920$	−1.03532	−	1.79323i	−0.0341336	−	0.0591212i
$921$	−25.6652	−	6.87696i	−0.845696	−	0.226603i
$922$	−6.62746	−	3.82636i	−0.218264	−	0.126015i
$923$			30.8786i			1.01638i
$924$	−16.8072	−	27.2457i	−0.552916	−	0.896318i
$925$	9.79044			0.321908
$926$	−1.89170	−	7.05990i	−0.0621650	−	0.232003i
$927$	−2.84297	−	4.92418i	−0.0933755	−	0.161731i
$928$	−22.9917	−	6.16060i	−0.754739	−	0.202232i
$929$	3.79921	+	14.1789i	0.124648	+	0.465193i	0.999827	−	0.0186064i	$-0.00592294\pi$
$929$	3.79921	+	14.1789i	0.124648	+	0.465193i	−0.875179	+	0.483800i	$0.839256\pi$
$930$	−1.05875	−	1.05875i	−0.0347176	−	0.0347176i
$931$	15.5818	+	3.21583i	0.510674	+	0.105395i
$932$	5.21344	+	5.21344i	0.170772	+	0.170772i
$933$	−0.223583	+	0.387257i	−0.00731977	+	0.0126782i
$934$	3.12953	−	1.80683i	0.102401	−	0.0591214i
$935$	−14.6786	+	8.47467i	−0.480040	+	0.277151i
$936$	−6.52316	+	1.74788i	−0.213216	+	0.0571311i
$937$	21.5397	−	21.5397i	0.703672	−	0.703672i	−0.261525	−	0.965197i	$-0.584225\pi$
$937$	21.5397	−	21.5397i	0.703672	−	0.703672i	0.965197	+	0.261525i	$0.0842254\pi$
$938$	−5.81925	−	1.37889i	−0.190005	−	0.0450225i
$939$	−12.5654			−0.410058
$940$	−21.6439	+	5.79946i	−0.705945	+	0.189157i
$941$	12.5961	−	7.27237i	0.410621	−	0.237072i	−0.280435	−	0.959873i	$-0.590479\pi$
$941$	12.5961	−	7.27237i	0.410621	−	0.237072i	0.691057	+	0.722801i	$0.257145\pi$
$942$	1.55536	+	2.69396i	0.0506763	+	0.0877739i
$943$	11.6165	+	9.14913i	0.378285	+	0.297937i
$944$	5.84488			0.190235
$945$	−9.40176	+	9.96624i	−0.305839	+	0.324202i
$946$	−10.1289	−	10.1289i	−0.329319	−	0.329319i
$947$	−6.85080	+	11.8659i	−0.222621	+	0.385591i	−0.955603	−	0.294657i	$-0.904795\pi$
$947$	−6.85080	+	11.8659i	−0.222621	+	0.385591i	0.732982	+	0.680248i	$0.238128\pi$
$948$	12.2038	−	7.04589i	0.396362	−	0.228840i
$949$	24.3881	+	6.53477i	0.791672	+	0.212128i
$950$	−1.96254	+	0.525861i	−0.0636732	+	0.0170612i
$951$		−	8.19876i		−	0.265863i
$952$	1.89902	+	6.34205i	0.0615475	+	0.205547i
$953$	−24.7965			−0.803238			−0.401619	−	0.915807i	$-0.631552\pi$
$953$	−24.7965			−0.803238			−0.401619	+	0.915807i	$0.631552\pi$
$954$	0.838155	−	0.224583i	0.0271363	−	0.00727114i
$955$	0.580282	−	2.16564i	0.0187775	−	0.0700785i
$956$	4.72541	−	17.6355i	0.152831	−	0.570372i
$957$	14.6730	+	54.7603i	0.474310	+	1.77015i
$958$	5.17516	−	5.17516i	0.167202	−	0.167202i
$959$	20.5328	−	6.14819i	0.663039	−	0.198535i
$960$	5.08046	−	5.08046i	0.163971	−	0.163971i
$961$	−4.47425	+	7.74963i	−0.144331	+	0.249988i
$962$	2.12644	+	0.569779i	0.0685593	+	0.0183704i
$963$	−0.640438	+	0.369757i	−0.0206378	+	0.0119153i
$964$	−36.6471	−	21.1582i	−1.18032	−	0.681460i
$965$	−11.6817	+	11.6817i	−0.376046	+	0.376046i
$966$	1.04189	+	0.982881i	0.0335223	+	0.0316237i
$967$	39.9067	−	39.9067i	1.28331	−	1.28331i	0.344541	−	0.938771i	$-0.388035\pi$
$967$	39.9067	−	39.9067i	1.28331	−	1.28331i	0.938771	−	0.344541i	$-0.111965\pi$
$968$	10.8156	−	18.7332i	0.347627	−	0.602108i
$969$	6.46015	+	1.73099i	0.207530	+	0.0556075i
$970$	1.85703	+	0.497591i	0.0596258	+	0.0159767i
$971$	−24.0149	+	6.43478i	−0.770676	+	0.206502i	−0.622670	−	0.782484i	$-0.713952\pi$
$971$	−24.0149	+	6.43478i	−0.770676	+	0.206502i	−0.148006	+	0.988986i	$0.547285\pi$
$972$	21.7488	+	21.7488i	0.697593	+	0.697593i
$973$	−49.6322	+	30.6169i	−1.59114	+	0.981533i
$974$	−3.78196			−0.121182
$975$	14.3184	+	8.26676i	0.458557	+	0.264748i
$976$	−24.5948	+	14.1998i	−0.787260	+	0.454525i
$977$	10.3180	−	38.5072i	0.330101	−	1.23195i	−0.578982	−	0.815340i	$-0.696550\pi$
$977$	10.3180	−	38.5072i	0.330101	−	1.23195i	0.909083	−	0.416614i	$-0.136783\pi$
$978$	0.00568018	+	0.0211987i	0.000181632	+	0.000677860i
$979$			3.66466i			0.117123i
$980$	12.3239	+	6.18782i	0.393673	+	0.197663i
$981$	14.6909	+	14.6909i	0.469046	+	0.469046i
$982$	−2.85202	−	1.64662i	−0.0910117	−	0.0525456i
$983$	16.8637	+	29.2088i	0.537869	+	0.931616i	0.999019	+	0.0442940i	$0.0141038\pi$
$983$	16.8637	+	29.2088i	0.537869	+	0.931616i	−0.461150	+	0.887322i	$0.652563\pi$
$984$	2.33780	−	5.44820i	0.0745262	−	0.173682i
$985$	−0.707133	+	1.22479i	−0.0225311	+	0.0390251i
$986$		−	5.78708i		−	0.184298i
$987$	26.7253	−	16.4862i	0.850676	−	0.524761i
$988$	17.6456			0.561381
$989$	−21.4381	−	12.3773i	−0.681691	−	0.393574i
$990$	−2.49283	−	0.667952i	−0.0792274	−	0.0212289i
$991$	2.12691	−	7.93775i	0.0675637	−	0.252151i	−0.923881	−	0.382680i	$-0.875001\pi$
$991$	2.12691	−	7.93775i	0.0675637	−	0.252151i	0.991444	+	0.130529i	$0.0416677\pi$
$992$	14.2636	+	8.23510i	0.452870	+	0.261465i
$993$		−	26.0368i		−	0.826252i
$994$	3.35268	+	3.16279i	0.106341	+	0.100318i
$995$	5.06495	+	5.06495i	0.160570	+	0.160570i
$996$	−35.6737	+	9.55873i	−1.13036	+	0.302880i
$997$	−0.535732	+	1.99938i	−0.0169668	+	0.0633210i	−0.973890	−	0.227019i	$-0.927102\pi$
$997$	−0.535732	+	1.99938i	−0.0169668	+	0.0633210i	0.956923	+	0.290340i	$0.0937686\pi$
$998$	4.86356	+	1.30319i	0.153953	+	0.0412517i
$999$	−3.26364	−	12.1801i	−0.103257	−	0.385361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.r.c.9.11	✓	96
7.4	even	3	inner	287.2.r.c.214.14	yes	96
41.32	even	4	inner	287.2.r.c.114.14	yes	96
287.32	even	12	inner	287.2.r.c.32.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.r.c.9.11	✓	96	1.1	even	1	trivial
287.2.r.c.32.11	yes	96	287.32	even	12	inner
287.2.r.c.114.14	yes	96	41.32	even	4	inner
287.2.r.c.214.14	yes	96	7.4	even	3	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.194567 - 0.112333i) q^{2} +(-0.270068 + 1.00791i) q^{3} +(-0.974763 - 1.68834i) q^{4} +(-0.875130 - 0.505256i) q^{5} +(0.165768 - 0.165768i) q^{6} +(-2.25178 + 1.38907i) q^{7} +0.887324i q^{8} +(1.65513 + 0.955593i) q^{9} +O(q^{10})\)	\(q+(-0.194567 - 0.112333i) q^{2} +(-0.270068 + 1.00791i) q^{3} +(-0.974763 - 1.68834i) q^{4} +(-0.875130 - 0.505256i) q^{5} +(0.165768 - 0.165768i) q^{6} +(-2.25178 + 1.38907i) q^{7} +0.887324i q^{8} +(1.65513 + 0.955593i) q^{9} +(0.113514 + 0.196612i) q^{10} +(-1.53944 + 5.74527i) q^{11} +(1.96494 - 0.526505i) q^{12} +(2.81588 + 2.81588i) q^{13} +(0.594158 - 0.0173167i) q^{14} +(0.745597 - 0.745597i) q^{15} +(-1.84985 + 3.20403i) q^{16} +(-2.72388 - 0.729861i) q^{17} +(-0.214689 - 0.371853i) q^{18} +(0.588267 + 2.19544i) q^{19} +1.97002i q^{20} +(-0.791917 - 2.64473i) q^{21} +(0.944908 - 0.944908i) q^{22} +(1.15466 - 1.99992i) q^{23} +(-0.894341 - 0.239638i) q^{24} +(-1.98943 - 3.44580i) q^{25} +(-0.231560 - 0.864192i) q^{26} +(-3.62367 + 3.62367i) q^{27} +(4.54016 + 2.44775i) q^{28} +(-6.45897 - 6.45897i) q^{29} +(-0.228823 + 0.0613130i) q^{30} +(3.16024 + 5.47370i) q^{31} +(2.25673 - 1.30292i) q^{32} +(-5.37495 - 3.10323i) q^{33} +(0.447988 + 0.447988i) q^{34} +(2.67243 - 0.0778880i) q^{35} -3.72590i q^{36} +(-1.23031 + 2.13095i) q^{37} +(0.132164 - 0.493241i) q^{38} +(-3.59863 + 2.07767i) q^{39} +(0.448326 - 0.776524i) q^{40} +(-0.915918 + 6.33728i) q^{41} +(-0.143009 + 0.603533i) q^{42} -10.7195i q^{43} +(11.2006 - 3.00118i) q^{44} +(-0.965639 - 1.67254i) q^{45} +(-0.449314 + 0.259412i) q^{46} +(2.94386 + 10.9866i) q^{47} +(-2.72978 - 2.72978i) q^{48} +(3.14099 - 6.25573i) q^{49} +0.893916i q^{50} +(1.47127 - 2.54831i) q^{51} +(2.00934 - 7.49897i) q^{52} +(-0.523042 + 1.95202i) q^{53} +(1.11210 - 0.297987i) q^{54} +(4.25005 - 4.25005i) q^{55} +(-1.23255 - 1.99806i) q^{56} -2.37167 q^{57} +(0.531144 + 1.98226i) q^{58} +(-0.789913 - 1.36817i) q^{59} +(-1.98560 - 0.532040i) q^{60} +(6.64778 + 3.83810i) q^{61} -1.42000i q^{62} +(-5.05437 + 0.147310i) q^{63} +6.81395 q^{64} +(-1.04152 - 3.88700i) q^{65} +(0.697190 + 1.20757i) q^{66} +(-9.71822 - 2.60399i) q^{67} +(1.42288 + 5.31027i) q^{68} +(1.70390 + 1.70390i) q^{69} +(-0.528715 - 0.285048i) q^{70} +(5.48294 + 5.48294i) q^{71} +(-0.847921 + 1.46864i) q^{72} +(5.49080 - 3.17012i) q^{73} +(0.478753 - 0.276408i) q^{74} +(4.01033 - 1.07456i) q^{75} +(3.13323 - 3.13323i) q^{76} +(-4.51408 - 15.0755i) q^{77} +0.933563 q^{78} +(6.69120 - 1.79290i) q^{79} +(3.23772 - 1.86930i) q^{80} +(0.193092 + 0.334445i) q^{81} +(0.890093 - 1.13013i) q^{82} -18.1551 q^{83} +(-3.69326 + 3.91500i) q^{84} +(2.01498 + 2.01498i) q^{85} +(-1.20415 + 2.08565i) q^{86} +(8.25441 - 4.76568i) q^{87} +(-5.09792 - 1.36598i) q^{88} +(0.595128 - 0.159464i) q^{89} +0.433893i q^{90} +(-10.2522 - 2.42929i) q^{91} -4.50206 q^{92} +(-6.37046 + 1.70696i) q^{93} +(0.661385 - 2.46832i) q^{94} +(0.594451 - 2.21852i) q^{95} +(0.703756 + 2.62645i) q^{96} +(5.98800 - 5.98800i) q^{97} +(-1.31386 + 0.864318i) q^{98} +(-8.03812 + 8.03812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7}+O(q^{10}) \) 96 * q - 4 * q^3 + 48 * q^4 - 28 * q^6 - 14 * q^7	\( 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7} - 28 q^{10} + 12 q^{12} - 8 q^{13} + 8 q^{14} - 20 q^{15} - 40 q^{16} - 20 q^{17} - 16 q^{18} - 8 q^{19} - 12 q^{22} + 12 q^{23} - 30 q^{24} + 40 q^{25} + 8 q^{26} - 4 q^{27} - 20 q^{28} - 72 q^{29} + 14 q^{30} + 24 q^{31} + 40 q^{34} + 20 q^{35} + 16 q^{37} - 18 q^{38} + 80 q^{40} - 88 q^{41} - 76 q^{42} + 4 q^{44} - 16 q^{45} + 14 q^{47} - 24 q^{48} - 8 q^{51} + 10 q^{52} - 4 q^{53} + 16 q^{54} - 60 q^{55} + 36 q^{56} + 128 q^{57} - 16 q^{58} - 8 q^{59} + 54 q^{60} + 30 q^{63} - 16 q^{64} + 48 q^{66} + 14 q^{67} - 30 q^{68} + 56 q^{69} - 34 q^{70} - 68 q^{71} + 112 q^{72} - 62 q^{75} - 84 q^{76} - 96 q^{78} - 26 q^{79} - 32 q^{81} + 14 q^{82} + 56 q^{83} - 92 q^{85} + 36 q^{86} + 6 q^{88} + 40 q^{89} - 160 q^{92} - 78 q^{93} + 96 q^{94} + 72 q^{95} + 24 q^{96} + 60 q^{97} - 116 q^{98} - 128 q^{99}+O(q^{100}) \) 96 * q - 4 * q^3 + 48 * q^4 - 28 * q^6 - 14 * q^7 - 28 * q^10 + 12 * q^12 - 8 * q^13 + 8 * q^14 - 20 * q^15 - 40 * q^16 - 20 * q^17 - 16 * q^18 - 8 * q^19 - 12 * q^22 + 12 * q^23 - 30 * q^24 + 40 * q^25 + 8 * q^26 - 4 * q^27 - 20 * q^28 - 72 * q^29 + 14 * q^30 + 24 * q^31 + 40 * q^34 + 20 * q^35 + 16 * q^37 - 18 * q^38 + 80 * q^40 - 88 * q^41 - 76 * q^42 + 4 * q^44 - 16 * q^45 + 14 * q^47 - 24 * q^48 - 8 * q^51 + 10 * q^52 - 4 * q^53 + 16 * q^54 - 60 * q^55 + 36 * q^56 + 128 * q^57 - 16 * q^58 - 8 * q^59 + 54 * q^60 + 30 * q^63 - 16 * q^64 + 48 * q^66 + 14 * q^67 - 30 * q^68 + 56 * q^69 - 34 * q^70 - 68 * q^71 + 112 * q^72 - 62 * q^75 - 84 * q^76 - 96 * q^78 - 26 * q^79 - 32 * q^81 + 14 * q^82 + 56 * q^83 - 92 * q^85 + 36 * q^86 + 6 * q^88 + 40 * q^89 - 160 * q^92 - 78 * q^93 + 96 * q^94 + 72 * q^95 + 24 * q^96 + 60 * q^97 - 116 * q^98 - 128 * q^99

Introduction

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