LMFDB - Embedded newform 525.2.bg.b.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53240 + 0.682267i) q^{2} +(0.669131 - 0.743145i) q^{3} +(0.544489 - 0.604717i) q^{4} +(1.08380 + 1.95586i) q^{5} +(-0.518350 + 1.59532i) q^{6} +(-2.12083 - 1.58180i) q^{7} +(0.614905 - 1.89248i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-1.53240 + 0.682267i) q^{2} +(0.669131 - 0.743145i) q^{3} +(0.544489 - 0.604717i) q^{4} +(1.08380 + 1.95586i) q^{5} +(-0.518350 + 1.59532i) q^{6} +(-2.12083 - 1.58180i) q^{7} +(0.614905 - 1.89248i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-2.99523 - 2.25771i) q^{10} +(-0.191010 + 1.81734i) q^{11} +(-0.0850576 - 0.809269i) q^{12} +(-5.18647 + 3.76819i) q^{13} +(4.32916 + 0.976980i) q^{14} +(2.17869 + 0.503303i) q^{15} +(0.519015 + 4.93810i) q^{16} +(-4.77243 + 1.01441i) q^{17} +(0.838708 + 1.45269i) q^{18} +(0.832880 + 0.925007i) q^{19} +(1.77286 + 0.409551i) q^{20} +(-2.59462 + 0.517647i) q^{21} +(-0.947207 - 2.91520i) q^{22} +(6.69573 - 2.98113i) q^{23} +(-0.994938 - 1.72328i) q^{24} +(-2.65075 + 4.23952i) q^{25} +(5.37681 - 9.31291i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.11131 + 0.421223i) q^{28} +(-0.326421 - 1.00462i) q^{29} +(-3.68200 + 0.715188i) q^{30} +(-5.58991 + 1.18817i) q^{31} +(-2.17457 - 3.76646i) q^{32} +(1.22274 + 1.35799i) q^{33} +(6.62115 - 4.81055i) q^{34} +(0.795229 - 5.86239i) q^{35} +(-0.658318 - 0.478296i) q^{36} +(0.439740 + 4.18384i) q^{37} +(-1.90740 - 0.849231i) q^{38} +(-0.670114 + 6.37571i) q^{39} +(4.36786 - 0.848408i) q^{40} +(-6.87687 + 4.99634i) q^{41} +(3.62281 - 2.56346i) q^{42} -10.4647 q^{43} +(0.994972 + 1.10503i) q^{44} +(1.83185 - 1.28231i) q^{45} +(-8.22659 + 9.13655i) q^{46} +(-3.16752 - 0.673276i) q^{47} +(4.01701 + 2.91853i) q^{48} +(1.99580 + 6.70946i) q^{49} +(1.16952 - 8.30514i) q^{50} +(-2.43952 + 4.22538i) q^{51} +(-0.545289 + 5.18808i) q^{52} +(1.30019 - 1.44401i) q^{53} +(1.64076 + 0.348755i) q^{54} +(-3.76147 + 1.59605i) q^{55} +(-4.29764 + 3.04097i) q^{56} +1.24472 q^{57} +(1.18562 + 1.31677i) q^{58} +(8.56659 + 3.81409i) q^{59} +(1.49063 - 1.04345i) q^{60} +(-6.50117 + 2.89451i) q^{61} +(7.75531 - 5.63456i) q^{62} +(-1.35145 + 2.27455i) q^{63} +(-2.13200 - 1.54899i) q^{64} +(-12.9911 - 6.06002i) q^{65} +(-2.80022 - 1.24674i) q^{66} +(-10.4123 + 2.21320i) q^{67} +(-1.98510 + 3.43830i) q^{68} +(2.26491 - 6.97067i) q^{69} +(2.78111 + 9.52606i) q^{70} +(0.0148052 + 0.0455658i) q^{71} +(-1.94639 - 0.413718i) q^{72} +(1.59127 - 15.1399i) q^{73} +(-3.52835 - 6.11129i) q^{74} +(1.37688 + 4.80668i) q^{75} +1.01286 q^{76} +(3.27977 - 3.55212i) q^{77} +(-3.32305 - 10.2273i) q^{78} +(14.2839 + 3.03614i) q^{79} +(-9.09571 + 6.36704i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(7.12926 - 12.3482i) q^{82} +(-1.14042 + 3.50984i) q^{83} +(-1.09971 + 1.85086i) q^{84} +(-7.15640 - 8.23476i) q^{85} +(16.0360 - 7.13971i) q^{86} +(-0.964996 - 0.429644i) q^{87} +(3.32183 + 1.47898i) q^{88} +(0.522387 - 0.232582i) q^{89} +(-1.93225 + 3.21481i) q^{90} +(16.9601 + 0.212299i) q^{91} +(1.84301 - 5.67221i) q^{92} +(-2.85740 + 4.94916i) q^{93} +(5.31324 - 1.12936i) q^{94} +(-0.906505 + 2.63152i) q^{95} +(-4.25409 - 0.904235i) q^{96} +(-2.18375 - 6.72090i) q^{97} +(-7.63599 - 8.91988i) q^{98} +1.82735 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.53240	+	0.682267i	−1.08357	+	0.482435i	−0.869272	−	0.494333i	$-0.835412\pi$
$2$	−1.53240	+	0.682267i	−1.08357	+	0.482435i	−0.214295	+	0.976769i	$0.568746\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	0.544489	−	0.604717i	0.272245	−	0.302358i
$5$	1.08380	+	1.95586i	0.484690	+	0.874686i
$5$	1.08380	+	1.95586i	0.484690	+	0.874686i
$6$	−0.518350	+	1.59532i	−0.211616	+	0.651286i
$7$	−2.12083	−	1.58180i	−0.801597	−	0.597865i
$7$	−2.12083	−	1.58180i	−0.801597	−	0.597865i
$8$	0.614905	−	1.89248i	0.217402	−	0.669094i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−2.99523	−	2.25771i	−0.947174	−	0.713950i
$11$	−0.191010	+	1.81734i	−0.0575917	+	0.547948i	0.927244	+	0.374458i	$0.122171\pi$
$11$	−0.191010	+	1.81734i	−0.0575917	+	0.547948i	−0.984836	+	0.173490i	$0.944495\pi$
$12$	−0.0850576	−	0.809269i	−0.0245540	−	0.233616i
$13$	−5.18647	+	3.76819i	−1.43847	+	1.04511i	−0.450107	+	0.892974i	$0.648614\pi$
$13$	−5.18647	+	3.76819i	−1.43847	+	1.04511i	−0.988360	+	0.152133i	$0.951386\pi$
$14$	4.32916	+	0.976980i	1.15702	+	0.261109i
$15$	2.17869	+	0.503303i	0.562535	+	0.129952i
$16$	0.519015	+	4.93810i	0.129754	+	1.23453i
$17$	−4.77243	+	1.01441i	−1.15748	+	0.246031i	−0.746356	−	0.665547i	$-0.768198\pi$
$17$	−4.77243	+	1.01441i	−1.15748	+	0.246031i	−0.411128	+	0.911578i	$0.634865\pi$
$18$	0.838708	+	1.45269i	0.197685	+	0.342401i
$19$	0.832880	+	0.925007i	0.191076	+	0.212211i	0.831069	−	0.556169i	$-0.187729\pi$
$19$	0.832880	+	0.925007i	0.191076	+	0.212211i	−0.639993	+	0.768381i	$0.721063\pi$
$20$	1.77286	+	0.409551i	0.396423	+	0.0915784i
$21$	−2.59462	+	0.517647i	−0.566192	+	0.112960i
$22$	−0.947207	−	2.91520i	−0.201945	−	0.621524i
$23$	6.69573	−	2.98113i	1.39616	−	0.621609i	0.435714	−	0.900085i	$-0.356496\pi$
$23$	6.69573	−	2.98113i	1.39616	−	0.621609i	0.960443	+	0.278476i	$0.0898294\pi$
$24$	−0.994938	−	1.72328i	−0.203091	−	0.351764i
$25$	−2.65075	+	4.23952i	−0.530150	+	0.847904i
$26$	5.37681	−	9.31291i	1.05448	−	1.82641i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−2.11131	+	0.421223i	−0.399000	+	0.0796037i
$29$	−0.326421	−	1.00462i	−0.0606148	−	0.186553i	0.916164	−	0.400804i	$-0.131269\pi$
$29$	−0.326421	−	1.00462i	−0.0606148	−	0.186553i	−0.976779	+	0.214251i	$0.931269\pi$
$30$	−3.68200	+	0.715188i	−0.672239	+	0.130575i
$31$	−5.58991	+	1.18817i	−1.00398	+	0.213402i	−0.680433	−	0.732810i	$-0.738208\pi$
$31$	−5.58991	+	1.18817i	−1.00398	+	0.213402i	−0.323545	+	0.946213i	$0.604875\pi$
$32$	−2.17457	−	3.76646i	−0.384412	−	0.665822i
$33$	1.22274	+	1.35799i	0.212851	+	0.236395i
$34$	6.62115	−	4.81055i	1.13552	−	0.825002i
$35$	0.795229	−	5.86239i	0.134418	−	0.990925i
$36$	−0.658318	−	0.478296i	−0.109720	−	0.0797161i
$37$	0.439740	+	4.18384i	0.0722928	+	0.687820i	0.969313	+	0.245830i	$0.0790605\pi$
$37$	0.439740	+	4.18384i	0.0722928	+	0.687820i	−0.897020	+	0.441990i	$0.854273\pi$
$38$	−1.90740	−	0.849231i	−0.309422	−	0.137763i
$39$	−0.670114	+	6.37571i	−0.107304	+	1.02093i
$40$	4.36786	−	0.848408i	0.690620	−	0.134145i
$41$	−6.87687	+	4.99634i	−1.07399	+	0.780297i	−0.976625	−	0.214952i	$-0.931041\pi$
$41$	−6.87687	+	4.99634i	−1.07399	+	0.780297i	−0.0973622	+	0.995249i	$0.531041\pi$
$42$	3.62281	−	2.56346i	0.559012	−	0.395551i
$43$	−10.4647			−1.59585			−0.797925	−	0.602757i	$-0.794069\pi$
$43$	−10.4647			−1.59585			−0.797925	+	0.602757i	$0.794069\pi$
$44$	0.994972	+	1.10503i	0.149998	+	0.166589i
$45$	1.83185	−	1.28231i	0.273077	−	0.191155i
$46$	−8.22659	+	9.13655i	−1.21294	+	1.34711i
$47$	−3.16752	−	0.673276i	−0.462030	−	0.0982074i	−0.0289849	−	0.999580i	$-0.509227\pi$
$47$	−3.16752	−	0.673276i	−0.462030	−	0.0982074i	−0.433045	+	0.901372i	$0.642561\pi$
$48$	4.01701	+	2.91853i	0.579806	+	0.421254i
$49$	1.99580	+	6.70946i	0.285114	+	0.958494i
$50$	1.16952	−	8.30514i	0.165395	−	1.17452i
$51$	−2.43952	+	4.22538i	−0.341601	+	0.591671i
$52$	−0.545289	+	5.18808i	−0.0756180	+	0.719457i
$53$	1.30019	−	1.44401i	0.178595	−	0.198350i	−0.647200	−	0.762320i	$-0.724060\pi$
$53$	1.30019	−	1.44401i	0.178595	−	0.198350i	0.825795	+	0.563970i	$0.190727\pi$
$54$	1.64076	+	0.348755i	0.223279	+	0.0474595i
$55$	−3.76147	+	1.59605i	−0.507197	+	0.215211i
$56$	−4.29764	+	3.04097i	−0.574297	+	0.406366i
$57$	1.24472			0.164867
$58$	1.18562	+	1.31677i	0.155680	+	0.172900i
$59$	8.56659	+	3.81409i	1.11527	+	0.496552i	0.879808	−	0.475330i	$-0.157671\pi$
$59$	8.56659	+	3.81409i	1.11527	+	0.496552i	0.235467	+	0.971882i	$0.424338\pi$
$60$	1.49063	−	1.04345i	0.192439	−	0.134708i
$61$	−6.50117	+	2.89451i	−0.832390	+	0.370604i	−0.778269	−	0.627930i	$-0.783902\pi$
$61$	−6.50117	+	2.89451i	−0.832390	+	0.370604i	−0.0541207	+	0.998534i	$0.517236\pi$
$62$	7.75531	−	5.63456i	0.984926	−	0.715590i
$63$	−1.35145	+	2.27455i	−0.170267	+	0.286566i
$64$	−2.13200	−	1.54899i	−0.266500	−	0.193624i
$65$	−12.9911	−	6.06002i	−1.61135	−	0.751653i
$66$	−2.80022	−	1.24674i	−0.344684	−	0.153463i
$67$	−10.4123	+	2.21320i	−1.27206	+	0.270386i	−0.793988	−	0.607933i	$-0.791999\pi$
$67$	−10.4123	+	2.21320i	−1.27206	+	0.270386i	−0.478076	+	0.878319i	$0.658666\pi$
$68$	−1.98510	+	3.43830i	−0.240729	+	0.416955i
$69$	2.26491	−	6.97067i	0.272663	−	0.839170i
$70$	2.78111	+	9.52606i	0.332406	+	1.13858i
$71$	0.0148052	+	0.0455658i	0.00175706	+	0.00540766i	0.951931	−	0.306312i	$-0.0990951\pi$
$71$	0.0148052	+	0.0455658i	0.00175706	+	0.00540766i	−0.950174	+	0.311720i	$0.899095\pi$
$72$	−1.94639	−	0.413718i	−0.229384	−	0.0487572i
$73$	1.59127	−	15.1399i	0.186244	−	1.77199i	−0.358637	−	0.933477i	$-0.616758\pi$
$73$	1.59127	−	15.1399i	0.186244	−	1.77199i	0.544881	−	0.838514i	$-0.316575\pi$
$74$	−3.52835	−	6.11129i	−0.410163	−	0.710423i
$75$	1.37688	+	4.80668i	0.158988	+	0.555028i
$76$	1.01286			0.116183
$77$	3.27977	−	3.55212i	0.373765	−	0.404802i
$78$	−3.32305	−	10.2273i	−0.376262	−	1.15801i
$79$	14.2839	+	3.03614i	1.60707	+	0.341592i	0.922091	−	0.386974i	$-0.126480\pi$
$79$	14.2839	+	3.03614i	1.60707	+	0.341592i	0.684975	+	0.728566i	$0.259813\pi$
$80$	−9.09571	+	6.36704i	−1.01693	+	0.711856i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	7.12926	−	12.3482i	0.787295	−	1.36363i
$83$	−1.14042	+	3.50984i	−0.125177	+	0.385255i	−0.993933	−	0.109985i	$-0.964920\pi$
$83$	−1.14042	+	3.50984i	−0.125177	+	0.385255i	0.868756	+	0.495240i	$0.164920\pi$
$84$	−1.09971	+	1.85086i	−0.119988	+	0.201946i
$85$	−7.15640	−	8.23476i	−0.776221	−	0.893186i
$86$	16.0360	−	7.13971i	1.72921	−	0.769894i
$87$	−0.964996	−	0.429644i	−0.103458	−	0.0460627i
$88$	3.32183	+	1.47898i	0.354109	+	0.157659i
$89$	0.522387	−	0.232582i	0.0553730	−	0.0246536i	−0.378863	−	0.925453i	$-0.623685\pi$
$89$	0.522387	−	0.232582i	0.0553730	−	0.0246536i	0.434236	+	0.900799i	$0.357018\pi$
$90$	−1.93225	+	3.21481i	−0.203677	+	0.338871i
$91$	16.9601	+	0.212299i	1.77790	+	0.0222550i
$92$	1.84301	−	5.67221i	0.192148	−	0.591369i
$93$	−2.85740	+	4.94916i	−0.296298	+	0.513204i
$94$	5.31324	−	1.12936i	0.548019	−	0.116485i
$95$	−0.906505	+	2.63152i	−0.0930055	+	0.269988i
$96$	−4.25409	−	0.904235i	−0.434181	−	0.0922881i
$97$	−2.18375	−	6.72090i	−0.221727	−	0.682404i	−0.998607	−	0.0527565i	$-0.983199\pi$
$97$	−2.18375	−	6.72090i	−0.221727	−	0.682404i	0.776881	−	0.629648i	$-0.216801\pi$
$98$	−7.63599	−	8.91988i	−0.771352	−	0.901044i
$99$	1.82735			0.183656
$100$	1.12040	+	3.91133i	0.112040	+	0.391133i
$101$	1.99383	+	3.45341i	0.198393	+	0.343628i	0.948008	−	0.318247i	$-0.103094\pi$
$101$	1.99383	+	3.45341i	0.198393	+	0.343628i	−0.749614	+	0.661875i	$0.769761\pi$
$102$	0.855481	−	8.13936i	0.0847052	−	0.805916i
$103$	0.915749	+	0.194648i	0.0902314	+	0.0191793i	0.252806	−	0.967517i	$-0.418647\pi$
$103$	0.915749	+	0.194648i	0.0902314	+	0.0191793i	−0.162575	+	0.986696i	$0.551980\pi$
$104$	3.94205	+	12.1324i	0.386550	+	1.18968i
$105$	−3.82449	−	4.51367i	−0.373232	−	0.440490i
$106$	−1.00721	+	3.09987i	−0.0978289	+	0.301086i
$107$	−2.93110	+	5.07681i	−0.283360	+	0.490794i	−0.972210	−	0.234110i	$-0.924782\pi$
$107$	−2.93110	+	5.07681i	−0.283360	+	0.490794i	0.688850	+	0.724904i	$0.258116\pi$
$108$	−0.795945	+	0.169183i	−0.0765898	+	0.0162797i
$109$	−11.5569	−	5.14546i	−1.10695	−	0.492846i	−0.229885	−	0.973218i	$-0.573835\pi$
$109$	−11.5569	−	5.14546i	−1.10695	−	0.492846i	−0.877065	+	0.480372i	$0.840502\pi$
$110$	4.67514	−	5.01210i	0.445757	−	0.477885i
$111$	3.40345	+	2.47275i	0.323041	+	0.234703i
$112$	6.71036	−	11.2938i	0.634070	−	1.06717i
$113$	13.1029	−	9.51978i	1.23261	−	0.895546i	0.235530	−	0.971867i	$-0.424318\pi$
$113$	13.1029	−	9.51978i	1.23261	−	0.895546i	0.997083	+	0.0763216i	$0.0243176\pi$
$114$	−1.90740	+	0.849231i	−0.178645	+	0.0795378i
$115$	13.0875	+	9.86494i	1.22042	+	0.919911i
$116$	−0.785243	−	0.349613i	−0.0729080	−	0.0324607i
$117$	4.28968	+	4.76417i	0.396581	+	0.440448i
$118$	−15.7296			−1.44803
$119$	11.7261	+	5.39765i	1.07493	+	0.494802i
$120$	2.29218	−	3.81365i	0.209246	−	0.348137i
$121$	7.49339	+	1.59277i	0.681217	+	0.144797i
$122$	7.98755	−	8.87107i	0.723159	−	0.803149i
$123$	−0.888521	+	8.45371i	−0.0801153	+	0.762246i
$124$	−2.32514	+	4.02726i	−0.208804	+	0.361659i
$125$	−11.1648	−	0.589700i	−0.998608	−	0.0527444i
$126$	0.519108	−	4.40756i	0.0462459	−	0.392657i
$127$	4.86988	+	3.53817i	0.432132	+	0.313962i	0.782501	−	0.622650i	$-0.213944\pi$
$127$	4.86988	+	3.53817i	0.432132	+	0.313962i	−0.350369	+	0.936612i	$0.613944\pi$
$128$	12.8321	+	2.72754i	1.13421	+	0.241083i
$129$	−7.00224	+	7.77678i	−0.616513	+	0.684707i
$130$	24.0421	+	0.422936i	2.10863	+	0.0370939i
$131$	8.28351	+	9.19977i	0.723733	+	0.803787i	0.986963	−	0.160946i	$-0.0514544\pi$
$131$	8.28351	+	9.19977i	0.723733	+	0.803787i	−0.263230	+	0.964733i	$0.584788\pi$
$132$	1.48696			0.129424
$133$	−0.303214	−	3.27923i	−0.0262920	−	0.284345i
$134$	14.4458	−	10.4955i	1.24792	−	0.906670i
$135$	0.272811	−	2.21936i	0.0234798	−	0.191012i
$136$	−1.01483	+	9.65551i	−0.0870213	+	0.827953i
$137$	16.4384	+	7.31886i	1.40443	+	0.625292i	0.962382	−	0.271700i	$-0.0875858\pi$
$137$	16.4384	+	7.31886i	1.40443	+	0.625292i	0.442047	+	0.896992i	$0.354252\pi$
$138$	1.28512	+	12.2271i	0.109397	+	1.04084i
$139$	10.0854	+	7.32750i	0.855435	+	0.621510i	0.926639	−	0.375952i	$-0.122684\pi$
$139$	10.0854	+	7.32750i	0.855435	+	0.621510i	−0.0712041	+	0.997462i	$0.522684\pi$
$140$	−3.11209	−	3.67290i	−0.263020	−	0.310416i
$141$	−2.61982	+	1.90341i	−0.220629	+	0.160296i
$142$	−0.0537755	−	0.0597237i	−0.00451274	−	0.00501190i
$143$	−5.85741	−	10.1453i	−0.489821	−	0.848396i
$144$	4.85680	−	1.03234i	0.404733	−	0.0860287i
$145$	1.61112	−	1.72724i	0.133796	−	0.143439i
$146$	7.89100	+	24.2860i	0.653064	+	2.00992i
$147$	6.32155	+	3.00633i	0.521392	+	0.247958i
$148$	2.76947	+	2.01214i	0.227649	+	0.165397i
$149$	1.12288	−	1.94489i	0.0919900	−	0.159331i	−0.816358	−	0.577546i	$-0.804011\pi$
$149$	1.12288	−	1.94489i	0.0919900	−	0.159331i	0.908348	+	0.418214i	$0.137344\pi$
$150$	−5.38936	−	6.42635i	−0.440039	−	0.524709i
$151$	−8.23717	−	14.2672i	−0.670332	−	1.16105i	−0.977810	−	0.209493i	$-0.932818\pi$
$151$	−8.23717	−	14.2672i	−0.670332	−	1.16105i	0.307478	−	0.951555i	$-0.400515\pi$
$152$	2.26270	−	1.00742i	0.183529	−	0.0817126i
$153$	1.50771	+	4.64025i	0.121891	+	0.375142i
$154$	−2.60242	+	7.68093i	−0.209709	+	0.618947i
$155$	−8.38225	−	9.64533i	−0.673278	−	0.774732i
$156$	3.49063	+	3.87673i	0.279474	+	0.310387i
$157$	5.59334	+	9.68795i	0.446397	+	0.773182i	0.998148	−	0.0608263i	$-0.0193736\pi$
$157$	5.59334	+	9.68795i	0.446397	+	0.773182i	−0.551751	+	0.834009i	$0.686040\pi$
$158$	−23.9601	+	5.09287i	−1.90616	+	0.405167i
$159$	−0.203110	−	1.93246i	−0.0161077	−	0.153254i
$160$	5.00986	−	8.33523i	0.396064	−	0.658958i
$161$	−18.9160	−	4.26887i	−1.49079	−	0.336434i
$162$	1.35706	−	0.985961i	0.106621	−	0.0774644i
$163$	1.48926	+	14.1693i	0.116648	+	1.10983i	0.883639	+	0.468170i	$0.155086\pi$
$163$	1.48926	+	14.1693i	0.116648	+	1.10983i	−0.766991	+	0.641658i	$0.778247\pi$
$164$	−0.723013	+	6.87901i	−0.0564578	+	0.537160i
$165$	−1.33082	+	3.86328i	−0.103604	+	0.300756i
$166$	−0.647077	−	6.15653i	−0.0502229	−	0.477839i
$167$	1.03979	−	3.20015i	0.0804616	−	0.247635i	−0.902731	−	0.430205i	$-0.858441\pi$
$167$	1.03979	−	3.20015i	0.0804616	−	0.247635i	0.983193	+	0.182569i	$0.0584414\pi$
$168$	−0.615805	+	5.22858i	−0.0475104	+	0.403393i
$169$	8.68298	−	26.7235i	0.667921	−	2.05565i
$170$	16.5847	+	7.73635i	1.27199	+	0.593351i
$171$	0.832880	−	0.925007i	0.0636919	−	0.0707371i
$172$	−5.69791	+	6.32817i	−0.434461	+	0.482518i
$173$	1.21154	−	0.539414i	0.0921120	−	0.0410109i	−0.360163	−	0.932889i	$-0.617279\pi$
$173$	1.21154	−	0.539414i	0.0921120	−	0.0410109i	0.452275	+	0.891878i	$0.350612\pi$
$174$	1.77189			0.134327
$175$	12.3279	−	4.79831i	0.931899	−	0.362718i
$176$	−9.07334			−0.683929
$177$	8.56659	−	3.81409i	0.643904	−	0.286685i
$178$	−0.641822	+	0.712815i	−0.0481066	+	0.0534278i
$179$	−6.09651	+	6.77086i	−0.455675	+	0.506078i	−0.926576	−	0.376108i	$-0.877262\pi$
$179$	−6.09651	+	6.77086i	−0.455675	+	0.506078i	0.470901	+	0.882186i	$0.343929\pi$
$180$	0.221993	−	1.80595i	0.0165464	−	0.134608i
$181$	−0.267349	+	0.822816i	−0.0198719	+	0.0611594i	−0.960501	−	0.278278i	$-0.910237\pi$
$181$	−0.267349	+	0.822816i	−0.0198719	+	0.0611594i	0.940629	+	0.339437i	$0.110237\pi$
$182$	−26.1345	+	11.2460i	−1.93722	+	0.833609i
$183$	−2.19910	+	6.76812i	−0.162562	+	0.500314i
$184$	−1.52450	−	14.5047i	−0.112388	−	1.06930i
$185$	−7.70641	+	5.39452i	−0.566587	+	0.396613i
$186$	1.00202	−	9.53358i	0.0734716	−	0.699036i
$187$	−0.931947	−	8.86688i	−0.0681507	−	0.648411i
$188$	−2.13182	+	1.54886i	−0.155479	+	0.112962i
$189$	0.786023	+	2.52630i	0.0571748	+	0.183761i
$190$	−0.406271	−	4.65101i	−0.0294740	−	0.337419i
$191$	−0.901456	−	8.57678i	−0.0652270	−	0.620594i	−0.977489	−	0.210987i	$-0.932332\pi$
$191$	−0.901456	−	8.57678i	−0.0652270	−	0.620594i	0.912262	−	0.409607i	$-0.134334\pi$
$192$	−2.57771	+	0.547910i	−0.186030	+	0.0395420i
$193$	4.19622	+	7.26806i	0.302050	+	0.523166i	0.976600	−	0.215063i	$-0.0689956\pi$
$193$	4.19622	+	7.26806i	0.302050	+	0.523166i	−0.674550	+	0.738229i	$0.735662\pi$
$194$	7.93182	+	8.80918i	0.569472	+	0.632462i
$195$	−13.1962	+	5.59935i	−0.945003	+	0.400978i
$196$	5.14401	+	2.44633i	0.367429	+	0.174738i
$197$	0.791751	+	2.43676i	0.0564099	+	0.173612i	0.975292	−	0.220921i	$-0.0709063\pi$
$197$	0.791751	+	2.43676i	0.0564099	+	0.173612i	−0.918882	+	0.394533i	$0.870906\pi$
$198$	−2.80022	+	1.24674i	−0.199003	+	0.0886020i
$199$	−12.8977	−	22.3395i	−0.914296	−	1.58361i	−0.807928	−	0.589281i	$-0.799411\pi$
$199$	−12.8977	−	22.3395i	−0.914296	−	1.58361i	−0.106368	−	0.994327i	$-0.533922\pi$
$200$	6.39326	+	7.62341i	0.452072	+	0.539056i
$201$	−5.32245	+	9.21876i	−0.375417	+	0.650241i
$202$	−5.41149	−	3.93168i	−0.380751	−	0.276632i
$203$	−0.896829	+	2.64696i	−0.0629451	+	0.185780i
$204$	1.22686	+	3.77589i	0.0858975	+	0.264365i
$205$	−17.2253	−	8.03514i	−1.20307	−	0.561199i
$206$	−1.53609	+	0.326506i	−0.107025	+	0.0227488i
$207$	−3.66470	−	6.34744i	−0.254714	−	0.441178i
$208$	−21.2996	−	23.6556i	−1.47686	−	1.64022i
$209$	−1.84014	+	1.33694i	−0.127285	+	0.0924781i
$210$	8.94017	+	4.30741i	0.616930	+	0.297240i
$211$	7.43195	+	5.39963i	0.511637	+	0.371726i	0.813444	−	0.581643i	$-0.197590\pi$
$211$	7.43195	+	5.39963i	0.511637	+	0.371726i	−0.301807	+	0.953369i	$0.597590\pi$
$212$	−0.165276	−	1.57250i	−0.0113512	−	0.107999i
$213$	0.0437686	+	0.0194870i	0.00299897	+	0.00133523i
$214$	1.02786	−	9.77948i	0.0702634	−	0.668511i
$215$	−11.3416	−	20.4674i	−0.773493	−	1.39587i
$216$	−1.60984	+	1.16962i	−0.109536	+	0.0795825i
$217$	13.7347	+	6.32224i	0.932371	+	0.429181i
$218$	21.2203			1.43722
$219$	−10.1864	−	11.3131i	−0.688331	−	0.764469i
$220$	−1.08293	+	3.14365i	−0.0730109	+	0.211945i
$221$	20.9295	−	23.2446i	1.40787	−	1.56360i
$222$	−6.90250	−	1.46717i	−0.463266	−	0.0984701i
$223$	11.6394	+	8.45650i	0.779430	+	0.566289i	0.904808	−	0.425820i	$-0.140014\pi$
$223$	11.6394	+	8.45650i	0.779430	+	0.566289i	−0.125378	+	0.992109i	$0.540014\pi$
$224$	−1.34592	+	11.4277i	−0.0899281	+	0.763547i
$225$	4.49337	+	2.19308i	0.299558	+	0.146205i
$226$	−13.5837	+	23.5277i	−0.903577	+	1.56504i
$227$	−0.595065	+	5.66166i	−0.0394958	+	0.375778i	0.956864	+	0.290535i	$0.0938332\pi$
$227$	−0.595065	+	5.66166i	−0.0394958	+	0.375778i	−0.996360	+	0.0852428i	$0.972833\pi$
$228$	0.677737	−	0.752703i	0.0448842	−	0.0498490i
$229$	−8.79005	−	1.86838i	−0.580863	−	0.123466i	−0.0918961	−	0.995769i	$-0.529293\pi$
$229$	−8.79005	−	1.86838i	−0.580863	−	0.123466i	−0.488967	+	0.872302i	$0.662626\pi$
$230$	−26.7858	−	6.18783i	−1.76620	−	0.408013i
$231$	−0.445143	−	4.81418i	−0.0292883	−	0.316750i
$232$	−2.10194			−0.137999
$233$	−13.7316	−	15.2505i	−0.899588	−	0.999094i	−0.999991	−	0.00414721i	$-0.998680\pi$
$233$	−13.7316	−	15.2505i	−0.899588	−	0.999094i	0.100403	−	0.994947i	$-0.467987\pi$
$234$	−9.82393	−	4.37389i	−0.642210	−	0.285930i
$235$	−2.11612	−	6.92490i	−0.138041	−	0.451731i
$236$	6.97086	−	3.10363i	0.453764	−	0.202029i
$237$	11.8141	−	8.58344i	0.767408	−	0.557555i
$238$	−21.6516	−	0.271026i	−1.40347	−	0.0175680i
$239$	14.6242	+	10.6251i	0.945961	+	0.687281i	0.949848	−	0.312712i	$-0.101237\pi$
$239$	14.6242	+	10.6251i	0.945961	+	0.687281i	−0.00388731	+	0.999992i	$0.501237\pi$
$240$	−1.35459	+	11.0198i	−0.0874383	+	0.711326i
$241$	19.1552	+	8.52844i	1.23389	+	0.549365i	0.916921	−	0.399069i	$-0.130667\pi$
$241$	19.1552	+	8.52844i	1.23389	+	0.549365i	0.316974	+	0.948434i	$0.397333\pi$
$242$	−12.5695	+	2.67174i	−0.808000	+	0.171746i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.78946	+	5.50740i	−0.114559	+	0.352575i
$245$	−10.9597	+	11.1752i	−0.700189	+	0.713958i
$246$	−4.40612	−	13.5606i	−0.280924	−	0.864595i
$247$	−7.80531	−	1.65907i	−0.496640	−	0.105564i
$248$	−1.18867	+	11.3094i	−0.0754806	+	0.718150i
$249$	1.84523	+	3.19603i	0.116937	+	0.202540i
$250$	17.5112	−	6.71370i	1.10751	−	0.424612i
$251$	18.8023			1.18679			0.593396	−	0.804911i	$-0.297787\pi$
$251$	18.8023			1.18679			0.593396	+	0.804911i	$0.297787\pi$
$252$	0.639608	+	2.05571i	0.0402915	+	0.129498i
$253$	4.13878	+	12.7378i	0.260203	+	0.800822i
$254$	−9.87656	−	2.09933i	−0.619710	−	0.131724i
$255$	−10.9082	−	0.191891i	−0.683097	−	0.0120167i
$256$	−16.3693	+	3.47941i	−1.02308	+	0.217463i
$257$	−6.75890	+	11.7068i	−0.421609	+	0.730248i	−0.996097	−	0.0882649i	$-0.971868\pi$
$257$	−6.75890	+	11.7068i	−0.421609	+	0.730248i	0.574488	+	0.818513i	$0.305201\pi$
$258$	5.42437	−	16.6945i	0.337707	−	1.03935i
$259$	5.68541	−	9.56878i	0.353274	−	0.594575i
$260$	−10.7381	+	4.55634i	−0.665951	+	0.282572i
$261$	−0.964996	+	0.429644i	−0.0597318	+	0.0265943i
$262$	−18.9703	−	8.44613i	−1.17199	−	0.521804i
$263$	9.15266	+	4.07503i	0.564377	+	0.251277i	0.669034	−	0.743231i	$-0.266708\pi$
$263$	9.15266	+	4.07503i	0.564377	+	0.251277i	−0.104657	+	0.994508i	$0.533375\pi$
$264$	3.32183	−	1.47898i	0.204445	−	0.0910246i
$265$	4.23343	+	0.977972i	0.260057	+	0.0600763i
$266$	2.70195	+	4.81821i	0.165667	+	0.295423i
$267$	0.176703	−	0.543837i	0.0108141	−	0.0332823i
$268$	−4.33102	+	7.50155i	−0.264559	+	0.458230i
$269$	−26.0775	+	5.54294i	−1.58997	+	0.337959i	−0.916119	−	0.400907i	$-0.868695\pi$
$269$	−26.0775	+	5.54294i	−1.58997	+	0.337959i	−0.673853	+	0.738866i	$0.735362\pi$
$270$	1.09614	+	3.58707i	0.0667092	+	0.218302i
$271$	−8.81085	−	1.87280i	−0.535221	−	0.113765i	−0.0676314	−	0.997710i	$-0.521544\pi$
$271$	−8.81085	−	1.87280i	−0.535221	−	0.113765i	−0.467590	+	0.883946i	$0.654878\pi$
$272$	−7.48623	−	23.0402i	−0.453919	−	1.39702i
$273$	11.5063	−	12.4618i	0.696393	−	0.754221i
$274$	−30.1836			−1.82346
$275$	−7.19832	−	5.62711i	−0.434075	−	0.339327i
$276$	−2.98206	−	5.16508i	−0.179499	−	0.310901i
$277$	−1.67974	+	15.9816i	−0.100926	+	0.960242i	0.820489	+	0.571662i	$0.193701\pi$
$277$	−1.67974	+	15.9816i	−0.100926	+	0.960242i	−0.921415	+	0.388580i	$0.872966\pi$
$278$	−20.4542	−	4.34767i	−1.22676	−	0.260756i
$279$	1.76597	+	5.43509i	0.105726	+	0.325391i
$280$	−10.6055	−	5.10977i	−0.633799	−	0.305367i
$281$	0.631247	−	1.94278i	0.0376570	−	0.115896i	−0.930461	−	0.366391i	$-0.880593\pi$
$281$	0.631247	−	1.94278i	0.0376570	−	0.115896i	0.968118	+	0.250495i	$0.0805932\pi$
$282$	2.71597	−	4.70420i	0.161734	−	0.280131i
$283$	−17.1155	+	3.63801i	−1.01741	+	0.216257i	−0.686288	−	0.727330i	$-0.740761\pi$
$283$	−17.1155	+	3.63801i	−1.01741	+	0.216257i	−0.331123	+	0.943588i	$0.607427\pi$
$284$	0.0356157	+	0.0158571i	0.00211340	+	0.000940946i
$285$	1.34903	+	2.43449i	0.0799095	+	0.144207i
$286$	15.8977	+	11.5504i	0.940051	+	0.682987i
$287$	22.4879	+	0.281493i	1.32742	+	0.0166160i
$288$	−3.51852	+	2.55635i	−0.207331	+	0.150635i
$289$	6.21675	−	2.76788i	0.365691	−	0.162816i
$290$	−1.29043	+	3.74603i	−0.0757768	+	0.219974i
$291$	−6.45582	−	2.87432i	−0.378447	−	0.168495i
$292$	−8.28892	−	9.20578i	−0.485072	−	0.538727i
$293$	−27.4172			−1.60173			−0.800865	−	0.598845i	$-0.795626\pi$
$293$	−27.4172			−1.60173			−0.800865	+	0.598845i	$0.795626\pi$
$294$	−11.7382	−	0.293914i	−0.684588	−	0.0171414i
$295$	1.82466	+	20.8887i	0.106236	+	1.21619i
$296$	8.18826	+	1.74047i	0.475933	+	0.101163i
$297$	1.22274	−	1.35799i	0.0709503	−	0.0787983i
$298$	−0.393767	+	3.74644i	−0.0228103	+	0.217026i
$299$	−23.4937	+	40.6923i	−1.35868	+	2.35330i
$300$	3.65638	+	1.78457i	0.211101	+	0.103032i
$301$	22.1938	+	16.5531i	1.27923	+	0.954103i
$302$	22.3567	+	16.2431i	1.28648	+	0.934683i
$303$	3.90052	+	0.829081i	0.224079	+	0.0476295i
$304$	−4.13550	+	4.59294i	−0.237187	+	0.263423i
$305$	−12.7072	−	9.57830i	−0.727614	−	0.548452i
$306$	−5.47629	−	6.08204i	−0.313059	−	0.347687i
$307$	12.3701			0.705998			0.352999	−	0.935624i	$-0.385162\pi$
$307$	12.3701			0.705998			0.352999	+	0.935624i	$0.385162\pi$
$308$	−0.362225	−	3.91742i	−0.0206397	−	0.223216i
$309$	0.757408	−	0.550289i	0.0430874	−	0.0313048i
$310$	19.4256	+	9.06154i	1.10330	+	0.514661i
$311$	0.876076	−	8.33530i	0.0496777	−	0.472652i	−0.941196	−	0.337860i	$-0.890297\pi$
$311$	0.876076	−	8.33530i	0.0496777	−	0.472652i	0.990874	−	0.134791i	$-0.0430365\pi$
$312$	11.6539	+	5.18864i	0.659770	+	0.293749i
$313$	−0.137909	−	1.31211i	−0.00779506	−	0.0741650i	0.989933	−	0.141538i	$-0.0452048\pi$
$313$	−0.137909	−	1.31211i	−0.00779506	−	0.0741650i	−0.997728	+	0.0673733i	$0.978538\pi$
$314$	−15.1810	−	11.0296i	−0.856712	−	0.622438i
$315$	−5.91340	−	0.178086i	−0.333182	−	0.0100340i
$316$	9.61344	−	6.98457i	0.540798	−	0.392913i
$317$	5.84255	+	6.48881i	0.328150	+	0.364448i	0.884532	−	0.466479i	$-0.154478\pi$
$317$	5.84255	+	6.48881i	0.328150	+	0.364448i	−0.556382	+	0.830927i	$0.687811\pi$
$318$	1.62970	+	2.82272i	0.0913891	+	0.158290i
$319$	1.88809	−	0.401325i	0.105712	−	0.0224699i
$320$	0.718938	−	5.84869i	0.0401899	−	0.326952i
$321$	1.81152	+	5.57528i	0.101109	+	0.311182i
$322$	31.8994	−	6.36419i	1.77768	−	0.354662i
$323$	−4.91320	−	3.56965i	−0.273378	−	0.198620i
$324$	−0.406863	+	0.704708i	−0.0226035	+	0.0391504i
$325$	−2.22726	−	31.9767i	−0.123546	−	1.77375i
$326$	−11.9494	−	20.6970i	−0.661816	−	1.14630i
$327$	−11.5569	+	5.14546i	−0.639098	+	0.284545i
$328$	5.22687	+	16.0866i	0.288605	+	0.888236i
$329$	5.65276	+	6.43829i	0.311647	+	0.354954i
$330$	−0.596439	−	6.82806i	−0.0328329	−	0.375872i
$331$	3.51979	+	3.90912i	0.193465	+	0.214865i	0.832071	−	0.554669i	$-0.187155\pi$
$331$	3.51979	+	3.90912i	0.193465	+	0.214865i	−0.638606	+	0.769534i	$0.720489\pi$
$332$	1.50151	+	2.60070i	0.0824062	+	0.142732i
$333$	4.11496	−	0.874662i	0.225498	−	0.0479312i
$334$	0.589983	+	5.61332i	0.0322825	+	0.307147i
$335$	−15.6136	−	17.9663i	−0.853059	−	0.981603i
$336$	−3.90284	−	12.5438i	−0.212918	−	0.684321i
$337$	−16.3543	+	11.8821i	−0.890877	+	0.647260i	−0.936107	−	0.351716i	$-0.885598\pi$
$337$	−16.3543	+	11.8821i	−0.890877	+	0.647260i	0.0452294	+	0.998977i	$0.485598\pi$
$338$	4.92676	+	46.8750i	0.267981	+	2.54967i
$339$	1.69294	−	16.1073i	0.0919481	−	0.874828i
$340$	−8.87628	−	0.156147i	−0.481384	−	0.00846824i
$341$	−1.09158	−	10.3857i	−0.0591126	−	0.562419i
$342$	−0.645201	+	1.98572i	−0.0348885	+	0.107376i
$343$	6.38030	−	17.3865i	0.344504	−	0.938785i
$344$	−6.43479	+	19.8042i	−0.346941	+	1.06777i
$345$	16.0883	−	3.12498i	0.866167	−	0.168243i
$346$	−1.48854	+	1.65319i	−0.0800245	+	0.0888762i
$347$	−16.0425	+	17.8170i	−0.861209	+	0.956469i	−0.999424	−	0.0339332i	$-0.989197\pi$
$347$	−16.0425	+	17.8170i	−0.861209	+	0.956469i	0.138216	+	0.990402i	$0.455863\pi$
$348$	−0.785243	+	0.349613i	−0.0420934	+	0.0187412i
$349$	−20.4122			−1.09264			−0.546320	−	0.837576i	$-0.683972\pi$
$349$	−20.4122			−1.09264			−0.546320	+	0.837576i	$0.683972\pi$
$350$	−15.6174	+	15.7638i	−0.834788	+	0.842611i
$351$	6.41083			0.342185
$352$	7.26030	−	3.23249i	0.386975	−	0.172292i
$353$	7.41979	−	8.24051i	0.394915	−	0.438598i	−0.512593	−	0.858632i	$-0.671315\pi$
$353$	7.41979	−	8.24051i	0.394915	−	0.438598i	0.907509	+	0.420034i	$0.137982\pi$
$354$	−10.5252	+	11.6894i	−0.559407	+	0.621284i
$355$	−0.0730742	+	0.0783411i	−0.00387838	+	0.00415791i
$356$	0.143788	−	0.442535i	0.00762076	−	0.0234543i
$357$	11.8575	−	5.10244i	0.627566	−	0.270050i
$358$	4.72274	−	14.5351i	0.249604	−	0.768204i
$359$	−1.03222	−	9.82096i	−0.0544787	−	0.518330i	−0.987399	−	0.158248i	$-0.949415\pi$
$359$	−1.03222	−	9.82096i	−0.0544787	−	0.518330i	0.932921	−	0.360082i	$-0.117251\pi$
$360$	−1.30033	−	4.25525i	−0.0685332	−	0.224271i
$361$	1.82409	−	17.3551i	0.0960048	−	0.913425i
$362$	−0.151695	−	1.44328i	−0.00797292	−	0.0758573i
$363$	6.19771	−	4.50290i	0.325295	−	0.236341i
$364$	9.36299	−	10.1405i	0.490754	−	0.531505i
$365$	31.3361	−	13.2963i	1.64021	−	0.695962i
$366$	−1.24778	−	11.8718i	−0.0652224	−	0.620549i
$367$	−9.67983	+	2.05751i	−0.505283	+	0.107401i	−0.453498	−	0.891257i	$-0.649824\pi$
$367$	−9.67983	+	2.05751i	−0.505283	+	0.107401i	−0.0517844	+	0.998658i	$0.516491\pi$
$368$	18.1963	+	31.5170i	0.948549	+	1.64293i
$369$	5.68780	+	6.31694i	0.296095	+	0.328847i
$370$	8.12877	−	13.5244i	0.422595	−	0.703099i
$371$	−5.04162	+	1.00584i	−0.261748	+	0.0522209i
$372$	1.43702	+	4.42268i	0.0745058	+	0.229305i
$373$	13.1923	−	5.87357i	0.683069	−	0.304122i	−0.0357081	−	0.999362i	$-0.511369\pi$
$373$	13.1923	−	5.87357i	0.683069	−	0.304122i	0.718778	+	0.695240i	$0.244702\pi$
$374$	7.47769	+	12.9517i	0.386662	+	0.669719i
$375$	−7.90893	+	7.90246i	−0.408415	+	0.408081i
$376$	−3.22189	+	5.58047i	−0.166156	+	0.287791i
$377$	5.47857	+	3.98041i	0.282161	+	0.205002i
$378$	−2.92811	−	3.33501i	−0.150606	−	0.171534i
$379$	2.45034	+	7.54138i	0.125866	+	0.387375i	0.994058	−	0.108854i	$-0.0347180\pi$
$379$	2.45034	+	7.54138i	0.125866	+	0.387375i	−0.868192	+	0.496228i	$0.834718\pi$
$380$	1.09774	+	1.98101i	0.0563129	+	0.101624i
$381$	5.88796	−	1.25152i	0.301649	−	0.0641175i
$382$	7.23304	+	12.5280i	0.370074	+	0.640988i
$383$	4.57108	+	5.07670i	0.233571	+	0.259407i	0.848524	−	0.529157i	$-0.177492\pi$
$383$	4.57108	+	5.07670i	0.233571	+	0.259407i	−0.614953	+	0.788564i	$0.710825\pi$
$384$	10.6133	−	7.71101i	0.541608	−	0.393501i
$385$	10.5021	+	2.56498i	0.535234	+	0.130723i
$386$	−11.3890	−	8.27461i	−0.579686	−	0.421166i
$387$	1.09386	+	10.4074i	0.0556039	+	0.529036i
$388$	−5.25327	−	2.33891i	−0.266694	−	0.118740i
$389$	4.01050	−	38.1574i	0.203340	−	1.93466i	−0.129308	−	0.991604i	$-0.541276\pi$
$389$	4.01050	−	38.1574i	0.203340	−	1.93466i	0.332648	−	0.943051i	$-0.392058\pi$
$390$	16.4016	−	17.5838i	0.830528	−	0.890389i
$391$	−28.9308	+	21.0195i	−1.46309	+	1.06300i
$392$	13.9248	+	0.348663i	0.703307	+	0.0176101i
$393$	12.3795			0.624464
$394$	−2.87580	−	3.19390i	−0.144881	−	0.160906i
$395$	9.54266	+	31.2279i	0.480143	+	1.57124i
$396$	0.994972	−	1.10503i	0.0499992	−	0.0555298i
$397$	−25.5491	−	5.43063i	−1.28227	−	0.272556i	−0.484116	−	0.875004i	$-0.660859\pi$
$397$	−25.5491	−	5.43063i	−1.28227	−	0.272556i	−0.798158	+	0.602448i	$0.794192\pi$
$398$	35.0060	+	25.4333i	1.75469	+	1.27486i
$399$	−2.63983	−	1.96890i	−0.132157	−	0.0985684i
$400$	−22.3110	−	10.8893i	−1.11555	−	0.544466i
$401$	−5.46719	+	9.46946i	−0.273019	+	0.472882i	−0.969633	−	0.244563i	$-0.921355\pi$
$401$	−5.46719	+	9.46946i	−0.273019	+	0.472882i	0.696615	+	0.717445i	$0.254689\pi$
$402$	1.86645	−	17.7581i	0.0930903	−	0.885695i
$403$	24.5147	−	27.2263i	1.22116	−	1.35624i
$404$	3.17396	+	0.674645i	0.157910	+	0.0335649i
$405$	−1.46676	−	1.68778i	−0.0728840	−	0.0838666i
$406$	−0.431633	−	4.66806i	−0.0214216	−	0.231672i
$407$	−7.68746			−0.381053
$408$	6.49638	+	7.21496i	0.321619	+	0.357194i
$409$	4.25841	+	1.89597i	0.210565	+	0.0937495i	0.509309	−	0.860584i	$-0.329901\pi$
$409$	4.25841	+	1.89597i	0.210565	+	0.0937495i	−0.298744	+	0.954333i	$0.596568\pi$
$410$	31.8781	+	0.560781i	1.57435	+	0.0276950i
$411$	16.4384	−	7.31886i	0.810847	−	0.361013i
$412$	0.616322	−	0.447784i	0.0303640	−	0.0220608i
$413$	−12.1351	−	21.6397i	−0.597129	−	1.06482i
$414$	9.94641	+	7.22649i	0.488840	+	0.355163i
$415$	−8.10072	+	1.57347i	−0.397649	+	0.0772388i
$416$	25.4710	+	11.3404i	1.24882	+	0.556011i
$417$	12.1939	−	2.59189i	0.597136	−	0.126925i
$418$	1.90767	−	3.30419i	0.0933074	−	0.161613i
$419$	6.30722	−	19.4116i	0.308128	−	0.948319i	−0.670364	−	0.742033i	$-0.733862\pi$
$419$	6.30722	−	19.4116i	0.308128	−	0.948319i	0.978492	−	0.206287i	$-0.0661380\pi$
$420$	−4.81189	−	0.144913i	−0.234796	−	0.00707104i
$421$	−4.99444	−	15.3713i	−0.243414	−	0.749151i	−0.995893	−	0.0905352i	$-0.971142\pi$
$421$	−4.99444	−	15.3713i	−0.243414	−	0.749151i	0.752479	−	0.658616i	$-0.228858\pi$
$422$	−15.0727	−	3.20380i	−0.733727	−	0.155958i
$423$	−0.338492	+	3.22054i	−0.0164581	+	0.156588i
$424$	−1.93327	−	3.34852i	−0.0938879	−	0.162619i
$425$	8.34991	−	22.9217i	0.405030	−	1.11187i
$426$	−0.0803662			−0.00389375
$427$	18.3664	+	4.14483i	0.888812	+	0.200582i
$428$	1.47408	+	4.53675i	0.0712524	+	0.219292i
$429$	−11.4588	−	2.43565i	−0.553237	−	0.117594i
$430$	31.3441	+	23.6262i	1.51155	+	1.13936i
$431$	26.6789	−	5.67078i	1.28508	−	0.273152i	0.485777	−	0.874083i	$-0.338537\pi$
$431$	26.6789	−	5.67078i	1.28508	−	0.273152i	0.799301	+	0.600931i	$0.205203\pi$
$432$	2.48265	−	4.30008i	0.119447	−	0.206888i
$433$	−9.99018	+	30.7466i	−0.480097	+	1.47759i	0.358860	+	0.933391i	$0.383165\pi$
$433$	−9.99018	+	30.7466i	−0.480097	+	1.47759i	−0.838958	+	0.544197i	$0.816835\pi$
$434$	−25.3604	−	0.317451i	−1.21734	−	0.0152381i
$435$	−0.205541	−	2.35304i	−0.00985495	−	0.112820i
$436$	−9.40415	+	4.18700i	−0.450377	+	0.200521i
$437$	8.33431	+	3.71067i	0.398684	+	0.177506i
$438$	23.3281	+	10.3863i	1.11466	+	0.496279i
$439$	17.3622	−	7.73015i	0.828653	−	0.368940i	0.0518273	−	0.998656i	$-0.483495\pi$
$439$	17.3622	−	7.73015i	0.828653	−	0.368940i	0.776825	+	0.629716i	$0.216829\pi$
$440$	0.707540	+	8.09994i	0.0337307	+	0.386150i
$441$	6.46408	−	2.68619i	0.307813	−	0.127914i
$442$	−16.2133	+	49.8995i	−0.771189	+	2.37348i
$443$	17.8438	−	30.9064i	0.847787	−	1.46841i	−0.0353923	−	0.999373i	$-0.511268\pi$
$443$	17.8438	−	30.9064i	0.847787	−	1.46841i	0.883179	−	0.469036i	$-0.155399\pi$
$444$	3.34845	−	0.711735i	0.158910	−	0.0337775i
$445$	1.02106	+	0.769643i	0.0484029	+	0.0364846i
$446$	−23.6057	−	5.01755i	−1.11776	−	0.237588i
$447$	−0.693979	−	2.13585i	−0.0328241	−	0.101022i
$448$	2.07141	+	6.65755i	0.0978648	+	0.314540i
$449$	7.40086			0.349268			0.174634	−	0.984633i	$-0.444126\pi$
$449$	7.40086			0.349268			0.174634	+	0.984633i	$0.444126\pi$
$450$	−8.38189	−	0.294991i	−0.395126	−	0.0139060i
$451$	−7.76649	−	13.4520i	−0.365710	−	0.633428i
$452$	1.37759	−	13.1069i	0.0647966	−	0.616498i
$453$	−16.1143	−	3.42521i	−0.757118	−	0.160930i
$454$	−2.95089	−	9.08190i	−0.138492	−	0.426235i
$455$	17.9662	+	33.4017i	0.842267	+	1.56589i
$456$	0.765385	−	2.35561i	0.0358424	−	0.110312i
$457$	−7.40708	+	12.8294i	−0.346489	+	0.600136i	−0.985623	−	0.168959i	$-0.945959\pi$
$457$	−7.40708	+	12.8294i	−0.346489	+	0.600136i	0.639134	+	0.769095i	$0.279293\pi$
$458$	14.7446	−	3.13406i	0.688969	−	0.146445i
$459$	4.45723	+	1.98449i	0.208046	+	0.0926279i
$460$	13.0915	−	2.54288i	0.610394	−	0.118562i
$461$	−26.7008	−	19.3993i	−1.24358	−	0.903514i	−0.245749	−	0.969334i	$-0.579034\pi$
$461$	−26.7008	−	19.3993i	−1.24358	−	0.903514i	−0.997832	+	0.0658198i	$0.979034\pi$
$462$	3.96669	+	7.07352i	0.184547	+	0.329090i
$463$	−10.8864	+	7.90943i	−0.505934	+	0.367582i	−0.811279	−	0.584659i	$-0.801228\pi$
$463$	−10.8864	+	7.90943i	−0.505934	+	0.367582i	0.305345	+	0.952242i	$0.401228\pi$
$464$	4.79150	−	2.13331i	0.222440	−	0.0990365i
$465$	−12.7767	−	0.224761i	−0.592505	−	0.0104230i
$466$	31.4472	+	14.0012i	1.45676	+	0.648593i
$467$	12.6108	+	14.0058i	0.583560	+	0.648109i	0.960550	−	0.278108i	$-0.0897075\pi$
$467$	12.6108	+	14.0058i	0.583560	+	0.648109i	−0.376990	+	0.926217i	$0.623041\pi$
$468$	5.21666			0.241140
$469$	25.5835	+	11.7764i	1.18134	+	0.543783i
$470$	7.96737	+	9.16794i	0.367507	+	0.422885i
$471$	10.9422	+	2.32584i	0.504191	+	0.107169i
$472$	12.4857	−	13.8668i	0.574703	−	0.638272i
$473$	1.99886	−	19.0179i	0.0919077	−	0.874443i
$474$	−12.2477	+	21.2136i	−0.562555	+	0.974373i
$475$	−6.12934	+	1.07905i	−0.281234	+	0.0495100i
$476$	9.64877	−	4.15199i	0.442251	−	0.190306i
$477$	−1.57201	−	1.14213i	−0.0719773	−	0.0522945i
$478$	−29.6592	−	6.30426i	−1.35658	−	0.288350i
$479$	−14.9887	+	16.6466i	−0.684851	+	0.760605i	−0.980888	−	0.194572i	$-0.937668\pi$
$479$	−14.9887	+	16.6466i	−0.684851	+	0.760605i	0.296037	+	0.955177i	$0.404335\pi$
$480$	−2.84203	−	9.30040i	−0.129720	−	0.424503i
$481$	−18.0462	−	20.0424i	−0.822837	−	0.913853i
$482$	−35.1720			−1.60204
$483$	−15.8297	+	11.2009i	−0.720276	+	0.509660i
$484$	5.04324	−	3.66413i	0.229238	−	0.166551i
$485$	10.7784	−	11.5552i	0.489420	−	0.524696i
$486$	0.175338	−	1.66823i	0.00795348	−	0.0756723i
$487$	−33.5584	−	14.9411i	−1.52067	−	0.677048i	−0.534868	−	0.844935i	$-0.679639\pi$
$487$	−33.5584	−	14.9411i	−1.52067	−	0.677048i	−0.985806	+	0.167887i	$0.946306\pi$
$488$	1.48021	+	14.0832i	0.0670058	+	0.637517i
$489$	11.5264	+	8.37440i	0.521241	+	0.378703i
$490$	9.17011	−	24.6023i	0.414263	−	1.11142i
$491$	−27.6237	+	20.0698i	−1.24664	+	0.905736i	−0.998022	−	0.0628659i	$-0.979976\pi$
$491$	−27.6237	+	20.0698i	−1.24664	+	0.905736i	−0.248617	+	0.968602i	$0.579976\pi$
$492$	4.62831	+	5.14026i	0.208660	+	0.231741i
$493$	2.57692	+	4.46335i	0.116058	+	0.201019i
$494$	13.0928	−	2.78295i	0.589071	−	0.125211i
$495$	1.98048	+	3.57404i	0.0890161	+	0.160641i
$496$	−8.76857	−	26.9869i	−0.393720	−	1.21175i
$497$	0.0406768	−	0.120056i	0.00182460	−	0.00538525i
$498$	−5.00817	−	3.63865i	−0.224422	−	0.163052i
$499$	−7.35594	+	12.7409i	−0.329297	+	0.570359i	−0.982373	−	0.186934i	$-0.940145\pi$
$499$	−7.35594	+	12.7409i	−0.329297	+	0.570359i	0.653076	+	0.757293i	$0.273478\pi$
$500$	−6.43570	+	6.43044i	−0.287813	+	0.287578i
$501$	−1.68242	−	2.91404i	−0.0751650	−	0.130190i
$502$	−28.8126	+	12.8282i	−1.28597	+	0.572551i
$503$	−0.673316	−	2.07225i	−0.0300217	−	0.0923973i	0.934923	−	0.354851i	$-0.115468\pi$
$503$	−0.673316	−	2.07225i	−0.0300217	−	0.0923973i	−0.964945	+	0.262454i	$0.915468\pi$
$504$	3.47354	+	3.95623i	0.154724	+	0.176225i
$505$	−4.59347	+	7.64246i	−0.204407	+	0.340085i
$506$	−15.0329	−	16.6957i	−0.668292	−	0.742213i
$507$	−14.0494	−	24.3342i	−0.623954	−	1.08072i
$508$	4.79119	−	1.01840i	0.212575	−	0.0451841i
$509$	1.20583	+	11.4727i	0.0534474	+	0.508518i	0.988195	+	0.153204i	$0.0489592\pi$
$509$	1.20583	+	11.4727i	0.0534474	+	0.508518i	−0.934747	+	0.355313i	$0.884374\pi$
$510$	16.8466	−	7.14824i	0.745980	−	0.316529i
$511$	−27.3231	+	29.5920i	−1.20870	+	1.30907i
$512$	1.48380	−	1.07805i	0.0655755	−	0.0476434i
$513$	−0.130109	−	1.23790i	−0.00574444	−	0.0546547i
$514$	2.37018	−	22.5508i	0.104544	−	0.994672i
$515$	0.611785	+	2.00203i	0.0269585	+	0.0882201i
$516$	0.890101	+	8.46874i	0.0391845	+	0.372816i
$517$	1.82860	−	5.62785i	0.0804217	−	0.247512i
$518$	−2.18383	+	18.5421i	−0.0959521	+	0.814695i
$519$	0.409818	−	1.26129i	0.0179890	−	0.0553645i
$520$	−19.4568	+	20.8592i	−0.853238	+	0.914735i
$521$	−14.9629	+	16.6180i	−0.655536	+	0.728047i	−0.975650	−	0.219332i	$-0.929612\pi$
$521$	−14.9629	+	16.6180i	−0.655536	+	0.728047i	0.320114	+	0.947379i	$0.396279\pi$
$522$	1.18562	−	1.31677i	0.0518934	−	0.0576334i
$523$	8.14177	−	3.62495i	0.356015	−	0.158508i	−0.220933	−	0.975289i	$-0.570910\pi$
$523$	8.14177	−	3.62495i	0.356015	−	0.158508i	0.576948	+	0.816781i	$0.304244\pi$
$524$	10.0735			0.440064
$525$	4.68311	−	12.3721i	0.204388	−	0.539962i
$526$	−16.8058			−0.732766
$527$	25.4722	−	11.3409i	1.10958	−	0.494019i
$528$	−6.07125	+	6.74281i	−0.264217	+	0.293443i
$529$	20.5557	−	22.8294i	0.893725	−	0.992582i
$530$	−7.15453	+	1.38969i	−0.310773	+	0.0603641i
$531$	2.89774	−	8.91834i	0.125751	−	0.387023i
$532$	−2.14810	−	1.60215i	−0.0931320	−	0.0694619i
$533$	16.8395	−	51.8267i	0.729400	−	2.24486i
$534$	0.100262	+	0.953933i	0.00433878	+	0.0412807i
$535$	−13.1062	−	0.230558i	−0.566632	−	0.00996788i
$536$	−2.21413	+	21.0660i	−0.0956357	+	0.909913i
$537$	0.952369	+	9.06118i	0.0410977	+	0.391019i
$538$	36.1793	−	26.2858i	1.55980	−	1.13326i
$539$	−12.5746	+	2.34547i	−0.541625	+	0.101027i
$540$	−1.19354	−	1.37339i	−0.0513619	−	0.0591014i
$541$	−1.81368	−	17.2560i	−0.0779763	−	0.741895i	−0.961740	−	0.273962i	$-0.911666\pi$
$541$	−1.81368	−	17.2560i	−0.0779763	−	0.741895i	0.883764	−	0.467933i	$-0.155001\pi$
$542$	14.7795	−	3.14147i	0.634833	−	0.134938i
$543$	0.432580	+	0.749250i	0.0185638	+	0.0321534i
$544$	14.1987	+	15.7692i	0.608764	+	0.676101i
$545$	−2.46158	−	28.1803i	−0.105443	−	1.20711i
$546$	−9.12997	+	26.9467i	−0.390727	+	1.15321i
$547$	7.41295	+	22.8147i	0.316955	+	0.975486i	0.974942	+	0.222458i	$0.0714079\pi$
$547$	7.41295	+	22.8147i	0.316955	+	0.975486i	−0.657988	+	0.753029i	$0.728592\pi$
$548$	13.3764	−	5.95555i	0.571410	−	0.254408i
$549$	3.55821	+	6.16300i	0.151861	+	0.263031i
$550$	14.8699	+	3.71178i	0.634053	+	0.158271i
$551$	0.657411	−	1.13867i	0.0280067	−	0.0485090i
$552$	−11.7992	−	8.57260i	−0.502206	−	0.364874i
$553$	−25.4911	−	29.0335i	−1.08399	−	1.23463i
$554$	−8.32971	−	25.6362i	−0.353895	−	1.08918i
$555$	−1.14768	+	9.33662i	−0.0487165	+	0.396317i
$556$	9.92247	−	2.10909i	0.420806	−	0.0894451i
$557$	−0.263186	−	0.455851i	−0.0111515	−	0.0193150i	0.860396	−	0.509626i	$-0.170216\pi$
$557$	−0.263186	−	0.455851i	−0.0111515	−	0.0193150i	−0.871547	+	0.490311i	$0.836883\pi$
$558$	−6.41435	−	7.12386i	−0.271541	−	0.301577i
$559$	54.2748	−	39.4329i	2.29558	−	1.66783i
$560$	29.3618	+	0.884250i	1.24076	+	0.0373664i
$561$	−7.21297	−	5.24053i	−0.304532	−	0.221255i
$562$	0.358173	+	3.40779i	0.0151086	+	0.143749i
$563$	33.8012	+	15.0493i	1.42455	+	0.634252i	0.966964	−	0.254913i	$-0.0820467\pi$
$563$	33.8012	+	15.0493i	1.42455	+	0.634252i	0.457588	+	0.889164i	$0.348713\pi$
$564$	−0.275440	+	2.62064i	−0.0115981	+	0.110349i
$565$	32.8202	+	15.3098i	1.38076	+	0.644087i
$566$	23.7456	−	17.2522i	0.998103	−	0.725164i
$567$	2.40336	+	1.10629i	0.100931	+	0.0464599i
$568$	0.0953363			0.00400022
$569$	−4.26106	−	4.73239i	−0.178633	−	0.198392i	0.647178	−	0.762339i	$-0.275949\pi$
$569$	−4.26106	−	4.73239i	−0.178633	−	0.198392i	−0.825811	+	0.563947i	$0.809282\pi$
$570$	−3.72822	−	2.81021i	−0.156158	−	0.117707i
$571$	4.66396	−	5.17986i	0.195181	−	0.216770i	−0.637608	−	0.770361i	$-0.720076\pi$
$571$	4.66396	−	5.17986i	0.195181	−	0.216770i	0.832789	+	0.553591i	$0.186743\pi$
$572$	−9.32435	−	1.98195i	−0.389871	−	0.0828696i
$573$	−6.97698	−	5.06907i	−0.291468	−	0.211764i
$574$	−34.6524	+	14.9114i	−1.44636	+	0.622388i
$575$	−5.11017	+	36.2889i	−0.213109	+	1.51335i
$576$	−1.31765	+	2.28224i	−0.0549021	+	0.0950932i
$577$	−3.89067	+	37.0172i	−0.161971	+	1.54105i	0.547796	+	0.836612i	$0.315467\pi$
$577$	−3.89067	+	37.0172i	−0.161971	+	1.54105i	−0.709767	+	0.704436i	$0.751200\pi$
$578$	−7.63810	+	8.48297i	−0.317703	+	0.352845i
$579$	8.20904	+	1.74488i	0.341156	+	0.0725149i
$580$	−0.167254	−	1.91473i	−0.00694486	−	0.0795050i
$581$	7.97049	−	5.63984i	0.330672	−	0.233980i
$582$	11.8539			0.491361
$583$	2.37591	+	2.63871i	0.0984000	+	0.109284i
$584$	−27.6735	−	12.3210i	−1.14514	−	0.509849i
$585$	−4.66888	+	13.5534i	−0.193035	+	0.560365i
$586$	42.0140	−	18.7058i	1.73558	−	0.772731i
$587$	−18.1831	+	13.2108i	−0.750498	+	0.545269i	−0.895981	−	0.444092i	$-0.853526\pi$
$587$	−18.1831	+	13.2108i	−0.750498	+	0.545269i	0.145483	+	0.989361i	$0.453526\pi$
$588$	5.25999	−	2.18583i	0.216919	−	0.0901420i
$589$	−5.75480	−	4.18110i	−0.237122	−	0.172279i
$590$	−17.0478	−	30.7649i	−0.701846	−	1.26657i
$591$	2.34065	+	1.04212i	0.0962815	+	0.0428673i
$592$	−20.4320	+	4.34296i	−0.839751	+	0.178495i
$593$	−15.1654	+	26.2673i	−0.622769	+	1.07867i	0.366199	+	0.930537i	$0.380659\pi$
$593$	−15.1654	+	26.2673i	−0.622769	+	1.07867i	−0.988968	+	0.148131i	$0.952674\pi$
$594$	−0.947207	+	2.91520i	−0.0388644	+	0.119612i
$595$	2.15170	+	28.7845i	0.0882111	+	1.18005i
$596$	−0.564709	−	1.73800i	−0.0231314	−	0.0711910i
$597$	−25.2318	−	5.36318i	−1.03267	−	0.219500i
$598$	8.23868	−	78.3858i	0.336905	−	3.20543i
$599$	−7.44963	−	12.9031i	−0.304384	−	0.527208i	0.672740	−	0.739879i	$-0.265117\pi$
$599$	−7.44963	−	12.9031i	−0.304384	−	0.527208i	−0.977124	+	0.212671i	$0.931784\pi$
$600$	9.94322	+	0.349940i	0.405930	+	0.0142862i
$601$	30.5650			1.24677			0.623387	−	0.781913i	$-0.285756\pi$
$601$	30.5650			1.24677			0.623387	+	0.781913i	$0.285756\pi$
$602$	−45.3033	−	10.2238i	−1.84642	−	0.416691i
$603$	3.28946	+	10.1239i	0.133957	+	0.412277i
$604$	−13.1127	−	2.78718i	−0.533547	−	0.113409i
$605$	5.00611	+	16.3822i	0.203527	+	0.666032i
$606$	−6.54280	+	1.39071i	−0.265783	+	0.0564939i
$607$	−18.2270	+	31.5701i	−0.739811	+	1.28139i	0.212769	+	0.977103i	$0.431752\pi$
$607$	−18.2270	+	31.5701i	−0.739811	+	1.28139i	−0.952580	+	0.304288i	$0.901581\pi$
$608$	1.67285	−	5.14850i	0.0678429	−	0.208799i
$609$	1.36698	+	2.43763i	0.0553927	+	0.0987779i
$610$	26.0075	+	6.00803i	1.05301	+	0.243258i
$611$	18.9652	−	8.44387i	0.767252	−	0.341603i
$612$	3.62697	+	1.61483i	0.146611	+	0.0652756i
$613$	9.45654	+	4.21032i	0.381946	+	0.170053i	0.588723	−	0.808335i	$-0.299631\pi$
$613$	9.45654	+	4.21032i	0.381946	+	0.170053i	−0.206777	+	0.978388i	$0.566297\pi$
$614$	−18.9559	+	8.43970i	−0.764997	+	0.340598i
$615$	−17.4972	+	7.42432i	−0.705557	+	0.299378i
$616$	−4.70558	−	8.39113i	−0.189593	−	0.338088i
$617$	−7.84476	+	24.1437i	−0.315818	+	0.971989i	0.659598	+	0.751619i	$0.270727\pi$
$617$	−7.84476	+	24.1437i	−0.315818	+	0.971989i	−0.975416	+	0.220370i	$0.929273\pi$
$618$	−0.785205	+	1.36001i	−0.0315856	+	0.0547078i
$619$	−20.1510	+	4.28323i	−0.809938	+	0.172158i	−0.594225	−	0.804299i	$-0.702541\pi$
$619$	−20.1510	+	4.28323i	−0.809938	+	0.172158i	−0.215714	+	0.976457i	$0.569208\pi$
$620$	−10.3967	−	0.182894i	−0.417543	−	0.00734518i
$621$	−7.16923	−	1.52387i	−0.287691	−	0.0611506i
$622$	4.34441	+	13.3707i	0.174195	+	0.536117i
$623$	−1.47579	−	0.333048i	−0.0591263	−	0.0133433i
$624$	−31.8317			−1.27429
$625$	−10.9470	−	22.4758i	−0.437881	−	0.899033i
$626$	1.10654	+	1.91659i	0.0442263	+	0.0766022i
$627$	−0.237754	+	2.26208i	−0.00949498	+	0.0903387i
$628$	8.90398	+	1.89260i	0.355307	+	0.0755229i
$629$	−6.34276	−	19.5210i	−0.252902	−	0.778354i
$630$	9.18317	−	3.76162i	0.365866	−	0.149866i
$631$	0.744097	−	2.29010i	0.0296220	−	0.0911673i	−0.935152	−	0.354245i	$-0.884738\pi$
$631$	0.744097	−	2.29010i	0.0296220	−	0.0911673i	0.964775	+	0.263078i	$0.0847377\pi$
$632$	14.5291	−	25.1651i	0.577936	−	1.00102i
$633$	8.98565	−	1.90996i	0.357148	−	0.0759141i
$634$	−13.3802	−	5.95725i	−0.531396	−	0.236593i
$635$	−1.64218	+	13.3595i	−0.0651681	+	0.530154i
$636$	−1.27918	−	0.929381i	−0.0507229	−	0.0368524i
$637$	−35.6336	−	27.2778i	−1.41186	−	1.08079i
$638$	−2.61948	+	1.90317i	−0.103706	+	0.0753471i
$639$	0.0437686	−	0.0194870i	0.00173146	−	0.000770895i
$640$	8.57273	+	28.0538i	0.338867	+	1.10892i
$641$	−32.1072	−	14.2950i	−1.26816	−	0.564620i	−0.341272	−	0.939965i	$-0.610858\pi$
$641$	−32.1072	−	14.2950i	−1.26816	−	0.564620i	−0.926885	+	0.375345i	$0.877524\pi$
$642$	−6.57979	−	7.30760i	−0.259684	−	0.288408i
$643$	−44.7387			−1.76432			−0.882161	−	0.470949i	$-0.843912\pi$
$643$	−44.7387			−1.76432			−0.882161	+	0.470949i	$0.843912\pi$
$644$	−12.8810	+	9.11449i	−0.507584	+	0.359161i
$645$	−22.7993	−	5.26691i	−0.897721	−	0.207384i
$646$	9.96441	+	2.11800i	0.392045	+	0.0833317i
$647$	19.5749	−	21.7401i	0.769569	−	0.854693i	−0.223195	−	0.974774i	$-0.571649\pi$
$647$	19.5749	−	21.7401i	0.769569	−	0.854693i	0.992764	+	0.120081i	$0.0383155\pi$
$648$	−0.207999	+	1.97897i	−0.00817096	+	0.0777415i
$649$	−8.56780	+	14.8399i	−0.336316	+	0.582516i
$650$	25.2297	+	47.4813i	0.989589	+	1.86237i
$651$	13.8886	−	5.97646i	0.544339	−	0.234236i
$652$	9.37931	+	6.81447i	0.367322	+	0.266875i
$653$	−11.1676	−	2.37375i	−0.437022	−	0.0928919i	−0.0158536	−	0.999874i	$-0.505047\pi$
$653$	−11.1676	−	2.37375i	−0.437022	−	0.0928919i	−0.421168	+	0.906982i	$0.638380\pi$
$654$	14.1992	−	15.7698i	0.555231	−	0.616647i
$655$	−9.01576	+	26.1721i	−0.352275	+	1.02263i
$656$	−28.2416	−	31.3655i	−1.10265	−	1.22462i
$657$	−15.2233			−0.593917
$658$	−13.0549	−	6.00932i	−0.508933	−	0.234268i
$659$	19.9679	−	14.5075i	0.777840	−	0.565134i	−0.126490	−	0.991968i	$-0.540371\pi$
$659$	19.9679	−	14.5075i	0.777840	−	0.565134i	0.904330	+	0.426834i	$0.140371\pi$
$660$	1.61157	+	2.90829i	0.0627303	+	0.113205i
$661$	−3.86989	+	36.8195i	−0.150521	+	1.43211i	0.614911	+	0.788596i	$0.289192\pi$
$661$	−3.86989	+	36.8195i	−0.150521	+	1.43211i	−0.765432	+	0.643516i	$0.777475\pi$
$662$	−8.06077	−	3.58889i	−0.313291	−	0.139486i
$663$	−3.26952	−	31.1074i	−0.126977	−	1.20811i
$664$	5.94106	+	4.31643i	0.230558	+	0.167510i
$665$	6.08508	−	4.14708i	0.235969	−	0.160817i
$666$	−5.70900	+	4.14783i	−0.221219	+	0.160725i
$667$	−5.18053	−	5.75356i	−0.200591	−	0.222779i
$668$	−1.36903	−	2.37123i	−0.0529693	−	0.0917456i
$669$	14.0727	−	2.99124i	0.544081	−	0.115648i
$670$	36.1839	+	16.8789i	1.39791	+	0.652087i
$671$	−4.01852	−	12.3677i	−0.155133	−	0.477451i
$672$	7.59186	+	8.64686i	0.292862	+	0.333560i
$673$	34.4149	+	25.0039i	1.32660	+	0.963828i	0.999825	+	0.0187250i	$0.00596071\pi$
$673$	34.4149	+	25.0039i	1.32660	+	0.963828i	0.326771	+	0.945103i	$0.394039\pi$
$674$	16.9545	−	29.3661i	0.653065	−	1.13114i
$675$	4.63643	−	1.87177i	0.178456	−	0.0720444i
$676$	−11.4323	−	19.8014i	−0.439705	−	0.761591i
$677$	43.8570	−	19.5264i	1.68556	−	0.750461i	0.685820	−	0.727771i	$-0.259444\pi$
$677$	43.8570	−	19.5264i	1.68556	−	0.750461i	0.999743	−	0.0226893i	$-0.00722285\pi$
$678$	8.39521	+	25.8378i	0.322416	+	0.992295i
$679$	−5.99978	+	17.7081i	−0.230251	+	0.679575i
$680$	−19.9847	+	8.47977i	−0.766377	+	0.325184i
$681$	3.80926	+	4.23061i	0.145971	+	0.162117i
$682$	8.75857	+	15.1703i	0.335383	+	0.580901i
$683$	−10.4734	+	2.22620i	−0.400755	+	0.0851830i	−0.403880	−	0.914812i	$-0.632339\pi$
$683$	−10.4734	+	2.22620i	−0.400755	+	0.0851830i	0.00312507	+	0.999995i	$0.499005\pi$
$684$	−0.105873	−	1.00731i	−0.00404815	−	0.0385156i
$685$	3.50133	+	40.0834i	0.133779	+	1.53151i
$686$	2.08512	+	30.9961i	0.0796101	+	1.18344i
$687$	−7.27017	+	5.28209i	−0.277374	+	0.201524i
$688$	−5.43133	−	51.6757i	−0.207068	−	1.97012i
$689$	−1.30210	+	12.3887i	−0.0496062	+	0.471971i
$690$	−22.5216	+	15.7652i	−0.857384	+	0.600172i
$691$	0.770287	+	7.32879i	0.0293031	+	0.278800i	0.999355	+	0.0359037i	$0.0114310\pi$
$691$	0.770287	+	7.32879i	0.0293031	+	0.278800i	−0.970052	+	0.242897i	$0.921902\pi$
$692$	0.333480	−	1.02635i	0.0126770	−	0.0390158i
$693$	−3.87549	−	2.89051i	−0.147218	−	0.109801i
$694$	12.4275	−	38.2481i	0.471743	−	1.45188i
$695$	−3.40093	+	27.6672i	−0.129005	+	1.04948i
$696$	−1.40648	+	1.56205i	−0.0533123	+	0.0592093i
$697$	27.7510	−	30.8206i	1.05114	−	1.16741i
$698$	31.2796	−	13.9266i	1.18395	−	0.527128i
$699$	−20.5216			−0.776198
$700$	3.81077	−	10.0675i	0.144034	−	0.380515i
$701$	−6.96902			−0.263216			−0.131608	−	0.991302i	$-0.542014\pi$
$701$	−6.96902			−0.263216			−0.131608	+	0.991302i	$0.542014\pi$
$702$	−9.82393	+	4.37389i	−0.370780	+	0.165082i
$703$	−3.50384	+	3.89140i	−0.132150	+	0.146767i
$704$	3.22228	−	3.57870i	0.121444	−	0.134877i
$705$	−6.56217	−	3.06108i	−0.247146	−	0.115287i
$706$	−5.74783	+	17.6900i	−0.216322	+	0.665772i
$707$	1.23406	−	10.4779i	0.0464115	−	0.394063i
$708$	2.35797	−	7.25709i	0.0886180	−	0.272738i
$709$	4.06588	+	38.6843i	0.152697	+	1.45282i	0.755616	+	0.655015i	$0.227338\pi$
$709$	4.06588	+	38.6843i	0.152697	+	1.45282i	−0.602918	+	0.797803i	$0.705995\pi$
$710$	0.0585291	−	0.169906i	0.00219656	−	0.00637645i
$711$	1.52643	−	14.5230i	0.0572457	−	0.544656i
$712$	−0.118939	−	1.13163i	−0.00445741	−	0.0424095i
$713$	−33.8865	+	24.6200i	−1.26906	+	0.922025i
$714$	−14.6892	+	15.9090i	−0.549729	+	0.595378i
$715$	13.4946	−	22.4518i	0.504668	−	0.839649i
$716$	0.774968	+	7.37332i	0.0289619	+	0.275554i
$717$	17.6815	−	3.75832i	0.660327	−	0.140357i
$718$	8.28229	+	14.3453i	0.309092	+	0.535364i
$719$	29.3195	+	32.5626i	1.09343	+	1.21438i	0.975184	+	0.221396i	$0.0710615\pi$
$719$	29.3195	+	32.5626i	1.09343	+	1.21438i	0.118249	+	0.992984i	$0.462272\pi$
$720$	7.28292	+	8.38035i	0.271418	+	0.312317i
$721$	−1.63425	−	1.86135i	−0.0608626	−	0.0693203i
$722$	9.04556	+	27.8394i	0.336641	+	1.03607i
$723$	19.1552	−	8.52844i	0.712390	−	0.317176i
$724$	0.352002	+	0.609685i	0.0130820	+	0.0226588i
$725$	5.12436	+	1.27913i	0.190314	+	0.0475058i
$726$	−6.42517	+	11.1287i	−0.238460	+	0.413026i
$727$	12.4807	+	9.06775i	0.462883	+	0.336304i	0.794661	−	0.607053i	$-0.207649\pi$
$727$	12.4807	+	9.06775i	0.462883	+	0.336304i	−0.331778	+	0.943357i	$0.607649\pi$
$728$	10.8306	−	31.9662i	0.401410	−	1.18475i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−38.9477	+	41.7548i	−1.44152	+	1.54542i
$731$	49.9419	−	10.6155i	1.84717	−	0.392628i
$732$	2.89541	+	5.01500i	0.107017	+	0.185360i
$733$	−13.9800	−	15.5264i	−0.516363	−	0.573479i	0.427416	−	0.904055i	$-0.359424\pi$
$733$	−13.9800	−	15.5264i	−0.516363	−	0.573479i	−0.943780	+	0.330576i	$0.892757\pi$
$734$	13.4296	−	9.75715i	0.495694	−	0.360143i
$735$	0.971336	+	15.6223i	0.0358283	+	0.576238i
$736$	−25.7886	−	18.7365i	−0.950581	−	0.690637i
$737$	−2.03328	−	19.3454i	−0.0748970	−	0.712597i
$738$	−13.0258	−	5.79946i	−0.479486	−	0.213481i
$739$	−0.0823922	+	0.783909i	−0.00303085	+	0.0288366i	−0.995933	−	0.0900992i	$-0.971282\pi$
$739$	−0.0823922	+	0.783909i	−0.00303085	+	0.0288366i	0.992902	+	0.118936i	$0.0379483\pi$
$740$	−0.933901	+	7.59745i	−0.0343309	+	0.279288i
$741$	−6.45570	+	4.69034i	−0.237156	+	0.172304i
$742$	7.03951	−	4.98108i	0.258428	−	0.182861i
$743$	20.8525			0.765002			0.382501	−	0.923955i	$-0.375063\pi$
$743$	20.8525			0.765002			0.382501	+	0.923955i	$0.375063\pi$
$744$	7.60917	+	8.45084i	0.278966	+	0.309823i
$745$	5.02090	+	0.0883249i	0.183952	+	0.00323597i
$746$	−16.2084	+	18.0013i	−0.593433	+	0.659074i
$747$	3.60982	+	0.767290i	0.132076	+	0.0280737i
$748$	−5.86939	−	4.26436i	−0.214606	−	0.155920i
$749$	14.2469	−	6.13061i	0.520569	−	0.224008i
$750$	6.72802	−	17.5057i	0.245673	−	0.639218i
$751$	9.42819	−	16.3301i	0.344039	−	0.595894i	−0.641139	−	0.767424i	$-0.721538\pi$
$751$	9.42819	−	16.3301i	0.344039	−	0.595894i	0.985179	+	0.171531i	$0.0548713\pi$
$752$	1.68072	−	15.9910i	0.0612894	−	0.583130i
$753$	12.5812	−	13.9728i	0.458485	−	0.509199i
$754$	−11.1110	−	2.36173i	−0.404640	−	0.0860090i
$755$	18.9772	−	31.5735i	0.690649	−	1.14908i
$756$	1.95567	+	0.900219i	0.0711272	+	0.0327407i
$757$	−20.9159			−0.760201			−0.380100	−	0.924945i	$-0.624111\pi$
$757$	−20.9159			−0.760201			−0.380100	+	0.924945i	$0.624111\pi$
$758$	−8.90013	−	9.88459i	−0.323267	−	0.359025i
$759$	12.2354	+	5.44757i	0.444119	+	0.197734i
$760$	4.42269	+	3.33368i	0.160428	+	0.120925i
$761$	1.25399	−	0.558312i	0.0454571	−	0.0202388i	−0.383882	−	0.923382i	$-0.625413\pi$
$761$	1.25399	−	0.558312i	0.0454571	−	0.0202388i	0.429339	+	0.903143i	$0.358746\pi$
$762$	−8.16881	+	5.93499i	−0.295925	+	0.215002i
$763$	16.3710	+	29.1933i	0.592672	+	1.05687i
$764$	−5.67735	−	4.12484i	−0.205399	−	0.149231i
$765$	−7.44161	+	7.97796i	−0.269052	+	0.288444i
$766$	−10.4684	−	4.66082i	−0.378238	−	0.168402i
$767$	−58.8026	+	12.4989i	−2.12324	+	0.451308i
$768$	−8.36751	+	14.4930i	−0.301937	+	0.522969i
$769$	3.53545	−	10.8810i	0.127491	−	0.392378i	−0.866855	−	0.498560i	$-0.833862\pi$
$769$	3.53545	−	10.8810i	0.127491	−	0.392378i	0.994347	+	0.106181i	$0.0338624\pi$
$770$	−17.8433	+	3.23464i	−0.643028	+	0.116568i
$771$	4.17723	+	12.8562i	0.150439	+	0.463005i
$772$	6.67991	+	1.41986i	0.240415	+	0.0511018i
$773$	−1.14639	+	10.9072i	−0.0412327	+	0.392303i	0.954370	+	0.298627i	$0.0965286\pi$
$773$	−1.14639	+	10.9072i	−0.0412327	+	0.392303i	−0.995603	+	0.0936764i	$0.970138\pi$
$774$	−8.77682	−	15.2019i	−0.315476	−	0.546421i
$775$	9.78020	−	26.8481i	0.351315	−	0.964412i
$776$	−14.0620			−0.504796
$777$	−3.30671	−	10.6278i	−0.118628	−	0.381272i
$778$	19.8878	+	61.2084i	0.713013	+	2.19443i
$779$	−10.3493	−	2.19980i	−0.370801	−	0.0788161i
$780$	−3.79919	+	11.0288i	−0.136033	+	0.394893i
$781$	−0.0856364	+	0.0182026i	−0.00306431	+	0.000651340i
$782$	29.9926	−	51.9487i	1.07253	−	1.85768i
$783$	−0.326421	+	1.00462i	−0.0116653	+	0.0359022i
$784$	−32.0961	+	13.3378i	−1.14629	+	0.476349i
$785$	−12.8862	+	21.4396i	−0.459927	+	0.765211i
$786$	−18.9703	+	8.44613i	−0.676649	+	0.301263i
$787$	−0.415664	−	0.185066i	−0.0148168	−	0.00659688i	0.399315	−	0.916814i	$-0.369248\pi$
$787$	−0.415664	−	0.185066i	−0.0148168	−	0.00659688i	−0.414132	+	0.910217i	$0.635915\pi$
$788$	1.90465	+	0.848004i	0.0678503	+	0.0302089i
$789$	9.15266	−	4.07503i	0.325843	−	0.145075i
$790$	−35.9289	−	41.3428i	−1.27829	−	1.47091i
$791$	−42.8473	−	0.536343i	−1.52347	−	0.0190702i
$792$	1.12365	−	3.45823i	0.0399271	−	0.122883i
$793$	22.8111	−	39.5099i	0.810045	−	1.40304i
$794$	42.8565	−	9.10943i	1.52092	−	0.323282i
$795$	3.55949	−	2.49166i	0.126242	−	0.0883700i
$796$	−20.5318	−	4.36416i	−0.727729	−	0.154684i
$797$	8.21803	+	25.2925i	0.291098	+	0.895906i	0.984504	+	0.175360i	$0.0561089\pi$
$797$	8.21803	+	25.2925i	0.291098	+	0.895906i	−0.693407	+	0.720546i	$0.743891\pi$
$798$	5.38859	+	1.21607i	0.190754	+	0.0430483i
$799$	15.7997			0.558954
$800$	21.7322	+	0.764838i	0.768349	+	0.0270411i
$801$	−0.285912	−	0.495214i	−0.0101022	−	0.0174975i
$802$	1.91721	−	18.2410i	0.0676991	−	0.644114i
$803$	27.2104	+	5.78375i	0.960234	+	0.204104i
$804$	2.67672	+	8.23809i	0.0944006	+	0.290535i
$805$	−12.1519	−	41.6237i	−0.428299	−	1.46704i
$806$	−18.9906	+	58.4470i	−0.668914	+	2.05871i
$807$	−13.3300	+	23.0883i	−0.469239	+	0.812746i
$808$	7.76155	−	1.64977i	0.273050	−	0.0580386i
$809$	−20.1644	−	8.97778i	−0.708944	−	0.315642i	0.0203978	−	0.999792i	$-0.493507\pi$
$809$	−20.1644	−	8.97778i	−0.708944	−	0.315642i	−0.729341	+	0.684150i	$0.760173\pi$
$810$	3.39918	+	1.58563i	0.119435	+	0.0557133i
$811$	16.1376	+	11.7246i	0.566667	+	0.411707i	0.833893	−	0.551926i	$-0.186107\pi$
$811$	16.1376	+	11.7246i	0.566667	+	0.411707i	−0.267226	+	0.963634i	$0.586107\pi$
$812$	1.11234	+	1.98357i	0.0390356	+	0.0696096i
$813$	−7.28738	+	5.29459i	−0.255579	+	0.185689i
$814$	11.7802	−	5.24490i	0.412897	−	0.183834i
$815$	−26.0991	+	18.2695i	−0.914212	+	0.639953i
$816$	−22.1315	−	9.85358i	−0.774757	−	0.344944i
$817$	−8.71583	−	9.67991i	−0.304928	−	0.338657i
$818$	−7.81913			−0.273389
$819$	−1.56168	−	16.8894i	−0.0545695	−	0.590164i
$820$	−14.2380	+	6.04137i	−0.497211	+	0.210974i
$821$	−15.1938	−	3.22954i	−0.530268	−	0.112712i	−0.0650057	−	0.997885i	$-0.520707\pi$
$821$	−15.1938	−	3.22954i	−0.530268	−	0.112712i	−0.465262	+	0.885173i	$0.654040\pi$
$822$	−20.1968	+	22.4308i	−0.704443	+	0.782363i
$823$	−1.12124	+	10.6679i	−0.0390839	+	0.371858i	0.957445	+	0.288615i	$0.0931947\pi$
$823$	−1.12124	+	10.6679i	−0.0390839	+	0.371858i	−0.996529	+	0.0832437i	$0.973472\pi$
$824$	0.931468	−	1.61335i	0.0324492	−	0.0562037i
$825$	−8.99837	+	1.58413i	−0.313283	+	0.0551522i
$826$	33.3598	+	24.8812i	1.16074	+	0.865727i
$827$	−15.1174	−	10.9834i	−0.525684	−	0.381931i	0.293057	−	0.956095i	$-0.405327\pi$
$827$	−15.1174	−	10.9834i	−0.525684	−	0.381931i	−0.818741	+	0.574163i	$0.805327\pi$
$828$	−5.83379	−	1.24001i	−0.202738	−	0.0430933i
$829$	−1.17623	+	1.30633i	−0.0408521	+	0.0453709i	−0.763225	−	0.646133i	$-0.776385\pi$
$829$	−1.17623	+	1.30633i	−0.0408521	+	0.0453709i	0.722372	+	0.691504i	$0.243052\pi$
$830$	11.3400	−	7.93804i	0.393617	−	0.275533i
$831$	10.7527	+	11.9421i	0.373007	+	0.414266i
$832$	16.8945			0.585710
$833$	−16.3309	−	29.9958i	−0.565834	−	1.03929i
$834$	−16.9175	+	12.2913i	−0.585804	+	0.425612i
$835$	7.38597	−	1.43464i	0.255602	−	0.0496478i
$836$	−0.193467	+	1.84071i	−0.00669119	+	0.0636624i
$837$	5.22073	+	2.32442i	0.180455	+	0.0803436i
$838$	3.57875	+	34.0495i	0.123626	+	1.17622i
$839$	4.13427	+	3.00372i	0.142731	+	0.103700i	0.656859	−	0.754013i	$-0.271885\pi$
$839$	4.13427	+	3.00372i	0.142731	+	0.103700i	−0.514129	+	0.857713i	$0.671885\pi$
$840$	−10.8938	+	4.46231i	−0.375870	+	0.153964i
$841$	22.5588	−	16.3899i	0.777889	−	0.565169i
$842$	18.1408	+	20.1474i	0.625173	+	0.694325i
$843$	−1.02138	−	1.76908i	−0.0351782	−	0.0609304i
$844$	7.31186	−	1.55418i	0.251685	−	0.0534972i
$845$	61.6779	−	11.9802i	2.12178	−	0.412133i
$846$	−1.67856	−	5.16609i	−0.0577102	−	0.177614i
$847$	−13.3727	−	15.2310i	−0.459492	−	0.523345i
$848$	7.80549	+	5.67102i	0.268042	+	0.194744i
$849$	−8.74893	+	15.1536i	−0.300263	+	0.520070i
$850$	2.84337	+	40.8221i	0.0975268	+	1.40018i
$851$	15.4170	+	26.7030i	0.528487	+	0.915366i
$852$	0.0356157	−	0.0158571i	0.00122017	−	0.000543256i
$853$	−4.12683	−	12.7011i	−0.141300	−	0.434876i	0.855217	−	0.518271i	$-0.173424\pi$
$853$	−4.12683	−	12.7011i	−0.141300	−	0.434876i	−0.996517	+	0.0833941i	$0.973424\pi$
$854$	−30.9725	+	6.17926i	−1.05986	+	0.211450i
$855$	2.71186	+	0.626471i	0.0927436	+	0.0214249i
$856$	7.80544	+	8.66881i	0.266784	+	0.296294i
$857$	−19.3410	−	33.4996i	−0.660676	−	1.14432i	−0.980438	−	0.196826i	$-0.936937\pi$
$857$	−19.3410	−	33.4996i	−0.660676	−	1.14432i	0.319763	−	0.947498i	$-0.396397\pi$
$858$	19.2212	−	4.08560i	0.656202	−	0.139480i
$859$	2.72433	+	25.9203i	0.0929530	+	0.884389i	0.937284	+	0.348567i	$0.113332\pi$
$859$	2.72433	+	25.9203i	0.0929530	+	0.884389i	−0.844331	+	0.535822i	$0.820002\pi$
$860$	−18.5524	−	4.28582i	−0.632631	−	0.146145i
$861$	15.2565	−	16.5234i	0.519940	−	0.563115i
$862$	−37.0137	+	26.8920i	−1.26069	+	0.915945i
$863$	2.80142	+	26.6537i	0.0953613	+	0.907302i	0.932709	+	0.360631i	$0.117439\pi$
$863$	2.80142	+	26.6537i	0.0953613	+	0.907302i	−0.837347	+	0.546671i	$0.815895\pi$
$864$	−0.454608	+	4.32531i	−0.0154661	+	0.147150i
$865$	2.36809	+	1.78499i	0.0805175	+	0.0606915i
$866$	−5.66848	−	53.9320i	−0.192623	−	1.83268i
$867$	2.10289	−	6.47202i	0.0714178	−	0.219801i
$868$	11.3015	−	4.86320i	0.383600	−	0.165068i
$869$	−8.24607	+	25.3788i	−0.279729	+	0.860916i
$870$	1.92037	+	3.46556i	0.0651068	+	0.117494i
$871$	45.6633	−	50.7142i	1.54724	−	1.71838i
$872$	−16.8441	+	18.7073i	−0.570413	+	0.633508i
$873$	−6.45582	+	2.87432i	−0.218496	+	0.0972808i
$874$	−15.3031			−0.517636
$875$	22.7458	+	18.9111i	0.768947	+	0.639313i
$876$	−12.3876			−0.418538
$877$	−15.6396	+	6.96319i	−0.528111	+	0.235130i	−0.653431	−	0.756986i	$-0.726671\pi$
$877$	−15.6396	+	6.96319i	−0.528111	+	0.235130i	0.125320	+	0.992116i	$0.460004\pi$
$878$	−21.3317	+	23.6913i	−0.719912	+	0.799543i
$879$	−18.3457	+	20.3749i	−0.618785	+	0.687230i
$880$	−9.83370	−	17.7462i	−0.331494	−	0.598223i
$881$	−3.45055	+	10.6197i	−0.116252	+	0.357787i	−0.992206	−	0.124608i	$-0.960233\pi$
$881$	−3.45055	+	10.6197i	−0.116252	+	0.357787i	0.875954	+	0.482394i	$0.160233\pi$
$882$	−8.07283	+	8.52654i	−0.271826	+	0.287104i
$883$	9.47283	−	29.1544i	0.318786	−	0.981122i	−0.655382	−	0.755298i	$-0.727492\pi$
$883$	9.47283	−	29.1544i	0.318786	−	0.981122i	0.974168	−	0.225825i	$-0.0725077\pi$
$884$	−2.66049	−	25.3129i	−0.0894820	−	0.851364i
$885$	16.7443	+	12.6213i	0.562853	+	0.424261i
$886$	−6.25740	+	59.5352i	−0.210221	+	2.00012i
$887$	−5.04440	−	47.9942i	−0.169374	−	1.61149i	−0.667654	−	0.744472i	$-0.732701\pi$
$887$	−5.04440	−	47.9942i	−0.169374	−	1.61149i	0.498279	−	0.867017i	$-0.333965\pi$
$888$	6.77243	−	4.92046i	0.227268	−	0.165120i
$889$	−4.73146	−	15.2070i	−0.158688	−	0.510027i
$890$	−2.08977	−	0.482762i	−0.0700493	−	0.0161822i
$891$	−0.191010	−	1.81734i	−0.00639908	−	0.0608832i
$892$	11.4513	−	2.43405i	0.383418	−	0.0814980i
$893$	−2.01538	−	3.49073i	−0.0674420	−	0.116813i
$894$	2.52067	+	2.79949i	0.0843037	+	0.0936288i
$895$	−19.8502	−	4.58564i	−0.663520	−	0.153281i
$896$	−22.9002	−	26.0825i	−0.765041	−	0.871354i
$897$	14.5199	+	44.6877i	0.484806	+	1.49208i
$898$	−11.3411	+	5.04936i	−0.378456	+	0.168499i
$899$	3.01833	+	5.22790i	0.100667	+	0.174360i
$900$	3.77279	−	1.52311i	0.125760	−	0.0507703i
$901$	−4.74025	+	8.21036i	−0.157921	+	0.273527i
$902$	21.0792	+	15.3149i	0.701860	+	0.509931i
$903$	27.1519	−	5.41702i	0.903557	−	0.180267i
$904$	−9.95902	−	30.6507i	−0.331232	−	1.01943i
$905$	−1.89906	+	0.368872i	−0.0631270	+	0.0122617i
$906$	27.0305	−	5.74550i	0.898027	−	0.190882i
$907$	4.65044	+	8.05479i	0.154415	+	0.267455i	0.932846	−	0.360276i	$-0.117317\pi$
$907$	4.65044	+	8.05479i	0.154415	+	0.267455i	−0.778431	+	0.627731i	$0.783984\pi$
$908$	3.09969	+	3.44256i	0.102867	+	0.114245i
$909$	3.22608	−	2.34389i	0.107002	−	0.0777418i
$910$	−50.3201	−	38.9269i	−1.66810	−	1.29041i
$911$	−45.6078	−	33.1360i	−1.51105	−	1.09785i	−0.965707	−	0.259635i	$-0.916398\pi$
$911$	−45.6078	−	33.1360i	−1.51105	−	1.09785i	−0.545348	−	0.838210i	$-0.683602\pi$
$912$	0.646029	+	6.14655i	0.0213921	+	0.203533i
$913$	−6.16074	−	2.74294i	−0.203891	−	0.0907779i
$914$	2.59748	−	24.7134i	0.0859171	−	0.817446i
$915$	−15.6209	+	3.03418i	−0.516409	+	0.100307i
$916$	−5.91593	+	4.29817i	−0.195468	+	0.142016i
$917$	−3.01565	−	32.6140i	−0.0995856	−	1.07701i
$918$	−8.18419			−0.270119
$919$	9.41067	+	10.4516i	0.310429	+	0.344767i	0.878090	−	0.478496i	$-0.158818\pi$
$919$	9.41067	+	10.4516i	0.310429	+	0.344767i	−0.567660	+	0.823263i	$0.692151\pi$
$920$	26.7168	−	18.7019i	0.880827	−	0.616583i
$921$	8.27720	−	9.19276i	0.272743	−	0.302912i
$922$	54.1517	+	11.5103i	1.78339	+	0.379071i
$923$	−0.248487	−	0.180537i	−0.00817906	−	0.00594243i
$924$	−3.15359	−	2.35208i	−0.103745	−	0.0773778i
$925$	−18.9031	−	9.22605i	−0.621531	−	0.303351i
$926$	11.2859	−	19.5478i	0.370879	−	0.642381i
$927$	0.0978603	−	0.931079i	0.00321415	−	0.0305806i
$928$	−3.07403	+	3.41406i	−0.100910	+	0.112072i
$929$	−15.4799	−	3.29035i	−0.507879	−	0.107953i	−0.0531563	−	0.998586i	$-0.516928\pi$
$929$	−15.4799	−	3.29035i	−0.507879	−	0.107953i	−0.454722	+	0.890633i	$0.650261\pi$
$930$	19.7323	−	8.37269i	0.647048	−	0.274551i
$931$	−4.54403	+	7.43430i	−0.148925	+	0.243649i
$932$	−16.6990			−0.546992
$933$	−5.60813	−	6.22846i	−0.183602	−	0.203911i
$934$	−28.8805	−	12.8584i	−0.944998	−	0.420740i
$935$	16.3323	−	11.4327i	0.534124	−	0.373889i
$936$	11.6539	−	5.18864i	0.380919	−	0.169596i
$937$	−12.6263	+	9.17353i	−0.412483	+	0.299686i	−0.774606	−	0.632444i	$-0.782052\pi$
$937$	−12.6263	+	9.17353i	−0.412483	+	0.299686i	0.362123	+	0.932130i	$0.382052\pi$
$938$	−47.2387	−	0.591313i	−1.54240	−	0.0193071i
$939$	−1.06737	−	0.775489i	−0.0348323	−	0.0253071i
$940$	−5.33981	−	2.49088i	−0.174165	−	0.0812436i
$941$	−15.6376	−	6.96232i	−0.509772	−	0.226965i	0.135699	−	0.990750i	$-0.456672\pi$
$941$	−15.6376	−	6.96232i	−0.509772	−	0.226965i	−0.645471	+	0.763785i	$0.723339\pi$
$942$	−18.3547	+	3.90140i	−0.598027	+	0.127115i
$943$	−31.1509	+	53.9550i	−1.01441	+	1.75702i
$944$	−14.3882	+	44.2823i	−0.468295	+	1.44126i
$945$	−4.08918	+	4.27535i	−0.133021	+	0.139077i
$946$	9.91223	+	30.5067i	0.322274	+	0.991858i
$947$	−17.4204	−	3.70281i	−0.566086	−	0.120325i	−0.0840261	−	0.996464i	$-0.526778\pi$
$947$	−17.4204	−	3.70281i	−0.566086	−	0.120325i	−0.482060	+	0.876138i	$0.660111\pi$
$948$	1.24210	−	11.8178i	0.0403415	−	0.383823i
$949$	48.7969	+	84.5188i	1.58402	+	2.74360i
$950$	8.65639	−	5.83537i	0.280850	−	0.189324i
$951$	8.73155			0.283140
$952$	17.4254	−	18.8724i	0.564760	−	0.611657i
$953$	−3.12833	−	9.62800i	−0.101336	−	0.311881i	0.887517	−	0.460775i	$-0.152429\pi$
$953$	−3.12833	−	9.62800i	−0.101336	−	0.311881i	−0.988853	+	0.148894i	$0.952429\pi$
$954$	3.18818	+	0.677668i	0.103221	+	0.0219403i
$955$	15.7980	−	11.0586i	0.511210	−	0.357849i
$956$	14.3879	−	3.05824i	0.465338	−	0.0989106i
$957$	0.965133	−	1.67166i	0.0311983	−	0.0540371i
$958$	11.6112	−	35.7356i	0.375140	−	1.15456i
$959$	−23.2860	−	41.5244i	−0.751945	−	1.34089i
$960$	−3.86536	−	4.44781i	−0.124754	−	0.143553i
$961$	1.51548	−	0.674735i	0.0488864	−	0.0217656i
$962$	41.3282	+	18.4005i	1.33247	+	0.593256i
$963$	5.35538	+	2.38437i	0.172575	+	0.0768353i
$964$	15.5871	−	6.93982i	0.502026	−	0.223517i
$965$	−9.66742	+	16.0843i	−0.311205	+	0.517773i
$966$	16.6153	−	27.9643i	0.534590	−	0.899738i
$967$	17.7172	−	54.5280i	0.569748	−	1.75350i	−0.0836569	−	0.996495i	$-0.526660\pi$
$967$	17.7172	−	54.5280i	0.569748	−	1.75350i	0.653405	−	0.757009i	$-0.273340\pi$
$968$	7.62201	−	13.2017i	0.244981	−	0.424319i
$969$	−5.94033	+	1.26266i	−0.190831	+	0.0405624i
$970$	−8.63298	+	25.0609i	−0.277188	+	0.804657i
$971$	39.9444	+	8.49045i	1.28188	+	0.272472i	0.797996	−	0.602662i	$-0.205893\pi$
$971$	39.9444	+	8.49045i	1.28188	+	0.272472i	0.483881	+	0.875134i	$0.339227\pi$
$972$	0.251455	+	0.773900i	0.00806543	+	0.0248228i
$973$	−9.79878	−	31.4935i	−0.314135	−	1.00964i
$974$	61.6186			1.97439
$975$	−25.2536	−	19.7414i	−0.808763	−	0.632230i
$976$	−17.6676	−	30.6012i	−0.565526	−	0.979519i
$977$	−4.63788	+	44.1265i	−0.148379	+	1.41173i	0.626401	+	0.779501i	$0.284527\pi$
$977$	−4.63788	+	44.1265i	−0.148379	+	1.41173i	−0.774780	+	0.632231i	$0.782139\pi$
$978$	−23.3765	−	4.96884i	−0.747499	−	0.158886i
$979$	0.322899	+	0.993781i	0.0103199	+	0.0317614i
$980$	0.790402	+	12.7123i	0.0252485	+	0.406079i
$981$	−3.90925	+	12.0314i	−0.124813	+	0.384134i
$982$	28.6375	−	49.6016i	0.913858	−	1.58285i
$983$	9.49934	−	2.01915i	0.302982	−	0.0644008i	−0.0539121	−	0.998546i	$-0.517169\pi$
$983$	9.49934	−	2.01915i	0.302982	−	0.0644008i	0.356894	+	0.934145i	$0.383836\pi$
$984$	15.4522	+	6.87974i	0.492597	+	0.219318i
$985$	−3.90785	+	4.18951i	−0.124515	+	0.133489i
$986$	−6.99405	−	5.08148i	−0.222736	−	0.161827i
$987$	8.56701	+	0.107238i	0.272691	+	0.00341343i
$988$	−5.25317	+	3.81665i	−0.167126	+	0.121424i
$989$	−70.0687	+	31.1966i	−2.22806	+	0.991994i
$990$	−5.47333	−	4.12562i	−0.173954	−	0.131121i
$991$	−26.1766	−	11.6546i	−0.831528	−	0.370220i	−0.0535914	−	0.998563i	$-0.517067\pi$
$991$	−26.1766	−	11.6546i	−0.831528	−	0.370220i	−0.777937	+	0.628343i	$0.783734\pi$
$992$	16.6308	+	18.4704i	0.528030	+	0.586436i
$993$	5.26024			0.166929
$994$	0.0195772	+	0.211726i	0.000620952	+	0.00671553i
$995$	29.7144	−	49.4377i	0.942009	−	1.56728i
$996$	2.93740	+	0.624364i	0.0930752	+	0.0197837i
$997$	9.66937	−	10.7389i	0.306232	−	0.340105i	−0.570311	−	0.821429i	$-0.693177\pi$
$997$	9.66937	−	10.7389i	0.306232	−	0.340105i	0.876543	+	0.481324i	$0.159844\pi$
$998$	2.57955	−	24.5428i	0.0816541	−	0.776887i
$999$	2.10345	−	3.64327i	0.0665501	−	0.115268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.5	✓	160
7.4	even	3	inner	525.2.bg.b.466.16	yes	160
25.11	even	5	inner	525.2.bg.b.436.16	yes	160
175.11	even	15	inner	525.2.bg.b.361.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.5	✓	160	1.1	even	1	trivial
525.2.bg.b.361.5	yes	160	175.11	even	15	inner
525.2.bg.b.436.16	yes	160	25.11	even	5	inner
525.2.bg.b.466.16	yes	160	7.4	even	3	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53240 + 0.682267i) q^{2} +(0.669131 - 0.743145i) q^{3} +(0.544489 - 0.604717i) q^{4} +(1.08380 + 1.95586i) q^{5} +(-0.518350 + 1.59532i) q^{6} +(-2.12083 - 1.58180i) q^{7} +(0.614905 - 1.89248i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-1.53240 + 0.682267i) q^{2} +(0.669131 - 0.743145i) q^{3} +(0.544489 - 0.604717i) q^{4} +(1.08380 + 1.95586i) q^{5} +(-0.518350 + 1.59532i) q^{6} +(-2.12083 - 1.58180i) q^{7} +(0.614905 - 1.89248i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-2.99523 - 2.25771i) q^{10} +(-0.191010 + 1.81734i) q^{11} +(-0.0850576 - 0.809269i) q^{12} +(-5.18647 + 3.76819i) q^{13} +(4.32916 + 0.976980i) q^{14} +(2.17869 + 0.503303i) q^{15} +(0.519015 + 4.93810i) q^{16} +(-4.77243 + 1.01441i) q^{17} +(0.838708 + 1.45269i) q^{18} +(0.832880 + 0.925007i) q^{19} +(1.77286 + 0.409551i) q^{20} +(-2.59462 + 0.517647i) q^{21} +(-0.947207 - 2.91520i) q^{22} +(6.69573 - 2.98113i) q^{23} +(-0.994938 - 1.72328i) q^{24} +(-2.65075 + 4.23952i) q^{25} +(5.37681 - 9.31291i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.11131 + 0.421223i) q^{28} +(-0.326421 - 1.00462i) q^{29} +(-3.68200 + 0.715188i) q^{30} +(-5.58991 + 1.18817i) q^{31} +(-2.17457 - 3.76646i) q^{32} +(1.22274 + 1.35799i) q^{33} +(6.62115 - 4.81055i) q^{34} +(0.795229 - 5.86239i) q^{35} +(-0.658318 - 0.478296i) q^{36} +(0.439740 + 4.18384i) q^{37} +(-1.90740 - 0.849231i) q^{38} +(-0.670114 + 6.37571i) q^{39} +(4.36786 - 0.848408i) q^{40} +(-6.87687 + 4.99634i) q^{41} +(3.62281 - 2.56346i) q^{42} -10.4647 q^{43} +(0.994972 + 1.10503i) q^{44} +(1.83185 - 1.28231i) q^{45} +(-8.22659 + 9.13655i) q^{46} +(-3.16752 - 0.673276i) q^{47} +(4.01701 + 2.91853i) q^{48} +(1.99580 + 6.70946i) q^{49} +(1.16952 - 8.30514i) q^{50} +(-2.43952 + 4.22538i) q^{51} +(-0.545289 + 5.18808i) q^{52} +(1.30019 - 1.44401i) q^{53} +(1.64076 + 0.348755i) q^{54} +(-3.76147 + 1.59605i) q^{55} +(-4.29764 + 3.04097i) q^{56} +1.24472 q^{57} +(1.18562 + 1.31677i) q^{58} +(8.56659 + 3.81409i) q^{59} +(1.49063 - 1.04345i) q^{60} +(-6.50117 + 2.89451i) q^{61} +(7.75531 - 5.63456i) q^{62} +(-1.35145 + 2.27455i) q^{63} +(-2.13200 - 1.54899i) q^{64} +(-12.9911 - 6.06002i) q^{65} +(-2.80022 - 1.24674i) q^{66} +(-10.4123 + 2.21320i) q^{67} +(-1.98510 + 3.43830i) q^{68} +(2.26491 - 6.97067i) q^{69} +(2.78111 + 9.52606i) q^{70} +(0.0148052 + 0.0455658i) q^{71} +(-1.94639 - 0.413718i) q^{72} +(1.59127 - 15.1399i) q^{73} +(-3.52835 - 6.11129i) q^{74} +(1.37688 + 4.80668i) q^{75} +1.01286 q^{76} +(3.27977 - 3.55212i) q^{77} +(-3.32305 - 10.2273i) q^{78} +(14.2839 + 3.03614i) q^{79} +(-9.09571 + 6.36704i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(7.12926 - 12.3482i) q^{82} +(-1.14042 + 3.50984i) q^{83} +(-1.09971 + 1.85086i) q^{84} +(-7.15640 - 8.23476i) q^{85} +(16.0360 - 7.13971i) q^{86} +(-0.964996 - 0.429644i) q^{87} +(3.32183 + 1.47898i) q^{88} +(0.522387 - 0.232582i) q^{89} +(-1.93225 + 3.21481i) q^{90} +(16.9601 + 0.212299i) q^{91} +(1.84301 - 5.67221i) q^{92} +(-2.85740 + 4.94916i) q^{93} +(5.31324 - 1.12936i) q^{94} +(-0.906505 + 2.63152i) q^{95} +(-4.25409 - 0.904235i) q^{96} +(-2.18375 - 6.72090i) q^{97} +(-7.63599 - 8.91988i) q^{98} +1.82735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more