LMFDB - Embedded newform 950.2.n.b.39.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.16
Character	$\chi$	$=$	950.39
Dual form			950.2.n.b.609.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-1.43673 - 0.466821i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.88711 + 1.19951i) q^{5} +(-0.466821 - 1.43673i) q^{6} +3.41486i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.580791 - 0.421969i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-1.43673 - 0.466821i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.88711 + 1.19951i) q^{5} +(-0.466821 - 1.43673i) q^{6} +3.41486i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.580791 - 0.421969i) q^{9} +(-2.07964 - 0.821650i) q^{10} +(-2.88941 + 2.09928i) q^{11} +(0.887946 - 1.22215i) q^{12} +(2.29183 - 3.15444i) q^{13} +(-2.76268 + 2.00720i) q^{14} +(3.27121 - 0.842423i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.323942 - 0.105255i) q^{17} -0.717897i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-0.557651 - 2.16542i) q^{20} +(1.59413 - 4.90622i) q^{21} +(-3.39671 - 1.10366i) q^{22} +(-1.84006 - 2.53262i) q^{23} +1.51066 q^{24} +(2.12236 - 4.52720i) q^{25} +3.89910 q^{26} +(3.30129 + 4.54384i) q^{27} +(-3.24772 - 1.05525i) q^{28} +(1.06249 - 3.27000i) q^{29} +(2.60431 + 2.15130i) q^{30} +(0.292544 + 0.900357i) q^{31} -1.00000i q^{32} +(5.13128 - 1.66726i) q^{33} +(0.275562 + 0.200207i) q^{34} +(-4.09615 - 6.44421i) q^{35} +(0.580791 - 0.421969i) q^{36} +(-0.952929 + 1.31159i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-4.76529 + 3.46219i) q^{39} +(1.42408 - 1.72395i) q^{40} +(-2.04954 - 1.48908i) q^{41} +(4.90622 - 1.59413i) q^{42} -8.45836i q^{43} +(-1.10366 - 3.39671i) q^{44} +(1.60217 + 0.0996387i) q^{45} +(0.967375 - 2.97727i) q^{46} +(-9.92451 - 3.22467i) q^{47} +(0.887946 + 1.22215i) q^{48} -4.66126 q^{49} +(4.91008 - 0.943998i) q^{50} -0.514551 q^{51} +(2.29183 + 3.15444i) q^{52} +(-5.01363 - 1.62903i) q^{53} +(-1.73559 + 5.34160i) q^{54} +(2.93453 - 7.42745i) q^{55} +(-1.05525 - 3.24772i) q^{56} +1.51066i q^{57} +(3.27000 - 1.06249i) q^{58} +(-0.185466 - 0.134749i) q^{59} +(-0.209669 + 3.37143i) q^{60} +(2.18446 - 1.58710i) q^{61} +(-0.556451 + 0.765889i) q^{62} +(1.44096 - 1.98332i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.541165 + 8.70183i) q^{65} +(4.36493 + 3.17131i) q^{66} +(10.3513 - 3.36334i) q^{67} +0.340613i q^{68} +(1.46138 + 4.49766i) q^{69} +(2.80582 - 7.10167i) q^{70} +(-1.86096 + 5.72745i) q^{71} +(0.682760 + 0.221842i) q^{72} +(-8.19116 - 11.2742i) q^{73} -1.62122 q^{74} +(-5.16264 + 5.51359i) q^{75} +1.00000 q^{76} +(-7.16875 - 9.86694i) q^{77} +(-5.60193 - 1.82018i) q^{78} +(-2.67376 + 8.22900i) q^{79} +(2.23176 + 0.138793i) q^{80} +(-1.95637 - 6.02108i) q^{81} -2.53337i q^{82} +(7.52580 - 2.44528i) q^{83} +(4.17348 + 3.03221i) q^{84} +(-0.485060 + 0.587199i) q^{85} +(6.84296 - 4.97170i) q^{86} +(-3.05301 + 4.20211i) q^{87} +(2.09928 - 2.88941i) q^{88} +(-14.3418 + 10.4199i) q^{89} +(0.861123 + 1.35475i) q^{90} +(10.7719 + 7.82628i) q^{91} +(2.97727 - 0.967375i) q^{92} -1.43013i q^{93} +(-3.22467 - 9.92451i) q^{94} +(1.72395 + 1.42408i) q^{95} +(-0.466821 + 1.43673i) q^{96} +(-14.0940 - 4.57943i) q^{97} +(-2.73982 - 3.77104i) q^{98} +2.56398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−1.43673	−	0.466821i	−0.829494	−	0.269519i	−0.136662	−	0.990618i	$-0.543637\pi$
$3$	−1.43673	−	0.466821i	−0.829494	−	0.269519i	−0.692832	+	0.721099i	$0.743637\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.88711	+	1.19951i	−0.843941	+	0.536436i
$5$	−1.88711	+	1.19951i	−0.843941	+	0.536436i
$6$	−0.466821	−	1.43673i	−0.190579	−	0.586541i
$7$			3.41486i			1.29070i	0.763889	+	0.645348i	$0.223287\pi$
$7$			3.41486i			1.29070i	−0.763889	+	0.645348i	$0.776713\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.580791	−	0.421969i	−0.193597	−	0.140656i
$10$	−2.07964	−	0.821650i	−0.657639	−	0.259829i
$11$	−2.88941	+	2.09928i	−0.871191	+	0.632957i	−0.930906	−	0.365258i	$-0.880981\pi$
$11$	−2.88941	+	2.09928i	−0.871191	+	0.632957i	0.0597153	+	0.998215i	$0.480981\pi$
$12$	0.887946	−	1.22215i	0.256328	−	0.352805i
$13$	2.29183	−	3.15444i	0.635640	−	0.874883i	−0.362734	−	0.931893i	$-0.618157\pi$
$13$	2.29183	−	3.15444i	0.635640	−	0.874883i	0.998374	+	0.0570098i	$0.0181566\pi$
$14$	−2.76268	+	2.00720i	−0.738357	+	0.536448i
$15$	3.27121	−	0.842423i	0.844624	−	0.217513i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.323942	−	0.105255i	0.0785675	−	0.0255281i	−0.269470	−	0.963009i	$-0.586848\pi$
$17$	0.323942	−	0.105255i	0.0785675	−	0.0255281i	0.348037	+	0.937481i	$0.386848\pi$
$18$		−	0.717897i		−	0.169210i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−0.557651	−	2.16542i	−0.124695	−	0.484202i
$21$	1.59413	−	4.90622i	0.347867	−	1.07062i
$22$	−3.39671	−	1.10366i	−0.724181	−	0.235301i
$23$	−1.84006	−	2.53262i	−0.383678	−	0.528088i	0.572876	−	0.819642i	$-0.305828\pi$
$23$	−1.84006	−	2.53262i	−0.383678	−	0.528088i	−0.956554	+	0.291554i	$0.905828\pi$
$24$	1.51066			0.308363
$25$	2.12236	−	4.52720i	0.424472	−	0.905441i
$26$	3.89910			0.764676
$27$	3.30129	+	4.54384i	0.635334	+	0.874462i
$28$	−3.24772	−	1.05525i	−0.613762	−	0.199423i
$29$	1.06249	−	3.27000i	0.197299	−	0.607224i	−0.802643	−	0.596460i	$-0.796573\pi$
$29$	1.06249	−	3.27000i	0.197299	−	0.607224i	0.999942	−	0.0107646i	$-0.00342654\pi$
$30$	2.60431	+	2.15130i	0.475479	+	0.392773i
$31$	0.292544	+	0.900357i	0.0525424	+	0.161709i	0.973885	−	0.227044i	$-0.0729061\pi$
$31$	0.292544	+	0.900357i	0.0525424	+	0.161709i	−0.921342	+	0.388753i	$0.872906\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.13128	−	1.66726i	0.893242	−	0.290232i
$34$	0.275562	+	0.200207i	0.0472584	+	0.0343353i
$35$	−4.09615	−	6.44421i	−0.692376	−	1.08927i
$36$	0.580791	−	0.421969i	0.0967984	−	0.0703282i
$37$	−0.952929	+	1.31159i	−0.156661	+	0.215625i	−0.880131	−	0.474730i	$-0.842546\pi$
$37$	−0.952929	+	1.31159i	−0.156661	+	0.215625i	0.723471	+	0.690355i	$0.242546\pi$
$38$	0.587785	−	0.809017i	0.0953514	−	0.131240i
$39$	−4.76529	+	3.46219i	−0.763057	+	0.554393i
$40$	1.42408	−	1.72395i	0.225167	−	0.272580i
$41$	−2.04954	−	1.48908i	−0.320085	−	0.232555i	0.416127	−	0.909307i	$-0.363387\pi$
$41$	−2.04954	−	1.48908i	−0.320085	−	0.232555i	−0.736212	+	0.676751i	$0.763387\pi$
$42$	4.90622	−	1.59413i	0.757046	−	0.245979i
$43$		−	8.45836i		−	1.28989i	−0.764230	−	0.644944i	$-0.776881\pi$
$43$		−	8.45836i		−	1.28989i	0.764230	−	0.644944i	$-0.223119\pi$
$44$	−1.10366	−	3.39671i	−0.166383	−	0.512073i
$45$	1.60217	+	0.0996387i	0.238838	+	0.0148533i
$46$	0.967375	−	2.97727i	0.142632	−	0.438975i
$47$	−9.92451	−	3.22467i	−1.44764	−	0.470366i	−0.523369	−	0.852106i	$-0.675325\pi$
$47$	−9.92451	−	3.22467i	−1.44764	−	0.470366i	−0.924270	+	0.381740i	$0.875325\pi$
$48$	0.887946	+	1.22215i	0.128164	+	0.176402i
$49$	−4.66126			−0.665894
$50$	4.91008	−	0.943998i	0.694390	−	0.133501i
$51$	−0.514551			−0.0720516
$52$	2.29183	+	3.15444i	0.317820	+	0.437441i
$53$	−5.01363	−	1.62903i	−0.688676	−	0.223764i	−0.0562859	−	0.998415i	$-0.517926\pi$
$53$	−5.01363	−	1.62903i	−0.688676	−	0.223764i	−0.632390	+	0.774650i	$0.717926\pi$
$54$	−1.73559	+	5.34160i	−0.236184	+	0.726900i
$55$	2.93453	−	7.42745i	0.395692	−	1.00152i
$56$	−1.05525	−	3.24772i	−0.141014	−	0.433995i
$57$			1.51066i			0.200092i
$58$	3.27000	−	1.06249i	0.429373	−	0.139512i
$59$	−0.185466	−	0.134749i	−0.0241456	−	0.0175428i	0.575647	−	0.817698i	$-0.304750\pi$
$59$	−0.185466	−	0.134749i	−0.0241456	−	0.0175428i	−0.599793	+	0.800155i	$0.704750\pi$
$60$	−0.209669	+	3.37143i	−0.0270681	+	0.435250i
$61$	2.18446	−	1.58710i	0.279691	−	0.203208i	−0.439091	−	0.898442i	$-0.644700\pi$
$61$	2.18446	−	1.58710i	0.279691	−	0.203208i	0.718783	+	0.695235i	$0.244700\pi$
$62$	−0.556451	+	0.765889i	−0.0706694	+	0.0972680i
$63$	1.44096	−	1.98332i	0.181545	−	0.249875i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−0.541165	+	8.70183i	−0.0671233	+	1.07933i
$66$	4.36493	+	3.17131i	0.537286	+	0.390361i
$67$	10.3513	−	3.36334i	1.26461	−	0.410897i	0.401476	−	0.915870i	$-0.368497\pi$
$67$	10.3513	−	3.36334i	1.26461	−	0.410897i	0.863136	+	0.504972i	$0.168497\pi$
$68$			0.340613i			0.0413054i
$69$	1.46138	+	4.49766i	0.175929	+	0.541454i
$70$	2.80582	−	7.10167i	0.335360	−	0.848812i
$71$	−1.86096	+	5.72745i	−0.220855	+	0.679723i	0.777831	+	0.628474i	$0.216320\pi$
$71$	−1.86096	+	5.72745i	−0.220855	+	0.679723i	−0.998686	+	0.0512489i	$0.983680\pi$
$72$	0.682760	+	0.221842i	0.0804641	+	0.0261444i
$73$	−8.19116	−	11.2742i	−0.958703	−	1.31954i	−0.947551	−	0.319604i	$-0.896450\pi$
$73$	−8.19116	−	11.2742i	−0.958703	−	1.31954i	−0.0111517	−	0.999938i	$-0.503550\pi$
$74$	−1.62122			−0.188463
$75$	−5.16264	+	5.51359i	−0.596131	+	0.636655i
$76$	1.00000			0.114708
$77$	−7.16875	−	9.86694i	−0.816955	−	1.12444i
$78$	−5.60193	−	1.82018i	−0.634294	−	0.206095i
$79$	−2.67376	+	8.22900i	−0.300822	+	0.925835i	0.680381	+	0.732858i	$0.261814\pi$
$79$	−2.67376	+	8.22900i	−0.300822	+	0.925835i	−0.981203	+	0.192977i	$0.938186\pi$
$80$	2.23176	+	0.138793i	0.249518	+	0.0155175i
$81$	−1.95637	−	6.02108i	−0.217374	−	0.669008i
$82$		−	2.53337i		−	0.279764i
$83$	7.52580	−	2.44528i	0.826064	−	0.268404i	0.134677	−	0.990890i	$-0.457000\pi$
$83$	7.52580	−	2.44528i	0.826064	−	0.268404i	0.691386	+	0.722485i	$0.257000\pi$
$84$	4.17348	+	3.03221i	0.455364	+	0.330841i
$85$	−0.485060	+	0.587199i	−0.0526121	+	0.0636907i
$86$	6.84296	−	4.97170i	0.737895	−	0.536112i
$87$	−3.05301	+	4.20211i	−0.327317	+	0.450513i
$88$	2.09928	−	2.88941i	0.223784	−	0.308013i
$89$	−14.3418	+	10.4199i	−1.52023	+	1.10451i	−0.558854	+	0.829266i	$0.688759\pi$
$89$	−14.3418	+	10.4199i	−1.52023	+	1.10451i	−0.961374	+	0.275245i	$0.911241\pi$
$90$	0.861123	+	1.35475i	0.0907703	+	0.142803i
$91$	10.7719	+	7.82628i	1.12921	+	0.820417i
$92$	2.97727	−	0.967375i	0.310402	−	0.100856i
$93$		−	1.43013i		−	0.148298i
$94$	−3.22467	−	9.92451i	−0.332599	−	1.02364i
$95$	1.72395	+	1.42408i	0.176873	+	0.146107i
$96$	−0.466821	+	1.43673i	−0.0476447	+	0.146635i
$97$	−14.0940	−	4.57943i	−1.43103	−	0.464970i	−0.511942	−	0.859020i	$-0.671074\pi$
$97$	−14.0940	−	4.57943i	−1.43103	−	0.464970i	−0.919089	+	0.394050i	$0.871074\pi$
$98$	−2.73982	−	3.77104i	−0.276764	−	0.380932i
$99$	2.56398			0.257689
$100$	3.64978	+	3.41747i	0.364978	+	0.341747i
$101$	2.31470			0.230321			0.115161	−	0.993347i	$-0.463262\pi$
$101$	2.31470			0.230321			0.115161	+	0.993347i	$0.463262\pi$
$102$	−0.302446	−	0.416281i	−0.0299466	−	0.0412180i
$103$	−7.23952	−	2.35226i	−0.713331	−	0.231775i	−0.0702018	−	0.997533i	$-0.522364\pi$
$103$	−7.23952	−	2.35226i	−0.713331	−	0.231775i	−0.643130	+	0.765757i	$0.722364\pi$
$104$	−1.20489	+	3.70826i	−0.118149	+	0.363625i
$105$	2.87676	+	11.1707i	0.280743	+	1.09015i
$106$	−1.62903	−	5.01363i	−0.158225	−	0.486967i
$107$		−	1.82459i		−	0.176390i	−0.996103	−	0.0881950i	$-0.971890\pi$
$107$		−	1.82459i		−	0.176390i	0.996103	−	0.0881950i	$-0.0281099\pi$
$108$	−5.34160	+	1.73559i	−0.513996	+	0.167007i
$109$	4.10192	+	2.98022i	0.392892	+	0.285453i	0.766640	−	0.642077i	$-0.221927\pi$
$109$	4.10192	+	2.98022i	0.392892	+	0.285453i	−0.373747	+	0.927531i	$0.621927\pi$
$110$	7.73381	−	1.99166i	0.737390	−	0.189897i
$111$	1.98138	−	1.43956i	0.188064	−	0.136637i
$112$	2.00720	−	2.76268i	0.189663	−	0.261049i
$113$	5.40744	−	7.44270i	0.508689	−	0.700150i	−0.475009	−	0.879981i	$-0.657555\pi$
$113$	5.40744	−	7.44270i	0.508689	−	0.700150i	0.983698	+	0.179831i	$0.0575551\pi$
$114$	−1.22215	+	0.887946i	−0.114465	+	0.0831637i
$115$	6.51029	+	2.57217i	0.607087	+	0.239856i
$116$	2.78163	+	2.02097i	0.258268	+	0.187643i
$117$	−2.66215	+	0.864984i	−0.246116	+	0.0799678i
$118$		−	0.229249i		−	0.0211040i
$119$	0.359432	+	1.10622i	0.0329490	+	0.101407i
$120$	−2.85079	+	1.81205i	−0.260240	+	0.165417i
$121$	0.542539	−	1.66976i	0.0493218	−	0.151797i
$122$	2.56799	+	0.834390i	0.232495	+	0.0755421i
$123$	2.24950	+	3.09617i	0.202830	+	0.279172i
$124$	−0.946691			−0.0850154
$125$	1.42529	+	11.0891i	0.127482	+	0.991841i
$126$	2.45152			0.218398
$127$	6.07394	+	8.36006i	0.538975	+	0.741836i	0.988465	−	0.151450i	$-0.0483942\pi$
$127$	6.07394	+	8.36006i	0.538975	+	0.741836i	−0.449490	+	0.893285i	$0.648394\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−3.94854	+	12.1523i	−0.347649	+	1.06995i
$130$	−7.35802	+	4.67700i	−0.645341	+	0.410200i
$131$	6.77402	+	20.8483i	0.591848	+	1.82152i	0.569827	+	0.821765i	$0.307010\pi$
$131$	6.77402	+	20.8483i	0.591848	+	1.82152i	0.0220217	+	0.999757i	$0.492990\pi$
$132$			5.39535i			0.469605i
$133$	3.24772	−	1.05525i	0.281613	−	0.0915017i
$134$	8.80534	+	6.39745i	0.760665	+	0.552656i
$135$	−11.6803	−	4.61479i	−1.00528	−	0.397178i
$136$	−0.275562	+	0.200207i	−0.0236292	+	0.0171676i
$137$	7.94061	−	10.9293i	0.678412	−	0.933754i	−0.321502	−	0.946909i	$-0.604188\pi$
$137$	7.94061	−	10.9293i	0.678412	−	0.933754i	0.999913	+	0.0131551i	$0.00418752\pi$
$138$	−2.77971	+	3.82594i	−0.236624	+	0.325685i
$139$	−4.64475	+	3.37461i	−0.393963	+	0.286231i	−0.767078	−	0.641554i	$-0.778290\pi$
$139$	−4.64475	+	3.37461i	−0.393963	+	0.286231i	0.373115	+	0.927785i	$0.378290\pi$
$140$	7.39459	−	1.90430i	0.624957	−	0.160943i
$141$	12.7535	+	9.26593i	1.07404	+	0.780332i
$142$	−5.72745	+	1.86096i	−0.480637	+	0.156168i
$143$			13.9257i			1.16452i
$144$	0.221842	+	0.682760i	0.0184869	+	0.0568967i
$145$	1.91736	+	7.44532i	0.159228	+	0.618300i
$146$	4.30635	−	13.2536i	0.356396	−	1.09687i
$147$	6.69695	+	2.17597i	0.552355	+	0.179471i
$148$	−0.952929	−	1.31159i	−0.0783303	−	0.107812i
$149$	−11.2702			−0.923291			−0.461646	−	0.887064i	$-0.652741\pi$
$149$	−11.2702			−0.923291			−0.461646	+	0.887064i	$0.652741\pi$
$150$	−7.49511	−	0.935859i	−0.611974	−	0.0764126i
$151$	−6.89085			−0.560770			−0.280385	−	0.959888i	$-0.590462\pi$
$151$	−6.89085			−0.560770			−0.280385	+	0.959888i	$0.590462\pi$
$152$	0.587785	+	0.809017i	0.0476757	+	0.0656199i
$153$	−0.232557	−	0.0755624i	−0.0188011	−	0.00610886i
$154$	3.76884	−	11.5993i	0.303701	−	0.934697i
$155$	−1.63205	−	1.34816i	−0.131089	−	0.108287i
$156$	−1.82018	−	5.60193i	−0.145731	−	0.448514i
$157$		−	7.49528i		−	0.598188i	−0.954224	−	0.299094i	$-0.903316\pi$
$157$		−	7.49528i		−	0.598188i	0.954224	−	0.299094i	$-0.0966845\pi$
$158$	−8.22900	+	2.67376i	−0.654664	+	0.212713i
$159$	6.44276	+	4.68094i	0.510944	+	0.371222i
$160$	1.19951	+	1.88711i	0.0948294	+	0.149189i
$161$	8.64854	−	6.28353i	0.681601	−	0.495212i
$162$	3.72123	−	5.12183i	0.292367	−	0.402409i
$163$	−13.1897	+	18.1541i	−1.03310	+	1.42194i	−0.130500	+	0.991448i	$0.541658\pi$
$163$	−13.1897	+	18.1541i	−1.03310	+	1.42194i	−0.902597	+	0.430487i	$0.858342\pi$
$164$	2.04954	−	1.48908i	0.160042	−	0.116278i
$165$	−7.68341	+	9.30131i	−0.598152	+	0.724106i
$166$	6.40183	+	4.65120i	0.496878	+	0.361003i
$167$	−13.0816	+	4.25049i	−1.01229	+	0.328912i	−0.767765	−	0.640731i	$-0.778631\pi$
$167$	−13.0816	+	4.25049i	−1.01229	+	0.328912i	−0.244523	+	0.969643i	$0.578631\pi$
$168$			5.15870i			0.398002i
$169$	−0.680749	−	2.09513i	−0.0523653	−	0.161164i
$170$	−0.760165	−	0.0472745i	−0.0583020	−	0.00362579i
$171$	−0.221842	+	0.682760i	−0.0169647	+	0.0522120i
$172$	8.04438	+	2.61378i	0.613378	+	0.199299i
$173$	3.12511	+	4.30134i	0.237598	+	0.327025i	0.911120	−	0.412142i	$-0.135219\pi$
$173$	3.12511	+	4.30134i	0.237598	+	0.327025i	−0.673522	+	0.739167i	$0.735219\pi$
$174$	−5.19409			−0.393763
$175$	15.4598	+	7.24756i	1.16865	+	0.547864i
$176$	3.57151			0.269213
$177$	0.203560	+	0.280177i	0.0153005	+	0.0210594i
$178$	−16.8598	−	5.47808i	−1.26370	−	0.410600i
$179$	4.44928	−	13.6935i	0.332555	−	1.02350i	−0.635360	−	0.772216i	$-0.719148\pi$
$179$	4.44928	−	13.6935i	0.332555	−	1.02350i	0.967914	−	0.251281i	$-0.0808519\pi$
$180$	−0.589860	+	1.49296i	−0.0439656	+	0.111279i
$181$	−5.13124	−	15.7923i	−0.381402	−	1.17384i	−0.939057	−	0.343762i	$-0.888299\pi$
$181$	−5.13124	−	15.7923i	−0.381402	−	1.17384i	0.557654	−	0.830073i	$-0.311701\pi$
$182$			13.3149i			0.986963i
$183$	−3.87936	+	1.26048i	−0.286771	+	0.0931775i
$184$	2.53262	+	1.84006i	0.186707	+	0.135651i
$185$	0.225013	−	3.61817i	0.0165433	−	0.266013i
$186$	1.15700	−	0.840610i	0.0848354	−	0.0616365i
$187$	−0.715043	+	0.984172i	−0.0522891	+	0.0719698i
$188$	6.13369	−	8.44229i	0.447345	−	0.615718i
$189$	−15.5166	+	11.2734i	−1.12866	+	0.820022i
$190$	−0.138793	+	2.23176i	−0.0100691	+	0.161909i
$191$	−8.84029	−	6.42285i	−0.639661	−	0.464741i	0.220073	−	0.975484i	$-0.429371\pi$
$191$	−8.84029	−	6.42285i	−0.639661	−	0.464741i	−0.859734	+	0.510742i	$0.829371\pi$
$192$	−1.43673	+	0.466821i	−0.103687	+	0.0336899i
$193$			21.0547i			1.51555i	0.652517	+	0.757774i	$0.273713\pi$
$193$			21.0547i			1.51555i	−0.652517	+	0.757774i	$0.726287\pi$
$194$	−4.57943	−	14.0940i	−0.328784	−	1.01189i
$195$	4.83970	−	12.2495i	0.346578	−	0.877207i
$196$	1.44041	−	4.43312i	0.102886	−	0.316651i
$197$	−18.6642	−	6.06438i	−1.32977	−	0.432069i	−0.443932	−	0.896060i	$-0.646417\pi$
$197$	−18.6642	−	6.06438i	−1.32977	−	0.432069i	−0.885840	+	0.463991i	$0.846417\pi$
$198$	1.50707	+	2.07430i	0.107103	+	0.147414i
$199$	16.5808			1.17538			0.587692	−	0.809085i	$-0.300037\pi$
$199$	16.5808			1.17538			0.587692	+	0.809085i	$0.300037\pi$
$200$	−0.619502	+	4.96147i	−0.0438054	+	0.350829i
$201$	−16.4420			−1.15973
$202$	1.36055	+	1.87263i	0.0957276	+	0.131758i
$203$	11.1666	+	3.62825i	0.783742	+	0.254653i
$204$	0.159005	−	0.489368i	0.0111326	−	0.0342626i
$205$	5.65387	+	0.351613i	0.394883	+	0.0245577i
$206$	−2.35226	−	7.23952i	−0.163890	−	0.504401i
$207$			2.24737i			0.156203i
$208$	−3.70826	+	1.20489i	−0.257122	+	0.0835439i
$209$	2.88941	+	2.09928i	0.199865	+	0.145210i
$210$	−7.34640	+	8.89334i	−0.506950	+	0.613698i
$211$	14.9619	−	10.8705i	1.03002	−	0.748355i	0.0617091	−	0.998094i	$-0.480345\pi$
$211$	14.9619	−	10.8705i	1.03002	−	0.748355i	0.968313	+	0.249739i	$0.0803449\pi$
$212$	3.09860	−	4.26485i	0.212812	−	0.292911i
$213$	5.34738	−	7.36004i	0.366397	−	0.504302i
$214$	1.47613	−	1.07247i	0.100906	−	0.0733124i
$215$	10.1459	+	15.9618i	0.691943	+	1.08859i
$216$	−4.54384	−	3.30129i	−0.309169	−	0.224624i
$217$	−3.07459	+	0.998995i	−0.208717	+	0.0678162i
$218$			5.07025i			0.343401i
$219$	6.50544	+	20.0217i	0.439597	+	1.35294i
$220$	6.15710	+	5.08611i	0.415112	+	0.342906i
$221$	0.410400	−	1.26308i	0.0276065	−	0.0849641i
$222$	2.32925	+	0.756819i	0.156329	+	0.0507944i
$223$	−3.13005	−	4.30814i	−0.209603	−	0.288494i	0.691252	−	0.722614i	$-0.257060\pi$
$223$	−3.13005	−	4.30814i	−0.209603	−	0.288494i	−0.900855	+	0.434120i	$0.857060\pi$
$224$	3.41486			0.228165
$225$	−3.14299	+	1.73379i	−0.209533	+	0.115586i
$226$	9.19968			0.611954
$227$	−10.4397	−	14.3690i	−0.692905	−	0.953702i	−0.999998	−	0.00202273i	$-0.999356\pi$
$227$	−10.4397	−	14.3690i	−0.692905	−	0.953702i	0.307093	−	0.951680i	$-0.400644\pi$
$228$	−1.43673	−	0.466821i	−0.0951495	−	0.0309159i
$229$	1.00600	−	3.09614i	0.0664782	−	0.204599i	−0.912300	−	0.409524i	$-0.865695\pi$
$229$	1.00600	−	3.09614i	0.0664782	−	0.204599i	0.978778	+	0.204925i	$0.0656950\pi$
$230$	1.74572	+	6.77882i	0.115109	+	0.446982i
$231$	5.69344	+	17.5226i	0.374601	+	1.15290i
$232$			3.43829i			0.225735i
$233$	1.05419	−	0.342529i	0.0690626	−	0.0224398i	−0.274282	−	0.961649i	$-0.588440\pi$
$233$	1.05419	−	0.342529i	0.0690626	−	0.0224398i	0.343345	+	0.939210i	$0.388440\pi$
$234$	−2.26456	−	1.64530i	−0.148039	−	0.107557i
$235$	22.5967	−	5.81923i	1.47404	−	0.379605i
$236$	0.185466	−	0.134749i	0.0120728	−	0.00877141i
$237$	7.68293	−	10.5747i	0.499060	−	0.686897i
$238$	−0.683680	+	0.941004i	−0.0443164	+	0.0609962i
$239$	−15.3604	+	11.1600i	−0.993580	+	0.721878i	−0.960702	−	0.277581i	$-0.910467\pi$
$239$	−15.3604	+	11.1600i	−0.993580	+	0.721878i	−0.0328780	+	0.999459i	$0.510467\pi$
$240$	−3.14163	−	1.24124i	−0.202791	−	0.0801215i
$241$	−19.9580	−	14.5003i	−1.28561	−	0.934048i	−0.285900	−	0.958259i	$-0.592293\pi$
$241$	−19.9580	−	14.5003i	−1.28561	−	0.934048i	−0.999707	+	0.0242114i	$0.992293\pi$
$242$	1.66976	−	0.542539i	0.107337	−	0.0348758i
$243$		−	7.28556i		−	0.467369i
$244$	0.834390	+	2.56799i	0.0534163	+	0.164399i
$245$	8.79630	−	5.59122i	0.561975	−	0.357210i
$246$	−1.18263	+	3.63976i	−0.0754018	+	0.232063i
$247$	−3.70826	−	1.20489i	−0.235951	−	0.0766651i
$248$	−0.556451	−	0.765889i	−0.0353347	−	0.0486340i
$249$	−11.9540			−0.757555
$250$	−8.13352	+	7.67111i	−0.514409	+	0.485163i
$251$	−23.2793			−1.46937			−0.734687	−	0.678406i	$-0.762671\pi$
$251$	−23.2793			−1.46937			−0.734687	+	0.678406i	$0.762671\pi$
$252$	1.44096	+	1.98332i	0.0907723	+	0.124937i
$253$	10.6334	+	3.45499i	0.668514	+	0.217213i
$254$	−3.19326	+	9.82784i	−0.200363	+	0.616654i
$255$	0.971015	−	0.617209i	0.0608073	−	0.0386511i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	25.6654i		−	1.60096i	−0.599358	−	0.800481i	$-0.704577\pi$
$257$		−	25.6654i		−	1.60096i	0.599358	−	0.800481i	$-0.295423\pi$
$258$	−12.1523	+	3.94854i	−0.756572	+	0.245825i
$259$	−4.47891	−	3.25412i	−0.278306	−	0.202201i
$260$	−8.10871	−	3.20369i	−0.502881	−	0.198685i
$261$	−1.99692	+	1.45085i	−0.123607	+	0.0898054i
$262$	−12.8849	+	17.7346i	−0.796034	+	1.09565i
$263$	−7.13717	+	9.82347i	−0.440096	+	0.605741i	−0.970234	−	0.242171i	$-0.922140\pi$
$263$	−7.13717	+	9.82347i	−0.440096	+	0.605741i	0.530137	+	0.847912i	$0.322140\pi$
$264$	−4.36493	+	3.17131i	−0.268643	+	0.195180i
$265$	11.4153	−	2.93974i	0.701237	−	0.180587i
$266$	2.76268	+	2.00720i	0.169391	+	0.123070i
$267$	25.4695	−	8.27554i	1.55871	−	0.506455i
$268$			10.8840i			0.664846i
$269$	5.81253	+	17.8891i	0.354396	+	1.09072i	0.956359	+	0.292196i	$0.0943858\pi$
$269$	5.81253	+	17.8891i	0.354396	+	1.09072i	−0.601962	+	0.798525i	$0.705614\pi$
$270$	−3.13204	−	12.1620i	−0.190610	−	0.740158i
$271$	3.41695	−	10.5163i	0.207565	−	0.638818i	−0.792034	−	0.610477i	$-0.790978\pi$
$271$	3.41695	−	10.5163i	0.207565	−	0.638818i	0.999598	−	0.0283410i	$-0.00902242\pi$
$272$	−0.323942	−	0.105255i	−0.0196419	−	0.00638203i
$273$	−11.8229	−	16.2728i	−0.715553	−	0.984874i
$274$	13.5094			0.816131
$275$	3.37150	+	17.5364i	0.203309	+	1.05748i
$276$	−4.72912			−0.284659
$277$	−0.873695	−	1.20254i	−0.0524952	−	0.0722535i	0.781962	−	0.623326i	$-0.214219\pi$
$277$	−0.873695	−	1.20254i	−0.0524952	−	0.0722535i	−0.834458	+	0.551072i	$0.814219\pi$
$278$	−5.46024	−	1.77414i	−0.327483	−	0.106406i
$279$	0.210016	−	0.646363i	0.0125733	−	0.0386968i
$280$	5.88704	+	4.86303i	0.351818	+	0.290622i
$281$	2.75512	+	8.47940i	0.164357	+	0.505838i	0.998988	−	0.0449704i	$-0.0143194\pi$
$281$	2.75512	+	8.47940i	0.164357	+	0.505838i	−0.834631	+	0.550809i	$0.814319\pi$
$282$			15.7641i			0.938741i
$283$	0.807675	−	0.262429i	0.0480113	−	0.0155998i	−0.284913	−	0.958553i	$-0.591965\pi$
$283$	0.807675	−	0.262429i	0.0480113	−	0.0155998i	0.332924	+	0.942954i	$0.391965\pi$
$284$	−4.87206	−	3.53976i	−0.289103	−	0.210046i
$285$	−1.81205	−	2.85079i	−0.107337	−	0.168866i
$286$	−11.2661	+	8.18530i	−0.666179	+	0.484007i
$287$	5.08499	−	6.99889i	0.300158	−	0.413132i
$288$	−0.421969	+	0.580791i	−0.0248648	+	0.0342234i
$289$	−13.6594	+	9.92416i	−0.803496	+	0.583774i
$290$	−4.89639	+	5.92743i	−0.287526	+	0.348071i
$291$	18.1115	+	13.1588i	1.06171	+	0.771380i
$292$	13.2536	−	4.30635i	0.775607	−	0.252010i
$293$		−	16.5749i		−	0.968318i	−0.874980	−	0.484159i	$-0.839126\pi$
$293$		−	16.5749i		−	0.968318i	0.874980	−	0.484159i	$-0.160874\pi$
$294$	2.17597	+	6.69695i	0.126905	+	0.390574i
$295$	0.511627	+	0.0318180i	0.0297881	+	0.00185252i
$296$	0.500985	−	1.54187i	0.0291191	−	0.0896195i
$297$	−19.0776	−	6.19868i	−1.10699	−	0.359684i
$298$	−6.62446	−	9.11779i	−0.383745	−	0.528179i
$299$	−12.2061			−0.705896
$300$	−3.64839	−	6.61376i	−0.210640	−	0.381846i
$301$	28.8841			1.66485
$302$	−4.05034	−	5.57482i	−0.233071	−	0.320795i
$303$	−3.32559	−	1.08055i	−0.191050	−	0.0620759i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	−2.21857	+	5.61531i	−0.127035	+	0.321532i
$306$	−0.0755624	−	0.232557i	−0.00431961	−	0.0132944i
$307$		−	19.3552i		−	1.10466i	−0.833626	−	0.552329i	$-0.813739\pi$
$307$		−	19.3552i		−	1.10466i	0.833626	−	0.552329i	$-0.186261\pi$
$308$	11.5993	−	3.76884i	0.660930	−	0.214749i
$309$	9.30312	+	6.75912i	0.529236	+	0.384513i
$310$	0.131394	−	2.11278i	0.00746266	−	0.119998i
$311$	−9.43121	+	6.85218i	−0.534795	+	0.388551i	−0.822148	−	0.569273i	$-0.807225\pi$
$311$	−9.43121	+	6.85218i	−0.534795	+	0.388551i	0.287353	+	0.957825i	$0.407225\pi$
$312$	3.46219	−	4.76529i	0.196008	−	0.269781i
$313$	13.7599	−	18.9389i	0.777756	−	1.07049i	−0.217770	−	0.976000i	$-0.569878\pi$
$313$	13.7599	−	18.9389i	0.777756	−	1.07049i	0.995526	−	0.0944893i	$-0.0301218\pi$
$314$	6.06381	−	4.40561i	0.342200	−	0.248623i
$315$	−0.340252	+	5.47119i	−0.0191710	+	0.308266i
$316$	−7.00001	−	5.08580i	−0.393781	−	0.286099i
$317$	4.59909	−	1.49434i	0.258311	−	0.0839303i	−0.176999	−	0.984211i	$-0.556639\pi$
$317$	4.59909	−	1.49434i	0.258311	−	0.0839303i	0.435310	+	0.900281i	$0.356639\pi$
$318$			7.96368i			0.446581i
$319$	3.79469	+	11.6789i	0.212462	+	0.653890i
$320$	−0.821650	+	2.07964i	−0.0459316	+	0.116255i
$321$	−0.851757	+	2.62144i	−0.0475405	+	0.146314i
$322$	10.1670	+	3.30345i	0.566583	+	0.184094i
$323$	−0.200207	−	0.275562i	−0.0111398	−	0.0153327i
$324$	6.33093			0.351719
$325$	−9.41668	−	17.0704i	−0.522343	−	0.946898i
$326$	−22.4396			−1.24282
$327$	−4.50211	−	6.19662i	−0.248967	−	0.342674i
$328$	2.40938	+	0.782855i	0.133036	+	0.0432259i
$329$	11.0118	−	33.8908i	0.607100	−	1.86846i
$330$	−12.0411	−	0.748834i	−0.662841	−	0.0412220i
$331$	8.39910	+	25.8498i	0.461656	+	1.42083i	0.863139	+	0.504966i	$0.168495\pi$
$331$	8.39910	+	25.8498i	0.461656	+	1.42083i	−0.401483	+	0.915867i	$0.631505\pi$
$332$			7.91309i			0.434287i
$333$	1.10691	−	0.359655i	0.0606580	−	0.0197090i
$334$	−11.1279	−	8.08490i	−0.608892	−	0.442386i
$335$	−15.4997	+	18.7634i	−0.846837	+	1.02516i
$336$	−4.17348	+	3.03221i	−0.227682	+	0.165421i
$337$	4.91924	−	6.77076i	0.267968	−	0.368827i	−0.653734	−	0.756724i	$-0.726799\pi$
$337$	4.91924	−	6.77076i	0.267968	−	0.368827i	0.921703	+	0.387898i	$0.126799\pi$
$338$	1.29486	−	1.78222i	0.0704312	−	0.0969403i
$339$	−11.2434	+	8.16881i	−0.610658	+	0.443669i
$340$	−0.408568	−	0.642774i	−0.0221577	−	0.0348593i
$341$	−2.73538	−	1.98737i	−0.148129	−	0.107622i
$342$	−0.682760	+	0.221842i	−0.0369195	+	0.0119959i
$343$			7.98647i			0.431229i
$344$	2.61378	+	8.04438i	0.140925	+	0.433724i
$345$	−8.15276	−	6.73464i	−0.438930	−	0.362581i
$346$	−1.64297	+	5.05653i	−0.0883265	+	0.271841i
$347$	−11.8196	−	3.84044i	−0.634512	−	0.206165i	−0.0259391	−	0.999664i	$-0.508258\pi$
$347$	−11.8196	−	3.84044i	−0.634512	−	0.206165i	−0.608573	+	0.793498i	$0.708258\pi$
$348$	−3.05301	−	4.20211i	−0.163659	−	0.225257i
$349$	−24.7634			−1.32555			−0.662777	−	0.748817i	$-0.730622\pi$
$349$	−24.7634			−1.32555			−0.662777	+	0.748817i	$0.730622\pi$
$350$	3.22362	+	16.7672i	0.172310	+	0.896246i
$351$	21.8992			1.16889
$352$	2.09928	+	2.88941i	0.111892	+	0.154006i
$353$	−22.1700	−	7.20347i	−1.17999	−	0.383402i	−0.347627	−	0.937633i	$-0.613013\pi$
$353$	−22.1700	−	7.20347i	−1.17999	−	0.383402i	−0.832363	+	0.554231i	$0.813013\pi$
$354$	−0.107018	+	0.329367i	−0.00568794	+	0.0175057i
$355$	−3.35828	−	13.0406i	−0.178239	−	0.692121i
$356$	−5.47808	−	16.8598i	−0.290338	−	0.893568i
$357$		−	1.75712i		−	0.0929967i
$358$	13.6935	−	4.44928i	0.723722	−	0.235152i
$359$	12.1650	+	8.83837i	0.642043	+	0.466471i	0.860551	−	0.509364i	$-0.170119\pi$
$359$	12.1650	+	8.83837i	0.642043	+	0.466471i	−0.218509	+	0.975835i	$0.570119\pi$
$360$	−1.55454	+	0.400336i	−0.0819317	+	0.0210996i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	9.76020	−	13.4338i	0.512985	−	0.706063i
$363$	−1.55896	+	2.14573i	−0.0818242	+	0.112621i
$364$	−10.7719	+	7.82628i	−0.564604	+	0.410208i
$365$	28.9811	+	11.4502i	1.51694	+	0.599332i
$366$	−3.29998	−	2.39758i	−0.172493	−	0.125323i
$367$	23.2482	−	7.55379i	1.21355	−	0.394305i	0.368818	−	0.929502i	$-0.379763\pi$
$367$	23.2482	−	7.55379i	1.21355	−	0.394305i	0.844727	+	0.535197i	$0.179763\pi$
$368$			3.13049i			0.163188i
$369$	0.562009	+	1.72969i	0.0292570	+	0.0900439i
$370$	3.05942	−	1.94467i	0.159052	−	0.101098i
$371$	5.56290	−	17.1209i	0.288811	−	0.888870i
$372$	1.36014	+	0.441935i	0.0705198	+	0.0229133i
$373$	4.72437	+	6.50253i	0.244618	+	0.336688i	0.913617	−	0.406575i	$-0.133277\pi$
$373$	4.72437	+	6.50253i	0.244618	+	0.336688i	−0.668999	+	0.743263i	$0.733277\pi$
$374$	−1.21650			−0.0629039
$375$	3.12888	−	16.5974i	0.161574	−	0.857085i
$376$	10.4352			0.538157
$377$	−7.87997	−	10.8458i	−0.405839	−	0.558590i
$378$	−18.2408	−	5.92680i	−0.938206	−	0.304842i
$379$	6.46171	−	19.8871i	0.331916	−	1.02153i	−0.636306	−	0.771437i	$-0.719538\pi$
$379$	6.46171	−	19.8871i	0.331916	−	1.02153i	0.968221	−	0.250095i	$-0.0804618\pi$
$380$	−1.88711	+	1.19951i	−0.0968067	+	0.0615335i
$381$	−4.82394	−	14.8466i	−0.247138	−	0.760612i
$382$		−	10.9272i		−	0.559084i
$383$	−30.3721	+	9.86849i	−1.55194	+	0.504256i	−0.954640	−	0.297761i	$-0.903760\pi$
$383$	−30.3721	+	9.86849i	−1.55194	+	0.504256i	−0.597301	+	0.802017i	$0.703760\pi$
$384$	−1.22215	−	0.887946i	−0.0623677	−	0.0453128i
$385$	25.3637	+	10.0210i	1.29265	+	0.510718i
$386$	−17.0336	+	12.3756i	−0.866987	+	0.629903i
$387$	−3.56917	+	4.91254i	−0.181431	+	0.249718i
$388$	8.71059	−	11.9891i	0.442213	−	0.608654i
$389$	−7.15646	+	5.19947i	−0.362847	+	0.263624i	−0.754239	−	0.656600i	$-0.771994\pi$
$389$	−7.15646	+	5.19947i	−0.362847	+	0.263624i	0.391392	+	0.920224i	$0.371994\pi$
$390$	12.7548	−	3.28469i	0.645863	−	0.166327i
$391$	−0.862643	−	0.626747i	−0.0436258	−	0.0316960i
$392$	4.43312	−	1.44041i	0.223906	−	0.0727516i
$393$		−	33.1155i		−	1.67046i
$394$	−6.06438	−	18.6642i	−0.305519	−	0.940291i
$395$	−4.82507	−	18.7362i	−0.242775	−	0.942722i
$396$	−0.792312	+	2.43849i	−0.0398152	+	0.122539i
$397$	26.4788	+	8.60347i	1.32893	+	0.431796i	0.885553	−	0.464539i	$-0.153780\pi$
$397$	26.4788	+	8.60347i	1.32893	+	0.431796i	0.443378	+	0.896335i	$0.353780\pi$
$398$	9.74597	+	13.4142i	0.488521	+	0.672392i
$399$	−5.15870			−0.258258
$400$	−4.37805	+	2.41509i	−0.218903	+	0.120755i
$401$	−6.41233			−0.320217			−0.160108	−	0.987099i	$-0.551184\pi$
$401$	−6.41233			−0.320217			−0.160108	+	0.987099i	$0.551184\pi$
$402$	−9.66439	−	13.3019i	−0.482016	−	0.663438i
$403$	3.51058	+	1.14066i	0.174874	+	0.0568201i
$404$	−0.715281	+	2.20141i	−0.0355866	+	0.109524i
$405$	10.9142	+	9.01575i	0.542331	+	0.447996i
$406$	3.62825	+	11.1666i	0.180067	+	0.554189i
$407$		−	5.79021i		−	0.287010i
$408$	0.489368	−	0.159005i	0.0242273	−	0.00787193i
$409$	−13.4055	−	9.73964i	−0.662858	−	0.481594i	0.204769	−	0.978810i	$-0.434356\pi$
$409$	−13.4055	−	9.73964i	−0.662858	−	0.481594i	−0.867627	+	0.497216i	$0.834356\pi$
$410$	3.03880	+	4.78075i	0.150076	+	0.236104i
$411$	−16.5105	+	11.9956i	−0.814403	+	0.591699i
$412$	4.47427	−	6.15831i	0.220431	−	0.303398i
$413$	0.460149	−	0.633340i	0.0226424	−	0.0311646i
$414$	−1.81816	+	1.32097i	−0.0893577	+	0.0649222i
$415$	−11.2689	+	13.6418i	−0.553167	+	0.669648i
$416$	−3.15444	−	2.29183i	−0.154659	−	0.112366i
$417$	8.24858	−	2.68013i	0.403935	−	0.131246i
$418$			3.57151i			0.174688i
$419$	−7.58092	−	23.3317i	−0.370352	−	1.13983i	−0.946561	−	0.322525i	$-0.895468\pi$
$419$	−7.58092	−	23.3317i	−0.370352	−	1.13983i	0.576209	−	0.817303i	$-0.304532\pi$
$420$	−11.5130	−	0.715989i	−0.561775	−	0.0349367i
$421$	−2.51354	+	7.73589i	−0.122503	+	0.377024i	−0.993438	−	0.114374i	$-0.963514\pi$
$421$	−2.51354	+	7.73589i	−0.122503	+	0.377024i	0.870935	+	0.491398i	$0.163514\pi$
$422$	17.5888	+	5.71495i	0.856210	+	0.278199i
$423$	4.40335	+	6.06070i	0.214098	+	0.294681i
$424$	5.27165			0.256014
$425$	0.211010	−	1.68994i	0.0102355	−	0.0819742i
$426$	9.09751			0.440776
$427$	5.41973	+	7.45962i	0.262279	+	0.360996i
$428$	1.73529	+	0.563830i	0.0838784	+	0.0272538i
$429$	6.50079	−	20.0074i	0.313861	−	0.965965i
$430$	−6.94981	+	17.5903i	−0.335150	+	0.848280i
$431$	8.27393	+	25.4645i	0.398541	+	1.22658i	0.926169	+	0.377108i	$0.123082\pi$
$431$	8.27393	+	25.4645i	0.398541	+	1.22658i	−0.527628	+	0.849476i	$0.676918\pi$
$432$		−	5.61649i		−	0.270223i
$433$	−21.4524	+	6.97032i	−1.03094	+	0.334972i	−0.775161	−	0.631763i	$-0.782331\pi$
$433$	−21.4524	+	6.97032i	−1.03094	+	0.334972i	−0.255778	+	0.966736i	$0.582331\pi$
$434$	−2.61540	−	1.90020i	−0.125543	−	0.0912126i
$435$	0.720901	−	11.5919i	0.0345646	−	0.555791i
$436$	−4.10192	+	2.98022i	−0.196446	+	0.142727i
$437$	−1.84006	+	2.53262i	−0.0880218	+	0.121152i
$438$	−12.3741	+	17.0315i	−0.591257	+	0.813795i
$439$	−13.3138	+	9.67305i	−0.635434	+	0.461670i	−0.858278	−	0.513184i	$-0.828466\pi$
$439$	−13.3138	+	9.67305i	−0.635434	+	0.461670i	0.222845	+	0.974854i	$0.428466\pi$
$440$	−0.495699	+	7.97074i	−0.0236315	+	0.379990i
$441$	2.70722	+	1.96691i	0.128915	+	0.0936622i
$442$	1.26308	−	0.410400i	0.0600787	−	0.0195207i
$443$			9.39956i			0.446587i	0.974751	+	0.223293i	$0.0716808\pi$
$443$			9.39956i			0.446587i	−0.974751	+	0.223293i	$0.928319\pi$
$444$	0.756819	+	2.32925i	0.0359170	+	0.110541i
$445$	14.5658	−	36.8667i	0.690483	−	1.74765i
$446$	1.64556	−	5.06452i	0.0779197	−	0.239812i
$447$	16.1922	+	5.26117i	0.765865	+	0.248845i
$448$	2.00720	+	2.76268i	0.0948314	+	0.130524i
$449$	16.6969			0.787974			0.393987	−	0.919116i	$-0.371096\pi$
$449$	16.6969			0.787974			0.393987	+	0.919116i	$0.371096\pi$
$450$	−3.25007	−	1.52364i	−0.153210	−	0.0718249i
$451$	9.04797			0.426052
$452$	5.40744	+	7.44270i	0.254344	+	0.350075i
$453$	9.90027	+	3.21679i	0.465155	+	0.151138i
$454$	5.48846	−	16.8917i	0.257586	−	0.792769i
$455$	−29.7155	−	1.84800i	−1.39309	−	0.0866357i
$456$	−0.466821	−	1.43673i	−0.0218609	−	0.0672809i
$457$			2.65622i			0.124253i	0.998068	+	0.0621263i	$0.0197882\pi$
$457$			2.65622i			0.124253i	−0.998068	+	0.0621263i	$0.980212\pi$
$458$	3.09614	−	1.00600i	0.144673	−	0.0470072i
$459$	1.54769	+	1.12446i	0.0722400	+	0.0524854i
$460$	−4.45807	+	5.39681i	−0.207858	+	0.251627i
$461$	20.4449	−	14.8541i	0.952215	−	0.691825i	0.000885598	−	1.00000i	$-0.499718\pi$
$461$	20.4449	−	14.8541i	0.952215	−	0.691825i	0.951330	+	0.308175i	$0.0997181\pi$
$462$	−10.8296	+	14.9056i	−0.503837	+	0.693472i
$463$	22.6305	−	31.1482i	1.05173	−	1.44758i	0.164426	−	0.986389i	$-0.447423\pi$
$463$	22.6305	−	31.1482i	1.05173	−	1.44758i	0.887302	−	0.461190i	$-0.152577\pi$
$464$	−2.78163	+	2.02097i	−0.129134	+	0.0938213i
$465$	1.71545	+	2.69881i	0.0795523	+	0.125155i
$466$	0.896751	+	0.651528i	0.0415412	+	0.0301815i
$467$	−4.28548	+	1.39244i	−0.198308	+	0.0644343i	−0.406487	−	0.913657i	$-0.633246\pi$
$467$	−4.28548	+	1.39244i	−0.198308	+	0.0644343i	0.208179	+	0.978091i	$0.433246\pi$
$468$		−	2.79915i		−	0.129391i
$469$	11.4853	+	35.3482i	0.530343	+	1.63223i
$470$	17.9898	+	14.8606i	0.829809	+	0.685469i
$471$	−3.49895	+	10.7687i	−0.161223	+	0.496194i
$472$	0.218028	+	0.0708417i	0.0100356	+	0.00326075i
$473$	17.7565	+	24.4397i	0.816444	+	1.12374i
$474$	13.0710			0.600370
$475$	−4.96147	−	0.619502i	−0.227648	−	0.0284247i
$476$	−1.16315			−0.0533127
$477$	2.22447	+	3.06172i	0.101852	+	0.140187i
$478$	−18.0572	−	5.86714i	−0.825917	−	0.268357i
$479$	−0.0265151	+	0.0816052i	−0.00121151	+	0.00372863i	−0.951660	−	0.307152i	$-0.900624\pi$
$479$	−0.0265151	+	0.0816052i	−0.00121151	+	0.00372863i	0.950449	+	0.310881i	$0.100624\pi$
$480$	−0.842423	−	3.27121i	−0.0384512	−	0.149310i
$481$	1.95339	+	6.01191i	0.0890668	+	0.274119i
$482$		−	24.6694i		−	1.12366i
$483$	−15.3589	+	4.99040i	−0.698853	+	0.227071i
$484$	1.42039	+	1.03197i	0.0645630	+	0.0469078i
$485$	32.0900	−	8.26402i	1.45713	−	0.375250i
$486$	5.89414	−	4.28235i	0.267364	−	0.194251i
$487$	−13.0688	+	17.9876i	−0.592203	+	0.815098i	−0.994967	−	0.100206i	$-0.968050\pi$
$487$	−13.0688	+	17.9876i	−0.592203	+	0.815098i	0.402764	+	0.915304i	$0.368050\pi$
$488$	−1.58710	+	2.18446i	−0.0718448	+	0.0988859i
$489$	27.4247	−	19.9252i	1.24019	−	0.901048i
$490$	9.69373	+	3.82992i	0.437918	+	0.173018i
$491$	−2.72206	−	1.97769i	−0.122845	−	0.0892520i	0.524666	−	0.851308i	$-0.324190\pi$
$491$	−2.72206	−	1.97769i	−0.122845	−	0.0892520i	−0.647511	+	0.762056i	$0.724190\pi$
$492$	−3.63976	+	1.18263i	−0.164093	+	0.0533171i
$493$		−	1.17112i		−	0.0527448i
$494$	−1.20489	−	3.70826i	−0.0542104	−	0.166843i
$495$	−4.83850	+	3.07551i	−0.217475	+	0.138234i
$496$	0.292544	−	0.900357i	0.0131356	−	0.0404272i
$497$	−19.5584	−	6.35492i	−0.877315	−	0.285057i
$498$	−7.02639	−	9.67100i	−0.314860	−	0.433368i
$499$	−5.34425			−0.239241			−0.119621	−	0.992820i	$-0.538168\pi$
$499$	−5.34425			−0.239241			−0.119621	+	0.992820i	$0.538168\pi$
$500$	−10.9868	−	2.07119i	−0.491345	−	0.0926266i
$501$	20.7790			0.928336
$502$	−13.6832	−	18.8333i	−0.610712	−	0.840573i
$503$	36.8970	+	11.9885i	1.64515	+	0.534543i	0.977682	−	0.210092i	$-0.0673763\pi$
$503$	36.8970	+	11.9885i	1.64515	+	0.534543i	0.667472	+	0.744635i	$0.267376\pi$
$504$	−0.757560	+	2.33153i	−0.0337444	+	0.103855i
$505$	−4.36809	+	2.77650i	−0.194377	+	0.123553i
$506$	3.45499	+	10.6334i	0.153593	+	0.472711i
$507$			3.32792i			0.147798i
$508$	−9.82784	+	3.19326i	−0.436040	+	0.141678i
$509$	11.6956	+	8.49732i	0.518397	+	0.376637i	0.816000	−	0.578053i	$-0.196187\pi$
$509$	11.6956	+	8.49732i	0.518397	+	0.376637i	−0.297603	+	0.954690i	$0.596187\pi$
$510$	1.07008	+	0.422781i	0.0473840	+	0.0187211i
$511$	38.4997	−	27.9717i	1.70313	−	1.23739i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	3.30129	−	4.54384i	0.145756	−	0.200615i
$514$	20.7637	−	15.0857i	0.915849	−	0.665403i
$515$	16.4833	−	4.24489i	0.726342	−	0.187052i
$516$	−10.3374	−	7.51056i	−0.455079	−	0.330634i
$517$	35.4455	−	11.5169i	1.55889	−	0.506515i
$518$		−	5.53624i		−	0.243248i
$519$	−2.48197	−	7.63872i	−0.108946	−	0.335302i
$520$	−2.17434	−	8.44316i	−0.0953509	−	0.370257i
$521$	8.91409	−	27.4347i	0.390533	−	1.20194i	−0.541852	−	0.840474i	$-0.682277\pi$
$521$	8.91409	−	27.4347i	0.390533	−	1.20194i	0.932386	−	0.361465i	$-0.117723\pi$
$522$	−2.34753	−	0.762757i	−0.102748	−	0.0333850i
$523$	10.3793	+	14.2859i	0.453856	+	0.624679i	0.973220	−	0.229874i	$-0.0738313\pi$
$523$	10.3793	+	14.2859i	0.453856	+	0.624679i	−0.519364	+	0.854553i	$0.673831\pi$
$524$	−21.9212			−0.957631
$525$	−18.8281	−	17.6297i	−0.821727	−	0.769423i
$526$	−12.1425			−0.529437
$527$	0.189534	+	0.260872i	0.00825625	+	0.0113638i
$528$	−5.13128	−	1.66726i	−0.223310	−	0.0725580i
$529$	4.07903	−	12.5540i	0.177349	−	0.545825i
$530$	9.08805	+	7.50724i	0.394760	+	0.326094i
$531$	0.0508570	+	0.156522i	0.00220701	+	0.00679247i
$532$			3.41486i			0.148053i
$533$	−9.39441	+	3.05243i	−0.406917	+	0.132215i
$534$	21.6656	+	15.7410i	0.937564	+	0.681180i
$535$	2.18861	+	3.44321i	0.0946220	+	0.148863i
$536$	−8.80534	+	6.39745i	−0.380333	+	0.276328i
$537$	−12.7848	+	17.5967i	−0.551704	+	0.759356i
$538$	−11.0561	+	15.2174i	−0.476662	+	0.656069i
$539$	13.4683	−	9.78530i	0.580121	−	0.421482i
$540$	7.99833	−	9.68254i	0.344193	−	0.416670i
$541$	−10.7912	−	7.84025i	−0.463949	−	0.337079i	0.331129	−	0.943585i	$-0.392570\pi$
$541$	−10.7912	−	7.84025i	−0.463949	−	0.337079i	−0.795078	+	0.606507i	$0.792570\pi$
$542$	10.5163	−	3.41695i	0.451713	−	0.146770i
$543$			25.0846i			1.07648i
$544$	−0.105255	−	0.323942i	−0.00451278	−	0.0138889i
$545$	−11.3156	−	0.703713i	−0.484705	−	0.0301437i
$546$	6.21565	−	19.1298i	0.266005	−	0.818680i
$547$	4.50744	+	1.46456i	0.192724	+	0.0626199i	0.403789	−	0.914852i	$-0.367693\pi$
$547$	4.50744	+	1.46456i	0.192724	+	0.0626199i	−0.211065	+	0.977472i	$0.567693\pi$
$548$	7.94061	+	10.9293i	0.339206	+	0.466877i
$549$	−1.93842			−0.0827299
$550$	−12.2055	+	13.0352i	−0.520445	+	0.555824i
$551$	−3.43829			−0.146476
$552$	−2.77971	−	3.82594i	−0.118312	−	0.162843i
$553$	−28.1009	−	9.13053i	−1.19497	−	0.388270i
$554$	0.459328	−	1.41367i	0.0195150	−	0.0600610i
$555$	−2.01232	+	5.09328i	−0.0854181	+	0.216198i
$556$	−1.77414	−	5.46024i	−0.0752402	−	0.231566i
$557$			4.47844i			0.189757i	0.995489	+	0.0948787i	$0.0302463\pi$
$557$			4.47844i			0.189757i	−0.995489	+	0.0948787i	$0.969754\pi$
$558$	0.646363	−	0.210016i	0.0273627	−	0.00889069i
$559$	−26.6813	−	19.3851i	−1.12850	−	0.819904i
$560$	−0.473957	+	7.62113i	−0.0200283	+	0.322052i
$561$	1.48675	−	1.08019i	0.0627707	−	0.0456056i
$562$	−5.24055	+	7.21300i	−0.221059	+	0.304262i
$563$	20.2329	−	27.8482i	0.852716	−	1.17366i	−0.130542	−	0.991443i	$-0.541672\pi$
$563$	20.2329	−	27.8482i	0.852716	−	1.17366i	0.983258	−	0.182220i	$-0.0583282\pi$
$564$	−12.7535	+	9.26593i	−0.537018	+	0.390166i
$565$	−1.27685	+	20.5314i	−0.0537173	+	0.863764i
$566$	0.687049	+	0.499171i	0.0288788	+	0.0209817i
$567$	20.5611	−	6.68071i	0.863486	−	0.280564i
$568$		−	6.02219i		−	0.252686i
$569$	0.302663	+	0.931500i	0.0126883	+	0.0390505i	0.957200	−	0.289427i	$-0.0934646\pi$
$569$	0.302663	+	0.931500i	0.0126883	+	0.0390505i	−0.944512	+	0.328477i	$0.893465\pi$
$570$	1.24124	−	3.14163i	0.0519897	−	0.131588i
$571$	−0.505686	+	1.55634i	−0.0211623	+	0.0651309i	−0.961080	−	0.276270i	$-0.910901\pi$
$571$	−0.505686	+	1.55634i	−0.0211623	+	0.0651309i	0.939918	+	0.341401i	$0.110901\pi$
$572$	−13.2441	−	4.30327i	−0.553763	−	0.179929i
$573$	9.70276	+	13.3547i	0.405339	+	0.557901i
$574$	8.65111			0.361090
$575$	−15.3710	+	2.95518i	−0.641013	+	0.123239i
$576$	−0.717897			−0.0299124
$577$	−0.293323	−	0.403725i	−0.0122112	−	0.0168073i	0.802868	−	0.596157i	$-0.203306\pi$
$577$	−0.293323	−	0.403725i	−0.0122112	−	0.0168073i	−0.815079	+	0.579350i	$0.803306\pi$
$578$	−16.0576	−	5.21744i	−0.667909	−	0.217017i
$579$	9.82875	−	30.2498i	0.408469	−	1.25714i
$580$	−7.67342	−	0.477208i	−0.318621	−	0.0198150i
$581$	8.35028	+	25.6995i	0.346428	+	1.06620i
$582$			22.3870i			0.927972i
$583$	17.9063	−	5.81809i	0.741601	−	0.240961i
$584$	11.2742	+	8.19116i	0.466528	+	0.338953i
$585$	3.98621	−	4.82559i	0.164809	−	0.199514i
$586$	13.4094	−	9.74250i	0.553937	−	0.402459i
$587$	−7.19010	+	9.89632i	−0.296767	+	0.408465i	−0.931197	−	0.364515i	$-0.881235\pi$
$587$	−7.19010	+	9.89632i	−0.296767	+	0.408465i	0.634430	+	0.772980i	$0.281235\pi$
$588$	−4.13894	+	5.69677i	−0.170687	+	0.234931i
$589$	0.765889	−	0.556451i	0.0315579	−	0.0229282i
$590$	0.274986	+	0.432617i	0.0113210	+	0.0178106i
$591$	23.9844	+	17.4257i	0.986587	+	0.716797i
$592$	1.54187	−	0.500985i	0.0633706	−	0.0205903i
$593$			19.8598i			0.815545i	0.913084	+	0.407773i	$0.133694\pi$
$593$			19.8598i			0.815545i	−0.913084	+	0.407773i	$0.866306\pi$
$594$	−6.19868	−	19.0776i	−0.254335	−	0.782763i
$595$	−2.00520	−	1.65641i	−0.0822053	−	0.0679062i
$596$	3.48269	−	10.7186i	0.142656	−	0.439051i
$597$	−23.8221	−	7.74027i	−0.974974	−	0.316788i
$598$	−7.17456	−	9.87493i	−0.293389	−	0.403816i
$599$	4.65791			0.190317			0.0951585	−	0.995462i	$-0.469664\pi$
$599$	4.65791			0.190317			0.0951585	+	0.995462i	$0.469664\pi$
$600$	3.20617	−	6.83908i	0.130891	−	0.279204i
$601$	2.26664			0.0924582			0.0462291	−	0.998931i	$-0.485280\pi$
$601$	2.26664			0.0924582			0.0462291	+	0.998931i	$0.485280\pi$
$602$	16.9776	+	23.3677i	0.691957	+	0.952397i
$603$	−7.43116	−	2.41453i	−0.302620	−	0.0983273i
$604$	2.12939	−	6.55359i	0.0866437	−	0.266662i
$605$	0.979065	+	3.80181i	0.0398047	+	0.154565i
$606$	−1.08055	−	3.32559i	−0.0438943	−	0.135093i
$607$		−	12.3731i		−	0.502210i	−0.967960	−	0.251105i	$-0.919206\pi$
$607$		−	12.3731i		−	0.502210i	0.967960	−	0.251105i	$-0.0807939\pi$
$608$	−0.951057	+	0.309017i	−0.0385704	+	0.0125323i
$609$	−14.3496	−	10.4256i	−0.581475	−	0.422467i
$610$	−5.84693	+	1.50574i	−0.236735	+	0.0609655i
$611$	−32.9173	+	23.9158i	−1.33169	+	0.967531i
$612$	0.143728	−	0.197825i	0.00580987	−	0.00799660i
$613$	−10.9151	+	15.0234i	−0.440858	+	0.606789i	−0.970402	−	0.241493i	$-0.922363\pi$
$613$	−10.9151	+	15.0234i	−0.440858	+	0.606789i	0.529545	+	0.848282i	$0.322363\pi$
$614$	15.6587	−	11.3767i	0.631932	−	0.459126i
$615$	−7.95892	−	3.14451i	−0.320935	−	0.126799i
$616$	9.86694	+	7.16875i	0.397550	+	0.288837i
$617$	−13.1698	+	4.27911i	−0.530194	+	0.172271i	−0.561867	−	0.827228i	$-0.689917\pi$
$617$	−13.1698	+	4.27911i	−0.530194	+	0.172271i	0.0316725	+	0.999498i	$0.489917\pi$
$618$			11.4993i			0.462569i
$619$	−14.7931	−	45.5286i	−0.594586	−	1.82995i	−0.556776	−	0.830663i	$-0.687962\pi$
$619$	−14.7931	−	45.5286i	−0.594586	−	1.82995i	−0.0378105	−	0.999285i	$-0.512038\pi$
$620$	1.78651	−	1.13556i	0.0717480	−	0.0456053i
$621$	5.43325	−	16.7218i	0.218029	−	0.671024i
$622$	−11.0871	−	3.60240i	−0.444550	−	0.144443i
$623$	−35.5826	−	48.9752i	−1.42559	−	1.96215i
$624$	5.89022			0.235798
$625$	−15.9912	−	19.2167i	−0.639647	−	0.768669i
$626$	23.4098			0.935642
$627$	−3.17131	−	4.36493i	−0.126650	−	0.174319i
$628$	7.12843	+	2.31617i	0.284455	+	0.0924252i
$629$	−0.170642	+	0.525182i	−0.00680394	+	0.0209404i
$630$	−4.62628	+	2.94061i	−0.184315	+	0.117157i
$631$	5.56767	+	17.1355i	0.221646	+	0.682155i	0.998615	+	0.0526165i	$0.0167561\pi$
$631$	5.56767	+	17.1355i	0.221646	+	0.682155i	−0.776969	+	0.629539i	$0.783244\pi$
$632$		−	8.65248i		−	0.344177i
$633$	−26.5708	+	8.63337i	−1.05609	+	0.343146i
$634$	3.91222	+	2.84240i	0.155374	+	0.112886i
$635$	−21.4902	−	8.49061i	−0.852811	−	0.336940i
$636$	−6.44276	+	4.68094i	−0.255472	+	0.185611i
$637$	−10.6828	+	14.7036i	−0.423269	+	0.582579i
$638$	−7.21793	+	9.93463i	−0.285761	+	0.393316i
$639$	3.49763	−	2.54118i	0.138364	−	0.100528i
$640$	−2.16542	+	0.557651i	−0.0855956	+	0.0220431i
$641$	−28.3480	−	20.5961i	−1.11968	−	0.813495i	−0.135519	−	0.990775i	$-0.543270\pi$
$641$	−28.3480	−	20.5961i	−1.11968	−	0.813495i	−0.984161	+	0.177280i	$0.943270\pi$
$642$	−2.62144	+	0.851757i	−0.103460	+	0.0336162i
$643$			27.0771i			1.06782i	0.845542	+	0.533909i	$0.179277\pi$
$643$			27.0771i			1.06782i	−0.845542	+	0.533909i	$0.820723\pi$
$644$	3.30345	+	10.1670i	0.130174	+	0.400635i
$645$	−7.12552	−	27.6691i	−0.280567	−	1.08947i
$646$	0.105255	−	0.323942i	0.00414121	−	0.0127453i
$647$	−35.5018	−	11.5352i	−1.39572	−	0.453496i	−0.487915	−	0.872891i	$-0.662242\pi$
$647$	−35.5018	−	11.5352i	−1.39572	−	0.453496i	−0.907804	+	0.419395i	$0.862242\pi$
$648$	3.72123	+	5.12183i	0.146184	+	0.201205i
$649$	0.818764			0.0321393
$650$	8.27529	−	17.6520i	0.324584	−	0.692369i
$651$	4.88370			0.191407
$652$	−13.1897	−	18.1541i	−0.516548	−	0.710968i
$653$	31.2671	+	10.1593i	1.22358	+	0.397564i	0.848383	−	0.529383i	$-0.177577\pi$
$653$	31.2671	+	10.1593i	1.22358	+	0.397564i	0.375192	+	0.926947i	$0.377577\pi$
$654$	2.36690	−	7.28456i	0.0925530	−	0.284849i
$655$	−37.7910	−	31.2175i	−1.47662	−	1.21977i
$656$	0.782855	+	2.40938i	0.0305654	+	0.0940705i
$657$			10.0043i			0.390307i
$658$	33.8908	−	11.0118i	1.32120	−	0.429284i
$659$	32.3510	+	23.5044i	1.26022	+	0.915601i	0.998768	−	0.0496164i	$-0.0157999\pi$
$659$	32.3510	+	23.5044i	1.26022	+	0.915601i	0.261448	+	0.965217i	$0.415800\pi$
$660$	−6.47177	−	10.1816i	−0.251913	−	0.396319i
$661$	−25.2210	+	18.3241i	−0.980983	+	0.712726i	−0.957928	−	0.287008i	$-0.907339\pi$
$661$	−25.2210	+	18.3241i	−0.980983	+	0.712726i	−0.0230551	+	0.999734i	$0.507339\pi$
$662$	−15.9760	+	21.9891i	−0.620927	+	0.854632i
$663$	−1.17927	+	1.62312i	−0.0457989	+	0.0630367i
$664$	−6.40183	+	4.65120i	−0.248439	+	0.180502i
$665$	−4.86303	+	5.88704i	−0.188580	+	0.228290i
$666$	0.941590	+	0.684105i	0.0364859	+	0.0265085i
$667$	−10.2367	+	3.32611i	−0.396367	+	0.128788i
$668$		−	13.7549i		−	0.532192i
$669$	2.48589	+	7.65079i	0.0961101	+	0.295797i
$670$	−24.2904	−	1.51062i	−0.938421	−	0.0583602i
$671$	−2.98003	+	9.17160i	−0.115043	+	0.354066i
$672$	−4.90622	−	1.59413i	−0.189261	−	0.0614948i
$673$	13.1137	+	18.0494i	0.505495	+	0.695754i	0.983152	−	0.182793i	$-0.0585137\pi$
$673$	13.1137	+	18.0494i	0.505495	+	0.695754i	−0.477657	+	0.878547i	$0.658514\pi$
$674$	8.36912			0.322366
$675$	27.5774	−	5.30195i	1.06145	−	0.204072i
$676$	2.20295			0.0847289
$677$	−25.1934	−	34.6757i	−0.968259	−	1.33269i	−0.942921	−	0.333016i	$-0.891934\pi$
$677$	−25.1934	−	34.6757i	−0.968259	−	1.33269i	−0.0253380	−	0.999679i	$-0.508066\pi$
$678$	−13.2174	−	4.29460i	−0.507612	−	0.164933i
$679$	15.6381	−	48.1291i	0.600135	−	1.84703i
$680$	0.279865	−	0.708351i	0.0107323	−	0.0271640i
$681$	8.29121	+	25.5177i	0.317720	+	0.977842i
$682$		−	3.38112i		−	0.129470i
$683$	−23.8613	+	7.75301i	−0.913027	+	0.296661i	−0.727603	−	0.685998i	$-0.759366\pi$
$683$	−23.8613	+	7.75301i	−0.913027	+	0.296661i	−0.185424	+	0.982659i	$0.559366\pi$
$684$	−0.580791	−	0.421969i	−0.0222071	−	0.0161344i
$685$	−1.87500	+	30.1496i	−0.0716400	+	1.15196i
$686$	−6.46119	+	4.69433i	−0.246689	+	0.179230i
$687$	−2.89069	+	3.97869i	−0.110287	+	0.151796i
$688$	−4.97170	+	6.84296i	−0.189544	+	0.260885i
$689$	−16.6291	+	12.0817i	−0.633517	+	0.460277i
$690$	0.656366	−	10.5542i	0.0249874	−	0.401793i
$691$	−26.8027	−	19.4733i	−1.01962	−	0.740798i	−0.0534162	−	0.998572i	$-0.517011\pi$
$691$	−26.8027	−	19.4733i	−1.01962	−	0.740798i	−0.966205	+	0.257774i	$0.917011\pi$
$692$	−5.05653	+	1.64297i	−0.192221	+	0.0624562i
$693$			8.75562i			0.332598i
$694$	−3.84044	−	11.8196i	−0.145781	−	0.448668i
$695$	4.71728	−	11.9397i	0.178937	−	0.452898i
$696$	1.60506	−	4.93987i	0.0608397	−	0.187245i
$697$	−0.820666	−	0.266651i	−0.0310850	−	0.0101001i
$698$	−14.5555	−	20.0340i	−0.550936	−	0.758298i
$699$	−1.67449			−0.0633350
$700$	−11.6702	+	12.4635i	−0.441091	+	0.471076i
$701$	21.7218			0.820422			0.410211	−	0.911991i	$-0.365455\pi$
$701$	21.7218			0.820422			0.410211	+	0.911991i	$0.365455\pi$
$702$	12.8720	+	17.7169i	0.485824	+	0.668679i
$703$	1.54187	+	0.500985i	0.0581528	+	0.0188950i
$704$	−1.10366	+	3.39671i	−0.0415957	+	0.128018i
$705$	−35.1817	−	2.18795i	−1.32502	−	0.0824028i
$706$	−7.20347	−	22.1700i	−0.271106	−	0.834379i
$707$			7.90437i			0.297274i
$708$	−0.329367	+	0.107018i	−0.0123784	+	0.00402198i
$709$	−20.4217	−	14.8373i	−0.766954	−	0.557225i	0.134081	−	0.990970i	$-0.457192\pi$
$709$	−20.4217	−	14.8373i	−0.766954	−	0.557225i	−0.901035	+	0.433746i	$0.857192\pi$
$710$	8.57608	−	10.3820i	0.321855	−	0.389628i
$711$	5.02528	−	3.65108i	0.188463	−	0.136926i
$712$	10.4199	−	14.3418i	0.390503	−	0.537482i
$713$	1.74197	−	2.39761i	0.0652371	−	0.0897912i
$714$	1.42154	−	1.03281i	0.0531998	−	0.0386519i
$715$	−16.7039	−	26.2793i	−0.624692	−	0.982788i
$716$	11.6484	+	8.46303i	0.435320	+	0.316278i
$717$	27.2784	−	8.86327i	1.01873	−	0.331005i
$718$			15.0367i			0.561166i
$719$	10.8926	+	33.5240i	0.406225	+	1.25023i	0.919868	+	0.392228i	$0.128296\pi$
$719$	10.8926	+	33.5240i	0.406225	+	1.25023i	−0.513643	+	0.858004i	$0.671704\pi$
$720$	−1.23762	−	1.02234i	−0.0461233	−	0.0381004i
$721$	8.03265	−	24.7219i	0.299151	−	0.920693i
$722$	−0.951057	−	0.309017i	−0.0353947	−	0.0115004i
$723$	21.9051	+	30.1498i	0.814660	+	1.12128i
$724$	16.6051			0.617122
$725$	−12.5490	−	11.7502i	−0.466058	−	0.436393i
$726$	−2.65226			−0.0984347
$727$	−19.5541	−	26.9139i	−0.725220	−	0.998180i	−0.999334	−	0.0364828i	$-0.988385\pi$
$727$	−19.5541	−	26.9139i	−0.725220	−	0.998180i	0.274114	−	0.961697i	$-0.411615\pi$
$728$	−12.6632	−	4.11452i	−0.469329	−	0.152494i
$729$	−9.27015	+	28.5306i	−0.343339	+	1.05669i
$730$	7.77122	+	30.1764i	0.287626	+	1.11688i
$731$	−0.890286	−	2.74002i	−0.0329284	−	0.101343i
$732$		−	4.07900i		−	0.150764i
$733$	34.0267	−	11.0559i	1.25680	−	0.408360i	0.396450	−	0.918056i	$-0.370242\pi$
$733$	34.0267	−	11.0559i	1.25680	−	0.408360i	0.860355	+	0.509696i	$0.170242\pi$
$734$	19.7761	+	14.3682i	0.729949	+	0.530339i
$735$	−15.2480	+	3.92675i	−0.562430	+	0.144840i
$736$	−2.53262	+	1.84006i	−0.0933536	+	0.0678254i
$737$	−22.8486	+	31.4484i	−0.841638	+	1.15842i
$738$	−1.06901	+	1.47136i	−0.0393506	+	0.0541615i
$739$	0.836356	−	0.607648i	0.0307659	−	0.0223527i	−0.572296	−	0.820047i	$-0.693947\pi$
$739$	0.836356	−	0.607648i	0.0307659	−	0.0223527i	0.603062	+	0.797694i	$0.293947\pi$
$740$	3.37155	+	1.33208i	0.123941	+	0.0489681i
$741$	4.76529	+	3.46219i	0.175057	+	0.127187i
$742$	17.1209	−	5.56290i	0.628526	−	0.204221i
$743$			1.57736i			0.0578676i	0.999581	+	0.0289338i	$0.00921120\pi$
$743$			1.57736i			0.0578676i	−0.999581	+	0.0289338i	$0.990789\pi$
$744$	0.441935	+	1.36014i	0.0162021	+	0.0498650i
$745$	21.2681	−	13.5187i	0.779203	−	0.495287i
$746$	−2.48375	+	7.64419i	−0.0909364	+	0.279874i
$747$	−5.40275	−	1.75546i	−0.197676	−	0.0642289i
$748$	−0.715043	−	0.984172i	−0.0261445	−	0.0359849i
$749$	6.23073			0.227666
$750$	15.2667	−	7.22438i	0.557460	−	0.263797i
$751$	4.70865			0.171821			0.0859106	−	0.996303i	$-0.472620\pi$
$751$	4.70865			0.171821			0.0859106	+	0.996303i	$0.472620\pi$
$752$	6.13369	+	8.44229i	0.223673	+	0.307859i
$753$	33.4459	+	10.8672i	1.21884	+	0.396024i
$754$	4.14275	−	12.7501i	0.150870	−	0.464330i
$755$	13.0038	−	8.26563i	0.473256	−	0.300817i
$756$	−5.92680	−	18.2408i	−0.215556	−	0.663412i
$757$		−	14.5843i		−	0.530074i	−0.964238	−	0.265037i	$-0.914616\pi$
$757$		−	14.5843i		−	0.530074i	0.964238	−	0.265037i	$-0.0853842\pi$
$758$	19.8871	−	6.46171i	0.722332	−	0.234700i
$759$	−13.6644	−	9.92775i	−0.495985	−	0.360355i
$760$	−2.07964	−	0.821650i	−0.0754364	−	0.0298044i
$761$	−33.4923	+	24.3336i	−1.21409	+	0.882091i	−0.995596	−	0.0937461i	$-0.970116\pi$
$761$	−33.4923	+	24.3336i	−1.21409	+	0.882091i	−0.218498	+	0.975837i	$0.570116\pi$
$762$	9.17568	−	12.6292i	0.332400	−	0.457509i
$763$	−10.1770	+	14.0075i	−0.368433	+	0.507104i
$764$	8.84029	−	6.42285i	0.319831	−	0.232371i
$765$	0.529498	−	0.136360i	0.0191440	−	0.00493009i
$766$	−25.8360	−	18.7710i	−0.933494	−	0.678223i
$767$	−0.850114	+	0.276219i	−0.0306958	+	0.00997368i
$768$		−	1.51066i		−	0.0545114i
$769$	−1.76986	−	5.44708i	−0.0638229	−	0.196427i	0.914060	−	0.405578i	$-0.132930\pi$
$769$	−1.76986	−	5.44708i	−0.0638229	−	0.196427i	−0.977883	+	0.209152i	$0.932930\pi$
$770$	6.80123	+	26.4099i	0.245099	+	0.951745i
$771$	−11.9811	+	36.8741i	−0.431490	+	1.32799i
$772$	−20.0242	−	6.50625i	−0.720686	−	0.234165i
$773$	3.45391	+	4.75390i	0.124229	+	0.170986i	0.866601	−	0.499001i	$-0.166300\pi$
$773$	3.45391	+	4.75390i	0.124229	+	0.170986i	−0.742373	+	0.669987i	$0.766300\pi$
$774$	−6.07223			−0.218262
$775$	4.69698	+	0.586477i	0.168721	+	0.0210669i
$776$	14.8193			0.531983
$777$	4.91588	+	6.76613i	0.176356	+	0.242733i
$778$	−8.41292	−	2.73352i	−0.301618	−	0.0980016i
$779$	−0.782855	+	2.40938i	−0.0280487	+	0.0863250i
$780$	10.1544	+	8.38814i	0.363587	+	0.300344i
$781$	−6.64644	−	20.4556i	−0.237828	−	0.731961i
$782$		−	1.06629i		−	0.0381303i
$783$	18.3659	−	5.96746i	0.656345	−	0.213260i
$784$	3.77104	+	2.73982i	0.134680	+	0.0978507i
$785$	8.99065	+	14.1444i	0.320890	+	0.504836i
$786$	26.7910	−	19.4648i	0.955604	−	0.694287i
$787$	−17.9994	+	24.7740i	−0.641608	+	0.883097i	−0.998700	−	0.0509718i	$-0.983768\pi$
$787$	−17.9994	+	24.7740i	−0.641608	+	0.883097i	0.357092	+	0.934069i	$0.383768\pi$
$788$	11.5351	−	15.8767i	0.410922	−	0.565586i
$789$	14.8399	−	10.7819i	0.528316	−	0.383844i
$790$	12.3218	−	14.9164i	0.438391	−	0.530703i
$791$	25.4158	+	18.4656i	0.903680	+	0.656562i
$792$	−2.43849	+	0.792312i	−0.0866479	+	0.0281536i
$793$		−	10.5281i		−	0.373864i
$794$	8.60347	+	26.4788i	0.305326	+	0.939696i
$795$	−17.7730	−	1.10530i	−0.630343	−	0.0392009i
$796$	−5.12376	+	15.7693i	−0.181607	+	0.558928i
$797$	17.4586	+	5.67266i	0.618417	+	0.200936i	0.601437	−	0.798920i	$-0.294595\pi$
$797$	17.4586	+	5.67266i	0.618417	+	0.200936i	0.0169797	+	0.999856i	$0.494595\pi$
$798$	−3.03221	−	4.17348i	−0.107339	−	0.147739i
$799$	−3.55438			−0.125745
$800$	−4.52720	−	2.12236i	−0.160061	−	0.0750368i
$801$	12.7265			0.449668
$802$	−3.76907	−	5.18769i	−0.133091	−	0.183184i
$803$	47.3353	+	15.3802i	1.67043	+	0.542755i
$804$	5.08087	−	15.6373i	0.179189	−	0.551486i
$805$	−8.78359	+	22.2317i	−0.309581	+	0.783565i
$806$	1.14066	+	3.51058i	0.0401779	+	0.123655i
$807$		−	28.4152i		−	1.00026i
$808$	−2.20141	+	0.715281i	−0.0774453	+	0.0251635i
$809$	9.77574	+	7.10249i	0.343697	+	0.249710i	0.746220	−	0.665700i	$-0.231867\pi$
$809$	9.77574	+	7.10249i	0.343697	+	0.249710i	−0.402523	+	0.915410i	$0.631867\pi$
$810$	−0.878686	+	14.1291i	−0.0308739	+	0.496446i
$811$	−24.1358	+	17.5357i	−0.847521	+	0.615760i	−0.924461	−	0.381276i	$-0.875485\pi$
$811$	−24.1358	+	17.5357i	−0.847521	+	0.615760i	0.0769403	+	0.997036i	$0.475485\pi$
$812$	−6.90134	+	9.49888i	−0.242190	+	0.333345i
$813$	−9.81843	+	13.5139i	−0.344347	+	0.473954i
$814$	4.68438	−	3.40340i	0.164187	−	0.119289i
$815$	3.11446	−	50.0798i	0.109095	−	1.75422i
$816$	0.416281	+	0.302446i	0.0145727	+	0.0105877i
$817$	−8.04438	+	2.61378i	−0.281437	+	0.0914445i
$818$		−	16.5701i		−	0.579359i
$819$	−2.95380	−	9.09086i	−0.103214	−	0.317660i
$820$	−2.08155	+	5.26850i	−0.0726907	+	0.183984i
$821$	2.90051	−	8.92684i	0.101228	−	0.311549i	−0.887598	−	0.460618i	$-0.847628\pi$
$821$	2.90051	−	8.92684i	0.101228	−	0.311549i	0.988827	+	0.149069i	$0.0476278\pi$
$822$	−19.4093	−	6.30645i	−0.676976	−	0.219963i
$823$	−14.8360	−	20.4200i	−0.517150	−	0.711796i	0.467954	−	0.883753i	$-0.344991\pi$
$823$	−14.8360	−	20.4200i	−0.517150	−	0.711796i	−0.985105	+	0.171956i	$0.944991\pi$
$824$	7.61208			0.265180
$825$	3.34243	−	26.7689i	0.116369	−	0.931973i
$826$	0.782852			0.0272389
$827$	21.2563	+	29.2568i	0.739155	+	1.01736i	0.998667	+	0.0516202i	$0.0164385\pi$
$827$	21.2563	+	29.2568i	0.739155	+	1.01736i	−0.259511	+	0.965740i	$0.583561\pi$
$828$	−2.13738	−	0.694475i	−0.0742789	−	0.0241347i
$829$	−8.63081	+	26.5629i	−0.299761	+	0.922568i	0.681820	+	0.731520i	$0.261189\pi$
$829$	−8.63081	+	26.5629i	−0.299761	+	0.922568i	−0.981581	+	0.191048i	$0.938811\pi$
$830$	−17.6601	−	1.09828i	−0.612991	−	0.0381218i
$831$	0.693891	+	2.13558i	0.0240708	+	0.0740823i
$832$		−	3.89910i		−	0.135177i
$833$	−1.50998	+	0.490622i	−0.0523176	+	0.0169990i
$834$	7.01666	+	5.09790i	0.242967	+	0.176526i
$835$	19.5880	−	23.7127i	0.677871	−	0.820611i
$836$	−2.88941	+	2.09928i	−0.0999325	+	0.0726052i
$837$	−3.12530	+	4.30161i	−0.108026	+	0.148685i
$838$	14.4198	−	19.8471i	0.498123	−	0.685607i
$839$	−28.6898	+	20.8443i	−0.990480	+	0.719626i	−0.960026	−	0.279910i	$-0.909695\pi$
$839$	−28.6898	+	20.8443i	−0.990480	+	0.719626i	−0.0304540	+	0.999536i	$0.509695\pi$
$840$	−6.18790	−	9.73503i	−0.213503	−	0.335890i
$841$	13.8974	+	10.0971i	0.479222	+	0.348175i
$842$	−7.73589	+	2.51354i	−0.266596	+	0.0866224i
$843$		−	13.4687i		−	0.463887i
$844$	5.71495	+	17.5888i	0.196717	+	0.605432i
$845$	3.79777	+	3.13718i	0.130647	+	0.107922i
$846$	−2.31498	+	7.12478i	−0.0795906	+	0.244955i
$847$	5.70201	+	1.85270i	0.195923	+	0.0636594i
$848$	3.09860	+	4.26485i	0.106406	+	0.146456i
$849$	−1.28291			−0.0440295
$850$	1.49122	−	0.822612i	0.0511485	−	0.0282154i
$851$	5.07522			0.173976
$852$	5.34738	+	7.36004i	0.183198	+	0.252151i
$853$	49.9510	+	16.2301i	1.71029	+	0.555707i	0.990382	−	0.138363i	$-0.0441840\pi$
$853$	49.9510	+	16.2301i	1.71029	+	0.555707i	0.719908	+	0.694069i	$0.244184\pi$
$854$	−2.84932	+	8.76931i	−0.0975018	+	0.300080i
$855$	−0.400336	−	1.55454i	−0.0136912	−	0.0531643i
$856$	0.563830	+	1.73529i	0.0192713	+	0.0593110i
$857$			51.3654i			1.75461i	0.479935	+	0.877304i	$0.340660\pi$
$857$			51.3654i			1.75461i	−0.479935	+	0.877304i	$0.659340\pi$
$858$	20.0074	−	6.50079i	0.683040	−	0.221933i
$859$	39.3431	+	28.5844i	1.34237	+	0.975287i	0.999353	+	0.0359570i	$0.0114479\pi$
$859$	39.3431	+	28.5844i	1.34237	+	0.975287i	0.343014	+	0.939330i	$0.388552\pi$
$860$	−18.3159	+	4.71681i	−0.624566	+	0.160842i
$861$	−10.5730	+	7.68171i	−0.360326	+	0.261792i
$862$	−15.7380	+	21.6614i	−0.536037	+	0.737791i
$863$	28.9284	−	39.8165i	0.984734	−	1.35537i	0.0504951	−	0.998724i	$-0.483920\pi$
$863$	28.9284	−	39.8165i	0.984734	−	1.35537i	0.934239	−	0.356646i	$-0.116080\pi$
$864$	4.54384	−	3.30129i	0.154584	−	0.112312i
$865$	−11.0569	−	4.36851i	−0.375946	−	0.148534i
$866$	−18.2485	−	13.2583i	−0.620111	−	0.450537i
$867$	24.2577	−	7.88179i	0.823833	−	0.267680i
$868$		−	3.23282i		−	0.109729i
$869$	−9.54938	−	29.3900i	−0.323941	−	0.996986i
$870$	9.80182	−	6.23035i	0.332313	−	0.211229i
$871$	13.1140	−	40.3607i	0.444350	−	1.36757i
$872$	−4.82209	−	1.56679i	−0.163297	−	0.0530583i
$873$	6.25330	+	8.60693i	0.211642	+	0.291300i
$874$	−3.13049			−0.105890
$875$	−37.8678	+	4.86717i	−1.28016	+	0.164540i
$876$	−21.0521			−0.711283
$877$	34.5617	+	47.5701i	1.16707	+	1.60633i	0.680670	+	0.732590i	$0.261689\pi$
$877$	34.5617	+	47.5701i	1.16707	+	1.60633i	0.486396	+	0.873739i	$0.338311\pi$
$878$	−15.6513	−	5.08543i	−0.528207	−	0.171625i
$879$	−7.73752	+	23.8136i	−0.260980	+	0.803214i
$880$	−6.73983	+	4.28406i	−0.227200	+	0.144416i
$881$	−4.49139	−	13.8231i	−0.151319	−	0.465711i	0.846451	−	0.532467i	$-0.178735\pi$
$881$	−4.49139	−	13.8231i	−0.151319	−	0.465711i	−0.997769	+	0.0667561i	$0.978735\pi$
$882$			3.34630i			0.112676i
$883$	11.5664	−	3.75814i	0.389239	−	0.126472i	−0.107858	−	0.994166i	$-0.534399\pi$
$883$	11.5664	−	3.75814i	0.389239	−	0.126472i	0.497097	+	0.867695i	$0.334399\pi$
$884$	1.07444	+	0.780627i	0.0361374	+	0.0262553i
$885$	−0.720215	−	0.284552i	−0.0242098	−	0.00956510i
$886$	−7.60440	+	5.52492i	−0.255475	+	0.185613i
$887$	−15.7248	+	21.6434i	−0.527988	+	0.726713i	−0.986822	−	0.161809i	$-0.948267\pi$
$887$	−15.7248	+	21.6434i	−0.527988	+	0.726713i	0.458834	+	0.888522i	$0.348267\pi$
$888$	−1.43956	+	1.98138i	−0.0483083	+	0.0664907i
$889$	−28.5484	+	20.7417i	−0.957484	+	0.695653i
$890$	38.3873	−	9.88573i	1.28675	−	0.331370i
$891$	18.2927	+	13.2904i	0.612828	+	0.445246i
$892$	5.06452	−	1.64556i	0.169573	−	0.0550975i
$893$			10.4352i			0.349202i
$894$	5.26117	+	16.1922i	0.175960	+	0.541548i
$895$	8.02915	+	31.1780i	0.268385	+	1.04217i
$896$	−1.05525	+	3.24772i	−0.0352534	+	0.108499i
$897$	17.5368	+	5.69805i	0.585537	+	0.190252i
$898$	9.81417	+	13.5080i	0.327503	+	0.450769i
$899$	3.25500			0.108560
$900$	−0.677693	−	3.52493i	−0.0225898	−	0.117498i
$901$	−1.79559			−0.0598198
$902$	5.31826	+	7.31996i	0.177079	+	0.243728i
$903$	−41.4985	−	13.4837i	−1.38098	−	0.448709i
$904$	−2.84286	+	8.74941i	−0.0945520	+	0.291001i
$905$	28.6263	+	23.6469i	0.951569	+	0.786050i
$906$	3.21679	+	9.90027i	0.106871	+	0.328914i
$907$			29.5222i			0.980268i	0.871647	+	0.490134i	$0.163052\pi$
$907$			29.5222i			0.980268i	−0.871647	+	0.490134i	$0.836948\pi$
$908$	16.8917	−	5.48846i	0.560572	−	0.182141i
$909$	−1.34436	−	0.976731i	−0.0445894	−	0.0323961i
$910$	−15.9713	−	25.1266i	−0.529443	−	0.832939i
$911$	−41.5652	+	30.1989i	−1.37712	+	1.00053i	−0.379973	+	0.924997i	$0.624067\pi$
$911$	−41.5652	+	30.1989i	−1.37712	+	1.00053i	−0.997143	+	0.0755360i	$0.975933\pi$
$912$	0.887946	−	1.22215i	0.0294028	−	0.0404695i
$913$	−16.6118	+	22.8642i	−0.549771	+	0.756694i
$914$	−2.14893	+	1.56129i	−0.0710802	+	0.0516428i
$915$	5.80882	−	7.03199i	0.192034	−	0.232471i
$916$	2.63374	+	1.91352i	0.0870211	+	0.0632245i
$917$	−71.1939	+	23.1323i	−2.35103	+	0.763896i
$918$			1.91305i			0.0631400i
$919$	15.5217	+	47.7709i	0.512014	+	1.57582i	0.788650	+	0.614843i	$0.210781\pi$
$919$	15.5217	+	47.7709i	0.512014	+	1.57582i	−0.276635	+	0.960975i	$0.589219\pi$
$920$	−6.98649	−	0.434489i	−0.230338	−	0.0143247i
$921$	−9.03539	+	27.8081i	−0.297726	+	0.916308i
$922$	24.0345	+	7.80927i	0.791533	+	0.257185i
$923$	13.8019	+	18.9966i	0.454294	+	0.625281i
$924$	−18.4244			−0.606117
$925$	3.91540	+	7.09778i	0.128737	+	0.233374i
$926$	38.5013			1.26523
$927$	3.21206	+	4.42103i	0.105498	+	0.145206i
$928$	−3.27000	−	1.06249i	−0.107343	−	0.0348779i
$929$	−14.7356	+	45.3515i	−0.483459	+	1.48793i	0.350741	+	0.936472i	$0.385930\pi$
$929$	−14.7356	+	45.3515i	−0.483459	+	1.48793i	−0.834200	+	0.551462i	$0.814070\pi$
$930$	−1.17507	+	2.97416i	−0.0385320	+	0.0975264i
$931$	1.44041	+	4.43312i	0.0472075	+	0.145290i
$932$			1.10845i			0.0363083i
$933$	16.7488	−	5.44202i	0.548331	−	0.178164i
$934$	−3.64545	−	2.64857i	−0.119283	−	0.0866639i
$935$	0.168842	−	2.71494i	0.00552171	−	0.0887880i
$936$	2.26456	−	1.64530i	0.0740194	−	0.0537783i
$937$	−24.5797	+	33.8310i	−0.802984	+	1.10521i	0.189385	+	0.981903i	$0.439351\pi$
$937$	−24.5797	+	33.8310i	−0.802984	+	1.10521i	−0.992368	+	0.123309i	$0.960649\pi$
$938$	−21.8464	+	30.0690i	−0.713310	+	0.981787i
$939$	−28.6103	+	20.7866i	−0.933661	+	0.678345i
$940$	−1.44833	+	23.2889i	−0.0472395	+	0.759601i
$941$	−1.85320	−	1.34643i	−0.0604125	−	0.0438923i	0.557169	−	0.830399i	$-0.311888\pi$
$941$	−1.85320	−	1.34643i	−0.0604125	−	0.0438923i	−0.617582	+	0.786507i	$0.711888\pi$
$942$	−10.7687	+	3.49895i	−0.350862	+	0.114002i
$943$			7.93070i			0.258259i
$944$	0.0708417	+	0.218028i	0.00230570	+	0.00709622i
$945$	15.7589	−	39.8864i	0.512636	−	1.29751i
$946$	−9.33513	+	28.7306i	−0.303511	+	0.934112i
$947$	−36.3364	−	11.8064i	−1.18077	−	0.383657i	−0.348120	−	0.937450i	$-0.613180\pi$
$947$	−36.3364	−	11.8064i	−1.18077	−	0.383657i	−0.832654	+	0.553793i	$0.813180\pi$
$948$	7.68293	+	10.5747i	0.249530	+	0.343449i
$949$	−54.3364			−1.76383
$950$	−2.41509	−	4.37805i	−0.0783560	−	0.142043i
$951$	−7.30523			−0.236888
$952$	−0.683680	−	0.941004i	−0.0221582	−	0.0304981i
$953$	−54.6135	−	17.7450i	−1.76910	−	0.574816i	−0.771026	−	0.636803i	$-0.780256\pi$
$953$	−54.6135	−	17.7450i	−1.76910	−	0.574816i	−0.998077	+	0.0619869i	$0.980256\pi$
$954$	−1.16947	+	3.59927i	−0.0378631	+	0.116531i
$955$	24.3869	+	1.51661i	0.789140	+	0.0490765i
$956$	−5.86714	−	18.0572i	−0.189757	−	0.584012i
$957$		−	18.5508i		−	0.599661i
$958$	−0.0816052	+	0.0265151i	−0.00263654	+	0.000856665i
$959$	37.3220	+	27.1161i	1.20519	+	0.875623i
$960$	2.15130	−	2.60431i	0.0694330	−	0.0840536i
$961$	24.3545	−	17.6946i	0.785628	−	0.570792i
$962$	−3.71556	+	5.11403i	−0.119795	+	0.164883i
$963$	−0.769922	+	1.05971i	−0.0248104	+	0.0341486i
$964$	19.9580	−	14.5003i	0.642803	−	0.467024i
$965$	−25.2552	−	39.7325i	−0.812995	−	1.27903i
$966$	−13.0650	−	9.49230i	−0.420361	−	0.305410i
$967$	44.5541	−	14.4765i	1.43276	−	0.465533i	0.513129	−	0.858311i	$-0.328486\pi$
$967$	44.5541	−	14.4765i	1.43276	−	0.465533i	0.919633	+	0.392779i	$0.128486\pi$
$968$			1.75569i			0.0564302i
$969$	0.159005	+	0.489368i	0.00510798	+	0.0157208i
$970$	25.5478	+	21.1039i	0.820289	+	0.677605i
$971$	−5.84746	+	17.9966i	−0.187654	+	0.577539i	−0.999984	−	0.00565864i	$-0.998199\pi$
$971$	−5.84746	+	17.9966i	−0.187654	+	0.577539i	0.812330	+	0.583198i	$0.198199\pi$
$972$	6.92898	+	2.25136i	0.222247	+	0.0722125i
$973$	−11.5238	−	15.8612i	−0.369437	−	0.508486i
$974$	−22.2339			−0.712421
$975$	5.56036	+	28.9214i	0.178074	+	0.926228i
$976$	−2.70014			−0.0864294
$977$	20.7344	+	28.5384i	0.663352	+	0.913025i	0.999587	−	0.0287528i	$-0.00915355\pi$
$977$	20.7344	+	28.5384i	0.663352	+	0.913025i	−0.336235	+	0.941778i	$0.609154\pi$
$978$	32.2396	+	10.4753i	1.03091	+	0.334963i
$979$	19.5650	−	60.2150i	0.625301	−	1.92448i
$980$	2.59936	+	10.0936i	0.0830334	+	0.322427i
$981$	−1.12480	−	3.46177i	−0.0359120	−	0.110526i
$982$		−	3.36465i		−	0.107370i
$983$	−29.0724	+	9.44621i	−0.927267	+	0.301287i	−0.733444	−	0.679749i	$-0.762089\pi$
$983$	−29.0724	+	9.44621i	−0.927267	+	0.301287i	−0.193822	+	0.981037i	$0.562089\pi$
$984$	−3.09617	−	2.24950i	−0.0987022	−	0.0717113i
$985$	42.4957	−	10.9438i	1.35403	−	0.348697i
$986$	0.947460	−	0.688370i	0.0301733	−	0.0219222i
$987$	−31.6419	+	43.5513i	−1.00717	+	1.38625i
$988$	2.29183	−	3.15444i	0.0729129	−	0.100356i
$989$	−21.4218	+	15.5639i	−0.681174	+	0.494902i
$990$	−5.33214	−	2.10669i	−0.169467	−	0.0669551i
$991$	−5.00779	−	3.63837i	−0.159078	−	0.115577i	0.505399	−	0.862886i	$-0.331345\pi$
$991$	−5.00779	−	3.63837i	−0.159078	−	0.115577i	−0.664476	+	0.747309i	$0.731345\pi$
$992$	0.900357	−	0.292544i	0.0285864	−	0.00928827i
$993$		−	41.0599i		−	1.30300i
$994$	−6.35492	−	19.5584i	−0.201566	−	0.620356i
$995$	−31.2898	+	19.8888i	−0.991954	+	0.630518i
$996$	3.69399	−	11.3689i	0.117049	−	0.360239i
$997$	28.3098	+	9.19840i	0.896579	+	0.291316i	0.720824	−	0.693118i	$-0.243763\pi$
$997$	28.3098	+	9.19840i	0.896579	+	0.291316i	0.175755	+	0.984434i	$0.443763\pi$
$998$	−3.14127	−	4.32359i	−0.0994352	−	0.136861i
$999$	−9.10557			−0.288087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.b.39.16	✓	96
25.9	even	10	inner	950.2.n.b.609.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.b.39.16	✓	96	1.1	even	1	trivial
950.2.n.b.609.16	yes	96	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.43673 - 0.466821i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.88711 + 1.19951i) q^{5} +(-0.466821 - 1.43673i) q^{6} +3.41486i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.580791 - 0.421969i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.43673 - 0.466821i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.88711 + 1.19951i) q^{5} +(-0.466821 - 1.43673i) q^{6} +3.41486i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.580791 - 0.421969i) q^{9} +(-2.07964 - 0.821650i) q^{10} +(-2.88941 + 2.09928i) q^{11} +(0.887946 - 1.22215i) q^{12} +(2.29183 - 3.15444i) q^{13} +(-2.76268 + 2.00720i) q^{14} +(3.27121 - 0.842423i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.323942 - 0.105255i) q^{17} -0.717897i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-0.557651 - 2.16542i) q^{20} +(1.59413 - 4.90622i) q^{21} +(-3.39671 - 1.10366i) q^{22} +(-1.84006 - 2.53262i) q^{23} +1.51066 q^{24} +(2.12236 - 4.52720i) q^{25} +3.89910 q^{26} +(3.30129 + 4.54384i) q^{27} +(-3.24772 - 1.05525i) q^{28} +(1.06249 - 3.27000i) q^{29} +(2.60431 + 2.15130i) q^{30} +(0.292544 + 0.900357i) q^{31} -1.00000i q^{32} +(5.13128 - 1.66726i) q^{33} +(0.275562 + 0.200207i) q^{34} +(-4.09615 - 6.44421i) q^{35} +(0.580791 - 0.421969i) q^{36} +(-0.952929 + 1.31159i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-4.76529 + 3.46219i) q^{39} +(1.42408 - 1.72395i) q^{40} +(-2.04954 - 1.48908i) q^{41} +(4.90622 - 1.59413i) q^{42} -8.45836i q^{43} +(-1.10366 - 3.39671i) q^{44} +(1.60217 + 0.0996387i) q^{45} +(0.967375 - 2.97727i) q^{46} +(-9.92451 - 3.22467i) q^{47} +(0.887946 + 1.22215i) q^{48} -4.66126 q^{49} +(4.91008 - 0.943998i) q^{50} -0.514551 q^{51} +(2.29183 + 3.15444i) q^{52} +(-5.01363 - 1.62903i) q^{53} +(-1.73559 + 5.34160i) q^{54} +(2.93453 - 7.42745i) q^{55} +(-1.05525 - 3.24772i) q^{56} +1.51066i q^{57} +(3.27000 - 1.06249i) q^{58} +(-0.185466 - 0.134749i) q^{59} +(-0.209669 + 3.37143i) q^{60} +(2.18446 - 1.58710i) q^{61} +(-0.556451 + 0.765889i) q^{62} +(1.44096 - 1.98332i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.541165 + 8.70183i) q^{65} +(4.36493 + 3.17131i) q^{66} +(10.3513 - 3.36334i) q^{67} +0.340613i q^{68} +(1.46138 + 4.49766i) q^{69} +(2.80582 - 7.10167i) q^{70} +(-1.86096 + 5.72745i) q^{71} +(0.682760 + 0.221842i) q^{72} +(-8.19116 - 11.2742i) q^{73} -1.62122 q^{74} +(-5.16264 + 5.51359i) q^{75} +1.00000 q^{76} +(-7.16875 - 9.86694i) q^{77} +(-5.60193 - 1.82018i) q^{78} +(-2.67376 + 8.22900i) q^{79} +(2.23176 + 0.138793i) q^{80} +(-1.95637 - 6.02108i) q^{81} -2.53337i q^{82} +(7.52580 - 2.44528i) q^{83} +(4.17348 + 3.03221i) q^{84} +(-0.485060 + 0.587199i) q^{85} +(6.84296 - 4.97170i) q^{86} +(-3.05301 + 4.20211i) q^{87} +(2.09928 - 2.88941i) q^{88} +(-14.3418 + 10.4199i) q^{89} +(0.861123 + 1.35475i) q^{90} +(10.7719 + 7.82628i) q^{91} +(2.97727 - 0.967375i) q^{92} -1.43013i q^{93} +(-3.22467 - 9.92451i) q^{94} +(1.72395 + 1.42408i) q^{95} +(-0.466821 + 1.43673i) q^{96} +(-14.0940 - 4.57943i) q^{97} +(-2.73982 - 3.77104i) q^{98} +2.56398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

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