LMFDB - Embedded newform 900.2.r.c.851.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(551,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("900.551");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			851.4
Root			$1.41203 - 0.0786378i$ of defining polynomial
Character	$\chi$	$=$	900.851
Dual form			900.2.r.c.551.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41203 - 0.0786378i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(1.98763 - 0.222077i) q^{4} +(-0.774115 + 2.32395i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +O(q^{10})$	\(q+(1.41203 - 0.0786378i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(1.98763 - 0.222077i) q^{4} +(-0.774115 + 2.32395i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +(1.71352 + 2.96790i) q^{11} +(-0.910320 + 3.34235i) q^{12} +(1.68614 - 2.92048i) q^{13} +(3.21352 - 2.10187i) q^{14} +(3.90136 - 0.882816i) q^{16} +2.52434i q^{17} +(-3.24844 - 2.72903i) q^{18} -2.20979i q^{19} +(0.686141 + 4.65253i) q^{21} +(2.65292 + 4.05600i) q^{22} +(-1.07561 + 1.86301i) q^{23} +(-1.02256 + 4.79107i) q^{24} +(2.15121 - 4.25639i) q^{26} +(4.70285 - 2.20979i) q^{27} +(4.37228 - 3.22060i) q^{28} +(-0.686141 + 0.396143i) q^{29} +(1.47603 + 0.852189i) q^{31} +(5.43940 - 1.55335i) q^{32} +(-5.87228 + 0.866025i) q^{33} +(0.198508 + 3.56443i) q^{34} +(-4.80149 - 3.59801i) q^{36} -4.74456 q^{37} +(-0.173773 - 3.12027i) q^{38} +(3.62725 + 4.57820i) q^{39} +(0.127719 + 0.0737384i) q^{41} +(1.33471 + 6.51554i) q^{42} +(-6.01594 + 3.47331i) q^{43} +(4.06494 + 5.51856i) q^{44} +(-1.37228 + 2.71519i) q^{46} +(5.77846 + 10.0086i) q^{47} +(-1.06712 + 6.84553i) q^{48} +(0.186141 - 0.322405i) q^{49} +(-4.06494 - 1.61030i) q^{51} +(2.70285 - 6.17930i) q^{52} -8.51278i q^{53} +(6.46678 - 3.49010i) q^{54} +(5.92051 - 4.89140i) q^{56} +(3.55842 + 1.40965i) q^{57} +(-0.937696 + 0.613321i) q^{58} +(-2.58891 + 4.48412i) q^{59} +(-1.68614 - 2.92048i) q^{61} +(2.15121 + 1.08724i) q^{62} +(-7.92967 - 1.86301i) q^{63} +(7.55842 - 2.62112i) q^{64} +(-8.22371 + 1.68463i) q^{66} +(-6.01594 - 3.47331i) q^{67} +(0.560598 + 5.01746i) q^{68} +(-2.31386 - 2.92048i) q^{69} +1.75079 q^{71} +(-7.06277 - 4.70290i) q^{72} +2.37228 q^{73} +(-6.69944 + 0.373102i) q^{74} +(-0.490743 - 4.39224i) q^{76} +(8.05842 + 4.65253i) q^{77} +(5.48179 + 6.17930i) q^{78} +(-8.80507 + 5.08361i) q^{79} +(0.558422 + 8.98266i) q^{81} +(0.186141 + 0.0940770i) q^{82} +(-3.62725 - 6.28258i) q^{83} +(2.39702 + 9.09515i) q^{84} +(-8.22153 + 5.37748i) q^{86} +(-0.200214 - 1.35760i) q^{87} +(6.17377 + 7.47269i) q^{88} -5.34363i q^{89} -9.15640i q^{91} +(-1.72418 + 3.94184i) q^{92} +(-2.31386 + 1.83324i) q^{93} +(8.94639 + 13.6780i) q^{94} +(-0.968484 + 9.74998i) q^{96} +(-6.24456 - 10.8159i) q^{97} +(0.237482 - 0.469882i) q^{98} +(2.35143 - 10.0086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{4} - 3 q^{6} - 6 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - q^4 - 3 * q^6 - 6 * q^9	$ 8 q + 3 q^{2} - q^{4} - 3 q^{6} - 6 q^{9} - 6 q^{12} + 2 q^{13} + 12 q^{14} - q^{16} - 18 q^{18} - 6 q^{21} - 3 q^{22} + 3 q^{24} + 12 q^{28} + 6 q^{29} + 33 q^{32} - 24 q^{33} + 7 q^{34} - 33 q^{36} + 8 q^{37} + 27 q^{38} + 24 q^{41} + 18 q^{42} + 12 q^{46} - 21 q^{48} - 10 q^{49} - 16 q^{52} + 39 q^{54} + 18 q^{56} - 6 q^{57} - 4 q^{58} - 2 q^{61} + 26 q^{64} - 24 q^{66} + 15 q^{68} - 30 q^{69} + 21 q^{72} - 4 q^{73} - 30 q^{74} - 3 q^{76} + 30 q^{77} + 12 q^{78} - 30 q^{81} - 10 q^{82} + 30 q^{84} + 21 q^{86} + 21 q^{88} - 24 q^{92} - 30 q^{93} - 18 q^{94} + 12 q^{96} - 4 q^{97}+O(q^{100}) $ 8 * q + 3 * q^2 - q^4 - 3 * q^6 - 6 * q^9 - 6 * q^12 + 2 * q^13 + 12 * q^14 - q^16 - 18 * q^18 - 6 * q^21 - 3 * q^22 + 3 * q^24 + 12 * q^28 + 6 * q^29 + 33 * q^32 - 24 * q^33 + 7 * q^34 - 33 * q^36 + 8 * q^37 + 27 * q^38 + 24 * q^41 + 18 * q^42 + 12 * q^46 - 21 * q^48 - 10 * q^49 - 16 * q^52 + 39 * q^54 + 18 * q^56 - 6 * q^57 - 4 * q^58 - 2 * q^61 + 26 * q^64 - 24 * q^66 + 15 * q^68 - 30 * q^69 + 21 * q^72 - 4 * q^73 - 30 * q^74 - 3 * q^76 + 30 * q^77 + 12 * q^78 - 30 * q^81 - 10 * q^82 + 30 * q^84 + 21 * q^86 + 21 * q^88 - 24 * q^92 - 30 * q^93 - 18 * q^94 + 12 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	1.41203	−	0.0786378i	0.998453	−	0.0556054i
$2$	1.41203	−	0.0786378i	0.998453	−	0.0556054i
$3$	−0.637910	+	1.61030i	−0.368298	+	0.929708i
$3$	−0.637910	+	1.61030i	−0.368298	+	0.929708i
$4$	1.98763	−	0.222077i	0.993816	−	0.111039i
$5$		0			0
$5$		0			0
$6$	−0.774115	+	2.32395i	−0.316031	+	0.948749i
$7$	2.35143	−	1.35760i	0.888756	−	0.513124i	0.0152206	−	0.999884i	$-0.495155\pi$
$7$	2.35143	−	1.35760i	0.888756	−	0.513124i	0.873535	+	0.486761i	$0.161822\pi$
$8$	2.78912	−	0.469882i	0.986104	−	0.166128i
$9$	−2.18614	−	2.05446i	−0.728714	−	0.684819i
$10$		0			0
$11$	1.71352	+	2.96790i	0.516645	+	0.894855i	0.999813	+	0.0193276i	$0.00615256\pi$
$11$	1.71352	+	2.96790i	0.516645	+	0.894855i	−0.483168	+	0.875527i	$0.660514\pi$
$12$	−0.910320	+	3.34235i	−0.262787	+	0.964854i
$13$	1.68614	−	2.92048i	0.467651	−	0.809996i	−0.531666	−	0.846954i	$-0.678434\pi$
$13$	1.68614	−	2.92048i	0.467651	−	0.809996i	0.999317	+	0.0369586i	$0.0117670\pi$
$14$	3.21352	−	2.10187i	0.858849	−	0.561749i
$15$		0			0
$16$	3.90136	−	0.882816i	0.975341	−	0.220704i
$17$			2.52434i			0.612242i	0.951993	+	0.306121i	$0.0990312\pi$
$17$			2.52434i			0.612242i	−0.951993	+	0.306121i	$0.900969\pi$
$18$	−3.24844	−	2.72903i	−0.765666	−	0.643239i
$19$		−	2.20979i		−	0.506960i	−0.967341	−	0.253480i	$-0.918425\pi$
$19$		−	2.20979i		−	0.506960i	0.967341	−	0.253480i	$-0.0815752\pi$
$20$		0			0
$21$	0.686141	+	4.65253i	0.149728	+	1.01527i
$22$	2.65292	+	4.05600i	0.565604	+	0.864742i
$23$	−1.07561	+	1.86301i	−0.224279	+	0.388463i	−0.956103	−	0.293031i	$-0.905336\pi$
$23$	−1.07561	+	1.86301i	−0.224279	+	0.388463i	0.731824	+	0.681494i	$0.238670\pi$
$24$	−1.02256	+	4.79107i	−0.208729	+	0.977973i
$25$		0			0
$26$	2.15121	−	4.25639i	0.421888	−	0.834746i
$27$	4.70285	−	2.20979i	0.905065	−	0.425274i
$28$	4.37228	−	3.22060i	0.826284	−	0.608637i
$29$	−0.686141	+	0.396143i	−0.127413	+	0.0735620i	−0.562352	−	0.826898i	$-0.690103\pi$
$29$	−0.686141	+	0.396143i	−0.127413	+	0.0735620i	0.434939	+	0.900460i	$0.356770\pi$
$30$		0			0
$31$	1.47603	+	0.852189i	0.265104	+	0.153058i	0.626660	−	0.779292i	$-0.284421\pi$
$31$	1.47603	+	0.852189i	0.265104	+	0.153058i	−0.361557	+	0.932350i	$0.617755\pi$
$32$	5.43940	−	1.55335i	0.961559	−	0.274597i
$33$	−5.87228	+	0.866025i	−1.02223	+	0.150756i
$34$	0.198508	+	3.56443i	0.0340439	+	0.611295i
$35$		0			0
$36$	−4.80149	−	3.59801i	−0.800249	−	0.599668i
$37$	−4.74456			−0.780001			−0.390001	−	0.920815i	$-0.627525\pi$
$37$	−4.74456			−0.780001			−0.390001	+	0.920815i	$0.627525\pi$
$38$	−0.173773	−	3.12027i	−0.0281897	−	0.506175i
$39$	3.62725	+	4.57820i	0.580825	+	0.733099i
$40$		0			0
$41$	0.127719	+	0.0737384i	0.0199463	+	0.0115160i	0.509940	−	0.860210i	$-0.329668\pi$
$41$	0.127719	+	0.0737384i	0.0199463	+	0.0115160i	−0.489994	+	0.871726i	$0.663001\pi$
$42$	1.33471	+	6.51554i	0.205951	+	1.00537i
$43$	−6.01594	+	3.47331i	−0.917423	+	0.529674i	−0.882812	−	0.469727i	$-0.844353\pi$
$43$	−6.01594	+	3.47331i	−0.917423	+	0.529674i	−0.0346108	+	0.999401i	$0.511019\pi$
$44$	4.06494	+	5.51856i	0.612813	+	0.831954i
$45$		0			0
$46$	−1.37228	+	2.71519i	−0.202332	+	0.400334i
$47$	5.77846	+	10.0086i	0.842875	+	1.45990i	0.887454	+	0.460897i	$0.152472\pi$
$47$	5.77846	+	10.0086i	0.842875	+	1.45990i	−0.0445785	+	0.999006i	$0.514194\pi$
$48$	−1.06712	+	6.84553i	−0.154026	+	0.988067i
$49$	0.186141	−	0.322405i	0.0265915	−	0.0460579i
$50$		0			0
$51$	−4.06494	−	1.61030i	−0.569206	−	0.225487i
$52$	2.70285	−	6.17930i	0.374819	−	0.856914i
$53$		−	8.51278i		−	1.16932i	−0.811278	−	0.584660i	$-0.801228\pi$
$53$		−	8.51278i		−	1.16932i	0.811278	−	0.584660i	$-0.198772\pi$
$54$	6.46678	−	3.49010i	0.880017	−	0.474942i
$55$		0			0
$56$	5.92051	−	4.89140i	0.791162	−	0.653641i
$57$	3.55842	+	1.40965i	0.471325	+	0.186712i
$58$	−0.937696	+	0.613321i	−0.123126	+	0.0805330i
$59$	−2.58891	+	4.48412i	−0.337047	+	0.583783i	−0.983876	−	0.178852i	$-0.942762\pi$
$59$	−2.58891	+	4.48412i	−0.337047	+	0.583783i	0.646829	+	0.762635i	$0.276095\pi$
$60$		0			0
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	0.737659	−	0.675174i	$-0.235931\pi$
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	−0.953547	+	0.301244i	$0.902598\pi$
$62$	2.15121	+	1.08724i	0.273204	+	0.138080i
$63$	−7.92967	−	1.86301i	−0.999045	−	0.234717i
$64$	7.55842	−	2.62112i	0.944803	−	0.327640i
$65$		0			0
$66$	−8.22371	+	1.68463i	−1.01227	+	0.207364i
$67$	−6.01594	−	3.47331i	−0.734964	−	0.424332i	0.0852711	−	0.996358i	$-0.472824\pi$
$67$	−6.01594	−	3.47331i	−0.734964	−	0.424332i	−0.820236	+	0.572026i	$0.806158\pi$
$68$	0.560598	+	5.01746i	0.0679825	+	0.608456i
$69$	−2.31386	−	2.92048i	−0.278556	−	0.351585i
$70$		0			0
$71$	1.75079			0.207780			0.103890	−	0.994589i	$-0.466871\pi$
$71$	1.75079			0.207780			0.103890	+	0.994589i	$0.466871\pi$
$72$	−7.06277	−	4.70290i	−0.832355	−	0.554243i
$73$	2.37228			0.277655			0.138827	−	0.990317i	$-0.455667\pi$
$73$	2.37228			0.277655			0.138827	+	0.990317i	$0.455667\pi$
$74$	−6.69944	+	0.373102i	−0.778794	+	0.0433722i
$75$		0			0
$76$	−0.490743	−	4.39224i	−0.0562921	−	0.503825i
$77$	8.05842	+	4.65253i	0.918342	+	0.530205i
$78$	5.48179	+	6.17930i	0.620690	+	0.699668i
$79$	−8.80507	+	5.08361i	−0.990647	+	0.571951i	−0.905468	−	0.424415i	$-0.860480\pi$
$79$	−8.80507	+	5.08361i	−0.990647	+	0.571951i	−0.0851797	+	0.996366i	$0.527146\pi$
$80$		0			0
$81$	0.558422	+	8.98266i	0.0620469	+	0.998073i
$82$	0.186141	+	0.0940770i	0.0205558	+	0.0103891i
$83$	−3.62725	−	6.28258i	−0.398142	−	0.689603i	0.595355	−	0.803463i	$-0.297012\pi$
$83$	−3.62725	−	6.28258i	−0.398142	−	0.689603i	−0.993497	+	0.113861i	$0.963678\pi$
$84$	2.39702	+	9.09515i	0.261536	+	0.992362i
$85$		0			0
$86$	−8.22153	+	5.37748i	−0.886551	+	0.579868i
$87$	−0.200214	−	1.35760i	−0.0214652	−	0.145550i
$88$	6.17377	+	7.47269i	0.658126	+	0.796591i
$89$		−	5.34363i		−	0.566424i	−0.959057	−	0.283212i	$-0.908600\pi$
$89$		−	5.34363i		−	0.566424i	0.959057	−	0.283212i	$-0.0913999\pi$
$90$		0			0
$91$		−	9.15640i		−	0.959852i
$92$	−1.72418	+	3.94184i	−0.179758	+	0.410965i
$93$	−2.31386	+	1.83324i	−0.239936	+	0.190098i
$94$	8.94639	+	13.6780i	0.922750	+	1.41078i
$95$		0			0
$96$	−0.968484	+	9.74998i	−0.0988455	+	0.995103i
$97$	−6.24456	−	10.8159i	−0.634039	−	1.09819i	−0.986718	−	0.162444i	$-0.948062\pi$
$97$	−6.24456	−	10.8159i	−0.634039	−	1.09819i	0.352679	−	0.935745i	$-0.385271\pi$
$98$	0.237482	−	0.469882i	0.0239893	−	0.0474652i
$99$	2.35143	−	10.0086i	0.236327	−	1.00590i
$100$		0			0
$101$	15.4307	−	8.90892i	1.53541	−	0.886471i	0.536314	−	0.844019i	$-0.319816\pi$
$101$	15.4307	−	8.90892i	1.53541	−	0.886471i	0.999099	−	0.0424521i	$-0.0135170\pi$
$102$	−5.86644	−	1.95413i	−0.580864	−	0.193488i
$103$	12.6325	+	7.29339i	1.24472	+	0.718640i	0.970051	−	0.242899i	$-0.0780985\pi$
$103$	12.6325	+	7.29339i	1.24472	+	0.718640i	0.274669	+	0.961539i	$0.411432\pi$
$104$	3.33057	−	8.93787i	0.326590	−	0.876430i
$105$		0			0
$106$	−0.669426	−	12.0203i	−0.0650204	−	1.16751i
$107$	−13.2332			−1.27930			−0.639650	−	0.768667i	$-0.720920\pi$
$107$	−13.2332			−1.27930			−0.639650	+	0.768667i	$0.720920\pi$
$108$	8.85680	−	5.43664i	0.852246	−	0.523141i
$109$	−9.48913			−0.908893			−0.454447	−	0.890774i	$-0.650163\pi$
$109$	−9.48913			−0.908893			−0.454447	+	0.890774i	$0.650163\pi$
$110$		0			0
$111$	3.02661	−	7.64018i	0.287273	−	0.725173i
$112$	7.97526	−	7.37236i	0.753592	−	0.696622i
$113$	−13.8030	−	7.96916i	−1.29848	−	0.749675i	−0.318335	−	0.947978i	$-0.603124\pi$
$113$	−13.8030	−	7.96916i	−1.29848	−	0.749675i	−0.980141	+	0.198303i	$0.936457\pi$
$114$	5.13543	+	1.71063i	0.480977	+	0.160215i
$115$		0			0
$116$	−1.27582	+	0.939764i	−0.118457	+	0.0872549i
$117$	−9.68614	+	2.92048i	−0.895484	+	0.269999i
$118$	−3.30298	+	6.53528i	−0.304064	+	0.601621i
$119$	3.42703	+	5.93580i	0.314156	+	0.544134i
$120$		0			0
$121$	−0.372281	+	0.644810i	−0.0338438	+	0.0586191i
$122$	−2.61053	−	3.99120i	−0.236347	−	0.361346i
$123$	−0.200214	+	0.158627i	−0.0180527	+	0.0143029i
$124$	3.12307	+	1.36604i	0.280460	+	0.122674i
$125$		0			0
$126$	−11.3434	−	2.00704i	−1.01055	−	0.178801i
$127$		−	16.2912i		−	1.44561i	−0.691053	−	0.722804i	$-0.742853\pi$
$127$		−	16.2912i		−	1.44561i	0.691053	−	0.722804i	$-0.257147\pi$
$128$	10.4666	−	4.29546i	0.925122	−	0.379669i
$129$	−1.75544	−	11.9031i	−0.154558	−	1.04801i
$130$		0			0
$131$	−3.62725	+	6.28258i	−0.316914	+	0.548911i	−0.979843	−	0.199771i	$-0.935980\pi$
$131$	−3.62725	+	6.28258i	−0.316914	+	0.548911i	0.662928	+	0.748683i	$0.269313\pi$
$132$	−11.4796	+	3.02544i	−0.999172	+	0.263331i
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	−8.76780	−	4.43132i	−0.757423	−	0.382807i
$135$		0			0
$136$	1.18614	+	7.04069i	0.101711	+	0.603734i
$137$	16.2446	−	9.37880i	1.38787	−	0.801285i	0.394792	−	0.918771i	$-0.370817\pi$
$137$	16.2446	−	9.37880i	1.38787	−	0.801285i	0.993075	+	0.117485i	$0.0374833\pi$
$138$	−3.49689	−	3.94184i	−0.297675	−	0.335551i
$139$	−8.09262	−	4.67228i	−0.686407	−	0.396297i	0.115858	−	0.993266i	$-0.463038\pi$
$139$	−8.09262	−	4.67228i	−0.686407	−	0.396297i	−0.802265	+	0.596968i	$0.796372\pi$
$140$		0			0
$141$	−19.8030	+	2.92048i	−1.66771	+	0.245949i
$142$	2.47215	−	0.137678i	0.207458	−	0.0115537i
$143$	11.5569			0.966438
$144$	−10.3426	−	6.08522i	−0.861886	−	0.507102i
$145$		0			0
$146$	3.34972	−	0.186551i	0.277225	−	0.0154391i
$147$	0.400428	+	0.505408i	0.0330268	+	0.0416854i
$148$	−9.43045	+	1.05366i	−0.775178	+	0.0866103i
$149$	−8.31386	−	4.80001i	−0.681098	−	0.393232i	0.119171	−	0.992874i	$-0.461976\pi$
$149$	−8.31386	−	4.80001i	−0.681098	−	0.393232i	−0.800269	+	0.599642i	$0.795310\pi$
$150$		0			0
$151$	7.92967	−	4.57820i	0.645308	−	0.372569i	−0.141348	−	0.989960i	$-0.545144\pi$
$151$	7.92967	−	4.57820i	0.645308	−	0.372569i	0.786656	+	0.617391i	$0.211810\pi$
$152$	−1.03834	−	6.16337i	−0.0842204	−	0.499915i
$153$	5.18614	−	5.51856i	0.419275	−	0.446149i
$154$	11.7446	+	5.93580i	0.946404	+	0.478320i
$155$		0			0
$156$	8.22635	+	8.29425i	0.658635	+	0.664071i
$157$	−8.43070	+	14.6024i	−0.672843	+	1.16540i	0.304251	+	0.952592i	$0.401594\pi$
$157$	−8.43070	+	14.6024i	−0.672843	+	1.16540i	−0.977094	+	0.212807i	$0.931739\pi$
$158$	−12.0332	+	7.87060i	−0.957311	+	0.626151i
$159$	13.7081	+	5.43039i	1.08713	+	0.430658i
$160$		0			0
$161$			5.84096i			0.460332i
$162$	1.49488	+	12.6398i	0.117449	+	0.993079i
$163$		−	11.8716i		−	0.929855i	−0.885349	−	0.464928i	$-0.846080\pi$
$163$		−	11.8716i		−	0.929855i	0.885349	−	0.464928i	$-0.153920\pi$
$164$	0.270233	+	0.118201i	0.0211017	+	0.00922998i
$165$		0			0
$166$	−5.61582	−	8.58592i	−0.435872	−	0.666397i
$167$	−9.60592	+	16.6379i	−0.743329	+	1.28748i	0.207643	+	0.978205i	$0.433421\pi$
$167$	−9.60592	+	16.6379i	−0.743329	+	1.28748i	−0.950972	+	0.309278i	$0.899913\pi$
$168$	4.09987	+	12.6541i	0.316312	+	0.976284i
$169$	0.813859	+	1.40965i	0.0626046	+	0.108434i
$170$		0			0
$171$	−4.53991	+	4.83090i	−0.347175	+	0.369428i
$172$	−11.1861	+	8.23966i	−0.852935	+	0.628268i
$173$	4.80298	−	2.77300i	0.365164	−	0.210828i	−0.306180	−	0.951974i	$-0.599051\pi$
$173$	4.80298	−	2.77300i	0.365164	−	0.210828i	0.671344	+	0.741146i	$0.265717\pi$
$174$	−0.389466	−	1.90122i	−0.0295253	−	0.144131i
$175$		0			0
$176$	9.30516	+	10.0661i	0.701403	+	0.758763i
$177$	−5.56930	−	7.02939i	−0.418614	−	0.528362i
$178$	−0.420211	−	7.54534i	−0.0314962	−	0.565547i
$179$	−18.8114			−1.40603			−0.703016	−	0.711174i	$-0.748164\pi$
$179$	−18.8114			−1.40603			−0.703016	+	0.711174i	$0.748164\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	−0.720040	−	12.9291i	−0.0533729	−	0.958366i
$183$	5.77846	−	0.852189i	0.427156	−	0.0629956i
$184$	−2.12461	+	5.70156i	−0.156628	+	0.420325i
$185$		0			0
$186$	−3.12307	+	2.77054i	−0.228994	+	0.203146i
$187$	−7.49198	+	4.32550i	−0.547868	+	0.316312i
$188$	13.7081	+	18.6101i	0.999769	+	1.35728i
$189$	8.05842	−	11.5807i	0.586164	−	0.842375i
$190$		0			0
$191$	−1.95100	−	3.37923i	−0.141169	−	0.244512i	0.786768	−	0.617249i	$-0.211753\pi$
$191$	−1.95100	−	3.37923i	−0.141169	−	0.244512i	−0.927937	+	0.372736i	$0.878420\pi$
$192$	−0.600807	+	13.8434i	−0.0433595	+	0.999060i
$193$	−1.87228	+	3.24289i	−0.134770	+	0.233428i	−0.925509	−	0.378724i	$-0.876363\pi$
$193$	−1.87228	+	3.24289i	−0.134770	+	0.233428i	0.790740	+	0.612153i	$0.209696\pi$
$194$	−9.66802	−	14.7813i	−0.694123	−	1.06123i
$195$		0			0
$196$	0.298380	−	0.682160i	0.0213129	−	0.0487257i
$197$		−	10.6873i		−	0.761436i	−0.924691	−	0.380718i	$-0.875677\pi$
$197$		−	10.6873i		−	0.761436i	0.924691	−	0.380718i	$-0.124323\pi$
$198$	2.53322	−	14.3173i	0.180028	−	1.01749i
$199$		−	19.3236i		−	1.36981i	−0.728630	−	0.684907i	$-0.759843\pi$
$199$		−	19.3236i		−	1.36981i	0.728630	−	0.684907i	$-0.240157\pi$
$200$		0			0
$201$	9.43070	−	7.47182i	0.665191	−	0.527022i
$202$	21.0880	−	13.7931i	1.48374	−	0.970476i
$203$	−1.07561	+	1.86301i	−0.0754928	+	0.130757i
$204$	−8.43723	−	2.29795i	−0.590724	−	0.160889i
$205$		0			0
$206$	18.4110	+	9.30506i	1.28275	+	0.648315i
$207$	6.17889	−	1.86301i	0.429463	−	0.129488i
$208$	4.00000	−	12.8824i	0.277350	−	0.893234i
$209$	6.55842	−	3.78651i	0.453656	−	0.261918i
$210$		0			0
$211$	5.30350	+	3.06198i	0.365108	+	0.210795i	0.671319	−	0.741169i	$-0.265728\pi$
$211$	5.30350	+	3.06198i	0.365108	+	0.210795i	−0.306211	+	0.951964i	$0.599061\pi$
$212$	−1.89049	−	16.9203i	−0.129840	−	1.16209i
$213$	−1.11684	+	2.81929i	−0.0765249	+	0.193175i
$214$	−18.6856	+	1.04063i	−1.27732	+	0.0711359i
$215$		0			0
$216$	12.0785	−	8.37315i	0.821838	−	0.569721i
$217$	4.62772			0.314150
$218$	−13.3989	+	0.746204i	−0.907487	+	0.0505393i
$219$	−1.51330	+	3.82009i	−0.102260	+	0.258138i
$220$		0			0
$221$	7.37228	+	4.25639i	0.495913	+	0.286316i
$222$	3.67284	−	11.0261i	0.246505	−	0.740025i
$223$	−1.47603	+	0.852189i	−0.0988426	+	0.0570668i	−0.548606	−	0.836081i	$-0.684841\pi$
$223$	−1.47603	+	0.852189i	−0.0988426	+	0.0570668i	0.449764	+	0.893147i	$0.351508\pi$
$224$	10.6815	−	11.0371i	0.713690	−	0.737448i
$225$		0			0
$226$	−20.1168	−	10.1672i	−1.33815	−	0.676313i
$227$	9.44298	+	16.3557i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489496\pi$
$227$	9.44298	+	16.3557i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$228$	7.38588	+	2.01161i	0.489142	+	0.133222i
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	−0.978290	−	0.207241i	$-0.933552\pi$
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	0.668621	+	0.743603i	$0.266885\pi$
$230$		0			0
$231$	−12.6325	+	10.0086i	−0.831159	+	0.658517i
$232$	−1.72759	+	1.42730i	−0.113422	+	0.0937067i
$233$			28.0627i			1.83845i	0.393737	+	0.919223i	$0.371182\pi$
$233$			28.0627i			1.83845i	−0.393737	+	0.919223i	$0.628818\pi$
$234$	−13.4474	+	4.88549i	−0.879085	+	0.319375i
$235$		0			0
$236$	−4.14998	+	9.48772i	−0.270141	+	0.617598i
$237$	−2.56930	−	17.4217i	−0.166894	−	1.13166i
$238$	5.30584	+	8.11200i	0.343926	+	0.525823i
$239$	−8.33010	+	14.4282i	−0.538830	+	0.933280i	0.460138	+	0.887847i	$0.347800\pi$
$239$	−8.33010	+	14.4282i	−0.538830	+	0.933280i	−0.998967	+	0.0454327i	$0.985533\pi$
$240$		0			0
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	−0.999342	−	0.0362667i	$-0.988453\pi$
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	0.468263	−	0.883589i	$-0.344880\pi$
$242$	−0.474964	+	0.939764i	−0.0305319	+	0.0604103i
$243$	−14.8210	−	4.83090i	−0.950768	−	0.309903i
$244$	−4.00000	−	5.43039i	−0.256074	−	0.347645i
$245$		0			0
$246$	−0.270233	+	0.239730i	−0.0172295	+	0.0152846i
$247$	−6.45364	−	3.72601i	−0.410635	−	0.237080i
$248$	4.51727	+	1.68330i	0.286847	+	0.106890i
$249$	12.4307	−	1.83324i	0.787764	−	0.116177i
$250$		0			0
$251$	16.7347			1.05629			0.528144	−	0.849155i	$-0.322888\pi$
$251$	16.7347			1.05629			0.528144	+	0.849155i	$0.322888\pi$
$252$	−16.1750	−	1.94197i	−1.01893	−	0.122333i
$253$	−7.37228			−0.463491
$254$	−1.28110	−	23.0035i	−0.0803835	−	1.44337i
$255$		0			0
$256$	14.4413	−	6.88837i	0.902580	−	0.430523i
$257$	9.98913	+	5.76722i	0.623105	+	0.359750i	0.778077	−	0.628169i	$-0.216195\pi$
$257$	9.98913	+	5.76722i	0.623105	+	0.359750i	−0.154972	+	0.987919i	$0.549529\pi$
$258$	−3.41476	−	16.6695i	−0.212594	−	1.03780i
$259$	−11.1565	+	6.44121i	−0.693231	+	0.400237i
$260$		0			0
$261$	2.31386	+	0.543620i	0.143224	+	0.0336493i
$262$	−4.62772	+	9.15640i	−0.285901	+	0.565684i
$263$	−6.25343	−	10.8313i	−0.385603	−	0.667884i	0.606250	−	0.795274i	$-0.292673\pi$
$263$	−6.25343	−	10.8313i	−0.385603	−	0.667884i	−0.991853	+	0.127391i	$0.959340\pi$
$264$	−15.9716	+	5.17473i	−0.982983	+	0.318483i
$265$		0			0
$266$	−4.64469	−	7.10119i	−0.284784	−	0.435402i
$267$	8.60485	+	3.40876i	0.526608	+	0.208613i
$268$	−12.7288	−	5.56765i	−0.777537	−	0.340098i
$269$			24.9484i			1.52113i	0.649260	+	0.760566i	$0.275079\pi$
$269$			24.9484i			1.52113i	−0.649260	+	0.760566i	$0.724921\pi$
$270$		0			0
$271$		−	1.38712i		−	0.0842618i	−0.999112	−	0.0421309i	$-0.986585\pi$
$271$		−	1.38712i		−	0.0842618i	0.999112	−	0.0421309i	$-0.0134147\pi$
$272$	2.22853	+	9.84836i	0.135124	+	0.597144i
$273$	14.7446	+	5.84096i	0.892382	+	0.353511i
$274$	22.2002	−	14.5205i	1.34116	−	0.877218i
$275$		0			0
$276$	−5.24767	−	5.29099i	−0.315873	−	0.318480i
$277$	0.313859	+	0.543620i	0.0188580	+	0.0326630i	0.875300	−	0.483580i	$-0.160664\pi$
$277$	0.313859	+	0.543620i	0.0188580	+	0.0326630i	−0.856442	+	0.516243i	$0.827330\pi$
$278$	−11.7944	−	5.96099i	−0.707381	−	0.357516i
$279$	−1.47603	−	4.89545i	−0.0883679	−	0.293083i
$280$		0			0
$281$	−5.56930	+	3.21543i	−0.332236	+	0.191817i	−0.656834	−	0.754036i	$-0.728105\pi$
$281$	−5.56930	+	3.21543i	−0.332236	+	0.191817i	0.324597	+	0.945852i	$0.394771\pi$
$282$	−27.7327	+	5.68106i	−1.65146	+	0.338302i
$283$	8.80507	+	5.08361i	0.523407	+	0.302189i	0.738327	−	0.674442i	$-0.235616\pi$
$283$	8.80507	+	5.08361i	0.523407	+	0.302189i	−0.214921	+	0.976632i	$0.568949\pi$
$284$	3.47992	−	0.388810i	0.206495	−	0.0230716i
$285$		0			0
$286$	16.3187	−	0.908812i	0.964943	−	0.0537392i
$287$	0.400428			0.0236365
$288$	−15.0826	−	7.77916i	−0.888750	−	0.458392i
$289$	10.6277			0.625160
$290$		0			0
$291$	21.4003	−	3.15605i	1.25451	−	0.185011i
$292$	4.71522	−	0.526830i	0.275938	−	0.0308304i
$293$	17.3139	+	9.99616i	1.01149	+	0.583982i	0.911627	−	0.411020i	$-0.134827\pi$
$293$	17.3139	+	9.99616i	1.01149	+	0.583982i	0.0998599	+	0.995002i	$0.468161\pi$
$294$	0.605159	+	0.682160i	0.0352936	+	0.0397844i
$295$		0			0
$296$	−13.2332	+	2.22938i	−0.769163	+	0.129580i
$297$	14.6168	+	10.1711i	0.848155	+	0.590186i
$298$	−12.1168	−	6.12395i	−0.701910	−	0.354751i
$299$	3.62725	+	6.28258i	0.209769	+	0.363331i
$300$		0			0
$301$	−9.43070	+	16.3345i	−0.543577	+	0.941502i
$302$	10.8369	−	7.08811i	0.623593	−	0.407875i
$303$	4.50264	+	30.5312i	0.258670	+	1.75397i
$304$	−1.95083	−	8.62118i	−0.111888	−	0.494459i
$305$		0			0
$306$	6.88900	−	8.20017i	0.393818	−	0.468773i
$307$		−	25.9530i		−	1.48121i	−0.671938	−	0.740607i	$-0.734538\pi$
$307$		−	25.9530i		−	1.48121i	0.671938	−	0.740607i	$-0.265462\pi$
$308$	17.0504	+	7.45793i	0.971537	+	0.424955i
$309$	−19.8030	+	15.6896i	−1.12655	+	0.892553i
$310$		0			0
$311$	−15.6591	+	27.1224i	−0.887948	+	1.53797i	−0.0456512	+	0.998957i	$0.514536\pi$
$311$	−15.6591	+	27.1224i	−0.887948	+	1.53797i	−0.842297	+	0.539014i	$0.818797\pi$
$312$	12.2681	+	11.0648i	0.694542	+	0.626420i
$313$	2.24456	+	3.88770i	0.126870	+	0.219746i	0.922462	−	0.386087i	$-0.126174\pi$
$313$	2.24456	+	3.88770i	0.126870	+	0.219746i	−0.795592	+	0.605832i	$0.792840\pi$
$314$	−10.7561	+	21.2819i	−0.607000	+	1.20101i
$315$		0			0
$316$	−16.3723	+	12.0597i	−0.921013	+	0.678414i
$317$	−20.6644	+	11.9306i	−1.16063	+	0.670089i	−0.951454	−	0.307790i	$-0.900411\pi$
$317$	−20.6644	+	11.9306i	−1.16063	+	0.670089i	−0.209173	+	0.977879i	$0.567077\pi$
$318$	19.7833	+	6.58987i	1.10939	+	0.369542i
$319$	−2.35143	−	1.35760i	−0.131655	−	0.0760109i
$320$		0			0
$321$	8.44158	−	21.3094i	0.471163	−	1.18937i
$322$	0.459321	+	8.24759i	0.0255969	+	0.459620i
$323$	5.57825			0.310382
$324$	3.10478	+	17.7302i	0.172488	+	0.985012i
$325$		0			0
$326$	−0.933557	−	16.7630i	−0.0517049	−	0.928416i
$327$	6.05321	−	15.2804i	0.334743	−	0.845005i
$328$	0.390872	+	0.145653i	0.0215823	+	0.00804233i
$329$	27.1753	+	15.6896i	1.49822	+	0.864998i
$330$		0			0
$331$	−24.1149	+	13.9228i	−1.32548	+	0.765264i	−0.984596	−	0.174843i	$-0.944058\pi$
$331$	−24.1149	+	13.9228i	−1.32548	+	0.765264i	−0.340879	+	0.940107i	$0.610725\pi$
$332$	−8.60485	−	11.6819i	−0.472253	−	0.641129i
$333$	10.3723	+	9.74749i	0.568398	+	0.534159i
$334$	−12.2554	+	24.2486i	−0.670588	+	1.32682i
$335$		0			0
$336$	6.78421	+	17.5455i	0.370109	+	0.957185i
$337$	−2.12772	+	3.68532i	−0.115904	+	0.200752i	−0.918141	−	0.396254i	$-0.870310\pi$
$337$	−2.12772	+	3.68532i	−0.115904	+	0.200752i	0.802237	+	0.597006i	$0.203643\pi$
$338$	1.26004	+	1.92646i	0.0685372	+	0.104785i
$339$	21.6378	−	17.1434i	1.17520	−	0.931099i
$340$		0			0
$341$			5.84096i			0.316306i
$342$	−6.03058	+	7.17837i	−0.326096	+	0.388162i
$343$			17.9955i			0.971668i
$344$	−15.1472	+	12.5143i	−0.816681	+	0.674724i
$345$		0			0
$346$	6.56387	−	4.29325i	0.352876	−	0.230807i
$347$	−3.86473	+	6.69391i	−0.207470	+	0.359348i	−0.950917	−	0.309447i	$-0.899856\pi$
$347$	−3.86473	+	6.69391i	−0.207470	+	0.359348i	0.743447	+	0.668795i	$0.233189\pi$
$348$	−0.699444	−	2.65394i	−0.0374941	−	0.142266i
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	0.977121	−	0.212683i	$-0.0682200\pi$
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	−0.672749	+	0.739871i	$0.734887\pi$
$350$		0			0
$351$	1.47603	−	17.4606i	0.0787849	−	0.931978i
$352$	13.9307	+	13.4819i	0.742509	+	0.718587i
$353$	4.24456	−	2.45060i	0.225915	−	0.130432i	−0.382771	−	0.923843i	$-0.625030\pi$
$353$	4.24456	−	2.45060i	0.225915	−	0.130432i	0.608686	+	0.793411i	$0.291697\pi$
$354$	−8.41677	−	9.48772i	−0.447346	−	0.504267i
$355$		0			0
$356$	−1.18670	−	10.6212i	−0.0628949	−	0.562921i
$357$	−11.7446	+	1.73205i	−0.621588	+	0.0916698i
$358$	−26.5622	+	1.47929i	−1.40386	+	0.0781829i
$359$	29.9679			1.58165			0.790823	−	0.612045i	$-0.209653\pi$
$359$	29.9679			1.58165			0.790823	+	0.612045i	$0.209653\pi$
$360$		0			0
$361$	14.1168			0.742992
$362$	−5.64810	+	0.314551i	−0.296858	+	0.0165325i
$363$	−0.800857	−	1.01082i	−0.0420341	−	0.0530541i
$364$	−2.03343	−	18.1996i	−0.106581	−	0.953916i
$365$		0			0
$366$	8.09232	−	1.65772i	0.422992	−	0.0866503i
$367$	−11.7571	+	6.78799i	−0.613718	+	0.354330i	−0.774419	−	0.632673i	$-0.781958\pi$
$367$	−11.7571	+	6.78799i	−0.613718	+	0.354330i	0.160701	+	0.987003i	$0.448624\pi$
$368$	−2.55164	+	8.21782i	−0.133014	+	0.428384i
$369$	−0.127719	−	0.423595i	−0.00664877	−	0.0220515i
$370$		0			0
$371$	−11.5569	−	20.0172i	−0.600006	−	1.03924i
$372$	−4.19198	+	4.15766i	−0.217344	+	0.215565i
$373$	4.43070	−	7.67420i	0.229413	−	0.397355i	−0.728221	−	0.685342i	$-0.759653\pi$
$373$	4.43070	−	7.67420i	0.229413	−	0.397355i	0.957634	+	0.287987i	$0.0929860\pi$
$374$	−10.2387	+	6.69686i	−0.529431	+	0.346287i
$375$		0			0
$376$	20.8197	+	25.2000i	1.07369	+	1.29959i
$377$			2.67181i			0.137605i
$378$	10.4680	−	16.9860i	0.538417	−	0.873665i
$379$		−	9.66181i		−	0.496294i	−0.968722	−	0.248147i	$-0.920178\pi$
$379$		−	9.66181i		−	0.496294i	0.968722	−	0.248147i	$-0.0798216\pi$
$380$		0			0
$381$	26.2337	+	10.3923i	1.34399	+	0.532414i
$382$	−3.02060	−	4.61814i	−0.154547	−	0.236284i
$383$	−0.200214	+	0.346781i	−0.0102305	+	0.0177197i	−0.871095	−	0.491114i	$-0.836590\pi$
$383$	−0.200214	+	0.346781i	−0.0102305	+	0.0177197i	0.860865	+	0.508834i	$0.169923\pi$
$384$	0.240258	+	19.5944i	0.0122606	+	0.999925i
$385$		0			0
$386$	−2.38870	+	4.72627i	−0.121581	+	0.240561i
$387$	20.2875	+	4.76635i	1.03127	+	0.242287i
$388$	−14.8139	−	20.1113i	−0.752060	−	1.02099i
$389$	7.19702	−	4.15520i	0.364903	−	0.210677i	−0.306326	−	0.951927i	$-0.599100\pi$
$389$	7.19702	−	4.15520i	0.364903	−	0.210677i	0.671229	+	0.741250i	$0.265767\pi$
$390$		0			0
$391$	−4.70285	−	2.71519i	−0.237834	−	0.137313i
$392$	0.367677	−	0.986692i	0.0185705	−	0.0498355i
$393$	−7.80298	−	9.84868i	−0.393609	−	0.496800i
$394$	−0.840423	−	15.0907i	−0.0423399	−	0.760258i
$395$		0			0
$396$	2.45109	−	20.4156i	0.123172	−	1.02592i
$397$	7.25544			0.364140			0.182070	−	0.983286i	$-0.441720\pi$
$397$	7.25544			0.364140			0.182070	+	0.983286i	$0.441720\pi$
$398$	−1.51957	−	27.2854i	−0.0761690	−	1.36770i
$399$	10.2811	−	1.51622i	0.514699	−	0.0759062i
$400$		0			0
$401$	−18.9891	−	10.9634i	−0.948272	−	0.547485i	−0.0557281	−	0.998446i	$-0.517748\pi$
$401$	−18.9891	−	10.9634i	−0.948272	−	0.547485i	−0.892544	+	0.450961i	$0.851081\pi$
$402$	12.7288	−	11.2920i	0.634856	−	0.563195i
$403$	4.97760	−	2.87382i	0.247952	−	0.143155i
$404$	28.6921	−	21.1345i	1.42749	−	1.05148i
$405$		0			0
$406$	−1.37228	+	2.71519i	−0.0681052	+	0.134753i
$407$	−8.12989	−	14.0814i	−0.402984	−	0.697988i
$408$	−12.0943	−	2.58129i	−0.598756	−	0.127793i
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	−0.892559	−	0.450931i	$-0.851092\pi$
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	0.836797	+	0.547513i	$0.184426\pi$
$410$		0			0
$411$	4.74012	+	32.1415i	0.233813	+	1.58542i
$412$	26.7285	+	11.6912i	1.31682	+	0.575983i
$413$			14.0588i			0.691788i
$414$	8.57825	−	3.11651i	0.421598	−	0.153168i
$415$		0			0
$416$	4.63506	−	18.5048i	0.227252	−	0.907275i
$417$	12.6861	−	10.0511i	0.621243	−	0.492203i
$418$	8.96290	−	5.86238i	0.438390	−	0.286739i
$419$	2.82639	−	4.89545i	0.138078	−	0.239159i	−0.788691	−	0.614790i	$-0.789241\pi$
$419$	2.82639	−	4.89545i	0.138078	−	0.239159i	0.926769	+	0.375631i	$0.122574\pi$
$420$		0			0
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	−0.960417	−	0.278565i	$-0.910141\pi$
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	0.238964	−	0.971028i	$-0.423192\pi$
$422$	7.72946	+	3.90653i	0.376264	+	0.190167i
$423$	7.92967	−	33.7518i	0.385554	−	1.64107i
$424$	−4.00000	−	23.7432i	−0.194257	−	1.15307i
$425$		0			0
$426$	−1.35531	+	4.06874i	−0.0656649	+	0.197131i
$427$	−7.92967	−	4.57820i	−0.383744	−	0.221555i
$428$	−26.3027	+	2.93879i	−1.27139	+	0.142052i
$429$	−7.37228	+	18.6101i	−0.355937	+	0.898505i
$430$		0			0
$431$	−14.6581			−0.706054			−0.353027	−	0.935613i	$-0.614848\pi$
$431$	−14.6581			−0.706054			−0.353027	+	0.935613i	$0.614848\pi$
$432$	16.3967	−	12.7729i	0.788887	−	0.614538i
$433$	14.3723			0.690688			0.345344	−	0.938476i	$-0.387762\pi$
$433$	14.3723			0.690688			0.345344	+	0.938476i	$0.387762\pi$
$434$	6.53446	−	0.363914i	0.313664	−	0.0174684i
$435$		0			0
$436$	−18.8609	+	2.10732i	−0.903273	+	0.100922i
$437$	4.11684	+	2.37686i	0.196935	+	0.113701i
$438$	−1.83642	+	5.51306i	−0.0877475	+	0.263424i
$439$	28.4919	−	16.4498i	1.35984	−	0.785106i	0.370241	−	0.928936i	$-0.379275\pi$
$439$	28.4919	−	16.4498i	1.35984	−	0.785106i	0.989602	+	0.143830i	$0.0459418\pi$
$440$		0			0
$441$	−1.06930	+	0.322405i	−0.0509189	+	0.0153526i
$442$	10.7446	+	5.43039i	0.511067	+	0.258297i
$443$	−2.58891	−	4.48412i	−0.123003	−	0.213047i	0.797948	−	0.602727i	$-0.205919\pi$
$443$	−2.58891	−	4.48412i	−0.123003	−	0.213047i	−0.920950	+	0.389680i	$0.872586\pi$
$444$	4.31907	−	15.8580i	0.204974	−	0.752587i
$445$		0			0
$446$	−2.01718	+	1.31939i	−0.0955165	+	0.0624747i
$447$	13.0330	−	10.3258i	0.616438	−	0.488396i
$448$	14.2147	−	16.4247i	0.671580	−	0.775992i
$449$		−	3.81396i		−	0.179992i	−0.995942	−	0.0899959i	$-0.971315\pi$
$449$		−	3.81396i		−	0.179992i	0.995942	−	0.0899959i	$-0.0286854\pi$
$450$		0			0
$451$			0.505408i			0.0237987i
$452$	−29.2050	−	12.7744i	−1.37369	−	0.600858i
$453$	2.31386	+	15.6896i	0.108715	+	0.737164i
$454$	14.6199	+	22.3521i	0.686146	+	1.04904i
$455$		0			0
$456$	10.5872	+	2.25964i	0.495793	+	0.105817i
$457$	−2.98913	−	5.17732i	−0.139825	−	0.242185i	0.787605	−	0.616180i	$-0.211321\pi$
$457$	−2.98913	−	5.17732i	−0.139825	−	0.242185i	−0.927430	+	0.373996i	$0.877987\pi$
$458$	−5.97868	+	11.8294i	−0.279365	+	0.552752i
$459$	5.57825	+	11.8716i	0.260370	+	0.554119i
$460$		0			0
$461$	−19.8030	+	11.4333i	−0.922317	+	0.532500i	−0.884373	−	0.466780i	$-0.845414\pi$
$461$	−19.8030	+	11.4333i	−0.922317	+	0.532500i	−0.0379435	+	0.999280i	$0.512081\pi$
$462$	−17.0504	+	15.1258i	−0.793256	+	0.703715i
$463$	−18.2108	−	10.5140i	−0.846327	−	0.488627i	0.0130831	−	0.999914i	$-0.495835\pi$
$463$	−18.2108	−	10.5140i	−0.846327	−	0.488627i	−0.859410	+	0.511288i	$0.829169\pi$
$464$	−2.32716	+	2.15124i	−0.108036	+	0.0998686i
$465$		0			0
$466$	2.20679	+	39.6252i	0.102227	+	1.83560i
$467$	24.3897			1.12862			0.564310	−	0.825563i	$-0.309142\pi$
$467$	24.3897			1.12862			0.564310	+	0.825563i	$0.309142\pi$
$468$	−18.6039	+	7.95591i	−0.859966	+	0.367762i
$469$	−18.8614			−0.870939
$470$		0			0
$471$	−18.1362	−	22.8910i	−0.835674	−	1.05476i
$472$	−5.11378	+	13.7233i	−0.235381	+	0.631664i
$473$	−20.6168	−	11.9031i	−0.947963	−	0.547307i
$474$	−4.99792	−	24.3978i	−0.229562	−	1.12063i
$475$		0			0
$476$	8.12989	+	11.0371i	0.372633	+	0.505885i
$477$	−17.4891	+	18.6101i	−0.800772	+	0.852099i
$478$	−10.6277	+	21.0280i	−0.486101	+	0.961798i
$479$	−4.90307	−	8.49236i	−0.224027	−	0.388026i	0.732000	−	0.681304i	$-0.238587\pi$
$479$	−4.90307	−	8.49236i	−0.224027	−	0.388026i	−0.956027	+	0.293278i	$0.905254\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−12.7645	−	19.5154i	−0.581406	−	0.888902i
$483$	−9.40571	−	3.72601i	−0.427975	−	0.169539i
$484$	−0.596761	+	1.36432i	−0.0271255	+	0.0620146i
$485$		0			0
$486$	−21.3075	−	5.65587i	−0.966530	−	0.256555i
$487$			17.9365i			0.812780i	0.913700	+	0.406390i	$0.133213\pi$
$487$			17.9365i			0.812780i	−0.913700	+	0.406390i	$0.866787\pi$
$488$	−6.07514	−	7.35330i	−0.275008	−	0.332868i
$489$	19.1168	+	7.57301i	0.864494	+	0.342464i
$490$		0			0
$491$	12.3950	−	21.4689i	0.559381	−	0.968876i	−0.438168	−	0.898893i	$-0.644372\pi$
$491$	12.3950	−	21.4689i	0.559381	−	0.968876i	0.997548	−	0.0699824i	$-0.0222943\pi$
$492$	−0.362725	+	0.359755i	−0.0163529	+	0.0162190i
$493$	−1.00000	−	1.73205i	−0.0450377	−	0.0780076i
$494$	−9.40571	−	4.75372i	−0.423183	−	0.213880i
$495$		0			0
$496$	6.51087	+	2.02163i	0.292347	+	0.0907740i
$497$	4.11684	−	2.37686i	0.184666	−	0.106617i
$498$	17.4083	−	3.56611i	0.780085	−	0.159801i
$499$	−0.437696	−	0.252704i	−0.0195940	−	0.0113126i	0.490171	−	0.871626i	$-0.336934\pi$
$499$	−0.437696	−	0.252704i	−0.0195940	−	0.0113126i	−0.509765	+	0.860314i	$0.670268\pi$
$500$		0			0
$501$	−20.6644	−	26.0820i	−0.923217	−	1.16526i
$502$	23.6299	−	1.31598i	1.05465	−	0.0587352i
$503$	12.9073			0.575507			0.287754	−	0.957704i	$-0.407092\pi$
$503$	12.9073			0.575507			0.287754	+	0.957704i	$0.407092\pi$
$504$	−22.9922	−	1.47014i	−1.02416	−	0.0654853i
$505$		0			0
$506$	−10.4098	+	0.579740i	−0.462774	+	0.0257726i
$507$	−2.78912	+	0.411331i	−0.123869	+	0.0182679i
$508$	−3.61790	−	32.3808i	−0.160518	−	1.43667i
$509$	15.6861	+	9.05640i	0.695276	+	0.401418i	0.805586	−	0.592480i	$-0.201851\pi$
$509$	15.6861	+	9.05640i	0.695276	+	0.401418i	−0.110310	+	0.993897i	$0.535184\pi$
$510$		0			0
$511$	5.57825	−	3.22060i	0.246767	−	0.142471i
$512$	19.8498	−	10.8622i	0.877244	−	0.480045i
$513$	−4.88316	−	10.3923i	−0.215597	−	0.458831i
$514$	14.5584	+	7.35794i	0.642144	+	0.324545i
$515$		0			0
$516$	−6.13258	−	23.2692i	−0.269972	−	1.02437i
$517$	−19.8030	+	34.2998i	−0.870934	+	1.50850i
$518$	−15.2467	+	9.97247i	−0.669903	+	0.438165i
$519$	1.40150	+	9.50318i	0.0615190	+	0.417143i
$520$		0			0
$521$			10.4472i			0.457700i	0.973462	+	0.228850i	$0.0734966\pi$
$521$			10.4472i			0.457700i	−0.973462	+	0.228850i	$0.926503\pi$
$522$	3.30998	+	0.585649i	0.144874	+	0.0256332i
$523$		−	4.41957i		−	0.193254i	−0.995321	−	0.0966272i	$-0.969195\pi$
$523$		−	4.41957i		−	0.193254i	0.995321	−	0.0966272i	$-0.0308055\pi$
$524$	−5.81442	+	13.2930i	−0.254004	+	0.580707i
$525$		0			0
$526$	−9.68174	−	14.8022i	−0.422144	−	0.645409i
$527$	−2.15121	+	3.72601i	−0.0937083	+	0.162308i
$528$	−22.1454	+	8.56282i	−0.963753	+	0.372649i
$529$	9.18614	+	15.9109i	0.399397	+	0.691777i
$530$		0			0
$531$	14.8722	−	4.48412i	0.645396	−	0.194594i
$532$	−7.11684	−	9.66181i	−0.308554	−	0.418892i
$533$	0.430703	−	0.248667i	0.0186558	−	0.0107709i
$534$	12.4183	+	4.13658i	0.537394	+	0.179008i
$535$		0			0
$536$	−18.4113	−	6.86070i	−0.795245	−	0.296337i
$537$	12.0000	−	30.2921i	0.517838	−	1.30720i
$538$	1.96189	+	35.2278i	0.0845831	+	1.51878i
$539$	1.27582			0.0549535
$540$		0			0
$541$	36.9783			1.58982			0.794910	−	0.606728i	$-0.207518\pi$
$541$	36.9783			1.58982			0.794910	+	0.606728i	$0.207518\pi$
$542$	−0.109080	−	1.95865i	−0.00468541	−	0.0841314i
$543$	2.55164	−	6.44121i	0.109501	−	0.276419i
$544$	3.92119	+	13.7309i	0.168120	+	0.588707i
$545$		0			0
$546$	21.2790	+	7.08811i	0.910658	+	0.303343i
$547$	−7.21723	+	4.16687i	−0.308586	+	0.178162i	−0.646294	−	0.763089i	$-0.723682\pi$
$547$	−7.21723	+	4.16687i	−0.308586	+	0.178162i	0.337707	+	0.941251i	$0.390349\pi$
$548$	30.2054	−	22.2492i	1.29031	−	0.950437i
$549$	−2.31386	+	9.84868i	−0.0987531	+	0.420332i
$550$		0			0
$551$	0.875393	+	1.51622i	0.0372930	+	0.0645933i
$552$	−7.82592	−	7.05834i	−0.333093	−	0.300423i
$553$	−13.8030	+	23.9075i	−0.586963	+	1.01665i
$554$	0.485927	+	0.742925i	0.0206450	+	0.0315638i
$555$		0			0
$556$	−17.1228	−	7.48958i	−0.726167	−	0.317629i
$557$			20.4897i			0.868175i	0.900871	+	0.434087i	$0.142929\pi$
$557$			20.4897i			0.868175i	−0.900871	+	0.434087i	$0.857071\pi$
$558$	−2.46917	−	6.79643i	−0.104528	−	0.287716i
$559$			23.4259i			0.990811i
$560$		0			0
$561$	−2.18614	−	14.8236i	−0.0922989	−	0.625854i
$562$	−7.61113	+	4.97823i	−0.321056	+	0.209994i
$563$	5.54098	−	9.59726i	0.233524	−	0.404476i	−0.725318	−	0.688414i	$-0.758307\pi$
$563$	5.54098	−	9.59726i	0.233524	−	0.404476i	0.958843	+	0.283937i	$0.0916408\pi$
$564$	−38.7125	+	10.2026i	−1.63009	+	0.429608i
$565$		0			0
$566$	12.8327	+	6.48577i	0.539400	+	0.272617i
$567$	13.5079	+	20.3640i	0.567279	+	0.855206i
$568$	4.88316	−	0.822662i	0.204893	−	0.0345181i
$569$	0.989125	−	0.571072i	0.0414663	−	0.0239406i	−0.479124	−	0.877747i	$-0.659045\pi$
$569$	0.989125	−	0.571072i	0.0414663	−	0.0239406i	0.520590	+	0.853807i	$0.325712\pi$
$570$		0			0
$571$	−14.5463	−	8.39829i	−0.608742	−	0.351457i	0.163731	−	0.986505i	$-0.447647\pi$
$571$	−14.5463	−	8.39829i	−0.608742	−	0.351457i	−0.772473	+	0.635048i	$0.780980\pi$
$572$	22.9709	−	2.56653i	0.960462	−	0.107312i
$573$	6.68614	−	0.986051i	0.279318	−	0.0411929i
$574$	0.565415	−	0.0314888i	0.0236000	−	0.00131432i
$575$		0			0
$576$	−21.9087	−	9.79831i	−0.912864	−	0.408263i
$577$	42.8397			1.78344			0.891719	−	0.452589i	$-0.149500\pi$
$577$	42.8397			1.78344			0.891719	+	0.452589i	$0.149500\pi$
$578$	15.0066	−	0.835741i	0.624193	−	0.0347622i
$579$	−4.02768	−	5.08361i	−0.167385	−	0.211268i
$580$		0			0
$581$	−17.0584	−	9.84868i	−0.707703	−	0.408592i
$582$	29.9696	−	6.13930i	1.24228	−	0.254482i
$583$	25.2651	−	14.5868i	1.04637	−	0.604123i
$584$	6.61659	−	1.11469i	0.273796	−	0.0461263i
$585$		0			0
$586$	25.2337	+	12.7533i	1.04239	+	0.526834i
$587$	−6.41637	−	11.1135i	−0.264832	−	0.458702i	0.702688	−	0.711499i	$-0.251983\pi$
$587$	−6.41637	−	11.1135i	−0.264832	−	0.458702i	−0.967520	+	0.252796i	$0.918650\pi$
$588$	0.908144	+	0.915639i	0.0374512	+	0.0377603i
$589$	1.88316	−	3.26172i	0.0775941	−	0.134397i
$590$		0			0
$591$	17.2097	+	6.81751i	0.707913	+	0.280435i
$592$	−18.5103	+	4.18858i	−0.760767	+	0.172149i
$593$		−	15.4410i		−	0.634085i	−0.948411	−	0.317043i	$-0.897310\pi$
$593$		−	15.4410i		−	0.634085i	0.948411	−	0.317043i	$-0.102690\pi$
$594$	21.4392	+	13.2124i	0.879661	+	0.542111i
$595$		0			0
$596$	−17.5909	−	7.69433i	−0.720550	−	0.315172i
$597$	31.1168	+	12.3267i	1.27353	+	0.504500i
$598$	5.61582	+	8.58592i	0.229648	+	0.351104i
$599$	−9.20550	+	15.9444i	−0.376126	+	0.651470i	−0.990495	−	0.137549i	$-0.956077\pi$
$599$	−9.20550	+	15.9444i	−0.376126	+	0.651470i	0.614369	+	0.789019i	$0.289411\pi$
$600$		0			0
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	0.991001	+	0.133851i	$0.0427344\pi$
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	−0.379582	+	0.925158i	$0.623932\pi$
$602$	−12.0319	+	23.8063i	−0.490383	+	0.970272i
$603$	6.01594	+	19.9526i	0.244988	+	0.812534i
$604$	14.7446	−	10.8608i	0.599948	−	0.441919i
$605$		0			0
$606$	8.75875	+	42.7567i	0.355800	+	1.73687i
$607$	33.1947	+	19.1650i	1.34733	+	0.777883i	0.987871	−	0.155277i	$-0.0496270\pi$
$607$	33.1947	+	19.1650i	1.34733	+	0.777883i	0.359462	+	0.933160i	$0.382960\pi$
$608$	−3.43258	−	12.0199i	−0.139209	−	0.487472i
$609$	−2.31386	−	2.92048i	−0.0937623	−	0.118344i
$610$		0			0
$611$	38.9732			1.57669
$612$	9.08259	−	12.1206i	0.367142	−	0.489946i
$613$	30.2337			1.22113			0.610564	−	0.791967i	$-0.290943\pi$
$613$	30.2337			1.22113			0.610564	+	0.791967i	$0.290943\pi$
$614$	−2.04089	−	36.6463i	−0.0823635	−	1.47892i
$615$		0			0
$616$	24.6621	+	9.18998i	0.993663	+	0.370275i
$617$	−7.24456	−	4.18265i	−0.291655	−	0.168387i	0.347033	−	0.937853i	$-0.387189\pi$
$617$	−7.24456	−	4.18265i	−0.291655	−	0.168387i	−0.638688	+	0.769466i	$0.720523\pi$
$618$	−26.7285	+	23.7114i	−1.07518	+	0.953814i
$619$	23.9520	−	13.8287i	0.962711	−	0.555821i	0.0657046	−	0.997839i	$-0.479070\pi$
$619$	23.9520	−	13.8287i	0.962711	−	0.555821i	0.897006	+	0.442018i	$0.145737\pi$
$620$		0			0
$621$	−0.941578	+	11.1383i	−0.0377842	+	0.446965i
$622$	−19.9783	+	39.5289i	−0.801055	+	1.58497i
$623$	−7.25450	−	12.5652i	−0.290645	−	0.503412i
$624$	18.1929	+	14.6590i	0.728300	+	0.586831i
$625$		0			0
$626$	3.47510	+	5.31302i	0.138893	+	0.212351i
$627$	1.91373	+	12.9765i	0.0764271	+	0.518231i
$628$	−13.5143	+	30.8965i	−0.539278	+	1.23290i
$629$		−	11.9769i		−	0.477549i
$630$		0			0
$631$			17.9365i			0.714040i	0.934097	+	0.357020i	$0.116207\pi$
$631$			17.9365i			0.714040i	−0.934097	+	0.357020i	$0.883793\pi$
$632$	−22.1697	+	18.3162i	−0.881864	+	0.728577i
$633$	−8.31386	+	6.58696i	−0.330446	+	0.261808i
$634$	−28.2405	+	18.4713i	−1.12157	+	0.733589i
$635$		0			0
$636$	28.4527	+	7.74935i	1.12822	+	0.307282i
$637$	−0.627719	−	1.08724i	−0.0248711	−	0.0430780i
$638$	−3.42703	−	1.73205i	−0.135678	−	0.0685725i
$639$	−3.82746	−	3.59691i	−0.151412	−	0.142292i
$640$		0			0
$641$	23.8723	−	13.7827i	0.942898	−	0.544383i	0.0520307	−	0.998645i	$-0.483431\pi$
$641$	23.8723	−	13.7827i	0.942898	−	0.544383i	0.890868	+	0.454263i	$0.150097\pi$
$642$	10.2440	−	30.7532i	0.404298	−	1.21373i
$643$	5.46644	+	3.15605i	0.215575	+	0.124463i	0.603900	−	0.797060i	$-0.293613\pi$
$643$	5.46644	+	3.15605i	0.215575	+	0.124463i	−0.388324	+	0.921523i	$0.626946\pi$
$644$	1.29715	+	11.6097i	0.0511147	+	0.457486i
$645$		0			0
$646$	7.87663	−	0.438661i	0.309902	−	0.0172589i
$647$	−36.9711			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$647$	−36.9711			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$648$	5.77830	+	24.7914i	0.226993	+	0.973896i
$649$	−17.7446			−0.696535
$650$		0			0
$651$	−2.95207	+	7.45202i	−0.115701	+	0.292068i
$652$	−2.63641	−	23.5964i	−0.103250	−	0.924105i
$653$	−6.68614	−	3.86025i	−0.261649	−	0.151063i	0.363438	−	0.931619i	$-0.381603\pi$
$653$	−6.68614	−	3.86025i	−0.261649	−	0.151063i	−0.625087	+	0.780555i	$0.714936\pi$
$654$	7.34568	−	22.0523i	0.287239	−	0.862311i
$655$		0			0
$656$	0.563374	+	0.174928i	0.0219961	+	0.00682980i
$657$	−5.18614	−	4.87375i	−0.202331	−	0.190143i
$658$	39.6060	+	20.0172i	1.54400	+	0.780351i
$659$	8.33010	+	14.4282i	0.324495	+	0.562041i	0.981410	−	0.191923i	$-0.0614724\pi$
$659$	8.33010	+	14.4282i	0.324495	+	0.562041i	−0.656915	+	0.753964i	$0.728139\pi$
$660$		0			0
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	−0.995496	−	0.0948069i	$-0.969777\pi$
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	0.579853	+	0.814721i	$0.303110\pi$
$662$	−32.9560	+	21.5556i	−1.28087	+	0.837783i
$663$	−11.5569	+	9.15640i	−0.448834	+	0.355605i
$664$	−13.0689	−	15.8185i	−0.507172	−	0.613877i
$665$		0			0
$666$	15.4124	+	12.9481i	0.597220	+	0.501727i
$667$		−	1.70438i		−	0.0659938i
$668$	−15.3981	+	35.2034i	−0.595772	+	1.36206i
$669$	−0.430703	−	2.92048i	−0.0166520	−	0.112912i
$670$		0			0
$671$	5.77846	−	10.0086i	0.223075	−	0.386377i
$672$	10.9592	+	24.2412i	0.422761	+	0.935124i
$673$	0.569297	+	0.986051i	0.0219448	+	0.0380095i	0.876789	−	0.480875i	$-0.159681\pi$
$673$	0.569297	+	0.986051i	0.0219448	+	0.0380095i	−0.854844	+	0.518884i	$0.826348\pi$
$674$	−2.71459	+	5.37108i	−0.104562	+	0.206886i
$675$		0			0
$676$	1.93070	+	2.62112i	0.0742578	+	0.100812i
$677$	−28.5475	+	16.4819i	−1.09717	+	0.633452i	−0.935477	−	0.353389i	$-0.885029\pi$
$677$	−28.5475	+	16.4819i	−1.09717	+	0.633452i	−0.161695	+	0.986841i	$0.551696\pi$
$678$	29.2050	−	25.9084i	1.12161	−	0.995006i
$679$	−29.3673	−	16.9552i	−1.12701	−	0.650681i
$680$		0			0
$681$	−32.3614	+	4.77256i	−1.24009	+	0.182885i
$682$	0.459321	+	8.24759i	0.0175883	+	0.315816i
$683$	−2.07668			−0.0794618			−0.0397309	−	0.999210i	$-0.512650\pi$
$683$	−2.07668			−0.0794618			−0.0397309	+	0.999210i	$0.512650\pi$
$684$	−7.95083	+	10.6103i	−0.304008	+	0.405694i
$685$		0			0
$686$	1.41513	+	25.4102i	0.0540299	+	0.970165i
$687$	−10.0809	−	12.7238i	−0.384610	−	0.485443i
$688$	−20.4041	+	18.8616i	−0.777899	+	0.719092i
$689$	−24.8614	−	14.3537i	−0.947144	−	0.546834i
$690$		0			0
$691$	−10.0064	+	5.77717i	−0.380660	+	0.219774i	−0.678105	−	0.734965i	$-0.737199\pi$
$691$	−10.0064	+	5.77717i	−0.380660	+	0.219774i	0.297446	+	0.954739i	$0.403865\pi$
$692$	8.93075	−	6.57835i	0.339496	−	0.250071i
$693$	−8.05842	−	26.7268i	−0.306114	−	1.01527i
$694$	−4.93070	+	9.75588i	−0.187167	+	0.370328i
$695$		0			0
$696$	−1.19633	−	3.69243i	−0.0453469	−	0.139961i
$697$	−0.186141	+	0.322405i	−0.00705058	+	0.0122120i
$698$	8.80346	+	13.4594i	0.333216	+	0.509448i
$699$	−45.1894	−	17.9015i	−1.70922	−	0.677096i
$700$		0			0
$701$		−	26.1282i		−	0.986850i	−0.869788	−	0.493425i	$-0.835745\pi$
$701$		−	26.1282i		−	0.986850i	0.869788	−	0.493425i	$-0.164255\pi$
$702$	0.711134	−	24.7709i	0.0268400	−	0.934917i
$703$			10.4845i			0.395429i
$704$	20.7307	+	17.9413i	0.781317	+	0.676188i
$705$		0			0
$706$	5.80072	−	3.79409i	0.218313	−	0.142793i
$707$	24.1895	−	41.8974i	0.909738	−	1.57571i
$708$	−12.6308	−	12.7350i	−0.474694	−	0.478612i
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	0.908053	−	0.418855i	$-0.137569\pi$
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	−0.816766	+	0.576969i	$0.804235\pi$
$710$		0			0
$711$	29.6932	+	6.97614i	1.11358	+	0.261626i
$712$	−2.51087	−	14.9040i	−0.0940990	−	0.558553i
$713$	−3.17527	+	1.83324i	−0.118915	+	0.0686554i
$714$	−16.4474	+	3.36927i	−0.615529	+	0.126092i
$715$		0			0
$716$	−37.3902	+	4.17759i	−1.39734	+	0.156124i
$717$	−17.9198	−	22.6179i	−0.669228	−	0.844679i
$718$	42.3155	−	2.35661i	1.57920	−	0.0879480i
$719$	−7.65492			−0.285481			−0.142740	−	0.989760i	$-0.545591\pi$
$719$	−7.65492			−0.285481			−0.142740	+	0.989760i	$0.545591\pi$
$720$		0			0
$721$	39.6060			1.47500
$722$	19.9333	−	1.11012i	0.741842	−	0.0413143i
$723$	28.2544	−	4.16687i	1.05079	−	0.154968i
$724$	−7.95053	+	0.888309i	−0.295479	+	0.0330137i
$725$		0			0
$726$	−1.21032	−	1.36432i	−0.0449191	−	0.0506347i
$727$	−2.67732	+	1.54575i	−0.0992963	+	0.0573287i	−0.548826	−	0.835937i	$-0.684925\pi$
$727$	−2.67732	+	1.54575i	−0.0992963	+	0.0573287i	0.449530	+	0.893265i	$0.351592\pi$
$728$	−4.30243	−	25.5383i	−0.159459	−	0.946514i
$729$	17.2337	−	20.7846i	0.638285	−	0.769800i
$730$		0			0
$731$	−8.76780	−	15.1863i	−0.324289	−	0.561685i
$732$	11.2962	−	2.97710i	0.417520	−	0.110037i
$733$	−2.68614	+	4.65253i	−0.0992149	+	0.171845i	−0.911360	−	0.411610i	$-0.864966\pi$
$733$	−2.68614	+	4.65253i	−0.0992149	+	0.171845i	0.812145	+	0.583456i	$0.198300\pi$
$734$	−16.0676	+	10.5094i	−0.593065	+	0.387908i
$735$		0			0
$736$	−2.95675	+	11.8044i	−0.108987	+	0.435117i
$737$		−	23.8063i		−	0.876916i
$738$	−0.213653	−	0.588083i	−0.00786466	−	0.0216476i
$739$			9.66181i			0.355415i	0.984083	+	0.177708i	$0.0568681\pi$
$739$			9.66181i			0.355415i	−0.984083	+	0.177708i	$0.943132\pi$
$740$		0			0
$741$	10.1168	−	8.01544i	0.371652	−	0.294455i
$742$	−17.8928	−	27.3560i	−0.656865	−	1.00427i
$743$	−22.5132	+	38.9940i	−0.825929	+	1.43055i	0.0752776	+	0.997163i	$0.476016\pi$
$743$	−22.5132	+	38.9940i	−0.825929	+	1.43055i	−0.901207	+	0.433389i	$0.857318\pi$
$744$	−5.59223	+	6.20038i	−0.205021	+	0.227317i
$745$		0			0
$746$	5.65278	−	11.1846i	0.206963	−	0.409497i
$747$	−4.97760	+	21.1866i	−0.182121	+	0.775178i
$748$	−13.9307	+	10.2613i	−0.509357	+	0.375190i
$749$	−31.1168	+	17.9653i	−1.13698	+	0.656438i
$750$		0			0
$751$	39.9743	+	23.0792i	1.45868	+	0.842170i	0.998947	−	0.0458859i	$-0.0146111\pi$
$751$	39.9743	+	23.0792i	1.45868	+	0.842170i	0.459735	+	0.888056i	$0.347944\pi$
$752$	31.3796	+	33.9458i	1.14430	+	1.23788i
$753$	−10.6753	+	26.9480i	−0.389028	+	0.982039i
$754$	0.210106	+	3.77267i	0.00765160	+	0.137393i
$755$		0			0
$756$	13.4454	−	24.8078i	0.489003	−	0.902252i
$757$	−14.0000			−0.508839			−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000			−0.508839			−0.254419	+	0.967094i	$0.581884\pi$
$758$	−0.759784	−	13.6427i	−0.0275966	−	0.495526i
$759$	4.70285	−	11.8716i	0.170703	−	0.430912i
$760$		0			0
$761$	−16.5475	−	9.55373i	−0.599848	−	0.346322i	0.169134	−	0.985593i	$-0.445903\pi$
$761$	−16.5475	−	9.55373i	−0.599848	−	0.346322i	−0.768982	+	0.639271i	$0.779236\pi$
$762$	37.8599	+	12.6112i	1.37152	+	0.456857i
$763$	−22.3130	+	12.8824i	−0.807784	+	0.466375i
$764$	−4.62832	−	6.28339i	−0.167447	−	0.227325i
$765$		0			0
$766$	−0.255437	+	0.505408i	−0.00922933	+	0.0182611i
$767$	8.73053	+	15.1217i	0.315241	+	0.546014i
$768$	1.88012	+	27.6490i	0.0678428	+	0.997696i
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.397285	−	0.917695i	$-0.369952\pi$
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.596105	−	0.802907i	$-0.296714\pi$
$770$		0			0
$771$	−15.6591	+	12.4065i	−0.563950	+	0.446810i
$772$	−3.00124	+	6.86146i	−0.108017	+	0.246949i
$773$		−	45.7330i		−	1.64490i	−0.568835	−	0.822451i	$-0.692606\pi$
$773$		−	45.7330i		−	1.64490i	0.568835	−	0.822451i	$-0.307394\pi$
$774$	29.0212	+	5.13485i	1.04315	+	0.184568i
$775$		0			0
$776$	−22.4991	−	27.2327i	−0.807669	−	0.977596i
$777$	−3.25544	−	22.0742i	−0.116788	−	0.791909i
$778$	9.83561	−	6.43320i	0.352624	−	0.230642i
$779$	0.162946	−	0.282231i	0.00583815	−	0.0101120i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−6.85407	−	3.46410i	−0.245101	−	0.123876i
$783$	−2.35143	+	3.37923i	−0.0840332	+	0.120764i
$784$	0.441578	−	1.42215i	0.0157706	−	0.0507910i
$785$		0			0
$786$	−11.7925	−	13.2930i	−0.420624	−	0.474145i
$787$	−17.0095	−	9.82043i	−0.606323	−	0.350061i	0.165202	−	0.986260i	$-0.447172\pi$
$787$	−17.0095	−	9.82043i	−0.606323	−	0.350061i	−0.771525	+	0.636199i	$0.780506\pi$
$788$	−2.37340	−	21.2423i	−0.0845488	−	0.756727i
$789$	21.4307	−	3.16053i	0.762953	−	0.112518i
$790$		0			0
$791$	−43.2756			−1.53870
$792$	1.85557	−	29.0201i	0.0659347	−	1.03118i
$793$	−11.3723			−0.403842
$794$	10.2449	−	0.570552i	0.363577	−	0.0202481i
$795$		0			0
$796$	−4.29134	−	38.4082i	−0.152102	−	1.36134i
$797$	−40.8030	−	23.5576i	−1.44532	−	0.834454i	−0.447119	−	0.894475i	$-0.647550\pi$
$797$	−40.8030	−	23.5576i	−1.44532	−	0.834454i	−0.998197	+	0.0600211i	$0.980883\pi$
$798$	14.3979	−	2.94943i	0.509682	−	0.104409i
$799$	−25.2651	+	14.5868i	−0.893814	+	0.516043i
$800$		0			0
$801$	−10.9783	+	11.6819i	−0.387897	+	0.412761i
$802$	−27.6753	−	13.9873i	−0.977248	−	0.493909i
$803$	4.06494	+	7.04069i	0.143449	+	0.248461i
$804$	17.0854	−	16.9456i	0.602557	−	0.597625i
$805$		0			0
$806$	6.80251	−	4.44934i	0.239608	−	0.156721i
$807$	−40.1745	−	15.9149i	−1.41421	−	0.560230i
$808$	38.8520	−	32.0987i	1.36681	−	1.12923i
$809$		−	27.1778i		−	0.955521i	−0.878490	−	0.477760i	$-0.841449\pi$
$809$		−	27.1778i		−	0.955521i	0.878490	−	0.477760i	$-0.158551\pi$
$810$		0			0
$811$		−	25.9530i		−	0.911332i	−0.890151	−	0.455666i	$-0.849401\pi$
$811$		−	25.9530i		−	0.911332i	0.890151	−	0.455666i	$-0.150599\pi$
$812$	−1.72418	+	3.94184i	−0.0605068	+	0.138331i
$813$	2.23369	+	0.884861i	0.0783389	+	0.0310334i
$814$	−12.5869	−	19.2440i	−0.441172	−	0.674500i
$815$		0			0
$816$	−17.2804	−	2.69377i	−0.604936	−	0.0943009i
$817$	7.67527	+	13.2940i	0.268524	+	0.465096i
$818$	−1.43877	+	2.84674i	−0.0503053	+	0.0995340i
$819$	−18.8114	+	20.0172i	−0.657324	+	0.699457i
$820$		0			0
$821$	−18.6861	+	10.7884i	−0.652151	+	0.376519i	−0.789280	−	0.614034i	$-0.789546\pi$
$821$	−18.6861	+	10.7884i	−0.652151	+	0.376519i	0.137129	+	0.990553i	$0.456213\pi$
$822$	9.22071	+	45.0118i	0.321609	+	1.56997i
$823$	−25.8657	−	14.9336i	−0.901622	−	0.520552i	−0.0238957	−	0.999714i	$-0.507607\pi$
$823$	−25.8657	−	14.9336i	−0.901622	−	0.520552i	−0.877726	+	0.479163i	$0.840940\pi$
$824$	38.6607	+	14.4064i	1.34681	+	0.501870i
$825$		0			0
$826$	1.10555	+	19.8514i	0.0384671	+	0.690717i
$827$	7.00314			0.243523			0.121762	−	0.992559i	$-0.461146\pi$
$827$	7.00314			0.243523			0.121762	+	0.992559i	$0.461146\pi$
$828$	11.8676	−	5.07516i	0.412429	−	0.176374i
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$		0			0
$831$	−1.07561	+	0.158627i	−0.0373124	+	0.00550271i
$832$	5.08964	−	26.4938i	0.176451	−	0.918507i
$833$	0.813859	+	0.469882i	0.0281986	+	0.0162804i
$834$	17.1228	−	15.1900i	0.592913	−	0.525986i
$835$		0			0
$836$	12.1948	−	8.98266i	0.421767	−	0.310672i
$837$	8.82473	+	0.746000i	0.305027	+	0.0257855i
$838$	3.60597	−	7.13477i	0.124566	−	0.246466i
$839$	−22.8391	−	39.5585i	−0.788493	−	1.36571i	−0.926890	−	0.375333i	$-0.877528\pi$
$839$	−22.8391	−	39.5585i	−0.788493	−	1.36571i	0.138397	−	0.990377i	$-0.455805\pi$
$840$		0			0
$841$	−14.1861	+	24.5711i	−0.489177	+	0.847280i
$842$	−22.9184	−	35.0396i	−0.789821	−	1.20754i
$843$	−1.62511	−	11.0194i	−0.0559717	−	0.379528i
$844$	11.2214	+	4.90829i	0.386256	+	0.168950i
$845$		0			0
$846$	8.54274	−	48.2819i	0.293705	−	1.65997i
$847$			2.02163i			0.0694641i
$848$	−7.51522	−	33.2114i	−0.258074	−	1.14049i
$849$	−13.8030	+	10.9359i	−0.473717	+	0.375320i
$850$		0			0
$851$	5.10328	−	8.83915i	0.174938	−	0.303002i
$852$	−1.59377	+	5.85174i	−0.0546018	+	0.200477i
$853$	2.19702	+	3.80534i	0.0752244	+	0.130292i	0.901184	−	0.433437i	$-0.142699\pi$
$853$	2.19702	+	3.80534i	0.0752244	+	0.130292i	−0.825959	+	0.563730i	$0.809366\pi$
$854$	−11.5569	−	5.84096i	−0.395470	−	0.199874i
$855$		0			0
$856$	−36.9090	+	6.21803i	−1.26152	+	0.212528i
$857$	22.0367	−	12.7229i	0.752758	−	0.434605i	−0.0739313	−	0.997263i	$-0.523555\pi$
$857$	22.0367	−	12.7229i	0.752758	−	0.434605i	0.826690	+	0.562658i	$0.190221\pi$
$858$	−8.94639	+	26.8577i	−0.305425	+	0.916907i
$859$	30.4056	+	17.5547i	1.03743	+	0.598958i	0.919103	−	0.394017i	$-0.128915\pi$
$859$	30.4056	+	17.5547i	1.03743	+	0.598958i	0.118323	+	0.992975i	$0.462248\pi$
$860$		0			0
$861$	−0.255437	+	0.644810i	−0.00870528	+	0.0219751i
$862$	−20.6976	+	1.15268i	−0.704962	+	0.0392604i
$863$	4.15335			0.141382			0.0706909	−	0.997498i	$-0.477480\pi$
$863$	4.15335			0.141382			0.0706909	+	0.997498i	$0.477480\pi$
$864$	22.1481	−	19.3251i	0.753495	−	0.657454i
$865$		0			0
$866$	20.2940	−	1.13021i	0.689619	−	0.0384059i
$867$	−6.77953	+	17.1138i	−0.230245	+	0.581216i
$868$	9.19820	−	1.02771i	0.312207	−	0.0348828i
$869$	−30.1753	−	17.4217i	−1.02363	−	0.590991i
$870$		0			0
$871$	−20.2875	+	11.7130i	−0.687414	+	0.396879i
$872$	−26.4663	+	4.45877i	−0.896264	+	0.150993i
$873$	−8.56930	+	36.4743i	−0.290027	+	1.23447i
$874$	6.00000	+	3.03245i	0.202953	+	0.102574i
$875$		0			0
$876$	−2.15953	+	7.92900i	−0.0729639	+	0.267896i
$877$	13.6861	−	23.7051i	0.462148	−	0.800464i	−0.536920	−	0.843633i	$-0.680412\pi$
$877$	13.6861	−	23.7051i	0.462148	−	0.800464i	0.999068	+	0.0431693i	$0.0137455\pi$
$878$	38.9377	−	25.4681i	1.31408	−	0.859506i
$879$	−27.1415	+	21.5039i	−0.915461	+	0.725308i
$880$		0			0
$881$			19.7899i			0.666740i	0.942796	+	0.333370i	$0.108186\pi$
$881$			19.7899i			0.666740i	−0.942796	+	0.333370i	$0.891814\pi$
$882$	−1.48452	+	0.539331i	−0.0499864	+	0.0181602i
$883$			34.7921i			1.17085i	0.810727	+	0.585424i	$0.199072\pi$
$883$			34.7921i			1.17085i	−0.810727	+	0.585424i	$0.800928\pi$
$884$	15.5986	+	6.82292i	0.524639	+	0.229480i
$885$		0			0
$886$	−4.00823	−	6.12811i	−0.134659	−	0.205878i
$887$	2.75186	−	4.76635i	0.0923983	−	0.160039i	−0.816122	−	0.577880i	$-0.803880\pi$
$887$	2.75186	−	4.76635i	0.0923983	−	0.160039i	0.908520	+	0.417842i	$0.137213\pi$
$888$	4.85160	−	22.7315i	0.162809	−	0.762821i
$889$	−22.1168	−	38.3075i	−0.741775	−	1.28479i
$890$		0			0
$891$	−25.7028	+	17.0493i	−0.861075	+	0.571172i
$892$	−2.74456	+	2.02163i	−0.0918948	+	0.0676893i
$893$	22.1168	−	12.7692i	0.740112	−	0.427304i
$894$	17.5909	−	15.6052i	0.588327	−	0.521917i
$895$		0			0
$896$	18.7799	−	24.3099i	0.627391	−	0.812135i
$897$	−12.4307	+	1.83324i	−0.415049	+	0.0612101i
$898$	−0.299921	−	5.38541i	−0.0100085	−	0.179713i
$899$	−1.35036			−0.0450369
$900$		0			0
$901$	21.4891			0.715907
$902$	0.0397442	+	0.713649i	0.00132334	+	0.0237619i
$903$	−20.2875	−	25.6062i	−0.675124	−	0.852121i
$904$	−42.2428	−	15.7412i	−1.40497	−	0.523544i
$905$		0			0
$906$	4.50103	+	21.9722i	0.149537	+	0.729978i
$907$	−21.3258	+	12.3125i	−0.708111	+	0.408828i	−0.810361	−	0.585930i	$-0.800729\pi$
$907$	−21.3258	+	12.3125i	−0.708111	+	0.408828i	0.102250	+	0.994759i	$0.467396\pi$
$908$	22.4014	+	30.4121i	0.743417	+	1.00926i
$909$	−52.0367	−	12.2255i	−1.72595	−	0.405496i
$910$		0			0
$911$	6.57932	+	11.3957i	0.217983	+	0.377557i	0.954191	−	0.299198i	$-0.0967191\pi$
$911$	6.57932	+	11.3957i	0.217983	+	0.377557i	−0.736209	+	0.676755i	$0.763386\pi$
$912$	15.1272	+	2.35811i	0.500910	+	0.0780848i
$913$	12.4307	−	21.5306i	0.411396	−	0.712559i
$914$	−4.62785	−	7.07545i	−0.153076	−	0.234035i
$915$		0			0
$916$	−7.51180	+	17.1736i	−0.248197	+	0.567431i
$917$			19.6974i			0.650464i
$918$	8.81018	+	16.3243i	0.290779	+	0.538783i
$919$			46.0993i			1.52067i	0.649529	+	0.760337i	$0.274966\pi$
$919$			46.0993i			1.52067i	−0.649529	+	0.760337i	$0.725034\pi$
$920$		0			0
$921$	41.7921	+	16.5557i	1.37710	+	0.545528i
$922$	−27.0632	+	17.7013i	−0.891280	+	0.582962i
$923$	2.95207	−	5.11313i	0.0971686	−	0.168301i
$924$	−22.8861	+	22.6988i	−0.752899	+	0.746735i
$925$		0			0
$926$	−26.5409	−	13.4140i	−0.872187	−	0.440811i
$927$	−12.6325	−	41.8974i	−0.414907	−	1.37609i
$928$	−3.11684	+	3.22060i	−0.102315	+	0.105721i
$929$	30.4307	−	17.5692i	0.998399	−	0.576426i	0.0906248	−	0.995885i	$-0.471114\pi$
$929$	30.4307	−	17.5692i	0.998399	−	0.576426i	0.907774	+	0.419459i	$0.137780\pi$
$930$		0			0
$931$	−0.712446	−	0.411331i	−0.0233495	−	0.0134808i
$932$	6.23208	+	55.7783i	0.204139	+	1.82708i
$933$	−33.6861	−	42.5176i	−1.10283	−	1.39196i
$934$	34.4388	−	1.91795i	1.12687	−	0.0627573i
$935$		0			0
$936$	−25.6436	+	12.6969i	−0.838186	+	0.415012i
$937$	11.7228			0.382968			0.191484	−	0.981496i	$-0.438670\pi$
$937$	11.7228			0.382968			0.191484	+	0.981496i	$0.438670\pi$
$938$	−26.6328	+	1.48322i	−0.869591	+	0.0484289i
$939$	−7.69219	+	1.13442i	−0.251025	+	0.0370204i
$940$		0			0
$941$	31.8030	+	18.3615i	1.03675	+	0.598567i	0.918910	−	0.394466i	$-0.129071\pi$
$941$	31.8030	+	18.3615i	1.03675	+	0.598567i	0.117837	+	0.993033i	$0.462404\pi$
$942$	−27.4089	−	30.8965i	−0.893031	−	1.00666i
$943$	−0.274750	+	0.158627i	−0.00894709	+	0.00516561i
$944$	−6.14162	+	19.7797i	−0.199893	+	0.643775i
$945$		0			0
$946$	−30.0475	−	15.1863i	−0.976930	−	0.493748i
$947$	−22.2757	−	38.5827i	−0.723864	−	1.25377i	−0.959440	−	0.281913i	$-0.909031\pi$
$947$	−22.2757	−	38.5827i	−0.723864	−	1.25377i	0.235576	−	0.971856i	$-0.424302\pi$
$948$	−8.97578	−	34.0573i	−0.291520	−	1.10613i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$	−6.02982	−	40.8865i	−0.195530	−	1.32584i
$952$	12.3475	+	14.9454i	0.400186	+	0.484382i
$953$			32.8164i			1.06303i	0.847050	+	0.531514i	$0.178377\pi$
$953$			32.8164i			1.06303i	−0.847050	+	0.531514i	$0.821623\pi$
$954$	−23.2316	+	27.6533i	−0.752152	+	0.895308i
$955$		0			0
$956$	−13.3530	+	30.5278i	−0.431867	+	0.987340i
$957$	3.68614	−	2.92048i	0.119156	−	0.0944058i
$958$	−7.59108	−	11.6059i	−0.245257	−	0.374969i
$959$	25.4653	−	44.1071i	0.822317	−	1.42429i
$960$		0			0
$961$	−14.0475	−	24.3311i	−0.453147	−	0.784873i
$962$	−10.2066	+	20.1947i	−0.329073	+	0.651103i
$963$	28.9296	+	27.1870i	0.932243	+	0.876088i
$964$	−19.5584	−	26.5525i	−0.629934	−	0.855197i
$965$		0			0
$966$	−13.5741	−	4.52158i	−0.436740	−	0.145479i
$967$	48.7282	+	28.1332i	1.56699	+	0.904704i	0.996517	+	0.0833895i	$0.0265746\pi$
$967$	48.7282	+	28.1332i	1.56699	+	0.904704i	0.570476	+	0.821314i	$0.306759\pi$
$968$	−0.735354	+	1.97338i	−0.0236352	+	0.0634270i
$969$	−3.55842	+	8.98266i	−0.114313	+	0.288565i
$970$		0			0
$971$	−24.7156			−0.793160			−0.396580	−	0.918000i	$-0.629803\pi$
$971$	−24.7156			−0.793160			−0.396580	+	0.918000i	$0.629803\pi$
$972$	−30.5316	−	6.31065i	−0.979300	−	0.202414i
$973$	−25.3723			−0.813398
$974$	1.41049	+	25.3268i	0.0451949	+	0.811523i
$975$		0			0
$976$	−9.15649	−	9.90531i	−0.293092	−	0.317061i
$977$	18.6386	+	10.7610i	0.596301	+	0.344275i	0.767585	−	0.640947i	$-0.221458\pi$
$977$	18.6386	+	10.7610i	0.596301	+	0.344275i	−0.171284	+	0.985222i	$0.554791\pi$
$978$	27.5890	+	9.18998i	0.882199	+	0.293863i
$979$	15.8593	−	9.15640i	0.506867	−	0.292640i
$980$		0			0
$981$	20.7446	+	19.4950i	0.662323	+	0.622427i
$982$	15.8139	−	31.2893i	0.504641	−	0.998481i
$983$	8.40464	+	14.5573i	0.268066	+	0.464305i	0.968362	−	0.249548i	$-0.0802820\pi$
$983$	8.40464	+	14.5573i	0.268066	+	0.464305i	−0.700296	+	0.713852i	$0.746949\pi$
$984$	−0.483886	+	0.536507i	−0.0154257	+	0.0171032i
$985$		0			0
$986$	−1.54823	−	2.36706i	−0.0493057	−	0.0753826i
$987$	−42.6004	+	33.7518i	−1.35599	+	1.07433i
$988$	−13.6549	−	5.97273i	−0.434421	−	0.190018i
$989$		−	14.9436i		−	0.475180i
$990$		0			0
$991$		−	16.2912i		−	0.517506i	−0.965944	−	0.258753i	$-0.916688\pi$
$991$		−	16.2912i		−	0.517506i	0.965944	−	0.258753i	$-0.0833116\pi$
$992$	9.35250	+	2.34260i	0.296942	+	0.0743775i
$993$	−7.03667	−	47.7138i	−0.223302	−	1.51415i
$994$	5.62618	−	3.67993i	0.178452	−	0.116720i
$995$		0			0
$996$	24.3005	−	6.40438i	0.769992	−	0.202931i
$997$	−26.4307	−	45.7793i	−0.837069	−	1.44985i	−0.892335	−	0.451374i	$-0.850934\pi$
$997$	−26.4307	−	45.7793i	−0.837069	−	1.44985i	0.0552661	−	0.998472i	$-0.482399\pi$
$998$	−0.637910	−	0.322405i	−0.0201927	−	0.0102056i
$999$	−22.3130	+	10.4845i	−0.705952	+	0.331714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.c.851.4		8
4.3	odd	2	inner	900.2.r.c.851.3		8
5.2	odd	4		900.2.o.a.599.5		16
5.3	odd	4		900.2.o.a.599.4		16
5.4	even	2		36.2.h.a.23.1	yes	8
9.2	odd	6	inner	900.2.r.c.551.3		8
15.14	odd	2		108.2.h.a.71.4		8
20.3	even	4		900.2.o.a.599.2		16
20.7	even	4		900.2.o.a.599.7		16
20.19	odd	2		36.2.h.a.23.2	yes	8
36.11	even	6	inner	900.2.r.c.551.4		8
40.19	odd	2		576.2.s.f.383.3		8
40.29	even	2		576.2.s.f.383.2		8
45.2	even	12		900.2.o.a.299.2		16
45.4	even	6		324.2.b.b.323.5		8
45.14	odd	6		324.2.b.b.323.4		8
45.29	odd	6		36.2.h.a.11.2	yes	8
45.34	even	6		108.2.h.a.35.3		8
45.38	even	12		900.2.o.a.299.7		16
60.59	even	2		108.2.h.a.71.3		8
120.29	odd	2		1728.2.s.f.1151.3		8
120.59	even	2		1728.2.s.f.1151.4		8
180.47	odd	12		900.2.o.a.299.4		16
180.59	even	6		324.2.b.b.323.6		8
180.79	odd	6		108.2.h.a.35.4		8
180.83	odd	12		900.2.o.a.299.5		16
180.119	even	6		36.2.h.a.11.1	✓	8
180.139	odd	6		324.2.b.b.323.3		8
360.29	odd	6		576.2.s.f.191.3		8
360.59	even	6		5184.2.c.j.5183.4		8
360.139	odd	6		5184.2.c.j.5183.6		8
360.149	odd	6		5184.2.c.j.5183.3		8
360.229	even	6		5184.2.c.j.5183.5		8
360.259	odd	6		1728.2.s.f.575.3		8
360.299	even	6		576.2.s.f.191.2		8
360.349	even	6		1728.2.s.f.575.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.1	✓	8	180.119	even	6
36.2.h.a.11.2	yes	8	45.29	odd	6
36.2.h.a.23.1	yes	8	5.4	even	2
36.2.h.a.23.2	yes	8	20.19	odd	2
108.2.h.a.35.3		8	45.34	even	6
108.2.h.a.35.4		8	180.79	odd	6
108.2.h.a.71.3		8	60.59	even	2
108.2.h.a.71.4		8	15.14	odd	2
324.2.b.b.323.3		8	180.139	odd	6
324.2.b.b.323.4		8	45.14	odd	6
324.2.b.b.323.5		8	45.4	even	6
324.2.b.b.323.6		8	180.59	even	6
576.2.s.f.191.2		8	360.299	even	6
576.2.s.f.191.3		8	360.29	odd	6
576.2.s.f.383.2		8	40.29	even	2
576.2.s.f.383.3		8	40.19	odd	2
900.2.o.a.299.2		16	45.2	even	12
900.2.o.a.299.4		16	180.47	odd	12
900.2.o.a.299.5		16	180.83	odd	12
900.2.o.a.299.7		16	45.38	even	12
900.2.o.a.599.2		16	20.3	even	4
900.2.o.a.599.4		16	5.3	odd	4
900.2.o.a.599.5		16	5.2	odd	4
900.2.o.a.599.7		16	20.7	even	4
900.2.r.c.551.3		8	9.2	odd	6	inner
900.2.r.c.551.4		8	36.11	even	6	inner
900.2.r.c.851.3		8	4.3	odd	2	inner
900.2.r.c.851.4		8	1.1	even	1	trivial
1728.2.s.f.575.3		8	360.259	odd	6
1728.2.s.f.575.4		8	360.349	even	6
1728.2.s.f.1151.3		8	120.29	odd	2
1728.2.s.f.1151.4		8	120.59	even	2
5184.2.c.j.5183.3		8	360.149	odd	6
5184.2.c.j.5183.4		8	360.59	even	6
5184.2.c.j.5183.5		8	360.229	even	6
5184.2.c.j.5183.6		8	360.139	odd	6

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41203 - 0.0786378i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(1.98763 - 0.222077i) q^{4} +(-0.774115 + 2.32395i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +O(q^{10})\)	\(q+(1.41203 - 0.0786378i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(1.98763 - 0.222077i) q^{4} +(-0.774115 + 2.32395i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 - 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +(1.71352 + 2.96790i) q^{11} +(-0.910320 + 3.34235i) q^{12} +(1.68614 - 2.92048i) q^{13} +(3.21352 - 2.10187i) q^{14} +(3.90136 - 0.882816i) q^{16} +2.52434i q^{17} +(-3.24844 - 2.72903i) q^{18} -2.20979i q^{19} +(0.686141 + 4.65253i) q^{21} +(2.65292 + 4.05600i) q^{22} +(-1.07561 + 1.86301i) q^{23} +(-1.02256 + 4.79107i) q^{24} +(2.15121 - 4.25639i) q^{26} +(4.70285 - 2.20979i) q^{27} +(4.37228 - 3.22060i) q^{28} +(-0.686141 + 0.396143i) q^{29} +(1.47603 + 0.852189i) q^{31} +(5.43940 - 1.55335i) q^{32} +(-5.87228 + 0.866025i) q^{33} +(0.198508 + 3.56443i) q^{34} +(-4.80149 - 3.59801i) q^{36} -4.74456 q^{37} +(-0.173773 - 3.12027i) q^{38} +(3.62725 + 4.57820i) q^{39} +(0.127719 + 0.0737384i) q^{41} +(1.33471 + 6.51554i) q^{42} +(-6.01594 + 3.47331i) q^{43} +(4.06494 + 5.51856i) q^{44} +(-1.37228 + 2.71519i) q^{46} +(5.77846 + 10.0086i) q^{47} +(-1.06712 + 6.84553i) q^{48} +(0.186141 - 0.322405i) q^{49} +(-4.06494 - 1.61030i) q^{51} +(2.70285 - 6.17930i) q^{52} -8.51278i q^{53} +(6.46678 - 3.49010i) q^{54} +(5.92051 - 4.89140i) q^{56} +(3.55842 + 1.40965i) q^{57} +(-0.937696 + 0.613321i) q^{58} +(-2.58891 + 4.48412i) q^{59} +(-1.68614 - 2.92048i) q^{61} +(2.15121 + 1.08724i) q^{62} +(-7.92967 - 1.86301i) q^{63} +(7.55842 - 2.62112i) q^{64} +(-8.22371 + 1.68463i) q^{66} +(-6.01594 - 3.47331i) q^{67} +(0.560598 + 5.01746i) q^{68} +(-2.31386 - 2.92048i) q^{69} +1.75079 q^{71} +(-7.06277 - 4.70290i) q^{72} +2.37228 q^{73} +(-6.69944 + 0.373102i) q^{74} +(-0.490743 - 4.39224i) q^{76} +(8.05842 + 4.65253i) q^{77} +(5.48179 + 6.17930i) q^{78} +(-8.80507 + 5.08361i) q^{79} +(0.558422 + 8.98266i) q^{81} +(0.186141 + 0.0940770i) q^{82} +(-3.62725 - 6.28258i) q^{83} +(2.39702 + 9.09515i) q^{84} +(-8.22153 + 5.37748i) q^{86} +(-0.200214 - 1.35760i) q^{87} +(6.17377 + 7.47269i) q^{88} -5.34363i q^{89} -9.15640i q^{91} +(-1.72418 + 3.94184i) q^{92} +(-2.31386 + 1.83324i) q^{93} +(8.94639 + 13.6780i) q^{94} +(-0.968484 + 9.74998i) q^{96} +(-6.24456 - 10.8159i) q^{97} +(0.237482 - 0.469882i) q^{98} +(2.35143 - 10.0086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{4} - 3 q^{6} - 6 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - q^4 - 3 * q^6 - 6 * q^9	\( 8 q + 3 q^{2} - q^{4} - 3 q^{6} - 6 q^{9} - 6 q^{12} + 2 q^{13} + 12 q^{14} - q^{16} - 18 q^{18} - 6 q^{21} - 3 q^{22} + 3 q^{24} + 12 q^{28} + 6 q^{29} + 33 q^{32} - 24 q^{33} + 7 q^{34} - 33 q^{36} + 8 q^{37} + 27 q^{38} + 24 q^{41} + 18 q^{42} + 12 q^{46} - 21 q^{48} - 10 q^{49} - 16 q^{52} + 39 q^{54} + 18 q^{56} - 6 q^{57} - 4 q^{58} - 2 q^{61} + 26 q^{64} - 24 q^{66} + 15 q^{68} - 30 q^{69} + 21 q^{72} - 4 q^{73} - 30 q^{74} - 3 q^{76} + 30 q^{77} + 12 q^{78} - 30 q^{81} - 10 q^{82} + 30 q^{84} + 21 q^{86} + 21 q^{88} - 24 q^{92} - 30 q^{93} - 18 q^{94} + 12 q^{96} - 4 q^{97}+O(q^{100}) \) 8 * q + 3 * q^2 - q^4 - 3 * q^6 - 6 * q^9 - 6 * q^12 + 2 * q^13 + 12 * q^14 - q^16 - 18 * q^18 - 6 * q^21 - 3 * q^22 + 3 * q^24 + 12 * q^28 + 6 * q^29 + 33 * q^32 - 24 * q^33 + 7 * q^34 - 33 * q^36 + 8 * q^37 + 27 * q^38 + 24 * q^41 + 18 * q^42 + 12 * q^46 - 21 * q^48 - 10 * q^49 - 16 * q^52 + 39 * q^54 + 18 * q^56 - 6 * q^57 - 4 * q^58 - 2 * q^61 + 26 * q^64 - 24 * q^66 + 15 * q^68 - 30 * q^69 + 21 * q^72 - 4 * q^73 - 30 * q^74 - 3 * q^76 + 30 * q^77 + 12 * q^78 - 30 * q^81 - 10 * q^82 + 30 * q^84 + 21 * q^86 + 21 * q^88 - 24 * q^92 - 30 * q^93 - 18 * q^94 + 12 * q^96 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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