LMFDB - Embedded newform 722.2.e.d.423.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			423.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	722.423
Dual form			722.2.e.d.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.06418 - 2.57115i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.06418 - 2.57115i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +(-3.75877 - 1.36808i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.173648 + 0.984808i) q^{13} +(-2.29813 - 1.92836i) q^{14} +(-3.06418 + 2.57115i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.81908 + 1.02606i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(-2.81908 + 1.02606i) q^{21} +(-0.347296 + 1.96962i) q^{22} +(-0.766044 + 0.642788i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(1.91013 + 10.8329i) q^{25} +(0.500000 + 0.866025i) q^{26} +(2.50000 - 4.33013i) q^{27} +(-2.81908 - 1.02606i) q^{28} +(-4.69846 - 1.71010i) q^{29} +(-2.00000 + 3.46410i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.53209 + 1.28558i) q^{33} +(-2.29813 + 1.92836i) q^{34} +(-2.08378 + 11.8177i) q^{35} +(1.87939 - 0.684040i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(-3.75877 + 1.36808i) q^{40} +(1.38919 - 7.87846i) q^{41} +(-2.29813 + 1.92836i) q^{42} +(3.06418 + 2.57115i) q^{43} +(0.347296 + 1.96962i) q^{44} +(-4.00000 - 6.92820i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-7.51754 - 2.73616i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(5.50000 + 9.52628i) q^{50} +(0.520945 + 2.95442i) q^{51} +(0.766044 + 0.642788i) q^{52} +(0.766044 - 0.642788i) q^{53} +(0.868241 - 4.92404i) q^{54} +(7.51754 - 2.73616i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(14.0954 - 5.13030i) q^{59} +(-0.694593 + 3.93923i) q^{60} +(1.53209 - 1.28558i) q^{61} +(-6.12836 - 5.14230i) q^{62} +(-1.04189 - 5.90885i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.00000 - 3.46410i) q^{65} +(1.87939 + 0.684040i) q^{66} +(2.81908 + 1.02606i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(0.500000 + 0.866025i) q^{69} +(2.08378 + 11.8177i) q^{70} +(-1.53209 - 1.28558i) q^{71} +(1.53209 - 1.28558i) q^{72} +(1.56283 - 8.86327i) q^{73} +(1.87939 - 0.684040i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(0.939693 - 0.342020i) q^{78} +(1.73648 - 9.84808i) q^{79} +(-3.06418 + 2.57115i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.38919 - 7.87846i) q^{82} +(3.00000 + 5.19615i) q^{83} +(-1.50000 + 2.59808i) q^{84} +(11.2763 + 4.10424i) q^{85} +(3.75877 + 1.36808i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-6.12836 - 5.14230i) q^{90} +(2.29813 - 1.92836i) q^{91} +(-0.173648 + 0.984808i) q^{92} +(-7.51754 + 2.73616i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(-1.87939 + 0.684040i) q^{97} +(-0.347296 + 1.96962i) q^{98} +(-3.06418 + 2.57115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 9 * q^7 + 3 * q^8	$ 6 q - 9 q^{7} + 3 q^{8} - 6 q^{11} - 3 q^{12} + 12 q^{18} - 24 q^{20} + 3 q^{26} + 15 q^{27} - 12 q^{30} - 24 q^{31} + 12 q^{37} + 6 q^{39} - 24 q^{45} - 3 q^{46} - 6 q^{49} + 33 q^{50} - 18 q^{56} - 30 q^{58} - 3 q^{64} + 12 q^{65} - 9 q^{68} + 3 q^{69} + 66 q^{75} + 36 q^{77} + 18 q^{83} - 9 q^{84} - 15 q^{87} + 6 q^{88} - 48 q^{94} - 6 q^{96}+O(q^{100}) $ 6 * q - 9 * q^7 + 3 * q^8 - 6 * q^11 - 3 * q^12 + 12 * q^18 - 24 * q^20 + 3 * q^26 + 15 * q^27 - 12 * q^30 - 24 * q^31 + 12 * q^37 + 6 * q^39 - 24 * q^45 - 3 * q^46 - 6 * q^49 + 33 * q^50 - 18 * q^56 - 30 * q^58 - 3 * q^64 + 12 * q^65 - 9 * q^68 + 3 * q^69 + 66 * q^75 + 36 * q^77 + 18 * q^83 - 9 * q^84 - 15 * q^87 + 6 * q^88 - 48 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i	−0.892754	−	0.450545i	$-0.851230\pi$
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i	0.993010	−	0.118034i	$-0.0376592\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−3.06418	−	2.57115i	−1.37034	−	1.14985i	−0.972634	−	0.232341i	$-0.925361\pi$
$5$	−3.06418	−	2.57115i	−1.37034	−	1.14985i	−0.397708	−	0.917512i	$-0.630194\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.87939	+	0.684040i	0.626462	+	0.228013i
$10$	−3.75877	−	1.36808i	−1.18863	−	0.432625i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.173648	+	0.984808i	0.0481613	+	0.273137i	0.999373	−	0.0354021i	$-0.0112712\pi$
$13$	0.173648	+	0.984808i	0.0481613	+	0.273137i	−0.951212	+	0.308539i	$0.900160\pi$
$14$	−2.29813	−	1.92836i	−0.614202	−	0.515377i
$15$	−3.06418	+	2.57115i	−0.791167	+	0.663868i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.81908	+	1.02606i	−0.683727	+	0.248856i	−0.660447	−	0.750873i	$-0.729633\pi$
$17$	−2.81908	+	1.02606i	−0.683727	+	0.248856i	−0.0232799	+	0.999729i	$0.507411\pi$
$18$	2.00000			0.471405
$19$		0			0
$19$		0			0
$20$	−4.00000			−0.894427
$21$	−2.81908	+	1.02606i	−0.615173	+	0.223905i
$22$	−0.347296	+	1.96962i	−0.0740438	+	0.419923i
$23$	−0.766044	+	0.642788i	−0.159731	+	0.134030i	−0.719150	−	0.694855i	$-0.755469\pi$
$23$	−0.766044	+	0.642788i	−0.159731	+	0.134030i	0.559419	+	0.828885i	$0.311024\pi$
$24$	−0.766044	−	0.642788i	−0.156368	−	0.131208i
$25$	1.91013	+	10.8329i	0.382026	+	2.16658i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	2.50000	−	4.33013i	0.481125	−	0.833333i
$28$	−2.81908	−	1.02606i	−0.532756	−	0.193907i
$29$	−4.69846	−	1.71010i	−0.872483	−	0.317558i	−0.133311	−	0.991074i	$-0.542561\pi$
$29$	−4.69846	−	1.71010i	−0.872483	−	0.317558i	−0.739172	+	0.673517i	$0.764783\pi$
$30$	−2.00000	+	3.46410i	−0.365148	+	0.632456i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	1.53209	+	1.28558i	0.266702	+	0.223790i
$34$	−2.29813	+	1.92836i	−0.394127	+	0.330711i
$35$	−2.08378	+	11.8177i	−0.352223	+	1.99755i
$36$	1.87939	−	0.684040i	0.313231	−	0.114007i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	1.00000			0.160128
$40$	−3.75877	+	1.36808i	−0.594314	+	0.216313i
$41$	1.38919	−	7.87846i	0.216954	−	1.23041i	−0.660529	−	0.750801i	$-0.729668\pi$
$41$	1.38919	−	7.87846i	0.216954	−	1.23041i	0.877483	−	0.479608i	$-0.159221\pi$
$42$	−2.29813	+	1.92836i	−0.354610	+	0.297553i
$43$	3.06418	+	2.57115i	0.467283	+	0.392097i	0.845802	−	0.533497i	$-0.179122\pi$
$43$	3.06418	+	2.57115i	0.467283	+	0.392097i	−0.378520	+	0.925593i	$0.623567\pi$
$44$	0.347296	+	1.96962i	0.0523569	+	0.296931i
$45$	−4.00000	−	6.92820i	−0.596285	−	1.03280i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−7.51754	−	2.73616i	−1.09655	−	0.399110i	−0.270504	−	0.962719i	$-0.587190\pi$
$47$	−7.51754	−	2.73616i	−1.09655	−	0.399110i	−0.826042	+	0.563609i	$0.809413\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	5.50000	+	9.52628i	0.777817	+	1.34722i
$51$	0.520945	+	2.95442i	0.0729468	+	0.413702i
$52$	0.766044	+	0.642788i	0.106231	+	0.0891386i
$53$	0.766044	−	0.642788i	0.105224	−	0.0882937i	−0.588658	−	0.808382i	$-0.700343\pi$
$53$	0.766044	−	0.642788i	0.105224	−	0.0882937i	0.693882	+	0.720089i	$0.255899\pi$
$54$	0.868241	−	4.92404i	0.118153	−	0.670077i
$55$	7.51754	−	2.73616i	1.01367	−	0.368944i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−5.00000			−0.656532
$59$	14.0954	−	5.13030i	1.83506	−	0.667908i	0.843692	−	0.536828i	$-0.180378\pi$
$59$	14.0954	−	5.13030i	1.83506	−	0.667908i	0.991372	−	0.131080i	$-0.0418446\pi$
$60$	−0.694593	+	3.93923i	−0.0896715	+	0.508553i
$61$	1.53209	−	1.28558i	0.196164	−	0.164601i	−0.539415	−	0.842040i	$-0.681355\pi$
$61$	1.53209	−	1.28558i	0.196164	−	0.164601i	0.735579	+	0.677439i	$0.236910\pi$
$62$	−6.12836	−	5.14230i	−0.778302	−	0.653073i
$63$	−1.04189	−	5.90885i	−0.131266	−	0.744445i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$	1.87939	+	0.684040i	0.231336	+	0.0841995i
$67$	2.81908	+	1.02606i	0.344405	+	0.125353i	0.508431	−	0.861103i	$-0.330226\pi$
$67$	2.81908	+	1.02606i	0.344405	+	0.125353i	−0.164026	+	0.986456i	$0.552448\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	0.500000	+	0.866025i	0.0601929	+	0.104257i
$70$	2.08378	+	11.8177i	0.249059	+	1.41248i
$71$	−1.53209	−	1.28558i	−0.181825	−	0.152570i	0.547332	−	0.836915i	$-0.315643\pi$
$71$	−1.53209	−	1.28558i	−0.181825	−	0.152570i	−0.729158	+	0.684346i	$0.760088\pi$
$72$	1.53209	−	1.28558i	0.180558	−	0.151506i
$73$	1.56283	−	8.86327i	0.182916	−	1.03737i	−0.745688	−	0.666295i	$-0.767879\pi$
$73$	1.56283	−	8.86327i	0.182916	−	1.03737i	0.928604	−	0.371072i	$-0.121010\pi$
$74$	1.87939	−	0.684040i	0.218474	−	0.0795181i
$75$	11.0000			1.27017
$76$		0			0
$77$	6.00000			0.683763
$78$	0.939693	−	0.342020i	0.106399	−	0.0387262i
$79$	1.73648	−	9.84808i	0.195369	−	1.10800i	−0.716522	−	0.697564i	$-0.754267\pi$
$79$	1.73648	−	9.84808i	0.195369	−	1.10800i	0.911892	−	0.410431i	$-0.134622\pi$
$80$	−3.06418	+	2.57115i	−0.342585	+	0.287463i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	−1.38919	−	7.87846i	−0.153410	−	0.870031i
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$	−1.50000	+	2.59808i	−0.163663	+	0.283473i
$85$	11.2763	+	4.10424i	1.22309	+	0.445168i
$86$	3.75877	+	1.36808i	0.405319	+	0.147524i
$87$	−2.50000	+	4.33013i	−0.268028	+	0.464238i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$89$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$90$	−6.12836	−	5.14230i	−0.645985	−	0.542046i
$91$	2.29813	−	1.92836i	0.240910	−	0.202147i
$92$	−0.173648	+	0.984808i	−0.0181041	+	0.102673i
$93$	−7.51754	+	2.73616i	−0.779533	+	0.283727i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−1.87939	+	0.684040i	−0.190823	+	0.0694538i	−0.435664	−	0.900109i	$-0.643486\pi$
$97$	−1.87939	+	0.684040i	−0.190823	+	0.0694538i	0.244841	+	0.969563i	$0.421264\pi$
$98$	−0.347296	+	1.96962i	−0.0350822	+	0.198961i
$99$	−3.06418	+	2.57115i	−0.307961	+	0.258410i
$100$	8.42649	+	7.07066i	0.842649	+	0.707066i
$101$	0.347296	+	1.96962i	0.0345573	+	0.195984i	0.997199	−	0.0747944i	$-0.0238300\pi$
$101$	0.347296	+	1.96962i	0.0345573	+	0.195984i	−0.962642	+	0.270778i	$0.912719\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	−0.975124	−	0.221660i	$-0.928852\pi$
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	0.679525	+	0.733652i	$0.262186\pi$
$104$	0.939693	+	0.342020i	0.0921444	+	0.0335378i
$105$	11.2763	+	4.10424i	1.10046	+	0.400533i
$106$	0.500000	−	0.866025i	0.0485643	−	0.0841158i
$107$	−3.50000	−	6.06218i	−0.338358	−	0.586053i	0.645766	−	0.763535i	$-0.276538\pi$
$107$	−3.50000	−	6.06218i	−0.338358	−	0.586053i	−0.984124	+	0.177482i	$0.943205\pi$
$108$	−0.868241	−	4.92404i	−0.0835465	−	0.473816i
$109$	11.4907	+	9.64181i	1.10061	+	0.923518i	0.997466	−	0.0711485i	$-0.0226664\pi$
$109$	11.4907	+	9.64181i	1.10061	+	0.923518i	0.103141	+	0.994667i	$0.467111\pi$
$110$	6.12836	−	5.14230i	0.584316	−	0.490299i
$111$	0.347296	−	1.96962i	0.0329639	−	0.186948i
$112$	−2.81908	+	1.02606i	−0.266378	+	0.0969536i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	4.00000			0.373002
$116$	−4.69846	+	1.71010i	−0.436241	+	0.158779i
$117$	−0.347296	+	1.96962i	−0.0321076	+	0.182091i
$118$	11.4907	−	9.64181i	1.05780	−	0.887601i
$119$	6.89440	+	5.78509i	0.632009	+	0.530318i
$120$	0.694593	+	3.93923i	0.0634073	+	0.359601i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$	−7.51754	−	2.73616i	−0.677834	−	0.246711i
$124$	−7.51754	−	2.73616i	−0.675095	−	0.245715i
$125$	12.0000	−	20.7846i	1.07331	−	1.85903i
$126$	−3.00000	−	5.19615i	−0.267261	−	0.462910i
$127$	−3.12567	−	17.7265i	−0.277358	−	1.57298i	−0.731370	−	0.681981i	$-0.761119\pi$
$127$	−3.12567	−	17.7265i	−0.277358	−	1.57298i	0.454012	−	0.890995i	$-0.349992\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	3.06418	−	2.57115i	0.269786	−	0.226377i
$130$	0.694593	−	3.93923i	0.0609198	−	0.345493i
$131$	−11.2763	+	4.10424i	−0.985216	+	0.358589i	−0.783866	−	0.620930i	$-0.786755\pi$
$131$	−11.2763	+	4.10424i	−0.985216	+	0.358589i	−0.201350	+	0.979519i	$0.564533\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	3.00000			0.259161
$135$	−18.7939	+	6.84040i	−1.61752	+	0.588728i
$136$	−0.520945	+	2.95442i	−0.0446706	+	0.253340i
$137$	−13.0228	+	10.9274i	−1.11261	+	0.933590i	−0.998208	−	0.0598447i	$-0.980939\pi$
$137$	−13.0228	+	10.9274i	−1.11261	+	0.933590i	−0.114401	+	0.993435i	$0.536495\pi$
$138$	0.766044	+	0.642788i	0.0652100	+	0.0547177i
$139$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$139$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$140$	6.00000	+	10.3923i	0.507093	+	0.878310i
$141$	−4.00000	+	6.92820i	−0.336861	+	0.583460i
$142$	−1.87939	−	0.684040i	−0.157715	−	0.0574034i
$143$	−1.87939	−	0.684040i	−0.157162	−	0.0572023i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	10.0000	+	17.3205i	0.830455	+	1.43839i
$146$	−1.56283	−	8.86327i	−0.129341	−	0.733529i
$147$	1.53209	+	1.28558i	0.126365	+	0.106032i
$148$	1.53209	−	1.28558i	0.125937	−	0.105674i
$149$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$149$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$150$	10.3366	−	3.76222i	0.843981	−	0.307184i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	5.63816	−	2.05212i	0.454336	−	0.165365i
$155$	−5.55674	+	31.5138i	−0.446328	+	2.53125i
$156$	0.766044	−	0.642788i	0.0613326	−	0.0514642i
$157$	−1.53209	−	1.28558i	−0.122274	−	0.102600i	0.579600	−	0.814901i	$-0.303209\pi$
$157$	−1.53209	−	1.28558i	−0.122274	−	0.102600i	−0.701874	+	0.712301i	$0.747653\pi$
$158$	−1.73648	−	9.84808i	−0.138147	−	0.783471i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	−2.00000	+	3.46410i	−0.158114	+	0.273861i
$161$	2.81908	+	1.02606i	0.222174	+	0.0808649i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	−4.00000	−	6.92820i	−0.312348	−	0.541002i
$165$	−1.38919	−	7.87846i	−0.108148	−	0.613337i
$166$	4.59627	+	3.85673i	0.356739	+	0.299340i
$167$	9.19253	−	7.71345i	0.711340	−	0.596885i	−0.213635	−	0.976914i	$-0.568530\pi$
$167$	9.19253	−	7.71345i	0.711340	−	0.596885i	0.924975	+	0.380029i	$0.124086\pi$
$168$	−0.520945	+	2.95442i	−0.0401917	+	0.227939i
$169$	11.2763	−	4.10424i	0.867409	−	0.315711i
$170$	12.0000			0.920358
$171$		0			0
$172$	4.00000			0.304997
$173$	−5.63816	+	2.05212i	−0.428661	+	0.156020i	−0.547335	−	0.836913i	$-0.684358\pi$
$173$	−5.63816	+	2.05212i	−0.428661	+	0.156020i	0.118674	+	0.992933i	$0.462136\pi$
$174$	−0.868241	+	4.92404i	−0.0658212	+	0.373290i
$175$	25.2795	−	21.2120i	1.91095	−	1.60348i
$176$	1.53209	+	1.28558i	0.115486	+	0.0969039i
$177$	−2.60472	−	14.7721i	−0.195783	−	1.11034i
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	−7.51754	−	2.73616i	−0.560324	−	0.203941i
$181$	20.6732	+	7.52444i	1.53663	+	0.559287i	0.965234	−	0.261387i	$-0.0841800\pi$
$181$	20.6732	+	7.52444i	1.53663	+	0.559287i	0.571396	+	0.820675i	$0.306402\pi$
$182$	1.50000	−	2.59808i	0.111187	−	0.192582i
$183$	−1.00000	−	1.73205i	−0.0739221	−	0.128037i
$184$	0.173648	+	0.984808i	0.0128015	+	0.0726010i
$185$	−6.12836	−	5.14230i	−0.450566	−	0.378069i
$186$	−6.12836	+	5.14230i	−0.449353	+	0.377052i
$187$	1.04189	−	5.90885i	0.0761905	−	0.432098i
$188$	−7.51754	+	2.73616i	−0.548273	+	0.199555i
$189$	−15.0000			−1.09109
$190$		0			0
$191$	7.00000			0.506502			0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000			0.506502			0.253251	+	0.967401i	$0.418500\pi$
$192$	−0.939693	+	0.342020i	−0.0678165	+	0.0246832i
$193$	1.04189	−	5.90885i	0.0749968	−	0.425328i	−0.924073	−	0.382215i	$-0.875161\pi$
$193$	1.04189	−	5.90885i	0.0749968	−	0.425328i	0.999070	−	0.0431130i	$-0.0137275\pi$
$194$	−1.53209	+	1.28558i	−0.109998	+	0.0922989i
$195$	−3.06418	−	2.57115i	−0.219430	−	0.184124i
$196$	0.347296	+	1.96962i	0.0248069	+	0.140687i
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	0.687618	−	0.726073i	$-0.258656\pi$
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	−0.972606	+	0.232458i	$0.925323\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$	23.4923	+	8.55050i	1.66533	+	0.606129i	0.991186	−	0.132475i	$-0.0422923\pi$
$199$	23.4923	+	8.55050i	1.66533	+	0.606129i	0.674140	+	0.738604i	$0.264515\pi$
$200$	10.3366	+	3.76222i	0.730909	+	0.266029i
$201$	1.50000	−	2.59808i	0.105802	−	0.183254i
$202$	1.00000	+	1.73205i	0.0703598	+	0.121867i
$203$	2.60472	+	14.7721i	0.182816	+	1.03680i
$204$	2.29813	+	1.92836i	0.160902	+	0.135012i
$205$	−24.5134	+	20.5692i	−1.71209	+	1.43662i
$206$	−1.04189	+	5.90885i	−0.0725919	+	0.411689i
$207$	−1.87939	+	0.684040i	−0.130626	+	0.0475441i
$208$	1.00000			0.0693375
$209$		0			0
$210$	12.0000			0.828079
$211$	25.3717	−	9.23454i	1.74666	−	0.635732i	0.747081	−	0.664734i	$-0.231455\pi$
$211$	25.3717	−	9.23454i	1.74666	−	0.635732i	0.999579	+	0.0290013i	$0.00923270\pi$
$212$	0.173648	−	0.984808i	0.0119262	−	0.0676369i
$213$	−1.53209	+	1.28558i	−0.104977	+	0.0880862i
$214$	−5.36231	−	4.49951i	−0.366560	−	0.307580i
$215$	−2.77837	−	15.7569i	−0.189483	−	1.07461i
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	−12.0000	+	20.7846i	−0.814613	+	1.41095i
$218$	14.0954	+	5.13030i	0.954660	+	0.347468i
$219$	−8.45723	−	3.07818i	−0.571487	−	0.208004i
$220$	4.00000	−	6.92820i	0.269680	−	0.467099i
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$	−0.347296	−	1.96962i	−0.0233090	−	0.132192i
$223$	−10.7246	−	8.99903i	−0.718174	−	0.602619i	0.208706	−	0.977979i	$-0.433075\pi$
$223$	−10.7246	−	8.99903i	−0.718174	−	0.602619i	−0.926879	+	0.375359i	$0.877519\pi$
$224$	−2.29813	+	1.92836i	−0.153550	+	0.128844i
$225$	−3.82026	+	21.6658i	−0.254684	+	1.44438i
$226$	−13.1557	+	4.78828i	−0.875104	+	0.318512i
$227$	17.0000			1.12833			0.564165	−	0.825662i	$-0.309198\pi$
$227$	17.0000			1.12833			0.564165	+	0.825662i	$0.309198\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	3.75877	−	1.36808i	0.247846	−	0.0902086i
$231$	1.04189	−	5.90885i	0.0685513	−	0.388774i
$232$	−3.83022	+	3.21394i	−0.251466	+	0.211005i
$233$	−4.59627	−	3.85673i	−0.301111	−	0.252662i	0.479695	−	0.877435i	$-0.340747\pi$
$233$	−4.59627	−	3.85673i	−0.301111	−	0.252662i	−0.780807	+	0.624773i	$0.785192\pi$
$234$	0.347296	+	1.96962i	0.0227035	+	0.128758i
$235$	16.0000	+	27.7128i	1.04372	+	1.80778i
$236$	7.50000	−	12.9904i	0.488208	−	0.845602i
$237$	−9.39693	−	3.42020i	−0.610396	−	0.222166i
$238$	8.45723	+	3.07818i	0.548201	+	0.199529i
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$	2.00000	+	3.46410i	0.129099	+	0.223607i
$241$	1.38919	+	7.87846i	0.0894853	+	0.507496i	0.996298	+	0.0859632i	$0.0273968\pi$
$241$	1.38919	+	7.87846i	0.0894853	+	0.507496i	−0.906813	+	0.421533i	$0.861492\pi$
$242$	5.36231	+	4.49951i	0.344702	+	0.289240i
$243$	12.2567	−	10.2846i	0.786268	−	0.659758i
$244$	0.347296	−	1.96962i	0.0222334	−	0.126092i
$245$	7.51754	−	2.73616i	0.480278	−	0.174807i
$246$	−8.00000			−0.510061
$247$		0			0
$248$	−8.00000			−0.508001
$249$	5.63816	−	2.05212i	0.357304	−	0.130048i
$250$	4.16756	−	23.6354i	0.263579	−	1.49483i
$251$	1.53209	−	1.28558i	0.0967046	−	0.0811448i	−0.593154	−	0.805089i	$-0.702117\pi$
$251$	1.53209	−	1.28558i	0.0967046	−	0.0811448i	0.689858	+	0.723945i	$0.257673\pi$
$252$	−4.59627	−	3.85673i	−0.289538	−	0.242951i
$253$	−0.347296	−	1.96962i	−0.0218343	−	0.123829i
$254$	−9.00000	−	15.5885i	−0.564710	−	0.978107i
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	7.51754	+	2.73616i	0.468931	+	0.170677i	0.565668	−	0.824633i	$-0.308618\pi$
$257$	7.51754	+	2.73616i	0.468931	+	0.170677i	−0.0967369	+	0.995310i	$0.530841\pi$
$258$	2.00000	−	3.46410i	0.124515	−	0.215666i
$259$	−3.00000	−	5.19615i	−0.186411	−	0.322873i
$260$	−0.694593	−	3.93923i	−0.0430768	−	0.244301i
$261$	−7.66044	−	6.42788i	−0.474170	−	0.397876i
$262$	−9.19253	+	7.71345i	−0.567917	+	0.476539i
$263$	4.16756	−	23.6354i	0.256983	−	1.45742i	−0.533950	−	0.845516i	$-0.679293\pi$
$263$	4.16756	−	23.6354i	0.256983	−	1.45742i	0.790932	−	0.611904i	$-0.209596\pi$
$264$	1.87939	−	0.684040i	0.115668	−	0.0420998i
$265$	−4.00000			−0.245718
$266$		0			0
$267$		0			0
$268$	2.81908	−	1.02606i	0.172203	−	0.0626766i
$269$	−5.20945	+	29.5442i	−0.317625	+	1.80134i	0.239479	+	0.970901i	$0.423023\pi$
$269$	−5.20945	+	29.5442i	−0.317625	+	1.80134i	−0.557105	+	0.830442i	$0.688088\pi$
$270$	−15.3209	+	12.8558i	−0.932400	+	0.782376i
$271$	5.36231	+	4.49951i	0.325737	+	0.273326i	0.790960	−	0.611868i	$-0.209581\pi$
$271$	5.36231	+	4.49951i	0.325737	+	0.273326i	−0.465223	+	0.885193i	$0.654026\pi$
$272$	0.520945	+	2.95442i	0.0315869	+	0.179138i
$273$	−1.50000	−	2.59808i	−0.0907841	−	0.157243i
$274$	−8.50000	+	14.7224i	−0.513504	+	0.889415i
$275$	−20.6732	−	7.52444i	−1.24664	−	0.453741i
$276$	0.939693	+	0.342020i	0.0565628	+	0.0205872i
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	0.0477206	+	0.998861i	$0.484804\pi$
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	−0.888899	+	0.458103i	$0.848529\pi$
$278$		0			0
$279$	−2.77837	−	15.7569i	−0.166337	−	0.943342i
$280$	9.19253	+	7.71345i	0.549359	+	0.460967i
$281$	6.12836	−	5.14230i	0.365587	−	0.306764i	−0.441426	−	0.897298i	$-0.645527\pi$
$281$	6.12836	−	5.14230i	0.365587	−	0.306764i	0.807013	+	0.590534i	$0.201083\pi$
$282$	−1.38919	+	7.87846i	−0.0827248	+	0.469156i
$283$	5.63816	−	2.05212i	0.335154	−	0.121986i	−0.168961	−	0.985623i	$-0.554041\pi$
$283$	5.63816	−	2.05212i	0.335154	−	0.121986i	0.504115	+	0.863637i	$0.331819\pi$
$284$	−2.00000			−0.118678
$285$		0			0
$286$	−2.00000			−0.118262
$287$	−22.5526	+	8.20848i	−1.33124	+	0.484531i
$288$	0.347296	−	1.96962i	0.0204646	−	0.116061i
$289$	−6.12836	+	5.14230i	−0.360492	+	0.302488i
$290$	15.3209	+	12.8558i	0.899674	+	0.754916i
$291$	0.347296	+	1.96962i	0.0203589	+	0.115461i
$292$	−4.50000	−	7.79423i	−0.263343	−	0.456123i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	1.87939	+	0.684040i	0.109608	+	0.0398940i
$295$	−56.3816	−	20.5212i	−3.28266	−	1.19479i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	5.00000	+	8.66025i	0.290129	+	0.502519i
$298$		0			0
$299$	−0.766044	−	0.642788i	−0.0443015	−	0.0371734i
$300$	8.42649	−	7.07066i	0.486504	−	0.408225i
$301$	2.08378	−	11.8177i	0.120107	−	0.681161i
$302$	−1.87939	+	0.684040i	−0.108146	+	0.0393621i
$303$	2.00000			0.114897
$304$		0			0
$305$	−8.00000			−0.458079
$306$	−5.63816	+	2.05212i	−0.322312	+	0.117312i
$307$	2.08378	−	11.8177i	0.118927	−	0.674471i	−0.865803	−	0.500385i	$-0.833192\pi$
$307$	2.08378	−	11.8177i	0.118927	−	0.674471i	0.984730	−	0.174086i	$-0.0556971\pi$
$308$	4.59627	−	3.85673i	0.261897	−	0.219757i
$309$	4.59627	+	3.85673i	0.261472	+	0.219401i
$310$	5.55674	+	31.5138i	0.315602	+	1.78987i
$311$	−3.50000	−	6.06218i	−0.198467	−	0.343755i	0.749565	−	0.661931i	$-0.230263\pi$
$311$	−3.50000	−	6.06218i	−0.198467	−	0.343755i	−0.948031	+	0.318177i	$0.896930\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	−27.2511	−	9.91858i	−1.54032	−	0.560632i	−0.574200	−	0.818715i	$-0.694687\pi$
$313$	−27.2511	−	9.91858i	−1.54032	−	0.560632i	−0.966123	+	0.258084i	$0.916909\pi$
$314$	−1.87939	−	0.684040i	−0.106060	−	0.0386026i
$315$	−12.0000	+	20.7846i	−0.676123	+	1.17108i
$316$	−5.00000	−	8.66025i	−0.281272	−	0.487177i
$317$	4.68850	+	26.5898i	0.263332	+	1.49343i	0.773742	+	0.633501i	$0.218383\pi$
$317$	4.68850	+	26.5898i	0.263332	+	1.49343i	−0.510409	+	0.859932i	$0.670506\pi$
$318$	−0.766044	−	0.642788i	−0.0429576	−	0.0360457i
$319$	7.66044	−	6.42788i	0.428903	−	0.359892i
$320$	−0.694593	+	3.93923i	−0.0388289	+	0.220210i
$321$	−6.57785	+	2.39414i	−0.367140	+	0.133628i
$322$	3.00000			0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	−10.3366	+	3.76222i	−0.573372	+	0.208691i
$326$	2.77837	−	15.7569i	0.153880	−	0.872695i
$327$	11.4907	−	9.64181i	0.635435	−	0.533194i
$328$	−6.12836	−	5.14230i	−0.338382	−	0.283936i
$329$	4.16756	+	23.6354i	0.229765	+	1.30306i
$330$	−4.00000	−	6.92820i	−0.220193	−	0.381385i
$331$	8.50000	−	14.7224i	0.467202	−	0.809218i	−0.532096	−	0.846684i	$-0.678595\pi$
$331$	8.50000	−	14.7224i	0.467202	−	0.809218i	0.999298	+	0.0374662i	$0.0119287\pi$
$332$	5.63816	+	2.05212i	0.309434	+	0.112625i
$333$	3.75877	+	1.36808i	0.205979	+	0.0749704i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$	0.520945	+	2.95442i	0.0284199	+	0.161177i
$337$	24.5134	+	20.5692i	1.33533	+	1.12048i	0.982799	+	0.184676i	$0.0591236\pi$
$337$	24.5134	+	20.5692i	1.33533	+	1.12048i	0.352532	+	0.935800i	$0.385321\pi$
$338$	9.19253	−	7.71345i	0.500008	−	0.419556i
$339$	−2.43107	+	13.7873i	−0.132038	+	0.748824i
$340$	11.2763	−	4.10424i	0.611544	−	0.222584i
$341$	16.0000			0.866449
$342$		0			0
$343$	−15.0000			−0.809924
$344$	3.75877	−	1.36808i	0.202659	−	0.0737620i
$345$	0.694593	−	3.93923i	0.0373956	−	0.212081i
$346$	−4.59627	+	3.85673i	−0.247097	+	0.207339i
$347$	−1.53209	−	1.28558i	−0.0822468	−	0.0690133i	0.600737	−	0.799446i	$-0.294874\pi$
$347$	−1.53209	−	1.28558i	−0.0822468	−	0.0690133i	−0.682984	+	0.730433i	$0.739318\pi$
$348$	0.868241	+	4.92404i	0.0465426	+	0.263956i
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	0.700609	−	0.713545i	$-0.252912\pi$
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	−0.968253	+	0.249973i	$0.919578\pi$
$350$	16.5000	−	28.5788i	0.881962	−	1.52760i
$351$	4.69846	+	1.71010i	0.250785	+	0.0912784i
$352$	1.87939	+	0.684040i	0.100172	+	0.0364595i
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$	−7.50000	−	12.9904i	−0.398621	−	0.690431i
$355$	1.38919	+	7.87846i	0.0737303	+	0.418145i
$356$		0			0
$357$	6.89440	−	5.78509i	0.364890	−	0.306179i
$358$		0			0
$359$	14.0954	−	5.13030i	0.743926	−	0.270767i	0.0578786	−	0.998324i	$-0.481566\pi$
$359$	14.0954	−	5.13030i	0.743926	−	0.270767i	0.686048	+	0.727557i	$0.259344\pi$
$360$	−8.00000			−0.421637
$361$		0			0
$362$	22.0000			1.15629
$363$	6.57785	−	2.39414i	0.345248	−	0.125660i
$364$	0.520945	−	2.95442i	0.0273049	−	0.154854i
$365$	−27.5776	+	23.1404i	−1.44348	+	1.21122i
$366$	−1.53209	−	1.28558i	−0.0800836	−	0.0671981i
$367$	4.86215	+	27.5746i	0.253802	+	1.43938i	0.799129	+	0.601160i	$0.205294\pi$
$367$	4.86215	+	27.5746i	0.253802	+	1.43938i	−0.545327	+	0.838224i	$0.683594\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	8.00000	−	13.8564i	0.416463	−	0.721336i
$370$	−7.51754	−	2.73616i	−0.390818	−	0.142246i
$371$	−2.81908	−	1.02606i	−0.146359	−	0.0532704i
$372$	−4.00000	+	6.92820i	−0.207390	+	0.359211i
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	0.947444	+	0.319921i	$0.103656\pi$
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	−0.196663	+	0.980471i	$0.563010\pi$
$374$	−1.04189	−	5.90885i	−0.0538748	−	0.305539i
$375$	−18.3851	−	15.4269i	−0.949401	−	0.796642i
$376$	−6.12836	+	5.14230i	−0.316046	+	0.265194i
$377$	0.868241	−	4.92404i	0.0447167	−	0.253601i
$378$	−14.0954	+	5.13030i	−0.724989	+	0.263874i
$379$	−15.0000			−0.770498			−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000			−0.770498			−0.385249	+	0.922813i	$0.625884\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	6.57785	−	2.39414i	0.336552	−	0.122495i
$383$	4.51485	−	25.6050i	0.230698	−	1.30835i	−0.620788	−	0.783978i	$-0.713187\pi$
$383$	4.51485	−	25.6050i	0.230698	−	1.30835i	0.851487	−	0.524376i	$-0.175701\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	−18.3851	−	15.4269i	−0.936990	−	0.786228i
$386$	−1.04189	−	5.90885i	−0.0530308	−	0.300752i
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	28.1908	+	10.2606i	1.42933	+	0.520233i	0.936739	−	0.350028i	$-0.113828\pi$
$389$	28.1908	+	10.2606i	1.42933	+	0.520233i	0.492590	+	0.870261i	$0.336050\pi$
$390$	−3.75877	−	1.36808i	−0.190333	−	0.0692755i
$391$	1.50000	−	2.59808i	0.0758583	−	0.131390i
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	2.08378	+	11.8177i	0.105113	+	0.596124i
$394$	−6.12836	−	5.14230i	−0.308742	−	0.259065i
$395$	−30.6418	+	25.7115i	−1.54176	+	1.29369i
$396$	−0.694593	+	3.93923i	−0.0349046	+	0.197954i
$397$	−7.51754	+	2.73616i	−0.377295	+	0.137324i	−0.523704	−	0.851900i	$-0.675450\pi$
$397$	−7.51754	+	2.73616i	−0.377295	+	0.137324i	0.146410	+	0.989224i	$0.453228\pi$
$398$	25.0000			1.25314
$399$		0			0
$400$	11.0000			0.550000
$401$	−7.51754	+	2.73616i	−0.375408	+	0.136637i	−0.522831	−	0.852436i	$-0.675124\pi$
$401$	−7.51754	+	2.73616i	−0.375408	+	0.136637i	0.147423	+	0.989073i	$0.452902\pi$
$402$	0.520945	−	2.95442i	0.0259824	−	0.147353i
$403$	6.12836	−	5.14230i	0.305275	−	0.256156i
$404$	1.53209	+	1.28558i	0.0762243	+	0.0639598i
$405$	−0.694593	−	3.93923i	−0.0345146	−	0.195742i
$406$	7.50000	+	12.9904i	0.372219	+	0.644702i
$407$	−2.00000	+	3.46410i	−0.0991363	+	0.171709i
$408$	2.81908	+	1.02606i	0.139565	+	0.0507976i
$409$	−18.7939	−	6.84040i	−0.929296	−	0.338236i	−0.167366	−	0.985895i	$-0.553526\pi$
$409$	−18.7939	−	6.84040i	−0.929296	−	0.338236i	−0.761931	+	0.647659i	$0.775748\pi$
$410$	−16.0000	+	27.7128i	−0.790184	+	1.36864i
$411$	8.50000	+	14.7224i	0.419274	+	0.726204i
$412$	1.04189	+	5.90885i	0.0513302	+	0.291108i
$413$	−34.4720	−	28.9254i	−1.69626	−	1.42333i
$414$	−1.53209	+	1.28558i	−0.0752981	+	0.0631826i
$415$	4.16756	−	23.6354i	0.204577	−	1.16022i
$416$	0.939693	−	0.342020i	0.0460722	−	0.0167689i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	11.2763	−	4.10424i	0.550228	−	0.200266i
$421$	2.25743	−	12.8025i	0.110020	−	0.623956i	−0.879076	−	0.476682i	$-0.841839\pi$
$421$	2.25743	−	12.8025i	0.110020	−	0.623956i	0.989096	−	0.147273i	$-0.0470497\pi$
$422$	20.6832	−	17.3553i	1.00684	−	0.844841i
$423$	−12.2567	−	10.2846i	−0.595942	−	0.500054i
$424$	−0.173648	−	0.984808i	−0.00843310	−	0.0478265i
$425$	−16.5000	−	28.5788i	−0.800368	−	1.38628i
$426$	−1.00000	+	1.73205i	−0.0484502	+	0.0839181i
$427$	−5.63816	−	2.05212i	−0.272849	−	0.0993091i
$428$	−6.57785	−	2.39414i	−0.317952	−	0.115725i
$429$	−1.00000	+	1.73205i	−0.0482805	+	0.0836242i
$430$	−8.00000	−	13.8564i	−0.385794	−	0.668215i
$431$	3.12567	+	17.7265i	0.150558	+	0.853857i	0.962735	+	0.270446i	$0.0871712\pi$
$431$	3.12567	+	17.7265i	0.150558	+	0.853857i	−0.812177	+	0.583411i	$0.801718\pi$
$432$	−3.83022	−	3.21394i	−0.184282	−	0.154631i
$433$	−10.7246	+	8.99903i	−0.515392	+	0.432466i	−0.863022	−	0.505166i	$-0.831431\pi$
$433$	−10.7246	+	8.99903i	−0.515392	+	0.432466i	0.347630	+	0.937632i	$0.386987\pi$
$434$	−4.16756	+	23.6354i	−0.200049	+	1.13453i
$435$	18.7939	−	6.84040i	0.901096	−	0.327972i
$436$	15.0000			0.718370
$437$		0			0
$438$	−9.00000			−0.430037
$439$	18.7939	−	6.84040i	0.896982	−	0.326475i	0.147939	−	0.988996i	$-0.452736\pi$
$439$	18.7939	−	6.84040i	0.896982	−	0.326475i	0.749043	+	0.662522i	$0.230514\pi$
$440$	1.38919	−	7.87846i	0.0662268	−	0.375591i
$441$	−3.06418	+	2.57115i	−0.145913	+	0.122436i
$442$	−2.29813	−	1.92836i	−0.109311	−	0.0917229i
$443$	−4.51485	−	25.6050i	−0.214507	−	1.21653i	−0.881760	−	0.471699i	$-0.843641\pi$
$443$	−4.51485	−	25.6050i	−0.214507	−	1.21653i	0.667253	−	0.744832i	$-0.267470\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$		0			0
$446$	−13.1557	−	4.78828i	−0.622940	−	0.226732i
$447$		0			0
$448$	−1.50000	+	2.59808i	−0.0708683	+	0.122748i
$449$	5.00000	+	8.66025i	0.235965	+	0.408703i	0.959553	−	0.281529i	$-0.0908417\pi$
$449$	5.00000	+	8.66025i	0.235965	+	0.408703i	−0.723588	+	0.690232i	$0.757508\pi$
$450$	3.82026	+	21.6658i	0.180089	+	1.02133i
$451$	12.2567	+	10.2846i	0.577146	+	0.484283i
$452$	−10.7246	+	8.99903i	−0.504444	+	0.423279i
$453$	−0.347296	+	1.96962i	−0.0163174	+	0.0925406i
$454$	15.9748	−	5.81434i	0.749733	−	0.272881i
$455$	−12.0000			−0.562569
$456$		0			0
$457$	−7.00000			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$458$	−9.39693	+	3.42020i	−0.439090	+	0.159816i
$459$	−2.60472	+	14.7721i	−0.121578	+	0.689503i
$460$	3.06418	−	2.57115i	0.142868	−	0.119881i
$461$	−21.4492	−	17.9981i	−0.998991	−	0.838253i	−0.0121466	−	0.999926i	$-0.503866\pi$
$461$	−21.4492	−	17.9981i	−0.998991	−	0.838253i	−0.986844	+	0.161673i	$0.948311\pi$
$462$	−1.04189	−	5.90885i	−0.0484731	−	0.274904i
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	0.815802	−	0.578331i	$-0.196296\pi$
$463$	−2.00000	−	3.46410i	−0.0929479	−	0.160990i	−0.908750	+	0.417340i	$0.862962\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$	30.0702	+	10.9446i	1.39447	+	0.507546i
$466$	−5.63816	−	2.05212i	−0.261183	−	0.0950627i
$467$	1.00000	−	1.73205i	0.0462745	−	0.0801498i	−0.841960	−	0.539539i	$-0.818598\pi$
$467$	1.00000	−	1.73205i	0.0462745	−	0.0801498i	0.888235	+	0.459390i	$0.151932\pi$
$468$	1.00000	+	1.73205i	0.0462250	+	0.0800641i
$469$	−1.56283	−	8.86327i	−0.0721650	−	0.409268i
$470$	24.5134	+	20.5692i	1.13072	+	0.948787i
$471$	−1.53209	+	1.28558i	−0.0705949	+	0.0592362i
$472$	2.60472	−	14.7721i	0.119892	−	0.679942i
$473$	−7.51754	+	2.73616i	−0.345657	+	0.125809i
$474$	−10.0000			−0.459315
$475$		0			0
$476$	9.00000			0.412514
$477$	1.87939	−	0.684040i	0.0860511	−	0.0313201i
$478$	−2.60472	+	14.7721i	−0.119137	+	0.675661i
$479$	−15.3209	+	12.8558i	−0.700029	+	0.587394i	−0.921782	−	0.387709i	$-0.873267\pi$
$479$	−15.3209	+	12.8558i	−0.700029	+	0.587394i	0.221753	+	0.975103i	$0.428822\pi$
$480$	3.06418	+	2.57115i	0.139860	+	0.117356i
$481$	0.347296	+	1.96962i	0.0158354	+	0.0898067i
$482$	4.00000	+	6.92820i	0.182195	+	0.315571i
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$	6.57785	+	2.39414i	0.298993	+	0.108825i
$485$	7.51754	+	2.73616i	0.341354	+	0.124243i
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	−0.347296	−	1.96962i	−0.0157214	−	0.0891603i
$489$	−12.2567	−	10.2846i	−0.554268	−	0.465086i
$490$	6.12836	−	5.14230i	0.276851	−	0.232305i
$491$	−4.86215	+	27.5746i	−0.219426	+	1.24443i	0.653634	+	0.756811i	$0.273244\pi$
$491$	−4.86215	+	27.5746i	−0.219426	+	1.24443i	−0.873059	+	0.487614i	$0.837867\pi$
$492$	−7.51754	+	2.73616i	−0.338917	+	0.123356i
$493$	15.0000			0.675566
$494$		0			0
$495$	16.0000			0.719147
$496$	−7.51754	+	2.73616i	−0.337548	+	0.122857i
$497$	−1.04189	+	5.90885i	−0.0467351	+	0.265048i
$498$	4.59627	−	3.85673i	0.205964	−	0.172824i
$499$	30.6418	+	25.7115i	1.37171	+	1.15101i	0.972166	+	0.234293i	$0.0752775\pi$
$499$	30.6418	+	25.7115i	1.37171	+	1.15101i	0.399548	+	0.916712i	$0.369167\pi$
$500$	−4.16756	−	23.6354i	−0.186379	−	1.05701i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	1.00000	−	1.73205i	0.0446322	−	0.0773052i
$503$	−36.6480	−	13.3388i	−1.63405	−	0.594747i	−0.648069	−	0.761581i	$-0.724423\pi$
$503$	−36.6480	−	13.3388i	−1.63405	−	0.594747i	−0.985985	+	0.166834i	$0.946645\pi$
$504$	−5.63816	−	2.05212i	−0.251143	−	0.0914087i
$505$	4.00000	−	6.92820i	0.177998	−	0.308301i
$506$	−1.00000	−	1.73205i	−0.0444554	−	0.0769991i
$507$	−2.08378	−	11.8177i	−0.0925438	−	0.524842i
$508$	−13.7888	−	11.5702i	−0.611779	−	0.513344i
$509$	22.9813	−	19.2836i	1.01863	−	0.854732i	0.0291750	−	0.999574i	$-0.490712\pi$
$509$	22.9813	−	19.2836i	1.01863	−	0.854732i	0.989455	+	0.144843i	$0.0462676\pi$
$510$	2.08378	−	11.8177i	0.0922712	−	0.523296i
$511$	−25.3717	+	9.23454i	−1.12238	+	0.408512i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	8.00000			0.352865
$515$	22.5526	−	8.20848i	0.993787	−	0.361709i
$516$	0.694593	−	3.93923i	0.0305777	−	0.173415i
$517$	12.2567	−	10.2846i	0.539050	−	0.452316i
$518$	−4.59627	−	3.85673i	−0.201948	−	0.169455i
$519$	1.04189	+	5.90885i	0.0457339	+	0.259370i
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$	−9.39693	−	3.42020i	−0.411292	−	0.149698i
$523$	27.2511	+	9.91858i	1.19161	+	0.433709i	0.860287	−	0.509809i	$-0.170284\pi$
$523$	27.2511	+	9.91858i	1.19161	+	0.433709i	0.331319	+	0.943519i	$0.392506\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$	−16.5000	−	28.5788i	−0.720119	−	1.24728i
$526$	−4.16756	−	23.6354i	−0.181714	−	1.03055i
$527$	18.3851	+	15.4269i	0.800866	+	0.672006i
$528$	1.53209	−	1.28558i	0.0666756	−	0.0559475i
$529$	−3.82026	+	21.6658i	−0.166098	+	0.941990i
$530$	−3.75877	+	1.36808i	−0.163271	+	0.0594256i
$531$	30.0000			1.30189
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	−4.86215	+	27.5746i	−0.210209	+	1.19215i
$536$	2.29813	−	1.92836i	0.0992642	−	0.0832926i
$537$		0			0
$538$	5.20945	+	29.5442i	0.224595	+	1.27374i
$539$	−2.00000	−	3.46410i	−0.0861461	−	0.149209i
$540$	−10.0000	+	17.3205i	−0.430331	+	0.745356i
$541$	−1.87939	−	0.684040i	−0.0808011	−	0.0294092i	0.301303	−	0.953528i	$-0.402578\pi$
$541$	−1.87939	−	0.684040i	−0.0808011	−	0.0294092i	−0.382104	+	0.924119i	$0.624801\pi$
$542$	6.57785	+	2.39414i	0.282543	+	0.102837i
$543$	11.0000	−	19.0526i	0.472055	−	0.817624i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−10.4189	−	59.0885i	−0.446296	−	2.53107i
$546$	−2.29813	−	1.92836i	−0.0983510	−	0.0825263i
$547$	−21.4492	+	17.9981i	−0.917103	+	0.769541i	−0.973457	−	0.228870i	$-0.926497\pi$
$547$	−21.4492	+	17.9981i	−0.917103	+	0.769541i	0.0563536	+	0.998411i	$0.482053\pi$
$548$	−2.95202	+	16.7417i	−0.126104	+	0.715171i
$549$	3.75877	−	1.36808i	0.160420	−	0.0583883i
$550$	−22.0000			−0.938083
$551$		0			0
$552$	1.00000			0.0425628
$553$	−28.1908	+	10.2606i	−1.19879	+	0.436325i
$554$	−4.86215	+	27.5746i	−0.206573	+	1.17153i
$555$	−6.12836	+	5.14230i	−0.260134	+	0.218279i
$556$		0			0
$557$	4.86215	+	27.5746i	0.206016	+	1.16837i	0.895833	+	0.444391i	$0.146580\pi$
$557$	4.86215	+	27.5746i	0.206016	+	1.16837i	−0.689817	+	0.723983i	$0.742309\pi$
$558$	−8.00000	−	13.8564i	−0.338667	−	0.586588i
$559$	−2.00000	+	3.46410i	−0.0845910	+	0.146516i
$560$	11.2763	+	4.10424i	0.476511	+	0.173436i
$561$	−5.63816	−	2.05212i	−0.238043	−	0.0866406i
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$	1.38919	+	7.87846i	0.0584953	+	0.331743i
$565$	42.8985	+	35.9961i	1.80475	+	1.51437i
$566$	4.59627	−	3.85673i	0.193195	−	0.162110i
$567$	0.520945	−	2.95442i	0.0218776	−	0.124074i
$568$	−1.87939	+	0.684040i	−0.0788573	+	0.0287017i
$569$	−40.0000			−1.67689			−0.838444	−	0.544988i	$-0.816534\pi$
$569$	−40.0000			−1.67689			−0.838444	+	0.544988i	$0.816534\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$	−1.87939	+	0.684040i	−0.0785810	+	0.0286012i
$573$	1.21554	−	6.89365i	0.0507798	−	0.287987i
$574$	−18.3851	+	15.4269i	−0.767378	+	0.643906i
$575$	−8.42649	−	7.07066i	−0.351409	−	0.294867i
$576$	−0.347296	−	1.96962i	−0.0144707	−	0.0820673i
$577$	18.5000	+	32.0429i	0.770165	+	1.33397i	0.937472	+	0.348060i	$0.113160\pi$
$577$	18.5000	+	32.0429i	0.770165	+	1.33397i	−0.167307	+	0.985905i	$0.553507\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−5.63816	−	2.05212i	−0.234314	−	0.0852832i
$580$	18.7939	+	6.84040i	0.780372	+	0.284032i
$581$	9.00000	−	15.5885i	0.373383	−	0.646718i
$582$	1.00000	+	1.73205i	0.0414513	+	0.0717958i
$583$	0.347296	+	1.96962i	0.0143835	+	0.0815731i
$584$	−6.89440	−	5.78509i	−0.285292	−	0.239389i
$585$	6.12836	−	5.14230i	0.253376	−	0.212608i
$586$	1.56283	−	8.86327i	0.0645601	−	0.366138i
$587$	11.2763	−	4.10424i	0.465423	−	0.169400i	−0.0986548	−	0.995122i	$-0.531454\pi$
$587$	11.2763	−	4.10424i	0.465423	−	0.169400i	0.564078	+	0.825722i	$0.309232\pi$
$588$	2.00000			0.0824786
$589$		0			0
$590$	−60.0000			−2.47016
$591$	−7.51754	+	2.73616i	−0.309230	+	0.112551i
$592$	0.347296	−	1.96962i	0.0142738	−	0.0809507i
$593$	26.0455	−	21.8548i	1.06956	−	0.897468i	0.0745483	−	0.997217i	$-0.476248\pi$
$593$	26.0455	−	21.8548i	1.06956	−	0.897468i	0.995013	+	0.0997492i	$0.0318040\pi$
$594$	7.66044	+	6.42788i	0.314312	+	0.263739i
$595$	−6.25133	−	35.4531i	−0.256280	−	1.45343i
$596$		0			0
$597$	12.5000	−	21.6506i	0.511591	−	0.886102i
$598$	−0.939693	−	0.342020i	−0.0384269	−	0.0139862i
$599$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$599$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$600$	5.50000	−	9.52628i	0.224537	−	0.388909i
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	0.772838	−	0.634603i	$-0.218836\pi$
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	−0.936002	+	0.351996i	$0.885503\pi$
$602$	−2.08378	−	11.8177i	−0.0849285	−	0.481653i
$603$	4.59627	+	3.85673i	0.187174	+	0.157058i
$604$	−1.53209	+	1.28558i	−0.0623398	+	0.0523093i
$605$	4.86215	−	27.5746i	0.197674	−	1.12107i
$606$	1.87939	−	0.684040i	0.0763448	−	0.0277872i
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$		0			0
$609$	15.0000			0.607831
$610$	−7.51754	+	2.73616i	−0.304376	+	0.110784i
$611$	1.38919	−	7.87846i	0.0562004	−	0.318728i
$612$	−4.59627	+	3.85673i	−0.185793	+	0.155899i
$613$	26.0455	+	21.8548i	1.05197	+	0.882706i	0.993299	−	0.115571i	$-0.0368699\pi$
$613$	26.0455	+	21.8548i	1.05197	+	0.882706i	0.0586691	+	0.998277i	$0.481314\pi$
$614$	−2.08378	−	11.8177i	−0.0840944	−	0.476923i
$615$	16.0000	+	27.7128i	0.645182	+	1.11749i
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−16.9145	−	6.15636i	−0.680951	−	0.247846i	−0.0216951	−	0.999765i	$-0.506906\pi$
$617$	−16.9145	−	6.15636i	−0.680951	−	0.247846i	−0.659256	+	0.751919i	$0.729129\pi$
$618$	5.63816	+	2.05212i	0.226800	+	0.0825484i
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$	16.0000	+	27.7128i	0.642575	+	1.11297i
$621$	0.868241	+	4.92404i	0.0348413	+	0.197595i
$622$	−5.36231	−	4.49951i	−0.215009	−	0.180414i
$623$		0			0
$624$	0.173648	−	0.984808i	0.00695149	−	0.0394239i
$625$	−38.5274	+	14.0228i	−1.54110	+	0.560913i
$626$	−29.0000			−1.15907
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−5.63816	+	2.05212i	−0.224808	+	0.0818234i
$630$	−4.16756	+	23.6354i	−0.166039	+	0.941656i
$631$	24.5134	−	20.5692i	0.975864	−	0.818847i	−0.00759632	−	0.999971i	$-0.502418\pi$
$631$	24.5134	−	20.5692i	0.975864	−	0.818847i	0.983460	+	0.181124i	$0.0579736\pi$
$632$	−7.66044	−	6.42788i	−0.304716	−	0.255687i
$633$	−4.68850	−	26.5898i	−0.186351	−	1.05685i
$634$	13.5000	+	23.3827i	0.536153	+	0.928645i
$635$	−36.0000	+	62.3538i	−1.42862	+	2.47444i
$636$	−0.939693	−	0.342020i	−0.0372612	−	0.0135620i
$637$	−1.87939	−	0.684040i	−0.0744640	−	0.0271027i
$638$	5.00000	−	8.66025i	0.197952	−	0.342863i
$639$	−2.00000	−	3.46410i	−0.0791188	−	0.137038i
$640$	0.694593	+	3.93923i	0.0274562	+	0.155712i
$641$	−32.1739	−	26.9971i	−1.27079	−	1.06632i	−0.994444	−	0.105263i	$-0.966432\pi$
$641$	−32.1739	−	26.9971i	−1.27079	−	1.06632i	−0.276347	−	0.961058i	$-0.589124\pi$
$642$	−5.36231	+	4.49951i	−0.211634	+	0.177582i
$643$	−4.51485	+	25.6050i	−0.178048	+	1.00976i	0.756518	+	0.653973i	$0.226899\pi$
$643$	−4.51485	+	25.6050i	−0.178048	+	1.00976i	−0.934566	+	0.355789i	$0.884212\pi$
$644$	2.81908	−	1.02606i	0.111087	−	0.0404324i
$645$	−16.0000			−0.629999
$646$		0			0
$647$	23.0000			0.904223			0.452112	−	0.891961i	$-0.350671\pi$
$647$	23.0000			0.904223			0.452112	+	0.891961i	$0.350671\pi$
$648$	0.939693	−	0.342020i	0.0369146	−	0.0134358i
$649$	−5.20945	+	29.5442i	−0.204489	+	1.15971i
$650$	−8.42649	+	7.07066i	−0.330514	+	0.277334i
$651$	18.3851	+	15.4269i	0.720568	+	0.604628i
$652$	−2.77837	−	15.7569i	−0.108809	−	0.617089i
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$	7.50000	−	12.9904i	0.293273	−	0.507964i
$655$	45.1052	+	16.4170i	1.76241	+	0.641464i
$656$	−7.51754	−	2.73616i	−0.293511	−	0.106829i
$657$	9.00000	−	15.5885i	0.351123	−	0.608164i
$658$	12.0000	+	20.7846i	0.467809	+	0.810268i
$659$	−0.868241	−	4.92404i	−0.0338219	−	0.191813i	0.963216	−	0.268729i	$-0.0866037\pi$
$659$	−0.868241	−	4.92404i	−0.0338219	−	0.191813i	−0.997038	+	0.0769161i	$0.975493\pi$
$660$	−6.12836	−	5.14230i	−0.238546	−	0.200164i
$661$	17.6190	−	14.7841i	0.685301	−	0.575035i	−0.232249	−	0.972656i	$-0.574609\pi$
$661$	17.6190	−	14.7841i	0.685301	−	0.575035i	0.917550	+	0.397621i	$0.130164\pi$
$662$	2.95202	−	16.7417i	0.114733	−	0.650686i
$663$	−2.81908	+	1.02606i	−0.109484	+	0.0398489i
$664$	6.00000			0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	4.69846	−	1.71010i	0.181925	−	0.0662154i
$668$	2.08378	−	11.8177i	0.0806238	−	0.457240i
$669$	−10.7246	+	8.99903i	−0.414638	+	0.347922i
$670$	−9.19253	−	7.71345i	−0.355139	−	0.297997i
$671$	0.694593	+	3.93923i	0.0268145	+	0.152072i
$672$	1.50000	+	2.59808i	0.0578638	+	0.100223i
$673$	22.0000	−	38.1051i	0.848038	−	1.46884i	−0.0349191	−	0.999390i	$-0.511117\pi$
$673$	22.0000	−	38.1051i	0.848038	−	1.46884i	0.882957	−	0.469454i	$-0.155549\pi$
$674$	30.0702	+	10.9446i	1.15826	+	0.421572i
$675$	51.6831	+	18.8111i	1.98928	+	0.724040i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	6.50000	+	11.2583i	0.249815	+	0.432693i	0.963474	−	0.267800i	$-0.0862968\pi$
$677$	6.50000	+	11.2583i	0.249815	+	0.432693i	−0.713659	+	0.700493i	$0.752963\pi$
$678$	2.43107	+	13.7873i	0.0933649	+	0.529498i
$679$	4.59627	+	3.85673i	0.176389	+	0.148008i
$680$	9.19253	−	7.71345i	0.352518	−	0.295797i
$681$	2.95202	−	16.7417i	0.113122	−	0.641545i
$682$	15.0351	−	5.47232i	0.575723	−	0.209546i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	68.0000			2.59815
$686$	−14.0954	+	5.13030i	−0.538164	+	0.195876i
$687$	−1.73648	+	9.84808i	−0.0662509	+	0.375728i
$688$	3.06418	−	2.57115i	0.116821	−	0.0980242i
$689$	0.766044	+	0.642788i	0.0291840	+	0.0244883i
$690$	−0.694593	−	3.93923i	−0.0264427	−	0.149964i
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	−0.920348	−	0.391102i	$-0.872094\pi$
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	0.121470	−	0.992595i	$-0.461239\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$	11.2763	+	4.10424i	0.428352	+	0.155907i
$694$	−1.87939	−	0.684040i	−0.0713405	−	0.0259658i
$695$		0			0
$696$	2.50000	+	4.33013i	0.0947623	+	0.164133i
$697$	4.16756	+	23.6354i	0.157857	+	0.895254i
$698$	−7.66044	−	6.42788i	−0.289952	−	0.243299i
$699$	−4.59627	+	3.85673i	−0.173847	+	0.145875i
$700$	5.73039	−	32.4987i	0.216588	−	1.22833i
$701$	26.3114	−	9.57656i	0.993768	−	0.361702i	0.206590	−	0.978428i	$-0.433764\pi$
$701$	26.3114	−	9.57656i	0.993768	−	0.361702i	0.787178	+	0.616726i	$0.211541\pi$
$702$	5.00000			0.188713
$703$		0			0
$704$	2.00000			0.0753778
$705$	30.0702	−	10.9446i	1.13251	−	0.412199i
$706$	−1.56283	+	8.86327i	−0.0588180	+	0.333574i
$707$	4.59627	−	3.85673i	0.172860	−	0.145047i
$708$	−11.4907	−	9.64181i	−0.431846	−	0.362362i
$709$	−5.20945	−	29.5442i	−0.195645	−	1.10956i	−0.911498	−	0.411306i	$-0.865073\pi$
$709$	−5.20945	−	29.5442i	−0.195645	−	1.10956i	0.715853	−	0.698251i	$-0.246038\pi$
$710$	4.00000	+	6.92820i	0.150117	+	0.260011i
$711$	10.0000	−	17.3205i	0.375029	−	0.649570i
$712$		0			0
$713$	7.51754	+	2.73616i	0.281534	+	0.102470i
$714$	4.50000	−	7.79423i	0.168408	−	0.291692i
$715$	4.00000	+	6.92820i	0.149592	+	0.259100i
$716$		0			0
$717$	11.4907	+	9.64181i	0.429127	+	0.360080i
$718$	11.4907	−	9.64181i	0.428828	−	0.359829i
$719$	−0.868241	+	4.92404i	−0.0323799	+	0.183636i	−0.996708	−	0.0810740i	$-0.974165\pi$
$719$	−0.868241	+	4.92404i	−0.0323799	+	0.183636i	0.964328	+	0.264710i	$0.0852761\pi$
$720$	−7.51754	+	2.73616i	−0.280162	+	0.101971i
$721$	18.0000			0.670355
$722$		0			0
$723$	8.00000			0.297523
$724$	20.6732	−	7.52444i	0.768315	−	0.279644i
$725$	9.55065	−	54.1644i	0.354702	−	2.01162i
$726$	5.36231	−	4.49951i	0.199014	−	0.166993i
$727$	−13.0228	−	10.9274i	−0.482987	−	0.405274i	0.368518	−	0.929621i	$-0.379865\pi$
$727$	−13.0228	−	10.9274i	−0.482987	−	0.405274i	−0.851505	+	0.524346i	$0.824310\pi$
$728$	−0.520945	−	2.95442i	−0.0193075	−	0.109498i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$	−18.0000	+	31.1769i	−0.666210	+	1.15391i
$731$	−11.2763	−	4.10424i	−0.417069	−	0.151801i
$732$	−1.87939	−	0.684040i	−0.0694641	−	0.0252829i
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	−0.314482	−	0.949263i	$-0.601831\pi$
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	0.979327	−	0.202282i	$-0.0648358\pi$
$734$	14.0000	+	24.2487i	0.516749	+	0.895036i
$735$	−1.38919	−	7.87846i	−0.0512409	−	0.290601i
$736$	0.766044	+	0.642788i	0.0282368	+	0.0236935i
$737$	−4.59627	+	3.85673i	−0.169306	+	0.142064i
$738$	2.77837	−	15.7569i	0.102273	−	0.580020i
$739$	37.5877	−	13.6808i	1.38269	−	0.503257i	0.459695	−	0.888077i	$-0.347959\pi$
$739$	37.5877	−	13.6808i	1.38269	−	0.503257i	0.922991	+	0.384820i	$0.125737\pi$
$740$	−8.00000			−0.294086
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−15.0351	+	5.47232i	−0.551584	+	0.200760i	−0.602750	−	0.797930i	$-0.705928\pi$
$743$	−15.0351	+	5.47232i	−0.551584	+	0.200760i	0.0511663	+	0.998690i	$0.483706\pi$
$744$	−1.38919	+	7.87846i	−0.0509300	+	0.288838i
$745$		0			0
$746$	22.2153	+	18.6408i	0.813360	+	0.682490i
$747$	2.08378	+	11.8177i	0.0762415	+	0.432387i
$748$	−3.00000	−	5.19615i	−0.109691	−	0.189990i
$749$	−10.5000	+	18.1865i	−0.383662	+	0.664521i
$750$	−22.5526	−	8.20848i	−0.823505	−	0.299731i
$751$	30.0702	+	10.9446i	1.09728	+	0.399376i	0.826311	−	0.563214i	$-0.190435\pi$
$751$	30.0702	+	10.9446i	1.09728	+	0.399376i	0.270965	+	0.962589i	$0.412657\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$	−1.00000	−	1.73205i	−0.0364420	−	0.0631194i
$754$	−0.868241	−	4.92404i	−0.0316195	−	0.179323i
$755$	6.12836	+	5.14230i	0.223034	+	0.187147i
$756$	−11.4907	+	9.64181i	−0.417912	+	0.350669i
$757$	−0.347296	+	1.96962i	−0.0126227	+	0.0715869i	−0.990468	−	0.137740i	$-0.956016\pi$
$757$	−0.347296	+	1.96962i	−0.0126227	+	0.0715869i	0.977846	+	0.209327i	$0.0671273\pi$
$758$	−14.0954	+	5.13030i	−0.511968	+	0.186341i
$759$	−2.00000			−0.0725954
$760$		0			0
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$	−16.9145	+	6.15636i	−0.612746	+	0.223021i
$763$	7.81417	−	44.3163i	0.282892	−	1.60436i
$764$	5.36231	−	4.49951i	0.194002	−	0.162787i
$765$	18.3851	+	15.4269i	0.664713	+	0.557761i
$766$	−4.51485	−	25.6050i	−0.163128	−	0.925146i
$767$	7.50000	+	12.9904i	0.270809	+	0.469055i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	32.8892	+	11.9707i	1.18602	+	0.431675i	0.858323	−	0.513110i	$-0.171507\pi$
$769$	32.8892	+	11.9707i	1.18602	+	0.431675i	0.327693	+	0.944784i	$0.393729\pi$
$770$	−22.5526	−	8.20848i	−0.812740	−	0.295813i
$771$	4.00000	−	6.92820i	0.144056	−	0.249513i
$772$	−3.00000	−	5.19615i	−0.107972	−	0.187014i
$773$	−1.56283	−	8.86327i	−0.0562112	−	0.318790i	0.943717	−	0.330753i	$-0.107303\pi$
$773$	−1.56283	−	8.86327i	−0.0562112	−	0.318790i	−0.999928	+	0.0119638i	$0.996192\pi$
$774$	6.12836	+	5.14230i	0.220279	+	0.184836i
$775$	67.4119	−	56.5653i	2.42151	−	2.03189i
$776$	−0.347296	+	1.96962i	−0.0124672	+	0.0707051i
$777$	−5.63816	+	2.05212i	−0.202268	+	0.0736194i
$778$	30.0000			1.07555
$779$		0			0
$780$	−4.00000			−0.143223
$781$	3.75877	−	1.36808i	0.134499	−	0.0489538i
$782$	0.520945	−	2.95442i	0.0186289	−	0.105650i
$783$	−19.1511	+	16.0697i	−0.684405	+	0.574284i
$784$	1.53209	+	1.28558i	0.0547175	+	0.0459134i
$785$	1.38919	+	7.87846i	0.0495822	+	0.281194i
$786$	6.00000	+	10.3923i	0.214013	+	0.370681i
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	−0.976812	−	0.214097i	$-0.931319\pi$
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	0.673820	+	0.738896i	$0.264652\pi$
$788$	−7.51754	−	2.73616i	−0.267801	−	0.0974717i
$789$	−22.5526	−	8.20848i	−0.802895	−	0.292230i
$790$	−20.0000	+	34.6410i	−0.711568	+	1.23247i
$791$	21.0000	+	36.3731i	0.746674	+	1.29328i
$792$	0.694593	+	3.93923i	0.0246813	+	0.139974i
$793$	1.53209	+	1.28558i	0.0544061	+	0.0456521i
$794$	−6.12836	+	5.14230i	−0.217487	+	0.182493i
$795$	−0.694593	+	3.93923i	−0.0246347	+	0.139710i
$796$	23.4923	−	8.55050i	0.832663	−	0.303065i
$797$	−3.00000			−0.106265			−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000			−0.106265			−0.0531327	+	0.998587i	$0.516921\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	10.3366	−	3.76222i	0.365455	−	0.133015i
$801$		0			0
$802$	−6.12836	+	5.14230i	−0.216400	+	0.181581i
$803$	13.7888	+	11.5702i	0.486596	+	0.408303i
$804$	−0.520945	−	2.95442i	−0.0183723	−	0.104194i
$805$	−6.00000	−	10.3923i	−0.211472	−	0.366281i
$806$	4.00000	−	6.92820i	0.140894	−	0.244036i
$807$	28.1908	+	10.2606i	0.992362	+	0.361190i
$808$	1.87939	+	0.684040i	0.0661165	+	0.0240645i
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	−0.703533	−	0.710663i	$-0.748395\pi$
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	0.967219	+	0.253946i	$0.0817284\pi$
$810$	−2.00000	−	3.46410i	−0.0702728	−	0.121716i
$811$	0.520945	+	2.95442i	0.0182928	+	0.103744i	0.992587	−	0.121535i	$-0.0387817\pi$
$811$	0.520945	+	2.95442i	0.0182928	+	0.103744i	−0.974294	+	0.225279i	$0.927671\pi$
$812$	11.4907	+	9.64181i	0.403243	+	0.338361i
$813$	5.36231	−	4.49951i	0.188064	−	0.157805i
$814$	−0.694593	+	3.93923i	−0.0243455	+	0.138070i
$815$	−60.1403	+	21.8893i	−2.10662	+	0.766748i
$816$	3.00000			0.105021
$817$		0			0
$818$	−20.0000			−0.699284
$819$	5.63816	−	2.05212i	0.197013	−	0.0717069i
$820$	−5.55674	+	31.5138i	−0.194050	+	1.10051i
$821$	9.19253	−	7.71345i	0.320822	−	0.269201i	−0.468126	−	0.883662i	$-0.655071\pi$
$821$	9.19253	−	7.71345i	0.320822	−	0.269201i	0.788948	+	0.614460i	$0.210626\pi$
$822$	13.0228	+	10.9274i	0.454221	+	0.381136i
$823$	5.03580	+	28.5594i	0.175537	+	0.995519i	0.937522	+	0.347925i	$0.113114\pi$
$823$	5.03580	+	28.5594i	0.175537	+	0.995519i	−0.761986	+	0.647594i	$0.775775\pi$
$824$	3.00000	+	5.19615i	0.104510	+	0.181017i
$825$	−11.0000	+	19.0526i	−0.382971	+	0.663325i
$826$	−42.2862	−	15.3909i	−1.47132	−	0.535518i
$827$	21.6129	+	7.86646i	0.751555	+	0.273544i	0.689260	−	0.724514i	$-0.257936\pi$
$827$	21.6129	+	7.86646i	0.751555	+	0.273544i	0.0622952	+	0.998058i	$0.480158\pi$
$828$	−1.00000	+	1.73205i	−0.0347524	+	0.0601929i
$829$	−7.50000	−	12.9904i	−0.260486	−	0.451175i	0.705885	−	0.708326i	$-0.250549\pi$
$829$	−7.50000	−	12.9904i	−0.260486	−	0.451175i	−0.966371	+	0.257152i	$0.917216\pi$
$830$	−4.16756	−	23.6354i	−0.144658	−	0.820396i
$831$	21.4492	+	17.9981i	0.744066	+	0.624346i
$832$	0.766044	−	0.642788i	0.0265578	−	0.0222847i
$833$	1.04189	−	5.90885i	0.0360993	−	0.204729i
$834$		0			0
$835$	−48.0000			−1.66111
$836$		0			0
$837$	−40.0000			−1.38260
$838$		0			0
$839$	−3.47296	+	19.6962i	−0.119900	+	0.679987i	0.864307	+	0.502965i	$0.167757\pi$
$839$	−3.47296	+	19.6962i	−0.119900	+	0.679987i	−0.984207	+	0.177022i	$0.943354\pi$
$840$	9.19253	−	7.71345i	0.317173	−	0.266139i
$841$	−3.06418	−	2.57115i	−0.105661	−	0.0886604i
$842$	−2.25743	−	12.8025i	−0.0777960	−	0.441203i
$843$	−4.00000	−	6.92820i	−0.137767	−	0.238620i
$844$	13.5000	−	23.3827i	0.464689	−	0.804865i
$845$	−45.1052	−	16.4170i	−1.55167	−	0.564761i
$846$	−15.0351	−	5.47232i	−0.516917	−	0.188142i
$847$	10.5000	−	18.1865i	0.360784	−	0.624897i
$848$	−0.500000	−	0.866025i	−0.0171701	−	0.0297394i
$849$	−1.04189	−	5.90885i	−0.0357575	−	0.202791i
$850$	−25.2795	−	21.2120i	−0.867079	−	0.727565i
$851$	−1.53209	+	1.28558i	−0.0525193	+	0.0440690i
$852$	−0.347296	+	1.96962i	−0.0118982	+	0.0674779i
$853$	5.63816	−	2.05212i	0.193047	−	0.0702633i	−0.243688	−	0.969854i	$-0.578357\pi$
$853$	5.63816	−	2.05212i	0.193047	−	0.0702633i	0.436734	+	0.899590i	$0.356135\pi$
$854$	−6.00000			−0.205316
$855$		0			0
$856$	−7.00000			−0.239255
$857$	−11.2763	+	4.10424i	−0.385191	+	0.140198i	−0.527355	−	0.849645i	$-0.676816\pi$
$857$	−11.2763	+	4.10424i	−0.385191	+	0.140198i	0.142164	+	0.989843i	$0.454594\pi$
$858$	−0.347296	+	1.96962i	−0.0118565	+	0.0672416i
$859$	−38.3022	+	32.1394i	−1.30685	+	1.09658i	−0.317938	+	0.948111i	$0.602990\pi$
$859$	−38.3022	+	32.1394i	−1.30685	+	1.09658i	−0.988917	+	0.148470i	$0.952565\pi$
$860$	−12.2567	−	10.2846i	−0.417950	−	0.350702i
$861$	4.16756	+	23.6354i	0.142030	+	0.805492i
$862$	9.00000	+	15.5885i	0.306541	+	0.530945i
$863$	27.0000	−	46.7654i	0.919091	−	1.59191i	0.118291	−	0.992979i	$-0.462258\pi$
$863$	27.0000	−	46.7654i	0.919091	−	1.59191i	0.800799	−	0.598933i	$-0.204408\pi$
$864$	−4.69846	−	1.71010i	−0.159845	−	0.0581788i
$865$	22.5526	+	8.20848i	0.766812	+	0.279097i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$	4.16756	+	23.6354i	0.141456	+	0.802237i
$869$	15.3209	+	12.8558i	0.519726	+	0.436102i
$870$	15.3209	−	12.8558i	0.519427	−	0.435851i
$871$	−0.520945	+	2.95442i	−0.0176515	+	0.100107i
$872$	14.0954	−	5.13030i	0.477330	−	0.173734i
$873$	−4.00000			−0.135379
$874$		0			0
$875$	−72.0000			−2.43404
$876$	−8.45723	+	3.07818i	−0.285743	+	0.104002i
$877$	−2.25743	+	12.8025i	−0.0762279	+	0.432310i	0.922679	+	0.385569i	$0.125995\pi$
$877$	−2.25743	+	12.8025i	−0.0762279	+	0.432310i	−0.998907	+	0.0467411i	$0.985116\pi$
$878$	15.3209	−	12.8558i	0.517055	−	0.433861i
$879$	−6.89440	−	5.78509i	−0.232542	−	0.195126i
$880$	−1.38919	−	7.87846i	−0.0468294	−	0.265583i
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	0.976863	−	0.213866i	$-0.0686057\pi$
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	−0.673645	+	0.739055i	$0.735272\pi$
$882$	−2.00000	+	3.46410i	−0.0673435	+	0.116642i
$883$	−31.9495	−	11.6287i	−1.07519	−	0.391336i	−0.257073	−	0.966392i	$-0.582758\pi$
$883$	−31.9495	−	11.6287i	−1.07519	−	0.391336i	−0.818114	+	0.575055i	$0.804980\pi$
$884$	−2.81908	−	1.02606i	−0.0948158	−	0.0345101i
$885$	−30.0000	+	51.9615i	−1.00844	+	1.74667i
$886$	−13.0000	−	22.5167i	−0.436744	−	0.756462i
$887$	0.347296	+	1.96962i	0.0116611	+	0.0661332i	0.990083	−	0.140484i	$-0.0448657\pi$
$887$	0.347296	+	1.96962i	0.0116611	+	0.0661332i	−0.978422	+	0.206617i	$0.933755\pi$
$888$	−1.53209	−	1.28558i	−0.0514135	−	0.0431411i
$889$	−41.3664	+	34.7105i	−1.38738	+	1.16415i
$890$		0			0
$891$	−1.87939	+	0.684040i	−0.0629618	+	0.0229162i
$892$	−14.0000			−0.468755
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.520945	+	2.95442i	−0.0174035	+	0.0987004i
$897$	−0.766044	+	0.642788i	−0.0255775	+	0.0214621i
$898$	7.66044	+	6.42788i	0.255632	+	0.214501i
$899$	6.94593	+	39.3923i	0.231660	+	1.31381i
$900$	11.0000	+	19.0526i	0.366667	+	0.635085i
$901$	−1.50000	+	2.59808i	−0.0499722	+	0.0865545i
$902$	15.0351	+	5.47232i	0.500613	+	0.182208i
$903$	−11.2763	−	4.10424i	−0.375252	−	0.136581i
$904$	−7.00000	+	12.1244i	−0.232817	+	0.403250i
$905$	−44.0000	−	76.2102i	−1.46261	−	2.53331i
$906$	0.347296	+	1.96962i	0.0115381	+	0.0654361i
$907$	−40.6004	−	34.0677i	−1.34811	−	1.13120i	−0.979461	−	0.201633i	$-0.935375\pi$
$907$	−40.6004	−	34.0677i	−1.34811	−	1.13120i	−0.368652	−	0.929568i	$-0.620180\pi$
$908$	13.0228	−	10.9274i	0.432175	−	0.362638i
$909$	−0.694593	+	3.93923i	−0.0230382	+	0.130656i
$910$	−11.2763	+	4.10424i	−0.373806	+	0.136054i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$	−6.57785	+	2.39414i	−0.217576	+	0.0791911i
$915$	−1.38919	+	7.87846i	−0.0459251	+	0.260454i
$916$	−7.66044	+	6.42788i	−0.253108	+	0.212383i
$917$	27.5776	+	23.1404i	0.910693	+	0.764162i
$918$	2.60472	+	14.7721i	0.0859687	+	0.487552i
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	0.821842	−	0.569716i	$-0.192947\pi$
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	−0.904309	+	0.426878i	$0.859613\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	−11.2763	−	4.10424i	−0.371567	−	0.135239i
$922$	−26.3114	−	9.57656i	−0.866520	−	0.315387i
$923$	1.00000	−	1.73205i	0.0329154	−	0.0570111i
$924$	−3.00000	−	5.19615i	−0.0986928	−	0.170941i
$925$	3.82026	+	21.6658i	0.125609	+	0.712366i
$926$	−3.06418	−	2.57115i	−0.100695	−	0.0844932i
$927$	−9.19253	+	7.71345i	−0.301922	+	0.253343i
$928$	−0.868241	+	4.92404i	−0.0285014	+	0.161639i
$929$	51.6831	−	18.8111i	1.69567	−	0.617172i	0.700347	−	0.713803i	$-0.253029\pi$
$929$	51.6831	−	18.8111i	1.69567	−	0.617172i	0.995320	+	0.0966302i	$0.0308064\pi$
$930$	32.0000			1.04932
$931$		0			0
$932$	−6.00000			−0.196537
$933$	−6.57785	+	2.39414i	−0.215349	+	0.0783807i
$934$	0.347296	−	1.96962i	0.0113639	−	0.0644478i
$935$	−18.3851	+	15.4269i	−0.601256	+	0.504514i
$936$	1.53209	+	1.28558i	0.0500779	+	0.0420203i
$937$	−1.21554	−	6.89365i	−0.0397099	−	0.225206i	0.958494	−	0.285112i	$-0.0920309\pi$
$937$	−1.21554	−	6.89365i	−0.0397099	−	0.225206i	−0.998204	+	0.0599064i	$0.980920\pi$
$938$	−4.50000	−	7.79423i	−0.146930	−	0.254491i
$939$	−14.5000	+	25.1147i	−0.473190	+	0.819588i
$940$	30.0702	+	10.9446i	0.980781	+	0.356975i
$941$	6.57785	+	2.39414i	0.214432	+	0.0780468i	0.447002	−	0.894533i	$-0.352492\pi$
$941$	6.57785	+	2.39414i	0.214432	+	0.0780468i	−0.232571	+	0.972579i	$0.574714\pi$
$942$	−1.00000	+	1.73205i	−0.0325818	+	0.0564333i
$943$	4.00000	+	6.92820i	0.130258	+	0.225613i
$944$	−2.60472	−	14.7721i	−0.0847765	−	0.480791i
$945$	45.9627	+	38.5673i	1.49517	+	1.25459i
$946$	−6.12836	+	5.14230i	−0.199250	+	0.167191i
$947$	−2.08378	+	11.8177i	−0.0677137	+	0.384023i	0.932051	+	0.362327i	$0.118018\pi$
$947$	−2.08378	+	11.8177i	−0.0677137	+	0.384023i	−0.999765	+	0.0216961i	$0.993093\pi$
$948$	−9.39693	+	3.42020i	−0.305198	+	0.111083i
$949$	9.00000			0.292152
$950$		0			0
$951$	27.0000			0.875535
$952$	8.45723	−	3.07818i	0.274101	−	0.0997644i
$953$	7.98782	−	45.3012i	0.258751	−	1.46745i	−0.527507	−	0.849550i	$-0.676873\pi$
$953$	7.98782	−	45.3012i	0.258751	−	1.46745i	0.786258	−	0.617898i	$-0.212016\pi$
$954$	1.53209	−	1.28558i	0.0496032	−	0.0416220i
$955$	−21.4492	−	17.9981i	−0.694081	−	0.582403i
$956$	2.60472	+	14.7721i	0.0842428	+	0.477764i
$957$	−5.00000	−	8.66025i	−0.161627	−	0.279946i
$958$	−10.0000	+	17.3205i	−0.323085	+	0.559600i
$959$	47.9243	+	17.4430i	1.54756	+	0.563265i
$960$	3.75877	+	1.36808i	0.121314	+	0.0441546i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	1.00000	+	1.73205i	0.0322413	+	0.0558436i
$963$	−2.43107	−	13.7873i	−0.0783403	−	0.444290i
$964$	6.12836	+	5.14230i	0.197381	+	0.165622i
$965$	−18.3851	+	15.4269i	−0.591836	+	0.496610i
$966$	0.520945	−	2.95442i	0.0167611	−	0.0950570i
$967$	−45.1052	+	16.4170i	−1.45049	+	0.527934i	−0.942727	−	0.333565i	$-0.891748\pi$
$967$	−45.1052	+	16.4170i	−1.45049	+	0.527934i	−0.507760	+	0.861499i	$0.669526\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	8.00000			0.256865
$971$	−26.3114	+	9.57656i	−0.844373	+	0.307327i	−0.727744	−	0.685849i	$-0.759431\pi$
$971$	−26.3114	+	9.57656i	−0.844373	+	0.307327i	−0.116629	+	0.993176i	$0.537209\pi$
$972$	2.77837	−	15.7569i	0.0891163	−	0.505404i
$973$		0			0
$974$	−1.53209	−	1.28558i	−0.0490913	−	0.0411925i
$975$	1.91013	+	10.8329i	0.0611731	+	0.346930i
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	4.00000	−	6.92820i	0.127971	−	0.221653i	−0.794919	−	0.606715i	$-0.792487\pi$
$977$	4.00000	−	6.92820i	0.127971	−	0.221653i	0.922890	+	0.385063i	$0.125820\pi$
$978$	−15.0351	−	5.47232i	−0.480769	−	0.174986i
$979$		0			0
$980$	4.00000	−	6.92820i	0.127775	−	0.221313i
$981$	15.0000	+	25.9808i	0.478913	+	0.829502i
$982$	4.86215	+	27.5746i	0.155157	+	0.879941i
$983$	4.59627	+	3.85673i	0.146598	+	0.123010i	0.713137	−	0.701024i	$-0.247274\pi$
$983$	4.59627	+	3.85673i	0.146598	+	0.123010i	−0.566539	+	0.824035i	$0.691718\pi$
$984$	−6.12836	+	5.14230i	−0.195365	+	0.163931i
$985$	−5.55674	+	31.5138i	−0.177053	+	1.00411i
$986$	14.0954	−	5.13030i	0.448889	−	0.163382i
$987$	24.0000			0.763928
$988$		0			0
$989$	−4.00000			−0.127193
$990$	15.0351	−	5.47232i	0.477846	−	0.173922i
$991$	1.38919	−	7.87846i	0.0441289	−	0.250268i	−0.954761	−	0.297374i	$-0.903889\pi$
$991$	1.38919	−	7.87846i	0.0441289	−	0.250268i	0.998890	+	0.0471069i	$0.0150001\pi$
$992$	−6.12836	+	5.14230i	−0.194575	+	0.163268i
$993$	−13.0228	−	10.9274i	−0.413265	−	0.346770i
$994$	1.04189	+	5.90885i	0.0330467	+	0.187417i
$995$	−50.0000	−	86.6025i	−1.58511	−	2.74549i
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	−26.3114	−	9.57656i	−0.833290	−	0.303293i	−0.110082	−	0.993923i	$-0.535111\pi$
$997$	−26.3114	−	9.57656i	−0.833290	−	0.303293i	−0.723209	+	0.690630i	$0.757333\pi$
$998$	37.5877	+	13.6808i	1.18982	+	0.433058i
$999$	5.00000	−	8.66025i	0.158193	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.d.423.1		6
19.2	odd	18		38.2.a.b.1.1	✓	1
19.3	odd	18		722.2.c.d.653.1		2
19.4	even	9	inner	722.2.e.d.99.1		6
19.5	even	9		722.2.c.f.429.1		2
19.6	even	9	inner	722.2.e.d.389.1		6
19.7	even	3	inner	722.2.e.d.245.1		6
19.8	odd	6		722.2.e.c.415.1		6
19.9	even	9	inner	722.2.e.d.595.1		6
19.10	odd	18		722.2.e.c.595.1		6
19.11	even	3	inner	722.2.e.d.415.1		6
19.12	odd	6		722.2.e.c.245.1		6
19.13	odd	18		722.2.e.c.389.1		6
19.14	odd	18		722.2.c.d.429.1		2
19.15	odd	18		722.2.e.c.99.1		6
19.16	even	9		722.2.c.f.653.1		2
19.17	even	9		722.2.a.b.1.1		1
19.18	odd	2		722.2.e.c.423.1		6
57.2	even	18		342.2.a.d.1.1		1
57.17	odd	18		6498.2.a.y.1.1		1
76.55	odd	18		5776.2.a.d.1.1		1
76.59	even	18		304.2.a.d.1.1		1
95.2	even	36		950.2.b.c.799.2		2
95.59	odd	18		950.2.a.b.1.1		1
95.78	even	36		950.2.b.c.799.1		2
133.97	even	18		1862.2.a.f.1.1		1
152.21	odd	18		1216.2.a.n.1.1		1
152.59	even	18		1216.2.a.g.1.1		1
209.21	even	18		4598.2.a.a.1.1		1
228.59	odd	18		2736.2.a.w.1.1		1
247.116	odd	18		6422.2.a.b.1.1		1
285.59	even	18		8550.2.a.u.1.1		1
380.59	even	18		7600.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.a.b.1.1	✓	1	19.2	odd	18
304.2.a.d.1.1		1	76.59	even	18
342.2.a.d.1.1		1	57.2	even	18
722.2.a.b.1.1		1	19.17	even	9
722.2.c.d.429.1		2	19.14	odd	18
722.2.c.d.653.1		2	19.3	odd	18
722.2.c.f.429.1		2	19.5	even	9
722.2.c.f.653.1		2	19.16	even	9
722.2.e.c.99.1		6	19.15	odd	18
722.2.e.c.245.1		6	19.12	odd	6
722.2.e.c.389.1		6	19.13	odd	18
722.2.e.c.415.1		6	19.8	odd	6
722.2.e.c.423.1		6	19.18	odd	2
722.2.e.c.595.1		6	19.10	odd	18
722.2.e.d.99.1		6	19.4	even	9	inner
722.2.e.d.245.1		6	19.7	even	3	inner
722.2.e.d.389.1		6	19.6	even	9	inner
722.2.e.d.415.1		6	19.11	even	3	inner
722.2.e.d.423.1		6	1.1	even	1	trivial
722.2.e.d.595.1		6	19.9	even	9	inner
950.2.a.b.1.1		1	95.59	odd	18
950.2.b.c.799.1		2	95.78	even	36
950.2.b.c.799.2		2	95.2	even	36
1216.2.a.g.1.1		1	152.59	even	18
1216.2.a.n.1.1		1	152.21	odd	18
1862.2.a.f.1.1		1	133.97	even	18
2736.2.a.w.1.1		1	228.59	odd	18
4598.2.a.a.1.1		1	209.21	even	18
5776.2.a.d.1.1		1	76.55	odd	18
6422.2.a.b.1.1		1	247.116	odd	18
6498.2.a.y.1.1		1	57.17	odd	18
7600.2.a.h.1.1		1	380.59	even	18
8550.2.a.u.1.1		1	285.59	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.06418 - 2.57115i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.06418 - 2.57115i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.87939 + 0.684040i) q^{9} +(-3.75877 - 1.36808i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.173648 + 0.984808i) q^{13} +(-2.29813 - 1.92836i) q^{14} +(-3.06418 + 2.57115i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.81908 + 1.02606i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(-2.81908 + 1.02606i) q^{21} +(-0.347296 + 1.96962i) q^{22} +(-0.766044 + 0.642788i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(1.91013 + 10.8329i) q^{25} +(0.500000 + 0.866025i) q^{26} +(2.50000 - 4.33013i) q^{27} +(-2.81908 - 1.02606i) q^{28} +(-4.69846 - 1.71010i) q^{29} +(-2.00000 + 3.46410i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.53209 + 1.28558i) q^{33} +(-2.29813 + 1.92836i) q^{34} +(-2.08378 + 11.8177i) q^{35} +(1.87939 - 0.684040i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(-3.75877 + 1.36808i) q^{40} +(1.38919 - 7.87846i) q^{41} +(-2.29813 + 1.92836i) q^{42} +(3.06418 + 2.57115i) q^{43} +(0.347296 + 1.96962i) q^{44} +(-4.00000 - 6.92820i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-7.51754 - 2.73616i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(5.50000 + 9.52628i) q^{50} +(0.520945 + 2.95442i) q^{51} +(0.766044 + 0.642788i) q^{52} +(0.766044 - 0.642788i) q^{53} +(0.868241 - 4.92404i) q^{54} +(7.51754 - 2.73616i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(14.0954 - 5.13030i) q^{59} +(-0.694593 + 3.93923i) q^{60} +(1.53209 - 1.28558i) q^{61} +(-6.12836 - 5.14230i) q^{62} +(-1.04189 - 5.90885i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.00000 - 3.46410i) q^{65} +(1.87939 + 0.684040i) q^{66} +(2.81908 + 1.02606i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(0.500000 + 0.866025i) q^{69} +(2.08378 + 11.8177i) q^{70} +(-1.53209 - 1.28558i) q^{71} +(1.53209 - 1.28558i) q^{72} +(1.56283 - 8.86327i) q^{73} +(1.87939 - 0.684040i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(0.939693 - 0.342020i) q^{78} +(1.73648 - 9.84808i) q^{79} +(-3.06418 + 2.57115i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.38919 - 7.87846i) q^{82} +(3.00000 + 5.19615i) q^{83} +(-1.50000 + 2.59808i) q^{84} +(11.2763 + 4.10424i) q^{85} +(3.75877 + 1.36808i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-6.12836 - 5.14230i) q^{90} +(2.29813 - 1.92836i) q^{91} +(-0.173648 + 0.984808i) q^{92} +(-7.51754 + 2.73616i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(-1.87939 + 0.684040i) q^{97} +(-0.347296 + 1.96962i) q^{98} +(-3.06418 + 2.57115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 9 * q^7 + 3 * q^8	\( 6 q - 9 q^{7} + 3 q^{8} - 6 q^{11} - 3 q^{12} + 12 q^{18} - 24 q^{20} + 3 q^{26} + 15 q^{27} - 12 q^{30} - 24 q^{31} + 12 q^{37} + 6 q^{39} - 24 q^{45} - 3 q^{46} - 6 q^{49} + 33 q^{50} - 18 q^{56} - 30 q^{58} - 3 q^{64} + 12 q^{65} - 9 q^{68} + 3 q^{69} + 66 q^{75} + 36 q^{77} + 18 q^{83} - 9 q^{84} - 15 q^{87} + 6 q^{88} - 48 q^{94} - 6 q^{96}+O(q^{100}) \) 6 * q - 9 * q^7 + 3 * q^8 - 6 * q^11 - 3 * q^12 + 12 * q^18 - 24 * q^20 + 3 * q^26 + 15 * q^27 - 12 * q^30 - 24 * q^31 + 12 * q^37 + 6 * q^39 - 24 * q^45 - 3 * q^46 - 6 * q^49 + 33 * q^50 - 18 * q^56 - 30 * q^58 - 3 * q^64 + 12 * q^65 - 9 * q^68 + 3 * q^69 + 66 * q^75 + 36 * q^77 + 18 * q^83 - 9 * q^84 - 15 * q^87 + 6 * q^88 - 48 * q^94 - 6 * q^96

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