LMFDB - Embedded newform 1110.2.o.b.253.19

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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.19
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.18349 + 0.482069i) q^{5} +(0.707107 - 0.707107i) q^{6} +(3.34184 - 3.34184i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.18349 + 0.482069i) q^{5} +(0.707107 - 0.707107i) q^{6} +(3.34184 - 3.34184i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-2.18349 + 0.482069i) q^{10} +0.666166i q^{11} +(0.707107 - 0.707107i) q^{12} -2.34770 q^{13} +(3.34184 - 3.34184i) q^{14} +(-1.20308 + 1.88483i) q^{15} +1.00000 q^{16} -2.53367i q^{17} -1.00000i q^{18} +(-2.61593 - 2.61593i) q^{19} +(-2.18349 + 0.482069i) q^{20} -4.72607i q^{21} +0.666166i q^{22} +7.61016 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.53522 - 2.10518i) q^{25} -2.34770 q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.34184 - 3.34184i) q^{28} +(1.83506 - 1.83506i) q^{29} +(-1.20308 + 1.88483i) q^{30} +(-3.00523 - 3.00523i) q^{31} +1.00000 q^{32} +(0.471050 + 0.471050i) q^{33} -2.53367i q^{34} +(-5.68586 + 8.90786i) q^{35} -1.00000i q^{36} +(5.08208 - 3.34252i) q^{37} +(-2.61593 - 2.61593i) q^{38} +(-1.66007 + 1.66007i) q^{39} +(-2.18349 + 0.482069i) q^{40} +6.19673i q^{41} -4.72607i q^{42} -9.47906 q^{43} +0.666166i q^{44} +(0.482069 + 2.18349i) q^{45} +7.61016 q^{46} +(-5.52416 + 5.52416i) q^{47} +(0.707107 - 0.707107i) q^{48} -15.3358i q^{49} +(4.53522 - 2.10518i) q^{50} +(-1.79158 - 1.79158i) q^{51} -2.34770 q^{52} +(3.00973 + 3.00973i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.321138 - 1.45456i) q^{55} +(3.34184 - 3.34184i) q^{56} -3.69948 q^{57} +(1.83506 - 1.83506i) q^{58} +(1.77437 + 1.77437i) q^{59} +(-1.20308 + 1.88483i) q^{60} +(-1.33334 - 1.33334i) q^{61} +(-3.00523 - 3.00523i) q^{62} +(-3.34184 - 3.34184i) q^{63} +1.00000 q^{64} +(5.12617 - 1.13175i) q^{65} +(0.471050 + 0.471050i) q^{66} +(9.44858 + 9.44858i) q^{67} -2.53367i q^{68} +(5.38119 - 5.38119i) q^{69} +(-5.68586 + 8.90786i) q^{70} +3.44750 q^{71} -1.00000i q^{72} +(7.93466 - 7.93466i) q^{73} +(5.08208 - 3.34252i) q^{74} +(1.71830 - 4.69547i) q^{75} +(-2.61593 - 2.61593i) q^{76} +(2.22622 + 2.22622i) q^{77} +(-1.66007 + 1.66007i) q^{78} +(-8.95760 - 8.95760i) q^{79} +(-2.18349 + 0.482069i) q^{80} -1.00000 q^{81} +6.19673i q^{82} +(6.18662 + 6.18662i) q^{83} -4.72607i q^{84} +(1.22140 + 5.53224i) q^{85} -9.47906 q^{86} -2.59517i q^{87} +0.666166i q^{88} +(-0.703752 + 0.703752i) q^{89} +(0.482069 + 2.18349i) q^{90} +(-7.84563 + 7.84563i) q^{91} +7.61016 q^{92} -4.25003 q^{93} +(-5.52416 + 5.52416i) q^{94} +(6.97289 + 4.45078i) q^{95} +(0.707107 - 0.707107i) q^{96} +6.06755i q^{97} -15.3358i q^{98} +0.666166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * 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
$5$	−2.18349	+	0.482069i	−0.976484	+	0.215588i
$5$	−2.18349	+	0.482069i	−0.976484	+	0.215588i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	3.34184	−	3.34184i	1.26310	−	1.26310i	0.313513	−	0.949584i	$-0.398494\pi$
$7$	3.34184	−	3.34184i	1.26310	−	1.26310i	0.949584	−	0.313513i	$-0.101506\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−2.18349	+	0.482069i	−0.690479	+	0.152444i
$11$			0.666166i			0.200856i	0.994944	+	0.100428i	$0.0320213\pi$
$11$			0.666166i			0.200856i	−0.994944	+	0.100428i	$0.967979\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−2.34770			−0.651134			−0.325567	−	0.945519i	$-0.605555\pi$
$13$	−2.34770			−0.651134			−0.325567	+	0.945519i	$0.605555\pi$
$14$	3.34184	−	3.34184i	0.893144	−	0.893144i
$15$	−1.20308	+	1.88483i	−0.310635	+	0.486661i
$16$	1.00000			0.250000
$17$		−	2.53367i		−	0.614506i	−0.951628	−	0.307253i	$-0.900590\pi$
$17$		−	2.53367i		−	0.614506i	0.951628	−	0.307253i	$-0.0994097\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−2.61593	−	2.61593i	−0.600135	−	0.600135i	0.340214	−	0.940348i	$-0.389501\pi$
$19$	−2.61593	−	2.61593i	−0.600135	−	0.600135i	−0.940348	+	0.340214i	$0.889501\pi$
$20$	−2.18349	+	0.482069i	−0.488242	+	0.107794i
$21$		−	4.72607i		−	1.03131i
$22$			0.666166i			0.142027i
$23$	7.61016			1.58683			0.793414	−	0.608683i	$-0.208302\pi$
$23$	7.61016			1.58683			0.793414	+	0.608683i	$0.208302\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	4.53522	−	2.10518i	0.907044	−	0.421036i
$26$	−2.34770			−0.460422
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	3.34184	−	3.34184i	0.631548	−	0.631548i
$29$	1.83506	−	1.83506i	0.340763	−	0.340763i	−0.515891	−	0.856654i	$-0.672539\pi$
$29$	1.83506	−	1.83506i	0.340763	−	0.340763i	0.856654	+	0.515891i	$0.172539\pi$
$30$	−1.20308	+	1.88483i	−0.219652	+	0.344122i
$31$	−3.00523	−	3.00523i	−0.539755	−	0.539755i	0.383702	−	0.923457i	$-0.374649\pi$
$31$	−3.00523	−	3.00523i	−0.539755	−	0.539755i	−0.923457	+	0.383702i	$0.874649\pi$
$32$	1.00000			0.176777
$33$	0.471050	+	0.471050i	0.0819993	+	0.0819993i
$34$		−	2.53367i		−	0.434521i
$35$	−5.68586	+	8.90786i	−0.961086	+	1.50570i
$36$		−	1.00000i		−	0.166667i
$37$	5.08208	−	3.34252i	0.835489	−	0.549507i
$37$	5.08208	−	3.34252i	0.835489	−	0.549507i
$38$	−2.61593	−	2.61593i	−0.424359	−	0.424359i
$39$	−1.66007	+	1.66007i	−0.265824	+	0.265824i
$40$	−2.18349	+	0.482069i	−0.345239	+	0.0762218i
$41$			6.19673i			0.967766i	0.875133	+	0.483883i	$0.160774\pi$
$41$			6.19673i			0.967766i	−0.875133	+	0.483883i	$0.839226\pi$
$42$		−	4.72607i		−	0.729249i
$43$	−9.47906			−1.44554			−0.722771	−	0.691087i	$-0.757132\pi$
$43$	−9.47906			−1.44554			−0.722771	+	0.691087i	$0.757132\pi$
$44$			0.666166i			0.100428i
$45$	0.482069	+	2.18349i	0.0718626	+	0.325495i
$46$	7.61016			1.12206
$47$	−5.52416	+	5.52416i	−0.805782	+	0.805782i	−0.983992	−	0.178210i	$-0.942969\pi$
$47$	−5.52416	+	5.52416i	−0.805782	+	0.805782i	0.178210	+	0.983992i	$0.442969\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	15.3358i		−	2.19083i
$50$	4.53522	−	2.10518i	0.641377	−	0.297717i
$51$	−1.79158	−	1.79158i	−0.250871	−	0.250871i
$52$	−2.34770			−0.325567
$53$	3.00973	+	3.00973i	0.413418	+	0.413418i	0.882927	−	0.469510i	$-0.155569\pi$
$53$	3.00973	+	3.00973i	0.413418	+	0.413418i	−0.469510	+	0.882927i	$0.655569\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−0.321138	−	1.45456i	−0.0433022	−	0.196133i
$56$	3.34184	−	3.34184i	0.446572	−	0.446572i
$57$	−3.69948			−0.490008
$58$	1.83506	−	1.83506i	0.240956	−	0.240956i
$59$	1.77437	+	1.77437i	0.231003	+	0.231003i	0.813111	−	0.582108i	$-0.197772\pi$
$59$	1.77437	+	1.77437i	0.231003	+	0.231003i	−0.582108	+	0.813111i	$0.697772\pi$
$60$	−1.20308	+	1.88483i	−0.155317	+	0.243331i
$61$	−1.33334	−	1.33334i	−0.170717	−	0.170717i	0.616577	−	0.787294i	$-0.288519\pi$
$61$	−1.33334	−	1.33334i	−0.170717	−	0.170717i	−0.787294	+	0.616577i	$0.788519\pi$
$62$	−3.00523	−	3.00523i	−0.381664	−	0.381664i
$63$	−3.34184	−	3.34184i	−0.421032	−	0.421032i
$64$	1.00000			0.125000
$65$	5.12617	−	1.13175i	0.635823	−	0.140377i
$66$	0.471050	+	0.471050i	0.0579823	+	0.0579823i
$67$	9.44858	+	9.44858i	1.15433	+	1.15433i	0.985676	+	0.168653i	$0.0539416\pi$
$67$	9.44858	+	9.44858i	1.15433	+	1.15433i	0.168653	+	0.985676i	$0.446058\pi$
$68$		−	2.53367i		−	0.307253i
$69$	5.38119	−	5.38119i	0.647819	−	0.647819i
$70$	−5.68586	+	8.90786i	−0.679591	+	1.06469i
$71$	3.44750			0.409143			0.204572	−	0.978852i	$-0.434420\pi$
$71$	3.44750			0.409143			0.204572	+	0.978852i	$0.434420\pi$
$72$		−	1.00000i		−	0.117851i
$73$	7.93466	−	7.93466i	0.928682	−	0.928682i	−0.0689386	−	0.997621i	$-0.521961\pi$
$73$	7.93466	−	7.93466i	0.928682	−	0.928682i	0.997621	+	0.0689386i	$0.0219613\pi$
$74$	5.08208	−	3.34252i	0.590780	−	0.388560i
$75$	1.71830	−	4.69547i	0.198412	−	0.542186i
$76$	−2.61593	−	2.61593i	−0.300067	−	0.300067i
$77$	2.22622	+	2.22622i	0.253701	+	0.253701i
$78$	−1.66007	+	1.66007i	−0.187966	+	0.187966i
$79$	−8.95760	−	8.95760i	−1.00781	−	1.00781i	−0.999969	−	0.00783976i	$-0.997505\pi$
$79$	−8.95760	−	8.95760i	−1.00781	−	1.00781i	−0.00783976	−	0.999969i	$-0.502495\pi$
$80$	−2.18349	+	0.482069i	−0.244121	+	0.0538969i
$81$	−1.00000			−0.111111
$82$			6.19673i			0.684314i
$83$	6.18662	+	6.18662i	0.679070	+	0.679070i	0.959790	−	0.280720i	$-0.0905732\pi$
$83$	6.18662	+	6.18662i	0.679070	+	0.679070i	−0.280720	+	0.959790i	$0.590573\pi$
$84$		−	4.72607i		−	0.515657i
$85$	1.22140	+	5.53224i	0.132480	+	0.600055i
$86$	−9.47906			−1.02215
$87$		−	2.59517i		−	0.278232i
$88$			0.666166i			0.0710135i
$89$	−0.703752	+	0.703752i	−0.0745976	+	0.0745976i	−0.743421	−	0.668824i	$-0.766798\pi$
$89$	−0.703752	+	0.703752i	−0.0745976	+	0.0745976i	0.668824	+	0.743421i	$0.266798\pi$
$90$	0.482069	+	2.18349i	0.0508145	+	0.230160i
$91$	−7.84563	+	7.84563i	−0.822446	+	0.822446i
$92$	7.61016			0.793414
$93$	−4.25003			−0.440708
$94$	−5.52416	+	5.52416i	−0.569774	+	0.569774i
$95$	6.97289	+	4.45078i	0.715404	+	0.456641i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$			6.06755i			0.616067i	0.951376	+	0.308033i	$0.0996708\pi$
$97$			6.06755i			0.616067i	−0.951376	+	0.308033i	$0.900329\pi$
$98$		−	15.3358i		−	1.54915i
$99$	0.666166			0.0669522
$100$	4.53522	−	2.10518i	0.453522	−	0.210518i
$101$			8.40742i			0.836570i	0.908316	+	0.418285i	$0.137369\pi$
$101$			8.40742i			0.836570i	−0.908316	+	0.418285i	$0.862631\pi$
$102$	−1.79158	−	1.79158i	−0.177392	−	0.177392i
$103$			2.52556i			0.248851i	0.992229	+	0.124426i	$0.0397088\pi$
$103$			2.52556i			0.248851i	−0.992229	+	0.124426i	$0.960291\pi$
$104$	−2.34770			−0.230211
$105$	2.27829	+	10.3193i	0.222339	+	1.00706i
$106$	3.00973	+	3.00973i	0.292331	+	0.292331i
$107$	0.430870	−	0.430870i	0.0416537	−	0.0416537i	−0.685973	−	0.727627i	$-0.740623\pi$
$107$	0.430870	−	0.430870i	0.0416537	−	0.0416537i	0.727627	+	0.685973i	$0.240623\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	11.4666	+	11.4666i	1.09830	+	1.09830i	0.994610	+	0.103687i	$0.0330640\pi$
$109$	11.4666	+	11.4666i	1.09830	+	1.09830i	0.103687	+	0.994610i	$0.466936\pi$
$110$	−0.321138	−	1.45456i	−0.0306193	−	0.138687i
$111$	1.23006	−	5.95709i	0.116752	−	0.565422i
$112$	3.34184	−	3.34184i	0.315774	−	0.315774i
$113$		−	13.9701i		−	1.31420i	−0.753803	−	0.657100i	$-0.771783\pi$
$113$		−	13.9701i		−	1.31420i	0.753803	−	0.657100i	$-0.228217\pi$
$114$	−3.69948			−0.346488
$115$	−16.6167	+	3.66862i	−1.54951	+	0.342100i
$116$	1.83506	−	1.83506i	0.170381	−	0.170381i
$117$			2.34770i			0.217045i
$118$	1.77437	+	1.77437i	0.163344	+	0.163344i
$119$	−8.46712	−	8.46712i	−0.776180	−	0.776180i
$120$	−1.20308	+	1.88483i	−0.109826	+	0.172061i
$121$	10.5562			0.959657
$122$	−1.33334	−	1.33334i	−0.120715	−	0.120715i
$123$	4.38175	+	4.38175i	0.395089	+	0.395089i
$124$	−3.00523	−	3.00523i	−0.269877	−	0.269877i
$125$	−8.88775	+	6.78292i	−0.794944	+	0.606683i
$126$	−3.34184	−	3.34184i	−0.297715	−	0.297715i
$127$	1.03742	−	1.03742i	0.0920561	−	0.0920561i	−0.659579	−	0.751635i	$-0.729265\pi$
$127$	1.03742	−	1.03742i	0.0920561	−	0.0920561i	0.751635	+	0.659579i	$0.229265\pi$
$128$	1.00000			0.0883883
$129$	−6.70270	+	6.70270i	−0.590140	+	0.590140i
$130$	5.12617	−	1.13175i	0.449594	−	0.0992612i
$131$	−1.52555	−	1.52555i	−0.133288	−	0.133288i	0.637315	−	0.770603i	$-0.280045\pi$
$131$	−1.52555	−	1.52555i	−0.133288	−	0.133288i	−0.770603	+	0.637315i	$0.780045\pi$
$132$	0.471050	+	0.471050i	0.0409997	+	0.0409997i
$133$	−17.4840			−1.51606
$134$	9.44858	+	9.44858i	0.816233	+	0.816233i
$135$	1.88483	+	1.20308i	0.162220	+	0.103545i
$136$		−	2.53367i		−	0.217261i
$137$	−11.0104	+	11.0104i	−0.940684	+	0.940684i	−0.998337	−	0.0576526i	$-0.981638\pi$
$137$	−11.0104	+	11.0104i	−0.940684	+	0.940684i	0.0576526	+	0.998337i	$0.481638\pi$
$138$	5.38119	−	5.38119i	0.458078	−	0.458078i
$139$	−15.7670			−1.33734			−0.668670	−	0.743559i	$-0.733136\pi$
$139$	−15.7670			−1.33734			−0.668670	+	0.743559i	$0.733136\pi$
$140$	−5.68586	+	8.90786i	−0.480543	+	0.752851i
$141$			7.81235i			0.657918i
$142$	3.44750			0.289308
$143$		−	1.56396i		−	0.130785i
$144$		−	1.00000i		−	0.0833333i
$145$	−3.12221	+	4.89146i	−0.259285	+	0.406214i
$146$	7.93466	−	7.93466i	0.656678	−	0.656678i
$147$	−10.8440	−	10.8440i	−0.894401	−	0.894401i
$148$	5.08208	−	3.34252i	0.417745	−	0.274753i
$149$			11.5084i			0.942804i	0.881918	+	0.471402i	$0.156252\pi$
$149$			11.5084i			0.942804i	−0.881918	+	0.471402i	$0.843748\pi$
$150$	1.71830	−	4.69547i	0.140298	−	0.383384i
$151$			10.3843i			0.845059i	0.906349	+	0.422530i	$0.138858\pi$
$151$			10.3843i			0.845059i	−0.906349	+	0.422530i	$0.861142\pi$
$152$	−2.61593	−	2.61593i	−0.212180	−	0.212180i
$153$	−2.53367			−0.204835
$154$	2.22622	+	2.22622i	0.179394	+	0.179394i
$155$	8.01060	+	5.11315i	0.643427	+	0.410698i
$156$	−1.66007	+	1.66007i	−0.132912	+	0.132912i
$157$	−16.9864	+	16.9864i	−1.35566	+	1.35566i	−0.476470	+	0.879191i	$0.658084\pi$
$157$	−16.9864	+	16.9864i	−1.35566	+	1.35566i	−0.879191	+	0.476470i	$0.841916\pi$
$158$	−8.95760	−	8.95760i	−0.712629	−	0.712629i
$159$	4.25640			0.337554
$160$	−2.18349	+	0.482069i	−0.172620	+	0.0381109i
$161$	25.4319	−	25.4319i	2.00432	−	2.00432i
$162$	−1.00000			−0.0785674
$163$			20.9453i			1.64056i	0.571961	+	0.820281i	$0.306183\pi$
$163$			20.9453i			1.64056i	−0.571961	+	0.820281i	$0.693817\pi$
$164$			6.19673i			0.483883i
$165$	−1.25561	−	0.801453i	−0.0977491	−	0.0623930i
$166$	6.18662	+	6.18662i	0.480175	+	0.480175i
$167$			5.80697i			0.449357i	0.974433	+	0.224678i	$0.0721331\pi$
$167$			5.80697i			0.449357i	−0.974433	+	0.224678i	$0.927867\pi$
$168$		−	4.72607i		−	0.364625i
$169$	−7.48831			−0.576024
$170$	1.22140	+	5.53224i	0.0936774	+	0.424303i
$171$	−2.61593	+	2.61593i	−0.200045	+	0.200045i
$172$	−9.47906			−0.722771
$173$	−12.6536	+	12.6536i	−0.962035	+	0.962035i	−0.999305	−	0.0372707i	$-0.988134\pi$
$173$	−12.6536	+	12.6536i	−0.962035	+	0.962035i	0.0372707	+	0.999305i	$0.488134\pi$
$174$		−	2.59517i		−	0.196739i
$175$	8.12080	−	22.1912i	0.613875	−	1.67749i
$176$			0.666166i			0.0502141i
$177$	2.50933			0.188613
$178$	−0.703752	+	0.703752i	−0.0527484	+	0.0527484i
$179$	−3.41628	+	3.41628i	−0.255345	+	0.255345i	−0.823158	−	0.567813i	$-0.807790\pi$
$179$	−3.41628	+	3.41628i	−0.255345	+	0.255345i	0.567813	+	0.823158i	$0.307790\pi$
$180$	0.482069	+	2.18349i	0.0359313	+	0.162747i
$181$	20.1683			1.49910			0.749548	−	0.661950i	$-0.230271\pi$
$181$	20.1683			1.49910			0.749548	+	0.661950i	$0.230271\pi$
$182$	−7.84563	+	7.84563i	−0.581557	+	0.581557i
$183$	−1.88563			−0.139390
$184$	7.61016			0.561028
$185$	−9.48533	+	9.74826i	−0.697375	+	0.716706i
$186$	−4.25003			−0.311628
$187$	1.68784			0.123427
$188$	−5.52416	+	5.52416i	−0.402891	+	0.402891i
$189$	−4.72607			−0.343771
$190$	6.97289	+	4.45078i	0.505867	+	0.322894i
$191$	−14.1273	+	14.1273i	−1.02222	+	1.02222i	−0.0224689	+	0.999748i	$0.507153\pi$
$191$	−14.1273	+	14.1273i	−1.02222	+	1.02222i	−0.999748	+	0.0224689i	$0.992847\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	7.65037			0.550686			0.275343	−	0.961346i	$-0.411209\pi$
$193$	7.65037			0.550686			0.275343	+	0.961346i	$0.411209\pi$
$194$			6.06755i			0.435625i
$195$	2.82448	−	4.42502i	0.202265	−	0.316882i
$196$		−	15.3358i		−	1.09541i
$197$	8.59297	−	8.59297i	0.612223	−	0.612223i	−0.331302	−	0.943525i	$-0.607488\pi$
$197$	8.59297	−	8.59297i	0.612223	−	0.612223i	0.943525	+	0.331302i	$0.107488\pi$
$198$	0.666166			0.0473423
$199$	−3.03831	+	3.03831i	−0.215380	+	0.215380i	−0.806548	−	0.591168i	$-0.798667\pi$
$199$	−3.03831	+	3.03831i	−0.215380	+	0.215380i	0.591168	+	0.806548i	$0.298667\pi$
$200$	4.53522	−	2.10518i	0.320688	−	0.148859i
$201$	13.3623			0.942505
$202$			8.40742i			0.591544i
$203$		−	12.2650i		−	0.860833i
$204$	−1.79158	−	1.79158i	−0.125435	−	0.125435i
$205$	−2.98725	−	13.5305i	−0.208638	−	0.945008i
$206$			2.52556i			0.175964i
$207$		−	7.61016i		−	0.528942i
$208$	−2.34770			−0.162784
$209$	1.74264	−	1.74264i	0.120541	−	0.120541i
$210$	2.27829	+	10.3193i	0.157217	+	0.712101i
$211$	23.8884			1.64454			0.822271	−	0.569096i	$-0.192707\pi$
$211$	23.8884			1.64454			0.822271	+	0.569096i	$0.192707\pi$
$212$	3.00973	+	3.00973i	0.206709	+	0.206709i
$213$	2.43775	−	2.43775i	0.167032	−	0.167032i
$214$	0.430870	−	0.430870i	0.0294536	−	0.0294536i
$215$	20.6974	−	4.56956i	1.41155	−	0.311641i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−20.0860			−1.36353
$218$	11.4666	+	11.4666i	0.776613	+	0.776613i
$219$		−	11.2213i		−	0.758266i
$220$	−0.321138	−	1.45456i	−0.0216511	−	0.0980666i
$221$			5.94830i			0.400126i
$222$	1.23006	−	5.95709i	0.0825560	−	0.399814i
$223$	8.08969	+	8.08969i	0.541726	+	0.541726i	0.924035	−	0.382309i	$-0.124871\pi$
$223$	8.08969	+	8.08969i	0.541726	+	0.541726i	−0.382309	+	0.924035i	$0.624871\pi$
$224$	3.34184	−	3.34184i	0.223286	−	0.223286i
$225$	−2.10518	−	4.53522i	−0.140345	−	0.302348i
$226$		−	13.9701i		−	0.929280i
$227$		−	20.7048i		−	1.37422i	−0.726551	−	0.687112i	$-0.758878\pi$
$227$		−	20.7048i		−	1.37422i	0.726551	−	0.687112i	$-0.241122\pi$
$228$	−3.69948			−0.245004
$229$		−	16.7178i		−	1.10475i	−0.833597	−	0.552373i	$-0.813722\pi$
$229$		−	16.7178i		−	1.10475i	0.833597	−	0.552373i	$-0.186278\pi$
$230$	−16.6167	+	3.66862i	−1.09567	+	0.241902i
$231$	3.14835			0.207146
$232$	1.83506	−	1.83506i	0.120478	−	0.120478i
$233$	6.42946	−	6.42946i	0.421208	−	0.421208i	−0.464411	−	0.885620i	$-0.653734\pi$
$233$	6.42946	−	6.42946i	0.421208	−	0.421208i	0.885620	+	0.464411i	$0.153734\pi$
$234$			2.34770i			0.153474i
$235$	9.39891	−	14.7250i	0.613117	−	0.960550i
$236$	1.77437	+	1.77437i	0.115501	+	0.115501i
$237$	−12.6680			−0.822873
$238$	−8.46712	−	8.46712i	−0.548842	−	0.548842i
$239$	−4.77321	−	4.77321i	−0.308754	−	0.308754i	0.535672	−	0.844426i	$-0.320058\pi$
$239$	−4.77321	−	4.77321i	−0.308754	−	0.308754i	−0.844426	+	0.535672i	$0.820058\pi$
$240$	−1.20308	+	1.88483i	−0.0776587	+	0.121665i
$241$	11.2042	−	11.2042i	0.721729	−	0.721729i	−0.247228	−	0.968957i	$-0.579520\pi$
$241$	11.2042	−	11.2042i	0.721729	−	0.721729i	0.968957	+	0.247228i	$0.0795197\pi$
$242$	10.5562			0.678580
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−1.33334	−	1.33334i	−0.0853584	−	0.0853584i
$245$	7.39290	+	33.4855i	0.472315	+	2.13931i
$246$	4.38175	+	4.38175i	0.279370	+	0.279370i
$247$	6.14141	+	6.14141i	0.390768	+	0.390768i
$248$	−3.00523	−	3.00523i	−0.190832	−	0.190832i
$249$	8.74920			0.554458
$250$	−8.88775	+	6.78292i	−0.562110	+	0.428989i
$251$	13.2650	+	13.2650i	0.837278	+	0.837278i	0.988500	−	0.151222i	$-0.0483209\pi$
$251$	13.2650	+	13.2650i	0.837278	+	0.837278i	−0.151222	+	0.988500i	$0.548321\pi$
$252$	−3.34184	−	3.34184i	−0.210516	−	0.210516i
$253$			5.06962i			0.318724i
$254$	1.03742	−	1.03742i	0.0650935	−	0.0650935i
$255$	4.77554	+	3.04822i	0.299056	+	0.190887i
$256$	1.00000			0.0625000
$257$			18.3578i			1.14513i	0.819859	+	0.572565i	$0.194052\pi$
$257$			18.3578i			1.14513i	−0.819859	+	0.572565i	$0.805948\pi$
$258$	−6.70270	+	6.70270i	−0.417292	+	0.417292i
$259$	5.81334	−	28.1537i	0.361223	−	1.74938i
$260$	5.12617	−	1.13175i	0.317911	−	0.0701883i
$261$	−1.83506	−	1.83506i	−0.113588	−	0.113588i
$262$	−1.52555	−	1.52555i	−0.0942487	−	0.0942487i
$263$	2.32615	−	2.32615i	0.143437	−	0.143437i	−0.631742	−	0.775179i	$-0.717660\pi$
$263$	2.32615	−	2.32615i	0.143437	−	0.143437i	0.775179	+	0.631742i	$0.217660\pi$
$264$	0.471050	+	0.471050i	0.0289911	+	0.0289911i
$265$	−8.02259	−	5.12080i	−0.492824	−	0.314568i
$266$	−17.4840			−1.07201
$267$			0.995256i			0.0609087i
$268$	9.44858	+	9.44858i	0.577164	+	0.577164i
$269$			13.2859i			0.810056i	0.914304	+	0.405028i	$0.132738\pi$
$269$			13.2859i			0.810056i	−0.914304	+	0.405028i	$0.867262\pi$
$270$	1.88483	+	1.20308i	0.114707	+	0.0732173i
$271$	−7.30510			−0.443753			−0.221877	−	0.975075i	$-0.571218\pi$
$271$	−7.30510			−0.443753			−0.221877	+	0.975075i	$0.571218\pi$
$272$		−	2.53367i		−	0.153626i
$273$			11.0954i			0.671524i
$274$	−11.0104	+	11.0104i	−0.665164	+	0.665164i
$275$	1.40240	+	3.02121i	0.0845678	+	0.182186i
$276$	5.38119	−	5.38119i	0.323910	−	0.323910i
$277$	−10.3515			−0.621963			−0.310982	−	0.950416i	$-0.600658\pi$
$277$	−10.3515			−0.621963			−0.310982	+	0.950416i	$0.600658\pi$
$278$	−15.7670			−0.945642
$279$	−3.00523	+	3.00523i	−0.179918	+	0.179918i
$280$	−5.68586	+	8.90786i	−0.339795	+	0.532346i
$281$	−2.33368	+	2.33368i	−0.139215	+	0.139215i	−0.773280	−	0.634065i	$-0.781385\pi$
$281$	−2.33368	+	2.33368i	−0.139215	+	0.139215i	0.634065	+	0.773280i	$0.281385\pi$
$282$			7.81235i			0.465219i
$283$		−	6.66578i		−	0.396239i	−0.980178	−	0.198120i	$-0.936517\pi$
$283$		−	6.66578i		−	0.396239i	0.980178	−	0.198120i	$-0.0634835\pi$
$284$	3.44750			0.204572
$285$	8.07776	−	1.78340i	0.478485	−	0.105640i
$286$		−	1.56396i		−	0.0924786i
$287$	20.7085	+	20.7085i	1.22238	+	1.22238i
$288$		−	1.00000i		−	0.0589256i
$289$	10.5805			0.622383
$290$	−3.12221	+	4.89146i	−0.183342	+	0.287237i
$291$	4.29041	+	4.29041i	0.251508	+	0.251508i
$292$	7.93466	−	7.93466i	0.464341	−	0.464341i
$293$	−7.71738	−	7.71738i	−0.450854	−	0.450854i	0.444784	−	0.895638i	$-0.353280\pi$
$293$	−7.71738	−	7.71738i	−0.450854	−	0.450854i	−0.895638	+	0.444784i	$0.853280\pi$
$294$	−10.8440	−	10.8440i	−0.632437	−	0.632437i
$295$	−4.72967	−	3.01894i	−0.275372	−	0.175769i
$296$	5.08208	−	3.34252i	0.295390	−	0.194280i
$297$	0.471050	−	0.471050i	0.0273331	−	0.0273331i
$298$			11.5084i			0.666663i
$299$	−17.8663			−1.03324
$300$	1.71830	−	4.69547i	0.0992059	−	0.271093i
$301$	−31.6775	+	31.6775i	−1.82586	+	1.82586i
$302$			10.3843i			0.597547i
$303$	5.94494	+	5.94494i	0.341528	+	0.341528i
$304$	−2.61593	−	2.61593i	−0.150034	−	0.150034i
$305$	3.55409	+	2.26857i	0.203507	+	0.129898i
$306$	−2.53367			−0.144840
$307$	−12.9567	−	12.9567i	−0.739476	−	0.739476i	0.233001	−	0.972477i	$-0.425146\pi$
$307$	−12.9567	−	12.9567i	−0.739476	−	0.739476i	−0.972477	+	0.233001i	$0.925146\pi$
$308$	2.22622	+	2.22622i	0.126851	+	0.126851i
$309$	1.78584	+	1.78584i	0.101593	+	0.101593i
$310$	8.01060	+	5.11315i	0.454971	+	0.290407i
$311$	15.2081	+	15.2081i	0.862371	+	0.862371i	0.991613	−	0.129242i	$-0.0412544\pi$
$311$	15.2081	+	15.2081i	0.862371	+	0.862371i	−0.129242	+	0.991613i	$0.541254\pi$
$312$	−1.66007	+	1.66007i	−0.0939831	+	0.0939831i
$313$	−16.4081			−0.927439			−0.463719	−	0.885982i	$-0.653485\pi$
$313$	−16.4081			−0.927439			−0.463719	+	0.885982i	$0.653485\pi$
$314$	−16.9864	+	16.9864i	−0.958597	+	0.958597i
$315$	8.90786	+	5.68586i	0.501901	+	0.320362i
$316$	−8.95760	−	8.95760i	−0.503905	−	0.503905i
$317$	−10.9552	−	10.9552i	−0.615304	−	0.615304i	0.329019	−	0.944323i	$-0.393282\pi$
$317$	−10.9552	−	10.9552i	−0.615304	−	0.615304i	−0.944323	+	0.329019i	$0.893282\pi$
$318$	4.25640			0.238687
$319$	1.22246	+	1.22246i	0.0684444	+	0.0684444i
$320$	−2.18349	+	0.482069i	−0.122061	+	0.0269485i
$321$		−	0.609342i		−	0.0340101i
$322$	25.4319	−	25.4319i	1.41727	−	1.41727i
$323$	−6.62790	+	6.62790i	−0.368786	+	0.368786i
$324$	−1.00000			−0.0555556
$325$	−10.6473	+	4.94233i	−0.590607	+	0.274151i
$326$			20.9453i			1.16005i
$327$	16.2162			0.896756
$328$			6.19673i			0.342157i
$329$			36.9217i			2.03556i
$330$	−1.25561	−	0.801453i	−0.0691191	−	0.0441185i
$331$	21.5320	−	21.5320i	1.18351	−	1.18351i	0.204677	−	0.978830i	$-0.434386\pi$
$331$	21.5320	−	21.5320i	1.18351	−	1.18351i	0.978830	−	0.204677i	$-0.0656144\pi$
$332$	6.18662	+	6.18662i	0.339535	+	0.339535i
$333$	−3.34252	−	5.08208i	−0.183169	−	0.278496i
$334$			5.80697i			0.317743i
$335$	−25.1857	−	16.0760i	−1.37604	−	0.878325i
$336$		−	4.72607i		−	0.257829i
$337$	−9.32924	−	9.32924i	−0.508196	−	0.508196i	0.405776	−	0.913972i	$-0.367001\pi$
$337$	−9.32924	−	9.32924i	−0.508196	−	0.508196i	−0.913972	+	0.405776i	$0.867001\pi$
$338$	−7.48831			−0.407311
$339$	−9.87838	−	9.87838i	−0.536520	−	0.536520i
$340$	1.22140	+	5.53224i	0.0662399	+	0.300028i
$341$	2.00198	−	2.00198i	0.108413	−	0.108413i
$342$	−2.61593	+	2.61593i	−0.141453	+	0.141453i
$343$	−27.8569	−	27.8569i	−1.50413	−	1.50413i
$344$	−9.47906			−0.511076
$345$	−9.15565	+	14.3439i	−0.492924	+	0.772248i
$346$	−12.6536	+	12.6536i	−0.680261	+	0.680261i
$347$	−22.7387			−1.22068			−0.610340	−	0.792140i	$-0.708967\pi$
$347$	−22.7387			−1.22068			−0.610340	+	0.792140i	$0.708967\pi$
$348$		−	2.59517i		−	0.139116i
$349$			22.0317i			1.17933i	0.807649	+	0.589664i	$0.200740\pi$
$349$			22.0317i			1.17933i	−0.807649	+	0.589664i	$0.799260\pi$
$350$	8.12080	−	22.1912i	0.434075	−	1.18617i
$351$	1.66007	+	1.66007i	0.0886082	+	0.0886082i
$352$			0.666166i			0.0355067i
$353$		−	19.8627i		−	1.05719i	−0.848875	−	0.528593i	$-0.822720\pi$
$353$		−	19.8627i		−	1.05719i	0.848875	−	0.528593i	$-0.177280\pi$
$354$	2.50933			0.133370
$355$	−7.52757	+	1.66193i	−0.399522	+	0.0882063i
$356$	−0.703752	+	0.703752i	−0.0372988	+	0.0372988i
$357$	−11.9743			−0.633748
$358$	−3.41628	+	3.41628i	−0.180556	+	0.180556i
$359$		−	34.9845i		−	1.84641i	−0.384304	−	0.923207i	$-0.625558\pi$
$359$		−	34.9845i		−	1.84641i	0.384304	−	0.923207i	$-0.374442\pi$
$360$	0.482069	+	2.18349i	0.0254073	+	0.115080i
$361$		−	5.31386i		−	0.279677i
$362$	20.1683			1.06002
$363$	7.46438	−	7.46438i	0.391778	−	0.391778i
$364$	−7.84563	+	7.84563i	−0.411223	+	0.411223i
$365$	−13.5002	+	21.1503i	−0.706631	+	1.10706i
$366$	−1.88563			−0.0985634
$367$	5.42620	−	5.42620i	0.283245	−	0.283245i	−0.551157	−	0.834402i	$-0.685813\pi$
$367$	5.42620	−	5.42620i	0.283245	−	0.283245i	0.834402	+	0.551157i	$0.185813\pi$
$368$	7.61016			0.396707
$369$	6.19673			0.322589
$370$	−9.48533	+	9.74826i	−0.493119	+	0.506788i
$371$	20.1161			1.04437
$372$	−4.25003			−0.220354
$373$	−18.4762	+	18.4762i	−0.956662	+	0.956662i	−0.999099	−	0.0424373i	$-0.986488\pi$
$373$	−18.4762	+	18.4762i	−0.956662	+	0.956662i	0.0424373	+	0.999099i	$0.486488\pi$
$374$	1.68784			0.0872764
$375$	−1.48834	+	11.0808i	−0.0768574	+	0.572212i
$376$	−5.52416	+	5.52416i	−0.284887	+	0.284887i
$377$	−4.30818	+	4.30818i	−0.221882	+	0.221882i
$378$	−4.72607			−0.243083
$379$		−	27.9090i		−	1.43359i	−0.697286	−	0.716793i	$-0.745609\pi$
$379$		−	27.9090i		−	1.43359i	0.697286	−	0.716793i	$-0.254391\pi$
$380$	6.97289	+	4.45078i	0.357702	+	0.228320i
$381$		−	1.46713i		−	0.0751635i
$382$	−14.1273	+	14.1273i	−0.722816	+	0.722816i
$383$	33.2956			1.70132			0.850662	−	0.525712i	$-0.176201\pi$
$383$	33.2956			1.70132			0.850662	+	0.525712i	$0.176201\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−5.93411	−	3.78773i	−0.302430	−	0.193040i
$386$	7.65037			0.389394
$387$			9.47906i			0.481847i
$388$			6.06755i			0.308033i
$389$	−19.1433	−	19.1433i	−0.970603	−	0.970603i	0.0289772	−	0.999580i	$-0.490775\pi$
$389$	−19.1433	−	19.1433i	−0.970603	−	0.970603i	−0.999580	+	0.0289772i	$0.990775\pi$
$390$	2.82448	−	4.42502i	0.143023	−	0.224069i
$391$		−	19.2816i		−	0.975114i
$392$		−	15.3358i		−	0.774574i
$393$	−2.15745			−0.108829
$394$	8.59297	−	8.59297i	0.432907	−	0.432907i
$395$	23.8770	+	15.2406i	1.20138	+	0.766839i
$396$	0.666166			0.0334761
$397$	15.3592	+	15.3592i	0.770858	+	0.770858i	0.978257	−	0.207399i	$-0.0664997\pi$
$397$	15.3592	+	15.3592i	0.770858	+	0.770858i	−0.207399	+	0.978257i	$0.566500\pi$
$398$	−3.03831	+	3.03831i	−0.152297	+	0.152297i
$399$	−12.3631	+	12.3631i	−0.618927	+	0.618927i
$400$	4.53522	−	2.10518i	0.226761	−	0.105259i
$401$	7.56046	+	7.56046i	0.377551	+	0.377551i	0.870218	−	0.492667i	$-0.163978\pi$
$401$	7.56046	+	7.56046i	0.377551	+	0.377551i	−0.492667	+	0.870218i	$0.663978\pi$
$402$	13.3623			0.666452
$403$	7.05537	+	7.05537i	0.351453	+	0.351453i
$404$			8.40742i			0.418285i
$405$	2.18349	−	0.482069i	0.108498	−	0.0239542i
$406$		−	12.2650i		−	0.608701i
$407$	2.22667	+	3.38551i	0.110372	+	0.167813i
$408$	−1.79158	−	1.79158i	−0.0886962	−	0.0886962i
$409$	16.6038	−	16.6038i	0.821004	−	0.821004i	−0.165248	−	0.986252i	$-0.552842\pi$
$409$	16.6038	−	16.6038i	0.821004	−	0.821004i	0.986252	+	0.165248i	$0.0528424\pi$
$410$	−2.98725	−	13.5305i	−0.147530	−	0.668222i
$411$			15.5711i			0.768065i
$412$			2.52556i			0.124426i
$413$	11.8593			0.583558
$414$		−	7.61016i		−	0.374019i
$415$	−16.4908	−	10.5260i	−0.809500	−	0.516702i
$416$	−2.34770			−0.115105
$417$	−11.1490	+	11.1490i	−0.545967	+	0.545967i
$418$	1.74264	−	1.74264i	0.0852353	−	0.0852353i
$419$		−	24.6470i		−	1.20409i	−0.798464	−	0.602043i	$-0.794354\pi$
$419$		−	24.6470i		−	1.20409i	0.798464	−	0.602043i	$-0.205646\pi$
$420$	2.27829	+	10.3193i	0.111169	+	0.503531i
$421$	−3.15671	−	3.15671i	−0.153849	−	0.153849i	0.625986	−	0.779834i	$-0.284697\pi$
$421$	−3.15671	−	3.15671i	−0.153849	−	0.153849i	−0.779834	+	0.625986i	$0.784697\pi$
$422$	23.8884			1.16287
$423$	5.52416	+	5.52416i	0.268594	+	0.268594i
$424$	3.00973	+	3.00973i	0.146165	+	0.146165i
$425$	−5.33384	−	11.4908i	−0.258729	−	0.557384i
$426$	2.43775	−	2.43775i	0.118109	−	0.118109i
$427$	−8.91162			−0.431263
$428$	0.430870	−	0.430870i	0.0208269	−	0.0208269i
$429$	−1.10588	−	1.10588i	−0.0533926	−	0.0533926i
$430$	20.6974	−	4.56956i	0.998116	−	0.220364i
$431$	−0.785388	−	0.785388i	−0.0378308	−	0.0378308i	0.687938	−	0.725769i	$-0.258516\pi$
$431$	−0.785388	−	0.785388i	−0.0378308	−	0.0378308i	−0.725769	+	0.687938i	$0.758516\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	20.8591	+	20.8591i	1.00243	+	1.00243i	0.999997	+	0.00242917i	$0.000773229\pi$
$433$	20.8591	+	20.8591i	1.00243	+	1.00243i	0.00242917	+	0.999997i	$0.499227\pi$
$434$	−20.0860			−0.964158
$435$	1.25105	+	5.66652i	0.0599833	+	0.271689i
$436$	11.4666	+	11.4666i	0.549148	+	0.549148i
$437$	−19.9076	−	19.9076i	−0.952310	−	0.952310i
$438$		−	11.2213i		−	0.536175i
$439$	17.9134	−	17.9134i	0.854961	−	0.854961i	−0.135778	−	0.990739i	$-0.543353\pi$
$439$	17.9134	−	17.9134i	0.854961	−	0.854961i	0.990739	+	0.135778i	$0.0433535\pi$
$440$	−0.321138	−	1.45456i	−0.0153096	−	0.0693436i
$441$	−15.3358			−0.730275
$442$			5.94830i			0.282932i
$443$	−6.57108	+	6.57108i	−0.312202	+	0.312202i	−0.845762	−	0.533560i	$-0.820854\pi$
$443$	−6.57108	+	6.57108i	−0.312202	+	0.312202i	0.533560	+	0.845762i	$0.320854\pi$
$444$	1.23006	−	5.95709i	0.0583759	−	0.282711i
$445$	1.19738	−	1.87589i	0.0567611	−	0.0889257i
$446$	8.08969	+	8.08969i	0.383058	+	0.383058i
$447$	8.13766	+	8.13766i	0.384898	+	0.384898i
$448$	3.34184	−	3.34184i	0.157887	−	0.157887i
$449$	−7.18617	−	7.18617i	−0.339136	−	0.339136i	0.516906	−	0.856042i	$-0.327084\pi$
$449$	−7.18617	−	7.18617i	−0.339136	−	0.339136i	−0.856042	+	0.516906i	$0.827084\pi$
$450$	−2.10518	−	4.53522i	−0.0992392	−	0.213792i
$451$	−4.12805			−0.194382
$452$		−	13.9701i		−	0.657100i
$453$	7.34278	+	7.34278i	0.344994	+	0.344994i
$454$		−	20.7048i		−	0.971723i
$455$	13.3487	−	20.9130i	0.625796	−	0.980414i
$456$	−3.69948			−0.173244
$457$		−	8.80871i		−	0.412054i	−0.978546	−	0.206027i	$-0.933947\pi$
$457$		−	8.80871i		−	0.412054i	0.978546	−	0.206027i	$-0.0660535\pi$
$458$		−	16.7178i		−	0.781173i
$459$	−1.79158	+	1.79158i	−0.0836236	+	0.0836236i
$460$	−16.6167	+	3.66862i	−0.774756	+	0.171050i
$461$	−12.7438	+	12.7438i	−0.593538	+	0.593538i	−0.938585	−	0.345048i	$-0.887863\pi$
$461$	−12.7438	+	12.7438i	−0.593538	+	0.593538i	0.345048	+	0.938585i	$0.387863\pi$
$462$	3.14835			0.146474
$463$	−19.6503			−0.913225			−0.456613	−	0.889666i	$-0.650937\pi$
$463$	−19.6503			−0.913225			−0.456613	+	0.889666i	$0.650937\pi$
$464$	1.83506	−	1.83506i	0.0851907	−	0.0851907i
$465$	9.27989	−	2.04881i	0.430345	−	0.0950112i
$466$	6.42946	−	6.42946i	0.297839	−	0.297839i
$467$			7.05736i			0.326576i	0.986578	+	0.163288i	$0.0522099\pi$
$467$			7.05736i			0.326576i	−0.986578	+	0.163288i	$0.947790\pi$
$468$			2.34770i			0.108522i
$469$	63.1513			2.91606
$470$	9.39891	−	14.7250i	0.433539	−	0.679212i
$471$			24.0224i			1.10689i
$472$	1.77437	+	1.77437i	0.0816718	+	0.0816718i
$473$		−	6.31462i		−	0.290347i
$474$	−12.6680			−0.581859
$475$	−17.3708	−	6.35680i	−0.797027	−	0.291670i
$476$	−8.46712	−	8.46712i	−0.388090	−	0.388090i
$477$	3.00973	−	3.00973i	0.137806	−	0.137806i
$478$	−4.77321	−	4.77321i	−0.218322	−	0.218322i
$479$	−2.30974	−	2.30974i	−0.105535	−	0.105535i	0.652368	−	0.757903i	$-0.273776\pi$
$479$	−2.30974	−	2.30974i	−0.105535	−	0.105535i	−0.757903	+	0.652368i	$0.773776\pi$
$480$	−1.20308	+	1.88483i	−0.0549130	+	0.0860304i
$481$	−11.9312	+	7.84723i	−0.544016	+	0.357803i
$482$	11.2042	−	11.2042i	0.510339	−	0.510339i
$483$		−	35.9662i		−	1.63652i
$484$	10.5562			0.479828
$485$	−2.92498	−	13.2484i	−0.132816	−	0.601579i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$		−	4.14854i		−	0.187988i	−0.995573	−	0.0939941i	$-0.970037\pi$
$487$		−	4.14854i		−	0.187988i	0.995573	−	0.0939941i	$-0.0299635\pi$
$488$	−1.33334	−	1.33334i	−0.0603575	−	0.0603575i
$489$	14.8106	+	14.8106i	0.669756	+	0.669756i
$490$	7.39290	+	33.4855i	0.333977	+	1.51272i
$491$	19.1216			0.862948			0.431474	−	0.902125i	$-0.357994\pi$
$491$	19.1216			0.862948			0.431474	+	0.902125i	$0.357994\pi$
$492$	4.38175	+	4.38175i	0.197544	+	0.197544i
$493$	−4.64945	−	4.64945i	−0.209401	−	0.209401i
$494$	6.14141	+	6.14141i	0.276315	+	0.276315i
$495$	−1.45456	+	0.321138i	−0.0653777	+	0.0144341i
$496$	−3.00523	−	3.00523i	−0.134939	−	0.134939i
$497$	11.5210	−	11.5210i	0.516788	−	0.516788i
$498$	8.74920			0.392061
$499$	15.5895	−	15.5895i	0.697884	−	0.697884i	−0.266070	−	0.963954i	$-0.585725\pi$
$499$	15.5895	−	15.5895i	0.697884	−	0.697884i	0.963954	+	0.266070i	$0.0857252\pi$
$500$	−8.88775	+	6.78292i	−0.397472	+	0.303341i
$501$	4.10615	+	4.10615i	0.183449	+	0.183449i
$502$	13.2650	+	13.2650i	0.592045	+	0.592045i
$503$	1.20397			0.0536823			0.0268412	−	0.999640i	$-0.491455\pi$
$503$	1.20397			0.0536823			0.0268412	+	0.999640i	$0.491455\pi$
$504$	−3.34184	−	3.34184i	−0.148857	−	0.148857i
$505$	−4.05296	−	18.3575i	−0.180354	−	0.816897i
$506$			5.06962i			0.225372i
$507$	−5.29504	+	5.29504i	−0.235161	+	0.235161i
$508$	1.03742	−	1.03742i	0.0460280	−	0.0460280i
$509$	14.0992			0.624938			0.312469	−	0.949928i	$-0.398844\pi$
$509$	14.0992			0.624938			0.312469	+	0.949928i	$0.398844\pi$
$510$	4.77554	+	3.04822i	0.211465	+	0.134977i
$511$		−	53.0328i		−	2.34603i
$512$	1.00000			0.0441942
$513$			3.69948i			0.163336i
$514$			18.3578i			0.809729i
$515$	−1.21750	−	5.51453i	−0.0536493	−	0.242999i
$516$	−6.70270	+	6.70270i	−0.295070	+	0.295070i
$517$	−3.68001	−	3.68001i	−0.161847	−	0.161847i
$518$	5.81334	−	28.1537i	0.255423	−	1.23700i
$519$			17.8949i			0.785498i
$520$	5.12617	−	1.13175i	0.224797	−	0.0496306i
$521$		−	34.0802i		−	1.49308i	−0.665339	−	0.746541i	$-0.731713\pi$
$521$		−	34.0802i		−	1.49308i	0.665339	−	0.746541i	$-0.268287\pi$
$522$	−1.83506	−	1.83506i	−0.0803185	−	0.0803185i
$523$	19.0590			0.833393			0.416696	−	0.909046i	$-0.363188\pi$
$523$	19.0590			0.833393			0.416696	+	0.909046i	$0.363188\pi$
$524$	−1.52555	−	1.52555i	−0.0666439	−	0.0666439i
$525$	−9.94924	−	21.4338i	−0.434220	−	0.935447i
$526$	2.32615	−	2.32615i	0.101425	−	0.101425i
$527$	−7.61426	+	7.61426i	−0.331682	+	0.331682i
$528$	0.471050	+	0.471050i	0.0204998	+	0.0204998i
$529$	34.9145			1.51802
$530$	−8.02259	−	5.12080i	−0.348479	−	0.222433i
$531$	1.77437	−	1.77437i	0.0770009	−	0.0770009i
$532$	−17.4840			−0.758028
$533$		−	14.5480i		−	0.630146i
$534$			0.995256i			0.0430689i
$535$	−0.733089	+	1.14851i	−0.0316942	+	0.0496542i
$536$	9.44858	+	9.44858i	0.408117	+	0.408117i
$537$			4.83135i			0.208488i
$538$			13.2859i			0.572796i
$539$	10.2162			0.440042
$540$	1.88483	+	1.20308i	0.0811102	+	0.0517725i
$541$	5.64524	−	5.64524i	0.242708	−	0.242708i	−0.575262	−	0.817969i	$-0.695100\pi$
$541$	5.64524	−	5.64524i	0.242708	−	0.242708i	0.817969	+	0.575262i	$0.195100\pi$
$542$	−7.30510			−0.313781
$543$	14.2611	−	14.2611i	0.612003	−	0.612003i
$544$		−	2.53367i		−	0.108630i
$545$	−30.5647	−	19.5094i	−1.30925	−	0.835691i
$546$			11.0954i			0.474839i
$547$	−29.3947			−1.25683			−0.628414	−	0.777879i	$-0.716295\pi$
$547$	−29.3947			−1.25683			−0.628414	+	0.777879i	$0.716295\pi$
$548$	−11.0104	+	11.0104i	−0.470342	+	0.470342i
$549$	−1.33334	+	1.33334i	−0.0569056	+	0.0569056i
$550$	1.40240	+	3.02121i	0.0597985	+	0.128825i
$551$	−9.60078			−0.409007
$552$	5.38119	−	5.38119i	0.229039	−	0.229039i
$553$	−59.8697			−2.54592
$554$	−10.3515			−0.439794
$555$	0.185918	+	13.6002i	0.00789178	+	0.577296i
$556$	−15.7670			−0.668670
$557$	27.6822			1.17293			0.586466	−	0.809974i	$-0.300519\pi$
$557$	27.6822			1.17293			0.586466	+	0.809974i	$0.300519\pi$
$558$	−3.00523	+	3.00523i	−0.127221	+	0.127221i
$559$	22.2540			0.941242
$560$	−5.68586	+	8.90786i	−0.240272	+	0.376426i
$561$	1.19349	−	1.19349i	0.0503890	−	0.0503890i
$562$	−2.33368	+	2.33368i	−0.0984402	+	0.0984402i
$563$	−27.5368			−1.16054			−0.580269	−	0.814425i	$-0.697053\pi$
$563$	−27.5368			−1.16054			−0.580269	+	0.814425i	$0.697053\pi$
$564$			7.81235i			0.328959i
$565$	6.73457	+	30.5036i	0.283325	+	1.28330i
$566$		−	6.66578i		−	0.280183i
$567$	−3.34184	+	3.34184i	−0.140344	+	0.140344i
$568$	3.44750			0.144654
$569$	−21.5462	+	21.5462i	−0.903262	+	0.903262i	−0.995717	−	0.0924552i	$-0.970529\pi$
$569$	−21.5462	+	21.5462i	−0.903262	+	0.903262i	0.0924552	+	0.995717i	$0.470529\pi$
$570$	8.07776	−	1.78340i	0.338340	−	0.0746985i
$571$	4.88567			0.204459			0.102229	−	0.994761i	$-0.467402\pi$
$571$	4.88567			0.204459			0.102229	+	0.994761i	$0.467402\pi$
$572$		−	1.56396i		−	0.0653923i
$573$			19.9790i			0.834636i
$574$	20.7085	+	20.7085i	0.864355	+	0.864355i
$575$	34.5137	−	16.0207i	1.43932	−	0.668111i
$576$		−	1.00000i		−	0.0416667i
$577$			4.20762i			0.175166i	0.996157	+	0.0875828i	$0.0279142\pi$
$577$			4.20762i			0.175166i	−0.996157	+	0.0875828i	$0.972086\pi$
$578$	10.5805			0.440091
$579$	5.40963	−	5.40963i	0.224816	−	0.224816i
$580$	−3.12221	+	4.89146i	−0.129643	+	0.203107i
$581$	41.3494			1.71546
$582$	4.29041	+	4.29041i	0.177843	+	0.177843i
$583$	−2.00498	+	2.00498i	−0.0830377	+	0.0830377i
$584$	7.93466	−	7.93466i	0.328339	−	0.328339i
$585$	−1.13175	−	5.12617i	−0.0467922	−	0.211941i
$586$	−7.71738	−	7.71738i	−0.318802	−	0.318802i
$587$	−37.1635			−1.53390			−0.766951	−	0.641706i	$-0.778227\pi$
$587$	−37.1635			−1.53390			−0.766951	+	0.641706i	$0.778227\pi$
$588$	−10.8440	−	10.8440i	−0.447201	−	0.447201i
$589$			15.7229i			0.647851i
$590$	−4.72967	−	3.01894i	−0.194717	−	0.124288i
$591$		−	12.1523i		−	0.499878i
$592$	5.08208	−	3.34252i	0.208872	−	0.137377i
$593$	21.0119	+	21.0119i	0.862855	+	0.862855i	0.991669	−	0.128814i	$-0.0411169\pi$
$593$	21.0119	+	21.0119i	0.862855	+	0.862855i	−0.128814	+	0.991669i	$0.541117\pi$
$594$	0.471050	−	0.471050i	0.0193274	−	0.0193274i
$595$	22.5696	+	14.4061i	0.925262	+	0.590593i
$596$			11.5084i			0.471402i
$597$			4.29682i			0.175857i
$598$	−17.8663			−0.730609
$599$			21.8033i			0.890860i	0.895317	+	0.445430i	$0.146949\pi$
$599$			21.8033i			0.890860i	−0.895317	+	0.445430i	$0.853051\pi$
$600$	1.71830	−	4.69547i	0.0701492	−	0.191692i
$601$	20.7593			0.846788			0.423394	−	0.905946i	$-0.360839\pi$
$601$	20.7593			0.846788			0.423394	+	0.905946i	$0.360839\pi$
$602$	−31.6775	+	31.6775i	−1.29108	+	1.29108i
$603$	9.44858	−	9.44858i	0.384776	−	0.384776i
$604$			10.3843i			0.422530i
$605$	−23.0494	+	5.08883i	−0.937090	+	0.206890i
$606$	5.94494	+	5.94494i	0.241497	+	0.241497i
$607$	−0.910829			−0.0369694			−0.0184847	−	0.999829i	$-0.505884\pi$
$607$	−0.910829			−0.0369694			−0.0184847	+	0.999829i	$0.505884\pi$
$608$	−2.61593	−	2.61593i	−0.106090	−	0.106090i
$609$	−8.67265	−	8.67265i	−0.351433	−	0.351433i
$610$	3.55409	+	2.26857i	0.143901	+	0.0918516i
$611$	12.9691	−	12.9691i	0.524672	−	0.524672i
$612$	−2.53367			−0.102418
$613$	−29.8661	+	29.8661i	−1.20628	+	1.20628i	−0.234057	+	0.972223i	$0.575200\pi$
$613$	−29.8661	+	29.8661i	−1.20628	+	1.20628i	−0.972223	+	0.234057i	$0.924800\pi$
$614$	−12.9567	−	12.9567i	−0.522889	−	0.522889i
$615$	−11.6798	−	7.45518i	−0.470974	−	0.300622i
$616$	2.22622	+	2.22622i	0.0896969	+	0.0896969i
$617$	−18.0552	−	18.0552i	−0.726876	−	0.726876i	0.243120	−	0.969996i	$-0.421829\pi$
$617$	−18.0552	−	18.0552i	−0.726876	−	0.726876i	−0.969996	+	0.243120i	$0.921829\pi$
$618$	1.78584	+	1.78584i	0.0718372	+	0.0718372i
$619$	6.78260			0.272616			0.136308	−	0.990667i	$-0.456476\pi$
$619$	6.78260			0.272616			0.136308	+	0.990667i	$0.456476\pi$
$620$	8.01060	+	5.11315i	0.321713	+	0.205349i
$621$	−5.38119	−	5.38119i	−0.215940	−	0.215940i
$622$	15.2081	+	15.2081i	0.609788	+	0.609788i
$623$			4.70365i			0.188448i
$624$	−1.66007	+	1.66007i	−0.0664561	+	0.0664561i
$625$	16.1364	−	19.0949i	0.645457	−	0.763796i
$626$	−16.4081			−0.655798
$627$		−	2.46447i		−	0.0984213i
$628$	−16.9864	+	16.9864i	−0.677830	+	0.677830i
$629$	−8.46885	−	12.8763i	−0.337675	−	0.513413i
$630$	8.90786	+	5.68586i	0.354897	+	0.226530i
$631$	−11.0789	−	11.0789i	−0.441043	−	0.441043i	0.451320	−	0.892362i	$-0.350953\pi$
$631$	−11.0789	−	11.0789i	−0.441043	−	0.441043i	−0.892362	+	0.451320i	$0.850953\pi$
$632$	−8.95760	−	8.95760i	−0.356314	−	0.356314i
$633$	16.8916	−	16.8916i	0.671381	−	0.671381i
$634$	−10.9552	−	10.9552i	−0.435086	−	0.435086i
$635$	−1.76508	+	2.76530i	−0.0700452	+	0.109737i
$636$	4.25640			0.168777
$637$			36.0038i			1.42652i
$638$	1.22246	+	1.22246i	0.0483975	+	0.0483975i
$639$		−	3.44750i		−	0.136381i
$640$	−2.18349	+	0.482069i	−0.0863099	+	0.0190554i
$641$	13.4956			0.533046			0.266523	−	0.963829i	$-0.414125\pi$
$641$	13.4956			0.533046			0.266523	+	0.963829i	$0.414125\pi$
$642$		−	0.609342i		−	0.0240488i
$643$		−	35.8341i		−	1.41316i	−0.707633	−	0.706580i	$-0.750237\pi$
$643$		−	35.8341i		−	1.41316i	0.707633	−	0.706580i	$-0.249763\pi$
$644$	25.4319	−	25.4319i	1.00216	−	1.00216i
$645$	11.4041	−	17.8664i	0.449036	−	0.703490i
$646$	−6.62790	+	6.62790i	−0.260771	+	0.260771i
$647$	−3.92354			−0.154250			−0.0771251	−	0.997021i	$-0.524574\pi$
$647$	−3.92354			−0.154250			−0.0771251	+	0.997021i	$0.524574\pi$
$648$	−1.00000			−0.0392837
$649$	−1.18202	+	1.18202i	−0.0463984	+	0.0463984i
$650$	−10.6473	+	4.94233i	−0.417623	+	0.193854i
$651$	−14.2029	+	14.2029i	−0.556657	+	0.556657i
$652$			20.9453i			0.820281i
$653$		−	13.2901i		−	0.520082i	−0.965598	−	0.260041i	$-0.916264\pi$
$653$		−	13.2901i		−	0.520082i	0.965598	−	0.260041i	$-0.0837361\pi$
$654$	16.2162			0.634102
$655$	4.06643	+	2.59559i	0.158889	+	0.101418i
$656$			6.19673i			0.241941i
$657$	−7.93466	−	7.93466i	−0.309561	−	0.309561i
$658$			36.9217i			1.43936i
$659$	3.96130			0.154310			0.0771552	−	0.997019i	$-0.475416\pi$
$659$	3.96130			0.154310			0.0771552	+	0.997019i	$0.475416\pi$
$660$	−1.25561	−	0.801453i	−0.0488746	−	0.0311965i
$661$	−8.74295	−	8.74295i	−0.340061	−	0.340061i	0.516329	−	0.856390i	$-0.327298\pi$
$661$	−8.74295	−	8.74295i	−0.340061	−	0.340061i	−0.856390	+	0.516329i	$0.827298\pi$
$662$	21.5320	−	21.5320i	0.836866	−	0.836866i
$663$	4.20608	+	4.20608i	0.163351	+	0.163351i
$664$	6.18662	+	6.18662i	0.240087	+	0.240087i
$665$	38.1761	−	8.42850i	1.48041	−	0.326843i
$666$	−3.34252	−	5.08208i	−0.129520	−	0.196927i
$667$	13.9651	−	13.9651i	0.540732	−	0.540732i
$668$			5.80697i			0.224678i
$669$	11.4406			0.442317
$670$	−25.1857	−	16.0760i	−0.973009	−	0.621069i
$671$	0.888225	−	0.888225i	0.0342896	−	0.0342896i
$672$		−	4.72607i		−	0.182312i
$673$	24.1381	+	24.1381i	0.930454	+	0.930454i	0.997734	−	0.0672798i	$-0.0214320\pi$
$673$	24.1381	+	24.1381i	0.930454	+	0.930454i	−0.0672798	+	0.997734i	$0.521432\pi$
$674$	−9.32924	−	9.32924i	−0.359349	−	0.359349i
$675$	−4.69547	−	1.71830i	−0.180729	−	0.0661373i
$676$	−7.48831			−0.288012
$677$	1.33458	+	1.33458i	0.0512920	+	0.0512920i	0.732288	−	0.680996i	$-0.238453\pi$
$677$	1.33458	+	1.33458i	0.0512920	+	0.0512920i	−0.680996	+	0.732288i	$0.738453\pi$
$678$	−9.87838	−	9.87838i	−0.379377	−	0.379377i
$679$	20.2768	+	20.2768i	0.778152	+	0.778152i
$680$	1.22140	+	5.53224i	0.0468387	+	0.212152i
$681$	−14.6405	−	14.6405i	−0.561025	−	0.561025i
$682$	2.00198	−	2.00198i	0.0766598	−	0.0766598i
$683$	−31.2844			−1.19706			−0.598532	−	0.801099i	$-0.704249\pi$
$683$	−31.2844			−1.19706			−0.598532	+	0.801099i	$0.704249\pi$
$684$	−2.61593	+	2.61593i	−0.100022	+	0.100022i
$685$	18.7333	−	29.3489i	0.715764	−	1.12136i
$686$	−27.8569	−	27.8569i	−1.06358	−	1.06358i
$687$	−11.8213	−	11.8213i	−0.451011	−	0.451011i
$688$	−9.47906			−0.361386
$689$	−7.06593	−	7.06593i	−0.269191	−	0.269191i
$690$	−9.15565	+	14.3439i	−0.348550	+	0.546061i
$691$		−	10.6548i		−	0.405329i	−0.979248	−	0.202665i	$-0.935040\pi$
$691$		−	10.6548i		−	0.405329i	0.979248	−	0.202665i	$-0.0649601\pi$
$692$	−12.6536	+	12.6536i	−0.481017	+	0.481017i
$693$	2.22622	−	2.22622i	0.0845670	−	0.0845670i
$694$	−22.7387			−0.863151
$695$	34.4270	−	7.60078i	1.30589	−	0.288314i
$696$		−	2.59517i		−	0.0983697i
$697$	15.7005			0.594698
$698$			22.0317i			0.833911i
$699$		−	9.09264i		−	0.343915i
$700$	8.12080	−	22.1912i	0.306937	−	0.838747i
$701$	−16.3034	+	16.3034i	−0.615769	+	0.615769i	−0.944443	−	0.328674i	$-0.893398\pi$
$701$	−16.3034	+	16.3034i	−0.615769	+	0.615769i	0.328674	+	0.944443i	$0.393398\pi$
$702$	1.66007	+	1.66007i	0.0626554	+	0.0626554i
$703$	−22.0381	−	4.55057i	−0.831184	−	0.171628i
$704$			0.666166i			0.0251071i
$705$	−3.76609	−	17.0581i	−0.141839	−	0.642447i
$706$		−	19.8627i		−	0.747544i
$707$	28.0963	+	28.0963i	1.05667	+	1.05667i
$708$	2.50933			0.0943065
$709$	27.8861	+	27.8861i	1.04728	+	1.04728i	0.998825	+	0.0484592i	$0.0154311\pi$
$709$	27.8861	+	27.8861i	1.04728	+	1.04728i	0.0484592	+	0.998825i	$0.484569\pi$
$710$	−7.52757	+	1.66193i	−0.282505	+	0.0623712i
$711$	−8.95760	+	8.95760i	−0.335936	+	0.335936i
$712$	−0.703752	+	0.703752i	−0.0263742	+	0.0263742i
$713$	−22.8703	−	22.8703i	−0.856498	−	0.856498i
$714$	−11.9743			−0.448128
$715$	0.753934	+	3.41487i	0.0281955	+	0.127709i
$716$	−3.41628	+	3.41628i	−0.127672	+	0.127672i
$717$	−6.75034			−0.252096
$718$		−	34.9845i		−	1.30561i
$719$		−	21.2641i		−	0.793016i	−0.918031	−	0.396508i	$-0.870222\pi$
$719$		−	21.2641i		−	0.793016i	0.918031	−	0.396508i	$-0.129778\pi$
$720$	0.482069	+	2.18349i	0.0179656	+	0.0813737i
$721$	8.44003	+	8.44003i	0.314323	+	0.314323i
$722$		−	5.31386i		−	0.197761i
$723$		−	15.8452i		−	0.589289i
$724$	20.1683			0.749548
$725$	4.45928	−	12.1856i	0.165613	−	0.452560i
$726$	7.46438	−	7.46438i	0.277029	−	0.277029i
$727$	−18.6250			−0.690761			−0.345381	−	0.938463i	$-0.612250\pi$
$727$	−18.6250			−0.690761			−0.345381	+	0.938463i	$0.612250\pi$
$728$	−7.84563	+	7.84563i	−0.290778	+	0.290778i
$729$			1.00000i			0.0370370i
$730$	−13.5002	+	21.1503i	−0.499664	+	0.782807i
$731$			24.0168i			0.888294i
$732$	−1.88563			−0.0696948
$733$	−4.53054	+	4.53054i	−0.167339	+	0.167339i	−0.785809	−	0.618469i	$-0.787753\pi$
$733$	−4.53054	+	4.53054i	−0.167339	+	0.167339i	0.618469	+	0.785809i	$0.287753\pi$
$734$	5.42620	−	5.42620i	0.200285	−	0.200285i
$735$	28.9054	+	18.4502i	1.06619	+	0.680547i
$736$	7.61016			0.280514
$737$	−6.29432	+	6.29432i	−0.231854	+	0.231854i
$738$	6.19673			0.228105
$739$	−39.3179			−1.44633			−0.723167	−	0.690674i	$-0.757314\pi$
$739$	−39.3179			−1.44633			−0.723167	+	0.690674i	$0.757314\pi$
$740$	−9.48533	+	9.74826i	−0.348688	+	0.358353i
$741$	8.68526			0.319061
$742$	20.1161			0.738484
$743$	−25.1428	+	25.1428i	−0.922401	+	0.922401i	−0.997199	−	0.0747978i	$-0.976169\pi$
$743$	−25.1428	+	25.1428i	−0.922401	+	0.922401i	0.0747978	+	0.997199i	$0.476169\pi$
$744$	−4.25003			−0.155814
$745$	−5.54783	−	25.1284i	−0.203257	−	0.920633i
$746$	−18.4762	+	18.4762i	−0.676462	+	0.676462i
$747$	6.18662	−	6.18662i	0.226357	−	0.226357i
$748$	1.68784			0.0617137
$749$		−	2.87979i		−	0.105225i
$750$	−1.48834	+	11.0808i	−0.0543464	+	0.404615i
$751$			36.7088i			1.33952i	0.742575	+	0.669762i	$0.233604\pi$
$751$			36.7088i			1.33952i	−0.742575	+	0.669762i	$0.766396\pi$
$752$	−5.52416	+	5.52416i	−0.201446	+	0.201446i
$753$	18.7595			0.683634
$754$	−4.30818	+	4.30818i	−0.156894	+	0.156894i
$755$	−5.00593	−	22.6739i	−0.182184	−	0.825187i
$756$	−4.72607			−0.171886
$757$			20.5947i			0.748529i	0.927322	+	0.374264i	$0.122105\pi$
$757$			20.5947i			0.748529i	−0.927322	+	0.374264i	$0.877895\pi$
$758$		−	27.9090i		−	1.01370i
$759$	3.58477	+	3.58477i	0.130119	+	0.130119i
$760$	6.97289	+	4.45078i	0.252933	+	0.161447i
$761$		−	27.0015i		−	0.978804i	−0.872058	−	0.489402i	$-0.837215\pi$
$761$		−	27.0015i		−	0.978804i	0.872058	−	0.489402i	$-0.162785\pi$
$762$		−	1.46713i		−	0.0531486i
$763$	76.6388			2.77451
$764$	−14.1273	+	14.1273i	−0.511108	+	0.511108i
$765$	5.53224	−	1.22140i	0.200018	−	0.0441599i
$766$	33.2956			1.20302
$767$	−4.16568	−	4.16568i	−0.150414	−	0.150414i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	7.48626	−	7.48626i	0.269961	−	0.269961i	−0.559123	−	0.829085i	$-0.688862\pi$
$769$	7.48626	−	7.48626i	0.269961	−	0.269961i	0.829085	+	0.559123i	$0.188862\pi$
$770$	−5.93411	−	3.78773i	−0.213850	−	0.136500i
$771$	12.9810	+	12.9810i	0.467498	+	0.467498i
$772$	7.65037			0.275343
$773$	−37.6580	−	37.6580i	−1.35446	−	1.35446i	−0.880596	−	0.473868i	$-0.842857\pi$
$773$	−37.6580	−	37.6580i	−1.35446	−	1.35446i	−0.473868	−	0.880596i	$-0.657143\pi$
$774$			9.47906i			0.340718i
$775$	−19.9559	−	7.30282i	−0.716838	−	0.262325i
$776$			6.06755i			0.217812i
$777$	−15.7970	−	24.0183i	−0.566714	−	0.861652i
$778$	−19.1433	−	19.1433i	−0.686320	−	0.686320i
$779$	16.2102	−	16.2102i	0.580790	−	0.580790i
$780$	2.82448	−	4.42502i	0.101132	−	0.158441i
$781$			2.29661i			0.0821791i
$782$		−	19.2816i		−	0.689510i
$783$	−2.59517			−0.0927439
$784$		−	15.3358i		−	0.547707i
$785$	28.9009	−	45.2781i	1.03152	−	1.61605i
$786$	−2.15745			−0.0769538
$787$	21.5902	−	21.5902i	0.769609	−	0.769609i	−0.208429	−	0.978038i	$-0.566835\pi$
$787$	21.5902	−	21.5902i	0.769609	−	0.769609i	0.978038	+	0.208429i	$0.0668350\pi$
$788$	8.59297	−	8.59297i	0.306112	−	0.306112i
$789$		−	3.28968i		−	0.117116i
$790$	23.8770	+	15.2406i	0.849505	+	0.542237i
$791$	−46.6860	−	46.6860i	−1.65996	−	1.65996i
$792$	0.666166			0.0236712
$793$	3.13028	+	3.13028i	0.111160	+	0.111160i
$794$	15.3592	+	15.3592i	0.545079	+	0.545079i
$795$	−9.29378	+	2.05188i	−0.329617	+	0.0727726i
$796$	−3.03831	+	3.03831i	−0.107690	+	0.107690i
$797$	30.2402			1.07116			0.535582	−	0.844483i	$-0.320092\pi$
$797$	30.2402			1.07116			0.535582	+	0.844483i	$0.320092\pi$
$798$	−12.3631	+	12.3631i	−0.437648	+	0.437648i
$799$	13.9964	+	13.9964i	0.495158	+	0.495158i
$800$	4.53522	−	2.10518i	0.160344	−	0.0744294i
$801$	0.703752	+	0.703752i	0.0248659	+	0.0248659i
$802$	7.56046	+	7.56046i	0.266969	+	0.266969i
$803$	5.28580	+	5.28580i	0.186532	+	0.186532i
$804$	13.3623			0.471252
$805$	−43.2703	+	67.7902i	−1.52508	+	2.38929i
$806$	7.05537	+	7.05537i	0.248515	+	0.248515i
$807$	9.39455	+	9.39455i	0.330704	+	0.330704i
$808$			8.40742i			0.295772i
$809$	−39.6464	+	39.6464i	−1.39389	+	1.39389i	−0.577507	+	0.816386i	$0.695974\pi$
$809$	−39.6464	+	39.6464i	−1.39389	+	1.39389i	−0.816386	+	0.577507i	$0.804026\pi$
$810$	2.18349	−	0.482069i	0.0767199	−	0.0169382i
$811$	−41.4057			−1.45395			−0.726976	−	0.686663i	$-0.759075\pi$
$811$	−41.4057			−1.45395			−0.726976	+	0.686663i	$0.759075\pi$
$812$		−	12.2650i		−	0.430416i
$813$	−5.16549	+	5.16549i	−0.181162	+	0.181162i
$814$	2.22667	+	3.38551i	0.0780448	+	0.118662i
$815$	−10.0971	−	45.7337i	−0.353685	−	1.60198i
$816$	−1.79158	−	1.79158i	−0.0627177	−	0.0627177i
$817$	24.7965	+	24.7965i	0.867520	+	0.867520i
$818$	16.6038	−	16.6038i	0.580538	−	0.580538i
$819$	7.84563	+	7.84563i	0.274149	+	0.274149i
$820$	−2.98725	−	13.5305i	−0.104319	−	0.472504i
$821$	41.3388			1.44273			0.721367	−	0.692553i	$-0.243514\pi$
$821$	41.3388			1.44273			0.721367	+	0.692553i	$0.243514\pi$
$822$			15.5711i			0.543104i
$823$	1.14103	+	1.14103i	0.0397738	+	0.0397738i	0.726714	−	0.686940i	$-0.241047\pi$
$823$	1.14103	+	1.14103i	0.0397738	+	0.0397738i	−0.686940	+	0.726714i	$0.741047\pi$
$824$			2.52556i			0.0879822i
$825$	3.12796	+	1.14467i	0.108902	+	0.0398523i
$826$	11.8593			0.412638
$827$		−	45.1292i		−	1.56929i	−0.619942	−	0.784647i	$-0.712844\pi$
$827$		−	45.1292i		−	1.56929i	0.619942	−	0.784647i	$-0.287156\pi$
$828$		−	7.61016i		−	0.264471i
$829$	−22.0647	+	22.0647i	−0.766339	+	0.766339i	−0.977460	−	0.211121i	$-0.932289\pi$
$829$	−22.0647	+	22.0647i	−0.766339	+	0.766339i	0.211121	+	0.977460i	$0.432289\pi$
$830$	−16.4908	−	10.5260i	−0.572403	−	0.365364i
$831$	−7.31964	+	7.31964i	−0.253915	+	0.253915i
$832$	−2.34770			−0.0813918
$833$	−38.8558			−1.34627
$834$	−11.1490	+	11.1490i	−0.386057	+	0.386057i
$835$	−2.79936	−	12.6794i	−0.0968758	−	0.438790i
$836$	1.74264	−	1.74264i	0.0602705	−	0.0602705i
$837$			4.25003i			0.146903i
$838$		−	24.6470i		−	0.851417i
$839$	−49.4222			−1.70625			−0.853123	−	0.521711i	$-0.825294\pi$
$839$	−49.4222			−1.70625			−0.853123	+	0.521711i	$0.825294\pi$
$840$	2.27829	+	10.3193i	0.0786086	+	0.356050i
$841$			22.2651i			0.767762i
$842$	−3.15671	−	3.15671i	−0.108787	−	0.108787i
$843$			3.30032i			0.113669i
$844$	23.8884			0.822271
$845$	16.3506	−	3.60988i	0.562479	−	0.124184i
$846$	5.52416	+	5.52416i	0.189925	+	0.189925i
$847$	35.2772	−	35.2772i	1.21214	−	1.21214i
$848$	3.00973	+	3.00973i	0.103354	+	0.103354i
$849$	−4.71342	−	4.71342i	−0.161764	−	0.161764i
$850$	−5.33384	−	11.4908i	−0.182949	−	0.394130i
$851$	38.6754	−	25.4371i	1.32578	−	0.871972i
$852$	2.43775	−	2.43775i	0.0835160	−	0.0835160i
$853$		−	1.41190i		−	0.0483425i	−0.999708	−	0.0241712i	$-0.992305\pi$
$853$		−	1.41190i		−	0.0483425i	0.999708	−	0.0241712i	$-0.00769469\pi$
$854$	−8.91162			−0.304949
$855$	4.45078	−	6.97289i	0.152214	−	0.238468i
$856$	0.430870	−	0.430870i	0.0147268	−	0.0147268i
$857$			14.7088i			0.502443i	0.967930	+	0.251221i	$0.0808322\pi$
$857$			14.7088i			0.502443i	−0.967930	+	0.251221i	$0.919168\pi$
$858$	−1.10588	−	1.10588i	−0.0377542	−	0.0377542i
$859$	23.0013	+	23.0013i	0.784795	+	0.784795i	0.980636	−	0.195841i	$-0.0627436\pi$
$859$	23.0013	+	23.0013i	0.784795	+	0.784795i	−0.195841	+	0.980636i	$0.562744\pi$
$860$	20.6974	−	4.56956i	0.705775	−	0.155821i
$861$	29.2862			0.998071
$862$	−0.785388	−	0.785388i	−0.0267504	−	0.0267504i
$863$	36.3139	+	36.3139i	1.23614	+	1.23614i	0.961566	+	0.274573i	$0.0885364\pi$
$863$	36.3139	+	36.3139i	1.23614	+	1.23614i	0.274573	+	0.961566i	$0.411464\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	21.5290	−	33.7288i	0.732009	−	1.14681i
$866$	20.8591	+	20.8591i	0.708822	+	0.708822i
$867$	7.48155	−	7.48155i	0.254087	−	0.254087i
$868$	−20.0860			−0.681763
$869$	5.96725	−	5.96725i	0.202425	−	0.202425i
$870$	1.25105	+	5.66652i	0.0424146	+	0.192113i
$871$	−22.1824	−	22.1824i	−0.751623	−	0.751623i
$872$	11.4666	+	11.4666i	0.388307	+	0.388307i
$873$	6.06755			0.205356
$874$	−19.9076	−	19.9076i	−0.673385	−	0.673385i
$875$	−7.03399	+	52.3688i	−0.237792	+	1.77039i
$876$		−	11.2213i		−	0.379133i
$877$	5.90242	−	5.90242i	0.199311	−	0.199311i	−0.600394	−	0.799704i	$-0.704990\pi$
$877$	5.90242	−	5.90242i	0.199311	−	0.199311i	0.799704	+	0.600394i	$0.204990\pi$
$878$	17.9134	−	17.9134i	0.604549	−	0.604549i
$879$	−10.9140			−0.368121
$880$	−0.321138	−	1.45456i	−0.0108255	−	0.0490333i
$881$		−	9.25067i		−	0.311663i	−0.987784	−	0.155831i	$-0.950194\pi$
$881$		−	9.25067i		−	0.311663i	0.987784	−	0.155831i	$-0.0498057\pi$
$882$	−15.3358			−0.516383
$883$		−	1.95004i		−	0.0656239i	−0.999462	−	0.0328120i	$-0.989554\pi$
$883$		−	1.95004i		−	0.0656239i	0.999462	−	0.0328120i	$-0.0104462\pi$
$884$			5.94830i			0.200063i
$885$	−5.47909	+	1.20967i	−0.184178	+	0.0406626i
$886$	−6.57108	+	6.57108i	−0.220760	+	0.220760i
$887$	−36.7233	−	36.7233i	−1.23305	−	1.23305i	−0.962787	−	0.270261i	$-0.912890\pi$
$887$	−36.7233	−	36.7233i	−1.23305	−	1.23305i	−0.270261	−	0.962787i	$-0.587110\pi$
$888$	1.23006	−	5.95709i	0.0412780	−	0.199907i
$889$		−	6.93378i		−	0.232551i
$890$	1.19738	−	1.87589i	0.0401361	−	0.0628800i
$891$		−	0.666166i		−	0.0223174i
$892$	8.08969	+	8.08969i	0.270863	+	0.270863i
$893$	28.9016			0.967156
$894$	8.13766	+	8.13766i	0.272164	+	0.272164i
$895$	5.81251	−	9.10628i	0.194291	−	0.304389i
$896$	3.34184	−	3.34184i	0.111643	−	0.111643i
$897$	−12.6334	+	12.6334i	−0.421817	+	0.421817i
$898$	−7.18617	−	7.18617i	−0.239806	−	0.239806i
$899$	−11.0296			−0.367857
$900$	−2.10518	−	4.53522i	−0.0701727	−	0.151174i
$901$	7.62566	−	7.62566i	0.254048	−	0.254048i
$902$	−4.12805			−0.137449
$903$			44.7987i			1.49081i
$904$		−	13.9701i		−	0.464640i
$905$	−44.0371	+	9.72249i	−1.46384	+	0.323187i
$906$	7.34278	+	7.34278i	0.243948	+	0.243948i
$907$			38.4909i			1.27807i	0.769178	+	0.639034i	$0.220666\pi$
$907$			38.4909i			1.27807i	−0.769178	+	0.639034i	$0.779334\pi$
$908$		−	20.7048i		−	0.687112i
$909$	8.40742			0.278857
$910$	13.3487	−	20.9130i	0.442505	−	0.693258i
$911$	−17.7171	+	17.7171i	−0.586992	+	0.586992i	−0.936816	−	0.349823i	$-0.886242\pi$
$911$	−17.7171	+	17.7171i	−0.586992	+	0.586992i	0.349823	+	0.936816i	$0.386242\pi$
$912$	−3.69948			−0.122502
$913$	−4.12131	+	4.12131i	−0.136396	+	0.136396i
$914$		−	8.80871i		−	0.291366i
$915$	4.11724	−	0.909002i	0.136112	−	0.0300507i
$916$		−	16.7178i		−	0.552373i
$917$	−10.1963			−0.336711
$918$	−1.79158	+	1.79158i	−0.0591308	+	0.0591308i
$919$	−22.2252	+	22.2252i	−0.733143	+	0.733143i	−0.971241	−	0.238098i	$-0.923476\pi$
$919$	−22.2252	+	22.2252i	−0.733143	+	0.733143i	0.238098	+	0.971241i	$0.423476\pi$
$920$	−16.6167	+	3.66862i	−0.547835	+	0.120951i
$921$	−18.3235			−0.603780
$922$	−12.7438	+	12.7438i	−0.419694	+	0.419694i
$923$	−8.09370			−0.266407
$924$	3.14835			0.103573
$925$	16.0118	−	25.8578i	0.526463	−	0.850198i
$926$	−19.6503			−0.645748
$927$	2.52556			0.0829504
$928$	1.83506	−	1.83506i	0.0602389	−	0.0602389i
$929$	59.5228			1.95288			0.976440	−	0.215790i	$-0.0692328\pi$
$929$	59.5228			1.95288			0.976440	+	0.215790i	$0.0692328\pi$
$930$	9.27989	−	2.04881i	0.304300	−	0.0671831i
$931$	−40.1173	+	40.1173i	−1.31479	+	1.31479i
$932$	6.42946	−	6.42946i	0.210604	−	0.210604i
$933$	21.5075			0.704123
$934$			7.05736i			0.230924i
$935$	−3.68538	+	0.813657i	−0.120525	+	0.0266094i
$936$			2.34770i			0.0767369i
$937$	0.439389	−	0.439389i	0.0143542	−	0.0143542i	−0.699893	−	0.714247i	$-0.746769\pi$
$937$	0.439389	−	0.439389i	0.0143542	−	0.0143542i	0.714247	+	0.699893i	$0.246769\pi$
$938$	63.1513			2.06196
$939$	−11.6023	+	11.6023i	−0.378625	+	0.378625i
$940$	9.39891	−	14.7250i	0.306559	−	0.480275i
$941$	−44.1829			−1.44032			−0.720160	−	0.693808i	$-0.755932\pi$
$941$	−44.1829			−1.44032			−0.720160	+	0.693808i	$0.755932\pi$
$942$			24.0224i			0.782691i
$943$			47.1580i			1.53568i
$944$	1.77437	+	1.77437i	0.0577507	+	0.0577507i
$945$	10.3193	−	2.27829i	0.335687	−	0.0741129i
$946$		−	6.31462i		−	0.205306i
$947$			21.4568i			0.697254i	0.937262	+	0.348627i	$0.113352\pi$
$947$			21.4568i			0.697254i	−0.937262	+	0.348627i	$0.886648\pi$
$948$	−12.6680			−0.411436
$949$	−18.6282	+	18.6282i	−0.604697	+	0.604697i
$950$	−17.3708	−	6.35680i	−0.563583	−	0.206242i
$951$	−15.4930			−0.502394
$952$	−8.46712	−	8.46712i	−0.274421	−	0.274421i
$953$	−12.2576	+	12.2576i	−0.397063	+	0.397063i	−0.877196	−	0.480133i	$-0.840589\pi$
$953$	−12.2576	+	12.2576i	−0.397063	+	0.397063i	0.480133	+	0.877196i	$0.340589\pi$
$954$	3.00973	−	3.00973i	0.0974435	−	0.0974435i
$955$	24.0364	−	37.6571i	0.777801	−	1.21856i
$956$	−4.77321	−	4.77321i	−0.154377	−	0.154377i
$957$	1.72881			0.0558846
$958$	−2.30974	−	2.30974i	−0.0746244	−	0.0746244i
$959$			73.5901i			2.37635i
$960$	−1.20308	+	1.88483i	−0.0388294	+	0.0608327i
$961$		−	12.9372i		−	0.417329i
$962$	−11.9312	+	7.84723i	−0.384677	+	0.253005i
$963$	−0.430870	−	0.430870i	−0.0138846	−	0.0138846i
$964$	11.2042	−	11.2042i	0.360865	−	0.360865i
$965$	−16.7045	+	3.68800i	−0.537736	+	0.118721i
$966$		−	35.9662i		−	1.15719i
$967$		−	32.2102i		−	1.03581i	−0.855438	−	0.517906i	$-0.826712\pi$
$967$		−	32.2102i		−	1.03581i	0.855438	−	0.517906i	$-0.173288\pi$
$968$	10.5562			0.339290
$969$			9.37326i			0.301113i
$970$	−2.92498	−	13.2484i	−0.0939154	−	0.425381i
$971$	33.2436			1.06684			0.533418	−	0.845852i	$-0.320907\pi$
$971$	33.2436			1.06684			0.533418	+	0.845852i	$0.320907\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−52.6908	+	52.6908i	−1.68919	+	1.68919i
$974$		−	4.14854i		−	0.132928i
$975$	−4.03404	+	11.0236i	−0.129193	+	0.353036i
$976$	−1.33334	−	1.33334i	−0.0426792	−	0.0426792i
$977$	−11.7694			−0.376538			−0.188269	−	0.982118i	$-0.560288\pi$
$977$	−11.7694			−0.376538			−0.188269	+	0.982118i	$0.560288\pi$
$978$	14.8106	+	14.8106i	0.473589	+	0.473589i
$979$	−0.468815	−	0.468815i	−0.0149834	−	0.0149834i
$980$	7.39290	+	33.4855i	0.236158	+	1.06965i
$981$	11.4666	−	11.4666i	0.366099	−	0.366099i
$982$	19.1216			0.610196
$983$	−26.8913	+	26.8913i	−0.857698	+	0.857698i	−0.991067	−	0.133368i	$-0.957421\pi$
$983$	−26.8913	+	26.8913i	−0.857698	+	0.857698i	0.133368	+	0.991067i	$0.457421\pi$
$984$	4.38175	+	4.38175i	0.139685	+	0.139685i
$985$	−14.6202	+	22.9050i	−0.465839	+	0.729814i
$986$	−4.64945	−	4.64945i	−0.148069	−	0.148069i
$987$	26.1076	+	26.1076i	0.831014	+	0.831014i
$988$	6.14141	+	6.14141i	0.195384	+	0.195384i
$989$	−72.1371			−2.29383
$990$	−1.45456	+	0.321138i	−0.0462290	+	0.0102064i
$991$	−13.7998	−	13.7998i	−0.438365	−	0.438365i	0.453096	−	0.891462i	$-0.350319\pi$
$991$	−13.7998	−	13.7998i	−0.438365	−	0.438365i	−0.891462	+	0.453096i	$0.850319\pi$
$992$	−3.00523	−	3.00523i	−0.0954161	−	0.0954161i
$993$		−	30.4509i		−	0.966329i
$994$	11.5210	−	11.5210i	0.365424	−	0.365424i
$995$	5.16943	−	8.09878i	0.163882	−	0.256749i
$996$	8.74920			0.277229
$997$			46.6554i			1.47759i	0.673930	+	0.738796i	$0.264605\pi$
$997$			46.6554i			1.47759i	−0.673930	+	0.738796i	$0.735395\pi$
$998$	15.5895	−	15.5895i	0.493478	−	0.493478i
$999$	−5.95709	−	1.23006i	−0.188474	−	0.0389173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.b.253.19	yes	40
5.2	odd	4		1110.2.l.b.697.2	yes	40
37.6	odd	4		1110.2.l.b.43.2	✓	40
185.117	even	4	inner	1110.2.o.b.487.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.2	✓	40	37.6	odd	4
1110.2.l.b.697.2	yes	40	5.2	odd	4
1110.2.o.b.253.19	yes	40	1.1	even	1	trivial
1110.2.o.b.487.19	yes	40	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.18349 + 0.482069i) q^{5} +(0.707107 - 0.707107i) q^{6} +(3.34184 - 3.34184i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.18349 + 0.482069i) q^{5} +(0.707107 - 0.707107i) q^{6} +(3.34184 - 3.34184i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-2.18349 + 0.482069i) q^{10} +0.666166i q^{11} +(0.707107 - 0.707107i) q^{12} -2.34770 q^{13} +(3.34184 - 3.34184i) q^{14} +(-1.20308 + 1.88483i) q^{15} +1.00000 q^{16} -2.53367i q^{17} -1.00000i q^{18} +(-2.61593 - 2.61593i) q^{19} +(-2.18349 + 0.482069i) q^{20} -4.72607i q^{21} +0.666166i q^{22} +7.61016 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.53522 - 2.10518i) q^{25} -2.34770 q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.34184 - 3.34184i) q^{28} +(1.83506 - 1.83506i) q^{29} +(-1.20308 + 1.88483i) q^{30} +(-3.00523 - 3.00523i) q^{31} +1.00000 q^{32} +(0.471050 + 0.471050i) q^{33} -2.53367i q^{34} +(-5.68586 + 8.90786i) q^{35} -1.00000i q^{36} +(5.08208 - 3.34252i) q^{37} +(-2.61593 - 2.61593i) q^{38} +(-1.66007 + 1.66007i) q^{39} +(-2.18349 + 0.482069i) q^{40} +6.19673i q^{41} -4.72607i q^{42} -9.47906 q^{43} +0.666166i q^{44} +(0.482069 + 2.18349i) q^{45} +7.61016 q^{46} +(-5.52416 + 5.52416i) q^{47} +(0.707107 - 0.707107i) q^{48} -15.3358i q^{49} +(4.53522 - 2.10518i) q^{50} +(-1.79158 - 1.79158i) q^{51} -2.34770 q^{52} +(3.00973 + 3.00973i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.321138 - 1.45456i) q^{55} +(3.34184 - 3.34184i) q^{56} -3.69948 q^{57} +(1.83506 - 1.83506i) q^{58} +(1.77437 + 1.77437i) q^{59} +(-1.20308 + 1.88483i) q^{60} +(-1.33334 - 1.33334i) q^{61} +(-3.00523 - 3.00523i) q^{62} +(-3.34184 - 3.34184i) q^{63} +1.00000 q^{64} +(5.12617 - 1.13175i) q^{65} +(0.471050 + 0.471050i) q^{66} +(9.44858 + 9.44858i) q^{67} -2.53367i q^{68} +(5.38119 - 5.38119i) q^{69} +(-5.68586 + 8.90786i) q^{70} +3.44750 q^{71} -1.00000i q^{72} +(7.93466 - 7.93466i) q^{73} +(5.08208 - 3.34252i) q^{74} +(1.71830 - 4.69547i) q^{75} +(-2.61593 - 2.61593i) q^{76} +(2.22622 + 2.22622i) q^{77} +(-1.66007 + 1.66007i) q^{78} +(-8.95760 - 8.95760i) q^{79} +(-2.18349 + 0.482069i) q^{80} -1.00000 q^{81} +6.19673i q^{82} +(6.18662 + 6.18662i) q^{83} -4.72607i q^{84} +(1.22140 + 5.53224i) q^{85} -9.47906 q^{86} -2.59517i q^{87} +0.666166i q^{88} +(-0.703752 + 0.703752i) q^{89} +(0.482069 + 2.18349i) q^{90} +(-7.84563 + 7.84563i) q^{91} +7.61016 q^{92} -4.25003 q^{93} +(-5.52416 + 5.52416i) q^{94} +(6.97289 + 4.45078i) q^{95} +(0.707107 - 0.707107i) q^{96} +6.06755i q^{97} -15.3358i q^{98} +0.666166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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