LMFDB - Embedded newform 1110.2.o.a.253.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.7
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.866398 + 2.06140i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.662100 + 0.662100i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.866398 + 2.06140i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.662100 + 0.662100i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(0.866398 - 2.06140i) q^{10} +3.51735i q^{11} +(-0.707107 + 0.707107i) q^{12} +6.87657 q^{13} +(0.662100 - 0.662100i) q^{14} +(-0.844991 - 2.07026i) q^{15} +1.00000 q^{16} +2.17458i q^{17} +1.00000i q^{18} +(-1.01389 - 1.01389i) q^{19} +(-0.866398 + 2.06140i) q^{20} -0.936350i q^{21} -3.51735i q^{22} +9.57399 q^{23} +(0.707107 - 0.707107i) q^{24} +(-3.49871 - 3.57198i) q^{25} -6.87657 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.662100 + 0.662100i) q^{28} +(-6.49970 + 6.49970i) q^{29} +(0.844991 + 2.07026i) q^{30} +(2.38699 + 2.38699i) q^{31} -1.00000 q^{32} +(-2.48714 - 2.48714i) q^{33} -2.17458i q^{34} +(-0.791208 - 1.93849i) q^{35} -1.00000i q^{36} +(-5.95481 + 1.24106i) q^{37} +(1.01389 + 1.01389i) q^{38} +(-4.86247 + 4.86247i) q^{39} +(0.866398 - 2.06140i) q^{40} +3.47992i q^{41} +0.936350i q^{42} +2.74581 q^{43} +3.51735i q^{44} +(2.06140 + 0.866398i) q^{45} -9.57399 q^{46} +(3.59071 - 3.59071i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.12325i q^{49} +(3.49871 + 3.57198i) q^{50} +(-1.53766 - 1.53766i) q^{51} +6.87657 q^{52} +(-2.93440 - 2.93440i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-7.25065 - 3.04742i) q^{55} +(0.662100 - 0.662100i) q^{56} +1.43385 q^{57} +(6.49970 - 6.49970i) q^{58} +(-3.45523 - 3.45523i) q^{59} +(-0.844991 - 2.07026i) q^{60} +(-9.99355 - 9.99355i) q^{61} +(-2.38699 - 2.38699i) q^{62} +(0.662100 + 0.662100i) q^{63} +1.00000 q^{64} +(-5.95785 + 14.1753i) q^{65} +(2.48714 + 2.48714i) q^{66} +(-1.14933 - 1.14933i) q^{67} +2.17458i q^{68} +(-6.76983 + 6.76983i) q^{69} +(0.791208 + 1.93849i) q^{70} -7.32848 q^{71} +1.00000i q^{72} +(-0.292649 + 0.292649i) q^{73} +(5.95481 - 1.24106i) q^{74} +(4.99973 + 0.0518094i) q^{75} +(-1.01389 - 1.01389i) q^{76} +(-2.32883 - 2.32883i) q^{77} +(4.86247 - 4.86247i) q^{78} +(7.95594 + 7.95594i) q^{79} +(-0.866398 + 2.06140i) q^{80} -1.00000 q^{81} -3.47992i q^{82} +(-1.46770 - 1.46770i) q^{83} -0.936350i q^{84} +(-4.48266 - 1.88405i) q^{85} -2.74581 q^{86} -9.19196i q^{87} -3.51735i q^{88} +(-6.43088 + 6.43088i) q^{89} +(-2.06140 - 0.866398i) q^{90} +(-4.55298 + 4.55298i) q^{91} +9.57399 q^{92} -3.37571 q^{93} +(-3.59071 + 3.59071i) q^{94} +(2.96845 - 1.21159i) q^{95} +(0.707107 - 0.707107i) q^{96} -0.301015i q^{97} -6.12325i q^{98} +3.51735 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−0.866398	+	2.06140i	−0.387465	+	0.921884i
$5$	−0.866398	+	2.06140i	−0.387465	+	0.921884i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−0.662100	+	0.662100i	−0.250250	+	0.250250i	−0.821073	−	0.570823i	$-0.806624\pi$
$7$	−0.662100	+	0.662100i	−0.250250	+	0.250250i	0.570823	+	0.821073i	$0.306624\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	0.866398	−	2.06140i	0.273979	−	0.651871i
$11$			3.51735i			1.06052i	0.847835	+	0.530260i	$0.177906\pi$
$11$			3.51735i			1.06052i	−0.847835	+	0.530260i	$0.822094\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	6.87657			1.90722			0.953609	−	0.301047i	$-0.0973362\pi$
$13$	6.87657			1.90722			0.953609	+	0.301047i	$0.0973362\pi$
$14$	0.662100	−	0.662100i	0.176954	−	0.176954i
$15$	−0.844991	−	2.07026i	−0.218176	−	0.534540i
$16$	1.00000			0.250000
$17$			2.17458i			0.527412i	0.964603	+	0.263706i	$0.0849449\pi$
$17$			2.17458i			0.527412i	−0.964603	+	0.263706i	$0.915055\pi$
$18$			1.00000i			0.235702i
$19$	−1.01389	−	1.01389i	−0.232601	−	0.232601i	0.581176	−	0.813778i	$-0.302593\pi$
$19$	−1.01389	−	1.01389i	−0.232601	−	0.232601i	−0.813778	+	0.581176i	$0.802593\pi$
$20$	−0.866398	+	2.06140i	−0.193732	+	0.460942i
$21$		−	0.936350i		−	0.204328i
$22$		−	3.51735i		−	0.749901i
$23$	9.57399			1.99632			0.998158	−	0.0606732i	$-0.0193247\pi$
$23$	9.57399			1.99632			0.998158	+	0.0606732i	$0.0193247\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−3.49871	−	3.57198i	−0.699742	−	0.714396i
$26$	−6.87657			−1.34861
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.662100	+	0.662100i	−0.125125	+	0.125125i
$29$	−6.49970	+	6.49970i	−1.20696	+	1.20696i	−0.234958	+	0.972006i	$0.575495\pi$
$29$	−6.49970	+	6.49970i	−1.20696	+	1.20696i	−0.972006	+	0.234958i	$0.924505\pi$
$30$	0.844991	+	2.07026i	0.154274	+	0.377977i
$31$	2.38699	+	2.38699i	0.428716	+	0.428716i	0.888191	−	0.459475i	$-0.151962\pi$
$31$	2.38699	+	2.38699i	0.428716	+	0.428716i	−0.459475	+	0.888191i	$0.651962\pi$
$32$	−1.00000			−0.176777
$33$	−2.48714	−	2.48714i	−0.432956	−	0.432956i
$34$		−	2.17458i		−	0.372937i
$35$	−0.791208	−	1.93849i	−0.133739	−	0.327665i
$36$		−	1.00000i		−	0.166667i
$37$	−5.95481	+	1.24106i	−0.978965	+	0.204029i
$37$	−5.95481	+	1.24106i	−0.978965	+	0.204029i
$38$	1.01389	+	1.01389i	0.164474	+	0.164474i
$39$	−4.86247	+	4.86247i	−0.778619	+	0.778619i
$40$	0.866398	−	2.06140i	0.136990	−	0.325935i
$41$			3.47992i			0.543472i	0.962372	+	0.271736i	$0.0875977\pi$
$41$			3.47992i			0.543472i	−0.962372	+	0.271736i	$0.912402\pi$
$42$			0.936350i			0.144482i
$43$	2.74581			0.418732			0.209366	−	0.977837i	$-0.432860\pi$
$43$	2.74581			0.418732			0.209366	+	0.977837i	$0.432860\pi$
$44$			3.51735i			0.530260i
$45$	2.06140	+	0.866398i	0.307295	+	0.129155i
$46$	−9.57399			−1.41161
$47$	3.59071	−	3.59071i	0.523759	−	0.523759i	−0.394946	−	0.918704i	$-0.629237\pi$
$47$	3.59071	−	3.59071i	0.523759	−	0.523759i	0.918704	+	0.394946i	$0.129237\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			6.12325i			0.874750i
$50$	3.49871	+	3.57198i	0.494792	+	0.505154i
$51$	−1.53766	−	1.53766i	−0.215315	−	0.215315i
$52$	6.87657			0.953609
$53$	−2.93440	−	2.93440i	−0.403071	−	0.403071i	0.476243	−	0.879314i	$-0.341998\pi$
$53$	−2.93440	−	2.93440i	−0.403071	−	0.403071i	−0.879314	+	0.476243i	$0.841998\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−7.25065	−	3.04742i	−0.977677	−	0.410914i
$56$	0.662100	−	0.662100i	0.0884768	−	0.0884768i
$57$	1.43385			0.189918
$58$	6.49970	−	6.49970i	0.853452	−	0.853452i
$59$	−3.45523	−	3.45523i	−0.449833	−	0.449833i	0.445466	−	0.895299i	$-0.353038\pi$
$59$	−3.45523	−	3.45523i	−0.449833	−	0.449833i	−0.895299	+	0.445466i	$0.853038\pi$
$60$	−0.844991	−	2.07026i	−0.109088	−	0.267270i
$61$	−9.99355	−	9.99355i	−1.27954	−	1.27954i	−0.940924	−	0.338619i	$-0.890040\pi$
$61$	−9.99355	−	9.99355i	−1.27954	−	1.27954i	−0.338619	−	0.940924i	$-0.609960\pi$
$62$	−2.38699	−	2.38699i	−0.303148	−	0.303148i
$63$	0.662100	+	0.662100i	0.0834167	+	0.0834167i
$64$	1.00000			0.125000
$65$	−5.95785	+	14.1753i	−0.738980	+	1.75824i
$66$	2.48714	+	2.48714i	0.306146	+	0.306146i
$67$	−1.14933	−	1.14933i	−0.140413	−	0.140413i	0.633406	−	0.773819i	$-0.281656\pi$
$67$	−1.14933	−	1.14933i	−0.140413	−	0.140413i	−0.773819	+	0.633406i	$0.781656\pi$
$68$			2.17458i			0.263706i
$69$	−6.76983	+	6.76983i	−0.814992	+	0.814992i
$70$	0.791208	+	1.93849i	0.0945674	+	0.231694i
$71$	−7.32848			−0.869730			−0.434865	−	0.900496i	$-0.643204\pi$
$71$	−7.32848			−0.869730			−0.434865	+	0.900496i	$0.643204\pi$
$72$			1.00000i			0.117851i
$73$	−0.292649	+	0.292649i	−0.0342519	+	0.0342519i	−0.724025	−	0.689773i	$-0.757710\pi$
$73$	−0.292649	+	0.292649i	−0.0342519	+	0.0342519i	0.689773	+	0.724025i	$0.257710\pi$
$74$	5.95481	−	1.24106i	0.692233	−	0.144270i
$75$	4.99973	+	0.0518094i	0.577319	+	0.00598243i
$76$	−1.01389	−	1.01389i	−0.116301	−	0.116301i
$77$	−2.32883	−	2.32883i	−0.265395	−	0.265395i
$78$	4.86247	−	4.86247i	0.550567	−	0.550567i
$79$	7.95594	+	7.95594i	0.895113	+	0.895113i	0.994999	−	0.0998861i	$-0.0318478\pi$
$79$	7.95594	+	7.95594i	0.895113	+	0.895113i	−0.0998861	+	0.994999i	$0.531848\pi$
$80$	−0.866398	+	2.06140i	−0.0968662	+	0.230471i
$81$	−1.00000			−0.111111
$82$		−	3.47992i		−	0.384293i
$83$	−1.46770	−	1.46770i	−0.161102	−	0.161102i	0.621953	−	0.783055i	$-0.286339\pi$
$83$	−1.46770	−	1.46770i	−0.161102	−	0.161102i	−0.783055	+	0.621953i	$0.786339\pi$
$84$		−	0.936350i		−	0.102164i
$85$	−4.48266	−	1.88405i	−0.486213	−	0.204354i
$86$	−2.74581			−0.296088
$87$		−	9.19196i		−	0.985481i
$88$		−	3.51735i		−	0.374951i
$89$	−6.43088	+	6.43088i	−0.681672	+	0.681672i	−0.960377	−	0.278705i	$-0.910095\pi$
$89$	−6.43088	+	6.43088i	−0.681672	+	0.681672i	0.278705	+	0.960377i	$0.410095\pi$
$90$	−2.06140	−	0.866398i	−0.217290	−	0.0913264i
$91$	−4.55298	+	4.55298i	−0.477282	+	0.477282i
$92$	9.57399			0.998158
$93$	−3.37571			−0.350045
$94$	−3.59071	+	3.59071i	−0.370353	+	0.370353i
$95$	2.96845	−	1.21159i	0.304556	−	0.124307i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$		−	0.301015i		−	0.0305635i	−0.999883	−	0.0152817i	$-0.995135\pi$
$97$		−	0.301015i		−	0.0305635i	0.999883	−	0.0152817i	$-0.00486451\pi$
$98$		−	6.12325i		−	0.618541i
$99$	3.51735			0.353507
$100$	−3.49871	−	3.57198i	−0.349871	−	0.357198i
$101$			7.88206i			0.784294i	0.919903	+	0.392147i	$0.128268\pi$
$101$			7.88206i			0.784294i	−0.919903	+	0.392147i	$0.871732\pi$
$102$	1.53766	+	1.53766i	0.152251	+	0.152251i
$103$		−	3.81714i		−	0.376114i	−0.982158	−	0.188057i	$-0.939781\pi$
$103$		−	3.81714i		−	0.376114i	0.982158	−	0.188057i	$-0.0602190\pi$
$104$	−6.87657			−0.674304
$105$	1.93019	+	0.811252i	0.188367	+	0.0791701i
$106$	2.93440	+	2.93440i	0.285014	+	0.285014i
$107$	−3.39625	+	3.39625i	−0.328328	+	0.328328i	−0.851950	−	0.523622i	$-0.824580\pi$
$107$	−3.39625	+	3.39625i	−0.328328	+	0.328328i	0.523622	+	0.851950i	$0.324580\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	−1.95485	−	1.95485i	−0.187241	−	0.187241i	0.607261	−	0.794502i	$-0.292268\pi$
$109$	−1.95485	−	1.95485i	−0.187241	−	0.187241i	−0.794502	+	0.607261i	$0.792268\pi$
$110$	7.25065	+	3.04742i	0.691322	+	0.290560i
$111$	3.33312	−	5.08825i	0.316366	−	0.482955i
$112$	−0.662100	+	0.662100i	−0.0625625	+	0.0625625i
$113$			18.3281i			1.72416i	0.506773	+	0.862079i	$0.330838\pi$
$113$			18.3281i			1.72416i	−0.506773	+	0.862079i	$0.669162\pi$
$114$	−1.43385			−0.134292
$115$	−8.29489	+	19.7358i	−0.773502	+	1.84037i
$116$	−6.49970	+	6.49970i	−0.603482	+	0.603482i
$117$		−	6.87657i		−	0.635739i
$118$	3.45523	+	3.45523i	0.318080	+	0.318080i
$119$	−1.43979	−	1.43979i	−0.131985	−	0.131985i
$120$	0.844991	+	2.07026i	0.0771368	+	0.188988i
$121$	−1.37173			−0.124703
$122$	9.99355	+	9.99355i	0.904773	+	0.904773i
$123$	−2.46067	−	2.46067i	−0.221871	−	0.221871i
$124$	2.38699	+	2.38699i	0.214358	+	0.214358i
$125$	10.3945	−	4.11747i	0.929716	−	0.368278i
$126$	−0.662100	−	0.662100i	−0.0589845	−	0.0589845i
$127$	−0.247513	+	0.247513i	−0.0219632	+	0.0219632i	−0.718003	−	0.696040i	$-0.754944\pi$
$127$	−0.247513	+	0.247513i	−0.0219632	+	0.0219632i	0.696040	+	0.718003i	$0.254944\pi$
$128$	−1.00000			−0.0883883
$129$	−1.94158	+	1.94158i	−0.170947	+	0.170947i
$130$	5.95785	−	14.1753i	0.522538	−	1.24326i
$131$	−1.31529	−	1.31529i	−0.114917	−	0.114917i	0.647310	−	0.762227i	$-0.275894\pi$
$131$	−1.31529	−	1.31529i	−0.114917	−	0.114917i	−0.762227	+	0.647310i	$0.775894\pi$
$132$	−2.48714	−	2.48714i	−0.216478	−	0.216478i
$133$	1.34259			0.116417
$134$	1.14933	+	1.14933i	0.0992872	+	0.0992872i
$135$	−2.07026	+	0.844991i	−0.178180	+	0.0727253i
$136$		−	2.17458i		−	0.186468i
$137$	−13.6827	+	13.6827i	−1.16899	+	1.16899i	−0.186544	+	0.982447i	$0.559729\pi$
$137$	−13.6827	+	13.6827i	−1.16899	+	1.16899i	−0.982447	+	0.186544i	$0.940271\pi$
$138$	6.76983	−	6.76983i	0.576287	−	0.576287i
$139$	−17.7419			−1.50484			−0.752422	−	0.658681i	$-0.771115\pi$
$139$	−17.7419			−1.50484			−0.752422	+	0.658681i	$0.771115\pi$
$140$	−0.791208	−	1.93849i	−0.0668693	−	0.163832i
$141$			5.07803i			0.427647i
$142$	7.32848			0.614992
$143$			24.1873i			2.02264i
$144$		−	1.00000i		−	0.0833333i
$145$	−7.76713	−	19.0298i	−0.645025	−	1.58034i
$146$	0.292649	−	0.292649i	0.0242198	−	0.0242198i
$147$	−4.32979	−	4.32979i	−0.357115	−	0.357115i
$148$	−5.95481	+	1.24106i	−0.489482	+	0.102015i
$149$		−	10.6094i		−	0.869159i	−0.900633	−	0.434579i	$-0.856897\pi$
$149$		−	10.6094i		−	0.869159i	0.900633	−	0.434579i	$-0.143103\pi$
$150$	−4.99973	−	0.0518094i	−0.408226	−	0.00423022i
$151$		−	3.90183i		−	0.317526i	−0.987317	−	0.158763i	$-0.949249\pi$
$151$		−	3.90183i		−	0.317526i	0.987317	−	0.158763i	$-0.0507506\pi$
$152$	1.01389	+	1.01389i	0.0822370	+	0.0822370i
$153$	2.17458			0.175804
$154$	2.32883	+	2.32883i	0.187663	+	0.187663i
$155$	−6.98861	+	2.85245i	−0.561339	+	0.229114i
$156$	−4.86247	+	4.86247i	−0.389309	+	0.389309i
$157$	1.75656	−	1.75656i	0.140188	−	0.140188i	−0.633530	−	0.773718i	$-0.718395\pi$
$157$	1.75656	−	1.75656i	0.140188	−	0.140188i	0.773718	+	0.633530i	$0.218395\pi$
$158$	−7.95594	−	7.95594i	−0.632940	−	0.632940i
$159$	4.14987			0.329106
$160$	0.866398	−	2.06140i	0.0684948	−	0.162968i
$161$	−6.33894	+	6.33894i	−0.499578	+	0.499578i
$162$	1.00000			0.0785674
$163$		−	9.39725i		−	0.736049i	−0.929816	−	0.368025i	$-0.880034\pi$
$163$		−	9.39725i		−	0.736049i	0.929816	−	0.368025i	$-0.119966\pi$
$164$			3.47992i			0.271736i
$165$	7.28184	−	2.97213i	0.566890	−	0.231380i
$166$	1.46770	+	1.46770i	0.113916	+	0.113916i
$167$			18.3360i			1.41888i	0.704765	+	0.709441i	$0.251052\pi$
$167$			18.3360i			1.41888i	−0.704765	+	0.709441i	$0.748948\pi$
$168$			0.936350i			0.0722410i
$169$	34.2873			2.63748
$170$	4.48266	+	1.88405i	0.343805	+	0.144500i
$171$	−1.01389	+	1.01389i	−0.0775338	+	0.0775338i
$172$	2.74581			0.209366
$173$	5.06991	−	5.06991i	0.385458	−	0.385458i	−0.487606	−	0.873064i	$-0.662130\pi$
$173$	5.06991	−	5.06991i	0.385458	−	0.385458i	0.873064	+	0.487606i	$0.162130\pi$
$174$			9.19196i			0.696841i
$175$	4.68150	+	0.0485117i	0.353888	+	0.00366714i
$176$			3.51735i			0.265130i
$177$	4.88643			0.367287
$178$	6.43088	−	6.43088i	0.482015	−	0.482015i
$179$	14.7313	−	14.7313i	1.10107	−	1.10107i	0.106786	−	0.994282i	$-0.465944\pi$
$179$	14.7313	−	14.7313i	1.10107	−	1.10107i	0.994282	−	0.106786i	$-0.0340560\pi$
$180$	2.06140	+	0.866398i	0.153647	+	0.0645775i
$181$	−4.07298			−0.302742			−0.151371	−	0.988477i	$-0.548369\pi$
$181$	−4.07298			−0.302742			−0.151371	+	0.988477i	$0.548369\pi$
$182$	4.55298	−	4.55298i	0.337489	−	0.337489i
$183$	14.1330			1.04474
$184$	−9.57399			−0.705804
$185$	2.60092	−	13.3505i	0.191223	−	0.981547i
$186$	3.37571			0.247519
$187$	−7.64874			−0.559331
$188$	3.59071	−	3.59071i	0.261879	−	0.261879i
$189$	−0.936350			−0.0681095
$190$	−2.96845	+	1.21159i	−0.215354	+	0.0878981i
$191$	0.841106	−	0.841106i	0.0608603	−	0.0608603i	−0.676022	−	0.736882i	$-0.736297\pi$
$191$	0.841106	−	0.841106i	0.0608603	−	0.0608603i	0.736882	+	0.676022i	$0.236297\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	2.71107			0.195147			0.0975736	−	0.995228i	$-0.468892\pi$
$193$	2.71107			0.195147			0.0975736	+	0.995228i	$0.468892\pi$
$194$			0.301015i			0.0216116i
$195$	−5.81065	−	14.2363i	−0.416109	−	1.01948i
$196$			6.12325i			0.437375i
$197$	14.0103	−	14.0103i	0.998195	−	0.998195i	−0.00180312	−	0.999998i	$-0.500574\pi$
$197$	14.0103	−	14.0103i	0.998195	−	0.998195i	0.999998	+	0.00180312i	$0.000573952\pi$
$198$	−3.51735			−0.249967
$199$	2.28257	−	2.28257i	0.161807	−	0.161807i	−0.621560	−	0.783367i	$-0.713501\pi$
$199$	2.28257	−	2.28257i	0.161807	−	0.161807i	0.783367	+	0.621560i	$0.213501\pi$
$200$	3.49871	+	3.57198i	0.247396	+	0.252577i
$201$	1.62540			0.114647
$202$		−	7.88206i		−	0.554580i
$203$		−	8.60689i		−	0.604085i
$204$	−1.53766	−	1.53766i	−0.107658	−	0.107658i
$205$	−7.17349	−	3.01499i	−0.501018	−	0.210576i
$206$			3.81714i			0.265953i
$207$		−	9.57399i		−	0.665438i
$208$	6.87657			0.476805
$209$	3.56619	−	3.56619i	0.246678	−	0.246678i
$210$	−1.93019	−	0.811252i	−0.133196	−	0.0559817i
$211$	16.7409			1.15249			0.576247	−	0.817276i	$-0.304517\pi$
$211$	16.7409			1.15249			0.576247	+	0.817276i	$0.304517\pi$
$212$	−2.93440	−	2.93440i	−0.201536	−	0.201536i
$213$	5.18202	−	5.18202i	0.355066	−	0.355066i
$214$	3.39625	−	3.39625i	0.232163	−	0.232163i
$215$	−2.37896	+	5.66020i	−0.162244	+	0.386022i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−3.16085			−0.214572
$218$	1.95485	+	1.95485i	0.132399	+	0.132399i
$219$		−	0.413868i		−	0.0279666i
$220$	−7.25065	−	3.04742i	−0.488839	−	0.205457i
$221$			14.9536i			1.00589i
$222$	−3.33312	+	5.08825i	−0.223705	+	0.341501i
$223$	16.5296	+	16.5296i	1.10690	+	1.10690i	0.993555	+	0.113349i	$0.0361580\pi$
$223$	16.5296	+	16.5296i	1.10690	+	1.10690i	0.113349	+	0.993555i	$0.463842\pi$
$224$	0.662100	−	0.662100i	0.0442384	−	0.0442384i
$225$	−3.57198	+	3.49871i	−0.238132	+	0.233247i
$226$		−	18.3281i		−	1.21916i
$227$		−	28.0799i		−	1.86373i	−0.362805	−	0.931865i	$-0.618181\pi$
$227$		−	28.0799i		−	1.86373i	0.362805	−	0.931865i	$-0.381819\pi$
$228$	1.43385			0.0949591
$229$		−	0.286568i		−	0.0189369i	−0.999955	−	0.00946847i	$-0.996986\pi$
$229$		−	0.286568i		−	0.0189369i	0.999955	−	0.00946847i	$-0.00301395\pi$
$230$	8.29489	−	19.7358i	0.546949	−	1.30134i
$231$	3.29347			0.216694
$232$	6.49970	−	6.49970i	0.426726	−	0.426726i
$233$	10.2080	−	10.2080i	0.668751	−	0.668751i	−0.288676	−	0.957427i	$-0.593215\pi$
$233$	10.2080	−	10.2080i	0.668751	−	0.668751i	0.957427	+	0.288676i	$0.0932150\pi$
$234$			6.87657i			0.449536i
$235$	4.29089	+	10.5129i	0.279907	+	0.685783i
$236$	−3.45523	−	3.45523i	−0.224916	−	0.224916i
$237$	−11.2514			−0.730857
$238$	1.43979	+	1.43979i	0.0933275	+	0.0933275i
$239$	−16.6011	−	16.6011i	−1.07384	−	1.07384i	−0.997047	−	0.0767893i	$-0.975533\pi$
$239$	−16.6011	−	16.6011i	−1.07384	−	1.07384i	−0.0767893	−	0.997047i	$-0.524467\pi$
$240$	−0.844991	−	2.07026i	−0.0545440	−	0.133635i
$241$	−17.4511	+	17.4511i	−1.12412	+	1.12412i	−0.133010	+	0.991115i	$0.542464\pi$
$241$	−17.4511	+	17.4511i	−1.12412	+	1.12412i	−0.991115	+	0.133010i	$0.957536\pi$
$242$	1.37173			0.0881784
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−9.99355	−	9.99355i	−0.639771	−	0.639771i
$245$	−12.6224	−	5.30517i	−0.806418	−	0.338935i
$246$	2.46067	+	2.46067i	0.156887	+	0.156887i
$247$	−6.97206	−	6.97206i	−0.443622	−	0.443622i
$248$	−2.38699	−	2.38699i	−0.151574	−	0.151574i
$249$	2.07565			0.131539
$250$	−10.3945	+	4.11747i	−0.657408	+	0.260412i
$251$	−0.992524	−	0.992524i	−0.0626476	−	0.0626476i	0.675089	−	0.737736i	$-0.264105\pi$
$251$	−0.992524	−	0.992524i	−0.0626476	−	0.0626476i	−0.737736	+	0.675089i	$0.764105\pi$
$252$	0.662100	+	0.662100i	0.0417084	+	0.0417084i
$253$			33.6751i			2.11713i
$254$	0.247513	−	0.247513i	0.0155303	−	0.0155303i
$255$	4.50195	−	1.83750i	0.281923	−	0.115069i
$256$	1.00000			0.0625000
$257$		−	9.19465i		−	0.573546i	−0.957998	−	0.286773i	$-0.907417\pi$
$257$		−	9.19465i		−	0.573546i	0.957998	−	0.286773i	$-0.0925826\pi$
$258$	1.94158	−	1.94158i	0.120877	−	0.120877i
$259$	3.12097	−	4.76438i	0.193928	−	0.296044i
$260$	−5.95785	+	14.1753i	−0.369490	+	0.879118i
$261$	6.49970	+	6.49970i	0.402321	+	0.402321i
$262$	1.31529	+	1.31529i	0.0812588	+	0.0812588i
$263$	10.1321	−	10.1321i	0.624774	−	0.624774i	−0.321974	−	0.946748i	$-0.604346\pi$
$263$	10.1321	−	10.1321i	0.624774	−	0.624774i	0.946748	+	0.321974i	$0.104346\pi$
$264$	2.48714	+	2.48714i	0.153073	+	0.153073i
$265$	8.59132	−	3.50660i	0.527761	−	0.215409i
$266$	−1.34259			−0.0823193
$267$		−	9.09463i		−	0.556582i
$268$	−1.14933	−	1.14933i	−0.0702067	−	0.0702067i
$269$			25.8428i			1.57566i	0.615890	+	0.787832i	$0.288796\pi$
$269$			25.8428i			1.57566i	−0.615890	+	0.787832i	$0.711204\pi$
$270$	2.07026	−	0.844991i	0.125992	−	0.0514245i
$271$	19.0523			1.15734			0.578672	−	0.815561i	$-0.303571\pi$
$271$	19.0523			1.15734			0.578672	+	0.815561i	$0.303571\pi$
$272$			2.17458i			0.131853i
$273$		−	6.43888i		−	0.389699i
$274$	13.6827	−	13.6827i	0.826601	−	0.826601i
$275$	12.5639	−	12.3062i	0.757631	−	0.742090i
$276$	−6.76983	+	6.76983i	−0.407496	+	0.407496i
$277$	2.31001			0.138795			0.0693974	−	0.997589i	$-0.477892\pi$
$277$	2.31001			0.138795			0.0693974	+	0.997589i	$0.477892\pi$
$278$	17.7419			1.06409
$279$	2.38699	−	2.38699i	0.142905	−	0.142905i
$280$	0.791208	+	1.93849i	0.0472837	+	0.115847i
$281$	−13.8796	+	13.8796i	−0.827987	+	0.827987i	−0.987238	−	0.159251i	$-0.949092\pi$
$281$	−13.8796	+	13.8796i	−0.827987	+	0.827987i	0.159251	+	0.987238i	$0.449092\pi$
$282$		−	5.07803i		−	0.302392i
$283$			20.9115i			1.24306i	0.783389	+	0.621531i	$0.213489\pi$
$283$			20.9115i			1.24306i	−0.783389	+	0.621531i	$0.786511\pi$
$284$	−7.32848			−0.434865
$285$	−1.24229	+	2.95573i	−0.0735866	+	0.175083i
$286$		−	24.1873i		−	1.43023i
$287$	−2.30405	−	2.30405i	−0.136004	−	0.136004i
$288$			1.00000i			0.0589256i
$289$	12.2712			0.721836
$290$	7.76713	+	19.0298i	0.456101	+	1.11747i
$291$	0.212850	+	0.212850i	0.0124775	+	0.0124775i
$292$	−0.292649	+	0.292649i	−0.0171260	+	0.0171260i
$293$	−6.11142	−	6.11142i	−0.357033	−	0.357033i	0.505685	−	0.862718i	$-0.331240\pi$
$293$	−6.11142	−	6.11142i	−0.357033	−	0.357033i	−0.862718	+	0.505685i	$0.831240\pi$
$294$	4.32979	+	4.32979i	0.252518	+	0.252518i
$295$	10.1162	−	4.12899i	0.588988	−	0.240399i
$296$	5.95481	−	1.24106i	0.346116	−	0.0721352i
$297$	−2.48714	+	2.48714i	−0.144319	+	0.144319i
$298$			10.6094i			0.614588i
$299$	65.8363			3.80741
$300$	4.99973	+	0.0518094i	0.288660	+	0.00299122i
$301$	−1.81800	+	1.81800i	−0.104788	+	0.104788i
$302$			3.90183i			0.224525i
$303$	−5.57346	−	5.57346i	−0.320187	−	0.320187i
$304$	−1.01389	−	1.01389i	−0.0581503	−	0.0581503i
$305$	29.2590	−	11.9423i	1.67537	−	0.683812i
$306$	−2.17458			−0.124312
$307$	11.2957	+	11.2957i	0.644681	+	0.644681i	0.951703	−	0.307022i	$-0.0993324\pi$
$307$	11.2957	+	11.2957i	0.644681	+	0.644681i	−0.307022	+	0.951703i	$0.599332\pi$
$308$	−2.32883	−	2.32883i	−0.132698	−	0.132698i
$309$	2.69912	+	2.69912i	0.153548	+	0.153548i
$310$	6.98861	−	2.85245i	0.396927	−	0.162008i
$311$	9.84746	+	9.84746i	0.558398	+	0.558398i	0.928851	−	0.370453i	$-0.120798\pi$
$311$	9.84746	+	9.84746i	0.558398	+	0.558398i	−0.370453	+	0.928851i	$0.620798\pi$
$312$	4.86247	−	4.86247i	0.275283	−	0.275283i
$313$	−12.1322			−0.685752			−0.342876	−	0.939381i	$-0.611401\pi$
$313$	−12.1322			−0.685752			−0.342876	+	0.939381i	$0.611401\pi$
$314$	−1.75656	+	1.75656i	−0.0991282	+	0.0991282i
$315$	−1.93849	+	0.791208i	−0.109222	+	0.0445795i
$316$	7.95594	+	7.95594i	0.447556	+	0.447556i
$317$	−9.66544	−	9.66544i	−0.542865	−	0.542865i	0.381502	−	0.924368i	$-0.375407\pi$
$317$	−9.66544	−	9.66544i	−0.542865	−	0.542865i	−0.924368	+	0.381502i	$0.875407\pi$
$318$	−4.14987			−0.232713
$319$	−22.8617	−	22.8617i	−1.28001	−	1.28001i
$320$	−0.866398	+	2.06140i	−0.0484331	+	0.115236i
$321$		−	4.80302i		−	0.268079i
$322$	6.33894	−	6.33894i	0.353255	−	0.353255i
$323$	2.20477	−	2.20477i	0.122677	−	0.122677i
$324$	−1.00000			−0.0555556
$325$	−24.0591	−	24.5630i	−1.33456	−	1.36251i
$326$			9.39725i			0.520465i
$327$	2.76458			0.152882
$328$		−	3.47992i		−	0.192146i
$329$			4.75481i			0.262141i
$330$	−7.28184	+	2.97213i	−0.400852	+	0.163610i
$331$	23.0765	−	23.0765i	1.26840	−	1.26840i	0.321487	−	0.946914i	$-0.395817\pi$
$331$	23.0765	−	23.0765i	1.26840	−	1.26840i	0.946914	−	0.321487i	$-0.104183\pi$
$332$	−1.46770	−	1.46770i	−0.0805508	−	0.0805508i
$333$	1.24106	+	5.95481i	0.0680097	+	0.326322i
$334$		−	18.3360i		−	1.00330i
$335$	3.36501	−	1.37345i	0.183850	−	0.0750396i
$336$		−	0.936350i		−	0.0510821i
$337$	10.8978	+	10.8978i	0.593640	+	0.593640i	0.938613	−	0.344973i	$-0.112112\pi$
$337$	10.8978	+	10.8978i	0.593640	+	0.593640i	−0.344973	+	0.938613i	$0.612112\pi$
$338$	−34.2873			−1.86498
$339$	−12.9599	−	12.9599i	−0.703885	−	0.703885i
$340$	−4.48266	−	1.88405i	−0.243107	−	0.102177i
$341$	−8.39587	+	8.39587i	−0.454662	+	0.454662i
$342$	1.01389	−	1.01389i	0.0548247	−	0.0548247i
$343$	−8.68890	−	8.68890i	−0.469156	−	0.469156i
$344$	−2.74581			−0.148044
$345$	−8.08994	−	19.8207i	−0.435548	−	1.06711i
$346$	−5.06991	+	5.06991i	−0.272560	+	0.272560i
$347$	0.330476			0.0177409			0.00887043	−	0.999961i	$-0.497176\pi$
$347$	0.330476			0.0177409			0.00887043	+	0.999961i	$0.497176\pi$
$348$		−	9.19196i		−	0.492741i
$349$			35.7141i			1.91173i	0.293799	+	0.955867i	$0.405080\pi$
$349$			35.7141i			1.91173i	−0.293799	+	0.955867i	$0.594920\pi$
$350$	−4.68150	−	0.0485117i	−0.250237	−	0.00259306i
$351$	4.86247	+	4.86247i	0.259540	+	0.259540i
$352$		−	3.51735i		−	0.187475i
$353$		−	19.1728i		−	1.02047i	−0.860036	−	0.510233i	$-0.829559\pi$
$353$		−	19.1728i		−	1.02047i	0.860036	−	0.510233i	$-0.170441\pi$
$354$	−4.88643			−0.259711
$355$	6.34938	−	15.1069i	0.336990	−	0.801791i
$356$	−6.43088	+	6.43088i	−0.340836	+	0.340836i
$357$	2.03617			0.107765
$358$	−14.7313	+	14.7313i	−0.778573	+	0.778573i
$359$			6.91664i			0.365046i	0.983202	+	0.182523i	$0.0584264\pi$
$359$			6.91664i			0.365046i	−0.983202	+	0.182523i	$0.941574\pi$
$360$	−2.06140	−	0.866398i	−0.108645	−	0.0456632i
$361$		−	16.9441i		−	0.891793i
$362$	4.07298			0.214071
$363$	0.969963	−	0.969963i	0.0509098	−	0.0509098i
$364$	−4.55298	+	4.55298i	−0.238641	+	0.238641i
$365$	−0.349715	−	0.856815i	−0.0183049	−	0.0448477i
$366$	−14.1330			−0.738744
$367$	17.2144	−	17.2144i	0.898582	−	0.898582i	−0.0967284	−	0.995311i	$-0.530838\pi$
$367$	17.2144	−	17.2144i	0.898582	−	0.898582i	0.995311	+	0.0967284i	$0.0308378\pi$
$368$	9.57399			0.499079
$369$	3.47992			0.181157
$370$	−2.60092	+	13.3505i	−0.135215	+	0.694058i
$371$	3.88573			0.201737
$372$	−3.37571			−0.175023
$373$	−13.8033	+	13.8033i	−0.714705	+	0.714705i	−0.967516	−	0.252811i	$-0.918645\pi$
$373$	−13.8033	+	13.8033i	−0.714705	+	0.714705i	0.252811	+	0.967516i	$0.418645\pi$
$374$	7.64874			0.395507
$375$	−4.43856	+	10.2615i	−0.229206	+	0.529904i
$376$	−3.59071	+	3.59071i	−0.185177	+	0.185177i
$377$	−44.6956	+	44.6956i	−2.30194	+	2.30194i
$378$	0.936350			0.0481607
$379$			0.729632i			0.0374787i	0.999824	+	0.0187393i	$0.00596527\pi$
$379$			0.729632i			0.0374787i	−0.999824	+	0.0187393i	$0.994035\pi$
$380$	2.96845	−	1.21159i	0.152278	−	0.0621533i
$381$		−	0.350036i		−	0.0179329i
$382$	−0.841106	+	0.841106i	−0.0430347	+	0.0430347i
$383$	28.2223			1.44209			0.721047	−	0.692887i	$-0.243661\pi$
$383$	28.2223			1.44209			0.721047	+	0.692887i	$0.243661\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	6.81835	−	2.78295i	0.347495	−	0.141832i
$386$	−2.71107			−0.137990
$387$		−	2.74581i		−	0.139577i
$388$		−	0.301015i		−	0.0152817i
$389$	−15.3299	−	15.3299i	−0.777258	−	0.777258i	0.202106	−	0.979364i	$-0.435222\pi$
$389$	−15.3299	−	15.3299i	−0.777258	−	0.777258i	−0.979364	+	0.202106i	$0.935222\pi$
$390$	5.81065	+	14.2363i	0.294234	+	0.720884i
$391$			20.8194i			1.05288i
$392$		−	6.12325i		−	0.309271i
$393$	1.86010			0.0938295
$394$	−14.0103	+	14.0103i	−0.705831	+	0.705831i
$395$	−23.2933	+	9.50733i	−1.17202	+	0.478366i
$396$	3.51735			0.176753
$397$	9.07360	+	9.07360i	0.455391	+	0.455391i	0.897139	−	0.441748i	$-0.145642\pi$
$397$	9.07360	+	9.07360i	0.455391	+	0.455391i	−0.441748	+	0.897139i	$0.645642\pi$
$398$	−2.28257	+	2.28257i	−0.114415	+	0.114415i
$399$	−0.949352	+	0.949352i	−0.0475271	+	0.0475271i
$400$	−3.49871	−	3.57198i	−0.174935	−	0.178599i
$401$	−23.0577	−	23.0577i	−1.15144	−	1.15144i	−0.986263	−	0.165182i	$-0.947179\pi$
$401$	−23.0577	−	23.0577i	−1.15144	−	1.15144i	−0.165182	−	0.986263i	$-0.552821\pi$
$402$	−1.62540			−0.0810677
$403$	16.4143	+	16.4143i	0.817655	+	0.817655i
$404$			7.88206i			0.392147i
$405$	0.866398	−	2.06140i	0.0430517	−	0.102432i
$406$			8.60689i			0.427153i
$407$	−4.36524	−	20.9451i	−0.216377	−	1.03821i
$408$	1.53766	+	1.53766i	0.0761254	+	0.0761254i
$409$	12.7245	−	12.7245i	0.629185	−	0.629185i	−0.318678	−	0.947863i	$-0.603239\pi$
$409$	12.7245	−	12.7245i	0.629185	−	0.629185i	0.947863	+	0.318678i	$0.103239\pi$
$410$	7.17349	+	3.01499i	0.354273	+	0.148900i
$411$		−	19.3502i		−	0.954477i
$412$		−	3.81714i		−	0.188057i
$413$	4.57541			0.225141
$414$			9.57399i			0.470536i
$415$	4.29714	−	1.75390i	0.210938	−	0.0860958i
$416$	−6.87657			−0.337152
$417$	12.5454	−	12.5454i	0.614350	−	0.614350i
$418$	−3.56619	+	3.56619i	−0.174428	+	0.174428i
$419$		−	4.07751i		−	0.199200i	−0.995028	−	0.0995998i	$-0.968244\pi$
$419$		−	4.07751i		−	0.199200i	0.995028	−	0.0995998i	$-0.0317563\pi$
$420$	1.93019	+	0.811252i	0.0941836	+	0.0395850i
$421$	−5.38925	−	5.38925i	−0.262656	−	0.262656i	0.563476	−	0.826132i	$-0.309464\pi$
$421$	−5.38925	−	5.38925i	−0.262656	−	0.262656i	−0.826132	+	0.563476i	$0.809464\pi$
$422$	−16.7409			−0.814936
$423$	−3.59071	−	3.59071i	−0.174586	−	0.174586i
$424$	2.93440	+	2.93440i	0.142507	+	0.142507i
$425$	7.76754	−	7.60821i	0.376781	−	0.369052i
$426$	−5.18202	+	5.18202i	−0.251070	+	0.251070i
$427$	13.2334			0.640411
$428$	−3.39625	+	3.39625i	−0.164164	+	0.164164i
$429$	−17.1030	−	17.1030i	−0.825741	−	0.825741i
$430$	2.37896	−	5.66020i	0.114724	−	0.272959i
$431$	9.41260	+	9.41260i	0.453389	+	0.453389i	0.896478	−	0.443089i	$-0.146117\pi$
$431$	9.41260	+	9.41260i	0.453389	+	0.453389i	−0.443089	+	0.896478i	$0.646117\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	18.0950	+	18.0950i	0.869588	+	0.869588i	0.992427	−	0.122839i	$-0.0391998\pi$
$433$	18.0950	+	18.0950i	0.869588	+	0.869588i	−0.122839	+	0.992427i	$0.539200\pi$
$434$	3.16085			0.151726
$435$	18.9483	+	7.96389i	0.908500	+	0.381840i
$436$	−1.95485	−	1.95485i	−0.0936205	−	0.0936205i
$437$	−9.70693	−	9.70693i	−0.464346	−	0.464346i
$438$			0.413868i			0.0197754i
$439$	−3.41744	+	3.41744i	−0.163106	+	0.163106i	−0.783941	−	0.620835i	$-0.786794\pi$
$439$	−3.41744	+	3.41744i	−0.163106	+	0.163106i	0.620835	+	0.783941i	$0.286794\pi$
$440$	7.25065	+	3.04742i	0.345661	+	0.145280i
$441$	6.12325			0.291583
$442$		−	14.9536i		−	0.711272i
$443$	−10.8466	+	10.8466i	−0.515340	+	0.515340i	−0.916158	−	0.400818i	$-0.868726\pi$
$443$	−10.8466	+	10.8466i	−0.515340	+	0.515340i	0.400818	+	0.916158i	$0.368726\pi$
$444$	3.33312	−	5.08825i	0.158183	−	0.241478i
$445$	−7.68489	−	18.8283i	−0.364299	−	0.892546i
$446$	−16.5296	−	16.5296i	−0.782700	−	0.782700i
$447$	7.50200	+	7.50200i	0.354833	+	0.354833i
$448$	−0.662100	+	0.662100i	−0.0312813	+	0.0312813i
$449$	10.3811	+	10.3811i	0.489913	+	0.489913i	0.908279	−	0.418366i	$-0.137397\pi$
$449$	10.3811	+	10.3811i	0.489913	+	0.489913i	−0.418366	+	0.908279i	$0.637397\pi$
$450$	3.57198	−	3.49871i	0.168385	−	0.164931i
$451$	−12.2401			−0.576363
$452$			18.3281i			0.862079i
$453$	2.75901	+	2.75901i	0.129630	+	0.129630i
$454$			28.0799i			1.31786i
$455$	−5.44080	−	13.3302i	−0.255069	−	0.624928i
$456$	−1.43385			−0.0671462
$457$			13.7780i			0.644509i	0.946653	+	0.322254i	$0.104441\pi$
$457$			13.7780i			0.644509i	−0.946653	+	0.322254i	$0.895559\pi$
$458$			0.286568i			0.0133904i
$459$	−1.53766	+	1.53766i	−0.0717717	+	0.0717717i
$460$	−8.29489	+	19.7358i	−0.386751	+	0.920186i
$461$	−28.3555	+	28.3555i	−1.32065	+	1.32065i	−0.407393	+	0.913253i	$0.633562\pi$
$461$	−28.3555	+	28.3555i	−1.32065	+	1.32065i	−0.913253	+	0.407393i	$0.866438\pi$
$462$	−3.29347			−0.153226
$463$	−27.1414			−1.26137			−0.630683	−	0.776040i	$-0.717225\pi$
$463$	−27.1414			−1.26137			−0.630683	+	0.776040i	$0.717225\pi$
$464$	−6.49970	+	6.49970i	−0.301741	+	0.301741i
$465$	2.92471	−	6.95868i	0.135630	−	0.322701i
$466$	−10.2080	+	10.2080i	−0.472878	+	0.472878i
$467$		−	15.3540i		−	0.710500i	−0.934771	−	0.355250i	$-0.884396\pi$
$467$		−	15.3540i		−	0.710500i	0.934771	−	0.355250i	$-0.115604\pi$
$468$		−	6.87657i		−	0.317870i
$469$	1.52195			0.0702769
$470$	−4.29089	−	10.5129i	−0.197924	−	0.484922i
$471$			2.48415i			0.114463i
$472$	3.45523	+	3.45523i	0.159040	+	0.159040i
$473$			9.65796i			0.444074i
$474$	11.2514			0.516794
$475$	−0.0742869	+	7.16887i	−0.00340852	+	0.328930i
$476$	−1.43979	−	1.43979i	−0.0659925	−	0.0659925i
$477$	−2.93440	+	2.93440i	−0.134357	+	0.134357i
$478$	16.6011	+	16.6011i	0.759317	+	0.759317i
$479$	11.3006	+	11.3006i	0.516338	+	0.516338i	0.916461	−	0.400123i	$-0.131033\pi$
$479$	11.3006	+	11.3006i	0.516338	+	0.516338i	−0.400123	+	0.916461i	$0.631033\pi$
$480$	0.844991	+	2.07026i	0.0385684	+	0.0944942i
$481$	−40.9487	+	8.53425i	−1.86710	+	0.389128i
$482$	17.4511	−	17.4511i	0.794876	−	0.794876i
$483$		−	8.96461i		−	0.407904i
$484$	−1.37173			−0.0623516
$485$	0.620511	+	0.260799i	0.0281760	+	0.0118423i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$			21.7950i			0.987628i	0.869568	+	0.493814i	$0.164398\pi$
$487$			21.7950i			0.987628i	−0.869568	+	0.493814i	$0.835602\pi$
$488$	9.99355	+	9.99355i	0.452387	+	0.452387i
$489$	6.64486	+	6.64486i	0.300491	+	0.300491i
$490$	12.6224	+	5.30517i	0.570224	+	0.239663i
$491$	−6.69716			−0.302239			−0.151119	−	0.988516i	$-0.548288\pi$
$491$	−6.69716			−0.302239			−0.151119	+	0.988516i	$0.548288\pi$
$492$	−2.46067	−	2.46067i	−0.110936	−	0.110936i
$493$	−14.1341	−	14.1341i	−0.636567	−	0.636567i
$494$	6.97206	+	6.97206i	0.313688	+	0.313688i
$495$	−3.04742	+	7.25065i	−0.136971	+	0.325892i
$496$	2.38699	+	2.38699i	0.107179	+	0.107179i
$497$	4.85218	−	4.85218i	0.217650	−	0.217650i
$498$	−2.07565			−0.0930120
$499$	−31.1536	+	31.1536i	−1.39463	+	1.39463i	−0.580034	+	0.814592i	$0.696961\pi$
$499$	−31.1536	+	31.1536i	−1.39463	+	1.39463i	−0.814592	+	0.580034i	$0.803039\pi$
$500$	10.3945	−	4.11747i	0.464858	−	0.184139i
$501$	−12.9655	−	12.9655i	−0.579256	−	0.579256i
$502$	0.992524	+	0.992524i	0.0442985	+	0.0442985i
$503$	−0.724954			−0.0323241			−0.0161621	−	0.999869i	$-0.505145\pi$
$503$	−0.724954			−0.0323241			−0.0161621	+	0.999869i	$0.505145\pi$
$504$	−0.662100	−	0.662100i	−0.0294923	−	0.0294923i
$505$	−16.2480	−	6.82900i	−0.723029	−	0.303886i
$506$		−	33.6751i		−	1.49704i
$507$	−24.2448	+	24.2448i	−1.07675	+	1.07675i
$508$	−0.247513	+	0.247513i	−0.0109816	+	0.0109816i
$509$	−23.7296			−1.05180			−0.525899	−	0.850547i	$-0.676271\pi$
$509$	−23.7296			−1.05180			−0.525899	+	0.850547i	$0.676271\pi$
$510$	−4.50195	+	1.83750i	−0.199350	+	0.0813658i
$511$		−	0.387525i		−	0.0171431i
$512$	−1.00000			−0.0441942
$513$		−	1.43385i		−	0.0633061i
$514$			9.19465i			0.405559i
$515$	7.86864	+	3.30716i	0.346734	+	0.145731i
$516$	−1.94158	+	1.94158i	−0.0854733	+	0.0854733i
$517$	12.6298	+	12.6298i	0.555456	+	0.555456i
$518$	−3.12097	+	4.76438i	−0.137128	+	0.209335i
$519$			7.16994i			0.314725i
$520$	5.95785	−	14.1753i	0.261269	−	0.621630i
$521$		−	23.1177i		−	1.01281i	−0.862297	−	0.506403i	$-0.830975\pi$
$521$		−	23.1177i		−	1.01281i	0.862297	−	0.506403i	$-0.169025\pi$
$522$	−6.49970	−	6.49970i	−0.284484	−	0.284484i
$523$	15.4427			0.675261			0.337631	−	0.941279i	$-0.390375\pi$
$523$	15.4427			0.675261			0.337631	+	0.941279i	$0.390375\pi$
$524$	−1.31529	−	1.31529i	−0.0574586	−	0.0574586i
$525$	−3.34462	+	3.27602i	−0.145971	+	0.142977i
$526$	−10.1321	+	10.1321i	−0.441782	+	0.441782i
$527$	−5.19069	+	5.19069i	−0.226110	+	0.226110i
$528$	−2.48714	−	2.48714i	−0.108239	−	0.108239i
$529$	68.6613			2.98528
$530$	−8.59132	+	3.50660i	−0.373183	+	0.152317i
$531$	−3.45523	+	3.45523i	−0.149944	+	0.149944i
$532$	1.34259			0.0582085
$533$			23.9299i			1.03652i
$534$			9.09463i			0.393563i
$535$	−4.05851	−	9.94353i	−0.175465	−	0.429896i
$536$	1.14933	+	1.14933i	0.0496436	+	0.0496436i
$537$			20.8332i			0.899018i
$538$		−	25.8428i		−	1.11416i
$539$	−21.5376			−0.927690
$540$	−2.07026	+	0.844991i	−0.0890899	+	0.0363626i
$541$	3.85083	−	3.85083i	0.165560	−	0.165560i	−0.619465	−	0.785025i	$-0.712650\pi$
$541$	3.85083	−	3.85083i	0.165560	−	0.165560i	0.785025	+	0.619465i	$0.212650\pi$
$542$	−19.0523			−0.818365
$543$	2.88003	−	2.88003i	0.123594	−	0.123594i
$544$		−	2.17458i		−	0.0932342i
$545$	5.72341	−	2.33605i	0.245164	−	0.100065i
$546$			6.43888i			0.275559i
$547$	5.49141			0.234796			0.117398	−	0.993085i	$-0.462545\pi$
$547$	5.49141			0.234796			0.117398	+	0.993085i	$0.462545\pi$
$548$	−13.6827	+	13.6827i	−0.584495	+	0.584495i
$549$	−9.99355	+	9.99355i	−0.426514	+	0.426514i
$550$	−12.5639	+	12.3062i	−0.535726	+	0.524737i
$551$	13.1799			0.561483
$552$	6.76983	−	6.76983i	0.288143	−	0.288143i
$553$	−10.5352			−0.448004
$554$	−2.31001			−0.0981428
$555$	7.60109	+	11.2793i	0.322648	+	0.478781i
$556$	−17.7419			−0.752422
$557$	−20.3979			−0.864285			−0.432142	−	0.901805i	$-0.642242\pi$
$557$	−20.3979			−0.864285			−0.432142	+	0.901805i	$0.642242\pi$
$558$	−2.38699	+	2.38699i	−0.101049	+	0.101049i
$559$	18.8818			0.798613
$560$	−0.791208	−	1.93849i	−0.0334346	−	0.0819162i
$561$	5.40848	−	5.40848i	0.228346	−	0.228346i
$562$	13.8796	−	13.8796i	0.585475	−	0.585475i
$563$	41.6497			1.75533			0.877663	−	0.479278i	$-0.159101\pi$
$563$	41.6497			1.75533			0.877663	+	0.479278i	$0.159101\pi$
$564$			5.07803i			0.213824i
$565$	−37.7814	−	15.8794i	−1.58948	−	0.668051i
$566$		−	20.9115i		−	0.878978i
$567$	0.662100	−	0.662100i	0.0278056	−	0.0278056i
$568$	7.32848			0.307496
$569$	29.9799	−	29.9799i	1.25682	−	1.25682i	0.304220	−	0.952602i	$-0.401604\pi$
$569$	29.9799	−	29.9799i	1.25682	−	1.25682i	0.952602	−	0.304220i	$-0.0983957\pi$
$570$	1.24229	−	2.95573i	0.0520336	−	0.123802i
$571$	−33.5003			−1.40195			−0.700973	−	0.713188i	$-0.747250\pi$
$571$	−33.5003			−1.40195			−0.700973	+	0.713188i	$0.747250\pi$
$572$			24.1873i			1.01132i
$573$			1.18950i			0.0496922i
$574$	2.30405	+	2.30405i	0.0961693	+	0.0961693i
$575$	−33.4966	−	34.1981i	−1.39691	−	1.42616i
$576$		−	1.00000i		−	0.0416667i
$577$		−	11.2900i		−	0.470008i	−0.971994	−	0.235004i	$-0.924490\pi$
$577$		−	11.2900i		−	0.470008i	0.971994	−	0.235004i	$-0.0755104\pi$
$578$	−12.2712			−0.510415
$579$	−1.91702	+	1.91702i	−0.0796685	+	0.0796685i
$580$	−7.76713	−	19.0298i	−0.322512	−	0.790168i
$581$	1.94353			0.0806313
$582$	−0.212850	−	0.212850i	−0.00882291	−	0.00882291i
$583$	10.3213	−	10.3213i	0.427465	−	0.427465i
$584$	0.292649	−	0.292649i	0.0121099	−	0.0121099i
$585$	14.1753	+	5.95785i	0.586078	+	0.246327i
$586$	6.11142	+	6.11142i	0.252461	+	0.252461i
$587$	−0.261793			−0.0108053			−0.00540267	−	0.999985i	$-0.501720\pi$
$587$	−0.261793			−0.0108053			−0.00540267	+	0.999985i	$0.501720\pi$
$588$	−4.32979	−	4.32979i	−0.178558	−	0.178558i
$589$		−	4.84027i		−	0.199440i
$590$	−10.1162	+	4.12899i	−0.416477	+	0.169988i
$591$			19.8136i			0.815023i
$592$	−5.95481	+	1.24106i	−0.244741	+	0.0510073i
$593$	−23.9024	−	23.9024i	−0.981553	−	0.981553i	0.0182800	−	0.999833i	$-0.494181\pi$
$593$	−23.9024	−	23.9024i	−0.981553	−	0.981553i	−0.999833	+	0.0182800i	$0.994181\pi$
$594$	2.48714	−	2.48714i	0.102049	−	0.102049i
$595$	4.21540	−	1.72054i	0.172814	−	0.0705354i
$596$		−	10.6094i		−	0.434579i
$597$			3.22805i			0.132115i
$598$	−65.8363			−2.69225
$599$			40.4441i			1.65250i	0.563303	+	0.826251i	$0.309530\pi$
$599$			40.4441i			1.65250i	−0.563303	+	0.826251i	$0.690470\pi$
$600$	−4.99973	−	0.0518094i	−0.204113	−	0.00211511i
$601$	38.4258			1.56742			0.783710	−	0.621127i	$-0.213325\pi$
$601$	38.4258			1.56742			0.783710	+	0.621127i	$0.213325\pi$
$602$	1.81800	−	1.81800i	0.0740961	−	0.0740961i
$603$	−1.14933	+	1.14933i	−0.0468044	+	0.0468044i
$604$		−	3.90183i		−	0.158763i
$605$	1.18847	−	2.82769i	0.0483181	−	0.114962i
$606$	5.57346	+	5.57346i	0.226406	+	0.226406i
$607$	−14.3687			−0.583208			−0.291604	−	0.956539i	$-0.594189\pi$
$607$	−14.3687			−0.583208			−0.291604	+	0.956539i	$0.594189\pi$
$608$	1.01389	+	1.01389i	0.0411185	+	0.0411185i
$609$	6.08599	+	6.08599i	0.246617	+	0.246617i
$610$	−29.2590	+	11.9423i	−1.18466	+	0.483528i
$611$	24.6918	−	24.6918i	0.998922	−	0.998922i
$612$	2.17458			0.0879020
$613$	−10.7011	+	10.7011i	−0.432213	+	0.432213i	−0.889381	−	0.457167i	$-0.848864\pi$
$613$	−10.7011	+	10.7011i	−0.432213	+	0.432213i	0.457167	+	0.889381i	$0.348864\pi$
$614$	−11.2957	−	11.2957i	−0.455858	−	0.455858i
$615$	7.20434	−	2.94050i	0.290507	−	0.118572i
$616$	2.32883	+	2.32883i	0.0938314	+	0.0938314i
$617$	14.0957	+	14.0957i	0.567470	+	0.567470i	0.931419	−	0.363949i	$-0.118572\pi$
$617$	14.0957	+	14.0957i	0.567470	+	0.567470i	−0.363949	+	0.931419i	$0.618572\pi$
$618$	−2.69912	−	2.69912i	−0.108575	−	0.108575i
$619$	−4.28502			−0.172230			−0.0861148	−	0.996285i	$-0.527445\pi$
$619$	−4.28502			−0.172230			−0.0861148	+	0.996285i	$0.527445\pi$
$620$	−6.98861	+	2.85245i	−0.280669	+	0.114557i
$621$	6.76983	+	6.76983i	0.271664	+	0.271664i
$622$	−9.84746	−	9.84746i	−0.394847	−	0.394847i
$623$		−	8.51576i		−	0.341177i
$624$	−4.86247	+	4.86247i	−0.194655	+	0.194655i
$625$	−0.518066	+	24.9946i	−0.0207226	+	0.999785i
$626$	12.1322			0.484900
$627$			5.04335i			0.201412i
$628$	1.75656	−	1.75656i	0.0700942	−	0.0700942i
$629$	−2.69878	−	12.9492i	−0.107607	−	0.516318i
$630$	1.93849	−	0.791208i	0.0772313	−	0.0315225i
$631$	−10.5038	−	10.5038i	−0.418149	−	0.418149i	0.466416	−	0.884565i	$-0.345545\pi$
$631$	−10.5038	−	10.5038i	−0.418149	−	0.418149i	−0.884565	+	0.466416i	$0.845545\pi$
$632$	−7.95594	−	7.95594i	−0.316470	−	0.316470i
$633$	−11.8376	+	11.8376i	−0.470504	+	0.470504i
$634$	9.66544	+	9.66544i	0.383864	+	0.383864i
$635$	−0.295777	−	0.724667i	−0.0117376	−	0.0287575i
$636$	4.14987			0.164553
$637$			42.1070i			1.66834i
$638$	22.8617	+	22.8617i	0.905103	+	0.905103i
$639$			7.32848i			0.289910i
$640$	0.866398	−	2.06140i	0.0342474	−	0.0814838i
$641$	41.6777			1.64617			0.823085	−	0.567919i	$-0.192251\pi$
$641$	41.6777			1.64617			0.823085	+	0.567919i	$0.192251\pi$
$642$			4.80302i			0.189560i
$643$			25.1480i			0.991742i	0.868396	+	0.495871i	$0.165151\pi$
$643$			25.1480i			0.991742i	−0.868396	+	0.495871i	$0.834849\pi$
$644$	−6.33894	+	6.33894i	−0.249789	+	0.249789i
$645$	−2.32018	−	5.68455i	−0.0913572	−	0.223829i
$646$	−2.20477	+	2.20477i	−0.0867456	+	0.0867456i
$647$	−29.9330			−1.17679			−0.588394	−	0.808575i	$-0.700239\pi$
$647$	−29.9330			−1.17679			−0.588394	+	0.808575i	$0.700239\pi$
$648$	1.00000			0.0392837
$649$	12.1532	−	12.1532i	0.477057	−	0.477057i
$650$	24.0591	+	24.5630i	0.943677	+	0.963439i
$651$	2.23506	−	2.23506i	0.0875988	−	0.0875988i
$652$		−	9.39725i		−	0.368025i
$653$		−	16.5783i		−	0.648759i	−0.945927	−	0.324380i	$-0.894844\pi$
$653$		−	16.5783i		−	0.648759i	0.945927	−	0.324380i	$-0.105156\pi$
$654$	−2.76458			−0.108104
$655$	3.85089	−	1.57177i	0.150467	−	0.0614140i
$656$			3.47992i			0.135868i
$657$	0.292649	+	0.292649i	0.0114173	+	0.0114173i
$658$		−	4.75481i		−	0.185362i
$659$	19.3767			0.754807			0.377404	−	0.926049i	$-0.376817\pi$
$659$	19.3767			0.754807			0.377404	+	0.926049i	$0.376817\pi$
$660$	7.28184	−	2.97213i	0.283445	−	0.115690i
$661$	−11.4801	−	11.4801i	−0.446523	−	0.446523i	0.447674	−	0.894197i	$-0.352252\pi$
$661$	−11.4801	−	11.4801i	−0.446523	−	0.446523i	−0.894197	+	0.447674i	$0.852252\pi$
$662$	−23.0765	+	23.0765i	−0.896895	+	0.896895i
$663$	−10.5738	−	10.5738i	−0.410653	−	0.410653i
$664$	1.46770	+	1.46770i	0.0569580	+	0.0569580i
$665$	−1.16321	+	2.76760i	−0.0451075	+	0.107323i
$666$	−1.24106	−	5.95481i	−0.0480901	−	0.230744i
$667$	−62.2280	+	62.2280i	−2.40948	+	2.40948i
$668$			18.3360i			0.709441i
$669$	−23.3764			−0.903784
$670$	−3.36501	+	1.37345i	−0.130002	+	0.0530610i
$671$	35.1508	−	35.1508i	1.35698	−	1.35698i
$672$			0.936350i			0.0361205i
$673$	24.2873	+	24.2873i	0.936205	+	0.936205i	0.998084	−	0.0618787i	$-0.0197092\pi$
$673$	24.2873	+	24.2873i	0.936205	+	0.936205i	−0.0618787	+	0.998084i	$0.519709\pi$
$674$	−10.8978	−	10.8978i	−0.419767	−	0.419767i
$675$	0.0518094	−	4.99973i	0.00199414	−	0.192440i
$676$	34.2873			1.31874
$677$	19.1232	+	19.1232i	0.734963	+	0.734963i	0.971599	−	0.236635i	$-0.0760446\pi$
$677$	19.1232	+	19.1232i	0.734963	+	0.734963i	−0.236635	+	0.971599i	$0.576045\pi$
$678$	12.9599	+	12.9599i	0.497722	+	0.497722i
$679$	0.199302	+	0.199302i	0.00764851	+	0.00764851i
$680$	4.48266	+	1.88405i	0.171902	+	0.0722500i
$681$	19.8555	+	19.8555i	0.760865	+	0.760865i
$682$	8.39587	−	8.39587i	0.321494	−	0.321494i
$683$	−5.31945			−0.203543			−0.101772	−	0.994808i	$-0.532451\pi$
$683$	−5.31945			−0.203543			−0.101772	+	0.994808i	$0.532451\pi$
$684$	−1.01389	+	1.01389i	−0.0387669	+	0.0387669i
$685$	−16.3508	−	40.0601i	−0.624732	−	1.53062i
$686$	8.68890	+	8.68890i	0.331744	+	0.331744i
$687$	0.202634	+	0.202634i	0.00773097	+	0.00773097i
$688$	2.74581			0.104683
$689$	−20.1786	−	20.1786i	−0.768745	−	0.768745i
$690$	8.08994	+	19.8207i	0.307979	+	0.754561i
$691$			35.7436i			1.35975i	0.733328	+	0.679875i	$0.237966\pi$
$691$			35.7436i			1.35975i	−0.733328	+	0.679875i	$0.762034\pi$
$692$	5.06991	−	5.06991i	0.192729	−	0.192729i
$693$	−2.32883	+	2.32883i	−0.0884651	+	0.0884651i
$694$	−0.330476			−0.0125447
$695$	15.3715	−	36.5730i	0.583074	−	1.38729i
$696$			9.19196i			0.348420i
$697$	−7.56735			−0.286634
$698$		−	35.7141i		−	1.35180i
$699$			14.4363i			0.546033i
$700$	4.68150	+	0.0485117i	0.176944	+	0.00183357i
$701$	−20.6265	+	20.6265i	−0.779051	+	0.779051i	−0.979669	−	0.200618i	$-0.935705\pi$
$701$	−20.6265	+	20.6265i	−0.779051	+	0.779051i	0.200618	+	0.979669i	$0.435705\pi$
$702$	−4.86247	−	4.86247i	−0.183522	−	0.183522i
$703$	7.29579	+	4.77920i	0.275166	+	0.180251i
$704$			3.51735i			0.132565i
$705$	−10.4678	−	4.39959i	−0.394241	−	0.165698i
$706$			19.1728i			0.721579i
$707$	−5.21871	−	5.21871i	−0.196270	−	0.196270i
$708$	4.88643			0.183643
$709$	−7.74624	−	7.74624i	−0.290916	−	0.290916i	0.546526	−	0.837442i	$-0.315950\pi$
$709$	−7.74624	−	7.74624i	−0.290916	−	0.290916i	−0.837442	+	0.546526i	$0.815950\pi$
$710$	−6.34938	+	15.1069i	−0.238288	+	0.566952i
$711$	7.95594	−	7.95594i	0.298371	−	0.298371i
$712$	6.43088	−	6.43088i	0.241007	−	0.241007i
$713$	22.8530	+	22.8530i	0.855852	+	0.855852i
$714$	−2.03617			−0.0762016
$715$	−49.8596	−	20.9558i	−1.86464	−	0.783704i
$716$	14.7313	−	14.7313i	0.550534	−	0.550534i
$717$	23.4775			0.876784
$718$		−	6.91664i		−	0.258127i
$719$		−	28.4115i		−	1.05957i	−0.848132	−	0.529785i	$-0.822273\pi$
$719$		−	28.4115i		−	1.05957i	0.848132	−	0.529785i	$-0.177727\pi$
$720$	2.06140	+	0.866398i	0.0768237	+	0.0322887i
$721$	2.52733	+	2.52733i	0.0941226	+	0.0941226i
$722$			16.9441i			0.630593i
$723$		−	24.6796i		−	0.917844i
$724$	−4.07298			−0.151371
$725$	45.9573	+	0.476230i	1.70681	+	0.0176867i
$726$	−0.969963	+	0.969963i	−0.0359987	+	0.0359987i
$727$	10.2341			0.379561			0.189780	−	0.981827i	$-0.439222\pi$
$727$	10.2341			0.379561			0.189780	+	0.981827i	$0.439222\pi$
$728$	4.55298	−	4.55298i	0.168745	−	0.168745i
$729$			1.00000i			0.0370370i
$730$	0.349715	+	0.856815i	0.0129435	+	0.0317121i
$731$			5.97097i			0.220844i
$732$	14.1330			0.522371
$733$	−27.1770	+	27.1770i	−1.00380	+	1.00380i	−0.00381081	+	0.999993i	$0.501213\pi$
$733$	−27.1770	+	27.1770i	−1.00380	+	1.00380i	−0.999993	+	0.00381081i	$0.998787\pi$
$734$	−17.2144	+	17.2144i	−0.635394	+	0.635394i
$735$	12.6767	−	5.17409i	0.467588	−	0.190849i
$736$	−9.57399			−0.352902
$737$	4.04260	−	4.04260i	0.148911	−	0.148911i
$738$	−3.47992			−0.128098
$739$	17.3037			0.636527			0.318264	−	0.948002i	$-0.396900\pi$
$739$	17.3037			0.636527			0.318264	+	0.948002i	$0.396900\pi$
$740$	2.60092	−	13.3505i	0.0956116	−	0.490773i
$741$	9.85998			0.362215
$742$	−3.88573			−0.142650
$743$	24.1248	−	24.1248i	0.885055	−	0.885055i	−0.108988	−	0.994043i	$-0.534761\pi$
$743$	24.1248	−	24.1248i	0.885055	−	0.885055i	0.994043	+	0.108988i	$0.0347611\pi$
$744$	3.37571			0.123760
$745$	21.8703	+	9.19199i	0.801264	+	0.336769i
$746$	13.8033	−	13.8033i	0.505373	−	0.505373i
$747$	−1.46770	+	1.46770i	−0.0537005	+	0.0537005i
$748$	−7.64874			−0.279666
$749$		−	4.49731i		−	0.164328i
$750$	4.43856	−	10.2615i	0.162073	−	0.374698i
$751$			49.1232i			1.79253i	0.443517	+	0.896266i	$0.353730\pi$
$751$			49.1232i			1.79253i	−0.443517	+	0.896266i	$0.646270\pi$
$752$	3.59071	−	3.59071i	0.130940	−	0.130940i
$753$	1.40364			0.0511515
$754$	44.6956	−	44.6956i	1.62772	−	1.62772i
$755$	8.04321	+	3.38053i	0.292722	+	0.123030i
$756$	−0.936350			−0.0340547
$757$			20.9126i			0.760081i	0.924970	+	0.380040i	$0.124090\pi$
$757$			20.9126i			0.760081i	−0.924970	+	0.380040i	$0.875910\pi$
$758$		−	0.729632i		−	0.0265014i
$759$	−23.8119	−	23.8119i	−0.864316	−	0.864316i
$760$	−2.96845	+	1.21159i	−0.107677	+	0.0439491i
$761$			22.5447i			0.817245i	0.912704	+	0.408622i	$0.133991\pi$
$761$			22.5447i			0.817245i	−0.912704	+	0.408622i	$0.866009\pi$
$762$			0.350036i			0.0126805i
$763$	2.58862			0.0937142
$764$	0.841106	−	0.841106i	0.0304301	−	0.0304301i
$765$	−1.88405	+	4.48266i	−0.0681179	+	0.162071i
$766$	−28.2223			−1.01971
$767$	−23.7601	−	23.7601i	−0.857929	−	0.857929i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	1.79332	−	1.79332i	0.0646688	−	0.0646688i	−0.674033	−	0.738701i	$-0.735439\pi$
$769$	1.79332	−	1.79332i	0.0646688	−	0.0646688i	0.738701	+	0.674033i	$0.235439\pi$
$770$	−6.81835	+	2.78295i	−0.245716	+	0.100291i
$771$	6.50160	+	6.50160i	0.234149	+	0.234149i
$772$	2.71107			0.0975736
$773$	−10.3091	−	10.3091i	−0.370791	−	0.370791i	0.496974	−	0.867765i	$-0.334444\pi$
$773$	−10.3091	−	10.3091i	−0.370791	−	0.370791i	−0.867765	+	0.496974i	$0.834444\pi$
$774$			2.74581i			0.0986961i
$775$	0.174894	−	16.8777i	0.00628236	−	0.606263i
$776$			0.301015i			0.0108058i
$777$	1.16207	+	5.57579i	0.0416890	+	0.200030i
$778$	15.3299	+	15.3299i	0.549604	+	0.549604i
$779$	3.52824	−	3.52824i	0.126412	−	0.126412i
$780$	−5.81065	−	14.2363i	−0.208055	−	0.509742i
$781$		−	25.7768i		−	0.922367i
$782$		−	20.8194i		−	0.744499i
$783$	−9.19196			−0.328494
$784$			6.12325i			0.218687i
$785$	2.09908	+	5.14283i	0.0749194	+	0.183556i
$786$	−1.86010			−0.0663475
$787$	34.8286	−	34.8286i	1.24151	−	1.24151i	0.282129	−	0.959376i	$-0.408959\pi$
$787$	34.8286	−	34.8286i	1.24151	−	1.24151i	0.959376	−	0.282129i	$-0.0910406\pi$
$788$	14.0103	−	14.0103i	0.499098	−	0.499098i
$789$			14.3290i			0.510126i
$790$	23.2933	−	9.50733i	0.828740	−	0.338256i
$791$	−12.1350	−	12.1350i	−0.431471	−	0.431471i
$792$	−3.51735			−0.124984
$793$	−68.7214	−	68.7214i	−2.44037	−	2.44037i
$794$	−9.07360	−	9.07360i	−0.322010	−	0.322010i
$795$	−3.59544	+	8.55453i	−0.127517	+	0.303398i
$796$	2.28257	−	2.28257i	0.0809037	−	0.0809037i
$797$	18.1150			0.641667			0.320833	−	0.947136i	$-0.396037\pi$
$797$	18.1150			0.641667			0.320833	+	0.947136i	$0.396037\pi$
$798$	0.949352	−	0.949352i	0.0336067	−	0.0336067i
$799$	7.80827	+	7.80827i	0.276237	+	0.276237i
$800$	3.49871	+	3.57198i	0.123698	+	0.126289i
$801$	6.43088	+	6.43088i	0.227224	+	0.227224i
$802$	23.0577	+	23.0577i	0.814194	+	0.814194i
$803$	−1.02935	−	1.02935i	−0.0363249	−	0.0363249i
$804$	1.62540			0.0573235
$805$	−7.57502	−	18.5591i	−0.266984	−	0.654122i
$806$	−16.4143	−	16.4143i	−0.578169	−	0.578169i
$807$	−18.2736	−	18.2736i	−0.643262	−	0.643262i
$808$		−	7.88206i		−	0.277290i
$809$	8.19124	−	8.19124i	0.287989	−	0.287989i	−0.548296	−	0.836284i	$-0.684723\pi$
$809$	8.19124	−	8.19124i	0.287989	−	0.287989i	0.836284	+	0.548296i	$0.184723\pi$
$810$	−0.866398	+	2.06140i	−0.0304421	+	0.0724301i
$811$	42.4868			1.49191			0.745956	−	0.665995i	$-0.231993\pi$
$811$	42.4868			1.49191			0.745956	+	0.665995i	$0.231993\pi$
$812$		−	8.60689i		−	0.302043i
$813$	−13.4720	+	13.4720i	−0.472483	+	0.472483i
$814$	4.36524	+	20.9451i	0.153002	+	0.734127i
$815$	19.3714	+	8.14175i	0.678552	+	0.285193i
$816$	−1.53766	−	1.53766i	−0.0538288	−	0.0538288i
$817$	−2.78394	−	2.78394i	−0.0973976	−	0.0973976i
$818$	−12.7245	+	12.7245i	−0.444901	+	0.444901i
$819$	4.55298	+	4.55298i	0.159094	+	0.159094i
$820$	−7.17349	−	3.01499i	−0.250509	−	0.105288i
$821$	47.2026			1.64738			0.823691	−	0.567039i	$-0.191911\pi$
$821$	47.2026			1.64738			0.823691	+	0.567039i	$0.191911\pi$
$822$			19.3502i			0.674917i
$823$	10.8159	+	10.8159i	0.377018	+	0.377018i	0.870025	−	0.493007i	$-0.164102\pi$
$823$	10.8159	+	10.8159i	0.377018	+	0.377018i	−0.493007	+	0.870025i	$0.664102\pi$
$824$			3.81714i			0.132976i
$825$	−0.182232	+	17.5858i	−0.00634449	+	0.612259i
$826$	−4.57541			−0.159199
$827$			8.86372i			0.308222i	0.988054	+	0.154111i	$0.0492513\pi$
$827$			8.86372i			0.308222i	−0.988054	+	0.154111i	$0.950749\pi$
$828$		−	9.57399i		−	0.332719i
$829$	−12.4726	+	12.4726i	−0.433190	+	0.433190i	−0.889712	−	0.456522i	$-0.849095\pi$
$829$	−12.4726	+	12.4726i	−0.433190	+	0.433190i	0.456522	+	0.889712i	$0.349095\pi$
$830$	−4.29714	+	1.75390i	−0.149156	+	0.0608789i
$831$	−1.63342	+	1.63342i	−0.0566628	+	0.0566628i
$832$	6.87657			0.238402
$833$	−13.3155			−0.461354
$834$	−12.5454	+	12.5454i	−0.434411	+	0.434411i
$835$	−37.7977	−	15.8863i	−1.30804	−	0.549767i
$836$	3.56619	−	3.56619i	0.123339	−	0.123339i
$837$			3.37571i			0.116682i
$838$			4.07751i			0.140855i
$839$	−52.3150			−1.80611			−0.903056	−	0.429522i	$-0.858682\pi$
$839$	−52.3150			−1.80611			−0.903056	+	0.429522i	$0.858682\pi$
$840$	−1.93019	−	0.811252i	−0.0665978	−	0.0279909i
$841$		−	55.4921i		−	1.91352i
$842$	5.38925	+	5.38925i	0.185726	+	0.185726i
$843$		−	19.6287i		−	0.676048i
$844$	16.7409			0.576247
$845$	−29.7064	+	70.6797i	−1.02193	+	2.43145i
$846$	3.59071	+	3.59071i	0.123451	+	0.123451i
$847$	0.908225	−	0.908225i	0.0312070	−	0.0312070i
$848$	−2.93440	−	2.93440i	−0.100768	−	0.100768i
$849$	−14.7867	−	14.7867i	−0.507478	−	0.507478i
$850$	−7.76754	+	7.60821i	−0.266424	+	0.260960i
$851$	−57.0113	+	11.8819i	−1.95432	+	0.407307i
$852$	5.18202	−	5.18202i	0.177533	−	0.177533i
$853$			38.2913i			1.31107i	0.755165	+	0.655535i	$0.227557\pi$
$853$			38.2913i			1.31107i	−0.755165	+	0.655535i	$0.772443\pi$
$854$	−13.2334			−0.452839
$855$	−1.21159	−	2.96845i	−0.0414356	−	0.101519i
$856$	3.39625	−	3.39625i	0.116081	−	0.116081i
$857$		−	23.6239i		−	0.806978i	−0.914984	−	0.403489i	$-0.867797\pi$
$857$		−	23.6239i		−	0.806978i	0.914984	−	0.403489i	$-0.132203\pi$
$858$	17.1030	+	17.1030i	0.583887	+	0.583887i
$859$	−25.3164	−	25.3164i	−0.863785	−	0.863785i	0.127991	−	0.991775i	$-0.459147\pi$
$859$	−25.3164	−	25.3164i	−0.863785	−	0.863785i	−0.991775	+	0.127991i	$0.959147\pi$
$860$	−2.37896	+	5.66020i	−0.0811220	+	0.193011i
$861$	3.25842			0.111047
$862$	−9.41260	−	9.41260i	−0.320594	−	0.320594i
$863$	−22.2626	−	22.2626i	−0.757827	−	0.757827i	0.218099	−	0.975927i	$-0.430014\pi$
$863$	−22.2626	−	22.2626i	−0.757827	−	0.757827i	−0.975927	+	0.218099i	$0.930014\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	6.05853	+	14.8437i	0.205996	+	0.504699i
$866$	−18.0950	−	18.0950i	−0.614892	−	0.614892i
$867$	−8.67706	+	8.67706i	−0.294688	+	0.294688i
$868$	−3.16085			−0.107286
$869$	−27.9838	+	27.9838i	−0.949285	+	0.949285i
$870$	−18.9483	−	7.96389i	−0.642407	−	0.270001i
$871$	−7.90347	−	7.90347i	−0.267799	−	0.267799i
$872$	1.95485	+	1.95485i	0.0661997	+	0.0661997i
$873$	−0.301015			−0.0101878
$874$	9.70693	+	9.70693i	0.328342	+	0.328342i
$875$	−4.15604	+	9.60840i	−0.140500	+	0.324823i
$876$		−	0.413868i		−	0.0139833i
$877$	13.1660	−	13.1660i	0.444583	−	0.444583i	−0.448966	−	0.893549i	$-0.648208\pi$
$877$	13.1660	−	13.1660i	0.444583	−	0.444583i	0.893549	+	0.448966i	$0.148208\pi$
$878$	3.41744	−	3.41744i	0.115333	−	0.115333i
$879$	8.64286			0.291516
$880$	−7.25065	−	3.04742i	−0.244419	−	0.102729i
$881$		−	12.7644i		−	0.430043i	−0.976609	−	0.215022i	$-0.931018\pi$
$881$		−	12.7644i		−	0.430043i	0.976609	−	0.215022i	$-0.0689822\pi$
$882$	−6.12325			−0.206180
$883$		−	23.3191i		−	0.784751i	−0.919805	−	0.392376i	$-0.871653\pi$
$883$		−	23.3191i		−	0.784751i	0.919805	−	0.392376i	$-0.128347\pi$
$884$			14.9536i			0.502945i
$885$	−4.23360	+	10.0729i	−0.142311	+	0.338596i
$886$	10.8466	−	10.8466i	0.364400	−	0.364400i
$887$	7.29393	+	7.29393i	0.244906	+	0.244906i	0.818876	−	0.573970i	$-0.194597\pi$
$887$	7.29393	+	7.29393i	0.244906	+	0.244906i	−0.573970	+	0.818876i	$0.694597\pi$
$888$	−3.33312	+	5.08825i	−0.111852	+	0.170750i
$889$		−	0.327756i		−	0.0109926i
$890$	7.68489	+	18.8283i	0.257598	+	0.631125i
$891$		−	3.51735i		−	0.117836i
$892$	16.5296	+	16.5296i	0.553452	+	0.553452i
$893$	−7.28113			−0.243654
$894$	−7.50200	−	7.50200i	−0.250905	−	0.250905i
$895$	17.6039	+	43.1302i	0.588432	+	1.44168i
$896$	0.662100	−	0.662100i	0.0221192	−	0.0221192i
$897$	−46.5533	+	46.5533i	−1.55437	+	1.55437i
$898$	−10.3811	−	10.3811i	−0.346421	−	0.346421i
$899$	−31.0294			−1.03489
$900$	−3.57198	+	3.49871i	−0.119066	+	0.116624i
$901$	6.38108	−	6.38108i	0.212585	−	0.212585i
$902$	12.2401			0.407550
$903$		−	2.57104i		−	0.0855588i
$904$		−	18.3281i		−	0.609582i
$905$	3.52882	−	8.39602i	0.117302	−	0.279093i
$906$	−2.75901	−	2.75901i	−0.0916619	−	0.0916619i
$907$		−	49.3619i		−	1.63904i	−0.573054	−	0.819518i	$-0.694241\pi$
$907$		−	49.3619i		−	1.63904i	0.573054	−	0.819518i	$-0.305759\pi$
$908$		−	28.0799i		−	0.931865i
$909$	7.88206			0.261431
$910$	5.44080	+	13.3302i	0.180361	+	0.441891i
$911$	6.70882	−	6.70882i	0.222273	−	0.222273i	−0.587182	−	0.809455i	$-0.699763\pi$
$911$	6.70882	−	6.70882i	0.222273	−	0.222273i	0.809455	+	0.587182i	$0.199763\pi$
$912$	1.43385			0.0474795
$913$	5.16243	−	5.16243i	0.170851	−	0.170851i
$914$		−	13.7780i		−	0.455737i
$915$	−12.2448	+	29.1337i	−0.404801	+	0.963131i
$916$		−	0.286568i		−	0.00946847i
$917$	1.74170			0.0575161
$918$	1.53766	−	1.53766i	0.0507503	−	0.0507503i
$919$	19.7075	−	19.7075i	0.650090	−	0.650090i	−0.302924	−	0.953015i	$-0.597963\pi$
$919$	19.7075	−	19.7075i	0.650090	−	0.650090i	0.953015	+	0.302924i	$0.0979630\pi$
$920$	8.29489	−	19.7358i	0.273474	−	0.650670i
$921$	−15.9746			−0.526380
$922$	28.3555	−	28.3555i	0.933838	−	0.933838i
$923$	−50.3948			−1.65877
$924$	3.29347			0.108347
$925$	25.2672	+	16.9283i	0.830780	+	0.556601i
$926$	27.1414			0.891921
$927$	−3.81714			−0.125371
$928$	6.49970	−	6.49970i	0.213363	−	0.213363i
$929$	32.0555			1.05171			0.525853	−	0.850575i	$-0.323746\pi$
$929$	32.0555			1.05171			0.525853	+	0.850575i	$0.323746\pi$
$930$	−2.92471	+	6.95868i	−0.0959050	+	0.228184i
$931$	6.20827	−	6.20827i	0.203468	−	0.203468i
$932$	10.2080	−	10.2080i	0.334375	−	0.334375i
$933$	−13.9264			−0.455930
$934$			15.3540i			0.502400i
$935$	6.62685	−	15.7671i	0.216721	−	0.515639i
$936$			6.87657i			0.224768i
$937$	31.6848	−	31.6848i	1.03510	−	1.03510i	0.0357367	−	0.999361i	$-0.488622\pi$
$937$	31.6848	−	31.6848i	1.03510	−	1.03510i	0.999361	−	0.0357367i	$-0.0113778\pi$
$938$	−1.52195			−0.0496933
$939$	8.57876	−	8.57876i	0.279957	−	0.279957i
$940$	4.29089	+	10.5129i	0.139953	+	0.342891i
$941$	22.9702			0.748808			0.374404	−	0.927266i	$-0.377847\pi$
$941$	22.9702			0.748808			0.374404	+	0.927266i	$0.377847\pi$
$942$		−	2.48415i		−	0.0809378i
$943$			33.3167i			1.08494i
$944$	−3.45523	−	3.45523i	−0.112458	−	0.112458i
$945$	0.811252	−	1.93019i	0.0263900	−	0.0627891i
$946$		−	9.65796i		−	0.314007i
$947$		−	47.0948i		−	1.53037i	−0.643808	−	0.765187i	$-0.722647\pi$
$947$		−	47.0948i		−	1.53037i	0.643808	−	0.765187i	$-0.277353\pi$
$948$	−11.2514			−0.365428
$949$	−2.01242	+	2.01242i	−0.0653259	+	0.0653259i
$950$	0.0742869	−	7.16887i	0.00241019	−	0.232589i
$951$	13.6690			0.443248
$952$	1.43979	+	1.43979i	0.0466637	+	0.0466637i
$953$	10.7627	−	10.7627i	0.348638	−	0.348638i	−0.510964	−	0.859602i	$-0.670711\pi$
$953$	10.7627	−	10.7627i	0.348638	−	0.348638i	0.859602	+	0.510964i	$0.170711\pi$
$954$	2.93440	−	2.93440i	0.0950048	−	0.0950048i
$955$	1.00512	+	2.46258i	0.0325249	+	0.0796874i
$956$	−16.6011	−	16.6011i	−0.536918	−	0.536918i
$957$	32.3313			1.04512
$958$	−11.3006	−	11.3006i	−0.365106	−	0.365106i
$959$		−	18.1186i		−	0.585080i
$960$	−0.844991	−	2.07026i	−0.0272720	−	0.0668175i
$961$		−	19.6046i		−	0.632405i
$962$	40.9487	−	8.53425i	1.32024	−	0.275155i
$963$	3.39625	+	3.39625i	0.109443	+	0.109443i
$964$	−17.4511	+	17.4511i	−0.562062	+	0.562062i
$965$	−2.34887	+	5.58860i	−0.0756127	+	0.179903i
$966$			8.96461i			0.288432i
$967$		−	25.7099i		−	0.826776i	−0.910555	−	0.413388i	$-0.864345\pi$
$967$		−	25.7099i		−	0.826776i	0.910555	−	0.413388i	$-0.135655\pi$
$968$	1.37173			0.0440892
$969$			3.11802i			0.100165i
$970$	−0.620511	−	0.260799i	−0.0199234	−	0.00837375i
$971$	−7.16138			−0.229820			−0.114910	−	0.993376i	$-0.536658\pi$
$971$	−7.16138			−0.229820			−0.114910	+	0.993376i	$0.536658\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	11.7469	−	11.7469i	0.376587	−	0.376587i
$974$		−	21.7950i		−	0.698358i
$975$	34.3810	+	0.356271i	1.10107	+	0.0114098i
$976$	−9.99355	−	9.99355i	−0.319886	−	0.319886i
$977$	−6.00481			−0.192111			−0.0960554	−	0.995376i	$-0.530623\pi$
$977$	−6.00481			−0.192111			−0.0960554	+	0.995376i	$0.530623\pi$
$978$	−6.64486	−	6.64486i	−0.212479	−	0.212479i
$979$	−22.6196	−	22.6196i	−0.722926	−	0.722926i
$980$	−12.6224	−	5.30517i	−0.403209	−	0.169467i
$981$	−1.95485	+	1.95485i	−0.0624137	+	0.0624137i
$982$	6.69716			0.213715
$983$	16.8252	−	16.8252i	0.536640	−	0.536640i	−0.385901	−	0.922540i	$-0.626109\pi$
$983$	16.8252	−	16.8252i	0.536640	−	0.536640i	0.922540	+	0.385901i	$0.126109\pi$
$984$	2.46067	+	2.46067i	0.0784434	+	0.0784434i
$985$	16.7423	+	41.0194i	0.533455	+	1.30699i
$986$	14.1341	+	14.1341i	0.450121	+	0.450121i
$987$	−3.36216	−	3.36216i	−0.107019	−	0.107019i
$988$	−6.97206	−	6.97206i	−0.221811	−	0.221811i
$989$	26.2883			0.835921
$990$	3.04742	−	7.25065i	0.0968534	−	0.230441i
$991$	21.1418	+	21.1418i	0.671592	+	0.671592i	0.958083	−	0.286491i	$-0.0924887\pi$
$991$	21.1418	+	21.1418i	0.671592	+	0.671592i	−0.286491	+	0.958083i	$0.592489\pi$
$992$	−2.38699	−	2.38699i	−0.0757870	−	0.0757870i
$993$			32.6352i			1.03565i
$994$	−4.85218	+	4.85218i	−0.153902	+	0.153902i
$995$	2.72767	+	6.68291i	0.0864731	+	0.211862i
$996$	2.07565			0.0657694
$997$			51.0135i			1.61561i	0.589447	+	0.807807i	$0.299346\pi$
$997$			51.0135i			1.61561i	−0.589447	+	0.807807i	$0.700654\pi$
$998$	31.1536	−	31.1536i	0.986150	−	0.986150i
$999$	−5.08825	−	3.33312i	−0.160985	−	0.105455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.7	yes	36
5.2	odd	4		1110.2.l.a.697.12	yes	36
37.6	odd	4		1110.2.l.a.43.12	✓	36
185.117	even	4	inner	1110.2.o.a.487.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.12	✓	36	37.6	odd	4
1110.2.l.a.697.12	yes	36	5.2	odd	4
1110.2.o.a.253.7	yes	36	1.1	even	1	trivial
1110.2.o.a.487.7	yes	36	185.117	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.866398 + 2.06140i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.662100 + 0.662100i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-0.866398 + 2.06140i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.662100 + 0.662100i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(0.866398 - 2.06140i) q^{10} +3.51735i q^{11} +(-0.707107 + 0.707107i) q^{12} +6.87657 q^{13} +(0.662100 - 0.662100i) q^{14} +(-0.844991 - 2.07026i) q^{15} +1.00000 q^{16} +2.17458i q^{17} +1.00000i q^{18} +(-1.01389 - 1.01389i) q^{19} +(-0.866398 + 2.06140i) q^{20} -0.936350i q^{21} -3.51735i q^{22} +9.57399 q^{23} +(0.707107 - 0.707107i) q^{24} +(-3.49871 - 3.57198i) q^{25} -6.87657 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.662100 + 0.662100i) q^{28} +(-6.49970 + 6.49970i) q^{29} +(0.844991 + 2.07026i) q^{30} +(2.38699 + 2.38699i) q^{31} -1.00000 q^{32} +(-2.48714 - 2.48714i) q^{33} -2.17458i q^{34} +(-0.791208 - 1.93849i) q^{35} -1.00000i q^{36} +(-5.95481 + 1.24106i) q^{37} +(1.01389 + 1.01389i) q^{38} +(-4.86247 + 4.86247i) q^{39} +(0.866398 - 2.06140i) q^{40} +3.47992i q^{41} +0.936350i q^{42} +2.74581 q^{43} +3.51735i q^{44} +(2.06140 + 0.866398i) q^{45} -9.57399 q^{46} +(3.59071 - 3.59071i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.12325i q^{49} +(3.49871 + 3.57198i) q^{50} +(-1.53766 - 1.53766i) q^{51} +6.87657 q^{52} +(-2.93440 - 2.93440i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-7.25065 - 3.04742i) q^{55} +(0.662100 - 0.662100i) q^{56} +1.43385 q^{57} +(6.49970 - 6.49970i) q^{58} +(-3.45523 - 3.45523i) q^{59} +(-0.844991 - 2.07026i) q^{60} +(-9.99355 - 9.99355i) q^{61} +(-2.38699 - 2.38699i) q^{62} +(0.662100 + 0.662100i) q^{63} +1.00000 q^{64} +(-5.95785 + 14.1753i) q^{65} +(2.48714 + 2.48714i) q^{66} +(-1.14933 - 1.14933i) q^{67} +2.17458i q^{68} +(-6.76983 + 6.76983i) q^{69} +(0.791208 + 1.93849i) q^{70} -7.32848 q^{71} +1.00000i q^{72} +(-0.292649 + 0.292649i) q^{73} +(5.95481 - 1.24106i) q^{74} +(4.99973 + 0.0518094i) q^{75} +(-1.01389 - 1.01389i) q^{76} +(-2.32883 - 2.32883i) q^{77} +(4.86247 - 4.86247i) q^{78} +(7.95594 + 7.95594i) q^{79} +(-0.866398 + 2.06140i) q^{80} -1.00000 q^{81} -3.47992i q^{82} +(-1.46770 - 1.46770i) q^{83} -0.936350i q^{84} +(-4.48266 - 1.88405i) q^{85} -2.74581 q^{86} -9.19196i q^{87} -3.51735i q^{88} +(-6.43088 + 6.43088i) q^{89} +(-2.06140 - 0.866398i) q^{90} +(-4.55298 + 4.55298i) q^{91} +9.57399 q^{92} -3.37571 q^{93} +(-3.59071 + 3.59071i) q^{94} +(2.96845 - 1.21159i) q^{95} +(0.707107 - 0.707107i) q^{96} -0.301015i q^{97} -6.12325i q^{98} +3.51735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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