LMFDB - Embedded newform 525.2.n.c.316.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			316.4
Character	$\chi$	$=$	525.316
Dual form			525.2.n.c.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728341 + 0.529171i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.367575 - 1.13128i) q^{4} +(-2.01165 - 0.976343i) q^{5} +(-0.278202 + 0.856217i) q^{6} +1.00000 q^{7} +(0.887323 - 2.73090i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.728341 + 0.529171i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.367575 - 1.13128i) q^{4} +(-2.01165 - 0.976343i) q^{5} +(-0.278202 + 0.856217i) q^{6} +1.00000 q^{7} +(0.887323 - 2.73090i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.948519 - 1.77562i) q^{10} +(-3.97096 - 2.88507i) q^{11} +(0.962323 - 0.699169i) q^{12} +(3.62273 - 2.63207i) q^{13} +(0.728341 + 0.529171i) q^{14} +(0.306921 - 2.21490i) q^{15} +(0.166740 - 0.121144i) q^{16} +(1.77993 - 5.47805i) q^{17} -0.900279 q^{18} +(-0.161781 + 0.497911i) q^{19} +(-0.365082 + 2.63462i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-1.36552 - 4.20263i) q^{22} +(3.20896 + 2.33145i) q^{23} +2.87144 q^{24} +(3.09351 + 3.92813i) q^{25} +4.03140 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.367575 - 1.13128i) q^{28} +(-1.85676 - 5.71452i) q^{29} +(1.39561 - 1.45079i) q^{30} +(-0.556378 + 1.71235i) q^{31} -5.55733 q^{32} +(1.51677 - 4.66814i) q^{33} +(4.19522 - 3.04801i) q^{34} +(-2.01165 - 0.976343i) q^{35} +(0.962323 + 0.699169i) q^{36} +(-5.96767 + 4.33576i) q^{37} +(-0.381312 + 0.277039i) q^{38} +(3.62273 + 2.63207i) q^{39} +(-4.45128 + 4.62730i) q^{40} +(6.66577 - 4.84297i) q^{41} +(-0.278202 + 0.856217i) q^{42} -1.87126 q^{43} +(-1.80420 + 5.55274i) q^{44} +(2.20134 - 0.392543i) q^{45} +(1.10349 + 3.39618i) q^{46} +(-3.34290 - 10.2884i) q^{47} +(0.166740 + 0.121144i) q^{48} +1.00000 q^{49} +(0.174480 + 4.49801i) q^{50} +5.75997 q^{51} +(-4.30923 - 3.13084i) q^{52} +(4.08133 + 12.5610i) q^{53} +(-0.278202 - 0.856217i) q^{54} +(5.17138 + 9.68078i) q^{55} +(0.887323 - 2.73090i) q^{56} -0.523534 q^{57} +(1.67160 - 5.14466i) q^{58} +(0.0854442 - 0.0620788i) q^{59} +(-2.61849 + 0.466929i) q^{60} +(5.41377 + 3.93333i) q^{61} +(-1.31136 + 0.952759i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-4.38111 - 3.18306i) q^{64} +(-9.85749 + 1.75779i) q^{65} +(3.57497 - 2.59737i) q^{66} +(0.265019 - 0.815644i) q^{67} -6.85146 q^{68} +(-1.22571 + 3.77236i) q^{69} +(-0.948519 - 1.77562i) q^{70} +(0.561335 + 1.72761i) q^{71} +(0.887323 + 2.73090i) q^{72} +(7.64336 + 5.55323i) q^{73} -6.64086 q^{74} +(-2.77992 + 4.15596i) q^{75} +0.622743 q^{76} +(-3.97096 - 2.88507i) q^{77} +(1.24577 + 3.83409i) q^{78} +(2.14674 + 6.60699i) q^{79} +(-0.453702 + 0.0809041i) q^{80} +(0.309017 - 0.951057i) q^{81} +7.41772 q^{82} +(-4.01564 + 12.3589i) q^{83} +(0.962323 - 0.699169i) q^{84} +(-8.92905 + 9.28213i) q^{85} +(-1.36292 - 0.990217i) q^{86} +(4.86106 - 3.53176i) q^{87} +(-11.4024 + 8.28430i) q^{88} +(5.20546 + 3.78199i) q^{89} +(1.81105 + 0.878981i) q^{90} +(3.62273 - 2.63207i) q^{91} +(1.45798 - 4.48721i) q^{92} -1.80048 q^{93} +(3.00954 - 9.26241i) q^{94} +(0.811579 - 0.843671i) q^{95} +(-1.71731 - 5.28533i) q^{96} +(-2.77759 - 8.54855i) q^{97} +(0.728341 + 0.529171i) q^{98} +4.90838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	0.728341	+	0.529171i	0.515015	+	0.374180i	0.814723	−	0.579851i	$-0.196889\pi$
$2$	0.728341	+	0.529171i	0.515015	+	0.374180i	−0.299708	+	0.954031i	$0.596889\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.367575	−	1.13128i	−0.183787	−	0.565639i
$5$	−2.01165	−	0.976343i	−0.899639	−	0.436634i
$5$	−2.01165	−	0.976343i	−0.899639	−	0.436634i
$6$	−0.278202	+	0.856217i	−0.113575	+	0.349549i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.887323	−	2.73090i	0.313716	−	0.965519i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.948519	−	1.77562i	−0.299948	−	0.561500i
$11$	−3.97096	−	2.88507i	−1.19729	−	0.869882i	−0.203274	−	0.979122i	$-0.565158\pi$
$11$	−3.97096	−	2.88507i	−1.19729	−	0.869882i	−0.994015	+	0.109240i	$0.965158\pi$
$12$	0.962323	−	0.699169i	0.277799	−	0.201833i
$13$	3.62273	−	2.63207i	1.00477	−	0.730005i	0.0416606	−	0.999132i	$-0.486735\pi$
$13$	3.62273	−	2.63207i	1.00477	−	0.730005i	0.963105	+	0.269127i	$0.0867352\pi$
$14$	0.728341	+	0.529171i	0.194657	+	0.141427i
$15$	0.306921	−	2.21490i	0.0792468	−	0.571886i
$16$	0.166740	−	0.121144i	0.0416851	−	0.0302860i
$17$	1.77993	−	5.47805i	0.431696	−	1.32862i	−0.464739	−	0.885448i	$-0.653852\pi$
$17$	1.77993	−	5.47805i	0.431696	−	1.32862i	0.896435	−	0.443175i	$-0.146148\pi$
$18$	−0.900279			−0.212198
$19$	−0.161781	+	0.497911i	−0.0371151	+	0.114229i	−0.967898	−	0.251345i	$-0.919127\pi$
$19$	−0.161781	+	0.497911i	−0.0371151	+	0.114229i	0.930782	+	0.365574i	$0.119127\pi$
$20$	−0.365082	+	2.63462i	−0.0816348	+	0.589119i
$21$	0.309017	+	0.951057i	0.0674330	+	0.207538i
$22$	−1.36552	−	4.20263i	−0.291129	−	0.896004i
$23$	3.20896	+	2.33145i	0.669115	+	0.486140i	0.869729	−	0.493530i	$-0.164294\pi$
$23$	3.20896	+	2.33145i	0.669115	+	0.486140i	−0.200614	+	0.979670i	$0.564294\pi$
$24$	2.87144			0.586130
$25$	3.09351	+	3.92813i	0.618702	+	0.785626i
$26$	4.03140			0.790623
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.367575	−	1.13128i	−0.0694651	−	0.213792i
$29$	−1.85676	−	5.71452i	−0.344791	−	1.06116i	−0.961695	−	0.274120i	$-0.911613\pi$
$29$	−1.85676	−	5.71452i	−0.344791	−	1.06116i	0.616904	−	0.787038i	$-0.288387\pi$
$30$	1.39561	−	1.45079i	0.254802	−	0.264877i
$31$	−0.556378	+	1.71235i	−0.0999284	+	0.307548i	−0.988507	−	0.151177i	$-0.951694\pi$
$31$	−0.556378	+	1.71235i	−0.0999284	+	0.307548i	0.888578	+	0.458725i	$0.151694\pi$
$32$	−5.55733			−0.982406
$33$	1.51677	−	4.66814i	0.264036	−	0.812619i
$34$	4.19522	−	3.04801i	0.719474	−	0.522729i
$35$	−2.01165	−	0.976343i	−0.340032	−	0.165032i
$36$	0.962323	+	0.699169i	0.160387	+	0.116528i
$37$	−5.96767	+	4.33576i	−0.981079	+	0.712795i	−0.957949	−	0.286937i	$-0.907363\pi$
$37$	−5.96767	+	4.33576i	−0.981079	+	0.712795i	−0.0231291	+	0.999732i	$0.507363\pi$
$38$	−0.381312	+	0.277039i	−0.0618569	+	0.0449417i
$39$	3.62273	+	2.63207i	0.580101	+	0.421468i
$40$	−4.45128	+	4.62730i	−0.703809	+	0.731640i
$41$	6.66577	−	4.84297i	1.04102	−	0.756344i	0.0705347	−	0.997509i	$-0.477529\pi$
$41$	6.66577	−	4.84297i	1.04102	−	0.756344i	0.970484	+	0.241165i	$0.0775294\pi$
$42$	−0.278202	+	0.856217i	−0.0429274	+	0.132117i
$43$	−1.87126			−0.285365			−0.142682	−	0.989769i	$-0.545573\pi$
$43$	−1.87126			−0.285365			−0.142682	+	0.989769i	$0.545573\pi$
$44$	−1.80420	+	5.55274i	−0.271993	+	0.837107i
$45$	2.20134	−	0.392543i	0.328157	−	0.0585169i
$46$	1.10349	+	3.39618i	0.162700	+	0.500739i
$47$	−3.34290	−	10.2884i	−0.487612	−	1.50071i	−0.828162	−	0.560488i	$-0.810614\pi$
$47$	−3.34290	−	10.2884i	−0.487612	−	1.50071i	0.340551	−	0.940226i	$-0.389386\pi$
$48$	0.166740	+	0.121144i	0.0240669	+	0.0174856i
$49$	1.00000			0.142857
$50$	0.174480	+	4.49801i	0.0246752	+	0.636115i
$51$	5.75997			0.806556
$52$	−4.30923	−	3.13084i	−0.597583	−	0.434169i
$53$	4.08133	+	12.5610i	0.560614	+	1.72539i	0.680637	+	0.732621i	$0.261703\pi$
$53$	4.08133	+	12.5610i	0.560614	+	1.72539i	−0.120023	+	0.992771i	$0.538297\pi$
$54$	−0.278202	−	0.856217i	−0.0378584	−	0.116516i
$55$	5.17138	+	9.68078i	0.697309	+	1.30536i
$56$	0.887323	−	2.73090i	0.118574	−	0.364932i
$57$	−0.523534			−0.0693438
$58$	1.67160	−	5.14466i	0.219492	−	0.675527i
$59$	0.0854442	−	0.0620788i	0.0111239	−	0.00808197i	−0.582209	−	0.813039i	$-0.697812\pi$
$59$	0.0854442	−	0.0620788i	0.0111239	−	0.00808197i	0.593333	+	0.804957i	$0.297812\pi$
$60$	−2.61849	+	0.466929i	−0.338046	+	0.0602803i
$61$	5.41377	+	3.93333i	0.693162	+	0.503612i	0.877698	−	0.479214i	$-0.159078\pi$
$61$	5.41377	+	3.93333i	0.693162	+	0.503612i	−0.184536	+	0.982826i	$0.559078\pi$
$62$	−1.31136	+	0.952759i	−0.166543	+	0.121001i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	−4.38111	−	3.18306i	−0.547639	−	0.397883i
$65$	−9.85749	+	1.75779i	−1.22267	+	0.218027i
$66$	3.57497	−	2.59737i	0.440049	−	0.319714i
$67$	0.265019	−	0.815644i	0.0323772	−	0.0996467i	−0.933562	−	0.358416i	$-0.883317\pi$
$67$	0.265019	−	0.815644i	0.0323772	−	0.0996467i	0.965939	+	0.258769i	$0.0833169\pi$
$68$	−6.85146			−0.830862
$69$	−1.22571	+	3.77236i	−0.147559	+	0.454139i
$70$	−0.948519	−	1.77562i	−0.113370	−	0.212227i
$71$	0.561335	+	1.72761i	0.0666183	+	0.205030i	0.978824	−	0.204702i	$-0.0656224\pi$
$71$	0.561335	+	1.72761i	0.0666183	+	0.205030i	−0.912206	+	0.409732i	$0.865622\pi$
$72$	0.887323	+	2.73090i	0.104572	+	0.321840i
$73$	7.64336	+	5.55323i	0.894588	+	0.649956i	0.937070	−	0.349141i	$-0.113527\pi$
$73$	7.64336	+	5.55323i	0.894588	+	0.649956i	−0.0424822	+	0.999097i	$0.513527\pi$
$74$	−6.64086			−0.771984
$75$	−2.77992	+	4.15596i	−0.320998	+	0.479889i
$76$	0.622743			0.0714335
$77$	−3.97096	−	2.88507i	−0.452533	−	0.328784i
$78$	1.24577	+	3.83409i	0.141056	+	0.434125i
$79$	2.14674	+	6.60699i	0.241527	+	0.743345i	0.996188	+	0.0872296i	$0.0278014\pi$
$79$	2.14674	+	6.60699i	0.241527	+	0.743345i	−0.754661	+	0.656115i	$0.772199\pi$
$80$	−0.453702	+	0.0809041i	−0.0507254	+	0.00904536i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	7.41772			0.819150
$83$	−4.01564	+	12.3589i	−0.440773	+	1.35656i	0.446280	+	0.894894i	$0.352749\pi$
$83$	−4.01564	+	12.3589i	−0.440773	+	1.35656i	−0.887053	+	0.461668i	$0.847251\pi$
$84$	0.962323	−	0.699169i	0.104998	−	0.0762856i
$85$	−8.92905	+	9.28213i	−0.968492	+	1.00679i
$86$	−1.36292	−	0.990217i	−0.146967	−	0.106778i
$87$	4.86106	−	3.53176i	0.521160	−	0.378645i
$88$	−11.4024	+	8.28430i	−1.21550	+	0.883110i
$89$	5.20546	+	3.78199i	0.551778	+	0.400890i	0.828441	−	0.560077i	$-0.189228\pi$
$89$	5.20546	+	3.78199i	0.551778	+	0.400890i	−0.276663	+	0.960967i	$0.589228\pi$
$90$	1.81105	+	0.878981i	0.190902	+	0.0926527i
$91$	3.62273	−	2.63207i	0.379766	−	0.275916i
$92$	1.45798	−	4.48721i	0.152005	−	0.467824i
$93$	−1.80048			−0.186701
$94$	3.00954	−	9.26241i	0.310410	−	0.955345i
$95$	0.811579	−	0.843671i	0.0832663	−	0.0865588i
$96$	−1.71731	−	5.28533i	−0.175272	−	0.539432i
$97$	−2.77759	−	8.54855i	−0.282022	−	0.867974i	−0.987276	−	0.159019i	$-0.949167\pi$
$97$	−2.77759	−	8.54855i	−0.282022	−	0.867974i	0.705254	−	0.708955i	$-0.250833\pi$
$98$	0.728341	+	0.529171i	0.0735736	+	0.0534543i
$99$	4.90838			0.493310
$100$	3.30671	−	4.94350i	0.330671	−	0.494350i
$101$	−6.48678			−0.645459			−0.322729	−	0.946491i	$-0.604600\pi$
$101$	−6.48678			−0.645459			−0.322729	+	0.946491i	$0.604600\pi$
$102$	4.19522	+	3.04801i	0.415389	+	0.301798i
$103$	−5.53991	−	17.0501i	−0.545864	−	1.68000i	−0.718927	−	0.695086i	$-0.755366\pi$
$103$	−5.53991	−	17.0501i	−0.545864	−	1.68000i	0.173063	−	0.984911i	$-0.444634\pi$
$104$	−3.97338	−	12.2288i	−0.389622	−	1.19913i
$105$	0.306921	−	2.21490i	0.0299525	−	0.216152i
$106$	−3.67434	+	11.3084i	−0.356883	+	1.09837i
$107$	−9.43379			−0.911998			−0.455999	−	0.889980i	$-0.650718\pi$
$107$	−9.43379			−0.911998			−0.455999	+	0.889980i	$0.650718\pi$
$108$	−0.367575	+	1.13128i	−0.0353699	+	0.108857i
$109$	8.09735	−	5.88307i	0.775586	−	0.563496i	−0.128065	−	0.991766i	$-0.540877\pi$
$109$	8.09735	−	5.88307i	0.775586	−	0.563496i	0.903651	+	0.428270i	$0.140877\pi$
$110$	−1.35626	+	9.78746i	−0.129314	+	0.933198i
$111$	−5.96767	−	4.33576i	−0.566426	−	0.411533i
$112$	0.166740	−	0.121144i	0.0157555	−	0.0114470i
$113$	14.8050	−	10.7565i	1.39274	−	1.01189i	0.397183	−	0.917740i	$-0.369988\pi$
$113$	14.8050	−	10.7565i	1.39274	−	1.01189i	0.995558	−	0.0941460i	$-0.0300120\pi$
$114$	−0.381312	−	0.277039i	−0.0357131	−	0.0259471i
$115$	−4.17903	−	7.82311i	−0.389697	−	0.729509i
$116$	−5.78221	+	4.20102i	−0.536865	+	0.390055i
$117$	−1.38376	+	4.25878i	−0.127929	+	0.393724i
$118$	0.0950828			0.00875308
$119$	1.77993	−	5.47805i	0.163166	−	0.502172i
$120$	−5.77634	−	2.80351i	−0.527306	−	0.255924i
$121$	4.04570	+	12.4514i	0.367791	+	1.13194i
$122$	1.86167	+	5.72962i	0.168547	+	0.518735i
$123$	6.66577	+	4.84297i	0.601033	+	0.436676i
$124$	2.14166			0.192327
$125$	−2.38788	−	10.9224i	−0.213578	−	0.976926i
$126$	−0.900279			−0.0802033
$127$	−4.49428	−	3.26529i	−0.398803	−	0.289747i	0.370250	−	0.928932i	$-0.379272\pi$
$127$	−4.49428	−	3.26529i	−0.398803	−	0.289747i	−0.769053	+	0.639185i	$0.779272\pi$
$128$	1.92806	+	5.93395i	0.170418	+	0.524492i
$129$	−0.578252	−	1.77968i	−0.0509122	−	0.156692i
$130$	−8.10979	−	3.93603i	−0.711275	−	0.345212i
$131$	−4.35447	+	13.4017i	−0.380452	+	1.17091i	0.559274	+	0.828983i	$0.311080\pi$
$131$	−4.35447	+	13.4017i	−0.380452	+	1.17091i	−0.939726	+	0.341928i	$0.888920\pi$
$132$	−5.83850			−0.508176
$133$	−0.161781	+	0.497911i	−0.0140282	+	0.0431743i
$134$	0.624639	−	0.453827i	0.0539606	−	0.0392047i
$135$	1.05358	+	1.97230i	0.0906780	+	0.169748i
$136$	−13.3806	−	9.72161i	−1.14738	−	0.833621i
$137$	−9.53811	+	6.92984i	−0.814895	+	0.592056i	−0.915246	−	0.402896i	$-0.868004\pi$
$137$	−9.53811	+	6.92984i	−0.814895	+	0.592056i	0.100350	+	0.994952i	$0.468004\pi$
$138$	−2.88896	+	2.09895i	−0.245925	+	0.178675i
$139$	11.1872	+	8.12798i	0.948886	+	0.689406i	0.950543	−	0.310593i	$-0.100527\pi$
$139$	11.1872	+	8.12798i	0.948886	+	0.689406i	−0.00165718	+	0.999999i	$0.500527\pi$
$140$	−0.365082	+	2.63462i	−0.0308551	+	0.222666i
$141$	8.75182	−	6.35857i	0.737036	−	0.535488i
$142$	−0.505359	+	1.55533i	−0.0424088	+	0.130521i
$143$	−21.9794			−1.83801
$144$	−0.0636891	+	0.196015i	−0.00530743	+	0.0163346i
$145$	−1.84417	+	13.3085i	−0.153150	+	1.10521i
$146$	2.62837	+	8.08929i	0.217525	+	0.669475i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	7.09852	+	5.15738i	0.583495	+	0.423934i
$149$	−6.38027			−0.522692			−0.261346	−	0.965245i	$-0.584166\pi$
$149$	−6.38027			−0.522692			−0.261346	+	0.965245i	$0.584166\pi$
$150$	−4.22395	+	1.55590i	−0.344884	+	0.127039i
$151$	12.0316			0.979121			0.489561	−	0.871969i	$-0.337157\pi$
$151$	12.0316			0.979121			0.489561	+	0.871969i	$0.337157\pi$
$152$	1.21619	+	0.883616i	0.0986463	+	0.0716707i
$153$	1.77993	+	5.47805i	0.143899	+	0.442874i
$154$	−1.36552	−	4.20263i	−0.110037	−	0.338658i
$155$	2.79108	−	2.90145i	0.224185	−	0.233050i
$156$	1.64598	−	5.06580i	0.131784	−	0.405589i
$157$	14.4967			1.15696			0.578482	−	0.815695i	$-0.303645\pi$
$157$	14.4967			1.15696			0.578482	+	0.815695i	$0.303645\pi$
$158$	−1.93267	+	5.94814i	−0.153755	+	0.473208i
$159$	−10.6851	+	7.76315i	−0.847381	+	0.615658i
$160$	11.1794	+	5.42585i	0.883811	+	0.428951i
$161$	3.20896	+	2.33145i	0.252902	+	0.183744i
$162$	0.728341	−	0.529171i	0.0572239	−	0.0415756i
$163$	0.358274	−	0.260301i	0.0280622	−	0.0203884i	−0.573666	−	0.819089i	$-0.694479\pi$
$163$	0.358274	−	0.260301i	0.0280622	−	0.0203884i	0.601728	+	0.798701i	$0.294479\pi$
$164$	−7.92892	−	5.76070i	−0.619144	−	0.449835i
$165$	−7.60893	+	7.90980i	−0.592354	+	0.615777i
$166$	−9.46470	+	6.87651i	−0.734604	+	0.533721i
$167$	4.63846	−	14.2757i	0.358934	−	1.10469i	−0.594758	−	0.803904i	$-0.702752\pi$
$167$	4.63846	−	14.2757i	0.358934	−	1.10469i	0.953693	−	0.300782i	$-0.0972477\pi$
$168$	2.87144			0.221536
$169$	2.17918	−	6.70683i	0.167629	−	0.515910i
$170$	−11.4152	+	2.03556i	−0.875508	+	0.156121i
$171$	−0.161781	−	0.497911i	−0.0123717	−	0.0380762i
$172$	0.687829	+	2.11692i	0.0524465	+	0.161414i
$173$	17.6707	+	12.8385i	1.34348	+	0.976096i	0.999308	+	0.0371902i	$0.0118407\pi$
$173$	17.6707	+	12.8385i	1.34348	+	0.976096i	0.344173	+	0.938906i	$0.388159\pi$
$174$	5.40942			0.410087
$175$	3.09351	+	3.92813i	0.233847	+	0.296939i
$176$	−1.01163			−0.0762543
$177$	0.0854442	+	0.0620788i	0.00642238	+	0.00466613i
$178$	1.79003	+	5.50916i	0.134169	+	0.412929i
$179$	−2.26671	−	6.97623i	−0.169422	−	0.521428i	0.829913	−	0.557893i	$-0.188390\pi$
$179$	−2.26671	−	6.97623i	−0.169422	−	0.521428i	−0.999335	+	0.0364654i	$0.988390\pi$
$180$	−1.25323	−	2.34604i	−0.0934106	−	0.174864i
$181$	5.17588	−	15.9297i	0.384720	−	1.18405i	−0.551963	−	0.833869i	$-0.686121\pi$
$181$	5.17588	−	15.9297i	0.384720	−	1.18405i	0.936683	−	0.350178i	$-0.113879\pi$
$182$	4.03140			0.298827
$183$	−2.06788	+	6.36427i	−0.152862	+	0.470460i
$184$	9.21434	−	6.69461i	0.679290	−	0.493533i
$185$	16.2381	−	2.89557i	1.19385	−	0.212887i
$186$	−1.31136	−	0.952759i	−0.0961536	−	0.0698597i
$187$	−22.8726	+	16.6179i	−1.67261	+	1.21522i
$188$	−10.4103	+	7.56350i	−0.759246	+	0.551625i
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	1.03755	−	0.185016i	0.0752720	−	0.0134225i
$191$	−3.38199	+	2.45716i	−0.244712	+	0.177794i	−0.703380	−	0.710814i	$-0.748327\pi$
$191$	−3.38199	+	2.45716i	−0.244712	+	0.177794i	0.458668	+	0.888608i	$0.348327\pi$
$192$	1.67344	−	5.15031i	0.120770	−	0.371691i
$193$	4.84015			0.348402			0.174201	−	0.984710i	$-0.444266\pi$
$193$	4.84015			0.348402			0.174201	+	0.984710i	$0.444266\pi$
$194$	2.50061	−	7.69608i	0.179533	−	0.552547i
$195$	−4.71789	−	8.83184i	−0.337855	−	0.632461i
$196$	−0.367575	−	1.13128i	−0.0262553	−	0.0808056i
$197$	3.28255	+	10.1026i	0.233872	+	0.719784i	0.997269	+	0.0738544i	$0.0235300\pi$
$197$	3.28255	+	10.1026i	0.233872	+	0.719784i	−0.763397	+	0.645929i	$0.776470\pi$
$198$	3.57497	+	2.59737i	0.254062	+	0.184587i
$199$	26.3051			1.86472			0.932359	−	0.361533i	$-0.117747\pi$
$199$	26.3051			1.86472			0.932359	+	0.361533i	$0.117747\pi$
$200$	13.4723	−	4.96255i	0.952633	−	0.350905i
$201$	0.857619			0.0604918
$202$	−4.72459	−	3.43262i	−0.332421	−	0.241518i
$203$	−1.85676	−	5.71452i	−0.130319	−	0.401080i
$204$	−2.11722	−	6.51613i	−0.148235	−	0.456220i
$205$	−18.1376	+	3.23430i	−1.26679	+	0.225893i
$206$	4.98747	−	15.3499i	0.347493	−	1.06947i
$207$	−3.96649			−0.275690
$208$	0.285196	−	0.877744i	0.0197748	−	0.0608606i
$209$	2.07893	−	1.51043i	0.143803	−	0.104479i
$210$	1.39561	−	1.45079i	0.0963060	−	0.100114i
$211$	13.7960	+	10.0234i	0.949758	+	0.690040i	0.950750	−	0.309960i	$-0.100316\pi$
$211$	13.7960	+	10.0234i	0.949758	+	0.690040i	−0.000991491		1.00000i	$0.500316\pi$
$212$	12.7099	−	9.23425i	0.872916	−	0.634211i
$213$	−1.46960	+	1.06772i	−0.100695	+	0.0731592i
$214$	−6.87102	−	4.99208i	−0.469693	−	0.341252i
$215$	3.76433	+	1.82699i	0.256725	+	0.124600i
$216$	−2.32304	+	1.68779i	−0.158063	+	0.114840i
$217$	−0.556378	+	1.71235i	−0.0377694	+	0.116242i
$218$	9.01079			0.610288
$219$	−2.91951	+	8.98531i	−0.197282	+	0.607171i
$220$	9.05080	−	9.40869i	0.610205	−	0.634334i
$221$	−7.97041	−	24.5304i	−0.536148	−	1.65009i
$222$	−2.05214	−	6.31583i	−0.137731	−	0.423891i
$223$	7.23638	+	5.25754i	0.484584	+	0.352071i	0.803098	−	0.595848i	$-0.203184\pi$
$223$	7.23638	+	5.25754i	0.484584	+	0.352071i	−0.318514	+	0.947918i	$0.603184\pi$
$224$	−5.55733			−0.371315
$225$	−4.81160	−	1.35960i	−0.320773	−	0.0906402i
$226$	16.4751			1.09591
$227$	6.50815	+	4.72845i	0.431961	+	0.313838i	0.782433	−	0.622735i	$-0.213979\pi$
$227$	6.50815	+	4.72845i	0.431961	+	0.313838i	−0.350471	+	0.936573i	$0.613979\pi$
$228$	0.192438	+	0.592264i	0.0127445	+	0.0392236i
$229$	−3.85963	−	11.8787i	−0.255052	−	0.784969i	−0.993819	−	0.111008i	$-0.964592\pi$
$229$	−3.85963	−	11.8787i	−0.255052	−	0.784969i	0.738768	−	0.673960i	$-0.235408\pi$
$230$	1.09600	−	7.90932i	0.0722682	−	0.521525i
$231$	1.51677	−	4.66814i	0.0997962	−	0.307141i
$232$	−17.2533			−1.13274
$233$	2.12399	−	6.53697i	0.139147	−	0.428251i	−0.857065	−	0.515209i	$-0.827714\pi$
$233$	2.12399	−	6.53697i	0.139147	−	0.428251i	0.996212	+	0.0869574i	$0.0277144\pi$
$234$	−3.26147	+	2.36960i	−0.213209	+	0.154905i
$235$	−3.32023	+	23.9605i	−0.216588	+	1.56301i
$236$	−0.101636	−	0.0738426i	−0.00661591	−	0.00480674i
$237$	−5.62024	+	4.08335i	−0.365074	+	0.265242i
$238$	4.19522	−	3.04801i	0.271936	−	0.197573i
$239$	12.8408	+	9.32938i	0.830601	+	0.603467i	0.919729	−	0.392553i	$-0.128408\pi$
$239$	12.8408	+	9.32938i	0.830601	+	0.603467i	−0.0891279	+	0.996020i	$0.528408\pi$
$240$	−0.217146	−	0.406495i	−0.0140167	−	0.0262392i
$241$	2.37441	−	1.72511i	0.152949	−	0.111124i	−0.508679	−	0.860956i	$-0.669866\pi$
$241$	2.37441	−	1.72511i	0.152949	−	0.111124i	0.661628	+	0.749832i	$0.269866\pi$
$242$	−3.64226	+	11.2097i	−0.234133	+	0.720588i
$243$	1.00000			0.0641500
$244$	2.45973	−	7.57027i	0.157468	−	0.484637i
$245$	−2.01165	−	0.976343i	−0.128520	−	0.0623762i
$246$	2.29220	+	7.05467i	0.146145	+	0.449789i
$247$	0.724446	+	2.22962i	0.0460954	+	0.141867i
$248$	4.18258	+	3.03882i	0.265594	+	0.192965i
$249$	−12.9949			−0.823517
$250$	4.04061	−	9.21880i	0.255551	−	0.583048i
$251$	5.68994			0.359146			0.179573	−	0.983745i	$-0.442528\pi$
$251$	5.68994			0.359146			0.179573	+	0.983745i	$0.442528\pi$
$252$	0.962323	+	0.699169i	0.0606207	+	0.0440435i
$253$	−6.01627	−	18.5162i	−0.378239	−	1.16410i
$254$	−1.54548	−	4.75649i	−0.0969718	−	0.298449i
$255$	−11.5871	−	5.62370i	−0.725610	−	0.352170i
$256$	−5.08266	+	15.6428i	−0.317666	+	0.977676i
$257$	14.7882			0.922461			0.461231	−	0.887280i	$-0.347408\pi$
$257$	14.7882			0.922461			0.461231	+	0.887280i	$0.347408\pi$
$258$	0.520588	−	1.60221i	0.0324104	−	0.0997490i
$259$	−5.96767	+	4.33576i	−0.370813	+	0.269411i
$260$	5.61191	+	10.5055i	0.348036	+	0.651520i
$261$	4.86106	+	3.53176i	0.300892	+	0.218611i
$262$	−10.2633	+	7.45674i	−0.634070	+	0.460679i
$263$	−19.8631	+	14.4314i	−1.22481	+	0.889878i	−0.996490	−	0.0837077i	$-0.973324\pi$
$263$	−19.8631	+	14.4314i	−1.22481	+	0.889878i	−0.228322	+	0.973586i	$0.573324\pi$
$264$	−11.4024	−	8.28430i	−0.701767	−	0.509864i
$265$	4.05365	−	29.2533i	0.249014	−	1.79701i
$266$	−0.381312	+	0.277039i	−0.0233797	+	0.0169864i
$267$	−1.98831	+	6.11939i	−0.121683	+	0.374501i
$268$	−1.02013			−0.0623147
$269$	−3.95694	+	12.1782i	−0.241259	+	0.742518i	0.754971	+	0.655759i	$0.227651\pi$
$269$	−3.95694	+	12.1782i	−0.241259	+	0.742518i	−0.996229	+	0.0867594i	$0.972349\pi$
$270$	−0.276315	+	1.99403i	−0.0168160	+	0.121353i
$271$	−3.46391	−	10.6608i	−0.210417	−	0.647598i	−0.999447	−	0.0332434i	$-0.989416\pi$
$271$	−3.46391	−	10.6608i	−0.210417	−	0.647598i	0.789030	−	0.614355i	$-0.210584\pi$
$272$	−0.366847	−	1.12904i	−0.0222434	−	0.0684581i
$273$	3.62273	+	2.63207i	0.219258	+	0.159300i
$274$	−10.6141			−0.641219
$275$	−0.951276	−	24.5234i	−0.0573641	−	1.47882i
$276$	4.71813			0.283998
$277$	−17.0686	−	12.4010i	−1.02555	−	0.745107i	−0.0581378	−	0.998309i	$-0.518516\pi$
$277$	−17.0686	−	12.4010i	−1.02555	−	0.745107i	−0.967413	+	0.253202i	$0.918516\pi$
$278$	3.84701	+	11.8399i	0.230728	+	0.710109i
$279$	−0.556378	−	1.71235i	−0.0333095	−	0.102516i
$280$	−4.45128	+	4.62730i	−0.266015	+	0.276534i
$281$	5.87600	−	18.0845i	0.350533	−	1.07883i	−0.608022	−	0.793920i	$-0.708037\pi$
$281$	5.87600	−	18.0845i	0.350533	−	1.07883i	0.958555	−	0.284909i	$-0.0919633\pi$
$282$	9.73908			0.579954
$283$	7.68442	−	23.6502i	0.456791	−	1.40586i	−0.412228	−	0.911081i	$-0.635249\pi$
$283$	7.68442	−	23.6502i	0.456791	−	1.40586i	0.869019	−	0.494779i	$-0.164751\pi$
$284$	1.74808	−	1.27005i	0.103729	−	0.0753638i
$285$	1.05317	+	0.511149i	0.0623844	+	0.0302779i
$286$	−16.0085	−	11.6309i	−0.946604	−	0.687748i
$287$	6.66577	−	4.84297i	0.393468	−	0.285871i
$288$	4.49597	−	3.26651i	0.264928	−	0.192481i
$289$	−13.0876	−	9.50872i	−0.769861	−	0.559337i
$290$	−8.38564	+	8.71723i	−0.492421	+	0.511893i
$291$	7.27183	−	5.28329i	0.426282	−	0.309712i
$292$	3.47274	−	10.6880i	0.203227	−	0.625468i
$293$	9.89689			0.578183			0.289091	−	0.957302i	$-0.406647\pi$
$293$	9.89689			0.578183			0.289091	+	0.957302i	$0.406647\pi$
$294$	−0.278202	+	0.856217i	−0.0162250	+	0.0499356i
$295$	−0.232494	+	0.0414584i	−0.0135363	+	0.00241380i
$296$	6.54529	+	20.1443i	0.380437	+	1.17087i
$297$	1.51677	+	4.66814i	0.0880120	+	0.270873i
$298$	−4.64702	−	3.37625i	−0.269194	−	0.195581i
$299$	17.7617			1.02719
$300$	5.72338	+	1.61724i	0.330440	+	0.0933716i
$301$	−1.87126			−0.107858
$302$	8.76314	+	6.36680i	0.504262	+	0.366368i
$303$	−2.00453	−	6.16930i	−0.115157	−	0.354417i
$304$	0.0333435	+	0.102621i	0.00191238	+	0.00588570i
$305$	−7.05035	−	13.1982i	−0.403702	−	0.755727i
$306$	−1.60243	+	4.93178i	−0.0916049	+	0.281931i
$307$	−25.8689			−1.47642			−0.738208	−	0.674573i	$-0.764328\pi$
$307$	−25.8689			−1.47642			−0.738208	+	0.674573i	$0.764328\pi$
$308$	−1.80420	+	5.55274i	−0.102804	+	0.316397i
$309$	14.5037	−	10.5375i	0.825086	−	0.599460i
$310$	3.56823	−	0.636286i	0.202662	−	0.0361386i
$311$	12.7212	+	9.24247i	0.721351	+	0.524092i	0.886816	−	0.462123i	$-0.152912\pi$
$311$	12.7212	+	9.24247i	0.721351	+	0.524092i	−0.165464	+	0.986216i	$0.552912\pi$
$312$	10.4025	−	7.55782i	0.588923	−	0.427878i
$313$	−16.9110	+	12.2865i	−0.955864	+	0.694476i	−0.952186	−	0.305518i	$-0.901171\pi$
$313$	−16.9110	+	12.2865i	−0.955864	+	0.694476i	−0.00367737	+	0.999993i	$0.501171\pi$
$314$	10.5586	+	7.67124i	0.595854	+	0.432913i
$315$	2.20134	−	0.392543i	0.124032	−	0.0221173i
$316$	6.68526	−	4.85713i	0.376075	−	0.273235i
$317$	8.13825	−	25.0470i	0.457090	−	1.40678i	−0.411575	−	0.911376i	$-0.635021\pi$
$317$	8.13825	−	25.0470i	0.457090	−	1.40678i	0.868664	−	0.495401i	$-0.164979\pi$
$318$	−11.8904			−0.666781
$319$	−9.11367	+	28.0490i	−0.510267	+	1.57044i
$320$	5.70552	+	10.6807i	0.318948	+	0.597069i
$321$	−2.91520	−	8.97206i	−0.162711	−	0.500772i
$322$	1.10349	+	3.39618i	0.0614948	+	0.189262i
$323$	2.43962	+	1.77249i	0.135744	+	0.0986240i
$324$	−1.18950			−0.0660832
$325$	21.5461	+	6.08822i	1.19516	+	0.337714i
$326$	0.398690			0.0220814
$327$	8.09735	+	5.88307i	0.447785	+	0.325335i
$328$	−7.31097	−	22.5008i	−0.403681	−	1.24240i
$329$	−3.34290	−	10.2884i	−0.184300	−	0.567217i
$330$	−9.72753	+	1.73461i	−0.535483	+	0.0954873i
$331$	−8.48109	+	26.1021i	−0.466163	+	1.43470i	0.391351	+	0.920241i	$0.372008\pi$
$331$	−8.48109	+	26.1021i	−0.466163	+	1.43470i	−0.857514	+	0.514460i	$0.827992\pi$
$332$	15.4574			0.848333
$333$	2.27945	−	7.01541i	0.124913	−	0.384442i
$334$	10.9327	−	7.94304i	0.598209	−	0.434624i
$335$	−1.32947	+	1.38204i	−0.0726369	+	0.0755092i
$336$	0.166740	+	0.121144i	0.00909643	+	0.00660894i
$337$	−11.2890	+	8.20196i	−0.614952	+	0.446789i	−0.851155	−	0.524915i	$-0.824097\pi$
$337$	−11.2890	+	8.20196i	−0.614952	+	0.446789i	0.236202	+	0.971704i	$0.424097\pi$
$338$	5.13625	−	3.73170i	0.279375	−	0.202978i
$339$	14.8050	+	10.7565i	0.804099	+	0.584212i
$340$	13.7828	+	6.68937i	0.747476	+	0.362782i
$341$	7.14962	−	5.19450i	0.387173	−	0.281298i
$342$	0.145648	−	0.448259i	0.00787575	−	0.0242391i
$343$	1.00000			0.0539949
$344$	−1.66041	+	5.11023i	−0.0895235	+	0.275525i
$345$	6.14883	−	6.39197i	0.331042	−	0.344132i
$346$	6.07654	+	18.7017i	0.326677	+	1.00541i
$347$	6.80399	+	20.9405i	0.365257	+	1.12415i	0.949820	+	0.312797i	$0.101266\pi$
$347$	6.80399	+	20.9405i	0.365257	+	1.12415i	−0.584563	+	0.811348i	$0.698734\pi$
$348$	−5.78221	−	4.20102i	−0.309959	−	0.225199i
$349$	5.10144			0.273074			0.136537	−	0.990635i	$-0.456403\pi$
$349$	5.10144			0.273074			0.136537	+	0.990635i	$0.456403\pi$
$350$	0.174480	+	4.49801i	0.00932636	+	0.240429i
$351$	−4.47794			−0.239015
$352$	22.0679	+	16.0333i	1.17622	+	0.854577i
$353$	−6.94729	−	21.3816i	−0.369767	−	1.13803i	−0.946942	−	0.321405i	$-0.895845\pi$
$353$	−6.94729	−	21.3816i	−0.369767	−	1.13803i	0.577175	−	0.816621i	$-0.304155\pi$
$354$	0.0293822	+	0.0904291i	0.00156165	+	0.00480625i
$355$	0.557529	−	4.02342i	0.0295906	−	0.213541i
$356$	2.36509	−	7.27900i	0.125349	−	0.385786i
$357$	5.75997			0.304850
$358$	2.04068	−	6.28055i	0.107853	−	0.331938i
$359$	−24.5229	+	17.8169i	−1.29427	+	0.940342i	−0.999882	−	0.0153444i	$-0.995116\pi$
$359$	−24.5229	+	17.8169i	−1.29427	+	0.940342i	−0.294387	+	0.955686i	$0.595116\pi$
$360$	0.881306	−	6.35996i	0.0464489	−	0.335199i
$361$	15.1496	+	11.0068i	0.797346	+	0.579306i
$362$	12.1994	−	8.86335i	0.641184	−	0.465847i
$363$	−10.5918	+	7.69537i	−0.555924	+	0.403902i
$364$	−4.30923	−	3.13084i	−0.225865	−	0.164101i
$365$	−9.95396	−	18.6337i	−0.521014	−	0.975334i
$366$	−4.87390	+	3.54110i	−0.254763	+	0.185096i
$367$	−3.20360	+	9.85966i	−0.167226	+	0.514670i	−0.999193	−	0.0401549i	$-0.987215\pi$
$367$	−3.20360	+	9.85966i	−0.167226	+	0.514670i	0.831967	+	0.554825i	$0.187215\pi$
$368$	0.817504			0.0426153
$369$	−2.54610	+	7.83609i	−0.132545	+	0.407930i
$370$	13.3591	+	6.48375i	0.694507	+	0.337074i
$371$	4.08133	+	12.5610i	0.211892	+	0.652137i
$372$	0.661810	+	2.03684i	0.0343132	+	0.105605i
$373$	−27.7743	−	20.1792i	−1.43810	−	1.04484i	−0.988435	−	0.151645i	$-0.951543\pi$
$373$	−27.7743	−	20.1792i	−1.43810	−	1.04484i	−0.449666	−	0.893197i	$-0.648457\pi$
$374$	−25.4528			−1.31613
$375$	9.64989	−	5.64620i	0.498318	−	0.291569i
$376$	−31.0628			−1.60194
$377$	−21.7675	−	15.8150i	−1.12109	−	0.814516i
$378$	−0.278202	−	0.856217i	−0.0143091	−	0.0440390i
$379$	−4.91920	−	15.1398i	−0.252683	−	0.777677i	−0.994277	−	0.106829i	$-0.965930\pi$
$379$	−4.91920	−	15.1398i	−0.252683	−	0.777677i	0.741595	−	0.670848i	$-0.234070\pi$
$380$	−1.25274	−	0.608010i	−0.0642644	−	0.0311903i
$381$	1.71666	−	5.28335i	0.0879473	−	0.270674i
$382$	−3.76350			−0.192558
$383$	2.86252	−	8.80993i	0.146268	−	0.450166i	−0.850904	−	0.525321i	$-0.823945\pi$
$383$	2.86252	−	8.80993i	0.146268	−	0.450166i	0.997172	+	0.0751550i	$0.0239452\pi$
$384$	−5.04772	+	3.66738i	−0.257590	+	0.187150i
$385$	5.17138	+	9.68078i	0.263558	+	0.493378i
$386$	3.52528	+	2.56127i	0.179432	+	0.130365i
$387$	1.51388	−	1.09990i	0.0769550	−	0.0559111i
$388$	−8.64982	+	6.28446i	−0.439128	+	0.319045i
$389$	8.87361	+	6.44705i	0.449910	+	0.326879i	0.789560	−	0.613673i	$-0.210309\pi$
$389$	8.87361	+	6.44705i	0.449910	+	0.326879i	−0.339650	+	0.940552i	$0.610309\pi$
$390$	1.23732	−	8.92916i	0.0626543	−	0.452146i
$391$	18.4835	−	13.4291i	0.934751	−	0.679136i
$392$	0.887323	−	2.73090i	0.0448166	−	0.137931i
$393$	−14.0914			−0.710815
$394$	−2.95521	+	9.09520i	−0.148881	+	0.458210i
$395$	2.13218	−	15.3869i	0.107282	−	0.774201i
$396$	−1.80420	−	5.55274i	−0.0906642	−	0.279036i
$397$	−5.04294	−	15.5206i	−0.253098	−	0.778955i	−0.994199	−	0.107561i	$-0.965696\pi$
$397$	−5.04294	−	15.5206i	−0.253098	−	0.778955i	0.741101	−	0.671394i	$-0.234304\pi$
$398$	19.1591	+	13.9199i	0.960358	+	0.697741i
$399$	−0.523534			−0.0262095
$400$	0.991682	+	0.280217i	0.0495841	+	0.0140109i
$401$	10.3512			0.516914			0.258457	−	0.966023i	$-0.416786\pi$
$401$	10.3512			0.516914			0.258457	+	0.966023i	$0.416786\pi$
$402$	0.624639	+	0.453827i	0.0311542	+	0.0226348i
$403$	2.49143	+	7.66783i	0.124107	+	0.381962i
$404$	2.38438	+	7.33836i	0.118627	+	0.365097i
$405$	−1.55019	+	1.61149i	−0.0770297	+	0.0800756i
$406$	1.67160	−	5.14466i	0.0829602	−	0.255325i
$407$	36.2064			1.79468
$408$	5.11095	−	15.7299i	0.253030	−	0.778746i
$409$	−11.9100	+	8.65313i	−0.588912	+	0.427870i	−0.841926	−	0.539593i	$-0.818578\pi$
$409$	−11.9100	+	8.65313i	−0.588912	+	0.427870i	0.253014	+	0.967463i	$0.418578\pi$
$410$	−14.9219	−	7.24223i	−0.736939	−	0.357668i
$411$	−9.53811	−	6.92984i	−0.470480	−	0.341824i
$412$	−17.2521	+	12.5344i	−0.849949	+	0.617524i
$413$	0.0854442	−	0.0620788i	0.00420443	−	0.00305470i
$414$	−2.88896	−	2.09895i	−0.141985	−	0.103158i
$415$	20.1446	−	20.9411i	0.988857	−	1.02796i
$416$	−20.1327	+	14.6273i	−0.987087	+	0.717161i
$417$	−4.27313	+	13.1513i	−0.209256	+	0.644024i
$418$	2.31345			0.113155
$419$	−9.55937	+	29.4207i	−0.467006	+	1.43730i	0.389436	+	0.921053i	$0.372670\pi$
$419$	−9.55937	+	29.4207i	−0.467006	+	1.43730i	−0.856442	+	0.516243i	$0.827330\pi$
$420$	−2.61849	+	0.466929i	−0.127769	+	0.0227838i
$421$	−0.974432	−	2.99899i	−0.0474909	−	0.146162i	0.924499	−	0.381184i	$-0.124484\pi$
$421$	−0.974432	−	2.99899i	−0.0474909	−	0.146162i	−0.971990	+	0.235022i	$0.924484\pi$
$422$	4.74413	+	14.6009i	0.230940	+	0.710762i
$423$	8.75182	+	6.35857i	0.425528	+	0.309164i
$424$	37.9244			1.84177
$425$	27.0247	−	9.95463i	1.31089	−	0.482871i
$426$	−1.63538			−0.0792342
$427$	5.41377	+	3.93333i	0.261991	+	0.190347i
$428$	3.46762	+	10.6722i	0.167614	+	0.515862i
$429$	−6.79202	−	20.9037i	−0.327922	−	1.00924i
$430$	1.77493	+	3.32265i	0.0855946	+	0.160232i
$431$	6.24893	−	19.2322i	0.301000	−	0.926384i	−0.680139	−	0.733083i	$-0.738081\pi$
$431$	6.24893	−	19.2322i	0.301000	−	0.926384i	0.981140	−	0.193301i	$-0.0619193\pi$
$432$	−0.206102			−0.00991610
$433$	−0.710157	+	2.18564i	−0.0341280	+	0.105035i	−0.966669	−	0.256028i	$-0.917586\pi$
$433$	−0.710157	+	2.18564i	−0.0341280	+	0.105035i	0.932541	+	0.361063i	$0.117586\pi$
$434$	−1.31136	+	0.952759i	−0.0629473	+	0.0457339i
$435$	−13.2270	+	2.35863i	−0.634185	+	0.113088i
$436$	−9.63178	−	6.99790i	−0.461279	−	0.335139i
$437$	−1.68000	+	1.22059i	−0.0803654	+	0.0583889i
$438$	−6.88116	+	4.99946i	−0.328795	+	0.238883i
$439$	9.67925	+	7.03239i	0.461966	+	0.335638i	0.794302	−	0.607523i	$-0.207837\pi$
$439$	9.67925	+	7.03239i	0.461966	+	0.335638i	−0.332336	+	0.943161i	$0.607837\pi$
$440$	31.0259	−	5.53254i	1.47910	−	0.263754i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	7.17560	−	22.0842i	0.341308	−	1.05044i
$443$	−4.96084			−0.235697			−0.117848	−	0.993032i	$-0.537600\pi$
$443$	−4.96084			−0.235697			−0.117848	+	0.993032i	$0.537600\pi$
$444$	−2.71139	+	8.34481i	−0.128677	+	0.396027i
$445$	−6.77908	−	12.6904i	−0.321359	−	0.601582i
$446$	2.48842	+	7.65856i	0.117830	+	0.362643i
$447$	−1.97161	−	6.06800i	−0.0932541	−	0.287007i
$448$	−4.38111	−	3.18306i	−0.206988	−	0.150386i
$449$	−38.5972			−1.82151			−0.910757	−	0.412943i	$-0.864501\pi$
$449$	−38.5972			−1.82151			−0.910757	+	0.412943i	$0.864501\pi$
$450$	−2.78502	−	3.53641i	−0.131287	−	0.166708i
$451$	−40.4418			−1.90433
$452$	−17.6106	−	12.7948i	−0.828331	−	0.601817i
$453$	3.71798	+	11.4428i	0.174686	+	0.537628i
$454$	2.23800	+	6.88785i	0.105034	+	0.323263i
$455$	−9.85749	+	1.75779i	−0.462126	+	0.0824063i
$456$	−0.464544	+	1.42972i	−0.0217543	+	0.0669528i
$457$	−20.3072			−0.949933			−0.474966	−	0.880004i	$-0.657540\pi$
$457$	−20.3072			−0.949933			−0.474966	+	0.880004i	$0.657540\pi$
$458$	3.47475	−	10.6942i	0.162364	−	0.499706i
$459$	−4.65991	+	3.38562i	−0.217506	+	0.158027i
$460$	−7.31402	+	7.60323i	−0.341018	+	0.354502i
$461$	−9.54948	−	6.93810i	−0.444763	−	0.323140i	0.342761	−	0.939423i	$-0.388638\pi$
$461$	−9.54948	−	6.93810i	−0.444763	−	0.323140i	−0.787525	+	0.616283i	$0.788638\pi$
$462$	3.57497	−	2.59737i	0.166323	−	0.120841i
$463$	2.80714	−	2.03951i	0.130459	−	0.0947840i	−0.520642	−	0.853775i	$-0.674307\pi$
$463$	2.80714	−	2.03951i	0.130459	−	0.0947840i	0.651101	+	0.758991i	$0.274307\pi$
$464$	−1.00188	−	0.727905i	−0.0465109	−	0.0337921i
$465$	3.62194	+	1.75788i	0.167963	+	0.0815198i
$466$	5.00617	−	3.63719i	0.231906	−	0.168490i
$467$	−9.51845	+	29.2948i	−0.440461	+	1.35560i	0.446924	+	0.894572i	$0.352519\pi$
$467$	−9.51845	+	29.2948i	−0.440461	+	1.35560i	−0.887385	+	0.461028i	$0.847481\pi$
$468$	5.32650			0.246218
$469$	0.265019	−	0.815644i	0.0122374	−	0.0376629i
$470$	−15.0974	+	15.6944i	−0.696393	+	0.723930i
$471$	4.47973	+	13.7872i	0.206415	+	0.635280i
$472$	−0.0937145	−	0.288423i	−0.00431356	−	0.0132758i
$473$	7.43071	+	5.39872i	0.341664	+	0.248234i
$474$	−6.25424			−0.287267
$475$	−2.45633	+	0.904796i	−0.112704	+	0.0415149i
$476$	−6.85146			−0.314036
$477$	−10.6851	−	7.76315i	−0.489235	−	0.355450i
$478$	4.41564	+	13.5899i	0.201967	+	0.621590i
$479$	3.12584	+	9.62034i	0.142823	+	0.439565i	0.996725	−	0.0808701i	$-0.0257699\pi$
$479$	3.12584	+	9.62034i	0.142823	+	0.439565i	−0.853901	+	0.520435i	$0.825770\pi$
$480$	−1.70566	+	12.3089i	−0.0778525	+	0.561824i
$481$	−10.2072	+	31.4146i	−0.465410	+	1.43238i
$482$	2.64226			0.120351
$483$	−1.22571	+	3.77236i	−0.0557719	+	0.171648i
$484$	12.5989	−	9.15363i	0.572677	−	0.416074i
$485$	−2.75876	+	19.9086i	−0.125269	+	0.904004i
$486$	0.728341	+	0.529171i	0.0330382	+	0.0240037i
$487$	32.7766	−	23.8136i	1.48525	−	1.07910i	0.509431	−	0.860512i	$-0.329856\pi$
$487$	32.7766	−	23.8136i	1.48525	−	1.07910i	0.975818	−	0.218585i	$-0.0701440\pi$
$488$	15.5453	−	11.2943i	0.703703	−	0.511270i
$489$	0.358274	+	0.260301i	0.0162017	+	0.0117712i
$490$	−0.948519	−	1.77562i	−0.0428497	−	0.0802143i
$491$	−5.09012	+	3.69819i	−0.229714	+	0.166897i	−0.696688	−	0.717374i	$-0.745344\pi$
$491$	−5.09012	+	3.69819i	−0.229714	+	0.166897i	0.466974	+	0.884271i	$0.345344\pi$
$492$	3.02858	−	9.32100i	0.136539	−	0.420223i
$493$	−34.6093			−1.55873
$494$	−0.652204	+	2.00728i	−0.0293441	+	0.0903117i
$495$	−9.87396	−	4.79226i	−0.443801	−	0.215396i
$496$	0.114671	+	0.352920i	0.00514887	+	0.0158466i
$497$	0.561335	+	1.72761i	0.0251793	+	0.0774940i
$498$	−9.46470	−	6.87651i	−0.424124	−	0.308144i
$499$	−8.13309			−0.364087			−0.182044	−	0.983290i	$-0.558271\pi$
$499$	−8.13309			−0.364087			−0.182044	+	0.983290i	$0.558271\pi$
$500$	−11.4785	+	6.71614i	−0.513335	+	0.300355i
$501$	15.0104			0.670613
$502$	4.14422	+	3.01095i	0.184966	+	0.134385i
$503$	3.73260	+	11.4878i	0.166428	+	0.512214i	0.999139	−	0.0414948i	$-0.0132120\pi$
$503$	3.73260	+	11.4878i	0.166428	+	0.512214i	−0.832710	+	0.553709i	$0.813212\pi$
$504$	0.887323	+	2.73090i	0.0395245	+	0.121644i
$505$	13.0492	+	6.33332i	0.580680	+	0.281829i
$506$	5.41632	−	16.6697i	0.240785	−	0.741059i
$507$	7.05198			0.313189
$508$	−2.04197	+	6.28452i	−0.0905976	+	0.278831i
$509$	14.9352	−	10.8510i	0.661990	−	0.480964i	−0.205344	−	0.978690i	$-0.565831\pi$
$509$	14.9352	−	10.8510i	0.661990	−	0.480964i	0.867335	+	0.497726i	$0.165831\pi$
$510$	−5.46344	−	10.2275i	−0.241925	−	0.452882i
$511$	7.64336	+	5.55323i	0.338123	+	0.245660i
$512$	−1.88420	+	1.36895i	−0.0832706	+	0.0604997i
$513$	0.423548	−	0.307726i	0.0187001	−	0.0135864i
$514$	10.7708	+	7.82548i	0.475082	+	0.345167i
$515$	−5.50234	+	39.7078i	−0.242462	+	1.74973i
$516$	−1.80076	+	1.30833i	−0.0792740	+	0.0575959i
$517$	−16.4082	+	50.4992i	−0.721631	+	2.22095i
$518$	−6.64086			−0.291783
$519$	−6.74962	+	20.7732i	−0.296276	+	0.911842i
$520$	−3.94644	+	28.4795i	−0.173063	+	1.24891i
$521$	1.62591	+	5.00404i	0.0712324	+	0.219231i	0.980335	−	0.197342i	$-0.0632310\pi$
$521$	1.62591	+	5.00404i	0.0712324	+	0.219231i	−0.909102	+	0.416573i	$0.863231\pi$
$522$	1.67160	+	5.14466i	0.0731640	+	0.225176i
$523$	−19.2727	−	14.0024i	−0.842734	−	0.612282i	0.0803987	−	0.996763i	$-0.474381\pi$
$523$	−19.2727	−	14.0024i	−0.842734	−	0.612282i	−0.923133	+	0.384480i	$0.874381\pi$
$524$	16.7616			0.732236
$525$	−2.77992	+	4.15596i	−0.121326	+	0.181381i
$526$	−22.1038			−0.963772
$527$	8.39006	+	6.09573i	0.365477	+	0.265534i
$528$	−0.312610	−	0.962115i	−0.0136046	−	0.0418707i
$529$	−2.24560	−	6.91125i	−0.0976349	−	0.300489i
$530$	18.4324	−	19.1613i	0.800653	−	0.832313i
$531$	−0.0326368	+	0.100446i	−0.00141632	+	0.00435897i
$532$	0.622743			0.0269993
$533$	11.4013	−	35.0896i	0.493845	−	1.51990i
$534$	−4.68637	+	3.40485i	−0.202799	+	0.147342i
$535$	18.9775	+	9.21061i	0.820470	+	0.398209i
$536$	−1.99228	−	1.44748i	−0.0860536	−	0.0625216i
$537$	5.93433	−	4.31155i	0.256085	−	0.186057i
$538$	−9.32635	+	6.77599i	−0.402088	+	0.292134i
$539$	−3.97096	−	2.88507i	−0.171041	−	0.124269i
$540$	1.84395	−	1.91686i	0.0793510	−	0.0824887i
$541$	−22.0825	+	16.0439i	−0.949402	+	0.689781i	−0.950665	−	0.310218i	$-0.899598\pi$
$541$	−22.0825	+	16.0439i	−0.949402	+	0.689781i	0.00126356	+	0.999999i	$0.499598\pi$
$542$	3.11848	−	9.59771i	0.133950	−	0.412257i
$543$	16.7495			0.718790
$544$	−9.89164	+	30.4433i	−0.424100	+	1.30525i
$545$	−22.0330	+	3.92892i	−0.943789	+	0.168296i
$546$	1.24577	+	3.83409i	0.0533141	+	0.164084i
$547$	0.167234	+	0.514693i	0.00715041	+	0.0220067i	0.954568	−	0.297993i	$-0.0963172\pi$
$547$	0.167234	+	0.514693i	0.00715041	+	0.0220067i	−0.947418	+	0.320000i	$0.896317\pi$
$548$	11.3455	+	8.24302i	0.484658	+	0.352125i
$549$	−6.69178			−0.285598
$550$	12.2842	−	18.3648i	0.523802	−	0.783078i
$551$	3.14571			0.134012
$552$	9.21434	+	6.69461i	0.392188	+	0.284941i
$553$	2.14674	+	6.60699i	0.0912887	+	0.280958i
$554$	−5.86947	−	18.0644i	−0.249370	−	0.767482i
$555$	7.77170	+	14.5485i	0.329890	+	0.617552i
$556$	5.08288	−	15.6435i	0.215562	−	0.663432i
$557$	−16.0207			−0.678820			−0.339410	−	0.940638i	$-0.610227\pi$
$557$	−16.0207			−0.678820			−0.339410	+	0.940638i	$0.610227\pi$
$558$	0.500895	−	1.54160i	0.0212046	−	0.0652610i
$559$	−6.77908	+	4.92529i	−0.286725	+	0.208318i
$560$	−0.453702	+	0.0809041i	−0.0191724	+	0.00341882i
$561$	−22.8726	−	16.6179i	−0.965681	−	0.701609i
$562$	13.8495	−	10.0623i	0.584206	−	0.424451i
$563$	−12.8304	+	9.32185i	−0.540738	+	0.392869i	−0.824359	−	0.566067i	$-0.808464\pi$
$563$	−12.8304	+	9.32185i	−0.540738	+	0.392869i	0.283621	+	0.958936i	$0.408464\pi$
$564$	−10.4103	−	7.56350i	−0.438351	−	0.318481i
$565$	−40.2847	+	7.18356i	−1.69479	+	0.302215i
$566$	18.1119	−	13.1591i	0.761299	−	0.553116i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	5.21602			0.218860
$569$	2.92362	−	8.99799i	0.122565	−	0.377215i	−0.870885	−	0.491487i	$-0.836453\pi$
$569$	2.92362	−	8.99799i	0.122565	−	0.377215i	0.993450	+	0.114272i	$0.0364535\pi$
$570$	0.496583	+	0.929598i	0.0207996	+	0.0389366i
$571$	−6.15720	−	18.9499i	−0.257671	−	0.793030i	−0.993292	−	0.115636i	$-0.963109\pi$
$571$	−6.15720	−	18.9499i	−0.257671	−	0.793030i	0.735621	−	0.677394i	$-0.236891\pi$
$572$	8.07909	+	24.8649i	0.337804	+	1.03965i
$573$	−3.38199	−	2.45716i	−0.141285	−	0.102649i
$574$	7.41772			0.309609
$575$	0.768733	+	19.8176i	0.0320584	+	0.826450i
$576$	5.41535			0.225640
$577$	1.20594	+	0.876164i	0.0502038	+	0.0364752i	0.612604	−	0.790390i	$-0.290122\pi$
$577$	1.20594	+	0.876164i	0.0502038	+	0.0364752i	−0.562400	+	0.826865i	$0.690122\pi$
$578$	−4.50052	−	13.8512i	−0.187197	−	0.576133i
$579$	1.49569	+	4.60326i	0.0621587	+	0.191305i
$580$	15.7335	−	2.80559i	0.653296	−	0.116496i
$581$	−4.01564	+	12.3589i	−0.166597	+	0.512732i
$582$	8.09214			0.335430
$583$	20.0327	−	61.6543i	0.829670	−	2.55346i
$584$	21.9474	−	15.9458i	0.908192	−	0.659840i
$585$	6.94167	−	7.21617i	0.287003	−	0.298352i
$586$	7.20831	+	5.23715i	0.297773	+	0.216345i
$587$	−22.4014	+	16.2755i	−0.924603	+	0.671764i	−0.944666	−	0.328035i	$-0.893614\pi$
$587$	−22.4014	+	16.2755i	−0.924603	+	0.671764i	0.0200621	+	0.999799i	$0.493614\pi$
$588$	0.962323	−	0.699169i	0.0396855	−	0.0288332i
$589$	−0.762588	−	0.554053i	−0.0314219	−	0.0228294i
$590$	−0.191274	−	0.0928334i	−0.00787462	−	0.00382189i
$591$	−8.59383	+	6.24378i	−0.353503	+	0.256835i
$592$	−0.469799	+	1.44589i	−0.0193086	+	0.0594259i
$593$	−5.92027			−0.243116			−0.121558	−	0.992584i	$-0.538789\pi$
$593$	−5.92027			−0.243116			−0.121558	+	0.992584i	$0.538789\pi$
$594$	−1.36552	+	4.20263i	−0.0560279	+	0.172436i
$595$	−8.92905	+	9.28213i	−0.366056	+	0.380530i
$596$	2.34523	+	7.21787i	0.0960643	+	0.295655i
$597$	8.12872	+	25.0176i	0.332686	+	1.02390i
$598$	12.9366	+	9.39900i	0.529017	+	0.384354i
$599$	−26.0292			−1.06353			−0.531763	−	0.846893i	$-0.678470\pi$
$599$	−26.0292			−1.06353			−0.531763	+	0.846893i	$0.678470\pi$
$600$	8.88282	+	11.2794i	0.362640	+	0.460479i
$601$	−28.6804			−1.16990			−0.584949	−	0.811070i	$-0.698885\pi$
$601$	−28.6804			−1.16990			−0.584949	+	0.811070i	$0.698885\pi$
$602$	−1.36292	−	0.990217i	−0.0555484	−	0.0403583i
$603$	0.265019	+	0.815644i	0.0107924	+	0.0332156i
$604$	−4.42253	−	13.6111i	−0.179950	−	0.553830i
$605$	4.01826	−	28.9979i	0.163366	−	1.17893i
$606$	1.80463	−	5.55409i	0.0733082	−	0.225619i
$607$	32.8114			1.33177			0.665887	−	0.746053i	$-0.268053\pi$
$607$	32.8114			1.33177			0.665887	+	0.746053i	$0.268053\pi$
$608$	0.899070	−	2.76705i	0.0364621	−	0.112219i
$609$	4.86106	−	3.53176i	0.196980	−	0.143114i
$610$	1.84904	−	13.3436i	0.0748654	−	0.540268i
$611$	−39.1901	−	28.4733i	−1.58546	−	1.15191i
$612$	5.54295	−	4.02719i	0.224060	−	0.162789i
$613$	15.1852	−	11.0327i	0.613326	−	0.445607i	−0.237258	−	0.971447i	$-0.576249\pi$
$613$	15.1852	−	11.0327i	0.613326	−	0.445607i	0.850584	+	0.525839i	$0.176249\pi$
$614$	−18.8414	−	13.6891i	−0.760376	−	0.552446i
$615$	−8.68084	−	16.2505i	−0.350045	−	0.655282i
$616$	−11.4024	+	8.28430i	−0.459414	+	0.333784i
$617$	1.21458	−	3.73810i	0.0488973	−	0.150490i	−0.923627	−	0.383293i	$-0.874790\pi$
$617$	1.21458	−	3.73810i	0.0488973	−	0.150490i	0.972524	+	0.232803i	$0.0747898\pi$
$618$	16.1398			0.649238
$619$	−10.7073	+	32.9536i	−0.430362	+	1.32452i	0.467404	+	0.884044i	$0.345189\pi$
$619$	−10.7073	+	32.9536i	−0.430362	+	1.32452i	−0.897766	+	0.440474i	$0.854811\pi$
$620$	−4.30828	−	2.09099i	−0.173025	−	0.0839764i
$621$	−1.22571	−	3.77236i	−0.0491862	−	0.151380i
$622$	4.37451	+	13.4633i	0.175402	+	0.539831i
$623$	5.20546	+	3.78199i	0.208553	+	0.151522i
$624$	0.922915			0.0369462
$625$	−5.86038	+	24.3034i	−0.234415	+	0.972137i
$626$	−18.8186			−0.752143
$627$	2.07893	+	1.51043i	0.0830246	+	0.0603209i
$628$	−5.32863	−	16.3998i	−0.212635	−	0.654424i
$629$	13.1295	+	40.4085i	0.523509	+	1.61119i
$630$	1.81105	+	0.878981i	0.0721540	+	0.0350194i
$631$	−13.0583	+	40.1894i	−0.519844	+	1.59992i	0.254447	+	0.967087i	$0.418107\pi$
$631$	−13.0583	+	40.1894i	−0.519844	+	1.59992i	−0.774291	+	0.632830i	$0.781893\pi$
$632$	19.9479			0.793484
$633$	−5.26962	+	16.2182i	−0.209448	+	0.644616i
$634$	19.1815	−	13.9362i	0.761796	−	0.553477i
$635$	5.85291	+	10.9566i	0.232265	+	0.434799i
$636$	12.7099	+	9.23425i	0.503978	+	0.366162i
$637$	3.62273	−	2.63207i	0.143538	−	0.104286i
$638$	−21.4806	+	15.6065i	−0.850424	+	0.617869i
$639$	−1.46960	−	1.06772i	−0.0581363	−	0.0422385i
$640$	1.91498	−	13.8195i	0.0756963	−	0.546264i
$641$	−13.3184	+	9.67635i	−0.526043	+	0.382193i	−0.818876	−	0.573971i	$-0.805402\pi$
$641$	−13.3184	+	9.67635i	−0.526043	+	0.382193i	0.292832	+	0.956164i	$0.405402\pi$
$642$	2.62449	−	8.07736i	0.103581	−	0.318788i
$643$	−25.4629			−1.00416			−0.502079	−	0.864822i	$-0.667431\pi$
$643$	−25.4629			−1.00416			−0.502079	+	0.864822i	$0.667431\pi$
$644$	1.45798	−	4.48721i	0.0574526	−	0.176821i
$645$	−0.574330	+	4.14467i	−0.0226142	+	0.163196i
$646$	0.838928	+	2.58196i	0.0330072	+	0.101586i
$647$	−3.53263	−	10.8723i	−0.138882	−	0.427435i	0.857292	−	0.514831i	$-0.172145\pi$
$647$	−3.53263	−	10.8723i	−0.138882	−	0.427435i	−0.996174	+	0.0873961i	$0.972145\pi$
$648$	−2.32304	−	1.68779i	−0.0912577	−	0.0663026i
$649$	−0.518397			−0.0203489
$650$	12.4712	+	15.8359i	0.489160	+	0.621133i
$651$	−1.80048			−0.0705662
$652$	−0.426166	−	0.309628i	−0.0166899	−	0.0121260i
$653$	−10.8637	−	33.4350i	−0.425129	−	1.30841i	−0.902871	−	0.429913i	$-0.858544\pi$
$653$	−10.8637	−	33.4350i	−0.425129	−	1.30841i	0.477741	−	0.878501i	$-0.341456\pi$
$654$	2.78449	+	8.56977i	0.108882	+	0.335105i
$655$	21.8443	−	22.7081i	0.853529	−	0.887279i
$656$	0.524757	−	1.61504i	0.0204883	−	0.0630566i
$657$	−9.44772			−0.368591
$658$	3.00954	−	9.26241i	0.117324	−	0.361086i
$659$	−12.3509	+	8.97342i	−0.481121	+	0.349555i	−0.801760	−	0.597647i	$-0.796103\pi$
$659$	−12.3509	+	8.97342i	−0.481121	+	0.349555i	0.320638	+	0.947202i	$0.396103\pi$
$660$	11.7450	+	5.70037i	0.457175	+	0.221887i
$661$	11.7217	+	8.51630i	0.455920	+	0.331246i	0.791929	−	0.610613i	$-0.209077\pi$
$661$	11.7217	+	8.51630i	0.455920	+	0.331246i	−0.336008	+	0.941859i	$0.609077\pi$
$662$	−19.9896	+	14.5233i	−0.776918	+	0.564464i
$663$	20.8668	−	15.1606i	0.810400	−	0.588790i
$664$	30.1876	+	21.9326i	1.17151	+	0.851150i
$665$	0.811579	−	0.843671i	0.0314717	−	0.0327162i
$666$	5.37257	−	3.90340i	0.208183	−	0.151254i
$667$	7.36482	−	22.6666i	0.285167	−	0.877654i
$668$	−17.8548			−0.690822
$669$	−2.76405	+	8.50687i	−0.106864	+	0.328895i
$670$	−1.69965	+	0.303081i	−0.0656632	+	0.0117091i
$671$	−10.1499	−	31.2382i	−0.391833	−	1.20594i
$672$	−1.71731	−	5.28533i	−0.0662466	−	0.203886i
$673$	35.3145	+	25.6575i	1.36127	+	0.989024i	0.998363	+	0.0572002i	$0.0182173\pi$
$673$	35.3145	+	25.6575i	1.36127	+	0.989024i	0.362912	+	0.931824i	$0.381783\pi$
$674$	−12.5625			−0.483889
$675$	−0.193807	−	4.99624i	−0.00745962	−	0.192305i
$676$	−8.38831			−0.322627
$677$	15.7617	+	11.4515i	0.605770	+	0.440117i	0.847922	−	0.530121i	$-0.177853\pi$
$677$	15.7617	+	11.4515i	0.605770	+	0.440117i	−0.242153	+	0.970238i	$0.577853\pi$
$678$	5.09110	+	15.6688i	0.195522	+	0.601756i
$679$	−2.77759	−	8.54855i	−0.106594	−	0.328063i
$680$	17.4256	+	32.6206i	0.668242	+	1.25094i
$681$	−2.48589	+	7.65079i	−0.0952596	+	0.293179i
$682$	7.95614			0.304656
$683$	8.41075	−	25.8856i	0.321829	−	0.990486i	−0.651023	−	0.759058i	$-0.725660\pi$
$683$	8.41075	−	25.8856i	0.321829	−	0.990486i	0.972852	−	0.231429i	$-0.0743400\pi$
$684$	−0.503809	+	0.366039i	−0.0192636	+	0.0139959i
$685$	25.9533	−	4.62799i	0.991624	−	0.176826i
$686$	0.728341	+	0.529171i	0.0278082	+	0.0202038i
$687$	10.1047	−	7.34146i	0.385517	−	0.280094i
$688$	−0.312015	+	0.226692i	−0.0118955	+	0.00864255i
$689$	47.8471	+	34.7630i	1.82283	+	1.32436i
$690$	7.86089	−	1.40175i	0.299259	−	0.0533639i
$691$	3.64078	−	2.64518i	0.138502	−	0.100627i	−0.516377	−	0.856361i	$-0.672720\pi$
$691$	3.64078	−	2.64518i	0.138502	−	0.100627i	0.654879	+	0.755734i	$0.272720\pi$
$692$	8.02866	−	24.7097i	0.305204	−	0.939320i
$693$	4.90838			0.186454
$694$	−6.12549	+	18.8523i	−0.232520	+	0.715624i
$695$	−14.5691	−	27.2732i	−0.552637	−	1.03453i
$696$	−5.33157	−	16.4089i	−0.202093	−	0.621977i
$697$	−14.6654	−	45.1356i	−0.555493	−	1.70963i
$698$	3.71559	+	2.69953i	0.140637	+	0.102179i
$699$	6.87338			0.259975
$700$	3.30671	−	4.94350i	0.124982	−	0.186847i
$701$	31.3840			1.18536			0.592678	−	0.805439i	$-0.298071\pi$
$701$	31.3840			1.18536			0.592678	+	0.805439i	$0.298071\pi$
$702$	−3.26147	−	2.36960i	−0.123096	−	0.0894347i
$703$	−1.19337	−	3.67281i	−0.0450088	−	0.138523i
$704$	8.21385	+	25.2796i	0.309571	+	0.952762i
$705$	−23.8138	+	4.24647i	−0.896879	+	0.159931i
$706$	6.25450	−	19.2494i	0.235391	−	0.724460i
$707$	−6.48678			−0.243961
$708$	0.0388213	−	0.119480i	0.00145900	−	0.00449033i
$709$	12.8387	−	9.32784i	0.482166	−	0.350314i	−0.319997	−	0.947418i	$-0.603682\pi$
$709$	12.8387	−	9.32784i	0.482166	−	0.350314i	0.802164	+	0.597104i	$0.203682\pi$
$710$	2.53515	−	2.63539i	0.0951423	−	0.0989045i
$711$	−5.62024	−	4.08335i	−0.210776	−	0.153137i
$712$	14.9472	−	10.8598i	0.560169	−	0.406987i
$713$	−5.77766	+	4.19771i	−0.216375	+	0.157206i
$714$	4.19522	+	3.04801i	0.157002	+	0.114069i
$715$	44.2150	+	21.4595i	1.65355	+	0.802538i
$716$	−7.05887	+	5.12857i	−0.263803	+	0.191664i
$717$	−4.90474	+	15.0953i	−0.183171	+	0.563742i
$718$	−27.2892			−1.01843
$719$	8.43302	−	25.9542i	0.314499	−	0.967927i	−0.661462	−	0.749979i	$-0.730064\pi$
$719$	8.43302	−	25.9542i	0.314499	−	0.967927i	0.975960	−	0.217948i	$-0.0699364\pi$
$720$	0.319498	−	0.332132i	0.0119070	−	0.0123778i
$721$	−5.53991	−	17.0501i	−0.206317	−	0.634979i
$722$	5.20958	+	16.0334i	0.193880	+	0.596703i
$723$	2.37441	+	1.72511i	0.0883052	+	0.0641575i
$724$	−19.9235			−0.740451
$725$	16.7034	−	24.9715i	0.620350	−	0.927418i
$726$	−11.7866			−0.437442
$727$	−13.4470	−	9.76979i	−0.498720	−	0.362341i	0.309808	−	0.950799i	$-0.399735\pi$
$727$	−13.4470	−	9.76979i	−0.498720	−	0.362341i	−0.808528	+	0.588458i	$0.799735\pi$
$728$	−3.97338	−	12.2288i	−0.147263	−	0.453230i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	2.61055	−	18.8391i	0.0966206	−	0.697265i
$731$	−3.33071	+	10.2509i	−0.123191	+	0.379142i
$732$	7.95986			0.294205
$733$	6.10931	−	18.8025i	0.225652	−	0.694486i	−0.772572	−	0.634927i	$-0.781030\pi$
$733$	6.10931	−	18.8025i	0.225652	−	0.694486i	0.998225	−	0.0595598i	$-0.0189697\pi$
$734$	−7.55076	+	5.48595i	−0.278704	+	0.202490i
$735$	0.306921	−	2.21490i	0.0113210	−	0.0816980i
$736$	−17.8332	−	12.9566i	−0.657342	−	0.477587i
$737$	−3.40557	+	2.47429i	−0.125446	+	0.0911417i
$738$	−6.00106	+	4.36002i	−0.220902	+	0.160495i
$739$	23.6008	+	17.1470i	0.868168	+	0.630761i	0.930095	−	0.367320i	$-0.119725\pi$
$739$	23.6008	+	17.1470i	0.868168	+	0.630761i	−0.0619269	+	0.998081i	$0.519725\pi$
$740$	−9.24441	−	17.3055i	−0.339831	−	0.636161i
$741$	−1.89663	+	1.37798i	−0.0696743	+	0.0506213i
$742$	−3.67434	+	11.3084i	−0.134889	+	0.415146i
$743$	−34.6908			−1.27268			−0.636340	−	0.771409i	$-0.719552\pi$
$743$	−34.6908			−1.27268			−0.636340	+	0.771409i	$0.719552\pi$
$744$	−1.59760	+	4.91692i	−0.0585710	+	0.180263i
$745$	12.8349	+	6.22933i	0.470235	+	0.228225i
$746$	−9.55093	−	29.3948i	−0.349685	−	1.07622i
$747$	−4.01564	−	12.3589i	−0.146924	−	0.452187i
$748$	27.2069	+	19.7670i	0.994782	+	0.722751i
$749$	−9.43379			−0.344703
$750$	10.0162	+	0.994080i	0.365741	+	0.0362987i
$751$	14.4010			0.525500			0.262750	−	0.964864i	$-0.415371\pi$
$751$	14.4010			0.525500			0.262750	+	0.964864i	$0.415371\pi$
$752$	−1.80377	−	1.31052i	−0.0657767	−	0.0477896i
$753$	1.75829	+	5.41146i	0.0640756	+	0.197204i
$754$	−7.48534	−	23.0375i	−0.272600	−	0.838976i
$755$	−24.2035	−	11.7470i	−0.880856	−	0.427517i
$756$	−0.367575	+	1.13128i	−0.0133686	+	0.0411442i
$757$	21.2525			0.772435			0.386218	−	0.922408i	$-0.373781\pi$
$757$	21.2525			0.772435			0.386218	+	0.922408i	$0.373781\pi$
$758$	4.42866	−	13.6300i	0.160856	−	0.495064i
$759$	15.7508	−	11.4436i	0.571717	−	0.415377i
$760$	−1.58385	−	2.96495i	−0.0574522	−	0.107550i
$761$	25.2452	+	18.3417i	0.915137	+	0.664886i	0.942309	−	0.334745i	$-0.108650\pi$
$761$	25.2452	+	18.3417i	0.915137	+	0.664886i	−0.0271715	+	0.999631i	$0.508650\pi$
$762$	4.04611	−	2.93967i	0.146575	−	0.106493i
$763$	8.09735	−	5.88307i	0.293144	−	0.212982i
$764$	4.02287	+	2.92279i	0.145542	+	0.105743i
$765$	1.76786	−	12.7578i	0.0639170	−	0.461258i
$766$	6.74685	−	4.90187i	0.243774	−	0.177112i
$767$	0.146146	−	0.449790i	0.00527701	−	0.0162410i
$768$	−16.4478			−0.593510
$769$	−1.20881	+	3.72033i	−0.0435908	+	0.134159i	−0.970483	−	0.241168i	$-0.922469\pi$
$769$	−1.20881	+	3.72033i	−0.0435908	+	0.134159i	0.926893	+	0.375327i	$0.122469\pi$
$770$	−1.35626	+	9.78746i	−0.0488761	+	0.352716i
$771$	4.56980	+	14.0644i	0.164577	+	0.506517i
$772$	−1.77912	−	5.47556i	−0.0640319	−	0.197070i
$773$	−15.8120	−	11.4881i	−0.568716	−	0.413197i	0.265922	−	0.963994i	$-0.414324\pi$
$773$	−15.8120	−	11.4881i	−0.568716	−	0.413197i	−0.834639	+	0.550798i	$0.814324\pi$
$774$	1.68466			0.0605538
$775$	−8.44751	+	3.11166i	−0.303443	+	0.111774i
$776$	−25.8099			−0.926520
$777$	−5.96767	−	4.33576i	−0.214089	−	0.155545i
$778$	3.05142	+	9.39131i	0.109399	+	0.336695i
$779$	1.33297	+	4.10246i	0.0477586	+	0.146986i
$780$	−8.25710	+	8.58361i	−0.295652	+	0.307343i
$781$	2.75525	−	8.47977i	0.0985904	−	0.303430i
$782$	20.5686			0.735530
$783$	−1.85676	+	5.71452i	−0.0663551	+	0.204220i
$784$	0.166740	−	0.121144i	0.00595501	−	0.00432657i
$785$	−29.1624	−	14.1538i	−1.04085	−	0.505169i
$786$	−10.2633	−	7.45674i	−0.366081	−	0.265973i
$787$	−11.1517	+	8.10215i	−0.397514	+	0.288811i	−0.768527	−	0.639817i	$-0.779010\pi$
$787$	−11.1517	+	8.10215i	−0.397514	+	0.288811i	0.371014	+	0.928627i	$0.379010\pi$
$788$	10.2223	−	7.42696i	0.364155	−	0.264574i
$789$	−19.8631	−	14.4314i	−0.707146	−	0.513771i
$790$	9.69528	−	10.0787i	0.344943	−	0.358582i
$791$	14.8050	−	10.7565i	0.526407	−	0.382457i
$792$	4.35532	−	13.4043i	0.154759	−	0.476300i
$793$	29.9654			1.06410
$794$	4.54005	−	13.9728i	0.161120	−	0.495877i
$795$	29.0742	−	5.18450i	1.03115	−	0.183875i
$796$	−9.66909	−	29.7584i	−0.342712	−	1.05476i
$797$	12.1509	+	37.3965i	0.430405	+	1.32465i	0.897723	+	0.440561i	$0.145221\pi$
$797$	12.1509	+	37.3965i	0.430405	+	1.32465i	−0.467317	+	0.884090i	$0.654779\pi$
$798$	−0.381312	−	0.277039i	−0.0134983	−	0.00980708i
$799$	−62.3104			−2.20438
$800$	−17.1916	−	21.8299i	−0.607817	−	0.771803i
$801$	−6.43431			−0.227345
$802$	7.53920	+	5.47755i	0.266219	+	0.193419i
$803$	−14.3300	−	44.1033i	−0.505696	−	1.55637i
$804$	−0.315239	−	0.970206i	−0.0111176	−	0.0342165i
$805$	−4.17903	−	7.82311i	−0.147292	−	0.275728i
$806$	−2.24298	+	6.90319i	−0.0790056	+	0.243154i
$807$	−12.8049			−0.450754
$808$	−5.75587	+	17.7148i	−0.202491	+	0.623203i
$809$	40.8970	−	29.7134i	1.43786	−	1.04467i	0.449378	−	0.893342i	$-0.351646\pi$
$809$	40.8970	−	29.7134i	1.43786	−	1.04467i	0.988484	−	0.151326i	$-0.0483542\pi$
$810$	−1.98182	+	0.353399i	−0.0696342	+	0.0124172i
$811$	6.45492	+	4.68977i	0.226663	+	0.164680i	0.695321	−	0.718700i	$-0.255262\pi$
$811$	6.45492	+	4.68977i	0.226663	+	0.164680i	−0.468658	+	0.883380i	$0.655262\pi$
$812$	−5.78221	+	4.20102i	−0.202916	+	0.147427i
$813$	9.06863	−	6.58874i	0.318051	−	0.231077i
$814$	26.3706	+	19.1593i	0.924288	+	0.671535i
$815$	−0.974867	+	0.173838i	−0.0341481	+	0.00608929i
$816$	0.960418	−	0.697785i	0.0336214	−	0.0244274i
$817$	0.302735	−	0.931722i	0.0105913	−	0.0325968i
$818$	−13.2535			−0.463399
$819$	−1.38376	+	4.25878i	−0.0483525	+	0.148814i
$820$	10.3258	+	19.3299i	0.360594	+	0.675028i
$821$	−9.30485	−	28.6374i	−0.324742	−	0.999452i	−0.971557	−	0.236805i	$-0.923900\pi$
$821$	−9.30485	−	28.6374i	−0.324742	−	0.999452i	0.646815	−	0.762647i	$-0.276100\pi$
$822$	−3.27993	−	10.0946i	−0.114401	−	0.352089i
$823$	12.4839	+	9.07006i	0.435160	+	0.316162i	0.783709	−	0.621128i	$-0.213325\pi$
$823$	12.4839	+	9.07006i	0.435160	+	0.316162i	−0.348549	+	0.937291i	$0.613325\pi$
$824$	−51.4778			−1.79331
$825$	23.0292	−	8.48288i	0.801774	−	0.295336i
$826$	0.0950828			0.00330835
$827$	−20.8038	−	15.1148i	−0.723418	−	0.525594i	0.164056	−	0.986451i	$-0.447542\pi$
$827$	−20.8038	−	15.1148i	−0.723418	−	0.525594i	−0.887474	+	0.460857i	$0.847542\pi$
$828$	1.45798	+	4.48721i	0.0506684	+	0.155941i
$829$	−6.48670	−	19.9640i	−0.225292	−	0.693378i	−0.998262	−	0.0589351i	$-0.981229\pi$
$829$	−6.48670	−	19.9640i	−0.225292	−	0.693378i	0.772970	−	0.634443i	$-0.218771\pi$
$830$	25.7535	−	4.59237i	0.893919	−	0.159404i
$831$	6.51962	−	20.0653i	0.226163	−	0.696058i
$832$	−24.2496			−0.840705
$833$	1.77993	−	5.47805i	0.0616708	−	0.189803i
$834$	−10.0716	+	7.31745i	−0.348751	+	0.253383i
$835$	−23.2689	+	24.1891i	−0.805255	+	0.837097i
$836$	−2.47289	−	1.79666i	−0.0855266	−	0.0621387i
$837$	1.45662	−	1.05829i	0.0503480	−	0.0365800i
$838$	−22.5311	+	16.3698i	−0.778323	+	0.565485i
$839$	39.1943	+	28.4763i	1.35314	+	0.983113i	0.998848	+	0.0479770i	$0.0152774\pi$
$839$	39.1943	+	28.4763i	1.35314	+	0.983113i	0.354290	+	0.935136i	$0.384723\pi$
$840$	−5.77634	−	2.80351i	−0.199303	−	0.0967302i
$841$	−5.74664	+	4.17518i	−0.198160	+	0.143972i
$842$	0.877261	−	2.69993i	0.0302324	−	0.0930458i
$843$	19.0151			0.654916
$844$	6.26819	−	19.2915i	0.215760	−	0.664041i
$845$	−10.9319	+	11.3642i	−0.376070	+	0.390940i
$846$	3.00954	+	9.26241i	0.103470	+	0.318448i
$847$	4.04570	+	12.4514i	0.139012	+	0.427834i
$848$	2.20222	+	1.60000i	0.0756244	+	0.0549444i
$849$	24.8673			0.853444
$850$	24.9509	+	7.05033i	0.855809	+	0.241824i
$851$	−29.2586			−1.00297
$852$	1.74808	+	1.27005i	0.0598882	+	0.0435113i
$853$	5.84062	+	17.9756i	0.199979	+	0.615472i	0.999882	+	0.0153431i	$0.00488404\pi$
$853$	5.84062	+	17.9756i	0.199979	+	0.615472i	−0.799903	+	0.600129i	$0.795116\pi$
$854$	1.86167	+	5.72962i	0.0637049	+	0.196063i
$855$	−0.160684	+	1.15958i	−0.00549527	+	0.0396568i
$856$	−8.37082	+	25.7627i	−0.286109	+	0.880552i
$857$	−31.8586			−1.08827			−0.544134	−	0.838998i	$-0.683142\pi$
$857$	−31.8586			−1.08827			−0.544134	+	0.838998i	$0.683142\pi$
$858$	6.11471	−	18.8192i	0.208753	−	0.642475i
$859$	6.05658	−	4.40036i	0.206648	−	0.150138i	−0.479648	−	0.877461i	$-0.659236\pi$
$859$	6.05658	−	4.40036i	0.206648	−	0.150138i	0.686296	+	0.727323i	$0.259236\pi$
$860$	0.683164	−	4.93007i	0.0232957	−	0.168114i
$861$	6.66577	+	4.84297i	0.227169	+	0.165048i
$862$	14.7285	−	10.7009i	0.501654	−	0.364473i
$863$	−36.8193	+	26.7508i	−1.25334	+	0.910608i	−0.998411	−	0.0563506i	$-0.982054\pi$
$863$	−36.8193	+	26.7508i	−1.25334	+	0.910608i	−0.254933	+	0.966959i	$0.582054\pi$
$864$	4.49597	+	3.26651i	0.152956	+	0.111129i
$865$	−23.0126	−	43.0794i	−0.782452	−	1.46474i
$866$	−1.67381	+	1.21610i	−0.0568785	+	0.0413246i
$867$	4.99903	−	15.3854i	0.169776	−	0.522517i
$868$	2.14166			0.0726927
$869$	10.5370	−	32.4296i	0.357444	−	1.10010i
$870$	−10.8819	−	5.28144i	−0.368930	−	0.179058i
$871$	−1.18674	−	3.65241i	−0.0402111	−	0.123757i
$872$	−8.88111	−	27.3333i	−0.300752	−	0.925621i
$873$	7.27183	+	5.28329i	0.246114	+	0.178812i
$874$	−1.86952			−0.0632374
$875$	−2.38788	−	10.9224i	−0.0807250	−	0.369243i
$876$	11.2380			0.379698
$877$	28.7294	+	20.8731i	0.970124	+	0.704836i	0.955480	−	0.295057i	$-0.0953385\pi$
$877$	28.7294	+	20.8731i	0.970124	+	0.704836i	0.0146439	+	0.999893i	$0.495339\pi$
$878$	3.32846	+	10.2440i	0.112330	+	0.345717i
$879$	3.05831	+	9.41250i	0.103154	+	0.317476i
$880$	2.03505	+	0.987695i	0.0686014	+	0.0332952i
$881$	−4.07364	+	12.5374i	−0.137244	+	0.422395i	−0.995932	−	0.0901038i	$-0.971280\pi$
$881$	−4.07364	+	12.5374i	−0.137244	+	0.422395i	0.858688	+	0.512499i	$0.171280\pi$
$882$	−0.900279			−0.0303140
$883$	16.3845	−	50.4264i	0.551383	−	1.69698i	−0.153925	−	0.988082i	$-0.549192\pi$
$883$	16.3845	−	50.4264i	0.551383	−	1.69698i	0.705309	−	0.708900i	$-0.250808\pi$
$884$	−24.8210	+	18.0335i	−0.834821	+	0.606533i
$885$	−0.111274	−	0.208304i	−0.00374043	−	0.00700206i
$886$	−3.61319	−	2.62513i	−0.121387	−	0.0881931i
$887$	10.7809	−	7.83280i	0.361988	−	0.263000i	−0.391893	−	0.920011i	$-0.628180\pi$
$887$	10.7809	−	7.83280i	0.361988	−	0.263000i	0.753881	+	0.657011i	$0.228180\pi$
$888$	−17.1358	+	12.4499i	−0.575039	+	0.417791i
$889$	−4.49428	−	3.26529i	−0.150733	−	0.109514i
$890$	1.77790	−	12.8302i	0.0595952	−	0.430070i
$891$	−3.97096	+	2.88507i	−0.133032	+	0.0966535i
$892$	3.28783	−	10.1189i	0.110085	−	0.338806i
$893$	5.66351			0.189522
$894$	1.77500	−	5.46289i	0.0593649	−	0.182707i
$895$	−2.25134	+	16.2469i	−0.0752541	+	0.543072i
$896$	1.92806	+	5.93395i	0.0644119	+	0.198239i
$897$	5.48868	+	16.8924i	0.183262	+	0.564021i
$898$	−28.1119	−	20.4245i	−0.938107	−	0.681575i
$899$	10.8183			0.360812
$900$	0.230533	+	5.94302i	0.00768442	+	0.198101i
$901$	76.0745			2.53441
$902$	−29.4554	−	21.4006i	−0.980759	−	0.712563i
$903$	−0.578252	−	1.77968i	−0.0192430	−	0.0592239i
$904$	−16.2380	−	49.9756i	−0.540069	−	1.66216i
$905$	−25.9650	+	26.9917i	−0.863104	+	0.897234i
$906$	−3.34722	+	10.3017i	−0.111204	+	0.342251i
$907$	7.41957			0.246363			0.123181	−	0.992384i	$-0.460690\pi$
$907$	7.41957			0.246363			0.123181	+	0.992384i	$0.460690\pi$
$908$	2.95696	−	9.10060i	0.0981302	−	0.302014i
$909$	5.24792	−	3.81283i	0.174062	−	0.126464i
$910$	−8.10979	−	3.93603i	−0.268837	−	0.130478i
$911$	43.8272	+	31.8423i	1.45206	+	1.05498i	0.985345	+	0.170574i	$0.0545622\pi$
$911$	43.8272	+	31.8423i	1.45206	+	1.05498i	0.466714	+	0.884408i	$0.345438\pi$
$912$	−0.0872943	+	0.0634230i	−0.00289060	+	0.00210015i
$913$	51.6021	−	37.4911i	1.70778	−	1.24078i
$914$	−14.7906	−	10.7460i	−0.489230	−	0.355446i
$915$	10.3736	−	10.7838i	0.342939	−	0.356500i
$916$	−12.0195	+	8.73264i	−0.397134	+	0.288535i
$917$	−4.35447	+	13.4017i	−0.143797	+	0.442563i
$918$	−5.18558			−0.171150
$919$	16.6231	−	51.1605i	0.548344	−	1.68763i	−0.164560	−	0.986367i	$-0.552620\pi$
$919$	16.6231	−	51.1605i	0.548344	−	1.68763i	0.712904	−	0.701262i	$-0.247380\pi$
$920$	−25.0723	+	4.47089i	−0.826609	+	0.147401i
$921$	−7.99393	−	24.6028i	−0.263409	−	0.810689i
$922$	−3.28384	−	10.1066i	−0.108147	−	0.332843i
$923$	6.58076	+	4.78121i	0.216609	+	0.157375i
$924$	−5.83850			−0.192073
$925$	−35.4925	−	10.0290i	−1.16699	−	0.329753i
$926$	3.12381			0.102655
$927$	14.5037	+	10.5375i	0.476363	+	0.346098i
$928$	10.3186	+	31.7574i	0.338725	+	1.04249i
$929$	7.38370	+	22.7247i	0.242251	+	0.745573i	0.996076	+	0.0884979i	$0.0282067\pi$
$929$	7.38370	+	22.7247i	0.242251	+	0.745573i	−0.753825	+	0.657075i	$0.771793\pi$
$930$	1.70779	+	3.19696i	0.0560005	+	0.104832i
$931$	−0.161781	+	0.497911i	−0.00530216	+	0.0163184i
$932$	−8.17587			−0.267809
$933$	−4.85905	+	14.9546i	−0.159078	+	0.489593i
$934$	−22.4346	+	16.2997i	−0.734083	+	0.533343i
$935$	62.2365	−	11.0980i	2.03535	−	0.362944i
$936$	10.4025	+	7.55782i	0.340015	+	0.247035i
$937$	−13.1425	+	9.54858i	−0.429347	+	0.311939i	−0.781388	−	0.624046i	$-0.785488\pi$
$937$	−13.1425	+	9.54858i	−0.429347	+	0.311939i	0.352041	+	0.935985i	$0.385488\pi$
$938$	0.624639	−	0.453827i	0.0203952	−	0.0148180i
$939$	−16.9110	−	12.2865i	−0.551868	−	0.400956i
$940$	28.3264	−	5.05117i	0.923906	−	0.164751i
$941$	−27.3543	+	19.8741i	−0.891725	+	0.647876i	−0.936327	−	0.351129i	$-0.885798\pi$
$941$	−27.3543	+	19.8741i	−0.891725	+	0.647876i	0.0446026	+	0.999005i	$0.485798\pi$
$942$	−4.03301	+	12.4123i	−0.131403	+	0.404415i
$943$	32.6813			1.06425
$944$	0.00672651	−	0.0207021i	0.000218929	−	0.000673795i
$945$	1.05358	+	1.97230i	0.0342731	+	0.0641589i
$946$	2.55524	+	7.86423i	0.0830781	+	0.255688i
$947$	5.37948	+	16.5563i	0.174810	+	0.538009i	0.999625	−	0.0273939i	$-0.00872084\pi$
$947$	5.37948	+	16.5563i	0.174810	+	0.538009i	−0.824815	+	0.565403i	$0.808721\pi$
$948$	6.68526	+	4.85713i	0.217127	+	0.157752i
$949$	42.3063			1.37332
$950$	−2.26784	−	0.640818i	−0.0735784	−	0.0207909i
$951$	26.3359			0.854001
$952$	−13.3806	−	9.72161i	−0.433669	−	0.315079i
$953$	12.7961	+	39.3824i	0.414507	+	1.27572i	0.912692	+	0.408649i	$0.134000\pi$
$953$	12.7961	+	39.3824i	0.414507	+	1.27572i	−0.498185	+	0.867071i	$0.666000\pi$
$954$	−3.67434	−	11.3084i	−0.118961	−	0.366125i
$955$	9.20243	−	1.64098i	0.297784	−	0.0531008i
$956$	5.83418	−	17.9558i	0.188691	−	0.580731i
$957$	−29.4925			−0.953356
$958$	−2.81413	+	8.66100i	−0.0909204	+	0.279824i
$959$	−9.53811	+	6.92984i	−0.308001	+	0.223776i
$960$	−8.39484	+	8.72679i	−0.270942	+	0.281656i
$961$	22.4569	+	16.3159i	0.724417	+	0.526320i
$962$	−24.0581	+	17.4792i	−0.775663	+	0.563552i
$963$	7.63209	−	5.54504i	0.245941	−	0.178686i
$964$	−2.82435	−	2.05201i	−0.0909662	−	0.0660908i
$965$	−9.73672	−	4.72565i	−0.313436	−	0.152124i
$966$	−2.88896	+	2.09895i	−0.0929508	+	0.0675327i
$967$	−15.6444	+	48.1487i	−0.503092	+	1.54836i	0.300864	+	0.953667i	$0.402725\pi$
$967$	−15.6444	+	48.1487i	−0.503092	+	1.54836i	−0.803955	+	0.594690i	$0.797275\pi$
$968$	37.5933			1.20829
$969$	−0.931853	+	2.86795i	−0.0299354	+	0.0921318i
$970$	−12.5444	+	13.0404i	−0.402776	+	0.418702i
$971$	2.69747	+	8.30195i	0.0865659	+	0.266422i	0.984964	−	0.172760i	$-0.0552684\pi$
$971$	2.69747	+	8.30195i	0.0865659	+	0.266422i	−0.898398	+	0.439182i	$0.855268\pi$
$972$	−0.367575	−	1.13128i	−0.0117900	−	0.0362858i
$973$	11.1872	+	8.12798i	0.358645	+	0.260571i
$974$	36.4740			1.16870
$975$	0.867856	+	22.3729i	0.0277936	+	0.716506i
$976$	1.37919			0.0441469
$977$	−17.1627	−	12.4695i	−0.549085	−	0.398933i	0.278363	−	0.960476i	$-0.410208\pi$
$977$	−17.1627	−	12.4695i	−0.549085	−	0.398933i	−0.827448	+	0.561543i	$0.810208\pi$
$978$	0.123202	+	0.379176i	0.00393956	+	0.0121247i
$979$	−9.75937	−	30.0363i	−0.311911	−	0.959963i
$980$	−0.365082	+	2.63462i	−0.0116621	+	0.0841599i
$981$	−3.09291	+	9.51901i	−0.0987492	+	0.303919i
$982$	−5.66432			−0.180756
$983$	−4.57450	+	14.0789i	−0.145904	+	0.449046i	−0.997126	−	0.0757595i	$-0.975862\pi$
$983$	−4.57450	+	14.0789i	−0.145904	+	0.449046i	0.851222	+	0.524805i	$0.175862\pi$
$984$	19.1404	−	13.9063i	0.610172	−	0.443316i
$985$	3.26029	−	23.5279i	0.103881	−	0.749662i
$986$	−25.2074	−	18.3142i	−0.802767	−	0.583244i
$987$	8.75182	−	6.35857i	0.278573	−	0.202395i
$988$	2.25603	−	1.63910i	0.0717739	−	0.0521468i
$989$	−6.00481	−	4.36275i	−0.190942	−	0.138727i
$990$	−4.65569	−	8.71541i	−0.147967	−	0.276994i
$991$	−17.0716	+	12.4033i	−0.542299	+	0.394003i	−0.824938	−	0.565223i	$-0.808790\pi$
$991$	−17.0716	+	12.4033i	−0.542299	+	0.394003i	0.282639	+	0.959226i	$0.408790\pi$
$992$	3.09197	−	9.51611i	0.0981702	−	0.302137i
$993$	−27.4454			−0.870953
$994$	−0.505359	+	1.55533i	−0.0160290	+	0.0493322i
$995$	−52.9168	−	25.6828i	−1.67757	−	0.814199i
$996$	4.77659	+	14.7008i	0.151352	+	0.465814i
$997$	−7.82252	−	24.0752i	−0.247742	−	0.762470i	−0.995173	−	0.0981317i	$-0.968713\pi$
$997$	−7.82252	−	24.0752i	−0.247742	−	0.762470i	0.747432	−	0.664338i	$-0.231287\pi$
$998$	−5.92367	−	4.30380i	−0.187510	−	0.136234i
$999$	7.37644			0.233380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.316.4	yes	24
25.11	even	5	inner	525.2.n.c.211.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.211.4	✓	24	25.11	even	5	inner
525.2.n.c.316.4	yes	24	1.1	even	1	trivial

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.728341 + 0.529171i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.367575 - 1.13128i) q^{4} +(-2.01165 - 0.976343i) q^{5} +(-0.278202 + 0.856217i) q^{6} +1.00000 q^{7} +(0.887323 - 2.73090i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.728341 + 0.529171i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.367575 - 1.13128i) q^{4} +(-2.01165 - 0.976343i) q^{5} +(-0.278202 + 0.856217i) q^{6} +1.00000 q^{7} +(0.887323 - 2.73090i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.948519 - 1.77562i) q^{10} +(-3.97096 - 2.88507i) q^{11} +(0.962323 - 0.699169i) q^{12} +(3.62273 - 2.63207i) q^{13} +(0.728341 + 0.529171i) q^{14} +(0.306921 - 2.21490i) q^{15} +(0.166740 - 0.121144i) q^{16} +(1.77993 - 5.47805i) q^{17} -0.900279 q^{18} +(-0.161781 + 0.497911i) q^{19} +(-0.365082 + 2.63462i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-1.36552 - 4.20263i) q^{22} +(3.20896 + 2.33145i) q^{23} +2.87144 q^{24} +(3.09351 + 3.92813i) q^{25} +4.03140 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.367575 - 1.13128i) q^{28} +(-1.85676 - 5.71452i) q^{29} +(1.39561 - 1.45079i) q^{30} +(-0.556378 + 1.71235i) q^{31} -5.55733 q^{32} +(1.51677 - 4.66814i) q^{33} +(4.19522 - 3.04801i) q^{34} +(-2.01165 - 0.976343i) q^{35} +(0.962323 + 0.699169i) q^{36} +(-5.96767 + 4.33576i) q^{37} +(-0.381312 + 0.277039i) q^{38} +(3.62273 + 2.63207i) q^{39} +(-4.45128 + 4.62730i) q^{40} +(6.66577 - 4.84297i) q^{41} +(-0.278202 + 0.856217i) q^{42} -1.87126 q^{43} +(-1.80420 + 5.55274i) q^{44} +(2.20134 - 0.392543i) q^{45} +(1.10349 + 3.39618i) q^{46} +(-3.34290 - 10.2884i) q^{47} +(0.166740 + 0.121144i) q^{48} +1.00000 q^{49} +(0.174480 + 4.49801i) q^{50} +5.75997 q^{51} +(-4.30923 - 3.13084i) q^{52} +(4.08133 + 12.5610i) q^{53} +(-0.278202 - 0.856217i) q^{54} +(5.17138 + 9.68078i) q^{55} +(0.887323 - 2.73090i) q^{56} -0.523534 q^{57} +(1.67160 - 5.14466i) q^{58} +(0.0854442 - 0.0620788i) q^{59} +(-2.61849 + 0.466929i) q^{60} +(5.41377 + 3.93333i) q^{61} +(-1.31136 + 0.952759i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-4.38111 - 3.18306i) q^{64} +(-9.85749 + 1.75779i) q^{65} +(3.57497 - 2.59737i) q^{66} +(0.265019 - 0.815644i) q^{67} -6.85146 q^{68} +(-1.22571 + 3.77236i) q^{69} +(-0.948519 - 1.77562i) q^{70} +(0.561335 + 1.72761i) q^{71} +(0.887323 + 2.73090i) q^{72} +(7.64336 + 5.55323i) q^{73} -6.64086 q^{74} +(-2.77992 + 4.15596i) q^{75} +0.622743 q^{76} +(-3.97096 - 2.88507i) q^{77} +(1.24577 + 3.83409i) q^{78} +(2.14674 + 6.60699i) q^{79} +(-0.453702 + 0.0809041i) q^{80} +(0.309017 - 0.951057i) q^{81} +7.41772 q^{82} +(-4.01564 + 12.3589i) q^{83} +(0.962323 - 0.699169i) q^{84} +(-8.92905 + 9.28213i) q^{85} +(-1.36292 - 0.990217i) q^{86} +(4.86106 - 3.53176i) q^{87} +(-11.4024 + 8.28430i) q^{88} +(5.20546 + 3.78199i) q^{89} +(1.81105 + 0.878981i) q^{90} +(3.62273 - 2.63207i) q^{91} +(1.45798 - 4.48721i) q^{92} -1.80048 q^{93} +(3.00954 - 9.26241i) q^{94} +(0.811579 - 0.843671i) q^{95} +(-1.71731 - 5.28533i) q^{96} +(-2.77759 - 8.54855i) q^{97} +(0.728341 + 0.529171i) q^{98} +4.90838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

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