LMFDB - Embedded newform 525.2.bg.b.16.10

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			16.10
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.195464 + 0.0870263i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-1.30763 + 1.45227i) q^{4} +(2.23437 - 0.0871077i) q^{5} +(-0.0661180 + 0.203490i) q^{6} +(-2.62302 - 0.346096i) q^{7} +(0.261445 - 0.804645i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.195464 + 0.0870263i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-1.30763 + 1.45227i) q^{4} +(2.23437 - 0.0871077i) q^{5} +(-0.0661180 + 0.203490i) q^{6} +(-2.62302 - 0.346096i) q^{7} +(0.261445 - 0.804645i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.429159 + 0.211475i) q^{10} +(0.636015 - 6.05127i) q^{11} +(0.204272 + 1.94351i) q^{12} +(1.17136 - 0.851045i) q^{13} +(0.542825 - 0.160622i) q^{14} +(1.43035 - 1.71875i) q^{15} +(-0.389621 - 3.70700i) q^{16} +(6.44967 - 1.37092i) q^{17} +(0.106981 + 0.185297i) q^{18} +(3.85781 + 4.28453i) q^{19} +(-2.79522 + 3.35881i) q^{20} +(-2.01234 + 1.71770i) q^{21} +(0.402302 + 1.23816i) q^{22} +(-0.163540 + 0.0728126i) q^{23} +(-0.423027 - 0.732704i) q^{24} +(4.98482 - 0.389262i) q^{25} +(-0.154896 + 0.268288i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.93256 - 3.35676i) q^{28} +(2.00313 + 6.16499i) q^{29} +(-0.130006 + 0.460432i) q^{30} +(0.525717 - 0.111745i) q^{31} +(1.24482 + 2.15609i) q^{32} +(-4.07140 - 4.52174i) q^{33} +(-1.14137 + 0.829256i) q^{34} +(-5.89094 - 0.544822i) q^{35} +(1.58100 + 1.14866i) q^{36} +(-1.02073 - 9.71158i) q^{37} +(-1.12693 - 0.501741i) q^{38} +(0.151345 - 1.43995i) q^{39} +(0.514074 - 1.82065i) q^{40} +(-4.27860 + 3.10858i) q^{41} +(0.243856 - 0.510875i) q^{42} -5.94246 q^{43} +(7.95640 + 8.83648i) q^{44} +(-0.320186 - 2.21303i) q^{45} +(0.0256296 - 0.0284645i) q^{46} +(3.47143 + 0.737875i) q^{47} +(-3.01554 - 2.19092i) q^{48} +(6.76043 + 1.81563i) q^{49} +(-0.940479 + 0.509897i) q^{50} +(3.29688 - 5.71036i) q^{51} +(-0.295762 + 2.81398i) q^{52} +(3.45737 - 3.83980i) q^{53} +(0.209287 + 0.0444852i) q^{54} +(0.893979 - 13.5762i) q^{55} +(-0.964259 + 2.02011i) q^{56} +5.76540 q^{57} +(-0.928055 - 1.03071i) q^{58} +(-12.7311 - 5.66827i) q^{59} +(0.625714 + 4.32474i) q^{60} +(0.891913 - 0.397105i) q^{61} +(-0.0930342 + 0.0675933i) q^{62} +(-0.0700204 + 2.64482i) q^{63} +(5.60013 + 4.06874i) q^{64} +(2.54313 - 2.00358i) q^{65} +(1.18932 + 0.529521i) q^{66} +(-6.87805 + 1.46197i) q^{67} +(-6.44283 + 11.1593i) q^{68} +(-0.0553192 + 0.170255i) q^{69} +(1.19888 - 0.406173i) q^{70} +(2.54845 + 7.84331i) q^{71} +(-0.827565 - 0.175904i) q^{72} +(1.09920 - 10.4582i) q^{73} +(1.04468 + 1.80944i) q^{74} +(3.04622 - 3.96491i) q^{75} -11.2669 q^{76} +(-3.76260 + 15.6525i) q^{77} +(0.0957311 + 0.294630i) q^{78} +(-11.3605 - 2.41475i) q^{79} +(-1.19347 - 8.24887i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.565784 - 0.979967i) q^{82} +(0.275453 - 0.847757i) q^{83} +(0.136835 - 5.16857i) q^{84} +(14.2915 - 3.62496i) q^{85} +(1.16154 - 0.517150i) q^{86} +(5.92183 + 2.63657i) q^{87} +(-4.70284 - 2.09384i) q^{88} +(-12.7348 + 5.66989i) q^{89} +(0.255176 + 0.404703i) q^{90} +(-3.36705 + 1.82690i) q^{91} +(0.108106 - 0.332716i) q^{92} +(0.268731 - 0.465456i) q^{93} +(-0.742754 + 0.157877i) q^{94} +(8.99299 + 9.23718i) q^{95} +(2.43523 + 0.517624i) q^{96} +(1.11470 + 3.43070i) q^{97} +(-1.47943 + 0.233444i) q^{98} -6.08461 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 $

$2$	−0.195464	+	0.0870263i	−0.138214	+	0.0615369i	−0.474678	−	0.880159i	$-0.657436\pi$
$2$	−0.195464	+	0.0870263i	−0.138214	+	0.0615369i	0.336464	+	0.941696i	$0.390769\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−1.30763	+	1.45227i	−0.653814	+	0.726134i
$5$	2.23437	−	0.0871077i	0.999241	−	0.0389558i
$5$	2.23437	−	0.0871077i	0.999241	−	0.0389558i
$6$	−0.0661180	+	0.203490i	−0.0269925	+	0.0830745i
$7$	−2.62302	−	0.346096i	−0.991407	−	0.130812i
$7$	−2.62302	−	0.346096i	−0.991407	−	0.130812i
$8$	0.261445	−	0.804645i	0.0924348	−	0.284485i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−0.429159	+	0.211475i	−0.135712	+	0.0668744i
$11$	0.636015	−	6.05127i	0.191766	−	1.82453i	−0.300158	−	0.953889i	$-0.597039\pi$
$11$	0.636015	−	6.05127i	0.191766	−	1.82453i	0.491924	−	0.870638i	$-0.336294\pi$
$12$	0.204272	+	1.94351i	0.0589681	+	0.561044i
$13$	1.17136	−	0.851045i	0.324878	−	0.236037i	−0.413376	−	0.910560i	$-0.635651\pi$
$13$	1.17136	−	0.851045i	0.324878	−	0.236037i	0.738254	+	0.674523i	$0.235651\pi$
$14$	0.542825	−	0.160622i	0.145076	−	0.0429280i
$15$	1.43035	−	1.71875i	0.369315	−	0.443779i
$16$	−0.389621	−	3.70700i	−0.0974053	−	0.926749i
$17$	6.44967	−	1.37092i	1.56427	−	0.332497i	0.657282	−	0.753645i	$-0.271706\pi$
$17$	6.44967	−	1.37092i	1.56427	−	0.332497i	0.906992	+	0.421148i	$0.138373\pi$
$18$	0.106981	+	0.185297i	0.0252157	+	0.0436749i
$19$	3.85781	+	4.28453i	0.885042	+	0.982938i	0.999946	−	0.0104384i	$-0.00332271\pi$
$19$	3.85781	+	4.28453i	0.885042	+	0.982938i	−0.114904	+	0.993377i	$0.536656\pi$
$20$	−2.79522	+	3.35881i	−0.625031	+	0.751053i
$21$	−2.01234	+	1.71770i	−0.439129	+	0.374832i
$22$	0.402302	+	1.23816i	0.0857710	+	0.263976i
$23$	−0.163540	+	0.0728126i	−0.0341004	+	0.0151825i	−0.423716	−	0.905795i	$-0.639275\pi$
$23$	−0.163540	+	0.0728126i	−0.0341004	+	0.0151825i	0.389616	+	0.920978i	$0.372608\pi$
$24$	−0.423027	−	0.732704i	−0.0863500	−	0.149563i
$25$	4.98482	−	0.389262i	0.996965	−	0.0778524i
$26$	−0.154896	+	0.268288i	−0.0303777	+	0.0526156i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	3.93256	−	3.35676i	0.743183	−	0.634368i
$29$	2.00313	+	6.16499i	0.371971	+	1.14481i	0.945499	+	0.325624i	$0.105574\pi$
$29$	2.00313	+	6.16499i	0.371971	+	1.14481i	−0.573528	+	0.819186i	$0.694426\pi$
$30$	−0.130006	+	0.460432i	−0.0237358	+	0.0840630i
$31$	0.525717	−	0.111745i	0.0944216	−	0.0200699i	−0.160459	−	0.987043i	$-0.551297\pi$
$31$	0.525717	−	0.111745i	0.0944216	−	0.0200699i	0.254880	+	0.966973i	$0.417964\pi$
$32$	1.24482	+	2.15609i	0.220055	+	0.381146i
$33$	−4.07140	−	4.52174i	−0.708739	−	0.787134i
$34$	−1.14137	+	0.829256i	−0.195744	+	0.142216i
$35$	−5.89094	−	0.544822i	−0.995751	−	0.0920918i
$36$	1.58100	+	1.14866i	0.263500	+	0.191444i
$37$	−1.02073	−	9.71158i	−0.167807	−	1.59657i	−0.677041	−	0.735946i	$-0.736738\pi$
$37$	−1.02073	−	9.71158i	−0.167807	−	1.59657i	0.509234	−	0.860628i	$-0.329929\pi$
$38$	−1.12693	−	0.501741i	−0.182812	−	0.0813932i
$39$	0.151345	−	1.43995i	0.0242346	−	0.230577i
$40$	0.514074	−	1.82065i	0.0812823	−	0.287870i
$41$	−4.27860	+	3.10858i	−0.668205	+	0.485479i	−0.869424	−	0.494067i	$-0.835510\pi$
$41$	−4.27860	+	3.10858i	−0.668205	+	0.485479i	0.201219	+	0.979546i	$0.435510\pi$
$42$	0.243856	−	0.510875i	0.0376278	−	0.0788297i
$43$	−5.94246			−0.906217			−0.453108	−	0.891455i	$-0.649685\pi$
$43$	−5.94246			−0.906217			−0.453108	+	0.891455i	$0.649685\pi$
$44$	7.95640	+	8.83648i	1.19947	+	1.33215i
$45$	−0.320186	−	2.21303i	−0.0477305	−	0.329898i
$46$	0.0256296	−	0.0284645i	0.00377888	−	0.00419687i
$47$	3.47143	+	0.737875i	0.506360	+	0.107630i	0.454006	−	0.890999i	$-0.349994\pi$
$47$	3.47143	+	0.737875i	0.506360	+	0.107630i	0.0523536	+	0.998629i	$0.483328\pi$
$48$	−3.01554	−	2.19092i	−0.435256	−	0.316232i
$49$	6.76043	+	1.81563i	0.965776	+	0.259376i
$50$	−0.940479	+	0.509897i	−0.133004	+	0.0721104i
$51$	3.29688	−	5.71036i	0.461655	−	0.799610i
$52$	−0.295762	+	2.81398i	−0.0410148	+	0.390229i
$53$	3.45737	−	3.83980i	0.474906	−	0.527437i	−0.457325	−	0.889299i	$-0.651192\pi$
$53$	3.45737	−	3.83980i	0.474906	−	0.527437i	0.932231	+	0.361863i	$0.117859\pi$
$54$	0.209287	+	0.0444852i	0.0284803	+	0.00605367i
$55$	0.893979	−	13.5762i	0.120544	−	1.83061i
$56$	−0.964259	+	2.02011i	−0.128855	+	0.269949i
$57$	5.76540			0.763646
$58$	−0.928055	−	1.03071i	−0.121860	−	0.135339i
$59$	−12.7311	−	5.66827i	−1.65745	−	0.737946i	−0.657572	−	0.753391i	$-0.728417\pi$
$59$	−12.7311	−	5.66827i	−1.65745	−	0.737946i	−0.999881	+	0.0154456i	$0.995083\pi$
$60$	0.625714	+	4.32474i	0.0807793	+	0.558321i
$61$	0.891913	−	0.397105i	0.114198	−	0.0508441i	−0.348843	−	0.937181i	$-0.613425\pi$
$61$	0.891913	−	0.397105i	0.114198	−	0.0508441i	0.463040	+	0.886337i	$0.346759\pi$
$62$	−0.0930342	+	0.0675933i	−0.0118154	+	0.00858436i
$63$	−0.0700204	+	2.64482i	−0.00882175	+	0.333217i
$64$	5.60013	+	4.06874i	0.700017	+	0.508592i
$65$	2.54313	−	2.00358i	0.315436	−	0.248514i
$66$	1.18932	+	0.529521i	0.146395	+	0.0651795i
$67$	−6.87805	+	1.46197i	−0.840287	+	0.178609i	−0.607899	−	0.794014i	$-0.707987\pi$
$67$	−6.87805	+	1.46197i	−0.840287	+	0.178609i	−0.232389	+	0.972623i	$0.574654\pi$
$68$	−6.44283	+	11.1593i	−0.781307	+	1.35326i
$69$	−0.0553192	+	0.170255i	−0.00665965	+	0.0204963i
$70$	1.19888	−	0.406173i	0.143294	−	0.0485470i
$71$	2.54845	+	7.84331i	0.302445	+	0.930829i	0.980618	+	0.195928i	$0.0627717\pi$
$71$	2.54845	+	7.84331i	0.302445	+	0.930829i	−0.678174	+	0.734902i	$0.737228\pi$
$72$	−0.827565	−	0.175904i	−0.0975295	−	0.0207305i
$73$	1.09920	−	10.4582i	0.128652	−	1.22404i	−0.719579	−	0.694410i	$-0.755665\pi$
$73$	1.09920	−	10.4582i	0.128652	−	1.22404i	0.848231	−	0.529627i	$-0.177668\pi$
$74$	1.04468	+	1.80944i	0.121441	+	0.210343i
$75$	3.04622	−	3.96491i	0.351747	−	0.457829i
$76$	−11.2669			−1.29240
$77$	−3.76260	+	15.6525i	−0.428788	+	1.78376i
$78$	0.0957311	+	0.294630i	0.0108394	+	0.0333603i
$79$	−11.3605	−	2.41475i	−1.27815	−	0.271680i	−0.481677	−	0.876349i	$-0.659972\pi$
$79$	−11.3605	−	2.41475i	−1.27815	−	0.271680i	−0.796477	+	0.604668i	$0.793306\pi$
$80$	−1.19347	−	8.24887i	−0.133434	−	0.922251i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.565784	−	0.979967i	0.0624804	−	0.108219i
$83$	0.275453	−	0.847757i	0.0302349	−	0.0930534i	−0.934800	−	0.355174i	$-0.884422\pi$
$83$	0.275453	−	0.847757i	0.0302349	−	0.0930534i	0.965035	+	0.262120i	$0.0844217\pi$
$84$	0.136835	−	5.16857i	0.0149300	−	0.563937i
$85$	14.2915	−	3.62496i	1.55013	−	0.393182i
$86$	1.16154	−	0.517150i	0.125252	−	0.0557657i
$87$	5.92183	+	2.63657i	0.634887	+	0.282670i
$88$	−4.70284	−	2.09384i	−0.501325	−	0.223204i
$89$	−12.7348	+	5.66989i	−1.34988	+	0.601007i	−0.949045	−	0.315141i	$-0.897948\pi$
$89$	−12.7348	+	5.66989i	−1.34988	+	0.601007i	−0.400840	+	0.916148i	$0.631282\pi$
$90$	0.255176	+	0.404703i	0.0268979	+	0.0426594i
$91$	−3.36705	+	1.82690i	−0.352963	+	0.191511i
$92$	0.108106	−	0.332716i	0.0112708	−	0.0346880i
$93$	0.268731	−	0.465456i	0.0278661	−	0.0482655i
$94$	−0.742754	+	0.157877i	−0.0766093	+	0.0162838i
$95$	8.99299	+	9.23718i	0.922661	+	0.947715i
$96$	2.43523	+	0.517624i	0.248545	+	0.0528298i
$97$	1.11470	+	3.43070i	0.113181	+	0.348335i	0.991563	−	0.129624i	$-0.0413769\pi$
$97$	1.11470	+	3.43070i	0.113181	+	0.348335i	−0.878382	+	0.477959i	$0.841377\pi$
$98$	−1.47943	+	0.233444i	−0.149445	+	0.0235814i
$99$	−6.08461			−0.611526
$100$	−5.95299	+	7.74831i	−0.595299	+	0.774831i
$101$	6.64013	+	11.5010i	0.660717	+	1.14440i	0.980427	+	0.196880i	$0.0630811\pi$
$101$	6.64013	+	11.5010i	0.660717	+	1.14440i	−0.319710	+	0.947515i	$0.603586\pi$
$102$	−0.147470	+	1.40309i	−0.0146017	+	0.138926i
$103$	6.22193	+	1.32251i	0.613065	+	0.130311i	0.503971	−	0.863720i	$-0.331872\pi$
$103$	6.22193	+	1.32251i	0.613065	+	0.130311i	0.109094	+	0.994031i	$0.465205\pi$
$104$	−0.378542	−	1.16503i	−0.0371191	−	0.114241i
$105$	−4.34669	+	4.01326i	−0.424193	+	0.391654i
$106$	−0.341629	+	1.05142i	−0.0331819	+	0.102123i
$107$	1.26542	−	2.19177i	0.122333	−	0.211887i	−0.798354	−	0.602188i	$-0.794296\pi$
$107$	1.26542	−	2.19177i	0.122333	−	0.211887i	0.920687	+	0.390301i	$0.127629\pi$
$108$	1.91152	−	0.406305i	0.183936	−	0.0390967i
$109$	10.5120	+	4.68025i	1.00687	+	0.448286i	0.842837	−	0.538169i	$-0.180884\pi$
$109$	10.5120	+	4.68025i	1.00687	+	0.448286i	0.164031	+	0.986455i	$0.447550\pi$
$110$	1.00674	+	2.73146i	0.0959893	+	0.260434i
$111$	−7.90011	−	5.73977i	−0.749845	−	0.544794i
$112$	−0.260995	+	9.85836i	−0.0246617	+	0.931528i
$113$	−2.90810	+	2.11286i	−0.273571	+	0.198761i	−0.716108	−	0.697989i	$-0.754078\pi$
$113$	−2.90810	+	2.11286i	−0.273571	+	0.198761i	0.442537	+	0.896750i	$0.354078\pi$
$114$	−1.12693	+	0.501741i	−0.105547	+	0.0469924i
$115$	−0.359066	+	0.176936i	−0.0334831	+	0.0164994i
$116$	−11.5726	−	5.15244i	−1.07449	−	0.478392i
$117$	−0.968824	−	1.07599i	−0.0895678	−	0.0994751i
$118$	2.98177			0.274494
$119$	−17.3921	+	1.36374i	−1.59433	+	0.125014i
$120$	−1.00902	−	1.60028i	−0.0921108	−	0.146085i
$121$	−25.4538	−	5.41037i	−2.31398	−	0.491852i
$122$	−0.139778	+	0.155240i	−0.0126549	+	0.0140547i
$123$	−0.552813	+	5.25967i	−0.0498455	+	0.474248i
$124$	−0.525160	+	0.909603i	−0.0471607	+	0.0816848i
$125$	11.1040	−	1.30397i	0.993175	−	0.116631i
$126$	−0.216483	−	0.523062i	−0.0192858	−	0.0465981i
$127$	4.05908	+	2.94909i	0.360185	+	0.261690i	0.753129	−	0.657873i	$-0.228544\pi$
$127$	4.05908	+	2.94909i	0.360185	+	0.261690i	−0.392944	+	0.919562i	$0.628544\pi$
$128$	−6.31917	−	1.34318i	−0.558541	−	0.118722i
$129$	−3.97628	+	4.41611i	−0.350092	+	0.388817i
$130$	−0.322726	+	0.612948i	−0.0283049	+	0.0537591i
$131$	−2.82374	−	3.13608i	−0.246711	−	0.274000i	0.607052	−	0.794662i	$-0.292352\pi$
$131$	−2.82374	−	3.13608i	−0.246711	−	0.274000i	−0.853763	+	0.520662i	$0.825685\pi$
$132$	11.8907			1.03495
$133$	−8.63623	−	12.5736i	−0.748856	−	1.09027i
$134$	1.21718	−	0.884335i	0.105149	−	0.0763949i
$135$	−1.85884	−	1.24286i	−0.159984	−	0.106968i
$136$	0.583130	−	5.54811i	0.0500030	−	0.475747i
$137$	1.94305	+	0.865103i	0.166006	+	0.0739107i	0.488057	−	0.872812i	$-0.337706\pi$
$137$	1.94305	+	0.865103i	0.166006	+	0.0739107i	−0.322051	+	0.946722i	$0.604372\pi$
$138$	−0.00400373	−	0.0380930i	−0.000340820	−	0.00324269i
$139$	10.0374	+	7.29257i	0.851358	+	0.618548i	0.925520	−	0.378699i	$-0.123628\pi$
$139$	10.0374	+	7.29257i	0.851358	+	0.618548i	−0.0741623	+	0.997246i	$0.523628\pi$
$140$	8.49439	−	7.84280i	0.717907	−	0.662838i
$141$	2.87119	−	2.08604i	0.241798	−	0.175676i
$142$	−1.18070	−	1.31130i	−0.0990824	−	0.110042i
$143$	−4.40490	−	7.62951i	−0.368356	−	0.638012i
$144$	−3.64596	+	0.774974i	−0.303830	+	0.0645811i
$145$	5.01274	+	13.6004i	0.416286	+	1.12945i
$146$	0.695282	+	2.13986i	0.0575420	+	0.177096i
$147$	5.87289	−	3.80909i	0.484388	−	0.314168i
$148$	15.4386	+	11.2168i	1.26904	+	0.922012i
$149$	−5.52037	+	9.56155i	−0.452246	+	0.783313i	−0.998525	−	0.0542901i	$-0.982710\pi$
$149$	−5.52037	+	9.56155i	−0.452246	+	0.783313i	0.546279	+	0.837603i	$0.316044\pi$
$150$	−0.250375	+	1.04010i	−0.0204431	+	0.0849238i
$151$	−3.07761	−	5.33058i	−0.250453	−	0.433797i	0.713198	−	0.700963i	$-0.247246\pi$
$151$	−3.07761	−	5.33058i	−0.250453	−	0.433797i	−0.963650	+	0.267166i	$0.913913\pi$
$152$	4.45613	−	1.98400i	0.361440	−	0.160923i
$153$	−2.03758	−	6.27103i	−0.164729	−	0.506983i
$154$	−0.626722	−	3.38694i	−0.0505027	−	0.272928i
$155$	1.16491	−	0.295473i	0.0935681	−	0.0237330i
$156$	1.89329	+	2.10272i	0.151585	+	0.168352i
$157$	2.76018	+	4.78078i	0.220287	+	0.381548i	0.954895	−	0.296944i	$-0.0959674\pi$
$157$	2.76018	+	4.78078i	0.220287	+	0.381548i	−0.734608	+	0.678491i	$0.762634\pi$
$158$	2.43072	−	0.516664i	0.193377	−	0.0411036i
$159$	−0.540094	−	5.13865i	−0.0428322	−	0.407521i
$160$	2.96919	+	4.70906i	0.234735	+	0.372284i
$161$	0.454168	−	0.134388i	0.0357935	−	0.0105913i
$162$	0.173099	−	0.125764i	0.0135999	−	0.00988094i
$163$	2.47727	+	23.5697i	0.194035	+	1.84612i	0.467202	+	0.884151i	$0.345262\pi$
$163$	2.47727	+	23.5697i	0.194035	+	1.84612i	−0.273167	+	0.961967i	$0.588071\pi$
$164$	1.08032	−	10.2785i	0.0843587	−	0.802620i
$165$	−9.49089	−	9.74860i	−0.738865	−	0.758928i
$166$	0.0199359	+	0.189678i	0.00154733	+	0.0147219i
$167$	1.66296	−	5.11808i	0.128684	−	0.396049i	−0.865870	−	0.500269i	$-0.833235\pi$
$167$	1.66296	−	5.11808i	0.128684	−	0.396049i	0.994554	+	0.104220i	$0.0332346\pi$
$168$	0.856020	+	2.06830i	0.0660434	+	0.159573i
$169$	−3.36941	+	10.3700i	−0.259185	+	0.797690i
$170$	−2.47802	+	1.95229i	−0.190055	+	0.149734i
$171$	3.85781	−	4.28453i	0.295014	−	0.327646i
$172$	7.77053	−	8.63005i	0.592497	−	0.658035i
$173$	15.1233	−	6.73332i	1.14980	−	0.511925i	0.258803	−	0.965930i	$-0.416672\pi$
$173$	15.1233	−	6.73332i	1.14980	−	0.511925i	0.890999	+	0.454006i	$0.150005\pi$
$174$	−1.38696			−0.105145
$175$	−13.2100	−	0.704189i	−0.998582	−	0.0532317i
$176$	−22.6799			−1.70956
$177$	−12.7311	+	5.66827i	−0.956931	+	0.426053i
$178$	1.99576	−	2.21652i	0.149589	−	0.166135i
$179$	1.20170	−	1.33462i	0.0898190	−	0.0997541i	−0.696560	−	0.717499i	$-0.745287\pi$
$179$	1.20170	−	1.33462i	0.0898190	−	0.0997541i	0.786379	+	0.617745i	$0.211954\pi$
$180$	3.63259	+	2.42882i	0.270757	+	0.181033i
$181$	−5.67649	+	17.4704i	−0.421930	+	1.29857i	0.483973	+	0.875083i	$0.339193\pi$
$181$	−5.67649	+	17.4704i	−0.421930	+	1.29857i	−0.905903	+	0.423485i	$0.860807\pi$
$182$	0.499149	−	0.650115i	0.0369994	−	0.0481898i
$183$	0.301700	−	0.928536i	0.0223023	−	0.0686393i
$184$	0.0158316	+	0.150628i	0.00116712	+	0.0111044i
$185$	−3.12664	−	21.6104i	−0.229875	−	1.58882i
$186$	−0.0120204	+	0.114367i	−0.000881380	+	0.00838577i
$187$	−4.19372	−	39.9006i	−0.306676	−	2.91782i
$188$	−5.61093	+	4.07658i	−0.409219	+	0.297315i
$189$	1.91863	+	1.82177i	0.139560	+	0.132514i
$190$	−2.56168	−	1.02291i	−0.185844	−	0.0742098i
$191$	2.79590	+	26.6012i	0.202304	+	1.92480i	0.351874	+	0.936047i	$0.385545\pi$
$191$	2.79590	+	26.6012i	0.202304	+	1.92480i	−0.149570	+	0.988751i	$0.547789\pi$
$192$	6.77088	−	1.43920i	0.488646	−	0.103865i
$193$	−10.2448	−	17.7445i	−0.737438	−	1.27728i	−0.953646	−	0.300932i	$-0.902702\pi$
$193$	−10.2448	−	17.7445i	−0.737438	−	1.27728i	0.216208	−	0.976347i	$-0.430631\pi$
$194$	−0.516445	−	0.573571i	−0.0370786	−	0.0411800i
$195$	0.212730	−	3.23057i	0.0152339	−	0.231346i
$196$	−11.4769	+	7.44379i	−0.819780	+	0.531700i
$197$	5.23446	+	16.1100i	0.372940	+	1.14779i	0.944858	+	0.327480i	$0.106199\pi$
$197$	5.23446	+	16.1100i	0.372940	+	1.14779i	−0.571918	+	0.820311i	$0.693801\pi$
$198$	1.18932	−	0.529521i	0.0845215	−	0.0376314i
$199$	−4.03684	−	6.99200i	−0.286164	−	0.495650i	0.686727	−	0.726915i	$-0.259047\pi$
$199$	−4.03684	−	6.99200i	−0.286164	−	0.495650i	−0.972891	+	0.231265i	$0.925713\pi$
$200$	0.990040	−	4.11278i	0.0700064	−	0.290818i
$201$	−3.51585	+	6.08964i	−0.247989	+	0.429530i
$202$	−2.29880	−	1.67018i	−0.161743	−	0.117513i
$203$	−3.12055	−	16.8641i	−0.219020	−	1.18363i
$204$	3.98189	+	12.2550i	0.278788	+	0.858020i
$205$	−9.28919	+	7.31843i	−0.648785	+	0.511141i
$206$	−1.33126	+	0.282968i	−0.0927532	+	0.0197153i
$207$	0.0895083	+	0.155033i	0.00622126	+	0.0107755i
$208$	−3.61121	−	4.01065i	−0.250392	−	0.278089i
$209$	28.3805	−	20.6196i	1.96312	−	1.42629i
$210$	0.500363	−	1.16273i	0.0345283	−	0.0802357i
$211$	−6.46634	−	4.69807i	−0.445161	−	0.323428i	0.342521	−	0.939510i	$-0.388719\pi$
$211$	−6.46634	−	4.69807i	−0.445161	−	0.323428i	−0.787682	+	0.616082i	$0.788719\pi$
$212$	1.05546	+	10.0421i	0.0724895	+	0.689691i
$213$	7.53396	+	3.35433i	0.516218	+	0.229835i
$214$	−0.0566027	+	0.538538i	−0.00386928	+	0.0368137i
$215$	−13.2777	+	0.517634i	−0.905529	+	0.0353024i
$216$	−0.684472	+	0.497298i	−0.0465724	+	0.0338368i
$217$	−1.41764	+	0.111159i	−0.0962357	+	0.00754599i
$218$	−2.46202			−0.166749
$219$	−7.03644	−	7.81475i	−0.475478	−	0.528072i
$220$	18.5473	+	19.0509i	1.25046	+	1.28441i
$221$	6.38819	−	7.09480i	0.429716	−	0.477248i
$222$	2.04370	+	0.434402i	0.137164	+	0.0291551i
$223$	−9.26807	−	6.73365i	−0.620636	−	0.450918i	0.232508	−	0.972595i	$-0.425307\pi$
$223$	−9.26807	−	6.73365i	−0.620636	−	0.450918i	−0.853144	+	0.521676i	$0.825307\pi$
$224$	−2.51896	−	6.08628i	−0.168305	−	0.406656i
$225$	−0.908186	−	4.91683i	−0.0605457	−	0.327789i
$226$	0.384555	−	0.666070i	0.0255803	−	0.0443063i
$227$	−1.19673	+	11.3862i	−0.0794300	+	0.755726i	0.880227	+	0.474553i	$0.157390\pi$
$227$	−1.19673	+	11.3862i	−0.0794300	+	0.755726i	−0.959657	+	0.281173i	$0.909276\pi$
$228$	−7.53900	+	8.37291i	−0.499283	+	0.554510i
$229$	4.64275	+	0.986847i	0.306802	+	0.0652127i	0.358740	−	0.933438i	$-0.383207\pi$
$229$	4.64275	+	0.986847i	0.306802	+	0.0652127i	−0.0519381	+	0.998650i	$0.516540\pi$
$230$	0.0547865	−	0.0658328i	0.00361251	−	0.00434089i
$231$	9.11438	+	13.2697i	0.599682	+	0.873082i
$232$	5.48433			0.360064
$233$	4.39416	+	4.88021i	0.287871	+	0.319713i	0.869684	−	0.493610i	$-0.164323\pi$
$233$	4.39416	+	4.88021i	0.287871	+	0.319713i	−0.581812	+	0.813323i	$0.697656\pi$
$234$	0.283010	+	0.126004i	0.0185009	+	0.00823714i
$235$	7.82073	+	1.34630i	0.510168	+	0.0878228i
$236$	24.8794	−	11.0770i	1.61951	−	0.721054i
$237$	−9.39616	+	6.82671i	−0.610346	+	0.443442i
$238$	3.28084	−	1.78013i	0.212665	−	0.115389i
$239$	11.6175	+	8.44063i	0.751475	+	0.545979i	0.896284	−	0.443481i	$-0.146257\pi$
$239$	11.6175	+	8.44063i	0.751475	+	0.545979i	−0.144809	+	0.989460i	$0.546257\pi$
$240$	−6.92869	−	4.63265i	−0.447245	−	0.299036i
$241$	−3.78222	−	1.68395i	−0.243634	−	0.108473i	0.281287	−	0.959624i	$-0.409239\pi$
$241$	−3.78222	−	1.68395i	−0.243634	−	0.108473i	−0.524921	+	0.851151i	$0.675905\pi$
$242$	5.44615	−	1.15761i	0.350092	−	0.0744142i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.589587	+	1.81456i	−0.0377445	+	0.116166i
$245$	15.2635	+	3.46791i	0.975147	+	0.221557i
$246$	−0.349674	−	1.07619i	−0.0222944	−	0.0686151i
$247$	8.16522	+	1.73557i	0.519540	+	0.110432i
$248$	0.0475314	−	0.452231i	0.00301825	−	0.0287167i
$249$	−0.445692	−	0.771962i	−0.0282446	−	0.0489211i
$250$	−2.05696	+	1.22122i	−0.130094	+	0.0772369i
$251$	12.3785			0.781324			0.390662	−	0.920534i	$-0.372246\pi$
$251$	12.3785			0.781324			0.390662	+	0.920534i	$0.372246\pi$
$252$	−3.74944	−	3.56014i	−0.236192	−	0.224268i
$253$	0.336596	+	1.03593i	0.0211616	+	0.0651286i
$254$	−1.05005	−	0.223196i	−0.0658861	−	0.0140045i
$255$	6.86903	−	13.0462i	0.430155	−	0.816988i
$256$	−12.1897	+	2.59100i	−0.761856	+	0.161938i
$257$	1.00646	−	1.74323i	0.0627810	−	0.108740i	−0.832927	−	0.553384i	$-0.813336\pi$
$257$	1.00646	−	1.74323i	0.0627810	−	0.108740i	0.895708	+	0.444644i	$0.146670\pi$
$258$	0.392903	−	1.20923i	0.0244611	−	0.0752835i
$259$	−0.683755	+	25.8269i	−0.0424864	+	1.60481i
$260$	−0.415721	+	6.31325i	−0.0257819	+	0.391531i
$261$	5.92183	−	2.63657i	0.366552	−	0.163200i
$262$	0.824861	+	0.367252i	0.0509601	+	0.0226889i
$263$	3.61668	+	1.61025i	0.223014	+	0.0992922i	0.515202	−	0.857069i	$-0.327717\pi$
$263$	3.61668	+	1.61025i	0.223014	+	0.0992922i	−0.292188	+	0.956361i	$0.594383\pi$
$264$	−4.70284	+	2.09384i	−0.289440	+	0.128867i
$265$	7.39057	−	8.88069i	0.453999	−	0.545537i
$266$	2.78230	+	1.70610i	0.170594	+	0.104608i
$267$	−4.30768	+	13.2577i	−0.263626	+	0.811357i
$268$	6.87075	−	11.9005i	0.419698	−	0.726938i
$269$	−7.85541	+	1.66972i	−0.478953	+	0.101805i	−0.441061	−	0.897477i	$-0.645398\pi$
$269$	−7.85541	+	1.66972i	−0.478953	+	0.101805i	−0.0378922	+	0.999282i	$0.512064\pi$
$270$	0.471499	+	0.0811660i	0.0286945	+	0.00493961i
$271$	13.9347	+	2.96190i	0.846470	+	0.179923i	0.610676	−	0.791880i	$-0.290898\pi$
$271$	13.9347	+	2.96190i	0.846470	+	0.179923i	0.235794	+	0.971803i	$0.424231\pi$
$272$	−7.59492	−	23.3748i	−0.460510	−	1.41730i
$273$	−0.895343	+	3.72464i	−0.0541886	+	0.225425i
$274$	−0.455084			−0.0274926
$275$	0.814890	−	30.4121i	0.0491397	−	1.83392i
$276$	−0.174919	−	0.302969i	−0.0105289	−	0.0182366i
$277$	0.0452989	−	0.430990i	0.00272175	−	0.0258957i	−0.993077	−	0.117467i	$-0.962522\pi$
$277$	0.0452989	−	0.430990i	0.00272175	−	0.0258957i	0.995798	+	0.0915718i	$0.0291891\pi$
$278$	−2.59659	−	0.551922i	−0.155733	−	0.0331021i
$279$	−0.166085	−	0.511157i	−0.00994325	−	0.0306022i
$280$	−1.97854	+	4.59767i	−0.118241	+	0.274764i
$281$	5.56107	−	17.1152i	0.331745	−	1.02101i	−0.636558	−	0.771229i	$-0.719642\pi$
$281$	5.56107	−	17.1152i	0.331745	−	1.02101i	0.968303	−	0.249778i	$-0.0803578\pi$
$282$	−0.379674	+	0.657615i	−0.0226093	+	0.0391604i
$283$	26.6373	−	5.66194i	1.58343	−	0.336567i	0.669615	−	0.742709i	$-0.266459\pi$
$283$	26.6373	−	5.66194i	1.58343	−	0.336567i	0.913810	+	0.406141i	$0.133126\pi$
$284$	−14.7230	−	6.55511i	−0.873650	−	0.388974i
$285$	12.8820	−	0.502211i	0.763066	−	0.0297484i
$286$	1.52497	+	1.10795i	0.0901733	+	0.0655147i
$287$	12.2987	−	6.67306i	0.725970	−	0.393898i
$288$	2.01416	−	1.46337i	0.118685	−	0.0862299i
$289$	24.1885	−	10.7694i	1.42285	−	0.633495i
$290$	−2.16340	−	2.22215i	−0.127039	−	0.130489i
$291$	3.29539	+	1.46720i	0.193179	+	0.0860089i
$292$	13.7507	+	15.2717i	0.804701	+	0.893711i
$293$	0.299317			0.0174863			0.00874315	−	0.999962i	$-0.497217\pi$
$293$	0.299317			0.0174863			0.00874315	+	0.999962i	$0.497217\pi$
$294$	−0.816450	+	1.25564i	−0.0476163	+	0.0732302i
$295$	−28.9398	−	11.5560i	−1.68494	−	0.672818i
$296$	−8.08124	−	1.71772i	−0.469712	−	0.0998404i
$297$	−4.07140	+	4.52174i	−0.236246	+	0.262378i
$298$	0.246928	−	2.34936i	0.0143041	−	0.136095i
$299$	−0.129598	+	0.224470i	−0.00749483	+	0.0129814i
$300$	1.77479	+	9.60856i	0.102468	+	0.554751i
$301$	15.5872	+	2.05666i	0.898430	+	0.118544i
$302$	1.06546	+	0.774105i	0.0613105	+	0.0445447i
$303$	12.9900	+	2.76112i	0.746259	+	0.158622i
$304$	14.3797	−	15.9702i	0.824730	−	0.915955i
$305$	1.95827	−	0.964973i	0.112130	−	0.0552542i
$306$	0.944019	+	1.04844i	0.0539660	+	0.0599353i
$307$	−11.0842			−0.632607			−0.316304	−	0.948658i	$-0.602442\pi$
$307$	−11.0842			−0.632607			−0.316304	+	0.948658i	$0.602442\pi$
$308$	−17.8115	−	25.9319i	−1.01490	−	1.47761i
$309$	5.14611	−	3.73886i	0.292752	−	0.212697i
$310$	−0.201985	+	0.159132i	−0.0114720	+	0.00903812i
$311$	1.33063	−	12.6601i	0.0754528	−	0.717886i	−0.889761	−	0.456426i	$-0.849129\pi$
$311$	1.33063	−	12.6601i	0.0754528	−	0.717886i	0.965214	−	0.261460i	$-0.0842039\pi$
$312$	−1.11908	−	0.498247i	−0.0633555	−	0.0282077i
$313$	−0.302652	−	2.87954i	−0.0171069	−	0.162761i	0.982633	−	0.185559i	$-0.0594094\pi$
$313$	−0.302652	−	2.87954i	−0.0171069	−	0.162761i	−0.999740	+	0.0227973i	$0.992743\pi$
$314$	−0.955571	−	0.694263i	−0.0539260	−	0.0391795i
$315$	0.0739331	+	5.91562i	0.00416566	+	0.333307i
$316$	18.3622	−	13.3409i	1.03295	−	0.750484i
$317$	3.32719	+	3.69522i	0.186874	+	0.207544i	0.829301	−	0.558803i	$-0.188739\pi$
$317$	3.32719	+	3.69522i	0.186874	+	0.207544i	−0.642427	+	0.766347i	$0.722072\pi$
$318$	0.552767	+	0.957420i	0.0309976	+	0.0536894i
$319$	38.5800	−	8.20044i	2.16007	−	0.459137i
$320$	12.8672	+	8.60325i	0.719298	+	0.480936i
$321$	−0.782074	−	2.40698i	−0.0436511	−	0.134344i
$322$	−0.0770783	+	0.0657926i	−0.00429540	+	0.00366648i
$323$	30.7553	+	22.3450i	1.71127	+	1.24331i
$324$	0.977110	−	1.69240i	0.0542839	−	0.0940225i
$325$	5.50776	−	4.69828i	0.305515	−	0.260613i
$326$	−2.53540	−	4.39144i	−0.140423	−	0.243219i
$327$	10.5120	−	4.68025i	0.581315	−	0.258818i
$328$	1.38269	+	4.25548i	0.0763462	+	0.234969i
$329$	−8.85024	−	3.13691i	−0.487929	−	0.172943i
$330$	2.70351	+	1.07955i	0.148823	+	0.0594270i
$331$	−10.5460	−	11.7125i	−0.579661	−	0.643779i	0.379984	−	0.924993i	$-0.375930\pi$
$331$	−10.5460	−	11.7125i	−0.579661	−	0.643779i	−0.959645	+	0.281214i	$0.909263\pi$
$332$	0.870981	+	1.50858i	0.0478013	+	0.0827943i
$333$	−9.55168	+	2.03027i	−0.523429	+	0.111258i
$334$	0.120357	+	1.14512i	0.00658565	+	0.0626583i
$335$	−15.2408	+	3.86572i	−0.832692	+	0.211207i
$336$	7.15155	+	6.79049i	0.390149	+	0.370452i
$337$	−15.9343	+	11.5770i	−0.867998	+	0.630638i	−0.930049	−	0.367435i	$-0.880236\pi$
$337$	−15.9343	+	11.5770i	−0.867998	+	0.630638i	0.0620509	+	0.998073i	$0.480236\pi$
$338$	−0.243861	−	2.32018i	−0.0132643	−	0.126201i
$339$	−0.375739	+	3.57492i	−0.0204074	+	0.194163i
$340$	−13.4236	+	25.4952i	−0.727997	+	1.38267i
$341$	−0.341834	−	3.25233i	−0.0185113	−	0.176124i
$342$	−0.381197	+	1.17320i	−0.0206127	+	0.0634395i
$343$	−17.1044	−	7.10220i	−0.923548	−	0.383483i
$344$	−1.55363	+	4.78157i	−0.0837659	+	0.257805i
$345$	−0.108773	+	0.385231i	−0.00585615	+	0.0207402i
$346$	−2.37008	+	2.63224i	−0.127416	+	0.141510i
$347$	−4.55739	+	5.06150i	−0.244654	+	0.271716i	−0.852948	−	0.521996i	$-0.825187\pi$
$347$	−4.55739	+	5.06150i	−0.244654	+	0.271716i	0.608294	+	0.793712i	$0.291854\pi$
$348$	−11.5726	+	5.15244i	−0.620354	+	0.276200i
$349$	−31.9435			−1.70990			−0.854949	−	0.518712i	$-0.826412\pi$
$349$	−31.9435			−1.70990			−0.854949	+	0.518712i	$0.826412\pi$
$350$	2.64337	−	1.01197i	0.141294	−	0.0540923i
$351$	−1.44788			−0.0772823
$352$	13.8388	−	6.16143i	0.737610	−	0.328405i
$353$	−19.3801	+	21.5238i	−1.03150	+	1.14560i	−0.0422870	+	0.999106i	$0.513464\pi$
$353$	−19.3801	+	21.5238i	−1.03150	+	1.14560i	−0.989212	+	0.146490i	$0.953202\pi$
$354$	1.99519	−	2.21589i	0.106043	−	0.117773i
$355$	6.37738	+	17.3029i	0.338476	+	0.918341i
$356$	8.41816	−	25.9084i	0.446162	−	1.37314i
$357$	−10.6241	+	13.8373i	−0.562287	+	0.732349i
$358$	−0.118742	+	0.365449i	−0.00627569	+	0.0193146i
$359$	0.632876	+	6.02141i	0.0334019	+	0.317798i	0.998447	+	0.0557133i	$0.0177433\pi$
$359$	0.632876	+	6.02141i	0.0334019	+	0.317798i	−0.965045	+	0.262085i	$0.915590\pi$
$360$	−1.86441	−	0.320948i	−0.0982631	−	0.0169155i
$361$	−1.48847	+	14.1618i	−0.0783405	+	0.745360i
$362$	−0.410837	−	3.90885i	−0.0215931	−	0.205445i
$363$	−21.0526	+	15.2956i	−1.10497	+	0.802811i
$364$	1.74970	−	7.27877i	0.0917091	−	0.381511i
$365$	1.54503	−	23.4632i	0.0808706	−	1.22812i
$366$	0.0218355	+	0.207751i	0.00114136	+	0.0108593i
$367$	−9.08673	+	1.93144i	−0.474323	+	0.100821i	−0.438870	−	0.898551i	$-0.644621\pi$
$367$	−9.08673	+	1.93144i	−0.474323	+	0.100821i	−0.0354537	+	0.999371i	$0.511288\pi$
$368$	0.333635	+	0.577873i	0.0173919	+	0.0301237i
$369$	3.53879	+	3.93022i	0.184222	+	0.204599i
$370$	2.49181	+	3.95195i	0.129543	+	0.205452i
$371$	−10.3977	+	8.87527i	−0.539820	+	0.460781i
$372$	0.324567	+	0.998913i	0.0168280	+	0.0517912i
$373$	28.8129	−	12.8283i	1.49188	−	0.664226i	0.511128	−	0.859504i	$-0.329228\pi$
$373$	28.8129	−	12.8283i	1.49188	−	0.664226i	0.980748	+	0.195278i	$0.0625610\pi$
$374$	4.29213	+	7.43418i	0.221941	+	0.384412i
$375$	6.46101	−	9.12444i	0.333645	−	0.471184i
$376$	1.50131	−	2.60035i	0.0774244	−	0.134103i
$377$	7.59307	+	5.51669i	0.391063	+	0.284124i
$378$	−0.533566	−	0.189119i	−0.0274437	−	0.00972722i
$379$	−2.36275	−	7.27180i	−0.121366	−	0.373527i	0.871855	−	0.489764i	$-0.162917\pi$
$379$	−2.36275	−	7.27180i	−0.121366	−	0.373527i	−0.993222	+	0.116236i	$0.962917\pi$
$380$	−25.1743	+	0.981431i	−1.29142	+	0.0503463i
$381$	4.90765	−	1.04315i	0.251427	−	0.0534424i
$382$	−2.86151	−	4.95627i	−0.146407	−	0.253585i
$383$	−15.1613	−	16.8383i	−0.774704	−	0.860396i	0.218613	−	0.975812i	$-0.429847\pi$
$383$	−15.1613	−	16.8383i	−0.774704	−	0.860396i	−0.993317	+	0.115416i	$0.963180\pi$
$384$	−5.22653	+	3.79730i	−0.266715	+	0.193780i
$385$	−7.04359	+	35.3012i	−0.358975	+	1.79911i
$386$	3.54673	+	2.57685i	0.180524	+	0.131158i
$387$	0.621156	+	5.90991i	0.0315751	+	0.300417i
$388$	−6.43992	−	2.86724i	−0.326937	−	0.145562i
$389$	−0.287250	+	2.73300i	−0.0145641	+	0.138568i	−0.999388	−	0.0349903i	$-0.988860\pi$
$389$	−0.287250	+	2.73300i	−0.0145641	+	0.138568i	0.984824	+	0.173559i	$0.0555266\pi$
$390$	0.239563	+	0.649974i	0.0121308	+	0.0329127i
$391$	−0.954957	+	0.693817i	−0.0482943	+	0.0350878i
$392$	3.22842	−	4.96506i	0.163060	−	0.250773i
$393$	−4.22001			−0.212871
$394$	−2.42514	−	2.69340i	−0.122177	−	0.135691i
$395$	−25.5939	−	4.40585i	−1.28777	−	0.221682i
$396$	7.95640	−	8.83648i	0.399824	−	0.444050i
$397$	−33.8929	−	7.20415i	−1.70103	−	0.361566i	−0.747829	−	0.663891i	$-0.768904\pi$
$397$	−33.8929	−	7.20415i	−1.70103	−	0.361566i	−0.953205	+	0.302325i	$0.902237\pi$
$398$	1.39754	+	1.01538i	0.0700526	+	0.0508962i
$399$	−15.1227	−	1.99538i	−0.757084	−	0.0998942i
$400$	−3.38519	−	18.3271i	−0.169259	−	0.916353i
$401$	1.19648	−	2.07236i	0.0597491	−	0.103489i	−0.834604	−	0.550851i	$-0.814303\pi$
$401$	1.19648	−	2.07236i	0.0597491	−	0.103489i	0.894353	+	0.447362i	$0.147637\pi$
$402$	0.157265	−	1.49628i	0.00784367	−	0.0746276i
$403$	0.520706	−	0.578303i	0.0259382	−	0.0288073i
$404$	−25.3854	−	5.39584i	−1.26297	−	0.268453i
$405$	−2.16743	+	0.549756i	−0.107701	+	0.0273176i
$406$	2.07758	+	3.02477i	0.103109	+	0.150117i
$407$	−59.4166			−2.94517
$408$	−3.73286	−	4.14576i	−0.184804	−	0.205246i
$409$	−12.7296	−	5.66758i	−0.629438	−	0.280244i	0.0671192	−	0.997745i	$-0.478619\pi$
$409$	−12.7296	−	5.66758i	−0.629438	−	0.280244i	−0.696557	+	0.717501i	$0.745286\pi$
$410$	1.17881	−	2.23889i	0.0582172	−	0.110571i
$411$	1.94305	−	0.865103i	0.0958437	−	0.0426724i
$412$	−10.0566	+	7.30656i	−0.495454	+	0.359969i
$413$	31.4322	+	19.2742i	1.54668	+	0.948420i
$414$	−0.0309876	−	0.0225138i	−0.00152296	−	0.00110649i
$415$	0.541618	−	1.91820i	0.0265870	−	0.0941606i
$416$	3.29306	+	1.46616i	0.161455	+	0.0718846i
$417$	12.1357	−	2.57953i	0.594290	−	0.126320i
$418$	−3.75292	+	6.50024i	−0.183561	+	0.317937i
$419$	−5.01901	+	15.4469i	−0.245195	+	0.754631i	0.750410	+	0.660973i	$0.229856\pi$
$419$	−5.01901	+	15.4469i	−0.245195	+	0.754631i	−0.995604	+	0.0936583i	$0.970144\pi$
$420$	−0.144481	−	11.5604i	−0.00704998	−	0.564091i
$421$	8.21907	+	25.2957i	0.400573	+	1.23284i	0.924536	+	0.381095i	$0.124453\pi$
$421$	8.21907	+	25.2957i	0.400573	+	1.23284i	−0.523963	+	0.851741i	$0.675547\pi$
$422$	1.67279	+	0.355563i	0.0814303	+	0.0173085i
$423$	0.370970	−	3.52954i	0.0180372	−	0.171612i
$424$	−2.18576	−	3.78585i	−0.106150	−	0.183857i
$425$	31.6168	−	9.34440i	1.53364	−	0.453270i
$426$	−1.76453			−0.0854919
$427$	−2.47694	+	0.732926i	−0.119868	+	0.0354688i
$428$	1.52834	+	4.70376i	0.0738753	+	0.227365i
$429$	−8.61729	−	1.83166i	−0.416047	−	0.0884334i
$430$	2.55026	−	1.25668i	0.122984	−	0.0606027i
$431$	19.3325	−	4.10925i	0.931214	−	0.197936i	0.282761	−	0.959190i	$-0.408750\pi$
$431$	19.3325	−	4.10925i	0.931214	−	0.197936i	0.648453	+	0.761255i	$0.275416\pi$
$432$	−1.86371	+	3.22804i	−0.0896677	+	0.155309i
$433$	6.02430	−	18.5409i	0.289510	−	0.891019i	−0.695501	−	0.718525i	$-0.744818\pi$
$433$	6.02430	−	18.5409i	0.289510	−	0.891019i	0.985011	−	0.172494i	$-0.0551825\pi$
$434$	0.267424	−	0.145100i	0.0128368	−	0.00696500i
$435$	13.4612	+	5.37524i	0.645417	+	0.257723i
$436$	−20.5428	+	9.14623i	−0.983820	+	0.438025i
$437$	−0.942873	−	0.419794i	−0.0451037	−	0.0200815i
$438$	2.05546	+	0.915150i	0.0982137	+	0.0437275i
$439$	−15.2149	+	6.77411i	−0.726168	+	0.323311i	−0.736316	−	0.676638i	$-0.763436\pi$
$439$	−15.2149	+	6.77411i	−0.726168	+	0.323311i	0.0101484	+	0.999949i	$0.496770\pi$
$440$	−10.6903	−	4.26876i	−0.509639	−	0.203505i
$441$	1.09903	−	6.91319i	0.0523347	−	0.329199i
$442$	−0.631228	+	1.94272i	−0.0300244	+	0.0924057i
$443$	−9.27023	+	16.0565i	−0.440442	+	0.762868i	−0.997722	−	0.0674564i	$-0.978512\pi$
$443$	−9.27023	+	16.0565i	−0.440442	+	0.762868i	0.557280	+	0.830325i	$0.311845\pi$
$444$	18.6661	−	3.96760i	0.885853	−	0.188294i
$445$	−27.9603	+	13.7779i	−1.32545	+	0.653137i
$446$	2.39758	+	0.509621i	0.113529	+	0.0241313i
$447$	3.41177	+	10.5004i	0.161371	+	0.496650i
$448$	−13.2811	−	12.6105i	−0.627472	−	0.595792i
$449$	1.57381			0.0742726			0.0371363	−	0.999310i	$-0.488176\pi$
$449$	1.57381			0.0742726			0.0371363	+	0.999310i	$0.488176\pi$
$450$	0.605411	+	0.882028i	0.0285393	+	0.0415792i
$451$	16.0896	+	27.8681i	0.757632	+	1.31226i
$452$	0.734277	−	6.98618i	0.0345375	−	0.328602i
$453$	−6.02072	−	1.27974i	−0.282878	−	0.0601276i
$454$	−0.756977	−	2.32973i	−0.0355267	−	0.109340i
$455$	−7.36410	+	4.37527i	−0.345234	+	0.205116i
$456$	1.50734	−	4.63910i	0.0705874	−	0.217246i
$457$	4.60768	−	7.98074i	0.215538	−	0.373323i	−0.737901	−	0.674909i	$-0.764183\pi$
$457$	4.60768	−	7.98074i	0.215538	−	0.373323i	0.953439	+	0.301586i	$0.0975160\pi$
$458$	−0.993374	+	0.211148i	−0.0464173	+	0.00986630i
$459$	−6.02370	−	2.68192i	−0.281162	−	0.125181i
$460$	0.212567	−	0.752827i	0.00991097	−	0.0351007i
$461$	4.19715	+	3.04941i	0.195481	+	0.142025i	0.681220	−	0.732079i	$-0.261450\pi$
$461$	4.19715	+	3.04941i	0.195481	+	0.142025i	−0.485740	+	0.874104i	$0.661450\pi$
$462$	−2.93635	−	1.80056i	−0.136611	−	0.0837697i
$463$	−22.6452	+	16.4527i	−1.05241	+	0.764621i	−0.972669	−	0.232195i	$-0.925409\pi$
$463$	−22.6452	+	16.4527i	−1.05241	+	0.764621i	−0.0797412	+	0.996816i	$0.525409\pi$
$464$	22.0731	−	9.82759i	1.02472	−	0.456234i
$465$	0.559900	−	1.06341i	0.0259647	−	0.0493144i
$466$	−1.28361	−	0.571499i	−0.0594620	−	0.0264742i
$467$	−14.5166	−	16.1224i	−0.671750	−	0.746054i	0.306865	−	0.951753i	$-0.400720\pi$
$467$	−14.5166	−	16.1224i	−0.671750	−	0.746054i	−0.978615	+	0.205699i	$0.934053\pi$
$468$	2.82948			0.130793
$469$	18.5472	−	1.45432i	0.856431	−	0.0671541i
$470$	−1.64584	+	0.417456i	−0.0759168	+	0.0192558i
$471$	5.39973	+	1.14775i	0.248807	+	0.0528855i
$472$	−7.88944	+	8.76211i	−0.363141	+	0.403309i
$473$	−3.77949	+	35.9594i	−0.173781	+	1.65342i
$474$	1.24251	−	2.15209i	0.0570703	−	0.0988487i
$475$	20.8983	+	19.8559i	0.958879	+	0.911052i
$476$	20.7618	−	27.0412i	0.951617	−	1.23943i
$477$	−4.18015	−	3.03706i	−0.191396	−	0.139057i
$478$	−3.00537	−	0.638810i	−0.137462	−	0.0292185i
$479$	−0.372676	+	0.413898i	−0.0170280	+	0.0189115i	−0.751599	−	0.659621i	$-0.770717\pi$
$479$	−0.372676	+	0.413898i	−0.0170280	+	0.0189115i	0.734571	+	0.678532i	$0.237384\pi$
$480$	5.48629	+	0.944436i	0.250414	+	0.0431074i
$481$	−9.46063	−	10.5071i	−0.431368	−	0.479082i
$482$	0.885836			0.0403487
$483$	0.204028	−	0.427436i	0.00928359	−	0.0194490i
$484$	41.1414	−	29.8910i	1.87006	−	1.35868i
$485$	2.78950	+	7.56836i	0.126665	+	0.343661i
$486$	0.0223651	−	0.212790i	0.00101450	−	0.00965235i
$487$	−8.33626	−	3.71154i	−0.377752	−	0.168186i	0.209073	−	0.977900i	$-0.432955\pi$
$487$	−8.33626	−	3.71154i	−0.377752	−	0.168186i	−0.586825	+	0.809714i	$0.699622\pi$
$488$	−0.0863425	−	0.821494i	−0.00390854	−	0.0371873i
$489$	19.1733	+	13.9302i	0.867046	+	0.629946i
$490$	−3.28526	+	0.650471i	−0.148413	+	0.0293853i
$491$	7.19992	−	5.23105i	0.324928	−	0.236074i	−0.413347	−	0.910573i	$-0.635640\pi$
$491$	7.19992	−	5.23105i	0.324928	−	0.236074i	0.738275	+	0.674499i	$0.235640\pi$
$492$	−6.91557	−	7.68052i	−0.311778	−	0.346265i
$493$	21.3712	+	37.0160i	0.962510	+	1.66712i
$494$	−1.74705	+	0.371346i	−0.0786034	+	0.0167077i
$495$	−13.5953	+	0.530016i	−0.611062	+	0.0238225i
$496$	−0.619068	−	1.90529i	−0.0277970	−	0.0855503i
$497$	−3.97007	−	21.4551i	−0.178082	−	0.962394i
$498$	0.154298	+	0.112104i	0.00691425	+	0.00502350i
$499$	−6.50506	+	11.2671i	−0.291207	+	0.504385i	−0.974095	−	0.226138i	$-0.927390\pi$
$499$	−6.50506	+	11.2671i	−0.291207	+	0.504385i	0.682889	+	0.730522i	$0.260723\pi$
$500$	−12.6262	+	17.8312i	−0.564663	+	0.797434i
$501$	−2.69073	−	4.66048i	−0.120213	−	0.208215i
$502$	−2.41955	+	1.07726i	−0.107990	+	0.0480802i
$503$	−2.42745	−	7.47093i	−0.108235	−	0.333112i	0.882241	−	0.470798i	$-0.156034\pi$
$503$	−2.42745	−	7.47093i	−0.108235	−	0.333112i	−0.990476	+	0.137685i	$0.956034\pi$
$504$	2.10984	+	0.747818i	0.0939797	+	0.0333104i
$505$	15.8383	+	25.1192i	0.704797	+	1.11779i
$506$	−0.155946	−	0.173195i	−0.00693264	−	0.00769948i
$507$	5.45182	+	9.44282i	0.242124	+	0.419370i
$508$	−9.59064	+	2.03855i	−0.425516	+	0.0904461i
$509$	1.31027	+	12.4664i	0.0580769	+	0.552565i	0.984414	+	0.175868i	$0.0562733\pi$
$509$	1.31027	+	12.4664i	0.0580769	+	0.552565i	−0.926337	+	0.376696i	$0.877060\pi$
$510$	−0.207284	+	3.14786i	−0.00917867	+	0.139390i
$511$	−6.50276	+	27.0516i	−0.287665	+	1.19669i
$512$	12.6102	−	9.16186i	0.557298	−	0.404901i
$513$	−0.602649	−	5.73382i	−0.0266076	−	0.253154i
$514$	−0.0450190	+	0.428328i	−0.00198570	+	0.0188927i
$515$	14.0173	+	2.41301i	0.617676	+	0.106330i
$516$	−1.21388	−	11.5493i	−0.0534379	−	0.508428i
$517$	6.67296	−	20.5373i	0.293476	−	0.903228i
$518$	−2.11397	−	5.10774i	−0.0928825	−	0.224421i
$519$	5.11562	−	15.7443i	0.224551	−	0.691096i
$520$	−0.947286	−	2.57014i	−0.0415413	−	0.112708i
$521$	−0.0509338	+	0.0565678i	−0.00223145	+	0.00247828i	−0.744260	−	0.667891i	$-0.767197\pi$
$521$	−0.0509338	+	0.0565678i	−0.00223145	+	0.00247828i	0.742028	+	0.670369i	$0.233864\pi$
$522$	−0.928055	+	1.03071i	−0.0406199	+	0.0451129i
$523$	22.8083	−	10.1549i	0.997336	−	0.444043i	0.157873	−	0.987459i	$-0.449536\pi$
$523$	22.8083	−	10.1549i	0.997336	−	0.444043i	0.839463	+	0.543417i	$0.182870\pi$
$524$	8.24683			0.360264
$525$	−9.36253	+	9.34575i	−0.408614	+	0.407882i
$526$	−0.847065			−0.0369338
$527$	3.23751	−	1.44143i	0.141028	−	0.0627898i
$528$	−15.1758	+	16.8544i	−0.660441	+	0.733495i
$529$	−15.3686	+	17.0685i	−0.668198	+	0.742109i
$530$	−0.671738	+	2.37903i	−0.0291784	+	0.103338i
$531$	−4.30645	+	13.2539i	−0.186884	+	0.575170i
$532$	29.5532	+	3.89942i	1.28129	+	0.169061i
$533$	−2.36625	+	7.28256i	−0.102494	+	0.315443i
$534$	−0.311769	−	2.96628i	−0.0134916	−	0.128364i
$535$	2.63650	−	5.00747i	0.113986	−	0.216492i
$536$	−0.621861	+	5.91661i	−0.0268603	+	0.255559i
$537$	−0.187723	−	1.78607i	−0.00810086	−	0.0770745i
$538$	1.39014	−	1.01000i	0.0599333	−	0.0435441i
$539$	15.2866	−	39.7545i	0.658442	−	1.71235i
$540$	4.23564	−	1.07434i	0.182273	−	0.0462324i
$541$	0.537043	+	5.10962i	0.0230893	+	0.219680i	0.999982	+	0.00595098i	$0.00189427\pi$
$541$	0.537043	+	5.10962i	0.0230893	+	0.219680i	−0.976893	+	0.213729i	$0.931439\pi$
$542$	−2.98149	+	0.633735i	−0.128066	+	0.0272213i
$543$	9.18475	+	15.9085i	0.394156	+	0.682697i
$544$	10.9845	+	12.1995i	0.470955	+	0.523049i
$545$	23.8954	+	9.54173i	1.02357	+	0.408723i
$546$	−0.149134	−	0.805952i	−0.00638235	−	0.0344916i
$547$	−11.6866	−	35.9676i	−0.499682	−	1.53786i	−0.809531	−	0.587077i	$-0.800279\pi$
$547$	−11.6866	−	35.9676i	−0.499682	−	1.53786i	0.309850	−	0.950786i	$-0.399721\pi$
$548$	−3.79715	+	1.69060i	−0.162206	+	0.0722189i
$549$	−0.488160	−	0.845518i	−0.0208342	−	0.0360858i
$550$	2.48737	+	6.01540i	0.106062	+	0.256497i
$551$	−18.6864	+	32.3658i	−0.796067	+	1.37883i
$552$	0.122532	+	0.0890246i	0.00521530	+	0.00378914i
$553$	28.9630	+	10.2657i	1.23163	+	0.436544i
$554$	0.0286531	+	0.0881853i	0.00121736	+	0.00374664i
$555$	−18.1518	−	12.1366i	−0.770499	−	0.515170i
$556$	−23.7159	+	5.04097i	−1.00578	+	0.213785i
$557$	−0.766934	−	1.32837i	−0.0324961	−	0.0562848i	0.849320	−	0.527878i	$-0.177012\pi$
$557$	−0.766934	−	1.32837i	−0.0324961	−	0.0562848i	−0.881816	+	0.471594i	$0.843679\pi$
$558$	0.0769477	+	0.0854591i	0.00325746	+	0.00361777i
$559$	−6.96078	+	5.05730i	−0.294409	+	0.213901i
$560$	0.275579	+	22.0500i	0.0116454	+	0.931781i
$561$	−32.4581	−	23.5822i	−1.37038	−	0.995641i
$562$	0.402483	+	3.82937i	0.0169777	+	0.161532i
$563$	−16.9195	−	7.53305i	−0.713072	−	0.317480i	0.0179452	−	0.999839i	$-0.494288\pi$
$563$	−16.9195	−	7.53305i	−0.713072	−	0.317480i	−0.731017	+	0.682359i	$0.760954\pi$
$564$	−0.724956	+	6.89750i	−0.0305262	+	0.290437i
$565$	−6.31373	+	4.97423i	−0.265621	+	0.209267i
$566$	−4.71391	+	3.42485i	−0.198140	+	0.143957i
$567$	2.63766	−	0.206823i	0.110771	−	0.00868573i
$568$	6.97735			0.292763
$569$	−9.14569	−	10.1573i	−0.383407	−	0.425817i	0.520290	−	0.853990i	$-0.325824\pi$
$569$	−9.14569	−	10.1573i	−0.383407	−	0.425817i	−0.903697	+	0.428173i	$0.859157\pi$
$570$	−2.47427	+	1.21924i	−0.103636	+	0.0510684i
$571$	26.4463	−	29.3715i	1.10674	−	1.22916i	0.135573	−	0.990767i	$-0.456713\pi$
$571$	26.4463	−	29.3715i	1.10674	−	1.22916i	0.971169	−	0.238393i	$-0.0766207\pi$
$572$	16.8401	+	3.57947i	0.704119	+	0.149665i
$573$	21.6394	+	15.7219i	0.903999	+	0.656794i
$574$	−1.82322	+	2.37465i	−0.0760999	+	0.0991162i
$575$	−0.786874	+	0.426618i	−0.0328149	+	0.0177912i
$576$	3.46107	−	5.99475i	0.144211	−	0.249781i
$577$	3.98265	−	37.8924i	0.165800	−	1.57748i	−0.522874	−	0.852410i	$-0.675140\pi$
$577$	3.98265	−	37.8924i	0.165800	−	1.57748i	0.688674	−	0.725072i	$-0.258193\pi$
$578$	−3.79077	+	4.21007i	−0.157675	+	0.175116i
$579$	−20.0419	−	4.26003i	−0.832912	−	0.177041i
$580$	−26.3062	−	10.5044i	−1.09231	−	0.436171i
$581$	−1.01592	+	2.12835i	−0.0421476	+	0.0882988i
$582$	−0.771816			−0.0319928
$583$	−21.0367	−	23.3636i	−0.871252	−	0.967623i
$584$	−8.12774	−	3.61870i	−0.336328	−	0.149743i
$585$	−2.25844	−	2.31976i	−0.0933749	−	0.0959104i
$586$	−0.0585058	+	0.0260485i	−0.00241685	+	0.00107605i
$587$	4.62549	−	3.36061i	0.190914	−	0.138707i	−0.488222	−	0.872719i	$-0.662354\pi$
$587$	4.62549	−	3.36061i	0.190914	−	0.138707i	0.679136	+	0.734012i	$0.262354\pi$
$588$	−2.14774	+	13.5099i	−0.0885715	+	0.557138i
$589$	2.50689	+	1.82136i	0.103295	+	0.0750479i
$590$	6.66238	−	0.259735i	0.274286	−	0.0106931i
$591$	15.4746	+	6.88974i	0.636540	+	0.283406i
$592$	−35.6031	+	7.56767i	−1.46328	+	0.311029i
$593$	−19.8524	+	34.3853i	−0.815239	+	1.41204i	0.0939170	+	0.995580i	$0.470061\pi$
$593$	−19.8524	+	34.3853i	−0.815239	+	1.41204i	−0.909156	+	0.416455i	$0.863272\pi$
$594$	0.402302	−	1.23816i	0.0165066	−	0.0508022i
$595$	−38.7415	+	4.56208i	−1.58825	+	0.187027i
$596$	−6.66736	−	20.5200i	−0.273106	−	0.840533i
$597$	−7.89724	−	1.67861i	−0.323213	−	0.0687010i
$598$	0.00579694	−	0.0551542i	0.000237055	−	0.00225542i
$599$	16.7826	+	29.0683i	0.685717	+	1.18770i	0.973211	+	0.229915i	$0.0738447\pi$
$599$	16.7826	+	29.0683i	0.685717	+	1.18770i	−0.287493	+	0.957783i	$0.592822\pi$
$600$	−2.39393	−	3.48773i	−0.0977317	−	0.142386i
$601$	9.01830			0.367864			0.183932	−	0.982939i	$-0.441117\pi$
$601$	9.01830			0.367864			0.183932	+	0.982939i	$0.441117\pi$
$602$	−3.22572	+	0.954489i	−0.131470	+	0.0389021i
$603$	2.17292	+	6.68755i	0.0884880	+	0.272338i
$604$	11.7658	+	2.50090i	0.478744	+	0.101760i
$605$	−57.3445	−	9.87154i	−2.33138	−	0.401335i
$606$	−2.77938	+	0.590775i	−0.112905	+	0.0239986i
$607$	22.0209	−	38.1414i	0.893802	−	1.54811i	0.0585227	−	0.998286i	$-0.481361\pi$
$607$	22.0209	−	38.1414i	0.893802	−	1.54811i	0.835280	−	0.549825i	$-0.185306\pi$
$608$	−4.43555	+	13.6512i	−0.179885	+	0.553630i
$609$	−14.6206	−	8.96529i	−0.592455	−	0.363292i
$610$	−0.298794	+	0.359039i	−0.0120978	+	0.0145371i
$611$	4.69427	−	2.09002i	0.189910	−	0.0845532i
$612$	11.7716	+	5.24107i	0.475840	+	0.211858i
$613$	24.3255	+	10.8304i	0.982496	+	0.437436i	0.834173	−	0.551503i	$-0.185946\pi$
$613$	24.3255	+	10.8304i	0.982496	+	0.437436i	0.148324	+	0.988939i	$0.452612\pi$
$614$	2.16656	−	0.964614i	0.0874352	−	0.0389287i
$615$	−0.777032	+	11.8002i	−0.0313330	+	0.475830i
$616$	11.6110	+	7.11982i	0.467819	+	0.286866i
$617$	−12.2898	+	37.8242i	−0.494769	+	1.52274i	0.322547	+	0.946554i	$0.395461\pi$
$617$	−12.2898	+	37.8242i	−0.494769	+	1.52274i	−0.817316	+	0.576190i	$0.804539\pi$
$618$	−0.680500	+	1.17866i	−0.0273737	+	0.0474127i
$619$	−10.3899	+	2.20843i	−0.417603	+	0.0887643i	−0.411921	−	0.911220i	$-0.635142\pi$
$619$	−10.3899	+	2.20843i	−0.417603	+	0.0887643i	−0.00568226	+	0.999984i	$0.501809\pi$
$620$	−1.09417	+	2.07814i	−0.0439428	+	0.0834600i
$621$	0.175105	+	0.0372197i	0.00702671	+	0.00149357i
$622$	0.841668	+	2.59039i	0.0337478	+	0.103865i
$623$	35.3659	−	10.4648i	1.41690	−	0.419262i
$624$	−5.39687			−0.216048
$625$	24.6970	−	3.88080i	0.987878	−	0.155232i
$626$	0.309753	+	0.536509i	0.0123802	+	0.0214432i
$627$	3.66688	−	34.8880i	0.146441	−	1.39329i
$628$	−10.5523	−	2.24295i	−0.421081	−	0.0895036i
$629$	−19.8971	−	61.2371i	−0.793351	−	2.44168i
$630$	−0.529265	−	1.14986i	−0.0210864	−	0.0458114i
$631$	5.08723	−	15.6569i	0.202519	−	0.623291i	−0.797287	−	0.603601i	$-0.793732\pi$
$631$	5.08723	−	15.6569i	0.202519	−	0.623291i	0.999806	−	0.0196900i	$-0.00626792\pi$
$632$	−4.91316	+	8.50984i	−0.195435	+	0.338503i
$633$	−7.81817	+	1.66180i	−0.310744	+	0.0660507i
$634$	−0.971927	−	0.432730i	−0.0386002	−	0.0171859i
$635$	9.32637	+	6.23579i	0.370106	+	0.247460i
$636$	8.16894	+	5.93508i	0.323920	+	0.235341i
$637$	9.46411	−	3.62667i	0.374982	−	0.143694i
$638$	−6.82736	+	4.96037i	−0.270298	+	0.196383i
$639$	7.53396	−	3.35433i	0.298039	−	0.132695i
$640$	−14.2364	−	2.45072i	−0.562742	−	0.0968731i
$641$	22.3634	+	9.95681i	0.883300	+	0.393270i	0.797697	−	0.603059i	$-0.206052\pi$
$641$	22.3634	+	9.95681i	0.883300	+	0.393270i	0.0856032	+	0.996329i	$0.472718\pi$
$642$	0.362337	+	0.402417i	0.0143003	+	0.0158821i
$643$	−15.0471			−0.593400			−0.296700	−	0.954971i	$-0.595886\pi$
$643$	−15.0471			−0.593400			−0.296700	+	0.954971i	$0.595886\pi$
$644$	−0.398715	+	0.835304i	−0.0157116	+	0.0329156i
$645$	−8.49981	+	10.2136i	−0.334680	+	0.402160i
$646$	−7.95617	−	1.69114i	−0.313031	−	0.0665368i
$647$	9.59966	−	10.6615i	0.377402	−	0.419147i	−0.524281	−	0.851545i	$-0.675666\pi$
$647$	9.59966	−	10.6615i	0.377402	−	0.419147i	0.901683	+	0.432398i	$0.142333\pi$
$648$	−0.0884367	+	0.841419i	−0.00347412	+	0.0330541i
$649$	−42.3974	+	73.4345i	−1.66424	+	2.88256i
$650$	−0.667696	+	1.39766i	−0.0261892	+	0.0548209i
$651$	−0.865979	+	1.12789i	−0.0339404	+	0.0442056i
$652$	−37.4688	−	27.2227i	−1.46739	−	1.06612i
$653$	43.2008	+	9.18262i	1.69058	+	0.359344i	0.949910	−	0.312525i	$-0.101175\pi$
$653$	43.2008	+	9.18262i	1.69058	+	0.359344i	0.740670	+	0.671869i	$0.234508\pi$
$654$	−1.64742	+	1.82964i	−0.0644191	+	0.0715446i
$655$	−6.58245	−	6.76119i	−0.257198	−	0.264182i
$656$	13.1905	+	14.6496i	0.515004	+	0.571970i
$657$	−10.5158			−0.410260
$658$	2.00290	−	0.157050i	0.0780811	−	0.00612246i
$659$	24.3021	−	17.6565i	0.946675	−	0.687799i	−0.00334347	−	0.999994i	$-0.501064\pi$
$659$	24.3021	−	17.6565i	0.946675	−	0.687799i	0.950018	+	0.312195i	$0.101064\pi$
$660$	26.5681	−	1.03577i	1.03416	−	0.0403172i
$661$	−2.18097	+	20.7506i	−0.0848301	+	0.807104i	0.866551	+	0.499088i	$0.166332\pi$
$661$	−2.18097	+	20.7506i	−0.0848301	+	0.807104i	−0.951381	+	0.308016i	$0.900335\pi$
$662$	3.08067	+	1.37160i	0.119734	+	0.0533088i
$663$	−0.997933	−	9.49470i	−0.0387565	−	0.368743i
$664$	−0.610128	−	0.443284i	−0.0236775	−	0.0172027i
$665$	−20.3918	−	27.3417i	−0.790760	−	1.06027i
$666$	1.69032	−	1.22809i	0.0654988	−	0.0475876i
$667$	−0.776480	−	0.862368i	−0.0300654	−	0.0333910i
$668$	5.25828	+	9.10761i	0.203449	+	0.352384i
$669$	−11.2056	+	2.38183i	−0.433235	+	0.0920868i
$670$	2.64260	−	2.08196i	0.102093	−	0.0804330i
$671$	−1.83572	−	5.64977i	−0.0708673	−	0.218107i
$672$	−6.20850	−	2.20056i	−0.239498	−	0.0848884i
$673$	14.6391	+	10.6359i	0.564296	+	0.409985i	0.833029	−	0.553230i	$-0.186605\pi$
$673$	14.6391	+	10.6359i	0.564296	+	0.409985i	−0.268733	+	0.963215i	$0.586605\pi$
$674$	2.10709	−	3.64959i	0.0811621	−	0.140577i
$675$	−4.26161	−	2.61509i	−0.164029	−	0.100655i
$676$	−10.6540	−	18.4534i	−0.409771	−	0.709744i
$677$	−2.86991	+	1.27777i	−0.110299	+	0.0491085i	−0.461145	−	0.887325i	$-0.652561\pi$
$677$	−2.86991	+	1.27777i	−0.110299	+	0.0491085i	0.350845	+	0.936434i	$0.385894\pi$
$678$	−0.237668	−	0.731468i	−0.00912760	−	0.0280919i
$679$	−1.73653	−	9.38458i	−0.0666419	−	0.360147i
$680$	0.819645	−	12.4473i	0.0314320	−	0.477333i
$681$	7.66080	+	8.50818i	0.293562	+	0.326034i
$682$	0.349854	+	0.605966i	0.0133966	+	0.0232036i
$683$	−23.6787	+	5.03305i	−0.906039	+	0.192584i	−0.637288	−	0.770625i	$-0.719944\pi$
$683$	−23.6787	+	5.03305i	−0.906039	+	0.192584i	−0.268750	+	0.963210i	$0.586611\pi$
$684$	1.17771	+	11.2051i	0.0450308	+	0.428439i
$685$	4.41686	+	1.76371i	0.168759	+	0.0673877i
$686$	3.96137	−	0.100302i	0.151246	−	0.00382957i
$687$	3.83998	−	2.78991i	0.146504	−	0.106442i
$688$	2.31531	+	22.0287i	0.0882703	+	0.839836i
$689$	0.781993	−	7.44017i	0.0297916	−	0.283448i
$690$	−0.0122640	−	0.0847651i	−0.000466883	−	0.00322695i
$691$	−1.12069	−	10.6626i	−0.0426329	−	0.405625i	−0.994939	−	0.100481i	$-0.967962\pi$
$691$	−1.12069	−	10.6626i	−0.0426329	−	0.405625i	0.952306	−	0.305144i	$-0.0987047\pi$
$692$	−9.99704	+	30.7677i	−0.380031	+	1.16961i
$693$	15.9600	+	2.10586i	0.606271	+	0.0799950i
$694$	0.450324	−	1.38596i	0.0170941	−	0.0526101i
$695$	23.0624	+	15.4200i	0.874808	+	0.584913i
$696$	3.66973	−	4.07565i	0.139101	−	0.154487i
$697$	−23.3339	+	25.9149i	−0.883835	+	0.981598i
$698$	6.24382	−	2.77993i	0.236332	−	0.105222i
$699$	6.56698			0.248386
$700$	18.2964	−	18.2637i	0.691541	−	0.690301i
$701$	−20.0479			−0.757200			−0.378600	−	0.925560i	$-0.623594\pi$
$701$	−20.0479			−0.757200			−0.378600	+	0.925560i	$0.623594\pi$
$702$	0.283010	−	0.126004i	0.0106815	−	0.00475571i
$703$	37.6718	−	41.8387i	1.42082	−	1.57798i
$704$	28.1828	−	31.3002i	1.06218	−	1.17967i
$705$	6.23358	−	4.91109i	0.234770	−	0.184962i
$706$	1.91498	−	5.89371i	0.0720713	−	0.221813i
$707$	−13.4367	−	32.4655i	−0.505339	−	1.22099i
$708$	8.41575	−	25.9010i	0.316283	−	0.973420i
$709$	−1.77791	−	16.9156i	−0.0667706	−	0.635280i	−0.975818	−	0.218587i	$-0.929855\pi$
$709$	−1.77791	−	16.9156i	−0.0667706	−	0.635280i	0.909047	−	0.416694i	$-0.136811\pi$
$710$	−2.75235	−	2.82709i	−0.103294	−	0.106099i
$711$	−1.21402	+	11.5507i	−0.0455294	+	0.433184i
$712$	1.23280	+	11.7293i	0.0462013	+	0.439576i
$713$	−0.0778393	+	0.0565536i	−0.00291511	+	0.00211795i
$714$	0.872420	−	3.62928i	0.0326495	−	0.135822i
$715$	−10.5068	−	16.6635i	−0.392931	−	0.623178i
$716$	0.366853	+	3.49037i	0.0137099	+	0.130441i
$717$	14.0462	−	2.98562i	0.524567	−	0.111500i
$718$	−0.647726	−	1.12189i	−0.0241729	−	0.0418687i
$719$	4.58612	+	5.09340i	0.171033	+	0.189952i	0.822567	−	0.568668i	$-0.192541\pi$
$719$	4.58612	+	5.09340i	0.171033	+	0.189952i	−0.651534	+	0.758619i	$0.725874\pi$
$720$	−8.07893	+	2.04917i	−0.301084	+	0.0763680i
$721$	−15.8625	−	5.62236i	−0.590751	−	0.209388i
$722$	−0.941510	−	2.89767i	−0.0350394	−	0.107840i
$723$	−3.78222	+	1.68395i	−0.140662	+	0.0626268i
$724$	−17.9490	−	31.0886i	−0.667071	−	1.15540i
$725$	12.3850	+	29.9516i	0.459968	+	1.11238i
$726$	2.78391	−	4.82187i	0.103321	−	0.178956i
$727$	5.37334	+	3.90396i	0.199286	+	0.144790i	0.682953	−	0.730462i	$-0.260695\pi$
$727$	5.37334	+	3.90396i	0.199286	+	0.144790i	−0.483667	+	0.875252i	$0.660695\pi$
$728$	0.589709	+	3.18691i	0.0218561	+	0.118115i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.73992	+	4.72067i	0.0643972	+	0.174720i
$731$	−38.3269	+	8.14663i	−1.41757	+	0.301314i
$732$	0.953972	+	1.65233i	0.0352598	+	0.0610718i
$733$	−12.7153	−	14.1218i	−0.469651	−	0.521601i	0.461053	−	0.887373i	$-0.347472\pi$
$733$	−12.7153	−	14.1218i	−0.469651	−	0.521601i	−0.930705	+	0.365772i	$0.880805\pi$
$734$	1.60804	−	1.16831i	0.0593540	−	0.0431232i
$735$	12.7904	−	9.02249i	0.471782	−	0.332799i
$736$	−0.360568	−	0.261968i	−0.0132907	−	0.00965625i
$737$	4.47227	+	42.5508i	0.164738	+	1.56738i
$738$	−1.03374	−	0.460250i	−0.0380525	−	0.0169421i
$739$	−0.588302	+	5.59732i	−0.0216410	+	0.205901i	−0.999999	−	0.00101653i	$-0.999676\pi$
$739$	−0.588302	+	5.59732i	−0.0216410	+	0.205901i	0.978358	+	0.206917i	$0.0663431\pi$
$740$	35.4725	+	23.7176i	1.30400	+	0.871876i
$741$	6.75338	−	4.90662i	0.248092	−	0.180249i
$742$	1.25999	−	2.63967i	0.0462557	−	0.0969053i
$743$	−5.34768			−0.196187			−0.0980937	−	0.995177i	$-0.531274\pi$
$743$	−5.34768			−0.196187			−0.0980937	+	0.995177i	$0.531274\pi$
$744$	−0.304268	−	0.337924i	−0.0111550	−	0.0123889i
$745$	−11.5017	+	21.8449i	−0.421388	+	0.800336i
$746$	−4.51549	+	5.01496i	−0.165324	+	0.183611i
$747$	−0.871906	−	0.185329i	−0.0319014	−	0.00678084i
$748$	63.4303	+	46.0848i	2.31924	+	1.68503i
$749$	−4.07779	+	5.31110i	−0.148999	+	0.194064i
$750$	−0.468831	+	2.34578i	−0.0171193	+	0.0856557i
$751$	8.03634	−	13.9193i	0.293250	−	0.507924i	−0.681326	−	0.731980i	$-0.738596\pi$
$751$	8.03634	−	13.9193i	0.293250	−	0.507924i	0.974576	+	0.224056i	$0.0719298\pi$
$752$	1.38276	−	13.1561i	0.0504240	−	0.479752i
$753$	8.28284	−	9.19902i	0.301843	−	0.335231i
$754$	−1.96427	−	0.417518i	−0.0715345	−	0.0152051i
$755$	−7.34086	−	11.6424i	−0.267161	−	0.423711i
$756$	−5.15456	+	0.404177i	−0.187469	+	0.0146998i
$757$	−30.7572			−1.11789			−0.558945	−	0.829205i	$-0.688794\pi$
$757$	−30.7572			−1.11789			−0.558945	+	0.829205i	$0.688794\pi$
$758$	1.09467	+	1.21576i	0.0397602	+	0.0441582i
$759$	0.995076	+	0.443036i	0.0361190	+	0.0160812i
$760$	9.78382	−	4.82115i	0.354896	−	0.174881i
$761$	29.6292	−	13.1918i	1.07406	−	0.478201i	0.207992	−	0.978131i	$-0.433307\pi$
$761$	29.6292	−	13.1918i	1.07406	−	0.478201i	0.866066	+	0.499929i	$0.166641\pi$
$762$	−0.868489	+	0.630994i	−0.0314620	+	0.0228585i
$763$	−25.9534	−	15.9145i	−0.939574	−	0.576145i
$764$	−42.2882	−	30.7241i	−1.52993	−	1.11156i
$765$	−5.09897	−	13.8343i	−0.184354	−	0.500181i
$766$	4.42885	+	1.97185i	0.160021	+	0.0712459i
$767$	−19.7367	+	4.19517i	−0.712652	+	0.151479i
$768$	−6.23101	+	10.7924i	−0.224842	+	0.389438i
$769$	10.0900	−	31.0537i	0.363853	−	1.11983i	−0.586843	−	0.809701i	$-0.699629\pi$
$769$	10.0900	−	31.0537i	0.363853	−	1.11983i	0.950696	−	0.310124i	$-0.100371\pi$
$770$	−1.69536	−	7.51309i	−0.0610965	−	0.270753i
$771$	−0.622024	−	1.91439i	−0.0224016	−	0.0689451i
$772$	39.1662	+	8.32504i	1.40962	+	0.299625i
$773$	3.62852	−	34.5230i	0.130509	−	1.24171i	−0.711672	−	0.702512i	$-0.752062\pi$
$773$	3.62852	−	34.5230i	0.130509	−	1.24171i	0.842181	−	0.539195i	$-0.181272\pi$
$774$	−0.635731	−	1.10112i	−0.0228509	−	0.0395789i
$775$	2.57711	−	0.761669i	0.0925726	−	0.0273600i
$776$	3.05193			0.109558
$777$	18.7356	+	17.7897i	0.672136	+	0.638202i
$778$	−0.181696	−	0.559201i	−0.00651410	−	0.0200483i
$779$	−29.8248	−	6.33946i	−1.06858	−	0.227135i
$780$	4.41348	+	4.53333i	0.158028	+	0.162319i
$781$	49.0828	−	10.4329i	1.75632	−	0.373318i
$782$	0.126280	−	0.218723i	0.00451575	−	0.00782151i
$783$	2.00313	−	6.16499i	0.0715859	−	0.220319i
$784$	4.09654	−	25.7683i	0.146305	−	0.920297i
$785$	6.58372	+	10.4416i	0.234983	+	0.372677i
$786$	0.824861	−	0.367252i	0.0294218	−	0.0130994i
$787$	4.74726	+	2.11362i	0.169222	+	0.0753423i	0.489599	−	0.871948i	$-0.337143\pi$
$787$	4.74726	+	2.11362i	0.169222	+	0.0753423i	−0.320378	+	0.947290i	$0.603810\pi$
$788$	−30.2408	−	13.4641i	−1.07728	−	0.479638i
$789$	3.61668	−	1.61025i	0.128757	−	0.0573264i
$790$	5.38611	−	1.36615i	0.191629	−	0.0486056i
$791$	8.35925	−	4.53558i	0.297221	−	0.161267i
$792$	−1.59079	+	4.89595i	−0.0565262	+	0.173970i
$793$	0.706799	−	1.22421i	0.0250992	−	0.0434731i
$794$	7.25179	−	1.54142i	0.257356	−	0.0547028i
$795$	−1.65439	−	11.4346i	−0.0586750	−	0.405544i
$796$	15.4329	+	3.28037i	0.547006	+	0.116270i
$797$	2.89610	+	8.91329i	0.102585	+	0.315725i	0.989156	−	0.146868i	$-0.0469192\pi$
$797$	2.89610	+	8.91329i	0.102585	+	0.315725i	−0.886571	+	0.462593i	$0.846919\pi$
$798$	3.12961	−	0.926050i	0.110787	−	0.0327818i
$799$	23.4011			0.827872
$800$	7.04448	+	10.2632i	0.249060	+	0.362857i
$801$	6.96998	+	12.0724i	0.246272	+	0.426556i
$802$	−0.0535187	+	0.509196i	−0.00188981	+	0.0179803i
$803$	−62.5862	−	13.3031i	−2.20862	−	0.469457i
$804$	−4.24636	−	13.0690i	−0.149758	−	0.460906i
$805$	1.00307	−	0.339835i	0.0353537	−	0.0119776i
$806$	−0.0514519	+	0.158353i	−0.00181231	+	0.00557773i
$807$	−4.01545	+	6.95497i	−0.141351	+	0.244827i
$808$	10.9903	−	2.33606i	0.386637	−	0.0821821i
$809$	7.93212	+	3.53161i	0.278879	+	0.124165i	0.541410	−	0.840759i	$-0.317891\pi$
$809$	7.93212	+	3.53161i	0.278879	+	0.124165i	−0.262531	+	0.964923i	$0.584557\pi$
$810$	0.375812	−	0.296081i	0.0132047	−	0.0104032i
$811$	−6.54037	−	4.75186i	−0.229663	−	0.166860i	0.467002	−	0.884256i	$-0.345334\pi$
$811$	−6.54037	−	4.75186i	−0.229663	−	0.166860i	−0.696666	+	0.717396i	$0.745334\pi$
$812$	28.5718	+	17.5201i	1.00267	+	0.614837i
$813$	11.5252	−	8.37357i	0.404207	−	0.293674i
$814$	11.6138	−	5.17081i	0.407064	−	0.181237i
$815$	7.58824	+	52.4475i	0.265804	+	1.83716i
$816$	−22.4528	−	9.99664i	−0.786006	−	0.349952i
$817$	−22.9249	−	25.4606i	−0.802039	−	0.890755i
$818$	2.98141			0.104243
$819$	2.16885	+	3.15764i	0.0757856	+	0.110337i
$820$	1.51849	−	23.0602i	0.0530280	−	0.805297i
$821$	48.6803	+	10.3473i	1.69896	+	0.361124i	0.952553	−	0.304372i	$-0.0984465\pi$
$821$	48.6803	+	10.3473i	1.69896	+	0.361124i	0.746402	+	0.665496i	$0.231780\pi$
$822$	−0.304511	+	0.338193i	−0.0106210	+	0.0117958i
$823$	−0.529263	+	5.03560i	−0.0184489	+	0.175530i	−0.999866	−	0.0163557i	$-0.994794\pi$
$823$	−0.529263	+	5.03560i	−0.0184489	+	0.175530i	0.981417	+	0.191886i	$0.0614603\pi$
$824$	2.69085	−	4.66068i	0.0937401	−	0.162363i
$825$	−22.0553	−	20.9553i	−0.767868	−	0.729568i
$826$	−7.82123	−	1.03198i	−0.272136	−	0.0359072i
$827$	42.7292	+	31.0446i	1.48584	+	1.07953i	0.975616	+	0.219485i	$0.0704377\pi$
$827$	42.7292	+	31.0446i	1.48584	+	1.07953i	0.510225	+	0.860041i	$0.329562\pi$
$828$	−0.342193	−	0.0727354i	−0.0118920	−	0.00252773i
$829$	17.3940	−	19.3180i	0.604118	−	0.670941i	−0.361058	−	0.932543i	$-0.617584\pi$
$829$	17.3940	−	19.3180i	0.604118	−	0.670941i	0.965176	+	0.261602i	$0.0842509\pi$
$830$	0.0610667	+	0.422074i	0.00211966	+	0.0146504i
$831$	−0.289977	−	0.322052i	−0.0100592	−	0.0111719i
$832$	10.0225			0.347466
$833$	46.0916	+	2.44222i	1.59698	+	0.0846179i
$834$	−2.14762	+	1.56033i	−0.0743658	+	0.0540299i
$835$	3.26985	−	11.5805i	0.113158	−	0.400761i
$836$	−7.16589	+	68.1789i	−0.247837	+	2.35802i
$837$	−0.490996	−	0.218606i	−0.0169713	−	0.00755611i
$838$	−0.363251	−	3.45610i	−0.0125483	−	0.119389i
$839$	29.4539	+	21.3995i	1.01686	+	0.738793i	0.965637	−	0.259894i	$-0.0836877\pi$
$839$	29.4539	+	21.3995i	1.01686	+	0.738793i	0.0512243	+	0.998687i	$0.483688\pi$
$840$	2.09283	+	4.54679i	0.0722096	+	0.156879i
$841$	−10.5331	+	7.65272i	−0.363209	+	0.263887i
$842$	−3.80792	−	4.22913i	−0.131230	−	0.145745i
$843$	−8.99800	−	15.5850i	−0.309907	−	0.536775i
$844$	15.2784	−	3.24753i	0.525905	−	0.111785i
$845$	−6.62520	+	23.4639i	−0.227914	+	0.807181i
$846$	0.234651	+	0.722183i	0.00806748	+	0.0248292i
$847$	64.8932	+	23.0009i	2.22976	+	0.790322i
$848$	−15.5812	−	11.3204i	−0.535060	−	0.388744i
$849$	13.6162	−	23.5840i	0.467307	−	0.809400i
$850$	−5.36675	+	4.57799i	−0.184078	+	0.157024i
$851$	0.874055	+	1.51391i	0.0299622	+	0.0518961i
$852$	−14.7230	+	6.55511i	−0.504402	+	0.224574i
$853$	12.7492	+	39.2381i	0.436525	+	1.34349i	0.891516	+	0.452990i	$0.149643\pi$
$853$	12.7492	+	39.2381i	0.436525	+	1.34349i	−0.454991	+	0.890496i	$0.650357\pi$
$854$	0.420369	−	0.358820i	0.0143847	−	0.0122786i
$855$	8.24655	−	9.90927i	0.282026	−	0.338890i
$856$	−1.43276	−	1.59124i	−0.0489708	−	0.0543876i
$857$	2.75167	+	4.76603i	0.0939952	+	0.162804i	0.909189	−	0.416384i	$-0.136703\pi$
$857$	2.75167	+	4.76603i	0.0939952	+	0.162804i	−0.815194	+	0.579189i	$0.803370\pi$
$858$	1.84377	−	0.391906i	0.0629454	−	0.0133795i
$859$	−4.73973	−	45.0955i	−0.161718	−	1.53864i	−0.711114	−	0.703077i	$-0.751809\pi$
$859$	−4.73973	−	45.0955i	−0.161718	−	1.53864i	0.549396	−	0.835562i	$-0.314858\pi$
$860$	16.6105	−	19.9596i	0.566413	−	0.680617i
$861$	3.27039	−	13.6049i	0.111455	−	0.463653i
$862$	−3.42120	+	2.48565i	−0.116527	+	0.0846615i
$863$	1.73904	+	16.5459i	0.0591977	+	0.563228i	0.983416	+	0.181364i	$0.0580512\pi$
$863$	1.73904	+	16.5459i	0.0591977	+	0.563228i	−0.924218	+	0.381864i	$0.875282\pi$
$864$	0.260238	−	2.47600i	0.00885346	−	0.0842351i
$865$	33.2045	−	16.3621i	1.12899	−	0.556327i
$866$	0.436010	+	4.14836i	0.0148162	+	0.140967i
$867$	8.18203	−	25.1817i	0.277876	−	0.855216i
$868$	1.69231	−	2.20415i	0.0574409	−	0.0748137i
$869$	−21.8377	+	67.2096i	−0.740794	+	2.27993i
$870$	−3.09898	+	0.120815i	−0.105065	+	0.00409600i
$871$	−6.81249	+	7.56603i	−0.230832	+	0.256365i
$872$	6.51425	−	7.23480i	0.220600	−	0.245001i
$873$	3.29539	−	1.46720i	0.111532	−	0.0496573i
$874$	0.220831			0.00746972
$875$	−29.5774	−	0.422725i	−0.999898	−	0.0142907i
$876$	20.5502			0.694326
$877$	0.437320	−	0.194707i	0.0147672	−	0.00657480i	−0.399340	−	0.916803i	$-0.630761\pi$
$877$	0.437320	−	0.194707i	0.0147672	−	0.00657480i	0.414107	+	0.910228i	$0.364094\pi$
$878$	2.38444	−	2.64819i	0.0804710	−	0.0893721i
$879$	0.200282	−	0.222436i	0.00675536	−	0.00750258i
$880$	−50.6752	+	1.97559i	−1.70826	+	0.0665972i
$881$	8.99255	−	27.6762i	0.302967	−	0.932436i	−0.677461	−	0.735558i	$-0.736920\pi$
$881$	8.99255	−	27.6762i	0.302967	−	0.932436i	0.980428	−	0.196878i	$-0.0630802\pi$
$882$	0.386808	+	1.44692i	0.0130245	+	0.0487205i
$883$	−3.18079	+	9.78946i	−0.107042	+	0.329441i	−0.990204	−	0.139626i	$-0.955410\pi$
$883$	−3.18079	+	9.78946i	−0.107042	+	0.329441i	0.883162	+	0.469068i	$0.155410\pi$
$884$	1.95018	+	18.5547i	0.0655917	+	0.624063i
$885$	−27.9523	+	13.7740i	−0.939607	+	0.463008i
$886$	0.414660	−	3.94523i	0.0139308	−	0.132543i
$887$	−0.367875	−	3.50009i	−0.0123520	−	0.117522i	0.986608	−	0.163107i	$-0.0521515\pi$
$887$	−0.367875	−	3.50009i	−0.0123520	−	0.117522i	−0.998960	+	0.0455850i	$0.985485\pi$
$888$	−6.68392	+	4.85615i	−0.224298	+	0.162962i
$889$	−9.62635	−	9.14035i	−0.322858	−	0.306557i
$890$	4.26620	−	5.12638i	0.143003	−	0.171837i
$891$	0.636015	+	6.05127i	0.0213073	+	0.202725i
$892$	21.8983	−	4.65462i	0.733208	−	0.155848i
$893$	10.2307	+	17.7200i	0.342356	+	0.592977i
$894$	−1.58069	−	1.75553i	−0.0528661	−	0.0587137i
$895$	2.56878	−	3.08671i	0.0858648	−	0.103177i
$896$	16.1104	+	5.71023i	0.538211	+	0.190765i
$897$	0.0800958	+	0.246509i	0.00267432	+	0.00823071i
$898$	−0.307623	+	0.136963i	−0.0102655	+	0.00457050i
$899$	1.74198	+	3.01720i	0.0580984	+	0.100629i
$900$	8.32812	+	5.11046i	0.277604	+	0.170349i
$901$	17.0348	−	29.5052i	0.567512	−	0.982960i
$902$	−5.57020	−	4.04699i	−0.185467	−	0.134750i
$903$	11.9583	−	10.2073i	0.397946	−	0.339679i
$904$	0.939793	+	2.89239i	0.0312571	+	0.0961993i
$905$	−11.1616	+	39.5299i	−0.371023	+	1.31402i
$906$	1.28821	−	0.273817i	0.0427978	−	0.00909695i
$907$	−6.81724	−	11.8078i	−0.226363	−	0.392072i	0.730365	−	0.683057i	$-0.239350\pi$
$907$	−6.81724	−	11.8078i	−0.226363	−	0.392072i	−0.956727	+	0.290986i	$0.906017\pi$
$908$	−14.9709	−	16.6269i	−0.496826	−	0.551781i
$909$	10.7439	−	7.80594i	0.356354	−	0.258907i
$910$	1.05865	−	1.49608i	0.0350940	−	0.0495945i
$911$	−32.9498	−	23.9395i	−1.09168	−	0.793149i	−0.111995	−	0.993709i	$-0.535724\pi$
$911$	−32.9498	−	23.9395i	−1.09168	−	0.793149i	−0.979682	+	0.200559i	$0.935724\pi$
$912$	−2.24632	−	21.3723i	−0.0743832	−	0.707709i
$913$	−4.95482	−	2.20603i	−0.163981	−	0.0730088i
$914$	−0.206103	+	1.96094i	−0.00681728	+	0.0648621i
$915$	0.593226	−	2.10097i	0.0196114	−	0.0694560i
$916$	−7.50416	+	5.45209i	−0.247945	+	0.180142i
$917$	6.32133	+	9.20327i	0.208749	+	0.303919i
$918$	1.41081			0.0465638
$919$	26.1975	+	29.0953i	0.864176	+	0.959765i	0.999518	−	0.0310338i	$-0.00987995\pi$
$919$	26.1975	+	29.0953i	0.864176	+	0.959765i	−0.135342	+	0.990799i	$0.543213\pi$
$920$	0.0484946	+	0.335180i	0.00159882	+	0.0110505i
$921$	−7.41676	+	8.23715i	−0.244391	+	0.271423i
$922$	−1.08577	−	0.230788i	−0.0357579	−	0.00760058i
$923$	9.66016	+	7.01852i	0.317968	+	0.231017i
$924$	−31.1894	−	4.11531i	−1.02606	−	0.135384i
$925$	−8.86850	−	48.0132i	−0.291594	−	1.57866i
$926$	2.99451	−	5.18664i	0.0984056	−	0.170443i
$927$	0.664899	−	6.32609i	0.0218381	−	0.207776i
$928$	−10.7987	+	11.9932i	−0.354485	+	0.393696i
$929$	27.0716	+	5.75424i	0.888189	+	0.188790i	0.629343	−	0.777128i	$-0.283324\pi$
$929$	27.0716	+	5.75424i	0.888189	+	0.188790i	0.258847	+	0.965918i	$0.416658\pi$
$930$	−0.0168958	+	0.256585i	−0.000554037	+	0.00841374i
$931$	18.3013	+	35.9696i	0.599801	+	1.17886i
$932$	−12.8333			−0.420369
$933$	−8.51789	−	9.46008i	−0.278863	−	0.309709i
$934$	4.24055	+	1.88802i	0.138755	+	0.0617778i
$935$	−12.8460	−	88.7875i	−0.420109	−	2.90366i
$936$	−1.11908	+	0.498247i	−0.0365783	+	0.0162857i
$937$	−44.9953	+	32.6910i	−1.46993	+	1.06797i	−0.489299	+	0.872116i	$0.662747\pi$
$937$	−44.9953	+	32.6910i	−1.46993	+	1.06797i	−0.980633	+	0.195852i	$0.937253\pi$
$938$	−3.49875	+	1.89836i	−0.114238	+	0.0619837i
$939$	−2.34243	−	1.70188i	−0.0764423	−	0.0555386i
$940$	−12.1818	+	9.59735i	−0.397326	+	0.313031i
$941$	−23.9261	−	10.6526i	−0.779970	−	0.347265i	−0.0221719	−	0.999754i	$-0.507058\pi$
$941$	−23.9261	−	10.6526i	−0.779970	−	0.347265i	−0.757798	+	0.652489i	$0.773725\pi$
$942$	−1.15534	+	0.245575i	−0.0376430	+	0.00800126i
$943$	0.473377	−	0.819913i	0.0154153	−	0.0267001i
$944$	−16.0519	+	49.4028i	−0.522446	+	1.60792i
$945$	4.44563	+	3.90338i	0.144616	+	0.126977i
$946$	−2.39066	−	7.35770i	−0.0777271	−	0.239219i
$947$	−55.6423	−	11.8271i	−1.80813	−	0.384330i	−0.824694	−	0.565578i	$-0.808653\pi$
$947$	−55.6423	−	11.8271i	−1.80813	−	0.384330i	−0.983437	+	0.181248i	$0.941986\pi$
$948$	2.37247	−	22.5725i	0.0770542	−	0.733122i
$949$	−7.61282	−	13.1858i	−0.247123	−	0.428029i
$950$	−5.81285	−	2.06242i	−0.188594	−	0.0669138i
$951$	4.97241			0.161241
$952$	−3.44974	+	14.3510i	−0.111807	+	0.465118i
$953$	−0.640849	−	1.97233i	−0.0207591	−	0.0638901i	0.940140	−	0.340788i	$-0.110694\pi$
$953$	−0.640849	−	1.97233i	−0.0207591	−	0.0638901i	−0.960899	+	0.276898i	$0.910694\pi$
$954$	1.08137	+	0.229853i	0.0350108	+	0.00744177i
$955$	8.56426	+	59.1935i	0.277133	+	1.91546i
$956$	−27.4495	+	5.83456i	−0.887779	+	0.188703i
$957$	19.7210	−	34.1577i	0.637488	−	1.10416i
$958$	0.0368247	−	0.113335i	0.00118975	−	0.00366168i
$959$	−4.79725	−	2.94166i	−0.154911	−	0.0949913i
$960$	15.0033	−	3.80549i	0.484229	−	0.122822i
$961$	−28.0560	+	12.4913i	−0.905033	+	0.402947i
$962$	2.76361	+	1.23044i	0.0891023	+	0.0396709i
$963$	−2.31204	−	1.02939i	−0.0745045	−	0.0331715i
$964$	7.39128	−	3.29081i	0.238057	−	0.105990i
$965$	−24.4364	−	38.7555i	−0.786635	−	1.24758i
$966$	−0.00268198	+	0.101304i	−8.62913e−5	+	0.00325941i
$967$	12.6030	−	38.7882i	0.405286	−	1.24734i	−0.515369	−	0.856968i	$-0.672345\pi$
$967$	12.6030	−	38.7882i	0.405286	−	1.24734i	0.920656	−	0.390375i	$-0.127655\pi$
$968$	−11.0082	+	19.0667i	−0.353816	+	0.612828i
$969$	37.1849	−	7.90390i	1.19455	−	0.253910i
$970$	−1.20389	−	1.23658i	−0.0386547	−	0.0397043i
$971$	18.5064	+	3.93366i	0.593899	+	0.126237i	0.495049	−	0.868865i	$-0.335150\pi$
$971$	18.5064	+	3.93366i	0.593899	+	0.126237i	0.0988502	+	0.995102i	$0.468484\pi$
$972$	−0.603887	−	1.85857i	−0.0193697	−	0.0596138i
$973$	−23.8042	−	22.6024i	−0.763129	−	0.724600i
$974$	1.95244			0.0625603
$975$	0.193910	−	7.23682i	0.00621009	−	0.231764i
$976$	−1.81958	−	3.15160i	−0.0582432	−	0.100880i
$977$	4.99142	−	47.4902i	0.159690	−	1.51935i	−0.562005	−	0.827134i	$-0.689970\pi$
$977$	4.99142	−	47.4902i	0.159690	−	1.51935i	0.721694	−	0.692212i	$-0.243364\pi$
$978$	−4.95998	−	1.05428i	−0.158603	−	0.0337121i
$979$	26.2106	+	80.6678i	0.837693	+	2.57815i
$980$	−24.9953	+	17.6319i	−0.798445	+	0.563231i
$981$	3.55580	−	10.9436i	0.113528	−	0.349403i
$982$	−0.952089	+	1.64907i	−0.0303824	+	0.0526238i
$983$	38.1196	−	8.10257i	1.21583	−	0.258432i	0.445031	−	0.895515i	$-0.353193\pi$
$983$	38.1196	−	8.10257i	1.21583	−	0.258432i	0.770795	+	0.637083i	$0.219859\pi$
$984$	4.08763	+	1.81993i	0.130309	+	0.0580173i
$985$	13.0990	+	35.5398i	0.417370	+	1.13239i
$986$	−7.39867	−	5.37545i	−0.235622	−	0.171189i
$987$	−8.25314	+	4.47801i	−0.262700	+	0.142537i
$988$	−13.1976	+	9.58861i	−0.419871	+	0.305054i
$989$	0.971829	−	0.432686i	0.0309024	−	0.0137586i
$990$	2.61126	−	1.28674i	0.0829914	−	0.0408954i
$991$	−17.2089	−	7.66189i	−0.546659	−	0.243388i	0.114775	−	0.993391i	$-0.463385\pi$
$991$	−17.2089	−	7.66189i	−0.546659	−	0.243388i	−0.661434	+	0.750003i	$0.730052\pi$
$992$	0.895353	+	0.994390i	0.0284275	+	0.0315719i
$993$	−15.7608			−0.500153
$994$	2.64317	+	3.84821i	0.0838362	+	0.122058i
$995$	−9.62884	−	15.2711i	−0.305255	−	0.484126i
$996$	1.70390	+	0.362174i	0.0539900	+	0.0114759i
$997$	−36.3995	+	40.4257i	−1.15278	+	1.28030i	−0.198933	+	0.980013i	$0.563748\pi$
$997$	−36.3995	+	40.4257i	−1.15278	+	1.28030i	−0.953850	+	0.300282i	$0.902919\pi$
$998$	0.290973	−	2.76843i	0.00921060	−	0.0876330i
$999$	−4.88254	+	8.45680i	−0.154477	+	0.267561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.10	✓	160
7.4	even	3	inner	525.2.bg.b.466.11	yes	160
25.11	even	5	inner	525.2.bg.b.436.11	yes	160
175.11	even	15	inner	525.2.bg.b.361.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.10	✓	160	1.1	even	1	trivial
525.2.bg.b.361.10	yes	160	175.11	even	15	inner
525.2.bg.b.436.11	yes	160	25.11	even	5	inner
525.2.bg.b.466.11	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)

\(f(q)\)	\(=\)	\(q+(-0.195464 + 0.0870263i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-1.30763 + 1.45227i) q^{4} +(2.23437 - 0.0871077i) q^{5} +(-0.0661180 + 0.203490i) q^{6} +(-2.62302 - 0.346096i) q^{7} +(0.261445 - 0.804645i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.195464 + 0.0870263i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-1.30763 + 1.45227i) q^{4} +(2.23437 - 0.0871077i) q^{5} +(-0.0661180 + 0.203490i) q^{6} +(-2.62302 - 0.346096i) q^{7} +(0.261445 - 0.804645i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.429159 + 0.211475i) q^{10} +(0.636015 - 6.05127i) q^{11} +(0.204272 + 1.94351i) q^{12} +(1.17136 - 0.851045i) q^{13} +(0.542825 - 0.160622i) q^{14} +(1.43035 - 1.71875i) q^{15} +(-0.389621 - 3.70700i) q^{16} +(6.44967 - 1.37092i) q^{17} +(0.106981 + 0.185297i) q^{18} +(3.85781 + 4.28453i) q^{19} +(-2.79522 + 3.35881i) q^{20} +(-2.01234 + 1.71770i) q^{21} +(0.402302 + 1.23816i) q^{22} +(-0.163540 + 0.0728126i) q^{23} +(-0.423027 - 0.732704i) q^{24} +(4.98482 - 0.389262i) q^{25} +(-0.154896 + 0.268288i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.93256 - 3.35676i) q^{28} +(2.00313 + 6.16499i) q^{29} +(-0.130006 + 0.460432i) q^{30} +(0.525717 - 0.111745i) q^{31} +(1.24482 + 2.15609i) q^{32} +(-4.07140 - 4.52174i) q^{33} +(-1.14137 + 0.829256i) q^{34} +(-5.89094 - 0.544822i) q^{35} +(1.58100 + 1.14866i) q^{36} +(-1.02073 - 9.71158i) q^{37} +(-1.12693 - 0.501741i) q^{38} +(0.151345 - 1.43995i) q^{39} +(0.514074 - 1.82065i) q^{40} +(-4.27860 + 3.10858i) q^{41} +(0.243856 - 0.510875i) q^{42} -5.94246 q^{43} +(7.95640 + 8.83648i) q^{44} +(-0.320186 - 2.21303i) q^{45} +(0.0256296 - 0.0284645i) q^{46} +(3.47143 + 0.737875i) q^{47} +(-3.01554 - 2.19092i) q^{48} +(6.76043 + 1.81563i) q^{49} +(-0.940479 + 0.509897i) q^{50} +(3.29688 - 5.71036i) q^{51} +(-0.295762 + 2.81398i) q^{52} +(3.45737 - 3.83980i) q^{53} +(0.209287 + 0.0444852i) q^{54} +(0.893979 - 13.5762i) q^{55} +(-0.964259 + 2.02011i) q^{56} +5.76540 q^{57} +(-0.928055 - 1.03071i) q^{58} +(-12.7311 - 5.66827i) q^{59} +(0.625714 + 4.32474i) q^{60} +(0.891913 - 0.397105i) q^{61} +(-0.0930342 + 0.0675933i) q^{62} +(-0.0700204 + 2.64482i) q^{63} +(5.60013 + 4.06874i) q^{64} +(2.54313 - 2.00358i) q^{65} +(1.18932 + 0.529521i) q^{66} +(-6.87805 + 1.46197i) q^{67} +(-6.44283 + 11.1593i) q^{68} +(-0.0553192 + 0.170255i) q^{69} +(1.19888 - 0.406173i) q^{70} +(2.54845 + 7.84331i) q^{71} +(-0.827565 - 0.175904i) q^{72} +(1.09920 - 10.4582i) q^{73} +(1.04468 + 1.80944i) q^{74} +(3.04622 - 3.96491i) q^{75} -11.2669 q^{76} +(-3.76260 + 15.6525i) q^{77} +(0.0957311 + 0.294630i) q^{78} +(-11.3605 - 2.41475i) q^{79} +(-1.19347 - 8.24887i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.565784 - 0.979967i) q^{82} +(0.275453 - 0.847757i) q^{83} +(0.136835 - 5.16857i) q^{84} +(14.2915 - 3.62496i) q^{85} +(1.16154 - 0.517150i) q^{86} +(5.92183 + 2.63657i) q^{87} +(-4.70284 - 2.09384i) q^{88} +(-12.7348 + 5.66989i) q^{89} +(0.255176 + 0.404703i) q^{90} +(-3.36705 + 1.82690i) q^{91} +(0.108106 - 0.332716i) q^{92} +(0.268731 - 0.465456i) q^{93} +(-0.742754 + 0.157877i) q^{94} +(8.99299 + 9.23718i) q^{95} +(2.43523 + 0.517624i) q^{96} +(1.11470 + 3.43070i) q^{97} +(-1.47943 + 0.233444i) q^{98} -6.08461 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

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