LMFDB - Embedded newform 525.2.z.a.169.5

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			169.5
Character	$\chi$	$=$	525.169
Dual form			525.2.z.a.379.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.752353 + 0.244454i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.11176 + 0.807738i) q^{4} +(2.10831 + 0.745003i) q^{5} +(0.639990 + 0.464980i) q^{6} +1.00000i q^{7} +(1.56894 - 2.15946i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.752353 + 0.244454i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.11176 + 0.807738i) q^{4} +(2.10831 + 0.745003i) q^{5} +(0.639990 + 0.464980i) q^{6} +1.00000i q^{7} +(1.56894 - 2.15946i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.76831 - 0.0451201i) q^{10} +(0.642878 + 1.97858i) q^{11} +(1.30695 + 0.424653i) q^{12} +(-3.10128 - 1.00767i) q^{13} +(-0.244454 - 0.752353i) q^{14} +(-0.636513 - 2.14356i) q^{15} +(0.196799 - 0.605686i) q^{16} +(-0.940152 + 1.29401i) q^{17} -0.791071i q^{18} +(3.15049 + 2.28897i) q^{19} +(-2.94569 + 0.874700i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-0.967344 - 1.33143i) q^{22} +(-1.74443 + 0.566798i) q^{23} -2.66924 q^{24} +(3.88994 + 3.14140i) q^{25} +2.57959 q^{26} +(0.951057 - 0.309017i) q^{27} +(-0.807738 - 1.11176i) q^{28} +(-5.52439 + 4.01370i) q^{29} +(1.00289 + 1.45712i) q^{30} +(2.85090 + 2.07130i) q^{31} +5.84227i q^{32} +(1.22283 - 1.68308i) q^{33} +(0.391000 - 1.20338i) q^{34} +(-0.745003 + 2.10831i) q^{35} +(-0.424653 - 1.30695i) q^{36} +(3.48612 + 1.13271i) q^{37} +(-2.92983 - 0.951961i) q^{38} +(1.00767 + 3.10128i) q^{39} +(4.91661 - 3.38394i) q^{40} +(-3.60907 + 11.1076i) q^{41} +(-0.464980 + 0.639990i) q^{42} +4.69230i q^{43} +(-2.31290 - 1.68042i) q^{44} +(-1.36004 + 1.77490i) q^{45} +(1.17387 - 0.852865i) q^{46} +(4.22504 + 5.81527i) q^{47} +(-0.605686 + 0.196799i) q^{48} -1.00000 q^{49} +(-3.69454 - 1.41253i) q^{50} +1.59948 q^{51} +(4.26180 - 1.38474i) q^{52} +(-3.92767 - 5.40598i) q^{53} +(-0.639990 + 0.464980i) q^{54} +(-0.118659 + 4.65040i) q^{55} +(2.15946 + 1.56894i) q^{56} -3.89423i q^{57} +(3.17512 - 4.37018i) q^{58} +(-0.701598 + 2.15930i) q^{59} +(2.43908 + 1.86898i) q^{60} +(2.98895 + 9.19904i) q^{61} +(-2.65122 - 0.861434i) q^{62} +(-0.951057 - 0.309017i) q^{63} +(-1.03457 - 3.18408i) q^{64} +(-5.78775 - 4.43494i) q^{65} +(-0.508563 + 1.56519i) q^{66} +(8.16200 - 11.2340i) q^{67} -2.19802i q^{68} +(1.48390 + 1.07811i) q^{69} +(0.0451201 - 1.76831i) q^{70} +(-0.804688 + 0.584640i) q^{71} +(1.56894 + 2.15946i) q^{72} +(3.18447 - 1.03470i) q^{73} -2.89969 q^{74} +(0.254993 - 4.99349i) q^{75} -5.35147 q^{76} +(-1.97858 + 0.642878i) q^{77} +(-1.51624 - 2.08693i) q^{78} +(-2.32761 + 1.69111i) q^{79} +(0.866152 - 1.13036i) q^{80} +(-0.809017 - 0.587785i) q^{81} -9.23908i q^{82} +(3.18233 - 4.38010i) q^{83} +(-0.424653 + 1.30695i) q^{84} +(-2.94617 + 2.02775i) q^{85} +(-1.14705 - 3.53026i) q^{86} +(6.49431 + 2.11013i) q^{87} +(5.28129 + 1.71600i) q^{88} +(-1.14403 - 3.52095i) q^{89} +(0.589351 - 1.66782i) q^{90} +(1.00767 - 3.10128i) q^{91} +(1.48155 - 2.03918i) q^{92} -3.52391i q^{93} +(-4.60029 - 3.34231i) q^{94} +(4.93693 + 7.17298i) q^{95} +(4.72650 - 3.43400i) q^{96} +(-9.87564 - 13.5926i) q^{97} +(0.752353 - 0.244454i) q^{98} -2.08040 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$1$

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 $

$2$	−0.752353	+	0.244454i	−0.531994	+	0.172855i	−0.562682	−	0.826674i	$-0.690230\pi$
$2$	−0.752353	+	0.244454i	−0.531994	+	0.172855i	0.0306875	+	0.999529i	$0.490230\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−1.11176	+	0.807738i	−0.555878	+	0.403869i
$5$	2.10831	+	0.745003i	0.942865	+	0.333176i
$5$	2.10831	+	0.745003i	0.942865	+	0.333176i
$6$	0.639990	+	0.464980i	0.261275	+	0.189827i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.56894	−	2.15946i	0.554703	−	0.763484i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−1.76831	−	0.0451201i	−0.559190	−	0.0142682i
$11$	0.642878	+	1.97858i	0.193835	+	0.596563i	0.999988	+	0.00485620i	$0.00154578\pi$
$11$	0.642878	+	1.97858i	0.193835	+	0.596563i	−0.806153	+	0.591707i	$0.798454\pi$
$12$	1.30695	+	0.424653i	0.377283	+	0.122587i
$13$	−3.10128	−	1.00767i	−0.860141	−	0.279477i	−0.154453	−	0.988000i	$-0.549362\pi$
$13$	−3.10128	−	1.00767i	−0.860141	−	0.279477i	−0.705687	+	0.708523i	$0.749362\pi$
$14$	−0.244454	−	0.752353i	−0.0653332	−	0.201075i
$15$	−0.636513	−	2.14356i	−0.164347	−	0.553465i
$16$	0.196799	−	0.605686i	0.0491998	−	0.151422i
$17$	−0.940152	+	1.29401i	−0.228020	+	0.313843i	−0.907663	−	0.419701i	$-0.862135\pi$
$17$	−0.940152	+	1.29401i	−0.228020	+	0.313843i	0.679642	+	0.733544i	$0.262135\pi$
$18$		−	0.791071i		−	0.186457i
$19$	3.15049	+	2.28897i	0.722773	+	0.525125i	0.887269	−	0.461252i	$-0.152600\pi$
$19$	3.15049	+	2.28897i	0.722773	+	0.525125i	−0.164496	+	0.986378i	$0.552600\pi$
$20$	−2.94569	+	0.874700i	−0.658677	+	0.195589i
$21$	0.809017	−	0.587785i	0.176542	−	0.128265i
$22$	−0.967344	−	1.33143i	−0.206238	−	0.283863i
$23$	−1.74443	+	0.566798i	−0.363738	+	0.118186i	−0.485183	−	0.874412i	$-0.661247\pi$
$23$	−1.74443	+	0.566798i	−0.363738	+	0.118186i	0.121445	+	0.992598i	$0.461247\pi$
$24$	−2.66924			−0.544856
$25$	3.88994	+	3.14140i	0.777988	+	0.628279i
$26$	2.57959			0.505899
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−0.807738	−	1.11176i	−0.152648	−	0.210102i
$29$	−5.52439	+	4.01370i	−1.02585	+	0.745326i	−0.967475	−	0.252969i	$-0.918593\pi$
$29$	−5.52439	+	4.01370i	−1.02585	+	0.745326i	−0.0583787	+	0.998295i	$0.518593\pi$
$30$	1.00289	+	1.45712i	0.183101	+	0.266032i
$31$	2.85090	+	2.07130i	0.512037	+	0.372016i	0.813596	−	0.581431i	$-0.197507\pi$
$31$	2.85090	+	2.07130i	0.512037	+	0.372016i	−0.301559	+	0.953448i	$0.597507\pi$
$32$			5.84227i			1.03278i
$33$	1.22283	−	1.68308i	0.212867	−	0.292986i
$34$	0.391000	−	1.20338i	0.0670560	−	0.206377i
$35$	−0.745003	+	2.10831i	−0.125929	+	0.356369i
$36$	−0.424653	−	1.30695i	−0.0707755	−	0.217825i
$37$	3.48612	+	1.13271i	0.573115	+	0.186216i	0.581214	−	0.813751i	$-0.302578\pi$
$37$	3.48612	+	1.13271i	0.573115	+	0.186216i	−0.00809884	+	0.999967i	$0.502578\pi$
$38$	−2.92983	−	0.951961i	−0.475282	−	0.154428i
$39$	1.00767	+	3.10128i	0.161356	+	0.496602i
$40$	4.91661	−	3.38394i	0.777385	−	0.535048i
$41$	−3.60907	+	11.1076i	−0.563642	+	1.73471i	0.108309	+	0.994117i	$0.465457\pi$
$41$	−3.60907	+	11.1076i	−0.563642	+	1.73471i	−0.671951	+	0.740596i	$0.734543\pi$
$42$	−0.464980	+	0.639990i	−0.0717480	+	0.0987526i
$43$			4.69230i			0.715568i	0.933804	+	0.357784i	$0.116468\pi$
$43$			4.69230i			0.715568i	−0.933804	+	0.357784i	$0.883532\pi$
$44$	−2.31290	−	1.68042i	−0.348682	−	0.253332i
$45$	−1.36004	+	1.77490i	−0.202743	+	0.264587i
$46$	1.17387	−	0.852865i	0.173077	−	0.125748i
$47$	4.22504	+	5.81527i	0.616286	+	0.848245i	0.997076	−	0.0764168i	$-0.0243480\pi$
$47$	4.22504	+	5.81527i	0.616286	+	0.848245i	−0.380790	+	0.924661i	$0.624348\pi$
$48$	−0.605686	+	0.196799i	−0.0874233	+	0.0284055i
$49$	−1.00000			−0.142857
$50$	−3.69454	−	1.41253i	−0.522487	−	0.199761i
$51$	1.59948			0.223972
$52$	4.26180	−	1.38474i	0.591005	−	0.192029i
$53$	−3.92767	−	5.40598i	−0.539507	−	0.742568i	0.449035	−	0.893514i	$-0.351768\pi$
$53$	−3.92767	−	5.40598i	−0.539507	−	0.742568i	−0.988542	+	0.150946i	$0.951768\pi$
$54$	−0.639990	+	0.464980i	−0.0870916	+	0.0632758i
$55$	−0.118659	+	4.65040i	−0.0160000	+	0.627060i
$56$	2.15946	+	1.56894i	0.288570	+	0.209658i
$57$		−	3.89423i		−	0.515803i
$58$	3.17512	−	4.37018i	0.416914	−	0.573833i
$59$	−0.701598	+	2.15930i	−0.0913403	+	0.281116i	−0.986283	−	0.165065i	$-0.947217\pi$
$59$	−0.701598	+	2.15930i	−0.0913403	+	0.281116i	0.894942	+	0.446182i	$0.147217\pi$
$60$	2.43908	+	1.86898i	0.314884	+	0.241284i
$61$	2.98895	+	9.19904i	0.382696	+	1.17782i	0.938138	+	0.346262i	$0.112549\pi$
$61$	2.98895	+	9.19904i	0.382696	+	1.17782i	−0.555442	+	0.831555i	$0.687451\pi$
$62$	−2.65122	−	0.861434i	−0.336706	−	0.109402i
$63$	−0.951057	−	0.309017i	−0.119822	−	0.0389325i
$64$	−1.03457	−	3.18408i	−0.129321	−	0.398010i
$65$	−5.78775	−	4.43494i	−0.717882	−	0.550087i
$66$	−0.508563	+	1.56519i	−0.0625997	+	0.192662i
$67$	8.16200	−	11.2340i	0.997146	−	1.37245i	0.0700866	−	0.997541i	$-0.477672\pi$
$67$	8.16200	−	11.2340i	0.997146	−	1.37245i	0.927060	−	0.374913i	$-0.122328\pi$
$68$		−	2.19802i		−	0.266549i
$69$	1.48390	+	1.07811i	0.178640	+	0.129790i
$70$	0.0451201	−	1.76831i	0.00539288	−	0.211354i
$71$	−0.804688	+	0.584640i	−0.0954989	+	0.0693840i	−0.634510	−	0.772915i	$-0.718798\pi$
$71$	−0.804688	+	0.584640i	−0.0954989	+	0.0693840i	0.539011	+	0.842299i	$0.318798\pi$
$72$	1.56894	+	2.15946i	0.184901	+	0.254495i
$73$	3.18447	−	1.03470i	0.372714	−	0.121102i	−0.116669	−	0.993171i	$-0.537222\pi$
$73$	3.18447	−	1.03470i	0.372714	−	0.121102i	0.489384	+	0.872069i	$0.337222\pi$
$74$	−2.89969			−0.337082
$75$	0.254993	−	4.99349i	0.0294440	−	0.576599i
$76$	−5.35147			−0.613856
$77$	−1.97858	+	0.642878i	−0.225480	+	0.0732628i
$78$	−1.51624	−	2.08693i	−0.171681	−	0.236298i
$79$	−2.32761	+	1.69111i	−0.261876	+	0.190264i	−0.710974	−	0.703218i	$-0.751746\pi$
$79$	−2.32761	+	1.69111i	−0.261876	+	0.190264i	0.449097	+	0.893483i	$0.351746\pi$
$80$	0.866152	−	1.13036i	0.0968388	−	0.126378i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		−	9.23908i		−	1.02029i
$83$	3.18233	−	4.38010i	0.349306	−	0.480779i	−0.597824	−	0.801627i	$-0.703968\pi$
$83$	3.18233	−	4.38010i	0.349306	−	0.480779i	0.947131	+	0.320848i	$0.103968\pi$
$84$	−0.424653	+	1.30695i	−0.0463335	+	0.142600i
$85$	−2.94617	+	2.02775i	−0.319557	+	0.219941i
$86$	−1.14705	−	3.53026i	−0.123690	−	0.380678i
$87$	6.49431	+	2.11013i	0.696263	+	0.226230i
$88$	5.28129	+	1.71600i	0.562987	+	0.182926i
$89$	−1.14403	−	3.52095i	−0.121266	−	0.373220i	0.871936	−	0.489620i	$-0.162864\pi$
$89$	−1.14403	−	3.52095i	−0.121266	−	0.373220i	−0.993202	+	0.116400i	$0.962864\pi$
$90$	0.589351	−	1.66782i	0.0621230	−	0.175804i
$91$	1.00767	−	3.10128i	0.105632	−	0.325103i
$92$	1.48155	−	2.03918i	0.154462	−	0.212599i
$93$		−	3.52391i		−	0.365412i
$94$	−4.60029	−	3.34231i	−0.474484	−	0.344733i
$95$	4.93693	+	7.17298i	0.506518	+	0.735933i
$96$	4.72650	−	3.43400i	0.482396	−	0.350481i
$97$	−9.87564	−	13.5926i	−1.00272	−	1.38012i	−0.923642	−	0.383256i	$-0.874803\pi$
$97$	−9.87564	−	13.5926i	−1.00272	−	1.38012i	−0.0790765	−	0.996869i	$-0.525197\pi$
$98$	0.752353	−	0.244454i	0.0759992	−	0.0246936i
$99$	−2.08040			−0.209088
$100$	−6.86209	−	0.350413i	−0.686209	−	0.0350413i
$101$	−15.3045			−1.52285			−0.761425	−	0.648253i	$-0.775500\pi$
$101$	−15.3045			−1.52285			−0.761425	+	0.648253i	$0.775500\pi$
$102$	−1.20338	+	0.391000i	−0.119152	+	0.0387148i
$103$	−3.80809	−	5.24139i	−0.375222	−	0.516449i	0.579089	−	0.815265i	$-0.303409\pi$
$103$	−3.80809	−	5.24139i	−0.375222	−	0.516449i	−0.954311	+	0.298815i	$0.903409\pi$
$104$	−7.04173	+	5.11612i	−0.690499	+	0.501677i
$105$	2.14356	−	0.636513i	0.209190	−	0.0621173i
$106$	4.27651	+	3.10707i	0.415372	+	0.301785i
$107$			2.26444i			0.218912i	0.993992	+	0.109456i	$0.0349108\pi$
$107$			2.26444i			0.218912i	−0.993992	+	0.109456i	$0.965089\pi$
$108$	−0.807738	+	1.11176i	−0.0777247	+	0.106979i
$109$	1.54134	−	4.74376i	0.147634	−	0.454370i	−0.849707	−	0.527256i	$-0.823221\pi$
$109$	1.54134	−	4.74376i	0.147634	−	0.454370i	0.997340	+	0.0728859i	$0.0232209\pi$
$110$	−1.04754	−	3.52775i	−0.0998787	−	0.336358i
$111$	−1.13271	−	3.48612i	−0.107512	−	0.330888i
$112$	0.605686	+	0.196799i	0.0572320	+	0.0185958i
$113$	−7.47830	−	2.42985i	−0.703499	−	0.228581i	−0.0646448	−	0.997908i	$-0.520591\pi$
$113$	−7.47830	−	2.42985i	−0.703499	−	0.228581i	−0.638855	+	0.769328i	$0.720591\pi$
$114$	0.951961	+	2.92983i	0.0891593	+	0.274404i
$115$	−4.10006	−	0.104617i	−0.382332	−	0.00975554i
$116$	2.89975	−	8.92452i	0.269235	−	0.828621i
$117$	1.91670	−	2.63811i	0.177199	−	0.243893i
$118$		−	1.79606i		−	0.165341i
$119$	−1.29401	−	0.940152i	−0.118622	−	0.0861836i
$120$	−5.62758	−	1.98859i	−0.513725	−	0.181533i
$121$	5.39771	−	3.92167i	0.490701	−	0.356515i
$122$	−4.49749	−	6.19027i	−0.407184	−	0.560441i
$123$	11.1076	−	3.60907i	1.00154	−	0.325419i
$124$	−4.84257			−0.434876
$125$	5.86085	+	9.52105i	0.524210	+	0.851589i
$126$	0.791071			0.0704742
$127$	13.0152	−	4.22890i	1.15491	−	0.375254i	0.331922	−	0.943307i	$-0.392303\pi$
$127$	13.0152	−	4.22890i	1.15491	−	0.375254i	0.822992	+	0.568053i	$0.192303\pi$
$128$	−5.31128	−	7.31035i	−0.469455	−	0.646150i
$129$	3.79615	−	2.75806i	0.334232	−	0.242834i
$130$	5.43857	+	1.92180i	0.476994	+	0.168553i
$131$	15.5048	+	11.2649i	1.35466	+	0.984218i	0.998765	+	0.0496926i	$0.0158242\pi$
$131$	15.5048	+	11.2649i	1.35466	+	0.984218i	0.355896	+	0.934526i	$0.384176\pi$
$132$			2.85890i			0.248835i
$133$	−2.28897	+	3.15049i	−0.198479	+	0.273183i
$134$	−3.39450	+	10.4472i	−0.293240	+	0.902500i
$135$	2.23534	+	0.0570367i	0.192387	+	0.00490893i
$136$	1.31932	+	4.06044i	0.113130	+	0.348180i
$137$	7.30315	+	2.37294i	0.623950	+	0.202734i	0.603893	−	0.797065i	$-0.293615\pi$
$137$	7.30315	+	2.37294i	0.623950	+	0.202734i	0.0200568	+	0.999799i	$0.493615\pi$
$138$	−1.37997	−	0.448378i	−0.117470	−	0.0381685i
$139$	−4.04779	−	12.4578i	−0.343329	−	1.05666i	−0.962472	−	0.271380i	$-0.912520\pi$
$139$	−4.04779	−	12.4578i	−0.343329	−	1.05666i	0.619143	−	0.785278i	$-0.287480\pi$
$140$	−0.874700	−	2.94569i	−0.0739257	−	0.248957i
$141$	2.22124	−	6.83626i	0.187062	−	0.575717i
$142$	0.462492	−	0.636566i	0.0388115	−	0.0534194i
$143$		−	6.78393i		−	0.567301i
$144$	0.515228	+	0.374335i	0.0429356	+	0.0311946i
$145$	−14.6373	+	4.34644i	−1.21557	+	0.360952i
$146$	−2.14291	+	1.55692i	−0.177349	+	0.128851i
$147$	0.587785	+	0.809017i	0.0484797	+	0.0667266i
$148$	−4.79065	+	1.55658i	−0.393789	+	0.127950i
$149$	7.44657			0.610047			0.305023	−	0.952345i	$-0.401336\pi$
$149$	7.44657			0.610047			0.305023	+	0.952345i	$0.401336\pi$
$150$	1.02884	+	3.81921i	0.0840042	+	0.311837i
$151$	15.0228			1.22254			0.611268	−	0.791423i	$-0.290660\pi$
$151$	15.0228			1.22254			0.611268	+	0.791423i	$0.290660\pi$
$152$	9.88586	−	3.21211i	0.801849	−	0.260537i
$153$	−0.940152	−	1.29401i	−0.0760068	−	0.104614i
$154$	1.33143	−	0.967344i	0.107290	−	0.0779508i
$155$	4.46745	+	6.49087i	0.358835	+	0.521359i
$156$	−3.62530	−	2.63394i	−0.290257	−	0.210884i
$157$			12.6392i			1.00872i	0.863494	+	0.504359i	$0.168271\pi$
$157$			12.6392i			1.00872i	−0.863494	+	0.504359i	$0.831729\pi$
$158$	1.33779	−	1.84130i	0.106429	−	0.146486i
$159$	−2.06490	+	6.35511i	−0.163757	+	0.503993i
$160$	−4.35251	+	12.3173i	−0.344096	+	0.973770i
$161$	−0.566798	−	1.74443i	−0.0446700	−	0.137480i
$162$	0.752353	+	0.244454i	0.0591105	+	0.0192062i
$163$	9.09384	+	2.95477i	0.712284	+	0.231435i	0.642675	−	0.766139i	$-0.277825\pi$
$163$	9.09384	+	2.95477i	0.712284	+	0.231435i	0.0696096	+	0.997574i	$0.477825\pi$
$164$	−4.95961	−	15.2641i	−0.387281	−	1.19193i
$165$	3.83200	−	2.63744i	0.298321	−	0.205324i
$166$	−1.32350	+	4.07332i	−0.102724	+	0.316151i
$167$	7.01316	−	9.65278i	0.542694	−	0.746955i	−0.446304	−	0.894881i	$-0.647260\pi$
$167$	7.01316	−	9.65278i	0.542694	−	0.746955i	0.988998	+	0.147927i	$0.0472600\pi$
$168$		−	2.66924i		−	0.205936i
$169$	−1.91467	−	1.39109i	−0.147282	−	0.107007i
$170$	1.72087	−	2.24579i	0.131985	−	0.172244i
$171$	−3.15049	+	2.28897i	−0.240924	+	0.175042i
$172$	−3.79015	−	5.21669i	−0.288996	−	0.397769i
$173$	−11.3088	+	3.67446i	−0.859793	+	0.279364i	−0.705542	−	0.708668i	$-0.749296\pi$
$173$	−11.3088	+	3.67446i	−0.859793	+	0.279364i	−0.154251	+	0.988032i	$0.549296\pi$
$174$	−5.40185			−0.409513
$175$	−3.14140	+	3.88994i	−0.237467	+	0.294052i
$176$	1.32491			0.0998692
$177$	2.15930	−	0.701598i	0.162303	−	0.0527353i
$178$	1.72142	+	2.36934i	0.129026	+	0.177589i
$179$	11.1559	−	8.10521i	0.833828	−	0.605812i	−0.0868115	−	0.996225i	$-0.527668\pi$
$179$	11.1559	−	8.10521i	0.833828	−	0.605812i	0.920640	+	0.390413i	$0.127668\pi$
$180$	0.0783801	−	3.07182i	0.00584211	−	0.228960i
$181$	−15.8546	−	11.5190i	−1.17846	−	0.856204i	−0.186466	−	0.982461i	$-0.559703\pi$
$181$	−15.8546	−	11.5190i	−1.17846	−	0.856204i	−0.991998	+	0.126257i	$0.959703\pi$
$182$			2.57959i			0.191212i
$183$	5.68532	−	7.82517i	0.420271	−	0.578453i
$184$	−1.51292	+	4.65629i	−0.111534	+	0.343266i
$185$	6.50595	+	4.98528i	0.478327	+	0.366525i
$186$	0.861434	+	2.65122i	0.0631634	+	0.194397i
$187$	−3.16470	−	1.02827i	−0.231426	−	0.0751947i
$188$	−9.39444	−	3.05244i	−0.685160	−	0.222622i
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	−5.46778	−	4.18976i	−0.396675	−	0.303957i
$191$	0.535107	−	1.64689i	0.0387190	−	0.119165i	−0.929829	−	0.367992i	$-0.880045\pi$
$191$	0.535107	−	1.64689i	0.0387190	−	0.119165i	0.968548	+	0.248828i	$0.0800453\pi$
$192$	−1.96787	+	2.70854i	−0.142019	+	0.195472i
$193$			13.3171i			0.958585i	0.877655	+	0.479293i	$0.159107\pi$
$193$			13.3171i			0.958585i	−0.877655	+	0.479293i	$0.840893\pi$
$194$	10.7527	+	7.81233i	0.772002	+	0.560893i
$195$	−0.185990	+	7.28918i	−0.0133190	+	0.521989i
$196$	1.11176	−	0.807738i	0.0794112	−	0.0576956i
$197$	−8.82724	−	12.1497i	−0.628915	−	0.865627i	0.369049	−	0.929410i	$-0.379684\pi$
$197$	−8.82724	−	12.1497i	−0.628915	−	0.865627i	−0.997964	+	0.0637828i	$0.979684\pi$
$198$	1.56519	−	0.508563i	0.111234	−	0.0361420i
$199$	2.46911			0.175031			0.0875154	−	0.996163i	$-0.472107\pi$
$199$	2.46911			0.175031			0.0875154	+	0.996163i	$0.472107\pi$
$200$	12.8868	−	3.47151i	0.911234	−	0.245473i
$201$	−13.8860			−0.979444
$202$	11.5144	−	3.74124i	0.810147	−	0.263233i
$203$	−4.01370	−	5.52439i	−0.281707	−	0.387736i
$204$	−1.77823	+	1.29196i	−0.124501	+	0.0904555i
$205$	−15.8842	+	20.7295i	−1.10940	+	1.44781i
$206$	4.14631	+	3.01247i	0.288887	+	0.209889i
$207$		−	1.83420i		−	0.127486i
$208$	−1.22066	+	1.68010i	−0.0846376	+	0.116494i
$209$	−2.50351	+	7.70502i	−0.173172	+	0.532968i
$210$	−1.45712	+	1.00289i	−0.100551	+	0.0692057i
$211$	1.88895	+	5.81360i	0.130041	+	0.400225i	0.994786	−	0.101987i	$-0.0325199\pi$
$211$	1.88895	+	5.81360i	0.130041	+	0.400225i	−0.864745	+	0.502211i	$0.832520\pi$
$212$	8.73323	+	2.83760i	0.599801	+	0.194887i
$213$	0.945968	+	0.307364i	0.0648167	+	0.0210602i
$214$	−0.553552	−	1.70366i	−0.0378400	−	0.116460i
$215$	−3.49578	+	9.89281i	−0.238410	+	0.674684i
$216$	0.824840	−	2.53860i	0.0561232	−	0.172730i
$217$	−2.07130	+	2.85090i	−0.140609	+	0.193532i
$218$			3.94577i			0.267242i
$219$	−2.70887	−	1.96811i	−0.183049	−	0.132993i
$220$	−3.62439	−	5.26596i	−0.244356	−	0.355031i
$221$	4.21961	−	3.06572i	0.283841	−	0.206223i
$222$	1.70440	+	2.34590i	0.114392	+	0.157447i
$223$	−9.85079	+	3.20072i	−0.659658	+	0.214336i	−0.619668	−	0.784864i	$-0.712733\pi$
$223$	−9.85079	+	3.20072i	−0.659658	+	0.214336i	−0.0399900	+	0.999200i	$0.512733\pi$
$224$	−5.84227			−0.390353
$225$	−4.18970	+	2.72881i	−0.279313	+	0.181921i
$226$	6.22031			0.413769
$227$	3.00278	−	0.975662i	0.199301	−	0.0647570i	−0.207665	−	0.978200i	$-0.566586\pi$
$227$	3.00278	−	0.975662i	0.199301	−	0.0647570i	0.406967	+	0.913443i	$0.366586\pi$
$228$	3.14552	+	4.32943i	0.208317	+	0.286724i
$229$	20.1648	−	14.6506i	1.33253	−	0.968138i	0.332844	−	0.942982i	$-0.391992\pi$
$229$	20.1648	−	14.6506i	1.33253	−	0.968138i	0.999684	−	0.0251558i	$-0.00800817\pi$
$230$	3.11027	−	0.923569i	0.205085	−	0.0608983i
$231$	1.68308	+	1.22283i	0.110738	+	0.0804561i
$232$			18.2269i			1.19666i
$233$	16.4574	−	22.6517i	1.07816	−	1.48396i	0.216631	−	0.976253i	$-0.430493\pi$
$233$	16.4574	−	22.6517i	1.07816	−	1.48396i	0.861530	−	0.507708i	$-0.169507\pi$
$234$	−0.797137	+	2.45333i	−0.0521104	+	0.160379i
$235$	4.57530	+	15.4081i	0.298460	+	1.00511i
$236$	−0.964140	−	2.96732i	−0.0627602	−	0.193156i
$237$	2.73627	+	0.889067i	0.177740	+	0.0577511i
$238$	1.20338	+	0.391000i	0.0780033	+	0.0253448i
$239$	3.22475	+	9.92477i	0.208592	+	0.641980i	0.999547	+	0.0301054i	$0.00958431\pi$
$239$	3.22475	+	9.92477i	0.208592	+	0.641980i	−0.790955	+	0.611875i	$0.790416\pi$
$240$	−1.42359	−	0.0363242i	−0.0918924	−	0.00234471i
$241$	−2.67734	+	8.24000i	−0.172463	+	0.530785i	−0.999508	−	0.0313491i	$-0.990020\pi$
$241$	−2.67734	+	8.24000i	−0.172463	+	0.530785i	0.827046	+	0.562134i	$0.190020\pi$
$242$	−3.10232	+	4.26998i	−0.199425	+	0.274484i
$243$			1.00000i			0.0641500i
$244$	−10.7534	−	7.81281i	−0.688416	−	0.500164i
$245$	−2.10831	−	0.745003i	−0.134695	−	0.0475965i
$246$	−7.47457	+	5.43060i	−0.476561	+	0.346242i
$247$	−7.46405	−	10.2734i	−0.474926	−	0.653680i
$248$	8.94577	−	2.90666i	0.568057	−	0.184573i
$249$	−5.41411			−0.343105
$250$	−6.73689	−	5.73049i	−0.426079	−	0.362428i
$251$	−13.8177			−0.872168			−0.436084	−	0.899906i	$-0.643635\pi$
$251$	−13.8177			−0.872168			−0.436084	+	0.899906i	$0.643635\pi$
$252$	1.30695	−	0.424653i	0.0823300	−	0.0267506i
$253$	−2.24291	−	3.08710i	−0.141010	−	0.194084i
$254$	−8.75827	+	6.36325i	−0.549543	+	0.399266i
$255$	3.37220	+	1.19162i	0.211176	+	0.0746221i
$256$	11.2001	+	8.13734i	0.700006	+	0.508584i
$257$			23.8832i			1.48980i	0.667179	+	0.744898i	$0.267502\pi$
$257$			23.8832i			1.48980i	−0.667179	+	0.744898i	$0.732498\pi$
$258$	−2.18182	+	3.00302i	−0.135834	+	0.186960i
$259$	−1.13271	+	3.48612i	−0.0703832	+	0.216617i
$260$	10.0168	+	0.255588i	0.621218	+	0.0158509i
$261$	−2.11013	−	6.49431i	−0.130614	−	0.401988i
$262$	−14.4188	−	4.68496i	−0.890799	−	0.289438i
$263$	1.84380	+	0.599087i	0.113694	+	0.0369413i	0.365311	−	0.930885i	$-0.380963\pi$
$263$	1.84380	+	0.599087i	0.113694	+	0.0369413i	−0.251618	+	0.967827i	$0.580963\pi$
$264$	−1.71600	−	5.28129i	−0.105612	−	0.325041i
$265$	−4.25328	−	14.3236i	−0.261277	−	0.879892i
$266$	0.951961	−	2.92983i	0.0583685	−	0.179640i
$267$	−2.17607	+	2.99510i	−0.133173	+	0.183297i
$268$			19.0823i			1.16563i
$269$	−22.1640	−	16.1031i	−1.35136	−	0.981821i	−0.998942	−	0.0459789i	$-0.985359\pi$
$269$	−22.1640	−	16.1031i	−1.35136	−	0.981821i	−0.352419	−	0.935842i	$-0.614641\pi$
$270$	−1.69571	+	0.503527i	−0.103198	+	0.0306437i
$271$	9.93058	−	7.21499i	0.603240	−	0.438280i	−0.243787	−	0.969829i	$-0.578390\pi$
$271$	9.93058	−	7.21499i	0.603240	−	0.438280i	0.847027	+	0.531549i	$0.178390\pi$
$272$	0.598742	+	0.824097i	0.0363040	+	0.0499682i
$273$	−3.10128	+	1.00767i	−0.187698	+	0.0609868i
$274$	−6.07462			−0.366981
$275$	−3.71473	+	9.71608i	−0.224007	+	0.585902i
$276$	−2.52057			−0.151720
$277$	13.2720	−	4.31233i	0.797437	−	0.259103i	0.118169	−	0.992993i	$-0.462298\pi$
$277$	13.2720	−	4.31233i	0.797437	−	0.259103i	0.679268	+	0.733891i	$0.262298\pi$
$278$	6.09074	+	8.38318i	0.365298	+	0.502790i
$279$	−2.85090	+	2.07130i	−0.170679	+	0.124005i
$280$	3.38394	+	4.91661i	0.202229	+	0.293824i
$281$	19.0539	+	13.8434i	1.13666	+	0.825831i	0.986650	−	0.162854i	$-0.0520700\pi$
$281$	19.0539	+	13.8434i	1.13666	+	0.825831i	0.150008	+	0.988685i	$0.452070\pi$
$282$			5.68628i			0.338613i
$283$	−12.6472	+	17.4074i	−0.751799	+	1.03476i	0.246053	+	0.969256i	$0.420866\pi$
$283$	−12.6472	+	17.4074i	−0.751799	+	1.03476i	−0.997852	+	0.0655067i	$0.979134\pi$
$284$	0.422381	−	1.29996i	0.0250637	−	0.0771381i
$285$	2.90121	−	8.21023i	0.171853	−	0.486332i
$286$	1.65836	+	5.10391i	0.0980610	+	0.301801i
$287$	−11.1076	−	3.60907i	−0.655660	−	0.213037i
$288$	−5.55633	−	1.80536i	−0.327410	−	0.106382i
$289$	4.46272	+	13.7348i	0.262513	+	0.807931i
$290$	9.94995	−	6.84822i	0.584281	−	0.402142i
$291$	−5.19193	+	15.9791i	−0.304356	+	0.936712i
$292$	−2.70459	+	3.72255i	−0.158274	+	0.217846i
$293$			23.3708i			1.36534i	0.730728	+	0.682669i	$0.239181\pi$
$293$			23.3708i			1.36534i	−0.730728	+	0.682669i	$0.760819\pi$
$294$	−0.639990	−	0.464980i	−0.0373250	−	0.0271182i
$295$	−3.08787	+	4.02977i	−0.179783	+	0.234622i
$296$	7.91555	−	5.75098i	0.460082	−	0.334269i
$297$	1.22283	+	1.68308i	0.0709557	+	0.0976621i
$298$	−5.60245	+	1.82035i	−0.324541	+	0.105450i
$299$	5.98110			0.345896
$300$	3.74995	+	5.75752i	0.216503	+	0.332410i
$301$	−4.69230			−0.270459
$302$	−11.3024	+	3.67239i	−0.650382	+	0.211322i
$303$	8.99573	+	12.3816i	0.516791	+	0.711302i
$304$	2.00641	−	1.45774i	0.115076	−	0.0836073i
$305$	−0.551684	+	21.6212i	−0.0315893	+	1.23803i
$306$	1.02365	+	0.743727i	0.0585183	+	0.0425161i
$307$		−	27.5337i		−	1.57143i	−0.618587	−	0.785716i	$-0.712295\pi$
$307$		−	27.5337i		−	1.57143i	0.618587	−	0.785716i	$-0.287705\pi$
$308$	1.68042	−	2.31290i	0.0957507	−	0.131789i
$309$	−2.00203	+	6.16162i	−0.113892	+	0.350522i
$310$	−4.94783	−	3.79134i	−0.281018	−	0.215334i
$311$	2.96623	+	9.12913i	0.168200	+	0.517665i	0.999258	−	0.0385202i	$-0.0122644\pi$
$311$	2.96623	+	9.12913i	0.168200	+	0.517665i	−0.831058	+	0.556186i	$0.812264\pi$
$312$	8.27806	+	2.68970i	0.468653	+	0.152274i
$313$	−4.08434	−	1.32708i	−0.230860	−	0.0750111i	0.191302	−	0.981531i	$-0.438729\pi$
$313$	−4.08434	−	1.32708i	−0.230860	−	0.0750111i	−0.422163	+	0.906520i	$0.638729\pi$
$314$	−3.08971	−	9.50915i	−0.174363	−	0.536633i
$315$	−1.77490	−	1.36004i	−0.100004	−	0.0766298i
$316$	1.22176	−	3.76020i	0.0687295	−	0.211528i
$317$	−2.00407	+	2.75837i	−0.112560	+	0.154925i	−0.861580	−	0.507622i	$-0.830525\pi$
$317$	−2.00407	+	2.75837i	−0.112560	+	0.154925i	0.749020	+	0.662547i	$0.230525\pi$
$318$		−	5.28606i		−	0.296428i
$319$	−11.4929	−	8.35010i	−0.643481	−	0.467516i
$320$	0.190955	−	7.48379i	0.0106747	−	0.418357i
$321$	1.83197	−	1.33100i	0.102251	−	0.0742894i
$322$	0.852865	+	1.17387i	0.0475283	+	0.0654171i
$323$	−5.92389	+	1.92479i	−0.329614	+	0.107098i
$324$	1.37421			0.0763448
$325$	−8.89832	−	13.6621i	−0.493590	−	0.757838i
$326$	−7.56409			−0.418936
$327$	−4.74376	+	1.54134i	−0.262331	+	0.0852364i
$328$	18.3240	+	25.2208i	1.01177	+	1.39258i
$329$	−5.81527	+	4.22504i	−0.320606	+	0.232934i
$330$	−2.23828	+	2.92103i	−0.123213	+	0.160798i
$331$	12.9168	+	9.38463i	0.709973	+	0.515826i	0.883165	−	0.469062i	$-0.155408\pi$
$331$	12.9168	+	9.38463i	0.709973	+	0.515826i	−0.173192	+	0.984888i	$0.555408\pi$
$332$			7.44010i			0.408329i
$333$	−2.15454	+	2.96547i	−0.118068	+	0.162507i
$334$	−2.91671	+	8.97670i	−0.159595	+	0.491183i
$335$	25.5774	−	17.6041i	1.39744	−	0.961814i
$336$	−0.196799	−	0.605686i	−0.0107363	−	0.0330429i
$337$	−28.0410	−	9.11108i	−1.52749	−	0.496312i	−0.579599	−	0.814901i	$-0.696791\pi$
$337$	−28.0410	−	9.11108i	−1.52749	−	0.496312i	−0.947893	+	0.318589i	$0.896791\pi$
$338$	1.78057	+	0.578541i	0.0968500	+	0.0314685i
$339$	2.42985	+	7.47830i	0.131971	+	0.406166i
$340$	1.63753	−	4.63410i	0.0888076	−	0.251320i
$341$	−2.26544	+	6.97232i	−0.122681	+	0.377572i
$342$	1.81074	−	2.49227i	0.0979134	−	0.134766i
$343$		−	1.00000i		−	0.0539949i
$344$	10.1328	+	7.36192i	0.546325	+	0.396928i
$345$	2.32532	+	3.37851i	0.125191	+	0.181893i
$346$	7.60999	−	5.52898i	0.409115	−	0.297240i
$347$	−12.8765	−	17.7230i	−0.691247	−	0.951420i	−1.00000		0.000277780i	$-0.999912\pi$
$347$	−12.8765	−	17.7230i	−0.691247	−	0.951420i	0.308753	−	0.951142i	$-0.400088\pi$
$348$	−8.92452	+	2.89975i	−0.478405	+	0.155443i
$349$	32.5762			1.74377			0.871883	−	0.489715i	$-0.162899\pi$
$349$	32.5762			1.74377			0.871883	+	0.489715i	$0.162899\pi$
$350$	1.41253	−	3.69454i	0.0755027	−	0.197481i
$351$	−3.26088			−0.174053
$352$	−11.5594	+	3.75587i	−0.616117	+	0.200189i
$353$	−2.30252	−	3.16915i	−0.122551	−	0.168677i	0.743333	−	0.668921i	$-0.233244\pi$
$353$	−2.30252	−	3.16915i	−0.122551	−	0.168677i	−0.865884	+	0.500244i	$0.833244\pi$
$354$	−1.45305	+	1.05570i	−0.0772285	+	0.0561098i
$355$	−2.13209	+	0.633107i	−0.113160	+	0.0336019i
$356$	4.11588	+	2.99036i	0.218141	+	0.158489i
$357$			1.59948i			0.0846536i
$358$	−6.41180	+	8.82508i	−0.338874	+	0.466420i
$359$	3.51393	−	10.8148i	0.185458	−	0.570782i	−0.814498	−	0.580167i	$-0.802987\pi$
$359$	3.51393	−	10.8148i	0.185458	−	0.570782i	0.999956	+	0.00938489i	$0.00298735\pi$
$360$	1.69900	+	5.72167i	0.0895454	+	0.301559i
$361$	−1.18508	−	3.64731i	−0.0623727	−	0.191964i
$362$	14.7441	+	4.79066i	0.774935	+	0.251792i
$363$	−6.34539	−	2.06174i	−0.333047	−	0.108213i
$364$	1.38474	+	4.26180i	0.0725803	+	0.223379i
$365$	7.48470	+	0.190979i	0.391767	+	0.00999628i
$366$	−2.36447	+	7.27710i	−0.123593	+	0.380380i
$367$	−16.7642	+	23.0739i	−0.875083	+	1.20445i	0.102676	+	0.994715i	$0.467259\pi$
$367$	−16.7642	+	23.0739i	−0.875083	+	1.20445i	−0.977759	+	0.209733i	$0.932741\pi$
$368$			1.16812i			0.0608925i
$369$	−9.44867	−	6.86486i	−0.491878	−	0.357371i
$370$	−6.11345	−	2.16028i	−0.317823	−	0.112308i
$371$	5.40598	−	3.92767i	0.280664	−	0.203915i
$372$	2.84639	+	3.91772i	0.147579	+	0.203125i
$373$	28.0280	−	9.10686i	1.45124	−	0.471536i	0.525856	−	0.850574i	$-0.323745\pi$
$373$	28.0280	−	9.10686i	1.45124	−	0.471536i	0.925381	+	0.379038i	$0.123745\pi$
$374$	2.63234			0.136115
$375$	4.25777	−	10.3379i	0.219870	−	0.533845i
$376$	19.1867			0.989477
$377$	21.1772	−	6.88088i	1.09068	−	0.354383i
$378$	−0.464980	−	0.639990i	−0.0239160	−	0.0329175i
$379$	22.4824	−	16.3344i	1.15484	−	0.839043i	0.165726	−	0.986172i	$-0.447003\pi$
$379$	22.4824	−	16.3344i	1.15484	−	0.839043i	0.989117	+	0.147129i	$0.0470033\pi$
$380$	−11.2826	−	3.98686i	−0.578783	−	0.204522i
$381$	−11.0714	−	8.04385i	−0.567205	−	0.412099i
$382$			1.36985i			0.0700877i
$383$	12.8243	−	17.6511i	0.655291	−	0.901930i	−0.344023	−	0.938961i	$-0.611790\pi$
$383$	12.8243	−	17.6511i	0.655291	−	0.901930i	0.999314	+	0.0370306i	$0.0117899\pi$
$384$	−2.79230	+	8.59383i	−0.142494	+	0.438552i
$385$	−4.65040	−	0.118659i	−0.237006	−	0.00604742i
$386$	−3.25542	−	10.0192i	−0.165697	−	0.509962i
$387$	−4.46264	−	1.45000i	−0.226849	−	0.0737076i
$388$	21.9586	+	7.13478i	1.11478	+	0.362214i
$389$	−5.62549	−	17.3135i	−0.285224	−	0.877828i	−0.986331	−	0.164773i	$-0.947311\pi$
$389$	−5.62549	−	17.3135i	−0.285224	−	0.877828i	0.701108	−	0.713055i	$-0.252689\pi$
$390$	−1.64194	−	5.52950i	−0.0831429	−	0.279997i
$391$	0.906584	−	2.79018i	0.0458479	−	0.141105i
$392$	−1.56894	+	2.15946i	−0.0792434	+	0.109069i
$393$		−	19.1650i		−	0.966745i
$394$	9.61124	+	6.98298i	0.484207	+	0.351797i
$395$	−6.16720	+	1.83130i	−0.310305	+	0.0921427i
$396$	2.31290	−	1.68042i	0.116227	−	0.0844442i
$397$	−15.5121	−	21.3506i	−0.778531	−	1.07156i	−0.995442	−	0.0953649i	$-0.969598\pi$
$397$	−15.5121	−	21.3506i	−0.778531	−	1.07156i	0.216911	−	0.976191i	$-0.430402\pi$
$398$	−1.85765	+	0.603586i	−0.0931154	+	0.0302550i
$399$	3.89423			0.194955
$400$	2.66824	−	1.73786i	0.133412	−	0.0868929i
$401$	−34.0042			−1.69809			−0.849046	−	0.528320i	$-0.822822\pi$
$401$	−34.0042			−1.69809			−0.849046	+	0.528320i	$0.822822\pi$
$402$	10.4472	−	3.39450i	0.521059	−	0.169302i
$403$	−6.75426	−	9.29644i	−0.336454	−	0.463089i
$404$	17.0148	−	12.3620i	0.846519	−	0.615032i
$405$	−1.26776	−	1.84195i	−0.0629953	−	0.0915274i
$406$	4.37018	+	3.17512i	0.216889	+	0.157579i
$407$			7.62576i			0.377995i
$408$	2.50949	−	3.45402i	0.124238	−	0.170999i
$409$	10.5192	−	32.3747i	0.520139	−	1.60082i	−0.253592	−	0.967311i	$-0.581612\pi$
$409$	10.5192	−	32.3747i	0.520139	−	1.60082i	0.773732	−	0.633513i	$-0.218388\pi$
$410$	6.88315	−	19.4788i	0.339934	−	0.961992i
$411$	−2.37294	−	7.30315i	−0.117048	−	0.360238i
$412$	8.46734	+	2.75120i	0.417156	+	0.135542i
$413$	−2.15930	−	0.701598i	−0.106252	−	0.0345234i
$414$	0.448378	+	1.37997i	0.0220366	+	0.0678216i
$415$	9.97253	−	6.86377i	0.489532	−	0.336929i
$416$	5.88707	−	18.1185i	0.288637	−	0.888334i
$417$	−7.69935	+	10.5973i	−0.377039	+	0.518950i
$418$		−	6.40890i		−	0.313469i
$419$	−7.93838	−	5.76757i	−0.387815	−	0.281764i	0.376744	−	0.926317i	$-0.377044\pi$
$419$	−7.93838	−	5.76757i	−0.387815	−	0.281764i	−0.764560	+	0.644553i	$0.777044\pi$
$420$	−1.86898	+	2.43908i	−0.0911969	+	0.119015i
$421$	27.1971	−	19.7599i	1.32551	−	0.963037i	0.325660	−	0.945487i	$-0.394413\pi$
$421$	27.1971	−	19.7599i	1.32551	−	0.963037i	0.999846	−	0.0175499i	$-0.00558660\pi$
$422$	−2.84232	−	3.91212i	−0.138362	−	0.190439i
$423$	−6.83626	+	2.22124i	−0.332390	+	0.108000i
$424$	−17.8363			−0.866205
$425$	−7.72213	+	2.08023i	−0.374578	+	0.100906i
$426$	−0.786839			−0.0381225
$427$	−9.19904	+	2.98895i	−0.445173	+	0.144645i
$428$	−1.82907	−	2.51750i	−0.0884116	−	0.121688i
$429$	−5.48831	+	3.98749i	−0.264978	+	0.192518i
$430$	0.211717	−	8.29745i	0.0102099	−	0.400139i
$431$	−22.5179	−	16.3602i	−1.08465	−	0.788044i	−0.106162	−	0.994349i	$-0.533856\pi$
$431$	−22.5179	−	16.3602i	−1.08465	−	0.788044i	−0.978488	+	0.206305i	$0.933856\pi$
$432$		−	0.636856i		−	0.0306408i
$433$	−7.92258	+	10.9045i	−0.380735	+	0.524037i	−0.955779	−	0.294086i	$-0.904985\pi$
$433$	−7.92258	+	10.9045i	−0.380735	+	0.524037i	0.575044	+	0.818122i	$0.304985\pi$
$434$	0.861434	−	2.65122i	0.0413502	−	0.127263i
$435$	12.1200	+	9.28709i	0.581108	+	0.445282i
$436$	2.11812	+	6.51891i	0.101440	+	0.312199i
$437$	−6.79319	−	2.20724i	−0.324962	−	0.105587i
$438$	2.51914	+	0.818519i	0.120369	+	0.0391104i
$439$	7.19846	+	22.1546i	0.343564	+	1.05738i	0.962348	+	0.271819i	$0.0876253\pi$
$439$	7.19846	+	22.1546i	0.343564	+	1.05738i	−0.618785	+	0.785561i	$0.712375\pi$
$440$	9.85617	+	7.55243i	0.469875	+	0.360048i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	−2.42521	+	3.33801i	−0.115355	+	0.158773i
$443$		−	11.2026i		−	0.532254i	−0.963938	−	0.266127i	$-0.914256\pi$
$443$		−	11.2026i		−	0.532254i	0.963938	−	0.266127i	$-0.0857440\pi$
$444$	4.07517	+	2.96079i	0.193399	+	0.140513i
$445$	0.211158	−	8.27555i	0.0100098	−	0.392299i
$446$	6.62885	−	4.81614i	0.313885	−	0.228051i
$447$	−4.37698	−	6.02440i	−0.207024	−	0.284944i
$448$	3.18408	−	1.03457i	0.150434	−	0.0488789i
$449$	40.6943			1.92048			0.960241	−	0.279172i	$-0.0900600\pi$
$449$	40.6943			1.92048			0.960241	+	0.279172i	$0.0900600\pi$
$450$	2.48507	−	3.07722i	0.117147	−	0.145062i
$451$	−24.2974			−1.14412
$452$	10.2767	−	3.33911i	0.483377	−	0.157059i
$453$	−8.83017	−	12.1537i	−0.414878	−	0.571030i
$454$	−2.02065	+	1.46809i	−0.0948336	+	0.0689006i
$455$	4.43494	−	5.78775i	0.207913	−	0.271334i
$456$	−8.40942	−	6.10980i	−0.393807	−	0.286118i
$457$			25.2812i			1.18261i	0.806450	+	0.591303i	$0.201386\pi$
$457$			25.2812i			1.18261i	−0.806450	+	0.591303i	$0.798614\pi$
$458$	−11.5897	+	15.9518i	−0.541549	+	0.745378i
$459$	−0.494267	+	1.52120i	−0.0230704	+	0.0710034i
$460$	4.64277	−	3.19546i	0.216470	−	0.148989i
$461$	3.47641	+	10.6993i	0.161913	+	0.498315i	0.998796	−	0.0490663i	$-0.0156246\pi$
$461$	3.47641	+	10.6993i	0.161913	+	0.498315i	−0.836883	+	0.547382i	$0.815625\pi$
$462$	−1.56519	−	0.508563i	−0.0728195	−	0.0236605i
$463$	−29.5304	−	9.59500i	−1.37239	−	0.445918i	−0.472232	−	0.881474i	$-0.656551\pi$
$463$	−29.5304	−	9.59500i	−1.37239	−	0.445918i	−0.900161	+	0.435557i	$0.856551\pi$
$464$	1.34385	+	4.13594i	0.0623866	+	0.192006i
$465$	2.62532	−	7.42949i	0.121746	−	0.344534i
$466$	−6.84448	+	21.0652i	−0.317065	+	0.975824i
$467$	−20.1101	+	27.6792i	−0.930584	+	1.28084i	0.0290478	+	0.999578i	$0.490752\pi$
$467$	−20.1101	+	27.6792i	−0.930584	+	1.28084i	−0.959631	+	0.281260i	$0.909248\pi$
$468$			4.48112i			0.207140i
$469$	11.2340	+	8.16200i	0.518739	+	0.376886i
$470$	−7.20881	−	10.4739i	−0.332518	−	0.483123i
$471$	10.2253	−	7.42914i	0.471159	−	0.342317i
$472$	3.56215	+	4.90287i	0.163961	+	0.225673i
$473$	−9.28407	+	3.01658i	−0.426882	+	0.138702i
$474$	−2.27598			−0.104539
$475$	5.06468	+	18.8009i	0.232384	+	0.862644i
$476$	2.19802			0.100746
$477$	6.35511	−	2.06490i	0.290980	−	0.0945453i
$478$	−4.85231	−	6.67863i	−0.221939	−	0.305473i
$479$	−4.59881	+	3.34123i	−0.210125	+	0.152665i	−0.687870	−	0.725834i	$-0.741454\pi$
$479$	−4.59881	+	3.34123i	−0.210125	+	0.152665i	0.477745	+	0.878498i	$0.341454\pi$
$480$	12.5233	−	3.71868i	0.571606	−	0.169734i
$481$	−9.67005	−	7.02570i	−0.440916	−	0.320345i
$482$		−	6.85388i		−	0.312186i
$483$	−1.07811	+	1.48390i	−0.0490559	+	0.0675197i
$484$	−2.83326	+	8.71988i	−0.128785	+	0.396358i
$485$	−10.6943	−	36.0149i	−0.485605	−	1.63535i
$486$	−0.244454	−	0.752353i	−0.0110887	−	0.0341274i
$487$	−19.3783	−	6.29640i	−0.878115	−	0.285317i	−0.164941	−	0.986303i	$-0.552743\pi$
$487$	−19.3783	−	6.29640i	−0.878115	−	0.285317i	−0.713174	+	0.700987i	$0.752743\pi$
$488$	24.5544	+	7.97822i	1.11153	+	0.361157i
$489$	−2.95477	−	9.09384i	−0.133619	−	0.411238i
$490$	1.76831	+	0.0451201i	0.0798843	+	0.00203832i
$491$	4.41133	−	13.5767i	0.199080	−	0.612707i	−0.800824	−	0.598899i	$-0.795605\pi$
$491$	4.41133	−	13.5767i	0.199080	−	0.612707i	0.999905	−	0.0138071i	$-0.00439508\pi$
$492$	−9.43374	+	12.9844i	−0.425306	+	0.585383i
$493$		−	10.9221i		−	0.491906i
$494$	8.12698	+	5.90460i	0.365650	+	0.265660i
$495$	−4.38612	−	1.54990i	−0.197142	−	0.0696630i
$496$	1.81561	−	1.31912i	0.0815234	−	0.0592302i
$497$	−0.584640	−	0.804688i	−0.0262247	−	0.0360952i
$498$	4.07332	−	1.32350i	0.182530	−	0.0593076i
$499$	43.1702			1.93256			0.966282	−	0.257485i	$-0.0828938\pi$
$499$	43.1702			1.93256			0.966282	+	0.257485i	$0.0828938\pi$
$500$	−14.2064	−	5.85106i	−0.635328	−	0.261667i
$501$	−11.9315			−0.533060
$502$	10.3958	−	3.37781i	0.463988	−	0.150759i
$503$	14.0392	+	19.3233i	0.625977	+	0.861583i	0.997771	−	0.0667319i	$-0.0212572\pi$
$503$	14.0392	+	19.3233i	0.625977	+	0.861583i	−0.371794	+	0.928315i	$0.621257\pi$
$504$	−2.15946	+	1.56894i	−0.0961899	+	0.0698861i
$505$	−32.2665	−	11.4019i	−1.43584	−	0.507376i
$506$	2.44211	+	1.77430i	0.108565	+	0.0788772i
$507$			2.36666i			0.105107i
$508$	−11.0539	+	15.2144i	−0.490438	+	0.675030i
$509$	−2.18983	+	6.73960i	−0.0970624	+	0.298727i	−0.987786	−	0.155819i	$-0.950198\pi$
$509$	−2.18983	+	6.73960i	−0.0970624	+	0.298727i	0.890723	+	0.454546i	$0.150198\pi$
$510$	−2.82839	−	0.0721687i	−0.125243	−	0.00319568i
$511$	1.03470	+	3.18447i	0.0457723	+	0.140873i
$512$	6.77203	+	2.20036i	0.299284	+	0.0972433i
$513$	3.70363	+	1.20338i	0.163519	+	0.0531306i
$514$	−5.83836	−	17.9686i	−0.257519	−	0.792563i
$515$	−4.12378	−	13.8875i	−0.181716	−	0.611957i
$516$	−1.99260	+	6.13259i	−0.0877192	+	0.269972i
$517$	−8.78977	+	12.0981i	−0.386574	+	0.532073i
$518$		−	2.89969i		−	0.127405i
$519$	9.61985	+	6.98923i	0.422265	+	0.306793i
$520$	−18.6577	+	5.54025i	−0.818194	+	0.242956i
$521$	−17.2693	+	12.5468i	−0.756580	+	0.549687i	−0.897859	−	0.440282i	$-0.854878\pi$
$521$	−17.2693	+	12.5468i	−0.756580	+	0.549687i	0.141280	+	0.989970i	$0.454878\pi$
$522$	3.17512	+	4.37018i	0.138971	+	0.191278i
$523$	4.91758	−	1.59782i	0.215031	−	0.0698677i	−0.199521	−	0.979894i	$-0.563938\pi$
$523$	4.91758	−	1.59782i	0.215031	−	0.0698677i	0.414551	+	0.910026i	$0.363938\pi$
$524$	−26.3366			−1.15052
$525$	4.99349	+	0.254993i	0.217934	+	0.0111288i
$526$	−1.53364			−0.0668698
$527$	−5.36056	+	1.74175i	−0.233510	+	0.0758719i
$528$	−0.778765	−	1.07188i	−0.0338914	−	0.0466475i
$529$	−15.8856	+	11.5416i	−0.690680	+	0.501808i
$530$	6.70144	+	9.73668i	0.291092	+	0.422934i
$531$	−1.83681	−	1.33452i	−0.0797106	−	0.0579132i
$532$		−	5.35147i		−	0.232016i
$533$	22.3855	−	30.8110i	0.969624	−	1.33457i
$534$	0.905006	−	2.78532i	0.0391634	−	0.120533i
$535$	−1.68701	+	4.77414i	−0.0729360	+	0.206404i
$536$	−11.4537	−	35.2510i	−0.494726	−	1.52261i
$537$	−13.1145	−	4.26116i	−0.565933	−	0.183883i
$538$	20.6116	+	6.69712i	0.888629	+	0.288733i
$539$	−0.642878	−	1.97858i	−0.0276907	−	0.0852233i
$540$	−2.53122	+	1.74216i	−0.108927	+	0.0749706i
$541$	4.00209	−	12.3172i	0.172063	−	0.529556i	−0.827424	−	0.561578i	$-0.810194\pi$
$541$	4.00209	−	12.3172i	0.172063	−	0.529556i	0.999487	+	0.0320215i	$0.0101945\pi$
$542$	−5.70757	+	7.85580i	−0.245161	+	0.337435i
$543$			19.5974i			0.841004i
$544$	−7.55995	−	5.49263i	−0.324130	−	0.235494i
$545$	6.78374	−	8.85302i	0.290584	−	0.379222i
$546$	2.08693	−	1.51624i	0.0893124	−	0.0648892i
$547$	−5.80597	−	7.99124i	−0.248246	−	0.341681i	0.666650	−	0.745371i	$-0.267727\pi$
$547$	−5.80597	−	7.99124i	−0.248246	−	0.341681i	−0.914896	+	0.403690i	$0.867727\pi$
$548$	−10.0360	+	3.26090i	−0.428718	+	0.139299i
$549$	−9.67245			−0.412810
$550$	0.419653	−	8.21801i	0.0178940	−	0.350417i
$551$	−26.5918			−1.13285
$552$	4.65629	−	1.51292i	0.198185	−	0.0643941i
$553$	−1.69111	−	2.32761i	−0.0719132	−	0.0989800i
$554$	−8.93106	+	6.48880i	−0.379444	+	0.275682i
$555$	0.209069	−	8.19370i	0.00887450	−	0.347803i
$556$	14.5628	+	10.5805i	0.617601	+	0.448713i
$557$			12.2950i			0.520956i	0.965480	+	0.260478i	$0.0838802\pi$
$557$			12.2950i			0.520956i	−0.965480	+	0.260478i	$0.916120\pi$
$558$	1.63855	−	2.25526i	0.0693652	−	0.0954730i
$559$	4.72827	−	14.5521i	0.199985	−	0.615489i
$560$	1.13036	+	0.866152i	0.0477663	+	0.0366016i
$561$	1.02827	+	3.16470i	0.0434137	+	0.133614i
$562$	−17.7193	−	5.75736i	−0.747445	−	0.242860i
$563$	41.3346	+	13.4304i	1.74205	+	0.566025i	0.995101	−	0.0988618i	$-0.0315202\pi$
$563$	41.3346	+	13.4304i	1.74205	+	0.566025i	0.746944	+	0.664887i	$0.231520\pi$
$564$	3.05244	+	9.39444i	0.128531	+	0.395577i
$565$	−13.9563	−	10.6942i	−0.587147	−	0.449910i
$566$	5.25986	−	16.1882i	0.221089	−	0.680441i
$567$	0.587785	−	0.809017i	0.0246847	−	0.0339755i
$568$			2.65496i			0.111399i
$569$	35.2860	+	25.6368i	1.47926	+	1.07475i	0.977793	+	0.209575i	$0.0672081\pi$
$569$	35.2860	+	25.6368i	1.47926	+	1.07475i	0.501472	+	0.865174i	$0.332792\pi$
$570$	−0.175708	+	6.88621i	−0.00735958	+	0.288432i
$571$	10.7527	−	7.81231i	0.449987	−	0.326935i	−0.339604	−	0.940569i	$-0.610293\pi$
$571$	10.7527	−	7.81231i	0.449987	−	0.326935i	0.789591	+	0.613634i	$0.210293\pi$
$572$	5.47964	+	7.54208i	0.229115	+	0.315350i
$573$	−1.64689	+	0.535107i	−0.0687998	+	0.0223544i
$574$	9.23908			0.385632
$575$	−8.56625	−	3.27512i	−0.357237	−	0.136582i
$576$	3.34794			0.139498
$577$	22.9013	−	7.44108i	0.953393	−	0.309776i	0.209299	−	0.977852i	$-0.432882\pi$
$577$	22.9013	−	7.44108i	0.953393	−	0.309776i	0.744094	+	0.668075i	$0.232882\pi$
$578$	−6.71508	−	9.24252i	−0.279311	−	0.384438i
$579$	10.7738	−	7.82759i	0.447742	−	0.325304i
$580$	12.7624	−	16.6553i	0.529929	−	0.691575i
$581$	4.38010	+	3.18233i	0.181717	+	0.132025i
$582$		−	13.2911i		−	0.550935i
$583$	8.17112	−	11.2466i	0.338413	−	0.465786i
$584$	2.76185	−	8.50011i	0.114286	−	0.351737i
$585$	6.00639	−	4.13400i	0.248334	−	0.170920i
$586$	−5.71310	−	17.5831i	−0.236006	−	0.726352i
$587$	24.8289	+	8.06740i	1.02480	+	0.332977i	0.772732	−	0.634733i	$-0.218890\pi$
$587$	24.8289	+	8.06740i	1.02480	+	0.332977i	0.252066	+	0.967710i	$0.418890\pi$
$588$	−1.30695	−	0.424653i	−0.0538976	−	0.0175124i
$589$	4.24060	+	13.0512i	0.174731	+	0.537767i
$590$	1.33807	−	3.78666i	0.0550876	−	0.155894i
$591$	−4.64076	+	14.2828i	−0.190895	+	0.587515i
$592$	1.37213	−	1.88858i	0.0563943	−	0.0776202i
$593$			1.80277i			0.0740309i	0.999315	+	0.0370155i	$0.0117851\pi$
$593$			1.80277i			0.0740309i	−0.999315	+	0.0370155i	$0.988215\pi$
$594$	−1.33143	−	0.967344i	−0.0546294	−	0.0396906i
$595$	−2.02775	−	2.94617i	−0.0831298	−	0.120781i
$596$	−8.27877	+	6.01488i	−0.339112	+	0.246379i
$597$	−1.45131	−	1.99755i	−0.0593981	−	0.0817545i
$598$	−4.49990	+	1.46211i	−0.184015	+	0.0597900i
$599$	−24.1820			−0.988048			−0.494024	−	0.869448i	$-0.664474\pi$
$599$	−24.1820			−0.988048			−0.494024	+	0.869448i	$0.664474\pi$
$600$	−10.3832	−	8.38513i	−0.423891	−	0.342321i
$601$	−41.6119			−1.69739			−0.848693	−	0.528885i	$-0.822610\pi$
$601$	−41.6119			−1.69739			−0.848693	+	0.528885i	$0.822610\pi$
$602$	3.53026	−	1.14705i	0.143883	−	0.0467504i
$603$	8.16200	+	11.2340i	0.332382	+	0.457485i
$604$	−16.7017	+	12.1345i	−0.679581	+	0.493745i
$605$	14.3017	−	4.24678i	0.581447	−	0.172656i
$606$	−9.79470	−	7.11626i	−0.397882	−	0.289078i
$607$		−	1.87483i		−	0.0760970i	−0.999276	−	0.0380485i	$-0.987886\pi$
$607$		−	1.87483i		−	0.0760970i	0.999276	−	0.0380485i	$-0.0121141\pi$
$608$	−13.3728	+	18.4061i	−0.542338	+	0.746464i
$609$	−2.11013	+	6.49431i	−0.0855067	+	0.263163i
$610$	−4.87034	−	16.4017i	−0.197194	−	0.664083i
$611$	−7.24319	−	22.2922i	−0.293028	−	0.901847i
$612$	2.09044	+	0.679225i	0.0845010	+	0.0274560i
$613$	−8.24991	−	2.68056i	−0.333211	−	0.108267i	0.137633	−	0.990483i	$-0.456051\pi$
$613$	−8.24991	−	2.68056i	−0.333211	−	0.108267i	−0.470844	+	0.882217i	$0.656051\pi$
$614$	6.73074	+	20.7151i	0.271631	+	0.835993i
$615$	26.1070	+	0.666143i	1.05274	+	0.0268615i
$616$	−1.71600	+	5.28129i	−0.0691394	+	0.212789i
$617$	−0.405303	+	0.557851i	−0.0163169	+	0.0224583i	−0.817097	−	0.576500i	$-0.804418\pi$
$617$	−0.405303	+	0.557851i	−0.0163169	+	0.0224583i	0.800781	+	0.598958i	$0.204418\pi$
$618$		−	5.12512i		−	0.206163i
$619$	7.25430	+	5.27055i	0.291575	+	0.211841i	0.723950	−	0.689852i	$-0.242324\pi$
$619$	7.25430	+	5.27055i	0.291575	+	0.211841i	−0.432375	+	0.901694i	$0.642324\pi$
$620$	−10.2096	−	3.60773i	−0.410029	−	0.144890i
$621$	−1.48390	+	1.07811i	−0.0595468	+	0.0432632i
$622$	−4.46331	−	6.14322i	−0.178962	−	0.246321i
$623$	3.52095	−	1.14403i	0.141064	−	0.0458344i
$624$	2.07671			0.0831350
$625$	5.26327	+	24.4397i	0.210531	+	0.977587i
$626$	3.39728			0.135782
$627$	7.70502	−	2.50351i	0.307709	−	0.0999807i
$628$	−10.2092	−	14.0517i	−0.407390	−	0.560725i
$629$	−4.74322	+	3.44615i	−0.189125	+	0.137407i
$630$	1.66782	+	0.589351i	0.0664477	+	0.0234803i
$631$	6.17840	+	4.48887i	0.245958	+	0.178699i	0.703934	−	0.710266i	$-0.251425\pi$
$631$	6.17840	+	4.48887i	0.245958	+	0.178699i	−0.457975	+	0.888965i	$0.651425\pi$
$632$			7.67962i			0.305479i
$633$	3.59300	−	4.94534i	0.142809	−	0.196560i
$634$	0.833474	−	2.56517i	0.0331015	−	0.101876i
$635$	30.5907	+	0.780547i	1.21395	+	0.0309751i
$636$	−2.83760	−	8.73323i	−0.112518	−	0.346295i
$637$	3.10128	+	1.00767i	0.122877	+	0.0399252i
$638$	10.6880	+	3.47273i	0.423141	+	0.137487i
$639$	−0.307364	−	0.945968i	−0.0121591	−	0.0374219i
$640$	−5.75159	−	19.3694i	−0.227351	−	0.765643i
$641$	−4.83089	+	14.8679i	−0.190809	+	0.587249i	−1.00000		0.000296639i	$-0.999906\pi$
$641$	−4.83089	+	14.8679i	−0.190809	+	0.587249i	0.809191	+	0.587545i	$0.199906\pi$
$642$	−1.05292	+	1.44922i	−0.0415554	+	0.0571961i
$643$			30.1733i			1.18992i	0.803755	+	0.594960i	$0.202832\pi$
$643$			30.1733i			1.18992i	−0.803755	+	0.594960i	$0.797168\pi$
$644$	2.03918	+	1.48155i	0.0803550	+	0.0583813i
$645$	10.0582	−	2.98671i	0.396042	−	0.117602i
$646$	3.98633	−	2.89624i	0.156840	−	0.113951i
$647$	−5.32854	−	7.33410i	−0.209486	−	0.288333i	0.691325	−	0.722544i	$-0.257027\pi$
$647$	−5.32854	−	7.33410i	−0.209486	−	0.288333i	−0.900811	+	0.434211i	$0.857027\pi$
$648$	−2.53860	+	0.824840i	−0.0997255	+	0.0324028i
$649$	−4.72338			−0.185409
$650$	10.0344	+	8.10351i	0.393583	+	0.317846i
$651$	3.52391			0.138113
$652$	−12.4968	+	4.06046i	−0.489413	+	0.159020i
$653$	−4.39864	−	6.05421i	−0.172132	−	0.236920i	0.714231	−	0.699910i	$-0.246777\pi$
$653$	−4.39864	−	6.05421i	−0.172132	−	0.236920i	−0.886363	+	0.462990i	$0.846777\pi$
$654$	3.19220	−	2.31927i	0.124825	−	0.0906905i
$655$	24.2965	+	35.3010i	0.949344	+	1.37932i
$656$	6.01745	+	4.37193i	0.234942	+	0.170695i
$657$			3.34835i			0.130632i
$658$	3.34231	−	4.60029i	0.130297	−	0.179338i
$659$	−12.2022	+	37.5545i	−0.475330	+	1.46291i	0.370183	+	0.928959i	$0.379295\pi$
$659$	−12.2022	+	37.5545i	−0.475330	+	1.46291i	−0.845513	+	0.533956i	$0.820705\pi$
$660$	−2.12989	+	6.02744i	−0.0829058	+	0.234618i
$661$	−7.34362	−	22.6013i	−0.285634	−	0.879090i	−0.986208	−	0.165510i	$-0.947073\pi$
$661$	−7.34362	−	22.6013i	−0.285634	−	0.879090i	0.700575	−	0.713579i	$-0.252927\pi$
$662$	−12.0121	−	3.90298i	−0.466865	−	0.151694i
$663$	−4.96044	−	1.61175i	−0.192648	−	0.0625950i
$664$	−4.46577	−	13.7442i	−0.173305	−	0.533379i
$665$	−7.17298	+	4.93693i	−0.278156	+	0.191446i
$666$	0.896054	−	2.75777i	0.0347214	−	0.106861i
$667$	7.36193	−	10.1328i	0.285055	−	0.392344i
$668$			16.3963i			0.634393i
$669$	8.37958	+	6.08812i	0.323973	+	0.235380i
$670$	−14.9398	+	19.4970i	−0.577177	+	0.753235i
$671$	−16.2795	+	11.8277i	−0.628462	+	0.456605i
$672$	3.43400	+	4.72650i	0.132470	+	0.182329i
$673$	30.3407	−	9.85830i	1.16955	−	0.380010i	0.341075	−	0.940036i	$-0.389209\pi$
$673$	30.3407	−	9.85830i	1.16955	−	0.380010i	0.828475	+	0.560027i	$0.189209\pi$
$674$	23.3240			0.898407
$675$	4.67030	+	1.78559i	0.179760	+	0.0687273i
$676$	3.25228			0.125088
$677$	−28.2054	+	9.16450i	−1.08402	+	0.352220i	−0.795934	−	0.605383i	$-0.793020\pi$
$677$	−28.2054	+	9.16450i	−1.08402	+	0.352220i	−0.288089	+	0.957604i	$0.593020\pi$
$678$	−3.65621	−	5.03234i	−0.140416	−	0.193266i
$679$	13.5926	−	9.87564i	0.521638	−	0.378992i
$680$	−0.243512	+	9.54356i	−0.00933827	+	0.365979i
$681$	−2.55432	−	1.85582i	−0.0978816	−	0.0711152i
$682$		−	5.79944i		−	0.222072i
$683$	−11.9108	+	16.3939i	−0.455755	+	0.627293i	−0.973622	−	0.228168i	$-0.926726\pi$
$683$	−11.9108	+	16.3939i	−0.455755	+	0.627293i	0.517866	+	0.855461i	$0.326726\pi$
$684$	1.65370	−	5.08955i	0.0632306	−	0.194604i
$685$	13.6295	+	10.4438i	0.520755	+	0.399035i
$686$	0.244454	+	0.752353i	0.00933331	+	0.0287250i
$687$	−23.7051	−	7.70227i	−0.904408	−	0.293860i
$688$	2.84206	+	0.923441i	0.108352	+	0.0352059i
$689$	6.73339	+	20.7232i	0.256522	+	0.789493i
$690$	−2.57535	−	1.97340i	−0.0980419	−	0.0751260i
$691$	−8.70480	+	26.7906i	−0.331146	+	1.01916i	0.637443	+	0.770497i	$0.279992\pi$
$691$	−8.70480	+	26.7906i	−0.331146	+	1.01916i	−0.968589	+	0.248665i	$0.920008\pi$
$692$	9.60464	−	13.2197i	0.365114	−	0.502536i
$693$		−	2.08040i		−	0.0790278i
$694$	14.0201	+	10.1862i	0.532198	+	0.386664i
$695$	0.747119	−	29.2806i	0.0283398	−	1.11067i
$696$	14.7459	−	10.7135i	0.558942	−	0.406095i
$697$	−10.9802	−	15.1130i	−0.415906	−	0.572445i
$698$	−24.5088	+	7.96340i	−0.927673	+	0.301419i
$699$	−27.9990			−1.05902
$700$	0.350413	−	6.86209i	0.0132444	−	0.259363i
$701$	−8.13535			−0.307268			−0.153634	−	0.988128i	$-0.549098\pi$
$701$	−8.13535			−0.307268			−0.153634	+	0.988128i	$0.549098\pi$
$702$	2.45333	−	0.797137i	0.0925951	−	0.0300860i
$703$	8.39027	+	11.5482i	0.316445	+	0.435549i
$704$	5.63485	−	4.09395i	0.212371	−	0.154297i
$705$	9.77609	−	12.7581i	0.368189	−	0.480499i
$706$	2.50702	+	1.82146i	0.0943531	+	0.0685515i
$707$		−	15.3045i		−	0.575583i
$708$	−1.83390	+	2.52415i	−0.0689223	+	0.0948635i
$709$	10.9126	−	33.5854i	0.409829	−	1.26133i	−0.506965	−	0.861967i	$-0.669233\pi$
$709$	10.9126	−	33.5854i	0.409829	−	1.26133i	0.916795	−	0.399359i	$-0.130767\pi$
$710$	1.44932	−	0.997520i	0.0543920	−	0.0374362i
$711$	−0.889067	−	2.73627i	−0.0333426	−	0.102618i
$712$	−9.39825	−	3.05368i	−0.352214	−	0.114441i
$713$	−6.14719	−	1.99734i	−0.230214	−	0.0748011i
$714$	−0.391000	−	1.20338i	−0.0146328	−	0.0450352i
$715$	5.05405	−	14.3026i	0.189011	−	0.534888i
$716$	−5.85571	+	18.0220i	−0.218838	+	0.673515i
$717$	6.13385	−	8.44251i	0.229073	−	0.315291i
$718$			8.99553i			0.335710i
$719$	−3.27800	−	2.38160i	−0.122249	−	0.0888189i	0.524981	−	0.851114i	$-0.324072\pi$
$719$	−3.27800	−	2.38160i	−0.122249	−	0.0888189i	−0.647230	+	0.762295i	$0.724072\pi$
$720$	0.807379	+	1.17306i	0.0300892	+	0.0437174i
$721$	5.24139	−	3.80809i	0.195199	−	0.141821i
$722$	1.78320	+	2.45437i	0.0663639	+	0.0913420i
$723$	8.24000	−	2.67734i	0.306449	−	0.0995713i
$724$	26.9308			1.00088
$725$	−34.0982	−	1.74122i	−1.26637	−	0.0646674i
$726$	5.27798			0.195884
$727$	10.7397	−	3.48955i	0.398314	−	0.129420i	−0.103009	−	0.994680i	$-0.532847\pi$
$727$	10.7397	−	3.48955i	0.398314	−	0.129420i	0.501323	+	0.865260i	$0.332847\pi$
$728$	−5.11612	−	7.04173i	−0.189616	−	0.260984i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−5.67783	+	1.68599i	−0.210146	+	0.0624011i
$731$	−6.07187	−	4.41147i	−0.224576	−	0.163164i
$732$			13.2919i			0.491284i
$733$	−10.0636	+	13.8513i	−0.371707	+	0.511610i	−0.953364	−	0.301824i	$-0.902405\pi$
$733$	−10.0636	+	13.8513i	−0.371707	+	0.511610i	0.581657	+	0.813434i	$0.302405\pi$
$734$	6.97206	−	21.4578i	0.257344	−	0.792022i
$735$	0.636513	+	2.14356i	0.0234781	+	0.0790664i
$736$	−3.31139	−	10.1914i	−0.122059	−	0.375660i
$737$	27.4745	+	8.92702i	1.01204	+	0.328831i
$738$	8.78689	+	2.85503i	0.323450	+	0.105095i
$739$	9.36403	+	28.8195i	0.344462	+	1.06014i	0.961871	+	0.273502i	$0.0881820\pi$
$739$	9.36403	+	28.8195i	0.344462	+	1.06014i	−0.617410	+	0.786642i	$0.711818\pi$
$740$	−11.2598	−	0.287304i	−0.413920	−	0.0105615i
$741$	−3.92408	+	12.0771i	−0.144155	+	0.443663i
$742$	−3.10707	+	4.27651i	−0.114064	+	0.156996i
$743$		−	15.9662i		−	0.585742i	−0.956152	−	0.292871i	$-0.905389\pi$
$743$		−	15.9662i		−	0.585742i	0.956152	−	0.292871i	$-0.0946107\pi$
$744$	−7.60973	−	5.52879i	−0.278986	−	0.202695i
$745$	15.6997	+	5.54772i	0.575192	+	0.203253i
$746$	−18.8608	+	13.7032i	−0.690542	+	0.501708i
$747$	3.18233	+	4.38010i	0.116435	+	0.160260i
$748$	4.34895	−	1.41306i	0.159013	−	0.0516666i
$749$	−2.26444			−0.0827408
$750$	−0.676214	+	8.81856i	−0.0246918	+	0.322008i
$751$	−9.53400			−0.347901			−0.173950	−	0.984754i	$-0.555653\pi$
$751$	−9.53400			−0.347901			−0.173950	+	0.984754i	$0.555653\pi$
$752$	4.35372	−	1.41461i	0.158764	−	0.0515855i
$753$	8.12186	+	11.1788i	0.295977	+	0.407378i
$754$	−14.2506	+	10.3537i	−0.518978	+	0.377060i
$755$	31.6727	+	11.1920i	1.15269	+	0.407319i
$756$	−1.11176	−	0.807738i	−0.0404342	−	0.0293772i
$757$			47.1305i			1.71299i	0.516158	+	0.856493i	$0.327362\pi$
$757$			47.1305i			1.71299i	−0.516158	+	0.856493i	$0.672638\pi$
$758$	−12.9217	+	17.7852i	−0.469337	+	0.645987i
$759$	−1.17917	+	3.62910i	−0.0428010	+	0.131728i
$760$	23.2355	+	0.592874i	0.842840	+	0.0215058i
$761$	−0.349340	−	1.07516i	−0.0126636	−	0.0389744i	0.944525	−	0.328439i	$-0.106523\pi$
$761$	−0.349340	−	1.07516i	−0.0126636	−	0.0389744i	−0.957189	+	0.289465i	$0.906523\pi$
$762$	10.2960	+	3.34536i	0.372983	+	0.121190i
$763$	4.74376	+	1.54134i	0.171736	+	0.0558003i
$764$	0.735347	+	2.26317i	0.0266039	+	0.0818785i
$765$	−1.01809	−	3.42859i	−0.0368092	−	0.123961i
$766$	−5.33351	+	16.4148i	−0.192707	+	0.593092i
$767$	4.35170	−	5.98961i	0.157131	−	0.216272i
$768$		−	13.8441i		−	0.499555i
$769$	−13.6967	−	9.95121i	−0.493914	−	0.358850i	0.312773	−	0.949828i	$-0.398742\pi$
$769$	−13.6967	−	9.95121i	−0.493914	−	0.358850i	−0.806688	+	0.590978i	$0.798742\pi$
$770$	3.52775	−	1.04754i	0.127131	−	0.0377506i
$771$	19.3219	−	14.0382i	0.695863	−	0.505574i
$772$	−10.7567	−	14.8054i	−0.387143	−	0.532857i
$773$	−0.571219	+	0.185600i	−0.0205453	+	0.00667558i	−0.319272	−	0.947663i	$-0.603438\pi$
$773$	−0.571219	+	0.185600i	−0.0205453	+	0.00667558i	0.298726	+	0.954339i	$0.403438\pi$
$774$	3.71194			0.133423
$775$	4.58306	+	17.0130i	0.164628	+	0.611126i
$776$	−44.8470			−1.60991
$777$	3.48612	−	1.13271i	0.125064	−	0.0406357i
$778$	8.46472	+	11.6507i	0.303475	+	0.417697i
$779$	−36.7953	+	26.7333i	−1.31833	+	0.957821i
$780$	−5.68097	−	8.25402i	−0.203411	−	0.295541i
$781$	−1.67407	−	1.21628i	−0.0599030	−	0.0435221i
$782$			2.32082i			0.0829923i
$783$	−4.01370	+	5.52439i	−0.143438	+	0.197426i
$784$	−0.196799	+	0.605686i	−0.00702855	+	0.0216317i
$785$	−9.41625	+	26.6474i	−0.336081	+	0.951086i
$786$	4.68496	+	14.4188i	0.167107	+	0.514303i
$787$	32.6670	+	10.6142i	1.16445	+	0.378354i	0.826570	−	0.562834i	$-0.190289\pi$
$787$	32.6670	+	10.6142i	1.16445	+	0.378354i	0.337883	+	0.941188i	$0.390289\pi$
$788$	19.6275	+	6.37736i	0.699200	+	0.227184i
$789$	−0.599087	−	1.84380i	−0.0213281	−	0.0656410i
$790$	4.19224	−	2.88538i	0.149153	−	0.102657i
$791$	2.42985	−	7.47830i	0.0863954	−	0.265898i
$792$	−3.26402	+	4.49253i	−0.115982	+	0.159635i
$793$		−	31.5407i		−	1.12004i
$794$	16.8898	+	12.2712i	0.599398	+	0.435488i
$795$	−9.08802	+	11.8602i	−0.322319	+	0.420637i
$796$	−2.74505	+	1.99440i	−0.0972958	+	0.0706895i
$797$	−9.99471	−	13.7565i	−0.354031	−	0.487282i	0.594443	−	0.804138i	$-0.297373\pi$
$797$	−9.99471	−	13.7565i	−0.354031	−	0.487282i	−0.948474	+	0.316856i	$0.897373\pi$
$798$	−2.92983	+	0.951961i	−0.103715	+	0.0336990i
$799$	−11.4972			−0.406741
$800$	−18.3529	+	22.7261i	−0.648873	+	0.803489i
$801$	3.70214			0.130809
$802$	25.5832	−	8.31249i	0.903375	−	0.293524i
$803$	4.09446	+	5.63553i	0.144490	+	0.198874i
$804$	15.4379	−	11.2163i	0.544452	−	0.395567i
$805$	0.104617	−	4.10006i	0.00368725	−	0.144508i
$806$	7.35415	+	5.34310i	0.259039	+	0.188203i
$807$			27.3962i			0.964391i
$808$	−24.0117	+	33.0493i	−0.844730	+	1.16267i
$809$	3.00067	−	9.23513i	0.105498	−	0.324690i	−0.884349	−	0.466826i	$-0.845397\pi$
$809$	3.00067	−	9.23513i	0.105498	−	0.324690i	0.989847	+	0.142137i	$0.0453973\pi$
$810$	1.40407	+	1.07589i	0.0493342	+	0.0378030i
$811$	−4.80487	−	14.7879i	−0.168722	−	0.519272i	0.830570	−	0.556915i	$-0.188015\pi$
$811$	−4.80487	−	14.7879i	−0.168722	−	0.519272i	−0.999291	+	0.0376429i	$0.988015\pi$
$812$	8.92452	+	2.89975i	0.313189	+	0.101761i
$813$	−11.6741	−	3.79315i	−0.409429	−	0.133031i
$814$	−1.86415	−	5.73726i	−0.0653384	−	0.201091i
$815$	16.9713	+	13.0045i	0.594479	+	0.455528i
$816$	0.314777	−	0.968784i	0.0110194	−	0.0339142i
$817$	−10.7405	+	14.7831i	−0.375763	+	0.517194i
$818$			26.9287i			0.941538i
$819$	2.63811	+	1.91670i	0.0921829	+	0.0669748i
$820$	0.915418	−	35.8764i	0.0319678	−	1.25286i
$821$	−7.92021	+	5.75437i	−0.276417	+	0.200829i	−0.717353	−	0.696710i	$-0.754647\pi$
$821$	−7.92021	+	5.75437i	−0.276417	+	0.200829i	0.440936	+	0.897539i	$0.354647\pi$
$822$	3.57057	+	4.91447i	0.124538	+	0.171412i
$823$	−42.5805	+	13.8352i	−1.48426	+	0.482266i	−0.935384	−	0.353635i	$-0.884946\pi$
$823$	−42.5805	+	13.8352i	−1.48426	+	0.482266i	−0.548880	+	0.835901i	$0.684946\pi$
$824$	−17.2932			−0.602438
$825$	10.0439	−	2.70569i	0.349685	−	0.0941999i
$826$	1.79606			0.0624930
$827$	45.8823	−	14.9081i	1.59548	−	0.518404i	0.629499	−	0.777001i	$-0.283260\pi$
$827$	45.8823	−	14.9081i	1.59548	−	0.518404i	0.965985	+	0.258597i	$0.0832601\pi$
$828$	1.48155	+	2.03918i	0.0514875	+	0.0708665i
$829$	16.6983	−	12.1320i	0.579957	−	0.421363i	−0.258752	−	0.965944i	$-0.583311\pi$
$829$	16.6983	−	12.1320i	0.579957	−	0.421363i	0.838709	+	0.544581i	$0.183311\pi$
$830$	−5.82499	+	7.60181i	−0.202188	+	0.263863i
$831$	−11.2898	−	8.20254i	−0.391640	−	0.284543i
$832$			10.9172i			0.378487i
$833$	0.940152	−	1.29401i	0.0325743	−	0.0448347i
$834$	3.20209	−	9.85502i	0.110879	−	0.341251i
$835$	21.9773	−	15.1262i	0.760554	−	0.523465i
$836$	−3.44034	−	10.5883i	−0.118987	−	0.366204i
$837$	3.35143	+	1.08895i	0.115842	+	0.0376395i
$838$	7.38237	+	2.39868i	0.255020	+	0.0828610i
$839$	1.32903	+	4.09032i	0.0458831	+	0.141214i	0.971373	−	0.237557i	$-0.0763468\pi$
$839$	1.32903	+	4.09032i	0.0458831	+	0.141214i	−0.925490	+	0.378771i	$0.876347\pi$
$840$	1.98859	−	5.62758i	0.0686129	−	0.194170i
$841$	5.44756	−	16.7659i	0.187847	−	0.578134i
$842$	−15.6315	+	21.5149i	−0.538696	+	0.741451i
$843$		−	23.5519i		−	0.811170i
$844$	−6.79592	−	4.93753i	−0.233925	−	0.169957i
$845$	−3.00035	−	4.35928i	−0.103215	−	0.149964i
$846$	4.60029	−	3.34231i	0.158161	−	0.114911i
$847$	3.92167	+	5.39771i	0.134750	+	0.185468i
$848$	−4.04729	+	1.31504i	−0.138985	+	0.0451588i
$849$	21.5167			0.738453
$850$	5.30125	−	3.45277i	0.181831	−	0.118429i
$851$	−6.72330			−0.230472
$852$	−1.29996	+	0.422381i	−0.0445357	+	0.0144705i
$853$	18.3504	+	25.2571i	0.628305	+	0.864787i	0.997924	−	0.0643958i	$-0.0205120\pi$
$853$	18.3504	+	25.2571i	0.628305	+	0.864787i	−0.369620	+	0.929183i	$0.620512\pi$
$854$	6.19027	−	4.49749i	0.211827	−	0.153901i
$855$	−8.34751	+	2.47873i	−0.285479	+	0.0847706i
$856$	4.88996	+	3.55276i	0.167135	+	0.121431i
$857$			11.9038i			0.406625i	0.979114	+	0.203313i	$0.0651708\pi$
$857$			11.9038i			0.406625i	−0.979114	+	0.203313i	$0.934829\pi$
$858$	3.15439	−	4.34165i	0.107689	−	0.148221i
$859$	2.13546	−	6.57227i	0.0728609	−	0.224243i	−0.907994	−	0.418983i	$-0.862387\pi$
$859$	2.13546	−	6.57227i	0.0728609	−	0.224243i	0.980855	+	0.194741i	$0.0623865\pi$
$860$	−4.10435	−	13.8221i	−0.139957	−	0.471329i
$861$	3.60907	+	11.1076i	0.122997	+	0.378545i
$862$	20.9408	+	6.80406i	0.713245	+	0.231747i
$863$	−42.0512	−	13.6633i	−1.43144	−	0.465103i	−0.512222	−	0.858853i	$-0.671177\pi$
$863$	−42.0512	−	13.6633i	−1.43144	−	0.465103i	−0.919217	+	0.393751i	$0.871177\pi$
$864$	1.80536	+	5.55633i	0.0614197	+	0.189030i
$865$	−26.5800	−	0.678211i	−0.903746	−	0.0230599i
$866$	3.29493	−	10.1407i	0.111966	−	0.344597i
$867$	8.48859	−	11.6835i	0.288288	−	0.396794i
$868$		−	4.84257i		−	0.164368i
$869$	−4.84235	−	3.51818i	−0.164266	−	0.119346i
$870$	−11.3888	−	4.02439i	−0.386115	−	0.136440i
$871$	−36.6328	+	26.6153i	−1.24126	+	0.901825i
$872$	−7.82569	−	10.7711i	−0.265011	−	0.364757i
$873$	15.9791	−	5.19193i	0.540811	−	0.175720i
$874$	5.65045			0.191129
$875$	−9.52105	+	5.86085i	−0.321870	+	0.198133i
$876$	4.60133			0.155464
$877$	−35.4625	+	11.5225i	−1.19748	+	0.389086i	−0.838835	−	0.544386i	$-0.816763\pi$
$877$	−35.4625	+	11.5225i	−1.19748	+	0.389086i	−0.358650	+	0.933472i	$0.616763\pi$
$878$	−10.8316	−	14.9084i	−0.365548	−	0.503133i
$879$	18.9074	−	13.7370i	0.637731	−	0.463338i
$880$	2.79333	+	0.987066i	0.0941632	+	0.0332740i
$881$	25.2394	+	18.3375i	0.850338	+	0.617807i	0.925239	−	0.379384i	$-0.123864\pi$
$881$	25.2394	+	18.3375i	0.850338	+	0.617807i	−0.0749014	+	0.997191i	$0.523864\pi$
$882$			0.791071i			0.0266368i
$883$	−7.67210	+	10.5597i	−0.258187	+	0.355364i	−0.918357	−	0.395752i	$-0.870484\pi$
$883$	−7.67210	+	10.5597i	−0.258187	+	0.355364i	0.660171	+	0.751116i	$0.270484\pi$
$884$	−2.21487	+	6.81667i	−0.0744942	+	0.229270i
$885$	5.07516	+	0.129497i	0.170600	+	0.00435300i
$886$	2.73854	+	8.42835i	0.0920029	+	0.283156i
$887$	−41.0291	−	13.3312i	−1.37762	−	0.447617i	−0.475735	−	0.879589i	$-0.657818\pi$
$887$	−41.0291	−	13.3312i	−1.37762	−	0.447617i	−0.901887	+	0.431972i	$0.857818\pi$
$888$	−9.30529	−	3.02347i	−0.312265	−	0.101461i
$889$	4.22890	+	13.0152i	0.141833	+	0.436516i
$890$	1.86413	+	6.27776i	0.0624858	+	0.210431i
$891$	0.642878	−	1.97858i	0.0215372	−	0.0662848i
$892$	8.36634	−	11.5153i	0.280126	−	0.385560i
$893$			27.9920i			0.936716i
$894$	4.76573	+	3.46251i	0.159390	+	0.115804i
$895$	29.5584	−	8.77714i	0.988029	−	0.293387i
$896$	7.31035	−	5.31128i	0.244222	−	0.177437i
$897$	−3.51560	−	4.83881i	−0.117383	−	0.161563i
$898$	−30.6165	+	9.94790i	−1.02169	+	0.331966i
$899$	−24.0631			−0.802548
$900$	2.45376	−	6.41795i	0.0817922	−	0.213932i
$901$	10.6880			0.356069
$902$	18.2802	−	5.93961i	0.608665	−	0.197767i
$903$	2.75806	+	3.79615i	0.0917826	+	0.126328i
$904$	−16.9801	+	12.3368i	−0.564751	+	0.410316i
$905$	−24.8447	−	36.0975i	−0.825866	−	1.19992i
$906$	9.61443	+	6.98529i	0.319418	+	0.232071i
$907$		−	47.4140i		−	1.57436i	−0.616725	−	0.787179i	$-0.711541\pi$
$907$		−	47.4140i		−	1.57436i	0.616725	−	0.787179i	$-0.288459\pi$
$908$	−2.55028	+	3.51016i	−0.0846340	+	0.116489i
$909$	4.72934	−	14.5554i	0.156862	−	0.482772i
$910$	−1.92180	+	5.43857i	−0.0637071	+	0.180287i
$911$	3.28422	+	10.1078i	0.108811	+	0.334886i	0.990606	−	0.136747i	$-0.0436647\pi$
$911$	3.28422	+	10.1078i	0.108811	+	0.334886i	−0.881795	+	0.471633i	$0.843665\pi$
$912$	−2.35868	−	0.766381i	−0.0781037	−	0.0253774i
$913$	10.7122	+	3.48061i	0.354523	+	0.115191i
$914$	−6.18011	−	19.0204i	−0.204420	−	0.629139i
$915$	17.8162	−	12.2623i	0.588985	−	0.405379i
$916$	−10.5845	+	32.5758i	−0.349722	+	1.07633i
$917$	−11.2649	+	15.5048i	−0.372000	+	0.512013i
$918$		−	1.26530i		−	0.0417613i
$919$	−8.17176	−	5.93713i	−0.269561	−	0.195848i	0.444790	−	0.895635i	$-0.353278\pi$
$919$	−8.17176	−	5.93713i	−0.269561	−	0.195848i	−0.714352	+	0.699787i	$0.753278\pi$
$920$	−6.65865	+	8.68977i	−0.219529	+	0.286493i
$921$	−22.2753	+	16.1839i	−0.733995	+	0.533278i
$922$	−5.23098	−	7.19982i	−0.172273	−	0.237113i
$923$	3.08469	−	1.00228i	0.101534	−	0.0329903i
$924$	−2.85890			−0.0940508
$925$	10.0025	+	15.3575i	0.328881	+	0.504950i
$926$	24.5628			0.807184
$927$	6.16162	−	2.00203i	0.202374	−	0.0657553i
$928$	−23.4492	−	32.2750i	−0.769756	−	1.05948i
$929$	−17.1299	+	12.4456i	−0.562012	+	0.408326i	−0.832195	−	0.554483i	$-0.812916\pi$
$929$	−17.1299	+	12.4456i	−0.562012	+	0.408326i	0.270183	+	0.962809i	$0.412916\pi$
$930$	−0.158999	+	6.23137i	−0.00521378	+	0.204335i
$931$	−3.15049	−	2.28897i	−0.103253	−	0.0750179i
$932$			38.4764i			1.26034i
$933$	5.64211	−	7.76570i	0.184714	−	0.254238i
$934$	8.36360	−	25.7405i	0.273665	−	0.842255i
$935$	−5.90610	−	4.52563i	−0.193150	−	0.148004i
$936$	−2.68970	−	8.27806i	−0.0879157	−	0.270577i
$937$	−4.92512	−	1.60027i	−0.160897	−	0.0522785i	0.227461	−	0.973787i	$-0.426958\pi$
$937$	−4.92512	−	1.60027i	−0.160897	−	0.0522785i	−0.388358	+	0.921509i	$0.626958\pi$
$938$	−10.4472	−	3.39450i	−0.341113	−	0.110834i
$939$	1.32708	+	4.08434i	0.0433077	+	0.133287i
$940$	−17.5323	−	13.4344i	−0.571841	−	0.438181i
$941$	7.42832	−	22.8620i	0.242156	−	0.745281i	−0.753935	−	0.656949i	$-0.771847\pi$
$941$	7.42832	−	22.8620i	0.242156	−	0.745281i	0.996091	−	0.0883315i	$-0.0281535\pi$
$942$	−5.87698	+	8.08897i	−0.191482	+	0.263553i
$943$		−	21.4220i		−	0.697595i
$944$	1.16978	+	0.849896i	0.0380732	+	0.0276618i
$945$	−0.0570367	+	2.23534i	−0.00185540	+	0.0727156i
$946$	6.24748	−	4.53906i	0.203123	−	0.147578i
$947$	−13.3487	−	18.3728i	−0.433773	−	0.597037i	0.535041	−	0.844826i	$-0.320296\pi$
$947$	−13.3487	−	18.3728i	−0.433773	−	0.597037i	−0.968814	+	0.247789i	$0.920296\pi$
$948$	−3.76020	+	1.22176i	−0.122126	+	0.0396810i
$949$	−10.9186			−0.354432
$950$	−8.40639	−	12.9068i	−0.272739	−	0.418753i
$951$	3.40953			0.110562
$952$	−4.06044	+	1.31932i	−0.131600	+	0.0427593i
$953$	6.10410	+	8.40157i	0.197731	+	0.272153i	0.896356	−	0.443334i	$-0.146205\pi$
$953$	6.10410	+	8.40157i	0.197731	+	0.272153i	−0.698625	+	0.715488i	$0.746205\pi$
$954$	−4.27651	+	3.10707i	−0.138457	+	0.100595i
$955$	2.35511	−	3.07350i	0.0762095	−	0.0994560i
$956$	−11.6018	−	8.42917i	−0.375228	−	0.272619i
$957$			14.2060i			0.459216i
$958$	2.64315	−	3.63798i	0.0853963	−	0.117538i
$959$	−2.37294	+	7.30315i	−0.0766261	+	0.235831i
$960$	−6.16675	+	4.24437i	−0.199031	+	0.136987i
$961$	−5.74218	−	17.6726i	−0.185232	−	0.570084i
$962$	8.99276	+	2.92193i	0.289938	+	0.0942066i
$963$	−2.15361	−	0.699750i	−0.0693991	−	0.0225491i
$964$	−3.67922	−	11.3235i	−0.118500	−	0.364704i
$965$	−9.92128	+	28.0766i	−0.319377	+	0.903816i
$966$	0.448378	−	1.37997i	0.0144263	−	0.0443996i
$967$	−26.1685	+	36.0179i	−0.841523	+	1.15826i	0.144145	+	0.989557i	$0.453957\pi$
$967$	−26.1685	+	36.0179i	−0.841523	+	1.15826i	−0.985667	+	0.168700i	$0.946043\pi$
$968$		−	17.8090i		−	0.572403i
$969$	5.03916	+	3.66116i	0.161881	+	0.117614i
$970$	16.8499	+	24.4816i	0.541018	+	0.786058i
$971$	28.1859	−	20.4782i	0.904527	−	0.657177i	−0.0350977	−	0.999384i	$-0.511174\pi$
$971$	28.1859	−	20.4782i	0.904527	−	0.657177i	0.939625	+	0.342207i	$0.111174\pi$
$972$	−0.807738	−	1.11176i	−0.0259082	−	0.0356596i
$973$	12.4578	−	4.04779i	0.399379	−	0.129766i
$974$	16.1185			0.516471
$975$	−5.82258	+	15.2293i	−0.186472	+	0.487727i
$976$	6.15996			0.197175
$977$	−3.87511	+	1.25910i	−0.123976	+	0.0402822i	−0.370348	−	0.928893i	$-0.620761\pi$
$977$	−3.87511	+	1.25910i	−0.123976	+	0.0402822i	0.246372	+	0.969175i	$0.420761\pi$
$978$	4.44606	+	6.11947i	0.142169	+	0.195679i
$979$	6.23100	−	4.52708i	0.199144	−	0.144686i
$980$	2.94569	−	0.874700i	0.0940968	−	0.0279413i
$981$	4.03529	+	2.93181i	0.128837	+	0.0936054i
$982$			11.2928i			0.360368i
$983$	21.4879	−	29.5755i	0.685357	−	0.943313i	−0.314626	−	0.949216i	$-0.601879\pi$
$983$	21.4879	−	29.5755i	0.685357	−	0.943313i	0.999983	+	0.00590281i	$0.00187893\pi$
$984$	9.63347	−	29.6488i	0.307104	−	0.945168i
$985$	−9.55903	−	32.1916i	−0.304576	−	1.02571i
$986$	2.66995	+	8.21728i	0.0850287	+	0.261691i
$987$	6.83626	+	2.22124i	0.217601	+	0.0707027i
$988$	16.5964	+	5.39250i	0.528002	+	0.171558i
$989$	−2.65959	−	8.18536i	−0.0845699	−	0.260279i
$990$	3.67880	+	0.0938677i	0.116920	+	0.00298331i
$991$	−6.83442	+	21.0342i	−0.217102	+	0.668172i	0.781895	+	0.623410i	$0.214253\pi$
$991$	−6.83442	+	21.0342i	−0.217102	+	0.668172i	−0.998998	+	0.0447626i	$0.985747\pi$
$992$	−12.1011	+	16.6557i	−0.384210	+	0.528820i
$993$		−	15.9661i		−	0.506668i
$994$	0.636566	+	0.462492i	0.0201906	+	0.0146694i
$995$	5.20566	+	1.83950i	0.165030	+	0.0583160i
$996$	6.01917	−	4.37318i	0.190725	−	0.138570i
$997$	22.8190	+	31.4076i	0.722683	+	0.994688i	0.999430	+	0.0337456i	$0.0107436\pi$
$997$	22.8190	+	31.4076i	0.722683	+	0.994688i	−0.276747	+	0.960943i	$0.589256\pi$
$998$	−32.4793	+	10.5532i	−1.02811	+	0.334054i
$999$	3.66553			0.115972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.169.5	✓	56
25.4	even	10	inner	525.2.z.a.379.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.169.5	✓	56	1.1	even	1	trivial
525.2.z.a.379.5	yes	56	25.4	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)

\(f(q)\)	\(=\)	\(q+(-0.752353 + 0.244454i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.11176 + 0.807738i) q^{4} +(2.10831 + 0.745003i) q^{5} +(0.639990 + 0.464980i) q^{6} +1.00000i q^{7} +(1.56894 - 2.15946i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.752353 + 0.244454i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.11176 + 0.807738i) q^{4} +(2.10831 + 0.745003i) q^{5} +(0.639990 + 0.464980i) q^{6} +1.00000i q^{7} +(1.56894 - 2.15946i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.76831 - 0.0451201i) q^{10} +(0.642878 + 1.97858i) q^{11} +(1.30695 + 0.424653i) q^{12} +(-3.10128 - 1.00767i) q^{13} +(-0.244454 - 0.752353i) q^{14} +(-0.636513 - 2.14356i) q^{15} +(0.196799 - 0.605686i) q^{16} +(-0.940152 + 1.29401i) q^{17} -0.791071i q^{18} +(3.15049 + 2.28897i) q^{19} +(-2.94569 + 0.874700i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-0.967344 - 1.33143i) q^{22} +(-1.74443 + 0.566798i) q^{23} -2.66924 q^{24} +(3.88994 + 3.14140i) q^{25} +2.57959 q^{26} +(0.951057 - 0.309017i) q^{27} +(-0.807738 - 1.11176i) q^{28} +(-5.52439 + 4.01370i) q^{29} +(1.00289 + 1.45712i) q^{30} +(2.85090 + 2.07130i) q^{31} +5.84227i q^{32} +(1.22283 - 1.68308i) q^{33} +(0.391000 - 1.20338i) q^{34} +(-0.745003 + 2.10831i) q^{35} +(-0.424653 - 1.30695i) q^{36} +(3.48612 + 1.13271i) q^{37} +(-2.92983 - 0.951961i) q^{38} +(1.00767 + 3.10128i) q^{39} +(4.91661 - 3.38394i) q^{40} +(-3.60907 + 11.1076i) q^{41} +(-0.464980 + 0.639990i) q^{42} +4.69230i q^{43} +(-2.31290 - 1.68042i) q^{44} +(-1.36004 + 1.77490i) q^{45} +(1.17387 - 0.852865i) q^{46} +(4.22504 + 5.81527i) q^{47} +(-0.605686 + 0.196799i) q^{48} -1.00000 q^{49} +(-3.69454 - 1.41253i) q^{50} +1.59948 q^{51} +(4.26180 - 1.38474i) q^{52} +(-3.92767 - 5.40598i) q^{53} +(-0.639990 + 0.464980i) q^{54} +(-0.118659 + 4.65040i) q^{55} +(2.15946 + 1.56894i) q^{56} -3.89423i q^{57} +(3.17512 - 4.37018i) q^{58} +(-0.701598 + 2.15930i) q^{59} +(2.43908 + 1.86898i) q^{60} +(2.98895 + 9.19904i) q^{61} +(-2.65122 - 0.861434i) q^{62} +(-0.951057 - 0.309017i) q^{63} +(-1.03457 - 3.18408i) q^{64} +(-5.78775 - 4.43494i) q^{65} +(-0.508563 + 1.56519i) q^{66} +(8.16200 - 11.2340i) q^{67} -2.19802i q^{68} +(1.48390 + 1.07811i) q^{69} +(0.0451201 - 1.76831i) q^{70} +(-0.804688 + 0.584640i) q^{71} +(1.56894 + 2.15946i) q^{72} +(3.18447 - 1.03470i) q^{73} -2.89969 q^{74} +(0.254993 - 4.99349i) q^{75} -5.35147 q^{76} +(-1.97858 + 0.642878i) q^{77} +(-1.51624 - 2.08693i) q^{78} +(-2.32761 + 1.69111i) q^{79} +(0.866152 - 1.13036i) q^{80} +(-0.809017 - 0.587785i) q^{81} -9.23908i q^{82} +(3.18233 - 4.38010i) q^{83} +(-0.424653 + 1.30695i) q^{84} +(-2.94617 + 2.02775i) q^{85} +(-1.14705 - 3.53026i) q^{86} +(6.49431 + 2.11013i) q^{87} +(5.28129 + 1.71600i) q^{88} +(-1.14403 - 3.52095i) q^{89} +(0.589351 - 1.66782i) q^{90} +(1.00767 - 3.10128i) q^{91} +(1.48155 - 2.03918i) q^{92} -3.52391i q^{93} +(-4.60029 - 3.34231i) q^{94} +(4.93693 + 7.17298i) q^{95} +(4.72650 - 3.43400i) q^{96} +(-9.87564 - 13.5926i) q^{97} +(0.752353 - 0.244454i) q^{98} -2.08040 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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