LMFDB - Embedded newform 240.2.y.e.187.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(163,240)]

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, 3, 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("240.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.3
Root			$1.40838 + 0.128355i$ of defining polynomial
Character	$\chi$	$=$	240.187
Dual form			240.2.y.e.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.481284 + 1.32980i) q^{2} +1.00000 q^{3} +(-1.53673 - 1.28002i) q^{4} +(-2.17005 + 0.539352i) q^{5} +(-0.481284 + 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(2.44178 - 1.42749i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.481284 + 1.32980i) q^{2} +1.00000 q^{3} +(-1.53673 - 1.28002i) q^{4} +(-2.17005 + 0.539352i) q^{5} +(-0.481284 + 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(2.44178 - 1.42749i) q^{8} +1.00000 q^{9} +(0.327178 - 3.14531i) q^{10} +(-2.91811 + 2.91811i) q^{11} +(-1.53673 - 1.28002i) q^{12} +4.96870i 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} +(-0.481284 + 1.32980i) q^{18} +(-0.174647 + 0.174647i) q^{19} +(4.02516 + 1.94887i) q^{20} +(3.00806 + 3.00806i) q^{21} +(-2.47606 - 5.28494i) 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} +1.00000 q^{27} +(-0.772196 - 8.47295i) q^{28} +(4.90621 + 4.90621i) q^{29} +(0.327178 - 3.14531i) q^{30} -5.24365i q^{31} +(-5.57957 - 0.931860i) q^{32} +(-2.91811 + 2.91811i) q^{33} +(4.65038 - 2.17876i) q^{34} +(-8.15002 - 4.90522i) q^{35} +(-1.53673 - 1.28002i) q^{36} +2.27540i q^{37} +(-0.148191 - 0.316301i) q^{38} +4.96870i q^{39} +(-4.52885 + 4.41470i) q^{40} -0.187334i q^{41} +(-5.44784 + 2.55238i) q^{42} -12.2767i q^{43} +(8.21960 - 0.749106i) q^{44} +(-2.17005 + 0.539352i) q^{45} +(2.48963 + 5.31390i) q^{46} +(0.0810813 - 0.0810813i) q^{47} +(0.723087 + 3.93410i) q^{48} +11.0968i q^{49} +(0.986437 + 7.00192i) q^{50} +(-2.56773 - 2.56773i) q^{51} +(6.36005 - 7.63556i) q^{52} +10.3383 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} +(-8.88555 + 4.16299i) q^{58} +(3.33519 + 3.33519i) q^{59} +(4.02516 + 1.94887i) q^{60} +(-1.32102 + 1.32102i) q^{61} +(6.97300 + 2.52369i) 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} -9.03323i q^{67} +(0.659161 + 7.23268i) q^{68} +(2.93410 - 2.93410i) q^{69} +(10.4454 - 8.47709i) q^{70} +4.47057 q^{71} +(2.44178 - 1.42749i) q^{72} +(-3.50820 - 3.50820i) q^{73} +(-3.02582 - 1.09511i) q^{74} +(4.41820 - 2.34084i) q^{75} +(0.491939 - 0.0448336i) q^{76} -17.5557 q^{77} +(-6.60738 - 2.39136i) q^{78} -6.75271 q^{79} +(-3.69100 - 8.14718i) q^{80} +1.00000 q^{81} +(0.249117 + 0.0901608i) q^{82} +0.203861 q^{83} +(-0.772196 - 8.47295i) q^{84} +(6.95702 + 4.18719i) q^{85} +(16.3255 + 5.90857i) q^{86} +(4.90621 + 4.90621i) q^{87} +(-2.95980 + 11.2909i) q^{88} +2.76590 q^{89} +(0.327178 - 3.14531i) q^{90} +(-14.9461 + 14.9461i) q^{91} +(-8.26464 + 0.753211i) q^{92} -5.24365i 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} +(-14.7565 - 5.34071i) q^{98} +(-2.91811 + 2.91811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.481284	+	1.32980i	−0.340319	+	0.940310i
$2$	−0.481284	+	1.32980i	−0.340319	+	0.940310i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.53673	−	1.28002i	−0.768366	−	0.640011i
$5$	−2.17005	+	0.539352i	−0.970474	+	0.241206i
$5$	−2.17005	+	0.539352i	−0.970474	+	0.241206i
$6$	−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	$0.452735\pi$
$8$	2.44178	−	1.42749i	0.863298	−	0.504694i
$9$	1.00000			0.333333
$10$	0.327178	−	3.14531i	0.103463	−	0.994633i
$11$	−2.91811	+	2.91811i	−0.879844	+	0.879844i	−0.993518	−	0.113675i	$-0.963738\pi$
$11$	−2.91811	+	2.91811i	−0.879844	+	0.879844i	0.113675	+	0.993518i	$0.463738\pi$
$12$	−1.53673	−	1.28002i	−0.443616	−	0.369511i
$13$			4.96870i			1.37807i	0.724728	+	0.689035i	$0.241966\pi$
$13$			4.96870i			1.37807i	−0.724728	+	0.689035i	$0.758034\pi$
$14$	−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	$0.895150\pi$
$18$	−0.481284	+	1.32980i	−0.113440	+	0.313437i
$19$	−0.174647	+	0.174647i	−0.0400669	+	0.0400669i	−0.726856	−	0.686789i	$-0.759019\pi$
$19$	−0.174647	+	0.174647i	−0.0400669	+	0.0400669i	0.686789	+	0.726856i	$0.259019\pi$
$20$	4.02516	+	1.94887i	0.900053	+	0.435780i
$21$	3.00806	+	3.00806i	0.656412	+	0.656412i
$22$	−2.47606	−	5.28494i	−0.527898	−	1.12675i
$23$	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
$27$	1.00000			0.192450
$28$	−0.772196	−	8.47295i	−0.145931	−	1.60124i
$29$	4.90621	+	4.90621i	0.911060	+	0.911060i	0.996356	−	0.0852961i	$-0.0271836\pi$
$29$	4.90621	+	4.90621i	0.911060	+	0.911060i	−0.0852961	+	0.996356i	$0.527184\pi$
$30$	0.327178	−	3.14531i	0.0597343	−	0.574252i
$31$		−	5.24365i		−	0.941788i	−0.882190	−	0.470894i	$-0.843931\pi$
$31$		−	5.24365i		−	0.941788i	0.882190	−	0.470894i	$-0.156069\pi$
$32$	−5.57957	−	0.931860i	−0.986339	−	0.164731i
$33$	−2.91811	+	2.91811i	−0.507978	+	0.507978i
$34$	4.65038	−	2.17876i	0.797534	−	0.373655i
$35$	−8.15002	−	4.90522i	−1.37760	−	0.829133i
$36$	−1.53673	−	1.28002i	−0.256122	−	0.213337i
$37$			2.27540i			0.374073i	0.982353	+	0.187036i	$0.0598883\pi$
$37$			2.27540i			0.374073i	−0.982353	+	0.187036i	$0.940112\pi$
$38$	−0.148191	−	0.316301i	−0.0240398	−	0.0513108i
$39$			4.96870i			0.795630i
$40$	−4.52885	+	4.41470i	−0.716074	+	0.698025i
$41$		−	0.187334i		−	0.0292566i	−0.999893	−	0.0146283i	$-0.995343\pi$
$41$		−	0.187334i		−	0.0292566i	0.999893	−	0.0146283i	$-0.00465651\pi$
$42$	−5.44784	+	2.55238i	−0.840620	+	0.393841i
$43$		−	12.2767i		−	1.87218i	−0.351764	−	0.936089i	$-0.614418\pi$
$43$		−	12.2767i		−	1.87218i	0.351764	−	0.936089i	$-0.385582\pi$
$44$	8.21960	−	0.749106i	1.23915	−	0.112932i
$45$	−2.17005	+	0.539352i	−0.323491	+	0.0804019i
$46$	2.48963	+	5.31390i	0.367076	+	0.783492i
$47$	0.0810813	−	0.0810813i	0.0118269	−	0.0118269i	−0.701169	−	0.712996i	$-0.747338\pi$
$47$	0.0810813	−	0.0810813i	0.0118269	−	0.0118269i	0.712996	+	0.701169i	$0.247338\pi$
$48$	0.723087	+	3.93410i	0.104369	+	0.567838i
$49$			11.0968i			1.58526i
$50$	0.986437	+	7.00192i	0.139503	+	0.990222i
$51$	−2.56773	−	2.56773i	−0.359555	−	0.359555i
$52$	6.36005	−	7.63556i	0.881981	−	1.05886i
$53$	10.3383			1.42007			0.710036	−	0.704166i	$-0.248679\pi$
$53$	10.3383			1.42007			0.710036	+	0.704166i	$0.248679\pi$
$54$	−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
$58$	−8.88555	+	4.16299i	−1.16673	+	0.546627i
$59$	3.33519	+	3.33519i	0.434204	+	0.434204i	0.890056	−	0.455852i	$-0.150665\pi$
$59$	3.33519	+	3.33519i	0.434204	+	0.434204i	−0.455852	+	0.890056i	$0.650665\pi$
$60$	4.02516	+	1.94887i	0.519646	+	0.251598i
$61$	−1.32102	+	1.32102i	−0.169139	+	0.169139i	−0.786601	−	0.617462i	$-0.788161\pi$
$61$	−1.32102	+	1.32102i	−0.169139	+	0.169139i	0.617462	+	0.786601i	$0.288161\pi$
$62$	6.97300	+	2.52369i	0.885572	+	0.320508i
$63$	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
$67$		−	9.03323i		−	1.10358i	−0.833982	−	0.551792i	$-0.813944\pi$
$67$		−	9.03323i		−	1.10358i	0.833982	−	0.551792i	$-0.186056\pi$
$68$	0.659161	+	7.23268i	0.0799350	+	0.877091i
$69$	2.93410	−	2.93410i	0.353224	−	0.353224i
$70$	10.4454	−	8.47709i	1.24847	−	1.01321i
$71$	4.47057			0.530560			0.265280	−	0.964171i	$-0.414536\pi$
$71$	4.47057			0.530560			0.265280	+	0.964171i	$0.414536\pi$
$72$	2.44178	−	1.42749i	0.287766	−	0.168231i
$73$	−3.50820	−	3.50820i	−0.410604	−	0.410604i	0.471345	−	0.881949i	$-0.343769\pi$
$73$	−3.50820	−	3.50820i	−0.410604	−	0.410604i	−0.881949	+	0.471345i	$0.843769\pi$
$74$	−3.02582	−	1.09511i	−0.351745	−	0.127304i
$75$	4.41820	−	2.34084i	0.510170	−	0.270297i
$76$	0.491939	−	0.0448336i	0.0564293	−	0.00514277i
$77$	−17.5557			−2.00066
$78$	−6.60738	−	2.39136i	−0.748138	−	0.270768i
$79$	−6.75271			−0.759740			−0.379870	−	0.925040i	$-0.624031\pi$
$79$	−6.75271			−0.759740			−0.379870	+	0.925040i	$0.624031\pi$
$80$	−3.69100	−	8.14718i	−0.412666	−	0.910882i
$81$	1.00000			0.111111
$82$	0.249117	+	0.0901608i	0.0275103	+	0.00995660i
$83$	0.203861			0.0223766			0.0111883	−	0.999937i	$-0.496439\pi$
$83$	0.203861			0.0223766			0.0111883	+	0.999937i	$0.496439\pi$
$84$	−0.772196	−	8.47295i	−0.0842534	−	0.924475i
$85$	6.95702	+	4.18719i	0.754594	+	0.454164i
$86$	16.3255	+	5.90857i	1.76043	+	0.637138i
$87$	4.90621	+	4.90621i	0.526000	+	0.526000i
$88$	−2.95980	+	11.2909i	−0.315516	+	1.20362i
$89$	2.76590			0.293184			0.146592	−	0.989197i	$-0.453169\pi$
$89$	2.76590			0.293184			0.146592	+	0.989197i	$0.453169\pi$
$90$	0.327178	−	3.14531i	0.0344876	−	0.331544i
$91$	−14.9461	+	14.9461i	−1.56678	+	1.56678i
$92$	−8.26464	+	0.753211i	−0.861648	+	0.0785276i
$93$		−	5.24365i		−	0.543741i
$94$	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	$0.498077\pi$
$98$	−14.7565	−	5.34071i	−1.49063	−	0.539493i
$99$	−2.91811	+	2.91811i	−0.293281	+	0.293281i
$100$	−9.78591	−	2.05815i	−0.978591	−	0.205815i
$101$	−9.51134	−	9.51134i	−0.946414	−	0.946414i	0.0522219	−	0.998636i	$-0.483370\pi$
$101$	−9.51134	−	9.51134i	−0.946414	−	0.946414i	−0.998636	+	0.0522219i	$0.983370\pi$
$102$	4.65038	−	2.17876i	0.460456	−	0.215730i
$103$	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
$107$	−5.04996			−0.488198			−0.244099	−	0.969750i	$-0.578492\pi$
$107$	−5.04996			−0.488198			−0.244099	+	0.969750i	$0.578492\pi$
$108$	−1.53673	−	1.28002i	−0.147872	−	0.123170i
$109$	6.77367	+	6.77367i	0.648800	+	0.648800i	0.952703	−	0.303903i	$-0.0982899\pi$
$109$	6.77367	+	6.77367i	0.648800	+	0.648800i	−0.303903	+	0.952703i	$0.598290\pi$
$110$	8.22361	+	10.1331i	0.784091	+	0.966153i
$111$			2.27540i			0.215971i
$112$	−9.65891	+	14.0091i	−0.912681	+	1.32373i
$113$	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
$115$	−4.78462	+	7.94965i	−0.446168	+	0.741308i
$116$	−1.25947	−	13.8196i	−0.116939	−	1.28312i
$117$			4.96870i			0.459357i
$118$	−6.04030	+	2.82996i	−0.556055	+	0.260519i
$119$		−	15.4478i		−	1.41610i
$120$	−4.52885	+	4.41470i	−0.413425	+	0.403005i
$121$		−	6.03074i		−	0.548249i
$122$	−1.12090	−	2.39247i	−0.101482	−	0.216604i
$123$		−	0.187334i		−	0.0168913i
$124$	−6.71199	+	8.05808i	−0.602755	+	0.723637i
$125$	−8.32516	+	7.46269i	−0.744625	+	0.667484i
$126$	−5.44784	+	2.55238i	−0.485332	+	0.227384i
$127$	−5.95445	+	5.95445i	−0.528372	+	0.528372i	−0.920087	−	0.391715i	$-0.871882\pi$
$127$	−5.95445	+	5.95445i	−0.528372	+	0.528372i	0.391715	+	0.920087i	$0.371882\pi$
$128$	7.38150	+	8.57400i	0.652439	+	0.757841i
$129$		−	12.2767i		−	1.08090i
$130$	15.6281	+	1.62565i	1.37068	+	0.142579i
$131$	1.07093	+	1.07093i	0.0935679	+	0.0935679i	0.752341	−	0.658773i	$-0.228924\pi$
$131$	1.07093	+	1.07093i	0.0935679	+	0.0935679i	−0.658773	+	0.752341i	$0.728924\pi$
$132$	8.21960	−	0.749106i	0.715424	−	0.0652013i
$133$	−1.05070			−0.0911071
$134$	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	−0.368036	−	0.929812i	$-0.619970\pi$
$137$	6.57542	−	6.57542i	0.561776	−	0.561776i	0.929812	+	0.368036i	$0.119970\pi$
$138$	2.48963	+	5.31390i	0.211931	+	0.452349i
$139$	−10.0808	−	10.0808i	−0.855039	−	0.855039i	0.135710	−	0.990749i	$-0.456669\pi$
$139$	−10.0808	−	10.0808i	−0.855039	−	0.855039i	−0.990749	+	0.135710i	$0.956669\pi$
$140$	6.24561	+	17.9702i	0.527850	+	1.51876i
$141$	0.0810813	−	0.0810813i	0.00682828	−	0.00682828i
$142$	−2.15162	+	5.94497i	−0.180560	+	0.498890i
$143$	−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
$147$			11.0968i			0.915248i
$148$	2.91256	−	3.49667i	0.239411	−	0.287425i
$149$	−15.1118	+	15.1118i	−1.23800	+	1.23800i	−0.277187	+	0.960816i	$0.589402\pi$
$149$	−15.1118	+	15.1118i	−1.23800	+	1.23800i	−0.960816	+	0.277187i	$0.910598\pi$
$150$	0.986437	+	7.00192i	0.0805423	+	0.571705i
$151$	−13.6260			−1.10886			−0.554432	−	0.832229i	$-0.687065\pi$
$151$	−13.6260			−1.10886			−0.554432	+	0.832229i	$0.687065\pi$
$152$	−0.177143	+	0.675758i	−0.0143682	+	0.0548112i
$153$	−2.56773	−	2.56773i	−0.207589	−	0.207589i
$154$	8.44927	−	23.3455i	0.680861	−	1.88124i
$155$	2.82818	+	11.3790i	0.227165	+	0.913980i
$156$	6.36005	−	7.63556i	0.509212	−	0.611334i
$157$	−7.13379			−0.569338			−0.284669	−	0.958626i	$-0.591884\pi$
$157$	−7.13379			−0.569338			−0.284669	+	0.958626i	$0.591884\pi$
$158$	3.24997	−	8.97975i	0.258554	−	0.714391i
$159$	10.3383			0.819878
$160$	12.6105	−	0.987178i	0.996950	−	0.0780432i
$161$	17.6519			1.39116
$162$	−0.481284	+	1.32980i	−0.0378132	+	0.104479i
$163$	15.7963			1.23727			0.618633	−	0.785680i	$-0.287687\pi$
$163$	15.7963			1.23727			0.618633	+	0.785680i	$0.287687\pi$
$164$	−0.239792	+	0.287882i	−0.0187246	+	0.0224798i
$165$	4.75854	−	7.90632i	0.370452	−	0.615507i
$166$	−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	$0.540997\pi$
$168$	11.6390	+	3.05103i	0.897966	+	0.235392i
$169$	−11.6880			−0.899079
$170$	−8.91642	+	7.23621i	−0.683858	+	0.554992i
$171$	−0.174647	+	0.174647i	−0.0133556	+	0.0133556i
$172$	−15.7144	+	18.8660i	−1.19821	+	1.43852i
$173$		−	24.3506i		−	1.85134i	−0.378334	−	0.925669i	$-0.623503\pi$
$173$		−	24.3506i		−	1.85134i	0.378334	−	0.925669i	$-0.376497\pi$
$174$	−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
$178$	−1.33118	+	3.67809i	−0.0997763	+	0.275684i
$179$	6.13094	−	6.13094i	0.458248	−	0.458248i	−0.439832	−	0.898080i	$-0.644962\pi$
$179$	6.13094	−	6.13094i	0.458248	−	0.458248i	0.898080	+	0.439832i	$0.144962\pi$
$180$	4.02516	+	1.94887i	0.300018	+	0.145260i
$181$	8.99477	+	8.99477i	0.668576	+	0.668576i	0.957386	−	0.288810i	$-0.0932597\pi$
$181$	8.99477	+	8.99477i	0.668576	+	0.668576i	−0.288810	+	0.957386i	$0.593260\pi$
$182$	−12.6820	−	27.0687i	−0.940054	−	2.00647i
$183$	−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
$187$	14.9859			1.09588
$188$	−0.228386	+	0.0208143i	−0.0166568	+	0.00151804i
$189$	3.00806	+	3.00806i	0.218804	+	0.218804i
$190$	0.492179	+	0.606461i	0.0357064	+	0.0439973i
$191$		−	0.148691i		−	0.0107589i	−0.999986	−	0.00537945i	$-0.998288\pi$
$191$		−	0.148691i		−	0.0107589i	0.999986	−	0.00537945i	$-0.00171234\pi$
$192$	3.92455	−	6.97122i	0.283230	−	0.503105i
$193$	−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
$195$	−2.67988	−	10.7823i	−0.191910	−	0.772138i
$196$	14.2041	−	17.0528i	1.01458	−	1.21806i
$197$			5.86883i			0.418137i	0.977901	+	0.209068i	$0.0670431\pi$
$197$			5.86883i			0.418137i	−0.977901	+	0.209068i	$0.932957\pi$
$198$	−2.47606	−	5.28494i	−0.175966	−	0.375584i
$199$			5.93363i			0.420624i	0.977634	+	0.210312i	$0.0674479\pi$
$199$			5.93363i			0.420624i	−0.977634	+	0.210312i	$0.932552\pi$
$200$	7.44673	−	12.0227i	0.526563	−	0.850136i
$201$		−	9.03323i		−	0.637155i
$202$	17.2258	−	8.07051i	1.21200	−	0.567839i
$203$			29.5163i			2.07164i
$204$	0.659161	+	7.23268i	0.0461505	+	0.506389i
$205$	0.101039	+	0.406523i	0.00705687	+	0.0283928i
$206$	4.38759	+	9.36493i	0.305698	+	0.652485i
$207$	2.93410	−	2.93410i	0.203934	−	0.203934i
$208$	−19.5474	+	3.59280i	−1.35537	+	0.249116i
$209$		−	1.01928i		−	0.0705052i
$210$	10.4454	−	8.47709i	0.720803	−	0.584975i
$211$	−7.09893	−	7.09893i	−0.488710	−	0.488710i	0.419189	−	0.907899i	$-0.362315\pi$
$211$	−7.09893	−	7.09893i	−0.488710	−	0.488710i	−0.907899	+	0.419189i	$0.862315\pi$
$212$	−15.8872	−	13.2332i	−1.09113	−	0.908861i
$213$	4.47057			0.306319
$214$	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
$218$	−12.2677	+	5.74756i	−0.830872	+	0.389274i
$219$	−3.50820	−	3.50820i	−0.237062	−	0.237062i
$220$	−17.4329	+	6.05885i	−1.17532	+	0.408488i
$221$	12.7583	−	12.7583i	0.858217	−	0.858217i
$222$	−3.02582	−	1.09511i	−0.203080	−	0.0734991i
$223$	19.9362	+	19.9362i	1.33503	+	1.33503i	0.900808	+	0.434217i	$0.142975\pi$
$223$	19.9362	+	19.9362i	1.33503	+	1.33503i	0.434217	+	0.900808i	$0.357025\pi$
$224$	−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
$227$		−	6.50202i		−	0.431554i	−0.976443	−	0.215777i	$-0.930772\pi$
$227$		−	6.50202i		−	0.431554i	0.976443	−	0.215777i	$-0.0692284\pi$
$228$	0.491939	−	0.0448336i	0.0325795	−	0.00296918i
$229$	−6.53144	+	6.53144i	−0.431610	+	0.431610i	−0.889176	−	0.457566i	$-0.848721\pi$
$229$	−6.53144	+	6.53144i	−0.431610	+	0.431610i	0.457566	+	0.889176i	$0.348721\pi$
$230$	−8.26867	−	10.1886i	−0.545220	−	0.671818i
$231$	−17.5557			−1.15508
$232$	18.9834	+	4.97630i	1.24632	+	0.326710i
$233$	14.3657	+	14.3657i	0.941130	+	0.941130i	0.998361	−	0.0572311i	$-0.0182272\pi$
$233$	14.3657	+	14.3657i	0.941130	+	0.941130i	−0.0572311	+	0.998361i	$0.518227\pi$
$234$	−6.60738	−	2.39136i	−0.431938	−	0.156328i
$235$	−0.132219	+	0.219682i	−0.00862500	+	0.0143304i
$236$	−0.856173	−	9.39440i	−0.0557321	−	0.611523i
$237$	−6.75271			−0.438636
$238$	20.5424	+	7.43477i	1.33157	+	0.481924i
$239$	6.65388			0.430404			0.215202	−	0.976570i	$-0.430959\pi$
$239$	6.65388			0.430404			0.215202	+	0.976570i	$0.430959\pi$
$240$	−3.69100	−	8.14718i	−0.238253	−	0.525898i
$241$	−15.6797			−1.01002			−0.505009	−	0.863114i	$-0.668511\pi$
$241$	−15.6797			−1.01002			−0.505009	+	0.863114i	$0.668511\pi$
$242$	8.01968	+	2.90250i	0.515524	+	0.186580i
$243$	1.00000			0.0641500
$244$	3.72098	−	0.339117i	0.238211	−	0.0217098i
$245$	−5.98508	−	24.0806i	−0.382373	−	1.53845i
$246$	0.249117	+	0.0901608i	0.0158831	+	0.00574844i
$247$	−0.867772	−	0.867772i	−0.0552150	−	0.0552150i
$248$	−7.48526	−	12.8038i	−0.475314	−	0.813044i
$249$	0.203861			0.0129192
$250$	−5.91712	−	14.6625i	−0.374231	−	0.927335i
$251$	−2.31676	+	2.31676i	−0.146233	+	0.146233i	−0.776433	−	0.630200i	$-0.782973\pi$
$251$	−2.31676	+	2.31676i	−0.146233	+	0.146233i	0.630200	+	0.776433i	$0.282973\pi$
$252$	−0.772196	−	8.47295i	−0.0486437	−	0.533746i
$253$			17.1241i			1.07658i
$254$	−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	$0.589196\pi$
$258$	16.3255	+	5.90857i	1.01638	+	0.367852i
$259$	−6.84452	+	6.84452i	−0.425298	+	0.425298i
$260$	−9.68335	+	19.9998i	−0.600536	+	1.24034i
$261$	4.90621	+	4.90621i	0.303687	+	0.303687i
$262$	−1.93955	+	0.908703i	−0.119826	+	0.0561399i
$263$	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
$267$	2.76590			0.169270
$268$	−11.5627	+	13.8816i	−0.706306	+	0.847957i
$269$	2.77544	+	2.77544i	0.169222	+	0.169222i	0.786637	−	0.617416i	$-0.211820\pi$
$269$	2.77544	+	2.77544i	0.169222	+	0.169222i	−0.617416	+	0.786637i	$0.711820\pi$
$270$	0.327178	−	3.14531i	0.0199114	−	0.191417i
$271$		−	3.86079i		−	0.234526i	−0.993101	−	0.117263i	$-0.962588\pi$
$271$		−	3.86079i		−	0.234526i	0.993101	−	0.117263i	$-0.0374121\pi$
$272$	8.24503	−	11.9584i	0.499928	−	0.725086i
$273$	−14.9461	+	14.9461i	−0.904582	+	0.904582i
$274$	5.57934	+	11.9086i	0.337060	+	0.719426i
$275$	−6.06196	+	19.7236i	−0.365550	+	1.18938i
$276$	−8.26464	+	0.753211i	−0.497473	+	0.0453379i
$277$		−	28.9073i		−	1.73687i	−0.495803	−	0.868435i	$-0.665126\pi$
$277$		−	28.9073i		−	1.73687i	0.495803	−	0.868435i	$-0.334874\pi$
$278$	18.2571	−	8.55368i	1.09499	−	0.513015i
$279$		−	5.24365i		−	0.313929i
$280$	−26.9027	−	0.343372i	−1.60774	−	0.0205204i
$281$			16.2395i			0.968770i	0.874855	+	0.484385i	$0.160957\pi$
$281$			16.2395i			0.968770i	−0.874855	+	0.484385i	$0.839043\pi$
$282$	0.0687987	+	0.146845i	0.00409690	+	0.00874449i
$283$		−	22.8092i		−	1.35587i	−0.735122	−	0.677934i	$-0.762875\pi$
$283$		−	22.8092i		−	1.35587i	0.735122	−	0.677934i	$-0.237125\pi$
$284$	−6.87007	−	5.72243i	−0.407664	−	0.339564i
$285$	0.284797	−	0.473190i	0.0168699	−	0.0280293i
$286$	26.2593	−	12.3028i	1.55275	−	0.727481i
$287$	0.563511	−	0.563511i	0.0332630	−	0.0332630i
$288$	−5.57957	−	0.931860i	−0.328780	−	0.0549104i
$289$		−	3.81348i		−	0.224322i
$290$	17.0367	−	13.8263i	1.00043	−	0.811909i
$291$	9.90816	+	9.90816i	0.580827	+	0.580827i
$292$	0.900588	+	9.88174i	0.0527029	+	0.578285i
$293$	−30.6990			−1.79346			−0.896728	−	0.442582i	$-0.854063\pi$
$293$	−30.6990			−1.79346			−0.896728	+	0.442582i	$0.854063\pi$
$294$	−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
$298$	−12.8226	−	27.3686i	−0.742790	−	1.58542i
$299$	14.5787	+	14.5787i	0.843107	+	0.843107i
$300$	−9.78591	−	2.05815i	−0.564990	−	0.118827i
$301$	36.9290	−	36.9290i	2.12855	−	2.12855i
$302$	6.55796	−	18.1198i	0.377368	−	1.04268i
$303$	−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
$307$		−	17.3607i		−	0.990829i	−0.868657	−	0.495415i	$-0.835016\pi$
$307$		−	17.3607i		−	0.990829i	0.868657	−	0.495415i	$-0.164984\pi$
$308$	26.9784	+	22.4717i	1.53723	+	1.28044i
$309$	5.17090	−	5.17090i	0.294162	−	0.294162i
$310$	−16.4929	−	1.71561i	−0.936733	−	0.0974400i
$311$	−20.0448			−1.13664			−0.568318	−	0.822809i	$-0.692406\pi$
$311$	−20.0448			−1.13664			−0.568318	+	0.822809i	$0.692406\pi$
$312$	7.09278	+	12.1325i	0.401549	+	0.686866i
$313$	10.7674	+	10.7674i	0.608610	+	0.608610i	0.942583	−	0.333973i	$-0.108389\pi$
$313$	10.7674	+	10.7674i	0.608610	+	0.608610i	−0.333973	+	0.942583i	$0.608389\pi$
$314$	3.43338	−	9.48651i	0.193757	−	0.535355i
$315$	−8.15002	−	4.90522i	−0.459202	−	0.276378i
$316$	10.3771	+	8.64362i	0.583758	+	0.486242i
$317$	11.6799			0.656006			0.328003	−	0.944677i	$-0.393624\pi$
$317$	11.6799			0.656006			0.328003	+	0.944677i	$0.393624\pi$
$318$	−4.97565	+	13.7478i	−0.279020	+	0.770940i
$319$	−28.6337			−1.60318
$320$	−4.75650	+	17.2446i	−0.265896	+	0.964002i
$321$	−5.04996			−0.281861
$322$	−8.49557	+	23.4734i	−0.473439	+	1.30812i
$323$	0.896897			0.0499047
$324$	−1.53673	−	1.28002i	−0.0853740	−	0.0711123i
$325$	11.6309	+	21.9527i	0.645168	+	1.21772i
$326$	−7.60253	+	21.0060i	−0.421065	+	1.16341i
$327$	6.77367	+	6.77367i	0.374585	+	0.374585i
$328$	−0.267417	−	0.457428i	−0.0147656	−	0.0252572i
$329$	0.487794			0.0268930
$330$	8.22361	+	10.1331i	0.452695	+	0.557809i
$331$	18.7327	−	18.7327i	1.02964	−	1.02964i	0.0300961	−	0.999547i	$-0.490419\pi$
$331$	18.7327	−	18.7327i	1.02964	−	1.02964i	0.999547	−	0.0300961i	$-0.00958132\pi$
$332$	−0.313279	−	0.260946i	−0.0171934	−	0.0143213i
$333$			2.27540i			0.124691i
$334$	−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	$0.826518\pi$
$338$	5.62526	−	15.5427i	0.305974	−	0.845413i
$339$	2.59004	−	2.59004i	0.140672	−	0.140672i
$340$	−5.33137	−	15.3397i	−0.289134	−	0.831913i
$341$	15.3016	+	15.3016i	0.828626	+	0.828626i
$342$	−0.148191	−	0.316301i	−0.00801325	−	0.0171036i
$343$	−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
$347$	−3.87988			−0.208283			−0.104142	−	0.994562i	$-0.533209\pi$
$347$	−3.87988			−0.208283			−0.104142	+	0.994562i	$0.533209\pi$
$348$	−1.25947	−	13.8196i	−0.0675146	−	0.740807i
$349$	1.56009	+	1.56009i	0.0835098	+	0.0835098i	0.747628	−	0.664118i	$-0.231193\pi$
$349$	1.56009	+	1.56009i	0.0835098	+	0.0835098i	−0.664118	+	0.747628i	$0.731193\pi$
$350$	−18.0949	+	24.0294i	−0.967214	+	1.28443i
$351$			4.96870i			0.265210i
$352$	19.0011	−	13.5625i	1.01276	−	0.722886i
$353$	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
$355$	−9.70135	+	2.41121i	−0.514894	+	0.127974i
$356$	−4.25044	−	3.54041i	−0.225273	−	0.187641i
$357$		−	15.4478i		−	0.817583i
$358$	5.20219	+	11.1036i	0.274944	+	0.586845i
$359$		−	18.0862i		−	0.954552i	−0.878753	−	0.477276i	$-0.841624\pi$
$359$		−	18.0862i		−	0.954552i	0.878753	−	0.477276i	$-0.158376\pi$
$360$	−4.52885	+	4.41470i	−0.238691	+	0.232675i
$361$			18.9390i			0.996789i
$362$	−16.2903	+	7.63220i	−0.856198	+	0.401139i
$363$		−	6.03074i		−	0.316532i
$364$	42.0996	−	3.83681i	2.20662	−	0.201104i
$365$	9.50512	+	5.72080i	0.497521	+	0.299440i
$366$	−1.12090	−	2.39247i	−0.0585905	−	0.125057i
$367$	−1.00068	+	1.00068i	−0.0522350	+	0.0522350i	−0.732742	−	0.680507i	$-0.761760\pi$
$367$	−1.00068	+	1.00068i	−0.0522350	+	0.0522350i	0.680507	+	0.732742i	$0.261760\pi$
$368$	13.6647	+	9.42144i	0.712319	+	0.491126i
$369$		−	0.187334i		−	0.00975222i
$370$	7.15682	+	0.744460i	0.372065	+	0.0387026i
$371$	31.0981	+	31.0981i	1.61453	+	1.61453i
$372$	−6.71199	+	8.05808i	−0.348001	+	0.417792i
$373$	−2.25365			−0.116689			−0.0583447	−	0.998296i	$-0.518582\pi$
$373$	−2.25365			−0.116689			−0.0583447	+	0.998296i	$0.518582\pi$
$374$	−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
$378$	−5.44784	+	2.55238i	−0.280207	+	0.131280i
$379$	7.91100	+	7.91100i	0.406361	+	0.406361i	0.880467	−	0.474107i	$-0.157229\pi$
$379$	7.91100	+	7.91100i	0.406361	+	0.406361i	−0.474107	+	0.880467i	$0.657229\pi$
$380$	−1.04335	+	0.362619i	−0.0535227	+	0.0186020i
$381$	−5.95445	+	5.95445i	−0.305056	+	0.305056i
$382$	0.197729	+	0.0715626i	0.0101167	+	0.00366146i
$383$	−19.7391	−	19.7391i	−1.00862	−	1.00862i	−0.999963	−	0.00865943i	$-0.997244\pi$
$383$	−19.7391	−	19.7391i	−1.00862	−	1.00862i	−0.00865943	−	0.999963i	$-0.502756\pi$
$384$	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
$387$		−	12.2767i		−	0.624059i
$388$	−2.54352	−	27.9089i	−0.129127	−	1.41686i
$389$	−5.49649	+	5.49649i	−0.278683	+	0.278683i	−0.832583	−	0.553900i	$-0.813139\pi$
$389$	−5.49649	+	5.49649i	−0.278683	+	0.278683i	0.553900	+	0.832583i	$0.313139\pi$
$390$	15.6281	+	1.62565i	0.791360	+	0.0823181i
$391$	−15.0680			−0.762021
$392$	15.8406	+	27.0959i	0.800069	+	1.36855i
$393$	1.07093	+	1.07093i	0.0540214	+	0.0540214i
$394$	−7.80437	−	2.82457i	−0.393178	−	0.142300i
$395$	14.6537	−	3.64209i	0.737308	−	0.183254i
$396$	8.21960	−	0.749106i	0.413050	−	0.0376440i
$397$	−25.4492			−1.27726			−0.638630	−	0.769514i	$-0.720499\pi$
$397$	−25.4492			−1.27726			−0.638630	+	0.769514i	$0.720499\pi$
$398$	−7.89053	−	2.85576i	−0.395517	−	0.143146i
$399$	−1.05070			−0.0526007
$400$	12.4038	+	15.6890i	0.620192	+	0.784450i
$401$	−1.45606			−0.0727124			−0.0363562	−	0.999339i	$-0.511575\pi$
$401$	−1.45606			−0.0727124			−0.0363562	+	0.999339i	$0.511575\pi$
$402$	12.0124	+	4.34755i	0.599123	+	0.216836i
$403$	26.0542			1.29785
$404$	2.44165	+	26.7911i	0.121477	+	1.33291i
$405$	−2.17005	+	0.539352i	−0.107830	+	0.0268006i
$406$	−39.2507	−	14.2057i	−1.94798	−	0.705018i
$407$	−6.63986	−	6.63986i	−0.329126	−	0.329126i
$408$	−9.93525	−	2.60442i	−0.491868	−	0.128938i
$409$	−14.9174			−0.737620			−0.368810	−	0.929505i	$-0.620235\pi$
$409$	−14.9174			−0.737620			−0.368810	+	0.929505i	$0.620235\pi$
$410$	−0.589223	−	0.0612916i	−0.0290996	−	0.00302697i
$411$	6.57542	−	6.57542i	0.324341	−	0.324341i
$412$	−14.5651	+	1.32742i	−0.717573	+	0.0653972i
$413$			20.0649i			0.987327i
$414$	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
$418$	1.35544	+	0.490564i	0.0662967	+	0.0239943i
$419$	−12.3766	+	12.3766i	−0.604638	+	0.604638i	−0.941540	−	0.336902i	$-0.890621\pi$
$419$	−12.3766	+	12.3766i	−0.604638	+	0.604638i	0.336902	+	0.941540i	$0.390621\pi$
$420$	6.24561	+	17.9702i	0.304754	+	0.876856i
$421$	−23.1411	−	23.1411i	−1.12783	−	1.12783i	−0.990530	−	0.137299i	$-0.956158\pi$
$421$	−23.1411	−	23.1411i	−1.12783	−	1.12783i	−0.137299	−	0.990530i	$-0.543842\pi$
$422$	12.8568	−	6.02355i	0.625857	−	0.293222i
$423$	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
$427$	−7.94739			−0.384601
$428$	7.76043	+	6.46406i	0.375115	+	0.312452i
$429$	−14.4992	−	14.4992i	−0.700030	−	0.700030i
$430$	−38.6139	−	4.01666i	−1.86213	−	0.193701i
$431$		−	16.0042i		−	0.770896i	−0.922730	−	0.385448i	$-0.874047\pi$
$431$		−	16.0042i		−	0.770896i	0.922730	−	0.385448i	$-0.125953\pi$
$432$	0.723087	+	3.93410i	0.0347895	+	0.189279i
$433$	−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
$435$	−13.2929	−	8.00052i	−0.637344	−	0.383595i
$436$	−1.73886	−	19.0798i	−0.0832764	−	0.913755i
$437$			1.02487i			0.0490260i
$438$	6.35365	−	2.97676i	0.303589	−	0.142235i
$439$		−	4.04860i		−	0.193229i	−0.995322	−	0.0966145i	$-0.969199\pi$
$439$		−	4.04860i		−	0.193229i	0.995322	−	0.0966145i	$-0.0308014\pi$
$440$	0.333105	−	26.0983i	0.0158801	−	1.24419i
$441$			11.0968i			0.528419i
$442$	10.8256	+	23.1064i	0.514922	+	1.09906i
$443$		−	24.3284i		−	1.15588i	−0.816081	−	0.577938i	$-0.803858\pi$
$443$		−	24.3284i		−	1.15588i	0.816081	−	0.577938i	$-0.196142\pi$
$444$	2.91256	−	3.49667i	0.138224	−	0.165945i
$445$	−6.00212	+	1.49179i	−0.284528	+	0.0707178i
$446$	−36.1061	+	16.9162i	−1.70967	+	0.801003i
$447$	−15.1118	+	15.1118i	−0.714761	+	0.714761i
$448$	32.7751	−	9.16457i	1.54848	−	0.432985i
$449$		−	26.9577i		−	1.27221i	−0.771602	−	0.636106i	$-0.780544\pi$
$449$		−	26.9577i		−	1.27221i	0.771602	−	0.636106i	$-0.219456\pi$
$450$	0.986437	+	7.00192i	0.0465011	+	0.330074i
$451$	0.546661	+	0.546661i	0.0257413	+	0.0257413i
$452$	−7.29552	+	0.664888i	−0.343152	+	0.0312737i
$453$	−13.6260			−0.640203
$454$	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	−0.409065	−	0.912505i	$-0.634145\pi$
$457$	10.7623	−	10.7623i	0.503440	−	0.503440i	0.912505	+	0.409065i	$0.134145\pi$
$458$	−5.54202	−	11.8290i	−0.258962	−	0.552732i
$459$	−2.56773	−	2.56773i	−0.119852	−	0.119852i
$460$	17.5284	−	6.09205i	0.817266	−	0.284043i
$461$	−4.26657	+	4.26657i	−0.198714	+	0.198714i	−0.799449	−	0.600734i	$-0.794875\pi$
$461$	−4.26657	+	4.26657i	−0.198714	+	0.198714i	0.600734	+	0.799449i	$0.294875\pi$
$462$	8.44927	−	23.3455i	0.393096	−	1.08613i
$463$	−23.4907	−	23.4907i	−1.09170	−	1.09170i	−0.995347	−	0.0963571i	$-0.969281\pi$
$463$	−23.4907	−	23.4907i	−1.09170	−	1.09170i	−0.0963571	−	0.995347i	$-0.530719\pi$
$464$	−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
$467$		−	28.5742i		−	1.32226i	−0.750273	−	0.661128i	$-0.770078\pi$
$467$		−	28.5742i		−	1.32226i	0.750273	−	0.661128i	$-0.229922\pi$
$468$	6.36005	−	7.63556i	0.293994	−	0.352954i
$469$	27.1725	−	27.1725i	1.25471	−	1.25471i
$470$	−0.228498	−	0.281554i	−0.0105398	−	0.0129871i
$471$	−7.13379			−0.328708
$472$	12.9047	+	3.38284i	0.593988	+	0.155708i
$473$	35.8247	+	35.8247i	1.64722	+	1.64722i
$474$	3.24997	−	8.97975i	0.149276	−	0.412454i
$475$	−0.362806	+	1.18045i	−0.0166467	+	0.0541627i
$476$	−19.7735	+	23.7391i	−0.906317	+	1.08808i
$477$	10.3383			0.473357
$478$	−3.20241	+	8.84833i	−0.146475	+	0.404713i
$479$	−3.27525			−0.149650			−0.0748250	−	0.997197i	$-0.523840\pi$
$479$	−3.27525			−0.149650			−0.0748250	+	0.997197i	$0.523840\pi$
$480$	12.6105	−	0.987178i	0.575589	−	0.0450583i
$481$	−11.3058			−0.515499
$482$	7.54638	−	20.8508i	0.343728	−	0.949729i
$483$	17.6519			0.803188
$484$	−7.71948	+	9.26763i	−0.350886	+	0.421256i
$485$	−26.8452	−	16.1572i	−1.21898	−	0.733660i
$486$	−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	$0.686809\pi$
$488$	−1.33989	+	5.11137i	−0.0606540	+	0.231381i
$489$	15.7963			0.714335
$490$	34.9028	+	3.63063i	1.57675	+	0.164015i
$491$	11.4090	−	11.4090i	0.514883	−	0.514883i	−0.401136	−	0.916019i	$-0.631384\pi$
$491$	11.4090	−	11.4090i	0.514883	−	0.514883i	0.916019	+	0.401136i	$0.131384\pi$
$492$	−0.239792	+	0.287882i	−0.0108106	+	0.0129787i
$493$		−	25.1957i		−	1.13476i
$494$	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
$498$	−0.0981149	+	0.271094i	−0.00439664	+	0.0121480i
$499$	10.8395	−	10.8395i	0.485242	−	0.485242i	−0.421559	−	0.906801i	$-0.638517\pi$
$499$	10.8395	−	10.8395i	0.485242	−	0.485242i	0.906801	+	0.421559i	$0.138517\pi$
$500$	22.3459	−	0.811772i	0.999341	−	0.0363035i
$501$	11.1560	+	11.1560i	0.498414	+	0.498414i
$502$	−1.96581	−	4.19585i	−0.0877383	−	0.187270i
$503$	−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
$507$	−11.6880			−0.519084
$508$	16.7722	−	1.52856i	0.744147	−	0.0678190i
$509$	11.1087	+	11.1087i	0.492385	+	0.492385i	0.909057	−	0.416672i	$-0.136804\pi$
$509$	11.1087	+	11.1087i	0.492385	+	0.492385i	−0.416672	+	0.909057i	$0.636804\pi$
$510$	−8.91642	+	7.23621i	−0.394826	+	0.320425i
$511$		−	21.1057i		−	0.933663i
$512$	−0.368484	−	22.6244i	−0.0162849	−	0.999867i
$513$	−0.174647	+	0.174647i	−0.00771088	+	0.00771088i
$514$	−19.8717	+	9.31012i	−0.876501	+	0.410652i
$515$	−8.43215	+	14.0100i	−0.371565	+	0.617355i
$516$	−15.7144	+	18.8660i	−0.691789	+	0.830528i
$517$			0.473208i			0.0208117i
$518$	−5.80768	−	12.3960i	−0.255175	−	0.544649i
$519$		−	24.3506i		−	1.06887i
$520$	−21.9353	−	22.5025i	−0.961928	−	0.986800i
$521$		−	15.9757i		−	0.699908i	−0.936767	−	0.349954i	$-0.886197\pi$
$521$		−	15.9757i		−	0.699908i	0.936767	−	0.349954i	$-0.113803\pi$
$522$	−8.88555	+	4.16299i	−0.388910	+	0.182209i
$523$			7.67260i			0.335499i	0.985830	+	0.167750i	$0.0536500\pi$
$523$			7.67260i			0.335499i	−0.985830	+	0.167750i	$0.946350\pi$
$524$	−0.274918	−	3.01656i	−0.0120099	−	0.131779i
$525$	20.3316	+	6.24881i	0.887342	+	0.272721i
$526$	8.03251	+	17.1447i	0.350234	+	0.747545i
$527$	−13.4643	+	13.4643i	−0.586514	+	0.586514i
$528$	−13.5902	−	9.37009i	−0.591437	−	0.407781i
$529$			5.78211i			0.251396i
$530$	3.38246	−	32.5170i	0.146925	−	1.41245i
$531$	3.33519	+	3.33519i	0.144735	+	0.144735i
$532$	1.61464	+	1.34492i	0.0700036	+	0.0583096i
$533$	0.930807			0.0403177
$534$	−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
$538$	−5.02655	+	2.35500i	−0.216710	+	0.101531i
$539$	−32.3817	−	32.3817i	−1.39478	−	1.39478i
$540$	4.02516	+	1.94887i	0.173215	+	0.0838659i
$541$	6.37490	−	6.37490i	0.274078	−	0.274078i	−0.556661	−	0.830740i	$-0.687918\pi$
$541$	6.37490	−	6.37490i	0.274078	−	0.274078i	0.830740	+	0.556661i	$0.187918\pi$
$542$	5.13408	+	1.85814i	0.220528	+	0.0798139i
$543$	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
$547$			44.7865i			1.91493i	0.288542	+	0.957467i	$0.406829\pi$
$547$			44.7865i			1.91493i	−0.288542	+	0.957467i	$0.593171\pi$
$548$	−18.5213	+	1.68797i	−0.791192	+	0.0721065i
$549$	−1.32102	+	1.32102i	−0.0563796	+	0.0563796i
$550$	−23.3109	−	17.5539i	−0.993981	−	0.748499i
$551$	−1.71371			−0.0730066
$552$	2.97602	−	11.3528i	0.126668	−	0.483208i
$553$	−20.3125	−	20.3125i	−0.863777	−	0.863777i
$554$	38.4409	+	13.9126i	1.63320	+	0.591090i
$555$	−1.22724	−	4.93772i	−0.0520935	−	0.209594i
$556$	2.58782	+	28.3950i	0.109748	+	1.20422i
$557$	10.4866			0.444331			0.222165	−	0.975009i	$-0.428687\pi$
$557$	10.4866			0.444331			0.222165	+	0.975009i	$0.428687\pi$
$558$	6.97300	+	2.52369i	0.295191	+	0.106836i
$559$	60.9992			2.57999
$560$	13.4044	−	35.6099i	0.566441	−	1.50479i
$561$	14.9859			0.632704
$562$	−21.5953	−	7.81583i	−0.910944	−	0.329691i
$563$	−31.5903			−1.33137			−0.665687	−	0.746231i	$-0.731861\pi$
$563$	−31.5903			−1.33137			−0.665687	+	0.746231i	$0.731861\pi$
$564$	−0.228386	+	0.0208143i	−0.00961679	+	0.000876441i
$565$	−4.22357	+	7.01746i	−0.177687	+	0.295227i
$566$	30.3317	+	10.9777i	1.27494	+	0.461428i
$567$	3.00806	+	3.00806i	0.126326	+	0.126326i
$568$	10.9161	−	6.38170i	0.458031	−	0.267770i
$569$	28.9118			1.21205			0.606023	−	0.795447i	$-0.292764\pi$
$569$	28.9118			1.21205			0.606023	+	0.795447i	$0.292764\pi$
$570$	0.492179	+	0.606461i	0.0206151	+	0.0254018i
$571$	−5.84635	+	5.84635i	−0.244662	+	0.244662i	−0.818776	−	0.574113i	$-0.805347\pi$
$571$	−5.84635	+	5.84635i	−0.244662	+	0.244662i	0.574113	+	0.818776i	$0.305347\pi$
$572$	3.72209	+	40.8408i	0.155628	+	1.70764i
$573$		−	0.148691i		−	0.00621165i
$574$	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	$0.845309\pi$
$578$	5.07116	+	1.83537i	0.210932	+	0.0763411i
$579$	−4.33825	+	4.33825i	−0.180291	+	0.180291i
$580$	10.1867	+	29.3098i	0.422981	+	1.21702i
$581$	0.613225	+	0.613225i	0.0254408	+	0.0254408i
$582$	−17.9445	+	8.40723i	−0.743824	+	0.348491i
$583$	−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
$587$	−3.79915			−0.156808			−0.0784039	−	0.996922i	$-0.524982\pi$
$587$	−3.79915			−0.156808			−0.0784039	+	0.996922i	$0.524982\pi$
$588$	14.2041	−	17.0528i	0.585769	−	0.703245i
$589$	0.915791	+	0.915791i	0.0377345	+	0.0377345i
$590$	11.5814	−	9.39898i	0.476798	−	0.386950i
$591$			5.86883i			0.241411i
$592$	−8.95164	+	1.64531i	−0.367910	+	0.0676218i
$593$	−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
$595$	8.33180	+	33.5224i	0.341570	+	1.37428i
$596$	42.5661	−	3.87933i	1.74357	−	0.158903i
$597$			5.93363i			0.242847i
$598$	−26.4032	+	12.3702i	−1.07971	+	0.505856i
$599$		−	21.2875i		−	0.869783i	−0.900483	−	0.434891i	$-0.856787\pi$
$599$		−	21.2875i		−	0.869783i	0.900483	−	0.434891i	$-0.143213\pi$
$600$	7.44673	−	12.0227i	0.304011	−	0.490826i
$601$			44.8560i			1.82971i	0.403779	+	0.914856i	$0.367696\pi$
$601$			44.8560i			1.82971i	−0.403779	+	0.914856i	$0.632304\pi$
$602$	31.3348	+	66.8814i	1.27711	+	2.72588i
$603$		−	9.03323i		−	0.367862i
$604$	20.9394	+	17.4415i	0.852014	+	0.709686i
$605$	3.25270	+	13.0870i	0.132241	+	0.532062i
$606$	17.2258	−	8.07051i	0.699751	−	0.327842i
$607$	−7.48042	+	7.48042i	−0.303621	+	0.303621i	−0.842429	−	0.538808i	$-0.818875\pi$
$607$	−7.48042	+	7.48042i	−0.303621	+	0.303621i	0.538808	+	0.842429i	$0.318875\pi$
$608$	1.13721	−	0.811712i	0.0461198	−	0.0329192i
$609$			29.5163i			1.19606i
$610$	3.72280	+	4.58721i	0.150732	+	0.185731i
$611$	0.402869	+	0.402869i	0.0162983	+	0.0162983i
$612$	0.659161	+	7.23268i	0.0266450	+	0.292364i
$613$	23.9275			0.966423			0.483211	−	0.875504i	$-0.339470\pi$
$613$	23.9275			0.966423			0.483211	+	0.875504i	$0.339470\pi$
$614$	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	−0.572569	−	0.819857i	$-0.694053\pi$
$617$	6.14250	−	6.14250i	0.247288	−	0.247288i	0.819857	+	0.572569i	$0.194053\pi$
$618$	4.38759	+	9.36493i	0.176495	+	0.376713i
$619$	−15.3689	−	15.3689i	−0.617729	−	0.617729i	0.327220	−	0.944948i	$-0.393888\pi$
$619$	−15.3689	−	15.3689i	−0.617729	−	0.617729i	−0.944948	+	0.327220i	$0.893888\pi$
$620$	10.2192	−	21.1065i	0.410412	−	0.847659i
$621$	2.93410	−	2.93410i	0.117741	−	0.117741i
$622$	9.64724	−	26.6556i	0.386819	−	1.06879i
$623$	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
$627$		−	1.01928i		−	0.0407062i
$628$	10.9627	+	9.13141i	0.437460	+	0.364383i
$629$	5.84262	−	5.84262i	0.232960	−	0.232960i
$630$	10.4454	−	8.47709i	0.416156	−	0.337735i
$631$	36.1280			1.43823			0.719116	−	0.694891i	$-0.244547\pi$
$631$	36.1280			1.43823			0.719116	+	0.694891i	$0.244547\pi$
$632$	−16.4886	+	9.63943i	−0.655882	+	0.383436i
$633$	−7.09893	−	7.09893i	−0.282157	−	0.282157i
$634$	−5.62133	+	15.5319i	−0.223252	+	0.616849i
$635$	9.70988	−	16.1330i	0.385325	−	0.640218i
$636$	−15.8872	−	13.2332i	−0.629967	−	0.524731i
$637$	−55.1367			−2.18460
$638$	13.7809	−	38.0771i	0.545593	−	1.50749i
$639$	4.47057			0.176853
$640$	−20.6426	−	14.6247i	−0.815971	−	0.578093i
$641$	−43.5468			−1.72000			−0.859998	−	0.510297i	$-0.829536\pi$
$641$	−43.5468			−1.72000			−0.859998	+	0.510297i	$0.829536\pi$
$642$	2.43047	−	6.71543i	0.0959228	−	0.265037i
$643$	−8.84133			−0.348668			−0.174334	−	0.984687i	$-0.555777\pi$
$643$	−8.84133			−0.348668			−0.174334	+	0.984687i	$0.555777\pi$
$644$	−27.1262	−	22.5948i	−1.06892	−	0.890359i
$645$	6.62146	+	26.6410i	0.260720	+	1.04899i
$646$	−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	$0.906606\pi$
$648$	2.44178	−	1.42749i	0.0959220	−	0.0560771i
$649$	−19.4649			−0.764064
$650$	−34.7905	+	4.90132i	−1.36460	+	0.192245i
$651$	15.7732	−	15.7732i	0.618200	−	0.618200i
$652$	−24.2747	−	20.2197i	−0.950672	−	0.791863i
$653$		−	35.7891i		−	1.40053i	−0.713881	−	0.700267i	$-0.753064\pi$
$653$		−	35.7891i		−	1.40053i	0.713881	−	0.700267i	$-0.246936\pi$
$654$	−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
$658$	−0.234767	+	0.648668i	−0.00915219	+	0.0252877i
$659$	11.8604	−	11.8604i	0.462014	−	0.462014i	−0.437301	−	0.899315i	$-0.644066\pi$
$659$	11.8604	−	11.8604i	0.462014	−	0.462014i	0.899315	+	0.437301i	$0.144066\pi$
$660$	−17.4329	+	6.05885i	−0.678574	+	0.235841i
$661$	−5.12628	−	5.12628i	−0.199389	−	0.199389i	0.600349	−	0.799738i	$-0.295028\pi$
$661$	−5.12628	−	5.12628i	−0.199389	−	0.199389i	−0.799738	+	0.600349i	$0.795028\pi$
$662$	15.8950	+	33.9265i	0.617776	+	1.31859i
$663$	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
$667$	28.7906			1.11478
$668$	−2.86385	−	31.4237i	−0.110806	−	1.21582i
$669$	19.9362	+	19.9362i	0.770777	+	0.770777i
$670$	−28.4123	−	2.95547i	−1.09766	−	0.114180i
$671$		−	7.70975i		−	0.297632i
$672$	−13.9806	−	19.5868i	−0.539313	−	0.755575i
$673$	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
$675$	4.41820	−	2.34084i	0.170057	−	0.0900989i
$676$	17.9614	+	14.9609i	0.690822	+	0.575421i
$677$			13.1467i			0.505268i	0.967562	+	0.252634i	$0.0812969\pi$
$677$			13.1467i			0.505268i	−0.967562	+	0.252634i	$0.918703\pi$
$678$	2.19769	+	4.69078i	0.0844018	+	0.180149i
$679$			59.6086i			2.28757i
$680$	22.9646	+	0.293109i	0.880654	+	0.0112402i
$681$		−	6.50202i		−	0.249158i
$682$	−27.7124	+	12.9836i	−1.06116	+	0.497168i
$683$			15.9674i			0.610977i	0.952196	+	0.305489i	$0.0988198\pi$
$683$			15.9674i			0.610977i	−0.952196	+	0.305489i	$0.901180\pi$
$684$	0.491939	−	0.0448336i	0.0188098	−	0.00171426i
$685$	−10.7225	+	17.8154i	−0.409685	+	0.680692i
$686$	−10.4566	−	22.3187i	−0.399234	−	0.852132i
$687$	−6.53144	+	6.53144i	−0.249190	+	0.249190i
$688$	48.2977	−	8.87711i	1.84133	−	0.338437i
$689$			51.3678i			1.95696i
$690$	−8.26867	−	10.1886i	−0.314783	−	0.387874i
$691$	−14.4031	−	14.4031i	−0.547919	−	0.547919i	0.377919	−	0.925839i	$-0.376640\pi$
$691$	−14.4031	−	14.4031i	−0.547919	−	0.547919i	−0.925839	+	0.377919i	$0.876640\pi$
$692$	−31.1693	+	37.4203i	−1.18488	+	1.42251i
$693$	−17.5557			−0.666885
$694$	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
$698$	−2.82546	+	1.32376i	−0.106945	+	0.0501051i
$699$	14.3657	+	14.3657i	0.543362	+	0.543362i
$700$	−23.2455	−	35.6276i	−0.878598	−	1.34660i
$701$	−9.70568	+	9.70568i	−0.366579	+	0.366579i	−0.866228	−	0.499649i	$-0.833462\pi$
$701$	−9.70568	+	9.70568i	−0.366579	+	0.366579i	0.499649	+	0.866228i	$0.333462\pi$
$702$	−6.60738	−	2.39136i	−0.249379	−	0.0902560i
$703$	−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
$707$		−	57.2213i		−	2.15203i
$708$	−0.856173	−	9.39440i	−0.0321769	−	0.353063i
$709$	−9.01713	+	9.01713i	−0.338645	+	0.338645i	−0.855857	−	0.517212i	$-0.826970\pi$
$709$	−9.01713	+	9.01713i	−0.338645	+	0.338645i	0.517212	+	0.855857i	$0.326970\pi$
$710$	1.46267	−	14.0613i	0.0548932	−	0.527712i
$711$	−6.75271			−0.253247
$712$	6.75370	−	3.94829i	0.253106	−	0.147968i
$713$	−15.3854	−	15.3854i	−0.576188	−	0.576188i
$714$	20.5424	+	7.43477i	0.768782	+	0.278239i
$715$	39.2842	+	23.6438i	1.46915	+	0.884228i
$716$	−17.2693	+	1.57387i	−0.645385	+	0.0588182i
$717$	6.65388			0.248494
$718$	24.0510	+	8.70459i	0.897575	+	0.324852i
$719$	24.3409			0.907762			0.453881	−	0.891062i	$-0.350039\pi$
$719$	24.3409			0.907762			0.453881	+	0.891062i	$0.350039\pi$
$720$	−3.69100	−	8.14718i	−0.137555	−	0.303627i
$721$	31.1087			1.15855
$722$	−25.1851	−	9.11504i	−0.937291	−	0.339227i
$723$	−15.6797			−0.583134
$724$	−2.30904	−	25.3360i	−0.0858148	−	0.941607i
$725$	33.1612	+	10.1920i	1.23158	+	0.378520i
$726$	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	$0.964376\pi$
$728$	−15.1597	+	57.8306i	−0.561855	+	2.14334i
$729$	1.00000			0.0370370
$730$	−12.1822	+	9.88656i	−0.450883	+	0.365918i
$731$	−31.5233	+	31.5233i	−1.16593	+	1.16593i
$732$	3.72098	−	0.339117i	0.137531	−	0.0125341i
$733$			14.8205i			0.547406i	0.961814	+	0.273703i	$0.0882486\pi$
$733$			14.8205i			0.547406i	−0.961814	+	0.273703i	$0.911751\pi$
$734$	−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
$738$	0.249117	+	0.0901608i	0.00917011	+	0.00331887i
$739$	−35.6500	+	35.6500i	−1.31141	+	1.31141i	−0.391029	+	0.920378i	$0.627881\pi$
$739$	−35.6500	+	35.6500i	−1.31141	+	1.31141i	−0.920378	+	0.391029i	$0.872119\pi$
$740$	−4.43445	+	9.15884i	−0.163013	+	0.336686i
$741$	−0.867772	−	0.867772i	−0.0318784	−	0.0318784i
$742$	−56.3213	+	26.3872i	−2.06762	+	0.968705i
$743$	−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
$747$	0.203861			0.00745888
$748$	−23.0293	−	19.1822i	−0.842033	−	0.701372i
$749$	−15.1906	−	15.1906i	−0.555051	−	0.555051i
$750$	−5.91712	−	14.6625i	−0.216063	−	0.535397i
$751$			25.6756i			0.936917i	0.883486	+	0.468458i	$0.155190\pi$
$751$			25.6756i			0.936917i	−0.883486	+	0.468458i	$0.844810\pi$
$752$	0.377611	+	0.260353i	0.0137700	+	0.00949410i
$753$	−2.31676	+	2.31676i	−0.0844275	+	0.0844275i
$754$	−20.6847	−	44.1497i	−0.753291	−	1.60784i
$755$	29.5690	−	7.34919i	1.07612	−	0.267465i
$756$	−0.772196	−	8.47295i	−0.0280845	−	0.308158i
$757$			21.4132i			0.778274i	0.921180	+	0.389137i	$0.127227\pi$
$757$			21.4132i			0.778274i	−0.921180	+	0.389137i	$0.872773\pi$
$758$	−14.3275	+	6.71260i	−0.520397	+	0.243813i
$759$			17.1241i			0.621564i
$760$	0.0199362	−	1.56197i	0.000723160	−	0.0566585i
$761$			15.6885i			0.568708i	0.958719	+	0.284354i	$0.0917791\pi$
$761$			15.6885i			0.568708i	−0.958719	+	0.284354i	$0.908221\pi$
$762$	−5.05244	−	10.7840i	−0.183031	−	0.390663i
$763$			40.7511i			1.47529i
$764$	−0.190328	+	0.228498i	−0.00688581	+	0.00826677i
$765$	6.95702	+	4.18719i	0.251531	+	0.151388i
$766$	35.7492	−	16.7489i	1.29167	−	0.605164i
$767$	−16.5716	+	16.5716i	−0.598364	+	0.598364i
$768$	−14.9543	+	5.68939i	−0.539617	+	0.205298i
$769$		−	51.0412i		−	1.84059i	−0.391221	−	0.920297i	$-0.627947\pi$
$769$		−	51.0412i		−	1.84059i	0.391221	−	0.920297i	$-0.372053\pi$
$770$	−5.74383	+	55.2180i	−0.206993	+	1.98992i
$771$	10.9722	+	10.9722i	0.395156	+	0.395156i
$772$	12.2198	−	1.11367i	0.439799	−	0.0400818i
$773$	15.9432			0.573437			0.286718	−	0.958015i	$-0.407436\pi$
$773$	15.9432			0.573437			0.286718	+	0.958015i	$0.407436\pi$
$774$	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
$778$	−4.66386	−	9.95460i	−0.167207	−	0.356890i
$779$	0.0327174	+	0.0327174i	0.00117222	+	0.00117222i
$780$	−9.68335	+	19.9998i	−0.346719	+	0.716109i
$781$	−13.0456	+	13.0456i	−0.466809	+	0.466809i
$782$	7.25198	−	20.0374i	0.259330	−	0.716536i
$783$	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
$787$		−	26.1398i		−	0.931784i	−0.884841	−	0.465892i	$-0.845733\pi$
$787$		−	26.1398i		−	0.931784i	0.884841	−	0.465892i	$-0.154267\pi$
$788$	7.51223	−	9.01882i	0.267612	−	0.321282i
$789$	9.46655	−	9.46655i	0.337018	−	0.337018i
$790$	−2.20934	+	21.2394i	−0.0786048	+	0.755662i
$791$	15.5820			0.554032
$792$	−2.95980	+	11.2909i	−0.105172	+	0.401206i
$793$	−6.56374	−	6.56374i	−0.233085	−	0.233085i
$794$	12.2483	−	33.8424i	0.434676	−	1.20102i
$795$	−22.4345	+	5.57597i	−0.795671	+	0.197759i
$796$	7.59517	−	9.11839i	0.269204	−	0.323193i
$797$	−34.0127			−1.20479			−0.602396	−	0.798197i	$-0.705787\pi$
$797$	−34.0127			−1.20479			−0.602396	+	0.798197i	$0.705787\pi$
$798$	0.505685	−	1.39722i	0.0179010	−	0.0494610i
$799$	−0.416390			−0.0147308
$800$	−26.8330	+	8.94374i	−0.948690	+	0.316209i
$801$	2.76590			0.0977282
$802$	0.700781	−	1.93627i	0.0247454	−	0.0683722i
$803$	20.4746			0.722534
$804$	−11.5627	+	13.8816i	−0.407786	+	0.489568i
$805$	−38.3054	+	9.52058i	−1.35009	+	0.335556i
$806$	−12.5395	+	34.6468i	−0.441683	+	1.22038i
$807$	2.77544	+	2.77544i	0.0977002	+	0.0977002i
$808$	−36.8019	−	9.64723i	−1.29469	−	0.339388i
$809$	−25.6058			−0.900253			−0.450127	−	0.892965i	$-0.648621\pi$
$809$	−25.6058			−0.900253			−0.450127	+	0.892965i	$0.648621\pi$
$810$	0.327178	−	3.14531i	0.0114959	−	0.110515i
$811$	−29.4467	+	29.4467i	−1.03401	+	1.03401i	−0.0346118	+	0.999401i	$0.511019\pi$
$811$	−29.4467	+	29.4467i	−1.03401	+	1.03401i	−0.999401	+	0.0346118i	$0.988981\pi$
$812$	37.7815	−	45.3586i	1.32587	−	1.59177i
$813$		−	3.86079i		−	0.135404i
$814$	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
$818$	7.17952	−	19.8372i	0.251026	−	0.693591i
$819$	−14.9461	+	14.9461i	−0.522260	+	0.522260i
$820$	0.365089	−	0.754049i	0.0127495	−	0.0263325i
$821$	−22.3951	−	22.3951i	−0.781595	−	0.781595i	0.198505	−	0.980100i	$-0.436392\pi$
$821$	−22.3951	−	22.3951i	−0.781595	−	0.781595i	−0.980100	+	0.198505i	$0.936392\pi$
$822$	5.57934	+	11.9086i	0.194602	+	0.415361i
$823$	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
$827$	45.0540			1.56668			0.783341	−	0.621592i	$-0.213514\pi$
$827$	45.0540			1.56668			0.783341	+	0.621592i	$0.213514\pi$
$828$	−8.26464	+	0.753211i	−0.287216	+	0.0261759i
$829$	20.1502	+	20.1502i	0.699844	+	0.699844i	0.964377	−	0.264533i	$-0.0852177\pi$
$829$	20.1502	+	20.1502i	0.699844	+	0.699844i	−0.264533	+	0.964377i	$0.585218\pi$
$830$	0.0666988	−	0.641205i	0.00231515	−	0.0222565i
$831$		−	28.9073i		−	1.00278i
$832$	34.6379	+	19.4999i	1.20085	+	0.676038i
$833$	28.4936	−	28.4936i	0.987246	−	0.987246i
$834$	18.2571	−	8.55368i	0.632191	−	0.296190i
$835$	−30.2261	−	18.1920i	−1.04602	−	0.629561i
$836$	−1.30470	+	1.56636i	−0.0451241	+	0.0541738i
$837$		−	5.24365i		−	0.181247i
$838$	−10.5018	−	22.4151i	−0.362777	−	0.774317i
$839$		−	10.9329i		−	0.377445i	−0.982030	−	0.188723i	$-0.939565\pi$
$839$		−	10.9329i		−	0.377445i	0.982030	−	0.188723i	$-0.0604347\pi$
$840$	−26.9027	−	0.343372i	−0.928231	−	0.0118475i
$841$			19.1417i			0.660059i
$842$	41.9105	−	19.6356i	1.44433	−	0.676687i
$843$			16.2395i			0.559319i
$844$	1.82236	+	19.9959i	0.0627282	+	0.688288i
$845$	25.3636	−	6.30397i	0.872533	−	0.216863i
$846$	0.0687987	+	0.146845i	0.00236535	+	0.00504863i
$847$	18.1408	−	18.1408i	0.623326	−	0.623326i
$848$	7.47547	+	40.6718i	0.256709	+	1.39668i
$849$		−	22.8092i		−	0.782811i
$850$	15.4462	−	20.5120i	0.529799	−	0.703556i
$851$	6.67624	+	6.67624i	0.228859	+	0.228859i
$852$	−6.87007	−	5.72243i	−0.235365	−	0.196047i
$853$	18.1959			0.623017			0.311508	−	0.950243i	$-0.399166\pi$
$853$	18.1959			0.623017			0.311508	+	0.950243i	$0.399166\pi$
$854$	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	$-0.316746\pi$
$857$	40.4936	−	40.4936i	1.38324	−	1.38324i	0.838807	−	0.544430i	$-0.183254\pi$
$858$	26.2593	−	12.3028i	0.896478	−	0.420011i
$859$	14.3628	+	14.3628i	0.490053	+	0.490053i	0.908323	−	0.418270i	$-0.137363\pi$
$859$	14.3628	+	14.3628i	0.490053	+	0.490053i	−0.418270	+	0.908323i	$0.637363\pi$
$860$	23.9256	−	49.4156i	0.815857	−	1.68506i
$861$	0.563511	−	0.563511i	0.0192044	−	0.0192044i
$862$	21.2824	+	7.70257i	0.724881	+	0.262351i
$863$	10.5835	+	10.5835i	0.360268	+	0.360268i	0.863911	−	0.503644i	$-0.168008\pi$
$863$	10.5835	+	10.5835i	0.360268	+	0.360268i	−0.503644	+	0.863911i	$0.668008\pi$
$864$	−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
$867$		−	3.81348i		−	0.129512i
$868$	−44.4292	+	4.04912i	−1.50803	+	0.137436i
$869$	19.7052	−	19.7052i	0.668452	−	0.668452i
$870$	17.0367	−	13.8263i	0.577599	−	0.468756i
$871$	44.8834			1.52082
$872$	26.2091	+	6.87044i	0.887553	+	0.232663i
$873$	9.90816	+	9.90816i	0.335341	+	0.335341i
$874$	−1.36287	−	0.493252i	−0.0460997	−	0.0166845i
$875$	−47.4907	−	2.59433i	−1.60548	−	0.0877045i
$876$	0.900588	+	9.88174i	0.0304280	+	0.333873i
$877$	55.3196			1.86801			0.934004	−	0.357262i	$-0.116290\pi$
$877$	55.3196			1.86801			0.934004	+	0.357262i	$0.116290\pi$
$878$	5.38382	+	1.94852i	0.181695	+	0.0657595i
$879$	−30.6990			−1.03545
$880$	34.5451	+	13.0036i	1.16452	+	0.438352i
$881$	−47.0634			−1.58561			−0.792804	−	0.609477i	$-0.791380\pi$
$881$	−47.0634			−1.58561			−0.792804	+	0.609477i	$0.791380\pi$
$882$	−14.7565	−	5.34071i	−0.496878	−	0.179831i
$883$	42.7619			1.43905			0.719526	−	0.694465i	$-0.244359\pi$
$883$	42.7619			1.43905			0.719526	+	0.694465i	$0.244359\pi$
$884$	−35.9370	+	3.27518i	−1.20869	+	0.110156i
$885$	−9.03635	−	5.43867i	−0.303753	−	0.182819i
$886$	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	$0.635365\pi$
$888$	3.24811	+	5.55601i	0.108999	+	0.186448i
$889$	−35.8226			−1.20145
$890$	0.904941	−	8.69959i	0.0303337	−	0.291611i
$891$	−2.91811	+	2.91811i	−0.0977604	+	0.0977604i
$892$	−5.11780	−	56.1553i	−0.171357	−	1.88022i
$893$			0.0283213i			0.000947736i
$894$	−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
$898$	35.8483	+	12.9743i	1.19627	+	0.432958i
$899$	25.7264	−	25.7264i	0.858025	−	0.858025i
$900$	−9.78591	−	2.05815i	−0.326197	−	0.0686050i
$901$	−26.5459	−	26.5459i	−0.884374	−	0.884374i
$902$	−0.990049	+	0.463850i	−0.0329650	+	0.0154445i
$903$	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
$907$	−31.3755			−1.04181			−0.520903	−	0.853616i	$-0.674405\pi$
$907$	−31.3755			−1.04181			−0.520903	+	0.853616i	$0.674405\pi$
$908$	−8.32273	+	9.99186i	−0.276199	+	0.331591i
$909$	−9.51134	−	9.51134i	−0.315471	−	0.315471i
$910$	42.1201	+	51.9002i	1.39627	+	1.72048i
$911$			20.9112i			0.692818i	0.938084	+	0.346409i	$0.112599\pi$
$911$			20.9112i			0.692818i	−0.938084	+	0.346409i	$0.887401\pi$
$912$	−0.813366	−	0.560796i	−0.0269332	−	0.0185698i
$913$	−0.594888	+	0.594888i	−0.0196879	+	0.0196879i
$914$	9.13200	+	19.4915i	0.302060	+	0.644720i
$915$	2.15417	−	3.57916i	0.0712148	−	0.118323i
$916$	18.3974	−	1.67668i	0.607869	−	0.0553991i
$917$			6.44286i			0.212762i
$918$	4.65038	−	2.17876i	0.153485	−	0.0719098i
$919$			19.8382i			0.654403i	0.944955	+	0.327201i	$0.106106\pi$
$919$			19.8382i			0.654403i	−0.944955	+	0.327201i	$0.893894\pi$
$920$	−0.334930	+	26.2413i	−0.0110423	+	0.865149i
$921$		−	17.3607i		−	0.572056i
$922$	−3.62025	−	7.72712i	−0.119227	−	0.254479i
$923$			22.2130i			0.731149i
$924$	26.9784	+	22.4717i	0.887523	+	0.739263i
$925$	5.32634	+	10.0532i	0.175129	+	0.330546i
$926$	42.5436	−	19.9322i	1.39807	−	0.655012i
$927$	5.17090	−	5.17090i	0.169835	−	0.169835i
$928$	−22.8026	−	31.9464i	−0.748533	−	1.04869i
$929$		−	20.2449i		−	0.664213i	−0.943242	−	0.332106i	$-0.892241\pi$
$929$		−	20.2449i		−	0.664213i	0.943242	−	0.332106i	$-0.107759\pi$
$930$	−16.4929	−	1.71561i	−0.540823	−	0.0562570i
$931$	−1.93803	−	1.93803i	−0.0635163	−	0.0635163i
$932$	−3.68781	−	40.4647i	−0.120798	−	1.32547i
$933$	−20.0448			−0.656237
$934$	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	−0.332103	−	0.943243i	$-0.607758\pi$
$937$	18.7073	−	18.7073i	0.611140	−	0.611140i	0.943243	+	0.332103i	$0.107758\pi$
$938$	23.0562	+	49.2116i	0.752813	+	1.60681i
$939$	10.7674	+	10.7674i	0.351381	+	0.351381i
$940$	0.484382	−	0.168349i	0.0157988	−	0.00549092i
$941$	−5.54352	+	5.54352i	−0.180713	+	0.180713i	−0.791667	−	0.610953i	$-0.790786\pi$
$941$	−5.54352	+	5.54352i	−0.180713	+	0.180713i	0.610953	+	0.791667i	$0.290786\pi$
$942$	3.43338	−	9.48651i	0.111866	−	0.309087i
$943$	−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
$947$			18.6075i			0.604664i	0.953203	+	0.302332i	$0.0977651\pi$
$947$			18.6075i			0.604664i	−0.953203	+	0.302332i	$0.902235\pi$
$948$	10.3771	+	8.64362i	0.337033	+	0.280732i
$949$	17.4312	−	17.4312i	0.565841	−	0.565841i
$950$	−1.39515	−	1.05059i	−0.0452646	−	0.0340856i
$951$	11.6799			0.378745
$952$	−22.0515	−	37.7200i	−0.714695	−	1.22251i
$953$	−39.8932	−	39.8932i	−1.29227	−	1.29227i	−0.933381	−	0.358888i	$-0.883156\pi$
$953$	−39.8932	−	39.8932i	−1.29227	−	1.29227i	−0.358888	−	0.933381i	$-0.616844\pi$
$954$	−4.97565	+	13.7478i	−0.161093	+	0.445102i
$955$	0.0801968	+	0.322666i	0.00259511	+	0.0104412i
$956$	−10.2252	−	8.51712i	−0.330708	−	0.275463i
$957$	−28.6337			−0.925596
$958$	1.57633	−	4.35542i	0.0509287	−	0.140717i
$959$	39.5584			1.27741
$960$	−4.75650	+	17.2446i	−0.153515	+	0.556567i
$961$	3.50411			0.113036
$962$	5.44129	−	15.0344i	0.175434	−	0.484729i
$963$	−5.04996			−0.162733
$964$	24.0955	+	20.0703i	0.776063	+	0.646422i
$965$	7.07435	−	11.7540i	0.227732	−	0.378376i
$966$	−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	$0.441522\pi$
$968$	−8.60882	−	14.7257i	−0.276698	−	0.473303i
$969$	0.896897			0.0288125
$970$	34.4059	−	27.9225i	1.10471	−	0.896537i
$971$	25.3075	−	25.3075i	0.812157	−	0.812157i	−0.172800	−	0.984957i	$-0.555281\pi$
$971$	25.3075	−	25.3075i	0.812157	−	0.812157i	0.984957	+	0.172800i	$0.0552814\pi$
$972$	−1.53673	−	1.28002i	−0.0492907	−	0.0410567i
$973$		−	60.6470i		−	1.94425i
$974$	−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	$0.928077\pi$
$978$	−7.60253	+	21.0060i	−0.243102	+	0.671697i
$979$	−8.07119	+	8.07119i	−0.257956	+	0.257956i
$980$	−21.6262	+	44.6664i	−0.690823	+	1.42682i
$981$	6.77367	+	6.77367i	0.216267	+	0.216267i
$982$	9.68074	+	20.6627i	0.308925	+	0.659374i
$983$	−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
$987$	0.487794			0.0155267
$988$	0.222765	+	2.44430i	0.00708710	+	0.0777635i
$989$	−36.0210	−	36.0210i	−1.14540	−	1.14540i
$990$	8.22361	+	10.1331i	0.261364	+	0.322051i
$991$			30.1804i			0.958711i	0.877621	+	0.479355i	$0.159130\pi$
$991$			30.1804i			0.958711i	−0.877621	+	0.479355i	$0.840870\pi$
$992$	−4.88635	+	29.2573i	−0.155142	+	0.928921i
$993$	18.7327	−	18.7327i	0.594465	−	0.594465i
$994$	−24.3550	+	11.4106i	−0.772493	+	0.361922i
$995$	−3.20032	−	12.8762i	−0.101457	−	0.408204i
$996$	−0.313279	−	0.260946i	−0.00992663	−	0.00826840i
$997$			41.2092i			1.30511i	0.757741	+	0.652555i	$0.226303\pi$
$997$			41.2092i			1.30511i	−0.757741	+	0.652555i	$0.773697\pi$
$998$	9.19746	+	19.6312i	0.291141	+	0.621415i
$999$			2.27540i			0.0719904i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.3	✓	16	80.3	even	4	inner
240.2.y.e.187.3	yes	16	1.1	even	1	trivial
240.2.bc.e.43.7	yes	16	5.3	odd	4
240.2.bc.e.67.7	yes	16	16.3	odd	4
720.2.z.f.163.6		16	240.83	odd	4
720.2.z.f.667.6		16	3.2	odd	2
720.2.bd.f.307.2		16	48.35	even	4
720.2.bd.f.523.2		16	15.8	even	4
960.2.y.e.847.1		16	4.3	odd	2
960.2.y.e.943.1		16	80.13	odd	4
960.2.bc.e.367.7		16	16.13	even	4
960.2.bc.e.463.7		16	20.3	even	4
1920.2.y.i.223.8		16	80.43	even	4
1920.2.y.i.1567.8		16	8.5	even	2
1920.2.y.j.223.8		16	80.53	odd	4
1920.2.y.j.1567.8		16	8.3	odd	2
1920.2.bc.i.607.2		16	16.11	odd	4
1920.2.bc.i.1183.2		16	40.13	odd	4
1920.2.bc.j.607.2		16	16.5	even	4
1920.2.bc.j.1183.2		16	40.3	even	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.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.481284 + 1.32980i) q^{2} +1.00000 q^{3} +(-1.53673 - 1.28002i) q^{4} +(-2.17005 + 0.539352i) q^{5} +(-0.481284 + 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(2.44178 - 1.42749i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.481284 + 1.32980i) q^{2} +1.00000 q^{3} +(-1.53673 - 1.28002i) q^{4} +(-2.17005 + 0.539352i) q^{5} +(-0.481284 + 1.32980i) q^{6} +(3.00806 + 3.00806i) q^{7} +(2.44178 - 1.42749i) q^{8} +1.00000 q^{9} +(0.327178 - 3.14531i) q^{10} +(-2.91811 + 2.91811i) q^{11} +(-1.53673 - 1.28002i) q^{12} +4.96870i 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} +(-0.481284 + 1.32980i) q^{18} +(-0.174647 + 0.174647i) q^{19} +(4.02516 + 1.94887i) q^{20} +(3.00806 + 3.00806i) q^{21} +(-2.47606 - 5.28494i) 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} +1.00000 q^{27} +(-0.772196 - 8.47295i) q^{28} +(4.90621 + 4.90621i) q^{29} +(0.327178 - 3.14531i) q^{30} -5.24365i q^{31} +(-5.57957 - 0.931860i) q^{32} +(-2.91811 + 2.91811i) q^{33} +(4.65038 - 2.17876i) q^{34} +(-8.15002 - 4.90522i) q^{35} +(-1.53673 - 1.28002i) q^{36} +2.27540i q^{37} +(-0.148191 - 0.316301i) q^{38} +4.96870i q^{39} +(-4.52885 + 4.41470i) q^{40} -0.187334i q^{41} +(-5.44784 + 2.55238i) q^{42} -12.2767i q^{43} +(8.21960 - 0.749106i) q^{44} +(-2.17005 + 0.539352i) q^{45} +(2.48963 + 5.31390i) q^{46} +(0.0810813 - 0.0810813i) q^{47} +(0.723087 + 3.93410i) q^{48} +11.0968i q^{49} +(0.986437 + 7.00192i) q^{50} +(-2.56773 - 2.56773i) q^{51} +(6.36005 - 7.63556i) q^{52} +10.3383 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} +(-8.88555 + 4.16299i) q^{58} +(3.33519 + 3.33519i) q^{59} +(4.02516 + 1.94887i) q^{60} +(-1.32102 + 1.32102i) q^{61} +(6.97300 + 2.52369i) 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} -9.03323i q^{67} +(0.659161 + 7.23268i) q^{68} +(2.93410 - 2.93410i) q^{69} +(10.4454 - 8.47709i) q^{70} +4.47057 q^{71} +(2.44178 - 1.42749i) q^{72} +(-3.50820 - 3.50820i) q^{73} +(-3.02582 - 1.09511i) q^{74} +(4.41820 - 2.34084i) q^{75} +(0.491939 - 0.0448336i) q^{76} -17.5557 q^{77} +(-6.60738 - 2.39136i) q^{78} -6.75271 q^{79} +(-3.69100 - 8.14718i) q^{80} +1.00000 q^{81} +(0.249117 + 0.0901608i) q^{82} +0.203861 q^{83} +(-0.772196 - 8.47295i) q^{84} +(6.95702 + 4.18719i) q^{85} +(16.3255 + 5.90857i) q^{86} +(4.90621 + 4.90621i) q^{87} +(-2.95980 + 11.2909i) q^{88} +2.76590 q^{89} +(0.327178 - 3.14531i) q^{90} +(-14.9461 + 14.9461i) q^{91} +(-8.26464 + 0.753211i) q^{92} -5.24365i 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} +(-14.7565 - 5.34071i) q^{98} +(-2.91811 + 2.91811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

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