LMFDB - Embedded newform 930.2.r.a.719.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.3
Character	$\chi$	$=$	930.719
Dual form			930.2.r.a.119.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.66709 + 0.469912i) q^{3} +1.00000 q^{4} +(-1.78081 + 1.35230i) q^{5} +(1.66709 - 0.469912i) q^{6} +(-2.19151 + 1.26527i) q^{7} -1.00000 q^{8} +(2.55837 - 1.56677i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.66709 + 0.469912i) q^{3} +1.00000 q^{4} +(-1.78081 + 1.35230i) q^{5} +(1.66709 - 0.469912i) q^{6} +(-2.19151 + 1.26527i) q^{7} -1.00000 q^{8} +(2.55837 - 1.56677i) q^{9} +(1.78081 - 1.35230i) q^{10} +(0.583678 - 1.01096i) q^{11} +(-1.66709 + 0.469912i) q^{12} +(3.18182 - 5.51107i) q^{13} +(2.19151 - 1.26527i) q^{14} +(2.33331 - 3.09123i) q^{15} +1.00000 q^{16} +(3.41739 - 1.97303i) q^{17} +(-2.55837 + 1.56677i) q^{18} +(1.33594 + 2.31391i) q^{19} +(-1.78081 + 1.35230i) q^{20} +(3.05888 - 3.13913i) q^{21} +(-0.583678 + 1.01096i) q^{22} +2.97331i q^{23} +(1.66709 - 0.469912i) q^{24} +(1.34257 - 4.81638i) q^{25} +(-3.18182 + 5.51107i) q^{26} +(-3.52878 + 3.81415i) q^{27} +(-2.19151 + 1.26527i) q^{28} -4.97367 q^{29} +(-2.33331 + 3.09123i) q^{30} +(-1.00997 + 5.47540i) q^{31} -1.00000 q^{32} +(-0.497981 + 1.95964i) q^{33} +(-3.41739 + 1.97303i) q^{34} +(2.19164 - 5.21678i) q^{35} +(2.55837 - 1.56677i) q^{36} +(2.60353 + 4.50944i) q^{37} +(-1.33594 - 2.31391i) q^{38} +(-2.71466 + 10.6826i) q^{39} +(1.78081 - 1.35230i) q^{40} +(0.504431 + 0.291233i) q^{41} +(-3.05888 + 3.13913i) q^{42} +(0.106364 + 0.184228i) q^{43} +(0.583678 - 1.01096i) q^{44} +(-2.43722 + 6.24980i) q^{45} -2.97331i q^{46} -2.60049 q^{47} +(-1.66709 + 0.469912i) q^{48} +(-0.298188 + 0.516477i) q^{49} +(-1.34257 + 4.81638i) q^{50} +(-4.76994 + 4.89509i) q^{51} +(3.18182 - 5.51107i) q^{52} +(-5.05784 - 2.92015i) q^{53} +(3.52878 - 3.81415i) q^{54} +(0.327702 + 2.58964i) q^{55} +(2.19151 - 1.26527i) q^{56} +(-3.31446 - 3.22972i) q^{57} +4.97367 q^{58} +(10.0172 - 5.78341i) q^{59} +(2.33331 - 3.09123i) q^{60} +7.81867i q^{61} +(1.00997 - 5.47540i) q^{62} +(-3.62430 + 6.67061i) q^{63} +1.00000 q^{64} +(1.78641 + 14.1170i) q^{65} +(0.497981 - 1.95964i) q^{66} +(2.19629 + 1.26803i) q^{67} +(3.41739 - 1.97303i) q^{68} +(-1.39719 - 4.95677i) q^{69} +(-2.19164 + 5.21678i) q^{70} +(13.2612 + 7.65636i) q^{71} +(-2.55837 + 1.56677i) q^{72} +(-3.80528 + 6.59093i) q^{73} +(-2.60353 - 4.50944i) q^{74} +(0.0250959 + 8.66022i) q^{75} +(1.33594 + 2.31391i) q^{76} +2.95404i q^{77} +(2.71466 - 10.6826i) q^{78} +(-9.30890 + 5.37450i) q^{79} +(-1.78081 + 1.35230i) q^{80} +(4.09047 - 8.01673i) q^{81} +(-0.504431 - 0.291233i) q^{82} +(2.79531 + 1.61388i) q^{83} +(3.05888 - 3.13913i) q^{84} +(-3.41759 + 8.13493i) q^{85} +(-0.106364 - 0.184228i) q^{86} +(8.29154 - 2.33718i) q^{87} +(-0.583678 + 1.01096i) q^{88} -12.6584 q^{89} +(2.43722 - 6.24980i) q^{90} +16.1034i q^{91} +2.97331i q^{92} +(-0.889250 - 9.60256i) q^{93} +2.60049 q^{94} +(-5.50816 - 2.31405i) q^{95} +(1.66709 - 0.469912i) q^{96} -11.6154i q^{97} +(0.298188 - 0.516477i) q^{98} +(-0.0906783 - 3.50089i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9	$ 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 - 6 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 2 * q^25 + 18 * q^31 - 64 * q^32 + 8 * q^33 + 6 * q^34 - 16 * q^35 - 4 * q^36 - 4 * q^38 - 8 * q^39 + 2 * q^40 + 5 * q^45 + 4 * q^47 + 30 * q^49 - 2 * q^50 - 8 * q^51 + 6 * q^53 - 6 * q^57 - 18 * q^62 - 12 * q^63 + 64 * q^64 - 8 * q^66 - 6 * q^68 - 10 * q^69 + 16 * q^70 + 4 * q^72 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.66709	+	0.469912i	−0.962494	+	0.271304i
$3$	−1.66709	+	0.469912i	−0.962494	+	0.271304i
$4$	1.00000			0.500000
$5$	−1.78081	+	1.35230i	−0.796402	+	0.604767i
$5$	−1.78081	+	1.35230i	−0.796402	+	0.604767i
$6$	1.66709	−	0.469912i	0.680586	−	0.191841i
$7$	−2.19151	+	1.26527i	−0.828313	+	0.478227i	−0.853275	−	0.521462i	$-0.825387\pi$
$7$	−2.19151	+	1.26527i	−0.828313	+	0.478227i	0.0249617	+	0.999688i	$0.492054\pi$
$8$	−1.00000			−0.353553
$9$	2.55837	−	1.56677i	0.852789	−	0.522256i
$10$	1.78081	−	1.35230i	0.563141	−	0.427635i
$11$	0.583678	−	1.01096i	0.175986	−	0.304816i	−0.764516	−	0.644604i	$-0.777022\pi$
$11$	0.583678	−	1.01096i	0.175986	−	0.304816i	0.940502	+	0.339788i	$0.110355\pi$
$12$	−1.66709	+	0.469912i	−0.481247	+	0.135652i
$13$	3.18182	−	5.51107i	0.882478	−	1.52850i	0.0339011	−	0.999425i	$-0.489207\pi$
$13$	3.18182	−	5.51107i	0.882478	−	1.52850i	0.848577	−	0.529072i	$-0.177460\pi$
$14$	2.19151	−	1.26527i	0.585706	−	0.338157i
$15$	2.33331	−	3.09123i	0.602457	−	0.798152i
$16$	1.00000			0.250000
$17$	3.41739	−	1.97303i	0.828839	−	0.478530i	−0.0246160	−	0.999697i	$-0.507836\pi$
$17$	3.41739	−	1.97303i	0.828839	−	0.478530i	0.853455	+	0.521167i	$0.174503\pi$
$18$	−2.55837	+	1.56677i	−0.603013	+	0.369291i
$19$	1.33594	+	2.31391i	0.306485	+	0.530848i	0.977591	−	0.210514i	$-0.0675137\pi$
$19$	1.33594	+	2.31391i	0.306485	+	0.530848i	−0.671106	+	0.741362i	$0.734180\pi$
$20$	−1.78081	+	1.35230i	−0.398201	+	0.302384i
$21$	3.05888	−	3.13913i	0.667501	−	0.685015i
$22$	−0.583678	+	1.01096i	−0.124441	+	0.215537i
$23$			2.97331i			0.619979i	0.950740	+	0.309989i	$0.100325\pi$
$23$			2.97331i			0.619979i	−0.950740	+	0.309989i	$0.899675\pi$
$24$	1.66709	−	0.469912i	0.340293	−	0.0959203i
$25$	1.34257	−	4.81638i	0.268513	−	0.963276i
$26$	−3.18182	+	5.51107i	−0.624006	+	1.08081i
$27$	−3.52878	+	3.81415i	−0.679114	+	0.734033i
$28$	−2.19151	+	1.26527i	−0.414157	+	0.239113i
$29$	−4.97367			−0.923586			−0.461793	−	0.886988i	$-0.652794\pi$
$29$	−4.97367			−0.923586			−0.461793	+	0.886988i	$0.652794\pi$
$30$	−2.33331	+	3.09123i	−0.426001	+	0.564378i
$31$	−1.00997	+	5.47540i	−0.181395	+	0.983410i
$31$	−1.00997	+	5.47540i	−0.181395	+	0.983410i
$32$	−1.00000			−0.176777
$33$	−0.497981	+	1.95964i	−0.0866873	+	0.341129i
$34$	−3.41739	+	1.97303i	−0.586078	+	0.338372i
$35$	2.19164	−	5.21678i	0.370455	−	0.881797i
$36$	2.55837	−	1.56677i	0.426394	−	0.261128i
$37$	2.60353	+	4.50944i	0.428017	+	0.741348i	0.996697	−	0.0812114i	$-0.0258789\pi$
$37$	2.60353	+	4.50944i	0.428017	+	0.741348i	−0.568680	+	0.822559i	$0.692546\pi$
$38$	−1.33594	−	2.31391i	−0.216718	−	0.375366i
$39$	−2.71466	+	10.6826i	−0.434693	+	1.71059i
$40$	1.78081	−	1.35230i	0.281571	−	0.213817i
$41$	0.504431	+	0.291233i	0.0787789	+	0.0454830i	0.538872	−	0.842388i	$-0.318851\pi$
$41$	0.504431	+	0.291233i	0.0787789	+	0.0454830i	−0.460093	+	0.887871i	$0.652184\pi$
$42$	−3.05888	+	3.13913i	−0.471995	+	0.484378i
$43$	0.106364	+	0.184228i	0.0162204	+	0.0280945i	0.874022	−	0.485887i	$-0.161503\pi$
$43$	0.106364	+	0.184228i	0.0162204	+	0.0280945i	−0.857801	+	0.513981i	$0.828170\pi$
$44$	0.583678	−	1.01096i	0.0879928	−	0.152408i
$45$	−2.43722	+	6.24980i	−0.363319	+	0.931665i
$46$		−	2.97331i		−	0.438391i
$47$	−2.60049			−0.379320			−0.189660	−	0.981850i	$-0.560739\pi$
$47$	−2.60049			−0.379320			−0.189660	+	0.981850i	$0.560739\pi$
$48$	−1.66709	+	0.469912i	−0.240623	+	0.0678259i
$49$	−0.298188	+	0.516477i	−0.0425983	+	0.0737825i
$50$	−1.34257	+	4.81638i	−0.189868	+	0.681139i
$51$	−4.76994	+	4.89509i	−0.667925	+	0.685450i
$52$	3.18182	−	5.51107i	0.441239	−	0.764249i
$53$	−5.05784	−	2.92015i	−0.694748	−	0.401113i	0.110640	−	0.993861i	$-0.464710\pi$
$53$	−5.05784	−	2.92015i	−0.694748	−	0.401113i	−0.805388	+	0.592748i	$0.798043\pi$
$54$	3.52878	−	3.81415i	0.480206	−	0.519040i
$55$	0.327702	+	2.58964i	0.0441873	+	0.349186i
$56$	2.19151	−	1.26527i	0.292853	−	0.169079i
$57$	−3.31446	−	3.22972i	−0.439011	−	0.427787i
$58$	4.97367			0.653074
$59$	10.0172	−	5.78341i	1.30412	−	0.752936i	0.323015	−	0.946394i	$-0.395304\pi$
$59$	10.0172	−	5.78341i	1.30412	−	0.752936i	0.981109	+	0.193458i	$0.0619703\pi$
$60$	2.33331	−	3.09123i	0.301228	−	0.399076i
$61$			7.81867i			1.00108i	0.865714	+	0.500539i	$0.166865\pi$
$61$			7.81867i			1.00108i	−0.865714	+	0.500539i	$0.833135\pi$
$62$	1.00997	−	5.47540i	0.128266	−	0.695376i
$63$	−3.62430	+	6.67061i	−0.456619	+	0.840418i
$64$	1.00000			0.125000
$65$	1.78641	+	14.1170i	0.221577	+	1.75099i
$66$	0.497981	−	1.95964i	0.0612972	−	0.241215i
$67$	2.19629	+	1.26803i	0.268320	+	0.154914i	0.628124	−	0.778113i	$-0.283823\pi$
$67$	2.19629	+	1.26803i	0.268320	+	0.154914i	−0.359804	+	0.933028i	$0.617156\pi$
$68$	3.41739	−	1.97303i	0.414419	−	0.239265i
$69$	−1.39719	−	4.95677i	−0.168202	−	0.596726i
$70$	−2.19164	+	5.21678i	−0.261951	+	0.623525i
$71$	13.2612	+	7.65636i	1.57381	+	0.908642i	0.995695	+	0.0926906i	$0.0295467\pi$
$71$	13.2612	+	7.65636i	1.57381	+	0.908642i	0.578120	+	0.815952i	$0.303787\pi$
$72$	−2.55837	+	1.56677i	−0.301506	+	0.184645i
$73$	−3.80528	+	6.59093i	−0.445374	+	0.771410i	−0.998078	−	0.0619672i	$-0.980263\pi$
$73$	−3.80528	+	6.59093i	−0.445374	+	0.771410i	0.552704	+	0.833377i	$0.313596\pi$
$74$	−2.60353	−	4.50944i	−0.302654	−	0.524212i
$75$	0.0250959	+	8.66022i	0.00289783	+	0.999996i
$76$	1.33594	+	2.31391i	0.153243	+	0.265424i
$77$			2.95404i			0.336644i
$78$	2.71466	−	10.6826i	0.307374	−	1.20957i
$79$	−9.30890	+	5.37450i	−1.04733	+	0.604678i	−0.921902	−	0.387424i	$-0.873365\pi$
$79$	−9.30890	+	5.37450i	−1.04733	+	0.604678i	−0.125432	+	0.992102i	$0.540032\pi$
$80$	−1.78081	+	1.35230i	−0.199101	+	0.151192i
$81$	4.09047	−	8.01673i	0.454497	−	0.890748i
$82$	−0.504431	−	0.291233i	−0.0557051	−	0.0321613i
$83$	2.79531	+	1.61388i	0.306826	+	0.177146i	0.645505	−	0.763756i	$-0.276647\pi$
$83$	2.79531	+	1.61388i	0.306826	+	0.177146i	−0.338680	+	0.940902i	$0.609980\pi$
$84$	3.05888	−	3.13913i	0.333751	−	0.342507i
$85$	−3.41759	+	8.13493i	−0.370690	+	0.882357i
$86$	−0.106364	−	0.184228i	−0.0114695	−	0.0198658i
$87$	8.29154	−	2.33718i	0.888946	−	0.250572i
$88$	−0.583678	+	1.01096i	−0.0622203	+	0.107769i
$89$	−12.6584			−1.34179			−0.670894	−	0.741553i	$-0.734089\pi$
$89$	−12.6584			−1.34179			−0.670894	+	0.741553i	$0.734089\pi$
$90$	2.43722	−	6.24980i	0.256906	−	0.658786i
$91$			16.1034i			1.68810i
$92$			2.97331i			0.309989i
$93$	−0.889250	−	9.60256i	−0.0922109	−	0.995739i
$94$	2.60049			0.268220
$95$	−5.50816	−	2.31405i	−0.565125	−	0.237416i
$96$	1.66709	−	0.469912i	0.170146	−	0.0479602i
$97$		−	11.6154i		−	1.17937i	−0.807635	−	0.589683i	$-0.799253\pi$
$97$		−	11.6154i		−	1.17937i	0.807635	−	0.589683i	$-0.200747\pi$
$98$	0.298188	−	0.516477i	0.0301216	−	0.0521721i
$99$	−0.0906783	−	3.50089i	−0.00911351	−	0.351853i
$100$	1.34257	−	4.81638i	0.134257	−	0.481638i
$101$			2.60547i			0.259254i	0.991563	+	0.129627i	$0.0413781\pi$
$101$			2.60547i			0.259254i	−0.991563	+	0.129627i	$0.958622\pi$
$102$	4.76994	−	4.89509i	0.472295	−	0.484686i
$103$	11.9006	+	6.87079i	1.17260	+	0.676999i	0.954290	−	0.298881i	$-0.0966135\pi$
$103$	11.9006	+	6.87079i	1.17260	+	0.676999i	0.218306	+	0.975880i	$0.429947\pi$
$104$	−3.18182	+	5.51107i	−0.312003	+	0.540405i
$105$	−1.20223	+	9.72672i	−0.117325	+	0.949230i
$106$	5.05784	+	2.92015i	0.491261	+	0.283630i
$107$	−1.02068	−	1.76788i	−0.0986733	−	0.170907i	0.812462	−	0.583014i	$-0.198127\pi$
$107$	−1.02068	−	1.76788i	−0.0986733	−	0.170907i	−0.911136	+	0.412106i	$0.864793\pi$
$108$	−3.52878	+	3.81415i	−0.339557	+	0.367017i
$109$	5.29320			0.506997			0.253498	−	0.967336i	$-0.418419\pi$
$109$	5.29320			0.506997			0.253498	+	0.967336i	$0.418419\pi$
$110$	−0.327702	−	2.58964i	−0.0312452	−	0.246912i
$111$	−6.45935	−	6.29421i	−0.613094	−	0.597420i
$112$	−2.19151	+	1.26527i	−0.207078	+	0.119557i
$113$	−6.29037	+	10.8952i	−0.591748	+	1.02494i	0.402249	+	0.915531i	$0.368229\pi$
$113$	−6.29037	+	10.8952i	−0.591748	+	1.02494i	−0.993997	+	0.109408i	$0.965105\pi$
$114$	3.31446	+	3.22972i	0.310428	+	0.302491i
$115$	−4.02081	−	5.29490i	−0.374943	−	0.493752i
$116$	−4.97367			−0.461793
$117$	−0.494317	−	19.0845i	−0.0456997	−	1.76436i
$118$	−10.0172	+	5.78341i	−0.922154	+	0.532406i
$119$	−4.99283	+	8.64784i	−0.457692	+	0.792746i
$120$	−2.33331	+	3.09123i	−0.213001	+	0.282189i
$121$	4.81864	+	8.34613i	0.438058	+	0.758739i
$122$		−	7.81867i		−	0.707869i
$123$	−0.977785	−	0.248474i	−0.0881639	−	0.0224041i
$124$	−1.00997	+	5.47540i	−0.0906977	+	0.491705i
$125$	4.12234	+	10.3926i	0.368713	+	0.929543i
$126$	3.62430	−	6.67061i	0.322878	−	0.594265i
$127$	9.47777	+	16.4160i	0.841016	+	1.45668i	0.889036	+	0.457837i	$0.151376\pi$
$127$	9.47777	+	16.4160i	0.841016	+	1.45668i	−0.0480201	+	0.998846i	$0.515291\pi$
$128$	−1.00000			−0.0883883
$129$	−0.263889	−	0.257142i	−0.0232341	−	0.0226401i
$130$	−1.78641	−	14.1170i	−0.156679	−	1.23814i
$131$	−4.32442	+	2.49670i	−0.377826	+	0.218138i	−0.676872	−	0.736101i	$-0.736665\pi$
$131$	−4.32442	+	2.49670i	−0.377826	+	0.218138i	0.299046	+	0.954239i	$0.403332\pi$
$132$	−0.497981	+	1.95964i	−0.0433437	+	0.170564i
$133$	−5.85544	−	3.38064i	−0.507731	−	0.293139i
$134$	−2.19629	−	1.26803i	−0.189731	−	0.109541i
$135$	1.12621	−	11.5642i	0.0969287	−	0.995291i
$136$	−3.41739	+	1.97303i	−0.293039	+	0.169186i
$137$	8.59916	+	4.96473i	0.734676	+	0.424165i	0.820130	−	0.572177i	$-0.193901\pi$
$137$	8.59916	+	4.96473i	0.734676	+	0.424165i	−0.0854546	+	0.996342i	$0.527234\pi$
$138$	1.39719	+	4.95677i	0.118937	+	0.421949i
$139$		−	5.27999i		−	0.447843i	−0.974607	−	0.223921i	$-0.928114\pi$
$139$		−	5.27999i		−	0.447843i	0.974607	−	0.223921i	$-0.0718859\pi$
$140$	2.19164	−	5.21678i	0.185227	−	0.440899i
$141$	4.33524	−	1.22200i	0.365093	−	0.102911i
$142$	−13.2612	−	7.65636i	−1.11286	−	0.642507i
$143$	−3.71432	−	6.43339i	−0.310607	−	0.537987i
$144$	2.55837	−	1.56677i	0.213197	−	0.130564i
$145$	8.85715	−	6.72589i	0.735546	−	0.558555i
$146$	3.80528	−	6.59093i	0.314927	−	0.545469i
$147$	0.254408	−	1.00114i	0.0209832	−	0.0825723i
$148$	2.60353	+	4.50944i	0.214009	+	0.370674i
$149$	13.6758	−	7.89572i	1.12036	−	0.646843i	0.178870	−	0.983873i	$-0.442756\pi$
$149$	13.6758	−	7.89572i	1.12036	−	0.646843i	0.941494	+	0.337030i	$0.109422\pi$
$150$	−0.0250959	−	8.66022i	−0.00204907	−	0.707104i
$151$			9.89798i			0.805486i	0.915313	+	0.402743i	$0.131943\pi$
$151$			9.89798i			0.805486i	−0.915313	+	0.402743i	$0.868057\pi$
$152$	−1.33594	−	2.31391i	−0.108359	−	0.187683i
$153$	5.65165	−	10.4020i	0.456909	−	0.840952i
$154$		−	2.95404i		−	0.238043i
$155$	−5.60582	−	11.1164i	−0.450271	−	0.892892i
$156$	−2.71466	+	10.6826i	−0.217346	+	0.855294i
$157$			4.41348i			0.352234i	0.984369	+	0.176117i	$0.0563537\pi$
$157$			4.41348i			0.352234i	−0.984369	+	0.176117i	$0.943646\pi$
$158$	9.30890	−	5.37450i	0.740577	−	0.427572i
$159$	9.80408	+	2.49140i	0.777514	+	0.197581i
$160$	1.78081	−	1.35230i	0.140785	−	0.106909i
$161$	−3.76204	−	6.51605i	−0.296490	−	0.513536i
$162$	−4.09047	+	8.01673i	−0.321378	+	0.629854i
$163$			2.35826i			0.184713i	0.995726	+	0.0923567i	$0.0294400\pi$
$163$			2.35826i			0.184713i	−0.995726	+	0.0923567i	$0.970560\pi$
$164$	0.504431	+	0.291233i	0.0393894	+	0.0227415i
$165$	−1.76321	−	4.16316i	−0.137266	−	0.324101i
$166$	−2.79531	−	1.61388i	−0.216958	−	0.125261i
$167$	−3.61526	+	2.08727i	−0.279758	+	0.161518i	−0.633314	−	0.773895i	$-0.718306\pi$
$167$	−3.61526	+	2.08727i	−0.279758	+	0.161518i	0.353556	+	0.935413i	$0.384972\pi$
$168$	−3.05888	+	3.13913i	−0.235997	+	0.242189i
$169$	−13.7480	−	23.8122i	−1.05754	−	1.83171i
$170$	3.41759	−	8.13493i	0.262117	−	0.623921i
$171$	7.04318	+	3.82673i	0.538606	+	0.292637i
$172$	0.106364	+	0.184228i	0.00811018	+	0.0140472i
$173$	6.74927	−	11.6901i	0.513137	−	0.888780i	−0.486747	−	0.873543i	$-0.661816\pi$
$173$	6.74927	−	11.6901i	0.513137	−	0.888780i	0.999884	−	0.0152367i	$-0.00485018\pi$
$174$	−8.29154	+	2.33718i	−0.628580	+	0.177181i
$175$	3.15177	+	12.2539i	0.238251	+	0.926304i
$176$	0.583678	−	1.01096i	0.0439964	−	0.0762040i
$177$	−13.9818	+	14.3486i	−1.05094	+	1.07851i
$178$	12.6584			0.948787
$179$	−7.50882	−	13.0057i	−0.561236	−	0.972089i	−0.997389	−	0.0722165i	$-0.976993\pi$
$179$	−7.50882	−	13.0057i	−0.561236	−	0.972089i	0.436153	−	0.899872i	$-0.356341\pi$
$180$	−2.43722	+	6.24980i	−0.181660	+	0.465832i
$181$	2.21896	+	1.28112i	0.164934	+	0.0952246i	0.580195	−	0.814478i	$-0.302976\pi$
$181$	2.21896	+	1.28112i	0.164934	+	0.0952246i	−0.415261	+	0.909702i	$0.636310\pi$
$182$		−	16.1034i		−	1.19367i
$183$	−3.67408	−	13.0344i	−0.271596	−	0.963531i
$184$		−	2.97331i		−	0.219196i
$185$	−10.7345	−	4.50971i	−0.789217	−	0.331560i
$186$	0.889250	+	9.60256i	0.0652030	+	0.704094i
$187$		−	4.60646i		−	0.336858i
$188$	−2.60049			−0.189660
$189$	2.90743	−	12.8236i	0.211485	−	0.932779i
$190$	5.50816	+	2.31405i	0.399604	+	0.167879i
$191$	6.67352	+	3.85296i	0.482879	+	0.278791i	0.721616	−	0.692294i	$-0.243400\pi$
$191$	6.67352	+	3.85296i	0.482879	+	0.278791i	−0.238736	+	0.971084i	$0.576733\pi$
$192$	−1.66709	+	0.469912i	−0.120312	+	0.0339130i
$193$	−7.14681	+	4.12622i	−0.514439	+	0.297011i	−0.734656	−	0.678439i	$-0.762657\pi$
$193$	−7.14681	+	4.12622i	−0.514439	+	0.297011i	0.220217	+	0.975451i	$0.429323\pi$
$194$			11.6154i			0.833938i
$195$	−9.61183	−	22.6947i	−0.688317	−	1.62520i
$196$	−0.298188	+	0.516477i	−0.0212992	+	0.0368912i
$197$	22.0501	+	12.7306i	1.57100	+	0.907020i	0.996046	+	0.0888373i	$0.0283151\pi$
$197$	22.0501	+	12.7306i	1.57100	+	0.907020i	0.574958	+	0.818183i	$0.305018\pi$
$198$	0.0906783	+	3.50089i	0.00644423	+	0.248798i
$199$	−15.1490	−	8.74625i	−1.07388	−	0.620006i	−0.144642	−	0.989484i	$-0.546203\pi$
$199$	−15.1490	−	8.74625i	−1.07388	−	0.620006i	−0.929239	+	0.369479i	$0.879536\pi$
$200$	−1.34257	+	4.81638i	−0.0949338	+	0.340569i
$201$	−4.25727	−	1.08185i	−0.300285	−	0.0763081i
$202$		−	2.60547i		−	0.183321i
$203$	10.8998	−	6.29302i	0.765019	−	0.441684i
$204$	−4.76994	+	4.89509i	−0.333963	+	0.342725i
$205$	−1.29213	+	0.163511i	−0.0902463	+	0.0114201i
$206$	−11.9006	−	6.87079i	−0.829151	−	0.478711i
$207$	4.65849	+	7.60682i	0.323788	+	0.528711i
$208$	3.18182	−	5.51107i	0.220620	−	0.382124i
$209$	3.11903			0.215748
$210$	1.20223	−	9.72672i	0.0829616	−	0.671207i
$211$	11.6155	+	20.1187i	0.799647	+	1.38503i	0.919846	+	0.392280i	$0.128314\pi$
$211$	11.6155	+	20.1187i	0.799647	+	1.38503i	−0.120198	+	0.992750i	$0.538353\pi$
$212$	−5.05784	−	2.92015i	−0.347374	−	0.200556i
$213$	−25.7054	−	6.53223i	−1.76131	−	0.447581i
$214$	1.02068	+	1.76788i	0.0697726	+	0.120850i
$215$	−0.438545	−	0.184239i	−0.0299085	−	0.0125650i
$216$	3.52878	−	3.81415i	0.240103	−	0.259520i
$217$	−4.71450	−	13.2773i	−0.320041	−	0.901320i
$218$	−5.29320			−0.358501
$219$	3.24658	−	12.7758i	0.219383	−	0.863309i
$220$	0.327702	+	2.58964i	0.0220937	+	0.174593i
$221$		−	25.1113i		−	1.68917i
$222$	6.45935	+	6.29421i	0.433523	+	0.422440i
$223$	−12.7804	−	22.1364i	−0.855841	−	1.48236i	−0.875863	−	0.482561i	$-0.839707\pi$
$223$	−12.7804	−	22.1364i	−0.855841	−	1.48236i	0.0200215	−	0.999800i	$-0.493627\pi$
$224$	2.19151	−	1.26527i	0.146426	−	0.0845393i
$225$	−4.11137	−	14.4256i	−0.274092	−	0.961704i
$226$	6.29037	−	10.8952i	0.418429	−	0.724741i
$227$	−9.83982	+	17.0431i	−0.653092	+	1.13119i	0.329277	+	0.944233i	$0.393195\pi$
$227$	−9.83982	+	17.0431i	−0.653092	+	1.13119i	−0.982369	+	0.186954i	$0.940138\pi$
$228$	−3.31446	−	3.22972i	−0.219506	−	0.213894i
$229$	0.583432	−	0.336845i	0.0385543	−	0.0222593i	−0.480599	−	0.876940i	$-0.659581\pi$
$229$	0.583432	−	0.336845i	0.0385543	−	0.0222593i	0.519153	+	0.854681i	$0.326247\pi$
$230$	4.02081	+	5.29490i	0.265125	+	0.349136i
$231$	−1.38814	−	4.92464i	−0.0913327	−	0.324018i
$232$	4.97367			0.326537
$233$	25.5858			1.67618			0.838090	−	0.545533i	$-0.183673\pi$
$233$	25.5858			1.67618			0.838090	+	0.545533i	$0.183673\pi$
$234$	0.494317	+	19.0845i	0.0323145	+	1.24759i
$235$	4.63098	−	3.51664i	0.302092	−	0.229400i
$236$	10.0172	−	5.78341i	0.652062	−	0.376468i
$237$	12.9932	−	13.3341i	0.844001	−	0.866145i
$238$	4.99283	−	8.64784i	0.323637	−	0.560556i
$239$	−12.1832	+	21.1019i	−0.788065	+	1.36497i	0.139086	+	0.990280i	$0.455584\pi$
$239$	−12.1832	+	21.1019i	−0.788065	+	1.36497i	−0.927151	+	0.374688i	$0.877750\pi$
$240$	2.33331	−	3.09123i	0.150614	−	0.199538i
$241$	22.6146	−	13.0565i	1.45673	−	0.841045i	0.457884	−	0.889012i	$-0.348607\pi$
$241$	22.6146	−	13.0565i	1.45673	−	0.841045i	0.998849	+	0.0479665i	$0.0152741\pi$
$242$	−4.81864	−	8.34613i	−0.309754	−	0.536510i
$243$	−3.05202	+	15.2868i	−0.195787	+	0.980646i
$244$			7.81867i			0.500539i
$245$	−0.167416	−	1.32299i	−0.0106958	−	0.0845226i
$246$	0.977785	+	0.248474i	0.0623413	+	0.0158421i
$247$	17.0029			1.08187
$248$	1.00997	−	5.47540i	0.0641329	−	0.347688i
$249$	−5.41841	−	1.37692i	−0.343378	−	0.0872589i
$250$	−4.12234	−	10.3926i	−0.260719	−	0.657286i
$251$	−8.56462	−	14.8344i	−0.540594	−	0.936337i	−0.998870	−	0.0475266i	$-0.984866\pi$
$251$	−8.56462	−	14.8344i	−0.540594	−	0.936337i	0.458276	−	0.888810i	$-0.348467\pi$
$252$	−3.62430	+	6.67061i	−0.228310	+	0.420209i
$253$	3.00590	+	1.73546i	0.188979	+	0.109107i
$254$	−9.47777	−	16.4160i	−0.594688	−	1.03003i
$255$	1.87473	−	15.1676i	0.117400	−	0.949833i
$256$	1.00000			0.0625000
$257$	−6.32974	+	10.9634i	−0.394838	+	0.683880i	−0.993081	−	0.117435i	$-0.962533\pi$
$257$	−6.32974	+	10.9634i	−0.394838	+	0.683880i	0.598242	+	0.801315i	$0.295866\pi$
$258$	0.263889	+	0.257142i	0.0164290	+	0.0160090i
$259$	−11.4113	−	6.58833i	−0.709065	−	0.409379i
$260$	1.78641	+	14.1170i	0.110789	+	0.875496i
$261$	−12.7245	+	7.79258i	−0.787624	+	0.482349i
$262$	4.32442	−	2.49670i	0.267163	−	0.154247i
$263$		−	7.65133i		−	0.471801i	−0.971777	−	0.235901i	$-0.924196\pi$
$263$		−	7.65133i		−	0.471801i	0.971777	−	0.235901i	$-0.0758040\pi$
$264$	0.497981	−	1.95964i	0.0306486	−	0.120607i
$265$	12.9560	−	1.63950i	0.795879	−	0.100713i
$266$	5.85544	+	3.38064i	0.359020	+	0.207280i
$267$	21.1027	−	5.94833i	1.29146	−	0.364032i
$268$	2.19629	+	1.26803i	0.134160	+	0.0774572i
$269$	−0.846925	+	1.46692i	−0.0516379	+	0.0894395i	−0.890689	−	0.454613i	$-0.849778\pi$
$269$	−0.846925	+	1.46692i	−0.0516379	+	0.0894395i	0.839051	+	0.544053i	$0.183111\pi$
$270$	−1.12621	+	11.5642i	−0.0685390	+	0.703777i
$271$			30.2591i			1.83811i	0.394130	+	0.919055i	$0.371046\pi$
$271$			30.2591i			1.83811i	−0.394130	+	0.919055i	$0.628954\pi$
$272$	3.41739	−	1.97303i	0.207210	−	0.119633i
$273$	−7.56719	−	26.8458i	−0.457987	−	1.62478i
$274$	−8.59916	−	4.96473i	−0.519494	−	0.299930i
$275$	−4.08554	−	4.16850i	−0.246367	−	0.251370i
$276$	−1.39719	−	4.95677i	−0.0841012	−	0.298363i
$277$	−32.9288			−1.97850			−0.989250	−	0.146235i	$-0.953284\pi$
$277$	−32.9288			−1.97850			−0.989250	+	0.146235i	$0.953284\pi$
$278$			5.27999i			0.316673i
$279$	5.99482	+	15.5905i	0.358900	+	0.933376i
$280$	−2.19164	+	5.21678i	−0.130975	+	0.311762i
$281$			13.9762i			0.833752i	0.908963	+	0.416876i	$0.136875\pi$
$281$			13.9762i			0.833752i	−0.908963	+	0.416876i	$0.863125\pi$
$282$	−4.33524	+	1.22200i	−0.258160	+	0.0727691i
$283$		−	11.4141i		−	0.678498i	−0.940697	−	0.339249i	$-0.889827\pi$
$283$		−	11.4141i		−	0.678498i	0.940697	−	0.339249i	$-0.110173\pi$
$284$	13.2612	+	7.65636i	0.786907	+	0.454321i
$285$	10.2700	+	1.26938i	0.608341	+	0.0751913i
$286$	3.71432	+	6.43339i	0.219632	+	0.380414i
$287$	−1.47395			−0.0870048
$288$	−2.55837	+	1.56677i	−0.150753	+	0.0923227i
$289$	−0.714295	+	1.23719i	−0.0420173	+	0.0727762i
$290$	−8.85715	+	6.72589i	−0.520110	+	0.394958i
$291$	5.45822	+	19.3639i	0.319967	+	1.13513i
$292$	−3.80528	+	6.59093i	−0.222687	+	0.385705i
$293$	2.33280	+	4.04052i	0.136283	+	0.236050i	0.926087	−	0.377310i	$-0.123151\pi$
$293$	2.33280	+	4.04052i	0.136283	+	0.236050i	−0.789804	+	0.613360i	$0.789818\pi$
$294$	−0.254408	+	1.00114i	−0.0148374	+	0.0583874i
$295$	−10.0177	+	23.8454i	−0.583256	+	1.38833i
$296$	−2.60353	−	4.50944i	−0.151327	−	0.262106i
$297$	1.79628	+	5.79369i	0.104231	+	0.336184i
$298$	−13.6758	+	7.89572i	−0.792217	+	0.457387i
$299$	16.3861	+	9.46055i	0.947635	+	0.547118i
$300$	0.0250959	+	8.66022i	0.00144891	+	0.499998i
$301$	−0.466195	−	0.269158i	−0.0268711	−	0.0155140i
$302$		−	9.89798i		−	0.569565i
$303$	−1.22434	−	4.34356i	−0.0703367	−	0.249531i
$304$	1.33594	+	2.31391i	0.0766213	+	0.132712i
$305$	−10.5732	−	13.9236i	−0.605419	−	0.797261i
$306$	−5.65165	+	10.4020i	−0.323083	+	0.594643i
$307$	6.69856	−	3.86742i	0.382307	−	0.220725i	−0.296514	−	0.955028i	$-0.595824\pi$
$307$	6.69856	−	3.86742i	0.382307	−	0.220725i	0.678822	+	0.734303i	$0.262491\pi$
$308$			2.95404i			0.168322i
$309$	−23.0679	−	5.86200i	−1.31229	−	0.333478i
$310$	5.60582	+	11.1164i	0.318389	+	0.631370i
$311$			3.48291i			0.197498i	0.995112	+	0.0987489i	$0.0314840\pi$
$311$			3.48291i			0.197498i	−0.995112	+	0.0987489i	$0.968516\pi$
$312$	2.71466	−	10.6826i	0.153687	−	0.604784i
$313$	−0.752791	−	1.30387i	−0.0425503	−	0.0736993i	0.843966	−	0.536397i	$-0.180215\pi$
$313$	−0.752791	−	1.30387i	−0.0425503	−	0.0736993i	−0.886516	+	0.462698i	$0.846882\pi$
$314$		−	4.41348i		−	0.249067i
$315$	−2.56648	−	16.7802i	−0.144605	−	0.945459i
$316$	−9.30890	+	5.37450i	−0.523667	+	0.302339i
$317$	8.17705	+	14.1631i	0.459269	+	0.795477i	0.998922	−	0.0464099i	$-0.0147780\pi$
$317$	8.17705	+	14.1631i	0.459269	+	0.795477i	−0.539653	+	0.841887i	$0.681445\pi$
$318$	−9.80408	−	2.49140i	−0.549785	−	0.139711i
$319$	−2.90302	+	5.02818i	−0.162538	+	0.281524i
$320$	−1.78081	+	1.35230i	−0.0995503	+	0.0755959i
$321$	2.53232	+	2.46758i	0.141340	+	0.137727i
$322$	3.76204	+	6.51605i	0.209650	+	0.363125i
$323$	9.13085	+	5.27170i	0.508054	+	0.293325i
$324$	4.09047	−	8.01673i	0.227248	−	0.445374i
$325$	−22.2716	−	22.7238i	−1.23541	−	1.26049i
$326$		−	2.35826i		−	0.130612i
$327$	−8.82424	+	2.48734i	−0.487981	+	0.137550i
$328$	−0.504431	−	0.291233i	−0.0278525	−	0.0160807i
$329$	5.69900	−	3.29032i	0.314196	−	0.181401i
$330$	1.76321	+	4.16316i	0.0970614	+	0.229174i
$331$	7.86876	+	4.54303i	0.432506	+	0.249707i	0.700414	−	0.713737i	$-0.252999\pi$
$331$	7.86876	+	4.54303i	0.432506	+	0.249707i	−0.267908	+	0.963445i	$0.586332\pi$
$332$	2.79531	+	1.61388i	0.153413	+	0.0885729i
$333$	13.7260	+	7.45768i	0.752182	+	0.408678i
$334$	3.61526	−	2.08727i	0.197818	−	0.114211i
$335$	−5.62593	+	0.711926i	−0.307378	+	0.0388967i
$336$	3.05888	−	3.13913i	0.166875	−	0.171254i
$337$	30.3494			1.65324			0.826619	−	0.562762i	$-0.190261\pi$
$337$	30.3494			1.65324			0.826619	+	0.562762i	$0.190261\pi$
$338$	13.7480	+	23.8122i	0.747790	+	1.29521i
$339$	5.36680	−	21.1193i	0.291485	−	1.14704i
$340$	−3.41759	+	8.13493i	−0.185345	+	0.441179i
$341$	4.94591	+	4.21690i	0.267836	+	0.228358i
$342$	−7.04318	−	3.82673i	−0.380852	−	0.206926i
$343$		−	19.2229i		−	1.03794i
$344$	−0.106364	−	0.184228i	−0.00573476	−	0.00993290i
$345$	9.19119	+	6.93765i	0.494837	+	0.373510i
$346$	−6.74927	+	11.6901i	−0.362843	+	0.628462i
$347$	8.16914	−	4.71646i	0.438542	−	0.253193i	−0.264437	−	0.964403i	$-0.585186\pi$
$347$	8.16914	−	4.71646i	0.438542	−	0.253193i	0.702979	+	0.711210i	$0.251853\pi$
$348$	8.29154	−	2.33718i	0.444473	−	0.125286i
$349$	−5.45162			−0.291819			−0.145909	−	0.989298i	$-0.546611\pi$
$349$	−5.45162			−0.291819			−0.145909	+	0.989298i	$0.546611\pi$
$350$	−3.15177	−	12.2539i	−0.168469	−	0.654996i
$351$	9.79211	+	31.5833i	0.522664	+	1.68579i
$352$	−0.583678	+	1.01096i	−0.0311101	+	0.0538843i
$353$	−20.6931	+	11.9472i	−1.10138	+	0.635883i	−0.936584	−	0.350444i	$-0.886031\pi$
$353$	−20.6931	+	11.9472i	−1.10138	+	0.635883i	−0.164798	+	0.986327i	$0.552697\pi$
$354$	13.9818	−	14.3486i	0.743124	−	0.762621i
$355$	−33.9694	+	4.29861i	−1.80291	+	0.228147i
$356$	−12.6584			−0.670894
$357$	4.25977	−	16.7629i	0.225451	−	0.887187i
$358$	7.50882	+	13.0057i	0.396854	+	0.687371i
$359$	−7.81527	−	4.51215i	−0.412474	−	0.238142i	0.279378	−	0.960181i	$-0.409872\pi$
$359$	−7.81527	−	4.51215i	−0.412474	−	0.238142i	−0.691852	+	0.722039i	$0.743205\pi$
$360$	2.43722	−	6.24980i	0.128453	−	0.329393i
$361$	5.93054	−	10.2720i	0.312134	−	0.540631i
$362$	−2.21896	−	1.28112i	−0.116626	−	0.0673339i
$363$	−11.9550	−	11.6494i	−0.627477	−	0.611435i
$364$			16.1034i			0.844049i
$365$	−2.13645	−	16.8831i	−0.111827	−	0.883700i
$366$	3.67408	+	13.0344i	0.192047	+	0.681319i
$367$	−15.7765	+	27.3257i	−0.823525	+	1.42639i	0.0795162	+	0.996834i	$0.474662\pi$
$367$	−15.7765	+	27.3257i	−0.823525	+	1.42639i	−0.903041	+	0.429554i	$0.858671\pi$
$368$			2.97331i			0.154995i
$369$	1.74681	−	0.0452451i	0.0909355	−	0.00235536i
$370$	10.7345	+	4.50971i	0.558061	+	0.234449i
$371$	14.7791			0.767292
$372$	−0.889250	−	9.60256i	−0.0461055	−	0.497870i
$373$			9.79690i			0.507264i	0.967301	+	0.253632i	$0.0816253\pi$
$373$			9.79690i			0.507264i	−0.967301	+	0.253632i	$0.918375\pi$
$374$			4.60646i			0.238194i
$375$	−11.7559	−	15.3883i	−0.607072	−	0.794646i
$376$	2.60049			0.134110
$377$	−15.8253	+	27.4102i	−0.815045	+	1.41170i
$378$	−2.90743	+	12.8236i	−0.149542	+	0.659575i
$379$	−10.2994	−	17.8392i	−0.529047	−	0.916336i	−0.999426	−	0.0338717i	$-0.989216\pi$
$379$	−10.2994	−	17.8392i	−0.529047	−	0.916336i	0.470379	−	0.882464i	$-0.344117\pi$
$380$	−5.50816	−	2.31405i	−0.282563	−	0.118708i
$381$	−23.5143	−	22.9132i	−1.20468	−	1.17388i
$382$	−6.67352	−	3.85296i	−0.341447	−	0.197135i
$383$	25.4503	+	14.6938i	1.30045	+	0.750816i	0.980481	−	0.196612i	$-0.0629939\pi$
$383$	25.4503	+	14.6938i	1.30045	+	0.750816i	0.319970	+	0.947428i	$0.396327\pi$
$384$	1.66709	−	0.469912i	0.0850732	−	0.0239801i
$385$	−3.99475	−	5.26058i	−0.203591	−	0.268104i
$386$	7.14681	−	4.12622i	0.363763	−	0.210019i
$387$	0.560760	+	0.304674i	0.0285050	+	0.0154875i
$388$		−	11.6154i		−	0.589683i
$389$	−1.62322	−	2.81150i	−0.0823006	−	0.142549i	0.821937	−	0.569578i	$-0.192893\pi$
$389$	−1.62322	−	2.81150i	−0.0823006	−	0.142549i	−0.904238	+	0.427029i	$0.859560\pi$
$390$	9.61183	+	22.6947i	0.486714	+	1.14919i
$391$	5.86644	+	10.1610i	0.296679	+	0.513862i
$392$	0.298188	−	0.516477i	0.0150608	−	0.0260861i
$393$	6.03596	−	6.19432i	0.304474	−	0.312462i
$394$	−22.0501	−	12.7306i	−1.11087	−	0.641360i
$395$	9.30945	−	22.1594i	0.468409	−	1.11496i
$396$	−0.0906783	−	3.50089i	−0.00455676	−	0.175927i
$397$	23.6825	−	13.6731i	1.18859	−	0.686232i	0.230603	−	0.973048i	$-0.425930\pi$
$397$	23.6825	−	13.6731i	1.18859	−	0.686232i	0.957986	+	0.286816i	$0.0925968\pi$
$398$	15.1490	+	8.74625i	0.759349	+	0.438410i
$399$	11.3501	+	2.88429i	0.568218	+	0.144395i
$400$	1.34257	−	4.81638i	0.0671283	−	0.240819i
$401$	9.60608			0.479705			0.239852	−	0.970809i	$-0.422901\pi$
$401$	9.60608			0.479705			0.239852	+	0.970809i	$0.422901\pi$
$402$	4.25727	+	1.08185i	0.212333	+	0.0539579i
$403$	26.9618	+	22.9877i	1.34306	+	1.14510i
$404$			2.60547i			0.129627i
$405$	3.55668	+	19.8078i	0.176733	+	0.984259i
$406$	−10.8998	+	6.29302i	−0.540950	+	0.312318i
$407$	6.07849			0.301299
$408$	4.76994	−	4.89509i	0.236147	−	0.242343i
$409$	26.5680	−	15.3390i	1.31370	−	0.758466i	0.330995	−	0.943633i	$-0.392616\pi$
$409$	26.5680	−	15.3390i	1.31370	−	0.758466i	0.982707	+	0.185167i	$0.0592824\pi$
$410$	1.29213	−	0.163511i	0.0638138	−	0.00807523i
$411$	−16.6685	−	4.23579i	−0.822198	−	0.208936i
$412$	11.9006	+	6.87079i	0.586298	+	0.338499i
$413$	−14.6351	+	25.3488i	−0.720148	+	1.24733i
$414$	−4.65849	−	7.60682i	−0.228952	−	0.373855i
$415$	−7.16037	+	0.906100i	−0.351489	+	0.0444787i
$416$	−3.18182	+	5.51107i	−0.156002	+	0.270203i
$417$	2.48113	+	8.80220i	0.121501	+	0.431046i
$418$	−3.11903			−0.152557
$419$			8.50389i			0.415442i	0.978188	+	0.207721i	$0.0666047\pi$
$419$			8.50389i			0.415442i	−0.978188	+	0.207721i	$0.933395\pi$
$420$	−1.20223	+	9.72672i	−0.0586627	+	0.474615i
$421$	2.12626	−	3.68278i	0.103627	−	0.179488i	−0.809549	−	0.587052i	$-0.800288\pi$
$421$	2.12626	−	3.68278i	0.103627	−	0.179488i	0.913177	+	0.407564i	$0.133622\pi$
$422$	−11.6155	−	20.1187i	−0.565436	−	0.979364i
$423$	−6.65300	+	4.07436i	−0.323480	+	0.198102i
$424$	5.05784	+	2.92015i	0.245630	+	0.141815i
$425$	−4.91479	−	19.1084i	−0.238402	−	0.926892i
$426$	25.7054	+	6.53223i	1.24543	+	0.316488i
$427$	−9.89272	−	17.1347i	−0.478742	−	0.829206i
$428$	−1.02068	−	1.76788i	−0.0493367	−	0.0854536i
$429$	9.21522	+	8.97962i	0.444915	+	0.433540i
$430$	0.438545	+	0.184239i	0.0211485	+	0.00888477i
$431$	3.67853	−	2.12380i	0.177189	−	0.102300i	−0.408782	−	0.912632i	$-0.634047\pi$
$431$	3.67853	−	2.12380i	0.177189	−	0.102300i	0.585971	+	0.810332i	$0.300713\pi$
$432$	−3.52878	+	3.81415i	−0.169778	+	0.183508i
$433$	−26.6589			−1.28115			−0.640573	−	0.767898i	$-0.721303\pi$
$433$	−26.6589			−1.28115			−0.640573	+	0.767898i	$0.721303\pi$
$434$	4.71450	+	13.2773i	0.226303	+	0.637329i
$435$	−11.6051	+	15.3747i	−0.556421	+	0.737162i
$436$	5.29320			0.253498
$437$	−6.87999	+	3.97216i	−0.329114	+	0.190014i
$438$	−3.24658	+	12.7758i	−0.155127	+	0.610452i
$439$	−5.46842	+	9.47159i	−0.260994	+	0.452054i	−0.966506	−	0.256643i	$-0.917384\pi$
$439$	−5.46842	+	9.47159i	−0.260994	+	0.452054i	0.705513	+	0.708697i	$0.250717\pi$
$440$	−0.327702	−	2.58964i	−0.0156226	−	0.123456i
$441$	0.0463256	+	1.78853i	0.00220598	+	0.0851681i
$442$			25.1113i			1.19442i
$443$	−17.1646	+	29.7300i	−0.815516	+	1.41251i	0.0934414	+	0.995625i	$0.470213\pi$
$443$	−17.1646	+	29.7300i	−0.815516	+	1.41251i	−0.908957	+	0.416890i	$0.863120\pi$
$444$	−6.45935	−	6.29421i	−0.306547	−	0.298710i
$445$	22.5422	−	17.1180i	1.06860	−	0.811469i
$446$	12.7804	+	22.1364i	0.605171	+	1.04819i
$447$	−19.0885	+	19.5893i	−0.902853	+	0.926541i
$448$	−2.19151	+	1.26527i	−0.103539	+	0.0597783i
$449$	20.8543			0.984176			0.492088	−	0.870546i	$-0.336234\pi$
$449$	20.8543			0.984176			0.492088	+	0.870546i	$0.336234\pi$
$450$	4.11137	+	14.4256i	0.193812	+	0.680027i
$451$	0.588850	−	0.339973i	0.0277279	−	0.0160087i
$452$	−6.29037	+	10.8952i	−0.295874	+	0.512469i
$453$	−4.65118	−	16.5008i	−0.218531	−	0.775276i
$454$	9.83982	−	17.0431i	0.461805	−	0.799870i
$455$	−21.7767	−	28.6772i	−1.02091	−	1.34441i
$456$	3.31446	+	3.22972i	0.155214	+	0.151246i
$457$	9.71757			0.454569			0.227284	−	0.973828i	$-0.427015\pi$
$457$	9.71757			0.454569			0.227284	+	0.973828i	$0.427015\pi$
$458$	−0.583432	+	0.336845i	−0.0272620	+	0.0157397i
$459$	−4.53378	+	19.9968i	−0.211619	+	0.933372i
$460$	−4.02081	−	5.29490i	−0.187471	−	0.246876i
$461$	28.0073			1.30443			0.652214	−	0.758035i	$-0.273840\pi$
$461$	28.0073			1.30443			0.652214	+	0.758035i	$0.273840\pi$
$462$	1.38814	+	4.92464i	0.0645820	+	0.229115i
$463$	−6.55196			−0.304496			−0.152248	−	0.988342i	$-0.548651\pi$
$463$	−6.55196			−0.304496			−0.152248	+	0.988342i	$0.548651\pi$
$464$	−4.97367			−0.230897
$465$	14.5691	+	15.8978i	0.675628	+	0.737243i
$466$	−25.5858			−1.18524
$467$	6.66673			0.308499			0.154250	−	0.988032i	$-0.450704\pi$
$467$	6.66673			0.308499			0.154250	+	0.988032i	$0.450704\pi$
$468$	−0.494317	−	19.0845i	−0.0228498	−	0.882182i
$469$	−6.41759			−0.296337
$470$	−4.63098	+	3.51664i	−0.213611	+	0.162211i
$471$	−2.07395	−	7.35766i	−0.0955624	−	0.339023i
$472$	−10.0172	+	5.78341i	−0.461077	+	0.266203i
$473$	0.248329			0.0114182
$474$	−12.9932	+	13.3341i	−0.596799	+	0.612457i
$475$	12.9383	−	3.32780i	0.593649	−	0.152690i
$476$	−4.99283	+	8.64784i	−0.228846	+	0.396373i
$477$	−17.5150	+	0.453664i	−0.801957	+	0.0207719i
$478$	12.1832	−	21.1019i	0.557246	−	0.965178i
$479$	−35.9059	+	20.7303i	−1.64058	+	0.947190i	−0.659954	+	0.751306i	$0.729424\pi$
$479$	−35.9059	+	20.7303i	−1.64058	+	0.947190i	−0.980627	+	0.195883i	$0.937243\pi$
$480$	−2.33331	+	3.09123i	−0.106500	+	0.141095i
$481$	33.1358			1.51086
$482$	−22.6146	+	13.0565i	−1.03007	+	0.594709i
$483$	9.33362	+	9.09500i	0.424694	+	0.413837i
$484$	4.81864	+	8.34613i	0.219029	+	0.379370i
$485$	15.7075	+	20.6848i	0.713242	+	0.939250i
$486$	3.05202	−	15.2868i	0.138442	−	0.693422i
$487$	7.67498	−	13.2935i	0.347787	−	0.602384i	−0.638069	−	0.769979i	$-0.720267\pi$
$487$	7.67498	−	13.2935i	0.347787	−	0.602384i	0.985856	+	0.167595i	$0.0536000\pi$
$488$		−	7.81867i		−	0.353934i
$489$	−1.10818	−	3.93143i	−0.0501134	−	0.177786i
$490$	0.167416	+	1.32299i	0.00756308	+	0.0597665i
$491$	8.51286	−	14.7447i	0.384180	−	0.665419i	−0.607475	−	0.794339i	$-0.707818\pi$
$491$	8.51286	−	14.7447i	0.384180	−	0.665419i	0.991655	+	0.128920i	$0.0411509\pi$
$492$	−0.977785	−	0.248474i	−0.0440819	−	0.0112021i
$493$	−16.9970	+	9.81320i	−0.765504	+	0.441964i
$494$	−17.0029			−0.764995
$495$	4.89574	+	6.11180i	0.220047	+	0.274705i
$496$	−1.00997	+	5.47540i	−0.0453488	+	0.245853i
$497$	−38.7494			−1.73815
$498$	5.41841	+	1.37692i	0.242805	+	0.0617013i
$499$	9.32152	−	5.38178i	0.417289	−	0.240922i	−0.276628	−	0.960977i	$-0.589217\pi$
$499$	9.32152	−	5.38178i	0.417289	−	0.240922i	0.693917	+	0.720055i	$0.255884\pi$
$500$	4.12234	+	10.3926i	0.184356	+	0.464772i
$501$	5.04613	−	5.17852i	0.225444	−	0.231359i
$502$	8.56462	+	14.8344i	0.382258	+	0.662090i
$503$	9.45987	+	16.3850i	0.421795	+	0.730570i	0.996115	−	0.0880609i	$-0.0280670\pi$
$503$	9.45987	+	16.3850i	0.421795	+	0.730570i	−0.574321	+	0.818631i	$0.694734\pi$
$504$	3.62430	−	6.67061i	0.161439	−	0.297133i
$505$	−3.52338	−	4.63985i	−0.156789	−	0.206471i
$506$	−3.00590	−	1.73546i	−0.133629	−	0.0771505i
$507$	34.1087	+	33.2367i	1.51482	+	1.47609i
$508$	9.47777	+	16.4160i	0.420508	+	0.728341i
$509$	14.0362	−	24.3114i	0.622144	−	1.07758i	−0.366942	−	0.930244i	$-0.619595\pi$
$509$	14.0362	−	24.3114i	0.622144	−	1.07758i	0.989086	−	0.147341i	$-0.0470714\pi$
$510$	−1.87473	+	15.1676i	−0.0830143	+	0.671633i
$511$		−	19.2588i		−	0.851959i
$512$	−1.00000			−0.0441942
$513$	−13.5398	−	3.06982i	−0.597798	−	0.135536i
$514$	6.32974	−	10.9634i	0.279193	−	0.483576i
$515$	−30.4840	+	3.85756i	−1.34329	+	0.169984i
$516$	−0.263889	−	0.257142i	−0.0116171	−	0.0113201i
$517$	−1.51785	+	2.62899i	−0.0667549	+	0.115623i
$518$	11.4113	+	6.58833i	0.501384	+	0.289474i
$519$	−5.75832	+	22.6599i	−0.252762	+	0.994661i
$520$	−1.78641	−	14.1170i	−0.0783393	−	0.619069i
$521$	−34.9512	+	20.1791i	−1.53124	+	0.884062i	−0.531935	+	0.846785i	$0.678535\pi$
$521$	−34.9512	+	20.1791i	−1.53124	+	0.884062i	−0.999305	+	0.0372764i	$0.988132\pi$
$522$	12.7245	−	7.79258i	0.556934	−	0.341072i
$523$	22.2396			0.972468			0.486234	−	0.873829i	$-0.338370\pi$
$523$	22.2396			0.972468			0.486234	+	0.873829i	$0.338370\pi$
$524$	−4.32442	+	2.49670i	−0.188913	+	0.109069i
$525$	−11.0125	−	18.9472i	−0.480625	−	0.826924i
$526$			7.65133i			0.333614i
$527$	7.35168	+	20.7043i	0.320244	+	0.901892i
$528$	−0.497981	+	1.95964i	−0.0216718	+	0.0852822i
$529$	14.1594			0.615627
$530$	−12.9560	+	1.63950i	−0.562771	+	0.0712152i
$531$	16.5663	−	30.4907i	0.718916	−	1.32318i
$532$	−5.85544	−	3.38064i	−0.253866	−	0.146569i
$533$	3.21002	−	1.85330i	0.139041	−	0.0802755i
$534$	−21.1027	+	5.94833i	−0.913202	+	0.257409i
$535$	4.20835	+	1.76798i	0.181943	+	0.0764365i
$536$	−2.19629	−	1.26803i	−0.0948653	−	0.0547705i
$537$	18.6294	+	18.1531i	0.803917	+	0.783364i
$538$	0.846925	−	1.46692i	0.0365135	−	0.0632433i
$539$	0.348092	+	0.602913i	0.0149934	+	0.0259693i
$540$	1.12621	−	11.5642i	0.0484644	−	0.497646i
$541$	−21.8294	−	37.8096i	−0.938518	−	1.62556i	−0.768238	−	0.640165i	$-0.778866\pi$
$541$	−21.8294	−	37.8096i	−0.938518	−	1.62556i	−0.170280	−	0.985396i	$-0.554467\pi$
$542$		−	30.2591i		−	1.29974i
$543$	−4.30121	−	1.09302i	−0.184583	−	0.0469059i
$544$	−3.41739	+	1.97303i	−0.146519	+	0.0845930i
$545$	−9.42619	+	7.15800i	−0.403774	+	0.306615i
$546$	7.56719	+	26.8458i	0.323846	+	1.14890i
$547$	−0.00396456	−	0.00228894i	−0.000169512	−	9.78679e-5i	0.499915	−	0.866074i	$-0.333364\pi$
$547$	−0.00396456	−	0.00228894i	−0.000169512	−	9.78679e-5i	−0.500085	+	0.865976i	$0.666698\pi$
$548$	8.59916	+	4.96473i	0.367338	+	0.212083i
$549$	12.2500	+	20.0030i	0.522819	+	0.853708i
$550$	4.08554	+	4.16850i	0.174208	+	0.177745i
$551$	−6.64451	−	11.5086i	−0.283066	−	0.490284i
$552$	1.39719	+	4.95677i	0.0594685	+	0.210974i
$553$	13.6004	−	23.5565i	0.578347	−	1.00173i
$554$	32.9288			1.39901
$555$	20.0145	+	2.47381i	0.849570	+	0.105007i
$556$		−	5.27999i		−	0.223921i
$557$			7.40927i			0.313941i	0.987603	+	0.156970i	$0.0501728\pi$
$557$			7.40927i			0.313941i	−0.987603	+	0.156970i	$0.949827\pi$
$558$	−5.99482	−	15.5905i	−0.253781	−	0.659996i
$559$	1.35372			0.0572564
$560$	2.19164	−	5.21678i	0.0926137	−	0.220449i
$561$	2.16463	+	7.67937i	0.0913907	+	0.324223i
$562$		−	13.9762i		−	0.589552i
$563$	−8.14483	+	14.1073i	−0.343264	+	0.594550i	−0.985037	−	0.172344i	$-0.944866\pi$
$563$	−8.14483	+	14.1073i	−0.343264	+	0.594550i	0.641773	+	0.766895i	$0.278199\pi$
$564$	4.33524	−	1.22200i	0.182547	−	0.0514555i
$565$	−3.53169	−	27.9088i	−0.148579	−	1.17413i
$566$			11.4141i			0.479771i
$567$	1.17901	+	22.7443i	0.0495139	+	0.955171i
$568$	−13.2612	−	7.65636i	−0.556428	−	0.321254i
$569$	5.77803	−	10.0078i	0.242228	−	0.419551i	−0.719121	−	0.694885i	$-0.755455\pi$
$569$	5.77803	−	10.0078i	0.242228	−	0.419551i	0.961349	+	0.275334i	$0.0887886\pi$
$570$	−10.2700	−	1.26938i	−0.430162	−	0.0531683i
$571$	−2.86065	−	1.65160i	−0.119715	−	0.0691173i	0.438947	−	0.898513i	$-0.355352\pi$
$571$	−2.86065	−	1.65160i	−0.119715	−	0.0691173i	−0.558662	+	0.829396i	$0.688685\pi$
$572$	−3.71432	−	6.43339i	−0.155303	−	0.268993i
$573$	−12.9359	−	3.28726i	−0.540405	−	0.137327i
$574$	1.47395			0.0615217
$575$	14.3206	+	3.99187i	0.597210	+	0.166473i
$576$	2.55837	−	1.56677i	0.106599	−	0.0652820i
$577$	−33.1201	+	19.1219i	−1.37881	+	0.796054i	−0.992016	−	0.126114i	$-0.959750\pi$
$577$	−33.1201	+	19.1219i	−1.37881	+	0.796054i	−0.386790	+	0.922168i	$0.626416\pi$
$578$	0.714295	−	1.23719i	0.0297107	−	0.0514605i
$579$	9.97541	−	10.2371i	0.414564	−	0.425441i
$580$	8.85715	−	6.72589i	0.367773	−	0.279277i
$581$	−8.16795			−0.338864
$582$	−5.45822	−	19.3639i	−0.226250	−	0.802660i
$583$	−5.90430	+	3.40885i	−0.244531	+	0.141180i
$584$	3.80528	−	6.59093i	0.157463	−	0.272735i
$585$	26.6883	+	33.3174i	1.10343	+	1.37751i
$586$	−2.33280	−	4.04052i	−0.0963669	−	0.166912i
$587$		−	28.9143i		−	1.19342i	−0.802457	−	0.596710i	$-0.796474\pi$
$587$		−	28.9143i		−	1.19342i	0.802457	−	0.596710i	$-0.203526\pi$
$588$	0.254408	−	1.00114i	0.0104916	−	0.0412861i
$589$	−14.0188	+	4.97782i	−0.577636	+	0.205107i
$590$	10.0177	−	23.8454i	0.412424	−	0.981698i
$591$	−42.7417	−	10.8615i	−1.75816	−	0.446782i
$592$	2.60353	+	4.50944i	0.107004	+	0.185337i
$593$	10.9026			0.447718			0.223859	−	0.974622i	$-0.428135\pi$
$593$	10.9026			0.447718			0.223859	+	0.974622i	$0.428135\pi$
$594$	−1.79628	−	5.79369i	−0.0737022	−	0.237718i
$595$	−2.80319	−	22.1520i	−0.114920	−	0.908142i
$596$	13.6758	−	7.89572i	0.560182	−	0.323421i
$597$	29.3646	+	7.46211i	1.20181	+	0.305404i
$598$	−16.3861	−	9.46055i	−0.670079	−	0.386871i
$599$	39.3112	+	22.6963i	1.60621	+	0.927348i	0.990207	+	0.139606i	$0.0445836\pi$
$599$	39.3112	+	22.6963i	1.60621	+	0.927348i	0.616006	+	0.787741i	$0.288750\pi$
$600$	−0.0250959	−	8.66022i	−0.00102454	−	0.353552i
$601$	10.1555	−	5.86329i	0.414252	−	0.239169i	−0.278363	−	0.960476i	$-0.589792\pi$
$601$	10.1555	−	5.86329i	0.414252	−	0.239169i	0.692615	+	0.721307i	$0.256458\pi$
$602$	0.466195	+	0.269158i	0.0190007	+	0.0109701i
$603$	7.60562	−	0.196997i	0.309725	−	0.00802233i
$604$			9.89798i			0.402743i
$605$	−19.8676	−	8.34662i	−0.807731	−	0.339338i
$606$	1.22434	+	4.34356i	0.0497355	+	0.176445i
$607$	−30.2803	−	17.4824i	−1.22904	−	0.709587i	−0.262212	−	0.965010i	$-0.584452\pi$
$607$	−30.2803	−	17.4824i	−1.22904	−	0.709587i	−0.966829	+	0.255423i	$0.917785\pi$
$608$	−1.33594	−	2.31391i	−0.0541794	−	0.0938416i
$609$	−15.2138	+	15.6130i	−0.616495	+	0.632670i
$610$	10.5732	+	13.9236i	0.428096	+	0.563748i
$611$	−8.27429	+	14.3315i	−0.334742	+	0.579790i
$612$	5.65165	−	10.4020i	0.228454	−	0.420476i
$613$	13.2279	+	22.9115i	0.534271	+	0.925385i	0.999198	+	0.0400358i	$0.0127472\pi$
$613$	13.2279	+	22.9115i	0.534271	+	0.925385i	−0.464927	+	0.885349i	$0.653919\pi$
$614$	−6.69856	+	3.86742i	−0.270332	+	0.156076i
$615$	2.07726	−	0.879775i	0.0837632	−	0.0354759i
$616$		−	2.95404i		−	0.119022i
$617$	12.1881	+	21.1104i	0.490674	+	0.849873i	0.999942	−	0.0107352i	$-0.00341717\pi$
$617$	12.1881	+	21.1104i	0.490674	+	0.849873i	−0.509268	+	0.860608i	$0.670084\pi$
$618$	23.0679	+	5.86200i	0.927929	+	0.235804i
$619$		−	42.7518i		−	1.71834i	−0.511690	−	0.859170i	$-0.670980\pi$
$619$		−	42.7518i		−	1.71834i	0.511690	−	0.859170i	$-0.329020\pi$
$620$	−5.60582	−	11.1164i	−0.225135	−	0.446446i
$621$	−11.3407	−	10.4922i	−0.455085	−	0.421036i
$622$		−	3.48291i		−	0.139652i
$623$	27.7410	−	16.0163i	1.11142	−	0.641679i
$624$	−2.71466	+	10.6826i	−0.108673	+	0.427647i
$625$	−21.3950	−	12.9326i	−0.855801	−	0.517305i
$626$	0.752791	+	1.30387i	0.0300876	+	0.0521132i
$627$	−5.19970	+	1.46567i	−0.207656	+	0.0585332i
$628$			4.41348i			0.176117i
$629$	17.7945	+	10.2737i	0.709515	+	0.409639i
$630$	2.56648	+	16.7802i	0.102251	+	0.668540i
$631$	−4.38109	−	2.52942i	−0.174408	−	0.100695i	0.410254	−	0.911971i	$-0.365440\pi$
$631$	−4.38109	−	2.52942i	−0.174408	−	0.100695i	−0.584663	+	0.811276i	$0.698773\pi$
$632$	9.30890	−	5.37450i	0.370288	−	0.213786i
$633$	−28.8182	−	28.0814i	−1.14542	−	1.11614i
$634$	−8.17705	−	14.1631i	−0.324752	−	0.562487i
$635$	−39.0775	−	16.4169i	−1.55074	−	0.651487i
$636$	9.80408	+	2.49140i	0.388757	+	0.0987905i
$637$	1.89756	+	3.28668i	0.0751842	+	0.130223i
$638$	2.90302	−	5.02818i	0.114932	−	0.199067i
$639$	45.9227	−	1.18947i	1.81668	−	0.0470546i
$640$	1.78081	−	1.35230i	0.0703927	−	0.0534544i
$641$	−22.9201	+	39.6989i	−0.905291	+	1.56801i	−0.0847654	+	0.996401i	$0.527014\pi$
$641$	−22.9201	+	39.6989i	−0.905291	+	1.56801i	−0.820526	+	0.571609i	$0.806319\pi$
$642$	−2.53232	−	2.46758i	−0.0999426	−	0.0973875i
$643$	−4.82979			−0.190468			−0.0952341	−	0.995455i	$-0.530360\pi$
$643$	−4.82979			−0.190468			−0.0952341	+	0.995455i	$0.530360\pi$
$644$	−3.76204	−	6.51605i	−0.148245	−	0.256768i
$645$	0.817670	+	0.101064i	0.0321957	+	0.00397941i
$646$	−9.13085	−	5.27170i	−0.359248	−	0.207412i
$647$		−	14.0203i		−	0.551194i	−0.961273	−	0.275597i	$-0.911124\pi$
$647$		−	14.0203i		−	0.551194i	0.961273	−	0.275597i	$-0.0888756\pi$
$648$	−4.09047	+	8.01673i	−0.160689	+	0.314927i
$649$		−	13.5026i		−	0.530023i
$650$	22.2716	+	22.7238i	0.873565	+	0.891302i
$651$	14.0986	+	19.9190i	0.552569	+	0.780686i
$652$			2.35826i			0.0923567i
$653$	32.7400			1.28121			0.640607	−	0.767869i	$-0.278683\pi$
$653$	32.7400			1.28121			0.640607	+	0.767869i	$0.278683\pi$
$654$	8.82424	−	2.48734i	0.345055	−	0.0972626i
$655$	4.32467	−	10.2941i	0.168979	−	0.402222i
$656$	0.504431	+	0.291233i	0.0196947	+	0.0113708i
$657$	0.591175	+	22.8240i	0.0230640	+	0.890449i
$658$	−5.69900	+	3.29032i	−0.222170	+	0.128270i
$659$		−	38.8028i		−	1.51154i	−0.654836	−	0.755771i	$-0.727262\pi$
$659$		−	38.8028i		−	1.51154i	0.654836	−	0.755771i	$-0.272738\pi$
$660$	−1.76321	−	4.16316i	−0.0686328	−	0.162051i
$661$	19.1710	−	33.2052i	0.745667	−	1.29153i	−0.204216	−	0.978926i	$-0.565464\pi$
$661$	19.1710	−	33.2052i	0.745667	−	1.29153i	0.949883	−	0.312607i	$-0.101202\pi$
$662$	−7.86876	−	4.54303i	−0.305828	−	0.176570i
$663$	11.8001	+	41.8628i	0.458278	+	1.62582i
$664$	−2.79531	−	1.61388i	−0.108479	−	0.0626305i
$665$	14.9991	−	1.89804i	0.581639	−	0.0736028i
$666$	−13.7260	−	7.45768i	−0.531873	−	0.288979i
$667$		−	14.7883i		−	0.572604i
$668$	−3.61526	+	2.08727i	−0.139879	+	0.0807591i
$669$	31.7082	+	30.8976i	1.22591	+	1.19457i
$670$	5.62593	−	0.711926i	0.217349	−	0.0275041i
$671$	7.90436	+	4.56358i	0.305144	+	0.176175i
$672$	−3.05888	+	3.13913i	−0.117999	+	0.121095i
$673$	−14.8730	+	25.7608i	−0.573312	+	0.993006i	0.422910	+	0.906172i	$0.361009\pi$
$673$	−14.8730	+	25.7608i	−0.573312	+	0.993006i	−0.996223	+	0.0868347i	$0.972325\pi$
$674$	−30.3494			−1.16902
$675$	13.6328	+	22.1167i	0.524725	+	0.851272i
$676$	−13.7480	−	23.8122i	−0.528768	−	0.915853i
$677$	−38.9582	−	22.4925i	−1.49729	−	0.864459i	−0.497291	−	0.867584i	$-0.665672\pi$
$677$	−38.9582	−	22.4925i	−1.49729	−	0.864459i	−0.999995	+	0.00312507i	$0.999005\pi$
$678$	−5.36680	+	21.1193i	−0.206111	+	0.811080i
$679$	14.6966	+	25.4553i	0.564005	+	0.976885i
$680$	3.41759	−	8.13493i	0.131059	−	0.311960i
$681$	8.39511	−	33.0361i	0.321701	−	1.26595i
$682$	−4.94591	−	4.21690i	−0.189389	−	0.161474i
$683$	19.9161			0.762068			0.381034	−	0.924561i	$-0.375568\pi$
$683$	19.9161			0.762068			0.381034	+	0.924561i	$0.375568\pi$
$684$	7.04318	+	3.82673i	0.269303	+	0.146319i
$685$	−22.0273	+	2.78741i	−0.841619	+	0.106502i
$686$			19.2229i			0.733935i
$687$	−0.814345	+	0.835711i	−0.0310692	+	0.0318844i
$688$	0.106364	+	0.184228i	0.00405509	+	0.00702362i
$689$	−32.1863	+	18.5828i	−1.22620	+	0.707947i
$690$	−9.19119	−	6.93765i	−0.349902	−	0.264112i
$691$	3.01668	−	5.22504i	0.114760	−	0.198770i	−0.802924	−	0.596082i	$-0.796723\pi$
$691$	3.01668	−	5.22504i	0.114760	−	0.198770i	0.917684	+	0.397312i	$0.130057\pi$
$692$	6.74927	−	11.6901i	0.256569	−	0.444390i
$693$	4.62829	+	7.55751i	0.175814	+	0.287086i
$694$	−8.16914	+	4.71646i	−0.310096	+	0.179034i
$695$	7.14013	+	9.40265i	0.270841	+	0.356663i
$696$	−8.29154	+	2.33718i	−0.314290	+	0.0885907i
$697$	2.29845			0.0870600
$698$	5.45162			0.206347
$699$	−42.6537	+	12.0231i	−1.61331	+	0.454754i
$700$	3.15177	+	12.2539i	0.119126	+	0.463152i
$701$	−13.1260	+	7.57832i	−0.495764	+	0.286229i	−0.726962	−	0.686677i	$-0.759069\pi$
$701$	−13.1260	+	7.57832i	−0.495764	+	0.286229i	0.231199	+	0.972907i	$0.425735\pi$
$702$	−9.79211	−	31.5833i	−0.369579	−	1.19203i
$703$	−6.95630	+	12.0487i	−0.262362	+	0.454424i
$704$	0.583678	−	1.01096i	0.0219982	−	0.0381020i
$705$	−6.06773	+	8.03870i	−0.228524	+	0.302755i
$706$	20.6931	−	11.9472i	0.778795	−	0.449637i
$707$	−3.29663	−	5.70992i	−0.123982	−	0.214744i
$708$	−13.9818	+	14.3486i	−0.525468	+	0.539255i
$709$			46.2342i			1.73636i	0.496247	+	0.868181i	$0.334711\pi$
$709$			46.2342i			1.73636i	−0.496247	+	0.868181i	$0.665289\pi$
$710$	33.9694	−	4.29861i	1.27485	−	0.161324i
$711$	−15.3950	+	28.3348i	−0.577357	+	1.06264i
$712$	12.6584			0.474394
$713$	−16.2801	−	3.00295i	−0.609693	−	0.112461i
$714$	−4.25977	+	16.7629i	−0.159418	+	0.627336i
$715$	15.3144	+	6.43376i	0.572725	+	0.240609i
$716$	−7.50882	−	13.0057i	−0.280618	−	0.486044i
$717$	10.3944	−	40.9038i	0.388187	−	1.52758i
$718$	7.81527	+	4.51215i	0.291663	+	0.168392i
$719$	−0.850396	−	1.47293i	−0.0317144	−	0.0549310i	0.849733	−	0.527214i	$-0.176763\pi$
$719$	−0.850396	−	1.47293i	−0.0317144	−	0.0549310i	−0.881447	+	0.472283i	$0.843430\pi$
$720$	−2.43722	+	6.24980i	−0.0908299	+	0.232916i
$721$	−34.7736			−1.29504
$722$	−5.93054	+	10.2720i	−0.220712	+	0.382284i
$723$	−31.5651	+	32.3933i	−1.17392	+	1.20472i
$724$	2.21896	+	1.28112i	0.0824669	+	0.0476123i
$725$	−6.67748	+	23.9551i	−0.247995	+	0.889669i
$726$	11.9550	+	11.6494i	0.443693	+	0.432350i
$727$	16.7604	−	9.67663i	0.621609	−	0.358886i	−0.155886	−	0.987775i	$-0.549823\pi$
$727$	16.7604	−	9.67663i	0.621609	−	0.358886i	0.777495	+	0.628889i	$0.216490\pi$
$728$		−	16.1034i		−	0.596833i
$729$	−2.09544	−	26.9186i	−0.0776089	−	0.996984i
$730$	2.13645	+	16.8831i	0.0790735	+	0.624871i
$731$	0.726974	+	0.419719i	0.0268881	+	0.0155239i
$732$	−3.67408	−	13.0344i	−0.135798	−	0.481765i
$733$	−7.87334	−	4.54568i	−0.290808	−	0.167898i	0.347498	−	0.937681i	$-0.387031\pi$
$733$	−7.87334	−	4.54568i	−0.290808	−	0.167898i	−0.638306	+	0.769782i	$0.720365\pi$
$734$	15.7765	−	27.3257i	0.582320	−	1.00861i
$735$	0.900785	+	2.12687i	0.0332260	+	0.0784507i
$736$		−	2.97331i		−	0.109598i
$737$	2.56385	−	1.48024i	0.0944407	−	0.0545254i
$738$	−1.74681	+	0.0452451i	−0.0643011	+	0.00166549i
$739$	−22.7174	−	13.1159i	−0.835674	−	0.482477i	0.0201174	−	0.999798i	$-0.493596\pi$
$739$	−22.7174	−	13.1159i	−0.835674	−	0.482477i	−0.855791	+	0.517321i	$0.826929\pi$
$740$	−10.7345	−	4.50971i	−0.394608	−	0.165780i
$741$	−28.3453	+	7.98984i	−1.04129	+	0.293514i
$742$	−14.7791			−0.542557
$743$			16.6662i			0.611425i	0.952124	+	0.305713i	$0.0988947\pi$
$743$			16.6662i			0.611425i	−0.952124	+	0.305713i	$0.901105\pi$
$744$	0.889250	+	9.60256i	0.0326015	+	0.352047i
$745$	−13.6766	+	32.5545i	−0.501071	+	1.19271i
$746$		−	9.79690i		−	0.358690i
$747$	9.68001	−	0.250726i	0.354173	−	0.00917360i
$748$		−	4.60646i		−	0.168429i
$749$	4.47368	+	2.58288i	0.163465	+	0.0943764i
$750$	11.7559	+	15.3883i	0.429265	+	0.561900i
$751$	−14.3994	−	24.9405i	−0.525441	−	0.910090i	−0.999561	−	0.0296299i	$-0.990567\pi$
$751$	−14.3994	−	24.9405i	−0.525441	−	0.910090i	0.474120	−	0.880460i	$-0.342766\pi$
$752$	−2.60049			−0.0948301
$753$	21.2488	+	20.7056i	0.774350	+	0.754553i
$754$	15.8253	−	27.4102i	0.576324	−	0.998222i
$755$	−13.3850	−	17.6264i	−0.487132	−	0.641491i
$756$	2.90743	−	12.8236i	0.105742	−	0.466390i
$757$	−6.97726	+	12.0850i	−0.253593	+	0.439235i	−0.964512	−	0.264038i	$-0.914946\pi$
$757$	−6.97726	+	12.0850i	−0.253593	+	0.439235i	0.710920	+	0.703273i	$0.248279\pi$
$758$	10.2994	+	17.8392i	0.374093	+	0.647947i
$759$	−5.82661	−	1.48065i	−0.211493	−	0.0537443i
$760$	5.50816	+	2.31405i	0.199802	+	0.0839394i
$761$	−5.28189	−	9.14850i	−0.191468	−	0.331633i	0.754269	−	0.656566i	$-0.227992\pi$
$761$	−5.28189	−	9.14850i	−0.191468	−	0.331633i	−0.945737	+	0.324933i	$0.894658\pi$
$762$	23.5143	+	22.9132i	0.851835	+	0.830057i
$763$	−11.6001	+	6.69733i	−0.419952	+	0.242460i
$764$	6.67352	+	3.85296i	0.241440	+	0.139395i
$765$	4.00211	+	26.1667i	0.144696	+	0.946059i
$766$	−25.4503	−	14.6938i	−0.919558	−	0.530907i
$767$		−	73.6071i		−	2.65780i
$768$	−1.66709	+	0.469912i	−0.0601559	+	0.0169565i
$769$	14.8007	+	25.6356i	0.533728	+	0.924445i	0.999224	+	0.0393944i	$0.0125429\pi$
$769$	14.8007	+	25.6356i	0.533728	+	0.924445i	−0.465495	+	0.885050i	$0.654124\pi$
$770$	3.99475	+	5.26058i	0.143961	+	0.189578i
$771$	5.40039	−	21.2514i	0.194490	−	0.765351i
$772$	−7.14681	+	4.12622i	−0.257219	+	0.148506i
$773$		−	19.0137i		−	0.683875i	−0.939723	−	0.341938i	$-0.888917\pi$
$773$		−	19.0137i		−	0.683875i	0.939723	−	0.341938i	$-0.111083\pi$
$774$	−0.560760	−	0.304674i	−0.0201561	−	0.0109513i
$775$	25.0156	+	12.2155i	0.898588	+	0.438793i
$776$			11.6154i			0.416969i
$777$	22.1196	+	5.62101i	0.793536	+	0.201653i
$778$	1.62322	+	2.81150i	0.0581953	+	0.100797i
$779$			1.55628i			0.0557595i
$780$	−9.61183	−	22.6947i	−0.344159	−	0.812602i
$781$	15.4805	−	8.93769i	0.553937	−	0.319816i
$782$	−5.86644	−	10.1610i	−0.209783	−	0.363356i
$783$	17.5510	−	18.9703i	0.627220	−	0.677943i
$784$	−0.298188	+	0.516477i	−0.0106496	+	0.0184456i
$785$	−5.96835	−	7.85957i	−0.213020	−	0.280520i
$786$	−6.03596	+	6.19432i	−0.215295	+	0.220944i
$787$	−16.8350	−	29.1591i	−0.600103	−	1.03941i	−0.992805	−	0.119744i	$-0.961793\pi$
$787$	−16.8350	−	29.1591i	−0.600103	−	1.03941i	0.392701	−	0.919666i	$-0.371541\pi$
$788$	22.0501	+	12.7306i	0.785502	+	0.453510i
$789$	3.59545	+	12.7554i	0.128001	+	0.454106i
$790$	−9.30945	+	22.1594i	−0.331215	+	0.788396i
$791$		−	31.8361i		−	1.13196i
$792$	0.0906783	+	3.50089i	0.00322211	+	0.124399i
$793$	43.0892	+	24.8776i	1.53014	+	0.883429i
$794$	−23.6825	+	13.6731i	−0.840459	+	0.485239i
$795$	−20.8283	+	8.82134i	−0.738704	+	0.312861i
$796$	−15.1490	−	8.74625i	−0.536941	−	0.310003i
$797$	11.8837	+	6.86104i	0.420941	+	0.243030i	0.695480	−	0.718546i	$-0.255192\pi$
$797$	11.8837	+	6.86104i	0.420941	+	0.243030i	−0.274539	+	0.961576i	$0.588525\pi$
$798$	−11.3501	−	2.88429i	−0.401791	−	0.102103i
$799$	−8.88689	+	5.13085i	−0.314395	+	0.181516i
$800$	−1.34257	+	4.81638i	−0.0474669	+	0.170285i
$801$	−32.3848	+	19.8328i	−1.14426	+	0.700757i
$802$	−9.60608			−0.339203
$803$	4.44211	+	7.69396i	0.156759	+	0.271514i
$804$	−4.25727	−	1.08185i	−0.150142	−	0.0381540i
$805$	15.5111	+	6.51643i	0.546696	+	0.229674i
$806$	−26.9618	−	22.9877i	−0.949688	−	0.809708i
$807$	0.722577	−	2.84346i	0.0254359	−	0.100095i
$808$		−	2.60547i		−	0.0916603i
$809$	−3.82153	−	6.61908i	−0.134358	−	0.232714i	0.790994	−	0.611824i	$-0.209564\pi$
$809$	−3.82153	−	6.61908i	−0.134358	−	0.232714i	−0.925352	+	0.379109i	$0.876230\pi$
$810$	−3.55668	−	19.8078i	−0.124969	−	0.695976i
$811$	1.11093	−	1.92419i	0.0390101	−	0.0675675i	−0.845861	−	0.533403i	$-0.820913\pi$
$811$	1.11093	−	1.92419i	0.0390101	−	0.0675675i	0.884871	+	0.465836i	$0.154246\pi$
$812$	10.8998	−	6.29302i	0.382509	−	0.220842i
$813$	−14.2191	−	50.4446i	−0.498686	−	1.76917i
$814$	−6.07849			−0.213051
$815$	−3.18908	−	4.19962i	−0.111709	−	0.147106i
$816$	−4.76994	+	4.89509i	−0.166981	+	0.171362i
$817$	−0.284191	+	0.492234i	−0.00994260	+	0.0172211i
$818$	−26.5680	+	15.3390i	−0.928927	+	0.536317i
$819$	25.2304	+	41.1985i	0.881620	+	1.43959i
$820$	−1.29213	+	0.163511i	−0.0451232	+	0.00571005i
$821$	−33.9218			−1.18388			−0.591939	−	0.805983i	$-0.701637\pi$
$821$	−33.9218			−1.18388			−0.591939	+	0.805983i	$0.701637\pi$
$822$	16.6685	+	4.23579i	0.581382	+	0.147740i
$823$	−4.08313	−	7.07218i	−0.142329	−	0.246521i	0.786044	−	0.618170i	$-0.212126\pi$
$823$	−4.08313	−	7.07218i	−0.142329	−	0.246521i	−0.928373	+	0.371649i	$0.878792\pi$
$824$	−11.9006	−	6.87079i	−0.414575	−	0.239355i
$825$	8.76978	+	5.02941i	0.305325	+	0.175101i
$826$	14.6351	−	25.3488i	0.509222	−	0.881998i
$827$	−8.07627	−	4.66284i	−0.280839	−	0.162143i	0.352964	−	0.935637i	$-0.385174\pi$
$827$	−8.07627	−	4.66284i	−0.280839	−	0.162143i	−0.633803	+	0.773494i	$0.718507\pi$
$828$	4.65849	+	7.60682i	0.161894	+	0.264355i
$829$		−	31.8726i		−	1.10698i	−0.832855	−	0.553491i	$-0.813295\pi$
$829$		−	31.8726i		−	1.10698i	0.832855	−	0.553491i	$-0.186705\pi$
$830$	7.16037	−	0.906100i	0.248540	−	0.0314512i
$831$	54.8952	−	15.4736i	1.90429	−	0.536774i
$832$	3.18182	−	5.51107i	0.110310	−	0.191062i
$833$			2.35334i			0.0815384i
$834$	−2.48113	−	8.80220i	−0.0859144	−	0.304795i
$835$	3.61548	−	8.60596i	0.125119	−	0.297822i
$836$	3.11903			0.107874
$837$	−17.3200	−	23.1736i	−0.598668	−	0.800998i
$838$		−	8.50389i		−	0.293762i
$839$		−	5.17690i		−	0.178726i	−0.995999	−	0.0893631i	$-0.971517\pi$
$839$		−	5.17690i		−	0.178726i	0.995999	−	0.0893631i	$-0.0284832\pi$
$840$	1.20223	−	9.72672i	0.0414808	−	0.335604i
$841$	−4.26265			−0.146988
$842$	−2.12626	+	3.68278i	−0.0732756	+	0.126917i
$843$	−6.56760	−	23.2996i	−0.226200	−	0.802481i
$844$	11.6155	+	20.1187i	0.399824	+	0.692515i
$845$	56.6837	+	23.8136i	1.94998	+	0.819212i
$846$	6.65300	−	4.07436i	0.228735	−	0.140080i
$847$	−21.1202	−	12.1938i	−0.725699	−	0.418982i
$848$	−5.05784	−	2.92015i	−0.173687	−	0.100278i
$849$	5.36362	+	19.0283i	0.184079	+	0.653050i
$850$	4.91479	+	19.1084i	0.168576	+	0.655412i
$851$	−13.4080	+	7.74110i	−0.459620	+	0.265362i
$852$	−25.7054	−	6.53223i	−0.880653	−	0.223790i
$853$		−	50.2504i		−	1.72054i	−0.509838	−	0.860270i	$-0.670295\pi$
$853$		−	50.2504i		−	1.72054i	0.509838	−	0.860270i	$-0.329705\pi$
$854$	9.89272	+	17.1347i	0.338522	+	0.586337i
$855$	−17.7175	+	2.70982i	−0.605924	+	0.0926740i
$856$	1.02068	+	1.76788i	0.0348863	+	0.0604248i
$857$	20.7236	−	35.8943i	0.707904	−	1.22613i	−0.257730	−	0.966217i	$-0.582974\pi$
$857$	20.7236	−	35.8943i	0.707904	−	1.22613i	0.965633	−	0.259908i	$-0.0836923\pi$
$858$	−9.21522	−	8.97962i	−0.314602	−	0.306559i
$859$	30.9828	+	17.8879i	1.05712	+	0.610328i	0.924634	−	0.380857i	$-0.124371\pi$
$859$	30.9828	+	17.8879i	1.05712	+	0.610328i	0.132485	+	0.991185i	$0.457704\pi$
$860$	−0.438545	−	0.184239i	−0.0149543	−	0.00628248i
$861$	2.45721	−	0.692628i	0.0837415	−	0.0236047i
$862$	−3.67853	+	2.12380i	−0.125291	+	0.0723370i
$863$	35.0518	+	20.2372i	1.19318	+	0.688882i	0.959026	−	0.283318i	$-0.0914352\pi$
$863$	35.0518	+	20.2372i	1.19318	+	0.688882i	0.234152	+	0.972200i	$0.424769\pi$
$864$	3.52878	−	3.81415i	0.120051	−	0.129760i
$865$	3.78933	+	29.9448i	0.128841	+	1.01816i
$866$	26.6589			0.905906
$867$	0.609420	−	2.39817i	0.0206970	−	0.0814461i
$868$	−4.71450	−	13.2773i	−0.160020	−	0.450660i
$869$			12.5479i			0.425659i
$870$	11.6051	−	15.3747i	0.393449	−	0.521252i
$871$	13.9764	−	8.06928i	0.473572	−	0.273417i
$872$	−5.29320			−0.179250
$873$	−18.1987	−	29.7165i	−0.615932	−	1.00575i
$874$	6.87999	−	3.97216i	0.232719	−	0.134360i
$875$	−22.1836	−	17.5596i	−0.749942	−	0.593624i
$876$	3.24658	−	12.7758i	0.109692	−	0.431655i
$877$	46.9146	+	27.0862i	1.58419	+	0.914635i	0.994238	+	0.107199i	$0.0341882\pi$
$877$	46.9146	+	27.0862i	1.58419	+	0.914635i	0.589956	+	0.807435i	$0.299145\pi$
$878$	5.46842	−	9.47159i	0.184550	−	0.319651i
$879$	−5.78766	−	5.63970i	−0.195213	−	0.190222i
$880$	0.327702	+	2.58964i	0.0110468	+	0.0872966i
$881$	18.4587	−	31.9714i	0.621889	−	1.07714i	−0.367244	−	0.930125i	$-0.619699\pi$
$881$	18.4587	−	31.9714i	0.621889	−	1.07714i	0.989134	−	0.147020i	$-0.0469680\pi$
$882$	−0.0463256	−	1.78853i	−0.00155986	−	0.0602230i
$883$	−27.6274			−0.929736			−0.464868	−	0.885380i	$-0.653898\pi$
$883$	−27.6274			−0.929736			−0.464868	+	0.885380i	$0.653898\pi$
$884$		−	25.1113i		−	0.844585i
$885$	5.49525	−	44.4598i	0.184721	−	1.49450i
$886$	17.1646	−	29.7300i	0.576657	−	0.998799i
$887$	−25.5426	−	44.2411i	−0.857637	−	1.48547i	−0.874176	−	0.485608i	$-0.838598\pi$
$887$	−25.5426	−	44.2411i	−0.857637	−	1.48547i	0.0165390	−	0.999863i	$-0.494735\pi$
$888$	6.45935	+	6.29421i	0.216762	+	0.211220i
$889$	−41.5413	−	23.9839i	−1.39325	−	0.804393i
$890$	−22.5422	+	17.1180i	−0.755616	+	0.573795i
$891$	−5.71708	−	8.81449i	−0.191529	−	0.295297i
$892$	−12.7804	−	22.1364i	−0.427921	−	0.741180i
$893$	−3.47409	−	6.01730i	−0.116256	−	0.201361i
$894$	19.0885	−	19.5893i	0.638413	−	0.655163i
$895$	30.9594	+	13.0064i	1.03486	+	0.434757i
$896$	2.19151	−	1.26527i	0.0732132	−	0.0422697i
$897$	−31.7628	−	8.07152i	−1.06053	−	0.269500i
$898$	−20.8543			−0.695917
$899$	5.02323	−	27.2328i	0.167534	−	0.908264i
$900$	−4.11137	−	14.4256i	−0.137046	−	0.480852i
$901$	−23.0462			−0.767779
$902$	−0.588850	+	0.339973i	−0.0196066	+	0.0113199i
$903$	0.903669	+	0.229640i	0.0300722	+	0.00764192i
$904$	6.29037	−	10.8952i	0.209215	−	0.362370i
$905$	−5.68399	+	0.719274i	−0.188942	+	0.0239095i
$906$	4.65118	+	16.5008i	0.154525	+	0.548203i
$907$		−	27.1776i		−	0.902418i	−0.892418	−	0.451209i	$-0.850993\pi$
$907$		−	27.1776i		−	0.902418i	0.892418	−	0.451209i	$-0.149007\pi$
$908$	−9.83982	+	17.0431i	−0.326546	+	0.565594i
$909$	4.08218	+	6.66576i	0.135397	+	0.221089i
$910$	21.7767	+	28.6772i	0.721890	+	0.950638i
$911$	−23.1209	−	40.0465i	−0.766028	−	1.32680i	−0.939701	−	0.341996i	$-0.888897\pi$
$911$	−23.1209	−	40.0465i	−0.766028	−	1.32680i	0.173673	−	0.984803i	$-0.444436\pi$
$912$	−3.31446	−	3.22972i	−0.109753	−	0.106947i
$913$	3.26313	−	1.88397i	0.107994	−	0.0623502i
$914$	−9.71757			−0.321429
$915$	24.1693	+	18.2433i	0.799012	+	0.603106i
$916$	0.583432	−	0.336845i	0.0192771	−	0.0111297i
$917$	6.31800	−	10.9431i	0.208639	−	0.361373i
$918$	4.53378	−	19.9968i	0.149637	−	0.659993i
$919$	−23.3930	+	40.5179i	−0.771664	+	1.33656i	0.164986	+	0.986296i	$0.447242\pi$
$919$	−23.3930	+	40.5179i	−0.771664	+	1.33656i	−0.936650	+	0.350265i	$0.886091\pi$
$920$	4.02081	+	5.29490i	0.132562	+	0.174568i
$921$	−9.34975	+	9.59506i	−0.308085	+	0.316168i
$922$	−28.0073			−0.922371
$923$	84.3895	−	48.7223i	2.77771	−	1.60371i
$924$	−1.38814	−	4.92464i	−0.0456664	−	0.162009i
$925$	25.2146	−	6.48535i	0.829051	−	0.213237i
$926$	6.55196			0.215311
$927$	41.2109	−	1.06742i	1.35354	−	0.0350588i
$928$	4.97367			0.163269
$929$	4.99976			0.164037			0.0820184	−	0.996631i	$-0.473863\pi$
$929$	4.99976			0.164037			0.0820184	+	0.996631i	$0.473863\pi$
$930$	−14.5691	−	15.8978i	−0.477741	−	0.521310i
$931$	−1.59345			−0.0522231
$932$	25.5858			0.838090
$933$	−1.63666	−	5.80632i	−0.0535818	−	0.190090i
$934$	−6.66673			−0.218142
$935$	6.22932	+	8.20323i	0.203720	+	0.268274i
$936$	0.494317	+	19.0845i	0.0161573	+	0.623797i
$937$	−30.5656	+	17.6471i	−0.998536	+	0.576505i	−0.907815	−	0.419371i	$-0.862251\pi$
$937$	−30.5656	+	17.6471i	−0.998536	+	0.576505i	−0.0907212	+	0.995876i	$0.528917\pi$
$938$	6.41759			0.209542
$939$	1.86768	+	1.81993i	0.0609493	+	0.0593910i
$940$	4.63098	−	3.51664i	0.151046	−	0.114700i
$941$	22.7805	−	39.4570i	0.742624	−	1.28626i	−0.208673	−	0.977985i	$-0.566914\pi$
$941$	22.7805	−	39.4570i	0.742624	−	1.28626i	0.951297	−	0.308277i	$-0.0997522\pi$
$942$	2.07395	+	7.35766i	0.0675728	+	0.239725i
$943$	−0.865928	+	1.49983i	−0.0281985	+	0.0488412i
$944$	10.0172	−	5.78341i	0.326031	−	0.188234i
$945$	12.1638	+	26.7681i	0.395688	+	0.870767i
$946$	−0.248329			−0.00807388
$947$	30.2955	−	17.4911i	0.984473	−	0.568386i	0.0808554	−	0.996726i	$-0.474235\pi$
$947$	30.2955	−	17.4911i	0.984473	−	0.568386i	0.903618	+	0.428340i	$0.140901\pi$
$948$	12.9932	−	13.3341i	0.422000	−	0.433072i
$949$	24.2154	+	41.9423i	0.786066	+	1.36151i
$950$	−12.9383	+	3.32780i	−0.419773	+	0.107968i
$951$	−20.2873	−	19.7686i	−0.657860	−	0.641041i
$952$	4.99283	−	8.64784i	0.161819	−	0.280278i
$953$		−	6.87324i		−	0.222646i	−0.993784	−	0.111323i	$-0.964491\pi$
$953$		−	6.87324i		−	0.222646i	0.993784	−	0.111323i	$-0.0355088\pi$
$954$	17.5150	−	0.453664i	0.567069	−	0.0146879i
$955$	−17.0946	+	2.16322i	−0.553170	+	0.0700001i
$956$	−12.1832	+	21.1019i	−0.394032	+	0.682484i
$957$	2.47679	−	9.74658i	0.0800632	−	0.315062i
$958$	35.9059	−	20.7303i	1.16007	−	0.669764i
$959$	−25.1269			−0.811389
$960$	2.33331	−	3.09123i	0.0753071	−	0.0997689i
$961$	−28.9599	−	11.0599i	−0.934191	−	0.356772i
$962$	−33.1358			−1.06834
$963$	−5.38114	−	2.92370i	−0.173405	−	0.0942150i
$964$	22.6146	−	13.0565i	0.728367	−	0.420523i
$965$	7.14723	−	17.0126i	0.230078	−	0.547656i
$966$	−9.33362	−	9.09500i	−0.300304	−	0.292627i
$967$	−4.20935	−	7.29080i	−0.135363	−	0.234456i	0.790373	−	0.612626i	$-0.209887\pi$
$967$	−4.20935	−	7.29080i	−0.135363	−	0.234456i	−0.925736	+	0.378170i	$0.876554\pi$
$968$	−4.81864	−	8.34613i	−0.154877	−	0.268255i
$969$	−17.6992	−	4.49769i	−0.568579	−	0.144487i
$970$	−15.7075	−	20.6848i	−0.504338	−	0.664150i
$971$	−18.3274	−	10.5813i	−0.588153	−	0.339570i	0.176214	−	0.984352i	$-0.443615\pi$
$971$	−18.3274	−	10.5813i	−0.588153	−	0.339570i	−0.764367	+	0.644782i	$0.776948\pi$
$972$	−3.05202	+	15.2868i	−0.0978936	+	0.490323i
$973$	6.68060	+	11.5711i	0.214170	+	0.370954i
$974$	−7.67498	+	13.2935i	−0.245922	+	0.425950i
$975$	47.8070	+	27.4170i	1.53105	+	0.878045i
$976$			7.81867i			0.250269i
$977$	37.4454			1.19799			0.598993	−	0.800754i	$-0.295568\pi$
$977$	37.4454			1.19799			0.598993	+	0.800754i	$0.295568\pi$
$978$	1.10818	+	3.93143i	0.0354355	+	0.125713i
$979$	−7.38843	+	12.7971i	−0.236135	+	0.408998i
$980$	−0.167416	−	1.32299i	−0.00534790	−	0.0422613i
$981$	13.5420	−	8.29323i	0.432361	−	0.264782i
$982$	−8.51286	+	14.7447i	−0.271656	+	0.470522i
$983$	−33.1751	−	19.1537i	−1.05812	−	0.610907i	−0.133210	−	0.991088i	$-0.542529\pi$
$983$	−33.1751	−	19.1537i	−1.05812	−	0.610907i	−0.924912	+	0.380180i	$0.875862\pi$
$984$	0.977785	+	0.248474i	0.0311706	+	0.00792105i
$985$	−56.4827	+	7.14753i	−1.79969	+	0.227739i
$986$	16.9970	−	9.81320i	0.541293	−	0.312516i
$987$	−7.95457	+	8.16328i	−0.253197	+	0.259840i
$988$	17.0029			0.540933
$989$	−0.547767	+	0.316253i	−0.0174180	+	0.0100563i
$990$	−4.89574	−	6.11180i	−0.155597	−	0.194246i
$991$			38.8224i			1.23323i	0.787263	+	0.616617i	$0.211497\pi$
$991$			38.8224i			1.23323i	−0.787263	+	0.616617i	$0.788503\pi$
$992$	1.00997	−	5.47540i	0.0320665	−	0.173844i
$993$	−15.2527	−	3.87601i	−0.484031	−	0.123001i
$994$	38.7494			1.22906
$995$	38.8050	−	4.91053i	1.23020	−	0.155674i
$996$	−5.41841	−	1.37692i	−0.171689	−	0.0436294i
$997$	19.4945	+	11.2552i	0.617398	+	0.356455i	0.775855	−	0.630911i	$-0.217319\pi$
$997$	19.4945	+	11.2552i	0.617398	+	0.356455i	−0.158457	+	0.987366i	$0.550652\pi$
$998$	−9.32152	+	5.38178i	−0.295068	+	0.170357i
$999$	−26.3870	−	5.98259i	−0.834846	−	0.189281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.a.719.3	yes	64
3.2	odd	2		930.2.r.b.719.24	yes	64
5.4	even	2		930.2.r.b.719.30	yes	64
15.14	odd	2	inner	930.2.r.a.719.9	yes	64
31.26	odd	6	inner	930.2.r.a.119.9	yes	64
93.26	even	6		930.2.r.b.119.30	yes	64
155.119	odd	6		930.2.r.b.119.24	yes	64
465.119	even	6	inner	930.2.r.a.119.3	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.3	✓	64	465.119	even	6	inner
930.2.r.a.119.9	yes	64	31.26	odd	6	inner
930.2.r.a.719.3	yes	64	1.1	even	1	trivial
930.2.r.a.719.9	yes	64	15.14	odd	2	inner
930.2.r.b.119.24	yes	64	155.119	odd	6
930.2.r.b.119.30	yes	64	93.26	even	6
930.2.r.b.719.24	yes	64	3.2	odd	2
930.2.r.b.719.30	yes	64	5.4	even	2

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.66709 + 0.469912i) q^{3} +1.00000 q^{4} +(-1.78081 + 1.35230i) q^{5} +(1.66709 - 0.469912i) q^{6} +(-2.19151 + 1.26527i) q^{7} -1.00000 q^{8} +(2.55837 - 1.56677i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.66709 + 0.469912i) q^{3} +1.00000 q^{4} +(-1.78081 + 1.35230i) q^{5} +(1.66709 - 0.469912i) q^{6} +(-2.19151 + 1.26527i) q^{7} -1.00000 q^{8} +(2.55837 - 1.56677i) q^{9} +(1.78081 - 1.35230i) q^{10} +(0.583678 - 1.01096i) q^{11} +(-1.66709 + 0.469912i) q^{12} +(3.18182 - 5.51107i) q^{13} +(2.19151 - 1.26527i) q^{14} +(2.33331 - 3.09123i) q^{15} +1.00000 q^{16} +(3.41739 - 1.97303i) q^{17} +(-2.55837 + 1.56677i) q^{18} +(1.33594 + 2.31391i) q^{19} +(-1.78081 + 1.35230i) q^{20} +(3.05888 - 3.13913i) q^{21} +(-0.583678 + 1.01096i) q^{22} +2.97331i q^{23} +(1.66709 - 0.469912i) q^{24} +(1.34257 - 4.81638i) q^{25} +(-3.18182 + 5.51107i) q^{26} +(-3.52878 + 3.81415i) q^{27} +(-2.19151 + 1.26527i) q^{28} -4.97367 q^{29} +(-2.33331 + 3.09123i) q^{30} +(-1.00997 + 5.47540i) q^{31} -1.00000 q^{32} +(-0.497981 + 1.95964i) q^{33} +(-3.41739 + 1.97303i) q^{34} +(2.19164 - 5.21678i) q^{35} +(2.55837 - 1.56677i) q^{36} +(2.60353 + 4.50944i) q^{37} +(-1.33594 - 2.31391i) q^{38} +(-2.71466 + 10.6826i) q^{39} +(1.78081 - 1.35230i) q^{40} +(0.504431 + 0.291233i) q^{41} +(-3.05888 + 3.13913i) q^{42} +(0.106364 + 0.184228i) q^{43} +(0.583678 - 1.01096i) q^{44} +(-2.43722 + 6.24980i) q^{45} -2.97331i q^{46} -2.60049 q^{47} +(-1.66709 + 0.469912i) q^{48} +(-0.298188 + 0.516477i) q^{49} +(-1.34257 + 4.81638i) q^{50} +(-4.76994 + 4.89509i) q^{51} +(3.18182 - 5.51107i) q^{52} +(-5.05784 - 2.92015i) q^{53} +(3.52878 - 3.81415i) q^{54} +(0.327702 + 2.58964i) q^{55} +(2.19151 - 1.26527i) q^{56} +(-3.31446 - 3.22972i) q^{57} +4.97367 q^{58} +(10.0172 - 5.78341i) q^{59} +(2.33331 - 3.09123i) q^{60} +7.81867i q^{61} +(1.00997 - 5.47540i) q^{62} +(-3.62430 + 6.67061i) q^{63} +1.00000 q^{64} +(1.78641 + 14.1170i) q^{65} +(0.497981 - 1.95964i) q^{66} +(2.19629 + 1.26803i) q^{67} +(3.41739 - 1.97303i) q^{68} +(-1.39719 - 4.95677i) q^{69} +(-2.19164 + 5.21678i) q^{70} +(13.2612 + 7.65636i) q^{71} +(-2.55837 + 1.56677i) q^{72} +(-3.80528 + 6.59093i) q^{73} +(-2.60353 - 4.50944i) q^{74} +(0.0250959 + 8.66022i) q^{75} +(1.33594 + 2.31391i) q^{76} +2.95404i q^{77} +(2.71466 - 10.6826i) q^{78} +(-9.30890 + 5.37450i) q^{79} +(-1.78081 + 1.35230i) q^{80} +(4.09047 - 8.01673i) q^{81} +(-0.504431 - 0.291233i) q^{82} +(2.79531 + 1.61388i) q^{83} +(3.05888 - 3.13913i) q^{84} +(-3.41759 + 8.13493i) q^{85} +(-0.106364 - 0.184228i) q^{86} +(8.29154 - 2.33718i) q^{87} +(-0.583678 + 1.01096i) q^{88} -12.6584 q^{89} +(2.43722 - 6.24980i) q^{90} +16.1034i q^{91} +2.97331i q^{92} +(-0.889250 - 9.60256i) q^{93} +2.60049 q^{94} +(-5.50816 - 2.31405i) q^{95} +(1.66709 - 0.469912i) q^{96} -11.6154i q^{97} +(0.298188 - 0.516477i) q^{98} +(-0.0906783 - 3.50089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 - 6 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 2 * q^25 + 18 * q^31 - 64 * q^32 + 8 * q^33 + 6 * q^34 - 16 * q^35 - 4 * q^36 - 4 * q^38 - 8 * q^39 + 2 * q^40 + 5 * q^45 + 4 * q^47 + 30 * q^49 - 2 * q^50 - 8 * q^51 + 6 * q^53 - 6 * q^57 - 18 * q^62 - 12 * q^63 + 64 * q^64 - 8 * q^66 - 6 * q^68 - 10 * q^69 + 16 * q^70 + 4 * q^72 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

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