LMFDB - Embedded newform 722.2.e.p.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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.6053445140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 $ x^12 - 4x^9 + 17x^6 + 4*x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			423.1
Root			$-1.23949 - 1.04005i$ of defining polynomial
Character	$\chi$	$=$	722.423
Dual form			722.2.e.p.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.561937 + 3.18690i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.05865 - 0.888311i) q^{5} +(-0.561937 - 3.18690i) q^{6} +(-0.618034 - 1.07047i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-7.02151 - 2.55562i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.561937 + 3.18690i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.05865 - 0.888311i) q^{5} +(-0.561937 - 3.18690i) q^{6} +(-0.618034 - 1.07047i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-7.02151 - 2.55562i) q^{9} +(1.29862 + 0.472660i) q^{10} +(-0.618034 + 1.07047i) q^{11} +(1.61803 + 2.80252i) q^{12} +(-0.628265 - 3.56307i) q^{13} +(0.946883 + 0.794529i) q^{14} +(3.42585 - 2.87463i) q^{15} +(0.173648 - 0.984808i) q^{16} +(5.27923 - 1.92148i) q^{17} +7.47214 q^{18} -1.38197 q^{20} +(3.75877 - 1.36808i) q^{21} +(0.214641 - 1.21729i) q^{22} +(0.585206 - 0.491046i) q^{23} +(-2.47897 - 2.08010i) q^{24} +(-0.536602 - 3.04322i) q^{25} +(1.80902 + 3.13331i) q^{26} +(7.23607 - 12.5332i) q^{27} +(-1.16152 - 0.422760i) q^{28} +(1.96412 + 0.714880i) q^{29} +(-2.23607 + 3.87298i) q^{30} +(1.61803 + 2.80252i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-3.06418 - 2.57115i) q^{33} +(-4.30366 + 3.61120i) q^{34} +(-0.296626 + 1.68225i) q^{35} +(-7.02151 + 2.55562i) q^{36} -10.6180 q^{37} +11.7082 q^{39} +(1.29862 - 0.472660i) q^{40} +(1.01655 - 5.76517i) q^{41} +(-3.06418 + 2.57115i) q^{42} +(-3.64938 - 3.06220i) q^{43} +(0.214641 + 1.21729i) q^{44} +(5.16312 + 8.94278i) q^{45} +(-0.381966 + 0.661585i) q^{46} +(4.20243 + 1.52956i) q^{47} +(3.04091 + 1.10680i) q^{48} +(2.73607 - 4.73901i) q^{49} +(1.54508 + 2.67617i) q^{50} +(3.15698 + 17.9041i) q^{51} +(-2.77157 - 2.32563i) q^{52} +(-3.89930 + 3.27190i) q^{53} +(-2.51306 + 14.2523i) q^{54} +(1.60519 - 0.584240i) q^{55} +1.23607 q^{56} -2.09017 q^{58} +(7.96120 - 2.89764i) q^{59} +(0.776578 - 4.40419i) q^{60} +(2.77157 - 2.32563i) q^{61} +(-2.47897 - 2.08010i) q^{62} +(1.60383 + 9.09575i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.50000 + 4.33013i) q^{65} +(3.75877 + 1.36808i) q^{66} +(-1.60519 - 0.584240i) q^{67} +(2.80902 - 4.86536i) q^{68} +(1.23607 + 2.14093i) q^{69} +(-0.296626 - 1.68225i) q^{70} +(11.4480 + 9.60599i) q^{71} +(5.72399 - 4.80300i) q^{72} +(-0.587272 + 3.33059i) q^{73} +(9.97769 - 3.63158i) q^{74} +10.0000 q^{75} +1.52786 q^{77} +(-11.0021 + 4.00444i) q^{78} +(1.25653 - 7.12614i) q^{79} +(-1.05865 + 0.888311i) q^{80} +(18.7041 + 15.6946i) q^{81} +(1.01655 + 5.76517i) q^{82} +(-4.23607 - 7.33708i) q^{83} +(2.00000 - 3.46410i) q^{84} +(-7.29571 - 2.65542i) q^{85} +(4.47663 + 1.62936i) q^{86} +(-3.38197 + 5.85774i) q^{87} +(-0.618034 - 1.07047i) q^{88} +(-0.372631 - 2.11330i) q^{89} +(-7.91036 - 6.63758i) q^{90} +(-3.42585 + 2.87463i) q^{91} +(0.132655 - 0.752326i) q^{92} +(-9.84059 + 3.58168i) q^{93} -4.47214 q^{94} -3.23607 q^{96} +(5.99709 - 2.18276i) q^{97} +(-0.950226 + 5.38900i) q^{98} +(7.07524 - 5.93683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{7} - 6 q^{8} + 6 q^{11} + 6 q^{12} + 36 q^{18} - 30 q^{20} + 15 q^{26} + 60 q^{27} + 6 q^{31} - 114 q^{37} + 60 q^{39} + 15 q^{45} - 18 q^{46} + 6 q^{49} - 15 q^{50} - 12 q^{56} + 42 q^{58} - 6 q^{64} - 30 q^{65} + 27 q^{68} - 12 q^{69} + 120 q^{75} + 72 q^{77} - 24 q^{83} + 24 q^{84} - 54 q^{87} + 6 q^{88} - 12 q^{96}+O(q^{100}) $ 12 * q + 6 * q^7 - 6 * q^8 + 6 * q^11 + 6 * q^12 + 36 * q^18 - 30 * q^20 + 15 * q^26 + 60 * q^27 + 6 * q^31 - 114 * q^37 + 60 * q^39 + 15 * q^45 - 18 * q^46 + 6 * q^49 - 15 * q^50 - 12 * q^56 + 42 * q^58 - 6 * q^64 - 30 * q^65 + 27 * q^68 - 12 * q^69 + 120 * q^75 + 72 * q^77 - 24 * q^83 + 24 * q^84 - 54 * q^87 + 6 * q^88 - 12 * 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
$3$	−0.561937	+	3.18690i	−0.324435	+	1.83996i	0.189184	+	0.981942i	$0.439416\pi$
$3$	−0.561937	+	3.18690i	−0.324435	+	1.83996i	−0.513618	+	0.858019i	$0.671695\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.05865	−	0.888311i	−0.473442	−	0.397265i	0.374607	−	0.927184i	$-0.377778\pi$
$5$	−1.05865	−	0.888311i	−0.473442	−	0.397265i	−0.848048	+	0.529919i	$0.822222\pi$
$6$	−0.561937	−	3.18690i	−0.229410	−	1.30105i
$7$	−0.618034	−	1.07047i	−0.233595	−	0.404598i	0.725269	−	0.688466i	$-0.241716\pi$
$7$	−0.618034	−	1.07047i	−0.233595	−	0.404598i	−0.958863	+	0.283868i	$0.908382\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−7.02151	−	2.55562i	−2.34050	−	0.851874i
$10$	1.29862	+	0.472660i	0.410661	+	0.149468i
$11$	−0.618034	+	1.07047i	−0.186344	+	0.322758i	−0.944029	−	0.329863i	$-0.892997\pi$
$11$	−0.618034	+	1.07047i	−0.186344	+	0.322758i	0.757684	+	0.652621i	$0.226331\pi$
$12$	1.61803	+	2.80252i	0.467086	+	0.809017i
$13$	−0.628265	−	3.56307i	−0.174249	−	0.988217i	−0.939007	−	0.343899i	$-0.888252\pi$
$13$	−0.628265	−	3.56307i	−0.174249	−	0.988217i	0.764757	−	0.644318i	$-0.222859\pi$
$14$	0.946883	+	0.794529i	0.253065	+	0.212347i
$15$	3.42585	−	2.87463i	0.884552	−	0.742227i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	5.27923	−	1.92148i	1.28040	−	0.466028i	0.389836	−	0.920884i	$-0.372532\pi$
$17$	5.27923	−	1.92148i	1.28040	−	0.466028i	0.890565	+	0.454857i	$0.150310\pi$
$18$	7.47214			1.76120
$19$		0			0
$19$		0			0
$20$	−1.38197			−0.309017
$21$	3.75877	−	1.36808i	0.820231	−	0.298540i
$22$	0.214641	−	1.21729i	0.0457616	−	0.259527i
$23$	0.585206	−	0.491046i	0.122024	−	0.102390i	−0.579734	−	0.814806i	$-0.696843\pi$
$23$	0.585206	−	0.491046i	0.122024	−	0.102390i	0.701758	+	0.712416i	$0.252399\pi$
$24$	−2.47897	−	2.08010i	−0.506018	−	0.424600i
$25$	−0.536602	−	3.04322i	−0.107320	−	0.608645i
$26$	1.80902	+	3.13331i	0.354777	+	0.614493i
$27$	7.23607	−	12.5332i	1.39258	−	2.41202i
$28$	−1.16152	−	0.422760i	−0.219507	−	0.0798942i
$29$	1.96412	+	0.714880i	0.364727	+	0.132750i	0.517881	−	0.855452i	$-0.326721\pi$
$29$	1.96412	+	0.714880i	0.364727	+	0.132750i	−0.153154	+	0.988202i	$0.548943\pi$
$30$	−2.23607	+	3.87298i	−0.408248	+	0.707107i
$31$	1.61803	+	2.80252i	0.290607	+	0.503347i	0.973954	−	0.226748i	$-0.0728093\pi$
$31$	1.61803	+	2.80252i	0.290607	+	0.503347i	−0.683346	+	0.730095i	$0.739476\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−3.06418	−	2.57115i	−0.533405	−	0.447580i
$34$	−4.30366	+	3.61120i	−0.738072	+	0.619316i
$35$	−0.296626	+	1.68225i	−0.0501390	+	0.284353i
$36$	−7.02151	+	2.55562i	−1.17025	+	0.425937i
$37$	−10.6180			−1.74559			−0.872797	−	0.488083i	$-0.837696\pi$
$37$	−10.6180			−1.74559			−0.872797	+	0.488083i	$0.837696\pi$
$38$		0			0
$39$	11.7082			1.87481
$40$	1.29862	−	0.472660i	0.205330	−	0.0747341i
$41$	1.01655	−	5.76517i	0.158759	−	0.900368i	−0.796509	−	0.604627i	$-0.793322\pi$
$41$	1.01655	−	5.76517i	0.158759	−	0.900368i	0.955268	−	0.295741i	$-0.0955665\pi$
$42$	−3.06418	+	2.57115i	−0.472813	+	0.396737i
$43$	−3.64938	−	3.06220i	−0.556526	−	0.466981i	0.320618	−	0.947209i	$-0.396109\pi$
$43$	−3.64938	−	3.06220i	−0.556526	−	0.466981i	−0.877144	+	0.480228i	$0.840554\pi$
$44$	0.214641	+	1.21729i	0.0323583	+	0.183513i
$45$	5.16312	+	8.94278i	0.769672	+	1.33311i
$46$	−0.381966	+	0.661585i	−0.0563178	+	0.0975453i
$47$	4.20243	+	1.52956i	0.612988	+	0.223109i	0.629810	−	0.776749i	$-0.283133\pi$
$47$	4.20243	+	1.52956i	0.612988	+	0.223109i	−0.0168222	+	0.999858i	$0.505355\pi$
$48$	3.04091	+	1.10680i	0.438917	+	0.159753i
$49$	2.73607	−	4.73901i	0.390867	−	0.677001i
$50$	1.54508	+	2.67617i	0.218508	+	0.378467i
$51$	3.15698	+	17.9041i	0.442066	+	2.50708i
$52$	−2.77157	−	2.32563i	−0.384348	−	0.322506i
$53$	−3.89930	+	3.27190i	−0.535610	+	0.449430i	−0.870033	−	0.492993i	$-0.835903\pi$
$53$	−3.89930	+	3.27190i	−0.535610	+	0.449430i	0.334424	+	0.942423i	$0.391458\pi$
$54$	−2.51306	+	14.2523i	−0.341984	+	1.93949i
$55$	1.60519	−	0.584240i	0.216443	−	0.0787789i
$56$	1.23607			0.165177
$57$		0			0
$58$	−2.09017			−0.274453
$59$	7.96120	−	2.89764i	1.03646	−	0.377241i	0.232923	−	0.972495i	$-0.425171\pi$
$59$	7.96120	−	2.89764i	1.03646	−	0.377241i	0.803537	+	0.595254i	$0.202949\pi$
$60$	0.776578	−	4.40419i	0.100256	−	0.568579i
$61$	2.77157	−	2.32563i	0.354864	−	0.297766i	−0.447876	−	0.894096i	$-0.647819\pi$
$61$	2.77157	−	2.32563i	0.354864	−	0.297766i	0.802740	+	0.596330i	$0.203375\pi$
$62$	−2.47897	−	2.08010i	−0.314830	−	0.264174i
$63$	1.60383	+	9.09575i	0.202063	+	1.14596i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$	3.75877	+	1.36808i	0.462673	+	0.168399i
$67$	−1.60519	−	0.584240i	−0.196105	−	0.0713763i	0.242101	−	0.970251i	$-0.422164\pi$
$67$	−1.60519	−	0.584240i	−0.196105	−	0.0713763i	−0.438205	+	0.898875i	$0.644386\pi$
$68$	2.80902	−	4.86536i	0.340643	−	0.590012i
$69$	1.23607	+	2.14093i	0.148805	+	0.257738i
$70$	−0.296626	−	1.68225i	−0.0354536	−	0.201068i
$71$	11.4480	+	9.60599i	1.35862	+	1.14002i	0.976404	+	0.215950i	$0.0692850\pi$
$71$	11.4480	+	9.60599i	1.35862	+	1.14002i	0.382221	+	0.924071i	$0.375159\pi$
$72$	5.72399	−	4.80300i	0.674578	−	0.566039i
$73$	−0.587272	+	3.33059i	−0.0687350	+	0.389816i	0.930960	+	0.365121i	$0.118972\pi$
$73$	−0.587272	+	3.33059i	−0.0687350	+	0.389816i	−0.999695	+	0.0246945i	$0.992139\pi$
$74$	9.97769	−	3.63158i	1.15988	−	0.422163i
$75$	10.0000			1.15470
$76$		0			0
$77$	1.52786			0.174116
$78$	−11.0021	+	4.00444i	−1.24574	+	0.453414i
$79$	1.25653	−	7.12614i	0.141371	−	0.801753i	−0.828839	−	0.559487i	$-0.810998\pi$
$79$	1.25653	−	7.12614i	0.141371	−	0.801753i	0.970210	−	0.242266i	$-0.0778907\pi$
$80$	−1.05865	+	0.888311i	−0.118360	+	0.0993161i
$81$	18.7041	+	15.6946i	2.07823	+	1.74384i
$82$	1.01655	+	5.76517i	0.112260	+	0.636656i
$83$	−4.23607	−	7.33708i	−0.464969	−	0.805350i	0.534231	−	0.845338i	$-0.320601\pi$
$83$	−4.23607	−	7.33708i	−0.464969	−	0.805350i	−0.999200	+	0.0399887i	$0.987268\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$	−7.29571	−	2.65542i	−0.791331	−	0.288021i
$86$	4.47663	+	1.62936i	0.482728	+	0.175698i
$87$	−3.38197	+	5.85774i	−0.362585	+	0.628015i
$88$	−0.618034	−	1.07047i	−0.0658826	−	0.114112i
$89$	−0.372631	−	2.11330i	−0.0394988	−	0.224009i	0.958668	−	0.284526i	$-0.0918362\pi$
$89$	−0.372631	−	2.11330i	−0.0394988	−	0.224009i	−0.998167	+	0.0605169i	$0.980725\pi$
$90$	−7.91036	−	6.63758i	−0.833825	−	0.699662i
$91$	−3.42585	+	2.87463i	−0.359127	+	0.301343i
$92$	0.132655	−	0.752326i	0.0138303	−	0.0784354i
$93$	−9.84059	+	3.58168i	−1.02042	+	0.371403i
$94$	−4.47214			−0.461266
$95$		0			0
$96$	−3.23607			−0.330280
$97$	5.99709	−	2.18276i	0.608912	−	0.221626i	−0.0191152	−	0.999817i	$-0.506085\pi$
$97$	5.99709	−	2.18276i	0.608912	−	0.221626i	0.628027	+	0.778191i	$0.283863\pi$
$98$	−0.950226	+	5.38900i	−0.0959874	+	0.544371i
$99$	7.07524	−	5.93683i	0.711088	−	0.596674i
$100$	−2.36721	−	1.98632i	−0.236721	−	0.198632i
$101$	−2.32375	−	13.1787i	−0.231222	−	1.31133i	−0.850426	−	0.526095i	$-0.823655\pi$
$101$	−2.32375	−	13.1787i	−0.231222	−	1.31133i	0.619203	−	0.785231i	$-0.287456\pi$
$102$	−9.09017	−	15.7446i	−0.900061	−	1.55895i
$103$	−8.32624	+	14.4215i	−0.820409	+	1.42099i	0.0849697	+	0.996384i	$0.472921\pi$
$103$	−8.32624	+	14.4215i	−0.820409	+	1.42099i	−0.905378	+	0.424606i	$0.860413\pi$
$104$	3.39984	+	1.23744i	0.333382	+	0.121341i
$105$	−5.19449	−	1.89064i	−0.506931	−	0.184508i
$106$	2.54508	−	4.40822i	0.247201	−	0.428164i
$107$	−8.70820	−	15.0831i	−0.841854	−	1.45813i	−0.888326	−	0.459214i	$-0.848131\pi$
$107$	−8.70820	−	15.0831i	−0.841854	−	1.45813i	0.0464718	−	0.998920i	$-0.485202\pi$
$108$	−2.51306	−	14.2523i	−0.241819	−	1.37143i
$109$	−13.8152	−	11.5923i	−1.32325	−	1.11034i	−0.985604	−	0.169071i	$-0.945923\pi$
$109$	−13.8152	−	11.5923i	−1.32325	−	1.11034i	−0.337651	−	0.941271i	$-0.609632\pi$
$110$	−1.30856	+	1.09801i	−0.124766	+	0.104691i
$111$	5.96667	−	33.8387i	0.566331	−	3.21182i
$112$	−1.16152	+	0.422760i	−0.109754	+	0.0399471i
$113$	3.14590			0.295941			0.147971	−	0.988992i	$-0.452726\pi$
$113$	3.14590			0.295941			0.147971	+	0.988992i	$0.452726\pi$
$114$		0			0
$115$	−1.05573			−0.0984472
$116$	1.96412	−	0.714880i	0.182364	−	0.0663750i
$117$	−4.69448	+	26.6237i	−0.434005	+	2.46136i
$118$	−6.49003	+	5.44578i	−0.597456	+	0.501325i
$119$	−5.31962	−	4.46369i	−0.487649	−	0.409186i
$120$	0.776578	+	4.40419i	0.0708916	+	0.402046i
$121$	4.73607	+	8.20311i	0.430552	+	0.745737i
$122$	−1.80902	+	3.13331i	−0.163781	+	0.283676i
$123$	17.8018	+	6.47932i	1.60513	+	0.584221i
$124$	3.04091	+	1.10680i	0.273082	+	0.0993936i
$125$	−5.59017	+	9.68246i	−0.500000	+	0.866025i
$126$	−4.61803	−	7.99867i	−0.411407	−	0.712578i
$127$	−2.67703	−	15.1822i	−0.237548	−	1.34720i	−0.837181	−	0.546927i	$-0.815798\pi$
$127$	−2.67703	−	15.1822i	−0.237548	−	1.34720i	0.599632	−	0.800276i	$-0.295313\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	11.8097	−	9.90948i	1.03978	−	0.872481i
$130$	0.868241	−	4.92404i	0.0761498	−	0.431867i
$131$	4.20243	−	1.52956i	0.367168	−	0.133638i	−0.151845	−	0.988404i	$-0.548522\pi$
$131$	4.20243	−	1.52956i	0.367168	−	0.133638i	0.519014	+	0.854766i	$0.326299\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$	1.70820			0.147566
$135$	−18.7939	+	6.84040i	−1.61752	+	0.588728i
$136$	−0.975561	+	5.53268i	−0.0836537	+	0.474424i
$137$	3.53762	−	2.96842i	0.302239	−	0.253609i	−0.479036	−	0.877795i	$-0.659014\pi$
$137$	3.53762	−	2.96842i	0.302239	−	0.253609i	0.781276	+	0.624186i	$0.214569\pi$
$138$	−1.89377	−	1.58906i	−0.161208	−	0.135270i
$139$	−2.43107	−	13.7873i	−0.206201	−	1.16942i	−0.895539	−	0.444984i	$-0.853209\pi$
$139$	−2.43107	−	13.7873i	−0.206201	−	1.16942i	0.689338	−	0.724440i	$-0.257902\pi$
$140$	0.854102	+	1.47935i	0.0721848	+	0.125028i
$141$	−7.23607	+	12.5332i	−0.609387	+	1.05549i
$142$	−14.0430	−	5.11124i	−1.17846	−	0.428926i
$143$	4.20243	+	1.52956i	0.351425	+	0.127908i
$144$	−3.73607	+	6.47106i	−0.311339	+	0.539255i
$145$	−1.44427	−	2.50155i	−0.119940	−	0.207743i
$146$	−0.587272	−	3.33059i	−0.0486030	−	0.275641i
$147$	13.5653	+	11.3826i	1.11884	+	0.938822i
$148$	−8.13389	+	6.82514i	−0.668601	+	0.561023i
$149$	−0.331639	+	1.88082i	−0.0271689	+	0.154082i	−0.995374	−	0.0960748i	$-0.969371\pi$
$149$	−0.331639	+	1.88082i	−0.0271689	+	0.154082i	0.968205	+	0.250157i	$0.0804823\pi$
$150$	−9.39693	+	3.42020i	−0.767256	+	0.279258i
$151$	−5.52786			−0.449851			−0.224926	−	0.974376i	$-0.572214\pi$
$151$	−5.52786			−0.449851			−0.224926	+	0.974376i	$0.572214\pi$
$152$		0			0
$153$	−41.9787			−3.39378
$154$	−1.43572	+	0.522560i	−0.115694	+	0.0421091i
$155$	0.776578	−	4.40419i	0.0623763	−	0.353753i
$156$	8.96900	−	7.52589i	0.718095	−	0.602553i
$157$	8.89993	+	7.46793i	0.710292	+	0.596006i	0.924681	−	0.380743i	$-0.124332\pi$
$157$	8.89993	+	7.46793i	0.710292	+	0.596006i	−0.214389	+	0.976748i	$0.568776\pi$
$158$	1.25653	+	7.12614i	0.0999642	+	0.566925i
$159$	−8.23607	−	14.2653i	−0.653163	−	1.13131i
$160$	0.690983	−	1.19682i	0.0546270	−	0.0946167i
$161$	−0.887325	−	0.322960i	−0.0699310	−	0.0254528i
$162$	−22.9439	−	8.35090i	−1.80264	−	0.656109i
$163$	10.3262	−	17.8856i	0.808813	−	1.40091i	−0.104873	−	0.994486i	$-0.533444\pi$
$163$	10.3262	−	17.8856i	0.808813	−	1.40091i	0.913686	−	0.406420i	$-0.133223\pi$
$164$	−2.92705	−	5.06980i	−0.228564	−	0.395885i
$165$	0.959904	+	5.44388i	0.0747284	+	0.423806i
$166$	6.49003	+	5.44578i	0.503724	+	0.422675i
$167$	2.70250	−	2.26767i	0.209126	−	0.175477i	−0.532209	−	0.846613i	$-0.678638\pi$
$167$	2.70250	−	2.26767i	0.209126	−	0.175477i	0.741334	+	0.671136i	$0.234193\pi$
$168$	−0.694593	+	3.93923i	−0.0535890	+	0.303918i
$169$	−0.0847320	+	0.0308399i	−0.00651785	+	0.00237230i
$170$	7.76393			0.595466
$171$		0			0
$172$	−4.76393			−0.363246
$173$	−13.4623	+	4.89986i	−1.02352	+	0.372530i	−0.798609	−	0.601850i	$-0.794430\pi$
$173$	−13.4623	+	4.89986i	−1.02352	+	0.372530i	−0.224908	+	0.974380i	$0.572208\pi$
$174$	1.17454	−	6.66117i	0.0890420	−	0.504982i
$175$	−2.92603	+	2.45523i	−0.221187	+	0.185598i
$176$	0.946883	+	0.794529i	0.0713740	+	0.0598899i
$177$	4.76081	+	26.9999i	0.357844	+	2.02944i
$178$	1.07295	+	1.85840i	0.0804209	+	0.139293i
$179$	1.70820	−	2.95870i	0.127677	−	0.221143i	−0.795099	−	0.606480i	$-0.792581\pi$
$179$	1.70820	−	2.95870i	0.127677	−	0.221143i	0.922776	+	0.385336i	$0.125915\pi$
$180$	9.70349	+	3.53178i	0.723255	+	0.263243i
$181$	−20.1248	−	7.32484i	−1.49587	−	0.544451i	−0.540881	−	0.841099i	$-0.681909\pi$
$181$	−20.1248	−	7.32484i	−1.49587	−	0.544451i	−0.954987	+	0.296648i	$0.904131\pi$
$182$	2.23607	−	3.87298i	0.165748	−	0.287085i
$183$	5.85410	+	10.1396i	0.432748	+	0.749541i
$184$	0.132655	+	0.752326i	0.00977949	+	0.0554622i
$185$	11.2408	+	9.43211i	0.826437	+	0.693463i
$186$	8.02212	−	6.73136i	0.588210	−	0.493567i
$187$	−1.20586	+	6.83877i	−0.0881812	+	0.500101i
$188$	4.20243	−	1.52956i	0.306494	−	0.111555i
$189$	−17.8885			−1.30120
$190$		0			0
$191$	12.4721			0.902452			0.451226	−	0.892410i	$-0.350987\pi$
$191$	12.4721			0.902452			0.451226	+	0.892410i	$0.350987\pi$
$192$	3.04091	−	1.10680i	0.219459	−	0.0798764i
$193$	3.55495	−	20.1611i	0.255891	−	1.45123i	−0.537885	−	0.843018i	$-0.680776\pi$
$193$	3.55495	−	20.1611i	0.255891	−	1.45123i	0.793776	−	0.608211i	$-0.208112\pi$
$194$	−4.88887	+	4.10225i	−0.351000	+	0.294524i
$195$	−12.3949	−	10.4005i	−0.887614	−	0.744797i
$196$	−0.950226	−	5.38900i	−0.0678733	−	0.384929i
$197$	5.42705	+	9.39993i	0.386661	+	0.669717i	0.991998	−	0.126252i	$-0.0402949\pi$
$197$	5.42705	+	9.39993i	0.386661	+	0.669717i	−0.605337	+	0.795969i	$0.706962\pi$
$198$	−4.61803	+	7.99867i	−0.328189	+	0.568441i
$199$	−1.43572	−	0.522560i	−0.101776	−	0.0370433i	0.290630	−	0.956835i	$-0.406135\pi$
$199$	−1.43572	−	0.522560i	−0.101776	−	0.0370433i	−0.392406	+	0.919792i	$0.628357\pi$
$200$	2.90381	+	1.05690i	0.205330	+	0.0747341i
$201$	2.76393	−	4.78727i	0.194953	−	0.337668i
$202$	6.69098	+	11.5891i	0.470776	+	0.815408i
$203$	−0.448636	−	2.54434i	−0.0314881	−	0.178578i
$204$	13.9269	+	11.6861i	0.975081	+	0.818190i
$205$	−6.19743	+	5.20026i	−0.432847	+	0.363202i
$206$	2.89167	−	16.3995i	0.201472	−	1.14261i
$207$	−5.36396	+	1.95232i	−0.372821	+	0.135696i
$208$	−3.61803			−0.250866
$209$		0			0
$210$	5.52786			0.381459
$211$	−2.59725	+	0.945320i	−0.178802	+	0.0650785i	−0.429870	−	0.902891i	$-0.641440\pi$
$211$	−2.59725	+	0.945320i	−0.178802	+	0.0650785i	0.251068	+	0.967969i	$0.419218\pi$
$212$	−0.883899	+	5.01284i	−0.0607064	+	0.344283i
$213$	−37.0464	+	31.0856i	−2.53838	+	2.12995i
$214$	13.3417	+	11.1951i	0.912023	+	0.765278i
$215$	1.14323	+	6.48357i	0.0779676	+	0.442176i
$216$	7.23607	+	12.5332i	0.492352	+	0.852779i
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	16.9468	+	6.16814i	1.14778	+	0.417759i
$219$	−10.2843	−	3.74316i	−0.694945	−	0.252939i
$220$	0.854102	−	1.47935i	0.0575835	−	0.0997376i
$221$	−10.1631	−	17.6030i	−0.683645	−	1.18411i
$222$	5.96667	+	33.8387i	0.400457	+	2.27110i
$223$	−10.9482	−	9.18659i	−0.733142	−	0.615180i	0.197844	−	0.980234i	$-0.436606\pi$
$223$	−10.9482	−	9.18659i	−0.733142	−	0.615180i	−0.930986	+	0.365054i	$0.881051\pi$
$224$	0.946883	−	0.794529i	0.0632663	−	0.0530867i
$225$	−4.00957	+	22.7394i	−0.267304	+	1.51596i
$226$	−2.95618	+	1.07596i	−0.196642	+	0.0715718i
$227$	−8.94427			−0.593652			−0.296826	−	0.954932i	$-0.595928\pi$
$227$	−8.94427			−0.593652			−0.296826	+	0.954932i	$0.595928\pi$
$228$		0			0
$229$	6.61803			0.437332			0.218666	−	0.975800i	$-0.429829\pi$
$229$	6.61803			0.437332			0.218666	+	0.975800i	$0.429829\pi$
$230$	0.992060	−	0.361080i	0.0654145	−	0.0238089i
$231$	−0.858564	+	4.86916i	−0.0564894	+	0.320367i
$232$	−1.60116	+	1.34354i	−0.105122	+	0.0882074i
$233$	−14.2196	−	11.9316i	−0.931554	−	0.781666i	0.0445419	−	0.999008i	$-0.485817\pi$
$233$	−14.2196	−	11.9316i	−0.931554	−	0.781666i	−0.976096	+	0.217341i	$0.930262\pi$
$234$	−4.69448	−	26.6237i	−0.306888	−	1.74045i
$235$	−3.09017	−	5.35233i	−0.201580	−	0.349148i
$236$	4.23607	−	7.33708i	0.275745	−	0.477604i
$237$	22.0042	+	8.00888i	1.42933	+	0.520233i
$238$	6.52548	+	2.37508i	0.422984	+	0.153954i
$239$	−3.90983	+	6.77202i	−0.252906	+	0.438046i	−0.964325	−	0.264723i	$-0.914720\pi$
$239$	−3.90983	+	6.77202i	−0.252906	+	0.438046i	0.711419	+	0.702768i	$0.248053\pi$
$240$	−2.23607	−	3.87298i	−0.144338	−	0.250000i
$241$	−0.245957	−	1.39489i	−0.0158435	−	0.0898527i	0.975861	−	0.218394i	$-0.0700817\pi$
$241$	−0.245957	−	1.39489i	−0.0158435	−	0.0898527i	−0.991704	+	0.128541i	$0.958971\pi$
$242$	−7.25608	−	6.08857i	−0.466438	−	0.391388i
$243$	−27.2687	+	22.8811i	−1.74929	+	1.46783i
$244$	0.628265	−	3.56307i	0.0402205	−	0.228102i
$245$	−7.10624	+	2.58646i	−0.454001	+	0.165243i
$246$	−18.9443			−1.20784
$247$		0			0
$248$	−3.23607			−0.205491
$249$	25.7630	−	9.37696i	1.63266	−	0.594241i
$250$	1.94145	−	11.0105i	0.122788	−	0.696364i
$251$	−12.0332	+	10.0970i	−0.759528	+	0.637319i	−0.938004	−	0.346625i	$-0.887328\pi$
$251$	−12.0332	+	10.0970i	−0.759528	+	0.637319i	0.178476	+	0.983944i	$0.442883\pi$
$252$	7.07524	+	5.93683i	0.445698	+	0.373985i
$253$	0.163971	+	0.929926i	0.0103088	+	0.0584640i
$254$	7.70820	+	13.3510i	0.483656	+	0.837716i
$255$	12.5623	−	21.7586i	0.786682	−	1.36257i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	19.3746	+	7.05178i	1.20856	+	0.439878i	0.866202	−	0.499693i	$-0.166554\pi$
$257$	19.3746	+	7.05178i	1.20856	+	0.439878i	0.342353	+	0.939571i	$0.388776\pi$
$258$	−7.70820	+	13.3510i	−0.479892	+	0.831197i
$259$	6.56231	+	11.3662i	0.407762	+	0.706264i
$260$	0.868241	+	4.92404i	0.0538460	+	0.305376i
$261$	−11.9641	−	10.0391i	−0.740560	−	0.621403i
$262$	−3.42585	+	2.87463i	−0.211650	+	0.177595i
$263$	−2.59505	+	14.7172i	−0.160017	+	0.907504i	0.794037	+	0.607870i	$0.207976\pi$
$263$	−2.59505	+	14.7172i	−0.160017	+	0.907504i	−0.954054	+	0.299634i	$0.903135\pi$
$264$	3.75877	−	1.36808i	0.231336	−	0.0841995i
$265$	7.03444			0.432122
$266$		0			0
$267$	6.94427			0.424983
$268$	−1.60519	+	0.584240i	−0.0980524	+	0.0356881i
$269$	0.230299	−	1.30609i	0.0140416	−	0.0796337i	−0.976982	−	0.213323i	$-0.931571\pi$
$269$	0.230299	−	1.30609i	0.0140416	−	0.0796337i	0.991023	+	0.133689i	$0.0426824\pi$
$270$	15.3209	−	12.8558i	0.932400	−	0.782376i
$271$	19.9172	+	16.7125i	1.20988	+	1.01521i	0.999292	+	0.0376362i	$0.0119828\pi$
$271$	19.9172	+	16.7125i	1.20988	+	1.01521i	0.210590	+	0.977575i	$0.432462\pi$
$272$	−0.975561	−	5.53268i	−0.0591521	−	0.335468i
$273$	−7.23607	−	12.5332i	−0.437947	−	0.758546i
$274$	−2.30902	+	3.99933i	−0.139493	+	0.241609i
$275$	3.58931	+	1.30640i	0.216443	+	0.0787789i
$276$	2.32305	+	0.845520i	0.139831	+	0.0508943i
$277$	−0.545085	+	0.944115i	−0.0327510	+	0.0567264i	−0.881936	−	0.471369i	$-0.843760\pi$
$277$	−0.545085	+	0.944115i	−0.0327510	+	0.0567264i	0.849185	+	0.528095i	$0.177093\pi$
$278$	7.00000	+	12.1244i	0.419832	+	0.727171i
$279$	−4.19887	−	23.8130i	−0.251380	−	1.42565i
$280$	−1.30856	−	1.09801i	−0.0782014	−	0.0656188i
$281$	19.9008	−	16.6988i	1.18719	−	0.996167i	0.187281	−	0.982306i	$-0.440032\pi$
$281$	19.9008	−	16.6988i	1.18719	−	0.996167i	0.999904	−	0.0138603i	$-0.00441200\pi$
$282$	2.51306	−	14.2523i	0.149651	−	0.848710i
$283$	−12.7120	+	4.62680i	−0.755652	+	0.275035i	−0.690982	−	0.722872i	$-0.742822\pi$
$283$	−12.7120	+	4.62680i	−0.755652	+	0.275035i	−0.0646699	+	0.997907i	$0.520599\pi$
$284$	14.9443			0.886779
$285$		0			0
$286$	−4.47214			−0.264443
$287$	−6.79968	+	2.47488i	−0.401372	+	0.146088i
$288$	1.29752	−	7.35862i	0.0764573	−	0.433611i
$289$	11.1554	−	9.36047i	0.656198	−	0.550616i
$290$	2.21275	+	1.85672i	0.129937	+	0.109030i
$291$	3.58626	+	20.3387i	0.210231	+	1.19228i
$292$	1.69098	+	2.92887i	0.0989573	+	0.171399i
$293$	2.52786	−	4.37839i	0.147679	−	0.255788i	−0.782690	−	0.622412i	$-0.786153\pi$
$293$	2.52786	−	4.37839i	0.147679	−	0.255788i	0.930369	+	0.366624i	$0.119486\pi$
$294$	−16.6403	−	6.05656i	−0.970480	−	0.353226i
$295$	−11.0021	−	4.00444i	−0.640568	−	0.233148i
$296$	5.30902	−	9.19549i	0.308580	−	0.534477i
$297$	8.94427	+	15.4919i	0.518999	+	0.898933i
$298$	−0.331639	−	1.88082i	−0.0192113	−	0.108953i
$299$	−2.11729	−	1.77662i	−0.122446	−	0.102745i
$300$	7.66044	−	6.42788i	0.442276	−	0.371114i
$301$	−1.02253	+	5.79908i	−0.0589379	+	0.334254i
$302$	5.19449	−	1.89064i	0.298909	−	0.108794i
$303$	43.3050			2.48780
$304$		0			0
$305$	−5.00000			−0.286299
$306$	39.4471	−	14.3576i	2.25504	−	0.820767i
$307$	0.296626	−	1.68225i	0.0169294	−	0.0960112i	−0.975172	−	0.221447i	$-0.928922\pi$
$307$	0.296626	−	1.68225i	0.0169294	−	0.0960112i	0.992102	+	0.125436i	$0.0400330\pi$
$308$	1.17041	−	0.982092i	0.0666904	−	0.0559599i
$309$	−41.2810	−	34.6389i	−2.34840	−	1.97054i
$310$	0.776578	+	4.40419i	0.0441067	+	0.250141i
$311$	−13.3820	−	23.1782i	−0.758822	−	1.31432i	−0.943452	−	0.331510i	$-0.892442\pi$
$311$	−13.3820	−	23.1782i	−0.758822	−	1.31432i	0.184630	−	0.982808i	$-0.440891\pi$
$312$	−5.85410	+	10.1396i	−0.331423	+	0.574042i
$313$	−21.1493	−	7.69770i	−1.19543	−	0.435100i	−0.333801	−	0.942644i	$-0.608331\pi$
$313$	−21.1493	−	7.69770i	−1.19543	−	0.435100i	−0.861626	+	0.507544i	$0.830554\pi$
$314$	−10.9174	−	3.97360i	−0.616103	−	0.224243i
$315$	6.38197	−	11.0539i	0.359583	−	0.622816i
$316$	−3.61803	−	6.26662i	−0.203530	−	0.352525i
$317$	2.48773	+	14.1086i	0.139725	+	0.792417i	0.971453	+	0.237234i	$0.0762408\pi$
$317$	2.48773	+	14.1086i	0.139725	+	0.792417i	−0.831728	+	0.555183i	$0.812648\pi$
$318$	12.6184	+	10.5881i	0.707604	+	0.593750i
$319$	−1.97915	+	1.66070i	−0.110811	+	0.0929814i
$320$	−0.239976	+	1.36097i	−0.0134151	+	0.0760806i
$321$	52.9617	−	19.2765i	2.95603	−	1.07591i
$322$	0.944272			0.0526222
$323$		0			0
$324$	24.4164			1.35647
$325$	−10.5061	+	3.82390i	−0.582773	+	0.212112i
$326$	−3.58626	+	20.3387i	−0.198625	+	1.12646i
$327$	44.7069	−	37.5135i	2.47230	−	2.07450i
$328$	4.48450	+	3.76294i	0.247615	+	0.207774i
$329$	−0.959904	−	5.44388i	−0.0529212	−	0.300131i
$330$	−2.76393	−	4.78727i	−0.152149	−	0.263531i
$331$	6.14590	−	10.6450i	0.337809	−	0.585103i	−0.646211	−	0.763159i	$-0.723648\pi$
$331$	6.14590	−	10.6450i	0.337809	−	0.585103i	0.984020	+	0.178056i	$0.0569808\pi$
$332$	−7.96120	−	2.89764i	−0.436928	−	0.159029i
$333$	74.5546	+	27.1357i	4.08557	+	1.48703i
$334$	−1.76393	+	3.05522i	−0.0965181	+	0.167174i
$335$	1.18034	+	2.04441i	0.0644889	+	0.111698i
$336$	−0.694593	−	3.93923i	−0.0378931	−	0.214903i
$337$	−3.53762	−	2.96842i	−0.192706	−	0.161700i	0.541329	−	0.840811i	$-0.317921\pi$
$337$	−3.53762	−	2.96842i	−0.192706	−	0.161700i	−0.734036	+	0.679111i	$0.762366\pi$
$338$	0.0690742	−	0.0579601i	0.00375714	−	0.00315262i
$339$	−1.76780	+	10.0257i	−0.0960136	+	0.544520i
$340$	−7.29571	+	2.65542i	−0.395665	+	0.144010i
$341$	−4.00000			−0.216612
$342$		0			0
$343$	−15.4164			−0.832408
$344$	4.47663	−	1.62936i	0.241364	−	0.0878492i
$345$	0.593253	−	3.36450i	0.0319397	−	0.181139i
$346$	10.9745	−	9.20873i	0.589995	−	0.495064i
$347$	21.9491	+	18.4175i	1.17829	+	0.988701i	0.999989	+	0.00472451i	$0.00150386\pi$
$347$	21.9491	+	18.4175i	1.17829	+	0.988701i	0.178299	+	0.983976i	$0.442941\pi$
$348$	1.17454	+	6.66117i	0.0629622	+	0.357076i
$349$	10.9549	+	18.9745i	0.586403	+	1.01568i	0.994699	+	0.102830i	$0.0327899\pi$
$349$	10.9549	+	18.9745i	0.586403	+	1.01568i	−0.408296	+	0.912850i	$0.633877\pi$
$350$	1.90983	−	3.30792i	0.102085	−	0.176816i
$351$	−49.2029	−	17.9084i	−2.62626	−	0.955880i
$352$	−1.16152	−	0.422760i	−0.0619094	−	0.0225332i
$353$	−9.37132	+	16.2316i	−0.498785	+	0.863921i	−0.999999	−	0.00140218i	$-0.999554\pi$
$353$	−9.37132	+	16.2316i	−0.498785	+	0.863921i	0.501214	+	0.865323i	$0.332887\pi$
$354$	−13.7082	−	23.7433i	−0.728583	−	1.26194i
$355$	−3.58626	−	20.3387i	−0.190339	−	1.07947i
$356$	−1.64385	−	1.37936i	−0.0871240	−	0.0731058i
$357$	17.2147	−	14.4448i	0.911096	−	0.764500i
$358$	−0.593253	+	3.36450i	−0.0313544	+	0.177820i
$359$	−19.2375	+	7.00188i	−1.01532	+	0.369545i	−0.795473	−	0.605990i	$-0.792777\pi$
$359$	−19.2375	+	7.00188i	−1.01532	+	0.369545i	−0.219845	+	0.975535i	$0.570555\pi$
$360$	−10.3262			−0.544241
$361$		0			0
$362$	21.4164			1.12562
$363$	−28.8039	+	10.4838i	−1.51181	+	0.550255i
$364$	−0.776578	+	4.40419i	−0.0407038	+	0.230842i
$365$	3.58031	−	3.00424i	0.187402	−	0.157249i
$366$	−8.96900	−	7.52589i	−0.468817	−	0.393384i
$367$	−6.04865	−	34.3036i	−0.315737	−	1.79063i	−0.568055	−	0.822990i	$-0.692304\pi$
$367$	−6.04865	−	34.3036i	−0.315737	−	1.79063i	0.252318	−	0.967644i	$-0.418807\pi$
$368$	−0.381966	−	0.661585i	−0.0199114	−	0.0344875i
$369$	−21.8713	+	37.8822i	−1.13858	+	1.97207i
$370$	−13.7888	−	5.01872i	−0.716847	−	0.260911i
$371$	5.91235	+	2.15192i	0.306954	+	0.111722i
$372$	−5.23607	+	9.06914i	−0.271477	+	0.470213i
$373$	1.33688	+	2.31555i	0.0692211	+	0.119894i	0.898559	−	0.438853i	$-0.144615\pi$
$373$	1.33688	+	2.31555i	0.0692211	+	0.119894i	−0.829338	+	0.558748i	$0.811282\pi$
$374$	−1.20586	−	6.83877i	−0.0623535	−	0.353625i
$375$	−27.7157	−	23.2563i	−1.43124	−	1.20095i
$376$	−3.42585	+	2.87463i	−0.176675	+	0.148248i
$377$	1.31318	−	7.44742i	0.0676322	−	0.383562i
$378$	16.8097	−	6.11824i	0.864599	−	0.314688i
$379$	8.58359			0.440910			0.220455	−	0.975397i	$-0.429246\pi$
$379$	8.58359			0.440910			0.220455	+	0.975397i	$0.429246\pi$
$380$		0			0
$381$	49.8885			2.55587
$382$	−11.7200	+	4.26572i	−0.599646	+	0.218253i
$383$	−4.38220	+	24.8527i	−0.223920	+	1.26991i	0.640820	+	0.767692i	$0.278595\pi$
$383$	−4.38220	+	24.8527i	−0.223920	+	1.26991i	−0.864739	+	0.502221i	$0.832516\pi$
$384$	−2.47897	+	2.08010i	−0.126505	+	0.106150i
$385$	−1.61747	−	1.35722i	−0.0824339	−	0.0691702i
$386$	3.55495	+	20.1611i	0.180942	+	1.02617i
$387$	17.7984	+	30.8277i	0.904742	+	1.56706i
$388$	3.19098	−	5.52694i	0.161998	−	0.280588i
$389$	11.0868	+	4.03528i	0.562125	+	0.204597i	0.607426	−	0.794377i	$-0.292202\pi$
$389$	11.0868	+	4.03528i	0.562125	+	0.204597i	−0.0453003	+	0.998973i	$0.514424\pi$
$390$	15.2045	+	5.53400i	0.769912	+	0.280225i
$391$	2.14590	−	3.71680i	0.108523	−	0.187967i
$392$	2.73607	+	4.73901i	0.138192	+	0.239356i
$393$	2.51306	+	14.2523i	0.126767	+	0.718932i
$394$	−8.31472	−	6.97688i	−0.418890	−	0.351490i
$395$	−7.66044	+	6.42788i	−0.385439	+	0.323422i
$396$	1.60383	−	9.09575i	0.0805953	−	0.457079i
$397$	−21.0122	+	7.64780i	−1.05457	+	0.383832i	−0.810386	−	0.585897i	$-0.800742\pi$
$397$	−21.0122	+	7.64780i	−1.05457	+	0.383832i	−0.244185	+	0.969729i	$0.578520\pi$
$398$	1.52786			0.0765849
$399$		0			0
$400$	−3.09017			−0.154508
$401$	0.992060	−	0.361080i	0.0495411	−	0.0180315i	−0.317131	−	0.948382i	$-0.602719\pi$
$401$	0.992060	−	0.361080i	0.0495411	−	0.0180315i	0.366672	+	0.930350i	$0.380497\pi$
$402$	−0.959904	+	5.44388i	−0.0478756	+	0.271516i
$403$	8.96900	−	7.52589i	0.446778	−	0.374891i
$404$	−10.2512	−	8.60176i	−0.510015	−	0.427954i
$405$	−5.85935	−	33.2300i	−0.291153	−	1.65121i
$406$	1.29180	+	2.23746i	0.0641108	+	0.111043i
$407$	6.56231	−	11.3662i	0.325281	−	0.563404i
$408$	−17.0839	−	6.21804i	−0.845781	−	0.307839i
$409$	−16.2290	−	5.90686i	−0.802471	−	0.292076i	−0.0919609	−	0.995763i	$-0.529313\pi$
$409$	−16.2290	−	5.90686i	−0.802471	−	0.292076i	−0.710510	+	0.703687i	$0.751536\pi$
$410$	4.04508	−	7.00629i	0.199773	−	0.346016i
$411$	7.47214	+	12.9421i	0.368573	+	0.638388i
$412$	2.89167	+	16.3995i	0.142462	+	0.807945i
$413$	−8.02212	−	6.73136i	−0.394743	−	0.331229i
$414$	4.37274	−	3.66916i	0.214908	−	0.180330i
$415$	−2.03311	+	11.5303i	−0.0998014	+	0.566002i
$416$	3.39984	−	1.23744i	0.166691	−	0.0606705i
$417$	45.3050			2.21859
$418$		0			0
$419$	2.47214			0.120772			0.0603859	−	0.998175i	$-0.480767\pi$
$419$	2.47214			0.120772			0.0603859	+	0.998175i	$0.480767\pi$
$420$	−5.19449	+	1.89064i	−0.253465	+	0.0922538i
$421$	−4.35686	+	24.7090i	−0.212340	+	1.20424i	0.673122	+	0.739532i	$0.264953\pi$
$421$	−4.35686	+	24.7090i	−0.212340	+	1.20424i	−0.885462	+	0.464711i	$0.846158\pi$
$422$	2.11729	−	1.77662i	0.103068	−	0.0864846i
$423$	−25.5985	−	21.4797i	−1.24464	−	1.04438i
$424$	−0.883899	−	5.01284i	−0.0429259	−	0.243445i
$425$	−8.68034	−	15.0348i	−0.421058	−	0.729294i
$426$	24.1803	−	41.8816i	1.17154	−	2.02917i
$427$	−4.20243	−	1.52956i	−0.203370	−	0.0740206i
$428$	−16.3661	−	5.95676i	−0.791084	−	0.287931i
$429$	−7.23607	+	12.5332i	−0.349361	+	0.605110i
$430$	−3.29180	−	5.70156i	−0.158745	−	0.274954i
$431$	4.28086	+	24.2779i	0.206202	+	1.16943i	0.895538	+	0.444986i	$0.146791\pi$
$431$	4.28086	+	24.2779i	0.206202	+	1.16943i	−0.689336	+	0.724442i	$0.742098\pi$
$432$	−11.0863	−	9.30251i	−0.533390	−	0.447567i
$433$	−3.09056	+	2.59329i	−0.148523	+	0.124626i	−0.714022	−	0.700124i	$-0.753128\pi$
$433$	−3.09056	+	2.59329i	−0.148523	+	0.124626i	0.565499	+	0.824749i	$0.308684\pi$
$434$	−0.694593	+	3.93923i	−0.0333415	+	0.189089i
$435$	8.78380	−	3.19704i	0.421151	−	0.153286i
$436$	−18.0344			−0.863693
$437$		0			0
$438$	10.9443			0.522938
$439$	23.2705	−	8.46976i	1.11064	−	0.404240i	0.279412	−	0.960171i	$-0.409861\pi$
$439$	23.2705	−	8.46976i	1.11064	−	0.404240i	0.831228	+	0.555932i	$0.187638\pi$
$440$	−0.296626	+	1.68225i	−0.0141411	+	0.0801982i
$441$	−31.3224	+	26.2826i	−1.49154	+	1.25155i
$442$	15.5708	+	13.0655i	0.740628	+	0.621460i
$443$	0.827248	+	4.69156i	0.0393037	+	0.222903i	0.998133	−	0.0610813i	$-0.0194549\pi$
$443$	0.827248	+	4.69156i	0.0393037	+	0.222903i	−0.958829	+	0.283984i	$0.908344\pi$
$444$	−17.1803	−	29.7572i	−0.815343	−	1.41222i
$445$	−1.48278	+	2.56825i	−0.0702905	+	0.121747i
$446$	13.4299	+	4.88808i	0.635924	+	0.231457i
$447$	−5.80762	−	2.11380i	−0.274691	−	0.0999793i
$448$	−0.618034	+	1.07047i	−0.0291994	+	0.0505748i
$449$	0.899187	+	1.55744i	0.0424353	+	0.0735000i	0.886463	−	0.462800i	$-0.153155\pi$
$449$	0.899187	+	1.55744i	0.0424353	+	0.0735000i	−0.844028	+	0.536300i	$0.819822\pi$
$450$	−4.00957	−	22.7394i	−0.189013	−	1.07194i
$451$	5.54315	+	4.65125i	0.261017	+	0.219019i
$452$	2.40990	−	2.02214i	0.113352	−	0.0951137i
$453$	3.10631	−	17.6168i	0.145947	−	0.827708i
$454$	8.40487	−	3.05912i	0.394460	−	0.143572i
$455$	6.18034			0.289739
$456$		0			0
$457$	−26.2148			−1.22628			−0.613138	−	0.789976i	$-0.710093\pi$
$457$	−26.2148			−1.22628			−0.613138	+	0.789976i	$0.710093\pi$
$458$	−6.21892	+	2.26350i	−0.290591	+	0.105766i
$459$	14.1185	−	80.0697i	0.658993	−	3.73734i
$460$	−0.808735	+	0.678609i	−0.0377074	+	0.0316403i
$461$	−4.14921	−	3.48160i	−0.193248	−	0.162154i	0.541030	−	0.841003i	$-0.318035\pi$
$461$	−4.14921	−	3.48160i	−0.193248	−	0.162154i	−0.734278	+	0.678849i	$0.762479\pi$
$462$	−0.858564	−	4.86916i	−0.0399440	−	0.226534i
$463$	11.4721	+	19.8703i	0.533155	+	0.923452i	0.999250	+	0.0387174i	$0.0123272\pi$
$463$	11.4721	+	19.8703i	0.533155	+	0.923452i	−0.466095	+	0.884735i	$0.654339\pi$
$464$	1.04508	−	1.81014i	0.0485169	−	0.0840337i
$465$	13.5994	+	4.94976i	0.630655	+	0.229540i
$466$	17.4429	+	6.34868i	0.808025	+	0.294097i
$467$	−14.6525	+	25.3788i	−0.678036	+	1.17439i	0.297536	+	0.954711i	$0.403835\pi$
$467$	−14.6525	+	25.3788i	−0.678036	+	1.17439i	−0.975572	+	0.219682i	$0.929498\pi$
$468$	13.5172	+	23.4125i	0.624834	+	1.08224i
$469$	0.366651	+	2.07938i	0.0169303	+	0.0960168i
$470$	4.73442	+	3.97265i	0.218382	+	0.183244i
$471$	−28.8008	+	24.1667i	−1.32707	+	1.11354i
$472$	−1.47117	+	8.34343i	−0.0677161	+	0.384037i
$473$	5.53342	−	2.01400i	0.254427	−	0.0926038i
$474$	−23.4164			−1.07555
$475$		0			0
$476$	−6.94427			−0.318290
$477$	35.7407	−	13.0085i	1.63645	−	0.595620i
$478$	1.35787	−	7.70086i	0.0621075	−	0.352229i
$479$	−4.37274	+	3.66916i	−0.199795	+	0.167648i	−0.737196	−	0.675679i	$-0.763851\pi$
$479$	−4.37274	+	3.66916i	−0.199795	+	0.167648i	0.537401	+	0.843327i	$0.319406\pi$
$480$	3.42585	+	2.87463i	0.156368	+	0.131208i
$481$	6.67094	+	37.8328i	0.304169	+	1.72503i
$482$	0.708204	+	1.22665i	0.0322578	+	0.0558722i
$483$	1.52786	−	2.64634i	0.0695202	−	0.120413i
$484$	8.90090	+	3.23966i	0.404586	+	0.147257i
$485$	−8.28777	−	3.01650i	−0.376328	−	0.136972i
$486$	17.7984	−	30.8277i	0.807351	−	1.39837i
$487$	7.38197	+	12.7859i	0.334509	+	0.579386i	0.983390	−	0.181503i	$-0.0580963\pi$
$487$	7.38197	+	12.7859i	0.334509	+	0.579386i	−0.648882	+	0.760889i	$0.724763\pi$
$488$	0.628265	+	3.56307i	0.0284402	+	0.161293i
$489$	51.1969	+	42.9593i	2.31520	+	1.94269i
$490$	5.79306	−	4.86096i	0.261704	−	0.219596i
$491$	−1.81847	+	10.3130i	−0.0820663	+	0.465421i	0.915885	+	0.401441i	$0.131491\pi$
$491$	−1.81847	+	10.3130i	−0.0820663	+	0.465421i	−0.997951	+	0.0639800i	$0.979621\pi$
$492$	17.8018	−	6.47932i	0.802567	−	0.292110i
$493$	11.7426			0.528862
$494$		0			0
$495$	−12.7639			−0.573696
$496$	3.04091	−	1.10680i	0.136541	−	0.0496968i
$497$	3.20765	−	18.1915i	0.143883	−	0.816000i
$498$	−21.0022	+	17.6229i	−0.941130	+	0.789702i
$499$	20.9168	+	17.5513i	0.936365	+	0.785703i	0.976949	−	0.213473i	$-0.0684774\pi$
$499$	20.9168	+	17.5513i	0.936365	+	0.785703i	−0.0405842	+	0.999176i	$0.512922\pi$
$500$	1.94145	+	11.0105i	0.0868241	+	0.492404i
$501$	5.70820	+	9.88690i	0.255024	+	0.441714i
$502$	7.85410	−	13.6037i	0.350546	−	0.607163i
$503$	−10.5585	−	3.84296i	−0.470778	−	0.171349i	0.0957267	−	0.995408i	$-0.469483\pi$
$503$	−10.5585	−	3.84296i	−0.470778	−	0.171349i	−0.566505	+	0.824058i	$0.691705\pi$
$504$	−8.67906	−	3.15892i	−0.386596	−	0.140710i
$505$	−9.24671	+	16.0158i	−0.411473	+	0.712693i
$506$	−0.472136	−	0.817763i	−0.0209890	−	0.0363540i
$507$	−0.0506699	−	0.287363i	−0.00225033	−	0.0127622i
$508$	−11.8097	−	9.90948i	−0.523969	−	0.439662i
$509$	13.5490	−	11.3689i	0.600547	−	0.503919i	−0.291074	−	0.956700i	$-0.594013\pi$
$509$	13.5490	−	11.3689i	0.600547	−	0.503919i	0.891622	+	0.452781i	$0.149568\pi$
$510$	−4.36284	+	24.7429i	−0.193190	+	1.09563i
$511$	3.92823	−	1.42976i	0.173775	−	0.0632489i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−20.6180			−0.909422
$515$	21.6253	−	7.87096i	0.952924	−	0.346836i
$516$	2.67703	−	15.1822i	0.117850	−	0.668359i
$517$	−4.23459	+	3.55324i	−0.186237	+	0.156271i
$518$	−10.0540	−	8.43634i	−0.441749	−	0.370671i
$519$	−8.05045	−	45.6564i	−0.353375	−	2.00409i
$520$	−2.50000	−	4.33013i	−0.109632	−	0.189889i
$521$	14.1353	−	24.4830i	0.619277	−	1.07262i	−0.370341	−	0.928896i	$-0.620759\pi$
$521$	14.1353	−	24.4830i	0.619277	−	1.07262i	0.989618	−	0.143723i	$-0.0459074\pi$
$522$	14.6762	+	5.34168i	0.642358	+	0.233799i
$523$	−3.75877	−	1.36808i	−0.164360	−	0.0598220i	0.258530	−	0.966003i	$-0.416762\pi$
$523$	−3.75877	−	1.36808i	−0.164360	−	0.0598220i	−0.422889	+	0.906181i	$0.638984\pi$
$524$	2.23607	−	3.87298i	0.0976831	−	0.169192i
$525$	−6.18034	−	10.7047i	−0.269732	−	0.467190i
$526$	−2.59505	−	14.7172i	−0.113149	−	0.641702i
$527$	13.9269	+	11.6861i	0.606667	+	0.509054i
$528$	−3.06418	+	2.57115i	−0.133351	+	0.111895i
$529$	−3.89257	+	22.0759i	−0.169242	+	0.959820i
$530$	−6.61021	+	2.40592i	−0.287129	+	0.104507i
$531$	−63.3050			−2.74720
$532$		0			0
$533$	−21.1803			−0.917422
$534$	−6.52548	+	2.37508i	−0.282385	+	0.102780i
$535$	−4.17952	+	23.7032i	−0.180696	+	1.02478i
$536$	1.30856	−	1.09801i	0.0565212	−	0.0474269i
$537$	8.46918	+	7.10649i	0.365472	+	0.306667i
$538$	0.230299	+	1.30609i	0.00992889	+	0.0563095i
$539$	3.38197	+	5.85774i	0.145672	+	0.252311i
$540$	−10.0000	+	17.3205i	−0.430331	+	0.745356i
$541$	22.9116	+	8.33912i	0.985045	+	0.358527i	0.783799	−	0.621014i	$-0.213279\pi$
$541$	22.9116	+	8.33912i	0.985045	+	0.358527i	0.201245	+	0.979541i	$0.435501\pi$
$542$	−24.4320	−	8.89252i	−1.04944	−	0.381967i
$543$	34.6525	−	60.0198i	1.48708	−	2.57570i
$544$	2.80902	+	4.86536i	0.120436	+	0.208601i
$545$	4.32783	+	24.5443i	0.185384	+	1.05136i
$546$	11.0863	+	9.30251i	0.474450	+	0.398111i
$547$	−17.5763	+	14.7483i	−0.751510	+	0.630592i	−0.935902	−	0.352261i	$-0.885413\pi$
$547$	−17.5763	+	14.7483i	−0.751510	+	0.630592i	0.184392	+	0.982853i	$0.440968\pi$
$548$	0.801913	−	4.54788i	0.0342560	−	0.194276i
$549$	−25.4041	+	9.24632i	−1.08422	+	0.394623i
$550$	−3.81966			−0.162871
$551$		0			0
$552$	−2.47214			−0.105221
$553$	−8.40487	+	3.05912i	−0.357411	+	0.130087i
$554$	0.189306	−	1.07361i	0.00804284	−	0.0456132i
$555$	−36.3758	+	30.5230i	−1.54407	+	1.29563i
$556$	−10.7246	−	8.99903i	−0.454825	−	0.381644i
$557$	3.98423	+	22.5957i	0.168817	+	0.957410i	0.945041	+	0.326953i	$0.106022\pi$
$557$	3.98423	+	22.5957i	0.168817	+	0.957410i	−0.776223	+	0.630458i	$0.782867\pi$
$558$	12.0902	+	20.9408i	0.511818	+	0.886494i
$559$	−8.61803	+	14.9269i	−0.364504	+	0.631339i
$560$	1.60519	+	0.584240i	0.0678315	+	0.0246887i
$561$	−21.1169	−	7.68592i	−0.891556	−	0.324500i
$562$	−12.9894	+	22.4982i	−0.547923	+	0.949030i
$563$	19.8541	+	34.3883i	0.836751	+	1.44929i	0.892597	+	0.450855i	$0.148881\pi$
$563$	19.8541	+	34.3883i	0.836751	+	1.44929i	−0.0558464	+	0.998439i	$0.517786\pi$
$564$	2.51306	+	14.2523i	0.105819	+	0.600129i
$565$	−3.33040	−	2.79453i	−0.140111	−	0.117567i
$566$	10.3629	−	8.69554i	0.435587	−	0.365501i
$567$	5.24076	−	29.7218i	0.220091	−	1.24820i
$568$	−14.0430	+	5.11124i	−0.589232	+	0.214463i
$569$	−19.0902			−0.800302			−0.400151	−	0.916449i	$-0.631042\pi$
$569$	−19.0902			−0.800302			−0.400151	+	0.916449i	$0.631042\pi$
$570$		0			0
$571$	34.5410			1.44550			0.722748	−	0.691111i	$-0.242879\pi$
$571$	34.5410			1.44550			0.722748	+	0.691111i	$0.242879\pi$
$572$	4.20243	−	1.52956i	0.175713	−	0.0639541i
$573$	−7.00856	+	39.7475i	−0.292787	+	1.66048i
$574$	5.54315	−	4.65125i	0.231367	−	0.194140i
$575$	−1.80839	−	1.51742i	−0.0754149	−	0.0632806i
$576$	1.29752	+	7.35862i	0.0540634	+	0.306609i
$577$	9.46149	+	16.3878i	0.393887	+	0.682232i	0.992958	−	0.118463i	$-0.0377968\pi$
$577$	9.46149	+	16.3878i	0.393887	+	0.682232i	−0.599071	+	0.800696i	$0.704463\pi$
$578$	−7.28115	+	12.6113i	−0.302856	+	0.524562i
$579$	62.2539	+	22.6586i	2.58718	+	0.941658i
$580$	−2.71434	−	0.987940i	−0.112707	−	0.0410220i
$581$	−5.23607	+	9.06914i	−0.217229	+	0.376251i
$582$	−10.3262	−	17.8856i	−0.428036	−	0.741381i
$583$	−1.09256	−	6.19621i	−0.0452492	−	0.256621i
$584$	−2.59074	−	2.17389i	−0.107205	−	0.0899560i
$585$	28.6199	−	24.0150i	1.18329	−	0.992897i
$586$	−0.877918	+	4.97892i	−0.0362665	+	0.205677i
$587$	−40.5239	+	14.7495i	−1.67260	+	0.608776i	−0.992266	−	0.124127i	$-0.960387\pi$
$587$	−40.5239	+	14.7495i	−1.67260	+	0.608776i	−0.680333	+	0.732903i	$0.738165\pi$
$588$	17.7082			0.730274
$589$		0			0
$590$	11.7082			0.482019
$591$	−33.0063	+	12.0133i	−1.35770	+	0.494162i
$592$	−1.84380	+	10.4567i	−0.0757798	+	0.429769i
$593$	22.9223	−	19.2341i	0.941308	−	0.789851i	−0.0365048	−	0.999333i	$-0.511622\pi$
$593$	22.9223	−	19.2341i	0.941308	−	0.789851i	0.977812	+	0.209483i	$0.0671780\pi$
$594$	−13.7034	−	11.4985i	−0.562258	−	0.471791i
$595$	1.66646	+	9.45095i	0.0683181	+	0.387451i
$596$	0.954915	+	1.65396i	0.0391148	+	0.0677489i
$597$	2.47214	−	4.28187i	0.101178	−	0.175245i
$598$	2.59725	+	0.945320i	0.106209	+	0.0386570i
$599$	1.05679	+	0.384640i	0.0431792	+	0.0157160i	0.363519	−	0.931587i	$-0.381575\pi$
$599$	1.05679	+	0.384640i	0.0431792	+	0.0157160i	−0.320340	+	0.947303i	$0.603797\pi$
$600$	−5.00000	+	8.66025i	−0.204124	+	0.353553i
$601$	3.76393	+	6.51932i	0.153534	+	0.265929i	0.932524	−	0.361107i	$-0.117601\pi$
$601$	3.76393	+	6.51932i	0.153534	+	0.265929i	−0.778990	+	0.627036i	$0.784268\pi$
$602$	−1.02253	−	5.79908i	−0.0416754	−	0.236353i
$603$	9.77774	+	8.20450i	0.398180	+	0.334113i
$604$	−4.23459	+	3.55324i	−0.172303	+	0.144579i
$605$	2.27308	−	12.8913i	0.0924140	−	0.524106i
$606$	−40.6933	+	14.8112i	−1.65305	+	0.601662i
$607$	−23.7771			−0.965082			−0.482541	−	0.875873i	$-0.660286\pi$
$607$	−23.7771			−0.965082			−0.482541	+	0.875873i	$0.660286\pi$
$608$		0			0
$609$	8.36068			0.338792
$610$	4.69846	−	1.71010i	0.190235	−	0.0692400i
$611$	2.80969	−	15.9345i	0.113668	−	0.644642i
$612$	−32.1576	+	26.9834i	−1.29989	+	1.09074i
$613$	8.13389	+	6.82514i	0.328525	+	0.275665i	0.792098	−	0.610393i	$-0.208989\pi$
$613$	8.13389	+	6.82514i	0.328525	+	0.275665i	−0.463574	+	0.886058i	$0.653433\pi$
$614$	0.296626	+	1.68225i	0.0119709	+	0.0678902i
$615$	−13.0902	−	22.6728i	−0.527847	−	0.914257i
$616$	−0.763932	+	1.32317i	−0.0307797	+	0.0533120i
$617$	−23.5447	−	8.56956i	−0.947873	−	0.344998i	−0.178603	−	0.983921i	$-0.557158\pi$
$617$	−23.5447	−	8.56956i	−0.947873	−	0.344998i	−0.769270	+	0.638924i	$0.779380\pi$
$618$	50.6387	+	18.4310i	2.03699	+	0.741402i
$619$	11.1803	−	19.3649i	0.449376	−	0.778342i	−0.548970	−	0.835842i	$-0.684980\pi$
$619$	11.1803	−	19.3649i	0.449376	−	0.778342i	0.998345	+	0.0575005i	$0.0183131\pi$
$620$	−2.23607	−	3.87298i	−0.0898027	−	0.155543i
$621$	−1.91981	−	10.8878i	−0.0770392	−	0.436911i
$622$	20.5024	+	17.2035i	0.822070	+	0.689798i
$623$	−2.03191	+	1.70498i	−0.0814069	+	0.0683085i
$624$	2.03311	−	11.5303i	0.0813895	−	0.461583i
$625$		0			0
$626$	22.5066			0.899544
$627$		0			0
$628$	11.6180			0.463610
$629$	−56.0550	+	20.4023i	−2.23506	+	0.813495i
$630$	−2.21643	+	12.5700i	−0.0883048	+	0.500802i
$631$	6.98986	−	5.86519i	0.278262	−	0.233489i	−0.492966	−	0.870049i	$-0.664087\pi$
$631$	6.98986	−	5.86519i	0.278262	−	0.233489i	0.771228	+	0.636559i	$0.219643\pi$
$632$	5.54315	+	4.65125i	0.220495	+	0.185017i
$633$	−1.55316	−	8.80839i	−0.0617324	−	0.350102i
$634$	−7.16312	−	12.4069i	−0.284484	−	0.492740i
$635$	−10.6525	+	18.4506i	−0.422731	+	0.732191i
$636$	−15.4787	−	5.63380i	−0.613772	−	0.223395i
$637$	−18.6044	−	6.77144i	−0.737133	−	0.268294i
$638$	1.29180	−	2.23746i	0.0511427	−	0.0885817i
$639$	−55.8328	−	96.7053i	−2.20871	−	3.82560i
$640$	−0.239976	−	1.36097i	−0.00948588	−	0.0537971i
$641$	−15.5281	−	13.0296i	−0.613324	−	0.514640i	0.282373	−	0.959305i	$-0.408878\pi$
$641$	−15.5281	−	13.0296i	−0.613324	−	0.514640i	−0.895697	+	0.444665i	$0.853323\pi$
$642$	−43.1748	+	36.2279i	−1.70397	+	1.42980i
$643$	2.57569	−	14.6075i	0.101575	−	0.576062i	−0.890958	−	0.454086i	$-0.849966\pi$
$643$	2.57569	−	14.6075i	0.101575	−	0.576062i	0.992533	−	0.121976i	$-0.0389231\pi$
$644$	−0.887325	+	0.322960i	−0.0349655	+	0.0127264i
$645$	−21.3050			−0.838882
$646$		0			0
$647$	−32.0689			−1.26076			−0.630379	−	0.776288i	$-0.717100\pi$
$647$	−32.0689			−1.26076			−0.630379	+	0.776288i	$0.717100\pi$
$648$	−22.9439	+	8.35090i	−0.901322	+	0.328054i
$649$	−1.81847	+	10.3130i	−0.0713811	+	0.404822i
$650$	8.56464	−	7.18658i	0.335933	−	0.281881i
$651$	9.91589	+	8.32042i	0.388634	+	0.326103i
$652$	−3.58626	−	20.3387i	−0.140449	−	0.796526i
$653$	−19.1976	−	33.2512i	−0.751259	−	1.30122i	−0.947213	−	0.320605i	$-0.896114\pi$
$653$	−19.1976	−	33.2512i	−0.751259	−	1.30122i	0.195954	−	0.980613i	$-0.437220\pi$
$654$	−29.1803	+	50.5418i	−1.14104	+	1.97634i
$655$	−5.80762	−	2.11380i	−0.226922	−	0.0825930i
$656$	−5.50106	−	2.00222i	−0.214780	−	0.0781736i
$657$	12.6353	−	21.8849i	0.492948	−	0.853811i
$658$	2.76393	+	4.78727i	0.107749	+	0.186627i
$659$	−3.21961	−	18.2593i	−0.125418	−	0.711283i	−0.981059	−	0.193712i	$-0.937947\pi$
$659$	−3.21961	−	18.2593i	−0.125418	−	0.711283i	0.855640	−	0.517571i	$-0.173164\pi$
$660$	4.23459	+	3.55324i	0.164831	+	0.138310i
$661$	−4.14921	+	3.48160i	−0.161386	+	0.135419i	−0.719904	−	0.694073i	$-0.755814\pi$
$661$	−4.14921	+	3.48160i	−0.161386	+	0.135419i	0.558519	+	0.829492i	$0.311370\pi$
$662$	−2.13445	+	12.1051i	−0.0829577	+	0.470476i
$663$	61.8102	−	22.4971i	2.40051	−	0.873715i
$664$	8.47214			0.328783
$665$		0			0
$666$	−79.3394			−3.07434
$667$	1.50045	−	0.546120i	0.0580977	−	0.0211458i
$668$	0.612607	−	3.47427i	0.0237025	−	0.134423i
$669$	35.4290	−	29.7284i	1.36976	−	1.14937i
$670$	−1.80839	−	1.51742i	−0.0698640	−	0.0586229i
$671$	0.776578	+	4.40419i	0.0299795	+	0.170022i
$672$	2.00000	+	3.46410i	0.0771517	+	0.133631i
$673$	16.3090	−	28.2480i	0.628666	−	1.08888i	−0.359153	−	0.933279i	$-0.616934\pi$
$673$	16.3090	−	28.2480i	0.628666	−	1.08888i	0.987820	−	0.155604i	$-0.0497322\pi$
$674$	4.33953	+	1.57946i	0.167153	+	0.0608386i
$675$	−42.0243	−	15.2956i	−1.61752	−	0.588728i
$676$	−0.0450850	+	0.0780895i	−0.00173404	+	0.00300344i
$677$	−2.19098	−	3.79489i	−0.0842063	−	0.145850i	0.820846	−	0.571149i	$-0.193502\pi$
$677$	−2.19098	−	3.79489i	−0.0842063	−	0.145850i	−0.905053	+	0.425299i	$0.860169\pi$
$678$	−1.76780	−	10.0257i	−0.0678919	−	0.385034i
$679$	−6.04298	−	5.07066i	−0.231908	−	0.194594i
$680$	5.94752	−	4.99056i	0.228077	−	0.191379i
$681$	5.02612	−	28.5045i	0.192601	−	1.09230i
$682$	3.75877	−	1.36808i	0.143931	−	0.0523865i
$683$	−2.18034			−0.0834284			−0.0417142	−	0.999130i	$-0.513282\pi$
$683$	−2.18034			−0.0834284			−0.0417142	+	0.999130i	$0.513282\pi$
$684$		0			0
$685$	−6.38197			−0.243842
$686$	14.4867	−	5.27272i	0.553104	−	0.201313i
$687$	−3.71892	+	21.0910i	−0.141886	+	0.804674i
$688$	−3.64938	+	3.06220i	−0.139131	+	0.116745i
$689$	14.1078	+	11.8378i	0.537464	+	0.450986i
$690$	0.593253	+	3.36450i	0.0225848	+	0.128085i
$691$	−11.1803	−	19.3649i	−0.425320	−	0.736676i	0.571130	−	0.820860i	$-0.306505\pi$
$691$	−11.1803	−	19.3649i	−0.425320	−	0.736676i	−0.996450	+	0.0841834i	$0.973172\pi$
$692$	−7.16312	+	12.4069i	−0.272301	+	0.471639i
$693$	−10.7279	−	3.90464i	−0.407520	−	0.148325i
$694$	−26.9245	−	9.79972i	−1.02204	−	0.371992i
$695$	−9.67376	+	16.7554i	−0.366947	+	0.635570i
$696$	−3.38197	−	5.85774i	−0.128193	−	0.222037i
$697$	−5.71104	−	32.3889i	−0.216321	−	1.22682i
$698$	−16.7839	−	14.0834i	−0.635280	−	0.533063i
$699$	46.0154	−	38.6115i	1.74046	−	1.46042i
$700$	−0.663277	+	3.76163i	−0.0250695	+	0.142176i
$701$	37.2411	−	13.5547i	1.40658	−	0.511953i	0.476455	−	0.879199i	$-0.341922\pi$
$701$	37.2411	−	13.5547i	1.40658	−	0.511953i	0.930124	+	0.367246i	$0.119699\pi$
$702$	52.3607			1.97623
$703$		0			0
$704$	1.23607			0.0465861
$705$	18.7939	−	6.84040i	0.707817	−	0.257624i
$706$	3.25463	−	18.4579i	0.122489	−	0.694672i
$707$	−12.6712	+	10.6324i	−0.476548	+	0.399871i
$708$	21.0022	+	17.6229i	0.789311	+	0.662310i
$709$	3.14133	+	17.8153i	0.117975	+	0.669069i	0.985234	+	0.171212i	$0.0547684\pi$
$709$	3.14133	+	17.8153i	0.117975	+	0.669069i	−0.867259	+	0.497857i	$0.834120\pi$
$710$	10.3262	+	17.8856i	0.387537	+	0.671233i
$711$	−27.0344	+	46.8250i	−1.01387	+	1.75608i
$712$	2.01648	+	0.733940i	0.0755710	+	0.0275056i
$713$	2.32305	+	0.845520i	0.0869988	+	0.0316650i
$714$	−11.2361	+	19.4614i	−0.420499	+	0.728326i
$715$	−3.09017	−	5.35233i	−0.115566	−	0.200166i
$716$	−0.593253	−	3.36450i	−0.0221709	−	0.125737i
$717$	−19.3847	−	16.2657i	−0.723936	−	0.607454i
$718$	15.6826	−	13.1592i	0.585268	−	0.491098i
$719$	4.46418	−	25.3176i	0.166486	−	0.944189i	−0.781033	−	0.624490i	$-0.785307\pi$
$719$	4.46418	−	25.3176i	0.166486	−	0.944189i	0.947519	−	0.319699i	$-0.103582\pi$
$720$	9.70349	−	3.53178i	0.361628	−	0.131622i
$721$	20.5836			0.766573
$722$		0			0
$723$	4.58359			0.170466
$724$	−20.1248	+	7.32484i	−0.747934	+	0.272226i
$725$	1.12159	−	6.36085i	0.0416548	−	0.236236i
$726$	23.4812	−	19.7030i	0.871468	−	0.731248i
$727$	−10.0013	−	8.39206i	−0.370926	−	0.311244i	0.438201	−	0.898877i	$-0.355616\pi$
$727$	−10.0013	−	8.39206i	−0.370926	−	0.311244i	−0.809128	+	0.587633i	$0.800060\pi$
$728$	−0.776578	−	4.40419i	−0.0287819	−	0.163230i
$729$	−20.9721	−	36.3248i	−0.776746	−	1.34536i
$730$	−2.33688	+	4.04760i	−0.0864918	+	0.149808i
$731$	−25.1499	−	9.15380i	−0.930202	−	0.338566i
$732$	11.0021	+	4.00444i	0.406650	+	0.148008i
$733$	−5.04508	+	8.73834i	−0.186344	+	0.322758i	−0.944029	−	0.329863i	$-0.892997\pi$
$733$	−5.04508	+	8.73834i	−0.186344	+	0.322758i	0.757684	+	0.652621i	$0.226331\pi$
$734$	17.4164	+	30.1661i	0.642851	+	1.11345i
$735$	−4.24954	−	24.1003i	−0.156747	−	0.888955i
$736$	0.585206	+	0.491046i	0.0215710	+	0.0181002i
$737$	1.61747	−	1.35722i	0.0595802	−	0.0499938i
$738$	7.59583	−	43.0781i	0.279606	−	1.58573i
$739$	29.2476	−	10.6452i	1.07589	−	0.391592i	0.257513	−	0.966275i	$-0.417097\pi$
$739$	29.2476	−	10.6452i	1.07589	−	0.391592i	0.818376	+	0.574683i	$0.194875\pi$
$740$	14.6738			0.539418
$741$		0			0
$742$	−6.29180			−0.230979
$743$	39.3624	−	14.3267i	1.44406	−	0.525597i	0.503138	−	0.864206i	$-0.332179\pi$
$743$	39.3624	−	14.3267i	1.44406	−	0.525597i	0.940927	+	0.338610i	$0.109957\pi$
$744$	1.81847	−	10.3130i	0.0666682	−	0.378094i
$745$	2.02184	−	1.69652i	0.0740744	−	0.0621558i
$746$	−2.04822	−	1.71866i	−0.0749907	−	0.0629247i
$747$	10.9928	+	62.3432i	0.402205	+	2.28102i
$748$	3.47214	+	6.01392i	0.126954	+	0.219891i
$749$	−10.7639	+	18.6437i	−0.393306	+	0.681225i
$750$	33.9984	+	12.3744i	1.24145	+	0.451849i
$751$	32.0143	+	11.6522i	1.16822	+	0.425196i	0.852026	−	0.523499i	$-0.175374\pi$
$751$	32.0143	+	11.6522i	1.16822	+	0.425196i	0.316191	+	0.948695i	$0.397596\pi$
$752$	2.23607	−	3.87298i	0.0815410	−	0.141233i
$753$	−25.4164	−	44.0225i	−0.926225	−	1.60427i
$754$	1.31318	+	7.44742i	0.0478232	+	0.271219i
$755$	5.85206	+	4.91046i	0.212978	+	0.178710i
$756$	−13.7034	+	11.4985i	−0.498389	+	0.418198i
$757$	4.26520	−	24.1891i	0.155021	−	0.879170i	−0.803745	−	0.594974i	$-0.797162\pi$
$757$	4.26520	−	24.1891i	0.155021	−	0.879170i	0.958766	−	0.284196i	$-0.0917265\pi$
$758$	−8.06594	+	2.93576i	−0.292968	+	0.106632i
$759$	−3.05573			−0.110916
$760$		0			0
$761$	−18.3607			−0.665574			−0.332787	−	0.943002i	$-0.607989\pi$
$761$	−18.3607			−0.665574			−0.332787	+	0.943002i	$0.607989\pi$
$762$	−46.8799	+	17.0629i	−1.69828	+	0.618123i
$763$	−3.87093	+	21.9531i	−0.140137	+	0.794757i
$764$	9.55421	−	8.01693i	0.345659	−	0.290043i
$765$	44.4407	+	37.2901i	1.60676	+	1.34823i
$766$	−4.38220	−	24.8527i	−0.158335	−	0.897964i
$767$	−15.3262	−	26.5458i	−0.553398	−	0.958514i
$768$	1.61803	−	2.80252i	0.0583858	−	0.101127i
$769$	3.51694	+	1.28006i	0.126824	+	0.0461602i	0.404653	−	0.914471i	$-0.367392\pi$
$769$	3.51694	+	1.28006i	0.126824	+	0.0461602i	−0.277829	+	0.960631i	$0.589615\pi$
$770$	1.98412	+	0.722161i	0.0715027	+	0.0260249i
$771$	−33.3607	+	57.7824i	−1.20146	+	2.08098i
$772$	−10.2361	−	17.7294i	−0.368404	−	0.638095i
$773$	2.57939	+	14.6284i	0.0927741	+	0.526148i	0.995407	+	0.0957363i	$0.0305206\pi$
$773$	2.57939	+	14.6284i	0.0927741	+	0.526148i	−0.902633	+	0.430412i	$0.858368\pi$
$774$	−27.2687	−	22.8811i	−0.980153	−	0.822446i
$775$	7.66044	−	6.42788i	0.275171	−	0.230896i
$776$	−1.10822	+	6.28501i	−0.0397827	+	0.225619i
$777$	−39.9108	+	14.5263i	−1.43179	+	0.521129i
$778$	−11.7984			−0.422992
$779$		0			0
$780$	−16.1803			−0.579349
$781$	−17.3581	+	6.31784i	−0.621123	+	0.226070i
$782$	−0.745263	+	4.22659i	−0.0266505	+	0.151143i
$783$	23.1722	−	19.4438i	0.828109	−	0.694866i
$784$	−4.19190	−	3.51742i	−0.149711	−	0.125622i
$785$	−2.78805	−	15.8118i	−0.0995097	−	0.564348i
$786$	−7.23607	−	12.5332i	−0.258102	−	0.447046i
$787$	9.76393	−	16.9116i	0.348047	−	0.602834i	−0.637856	−	0.770156i	$-0.720178\pi$
$787$	9.76393	−	16.9116i	0.348047	−	0.602834i	0.985902	+	0.167321i	$0.0535118\pi$
$788$	10.1995	+	3.71232i	0.363343	+	0.132246i
$789$	−45.4442	−	16.5403i	−1.61786	−	0.588851i
$790$	5.00000	−	8.66025i	0.177892	−	0.308118i
$791$	−1.94427	−	3.36758i	−0.0691304	−	0.119737i
$792$	1.60383	+	9.09575i	0.0569895	+	0.323203i
$793$	−10.0277	−	8.41420i	−0.356092	−	0.298797i
$794$	17.1293	−	14.3732i	0.607895	−	0.510085i
$795$	−3.95292	+	22.4181i	−0.140195	+	0.795088i
$796$	−1.43572	+	0.522560i	−0.0508878	+	0.0185217i
$797$	−48.5623			−1.72017			−0.860083	−	0.510155i	$-0.829588\pi$
$797$	−48.5623			−1.72017			−0.860083	+	0.510155i	$0.829588\pi$
$798$		0			0
$799$	25.1246			0.888845
$800$	2.90381	−	1.05690i	0.102665	−	0.0373671i
$801$	−2.78435	+	15.7908i	−0.0983802	+	0.557942i
$802$	−0.808735	+	0.678609i	−0.0285574	+	0.0239625i
$803$	−3.20233	−	2.68707i	−0.113008	−	0.0948247i
$804$	−0.959904	−	5.44388i	−0.0338532	−	0.191991i
$805$	0.652476	+	1.13012i	0.0229968	+	0.0398315i
$806$	−5.85410	+	10.1396i	−0.206202	+	0.357152i
$807$	4.03297	+	1.46788i	0.141967	+	0.0516718i
$808$	12.5749	+	4.57690i	0.442385	+	0.161015i
$809$	19.8713	−	34.4181i	0.698639	−	1.21008i	−0.270300	−	0.962776i	$-0.587123\pi$
$809$	19.8713	−	34.4181i	0.698639	−	1.21008i	0.968939	−	0.247301i	$-0.0795437\pi$
$810$	16.8713	+	29.2220i	0.592798	+	1.02676i
$811$	7.57050	+	42.9344i	0.265836	+	1.50763i	0.766644	+	0.642073i	$0.221925\pi$
$811$	7.57050	+	42.9344i	0.265836	+	1.50763i	−0.500808	+	0.865559i	$0.666964\pi$
$812$	−1.97915	−	1.66070i	−0.0694544	−	0.0582792i
$813$	−64.4533	+	54.0827i	−2.26047	+	1.89676i
$814$	−2.27906	+	12.9252i	−0.0798812	+	0.453029i
$815$	−26.8198	+	9.76160i	−0.939456	+	0.341934i
$816$	18.1803			0.636439
$817$		0			0
$818$	17.2705			0.603849
$819$	31.4012	−	11.4291i	1.09725	−	0.399365i
$820$	−1.40484	+	7.96726i	−0.0490593	+	0.278229i
$821$	−10.9318	+	9.17291i	−0.381524	+	0.320137i	−0.813300	−	0.581844i	$-0.802331\pi$
$821$	−10.9318	+	9.17291i	−0.381524	+	0.320137i	0.431776	+	0.901981i	$0.357887\pi$
$822$	−11.4480	−	9.60599i	−0.399294	−	0.335047i
$823$	5.70136	+	32.3340i	0.198737	+	1.12709i	0.906996	+	0.421140i	$0.138370\pi$
$823$	5.70136	+	32.3340i	0.198737	+	1.12709i	−0.708259	+	0.705953i	$0.750519\pi$
$824$	−8.32624	−	14.4215i	−0.290058	−	0.502396i
$825$	−6.18034	+	10.7047i	−0.215172	+	0.372689i
$826$	9.84059	+	3.58168i	0.342398	+	0.124623i
$827$	34.3373	+	12.4978i	1.19403	+	0.434590i	0.861135	−	0.508376i	$-0.169754\pi$
$827$	34.3373	+	12.4978i	1.19403	+	0.434590i	0.332890	+	0.942966i	$0.391976\pi$
$828$	−2.85410	+	4.94345i	−0.0991869	+	0.171797i
$829$	−21.6353	−	37.4734i	−0.751423	−	1.30150i	−0.947133	−	0.320842i	$-0.896034\pi$
$829$	−21.6353	−	37.4734i	−0.751423	−	1.30150i	0.195709	−	0.980662i	$-0.437299\pi$
$830$	−2.03311	−	11.5303i	−0.0705702	−	0.400224i
$831$	−2.70250	−	2.26767i	−0.0937487	−	0.0786645i
$832$	−2.77157	+	2.32563i	−0.0960871	+	0.0806266i
$833$	5.33840	−	30.2756i	0.184965	−	1.04899i
$834$	−42.5727	+	15.4952i	−1.47417	+	0.536555i
$835$	−4.87539			−0.168720
$836$		0			0
$837$	46.8328			1.61878
$838$	−2.32305	+	0.845520i	−0.0802484	+	0.0292080i
$839$	−3.82026	+	21.6658i	−0.131890	+	0.747985i	0.845085	+	0.534632i	$0.179550\pi$
$839$	−3.82026	+	21.6658i	−0.131890	+	0.747985i	−0.976975	+	0.213354i	$0.931561\pi$
$840$	4.23459	−	3.55324i	0.146107	−	0.122599i
$841$	−18.8686	−	15.8326i	−0.650641	−	0.545953i
$842$	−4.35686	−	24.7090i	−0.150147	−	0.851528i
$843$	42.0344	+	72.8058i	1.44774	+	2.50756i
$844$	−1.38197	+	2.39364i	−0.0475692	+	0.0823923i
$845$	0.117097	+	0.0426197i	0.00402825	+	0.00146616i
$846$	31.4012	+	11.4291i	1.07959	+	0.392940i
$847$	5.85410	−	10.1396i	0.201149	−	0.348401i
$848$	2.54508	+	4.40822i	0.0873986	+	0.151379i
$849$	−7.60181	−	43.1120i	−0.260893	−	1.47960i
$850$	13.2991	+	11.1592i	0.456154	+	0.382758i
$851$	−6.21374	+	5.21394i	−0.213004	+	0.178732i
$852$	−8.39774	+	47.6260i	−0.287702	+	1.63164i
$853$	16.8297	−	6.12552i	0.576239	−	0.209734i	−0.0374272	−	0.999299i	$-0.511916\pi$
$853$	16.8297	−	6.12552i	0.576239	−	0.209734i	0.613666	+	0.789565i	$0.289694\pi$
$854$	4.47214			0.153033
$855$		0			0
$856$	17.4164			0.595281
$857$	−13.6841	+	4.98060i	−0.467440	+	0.170134i	−0.564992	−	0.825096i	$-0.691121\pi$
$857$	−13.6841	+	4.98060i	−0.467440	+	0.170134i	0.0975525	+	0.995230i	$0.468899\pi$
$858$	2.51306	−	14.2523i	0.0857945	−	0.486565i
$859$	−23.0341	+	19.3279i	−0.785913	+	0.659460i	−0.944730	−	0.327848i	$-0.893676\pi$
$859$	−23.0341	+	19.3279i	−0.785913	+	0.659460i	0.158817	+	0.987308i	$0.449232\pi$
$860$	5.04332	+	4.23185i	0.171976	+	0.144305i
$861$	−4.06622	−	23.0607i	−0.138576	−	0.785905i
$862$	−12.3262	−	21.3497i	−0.419833	−	0.727173i
$863$	4.94427	−	8.56373i	0.168305	−	0.291513i	−0.769519	−	0.638624i	$-0.779504\pi$
$863$	4.94427	−	8.56373i	0.168305	−	0.291513i	0.937824	+	0.347111i	$0.112837\pi$
$864$	13.5994	+	4.94976i	0.462660	+	0.168394i
$865$	18.6044	+	6.77144i	0.632568	+	0.230236i
$866$	2.01722	−	3.49393i	0.0685480	−	0.118729i
$867$	23.5623	+	40.8111i	0.800218	+	1.38602i
$868$	−0.694593	−	3.93923i	−0.0235760	−	0.133706i
$869$	6.85171	+	5.74927i	0.232428	+	0.195031i
$870$	−7.16062	+	6.00847i	−0.242768	+	0.203706i
$871$	−1.07320	+	6.08645i	−0.0363642	+	0.206231i
$872$	16.9468	−	6.16814i	0.573892	−	0.208880i
$873$	−47.6869			−1.61396
$874$		0			0
$875$	13.8197			0.467190
$876$	−10.2843	+	3.74316i	−0.347473	+	0.126470i
$877$	7.07489	−	40.1237i	0.238902	−	1.35488i	−0.595337	−	0.803476i	$-0.702981\pi$
$877$	7.07489	−	40.1237i	0.238902	−	1.35488i	0.834239	−	0.551404i	$-0.185908\pi$
$878$	−18.9703	+	15.9179i	−0.640216	+	0.537205i
$879$	12.5330	+	10.5164i	0.422728	+	0.354711i
$880$	−0.296626	−	1.68225i	−0.00999928	−	0.0567087i
$881$	23.1074	+	40.0232i	0.778508	+	1.34842i	0.932802	+	0.360390i	$0.117356\pi$
$881$	23.1074	+	40.0232i	0.778508	+	1.34842i	−0.154294	+	0.988025i	$0.549310\pi$
$882$	20.4443	−	35.4105i	0.688394	−	1.19233i
$883$	37.7572	+	13.7425i	1.27063	+	0.462471i	0.887323	−	0.461149i	$-0.152563\pi$
$883$	37.7572	+	13.7425i	1.27063	+	0.462471i	0.383307	+	0.923621i	$0.374785\pi$
$884$	−19.1004	−	6.95198i	−0.642417	−	0.233820i
$885$	18.9443	−	32.8124i	0.636805	−	1.10298i
$886$	−2.38197	−	4.12569i	−0.0800237	−	0.138605i
$887$	1.90045	+	10.7780i	0.0638110	+	0.361890i	0.999947	+	0.0102531i	$0.00326371\pi$
$887$	1.90045	+	10.7780i	0.0638110	+	0.361890i	−0.936136	+	0.351637i	$0.885625\pi$
$888$	26.3218	+	22.0866i	0.883302	+	0.741178i
$889$	−14.5975	+	12.2488i	−0.489586	+	0.410811i
$890$	0.514964	−	2.92050i	0.0172616	−	0.0978955i
$891$	−28.3602	+	10.3223i	−0.950104	+	0.345810i
$892$	−14.2918			−0.478525
$893$		0			0
$894$	6.18034			0.206701
$895$	−4.43663	+	1.61480i	−0.148300	+	0.0539768i
$896$	0.214641	−	1.21729i	0.00717065	−	0.0406668i
$897$	6.85171	−	5.74927i	0.228772	−	0.191962i
$898$	−1.37763	−	1.15597i	−0.0459723	−	0.0385753i
$899$	1.17454	+	6.66117i	0.0391733	+	0.222163i
$900$	11.5451	+	19.9967i	0.384836	+	0.666556i
$901$	−14.2984	+	24.7655i	−0.476348	+	0.825059i
$902$	−6.79968	−	2.47488i	−0.226405	−	0.0824045i
$903$	−17.9065	−	6.51744i	−0.595892	−	0.216887i
$904$	−1.57295	+	2.72443i	−0.0523155	+	0.0906131i
$905$	14.7984	+	25.6315i	0.491915	+	0.852021i
$906$	3.10631	+	17.6168i	0.103200	+	0.585278i
$907$	10.5011	+	8.81146i	0.348683	+	0.292580i	0.800261	−	0.599652i	$-0.204694\pi$
$907$	10.5011	+	8.81146i	0.348683	+	0.292580i	−0.451578	+	0.892232i	$0.649139\pi$
$908$	−6.85171	+	5.74927i	−0.227382	+	0.190796i
$909$	−17.3634	+	98.4728i	−0.575908	+	3.26614i
$910$	−5.80762	+	2.11380i	−0.192521	+	0.0700718i
$911$	46.0689			1.52633			0.763165	−	0.646204i	$-0.223644\pi$
$911$	46.0689			1.52633			0.763165	+	0.646204i	$0.223644\pi$
$912$		0			0
$913$	10.4721			0.346577
$914$	24.6338	−	8.96598i	0.814815	−	0.296568i
$915$	2.80969	−	15.9345i	0.0928854	−	0.526779i
$916$	5.06971	−	4.25399i	0.167508	−	0.140556i
$917$	−4.23459	−	3.55324i	−0.139838	−	0.117338i
$918$	14.1185	+	80.0697i	0.465979	+	2.64270i
$919$	−5.05573	−	8.75678i	−0.166773	−	0.288859i	0.770510	−	0.637427i	$-0.220001\pi$
$919$	−5.05573	−	8.75678i	−0.166773	−	0.288859i	−0.937284	+	0.348568i	$0.886668\pi$
$920$	0.527864	−	0.914287i	0.0174032	−	0.0301432i
$921$	5.19449	+	1.89064i	0.171164	+	0.0622987i
$922$	5.08976	+	1.85252i	0.167622	+	0.0610095i
$923$	27.0344	−	46.8250i	0.889849	−	1.54126i
$924$	2.47214	+	4.28187i	0.0813273	+	0.140863i
$925$	5.69766	+	32.3130i	0.187338	+	1.06245i
$926$	−17.5763	−	14.7483i	−0.577594	−	0.484659i
$927$	95.3186	−	79.9818i	3.13067	−	2.62695i
$928$	−0.362954	+	2.05842i	−0.0119146	+	0.0675708i
$929$	−9.54639	+	3.47460i	−0.313207	+	0.113998i	−0.493841	−	0.869552i	$-0.664407\pi$
$929$	−9.54639	+	3.47460i	−0.313207	+	0.113998i	0.180634	+	0.983550i	$0.442185\pi$
$930$	−14.4721			−0.474560
$931$		0			0
$932$	−18.5623			−0.608029
$933$	81.3867	−	29.6223i	2.66448	−	0.969792i
$934$	5.08875	−	28.8597i	0.166509	−	0.944320i
$935$	7.35154	−	6.16867i	0.240421	−	0.201737i
$936$	−20.7096	−	17.3774i	−0.676914	−	0.567998i
$937$	−3.45361	−	19.5864i	−0.112825	−	0.639860i	−0.987804	−	0.155700i	$-0.950237\pi$
$937$	−3.45361	−	19.5864i	−0.112825	−	0.639860i	0.874980	−	0.484159i	$-0.160874\pi$
$938$	−1.05573	−	1.82857i	−0.0344707	−	0.0597051i
$939$	36.4164	−	63.0751i	1.18840	−	2.05838i
$940$	−5.80762	−	2.11380i	−0.189424	−	0.0689446i
$941$	24.4320	+	8.89252i	0.796461	+	0.289888i	0.708019	−	0.706193i	$-0.249589\pi$
$941$	24.4320	+	8.89252i	0.796461	+	0.289888i	0.0884417	+	0.996081i	$0.471811\pi$
$942$	18.7984	−	32.5597i	0.612484	−	1.06085i
$943$	−2.23607	−	3.87298i	−0.0728164	−	0.126122i
$944$	−1.47117	−	8.34343i	−0.0478825	−	0.271555i
$945$	18.9377	+	15.8906i	0.616042	+	0.516921i
$946$	−4.51089	+	3.78508i	−0.146662	+	0.123064i
$947$	−2.46239	+	13.9649i	−0.0800169	+	0.453799i	0.918304	+	0.395876i	$0.129559\pi$
$947$	−2.46239	+	13.9649i	−0.0800169	+	0.453799i	−0.998321	+	0.0579229i	$0.981552\pi$
$948$	22.0042	−	8.00888i	0.714664	−	0.260116i
$949$	12.2361			0.397200
$950$		0			0
$951$	−46.3607			−1.50335
$952$	6.52548	−	2.37508i	0.211492	−	0.0769768i
$953$	9.17063	−	52.0092i	0.297066	−	1.68474i	−0.361620	−	0.932325i	$-0.617776\pi$
$953$	9.17063	−	52.0092i	0.297066	−	1.68474i	0.658686	−	0.752418i	$-0.271113\pi$
$954$	−29.1361	+	24.4481i	−0.943315	+	0.791535i
$955$	−13.2036	−	11.0791i	−0.427258	−	0.358512i
$956$	1.35787	+	7.70086i	0.0439166	+	0.249064i
$957$	−4.18034	−	7.24056i	−0.135131	−	0.234054i
$958$	2.85410	−	4.94345i	0.0922118	−	0.159716i
$959$	−5.36396	−	1.95232i	−0.173211	−	0.0630437i
$960$	−4.20243	−	1.52956i	−0.135633	−	0.0493664i
$961$	10.2639	−	17.7777i	0.331095	−	0.573473i
$962$	−19.2082	−	33.2696i	−0.619297	−	1.07265i
$963$	22.5982	+	128.161i	0.728216	+	4.12992i
$964$	−1.08503	−	0.910449i	−0.0349465	−	0.0293236i
$965$	−21.6728	+	18.1856i	−0.697671	+	0.585416i
$966$	−0.530622	+	3.00930i	−0.0170725	+	0.0968228i
$967$	42.1291	−	15.3337i	1.35478	−	0.493099i	0.440343	−	0.897830i	$-0.354857\pi$
$967$	42.1291	−	15.3337i	1.35478	−	0.493099i	0.914436	+	0.404730i	$0.132635\pi$
$968$	−9.47214			−0.304446
$969$		0			0
$970$	8.81966			0.283182
$971$	−6.14655	+	2.23716i	−0.197252	+	0.0717939i	−0.438757	−	0.898606i	$-0.644581\pi$
$971$	−6.14655	+	2.23716i	−0.197252	+	0.0717939i	0.241505	+	0.970400i	$0.422359\pi$
$972$	−6.18131	+	35.0560i	−0.198266	+	1.12442i
$973$	−13.2564	+	11.1234i	−0.424979	+	0.356600i
$974$	−11.3098	−	9.49007i	−0.362390	−	0.304082i
$975$	−6.28265	−	35.6307i	−0.201206	−	1.14109i
$976$	−1.80902	−	3.13331i	−0.0579052	−	0.100295i
$977$	10.0172	−	17.3503i	0.320479	−	0.555086i	−0.660108	−	0.751171i	$-0.729489\pi$
$977$	10.0172	−	17.3503i	0.320479	−	0.555086i	0.980587	+	0.196085i	$0.0628227\pi$
$978$	−62.8023	−	22.8582i	−2.00820	−	0.730924i
$979$	2.49251	+	0.907200i	0.0796610	+	0.0289942i
$980$	−3.78115	+	6.54915i	−0.120785	+	0.209205i
$981$	67.3779	+	116.702i	2.15121	+	3.72601i
$982$	−1.81847	−	10.3130i	−0.0580296	−	0.329102i
$983$	22.6724	+	19.0244i	0.723138	+	0.606785i	0.928251	−	0.371953i	$-0.121312\pi$
$983$	22.6724	+	19.0244i	0.723138	+	0.606785i	−0.205113	+	0.978738i	$0.565756\pi$
$984$	−14.5122	+	12.1771i	−0.462631	+	0.388193i
$985$	2.60472	−	14.7721i	0.0829934	−	0.470679i
$986$	−11.0345	+	4.01622i	−0.351409	+	0.127903i
$987$	17.8885			0.569399
$988$		0			0
$989$	−3.63932			−0.115724
$990$	11.9942	−	4.36552i	0.381200	−	0.138745i
$991$	−0.113301	+	0.642563i	−0.00359913	+	0.0204117i	−0.986554	−	0.163433i	$-0.947743\pi$
$991$	−0.113301	+	0.642563i	−0.00359913	+	0.0204117i	0.982955	+	0.183845i	$0.0588544\pi$
$992$	−2.47897	+	2.08010i	−0.0787074	+	0.0660434i
$993$	30.4710	+	25.5682i	0.966968	+	0.811383i
$994$	3.20765	+	18.1915i	0.101741	+	0.576999i
$995$	1.05573	+	1.82857i	0.0334688	+	0.0579697i
$996$	13.7082	−	23.7433i	0.434361	−	0.752335i
$997$	−23.0287	−	8.38174i	−0.729325	−	0.265452i	−0.0494457	−	0.998777i	$-0.515745\pi$
$997$	−23.0287	−	8.38174i	−0.729325	−	0.265452i	−0.679879	+	0.733324i	$0.737968\pi$
$998$	−25.6583	−	9.33884i	−0.812198	−	0.295616i
$999$	−76.8328	+	133.078i	−2.43088	+	4.21041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.p.423.1		12
19.2	odd	18		722.2.a.h.1.2	✓	2
19.3	odd	18		722.2.c.i.653.1		4
19.4	even	9	inner	722.2.e.p.99.1		12
19.5	even	9		722.2.c.h.429.2		4
19.6	even	9	inner	722.2.e.p.389.1		12
19.7	even	3	inner	722.2.e.p.245.1		12
19.8	odd	6		722.2.e.q.415.1		12
19.9	even	9	inner	722.2.e.p.595.2		12
19.10	odd	18		722.2.e.q.595.1		12
19.11	even	3	inner	722.2.e.p.415.2		12
19.12	odd	6		722.2.e.q.245.2		12
19.13	odd	18		722.2.e.q.389.2		12
19.14	odd	18		722.2.c.i.429.1		4
19.15	odd	18		722.2.e.q.99.2		12
19.16	even	9		722.2.c.h.653.2		4
19.17	even	9		722.2.a.i.1.1	yes	2
19.18	odd	2		722.2.e.q.423.2		12
57.2	even	18		6498.2.a.bk.1.1		2
57.17	odd	18		6498.2.a.be.1.1		2
76.55	odd	18		5776.2.a.be.1.2		2
76.59	even	18		5776.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.h.1.2	✓	2	19.2	odd	18
722.2.a.i.1.1	yes	2	19.17	even	9
722.2.c.h.429.2		4	19.5	even	9
722.2.c.h.653.2		4	19.16	even	9
722.2.c.i.429.1		4	19.14	odd	18
722.2.c.i.653.1		4	19.3	odd	18
722.2.e.p.99.1		12	19.4	even	9	inner
722.2.e.p.245.1		12	19.7	even	3	inner
722.2.e.p.389.1		12	19.6	even	9	inner
722.2.e.p.415.2		12	19.11	even	3	inner
722.2.e.p.423.1		12	1.1	even	1	trivial
722.2.e.p.595.2		12	19.9	even	9	inner
722.2.e.q.99.2		12	19.15	odd	18
722.2.e.q.245.2		12	19.12	odd	6
722.2.e.q.389.2		12	19.13	odd	18
722.2.e.q.415.1		12	19.8	odd	6
722.2.e.q.423.2		12	19.18	odd	2
722.2.e.q.595.1		12	19.10	odd	18
5776.2.a.t.1.1		2	76.59	even	18
5776.2.a.be.1.2		2	76.55	odd	18
6498.2.a.be.1.1		2	57.17	odd	18
6498.2.a.bk.1.1		2	57.2	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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.561937 + 3.18690i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.05865 - 0.888311i) q^{5} +(-0.561937 - 3.18690i) q^{6} +(-0.618034 - 1.07047i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-7.02151 - 2.55562i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.561937 + 3.18690i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.05865 - 0.888311i) q^{5} +(-0.561937 - 3.18690i) q^{6} +(-0.618034 - 1.07047i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-7.02151 - 2.55562i) q^{9} +(1.29862 + 0.472660i) q^{10} +(-0.618034 + 1.07047i) q^{11} +(1.61803 + 2.80252i) q^{12} +(-0.628265 - 3.56307i) q^{13} +(0.946883 + 0.794529i) q^{14} +(3.42585 - 2.87463i) q^{15} +(0.173648 - 0.984808i) q^{16} +(5.27923 - 1.92148i) q^{17} +7.47214 q^{18} -1.38197 q^{20} +(3.75877 - 1.36808i) q^{21} +(0.214641 - 1.21729i) q^{22} +(0.585206 - 0.491046i) q^{23} +(-2.47897 - 2.08010i) q^{24} +(-0.536602 - 3.04322i) q^{25} +(1.80902 + 3.13331i) q^{26} +(7.23607 - 12.5332i) q^{27} +(-1.16152 - 0.422760i) q^{28} +(1.96412 + 0.714880i) q^{29} +(-2.23607 + 3.87298i) q^{30} +(1.61803 + 2.80252i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-3.06418 - 2.57115i) q^{33} +(-4.30366 + 3.61120i) q^{34} +(-0.296626 + 1.68225i) q^{35} +(-7.02151 + 2.55562i) q^{36} -10.6180 q^{37} +11.7082 q^{39} +(1.29862 - 0.472660i) q^{40} +(1.01655 - 5.76517i) q^{41} +(-3.06418 + 2.57115i) q^{42} +(-3.64938 - 3.06220i) q^{43} +(0.214641 + 1.21729i) q^{44} +(5.16312 + 8.94278i) q^{45} +(-0.381966 + 0.661585i) q^{46} +(4.20243 + 1.52956i) q^{47} +(3.04091 + 1.10680i) q^{48} +(2.73607 - 4.73901i) q^{49} +(1.54508 + 2.67617i) q^{50} +(3.15698 + 17.9041i) q^{51} +(-2.77157 - 2.32563i) q^{52} +(-3.89930 + 3.27190i) q^{53} +(-2.51306 + 14.2523i) q^{54} +(1.60519 - 0.584240i) q^{55} +1.23607 q^{56} -2.09017 q^{58} +(7.96120 - 2.89764i) q^{59} +(0.776578 - 4.40419i) q^{60} +(2.77157 - 2.32563i) q^{61} +(-2.47897 - 2.08010i) q^{62} +(1.60383 + 9.09575i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.50000 + 4.33013i) q^{65} +(3.75877 + 1.36808i) q^{66} +(-1.60519 - 0.584240i) q^{67} +(2.80902 - 4.86536i) q^{68} +(1.23607 + 2.14093i) q^{69} +(-0.296626 - 1.68225i) q^{70} +(11.4480 + 9.60599i) q^{71} +(5.72399 - 4.80300i) q^{72} +(-0.587272 + 3.33059i) q^{73} +(9.97769 - 3.63158i) q^{74} +10.0000 q^{75} +1.52786 q^{77} +(-11.0021 + 4.00444i) q^{78} +(1.25653 - 7.12614i) q^{79} +(-1.05865 + 0.888311i) q^{80} +(18.7041 + 15.6946i) q^{81} +(1.01655 + 5.76517i) q^{82} +(-4.23607 - 7.33708i) q^{83} +(2.00000 - 3.46410i) q^{84} +(-7.29571 - 2.65542i) q^{85} +(4.47663 + 1.62936i) q^{86} +(-3.38197 + 5.85774i) q^{87} +(-0.618034 - 1.07047i) q^{88} +(-0.372631 - 2.11330i) q^{89} +(-7.91036 - 6.63758i) q^{90} +(-3.42585 + 2.87463i) q^{91} +(0.132655 - 0.752326i) q^{92} +(-9.84059 + 3.58168i) q^{93} -4.47214 q^{94} -3.23607 q^{96} +(5.99709 - 2.18276i) q^{97} +(-0.950226 + 5.38900i) q^{98} +(7.07524 - 5.93683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{7} - 6 q^{8} + 6 q^{11} + 6 q^{12} + 36 q^{18} - 30 q^{20} + 15 q^{26} + 60 q^{27} + 6 q^{31} - 114 q^{37} + 60 q^{39} + 15 q^{45} - 18 q^{46} + 6 q^{49} - 15 q^{50} - 12 q^{56} + 42 q^{58} - 6 q^{64} - 30 q^{65} + 27 q^{68} - 12 q^{69} + 120 q^{75} + 72 q^{77} - 24 q^{83} + 24 q^{84} - 54 q^{87} + 6 q^{88} - 12 q^{96}+O(q^{100}) \) 12 * q + 6 * q^7 - 6 * q^8 + 6 * q^11 + 6 * q^12 + 36 * q^18 - 30 * q^20 + 15 * q^26 + 60 * q^27 + 6 * q^31 - 114 * q^37 + 60 * q^39 + 15 * q^45 - 18 * q^46 + 6 * q^49 - 15 * q^50 - 12 * q^56 + 42 * q^58 - 6 * q^64 - 30 * q^65 + 27 * q^68 - 12 * q^69 + 120 * q^75 + 72 * q^77 - 24 * q^83 + 24 * q^84 - 54 * q^87 + 6 * q^88 - 12 * q^96

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