LMFDB - Embedded newform 240.2.bc.e.67.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.7
Root			$1.40838 + 0.128355i$ of defining polynomial
Character	$\chi$	$=$	240.67
Dual form			240.2.bc.e.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32980 - 0.481284i) q^{2} -1.00000i q^{3} +(1.53673 - 1.28002i) q^{4} +(0.539352 + 2.17005i) q^{5} +(-0.481284 - 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(1.42749 - 2.44178i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.32980 - 0.481284i) q^{2} -1.00000i q^{3} +(1.53673 - 1.28002i) q^{4} +(0.539352 + 2.17005i) q^{5} +(-0.481284 - 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(1.42749 - 2.44178i) q^{8} -1.00000 q^{9} +(1.76164 + 2.62614i) q^{10} +(-2.91811 - 2.91811i) q^{11} +(-1.28002 - 1.53673i) q^{12} -4.96870 q^{13} +(5.44784 + 2.55238i) q^{14} +(2.17005 - 0.539352i) q^{15} +(0.723087 - 3.93410i) q^{16} +(-2.56773 - 2.56773i) q^{17} +(-1.32980 + 0.481284i) q^{18} +(0.174647 + 0.174647i) q^{19} +(3.60655 + 2.64439i) q^{20} +(3.00806 - 3.00806i) q^{21} +(-5.28494 - 2.47606i) q^{22} +(2.93410 - 2.93410i) q^{23} +(-2.44178 - 1.42749i) q^{24} +(-4.41820 + 2.34084i) q^{25} +(-6.60738 + 2.39136i) q^{26} +1.00000i q^{27} +(8.47295 + 0.772196i) q^{28} +(-4.90621 + 4.90621i) q^{29} +(2.62614 - 1.76164i) q^{30} +5.24365i q^{31} +(-0.931860 - 5.57957i) q^{32} +(-2.91811 + 2.91811i) q^{33} +(-4.65038 - 2.17876i) q^{34} +(-4.90522 + 8.15002i) q^{35} +(-1.53673 + 1.28002i) q^{36} +2.27540 q^{37} +(0.316301 + 0.148191i) q^{38} +4.96870i q^{39} +(6.06869 + 1.78074i) q^{40} +0.187334i q^{41} +(2.55238 - 5.44784i) q^{42} +12.2767 q^{43} +(-8.21960 - 0.749106i) q^{44} +(-0.539352 - 2.17005i) q^{45} +(2.48963 - 5.31390i) q^{46} +(-0.0810813 + 0.0810813i) q^{47} +(-3.93410 - 0.723087i) q^{48} +11.0968i q^{49} +(-4.74871 + 5.23925i) q^{50} +(-2.56773 + 2.56773i) q^{51} +(-7.63556 + 6.36005i) q^{52} -10.3383i q^{53} +(0.481284 + 1.32980i) q^{54} +(4.75854 - 7.90632i) q^{55} +(11.6390 - 3.05103i) q^{56} +(0.174647 - 0.174647i) q^{57} +(-4.16299 + 8.88555i) q^{58} +(-3.33519 + 3.33519i) q^{59} +(2.64439 - 3.60655i) q^{60} +(-1.32102 - 1.32102i) q^{61} +(2.52369 + 6.97300i) q^{62} +(-3.00806 - 3.00806i) q^{63} +(-3.92455 - 6.97122i) q^{64} +(-2.67988 - 10.7823i) q^{65} +(-2.47606 + 5.28494i) q^{66} -9.03323 q^{67} +(-7.23268 - 0.659161i) q^{68} +(-2.93410 - 2.93410i) q^{69} +(-2.60048 + 13.1987i) q^{70} +4.47057 q^{71} +(-1.42749 + 2.44178i) q^{72} +(3.50820 + 3.50820i) q^{73} +(3.02582 - 1.09511i) q^{74} +(2.34084 + 4.41820i) q^{75} +(0.491939 + 0.0448336i) q^{76} -17.5557i q^{77} +(2.39136 + 6.60738i) q^{78} +6.75271 q^{79} +(8.92718 - 0.552736i) q^{80} +1.00000 q^{81} +(0.0901608 + 0.249117i) q^{82} -0.203861i q^{83} +(0.772196 - 8.47295i) q^{84} +(4.18719 - 6.95702i) q^{85} +(16.3255 - 5.90857i) q^{86} +(4.90621 + 4.90621i) q^{87} +(-11.2909 + 2.95980i) q^{88} -2.76590 q^{89} +(-1.76164 - 2.62614i) q^{90} +(-14.9461 - 14.9461i) q^{91} +(0.753211 - 8.26464i) q^{92} +5.24365 q^{93} +(-0.0687987 + 0.146845i) q^{94} +(-0.284797 + 0.473190i) q^{95} +(-5.57957 + 0.931860i) q^{96} +(9.90816 + 9.90816i) q^{97} +(5.34071 + 14.7565i) q^{98} +(2.91811 + 2.91811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.32980	−	0.481284i	0.940310	−	0.340319i
$2$	1.32980	−	0.481284i	0.940310	−	0.340319i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.53673	−	1.28002i	0.768366	−	0.640011i
$5$	0.539352	+	2.17005i	0.241206	+	0.970474i
$5$	0.539352	+	2.17005i	0.241206	+	0.970474i
$6$	−0.481284	−	1.32980i	−0.196483	−	0.542888i
$7$	3.00806	+	3.00806i	1.13694	+	1.13694i	0.988996	+	0.147942i	$0.0472649\pi$
$7$	3.00806	+	3.00806i	1.13694	+	1.13694i	0.147942	+	0.988996i	$0.452735\pi$
$8$	1.42749	−	2.44178i	0.504694	−	0.863298i
$9$	−1.00000			−0.333333
$10$	1.76164	+	2.62614i	0.557079	+	0.830459i
$11$	−2.91811	−	2.91811i	−0.879844	−	0.879844i	0.113675	−	0.993518i	$-0.463738\pi$
$11$	−2.91811	−	2.91811i	−0.879844	−	0.879844i	−0.993518	+	0.113675i	$0.963738\pi$
$12$	−1.28002	−	1.53673i	−0.369511	−	0.443616i
$13$	−4.96870			−1.37807			−0.689035	−	0.724728i	$-0.741966\pi$
$13$	−4.96870			−1.37807			−0.689035	+	0.724728i	$0.741966\pi$
$14$	5.44784	+	2.55238i	1.45600	+	0.682152i
$15$	2.17005	−	0.539352i	0.560303	−	0.139260i
$16$	0.723087	−	3.93410i	0.180772	−	0.983525i
$17$	−2.56773	−	2.56773i	−0.622767	−	0.622767i	0.323471	−	0.946238i	$-0.395150\pi$
$17$	−2.56773	−	2.56773i	−0.622767	−	0.622767i	−0.946238	+	0.323471i	$0.895150\pi$
$18$	−1.32980	+	0.481284i	−0.313437	+	0.113440i
$19$	0.174647	+	0.174647i	0.0400669	+	0.0400669i	0.726856	−	0.686789i	$-0.240981\pi$
$19$	0.174647	+	0.174647i	0.0400669	+	0.0400669i	−0.686789	+	0.726856i	$0.740981\pi$
$20$	3.60655	+	2.64439i	0.806448	+	0.591305i
$21$	3.00806	−	3.00806i	0.656412	−	0.656412i
$22$	−5.28494	−	2.47606i	−1.12675	−	0.527898i
$23$	2.93410	−	2.93410i	0.611802	−	0.611802i	−0.331613	−	0.943415i	$-0.607593\pi$
$23$	2.93410	−	2.93410i	0.611802	−	0.611802i	0.943415	+	0.331613i	$0.107593\pi$
$24$	−2.44178	−	1.42749i	−0.498426	−	0.291385i
$25$	−4.41820	+	2.34084i	−0.883640	+	0.468168i
$26$	−6.60738	+	2.39136i	−1.29581	+	0.468984i
$27$			1.00000i			0.192450i
$28$	8.47295	+	0.772196i	1.60124	+	0.145931i
$29$	−4.90621	+	4.90621i	−0.911060	+	0.911060i	−0.996356	−	0.0852961i	$-0.972816\pi$
$29$	−4.90621	+	4.90621i	−0.911060	+	0.911060i	0.0852961	+	0.996356i	$0.472816\pi$
$30$	2.62614	−	1.76164i	0.479466	−	0.321630i
$31$			5.24365i			0.941788i	0.882190	+	0.470894i	$0.156069\pi$
$31$			5.24365i			0.941788i	−0.882190	+	0.470894i	$0.843931\pi$
$32$	−0.931860	−	5.57957i	−0.164731	−	0.986339i
$33$	−2.91811	+	2.91811i	−0.507978	+	0.507978i
$34$	−4.65038	−	2.17876i	−0.797534	−	0.373655i
$35$	−4.90522	+	8.15002i	−0.829133	+	1.37760i
$36$	−1.53673	+	1.28002i	−0.256122	+	0.213337i
$37$	2.27540			0.374073			0.187036	−	0.982353i	$-0.440112\pi$
$37$	2.27540			0.374073			0.187036	+	0.982353i	$0.440112\pi$
$38$	0.316301	+	0.148191i	0.0513108	+	0.0240398i
$39$			4.96870i			0.795630i
$40$	6.06869	+	1.78074i	0.959544	+	0.281560i
$41$			0.187334i			0.0292566i	0.999893	+	0.0146283i	$0.00465651\pi$
$41$			0.187334i			0.0292566i	−0.999893	+	0.0146283i	$0.995343\pi$
$42$	2.55238	−	5.44784i	0.393841	−	0.840620i
$43$	12.2767			1.87218			0.936089	−	0.351764i	$-0.114418\pi$
$43$	12.2767			1.87218			0.936089	+	0.351764i	$0.114418\pi$
$44$	−8.21960	−	0.749106i	−1.23915	−	0.112932i
$45$	−0.539352	−	2.17005i	−0.0804019	−	0.323491i
$46$	2.48963	−	5.31390i	0.367076	−	0.783492i
$47$	−0.0810813	+	0.0810813i	−0.0118269	+	0.0118269i	−0.712996	−	0.701169i	$-0.752662\pi$
$47$	−0.0810813	+	0.0810813i	−0.0118269	+	0.0118269i	0.701169	+	0.712996i	$0.252662\pi$
$48$	−3.93410	−	0.723087i	−0.567838	−	0.104369i
$49$			11.0968i			1.58526i
$50$	−4.74871	+	5.23925i	−0.671569	+	0.740942i
$51$	−2.56773	+	2.56773i	−0.359555	+	0.359555i
$52$	−7.63556	+	6.36005i	−1.05886	+	0.881981i
$53$		−	10.3383i		−	1.42007i	−0.704166	−	0.710036i	$-0.748679\pi$
$53$		−	10.3383i		−	1.42007i	0.704166	−	0.710036i	$-0.251321\pi$
$54$	0.481284	+	1.32980i	0.0654945	+	0.180963i
$55$	4.75854	−	7.90632i	0.641642	−	1.06609i
$56$	11.6390	−	3.05103i	1.55532	−	0.407711i
$57$	0.174647	−	0.174647i	0.0231326	−	0.0231326i
$58$	−4.16299	+	8.88555i	−0.546627	+	1.16673i
$59$	−3.33519	+	3.33519i	−0.434204	+	0.434204i	−0.890056	−	0.455852i	$-0.849335\pi$
$59$	−3.33519	+	3.33519i	−0.434204	+	0.434204i	0.455852	+	0.890056i	$0.349335\pi$
$60$	2.64439	−	3.60655i	0.341390	−	0.465603i
$61$	−1.32102	−	1.32102i	−0.169139	−	0.169139i	0.617462	−	0.786601i	$-0.288161\pi$
$61$	−1.32102	−	1.32102i	−0.169139	−	0.169139i	−0.786601	+	0.617462i	$0.788161\pi$
$62$	2.52369	+	6.97300i	0.320508	+	0.885572i
$63$	−3.00806	−	3.00806i	−0.378979	−	0.378979i
$64$	−3.92455	−	6.97122i	−0.490568	−	0.871403i
$65$	−2.67988	−	10.7823i	−0.332399	−	1.33738i
$66$	−2.47606	+	5.28494i	−0.304782	+	0.650531i
$67$	−9.03323			−1.10358			−0.551792	−	0.833982i	$-0.686056\pi$
$67$	−9.03323			−1.10358			−0.551792	+	0.833982i	$0.686056\pi$
$68$	−7.23268	−	0.659161i	−0.877091	−	0.0799350i
$69$	−2.93410	−	2.93410i	−0.353224	−	0.353224i
$70$	−2.60048	+	13.1987i	−0.310817	+	1.57755i
$71$	4.47057			0.530560			0.265280	−	0.964171i	$-0.414536\pi$
$71$	4.47057			0.530560			0.265280	+	0.964171i	$0.414536\pi$
$72$	−1.42749	+	2.44178i	−0.168231	+	0.287766i
$73$	3.50820	+	3.50820i	0.410604	+	0.410604i	0.881949	−	0.471345i	$-0.156231\pi$
$73$	3.50820	+	3.50820i	0.410604	+	0.410604i	−0.471345	+	0.881949i	$0.656231\pi$
$74$	3.02582	−	1.09511i	0.351745	−	0.127304i
$75$	2.34084	+	4.41820i	0.270297	+	0.510170i
$76$	0.491939	+	0.0448336i	0.0564293	+	0.00514277i
$77$		−	17.5557i		−	2.00066i
$78$	2.39136	+	6.60738i	0.270768	+	0.748138i
$79$	6.75271			0.759740			0.379870	−	0.925040i	$-0.375969\pi$
$79$	6.75271			0.759740			0.379870	+	0.925040i	$0.375969\pi$
$80$	8.92718	−	0.552736i	0.998089	−	0.0617977i
$81$	1.00000			0.111111
$82$	0.0901608	+	0.249117i	0.00995660	+	0.0275103i
$83$		−	0.203861i		−	0.0223766i	−0.999937	−	0.0111883i	$-0.996439\pi$
$83$		−	0.203861i		−	0.0223766i	0.999937	−	0.0111883i	$-0.00356143\pi$
$84$	0.772196	−	8.47295i	0.0842534	−	0.924475i
$85$	4.18719	−	6.95702i	0.454164	−	0.754594i
$86$	16.3255	−	5.90857i	1.76043	−	0.637138i
$87$	4.90621	+	4.90621i	0.526000	+	0.526000i
$88$	−11.2909	+	2.95980i	−1.20362	+	0.315516i
$89$	−2.76590			−0.293184			−0.146592	−	0.989197i	$-0.546831\pi$
$89$	−2.76590			−0.293184			−0.146592	+	0.989197i	$0.546831\pi$
$90$	−1.76164	−	2.62614i	−0.185693	−	0.276820i
$91$	−14.9461	−	14.9461i	−1.56678	−	1.56678i
$92$	0.753211	−	8.26464i	0.0785276	−	0.861648i
$93$	5.24365			0.543741
$94$	−0.0687987	+	0.146845i	−0.00709604	+	0.0151459i
$95$	−0.284797	+	0.473190i	−0.0292195	+	0.0485482i
$96$	−5.57957	+	0.931860i	−0.569463	+	0.0951075i
$97$	9.90816	+	9.90816i	1.00602	+	1.00602i	0.999982	+	0.00603974i	$0.00192252\pi$
$97$	9.90816	+	9.90816i	1.00602	+	1.00602i	0.00603974	+	0.999982i	$0.498077\pi$
$98$	5.34071	+	14.7565i	0.539493	+	1.49063i
$99$	2.91811	+	2.91811i	0.293281	+	0.293281i
$100$	−3.79326	+	9.25263i	−0.379326	+	0.925263i
$101$	−9.51134	+	9.51134i	−0.946414	+	0.946414i	−0.998636	−	0.0522219i	$-0.983370\pi$
$101$	−9.51134	+	9.51134i	−0.946414	+	0.946414i	0.0522219	+	0.998636i	$0.483370\pi$
$102$	−2.17876	+	4.65038i	−0.215730	+	0.460456i
$103$	5.17090	−	5.17090i	0.509504	−	0.509504i	−0.404870	−	0.914374i	$-0.632683\pi$
$103$	5.17090	−	5.17090i	0.509504	−	0.509504i	0.914374	+	0.404870i	$0.132683\pi$
$104$	−7.09278	+	12.1325i	−0.695504	+	1.18969i
$105$	8.15002	+	4.90522i	0.795361	+	0.478700i
$106$	−4.97565	−	13.7478i	−0.483278	−	1.33531i
$107$		−	5.04996i		−	0.488198i	−0.969750	−	0.244099i	$-0.921508\pi$
$107$		−	5.04996i		−	0.488198i	0.969750	−	0.244099i	$-0.0784922\pi$
$108$	1.28002	+	1.53673i	0.123170	+	0.147872i
$109$	−6.77367	+	6.77367i	−0.648800	+	0.648800i	−0.952703	−	0.303903i	$-0.901710\pi$
$109$	−6.77367	+	6.77367i	−0.648800	+	0.648800i	0.303903	+	0.952703i	$0.401710\pi$
$110$	2.52272	−	12.8040i	0.240532	−	1.22082i
$111$		−	2.27540i		−	0.215971i
$112$	14.0091	−	9.65891i	1.32373	−	0.912681i
$113$	2.59004	−	2.59004i	0.243651	−	0.243651i	−0.574708	−	0.818359i	$-0.694884\pi$
$113$	2.59004	−	2.59004i	0.243651	−	0.243651i	0.818359	+	0.574708i	$0.194884\pi$
$114$	0.148191	−	0.316301i	0.0138794	−	0.0296243i
$115$	7.94965	+	4.78462i	0.741308	+	0.446168i
$116$	−1.25947	+	13.8196i	−0.116939	+	1.28312i
$117$	4.96870			0.459357
$118$	−2.82996	+	6.04030i	−0.260519	+	0.556055i
$119$		−	15.4478i		−	1.41610i
$120$	1.78074	−	6.06869i	0.162559	−	0.553993i
$121$			6.03074i			0.548249i
$122$	−2.39247	−	1.12090i	−0.216604	−	0.101482i
$123$	0.187334			0.0168913
$124$	6.71199	+	8.05808i	0.602755	+	0.723637i
$125$	−7.46269	−	8.32516i	−0.667484	−	0.744625i
$126$	−5.44784	−	2.55238i	−0.485332	−	0.227384i
$127$	5.95445	−	5.95445i	0.528372	−	0.528372i	−0.391715	−	0.920087i	$-0.628118\pi$
$127$	5.95445	−	5.95445i	0.528372	−	0.528372i	0.920087	+	0.391715i	$0.128118\pi$
$128$	−8.57400	−	7.38150i	−0.757841	−	0.652439i
$129$		−	12.2767i		−	1.08090i
$130$	−8.75306	−	13.0485i	−0.767694	−	1.14443i
$131$	1.07093	−	1.07093i	0.0935679	−	0.0935679i	−0.658773	−	0.752341i	$-0.728924\pi$
$131$	1.07093	−	1.07093i	0.0935679	−	0.0935679i	0.752341	+	0.658773i	$0.228924\pi$
$132$	−0.749106	+	8.21960i	−0.0652013	+	0.715424i
$133$			1.05070i			0.0911071i
$134$	−12.0124	+	4.34755i	−1.03771	+	0.375571i
$135$	−2.17005	+	0.539352i	−0.186768	+	0.0464201i
$136$	−9.93525	+	2.60442i	−0.851941	+	0.223327i
$137$	−6.57542	+	6.57542i	−0.561776	+	0.561776i	−0.929812	−	0.368036i	$-0.880030\pi$
$137$	−6.57542	+	6.57542i	−0.561776	+	0.561776i	0.368036	+	0.929812i	$0.380030\pi$
$138$	−5.31390	−	2.48963i	−0.452349	−	0.211931i
$139$	10.0808	−	10.0808i	0.855039	−	0.855039i	−0.135710	−	0.990749i	$-0.543331\pi$
$139$	10.0808	−	10.0808i	0.855039	−	0.855039i	0.990749	+	0.135710i	$0.0433315\pi$
$140$	2.89421	+	18.8032i	0.244605	+	1.58916i
$141$	0.0810813	+	0.0810813i	0.00682828	+	0.00682828i
$142$	5.94497	−	2.15162i	0.498890	−	0.180560i
$143$	14.4992	+	14.4992i	1.21249	+	1.21249i
$144$	−0.723087	+	3.93410i	−0.0602572	+	0.327842i
$145$	−13.2929	−	8.00052i	−1.10391	−	0.664407i
$146$	6.35365	+	2.97676i	0.525831	+	0.246359i
$147$	11.0968			0.915248
$148$	3.49667	−	2.91256i	0.287425	−	0.239411i
$149$	15.1118	+	15.1118i	1.23800	+	1.23800i	0.960816	+	0.277187i	$0.0894023\pi$
$149$	15.1118	+	15.1118i	1.23800	+	1.23800i	0.277187	+	0.960816i	$0.410598\pi$
$150$	5.23925	+	4.74871i	0.427783	+	0.387730i
$151$	−13.6260			−1.10886			−0.554432	−	0.832229i	$-0.687065\pi$
$151$	−13.6260			−1.10886			−0.554432	+	0.832229i	$0.687065\pi$
$152$	0.675758	−	0.177143i	0.0548112	−	0.0143682i
$153$	2.56773	+	2.56773i	0.207589	+	0.207589i
$154$	−8.44927	−	23.3455i	−0.680861	−	1.88124i
$155$	−11.3790	+	2.82818i	−0.913980	+	0.227165i
$156$	6.36005	+	7.63556i	0.509212	+	0.611334i
$157$		−	7.13379i		−	0.569338i	−0.958626	−	0.284669i	$-0.908116\pi$
$157$		−	7.13379i		−	0.569338i	0.958626	−	0.284669i	$-0.0918838\pi$
$158$	8.97975	−	3.24997i	0.714391	−	0.258554i
$159$	−10.3383			−0.819878
$160$	11.6053	−	5.03153i	0.917482	−	0.397778i
$161$	17.6519			1.39116
$162$	1.32980	−	0.481284i	0.104479	−	0.0378132i
$163$		−	15.7963i		−	1.23727i	−0.785680	−	0.618633i	$-0.787687\pi$
$163$		−	15.7963i		−	1.23727i	0.785680	−	0.618633i	$-0.212313\pi$
$164$	0.239792	+	0.287882i	0.0187246	+	0.0224798i
$165$	−7.90632	−	4.75854i	−0.615507	−	0.370452i
$166$	−0.0981149	−	0.271094i	−0.00761520	−	0.0210410i
$167$	11.1560	+	11.1560i	0.863278	+	0.863278i	0.991717	−	0.128439i	$-0.0409968\pi$
$167$	11.1560	+	11.1560i	0.863278	+	0.863278i	−0.128439	+	0.991717i	$0.540997\pi$
$168$	−3.05103	−	11.6390i	−0.235392	−	0.897966i
$169$	11.6880			0.899079
$170$	2.21982	−	11.2667i	0.170252	−	0.864113i
$171$	−0.174647	−	0.174647i	−0.0133556	−	0.0133556i
$172$	18.8660	−	15.7144i	1.43852	−	1.19821i
$173$	24.3506			1.85134			0.925669	−	0.378334i	$-0.123503\pi$
$173$	24.3506			1.85134			0.925669	+	0.378334i	$0.123503\pi$
$174$	8.88555	+	4.16299i	0.673612	+	0.315595i
$175$	−20.3316	−	6.24881i	−1.53692	−	0.472366i
$176$	−13.5902	+	9.37009i	−1.02440	+	0.706297i
$177$	3.33519	+	3.33519i	0.250688	+	0.250688i
$178$	−3.67809	+	1.33118i	−0.275684	+	0.0997763i
$179$	−6.13094	−	6.13094i	−0.458248	−	0.458248i	0.439832	−	0.898080i	$-0.355038\pi$
$179$	−6.13094	−	6.13094i	−0.458248	−	0.458248i	−0.898080	+	0.439832i	$0.855038\pi$
$180$	−3.60655	−	2.64439i	−0.268816	−	0.197102i
$181$	8.99477	−	8.99477i	0.668576	−	0.668576i	−0.288810	−	0.957386i	$-0.593260\pi$
$181$	8.99477	−	8.99477i	0.668576	−	0.668576i	0.957386	+	0.288810i	$0.0932597\pi$
$182$	−27.0687	−	12.6820i	−2.00647	−	0.940054i
$183$	−1.32102	+	1.32102i	−0.0976524	+	0.0976524i
$184$	−2.97602	−	11.3528i	−0.219395	−	0.836941i
$185$	1.22724	+	4.93772i	0.0902285	+	0.363028i
$186$	6.97300	−	2.52369i	0.511285	−	0.185046i
$187$			14.9859i			1.09588i
$188$	−0.0208143	+	0.228386i	−0.00151804	+	0.0166568i
$189$	−3.00806	+	3.00806i	−0.218804	+	0.218804i
$190$	−0.150984	+	0.766315i	−0.0109535	+	0.0555943i
$191$			0.148691i			0.0107589i	0.999986	+	0.00537945i	$0.00171234\pi$
$191$			0.148691i			0.0107589i	−0.999986	+	0.00537945i	$0.998288\pi$
$192$	−6.97122	+	3.92455i	−0.503105	+	0.283230i
$193$	−4.33825	+	4.33825i	−0.312274	+	0.312274i	−0.845790	−	0.533516i	$-0.820870\pi$
$193$	−4.33825	+	4.33825i	−0.312274	+	0.312274i	0.533516	+	0.845790i	$0.320870\pi$
$194$	17.9445	+	8.40723i	1.28834	+	0.603604i
$195$	−10.7823	+	2.67988i	−0.772138	+	0.191910i
$196$	14.2041	+	17.0528i	1.01458	+	1.21806i
$197$	5.86883			0.418137			0.209068	−	0.977901i	$-0.432957\pi$
$197$	5.86883			0.418137			0.209068	+	0.977901i	$0.432957\pi$
$198$	5.28494	+	2.47606i	0.375584	+	0.175966i
$199$			5.93363i			0.420624i	0.977634	+	0.210312i	$0.0674479\pi$
$199$			5.93363i			0.420624i	−0.977634	+	0.210312i	$0.932552\pi$
$200$	−0.591127	+	14.1298i	−0.0417990	+	0.999126i
$201$			9.03323i			0.637155i
$202$	−8.07051	+	17.2258i	−0.567839	+	1.21200i
$203$	−29.5163			−2.07164
$204$	−0.659161	+	7.23268i	−0.0461505	+	0.506389i
$205$	−0.406523	+	0.101039i	−0.0283928	+	0.00705687i
$206$	4.38759	−	9.36493i	0.305698	−	0.652485i
$207$	−2.93410	+	2.93410i	−0.203934	+	0.203934i
$208$	−3.59280	+	19.5474i	−0.249116	+	1.35537i
$209$		−	1.01928i		−	0.0705052i
$210$	13.1987	+	2.60048i	0.910796	+	0.179450i
$211$	−7.09893	+	7.09893i	−0.488710	+	0.488710i	−0.907899	−	0.419189i	$-0.862315\pi$
$211$	−7.09893	+	7.09893i	−0.488710	+	0.488710i	0.419189	+	0.907899i	$0.362315\pi$
$212$	−13.2332	−	15.8872i	−0.908861	−	1.09113i
$213$		−	4.47057i		−	0.306319i
$214$	−2.43047	−	6.71543i	−0.166143	−	0.459058i
$215$	6.62146	+	26.6410i	0.451580	+	1.81690i
$216$	2.44178	+	1.42749i	0.166142	+	0.0971284i
$217$	−15.7732	+	15.7732i	−1.07075	+	1.07075i
$218$	−5.74756	+	12.2677i	−0.389274	+	0.830872i
$219$	3.50820	−	3.50820i	0.237062	−	0.237062i
$220$	−2.80767	−	18.2409i	−0.189293	−	1.22980i
$221$	12.7583	+	12.7583i	0.858217	+	0.858217i
$222$	−1.09511	−	3.02582i	−0.0734991	−	0.203080i
$223$	−19.9362	−	19.9362i	−1.33503	−	1.33503i	−0.900808	−	0.434217i	$-0.857025\pi$
$223$	−19.9362	−	19.9362i	−1.33503	−	1.33503i	−0.434217	−	0.900808i	$-0.642975\pi$
$224$	13.9806	−	19.5868i	0.934117	−	1.30869i
$225$	4.41820	−	2.34084i	0.294547	−	0.156056i
$226$	2.19769	−	4.69078i	0.146188	−	0.312026i
$227$	−6.50202			−0.431554			−0.215777	−	0.976443i	$-0.569228\pi$
$227$	−6.50202			−0.431554			−0.215777	+	0.976443i	$0.569228\pi$
$228$	0.0448336	−	0.491939i	0.00296918	−	0.0325795i
$229$	6.53144	+	6.53144i	0.431610	+	0.431610i	0.889176	−	0.457566i	$-0.151279\pi$
$229$	6.53144	+	6.53144i	0.431610	+	0.431610i	−0.457566	+	0.889176i	$0.651279\pi$
$230$	12.8742	+	2.53654i	0.848899	+	0.167255i
$231$	−17.5557			−1.15508
$232$	4.97630	+	18.9834i	0.326710	+	1.24632i
$233$	−14.3657	−	14.3657i	−0.941130	−	0.941130i	0.0572311	−	0.998361i	$-0.481773\pi$
$233$	−14.3657	−	14.3657i	−0.941130	−	0.941130i	−0.998361	+	0.0572311i	$0.981773\pi$
$234$	6.60738	−	2.39136i	0.431938	−	0.156328i
$235$	−0.219682	−	0.132219i	−0.0143304	−	0.00862500i
$236$	−0.856173	+	9.39440i	−0.0557321	+	0.611523i
$237$		−	6.75271i		−	0.438636i
$238$	−7.43477	−	20.5424i	−0.481924	−	1.33157i
$239$	−6.65388			−0.430404			−0.215202	−	0.976570i	$-0.569041\pi$
$239$	−6.65388			−0.430404			−0.215202	+	0.976570i	$0.569041\pi$
$240$	−0.552736	−	8.92718i	−0.0356789	−	0.576247i
$241$	−15.6797			−1.01002			−0.505009	−	0.863114i	$-0.668511\pi$
$241$	−15.6797			−1.01002			−0.505009	+	0.863114i	$0.668511\pi$
$242$	2.90250	+	8.01968i	0.186580	+	0.515524i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.72098	−	0.339117i	−0.238211	−	0.0217098i
$245$	−24.0806	+	5.98508i	−1.53845	+	0.382373i
$246$	0.249117	−	0.0901608i	0.0158831	−	0.00574844i
$247$	−0.867772	−	0.867772i	−0.0552150	−	0.0552150i
$248$	12.8038	+	7.48526i	0.813044	+	0.475314i
$249$	−0.203861			−0.0129192
$250$	−13.9306	−	7.47911i	−0.881051	−	0.473020i
$251$	−2.31676	−	2.31676i	−0.146233	−	0.146233i	0.630200	−	0.776433i	$-0.282973\pi$
$251$	−2.31676	−	2.31676i	−0.146233	−	0.146233i	−0.776433	+	0.630200i	$0.782973\pi$
$252$	−8.47295	−	0.772196i	−0.533746	−	0.0486437i
$253$	−17.1241			−1.07658
$254$	5.05244	−	10.7840i	0.317018	−	0.676649i
$255$	−6.95702	−	4.18719i	−0.435665	−	0.262212i
$256$	−14.9543	−	5.68939i	−0.934643	−	0.355587i
$257$	10.9722	+	10.9722i	0.684430	+	0.684430i	0.960995	−	0.276565i	$-0.0891962\pi$
$257$	10.9722	+	10.9722i	0.684430	+	0.684430i	−0.276565	+	0.960995i	$0.589196\pi$
$258$	−5.90857	−	16.3255i	−0.367852	−	1.01638i
$259$	6.84452	+	6.84452i	0.425298	+	0.425298i
$260$	−17.9199	−	13.1392i	−1.11134	−	0.814860i
$261$	4.90621	−	4.90621i	0.303687	−	0.303687i
$262$	0.908703	−	1.93955i	0.0561399	−	0.119826i
$263$	9.46655	−	9.46655i	0.583733	−	0.583733i	−0.352194	−	0.935927i	$-0.614564\pi$
$263$	9.46655	−	9.46655i	0.583733	−	0.583733i	0.935927	+	0.352194i	$0.114564\pi$
$264$	2.95980	+	11.2909i	0.182163	+	0.694910i
$265$	22.4345	−	5.57597i	1.37814	−	0.342529i
$266$	0.505685	+	1.39722i	0.0310055	+	0.0856690i
$267$			2.76590i			0.169270i
$268$	−13.8816	+	11.5627i	−0.847957	+	0.706306i
$269$	−2.77544	+	2.77544i	−0.169222	+	0.169222i	−0.786637	−	0.617416i	$-0.788180\pi$
$269$	−2.77544	+	2.77544i	−0.169222	+	0.169222i	0.617416	+	0.786637i	$0.288180\pi$
$270$	−2.62614	+	1.76164i	−0.159822	+	0.107210i
$271$			3.86079i			0.234526i	0.993101	+	0.117263i	$0.0374121\pi$
$271$			3.86079i			0.234526i	−0.993101	+	0.117263i	$0.962588\pi$
$272$	−11.9584	+	8.24503i	−0.725086	+	0.499928i
$273$	−14.9461	+	14.9461i	−0.904582	+	0.904582i
$274$	−5.57934	+	11.9086i	−0.337060	+	0.719426i
$275$	19.7236	+	6.06196i	1.18938	+	0.365550i
$276$	−8.26464	−	0.753211i	−0.497473	−	0.0453379i
$277$	−28.9073			−1.73687			−0.868435	−	0.495803i	$-0.834874\pi$
$277$	−28.9073			−1.73687			−0.868435	+	0.495803i	$0.834874\pi$
$278$	8.55368	−	18.2571i	0.513015	−	1.09499i
$279$		−	5.24365i		−	0.313929i
$280$	12.8984	+	23.6115i	0.770826	+	1.41106i
$281$		−	16.2395i		−	0.968770i	−0.874855	−	0.484385i	$-0.839043\pi$
$281$		−	16.2395i		−	0.968770i	0.874855	−	0.484385i	$-0.160957\pi$
$282$	0.146845	+	0.0687987i	0.00874449	+	0.00409690i
$283$	22.8092			1.35587			0.677934	−	0.735122i	$-0.262875\pi$
$283$	22.8092			1.35587			0.677934	+	0.735122i	$0.262875\pi$
$284$	6.87007	−	5.72243i	0.407664	−	0.339564i
$285$	0.473190	+	0.284797i	0.0280293	+	0.0168699i
$286$	26.2593	+	12.3028i	1.55275	+	0.727481i
$287$	−0.563511	+	0.563511i	−0.0332630	+	0.0332630i
$288$	0.931860	+	5.57957i	0.0549104	+	0.328780i
$289$		−	3.81348i		−	0.224322i
$290$	−21.5274	−	4.24144i	−1.26413	−	0.249066i
$291$	9.90816	−	9.90816i	0.580827	−	0.580827i
$292$	9.88174	+	0.900588i	0.578285	+	0.0527029i
$293$			30.6990i			1.79346i	0.442582	+	0.896728i	$0.354063\pi$
$293$			30.6990i			1.79346i	−0.442582	+	0.896728i	$0.645937\pi$
$294$	14.7565	−	5.34071i	0.860617	−	0.311477i
$295$	−9.03635	−	5.43867i	−0.526116	−	0.316651i
$296$	3.24811	−	5.55601i	0.188792	−	0.322937i
$297$	2.91811	−	2.91811i	0.169326	−	0.169326i
$298$	27.3686	+	12.8226i	1.58542	+	0.742790i
$299$	−14.5787	+	14.5787i	−0.843107	+	0.843107i
$300$	9.25263	+	3.79326i	0.534201	+	0.219004i
$301$	36.9290	+	36.9290i	2.12855	+	2.12855i
$302$	−18.1198	+	6.55796i	−1.04268	+	0.377368i
$303$	9.51134	+	9.51134i	0.546412	+	0.546412i
$304$	0.813366	−	0.560796i	0.0466497	−	0.0321638i
$305$	2.15417	−	3.57916i	0.123348	−	0.204942i
$306$	4.65038	+	2.17876i	0.265845	+	0.124552i
$307$	−17.3607			−0.990829			−0.495415	−	0.868657i	$-0.664984\pi$
$307$	−17.3607			−0.990829			−0.495415	+	0.868657i	$0.664984\pi$
$308$	−22.4717	−	26.9784i	−1.28044	−	1.53723i
$309$	−5.17090	−	5.17090i	−0.294162	−	0.294162i
$310$	−13.7706	+	9.23742i	−0.782116	+	0.524650i
$311$	−20.0448			−1.13664			−0.568318	−	0.822809i	$-0.692406\pi$
$311$	−20.0448			−1.13664			−0.568318	+	0.822809i	$0.692406\pi$
$312$	12.1325	+	7.09278i	0.686866	+	0.401549i
$313$	−10.7674	−	10.7674i	−0.608610	−	0.608610i	0.333973	−	0.942583i	$-0.391611\pi$
$313$	−10.7674	−	10.7674i	−0.608610	−	0.608610i	−0.942583	+	0.333973i	$0.891611\pi$
$314$	−3.43338	−	9.48651i	−0.193757	−	0.535355i
$315$	4.90522	−	8.15002i	0.276378	−	0.459202i
$316$	10.3771	−	8.64362i	0.583758	−	0.486242i
$317$			11.6799i			0.656006i	0.944677	+	0.328003i	$0.106376\pi$
$317$			11.6799i			0.656006i	−0.944677	+	0.328003i	$0.893624\pi$
$318$	−13.7478	+	4.97565i	−0.770940	+	0.279020i
$319$	28.6337			1.60318
$320$	13.0112	−	12.2764i	0.727346	−	0.686271i
$321$	−5.04996			−0.281861
$322$	23.4734	−	8.49557i	1.30812	−	0.473439i
$323$		−	0.896897i		−	0.0499047i
$324$	1.53673	−	1.28002i	0.0853740	−	0.0711123i
$325$	21.9527	−	11.6309i	1.21772	−	0.645168i
$326$	−7.60253	−	21.0060i	−0.421065	−	1.16341i
$327$	6.77367	+	6.77367i	0.374585	+	0.374585i
$328$	0.457428	+	0.267417i	0.0252572	+	0.0147656i
$329$	−0.487794			−0.0268930
$330$	−12.8040	−	2.52272i	−0.704839	−	0.138871i
$331$	18.7327	+	18.7327i	1.02964	+	1.02964i	0.999547	+	0.0300961i	$0.00958132\pi$
$331$	18.7327	+	18.7327i	1.02964	+	1.02964i	0.0300961	+	0.999547i	$0.490419\pi$
$332$	−0.260946	−	0.313279i	−0.0143213	−	0.0171934i
$333$	−2.27540			−0.124691
$334$	20.2045	+	9.46604i	1.10554	+	0.517959i
$335$	−4.87209	−	19.6025i	−0.266191	−	1.07100i
$336$	−9.65891	−	14.0091i	−0.526937	−	0.764258i
$337$	−6.18087	−	6.18087i	−0.336694	−	0.336694i	0.518428	−	0.855121i	$-0.326518\pi$
$337$	−6.18087	−	6.18087i	−0.336694	−	0.336694i	−0.855121	+	0.518428i	$0.826518\pi$
$338$	15.5427	−	5.62526i	0.845413	−	0.305974i
$339$	−2.59004	−	2.59004i	−0.140672	−	0.140672i
$340$	−2.47055	−	16.0508i	−0.133984	−	0.870475i
$341$	15.3016	−	15.3016i	0.828626	−	0.828626i
$342$	−0.316301	−	0.148191i	−0.0171036	−	0.00801325i
$343$	−12.3234	+	12.3234i	−0.665401	+	0.665401i
$344$	17.5248	−	29.9769i	0.944876	−	1.61625i
$345$	4.78462	−	7.94965i	0.257595	−	0.427995i
$346$	32.3814	−	11.7195i	1.74083	−	0.630046i
$347$		−	3.87988i		−	0.208283i	−0.994562	−	0.104142i	$-0.966791\pi$
$347$		−	3.87988i		−	0.208283i	0.994562	−	0.104142i	$-0.0332095\pi$
$348$	13.8196	+	1.25947i	0.740807	+	0.0675146i
$349$	−1.56009	+	1.56009i	−0.0835098	+	0.0835098i	−0.747628	−	0.664118i	$-0.768807\pi$
$349$	−1.56009	+	1.56009i	−0.0835098	+	0.0835098i	0.664118	+	0.747628i	$0.268807\pi$
$350$	−30.0443	+	1.47559i	−1.60594	+	0.0788736i
$351$		−	4.96870i		−	0.265210i
$352$	−13.5625	+	19.0011i	−0.722886	+	1.01276i
$353$	5.74300	−	5.74300i	0.305669	−	0.305669i	−0.537558	−	0.843227i	$-0.680653\pi$
$353$	5.74300	−	5.74300i	0.305669	−	0.305669i	0.843227	+	0.537558i	$0.180653\pi$
$354$	6.04030	+	2.82996i	0.321038	+	0.150410i
$355$	2.41121	+	9.70135i	0.127974	+	0.514894i
$356$	−4.25044	+	3.54041i	−0.225273	+	0.187641i
$357$	−15.4478			−0.817583
$358$	−11.1036	−	5.20219i	−0.586845	−	0.274944i
$359$		−	18.0862i		−	0.954552i	−0.878753	−	0.477276i	$-0.841624\pi$
$359$		−	18.0862i		−	0.954552i	0.878753	−	0.477276i	$-0.158376\pi$
$360$	−6.06869	−	1.78074i	−0.319848	−	0.0938532i
$361$		−	18.9390i		−	0.996789i
$362$	7.63220	−	16.2903i	0.401139	−	0.856198i
$363$	6.03074			0.316532
$364$	−42.0996	−	3.83681i	−2.20662	−	0.201104i
$365$	−5.72080	+	9.50512i	−0.299440	+	0.497521i
$366$	−1.12090	+	2.39247i	−0.0585905	+	0.125057i
$367$	1.00068	−	1.00068i	0.0522350	−	0.0522350i	−0.680507	−	0.732742i	$-0.738240\pi$
$367$	1.00068	−	1.00068i	0.0522350	−	0.0522350i	0.732742	+	0.680507i	$0.238240\pi$
$368$	−9.42144	−	13.6647i	−0.491126	−	0.712319i
$369$		−	0.187334i		−	0.00975222i
$370$	4.00843	+	5.97552i	0.208388	+	0.310652i
$371$	31.0981	−	31.0981i	1.61453	−	1.61453i
$372$	8.05808	−	6.71199i	0.417792	−	0.348001i
$373$			2.25365i			0.116689i	0.998296	+	0.0583447i	$0.0185822\pi$
$373$			2.25365i			0.116689i	−0.998296	+	0.0583447i	$0.981418\pi$
$374$	7.21246	+	19.9282i	0.372947	+	1.03046i
$375$	−8.32516	+	7.46269i	−0.429909	+	0.385372i
$376$	0.0822397	+	0.313725i	0.00424119	+	0.0161791i
$377$	24.3775	−	24.3775i	1.25550	−	1.25550i
$378$	−2.55238	+	5.44784i	−0.131280	+	0.280207i
$379$	−7.91100	+	7.91100i	−0.406361	+	0.406361i	−0.880467	−	0.474107i	$-0.842771\pi$
$379$	−7.91100	+	7.91100i	−0.406361	+	0.406361i	0.474107	+	0.880467i	$0.342771\pi$
$380$	0.168037	+	1.09171i	0.00862014	+	0.0560036i
$381$	−5.95445	−	5.95445i	−0.305056	−	0.305056i
$382$	0.0715626	+	0.197729i	0.00366146	+	0.0101167i
$383$	19.7391	+	19.7391i	1.00862	+	1.00862i	0.999963	+	0.00865943i	$0.00275642\pi$
$383$	19.7391	+	19.7391i	1.00862	+	1.00862i	0.00865943	+	0.999963i	$0.497244\pi$
$384$	−7.38150	+	8.57400i	−0.376686	+	0.437540i
$385$	38.0966	−	9.46870i	1.94158	−	0.482570i
$386$	−3.68107	+	7.85693i	−0.187362	+	0.399907i
$387$	−12.2767			−0.624059
$388$	27.9089	+	2.54352i	1.41686	+	0.129127i
$389$	5.49649	+	5.49649i	0.278683	+	0.278683i	0.832583	−	0.553900i	$-0.186861\pi$
$389$	5.49649	+	5.49649i	0.278683	+	0.278683i	−0.553900	+	0.832583i	$0.686861\pi$
$390$	−13.0485	+	8.75306i	−0.660738	+	0.443229i
$391$	−15.0680			−0.762021
$392$	27.0959	+	15.8406i	1.36855	+	0.800069i
$393$	−1.07093	−	1.07093i	−0.0540214	−	0.0540214i
$394$	7.80437	−	2.82457i	0.393178	−	0.142300i
$395$	3.64209	+	14.6537i	0.183254	+	0.737308i
$396$	8.21960	+	0.749106i	0.413050	+	0.0376440i
$397$		−	25.4492i		−	1.27726i	−0.769514	−	0.638630i	$-0.779501\pi$
$397$		−	25.4492i		−	1.27726i	0.769514	−	0.638630i	$-0.220499\pi$
$398$	2.85576	+	7.89053i	0.143146	+	0.395517i
$399$	1.05070			0.0526007
$400$	6.01436	+	19.0743i	0.300718	+	0.953713i
$401$	−1.45606			−0.0727124			−0.0363562	−	0.999339i	$-0.511575\pi$
$401$	−1.45606			−0.0727124			−0.0363562	+	0.999339i	$0.511575\pi$
$402$	4.34755	+	12.0124i	0.216836	+	0.599123i
$403$		−	26.0542i		−	1.29785i
$404$	−2.44165	+	26.7911i	−0.121477	+	1.33291i
$405$	0.539352	+	2.17005i	0.0268006	+	0.107830i
$406$	−39.2507	+	14.2057i	−1.94798	+	0.705018i
$407$	−6.63986	−	6.63986i	−0.329126	−	0.329126i
$408$	2.60442	+	9.93525i	0.128938	+	0.491868i
$409$	14.9174			0.737620			0.368810	−	0.929505i	$-0.379765\pi$
$409$	14.9174			0.737620			0.368810	+	0.929505i	$0.379765\pi$
$410$	−0.491966	+	0.330015i	−0.0242965	+	0.0162983i
$411$	6.57542	+	6.57542i	0.324341	+	0.324341i
$412$	1.32742	−	14.5651i	0.0653972	−	0.717573i
$413$	−20.0649			−0.987327
$414$	−2.48963	+	5.31390i	−0.122359	+	0.261164i
$415$	0.442387	−	0.109953i	0.0217159	−	0.00539737i
$416$	4.63014	+	27.7233i	0.227011	+	1.35924i
$417$	−10.0808	−	10.0808i	−0.493657	−	0.493657i
$418$	−0.490564	−	1.35544i	−0.0239943	−	0.0662967i
$419$	12.3766	+	12.3766i	0.604638	+	0.604638i	0.941540	−	0.336902i	$-0.109379\pi$
$419$	12.3766	+	12.3766i	0.604638	+	0.604638i	−0.336902	+	0.941540i	$0.609379\pi$
$420$	18.8032	−	2.89421i	0.917501	−	0.141223i
$421$	−23.1411	+	23.1411i	−1.12783	+	1.12783i	−0.137299	+	0.990530i	$0.543842\pi$
$421$	−23.1411	+	23.1411i	−1.12783	+	1.12783i	−0.990530	+	0.137299i	$0.956158\pi$
$422$	−6.02355	+	12.8568i	−0.293222	+	0.625857i
$423$	0.0810813	−	0.0810813i	0.00394231	−	0.00394231i
$424$	−25.2438	−	14.7578i	−1.22595	−	0.716701i
$425$	17.3554	+	5.33411i	0.841861	+	0.258742i
$426$	−2.15162	−	5.94497i	−0.104246	−	0.288035i
$427$		−	7.94739i		−	0.384601i
$428$	−6.46406	−	7.76043i	−0.312452	−	0.375115i
$429$	14.4992	−	14.4992i	0.700030	−	0.700030i
$430$	21.6271	+	32.2403i	1.04295	+	1.55477i
$431$			16.0042i			0.770896i	0.922730	+	0.385448i	$0.125953\pi$
$431$			16.0042i			0.770896i	−0.922730	+	0.385448i	$0.874047\pi$
$432$	3.93410	+	0.723087i	0.189279	+	0.0347895i
$433$	−21.6931	+	21.6931i	−1.04250	+	1.04250i	−0.0434459	+	0.999056i	$0.513834\pi$
$433$	−21.6931	+	21.6931i	−1.04250	+	1.04250i	−0.999056	+	0.0434459i	$0.986166\pi$
$434$	−13.3838	+	28.5666i	−0.642443	+	1.37124i
$435$	−8.00052	+	13.2929i	−0.383595	+	0.637344i
$436$	−1.73886	+	19.0798i	−0.0832764	+	0.913755i
$437$	1.02487			0.0490260
$438$	2.97676	−	6.35365i	0.142235	−	0.303589i
$439$		−	4.04860i		−	0.193229i	−0.995322	−	0.0966145i	$-0.969199\pi$
$439$		−	4.04860i		−	0.193229i	0.995322	−	0.0966145i	$-0.0308014\pi$
$440$	−12.5127	−	22.9055i	−0.596520	−	1.09198i
$441$		−	11.0968i		−	0.528419i
$442$	23.1064	+	10.8256i	1.09906	+	0.514922i
$443$	24.3284			1.15588			0.577938	−	0.816081i	$-0.303858\pi$
$443$	24.3284			1.15588			0.577938	+	0.816081i	$0.303858\pi$
$444$	−2.91256	−	3.49667i	−0.138224	−	0.165945i
$445$	−1.49179	−	6.00212i	−0.0707178	−	0.284528i
$446$	−36.1061	−	16.9162i	−1.70967	−	0.801003i
$447$	15.1118	−	15.1118i	0.714761	−	0.714761i
$448$	9.16457	−	32.7751i	0.432985	−	1.54848i
$449$		−	26.9577i		−	1.27221i	−0.771602	−	0.636106i	$-0.780544\pi$
$449$		−	26.9577i		−	1.27221i	0.771602	−	0.636106i	$-0.219456\pi$
$450$	4.74871	−	5.23925i	0.223856	−	0.246981i
$451$	0.546661	−	0.546661i	0.0257413	−	0.0257413i
$452$	0.664888	−	7.29552i	0.0312737	−	0.343152i
$453$			13.6260i			0.640203i
$454$	−8.64638	+	3.12932i	−0.405795	+	0.146866i
$455$	24.3726	−	40.4950i	1.14260	−	1.89844i
$456$	−0.177143	−	0.675758i	−0.00829546	−	0.0316453i
$457$	−10.7623	+	10.7623i	−0.503440	+	0.503440i	−0.912505	−	0.409065i	$-0.865855\pi$
$457$	−10.7623	+	10.7623i	−0.503440	+	0.503440i	0.409065	+	0.912505i	$0.365855\pi$
$458$	11.8290	+	5.54202i	0.552732	+	0.258962i
$459$	2.56773	−	2.56773i	0.119852	−	0.119852i
$460$	18.3409	−	2.82305i	0.855148	−	0.131625i
$461$	−4.26657	−	4.26657i	−0.198714	−	0.198714i	0.600734	−	0.799449i	$-0.294875\pi$
$461$	−4.26657	−	4.26657i	−0.198714	−	0.198714i	−0.799449	+	0.600734i	$0.794875\pi$
$462$	−23.3455	+	8.44927i	−1.08613	+	0.393096i
$463$	23.4907	+	23.4907i	1.09170	+	1.09170i	0.995347	+	0.0963571i	$0.0307191\pi$
$463$	23.4907	+	23.4907i	1.09170	+	1.09170i	0.0963571	+	0.995347i	$0.469281\pi$
$464$	15.7539	+	22.8491i	0.731356	+	1.06074i
$465$	2.82818	+	11.3790i	0.131154	+	0.527687i
$466$	−26.0175	−	12.1895i	−1.20524	−	0.564669i
$467$	−28.5742			−1.32226			−0.661128	−	0.750273i	$-0.729922\pi$
$467$	−28.5742			−1.32226			−0.661128	+	0.750273i	$0.729922\pi$
$468$	7.63556	−	6.36005i	0.352954	−	0.293994i
$469$	−27.1725	−	27.1725i	−1.25471	−	1.25471i
$470$	−0.355767	−	0.0700951i	−0.0164103	−	0.00323325i
$471$	−7.13379			−0.328708
$472$	3.38284	+	12.9047i	0.155708	+	0.593988i
$473$	−35.8247	−	35.8247i	−1.64722	−	1.64722i
$474$	−3.24997	−	8.97975i	−0.149276	−	0.412454i
$475$	−1.18045	−	0.362806i	−0.0541627	−	0.0166467i
$476$	−19.7735	−	23.7391i	−0.906317	−	1.08808i
$477$			10.3383i			0.473357i
$478$	−8.84833	+	3.20241i	−0.404713	+	0.146475i
$479$	3.27525			0.149650			0.0748250	−	0.997197i	$-0.476160\pi$
$479$	3.27525			0.149650			0.0748250	+	0.997197i	$0.476160\pi$
$480$	−5.03153	−	11.6053i	−0.229657	−	0.529708i
$481$	−11.3058			−0.515499
$482$	−20.8508	+	7.54638i	−0.949729	+	0.343728i
$483$		−	17.6519i		−	0.803188i
$484$	7.71948	+	9.26763i	0.350886	+	0.421256i
$485$	−16.1572	+	26.8452i	−0.733660	+	1.21898i
$486$	−0.481284	−	1.32980i	−0.0218315	−	0.0603209i
$487$	6.15496	+	6.15496i	0.278908	+	0.278908i	0.832673	−	0.553765i	$-0.186809\pi$
$487$	6.15496	+	6.15496i	0.278908	+	0.278908i	−0.553765	+	0.832673i	$0.686809\pi$
$488$	−5.11137	+	1.33989i	−0.231381	+	0.0606540i
$489$	−15.7963			−0.714335
$490$	−29.1418	+	19.5485i	−1.31649	+	0.883113i
$491$	11.4090	+	11.4090i	0.514883	+	0.514883i	0.916019	−	0.401136i	$-0.131384\pi$
$491$	11.4090	+	11.4090i	0.514883	+	0.514883i	−0.401136	+	0.916019i	$0.631384\pi$
$492$	0.287882	−	0.239792i	0.0129787	−	0.0108106i
$493$	25.1957			1.13476
$494$	−1.57161	−	0.736318i	−0.0707099	−	0.0331285i
$495$	−4.75854	+	7.90632i	−0.213881	+	0.355363i
$496$	20.6291	+	3.79161i	0.926272	+	0.170249i
$497$	13.4477	+	13.4477i	0.603213	+	0.603213i
$498$	−0.271094	+	0.0981149i	−0.0121480	+	0.00439664i
$499$	−10.8395	−	10.8395i	−0.485242	−	0.485242i	0.421559	−	0.906801i	$-0.361483\pi$
$499$	−10.8395	−	10.8395i	−0.485242	−	0.485242i	−0.906801	+	0.421559i	$0.861483\pi$
$500$	−22.1245	−	3.24111i	−0.989439	−	0.144947i
$501$	11.1560	−	11.1560i	0.498414	−	0.498414i
$502$	−4.19585	−	1.96581i	−0.187270	−	0.0877383i
$503$	−25.2060	+	25.2060i	−1.12388	+	1.12388i	−0.132726	+	0.991153i	$0.542373\pi$
$503$	−25.2060	+	25.2060i	−1.12388	+	1.12388i	−0.991153	+	0.132726i	$0.957627\pi$
$504$	−11.6390	+	3.05103i	−0.518441	+	0.135904i
$505$	−25.7700	−	15.5101i	−1.14675	−	0.690189i
$506$	−22.7716	+	8.24154i	−1.01232	+	0.366381i
$507$		−	11.6880i		−	0.519084i
$508$	1.52856	−	16.7722i	0.0678190	−	0.744147i
$509$	−11.1087	+	11.1087i	−0.492385	+	0.492385i	−0.909057	−	0.416672i	$-0.863196\pi$
$509$	−11.1087	+	11.1087i	−0.492385	+	0.492385i	0.416672	+	0.909057i	$0.363196\pi$
$510$	−11.2667	−	2.21982i	−0.498896	−	0.0982952i
$511$			21.1057i			0.933663i
$512$	−22.6244	−	0.368484i	−0.999867	−	0.0162849i
$513$	−0.174647	+	0.174647i	−0.00771088	+	0.00771088i
$514$	19.8717	+	9.31012i	0.876501	+	0.410652i
$515$	14.0100	+	8.43215i	0.617355	+	0.371565i
$516$	−15.7144	−	18.8660i	−0.691789	−	0.830528i
$517$	0.473208			0.0208117
$518$	12.3960	+	5.80768i	0.544649	+	0.255175i
$519$		−	24.3506i		−	1.06887i
$520$	−30.1535	−	8.84797i	−1.32232	−	0.388009i
$521$			15.9757i			0.699908i	0.936767	+	0.349954i	$0.113803\pi$
$521$			15.9757i			0.699908i	−0.936767	+	0.349954i	$0.886197\pi$
$522$	4.16299	−	8.88555i	0.182209	−	0.388910i
$523$	−7.67260			−0.335499			−0.167750	−	0.985830i	$-0.553650\pi$
$523$	−7.67260			−0.335499			−0.167750	+	0.985830i	$0.553650\pi$
$524$	0.274918	−	3.01656i	0.0120099	−	0.131779i
$525$	−6.24881	+	20.3316i	−0.272721	+	0.887342i
$526$	8.03251	−	17.1447i	0.350234	−	0.747545i
$527$	13.4643	−	13.4643i	0.586514	−	0.586514i
$528$	9.37009	+	13.5902i	0.407781	+	0.591437i
$529$			5.78211i			0.251396i
$530$	27.1498	−	18.2123i	1.17931	−	0.791092i
$531$	3.33519	−	3.33519i	0.144735	−	0.144735i
$532$	1.34492	+	1.61464i	0.0583096	+	0.0700036i
$533$		−	0.930807i		−	0.0403177i
$534$	1.33118	+	3.67809i	0.0576059	+	0.159166i
$535$	10.9586	−	2.72371i	0.473784	−	0.117756i
$536$	−12.8948	+	22.0571i	−0.556972	+	0.952723i
$537$	−6.13094	+	6.13094i	−0.264569	+	0.264569i
$538$	−2.35500	+	5.02655i	−0.101531	+	0.216710i
$539$	32.3817	−	32.3817i	1.39478	−	1.39478i
$540$	−2.64439	+	3.60655i	−0.113797	+	0.155201i
$541$	6.37490	+	6.37490i	0.274078	+	0.274078i	0.830740	−	0.556661i	$-0.187918\pi$
$541$	6.37490	+	6.37490i	0.274078	+	0.274078i	−0.556661	+	0.830740i	$0.687918\pi$
$542$	1.85814	+	5.13408i	0.0798139	+	0.220528i
$543$	−8.99477	−	8.99477i	−0.386002	−	0.386002i
$544$	−11.9341	+	16.7196i	−0.511670	+	0.716848i
$545$	−18.3526	−	11.0458i	−0.786138	−	0.473149i
$546$	−12.6820	+	27.0687i	−0.542741	+	1.15843i
$547$	44.7865			1.91493			0.957467	−	0.288542i	$-0.0931706\pi$
$547$	44.7865			1.91493			0.957467	+	0.288542i	$0.0931706\pi$
$548$	−1.68797	+	18.5213i	−0.0721065	+	0.791192i
$549$	1.32102	+	1.32102i	0.0563796	+	0.0563796i
$550$	29.1460	−	1.43147i	1.24279	−	0.0610380i
$551$	−1.71371			−0.0730066
$552$	−11.3528	+	2.97602i	−0.483208	+	0.126668i
$553$	20.3125	+	20.3125i	0.863777	+	0.863777i
$554$	−38.4409	+	13.9126i	−1.63320	+	0.591090i
$555$	4.93772	−	1.22724i	0.209594	−	0.0520935i
$556$	2.58782	−	28.3950i	0.109748	−	1.20422i
$557$			10.4866i			0.444331i	0.975009	+	0.222165i	$0.0713125\pi$
$557$			10.4866i			0.444331i	−0.975009	+	0.222165i	$0.928687\pi$
$558$	−2.52369	−	6.97300i	−0.106836	−	0.295191i
$559$	−60.9992			−2.57999
$560$	28.5161	+	25.1908i	1.20503	+	1.06450i
$561$	14.9859			0.632704
$562$	−7.81583	−	21.5953i	−0.329691	−	0.910944i
$563$			31.5903i			1.33137i	0.746231	+	0.665687i	$0.231861\pi$
$563$			31.5903i			1.33137i	−0.746231	+	0.665687i	$0.768139\pi$
$564$	0.228386	+	0.0208143i	0.00961679	+	0.000876441i
$565$	7.01746	+	4.22357i	0.295227	+	0.177687i
$566$	30.3317	−	10.9777i	1.27494	−	0.461428i
$567$	3.00806	+	3.00806i	0.126326	+	0.126326i
$568$	6.38170	−	10.9161i	0.267770	−	0.458031i
$569$	−28.9118			−1.21205			−0.606023	−	0.795447i	$-0.707236\pi$
$569$	−28.9118			−1.21205			−0.606023	+	0.795447i	$0.707236\pi$
$570$	0.766315	+	0.150984i	0.0320974	+	0.00632401i
$571$	−5.84635	−	5.84635i	−0.244662	−	0.244662i	0.574113	−	0.818776i	$-0.305347\pi$
$571$	−5.84635	−	5.84635i	−0.244662	−	0.244662i	−0.818776	+	0.574113i	$0.805347\pi$
$572$	40.8408	+	3.72209i	1.70764	+	0.155628i
$573$	0.148691			0.00621165
$574$	−0.478148	+	1.02057i	−0.0199575	+	0.0425976i
$575$	−6.09518	+	19.8317i	−0.254187	+	0.827039i
$576$	3.92455	+	6.97122i	0.163523	+	0.290468i
$577$	−10.0202	−	10.0202i	−0.417147	−	0.417147i	0.467072	−	0.884219i	$-0.345309\pi$
$577$	−10.0202	−	10.0202i	−0.417147	−	0.417147i	−0.884219	+	0.467072i	$0.845309\pi$
$578$	−1.83537	−	5.07116i	−0.0763411	−	0.210932i
$579$	4.33825	+	4.33825i	0.180291	+	0.180291i
$580$	−30.6684	+	4.72052i	−1.27344	+	0.196009i
$581$	0.613225	−	0.613225i	0.0254408	−	0.0254408i
$582$	8.40723	−	17.9445i	0.348491	−	0.743824i
$583$	−30.1682	+	30.1682i	−1.24944	+	1.24944i
$584$	13.5742	−	3.55832i	0.561703	−	0.147244i
$585$	2.67988	+	10.7823i	0.110800	+	0.445794i
$586$	14.7750	+	40.8235i	0.610348	+	1.68640i
$587$		−	3.79915i		−	0.156808i	−0.996922	−	0.0784039i	$-0.975018\pi$
$587$		−	3.79915i		−	0.156808i	0.996922	−	0.0784039i	$-0.0249824\pi$
$588$	17.0528	−	14.2041i	0.703245	−	0.585769i
$589$	−0.915791	+	0.915791i	−0.0377345	+	0.0377345i
$590$	−14.6341	−	2.88328i	−0.602475	−	0.118703i
$591$		−	5.86883i		−	0.241411i
$592$	1.64531	−	8.95164i	0.0676218	−	0.367910i
$593$	−11.5151	+	11.5151i	−0.472869	+	0.472869i	−0.902842	−	0.429973i	$-0.858523\pi$
$593$	−11.5151	+	11.5151i	−0.472869	+	0.472869i	0.429973	+	0.902842i	$0.358523\pi$
$594$	2.47606	−	5.28494i	0.101594	−	0.216844i
$595$	33.5224	−	8.33180i	1.37428	−	0.341570i
$596$	42.5661	+	3.87933i	1.74357	+	0.158903i
$597$	5.93363			0.242847
$598$	−12.3702	+	26.4032i	−0.505856	+	1.07971i
$599$		−	21.2875i		−	0.869783i	−0.900483	−	0.434891i	$-0.856787\pi$
$599$		−	21.2875i		−	0.869783i	0.900483	−	0.434891i	$-0.143213\pi$
$600$	14.1298	+	0.591127i	0.576846	+	0.0241327i
$601$		−	44.8560i		−	1.82971i	−0.403779	−	0.914856i	$-0.632304\pi$
$601$		−	44.8560i		−	1.82971i	0.403779	−	0.914856i	$-0.367696\pi$
$602$	66.8814	+	31.3348i	2.72588	+	1.27711i
$603$	9.03323			0.367862
$604$	−20.9394	+	17.4415i	−0.852014	+	0.709686i
$605$	−13.0870	+	3.25270i	−0.532062	+	0.132241i
$606$	17.2258	+	8.07051i	0.699751	+	0.327842i
$607$	7.48042	−	7.48042i	0.303621	−	0.303621i	−0.538808	−	0.842429i	$-0.681125\pi$
$607$	7.48042	−	7.48042i	0.303621	−	0.303621i	0.842429	+	0.538808i	$0.181125\pi$
$608$	0.811712	−	1.13721i	0.0329192	−	0.0461198i
$609$			29.5163i			1.19606i
$610$	1.14203	−	5.79634i	0.0462393	−	0.234687i
$611$	0.402869	−	0.402869i	0.0162983	−	0.0162983i
$612$	7.23268	+	0.659161i	0.292364	+	0.0266450i
$613$		−	23.9275i		−	0.966423i	−0.875504	−	0.483211i	$-0.839470\pi$
$613$		−	23.9275i		−	0.966423i	0.875504	−	0.483211i	$-0.160530\pi$
$614$	−23.0863	+	8.35544i	−0.931687	+	0.337198i
$615$	0.101039	+	0.406523i	0.00407429	+	0.0163926i
$616$	−42.8670	−	25.0606i	−1.72716	−	1.00972i
$617$	−6.14250	+	6.14250i	−0.247288	+	0.247288i	−0.819857	−	0.572569i	$-0.805947\pi$
$617$	−6.14250	+	6.14250i	−0.247288	+	0.247288i	0.572569	+	0.819857i	$0.305947\pi$
$618$	−9.36493	−	4.38759i	−0.376713	−	0.176495i
$619$	15.3689	−	15.3689i	0.617729	−	0.617729i	−0.327220	−	0.944948i	$-0.606112\pi$
$619$	15.3689	−	15.3689i	0.617729	−	0.617729i	0.944948	+	0.327220i	$0.106112\pi$
$620$	−13.8663	+	18.9115i	−0.556883	+	0.759503i
$621$	2.93410	+	2.93410i	0.117741	+	0.117741i
$622$	−26.6556	+	9.64724i	−1.06879	+	0.386819i
$623$	−8.31997	−	8.31997i	−0.333333	−	0.333333i
$624$	19.5474	+	3.59280i	0.782522	+	0.143827i
$625$	14.0409	−	20.6846i	0.561638	−	0.827383i
$626$	−19.5007	−	9.13631i	−0.779404	−	0.365160i
$627$	−1.01928			−0.0407062
$628$	−9.13141	−	10.9627i	−0.364383	−	0.437460i
$629$	−5.84262	−	5.84262i	−0.232960	−	0.232960i
$630$	2.60048	−	13.1987i	0.103606	−	0.525849i
$631$	36.1280			1.43823			0.719116	−	0.694891i	$-0.244547\pi$
$631$	36.1280			1.43823			0.719116	+	0.694891i	$0.244547\pi$
$632$	9.63943	−	16.4886i	0.383436	−	0.655882i
$633$	7.09893	+	7.09893i	0.282157	+	0.282157i
$634$	5.62133	+	15.5319i	0.223252	+	0.616849i
$635$	16.1330	+	9.70988i	0.640218	+	0.385325i
$636$	−15.8872	+	13.2332i	−0.629967	+	0.524731i
$637$		−	55.1367i		−	2.18460i
$638$	38.0771	−	13.7809i	1.50749	−	0.545593i
$639$	−4.47057			−0.176853
$640$	11.3938	−	22.5872i	0.450379	−	0.892837i
$641$	−43.5468			−1.72000			−0.859998	−	0.510297i	$-0.829536\pi$
$641$	−43.5468			−1.72000			−0.859998	+	0.510297i	$0.829536\pi$
$642$	−6.71543	+	2.43047i	−0.265037	+	0.0959228i
$643$			8.84133i			0.348668i	0.984687	+	0.174334i	$0.0557772\pi$
$643$			8.84133i			0.348668i	−0.984687	+	0.174334i	$0.944223\pi$
$644$	27.1262	−	22.5948i	1.06892	−	0.890359i
$645$	26.6410	−	6.62146i	1.04899	−	0.260720i
$646$	−0.431662	−	1.19269i	−0.0169835	−	0.0469259i
$647$	−16.9926	−	16.9926i	−0.668049	−	0.668049i	0.289215	−	0.957264i	$-0.406606\pi$
$647$	−16.9926	−	16.9926i	−0.668049	−	0.668049i	−0.957264	+	0.289215i	$0.906606\pi$
$648$	1.42749	−	2.44178i	0.0560771	−	0.0959220i
$649$	19.4649			0.764064
$650$	23.5949	−	26.0323i	0.925469	−	1.02107i
$651$	15.7732	+	15.7732i	0.618200	+	0.618200i
$652$	−20.2197	−	24.2747i	−0.791863	−	0.950672i
$653$	35.7891			1.40053			0.700267	−	0.713881i	$-0.253064\pi$
$653$	35.7891			1.40053			0.700267	+	0.713881i	$0.253064\pi$
$654$	12.2677	+	5.74756i	0.479704	+	0.224747i
$655$	2.90159	+	1.74636i	0.113374	+	0.0682361i
$656$	0.736991	+	0.135459i	0.0287746	+	0.00528877i
$657$	−3.50820	−	3.50820i	−0.136868	−	0.136868i
$658$	−0.648668	+	0.234767i	−0.0252877	+	0.00915219i
$659$	−11.8604	−	11.8604i	−0.462014	−	0.462014i	0.437301	−	0.899315i	$-0.355934\pi$
$659$	−11.8604	−	11.8604i	−0.462014	−	0.462014i	−0.899315	+	0.437301i	$0.855934\pi$
$660$	−18.2409	+	2.80767i	−0.710028	+	0.109288i
$661$	−5.12628	+	5.12628i	−0.199389	+	0.199389i	−0.799738	−	0.600349i	$-0.795028\pi$
$661$	−5.12628	+	5.12628i	−0.199389	+	0.199389i	0.600349	+	0.799738i	$0.295028\pi$
$662$	33.9265	+	15.8950i	1.31859	+	0.617776i
$663$	12.7583	−	12.7583i	0.495492	−	0.495492i
$664$	−0.497783	−	0.291009i	−0.0193177	−	0.0112933i
$665$	−2.28006	+	0.566697i	−0.0884171	+	0.0219756i
$666$	−3.02582	+	1.09511i	−0.117248	+	0.0424347i
$667$			28.7906i			1.11478i
$668$	31.4237	+	2.86385i	1.21582	+	0.110806i
$669$	−19.9362	+	19.9362i	−0.770777	+	0.770777i
$670$	−15.9133	−	23.7226i	−0.614784	−	0.916482i
$671$			7.70975i			0.297632i
$672$	−19.5868	−	13.9806i	−0.755575	−	0.539313i
$673$	8.42753	−	8.42753i	0.324858	−	0.324858i	−0.525770	−	0.850627i	$-0.676223\pi$
$673$	8.42753	−	8.42753i	0.324858	−	0.324858i	0.850627	+	0.525770i	$0.176223\pi$
$674$	−11.1941	−	5.24457i	−0.431180	−	0.202013i
$675$	−2.34084	−	4.41820i	−0.0900989	−	0.170057i
$676$	17.9614	−	14.9609i	0.690822	−	0.575421i
$677$	13.1467			0.505268			0.252634	−	0.967562i	$-0.418703\pi$
$677$	13.1467			0.505268			0.252634	+	0.967562i	$0.418703\pi$
$678$	−4.69078	−	2.19769i	−0.180149	−	0.0844018i
$679$			59.6086i			2.28757i
$680$	−11.0103	−	20.1552i	−0.422226	−	0.772918i
$681$			6.50202i			0.249158i
$682$	12.9836	−	27.7124i	0.497168	−	1.06116i
$683$	−15.9674			−0.610977			−0.305489	−	0.952196i	$-0.598820\pi$
$683$	−15.9674			−0.610977			−0.305489	+	0.952196i	$0.598820\pi$
$684$	−0.491939	−	0.0448336i	−0.0188098	−	0.00171426i
$685$	−17.8154	−	10.7225i	−0.680692	−	0.409685i
$686$	−10.4566	+	22.3187i	−0.399234	+	0.852132i
$687$	6.53144	−	6.53144i	0.249190	−	0.249190i
$688$	8.87711	−	48.2977i	0.338437	−	1.84133i
$689$			51.3678i			1.95696i
$690$	2.53654	−	12.8742i	0.0965646	−	0.490112i
$691$	−14.4031	+	14.4031i	−0.547919	+	0.547919i	−0.925839	−	0.377919i	$-0.876640\pi$
$691$	−14.4031	+	14.4031i	−0.547919	+	0.547919i	0.377919	+	0.925839i	$0.376640\pi$
$692$	37.4203	−	31.1693i	1.42251	−	1.18488i
$693$			17.5557i			0.666885i
$694$	−1.86733	−	5.15946i	−0.0708827	−	0.195851i
$695$	27.3128	+	16.4386i	1.03603	+	0.623553i
$696$	18.9834	−	4.97630i	0.719565	−	0.188626i
$697$	0.481024	−	0.481024i	0.0182201	−	0.0182201i
$698$	−1.32376	+	2.82546i	−0.0501051	+	0.106945i
$699$	−14.3657	+	14.3657i	−0.543362	+	0.543362i
$700$	−39.2428	+	16.4221i	−1.48324	+	0.620697i
$701$	−9.70568	−	9.70568i	−0.366579	−	0.366579i	0.499649	−	0.866228i	$-0.333462\pi$
$701$	−9.70568	−	9.70568i	−0.366579	−	0.366579i	−0.866228	+	0.499649i	$0.833462\pi$
$702$	−2.39136	−	6.60738i	−0.0902560	−	0.249379i
$703$	0.397392	+	0.397392i	0.0149879	+	0.0149879i
$704$	−8.89054	+	31.7951i	−0.335075	+	1.19832i
$705$	−0.132219	+	0.219682i	−0.00497965	+	0.00827368i
$706$	4.87302	−	10.4011i	0.183399	−	0.391449i
$707$	−57.2213			−2.15203
$708$	9.39440	+	0.856173i	0.353063	+	0.0321769i
$709$	9.01713	+	9.01713i	0.338645	+	0.338645i	0.855857	−	0.517212i	$-0.173030\pi$
$709$	9.01713	+	9.01713i	0.338645	+	0.338645i	−0.517212	+	0.855857i	$0.673030\pi$
$710$	7.87554	+	11.7404i	0.295564	+	0.440608i
$711$	−6.75271			−0.253247
$712$	−3.94829	+	6.75370i	−0.147968	+	0.253106i
$713$	15.3854	+	15.3854i	0.576188	+	0.576188i
$714$	−20.5424	+	7.43477i	−0.768782	+	0.278239i
$715$	−23.6438	+	39.2842i	−0.884228	+	1.46915i
$716$	−17.2693	−	1.57387i	−0.645385	−	0.0588182i
$717$			6.65388i			0.248494i
$718$	−8.70459	−	24.0510i	−0.324852	−	0.897575i
$719$	−24.3409			−0.907762			−0.453881	−	0.891062i	$-0.649961\pi$
$719$	−24.3409			−0.907762			−0.453881	+	0.891062i	$0.649961\pi$
$720$	−8.92718	+	0.552736i	−0.332696	+	0.0205992i
$721$	31.1087			1.15855
$722$	−9.11504	−	25.1851i	−0.339227	−	0.937291i
$723$			15.6797i			0.583134i
$724$	2.30904	−	25.3360i	0.0858148	−	0.941607i
$725$	10.1920	−	33.1612i	0.378520	−	1.23158i
$726$	8.01968	−	2.90250i	0.297638	−	0.107722i
$727$	−23.7830	−	23.7830i	−0.882062	−	0.882062i	0.111682	−	0.993744i	$-0.464376\pi$
$727$	−23.7830	−	23.7830i	−0.882062	−	0.882062i	−0.993744	+	0.111682i	$0.964376\pi$
$728$	−57.8306	+	15.1597i	−2.14334	+	0.561855i
$729$	−1.00000			−0.0370370
$730$	−3.03286	+	15.3932i	−0.112251	+	0.569729i
$731$	−31.5233	−	31.5233i	−1.16593	−	1.16593i
$732$	−0.339117	+	3.72098i	−0.0125341	+	0.137531i
$733$	−14.8205			−0.547406			−0.273703	−	0.961814i	$-0.588249\pi$
$733$	−14.8205			−0.547406			−0.273703	+	0.961814i	$0.588249\pi$
$734$	0.849091	−	1.81231i	0.0313405	−	0.0668937i
$735$	5.98508	+	24.0806i	0.220763	+	0.888225i
$736$	−19.1052	−	13.6369i	−0.704227	−	0.502661i
$737$	26.3600	+	26.3600i	0.970982	+	0.970982i
$738$	−0.0901608	−	0.249117i	−0.00331887	−	0.00917011i
$739$	35.6500	+	35.6500i	1.31141	+	1.31141i	0.920378	+	0.391029i	$0.127881\pi$
$739$	35.6500	+	35.6500i	1.31141	+	1.31141i	0.391029	+	0.920378i	$0.372119\pi$
$740$	8.20633	+	6.01705i	0.301671	+	0.221191i
$741$	−0.867772	+	0.867772i	−0.0318784	+	0.0318784i
$742$	26.3872	−	56.3213i	0.968705	−	2.06762i
$743$	−24.3691	+	24.3691i	−0.894016	+	0.894016i	−0.994898	−	0.100883i	$-0.967833\pi$
$743$	−24.3691	+	24.3691i	−0.894016	+	0.894016i	0.100883	+	0.994898i	$0.467833\pi$
$744$	7.48526	−	12.8038i	0.274423	−	0.469411i
$745$	−24.6426	+	40.9438i	−0.902836	+	1.50006i
$746$	1.08464	+	2.99690i	0.0397116	+	0.109724i
$747$			0.203861i			0.00745888i
$748$	19.1822	+	23.0293i	0.701372	+	0.842033i
$749$	15.1906	−	15.1906i	0.555051	−	0.555051i
$750$	−7.47911	+	13.9306i	−0.273098	+	0.508675i
$751$		−	25.6756i		−	0.936917i	−0.883486	−	0.468458i	$-0.844810\pi$
$751$		−	25.6756i		−	0.936917i	0.883486	−	0.468458i	$-0.155190\pi$
$752$	0.260353	+	0.377611i	0.00949410	+	0.0137700i
$753$	−2.31676	+	2.31676i	−0.0844275	+	0.0844275i
$754$	20.6847	−	44.1497i	0.753291	−	1.60784i
$755$	−7.34919	−	29.5690i	−0.267465	−	1.07612i
$756$	−0.772196	+	8.47295i	−0.0280845	+	0.308158i
$757$	21.4132			0.778274			0.389137	−	0.921180i	$-0.372773\pi$
$757$	21.4132			0.778274			0.389137	+	0.921180i	$0.372773\pi$
$758$	−6.71260	+	14.3275i	−0.243813	+	0.520397i
$759$			17.1241i			0.621564i
$760$	0.748879	+	1.37088i	0.0271647	+	0.0497271i
$761$		−	15.6885i		−	0.568708i	−0.958719	−	0.284354i	$-0.908221\pi$
$761$		−	15.6885i		−	0.568708i	0.958719	−	0.284354i	$-0.0917791\pi$
$762$	−10.7840	−	5.05244i	−0.390663	−	0.183031i
$763$	−40.7511			−1.47529
$764$	0.190328	+	0.228498i	0.00688581	+	0.00826677i
$765$	−4.18719	+	6.95702i	−0.151388	+	0.251531i
$766$	35.7492	+	16.7489i	1.29167	+	0.605164i
$767$	16.5716	−	16.5716i	0.598364	−	0.598364i
$768$	−5.68939	+	14.9543i	−0.205298	+	0.539617i
$769$		−	51.0412i		−	1.84059i	−0.391221	−	0.920297i	$-0.627947\pi$
$769$		−	51.0412i		−	1.84059i	0.391221	−	0.920297i	$-0.372053\pi$
$770$	46.1037	−	30.9268i	1.66146	−	1.11452i
$771$	10.9722	−	10.9722i	0.395156	−	0.395156i
$772$	−1.11367	+	12.2198i	−0.0400818	+	0.439799i
$773$		−	15.9432i		−	0.573437i	−0.958015	−	0.286718i	$-0.907436\pi$
$773$		−	15.9432i		−	0.573437i	0.958015	−	0.286718i	$-0.0925644\pi$
$774$	−16.3255	+	5.90857i	−0.586809	+	0.212379i
$775$	−12.2745	−	23.1675i	−0.440915	−	0.832201i
$776$	38.3373	−	10.0497i	1.37623	−	0.360764i
$777$	6.84452	−	6.84452i	0.245546	−	0.245546i
$778$	9.95460	+	4.66386i	0.356890	+	0.167207i
$779$	−0.0327174	+	0.0327174i	−0.00117222	+	0.00117222i
$780$	−13.1392	+	17.9199i	−0.470459	+	0.641634i
$781$	−13.0456	−	13.0456i	−0.466809	−	0.466809i
$782$	−20.0374	+	7.25198i	−0.716536	+	0.259330i
$783$	−4.90621	−	4.90621i	−0.175333	−	0.175333i
$784$	43.6559	+	8.02395i	1.55914	+	0.286569i
$785$	15.4807	−	3.84763i	0.552528	−	0.137328i
$786$	−1.93955	−	0.908703i	−0.0691814	−	0.0324124i
$787$	−26.1398			−0.931784			−0.465892	−	0.884841i	$-0.654267\pi$
$787$	−26.1398			−0.931784			−0.465892	+	0.884841i	$0.654267\pi$
$788$	9.01882	−	7.51223i	0.321282	−	0.267612i
$789$	−9.46655	−	9.46655i	−0.337018	−	0.337018i
$790$	11.8958	+	17.7336i	0.423235	+	0.630933i
$791$	15.5820			0.554032
$792$	11.2909	−	2.95980i	0.401206	−	0.105172i
$793$	6.56374	+	6.56374i	0.233085	+	0.233085i
$794$	−12.2483	−	33.8424i	−0.434676	−	1.20102i
$795$	−5.57597	−	22.4345i	−0.197759	−	0.795671i
$796$	7.59517	+	9.11839i	0.269204	+	0.323193i
$797$		−	34.0127i		−	1.20479i	−0.798197	−	0.602396i	$-0.794213\pi$
$797$		−	34.0127i		−	1.20479i	0.798197	−	0.602396i	$-0.205787\pi$
$798$	1.39722	−	0.505685i	0.0494610	−	0.0179010i
$799$	0.416390			0.0147308
$800$	17.1780	+	22.4703i	0.607335	+	0.794446i
$801$	2.76590			0.0977282
$802$	−1.93627	+	0.700781i	−0.0683722	+	0.0247454i
$803$		−	20.4746i		−	0.722534i
$804$	11.5627	+	13.8816i	0.407786	+	0.489568i
$805$	9.52058	+	38.3054i	0.335556	+	1.35009i
$806$	−12.5395	−	34.6468i	−0.441683	−	1.22038i
$807$	2.77544	+	2.77544i	0.0977002	+	0.0977002i
$808$	9.64723	+	36.8019i	0.339388	+	1.29469i
$809$	25.6058			0.900253			0.450127	−	0.892965i	$-0.351379\pi$
$809$	25.6058			0.900253			0.450127	+	0.892965i	$0.351379\pi$
$810$	1.76164	+	2.62614i	0.0618977	+	0.0922733i
$811$	−29.4467	−	29.4467i	−1.03401	−	1.03401i	−0.999401	−	0.0346118i	$-0.988981\pi$
$811$	−29.4467	−	29.4467i	−1.03401	−	1.03401i	−0.0346118	−	0.999401i	$-0.511019\pi$
$812$	−45.3586	+	37.7815i	−1.59177	+	1.32587i
$813$	3.86079			0.135404
$814$	−12.0253	−	5.63402i	−0.421488	−	0.197472i
$815$	34.2788	−	8.51980i	1.20073	−	0.298435i
$816$	8.24503	+	11.9584i	0.288634	+	0.418628i
$817$	2.14409	+	2.14409i	0.0750123	+	0.0750123i
$818$	19.8372	−	7.17952i	0.693591	−	0.251026i
$819$	14.9461	+	14.9461i	0.522260	+	0.522260i
$820$	−0.495385	+	0.675629i	−0.0172996	+	0.0235940i
$821$	−22.3951	+	22.3951i	−0.781595	+	0.781595i	−0.980100	−	0.198505i	$-0.936392\pi$
$821$	−22.3951	+	22.3951i	−0.781595	+	0.781595i	0.198505	+	0.980100i	$0.436392\pi$
$822$	11.9086	+	5.57934i	0.415361	+	0.194602i
$823$	19.7666	−	19.7666i	0.689019	−	0.689019i	−0.272996	−	0.962015i	$-0.588015\pi$
$823$	19.7666	−	19.7666i	0.689019	−	0.689019i	0.962015	+	0.272996i	$0.0880146\pi$
$824$	−5.24477	−	20.0076i	−0.182710	−	0.696997i
$825$	6.06196	−	19.7236i	0.211051	−	0.686688i
$826$	−26.6822	+	9.65689i	−0.928393	+	0.336006i
$827$			45.0540i			1.56668i	0.621592	+	0.783341i	$0.286486\pi$
$827$			45.0540i			1.56668i	−0.621592	+	0.783341i	$0.713514\pi$
$828$	−0.753211	+	8.26464i	−0.0261759	+	0.287216i
$829$	−20.1502	+	20.1502i	−0.699844	+	0.699844i	−0.964377	−	0.264533i	$-0.914782\pi$
$829$	−20.1502	+	20.1502i	−0.699844	+	0.699844i	0.264533	+	0.964377i	$0.414782\pi$
$830$	0.535368	−	0.359129i	0.0185829	−	0.0124656i
$831$			28.9073i			1.00278i
$832$	19.4999	+	34.6379i	0.676038	+	1.20085i
$833$	28.4936	−	28.4936i	0.987246	−	0.987246i
$834$	−18.2571	−	8.55368i	−0.632191	−	0.296190i
$835$	−18.1920	+	30.2261i	−0.629561	+	1.04602i
$836$	−1.30470	−	1.56636i	−0.0451241	−	0.0541738i
$837$	−5.24365			−0.181247
$838$	22.4151	+	10.5018i	0.774317	+	0.362777i
$839$		−	10.9329i		−	0.377445i	−0.982030	−	0.188723i	$-0.939565\pi$
$839$		−	10.9329i		−	0.377445i	0.982030	−	0.188723i	$-0.0604347\pi$
$840$	23.6115	−	12.8984i	0.814675	−	0.445037i
$841$		−	19.1417i		−	0.660059i
$842$	−19.6356	+	41.9105i	−0.676687	+	1.44433i
$843$	−16.2395			−0.559319
$844$	−1.82236	+	19.9959i	−0.0627282	+	0.688288i
$845$	6.30397	+	25.3636i	0.216863	+	0.872533i
$846$	0.0687987	−	0.146845i	0.00236535	−	0.00504863i
$847$	−18.1408	+	18.1408i	−0.623326	+	0.623326i
$848$	−40.6718	−	7.47547i	−1.39668	−	0.256709i
$849$		−	22.8092i		−	0.782811i
$850$	25.6464	−	1.25959i	0.879665	−	0.0432037i
$851$	6.67624	−	6.67624i	0.228859	−	0.228859i
$852$	−5.72243	−	6.87007i	−0.196047	−	0.235365i
$853$		−	18.1959i		−	0.623017i	−0.950243	−	0.311508i	$-0.899166\pi$
$853$		−	18.1959i		−	0.623017i	0.950243	−	0.311508i	$-0.100834\pi$
$854$	−3.82495	−	10.5684i	−0.130887	−	0.361644i
$855$	0.284797	−	0.473190i	0.00973984	−	0.0161827i
$856$	−12.3309	−	7.20877i	−0.421461	−	0.246391i
$857$	−40.4936	+	40.4936i	−1.38324	+	1.38324i	−0.544430	+	0.838807i	$0.683254\pi$
$857$	−40.4936	+	40.4936i	−1.38324	+	1.38324i	−0.838807	+	0.544430i	$0.816746\pi$
$858$	12.3028	−	26.2593i	0.420011	−	0.896478i
$859$	−14.3628	+	14.3628i	−0.490053	+	0.490053i	−0.908323	−	0.418270i	$-0.862637\pi$
$859$	−14.3628	+	14.3628i	−0.490053	+	0.490053i	0.418270	+	0.908323i	$0.362637\pi$
$860$	44.2764	+	32.4644i	1.50981	+	1.10703i
$861$	0.563511	+	0.563511i	0.0192044	+	0.0192044i
$862$	7.70257	+	21.2824i	0.262351	+	0.724881i
$863$	−10.5835	−	10.5835i	−0.360268	−	0.360268i	0.503644	−	0.863911i	$-0.331992\pi$
$863$	−10.5835	−	10.5835i	−0.360268	−	0.360268i	−0.863911	+	0.503644i	$0.831992\pi$
$864$	5.57957	−	0.931860i	0.189821	−	0.0317025i
$865$	13.1335	+	52.8418i	0.446553	+	1.79668i
$866$	−18.4069	+	39.2879i	−0.625491	+	1.33506i
$867$	−3.81348			−0.129512
$868$	−4.04912	+	44.4292i	−0.137436	+	1.50803i
$869$	−19.7052	−	19.7052i	−0.668452	−	0.668452i
$870$	−4.24144	+	21.5274i	−0.143798	+	0.729846i
$871$	44.8834			1.52082
$872$	6.87044	+	26.2091i	0.232663	+	0.887553i
$873$	−9.90816	−	9.90816i	−0.335341	−	0.335341i
$874$	1.36287	−	0.493252i	0.0460997	−	0.0166845i
$875$	2.59433	−	47.4907i	0.0877045	−	1.60548i
$876$	0.900588	−	9.88174i	0.0304280	−	0.333873i
$877$			55.3196i			1.86801i	0.357262	+	0.934004i	$0.383710\pi$
$877$			55.3196i			1.86801i	−0.357262	+	0.934004i	$0.616290\pi$
$878$	−1.94852	−	5.38382i	−0.0657595	−	0.181695i
$879$	30.6990			1.03545
$880$	−27.6634	−	24.4375i	−0.932534	−	0.823790i
$881$	−47.0634			−1.58561			−0.792804	−	0.609477i	$-0.791380\pi$
$881$	−47.0634			−1.58561			−0.792804	+	0.609477i	$0.791380\pi$
$882$	−5.34071	−	14.7565i	−0.179831	−	0.496878i
$883$		−	42.7619i		−	1.43905i	−0.694465	−	0.719526i	$-0.744359\pi$
$883$		−	42.7619i		−	1.43905i	0.694465	−	0.719526i	$-0.255641\pi$
$884$	35.9370	+	3.27518i	1.20869	+	0.110156i
$885$	−5.43867	+	9.03635i	−0.182819	+	0.303753i
$886$	32.3518	−	11.7088i	1.08688	−	0.393366i
$887$	14.8427	+	14.8427i	0.498370	+	0.498370i	0.910930	−	0.412560i	$-0.135365\pi$
$887$	14.8427	+	14.8427i	0.498370	+	0.498370i	−0.412560	+	0.910930i	$0.635365\pi$
$888$	−5.55601	−	3.24811i	−0.186448	−	0.108999i
$889$	35.8226			1.20145
$890$	−4.87251	−	7.26364i	−0.163327	−	0.243478i
$891$	−2.91811	−	2.91811i	−0.0977604	−	0.0977604i
$892$	−56.1553	−	5.11780i	−1.88022	−	0.171357i
$893$	−0.0283213			−0.000947736
$894$	12.8226	−	27.3686i	0.428850	−	0.915344i
$895$	9.99768	−	16.6111i	0.334185	−	0.555249i
$896$	−3.58708	−	47.9950i	−0.119836	−	1.60340i
$897$	14.5787	+	14.5787i	0.486768	+	0.486768i
$898$	−12.9743	−	35.8483i	−0.432958	−	1.19627i
$899$	−25.7264	−	25.7264i	−0.858025	−	0.858025i
$900$	3.79326	−	9.25263i	0.126442	−	0.308421i
$901$	−26.5459	+	26.5459i	−0.884374	+	0.884374i
$902$	0.463850	−	0.990049i	0.0154445	−	0.0329650i
$903$	36.9290	−	36.9290i	1.22892	−	1.22892i
$904$	−2.62705	−	10.0216i	−0.0873743	−	0.333312i
$905$	24.3704	+	14.6677i	0.810100	+	0.487571i
$906$	6.55796	+	18.1198i	0.217874	+	0.601990i
$907$		−	31.3755i		−	1.04181i	−0.853616	−	0.520903i	$-0.825595\pi$
$907$		−	31.3755i		−	1.04181i	0.853616	−	0.520903i	$-0.174405\pi$
$908$	−9.99186	+	8.32273i	−0.331591	+	0.276199i
$909$	9.51134	−	9.51134i	0.315471	−	0.315471i
$910$	12.9210	−	65.5804i	0.428327	−	2.17397i
$911$		−	20.9112i		−	0.692818i	−0.938084	−	0.346409i	$-0.887401\pi$
$911$		−	20.9112i		−	0.692818i	0.938084	−	0.346409i	$-0.112599\pi$
$912$	−0.560796	−	0.813366i	−0.0185698	−	0.0269332i
$913$	−0.594888	+	0.594888i	−0.0196879	+	0.0196879i
$914$	−9.13200	+	19.4915i	−0.302060	+	0.644720i
$915$	−3.57916	−	2.15417i	−0.118323	−	0.0712148i
$916$	18.3974	+	1.67668i	0.607869	+	0.0553991i
$917$	6.44286			0.212762
$918$	2.17876	−	4.65038i	0.0719098	−	0.153485i
$919$			19.8382i			0.654403i	0.944955	+	0.327201i	$0.106106\pi$
$919$			19.8382i			0.654403i	−0.944955	+	0.327201i	$0.893894\pi$
$920$	23.0310	−	12.5813i	0.759310	−	0.414792i
$921$			17.3607i			0.572056i
$922$	−7.72712	−	3.62025i	−0.254479	−	0.119227i
$923$	−22.2130			−0.731149
$924$	−26.9784	+	22.4717i	−0.887523	+	0.739263i
$925$	−10.0532	+	5.32634i	−0.330546	+	0.175129i
$926$	42.5436	+	19.9322i	1.39807	+	0.655012i
$927$	−5.17090	+	5.17090i	−0.169835	+	0.169835i
$928$	31.9464	+	22.8026i	1.04869	+	0.748533i
$929$		−	20.2449i		−	0.664213i	−0.943242	−	0.332106i	$-0.892241\pi$
$929$		−	20.2449i		−	0.664213i	0.943242	−	0.332106i	$-0.107759\pi$
$930$	9.23742	+	13.7706i	0.302907	+	0.451555i
$931$	−1.93803	+	1.93803i	−0.0635163	+	0.0635163i
$932$	−40.4647	−	3.68781i	−1.32547	−	0.120798i
$933$			20.0448i			0.656237i
$934$	−37.9979	+	13.7523i	−1.24333	+	0.449989i
$935$	−32.5200	+	8.08266i	−1.06352	+	0.264331i
$936$	7.09278	−	12.1325i	0.231835	−	0.396562i
$937$	−18.7073	+	18.7073i	−0.611140	+	0.611140i	−0.943243	−	0.332103i	$-0.892242\pi$
$937$	−18.7073	+	18.7073i	−0.611140	+	0.611140i	0.332103	+	0.943243i	$0.392242\pi$
$938$	−49.2116	−	23.0562i	−1.60681	−	0.752813i
$939$	−10.7674	+	10.7674i	−0.351381	+	0.351381i
$940$	−0.506834	+	0.0780125i	−0.0165311	+	0.00254449i
$941$	−5.54352	−	5.54352i	−0.180713	−	0.180713i	0.610953	−	0.791667i	$-0.290786\pi$
$941$	−5.54352	−	5.54352i	−0.180713	−	0.180713i	−0.791667	+	0.610953i	$0.790786\pi$
$942$	−9.48651	+	3.43338i	−0.309087	+	0.111866i
$943$	0.549657	+	0.549657i	0.0178993	+	0.0178993i
$944$	10.7093	+	15.5326i	0.348559	+	0.505543i
$945$	−8.15002	−	4.90522i	−0.265120	−	0.159567i
$946$	−64.8816	−	30.3978i	−2.10948	−	0.988319i
$947$	18.6075			0.604664			0.302332	−	0.953203i	$-0.402235\pi$
$947$	18.6075			0.604664			0.302332	+	0.953203i	$0.402235\pi$
$948$	−8.64362	−	10.3771i	−0.280732	−	0.337033i
$949$	−17.4312	−	17.4312i	−0.565841	−	0.565841i
$950$	−1.74437	+	0.0856727i	−0.0565949	+	0.00277959i
$951$	11.6799			0.378745
$952$	−37.7200	−	22.0515i	−1.22251	−	0.714695i
$953$	39.8932	+	39.8932i	1.29227	+	1.29227i	0.933381	+	0.358888i	$0.116844\pi$
$953$	39.8932	+	39.8932i	1.29227	+	1.29227i	0.358888	+	0.933381i	$0.383156\pi$
$954$	4.97565	+	13.7478i	0.161093	+	0.445102i
$955$	−0.322666	+	0.0801968i	−0.0104412	+	0.00259511i
$956$	−10.2252	+	8.51712i	−0.330708	+	0.275463i
$957$		−	28.6337i		−	0.925596i
$958$	4.35542	−	1.57633i	0.140717	−	0.0509287i
$959$	−39.5584			−1.27741
$960$	−12.2764	−	13.0112i	−0.396219	−	0.419933i
$961$	3.50411			0.113036
$962$	−15.0344	+	5.44129i	−0.484729	+	0.175434i
$963$			5.04996i			0.162733i
$964$	−24.0955	+	20.0703i	−0.776063	+	0.646422i
$965$	−11.7540	−	7.07435i	−0.378376	−	0.227732i
$966$	−8.49557	−	23.4734i	−0.273340	−	0.755246i
$967$	36.2541	+	36.2541i	1.16585	+	1.16585i	0.983172	+	0.182682i	$0.0584778\pi$
$967$	36.2541	+	36.2541i	1.16585	+	1.16585i	0.182682	+	0.983172i	$0.441522\pi$
$968$	14.7257	+	8.60882i	0.473303	+	0.276698i
$969$	−0.896897			−0.0288125
$970$	−8.56565	+	43.4749i	−0.275027	+	1.39589i
$971$	25.3075	+	25.3075i	0.812157	+	0.812157i	0.984957	−	0.172800i	$-0.0552814\pi$
$971$	25.3075	+	25.3075i	0.812157	+	0.812157i	−0.172800	+	0.984957i	$0.555281\pi$
$972$	−1.28002	−	1.53673i	−0.0410567	−	0.0492907i
$973$	60.6470			1.94425
$974$	11.1471	+	5.22258i	0.357178	+	0.167342i
$975$	−11.6309	−	21.9527i	−0.372488	−	0.703050i
$976$	−6.15222	+	4.24180i	−0.196928	+	0.135777i
$977$	−23.4598	−	23.4598i	−0.750547	−	0.750547i	0.224035	−	0.974581i	$-0.428077\pi$
$977$	−23.4598	−	23.4598i	−0.750547	−	0.750547i	−0.974581	+	0.224035i	$0.928077\pi$
$978$	−21.0060	+	7.60253i	−0.671697	+	0.243102i
$979$	8.07119	+	8.07119i	0.257956	+	0.257956i
$980$	−29.3443	+	40.0211i	−0.937370	+	1.27843i
$981$	6.77367	−	6.77367i	0.216267	−	0.216267i
$982$	20.6627	+	9.68074i	0.659374	+	0.308925i
$983$	−15.8155	+	15.8155i	−0.504437	+	0.504437i	−0.912814	−	0.408377i	$-0.866095\pi$
$983$	−15.8155	+	15.8155i	−0.504437	+	0.504437i	0.408377	+	0.912814i	$0.366095\pi$
$984$	0.267417	−	0.457428i	0.00852495	−	0.0145823i
$985$	3.16537	+	12.7356i	0.100857	+	0.405791i
$986$	33.5052	−	12.1263i	1.06702	−	0.386179i
$987$			0.487794i			0.0155267i
$988$	−2.44430	−	0.222765i	−0.0777635	−	0.00708710i
$989$	36.0210	−	36.0210i	1.14540	−	1.14540i
$990$	−2.52272	+	12.8040i	−0.0801773	+	0.406939i
$991$		−	30.1804i		−	0.958711i	−0.877621	−	0.479355i	$-0.840870\pi$
$991$		−	30.1804i		−	0.958711i	0.877621	−	0.479355i	$-0.159130\pi$
$992$	29.2573	−	4.88635i	0.928921	−	0.155142i
$993$	18.7327	−	18.7327i	0.594465	−	0.594465i
$994$	24.3550	+	11.4106i	0.772493	+	0.361922i
$995$	−12.8762	+	3.20032i	−0.408204	+	0.101457i
$996$	−0.313279	+	0.260946i	−0.00992663	+	0.00826840i
$997$	41.2092			1.30511			0.652555	−	0.757741i	$-0.273697\pi$
$997$	41.2092			1.30511			0.652555	+	0.757741i	$0.273697\pi$
$998$	−19.6312	−	9.19746i	−0.621415	−	0.291141i
$999$			2.27540i			0.0719904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bc.e.67.7	yes	16
3.2	odd	2		720.2.bd.f.307.2		16
4.3	odd	2		960.2.bc.e.367.7		16
5.3	odd	4		240.2.y.e.163.3	✓	16
8.3	odd	2		1920.2.bc.j.607.2		16
8.5	even	2		1920.2.bc.i.607.2		16
15.8	even	4		720.2.z.f.163.6		16
16.3	odd	4		1920.2.y.i.1567.8		16
16.5	even	4		960.2.y.e.847.1		16
16.11	odd	4		240.2.y.e.187.3	yes	16
16.13	even	4		1920.2.y.j.1567.8		16
20.3	even	4		960.2.y.e.943.1		16
40.3	even	4		1920.2.y.j.223.8		16
40.13	odd	4		1920.2.y.i.223.8		16
48.11	even	4		720.2.z.f.667.6		16
80.3	even	4		1920.2.bc.i.1183.2		16
80.13	odd	4		1920.2.bc.j.1183.2		16
80.43	even	4	inner	240.2.bc.e.43.7	yes	16
80.53	odd	4		960.2.bc.e.463.7		16
240.203	odd	4		720.2.bd.f.523.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.3	✓	16	5.3	odd	4
240.2.y.e.187.3	yes	16	16.11	odd	4
240.2.bc.e.43.7	yes	16	80.43	even	4	inner
240.2.bc.e.67.7	yes	16	1.1	even	1	trivial
720.2.z.f.163.6		16	15.8	even	4
720.2.z.f.667.6		16	48.11	even	4
720.2.bd.f.307.2		16	3.2	odd	2
720.2.bd.f.523.2		16	240.203	odd	4
960.2.y.e.847.1		16	16.5	even	4
960.2.y.e.943.1		16	20.3	even	4
960.2.bc.e.367.7		16	4.3	odd	2
960.2.bc.e.463.7		16	80.53	odd	4
1920.2.y.i.223.8		16	40.13	odd	4
1920.2.y.i.1567.8		16	16.3	odd	4
1920.2.y.j.223.8		16	40.3	even	4
1920.2.y.j.1567.8		16	16.13	even	4
1920.2.bc.i.607.2		16	8.5	even	2
1920.2.bc.i.1183.2		16	80.3	even	4
1920.2.bc.j.607.2		16	8.3	odd	2
1920.2.bc.j.1183.2		16	80.13	odd	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32980 - 0.481284i) q^{2} -1.00000i q^{3} +(1.53673 - 1.28002i) q^{4} +(0.539352 + 2.17005i) q^{5} +(-0.481284 - 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(1.42749 - 2.44178i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.32980 - 0.481284i) q^{2} -1.00000i q^{3} +(1.53673 - 1.28002i) q^{4} +(0.539352 + 2.17005i) q^{5} +(-0.481284 - 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(1.42749 - 2.44178i) q^{8} -1.00000 q^{9} +(1.76164 + 2.62614i) q^{10} +(-2.91811 - 2.91811i) q^{11} +(-1.28002 - 1.53673i) q^{12} -4.96870 q^{13} +(5.44784 + 2.55238i) q^{14} +(2.17005 - 0.539352i) q^{15} +(0.723087 - 3.93410i) q^{16} +(-2.56773 - 2.56773i) q^{17} +(-1.32980 + 0.481284i) q^{18} +(0.174647 + 0.174647i) q^{19} +(3.60655 + 2.64439i) q^{20} +(3.00806 - 3.00806i) q^{21} +(-5.28494 - 2.47606i) q^{22} +(2.93410 - 2.93410i) q^{23} +(-2.44178 - 1.42749i) q^{24} +(-4.41820 + 2.34084i) q^{25} +(-6.60738 + 2.39136i) q^{26} +1.00000i q^{27} +(8.47295 + 0.772196i) q^{28} +(-4.90621 + 4.90621i) q^{29} +(2.62614 - 1.76164i) q^{30} +5.24365i q^{31} +(-0.931860 - 5.57957i) q^{32} +(-2.91811 + 2.91811i) q^{33} +(-4.65038 - 2.17876i) q^{34} +(-4.90522 + 8.15002i) q^{35} +(-1.53673 + 1.28002i) q^{36} +2.27540 q^{37} +(0.316301 + 0.148191i) q^{38} +4.96870i q^{39} +(6.06869 + 1.78074i) q^{40} +0.187334i q^{41} +(2.55238 - 5.44784i) q^{42} +12.2767 q^{43} +(-8.21960 - 0.749106i) q^{44} +(-0.539352 - 2.17005i) q^{45} +(2.48963 - 5.31390i) q^{46} +(-0.0810813 + 0.0810813i) q^{47} +(-3.93410 - 0.723087i) q^{48} +11.0968i q^{49} +(-4.74871 + 5.23925i) q^{50} +(-2.56773 + 2.56773i) q^{51} +(-7.63556 + 6.36005i) q^{52} -10.3383i q^{53} +(0.481284 + 1.32980i) q^{54} +(4.75854 - 7.90632i) q^{55} +(11.6390 - 3.05103i) q^{56} +(0.174647 - 0.174647i) q^{57} +(-4.16299 + 8.88555i) q^{58} +(-3.33519 + 3.33519i) q^{59} +(2.64439 - 3.60655i) q^{60} +(-1.32102 - 1.32102i) q^{61} +(2.52369 + 6.97300i) q^{62} +(-3.00806 - 3.00806i) q^{63} +(-3.92455 - 6.97122i) q^{64} +(-2.67988 - 10.7823i) q^{65} +(-2.47606 + 5.28494i) q^{66} -9.03323 q^{67} +(-7.23268 - 0.659161i) q^{68} +(-2.93410 - 2.93410i) q^{69} +(-2.60048 + 13.1987i) q^{70} +4.47057 q^{71} +(-1.42749 + 2.44178i) q^{72} +(3.50820 + 3.50820i) q^{73} +(3.02582 - 1.09511i) q^{74} +(2.34084 + 4.41820i) q^{75} +(0.491939 + 0.0448336i) q^{76} -17.5557i q^{77} +(2.39136 + 6.60738i) q^{78} +6.75271 q^{79} +(8.92718 - 0.552736i) q^{80} +1.00000 q^{81} +(0.0901608 + 0.249117i) q^{82} -0.203861i q^{83} +(0.772196 - 8.47295i) q^{84} +(4.18719 - 6.95702i) q^{85} +(16.3255 - 5.90857i) q^{86} +(4.90621 + 4.90621i) q^{87} +(-11.2909 + 2.95980i) q^{88} -2.76590 q^{89} +(-1.76164 - 2.62614i) q^{90} +(-14.9461 - 14.9461i) q^{91} +(0.753211 - 8.26464i) q^{92} +5.24365 q^{93} +(-0.0687987 + 0.146845i) q^{94} +(-0.284797 + 0.473190i) q^{95} +(-5.57957 + 0.931860i) q^{96} +(9.90816 + 9.90816i) q^{97} +(5.34071 + 14.7565i) q^{98} +(2.91811 + 2.91811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

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