LMFDB - Embedded newform 525.2.z.a.64.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.6
Character	$\chi$	$=$	525.64
Dual form			525.2.z.a.484.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292589 - 0.402714i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.541463 - 1.66645i) q^{4} +(-1.58524 + 1.57703i) q^{5} +(0.153823 + 0.473419i) q^{6} -1.00000i q^{7} +(-1.77637 + 0.577177i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.292589 - 0.402714i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.541463 - 1.66645i) q^{4} +(-1.58524 + 1.57703i) q^{5} +(0.153823 + 0.473419i) q^{6} -1.00000i q^{7} +(-1.77637 + 0.577177i) q^{8} +(0.809017 + 0.587785i) q^{9} +(1.09892 + 0.176977i) q^{10} +(-2.86463 + 2.08127i) q^{11} +(-1.02992 + 1.41757i) q^{12} +(0.234859 - 0.323255i) q^{13} +(-0.402714 + 0.292589i) q^{14} +(1.99498 - 1.00998i) q^{15} +(-2.08296 - 1.51336i) q^{16} +(-2.07673 + 0.674772i) q^{17} -0.497782i q^{18} +(2.55033 + 7.84910i) q^{19} +(1.76970 + 3.49563i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(1.67632 + 0.544669i) q^{22} +(-1.62786 - 2.24056i) q^{23} +1.86779 q^{24} +(0.0259608 - 4.99993i) q^{25} -0.198897 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.66645 - 0.541463i) q^{28} +(-1.81610 + 5.58937i) q^{29} +(-0.990442 - 0.507899i) q^{30} +(0.907157 + 2.79194i) q^{31} +5.01720i q^{32} +(3.36757 - 1.09419i) q^{33} +(0.879371 + 0.638900i) q^{34} +(1.57703 + 1.58524i) q^{35} +(1.41757 - 1.02992i) q^{36} +(-5.40304 + 7.43664i) q^{37} +(2.41475 - 3.32362i) q^{38} +(-0.323255 + 0.234859i) q^{39} +(1.90574 - 3.71635i) q^{40} +(6.23359 + 4.52897i) q^{41} +(0.473419 - 0.153823i) q^{42} -3.76543i q^{43} +(1.91726 + 5.90070i) q^{44} +(-2.20944 + 0.344063i) q^{45} +(-0.426011 + 1.31113i) q^{46} +(-1.72055 - 0.559041i) q^{47} +(1.51336 + 2.08296i) q^{48} -1.00000 q^{49} +(-2.02114 + 1.45247i) q^{50} +2.18361 q^{51} +(-0.411522 - 0.566412i) q^{52} +(-2.93970 - 0.955166i) q^{53} +(-0.153823 + 0.473419i) q^{54} +(1.25889 - 7.81692i) q^{55} +(0.577177 + 1.77637i) q^{56} -8.25303i q^{57} +(2.78229 - 0.904021i) q^{58} +(0.0179096 + 0.0130121i) q^{59} +(-0.602872 - 3.87141i) q^{60} +(-3.73814 + 2.71592i) q^{61} +(0.858931 - 1.18222i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-2.14541 + 1.55873i) q^{64} +(0.137476 + 0.882816i) q^{65} +(-1.42596 - 1.03602i) q^{66} +(-15.0622 + 4.89400i) q^{67} +3.82615i q^{68} +(0.855818 + 2.63394i) q^{69} +(0.176977 - 1.09892i) q^{70} +(2.30888 - 7.10601i) q^{71} +(-1.77637 - 0.577177i) q^{72} +(0.899704 + 1.23834i) q^{73} +4.57571 q^{74} +(-1.56975 + 4.74720i) q^{75} +14.4611 q^{76} +(2.08127 + 2.86463i) q^{77} +(0.189162 + 0.0614625i) q^{78} +(4.68999 - 14.4343i) q^{79} +(5.68859 - 0.885851i) q^{80} +(0.309017 + 0.951057i) q^{81} -3.83548i q^{82} +(1.20159 - 0.390419i) q^{83} +(1.41757 + 1.02992i) q^{84} +(2.22798 - 4.34475i) q^{85} +(-1.51639 + 1.10172i) q^{86} +(3.45442 - 4.75460i) q^{87} +(3.88737 - 5.35051i) q^{88} +(-14.5924 + 10.6020i) q^{89} +(0.785017 + 0.789104i) q^{90} +(-0.323255 - 0.234859i) q^{91} +(-4.61522 + 1.49958i) q^{92} -2.93562i q^{93} +(0.278281 + 0.856460i) q^{94} +(-16.4211 - 8.42076i) q^{95} +(1.55040 - 4.77164i) q^{96} +(0.963488 + 0.313056i) q^{97} +(0.292589 + 0.402714i) q^{98} -3.54088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	−0.292589	−	0.402714i	−0.206892	−	0.284762i	0.692944	−	0.720992i	$-0.256314\pi$
$2$	−0.292589	−	0.402714i	−0.206892	−	0.284762i	−0.899835	+	0.436230i	$0.856314\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	0.541463	−	1.66645i	0.270732	−	0.833227i
$5$	−1.58524	+	1.57703i	−0.708940	+	0.705269i
$5$	−1.58524	+	1.57703i	−0.708940	+	0.705269i
$6$	0.153823	+	0.473419i	0.0627981	+	0.193273i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.77637	+	0.577177i	−0.628041	+	0.204063i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	1.09892	+	0.176977i	0.347508	+	0.0559650i
$11$	−2.86463	+	2.08127i	−0.863718	+	0.627528i	−0.928894	−	0.370346i	$-0.879239\pi$
$11$	−2.86463	+	2.08127i	−0.863718	+	0.627528i	0.0651758	+	0.997874i	$0.479239\pi$
$12$	−1.02992	+	1.41757i	−0.297314	+	0.409217i
$13$	0.234859	−	0.323255i	0.0651381	−	0.0896549i	−0.775205	−	0.631710i	$-0.782353\pi$
$13$	0.234859	−	0.323255i	0.0651381	−	0.0896549i	0.840343	+	0.542055i	$0.182353\pi$
$14$	−0.402714	+	0.292589i	−0.107630	+	0.0781977i
$15$	1.99498	−	1.00998i	0.515102	−	0.260775i
$16$	−2.08296	−	1.51336i	−0.520739	−	0.378339i
$17$	−2.07673	+	0.674772i	−0.503682	+	0.163656i	−0.549827	−	0.835278i	$-0.685306\pi$
$17$	−2.07673	+	0.674772i	−0.503682	+	0.163656i	0.0461449	+	0.998935i	$0.485306\pi$
$18$		−	0.497782i		−	0.117328i
$19$	2.55033	+	7.84910i	0.585085	+	1.80071i	0.598928	+	0.800803i	$0.295594\pi$
$19$	2.55033	+	7.84910i	0.585085	+	1.80071i	−0.0138425	+	0.999904i	$0.504406\pi$
$20$	1.76970	+	3.49563i	0.395716	+	0.781646i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	1.67632	+	0.544669i	0.357392	+	0.116124i
$23$	−1.62786	−	2.24056i	−0.339433	−	0.467189i	0.604843	−	0.796345i	$-0.293236\pi$
$23$	−1.62786	−	2.24056i	−0.339433	−	0.467189i	−0.944276	+	0.329156i	$0.893236\pi$
$24$	1.86779			0.381260
$25$	0.0259608	−	4.99993i	0.00519215	−	0.999987i
$26$	−0.198897			−0.0390068
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−1.66645	−	0.541463i	−0.314930	−	0.102327i
$29$	−1.81610	+	5.58937i	−0.337241	+	1.03792i	0.628367	+	0.777917i	$0.283724\pi$
$29$	−1.81610	+	5.58937i	−0.337241	+	1.03792i	−0.965608	+	0.260003i	$0.916276\pi$
$30$	−0.990442	−	0.507899i	−0.180829	−	0.0927292i
$31$	0.907157	+	2.79194i	0.162930	+	0.501448i	0.998878	−	0.0473616i	$-0.0150813\pi$
$31$	0.907157	+	2.79194i	0.162930	+	0.501448i	−0.835948	+	0.548809i	$0.815081\pi$
$32$			5.01720i			0.886924i
$33$	3.36757	−	1.09419i	0.586219	−	0.190474i
$34$	0.879371	+	0.638900i	0.150811	+	0.109570i
$35$	1.57703	+	1.58524i	0.266567	+	0.267954i
$36$	1.41757	−	1.02992i	0.236262	−	0.171654i
$37$	−5.40304	+	7.43664i	−0.888254	+	1.22258i	0.0858115	+	0.996311i	$0.472652\pi$
$37$	−5.40304	+	7.43664i	−0.888254	+	1.22258i	−0.974066	+	0.226266i	$0.927348\pi$
$38$	2.41475	−	3.32362i	0.391724	−	0.539162i
$39$	−0.323255	+	0.234859i	−0.0517623	+	0.0376075i
$40$	1.90574	−	3.71635i	0.301325	−	0.587606i
$41$	6.23359	+	4.52897i	0.973523	+	0.707306i	0.956252	−	0.292545i	$-0.0945022\pi$
$41$	6.23359	+	4.52897i	0.973523	+	0.707306i	0.0172710	+	0.999851i	$0.494502\pi$
$42$	0.473419	−	0.153823i	0.0730502	−	0.0237354i
$43$		−	3.76543i		−	0.574222i	−0.957897	−	0.287111i	$-0.907305\pi$
$43$		−	3.76543i		−	0.574222i	0.957897	−	0.287111i	$-0.0926949\pi$
$44$	1.91726	+	5.90070i	0.289037	+	0.889565i
$45$	−2.20944	+	0.344063i	−0.329364	+	0.0512899i
$46$	−0.426011	+	1.31113i	−0.0628119	+	0.193315i
$47$	−1.72055	−	0.559041i	−0.250968	−	0.0815445i	0.180831	−	0.983514i	$-0.442121\pi$
$47$	−1.72055	−	0.559041i	−0.250968	−	0.0815445i	−0.431799	+	0.901970i	$0.642121\pi$
$48$	1.51336	+	2.08296i	0.218434	+	0.300649i
$49$	−1.00000			−0.142857
$50$	−2.02114	+	1.45247i	−0.285832	+	0.205410i
$51$	2.18361			0.305766
$52$	−0.411522	−	0.566412i	−0.0570679	−	0.0785472i
$53$	−2.93970	−	0.955166i	−0.403799	−	0.131202i	0.100074	−	0.994980i	$-0.468092\pi$
$53$	−2.93970	−	0.955166i	−0.403799	−	0.131202i	−0.503873	+	0.863778i	$0.668092\pi$
$54$	−0.153823	+	0.473419i	−0.0209327	+	0.0644242i
$55$	1.25889	−	7.81692i	0.169749	−	1.05403i
$56$	0.577177	+	1.77637i	0.0771286	+	0.237377i
$57$		−	8.25303i		−	1.09314i
$58$	2.78229	−	0.904021i	0.365333	−	0.118704i
$59$	0.0179096	+	0.0130121i	0.00233163	+	0.00169403i	0.588950	−	0.808169i	$-0.299541\pi$
$59$	0.0179096	+	0.0130121i	0.00233163	+	0.00169403i	−0.586619	+	0.809863i	$0.699541\pi$
$60$	−0.602872	−	3.87141i	−0.0778305	−	0.499796i
$61$	−3.73814	+	2.71592i	−0.478620	+	0.347738i	−0.800791	−	0.598944i	$-0.795587\pi$
$61$	−3.73814	+	2.71592i	−0.478620	+	0.347738i	0.322171	+	0.946681i	$0.395587\pi$
$62$	0.858931	−	1.18222i	0.109084	−	0.150142i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−2.14541	+	1.55873i	−0.268177	+	0.194842i
$65$	0.137476	+	0.882816i	0.0170518	+	0.109500i
$66$	−1.42596	−	1.03602i	−0.175524	−	0.127525i
$67$	−15.0622	+	4.89400i	−1.84014	+	0.597897i	−0.841830	+	0.539744i	$0.818521\pi$
$67$	−15.0622	+	4.89400i	−1.84014	+	0.597897i	−0.998308	+	0.0581533i	$0.981479\pi$
$68$			3.82615i			0.463988i
$69$	0.855818	+	2.63394i	0.103028	+	0.317089i
$70$	0.176977	−	1.09892i	0.0211528	−	0.131346i
$71$	2.30888	−	7.10601i	0.274014	−	0.843329i	−0.715464	−	0.698649i	$-0.753785\pi$
$71$	2.30888	−	7.10601i	0.274014	−	0.843329i	0.989479	−	0.144680i	$-0.0462151\pi$
$72$	−1.77637	−	0.577177i	−0.209347	−	0.0680210i
$73$	0.899704	+	1.23834i	0.105302	+	0.144936i	0.858416	−	0.512954i	$-0.171449\pi$
$73$	0.899704	+	1.23834i	0.105302	+	0.144936i	−0.753114	+	0.657890i	$0.771449\pi$
$74$	4.57571			0.531916
$75$	−1.56975	+	4.74720i	−0.181260	+	0.548159i
$76$	14.4611			1.65880
$77$	2.08127	+	2.86463i	0.237183	+	0.326455i
$78$	0.189162	+	0.0614625i	0.0214184	+	0.00695925i
$79$	4.68999	−	14.4343i	0.527665	−	1.62399i	−0.231319	−	0.972878i	$-0.574304\pi$
$79$	4.68999	−	14.4343i	0.527665	−	1.62399i	0.758985	−	0.651109i	$-0.225696\pi$
$80$	5.68859	−	0.885851i	0.636003	−	0.0990412i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	3.83548i		−	0.423558i
$83$	1.20159	−	0.390419i	0.131891	−	0.0428541i	−0.242328	−	0.970194i	$-0.577911\pi$
$83$	1.20159	−	0.390419i	0.131891	−	0.0428541i	0.374219	+	0.927340i	$0.377911\pi$
$84$	1.41757	+	1.02992i	0.154670	+	0.112374i
$85$	2.22798	−	4.34475i	0.241659	−	0.471254i
$86$	−1.51639	+	1.10172i	−0.163517	+	0.118802i
$87$	3.45442	−	4.75460i	0.370353	−	0.509747i
$88$	3.88737	−	5.35051i	0.414396	−	0.570367i
$89$	−14.5924	+	10.6020i	−1.54679	+	1.12381i	−0.600893	+	0.799329i	$0.705188\pi$
$89$	−14.5924	+	10.6020i	−1.54679	+	1.12381i	−0.945894	+	0.324477i	$0.894812\pi$
$90$	0.785017	+	0.789104i	0.0827481	+	0.0831788i
$91$	−0.323255	−	0.234859i	−0.0338864	−	0.0246199i
$92$	−4.61522	+	1.49958i	−0.481170	+	0.156342i
$93$		−	2.93562i		−	0.304410i
$94$	0.278281	+	0.856460i	0.0287025	+	0.0883371i
$95$	−16.4211	−	8.42076i	−1.68477	−	0.863951i
$96$	1.55040	−	4.77164i	0.158237	−	0.487003i
$97$	0.963488	+	0.313056i	0.0978274	+	0.0317860i	0.357522	−	0.933905i	$-0.383622\pi$
$97$	0.963488	+	0.313056i	0.0978274	+	0.0317860i	−0.259694	+	0.965691i	$0.583622\pi$
$98$	0.292589	+	0.402714i	0.0295560	+	0.0406803i
$99$	−3.54088			−0.355871
$100$	−8.31810	−	2.75054i	−0.831810	−	0.275054i
$101$	2.55990			0.254719			0.127360	−	0.991857i	$-0.459350\pi$
$101$	2.55990			0.254719			0.127360	+	0.991857i	$0.459350\pi$
$102$	−0.638900	−	0.879371i	−0.0632605	−	0.0870707i
$103$	−10.3215	−	3.35367i	−1.01701	−	0.330447i	−0.247369	−	0.968921i	$-0.579566\pi$
$103$	−10.3215	−	3.35367i	−1.01701	−	0.330447i	−0.769643	+	0.638474i	$0.779566\pi$
$104$	−0.230620	+	0.709776i	−0.0226142	+	0.0695993i
$105$	−1.00998	−	1.99498i	−0.0985637	−	0.194690i
$106$	0.475465	+	1.46333i	0.0461812	+	0.142131i
$107$		−	9.34224i		−	0.903148i	−0.892234	−	0.451574i	$-0.850863\pi$
$107$		−	9.34224i		−	0.903148i	0.892234	−	0.451574i	$-0.149137\pi$
$108$	−1.66645	+	0.541463i	−0.160355	+	0.0521023i
$109$	−11.9890	−	8.71054i	−1.14834	−	0.834319i	−0.160082	−	0.987104i	$-0.551176\pi$
$109$	−11.9890	−	8.71054i	−1.14834	−	0.834319i	−0.988259	+	0.152785i	$0.951176\pi$
$110$	−3.51632	+	1.78017i	−0.335268	+	0.169733i
$111$	7.43664	−	5.40304i	0.705855	−	0.512834i
$112$	−1.51336	+	2.08296i	−0.142999	+	0.196821i
$113$	8.31496	−	11.4446i	0.782205	−	1.07661i	−0.212830	−	0.977089i	$-0.568268\pi$
$113$	8.31496	−	11.4446i	0.782205	−	1.07661i	0.995035	−	0.0995240i	$-0.0317320\pi$
$114$	−3.32362	+	2.41475i	−0.311285	+	0.226162i
$115$	6.11398	+	0.984637i	0.570132	+	0.0918178i
$116$	8.33108	+	6.05288i	0.773521	+	0.561996i
$117$	0.380009	−	0.123473i	0.0351319	−	0.0114150i
$118$		−	0.0110196i		−	0.00101444i
$119$	0.674772	+	2.07673i	0.0618563	+	0.190374i
$120$	−2.96089	+	2.94555i	−0.270291	+	0.268891i
$121$	0.475207	−	1.46254i	0.0432007	−	0.132958i
$122$	2.18748	+	0.710755i	0.198045	+	0.0643488i
$123$	−4.52897	−	6.23359i	−0.408363	−	0.562064i
$124$	5.14383			0.461930
$125$	7.84388	+	7.96703i	0.701578	+	0.712592i
$126$	−0.497782			−0.0443460
$127$	4.34916	+	5.98611i	0.385926	+	0.531181i	0.957142	−	0.289618i	$-0.0935284\pi$
$127$	4.34916	+	5.98611i	0.385926	+	0.531181i	−0.571217	+	0.820799i	$0.693528\pi$
$128$	10.7987	+	3.50872i	0.954482	+	0.310130i
$129$	−1.16358	+	3.58113i	−0.102448	+	0.315301i
$130$	0.315299	−	0.313666i	0.0276535	−	0.0275103i
$131$	−6.37843	−	19.6308i	−0.557286	−	1.71515i	−0.689830	−	0.723972i	$-0.742315\pi$
$131$	−6.37843	−	19.6308i	−0.557286	−	1.71515i	0.132544	−	0.991177i	$-0.457685\pi$
$132$		−	6.20437i		−	0.540021i
$133$	7.84910	−	2.55033i	0.680603	−	0.221141i
$134$	6.37791	+	4.63382i	0.550968	+	0.400301i
$135$	2.20762	+	0.355530i	0.190002	+	0.0305992i
$136$	3.29959	−	2.39729i	0.282937	−	0.205566i
$137$	−1.00313	+	1.38069i	−0.0857032	+	0.117960i	−0.849716	−	0.527241i	$-0.823227\pi$
$137$	−1.00313	+	1.38069i	−0.0857032	+	0.117960i	0.764013	+	0.645201i	$0.223227\pi$
$138$	0.810322	−	1.11531i	0.0689791	−	0.0949417i
$139$	16.6955	−	12.1300i	1.41609	−	1.02885i	0.423693	−	0.905806i	$-0.360733\pi$
$139$	16.6955	−	12.1300i	1.41609	−	1.02885i	0.992401	−	0.123047i	$-0.0392666\pi$
$140$	3.49563	−	1.76970i	0.295435	−	0.149567i
$141$	1.46359	+	1.06336i	0.123256	+	0.0895509i
$142$	−3.53725	+	1.14932i	−0.296839	+	0.0964489i
$143$			1.41481i			0.118313i
$144$	−0.795618	−	2.44866i	−0.0663015	−	0.204055i
$145$	−5.93565	−	11.7245i	−0.492929	−	0.973669i
$146$	0.235452	−	0.724647i	0.0194862	−	0.0599722i
$147$	0.951057	+	0.309017i	0.0784418	+	0.0254873i
$148$	9.46727	+	13.0306i	0.778205	+	1.07111i
$149$	−3.20626			−0.262667			−0.131334	−	0.991338i	$-0.541926\pi$
$149$	−3.20626			−0.262667			−0.131334	+	0.991338i	$0.541926\pi$
$150$	2.37106	−	0.756815i	0.193596	−	0.0617937i
$151$	1.14659			0.0933085			0.0466543	−	0.998911i	$-0.485144\pi$
$151$	1.14659			0.0933085			0.0466543	+	0.998911i	$0.485144\pi$
$152$	−9.06065	−	12.4709i	−0.734916	−	1.01152i
$153$	−2.07673	−	0.674772i	−0.167894	−	0.0545521i
$154$	0.544669	−	1.67632i	0.0438907	−	0.135082i
$155$	−5.84103	−	2.99528i	−0.469163	−	0.240587i
$156$	0.216350	+	0.665857i	0.0173219	+	0.0533112i
$157$			18.3520i			1.46465i	0.680958	+	0.732323i	$0.261564\pi$
$157$			18.3520i			1.46465i	−0.680958	+	0.732323i	$0.738436\pi$
$158$	−7.18514	+	2.33459i	−0.571619	+	0.185730i
$159$	2.50066	+	1.81683i	0.198315	+	0.144084i
$160$	−7.91227	−	7.95346i	−0.625520	−	0.628776i
$161$	−2.24056	+	1.62786i	−0.176581	+	0.128294i
$162$	0.292589	−	0.402714i	0.0229880	−	0.0316402i
$163$	5.24155	−	7.21438i	0.410550	−	0.565074i	−0.552802	−	0.833312i	$-0.686442\pi$
$163$	5.24155	−	7.21438i	0.410550	−	0.565074i	0.963353	+	0.268239i	$0.0864415\pi$
$164$	10.9226	−	7.93571i	0.852909	−	0.619675i
$165$	−3.61284	+	7.04531i	−0.281259	+	0.548477i
$166$	−0.508799	−	0.369664i	−0.0394904	−	0.0286915i
$167$	−16.8782	+	5.48407i	−1.30608	+	0.424370i	−0.877691	−	0.479227i	$-0.840917\pi$
$167$	−16.8782	+	5.48407i	−1.30608	+	0.424370i	−0.428385	+	0.903596i	$0.640917\pi$
$168$		−	1.86779i		−	0.144103i
$169$	3.96789	+	12.2119i	0.305222	+	0.939377i
$170$	−2.40158	+	0.373984i	−0.184192	+	0.0286832i
$171$	−2.55033	+	7.84910i	−0.195028	+	0.600236i
$172$	−6.27491	−	2.03884i	−0.478457	−	0.155460i
$173$	−8.39312	−	11.5521i	−0.638117	−	0.878292i	0.360397	−	0.932799i	$-0.382641\pi$
$173$	−8.39312	−	11.5521i	−0.638117	−	0.878292i	−0.998513	+	0.0545068i	$0.982641\pi$
$174$	−2.92547			−0.221780
$175$	−4.99993	−	0.0259608i	−0.377959	−	0.00196245i
$176$	9.11660			0.687190
$177$	−0.0130121	−	0.0179096i	−0.000978048	−	0.00134617i
$178$	8.53913	+	2.77453i	0.640035	+	0.207960i
$179$	−6.76981	+	20.8353i	−0.506000	+	1.55731i	0.293084	+	0.956087i	$0.405319\pi$
$179$	−6.76981	+	20.8353i	−0.506000	+	1.55731i	−0.799083	+	0.601220i	$0.794681\pi$
$180$	−0.622965	+	3.86822i	−0.0464331	+	0.288320i
$181$	1.67922	+	5.16812i	0.124816	+	0.384143i	0.993867	−	0.110578i	$-0.0352702\pi$
$181$	1.67922	+	5.16812i	0.124816	+	0.384143i	−0.869052	+	0.494721i	$0.835270\pi$
$182$			0.198897i			0.0147432i
$183$	4.39445	−	1.42784i	0.324847	−	0.105549i
$184$	4.18489	+	3.04050i	0.308514	+	0.224149i
$185$	−3.16270	−	20.3096i	−0.232526	−	1.49319i
$186$	−1.18222	+	0.858931i	−0.0866844	+	0.0629799i
$187$	4.54469	−	6.25523i	0.332341	−	0.457428i
$188$	−1.86323	+	2.56452i	−0.135890	+	0.187037i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	1.41349	+	9.07685i	0.102545	+	0.658504i
$191$	2.54427	+	1.84852i	0.184097	+	0.133754i	0.676017	−	0.736886i	$-0.263705\pi$
$191$	2.54427	+	1.84852i	0.184097	+	0.133754i	−0.491920	+	0.870640i	$0.663705\pi$
$192$	2.52208	−	0.819475i	0.182016	−	0.0591405i
$193$			13.0851i			0.941884i	0.882164	+	0.470942i	$0.156086\pi$
$193$			13.0851i			0.941884i	−0.882164	+	0.470942i	$0.843914\pi$
$194$	−0.155834	−	0.479607i	−0.0111882	−	0.0344338i
$195$	0.142058	−	0.882090i	0.0101730	−	0.0631678i
$196$	−0.541463	+	1.66645i	−0.0386760	+	0.119032i
$197$	−9.99096	−	3.24626i	−0.711826	−	0.231286i	−0.0693506	−	0.997592i	$-0.522093\pi$
$197$	−9.99096	−	3.24626i	−0.711826	−	0.231286i	−0.642476	+	0.766306i	$0.722093\pi$
$198$	1.03602	+	1.42596i	0.0736269	+	0.101339i
$199$	6.82331			0.483692			0.241846	−	0.970315i	$-0.422247\pi$
$199$	6.82331			0.483692			0.241846	+	0.970315i	$0.422247\pi$
$200$	2.83973	+	8.89671i	0.200799	+	0.629093i
$201$	15.8373			1.11708
$202$	−0.748999	−	1.03091i	−0.0526994	−	0.0725345i
$203$	5.58937	+	1.81610i	0.392297	+	0.127465i
$204$	1.18234	−	3.63888i	0.0827806	−	0.254773i
$205$	−17.0240	+	2.65106i	−1.18901	+	0.185158i
$206$	1.66940	+	5.13788i	0.116313	+	0.357973i
$207$		−	2.76949i		−	0.192493i
$208$	−0.978400	+	0.317902i	−0.0678399	+	0.0220425i
$209$	−23.6419	−	17.1768i	−1.63534	−	1.18815i
$210$	−0.507899	+	0.990442i	−0.0350483	+	0.0683470i
$211$	2.61793	−	1.90204i	0.180226	−	0.130942i	−0.494015	−	0.869454i	$-0.664471\pi$
$211$	2.61793	−	1.90204i	0.180226	−	0.130942i	0.674241	+	0.738512i	$0.264471\pi$
$212$	−3.18348	+	4.38168i	−0.218642	+	0.300935i
$213$	−4.39176	+	6.04474i	−0.300918	+	0.414178i
$214$	−3.76225	+	2.73344i	−0.257182	+	0.186854i
$215$	5.93818	+	5.96910i	0.404981	+	0.407089i
$216$	1.51107	+	1.09786i	0.102815	+	0.0746997i
$217$	2.79194	−	0.907157i	0.189529	−	0.0615818i
$218$			7.37677i			0.499618i
$219$	−0.473002	−	1.45575i	−0.0319625	−	0.0983705i
$220$	−12.3449	−	6.33046i	−0.832292	−	0.426799i
$221$	−0.269616	+	0.829792i	−0.0181363	+	0.0558178i
$222$	−4.35176	−	1.41397i	−0.292071	−	0.0948997i
$223$	2.42027	+	3.33122i	0.162073	+	0.223075i	0.882328	−	0.470635i	$-0.155975\pi$
$223$	2.42027	+	3.33122i	0.162073	+	0.223075i	−0.720255	+	0.693710i	$0.755975\pi$
$224$	5.01720			0.335226
$225$	2.95989	−	4.02977i	0.197326	−	0.268651i
$226$	−7.04175			−0.468411
$227$	15.7162	+	21.6315i	1.04312	+	1.43573i	0.894626	+	0.446817i	$0.147442\pi$
$227$	15.7162	+	21.6315i	1.04312	+	1.43573i	0.148493	+	0.988913i	$0.452558\pi$
$228$	−13.7533	−	4.46872i	−0.910834	−	0.295948i
$229$	−4.56928	+	14.0628i	−0.301947	+	0.929296i	0.678852	+	0.734275i	$0.262478\pi$
$229$	−4.56928	+	14.0628i	−0.301947	+	0.929296i	−0.980799	+	0.195021i	$0.937522\pi$
$230$	−1.39236	−	2.75028i	−0.0918093	−	0.181348i
$231$	−1.09419	−	3.36757i	−0.0719925	−	0.221570i
$232$		−	10.9770i		−	0.720676i
$233$	13.6076	−	4.42138i	0.891464	−	0.289654i	0.172754	−	0.984965i	$-0.444733\pi$
$233$	13.6076	−	4.42138i	0.891464	−	0.289654i	0.718709	+	0.695311i	$0.244733\pi$
$234$	−0.160911	−	0.116909i	−0.0105191	−	0.00764255i
$235$	3.60911	−	1.82714i	0.235432	−	0.119190i
$236$	0.0313814	−	0.0227999i	0.00204276	−	0.00148415i
$237$	−8.92089	+	12.2786i	−0.579474	+	0.797578i
$238$	0.638900	−	0.879371i	0.0414137	−	0.0570011i
$239$	−12.1645	+	8.83803i	−0.786857	+	0.571685i	−0.907029	−	0.421068i	$-0.861655\pi$
$239$	−12.1645	+	8.83803i	−0.786857	+	0.571685i	0.120172	+	0.992753i	$0.461655\pi$
$240$	−5.68391	−	0.915375i	−0.366895	−	0.0590872i
$241$	−8.94450	−	6.49856i	−0.576166	−	0.418609i	0.261174	−	0.965292i	$-0.415890\pi$
$241$	−8.94450	−	6.49856i	−0.576166	−	0.418609i	−0.837340	+	0.546683i	$0.815890\pi$
$242$	−0.728026	+	0.236550i	−0.0467993	+	0.0152060i
$243$		−	1.00000i		−	0.0641500i
$244$	2.50188	+	7.70001i	0.160167	+	0.492943i
$245$	1.58524	−	1.57703i	0.101277	−	0.100753i
$246$	−1.18523	+	3.64776i	−0.0755674	+	0.232573i
$247$	3.13623	+	1.01902i	0.199554	+	0.0648389i
$248$	−3.22289	−	4.43593i	−0.204654	−	0.281682i
$249$	−1.26342			−0.0800662
$250$	0.913401	−	5.48991i	0.0577685	−	0.347212i
$251$	4.91954			0.310519			0.155259	−	0.987874i	$-0.450379\pi$
$251$	4.91954			0.310519			0.155259	+	0.987874i	$0.450379\pi$
$252$	−1.02992	−	1.41757i	−0.0648792	−	0.0892985i
$253$	9.32645	+	3.03035i	0.586349	+	0.190516i
$254$	1.13817	−	3.50294i	0.0714154	−	0.219794i
$255$	−3.46154	+	3.44361i	−0.216770	+	0.215647i
$256$	−0.107629	−	0.331249i	−0.00672684	−	0.0207031i
$257$		−	5.36812i		−	0.334854i	−0.985884	−	0.167427i	$-0.946454\pi$
$257$		−	5.36812i		−	0.334854i	0.985884	−	0.167427i	$-0.0535459\pi$
$258$	1.78262	−	0.579210i	0.110981	−	0.0360600i
$259$	7.43664	+	5.40304i	0.462091	+	0.335728i
$260$	1.54561	+	0.248915i	0.0958546	+	0.0154371i
$261$	−4.75460	+	3.45442i	−0.294303	+	0.213823i
$262$	−6.03934	+	8.31244i	−0.373112	+	0.513544i
$263$	13.0709	−	17.9906i	0.805986	−	1.10935i	−0.185944	−	0.982560i	$-0.559534\pi$
$263$	13.0709	−	17.9906i	0.805986	−	1.10935i	0.991930	−	0.126785i	$-0.0404657\pi$
$264$	−5.35051	+	3.88737i	−0.329301	+	0.239251i
$265$	6.16645	−	3.12182i	0.378802	−	0.191772i
$266$	−3.32362	−	2.41475i	−0.203784	−	0.148058i
$267$	17.1543	−	5.57378i	1.04983	−	0.341110i
$268$			27.7503i			1.69512i
$269$	4.50510	+	13.8653i	0.274681	+	0.845381i	0.989304	+	0.145871i	$0.0465984\pi$
$269$	4.50510	+	13.8653i	0.274681	+	0.845381i	−0.714623	+	0.699510i	$0.753402\pi$
$270$	−0.502749	−	0.993066i	−0.0305963	−	0.0604361i
$271$	−6.46564	+	19.8992i	−0.392760	+	1.20879i	0.537933	+	0.842988i	$0.319206\pi$
$271$	−6.46564	+	19.8992i	−0.392760	+	1.20879i	−0.930692	+	0.365803i	$0.880794\pi$
$272$	5.34692	+	1.73732i	0.324204	+	0.105340i
$273$	0.234859	+	0.323255i	0.0142143	+	0.0195643i
$274$	0.849529			0.0513219
$275$	10.3319	+	14.3770i	0.623035	+	0.866965i
$276$	4.85273			0.292100
$277$	7.43412	+	10.2322i	0.446673	+	0.614792i	0.971679	−	0.236306i	$-0.0759369\pi$
$277$	7.43412	+	10.2322i	0.446673	+	0.614792i	−0.525006	+	0.851099i	$0.675937\pi$
$278$	−9.76985	−	3.17442i	−0.585957	−	0.190389i
$279$	−0.907157	+	2.79194i	−0.0543101	+	0.167149i
$280$	−3.71635	−	1.90574i	−0.222094	−	0.113890i
$281$	5.14789	+	15.8436i	0.307097	+	0.945148i	0.978886	+	0.204406i	$0.0655261\pi$
$281$	5.14789	+	15.8436i	0.307097	+	0.945148i	−0.671789	+	0.740743i	$0.734474\pi$
$282$		−	0.900535i		−	0.0536261i
$283$	2.70788	−	0.879843i	0.160967	−	0.0523012i	−0.227425	−	0.973796i	$-0.573031\pi$
$283$	2.70788	−	0.879843i	0.160967	−	0.0523012i	0.388392	+	0.921494i	$0.373031\pi$
$284$	−10.5917	−	7.69529i	−0.628500	−	0.456632i
$285$	13.0153	+	13.0830i	0.770958	+	0.774971i
$286$	0.569765	−	0.413959i	0.0336909	−	0.0244779i
$287$	4.52897	−	6.23359i	0.267336	−	0.367957i
$288$	−2.94904	+	4.05900i	−0.173774	+	0.239179i
$289$	−9.89578	+	7.18970i	−0.582105	+	0.422924i
$290$	−2.98493	+	5.82084i	−0.175281	+	0.341812i
$291$	−0.819592	−	0.595468i	−0.0480453	−	0.0349070i
$292$	2.55079	−	0.828800i	0.149273	−	0.0485019i
$293$		−	0.285793i		−	0.0166962i	−0.999965	−	0.00834810i	$-0.997343\pi$
$293$		−	0.285793i		−	0.0166962i	0.999965	−	0.00834810i	$-0.00265731\pi$
$294$	−0.153823	−	0.473419i	−0.00897115	−	0.0276104i
$295$	−0.0489114	+	0.00761669i	−0.00284773	+	0.000443461i
$296$	5.30553	−	16.3287i	0.308378	−	0.949089i
$297$	3.36757	+	1.09419i	0.195406	+	0.0634914i
$298$	0.938118	+	1.29121i	0.0543437	+	0.0747977i
$299$	−1.10659			−0.0639958
$300$	7.06102	+	5.18636i	0.407668	+	0.299434i
$301$	−3.76543			−0.217036
$302$	−0.335481	−	0.461750i	−0.0193048	−	0.0265707i
$303$	−2.43461	−	0.791052i	−0.139865	−	0.0454448i
$304$	6.56626	−	20.2089i	0.376601	−	1.15906i
$305$	1.64276	−	10.2005i	0.0940644	−	0.584081i
$306$	0.335890	+	1.03376i	0.0192015	+	0.0590962i
$307$			26.7675i			1.52770i	0.645393	+	0.763851i	$0.276694\pi$
$307$			26.7675i			1.52770i	−0.645393	+	0.763851i	$0.723306\pi$
$308$	5.90070	−	1.91726i	0.336224	−	0.109246i
$309$	8.78003	+	6.37906i	0.499478	+	0.362892i
$310$	0.502780	+	3.22866i	0.0285560	+	0.183375i
$311$	9.63149	−	6.99769i	0.546152	−	0.396802i	−0.280213	−	0.959938i	$-0.590405\pi$
$311$	9.63149	−	6.99769i	0.546152	−	0.396802i	0.826365	+	0.563135i	$0.190405\pi$
$312$	0.438666	−	0.603772i	0.0248346	−	0.0341818i
$313$	3.02108	−	4.15815i	0.170761	−	0.235033i	−0.715056	−	0.699067i	$-0.753599\pi$
$313$	3.02108	−	4.15815i	0.170761	−	0.235033i	0.885817	+	0.464035i	$0.153599\pi$
$314$	7.39060	−	5.36958i	0.417076	−	0.303023i
$315$	0.344063	+	2.20944i	0.0193858	+	0.124488i
$316$	−21.5146	−	15.6313i	−1.21029	−	0.879329i
$317$	26.4373	−	8.59001i	1.48487	−	0.482463i	0.549306	−	0.835622i	$-0.314892\pi$
$317$	26.4373	−	8.59001i	1.48487	−	0.482463i	0.935564	+	0.353158i	$0.114892\pi$
$318$		−	1.53864i		−	0.0862825i
$319$	−6.43058	−	19.7913i	−0.360043	−	1.10810i
$320$	0.942823	−	5.85434i	0.0527054	−	0.327268i
$321$	−2.88691	+	8.88500i	−0.161132	+	0.495912i
$322$	1.31113	+	0.426011i	0.0730663	+	0.0237407i
$323$	−10.5927	−	14.5796i	−0.589394	−	0.811231i
$324$	1.75221			0.0973451
$325$	−1.61016	−	1.18267i	−0.0893155	−	0.0656027i
$326$	−4.43896			−0.245851
$327$	8.71054	+	11.9890i	0.481694	+	0.662995i
$328$	−13.6872	−	4.44723i	−0.755748	−	0.245557i
$329$	−0.559041	+	1.72055i	−0.0308209	+	0.0948570i
$330$	3.89433	−	0.606441i	0.214376	−	0.0333835i
$331$	−3.70930	−	11.4161i	−0.203882	−	0.627483i	−0.999757	−	0.0220233i	$-0.992989\pi$
$331$	−3.70930	−	11.4161i	−0.203882	−	0.627483i	0.795876	−	0.605460i	$-0.207011\pi$
$332$		−	2.21379i		−	0.121497i
$333$	−8.74230	+	2.84055i	−0.479075	+	0.155661i
$334$	7.14690	+	5.19252i	0.391061	+	0.284122i
$335$	16.1592	−	31.5116i	0.882869	−	1.72166i
$336$	2.08296	−	1.51336i	0.113635	−	0.0825603i
$337$	−14.3451	+	19.7444i	−0.781429	+	1.07554i	0.213694	+	0.976901i	$0.431450\pi$
$337$	−14.3451	+	19.7444i	−0.781429	+	1.07554i	−0.995123	+	0.0986438i	$0.968550\pi$
$338$	3.75695	−	5.17099i	0.204351	−	0.281265i
$339$	−11.4446	+	8.31496i	−0.621583	+	0.451606i
$340$	−6.03394	−	6.06535i	−0.327236	−	0.328940i
$341$	−8.40947	−	6.10984i	−0.455398	−	0.330866i
$342$	3.90714	−	1.26951i	0.211274	−	0.0686471i
$343$			1.00000i			0.0539949i
$344$	2.17332	+	6.68879i	0.117177	+	0.360635i
$345$	−5.51047	−	2.82577i	−0.296674	−	0.152134i
$346$	−2.19648	+	6.76006i	−0.118083	+	0.363423i
$347$	28.2683	+	9.18492i	1.51752	+	0.493073i	0.945071	−	0.326866i	$-0.105993\pi$
$347$	28.2683	+	9.18492i	1.51752	+	0.493073i	0.572451	+	0.819939i	$0.305993\pi$
$348$	−6.05288	−	8.33108i	−0.324469	−	0.446593i
$349$	7.00703			0.375078			0.187539	−	0.982257i	$-0.439949\pi$
$349$	7.00703			0.375078			0.187539	+	0.982257i	$0.439949\pi$
$350$	1.45247	+	2.02114i	0.0776379	+	0.108035i
$351$	−0.399566			−0.0213272
$352$	−10.4422	−	14.3724i	−0.556569	−	0.766052i
$353$	−27.2639	−	8.85856i	−1.45111	−	0.471494i	−0.525767	−	0.850628i	$-0.676222\pi$
$353$	−27.2639	−	8.85856i	−1.45111	−	0.471494i	−0.925342	+	0.379135i	$0.876222\pi$
$354$	−0.00340526	+	0.0104803i	−0.000180987	+	0.000557022i
$355$	7.54626	+	14.9059i	0.400514	+	0.791123i
$356$	9.76646	+	30.0581i	0.517621	+	1.59307i
$357$		−	2.18361i		−	0.115569i
$358$	10.3715	−	3.36989i	0.548149	−	0.178104i
$359$	−9.86300	−	7.16589i	−0.520549	−	0.378201i	0.296262	−	0.955107i	$-0.404260\pi$
$359$	−9.86300	−	7.16589i	−0.520549	−	0.378201i	−0.816811	+	0.576906i	$0.804260\pi$
$360$	3.72619	−	1.88642i	0.196388	−	0.0994232i
$361$	−39.7329	+	28.8676i	−2.09120	+	1.51935i
$362$	1.58995	−	2.18838i	0.0835661	−	0.115019i
$363$	−0.903898	+	1.24411i	−0.0474424	+	0.0652988i
$364$	−0.566412	+	0.411522i	−0.0296881	+	0.0215696i
$365$	−3.37914	−	0.544199i	−0.176872	−	0.0284847i
$366$	−1.86078	−	1.35194i	−0.0972646	−	0.0706669i
$367$	20.3215	−	6.60285i	1.06077	−	0.344666i	0.273885	−	0.961762i	$-0.411691\pi$
$367$	20.3215	−	6.60285i	1.06077	−	0.344666i	0.786888	+	0.617096i	$0.211691\pi$
$368$			7.13052i			0.371704i
$369$	2.38102	+	7.32802i	0.123951	+	0.381482i
$370$	−7.25360	+	7.21603i	−0.377097	+	0.375144i
$371$	−0.955166	+	2.93970i	−0.0495898	+	0.152622i
$372$	−4.89208	−	1.58953i	−0.253642	−	0.0824134i
$373$	4.36614	+	6.00947i	0.226070	+	0.311159i	0.906952	−	0.421235i	$-0.138403\pi$
$373$	4.36614	+	6.00947i	0.226070	+	0.311159i	−0.680882	+	0.732394i	$0.738403\pi$
$374$	−3.84880			−0.199017
$375$	−4.99803	−	10.0010i	−0.258097	−	0.516449i
$376$	3.37900			0.174259
$377$	1.38027	+	1.89978i	0.0710874	+	0.0978434i
$378$	0.473419	+	0.153823i	0.0243501	+	0.00791181i
$379$	6.18748	−	19.0431i	0.317830	−	0.978179i	−0.656744	−	0.754113i	$-0.728067\pi$
$379$	6.18748	−	19.0431i	0.317830	−	0.978179i	0.974574	−	0.224066i	$-0.0719330\pi$
$380$	−22.9242	+	22.8055i	−1.17599	+	1.16990i
$381$	−2.28649	−	7.03709i	−0.117140	−	0.360521i
$382$		−	1.56547i		−	0.0800964i
$383$	−6.37394	+	2.07102i	−0.325693	+	0.105824i	−0.467300	−	0.884099i	$-0.654773\pi$
$383$	−6.37394	+	2.07102i	−0.325693	+	0.105824i	0.141607	+	0.989923i	$0.454773\pi$
$384$	−9.18595	−	6.67398i	−0.468768	−	0.340580i
$385$	−7.81692	−	1.25889i	−0.398387	−	0.0641589i
$386$	5.26955	−	3.82855i	0.268213	−	0.194868i
$387$	2.21326	−	3.04629i	0.112506	−	0.154852i
$388$	1.04339	−	1.43610i	0.0529700	−	0.0729069i
$389$	6.34596	−	4.61061i	0.321753	−	0.233767i	−0.415170	−	0.909744i	$-0.636278\pi$
$389$	6.34596	−	4.61061i	0.321753	−	0.233767i	0.736923	+	0.675977i	$0.236278\pi$
$390$	−0.396795	+	0.200881i	−0.0200925	+	0.0101720i
$391$	4.89251	+	3.55461i	0.247425	+	0.179765i
$392$	1.77637	−	0.577177i	0.0897202	−	0.0291519i
$393$			20.6410i			1.04120i
$394$	1.61593	+	4.97332i	0.0814094	+	0.250552i
$395$	15.3286	+	30.2781i	0.771264	+	1.52345i
$396$	−1.91726	+	5.90070i	−0.0963457	+	0.296522i
$397$	1.92150	+	0.624335i	0.0964376	+	0.0313345i	0.356838	−	0.934166i	$-0.383855\pi$
$397$	1.92150	+	0.624335i	0.0964376	+	0.0313345i	−0.260401	+	0.965501i	$0.583855\pi$
$398$	−1.99643	−	2.74785i	−0.100072	−	0.137737i
$399$	−8.25303			−0.413168
$400$	−7.62075	+	10.3753i	−0.381038	+	0.518767i
$401$	−3.47082			−0.173325			−0.0866623	−	0.996238i	$-0.527620\pi$
$401$	−3.47082			−0.173325			−0.0866623	+	0.996238i	$0.527620\pi$
$402$	−4.63382	−	6.37791i	−0.231114	−	0.318101i
$403$	1.11556	+	0.362469i	0.0555702	+	0.0180559i
$404$	1.38609	−	4.26595i	0.0689607	−	0.212239i
$405$	−1.98971	−	1.02032i	−0.0988694	−	0.0507002i
$406$	−0.904021	−	2.78229i	−0.0448658	−	0.138083i
$407$		−	32.5484i		−	1.61337i
$408$	−3.87890	+	1.26033i	−0.192034	+	0.0623956i
$409$	−15.1819	−	11.0303i	−0.750698	−	0.545414i	0.145345	−	0.989381i	$-0.453571\pi$
$409$	−15.1819	−	11.0303i	−0.750698	−	0.545414i	−0.896043	+	0.443967i	$0.853571\pi$
$410$	6.04866	+	6.08015i	0.298722	+	0.300277i
$411$	1.38069	−	1.00313i	0.0681044	−	0.0494808i
$412$	−11.1775	+	15.3845i	−0.550675	+	0.757939i
$413$	0.0130121	−	0.0179096i	0.000640283	−	0.000881274i
$414$	−1.11531	+	0.810322i	−0.0548146	+	0.0398251i
$415$	−1.28910	+	2.51384i	−0.0632794	+	0.123400i
$416$	1.62184	+	1.17833i	0.0795171	+	0.0577725i
$417$	−19.6267	+	6.37712i	−0.961126	+	0.312289i
$418$			14.5467i			0.711501i
$419$	−4.12995	−	12.7107i	−0.201761	−	0.620957i	−0.999831	−	0.0183920i	$-0.994145\pi$
$419$	−4.12995	−	12.7107i	−0.201761	−	0.620957i	0.798070	−	0.602565i	$-0.205855\pi$
$420$	−3.87141	+	0.602872i	−0.188905	+	0.0294172i
$421$	4.35102	−	13.3911i	0.212056	−	0.652641i	−0.787294	−	0.616578i	$-0.788518\pi$
$421$	4.35102	−	13.3911i	0.212056	−	0.652641i	0.999350	−	0.0360625i	$-0.0114815\pi$
$422$	−1.53196	−	0.497763i	−0.0745745	−	0.0242307i
$423$	−1.06336	−	1.46359i	−0.0517023	−	0.0711621i
$424$	5.77329			0.280376
$425$	3.31990	+	10.4011i	0.161039	+	0.504525i
$426$	3.71928			0.180200
$427$	2.71592	+	3.73814i	0.131433	+	0.180901i
$428$	−15.5684	−	5.05848i	−0.752527	−	0.244511i
$429$	0.437201	−	1.34557i	0.0211083	−	0.0649645i
$430$	0.666393	−	4.13789i	0.0321363	−	0.199547i
$431$	−7.34181	−	22.5958i	−0.353642	−	1.08840i	−0.956792	−	0.290772i	$-0.906088\pi$
$431$	−7.34181	−	22.5958i	−0.353642	−	1.08840i	0.603150	−	0.797628i	$-0.293912\pi$
$432$			2.57467i			0.123874i
$433$	−20.7211	+	6.73270i	−0.995793	+	0.323553i	−0.761183	−	0.648537i	$-0.775381\pi$
$433$	−20.7211	+	6.73270i	−0.995793	+	0.323553i	−0.234610	+	0.972090i	$0.575381\pi$
$434$	−1.18222	−	0.858931i	−0.0567482	−	0.0412300i
$435$	2.02207	+	12.9849i	0.0969506	+	0.622579i
$436$	−21.0073	+	15.2627i	−1.00607	+	0.730952i
$437$	13.4348	−	18.4914i	0.642674	−	0.884565i
$438$	−0.447857	+	0.616422i	−0.0213994	+	0.0294538i
$439$	23.0661	−	16.7585i	1.10088	−	0.799838i	0.119679	−	0.992813i	$-0.461813\pi$
$439$	23.0661	−	16.7585i	1.10088	−	0.799838i	0.981204	+	0.192974i	$0.0618134\pi$
$440$	2.27550	+	14.6123i	0.108480	+	0.696616i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	0.413056	−	0.134210i	0.0196471	−	0.00638372i
$443$			21.1793i			1.00626i	0.864211	+	0.503130i	$0.167818\pi$
$443$			21.1793i			1.00626i	−0.864211	+	0.503130i	$0.832182\pi$
$444$	−4.97724	−	15.3184i	−0.236209	−	0.726978i
$445$	6.41275	−	39.8192i	0.303994	−	1.88761i
$446$	0.633385	−	1.94936i	0.0299916	−	0.0923048i
$447$	3.04934	+	0.990790i	0.144229	+	0.0468627i
$448$	1.55873	+	2.14541i	0.0736432	+	0.101361i
$449$	24.9499			1.17746			0.588728	−	0.808331i	$-0.299629\pi$
$449$	24.9499			1.17746			0.588728	+	0.808331i	$0.299629\pi$
$450$	−2.48888	−	0.0129228i	−0.117327	−	0.000609187i
$451$	−27.2829			−1.28470
$452$	−14.5696	−	20.0533i	−0.685295	−	0.943228i
$453$	−1.09048	−	0.354317i	−0.0512350	−	0.0166473i
$454$	4.11292	−	12.6583i	0.193029	−	0.594081i
$455$	0.882816	−	0.137476i	0.0413870	−	0.00644497i
$456$	4.76346	+	14.6604i	0.223070	+	0.686538i
$457$		−	16.9448i		−	0.792644i	−0.918111	−	0.396322i	$-0.870286\pi$
$457$		−	16.9448i		−	0.792644i	0.918111	−	0.396322i	$-0.129714\pi$
$458$	7.00021	−	2.27451i	0.327099	−	0.106281i
$459$	1.76658	+	1.28349i	0.0824567	+	0.0599083i
$460$	4.95135	−	9.65552i	0.230858	−	0.450191i
$461$	6.62577	−	4.81390i	0.308593	−	0.224206i	−0.422700	−	0.906270i	$-0.638917\pi$
$461$	6.62577	−	4.81390i	0.308593	−	0.224206i	0.731292	+	0.682064i	$0.238917\pi$
$462$	−1.03602	+	1.42596i	−0.0482001	+	0.0663418i
$463$	21.7939	−	29.9967i	1.01285	−	1.39406i	0.0957467	−	0.995406i	$-0.469476\pi$
$463$	21.7939	−	29.9967i	1.01285	−	1.39406i	0.917100	−	0.398658i	$-0.130524\pi$
$464$	12.2416	−	8.89401i	0.568300	−	0.412894i
$465$	4.62956	+	4.65366i	0.214691	+	0.215808i
$466$	−5.76199	−	4.18633i	−0.266919	−	0.193928i
$467$	−0.260600	+	0.0846739i	−0.0120591	+	0.00391824i	−0.315040	−	0.949078i	$-0.602018\pi$
$467$	−0.260600	+	0.0846739i	−0.0120591	+	0.00391824i	0.302981	+	0.952997i	$0.402018\pi$
$468$		−	0.700124i		−	0.0323632i
$469$	4.89400	+	15.0622i	0.225984	+	0.695506i
$470$	−1.79180	−	0.918836i	−0.0826497	−	0.0423828i
$471$	5.67107	−	17.4537i	0.261309	−	0.804226i
$472$	−0.0393243	−	0.0127773i	−0.00181005	−	0.000588121i
$473$	7.83689	+	10.7865i	0.360340	+	0.495966i
$474$	7.55491			0.347008
$475$	39.3112	−	12.5477i	1.80372	−	0.575728i
$476$	3.82615			0.175371
$477$	−1.81683	−	2.50066i	−0.0831871	−	0.114497i
$478$	7.11841	+	2.31291i	0.325588	+	0.105790i
$479$	4.30452	−	13.2480i	0.196679	−	0.605315i	−0.803274	−	0.595609i	$-0.796911\pi$
$479$	4.30452	−	13.2480i	0.196679	−	0.605315i	0.999953	−	0.00970538i	$-0.00308937\pi$
$480$	5.06726	+	10.0092i	0.231288	+	0.456856i
$481$	1.13498	+	3.49312i	0.0517508	+	0.159273i
$482$			5.50349i			0.250677i
$483$	2.63394	−	0.855818i	0.119848	−	0.0389411i
$484$	−2.17994	−	1.58382i	−0.0990884	−	0.0719919i
$485$	−2.02106	+	1.02318i	−0.0917715	+	0.0464602i
$486$	−0.402714	+	0.292589i	−0.0182675	+	0.0132721i
$487$	2.62547	−	3.61365i	0.118971	−	0.163750i	−0.745378	−	0.666642i	$-0.767731\pi$
$487$	2.62547	−	3.61365i	0.118971	−	0.163750i	0.864349	+	0.502892i	$0.167731\pi$
$488$	5.07275	−	6.98205i	0.229633	−	0.316062i
$489$	−7.21438	+	5.24155i	−0.326246	+	0.237031i
$490$	−1.09892	−	0.176977i	−0.0496440	−	0.00799500i
$491$	−6.72560	−	4.88643i	−0.303522	−	0.220522i	0.425590	−	0.904916i	$-0.360067\pi$
$491$	−6.72560	−	4.88643i	−0.303522	−	0.220522i	−0.729112	+	0.684394i	$0.760067\pi$
$492$	−12.8403	+	4.17205i	−0.578883	+	0.188091i
$493$		−	12.8331i		−	0.577974i
$494$	−0.507252	−	1.56116i	−0.0228223	−	0.0702399i
$495$	5.61313	−	5.58406i	0.252292	−	0.250985i
$496$	2.33563	−	7.18834i	0.104873	−	0.322766i
$497$	−7.10601	−	2.30888i	−0.318748	−	0.103568i
$498$	0.369664	+	0.508799i	0.0165650	+	0.0227998i
$499$	33.8203			1.51400			0.757001	−	0.653413i	$-0.226664\pi$
$499$	33.8203			1.51400			0.757001	+	0.653413i	$0.226664\pi$
$500$	17.5239	−	8.75761i	0.783690	−	0.391652i
$501$	17.7468			0.792869
$502$	−1.43940	−	1.98117i	−0.0642438	−	0.0884240i
$503$	−39.1427	−	12.7182i	−1.74529	−	0.567079i	−0.749775	−	0.661693i	$-0.769838\pi$
$503$	−39.1427	−	12.7182i	−1.74529	−	0.567079i	−0.995514	+	0.0946144i	$0.969838\pi$
$504$	−0.577177	+	1.77637i	−0.0257095	+	0.0791258i
$505$	−4.05805	+	4.03703i	−0.180581	+	0.179646i
$506$	−1.50845	−	4.64254i	−0.0670589	−	0.206386i
$507$		−	12.8403i		−	0.570260i
$508$	12.3305	−	4.00642i	0.547077	−	0.177756i
$509$	−23.0367	−	16.7372i	−1.02108	−	0.741862i	−0.0545798	−	0.998509i	$-0.517382\pi$
$509$	−23.0367	−	16.7372i	−1.02108	−	0.741862i	−0.966505	+	0.256648i	$0.917382\pi$
$510$	2.39960	+	0.386448i	0.106256	+	0.0171122i
$511$	1.23834	−	0.899704i	0.0547807	−	0.0398005i
$512$	13.2461	−	18.2316i	0.585398	−	0.805732i
$513$	4.85101	−	6.67684i	0.214177	−	0.294790i
$514$	−2.16182	+	1.57065i	−0.0953538	+	0.0692786i
$515$	21.6509	−	10.9610i	0.954055	−	0.482999i
$516$	5.33775	+	3.87810i	0.234981	+	0.170724i
$517$	6.09226	−	1.97949i	0.267937	−	0.0870580i
$518$		−	4.57571i		−	0.201045i
$519$	4.41252	+	13.5803i	0.193688	+	0.596111i
$520$	−0.753749	−	1.48886i	−0.0330541	−	0.0652908i
$521$	−6.65558	+	20.4838i	−0.291586	+	0.897410i	0.692760	+	0.721168i	$0.256394\pi$
$521$	−6.65558	+	20.4838i	−0.291586	+	0.897410i	−0.984347	+	0.176243i	$0.943606\pi$
$522$	2.78229	+	0.904021i	0.121778	+	0.0395679i
$523$	19.1306	+	26.3310i	0.836522	+	1.15137i	0.986674	+	0.162711i	$0.0520239\pi$
$523$	19.1306	+	26.3310i	0.836522	+	1.15137i	−0.150151	+	0.988663i	$0.547976\pi$
$524$	−36.1675			−1.57998
$525$	4.74720	+	1.56975i	0.207185	+	0.0685097i
$526$	−11.0695			−0.482651
$527$	−3.76785	−	5.18600i	−0.164130	−	0.225906i
$528$	−8.67041	−	2.81719i	−0.377331	−	0.122602i
$529$	4.73721	−	14.5796i	0.205966	−	0.633898i
$530$	−3.06144	−	1.56991i	−0.132980	−	0.0681924i
$531$	0.00684086	+	0.0210540i	0.000296868	+	0.000913665i
$532$		−	14.4611i		−	0.626967i
$533$	2.92802	−	0.951373i	0.126827	−	0.0412085i
$534$	−7.26382	−	5.27747i	−0.314336	−	0.228379i
$535$	14.7330	+	14.8097i	0.636962	+	0.640278i
$536$	23.9313	−	17.3871i	1.03367	−	0.751008i
$537$	12.8770	−	17.7236i	0.555682	−	0.764830i
$538$	4.26560	−	5.87110i	0.183903	−	0.253121i
$539$	2.86463	−	2.08127i	0.123388	−	0.0896468i
$540$	1.78782	−	3.48639i	0.0769356	−	0.150030i
$541$	−7.78039	−	5.65278i	−0.334505	−	0.243032i	0.407835	−	0.913056i	$-0.366284\pi$
$541$	−7.78039	−	5.65278i	−0.334505	−	0.243032i	−0.742340	+	0.670024i	$0.766284\pi$
$542$	9.90547	−	3.21848i	0.425477	−	0.138246i
$543$		−	5.43408i		−	0.233199i
$544$	−3.38547	−	10.4194i	−0.145151	−	0.446728i
$545$	32.7423	−	5.09877i	1.40252	−	0.218407i
$546$	0.0614625	−	0.189162i	0.00263035	−	0.00809539i
$547$	−17.1740	−	5.58016i	−0.734306	−	0.238591i	−0.0820915	−	0.996625i	$-0.526160\pi$
$547$	−17.1740	−	5.58016i	−0.734306	−	0.238591i	−0.652215	+	0.758034i	$0.726160\pi$
$548$	1.75770	+	2.41926i	0.0750851	+	0.103346i
$549$	−4.62060			−0.197202
$550$	2.76683	−	8.36734i	0.117978	−	0.356785i
$551$	−48.5032			−2.06631
$552$	−3.04050	−	4.18489i	−0.129412	−	0.178121i
$553$	−14.4343	−	4.68999i	−0.613809	−	0.199439i
$554$	1.94551	−	5.98765i	0.0826566	−	0.254391i
$555$	−3.26811	+	20.2929i	−0.138723	+	0.861386i
$556$	−11.1741	−	34.3902i	−0.473886	−	1.45847i
$557$			41.7798i			1.77027i	0.465336	+	0.885134i	$0.345934\pi$
$557$			41.7798i			1.77027i	−0.465336	+	0.885134i	$0.654066\pi$
$558$	1.38978	−	0.451567i	0.0588341	−	0.0191163i
$559$	−1.21719	−	0.884343i	−0.0514818	−	0.0374037i
$560$	−0.885851	−	5.68859i	−0.0374340	−	0.240387i
$561$	−6.25523	+	4.54469i	−0.264096	+	0.191877i
$562$	4.87422	−	6.70879i	0.205606	−	0.282993i
$563$	−6.94520	+	9.55925i	−0.292705	+	0.402874i	−0.929890	−	0.367837i	$-0.880099\pi$
$563$	−6.94520	+	9.55925i	−0.292705	+	0.402874i	0.637185	+	0.770711i	$0.280099\pi$
$564$	2.56452	−	1.86323i	0.107986	−	0.0784562i
$565$	4.86721	+	31.2553i	0.204765	+	1.31492i
$566$	−1.14662	−	0.833069i	−0.0481961	−	0.0350165i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$			13.9555i			0.585561i
$569$	1.97904	+	6.09087i	0.0829658	+	0.255343i	0.983931	−	0.178549i	$-0.0571402\pi$
$569$	1.97904	+	6.09087i	0.0829658	+	0.255343i	−0.900965	+	0.433891i	$0.857140\pi$
$570$	1.46060	−	9.06939i	0.0611776	−	0.379875i
$571$	−2.88353	+	8.87460i	−0.120672	+	0.371390i	−0.993088	−	0.117374i	$-0.962552\pi$
$571$	−2.88353	+	8.87460i	−0.120672	+	0.371390i	0.872416	+	0.488765i	$0.162552\pi$
$572$	2.35772	+	0.766069i	0.0985811	+	0.0320310i
$573$	−1.84852	−	2.54427i	−0.0772230	−	0.106288i
$574$	−3.83548			−0.160090
$575$	−11.2449	+	8.08104i	−0.468945	+	0.337003i
$576$	−2.65188			−0.110495
$577$	8.09190	+	11.1375i	0.336870	+	0.463662i	0.943524	−	0.331304i	$-0.107489\pi$
$577$	8.09190	+	11.1375i	0.336870	+	0.463662i	−0.606654	+	0.794966i	$0.707489\pi$
$578$	5.79080	+	1.88154i	0.240865	+	0.0782619i
$579$	4.04351	−	12.4446i	0.168042	−	0.517182i
$580$	−22.7523	+	3.54309i	−0.944738	+	0.147119i
$581$	−0.390419	−	1.20159i	−0.0161973	−	0.0498502i
$582$			0.504289i			0.0209035i
$583$	10.4091	−	3.38213i	0.431101	−	0.140073i
$584$	−2.31295	−	1.68045i	−0.0957104	−	0.0695377i
$585$	−0.407686	+	0.795019i	−0.0168557	+	0.0328700i
$586$	−0.115093	+	0.0836199i	−0.00475444	+	0.00345431i
$587$	−3.06790	+	4.22260i	−0.126626	+	0.174285i	−0.867623	−	0.497223i	$-0.834353\pi$
$587$	−3.06790	+	4.22260i	−0.126626	+	0.174285i	0.740997	+	0.671508i	$0.234353\pi$
$588$	1.02992	−	1.41757i	0.0424734	−	0.0584596i
$589$	−19.6007	+	14.2407i	−0.807632	+	0.586779i
$590$	0.0173783	+	0.0174688i	0.000715453	+	0.000719178i
$591$	8.49882	+	6.17475i	0.349595	+	0.253995i
$592$	22.5086	−	7.31348i	0.925097	−	0.300582i
$593$			13.0856i			0.537362i	0.963229	+	0.268681i	$0.0865877\pi$
$593$			13.0856i			0.537362i	−0.963229	+	0.268681i	$0.913412\pi$
$594$	−0.544669	−	1.67632i	−0.0223480	−	0.0687802i
$595$	−4.34475	−	2.22798i	−0.178117	−	0.0913385i
$596$	−1.73607	+	5.34309i	−0.0711124	+	0.218861i
$597$	−6.48935	−	2.10852i	−0.265592	−	0.0862959i
$598$	0.323777	+	0.445640i	0.0132402	+	0.0182236i
$599$	43.5625			1.77991			0.889957	−	0.456044i	$-0.150734\pi$
$599$	43.5625			1.77991			0.889957	+	0.456044i	$0.150734\pi$
$600$	0.0484891	−	9.33880i	0.00197956	−	0.381255i
$601$	11.9241			0.486395			0.243197	−	0.969977i	$-0.421804\pi$
$601$	11.9241			0.486395			0.243197	+	0.969977i	$0.421804\pi$
$602$	1.10172	+	1.51639i	0.0449029	+	0.0618035i
$603$	−15.0622	−	4.89400i	−0.613379	−	0.199299i
$604$	0.620839	−	1.91075i	0.0252616	−	0.0777471i
$605$	1.55315	+	3.06789i	0.0631444	+	0.124727i
$606$	0.393772	+	1.21191i	0.0159959	+	0.0492303i
$607$			14.9614i			0.607263i	0.952790	+	0.303631i	$0.0981991\pi$
$607$			14.9614i			0.607263i	−0.952790	+	0.303631i	$0.901801\pi$
$608$	−39.3805	+	12.7955i	−1.59709	+	0.518926i
$609$	−4.75460	−	3.45442i	−0.192666	−	0.139980i
$610$	−4.58856	+	2.32300i	−0.185785	+	0.0940556i
$611$	−0.584799	+	0.424881i	−0.0236584	+	0.0171889i
$612$	−2.24895	+	3.09542i	−0.0909085	+	0.125125i
$613$	−10.1476	+	13.9669i	−0.409857	+	0.564119i	−0.963183	−	0.268845i	$-0.913358\pi$
$613$	−10.1476	+	13.9669i	−0.409857	+	0.564119i	0.553327	+	0.832964i	$0.313358\pi$
$614$	10.7797	−	7.83188i	0.435031	−	0.316069i
$615$	17.0100	+	2.73941i	0.685911	+	0.110464i
$616$	−5.35051	−	3.88737i	−0.215578	−	0.156627i
$617$	−3.83940	+	1.24750i	−0.154569	+	0.0502224i	−0.385279	−	0.922800i	$-0.625895\pi$
$617$	−3.83940	+	1.24750i	−0.154569	+	0.0502224i	0.230711	+	0.973022i	$0.425895\pi$
$618$		−	5.40229i		−	0.217312i
$619$	6.74733	+	20.7661i	0.271198	+	0.834661i	0.990200	+	0.139654i	$0.0445990\pi$
$619$	6.74733	+	20.7661i	0.271198	+	0.834661i	−0.719002	+	0.695008i	$0.755401\pi$
$620$	−8.15420	+	8.11197i	−0.327481	+	0.325785i
$621$	−0.855818	+	2.63394i	−0.0343428	+	0.105696i
$622$	−5.63614	−	1.83129i	−0.225989	−	0.0734282i
$623$	10.6020	+	14.5924i	0.424759	+	0.584630i
$624$	1.02875			0.0411830
$625$	−24.9987	−	0.259604i	−0.999946	−	0.0103842i
$626$	−2.55848			−0.102258
$627$	17.1768	+	23.6419i	0.685977	+	0.944166i
$628$	30.5827	+	9.93691i	1.22038	+	0.396526i
$629$	6.20264	−	19.0898i	0.247315	−	0.761159i
$630$	0.789104	−	0.785017i	0.0314386	−	0.0312758i
$631$	−10.2968	−	31.6904i	−0.409911	−	1.26158i	−0.916724	−	0.399520i	$-0.869177\pi$
$631$	−10.2968	−	31.6904i	−0.409911	−	1.26158i	0.506813	−	0.862056i	$-0.330823\pi$
$632$			28.3476i			1.12761i
$633$	−3.07756	+	0.999961i	−0.122322	+	0.0397449i
$634$	−11.1946	−	8.13335i	−0.444594	−	0.323017i
$635$	−16.3347	−	2.63065i	−0.648224	−	0.104394i
$636$	4.38168	−	3.18348i	0.173745	−	0.126233i
$637$	−0.234859	+	0.323255i	−0.00930544	+	0.0128078i
$638$	−6.08872	+	8.38040i	−0.241055	+	0.331783i
$639$	6.04474	−	4.39176i	0.239126	−	0.173735i
$640$	−22.6519	+	11.4677i	−0.895395	+	0.453303i
$641$	32.4090	+	23.5465i	1.28008	+	0.930032i	0.999555	−	0.0298146i	$-0.00949168\pi$
$641$	32.4090	+	23.5465i	1.28008	+	0.930032i	0.280524	+	0.959847i	$0.409492\pi$
$642$	4.42279	−	1.43705i	0.174554	−	0.0567160i
$643$			23.5368i			0.928200i	0.885783	+	0.464100i	$0.153622\pi$
$643$			23.5368i			0.928200i	−0.885783	+	0.464100i	$0.846378\pi$
$644$	1.49958	+	4.61522i	0.0590916	+	0.181865i
$645$	−3.80300	−	7.51195i	−0.149743	−	0.295783i
$646$	−2.77211	+	8.53167i	−0.109067	+	0.335674i
$647$	−45.0338	−	14.6324i	−1.77046	−	0.575258i	−0.772266	−	0.635299i	$-0.780877\pi$
$647$	−45.0338	−	14.6324i	−1.77046	−	0.575258i	−0.998196	+	0.0600409i	$0.980877\pi$
$648$	−1.09786	−	1.51107i	−0.0431279	−	0.0593604i
$649$	−0.0783861			−0.00307692
$650$	−0.00516351	+	0.994470i	−0.000202530	+	0.0390063i
$651$	−2.93562			−0.115056
$652$	−9.18432	−	12.6411i	−0.359686	−	0.495065i
$653$	2.06130	+	0.669758i	0.0806650	+	0.0262097i	0.349072	−	0.937096i	$-0.386497\pi$
$653$	2.06130	+	0.669758i	0.0806650	+	0.0262097i	−0.268406	+	0.963306i	$0.586497\pi$
$654$	2.27955	−	7.01572i	0.0891373	−	0.274337i
$655$	41.0696	+	21.0605i	1.60472	+	0.822902i
$656$	−6.13035	−	18.8673i	−0.239350	−	0.736643i
$657$			1.53067i			0.0597170i
$658$	0.856460	−	0.278281i	0.0333883	−	0.0108485i
$659$	−41.0625	−	29.8336i	−1.59957	−	1.16215i	−0.888335	−	0.459196i	$-0.848138\pi$
$659$	−41.0625	−	29.8336i	−1.59957	−	1.16215i	−0.711232	−	0.702958i	$-0.751862\pi$
$660$	9.78447	+	9.83540i	0.380860	+	0.382842i
$661$	36.0335	−	26.1799i	1.40154	−	1.01828i	0.407055	−	0.913404i	$-0.366556\pi$
$661$	36.0335	−	26.1799i	1.40154	−	1.01828i	0.994485	−	0.104875i	$-0.0334442\pi$
$662$	−3.51211	+	4.83400i	−0.136502	+	0.187879i
$663$	0.512839	−	0.705863i	0.0199170	−	0.0274134i
$664$	−1.90912	+	1.38706i	−0.0740883	+	0.0538283i
$665$	−8.42076	+	16.4211i	−0.326543	+	0.636784i
$666$	3.70183	+	2.68954i	0.143443	+	0.104217i
$667$	15.4797	−	5.02966i	0.599376	−	0.194749i
$668$			31.0962i			1.20315i
$669$	−1.27241	−	3.91608i	−0.0491943	−	0.151405i
$670$	−17.4182	+	2.71243i	−0.672923	+	0.104790i
$671$	5.05582	−	15.5602i	0.195178	−	0.600695i
$672$	−4.77164	−	1.55040i	−0.184070	−	0.0598080i
$673$	19.0073	+	26.1614i	0.732679	+	1.00845i	0.999007	+	0.0445634i	$0.0141897\pi$
$673$	19.0073	+	26.1614i	0.732679	+	1.00845i	−0.266328	+	0.963883i	$0.585810\pi$
$674$	12.1486			0.467946
$675$	−4.06029	+	2.91788i	−0.156281	+	0.112309i
$676$	22.4990			0.865347
$677$	−4.36102	−	6.00243i	−0.167608	−	0.230692i	0.716948	−	0.697126i	$-0.245538\pi$
$677$	−4.36102	−	6.00243i	−0.167608	−	0.230692i	−0.884556	+	0.466434i	$0.845538\pi$
$678$	6.69711	+	2.17602i	0.257201	+	0.0835696i
$679$	0.313056	−	0.963488i	0.0120140	−	0.0369753i
$680$	−1.45004	+	9.00382i	−0.0556063	+	0.345281i
$681$	−8.26248	−	25.4293i	−0.316619	−	0.974453i
$682$			5.17429i			0.198134i
$683$	−16.5692	+	5.38367i	−0.634004	+	0.206000i	−0.608348	−	0.793671i	$-0.708167\pi$
$683$	−16.5692	+	5.38367i	−0.634004	+	0.206000i	−0.0256559	+	0.999671i	$0.508167\pi$
$684$	11.6993	+	8.50000i	0.447332	+	0.325006i
$685$	−0.587188	−	3.77069i	−0.0224353	−	0.144071i
$686$	0.402714	−	0.292589i	0.0153757	−	0.0111711i
$687$	8.69129	−	11.9625i	0.331593	−	0.456399i
$688$	−5.69843	+	7.84321i	−0.217251	+	0.299020i
$689$	−0.999177	+	0.725944i	−0.0380656	+	0.0276563i
$690$	0.474326	+	3.04594i	0.0180573	+	0.115957i
$691$	−16.2098	−	11.7771i	−0.616648	−	0.448021i	0.235101	−	0.971971i	$-0.424458\pi$
$691$	−16.2098	−	11.7771i	−0.616648	−	0.448021i	−0.851749	+	0.523950i	$0.824458\pi$
$692$	−23.7957	+	7.73168i	−0.904575	+	0.293914i
$693$			3.54088i			0.134507i
$694$	−4.57209	−	14.0715i	−0.173554	−	0.534145i
$695$	−7.33700	+	45.5582i	−0.278308	+	1.72812i
$696$	−3.39208	+	10.4397i	−0.128576	+	0.395718i
$697$	−16.0015	−	5.19921i	−0.606101	−	0.196934i
$698$	−2.05018	−	2.82183i	−0.0776005	−	0.106808i
$699$	−14.3079			−0.541174
$700$	−2.75054	+	8.31810i	−0.103961	+	0.314395i
$701$	−47.7641			−1.80403			−0.902013	−	0.431709i	$-0.857911\pi$
$701$	−47.7641			−1.80403			−0.902013	+	0.431709i	$0.857911\pi$
$702$	0.116909	+	0.160911i	0.00441243	+	0.00607319i
$703$	−72.1505	−	23.4431i	−2.72121	−	0.884174i
$704$	2.90166	−	8.93039i	0.109360	−	0.336577i
$705$	−3.99708	+	0.622443i	−0.150539	+	0.0234426i
$706$	4.40964	+	13.5715i	0.165959	+	0.510769i
$707$		−	2.55990i		−	0.0962749i
$708$	−0.0368911	+	0.0119866i	−0.00138645	+	0.000450485i
$709$	9.61321	+	6.98440i	0.361032	+	0.262305i	0.753482	−	0.657468i	$-0.228373\pi$
$709$	9.61321	+	6.98440i	0.361032	+	0.262305i	−0.392451	+	0.919773i	$0.628373\pi$
$710$	3.79487	−	7.40029i	0.142419	−	0.277728i
$711$	12.2786	−	8.92089i	0.460482	−	0.334560i
$712$	19.8022	−	27.2554i	0.742119	−	1.02144i
$713$	4.77879	−	6.57744i	0.178967	−	0.246327i
$714$	−0.879371	+	0.638900i	−0.0329096	+	0.0239102i
$715$	−2.23120	−	2.24281i	−0.0834421	−	0.0838765i
$716$	31.0555	+	22.5632i	1.16060	+	0.843225i
$717$	14.3002	−	4.64643i	0.534052	−	0.173524i
$718$			6.06863i			0.226479i
$719$	9.55556	+	29.4090i	0.356362	+	1.09677i	0.955216	+	0.295911i	$0.0956232\pi$
$719$	9.55556	+	29.4090i	0.356362	+	1.09677i	−0.598853	+	0.800859i	$0.704377\pi$
$720$	5.12285	+	2.62700i	0.190917	+	0.0979025i
$721$	−3.35367	+	10.3215i	−0.124897	+	0.384394i
$722$	23.2508	+	7.55465i	0.865306	+	0.281155i
$723$	6.49856	+	8.94450i	0.241684	+	0.332650i
$724$	9.52167			0.353870
$725$	27.8993	+	9.22547i	1.03616	+	0.342625i
$726$	0.765492			0.0284101
$727$	23.8073	+	32.7679i	0.882962	+	1.21529i	0.975592	+	0.219593i	$0.0704729\pi$
$727$	23.8073	+	32.7679i	0.882962	+	1.21529i	−0.0926291	+	0.995701i	$0.529527\pi$
$728$	0.709776	+	0.230620i	0.0263060	+	0.00854735i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	0.769542	+	1.52005i	0.0284820	+	0.0562597i
$731$	2.54080	+	7.81979i	0.0939750	+	0.289225i
$732$		−	8.09627i		−	0.299247i
$733$	12.7731	−	4.15024i	0.471786	−	0.153292i	−0.0634679	−	0.997984i	$-0.520216\pi$
$733$	12.7731	−	4.15024i	0.471786	−	0.153292i	0.535254	+	0.844691i	$0.320216\pi$
$734$	−8.60491	−	6.25183i	−0.317613	−	0.230759i
$735$	−1.99498	+	1.00998i	−0.0735859	+	0.0372536i
$736$	11.2413	−	8.16731i	0.414361	−	0.301051i
$737$	32.9618	−	45.3680i	1.21416	−	1.67115i
$738$	2.25444	−	3.10297i	0.0829871	−	0.114222i
$739$	−32.1073	+	23.3273i	−1.18109	+	0.858110i	−0.992294	−	0.123907i	$-0.960458\pi$
$739$	−32.1073	+	23.3273i	−1.18109	+	0.858110i	−0.188793	+	0.982017i	$0.560458\pi$
$740$	−35.5575	−	5.72642i	−1.30712	−	0.210507i
$741$	−2.66784	−	1.93830i	−0.0980054	−	0.0712051i
$742$	1.46333	−	0.475465i	0.0537206	−	0.0174549i
$743$			20.8718i			0.765713i	0.923808	+	0.382857i	$0.125060\pi$
$743$			20.8718i			0.765713i	−0.923808	+	0.382857i	$0.874940\pi$
$744$	1.69437	+	5.21475i	0.0621188	+	0.191182i
$745$	5.08269	−	5.05637i	0.186215	−	0.185251i
$746$	1.14262	−	3.51661i	0.0418342	−	0.128752i
$747$	1.20159	+	0.390419i	0.0439638	+	0.0142847i
$748$	−7.96326	−	10.9605i	−0.291166	−	0.400755i
$749$	−9.34224			−0.341358
$750$	−2.56517	+	4.93896i	−0.0936668	+	0.180345i
$751$	−43.0147			−1.56963			−0.784815	−	0.619731i	$-0.787242\pi$
$751$	−43.0147			−1.56963			−0.784815	+	0.619731i	$0.787242\pi$
$752$	2.73780	+	3.76826i	0.0998374	+	0.137414i
$753$	−4.67876	−	1.52022i	−0.170504	−	0.0554000i
$754$	0.361216	−	1.11171i	0.0131547	−	0.0404860i
$755$	−1.81763	+	1.80821i	−0.0661502	+	0.0658076i
$756$	0.541463	+	1.66645i	0.0196928	+	0.0606083i
$757$			29.6897i			1.07909i	0.841956	+	0.539546i	$0.181404\pi$
$757$			29.6897i			1.07909i	−0.841956	+	0.539546i	$0.818596\pi$
$758$	−9.47933	+	3.08002i	−0.344305	+	0.111871i
$759$	−7.93355	−	5.76406i	−0.287970	−	0.209222i
$760$	34.0303	+	5.48047i	1.23441	+	0.198797i
$761$	15.2793	−	11.1011i	0.553874	−	0.402413i	−0.275338	−	0.961348i	$-0.588790\pi$
$761$	15.2793	−	11.1011i	0.553874	−	0.402413i	0.829212	+	0.558935i	$0.188790\pi$
$762$	−2.16494	+	2.97978i	−0.0784273	+	0.107946i
$763$	−8.71054	+	11.9890i	−0.315343	+	0.434032i
$764$	4.45810	−	3.23900i	0.161288	−	0.117183i
$765$	4.35625	−	2.20540i	0.157501	−	0.0797363i
$766$	2.69897	+	1.96092i	0.0975179	+	0.0708509i
$767$	0.00841245	−	0.00273337i	0.000303756	−	9.86963e-5i
$768$			0.348296i			0.0125681i
$769$	−10.8657	−	33.4411i	−0.391826	−	1.20592i	−0.931406	−	0.363982i	$-0.881417\pi$
$769$	−10.8657	−	33.4411i	−0.391826	−	1.20592i	0.539580	−	0.841935i	$-0.318583\pi$
$770$	1.78017	+	3.51632i	0.0641530	+	0.126719i
$771$	−1.65884	+	5.10539i	−0.0597417	+	0.183866i
$772$	21.8057	+	7.08509i	0.784803	+	0.254998i
$773$	30.8572	+	42.4714i	1.10986	+	1.52759i	0.821625	+	0.570028i	$0.193068\pi$
$773$	30.8572	+	42.4714i	1.10986	+	1.52759i	0.288233	+	0.957560i	$0.406932\pi$
$774$	−1.87436			−0.0673726
$775$	13.9831	−	4.46324i	0.502287	−	0.160324i
$776$	−1.89220			−0.0679260
$777$	−5.40304	−	7.43664i	−0.193833	−	0.266788i
$778$	−3.71352	−	1.20660i	−0.133136	−	0.0432585i
$779$	−19.6506	+	60.4784i	−0.704057	+	2.16686i
$780$	−1.39304	−	0.714352i	−0.0498789	−	0.0255779i
$781$	8.17547	+	25.1615i	0.292541	+	0.900350i
$782$		−	3.01033i		−	0.107649i
$783$	5.58937	−	1.81610i	0.199748	−	0.0649020i
$784$	2.08296	+	1.51336i	0.0743913	+	0.0540484i
$785$	−28.9416	−	29.0922i	−1.03297	−	1.03835i
$786$	8.31244	−	6.03934i	0.296495	−	0.215416i
$787$	−16.6793	+	22.9571i	−0.594552	+	0.818331i	−0.995196	−	0.0979030i	$-0.968787\pi$
$787$	−16.6793	+	22.9571i	−0.594552	+	0.818331i	0.400644	+	0.916234i	$0.368787\pi$
$788$	−10.8195	+	14.8917i	−0.385428	+	0.530496i
$789$	−17.9906	+	13.0709i	−0.640481	+	0.465336i
$790$	7.70844	−	15.0321i	0.274254	−	0.534817i
$791$	−11.4446	−	8.31496i	−0.406922	−	0.295646i
$792$	6.28990	−	2.04371i	0.223502	−	0.0726202i
$793$			1.84623i			0.0655616i
$794$	−0.310783	−	0.956491i	−0.0110293	−	0.0339446i
$795$	−6.82934	+	1.06349i	−0.242212	+	0.0377182i
$796$	3.69457	−	11.3707i	0.130951	−	0.403025i
$797$	6.30880	+	2.04985i	0.223469	+	0.0726095i	0.418611	−	0.908165i	$-0.362517\pi$
$797$	6.30880	+	2.04985i	0.223469	+	0.0726095i	−0.195142	+	0.980775i	$0.562517\pi$
$798$	2.41475	+	3.32362i	0.0854812	+	0.117655i
$799$	3.95035			0.139753
$800$	25.0857	+	0.130250i	0.886912	+	0.00460504i
$801$	−18.0371			−0.637311
$802$	1.01553	+	1.39775i	0.0358595	+	0.0493563i
$803$	−5.15463	−	1.67484i	−0.181903	−	0.0591039i
$804$	8.57532	−	26.3921i	0.302428	−	0.930779i
$805$	0.984637	−	6.11398i	0.0347039	−	0.215489i
$806$	−0.180431	−	0.555308i	−0.00635539	−	0.0195599i
$807$		−	14.5788i		−	0.513199i
$808$	−4.54733	+	1.47752i	−0.159974	+	0.0519788i
$809$	14.5341	+	10.5596i	0.510991	+	0.371257i	0.813199	−	0.581985i	$-0.197724\pi$
$809$	14.5341	+	10.5596i	0.510991	+	0.371257i	−0.302208	+	0.953242i	$0.597724\pi$
$810$	0.171269	+	1.09982i	0.00601777	+	0.0386437i
$811$	−23.1507	+	16.8200i	−0.812932	+	0.590630i	−0.914679	−	0.404181i	$-0.867557\pi$
$811$	−23.1507	+	16.8200i	−0.812932	+	0.590630i	0.101747	+	0.994810i	$0.467557\pi$
$812$	6.05288	−	8.33108i	0.212415	−	0.292364i
$813$	12.2984	−	16.9273i	0.431323	−	0.593665i
$814$	−13.1077	+	9.52332i	−0.459426	+	0.333792i
$815$	3.06817	+	19.7026i	0.107473	+	0.690152i
$816$	−4.54836	−	3.30458i	−0.159224	−	0.115683i
$817$	29.5552	−	9.60307i	1.03401	−	0.335969i
$818$			9.34134i			0.326612i
$819$	−0.123473	−	0.380009i	−0.00431448	−	0.0132786i
$820$	−4.80003	+	29.8052i	−0.167624	+	1.04084i
$821$	13.0530	−	40.1729i	0.455551	−	1.40204i	−0.414935	−	0.909851i	$-0.636196\pi$
$821$	13.0530	−	40.1729i	0.455551	−	1.40204i	0.870487	−	0.492192i	$-0.163804\pi$
$822$	−0.807950	−	0.262519i	−0.0281805	−	0.00915640i
$823$	−0.225120	−	0.309852i	−0.00784720	−	0.0108007i	0.805075	−	0.593173i	$-0.202125\pi$
$823$	−0.225120	−	0.309852i	−0.00784720	−	0.0108007i	−0.812923	+	0.582372i	$0.802125\pi$
$824$	20.2705			0.706158
$825$	−5.38346	−	16.8660i	−0.187428	−	0.587200i
$826$	−0.0110196			−0.000383423
$827$	−9.36599	−	12.8912i	−0.325687	−	0.448270i	0.614506	−	0.788912i	$-0.289355\pi$
$827$	−9.36599	−	12.8912i	−0.325687	−	0.448270i	−0.940193	+	0.340642i	$0.889355\pi$
$828$	−4.61522	−	1.49958i	−0.160390	−	0.0521138i
$829$	7.45907	−	22.9567i	0.259064	−	0.797317i	−0.733938	−	0.679217i	$-0.762320\pi$
$829$	7.45907	−	22.9567i	0.259064	−	0.797317i	0.993002	−	0.118100i	$-0.0376805\pi$
$830$	1.38954	−	0.216385i	0.0482316	−	0.00751083i
$831$	−3.90835	−	12.0287i	−0.135579	−	0.417269i
$832$			1.05960i			0.0367350i
$833$	2.07673	−	0.674772i	0.0719546	−	0.0233795i
$834$	8.31073	+	6.03810i	0.287777	+	0.209082i
$835$	18.1075	−	35.3110i	0.626635	−	1.22199i
$836$	−41.4256	+	30.0975i	−1.43273	+	1.04094i
$837$	1.72552	−	2.37497i	0.0596425	−	0.0820909i
$838$	−3.91039	+	5.38220i	−0.135082	+	0.185925i
$839$	6.84811	−	4.97545i	0.236423	−	0.171771i	−0.463265	−	0.886220i	$-0.653322\pi$
$839$	6.84811	−	4.97545i	0.236423	−	0.171771i	0.699688	+	0.714448i	$0.253322\pi$
$840$	2.94555	+	2.96089i	0.101631	+	0.102160i
$841$	−4.48139	−	3.25592i	−0.154531	−	0.112273i
$842$	−6.66584	+	2.16586i	−0.229720	+	0.0746405i
$843$		−	16.6589i		−	0.573764i
$844$	−1.75214	−	5.39255i	−0.0603113	−	0.185619i
$845$	−25.5486	−	13.1013i	−0.878897	−	0.450698i
$846$	−0.278281	+	0.856460i	−0.00956749	+	0.0294457i
$847$	−1.46254	−	0.475207i	−0.0502534	−	0.0163283i
$848$	4.67776	+	6.43838i	0.160635	+	0.221095i
$849$	−2.84723			−0.0977167
$850$	3.21729	−	4.38021i	0.110352	−	0.150240i
$851$	25.4577			0.872677
$852$	7.69529	+	10.5917i	0.263636	+	0.362864i
$853$	−23.9383	−	7.77803i	−0.819633	−	0.266315i	−0.130960	−	0.991388i	$-0.541806\pi$
$853$	−23.9383	−	7.77803i	−0.819633	−	0.266315i	−0.688672	+	0.725073i	$0.741806\pi$
$854$	0.710755	−	2.18748i	0.0243215	−	0.0748540i
$855$	−8.33538	−	16.4646i	−0.285064	−	0.563079i
$856$	5.39213	+	16.5953i	0.184299	+	0.567215i
$857$			38.0004i			1.29807i	0.760760	+	0.649034i	$0.224827\pi$
$857$			38.0004i			1.29807i	−0.760760	+	0.649034i	$0.775173\pi$
$858$	−0.669799	+	0.217631i	−0.0228666	+	0.00742980i
$859$	−0.652550	−	0.474105i	−0.0222647	−	0.0161763i	0.576597	−	0.817029i	$-0.304380\pi$
$859$	−0.652550	−	0.474105i	−0.0222647	−	0.0161763i	−0.598862	+	0.800852i	$0.704380\pi$
$860$	13.1625	−	6.66366i	0.448839	−	0.227229i
$861$	−6.23359	+	4.52897i	−0.212440	+	0.154347i
$862$	−6.95151	+	9.56793i	−0.236769	+	0.325885i
$863$	18.4327	−	25.3704i	0.627457	−	0.863620i	−0.370412	−	0.928867i	$-0.620784\pi$
$863$	18.4327	−	25.3704i	0.627457	−	0.863620i	0.997869	+	0.0652474i	$0.0207836\pi$
$864$	4.05900	−	2.94904i	0.138090	−	0.100328i
$865$	31.5231	+	5.07670i	1.07182	+	0.172613i
$866$	8.77412	+	6.37477i	0.298157	+	0.216624i
$867$	11.6332	−	3.77985i	0.395084	−	0.128370i
$868$		−	5.14383i		−	0.174593i
$869$	16.6067	+	51.1101i	0.563343	+	1.73379i
$870$	4.63757	−	4.61356i	0.157228	−	0.156414i
$871$	−1.95547	+	6.01832i	−0.0662586	+	0.203923i
$872$	26.3245	+	8.55334i	0.891460	+	0.289653i
$873$	0.595468	+	0.819592i	0.0201536	+	0.0277390i
$874$	−11.3776			−0.384854
$875$	7.96703	−	7.84388i	0.269335	−	0.265172i
$876$	−2.68205			−0.0906182
$877$	−21.6138	−	29.7489i	−0.729847	−	1.00455i	−0.999139	−	0.0414900i	$-0.986790\pi$
$877$	−21.6138	−	29.7489i	−0.729847	−	1.00455i	0.269292	−	0.963059i	$-0.413210\pi$
$878$	−13.4978	−	4.38569i	−0.455527	−	0.148010i
$879$	−0.0883148	+	0.271805i	−0.00297879	+	0.00916776i
$880$	−14.4520	+	14.3771i	−0.487176	+	0.484653i
$881$	4.90883	+	15.1078i	0.165383	+	0.508996i	0.999064	−	0.0432498i	$-0.0137711\pi$
$881$	4.90883	+	15.1078i	0.165383	+	0.508996i	−0.833682	+	0.552245i	$0.813771\pi$
$882$			0.497782i			0.0167612i
$883$	34.6674	−	11.2641i	1.16665	−	0.379068i	0.339258	−	0.940693i	$-0.389824\pi$
$883$	34.6674	−	11.2641i	1.16665	−	0.379068i	0.827391	+	0.561626i	$0.189824\pi$
$884$	1.23682	+	0.898604i	0.0415988	+	0.0302233i
$885$	0.0488712	+	0.00787055i	0.00164279	+	0.000264566i
$886$	8.52922	−	6.19684i	0.286545	−	0.208187i
$887$	−6.16123	+	8.48021i	−0.206874	+	0.284738i	−0.899829	−	0.436244i	$-0.856309\pi$
$887$	−6.16123	+	8.48021i	−0.206874	+	0.284738i	0.692955	+	0.720981i	$0.256309\pi$
$888$	−10.0917	+	13.8901i	−0.338656	+	0.466120i
$889$	5.98611	−	4.34916i	0.200768	−	0.145866i
$890$	−17.9121	+	9.06816i	−0.600414	+	0.303965i
$891$	−2.86463	−	2.08127i	−0.0959687	−	0.0697253i
$892$	6.86181	−	2.22954i	0.229750	−	0.0746505i
$893$		−	14.9305i		−	0.499630i
$894$	−0.493198	−	1.51791i	−0.0164950	−	0.0507664i
$895$	−22.1262	−	43.7052i	−0.739596	−	1.46090i
$896$	3.50872	−	10.7987i	0.117218	−	0.360760i
$897$	1.05243	+	0.341955i	0.0351396	+	0.0114176i
$898$	−7.30006	−	10.0477i	−0.243606	−	0.335295i
$899$	−17.2527			−0.575410
$900$	−5.11275	−	7.11449i	−0.170425	−	0.237150i
$901$	6.74950			0.224858
$902$	7.98269	+	10.9872i	0.265795	+	0.365835i
$903$	3.58113	+	1.16358i	0.119173	+	0.0387215i
$904$	−8.16490	+	25.1290i	−0.271560	+	0.835777i
$905$	−10.8122	−	5.54452i	−0.359411	−	0.184306i
$906$	0.176373	+	0.542820i	0.00585959	+	0.0180340i
$907$		−	14.0893i		−	0.467827i	−0.972257	−	0.233913i	$-0.924847\pi$
$907$		−	14.0893i		−	0.467827i	0.972257	−	0.233913i	$-0.0751532\pi$
$908$	44.5575	−	14.4776i	1.47869	−	0.480457i
$909$	2.07100	+	1.50467i	0.0686908	+	0.0499068i
$910$	−0.313666	−	0.315299i	−0.0103979	−	0.0104520i
$911$	−43.3245	+	31.4771i	−1.43541	+	1.04288i	−0.446428	+	0.894819i	$0.647304\pi$
$911$	−43.3245	+	31.4771i	−1.43541	+	1.04288i	−0.988978	+	0.148064i	$0.952696\pi$
$912$	−12.4898	+	17.1907i	−0.413578	+	0.569241i
$913$	−2.62953	+	3.61924i	−0.0870248	+	0.119779i
$914$	−6.82392	+	4.95787i	−0.225715	+	0.163992i
$915$	−4.71450	+	9.19364i	−0.155857	+	0.303933i
$916$	20.9609	+	15.2290i	0.692568	+	0.503180i
$917$	−19.6308	+	6.37843i	−0.648265	+	0.210634i
$918$		−	1.08696i		−	0.0358751i
$919$	−4.77776	−	14.7044i	−0.157604	−	0.485055i	0.840812	−	0.541328i	$-0.182078\pi$
$919$	−4.77776	−	14.7044i	−0.157604	−	0.485055i	−0.998415	+	0.0562732i	$0.982078\pi$
$920$	−11.4290	+	1.77977i	−0.376803	+	0.0586774i
$921$	8.27161	−	25.4574i	0.272559	−	0.838850i
$922$	−3.87726	−	1.25980i	−0.127691	−	0.0414892i
$923$	−1.75479	−	2.41527i	−0.0577598	−	0.0794995i
$924$	−6.20437			−0.204109
$925$	37.0425	+	27.2079i	1.21795	+	0.894590i
$926$	−18.4567			−0.606526
$927$	−6.37906	−	8.78003i	−0.209516	−	0.288374i
$928$	−28.0430	−	9.11172i	−0.920556	−	0.299107i
$929$	−12.8653	+	39.5953i	−0.422097	+	1.29908i	0.483650	+	0.875261i	$0.339311\pi$
$929$	−12.8653	+	39.5953i	−0.422097	+	1.29908i	−0.905747	+	0.423819i	$0.860689\pi$
$930$	0.519537	−	3.22600i	0.0170363	−	0.105785i
$931$	−2.55033	−	7.84910i	−0.0835836	−	0.257244i
$932$		−	25.0704i		−	0.821210i
$933$	−11.3225	+	3.67890i	−0.370682	+	0.120442i
$934$	0.110348	+	0.0801725i	0.00361070	+	0.00262332i
$935$	2.66026	+	17.0831i	0.0869998	+	0.558678i
$936$	−0.603772	+	0.438666i	−0.0197349	+	0.0143382i
$937$	−35.0308	+	48.2157i	−1.14440	+	1.57514i	−0.387153	+	0.922015i	$0.626541\pi$
$937$	−35.0308	+	48.2157i	−1.14440	+	1.57514i	−0.757252	+	0.653123i	$0.773459\pi$
$938$	4.63382	−	6.37791i	0.151300	−	0.208246i
$939$	−4.15815	+	3.02108i	−0.135696	+	0.0985891i
$940$	−1.09065	−	7.00374i	−0.0355732	−	0.228437i
$941$	−6.98676	−	5.07617i	−0.227762	−	0.165479i	0.468052	−	0.883701i	$-0.344956\pi$
$941$	−6.98676	−	5.07617i	−0.227762	−	0.165479i	−0.695814	+	0.718222i	$0.744956\pi$
$942$	−8.68817	+	2.82296i	−0.283076	+	0.0919769i
$943$		−	21.3393i		−	0.694902i
$944$	−0.0176130	−	0.0542072i	−0.000573254	−	0.00176429i
$945$	0.355530	−	2.20762i	0.0115654	−	0.0718140i
$946$	2.05091	−	6.31205i	0.0666809	−	0.205223i
$947$	28.2977	+	9.19448i	0.919552	+	0.298780i	0.730283	−	0.683145i	$-0.239388\pi$
$947$	28.2977	+	9.19448i	0.919552	+	0.298780i	0.189269	+	0.981925i	$0.439388\pi$
$948$	15.6313	+	21.5146i	0.507681	+	0.698763i
$949$	0.611602			0.0198534
$950$	−16.5552	−	12.1599i	−0.537120	−	0.394518i
$951$	−27.7979			−0.901408
$952$	−2.39729	−	3.29959i	−0.0776966	−	0.106940i
$953$	45.1732	+	14.6777i	1.46330	+	0.475456i	0.929077	−	0.369885i	$-0.120603\pi$
$953$	45.1732	+	14.6777i	1.46330	+	0.475456i	0.534226	+	0.845342i	$0.320603\pi$
$954$	−0.475465	+	1.46333i	−0.0153937	+	0.0473771i
$955$	−6.94844	+	1.08204i	−0.224846	+	0.0350140i
$956$	8.14153	+	25.0571i	0.263316	+	0.810403i
$957$			20.8098i			0.672685i
$958$	−6.59460	+	2.14272i	−0.213062	+	0.0692280i
$959$	1.38069	+	1.00313i	0.0445848	+	0.0323928i
$960$	−2.70577	+	5.27646i	−0.0873283	+	0.170297i
$961$	18.1075	−	13.1559i	0.584114	−	0.424383i
$962$	1.07465	−	1.47912i	0.0346480	−	0.0476889i
$963$	5.49123	−	7.55803i	0.176952	−	0.243554i
$964$	−15.6727	+	11.3869i	−0.504783	+	0.366746i
$965$	−20.6355	−	20.7429i	−0.664281	−	0.667739i
$966$	−1.11531	−	0.810322i	−0.0358846	−	0.0260717i
$967$	−3.09131	+	1.00443i	−0.0994099	+	0.0323002i	−0.358300	−	0.933607i	$-0.616643\pi$
$967$	−3.09131	+	1.00443i	−0.0994099	+	0.0323002i	0.258890	+	0.965907i	$0.416643\pi$
$968$			2.87229i			0.0923188i
$969$	5.56892	+	17.1394i	0.178899	+	0.550596i
$970$	1.00339	+	0.514537i	0.0322169	+	0.0165208i
$971$	−11.1711	+	34.3812i	−0.358499	+	1.10335i	0.595454	+	0.803390i	$0.296972\pi$
$971$	−11.1711	+	34.3812i	−0.358499	+	1.10335i	−0.953953	+	0.299957i	$0.903028\pi$
$972$	−1.66645	−	0.541463i	−0.0534515	−	0.0173674i
$973$	−12.1300	−	16.6955i	−0.388870	−	0.535233i
$974$	−2.22345			−0.0712439
$975$	1.16589	+	1.62235i	0.0373382	+	0.0519568i
$976$	11.8965			0.380799
$977$	−10.5823	−	14.5652i	−0.338557	−	0.465984i	0.605462	−	0.795874i	$-0.292988\pi$
$977$	−10.5823	−	14.5652i	−0.338557	−	0.465984i	−0.944019	+	0.329890i	$0.892988\pi$
$978$	4.22170	+	1.37171i	0.134995	+	0.0438626i
$979$	19.7361	−	60.7414i	0.630768	−	1.94130i
$980$	−1.76970	−	3.49563i	−0.0565309	−	0.111664i
$981$	−4.57940	−	14.0940i	−0.146209	−	0.449985i
$982$			4.13821i			0.132056i
$983$	−14.1996	+	4.61374i	−0.452898	+	0.147156i	−0.526579	−	0.850126i	$-0.676525\pi$
$983$	−14.1996	+	4.61374i	−0.452898	+	0.147156i	0.0736805	+	0.997282i	$0.476525\pi$
$984$	11.6430	+	8.45914i	0.371165	+	0.269667i
$985$	20.9575	−	10.6099i	0.667761	−	0.338061i
$986$	−5.16807	+	3.75483i	−0.164585	+	0.119578i
$987$	1.06336	−	1.46359i	0.0338471	−	0.0465865i
$988$	3.39631	−	4.67462i	0.108051	−	0.148719i
$989$	−8.43667	+	6.12960i	−0.268270	+	0.194910i
$990$	−3.89112	−	0.626653i	−0.123668	−	0.0199163i
$991$	28.9914	+	21.0635i	0.920942	+	0.669104i	0.943758	−	0.330636i	$-0.107263\pi$
$991$	28.9914	+	21.0635i	0.920942	+	0.669104i	−0.0228163	+	0.999740i	$0.507263\pi$
$992$	−14.0077	+	4.55139i	−0.444746	+	0.144507i
$993$			12.0036i			0.380921i
$994$	1.14932	+	3.53725i	0.0364543	+	0.112195i
$995$	−10.8166	+	10.7606i	−0.342908	+	0.341133i
$996$	−0.684097	+	2.10544i	−0.0216765	+	0.0667133i
$997$	−44.8042	−	14.5578i	−1.41896	−	0.461049i	−0.503691	−	0.863884i	$-0.668025\pi$
$997$	−44.8042	−	14.5578i	−1.41896	−	0.461049i	−0.915273	+	0.402835i	$0.868025\pi$
$998$	−9.89544	−	13.6199i	−0.313235	−	0.431131i
$999$	9.19220			0.290828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.64.6	✓	56
25.9	even	10	inner	525.2.z.a.484.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.64.6	✓	56	1.1	even	1	trivial
525.2.z.a.484.6	yes	56	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292589 - 0.402714i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.541463 - 1.66645i) q^{4} +(-1.58524 + 1.57703i) q^{5} +(0.153823 + 0.473419i) q^{6} -1.00000i q^{7} +(-1.77637 + 0.577177i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.292589 - 0.402714i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.541463 - 1.66645i) q^{4} +(-1.58524 + 1.57703i) q^{5} +(0.153823 + 0.473419i) q^{6} -1.00000i q^{7} +(-1.77637 + 0.577177i) q^{8} +(0.809017 + 0.587785i) q^{9} +(1.09892 + 0.176977i) q^{10} +(-2.86463 + 2.08127i) q^{11} +(-1.02992 + 1.41757i) q^{12} +(0.234859 - 0.323255i) q^{13} +(-0.402714 + 0.292589i) q^{14} +(1.99498 - 1.00998i) q^{15} +(-2.08296 - 1.51336i) q^{16} +(-2.07673 + 0.674772i) q^{17} -0.497782i q^{18} +(2.55033 + 7.84910i) q^{19} +(1.76970 + 3.49563i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(1.67632 + 0.544669i) q^{22} +(-1.62786 - 2.24056i) q^{23} +1.86779 q^{24} +(0.0259608 - 4.99993i) q^{25} -0.198897 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.66645 - 0.541463i) q^{28} +(-1.81610 + 5.58937i) q^{29} +(-0.990442 - 0.507899i) q^{30} +(0.907157 + 2.79194i) q^{31} +5.01720i q^{32} +(3.36757 - 1.09419i) q^{33} +(0.879371 + 0.638900i) q^{34} +(1.57703 + 1.58524i) q^{35} +(1.41757 - 1.02992i) q^{36} +(-5.40304 + 7.43664i) q^{37} +(2.41475 - 3.32362i) q^{38} +(-0.323255 + 0.234859i) q^{39} +(1.90574 - 3.71635i) q^{40} +(6.23359 + 4.52897i) q^{41} +(0.473419 - 0.153823i) q^{42} -3.76543i q^{43} +(1.91726 + 5.90070i) q^{44} +(-2.20944 + 0.344063i) q^{45} +(-0.426011 + 1.31113i) q^{46} +(-1.72055 - 0.559041i) q^{47} +(1.51336 + 2.08296i) q^{48} -1.00000 q^{49} +(-2.02114 + 1.45247i) q^{50} +2.18361 q^{51} +(-0.411522 - 0.566412i) q^{52} +(-2.93970 - 0.955166i) q^{53} +(-0.153823 + 0.473419i) q^{54} +(1.25889 - 7.81692i) q^{55} +(0.577177 + 1.77637i) q^{56} -8.25303i q^{57} +(2.78229 - 0.904021i) q^{58} +(0.0179096 + 0.0130121i) q^{59} +(-0.602872 - 3.87141i) q^{60} +(-3.73814 + 2.71592i) q^{61} +(0.858931 - 1.18222i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-2.14541 + 1.55873i) q^{64} +(0.137476 + 0.882816i) q^{65} +(-1.42596 - 1.03602i) q^{66} +(-15.0622 + 4.89400i) q^{67} +3.82615i q^{68} +(0.855818 + 2.63394i) q^{69} +(0.176977 - 1.09892i) q^{70} +(2.30888 - 7.10601i) q^{71} +(-1.77637 - 0.577177i) q^{72} +(0.899704 + 1.23834i) q^{73} +4.57571 q^{74} +(-1.56975 + 4.74720i) q^{75} +14.4611 q^{76} +(2.08127 + 2.86463i) q^{77} +(0.189162 + 0.0614625i) q^{78} +(4.68999 - 14.4343i) q^{79} +(5.68859 - 0.885851i) q^{80} +(0.309017 + 0.951057i) q^{81} -3.83548i q^{82} +(1.20159 - 0.390419i) q^{83} +(1.41757 + 1.02992i) q^{84} +(2.22798 - 4.34475i) q^{85} +(-1.51639 + 1.10172i) q^{86} +(3.45442 - 4.75460i) q^{87} +(3.88737 - 5.35051i) q^{88} +(-14.5924 + 10.6020i) q^{89} +(0.785017 + 0.789104i) q^{90} +(-0.323255 - 0.234859i) q^{91} +(-4.61522 + 1.49958i) q^{92} -2.93562i q^{93} +(0.278281 + 0.856460i) q^{94} +(-16.4211 - 8.42076i) q^{95} +(1.55040 - 4.77164i) q^{96} +(0.963488 + 0.313056i) q^{97} +(0.292589 + 0.402714i) q^{98} -3.54088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

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