LMFDB - Embedded newform 961.2.c.j.521.5

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.5
Root			$-2.16544i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.j.439.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23217 q^{2} +(-1.03749 - 1.79698i) q^{3} -0.481752 q^{4} +(0.772811 - 1.33855i) q^{5} +(-1.27836 - 2.21419i) q^{6} +(1.90188 + 3.29415i) q^{7} -3.05795 q^{8} +(-0.652760 + 1.13061i) q^{9} +O(q^{10})$	\(q+1.23217 q^{2} +(-1.03749 - 1.79698i) q^{3} -0.481752 q^{4} +(0.772811 - 1.33855i) q^{5} +(-1.27836 - 2.21419i) q^{6} +(1.90188 + 3.29415i) q^{7} -3.05795 q^{8} +(-0.652760 + 1.13061i) q^{9} +(0.952237 - 1.64932i) q^{10} +(1.88076 - 3.25758i) q^{11} +(0.499811 + 0.865698i) q^{12} +(1.31753 - 2.28203i) q^{13} +(2.34344 + 4.05896i) q^{14} -3.20713 q^{15} -2.80441 q^{16} +(-1.88717 - 3.26867i) q^{17} +(-0.804313 + 1.39311i) q^{18} +(-3.04916 - 5.28130i) q^{19} +(-0.372303 + 0.644848i) q^{20} +(3.94635 - 6.83528i) q^{21} +(2.31742 - 4.01389i) q^{22} +0.909847 q^{23} +(3.17258 + 5.49507i) q^{24} +(1.30553 + 2.26124i) q^{25} +(1.62343 - 2.81186i) q^{26} -3.51600 q^{27} +(-0.916233 - 1.58696i) q^{28} -6.80859 q^{29} -3.95173 q^{30} +2.66037 q^{32} -7.80507 q^{33} +(-2.32532 - 4.02757i) q^{34} +5.87917 q^{35} +(0.314468 - 0.544675i) q^{36} +(0.907032 + 1.57103i) q^{37} +(-3.75709 - 6.50747i) q^{38} -5.46769 q^{39} +(-2.36321 + 4.09321i) q^{40} +(-0.168572 + 0.291976i) q^{41} +(4.86258 - 8.42224i) q^{42} +(-1.94200 - 3.36364i) q^{43} +(-0.906060 + 1.56934i) q^{44} +(1.00892 + 1.74750i) q^{45} +1.12109 q^{46} -1.18915 q^{47} +(2.90954 + 5.03948i) q^{48} +(-3.73429 + 6.46798i) q^{49} +(1.60863 + 2.78623i) q^{50} +(-3.91583 + 6.78242i) q^{51} +(-0.634723 + 1.09937i) q^{52} +(1.17206 - 2.03007i) q^{53} -4.33232 q^{54} +(-2.90695 - 5.03498i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(-6.32692 + 10.9586i) q^{57} -8.38936 q^{58} +(-3.88942 - 6.73667i) q^{59} +1.54504 q^{60} -2.72343 q^{61} -4.96588 q^{63} +8.88686 q^{64} +(-2.03641 - 3.52716i) q^{65} -9.61719 q^{66} +(3.71059 - 6.42693i) q^{67} +(0.909147 + 1.57469i) q^{68} +(-0.943955 - 1.63498i) q^{69} +7.24416 q^{70} +(2.54909 - 4.41515i) q^{71} +(1.99610 - 3.45735i) q^{72} +(-2.69587 + 4.66939i) q^{73} +(1.11762 + 1.93577i) q^{74} +(2.70893 - 4.69201i) q^{75} +(1.46894 + 2.54427i) q^{76} +14.3079 q^{77} -6.73714 q^{78} +(4.86861 + 8.43268i) q^{79} +(-2.16728 + 3.75384i) q^{80} +(5.60609 + 9.71003i) q^{81} +(-0.207710 + 0.359765i) q^{82} +(4.19757 - 7.27041i) q^{83} +(-1.90116 + 3.29291i) q^{84} -5.83370 q^{85} +(-2.39288 - 4.14458i) q^{86} +(7.06383 + 12.2349i) q^{87} +(-5.75127 + 9.96149i) q^{88} +5.09560 q^{89} +(1.24316 + 2.15322i) q^{90} +10.0231 q^{91} -0.438320 q^{92} -1.46523 q^{94} -9.42569 q^{95} +(-2.76010 - 4.78064i) q^{96} +10.9142 q^{97} +(-4.60129 + 7.96966i) q^{98} +(2.45537 + 4.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 3 q^{3} + 16 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 3 * q^3 + 16 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9	\( 16 q + 4 q^{2} + 3 q^{3} + 16 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} + 18 q^{11} + 8 q^{13} + 9 q^{14} - 36 q^{15} + 8 q^{16} + 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20} - q^{21} + 4 q^{22} - 44 q^{23} + 30 q^{24} - 13 q^{25} + 9 q^{26} - 36 q^{27} + 5 q^{28} - 24 q^{29} - 22 q^{30} - 42 q^{32} + 12 q^{33} - 7 q^{34} - 24 q^{35} + q^{36} - 8 q^{37} - 7 q^{38} + 2 q^{39} - 11 q^{40} + 22 q^{41} - 6 q^{42} - 2 q^{43} + 4 q^{44} - 36 q^{46} - 36 q^{47} - q^{48} + 2 q^{49} - 27 q^{50} - 2 q^{51} - q^{52} + 6 q^{53} + 14 q^{54} + 28 q^{55} - 30 q^{56} - 17 q^{57} + 10 q^{58} + 4 q^{59} + 80 q^{60} - 60 q^{61} - 46 q^{63} + 18 q^{64} + 3 q^{65} + 20 q^{66} + 13 q^{67} + 30 q^{68} - 22 q^{69} - 78 q^{70} + q^{71} - 3 q^{72} + 2 q^{73} + 8 q^{74} + 23 q^{75} + 33 q^{76} + 48 q^{77} + 8 q^{79} - 24 q^{80} + 28 q^{81} + 19 q^{82} + 39 q^{83} + 8 q^{84} + 52 q^{85} - 16 q^{86} + 15 q^{87} - 17 q^{88} - 54 q^{89} - 8 q^{90} - 32 q^{91} - 64 q^{92} + 44 q^{94} - 12 q^{95} - 12 q^{96} + 68 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 16 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 + 18 * q^11 + 8 * q^13 + 9 * q^14 - 36 * q^15 + 8 * q^16 + 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 - q^21 + 4 * q^22 - 44 * q^23 + 30 * q^24 - 13 * q^25 + 9 * q^26 - 36 * q^27 + 5 * q^28 - 24 * q^29 - 22 * q^30 - 42 * q^32 + 12 * q^33 - 7 * q^34 - 24 * q^35 + q^36 - 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 - 6 * q^42 - 2 * q^43 + 4 * q^44 - 36 * q^46 - 36 * q^47 - q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 - q^52 + 6 * q^53 + 14 * q^54 + 28 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 + 4 * q^59 + 80 * q^60 - 60 * q^61 - 46 * q^63 + 18 * q^64 + 3 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 + 2 * q^73 + 8 * q^74 + 23 * q^75 + 33 * q^76 + 48 * q^77 + 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 + 39 * q^83 + 8 * q^84 + 52 * q^85 - 16 * q^86 + 15 * q^87 - 17 * q^88 - 54 * q^89 - 8 * q^90 - 32 * q^91 - 64 * q^92 + 44 * q^94 - 12 * q^95 - 12 * q^96 + 68 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.23217			0.871277			0.435639	−	0.900122i	$-0.356523\pi$
$2$	1.23217			0.871277			0.435639	+	0.900122i	$0.356523\pi$
$3$	−1.03749	−	1.79698i	−0.598994	−	1.03749i	−0.992970	−	0.118367i	$-0.962234\pi$
$3$	−1.03749	−	1.79698i	−0.598994	−	1.03749i	0.393976	−	0.919121i	$-0.371099\pi$
$4$	−0.481752			−0.240876
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	−0.639853	−	0.768497i	$-0.721005\pi$
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	0.985465	+	0.169880i	$0.0543381\pi$
$6$	−1.27836	−	2.21419i	−0.521890	−	0.903939i
$7$	1.90188	+	3.29415i	0.718843	+	1.24507i	0.961459	+	0.274950i	$0.0886612\pi$
$7$	1.90188	+	3.29415i	0.718843	+	1.24507i	−0.242616	+	0.970122i	$0.578005\pi$
$8$	−3.05795			−1.08115
$9$	−0.652760	+	1.13061i	−0.217587	+	0.376871i
$10$	0.952237	−	1.64932i	0.301124	−	0.521562i
$11$	1.88076	−	3.25758i	0.567071	−	0.982196i	−0.429783	−	0.902932i	$-0.641410\pi$
$11$	1.88076	−	3.25758i	0.567071	−	0.982196i	0.996854	−	0.0792636i	$-0.0252569\pi$
$12$	0.499811	+	0.865698i	0.144283	+	0.249906i
$13$	1.31753	−	2.28203i	0.365418	−	0.632922i	−0.623426	−	0.781883i	$-0.714260\pi$
$13$	1.31753	−	2.28203i	0.365418	−	0.632922i	0.988843	+	0.148961i	$0.0475929\pi$
$14$	2.34344	+	4.05896i	0.626311	+	1.08480i
$15$	−3.20713			−0.828077
$16$	−2.80441			−0.701103
$17$	−1.88717	−	3.26867i	−0.457706	−	0.792770i	0.541133	−	0.840937i	$-0.317995\pi$
$17$	−1.88717	−	3.26867i	−0.457706	−	0.792770i	−0.998839	+	0.0481669i	$0.984662\pi$
$18$	−0.804313	+	1.39311i	−0.189578	+	0.328359i
$19$	−3.04916	−	5.28130i	−0.699525	−	1.21161i	−0.968631	−	0.248502i	$-0.920062\pi$
$19$	−3.04916	−	5.28130i	−0.699525	−	1.21161i	0.269107	−	0.963110i	$-0.413272\pi$
$20$	−0.372303	+	0.644848i	−0.0832495	+	0.144192i
$21$	3.94635	−	6.83528i	0.861164	−	1.49158i
$22$	2.31742	−	4.01389i	0.494076	−	0.855765i
$23$	0.909847			0.189716			0.0948581	−	0.995491i	$-0.469760\pi$
$23$	0.909847			0.189716			0.0948581	+	0.995491i	$0.469760\pi$
$24$	3.17258	+	5.49507i	0.647600	+	1.12168i
$25$	1.30553	+	2.26124i	0.261105	+	0.452247i
$26$	1.62343	−	2.81186i	0.318380	−	0.551450i
$27$	−3.51600			−0.676655
$28$	−0.916233	−	1.58696i	−0.173152	−	0.299908i
$29$	−6.80859			−1.26432			−0.632162	−	0.774836i	$-0.717832\pi$
$29$	−6.80859			−1.26432			−0.632162	+	0.774836i	$0.717832\pi$
$30$	−3.95173			−0.721485
$31$		0			0
$31$		0			0
$32$	2.66037			0.470292
$33$	−7.80507			−1.35869
$34$	−2.32532	−	4.02757i	−0.398789	−	0.690722i
$35$	5.87917			0.993762
$36$	0.314468	−	0.544675i	0.0524114	−	0.0907792i
$37$	0.907032	+	1.57103i	0.149115	+	0.258275i	0.930901	−	0.365272i	$-0.119024\pi$
$37$	0.907032	+	1.57103i	0.149115	+	0.258275i	−0.781786	+	0.623547i	$0.785691\pi$
$38$	−3.75709	−	6.50747i	−0.609480	−	1.05565i
$39$	−5.46769			−0.875531
$40$	−2.36321	+	4.09321i	−0.373657	+	0.647193i
$41$	−0.168572	+	0.291976i	−0.0263266	+	0.0455990i	−0.878889	−	0.477027i	$-0.841714\pi$
$41$	−0.168572	+	0.291976i	−0.0263266	+	0.0455990i	0.852562	+	0.522626i	$0.175048\pi$
$42$	4.86258	−	8.42224i	0.750313	−	1.29958i
$43$	−1.94200	−	3.36364i	−0.296152	−	0.512950i	0.679100	−	0.734045i	$-0.262370\pi$
$43$	−1.94200	−	3.36364i	−0.296152	−	0.512950i	−0.975252	+	0.221095i	$0.929037\pi$
$44$	−0.906060	+	1.56934i	−0.136594	+	0.236587i
$45$	1.00892	+	1.74750i	0.150401	+	0.260502i
$46$	1.12109			0.165295
$47$	−1.18915			−0.173455			−0.0867275	−	0.996232i	$-0.527641\pi$
$47$	−1.18915			−0.173455			−0.0867275	+	0.996232i	$0.527641\pi$
$48$	2.90954	+	5.03948i	0.419956	+	0.727386i
$49$	−3.73429	+	6.46798i	−0.533470	+	0.923997i
$50$	1.60863	+	2.78623i	0.227495	+	0.394033i
$51$	−3.91583	+	6.78242i	−0.548326	+	0.949728i
$52$	−0.634723	+	1.09937i	−0.0880202	+	0.152456i
$53$	1.17206	−	2.03007i	0.160995	−	0.278852i	−0.774231	−	0.632904i	$-0.781863\pi$
$53$	1.17206	−	2.03007i	0.160995	−	0.278852i	0.935226	+	0.354052i	$0.115196\pi$
$54$	−4.33232			−0.589554
$55$	−2.90695	−	5.03498i	−0.391973	−	0.678917i
$56$	−5.81584	−	10.0733i	−0.777175	−	1.34611i
$57$	−6.32692	+	10.9586i	−0.838022	+	1.45150i
$58$	−8.38936			−1.10158
$59$	−3.88942	−	6.73667i	−0.506359	−	0.877039i	−0.999973	−	0.00735816i	$-0.997658\pi$
$59$	−3.88942	−	6.73667i	−0.506359	−	0.877039i	0.493614	−	0.869681i	$-0.335676\pi$
$60$	1.54504			0.199464
$61$	−2.72343			−0.348700			−0.174350	−	0.984684i	$-0.555782\pi$
$61$	−2.72343			−0.348700			−0.174350	+	0.984684i	$0.555782\pi$
$62$		0			0
$63$	−4.96588			−0.625642
$64$	8.88686			1.11086
$65$	−2.03641	−	3.52716i	−0.252585	−	0.437490i
$66$	−9.61719			−1.18379
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	−0.545269	−	0.838261i	$-0.683573\pi$
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	0.998590	+	0.0530864i	$0.0169059\pi$
$68$	0.909147	+	1.57469i	0.110250	+	0.190959i
$69$	−0.943955	−	1.63498i	−0.113639	−	0.196828i
$70$	7.24416			0.865842
$71$	2.54909	−	4.41515i	0.302521	−	0.523982i	−0.674185	−	0.738562i	$-0.735505\pi$
$71$	2.54909	−	4.41515i	0.302521	−	0.523982i	0.976706	+	0.214580i	$0.0688383\pi$
$72$	1.99610	−	3.45735i	0.235243	−	0.407453i
$73$	−2.69587	+	4.66939i	−0.315528	+	0.546510i	−0.979550	−	0.201203i	$-0.935515\pi$
$73$	−2.69587	+	4.66939i	−0.315528	+	0.546510i	0.664022	+	0.747713i	$0.268848\pi$
$74$	1.11762	+	1.93577i	0.129921	+	0.225029i
$75$	2.70893	−	4.69201i	0.312801	−	0.541786i
$76$	1.46894	+	2.54427i	0.168499	+	0.291848i
$77$	14.3079			1.63054
$78$	−6.73714			−0.762830
$79$	4.86861	+	8.43268i	0.547762	+	0.948751i	0.998427	+	0.0560584i	$0.0178533\pi$
$79$	4.86861	+	8.43268i	0.547762	+	0.948751i	−0.450666	+	0.892693i	$0.648813\pi$
$80$	−2.16728	+	3.75384i	−0.242309	+	0.419692i
$81$	5.60609	+	9.71003i	0.622899	+	1.07889i
$82$	−0.207710	+	0.359765i	−0.0229377	+	0.0397293i
$83$	4.19757	−	7.27041i	0.460743	−	0.798031i	−0.538255	−	0.842782i	$-0.680916\pi$
$83$	4.19757	−	7.27041i	0.460743	−	0.798031i	0.998998	+	0.0447511i	$0.0142495\pi$
$84$	−1.90116	+	3.29291i	−0.207434	+	0.359286i
$85$	−5.83370			−0.632754
$86$	−2.39288	−	4.14458i	−0.258030	−	0.446922i
$87$	7.06383	+	12.2349i	0.757322	+	1.31172i
$88$	−5.75127	+	9.96149i	−0.613087	+	1.06190i
$89$	5.09560			0.540132			0.270066	−	0.962842i	$-0.412954\pi$
$89$	5.09560			0.540132			0.270066	+	0.962842i	$0.412954\pi$
$90$	1.24316	+	2.15322i	0.131041	+	0.226970i
$91$	10.0231			1.05071
$92$	−0.438320			−0.0456980
$93$		0			0
$94$	−1.46523			−0.151127
$95$	−9.42569			−0.967056
$96$	−2.76010	−	4.78064i	−0.281702	−	0.487922i
$97$	10.9142			1.10817			0.554086	−	0.832460i	$-0.313068\pi$
$97$	10.9142			1.10817			0.554086	+	0.832460i	$0.313068\pi$
$98$	−4.60129	+	7.96966i	−0.464800	+	0.805057i
$99$	2.45537	+	4.25283i	0.246774	+	0.427426i
$100$	−0.628939	−	1.08935i	−0.0628939	−	0.108935i
$101$	−0.398727			−0.0396748			−0.0198374	−	0.999803i	$-0.506315\pi$
$101$	−0.398727			−0.0396748			−0.0198374	+	0.999803i	$0.506315\pi$
$102$	−4.82498	+	8.35710i	−0.477744	+	0.827477i
$103$	−1.63840	+	2.83779i	−0.161436	+	0.279616i	−0.935384	−	0.353633i	$-0.884946\pi$
$103$	−1.63840	+	2.83779i	−0.161436	+	0.279616i	0.773948	+	0.633250i	$0.218279\pi$
$104$	−4.02894	+	6.97833i	−0.395070	+	0.684281i
$105$	−6.09957	−	10.5648i	−0.595257	−	1.03102i
$106$	1.44418	−	2.50140i	0.140271	−	0.242957i
$107$	−1.57842	−	2.73391i	−0.152592	−	0.264297i	0.779588	−	0.626293i	$-0.215429\pi$
$107$	−1.57842	−	2.73391i	−0.152592	−	0.264297i	−0.932180	+	0.361996i	$0.882095\pi$
$108$	1.69384			0.162990
$109$	6.95622			0.666285			0.333142	−	0.942877i	$-0.391891\pi$
$109$	6.95622			0.666285			0.333142	+	0.942877i	$0.391891\pi$
$110$	−3.58186	−	6.20397i	−0.341517	−	0.591525i
$111$	1.88207	−	3.25984i	0.178638	−	0.309410i
$112$	−5.33365	−	9.23816i	−0.503983	−	0.872924i
$113$	7.62339	−	13.2041i	0.717148	−	1.24214i	−0.244977	−	0.969529i	$-0.578780\pi$
$113$	7.62339	−	13.2041i	0.717148	−	1.24214i	0.962125	−	0.272609i	$-0.0878864\pi$
$114$	−7.79586	+	13.5028i	−0.730149	+	1.26466i
$115$	0.703140	−	1.21787i	0.0655682	−	0.113567i
$116$	3.28005			0.304545
$117$	1.72006	+	2.97924i	0.159020	+	0.275431i
$118$	−4.79243	−	8.30073i	−0.441179	−	0.764144i
$119$	7.17834	−	12.4332i	0.658037	−	1.13975i
$120$	9.80722			0.895273
$121$	−1.57453	−	2.72717i	−0.143139	−	0.247925i
$122$	−3.35574			−0.303814
$123$	0.699567			0.0630778
$124$		0			0
$125$	11.7638			1.05219
$126$	−6.11882			−0.545108
$127$	10.1132	+	17.5165i	0.897400	+	1.55434i	0.830806	+	0.556562i	$0.187880\pi$
$127$	10.1132	+	17.5165i	0.897400	+	1.55434i	0.0665942	+	0.997780i	$0.478787\pi$
$128$	5.62940			0.497573
$129$	−4.02960	+	6.97946i	−0.354786	+	0.614508i
$130$	−2.50920	−	4.34607i	−0.220072	−	0.381175i
$131$	−6.32564	−	10.9563i	−0.552674	−	0.957259i	−0.998080	−	0.0619307i	$-0.980274\pi$
$131$	−6.32564	−	10.9563i	−0.552674	−	0.957259i	0.445407	−	0.895328i	$-0.353059\pi$
$132$	3.76010			0.327275
$133$	11.5983	−	20.0888i	1.00570	−	1.74192i
$134$	4.57209	−	7.91909i	0.394968	−	0.684105i
$135$	−2.71721	+	4.70634i	−0.233860	+	0.405057i
$136$	5.77086	+	9.99543i	0.494847	+	0.857101i
$137$	4.93901	−	8.55461i	0.421968	−	0.730870i	−0.574164	−	0.818740i	$-0.694673\pi$
$137$	4.93901	−	8.55461i	0.421968	−	0.730870i	0.996132	+	0.0878706i	$0.0280062\pi$
$138$	−1.16311	−	2.01457i	−0.0990109	−	0.171492i
$139$	−15.4990			−1.31461			−0.657303	−	0.753626i	$-0.728303\pi$
$139$	−15.4990			−1.31461			−0.657303	+	0.753626i	$0.728303\pi$
$140$	−2.83230			−0.239373
$141$	1.23373	+	2.13687i	0.103898	+	0.179957i
$142$	3.14092	−	5.44023i	0.263580	−	0.456534i
$143$	−4.95593	−	8.58392i	−0.414435	−	0.717823i
$144$	1.83061	−	3.17071i	0.152551	−	0.264226i
$145$	−5.26176	+	9.11363i	−0.436965	+	0.756846i
$146$	−3.32178	+	5.75349i	−0.274912	+	0.476162i
$147$	15.4971			1.27818
$148$	−0.436964	−	0.756844i	−0.0359182	−	0.0622122i
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	0.988659	+	0.150178i	$0.0479848\pi$
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	−0.364271	+	0.931293i	$0.618682\pi$
$150$	3.33787	−	5.78136i	0.272536	−	0.472046i
$151$	−0.261828			−0.0213073			−0.0106536	−	0.999943i	$-0.503391\pi$
$151$	−0.261828			−0.0213073			−0.0106536	+	0.999943i	$0.503391\pi$
$152$	9.32416	+	16.1499i	0.756289	+	1.30993i
$153$	4.92748			0.398363
$154$	17.6298			1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	15.9265			1.27108			0.635538	−	0.772070i	$-0.280778\pi$
$157$	15.9265			1.27108			0.635538	+	0.772070i	$0.280778\pi$
$158$	5.99897	+	10.3905i	0.477252	+	0.826625i
$159$	−4.86400			−0.385740
$160$	2.05597	−	3.56104i	0.162538	−	0.281525i
$161$	1.73042	+	2.99717i	0.136376	+	0.236210i
$162$	6.90767	+	11.9644i	0.542718	+	0.940014i
$163$	−0.133175			−0.0104311			−0.00521555	−	0.999986i	$-0.501660\pi$
$163$	−0.133175			−0.0104311			−0.00521555	+	0.999986i	$0.501660\pi$
$164$	0.0812100	−	0.140660i	0.00634143	−	0.0109837i
$165$	−6.03185	+	10.4475i	−0.469579	+	0.813334i
$166$	5.17213	−	8.95840i	0.401435	−	0.695306i
$167$	1.97439	+	3.41974i	0.152783	+	0.264628i	0.932250	−	0.361816i	$-0.117843\pi$
$167$	1.97439	+	3.41974i	0.152783	+	0.264628i	−0.779467	+	0.626444i	$0.784510\pi$
$168$	−12.0677	+	20.9019i	−0.931045	+	1.61262i
$169$	3.02822	+	5.24503i	0.232940	+	0.403464i
$170$	−7.18813			−0.551304
$171$	7.96147			0.608829
$172$	0.935560	+	1.62044i	0.0713358	+	0.123557i
$173$	7.22847	−	12.5201i	0.549570	−	0.951884i	−0.448733	−	0.893666i	$-0.648125\pi$
$173$	7.22847	−	12.5201i	0.549570	−	0.951884i	0.998304	−	0.0582182i	$-0.0185419\pi$
$174$	8.70385	+	15.0755i	0.659837	+	1.14287i
$175$	−4.96590	+	8.60120i	−0.375387	+	0.650189i
$176$	−5.27443	+	9.13559i	−0.397575	+	0.688621i
$177$	−8.07044	+	13.9784i	−0.606611	+	1.05068i
$178$	6.27865			0.470605
$179$	8.85994	+	15.3459i	0.662223	+	1.14700i	0.980030	+	0.198849i	$0.0637203\pi$
$179$	8.85994	+	15.3459i	0.662223	+	1.14700i	−0.317807	+	0.948155i	$0.602946\pi$
$180$	−0.486049	−	0.841862i	−0.0362280	−	0.0627487i
$181$	6.02958	−	10.4435i	0.448175	−	0.776262i	−0.550092	−	0.835104i	$-0.685407\pi$
$181$	6.02958	−	10.4435i	0.448175	−	0.776262i	0.998267	+	0.0588418i	$0.0187408\pi$
$182$	12.3502			0.915461
$183$	2.82553	+	4.89396i	0.208869	+	0.361772i
$184$	−2.78226			−0.205111
$185$	2.80386			0.206144
$186$		0			0
$187$	−14.1973			−1.03821
$188$	0.572874			0.0417811
$189$	−6.68701	−	11.5822i	−0.486409	−	0.842484i
$190$	−11.6141			−0.842574
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	−0.943064	−	0.332612i	$-0.892070\pi$
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	0.759583	+	0.650411i	$0.225403\pi$
$192$	−9.22001	−	15.9695i	−0.665397	−	1.15250i
$193$	10.0209	+	17.3567i	0.721318	+	1.24936i	0.960472	+	0.278378i	$0.0897968\pi$
$193$	10.0209	+	17.3567i	0.721318	+	1.24936i	−0.239153	+	0.970982i	$0.576870\pi$
$194$	13.4482			0.965525
$195$	−4.22549	+	7.31877i	−0.302594	+	0.524108i
$196$	1.79900	−	3.11596i	0.128500	−	0.222568i
$197$	−10.8542	+	18.8000i	−0.773328	+	1.33944i	0.162401	+	0.986725i	$0.448076\pi$
$197$	−10.8542	+	18.8000i	−0.773328	+	1.33944i	−0.935729	+	0.352719i	$0.885257\pi$
$198$	3.02544	+	5.24022i	0.215009	+	0.372406i
$199$	−7.58275	+	13.1337i	−0.537527	+	0.931024i	0.461509	+	0.887135i	$0.347308\pi$
$199$	−7.58275	+	13.1337i	−0.537527	+	0.931024i	−0.999036	+	0.0438890i	$0.986025\pi$
$200$	−3.99222	−	6.91474i	−0.282293	−	0.488946i
$201$	−15.3988			−1.08615
$202$	−0.491300			−0.0345678
$203$	−12.9491	−	22.4285i	−0.908850	−	1.57417i
$204$	1.88646	−	3.26744i	0.132078	−	0.228767i
$205$	0.260549	+	0.451284i	0.0181975	+	0.0315191i
$206$	−2.01879	+	3.49665i	−0.140656	+	0.243623i
$207$	−0.593912	+	1.02869i	−0.0412797	+	0.0714986i
$208$	−3.69490	+	6.39976i	−0.256195	+	0.443743i
$209$	−22.9390			−1.58672
$210$	−7.51572	−	13.0176i	−0.518634	−	0.898300i
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	0.736885	−	0.676018i	$-0.236296\pi$
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	−0.953891	+	0.300152i	$0.902963\pi$
$212$	−0.564643	+	0.977990i	−0.0387798	+	0.0671687i
$213$	−10.5786			−0.724833
$214$	−1.94489	−	3.36865i	−0.132950	−	0.230276i
$215$	−6.00319			−0.409414
$216$	10.7517			0.731564
$217$		0			0
$218$	8.57126			0.580519
$219$	11.1877			0.755997
$220$	1.40043	+	2.42561i	0.0944168	+	0.163535i
$221$	−9.94562			−0.669015
$222$	2.31903	−	4.01668i	0.155643	−	0.269582i
$223$	−3.69455	−	6.39915i	−0.247406	−	0.428519i	0.715400	−	0.698716i	$-0.246245\pi$
$223$	−3.69455	−	6.39915i	−0.247406	−	0.428519i	−0.962805	+	0.270196i	$0.912911\pi$
$224$	5.05971	+	8.76367i	0.338066	+	0.585547i
$225$	−3.40878			−0.227252
$226$	9.39333	−	16.2697i	0.624835	−	1.08225i
$227$	−9.61989	+	16.6621i	−0.638495	+	1.10591i	0.347269	+	0.937766i	$0.387109\pi$
$227$	−9.61989	+	16.6621i	−0.638495	+	1.10591i	−0.985763	+	0.168140i	$0.946224\pi$
$228$	3.04801	−	5.27930i	0.201859	−	0.349630i
$229$	3.04355	+	5.27159i	0.201124	+	0.348356i	0.948891	−	0.315605i	$-0.102207\pi$
$229$	3.04355	+	5.27159i	0.201124	+	0.348356i	−0.747767	+	0.663961i	$0.768874\pi$
$230$	0.866390	−	1.50063i	0.0571280	−	0.0989487i
$231$	−14.8443	−	25.7111i	−0.976683	−	1.69166i
$232$	20.8203			1.36692
$233$	17.5280			1.14830			0.574150	−	0.818750i	$-0.305333\pi$
$233$	17.5280			1.14830			0.574150	+	0.818750i	$0.305333\pi$
$234$	2.11942	+	3.67094i	0.138551	+	0.239977i
$235$	−0.918986	+	1.59173i	−0.0599481	+	0.103833i
$236$	1.87373	+	3.24540i	0.121970	+	0.211257i
$237$	10.1022	−	17.4976i	0.656212	−	1.13659i
$238$	8.84495	−	15.3199i	0.573333	−	0.993042i
$239$	13.9560	−	24.1725i	0.902740	−	1.56359i	0.0788174	−	0.996889i	$-0.474886\pi$
$239$	13.9560	−	24.1725i	0.902740	−	1.56359i	0.823923	−	0.566702i	$-0.191781\pi$
$240$	8.99411			0.580567
$241$	−11.3749	−	19.7018i	−0.732720	−	1.26911i	−0.955717	−	0.294289i	$-0.904917\pi$
$241$	−11.3749	−	19.7018i	−0.732720	−	1.26911i	0.222997	−	0.974819i	$-0.428416\pi$
$242$	−1.94010	−	3.36034i	−0.124714	−	0.216011i
$243$	6.35849	−	11.0132i	0.407897	−	0.706499i
$244$	1.31202			0.0839933
$245$	5.77180	+	9.99705i	0.368747	+	0.638688i
$246$	0.861987			0.0549583
$247$	−16.0694			−1.02247
$248$		0			0
$249$	−17.4197			−1.10393
$250$	14.4950			0.916747
$251$	8.11725	+	14.0595i	0.512356	+	0.887427i	0.999897	+	0.0143270i	$0.00456059\pi$
$251$	8.11725	+	14.0595i	0.512356	+	0.887427i	−0.487541	+	0.873100i	$0.662106\pi$
$252$	2.39232			0.150702
$253$	1.71121	−	2.96390i	0.107583	−	0.186339i
$254$	12.4612	+	21.5834i	0.781884	+	1.35426i
$255$	6.05239	+	10.4831i	0.379016	+	0.656474i
$256$	−10.8373			−0.677333
$257$	−11.6761	+	20.2235i	−0.728332	+	1.26151i	0.229256	+	0.973366i	$0.426371\pi$
$257$	−11.6761	+	20.2235i	−0.728332	+	1.26151i	−0.957588	+	0.288142i	$0.906963\pi$
$258$	−4.96516	+	8.59990i	−0.309117	+	0.535407i
$259$	−3.45013	+	5.97580i	−0.214381	+	0.371318i
$260$	0.981042	+	1.69921i	0.0608417	+	0.105381i
$261$	4.44438	−	7.69789i	0.275100	−	0.476487i
$262$	−7.79428	−	13.5001i	−0.481532	−	0.834038i
$263$	−10.3944			−0.640944			−0.320472	−	0.947258i	$-0.603841\pi$
$263$	−10.3944			−0.640944			−0.320472	+	0.947258i	$0.603841\pi$
$264$	23.8675			1.46894
$265$	−1.81157	−	3.13773i	−0.111284	−	0.192749i
$266$	14.2911	−	24.7528i	0.876240	−	1.51769i
$267$	−5.28662	−	9.15669i	−0.323536	−	0.560380i
$268$	−1.78758	+	3.09618i	−0.109194	+	0.189130i
$269$	2.20902	−	3.82614i	0.134686	−	0.233284i	−0.790791	−	0.612086i	$-0.790331\pi$
$269$	2.20902	−	3.82614i	0.134686	−	0.233284i	0.925478	+	0.378802i	$0.123664\pi$
$270$	−3.34807	+	5.79902i	−0.203757	+	0.352917i
$271$	6.15286			0.373760			0.186880	−	0.982383i	$-0.440162\pi$
$271$	6.15286			0.373760			0.186880	+	0.982383i	$0.440162\pi$
$272$	5.29240	+	9.16671i	0.320899	+	0.555813i
$273$	−10.3989	−	18.0114i	−0.629369	−	1.09010i
$274$	6.08571	−	10.5408i	0.367651	−	0.636790i
$275$	9.82153			0.592261
$276$	0.454752	+	0.787653i	0.0273728	+	0.0474111i
$277$	22.0474			1.32470			0.662350	−	0.749194i	$-0.269559\pi$
$277$	22.0474			1.32470			0.662350	+	0.749194i	$0.269559\pi$
$278$	−19.0974			−1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	−30.7736			−1.83580			−0.917899	−	0.396815i	$-0.870115\pi$
$281$	−30.7736			−1.83580			−0.917899	+	0.396815i	$0.870115\pi$
$282$	1.52016	+	2.63300i	0.0905243	+	0.156793i
$283$	−21.3453			−1.26884			−0.634422	−	0.772987i	$-0.718762\pi$
$283$	−21.3453			−1.26884			−0.634422	+	0.772987i	$0.718762\pi$
$284$	−1.22803	+	2.12701i	−0.0728701	+	0.126215i
$285$	9.77904	+	16.9378i	0.579260	+	1.00331i
$286$	−6.10656	−	10.5769i	−0.361088	−	0.625423i
$287$	−1.28242			−0.0756987
$288$	−1.73658	+	3.00785i	−0.102329	+	0.177239i
$289$	1.37718	−	2.38535i	0.0810107	−	0.140315i
$290$	−6.48339	+	11.2296i	−0.380718	+	0.659422i
$291$	−11.3234	−	19.6126i	−0.663788	−	1.14971i
$292$	1.29874	−	2.24948i	0.0760030	−	0.131641i
$293$	0.899514	+	1.55800i	0.0525501	+	0.0910195i	0.891104	−	0.453799i	$-0.149932\pi$
$293$	0.899514	+	1.55800i	0.0525501	+	0.0910195i	−0.838554	+	0.544819i	$0.816598\pi$
$294$	19.0951			1.11365
$295$	−12.0231			−0.700014
$296$	−2.77365	−	4.80411i	−0.161215	−	0.279233i
$297$	−6.61276	+	11.4536i	−0.383712	+	0.664608i
$298$	9.39115	+	16.2660i	0.544015	+	0.942261i
$299$	1.19875	−	2.07630i	0.0693256	−	0.120076i
$300$	−1.30503	+	2.26038i	−0.0753461	+	0.130503i
$301$	7.38689	−	12.7945i	0.425773	−	0.737461i
$302$	−0.322617			−0.0185645
$303$	0.413674	+	0.716505i	0.0237650	+	0.0411621i
$304$	8.55109	+	14.8109i	0.490439	+	0.849465i
$305$	−2.10470	+	3.64545i	−0.120515	+	0.208738i
$306$	6.07150			0.347085
$307$	−13.3847	−	23.1830i	−0.763905	−	1.32312i	−0.940823	−	0.338897i	$-0.889946\pi$
$307$	−13.3847	−	23.1830i	−0.763905	−	1.32312i	0.176918	−	0.984226i	$-0.443387\pi$
$308$	−6.89287			−0.392758
$309$	6.79928			0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	16.7199			0.946578
$313$	5.67141	+	9.82318i	0.320567	+	0.555239i	0.980605	−	0.195993i	$-0.0627931\pi$
$313$	5.67141	+	9.82318i	0.320567	+	0.555239i	−0.660038	+	0.751232i	$0.729460\pi$
$314$	19.6242			1.10746
$315$	−3.83769	+	6.64708i	−0.216229	+	0.374520i
$316$	−2.34546	−	4.06246i	−0.131943	−	0.228531i
$317$	−12.9407	−	22.4139i	−0.726820	−	1.25889i	−0.958220	−	0.286031i	$-0.907664\pi$
$317$	−12.9407	−	22.4139i	−0.726820	−	1.25889i	0.231400	−	0.972859i	$-0.425669\pi$
$318$	−5.99329			−0.336087
$319$	−12.8053	+	22.1795i	−0.716961	+	1.24181i
$320$	6.86787	−	11.8955i	0.383925	−	0.664978i
$321$	−3.27519	+	5.67279i	−0.182803	+	0.316624i
$322$	2.13217	+	3.69303i	0.118821	+	0.205805i
$323$	−11.5086	+	19.9334i	−0.640353	+	1.10912i
$324$	−2.70074	−	4.67782i	−0.150041	−	0.259879i
$325$	6.88028			0.381649
$326$	−0.164095			−0.00908838
$327$	−7.21699	−	12.5002i	−0.399100	−	0.691262i
$328$	0.515485	−	0.892846i	0.0284629	−	0.0492992i
$329$	−2.26161	−	3.91723i	−0.124687	−	0.215964i
$330$	−7.43227	+	12.8731i	−0.409133	+	0.708639i
$331$	−0.382894	+	0.663192i	−0.0210457	+	0.0364523i	−0.876356	−	0.481663i	$-0.840033\pi$
$331$	−0.382894	+	0.663192i	−0.0210457	+	0.0364523i	0.855311	+	0.518115i	$0.173366\pi$
$332$	−2.02219	+	3.50253i	−0.110982	+	0.192226i
$333$	−2.36830			−0.129782
$334$	2.43279	+	4.21371i	0.133116	+	0.230564i
$335$	−5.73517	−	9.93361i	−0.313346	−	0.542731i
$336$	−11.0672	+	19.1689i	−0.603765	+	1.04575i
$337$	2.39434			0.130428			0.0652140	−	0.997871i	$-0.479227\pi$
$337$	2.39434			0.130428			0.0652140	+	0.997871i	$0.479227\pi$
$338$	3.73129	+	6.46278i	0.202955	+	0.351529i
$339$	−31.6367			−1.71827
$340$	2.81040			0.152415
$341$		0			0
$342$	9.80991			0.530459
$343$	−1.78235			−0.0962378
$344$	5.93852	+	10.2858i	0.320184	+	0.554574i
$345$	−2.91800			−0.157100
$346$	8.90672	−	15.4269i	0.478828	−	0.829355i
$347$	−2.82890	−	4.89980i	−0.151863	−	0.263035i	0.780049	−	0.625718i	$-0.215194\pi$
$347$	−2.82890	−	4.89980i	−0.151863	−	0.263035i	−0.931912	+	0.362683i	$0.881861\pi$
$348$	−3.40301	−	5.89419i	−0.182420	−	0.315962i
$349$	29.0676			1.55595			0.777977	−	0.628293i	$-0.216246\pi$
$349$	29.0676			1.55595			0.777977	+	0.628293i	$0.216246\pi$
$350$	−6.11885	+	10.5982i	−0.327066	+	0.566495i
$351$	−4.63244	+	8.02363i	−0.247262	+	0.428270i
$352$	5.00353	−	8.66636i	0.266689	−	0.461919i
$353$	9.63760	+	16.6928i	0.512958	+	0.888469i	0.999887	+	0.0150275i	$0.00478359\pi$
$353$	9.63760	+	16.6928i	0.512958	+	0.888469i	−0.486929	+	0.873441i	$0.661883\pi$
$354$	−9.94417	+	17.2238i	−0.528527	+	0.915435i
$355$	−3.93993	−	6.82416i	−0.209110	−	0.362189i
$356$	−2.45481			−0.130105
$357$	−29.7897			−1.57664
$358$	10.9170	+	18.9088i	0.576980	+	0.999359i
$359$	−5.17214	+	8.95840i	−0.272975	+	0.472806i	−0.969622	−	0.244607i	$-0.921341\pi$
$359$	−5.17214	+	8.95840i	−0.272975	+	0.472806i	0.696647	+	0.717414i	$0.254674\pi$
$360$	−3.08522	−	5.34377i	−0.162606	−	0.281641i
$361$	−9.09472	+	15.7525i	−0.478669	+	0.829080i
$362$	7.42948	−	12.8682i	0.390485	−	0.676340i
$363$	−3.26712	+	5.65881i	−0.171479	+	0.297010i
$364$	−4.82867			−0.253091
$365$	4.16680	+	7.21711i	0.218100	+	0.377761i
$366$	3.48154	+	6.03020i	0.181983	+	0.315203i
$367$	0.0682819	−	0.118268i	0.00356428	−	0.00617352i	−0.864238	−	0.503084i	$-0.832199\pi$
$367$	0.0682819	−	0.118268i	0.00356428	−	0.00617352i	0.867802	+	0.496910i	$0.165532\pi$
$368$	−2.55159			−0.133011
$369$	−0.220075	−	0.381180i	−0.0114566	−	0.0198435i
$370$	3.45484			0.179608
$371$	8.91649			0.462921
$372$		0			0
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	−17.4935			−0.904566
$375$	−12.2048	−	21.1393i	−0.630254	−	1.09163i
$376$	3.63635			0.187530
$377$	−8.97053	+	15.5374i	−0.462006	+	0.800218i
$378$	−8.23955	−	14.2713i	−0.423797	−	0.734038i
$379$	2.30407	+	3.99076i	0.118352	+	0.204992i	0.919115	−	0.393990i	$-0.128906\pi$
$379$	2.30407	+	3.99076i	0.118352	+	0.204992i	−0.800763	+	0.598982i	$0.795572\pi$
$380$	4.54084			0.232940
$381$	20.9846	−	36.3464i	1.07507	−	1.86208i
$382$	−3.12449	+	5.41178i	−0.159863	+	0.276891i
$383$	16.1474	−	27.9681i	0.825093	−	1.42910i	−0.0767550	−	0.997050i	$-0.524456\pi$
$383$	16.1474	−	27.9681i	0.825093	−	1.42910i	0.901848	−	0.432053i	$-0.142211\pi$
$384$	−5.84043	−	10.1159i	−0.298043	−	0.516226i
$385$	11.0573	−	19.1519i	0.563534	−	0.976069i
$386$	12.3474	+	21.3864i	0.628468	+	1.08854i
$387$	5.07063			0.257755
$388$	−5.25794			−0.266932
$389$	17.6356	+	30.5458i	0.894162	+	1.54873i	0.834838	+	0.550496i	$0.185561\pi$
$389$	17.6356	+	30.5458i	0.894162	+	1.54873i	0.0593242	+	0.998239i	$0.481105\pi$
$390$	−5.20653	+	9.01798i	−0.263643	+	0.456643i
$391$	−1.71704	−	2.97399i	−0.0868342	−	0.150401i
$392$	11.4192	−	19.7787i	0.576759	−	0.998976i
$393$	−13.1255	+	22.7341i	−0.662096	+	1.14678i
$394$	−13.3742	+	23.1648i	−0.673783	+	1.16703i
$395$	15.0501			0.757252
$396$	−1.18288	−	2.04881i	−0.0594419	−	0.102956i
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	0.912192	−	0.409763i	$-0.134389\pi$
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	−0.810961	+	0.585100i	$0.801055\pi$
$398$	−9.34326	+	16.1830i	−0.468335	+	0.811181i
$399$	−48.1322			−2.40962
$400$	−3.66123	−	6.34144i	−0.183062	−	0.317072i
$401$	24.8832			1.24261			0.621304	−	0.783570i	$-0.286603\pi$
$401$	24.8832			1.24261			0.621304	+	0.783570i	$0.286603\pi$
$402$	−18.9739			−0.946334
$403$		0			0
$404$	0.192087			0.00955671
$405$	17.3298			0.861124
$406$	−15.9555	−	27.6358i	−0.791860	−	1.37154i
$407$	6.82365			0.338236
$408$	11.9744	−	20.7403i	0.592821	−	1.02680i
$409$	−1.75361	−	3.03734i	−0.0867105	−	0.150187i	0.819408	−	0.573210i	$-0.194302\pi$
$409$	−1.75361	−	3.03734i	−0.0867105	−	0.150187i	−0.906119	+	0.423023i	$0.860969\pi$
$410$	0.321042	+	0.556060i	0.0158551	+	0.0274619i
$411$	−20.4966			−1.01102
$412$	0.789302	−	1.36711i	0.0388861	−	0.0673528i
$413$	14.7944	−	25.6246i	0.727985	−	1.26091i
$414$	−0.731802	+	1.26752i	−0.0359661	+	0.0622951i
$415$	−6.48786	−	11.2373i	−0.318477	−	0.551618i
$416$	3.50512	−	6.07105i	0.171853	−	0.297658i
$417$	16.0800	+	27.8514i	0.787441	+	1.36389i
$418$	−28.2647			−1.38247
$419$	4.12031			0.201290			0.100645	−	0.994922i	$-0.467909\pi$
$419$	4.12031			0.201290			0.100645	+	0.994922i	$0.467909\pi$
$420$	2.93848	+	5.08959i	0.143383	+	0.248347i
$421$	−13.8007	+	23.9035i	−0.672605	+	1.16499i	0.304558	+	0.952494i	$0.401491\pi$
$421$	−13.8007	+	23.9035i	−0.672605	+	1.16499i	−0.977163	+	0.212492i	$0.931842\pi$
$422$	−3.88406	−	6.72739i	−0.189073	−	0.327484i
$423$	0.776228	−	1.34447i	0.0377415	−	0.0653702i
$424$	−3.58410	+	6.20785i	−0.174059	+	0.301480i
$425$	4.92750	−	8.53467i	0.239019	−	0.413992i
$426$	−13.0347			−0.631531
$427$	−5.17964	−	8.97140i	−0.250660	−	0.434156i
$428$	0.760408	+	1.31706i	0.0367557	+	0.0636627i
$429$	−10.2834	+	17.8114i	−0.496488	+	0.859943i
$430$	−7.39697			−0.356713
$431$	7.43697	+	12.8812i	0.358226	+	0.620466i	0.987665	−	0.156584i	$-0.0500483\pi$
$431$	7.43697	+	12.8812i	0.358226	+	0.620466i	−0.629438	+	0.777050i	$0.716715\pi$
$432$	9.86032			0.474405
$433$	9.26195			0.445101			0.222550	−	0.974921i	$-0.428562\pi$
$433$	9.26195			0.445101			0.222550	+	0.974921i	$0.428562\pi$
$434$		0			0
$435$	21.8360			1.04696
$436$	−3.35117			−0.160492
$437$	−2.77427	−	4.80517i	−0.132711	−	0.229863i
$438$	13.7852			0.658683
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	−0.996214	−	0.0869324i	$-0.972294\pi$
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	0.573393	+	0.819281i	$0.305627\pi$
$440$	8.88929	+	15.3967i	0.423780	+	0.734009i
$441$	−4.87519	−	8.44407i	−0.232152	−	0.402099i
$442$	−12.2547			−0.582898
$443$	9.22512	−	15.9784i	0.438299	−	0.759155i	−0.559260	−	0.828992i	$-0.688915\pi$
$443$	9.22512	−	15.9784i	0.438299	−	0.759155i	0.997558	+	0.0698371i	$0.0222479\pi$
$444$	−0.906689	+	1.57043i	−0.0430296	+	0.0745294i
$445$	3.93794	−	6.82070i	0.186676	−	0.323332i
$446$	−4.55233	−	7.88486i	−0.215559	−	0.373359i
$447$	15.8147	−	27.3918i	0.748009	−	1.29559i
$448$	16.9017	+	29.2747i	0.798532	+	1.38310i
$449$	22.7102			1.07176			0.535881	−	0.844294i	$-0.319980\pi$
$449$	22.7102			1.07176			0.535881	+	0.844294i	$0.319980\pi$
$450$	−4.20020			−0.197999
$451$	0.634089	+	1.09827i	0.0298581	+	0.0517157i
$452$	−3.67258	+	6.36110i	−0.172744	+	0.299201i
$453$	0.271643	+	0.470500i	0.0127629	+	0.0221060i
$454$	−11.8534	+	20.5306i	−0.556306	+	0.963550i
$455$	7.74600	−	13.4165i	0.363138	−	0.628974i
$456$	19.3474	−	33.5107i	0.906025	−	1.56928i
$457$	−16.1619			−0.756020			−0.378010	−	0.925802i	$-0.623392\pi$
$457$	−16.1619			−0.756020			−0.378010	+	0.925802i	$0.623392\pi$
$458$	3.75018	+	6.49550i	0.175234	+	0.303515i
$459$	6.63529	+	11.4927i	0.309709	+	0.536432i
$460$	−0.338739	+	0.586713i	−0.0157938	+	0.0273556i
$461$	21.5388			1.00316			0.501580	−	0.865111i	$-0.332752\pi$
$461$	21.5388			1.00316			0.501580	+	0.865111i	$0.332752\pi$
$462$	−18.2907	−	31.6805i	−0.850962	−	1.47391i
$463$	−17.5098			−0.813750			−0.406875	−	0.913484i	$-0.633381\pi$
$463$	−17.5098			−0.813750			−0.406875	+	0.913484i	$0.633381\pi$
$464$	19.0941			0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	−11.8066			−0.546346			−0.273173	−	0.961965i	$-0.588073\pi$
$467$	−11.8066			−0.546346			−0.273173	+	0.961965i	$0.588073\pi$
$468$	−0.828644	−	1.43525i	−0.0383041	−	0.0663446i
$469$	28.2284			1.30347
$470$	−1.13235	+	1.96129i	−0.0522314	+	0.0904674i
$471$	−16.5236	−	28.6197i	−0.761366	−	1.31872i
$472$	11.8936	+	20.6004i	0.547448	+	0.948208i
$473$	−14.6097			−0.671757
$474$	12.4477	−	21.5601i	0.571742	−	0.990287i
$475$	7.96150	−	13.7897i	0.365299	−	0.632716i
$476$	−3.45818	+	5.98973i	−0.158505	+	0.274539i
$477$	1.53015	+	2.65030i	0.0700608	+	0.121349i
$478$	17.1962	−	29.7847i	0.786537	−	1.36232i
$479$	7.90436	+	13.6908i	0.361159	+	0.625546i	0.988152	−	0.153479i	$-0.0490477\pi$
$479$	7.90436	+	13.6908i	0.361159	+	0.625546i	−0.626993	+	0.779025i	$0.715714\pi$
$480$	−8.53215			−0.389438
$481$	4.78017			0.217957
$482$	−14.0158	−	24.2761i	−0.638402	−	1.10574i
$483$	3.59058	−	6.21906i	0.163377	−	0.282977i
$484$	0.758534	+	1.31382i	0.0344788	+	0.0597190i
$485$	8.43464	−	14.6092i	0.382997	−	0.663370i
$486$	7.83475	−	13.5702i	0.355392	−	0.615556i
$487$	−6.39582	+	11.0779i	−0.289822	+	0.501987i	−0.973767	−	0.227547i	$-0.926930\pi$
$487$	−6.39582	+	11.0779i	−0.289822	+	0.501987i	0.683945	+	0.729534i	$0.260263\pi$
$488$	8.32811			0.376996
$489$	0.138168	+	0.239314i	0.00624816	+	0.0108221i
$490$	7.11185	+	12.3181i	0.321281	+	0.556475i
$491$	9.26410	−	16.0459i	0.418083	−	0.724141i	−0.577664	−	0.816275i	$-0.696036\pi$
$491$	9.26410	−	16.0459i	0.418083	−	0.724141i	0.995747	+	0.0921341i	$0.0293688\pi$
$492$	−0.337017			−0.0151939
$493$	12.8490	+	22.2551i	0.578688	+	1.00232i
$494$	−19.8003			−0.890859
$495$	7.59016			0.341152
$496$		0			0
$497$	19.3922			0.869861
$498$	−21.4641			−0.961829
$499$	−20.4436	−	35.4094i	−0.915182	−	1.58514i	−0.806634	−	0.591051i	$-0.798713\pi$
$499$	−20.4436	−	35.4094i	−0.915182	−	1.58514i	−0.108548	−	0.994091i	$-0.534620\pi$
$500$	−5.66723			−0.253446
$501$	4.09681	−	7.09588i	0.183032	−	0.317021i
$502$	10.0018	+	17.3237i	0.446404	+	0.773195i
$503$	−10.0385	−	17.3873i	−0.447597	−	0.775260i	0.550632	−	0.834748i	$-0.314387\pi$
$503$	−10.0385	−	17.3873i	−0.447597	−	0.775260i	−0.998229	+	0.0594876i	$0.981053\pi$
$504$	15.1854			0.676411
$505$	−0.308141	+	0.533716i	−0.0137121	+	0.0237500i
$506$	2.10850	−	3.65203i	0.0937343	−	0.162353i
$507$	6.28348	−	10.8833i	0.279059	−	0.483345i
$508$	−4.87204	−	8.43863i	−0.216162	−	0.374403i
$509$	15.9556	−	27.6359i	0.707220	−	1.22494i	−0.258665	−	0.965967i	$-0.583282\pi$
$509$	15.9556	−	27.6359i	0.707220	−	1.22494i	0.965884	−	0.258973i	$-0.0833842\pi$
$510$	7.45759	+	12.9169i	0.330228	+	0.571971i
$511$	−20.5089			−0.907260
$512$	−24.6123			−1.08772
$513$	10.7208	+	18.5690i	0.473337	+	0.819844i
$514$	−14.3869	+	24.9189i	−0.634579	+	1.09912i
$515$	2.53235	+	4.38616i	0.111589	+	0.193277i
$516$	1.94126	−	3.36237i	0.0854594	−	0.148020i
$517$	−2.23650	+	3.87374i	−0.0983613	+	0.170367i
$518$	−4.25115	+	7.36322i	−0.186785	+	0.323521i
$519$	−29.9978			−1.31676
$520$	6.22722	+	10.7859i	0.273082	+	0.472991i
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	0.842019	−	0.539449i	$-0.181367\pi$
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	−0.888185	+	0.459485i	$0.848034\pi$
$522$	5.47624	−	9.48512i	0.239688	−	0.415152i
$523$	4.90777			0.214602			0.107301	−	0.994227i	$-0.465779\pi$
$523$	4.90777			0.214602			0.107301	+	0.994227i	$0.465779\pi$
$524$	3.04739	+	5.27823i	0.133126	+	0.230581i
$525$	20.6082			0.899418
$526$	−12.8076			−0.558440
$527$		0			0
$528$	21.8886			0.952580
$529$	−22.1722			−0.964008
$530$	−2.23216	−	3.86622i	−0.0969589	−	0.167938i
$531$	10.1554			0.440708
$532$	−5.58748	+	9.67780i	−0.242248	+	0.419586i
$533$	0.444199	+	0.769375i	0.0192404	+	0.0333253i
$534$	−6.51402	−	11.2826i	−0.281889	−	0.488247i
$535$	−4.87929			−0.210950
$536$	−11.3468	+	19.6532i	−0.490106	+	0.848889i
$537$	18.3842	−	31.8423i	0.793335	−	1.37410i
$538$	2.72190	−	4.71446i	0.117349	−	0.203255i
$539$	14.0466	+	24.3295i	0.605031	+	1.04794i
$540$	1.30902	−	2.26729i	0.0563312	−	0.0975685i
$541$	6.21851	+	10.7708i	0.267355	+	0.463072i	0.968178	−	0.250263i	$-0.0805172\pi$
$541$	6.21851	+	10.7708i	0.267355	+	0.463072i	−0.700823	+	0.713335i	$0.747184\pi$
$542$	7.58139			0.325648
$543$	−25.0225			−1.07382
$544$	−5.02057	−	8.69589i	−0.215255	−	0.372833i
$545$	5.37584	−	9.31124i	0.230276	−	0.398849i
$546$	−12.8132	−	22.1931i	−0.548355	−	0.949779i
$547$	6.98250	−	12.0941i	0.298550	−	0.517104i	−0.677254	−	0.735749i	$-0.736830\pi$
$547$	6.98250	−	12.0941i	0.298550	−	0.517104i	0.975805	+	0.218645i	$0.0701636\pi$
$548$	−2.37937	+	4.12120i	−0.101642	+	0.176049i
$549$	1.77775	−	3.07915i	0.0758725	−	0.131415i
$550$	12.1018			0.516023
$551$	20.7605	+	35.9582i	0.884425	+	1.53187i
$552$	2.88656	+	4.99967i	0.122860	+	0.212800i
$553$	−18.5190	+	32.0759i	−0.787509	+	1.36401i
$554$	27.1662			1.15418
$555$	−2.90897	−	5.03848i	−0.123479	−	0.213872i
$556$	7.46666			0.316657
$557$	−37.2207			−1.57709			−0.788546	−	0.614976i	$-0.789166\pi$
$557$	−37.2207			−1.57709			−0.788546	+	0.614976i	$0.789166\pi$
$558$		0			0
$559$	−10.2346			−0.432876
$560$	−16.4876			−0.696730
$561$	14.7295	+	25.5122i	0.621879	+	1.07713i
$562$	−37.9183			−1.59949
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	−0.354252	−	0.935150i	$-0.615264\pi$
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	0.986990	−	0.160784i	$-0.0514023\pi$
$564$	−0.594349	−	1.02944i	−0.0250266	−	0.0433474i
$565$	−11.7829	−	20.4086i	−0.495710	−	0.858595i
$566$	−26.3010			−1.10551
$567$	−21.3242	+	36.9346i	−0.895532	+	1.55111i
$568$	−7.79498	+	13.5013i	−0.327070	+	0.566502i
$569$	20.1857	−	34.9626i	0.846227	−	1.46571i	−0.0383249	−	0.999265i	$-0.512202\pi$
$569$	20.1857	−	34.9626i	0.846227	−	1.46571i	0.884552	−	0.466442i	$-0.154464\pi$
$570$	12.0495	+	20.8703i	0.504696	+	0.874160i
$571$	−21.3008	+	36.8940i	−0.891410	+	1.54397i	−0.0532231	+	0.998583i	$0.516949\pi$
$571$	−21.3008	+	36.8940i	−0.891410	+	1.54397i	−0.838186	+	0.545384i	$0.816384\pi$
$572$	2.38753	+	4.13532i	0.0998275	+	0.172906i
$573$	10.5233			0.439616
$574$	−1.58016			−0.0659545
$575$	1.18783	+	2.05738i	0.0495359	+	0.0857986i
$576$	−5.80099	+	10.0476i	−0.241708	+	0.418650i
$577$	3.26888	+	5.66187i	0.136085	+	0.235707i	0.926012	−	0.377495i	$-0.123215\pi$
$577$	3.26888	+	5.66187i	0.136085	+	0.235707i	−0.789926	+	0.613202i	$0.789881\pi$
$578$	1.69692	−	2.93916i	0.0705827	−	0.122253i
$579$	20.7931	−	36.0146i	0.864130	−	1.49672i
$580$	2.53486	−	4.39050i	0.105254	−	0.182306i
$581$	31.9331			1.32481
$582$	−13.9523	−	24.1662i	−0.578343	−	1.00172i
$583$	−4.40874	−	7.63617i	−0.182591	−	0.316258i
$584$	8.24383	−	14.2787i	0.341132	−	0.590858i
$585$	5.31714			0.219837
$586$	1.10836	+	1.91973i	0.0457857	+	0.0793032i
$587$	−21.3777			−0.882352			−0.441176	−	0.897421i	$-0.645439\pi$
$587$	−21.3777			−0.882352			−0.441176	+	0.897421i	$0.645439\pi$
$588$	−7.46576			−0.307883
$589$		0			0
$590$	−14.8146			−0.609907
$591$	45.0443			1.85287
$592$	−2.54369	−	4.40580i	−0.104545	−	0.181077i
$593$	25.9906			1.06731			0.533653	−	0.845704i	$-0.320819\pi$
$593$	25.9906			1.06731			0.533653	+	0.845704i	$0.320819\pi$
$594$	−8.14807	+	14.1129i	−0.334319	+	0.579058i
$595$	−11.0950	−	19.2171i	−0.454851	−	0.787824i
$596$	−3.67173	−	6.35962i	−0.150400	−	0.260500i
$597$	31.4680			1.28790
$598$	1.47707	−	2.55836i	0.0604019	−	0.104619i
$599$	4.59398	−	7.95700i	0.187705	−	0.325114i	−0.756780	−	0.653670i	$-0.773228\pi$
$599$	4.59398	−	7.95700i	0.187705	−	0.325114i	0.944485	+	0.328556i	$0.106562\pi$
$600$	−8.28377	+	14.3479i	−0.338183	+	0.585751i
$601$	−16.6595	−	28.8551i	−0.679556	−	1.17703i	−0.975115	−	0.221701i	$-0.928839\pi$
$601$	−16.6595	−	28.8551i	−0.679556	−	1.17703i	0.295559	−	0.955325i	$-0.404494\pi$
$602$	9.10192	−	15.7650i	0.370967	−	0.642533i
$603$	4.84425	+	8.39049i	0.197273	+	0.341687i
$604$	0.126136			0.00513240
$605$	−4.86727			−0.197883
$606$	0.509718	+	0.882858i	0.0207059	+	0.0358636i
$607$	24.3504	−	42.1761i	0.988352	−	1.71188i	0.362377	−	0.932032i	$-0.381965\pi$
$607$	24.3504	−	42.1761i	0.988352	−	1.71188i	0.625975	−	0.779843i	$-0.284701\pi$
$608$	−8.11189	−	14.0502i	−0.328981	−	0.569811i
$609$	−26.8691	+	46.5386i	−1.08879	+	1.88584i
$610$	−2.59335	+	4.49182i	−0.105002	+	0.181868i
$611$	−1.56674	+	2.71367i	−0.0633835	+	0.109783i
$612$	−2.37382			−0.0959560
$613$	−10.4570	−	18.1121i	−0.422354	−	0.731539i	0.573815	−	0.818985i	$-0.305463\pi$
$613$	−10.4570	−	18.1121i	−0.422354	−	0.731539i	−0.996169	+	0.0874458i	$0.972130\pi$
$614$	−16.4923	−	28.5654i	−0.665573	−	1.15281i
$615$	0.540633	−	0.936404i	0.0218004	−	0.0377594i
$616$	−43.7529			−1.76285
$617$	−22.6920	−	39.3037i	−0.913545	−	1.58231i	−0.809018	−	0.587784i	$-0.800001\pi$
$617$	−22.6920	−	39.3037i	−0.913545	−	1.58231i	−0.104527	−	0.994522i	$-0.533333\pi$
$618$	8.37789			0.337008
$619$	−10.2462			−0.411832			−0.205916	−	0.978570i	$-0.566017\pi$
$619$	−10.2462			−0.411832			−0.205916	+	0.978570i	$0.566017\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	5.15188			0.206572
$623$	9.69121	+	16.7857i	0.388270	+	0.672504i
$624$	15.3337			0.613838
$625$	2.56358	−	4.44025i	0.102543	−	0.177610i
$626$	6.98816	+	12.1038i	0.279303	+	0.483767i
$627$	23.7989	+	41.2209i	0.950436	+	1.64620i
$628$	−7.67263			−0.306171
$629$	3.42345	−	5.92958i	0.136502	−	0.236428i
$630$	−4.72870	+	8.19034i	−0.188396	+	0.326311i
$631$	5.33848	−	9.24653i	0.212522	−	0.368098i	−0.739981	−	0.672627i	$-0.765166\pi$
$631$	5.33848	−	9.24653i	0.212522	−	0.368098i	0.952503	+	0.304529i	$0.0984991\pi$
$632$	−14.8880	−	25.7867i	−0.592211	−	1.02574i
$633$	−6.54074	+	11.3289i	−0.259971	+	0.450283i
$634$	−15.9451	−	27.6178i	−0.633262	−	1.09684i
$635$	31.2623			1.24061
$636$	2.34324			0.0929155
$637$	9.84009	+	17.0435i	0.389878	+	0.675289i
$638$	−15.7784	+	27.3290i	−0.624672	+	1.08196i
$639$	3.32789	+	5.76407i	0.131649	+	0.228023i
$640$	4.35046	−	7.53522i	0.171967	−	0.297856i
$641$	−11.9310	+	20.6652i	−0.471248	+	0.816226i	−0.999459	−	0.0328875i	$-0.989530\pi$
$641$	−11.9310	+	20.6652i	−0.471248	+	0.816226i	0.528211	+	0.849113i	$0.322863\pi$
$642$	−4.03560	+	6.98986i	−0.159272	+	0.275868i
$643$	−7.93926			−0.313094			−0.156547	−	0.987671i	$-0.550036\pi$
$643$	−7.93926			−0.313094			−0.156547	+	0.987671i	$0.550036\pi$
$644$	−0.833632	−	1.44389i	−0.0328497	−	0.0568974i
$645$	6.22823	+	10.7876i	0.245237	+	0.424762i
$646$	−14.1805	+	24.5614i	−0.557925	+	0.966355i
$647$	2.47761			0.0974050			0.0487025	−	0.998813i	$-0.484491\pi$
$647$	2.47761			0.0974050			0.0487025	+	0.998813i	$0.484491\pi$
$648$	−17.1431	−	29.6927i	−0.673445	−	1.16644i
$649$	−29.2603			−1.14857
$650$	8.47769			0.332523
$651$		0			0
$652$	0.0641574			0.00251260
$653$	22.4940			0.880260			0.440130	−	0.897934i	$-0.354932\pi$
$653$	22.4940			0.880260			0.440130	+	0.897934i	$0.354932\pi$
$654$	−8.89257	−	15.4024i	−0.347727	−	0.602281i
$655$	−19.5541			−0.764042
$656$	0.472746	−	0.818821i	0.0184576	−	0.0319696i
$657$	−3.51952	−	6.09598i	−0.137309	−	0.237827i
$658$	−2.78670	−	4.82670i	−0.108637	−	0.188164i
$659$	−11.9596			−0.465881			−0.232941	−	0.972491i	$-0.574835\pi$
$659$	−11.9596			−0.465881			−0.232941	+	0.972491i	$0.574835\pi$
$660$	2.90585	−	5.03308i	0.113110	−	0.195912i
$661$	−11.9180	+	20.6426i	−0.463556	+	0.802902i	−0.999135	−	0.0415827i	$-0.986760\pi$
$661$	−11.9180	+	20.6426i	−0.463556	+	0.802902i	0.535579	+	0.844485i	$0.320093\pi$
$662$	−0.471791	+	0.817166i	−0.0183367	+	0.0317601i
$663$	10.3185	+	17.8721i	0.400736	+	0.694095i
$664$	−12.8359	+	22.2325i	−0.498131	+	0.862789i
$665$	−17.9265	−	31.0497i	−0.695161	−	1.20405i
$666$	−2.91815			−0.113076
$667$	−6.19478			−0.239863
$668$	−0.951165	−	1.64747i	−0.0368017	−	0.0637424i
$669$	−7.66610	+	13.2781i	−0.296389	+	0.513360i
$670$	−7.06672	−	12.2399i	−0.273011	−	0.472869i
$671$	−5.12213	+	8.87179i	−0.197738	+	0.342492i
$672$	10.4988	−	18.1844i	0.404998	−	0.701478i
$673$	−1.74706	+	3.02600i	−0.0673442	+	0.116644i	−0.897731	−	0.440543i	$-0.854786\pi$
$673$	−1.74706	+	3.02600i	−0.0673442	+	0.116644i	0.830387	+	0.557187i	$0.188119\pi$
$674$	2.95024			0.113639
$675$	−4.59023	−	7.95051i	−0.176678	−	0.306015i
$676$	−1.45885	−	2.52680i	−0.0561096	−	0.0971847i
$677$	9.62287	−	16.6673i	0.369837	−	0.640576i	−0.619703	−	0.784836i	$-0.712747\pi$
$677$	9.62287	−	16.6673i	0.369837	−	0.640576i	0.989540	+	0.144260i	$0.0460803\pi$
$678$	−38.9819			−1.49709
$679$	20.7575	+	35.9531i	0.796601	+	1.37975i
$680$	17.8391			0.684100
$681$	39.9221			1.52982
$682$		0			0
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	−3.83545			−0.146652
$685$	−7.63384	−	13.2222i	−0.291674	−	0.505194i
$686$	−2.19616			−0.0838498
$687$	6.31529	−	10.9384i	0.240944	−	0.417326i
$688$	5.44616	+	9.43303i	0.207633	+	0.359631i
$689$	−3.08846	−	5.34937i	−0.117661	−	0.203795i
$690$	−3.59547			−0.136877
$691$	−19.2052	+	33.2644i	−0.730601	+	1.26544i	0.226025	+	0.974121i	$0.427427\pi$
$691$	−19.2052	+	33.2644i	−0.730601	+	1.26544i	−0.956627	+	0.291317i	$0.905907\pi$
$692$	−3.48233	+	6.03157i	−0.132378	+	0.229286i
$693$	−9.33965	+	16.1767i	−0.354784	+	0.614504i
$694$	−3.48569	−	6.03740i	−0.132315	−	0.229176i
$695$	−11.9778	+	20.7461i	−0.454343	+	0.786946i
$696$	−21.6008	−	37.4137i	−0.818776	−	1.41816i
$697$	1.27250			0.0481993
$698$	35.8163			1.35567
$699$	−18.1851	−	31.4976i	−0.687825	−	1.19135i
$700$	2.39233	−	4.14364i	0.0904216	−	0.156615i
$701$	17.7127	+	30.6794i	0.669001	+	1.15874i	0.978184	+	0.207741i	$0.0666110\pi$
$701$	17.7127	+	30.6794i	0.669001	+	1.15874i	−0.309183	+	0.951002i	$0.600056\pi$
$702$	−5.70797	+	9.88649i	−0.215433	+	0.373142i
$703$	5.53137	−	9.58061i	0.208619	−	0.361339i
$704$	16.7141	−	28.9496i	0.629935	−	1.09108i
$705$	3.81375			0.143634
$706$	11.8752	+	20.5684i	0.446928	+	0.774103i
$707$	−0.758331	−	1.31347i	−0.0285200	−	0.0493980i
$708$	3.88795	−	6.73412i	0.146118	−	0.253084i
$709$	−25.8093			−0.969288			−0.484644	−	0.874711i	$-0.661051\pi$
$709$	−25.8093			−0.969288			−0.484644	+	0.874711i	$0.661051\pi$
$710$	−4.85467	−	8.40854i	−0.182193	−	0.315567i
$711$	−12.7121			−0.476743
$712$	−15.5821			−0.583962
$713$		0			0
$714$	−36.7061			−1.37369
$715$	−15.3200			−0.572935
$716$	−4.26829	−	7.39290i	−0.159514	−	0.276286i
$717$	−57.9168			−2.16294
$718$	−6.37296	+	11.0383i	−0.237837	+	0.411945i
$719$	19.5234	+	33.8155i	0.728099	+	1.26110i	0.957686	+	0.287816i	$0.0929291\pi$
$719$	19.5234	+	33.8155i	0.728099	+	1.26110i	−0.229587	+	0.973288i	$0.573738\pi$
$720$	−2.82943	−	4.90072i	−0.105447	−	0.182639i
$721$	−12.4642			−0.464190
$722$	−11.2063	+	19.4098i	−0.417054	+	0.722359i
$723$	−23.6026	+	40.8808i	−0.877789	+	1.52037i
$724$	−2.90476	+	5.03119i	−0.107955	+	0.186983i
$725$	−8.88879	−	15.3958i	−0.330121	−	0.571787i
$726$	−4.02565	+	6.97263i	−0.149406	+	0.258779i
$727$	−12.4918	−	21.6365i	−0.463296	−	0.802452i	0.535827	−	0.844328i	$-0.320000\pi$
$727$	−12.4918	−	21.6365i	−0.463296	−	0.802452i	−0.999123	+	0.0418757i	$0.986667\pi$
$728$	−30.6502			−1.13597
$729$	7.24913			0.268486
$730$	5.13422	+	8.89272i	0.190026	+	0.329134i
$731$	−7.32976	+	12.6955i	−0.271101	+	0.469561i
$732$	−1.36120	−	2.35767i	−0.0503115	−	0.0871420i
$733$	8.47452	−	14.6783i	0.313014	−	0.542156i	−0.666000	−	0.745952i	$-0.731995\pi$
$733$	8.47452	−	14.6783i	0.313014	−	0.542156i	0.979013	+	0.203797i	$0.0653281\pi$
$734$	0.0841350	−	0.145726i	0.00310548	−	0.00537885i
$735$	11.9763	−	20.7436i	0.441754	−	0.765140i
$736$	2.42053			0.0892220
$737$	−13.9575	−	24.1751i	−0.514130	−	0.890500i
$738$	−0.271170	−	0.469680i	−0.00998190	−	0.0172892i
$739$	−7.19107	+	12.4553i	−0.264528	+	0.458175i	−0.967440	−	0.253101i	$-0.918549\pi$
$739$	−7.19107	+	12.4553i	−0.264528	+	0.458175i	0.702912	+	0.711277i	$0.251883\pi$
$740$	−1.35076			−0.0496550
$741$	16.6718	+	28.8765i	0.612456	+	1.06080i
$742$	10.9866			0.403333
$743$	−27.7705			−1.01880			−0.509400	−	0.860530i	$-0.670133\pi$
$743$	−27.7705			−1.01880			−0.509400	+	0.860530i	$0.670133\pi$
$744$		0			0
$745$	23.5603			0.863183
$746$	−9.07363			−0.332209
$747$	5.48002	+	9.49167i	0.200503	+	0.347282i
$748$	6.83956			0.250079
$749$	6.00394	−	10.3991i	0.219379	−	0.379976i
$750$	−15.0384	−	26.0473i	−0.549126	−	0.951113i
$751$	21.7851	+	37.7329i	0.794950	+	1.37689i	0.922871	+	0.385109i	$0.125836\pi$
$751$	21.7851	+	37.7329i	0.794950	+	1.37689i	−0.127922	+	0.991784i	$0.540831\pi$
$752$	3.33486			0.121610
$753$	16.8431	−	29.1731i	0.613796	−	1.06313i
$754$	−11.0532	+	19.1448i	−0.402535	+	0.697212i
$755$	−0.202344	+	0.350469i	−0.00736404	+	0.0127549i
$756$	3.22148	+	5.57976i	0.117164	+	0.202934i
$757$	−12.6086	+	21.8387i	−0.458266	+	0.793739i	−0.998869	−	0.0475380i	$-0.984862\pi$
$757$	−12.6086	+	21.8387i	−0.458266	+	0.793739i	0.540604	+	0.841277i	$0.318196\pi$
$758$	2.83901	+	4.91731i	0.103117	+	0.178605i
$759$	−7.10142			−0.257765
$760$	28.8233			1.04553
$761$	1.30797	+	2.26546i	0.0474137	+	0.0821229i	0.888758	−	0.458376i	$-0.151569\pi$
$761$	1.30797	+	2.26546i	0.0474137	+	0.0821229i	−0.841345	+	0.540499i	$0.818235\pi$
$762$	25.8566	−	44.7850i	0.936687	−	1.62239i
$763$	13.2299	+	22.9148i	0.478954	+	0.829573i
$764$	1.22161	−	2.11588i	0.0441962	−	0.0765500i
$765$	3.80801	−	6.59567i	0.137679	−	0.238467i
$766$	19.8964	−	34.4615i	0.718885	−	1.24515i
$767$	−20.4977			−0.740130
$768$	11.2436	+	19.4745i	0.405718	+	0.702725i
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	0.745366	−	0.666656i	$-0.232275\pi$
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	−0.950024	+	0.312178i	$0.898942\pi$
$770$	13.6245	−	23.5984i	0.490994	−	0.850427i
$771$	48.4550			1.74507
$772$	−4.82757	−	8.36160i	−0.173748	−	0.300941i
$773$	−11.4174			−0.410655			−0.205327	−	0.978693i	$-0.565826\pi$
$773$	−11.4174			−0.410655			−0.205327	+	0.978693i	$0.565826\pi$
$774$	6.24789			0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	14.3179			0.513651
$778$	21.7301	+	37.6377i	0.779063	+	1.34938i
$779$	2.05601			0.0736644
$780$	2.03564	−	3.52583i	0.0728875	−	0.126245i
$781$	−9.58846	−	16.6077i	−0.343102	−	0.594270i
$782$	−2.11568	−	3.66447i	−0.0756567	−	0.131041i
$783$	23.9390			0.855511
$784$	10.4725	−	18.1389i	0.374017	−	0.647817i
$785$	12.3082	−	21.3184i	0.439299	−	0.760888i
$786$	−16.1729	+	28.0123i	−0.576869	+	0.999167i
$787$	13.5446	+	23.4599i	0.482813	+	0.836257i	0.999805	−	0.0197334i	$-0.00628175\pi$
$787$	13.5446	+	23.4599i	0.482813	+	0.836257i	−0.516992	+	0.855990i	$0.672948\pi$
$788$	5.22902	−	9.05692i	0.186276	−	0.322640i
$789$	10.7840	+	18.6785i	0.383921	+	0.664971i
$790$	18.5443			0.659776
$791$	57.9951			2.06207
$792$	−7.50840	−	13.0049i	−0.266799	−	0.462110i
$793$	−3.58821	+	6.21496i	−0.127421	+	0.220700i
$794$	2.48530	+	4.30467i	0.0882001	+	0.152767i
$795$	−3.75896	+	6.51070i	−0.133316	+	0.230911i
$796$	3.65300	−	6.32719i	0.129477	−	0.224261i
$797$	−24.3279	+	42.1372i	−0.861739	+	1.49258i	0.00851025	+	0.999964i	$0.497291\pi$
$797$	−24.3279	+	42.1372i	−0.861739	+	1.49258i	−0.870249	+	0.492612i	$0.836042\pi$
$798$	−59.3071			−2.09945
$799$	2.24412	+	3.88693i	0.0793914	+	0.137510i
$800$	3.47318	+	6.01573i	0.122796	+	0.212688i
$801$	−3.32620	+	5.76115i	−0.117526	+	0.203560i
$802$	30.6604			1.08266
$803$	10.1406	+	17.5640i	0.357854	+	0.619821i
$804$	7.41838			0.261626
$805$	5.34915			0.188533
$806$		0			0
$807$	−9.16733			−0.322705
$808$	1.21929			0.0428943
$809$	9.40457	+	16.2892i	0.330647	+	0.572697i	0.982639	−	0.185529i	$-0.0593997\pi$
$809$	9.40457	+	16.2892i	0.330647	+	0.572697i	−0.651992	+	0.758226i	$0.726066\pi$
$810$	21.3533			0.750278
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	−0.276259	−	0.961083i	$-0.589095\pi$
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	0.970452	−	0.241294i	$-0.0775720\pi$
$812$	6.23826	+	10.8050i	0.218920	+	0.379180i
$813$	−6.38352	−	11.0566i	−0.223880	−	0.387771i
$814$	8.40791			0.294697
$815$	−0.102919	+	0.178262i	−0.00360511	+	0.00624423i
$816$	10.9816	−	19.0207i	0.384433	−	0.665857i
$817$	−11.8429	+	20.5125i	−0.414331	+	0.717642i
$818$	−2.16075	−	3.74253i	−0.0755489	−	0.130855i
$819$	−6.54271	+	11.3323i	−0.228621	+	0.395983i
$820$	−0.125520	−	0.217407i	−0.00438335	−	0.00759218i
$821$	−14.6367			−0.510825			−0.255412	−	0.966832i	$-0.582211\pi$
$821$	−14.6367			−0.510825			−0.255412	+	0.966832i	$0.582211\pi$
$822$	−25.2554			−0.880882
$823$	−20.8934	−	36.1883i	−0.728296	−	1.26145i	−0.957603	−	0.288092i	$-0.906979\pi$
$823$	−20.8934	−	36.1883i	−0.728296	−	1.26145i	0.229306	−	0.973354i	$-0.426354\pi$
$824$	5.01014	−	8.67782i	0.174537	−	0.302306i
$825$	−10.1897	−	17.6491i	−0.354760	−	0.614463i
$826$	18.2292	−	31.5740i	0.634277	−	1.09860i
$827$	4.70307	−	8.14595i	0.163542	−	0.283262i	−0.772595	−	0.634899i	$-0.781042\pi$
$827$	4.70307	−	8.14595i	0.163542	−	0.283262i	0.936136	+	0.351637i	$0.114375\pi$
$828$	0.286118	−	0.495571i	0.00994329	−	0.0172223i
$829$	40.3307			1.40074			0.700372	−	0.713778i	$-0.253017\pi$
$829$	40.3307			1.40074			0.700372	+	0.713778i	$0.253017\pi$
$830$	−7.99417	−	13.8463i	−0.277482	−	0.480612i
$831$	−22.8739	−	39.6188i	−0.793487	−	1.37436i
$832$	11.7087	−	20.2801i	0.405927	−	0.703086i
$833$	28.1889			0.976689
$834$	19.8133	+	34.3177i	0.686079	+	1.18832i
$835$	6.10332			0.211214
$836$	11.0509			0.382203
$837$		0			0
$838$	5.07693			0.175380
$839$	7.14965			0.246833			0.123417	−	0.992355i	$-0.460615\pi$
$839$	7.14965			0.246833			0.123417	+	0.992355i	$0.460615\pi$
$840$	18.6522	+	32.3065i	0.643560	+	1.11468i
$841$	17.3569			0.598514
$842$	−17.0048	+	29.4532i	−0.586025	+	1.01503i
$843$	31.9272	+	55.2995i	1.09963	+	1.90462i
$844$	1.51858	+	2.63026i	0.0522716	+	0.0905371i
$845$	9.36097			0.322027
$846$	0.956446	−	1.65661i	0.0328833	−	0.0569556i
$847$	5.98914	−	10.3735i	0.205789	−	0.356438i
$848$	−3.28695	+	5.69316i	−0.112874	+	0.195504i
$849$	22.1454	+	38.3570i	0.760029	+	1.31641i
$850$	6.07152	−	10.5162i	0.208252	−	0.360702i
$851$	0.825260	+	1.42939i	0.0282896	+	0.0489990i
$852$	5.09625			0.174595
$853$	1.12667			0.0385765			0.0192882	−	0.999814i	$-0.493860\pi$
$853$	1.12667			0.0385765			0.0192882	+	0.999814i	$0.493860\pi$
$854$	−6.38221	−	11.0543i	−0.218395	−	0.378271i
$855$	6.15272	−	10.6568i	0.210418	−	0.364455i
$856$	4.82673	+	8.36014i	0.164974	+	0.285744i
$857$	11.9270	−	20.6582i	0.407419	−	0.705671i	−0.587181	−	0.809456i	$-0.699762\pi$
$857$	11.9270	−	20.6582i	0.407419	−	0.705671i	0.994600	+	0.103785i	$0.0330955\pi$
$858$	−12.6710	+	21.9467i	−0.432579	+	0.749249i
$859$	−16.2328	+	28.1161i	−0.553857	+	0.959309i	0.444134	+	0.895960i	$0.353511\pi$
$859$	−16.2328	+	28.1161i	−0.553857	+	0.959309i	−0.997991	+	0.0633488i	$0.979822\pi$
$860$	2.89205			0.0986180
$861$	1.33049	+	2.30448i	0.0453430	+	0.0785364i
$862$	9.16363	+	15.8719i	0.312114	+	0.540598i
$863$	11.9209	−	20.6476i	0.405793	−	0.702853i	−0.588621	−	0.808409i	$-0.700329\pi$
$863$	11.9209	−	20.6476i	0.405793	−	0.702853i	0.994413	+	0.105556i	$0.0336622\pi$
$864$	−9.35387			−0.318225
$865$	−11.1725	−	19.3513i	−0.379876	−	0.657964i
$866$	11.4123			0.387806
$867$	−5.71523			−0.194099
$868$		0			0
$869$	36.6268			1.24248
$870$	26.9057			0.912190
$871$	−9.77764	−	16.9354i	−0.331303	−	0.573833i
$872$	−21.2717			−0.720352
$873$	−7.12437	+	12.3398i	−0.241123	+	0.417638i
$874$	−3.41837	−	5.92080i	−0.115628	−	0.200274i
$875$	22.3733	+	38.7518i	0.756357	+	1.31005i
$876$	−5.38971			−0.182101
$877$	−14.6373	+	25.3526i	−0.494267	+	0.856096i	−0.999978	−	0.00660717i	$-0.997897\pi$
$877$	−14.6373	+	25.3526i	−0.494267	+	0.856096i	0.505711	+	0.862703i	$0.331230\pi$
$878$	−10.9159	+	18.9069i	−0.368395	+	0.638078i
$879$	1.86647	−	3.23282i	0.0629544	−	0.109040i
$880$	8.15228	+	14.1202i	0.274813	+	0.475991i
$881$	−4.51504	+	7.82028i	−0.152116	+	0.263472i	−0.932005	−	0.362445i	$-0.881942\pi$
$881$	−4.51504	+	7.82028i	−0.152116	+	0.263472i	0.779889	+	0.625917i	$0.215275\pi$
$882$	−6.00707	−	10.4046i	−0.202269	−	0.350340i
$883$	21.4076			0.720422			0.360211	−	0.932871i	$-0.382705\pi$
$883$	21.4076			0.720422			0.360211	+	0.932871i	$0.382705\pi$
$884$	4.79132			0.161150
$885$	12.4739	+	21.6054i	0.419304	+	0.726256i
$886$	11.3669	−	19.6881i	0.381880	−	0.661435i
$887$	−12.2975	−	21.2999i	−0.412910	−	0.715181i	0.582297	−	0.812976i	$-0.302154\pi$
$887$	−12.2975	−	21.2999i	−0.412910	−	0.715181i	−0.995207	+	0.0977956i	$0.968821\pi$
$888$	−5.75526	+	9.96841i	−0.193134	+	0.334518i
$889$	−38.4681	+	66.6287i	−1.29018	+	2.23466i
$890$	4.85222	−	8.40428i	0.162647	−	0.281712i
$891$	42.1749			1.41291
$892$	1.77986	+	3.08280i	0.0595940	+	0.103220i
$893$	3.62590	+	6.28024i	0.121336	+	0.210160i
$894$	19.4864	−	33.7514i	0.651723	−	1.12882i
$895$	27.3883			0.915488
$896$	10.7064	+	18.5441i	0.357677	+	0.619515i
$897$	−4.97476			−0.166102
$898$	27.9829			0.933801
$899$		0			0
$900$	1.64218			0.0547395
$901$	−8.84753			−0.294754
$902$	0.781307	+	1.35326i	0.0260147	+	0.0450587i
$903$	−30.6552			−1.02014
$904$	−23.3119	+	40.3774i	−0.775343	+	1.34293i
$905$	−9.31946	−	16.1418i	−0.309789	−	0.536571i
$906$	0.334711	+	0.579737i	0.0111200	+	0.0192605i
$907$	−19.7663			−0.656329			−0.328165	−	0.944621i	$-0.606430\pi$
$907$	−19.7663			−0.656329			−0.328165	+	0.944621i	$0.606430\pi$
$908$	4.63440	−	8.02701i	0.153798	−	0.266386i
$909$	0.260273	−	0.450806i	0.00863272	−	0.0149523i
$910$	9.54441	−	16.5314i	0.316394	−	0.548010i
$911$	17.8108	+	30.8492i	0.590098	+	1.02208i	0.994219	+	0.107374i	$0.0342442\pi$
$911$	17.8108	+	30.8492i	0.590098	+	1.02208i	−0.404121	+	0.914706i	$0.632422\pi$
$912$	17.7433	−	30.7323i	0.587540	−	1.01765i
$913$	−15.7893	−	27.3478i	−0.522549	−	0.905081i
$914$	−19.9142			−0.658703
$915$	8.73440			0.288750
$916$	−1.46624	−	2.53960i	−0.0484458	−	0.0839106i
$917$	24.0612	−	41.6752i	0.794571	−	1.37624i
$918$	8.17582	+	14.1609i	0.269842	+	0.467381i
$919$	8.57816	−	14.8578i	0.282968	−	0.490114i	−0.689147	−	0.724622i	$-0.742014\pi$
$919$	8.57816	−	14.8578i	0.282968	−	0.490114i	0.972114	+	0.234508i	$0.0753478\pi$
$920$	−2.15016	+	3.72419i	−0.0708888	+	0.122783i
$921$	−27.7729	+	48.1041i	−0.915149	+	1.58508i
$922$	26.5395			0.874030
$923$	−6.71701	−	11.6342i	−0.221093	−	0.382945i
$924$	7.15126	+	12.3863i	0.235259	+	0.407481i
$925$	−2.36831	+	4.10203i	−0.0778694	+	0.134874i
$926$	−21.5751			−0.709002
$927$	−2.13897	−	3.70480i	−0.0702529	−	0.121682i
$928$	−18.1134			−0.594601
$929$	45.5222			1.49353			0.746767	−	0.665086i	$-0.231605\pi$
$929$	45.5222			1.49353			0.746767	+	0.665086i	$0.231605\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	−8.44416			−0.276598
$933$	−4.33788	−	7.51342i	−0.142016	−	0.245978i
$934$	−14.5478			−0.476018
$935$	−10.9718	+	19.0037i	−0.358817	+	0.621489i
$936$	−5.25986	−	9.11035i	−0.171924	−	0.297781i
$937$	−12.8087	−	22.1854i	−0.418443	−	0.724765i	0.577340	−	0.816504i	$-0.304091\pi$
$937$	−12.8087	−	22.1854i	−0.418443	−	0.724765i	−0.995783	+	0.0917389i	$0.970757\pi$
$938$	34.7822			1.13568
$939$	11.7680	−	20.3828i	0.384036	−	0.665169i
$940$	0.442723	−	0.766819i	0.0144400	−	0.0250109i
$941$	−6.06192	+	10.4996i	−0.197613	+	0.342276i	−0.947754	−	0.319002i	$-0.896652\pi$
$941$	−6.06192	+	10.4996i	−0.197613	+	0.342276i	0.750141	+	0.661278i	$0.229986\pi$
$942$	−20.3599	−	35.2644i	−0.663361	−	1.14898i
$943$	−0.153375	+	0.265653i	−0.00499458	+	0.00865086i
$944$	10.9075	+	18.8924i	0.355010	+	0.614895i
$945$	−20.6712			−0.672434
$946$	−18.0017			−0.585286
$947$	13.6005	+	23.5568i	0.441958	+	0.765494i	0.997835	−	0.0657711i	$-0.0209507\pi$
$947$	13.6005	+	23.5568i	0.441958	+	0.765494i	−0.555877	+	0.831265i	$0.687617\pi$
$948$	−4.86677	+	8.42950i	−0.158065	+	0.273777i
$949$	7.10379	+	12.3041i	0.230599	+	0.399409i
$950$	9.80994	−	16.9913i	0.318277	−	0.551271i
$951$	−26.8516	+	46.5083i	−0.870722	+	1.50813i
$952$	−21.9510	+	38.0202i	−0.711435	+	1.23224i
$953$	24.8927			0.806353			0.403177	−	0.915122i	$-0.367906\pi$
$953$	24.8927			0.806353			0.403177	+	0.915122i	$0.367906\pi$
$954$	1.88541	+	3.26563i	0.0610424	+	0.105729i
$955$	3.91933	+	6.78848i	0.126826	+	0.219670i
$956$	−6.72333	+	11.6452i	−0.217448	+	0.376631i
$957$	53.1415			1.71782
$958$	9.73953	+	16.8694i	0.314670	+	0.545024i
$959$	37.5736			1.21331
$960$	−28.5013			−0.919876
$961$		0			0
$962$	5.89000			0.189901
$963$	4.12133			0.132808
$964$	5.47986	+	9.49140i	0.176494	+	0.305697i
$965$	30.9770			0.997184
$966$	4.42421	−	7.66295i	0.142347	−	0.246551i
$967$	−26.0999	−	45.2064i	−0.839316	−	1.45374i	−0.890467	−	0.455048i	$-0.849622\pi$
$967$	−26.0999	−	45.2064i	−0.839316	−	1.45374i	0.0511507	−	0.998691i	$-0.483711\pi$
$968$	4.81483	+	8.33954i	0.154755	+	0.268043i
$969$	47.7599			1.53427
$970$	10.3929	−	18.0011i	0.333697	−	0.577980i
$971$	9.98042	−	17.2866i	0.320287	−	0.554753i	−0.660260	−	0.751037i	$-0.729554\pi$
$971$	9.98042	−	17.2866i	0.320287	−	0.554753i	0.980547	+	0.196284i	$0.0628874\pi$
$972$	−3.06321	+	5.30564i	−0.0982526	+	0.170178i
$973$	−29.4772	−	51.0560i	−0.944995	−	1.63678i
$974$	−7.88075	+	13.6499i	−0.252516	+	0.437370i
$975$	−7.13821	−	12.3637i	−0.228606	−	0.395957i
$976$	7.63763			0.244475
$977$	−60.2506			−1.92759			−0.963794	−	0.266648i	$-0.914084\pi$
$977$	−60.2506			−1.92759			−0.963794	+	0.266648i	$0.914084\pi$
$978$	0.170246	+	0.294876i	0.00544388	+	0.00942908i
$979$	9.58361	−	16.5993i	0.306293	−	0.530516i
$980$	−2.78057	−	4.81609i	−0.0888222	−	0.153845i
$981$	−4.54074	+	7.86480i	−0.144975	+	0.251104i
$982$	11.4150	−	19.7713i	0.364266	−	0.630927i
$983$	5.76936	−	9.99283i	0.184014	−	0.318722i	−0.759230	−	0.650823i	$-0.774424\pi$
$983$	5.76936	−	9.99283i	0.184014	−	0.318722i	0.943244	+	0.332101i	$0.107757\pi$
$984$	−2.13924			−0.0681964
$985$	16.7765	+	29.0577i	0.534543	+	0.925855i
$986$	15.8321	+	27.4221i	0.504198	+	0.873297i
$987$	−4.69279	+	8.12816i	−0.149373	+	0.258722i
$988$	7.74148			0.246289
$989$	−1.76692	−	3.06040i	−0.0561848	−	0.0973149i
$990$	9.35239			0.297238
$991$	37.3423			1.18622			0.593109	−	0.805122i	$-0.297900\pi$
$991$	37.3423			1.18622			0.593109	+	0.805122i	$0.297900\pi$
$992$		0			0
$993$	1.58899			0.0504251
$994$	23.8946			0.757890
$995$	11.7201	+	20.2998i	0.371551	+	0.643546i
$996$	8.39197			0.265910
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	−0.982395	−	0.186816i	$-0.940183\pi$
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	0.652985	+	0.757371i	$0.273516\pi$
$998$	−25.1901	−	43.6305i	−0.797378	−	1.38110i
$999$	−3.18913	−	5.52373i	−0.100900	−	0.174763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.j.521.5		16
31.2	even	5		31.2.g.a.7.2	✓	16
31.3	odd	30		961.2.d.n.628.3		16
31.4	even	5		961.2.g.s.338.1		16
31.5	even	3	inner	961.2.c.j.439.5		16
31.6	odd	6		961.2.a.j.1.5		8
31.7	even	15		961.2.d.p.388.2		16
31.8	even	5		961.2.g.t.732.1		16
31.9	even	15		961.2.g.s.816.1		16
31.10	even	15		961.2.g.k.547.2		16
31.11	odd	30		961.2.g.n.235.1		16
31.12	odd	30		961.2.d.n.531.3		16
31.13	odd	30		961.2.g.l.846.2		16
31.14	even	15		961.2.d.p.374.2		16
31.15	odd	10		961.2.g.j.448.2		16
31.16	even	5		961.2.g.k.448.2		16
31.17	odd	30		961.2.d.q.374.2		16
31.18	even	15		31.2.g.a.9.2	yes	16
31.19	even	15		961.2.d.o.531.3		16
31.20	even	15		961.2.g.t.235.1		16
31.21	odd	30		961.2.g.j.547.2		16
31.22	odd	30		961.2.g.m.816.1		16
31.23	odd	10		961.2.g.n.732.1		16
31.24	odd	30		961.2.d.q.388.2		16
31.25	even	3		961.2.a.i.1.5		8
31.26	odd	6		961.2.c.i.439.5		16
31.27	odd	10		961.2.g.m.338.1		16
31.28	even	15		961.2.d.o.628.3		16
31.29	odd	10		961.2.g.l.844.2		16
31.30	odd	2		961.2.c.i.521.5		16
93.2	odd	10		279.2.y.c.100.1		16
93.56	odd	6		8649.2.a.bf.1.4		8
93.68	even	6		8649.2.a.be.1.4		8
93.80	odd	30		279.2.y.c.226.1		16
124.95	odd	10		496.2.bg.c.193.2		16
124.111	odd	30		496.2.bg.c.257.2		16
155.2	odd	20		775.2.ck.a.224.2		32
155.18	odd	60		775.2.ck.a.474.2		32
155.33	odd	20		775.2.ck.a.224.3		32
155.49	even	30		775.2.bl.a.226.1		16
155.64	even	10		775.2.bl.a.751.1		16
155.142	odd	60		775.2.ck.a.474.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.2	even	5
31.2.g.a.9.2	yes	16	31.18	even	15
279.2.y.c.100.1		16	93.2	odd	10
279.2.y.c.226.1		16	93.80	odd	30
496.2.bg.c.193.2		16	124.95	odd	10
496.2.bg.c.257.2		16	124.111	odd	30
775.2.bl.a.226.1		16	155.49	even	30
775.2.bl.a.751.1		16	155.64	even	10
775.2.ck.a.224.2		32	155.2	odd	20
775.2.ck.a.224.3		32	155.33	odd	20
775.2.ck.a.474.2		32	155.18	odd	60
775.2.ck.a.474.3		32	155.142	odd	60
961.2.a.i.1.5		8	31.25	even	3
961.2.a.j.1.5		8	31.6	odd	6
961.2.c.i.439.5		16	31.26	odd	6
961.2.c.i.521.5		16	31.30	odd	2
961.2.c.j.439.5		16	31.5	even	3	inner
961.2.c.j.521.5		16	1.1	even	1	trivial
961.2.d.n.531.3		16	31.12	odd	30
961.2.d.n.628.3		16	31.3	odd	30
961.2.d.o.531.3		16	31.19	even	15
961.2.d.o.628.3		16	31.28	even	15
961.2.d.p.374.2		16	31.14	even	15
961.2.d.p.388.2		16	31.7	even	15
961.2.d.q.374.2		16	31.17	odd	30
961.2.d.q.388.2		16	31.24	odd	30
961.2.g.j.448.2		16	31.15	odd	10
961.2.g.j.547.2		16	31.21	odd	30
961.2.g.k.448.2		16	31.16	even	5
961.2.g.k.547.2		16	31.10	even	15
961.2.g.l.844.2		16	31.29	odd	10
961.2.g.l.846.2		16	31.13	odd	30
961.2.g.m.338.1		16	31.27	odd	10
961.2.g.m.816.1		16	31.22	odd	30
961.2.g.n.235.1		16	31.11	odd	30
961.2.g.n.732.1		16	31.23	odd	10
961.2.g.s.338.1		16	31.4	even	5
961.2.g.s.816.1		16	31.9	even	15
961.2.g.t.235.1		16	31.20	even	15
961.2.g.t.732.1		16	31.8	even	5
8649.2.a.be.1.4		8	93.68	even	6
8649.2.a.bf.1.4		8	93.56	odd	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)

\(f(q)\)	\(=\)	\(q+1.23217 q^{2} +(-1.03749 - 1.79698i) q^{3} -0.481752 q^{4} +(0.772811 - 1.33855i) q^{5} +(-1.27836 - 2.21419i) q^{6} +(1.90188 + 3.29415i) q^{7} -3.05795 q^{8} +(-0.652760 + 1.13061i) q^{9} +O(q^{10})\)	\(q+1.23217 q^{2} +(-1.03749 - 1.79698i) q^{3} -0.481752 q^{4} +(0.772811 - 1.33855i) q^{5} +(-1.27836 - 2.21419i) q^{6} +(1.90188 + 3.29415i) q^{7} -3.05795 q^{8} +(-0.652760 + 1.13061i) q^{9} +(0.952237 - 1.64932i) q^{10} +(1.88076 - 3.25758i) q^{11} +(0.499811 + 0.865698i) q^{12} +(1.31753 - 2.28203i) q^{13} +(2.34344 + 4.05896i) q^{14} -3.20713 q^{15} -2.80441 q^{16} +(-1.88717 - 3.26867i) q^{17} +(-0.804313 + 1.39311i) q^{18} +(-3.04916 - 5.28130i) q^{19} +(-0.372303 + 0.644848i) q^{20} +(3.94635 - 6.83528i) q^{21} +(2.31742 - 4.01389i) q^{22} +0.909847 q^{23} +(3.17258 + 5.49507i) q^{24} +(1.30553 + 2.26124i) q^{25} +(1.62343 - 2.81186i) q^{26} -3.51600 q^{27} +(-0.916233 - 1.58696i) q^{28} -6.80859 q^{29} -3.95173 q^{30} +2.66037 q^{32} -7.80507 q^{33} +(-2.32532 - 4.02757i) q^{34} +5.87917 q^{35} +(0.314468 - 0.544675i) q^{36} +(0.907032 + 1.57103i) q^{37} +(-3.75709 - 6.50747i) q^{38} -5.46769 q^{39} +(-2.36321 + 4.09321i) q^{40} +(-0.168572 + 0.291976i) q^{41} +(4.86258 - 8.42224i) q^{42} +(-1.94200 - 3.36364i) q^{43} +(-0.906060 + 1.56934i) q^{44} +(1.00892 + 1.74750i) q^{45} +1.12109 q^{46} -1.18915 q^{47} +(2.90954 + 5.03948i) q^{48} +(-3.73429 + 6.46798i) q^{49} +(1.60863 + 2.78623i) q^{50} +(-3.91583 + 6.78242i) q^{51} +(-0.634723 + 1.09937i) q^{52} +(1.17206 - 2.03007i) q^{53} -4.33232 q^{54} +(-2.90695 - 5.03498i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(-6.32692 + 10.9586i) q^{57} -8.38936 q^{58} +(-3.88942 - 6.73667i) q^{59} +1.54504 q^{60} -2.72343 q^{61} -4.96588 q^{63} +8.88686 q^{64} +(-2.03641 - 3.52716i) q^{65} -9.61719 q^{66} +(3.71059 - 6.42693i) q^{67} +(0.909147 + 1.57469i) q^{68} +(-0.943955 - 1.63498i) q^{69} +7.24416 q^{70} +(2.54909 - 4.41515i) q^{71} +(1.99610 - 3.45735i) q^{72} +(-2.69587 + 4.66939i) q^{73} +(1.11762 + 1.93577i) q^{74} +(2.70893 - 4.69201i) q^{75} +(1.46894 + 2.54427i) q^{76} +14.3079 q^{77} -6.73714 q^{78} +(4.86861 + 8.43268i) q^{79} +(-2.16728 + 3.75384i) q^{80} +(5.60609 + 9.71003i) q^{81} +(-0.207710 + 0.359765i) q^{82} +(4.19757 - 7.27041i) q^{83} +(-1.90116 + 3.29291i) q^{84} -5.83370 q^{85} +(-2.39288 - 4.14458i) q^{86} +(7.06383 + 12.2349i) q^{87} +(-5.75127 + 9.96149i) q^{88} +5.09560 q^{89} +(1.24316 + 2.15322i) q^{90} +10.0231 q^{91} -0.438320 q^{92} -1.46523 q^{94} -9.42569 q^{95} +(-2.76010 - 4.78064i) q^{96} +10.9142 q^{97} +(-4.60129 + 7.96966i) q^{98} +(2.45537 + 4.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 3 q^{3} + 16 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 3 * q^3 + 16 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9	\( 16 q + 4 q^{2} + 3 q^{3} + 16 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} + 18 q^{11} + 8 q^{13} + 9 q^{14} - 36 q^{15} + 8 q^{16} + 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20} - q^{21} + 4 q^{22} - 44 q^{23} + 30 q^{24} - 13 q^{25} + 9 q^{26} - 36 q^{27} + 5 q^{28} - 24 q^{29} - 22 q^{30} - 42 q^{32} + 12 q^{33} - 7 q^{34} - 24 q^{35} + q^{36} - 8 q^{37} - 7 q^{38} + 2 q^{39} - 11 q^{40} + 22 q^{41} - 6 q^{42} - 2 q^{43} + 4 q^{44} - 36 q^{46} - 36 q^{47} - q^{48} + 2 q^{49} - 27 q^{50} - 2 q^{51} - q^{52} + 6 q^{53} + 14 q^{54} + 28 q^{55} - 30 q^{56} - 17 q^{57} + 10 q^{58} + 4 q^{59} + 80 q^{60} - 60 q^{61} - 46 q^{63} + 18 q^{64} + 3 q^{65} + 20 q^{66} + 13 q^{67} + 30 q^{68} - 22 q^{69} - 78 q^{70} + q^{71} - 3 q^{72} + 2 q^{73} + 8 q^{74} + 23 q^{75} + 33 q^{76} + 48 q^{77} + 8 q^{79} - 24 q^{80} + 28 q^{81} + 19 q^{82} + 39 q^{83} + 8 q^{84} + 52 q^{85} - 16 q^{86} + 15 q^{87} - 17 q^{88} - 54 q^{89} - 8 q^{90} - 32 q^{91} - 64 q^{92} + 44 q^{94} - 12 q^{95} - 12 q^{96} + 68 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 16 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 + 18 * q^11 + 8 * q^13 + 9 * q^14 - 36 * q^15 + 8 * q^16 + 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 - q^21 + 4 * q^22 - 44 * q^23 + 30 * q^24 - 13 * q^25 + 9 * q^26 - 36 * q^27 + 5 * q^28 - 24 * q^29 - 22 * q^30 - 42 * q^32 + 12 * q^33 - 7 * q^34 - 24 * q^35 + q^36 - 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 - 6 * q^42 - 2 * q^43 + 4 * q^44 - 36 * q^46 - 36 * q^47 - q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 - q^52 + 6 * q^53 + 14 * q^54 + 28 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 + 4 * q^59 + 80 * q^60 - 60 * q^61 - 46 * q^63 + 18 * q^64 + 3 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 + 2 * q^73 + 8 * q^74 + 23 * q^75 + 33 * q^76 + 48 * q^77 + 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 + 39 * q^83 + 8 * q^84 + 52 * q^85 - 16 * q^86 + 15 * q^87 - 17 * q^88 - 54 * q^89 - 8 * q^90 - 32 * q^91 - 64 * q^92 + 44 * q^94 - 12 * q^95 - 12 * q^96 + 68 * q^97 - 10 * q^98 + 6 * q^99

Introduction

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