LMFDB - Embedded newform 690.3.k.a.277.4

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			277.4
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.4

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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	0.856137	−	0.516748i	$-0.172858\pi$
$7$	2.37572	+	2.37572i	0.339389	+	0.339389i	−0.516748	+	0.856137i	$0.672858\pi$
$8$	−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	−0.932410	−	0.361402i	$-0.882298\pi$
$13$	−7.42310	+	7.42310i	−0.571008	+	0.571008i	0.361402	+	0.932410i	$0.382298\pi$
$14$			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	0.906512	−	0.422179i	$-0.138735\pi$
$17$	8.23366	+	8.23366i	0.484333	+	0.484333i	−0.422179	+	0.906512i	$0.638735\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	2.11038i		−	0.111073i	−0.998457	−	0.0555364i	$-0.982313\pi$
$19$		−	2.11038i		−	0.111073i	0.998457	−	0.0555364i	$-0.0176869\pi$
$20$	−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	$-0.911914\pi$
$29$		−	15.8463i		−	0.546424i	0.961954	−	0.273212i	$-0.0880860\pi$
$30$	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	0.488413	−	0.872612i	$-0.337576\pi$
$37$	−14.2154	−	14.2154i	−0.384199	−	0.384199i	−0.872612	+	0.488413i	$0.837576\pi$
$38$	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	−0.742497	−	0.669849i	$-0.766359\pi$
$43$	−3.12385	+	3.12385i	−0.0726476	+	0.0726476i	0.669849	+	0.742497i	$0.266359\pi$
$44$		−	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	0.948625	−	0.316404i	$-0.102475\pi$
$47$	29.7144	+	29.7144i	0.632221	+	0.632221i	−0.316404	+	0.948625i	$0.602475\pi$
$48$	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	−0.521155	−	0.853462i	$-0.674499\pi$
$53$	17.6122	−	17.6122i	0.332306	−	0.332306i	0.853462	+	0.521155i	$0.174499\pi$
$54$			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	$0.0718944\pi$
$59$			26.4258i			0.447895i	−0.974601	+	0.223947i	$0.928106\pi$
$60$	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	0.000778970	−	1.00000i	$-0.499752\pi$
$67$	−66.9478	−	66.9478i	−0.999221	−	0.999221i	−1.00000		0.000778970i	$0.999752\pi$
$68$	−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	−0.581089	−	0.813840i	$-0.697373\pi$
$73$	16.9909	−	16.9909i	0.232752	−	0.232752i	0.813840	+	0.581089i	$0.197373\pi$
$74$		−	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	$-0.841277\pi$
$79$		−	75.5612i		−	0.956471i	0.878232	−	0.478235i	$-0.158723\pi$
$80$	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	−0.952624	−	0.304151i	$-0.901627\pi$
$83$	−53.8232	+	53.8232i	−0.648473	+	0.648473i	0.304151	+	0.952624i	$0.401627\pi$
$84$		−	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	$0.141610\pi$
$89$			76.6024i			0.860701i	−0.902662	+	0.430351i	$0.858390\pi$
$90$	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	0.863319	−	0.504659i	$-0.168382\pi$
$97$	34.7900	+	34.7900i	0.358660	+	0.358660i	−0.504659	+	0.863319i	$0.668382\pi$
$98$	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	−0.764418	−	0.644720i	$-0.776974\pi$
$103$	−12.3289	+	12.3289i	−0.119698	+	0.119698i	0.644720	+	0.764418i	$0.276974\pi$
$104$		−	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	0.840062	−	0.542491i	$-0.182519\pi$
$107$	31.8401	+	31.8401i	0.297571	+	0.297571i	−0.542491	+	0.840062i	$0.682519\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			178.228i			1.63512i	0.575844	+	0.817559i	$0.304673\pi$
$109$			178.228i			1.63512i	−0.575844	+	0.817559i	$0.695327\pi$
$110$	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	−0.953609	−	0.301047i	$-0.902664\pi$
$113$	−73.7395	+	73.7395i	−0.652562	+	0.652562i	0.301047	+	0.953609i	$0.402664\pi$
$114$			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	0.750114	−	0.661308i	$-0.229999\pi$
$127$	11.2783	+	11.2783i	0.0888056	+	0.0888056i	−0.661308	+	0.750114i	$0.729999\pi$
$128$	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	0.953521	−	0.301327i	$-0.0974296\pi$
$137$	89.3505	+	89.3505i	0.652194	+	0.652194i	−0.301327	+	0.953521i	$0.597430\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			61.2074i			0.440341i	0.975461	+	0.220170i	$0.0706613\pi$
$139$			61.2074i			0.440341i	−0.975461	+	0.220170i	$0.929339\pi$
$140$	−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	$0.308898\pi$
$149$			245.889i			1.65026i	−0.564943	+	0.825130i	$0.691102\pi$
$150$	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	0.498114	−	0.867111i	$-0.334026\pi$
$157$	−57.9326	−	57.9326i	−0.368997	−	0.368997i	−0.867111	+	0.498114i	$0.834026\pi$
$158$	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	−0.855174	−	0.518341i	$-0.826550\pi$
$163$	−54.9037	+	54.9037i	−0.336832	+	0.336832i	0.518341	+	0.855174i	$0.326550\pi$
$164$			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	0.816735	−	0.577013i	$-0.195782\pi$
$167$	40.0337	+	40.0337i	0.239723	+	0.239723i	−0.577013	+	0.816735i	$0.695782\pi$
$168$	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	−0.465347	−	0.885128i	$-0.654071\pi$
$173$	72.6221	−	72.6221i	0.419781	−	0.419781i	0.885128	+	0.465347i	$0.154071\pi$
$174$			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	$0.307792\pi$
$179$			294.692i			1.64632i	−0.567808	+	0.823161i	$0.692208\pi$
$180$	−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	−0.779852	−	0.625964i	$-0.784706\pi$
$193$	−29.7003	+	29.7003i	−0.153888	+	0.153888i	0.625964	+	0.779852i	$0.284706\pi$
$194$			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	0.946312	−	0.323255i	$-0.104777\pi$
$197$	122.742	+	122.742i	0.623057	+	0.623057i	−0.323255	+	0.946312i	$0.604777\pi$
$198$	−24.5691	+	24.5691i	−0.124087	+	0.124087i
$199$		−	10.9495i		−	0.0550228i	−0.999621	−	0.0275114i	$-0.991242\pi$
$199$		−	10.9495i		−	0.0550228i	0.999621	−	0.0275114i	$-0.00875825\pi$
$200$	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	−0.856659	−	0.515883i	$-0.827464\pi$
$223$	−75.9931	+	75.9931i	−0.340776	+	0.340776i	0.515883	+	0.856659i	$0.327464\pi$
$224$		−	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	0.976374	−	0.216087i	$-0.0693295\pi$
$227$	172.585	+	172.585i	0.760287	+	0.760287i	−0.216087	+	0.976374i	$0.569330\pi$
$228$	−5.16936	+	5.16936i	−0.0226726	+	0.0226726i
$229$			73.4614i			0.320792i	0.987053	+	0.160396i	$0.0512772\pi$
$229$			73.4614i			0.320792i	−0.987053	+	0.160396i	$0.948723\pi$
$230$	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	0.256519	−	0.966539i	$-0.417424\pi$
$233$	284.973	−	284.973i	1.22306	−	1.22306i	0.966539	−	0.256519i	$-0.0825757\pi$
$234$			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	$0.0787895\pi$
$239$			117.112i			0.490009i	−0.969522	+	0.245005i	$0.921211\pi$
$240$	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	0.885424	−	0.464785i	$-0.153868\pi$
$257$	108.104	+	108.104i	0.420639	+	0.420639i	−0.464785	+	0.885424i	$0.653868\pi$
$258$	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	−0.542210	−	0.840243i	$-0.682412\pi$
$263$	78.3826	−	78.3826i	0.298033	−	0.298033i	0.840243	+	0.542210i	$0.182412\pi$
$264$			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	$0.207798\pi$
$269$			326.796i			1.21485i	−0.794376	+	0.607427i	$0.792202\pi$
$270$	−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	0.580140	−	0.814517i	$-0.302998\pi$
$277$	−64.9224	−	64.9224i	−0.234377	−	0.234377i	−0.814517	+	0.580140i	$0.802998\pi$
$278$	−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	−0.997927	−	0.0643532i	$-0.979502\pi$
$283$	−264.201	+	264.201i	−0.933574	+	0.933574i	0.0643532	+	0.997927i	$0.479502\pi$
$284$		−	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	−0.402483	−	0.915428i	$-0.631853\pi$
$293$	150.293	−	150.293i	0.512945	−	0.512945i	0.915428	+	0.402483i	$0.131853\pi$
$294$			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	−0.970780	−	0.239971i	$-0.922862\pi$
$307$	−371.701	−	371.701i	−1.21075	−	1.21075i	−0.239971	−	0.970780i	$-0.577138\pi$
$308$	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	−0.405088	−	0.914277i	$-0.632759\pi$
$313$	159.376	−	159.376i	0.509189	−	0.509189i	0.914277	+	0.405088i	$0.132759\pi$
$314$		−	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	0.914582	−	0.404400i	$-0.132520\pi$
$317$	161.728	+	161.728i	0.510182	+	0.510182i	−0.404400	+	0.914582i	$0.632520\pi$
$318$	−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	0.629618	−	0.776905i	$-0.283212\pi$
$337$	−49.6359	−	49.6359i	−0.147288	−	0.147288i	−0.776905	+	0.629618i	$0.783212\pi$
$338$	−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	0.650499	−	0.759507i	$-0.274560\pi$
$347$	−37.8258	−	37.8258i	−0.109008	−	0.109008i	−0.759507	+	0.650499i	$0.774560\pi$
$348$	−38.8153	+	38.8153i	−0.111538	+	0.111538i
$349$			608.019i			1.74217i	0.491129	+	0.871087i	$0.336584\pi$
$349$			608.019i			1.74217i	−0.491129	+	0.871087i	$0.663416\pi$
$350$	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	−0.547603	−	0.836738i	$-0.684460\pi$
$353$	102.065	−	102.065i	0.289135	−	0.289135i	0.836738	+	0.547603i	$0.184460\pi$
$354$		−	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	$-0.815773\pi$
$359$		−	392.739i		−	1.09398i	0.837139	−	0.546990i	$-0.184227\pi$
$360$	−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	0.761421	−	0.648258i	$-0.224502\pi$
$367$	41.5309	+	41.5309i	0.113163	+	0.113163i	−0.648258	+	0.761421i	$0.724502\pi$
$368$	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	−0.913278	−	0.407337i	$-0.866457\pi$
$373$	−188.716	+	188.716i	−0.505941	+	0.505941i	0.407337	+	0.913278i	$0.366457\pi$
$374$		−	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	$-0.939289\pi$
$379$		−	143.699i		−	0.379152i	0.981866	−	0.189576i	$-0.0607113\pi$
$380$	−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	−0.567173	−	0.823599i	$-0.691963\pi$
$383$	98.2112	−	98.2112i	0.256426	−	0.256426i	0.823599	+	0.567173i	$0.191963\pi$
$384$			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	$-0.898439\pi$
$389$		−	244.042i		−	0.627357i	0.949529	−	0.313678i	$-0.101561\pi$
$390$	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	0.461612	−	0.887082i	$-0.347271\pi$
$397$	−168.912	−	168.912i	−0.425470	−	0.425470i	−0.887082	+	0.461612i	$0.847271\pi$
$398$	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	$0.0758399\pi$
$409$			193.056i			0.472021i	−0.971751	+	0.236010i	$0.924160\pi$
$410$	−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	$-0.833417\pi$
$419$		−	418.810i		−	0.999546i	0.866156	−	0.499773i	$-0.166583\pi$
$420$	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	−0.405950	−	0.913895i	$-0.633059\pi$
$433$	219.940	−	219.940i	0.507945	−	0.507945i	0.913895	+	0.405950i	$0.133059\pi$
$434$		−	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	$0.0581754\pi$
$439$			159.575i			0.363496i	−0.983345	+	0.181748i	$0.941825\pi$
$440$	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	−0.706846	−	0.707367i	$-0.749883\pi$
$443$	0.230949	−	0.230949i	0.000521329	−	0.000521329i	0.707367	+	0.706846i	$0.249883\pi$
$444$			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	$0.294770\pi$
$449$			717.728i			1.59850i	−0.600997	+	0.799251i	$0.705230\pi$
$450$	−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	0.755883	−	0.654706i	$-0.227208\pi$
$457$	46.2379	+	46.2379i	0.101177	+	0.101177i	−0.654706	+	0.755883i	$0.727208\pi$
$458$	−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	−0.502323	−	0.864680i	$-0.667521\pi$
$463$	167.771	−	167.771i	0.362357	−	0.362357i	0.864680	+	0.502323i	$0.167521\pi$
$464$			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	0.636937	−	0.770916i	$-0.280201\pi$
$467$	−62.5685	−	62.5685i	−0.133980	−	0.133980i	−0.770916	+	0.636937i	$0.780201\pi$
$468$	−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	$-0.779175\pi$
$479$		−	612.563i		−	1.27884i	0.768858	−	0.639419i	$-0.220825\pi$
$480$	−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	0.261139	−	0.965301i	$-0.415902\pi$
$487$	−342.927	−	342.927i	−0.704162	−	0.704162i	−0.965301	+	0.261139i	$0.915902\pi$
$488$	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	$0.286870\pi$
$499$			782.522i			1.56818i	−0.620647	+	0.784090i	$0.713130\pi$
$500$	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	−0.632379	−	0.774659i	$-0.717921\pi$
$503$	71.5670	−	71.5670i	0.142280	−	0.142280i	0.774659	+	0.632379i	$0.217921\pi$
$504$			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	$-0.853765\pi$
$509$		−	451.402i		−	0.886840i	0.896314	−	0.443420i	$-0.146235\pi$
$510$	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	−0.522788	−	0.852463i	$-0.675108\pi$
$523$	172.420	−	172.420i	0.329674	−	0.329674i	0.852463	+	0.522788i	$0.175108\pi$
$524$		−	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	0.504341	−	0.863505i	$-0.331736\pi$
$547$	−196.463	−	196.463i	−0.359164	−	0.359164i	−0.863505	+	0.504341i	$0.831736\pi$
$548$	−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	0.531337	−	0.847160i	$-0.321690\pi$
$557$	−175.913	−	175.913i	−0.315823	−	0.315823i	−0.847160	+	0.531337i	$0.821690\pi$
$558$	−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	−0.276305	−	0.961070i	$-0.589110\pi$
$563$	385.523	−	385.523i	0.684765	−	0.684765i	0.961070	+	0.276305i	$0.0891100\pi$
$564$		−	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	$-0.962675\pi$
$569$		−	133.135i		−	0.233981i	0.993133	−	0.116990i	$-0.0373247\pi$
$570$	−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	0.351101	−	0.936338i	$-0.385807\pi$
$577$	−337.682	−	337.682i	−0.585237	−	0.585237i	−0.936338	+	0.351101i	$0.885807\pi$
$578$	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	0.293150	−	0.956066i	$-0.405296\pi$
$587$	−389.132	−	389.132i	−0.662916	−	0.662916i	−0.956066	+	0.293150i	$0.905296\pi$
$588$	−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	−0.991602	−	0.129329i	$-0.958718\pi$
$593$	−511.328	+	511.328i	−0.862273	+	0.862273i	0.129329	+	0.991602i	$0.458718\pi$
$594$		−	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	$0.0436602\pi$
$599$			163.806i			0.273466i	−0.990608	+	0.136733i	$0.956340\pi$
$600$	−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	0.569464	−	0.822016i	$-0.307151\pi$
$607$	−153.299	−	153.299i	−0.252553	−	0.252553i	−0.822016	+	0.569464i	$0.807151\pi$
$608$	−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	0.180228	−	0.983625i	$-0.442317\pi$
$613$	713.442	−	713.442i	1.16385	−	1.16385i	0.983625	−	0.180228i	$-0.0576834\pi$
$614$		−	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	0.870153	−	0.492781i	$-0.164020\pi$
$617$	232.838	+	232.838i	0.377372	+	0.377372i	−0.492781	+	0.870153i	$0.664020\pi$
$618$	30.1995	−	30.1995i	0.0488665	−	0.0488665i
$619$			126.186i			0.203854i	0.994792	+	0.101927i	$0.0325009\pi$
$619$			126.186i			0.203854i	−0.994792	+	0.101927i	$0.967499\pi$
$620$	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	0.210283	−	0.977641i	$-0.432562\pi$
$643$	763.835	−	763.835i	1.18792	−	1.18792i	0.977641	−	0.210283i	$-0.0674385\pi$
$644$		−	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	0.893054	+	0.449949i	$0.148558\pi$
$647$	868.923	+	868.923i	1.34300	+	1.34300i	0.449949	+	0.893054i	$0.351442\pi$
$648$	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	−0.959069	−	0.283174i	$-0.908613\pi$
$653$	−441.359	+	441.359i	−0.675894	+	0.675894i	0.283174	+	0.959069i	$0.408613\pi$
$654$		−	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	$0.0813441\pi$
$659$			333.161i			0.505555i	−0.967524	+	0.252778i	$0.918656\pi$
$660$	−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	−0.572735	−	0.819740i	$-0.694118\pi$
$673$	166.235	−	166.235i	0.247005	−	0.247005i	0.819740	+	0.572735i	$0.194118\pi$
$674$		−	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	0.747817	−	0.663905i	$-0.231102\pi$
$677$	56.8084	+	56.8084i	0.0839119	+	0.0839119i	−0.663905	+	0.747817i	$0.731102\pi$
$678$	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	−0.0180741	+	0.999837i	$0.505753\pi$
$683$	−695.233	+	695.233i	−1.01791	+	1.01791i	−0.999837	+	0.0180741i	$0.994247\pi$
$684$		−	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	$-0.840726\pi$
$709$		−	680.289i		−	0.959505i	0.877404	−	0.479753i	$-0.159274\pi$
$710$	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	$0.207609\pi$
$719$			872.799i			1.21391i	−0.794737	+	0.606953i	$0.792391\pi$
$720$	−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	0.999913	+	0.0132213i	$0.00420860\pi$
$727$	736.548	+	736.548i	1.01313	+	1.01313i	0.0132213	+	0.999913i	$0.495791\pi$
$728$	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	−0.692645	−	0.721279i	$-0.743555\pi$
$733$	20.9889	−	20.9889i	0.0286342	−	0.0286342i	0.721279	+	0.692645i	$0.243555\pi$
$734$			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	$0.182032\pi$
$739$			799.903i			1.08241i	−0.840890	+	0.541206i	$0.817968\pi$
$740$	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	−0.876486	−	0.481427i	$-0.840119\pi$
$743$	−293.529	+	293.529i	−0.395059	+	0.395059i	0.481427	+	0.876486i	$0.340119\pi$
$744$			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	0.808007	−	0.589173i	$-0.200546\pi$
$757$	165.657	+	165.657i	0.218834	+	0.218834i	−0.589173	+	0.808007i	$0.700546\pi$
$758$	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	$0.167863\pi$
$769$			774.000i			1.00650i	−0.864140	+	0.503251i	$0.832137\pi$
$770$	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	−0.962546	−	0.271118i	$-0.912607\pi$
$773$	−534.474	+	534.474i	−0.691429	+	0.691429i	0.271118	+	0.962546i	$0.412607\pi$
$774$			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	0.946646	−	0.322277i	$-0.104448\pi$
$787$	491.378	+	491.378i	0.624369	+	0.624369i	−0.322277	+	0.946646i	$0.604448\pi$
$788$	−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	0.993060	−	0.117611i	$-0.0375237\pi$
$797$	697.732	+	697.732i	0.875449	+	0.875449i	−0.117611	+	0.993060i	$0.537524\pi$
$798$	−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	$0.135061\pi$
$809$			666.114i			0.823380i	−0.911324	+	0.411690i	$0.864939\pi$
$810$	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	−0.857727	−	0.514106i	$-0.828124\pi$
$823$	−282.800	+	282.800i	−0.343621	+	0.343621i	0.514106	+	0.857727i	$0.328124\pi$
$824$		−	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	0.894192	+	0.447683i	$0.147751\pi$
$827$	1109.73	+	1109.73i	1.34188	+	1.34188i	0.447683	+	0.894192i	$0.352249\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	530.827i		−	0.640322i	−0.947363	−	0.320161i	$-0.896263\pi$
$829$		−	530.827i		−	0.640322i	0.947363	−	0.320161i	$-0.103737\pi$
$830$	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	$-0.842130\pi$
$839$		−	798.526i		−	0.951759i	0.879510	−	0.475880i	$-0.157870\pi$
$840$	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	−0.458681	−	0.888601i	$-0.651678\pi$
$853$	366.721	−	366.721i	0.429919	−	0.429919i	0.888601	+	0.458681i	$0.151678\pi$
$854$		−	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	0.990525	−	0.137333i	$-0.0438530\pi$
$857$	731.186	+	731.186i	0.853192	+	0.853192i	−0.137333	+	0.990525i	$0.543853\pi$
$858$	−148.912	+	148.912i	−0.173557	+	0.173557i
$859$			802.675i			0.934429i	0.884144	+	0.467215i	$0.154742\pi$
$859$			802.675i			0.934429i	−0.884144	+	0.467215i	$0.845258\pi$
$860$	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	−0.158048	−	0.987431i	$-0.550520\pi$
$863$	715.758	−	715.758i	0.829383	−	0.829383i	0.987431	+	0.158048i	$0.0505202\pi$
$864$		−	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	0.999736	−	0.0229612i	$-0.00730941\pi$
$877$	856.632	+	856.632i	0.976775	+	0.976775i	−0.0229612	+	0.999736i	$0.507309\pi$
$878$	−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	−0.872779	−	0.488116i	$-0.837684\pi$
$883$	−339.658	+	339.658i	−0.384663	+	0.384663i	0.488116	+	0.872779i	$0.337684\pi$
$884$		−	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	0.191719	−	0.981450i	$-0.438594\pi$
$887$	−700.491	−	700.491i	−0.789731	−	0.789731i	−0.981450	+	0.191719i	$0.938594\pi$
$888$	−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	0.999988	−	0.00493230i	$-0.00157001\pi$
$907$	902.515	+	902.515i	0.995056	+	0.995056i	−0.00493230	+	0.999988i	$0.501570\pi$
$908$	−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	$-0.898151\pi$
$919$		−	578.120i		−	0.629075i	0.949245	−	0.314537i	$-0.101849\pi$
$920$	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	$-0.855343\pi$
$929$		−	815.607i		−	0.877941i	0.898501	−	0.438971i	$-0.144657\pi$
$930$	−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	0.981072	+	0.193646i	$0.0620312\pi$
$937$	1100.71	+	1100.71i	1.17472	+	1.17472i	0.193646	+	0.981072i	$0.437969\pi$
$938$	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	0.543062	−	0.839693i	$-0.317265\pi$
$947$	−280.909	−	280.909i	−0.296631	−	0.296631i	−0.839693	+	0.543062i	$0.817265\pi$
$948$	−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	−0.884204	−	0.467102i	$-0.845298\pi$
$953$	−397.498	+	397.498i	−0.417102	+	0.417102i	0.467102	+	0.884204i	$0.345298\pi$
$954$		−	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	0.998563	−	0.0535914i	$-0.0170668\pi$
$967$	913.788	+	913.788i	0.944972	+	0.944972i	−0.0535914	+	0.998563i	$0.517067\pi$
$968$	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	0.930548	−	0.366171i	$-0.119331\pi$
$977$	551.397	+	551.397i	0.564377	+	0.564377i	−0.366171	+	0.930548i	$0.619331\pi$
$978$	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	−0.374251	−	0.927327i	$-0.622100\pi$
$983$	543.674	−	543.674i	0.553076	−	0.553076i	0.927327	+	0.374251i	$0.122100\pi$
$984$		−	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	0.757738	−	0.652559i	$-0.226305\pi$
$997$	104.863	+	104.863i	0.105178	+	0.105178i	−0.652559	+	0.757738i	$0.726305\pi$
$998$	−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.277.4	✓	40
5.3	odd	4	inner	690.3.k.a.553.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.4	✓	40	1.1	even	1	trivial
690.3.k.a.553.4	yes	40	5.3	odd	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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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