LMFDB - Embedded newform 961.2.c.e.439.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(439,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("961.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	961.439
Dual form			961.2.c.e.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} +(1.61803 - 2.80252i) q^{3} +0.618034 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})$	\(q+1.61803 q^{2} +(1.61803 - 2.80252i) q^{3} +0.618034 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(-3.73607 - 6.47106i) q^{9} +(-0.809017 - 1.40126i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{12} +(1.61803 + 2.80252i) q^{13} +(-0.190983 + 0.330792i) q^{14} -3.23607 q^{15} -4.85410 q^{16} +(-0.381966 + 0.661585i) q^{17} +(-6.04508 - 10.4704i) q^{18} +(1.11803 - 1.93649i) q^{19} +(-0.309017 - 0.535233i) q^{20} +(0.381966 + 0.661585i) q^{21} +(-1.61803 - 2.80252i) q^{22} +5.70820 q^{23} +(-3.61803 + 6.26662i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.61803 + 4.53457i) q^{26} -14.4721 q^{27} +(-0.0729490 + 0.126351i) q^{28} +2.76393 q^{29} -5.23607 q^{30} -3.38197 q^{32} -6.47214 q^{33} +(-0.618034 + 1.07047i) q^{34} +0.236068 q^{35} +(-2.30902 - 3.99933i) q^{36} +(1.00000 - 1.73205i) q^{37} +(1.80902 - 3.13331i) q^{38} +10.4721 q^{39} +(1.11803 + 1.93649i) q^{40} +(-3.50000 - 6.06218i) q^{41} +(0.618034 + 1.07047i) q^{42} +(-0.618034 + 1.07047i) q^{43} +(-0.618034 - 1.07047i) q^{44} +(-3.73607 + 6.47106i) q^{45} +9.23607 q^{46} +2.47214 q^{47} +(-7.85410 + 13.6037i) q^{48} +(3.47214 + 6.01392i) q^{49} +(3.23607 - 5.60503i) q^{50} +(1.23607 + 2.14093i) q^{51} +(1.00000 + 1.73205i) q^{52} +(5.23607 + 9.06914i) q^{53} -23.4164 q^{54} +(-1.00000 + 1.73205i) q^{55} +(0.263932 - 0.457144i) q^{56} +(-3.61803 - 6.26662i) q^{57} +4.47214 q^{58} +(-1.11803 + 1.93649i) q^{59} -2.00000 q^{60} +8.18034 q^{61} +1.76393 q^{63} +4.23607 q^{64} +(1.61803 - 2.80252i) q^{65} -10.4721 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(9.23607 - 15.9973i) q^{69} +0.381966 q^{70} +(4.59017 + 7.95041i) q^{71} +(8.35410 + 14.4697i) q^{72} +(-4.23607 - 7.33708i) q^{73} +(1.61803 - 2.80252i) q^{74} +(-6.47214 - 11.2101i) q^{75} +(0.690983 - 1.19682i) q^{76} +0.472136 q^{77} +16.9443 q^{78} +(5.85410 - 10.1396i) q^{79} +(2.42705 + 4.20378i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(-5.66312 - 9.80881i) q^{82} +(7.47214 + 12.9421i) q^{83} +(0.236068 + 0.408882i) q^{84} +0.763932 q^{85} +(-1.00000 + 1.73205i) q^{86} +(4.47214 - 7.74597i) q^{87} +(2.23607 + 3.87298i) q^{88} +11.7082 q^{89} +(-6.04508 + 10.4704i) q^{90} -0.763932 q^{91} +3.52786 q^{92} +4.00000 q^{94} -2.23607 q^{95} +(-5.47214 + 9.47802i) q^{96} -15.9443 q^{97} +(5.61803 + 9.73072i) q^{98} +(-7.47214 + 12.9421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 6 q^{6} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 6 * q^6 + 4 * q^7 - 6 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 6 q^{6} + 4 q^{7} - 6 q^{9} - q^{10} - 4 q^{11} + 4 q^{12} + 2 q^{13} - 3 q^{14} - 4 q^{15} - 6 q^{16} - 6 q^{17} - 13 q^{18} + q^{20} + 6 q^{21} - 2 q^{22} - 4 q^{23} - 10 q^{24} + 8 q^{25} + 6 q^{26} - 40 q^{27} - 7 q^{28} + 20 q^{29} - 12 q^{30} - 18 q^{32} - 8 q^{33} + 2 q^{34} - 8 q^{35} - 7 q^{36} + 4 q^{37} + 5 q^{38} + 24 q^{39} - 14 q^{41} - 2 q^{42} + 2 q^{43} + 2 q^{44} - 6 q^{45} + 28 q^{46} - 8 q^{47} - 18 q^{48} - 4 q^{49} + 4 q^{50} - 4 q^{51} + 4 q^{52} + 12 q^{53} - 40 q^{54} - 4 q^{55} + 10 q^{56} - 10 q^{57} - 8 q^{60} - 12 q^{61} + 16 q^{63} + 8 q^{64} + 2 q^{65} - 24 q^{66} - 16 q^{67} + 8 q^{68} + 28 q^{69} + 6 q^{70} - 4 q^{71} + 20 q^{72} - 8 q^{73} + 2 q^{74} - 8 q^{75} + 5 q^{76} - 16 q^{77} + 32 q^{78} + 10 q^{79} + 3 q^{80} - 22 q^{81} - 7 q^{82} + 12 q^{83} - 8 q^{84} + 12 q^{85} - 4 q^{86} + 20 q^{89} - 13 q^{90} - 12 q^{91} + 32 q^{92} + 16 q^{94} - 4 q^{96} - 28 q^{97} + 18 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 6 * q^6 + 4 * q^7 - 6 * q^9 - q^10 - 4 * q^11 + 4 * q^12 + 2 * q^13 - 3 * q^14 - 4 * q^15 - 6 * q^16 - 6 * q^17 - 13 * q^18 + q^20 + 6 * q^21 - 2 * q^22 - 4 * q^23 - 10 * q^24 + 8 * q^25 + 6 * q^26 - 40 * q^27 - 7 * q^28 + 20 * q^29 - 12 * q^30 - 18 * q^32 - 8 * q^33 + 2 * q^34 - 8 * q^35 - 7 * q^36 + 4 * q^37 + 5 * q^38 + 24 * q^39 - 14 * q^41 - 2 * q^42 + 2 * q^43 + 2 * q^44 - 6 * q^45 + 28 * q^46 - 8 * q^47 - 18 * q^48 - 4 * q^49 + 4 * q^50 - 4 * q^51 + 4 * q^52 + 12 * q^53 - 40 * q^54 - 4 * q^55 + 10 * q^56 - 10 * q^57 - 8 * q^60 - 12 * q^61 + 16 * q^63 + 8 * q^64 + 2 * q^65 - 24 * q^66 - 16 * q^67 + 8 * q^68 + 28 * q^69 + 6 * q^70 - 4 * q^71 + 20 * q^72 - 8 * q^73 + 2 * q^74 - 8 * q^75 + 5 * q^76 - 16 * q^77 + 32 * q^78 + 10 * q^79 + 3 * q^80 - 22 * q^81 - 7 * q^82 + 12 * q^83 - 8 * q^84 + 12 * q^85 - 4 * q^86 + 20 * q^89 - 13 * q^90 - 12 * q^91 + 32 * q^92 + 16 * q^94 - 4 * q^96 - 28 * q^97 + 18 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.61803			1.14412			0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803			1.14412			0.572061	+	0.820211i	$0.306144\pi$
$3$	1.61803	−	2.80252i	0.934172	−	1.61803i	0.158069	−	0.987428i	$-0.449473\pi$
$3$	1.61803	−	2.80252i	0.934172	−	1.61803i	0.776103	−	0.630606i	$-0.217194\pi$
$4$	0.618034			0.309017
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	2.61803	−	4.53457i	1.06881	−	1.85123i
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	−0.887469	−	0.460866i	$-0.847539\pi$
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	0.842857	+	0.538138i	$0.180872\pi$
$8$	−2.23607			−0.790569
$9$	−3.73607	−	6.47106i	−1.24536	−	2.15702i
$10$	−0.809017	−	1.40126i	−0.255834	−	0.443117i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	1.61803	+	2.80252i	0.448762	+	0.777278i	0.998306	−	0.0581865i	$-0.0185318\pi$
$13$	1.61803	+	2.80252i	0.448762	+	0.777278i	−0.549544	+	0.835465i	$0.685198\pi$
$14$	−0.190983	+	0.330792i	−0.0510424	+	0.0884080i
$15$	−3.23607			−0.835549
$16$	−4.85410			−1.21353
$17$	−0.381966	+	0.661585i	−0.0926404	+	0.160458i	−0.908621	−	0.417621i	$-0.862864\pi$
$17$	−0.381966	+	0.661585i	−0.0926404	+	0.160458i	0.815981	+	0.578079i	$0.196197\pi$
$18$	−6.04508	−	10.4704i	−1.42484	−	2.46790i
$19$	1.11803	−	1.93649i	0.256495	−	0.444262i	−0.708806	−	0.705404i	$-0.750766\pi$
$19$	1.11803	−	1.93649i	0.256495	−	0.444262i	0.965300	+	0.261142i	$0.0840991\pi$
$20$	−0.309017	−	0.535233i	−0.0690983	−	0.119682i
$21$	0.381966	+	0.661585i	0.0833518	+	0.144370i
$22$	−1.61803	−	2.80252i	−0.344966	−	0.597499i
$23$	5.70820			1.19024			0.595121	−	0.803636i	$-0.297104\pi$
$23$	5.70820			1.19024			0.595121	+	0.803636i	$0.297104\pi$
$24$	−3.61803	+	6.26662i	−0.738528	+	1.27917i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	2.61803	+	4.53457i	0.513439	+	0.889302i
$27$	−14.4721			−2.78516
$28$	−0.0729490	+	0.126351i	−0.0137861	+	0.0238782i
$29$	2.76393			0.513249			0.256625	−	0.966511i	$-0.417390\pi$
$29$	2.76393			0.513249			0.256625	+	0.966511i	$0.417390\pi$
$30$	−5.23607			−0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	−6.47214			−1.12665
$34$	−0.618034	+	1.07047i	−0.105992	+	0.183583i
$35$	0.236068			0.0399028
$36$	−2.30902	−	3.99933i	−0.384836	−	0.666556i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	1.80902	−	3.13331i	0.293461	−	0.508290i
$39$	10.4721			1.67688
$40$	1.11803	+	1.93649i	0.176777	+	0.306186i
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	−0.998504	−	0.0546823i	$-0.982585\pi$
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	0.451896	−	0.892071i	$-0.350748\pi$
$42$	0.618034	+	1.07047i	0.0953647	+	0.165177i
$43$	−0.618034	+	1.07047i	−0.0942493	+	0.163245i	−0.909295	−	0.416152i	$-0.863378\pi$
$43$	−0.618034	+	1.07047i	−0.0942493	+	0.163245i	0.815046	+	0.579397i	$0.196712\pi$
$44$	−0.618034	−	1.07047i	−0.0931721	−	0.161379i
$45$	−3.73607	+	6.47106i	−0.556940	+	0.964649i
$46$	9.23607			1.36178
$47$	2.47214			0.360598			0.180299	−	0.983612i	$-0.442293\pi$
$47$	2.47214			0.360598			0.180299	+	0.983612i	$0.442293\pi$
$48$	−7.85410	+	13.6037i	−1.13364	+	1.96353i
$49$	3.47214	+	6.01392i	0.496019	+	0.859131i
$50$	3.23607	−	5.60503i	0.457649	−	0.792672i
$51$	1.23607	+	2.14093i	0.173084	+	0.299791i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	5.23607	+	9.06914i	0.719229	+	1.24574i	0.961306	+	0.275484i	$0.0888382\pi$
$53$	5.23607	+	9.06914i	0.719229	+	1.24574i	−0.242076	+	0.970257i	$0.577828\pi$
$54$	−23.4164			−3.18657
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	0.263932	−	0.457144i	0.0352694	−	0.0610884i
$57$	−3.61803	−	6.26662i	−0.479220	−	0.830034i
$58$	4.47214			0.587220
$59$	−1.11803	+	1.93649i	−0.145556	+	0.252110i	−0.929580	−	0.368620i	$-0.879830\pi$
$59$	−1.11803	+	1.93649i	−0.145556	+	0.252110i	0.784024	+	0.620730i	$0.213164\pi$
$60$	−2.00000			−0.258199
$61$	8.18034			1.04739			0.523693	−	0.851907i	$-0.324554\pi$
$61$	8.18034			1.04739			0.523693	+	0.851907i	$0.324554\pi$
$62$		0			0
$63$	1.76393			0.222235
$64$	4.23607			0.529508
$65$	1.61803	−	2.80252i	0.200692	−	0.347609i
$66$	−10.4721			−1.28903
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−0.236068	+	0.408882i	−0.0286274	+	0.0495842i
$69$	9.23607	−	15.9973i	1.11189	−	1.92585i
$70$	0.381966			0.0456537
$71$	4.59017	+	7.95041i	0.544753	+	0.943540i	0.998622	+	0.0524716i	$0.0167099\pi$
$71$	4.59017	+	7.95041i	0.544753	+	0.943540i	−0.453869	+	0.891068i	$0.649957\pi$
$72$	8.35410	+	14.4697i	0.984540	+	1.70527i
$73$	−4.23607	−	7.33708i	−0.495794	−	0.858741i	0.504194	−	0.863590i	$-0.331790\pi$
$73$	−4.23607	−	7.33708i	−0.495794	−	0.858741i	−0.999988	+	0.00484959i	$0.998456\pi$
$74$	1.61803	−	2.80252i	0.188093	−	0.325786i
$75$	−6.47214	−	11.2101i	−0.747338	−	1.29443i
$76$	0.690983	−	1.19682i	0.0792612	−	0.137284i
$77$	0.472136			0.0538049
$78$	16.9443			1.91856
$79$	5.85410	−	10.1396i	0.658638	−	1.14079i	−0.322331	−	0.946627i	$-0.604466\pi$
$79$	5.85410	−	10.1396i	0.658638	−	1.14079i	0.980968	−	0.194167i	$-0.0622004\pi$
$80$	2.42705	+	4.20378i	0.271353	+	0.469996i
$81$	−12.2082	+	21.1452i	−1.35647	+	2.34947i
$82$	−5.66312	−	9.80881i	−0.625387	−	1.08320i
$83$	7.47214	+	12.9421i	0.820173	+	1.42058i	0.905553	+	0.424234i	$0.139456\pi$
$83$	7.47214	+	12.9421i	0.820173	+	1.42058i	−0.0853793	+	0.996349i	$0.527210\pi$
$84$	0.236068	+	0.408882i	0.0257571	+	0.0446127i
$85$	0.763932			0.0828601
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	4.47214	−	7.74597i	0.479463	−	0.830455i
$88$	2.23607	+	3.87298i	0.238366	+	0.412861i
$89$	11.7082			1.24107			0.620534	−	0.784180i	$-0.286916\pi$
$89$	11.7082			1.24107			0.620534	+	0.784180i	$0.286916\pi$
$90$	−6.04508	+	10.4704i	−0.637208	+	1.10368i
$91$	−0.763932			−0.0800818
$92$	3.52786			0.367805
$93$		0			0
$94$	4.00000			0.412568
$95$	−2.23607			−0.229416
$96$	−5.47214	+	9.47802i	−0.558498	+	0.967346i
$97$	−15.9443			−1.61890			−0.809448	−	0.587192i	$-0.800233\pi$
$97$	−15.9443			−1.61890			−0.809448	+	0.587192i	$0.800233\pi$
$98$	5.61803	+	9.73072i	0.567507	+	0.982951i
$99$	−7.47214	+	12.9421i	−0.750978	+	1.30073i
$100$	1.23607	−	2.14093i	0.123607	−	0.214093i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	−3.11803	−	5.40059i	−0.307229	−	0.532136i	0.670526	−	0.741886i	$-0.266068\pi$
$103$	−3.11803	−	5.40059i	−0.307229	−	0.532136i	−0.977755	+	0.209750i	$0.932735\pi$
$104$	−3.61803	−	6.26662i	−0.354777	−	0.614493i
$105$	0.381966	−	0.661585i	0.0372761	−	0.0645640i
$106$	8.47214	+	14.6742i	0.822887	+	1.42528i
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	−0.971040	−	0.238919i	$-0.923207\pi$
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	0.692429	+	0.721486i	$0.256540\pi$
$108$	−8.94427			−0.860663
$109$	−13.9443			−1.33562			−0.667810	−	0.744332i	$-0.732768\pi$
$109$	−13.9443			−1.33562			−0.667810	+	0.744332i	$0.732768\pi$
$110$	−1.61803	+	2.80252i	−0.154273	+	0.267210i
$111$	−3.23607	−	5.60503i	−0.307154	−	0.532006i
$112$	0.572949	−	0.992377i	0.0541386	−	0.0937708i
$113$	−1.73607	−	3.00696i	−0.163316	−	0.282871i	0.772740	−	0.634722i	$-0.218886\pi$
$113$	−1.73607	−	3.00696i	−0.163316	−	0.282871i	−0.936056	+	0.351852i	$0.885552\pi$
$114$	−5.85410	−	10.1396i	−0.548287	−	0.949661i
$115$	−2.85410	−	4.94345i	−0.266146	−	0.460979i
$116$	1.70820			0.158603
$117$	12.0902	−	20.9408i	1.11774	−	1.93598i
$118$	−1.80902	+	3.13331i	−0.166534	+	0.288445i
$119$	−0.0901699	−	0.156179i	−0.00826587	−	0.0143169i
$120$	7.23607			0.660560
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	13.2361			1.19834
$123$	−22.6525			−2.04250
$124$		0			0
$125$	−9.00000			−0.804984
$126$	2.85410			0.254264
$127$	−6.23607	+	10.8012i	−0.553362	+	0.958450i	0.444667	+	0.895696i	$0.353322\pi$
$127$	−6.23607	+	10.8012i	−0.553362	+	0.958450i	−0.998029	+	0.0627546i	$0.980011\pi$
$128$	13.6180			1.20368
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	2.61803	−	4.53457i	0.229617	−	0.397708i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−4.00000			−0.348155
$133$	0.263932	+	0.457144i	0.0228858	+	0.0396394i
$134$	−6.47214	−	11.2101i	−0.559107	−	0.968402i
$135$	7.23607	+	12.5332i	0.622782	+	1.07869i
$136$	0.854102	−	1.47935i	0.0732386	−	0.126853i
$137$	−3.14590	−	5.44886i	−0.268772	−	0.465527i	0.699773	−	0.714365i	$-0.253285\pi$
$137$	−3.14590	−	5.44886i	−0.268772	−	0.465527i	−0.968545	+	0.248838i	$0.919951\pi$
$138$	14.9443	−	25.8842i	1.27214	−	2.20341i
$139$	13.4164			1.13796			0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164			1.13796			0.568982	+	0.822350i	$0.307337\pi$
$140$	0.145898			0.0123306
$141$	4.00000	−	6.92820i	0.336861	−	0.583460i
$142$	7.42705	+	12.8640i	0.623264	+	1.07953i
$143$	3.23607	−	5.60503i	0.270614	−	0.468717i
$144$	18.1353	+	31.4112i	1.51127	+	2.61760i
$145$	−1.38197	−	2.39364i	−0.114766	−	0.198781i
$146$	−6.85410	−	11.8717i	−0.567250	−	0.982505i
$147$	22.4721			1.85347
$148$	0.618034	−	1.07047i	0.0508021	−	0.0879918i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	−10.4721	−	18.1383i	−0.855046	−	1.48098i
$151$	−14.1803			−1.15398			−0.576990	−	0.816751i	$-0.695773\pi$
$151$	−14.1803			−1.15398			−0.576990	+	0.816751i	$0.695773\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$	5.70820			0.461481
$154$	0.763932			0.0615594
$155$		0			0
$156$	6.47214			0.518186
$157$	20.8885			1.66709			0.833544	−	0.552454i	$-0.186308\pi$
$157$	20.8885			1.66709			0.833544	+	0.552454i	$0.186308\pi$
$158$	9.47214	−	16.4062i	0.753563	−	1.30521i
$159$	33.8885			2.68754
$160$	1.69098	+	2.92887i	0.133684	+	0.231547i
$161$	−0.673762	+	1.16699i	−0.0530999	+	0.0919717i
$162$	−19.7533	+	34.2137i	−1.55196	+	2.68808i
$163$	10.7082			0.838731			0.419366	−	0.907817i	$-0.362253\pi$
$163$	10.7082			0.838731			0.419366	+	0.907817i	$0.362253\pi$
$164$	−2.16312	−	3.74663i	−0.168911	−	0.292563i
$165$	3.23607	+	5.60503i	0.251928	+	0.436351i
$166$	12.0902	+	20.9408i	0.938379	+	1.62532i
$167$	3.23607	−	5.60503i	0.250414	−	0.433731i	−0.713226	−	0.700935i	$-0.752766\pi$
$167$	3.23607	−	5.60503i	0.250414	−	0.433731i	0.963640	+	0.267204i	$0.0860998\pi$
$168$	−0.854102	−	1.47935i	−0.0658954	−	0.114134i
$169$	1.26393	−	2.18919i	0.0972255	−	0.168400i
$170$	1.23607			0.0948021
$171$	−16.7082			−1.27771
$172$	−0.381966	+	0.661585i	−0.0291246	+	0.0504453i
$173$	−1.47214	−	2.54981i	−0.111924	−	0.193859i	0.804622	−	0.593788i	$-0.202368\pi$
$173$	−1.47214	−	2.54981i	−0.111924	−	0.193859i	−0.916546	+	0.399929i	$0.869035\pi$
$174$	7.23607	−	12.5332i	0.548565	−	0.950142i
$175$	0.472136	+	0.817763i	0.0356901	+	0.0618171i
$176$	4.85410	+	8.40755i	0.365892	+	0.633743i
$177$	3.61803	+	6.26662i	0.271948	+	0.471028i
$178$	18.9443			1.41993
$179$	−0.854102	+	1.47935i	−0.0638386	+	0.110572i	−0.896178	−	0.443694i	$-0.853668\pi$
$179$	−0.854102	+	1.47935i	−0.0638386	+	0.110572i	0.832340	+	0.554266i	$0.187001\pi$
$180$	−2.30902	+	3.99933i	−0.172104	+	0.298093i
$181$	2.09017	+	3.62028i	0.155361	+	0.269093i	0.933190	−	0.359382i	$-0.117013\pi$
$181$	2.09017	+	3.62028i	0.155361	+	0.269093i	−0.777829	+	0.628476i	$0.783679\pi$
$182$	−1.23607			−0.0916235
$183$	13.2361	−	22.9255i	0.978438	−	1.69470i
$184$	−12.7639			−0.940970
$185$	−2.00000			−0.147043
$186$		0			0
$187$	1.52786			0.111728
$188$	1.52786			0.111431
$189$	1.70820	−	2.95870i	0.124254	−	0.215213i
$190$	−3.61803			−0.262480
$191$	9.59017	+	16.6107i	0.693920	+	1.20191i	0.970543	+	0.240927i	$0.0774514\pi$
$191$	9.59017	+	16.6107i	0.693920	+	1.20191i	−0.276623	+	0.960979i	$0.589215\pi$
$192$	6.85410	−	11.8717i	0.494652	−	0.856763i
$193$	−1.73607	+	3.00696i	−0.124965	+	0.216446i	−0.921719	−	0.387858i	$-0.873215\pi$
$193$	−1.73607	+	3.00696i	−0.124965	+	0.216446i	0.796754	+	0.604303i	$0.206548\pi$
$194$	−25.7984			−1.85222
$195$	−5.23607	−	9.06914i	−0.374963	−	0.649454i
$196$	2.14590	+	3.71680i	0.153278	+	0.265486i
$197$	−5.70820	−	9.88690i	−0.406693	−	0.704412i	0.587824	−	0.808989i	$-0.299985\pi$
$197$	−5.70820	−	9.88690i	−0.406693	−	0.704412i	−0.994517	+	0.104576i	$0.966651\pi$
$198$	−12.0902	+	20.9408i	−0.859211	+	1.48820i
$199$	9.47214	+	16.4062i	0.671462	+	1.16301i	0.977490	+	0.210984i	$0.0676666\pi$
$199$	9.47214	+	16.4062i	0.671462	+	1.16301i	−0.306028	+	0.952023i	$0.599000\pi$
$200$	−4.47214	+	7.74597i	−0.316228	+	0.547723i
$201$	−25.8885			−1.82604
$202$	−4.85410			−0.341533
$203$	−0.326238	+	0.565061i	−0.0228974	+	0.0396595i
$204$	0.763932	+	1.32317i	0.0534859	+	0.0926404i
$205$	−3.50000	+	6.06218i	−0.244451	+	0.423401i
$206$	−5.04508	−	8.73834i	−0.351508	−	0.608829i
$207$	−21.3262	−	36.9381i	−1.48228	−	2.56738i
$208$	−7.85410	−	13.6037i	−0.544584	−	0.943247i
$209$	−4.47214			−0.309344
$210$	0.618034	−	1.07047i	0.0426484	−	0.0738692i
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	0.123081	+	0.992397i	$0.460723\pi$
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	−0.920981	+	0.389607i	$0.872611\pi$
$212$	3.23607	+	5.60503i	0.222254	+	0.384955i
$213$	29.7082			2.03557
$214$	−4.66312	+	8.07676i	−0.318764	+	0.552116i
$215$	1.23607			0.0842991
$216$	32.3607			2.20187
$217$		0			0
$218$	−22.5623			−1.52811
$219$	−27.4164			−1.85263
$220$	−0.618034	+	1.07047i	−0.0416678	+	0.0721708i
$221$	−2.47214			−0.166294
$222$	−5.23607	−	9.06914i	−0.351422	−	0.608681i
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$	0.399187	−	0.691412i	0.0266718	−	0.0461969i
$225$	−29.8885			−1.99257
$226$	−2.80902	−	4.86536i	−0.186853	−	0.323639i
$227$	3.23607	+	5.60503i	0.214785	+	0.372019i	0.953206	−	0.302321i	$-0.0977615\pi$
$227$	3.23607	+	5.60503i	0.214785	+	0.372019i	−0.738421	+	0.674340i	$0.764428\pi$
$228$	−2.23607	−	3.87298i	−0.148087	−	0.256495i
$229$	6.70820	−	11.6190i	0.443291	−	0.767802i	−0.554641	−	0.832090i	$-0.687144\pi$
$229$	6.70820	−	11.6190i	0.443291	−	0.767802i	0.997931	+	0.0642881i	$0.0204776\pi$
$230$	−4.61803	−	7.99867i	−0.304504	−	0.527417i
$231$	0.763932	−	1.32317i	0.0502630	−	0.0870581i
$232$	−6.18034			−0.405759
$233$	17.9443			1.17557			0.587784	−	0.809018i	$-0.300000\pi$
$233$	17.9443			1.17557			0.587784	+	0.809018i	$0.300000\pi$
$234$	19.5623	−	33.8829i	1.27883	−	2.21499i
$235$	−1.23607	−	2.14093i	−0.0806322	−	0.139659i
$236$	−0.690983	+	1.19682i	−0.0449792	+	0.0779062i
$237$	−18.9443	−	32.8124i	−1.23056	−	2.13140i
$238$	−0.145898	−	0.252703i	−0.00945716	−	0.0163803i
$239$	5.85410	+	10.1396i	0.378670	+	0.655876i	0.990869	−	0.134828i	$-0.0430481\pi$
$239$	5.85410	+	10.1396i	0.378670	+	0.655876i	−0.612199	+	0.790704i	$0.709715\pi$
$240$	15.7082			1.01396
$241$	−7.18034	+	12.4367i	−0.462526	+	0.801119i	−0.999086	−	0.0427432i	$-0.986390\pi$
$241$	−7.18034	+	12.4367i	−0.462526	+	0.801119i	0.536560	+	0.843862i	$0.319724\pi$
$242$	5.66312	−	9.80881i	0.364039	−	0.630534i
$243$	17.7984	+	30.8277i	1.14177	+	1.97760i
$244$	5.05573			0.323660
$245$	3.47214	−	6.01392i	0.221827	−	0.384215i
$246$	−36.6525			−2.33688
$247$	7.23607			0.460420
$248$		0			0
$249$	48.3607			3.06473
$250$	−14.5623			−0.921001
$251$	0.909830	−	1.57587i	0.0574280	−	0.0994682i	−0.835882	−	0.548909i	$-0.815043\pi$
$251$	0.909830	−	1.57587i	0.0574280	−	0.0994682i	0.893310	+	0.449441i	$0.148377\pi$
$252$	1.09017			0.0686743
$253$	−5.70820	−	9.88690i	−0.358872	−	0.621584i
$254$	−10.0902	+	17.4767i	−0.633114	+	1.09658i
$255$	1.23607	−	2.14093i	0.0774056	−	0.134070i
$256$	13.5623			0.847644
$257$	−0.972136	−	1.68379i	−0.0606402	−	0.105032i	0.834112	−	0.551596i	$-0.185981\pi$
$257$	−0.972136	−	1.68379i	−0.0606402	−	0.105032i	−0.894752	+	0.446564i	$0.852648\pi$
$258$	3.23607	+	5.60503i	0.201469	+	0.348954i
$259$	0.236068	+	0.408882i	0.0146686	+	0.0254067i
$260$	1.00000	−	1.73205i	0.0620174	−	0.107417i
$261$	−10.3262	−	17.8856i	−0.639178	−	1.10709i
$262$	−9.70820	+	16.8151i	−0.599775	+	1.03884i
$263$	−23.2361			−1.43280			−0.716399	−	0.697691i	$-0.754211\pi$
$263$	−23.2361			−1.43280			−0.716399	+	0.697691i	$0.754211\pi$
$264$	14.4721			0.890698
$265$	5.23607	−	9.06914i	0.321649	−	0.557113i
$266$	0.427051	+	0.739674i	0.0261842	+	0.0453523i
$267$	18.9443	−	32.8124i	1.15937	−	2.00809i
$268$	−2.47214	−	4.28187i	−0.151010	−	0.261557i
$269$	5.52786	+	9.57454i	0.337040	+	0.583770i	0.983875	−	0.178860i	$-0.0572410\pi$
$269$	5.52786	+	9.57454i	0.337040	+	0.583770i	−0.646835	+	0.762630i	$0.723908\pi$
$270$	11.7082	+	20.2792i	0.712539	+	1.23415i
$271$	−14.1803			−0.861394			−0.430697	−	0.902497i	$-0.641732\pi$
$271$	−14.1803			−0.861394			−0.430697	+	0.902497i	$0.641732\pi$
$272$	1.85410	−	3.21140i	0.112421	−	0.194720i
$273$	−1.23607	+	2.14093i	−0.0748102	+	0.129575i
$274$	−5.09017	−	8.81643i	−0.307508	−	0.532620i
$275$	−8.00000			−0.482418
$276$	5.70820	−	9.88690i	0.343594	−	0.595121i
$277$	−12.6525			−0.760214			−0.380107	−	0.924943i	$-0.624113\pi$
$277$	−12.6525			−0.760214			−0.380107	+	0.924943i	$0.624113\pi$
$278$	21.7082			1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$	6.47214	−	11.2101i	0.385410	−	0.667550i
$283$	−13.8885			−0.825588			−0.412794	−	0.910824i	$-0.635447\pi$
$283$	−13.8885			−0.825588			−0.412794	+	0.910824i	$0.635447\pi$
$284$	2.83688	+	4.91362i	0.168338	+	0.291570i
$285$	−3.61803	+	6.26662i	−0.214314	+	0.371202i
$286$	5.23607	−	9.06914i	0.309615	−	0.536269i
$287$	1.65248			0.0975426
$288$	12.6353	+	21.8849i	0.744540	+	1.28958i
$289$	8.20820	+	14.2170i	0.482836	+	0.836296i
$290$	−2.23607	−	3.87298i	−0.131306	−	0.227429i
$291$	−25.7984	+	44.6841i	−1.51233	+	2.61943i
$292$	−2.61803	−	4.53457i	−0.153209	−	0.265366i
$293$	0.236068	−	0.408882i	0.0137912	−	0.0238871i	−0.859047	−	0.511896i	$-0.828943\pi$
$293$	0.236068	−	0.408882i	0.0137912	−	0.0238871i	0.872839	+	0.488009i	$0.162277\pi$
$294$	36.3607			2.12060
$295$	2.23607			0.130189
$296$	−2.23607	+	3.87298i	−0.129969	+	0.225113i
$297$	14.4721	+	25.0665i	0.839759	+	1.45450i
$298$	−8.09017	+	14.0126i	−0.468651	+	0.811727i
$299$	9.23607	+	15.9973i	0.534136	+	0.925150i
$300$	−4.00000	−	6.92820i	−0.230940	−	0.400000i
$301$	−0.145898	−	0.252703i	−0.00840942	−	0.0145655i
$302$	−22.9443			−1.32029
$303$	−4.85410	+	8.40755i	−0.278861	+	0.483001i
$304$	−5.42705	+	9.39993i	−0.311263	+	0.539123i
$305$	−4.09017	−	7.08438i	−0.234202	−	0.405651i
$306$	9.23607			0.527991
$307$	14.3541	−	24.8620i	0.819232	−	1.41895i	−0.0870171	−	0.996207i	$-0.527733\pi$
$307$	14.3541	−	24.8620i	0.819232	−	1.41895i	0.906249	−	0.422744i	$-0.138933\pi$
$308$	0.291796			0.0166266
$309$	−20.1803			−1.14802
$310$		0			0
$311$	−29.1803			−1.65467			−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803			−1.65467			−0.827333	+	0.561712i	$0.810143\pi$
$312$	−23.4164			−1.32569
$313$	−8.38197	+	14.5180i	−0.473777	+	0.820605i	−0.999549	−	0.0300198i	$-0.990443\pi$
$313$	−8.38197	+	14.5180i	−0.473777	+	0.820605i	0.525773	+	0.850625i	$0.323776\pi$
$314$	33.7984			1.90735
$315$	−0.881966	−	1.52761i	−0.0496932	−	0.0860711i
$316$	3.61803	−	6.26662i	0.203530	−	0.352525i
$317$	−2.02786	+	3.51236i	−0.113896	+	0.197274i	−0.917338	−	0.398109i	$-0.869666\pi$
$317$	−2.02786	+	3.51236i	−0.113896	+	0.197274i	0.803442	+	0.595383i	$0.203000\pi$
$318$	54.8328			3.07487
$319$	−2.76393	−	4.78727i	−0.154750	−	0.268036i
$320$	−2.11803	−	3.66854i	−0.118402	−	0.205078i
$321$	9.32624	+	16.1535i	0.520540	+	0.901601i
$322$	−1.09017	+	1.88823i	−0.0607528	+	0.105227i
$323$	0.854102	+	1.47935i	0.0475235	+	0.0823131i
$324$	−7.54508	+	13.0685i	−0.419171	+	0.726026i
$325$	12.9443			0.718019
$326$	17.3262			0.959612
$327$	−22.5623	+	39.0791i	−1.24770	+	2.16108i
$328$	7.82624	+	13.5554i	0.432132	+	0.748474i
$329$	−0.291796	+	0.505406i	−0.0160872	+	0.0278639i
$330$	5.23607	+	9.06914i	0.288236	+	0.499239i
$331$	−1.00000	−	1.73205i	−0.0549650	−	0.0952021i	0.837234	−	0.546845i	$-0.184171\pi$
$331$	−1.00000	−	1.73205i	−0.0549650	−	0.0952021i	−0.892199	+	0.451643i	$0.850838\pi$
$332$	4.61803	+	7.99867i	0.253448	+	0.438984i
$333$	−14.9443			−0.818941
$334$	5.23607	−	9.06914i	0.286505	−	0.496241i
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$	−1.85410	−	3.21140i	−0.101150	−	0.175196i
$337$	−14.7639			−0.804243			−0.402121	−	0.915586i	$-0.631727\pi$
$337$	−14.7639			−0.804243			−0.402121	+	0.915586i	$0.631727\pi$
$338$	2.04508	−	3.54219i	0.111238	−	0.192670i
$339$	−11.2361			−0.610259
$340$	0.472136			0.0256052
$341$		0			0
$342$	−27.0344			−1.46186
$343$	−3.29180			−0.177740
$344$	1.38197	−	2.39364i	0.0745106	−	0.129056i
$345$	−18.4721			−0.994506
$346$	−2.38197	−	4.12569i	−0.128055	−	0.221798i
$347$	−12.0902	+	20.9408i	−0.649034	+	1.12416i	0.334320	+	0.942460i	$0.391494\pi$
$347$	−12.0902	+	20.9408i	−0.649034	+	1.12416i	−0.983354	+	0.181701i	$0.941840\pi$
$348$	2.76393	−	4.78727i	0.148162	−	0.256625i
$349$	−7.88854			−0.422264			−0.211132	−	0.977458i	$-0.567715\pi$
$349$	−7.88854			−0.422264			−0.211132	+	0.977458i	$0.567715\pi$
$350$	0.763932	+	1.32317i	0.0408339	+	0.0707264i
$351$	−23.4164	−	40.5584i	−1.24988	−	2.16485i
$352$	3.38197	+	5.85774i	0.180259	+	0.312218i
$353$	−3.70820	+	6.42280i	−0.197368	+	0.341851i	−0.947674	−	0.319239i	$-0.896573\pi$
$353$	−3.70820	+	6.42280i	−0.197368	+	0.341851i	0.750306	+	0.661090i	$0.229906\pi$
$354$	5.85410	+	10.1396i	0.311142	+	0.538914i
$355$	4.59017	−	7.95041i	0.243621	−	0.421964i
$356$	7.23607			0.383511
$357$	−0.583592			−0.0308870
$358$	−1.38197	+	2.39364i	−0.0730392	+	0.126508i
$359$	−11.1180	−	19.2570i	−0.586787	−	1.01635i	−0.994650	−	0.103302i	$-0.967059\pi$
$359$	−11.1180	−	19.2570i	−0.586787	−	1.01635i	0.407863	−	0.913043i	$-0.366274\pi$
$360$	8.35410	−	14.4697i	0.440300	−	0.762622i
$361$	7.00000	+	12.1244i	0.368421	+	0.638124i
$362$	3.38197	+	5.85774i	0.177752	+	0.307876i
$363$	−11.3262	−	19.6176i	−0.594473	−	1.02966i
$364$	−0.472136			−0.0247466
$365$	−4.23607	+	7.33708i	−0.221726	+	0.384041i
$366$	21.4164	−	37.0943i	1.11945	−	1.93895i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−27.7082			−1.44439
$369$	−26.1525	+	45.2974i	−1.36144	+	2.35809i
$370$	−3.23607			−0.168235
$371$	−2.47214			−0.128347
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	2.47214			0.127831
$375$	−14.5623	+	25.2227i	−0.751994	+	1.30249i
$376$	−5.52786			−0.285078
$377$	4.47214	+	7.74597i	0.230327	+	0.398938i
$378$	2.76393	−	4.78727i	0.142161	−	0.246231i
$379$	1.05573	−	1.82857i	0.0542291	−	0.0939276i	−0.837637	−	0.546228i	$-0.816063\pi$
$379$	1.05573	−	1.82857i	0.0542291	−	0.0939276i	0.891866	+	0.452300i	$0.149397\pi$
$380$	−1.38197			−0.0708934
$381$	20.1803	+	34.9534i	1.03387	+	1.79072i
$382$	15.5172	+	26.8766i	0.793930	+	1.37513i
$383$	11.9443	+	20.6881i	0.610324	+	1.05711i	0.991186	+	0.132480i	$0.0422940\pi$
$383$	11.9443	+	20.6881i	0.610324	+	1.05711i	−0.380862	+	0.924632i	$0.624373\pi$
$384$	22.0344	−	38.1648i	1.12444	−	1.94759i
$385$	−0.236068	−	0.408882i	−0.0120311	−	0.0208385i
$386$	−2.80902	+	4.86536i	−0.142975	+	0.247640i
$387$	9.23607			0.469496
$388$	−9.85410			−0.500266
$389$	8.94427	−	15.4919i	0.453493	−	0.785472i	−0.545108	−	0.838366i	$-0.683511\pi$
$389$	8.94427	−	15.4919i	0.453493	−	0.785472i	0.998600	+	0.0528939i	$0.0168445\pi$
$390$	−8.47214	−	14.6742i	−0.429003	−	0.743055i
$391$	−2.18034	+	3.77646i	−0.110265	+	0.190984i
$392$	−7.76393	−	13.4475i	−0.392138	−	0.679203i
$393$	19.4164	+	33.6302i	0.979428	+	1.69642i
$394$	−9.23607	−	15.9973i	−0.465306	−	0.805934i
$395$	−11.7082			−0.589104
$396$	−4.61803	+	7.99867i	−0.232065	+	0.401948i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	15.3262	+	26.5458i	0.768235	+	1.33062i
$399$	1.70820			0.0855172
$400$	−9.70820	+	16.8151i	−0.485410	+	0.840755i
$401$	38.1803			1.90664			0.953318	−	0.301969i	$-0.0976441\pi$
$401$	38.1803			1.90664			0.953318	+	0.301969i	$0.0976441\pi$
$402$	−41.8885			−2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	24.4164			1.21326
$406$	−0.527864	+	0.914287i	−0.0261975	+	0.0453753i
$407$	−4.00000			−0.198273
$408$	−2.76393	−	4.78727i	−0.136835	−	0.237005i
$409$	1.90983	−	3.30792i	0.0944350	−	0.163566i	−0.814938	−	0.579549i	$-0.803229\pi$
$409$	1.90983	−	3.30792i	0.0944350	−	0.163566i	0.909373	+	0.415982i	$0.136562\pi$
$410$	−5.66312	+	9.80881i	−0.279682	+	0.484423i
$411$	−20.3607			−1.00432
$412$	−1.92705	−	3.33775i	−0.0949390	−	0.164439i
$413$	−0.263932	−	0.457144i	−0.0129872	−	0.0224946i
$414$	−34.5066	−	59.7671i	−1.69591	−	2.93739i
$415$	7.47214	−	12.9421i	0.366793	−	0.635304i
$416$	−5.47214	−	9.47802i	−0.268294	−	0.464698i
$417$	21.7082	−	37.5997i	1.06306	−	1.84127i
$418$	−7.23607			−0.353928
$419$	−10.1246			−0.494620			−0.247310	−	0.968936i	$-0.579547\pi$
$419$	−10.1246			−0.494620			−0.247310	+	0.968936i	$0.579547\pi$
$420$	0.236068	−	0.408882i	0.0115189	−	0.0199514i
$421$	−14.6803	−	25.4271i	−0.715476	−	1.23924i	−0.962776	−	0.270302i	$-0.912877\pi$
$421$	−14.6803	−	25.4271i	−0.715476	−	1.23924i	0.247300	−	0.968939i	$-0.420457\pi$
$422$	−18.7533	+	32.4816i	−0.912896	+	1.58118i
$423$	−9.23607	−	15.9973i	−0.449073	−	0.777817i
$424$	−11.7082	−	20.2792i	−0.568601	−	0.984845i
$425$	1.52786	+	2.64634i	0.0741123	+	0.128366i
$426$	48.0689			2.32895
$427$	−0.965558	+	1.67240i	−0.0467266	+	0.0809329i
$428$	−1.78115	+	3.08505i	−0.0860953	+	0.149121i
$429$	−10.4721	−	18.1383i	−0.505599	−	0.875724i
$430$	2.00000			0.0964486
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	70.2492			3.37987
$433$	10.1803			0.489236			0.244618	−	0.969620i	$-0.421337\pi$
$433$	10.1803			0.489236			0.244618	+	0.969620i	$0.421337\pi$
$434$		0			0
$435$	−8.94427			−0.428845
$436$	−8.61803			−0.412729
$437$	6.38197	−	11.0539i	0.305291	−	0.528779i
$438$	−44.3607			−2.11964
$439$	0.590170	+	1.02220i	0.0281673	+	0.0487872i	0.879765	−	0.475408i	$-0.157700\pi$
$439$	0.590170	+	1.02220i	0.0281673	+	0.0487872i	−0.851598	+	0.524195i	$0.824366\pi$
$440$	2.23607	−	3.87298i	0.106600	−	0.184637i
$441$	25.9443	−	44.9368i	1.23544	−	2.13985i
$442$	−4.00000			−0.190261
$443$	−15.3541	−	26.5941i	−0.729495	−	1.26352i	−0.957097	−	0.289769i	$-0.906422\pi$
$443$	−15.3541	−	26.5941i	−0.729495	−	1.26352i	0.227601	−	0.973754i	$-0.426912\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	−5.85410	−	10.1396i	−0.277511	−	0.480663i
$446$	−3.23607	+	5.60503i	−0.153232	+	0.265406i
$447$	16.1803	+	28.0252i	0.765304	+	1.32555i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−31.3050			−1.47737			−0.738686	−	0.674050i	$-0.764553\pi$
$449$	−31.3050			−1.47737			−0.738686	+	0.674050i	$0.764553\pi$
$450$	−48.3607			−2.27974
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	−1.07295	−	1.85840i	−0.0504673	−	0.0874119i
$453$	−22.9443	+	39.7406i	−1.07802	+	1.86718i
$454$	5.23607	+	9.06914i	0.245741	+	0.425636i
$455$	0.381966	+	0.661585i	0.0179068	+	0.0310156i
$456$	8.09017	+	14.0126i	0.378857	+	0.656199i
$457$	−3.05573			−0.142941			−0.0714705	−	0.997443i	$-0.522769\pi$
$457$	−3.05573			−0.142941			−0.0714705	+	0.997443i	$0.522769\pi$
$458$	10.8541	−	18.7999i	0.507179	−	0.878460i
$459$	5.52786	−	9.57454i	0.258019	−	0.446901i
$460$	−1.76393	−	3.05522i	−0.0822438	−	0.142450i
$461$	34.3607			1.60034			0.800168	−	0.599776i	$-0.204744\pi$
$461$	34.3607			1.60034			0.800168	+	0.599776i	$0.204744\pi$
$462$	1.23607	−	2.14093i	0.0575071	−	0.0996052i
$463$	−2.58359			−0.120070			−0.0600349	−	0.998196i	$-0.519121\pi$
$463$	−2.58359			−0.120070			−0.0600349	+	0.998196i	$0.519121\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	4.70820			0.217870			0.108935	−	0.994049i	$-0.465256\pi$
$467$	4.70820			0.217870			0.108935	+	0.994049i	$0.465256\pi$
$468$	7.47214	−	12.9421i	0.345400	−	0.598250i
$469$	1.88854			0.0872049
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	33.7984	−	58.5405i	1.55735	−	2.69740i
$472$	2.50000	−	4.33013i	0.115072	−	0.199310i
$473$	2.47214			0.113669
$474$	−30.6525	−	53.0916i	−1.40791	−	2.43858i
$475$	−4.47214	−	7.74597i	−0.205196	−	0.355409i
$476$	−0.0557281	−	0.0965239i	−0.00255429	−	0.00442416i
$477$	39.1246	−	67.7658i	1.79139	−	3.10278i
$478$	9.47214	+	16.4062i	0.433245	+	0.750403i
$479$	−11.6459	+	20.1713i	−0.532115	+	0.921650i	0.467182	+	0.884161i	$0.345269\pi$
$479$	−11.6459	+	20.1713i	−0.532115	+	0.921650i	−0.999297	+	0.0374887i	$0.988064\pi$
$480$	10.9443			0.499535
$481$	6.47214			0.295104
$482$	−11.6180	+	20.1230i	−0.529187	+	0.916579i
$483$	2.18034	+	3.77646i	0.0992089	+	0.171835i
$484$	2.16312	−	3.74663i	0.0983236	−	0.170301i
$485$	7.97214	+	13.8081i	0.361996	+	0.626996i
$486$	28.7984	+	49.8802i	1.30632	+	2.26261i
$487$	9.61803	+	16.6589i	0.435835	+	0.754888i	0.997363	−	0.0725694i	$-0.0231199\pi$
$487$	9.61803	+	16.6589i	0.435835	+	0.754888i	−0.561529	+	0.827457i	$0.689787\pi$
$488$	−18.2918			−0.828031
$489$	17.3262	−	30.0099i	0.783520	−	1.35710i
$490$	5.61803	−	9.73072i	0.253797	−	0.439589i
$491$	−2.18034	−	3.77646i	−0.0983974	−	0.170429i	0.812624	−	0.582788i	$-0.198038\pi$
$491$	−2.18034	−	3.77646i	−0.0983974	−	0.170429i	−0.911021	+	0.412359i	$0.864705\pi$
$492$	−14.0000			−0.631169
$493$	−1.05573	+	1.82857i	−0.0475476	+	0.0823549i
$494$	11.7082			0.526777
$495$	14.9443			0.671695
$496$		0			0
$497$	−2.16718			−0.0972115
$498$	78.2492			3.50643
$499$	3.29180	−	5.70156i	0.147361	−	0.255237i	−0.782890	−	0.622160i	$-0.786255\pi$
$499$	3.29180	−	5.70156i	0.147361	−	0.255237i	0.930251	+	0.366923i	$0.119589\pi$
$500$	−5.56231			−0.248754
$501$	−10.4721	−	18.1383i	−0.467861	−	0.810358i
$502$	1.47214	−	2.54981i	0.0657046	−	0.113804i
$503$	−14.8262	+	25.6798i	−0.661069	+	1.14501i	0.319266	+	0.947665i	$0.396564\pi$
$503$	−14.8262	+	25.6798i	−0.661069	+	1.14501i	−0.980335	+	0.197340i	$0.936770\pi$
$504$	−3.94427			−0.175692
$505$	1.50000	+	2.59808i	0.0667491	+	0.115613i
$506$	−9.23607	−	15.9973i	−0.410593	−	0.711168i
$507$	−4.09017	−	7.08438i	−0.181651	−	0.314628i
$508$	−3.85410	+	6.67550i	−0.170998	+	0.296177i
$509$	−14.7984	−	25.6315i	−0.655926	−	1.13610i	−0.981661	−	0.190636i	$-0.938945\pi$
$509$	−14.7984	−	25.6315i	−0.655926	−	1.13610i	0.325734	−	0.945461i	$-0.394389\pi$
$510$	2.00000	−	3.46410i	0.0885615	−	0.153393i
$511$	2.00000			0.0884748
$512$	−5.29180			−0.233867
$513$	−16.1803	+	28.0252i	−0.714379	+	1.23734i
$514$	−1.57295	−	2.72443i	−0.0693798	−	0.120169i
$515$	−3.11803	+	5.40059i	−0.137397	+	0.237979i
$516$	1.23607	+	2.14093i	0.0544149	+	0.0942493i
$517$	−2.47214	−	4.28187i	−0.108724	−	0.188316i
$518$	0.381966	+	0.661585i	0.0167826	+	0.0290684i
$519$	−9.52786			−0.418227
$520$	−3.61803	+	6.26662i	−0.158661	+	0.274809i
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	−0.887099	−	0.461579i	$-0.847283\pi$
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	0.843288	+	0.537461i	$0.180617\pi$
$522$	−16.7082	−	28.9395i	−0.731298	−	1.26665i
$523$	−17.7082			−0.774326			−0.387163	−	0.922011i	$-0.626545\pi$
$523$	−17.7082			−0.774326			−0.387163	+	0.922011i	$0.626545\pi$
$524$	−3.70820	+	6.42280i	−0.161994	+	0.280581i
$525$	3.05573			0.133363
$526$	−37.5967			−1.63930
$527$		0			0
$528$	31.4164			1.36722
$529$	9.58359			0.416678
$530$	8.47214	−	14.6742i	0.368006	−	0.637405i
$531$	16.7082			0.725074
$532$	0.163119	+	0.282530i	0.00707210	+	0.0122492i
$533$	11.3262	−	19.6176i	0.490594	−	0.849733i
$534$	30.6525	−	53.0916i	1.32646	−	2.29750i
$535$	5.76393			0.249197
$536$	8.94427	+	15.4919i	0.386334	+	0.669150i
$537$	2.76393	+	4.78727i	0.119272	+	0.206586i
$538$	8.94427	+	15.4919i	0.385615	+	0.667905i
$539$	6.94427	−	12.0278i	0.299111	−	0.518075i
$540$	4.47214	+	7.74597i	0.192450	+	0.333333i
$541$	12.6803	−	21.9630i	0.545170	−	0.944263i	−0.453426	−	0.891294i	$-0.649798\pi$
$541$	12.6803	−	21.9630i	0.545170	−	0.944263i	0.998596	−	0.0529688i	$-0.0168684\pi$
$542$	−22.9443			−0.985541
$543$	13.5279			0.580536
$544$	1.29180	−	2.23746i	0.0553853	−	0.0959302i
$545$	6.97214	+	12.0761i	0.298653	+	0.517283i
$546$	−2.00000	+	3.46410i	−0.0855921	+	0.148250i
$547$	6.06231	+	10.5002i	0.259205	+	0.448957i	0.966029	−	0.258433i	$-0.0832060\pi$
$547$	6.06231	+	10.5002i	0.259205	+	0.448957i	−0.706824	+	0.707390i	$0.749873\pi$
$548$	−1.94427	−	3.36758i	−0.0830552	−	0.143856i
$549$	−30.5623	−	52.9355i	−1.30437	−	2.25923i
$550$	−12.9443			−0.551946
$551$	3.09017	−	5.35233i	0.131646	−	0.228017i
$552$	−20.6525	+	35.7711i	−0.879028	+	1.52252i
$553$	1.38197	+	2.39364i	0.0587672	+	0.101788i
$554$	−20.4721			−0.869778
$555$	−3.23607	+	5.60503i	−0.137363	+	0.237920i
$556$	8.29180			0.351650
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−1.14590			−0.0484230
$561$	2.47214	−	4.28187i	0.104374	−	0.180780i
$562$	27.5066			1.16029
$563$	−13.7705	−	23.8512i	−0.580358	−	1.00521i	−0.995437	−	0.0954238i	$-0.969579\pi$
$563$	−13.7705	−	23.8512i	−0.580358	−	1.00521i	0.415079	−	0.909785i	$-0.363754\pi$
$564$	2.47214	−	4.28187i	0.104096	−	0.180299i
$565$	−1.73607	+	3.00696i	−0.0730369	+	0.126504i
$566$	−22.4721			−0.944574
$567$	−2.88197	−	4.99171i	−0.121031	−	0.209632i
$568$	−10.2639	−	17.7777i	−0.430665	−	0.745934i
$569$	−2.76393	−	4.78727i	−0.115870	−	0.200693i	0.802257	−	0.596979i	$-0.203632\pi$
$569$	−2.76393	−	4.78727i	−0.115870	−	0.200693i	−0.918127	+	0.396286i	$0.870299\pi$
$570$	−5.85410	+	10.1396i	−0.245201	+	0.424701i
$571$	−14.0902	−	24.4049i	−0.589655	−	1.02131i	−0.994277	−	0.106829i	$-0.965930\pi$
$571$	−14.0902	−	24.4049i	−0.589655	−	1.02131i	0.404622	−	0.914484i	$-0.367403\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	62.0689			2.59296
$574$	2.67376			0.111601
$575$	11.4164	−	19.7738i	0.476097	−	0.824624i
$576$	−15.8262	−	27.4118i	−0.659427	−	1.14216i
$577$	14.4164	−	24.9700i	0.600163	−	1.03951i	−0.392633	−	0.919695i	$-0.628436\pi$
$577$	14.4164	−	24.9700i	0.600163	−	1.03951i	0.992796	−	0.119817i	$-0.0382309\pi$
$578$	13.2812	+	23.0036i	0.552423	+	0.956825i
$579$	5.61803	+	9.73072i	0.233478	+	0.404395i
$580$	−0.854102	−	1.47935i	−0.0354647	−	0.0614266i
$581$	−3.52786			−0.146360
$582$	−41.7426	+	72.3004i	−1.73029	+	2.99695i
$583$	10.4721	−	18.1383i	0.433712	−	0.751210i
$584$	9.47214	+	16.4062i	0.391960	+	0.678894i
$585$	−24.1803			−0.999734
$586$	0.381966	−	0.661585i	0.0157789	−	0.0273298i
$587$	−6.47214			−0.267134			−0.133567	−	0.991040i	$-0.542643\pi$
$587$	−6.47214			−0.267134			−0.133567	+	0.991040i	$0.542643\pi$
$588$	13.8885			0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	−36.9443			−1.51968
$592$	−4.85410	+	8.40755i	−0.199502	+	0.345548i
$593$	−6.52786			−0.268067			−0.134034	−	0.990977i	$-0.542793\pi$
$593$	−6.52786			−0.268067			−0.134034	+	0.990977i	$0.542793\pi$
$594$	23.4164	+	40.5584i	0.960787	+	1.66413i
$595$	−0.0901699	+	0.156179i	−0.00369661	+	0.00640271i
$596$	−3.09017	+	5.35233i	−0.126578	+	0.219240i
$597$	61.3050			2.50904
$598$	14.9443	+	25.8842i	0.611117	+	1.05849i
$599$	7.29837	+	12.6412i	0.298203	+	0.516504i	0.975725	−	0.218999i	$-0.0702793\pi$
$599$	7.29837	+	12.6412i	0.298203	+	0.516504i	−0.677522	+	0.735503i	$0.736946\pi$
$600$	14.4721	+	25.0665i	0.590822	+	1.02333i
$601$	−15.2705	+	26.4493i	−0.622897	+	1.07889i	0.366046	+	0.930597i	$0.380711\pi$
$601$	−15.2705	+	26.4493i	−0.622897	+	1.07889i	−0.988943	+	0.148293i	$0.952622\pi$
$602$	−0.236068	−	0.408882i	−0.00962141	−	0.0166648i
$603$	−29.8885	+	51.7685i	−1.21716	+	2.10818i
$604$	−8.76393			−0.356599
$605$	−7.00000			−0.284590
$606$	−7.85410	+	13.6037i	−0.319051	+	0.552613i
$607$	−11.2361	−	19.4614i	−0.456058	−	0.789916i	0.542690	−	0.839933i	$-0.317406\pi$
$607$	−11.2361	−	19.4614i	−0.456058	−	0.789916i	−0.998748	+	0.0500173i	$0.984072\pi$
$608$	−3.78115	+	6.54915i	−0.153346	+	0.265603i
$609$	1.05573	+	1.82857i	0.0427803	+	0.0740976i
$610$	−6.61803	−	11.4628i	−0.267956	−	0.464114i
$611$	4.00000	+	6.92820i	0.161823	+	0.280285i
$612$	3.52786			0.142605
$613$	21.9443	−	38.0086i	0.886321	−	1.53515i	0.0421285	−	0.999112i	$-0.486586\pi$
$613$	21.9443	−	38.0086i	0.886321	−	1.53515i	0.844192	−	0.536040i	$-0.180081\pi$
$614$	23.2254	−	40.2276i	0.937302	−	1.62345i
$615$	11.3262	+	19.6176i	0.456718	+	0.791059i
$616$	−1.05573			−0.0425365
$617$	−16.2361	+	28.1217i	−0.653639	+	1.13214i	0.328594	+	0.944471i	$0.393425\pi$
$617$	−16.2361	+	28.1217i	−0.653639	+	1.13214i	−0.982233	+	0.187665i	$0.939908\pi$
$618$	−32.6525			−1.31348
$619$	6.18034			0.248409			0.124204	−	0.992257i	$-0.460362\pi$
$619$	6.18034			0.248409			0.124204	+	0.992257i	$0.460362\pi$
$620$		0			0
$621$	−82.6099			−3.31502
$622$	−47.2148			−1.89314
$623$	−1.38197	+	2.39364i	−0.0553673	+	0.0958990i
$624$	−50.8328			−2.03494
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−13.5623	+	23.4906i	−0.542059	+	0.938873i
$627$	−7.23607	+	12.5332i	−0.288981	+	0.500529i
$628$	12.9098			0.515158
$629$	0.763932	+	1.32317i	0.0304600	+	0.0527582i
$630$	−1.42705	−	2.47172i	−0.0568551	−	0.0984759i
$631$	−17.1803	−	29.7572i	−0.683939	−	1.18462i	−0.973769	−	0.227538i	$-0.926932\pi$
$631$	−17.1803	−	29.7572i	−0.683939	−	1.18462i	0.289831	−	0.957078i	$-0.406401\pi$
$632$	−13.0902	+	22.6728i	−0.520699	+	0.901877i
$633$	37.5066	+	64.9633i	1.49075	+	2.58206i
$634$	−3.28115	+	5.68312i	−0.130311	+	0.225706i
$635$	12.4721			0.494942
$636$	20.9443			0.830494
$637$	−11.2361	+	19.4614i	−0.445189	+	0.771090i
$638$	−4.47214	−	7.74597i	−0.177054	−	0.306666i
$639$	34.2984	−	59.4065i	1.35682	−	2.35009i
$640$	−6.80902	−	11.7936i	−0.269150	−	0.466182i
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$	15.0902	+	26.1369i	0.595562	+	1.03154i
$643$	19.5279			0.770104			0.385052	−	0.922895i	$-0.374184\pi$
$643$	19.5279			0.770104			0.385052	+	0.922895i	$0.374184\pi$
$644$	−0.416408	+	0.721240i	−0.0164088	+	0.0284208i
$645$	2.00000	−	3.46410i	0.0787499	−	0.136399i
$646$	1.38197	+	2.39364i	0.0543727	+	0.0941763i
$647$	−0.944272			−0.0371232			−0.0185616	−	0.999828i	$-0.505909\pi$
$647$	−0.944272			−0.0371232			−0.0185616	+	0.999828i	$0.505909\pi$
$648$	27.2984	−	47.2822i	1.07238	−	1.85742i
$649$	4.47214			0.175547
$650$	20.9443			0.821502
$651$		0			0
$652$	6.61803			0.259182
$653$	−47.3050			−1.85119			−0.925593	−	0.378521i	$-0.876433\pi$
$653$	−47.3050			−1.85119			−0.925593	+	0.378521i	$0.876433\pi$
$654$	−36.5066	+	63.2312i	−1.42752	+	2.47254i
$655$	12.0000			0.468879
$656$	16.9894	+	29.4264i	0.663323	+	1.14891i
$657$	−31.6525	+	54.8237i	−1.23488	+	2.13888i
$658$	−0.472136	+	0.817763i	−0.0184058	+	0.0318797i
$659$	25.6525			0.999279			0.499639	−	0.866234i	$-0.333466\pi$
$659$	25.6525			0.999279			0.499639	+	0.866234i	$0.333466\pi$
$660$	2.00000	+	3.46410i	0.0778499	+	0.134840i
$661$	0.319660	+	0.553668i	0.0124333	+	0.0215352i	0.872175	−	0.489194i	$-0.162709\pi$
$661$	0.319660	+	0.553668i	0.0124333	+	0.0215352i	−0.859742	+	0.510729i	$0.829376\pi$
$662$	−1.61803	−	2.80252i	−0.0628867	−	0.108923i
$663$	−4.00000	+	6.92820i	−0.155347	+	0.269069i
$664$	−16.7082	−	28.9395i	−0.648404	−	1.12307i
$665$	0.263932	−	0.457144i	0.0102348	−	0.0177273i
$666$	−24.1803			−0.936969
$667$	15.7771			0.610891
$668$	2.00000	−	3.46410i	0.0773823	−	0.134030i
$669$	6.47214	+	11.2101i	0.250227	+	0.433406i
$670$	−6.47214	+	11.2101i	−0.250040	+	0.433083i
$671$	−8.18034	−	14.1688i	−0.315799	−	0.546979i
$672$	−1.29180	−	2.23746i	−0.0498321	−	0.0863118i
$673$	14.5066	+	25.1261i	0.559187	+	0.968541i	0.997565	+	0.0697499i	$0.0222201\pi$
$673$	14.5066	+	25.1261i	0.559187	+	0.968541i	−0.438377	+	0.898791i	$0.644447\pi$
$674$	−23.8885			−0.920152
$675$	−28.9443	+	50.1329i	−1.11407	+	1.92962i
$676$	0.781153	−	1.35300i	0.0300443	−	0.0520383i
$677$	23.3607	+	40.4619i	0.897824	+	1.55508i	0.830270	+	0.557361i	$0.188186\pi$
$677$	23.3607	+	40.4619i	0.897824	+	1.55508i	0.0675535	+	0.997716i	$0.478481\pi$
$678$	−18.1803			−0.698212
$679$	1.88197	−	3.25966i	0.0722232	−	0.125094i
$680$	−1.70820			−0.0655066
$681$	20.9443			0.802586
$682$		0			0
$683$	5.18034			0.198220			0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034			0.198220			0.0991101	+	0.995076i	$0.468400\pi$
$684$	−10.3262			−0.394834
$685$	−3.14590	+	5.44886i	−0.120199	+	0.208190i
$686$	−5.32624			−0.203357
$687$	−21.7082	−	37.5997i	−0.828220	−	1.43452i
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−16.9443	+	29.3483i	−0.645525	+	1.11808i
$690$	−29.8885			−1.13784
$691$	−1.59017	−	2.75426i	−0.0604929	−	0.104777i	0.834193	−	0.551473i	$-0.185934\pi$
$691$	−1.59017	−	2.75426i	−0.0604929	−	0.104777i	−0.894686	+	0.446696i	$0.852601\pi$
$692$	−0.909830	−	1.57587i	−0.0345865	−	0.0599057i
$693$	−1.76393	−	3.05522i	−0.0670062	−	0.116058i
$694$	−19.5623	+	33.8829i	−0.742575	+	1.28618i
$695$	−6.70820	−	11.6190i	−0.254457	−	0.440732i
$696$	−10.0000	+	17.3205i	−0.379049	+	0.656532i
$697$	5.34752			0.202552
$698$	−12.7639			−0.483122
$699$	29.0344	−	50.2891i	1.09818	−	1.90211i
$700$	0.291796	+	0.505406i	0.0110289	+	0.0191025i
$701$	−3.50000	+	6.06218i	−0.132193	+	0.228965i	−0.924522	−	0.381129i	$-0.875535\pi$
$701$	−3.50000	+	6.06218i	−0.132193	+	0.228965i	0.792329	+	0.610095i	$0.208869\pi$
$702$	−37.8885	−	65.6249i	−1.43001	−	2.47685i
$703$	−2.23607	−	3.87298i	−0.0843349	−	0.146072i
$704$	−4.23607	−	7.33708i	−0.159653	−	0.276527i
$705$	−8.00000			−0.301297
$706$	−6.00000	+	10.3923i	−0.225813	+	0.391120i
$707$	0.354102	−	0.613323i	0.0133174	−	0.0230664i
$708$	2.23607	+	3.87298i	0.0840366	+	0.145556i
$709$	25.5279			0.958719			0.479360	−	0.877619i	$-0.340869\pi$
$709$	25.5279			0.958719			0.479360	+	0.877619i	$0.340869\pi$
$710$	7.42705	−	12.8640i	0.278732	−	0.482778i
$711$	−87.4853			−3.28095
$712$	−26.1803			−0.981150
$713$		0			0
$714$	−0.944272			−0.0353385
$715$	−6.47214			−0.242044
$716$	−0.527864	+	0.914287i	−0.0197272	+	0.0341685i
$717$	37.8885			1.41497
$718$	−17.9894	−	31.1585i	−0.671357	−	1.16282i
$719$	6.90983	−	11.9682i	0.257693	−	0.446338i	−0.707930	−	0.706282i	$-0.750371\pi$
$719$	6.90983	−	11.9682i	0.257693	−	0.446338i	0.965624	+	0.259945i	$0.0837043\pi$
$720$	18.1353	−	31.4112i	0.675861	−	1.17063i
$721$	1.47214			0.0548252
$722$	11.3262	+	19.6176i	0.421519	+	0.730092i
$723$	23.2361	+	40.2461i	0.864159	+	1.49677i
$724$	1.29180	+	2.23746i	0.0480092	+	0.0831544i
$725$	5.52786	−	9.57454i	0.205300	−	0.355590i
$726$	−18.3262	−	31.7420i	−0.680150	−	1.17806i
$727$	22.1180	−	38.3096i	0.820312	−	1.42082i	−0.0851372	−	0.996369i	$-0.527133\pi$
$727$	22.1180	−	38.3096i	0.820312	−	1.42082i	0.905450	−	0.424454i	$-0.139534\pi$
$728$	1.70820			0.0633102
$729$	41.9443			1.55349
$730$	−6.85410	+	11.8717i	−0.253682	+	0.439390i
$731$	−0.472136	−	0.817763i	−0.0174626	−	0.0302461i
$732$	8.18034	−	14.1688i	0.302354	−	0.523693i
$733$	−1.73607	−	3.00696i	−0.0641231	−	0.111065i	0.832182	−	0.554503i	$-0.187092\pi$
$733$	−1.73607	−	3.00696i	−0.0641231	−	0.111065i	−0.896305	+	0.443439i	$0.853758\pi$
$734$	−14.5623	−	25.2227i	−0.537505	−	0.930985i
$735$	−11.2361	−	19.4614i	−0.414449	−	0.717846i
$736$	−19.3050			−0.711590
$737$	−8.00000	+	13.8564i	−0.294684	+	0.510407i
$738$	−42.3156	+	73.2928i	−1.55766	+	2.69794i
$739$	−3.09017	−	5.35233i	−0.113674	−	0.196889i	0.803575	−	0.595203i	$-0.202929\pi$
$739$	−3.09017	−	5.35233i	−0.113674	−	0.196889i	−0.917249	+	0.398315i	$0.869595\pi$
$740$	−1.23607			−0.0454388
$741$	11.7082	−	20.2792i	0.430112	−	0.744975i
$742$	−4.00000			−0.146845
$743$	50.1803			1.84094			0.920469	−	0.390815i	$-0.127807\pi$
$743$	50.1803			1.84094			0.920469	+	0.390815i	$0.127807\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	30.7426			1.12557
$747$	55.8328	−	96.7053i	2.04282	−	3.53826i
$748$	0.944272			0.0345260
$749$	−0.680340	−	1.17838i	−0.0248591	−	0.0430572i
$750$	−23.5623	+	40.8111i	−0.860374	+	1.49021i
$751$	10.7705	−	18.6551i	0.393021	−	0.680733i	−0.599825	−	0.800131i	$-0.704763\pi$
$751$	10.7705	−	18.6551i	0.393021	−	0.680733i	0.992846	+	0.119398i	$0.0380965\pi$
$752$	−12.0000			−0.437595
$753$	−2.94427	−	5.09963i	−0.107295	−	0.185841i
$754$	7.23607	+	12.5332i	0.263522	+	0.456434i
$755$	7.09017	+	12.2805i	0.258038	+	0.446934i
$756$	1.05573	−	1.82857i	0.0383965	−	0.0665046i
$757$	−4.32624	−	7.49326i	−0.157240	−	0.272347i	0.776633	−	0.629954i	$-0.216926\pi$
$757$	−4.32624	−	7.49326i	−0.157240	−	0.272347i	−0.933872	+	0.357607i	$0.883593\pi$
$758$	1.70820	−	2.95870i	0.0620448	−	0.107465i
$759$	−36.9443			−1.34099
$760$	5.00000			0.181369
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	−0.883581	−	0.468278i	$-0.844875\pi$
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	0.847331	+	0.531065i	$0.178208\pi$
$762$	32.6525	+	56.5557i	1.18287	+	2.04880i
$763$	1.64590	−	2.85078i	0.0595855	−	0.103205i
$764$	5.92705	+	10.2660i	0.214433	+	0.371409i
$765$	−2.85410	−	4.94345i	−0.103190	−	0.178731i
$766$	19.3262	+	33.4740i	0.698285	+	1.20947i
$767$	−7.23607			−0.261279
$768$	21.9443	−	38.0086i	0.791846	−	1.37152i
$769$	23.6803	−	41.0156i	0.853935	−	1.47906i	−0.0236947	−	0.999719i	$-0.507543\pi$
$769$	23.6803	−	41.0156i	0.853935	−	1.47906i	0.877630	−	0.479339i	$-0.159124\pi$
$770$	−0.381966	−	0.661585i	−0.0137651	−	0.0238419i
$771$	−6.29180			−0.226594
$772$	−1.07295	+	1.85840i	−0.0386163	+	0.0668854i
$773$	−11.1246			−0.400124			−0.200062	−	0.979783i	$-0.564114\pi$
$773$	−11.1246			−0.400124			−0.200062	+	0.979783i	$0.564114\pi$
$774$	14.9443			0.537161
$775$		0			0
$776$	35.6525			1.27985
$777$	1.52786			0.0548118
$778$	14.4721	−	25.0665i	0.518851	−	0.898677i
$779$	−15.6525			−0.560808
$780$	−3.23607	−	5.60503i	−0.115870	−	0.200692i
$781$	9.18034	−	15.9008i	0.328498	−	0.568976i
$782$	−3.52786	+	6.11044i	−0.126156	+	0.218509i
$783$	−40.0000			−1.42948
$784$	−16.8541	−	29.1922i	−0.601932	−	1.04258i
$785$	−10.4443	−	18.0900i	−0.372772	−	0.645660i
$786$	31.4164	+	54.4148i	1.12059	+	1.94091i
$787$	−3.67376	+	6.36314i	−0.130955	+	0.226822i	−0.924045	−	0.382283i	$-0.875138\pi$
$787$	−3.67376	+	6.36314i	−0.130955	+	0.226822i	0.793090	+	0.609105i	$0.208471\pi$
$788$	−3.52786	−	6.11044i	−0.125675	−	0.217675i
$789$	−37.5967	+	65.1195i	−1.33848	+	2.31831i
$790$	−18.9443			−0.674007
$791$	0.819660			0.0291438
$792$	16.7082	−	28.9395i	0.593700	−	1.02832i
$793$	13.2361	+	22.9255i	0.470027	+	0.814110i
$794$	5.66312	−	9.80881i	0.200977	−	0.348102i
$795$	−16.9443	−	29.3483i	−0.600951	−	1.04088i
$796$	5.85410	+	10.1396i	0.207493	+	0.359389i
$797$	27.7082	+	47.9920i	0.981475	+	1.69996i	0.656660	+	0.754187i	$0.271969\pi$
$797$	27.7082	+	47.9920i	0.981475	+	1.69996i	0.324815	+	0.945778i	$0.394698\pi$
$798$	2.76393			0.0978421
$799$	−0.944272	+	1.63553i	−0.0334059	+	0.0578608i
$800$	−6.76393	+	11.7155i	−0.239141	+	0.414205i
$801$	−43.7426	−	75.7645i	−1.54557	−	2.67701i
$802$	61.7771			2.18142
$803$	−8.47214	+	14.6742i	−0.298975	+	0.517840i
$804$	−16.0000			−0.564276
$805$	1.34752			0.0474940
$806$		0			0
$807$	35.7771			1.25941
$808$	6.70820			0.235994
$809$	−11.7082	+	20.2792i	−0.411639	+	0.712979i	−0.995069	−	0.0991842i	$-0.968377\pi$
$809$	−11.7082	+	20.2792i	−0.411639	+	0.712979i	0.583431	+	0.812163i	$0.301710\pi$
$810$	39.5066			1.38812
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	0.999953	−	0.00966502i	$-0.00307652\pi$
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	−0.508347	+	0.861152i	$0.669743\pi$
$812$	−0.201626	+	0.349227i	−0.00707569	+	0.0122555i
$813$	−22.9443	+	39.7406i	−0.804691	+	1.39377i
$814$	−6.47214			−0.226848
$815$	−5.35410	−	9.27358i	−0.187546	−	0.324839i
$816$	−6.00000	−	10.3923i	−0.210042	−	0.363803i
$817$	1.38197	+	2.39364i	0.0483489	+	0.0837427i
$818$	3.09017	−	5.35233i	0.108045	−	0.187140i
$819$	2.85410	+	4.94345i	0.0997304	+	0.172738i
$820$	−2.16312	+	3.74663i	−0.0755394	+	0.130838i
$821$	30.5410			1.06589			0.532944	−	0.846150i	$-0.321085\pi$
$821$	30.5410			1.06589			0.532944	+	0.846150i	$0.321085\pi$
$822$	−32.9443			−1.14906
$823$	7.14590	−	12.3771i	0.249090	−	0.431437i	−0.714183	−	0.699959i	$-0.753202\pi$
$823$	7.14590	−	12.3771i	0.249090	−	0.431437i	0.963274	+	0.268522i	$0.0865351\pi$
$824$	6.97214	+	12.0761i	0.242886	+	0.420691i
$825$	−12.9443	+	22.4201i	−0.450662	+	0.780569i
$826$	−0.427051	−	0.739674i	−0.0148590	−	0.0257366i
$827$	−8.67376	−	15.0234i	−0.301616	−	0.522415i	0.674886	−	0.737922i	$-0.264193\pi$
$827$	−8.67376	−	15.0234i	−0.301616	−	0.522415i	−0.976502	+	0.215507i	$0.930859\pi$
$828$	−13.1803	−	22.8290i	−0.458048	−	0.793363i
$829$	16.8328			0.584628			0.292314	−	0.956322i	$-0.405575\pi$
$829$	16.8328			0.584628			0.292314	+	0.956322i	$0.405575\pi$
$830$	12.0902	−	20.9408i	0.419656	−	0.726865i
$831$	−20.4721	+	35.4588i	−0.710171	+	1.23005i
$832$	6.85410	+	11.8717i	0.237623	+	0.411576i
$833$	−5.30495			−0.183806
$834$	35.1246	−	60.8376i	1.21627	−	2.10663i
$835$	−6.47214			−0.223978
$836$	−2.76393			−0.0955926
$837$		0			0
$838$	−16.3820			−0.565906
$839$	28.9443			0.999267			0.499634	−	0.866237i	$-0.333468\pi$
$839$	28.9443			0.999267			0.499634	+	0.866237i	$0.333468\pi$
$840$	−0.854102	+	1.47935i	−0.0294693	+	0.0510424i
$841$	−21.3607			−0.736575
$842$	−23.7533	−	41.1419i	−0.818592	−	1.41784i
$843$	27.5066	−	47.6428i	0.947377	−	1.64090i
$844$	−7.16312	+	12.4069i	−0.246565	+	0.427063i
$845$	−2.52786			−0.0869612
$846$	−14.9443	−	25.8842i	−0.513795	−	0.889918i
$847$	0.826238	+	1.43109i	0.0283899	+	0.0491727i
$848$	−25.4164	−	44.0225i	−0.872803	−	1.51174i
$849$	−22.4721	+	38.9229i	−0.771242	+	1.33583i
$850$	2.47214	+	4.28187i	0.0847936	+	0.146867i
$851$	5.70820	−	9.88690i	0.195675	−	0.338919i
$852$	18.3607			0.629027
$853$	10.5836			0.362375			0.181188	−	0.983449i	$-0.442006\pi$
$853$	10.5836			0.362375			0.181188	+	0.983449i	$0.442006\pi$
$854$	−1.56231	+	2.70599i	−0.0534610	+	0.0925972i
$855$	8.35410	+	14.4697i	0.285704	+	0.494854i
$856$	6.44427	−	11.1618i	0.220261	−	0.381503i
$857$	27.8328	+	48.2079i	0.950751	+	1.64675i	0.743805	+	0.668396i	$0.233019\pi$
$857$	27.8328	+	48.2079i	0.950751	+	1.64675i	0.206946	+	0.978352i	$0.433648\pi$
$858$	−16.9443	−	29.3483i	−0.578468	−	1.00194i
$859$	−1.05573	−	1.82857i	−0.0360210	−	0.0623902i	0.847453	−	0.530871i	$-0.178135\pi$
$859$	−1.05573	−	1.82857i	−0.0360210	−	0.0623902i	−0.883474	+	0.468480i	$0.844802\pi$
$860$	0.763932			0.0260499
$861$	2.67376	−	4.63109i	0.0911216	−	0.157827i
$862$	−9.70820	+	16.8151i	−0.330663	+	0.572725i
$863$	4.90983	+	8.50408i	0.167133	+	0.289482i	0.937411	−	0.348226i	$-0.113216\pi$
$863$	4.90983	+	8.50408i	0.167133	+	0.289482i	−0.770278	+	0.637708i	$0.779883\pi$
$864$	48.9443			1.66512
$865$	−1.47214	+	2.54981i	−0.0500541	+	0.0866963i
$866$	16.4721			0.559746
$867$	53.1246			1.80421
$868$		0			0
$869$	−23.4164			−0.794347
$870$	−14.4721			−0.490651
$871$	12.9443	−	22.4201i	0.438600	−	0.759677i
$872$	31.1803			1.05590
$873$	59.5689	+	103.176i	2.01610	+	3.49199i
$874$	10.3262	−	17.8856i	0.349290	−	0.604988i
$875$	1.06231	−	1.83997i	0.0359125	−	0.0622023i
$876$	−16.9443			−0.572494
$877$	9.02786	+	15.6367i	0.304849	+	0.528014i	0.977228	−	0.212193i	$-0.0680606\pi$
$877$	9.02786	+	15.6367i	0.304849	+	0.528014i	−0.672378	+	0.740208i	$0.734727\pi$
$878$	0.954915	+	1.65396i	0.0322268	+	0.0558185i
$879$	−0.763932	−	1.32317i	−0.0257668	−	0.0446294i
$880$	4.85410	−	8.40755i	0.163632	−	0.283418i
$881$	10.1803	+	17.6329i	0.342984	+	0.594066i	0.984985	−	0.172637i	$-0.0552289\pi$
$881$	10.1803	+	17.6329i	0.342984	+	0.594066i	−0.642001	+	0.766704i	$0.721896\pi$
$882$	41.9787	−	72.7093i	1.41350	−	2.44825i
$883$	−31.7771			−1.06938			−0.534692	−	0.845047i	$-0.679572\pi$
$883$	−31.7771			−1.06938			−0.534692	+	0.845047i	$0.679572\pi$
$884$	−1.52786			−0.0513876
$885$	3.61803	−	6.26662i	0.121619	−	0.210650i
$886$	−24.8435	−	43.0301i	−0.834632	−	1.44563i
$887$	−13.5344	+	23.4423i	−0.454442	+	0.787117i	−0.998656	−	0.0518298i	$-0.983495\pi$
$887$	−13.5344	+	23.4423i	−0.454442	+	0.787117i	0.544214	+	0.838947i	$0.316828\pi$
$888$	7.23607	+	12.5332i	0.242827	+	0.420588i
$889$	−1.47214	−	2.54981i	−0.0493739	−	0.0855180i
$890$	−9.47214	−	16.4062i	−0.317507	−	0.549938i
$891$	48.8328			1.63596
$892$	−1.23607	+	2.14093i	−0.0413866	+	0.0716837i
$893$	2.76393	−	4.78727i	0.0924915	−	0.160200i
$894$	26.1803	+	45.3457i	0.875602	+	1.51659i
$895$	1.70820			0.0570990
$896$	−1.60739	+	2.78408i	−0.0536992	+	0.0930097i
$897$	59.7771			1.99590
$898$	−50.6525			−1.69030
$899$		0			0
$900$	−18.4721			−0.615738
$901$	−8.00000			−0.266519
$902$	−11.3262	+	19.6176i	−0.377122	+	0.653195i
$903$	−0.944272			−0.0314234
$904$	3.88197	+	6.72376i	0.129112	+	0.223629i
$905$	2.09017	−	3.62028i	0.0694796	−	0.120342i
$906$	−37.1246	+	64.3017i	−1.23338	+	2.13628i
$907$	−24.2361			−0.804745			−0.402373	−	0.915476i	$-0.631814\pi$
$907$	−24.2361			−0.804745			−0.402373	+	0.915476i	$0.631814\pi$
$908$	2.00000	+	3.46410i	0.0663723	+	0.114960i
$909$	11.2082	+	19.4132i	0.371753	+	0.643894i
$910$	0.618034	+	1.07047i	0.0204876	+	0.0354856i
$911$	−9.09017	+	15.7446i	−0.301171	+	0.521643i	−0.976401	−	0.215964i	$-0.930711\pi$
$911$	−9.09017	+	15.7446i	−0.301171	+	0.521643i	0.675231	+	0.737607i	$0.264044\pi$
$912$	17.5623	+	30.4188i	0.581546	+	1.00727i
$913$	14.9443	−	25.8842i	0.494583	−	0.856643i
$914$	−4.94427			−0.163542
$915$	−26.4721			−0.875142
$916$	4.14590	−	7.18091i	0.136984	−	0.237264i
$917$	−1.41641	−	2.45329i	−0.0467739	−	0.0810148i
$918$	8.94427	−	15.4919i	0.295205	−	0.511310i
$919$	7.23607	+	12.5332i	0.238696	+	0.413433i	0.960340	−	0.278831i	$-0.0899468\pi$
$919$	7.23607	+	12.5332i	0.238696	+	0.413433i	−0.721644	+	0.692264i	$0.756613\pi$
$920$	6.38197	+	11.0539i	0.210407	+	0.364436i
$921$	−46.4508	−	80.4552i	−1.53061	−	2.65109i
$922$	55.5967			1.83098
$923$	−14.8541	+	25.7281i	−0.488929	+	0.846849i
$924$	0.472136	−	0.817763i	0.0155321	−	0.0269024i
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	−4.18034			−0.137374
$927$	−23.2984	+	40.3540i	−0.765219	+	1.32540i
$928$	−9.34752			−0.306848
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	15.5279			0.508905
$932$	11.0902			0.363271
$933$	−47.2148	+	81.7784i	−1.54574	+	2.67730i
$934$	7.61803			0.249270
$935$	−0.763932	−	1.32317i	−0.0249832	−	0.0432723i
$936$	−27.0344	+	46.8250i	−0.883648	+	1.53052i
$937$	−4.52786	+	7.84249i	−0.147919	+	0.256203i	−0.930458	−	0.366398i	$-0.880591\pi$
$937$	−4.52786	+	7.84249i	−0.147919	+	0.256203i	0.782539	+	0.622601i	$0.213924\pi$
$938$	3.05573			0.0997731
$939$	27.1246	+	46.9812i	0.885178	+	1.53317i
$940$	−0.763932	−	1.32317i	−0.0249167	−	0.0431570i
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	0.989599	+	0.143856i	$0.0459502\pi$
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	−0.370216	+	0.928946i	$0.620716\pi$
$942$	54.6869	−	94.7205i	1.78180	−	3.08616i
$943$	−19.9787	−	34.6041i	−0.650596	−	1.12687i
$944$	5.42705	−	9.39993i	0.176635	−	0.305942i
$945$	−3.41641			−0.111136
$946$	4.00000			0.130051
$947$	6.52786	−	11.3066i	0.212127	−	0.367415i	−0.740253	−	0.672328i	$-0.765294\pi$
$947$	6.52786	−	11.3066i	0.212127	−	0.367415i	0.952380	+	0.304914i	$0.0986276\pi$
$948$	−11.7082	−	20.2792i	−0.380265	−	0.658638i
$949$	13.7082	−	23.7433i	0.444987	−	0.770740i
$950$	−7.23607	−	12.5332i	−0.234769	−	0.406632i
$951$	6.56231	+	11.3662i	0.212797	+	0.368576i
$952$	0.201626	+	0.349227i	0.00653474	+	0.0113185i
$953$	45.7082			1.48063			0.740317	−	0.672258i	$-0.234675\pi$
$953$	45.7082			1.48063			0.740317	+	0.672258i	$0.234675\pi$
$954$	63.3050	−	109.647i	2.04957	−	3.54997i
$955$	9.59017	−	16.6107i	0.310331	−	0.537508i
$956$	3.61803	+	6.26662i	0.117016	+	0.202677i
$957$	−17.8885			−0.578254
$958$	−18.8435	+	32.6378i	−0.608805	+	1.05448i
$959$	1.48529			0.0479626
$960$	−13.7082			−0.442430
$961$		0			0
$962$	10.4721			0.337635
$963$	43.0689			1.38788
$964$	−4.43769	+	7.68631i	−0.142929	+	0.247559i
$965$	3.47214			0.111772
$966$	3.52786	+	6.11044i	0.113507	+	0.196600i
$967$	−30.1803	+	52.2739i	−0.970534	+	1.68101i	−0.276587	+	0.960989i	$0.589203\pi$
$967$	−30.1803	+	52.2739i	−0.970534	+	1.68101i	−0.693947	+	0.720026i	$0.744130\pi$
$968$	−7.82624	+	13.5554i	−0.251545	+	0.435688i
$969$	5.52786			0.177581
$970$	12.8992	+	22.3420i	0.414168	+	0.717360i
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	0.998339	−	0.0576061i	$-0.0183467\pi$
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	−0.549058	+	0.835784i	$0.685013\pi$
$972$	11.0000	+	19.0526i	0.352825	+	0.611111i
$973$	−1.58359	+	2.74286i	−0.0507676	+	0.0879321i
$974$	15.5623	+	26.9547i	0.498648	+	0.863684i
$975$	20.9443	−	36.2765i	0.670754	−	1.16178i
$976$	−39.7082			−1.27103
$977$	−47.2492			−1.51164			−0.755818	−	0.654781i	$-0.772761\pi$
$977$	−47.2492			−1.51164			−0.755818	+	0.654781i	$0.772761\pi$
$978$	28.0344	−	48.5571i	0.896443	−	1.55268i
$979$	−11.7082	−	20.2792i	−0.374196	−	0.648126i
$980$	2.14590	−	3.71680i	0.0685482	−	0.118729i
$981$	52.0967	+	90.2342i	1.66332	+	2.88096i
$982$	−3.52786	−	6.11044i	−0.112579	−	0.194992i
$983$	−19.7639	−	34.2321i	−0.630372	−	1.09184i	−0.987476	−	0.157771i	$-0.949569\pi$
$983$	−19.7639	−	34.2321i	−0.630372	−	1.09184i	0.357104	−	0.934065i	$-0.383764\pi$
$984$	50.6525			1.61474
$985$	−5.70820	+	9.88690i	−0.181879	+	0.315023i
$986$	−1.70820	+	2.95870i	−0.0544003	+	0.0942241i
$987$	0.944272	+	1.63553i	0.0300565	+	0.0520594i
$988$	4.47214			0.142278
$989$	−3.52786	+	6.11044i	−0.112180	+	0.194301i
$990$	24.1803			0.768502
$991$	−16.5410			−0.525443			−0.262721	−	0.964872i	$-0.584620\pi$
$991$	−16.5410			−0.525443			−0.262721	+	0.964872i	$0.584620\pi$
$992$		0			0
$993$	−6.47214			−0.205387
$994$	−3.50658			−0.111222
$995$	9.47214	−	16.4062i	0.300287	−	0.520112i
$996$	29.8885			0.947055
$997$	14.6803	+	25.4271i	0.464931	+	0.805284i	0.999198	−	0.0400314i	$-0.0127458\pi$
$997$	14.6803	+	25.4271i	0.464931	+	0.805284i	−0.534267	+	0.845316i	$0.679412\pi$
$998$	5.32624	−	9.22531i	0.168599	−	0.292022i
$999$	−14.4721	+	25.0665i	−0.457878	+	0.793068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.e.439.2		4
31.2	even	5		961.2.g.h.547.1		8
31.3	odd	30		961.2.g.e.448.1		8
31.4	even	5		961.2.g.a.235.1		8
31.5	even	3		31.2.a.a.1.2	✓	2
31.6	odd	6		961.2.c.c.521.2		4
31.7	even	15		961.2.g.a.338.1		8
31.8	even	5		961.2.g.a.816.1		8
31.9	even	15		961.2.d.c.374.1		4
31.10	even	15		961.2.d.d.531.1		4
31.11	odd	30		961.2.d.a.388.1		4
31.12	odd	30		961.2.g.e.844.1		8
31.13	odd	30		961.2.d.g.628.1		4
31.14	even	15		961.2.g.a.732.1		8
31.15	odd	10		961.2.g.e.846.1		8
31.16	even	5		961.2.g.h.846.1		8
31.17	odd	30		961.2.g.d.732.1		8
31.18	even	15		961.2.d.d.628.1		4
31.19	even	15		961.2.g.h.844.1		8
31.20	even	15		961.2.d.c.388.1		4
31.21	odd	30		961.2.d.g.531.1		4
31.22	odd	30		961.2.d.a.374.1		4
31.23	odd	10		961.2.g.d.816.1		8
31.24	odd	30		961.2.g.d.338.1		8
31.25	even	3	inner	961.2.c.e.521.2		4
31.26	odd	6		961.2.a.f.1.2		2
31.27	odd	10		961.2.g.d.235.1		8
31.28	even	15		961.2.g.h.448.1		8
31.29	odd	10		961.2.g.e.547.1		8
31.30	odd	2		961.2.c.c.439.2		4
93.5	odd	6		279.2.a.a.1.1		2
93.26	even	6		8649.2.a.c.1.1		2
124.67	odd	6		496.2.a.i.1.2		2
155.67	odd	12		775.2.b.d.249.4		4
155.98	odd	12		775.2.b.d.249.1		4
155.129	even	6		775.2.a.d.1.1		2
217.160	odd	6		1519.2.a.a.1.2		2
248.5	even	6		1984.2.a.r.1.2		2
248.67	odd	6		1984.2.a.n.1.1		2
341.98	odd	6		3751.2.a.b.1.1		2
372.191	even	6		4464.2.a.bf.1.1		2
403.129	even	6		5239.2.a.f.1.1		2
465.284	odd	6		6975.2.a.y.1.2		2
527.67	even	6		8959.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	31.5	even	3
279.2.a.a.1.1		2	93.5	odd	6
496.2.a.i.1.2		2	124.67	odd	6
775.2.a.d.1.1		2	155.129	even	6
775.2.b.d.249.1		4	155.98	odd	12
775.2.b.d.249.4		4	155.67	odd	12
961.2.a.f.1.2		2	31.26	odd	6
961.2.c.c.439.2		4	31.30	odd	2
961.2.c.c.521.2		4	31.6	odd	6
961.2.c.e.439.2		4	1.1	even	1	trivial
961.2.c.e.521.2		4	31.25	even	3	inner
961.2.d.a.374.1		4	31.22	odd	30
961.2.d.a.388.1		4	31.11	odd	30
961.2.d.c.374.1		4	31.9	even	15
961.2.d.c.388.1		4	31.20	even	15
961.2.d.d.531.1		4	31.10	even	15
961.2.d.d.628.1		4	31.18	even	15
961.2.d.g.531.1		4	31.21	odd	30
961.2.d.g.628.1		4	31.13	odd	30
961.2.g.a.235.1		8	31.4	even	5
961.2.g.a.338.1		8	31.7	even	15
961.2.g.a.732.1		8	31.14	even	15
961.2.g.a.816.1		8	31.8	even	5
961.2.g.d.235.1		8	31.27	odd	10
961.2.g.d.338.1		8	31.24	odd	30
961.2.g.d.732.1		8	31.17	odd	30
961.2.g.d.816.1		8	31.23	odd	10
961.2.g.e.448.1		8	31.3	odd	30
961.2.g.e.547.1		8	31.29	odd	10
961.2.g.e.844.1		8	31.12	odd	30
961.2.g.e.846.1		8	31.15	odd	10
961.2.g.h.448.1		8	31.28	even	15
961.2.g.h.547.1		8	31.2	even	5
961.2.g.h.844.1		8	31.19	even	15
961.2.g.h.846.1		8	31.16	even	5
1519.2.a.a.1.2		2	217.160	odd	6
1984.2.a.n.1.1		2	248.67	odd	6
1984.2.a.r.1.2		2	248.5	even	6
3751.2.a.b.1.1		2	341.98	odd	6
4464.2.a.bf.1.1		2	372.191	even	6
5239.2.a.f.1.1		2	403.129	even	6
6975.2.a.y.1.2		2	465.284	odd	6
8649.2.a.c.1.1		2	93.26	even	6
8959.2.a.b.1.2		2	527.67	even	6

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +(1.61803 - 2.80252i) q^{3} +0.618034 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} +(1.61803 - 2.80252i) q^{3} +0.618034 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(-3.73607 - 6.47106i) q^{9} +(-0.809017 - 1.40126i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{12} +(1.61803 + 2.80252i) q^{13} +(-0.190983 + 0.330792i) q^{14} -3.23607 q^{15} -4.85410 q^{16} +(-0.381966 + 0.661585i) q^{17} +(-6.04508 - 10.4704i) q^{18} +(1.11803 - 1.93649i) q^{19} +(-0.309017 - 0.535233i) q^{20} +(0.381966 + 0.661585i) q^{21} +(-1.61803 - 2.80252i) q^{22} +5.70820 q^{23} +(-3.61803 + 6.26662i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.61803 + 4.53457i) q^{26} -14.4721 q^{27} +(-0.0729490 + 0.126351i) q^{28} +2.76393 q^{29} -5.23607 q^{30} -3.38197 q^{32} -6.47214 q^{33} +(-0.618034 + 1.07047i) q^{34} +0.236068 q^{35} +(-2.30902 - 3.99933i) q^{36} +(1.00000 - 1.73205i) q^{37} +(1.80902 - 3.13331i) q^{38} +10.4721 q^{39} +(1.11803 + 1.93649i) q^{40} +(-3.50000 - 6.06218i) q^{41} +(0.618034 + 1.07047i) q^{42} +(-0.618034 + 1.07047i) q^{43} +(-0.618034 - 1.07047i) q^{44} +(-3.73607 + 6.47106i) q^{45} +9.23607 q^{46} +2.47214 q^{47} +(-7.85410 + 13.6037i) q^{48} +(3.47214 + 6.01392i) q^{49} +(3.23607 - 5.60503i) q^{50} +(1.23607 + 2.14093i) q^{51} +(1.00000 + 1.73205i) q^{52} +(5.23607 + 9.06914i) q^{53} -23.4164 q^{54} +(-1.00000 + 1.73205i) q^{55} +(0.263932 - 0.457144i) q^{56} +(-3.61803 - 6.26662i) q^{57} +4.47214 q^{58} +(-1.11803 + 1.93649i) q^{59} -2.00000 q^{60} +8.18034 q^{61} +1.76393 q^{63} +4.23607 q^{64} +(1.61803 - 2.80252i) q^{65} -10.4721 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(9.23607 - 15.9973i) q^{69} +0.381966 q^{70} +(4.59017 + 7.95041i) q^{71} +(8.35410 + 14.4697i) q^{72} +(-4.23607 - 7.33708i) q^{73} +(1.61803 - 2.80252i) q^{74} +(-6.47214 - 11.2101i) q^{75} +(0.690983 - 1.19682i) q^{76} +0.472136 q^{77} +16.9443 q^{78} +(5.85410 - 10.1396i) q^{79} +(2.42705 + 4.20378i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(-5.66312 - 9.80881i) q^{82} +(7.47214 + 12.9421i) q^{83} +(0.236068 + 0.408882i) q^{84} +0.763932 q^{85} +(-1.00000 + 1.73205i) q^{86} +(4.47214 - 7.74597i) q^{87} +(2.23607 + 3.87298i) q^{88} +11.7082 q^{89} +(-6.04508 + 10.4704i) q^{90} -0.763932 q^{91} +3.52786 q^{92} +4.00000 q^{94} -2.23607 q^{95} +(-5.47214 + 9.47802i) q^{96} -15.9443 q^{97} +(5.61803 + 9.73072i) q^{98} +(-7.47214 + 12.9421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 6 q^{6} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 6 * q^6 + 4 * q^7 - 6 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 6 q^{6} + 4 q^{7} - 6 q^{9} - q^{10} - 4 q^{11} + 4 q^{12} + 2 q^{13} - 3 q^{14} - 4 q^{15} - 6 q^{16} - 6 q^{17} - 13 q^{18} + q^{20} + 6 q^{21} - 2 q^{22} - 4 q^{23} - 10 q^{24} + 8 q^{25} + 6 q^{26} - 40 q^{27} - 7 q^{28} + 20 q^{29} - 12 q^{30} - 18 q^{32} - 8 q^{33} + 2 q^{34} - 8 q^{35} - 7 q^{36} + 4 q^{37} + 5 q^{38} + 24 q^{39} - 14 q^{41} - 2 q^{42} + 2 q^{43} + 2 q^{44} - 6 q^{45} + 28 q^{46} - 8 q^{47} - 18 q^{48} - 4 q^{49} + 4 q^{50} - 4 q^{51} + 4 q^{52} + 12 q^{53} - 40 q^{54} - 4 q^{55} + 10 q^{56} - 10 q^{57} - 8 q^{60} - 12 q^{61} + 16 q^{63} + 8 q^{64} + 2 q^{65} - 24 q^{66} - 16 q^{67} + 8 q^{68} + 28 q^{69} + 6 q^{70} - 4 q^{71} + 20 q^{72} - 8 q^{73} + 2 q^{74} - 8 q^{75} + 5 q^{76} - 16 q^{77} + 32 q^{78} + 10 q^{79} + 3 q^{80} - 22 q^{81} - 7 q^{82} + 12 q^{83} - 8 q^{84} + 12 q^{85} - 4 q^{86} + 20 q^{89} - 13 q^{90} - 12 q^{91} + 32 q^{92} + 16 q^{94} - 4 q^{96} - 28 q^{97} + 18 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 6 * q^6 + 4 * q^7 - 6 * q^9 - q^10 - 4 * q^11 + 4 * q^12 + 2 * q^13 - 3 * q^14 - 4 * q^15 - 6 * q^16 - 6 * q^17 - 13 * q^18 + q^20 + 6 * q^21 - 2 * q^22 - 4 * q^23 - 10 * q^24 + 8 * q^25 + 6 * q^26 - 40 * q^27 - 7 * q^28 + 20 * q^29 - 12 * q^30 - 18 * q^32 - 8 * q^33 + 2 * q^34 - 8 * q^35 - 7 * q^36 + 4 * q^37 + 5 * q^38 + 24 * q^39 - 14 * q^41 - 2 * q^42 + 2 * q^43 + 2 * q^44 - 6 * q^45 + 28 * q^46 - 8 * q^47 - 18 * q^48 - 4 * q^49 + 4 * q^50 - 4 * q^51 + 4 * q^52 + 12 * q^53 - 40 * q^54 - 4 * q^55 + 10 * q^56 - 10 * q^57 - 8 * q^60 - 12 * q^61 + 16 * q^63 + 8 * q^64 + 2 * q^65 - 24 * q^66 - 16 * q^67 + 8 * q^68 + 28 * q^69 + 6 * q^70 - 4 * q^71 + 20 * q^72 - 8 * q^73 + 2 * q^74 - 8 * q^75 + 5 * q^76 - 16 * q^77 + 32 * q^78 + 10 * q^79 + 3 * q^80 - 22 * q^81 - 7 * q^82 + 12 * q^83 - 8 * q^84 + 12 * q^85 - 4 * q^86 + 20 * q^89 - 13 * q^90 - 12 * q^91 + 32 * q^92 + 16 * q^94 - 4 * q^96 - 28 * q^97 + 18 * q^98 - 12 * q^99

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