LMFDB - Embedded newform 605.2.g.q.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	605.251
Dual form			605.2.g.q.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.424181 + 1.30550i) q^{2} +(-2.63885 + 1.91724i) q^{3} +(0.0936432 + 0.0680358i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.38360 - 4.25827i) q^{6} +(-1.11052 - 0.806841i) q^{7} +(-2.34959 + 1.70707i) q^{8} +(2.36069 - 7.26546i) q^{9} +O(q^{10})$	\(q+(-0.424181 + 1.30550i) q^{2} +(-2.63885 + 1.91724i) q^{3} +(0.0936432 + 0.0680358i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.38360 - 4.25827i) q^{6} +(-1.11052 - 0.806841i) q^{7} +(-2.34959 + 1.70707i) q^{8} +(2.36069 - 7.26546i) q^{9} -1.37268 q^{10} -0.377552 q^{12} +(0.597186 - 1.83795i) q^{13} +(1.52439 - 1.10753i) q^{14} +(-2.63885 - 1.91724i) q^{15} +(-1.16039 - 3.57132i) q^{16} +(-1.91883 - 5.90555i) q^{17} +(8.48367 + 6.16374i) q^{18} +(0.657590 - 0.477767i) q^{19} +(-0.0357685 + 0.110084i) q^{20} +4.47741 q^{21} -3.63935 q^{23} +(2.92734 - 9.00943i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.14612 + 1.55925i) q^{26} +(4.67625 + 14.3920i) q^{27} +(-0.0490987 - 0.151110i) q^{28} +(-6.33874 - 4.60536i) q^{29} +(3.62230 - 2.63176i) q^{30} +(-1.05309 + 3.24106i) q^{31} -0.653939 q^{32} +8.52360 q^{34} +(0.424181 - 1.30550i) q^{35} +(0.715374 - 0.519749i) q^{36} +(3.65967 + 2.65891i) q^{37} +(0.344786 + 1.06114i) q^{38} +(1.94790 + 5.99503i) q^{39} +(-2.34959 - 1.70707i) q^{40} +(1.47737 - 1.07338i) q^{41} +(-1.89923 + 5.84524i) q^{42} +6.46243 q^{43} +7.63935 q^{45} +(1.54375 - 4.75116i) q^{46} +(-3.83328 + 2.78504i) q^{47} +(9.90917 + 7.19943i) q^{48} +(-1.58085 - 4.86537i) q^{49} +(-0.424181 - 1.30550i) q^{50} +(16.3859 + 11.9050i) q^{51} +(0.180969 - 0.131482i) q^{52} +(-2.59403 + 7.98360i) q^{53} -20.7723 q^{54} +3.98660 q^{56} +(-0.819289 + 2.52151i) q^{57} +(8.70106 - 6.32169i) q^{58} +(-0.902660 - 0.655821i) q^{59} +(-0.116670 - 0.359073i) q^{60} +(0.786410 + 2.42032i) q^{61} +(-3.78450 - 2.74960i) q^{62} +(-8.48367 + 6.16374i) q^{63} +(2.59817 - 7.99635i) q^{64} +1.93253 q^{65} +2.73820 q^{67} +(0.222103 - 0.683564i) q^{68} +(9.60372 - 6.97751i) q^{69} +(1.52439 + 1.10753i) q^{70} +(-0.344786 - 1.06114i) q^{71} +(6.85603 + 21.1007i) q^{72} +(-10.0471 - 7.29966i) q^{73} +(-5.02356 + 3.64983i) q^{74} +(1.00795 - 3.10216i) q^{75} +0.0940841 q^{76} -8.65275 q^{78} +(-1.79492 + 5.52421i) q^{79} +(3.03794 - 2.20719i) q^{80} +(-21.3918 - 15.5420i) q^{81} +(0.774613 + 2.38401i) q^{82} +(-4.93720 - 15.1951i) q^{83} +(0.419279 + 0.304624i) q^{84} +(5.02356 - 3.64983i) q^{85} +(-2.74124 + 8.43668i) q^{86} +25.5566 q^{87} -2.70789 q^{89} +(-3.24047 + 9.97315i) q^{90} +(-2.14612 + 1.55925i) q^{91} +(-0.340801 - 0.247606i) q^{92} +(-3.43496 - 10.5717i) q^{93} +(-2.00986 - 6.18570i) q^{94} +(0.657590 + 0.477767i) q^{95} +(1.72565 - 1.25376i) q^{96} +(4.37659 - 13.4698i) q^{97} +7.02229 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.424181	+	1.30550i	−0.299942	+	0.923125i	0.681575	+	0.731748i	$0.261295\pi$
$2$	−0.424181	+	1.30550i	−0.299942	+	0.923125i	−0.981517	+	0.191377i	$0.938705\pi$
$3$	−2.63885	+	1.91724i	−1.52354	+	1.10692i	−0.563846	+	0.825880i	$0.690679\pi$
$3$	−2.63885	+	1.91724i	−1.52354	+	1.10692i	−0.959696	+	0.281039i	$0.909321\pi$
$4$	0.0936432	+	0.0680358i	0.0468216	+	0.0340179i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$	−1.38360	−	4.25827i	−0.564851	−	1.73843i
$7$	−1.11052	−	0.806841i	−0.419738	−	0.304957i	0.357795	−	0.933800i	$-0.383529\pi$
$7$	−1.11052	−	0.806841i	−0.419738	−	0.304957i	−0.777532	+	0.628843i	$0.783529\pi$
$8$	−2.34959	+	1.70707i	−0.830704	+	0.603542i
$9$	2.36069	−	7.26546i	0.786897	−	2.42182i
$10$	−1.37268			−0.434080
$11$		0			0
$11$		0			0
$12$	−0.377552			−0.108990
$13$	0.597186	−	1.83795i	0.165630	−	0.509756i	−0.833453	−	0.552591i	$-0.813639\pi$
$13$	0.597186	−	1.83795i	0.165630	−	0.509756i	0.999082	+	0.0428355i	$0.0136392\pi$
$14$	1.52439	−	1.10753i	0.407411	−	0.296001i
$15$	−2.63885	−	1.91724i	−0.681349	−	0.495029i
$16$	−1.16039	−	3.57132i	−0.290098	−	0.892829i
$17$	−1.91883	−	5.90555i	−0.465384	−	1.43231i	−0.858498	−	0.512816i	$-0.828602\pi$
$17$	−1.91883	−	5.90555i	−0.465384	−	1.43231i	0.393114	−	0.919490i	$-0.371398\pi$
$18$	8.48367	+	6.16374i	1.99962	+	1.45281i
$19$	0.657590	−	0.477767i	0.150861	−	0.109607i	−0.509794	−	0.860296i	$-0.670278\pi$
$19$	0.657590	−	0.477767i	0.150861	−	0.109607i	0.660656	+	0.750689i	$0.270278\pi$
$20$	−0.0357685	+	0.110084i	−0.00799809	+	0.0246156i
$21$	4.47741			0.977051
$22$		0			0
$23$	−3.63935			−0.758858			−0.379429	−	0.925221i	$-0.623880\pi$
$23$	−3.63935			−0.758858			−0.379429	+	0.925221i	$0.623880\pi$
$24$	2.92734	−	9.00943i	0.597541	−	1.83904i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	2.14612	+	1.55925i	0.420889	+	0.305794i
$27$	4.67625	+	14.3920i	0.899944	+	2.76974i
$28$	−0.0490987	−	0.151110i	−0.00927879	−	0.0285572i
$29$	−6.33874	−	4.60536i	−1.17707	−	0.855195i	−0.185236	−	0.982694i	$-0.559305\pi$
$29$	−6.33874	−	4.60536i	−1.17707	−	0.855195i	−0.991839	+	0.127500i	$0.959305\pi$
$30$	3.62230	−	2.63176i	0.661339	−	0.480491i
$31$	−1.05309	+	3.24106i	−0.189140	+	0.582112i	−0.999995	−	0.00313447i	$-0.999002\pi$
$31$	−1.05309	+	3.24106i	−0.189140	+	0.582112i	0.810855	+	0.585247i	$0.199002\pi$
$32$	−0.653939			−0.115601
$33$		0			0
$34$	8.52360			1.46179
$35$	0.424181	−	1.30550i	0.0716998	−	0.220669i
$36$	0.715374	−	0.519749i	0.119229	−	0.0866249i
$37$	3.65967	+	2.65891i	0.601647	+	0.437122i	0.846463	−	0.532448i	$-0.178728\pi$
$37$	3.65967	+	2.65891i	0.601647	+	0.437122i	−0.244816	+	0.969569i	$0.578728\pi$
$38$	0.344786	+	1.06114i	0.0559316	+	0.172140i
$39$	1.94790	+	5.99503i	0.311914	+	0.959973i
$40$	−2.34959	−	1.70707i	−0.371502	−	0.269912i
$41$	1.47737	−	1.07338i	0.230727	−	0.167633i	−0.466415	−	0.884566i	$-0.654455\pi$
$41$	1.47737	−	1.07338i	0.230727	−	0.167633i	0.697142	+	0.716933i	$0.254455\pi$
$42$	−1.89923	+	5.84524i	−0.293058	+	0.901941i
$43$	6.46243			0.985512			0.492756	−	0.870168i	$-0.335990\pi$
$43$	6.46243			0.985512			0.492756	+	0.870168i	$0.335990\pi$
$44$		0			0
$45$	7.63935			1.13881
$46$	1.54375	−	4.75116i	0.227613	−	0.700521i
$47$	−3.83328	+	2.78504i	−0.559142	+	0.406240i	−0.831145	−	0.556056i	$-0.812314\pi$
$47$	−3.83328	+	2.78504i	−0.559142	+	0.406240i	0.272003	+	0.962296i	$0.412314\pi$
$48$	9.90917	+	7.19943i	1.43027	+	1.03915i
$49$	−1.58085	−	4.86537i	−0.225836	−	0.695052i
$50$	−0.424181	−	1.30550i	−0.0599883	−	0.184625i
$51$	16.3859	+	11.9050i	2.29448	+	1.66704i
$52$	0.180969	−	0.131482i	0.0250959	−	0.0182332i
$53$	−2.59403	+	7.98360i	−0.356317	+	1.09663i	0.598924	+	0.800806i	$0.295595\pi$
$53$	−2.59403	+	7.98360i	−0.356317	+	1.09663i	−0.955242	+	0.295827i	$0.904405\pi$
$54$	−20.7723			−2.82675
$55$		0			0
$56$	3.98660			0.532732
$57$	−0.819289	+	2.52151i	−0.108518	+	0.333983i
$58$	8.70106	−	6.32169i	1.14251	−	0.830079i
$59$	−0.902660	−	0.655821i	−0.117516	−	0.0853806i	0.527475	−	0.849571i	$-0.323139\pi$
$59$	−0.902660	−	0.655821i	−0.117516	−	0.0853806i	−0.644991	+	0.764190i	$0.723139\pi$
$60$	−0.116670	−	0.359073i	−0.0150620	−	0.0463561i
$61$	0.786410	+	2.42032i	0.100689	+	0.309890i	0.988695	−	0.149943i	$-0.0479091\pi$
$61$	0.786410	+	2.42032i	0.100689	+	0.309890i	−0.888005	+	0.459834i	$0.847909\pi$
$62$	−3.78450	−	2.74960i	−0.480632	−	0.349199i
$63$	−8.48367	+	6.16374i	−1.06884	+	0.776559i
$64$	2.59817	−	7.99635i	0.324771	−	0.999543i
$65$	1.93253			0.239701
$66$		0			0
$67$	2.73820			0.334524			0.167262	−	0.985912i	$-0.446507\pi$
$67$	2.73820			0.334524			0.167262	+	0.985912i	$0.446507\pi$
$68$	0.222103	−	0.683564i	0.0269340	−	0.0828943i
$69$	9.60372	−	6.97751i	1.15615	−	0.839994i
$70$	1.52439	+	1.10753i	0.182200	+	0.132376i
$71$	−0.344786	−	1.06114i	−0.0409185	−	0.125934i	0.928511	−	0.371306i	$-0.121090\pi$
$71$	−0.344786	−	1.06114i	−0.0409185	−	0.125934i	−0.969429	+	0.245372i	$0.921090\pi$
$72$	6.85603	+	21.1007i	0.807991	+	2.48674i
$73$	−10.0471	−	7.29966i	−1.17593	−	0.854361i	−0.184220	−	0.982885i	$-0.558976\pi$
$73$	−10.0471	−	7.29966i	−1.17593	−	0.854361i	−0.991706	+	0.128524i	$0.958976\pi$
$74$	−5.02356	+	3.64983i	−0.583977	+	0.424284i
$75$	1.00795	−	3.10216i	0.116388	−	0.358206i
$76$	0.0940841			0.0107922
$77$		0			0
$78$	−8.65275			−0.979731
$79$	−1.79492	+	5.52421i	−0.201945	+	0.621522i	0.797880	+	0.602816i	$0.205955\pi$
$79$	−1.79492	+	5.52421i	−0.201945	+	0.621522i	−0.999825	+	0.0187059i	$0.994045\pi$
$80$	3.03794	−	2.20719i	0.339652	−	0.246772i
$81$	−21.3918	−	15.5420i	−2.37686	−	1.72689i
$82$	0.774613	+	2.38401i	0.0855416	+	0.263270i
$83$	−4.93720	−	15.1951i	−0.541928	−	1.66788i	−0.728184	−	0.685381i	$-0.759635\pi$
$83$	−4.93720	−	15.1951i	−0.541928	−	1.66788i	0.186256	−	0.982501i	$-0.440365\pi$
$84$	0.419279	+	0.304624i	0.0457471	+	0.0332372i
$85$	5.02356	−	3.64983i	0.544882	−	0.395880i
$86$	−2.74124	+	8.43668i	−0.295596	+	0.909751i
$87$	25.5566			2.73995
$88$		0			0
$89$	−2.70789			−0.287036			−0.143518	−	0.989648i	$-0.545842\pi$
$89$	−2.70789			−0.287036			−0.143518	+	0.989648i	$0.545842\pi$
$90$	−3.24047	+	9.97315i	−0.341576	+	1.05126i
$91$	−2.14612	+	1.55925i	−0.224975	+	0.163454i
$92$	−0.340801	−	0.247606i	−0.0355309	−	0.0258147i
$93$	−3.43496	−	10.5717i	−0.356188	−	1.09623i
$94$	−2.00986	−	6.18570i	−0.207301	−	0.638006i
$95$	0.657590	+	0.477767i	0.0674673	+	0.0490178i
$96$	1.72565	−	1.25376i	0.176123	−	0.127961i
$97$	4.37659	−	13.4698i	0.444376	−	1.36765i	−0.438791	−	0.898589i	$-0.644593\pi$
$97$	4.37659	−	13.4698i	0.444376	−	1.36765i	0.883167	−	0.469059i	$-0.155407\pi$
$98$	7.02229			0.709358
$99$		0			0
$100$	−0.115749			−0.0115749
$101$	−3.52453	+	10.8474i	−0.350704	+	1.07936i	0.607755	+	0.794124i	$0.292070\pi$
$101$	−3.52453	+	10.8474i	−0.350704	+	1.07936i	−0.958459	+	0.285231i	$0.907930\pi$
$102$	−22.4925	+	16.3418i	−2.22709	+	1.61808i
$103$	−11.2218	−	8.15308i	−1.10571	−	0.803347i	−0.123729	−	0.992316i	$-0.539485\pi$
$103$	−11.2218	−	8.15308i	−1.10571	−	0.803347i	−0.981983	+	0.188969i	$0.939485\pi$
$104$	1.73438	+	5.33786i	0.170070	+	0.523420i
$105$	1.38360	+	4.25827i	0.135025	+	0.415565i
$106$	−9.32223	−	6.77299i	−0.905455	−	0.657851i
$107$	−0.862247	+	0.626459i	−0.0833566	+	0.0605621i	−0.628683	−	0.777662i	$-0.716406\pi$
$107$	−0.862247	+	0.626459i	−0.0833566	+	0.0605621i	0.545326	+	0.838224i	$0.316406\pi$
$108$	−0.541273	+	1.66587i	−0.0520840	+	0.160298i
$109$	−11.3115			−1.08345			−0.541724	−	0.840556i	$-0.682228\pi$
$109$	−11.3115			−1.08345			−0.541724	+	0.840556i	$0.682228\pi$
$110$		0			0
$111$	−14.7551			−1.40049
$112$	−1.59285	+	4.90227i	−0.150510	+	0.463221i
$113$	3.04878	−	2.21507i	0.286805	−	0.208376i	−0.435075	−	0.900394i	$-0.643278\pi$
$113$	3.04878	−	2.21507i	0.286805	−	0.208376i	0.721880	+	0.692018i	$0.243278\pi$
$114$	−2.94430	−	2.13916i	−0.275759	−	0.200351i
$115$	−1.12462	−	3.46123i	−0.104872	−	0.322761i
$116$	−0.280250	−	0.862522i	−0.0260206	−	0.0800832i
$117$	−11.9438	−	8.67766i	−1.10420	−	0.802250i
$118$	1.23906	−	0.900232i	0.114065	−	0.0828731i
$119$	−2.63394	+	8.10643i	−0.241453	+	0.743115i
$120$	9.47308			0.864770
$121$		0			0
$122$	−3.49330			−0.316269
$123$	−1.84066	+	5.66496i	−0.165966	+	0.510792i
$124$	−0.319123	+	0.231856i	−0.0286581	+	0.0208213i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	−4.44813	−	13.6899i	−0.396271	−	1.21960i
$127$	0.519014	+	1.59736i	0.0460550	+	0.141743i	0.971440	−	0.237286i	$-0.0762580\pi$
$127$	0.519014	+	1.59736i	0.0460550	+	0.141743i	−0.925385	+	0.379029i	$0.876258\pi$
$128$	8.27901	+	6.01505i	0.731768	+	0.531661i
$129$	−17.0534	+	12.3900i	−1.50147	+	1.09088i
$130$	−0.819745	+	2.52292i	−0.0718964	+	0.221274i
$131$	−11.7943			−1.03047			−0.515235	−	0.857049i	$-0.672295\pi$
$131$	−11.7943			−1.03047			−0.515235	+	0.857049i	$0.672295\pi$
$132$		0			0
$133$	−1.11575			−0.0967477
$134$	−1.16149	+	3.57471i	−0.100338	+	0.308808i
$135$	−12.2426	+	8.89475i	−1.05367	+	0.765538i
$136$	14.5897	+	10.6000i	1.25105	+	0.908943i
$137$	−2.28915	−	7.04529i	−0.195576	−	0.601920i	−0.999969	−	0.00782325i	$-0.997510\pi$
$137$	−2.28915	−	7.04529i	−0.195576	−	0.601920i	0.804394	−	0.594096i	$-0.202490\pi$
$138$	5.03540	+	15.4974i	0.428641	+	1.31922i
$139$	−2.14493	−	1.55838i	−0.181930	−	0.132180i	0.493093	−	0.869977i	$-0.335866\pi$
$139$	−2.14493	−	1.55838i	−0.181930	−	0.132180i	−0.675023	+	0.737797i	$0.735866\pi$
$140$	0.128542	−	0.0933914i	0.0108638	−	0.00789301i
$141$	4.77588	−	14.6986i	0.402201	−	1.23785i
$142$	1.53157			0.128526
$143$		0			0
$144$	−28.6866			−2.39055
$145$	2.42118	−	7.45164i	0.201068	−	0.618825i
$146$	13.7915	−	10.0201i	1.14139	−	0.829269i
$147$	13.4997	+	9.80812i	1.11344	+	0.808960i
$148$	0.161803	+	0.497977i	0.0133001	+	0.0409335i
$149$	−2.58133	−	7.94453i	−0.211471	−	0.650841i	−0.999385	−	0.0350561i	$-0.988839\pi$
$149$	−2.58133	−	7.94453i	−0.211471	−	0.650841i	0.787914	−	0.615785i	$-0.211161\pi$
$150$	3.62230	+	2.63176i	0.295760	+	0.214882i
$151$	6.00554	−	4.36328i	0.488724	−	0.355079i	−0.315969	−	0.948769i	$-0.602330\pi$
$151$	6.00554	−	4.36328i	0.488724	−	0.355079i	0.804693	+	0.593691i	$0.202330\pi$
$152$	−0.729480	+	2.24511i	−0.0591686	+	0.182102i
$153$	−47.4363			−3.83500
$154$		0			0
$155$	−3.40786			−0.273726
$156$	−0.225469	+	0.693921i	−0.0180519	+	0.0555581i
$157$	6.94477	−	5.04567i	0.554253	−	0.402689i	−0.275098	−	0.961416i	$-0.588710\pi$
$157$	6.94477	−	5.04567i	0.554253	−	0.402689i	0.829351	+	0.558728i	$0.188710\pi$
$158$	−6.45046	−	4.68653i	−0.513171	−	0.372840i
$159$	−8.46121	−	26.0409i	−0.671018	−	2.06518i
$160$	−0.202078	−	0.621933i	−0.0159757	−	0.0491681i
$161$	4.04158	+	2.93638i	0.318521	+	0.231419i
$162$	29.3640	−	21.3342i	2.30706	−	1.67617i
$163$	5.06094	−	15.5760i	0.396404	−	1.22000i	−0.531460	−	0.847084i	$-0.678356\pi$
$163$	5.06094	−	15.5760i	0.396404	−	1.22000i	0.927863	−	0.372921i	$-0.121644\pi$
$164$	0.211374			0.0165055
$165$		0			0
$166$	21.9315			1.70221
$167$	−6.62488	+	20.3893i	−0.512648	+	1.57777i	0.274872	+	0.961481i	$0.411364\pi$
$167$	−6.62488	+	20.3893i	−0.512648	+	1.57777i	−0.787521	+	0.616288i	$0.788636\pi$
$168$	−10.5201	+	7.64327i	−0.811640	+	0.589691i
$169$	7.49579	+	5.44601i	0.576599	+	0.418924i
$170$	2.63394	+	8.10643i	0.202014	+	0.621735i
$171$	−1.91883	−	5.90555i	−0.146737	−	0.451609i
$172$	0.605163	+	0.439677i	0.0461433	+	0.0335250i
$173$	11.1140	−	8.07481i	0.844984	−	0.613917i	−0.0787746	−	0.996892i	$-0.525101\pi$
$173$	11.1140	−	8.07481i	0.844984	−	0.613917i	0.923758	+	0.382976i	$0.125101\pi$
$174$	−10.8406	+	33.3640i	−0.821826	+	2.52932i
$175$	1.37268			0.103765
$176$		0			0
$177$	3.63935			0.273551
$178$	1.14864	−	3.53515i	0.0860941	−	0.264970i
$179$	3.04878	−	2.21507i	0.227877	−	0.165562i	−0.467988	−	0.883735i	$-0.655021\pi$
$179$	3.04878	−	2.21507i	0.227877	−	0.165562i	0.695865	+	0.718172i	$0.255021\pi$
$180$	0.715374	+	0.519749i	0.0533208	+	0.0387398i
$181$	−0.00414019	−	0.0127422i	−0.000307738	−	0.000947119i	0.950903	−	0.309491i	$-0.100158\pi$
$181$	−0.00414019	−	0.0127422i	−0.000307738	−	0.000947119i	−0.951210	+	0.308543i	$0.900158\pi$
$182$	−1.12525	−	3.46316i	−0.0834089	−	0.256706i
$183$	−6.71556	−	4.87914i	−0.496428	−	0.360676i
$184$	8.55097	−	6.21264i	0.630386	−	0.458002i
$185$	−1.39787	+	4.30220i	−0.102773	+	0.316304i
$186$	15.2584			1.11880
$187$		0			0
$188$	−0.548444			−0.0399994
$189$	6.41899	−	19.7556i	0.466913	−	1.43701i
$190$	−0.902660	+	0.655821i	−0.0654859	+	0.0475783i
$191$	13.4507	+	9.77249i	0.973257	+	0.707113i	0.956192	−	0.292742i	$-0.0945676\pi$
$191$	13.4507	+	9.77249i	0.973257	+	0.707113i	0.0170656	+	0.999854i	$0.494568\pi$
$192$	8.47472	+	26.0825i	0.611610	+	1.88234i
$193$	8.27587	+	25.4705i	0.595710	+	1.83341i	0.551160	+	0.834400i	$0.314186\pi$
$193$	8.27587	+	25.4705i	0.595710	+	1.83341i	0.0445504	+	0.999007i	$0.485814\pi$
$194$	15.7283	+	11.4273i	1.12922	+	0.820429i
$195$	−5.09968	+	3.70513i	−0.365195	+	0.265330i
$196$	0.182983	−	0.563163i	0.0130702	−	0.0402259i
$197$	2.55719			0.182192			0.0910962	−	0.995842i	$-0.470963\pi$
$197$	2.55719			0.182192			0.0910962	+	0.995842i	$0.470963\pi$
$198$		0			0
$199$	−21.8629			−1.54982			−0.774911	−	0.632071i	$-0.782205\pi$
$199$	−21.8629			−1.54982			−0.774911	+	0.632071i	$0.782205\pi$
$200$	0.897462	−	2.76210i	0.0634601	−	0.195310i
$201$	−7.22570	+	5.24978i	−0.509662	+	0.370291i
$202$	−12.6662	−	9.20252i	−0.891189	−	0.647487i
$203$	3.32351	+	10.2287i	0.233265	+	0.717915i
$204$	0.724457	+	2.22965i	0.0507221	+	0.156107i
$205$	1.47737	+	1.07338i	0.103184	+	0.0749678i
$206$	15.4039	−	11.1916i	1.07324	−	0.779754i
$207$	−8.59139	+	26.4416i	−0.597143	+	1.83782i
$208$	−7.25687			−0.503173
$209$		0			0
$210$	−6.14605			−0.424118
$211$	3.96493	−	12.2028i	0.272957	−	0.840075i	−0.716796	−	0.697283i	$-0.754392\pi$
$211$	3.96493	−	12.2028i	0.272957	−	0.840075i	0.989753	−	0.142792i	$-0.0456080\pi$
$212$	−0.786084	+	0.571124i	−0.0539885	+	0.0392249i
$213$	2.94430	+	2.13916i	0.201740	+	0.146573i
$214$	−0.452091	−	1.39139i	−0.0309043	−	0.0951137i
$215$	1.99700	+	6.14614i	0.136194	+	0.419163i
$216$	−35.5555	−	25.8326i	−2.41924	−	1.75768i
$217$	3.78450	−	2.74960i	0.256908	−	0.186655i
$218$	4.79814	−	14.7672i	0.324971	−	1.00016i
$219$	40.5081			2.73728
$220$		0			0
$221$	−12.0000			−0.807207
$222$	6.25884	−	19.2627i	0.420066	−	1.29283i
$223$	5.95773	−	4.32854i	0.398959	−	0.289861i	−0.370158	−	0.928969i	$-0.620696\pi$
$223$	5.95773	−	4.32854i	0.398959	−	0.289861i	0.769117	+	0.639108i	$0.220696\pi$
$224$	0.726213	+	0.527625i	0.0485221	+	0.0352534i
$225$	2.36069	+	7.26546i	0.157379	+	0.484364i
$226$	1.59853	+	4.91976i	0.106333	+	0.327258i
$227$	−1.11052	−	0.806841i	−0.0737079	−	0.0535519i	0.550321	−	0.834953i	$-0.314505\pi$
$227$	−1.11052	−	0.806841i	−0.0737079	−	0.0535519i	−0.624029	+	0.781401i	$0.714505\pi$
$228$	−0.248274	+	0.180382i	−0.0164424	+	0.0119461i
$229$	9.11502	−	28.0531i	0.602337	−	1.85380i	0.0881851	−	0.996104i	$-0.471893\pi$
$229$	9.11502	−	28.0531i	0.602337	−	1.85380i	0.514152	−	0.857699i	$-0.328107\pi$
$230$	4.99567			0.329405
$231$		0			0
$232$	22.7551			1.49395
$233$	6.79788	−	20.9217i	0.445344	−	1.37063i	−0.436762	−	0.899577i	$-0.643875\pi$
$233$	6.79788	−	20.9217i	0.445344	−	1.37063i	0.882106	−	0.471051i	$-0.156125\pi$
$234$	16.3950	−	11.9117i	1.07177	−	0.778689i
$235$	−3.83328	−	2.78504i	−0.250056	−	0.181676i
$236$	−0.0399087	−	0.122826i	−0.00259784	−	0.00799532i
$237$	−5.85469	−	18.0189i	−0.380303	−	1.17045i
$238$	−9.46565	−	6.87719i	−0.613567	−	0.445782i
$239$	−15.1468	+	11.0048i	−0.979765	+	0.711841i	−0.957656	−	0.287915i	$-0.907038\pi$
$239$	−15.1468	+	11.0048i	−0.979765	+	0.711841i	−0.0221087	+	0.999756i	$0.507038\pi$
$240$	−3.78497	+	11.6489i	−0.244318	+	0.751935i
$241$	−26.2630			−1.69175			−0.845875	−	0.533382i	$-0.820921\pi$
$241$	−26.2630			−1.69175			−0.845875	+	0.533382i	$0.820921\pi$
$242$		0			0
$243$	40.8495			2.62050
$244$	−0.0910265	+	0.280151i	−0.00582737	+	0.0179348i
$245$	4.13873	−	3.00696i	0.264414	−	0.192108i
$246$	−6.61481	−	4.80594i	−0.421745	−	0.306416i
$247$	−0.485408	−	1.49393i	−0.0308858	−	0.0950566i
$248$	−3.05842	−	9.41285i	−0.194210	−	0.597716i
$249$	42.1612	+	30.6319i	2.67186	+	1.94122i
$250$	1.11052	−	0.806841i	0.0702355	−	0.0510291i
$251$	−6.99180	+	21.5186i	−0.441319	+	1.35824i	0.445152	+	0.895455i	$0.353150\pi$
$251$	−6.99180	+	21.5186i	−0.441319	+	1.35824i	−0.886471	+	0.462785i	$0.846850\pi$
$252$	−1.21379			−0.0764618
$253$		0			0
$254$	−2.30550			−0.144660
$255$	−6.25884	+	19.2627i	−0.391944	+	1.20628i
$256$	2.23976	−	1.62728i	0.139985	−	0.101705i
$257$	−13.9233	−	10.1159i	−0.868513	−	0.631011i	0.0616747	−	0.998096i	$-0.480356\pi$
$257$	−13.9233	−	10.1159i	−0.868513	−	0.631011i	−0.930187	+	0.367085i	$0.880356\pi$
$258$	−8.94140	−	27.5188i	−0.556667	−	1.71324i
$259$	−1.91883	−	5.90555i	−0.119230	−	0.366953i
$260$	0.180969	+	0.131482i	0.0112232	+	0.00815414i
$261$	−48.4239	+	35.1820i	−2.99736	+	2.17771i
$262$	5.00291	−	15.3974i	0.309081	−	0.951253i
$263$	5.71441			0.352366			0.176183	−	0.984357i	$-0.443625\pi$
$263$	5.71441			0.352366			0.176183	+	0.984357i	$0.443625\pi$
$264$		0			0
$265$	−8.39446			−0.515667
$266$	0.473280	−	1.45661i	0.0290187	−	0.0893103i
$267$	7.14574	−	5.19168i	0.437312	−	0.317726i
$268$	0.256414	+	0.186295i	0.0156630	+	0.0113798i
$269$	−0.887142	−	2.73034i	−0.0540900	−	0.166472i	0.920362	−	0.391067i	$-0.127894\pi$
$269$	−0.887142	−	2.73034i	−0.0540900	−	0.166472i	−0.974452	+	0.224595i	$0.927894\pi$
$270$	−6.41899	−	19.7556i	−0.390647	−	1.20229i
$271$	6.18651	+	4.49476i	0.375804	+	0.273037i	0.759613	−	0.650375i	$-0.225388\pi$
$271$	6.18651	+	4.49476i	0.375804	+	0.273037i	−0.383810	+	0.923412i	$0.625388\pi$
$272$	−18.8640	+	13.7055i	−1.14380	+	0.831017i
$273$	2.67385	−	8.22926i	0.161829	−	0.498057i
$274$	10.1686			0.614309
$275$		0			0
$276$	1.37404			0.0827077
$277$	−9.08418	+	27.9582i	−0.545816	+	1.67985i	0.173227	+	0.984882i	$0.444580\pi$
$277$	−9.08418	+	27.9582i	−0.545816	+	1.67985i	−0.719043	+	0.694966i	$0.755420\pi$
$278$	2.94430	−	2.13916i	0.176587	−	0.128298i
$279$	21.0618	+	15.3023i	1.26094	+	0.916124i
$280$	1.23193	+	3.79148i	0.0736218	+	0.226585i
$281$	7.48565	+	23.0385i	0.446557	+	1.37436i	0.880768	+	0.473549i	$0.157027\pi$
$281$	7.48565	+	23.0385i	0.446557	+	1.37436i	−0.434211	+	0.900811i	$0.642973\pi$
$282$	17.1632	+	12.4698i	1.02205	+	0.742565i
$283$	−4.14139	+	3.00889i	−0.246180	+	0.178860i	−0.704032	−	0.710168i	$-0.748619\pi$
$283$	−4.14139	+	3.00889i	−0.246180	+	0.178860i	0.457852	+	0.889028i	$0.348619\pi$
$284$	0.0399087	−	0.122826i	0.00236815	−	0.00728841i
$285$	−2.65128			−0.157048
$286$		0			0
$287$	−2.50670			−0.147966
$288$	−1.54375	+	4.75116i	−0.0909661	+	0.279965i
$289$	−17.4403	+	12.6711i	−1.02590	+	0.745361i
$290$	8.70106	+	6.32169i	0.510944	+	0.371222i
$291$	14.2756	+	43.9357i	0.836850	+	2.57556i
$292$	−0.444207	−	1.36713i	−0.0259952	−	0.0800051i
$293$	−8.89298	−	6.46113i	−0.519534	−	0.377463i	0.296895	−	0.954910i	$-0.404049\pi$
$293$	−8.89298	−	6.46113i	−0.519534	−	0.377463i	−0.816428	+	0.577447i	$0.804049\pi$
$294$	−18.5308	+	13.4634i	−1.08074	+	0.785202i
$295$	0.344786	−	1.06114i	0.0200742	−	0.0617820i
$296$	−13.1377			−0.763611
$297$		0			0
$298$	11.4665			0.664237
$299$	−2.17337	+	6.68895i	−0.125689	+	0.386832i
$300$	0.305446	−	0.221919i	0.0176349	−	0.0128125i
$301$	−7.17667	−	5.21416i	−0.413656	−	0.300539i
$302$	3.14881	+	9.69103i	0.181193	+	0.557656i
$303$	−11.4963	−	35.3820i	−0.660446	−	2.03264i
$304$	−2.46932	−	1.79406i	−0.141625	−	0.102897i
$305$	−2.05885	+	1.49584i	−0.117889	+	0.0856516i
$306$	20.1216	−	61.9279i	1.15027	−	3.54018i
$307$	−14.3515			−0.819081			−0.409540	−	0.912292i	$-0.634311\pi$
$307$	−14.3515			−0.819081			−0.409540	+	0.912292i	$0.634311\pi$
$308$		0			0
$309$	45.2440			2.57384
$310$	1.44555	−	4.44894i	0.0821017	−	0.252683i
$311$	−22.1517	+	16.0942i	−1.25611	+	0.912617i	−0.998560	−	0.0536476i	$-0.982915\pi$
$311$	−22.1517	+	16.0942i	−1.25611	+	0.912617i	−0.257550	+	0.966265i	$0.582915\pi$
$312$	−14.8107	−	10.7606i	−0.838492	−	0.609200i
$313$	1.19616	+	3.68140i	0.0676109	+	0.208085i	0.979154	−	0.203120i	$-0.0651081\pi$
$313$	1.19616	+	3.68140i	0.0676109	+	0.208085i	−0.911543	+	0.411205i	$0.865108\pi$
$314$	3.64126	+	11.2067i	0.205488	+	0.632428i
$315$	−8.48367	−	6.16374i	−0.478000	−	0.347288i
$316$	−0.543926	+	0.395185i	−0.0305982	+	0.0222309i
$317$	−4.79292	+	14.7511i	−0.269197	+	0.828503i	0.721500	+	0.692415i	$0.243453\pi$
$317$	−4.79292	+	14.7511i	−0.269197	+	0.828503i	−0.990697	+	0.136089i	$0.956547\pi$
$318$	37.5854			2.10769
$319$		0			0
$320$	8.40786			0.470013
$321$	1.07427	−	3.30627i	0.0599600	−	0.184538i
$322$	−5.54780	+	4.03071i	−0.309167	+	0.224623i
$323$	−4.08328	−	2.96668i	−0.227200	−	0.165070i
$324$	−0.945780	−	2.91081i	−0.0525433	−	0.161712i
$325$	0.597186	+	1.83795i	0.0331259	+	0.101951i
$326$	18.1876	+	13.2141i	1.00732	+	0.731860i
$327$	29.8495	−	21.6869i	1.65068	−	1.19929i
$328$	−1.63889	+	5.04397i	−0.0904923	+	0.278507i
$329$	6.50403			0.358579
$330$		0			0
$331$	26.8575			1.47622			0.738110	−	0.674681i	$-0.235719\pi$
$331$	26.8575			1.47622			0.738110	+	0.674681i	$0.235719\pi$
$332$	0.571478	−	1.75883i	0.0313639	−	0.0965282i
$333$	27.9575	−	20.3123i	1.53206	−	1.11311i
$334$	−23.8080	−	17.2975i	−1.30271	−	0.946477i
$335$	0.846150	+	2.60418i	0.0462301	+	0.142282i
$336$	−5.19555	−	15.9902i	−0.283440	−	0.872339i
$337$	1.56345	+	1.13592i	0.0851667	+	0.0618773i	0.629554	−	0.776957i	$-0.283238\pi$
$337$	1.56345	+	1.13592i	0.0851667	+	0.0618773i	−0.544387	+	0.838834i	$0.683238\pi$
$338$	−10.2893	+	7.47563i	−0.559666	+	0.406621i
$339$	−3.79847	+	11.6905i	−0.206305	+	0.634940i
$340$	0.718741			0.0389792
$341$		0			0
$342$	8.52360			0.460904
$343$	−5.13928	+	15.8171i	−0.277495	+	0.854041i
$344$	−15.1840	+	11.0318i	−0.818668	+	0.594797i
$345$	9.60372	+	6.97751i	0.517047	+	0.375657i
$346$	5.82727	+	17.9345i	0.313276	+	0.964165i
$347$	−1.17435	−	3.61427i	−0.0630422	−	0.194024i	0.914575	−	0.404417i	$-0.132526\pi$
$347$	−1.17435	−	3.61427i	−0.0630422	−	0.194024i	−0.977617	+	0.210393i	$0.932526\pi$
$348$	2.39320	+	1.73876i	0.128289	+	0.0932075i
$349$	13.9077	−	10.1046i	0.744464	−	0.540885i	−0.149642	−	0.988740i	$-0.547812\pi$
$349$	13.9077	−	10.1046i	0.744464	−	0.540885i	0.894106	+	0.447856i	$0.147812\pi$
$350$	−0.582265	+	1.79203i	−0.0311234	+	0.0957880i
$351$	29.2444			1.56095
$352$		0			0
$353$	−1.99207			−0.106027			−0.0530135	−	0.998594i	$-0.516883\pi$
$353$	−1.99207			−0.106027			−0.0530135	+	0.998594i	$0.516883\pi$
$354$	−1.54375	+	4.75116i	−0.0820492	+	0.252521i
$355$	0.902660	−	0.655821i	0.0479082	−	0.0348074i
$356$	−0.253576	−	0.184234i	−0.0134395	−	0.00976437i
$357$	−8.59139	−	26.4416i	−0.454704	−	1.39944i
$358$	1.59853	+	4.91976i	0.0844849	+	0.260018i
$359$	−12.6014	−	9.15543i	−0.665075	−	0.483205i	0.203298	−	0.979117i	$-0.434834\pi$
$359$	−12.6014	−	9.15543i	−0.665075	−	0.483205i	−0.868373	+	0.495912i	$0.834834\pi$
$360$	−17.9493	+	13.0409i	−0.946012	+	0.687318i
$361$	−5.66716	+	17.4417i	−0.298272	+	0.917986i
$362$	0.0183911			0.000966613
$363$		0			0
$364$	−0.307054			−0.0160940
$365$	3.83766	−	11.8111i	0.200872	−	0.618221i
$366$	9.21831	−	6.69749i	0.481849	−	0.350084i
$367$	−15.1869	−	11.0339i	−0.792748	−	0.575965i	0.116029	−	0.993246i	$-0.462983\pi$
$367$	−15.1869	−	11.0339i	−0.792748	−	0.575965i	−0.908778	+	0.417280i	$0.862983\pi$
$368$	4.22307	+	12.9973i	0.220143	+	0.677530i
$369$	−4.31094	−	13.2677i	−0.224419	−	0.690689i
$370$	−5.02356	−	3.64983i	−0.261162	−	0.189746i
$371$	9.32223	−	6.77299i	0.483986	−	0.351636i
$372$	0.397594	−	1.22367i	0.0206143	−	0.0634443i
$373$	2.62664			0.136003			0.0680013	−	0.997685i	$-0.478338\pi$
$373$	2.62664			0.136003			0.0680013	+	0.997685i	$0.478338\pi$
$374$		0			0
$375$	3.26180			0.168439
$376$	4.25235	−	13.0874i	0.219298	−	0.674931i
$377$	−12.2498	+	8.90003i	−0.630899	+	0.458375i
$378$	23.0681	+	16.7599i	1.18649	+	0.862038i
$379$	0.822197	+	2.53046i	0.0422334	+	0.129981i	0.969950	−	0.243304i	$-0.0782313\pi$
$379$	0.822197	+	2.53046i	0.0422334	+	0.129981i	−0.927717	+	0.373285i	$0.878231\pi$
$380$	0.0290736	+	0.0894793i	0.00149144	+	0.00459019i
$381$	−4.43212	−	3.22013i	−0.227065	−	0.164972i
$382$	−18.4635	+	13.4145i	−0.944674	+	0.686346i
$383$	6.77719	−	20.8581i	0.346298	−	1.06580i	−0.614587	−	0.788849i	$-0.710677\pi$
$383$	6.77719	−	20.8581i	0.346298	−	1.06580i	0.960885	−	0.276948i	$-0.0893228\pi$
$384$	−33.3794			−1.70338
$385$		0			0
$386$	−36.7621			−1.87114
$387$	15.2558	−	46.9525i	0.775496	−	2.38673i
$388$	1.32627	−	0.963588i	0.0673309	−	0.0489188i
$389$	2.76785	+	2.01096i	0.140336	+	0.101960i	0.655738	−	0.754988i	$-0.272358\pi$
$389$	2.76785	+	2.01096i	0.140336	+	0.101960i	−0.515402	+	0.856948i	$0.672358\pi$
$390$	−2.67385	−	8.22926i	−0.135396	−	0.416705i
$391$	6.98330	+	21.4924i	0.353161	+	1.08692i
$392$	12.0199	+	8.73296i	0.607096	+	0.441081i
$393$	31.1233	−	22.6124i	1.56996	−	1.14065i
$394$	−1.08471	+	3.33840i	−0.0546471	+	0.168186i
$395$	−5.80849			−0.292257
$396$		0			0
$397$	5.51021			0.276549			0.138275	−	0.990394i	$-0.455844\pi$
$397$	5.51021			0.276549			0.138275	+	0.990394i	$0.455844\pi$
$398$	9.27385	−	28.5420i	0.464856	−	1.43068i
$399$	2.94430	−	2.13916i	0.147399	−	0.107092i
$400$	3.03794	+	2.20719i	0.151897	+	0.110360i
$401$	−5.53944	−	17.0486i	−0.276626	−	0.851368i	−0.988785	−	0.149349i	$-0.952282\pi$
$401$	−5.53944	−	17.0486i	−0.276626	−	0.851368i	0.712158	−	0.702019i	$-0.247718\pi$
$402$	−3.78856	−	11.6600i	−0.188956	−	0.581547i
$403$	5.32802	+	3.87103i	0.265408	+	0.192830i
$404$	−1.06806	+	0.775990i	−0.0531379	+	0.0386069i
$405$	8.17092	−	25.1475i	0.406016	−	1.24959i
$406$	−14.7633			−0.732691
$407$		0			0
$408$	−58.8227			−2.91216
$409$	9.06228	−	27.8908i	0.448101	−	1.37911i	−0.430946	−	0.902378i	$-0.641820\pi$
$409$	9.06228	−	27.8908i	0.448101	−	1.37911i	0.879047	−	0.476735i	$-0.158180\pi$
$410$	−2.02796	+	1.47340i	−0.100154	+	0.0727661i
$411$	19.5482	+	14.2026i	0.964244	+	0.700564i
$412$	−0.496140	−	1.52696i	−0.0244431	−	0.0752280i
$413$	0.473280	+	1.45661i	0.0232886	+	0.0716749i
$414$	−30.8751	−	22.4320i	−1.51743	−	1.10248i
$415$	12.9258	−	9.39111i	0.634500	−	0.460991i
$416$	−0.390523	+	1.20191i	−0.0191470	+	0.0589283i
$417$	8.64794			0.423491
$418$		0			0
$419$	2.65275			0.129595			0.0647977	−	0.997898i	$-0.479360\pi$
$419$	2.65275			0.129595			0.0647977	+	0.997898i	$0.479360\pi$
$420$	−0.160150	+	0.492892i	−0.00781454	+	0.0240507i
$421$	9.03102	−	6.56142i	0.440145	−	0.319784i	−0.345547	−	0.938401i	$-0.612307\pi$
$421$	9.03102	−	6.56142i	0.440145	−	0.319784i	0.785693	+	0.618617i	$0.212307\pi$
$422$	14.2489	+	10.3524i	0.693624	+	0.503947i
$423$	11.1854	+	34.4252i	0.543854	+	1.67381i
$424$	−7.53370	−	23.1864i	−0.365869	−	1.12603i
$425$	5.02356	+	3.64983i	0.243678	+	0.177043i
$426$	−4.04158	+	2.93638i	−0.195815	+	0.142268i
$427$	1.07949	−	3.32233i	0.0522402	−	0.160779i
$428$	−0.123365			−0.00596309
$429$		0			0
$430$	−8.87085			−0.427791
$431$	1.40886	−	4.33604i	0.0678626	−	0.208860i	−0.911374	−	0.411578i	$-0.864978\pi$
$431$	1.40886	−	4.33604i	0.0678626	−	0.208860i	0.979237	+	0.202719i	$0.0649777\pi$
$432$	45.9721	−	33.4007i	2.21184	−	1.60699i
$433$	−16.3122	−	11.8515i	−0.783913	−	0.569546i	0.122238	−	0.992501i	$-0.460993\pi$
$433$	−16.3122	−	11.8515i	−0.783913	−	0.569546i	−0.906151	+	0.422955i	$0.860993\pi$
$434$	1.98428	+	6.10697i	0.0952483	+	0.293144i
$435$	7.89742	+	24.3058i	0.378652	+	1.16537i
$436$	−1.05925	−	0.769589i	−0.0507288	−	0.0368566i
$437$	−2.39320	+	1.73876i	−0.114482	+	0.0831763i
$438$	−17.1828	+	52.8831i	−0.821025	+	2.52685i
$439$	−34.4868			−1.64596			−0.822982	−	0.568067i	$-0.807691\pi$
$439$	−34.4868			−1.64596			−0.822982	+	0.568067i	$0.807691\pi$
$440$		0			0
$441$	−39.0810			−1.86100
$442$	5.09018	−	15.6660i	0.242115	−	0.745154i
$443$	−25.4505	+	18.4909i	−1.20919	+	0.878528i	−0.995157	−	0.0982979i	$-0.968660\pi$
$443$	−25.4505	+	18.4909i	−1.20919	+	0.878528i	−0.214034	+	0.976826i	$0.568660\pi$
$444$	−1.38172	−	1.00388i	−0.0655733	−	0.0476418i
$445$	−0.836785	−	2.57536i	−0.0396674	−	0.122084i
$446$	3.12374	+	9.61388i	0.147913	+	0.455230i
$447$	22.0433	+	16.0154i	1.04261	+	0.757503i
$448$	−9.33710	+	6.78380i	−0.441137	+	0.320505i
$449$	−1.47600	+	4.54266i	−0.0696567	+	0.214381i	−0.979825	−	0.199857i	$-0.935952\pi$
$449$	−1.47600	+	4.54266i	−0.0696567	+	0.214381i	0.910168	+	0.414239i	$0.135952\pi$
$450$	−10.4864			−0.494333
$451$		0			0
$452$	0.436202			0.0205172
$453$	−7.48229	+	23.0281i	−0.351549	+	1.08196i
$454$	1.52439	−	1.10753i	0.0715432	−	0.0519792i
$455$	−2.14612	−	1.55925i	−0.100612	−	0.0730987i
$456$	−2.37942	−	7.32310i	−0.111426	−	0.342935i
$457$	0.473280	+	1.45661i	0.0221391	+	0.0681372i	0.961516	−	0.274750i	$-0.0885951\pi$
$457$	0.473280	+	1.45661i	0.0221391	+	0.0681372i	−0.939377	+	0.342887i	$0.888595\pi$
$458$	32.7568	+	23.7992i	1.53063	+	1.11207i
$459$	76.0198	−	55.2316i	3.54830	−	2.57799i
$460$	0.130174	−	0.400635i	0.00606941	−	0.0186797i
$461$	18.5220			0.862655			0.431327	−	0.902195i	$-0.358045\pi$
$461$	18.5220			0.862655			0.431327	+	0.902195i	$0.358045\pi$
$462$		0			0
$463$	9.68306			0.450010			0.225005	−	0.974358i	$-0.427760\pi$
$463$	9.68306			0.450010			0.225005	+	0.974358i	$0.427760\pi$
$464$	−9.09179	+	27.9817i	−0.422076	+	1.29902i
$465$	8.99283	−	6.53367i	0.417033	−	0.302992i
$466$	24.4297	+	17.7492i	1.13168	+	0.822217i
$467$	−9.79522	−	30.1466i	−0.453269	−	1.39502i	−0.873156	−	0.487441i	$-0.837930\pi$
$467$	−9.79522	−	30.1466i	−0.453269	−	1.39502i	0.419887	−	0.907576i	$-0.362070\pi$
$468$	−0.528062	−	1.62521i	−0.0244097	−	0.0751253i
$469$	−3.04083	−	2.20929i	−0.140412	−	0.102016i
$470$	5.26187	−	3.82297i	0.242712	−	0.176341i
$471$	−8.65248	+	26.6296i	−0.398685	+	1.22703i
$472$	3.24041			0.149152
$473$		0			0
$474$	26.0070			1.19454
$475$	−0.251177	+	0.773043i	−0.0115248	+	0.0354696i
$476$	−0.798178	+	0.579910i	−0.0365844	+	0.0265801i
$477$	51.8808	+	37.6936i	2.37546	+	1.72587i
$478$	−7.94172	−	24.4421i	−0.363246	−	1.11796i
$479$	9.52839	+	29.3254i	0.435363	+	1.33991i	0.892714	+	0.450624i	$0.148798\pi$
$479$	9.52839	+	29.3254i	0.435363	+	1.33991i	−0.457351	+	0.889286i	$0.651202\pi$
$480$	1.72565	+	1.25376i	0.0787647	+	0.0572259i
$481$	7.07244	−	5.13843i	0.322476	−	0.234292i
$482$	11.1403	−	34.2863i	0.507426	−	1.56170i
$483$	−16.2949			−0.741443
$484$		0			0
$485$	14.1630			0.643107
$486$	−17.3276	+	53.3289i	−0.785996	+	2.41905i
$487$	−24.2641	+	17.6289i	−1.09951	+	0.798841i	−0.980980	−	0.194109i	$-0.937818\pi$
$487$	−24.2641	+	17.6289i	−1.09951	+	0.798841i	−0.118531	+	0.992950i	$0.537818\pi$
$488$	−5.97940	−	4.34429i	−0.270675	−	0.196657i
$489$	16.5078	+	50.8058i	0.746508	+	2.29752i
$490$	2.17001	+	6.67859i	0.0980309	+	0.301708i
$491$	−27.9203	−	20.2853i	−1.26003	−	0.915463i	−0.261267	−	0.965266i	$-0.584140\pi$
$491$	−27.9203	−	20.2853i	−1.26003	−	0.915463i	−0.998759	+	0.0498038i	$0.984140\pi$
$492$	−0.557785	+	0.405255i	−0.0251469	+	0.0182703i
$493$	−15.0342	+	46.2706i	−0.677108	+	2.08392i
$494$	2.15622			0.0970131
$495$		0			0
$496$	12.7968			0.574595
$497$	−0.473280	+	1.45661i	−0.0212295	+	0.0653377i
$498$	−57.8739	+	42.0479i	−2.59339	+	1.88421i
$499$	−14.4514	−	10.4996i	−0.646934	−	0.470025i	0.215292	−	0.976550i	$-0.430930\pi$
$499$	−14.4514	−	10.4996i	−0.646934	−	0.470025i	−0.862225	+	0.506525i	$0.830930\pi$
$500$	−0.0357685	−	0.110084i	−0.00159962	−	0.00492312i
$501$	−21.6090	−	66.5058i	−0.965420	−	2.97126i
$502$	−25.1266	−	18.2556i	−1.12146	−	0.814785i
$503$	−4.14139	+	3.00889i	−0.184655	+	0.134160i	−0.676273	−	0.736651i	$-0.736406\pi$
$503$	−4.14139	+	3.00889i	−0.184655	+	0.134160i	0.491617	+	0.870811i	$0.336406\pi$
$504$	9.41113	−	28.9645i	0.419205	−	1.29018i
$505$	−11.4056			−0.507543
$506$		0			0
$507$	−30.2216			−1.34219
$508$	−0.0600755	+	0.184893i	−0.00266542	+	0.00820332i
$509$	14.6495	−	10.6435i	0.649329	−	0.471765i	−0.213714	−	0.976896i	$-0.568556\pi$
$509$	14.6495	−	10.6435i	0.649329	−	0.471765i	0.863043	+	0.505131i	$0.168556\pi$
$510$	−22.4925	−	16.3418i	−0.995987	−	0.723627i
$511$	5.26788	+	16.2129i	0.233037	+	0.717215i
$512$	7.49895	+	23.0794i	0.331410	+	1.01997i
$513$	9.95108	+	7.22988i	0.439351	+	0.319207i
$514$	19.1123	−	13.8859i	0.843006	−	0.612479i
$515$	4.28633	−	13.1920i	0.188878	−	0.581307i
$516$	−2.43990			−0.107411
$517$		0			0
$518$	8.52360			0.374506
$519$	−13.8469	+	42.6165i	−0.607813	+	1.87066i
$520$	−4.54065	+	3.29898i	−0.199121	+	0.144670i
$521$	27.9684	+	20.3202i	1.22532	+	0.890245i	0.996530	−	0.0832319i	$-0.0265242\pi$
$521$	27.9684	+	20.3202i	1.22532	+	0.890245i	0.228787	+	0.973477i	$0.426524\pi$
$522$	−25.3895	−	78.1407i	−1.11127	−	3.42013i
$523$	10.1332	+	31.1867i	0.443093	+	1.36370i	0.884561	+	0.466424i	$0.154458\pi$
$523$	10.1332	+	31.1867i	0.443093	+	1.36370i	−0.441468	+	0.897277i	$0.645542\pi$
$524$	−1.10445	−	0.802432i	−0.0482483	−	0.0350544i
$525$	−3.62230	+	2.63176i	−0.158090	+	0.114859i
$526$	−2.42395	+	7.46014i	−0.105689	+	0.325278i
$527$	21.1609			0.921785
$528$		0			0
$529$	−9.75510			−0.424135
$530$	3.56077	−	10.9589i	0.154670	−	0.476026i
$531$	−6.89574	+	5.01005i	−0.299250	+	0.217418i
$532$	−0.104482	−	0.0759109i	−0.00452989	−	0.00329115i
$533$	−1.09054	−	3.35634i	−0.0472366	−	0.145379i
$534$	3.74663	+	11.5309i	0.162133	+	0.498993i
$535$	−0.862247	−	0.626459i	−0.0372782	−	0.0270842i
$536$	−6.43363	+	4.67431i	−0.277890	+	0.201899i
$537$	−3.79847	+	11.6905i	−0.163916	+	0.504482i
$538$	3.94076			0.169898
$539$		0			0
$540$	−1.75160			−0.0753767
$541$	1.35116	−	4.15843i	0.0580908	−	0.178785i	−0.917801	−	0.397041i	$-0.870037\pi$
$541$	1.35116	−	4.15843i	0.0580908	−	0.178785i	0.975891	+	0.218256i	$0.0700369\pi$
$542$	−8.49210	+	6.16987i	−0.364767	+	0.265019i
$543$	0.0353552	+	0.0256870i	0.00151723	+	0.00110234i
$544$	1.25480	+	3.86187i	0.0537990	+	0.165576i
$545$	−3.49546	−	10.7579i	−0.149729	−	0.460818i
$546$	9.60907	+	6.98140i	0.411230	+	0.298776i
$547$	−25.6032	+	18.6018i	−1.09472	+	0.795357i	−0.980189	−	0.198063i	$-0.936535\pi$
$547$	−25.6032	+	18.6018i	−1.09472	+	0.795357i	−0.114526	+	0.993420i	$0.536535\pi$
$548$	0.264968	−	0.815488i	0.0113189	−	0.0348359i
$549$	19.4412			0.829731
$550$		0			0
$551$	−6.36858			−0.271311
$552$	−10.6536	+	32.7885i	−0.453449	+	1.39557i
$553$	6.45046	−	4.68653i	0.274301	−	0.199292i
$554$	−32.6460	−	23.7187i	−1.38700	−	1.00771i
$555$	−4.55958	−	14.0329i	−0.193543	−	0.595665i
$556$	−0.0948323	−	0.291864i	−0.00402178	−	0.0123778i
$557$	−1.23025	−	0.893831i	−0.0521275	−	0.0378729i	0.561416	−	0.827533i	$-0.310257\pi$
$557$	−1.23025	−	0.893831i	−0.0521275	−	0.0378729i	−0.613544	+	0.789661i	$0.710257\pi$
$558$	−28.9111	+	21.0051i	−1.22390	+	0.889219i
$559$	3.85927	−	11.8776i	0.163230	−	0.502370i
$560$	−5.15456			−0.217820
$561$		0			0
$562$	−33.2519			−1.40265
$563$	0.202078	−	0.621933i	0.00851658	−	0.0262113i	−0.946708	−	0.322093i	$-0.895614\pi$
$563$	0.202078	−	0.621933i	0.00851658	−	0.0262113i	0.955225	+	0.295882i	$0.0956135\pi$
$564$	1.44726	−	1.05150i	0.0609407	−	0.0442760i
$565$	3.04878	+	2.21507i	0.128263	+	0.0931887i
$566$	−2.17140	−	6.68288i	−0.0912707	−	0.280902i
$567$	11.2161	+	34.5195i	0.471030	+	1.44968i
$568$	2.62155	+	1.90467i	0.109998	+	0.0799180i
$569$	−26.4230	+	19.1974i	−1.10771	+	0.804799i	−0.982302	−	0.187306i	$-0.940024\pi$
$569$	−26.4230	+	19.1974i	−1.10771	+	0.804799i	−0.125409	+	0.992105i	$0.540024\pi$
$570$	1.12462	−	3.46123i	0.0471052	−	0.144975i
$571$	26.1457			1.09416			0.547082	−	0.837079i	$-0.315738\pi$
$571$	26.1457			1.09416			0.547082	+	0.837079i	$0.315738\pi$
$572$		0			0
$573$	−54.2306			−2.26552
$574$	1.06330	−	3.27249i	0.0443811	−	0.136591i
$575$	2.94430	−	2.13916i	0.122786	−	0.0892091i
$576$	−51.9636	−	37.7538i	−2.16515	−	1.57307i
$577$	1.77183	+	5.45314i	0.0737624	+	0.227017i	0.981140	−	0.193300i	$-0.0619189\pi$
$577$	1.77183	+	5.45314i	0.0737624	+	0.227017i	−0.907377	+	0.420317i	$0.861919\pi$
$578$	−9.14426	−	28.1431i	−0.380351	−	1.17060i
$579$	−70.6719	−	51.3461i	−2.93702	−	2.13387i
$580$	0.733705	−	0.533068i	0.0304655	−	0.0221344i
$581$	−6.77719	+	20.8581i	−0.281165	+	0.865338i
$582$	−63.4134			−2.62857
$583$		0			0
$584$	36.0676			1.49249
$585$	4.56212	−	14.0407i	0.188620	−	0.580513i
$586$	12.2072	−	8.86906i	0.504276	−	0.366378i
$587$	−35.1587	−	25.5443i	−1.45116	−	1.05433i	−0.985560	−	0.169329i	$-0.945840\pi$
$587$	−35.1587	−	25.5443i	−1.45116	−	1.05433i	−0.465596	−	0.884997i	$-0.654160\pi$
$588$	0.596854	+	1.83693i	0.0246138	+	0.0757536i
$589$	0.855974	+	2.63442i	0.0352698	+	0.108549i
$590$	1.23906	+	0.900232i	0.0510114	+	0.0370620i
$591$	−6.74806	+	4.90275i	−0.277578	+	0.201672i
$592$	5.24915	−	16.1552i	0.215739	−	0.663975i
$593$	9.23707			0.379321			0.189661	−	0.981850i	$-0.439261\pi$
$593$	9.23707			0.379321			0.189661	+	0.981850i	$0.439261\pi$
$594$		0			0
$595$	−8.52360			−0.349434
$596$	0.298788	−	0.919574i	0.0122388	−	0.0376672i
$597$	57.6930	−	41.9164i	2.36122	−	1.71553i
$598$	−7.81049	−	5.67466i	−0.319395	−	0.232054i
$599$	−11.1513	−	34.3203i	−0.455631	−	1.40229i	−0.870392	−	0.492359i	$-0.836135\pi$
$599$	−11.1513	−	34.3203i	−0.455631	−	1.40229i	0.414761	−	0.909930i	$-0.363865\pi$
$600$	2.92734	+	9.00943i	0.119508	+	0.367809i
$601$	18.7118	+	13.5949i	0.763268	+	0.554547i	0.899911	−	0.436073i	$-0.143631\pi$
$601$	18.7118	+	13.5949i	0.763268	+	0.554547i	−0.136643	+	0.990620i	$0.543631\pi$
$602$	9.85127	−	7.15737i	0.401508	−	0.291713i
$603$	6.46404	−	19.8943i	0.263236	−	0.810157i
$604$	0.859237			0.0349619
$605$		0			0
$606$	51.0676			2.07448
$607$	6.79788	−	20.9217i	0.275917	−	0.849187i	−0.713058	−	0.701105i	$-0.752690\pi$
$607$	6.79788	−	20.9217i	0.275917	−	0.849187i	0.988975	−	0.148081i	$-0.0473097\pi$
$608$	−0.430023	+	0.312430i	−0.0174397	+	0.0126707i
$609$	−28.3811	−	20.6201i	−1.15006	−	0.835569i
$610$	−1.07949	−	3.32233i	−0.0437072	−	0.134517i
$611$	2.82959	+	8.70857i	0.114473	+	0.352311i
$612$	−4.44209	−	3.22736i	−0.179561	−	0.130458i
$613$	−6.81536	+	4.95165i	−0.275270	+	0.199995i	−0.716852	−	0.697226i	$-0.754418\pi$
$613$	−6.81536	+	4.95165i	−0.275270	+	0.199995i	0.441582	+	0.897221i	$0.354418\pi$
$614$	6.08762	−	18.7358i	0.245676	−	0.756114i
$615$	−5.95649			−0.240189
$616$		0			0
$617$	−17.8709			−0.719453			−0.359727	−	0.933058i	$-0.617130\pi$
$617$	−17.8709			−0.719453			−0.359727	+	0.933058i	$0.617130\pi$
$618$	−19.1917	+	59.0658i	−0.772002	+	2.37598i
$619$	−23.8743	+	17.3457i	−0.959587	+	0.697181i	−0.953055	−	0.302798i	$-0.902079\pi$
$619$	−23.8743	+	17.3457i	−0.959587	+	0.697181i	−0.00653257	+	0.999979i	$0.502079\pi$
$620$	−0.319123	−	0.231856i	−0.0128163	−	0.00931157i
$621$	−17.0185	−	52.3776i	−0.682930	−	2.10184i
$622$	−11.6145	−	35.7459i	−0.465701	−	1.43328i
$623$	3.00717	+	2.18484i	0.120480	+	0.0875338i
$624$	19.1498	−	13.9132i	0.766606	−	0.556972i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−5.31344			−0.212368
$627$		0			0
$628$	0.993617			0.0396496
$629$	8.68002	−	26.7144i	0.346095	−	1.06517i
$630$	11.6454	−	8.46085i	0.463962	−	0.337088i
$631$	−18.6239	−	13.5311i	−0.741406	−	0.538663i	0.151745	−	0.988420i	$-0.451511\pi$
$631$	−18.6239	−	13.5311i	−0.741406	−	0.538663i	−0.893151	+	0.449757i	$0.851511\pi$
$632$	−5.21290	−	16.0437i	−0.207358	−	0.638183i
$633$	12.9328	+	39.8031i	0.514033	+	1.58203i
$634$	−17.2244	−	12.5143i	−0.684069	−	0.497005i
$635$	−1.35880	+	0.987223i	−0.0539222	+	0.0391767i
$636$	0.979380	−	3.01422i	0.0388350	−	0.119522i
$637$	−9.88636			−0.391712
$638$		0			0
$639$	−8.52360			−0.337189
$640$	−3.16230	+	9.73256i	−0.125001	+	0.384713i
$641$	3.04878	−	2.21507i	0.120420	−	0.0874900i	−0.525945	−	0.850518i	$-0.676288\pi$
$641$	3.04878	−	2.21507i	0.120420	−	0.0874900i	0.646365	+	0.763028i	$0.276288\pi$
$642$	3.86064	+	2.80492i	0.152367	+	0.110701i
$643$	8.74551	+	26.9159i	0.344889	+	1.06146i	0.961643	+	0.274304i	$0.0884475\pi$
$643$	8.74551	+	26.9159i	0.344889	+	1.06146i	−0.616754	+	0.787156i	$0.711552\pi$
$644$	0.178688	+	0.549944i	0.00704128	+	0.0216708i
$645$	−17.0534	−	12.3900i	−0.671477	−	0.487857i
$646$	5.60503	−	4.07230i	0.220527	−	0.160222i
$647$	3.63944	−	11.2010i	0.143081	−	0.440358i	−0.853678	−	0.520801i	$-0.825633\pi$
$647$	3.63944	−	11.2010i	0.143081	−	0.440358i	0.996759	+	0.0804426i	$0.0256334\pi$
$648$	76.7931			3.01672
$649$		0			0
$650$	−2.65275			−0.104049
$651$	−4.71509	+	14.5116i	−0.184799	+	0.568753i
$652$	1.53365	−	1.11426i	0.0600622	−	0.0436378i
$653$	37.3185	+	27.1135i	1.46039	+	1.06103i	0.983262	+	0.182197i	$0.0583210\pi$
$653$	37.3185	+	27.1135i	1.46039	+	1.06103i	0.477125	+	0.878836i	$0.341679\pi$
$654$	15.6506	+	48.1676i	0.611986	+	1.88350i
$655$	−3.64463	−	11.2170i	−0.142407	−	0.438285i
$656$	−5.54769	−	4.03063i	−0.216601	−	0.157370i
$657$	−76.7535	+	55.7647i	−2.99444	+	2.17559i
$658$	−2.75889	+	8.49099i	−0.107553	+	0.331013i
$659$	15.7781			0.614626			0.307313	−	0.951609i	$-0.400570\pi$
$659$	15.7781			0.614626			0.307313	+	0.951609i	$0.400570\pi$
$660$		0			0
$661$	−38.6732			−1.50421			−0.752106	−	0.659042i	$-0.770962\pi$
$661$	−38.6732			−1.50421			−0.752106	+	0.659042i	$0.770962\pi$
$662$	−11.3924	+	35.0623i	−0.442780	+	1.36274i
$663$	31.6662	−	23.0069i	1.22981	−	0.893513i
$664$	37.5396	+	27.2741i	1.45682	+	1.05844i
$665$	−0.344786	−	1.06114i	−0.0133702	−	0.0411493i
$666$	14.6586	+	45.1146i	0.568010	+	1.74815i
$667$	23.0689	+	16.7605i	0.893232	+	0.648971i
$668$	−2.00757	+	1.45859i	−0.0776754	+	0.0564345i
$669$	−7.42272	+	22.8448i	−0.286979	+	0.883230i
$670$	−3.75867			−0.145210
$671$		0			0
$672$	−2.92795			−0.112948
$673$	−13.6830	+	42.1119i	−0.527440	+	1.62329i	0.231999	+	0.972716i	$0.425473\pi$
$673$	−13.6830	+	42.1119i	−0.527440	+	1.62329i	−0.759439	+	0.650578i	$0.774527\pi$
$674$	−2.14612	+	1.55925i	−0.0826655	+	0.0600600i
$675$	−12.2426	−	8.89475i	−0.471217	−	0.342359i
$676$	0.331407	+	1.01996i	0.0127464	+	0.0392294i
$677$	−2.08279	−	6.41015i	−0.0800479	−	0.246362i	0.903022	−	0.429595i	$-0.141344\pi$
$677$	−2.08279	−	6.41015i	−0.0800479	−	0.246362i	−0.983070	+	0.183233i	$0.941344\pi$
$678$	−13.6506	−	9.91778i	−0.524250	−	0.380890i
$679$	−15.7283	+	11.4273i	−0.603596	+	0.438538i
$680$	−5.57275	+	17.1512i	−0.213705	+	0.657717i
$681$	4.47741			0.171575
$682$		0			0
$683$	33.3303			1.27535			0.637675	−	0.770305i	$-0.279896\pi$
$683$	33.3303			1.27535			0.637675	+	0.770305i	$0.279896\pi$
$684$	0.222103	−	0.683564i	0.00849233	−	0.0261367i
$685$	5.99308	−	4.35423i	0.228984	−	0.166366i
$686$	−18.4691	−	13.4186i	−0.705155	−	0.512325i
$687$	29.7314	+	91.5038i	1.13432	+	3.49109i
$688$	−7.49895	−	23.0794i	−0.285895	−	0.879893i
$689$	13.1243	+	9.53539i	0.499998	+	0.363270i
$690$	−13.1828	+	9.57789i	−0.501862	+	0.364624i
$691$	2.78284	−	8.56471i	0.105864	−	0.325817i	−0.884068	−	0.467358i	$-0.845206\pi$
$691$	2.78284	−	8.56471i	0.105864	−	0.325817i	0.989932	+	0.141541i	$0.0452058\pi$
$692$	1.59013			0.0604477
$693$		0			0
$694$	5.21655			0.198018
$695$	0.819289	−	2.52151i	0.0310774	−	0.0956465i
$696$	−60.0474	+	43.6270i	−2.27609	+	1.65368i
$697$	−9.17370	−	6.66508i	−0.347479	−	0.252458i
$698$	7.29206	+	22.4427i	0.276009	+	0.849467i
$699$	22.1733	+	68.2425i	0.838673	+	2.58117i
$700$	0.128542	+	0.0933914i	0.00485844	+	0.00352986i
$701$	37.1289	−	26.9757i	1.40234	−	1.01886i	0.407957	−	0.913001i	$-0.366241\pi$
$701$	37.1289	−	26.9757i	1.40234	−	1.01886i	0.994381	−	0.105857i	$-0.0337587\pi$
$702$	−12.4049	+	38.1784i	−0.468194	+	1.44095i
$703$	3.67690			0.138677
$704$		0			0
$705$	15.4551			0.582071
$706$	0.844998	−	2.60064i	0.0318019	−	0.0978762i
$707$	12.6662	−	9.20252i	0.476361	−	0.346096i
$708$	0.340801	+	0.247606i	0.0128081	+	0.00930561i
$709$	−2.62980	−	8.09369i	−0.0987642	−	0.303965i	0.889452	−	0.457028i	$-0.151086\pi$
$709$	−2.62980	−	8.09369i	−0.0987642	−	0.303965i	−0.988216	+	0.153063i	$0.951086\pi$
$710$	0.473280	+	1.45661i	0.0177619	+	0.0546655i
$711$	35.8986	+	26.0819i	1.34630	+	0.978147i
$712$	6.36243	−	4.62257i	0.238442	−	0.173238i
$713$	3.83255	−	11.7954i	0.143530	−	0.441740i
$714$	38.1637			1.42824
$715$		0			0
$716$	0.436202			0.0163016
$717$	18.8714	−	58.0801i	0.704764	−	2.16904i
$718$	17.2976	−	12.5675i	0.645542	−	0.469014i
$719$	7.77105	+	5.64600i	0.289811	+	0.210560i	0.723185	−	0.690654i	$-0.242677\pi$
$719$	7.77105	+	5.64600i	0.289811	+	0.210560i	−0.433374	+	0.901214i	$0.642677\pi$
$720$	−8.86464	−	27.2825i	−0.330365	−	1.01676i
$721$	5.88376	+	18.1083i	0.219123	+	0.674390i
$722$	−20.3662	−	14.7969i	−0.757952	−	0.550684i
$723$	69.3042	−	50.3525i	2.57745	−	1.87263i
$724$	0.000479224	−	0.00147490i	1.78102e−5	−	5.48142e-5i
$725$	7.83511			0.290989
$726$		0			0
$727$	32.9688			1.22274			0.611372	−	0.791343i	$-0.290618\pi$
$727$	32.9688			1.22274			0.611372	+	0.791343i	$0.290618\pi$
$728$	2.38074	−	7.32717i	0.0882362	−	0.271563i
$729$	−43.6206	+	31.6922i	−1.61558	+	1.17379i
$730$	13.7915	+	10.0201i	0.510446	+	0.370860i
$731$	−12.4003	−	38.1642i	−0.458642	−	1.41155i
$732$	−0.296910	−	0.913796i	−0.0109741	−	0.0337749i
$733$	−22.1431	−	16.0879i	−0.817875	−	0.594221i	0.0982280	−	0.995164i	$-0.468683\pi$
$733$	−22.1431	−	16.0879i	−0.817875	−	0.594221i	−0.916103	+	0.400943i	$0.868683\pi$
$734$	20.8467	−	15.1460i	0.769466	−	0.559050i
$735$	−5.15643	+	15.8699i	−0.190198	+	0.585369i
$736$	2.37991			0.0877248
$737$		0			0
$738$	19.1496			0.704905
$739$	−11.9171	+	36.6772i	−0.438379	+	1.34919i	0.451206	+	0.892420i	$0.350994\pi$
$739$	−11.9171	+	36.6772i	−0.438379	+	1.34919i	−0.889584	+	0.456771i	$0.849006\pi$
$740$	−0.423605	+	0.307767i	−0.0155720	+	0.0113137i
$741$	4.14515	+	3.01163i	0.152276	+	0.110635i
$742$	4.88780	+	15.0431i	0.179437	+	0.552250i
$743$	−10.5574	−	32.4922i	−0.387312	−	1.19202i	−0.934789	−	0.355204i	$-0.884412\pi$
$743$	−10.5574	−	32.4922i	−0.387312	−	1.19202i	0.547477	−	0.836821i	$-0.315588\pi$
$744$	26.1174	+	18.9754i	0.957510	+	0.695672i
$745$	6.75802	−	4.90999i	0.247595	−	0.179888i
$746$	−1.11417	+	3.42908i	−0.0407928	+	0.125547i
$747$	−122.055			−4.46575
$748$		0			0
$749$	1.46300			0.0534568
$750$	−1.38360	+	4.25827i	−0.0505218	+	0.155490i
$751$	37.1586	−	26.9973i	1.35594	−	0.985145i	0.357244	−	0.934011i	$-0.383716\pi$
$751$	37.1586	−	26.9973i	1.35594	−	0.985145i	0.998692	−	0.0511343i	$-0.0162837\pi$
$752$	14.3944	+	10.4581i	0.524909	+	0.381369i
$753$	−22.8059	−	70.1893i	−0.831093	−	2.55784i
$754$	−6.42280	−	19.7673i	−0.233904	−	0.719884i
$755$	6.00554	+	4.36328i	0.218564	+	0.158796i
$756$	1.94518	−	1.41326i	0.0707457	−	0.0513997i
$757$	−9.33960	+	28.7443i	−0.339453	+	1.04473i	0.625033	+	0.780598i	$0.285085\pi$
$757$	−9.33960	+	28.7443i	−0.339453	+	1.04473i	−0.964487	+	0.264132i	$0.914915\pi$
$758$	−3.65227			−0.132656
$759$		0			0
$760$	−2.36065			−0.0856296
$761$	4.15035	−	12.7735i	0.150450	−	0.463037i	−0.847222	−	0.531240i	$-0.821726\pi$
$761$	4.15035	−	12.7735i	0.150450	−	0.463037i	0.997672	+	0.0682023i	$0.0217263\pi$
$762$	6.08389	−	4.42020i	0.220396	−	0.160127i
$763$	12.5617	+	9.12661i	0.454764	+	0.330405i
$764$	0.594686	+	1.83026i	0.0215150	+	0.0662163i
$765$	−14.6586	−	45.1146i	−0.529983	−	1.63112i
$766$	24.3554	+	17.6952i	0.879995	+	0.639354i
$767$	−1.74442	+	1.26740i	−0.0629874	+	0.0457630i
$768$	−2.79052	+	8.58833i	−0.100694	+	0.309905i
$769$	−10.8982			−0.393001			−0.196500	−	0.980504i	$-0.562958\pi$
$769$	−10.8982			−0.393001			−0.196500	+	0.980504i	$0.562958\pi$
$770$		0			0
$771$	56.1362			2.02169
$772$	−0.957927	+	2.94820i	−0.0344765	+	0.106108i
$773$	−10.6382	+	7.72912i	−0.382630	+	0.277997i	−0.762429	−	0.647072i	$-0.775993\pi$
$773$	−10.6382	+	7.72912i	−0.382630	+	0.277997i	0.379799	+	0.925069i	$0.375993\pi$
$774$	54.8251	+	39.8328i	1.97065	+	1.43176i
$775$	−1.05309	−	3.24106i	−0.0378279	−	0.116422i
$776$	12.7107	+	39.1196i	0.456288	+	1.40431i
$777$	16.3859	+	11.9050i	0.587839	+	0.427090i
$778$	−3.79938	+	2.76041i	−0.136214	+	0.0989654i
$779$	0.458683	−	1.41168i	0.0164340	−	0.0505787i
$780$	−0.729632			−0.0261250
$781$		0			0
$782$	−31.0204			−1.10929
$783$	36.6389	−	112.763i	1.30937	−	4.02982i
$784$	−15.5414	+	11.2915i	−0.555048	+	0.403266i
$785$	6.94477	+	5.04567i	0.247870	+	0.180088i
$786$	16.3185	+	50.2232i	0.582062	+	1.79140i
$787$	−3.56646	−	10.9764i	−0.127130	−	0.391267i	0.867153	−	0.498042i	$-0.165948\pi$
$787$	−3.56646	−	10.9764i	−0.127130	−	0.391267i	−0.994283	+	0.106775i	$0.965948\pi$
$788$	0.239464	+	0.173981i	0.00853054	+	0.00619780i
$789$	−15.0795	+	10.9559i	−0.536844	+	0.390040i
$790$	2.46386	−	7.58297i	0.0876600	−	0.269790i
$791$	−5.17295			−0.183929
$792$		0			0
$793$	4.91806			0.174645
$794$	−2.33733	+	7.19355i	−0.0829487	+	0.255290i
$795$	22.1517	−	16.0942i	0.785641	−	0.570802i
$796$	−2.04731	−	1.48746i	−0.0725651	−	0.0527217i
$797$	−1.71348	−	5.27355i	−0.0606946	−	0.186799i	0.916112	−	0.400923i	$-0.131310\pi$
$797$	−1.71348	−	5.27355i	−0.0606946	−	0.186799i	−0.976807	+	0.214124i	$0.931310\pi$
$798$	1.54375	+	4.75116i	0.0546480	+	0.168189i
$799$	23.8026	+	17.2936i	0.842076	+	0.611804i
$800$	0.529047	−	0.384375i	0.0187047	−	0.0135897i
$801$	−6.39250	+	19.6741i	−0.225868	+	0.695150i
$802$	24.6067			0.868891
$803$		0			0
$804$	−1.03381			−0.0364597
$805$	−1.54375	+	4.75116i	−0.0544099	+	0.167456i
$806$	−7.31367	+	5.31369i	−0.257613	+	0.187167i
$807$	7.57576	+	5.50411i	0.266679	+	0.193754i
$808$	−10.2361	−	31.5035i	−0.360105	−	1.10829i
$809$	5.69834	+	17.5377i	0.200343	+	0.616592i	0.999873	+	0.0159656i	$0.00508221\pi$
$809$	5.69834	+	17.5377i	0.200343	+	0.616592i	−0.799530	+	0.600627i	$0.794918\pi$
$810$	29.3640	+	21.3342i	1.03175	+	0.749608i
$811$	−5.11960	+	3.71961i	−0.179774	+	0.130613i	−0.674033	−	0.738701i	$-0.735439\pi$
$811$	−5.11960	+	3.71961i	−0.179774	+	0.130613i	0.494259	+	0.869315i	$0.335439\pi$
$812$	−0.384694	+	1.18397i	−0.0135001	+	0.0415491i
$813$	−24.9428			−0.874783
$814$		0			0
$815$	16.3776			0.573681
$816$	23.5026	−	72.3336i	0.822755	−	2.53218i
$817$	4.24963	−	3.08754i	0.148676	−	0.108019i
$818$	32.5673	+	23.6615i	1.13869	+	0.827306i
$819$	6.26233	+	19.2735i	0.218823	+	0.673469i
$820$	0.0653182	+	0.201029i	0.00228101	+	0.00702022i
$821$	−6.43363	−	4.67431i	−0.224535	−	0.163134i	0.469831	−	0.882757i	$-0.344315\pi$
$821$	−6.43363	−	4.67431i	−0.224535	−	0.163134i	−0.694366	+	0.719622i	$0.744315\pi$
$822$	−26.8335	+	19.4957i	−0.935925	+	0.679990i
$823$	0.408647	−	1.25769i	0.0142445	−	0.0438402i	−0.943682	−	0.330855i	$-0.892663\pi$
$823$	0.408647	−	1.25769i	0.0142445	−	0.0438402i	0.957926	+	0.287015i	$0.0926629\pi$
$824$	40.2844			1.40337
$825$		0			0
$826$	−2.10235			−0.0731502
$827$	−1.39982	+	4.30819i	−0.0486764	+	0.149810i	−0.972440	−	0.233152i	$-0.925096\pi$
$827$	−1.39982	+	4.30819i	−0.0486764	+	0.149810i	0.923764	+	0.382962i	$0.125096\pi$
$828$	−2.60350	+	1.89155i	−0.0904778	+	0.0657360i
$829$	30.5928	+	22.2270i	1.06253	+	0.771975i	0.974555	−	0.224148i	$-0.0719598\pi$
$829$	30.5928	+	22.2270i	1.06253	+	0.771975i	0.0879770	+	0.996123i	$0.471960\pi$
$830$	6.77719	+	20.8581i	0.235240	+	0.723994i
$831$	−29.6308	−	91.1942i	−1.02788	−	3.16349i
$832$	−13.1453	−	9.55061i	−0.455731	−	0.331108i
$833$	−25.6993	+	18.6716i	−0.890427	+	0.646933i
$834$	−3.66830	+	11.2899i	−0.127023	+	0.390936i
$835$	−21.4385			−0.741912
$836$		0			0
$837$	−51.5699			−1.78252
$838$	−1.12525	+	3.46316i	−0.0388711	+	0.119633i
$839$	31.7555	−	23.0717i	1.09632	−	0.796523i	0.115865	−	0.993265i	$-0.463036\pi$
$839$	31.7555	−	23.0717i	1.09632	−	0.796523i	0.980455	+	0.196742i	$0.0630360\pi$
$840$	−10.5201	−	7.64327i	−0.362977	−	0.263718i
$841$	10.0087	+	30.8038i	0.345129	+	1.06220i
$842$	4.73512	+	14.5732i	0.163183	+	0.502226i
$843$	−63.9238	−	46.4434i	−2.20165	−	1.59959i
$844$	1.20152	−	0.872952i	0.0413579	−	0.0300483i
$845$	−2.86314	+	8.81183i	−0.0984949	+	0.303136i
$846$	−49.6866			−1.70826
$847$		0			0
$848$	31.5221			1.08247
$849$	5.15974	−	15.8801i	0.177082	−	0.545002i
$850$	−6.89574	+	5.01005i	−0.236522	+	0.171843i
$851$	−13.3188	−	9.67671i	−0.456564	−	0.331713i
$852$	0.130174	+	0.400635i	0.00445970	+	0.0137255i
$853$	10.3186	+	31.7574i	0.353302	+	1.08735i	0.956987	+	0.290130i	$0.0936984\pi$
$853$	10.3186	+	31.7574i	0.353302	+	1.08735i	−0.603685	+	0.797223i	$0.706302\pi$
$854$	3.87939	+	2.81854i	0.132750	+	0.0964484i
$855$	5.02356	−	3.64983i	0.171802	−	0.124822i
$856$	0.956512	−	2.94384i	0.0326929	−	0.100618i
$857$	−16.9781			−0.579961			−0.289980	−	0.957033i	$-0.593649\pi$
$857$	−16.9781			−0.579961			−0.289980	+	0.957033i	$0.593649\pi$
$858$		0			0
$859$	−40.8148			−1.39258			−0.696291	−	0.717759i	$-0.745168\pi$
$859$	−40.8148			−1.39258			−0.696291	+	0.717759i	$0.745168\pi$
$860$	−0.231152	+	0.711412i	−0.00788221	+	0.0242589i
$861$	6.61481	−	4.80594i	0.225432	−	0.163786i
$862$	5.06307	+	3.67853i	0.172449	+	0.125291i
$863$	10.8250	+	33.3158i	0.368486	+	1.13408i	0.947769	+	0.318957i	$0.103332\pi$
$863$	10.8250	+	33.3158i	0.368486	+	1.13408i	−0.579283	+	0.815126i	$0.696668\pi$
$864$	−3.05798	−	9.41149i	−0.104035	−	0.320185i
$865$	11.1140	+	8.07481i	0.377888	+	0.274552i
$866$	22.3914	−	16.2683i	0.760891	−	0.552819i
$867$	21.7288	−	66.8745i	0.737950	−	2.27118i
$868$	0.541464			0.0183785
$869$		0			0
$870$	−35.0810			−1.18936
$871$	1.63521	−	5.03267i	0.0554071	−	0.170526i
$872$	26.5774	−	19.3096i	0.900024	−	0.653906i
$873$	−87.5323	−	63.5959i	−2.96252	−	2.15240i
$874$	−1.25480	−	3.86187i	−0.0424441	−	0.130630i
$875$	0.424181	+	1.30550i	0.0143400	+	0.0441338i
$876$	3.79331	+	2.75600i	0.128164	+	0.0931166i
$877$	21.5705	−	15.6719i	0.728383	−	0.529201i	−0.160669	−	0.987008i	$-0.551365\pi$
$877$	21.5705	−	15.6719i	0.728383	−	0.529201i	0.889051	+	0.457807i	$0.151365\pi$
$878$	14.6287	−	45.0224i	0.493693	−	1.51943i
$879$	35.8548			1.20935
$880$		0			0
$881$	−4.66615			−0.157207			−0.0786033	−	0.996906i	$-0.525046\pi$
$881$	−4.66615			−0.157207			−0.0786033	+	0.996906i	$0.525046\pi$
$882$	16.5774	−	51.0201i	0.558192	−	1.71794i
$883$	−5.23509	+	3.80352i	−0.176175	+	0.127999i	−0.672378	−	0.740208i	$-0.734727\pi$
$883$	−5.23509	+	3.80352i	−0.176175	+	0.127999i	0.496203	+	0.868206i	$0.334727\pi$
$884$	−1.12372	−	0.816429i	−0.0377948	−	0.0274595i
$885$	1.12462	+	3.46123i	0.0378038	+	0.116348i
$886$	−13.3441	−	41.0691i	−0.448305	−	1.37974i
$887$	−14.8461	−	10.7863i	−0.498483	−	0.362169i	0.309954	−	0.950751i	$-0.399686\pi$
$887$	−14.8461	−	10.7863i	−0.498483	−	0.362169i	−0.808437	+	0.588582i	$0.799686\pi$
$888$	34.6684	−	25.1880i	1.16339	−	0.845256i
$889$	0.712440	−	2.19266i	0.0238945	−	0.0735396i
$890$	3.71707			0.124597
$891$		0			0
$892$	0.852396			0.0285403
$893$	−1.19013	+	3.66283i	−0.0398260	+	0.122572i
$894$	−30.2584	+	21.9840i	−1.01199	+	0.735256i
$895$	3.04878	+	2.21507i	0.101910	+	0.0740416i
$896$	−4.34083	−	13.3597i	−0.145017	−	0.446316i
$897$	−7.08911	−	21.8180i	−0.236698	−	0.728483i
$898$	−5.30433	−	3.85382i	−0.177008	−	0.128604i
$899$	21.6015	−	15.6944i	0.720451	−	0.523438i
$900$	−0.273248	+	0.840972i	−0.00910828	+	0.0280324i
$901$	52.1251			1.73654
$902$		0			0
$903$	28.9350			0.962895
$904$	−3.38209	+	10.4090i	−0.112486	+	0.346198i
$905$	0.0108391	−	0.00787510i	0.000360305	−	0.000261777i
$906$	−26.8893	−	19.5362i	−0.893336	−	0.649047i
$907$	−9.20391	−	28.3267i	−0.305611	−	0.940574i	−0.979449	−	0.201694i	$-0.935355\pi$
$907$	−9.20391	−	28.3267i	−0.305611	−	0.940574i	0.673838	−	0.738879i	$-0.264645\pi$
$908$	−0.0490987	−	0.151110i	−0.00162940	−	0.00501478i
$909$	70.4909	+	51.2146i	2.33804	+	1.69868i
$910$	2.94594	−	2.14035i	0.0976569	−	0.0709519i
$911$	14.1746	−	43.6249i	0.469625	−	1.44536i	−0.383446	−	0.923563i	$-0.625263\pi$
$911$	14.1746	−	43.6249i	0.469625	−	1.44536i	0.853071	−	0.521794i	$-0.174737\pi$
$912$	9.95582			0.329670
$913$		0			0
$914$	−2.10235			−0.0695396
$915$	2.56511	−	7.89461i	0.0848001	−	0.260988i
$916$	2.76218	−	2.00684i	0.0912649	−	0.0663078i
$917$	13.0978	+	9.51610i	0.432527	+	0.314249i
$918$	39.8585	+	122.672i	1.31553	+	4.04877i
$919$	−17.9648	−	55.2901i	−0.592606	−	1.82385i	−0.566301	−	0.824199i	$-0.691626\pi$
$919$	−17.9648	−	55.2901i	−0.592606	−	1.82385i	−0.0263047	−	0.999654i	$-0.508374\pi$
$920$	8.55097	+	6.21264i	0.281917	+	0.204825i
$921$	37.8714	−	27.5152i	1.24790	−	0.906656i
$922$	−7.85668	+	24.1804i	−0.258746	+	0.796339i
$923$	−2.15622			−0.0709730
$924$		0			0
$925$	−4.52360			−0.148735
$926$	−4.10737	+	12.6412i	−0.134977	+	0.415415i
$927$	−85.7270	+	62.2843i	−2.81564	+	2.04568i
$928$	4.14515	+	3.01163i	0.136071	+	0.0988614i
$929$	12.3100	+	37.8864i	0.403879	+	1.24301i	0.921827	+	0.387601i	$0.126696\pi$
$929$	12.3100	+	37.8864i	0.403879	+	1.24301i	−0.517948	+	0.855412i	$0.673304\pi$
$930$	4.71509	+	14.5116i	0.154614	+	0.475853i
$931$	−3.36406	−	2.44414i	−0.110253	−	0.0801033i
$932$	2.06000	−	1.49668i	0.0674776	−	0.0490253i
$933$	27.5988	−	84.9404i	0.903544	−	2.78082i
$934$	43.5112			1.42373
$935$		0			0
$936$	42.8763			1.40146
$937$	2.98930	−	9.20011i	0.0976560	−	0.300554i	−0.890281	−	0.455412i	$-0.849492\pi$
$937$	2.98930	−	9.20011i	0.0976560	−	0.300554i	0.987937	+	0.154858i	$0.0494919\pi$
$938$	4.17408	−	3.03265i	0.136289	−	0.0990195i
$939$	−10.2146	−	7.42135i	−0.333341	−	0.242187i
$940$	−0.169478	−	0.521601i	−0.00552777	−	0.0170127i
$941$	1.22725	+	3.77709i	0.0400073	+	0.123130i	0.969065	−	0.246804i	$-0.0793804\pi$
$941$	1.22725	+	3.77709i	0.0400073	+	0.123130i	−0.929058	+	0.369934i	$0.879380\pi$
$942$	−31.0946	−	22.5916i	−1.01312	−	0.736073i
$943$	−5.37669	+	3.90639i	−0.175089	+	0.127210i
$944$	−1.29471	+	3.98469i	−0.0421391	+	0.129691i
$945$	20.7723			0.675723
$946$		0			0
$947$	2.65275			0.0862029			0.0431014	−	0.999071i	$-0.486276\pi$
$947$	2.65275			0.0862029			0.0431014	+	0.999071i	$0.486276\pi$
$948$	0.677676	−	2.08567i	0.0220099	−	0.0677395i
$949$	−19.4164	+	14.1068i	−0.630283	+	0.457928i
$950$	−0.902660	−	0.655821i	−0.0292862	−	0.0212776i
$951$	−15.6335	−	48.1151i	−0.506953	−	1.56024i
$952$	−7.64961	−	23.5431i	−0.247925	−	0.763035i
$953$	16.8824	+	12.2658i	0.546875	+	0.397328i	0.826632	−	0.562743i	$-0.190254\pi$
$953$	16.8824	+	12.2658i	0.546875	+	0.397328i	−0.279757	+	0.960071i	$0.590254\pi$
$954$	−71.2158	+	51.7413i	−2.30570	+	1.67519i
$955$	−5.13770	+	15.8122i	−0.166252	+	0.511672i
$956$	−2.16711			−0.0700895
$957$		0			0
$958$	−42.3259			−1.36749
$959$	−3.14227	+	9.67093i	−0.101469	+	0.312291i
$960$	−22.1871	+	16.1199i	−0.716085	+	0.520267i
$961$	15.6840	+	11.3951i	0.505936	+	0.367584i
$962$	3.70820	+	11.4127i	0.119557	+	0.367960i
$963$	2.51602	+	7.74350i	0.0810775	+	0.249531i
$964$	−2.45935	−	1.78682i	−0.0792104	−	0.0575498i
$965$	−21.6665	+	15.7416i	−0.697469	+	0.506741i
$966$	6.91199	−	21.2729i	0.222390	−	0.684445i
$967$	58.5364			1.88240			0.941202	−	0.337843i	$-0.109697\pi$
$967$	58.5364			1.88240			0.941202	+	0.337843i	$0.109697\pi$
$968$		0			0
$969$	16.4630			0.528868
$970$	−6.00766	+	18.4897i	−0.192894	+	0.593668i
$971$	45.5196	−	33.0719i	1.46079	−	1.06133i	0.477638	−	0.878557i	$-0.341493\pi$
$971$	45.5196	−	33.0719i	1.46079	−	1.06133i	0.983155	−	0.182772i	$-0.0585069\pi$
$972$	3.82528	+	2.77923i	0.122696	+	0.0891438i
$973$	1.12462	+	3.46123i	0.0360537	+	0.110962i
$974$	−12.7221	−	39.1545i	−0.407642	−	1.25459i
$975$	−5.09968	−	3.70513i	−0.163320	−	0.118659i
$976$	7.73119	−	5.61704i	0.247469	−	0.179797i
$977$	11.4295	−	35.1763i	0.365662	−	1.12539i	−0.583904	−	0.811823i	$-0.698476\pi$
$977$	11.4295	−	35.1763i	0.365662	−	1.12539i	0.949566	−	0.313568i	$-0.101524\pi$
$978$	−73.3290			−2.34480
$979$		0			0
$980$	0.592145			0.0189154
$981$	−26.7030	+	82.1834i	−0.852562	+	2.62392i
$982$	38.3257	−	27.8452i	1.22302	−	0.888577i
$983$	15.9087	+	11.5583i	0.507408	+	0.368653i	0.811839	−	0.583881i	$-0.198467\pi$
$983$	15.9087	+	11.5583i	0.507408	+	0.368653i	−0.304432	+	0.952534i	$0.598467\pi$
$984$	−5.34572	−	16.4524i	−0.170415	−	0.524485i
$985$	0.790216	+	2.43203i	0.0251784	+	0.0774911i
$986$	−54.0289	−	39.2543i	−1.72063	−	1.25011i
$987$	−17.1632	+	12.4698i	−0.546310	+	0.396918i
$988$	0.0561857	−	0.172922i	0.00178750	−	0.00550137i
$989$	−23.5191			−0.747863
$990$		0			0
$991$	18.5763			0.590095			0.295047	−	0.955483i	$-0.404665\pi$
$991$	18.5763			0.590095			0.295047	+	0.955483i	$0.404665\pi$
$992$	0.688653	−	2.11946i	0.0218648	−	0.0672928i
$993$	−70.8729	+	51.4922i	−2.24908	+	1.63405i
$994$	−1.70084	−	1.23573i	−0.0539473	−	0.0391950i
$995$	−6.75601	−	20.7929i	−0.214180	−	0.659178i
$996$	1.86405	+	5.73695i	0.0590646	+	0.181782i
$997$	24.3554	+	17.6952i	0.771342	+	0.560413i	0.902368	−	0.430966i	$-0.141827\pi$
$997$	24.3554	+	17.6952i	0.771342	+	0.560413i	−0.131026	+	0.991379i	$0.541827\pi$
$998$	19.8372	−	14.4125i	0.627934	−	0.456221i
$999$	−21.1535	+	65.1038i	−0.669267	+	2.05979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.q.251.2		24
11.2	odd	10	inner	605.2.g.q.366.2		24
11.3	even	5	inner	605.2.g.q.81.5		24
11.4	even	5		605.2.a.m.1.2	✓	6
11.5	even	5	inner	605.2.g.q.511.2		24
11.6	odd	10	inner	605.2.g.q.511.5		24
11.7	odd	10		605.2.a.m.1.5	yes	6
11.8	odd	10	inner	605.2.g.q.81.2		24
11.9	even	5	inner	605.2.g.q.366.5		24
11.10	odd	2	inner	605.2.g.q.251.5		24
33.26	odd	10		5445.2.a.bx.1.5		6
33.29	even	10		5445.2.a.bx.1.2		6
44.7	even	10		9680.2.a.cw.1.2		6
44.15	odd	10		9680.2.a.cw.1.1		6
55.4	even	10		3025.2.a.bg.1.5		6
55.29	odd	10		3025.2.a.bg.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.2	✓	6	11.4	even	5
605.2.a.m.1.5	yes	6	11.7	odd	10
605.2.g.q.81.2		24	11.8	odd	10	inner
605.2.g.q.81.5		24	11.3	even	5	inner
605.2.g.q.251.2		24	1.1	even	1	trivial
605.2.g.q.251.5		24	11.10	odd	2	inner
605.2.g.q.366.2		24	11.2	odd	10	inner
605.2.g.q.366.5		24	11.9	even	5	inner
605.2.g.q.511.2		24	11.5	even	5	inner
605.2.g.q.511.5		24	11.6	odd	10	inner
3025.2.a.bg.1.2		6	55.29	odd	10
3025.2.a.bg.1.5		6	55.4	even	10
5445.2.a.bx.1.2		6	33.29	even	10
5445.2.a.bx.1.5		6	33.26	odd	10
9680.2.a.cw.1.1		6	44.15	odd	10
9680.2.a.cw.1.2		6	44.7	even	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.424181 + 1.30550i) q^{2} +(-2.63885 + 1.91724i) q^{3} +(0.0936432 + 0.0680358i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.38360 - 4.25827i) q^{6} +(-1.11052 - 0.806841i) q^{7} +(-2.34959 + 1.70707i) q^{8} +(2.36069 - 7.26546i) q^{9} +O(q^{10})\)	\(q+(-0.424181 + 1.30550i) q^{2} +(-2.63885 + 1.91724i) q^{3} +(0.0936432 + 0.0680358i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.38360 - 4.25827i) q^{6} +(-1.11052 - 0.806841i) q^{7} +(-2.34959 + 1.70707i) q^{8} +(2.36069 - 7.26546i) q^{9} -1.37268 q^{10} -0.377552 q^{12} +(0.597186 - 1.83795i) q^{13} +(1.52439 - 1.10753i) q^{14} +(-2.63885 - 1.91724i) q^{15} +(-1.16039 - 3.57132i) q^{16} +(-1.91883 - 5.90555i) q^{17} +(8.48367 + 6.16374i) q^{18} +(0.657590 - 0.477767i) q^{19} +(-0.0357685 + 0.110084i) q^{20} +4.47741 q^{21} -3.63935 q^{23} +(2.92734 - 9.00943i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.14612 + 1.55925i) q^{26} +(4.67625 + 14.3920i) q^{27} +(-0.0490987 - 0.151110i) q^{28} +(-6.33874 - 4.60536i) q^{29} +(3.62230 - 2.63176i) q^{30} +(-1.05309 + 3.24106i) q^{31} -0.653939 q^{32} +8.52360 q^{34} +(0.424181 - 1.30550i) q^{35} +(0.715374 - 0.519749i) q^{36} +(3.65967 + 2.65891i) q^{37} +(0.344786 + 1.06114i) q^{38} +(1.94790 + 5.99503i) q^{39} +(-2.34959 - 1.70707i) q^{40} +(1.47737 - 1.07338i) q^{41} +(-1.89923 + 5.84524i) q^{42} +6.46243 q^{43} +7.63935 q^{45} +(1.54375 - 4.75116i) q^{46} +(-3.83328 + 2.78504i) q^{47} +(9.90917 + 7.19943i) q^{48} +(-1.58085 - 4.86537i) q^{49} +(-0.424181 - 1.30550i) q^{50} +(16.3859 + 11.9050i) q^{51} +(0.180969 - 0.131482i) q^{52} +(-2.59403 + 7.98360i) q^{53} -20.7723 q^{54} +3.98660 q^{56} +(-0.819289 + 2.52151i) q^{57} +(8.70106 - 6.32169i) q^{58} +(-0.902660 - 0.655821i) q^{59} +(-0.116670 - 0.359073i) q^{60} +(0.786410 + 2.42032i) q^{61} +(-3.78450 - 2.74960i) q^{62} +(-8.48367 + 6.16374i) q^{63} +(2.59817 - 7.99635i) q^{64} +1.93253 q^{65} +2.73820 q^{67} +(0.222103 - 0.683564i) q^{68} +(9.60372 - 6.97751i) q^{69} +(1.52439 + 1.10753i) q^{70} +(-0.344786 - 1.06114i) q^{71} +(6.85603 + 21.1007i) q^{72} +(-10.0471 - 7.29966i) q^{73} +(-5.02356 + 3.64983i) q^{74} +(1.00795 - 3.10216i) q^{75} +0.0940841 q^{76} -8.65275 q^{78} +(-1.79492 + 5.52421i) q^{79} +(3.03794 - 2.20719i) q^{80} +(-21.3918 - 15.5420i) q^{81} +(0.774613 + 2.38401i) q^{82} +(-4.93720 - 15.1951i) q^{83} +(0.419279 + 0.304624i) q^{84} +(5.02356 - 3.64983i) q^{85} +(-2.74124 + 8.43668i) q^{86} +25.5566 q^{87} -2.70789 q^{89} +(-3.24047 + 9.97315i) q^{90} +(-2.14612 + 1.55925i) q^{91} +(-0.340801 - 0.247606i) q^{92} +(-3.43496 - 10.5717i) q^{93} +(-2.00986 - 6.18570i) q^{94} +(0.657590 + 0.477767i) q^{95} +(1.72565 - 1.25376i) q^{96} +(4.37659 - 13.4698i) q^{97} +7.02229 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more