LMFDB - Embedded newform 456.2.j.d.419.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(419,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("456.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.j (of order $2$, degree $1$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.22
Character	$\chi$	$=$	456.419
Dual form			456.2.j.d.419.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40055 + 0.196117i) q^{2} +(0.165731 + 1.72410i) q^{3} +(1.92308 + 0.549342i) q^{4} +0.906854 q^{5} +(-0.106011 + 2.44719i) q^{6} +1.41867i q^{7} +(2.58563 + 1.14653i) q^{8} +(-2.94507 + 0.571475i) q^{9} +O(q^{10})$	\(q+(1.40055 + 0.196117i) q^{2} +(0.165731 + 1.72410i) q^{3} +(1.92308 + 0.549342i) q^{4} +0.906854 q^{5} +(-0.106011 + 2.44719i) q^{6} +1.41867i q^{7} +(2.58563 + 1.14653i) q^{8} +(-2.94507 + 0.571475i) q^{9} +(1.27009 + 0.177849i) q^{10} -5.37260i q^{11} +(-0.628409 + 3.40663i) q^{12} +3.78965i q^{13} +(-0.278225 + 1.98692i) q^{14} +(0.150294 + 1.56351i) q^{15} +(3.39645 + 2.11285i) q^{16} -1.79438i q^{17} +(-4.23679 + 0.222802i) q^{18} -1.00000 q^{19} +(1.74395 + 0.498173i) q^{20} +(-2.44594 + 0.235118i) q^{21} +(1.05366 - 7.52459i) q^{22} +4.59129 q^{23} +(-1.54821 + 4.64791i) q^{24} -4.17762 q^{25} +(-0.743213 + 5.30759i) q^{26} +(-1.47337 - 4.98289i) q^{27} +(-0.779335 + 2.72821i) q^{28} -9.30823 q^{29} +(-0.0961364 + 2.21925i) q^{30} -8.16173i q^{31} +(4.34253 + 3.62525i) q^{32} +(9.26292 - 0.890406i) q^{33} +(0.351908 - 2.51312i) q^{34} +1.28653i q^{35} +(-5.97752 - 0.518858i) q^{36} +8.95844i q^{37} +(-1.40055 - 0.196117i) q^{38} +(-6.53375 + 0.628063i) q^{39} +(2.34479 + 1.03973i) q^{40} -7.10829i q^{41} +(-3.47177 - 0.150394i) q^{42} +8.04671 q^{43} +(2.95139 - 10.3319i) q^{44} +(-2.67075 + 0.518244i) q^{45} +(6.43032 + 0.900427i) q^{46} +10.6647 q^{47} +(-3.07988 + 6.20599i) q^{48} +4.98737 q^{49} +(-5.85096 - 0.819299i) q^{50} +(3.09370 - 0.297384i) q^{51} +(-2.08181 + 7.28779i) q^{52} -4.23811 q^{53} +(-1.08630 - 7.26773i) q^{54} -4.87216i q^{55} +(-1.62655 + 3.66816i) q^{56} +(-0.165731 - 1.72410i) q^{57} +(-13.0366 - 1.82550i) q^{58} -3.03104i q^{59} +(-0.569875 + 3.08931i) q^{60} -0.173612i q^{61} +(1.60065 - 11.4309i) q^{62} +(-0.810735 - 4.17808i) q^{63} +(5.37095 + 5.92899i) q^{64} +3.43666i q^{65} +(13.1478 + 0.569553i) q^{66} -13.1496 q^{67} +(0.985728 - 3.45073i) q^{68} +(0.760918 + 7.91585i) q^{69} +(-0.252309 + 1.80185i) q^{70} -6.74099 q^{71} +(-8.27006 - 1.89898i) q^{72} -3.12997 q^{73} +(-1.75690 + 12.5467i) q^{74} +(-0.692360 - 7.20264i) q^{75} +(-1.92308 - 0.549342i) q^{76} +7.62195 q^{77} +(-9.27401 - 0.401744i) q^{78} -2.42669i q^{79} +(3.08008 + 1.91605i) q^{80} +(8.34683 - 3.36606i) q^{81} +(1.39405 - 9.95552i) q^{82} -5.13329i q^{83} +(-4.83288 - 0.891505i) q^{84} -1.62724i q^{85} +(11.2698 + 1.57809i) q^{86} +(-1.54266 - 16.0484i) q^{87} +(6.15983 - 13.8915i) q^{88} -4.35387i q^{89} +(-3.84215 + 0.202049i) q^{90} -5.37627 q^{91} +(8.82939 + 2.52218i) q^{92} +(14.0717 - 1.35265i) q^{93} +(14.9364 + 2.09153i) q^{94} -0.906854 q^{95} +(-5.53062 + 8.08778i) q^{96} +0.911172 q^{97} +(6.98506 + 0.978106i) q^{98} +(3.07030 + 15.8227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} + 2 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 + 2 * q^4 - 10 * q^6 - 6 * q^9	$ 24 q + 2 q^{3} + 2 q^{4} - 10 q^{6} - 6 q^{9} + 8 q^{10} - 16 q^{12} + 18 q^{16} + 18 q^{18} - 24 q^{19} + 44 q^{22} - 22 q^{24} - 8 q^{25} - 16 q^{27} + 44 q^{28} + 2 q^{30} + 24 q^{33} - 16 q^{34} + 22 q^{36} + 64 q^{40} + 8 q^{42} - 40 q^{43} - 20 q^{46} - 8 q^{48} - 12 q^{49} - 18 q^{51} - 48 q^{52} + 4 q^{54} - 2 q^{57} - 40 q^{58} + 48 q^{60} + 26 q^{64} + 22 q^{66} - 92 q^{67} + 56 q^{70} - 8 q^{72} + 44 q^{73} - 34 q^{75} - 2 q^{76} - 42 q^{78} + 2 q^{81} - 100 q^{82} + 32 q^{84} + 16 q^{88} + 24 q^{90} + 44 q^{91} + 16 q^{94} + 2 q^{96} - 96 q^{97} - 56 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 + 2 * q^4 - 10 * q^6 - 6 * q^9 + 8 * q^10 - 16 * q^12 + 18 * q^16 + 18 * q^18 - 24 * q^19 + 44 * q^22 - 22 * q^24 - 8 * q^25 - 16 * q^27 + 44 * q^28 + 2 * q^30 + 24 * q^33 - 16 * q^34 + 22 * q^36 + 64 * q^40 + 8 * q^42 - 40 * q^43 - 20 * q^46 - 8 * q^48 - 12 * q^49 - 18 * q^51 - 48 * q^52 + 4 * q^54 - 2 * q^57 - 40 * q^58 + 48 * q^60 + 26 * q^64 + 22 * q^66 - 92 * q^67 + 56 * q^70 - 8 * q^72 + 44 * q^73 - 34 * q^75 - 2 * q^76 - 42 * q^78 + 2 * q^81 - 100 * q^82 + 32 * q^84 + 16 * q^88 + 24 * q^90 + 44 * q^91 + 16 * q^94 + 2 * q^96 - 96 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.40055	+	0.196117i	0.990338	+	0.138675i
$2$	1.40055	+	0.196117i	0.990338	+	0.138675i
$3$	0.165731	+	1.72410i	0.0956848	+	0.995412i
$3$	0.165731	+	1.72410i	0.0956848	+	0.995412i
$4$	1.92308	+	0.549342i	0.961538	+	0.274671i
$5$	0.906854			0.405558			0.202779	−	0.979225i	$-0.435003\pi$
$5$	0.906854			0.405558			0.202779	+	0.979225i	$0.435003\pi$
$6$	−0.106011	+	2.44719i	−0.0432787	+	0.999063i
$7$			1.41867i			0.536207i	0.963390	+	0.268104i	$0.0863970\pi$
$7$			1.41867i			0.536207i	−0.963390	+	0.268104i	$0.913603\pi$
$8$	2.58563	+	1.14653i	0.914158	+	0.405359i
$9$	−2.94507	+	0.571475i	−0.981689	+	0.190492i
$10$	1.27009	+	0.177849i	0.401639	+	0.0562408i
$11$		−	5.37260i		−	1.61990i	−0.586499	−	0.809950i	$-0.699494\pi$
$11$		−	5.37260i		−	1.61990i	0.586499	−	0.809950i	$-0.300506\pi$
$12$	−0.628409	+	3.40663i	−0.181406	+	0.983408i
$13$			3.78965i			1.05106i	0.850775	+	0.525530i	$0.176133\pi$
$13$			3.78965i			1.05106i	−0.850775	+	0.525530i	$0.823867\pi$
$14$	−0.278225	+	1.98692i	−0.0743587	+	0.531027i
$15$	0.150294	+	1.56351i	0.0388057	+	0.403697i
$16$	3.39645	+	2.11285i	0.849112	+	0.528213i
$17$		−	1.79438i		−	0.435201i	−0.976038	−	0.217601i	$-0.930177\pi$
$17$		−	1.79438i		−	0.435201i	0.976038	−	0.217601i	$-0.0698230\pi$
$18$	−4.23679	+	0.222802i	−0.998620	+	0.0525150i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.74395	+	0.498173i	0.389959	+	0.111395i
$21$	−2.44594	+	0.235118i	−0.533747	+	0.0513069i
$22$	1.05366	−	7.52459i	0.224640	−	1.60425i
$23$	4.59129			0.957349			0.478675	−	0.877992i	$-0.341117\pi$
$23$	4.59129			0.957349			0.478675	+	0.877992i	$0.341117\pi$
$24$	−1.54821	+	4.64791i	−0.316028	+	0.948750i
$25$	−4.17762			−0.835523
$26$	−0.743213	+	5.30759i	−0.145756	+	1.04090i
$27$	−1.47337	−	4.98289i	−0.283550	−	0.958957i
$28$	−0.779335	+	2.72821i	−0.147281	+	0.515584i
$29$	−9.30823			−1.72850			−0.864248	−	0.503067i	$-0.832205\pi$
$29$	−9.30823			−1.72850			−0.864248	+	0.503067i	$0.832205\pi$
$30$	−0.0961364	+	2.21925i	−0.0175520	+	0.405178i
$31$		−	8.16173i		−	1.46589i	−0.680288	−	0.732945i	$-0.738145\pi$
$31$		−	8.16173i		−	1.46589i	0.680288	−	0.732945i	$-0.261855\pi$
$32$	4.34253	+	3.62525i	0.767657	+	0.640860i
$33$	9.26292	−	0.890406i	1.61247	−	0.155000i
$34$	0.351908	−	2.51312i	0.0603517	−	0.430996i
$35$			1.28653i			0.217463i
$36$	−5.97752	−	0.518858i	−0.996254	−	0.0864764i
$37$			8.95844i			1.47276i	0.676569	+	0.736379i	$0.263466\pi$
$37$			8.95844i			1.47276i	−0.676569	+	0.736379i	$0.736534\pi$
$38$	−1.40055	−	0.196117i	−0.227199	−	0.0318143i
$39$	−6.53375	+	0.628063i	−1.04624	+	0.100571i
$40$	2.34479	+	1.03973i	0.370744	+	0.164396i
$41$		−	7.10829i		−	1.11013i	−0.831807	−	0.555065i	$-0.812694\pi$
$41$		−	7.10829i		−	1.11013i	0.831807	−	0.555065i	$-0.187306\pi$
$42$	−3.47177	−	0.150394i	−0.535705	−	0.0232064i
$43$	8.04671			1.22711			0.613556	−	0.789651i	$-0.289739\pi$
$43$	8.04671			1.22711			0.613556	+	0.789651i	$0.289739\pi$
$44$	2.95139	−	10.3319i	0.444939	−	1.55760i
$45$	−2.67075	+	0.518244i	−0.398131	+	0.0772553i
$46$	6.43032	+	0.900427i	0.948099	+	0.132761i
$47$	10.6647			1.55561			0.777804	−	0.628507i	$-0.216334\pi$
$47$	10.6647			1.55561			0.777804	+	0.628507i	$0.216334\pi$
$48$	−3.07988	+	6.20599i	−0.444542	+	0.895758i
$49$	4.98737			0.712482
$50$	−5.85096	−	0.819299i	−0.827450	−	0.115866i
$51$	3.09370	−	0.297384i	0.433204	−	0.0416422i
$52$	−2.08181	+	7.28779i	−0.288696	+	1.01063i
$53$	−4.23811			−0.582149			−0.291074	−	0.956700i	$-0.594013\pi$
$53$	−4.23811			−0.582149			−0.291074	+	0.956700i	$0.594013\pi$
$54$	−1.08630	−	7.26773i	−0.147827	−	0.989013i
$55$		−	4.87216i		−	0.656962i
$56$	−1.62655	+	3.66816i	−0.217356	+	0.490178i
$57$	−0.165731	−	1.72410i	−0.0219516	−	0.228363i
$58$	−13.0366	−	1.82550i	−1.71179	−	0.239700i
$59$		−	3.03104i		−	0.394608i	−0.980342	−	0.197304i	$-0.936781\pi$
$59$		−	3.03104i		−	0.394608i	0.980342	−	0.197304i	$-0.0632186\pi$
$60$	−0.569875	+	3.08931i	−0.0735706	+	0.398829i
$61$		−	0.173612i		−	0.0222288i	−0.999938	−	0.0111144i	$-0.996462\pi$
$61$		−	0.173612i		−	0.0222288i	0.999938	−	0.0111144i	$-0.00353789\pi$
$62$	1.60065	−	11.4309i	0.203283	−	1.45173i
$63$	−0.810735	−	4.17808i	−0.102143	−	0.526389i
$64$	5.37095	+	5.92899i	0.671369	+	0.741123i
$65$			3.43666i			0.426265i
$66$	13.1478	+	0.569553i	1.61838	+	0.0701072i
$67$	−13.1496			−1.60647			−0.803237	−	0.595659i	$-0.796891\pi$
$67$	−13.1496			−1.60647			−0.803237	+	0.595659i	$0.796891\pi$
$68$	0.985728	−	3.45073i	0.119537	−	0.418463i
$69$	0.760918	+	7.91585i	0.0916038	+	0.952957i
$70$	−0.252309	+	1.80185i	−0.0301568	+	0.215362i
$71$	−6.74099			−0.800009			−0.400004	−	0.916513i	$-0.630991\pi$
$71$	−6.74099			−0.800009			−0.400004	+	0.916513i	$0.630991\pi$
$72$	−8.27006	−	1.89898i	−0.974636	−	0.223797i
$73$	−3.12997			−0.366335			−0.183168	−	0.983082i	$-0.558635\pi$
$73$	−3.12997			−0.366335			−0.183168	+	0.983082i	$0.558635\pi$
$74$	−1.75690	+	12.5467i	−0.204235	+	1.45853i
$75$	−0.692360	−	7.20264i	−0.0799469	−	0.831689i
$76$	−1.92308	−	0.549342i	−0.220592	−	0.0630138i
$77$	7.62195			0.868602
$78$	−9.27401	−	0.401744i	−1.05008	−	0.0454885i
$79$		−	2.42669i		−	0.273024i	−0.990638	−	0.136512i	$-0.956411\pi$
$79$		−	2.42669i		−	0.273024i	0.990638	−	0.136512i	$-0.0435892\pi$
$80$	3.08008	+	1.91605i	0.344364	+	0.214221i
$81$	8.34683	−	3.36606i	0.927426	−	0.374007i
$82$	1.39405	−	9.95552i	0.153948	−	1.09940i
$83$		−	5.13329i		−	0.563451i	−0.959495	−	0.281726i	$-0.909093\pi$
$83$		−	5.13329i		−	0.563451i	0.959495	−	0.281726i	$-0.0909068\pi$
$84$	−4.83288	−	0.891505i	−0.527311	−	0.0972712i
$85$		−	1.62724i		−	0.176499i
$86$	11.2698	+	1.57809i	1.21526	+	0.170170i
$87$	−1.54266	−	16.0484i	−0.165391	−	1.72056i
$88$	6.15983	−	13.8915i	0.656640	−	1.48084i
$89$		−	4.35387i		−	0.461509i	−0.973012	−	0.230755i	$-0.925881\pi$
$89$		−	4.35387i		−	0.461509i	0.973012	−	0.230755i	$-0.0741195\pi$
$90$	−3.84215	+	0.202049i	−0.404998	+	0.0212979i
$91$	−5.37627			−0.563586
$92$	8.82939	+	2.52218i	0.920528	+	0.262956i
$93$	14.0717	−	1.35265i	1.45916	−	0.140263i
$94$	14.9364	+	2.09153i	1.54058	+	0.215724i
$95$	−0.906854			−0.0930413
$96$	−5.53062	+	8.08778i	−0.564467	+	0.825456i
$97$	0.911172			0.0925155			0.0462577	−	0.998930i	$-0.485270\pi$
$97$	0.911172			0.0925155			0.0462577	+	0.998930i	$0.485270\pi$
$98$	6.98506	+	0.978106i	0.705598	+	0.0988036i
$99$	3.07030	+	15.8227i	0.308577	+	1.59024i
$100$	−8.03387	−	2.29494i	−0.803387	−	0.229494i
$101$	10.2429			1.01920			0.509602	−	0.860410i	$-0.329793\pi$
$101$	10.2429			1.01920			0.509602	+	0.860410i	$0.329793\pi$
$102$	4.39120	+	0.190224i	0.434793	+	0.0188350i
$103$		−	3.63405i		−	0.358074i	−0.983842	−	0.179037i	$-0.942702\pi$
$103$		−	3.63405i		−	0.358074i	0.983842	−	0.179037i	$-0.0572981\pi$
$104$	−4.34494	+	9.79863i	−0.426056	+	0.960835i
$105$	−2.21811	+	0.213218i	−0.216465	+	0.0208079i
$106$	−5.93568	−	0.831163i	−0.576524	−	0.0807297i
$107$			13.5981i			1.31458i	0.753639	+	0.657288i	$0.228297\pi$
$107$			13.5981i			1.31458i	−0.753639	+	0.657288i	$0.771703\pi$
$108$	−0.0960958	−	10.3919i	−0.00924682	−	0.999957i
$109$		−	3.84720i		−	0.368495i	−0.982880	−	0.184247i	$-0.941015\pi$
$109$		−	3.84720i		−	0.368495i	0.982880	−	0.184247i	$-0.0589847\pi$
$110$	0.955512	−	6.82371i	0.0911045	−	0.650615i
$111$	−15.4453	+	1.48469i	−1.46600	+	0.140921i
$112$	−2.99744	+	4.81844i	−0.283232	+	0.455300i
$113$		−	7.99904i		−	0.752486i	−0.926521	−	0.376243i	$-0.877216\pi$
$113$		−	7.99904i		−	0.752486i	0.926521	−	0.376243i	$-0.122784\pi$
$114$	0.106011	−	2.44719i	0.00992882	−	0.229201i
$115$	4.16363			0.388260
$116$	−17.9004	−	5.11340i	−1.66201	−	0.474767i
$117$	−2.16569	−	11.1608i	−0.200218	−	1.03181i
$118$	0.594437	−	4.24512i	0.0547224	−	0.390795i
$119$	2.54564			0.233358
$120$	−1.40400	+	4.21497i	−0.128167	+	0.384773i
$121$	−17.8648			−1.62407
$122$	0.0340483	−	0.243153i	0.00308258	−	0.0220140i
$123$	12.2554	−	1.17806i	1.10504	−	0.106223i
$124$	4.48358	−	15.6956i	0.402637	−	1.40951i
$125$	−8.32276			−0.744410
$126$	−0.316083	−	6.01061i	−0.0281590	−	0.535468i
$127$		−	6.66469i		−	0.591396i	−0.955281	−	0.295698i	$-0.904448\pi$
$127$		−	6.66469i		−	0.591396i	0.955281	−	0.295698i	$-0.0955522\pi$
$128$	6.35951	+	9.35717i	0.562106	+	0.827065i
$129$	1.33359	+	13.8734i	0.117416	+	1.22148i
$130$	−0.673986	+	4.81321i	−0.0591125	+	0.422147i
$131$		−	3.08503i		−	0.269540i	−0.990877	−	0.134770i	$-0.956970\pi$
$131$		−	3.08503i		−	0.269540i	0.990877	−	0.134770i	$-0.0430295\pi$
$132$	18.3024	+	3.37619i	1.59302	+	0.293859i
$133$		−	1.41867i		−	0.123014i
$134$	−18.4166	−	2.57885i	−1.59095	−	0.222778i
$135$	−1.33613	−	4.51875i	−0.114996	−	0.388912i
$136$	2.05731	−	4.63960i	0.176413	−	0.397843i
$137$			14.6126i			1.24844i	0.781249	+	0.624219i	$0.214583\pi$
$137$			14.6126i			1.24844i	−0.781249	+	0.624219i	$0.785417\pi$
$138$	−0.486726	+	11.2358i	−0.0414329	+	0.956452i
$139$	−17.6880			−1.50028			−0.750139	−	0.661280i	$-0.770014\pi$
$139$	−17.6880			−1.50028			−0.750139	+	0.661280i	$0.770014\pi$
$140$	−0.706744	+	2.47409i	−0.0597307	+	0.209099i
$141$	1.76747	+	18.3871i	0.148848	+	1.54847i
$142$	−9.44109	−	1.32202i	−0.792279	−	0.110941i
$143$	20.3603			1.70261
$144$	−11.2102	−	4.28151i	−0.934184	−	0.356792i
$145$	−8.44121			−0.701004
$146$	−4.38368	−	0.613839i	−0.362796	−	0.0508017i
$147$	0.826562	+	8.59874i	0.0681737	+	0.709213i
$148$	−4.92124	+	17.2278i	−0.404524	+	1.41611i
$149$	5.30590			0.434676			0.217338	−	0.976096i	$-0.430263\pi$
$149$	5.30590			0.434676			0.217338	+	0.976096i	$0.430263\pi$
$150$	0.442872	−	10.2234i	0.0361604	−	0.834740i
$151$			14.2225i			1.15741i	0.815538	+	0.578704i	$0.196441\pi$
$151$			14.2225i			1.15741i	−0.815538	+	0.578704i	$0.803559\pi$
$152$	−2.58563	−	1.14653i	−0.209722	−	0.0929956i
$153$	1.02544	+	5.28457i	0.0829022	+	0.427232i
$154$	10.6749	+	1.49479i	0.860209	+	0.120454i
$155$		−	7.40150i		−	0.594503i
$156$	−12.9099	−	2.38145i	−1.03362	−	0.190669i
$157$			19.8137i			1.58131i	0.612262	+	0.790655i	$0.290260\pi$
$157$			19.8137i			1.58131i	−0.612262	+	0.790655i	$0.709740\pi$
$158$	0.475914	−	3.39870i	0.0378617	−	0.270386i
$159$	−0.702386	−	7.30694i	−0.0557028	−	0.579478i
$160$	3.93804	+	3.28758i	0.311329	+	0.259906i
$161$			6.51353i			0.513338i
$162$	12.3503	−	3.07738i	0.970331	−	0.241782i
$163$	−4.44830			−0.348418			−0.174209	−	0.984709i	$-0.555737\pi$
$163$	−4.44830			−0.348418			−0.174209	+	0.984709i	$0.555737\pi$
$164$	3.90488	−	13.6698i	0.304920	−	1.06743i
$165$	8.40012	−	0.807469i	0.653948	−	0.0628613i
$166$	1.00672	−	7.18942i	0.0781368	−	0.558007i
$167$	6.04734			0.467958			0.233979	−	0.972242i	$-0.424825\pi$
$167$	6.04734			0.467958			0.233979	+	0.972242i	$0.424825\pi$
$168$	−6.59385	−	2.19641i	−0.508727	−	0.169456i
$169$	−1.36145			−0.104727
$170$	0.319129	−	2.27903i	0.0244761	−	0.174794i
$171$	2.94507	−	0.571475i	0.225215	−	0.0437018i
$172$	15.4744	+	4.42039i	1.17991	+	0.337052i
$173$	−20.3344			−1.54599			−0.772997	−	0.634410i	$-0.781243\pi$
$173$	−20.3344			−1.54599			−0.772997	+	0.634410i	$0.781243\pi$
$174$	0.986773	−	22.7791i	0.0748071	−	1.72688i
$175$		−	5.92666i		−	0.448014i
$176$	11.3515	−	18.2477i	0.855652	−	1.37548i
$177$	5.22583	−	0.502337i	0.392797	−	0.0377580i
$178$	0.853866	−	6.09781i	0.0639999	−	0.457050i
$179$			19.7670i			1.47746i	0.674002	+	0.738729i	$0.264574\pi$
$179$			19.7670i			1.47746i	−0.674002	+	0.738729i	$0.735426\pi$
$180$	−5.42074	−	0.470529i	−0.404038	−	0.0350711i
$181$			15.9008i			1.18190i	0.806708	+	0.590950i	$0.201247\pi$
$181$			15.9008i			1.18190i	−0.806708	+	0.590950i	$0.798753\pi$
$182$	−7.52973	−	1.05438i	−0.558141	−	0.0781555i
$183$	0.299326	−	0.0287729i	0.0221268	−	0.00212696i
$184$	11.8714	+	5.26403i	0.875168	+	0.388070i
$185$			8.12400i			0.597288i
$186$	19.9733	+	0.865232i	1.46452	+	0.0634419i
$187$	−9.64048			−0.704982
$188$	20.5090	+	5.85857i	1.49578	+	0.427280i
$189$	7.06908	−	2.09023i	0.514200	−	0.152042i
$190$	−1.27009	−	0.177849i	−0.0921423	−	0.0129025i
$191$	−19.8967			−1.43967			−0.719836	−	0.694144i	$-0.755783\pi$
$191$	−19.8967			−1.43967			−0.719836	+	0.694144i	$0.755783\pi$
$192$	−9.33206	+	10.2427i	−0.673483	+	0.739203i
$193$	−5.60633			−0.403552			−0.201776	−	0.979432i	$-0.564671\pi$
$193$	−5.60633			−0.403552			−0.201776	+	0.979432i	$0.564671\pi$
$194$	1.27614	+	0.178696i	0.0916216	+	0.0128296i
$195$	−5.92516	+	0.569561i	−0.424310	+	0.0407871i
$196$	9.59110	+	2.73977i	0.685078	+	0.195698i
$197$	−7.62957			−0.543584			−0.271792	−	0.962356i	$-0.587616\pi$
$197$	−7.62957			−0.543584			−0.271792	+	0.962356i	$0.587616\pi$
$198$	1.19703	+	22.7626i	0.0850691	+	1.61766i
$199$			13.2751i			0.941044i	0.882388	+	0.470522i	$0.155934\pi$
$199$			13.2751i			0.941044i	−0.882388	+	0.470522i	$0.844066\pi$
$200$	−10.8018	−	4.78975i	−0.763800	−	0.338686i
$201$	−2.17929	−	22.6712i	−0.153715	−	1.59910i
$202$	14.3457	+	2.00880i	1.00936	+	0.141339i
$203$		−	13.2053i		−	0.926832i
$204$	6.11278	+	1.12760i	0.427980	+	0.0789481i
$205$		−	6.44619i		−	0.450221i
$206$	0.712697	−	5.08967i	0.0496560	−	0.354614i
$207$	−13.5216	+	2.62380i	−0.939819	+	0.182367i
$208$	−8.00697	+	12.8713i	−0.555184	+	0.892467i
$209$			5.37260i			0.371630i
$210$	−3.14839	−	0.136386i	−0.217259	−	0.00941152i
$211$	13.9831			0.962635			0.481318	−	0.876546i	$-0.340158\pi$
$211$	13.9831			0.962635			0.481318	+	0.876546i	$0.340158\pi$
$212$	−8.15021	−	2.32817i	−0.559758	−	0.159899i
$213$	−1.11719	−	11.6222i	−0.0765487	−	0.796338i
$214$	−2.66681	+	19.0448i	−0.182299	+	1.30187i
$215$	7.29719			0.497664
$216$	1.90343	−	14.5732i	0.129512	−	0.991578i
$217$	11.5788			0.786021
$218$	0.754499	−	5.38819i	0.0511011	−	0.364934i
$219$	−0.518733	−	5.39639i	−0.0350527	−	0.364654i
$220$	2.67648	−	9.36954i	0.180448	−	0.631695i
$221$	6.80008			0.457423
$222$	−21.9230	−	0.949691i	−1.47138	−	0.0637391i
$223$			12.9037i			0.864095i	0.901851	+	0.432048i	$0.142209\pi$
$223$			12.9037i			0.864095i	−0.901851	+	0.432048i	$0.857791\pi$
$224$	−5.14304	+	6.16062i	−0.343634	+	0.411624i
$225$	12.3034	−	2.38740i	0.820224	−	0.159160i
$226$	1.56874	−	11.2030i	0.104351	−	0.745215i
$227$		−	5.43835i		−	0.360956i	−0.983579	−	0.180478i	$-0.942236\pi$
$227$		−	5.43835i		−	0.360956i	0.983579	−	0.180478i	$-0.0577645\pi$
$228$	0.628409	−	3.40663i	0.0416174	−	0.225609i
$229$			11.1866i			0.739229i	0.929185	+	0.369614i	$0.120510\pi$
$229$			11.1866i			0.739229i	−0.929185	+	0.369614i	$0.879490\pi$
$230$	5.83136	+	0.816556i	0.384509	+	0.0538421i
$231$	1.26319	+	13.1410i	0.0831120	+	0.864617i
$232$	−24.0676	−	10.6721i	−1.58012	−	0.700660i
$233$			12.4167i			0.813446i	0.913552	+	0.406723i	$0.133329\pi$
$233$			12.4167i			0.813446i	−0.913552	+	0.406723i	$0.866671\pi$
$234$	−0.844343	−	16.0559i	−0.0551965	−	1.04961i
$235$	9.67133			0.630888
$236$	1.66508	−	5.82892i	0.108387	−	0.379430i
$237$	4.18387	−	0.402178i	0.271771	−	0.0261243i
$238$	3.56529	+	0.499241i	0.231103	+	0.0323610i
$239$	1.98767			0.128572			0.0642858	−	0.997932i	$-0.479523\pi$
$239$	1.98767			0.128572			0.0642858	+	0.997932i	$0.479523\pi$
$240$	−2.79300	+	5.62793i	−0.180288	+	0.363281i
$241$	10.6849			0.688277			0.344138	−	0.938919i	$-0.388171\pi$
$241$	10.6849			0.688277			0.344138	+	0.938919i	$0.388171\pi$
$242$	−25.0205	−	3.50358i	−1.60838	−	0.225219i
$243$	7.18677	+	13.8329i	0.461032	+	0.887384i
$244$	0.0953725	−	0.333870i	0.00610560	−	0.0213738i
$245$	4.52282			0.288952
$246$	17.3954	+	0.753556i	1.10909	+	0.0480450i
$247$		−	3.78965i		−	0.241130i
$248$	9.35765	−	21.1032i	0.594211	−	1.34005i
$249$	8.85032	−	0.850745i	0.560866	−	0.0539138i
$250$	−11.6564	−	1.63223i	−0.737218	−	0.103231i
$251$		−	10.4932i		−	0.662328i	−0.943573	−	0.331164i	$-0.892559\pi$
$251$		−	10.4932i		−	0.662328i	0.943573	−	0.331164i	$-0.107441\pi$
$252$	0.736089	−	8.48014i	0.0463693	−	0.534199i
$253$		−	24.6671i		−	1.55081i
$254$	1.30706	−	9.33423i	0.0820120	−	0.585682i
$255$	2.80553	−	0.269684i	0.175689	−	0.0168883i
$256$	7.07171	+	14.3524i	0.441982	+	0.897024i
$257$			20.1461i			1.25668i	0.777939	+	0.628340i	$0.216265\pi$
$257$			20.1461i			1.25668i	−0.777939	+	0.628340i	$0.783735\pi$
$258$	−0.853038	+	19.6919i	−0.0531078	+	1.22596i
$259$	−12.7091			−0.789704
$260$	−1.88790	+	6.60896i	−0.117083	+	0.409870i
$261$	27.4134	−	5.31942i	1.69684	−	0.329264i
$262$	0.605025	−	4.32073i	0.0373785	−	0.266936i
$263$	13.6909			0.844220			0.422110	−	0.906545i	$-0.361290\pi$
$263$	13.6909			0.844220			0.422110	+	0.906545i	$0.361290\pi$
$264$	24.9713	+	8.31793i	1.53688	+	0.511933i
$265$	−3.84335			−0.236095
$266$	0.278225	−	1.98692i	0.0170591	−	0.121826i
$267$	7.50652	−	0.721571i	0.459392	−	0.0441594i
$268$	−25.2876	−	7.22360i	−1.54469	−	0.441252i
$269$	−13.0148			−0.793525			−0.396763	−	0.917921i	$-0.629866\pi$
$269$	−13.0148			−0.793525			−0.396763	+	0.917921i	$0.629866\pi$
$270$	−0.985117	−	6.59078i	−0.0599523	−	0.401102i
$271$		−	28.4457i		−	1.72795i	−0.503531	−	0.863977i	$-0.667966\pi$
$271$		−	28.4457i		−	1.72795i	0.503531	−	0.863977i	$-0.332034\pi$
$272$	3.79126	−	6.09452i	0.229879	−	0.369534i
$273$	−0.891015	−	9.26925i	−0.0539267	−	0.561000i
$274$	−2.86577	+	20.4657i	−0.173128	+	1.23638i
$275$			22.4446i			1.35346i
$276$	−2.88520	+	15.6408i	−0.173669	+	0.941465i
$277$		−	4.93252i		−	0.296366i	−0.988960	−	0.148183i	$-0.952657\pi$
$277$		−	4.93252i		−	0.296366i	0.988960	−	0.148183i	$-0.0473425\pi$
$278$	−24.7729	−	3.46891i	−1.48578	−	0.208052i
$279$	4.66422	+	24.0368i	0.279240	+	1.43905i
$280$	−1.47504	+	3.32648i	−0.0881505	+	0.198795i
$281$		−	12.4880i		−	0.744969i	−0.928038	−	0.372485i	$-0.878506\pi$
$281$		−	12.4880i		−	0.744969i	0.928038	−	0.372485i	$-0.121494\pi$
$282$	−1.13057	+	26.0986i	−0.0673247	+	1.55415i
$283$	−4.83408			−0.287356			−0.143678	−	0.989624i	$-0.545893\pi$
$283$	−4.83408			−0.287356			−0.143678	+	0.989624i	$0.545893\pi$
$284$	−12.9634	−	3.70311i	−0.769239	−	0.219739i
$285$	−0.150294	−	1.56351i	−0.00890264	−	0.0926144i
$286$	28.5156	+	3.99299i	1.68616	+	0.236110i
$287$	10.0843			0.595259
$288$	−14.8608	−	8.19497i	−0.875679	−	0.482893i
$289$	13.7802			0.810600
$290$	−11.8223	−	1.65546i	−0.694231	−	0.0972120i
$291$	0.151009	+	1.57095i	0.00885233	+	0.0920910i
$292$	−6.01917	−	1.71942i	−0.352245	−	0.100622i
$293$	−18.0207			−1.05278			−0.526390	−	0.850243i	$-0.676455\pi$
$293$	−18.0207			−1.05278			−0.526390	+	0.850243i	$0.676455\pi$
$294$	−0.528715	+	12.2051i	−0.0308353	+	0.711814i
$295$		−	2.74871i		−	0.160036i
$296$	−10.2711	+	23.1632i	−0.596995	+	1.34633i
$297$	−26.7711	+	7.91583i	−1.55341	+	0.459323i
$298$	7.43118	+	1.04057i	0.430476	+	0.0602789i
$299$			17.3994i			1.00623i
$300$	2.62525	−	14.2316i	0.151569	−	0.821660i
$301$			11.4156i			0.657986i
$302$	−2.78926	+	19.9193i	−0.160504	+	1.14623i
$303$	1.69756	+	17.6598i	0.0975224	+	1.01453i
$304$	−3.39645	−	2.11285i	−0.194800	−	0.121180i
$305$		−	0.157441i		−	0.00901505i
$306$	0.399792	+	7.60241i	0.0228546	+	0.434601i
$307$	4.81674			0.274906			0.137453	−	0.990508i	$-0.456108\pi$
$307$	4.81674			0.274906			0.137453	+	0.990508i	$0.456108\pi$
$308$	14.6576	+	4.18706i	0.835194	+	0.238580i
$309$	6.26548	−	0.602275i	0.356431	−	0.0342622i
$310$	1.45156	−	10.3662i	0.0824429	−	0.588759i
$311$	−1.43274			−0.0812430			−0.0406215	−	0.999175i	$-0.512934\pi$
$311$	−1.43274			−0.0812430			−0.0406215	+	0.999175i	$0.512934\pi$
$312$	−17.6139	−	5.86719i	−0.997193	−	0.332164i
$313$	14.9330			0.844061			0.422030	−	0.906582i	$-0.361318\pi$
$313$	14.9330			0.844061			0.422030	+	0.906582i	$0.361318\pi$
$314$	−3.88580	+	27.7501i	−0.219289	+	1.56603i
$315$	−0.735219	−	3.78891i	−0.0414249	−	0.213481i
$316$	1.33308	−	4.66671i	0.0749918	−	0.262523i
$317$	−7.15073			−0.401625			−0.200812	−	0.979630i	$-0.564358\pi$
$317$	−7.15073			−0.401625			−0.200812	+	0.979630i	$0.564358\pi$
$318$	0.449285	−	10.3715i	0.0251947	−	0.581603i
$319$			50.0094i			2.79999i
$320$	4.87067	+	5.37673i	0.272279	+	0.300568i
$321$	−23.4445	+	2.25362i	−1.30854	+	0.125785i
$322$	−1.27741	+	9.12251i	−0.0711873	+	0.508378i
$323$			1.79438i			0.0998420i
$324$	17.9007	−	1.88793i	0.994484	−	0.104885i
$325$		−	15.8317i		−	0.878185i
$326$	−6.23007	−	0.872386i	−0.345052	−	0.0483170i
$327$	6.63297	−	0.637600i	0.366804	−	0.0352593i
$328$	8.14985	−	18.3794i	0.450000	−	1.01483i
$329$			15.1297i			0.834128i
$330$	11.9231	+	0.516502i	0.656347	+	0.0284325i
$331$	23.9732			1.31769			0.658844	−	0.752279i	$-0.271046\pi$
$331$	23.9732			1.31769			0.658844	+	0.752279i	$0.271046\pi$
$332$	2.81993	−	9.87171i	0.154764	−	0.541780i
$333$	−5.11952	−	26.3832i	−0.280548	−	1.44579i
$334$	8.46960	+	1.18598i	0.463436	+	0.0648942i
$335$	−11.9247			−0.651518
$336$	−8.80426	−	4.36934i	−0.480312	−	0.238367i
$337$	−12.8803			−0.701636			−0.350818	−	0.936444i	$-0.614096\pi$
$337$	−12.8803			−0.701636			−0.350818	+	0.936444i	$0.614096\pi$
$338$	−1.90678	−	0.267004i	−0.103715	−	0.0145231i
$339$	13.7912	−	1.32569i	0.749033	−	0.0720015i
$340$	0.893912	−	3.12931i	0.0484792	−	0.169711i
$341$	−43.8497			−2.37459
$342$	4.23679	−	0.222802i	0.229099	−	0.0120478i
$343$			17.0061i			0.918245i
$344$	20.8058	+	9.22577i	1.12177	+	0.497420i
$345$	0.690042	+	7.17852i	0.0371506	+	0.386479i
$346$	−28.4793	−	3.98791i	−1.53106	−	0.214391i
$347$			4.56944i			0.245301i	0.992450	+	0.122650i	$0.0391394\pi$
$347$			4.56944i			0.245301i	−0.992450	+	0.122650i	$0.960861\pi$
$348$	5.84937	−	31.7097i	0.313559	−	1.69982i
$349$		−	32.9942i		−	1.76614i	−0.469241	−	0.883070i	$-0.655473\pi$
$349$		−	32.9942i		−	1.76614i	0.469241	−	0.883070i	$-0.344527\pi$
$350$	1.16232	−	8.30058i	0.0621284	−	0.443685i
$351$	18.8834	−	5.58356i	1.00792	−	0.298028i
$352$	19.4770	−	23.3306i	1.03813	−	1.24353i
$353$		−	7.40581i		−	0.394172i	−0.980386	−	0.197086i	$-0.936852\pi$
$353$		−	7.40581i		−	0.394172i	0.980386	−	0.197086i	$-0.0631477\pi$
$354$	7.41754	+	0.321323i	0.394238	+	0.0170781i
$355$	−6.11310			−0.324450
$356$	2.39176	−	8.37282i	0.126763	−	0.443759i
$357$	0.421891	+	4.38894i	0.0223288	+	0.232287i
$358$	−3.87664	+	27.6847i	−0.204887	+	1.46318i
$359$	−17.3266			−0.914461			−0.457231	−	0.889348i	$-0.651159\pi$
$359$	−17.3266			−0.914461			−0.457231	+	0.889348i	$0.651159\pi$
$360$	−7.49974	−	1.72210i	−0.395271	−	0.0907624i
$361$	1.00000			0.0526316
$362$	−3.11842	+	22.2699i	−0.163900	+	1.17048i
$363$	−2.96075	−	30.8008i	−0.155399	−	1.61662i
$364$	−10.3390	−	2.95341i	−0.541910	−	0.154801i
$365$	−2.83843			−0.148570
$366$	0.424863	+	0.0184048i	0.0222080	+	0.000962033i
$367$		−	2.52764i		−	0.131942i	−0.997822	−	0.0659710i	$-0.978986\pi$
$367$		−	2.52764i		−	0.131942i	0.997822	−	0.0659710i	$-0.0210145\pi$
$368$	15.5941	+	9.70071i	0.812896	+	0.505684i
$369$	4.06221	+	20.9344i	0.211470	+	1.08980i
$370$	−1.59325	+	11.3781i	−0.0828291	+	0.591517i
$371$		−	6.01248i		−	0.312153i
$372$	27.8040	+	5.12890i	1.44157	+	0.265921i
$373$			15.9807i			0.827449i	0.910402	+	0.413724i	$0.135772\pi$
$373$			15.9807i			0.827449i	−0.910402	+	0.413724i	$0.864228\pi$
$374$	−13.5020	−	1.89066i	−0.698170	−	0.0977636i
$375$	−1.37934	−	14.3493i	−0.0712288	−	0.740995i
$376$	27.5750	+	12.2274i	1.42207	+	0.630579i
$377$		−	35.2749i		−	1.81675i
$378$	10.3105	−	1.54110i	0.530316	−	0.0792659i
$379$	8.40288			0.431627			0.215813	−	0.976435i	$-0.430760\pi$
$379$	8.40288			0.431627			0.215813	+	0.976435i	$0.430760\pi$
$380$	−1.74395	−	0.498173i	−0.0894628	−	0.0255557i
$381$	11.4906	−	1.10455i	0.588683	−	0.0565876i
$382$	−27.8663	−	3.90207i	−1.42576	−	0.199647i
$383$	14.5868			0.745351			0.372676	−	0.927962i	$-0.378440\pi$
$383$	14.5868			0.745351			0.372676	+	0.927962i	$0.378440\pi$
$384$	−15.0788	+	12.5152i	−0.769485	+	0.638665i
$385$	6.91200			0.352268
$386$	−7.85194	−	1.09949i	−0.399653	−	0.0559627i
$387$	−23.6981	+	4.59849i	−1.20464	+	0.233754i
$388$	1.75225	+	0.500545i	0.0889572	+	0.0254113i
$389$	−9.07532			−0.460137			−0.230069	−	0.973174i	$-0.573895\pi$
$389$	−9.07532			−0.460137			−0.230069	+	0.973174i	$0.573895\pi$
$390$	−8.41018	−	0.364323i	−0.425866	−	0.0184482i
$391$		−	8.23851i		−	0.416639i
$392$	12.8955	+	5.71816i	0.651321	+	0.288811i
$393$	5.31890	−	0.511284i	0.268303	−	0.0257909i
$394$	−10.6856	−	1.49628i	−0.538332	−	0.0753817i
$395$		−	2.20066i		−	0.110727i
$396$	−2.78762	+	32.1148i	−0.140083	+	1.61383i
$397$		−	30.1790i		−	1.51464i	−0.653043	−	0.757320i	$-0.726508\pi$
$397$		−	30.1790i		−	1.51464i	0.653043	−	0.757320i	$-0.273492\pi$
$398$	−2.60346	+	18.5924i	−0.130500	+	0.931951i
$399$	2.44594	−	0.235118i	0.122450	−	0.0117706i
$400$	−14.1890	−	8.82669i	−0.709452	−	0.441334i
$401$		−	32.0625i		−	1.60112i	−0.599250	−	0.800562i	$-0.704534\pi$
$401$		−	32.0625i		−	1.60112i	0.599250	−	0.800562i	$-0.295466\pi$
$402$	1.39400	−	32.1795i	0.0695262	−	1.60497i
$403$	30.9301			1.54074
$404$	19.6978	+	5.62684i	0.980004	+	0.279946i
$405$	7.56936	−	3.05253i	0.376125	−	0.151681i
$406$	2.58978	−	18.4947i	0.128529	−	0.917877i
$407$	48.1301			2.38572
$408$	8.34011	+	2.77808i	0.412897	+	0.137536i
$409$	−6.63235			−0.327949			−0.163974	−	0.986465i	$-0.552431\pi$
$409$	−6.63235			−0.327949			−0.163974	+	0.986465i	$0.552431\pi$
$410$	1.26420	−	9.02820i	0.0624346	−	0.445871i
$411$	−25.1936	+	2.42176i	−1.24271	+	0.119457i
$412$	1.99634	−	6.98855i	0.0983524	−	0.344301i
$413$	4.30005			0.211592
$414$	−19.4523	+	1.02295i	−0.956028	+	0.0502752i
$415$		−	4.65514i		−	0.228512i
$416$	−13.7384	+	16.4567i	−0.673583	+	0.806854i
$417$	−2.93145	−	30.4960i	−0.143554	−	1.49339i
$418$	−1.05366	+	7.52459i	−0.0515360	+	0.368040i
$419$			0.620727i			0.0303245i	0.999885	+	0.0151623i	$0.00482648\pi$
$419$			0.620727i			0.0303245i	−0.999885	+	0.0151623i	$0.995174\pi$
$420$	−4.38272	−	0.808466i	−0.213855	−	0.0394491i
$421$		−	28.4205i		−	1.38513i	−0.721355	−	0.692565i	$-0.756480\pi$
$421$		−	28.4205i		−	1.38513i	0.721355	−	0.692565i	$-0.243520\pi$
$422$	19.5840	+	2.74231i	0.953334	+	0.133494i
$423$	−31.4083	+	6.09461i	−1.52712	+	0.296330i
$424$	−10.9582	−	4.85911i	−0.532176	−	0.235979i
$425$			7.49623i			0.363621i
$426$	0.714618	−	16.4965i	0.0346234	−	0.799259i
$427$	0.246299			0.0119192
$428$	−7.47000	+	26.1502i	−0.361076	+	1.26402i
$429$	3.37433	+	35.1032i	0.162914	+	1.69480i
$430$	10.2201	+	1.43110i	0.492856	+	0.0690138i
$431$	−23.1164			−1.11348			−0.556740	−	0.830687i	$-0.687948\pi$
$431$	−23.1164			−1.11348			−0.556740	+	0.830687i	$0.687948\pi$
$432$	5.52388	−	20.0371i	0.265768	−	0.964037i
$433$	−6.97713			−0.335299			−0.167650	−	0.985847i	$-0.553618\pi$
$433$	−6.97713			−0.335299			−0.167650	+	0.985847i	$0.553618\pi$
$434$	16.2167	+	2.27080i	0.778427	+	0.109002i
$435$	−1.39897	−	14.5535i	−0.0670755	−	0.697788i
$436$	2.11343	−	7.39845i	0.101215	−	0.354322i
$437$	−4.59129			−0.219631
$438$	0.331811	−	7.65965i	0.0158545	−	0.365992i
$439$		−	12.0559i		−	0.575398i	−0.957721	−	0.287699i	$-0.907110\pi$
$439$		−	12.0559i		−	0.575398i	0.957721	−	0.287699i	$-0.0928903\pi$
$440$	5.58607	−	12.5976i	0.266305	−	0.600567i
$441$	−14.6881	+	2.85016i	−0.699435	+	0.135722i
$442$	9.52384	+	1.33361i	0.453003	+	0.0634332i
$443$		−	4.06974i		−	0.193359i	−0.995316	−	0.0966795i	$-0.969178\pi$
$443$		−	4.06974i		−	0.193359i	0.995316	−	0.0966795i	$-0.0308222\pi$
$444$	−30.5180	−	5.62956i	−1.44832	−	0.267167i
$445$		−	3.94832i		−	0.187169i
$446$	−2.53063	+	18.0723i	−0.119829	+	0.855746i
$447$	0.879352	+	9.14792i	0.0415919	+	0.432682i
$448$	−8.41129	+	7.61961i	−0.397396	+	0.359993i
$449$			20.6460i			0.974343i	0.873306	+	0.487172i	$0.161971\pi$
$449$			20.6460i			0.974343i	−0.873306	+	0.487172i	$0.838029\pi$
$450$	17.6997	−	0.930783i	0.834370	−	0.0438775i
$451$	−38.1900			−1.79830
$452$	4.39420	−	15.3828i	0.206686	−	0.723544i
$453$	−24.5210	+	2.35710i	−1.15210	+	0.110746i
$454$	1.06655	−	7.61668i	0.0500557	−	0.357469i
$455$	−4.87549			−0.228567
$456$	1.54821	−	4.64791i	0.0725017	−	0.217658i
$457$	5.73578			0.268309			0.134154	−	0.990960i	$-0.457168\pi$
$457$	5.73578			0.268309			0.134154	+	0.990960i	$0.457168\pi$
$458$	−2.19387	+	15.6673i	−0.102513	+	0.732086i
$459$	−8.94120	+	2.64379i	−0.417339	+	0.123401i
$460$	8.00697	+	2.28725i	0.373327	+	0.106644i
$461$	37.3891			1.74138			0.870692	−	0.491828i	$-0.163671\pi$
$461$	37.3891			1.74138			0.870692	+	0.491828i	$0.163671\pi$
$462$	−0.808009	+	18.6524i	−0.0375920	+	0.867788i
$463$			22.6647i			1.05332i	0.850077	+	0.526658i	$0.176555\pi$
$463$			22.6647i			1.05332i	−0.850077	+	0.526658i	$0.823445\pi$
$464$	−31.6149	−	19.6669i	−1.46769	−	0.913014i
$465$	12.7610	−	1.22666i	0.591775	−	0.0568849i
$466$	−2.43512	+	17.3902i	−0.112805	+	0.805586i
$467$		−	22.1762i		−	1.02619i	−0.858331	−	0.513096i	$-0.828498\pi$
$467$		−	22.1762i		−	1.02619i	0.858331	−	0.513096i	$-0.171502\pi$
$468$	1.96629	−	22.6527i	0.0908918	−	1.04712i
$469$		−	18.6549i		−	0.861404i
$470$	13.5452	+	1.89671i	0.624793	+	0.0874886i
$471$	−34.1610	+	3.28375i	−1.57405	+	0.151307i
$472$	3.47517	−	7.83714i	0.159958	−	0.360734i
$473$		−	43.2317i		−	1.98780i
$474$	5.93859	+	0.257255i	0.272768	+	0.0118161i
$475$	4.17762			0.191682
$476$	4.89545	+	1.39842i	0.224383	+	0.0640967i
$477$	12.4815	−	2.42197i	0.571489	−	0.110894i
$478$	2.78383	+	0.389814i	0.127329	+	0.0178297i
$479$	18.4304			0.842107			0.421054	−	0.907036i	$-0.361660\pi$
$479$	18.4304			0.842107			0.421054	+	0.907036i	$0.361660\pi$
$480$	−5.01547	+	7.33444i	−0.228924	+	0.334770i
$481$	−33.9494			−1.54796
$482$	14.9648	+	2.09549i	0.681627	+	0.0954470i
$483$	−11.2300	+	1.07949i	−0.510982	+	0.0491186i
$484$	−34.3554	−	9.81389i	−1.56161	−	0.446086i
$485$	0.826300			0.0375204
$486$	7.35256	+	20.7832i	0.333519	+	0.942743i
$487$		−	20.2860i		−	0.919247i	−0.888114	−	0.459624i	$-0.847984\pi$
$487$		−	20.2860i		−	0.919247i	0.888114	−	0.459624i	$-0.152016\pi$
$488$	0.199051	−	0.448897i	0.00901063	−	0.0203206i
$489$	−0.737222	−	7.66933i	−0.0333383	−	0.346819i
$490$	6.33443	+	0.887000i	0.286160	+	0.0400706i
$491$		−	35.9813i		−	1.62381i	−0.583787	−	0.811907i	$-0.698430\pi$
$491$		−	35.9813i		−	1.62381i	0.583787	−	0.811907i	$-0.301570\pi$
$492$	24.2153	+	4.46691i	1.09171	+	0.201384i
$493$			16.7025i			0.752243i
$494$	0.743213	−	5.30759i	0.0334387	−	0.238800i
$495$	2.78432	+	14.3488i	0.125146	+	0.644933i
$496$	17.2445	−	27.7209i	0.774303	−	1.24470i
$497$		−	9.56325i		−	0.428971i
$498$	12.5622	+	0.544184i	0.562924	+	0.0243855i
$499$	5.57878			0.249741			0.124870	−	0.992173i	$-0.460149\pi$
$499$	5.57878			0.249741			0.124870	+	0.992173i	$0.460149\pi$
$500$	−16.0053	−	4.57204i	−0.715779	−	0.204468i
$501$	1.00223	+	10.4262i	0.0447764	+	0.465810i
$502$	2.05790	−	14.6963i	0.0918485	−	0.655928i
$503$	−31.8202			−1.41879			−0.709395	−	0.704811i	$-0.751032\pi$
$503$	−31.8202			−1.41879			−0.709395	+	0.704811i	$0.751032\pi$
$504$	2.69403	−	11.7325i	0.120001	−	0.522607i
$505$	9.28880			0.413346
$506$	4.83763	−	34.5475i	0.215059	−	1.53583i
$507$	−0.225635	−	2.34729i	−0.0100208	−	0.104247i
$508$	3.66120	−	12.8167i	0.162439	−	0.568650i
$509$	25.9539			1.15039			0.575193	−	0.818018i	$-0.304927\pi$
$509$	25.9539			1.15039			0.575193	+	0.818018i	$0.304927\pi$
$510$	3.98218	+	0.172505i	0.176334	+	0.00763866i
$511$		−	4.44040i		−	0.196432i
$512$	7.08954	+	21.4881i	0.313316	+	0.949649i
$513$	1.47337	+	4.98289i	0.0650509	+	0.220000i
$514$	−3.95099	+	28.2156i	−0.174270	+	1.24454i
$515$		−	3.29555i		−	0.145219i
$516$	−5.05662	+	27.4121i	−0.222605	+	1.20675i
$517$		−	57.2972i		−	2.51993i
$518$	−17.7997	−	2.49246i	−0.782074	−	0.109512i
$519$	−3.37004	−	35.0586i	−0.147928	−	1.53890i
$520$	−3.94023	+	8.88593i	−0.172790	+	0.389674i
$521$			16.2458i			0.711741i	0.934535	+	0.355870i	$0.115816\pi$
$521$			16.2458i			0.711741i	−0.934535	+	0.355870i	$0.884184\pi$
$522$	39.4370	−	2.07390i	1.72611	−	0.0907720i
$523$	1.95795			0.0856151			0.0428075	−	0.999083i	$-0.486370\pi$
$523$	1.95795			0.0856151			0.0428075	+	0.999083i	$0.486370\pi$
$524$	1.69473	−	5.93274i	0.0740348	−	0.259173i
$525$	10.2182	−	0.982232i	0.445958	−	0.0428681i
$526$	19.1748	+	2.68502i	0.836063	+	0.117072i
$527$	−14.6453			−0.637957
$528$	33.3423	+	16.5470i	1.45104	+	0.720114i
$529$	−1.92010			−0.0834826
$530$	−5.38280	−	0.753744i	−0.233814	−	0.0327405i
$531$	1.73216	+	8.92661i	0.0751695	+	0.387382i
$532$	0.779335	−	2.72821i	0.0337885	−	0.118283i
$533$	26.9380			1.16681
$534$	10.6548	+	0.461557i	0.461077	+	0.0199735i
$535$			12.3315i			0.533136i
$536$	−33.9999	−	15.0763i	−1.46857	−	0.651198i
$537$	−34.0804	+	3.27601i	−1.47068	+	0.141370i
$538$	−18.2278	−	2.55241i	−0.785858	−	0.110042i
$539$		−	26.7951i		−	1.15415i
$540$	−0.0871449	−	9.42390i	−0.00375012	−	0.405540i
$541$			39.0691i			1.67971i	0.542810	+	0.839856i	$0.317361\pi$
$541$			39.0691i			1.67971i	−0.542810	+	0.839856i	$0.682639\pi$
$542$	5.57868	−	39.8396i	0.239625	−	1.71126i
$543$	−27.4147	+	2.63526i	−1.17648	+	0.113090i
$544$	6.50508	−	7.79214i	0.278903	−	0.334085i
$545$		−	3.48885i		−	0.149446i
$546$	0.569943	−	13.1568i	0.0243913	−	0.563058i
$547$	39.9371			1.70759			0.853793	−	0.520612i	$-0.174296\pi$
$547$	39.9371			1.70759			0.853793	+	0.520612i	$0.174296\pi$
$548$	−8.02731	+	28.1011i	−0.342910	+	1.20042i
$549$	0.0992151	+	0.511300i	0.00423440	+	0.0218217i
$550$	−4.40177	+	31.4348i	−0.187692	+	1.34039i
$551$	9.30823			0.396544
$552$	−7.10829	+	21.3399i	−0.302549	+	0.908285i
$553$	3.44268			0.146398
$554$	0.967348	−	6.90824i	0.0410987	−	0.293503i
$555$	−14.0066	+	1.34640i	−0.594548	+	0.0571514i
$556$	−34.0154	−	9.71677i	−1.44258	−	0.412083i
$557$	−39.8951			−1.69041			−0.845204	−	0.534444i	$-0.820521\pi$
$557$	−39.8951			−1.69041			−0.845204	+	0.534444i	$0.820521\pi$
$558$	1.81845	+	34.5795i	0.0769813	+	1.46387i
$559$			30.4942i			1.28977i
$560$	−2.71824	+	4.36963i	−0.114867	+	0.184650i
$561$	−1.59773	−	16.6212i	−0.0674561	−	0.701747i
$562$	2.44910	−	17.4900i	0.103309	−	0.737771i
$563$			36.0667i			1.52003i	0.649906	+	0.760015i	$0.274808\pi$
$563$			36.0667i			1.52003i	−0.649906	+	0.760015i	$0.725192\pi$
$564$	−6.70179	+	36.3307i	−0.282196	+	1.52980i
$565$		−	7.25396i		−	0.305176i
$566$	−6.77036	−	0.948043i	−0.284580	−	0.0398492i
$567$	4.77534	+	11.8414i	0.200545	+	0.497293i
$568$	−17.4297	−	7.72873i	−0.731334	−	0.324290i
$569$			16.3775i			0.686582i	0.939229	+	0.343291i	$0.111542\pi$
$569$			16.3775i			0.686582i	−0.939229	+	0.343291i	$0.888458\pi$
$570$	0.0961364	−	2.21925i	0.00402671	−	0.0929541i
$571$	−11.3510			−0.475026			−0.237513	−	0.971384i	$-0.576332\pi$
$571$	−11.3510			−0.475026			−0.237513	+	0.971384i	$0.576332\pi$
$572$	39.1544	+	11.1847i	1.63713	+	0.467658i
$573$	−3.29750	−	34.3039i	−0.137755	−	1.43307i
$574$	14.1236	+	1.97770i	0.589508	+	0.0825478i
$575$	−19.1806			−0.799887
$576$	−19.2061	−	14.3919i	−0.800253	−	0.599663i
$577$	24.2018			1.00753			0.503767	−	0.863840i	$-0.331947\pi$
$577$	24.2018			1.00753			0.503767	+	0.863840i	$0.331947\pi$
$578$	19.2998	+	2.70252i	0.802768	+	0.112410i
$579$	−0.929142	−	9.66589i	−0.0386138	−	0.401701i
$580$	−16.2331	−	4.63711i	−0.674043	−	0.192545i
$581$	7.28245			0.302127
$582$	−0.0965941	+	2.22981i	−0.00400395	+	0.0924288i
$583$			22.7697i			0.943023i
$584$	−8.09294	−	3.58860i	−0.334888	−	0.148497i
$585$	−1.96397	−	10.1212i	−0.0812000	−	0.418460i
$586$	−25.2388	−	3.53415i	−1.04261	−	0.145995i
$587$		−	27.2372i		−	1.12420i	−0.827069	−	0.562101i	$-0.809993\pi$
$587$		−	27.2372i		−	1.12420i	0.827069	−	0.562101i	$-0.190007\pi$
$588$	−3.13411	+	16.9901i	−0.129248	+	0.700660i
$589$			8.16173i			0.336298i
$590$	0.539068	−	3.84971i	0.0221931	−	0.158490i
$591$	−1.26446	−	13.1542i	−0.0520128	−	0.541090i
$592$	−18.9279	+	30.4269i	−0.777930	+	1.25054i
$593$		−	15.0669i		−	0.618723i	−0.950945	−	0.309361i	$-0.899885\pi$
$593$		−	15.0669i		−	0.618723i	0.950945	−	0.309361i	$-0.100115\pi$
$594$	−39.0466	+	5.83626i	−1.60210	+	0.239465i
$595$	2.30852			0.0946401
$596$	10.2037	+	2.91475i	0.417958	+	0.119393i
$597$	−22.8876	+	2.20009i	−0.936726	+	0.0900436i
$598$	−3.41230	+	24.3687i	−0.139539	+	0.996509i
$599$	−9.41326			−0.384615			−0.192308	−	0.981335i	$-0.561597\pi$
$599$	−9.41326			−0.384615			−0.192308	+	0.981335i	$0.561597\pi$
$600$	6.46784	−	19.4172i	0.264048	−	0.792702i
$601$	43.3139			1.76681			0.883406	−	0.468608i	$-0.155244\pi$
$601$	43.3139			1.76681			0.883406	+	0.468608i	$0.155244\pi$
$602$	−2.23880	+	15.9882i	−0.0912465	+	0.651629i
$603$	38.7263	−	7.51464i	1.57706	−	0.306020i
$604$	−7.81300	+	27.3509i	−0.317906	+	1.11289i
$605$	−16.2008			−0.658655
$606$	−1.08586	+	25.0663i	−0.0441099	+	1.01825i
$607$		−	21.9585i		−	0.891268i	−0.895215	−	0.445634i	$-0.852978\pi$
$607$		−	21.9585i		−	0.891268i	0.895215	−	0.445634i	$-0.147022\pi$
$608$	−4.34253	−	3.62525i	−0.176113	−	0.147023i
$609$	22.7673	−	2.18853i	0.922579	−	0.0886838i
$610$	0.0308768	−	0.220504i	0.00125017	−	0.00892795i
$611$			40.4155i			1.63504i
$612$	−0.931029	+	10.7260i	−0.0376346	+	0.433571i
$613$			32.3634i			1.30715i	0.756864	+	0.653573i	$0.226731\pi$
$613$			32.3634i			1.30715i	−0.756864	+	0.653573i	$0.773269\pi$
$614$	6.74608	+	0.944643i	0.272250	+	0.0381227i
$615$	11.1139	−	1.06833i	0.448155	−	0.0430793i
$616$	19.7075	+	8.73878i	0.794039	+	0.352095i
$617$			15.9725i			0.643027i	0.946905	+	0.321514i	$0.104192\pi$
$617$			15.9725i			0.643027i	−0.946905	+	0.321514i	$0.895808\pi$
$618$	8.89323	+	0.385248i	0.357738	+	0.0154970i
$619$	49.6645			1.99619			0.998093	−	0.0617308i	$-0.0196620\pi$
$619$	49.6645			1.99619			0.998093	+	0.0617308i	$0.0196620\pi$
$620$	4.06595	−	14.2337i	0.163293	−	0.571637i
$621$	−6.76466	−	22.8779i	−0.271457	−	0.918057i
$622$	−2.00662	−	0.280983i	−0.0804581	−	0.0112664i
$623$	6.17671			0.247465
$624$	−23.5185	−	11.6717i	−0.941495	−	0.467241i
$625$	13.3405			0.533622
$626$	20.9143	+	2.92860i	0.835905	+	0.117050i
$627$	−9.26292	+	0.890406i	−0.369925	+	0.0355594i
$628$	−10.8845	+	38.1034i	−0.434340	+	1.52049i
$629$	16.0748			0.640946
$630$	−0.286642	−	5.45075i	−0.0114201	−	0.217163i
$631$			23.8892i			0.951014i	0.879712	+	0.475507i	$0.157735\pi$
$631$			23.8892i			0.951014i	−0.879712	+	0.475507i	$0.842265\pi$
$632$	2.78227	−	6.27452i	0.110673	−	0.249587i
$633$	2.31743	+	24.1083i	0.0921096	+	0.958218i
$634$	−10.0149	−	1.40238i	−0.397744	−	0.0556955i
$635$		−	6.04391i		−	0.239845i
$636$	2.66326	−	14.4377i	0.105605	−	0.572490i
$637$			18.9004i			0.748861i
$638$	−9.80767	+	70.0406i	−0.388289	+	2.77293i
$639$	19.8527	−	3.85231i	0.785359	−	0.152395i
$640$	5.76715	+	8.48559i	0.227967	+	0.335422i
$641$			17.2980i			0.683232i	0.939840	+	0.341616i	$0.110974\pi$
$641$			17.2980i			0.683232i	−0.939840	+	0.341616i	$0.889026\pi$
$642$	−33.2772	−	1.44154i	−1.31334	−	0.0568932i
$643$	−2.76352			−0.108983			−0.0544914	−	0.998514i	$-0.517354\pi$
$643$	−2.76352			−0.108983			−0.0544914	+	0.998514i	$0.517354\pi$
$644$	−3.57815	+	12.5260i	−0.140999	+	0.493594i
$645$	1.20937	+	12.5811i	0.0476189	+	0.495381i
$646$	−0.351908	+	2.51312i	−0.0138456	+	0.0988773i
$647$	13.7500			0.540569			0.270285	−	0.962780i	$-0.412882\pi$
$647$	13.7500			0.540569			0.270285	+	0.962780i	$0.412882\pi$
$648$	25.4411	+	0.866484i	0.999421	+	0.0340387i
$649$	−16.2846			−0.639225
$650$	3.10486	−	22.1731i	0.121783	−	0.869700i
$651$	1.91897	+	19.9631i	0.0752103	+	0.782415i
$652$	−8.55443	−	2.44364i	−0.335017	−	0.0957003i
$653$	43.2808			1.69371			0.846855	−	0.531824i	$-0.178493\pi$
$653$	43.2808			1.69371			0.846855	+	0.531824i	$0.178493\pi$
$654$	9.41484	+	0.407844i	0.368149	+	0.0159480i
$655$		−	2.79767i		−	0.109314i
$656$	15.0188	−	24.1429i	0.586385	−	0.942624i
$657$	9.21797	−	1.78870i	0.359627	−	0.0697838i
$658$	−2.96719	+	21.1899i	−0.115673	+	0.826069i
$659$			25.3751i			0.988475i	0.869327	+	0.494237i	$0.164553\pi$
$659$			25.3751i			0.988475i	−0.869327	+	0.494237i	$0.835447\pi$
$660$	16.5976	+	3.06171i	0.646062	+	0.119177i
$661$		−	10.7539i		−	0.418279i	−0.977886	−	0.209140i	$-0.932934\pi$
$661$		−	10.7539i		−	0.418279i	0.977886	−	0.209140i	$-0.0670664\pi$
$662$	33.5757	+	4.70155i	1.30496	+	0.182731i
$663$	1.12698	+	11.7240i	0.0437684	+	0.455324i
$664$	5.88545	−	13.2728i	0.228400	−	0.515084i
$665$		−	1.28653i		−	0.0498894i
$666$	−1.99596	−	37.9550i	−0.0773419	−	1.47073i
$667$	−42.7367			−1.65477
$668$	11.6295	+	3.32206i	0.449959	+	0.128534i
$669$	−22.2473	+	2.13854i	−0.860130	+	0.0826808i
$670$	−16.7012	−	2.33864i	−0.645223	−	0.0903495i
$671$	−0.932749			−0.0360084
$672$	−11.4739	−	7.84613i	−0.442616	−	0.302671i
$673$	−1.87056			−0.0721048			−0.0360524	−	0.999350i	$-0.511478\pi$
$673$	−1.87056			−0.0721048			−0.0360524	+	0.999350i	$0.511478\pi$
$674$	−18.0395	−	2.52604i	−0.694857	−	0.0972996i
$675$	6.15518	+	20.8166i	0.236913	+	0.801231i
$676$	−2.61818	−	0.747903i	−0.100699	−	0.0287655i
$677$	30.8820			1.18689			0.593445	−	0.804875i	$-0.297767\pi$
$677$	30.8820			1.18689			0.593445	+	0.804875i	$0.297767\pi$
$678$	19.5752	+	0.847984i	0.751781	+	0.0325666i
$679$			1.29265i			0.0496075i
$680$	1.86568	−	4.20744i	0.0715454	−	0.161348i
$681$	9.37628	−	0.901304i	0.359300	−	0.0345380i
$682$	−61.4137	−	8.59965i	−2.35165	−	0.329298i
$683$		−	36.7025i		−	1.40438i	−0.711989	−	0.702190i	$-0.752206\pi$
$683$		−	36.7025i		−	1.40438i	0.711989	−	0.702190i	$-0.247794\pi$
$684$	5.97752	+	0.518858i	0.228556	+	0.0198390i
$685$			13.2515i			0.506314i
$686$	−3.33519	+	23.8179i	−0.127338	+	0.909373i
$687$	−19.2868	+	1.85396i	−0.735837	+	0.0707330i
$688$	27.3302	+	17.0015i	1.04195	+	0.648177i
$689$		−	16.0609i		−	0.611873i
$690$	−0.441389	+	10.1892i	−0.0168034	+	0.387896i
$691$	−30.1094			−1.14542			−0.572708	−	0.819759i	$-0.694107\pi$
$691$	−30.1094			−1.14542			−0.572708	+	0.819759i	$0.694107\pi$
$692$	−39.1046	−	11.1705i	−1.48653	−	0.424640i
$693$	−22.4472	+	4.35575i	−0.852697	+	0.165461i
$694$	−0.896144	+	6.39973i	−0.0340171	+	0.242930i
$695$	−16.0405			−0.608449
$696$	14.4111	−	43.2638i	0.546252	−	1.63991i
$697$	−12.7550			−0.483129
$698$	6.47071	−	46.2100i	0.244920	−	1.74908i
$699$	−21.4077	+	2.05783i	−0.809713	+	0.0778344i
$700$	3.25576	−	11.3974i	0.123056	−	0.430782i
$701$	−22.0531			−0.832934			−0.416467	−	0.909151i	$-0.636732\pi$
$701$	−22.0531			−0.832934			−0.416467	+	0.909151i	$0.636732\pi$
$702$	27.5422	−	4.11670i	1.03951	−	0.155375i
$703$		−	8.95844i		−	0.337874i
$704$	31.8541	−	28.8560i	1.20055	−	1.08755i
$705$	1.60284	+	16.6744i	0.0603664	+	0.627994i
$706$	1.45240	−	10.3722i	0.0546619	−	0.390363i
$707$			14.5313i			0.546505i
$708$	10.3256	+	1.90473i	0.388061	+	0.0715842i
$709$			31.4590i			1.18147i	0.806866	+	0.590734i	$0.201162\pi$
$709$			31.4590i			1.18147i	−0.806866	+	0.590734i	$0.798838\pi$
$710$	−8.56169	−	1.19888i	−0.321315	−	0.0449931i
$711$	1.38679	+	7.14677i	0.0520088	+	0.268025i
$712$	4.99183	−	11.2575i	0.187077	−	0.421892i
$713$		−	37.4728i		−	1.40337i
$714$	−0.269865	+	6.22967i	−0.0100994	+	0.233139i
$715$	18.4638			0.690507
$716$	−10.8589	+	38.0135i	−0.405815	+	1.42063i
$717$	0.329418	+	3.42694i	0.0123023	+	0.127982i
$718$	−24.2667	−	3.39803i	−0.905626	−	0.126813i
$719$	46.1801			1.72223			0.861113	−	0.508414i	$-0.169768\pi$
$719$	46.1801			1.72223			0.861113	+	0.508414i	$0.169768\pi$
$720$	−10.1660	−	3.88270i	−0.378865	−	0.144700i
$721$	5.15552			0.192002
$722$	1.40055	+	0.196117i	0.0521230	+	0.00729870i
$723$	1.77082	+	18.4219i	0.0658577	+	0.685119i
$724$	−8.73499	+	30.5785i	−0.324633	+	1.13644i
$725$	38.8862			1.44420
$726$	1.89386	−	43.7187i	0.0702878	−	1.62255i
$727$		−	50.5911i		−	1.87632i	−0.346202	−	0.938160i	$-0.612529\pi$
$727$		−	50.5911i		−	1.87632i	0.346202	−	0.938160i	$-0.387471\pi$
$728$	−13.9010	−	6.16404i	−0.515207	−	0.228455i
$729$	−22.6584	+	14.6833i	−0.839198	+	0.543825i
$730$	−3.97536	−	0.556663i	−0.147135	−	0.0206030i
$731$		−	14.4389i		−	0.534040i
$732$	0.591432	+	0.109100i	0.0218600	+	0.00403243i
$733$		−	9.29883i		−	0.343460i	−0.985144	−	0.171730i	$-0.945064\pi$
$733$		−	9.29883i		−	0.343460i	0.985144	−	0.171730i	$-0.0549357\pi$
$734$	0.495713	−	3.54009i	0.0182971	−	0.130667i
$735$	0.749571	+	7.79781i	0.0276484	+	0.287627i
$736$	19.9378	+	16.6446i	0.734916	+	0.613527i
$737$			70.6473i			2.60233i
$738$	1.58375	+	30.1163i	0.0582985	+	1.10860i
$739$	36.3369			1.33668			0.668338	−	0.743858i	$-0.267006\pi$
$739$	36.3369			1.33668			0.668338	+	0.743858i	$0.267006\pi$
$740$	−4.46285	+	15.6231i	−0.164058	+	0.574316i
$741$	6.53375	−	0.628063i	0.240023	−	0.0230725i
$742$	1.17915	−	8.42078i	0.0432879	−	0.309137i
$743$	−39.7037			−1.45659			−0.728294	−	0.685264i	$-0.759687\pi$
$743$	−39.7037			−1.45659			−0.728294	+	0.685264i	$0.759687\pi$
$744$	37.9350	+	12.6361i	1.39076	+	0.463262i
$745$	4.81168			0.176286
$746$	−3.13408	+	22.3817i	−0.114747	+	0.819454i
$747$	2.93354	+	15.1179i	0.107333	+	0.553134i
$748$	−18.5394	−	5.29592i	−0.677867	−	0.193638i
$749$	−19.2912			−0.704886
$750$	0.882302	−	20.3674i	0.0322171	−	0.743713i
$751$		−	48.3249i		−	1.76340i	−0.471809	−	0.881701i	$-0.656399\pi$
$751$		−	48.3249i		−	1.76340i	0.471809	−	0.881701i	$-0.343601\pi$
$752$	36.2221	+	22.5330i	1.32088	+	0.821692i
$753$	18.0914	−	1.73906i	0.659289	−	0.0633747i
$754$	6.91800	−	49.4043i	0.251939	−	1.79920i
$755$			12.8977i			0.469396i
$756$	14.7426	−	0.136328i	0.536184	−	0.00495821i
$757$			31.8263i			1.15675i	0.815772	+	0.578373i	$0.196312\pi$
$757$			31.8263i			1.15675i	−0.815772	+	0.578373i	$0.803688\pi$
$758$	11.7686	+	1.64794i	0.427456	+	0.0598560i
$759$	42.5287	−	4.08811i	1.54369	−	0.148389i
$760$	−2.34479	−	1.03973i	−0.0850544	−	0.0377151i
$761$			29.3316i			1.06327i	0.846974	+	0.531635i	$0.178422\pi$
$761$			29.3316i			1.06327i	−0.846974	+	0.531635i	$0.821578\pi$
$762$	16.3098	+	0.706530i	0.590842	+	0.0255949i
$763$	5.45791			0.197590
$764$	−38.2628	−	10.9301i	−1.38430	−	0.395436i
$765$	0.929928	+	4.79233i	0.0336216	+	0.173267i
$766$	20.4296	+	2.86072i	0.738150	+	0.103362i
$767$	11.4866			0.414756
$768$	−23.5730	+	14.5710i	−0.850617	+	0.525785i
$769$	−8.41827			−0.303571			−0.151785	−	0.988413i	$-0.548502\pi$
$769$	−8.41827			−0.303571			−0.151785	+	0.988413i	$0.548502\pi$
$770$	9.68060	+	1.35556i	0.348864	+	0.0488509i
$771$	−34.7340	+	3.33884i	−1.25091	+	0.120245i
$772$	−10.7814	−	3.07979i	−0.388031	−	0.110844i
$773$	−9.02003			−0.324428			−0.162214	−	0.986756i	$-0.551863\pi$
$773$	−9.02003			−0.324428			−0.162214	+	0.986756i	$0.551863\pi$
$774$	−34.0922	+	1.79283i	−1.22542	+	0.0644418i
$775$			34.0966i			1.22479i
$776$	2.35595	+	1.04468i	0.0845737	+	0.0375020i
$777$	−2.10629	−	21.9118i	−0.0755627	−	0.786080i
$778$	−12.7104	−	1.77982i	−0.455691	−	0.0638097i
$779$			7.10829i			0.254681i
$780$	−11.7074	−	2.15963i	−0.419193	−	0.0773271i
$781$			36.2166i			1.29593i
$782$	1.61571	−	11.5384i	0.0577776	−	0.412614i
$783$	13.7145	+	46.3819i	0.490115	+	1.65755i
$784$	16.9393	+	10.5376i	0.604977	+	0.376342i
$785$			17.9682i			0.641312i
$786$	7.54966	+	0.327046i	0.269287	+	0.0116653i
$787$	−5.37802			−0.191706			−0.0958529	−	0.995396i	$-0.530558\pi$
$787$	−5.37802			−0.191706			−0.0958529	+	0.995396i	$0.530558\pi$
$788$	−14.6722	−	4.19124i	−0.522677	−	0.149307i
$789$	2.26901	+	23.6046i	0.0807791	+	0.840346i
$790$	0.431585	−	3.08213i	0.0153551	−	0.109657i
$791$	11.3480			0.403489
$792$	−10.2024	+	44.4317i	−0.362528	+	1.57881i
$793$	0.657930			0.0233638
$794$	5.91860	−	42.2672i	0.210043	−	1.50001i
$795$	−0.636962	−	6.62633i	−0.0225907	−	0.235012i
$796$	−7.29254	+	25.5289i	−0.258477	+	0.904850i
$797$	−1.99116			−0.0705305			−0.0352652	−	0.999378i	$-0.511228\pi$
$797$	−1.99116			−0.0705305			−0.0352652	+	0.999378i	$0.511228\pi$
$798$	3.47177	+	0.150394i	0.122899	+	0.00532391i
$799$		−	19.1365i		−	0.677002i
$800$	−18.1414	−	15.1449i	−0.641396	−	0.535454i
$801$	2.48813	+	12.8224i	0.0879136	+	0.453058i
$802$	6.28798	−	44.9051i	0.222036	−	1.58565i
$803$			16.8161i			0.593426i
$804$	8.26330	−	44.7956i	0.291424	−	1.57982i
$805$			5.90682i			0.208188i
$806$	43.3191	+	6.06591i	1.52585	+	0.213662i
$807$	−2.15695	−	22.4388i	−0.0759283	−	0.789884i
$808$	26.4843	+	11.7437i	0.931714	+	0.413143i
$809$		−	23.9271i		−	0.841233i	−0.907238	−	0.420617i	$-0.861814\pi$
$809$		−	23.9271i		−	0.841233i	0.907238	−	0.420617i	$-0.138186\pi$
$810$	11.1999	−	2.79074i	0.393525	−	0.0980566i
$811$	26.7827			0.940469			0.470235	−	0.882541i	$-0.344169\pi$
$811$	26.7827			0.940469			0.470235	+	0.882541i	$0.344169\pi$
$812$	7.25423	−	25.3948i	0.254574	−	0.891184i
$813$	49.0434	−	4.71434i	1.72003	−	0.165339i
$814$	67.4086	+	9.43911i	2.36267	+	0.330840i
$815$	−4.03396			−0.141304
$816$	11.1359	+	5.52648i	0.389835	+	0.193465i
$817$	−8.04671			−0.281519
$818$	−9.28893	−	1.30071i	−0.324780	−	0.0454784i
$819$	15.8335	−	3.07240i	0.553266	−	0.107358i
$820$	3.54116	−	12.3965i	0.123663	−	0.432905i
$821$	−1.91127			−0.0667039			−0.0333519	−	0.999444i	$-0.510618\pi$
$821$	−1.91127			−0.0667039			−0.0333519	+	0.999444i	$0.510618\pi$
$822$	−35.7599	−	1.54909i	−1.24727	−	0.0540308i
$823$		−	2.69862i		−	0.0940681i	−0.998893	−	0.0470340i	$-0.985023\pi$
$823$		−	2.69862i		−	0.0940681i	0.998893	−	0.0470340i	$-0.0149769\pi$
$824$	4.16654	−	9.39630i	0.145148	−	0.327336i
$825$	−38.6969	+	3.71977i	−1.34725	+	0.129506i
$826$	6.02243	+	0.843311i	0.209547	+	0.0293425i
$827$		−	33.0233i		−	1.14833i	−0.818738	−	0.574167i	$-0.805326\pi$
$827$		−	33.0233i		−	1.14833i	0.818738	−	0.574167i	$-0.194674\pi$
$828$	−27.4445	−	2.38223i	−0.953763	−	0.0827881i
$829$			2.69842i			0.0937202i	0.998901	+	0.0468601i	$0.0149215\pi$
$829$			2.69842i			0.0937202i	−0.998901	+	0.0468601i	$0.985079\pi$
$830$	0.912951	−	6.51976i	0.0316890	−	0.226304i
$831$	8.50417	−	0.817471i	0.295006	−	0.0283578i
$832$	−22.4688	+	20.3540i	−0.778965	+	0.705649i
$833$		−	8.94924i		−	0.310073i
$834$	1.87512	−	43.2860i	0.0649301	−	1.49887i
$835$	5.48406			0.189784
$836$	−2.95139	+	10.3319i	−0.102076	+	0.357337i
$837$	−40.6690	+	12.0253i	−1.40573	+	0.415654i
$838$	−0.121735	+	0.869359i	−0.00420526	+	0.0300315i
$839$	26.5001			0.914885			0.457442	−	0.889239i	$-0.348766\pi$
$839$	26.5001			0.914885			0.457442	+	0.889239i	$0.348766\pi$
$840$	−5.97966	−	1.99182i	−0.206318	−	0.0687243i
$841$	57.6432			1.98770
$842$	5.57373	−	39.8043i	0.192083	−	1.37175i
$843$	21.5305	−	2.06964i	0.741551	−	0.0712823i
$844$	26.8905	+	7.68149i	0.925611	+	0.264408i
$845$	−1.23464			−0.0424729
$846$	−45.1841	+	2.37612i	−1.55346	+	0.0816928i
$847$		−	25.3443i		−	0.870840i
$848$	−14.3945	−	8.95450i	−0.494310	−	0.307499i
$849$	−0.801157	−	8.33445i	−0.0274956	−	0.286038i
$850$	−1.47013	+	10.4988i	−0.0504252	+	0.360107i
$851$			41.1307i			1.40994i
$852$	4.23610	−	22.9640i	0.145126	−	0.786735i
$853$		−	12.5910i		−	0.431106i	−0.976492	−	0.215553i	$-0.930845\pi$
$853$		−	12.5910i		−	0.431106i	0.976492	−	0.215553i	$-0.0691554\pi$
$854$	0.344954	+	0.0483033i	0.0118041	+	0.00165290i
$855$	2.67075	−	0.518244i	0.0913376	−	0.0177236i
$856$	−15.5906	+	35.1596i	−0.532875	+	1.20173i
$857$		−	23.6684i		−	0.808496i	−0.914649	−	0.404248i	$-0.867533\pi$
$857$		−	23.6684i		−	0.808496i	0.914649	−	0.404248i	$-0.132467\pi$
$858$	−2.15841	+	49.8255i	−0.0736869	+	1.70102i
$859$	−50.3558			−1.71812			−0.859059	−	0.511876i	$-0.828951\pi$
$859$	−50.3558			−1.71812			−0.859059	+	0.511876i	$0.828951\pi$
$860$	14.0331	+	4.00865i	0.478523	+	0.136694i
$861$	1.67129	+	17.3864i	0.0569573	+	0.592528i
$862$	−32.3757	−	4.53351i	−1.10272	−	0.154412i
$863$	10.5540			0.359261			0.179630	−	0.983734i	$-0.442510\pi$
$863$	10.5540			0.359261			0.179630	+	0.983734i	$0.442510\pi$
$864$	11.6661	−	26.9797i	0.396888	−	0.917867i
$865$	−18.4403			−0.626990
$866$	−9.77181	−	1.36833i	−0.332060	−	0.0464977i
$867$	2.28381	+	23.7585i	0.0775621	+	0.806881i
$868$	22.2669	+	6.36073i	0.755789	+	0.215897i
$869$	−13.0376			−0.442272
$870$	0.894859	−	20.6573i	0.0303386	−	0.700348i
$871$		−	49.8322i		−	1.68850i
$872$	4.41092	−	9.94742i	0.149372	−	0.336862i
$873$	−2.68346	+	0.520712i	−0.0908214	+	0.0176234i
$874$	−6.43032	−	0.900427i	−0.217509	−	0.0304574i
$875$		−	11.8073i		−	0.399158i
$876$	1.96690	−	10.6626i	0.0664554	−	0.360257i
$877$			1.64273i			0.0554711i	0.999615	+	0.0277355i	$0.00882963\pi$
$877$			1.64273i			0.0554711i	−0.999615	+	0.0277355i	$0.991170\pi$
$878$	2.36437	−	16.8849i	0.0797935	−	0.569838i
$879$	−2.98659	−	31.0695i	−0.100735	−	1.04795i
$880$	10.2942	−	16.5480i	0.347016	−	0.557835i
$881$		−	36.9963i		−	1.24644i	−0.782047	−	0.623219i	$-0.785824\pi$
$881$		−	36.9963i		−	1.24644i	0.782047	−	0.623219i	$-0.214176\pi$
$882$	−21.1304	+	1.11120i	−0.711498	+	0.0374160i
$883$	−31.9223			−1.07427			−0.537135	−	0.843496i	$-0.680494\pi$
$883$	−31.9223			−1.07427			−0.537135	+	0.843496i	$0.680494\pi$
$884$	13.0771	+	3.73557i	0.439829	+	0.125641i
$885$	4.73906	−	0.455547i	0.159302	−	0.0153130i
$886$	0.798143	−	5.69987i	0.0268141	−	0.191491i
$887$	−19.6517			−0.659840			−0.329920	−	0.944009i	$-0.607022\pi$
$887$	−19.6517			−0.659840			−0.329920	+	0.944009i	$0.607022\pi$
$888$	−41.6380	−	13.8696i	−1.39728	−	0.465432i
$889$	9.45501			0.317111
$890$	0.774332	−	5.52982i	0.0259557	−	0.185360i
$891$	−18.0845	−	44.8442i	−0.605854	−	1.50234i
$892$	−7.08854	+	24.8148i	−0.237342	+	0.830860i
$893$	−10.6647			−0.356881
$894$	−0.562483	+	12.9846i	−0.0188122	+	0.434269i
$895$			17.9258i			0.599194i
$896$	−13.2748	+	9.02205i	−0.443478	+	0.301406i
$897$	−29.9983	+	2.88361i	−1.00161	+	0.0962811i
$898$	−4.04901	+	28.9157i	−0.135117	+	0.964929i
$899$			75.9713i			2.53378i
$900$	24.9718	+	2.16759i	0.832393	+	0.0722530i
$901$			7.60478i			0.253352i
$902$	−53.4870	−	7.48969i	−1.78092	−	0.249379i
$903$	−19.6817	+	1.89192i	−0.654967	+	0.0629593i
$904$	9.17111	−	20.6825i	0.305027	−	0.687891i
$905$			14.4197i			0.479328i
$906$	−34.8052	−	1.50774i	−1.15632	−	0.0500912i
$907$	37.9424			1.25986			0.629928	−	0.776653i	$-0.283084\pi$
$907$	37.9424			1.25986			0.629928	+	0.776653i	$0.283084\pi$
$908$	2.98751	−	10.4584i	0.0991441	−	0.347073i
$909$	−30.1660	+	5.85355i	−1.00054	+	0.194150i
$910$	−6.82837	−	0.956165i	−0.226358	−	0.0316966i
$911$	−12.7858			−0.423613			−0.211806	−	0.977312i	$-0.567935\pi$
$911$	−12.7858			−0.423613			−0.211806	+	0.977312i	$0.567935\pi$
$912$	3.07988	−	6.20599i	0.101985	−	0.205501i
$913$	−27.5791			−0.912735
$914$	8.03325	+	1.12488i	0.265716	+	0.0372078i
$915$	0.271445	−	0.0260929i	0.00897369	−	0.000862604i
$916$	−6.14525	+	21.5126i	−0.203045	+	0.710797i
$917$	4.37664			0.144529
$918$	−13.0411	+	1.94924i	−0.430420	+	0.0643344i
$919$		−	22.4859i		−	0.741742i	−0.928684	−	0.370871i	$-0.879059\pi$
$919$		−	22.4859i		−	0.741742i	0.928684	−	0.370871i	$-0.120941\pi$
$920$	10.7656	+	4.77371i	0.354931	+	0.157385i
$921$	0.798283	+	8.30456i	0.0263043	+	0.273645i
$922$	52.3653	+	7.33262i	1.72456	+	0.241487i
$923$		−	25.5460i		−	0.840857i
$924$	−4.78970	+	25.9651i	−0.157570	+	0.854190i
$925$		−	37.4249i		−	1.23052i
$926$	−4.44491	+	31.7430i	−0.146069	+	1.04314i
$927$	2.07677	+	10.7025i	0.0682100	+	0.351517i
$928$	−40.4212	−	33.7447i	−1.32689	−	1.10772i
$929$		−	8.53573i		−	0.280048i	−0.990148	−	0.140024i	$-0.955282\pi$
$929$		−	8.53573i		−	0.280048i	0.990148	−	0.140024i	$-0.0447180\pi$
$930$	18.1129	+	0.784639i	0.593946	+	0.0257293i
$931$	−4.98737			−0.163454
$932$	−6.82102	+	23.8783i	−0.223430	+	0.782159i
$933$	−0.237449	−	2.47019i	−0.00777373	−	0.0808703i
$934$	4.34912	−	31.0589i	0.142308	−	1.01628i
$935$	−8.74252			−0.285911
$936$	7.19646	−	31.3406i	0.235224	−	1.02440i
$937$	2.86781			0.0936873			0.0468437	−	0.998902i	$-0.485084\pi$
$937$	2.86781			0.0936873			0.0468437	+	0.998902i	$0.485084\pi$
$938$	3.65854	−	26.1271i	0.119455	−	0.853081i
$939$	2.47485	+	25.7460i	0.0807638	+	0.840188i
$940$	18.5987	+	5.31287i	0.606623	+	0.173287i
$941$	−6.43217			−0.209683			−0.104841	−	0.994489i	$-0.533433\pi$
$941$	−6.43217			−0.209683			−0.104841	+	0.994489i	$0.533433\pi$
$942$	−48.4881	−	2.10047i	−1.57983	−	0.0684370i
$943$		−	32.6362i		−	1.06278i
$944$	6.40414	−	10.2948i	0.208437	−	0.335066i
$945$	6.41063	−	1.89553i	0.208538	−	0.0616617i
$946$	8.47846	−	60.5482i	0.275658	−	1.96859i
$947$		−	21.3917i		−	0.695137i	−0.937655	−	0.347569i	$-0.887007\pi$
$947$		−	21.3917i		−	0.695137i	0.937655	−	0.347569i	$-0.112993\pi$
$948$	8.26683	+	1.52495i	0.268494	+	0.0495282i
$949$		−	11.8615i		−	0.385040i
$950$	5.85096	+	0.819299i	0.189830	+	0.0265816i
$951$	−1.18510	−	12.3286i	−0.0384294	−	0.399782i
$952$	6.58207	+	2.91864i	0.213326	+	0.0945937i
$953$			45.7026i			1.48045i	0.672358	+	0.740226i	$0.265281\pi$
$953$			45.7026i			1.48045i	−0.672358	+	0.740226i	$0.734719\pi$
$954$	17.9560	−	0.944261i	0.581346	−	0.0305716i
$955$	−18.0434			−0.583870
$956$	3.82244	+	1.09191i	0.123626	+	0.0353149i
$957$	−86.2214	+	8.28811i	−2.78714	+	0.267916i
$958$	25.8127	+	3.61451i	0.833971	+	0.116779i
$959$	−20.7305			−0.669422
$960$	−8.46282	+	9.28863i	−0.273136	+	0.299789i
$961$	−35.6139			−1.14883
$962$	−47.5477	−	6.65803i	−1.53300	−	0.214663i
$963$	−7.77096	−	40.0473i	−0.250416	−	1.29050i
$964$	20.5479	+	5.86968i	0.661805	+	0.189050i
$965$	−5.08412			−0.163664
$966$	−15.9399	−	0.690504i	−0.512857	−	0.0222166i
$967$			15.5526i			0.500137i	0.968228	+	0.250068i	$0.0804531\pi$
$967$			15.5526i			0.500137i	−0.968228	+	0.250068i	$0.919547\pi$
$968$	−46.1918	−	20.4825i	−1.48466	−	0.658332i
$969$	−3.09370	+	0.297384i	−0.0993839	+	0.00955337i
$970$	1.15727	+	0.162051i	0.0371578	+	0.00520315i
$971$		−	0.0487845i		−	0.00156557i	−1.00000		0.000782784i	$-0.999751\pi$
$971$		−	0.0487845i		−	0.00156557i	1.00000		0.000782784i	$-0.000249168\pi$
$972$	6.22170	+	30.5498i	0.199561	+	0.979885i
$973$		−	25.0935i		−	0.804460i
$974$	3.97842	−	28.4116i	0.127477	−	0.910366i
$975$	27.2955	−	2.62380i	0.874155	−	0.0840290i
$976$	0.366817	−	0.589665i	0.0117415	−	0.0188747i
$977$		−	6.20591i		−	0.198545i	−0.995060	−	0.0992724i	$-0.968348\pi$
$977$		−	6.20591i		−	0.198545i	0.995060	−	0.0992724i	$-0.0316515\pi$
$978$	0.471568	−	10.8859i	0.0150791	−	0.348092i
$979$	−23.3916			−0.747598
$980$	8.69773	+	2.48457i	0.277839	+	0.0793668i
$981$	2.19858	+	11.3303i	0.0701951	+	0.361747i
$982$	7.05653	−	50.3936i	0.225183	−	1.60812i
$983$	10.5409			0.336202			0.168101	−	0.985770i	$-0.446237\pi$
$983$	10.5409			0.336202			0.168101	+	0.985770i	$0.446237\pi$
$984$	33.0387	+	11.0052i	1.05323	+	0.350832i
$985$	−6.91891			−0.220455
$986$	−3.27564	+	23.3927i	−0.104318	+	0.744975i
$987$	−26.0852	+	2.50746i	−0.830301	+	0.0798134i
$988$	2.08181	−	7.28779i	0.0662313	−	0.231855i
$989$	36.9447			1.17477
$990$	1.08553	+	20.6423i	0.0345004	+	0.656056i
$991$			23.4333i			0.744383i	0.928156	+	0.372192i	$0.121394\pi$
$991$			23.4333i			0.744383i	−0.928156	+	0.372192i	$0.878606\pi$
$992$	29.5883	−	35.4425i	0.939431	−	1.12530i
$993$	3.97311	+	41.3323i	0.126083	+	1.31164i
$994$	1.87551	−	13.3938i	0.0594876	−	0.424826i
$995$			12.0385i			0.381647i
$996$	17.4872	+	3.22580i	0.554103	+	0.102213i
$997$			10.4100i			0.329687i	0.986320	+	0.164844i	$0.0527120\pi$
$997$			10.4100i			0.329687i	−0.986320	+	0.164844i	$0.947288\pi$
$998$	7.81336	+	1.09409i	0.247328	+	0.0346329i
$999$	44.6389	−	13.1991i	1.41231	−	0.417601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.j.d.419.22	yes	24
3.2	odd	2	inner	456.2.j.d.419.3	✓	24
4.3	odd	2		1824.2.j.e.1103.14		24
8.3	odd	2	inner	456.2.j.d.419.4	yes	24
8.5	even	2		1824.2.j.e.1103.13		24
12.11	even	2		1824.2.j.e.1103.15		24
24.5	odd	2		1824.2.j.e.1103.16		24
24.11	even	2	inner	456.2.j.d.419.21	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.j.d.419.3	✓	24	3.2	odd	2	inner
456.2.j.d.419.4	yes	24	8.3	odd	2	inner
456.2.j.d.419.21	yes	24	24.11	even	2	inner
456.2.j.d.419.22	yes	24	1.1	even	1	trivial
1824.2.j.e.1103.13		24	8.5	even	2
1824.2.j.e.1103.14		24	4.3	odd	2
1824.2.j.e.1103.15		24	12.11	even	2
1824.2.j.e.1103.16		24	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40055 + 0.196117i) q^{2} +(0.165731 + 1.72410i) q^{3} +(1.92308 + 0.549342i) q^{4} +0.906854 q^{5} +(-0.106011 + 2.44719i) q^{6} +1.41867i q^{7} +(2.58563 + 1.14653i) q^{8} +(-2.94507 + 0.571475i) q^{9} +O(q^{10})\)	\(q+(1.40055 + 0.196117i) q^{2} +(0.165731 + 1.72410i) q^{3} +(1.92308 + 0.549342i) q^{4} +0.906854 q^{5} +(-0.106011 + 2.44719i) q^{6} +1.41867i q^{7} +(2.58563 + 1.14653i) q^{8} +(-2.94507 + 0.571475i) q^{9} +(1.27009 + 0.177849i) q^{10} -5.37260i q^{11} +(-0.628409 + 3.40663i) q^{12} +3.78965i q^{13} +(-0.278225 + 1.98692i) q^{14} +(0.150294 + 1.56351i) q^{15} +(3.39645 + 2.11285i) q^{16} -1.79438i q^{17} +(-4.23679 + 0.222802i) q^{18} -1.00000 q^{19} +(1.74395 + 0.498173i) q^{20} +(-2.44594 + 0.235118i) q^{21} +(1.05366 - 7.52459i) q^{22} +4.59129 q^{23} +(-1.54821 + 4.64791i) q^{24} -4.17762 q^{25} +(-0.743213 + 5.30759i) q^{26} +(-1.47337 - 4.98289i) q^{27} +(-0.779335 + 2.72821i) q^{28} -9.30823 q^{29} +(-0.0961364 + 2.21925i) q^{30} -8.16173i q^{31} +(4.34253 + 3.62525i) q^{32} +(9.26292 - 0.890406i) q^{33} +(0.351908 - 2.51312i) q^{34} +1.28653i q^{35} +(-5.97752 - 0.518858i) q^{36} +8.95844i q^{37} +(-1.40055 - 0.196117i) q^{38} +(-6.53375 + 0.628063i) q^{39} +(2.34479 + 1.03973i) q^{40} -7.10829i q^{41} +(-3.47177 - 0.150394i) q^{42} +8.04671 q^{43} +(2.95139 - 10.3319i) q^{44} +(-2.67075 + 0.518244i) q^{45} +(6.43032 + 0.900427i) q^{46} +10.6647 q^{47} +(-3.07988 + 6.20599i) q^{48} +4.98737 q^{49} +(-5.85096 - 0.819299i) q^{50} +(3.09370 - 0.297384i) q^{51} +(-2.08181 + 7.28779i) q^{52} -4.23811 q^{53} +(-1.08630 - 7.26773i) q^{54} -4.87216i q^{55} +(-1.62655 + 3.66816i) q^{56} +(-0.165731 - 1.72410i) q^{57} +(-13.0366 - 1.82550i) q^{58} -3.03104i q^{59} +(-0.569875 + 3.08931i) q^{60} -0.173612i q^{61} +(1.60065 - 11.4309i) q^{62} +(-0.810735 - 4.17808i) q^{63} +(5.37095 + 5.92899i) q^{64} +3.43666i q^{65} +(13.1478 + 0.569553i) q^{66} -13.1496 q^{67} +(0.985728 - 3.45073i) q^{68} +(0.760918 + 7.91585i) q^{69} +(-0.252309 + 1.80185i) q^{70} -6.74099 q^{71} +(-8.27006 - 1.89898i) q^{72} -3.12997 q^{73} +(-1.75690 + 12.5467i) q^{74} +(-0.692360 - 7.20264i) q^{75} +(-1.92308 - 0.549342i) q^{76} +7.62195 q^{77} +(-9.27401 - 0.401744i) q^{78} -2.42669i q^{79} +(3.08008 + 1.91605i) q^{80} +(8.34683 - 3.36606i) q^{81} +(1.39405 - 9.95552i) q^{82} -5.13329i q^{83} +(-4.83288 - 0.891505i) q^{84} -1.62724i q^{85} +(11.2698 + 1.57809i) q^{86} +(-1.54266 - 16.0484i) q^{87} +(6.15983 - 13.8915i) q^{88} -4.35387i q^{89} +(-3.84215 + 0.202049i) q^{90} -5.37627 q^{91} +(8.82939 + 2.52218i) q^{92} +(14.0717 - 1.35265i) q^{93} +(14.9364 + 2.09153i) q^{94} -0.906854 q^{95} +(-5.53062 + 8.08778i) q^{96} +0.911172 q^{97} +(6.98506 + 0.978106i) q^{98} +(3.07030 + 15.8227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} + 2 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 + 2 * q^4 - 10 * q^6 - 6 * q^9	\( 24 q + 2 q^{3} + 2 q^{4} - 10 q^{6} - 6 q^{9} + 8 q^{10} - 16 q^{12} + 18 q^{16} + 18 q^{18} - 24 q^{19} + 44 q^{22} - 22 q^{24} - 8 q^{25} - 16 q^{27} + 44 q^{28} + 2 q^{30} + 24 q^{33} - 16 q^{34} + 22 q^{36} + 64 q^{40} + 8 q^{42} - 40 q^{43} - 20 q^{46} - 8 q^{48} - 12 q^{49} - 18 q^{51} - 48 q^{52} + 4 q^{54} - 2 q^{57} - 40 q^{58} + 48 q^{60} + 26 q^{64} + 22 q^{66} - 92 q^{67} + 56 q^{70} - 8 q^{72} + 44 q^{73} - 34 q^{75} - 2 q^{76} - 42 q^{78} + 2 q^{81} - 100 q^{82} + 32 q^{84} + 16 q^{88} + 24 q^{90} + 44 q^{91} + 16 q^{94} + 2 q^{96} - 96 q^{97} - 56 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 + 2 * q^4 - 10 * q^6 - 6 * q^9 + 8 * q^10 - 16 * q^12 + 18 * q^16 + 18 * q^18 - 24 * q^19 + 44 * q^22 - 22 * q^24 - 8 * q^25 - 16 * q^27 + 44 * q^28 + 2 * q^30 + 24 * q^33 - 16 * q^34 + 22 * q^36 + 64 * q^40 + 8 * q^42 - 40 * q^43 - 20 * q^46 - 8 * q^48 - 12 * q^49 - 18 * q^51 - 48 * q^52 + 4 * q^54 - 2 * q^57 - 40 * q^58 + 48 * q^60 + 26 * q^64 + 22 * q^66 - 92 * q^67 + 56 * q^70 - 8 * q^72 + 44 * q^73 - 34 * q^75 - 2 * q^76 - 42 * q^78 + 2 * q^81 - 100 * q^82 + 32 * q^84 + 16 * q^88 + 24 * q^90 + 44 * q^91 + 16 * q^94 + 2 * q^96 - 96 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

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Database

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