LMFDB - Embedded newform 690.3.k.a.553.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.4
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-1.90173 - 4.62422i) q^{5} -2.44949 q^{6} +(2.37572 - 2.37572i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-1.90173 - 4.62422i) q^{5} -2.44949 q^{6} +(2.37572 - 2.37572i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-6.52595 - 2.72250i) q^{10} -8.18971 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.42310 - 7.42310i) q^{13} -4.75145i q^{14} +(-3.33436 + 7.99262i) q^{15} -4.00000 q^{16} +(8.23366 - 8.23366i) q^{17} +(3.00000 + 3.00000i) q^{18} +2.11038i q^{19} +(-9.24845 + 3.80345i) q^{20} -5.81931 q^{21} +(-8.18971 + 8.18971i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-17.7669 + 17.5880i) q^{25} -14.8462 q^{26} +(3.67423 - 3.67423i) q^{27} +(-4.75145 - 4.75145i) q^{28} +15.8463i q^{29} +(4.65826 + 11.3270i) q^{30} -15.0787 q^{31} +(-4.00000 + 4.00000i) q^{32} +(10.0303 + 10.0303i) q^{33} -16.4673i q^{34} +(-15.5039 - 6.46790i) q^{35} +6.00000 q^{36} +(-14.2154 + 14.2154i) q^{37} +(2.11038 + 2.11038i) q^{38} +18.1828i q^{39} +(-5.44499 + 13.0519i) q^{40} +7.01600 q^{41} +(-5.81931 + 5.81931i) q^{42} +(-3.12385 - 3.12385i) q^{43} +16.3794i q^{44} +(13.8727 - 5.70518i) q^{45} -6.78233 q^{46} +(29.7144 - 29.7144i) q^{47} +(4.89898 + 4.89898i) q^{48} +37.7119i q^{49} +(-0.178849 + 35.3549i) q^{50} -20.1683 q^{51} +(-14.8462 + 14.8462i) q^{52} +(17.6122 + 17.6122i) q^{53} -7.34847i q^{54} +(15.5746 + 37.8710i) q^{55} -9.50289 q^{56} +(2.58468 - 2.58468i) q^{57} +(15.8463 + 15.8463i) q^{58} -26.4258i q^{59} +(15.9852 + 6.66872i) q^{60} -28.1753 q^{61} +(-15.0787 + 15.0787i) q^{62} +(7.12717 + 7.12717i) q^{63} +8.00000i q^{64} +(-20.2094 + 48.4428i) q^{65} +20.0606 q^{66} +(-66.9478 + 66.9478i) q^{67} +(-16.4673 - 16.4673i) q^{68} +8.30662i q^{69} +(-21.9717 + 9.03595i) q^{70} -67.4077 q^{71} +(6.00000 - 6.00000i) q^{72} +(16.9909 + 16.9909i) q^{73} +28.4307i q^{74} +(43.3007 + 0.219044i) q^{75} +4.22077 q^{76} +(-19.4565 + 19.4565i) q^{77} +(18.1828 + 18.1828i) q^{78} +75.5612i q^{79} +(7.60691 + 18.4969i) q^{80} -9.00000 q^{81} +(7.01600 - 7.01600i) q^{82} +(-53.8232 - 53.8232i) q^{83} +11.6386i q^{84} +(-53.7325 - 22.4161i) q^{85} -6.24770 q^{86} +(19.4077 - 19.4077i) q^{87} +(16.3794 + 16.3794i) q^{88} -76.6024i q^{89} +(8.16749 - 19.5778i) q^{90} -35.2705 q^{91} +(-6.78233 + 6.78233i) q^{92} +(18.4675 + 18.4675i) q^{93} -59.4288i q^{94} +(9.75888 - 4.01337i) q^{95} +9.79796 q^{96} +(34.7900 - 34.7900i) q^{97} +(37.7119 + 37.7119i) q^{98} -24.5691i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−1.90173	−	4.62422i	−0.380345	−	0.924845i
$5$	−1.90173	−	4.62422i	−0.380345	−	0.924845i
$6$	−2.44949			−0.408248
$7$	2.37572	−	2.37572i	0.339389	−	0.339389i	−0.516748	−	0.856137i	$-0.672858\pi$
$7$	2.37572	−	2.37572i	0.339389	−	0.339389i	0.856137	+	0.516748i	$0.172858\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	−6.52595	−	2.72250i	−0.652595	−	0.272250i
$11$	−8.18971			−0.744519			−0.372260	−	0.928129i	$-0.621417\pi$
$11$	−8.18971			−0.744519			−0.372260	+	0.928129i	$0.621417\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−7.42310	−	7.42310i	−0.571008	−	0.571008i	0.361402	−	0.932410i	$-0.382298\pi$
$13$	−7.42310	−	7.42310i	−0.571008	−	0.571008i	−0.932410	+	0.361402i	$0.882298\pi$
$14$		−	4.75145i		−	0.339389i
$15$	−3.33436	+	7.99262i	−0.222291	+	0.532842i
$16$	−4.00000			−0.250000
$17$	8.23366	−	8.23366i	0.484333	−	0.484333i	−0.422179	−	0.906512i	$-0.638735\pi$
$17$	8.23366	−	8.23366i	0.484333	−	0.484333i	0.906512	+	0.422179i	$0.138735\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			2.11038i			0.111073i	0.998457	+	0.0555364i	$0.0176869\pi$
$19$			2.11038i			0.111073i	−0.998457	+	0.0555364i	$0.982313\pi$
$20$	−9.24845	+	3.80345i	−0.462422	+	0.190173i
$21$	−5.81931			−0.277110
$22$	−8.18971	+	8.18971i	−0.372260	+	0.372260i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	−17.7669	+	17.5880i	−0.710675	+	0.703521i
$26$	−14.8462			−0.571008
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−4.75145	−	4.75145i	−0.169695	−	0.169695i
$29$			15.8463i			0.546424i	0.961954	+	0.273212i	$0.0880860\pi$
$29$			15.8463i			0.546424i	−0.961954	+	0.273212i	$0.911914\pi$
$30$	4.65826	+	11.3270i	0.155275	+	0.377566i
$31$	−15.0787			−0.486409			−0.243204	−	0.969975i	$-0.578199\pi$
$31$	−15.0787			−0.486409			−0.243204	+	0.969975i	$0.578199\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	10.0303	+	10.0303i	0.303949	+	0.303949i
$34$		−	16.4673i		−	0.484333i
$35$	−15.5039	−	6.46790i	−0.442967	−	0.184797i
$36$	6.00000			0.166667
$37$	−14.2154	+	14.2154i	−0.384199	+	0.384199i	−0.872612	−	0.488413i	$-0.837576\pi$
$37$	−14.2154	+	14.2154i	−0.384199	+	0.384199i	0.488413	+	0.872612i	$0.337576\pi$
$38$	2.11038	+	2.11038i	0.0555364	+	0.0555364i
$39$			18.1828i			0.466226i
$40$	−5.44499	+	13.0519i	−0.136125	+	0.326297i
$41$	7.01600			0.171122			0.0855609	−	0.996333i	$-0.472732\pi$
$41$	7.01600			0.171122			0.0855609	+	0.996333i	$0.472732\pi$
$42$	−5.81931	+	5.81931i	−0.138555	+	0.138555i
$43$	−3.12385	−	3.12385i	−0.0726476	−	0.0726476i	0.669849	−	0.742497i	$-0.266359\pi$
$43$	−3.12385	−	3.12385i	−0.0726476	−	0.0726476i	−0.742497	+	0.669849i	$0.766359\pi$
$44$			16.3794i			0.372260i
$45$	13.8727	−	5.70518i	0.308282	−	0.126782i
$46$	−6.78233			−0.147442
$47$	29.7144	−	29.7144i	0.632221	−	0.632221i	−0.316404	−	0.948625i	$-0.602475\pi$
$47$	29.7144	−	29.7144i	0.632221	−	0.632221i	0.948625	+	0.316404i	$0.102475\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$			37.7119i			0.769630i
$50$	−0.178849	+	35.3549i	−0.00357698	+	0.707098i
$51$	−20.1683			−0.395456
$52$	−14.8462	+	14.8462i	−0.285504	+	0.285504i
$53$	17.6122	+	17.6122i	0.332306	+	0.332306i	0.853462	−	0.521155i	$-0.174499\pi$
$53$	17.6122	+	17.6122i	0.332306	+	0.332306i	−0.521155	+	0.853462i	$0.674499\pi$
$54$		−	7.34847i		−	0.136083i
$55$	15.5746	+	37.8710i	0.283174	+	0.688565i
$56$	−9.50289			−0.169695
$57$	2.58468	−	2.58468i	0.0453453	−	0.0453453i
$58$	15.8463	+	15.8463i	0.273212	+	0.273212i
$59$		−	26.4258i		−	0.447895i	−0.974601	−	0.223947i	$-0.928106\pi$
$59$		−	26.4258i		−	0.447895i	0.974601	−	0.223947i	$-0.0718944\pi$
$60$	15.9852	+	6.66872i	0.266421	+	0.111145i
$61$	−28.1753			−0.461889			−0.230945	−	0.972967i	$-0.574182\pi$
$61$	−28.1753			−0.461889			−0.230945	+	0.972967i	$0.574182\pi$
$62$	−15.0787	+	15.0787i	−0.243204	+	0.243204i
$63$	7.12717	+	7.12717i	0.113130	+	0.113130i
$64$			8.00000i			0.125000i
$65$	−20.2094	+	48.4428i	−0.310913	+	0.745273i
$66$	20.0606			0.303949
$67$	−66.9478	+	66.9478i	−0.999221	+	0.999221i	−1.00000		0.000778970i	$-0.999752\pi$
$67$	−66.9478	+	66.9478i	−0.999221	+	0.999221i	0.000778970		1.00000i	$0.499752\pi$
$68$	−16.4673	−	16.4673i	−0.242166	−	0.242166i
$69$			8.30662i			0.120386i
$70$	−21.9717	+	9.03595i	−0.313882	+	0.129085i
$71$	−67.4077			−0.949405			−0.474702	−	0.880146i	$-0.657444\pi$
$71$	−67.4077			−0.949405			−0.474702	+	0.880146i	$0.657444\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	16.9909	+	16.9909i	0.232752	+	0.232752i	0.813840	−	0.581089i	$-0.197373\pi$
$73$	16.9909	+	16.9909i	0.232752	+	0.232752i	−0.581089	+	0.813840i	$0.697373\pi$
$74$			28.4307i			0.384199i
$75$	43.3007	+	0.219044i	0.577343	+	0.00292059i
$76$	4.22077			0.0555364
$77$	−19.4565	+	19.4565i	−0.252682	+	0.252682i
$78$	18.1828	+	18.1828i	0.233113	+	0.233113i
$79$			75.5612i			0.956471i	0.878232	+	0.478235i	$0.158723\pi$
$79$			75.5612i			0.956471i	−0.878232	+	0.478235i	$0.841277\pi$
$80$	7.60691	+	18.4969i	0.0950864	+	0.231211i
$81$	−9.00000			−0.111111
$82$	7.01600	−	7.01600i	0.0855609	−	0.0855609i
$83$	−53.8232	−	53.8232i	−0.648473	−	0.648473i	0.304151	−	0.952624i	$-0.401627\pi$
$83$	−53.8232	−	53.8232i	−0.648473	−	0.648473i	−0.952624	+	0.304151i	$0.901627\pi$
$84$			11.6386i			0.138555i
$85$	−53.7325	−	22.4161i	−0.632147	−	0.263719i
$86$	−6.24770			−0.0726476
$87$	19.4077	−	19.4077i	0.223076	−	0.223076i
$88$	16.3794	+	16.3794i	0.186130	+	0.186130i
$89$		−	76.6024i		−	0.860701i	−0.902662	−	0.430351i	$-0.858390\pi$
$89$		−	76.6024i		−	0.860701i	0.902662	−	0.430351i	$-0.141610\pi$
$90$	8.16749	−	19.5778i	0.0907498	−	0.217532i
$91$	−35.2705			−0.387587
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	18.4675	+	18.4675i	0.198576	+	0.198576i
$94$		−	59.4288i		−	0.632221i
$95$	9.75888	−	4.01337i	0.102725	−	0.0422460i
$96$	9.79796			0.102062
$97$	34.7900	−	34.7900i	0.358660	−	0.358660i	−0.504659	−	0.863319i	$-0.668382\pi$
$97$	34.7900	−	34.7900i	0.358660	−	0.358660i	0.863319	+	0.504659i	$0.168382\pi$
$98$	37.7119	+	37.7119i	0.384815	+	0.384815i
$99$		−	24.5691i		−	0.248173i
$100$	35.1760	+	35.5337i	0.351760	+	0.355337i
$101$	−0.567660			−0.00562040			−0.00281020	−	0.999996i	$-0.500895\pi$
$101$	−0.567660			−0.00562040			−0.00281020	+	0.999996i	$0.500895\pi$
$102$	−20.1683	+	20.1683i	−0.197728	+	0.197728i
$103$	−12.3289	−	12.3289i	−0.119698	−	0.119698i	0.644720	−	0.764418i	$-0.276974\pi$
$103$	−12.3289	−	12.3289i	−0.119698	−	0.119698i	−0.764418	+	0.644720i	$0.776974\pi$
$104$			29.6924i			0.285504i
$105$	11.0667	+	26.9098i	0.105398	+	0.256284i
$106$	35.2245			0.332306
$107$	31.8401	−	31.8401i	0.297571	−	0.297571i	−0.542491	−	0.840062i	$-0.682519\pi$
$107$	31.8401	−	31.8401i	0.297571	−	0.297571i	0.840062	+	0.542491i	$0.182519\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	178.228i		−	1.63512i	−0.575844	−	0.817559i	$-0.695327\pi$
$109$		−	178.228i		−	1.63512i	0.575844	−	0.817559i	$-0.304673\pi$
$110$	53.4456	+	22.2965i	0.485870	+	0.202695i
$111$	34.8204			0.313697
$112$	−9.50289	+	9.50289i	−0.0848473	+	0.0848473i
$113$	−73.7395	−	73.7395i	−0.652562	−	0.652562i	0.301047	−	0.953609i	$-0.402664\pi$
$113$	−73.7395	−	73.7395i	−0.652562	−	0.652562i	−0.953609	+	0.301047i	$0.902664\pi$
$114$		−	5.16936i		−	0.0453453i
$115$	−9.23243	+	22.1306i	−0.0802820	+	0.192440i
$116$	31.6926			0.273212
$117$	22.2693	−	22.2693i	0.190336	−	0.190336i
$118$	−26.4258	−	26.4258i	−0.223947	−	0.223947i
$119$		−	39.1218i		−	0.328755i
$120$	22.6540	−	9.31652i	0.188783	−	0.0776377i
$121$	−53.9286			−0.445691
$122$	−28.1753	+	28.1753i	−0.230945	+	0.230945i
$123$	−8.59281	−	8.59281i	−0.0698602	−	0.0698602i
$124$			30.1573i			0.243204i
$125$	115.119	+	48.7103i	0.920949	+	0.389683i
$126$	14.2543			0.113130
$127$	11.2783	−	11.2783i	0.0888056	−	0.0888056i	−0.661308	−	0.750114i	$-0.729999\pi$
$127$	11.2783	−	11.2783i	0.0888056	−	0.0888056i	0.750114	+	0.661308i	$0.229999\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			7.65183i			0.0593165i
$130$	28.2334	+	68.6521i	0.217180	+	0.528093i
$131$	−125.767			−0.960057			−0.480028	−	0.877253i	$-0.659374\pi$
$131$	−125.767			−0.960057			−0.480028	+	0.877253i	$0.659374\pi$
$132$	20.0606	−	20.0606i	0.151974	−	0.151974i
$133$	5.01369	+	5.01369i	0.0376969	+	0.0376969i
$134$			133.896i			0.999221i
$135$	−23.9779	−	10.0031i	−0.177614	−	0.0740969i
$136$	−32.9346			−0.242166
$137$	89.3505	−	89.3505i	0.652194	−	0.652194i	−0.301327	−	0.953521i	$-0.597430\pi$
$137$	89.3505	−	89.3505i	0.652194	−	0.652194i	0.953521	+	0.301327i	$0.0974296\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	61.2074i		−	0.440341i	−0.975461	−	0.220170i	$-0.929339\pi$
$139$		−	61.2074i		−	0.440341i	0.975461	−	0.220170i	$-0.0706613\pi$
$140$	−12.9358	+	31.0077i	−0.0923985	+	0.221484i
$141$	−72.7851			−0.516206
$142$	−67.4077	+	67.4077i	−0.474702	+	0.474702i
$143$	60.7930	+	60.7930i	0.425126	+	0.425126i
$144$		−	12.0000i		−	0.0833333i
$145$	73.2767	−	30.1353i	0.505357	−	0.207830i
$146$	33.9817			0.232752
$147$	46.1874	−	46.1874i	0.314200	−	0.314200i
$148$	28.4307	+	28.4307i	0.192099	+	0.192099i
$149$		−	245.889i		−	1.65026i	−0.564943	−	0.825130i	$-0.691102\pi$
$149$		−	245.889i		−	1.65026i	0.564943	−	0.825130i	$-0.308898\pi$
$150$	43.5198	−	43.0817i	0.290132	−	0.287211i
$151$	−8.23880			−0.0545616			−0.0272808	−	0.999628i	$-0.508685\pi$
$151$	−8.23880			−0.0545616			−0.0272808	+	0.999628i	$0.508685\pi$
$152$	4.22077	−	4.22077i	0.0277682	−	0.0277682i
$153$	24.7010	+	24.7010i	0.161444	+	0.161444i
$154$			38.9130i			0.252682i
$155$	28.6755	+	69.7271i	0.185003	+	0.449852i
$156$	36.3656			0.233113
$157$	−57.9326	+	57.9326i	−0.368997	+	0.368997i	−0.867111	−	0.498114i	$-0.834026\pi$
$157$	−57.9326	+	57.9326i	−0.368997	+	0.368997i	0.498114	+	0.867111i	$0.334026\pi$
$158$	75.5612	+	75.5612i	0.478235	+	0.478235i
$159$		−	43.1410i		−	0.271327i
$160$	26.1038	+	10.8900i	0.163149	+	0.0680624i
$161$	−16.1129			−0.100080
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−54.9037	−	54.9037i	−0.336832	−	0.336832i	0.518341	−	0.855174i	$-0.326550\pi$
$163$	−54.9037	−	54.9037i	−0.336832	−	0.336832i	−0.855174	+	0.518341i	$0.826550\pi$
$164$		−	14.0320i		−	0.0855609i
$165$	27.3075	−	65.4573i	0.165500	−	0.396711i
$166$	−107.646			−0.648473
$167$	40.0337	−	40.0337i	0.239723	−	0.239723i	−0.577013	−	0.816735i	$-0.695782\pi$
$167$	40.0337	−	40.0337i	0.239723	−	0.239723i	0.816735	+	0.577013i	$0.195782\pi$
$168$	11.6386	+	11.6386i	0.0692775	+	0.0692775i
$169$		−	58.7952i		−	0.347901i
$170$	−76.1486	+	31.3164i	−0.447933	+	0.184214i
$171$	−6.33115			−0.0370243
$172$	−6.24770	+	6.24770i	−0.0363238	+	0.0363238i
$173$	72.6221	+	72.6221i	0.419781	+	0.419781i	0.885128	−	0.465347i	$-0.154071\pi$
$173$	72.6221	+	72.6221i	0.419781	+	0.419781i	−0.465347	+	0.885128i	$0.654071\pi$
$174$		−	38.8153i		−	0.223076i
$175$	−0.424896	+	83.9934i	−0.00242798	+	0.479962i
$176$	32.7588			0.186130
$177$	−32.3649	+	32.3649i	−0.182852	+	0.182852i
$178$	−76.6024	−	76.6024i	−0.430351	−	0.430351i
$179$		−	294.692i		−	1.64632i	−0.567808	−	0.823161i	$-0.692208\pi$
$179$		−	294.692i		−	1.64632i	0.567808	−	0.823161i	$-0.307792\pi$
$180$	−11.4104	−	27.7453i	−0.0633909	−	0.154141i
$181$	15.6531			0.0864813			0.0432407	−	0.999065i	$-0.486232\pi$
$181$	15.6531			0.0864813			0.0432407	+	0.999065i	$0.486232\pi$
$182$	−35.2705	+	35.2705i	−0.193794	+	0.193794i
$183$	34.5075	+	34.5075i	0.188566	+	0.188566i
$184$			13.5647i			0.0737210i
$185$	92.7687	+	38.7012i	0.501452	+	0.209196i
$186$	36.9351			0.198576
$187$	−67.4313	+	67.4313i	−0.360595	+	0.360595i
$188$	−59.4288	−	59.4288i	−0.316111	−	0.316111i
$189$		−	17.4579i		−	0.0923700i
$190$	5.74551	−	13.7723i	0.0302395	−	0.0724855i
$191$	128.180			0.671097			0.335548	−	0.942023i	$-0.391078\pi$
$191$	128.180			0.671097			0.335548	+	0.942023i	$0.391078\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	−29.7003	−	29.7003i	−0.153888	−	0.153888i	0.625964	−	0.779852i	$-0.284706\pi$
$193$	−29.7003	−	29.7003i	−0.153888	−	0.153888i	−0.779852	+	0.625964i	$0.784706\pi$
$194$		−	69.5800i		−	0.358660i
$195$	84.0813	−	34.5787i	0.431186	−	0.177327i
$196$	75.4238			0.384815
$197$	122.742	−	122.742i	0.623057	−	0.623057i	−0.323255	−	0.946312i	$-0.604777\pi$
$197$	122.742	−	122.742i	0.623057	−	0.623057i	0.946312	+	0.323255i	$0.104777\pi$
$198$	−24.5691	−	24.5691i	−0.124087	−	0.124087i
$199$			10.9495i			0.0550228i	0.999621	+	0.0275114i	$0.00875825\pi$
$199$			10.9495i			0.0550228i	−0.999621	+	0.0275114i	$0.991242\pi$
$200$	70.7098	+	0.357698i	0.353549	+	0.00178849i
$201$	163.988			0.815860
$202$	−0.567660	+	0.567660i	−0.00281020	+	0.00281020i
$203$	37.6464	+	37.6464i	0.185450	+	0.185450i
$204$			40.3365i			0.197728i
$205$	−13.3425	−	32.4435i	−0.0650854	−	0.158261i
$206$	−24.6578			−0.119698
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	29.6924	+	29.6924i	0.142752	+	0.142752i
$209$		−	17.2834i		−	0.0826958i
$210$	37.9765	+	15.8430i	0.180841	+	0.0754431i
$211$	−371.360			−1.76000			−0.879999	−	0.474975i	$-0.842457\pi$
$211$	−371.360			−1.76000			−0.879999	+	0.474975i	$0.842457\pi$
$212$	35.2245	−	35.2245i	0.166153	−	0.166153i
$213$	82.5573	+	82.5573i	0.387593	+	0.387593i
$214$		−	63.6802i		−	0.297571i
$215$	−8.50466	+	20.3861i	−0.0395566	+	0.0948190i
$216$	−14.6969			−0.0680414
$217$	−35.8228	+	35.8228i	−0.165082	+	0.165082i
$218$	−178.228	−	178.228i	−0.817559	−	0.817559i
$219$		−	41.6189i		−	0.190041i
$220$	75.7421	−	31.1492i	0.344282	−	0.141587i
$221$	−122.239			−0.553116
$222$	34.8204	−	34.8204i	0.156849	−	0.156849i
$223$	−75.9931	−	75.9931i	−0.340776	−	0.340776i	0.515883	−	0.856659i	$-0.327464\pi$
$223$	−75.9931	−	75.9931i	−0.340776	−	0.340776i	−0.856659	+	0.515883i	$0.827464\pi$
$224$			19.0058i			0.0848473i
$225$	−52.7641	−	53.3006i	−0.234507	−	0.236892i
$226$	−147.479			−0.652562
$227$	172.585	−	172.585i	0.760287	−	0.760287i	−0.216087	−	0.976374i	$-0.569330\pi$
$227$	172.585	−	172.585i	0.760287	−	0.760287i	0.976374	+	0.216087i	$0.0693295\pi$
$228$	−5.16936	−	5.16936i	−0.0226726	−	0.0226726i
$229$		−	73.4614i		−	0.320792i	−0.987053	−	0.160396i	$-0.948723\pi$
$229$		−	73.4614i		−	0.320792i	0.987053	−	0.160396i	$-0.0512772\pi$
$230$	12.8981	+	31.3630i	0.0560789	+	0.136361i
$231$	47.6585			0.206314
$232$	31.6926	−	31.6926i	0.136606	−	0.136606i
$233$	284.973	+	284.973i	1.22306	+	1.22306i	0.966539	+	0.256519i	$0.0825757\pi$
$233$	284.973	+	284.973i	1.22306	+	1.22306i	0.256519	+	0.966539i	$0.417424\pi$
$234$		−	44.5386i		−	0.190336i
$235$	−193.915	−	80.8973i	−0.825168	−	0.344244i
$236$	−52.8516			−0.223947
$237$	92.5432	−	92.5432i	0.390478	−	0.390478i
$238$	−39.1218	−	39.1218i	−0.164377	−	0.164377i
$239$		−	117.112i		−	0.490009i	−0.969522	−	0.245005i	$-0.921211\pi$
$239$		−	117.112i		−	0.490009i	0.969522	−	0.245005i	$-0.0787895\pi$
$240$	13.3374	−	31.9705i	0.0555727	−	0.133210i
$241$	178.634			0.741219			0.370610	−	0.928789i	$-0.379149\pi$
$241$	178.634			0.741219			0.370610	+	0.928789i	$0.379149\pi$
$242$	−53.9286	+	53.9286i	−0.222846	+	0.222846i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			56.3505i			0.230945i
$245$	174.388	−	71.7177i	0.711788	−	0.292725i
$246$	−17.1856			−0.0698602
$247$	15.6656	−	15.6656i	0.0634234	−	0.0634234i
$248$	30.1573	+	30.1573i	0.121602	+	0.121602i
$249$			131.839i			0.529476i
$250$	163.829	−	66.4083i	0.655316	−	0.265633i
$251$	−350.780			−1.39753			−0.698765	−	0.715351i	$-0.746267\pi$
$251$	−350.780			−1.39753			−0.698765	+	0.715351i	$0.746267\pi$
$252$	14.2543	−	14.2543i	0.0565648	−	0.0565648i
$253$	27.7727	+	27.7727i	0.109773	+	0.109773i
$254$		−	22.5566i		−	0.0888056i
$255$	38.3545	+	93.2626i	0.150410	+	0.365736i
$256$	16.0000			0.0625000
$257$	108.104	−	108.104i	0.420639	−	0.420639i	−0.464785	−	0.885424i	$-0.653868\pi$
$257$	108.104	−	108.104i	0.420639	−	0.420639i	0.885424	+	0.464785i	$0.153868\pi$
$258$	7.65183	+	7.65183i	0.0296583	+	0.0296583i
$259$			67.5435i			0.260786i
$260$	96.8855	+	40.4187i	0.372637	+	0.155457i
$261$	−47.5388			−0.182141
$262$	−125.767	+	125.767i	−0.480028	+	0.480028i
$263$	78.3826	+	78.3826i	0.298033	+	0.298033i	0.840243	−	0.542210i	$-0.182412\pi$
$263$	78.3826	+	78.3826i	0.298033	+	0.298033i	−0.542210	+	0.840243i	$0.682412\pi$
$264$		−	40.1212i		−	0.151974i
$265$	47.9492	−	114.937i	0.180941	−	0.433723i
$266$	10.0274			0.0376969
$267$	−93.8184	+	93.8184i	−0.351380	+	0.351380i
$268$	133.896	+	133.896i	0.499610	+	0.499610i
$269$		−	326.796i		−	1.21485i	−0.794376	−	0.607427i	$-0.792202\pi$
$269$		−	326.796i		−	1.21485i	0.794376	−	0.607427i	$-0.207798\pi$
$270$	−33.9810	+	13.9748i	−0.125855	+	0.0517585i
$271$	−312.784			−1.15419			−0.577093	−	0.816679i	$-0.695813\pi$
$271$	−312.784			−1.15419			−0.577093	+	0.816679i	$0.695813\pi$
$272$	−32.9346	+	32.9346i	−0.121083	+	0.121083i
$273$	43.1973	+	43.1973i	0.158232	+	0.158232i
$274$		−	178.701i		−	0.652194i
$275$	145.506	−	144.041i	0.529111	−	0.523785i
$276$	16.6132			0.0601929
$277$	−64.9224	+	64.9224i	−0.234377	+	0.234377i	−0.814517	−	0.580140i	$-0.802998\pi$
$277$	−64.9224	+	64.9224i	−0.234377	+	0.234377i	0.580140	+	0.814517i	$0.302998\pi$
$278$	−61.2074	−	61.2074i	−0.220170	−	0.220170i
$279$		−	45.2360i		−	0.162136i
$280$	18.0719	+	43.9435i	0.0645425	+	0.156941i
$281$	−222.033			−0.790154			−0.395077	−	0.918648i	$-0.629282\pi$
$281$	−222.033			−0.790154			−0.395077	+	0.918648i	$0.629282\pi$
$282$	−72.7851	+	72.7851i	−0.258103	+	0.258103i
$283$	−264.201	−	264.201i	−0.933574	−	0.933574i	0.0643532	−	0.997927i	$-0.479502\pi$
$283$	−264.201	−	264.201i	−0.933574	−	0.933574i	−0.997927	+	0.0643532i	$0.979502\pi$
$284$			134.815i			0.474702i
$285$	−16.8675	−	7.03678i	−0.0591842	−	0.0246905i
$286$	121.586			0.425126
$287$	16.6681	−	16.6681i	0.0580769	−	0.0580769i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$			153.414i			0.530843i
$290$	43.1414	−	103.412i	0.148764	−	0.356593i
$291$	−85.2178			−0.292845
$292$	33.9817	−	33.9817i	0.116376	−	0.116376i
$293$	150.293	+	150.293i	0.512945	+	0.512945i	0.915428	−	0.402483i	$-0.131853\pi$
$293$	150.293	+	150.293i	0.512945	+	0.512945i	−0.402483	+	0.915428i	$0.631853\pi$
$294$		−	92.3749i		−	0.314200i
$295$	−122.199	+	50.2546i	−0.414233	+	0.170355i
$296$	56.8614			0.192099
$297$	−30.0909	+	30.0909i	−0.101316	+	0.101316i
$298$	−245.889	−	245.889i	−0.825130	−	0.825130i
$299$			50.3459i			0.168381i
$300$	0.438089	−	86.6014i	0.00146030	−	0.288671i
$301$	−14.8428			−0.0493116
$302$	−8.23880	+	8.23880i	−0.0272808	+	0.0272808i
$303$	0.695239	+	0.695239i	0.00229452	+	0.00229452i
$304$		−	8.44153i		−	0.0277682i
$305$	53.5816	+	130.289i	0.175678	+	0.427176i
$306$	49.4020			0.161444
$307$	−371.701	+	371.701i	−1.21075	+	1.21075i	−0.239971	+	0.970780i	$0.577138\pi$
$307$	−371.701	+	371.701i	−1.21075	+	1.21075i	−0.970780	+	0.239971i	$0.922862\pi$
$308$	38.9130	+	38.9130i	0.126341	+	0.126341i
$309$			30.1995i			0.0977331i
$310$	98.4027	+	41.0516i	0.317428	+	0.132425i
$311$	24.8526			0.0799118			0.0399559	−	0.999201i	$-0.487278\pi$
$311$	24.8526			0.0799118			0.0399559	+	0.999201i	$0.487278\pi$
$312$	36.3656	−	36.3656i	0.116556	−	0.116556i
$313$	159.376	+	159.376i	0.509189	+	0.509189i	0.914277	−	0.405088i	$-0.132759\pi$
$313$	159.376	+	159.376i	0.509189	+	0.509189i	−0.405088	+	0.914277i	$0.632759\pi$
$314$			115.865i			0.368997i
$315$	19.4037	−	46.5116i	0.0615990	−	0.147656i
$316$	151.122			0.478235
$317$	161.728	−	161.728i	0.510182	−	0.510182i	−0.404400	−	0.914582i	$-0.632520\pi$
$317$	161.728	−	161.728i	0.510182	−	0.510182i	0.914582	+	0.404400i	$0.132520\pi$
$318$	−43.1410	−	43.1410i	−0.135664	−	0.135664i
$319$		−	129.776i		−	0.406823i
$320$	36.9938	−	15.2138i	0.115606	−	0.0475432i
$321$	−77.9920			−0.242966
$322$	−16.1129	+	16.1129i	−0.0500402	+	0.0500402i
$323$	17.3762	+	17.3762i	0.0537962	+	0.0537962i
$324$			18.0000i			0.0555556i
$325$	262.443	+	1.32761i	0.807516	+	0.00408497i
$326$	−109.807			−0.336832
$327$	−218.284	+	218.284i	−0.667534	+	0.667534i
$328$	−14.0320	−	14.0320i	−0.0427805	−	0.0427805i
$329$		−	141.186i		−	0.429138i
$330$	−38.1498	−	92.7647i	−0.115606	−	0.281105i
$331$	−404.107			−1.22087			−0.610434	−	0.792067i	$-0.709005\pi$
$331$	−404.107			−1.22087			−0.610434	+	0.792067i	$0.709005\pi$
$332$	−107.646	+	107.646i	−0.324236	+	0.324236i
$333$	−42.6461	−	42.6461i	−0.128066	−	0.128066i
$334$		−	80.0673i		−	0.239723i
$335$	436.898	+	182.265i	1.30417	+	0.544075i
$336$	23.2772			0.0692775
$337$	−49.6359	+	49.6359i	−0.147288	+	0.147288i	−0.776905	−	0.629618i	$-0.783212\pi$
$337$	−49.6359	+	49.6359i	−0.147288	+	0.147288i	0.629618	+	0.776905i	$0.283212\pi$
$338$	−58.7952	−	58.7952i	−0.173950	−	0.173950i
$339$			180.624i			0.532815i
$340$	−44.8322	+	107.465i	−0.131859	+	0.316073i
$341$	123.490			0.362141
$342$	−6.33115	+	6.33115i	−0.0185121	+	0.0185121i
$343$	206.003	+	206.003i	0.600593	+	0.600593i
$344$			12.4954i			0.0363238i
$345$	38.4117	−	15.7969i	0.111338	−	0.0457882i
$346$	145.244			0.419781
$347$	−37.8258	+	37.8258i	−0.109008	+	0.109008i	−0.759507	−	0.650499i	$-0.774560\pi$
$347$	−37.8258	+	37.8258i	−0.109008	+	0.109008i	0.650499	+	0.759507i	$0.274560\pi$
$348$	−38.8153	−	38.8153i	−0.111538	−	0.111538i
$349$		−	608.019i		−	1.74217i	−0.491129	−	0.871087i	$-0.663416\pi$
$349$		−	608.019i		−	1.74217i	0.491129	−	0.871087i	$-0.336584\pi$
$350$	83.5685	+	84.4183i	0.238767	+	0.241195i
$351$	−54.5484			−0.155409
$352$	32.7588	−	32.7588i	0.0930649	−	0.0930649i
$353$	102.065	+	102.065i	0.289135	+	0.289135i	0.836738	−	0.547603i	$-0.184460\pi$
$353$	102.065	+	102.065i	0.289135	+	0.289135i	−0.547603	+	0.836738i	$0.684460\pi$
$354$			64.7297i			0.182852i
$355$	128.191	+	311.708i	0.361102	+	0.878052i
$356$	−153.205			−0.430351
$357$	−47.9142	+	47.9142i	−0.134214	+	0.134214i
$358$	−294.692	−	294.692i	−0.823161	−	0.823161i
$359$			392.739i			1.09398i	0.837139	+	0.546990i	$0.184227\pi$
$359$			392.739i			1.09398i	−0.837139	+	0.546990i	$0.815773\pi$
$360$	−39.1557	−	16.3350i	−0.108766	−	0.0453749i
$361$	356.546			0.987663
$362$	15.6531	−	15.6531i	0.0432407	−	0.0432407i
$363$	66.0488	+	66.0488i	0.181953	+	0.181953i
$364$			70.5409i			0.193794i
$365$	46.2575	−	110.882i	0.126733	−	0.303785i
$366$	69.0150			0.188566
$367$	41.5309	−	41.5309i	0.113163	−	0.113163i	−0.648258	−	0.761421i	$-0.724502\pi$
$367$	41.5309	−	41.5309i	0.113163	−	0.113163i	0.761421	+	0.648258i	$0.224502\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$			21.0480i			0.0570406i
$370$	131.470	−	54.0675i	0.355324	−	0.146128i
$371$	83.6836			0.225562
$372$	36.9351	−	36.9351i	0.0992878	−	0.0992878i
$373$	−188.716	−	188.716i	−0.505941	−	0.505941i	0.407337	−	0.913278i	$-0.366457\pi$
$373$	−188.716	−	188.716i	−0.505941	−	0.505941i	−0.913278	+	0.407337i	$0.866457\pi$
$374$			134.863i			0.360595i
$375$	−81.3332	−	200.649i	−0.216889	−	0.535063i
$376$	−118.858			−0.316111
$377$	117.629	−	117.629i	0.312012	−	0.312012i
$378$	−17.4579	−	17.4579i	−0.0461850	−	0.0461850i
$379$			143.699i			0.379152i	0.981866	+	0.189576i	$0.0607113\pi$
$379$			143.699i			0.379152i	−0.981866	+	0.189576i	$0.939289\pi$
$380$	−8.02675	−	19.5178i	−0.0211230	−	0.0513625i
$381$	−27.6261			−0.0725095
$382$	128.180	−	128.180i	0.335548	−	0.335548i
$383$	98.2112	+	98.2112i	0.256426	+	0.256426i	0.823599	−	0.567173i	$-0.191963\pi$
$383$	98.2112	+	98.2112i	0.256426	+	0.256426i	−0.567173	+	0.823599i	$0.691963\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	126.972	+	52.9702i	0.329798	+	0.137585i
$386$	−59.4006			−0.153888
$387$	9.37154	−	9.37154i	0.0242159	−	0.0242159i
$388$	−69.5800	−	69.5800i	−0.179330	−	0.179330i
$389$			244.042i			0.627357i	0.949529	+	0.313678i	$0.101561\pi$
$389$			244.042i			0.627357i	−0.949529	+	0.313678i	$0.898439\pi$
$390$	49.5026	−	118.660i	0.126930	−	0.304257i
$391$	−55.8434			−0.142822
$392$	75.4238	−	75.4238i	0.192408	−	0.192408i
$393$	154.033	+	154.033i	0.391941	+	0.391941i
$394$		−	245.484i		−	0.623057i
$395$	349.412	−	143.697i	0.884587	−	0.363789i
$396$	−49.1383			−0.124087
$397$	−168.912	+	168.912i	−0.425470	+	0.425470i	−0.887082	−	0.461612i	$-0.847271\pi$
$397$	−168.912	+	168.912i	−0.425470	+	0.425470i	0.461612	+	0.887082i	$0.347271\pi$
$398$	10.9495	+	10.9495i	0.0275114	+	0.0275114i
$399$		−	12.2810i		−	0.0307794i
$400$	71.0675	−	70.3521i	0.177669	−	0.175880i
$401$	−226.855			−0.565724			−0.282862	−	0.959161i	$-0.591284\pi$
$401$	−226.855			−0.565724			−0.282862	+	0.959161i	$0.591284\pi$
$402$	163.988	−	163.988i	0.407930	−	0.407930i
$403$	111.930	+	111.930i	0.277743	+	0.277743i
$404$			1.13532i			0.00281020i
$405$	17.1155	+	41.6180i	0.0422606	+	0.102761i
$406$	75.2928			0.185450
$407$	116.420	−	116.420i	0.286043	−	0.286043i
$408$	40.3365	+	40.3365i	0.0988641	+	0.0988641i
$409$		−	193.056i		−	0.472021i	−0.971751	−	0.236010i	$-0.924160\pi$
$409$		−	193.056i		−	0.472021i	0.971751	−	0.236010i	$-0.0758399\pi$
$410$	−45.7860	−	19.1010i	−0.111673	−	0.0465878i
$411$	−218.863			−0.532514
$412$	−24.6578	+	24.6578i	−0.0598490	+	0.0598490i
$413$	−62.7804	−	62.7804i	−0.152011	−	0.152011i
$414$		−	20.3470i		−	0.0491473i
$415$	−146.533	+	351.248i	−0.353093	+	0.846380i
$416$	59.3848			0.142752
$417$	−74.9634	+	74.9634i	−0.179768	+	0.179768i
$418$	−17.2834	−	17.2834i	−0.0413479	−	0.0413479i
$419$			418.810i			0.999546i	0.866156	+	0.499773i	$0.166583\pi$
$419$			418.810i			0.999546i	−0.866156	+	0.499773i	$0.833417\pi$
$420$	53.8196	−	22.1335i	0.128142	−	0.0526988i
$421$	781.367			1.85598			0.927989	−	0.372607i	$-0.121536\pi$
$421$	781.367			1.85598			0.927989	+	0.372607i	$0.121536\pi$
$422$	−371.360	+	371.360i	−0.879999	+	0.879999i
$423$	89.1432	+	89.1432i	0.210740	+	0.210740i
$424$		−	70.4490i		−	0.166153i
$425$	−1.47258	+	291.100i	−0.00346490	+	0.684942i
$426$	165.115			0.387593
$427$	−66.9366	+	66.9366i	−0.156760	+	0.156760i
$428$	−63.6802	−	63.6802i	−0.148785	−	0.148785i
$429$		−	148.912i		−	0.347114i
$430$	11.8814	+	28.8907i	0.0276312	+	0.0671878i
$431$	−127.925			−0.296809			−0.148404	−	0.988927i	$-0.547414\pi$
$431$	−127.925			−0.296809			−0.148404	+	0.988927i	$0.547414\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	219.940	+	219.940i	0.507945	+	0.507945i	0.913895	−	0.405950i	$-0.133059\pi$
$433$	219.940	+	219.940i	0.507945	+	0.507945i	−0.405950	+	0.913895i	$0.633059\pi$
$434$			71.6455i			0.165082i
$435$	−126.653	−	52.8372i	−0.291157	−	0.121465i
$436$	−356.456			−0.817559
$437$	7.15666	−	7.15666i	0.0163768	−	0.0163768i
$438$	−41.6189	−	41.6189i	−0.0950204	−	0.0950204i
$439$		−	159.575i		−	0.363496i	−0.983345	−	0.181748i	$-0.941825\pi$
$439$		−	159.575i		−	0.363496i	0.983345	−	0.181748i	$-0.0581754\pi$
$440$	44.5929	−	106.891i	0.101348	−	0.242935i
$441$	−113.136			−0.256543
$442$	−122.239	+	122.239i	−0.276558	+	0.276558i
$443$	0.230949	+	0.230949i	0.000521329	+	0.000521329i	0.707367	−	0.706846i	$-0.249883\pi$
$443$	0.230949	+	0.230949i	0.000521329	+	0.000521329i	−0.706846	+	0.707367i	$0.749883\pi$
$444$		−	69.6407i		−	0.156849i
$445$	−354.227	+	145.677i	−0.796015	+	0.327364i
$446$	−151.986			−0.340776
$447$	−301.151	+	301.151i	−0.673716	+	0.673716i
$448$	19.0058	+	19.0058i	0.0424236	+	0.0424236i
$449$		−	717.728i		−	1.59850i	−0.600997	−	0.799251i	$-0.705230\pi$
$449$		−	717.728i		−	1.59850i	0.600997	−	0.799251i	$-0.294770\pi$
$450$	−106.065	−	0.536547i	−0.235699	−	0.00119233i
$451$	−57.4590			−0.127404
$452$	−147.479	+	147.479i	−0.326281	+	0.326281i
$453$	10.0904	+	10.0904i	0.0222747	+	0.0222747i
$454$		−	345.170i		−	0.760287i
$455$	67.0748	+	163.098i	0.147417	+	0.358458i
$456$	−10.3387			−0.0226726
$457$	46.2379	−	46.2379i	0.101177	−	0.101177i	−0.654706	−	0.755883i	$-0.727208\pi$
$457$	46.2379	−	46.2379i	0.101177	−	0.101177i	0.755883	+	0.654706i	$0.227208\pi$
$458$	−73.4614	−	73.4614i	−0.160396	−	0.160396i
$459$		−	60.5048i		−	0.131819i
$460$	44.2611	+	18.4649i	0.0962199	+	0.0401410i
$461$	−88.2710			−0.191477			−0.0957386	−	0.995407i	$-0.530521\pi$
$461$	−88.2710			−0.191477			−0.0957386	+	0.995407i	$0.530521\pi$
$462$	47.6585	−	47.6585i	0.103157	−	0.103157i
$463$	167.771	+	167.771i	0.362357	+	0.362357i	0.864680	−	0.502323i	$-0.167521\pi$
$463$	167.771	+	167.771i	0.362357	+	0.362357i	−0.502323	+	0.864680i	$0.667521\pi$
$464$		−	63.3851i		−	0.136606i
$465$	50.2778	−	120.518i	0.108124	−	0.259179i
$466$	569.945			1.22306
$467$	−62.5685	+	62.5685i	−0.133980	+	0.133980i	−0.770916	−	0.636937i	$-0.780201\pi$
$467$	−62.5685	+	62.5685i	−0.133980	+	0.133980i	0.636937	+	0.770916i	$0.280201\pi$
$468$	−44.5386	−	44.5386i	−0.0951679	−	0.0951679i
$469$			318.099i			0.678249i
$470$	−274.812	+	113.017i	−0.584706	+	0.240462i
$471$	141.905			0.301285
$472$	−52.8516	+	52.8516i	−0.111974	+	0.111974i
$473$	25.5834	+	25.5834i	0.0540876	+	0.0540876i
$474$		−	185.086i		−	0.390478i
$475$	−37.1175	−	37.4949i	−0.0781420	−	0.0789366i
$476$	−78.2436			−0.164377
$477$	−52.8367	+	52.8367i	−0.110769	+	0.110769i
$478$	−117.112	−	117.112i	−0.245005	−	0.245005i
$479$			612.563i			1.27884i	0.768858	+	0.639419i	$0.220825\pi$
$479$			612.563i			1.27884i	−0.768858	+	0.639419i	$0.779175\pi$
$480$	−18.6330	−	45.3079i	−0.0388188	−	0.0943915i
$481$	211.044			0.438761
$482$	178.634	−	178.634i	0.370610	−	0.370610i
$483$	19.7342	+	19.7342i	0.0408576	+	0.0408576i
$484$			107.857i			0.222846i
$485$	−227.038	−	94.7157i	−0.468119	−	0.195290i
$486$	22.0454			0.0453609
$487$	−342.927	+	342.927i	−0.704162	+	0.704162i	−0.965301	−	0.261139i	$-0.915902\pi$
$487$	−342.927	+	342.927i	−0.704162	+	0.704162i	0.261139	+	0.965301i	$0.415902\pi$
$488$	56.3505	+	56.3505i	0.115472	+	0.115472i
$489$			134.486i			0.275022i
$490$	102.670	−	246.106i	0.209531	−	0.502257i
$491$	−850.889			−1.73297			−0.866486	−	0.499202i	$-0.833627\pi$
$491$	−850.889			−1.73297			−0.866486	+	0.499202i	$0.833627\pi$
$492$	−17.1856	+	17.1856i	−0.0349301	+	0.0349301i
$493$	130.473	+	130.473i	0.264651	+	0.264651i
$494$		−	31.3312i		−	0.0634234i
$495$	−113.613	+	46.7238i	−0.229522	+	0.0943915i
$496$	60.3147			0.121602
$497$	−160.142	+	160.142i	−0.322218	+	0.322218i
$498$	131.839	+	131.839i	0.264738	+	0.264738i
$499$		−	782.522i		−	1.56818i	−0.620647	−	0.784090i	$-0.713130\pi$
$499$		−	782.522i		−	1.56818i	0.620647	−	0.784090i	$-0.286870\pi$
$500$	97.4207	−	230.237i	0.194841	−	0.460475i
$501$	−98.0621			−0.195733
$502$	−350.780	+	350.780i	−0.698765	+	0.698765i
$503$	71.5670	+	71.5670i	0.142280	+	0.142280i	0.774659	−	0.632379i	$-0.217921\pi$
$503$	71.5670	+	71.5670i	0.142280	+	0.142280i	−0.632379	+	0.774659i	$0.717921\pi$
$504$		−	28.5087i		−	0.0565648i
$505$	1.07953	+	2.62499i	0.00213769	+	0.00519799i
$506$	55.5453			0.109773
$507$	−72.0091	+	72.0091i	−0.142030	+	0.142030i
$508$	−22.5566	−	22.5566i	−0.0444028	−	0.0444028i
$509$			451.402i			0.886840i	0.896314	+	0.443420i	$0.146235\pi$
$509$			451.402i			0.886840i	−0.896314	+	0.443420i	$0.853765\pi$
$510$	131.617	+	54.9080i	0.258073	+	0.107663i
$511$	80.7312			0.157987
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	7.75404	+	7.75404i	0.0151151	+	0.0151151i
$514$		−	216.209i		−	0.420639i
$515$	−33.5654	+	80.4578i	−0.0651755	+	0.156229i
$516$	15.3037			0.0296583
$517$	−243.352	+	243.352i	−0.470701	+	0.470701i
$518$	67.5435	+	67.5435i	0.130393	+	0.130393i
$519$		−	177.887i		−	0.342749i
$520$	137.304	−	56.4668i	0.264047	−	0.108590i
$521$	595.887			1.14374			0.571869	−	0.820345i	$-0.306219\pi$
$521$	595.887			1.14374			0.571869	+	0.820345i	$0.306219\pi$
$522$	−47.5388	+	47.5388i	−0.0910706	+	0.0910706i
$523$	172.420	+	172.420i	0.329674	+	0.329674i	0.852463	−	0.522788i	$-0.175108\pi$
$523$	172.420	+	172.420i	0.329674	+	0.329674i	−0.522788	+	0.852463i	$0.675108\pi$
$524$			251.535i			0.480028i
$525$	103.391	−	102.350i	0.196935	−	0.194953i
$526$	156.765			0.298033
$527$	−124.153	+	124.153i	−0.235584	+	0.235584i
$528$	−40.1212	−	40.1212i	−0.0759872	−	0.0759872i
$529$			23.0000i			0.0434783i
$530$	−66.9873	−	162.886i	−0.126391	−	0.307332i
$531$	79.2774			0.149298
$532$	10.0274	−	10.0274i	0.0188484	−	0.0188484i
$533$	−52.0804	−	52.0804i	−0.0977119	−	0.0977119i
$534$			187.637i			0.351380i
$535$	−207.787	−	86.6845i	−0.388387	−	0.162027i
$536$	267.791			0.499610
$537$	−360.922	+	360.922i	−0.672108	+	0.672108i
$538$	−326.796	−	326.796i	−0.607427	−	0.607427i
$539$		−	308.849i		−	0.573004i
$540$	−20.0062	+	47.9557i	−0.0370485	+	0.0888069i
$541$	576.448			1.06552			0.532762	−	0.846265i	$-0.321154\pi$
$541$	576.448			1.06552			0.532762	+	0.846265i	$0.321154\pi$
$542$	−312.784	+	312.784i	−0.577093	+	0.577093i
$543$	−19.1711	−	19.1711i	−0.0353059	−	0.0353059i
$544$			65.8693i			0.121083i
$545$	−824.166	+	338.941i	−1.51223	+	0.621910i
$546$	86.3946			0.158232
$547$	−196.463	+	196.463i	−0.359164	+	0.359164i	−0.863505	−	0.504341i	$-0.831736\pi$
$547$	−196.463	+	196.463i	−0.359164	+	0.359164i	0.504341	+	0.863505i	$0.331736\pi$
$548$	−178.701	−	178.701i	−0.326097	−	0.326097i
$549$		−	84.5258i		−	0.153963i
$550$	1.46472	−	289.546i	0.00266313	−	0.526448i
$551$	−33.4417			−0.0606928
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	179.512	+	179.512i	0.324616	+	0.324616i
$554$			129.845i			0.234377i
$555$	−66.2188	−	161.017i	−0.119313	−	0.290121i
$556$	−122.415			−0.220170
$557$	−175.913	+	175.913i	−0.315823	+	0.315823i	−0.847160	−	0.531337i	$-0.821690\pi$
$557$	−175.913	+	175.913i	−0.315823	+	0.315823i	0.531337	+	0.847160i	$0.321690\pi$
$558$	−45.2360	−	45.2360i	−0.0810681	−	0.0810681i
$559$			46.3773i			0.0829647i
$560$	62.0154	+	25.8716i	0.110742	+	0.0461993i
$561$	165.172			0.294425
$562$	−222.033	+	222.033i	−0.395077	+	0.395077i
$563$	385.523	+	385.523i	0.684765	+	0.684765i	0.961070	−	0.276305i	$-0.0891100\pi$
$563$	385.523	+	385.523i	0.684765	+	0.684765i	−0.276305	+	0.961070i	$0.589110\pi$
$564$			145.570i			0.258103i
$565$	−200.755	+	481.220i	−0.355319	+	0.851717i
$566$	−528.403			−0.933574
$567$	−21.3815	+	21.3815i	−0.0377099	+	0.0377099i
$568$	134.815	+	134.815i	0.237351	+	0.237351i
$569$			133.135i			0.233981i	0.993133	+	0.116990i	$0.0373247\pi$
$569$			133.135i			0.233981i	−0.993133	+	0.116990i	$0.962675\pi$
$570$	−23.9043	+	9.83072i	−0.0419373	+	0.0172469i
$571$	−296.967			−0.520082			−0.260041	−	0.965598i	$-0.583736\pi$
$571$	−296.967			−0.520082			−0.260041	+	0.965598i	$0.583736\pi$
$572$	121.586	−	121.586i	0.212563	−	0.212563i
$573$	−156.987	−	156.987i	−0.273974	−	0.273974i
$574$		−	33.3361i		−	0.0580769i
$575$	119.894	+	0.606507i	0.208512	+	0.00105479i
$576$	−24.0000			−0.0416667
$577$	−337.682	+	337.682i	−0.585237	+	0.585237i	−0.936338	−	0.351101i	$-0.885807\pi$
$577$	−337.682	+	337.682i	−0.585237	+	0.585237i	0.351101	+	0.936338i	$0.385807\pi$
$578$	153.414	+	153.414i	0.265422	+	0.265422i
$579$			72.7506i			0.125649i
$580$	−60.2706	−	146.553i	−0.103915	−	0.252678i
$581$	−255.738			−0.440169
$582$	−85.2178	+	85.2178i	−0.146422	+	0.146422i
$583$	−144.239	−	144.239i	−0.247408	−	0.247408i
$584$		−	67.9635i		−	0.116376i
$585$	−145.328	−	60.6281i	−0.248424	−	0.103638i
$586$	300.586			0.512945
$587$	−389.132	+	389.132i	−0.662916	+	0.662916i	−0.956066	−	0.293150i	$-0.905296\pi$
$587$	−389.132	+	389.132i	−0.662916	+	0.662916i	0.293150	+	0.956066i	$0.405296\pi$
$588$	−92.3749	−	92.3749i	−0.157100	−	0.157100i
$589$		−	31.8218i		−	0.0540268i
$590$	−71.9441	+	172.453i	−0.121939	+	0.292294i
$591$	−300.656			−0.508724
$592$	56.8614	−	56.8614i	0.0960497	−	0.0960497i
$593$	−511.328	−	511.328i	−0.862273	−	0.862273i	0.129329	−	0.991602i	$-0.458718\pi$
$593$	−511.328	−	511.328i	−0.862273	−	0.862273i	−0.991602	+	0.129329i	$0.958718\pi$
$594$			60.1818i			0.101316i
$595$	−180.908	+	74.3990i	−0.304047	+	0.125040i
$596$	−491.778			−0.825130
$597$	13.4104	−	13.4104i	0.0224630	−	0.0224630i
$598$	50.3459	+	50.3459i	0.0841905	+	0.0841905i
$599$		−	163.806i		−	0.273466i	−0.990608	−	0.136733i	$-0.956340\pi$
$599$		−	163.806i		−	0.273466i	0.990608	−	0.136733i	$-0.0436602\pi$
$600$	−86.1633	−	87.0395i	−0.143606	−	0.145066i
$601$	686.382			1.14207			0.571033	−	0.820927i	$-0.306543\pi$
$601$	686.382			1.14207			0.571033	+	0.820927i	$0.306543\pi$
$602$	−14.8428	+	14.8428i	−0.0246558	+	0.0246558i
$603$	−200.843	−	200.843i	−0.333074	−	0.333074i
$604$			16.4776i			0.0272808i
$605$	102.558	+	249.378i	0.169517	+	0.412195i
$606$	1.39048			0.00229452
$607$	−153.299	+	153.299i	−0.252553	+	0.252553i	−0.822016	−	0.569464i	$-0.807151\pi$
$607$	−153.299	+	153.299i	−0.252553	+	0.252553i	0.569464	+	0.822016i	$0.307151\pi$
$608$	−8.44153	−	8.44153i	−0.0138841	−	0.0138841i
$609$		−	92.2144i		−	0.151419i
$610$	183.870	+	76.7070i	0.301427	+	0.125749i
$611$	−441.146			−0.722006
$612$	49.4020	−	49.4020i	0.0807222	−	0.0807222i
$613$	713.442	+	713.442i	1.16385	+	1.16385i	0.983625	+	0.180228i	$0.0576834\pi$
$613$	713.442	+	713.442i	1.16385	+	1.16385i	0.180228	+	0.983625i	$0.442317\pi$
$614$			743.401i			1.21075i
$615$	−23.3939	+	56.0762i	−0.0380388	+	0.0911808i
$616$	77.8260			0.126341
$617$	232.838	−	232.838i	0.377372	−	0.377372i	−0.492781	−	0.870153i	$-0.664020\pi$
$617$	232.838	−	232.838i	0.377372	−	0.377372i	0.870153	+	0.492781i	$0.164020\pi$
$618$	30.1995	+	30.1995i	0.0488665	+	0.0488665i
$619$		−	126.186i		−	0.203854i	−0.994792	−	0.101927i	$-0.967499\pi$
$619$		−	126.186i		−	0.203854i	0.994792	−	0.101927i	$-0.0325009\pi$
$620$	139.454	−	57.3510i	0.224926	−	0.0925017i
$621$	−24.9199			−0.0401286
$622$	24.8526	−	24.8526i	0.0399559	−	0.0399559i
$623$	−181.986	−	181.986i	−0.292113	−	0.292113i
$624$		−	72.7312i		−	0.116556i
$625$	6.32319	−	624.968i	0.0101171	−	0.999949i
$626$	318.752			0.509189
$627$	−21.1678	+	21.1678i	−0.0337604	+	0.0337604i
$628$	115.865	+	115.865i	0.184499	+	0.184499i
$629$			234.089i			0.372160i
$630$	−27.1079	−	65.9152i	−0.0430284	−	0.104627i
$631$	−632.532			−1.00243			−0.501214	−	0.865323i	$-0.667113\pi$
$631$	−632.532			−1.00243			−0.501214	+	0.865323i	$0.667113\pi$
$632$	151.122	−	151.122i	0.239118	−	0.239118i
$633$	454.821	+	454.821i	0.718516	+	0.718516i
$634$		−	323.455i		−	0.510182i
$635$	−73.6017	−	30.7052i	−0.115908	−	0.0483546i
$636$	−86.2820			−0.135664
$637$	279.939	−	279.939i	0.439465	−	0.439465i
$638$	−129.776	−	129.776i	−0.203411	−	0.203411i
$639$		−	202.223i		−	0.316468i
$640$	21.7800	−	52.2076i	0.0340312	−	0.0815744i
$641$	216.571			0.337864			0.168932	−	0.985628i	$-0.445968\pi$
$641$	216.571			0.337864			0.168932	+	0.985628i	$0.445968\pi$
$642$	−77.9920	+	77.9920i	−0.121483	+	0.121483i
$643$	763.835	+	763.835i	1.18792	+	1.18792i	0.977641	+	0.210283i	$0.0674385\pi$
$643$	763.835	+	763.835i	1.18792	+	1.18792i	0.210283	+	0.977641i	$0.432562\pi$
$644$			32.2259i			0.0500402i
$645$	35.3838	−	14.5517i	0.0548586	−	0.0225608i
$646$	34.7524			0.0537962
$647$	868.923	−	868.923i	1.34300	−	1.34300i	0.449949	−	0.893054i	$-0.351442\pi$
$647$	868.923	−	868.923i	1.34300	−	1.34300i	0.893054	−	0.449949i	$-0.148558\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			216.420i			0.333466i
$650$	263.770	−	261.115i	0.405801	−	0.401716i
$651$	87.7475			0.134789
$652$	−109.807	+	109.807i	−0.168416	+	0.168416i
$653$	−441.359	−	441.359i	−0.675894	−	0.675894i	0.283174	−	0.959069i	$-0.408613\pi$
$653$	−441.359	−	441.359i	−0.675894	−	0.675894i	−0.959069	+	0.283174i	$0.908613\pi$
$654$			436.568i			0.667534i
$655$	239.175	+	581.577i	0.365153	+	0.887903i
$656$	−28.0640			−0.0427805
$657$	−50.9726	+	50.9726i	−0.0775839	+	0.0775839i
$658$	−141.186	−	141.186i	−0.214569	−	0.214569i
$659$		−	333.161i		−	0.505555i	−0.967524	−	0.252778i	$-0.918656\pi$
$659$		−	333.161i		−	0.505555i	0.967524	−	0.252778i	$-0.0813441\pi$
$660$	−130.915	−	54.6149i	−0.198355	−	0.0827499i
$661$	1104.51			1.67096			0.835481	−	0.549520i	$-0.185189\pi$
$661$	1104.51			1.67096			0.835481	+	0.549520i	$0.185189\pi$
$662$	−404.107	+	404.107i	−0.610434	+	0.610434i
$663$	149.711	+	149.711i	0.225809	+	0.225809i
$664$			215.293i			0.324236i
$665$	13.6497	−	32.7191i	0.0205259	−	0.0492016i
$666$	−85.2921			−0.128066
$667$	53.7374	−	53.7374i	0.0805658	−	0.0805658i
$668$	−80.0673	−	80.0673i	−0.119861	−	0.119861i
$669$			186.144i			0.278242i
$670$	619.163	−	254.633i	0.924124	−	0.380049i
$671$	230.747			0.343886
$672$	23.2772	−	23.2772i	0.0346387	−	0.0346387i
$673$	166.235	+	166.235i	0.247005	+	0.247005i	0.819740	−	0.572735i	$-0.194118\pi$
$673$	166.235	+	166.235i	0.247005	+	0.247005i	−0.572735	+	0.819740i	$0.694118\pi$
$674$			99.2719i			0.147288i
$675$	−0.657133	+	129.902i	−0.000973531	+	0.192448i
$676$	−117.590			−0.173950
$677$	56.8084	−	56.8084i	0.0839119	−	0.0839119i	−0.663905	−	0.747817i	$-0.731102\pi$
$677$	56.8084	−	56.8084i	0.0839119	−	0.0839119i	0.747817	+	0.663905i	$0.231102\pi$
$678$	180.624	+	180.624i	0.266407	+	0.266407i
$679$		−	165.303i		−	0.243451i
$680$	62.6327	+	152.297i	0.0921069	+	0.223966i
$681$	−422.745			−0.620772
$682$	123.490	−	123.490i	0.181070	−	0.181070i
$683$	−695.233	−	695.233i	−1.01791	−	1.01791i	−0.999837	−	0.0180741i	$-0.994247\pi$
$683$	−695.233	−	695.233i	−1.01791	−	1.01791i	−0.0180741	−	0.999837i	$-0.505753\pi$
$684$			12.6623i			0.0185121i
$685$	−583.097	−	243.256i	−0.851237	−	0.355119i
$686$	412.007			0.600593
$687$	−89.9715	+	89.9715i	−0.130963	+	0.130963i
$688$	12.4954	+	12.4954i	0.0181619	+	0.0181619i
$689$		−	261.475i		−	0.379499i
$690$	22.6147	−	54.2086i	0.0327750	−	0.0785632i
$691$	667.858			0.966509			0.483255	−	0.875480i	$-0.339455\pi$
$691$	667.858			0.966509			0.483255	+	0.875480i	$0.339455\pi$
$692$	145.244	−	145.244i	0.209890	−	0.209890i
$693$	−58.3695	−	58.3695i	−0.0842272	−	0.0842272i
$694$			75.6516i			0.109008i
$695$	−283.037	+	116.400i	−0.407247	+	0.167482i
$696$	−77.6306			−0.111538
$697$	57.7673	−	57.7673i	0.0828800	−	0.0828800i
$698$	−608.019	−	608.019i	−0.871087	−	0.871087i
$699$		−	698.037i		−	0.998623i
$700$	167.987	+	0.849792i	0.239981	+	0.00121399i
$701$	−936.912			−1.33654			−0.668268	−	0.743920i	$-0.732964\pi$
$701$	−936.912			−1.33654			−0.668268	+	0.743920i	$0.732964\pi$
$702$	−54.5484	+	54.5484i	−0.0777043	+	0.0777043i
$703$	−29.9998	−	29.9998i	−0.0426740	−	0.0426740i
$704$		−	65.5177i		−	0.0930649i
$705$	138.417	+	336.574i	0.196337	+	0.477411i
$706$	204.130			0.289135
$707$	−1.34860	+	1.34860i	−0.00190750	+	0.00190750i
$708$	64.7297	+	64.7297i	0.0914261	+	0.0914261i
$709$			680.289i			0.959505i	0.877404	+	0.479753i	$0.159274\pi$
$709$			680.289i			0.959505i	−0.877404	+	0.479753i	$0.840726\pi$
$710$	439.900	+	183.517i	0.619577	+	0.258475i
$711$	−226.684			−0.318824
$712$	−153.205	+	153.205i	−0.215175	+	0.215175i
$713$	51.1343	+	51.1343i	0.0717171	+	0.0717171i
$714$			95.8284i			0.134214i
$715$	165.509	−	396.732i	0.231481	−	0.554870i
$716$	−589.383			−0.823161
$717$	−143.433	+	143.433i	−0.200045	+	0.200045i
$718$	392.739	+	392.739i	0.546990	+	0.546990i
$719$		−	872.799i		−	1.21391i	−0.794737	−	0.606953i	$-0.792391\pi$
$719$		−	872.799i		−	1.21391i	0.794737	−	0.606953i	$-0.207609\pi$
$720$	−55.4907	+	22.8207i	−0.0770704	+	0.0316955i
$721$	−58.5801			−0.0812484
$722$	356.546	−	356.546i	0.493831	−	0.493831i
$723$	−218.781	−	218.781i	−0.302601	−	0.302601i
$724$		−	31.3062i		−	0.0432407i
$725$	−278.705	−	281.539i	−0.384420	−	0.388329i
$726$	132.098			0.181953
$727$	736.548	−	736.548i	1.01313	−	1.01313i	0.0132213	−	0.999913i	$-0.495791\pi$
$727$	736.548	−	736.548i	1.01313	−	1.01313i	0.999913	−	0.0132213i	$-0.00420860\pi$
$728$	70.5409	+	70.5409i	0.0968969	+	0.0968969i
$729$		−	27.0000i		−	0.0370370i
$730$	−64.6240	−	157.139i	−0.0885260	−	0.215259i
$731$	−51.4414			−0.0703713
$732$	69.0150	−	69.0150i	0.0942828	−	0.0942828i
$733$	20.9889	+	20.9889i	0.0286342	+	0.0286342i	0.721279	−	0.692645i	$-0.243555\pi$
$733$	20.9889	+	20.9889i	0.0286342	+	0.0286342i	−0.692645	+	0.721279i	$0.743555\pi$
$734$		−	83.0619i		−	0.113163i
$735$	−301.417	−	125.745i	−0.410091	−	0.171082i
$736$	27.1293			0.0368605
$737$	548.283	−	548.283i	0.743939	−	0.743939i
$738$	21.0480	+	21.0480i	0.0285203	+	0.0285203i
$739$		−	799.903i		−	1.08241i	−0.840890	−	0.541206i	$-0.817968\pi$
$739$		−	799.903i		−	1.08241i	0.840890	−	0.541206i	$-0.182032\pi$
$740$	77.4025	−	185.537i	0.104598	−	0.250726i
$741$	−38.3727			−0.0517850
$742$	83.6836	−	83.6836i	0.112781	−	0.112781i
$743$	−293.529	−	293.529i	−0.395059	−	0.395059i	0.481427	−	0.876486i	$-0.340119\pi$
$743$	−293.529	−	293.529i	−0.395059	−	0.395059i	−0.876486	+	0.481427i	$0.840119\pi$
$744$		−	73.8701i		−	0.0992878i
$745$	−1137.04	+	467.613i	−1.52623	+	0.627669i
$746$	−377.432			−0.505941
$747$	161.470	−	161.470i	0.216158	−	0.216158i
$748$	134.863	+	134.863i	0.180298	+	0.180298i
$749$		−	151.286i		−	0.201985i
$750$	−281.982	−	119.315i	−0.375976	−	0.159087i
$751$	1348.43			1.79551			0.897757	−	0.440491i	$-0.145196\pi$
$751$	1348.43			1.79551			0.897757	+	0.440491i	$0.145196\pi$
$752$	−118.858	+	118.858i	−0.158055	+	0.158055i
$753$	429.616	+	429.616i	0.570539	+	0.570539i
$754$		−	235.257i		−	0.312012i
$755$	15.6680	+	38.0981i	0.0207523	+	0.0504610i
$756$	−34.9159			−0.0461850
$757$	165.657	−	165.657i	0.218834	−	0.218834i	−0.589173	−	0.808007i	$-0.700546\pi$
$757$	165.657	−	165.657i	0.218834	−	0.218834i	0.808007	+	0.589173i	$0.200546\pi$
$758$	143.699	+	143.699i	0.189576	+	0.189576i
$759$		−	68.0289i		−	0.0896296i
$760$	−27.5445	−	11.4910i	−0.0362428	−	0.0151198i
$761$	−650.491			−0.854785			−0.427392	−	0.904066i	$-0.640568\pi$
$761$	−650.491			−0.854785			−0.427392	+	0.904066i	$0.640568\pi$
$762$	−27.6261	+	27.6261i	−0.0362547	+	0.0362547i
$763$	−423.420	−	423.420i	−0.554941	−	0.554941i
$764$		−	256.359i		−	0.335548i
$765$	67.2483	−	161.197i	0.0879063	−	0.210716i
$766$	196.422			0.256426
$767$	−196.161	+	196.161i	−0.255751	+	0.255751i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$		−	774.000i		−	1.00650i	−0.864140	−	0.503251i	$-0.832137\pi$
$769$		−	774.000i		−	1.00650i	0.864140	−	0.503251i	$-0.167863\pi$
$770$	179.942	−	74.0019i	0.233691	−	0.0961063i
$771$	−264.800			−0.343450
$772$	−59.4006	+	59.4006i	−0.0769438	+	0.0769438i
$773$	−534.474	−	534.474i	−0.691429	−	0.691429i	0.271118	−	0.962546i	$-0.412607\pi$
$773$	−534.474	−	534.474i	−0.691429	−	0.691429i	−0.962546	+	0.271118i	$0.912607\pi$
$774$		−	18.7431i		−	0.0242159i
$775$	267.901	−	265.204i	0.345678	−	0.342199i
$776$	−139.160			−0.179330
$777$	82.7236	−	82.7236i	0.106465	−	0.106465i
$778$	244.042	+	244.042i	0.313678	+	0.313678i
$779$			14.8064i			0.0190070i
$780$	−69.1575	−	168.163i	−0.0886634	−	0.215593i
$781$	552.050			0.706850
$782$	−55.8434	+	55.8434i	−0.0714110	+	0.0714110i
$783$	58.2230	+	58.2230i	0.0743588	+	0.0743588i
$784$		−	150.848i		−	0.192408i
$785$	378.065	+	157.721i	0.481611	+	0.200919i
$786$	308.066			0.391941
$787$	491.378	−	491.378i	0.624369	−	0.624369i	−0.322277	−	0.946646i	$-0.604448\pi$
$787$	491.378	−	491.378i	0.624369	−	0.624369i	0.946646	+	0.322277i	$0.104448\pi$
$788$	−245.484	−	245.484i	−0.311528	−	0.311528i
$789$		−	191.997i		−	0.243343i
$790$	205.715	−	493.109i	0.260399	−	0.624188i
$791$	−350.369			−0.442945
$792$	−49.1383	+	49.1383i	−0.0620433	+	0.0620433i
$793$	209.148	+	209.148i	0.263742	+	0.263742i
$794$			337.823i			0.425470i
$795$	−199.494	+	82.0424i	−0.250935	+	0.103198i
$796$	21.8991			0.0275114
$797$	697.732	−	697.732i	0.875449	−	0.875449i	−0.117611	−	0.993060i	$-0.537524\pi$
$797$	697.732	−	697.732i	0.875449	−	0.875449i	0.993060	+	0.117611i	$0.0375237\pi$
$798$	−12.2810	−	12.2810i	−0.0153897	−	0.0153897i
$799$		−	489.316i		−	0.612411i
$800$	0.715396	−	141.420i	0.000894245	−	0.176774i
$801$	229.807			0.286900
$802$	−226.855	+	226.855i	−0.282862	+	0.282862i
$803$	−139.150	−	139.150i	−0.173288	−	0.173288i
$804$		−	327.976i		−	0.407930i
$805$	30.6424	+	74.5098i	0.0380651	+	0.0925588i
$806$	223.861			0.277743
$807$	−400.241	+	400.241i	−0.495962	+	0.495962i
$808$	1.13532	+	1.13532i	0.00140510	+	0.00140510i
$809$		−	666.114i		−	0.823380i	−0.911324	−	0.411690i	$-0.864939\pi$
$809$		−	666.114i		−	0.823380i	0.911324	−	0.411690i	$-0.135061\pi$
$810$	58.7335	+	24.5025i	0.0725106	+	0.0302499i
$811$	182.199			0.224660			0.112330	−	0.993671i	$-0.464169\pi$
$811$	182.199			0.224660			0.112330	+	0.993671i	$0.464169\pi$
$812$	75.2928	−	75.2928i	0.0927251	−	0.0927251i
$813$	383.081	+	383.081i	0.471194	+	0.471194i
$814$		−	232.839i		−	0.286043i
$815$	−149.475	+	358.298i	−0.183405	+	0.439630i
$816$	80.6731			0.0988641
$817$	6.59252	−	6.59252i	0.00806918	−	0.00806918i
$818$	−193.056	−	193.056i	−0.236010	−	0.236010i
$819$		−	105.811i		−	0.129196i
$820$	−64.8871	+	26.6850i	−0.0791306	+	0.0325427i
$821$	−840.318			−1.02353			−0.511765	−	0.859126i	$-0.671008\pi$
$821$	−840.318			−1.02353			−0.511765	+	0.859126i	$0.671008\pi$
$822$	−218.863	+	218.863i	−0.266257	+	0.266257i
$823$	−282.800	−	282.800i	−0.343621	−	0.343621i	0.514106	−	0.857727i	$-0.328124\pi$
$823$	−282.800	−	282.800i	−0.343621	−	0.343621i	−0.857727	+	0.514106i	$0.828124\pi$
$824$			49.3156i			0.0598490i
$825$	−354.620	−	1.79391i	−0.429843	−	0.00217444i
$826$	−125.561			−0.152011
$827$	1109.73	−	1109.73i	1.34188	−	1.34188i	0.447683	−	0.894192i	$-0.352249\pi$
$827$	1109.73	−	1109.73i	1.34188	−	1.34188i	0.894192	−	0.447683i	$-0.147751\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$			530.827i			0.640322i	0.947363	+	0.320161i	$0.103737\pi$
$829$			530.827i			0.640322i	−0.947363	+	0.320161i	$0.896263\pi$
$830$	204.714	+	497.781i	0.246644	+	0.599736i
$831$	159.027			0.191368
$832$	59.3848	−	59.3848i	0.0713760	−	0.0713760i
$833$	310.507	+	310.507i	0.372757	+	0.372757i
$834$			149.927i			0.179768i
$835$	−261.258	−	108.991i	−0.312883	−	0.130529i
$836$	−34.5669			−0.0413479
$837$	−55.4026	+	55.4026i	−0.0661919	+	0.0661919i
$838$	418.810	+	418.810i	0.499773	+	0.499773i
$839$			798.526i			0.951759i	0.879510	+	0.475880i	$0.157870\pi$
$839$			798.526i			0.951759i	−0.879510	+	0.475880i	$0.842130\pi$
$840$	31.6861	−	75.9530i	0.0377215	−	0.0904203i
$841$	589.895			0.701421
$842$	781.367	−	781.367i	0.927989	−	0.927989i
$843$	271.934	+	271.934i	0.322579	+	0.322579i
$844$			742.719i			0.879999i
$845$	−271.882	+	111.812i	−0.321754	+	0.132322i
$846$	178.286			0.210740
$847$	−128.119	+	128.119i	−0.151263	+	0.151263i
$848$	−70.4490	−	70.4490i	−0.0830766	−	0.0830766i
$849$			647.159i			0.762260i
$850$	289.628	+	292.573i	0.340738	+	0.344203i
$851$	96.4132			0.113294
$852$	165.115	−	165.115i	0.193796	−	0.193796i
$853$	366.721	+	366.721i	0.429919	+	0.429919i	0.888601	−	0.458681i	$-0.151678\pi$
$853$	366.721	+	366.721i	0.429919	+	0.429919i	−0.458681	+	0.888601i	$0.651678\pi$
$854$			133.873i			0.156760i
$855$	12.0401	+	29.2766i	0.0140820	+	0.0342417i
$856$	−127.360			−0.148785
$857$	731.186	−	731.186i	0.853192	−	0.853192i	−0.137333	−	0.990525i	$-0.543853\pi$
$857$	731.186	−	731.186i	0.853192	−	0.853192i	0.990525	+	0.137333i	$0.0438530\pi$
$858$	−148.912	−	148.912i	−0.173557	−	0.173557i
$859$		−	802.675i		−	0.934429i	−0.884144	−	0.467215i	$-0.845258\pi$
$859$		−	802.675i		−	0.934429i	0.884144	−	0.467215i	$-0.154742\pi$
$860$	40.7722	+	17.0093i	0.0474095	+	0.0197783i
$861$	−40.8283			−0.0474196
$862$	−127.925	+	127.925i	−0.148404	+	0.148404i
$863$	715.758	+	715.758i	0.829383	+	0.829383i	0.987431	−	0.158048i	$-0.0505202\pi$
$863$	715.758	+	715.758i	0.829383	+	0.829383i	−0.158048	+	0.987431i	$0.550520\pi$
$864$			29.3939i			0.0340207i
$865$	197.713	−	473.928i	0.228570	−	0.547893i
$866$	439.880			0.507945
$867$	187.893	−	187.893i	0.216716	−	0.216716i
$868$	71.6455	+	71.6455i	0.0825409	+	0.0825409i
$869$		−	618.824i		−	0.712111i
$870$	−179.491	+	73.8161i	−0.206311	+	0.0848461i
$871$	993.920			1.14113
$872$	−356.456	+	356.456i	−0.408780	+	0.408780i
$873$	104.370	+	104.370i	0.119553	+	0.119553i
$874$		−	14.3133i		−	0.0163768i
$875$	389.212	−	157.768i	0.444814	−	0.180306i
$876$	−83.2379			−0.0950204
$877$	856.632	−	856.632i	0.976775	−	0.976775i	−0.0229612	−	0.999736i	$-0.507309\pi$
$877$	856.632	−	856.632i	0.976775	−	0.976775i	0.999736	+	0.0229612i	$0.00730941\pi$
$878$	−159.575	−	159.575i	−0.181748	−	0.181748i
$879$		−	368.141i		−	0.418818i
$880$	−62.2984	−	151.484i	−0.0707936	−	0.172141i
$881$	1144.37			1.29895			0.649473	−	0.760385i	$-0.274990\pi$
$881$	1144.37			1.29895			0.649473	+	0.760385i	$0.274990\pi$
$882$	−113.136	+	113.136i	−0.128272	+	0.128272i
$883$	−339.658	−	339.658i	−0.384663	−	0.384663i	0.488116	−	0.872779i	$-0.337684\pi$
$883$	−339.658	−	339.658i	−0.384663	−	0.384663i	−0.872779	+	0.488116i	$0.837684\pi$
$884$			244.477i			0.276558i
$885$	211.211	+	88.1132i	0.238657	+	0.0995629i
$886$	0.461898			0.000521329
$887$	−700.491	+	700.491i	−0.789731	+	0.789731i	−0.981450	−	0.191719i	$-0.938594\pi$
$887$	−700.491	+	700.491i	−0.789731	+	0.789731i	0.191719	+	0.981450i	$0.438594\pi$
$888$	−69.6407	−	69.6407i	−0.0784243	−	0.0784243i
$889$		−	53.5883i		−	0.0602793i
$890$	−208.550	+	499.903i	−0.234326	+	0.561689i
$891$	73.7074			0.0827244
$892$	−151.986	+	151.986i	−0.170388	+	0.170388i
$893$	62.7087	+	62.7087i	0.0702226	+	0.0702226i
$894$			602.302i			0.673716i
$895$	−1362.72	+	560.423i	−1.52259	+	0.626171i
$896$	38.0116			0.0424236
$897$	61.6609	−	61.6609i	0.0687412	−	0.0687412i
$898$	−717.728	−	717.728i	−0.799251	−	0.799251i
$899$		−	238.941i		−	0.265785i
$900$	−106.601	+	105.528i	−0.118446	+	0.117253i
$901$	290.026			0.321894
$902$	−57.4590	+	57.4590i	−0.0637018	+	0.0637018i
$903$	18.1786	+	18.1786i	0.0201314	+	0.0201314i
$904$			294.958i			0.326281i
$905$	−29.7680	−	72.3835i	−0.0328928	−	0.0799818i
$906$	20.1809			0.0222747
$907$	902.515	−	902.515i	0.995056	−	0.995056i	−0.00493230	−	0.999988i	$-0.501570\pi$
$907$	902.515	−	902.515i	0.995056	−	0.995056i	0.999988	+	0.00493230i	$0.00157001\pi$
$908$	−345.170	−	345.170i	−0.380143	−	0.380143i
$909$		−	1.70298i		−	0.00187347i
$910$	230.173	+	96.0237i	0.252938	+	0.105521i
$911$	−172.360			−0.189199			−0.0945995	−	0.995515i	$-0.530157\pi$
$911$	−172.360			−0.189199			−0.0945995	+	0.995515i	$0.530157\pi$
$912$	−10.3387	+	10.3387i	−0.0113363	+	0.0113363i
$913$	440.797	+	440.797i	0.482800	+	0.482800i
$914$		−	92.4758i		−	0.101177i
$915$	93.9465	−	225.194i	0.102674	−	0.246114i
$916$	−146.923			−0.160396
$917$	−298.789	+	298.789i	−0.325833	+	0.325833i
$918$	−60.5048	−	60.5048i	−0.0659094	−	0.0659094i
$919$			578.120i			0.629075i	0.949245	+	0.314537i	$0.101849\pi$
$919$			578.120i			0.629075i	−0.949245	+	0.314537i	$0.898151\pi$
$920$	62.7260	−	25.7963i	0.0681804	−	0.0280394i
$921$	910.477			0.988574
$922$	−88.2710	+	88.2710i	−0.0957386	+	0.0957386i
$923$	500.374	+	500.374i	0.542117	+	0.542117i
$924$		−	95.3169i		−	0.103157i
$925$	2.54240	−	502.582i	0.00274854	−	0.543332i
$926$	335.543			0.362357
$927$	36.9867	−	36.9867i	0.0398994	−	0.0398994i
$928$	−63.3851	−	63.3851i	−0.0683029	−	0.0683029i
$929$			815.607i			0.877941i	0.898501	+	0.438971i	$0.144657\pi$
$929$			815.607i			0.877941i	−0.898501	+	0.438971i	$0.855343\pi$
$930$	−70.2404	−	170.796i	−0.0755273	−	0.183652i
$931$	−79.5865			−0.0854850
$932$	569.945	−	569.945i	0.611529	−	0.611529i
$933$	−30.4381	−	30.4381i	−0.0326238	−	0.0326238i
$934$			125.137i			0.133980i
$935$	440.053	+	183.581i	0.470645	+	0.196344i
$936$	−89.0772			−0.0951679
$937$	1100.71	−	1100.71i	1.17472	−	1.17472i	0.193646	−	0.981072i	$-0.437969\pi$
$937$	1100.71	−	1100.71i	1.17472	−	1.17472i	0.981072	−	0.193646i	$-0.0620312\pi$
$938$	318.099	+	318.099i	0.339125	+	0.339125i
$939$		−	390.390i		−	0.415751i
$940$	−161.795	+	387.829i	−0.172122	+	0.412584i
$941$	333.594			0.354510			0.177255	−	0.984165i	$-0.443278\pi$
$941$	333.594			0.354510			0.177255	+	0.984165i	$0.443278\pi$
$942$	141.905	−	141.905i	0.150642	−	0.150642i
$943$	−23.7924	−	23.7924i	−0.0252305	−	0.0252305i
$944$			105.703i			0.111974i
$945$	−80.7293	+	33.2002i	−0.0854279	+	0.0351325i
$946$	51.1668			0.0540876
$947$	−280.909	+	280.909i	−0.296631	+	0.296631i	−0.839693	−	0.543062i	$-0.817265\pi$
$947$	−280.909	+	280.909i	−0.296631	+	0.296631i	0.543062	+	0.839693i	$0.317265\pi$
$948$	−185.086	−	185.086i	−0.195239	−	0.195239i
$949$		−	252.250i		−	0.265806i
$950$	−74.6124	−	0.377440i	−0.0785393	−	0.000397305i
$951$	−396.150			−0.416562
$952$	−78.2436	+	78.2436i	−0.0821887	+	0.0821887i
$953$	−397.498	−	397.498i	−0.417102	−	0.417102i	0.467102	−	0.884204i	$-0.345298\pi$
$953$	−397.498	−	397.498i	−0.417102	−	0.417102i	−0.884204	+	0.467102i	$0.845298\pi$
$954$			105.673i			0.110769i
$955$	−243.762	−	592.731i	−0.255249	−	0.620660i
$956$	−234.224			−0.245005
$957$	−158.943	+	158.943i	−0.166085	+	0.166085i
$958$	612.563	+	612.563i	0.639419	+	0.639419i
$959$		−	424.544i		−	0.442695i
$960$	−63.9410	−	26.6749i	−0.0666052	−	0.0277864i
$961$	−733.634			−0.763406
$962$	211.044	−	211.044i	0.219380	−	0.219380i
$963$	95.5203	+	95.5203i	0.0991903	+	0.0991903i
$964$		−	357.268i		−	0.370610i
$965$	−80.8589	+	193.823i	−0.0837916	+	0.200853i
$966$	39.4685			0.0408576
$967$	913.788	−	913.788i	0.944972	−	0.944972i	−0.0535914	−	0.998563i	$-0.517067\pi$
$967$	913.788	−	913.788i	0.944972	−	0.944972i	0.998563	+	0.0535914i	$0.0170668\pi$
$968$	107.857	+	107.857i	0.111423	+	0.111423i
$969$		−	42.5628i		−	0.0439244i
$970$	−321.754	+	132.322i	−0.331705	+	0.136415i
$971$	−642.646			−0.661839			−0.330920	−	0.943659i	$-0.607359\pi$
$971$	−642.646			−0.661839			−0.330920	+	0.943659i	$0.607359\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−145.412	−	145.412i	−0.149447	−	0.149447i
$974$			685.854i			0.704162i
$975$	−319.800	−	323.051i	−0.328000	−	0.331335i
$976$	112.701			0.115472
$977$	551.397	−	551.397i	0.564377	−	0.564377i	−0.366171	−	0.930548i	$-0.619331\pi$
$977$	551.397	−	551.397i	0.564377	−	0.564377i	0.930548	+	0.366171i	$0.119331\pi$
$978$	134.486	+	134.486i	0.137511	+	0.137511i
$979$			627.352i			0.640809i
$980$	−143.435	−	348.776i	−0.146363	−	0.355894i
$981$	534.684			0.545040
$982$	−850.889	+	850.889i	−0.866486	+	0.866486i
$983$	543.674	+	543.674i	0.553076	+	0.553076i	0.927327	−	0.374251i	$-0.122100\pi$
$983$	543.674	+	543.674i	0.553076	+	0.553076i	−0.374251	+	0.927327i	$0.622100\pi$
$984$			34.3712i			0.0349301i
$985$	−801.009	−	334.165i	−0.813207	−	0.339254i
$986$	260.946			0.264651
$987$	−172.917	+	172.917i	−0.175195	+	0.175195i
$988$	−31.3312	−	31.3312i	−0.0317117	−	0.0317117i
$989$			21.1870i			0.0214226i
$990$	−66.8894	+	160.337i	−0.0675650	+	0.161957i
$991$	−433.622			−0.437560			−0.218780	−	0.975774i	$-0.570208\pi$
$991$	−433.622			−0.437560			−0.218780	+	0.975774i	$0.570208\pi$
$992$	60.3147	−	60.3147i	0.0608011	−	0.0608011i
$993$	494.929	+	494.929i	0.498417	+	0.498417i
$994$			320.284i			0.322218i
$995$	50.6331	−	20.8230i	0.0508875	−	0.0209277i
$996$	263.679			0.264738
$997$	104.863	−	104.863i	0.105178	−	0.105178i	−0.652559	−	0.757738i	$-0.726305\pi$
$997$	104.863	−	104.863i	0.105178	−	0.105178i	0.757738	+	0.652559i	$0.226305\pi$
$998$	−782.522	−	782.522i	−0.784090	−	0.784090i
$999$			104.461i			0.104566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.4	yes	40
5.2	odd	4	inner	690.3.k.a.277.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.4	✓	40	5.2	odd	4	inner
690.3.k.a.553.4	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-1.90173 - 4.62422i) q^{5} -2.44949 q^{6} +(2.37572 - 2.37572i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-1.90173 - 4.62422i) q^{5} -2.44949 q^{6} +(2.37572 - 2.37572i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-6.52595 - 2.72250i) q^{10} -8.18971 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.42310 - 7.42310i) q^{13} -4.75145i q^{14} +(-3.33436 + 7.99262i) q^{15} -4.00000 q^{16} +(8.23366 - 8.23366i) q^{17} +(3.00000 + 3.00000i) q^{18} +2.11038i q^{19} +(-9.24845 + 3.80345i) q^{20} -5.81931 q^{21} +(-8.18971 + 8.18971i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-17.7669 + 17.5880i) q^{25} -14.8462 q^{26} +(3.67423 - 3.67423i) q^{27} +(-4.75145 - 4.75145i) q^{28} +15.8463i q^{29} +(4.65826 + 11.3270i) q^{30} -15.0787 q^{31} +(-4.00000 + 4.00000i) q^{32} +(10.0303 + 10.0303i) q^{33} -16.4673i q^{34} +(-15.5039 - 6.46790i) q^{35} +6.00000 q^{36} +(-14.2154 + 14.2154i) q^{37} +(2.11038 + 2.11038i) q^{38} +18.1828i q^{39} +(-5.44499 + 13.0519i) q^{40} +7.01600 q^{41} +(-5.81931 + 5.81931i) q^{42} +(-3.12385 - 3.12385i) q^{43} +16.3794i q^{44} +(13.8727 - 5.70518i) q^{45} -6.78233 q^{46} +(29.7144 - 29.7144i) q^{47} +(4.89898 + 4.89898i) q^{48} +37.7119i q^{49} +(-0.178849 + 35.3549i) q^{50} -20.1683 q^{51} +(-14.8462 + 14.8462i) q^{52} +(17.6122 + 17.6122i) q^{53} -7.34847i q^{54} +(15.5746 + 37.8710i) q^{55} -9.50289 q^{56} +(2.58468 - 2.58468i) q^{57} +(15.8463 + 15.8463i) q^{58} -26.4258i q^{59} +(15.9852 + 6.66872i) q^{60} -28.1753 q^{61} +(-15.0787 + 15.0787i) q^{62} +(7.12717 + 7.12717i) q^{63} +8.00000i q^{64} +(-20.2094 + 48.4428i) q^{65} +20.0606 q^{66} +(-66.9478 + 66.9478i) q^{67} +(-16.4673 - 16.4673i) q^{68} +8.30662i q^{69} +(-21.9717 + 9.03595i) q^{70} -67.4077 q^{71} +(6.00000 - 6.00000i) q^{72} +(16.9909 + 16.9909i) q^{73} +28.4307i q^{74} +(43.3007 + 0.219044i) q^{75} +4.22077 q^{76} +(-19.4565 + 19.4565i) q^{77} +(18.1828 + 18.1828i) q^{78} +75.5612i q^{79} +(7.60691 + 18.4969i) q^{80} -9.00000 q^{81} +(7.01600 - 7.01600i) q^{82} +(-53.8232 - 53.8232i) q^{83} +11.6386i q^{84} +(-53.7325 - 22.4161i) q^{85} -6.24770 q^{86} +(19.4077 - 19.4077i) q^{87} +(16.3794 + 16.3794i) q^{88} -76.6024i q^{89} +(8.16749 - 19.5778i) q^{90} -35.2705 q^{91} +(-6.78233 + 6.78233i) q^{92} +(18.4675 + 18.4675i) q^{93} -59.4288i q^{94} +(9.75888 - 4.01337i) q^{95} +9.79796 q^{96} +(34.7900 - 34.7900i) q^{97} +(37.7119 + 37.7119i) q^{98} -24.5691i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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