LMFDB - Embedded newform 435.2.q.d.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	435.41
Dual form			435.2.q.d.191.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203088 - 0.203088i) q^{2} +(0.407389 - 1.68346i) q^{3} +1.91751i q^{4} +1.00000 q^{5} +(-0.259155 - 0.424627i) q^{6} +4.71926 q^{7} +(0.795601 + 0.795601i) q^{8} +(-2.66807 - 1.37164i) q^{9} +O(q^{10})$	\(q+(0.203088 - 0.203088i) q^{2} +(0.407389 - 1.68346i) q^{3} +1.91751i q^{4} +1.00000 q^{5} +(-0.259155 - 0.424627i) q^{6} +4.71926 q^{7} +(0.795601 + 0.795601i) q^{8} +(-2.66807 - 1.37164i) q^{9} +(0.203088 - 0.203088i) q^{10} +(-1.95511 + 1.95511i) q^{11} +(3.22805 + 0.781172i) q^{12} +5.24447i q^{13} +(0.958428 - 0.958428i) q^{14} +(0.407389 - 1.68346i) q^{15} -3.51187 q^{16} +(2.21348 - 2.21348i) q^{17} +(-0.820419 + 0.263289i) q^{18} +(0.0703377 + 0.0703377i) q^{19} +1.91751i q^{20} +(1.92257 - 7.94469i) q^{21} +0.794119i q^{22} -7.77411i q^{23} +(1.66348 - 1.01524i) q^{24} +1.00000 q^{25} +(1.06509 + 1.06509i) q^{26} +(-3.39605 + 3.93279i) q^{27} +9.04924i q^{28} +(5.31383 + 0.873632i) q^{29} +(-0.259155 - 0.424627i) q^{30} +(-0.672629 - 0.672629i) q^{31} +(-2.30442 + 2.30442i) q^{32} +(2.49485 + 4.08783i) q^{33} -0.899066i q^{34} +4.71926 q^{35} +(2.63014 - 5.11605i) q^{36} +(2.42602 - 2.42602i) q^{37} +0.0285696 q^{38} +(8.82885 + 2.13654i) q^{39} +(0.795601 + 0.795601i) q^{40} +(-6.09464 - 6.09464i) q^{41} +(-1.22302 - 2.00393i) q^{42} +(-6.01660 - 6.01660i) q^{43} +(-3.74893 - 3.74893i) q^{44} +(-2.66807 - 1.37164i) q^{45} +(-1.57883 - 1.57883i) q^{46} +(-5.31905 - 5.31905i) q^{47} +(-1.43069 + 5.91208i) q^{48} +15.2714 q^{49} +(0.203088 - 0.203088i) q^{50} +(-2.82456 - 4.62806i) q^{51} -10.0563 q^{52} +4.43540i q^{53} +(0.109007 + 1.48840i) q^{54} +(-1.95511 + 1.95511i) q^{55} +(3.75465 + 3.75465i) q^{56} +(0.147065 - 0.0897559i) q^{57} +(1.25660 - 0.901753i) q^{58} +2.33428i q^{59} +(3.22805 + 0.781172i) q^{60} +(-2.26452 - 2.26452i) q^{61} -0.273206 q^{62} +(-12.5913 - 6.47315i) q^{63} -6.08773i q^{64} +5.24447i q^{65} +(1.33687 + 0.323515i) q^{66} +14.8576i q^{67} +(4.24438 + 4.24438i) q^{68} +(-13.0874 - 3.16709i) q^{69} +(0.958428 - 0.958428i) q^{70} -3.36785 q^{71} +(-1.03144 - 3.21400i) q^{72} +(-8.05912 + 8.05912i) q^{73} -0.985393i q^{74} +(0.407389 - 1.68346i) q^{75} +(-0.134873 + 0.134873i) q^{76} +(-9.22666 + 9.22666i) q^{77} +(2.22694 - 1.35913i) q^{78} +(-1.03247 - 1.03247i) q^{79} -3.51187 q^{80} +(5.23718 + 7.31928i) q^{81} -2.47550 q^{82} -8.25497i q^{83} +(15.2340 + 3.68656i) q^{84} +(2.21348 - 2.21348i) q^{85} -2.44381 q^{86} +(3.63552 - 8.58970i) q^{87} -3.11097 q^{88} +(-3.11970 + 3.11970i) q^{89} +(-0.820419 + 0.263289i) q^{90} +24.7500i q^{91} +14.9069 q^{92} +(-1.40636 + 0.858322i) q^{93} -2.16047 q^{94} +(0.0703377 + 0.0703377i) q^{95} +(2.94060 + 4.81819i) q^{96} +(3.99867 - 3.99867i) q^{97} +(3.10146 - 3.10146i) q^{98} +(7.89806 - 2.53465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8}+O(q^{10}) $ 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8	$ 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8} + 4 q^{10} + 12 q^{11} + 10 q^{12} - 28 q^{14} + 2 q^{15} - 60 q^{16} + 20 q^{17} + 32 q^{18} + 16 q^{19} - 12 q^{21} + 24 q^{24} + 36 q^{25} - 4 q^{26} - 22 q^{27} + 28 q^{29} - 8 q^{30} - 8 q^{31} + 16 q^{32} + 8 q^{33} + 8 q^{35} - 28 q^{36} - 4 q^{37} - 24 q^{38} - 24 q^{39} - 4 q^{40} - 48 q^{41} + 8 q^{42} + 4 q^{43} - 16 q^{44} + 20 q^{46} + 20 q^{47} - 66 q^{48} + 28 q^{49} + 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} + 84 q^{56} - 28 q^{57} - 64 q^{58} + 10 q^{60} + 20 q^{61} - 8 q^{62} - 32 q^{63} - 8 q^{66} - 60 q^{68} - 36 q^{69} - 28 q^{70} + 16 q^{71} + 64 q^{72} + 8 q^{73} + 2 q^{75} + 16 q^{76} - 32 q^{77} + 48 q^{78} + 12 q^{79} - 60 q^{80} - 60 q^{81} + 56 q^{82} + 100 q^{84} + 20 q^{85} - 8 q^{86} - 10 q^{87} - 24 q^{88} - 20 q^{89} + 32 q^{90} + 16 q^{92} - 24 q^{93} + 52 q^{94} + 16 q^{95} + 8 q^{96} + 4 q^{97} + 8 q^{98} + 32 q^{99}+O(q^{100}) $ 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8 + 4 * q^10 + 12 * q^11 + 10 * q^12 - 28 * q^14 + 2 * q^15 - 60 * q^16 + 20 * q^17 + 32 * q^18 + 16 * q^19 - 12 * q^21 + 24 * q^24 + 36 * q^25 - 4 * q^26 - 22 * q^27 + 28 * q^29 - 8 * q^30 - 8 * q^31 + 16 * q^32 + 8 * q^33 + 8 * q^35 - 28 * q^36 - 4 * q^37 - 24 * q^38 - 24 * q^39 - 4 * q^40 - 48 * q^41 + 8 * q^42 + 4 * q^43 - 16 * q^44 + 20 * q^46 + 20 * q^47 - 66 * q^48 + 28 * q^49 + 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 + 84 * q^56 - 28 * q^57 - 64 * q^58 + 10 * q^60 + 20 * q^61 - 8 * q^62 - 32 * q^63 - 8 * q^66 - 60 * q^68 - 36 * q^69 - 28 * q^70 + 16 * q^71 + 64 * q^72 + 8 * q^73 + 2 * q^75 + 16 * q^76 - 32 * q^77 + 48 * q^78 + 12 * q^79 - 60 * q^80 - 60 * q^81 + 56 * q^82 + 100 * q^84 + 20 * q^85 - 8 * q^86 - 10 * q^87 - 24 * q^88 - 20 * q^89 + 32 * q^90 + 16 * q^92 - 24 * q^93 + 52 * q^94 + 16 * q^95 + 8 * q^96 + 4 * q^97 + 8 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.203088	−	0.203088i	0.143605	−	0.143605i	−0.631649	−	0.775254i	$-0.717622\pi$
$2$	0.203088	−	0.203088i	0.143605	−	0.143605i	0.775254	+	0.631649i	$0.217622\pi$
$3$	0.407389	−	1.68346i	0.235206	−	0.971946i
$3$	0.407389	−	1.68346i	0.235206	−	0.971946i
$4$			1.91751i			0.958755i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.259155	−	0.424627i	−0.105800	−	0.173353i
$7$	4.71926			1.78371			0.891857	−	0.452318i	$-0.149403\pi$
$7$	4.71926			1.78371			0.891857	+	0.452318i	$0.149403\pi$
$8$	0.795601	+	0.795601i	0.281287	+	0.281287i
$9$	−2.66807	−	1.37164i	−0.889356	−	0.457215i
$10$	0.203088	−	0.203088i	0.0642222	−	0.0642222i
$11$	−1.95511	+	1.95511i	−0.589486	+	0.589486i	−0.937492	−	0.348006i	$-0.886859\pi$
$11$	−1.95511	+	1.95511i	−0.589486	+	0.589486i	0.348006	+	0.937492i	$0.386859\pi$
$12$	3.22805	+	0.781172i	0.931858	+	0.225505i
$13$			5.24447i			1.45455i	0.686344	+	0.727277i	$0.259214\pi$
$13$			5.24447i			1.45455i	−0.686344	+	0.727277i	$0.740786\pi$
$14$	0.958428	−	0.958428i	0.256151	−	0.256151i
$15$	0.407389	−	1.68346i	0.105187	−	0.434667i
$16$	−3.51187			−0.877966
$17$	2.21348	−	2.21348i	0.536849	−	0.536849i	−0.385753	−	0.922602i	$-0.626058\pi$
$17$	2.21348	−	2.21348i	0.536849	−	0.536849i	0.922602	+	0.385753i	$0.126058\pi$
$18$	−0.820419	+	0.263289i	−0.193375	+	0.0620578i
$19$	0.0703377	+	0.0703377i	0.0161366	+	0.0161366i	0.715129	−	0.698992i	$-0.246368\pi$
$19$	0.0703377	+	0.0703377i	0.0161366	+	0.0161366i	−0.698992	+	0.715129i	$0.746368\pi$
$20$			1.91751i			0.428768i
$21$	1.92257	−	7.94469i	0.419540	−	1.73367i
$22$			0.794119i			0.169307i
$23$		−	7.77411i		−	1.62101i	−0.585729	−	0.810507i	$-0.699192\pi$
$23$		−	7.77411i		−	1.62101i	0.585729	−	0.810507i	$-0.300808\pi$
$24$	1.66348	−	1.01524i	0.339557	−	0.207236i
$25$	1.00000			0.200000
$26$	1.06509	+	1.06509i	0.208882	+	0.208882i
$27$	−3.39605	+	3.93279i	−0.653570	+	0.756866i
$28$			9.04924i			1.71014i
$29$	5.31383	+	0.873632i	0.986753	+	0.162229i
$29$	5.31383	+	0.873632i	0.986753	+	0.162229i
$30$	−0.259155	−	0.424627i	−0.0473151	−	0.0775259i
$31$	−0.672629	−	0.672629i	−0.120808	−	0.120808i	0.644118	−	0.764926i	$-0.277224\pi$
$31$	−0.672629	−	0.672629i	−0.120808	−	0.120808i	−0.764926	+	0.644118i	$0.777224\pi$
$32$	−2.30442	+	2.30442i	−0.407368	+	0.407368i
$33$	2.49485	+	4.08783i	0.434298	+	0.711599i
$34$		−	0.899066i		−	0.154189i
$35$	4.71926			0.797701
$36$	2.63014	−	5.11605i	0.438357	−	0.852675i
$37$	2.42602	−	2.42602i	0.398835	−	0.398835i	−0.478987	−	0.877822i	$-0.658996\pi$
$37$	2.42602	−	2.42602i	0.398835	−	0.398835i	0.877822	+	0.478987i	$0.158996\pi$
$38$	0.0285696			0.00463459
$39$	8.82885	+	2.13654i	1.41375	+	0.342120i
$40$	0.795601	+	0.795601i	0.125796	+	0.125796i
$41$	−6.09464	−	6.09464i	−0.951824	−	0.951824i	0.0470681	−	0.998892i	$-0.485012\pi$
$41$	−6.09464	−	6.09464i	−0.951824	−	0.951824i	−0.998892	+	0.0470681i	$0.985012\pi$
$42$	−1.22302	−	2.00393i	−0.188716	−	0.309213i
$43$	−6.01660	−	6.01660i	−0.917523	−	0.917523i	0.0793255	−	0.996849i	$-0.474723\pi$
$43$	−6.01660	−	6.01660i	−0.917523	−	0.917523i	−0.996849	+	0.0793255i	$0.974723\pi$
$44$	−3.74893	−	3.74893i	−0.565173	−	0.565173i
$45$	−2.66807	−	1.37164i	−0.397732	−	0.204473i
$46$	−1.57883	−	1.57883i	−0.232786	−	0.232786i
$47$	−5.31905	−	5.31905i	−0.775863	−	0.775863i	0.203262	−	0.979124i	$-0.434846\pi$
$47$	−5.31905	−	5.31905i	−0.775863	−	0.775863i	−0.979124	+	0.203262i	$0.934846\pi$
$48$	−1.43069	+	5.91208i	−0.206503	+	0.853336i
$49$	15.2714			2.18164
$50$	0.203088	−	0.203088i	0.0287210	−	0.0287210i
$51$	−2.82456	−	4.62806i	−0.395518	−	0.648058i
$52$	−10.0563			−1.39456
$53$			4.43540i			0.609249i	0.952473	+	0.304625i	$0.0985310\pi$
$53$			4.43540i			0.609249i	−0.952473	+	0.304625i	$0.901469\pi$
$54$	0.109007	+	1.48840i	0.0148339	+	0.202546i
$55$	−1.95511	+	1.95511i	−0.263626	+	0.263626i
$56$	3.75465	+	3.75465i	0.501736	+	0.501736i
$57$	0.147065	−	0.0897559i	0.0194793	−	0.0118885i
$58$	1.25660	−	0.901753i	0.165000	−	0.118406i
$59$			2.33428i			0.303898i	0.988388	+	0.151949i	$0.0485549\pi$
$59$			2.33428i			0.303898i	−0.988388	+	0.151949i	$0.951445\pi$
$60$	3.22805	+	0.781172i	0.416739	+	0.100849i
$61$	−2.26452	−	2.26452i	−0.289943	−	0.289943i	0.547115	−	0.837058i	$-0.315726\pi$
$61$	−2.26452	−	2.26452i	−0.289943	−	0.289943i	−0.837058	+	0.547115i	$0.815726\pi$
$62$	−0.273206			−0.0346972
$63$	−12.5913	−	6.47315i	−1.58636	−	0.815540i
$64$		−	6.08773i		−	0.760966i
$65$			5.24447i			0.650496i
$66$	1.33687	+	0.323515i	0.164557	+	0.0398219i
$67$			14.8576i			1.81514i	0.419896	+	0.907572i	$0.362067\pi$
$67$			14.8576i			1.81514i	−0.419896	+	0.907572i	$0.637933\pi$
$68$	4.24438	+	4.24438i	0.514706	+	0.514706i
$69$	−13.0874	−	3.16709i	−1.57554	−	0.381272i
$70$	0.958428	−	0.958428i	0.114554	−	0.114554i
$71$	−3.36785			−0.399691			−0.199845	−	0.979827i	$-0.564044\pi$
$71$	−3.36785			−0.399691			−0.199845	+	0.979827i	$0.564044\pi$
$72$	−1.03144	−	3.21400i	−0.121556	−	0.378774i
$73$	−8.05912	+	8.05912i	−0.943248	+	0.943248i	−0.998474	−	0.0552256i	$-0.982412\pi$
$73$	−8.05912	+	8.05912i	−0.943248	+	0.943248i	0.0552256	+	0.998474i	$0.482412\pi$
$74$		−	0.985393i		−	0.114550i
$75$	0.407389	−	1.68346i	0.0470412	−	0.194389i
$76$	−0.134873	+	0.134873i	−0.0154710	+	0.0154710i
$77$	−9.22666	+	9.22666i	−1.05148	+	1.05148i
$78$	2.22694	−	1.35913i	0.252152	−	0.153891i
$79$	−1.03247	−	1.03247i	−0.116162	−	0.116162i	0.646637	−	0.762798i	$-0.276175\pi$
$79$	−1.03247	−	1.03247i	−0.116162	−	0.116162i	−0.762798	+	0.646637i	$0.776175\pi$
$80$	−3.51187			−0.392638
$81$	5.23718	+	7.31928i	0.581909	+	0.813254i
$82$	−2.47550			−0.273374
$83$		−	8.25497i		−	0.906101i	−0.891485	−	0.453050i	$-0.850336\pi$
$83$		−	8.25497i		−	0.906101i	0.891485	−	0.453050i	$-0.149664\pi$
$84$	15.2340	+	3.68656i	1.66217	+	0.402236i
$85$	2.21348	−	2.21348i	0.240086	−	0.240086i
$86$	−2.44381			−0.263522
$87$	3.63552	−	8.58970i	0.389768	−	0.920913i
$88$	−3.11097			−0.331630
$89$	−3.11970	+	3.11970i	−0.330688	+	0.330688i	−0.852848	−	0.522160i	$-0.825126\pi$
$89$	−3.11970	+	3.11970i	−0.330688	+	0.330688i	0.522160	+	0.852848i	$0.325126\pi$
$90$	−0.820419	+	0.263289i	−0.0864798	+	0.0277531i
$91$			24.7500i			2.59451i
$92$	14.9069			1.55416
$93$	−1.40636	+	0.858322i	−0.145833	+	0.0890038i
$94$	−2.16047			−0.222836
$95$	0.0703377	+	0.0703377i	0.00721650	+	0.00721650i
$96$	2.94060	+	4.81819i	0.300124	+	0.491755i
$97$	3.99867	−	3.99867i	0.406003	−	0.406003i	−0.474339	−	0.880342i	$-0.657313\pi$
$97$	3.99867	−	3.99867i	0.406003	−	0.406003i	0.880342	+	0.474339i	$0.157313\pi$
$98$	3.10146	−	3.10146i	0.313294	−	0.313294i
$99$	7.89806	−	2.53465i	0.793785	−	0.254742i
$100$			1.91751i			0.191751i
$101$	−8.18434	+	8.18434i	−0.814373	+	0.814373i	−0.985286	−	0.170913i	$-0.945328\pi$
$101$	−8.18434	+	8.18434i	−0.814373	+	0.814373i	0.170913	+	0.985286i	$0.445328\pi$
$102$	−1.51354	−	0.366269i	−0.149863	−	0.0362661i
$103$	−2.46747			−0.243127			−0.121564	−	0.992584i	$-0.538791\pi$
$103$	−2.46747			−0.243127			−0.121564	+	0.992584i	$0.538791\pi$
$104$	−4.17250	+	4.17250i	−0.409148	+	0.409148i
$105$	1.92257	−	7.94469i	0.187624	−	0.775322i
$106$	0.900779	+	0.900779i	0.0874914	+	0.0874914i
$107$			4.25718i			0.411558i	0.978599	+	0.205779i	$0.0659727\pi$
$107$			4.25718i			0.411558i	−0.978599	+	0.205779i	$0.934027\pi$
$108$	−7.54117	−	6.51196i	−0.725649	−	0.626613i
$109$		−	13.0164i		−	1.24675i	−0.781924	−	0.623374i	$-0.785761\pi$
$109$		−	13.0164i		−	1.24675i	0.781924	−	0.623374i	$-0.214239\pi$
$110$			0.794119i			0.0757162i
$111$	−3.09577	−	5.07243i	−0.293838	−	0.481454i
$112$	−16.5734			−1.56604
$113$	3.55560	+	3.55560i	0.334483	+	0.334483i	0.854286	−	0.519803i	$-0.173995\pi$
$113$	3.55560	+	3.55560i	0.334483	+	0.334483i	−0.519803	+	0.854286i	$0.673995\pi$
$114$	0.0116389	−	0.0480957i	0.00109008	−	0.00450457i
$115$		−	7.77411i		−	0.724940i
$116$	−1.67520	+	10.1893i	−0.155538	+	0.946055i
$117$	7.19354	−	13.9926i	0.665043	−	1.29362i
$118$	0.474066	+	0.474066i	0.0436413	+	0.0436413i
$119$	10.4460	−	10.4460i	0.957584	−	0.957584i
$120$	1.66348	−	1.01524i	0.151854	−	0.0926786i
$121$			3.35513i			0.305012i
$122$	−0.919798			−0.0832746
$123$	−12.7430	+	7.77720i	−1.14900	+	0.701246i
$124$	1.28977	−	1.28977i	0.115825	−	0.115825i
$125$	1.00000			0.0894427
$126$	−3.87177	+	1.24253i	−0.344925	+	0.110693i
$127$	1.72721	+	1.72721i	0.153265	+	0.153265i	0.779575	−	0.626309i	$-0.215435\pi$
$127$	1.72721	+	1.72721i	0.153265	+	0.153265i	−0.626309	+	0.779575i	$0.715435\pi$
$128$	−5.84519	−	5.84519i	−0.516647	−	0.516647i
$129$	−12.5798	+	7.67761i	−1.10759	+	0.675976i
$130$	1.06509	+	1.06509i	0.0934147	+	0.0934147i
$131$	−1.74025	−	1.74025i	−0.152046	−	0.152046i	0.626985	−	0.779031i	$-0.284289\pi$
$131$	−1.74025	−	1.74025i	−0.152046	−	0.152046i	−0.779031	+	0.626985i	$0.784289\pi$
$132$	−7.83845	+	4.78390i	−0.682250	+	0.416385i
$133$	0.331942	+	0.331942i	0.0287830	+	0.0287830i
$134$	3.01741	+	3.01741i	0.260664	+	0.260664i
$135$	−3.39605	+	3.93279i	−0.292285	+	0.338481i
$136$	3.52210			0.302018
$137$	−11.2136	+	11.2136i	−0.958044	+	0.958044i	−0.999155	−	0.0411108i	$-0.986910\pi$
$137$	−11.2136	+	11.2136i	−0.958044	+	0.958044i	0.0411108	+	0.999155i	$0.486910\pi$
$138$	−3.30110	+	2.01470i	−0.281008	+	0.171503i
$139$	3.14057			0.266380			0.133190	−	0.991091i	$-0.457478\pi$
$139$	3.14057			0.266380			0.133190	+	0.991091i	$0.457478\pi$
$140$			9.04924i			0.764800i
$141$	−11.1213	+	6.78748i	−0.936584	+	0.571609i
$142$	−0.683972	+	0.683972i	−0.0573977	+	0.0573977i
$143$	−10.2535	−	10.2535i	−0.857440	−	0.857440i
$144$	9.36990	+	4.81703i	0.780825	+	0.401419i
$145$	5.31383	+	0.873632i	0.441289	+	0.0725512i
$146$			3.27343i			0.270911i
$147$	6.22141	−	25.7089i	0.513134	−	2.12043i
$148$	4.65191	+	4.65191i	0.382385	+	0.382385i
$149$	−8.69252			−0.712119			−0.356060	−	0.934463i	$-0.615880\pi$
$149$	−8.69252			−0.712119			−0.356060	+	0.934463i	$0.615880\pi$
$150$	−0.259155	−	0.424627i	−0.0211599	−	0.0346707i
$151$		−	12.7333i		−	1.03622i	−0.855313	−	0.518112i	$-0.826635\pi$
$151$		−	12.7333i		−	1.03622i	0.855313	−	0.518112i	$-0.173365\pi$
$152$			0.111922i			0.00907804i
$153$	−8.94184	+	2.86962i	−0.722905	+	0.231995i
$154$			3.74766i			0.301995i
$155$	−0.672629	−	0.672629i	−0.0540268	−	0.0540268i
$156$	−4.09683	+	16.9294i	−0.328009	+	1.35544i
$157$	14.1320	−	14.1320i	1.12786	−	1.12786i	0.137330	−	0.990525i	$-0.456148\pi$
$157$	14.1320	−	14.1320i	1.12786	−	1.12786i	0.990525	−	0.137330i	$-0.0438522\pi$
$158$	−0.419364			−0.0333628
$159$	7.46681	+	1.80693i	0.592157	+	0.143299i
$160$	−2.30442	+	2.30442i	−0.182181	+	0.182181i
$161$		−	36.6881i		−	2.89143i
$162$	2.55007	+	0.422850i	0.200353	+	0.0332222i
$163$	10.9092	−	10.9092i	0.854474	−	0.854474i	−0.136206	−	0.990681i	$-0.543491\pi$
$163$	10.9092	−	10.9092i	0.854474	−	0.854474i	0.990681	+	0.136206i	$0.0434909\pi$
$164$	11.6865	−	11.6865i	0.912566	−	0.912566i
$165$	2.49485	+	4.08783i	0.194224	+	0.318237i
$166$	−1.67649	−	1.67649i	−0.130121	−	0.130121i
$167$	19.7842			1.53095			0.765474	−	0.643467i	$-0.222505\pi$
$167$	19.7842			1.53095			0.765474	+	0.643467i	$0.222505\pi$
$168$	7.85040	−	4.79120i	0.605672	−	0.369649i
$169$	−14.5044			−1.11573
$170$		−	0.899066i		−	0.0689552i
$171$	−0.0911876	−	0.284144i	−0.00697329	−	0.0217290i
$172$	11.5369	−	11.5369i	0.879680	−	0.879680i
$173$	−24.4547			−1.85925			−0.929627	−	0.368501i	$-0.879871\pi$
$173$	−24.4547			−1.85925			−0.929627	+	0.368501i	$0.879871\pi$
$174$	−1.00614	−	2.48280i	−0.0762752	−	0.188221i
$175$	4.71926			0.356743
$176$	6.86607	−	6.86607i	0.517549	−	0.517549i
$177$	3.92967	+	0.950960i	0.295372	+	0.0714786i
$178$			1.26715i			0.0949771i
$179$	3.12174			0.233330			0.116665	−	0.993171i	$-0.462780\pi$
$179$	3.12174			0.233330			0.116665	+	0.993171i	$0.462780\pi$
$180$	2.63014	−	5.11605i	0.196039	−	0.381328i
$181$	−7.09274			−0.527199			−0.263600	−	0.964632i	$-0.584910\pi$
$181$	−7.09274			−0.527199			−0.263600	+	0.964632i	$0.584910\pi$
$182$	5.02644	+	5.02644i	0.372585	+	0.372585i
$183$	−4.73478	+	2.88969i	−0.350005	+	0.213612i
$184$	6.18509	−	6.18509i	0.455971	−	0.455971i
$185$	2.42602	−	2.42602i	0.178364	−	0.178364i
$186$	−0.111301	+	0.459932i	−0.00816100	+	0.0337238i
$187$			8.65519i			0.632930i
$188$	10.1993	−	10.1993i	0.743862	−	0.743862i
$189$	−16.0268	+	18.5599i	−1.16578	+	1.35003i
$190$	0.0285696			0.00207265
$191$	11.6603	−	11.6603i	0.843708	−	0.843708i	−0.145631	−	0.989339i	$-0.546521\pi$
$191$	11.6603	−	11.6603i	0.843708	−	0.843708i	0.989339	+	0.145631i	$0.0465212\pi$
$192$	−10.2484	−	2.48007i	−0.739618	−	0.178984i
$193$	−2.18804	−	2.18804i	−0.157498	−	0.157498i	0.623959	−	0.781457i	$-0.285523\pi$
$193$	−2.18804	−	2.18804i	−0.157498	−	0.157498i	−0.781457	+	0.623959i	$0.785523\pi$
$194$		−	1.62417i		−	0.116608i
$195$	8.82885	+	2.13654i	0.632247	+	0.153001i
$196$			29.2832i			2.09165i
$197$			24.6926i			1.75927i	0.475648	+	0.879636i	$0.342214\pi$
$197$			24.6926i			1.75927i	−0.475648	+	0.879636i	$0.657786\pi$
$198$	1.08925	−	2.11876i	0.0774095	−	0.150574i
$199$	18.4161			1.30548			0.652740	−	0.757582i	$-0.273620\pi$
$199$	18.4161			1.30548			0.652740	+	0.757582i	$0.273620\pi$
$200$	0.795601	+	0.795601i	0.0562575	+	0.0562575i
$201$	25.0122	+	6.05282i	1.76422	+	0.426933i
$202$			3.32429i			0.233896i
$203$	25.0774	+	4.12290i	1.76009	+	0.289371i
$204$	8.87435	−	5.41612i	0.621329	−	0.379205i
$205$	−6.09464	−	6.09464i	−0.425668	−	0.425668i
$206$	−0.501115	+	0.501115i	−0.0349144	+	0.0349144i
$207$	−10.6633	+	20.7419i	−0.741152	+	1.44166i
$208$		−	18.4179i		−	1.27705i
$209$	−0.275035			−0.0190246
$210$	−1.22302	−	2.00393i	−0.0843965	−	0.138284i
$211$	−1.86299	+	1.86299i	−0.128253	+	0.128253i	−0.768320	−	0.640066i	$-0.778907\pi$
$211$	−1.86299	+	1.86299i	−0.128253	+	0.128253i	0.640066	+	0.768320i	$0.278907\pi$
$212$	−8.50492			−0.584121
$213$	−1.37202	+	5.66964i	−0.0940096	+	0.388477i
$214$	0.864585	+	0.864585i	0.0591018	+	0.0591018i
$215$	−6.01660	−	6.01660i	−0.410329	−	0.410329i
$216$	−5.83083	+	0.427035i	−0.396738	+	0.0290561i
$217$	−3.17431	−	3.17431i	−0.215486	−	0.215486i
$218$	−2.64349	−	2.64349i	−0.179040	−	0.179040i
$219$	10.2840	+	16.8504i	0.694928	+	1.13864i
$220$	−3.74893	−	3.74893i	−0.252753	−	0.252753i
$221$	11.6085	+	11.6085i	0.780875	+	0.780875i
$222$	−1.65887	−	0.401438i	−0.111336	−	0.0269427i
$223$	−9.27265			−0.620942			−0.310471	−	0.950583i	$-0.600487\pi$
$223$	−9.27265			−0.620942			−0.310471	+	0.950583i	$0.600487\pi$
$224$	−10.8752	+	10.8752i	−0.726628	+	0.726628i
$225$	−2.66807	−	1.37164i	−0.177871	−	0.0914429i
$226$	1.44420			0.0960669
$227$		−	0.506969i		−	0.0336487i	−0.999858	−	0.0168244i	$-0.994644\pi$
$227$		−	0.506969i		−	0.0336487i	0.999858	−	0.0168244i	$-0.00535561\pi$
$228$	0.172108	+	0.281999i	0.0113981	+	0.0186759i
$229$	−11.5698	+	11.5698i	−0.764554	+	0.764554i	−0.977142	−	0.212588i	$-0.931811\pi$
$229$	−11.5698	+	11.5698i	−0.764554	+	0.764554i	0.212588	+	0.977142i	$0.431811\pi$
$230$	−1.57883	−	1.57883i	−0.104105	−	0.104105i
$231$	11.7739	+	19.2915i	0.774663	+	1.26929i
$232$	3.53263	+	4.92275i	0.231928	+	0.323194i
$233$			11.8274i			0.774836i	0.921904	+	0.387418i	$0.126633\pi$
$233$			11.8274i			0.774836i	−0.921904	+	0.387418i	$0.873367\pi$
$234$	−1.38081	−	4.30266i	−0.0902664	−	0.281274i
$235$	−5.31905	−	5.31905i	−0.346976	−	0.346976i
$236$	−4.47601			−0.291364
$237$	−2.15873	+	1.31750i	−0.140225	+	0.0855809i
$238$		−	4.24293i		−	0.275028i
$239$		−	14.0319i		−	0.907646i	−0.891092	−	0.453823i	$-0.850060\pi$
$239$		−	14.0319i		−	0.907646i	0.891092	−	0.453823i	$-0.149940\pi$
$240$	−1.43069	+	5.91208i	−0.0923509	+	0.381623i
$241$		−	12.2077i		−	0.786364i	−0.919461	−	0.393182i	$-0.871374\pi$
$241$		−	12.2077i		−	0.786364i	0.919461	−	0.393182i	$-0.128626\pi$
$242$	0.681388	+	0.681388i	0.0438012	+	0.0438012i
$243$	14.4553	−	5.83479i	0.927307	−	0.374302i
$244$	4.34225	−	4.34225i	0.277984	−	0.277984i
$245$	15.2714			0.975657
$246$	−1.00849	+	4.16741i	−0.0642991	+	0.265704i
$247$	−0.368884	+	0.368884i	−0.0234715	+	0.0234715i
$248$		−	1.07029i		−	0.0679634i
$249$	−13.8969	−	3.36298i	−0.880681	−	0.213120i
$250$	0.203088	−	0.203088i	0.0128444	−	0.0128444i
$251$	13.5826	−	13.5826i	0.857327	−	0.857327i	−0.133695	−	0.991022i	$-0.542684\pi$
$251$	13.5826	−	13.5826i	0.857327	−	0.857327i	0.991022	+	0.133695i	$0.0426844\pi$
$252$	12.4123	−	24.1440i	0.781903	−	1.52093i
$253$	15.1992	+	15.1992i	0.955566	+	0.955566i
$254$	0.701553			0.0440193
$255$	−2.82456	−	4.62806i	−0.176881	−	0.289820i
$256$	9.80127			0.612580
$257$			16.8820i			1.05307i	0.850153	+	0.526535i	$0.176509\pi$
$257$			16.8820i			1.05307i	−0.850153	+	0.526535i	$0.823491\pi$
$258$	−0.995578	+	4.11405i	−0.0619820	+	0.256129i
$259$	11.4490	−	11.4490i	0.711407	−	0.711407i
$260$	−10.0563			−0.623666
$261$	−12.9793	−	9.61959i	−0.803401	−	0.595438i
$262$	−0.706848			−0.0436692
$263$	−15.1991	+	15.1991i	−0.937214	+	0.937214i	−0.998142	−	0.0609278i	$-0.980594\pi$
$263$	−15.1991	+	15.1991i	−0.937214	+	0.937214i	0.0609278	+	0.998142i	$0.480594\pi$
$264$	−1.26737	+	5.23719i	−0.0780014	+	0.322327i
$265$			4.43540i			0.272464i
$266$	0.134827			0.00826679
$267$	3.98096	+	6.52283i	0.243631	+	0.399191i
$268$	−28.4896			−1.74028
$269$	9.68332	+	9.68332i	0.590403	+	0.590403i	0.937740	−	0.347337i	$-0.112914\pi$
$269$	9.68332	+	9.68332i	0.590403	+	0.590403i	−0.347337	+	0.937740i	$0.612914\pi$
$270$	0.109007	+	1.48840i	0.00663394	+	0.0905813i
$271$	10.6559	−	10.6559i	0.647302	−	0.647302i	−0.305038	−	0.952340i	$-0.598669\pi$
$271$	10.6559	−	10.6559i	0.647302	−	0.647302i	0.952340	+	0.305038i	$0.0986692\pi$
$272$	−7.77346	+	7.77346i	−0.471335	+	0.471335i
$273$	41.6657	+	10.0829i	2.52172	+	0.610244i
$274$			4.55471i			0.275160i
$275$	−1.95511	+	1.95511i	−0.117897	+	0.117897i
$276$	6.07292	−	25.0952i	0.365547	−	1.51056i
$277$	6.21849			0.373633			0.186816	−	0.982395i	$-0.440183\pi$
$277$	6.21849			0.373633			0.186816	+	0.982395i	$0.440183\pi$
$278$	0.637814	−	0.637814i	0.0382536	−	0.0382536i
$279$	0.872013	+	2.71723i	0.0522060	+	0.162676i
$280$	3.75465	+	3.75465i	0.224383	+	0.224383i
$281$		−	10.7814i		−	0.643166i	−0.946881	−	0.321583i	$-0.895785\pi$
$281$		−	10.7814i		−	0.643166i	0.946881	−	0.321583i	$-0.104215\pi$
$282$	−0.880153	+	3.63707i	−0.0524123	+	0.216584i
$283$			7.63015i			0.453565i	0.973945	+	0.226783i	$0.0728207\pi$
$283$			7.63015i			0.453565i	−0.973945	+	0.226783i	$0.927179\pi$
$284$		−	6.45789i		−	0.383205i
$285$	0.147065	−	0.0897559i	0.00871141	−	0.00531668i
$286$	−4.16473			−0.246266
$287$	−28.7622	−	28.7622i	−1.69778	−	1.69778i
$288$	9.30920	−	2.98751i	0.548550	−	0.176041i
$289$			7.20098i			0.423587i
$290$	1.25660	−	0.901753i	0.0737902	−	0.0529527i
$291$	−5.10258	−	8.36060i	−0.299119	−	0.490107i
$292$	−15.4534	−	15.4534i	−0.904344	−	0.904344i
$293$	21.3425	−	21.3425i	1.24684	−	1.24684i	0.289739	−	0.957106i	$-0.406432\pi$
$293$	21.3425	−	21.3425i	1.24684	−	1.24684i	0.957106	−	0.289739i	$-0.0935684\pi$
$294$	−3.95768	−	6.48467i	−0.230816	−	0.378194i
$295$			2.33428i			0.135907i
$296$	3.86029			0.224375
$297$	−1.04939	−	14.3287i	−0.0608920	−	0.831433i
$298$	−1.76535	+	1.76535i	−0.102264	+	0.102264i
$299$	40.7711			2.35785
$300$	3.22805	+	0.781172i	0.186372	+	0.0451010i
$301$	−28.3939	−	28.3939i	−1.63660	−	1.63660i
$302$	−2.58600	−	2.58600i	−0.148807	−	0.148807i
$303$	10.4438	+	17.1122i	0.599981	+	0.983071i
$304$	−0.247017	−	0.247017i	−0.0141674	−	0.0141674i
$305$	−2.26452	−	2.26452i	−0.129666	−	0.129666i
$306$	−1.23320	+	2.39877i	−0.0704973	+	0.137129i
$307$	24.3814	+	24.3814i	1.39152	+	1.39152i	0.821929	+	0.569589i	$0.192898\pi$
$307$	24.3814	+	24.3814i	1.39152	+	1.39152i	0.569589	+	0.821929i	$0.307102\pi$
$308$	−17.6922	−	17.6922i	−1.00811	−	1.00811i
$309$	−1.00522	+	4.15389i	−0.0571850	+	0.236306i
$310$	−0.273206			−0.0155171
$311$	−14.0474	+	14.0474i	−0.796555	+	0.796555i	−0.982551	−	0.185995i	$-0.940449\pi$
$311$	−14.0474	+	14.0474i	−0.796555	+	0.796555i	0.185995	+	0.982551i	$0.440449\pi$
$312$	5.32441	+	8.72407i	0.301435	+	0.493903i
$313$	6.74963			0.381512			0.190756	−	0.981637i	$-0.438906\pi$
$313$	6.74963			0.381512			0.190756	+	0.981637i	$0.438906\pi$
$314$		−	5.74009i		−	0.323932i
$315$	−12.5913	−	6.47315i	−0.709441	−	0.364721i
$316$	1.97977	−	1.97977i	0.111371	−	0.111371i
$317$	11.8717	+	11.8717i	0.666781	+	0.666781i	0.956969	−	0.290189i	$-0.0937181\pi$
$317$	11.8717	+	11.8717i	0.666781	+	0.666781i	−0.290189	+	0.956969i	$0.593718\pi$
$318$	1.88339	−	1.14946i	0.105615	−	0.0644583i
$319$	−12.0971	+	8.68105i	−0.677310	+	0.486046i
$320$		−	6.08773i		−	0.340314i
$321$	7.16680	+	1.73433i	0.400012	+	0.0968008i
$322$	−7.45093	−	7.45093i	−0.415224	−	0.415224i
$323$	0.311383			0.0173258
$324$	−14.0348	+	10.0424i	−0.779711	+	0.557909i
$325$			5.24447i			0.290911i
$326$		−	4.43107i		−	0.245414i
$327$	−21.9126	−	5.30275i	−1.21177	−	0.293243i
$328$		−	9.69781i		−	0.535472i
$329$	−25.1020	−	25.1020i	−1.38392	−	1.38392i
$330$	1.33687	+	0.323515i	0.0735921	+	0.0178089i
$331$	10.3819	−	10.3819i	0.570640	−	0.570640i	−0.361667	−	0.932307i	$-0.617792\pi$
$331$	10.3819	−	10.3819i	0.570640	−	0.570640i	0.932307	+	0.361667i	$0.117792\pi$
$332$	15.8290			0.868729
$333$	−9.80042	+	3.14515i	−0.537060	+	0.172353i
$334$	4.01794	−	4.01794i	0.219852	−	0.219852i
$335$			14.8576i			0.811757i
$336$	−6.75182	+	27.9007i	−0.368342	+	1.52211i
$337$	−8.35554	+	8.35554i	−0.455155	+	0.455155i	−0.897061	−	0.441906i	$-0.854302\pi$
$337$	−8.35554	+	8.35554i	−0.455155	+	0.455155i	0.441906	+	0.897061i	$0.354302\pi$
$338$	−2.94568	+	2.94568i	−0.160224	+	0.160224i
$339$	7.43422	−	4.53719i	0.403771	−	0.246427i
$340$	4.24438	+	4.24438i	0.230184	+	0.230184i
$341$	2.63012			0.142429
$342$	−0.0762256	−	0.0391873i	−0.00412181	−	0.00211900i
$343$	39.0351			2.10770
$344$		−	9.57363i		−	0.516176i
$345$	−13.0874	−	3.16709i	−0.704602	−	0.170510i
$346$	−4.96646	+	4.96646i	−0.266999	+	0.266999i
$347$	0.378036			0.0202940			0.0101470	−	0.999949i	$-0.496770\pi$
$347$	0.378036			0.0202940			0.0101470	+	0.999949i	$0.496770\pi$
$348$	16.4708	+	6.97114i	0.882930	+	0.373692i
$349$	15.8477			0.848308			0.424154	−	0.905590i	$-0.360571\pi$
$349$	15.8477			0.848308			0.424154	+	0.905590i	$0.360571\pi$
$350$	0.958428	−	0.958428i	0.0512301	−	0.0512301i
$351$	−20.6254	−	17.8105i	−1.10090	−	0.950652i
$352$		−	9.01077i		−	0.480276i
$353$	−31.9300			−1.69946			−0.849732	−	0.527215i	$-0.823236\pi$
$353$	−31.9300			−1.69946			−0.849732	+	0.527215i	$0.823236\pi$
$354$	0.991200	−	0.604942i	0.0526817	−	0.0321523i
$355$	−3.36785			−0.178747
$356$	−5.98207	−	5.98207i	−0.317049	−	0.317049i
$357$	−13.3298	−	21.8410i	−0.705490	−	1.15595i
$358$	0.633990	−	0.633990i	0.0335074	−	0.0335074i
$359$	−9.12815	+	9.12815i	−0.481765	+	0.481765i	−0.905695	−	0.423930i	$-0.860650\pi$
$359$	−9.12815	+	9.12815i	−0.481765	+	0.481765i	0.423930	+	0.905695i	$0.360650\pi$
$360$	−1.03144	−	3.21400i	−0.0543615	−	0.169393i
$361$		−	18.9901i		−	0.999479i
$362$	−1.44045	+	1.44045i	−0.0757086	+	0.0757086i
$363$	5.64822	+	1.36684i	0.296455	+	0.0717405i
$364$	−47.4584			−2.48750
$365$	−8.05912	+	8.05912i	−0.421833	+	0.421833i
$366$	−0.374715	+	1.54844i	−0.0195867	+	0.0809383i
$367$	−17.2870	−	17.2870i	−0.902372	−	0.902372i	0.0932692	−	0.995641i	$-0.470268\pi$
$367$	−17.2870	−	17.2870i	−0.902372	−	0.902372i	−0.995641	+	0.0932692i	$0.970268\pi$
$368$			27.3016i			1.42320i
$369$	7.90125	+	24.6206i	0.411323	+	1.28170i
$370$		−	0.985393i		−	0.0512281i
$371$			20.9318i			1.08673i
$372$	−1.64584	−	2.69672i	−0.0853329	−	0.139818i
$373$	−22.0966			−1.14412			−0.572060	−	0.820212i	$-0.693856\pi$
$373$	−22.0966			−1.14412			−0.572060	+	0.820212i	$0.693856\pi$
$374$	1.75777	+	1.75777i	0.0908921	+	0.0908921i
$375$	0.407389	−	1.68346i	0.0210375	−	0.0869335i
$376$		−	8.46368i		−	0.436481i
$377$	−4.58173	+	27.8682i	−0.235971	+	1.43529i
$378$	0.514432	+	7.02417i	0.0264595	+	0.361284i
$379$	−15.2619	−	15.2619i	−0.783953	−	0.783953i	0.196542	−	0.980495i	$-0.437029\pi$
$379$	−15.2619	−	15.2619i	−0.783953	−	0.783953i	−0.980495	+	0.196542i	$0.937029\pi$
$380$	−0.134873	+	0.134873i	−0.00691885	+	0.00691885i
$381$	3.61133	−	2.20404i	0.185014	−	0.112916i
$382$		−	4.73614i		−	0.242322i
$383$	21.5927			1.10334			0.551668	−	0.834064i	$-0.313992\pi$
$383$	21.5927			1.10334			0.551668	+	0.834064i	$0.313992\pi$
$384$	−12.2214	+	7.45888i	−0.623671	+	0.380634i
$385$	−9.22666	+	9.22666i	−0.470234	+	0.470234i
$386$	−0.888730			−0.0452352
$387$	7.80007	+	24.3053i	0.396500	+	1.23551i
$388$	7.66748	+	7.66748i	0.389258	+	0.389258i
$389$	−3.91014	−	3.91014i	−0.198252	−	0.198252i	0.600998	−	0.799250i	$-0.294770\pi$
$389$	−3.91014	−	3.91014i	−0.198252	−	0.198252i	−0.799250	+	0.600998i	$0.794770\pi$
$390$	2.22694	−	1.35913i	0.112766	−	0.0688223i
$391$	−17.2079	−	17.2079i	−0.870240	−	0.870240i
$392$	12.1500	+	12.1500i	0.613667	+	0.613667i
$393$	−3.63859	+	2.22068i	−0.183543	+	0.112018i
$394$	5.01477	+	5.01477i	0.252641	+	0.252641i
$395$	−1.03247	−	1.03247i	−0.0519491	−	0.0519491i
$396$	4.86021	+	15.1446i	0.244235	+	0.761046i
$397$	11.8365			0.594059			0.297029	−	0.954868i	$-0.404004\pi$
$397$	11.8365			0.594059			0.297029	+	0.954868i	$0.404004\pi$
$398$	3.74009	−	3.74009i	0.187474	−	0.187474i
$399$	0.694041	−	0.423582i	0.0347455	−	0.0212056i
$400$	−3.51187			−0.175593
$401$			31.6053i			1.57829i	0.614205	+	0.789146i	$0.289477\pi$
$401$			31.6053i			1.57829i	−0.614205	+	0.789146i	$0.710523\pi$
$402$	6.30894	−	3.85042i	0.314661	−	0.192042i
$403$	3.52758	−	3.52758i	0.175721	−	0.175721i
$404$	−15.6936	−	15.6936i	−0.780784	−	0.780784i
$405$	5.23718	+	7.31928i	0.260238	+	0.363698i
$406$	5.93023	−	4.25561i	0.294313	−	0.211202i
$407$			9.48624i			0.470216i
$408$	1.43486	−	5.92931i	0.0710363	−	0.293545i
$409$	−13.3758	−	13.3758i	−0.661390	−	0.661390i	0.294318	−	0.955708i	$-0.404908\pi$
$409$	−13.3758	−	13.3758i	−0.661390	−	0.661390i	−0.955708	+	0.294318i	$0.904908\pi$
$410$	−2.47550			−0.122256
$411$	14.3094	+	23.4460i	0.705829	+	1.15650i
$412$		−	4.73140i		−	0.233100i
$413$			11.0161i			0.542067i
$414$	2.04684	+	6.37803i	0.100597	+	0.313463i
$415$		−	8.25497i		−	0.405221i
$416$	−12.0855	−	12.0855i	−0.592539	−	0.592539i
$417$	1.27943	−	5.28703i	0.0626541	−	0.258907i
$418$	−0.0558565	+	0.0558565i	−0.00273203	+	0.00273203i
$419$	−20.5409			−1.00349			−0.501743	−	0.865017i	$-0.667308\pi$
$419$	−20.5409			−1.00349			−0.501743	+	0.865017i	$0.667308\pi$
$420$	15.2340	+	3.68656i	0.743344	+	0.179885i
$421$	2.07899	−	2.07899i	0.101324	−	0.101324i	−0.654628	−	0.755951i	$-0.727175\pi$
$421$	2.07899	−	2.07899i	0.101324	−	0.101324i	0.755951	+	0.654628i	$0.227175\pi$
$422$			0.756703i			0.0368357i
$423$	6.89575	+	21.4874i	0.335283	+	1.04475i
$424$	−3.52881	+	3.52881i	−0.171374	+	0.171374i
$425$	2.21348	−	2.21348i	0.107370	−	0.107370i
$426$	0.872797	+	1.43008i	0.0422871	+	0.0692877i
$427$	−10.6869	−	10.6869i	−0.517175	−	0.517175i
$428$	−8.16320			−0.394583
$429$	−21.4385	+	13.0842i	−1.03506	+	0.631710i
$430$	−2.44381			−0.117851
$431$			17.3078i			0.833687i	0.908978	+	0.416844i	$0.136864\pi$
$431$			17.3078i			0.833687i	−0.908978	+	0.416844i	$0.863136\pi$
$432$	11.9265	−	13.8114i	0.573812	−	0.664503i
$433$	21.4943	−	21.4943i	1.03295	−	1.03295i	0.0335114	−	0.999438i	$-0.489331\pi$
$433$	21.4943	−	21.4943i	1.03295	−	1.03295i	0.999438	−	0.0335114i	$-0.0106690\pi$
$434$	−1.28933			−0.0618899
$435$	3.63552	−	8.58970i	0.174310	−	0.411845i
$436$	24.9591			1.19533
$437$	0.546813	−	0.546813i	0.0261576	−	0.0261576i
$438$	5.51068	+	1.33356i	0.263311	+	0.0637198i
$439$			15.5251i			0.740973i	0.928838	+	0.370486i	$0.120809\pi$
$439$			15.5251i			0.740973i	−0.928838	+	0.370486i	$0.879191\pi$
$440$	−3.11097			−0.148310
$441$	−40.7453	−	20.9470i	−1.94025	−	0.997476i
$442$	4.71512			0.224276
$443$	8.06242	+	8.06242i	0.383057	+	0.383057i	0.872202	−	0.489145i	$-0.162691\pi$
$443$	8.06242	+	8.06242i	0.383057	+	0.383057i	−0.489145	+	0.872202i	$0.662691\pi$
$444$	9.72645	−	5.93617i	0.461597	−	0.281718i
$445$	−3.11970	+	3.11970i	−0.147888	+	0.147888i
$446$	−1.88317	+	1.88317i	−0.0891706	+	0.0891706i
$447$	−3.54123	+	14.6335i	−0.167495	+	0.692141i
$448$		−	28.7296i		−	1.35735i
$449$	16.1974	−	16.1974i	0.764401	−	0.764401i	−0.212714	−	0.977115i	$-0.568230\pi$
$449$	16.1974	−	16.1974i	0.764401	−	0.764401i	0.977115	+	0.212714i	$0.0682302\pi$
$450$	−0.820419	+	0.263289i	−0.0386749	+	0.0124116i
$451$	23.8313			1.12217
$452$	−6.81790	+	6.81790i	−0.320687	+	0.320687i
$453$	−21.4361	−	5.18742i	−1.00715	−	0.243726i
$454$	−0.102960	−	0.102960i	−0.00483213	−	0.00483213i
$455$			24.7500i			1.16030i
$456$	0.188415	+	0.0455956i	0.00882336	+	0.00213521i
$457$		−	17.1020i		−	0.799996i	−0.916516	−	0.399998i	$-0.869011\pi$
$457$		−	17.1020i		−	0.799996i	0.916516	−	0.399998i	$-0.130989\pi$
$458$			4.69939i			0.219588i
$459$	1.18808	+	16.2223i	0.0554547	+	0.757191i
$460$	14.9069			0.695040
$461$	7.72915	+	7.72915i	0.359983	+	0.359983i	0.863806	−	0.503824i	$-0.168074\pi$
$461$	7.72915	+	7.72915i	0.359983	+	0.359983i	−0.503824	+	0.863806i	$0.668074\pi$
$462$	6.30902	+	1.52675i	0.293522	+	0.0710309i
$463$			23.1981i			1.07811i	0.842271	+	0.539054i	$0.181218\pi$
$463$			23.1981i			1.07811i	−0.842271	+	0.539054i	$0.818782\pi$
$464$	−18.6614	−	3.06808i	−0.866336	−	0.142432i
$465$	−1.40636	+	0.858322i	−0.0652186	+	0.0398037i
$466$	2.40200	+	2.40200i	0.111270	+	0.111270i
$467$	10.4436	−	10.4436i	0.483273	−	0.483273i	−0.422902	−	0.906175i	$-0.638989\pi$
$467$	10.4436	−	10.4436i	0.483273	−	0.483273i	0.906175	+	0.422902i	$0.138989\pi$
$468$	26.8310	+	13.7937i	1.24026	+	0.637614i
$469$			70.1169i			3.23770i
$470$	−2.16047			−0.0996553
$471$	−18.0334	−	29.5478i	−0.830936	−	1.36149i
$472$	−1.85716	+	1.85716i	−0.0854826	+	0.0854826i
$473$	23.5262			1.08173
$474$	−0.170844	+	0.705983i	−0.00784714	+	0.0324269i
$475$	0.0703377	+	0.0703377i	0.00322732	+	0.00322732i
$476$	20.0303	+	20.0303i	0.918089	+	0.918089i
$477$	6.08379	−	11.8340i	0.278558	−	0.541839i
$478$	−2.84971	−	2.84971i	−0.130343	−	0.130343i
$479$	−23.4401	−	23.4401i	−1.07100	−	1.07100i	−0.997279	−	0.0737262i	$-0.976511\pi$
$479$	−23.4401	−	23.4401i	−1.07100	−	1.07100i	−0.0737262	−	0.997279i	$-0.523489\pi$
$480$	2.94060	+	4.81819i	0.134220	+	0.219920i
$481$	12.7232	+	12.7232i	0.580127	+	0.580127i
$482$	−2.47923	−	2.47923i	−0.112926	−	0.112926i
$483$	−61.7629	−	14.9463i	−2.81031	−	0.680081i
$484$	−6.43349			−0.292431
$485$	3.99867	−	3.99867i	0.181570	−	0.181570i
$486$	1.75072	−	4.12068i	0.0794143	−	0.186918i
$487$	27.5891			1.25018			0.625091	−	0.780552i	$-0.285062\pi$
$487$	27.5891			1.25018			0.625091	+	0.780552i	$0.285062\pi$
$488$		−	3.60332i		−	0.163114i
$489$	−13.9209	−	22.8095i	−0.629525	−	1.03148i
$490$	3.10146	−	3.10146i	0.140109	−	0.140109i
$491$	10.5169	+	10.5169i	0.474619	+	0.474619i	0.903406	−	0.428786i	$-0.141059\pi$
$491$	10.5169	+	10.5169i	0.474619	+	0.474619i	−0.428786	+	0.903406i	$0.641059\pi$
$492$	−14.9129	−	24.4348i	−0.672323	−	1.10161i
$493$	13.6958	−	9.82830i	0.616830	−	0.442644i
$494$			0.149832i			0.00674127i
$495$	7.89806	−	2.53465i	0.354992	−	0.113924i
$496$	2.36218	+	2.36218i	0.106065	+	0.106065i
$497$	−15.8938			−0.712934
$498$	−3.50528	+	2.13932i	−0.157076	+	0.0958652i
$499$		−	3.44902i		−	0.154399i	−0.997016	−	0.0771996i	$-0.975402\pi$
$499$		−	3.44902i		−	0.154399i	0.997016	−	0.0771996i	$-0.0245979\pi$
$500$			1.91751i			0.0857537i
$501$	8.05986	−	33.3059i	0.360088	−	1.48800i
$502$		−	5.51695i		−	0.246233i
$503$	−0.214470	−	0.214470i	−0.00956276	−	0.00956276i	0.702309	−	0.711872i	$-0.252152\pi$
$503$	−0.214470	−	0.214470i	−0.00956276	−	0.00956276i	−0.711872	+	0.702309i	$0.752152\pi$
$504$	−4.86762	−	15.1677i	−0.216821	−	0.675624i
$505$	−8.18434	+	8.18434i	−0.364199	+	0.364199i
$506$	6.17357			0.274449
$507$	−5.90894	+	24.4176i	−0.262425	+	1.08443i
$508$	−3.31194	+	3.31194i	−0.146944	+	0.146944i
$509$		−	26.0050i		−	1.15265i	−0.817220	−	0.576326i	$-0.804486\pi$
$509$		−	26.0050i		−	1.15265i	0.817220	−	0.576326i	$-0.195514\pi$
$510$	−1.51354	−	0.366269i	−0.0670207	−	0.0162187i
$511$	−38.0331	+	38.0331i	−1.68249	+	1.68249i
$512$	13.6809	−	13.6809i	0.604616	−	0.604616i
$513$	−0.515494	+	0.0377534i	−0.0227596	+	0.00166685i
$514$	3.42854	+	3.42854i	0.151226	+	0.151226i
$515$	−2.46747			−0.108730
$516$	−14.7219	−	24.1219i	−0.648095	−	1.06191i
$517$	20.7986			0.914721
$518$		−	4.65033i		−	0.204324i
$519$	−9.96256	+	41.1684i	−0.437308	+	1.80709i
$520$	−4.17250	+	4.17250i	−0.182976	+	0.182976i
$521$	−9.29252			−0.407113			−0.203556	−	0.979063i	$-0.565250\pi$
$521$	−9.29252			−0.407113			−0.203556	+	0.979063i	$0.565250\pi$
$522$	−4.58958	+	0.682328i	−0.200881	+	0.0298647i
$523$	−14.1771			−0.619923			−0.309961	−	0.950749i	$-0.600316\pi$
$523$	−14.1771			−0.619923			−0.309961	+	0.950749i	$0.600316\pi$
$524$	3.33694	−	3.33694i	0.145775	−	0.145775i
$525$	1.92257	−	7.94469i	0.0839080	−	0.346735i
$526$			6.17351i			0.269178i
$527$	−2.97771			−0.129711
$528$	−8.76159	−	14.3559i	−0.381299	−	0.624760i
$529$	−37.4368			−1.62769
$530$	0.900779	+	0.900779i	0.0391273	+	0.0391273i
$531$	3.20181	−	6.22803i	0.138947	−	0.270273i
$532$	−0.636503	+	0.636503i	−0.0275959	+	0.0275959i
$533$	31.9632	−	31.9632i	1.38448	−	1.38448i
$534$	2.13320	+	0.516223i	0.0923125	+	0.0223392i
$535$			4.25718i			0.184054i
$536$	−11.8207	+	11.8207i	−0.510577	+	0.510577i
$537$	1.27176	−	5.25532i	0.0548806	−	0.226784i
$538$	3.93314			0.169570
$539$	−29.8573	+	29.8573i	−1.28604	+	1.28604i
$540$	−7.54117	−	6.51196i	−0.324520	−	0.280230i
$541$	15.3537	+	15.3537i	0.660107	+	0.660107i	0.955405	−	0.295298i	$-0.0954191\pi$
$541$	15.3537	+	15.3537i	0.660107	+	0.660107i	−0.295298	+	0.955405i	$0.595419\pi$
$542$		−	4.32820i		−	0.185912i
$543$	−2.88950	+	11.9403i	−0.124000	+	0.512409i
$544$			10.2016i			0.437390i
$545$		−	13.0164i		−	0.557563i
$546$	10.5095	−	6.41410i	0.449766	−	0.274498i
$547$	−15.6141			−0.667609			−0.333805	−	0.942642i	$-0.608333\pi$
$547$	−15.6141			−0.667609			−0.333805	+	0.942642i	$0.608333\pi$
$548$	−21.5022	−	21.5022i	−0.918529	−	0.918529i
$549$	2.93579	+	9.14803i	0.125296	+	0.390428i
$550$			0.794119i			0.0338613i
$551$	0.312313	+	0.435212i	0.0133050	+	0.0185406i
$552$	−7.89262	−	12.9321i	−0.335932	−	0.550426i
$553$	−4.87248	−	4.87248i	−0.207199	−	0.207199i
$554$	1.26290	−	1.26290i	0.0536556	−	0.0536556i
$555$	−3.09577	−	5.07243i	−0.131408	−	0.215313i
$556$			6.02208i			0.255393i
$557$	26.8663			1.13836			0.569182	−	0.822212i	$-0.307260\pi$
$557$	26.8663			1.13836			0.569182	+	0.822212i	$0.307260\pi$
$558$	0.728933	+	0.374742i	0.0308582	+	0.0158641i
$559$	31.5539	−	31.5539i	1.33459	−	1.33459i
$560$	−16.5734			−0.700355
$561$	14.5707	+	3.52602i	0.615173	+	0.148869i
$562$	−2.18958	−	2.18958i	−0.0923620	−	0.0923620i
$563$	3.63196	+	3.63196i	0.153069	+	0.153069i	0.779487	−	0.626418i	$-0.215480\pi$
$563$	3.63196	+	3.63196i	0.153069	+	0.153069i	−0.626418	+	0.779487i	$0.715480\pi$
$564$	−13.0151	−	21.3252i	−0.548033	−	0.897955i
$565$	3.55560	+	3.55560i	0.149585	+	0.149585i
$566$	1.54960	+	1.54960i	0.0651344	+	0.0651344i
$567$	24.7157	+	34.5416i	1.03796	+	1.45061i
$568$	−2.67947	−	2.67947i	−0.112428	−	0.112428i
$569$	−0.454125	−	0.454125i	−0.0190379	−	0.0190379i	0.697524	−	0.716562i	$-0.254285\pi$
$569$	−0.454125	−	0.454125i	−0.0190379	−	0.0190379i	−0.716562	+	0.697524i	$0.754285\pi$
$570$	0.0116389	−	0.0480957i	0.000487500	−	0.00201451i
$571$	23.9077			1.00051			0.500253	−	0.865879i	$-0.333240\pi$
$571$	23.9077			1.00051			0.500253	+	0.865879i	$0.333240\pi$
$572$	19.6612	−	19.6612i	0.822075	−	0.822075i
$573$	−14.8793	−	24.3799i	−0.621593	−	1.01848i
$574$	−11.6826			−0.487620
$575$		−	7.77411i		−	0.324203i
$576$	−8.35020	+	16.2425i	−0.347925	+	0.676770i
$577$	−30.6872	+	30.6872i	−1.27752	+	1.27752i	−0.335474	+	0.942050i	$0.608896\pi$
$577$	−30.6872	+	30.6872i	−1.27752	+	1.27752i	−0.942050	+	0.335474i	$0.891104\pi$
$578$	1.46244	+	1.46244i	0.0608293	+	0.0608293i
$579$	−4.57485	+	2.79209i	−0.190124	+	0.116035i
$580$	−1.67520	+	10.1893i	−0.0695588	+	0.423088i
$581$		−	38.9574i		−	1.61622i
$582$	−2.73422	−	0.661667i	−0.113337	−	0.0274270i
$583$	−8.67167	−	8.67167i	−0.359144	−	0.359144i
$584$	−12.8237			−0.530648
$585$	7.19354	−	13.9926i	0.297416	−	0.578523i
$586$		−	8.66885i		−	0.358107i
$587$		−	5.51433i		−	0.227601i	−0.993504	−	0.113800i	$-0.963698\pi$
$587$		−	5.51433i		−	0.227601i	0.993504	−	0.113800i	$-0.0363025\pi$
$588$	49.2970	+	11.9296i	2.03297	+	0.491969i
$589$		−	0.0946223i		−	0.00389885i
$590$	0.474066	+	0.474066i	0.0195170	+	0.0195170i
$591$	41.5689	+	10.0595i	1.70992	+	0.413791i
$592$	−8.51985	+	8.51985i	−0.350164	+	0.350164i
$593$	−1.54501			−0.0634461			−0.0317231	−	0.999497i	$-0.510099\pi$
$593$	−1.54501			−0.0634461			−0.0317231	+	0.999497i	$0.510099\pi$
$594$	−3.12310	−	2.69687i	−0.128143	−	0.110654i
$595$	10.4460	−	10.4460i	0.428245	−	0.428245i
$596$		−	16.6680i		−	0.682748i
$597$	7.50249	−	31.0027i	0.307056	−	1.26885i
$598$	8.28014	−	8.28014i	0.338600	−	0.338600i
$599$	−7.87150	+	7.87150i	−0.321621	+	0.321621i	−0.849389	−	0.527768i	$-0.823029\pi$
$599$	−7.87150	+	7.87150i	−0.321621	+	0.321621i	0.527768	+	0.849389i	$0.323029\pi$
$600$	1.66348	−	1.01524i	0.0679113	−	0.0414471i
$601$	16.2882	+	16.2882i	0.664409	+	0.664409i	0.956416	−	0.292007i	$-0.0943231\pi$
$601$	16.2882	+	16.2882i	0.664409	+	0.664409i	−0.292007	+	0.956416i	$0.594323\pi$
$602$	−11.5330			−0.470048
$603$	20.3793	−	39.6411i	0.829911	−	1.61431i
$604$	24.4163			0.993486
$605$			3.35513i			0.136405i
$606$	5.59631	+	1.35428i	0.227335	+	0.0550138i
$607$	−11.4375	+	11.4375i	−0.464235	+	0.464235i	−0.900041	−	0.435806i	$-0.856463\pi$
$607$	−11.4375	+	11.4375i	−0.464235	+	0.464235i	0.435806	+	0.900041i	$0.356463\pi$
$608$	−0.324176			−0.0131471
$609$	17.1570	−	40.5371i	0.695235	−	1.64265i
$610$	−0.919798			−0.0372415
$611$	27.8956	−	27.8956i	1.12853	−	1.12853i
$612$	−5.50252	−	17.1461i	−0.222426	−	0.693089i
$613$			4.43097i			0.178965i	0.995988	+	0.0894827i	$0.0285214\pi$
$613$			4.43097i			0.178965i	−0.995988	+	0.0894827i	$0.971479\pi$
$614$	9.90315			0.399659
$615$	−12.7430	+	7.77720i	−0.513846	+	0.313607i
$616$	−14.6815			−0.591534
$617$	−26.7888	−	26.7888i	−1.07848	−	1.07848i	−0.996646	−	0.0818305i	$-0.973923\pi$
$617$	−26.7888	−	26.7888i	−1.07848	−	1.07848i	−0.0818305	−	0.996646i	$-0.526077\pi$
$618$	0.639458	+	1.04776i	0.0257228	+	0.0421469i
$619$	−13.3155	+	13.3155i	−0.535194	+	0.535194i	−0.922113	−	0.386920i	$-0.873539\pi$
$619$	−13.3155	+	13.3155i	−0.535194	+	0.535194i	0.386920	+	0.922113i	$0.373539\pi$
$620$	1.28977	−	1.28977i	0.0517985	−	0.0517985i
$621$	30.5740	+	26.4013i	1.22689	+	1.05945i
$622$			5.70573i			0.228779i
$623$	−14.7227	+	14.7227i	−0.589853	+	0.589853i
$624$	−31.0057	−	7.50323i	−1.24122	−	0.300370i
$625$	1.00000			0.0400000
$626$	1.37077	−	1.37077i	0.0547871	−	0.0547871i
$627$	−0.112046	+	0.463011i	−0.00447470	+	0.0184909i
$628$	27.0982	+	27.0982i	1.08134	+	1.08134i
$629$		−	10.7399i		−	0.428228i
$630$	−3.87177	+	1.24253i	−0.154255	+	0.0495036i
$631$		−	2.14915i		−	0.0855565i	−0.999085	−	0.0427782i	$-0.986379\pi$
$631$		−	2.14915i		−	0.0855565i	0.999085	−	0.0427782i	$-0.0136209\pi$
$632$		−	1.64286i		−	0.0653496i
$633$	2.37731	+	3.89523i	0.0944894	+	0.154821i
$634$	4.82201			0.191506
$635$	1.72721	+	1.72721i	0.0685422	+	0.0685422i
$636$	−3.46481	+	14.3177i	−0.137389	+	0.567733i
$637$			80.0906i			3.17331i
$638$	−0.693767	+	4.21981i	−0.0274665	+	0.167064i
$639$	8.98566	+	4.61950i	0.355467	+	0.182744i
$640$	−5.84519	−	5.84519i	−0.231051	−	0.231051i
$641$	−18.8981	+	18.8981i	−0.746432	+	0.746432i	−0.973807	−	0.227375i	$-0.926986\pi$
$641$	−18.8981	+	18.8981i	−0.746432	+	0.746432i	0.227375	+	0.973807i	$0.426986\pi$
$642$	1.80772	−	1.10327i	0.0713449	−	0.0435427i
$643$		−	24.8596i		−	0.980367i	−0.871619	−	0.490184i	$-0.836930\pi$
$643$		−	24.8596i		−	0.980367i	0.871619	−	0.490184i	$-0.163070\pi$
$644$	70.3498			2.77217
$645$	−12.5798	+	7.67761i	−0.495329	+	0.302306i
$646$	0.0632383	−	0.0632383i	0.00248808	−	0.00248808i
$647$	44.5564			1.75169			0.875847	−	0.482590i	$-0.160304\pi$
$647$	44.5564			1.75169			0.875847	+	0.482590i	$0.160304\pi$
$648$	−1.65652	+	9.98994i	−0.0650742	+	0.392442i
$649$	−4.56377	−	4.56377i	−0.179144	−	0.179144i
$650$	1.06509	+	1.06509i	0.0417763	+	0.0417763i
$651$	−6.63700	+	4.05065i	−0.260125	+	0.158757i
$652$	20.9185	+	20.9185i	0.819232	+	0.819232i
$653$	31.3983	+	31.3983i	1.22871	+	1.22871i	0.964452	+	0.264259i	$0.0851274\pi$
$653$	31.3983	+	31.3983i	1.22871	+	1.22871i	0.264259	+	0.964452i	$0.414873\pi$
$654$	−5.52713	+	3.37328i	−0.216128	+	0.131906i
$655$	−1.74025	−	1.74025i	−0.0679970	−	0.0679970i
$656$	21.4036	+	21.4036i	0.835669	+	0.835669i
$657$	32.5565	−	10.4480i	1.27015	−	0.407617i
$658$	−10.1958			−0.397476
$659$	30.6643	−	30.6643i	1.19451	−	1.19451i	0.218727	−	0.975786i	$-0.429810\pi$
$659$	30.6643	−	30.6643i	1.19451	−	1.19451i	0.975786	−	0.218727i	$-0.0701905\pi$
$660$	−7.83845	+	4.78390i	−0.305111	+	0.186213i
$661$	−13.8136			−0.537288			−0.268644	−	0.963239i	$-0.586576\pi$
$661$	−13.8136			−0.537288			−0.268644	+	0.963239i	$0.586576\pi$
$662$		−	4.21688i		−	0.163894i
$663$	24.2717	−	14.8133i	0.942635	−	0.575302i
$664$	6.56766	−	6.56766i	0.254875	−	0.254875i
$665$	0.331942	+	0.331942i	0.0128722	+	0.0128722i
$666$	−1.35161	+	2.62910i	−0.0523738	+	0.101875i
$667$	6.79171	−	41.3103i	0.262976	−	1.59954i
$668$			37.9364i			1.46780i
$669$	−3.77757	+	15.6101i	−0.146049	+	0.603522i
$670$	3.01741	+	3.01741i	0.116573	+	0.116573i
$671$	8.85477			0.341835
$672$	13.8775	+	22.7383i	0.535336	+	0.877150i
$673$			29.7784i			1.14787i	0.818900	+	0.573936i	$0.194584\pi$
$673$			29.7784i			1.14787i	−0.818900	+	0.573936i	$0.805416\pi$
$674$			3.39383i			0.130725i
$675$	−3.39605	+	3.93279i	−0.130714	+	0.151373i
$676$		−	27.8124i		−	1.06971i
$677$	25.9892	+	25.9892i	0.998845	+	0.998845i	0.999999	−	0.00115385i	$-0.000367282\pi$
$677$	25.9892	+	25.9892i	0.998845	+	0.998845i	−0.00115385	+	0.999999i	$0.500367\pi$
$678$	0.588352	−	2.43126i	0.0225955	−	0.0933718i
$679$	18.8708	−	18.8708i	0.724193	−	0.724193i
$680$	3.52210			0.135066
$681$	−0.853462	−	0.206533i	−0.0327047	−	0.00791438i
$682$	0.534147	−	0.534147i	0.0204536	−	0.0204536i
$683$		−	35.6041i		−	1.36235i	−0.732119	−	0.681177i	$-0.761468\pi$
$683$		−	35.6041i		−	1.36235i	0.732119	−	0.681177i	$-0.238532\pi$
$684$	0.544849	−	0.174853i	0.0208328	−	0.00668567i
$685$	−11.2136	+	11.2136i	−0.428450	+	0.428450i
$686$	7.92759	−	7.92759i	0.302677	−	0.302677i
$687$	14.7639	+	24.1907i	0.563277	+	0.922933i
$688$	21.1295	+	21.1295i	0.805555	+	0.805555i
$689$	−23.2613			−0.886185
$690$	−3.30110	+	2.01470i	−0.125671	+	0.0766984i
$691$	−15.0468			−0.572409			−0.286204	−	0.958169i	$-0.592394\pi$
$691$	−15.0468			−0.572409			−0.286204	+	0.958169i	$0.592394\pi$
$692$		−	46.8921i		−	1.78257i
$693$	37.2730	−	11.9617i	1.41589	−	0.454386i
$694$	0.0767747	−	0.0767747i	0.00291433	−	0.00291433i
$695$	3.14057			0.119129
$696$	9.72640	−	3.94156i	0.368678	−	0.149404i
$697$	−26.9808			−1.02197
$698$	3.21849	−	3.21849i	0.121821	−	0.121821i
$699$	19.9109	+	4.81833i	0.753098	+	0.182246i
$700$			9.04924i			0.342029i
$701$	−30.1222			−1.13770			−0.568849	−	0.822442i	$-0.692611\pi$
$701$	−30.1222			−1.13770			−0.568849	+	0.822442i	$0.692611\pi$
$702$	−7.80588	+	0.571682i	−0.294614	+	0.0215768i
$703$	0.341281			0.0128717
$704$	11.9021	+	11.9021i	0.448579	+	0.448579i
$705$	−11.1213	+	6.78748i	−0.418853	+	0.255631i
$706$	−6.48462	+	6.48462i	−0.244052	+	0.244052i
$707$	−38.6241	+	38.6241i	−1.45261	+	1.45261i
$708$	−1.82348	+	7.53518i	−0.0685304	+	0.283189i
$709$			40.9198i			1.53678i	0.639984	+	0.768388i	$0.278941\pi$
$709$			40.9198i			1.53678i	−0.639984	+	0.768388i	$0.721059\pi$
$710$	−0.683972	+	0.683972i	−0.0256690	+	0.0256690i
$711$	1.33852	+	4.17087i	0.0501983	+	0.156420i
$712$	−4.96408			−0.186037
$713$	−5.22909	+	5.22909i	−0.195831	+	0.195831i
$714$	−7.14280	−	1.72852i	−0.267313	−	0.0646883i
$715$	−10.2535	−	10.2535i	−0.383459	−	0.383459i
$716$			5.98597i			0.223706i
$717$	−23.6221	−	5.71642i	−0.882182	−	0.213484i
$718$			3.70765i			0.138368i
$719$			10.9289i			0.407578i	0.979015	+	0.203789i	$0.0653257\pi$
$719$			10.9289i			0.407578i	−0.979015	+	0.203789i	$0.934674\pi$
$720$	9.36990	+	4.81703i	0.349196	+	0.179520i
$721$	−11.6447			−0.433670
$722$	−3.85667	−	3.85667i	−0.143530	−	0.143530i
$723$	−20.5511	−	4.97326i	−0.764303	−	0.184958i
$724$		−	13.6004i		−	0.505455i
$725$	5.31383	+	0.873632i	0.197351	+	0.0324459i
$726$	1.42468	−	0.869499i	0.0528747	−	0.0322701i
$727$	−18.0365	−	18.0365i	−0.668936	−	0.668936i	0.288534	−	0.957470i	$-0.406832\pi$
$727$	−18.0365	−	18.0365i	−0.668936	−	0.668936i	−0.957470	+	0.288534i	$0.906832\pi$
$728$	−19.6911	+	19.6911i	−0.729802	+	0.729802i
$729$	−3.93372	−	26.7119i	−0.145693	−	0.989330i
$730$			3.27343i			0.121155i
$731$	−26.6353			−0.985142
$732$	−5.54102	−	9.07898i	−0.204802	−	0.335569i
$733$	16.8842	−	16.8842i	0.623631	−	0.623631i	−0.322827	−	0.946458i	$-0.604633\pi$
$733$	16.8842	−	16.8842i	0.623631	−	0.623631i	0.946458	+	0.322827i	$0.104633\pi$
$734$	−7.02156			−0.259171
$735$	6.22141	−	25.7089i	0.229480	−	0.948286i
$736$	17.9148	+	17.9148i	0.660350	+	0.660350i
$737$	−29.0482	−	29.0482i	−1.07000	−	1.07000i
$738$	6.60482	+	3.39551i	0.243127	+	0.124990i
$739$	28.7931	+	28.7931i	1.05917	+	1.05917i	0.998136	+	0.0610363i	$0.0194405\pi$
$739$	28.7931	+	28.7931i	1.05917	+	1.05917i	0.0610363	+	0.998136i	$0.480559\pi$
$740$	4.65191	+	4.65191i	0.171008	+	0.171008i
$741$	0.470722	+	0.771280i	0.0172924	+	0.0283337i
$742$	4.25101	+	4.25101i	0.156060	+	0.156060i
$743$	0.554124	+	0.554124i	0.0203288	+	0.0203288i	0.717198	−	0.696869i	$-0.245424\pi$
$743$	0.554124	+	0.554124i	0.0203288	+	0.0203288i	−0.696869	+	0.717198i	$0.745424\pi$
$744$	−1.80179	−	0.436023i	−0.0660567	−	0.0159854i
$745$	−8.69252			−0.318469
$746$	−4.48757	+	4.48757i	−0.164302	+	0.164302i
$747$	−11.3229	+	22.0248i	−0.414283	+	0.805846i
$748$	−16.5964			−0.606825
$749$			20.0908i			0.734101i
$750$	−0.259155	−	0.424627i	−0.00946301	−	0.0155052i
$751$	11.2124	−	11.2124i	0.409146	−	0.409146i	−0.472295	−	0.881441i	$-0.656574\pi$
$751$	11.2124	−	11.2124i	0.409146	−	0.409146i	0.881441	+	0.472295i	$0.156574\pi$
$752$	18.6798	+	18.6798i	0.681182	+	0.681182i
$753$	−17.3324	−	28.3992i	−0.631627	−	1.03492i
$754$	4.72921	+	6.59021i	0.172228	+	0.240001i
$755$		−	12.7333i		−	0.463414i
$756$	−35.5888	−	30.7316i	−1.29435	−	1.11770i
$757$	13.1485	+	13.1485i	0.477890	+	0.477890i	0.904456	−	0.426566i	$-0.140277\pi$
$757$	13.1485	+	13.1485i	0.477890	+	0.477890i	−0.426566	+	0.904456i	$0.640277\pi$
$758$	−6.19905			−0.225160
$759$	31.7792	−	19.3953i	1.15351	−	0.704003i
$760$			0.111922i			0.00405982i
$761$		−	27.9838i		−	1.01441i	−0.861825	−	0.507207i	$-0.830678\pi$
$761$		−	27.9838i		−	1.01441i	0.861825	−	0.507207i	$-0.169322\pi$
$762$	0.285805	−	1.18104i	0.0103536	−	0.0427844i
$763$		−	61.4280i		−	2.22384i
$764$	22.3587	+	22.3587i	0.808909	+	0.808909i
$765$	−8.94184	+	2.86962i	−0.323293	+	0.103751i
$766$	4.38523	−	4.38523i	0.158445	−	0.158445i
$767$	−12.2421			−0.442036
$768$	3.99293	−	16.5000i	0.144082	−	0.595394i
$769$	11.6609	−	11.6609i	0.420503	−	0.420503i	−0.464874	−	0.885377i	$-0.653900\pi$
$769$	11.6609	−	11.6609i	0.420503	−	0.420503i	0.885377	+	0.464874i	$0.153900\pi$
$770$			3.74766i			0.135056i
$771$	28.4202	+	6.87753i	1.02353	+	0.247688i
$772$	4.19558	−	4.19558i	0.151002	−	0.151002i
$773$	1.94218	−	1.94218i	0.0698553	−	0.0698553i	−0.671316	−	0.741171i	$-0.734271\pi$
$773$	1.94218	−	1.94218i	0.0698553	−	0.0698553i	0.741171	+	0.671316i	$0.234271\pi$
$774$	6.52024	+	3.35203i	0.234365	+	0.120486i
$775$	−0.672629	−	0.672629i	−0.0241615	−	0.0241615i
$776$	6.36269			0.228407
$777$	−14.6098	−	23.9382i	−0.524122	−	0.858777i
$778$	−1.58821			−0.0569400
$779$		−	0.857367i		−	0.0307184i
$780$	−4.09683	+	16.9294i	−0.146690	+	0.606170i
$781$	6.58451	−	6.58451i	0.235612	−	0.235612i
$782$	−6.98944			−0.249942
$783$	−21.4818	+	17.9313i	−0.767698	+	0.640812i
$784$	−53.6313			−1.91540
$785$	14.1320	−	14.1320i	0.504392	−	0.504392i
$786$	−0.287962	+	1.18995i	−0.0102713	+	0.0424441i
$787$			4.34151i			0.154758i	0.997002	+	0.0773790i	$0.0246552\pi$
$787$			4.34151i			0.154758i	−0.997002	+	0.0773790i	$0.975345\pi$
$788$	−47.3482			−1.68671
$789$	19.3951	+	31.7789i	0.690483	+	1.13136i
$790$	−0.419364			−0.0149203
$791$	16.7798	+	16.7798i	0.596621	+	0.596621i
$792$	8.30028	+	4.26714i	0.294938	+	0.151626i
$793$	11.8762	−	11.8762i	0.421737	−	0.421737i
$794$	2.40386	−	2.40386i	0.0853099	−	0.0853099i
$795$	7.46681	+	1.80693i	0.264821	+	0.0640853i
$796$			35.3130i			1.25163i
$797$	−30.1648	+	30.1648i	−1.06849	+	1.06849i	−0.0710167	+	0.997475i	$0.522624\pi$
$797$	−30.1648	+	30.1648i	−1.06849	+	1.06849i	−0.997475	+	0.0710167i	$0.977376\pi$
$798$	0.0549271	−	0.226976i	0.00194440	−	0.00803487i
$799$	−23.5473			−0.833042
$800$	−2.30442	+	2.30442i	−0.0814736	+	0.0814736i
$801$	12.6027	−	4.04446i	0.445295	−	0.142904i
$802$	6.41867	+	6.41867i	0.226651	+	0.226651i
$803$		−	31.5128i		−	1.11206i
$804$	−11.6063	+	47.9611i	−0.409324	+	1.69146i
$805$		−	36.6881i		−	1.29309i
$806$		−	1.43282i		−	0.0504690i
$807$	20.2464	−	12.3566i	0.712706	−	0.434973i
$808$	−13.0229			−0.458146
$809$	6.19246	+	6.19246i	0.217715	+	0.217715i	0.807535	−	0.589820i	$-0.200801\pi$
$809$	6.19246	+	6.19246i	0.217715	+	0.217715i	−0.589820	+	0.807535i	$0.700801\pi$
$810$	2.55007	+	0.422850i	0.0896005	+	0.0148574i
$811$		−	5.46729i		−	0.191983i	−0.995382	−	0.0959913i	$-0.969398\pi$
$811$		−	5.46729i		−	0.191983i	0.995382	−	0.0959913i	$-0.0306021\pi$
$812$	−7.90570	+	48.0861i	−0.277436	+	1.68749i
$813$	−13.5977	−	22.2799i	−0.476893	−	0.781392i
$814$	1.92655	+	1.92655i	0.0675254	+	0.0675254i
$815$	10.9092	−	10.9092i	0.382133	−	0.382133i
$816$	9.91948	+	16.2531i	0.347251	+	0.568973i
$817$		−	0.846388i		−	0.0296114i
$818$	−5.43293			−0.189958
$819$	33.9482	−	66.0348i	1.18625	−	2.30744i
$820$	11.6865	−	11.6865i	0.408112	−	0.408112i
$821$	−21.1184			−0.737038			−0.368519	−	0.929620i	$-0.620135\pi$
$821$	−21.1184			−0.737038			−0.368519	+	0.929620i	$0.620135\pi$
$822$	7.66767	+	1.85554i	0.267441	+	0.0647193i
$823$	−0.538591	−	0.538591i	−0.0187741	−	0.0187741i	0.697657	−	0.716432i	$-0.254226\pi$
$823$	−0.538591	−	0.538591i	−0.0187741	−	0.0187741i	−0.716432	+	0.697657i	$0.754226\pi$
$824$	−1.96312	−	1.96312i	−0.0683887	−	0.0683887i
$825$	2.49485	+	4.08783i	0.0868596	+	0.142320i
$826$	2.23724	+	2.23724i	0.0778436	+	0.0778436i
$827$	12.1041	+	12.1041i	0.420901	+	0.420901i	0.885514	−	0.464613i	$-0.153807\pi$
$827$	12.1041	+	12.1041i	0.420901	+	0.420901i	−0.464613	+	0.885514i	$0.653807\pi$
$828$	−39.7727	−	20.4470i	−1.38220	−	0.710583i
$829$	1.32966	+	1.32966i	0.0461810	+	0.0461810i	0.729820	−	0.683639i	$-0.239604\pi$
$829$	1.32966	+	1.32966i	0.0461810	+	0.0461810i	−0.683639	+	0.729820i	$0.739604\pi$
$830$	−1.67649	−	1.67649i	−0.0581918	−	0.0581918i
$831$	2.53334	−	10.4686i	0.0878807	−	0.363151i
$832$	31.9269			1.10687
$833$	33.8031	−	33.8031i	1.17121	−	1.17121i
$834$	−0.813896	−	1.33357i	−0.0281829	−	0.0461778i
$835$	19.7842			0.684661
$836$		−	0.527383i		−	0.0182399i
$837$	4.92959	−	0.361030i	0.170392	−	0.0124790i
$838$	−4.17161	+	4.17161i	−0.144106	+	0.144106i
$839$	7.18039	+	7.18039i	0.247895	+	0.247895i	0.820106	−	0.572211i	$-0.193914\pi$
$839$	7.18039	+	7.18039i	0.247895	+	0.247895i	−0.572211	+	0.820106i	$0.693914\pi$
$840$	7.85040	−	4.79120i	0.270865	−	0.165312i
$841$	27.4735	+	9.28466i	0.947363	+	0.320161i
$842$		−	0.844437i		−	0.0291012i
$843$	−18.1501	−	4.39223i	−0.625122	−	0.151276i
$844$	−3.57230	−	3.57230i	−0.122964	−	0.122964i
$845$	−14.5044			−0.498968
$846$	5.76430	+	2.96340i	0.198181	+	0.101884i
$847$			15.8337i			0.544053i
$848$		−	15.5765i		−	0.534900i
$849$	12.8450	+	3.10844i	0.440841	+	0.106681i
$850$		−	0.899066i		−	0.0308377i
$851$	−18.8601	−	18.8601i	−0.646517	−	0.646517i
$852$	−10.8716	−	2.63087i	−0.372455	−	0.0901322i
$853$	−39.4619	+	39.4619i	−1.35115	+	1.35115i	−0.466774	+	0.884377i	$0.654584\pi$
$853$	−39.4619	+	39.4619i	−1.35115	+	1.35115i	−0.884377	+	0.466774i	$0.845416\pi$
$854$	−4.34077			−0.148538
$855$	−0.0911876	−	0.284144i	−0.00311855	−	0.00971753i
$856$	−3.38702	+	3.38702i	−0.115766	+	0.115766i
$857$			8.83514i			0.301803i	0.988549	+	0.150901i	$0.0482176\pi$
$857$			8.83514i			0.301803i	−0.988549	+	0.150901i	$0.951782\pi$
$858$	−1.69666	+	7.01115i	−0.0579231	+	0.239357i
$859$	5.44548	−	5.44548i	0.185797	−	0.185797i	−0.608079	−	0.793876i	$-0.708060\pi$
$859$	5.44548	−	5.44548i	0.185797	−	0.185797i	0.793876	+	0.608079i	$0.208060\pi$
$860$	11.5369	−	11.5369i	0.393405	−	0.393405i
$861$	−60.1375	+	36.7026i	−2.04948	+	1.25082i
$862$	3.51501	+	3.51501i	0.119722	+	0.119722i
$863$	19.4888			0.663407			0.331703	−	0.943384i	$-0.392377\pi$
$863$	19.4888			0.663407			0.331703	+	0.943384i	$0.392377\pi$
$864$	−1.23689	−	16.8887i	−0.0420798	−	0.574567i
$865$	−24.4547			−0.831484
$866$		−	8.73049i		−	0.296674i
$867$	12.1226	+	2.93360i	0.411704	+	0.0996302i
$868$	6.08678	−	6.08678i	0.206599	−	0.206599i
$869$	4.03716			0.136951
$870$	−1.00614	−	2.48280i	−0.0341113	−	0.0841749i
$871$	−77.9202			−2.64023
$872$	10.3559	−	10.3559i	0.350695	−	0.350695i
$873$	−16.1535	+	5.18397i	−0.546712	+	0.175451i
$874$		−	0.222103i		−	0.00751275i
$875$	4.71926			0.159540
$876$	−32.3108	+	19.7197i	−1.09168	+	0.666266i
$877$	−11.8037			−0.398583			−0.199292	−	0.979940i	$-0.563864\pi$
$877$	−11.8037			−0.398583			−0.199292	+	0.979940i	$0.563864\pi$
$878$	3.15297	+	3.15297i	0.106408	+	0.106408i
$879$	−27.2346	−	44.6240i	−0.918600	−	1.50513i
$880$	6.86607	−	6.86607i	0.231455	−	0.231455i
$881$	5.23474	−	5.23474i	0.176363	−	0.176363i	−0.613405	−	0.789768i	$-0.710201\pi$
$881$	5.23474	−	5.23474i	0.176363	−	0.176363i	0.789768	+	0.613405i	$0.210201\pi$
$882$	−12.5290	+	4.02080i	−0.421873	+	0.135388i
$883$			42.9410i			1.44508i	0.691329	+	0.722540i	$0.257026\pi$
$883$			42.9410i			1.44508i	−0.691329	+	0.722540i	$0.742974\pi$
$884$	−22.2595	+	22.2595i	−0.748668	+	0.748668i
$885$	3.92967	+	0.950960i	0.132094	+	0.0319662i
$886$	3.27477			0.110018
$887$	26.9817	−	26.9817i	0.905957	−	0.905957i	−0.0899859	−	0.995943i	$-0.528682\pi$
$887$	26.9817	−	26.9817i	0.905957	−	0.905957i	0.995943	+	0.0899859i	$0.0286822\pi$
$888$	1.57264	−	6.49863i	0.0527742	−	0.218080i
$889$	8.15116	+	8.15116i	0.273381	+	0.273381i
$890$			1.26715i			0.0424750i
$891$	−24.5492	−	4.07072i	−0.822430	−	0.136374i
$892$		−	17.7804i		−	0.595332i
$893$		−	0.748259i		−	0.0250395i
$894$	2.25271	+	3.69108i	0.0753420	+	0.123448i
$895$	3.12174			0.104348
$896$	−27.5850	−	27.5850i	−0.921550	−	0.921550i
$897$	16.6097	−	68.6365i	0.554581	−	2.29170i
$898$		−	6.57900i		−	0.219544i
$899$	−2.98660	−	4.16186i	−0.0996088	−	0.138806i
$900$	2.63014	−	5.11605i	0.0876714	−	0.170535i
$901$	9.81769	+	9.81769i	0.327075	+	0.327075i
$902$	4.83987	−	4.83987i	0.161150	−	0.161150i
$903$	−59.3674	+	36.2327i	−1.97562	+	1.20575i
$904$			5.65768i			0.188172i
$905$	−7.09274			−0.235771
$906$	−5.40692	+	3.29991i	−0.179633	+	0.109632i
$907$	13.5415	−	13.5415i	0.449637	−	0.449637i	−0.445597	−	0.895234i	$-0.647008\pi$
$907$	13.5415	−	13.5415i	0.449637	−	0.449637i	0.895234	+	0.445597i	$0.147008\pi$
$908$	0.972119			0.0322609
$909$	33.0624	−	10.6104i	1.09661	−	0.351924i
$910$	5.02644	+	5.02644i	0.166625	+	0.166625i
$911$	−0.159234	−	0.159234i	−0.00527565	−	0.00527565i	0.704464	−	0.709740i	$-0.251187\pi$
$911$	−0.159234	−	0.159234i	−0.00527565	−	0.00527565i	−0.709740	+	0.704464i	$0.751187\pi$
$912$	−0.516474	+	0.315211i	−0.0171022	+	0.0104377i
$913$	16.1393	+	16.1393i	0.534134	+	0.534134i
$914$	−3.47321	−	3.47321i	−0.114884	−	0.114884i
$915$	−4.73478	+	2.88969i	−0.156527	+	0.0955303i
$916$	−22.1852	−	22.1852i	−0.733020	−	0.733020i
$917$	−8.21268	−	8.21268i	−0.271207	−	0.271207i
$918$	3.53584	+	3.05327i	0.116700	+	0.100773i
$919$	−33.8228			−1.11571			−0.557856	−	0.829938i	$-0.688376\pi$
$919$	−33.8228			−1.11571			−0.557856	+	0.829938i	$0.688376\pi$
$920$	6.18509	−	6.18509i	0.203916	−	0.203916i
$921$	50.9777	−	31.1124i	1.67977	−	1.02519i
$922$	3.13940			0.103391
$923$		−	17.6626i		−	0.581371i
$924$	−36.9917	+	22.5765i	−1.21694	+	0.742712i
$925$	2.42602	−	2.42602i	0.0797670	−	0.0797670i
$926$	4.71127	+	4.71127i	0.154822	+	0.154822i
$927$	6.58339	+	3.38449i	0.216227	+	0.111161i
$928$	−14.2585	+	10.2321i	−0.468059	+	0.335885i
$929$		−	13.2730i		−	0.435472i	−0.976008	−	0.217736i	$-0.930133\pi$
$929$		−	13.2730i		−	0.435472i	0.976008	−	0.217736i	$-0.0698672\pi$
$930$	−0.111301	+	0.459932i	−0.00364971	+	0.0150818i
$931$	1.07416	+	1.07416i	0.0352041	+	0.0352041i
$932$	−22.6791			−0.742878
$933$	17.9255	+	29.3710i	0.586854	+	0.961563i
$934$		−	4.24196i		−	0.138801i
$935$			8.65519i			0.283055i
$936$	16.8557	−	5.40934i	0.550946	−	0.176810i
$937$		−	9.86335i		−	0.322222i	−0.986936	−	0.161111i	$-0.948492\pi$
$937$		−	9.86335i		−	0.322222i	0.986936	−	0.161111i	$-0.0515077\pi$
$938$	14.2399	+	14.2399i	0.464950	+	0.464950i
$939$	2.74972	−	11.3627i	0.0897339	−	0.370809i
$940$	10.1993	−	10.1993i	0.332665	−	0.332665i
$941$	−4.43751			−0.144659			−0.0723293	−	0.997381i	$-0.523043\pi$
$941$	−4.43751			−0.144659			−0.0723293	+	0.997381i	$0.523043\pi$
$942$	−9.66320	−	2.33845i	−0.314844	−	0.0761907i
$943$	−47.3805	+	47.3805i	−1.54292	+	1.54292i
$944$		−	8.19769i		−	0.266812i
$945$	−16.0268	+	18.5599i	−0.521353	+	0.603753i
$946$	4.77790	−	4.77790i	0.155343	−	0.155343i
$947$	−28.0807	+	28.0807i	−0.912500	+	0.912500i	−0.996468	−	0.0839685i	$-0.973240\pi$
$947$	−28.0807	+	28.0807i	−0.912500	+	0.912500i	0.0839685	+	0.996468i	$0.473240\pi$
$948$	−2.52632	−	4.13939i	−0.0820511	−	0.134441i
$949$	−42.2658	−	42.2658i	−1.37201	−	1.37201i
$950$	0.0285696			0.000926919
$951$	24.8219	−	15.1491i	0.804905	−	0.491244i
$952$	16.6217			0.538713
$953$			55.2531i			1.78982i	0.446244	+	0.894911i	$0.352761\pi$
$953$			55.2531i			1.78982i	−0.446244	+	0.894911i	$0.647239\pi$
$954$	−1.16779	−	3.63889i	−0.0378087	−	0.117813i
$955$	11.6603	−	11.6603i	0.377318	−	0.377318i
$956$	26.9062			0.870210
$957$	9.68596	+	23.9016i	0.313103	+	0.772629i
$958$	−9.52082			−0.307604
$959$	−52.9200	+	52.9200i	−1.70888	+	1.70888i
$960$	−10.2484	−	2.48007i	−0.330767	−	0.0800439i
$961$		−	30.0951i		−	0.970811i
$962$	5.16786			0.166618
$963$	5.83934	−	11.3585i	0.188170	−	0.366021i
$964$	23.4083			0.753931
$965$	−2.18804	−	2.18804i	−0.0704354	−	0.0704354i
$966$	−15.5788	+	9.50791i	−0.501238	+	0.305912i
$967$	25.0324	−	25.0324i	0.804987	−	0.804987i	−0.178883	−	0.983870i	$-0.557248\pi$
$967$	25.0324	−	25.0324i	0.804987	−	0.804987i	0.983870	+	0.178883i	$0.0572484\pi$
$968$	−2.66934	+	2.66934i	−0.0857959	+	0.0857959i
$969$	0.126854	−	0.524200i	0.00407513	−	0.0168397i
$970$		−	1.62417i		−	0.0521488i
$971$	27.9886	−	27.9886i	0.898196	−	0.898196i	−0.0970808	−	0.995276i	$-0.530951\pi$
$971$	27.9886	−	27.9886i	0.898196	−	0.898196i	0.995276	+	0.0970808i	$0.0309505\pi$
$972$	11.1883	+	27.7181i	0.358864	+	0.889060i
$973$	14.8212			0.475146
$974$	5.60303	−	5.60303i	0.179533	−	0.179533i
$975$	8.82885	+	2.13654i	0.282749	+	0.0684239i
$976$	7.95271	+	7.95271i	0.254560	+	0.254560i
$977$			34.0288i			1.08868i	0.838866	+	0.544338i	$0.183219\pi$
$977$			34.0288i			1.08868i	−0.838866	+	0.544338i	$0.816781\pi$
$978$	−7.45952	−	1.80517i	−0.238529	−	0.0577228i
$979$		−	12.1987i		−	0.389872i
$980$			29.2832i			0.935416i
$981$	−17.8539	+	34.7287i	−0.570032	+	1.10880i
$982$	4.27171			0.136316
$983$	18.2114	+	18.2114i	0.580852	+	0.580852i	0.935137	−	0.354285i	$-0.115276\pi$
$983$	18.2114	+	18.2114i	0.580852	+	0.580852i	−0.354285	+	0.935137i	$0.615276\pi$
$984$	−16.3259	−	3.95078i	−0.520450	−	0.125946i
$985$			24.6926i			0.786770i
$986$	0.785453	−	4.77748i	0.0250139	−	0.152146i
$987$	−52.4844	+	32.0319i	−1.67060	+	1.01959i
$988$	−0.707339	−	0.707339i	−0.0225034	−	0.0225034i
$989$	−46.7737	+	46.7737i	−1.48732	+	1.48732i
$990$	1.08925	−	2.11876i	0.0346186	−	0.0673387i
$991$		−	19.5569i		−	0.621244i	−0.950534	−	0.310622i	$-0.899463\pi$
$991$		−	19.5569i		−	0.621244i	0.950534	−	0.310622i	$-0.100537\pi$
$992$	3.10004			0.0984264
$993$	−13.2480	−	21.7069i	−0.420413	−	0.688849i
$994$	−3.22784	+	3.22784i	−0.102381	+	0.102381i
$995$	18.4161			0.583828
$996$	6.44855	−	26.6475i	0.204330	−	0.844357i
$997$	−0.181138	−	0.181138i	−0.00573669	−	0.00573669i	0.704233	−	0.709969i	$-0.251291\pi$
$997$	−0.181138	−	0.181138i	−0.00573669	−	0.00573669i	−0.709969	+	0.704233i	$0.751291\pi$
$998$	−0.700456	−	0.700456i	−0.0221725	−	0.0221725i
$999$	1.30215	+	17.7799i	0.0411983	+	0.562531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.d.41.9	yes	36
3.2	odd	2		435.2.q.c.41.10	✓	36
29.17	odd	4		435.2.q.c.191.10	yes	36
87.17	even	4	inner	435.2.q.d.191.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.10	✓	36	3.2	odd	2
435.2.q.c.191.10	yes	36	29.17	odd	4
435.2.q.d.41.9	yes	36	1.1	even	1	trivial
435.2.q.d.191.9	yes	36	87.17	even	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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203088 - 0.203088i) q^{2} +(0.407389 - 1.68346i) q^{3} +1.91751i q^{4} +1.00000 q^{5} +(-0.259155 - 0.424627i) q^{6} +4.71926 q^{7} +(0.795601 + 0.795601i) q^{8} +(-2.66807 - 1.37164i) q^{9} +O(q^{10})\)	\(q+(0.203088 - 0.203088i) q^{2} +(0.407389 - 1.68346i) q^{3} +1.91751i q^{4} +1.00000 q^{5} +(-0.259155 - 0.424627i) q^{6} +4.71926 q^{7} +(0.795601 + 0.795601i) q^{8} +(-2.66807 - 1.37164i) q^{9} +(0.203088 - 0.203088i) q^{10} +(-1.95511 + 1.95511i) q^{11} +(3.22805 + 0.781172i) q^{12} +5.24447i q^{13} +(0.958428 - 0.958428i) q^{14} +(0.407389 - 1.68346i) q^{15} -3.51187 q^{16} +(2.21348 - 2.21348i) q^{17} +(-0.820419 + 0.263289i) q^{18} +(0.0703377 + 0.0703377i) q^{19} +1.91751i q^{20} +(1.92257 - 7.94469i) q^{21} +0.794119i q^{22} -7.77411i q^{23} +(1.66348 - 1.01524i) q^{24} +1.00000 q^{25} +(1.06509 + 1.06509i) q^{26} +(-3.39605 + 3.93279i) q^{27} +9.04924i q^{28} +(5.31383 + 0.873632i) q^{29} +(-0.259155 - 0.424627i) q^{30} +(-0.672629 - 0.672629i) q^{31} +(-2.30442 + 2.30442i) q^{32} +(2.49485 + 4.08783i) q^{33} -0.899066i q^{34} +4.71926 q^{35} +(2.63014 - 5.11605i) q^{36} +(2.42602 - 2.42602i) q^{37} +0.0285696 q^{38} +(8.82885 + 2.13654i) q^{39} +(0.795601 + 0.795601i) q^{40} +(-6.09464 - 6.09464i) q^{41} +(-1.22302 - 2.00393i) q^{42} +(-6.01660 - 6.01660i) q^{43} +(-3.74893 - 3.74893i) q^{44} +(-2.66807 - 1.37164i) q^{45} +(-1.57883 - 1.57883i) q^{46} +(-5.31905 - 5.31905i) q^{47} +(-1.43069 + 5.91208i) q^{48} +15.2714 q^{49} +(0.203088 - 0.203088i) q^{50} +(-2.82456 - 4.62806i) q^{51} -10.0563 q^{52} +4.43540i q^{53} +(0.109007 + 1.48840i) q^{54} +(-1.95511 + 1.95511i) q^{55} +(3.75465 + 3.75465i) q^{56} +(0.147065 - 0.0897559i) q^{57} +(1.25660 - 0.901753i) q^{58} +2.33428i q^{59} +(3.22805 + 0.781172i) q^{60} +(-2.26452 - 2.26452i) q^{61} -0.273206 q^{62} +(-12.5913 - 6.47315i) q^{63} -6.08773i q^{64} +5.24447i q^{65} +(1.33687 + 0.323515i) q^{66} +14.8576i q^{67} +(4.24438 + 4.24438i) q^{68} +(-13.0874 - 3.16709i) q^{69} +(0.958428 - 0.958428i) q^{70} -3.36785 q^{71} +(-1.03144 - 3.21400i) q^{72} +(-8.05912 + 8.05912i) q^{73} -0.985393i q^{74} +(0.407389 - 1.68346i) q^{75} +(-0.134873 + 0.134873i) q^{76} +(-9.22666 + 9.22666i) q^{77} +(2.22694 - 1.35913i) q^{78} +(-1.03247 - 1.03247i) q^{79} -3.51187 q^{80} +(5.23718 + 7.31928i) q^{81} -2.47550 q^{82} -8.25497i q^{83} +(15.2340 + 3.68656i) q^{84} +(2.21348 - 2.21348i) q^{85} -2.44381 q^{86} +(3.63552 - 8.58970i) q^{87} -3.11097 q^{88} +(-3.11970 + 3.11970i) q^{89} +(-0.820419 + 0.263289i) q^{90} +24.7500i q^{91} +14.9069 q^{92} +(-1.40636 + 0.858322i) q^{93} -2.16047 q^{94} +(0.0703377 + 0.0703377i) q^{95} +(2.94060 + 4.81819i) q^{96} +(3.99867 - 3.99867i) q^{97} +(3.10146 - 3.10146i) q^{98} +(7.89806 - 2.53465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8}+O(q^{10}) \) 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8	\( 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8} + 4 q^{10} + 12 q^{11} + 10 q^{12} - 28 q^{14} + 2 q^{15} - 60 q^{16} + 20 q^{17} + 32 q^{18} + 16 q^{19} - 12 q^{21} + 24 q^{24} + 36 q^{25} - 4 q^{26} - 22 q^{27} + 28 q^{29} - 8 q^{30} - 8 q^{31} + 16 q^{32} + 8 q^{33} + 8 q^{35} - 28 q^{36} - 4 q^{37} - 24 q^{38} - 24 q^{39} - 4 q^{40} - 48 q^{41} + 8 q^{42} + 4 q^{43} - 16 q^{44} + 20 q^{46} + 20 q^{47} - 66 q^{48} + 28 q^{49} + 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} + 84 q^{56} - 28 q^{57} - 64 q^{58} + 10 q^{60} + 20 q^{61} - 8 q^{62} - 32 q^{63} - 8 q^{66} - 60 q^{68} - 36 q^{69} - 28 q^{70} + 16 q^{71} + 64 q^{72} + 8 q^{73} + 2 q^{75} + 16 q^{76} - 32 q^{77} + 48 q^{78} + 12 q^{79} - 60 q^{80} - 60 q^{81} + 56 q^{82} + 100 q^{84} + 20 q^{85} - 8 q^{86} - 10 q^{87} - 24 q^{88} - 20 q^{89} + 32 q^{90} + 16 q^{92} - 24 q^{93} + 52 q^{94} + 16 q^{95} + 8 q^{96} + 4 q^{97} + 8 q^{98} + 32 q^{99}+O(q^{100}) \) 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8 + 4 * q^10 + 12 * q^11 + 10 * q^12 - 28 * q^14 + 2 * q^15 - 60 * q^16 + 20 * q^17 + 32 * q^18 + 16 * q^19 - 12 * q^21 + 24 * q^24 + 36 * q^25 - 4 * q^26 - 22 * q^27 + 28 * q^29 - 8 * q^30 - 8 * q^31 + 16 * q^32 + 8 * q^33 + 8 * q^35 - 28 * q^36 - 4 * q^37 - 24 * q^38 - 24 * q^39 - 4 * q^40 - 48 * q^41 + 8 * q^42 + 4 * q^43 - 16 * q^44 + 20 * q^46 + 20 * q^47 - 66 * q^48 + 28 * q^49 + 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 + 84 * q^56 - 28 * q^57 - 64 * q^58 + 10 * q^60 + 20 * q^61 - 8 * q^62 - 32 * q^63 - 8 * q^66 - 60 * q^68 - 36 * q^69 - 28 * q^70 + 16 * q^71 + 64 * q^72 + 8 * q^73 + 2 * q^75 + 16 * q^76 - 32 * q^77 + 48 * q^78 + 12 * q^79 - 60 * q^80 - 60 * q^81 + 56 * q^82 + 100 * q^84 + 20 * q^85 - 8 * q^86 - 10 * q^87 - 24 * q^88 - 20 * q^89 + 32 * q^90 + 16 * q^92 - 24 * q^93 + 52 * q^94 + 16 * q^95 + 8 * q^96 + 4 * q^97 + 8 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more