LMFDB - Embedded newform 1001.2.i.d.716.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, degree $2$, 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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			716.21
Character	$\chi$	$=$	1001.716
Dual form			1001.2.i.d.144.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.865559 - 1.49919i) q^{2} +(0.0316961 + 0.0548993i) q^{3} +(-0.498384 - 0.863226i) q^{4} +(-1.64023 + 2.84097i) q^{5} +0.109739 q^{6} +(-2.63578 + 0.229444i) q^{7} +1.73671 q^{8} +(1.49799 - 2.59460i) q^{9} +O(q^{10})$	\(q+(0.865559 - 1.49919i) q^{2} +(0.0316961 + 0.0548993i) q^{3} +(-0.498384 - 0.863226i) q^{4} +(-1.64023 + 2.84097i) q^{5} +0.109739 q^{6} +(-2.63578 + 0.229444i) q^{7} +1.73671 q^{8} +(1.49799 - 2.59460i) q^{9} +(2.83944 + 4.91805i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.0315937 - 0.0547219i) q^{12} -1.00000 q^{13} +(-1.93744 + 4.15014i) q^{14} -0.207956 q^{15} +(2.49999 - 4.33012i) q^{16} +(3.93858 + 6.82182i) q^{17} +(-2.59320 - 4.49155i) q^{18} +(-3.87047 + 6.70386i) q^{19} +3.26986 q^{20} +(-0.0961405 - 0.137430i) q^{21} -1.73112 q^{22} +(-4.05683 + 7.02664i) q^{23} +(0.0550471 + 0.0953444i) q^{24} +(-2.88073 - 4.98957i) q^{25} +(-0.865559 + 1.49919i) q^{26} +0.380099 q^{27} +(1.51169 + 2.16093i) q^{28} +5.70844 q^{29} +(-0.179998 + 0.311766i) q^{30} +(2.04467 + 3.54147i) q^{31} +(-2.59107 - 4.48787i) q^{32} +(0.0316961 - 0.0548993i) q^{33} +13.6363 q^{34} +(3.67146 - 7.86452i) q^{35} -2.98630 q^{36} +(-1.05726 + 1.83123i) q^{37} +(6.70024 + 11.6052i) q^{38} +(-0.0316961 - 0.0548993i) q^{39} +(-2.84861 + 4.93394i) q^{40} -3.97994 q^{41} +(-0.289250 + 0.0251791i) q^{42} -1.44901 q^{43} +(-0.498384 + 0.863226i) q^{44} +(4.91411 + 8.51148i) q^{45} +(7.02286 + 12.1639i) q^{46} +(-2.32254 + 4.02275i) q^{47} +0.316961 q^{48} +(6.89471 - 1.20953i) q^{49} -9.97376 q^{50} +(-0.249675 + 0.432451i) q^{51} +(0.498384 + 0.863226i) q^{52} +(5.99360 + 10.3812i) q^{53} +(0.328998 - 0.569841i) q^{54} +3.28047 q^{55} +(-4.57760 + 0.398479i) q^{56} -0.490716 q^{57} +(4.94099 - 8.55805i) q^{58} +(-4.78753 - 8.29225i) q^{59} +(0.103642 + 0.179513i) q^{60} +(4.80245 - 8.31809i) q^{61} +7.07912 q^{62} +(-3.35306 + 7.18250i) q^{63} +1.02908 q^{64} +(1.64023 - 2.84097i) q^{65} +(-0.0548697 - 0.0950372i) q^{66} +(1.40360 + 2.43111i) q^{67} +(3.92585 - 6.79977i) q^{68} -0.514344 q^{69} +(-8.61256 - 12.3114i) q^{70} -6.59212 q^{71} +(2.60158 - 4.50607i) q^{72} +(-5.23596 - 9.06894i) q^{73} +(1.83025 + 3.17008i) q^{74} +(0.182616 - 0.316300i) q^{75} +7.71592 q^{76} +(1.51660 + 2.16793i) q^{77} -0.109739 q^{78} +(-3.20499 + 5.55120i) q^{79} +(8.20115 + 14.2048i) q^{80} +(-4.48192 - 7.76292i) q^{81} +(-3.44487 + 5.96670i) q^{82} +12.1151 q^{83} +(-0.0707185 + 0.151484i) q^{84} -25.8407 q^{85} +(-1.25421 + 2.17235i) q^{86} +(0.180936 + 0.313390i) q^{87} +(-0.868357 - 1.50404i) q^{88} +(6.65199 - 11.5216i) q^{89} +17.0138 q^{90} +(2.63578 - 0.229444i) q^{91} +8.08744 q^{92} +(-0.129616 + 0.224502i) q^{93} +(4.02058 + 6.96385i) q^{94} +(-12.6970 - 21.9918i) q^{95} +(0.164254 - 0.284496i) q^{96} -10.6903 q^{97} +(4.15446 - 11.3834i) q^{98} -2.99598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.865559	−	1.49919i	0.612042	−	1.06009i	−0.378853	−	0.925457i	$-0.623681\pi$
$2$	0.865559	−	1.49919i	0.612042	−	1.06009i	0.990896	−	0.134632i	$-0.0429852\pi$
$3$	0.0316961	+	0.0548993i	0.0182998	+	0.0316961i	0.875030	−	0.484068i	$-0.160841\pi$
$3$	0.0316961	+	0.0548993i	0.0182998	+	0.0316961i	−0.856730	+	0.515764i	$0.827508\pi$
$4$	−0.498384	−	0.863226i	−0.249192	−	0.431613i
$5$	−1.64023	+	2.84097i	−0.733535	+	1.27052i	0.221829	+	0.975086i	$0.428797\pi$
$5$	−1.64023	+	2.84097i	−0.733535	+	1.27052i	−0.955363	+	0.295433i	$0.904536\pi$
$6$	0.109739			0.0448010
$7$	−2.63578	+	0.229444i	−0.996233	+	0.0867218i
$7$	−2.63578	+	0.229444i	−0.996233	+	0.0867218i
$8$	1.73671			0.614021
$9$	1.49799	−	2.59460i	0.499330	−	0.864865i
$10$	2.83944	+	4.91805i	0.897908	+	1.55522i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	0.0315937	−	0.0547219i	0.00912031	−	0.0157968i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−1.93744	+	4.15014i	−0.517804	+	1.10917i
$15$	−0.207956			−0.0536941
$16$	2.49999	−	4.33012i	0.624999	−	1.08253i
$17$	3.93858	+	6.82182i	0.955246	+	1.65453i	0.733805	+	0.679360i	$0.237742\pi$
$17$	3.93858	+	6.82182i	0.955246	+	1.65453i	0.221440	+	0.975174i	$0.428924\pi$
$18$	−2.59320	−	4.49155i	−0.611223	−	1.05867i
$19$	−3.87047	+	6.70386i	−0.887947	+	1.53797i	−0.0456497	+	0.998958i	$0.514536\pi$
$19$	−3.87047	+	6.70386i	−0.887947	+	1.53797i	−0.842298	+	0.539013i	$0.818798\pi$
$20$	3.26986			0.731163
$21$	−0.0961405	−	0.137430i	−0.0209796	−	0.0299897i
$22$	−1.73112			−0.369075
$23$	−4.05683	+	7.02664i	−0.845908	+	1.46516i	0.0389214	+	0.999242i	$0.487608\pi$
$23$	−4.05683	+	7.02664i	−0.845908	+	1.46516i	−0.884830	+	0.465914i	$0.845726\pi$
$24$	0.0550471	+	0.0953444i	0.0112364	+	0.0194621i
$25$	−2.88073	−	4.98957i	−0.576146	−	0.997914i
$26$	−0.865559	+	1.49919i	−0.169750	+	0.294016i
$27$	0.380099			0.0731501
$28$	1.51169	+	2.16093i	0.285683	+	0.408377i
$29$	5.70844			1.06003			0.530015	−	0.847988i	$-0.322186\pi$
$29$	5.70844			1.06003			0.530015	+	0.847988i	$0.322186\pi$
$30$	−0.179998	+	0.311766i	−0.0328630	+	0.0569205i
$31$	2.04467	+	3.54147i	0.367233	+	0.636067i	0.989132	−	0.147031i	$-0.0469717\pi$
$31$	2.04467	+	3.54147i	0.367233	+	0.636067i	−0.621899	+	0.783098i	$0.713638\pi$
$32$	−2.59107	−	4.48787i	−0.458041	−	0.793350i
$33$	0.0316961	−	0.0548993i	0.00551759	−	0.00955675i
$34$	13.6363			2.33860
$35$	3.67146	−	7.86452i	0.620589	−	1.32935i
$36$	−2.98630			−0.497716
$37$	−1.05726	+	1.83123i	−0.173813	+	0.301053i	−0.939750	−	0.341863i	$-0.888942\pi$
$37$	−1.05726	+	1.83123i	−0.173813	+	0.301053i	0.765937	+	0.642916i	$0.222275\pi$
$38$	6.70024	+	11.6052i	1.08692	+	1.88261i
$39$	−0.0316961	−	0.0548993i	−0.00507544	−	0.00879093i
$40$	−2.84861	+	4.93394i	−0.450405	+	0.780125i
$41$	−3.97994			−0.621563			−0.310781	−	0.950481i	$-0.600591\pi$
$41$	−3.97994			−0.621563			−0.310781	+	0.950481i	$0.600591\pi$
$42$	−0.289250	+	0.0251791i	−0.0446322	+	0.00388522i
$43$	−1.44901			−0.220973			−0.110486	−	0.993878i	$-0.535241\pi$
$43$	−1.44901			−0.220973			−0.110486	+	0.993878i	$0.535241\pi$
$44$	−0.498384	+	0.863226i	−0.0751342	+	0.130136i
$45$	4.91411	+	8.51148i	0.732552	+	1.26882i
$46$	7.02286	+	12.1639i	1.03546	+	1.79348i
$47$	−2.32254	+	4.02275i	−0.338777	+	0.586778i	−0.984203	−	0.177044i	$-0.943346\pi$
$47$	−2.32254	+	4.02275i	−0.338777	+	0.586778i	0.645426	+	0.763823i	$0.276680\pi$
$48$	0.316961			0.0457493
$49$	6.89471	−	1.20953i	0.984959	−	0.172790i
$50$	−9.97376			−1.41050
$51$	−0.249675	+	0.432451i	−0.0349616	+	0.0605552i
$52$	0.498384	+	0.863226i	0.0691134	+	0.119708i
$53$	5.99360	+	10.3812i	0.823284	+	1.42597i	0.903224	+	0.429170i	$0.141194\pi$
$53$	5.99360	+	10.3812i	0.823284	+	1.42597i	−0.0799398	+	0.996800i	$0.525473\pi$
$54$	0.328998	−	0.569841i	0.0447709	−	0.0775456i
$55$	3.28047			0.442338
$56$	−4.57760	+	0.398479i	−0.611708	+	0.0532490i
$57$	−0.490716			−0.0649970
$58$	4.94099	−	8.55805i	0.648784	−	1.12373i
$59$	−4.78753	−	8.29225i	−0.623283	−	1.07956i	−0.988870	−	0.148781i	$-0.952465\pi$
$59$	−4.78753	−	8.29225i	−0.623283	−	1.07956i	0.365587	−	0.930777i	$-0.380868\pi$
$60$	0.103642	+	0.179513i	0.0133801	+	0.0231751i
$61$	4.80245	−	8.31809i	0.614891	−	1.06502i	−0.375513	−	0.926817i	$-0.622533\pi$
$61$	4.80245	−	8.31809i	0.614891	−	1.06502i	0.990404	−	0.138205i	$-0.0441333\pi$
$62$	7.07912			0.899050
$63$	−3.35306	+	7.18250i	−0.422446	+	0.904910i
$64$	1.02908			0.128635
$65$	1.64023	−	2.84097i	0.203446	−	0.352379i
$66$	−0.0548697	−	0.0950372i	−0.00675400	−	0.0116983i
$67$	1.40360	+	2.43111i	0.171478	+	0.297008i	0.938937	−	0.344090i	$-0.111813\pi$
$67$	1.40360	+	2.43111i	0.171478	+	0.297008i	−0.767459	+	0.641098i	$0.778479\pi$
$68$	3.92585	−	6.79977i	0.476079	−	0.824593i
$69$	−0.514344			−0.0619197
$70$	−8.61256	−	12.3114i	−1.02940	−	1.47150i
$71$	−6.59212			−0.782341			−0.391171	−	0.920318i	$-0.627930\pi$
$71$	−6.59212			−0.782341			−0.391171	+	0.920318i	$0.627930\pi$
$72$	2.60158	−	4.50607i	0.306599	−	0.531045i
$73$	−5.23596	−	9.06894i	−0.612822	−	1.06144i	−0.990762	−	0.135609i	$-0.956701\pi$
$73$	−5.23596	−	9.06894i	−0.612822	−	1.06144i	0.377940	−	0.925830i	$-0.376633\pi$
$74$	1.83025	+	3.17008i	0.212762	+	0.368514i
$75$	0.182616	−	0.316300i	0.0210867	−	0.0365232i
$76$	7.71592			0.885077
$77$	1.51660	+	2.16793i	0.172832	+	0.247059i
$78$	−0.109739			−0.0124255
$79$	−3.20499	+	5.55120i	−0.360589	+	0.624559i	−0.988058	−	0.154083i	$-0.950758\pi$
$79$	−3.20499	+	5.55120i	−0.360589	+	0.624559i	0.627469	+	0.778642i	$0.284091\pi$
$80$	8.20115	+	14.2048i	0.916916	+	1.58815i
$81$	−4.48192	−	7.76292i	−0.497992	−	0.862547i
$82$	−3.44487	+	5.96670i	−0.380423	+	0.658911i
$83$	12.1151			1.32980			0.664902	−	0.746930i	$-0.268473\pi$
$83$	12.1151			1.32980			0.664902	+	0.746930i	$0.268473\pi$
$84$	−0.0707185	+	0.151484i	−0.00771602	+	0.0165283i
$85$	−25.8407			−2.80282
$86$	−1.25421	+	2.17235i	−0.135245	+	0.234251i
$87$	0.180936	+	0.313390i	0.0193983	+	0.0335989i
$88$	−0.868357	−	1.50404i	−0.0925671	−	0.160331i
$89$	6.65199	−	11.5216i	0.705109	−	1.22129i	−0.261543	−	0.965192i	$-0.584231\pi$
$89$	6.65199	−	11.5216i	0.705109	−	1.22129i	0.966652	−	0.256093i	$-0.0824354\pi$
$90$	17.0138			1.79341
$91$	2.63578	−	0.229444i	0.276305	−	0.0240523i
$92$	8.08744			0.843174
$93$	−0.129616	+	0.224502i	−0.0134406	+	0.0232798i
$94$	4.02058	+	6.96385i	0.414691	+	0.718267i
$95$	−12.6970	−	21.9918i	−1.30268	−	2.25631i
$96$	0.164254	−	0.284496i	0.0167641	−	0.0290363i
$97$	−10.6903			−1.08543			−0.542717	−	0.839916i	$-0.682604\pi$
$97$	−10.6903			−1.08543			−0.542717	+	0.839916i	$0.682604\pi$
$98$	4.15446	−	11.3834i	0.419664	−	1.14990i
$99$	−2.99598			−0.301107
$100$	−2.87142	+	4.97344i	−0.287142	+	0.497344i
$101$	−5.43468	−	9.41314i	−0.540771	−	0.936642i	−0.998860	−	0.0477361i	$-0.984799\pi$
$101$	−5.43468	−	9.41314i	−0.540771	−	0.936642i	0.458089	−	0.888906i	$-0.348534\pi$
$102$	0.432218	+	0.748623i	0.0427959	+	0.0741247i
$103$	−2.95639	+	5.12062i	−0.291302	+	0.504549i	−0.974118	−	0.226041i	$-0.927422\pi$
$103$	−2.95639	+	5.12062i	−0.291302	+	0.504549i	0.682816	+	0.730590i	$0.260755\pi$
$104$	−1.73671			−0.170299
$105$	0.548128	−	0.0477144i	0.0534918	−	0.00465645i
$106$	20.7512			2.01554
$107$	0.987584	−	1.71055i	0.0954734	−	0.165365i	−0.814333	−	0.580398i	$-0.802897\pi$
$107$	0.987584	−	1.71055i	0.0954734	−	0.165365i	0.909806	+	0.415034i	$0.136230\pi$
$108$	−0.189435	−	0.328111i	−0.0182284	−	0.0315725i
$109$	−2.54733	−	4.41211i	−0.243990	−	0.422604i	0.717857	−	0.696191i	$-0.245123\pi$
$109$	−2.54733	−	4.41211i	−0.243990	−	0.422604i	−0.961847	+	0.273587i	$0.911790\pi$
$110$	2.83944	−	4.91805i	0.270730	−	0.468917i
$111$	−0.134045			−0.0127230
$112$	−5.59592	+	11.9869i	−0.528765	+	1.13265i
$113$	8.55799			0.805068			0.402534	−	0.915405i	$-0.368130\pi$
$113$	8.55799			0.805068			0.402534	+	0.915405i	$0.368130\pi$
$114$	−0.424744	+	0.735678i	−0.0397809	+	0.0689025i
$115$	−13.3083	−	23.0507i	−1.24101	−	2.14949i
$116$	−2.84499	−	4.92767i	−0.264151	−	0.457523i
$117$	−1.49799	+	2.59460i	−0.138489	+	0.239870i
$118$	−16.5756			−1.52590
$119$	−11.9465	−	17.0772i	−1.09513	−	1.56546i
$120$	−0.361160			−0.0329693
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−8.31361	−	14.3996i	−0.752679	−	1.30368i
$123$	−0.126149	−	0.218496i	−0.0113745	−	0.0197011i
$124$	2.03806	−	3.53002i	0.183023	−	0.317005i
$125$	2.49794			0.223422
$126$	7.86567	+	11.2438i	0.700730	+	1.00167i
$127$	12.1496			1.07810			0.539052	−	0.842273i	$-0.318783\pi$
$127$	12.1496			1.07810			0.539052	+	0.842273i	$0.318783\pi$
$128$	6.07287	−	10.5185i	0.536771	−	0.929715i
$129$	−0.0459282	−	0.0795499i	−0.00404375	−	0.00700398i
$130$	−2.83944	−	4.91805i	−0.249035	−	0.431341i
$131$	−7.04252	+	12.1980i	−0.615308	+	1.06574i	0.375023	+	0.927016i	$0.377635\pi$
$131$	−7.04252	+	12.1980i	−0.615308	+	1.06574i	−0.990330	+	0.138729i	$0.955698\pi$
$132$	−0.0631874			−0.00549975
$133$	8.66357	−	18.5580i	0.751227	−	1.60918i
$134$	4.85961			0.419806
$135$	−0.623451	+	1.07985i	−0.0536581	+	0.0929386i
$136$	6.84018	+	11.8475i	0.586541	+	1.01592i
$137$	−3.83013	−	6.63398i	−0.327230	−	0.566779i	0.654731	−	0.755862i	$-0.272782\pi$
$137$	−3.83013	−	6.63398i	−0.327230	−	0.566779i	−0.981961	+	0.189083i	$0.939449\pi$
$138$	−0.445195	+	0.771100i	−0.0378975	+	0.0656404i
$139$	11.8486			1.00498			0.502492	−	0.864582i	$-0.332417\pi$
$139$	11.8486			1.00498			0.502492	+	0.864582i	$0.332417\pi$
$140$	−8.61865	+	0.750252i	−0.728409	+	0.0634078i
$141$	−0.294462			−0.0247982
$142$	−5.70587	+	9.88286i	−0.478826	+	0.829351i
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	−7.48994	−	12.9730i	−0.624161	−	1.08108i
$145$	−9.36317	+	16.2175i	−0.777569	+	1.34679i
$146$	−18.1281			−1.50029
$147$	0.284938	+	0.340177i	0.0235013	+	0.0280574i
$148$	2.10769			0.173251
$149$	1.26811	−	2.19644i	0.103888	−	0.179939i	−0.809395	−	0.587264i	$-0.800205\pi$
$149$	1.26811	−	2.19644i	0.103888	−	0.179939i	0.913283	+	0.407325i	$0.133538\pi$
$150$	−0.316130	−	0.547553i	−0.0258119	−	0.0447075i
$151$	7.68290	+	13.3072i	0.625226	+	1.08292i	0.988497	+	0.151239i	$0.0483264\pi$
$151$	7.68290	+	13.3072i	0.625226	+	1.08292i	−0.363271	+	0.931683i	$0.618340\pi$
$152$	−6.72190	+	11.6427i	−0.545218	+	0.944346i
$153$	23.5998			1.90793
$154$	4.56285	−	0.397195i	0.367685	−	0.0320069i
$155$	−13.4149			−1.07751
$156$	−0.0315937	+	0.0547219i	−0.00252952	+	0.00438126i
$157$	−1.68225	−	2.91374i	−0.134258	−	0.232542i	0.791056	−	0.611744i	$-0.209532\pi$
$157$	−1.68225	−	2.91374i	−0.134258	−	0.232542i	−0.925314	+	0.379202i	$0.876198\pi$
$158$	5.54821	+	9.60978i	0.441392	+	0.764513i
$159$	−0.379948	+	0.658089i	−0.0301318	+	0.0521898i
$160$	16.9998			1.34396
$161$	9.08071	−	19.4515i	0.715661	−	1.53300i
$162$	−15.5175			−1.21917
$163$	1.12011	−	1.94009i	0.0877338	−	0.151959i	−0.818819	−	0.574052i	$-0.805371\pi$
$163$	1.12011	−	1.94009i	0.0877338	−	0.151959i	0.906553	+	0.422092i	$0.138704\pi$
$164$	1.98354	+	3.43559i	0.154888	+	0.268275i
$165$	0.103978	+	0.180095i	0.00809468	+	0.0140204i
$166$	10.4863	−	18.1628i	0.813897	−	1.40971i
$167$	17.5678			1.35944			0.679718	−	0.733473i	$-0.262102\pi$
$167$	17.5678			1.35944			0.679718	+	0.733473i	$0.262102\pi$
$168$	−0.166968	−	0.238677i	−0.0128819	−	0.0184143i
$169$	1.00000			0.0769231
$170$	−22.3667	+	38.7402i	−1.71545	+	2.97124i
$171$	11.5959	+	20.0846i	0.886758	+	1.53591i
$172$	0.722165	+	1.25083i	0.0550646	+	0.0953747i
$173$	1.28124	−	2.21917i	0.0974107	−	0.168720i	−0.813201	−	0.581982i	$-0.802277\pi$
$173$	1.28124	−	2.21917i	0.0974107	−	0.168720i	0.910612	+	0.413262i	$0.135611\pi$
$174$	0.626441			0.0474904
$175$	8.73781	+	12.4905i	0.660516	+	0.944190i
$176$	−4.99999			−0.376888
$177$	0.303492	−	0.525664i	0.0228119	−	0.0395114i
$178$	−11.5154	−	19.9452i	−0.863114	−	1.49496i
$179$	0.157020	+	0.271967i	0.0117363	+	0.0203278i	0.871834	−	0.489802i	$-0.162931\pi$
$179$	0.157020	+	0.271967i	0.0117363	+	0.0203278i	−0.860098	+	0.510129i	$0.829597\pi$
$180$	4.89822	−	8.48397i	0.365092	−	0.632358i
$181$	−17.6939			−1.31517			−0.657587	−	0.753379i	$-0.728423\pi$
$181$	−17.6939			−1.31517			−0.657587	+	0.753379i	$0.728423\pi$
$182$	1.93744	−	4.15014i	0.143613	−	0.307629i
$183$	0.608877			0.0450095
$184$	−7.04556	+	12.2033i	−0.519405	+	0.899637i
$185$	−3.46831	−	6.00730i	−0.254996	−	0.441665i
$186$	0.224381	+	0.388639i	0.0164524	+	0.0284964i
$187$	3.93858	−	6.82182i	0.288017	−	0.498861i
$188$	4.63006			0.337682
$189$	−1.00186	+	0.0872116i	−0.0728745	+	0.00634371i
$190$	−43.9598			−3.18918
$191$	−5.15359	+	8.92627i	−0.372900	+	0.645882i	−0.990010	−	0.140994i	$-0.954970\pi$
$191$	−5.15359	+	8.92627i	−0.372900	+	0.645882i	0.617110	+	0.786877i	$0.288303\pi$
$192$	0.0326179	+	0.0564959i	0.00235399	+	0.00407724i
$193$	−1.43769	−	2.49015i	−0.103487	−	0.179245i	0.809632	−	0.586938i	$-0.199667\pi$
$193$	−1.43769	−	2.49015i	−0.103487	−	0.179245i	−0.913119	+	0.407693i	$0.866333\pi$
$194$	−9.25307	+	16.0268i	−0.664332	+	1.15066i
$195$	0.207956			0.0148921
$196$	−4.48031	−	5.34888i	−0.320022	−	0.382063i
$197$	19.3960			1.38191			0.690953	−	0.722900i	$-0.257191\pi$
$197$	19.3960			1.38191			0.690953	+	0.722900i	$0.257191\pi$
$198$	−2.59320	+	4.49155i	−0.184291	+	0.319201i
$199$	4.19217	+	7.26104i	0.297175	+	0.514722i	0.975488	−	0.220051i	$-0.0706223\pi$
$199$	4.19217	+	7.26104i	0.297175	+	0.514722i	−0.678314	+	0.734772i	$0.737289\pi$
$200$	−5.00300	−	8.66545i	−0.353765	−	0.612740i
$201$	−0.0889777	+	0.154114i	−0.00627600	+	0.0108704i
$202$	−18.8161			−1.32390
$203$	−15.0462	+	1.30977i	−1.05604	+	0.0919278i
$204$	0.497737			0.0348485
$205$	6.52803	−	11.3069i	0.455938	−	0.789707i
$206$	5.11786	+	8.86439i	0.356578	+	0.617611i
$207$	12.1542	+	21.0517i	0.844775	+	1.46319i
$208$	−2.49999	+	4.33012i	−0.173343	+	0.300240i
$209$	7.74095			0.535452
$210$	0.402904	−	0.863048i	0.0278030	−	0.0595560i
$211$	−6.50419			−0.447767			−0.223883	−	0.974616i	$-0.571873\pi$
$211$	−6.50419			−0.447767			−0.223883	+	0.974616i	$0.571873\pi$
$212$	5.97422	−	10.3477i	0.410311	−	0.710680i
$213$	−0.208945	−	0.361903i	−0.0143167	−	0.0247972i
$214$	−1.70962	−	2.96116i	−0.116868	−	0.202420i
$215$	2.37672	−	4.11660i	0.162091	−	0.280750i
$216$	0.660123			0.0449157
$217$	−6.20187	−	8.86541i	−0.421011	−	0.601823i
$218$	−8.81947			−0.597330
$219$	0.331919	−	0.574901i	0.0224290	−	0.0388482i
$220$	−1.63493	−	2.83178i	−0.110227	−	0.190919i
$221$	−3.93858	−	6.82182i	−0.264937	−	0.458885i
$222$	−0.116023	+	0.200959i	−0.00778699	+	0.0134875i
$223$	8.32303			0.557352			0.278676	−	0.960385i	$-0.410105\pi$
$223$	8.32303			0.557352			0.278676	+	0.960385i	$0.410105\pi$
$224$	7.85922	+	11.2345i	0.525116	+	0.750639i
$225$	−17.2612			−1.15075
$226$	7.40744	−	12.8301i	0.492736	−	0.853443i
$227$	0.870123	+	1.50710i	0.0577521	+	0.100030i	0.893456	−	0.449151i	$-0.148273\pi$
$227$	0.870123	+	1.50710i	0.0577521	+	0.100030i	−0.835704	+	0.549180i	$0.814940\pi$
$228$	0.244565	+	0.423599i	0.0161967	+	0.0280535i
$229$	4.82245	−	8.35272i	0.318676	−	0.551963i	−0.661536	−	0.749913i	$-0.730095\pi$
$229$	4.82245	−	8.35272i	0.318676	−	0.551963i	0.980212	+	0.197950i	$0.0634284\pi$
$230$	−46.0765			−3.03819
$231$	−0.0709478	+	0.151975i	−0.00466802	+	0.00999924i
$232$	9.91392			0.650881
$233$	9.46510	−	16.3940i	0.620079	−	1.07401i	−0.369391	−	0.929274i	$-0.620434\pi$
$233$	9.46510	−	16.3940i	0.620079	−	1.07401i	0.989470	−	0.144735i	$-0.0462329\pi$
$234$	2.59320	+	4.49155i	0.169523	+	0.293622i
$235$	−7.61900	−	13.1965i	−0.497009	−	0.860845i
$236$	−4.77206	+	8.26544i	−0.310634	+	0.538034i
$237$	−0.406343			−0.0263948
$238$	−35.9423	+	3.12877i	−2.32979	+	0.202808i
$239$	0.211954			0.0137102			0.00685508	−	0.999977i	$-0.497818\pi$
$239$	0.211954			0.0137102			0.00685508	+	0.999977i	$0.497818\pi$
$240$	−0.519889	+	0.900475i	−0.0335587	+	0.0581254i
$241$	12.6889	+	21.9779i	0.817367	+	1.41572i	0.907616	+	0.419802i	$0.137900\pi$
$241$	12.6889	+	21.9779i	0.817367	+	1.41572i	−0.0902487	+	0.995919i	$0.528766\pi$
$242$	0.865559	+	1.49919i	0.0556402	+	0.0963717i
$243$	0.854268	−	1.47964i	0.0548013	−	0.0949186i
$244$	−9.57385			−0.612903
$245$	−7.87269	+	21.5716i	−0.502968	+	1.37816i
$246$	−0.436757			−0.0278466
$247$	3.87047	−	6.70386i	0.246272	−	0.426556i
$248$	3.55100	+	6.15052i	0.225489	+	0.390558i
$249$	0.384002	+	0.665110i	0.0243351	+	0.0421497i
$250$	2.16211	−	3.74488i	0.136744	−	0.236847i
$251$	17.6077			1.11139			0.555693	−	0.831387i	$-0.312453\pi$
$251$	17.6077			1.11139			0.555693	+	0.831387i	$0.312453\pi$
$252$	7.87123	−	0.685189i	0.495841	−	0.0431629i
$253$	8.11367			0.510102
$254$	10.5162	−	18.2146i	0.659845	−	1.14289i
$255$	−0.819052	−	1.41864i	−0.0512910	−	0.0888386i
$256$	−9.48378	−	16.4264i	−0.592736	−	1.02665i
$257$	−1.02810	+	1.78072i	−0.0641312	+	0.111079i	−0.896308	−	0.443431i	$-0.853761\pi$
$257$	−1.02810	+	1.78072i	−0.0641312	+	0.111079i	0.832177	+	0.554510i	$0.187094\pi$
$258$	−0.159014			−0.00989978
$259$	2.36655	−	5.06932i	0.147050	−	0.314992i
$260$	−3.26986			−0.202788
$261$	8.55119	−	14.8111i	0.529305	−	0.916784i
$262$	12.1914	+	21.1162i	0.753189	+	1.30456i
$263$	−5.39371	−	9.34218i	−0.332590	−	0.576064i	0.650429	−	0.759567i	$-0.274589\pi$
$263$	−5.39371	−	9.34218i	−0.332590	−	0.576064i	−0.983019	+	0.183504i	$0.941256\pi$
$264$	0.0550471	−	0.0953444i	0.00338791	−	0.00586804i
$265$	−39.3236			−2.41563
$266$	−20.3231	−	29.0514i	−1.24609	−	1.78125i
$267$	0.843369			0.0516134
$268$	1.39907	−	2.42326i	0.0854616	−	0.148024i
$269$	−7.68576	−	13.3121i	−0.468609	−	0.811655i	0.530747	−	0.847530i	$-0.321911\pi$
$269$	−7.68576	−	13.3121i	−0.468609	−	0.811655i	−0.999356	+	0.0358754i	$0.988578\pi$
$270$	1.07927	+	1.86934i	0.0656821	+	0.113765i
$271$	−0.838666	+	1.45261i	−0.0509453	+	0.0882399i	−0.890373	−	0.455231i	$-0.849557\pi$
$271$	−0.838666	+	1.45261i	−0.0509453	+	0.0882399i	0.839428	+	0.543471i	$0.182890\pi$
$272$	39.3857			2.38811
$273$	0.0961405	+	0.137430i	0.00581869	+	0.00831766i
$274$	−13.2608			−0.801115
$275$	−2.88073	+	4.98957i	−0.173714	+	0.300882i
$276$	0.256341	+	0.443995i	0.0154299	+	0.0267254i
$277$	13.0269	+	22.5632i	0.782710	+	1.35569i	0.930357	+	0.366654i	$0.119497\pi$
$277$	13.0269	+	22.5632i	0.782710	+	1.35569i	−0.147647	+	0.989040i	$0.547170\pi$
$278$	10.2556	−	17.7633i	0.615092	−	1.06537i
$279$	12.2516			0.733483
$280$	6.37626	−	13.6584i	0.381055	−	0.816246i
$281$	−1.90320			−0.113536			−0.0567678	−	0.998387i	$-0.518079\pi$
$281$	−1.90320			−0.113536			−0.0567678	+	0.998387i	$0.518079\pi$
$282$	−0.254874	+	0.441455i	−0.0151775	+	0.0262882i
$283$	−6.56839	−	11.3768i	−0.390450	−	0.676280i	0.602059	−	0.798452i	$-0.294347\pi$
$283$	−6.56839	−	11.3768i	−0.390450	−	0.676280i	−0.992509	+	0.122172i	$0.961014\pi$
$284$	3.28541	+	5.69049i	0.194953	+	0.337669i
$285$	0.804889	−	1.39411i	0.0476775	−	0.0825799i
$286$	1.73112			0.102363
$287$	10.4903	−	0.913176i	0.619221	−	0.0539031i
$288$	−15.5256			−0.914855
$289$	−22.5248	+	39.0141i	−1.32499	+	2.29495i
$290$	16.2088	+	28.0744i	0.951811	+	1.64858i
$291$	−0.338841	−	0.586890i	−0.0198632	−	0.0344041i
$292$	−5.21903	+	9.03963i	−0.305421	+	0.529004i
$293$	−19.3763			−1.13198			−0.565989	−	0.824413i	$-0.691505\pi$
$293$	−19.3763			−1.13198			−0.565989	+	0.824413i	$0.691505\pi$
$294$	0.756622	−	0.132733i	0.0441271	−	0.00774117i
$295$	31.4107			1.82880
$296$	−1.83616	+	3.18033i	−0.106725	+	0.184853i
$297$	−0.190049	−	0.329175i	−0.0110278	−	0.0191007i
$298$	−2.19526	−	3.80229i	−0.127168	−	0.220261i
$299$	4.05683	−	7.02664i	0.234613	−	0.406361i
$300$	−0.364051			−0.0210185
$301$	3.81929	−	0.332468i	0.220140	−	0.0191632i
$302$	26.6000			1.53066
$303$	0.344517	−	0.596720i	0.0197920	−	0.0342807i
$304$	19.3523	+	33.5192i	1.10993	+	1.92246i
$305$	15.7543	+	27.2872i	0.902087	+	1.56246i
$306$	20.4270	−	35.3806i	1.16774	−	2.02258i
$307$	2.27783			0.130003			0.0650013	−	0.997885i	$-0.479295\pi$
$307$	2.27783			0.130003			0.0650013	+	0.997885i	$0.479295\pi$
$308$	1.11557	−	2.38963i	0.0635655	−	0.136162i
$309$	−0.374825			−0.0213230
$310$	−11.6114	+	20.1116i	−0.659484	+	1.14226i
$311$	2.77651	+	4.80905i	0.157441	+	0.272696i	0.933945	−	0.357416i	$-0.116342\pi$
$311$	2.77651	+	4.80905i	0.157441	+	0.272696i	−0.776504	+	0.630112i	$0.783009\pi$
$312$	−0.0550471	−	0.0953444i	−0.00311643	−	0.00539781i
$313$	−13.6158	+	23.5833i	−0.769610	+	1.33300i	0.168164	+	0.985759i	$0.446216\pi$
$313$	−13.6158	+	23.5833i	−0.769610	+	1.33300i	−0.937774	+	0.347245i	$0.887117\pi$
$314$	−5.82434			−0.328686
$315$	−14.9054	−	21.3069i	−0.839826	−	1.20051i
$316$	6.38926			0.359424
$317$	−2.72301	+	4.71639i	−0.152939	+	0.264899i	−0.932307	−	0.361668i	$-0.882207\pi$
$317$	−2.72301	+	4.71639i	−0.152939	+	0.264899i	0.779367	+	0.626567i	$0.215541\pi$
$318$	0.657734	+	1.13923i	0.0368839	+	0.0638848i
$319$	−2.85422	−	4.94365i	−0.159806	−	0.276792i
$320$	−1.68793	+	2.92359i	−0.0943583	+	0.163433i
$321$	0.125210			0.00698856
$322$	−21.3017	−	30.4502i	−1.18710	−	1.69692i
$323$	−60.9766			−3.39283
$324$	−4.46744	+	7.73783i	−0.248191	+	0.429879i
$325$	2.88073	+	4.98957i	0.159794	+	0.276771i
$326$	−1.93904	−	3.35852i	−0.107394	−	0.186011i
$327$	0.161481	−	0.279694i	0.00892993	−	0.0154671i
$328$	−6.91202			−0.381652
$329$	5.19871	−	11.1360i	0.286614	−	0.613947i
$330$	0.359997			0.0198172
$331$	−8.24185	+	14.2753i	−0.453013	+	0.784641i	−0.998572	−	0.0534314i	$-0.982984\pi$
$331$	−8.24185	+	14.2753i	−0.453013	+	0.784641i	0.545559	+	0.838073i	$0.316317\pi$
$332$	−6.03797	−	10.4581i	−0.331376	−	0.573961i
$333$	3.16754	+	5.48634i	0.173580	+	0.300650i
$334$	15.2060	−	26.3375i	0.832033	−	1.44112i
$335$	−9.20895			−0.503139
$336$	−0.835440	+	0.0727249i	−0.0455770	+	0.00396747i
$337$	31.4117			1.71110			0.855551	−	0.517719i	$-0.173219\pi$
$337$	31.4117			1.71110			0.855551	+	0.517719i	$0.173219\pi$
$338$	0.865559	−	1.49919i	0.0470802	−	0.0815453i
$339$	0.271255	+	0.469828i	0.0147326	+	0.0255175i
$340$	12.8786	+	22.3064i	0.698441	+	1.20973i
$341$	2.04467	−	3.54147i	0.110725	−	0.191781i
$342$	40.1476			2.17093
$343$	−17.8954	+	4.77002i	−0.966263	+	0.257557i
$344$	−2.51652			−0.135682
$345$	0.843644	−	1.46123i	0.0454203	−	0.0786702i
$346$	−2.21797	−	3.84164i	−0.119239	−	0.206528i
$347$	−8.69952	−	15.0680i	−0.467014	−	0.808893i	0.532275	−	0.846571i	$-0.321337\pi$
$347$	−8.69952	−	15.0680i	−0.467014	−	0.808893i	−0.999290	+	0.0376784i	$0.988004\pi$
$348$	0.180351	−	0.312377i	0.00966781	−	0.0167451i
$349$	30.4009			1.62732			0.813660	−	0.581341i	$-0.197472\pi$
$349$	30.4009			1.62732			0.813660	+	0.581341i	$0.197472\pi$
$350$	26.2887	−	2.28842i	1.40519	−	0.122321i
$351$	−0.380099			−0.0202882
$352$	−2.59107	+	4.48787i	−0.138105	+	0.239204i
$353$	−11.2457	−	19.4781i	−0.598546	−	1.03671i	−0.993036	−	0.117812i	$-0.962412\pi$
$353$	−11.2457	−	19.4781i	−0.598546	−	1.03671i	0.394490	−	0.918900i	$-0.370921\pi$
$354$	−0.525381	−	0.909987i	−0.0279237	−	0.0483653i
$355$	10.8126	−	18.7280i	0.573874	−	0.993979i
$356$	−13.2610			−0.702830
$357$	0.558867	−	1.19713i	0.0295784	−	0.0633590i
$358$	0.543641			0.0287323
$359$	1.71525	−	2.97089i	0.0905273	−	0.156798i	−0.817206	−	0.576346i	$-0.804478\pi$
$359$	1.71525	−	2.97089i	0.0905273	−	0.156798i	0.907733	+	0.419548i	$0.137811\pi$
$360$	8.53440	+	14.7820i	0.449802	+	0.779080i
$361$	−20.4611	−	35.4397i	−1.07690	−	1.86525i
$362$	−15.3151	+	26.5265i	−0.804942	+	1.39420i
$363$	−0.0633923			−0.00332723
$364$	−1.51169	−	2.16093i	−0.0792343	−	0.113263i
$365$	34.3528			1.79811
$366$	0.527018	−	0.912823i	0.0275477	−	0.0477140i
$367$	14.7869	+	25.6117i	0.771871	+	1.33692i	0.936536	+	0.350571i	$0.114012\pi$
$367$	14.7869	+	25.6117i	0.771871	+	1.33692i	−0.164665	+	0.986350i	$0.552654\pi$
$368$	20.2841	+	35.1331i	1.05738	+	1.83144i
$369$	−5.96192	+	10.3263i	−0.310365	+	0.537568i
$370$	−12.0081			−0.624272
$371$	−18.1797	−	25.9874i	−0.943845	−	1.34920i
$372$	0.258394			0.0133971
$373$	−10.4131	+	18.0360i	−0.539170	+	0.933869i	0.459779	+	0.888033i	$0.347928\pi$
$373$	−10.4131	+	18.0360i	−0.539170	+	0.933869i	−0.998949	+	0.0458359i	$0.985405\pi$
$374$	−6.81814	−	11.8094i	−0.352558	−	0.610648i
$375$	0.0791749	+	0.137135i	0.00408857	+	0.00708162i
$376$	−4.03358	+	6.98636i	−0.208016	+	0.360294i
$377$	−5.70844			−0.294000
$378$	−0.736420	+	1.57746i	−0.0378774	+	0.0811360i
$379$	−8.00844			−0.411366			−0.205683	−	0.978619i	$-0.565942\pi$
$379$	−8.00844			−0.411366			−0.205683	+	0.978619i	$0.565942\pi$
$380$	−12.6559	+	21.9207i	−0.649235	+	1.12451i
$381$	0.385096	+	0.667005i	0.0197291	+	0.0341717i
$382$	8.92146	+	15.4524i	0.456462	+	0.790615i
$383$	8.87867	−	15.3783i	0.453679	−	0.785794i	−0.544933	−	0.838480i	$-0.683445\pi$
$383$	8.87867	−	15.3783i	0.453679	−	0.785794i	0.998611	+	0.0526854i	$0.0167781\pi$
$384$	0.769947			0.0392912
$385$	−8.64660	+	0.752685i	−0.440671	+	0.0383604i
$386$	−4.97761			−0.253354
$387$	−2.17061	+	3.75961i	−0.110338	+	0.191112i
$388$	5.32787	+	9.22813i	0.270481	+	0.468488i
$389$	−13.8728	−	24.0283i	−0.703377	−	1.21828i	−0.967274	−	0.253734i	$-0.918341\pi$
$389$	−13.8728	−	24.0283i	−0.703377	−	1.21828i	0.263897	−	0.964551i	$-0.414992\pi$
$390$	0.179998	−	0.311766i	0.00911457	−	0.0157869i
$391$	−63.9126			−3.23220
$392$	11.9741	−	2.10061i	0.604785	−	0.106097i
$393$	−0.892883			−0.0450400
$394$	16.7883	−	29.0783i	0.845785	−	1.46494i
$395$	−10.5139	−	18.2105i	−0.529010	−	0.916271i
$396$	1.49315	+	2.58621i	0.0750335	+	0.129962i
$397$	4.46166	−	7.72782i	0.223924	−	0.387848i	−0.732072	−	0.681227i	$-0.761446\pi$
$397$	4.46166	−	7.72782i	0.223924	−	0.387848i	0.955996	+	0.293379i	$0.0947798\pi$
$398$	14.5143			0.727534
$399$	1.29342	−	0.112592i	0.0647521	−	0.00563666i
$400$	−28.8072			−1.44036
$401$	−1.29577	+	2.24435i	−0.0647079	+	0.112077i	−0.896564	−	0.442913i	$-0.853945\pi$
$401$	−1.29577	+	2.24435i	−0.0647079	+	0.112077i	0.831856	+	0.554991i	$0.187278\pi$
$402$	0.154031	+	0.266789i	0.00768236	+	0.0133062i
$403$	−2.04467	−	3.54147i	−0.101852	−	0.176413i
$404$	−5.41711	+	9.38271i	−0.269511	+	0.466807i
$405$	29.4056			1.46118
$406$	−11.0598	+	23.6908i	−0.548888	+	1.17576i
$407$	2.11453			0.104813
$408$	−0.433615	+	0.751043i	−0.0214671	+	0.0371822i
$409$	1.39339	+	2.41342i	0.0688985	+	0.119336i	0.898417	−	0.439144i	$-0.144718\pi$
$409$	1.39339	+	2.41342i	0.0688985	+	0.119336i	−0.829518	+	0.558480i	$0.811385\pi$
$410$	−11.3008	−	19.5735i	−0.558106	−	0.966669i
$411$	0.242801	−	0.420543i	0.0119765	−	0.0207439i
$412$	5.89367			0.290360
$413$	14.5215	+	20.7581i	0.714557	+	1.02144i
$414$	42.0807			2.06815
$415$	−19.8716	+	34.4186i	−0.975457	+	1.68954i
$416$	2.59107	+	4.48787i	0.127038	+	0.220036i
$417$	0.375554	+	0.650479i	0.0183910	+	0.0318541i
$418$	6.70024	−	11.6052i	0.327720	−	0.567627i
$419$	−4.64779			−0.227059			−0.113530	−	0.993535i	$-0.536216\pi$
$419$	−4.64779			−0.227059			−0.113530	+	0.993535i	$0.536216\pi$
$420$	−0.314366	−	0.449378i	−0.0153395	−	0.0219274i
$421$	3.96492			0.193238			0.0966192	−	0.995321i	$-0.469197\pi$
$421$	3.96492			0.193238			0.0966192	+	0.995321i	$0.469197\pi$
$422$	−5.62975	+	9.75102i	−0.274052	+	0.474672i
$423$	6.95828	+	12.0521i	0.338323	+	0.585992i
$424$	10.4092	+	18.0292i	0.505513	+	0.875575i
$425$	22.6920	−	39.3036i	1.10072	−	1.90651i
$426$	−0.723416			−0.0350496
$427$	−10.7497	+	23.0266i	−0.520214	+	1.11433i
$428$	−1.96878			−0.0951648
$429$	−0.0316961	+	0.0548993i	−0.00153030	+	0.00265056i
$430$	−4.11438	−	7.12632i	−0.198413	−	0.343662i
$431$	4.04359	+	7.00370i	0.194773	+	0.337357i	0.946826	−	0.321746i	$-0.104270\pi$
$431$	4.04359	+	7.00370i	0.194773	+	0.337357i	−0.752053	+	0.659102i	$0.770936\pi$
$432$	0.950245	−	1.64587i	0.0457187	−	0.0791871i
$433$	−9.71766			−0.467001			−0.233501	−	0.972357i	$-0.575018\pi$
$433$	−9.71766			−0.467001			−0.233501	+	0.972357i	$0.575018\pi$
$434$	−18.6590	+	1.62427i	−0.895662	+	0.0779672i
$435$	−1.18711			−0.0569174
$436$	−2.53910	+	4.39785i	−0.121601	+	0.210619i
$437$	−31.4037	−	54.3929i	−1.50224	−	2.60196i
$438$	−0.574591	−	0.995221i	−0.0274550	−	0.0475535i
$439$	−0.182068	+	0.315350i	−0.00868962	+	0.0150509i	−0.870338	−	0.492456i	$-0.836099\pi$
$439$	−0.182068	+	0.315350i	−0.00868962	+	0.0150509i	0.861648	+	0.507507i	$0.169433\pi$
$440$	5.69723			0.271605
$441$	7.18997	−	19.7009i	0.342379	−	0.938136i
$442$	−13.6363			−0.648612
$443$	16.3139	−	28.2564i	0.775094	−	1.34250i	−0.159647	−	0.987174i	$-0.551036\pi$
$443$	16.3139	−	28.2564i	0.775094	−	1.34250i	0.934741	−	0.355329i	$-0.115631\pi$
$444$	0.0668057	+	0.115711i	0.00317046	+	0.00549139i
$445$	21.8216	+	37.7962i	1.03444	+	1.79171i
$446$	7.20408	−	12.4778i	0.341123	−	0.590842i
$447$	0.160777			0.00760451
$448$	−2.71244	+	0.236117i	−0.128151	+	0.0111555i
$449$	6.89782			0.325528			0.162764	−	0.986665i	$-0.447959\pi$
$449$	6.89782			0.325528			0.162764	+	0.986665i	$0.447959\pi$
$450$	−14.9406	+	25.8779i	−0.704307	+	1.21989i
$451$	1.98997	+	3.44673i	0.0937041	+	0.162300i
$452$	−4.26516	−	7.38748i	−0.200616	−	0.347478i
$453$	−0.487037	+	0.843572i	−0.0228830	+	0.0396345i
$454$	3.01257			0.141387
$455$	−3.67146	+	7.86452i	−0.172120	+	0.368694i
$456$	−0.852233			−0.0399095
$457$	−7.63926	+	13.2316i	−0.357350	+	0.618948i	−0.987517	−	0.157512i	$-0.949653\pi$
$457$	−7.63926	+	13.2316i	−0.357350	+	0.618948i	0.630168	+	0.776459i	$0.282986\pi$
$458$	−8.34822	−	14.4595i	−0.390087	−	0.675650i
$459$	1.49705	+	2.59297i	0.0698763	+	0.121029i
$460$	−13.2653	+	22.9762i	−0.618497	+	1.07127i
$461$	6.93595			0.323040			0.161520	−	0.986869i	$-0.448360\pi$
$461$	6.93595			0.323040			0.161520	+	0.986869i	$0.448360\pi$
$462$	0.166431	+	0.237908i	0.00774305	+	0.0110685i
$463$	−7.86662			−0.365593			−0.182796	−	0.983151i	$-0.558515\pi$
$463$	−7.86662			−0.365593			−0.182796	+	0.983151i	$0.558515\pi$
$464$	14.2711	−	24.7182i	0.662518	−	1.14751i
$465$	−0.425202	−	0.736471i	−0.0197183	−	0.0341530i
$466$	−16.3852	−	28.3800i	−0.759030	−	1.31468i
$467$	4.66437	−	8.07892i	0.215841	−	0.373848i	−0.737691	−	0.675138i	$-0.764084\pi$
$467$	4.66437	−	8.07892i	0.215841	−	0.373848i	0.953532	+	0.301290i	$0.0974173\pi$
$468$	2.98630			0.138042
$469$	−4.25740	−	6.08584i	−0.196589	−	0.281018i
$470$	−26.3788			−1.21676
$471$	0.106642	−	0.184709i	0.00491378	−	0.00851092i
$472$	−8.31457	−	14.4013i	−0.382709	−	0.662871i
$473$	0.724507	+	1.25488i	0.0333129	+	0.0576996i
$474$	−0.351714	+	0.609186i	−0.0161547	+	0.0279808i
$475$	44.5991			2.04635
$476$	−8.78752	+	18.8235i	−0.402775	+	0.862773i
$477$	35.9134			1.64436
$478$	0.183459	−	0.317759i	0.00839120	−	0.0145340i
$479$	11.2857	+	19.5474i	0.515657	+	0.893144i	0.999835	+	0.0181743i	$0.00578536\pi$
$479$	11.2857	+	19.5474i	0.515657	+	0.893144i	−0.484178	+	0.874969i	$0.660881\pi$
$480$	0.538829	+	0.933280i	0.0245941	+	0.0425982i
$481$	1.05726	−	1.83123i	0.0482070	−	0.0834970i
$482$	43.9321			2.00105
$483$	1.35570	−	0.118013i	0.0616865	−	0.00536979i
$484$	0.996768			0.0453076
$485$	17.5346	−	30.3708i	0.796203	−	1.37906i
$486$	−1.47884	−	2.56142i	−0.0670814	−	0.116188i
$487$	5.90698	+	10.2312i	0.267671	+	0.463620i	0.968260	−	0.249945i	$-0.0804127\pi$
$487$	5.90698	+	10.2312i	0.267671	+	0.463620i	−0.700589	+	0.713565i	$0.747079\pi$
$488$	8.34048	−	14.4461i	0.377556	−	0.653946i
$489$	0.142013			0.00642203
$490$	25.5256	+	30.4741i	1.15313	+	1.37668i
$491$	27.4431			1.23849			0.619246	−	0.785197i	$-0.287438\pi$
$491$	27.4431			1.23849			0.619246	+	0.785197i	$0.287438\pi$
$492$	−0.125741	+	0.217790i	−0.00566884	+	0.00981873i
$493$	22.4831	+	38.9419i	1.01259	+	1.75386i
$494$	−6.70024	−	11.6052i	−0.301458	−	0.522141i
$495$	4.91411	−	8.51148i	0.220873	−	0.382563i
$496$	20.4466			0.918081
$497$	17.3754	−	1.51253i	0.779394	−	0.0678461i
$498$	1.32950			0.0595765
$499$	−11.4273	+	19.7926i	−0.511556	+	0.886041i	0.488354	+	0.872645i	$0.337597\pi$
$499$	−11.4273	+	19.7926i	−0.511556	+	0.886041i	−0.999910	+	0.0133953i	$0.995736\pi$
$500$	−1.24493	−	2.15628i	−0.0556750	−	0.0964319i
$501$	0.556831	+	0.964460i	0.0248774	+	0.0430889i
$502$	15.2405	−	26.3973i	0.680216	−	1.17817i
$503$	17.0114			0.758502			0.379251	−	0.925294i	$-0.376182\pi$
$503$	17.0114			0.758502			0.379251	+	0.925294i	$0.376182\pi$
$504$	−5.82331	+	12.4739i	−0.259391	+	0.555633i
$505$	35.6566			1.58670
$506$	7.02286	−	12.1639i	0.312204	−	0.540753i
$507$	0.0316961	+	0.0548993i	0.00140767	+	0.00243816i
$508$	−6.05517	−	10.4879i	−0.268655	−	0.465324i
$509$	2.47160	−	4.28094i	0.109552	−	0.189750i	−0.806037	−	0.591865i	$-0.798392\pi$
$509$	2.47160	−	4.28094i	0.109552	−	0.189750i	0.915589	+	0.402116i	$0.131725\pi$
$510$	−2.83575			−0.125569
$511$	15.8817	+	22.7024i	0.702563	+	1.00430i
$512$	−8.54356			−0.377576
$513$	−1.47116	+	2.54813i	−0.0649534	+	0.112503i
$514$	1.77977	+	3.08264i	0.0785021	+	0.135970i
$515$	−9.69833	−	16.7980i	−0.427360	−	0.740209i
$516$	−0.0457797	+	0.0792928i	−0.00201534	+	0.00349067i
$517$	4.64507			0.204290
$518$	−5.55149	−	7.93570i	−0.243918	−	0.348675i
$519$	0.162441			0.00713037
$520$	2.84861	−	4.93394i	0.124920	−	0.216368i
$521$	15.0047	+	25.9888i	0.657366	+	1.13859i	0.981295	+	0.192510i	$0.0616629\pi$
$521$	15.0047	+	25.9888i	0.657366	+	1.13859i	−0.323929	+	0.946081i	$0.605004\pi$
$522$	−14.8031	−	25.6397i	−0.647915	−	1.12222i
$523$	11.2086	−	19.4138i	0.490116	−	0.848906i	−0.509819	−	0.860282i	$-0.670288\pi$
$523$	11.2086	−	19.4138i	0.490116	−	0.848906i	0.999935	+	0.0113756i	$0.00362105\pi$
$524$	14.0395			0.613319
$525$	−0.408763	+	0.875599i	−0.0178399	+	0.0382143i
$526$	−18.6743			−0.814238
$527$	−16.1062	+	27.8967i	−0.701596	+	1.21520i
$528$	−0.158480	−	0.274496i	−0.00689697	−	0.0119459i
$529$	−21.4158	−	37.0933i	−0.931122	−	1.61275i
$530$	−34.0369	+	58.9536i	−1.47847	+	2.56078i
$531$	−28.6867			−1.24490
$532$	−20.3375	+	1.77038i	−0.881743	+	0.0767555i
$533$	3.97994			0.172390
$534$	0.729986	−	1.26437i	0.0315896	−	0.0547147i
$535$	3.23974	+	5.61139i	0.140066	+	0.242601i
$536$	2.43766	+	4.22215i	0.105291	+	0.182369i
$537$	−0.00995388	+	0.0172406i	−0.000429542	+	0.000743988i
$538$	−26.6099			−1.14723
$539$	−4.49484	−	5.36623i	−0.193606	−	0.231140i
$540$	1.24287			0.0534847
$541$	−7.62529	+	13.2074i	−0.327837	+	0.567830i	−0.982082	−	0.188452i	$-0.939653\pi$
$541$	−7.62529	+	13.2074i	−0.327837	+	0.567830i	0.654245	+	0.756282i	$0.272986\pi$
$542$	1.45183	+	2.51464i	0.0623614	+	0.108013i
$543$	−0.560827	−	0.971381i	−0.0240674	−	0.0416859i
$544$	20.4103	−	35.3516i	0.875083	−	1.51569i
$545$	16.7129			0.715901
$546$	0.289250	−	0.0251791i	0.0123787	−	0.00107757i
$547$	22.6089			0.966686			0.483343	−	0.875431i	$-0.339422\pi$
$547$	22.6089			0.966686			0.483343	+	0.875431i	$0.339422\pi$
$548$	−3.81775	+	6.61253i	−0.163086	+	0.282473i
$549$	−14.3881	−	24.9208i	−0.614067	−	1.06360i
$550$	4.98688	+	8.63753i	0.212641	+	0.368305i
$551$	−22.0944	+	38.2686i	−0.941252	+	1.63030i
$552$	−0.893268			−0.0380200
$553$	7.17396	−	15.3671i	0.305068	−	0.653477i
$554$	45.1022			1.91621
$555$	0.219864	−	0.380816i	0.00933272	−	0.0161648i
$556$	−5.90514	−	10.2280i	−0.250434	−	0.433764i
$557$	5.75174	+	9.96231i	0.243709	+	0.422117i	0.961768	−	0.273866i	$-0.0883024\pi$
$557$	5.75174	+	9.96231i	0.243709	+	0.422117i	−0.718059	+	0.695983i	$0.754969\pi$
$558$	10.6045	−	18.3675i	0.448923	−	0.777557i
$559$	1.44901			0.0612868
$560$	−24.8757	−	35.5591i	−1.05119	−	1.50265i
$561$	0.499351			0.0210826
$562$	−1.64734	+	2.85327i	−0.0694887	+	0.120358i
$563$	−13.2143	−	22.8879i	−0.556918	−	0.964610i	−0.997752	−	0.0670211i	$-0.978651\pi$
$563$	−13.2143	−	22.8879i	−0.556918	−	0.964610i	0.440834	−	0.897589i	$-0.354683\pi$
$564$	0.146755	+	0.254187i	0.00617950	+	0.0107032i
$565$	−14.0371	+	24.3130i	−0.590545	+	1.02285i
$566$	−22.7413			−0.955889
$567$	13.5945	+	19.4330i	0.570917	+	0.816110i
$568$	−11.4486			−0.480374
$569$	10.8980	−	18.8758i	0.456866	−	0.791315i	−0.541927	−	0.840425i	$-0.682305\pi$
$569$	10.8980	−	18.8758i	0.456866	−	0.791315i	0.998793	+	0.0491102i	$0.0156385\pi$
$570$	−1.39336	−	2.41337i	−0.0583613	−	0.101085i
$571$	−19.0181	−	32.9403i	−0.795882	−	1.37851i	−0.922278	−	0.386528i	$-0.873674\pi$
$571$	−19.0181	−	32.9403i	−0.795882	−	1.37851i	0.126395	−	0.991980i	$-0.459659\pi$
$572$	0.498384	−	0.863226i	0.0208385	−	0.0360933i
$573$	−0.653395			−0.0272960
$574$	7.71092	−	16.5173i	0.321847	−	0.689420i
$575$	46.7466			1.94947
$576$	1.54155	−	2.67005i	0.0642314	−	0.111252i
$577$	12.5479	+	21.7336i	0.522375	+	0.904781i	0.999661	+	0.0260325i	$0.00828733\pi$
$577$	12.5479	+	21.7336i	0.522375	+	0.904781i	−0.477286	+	0.878748i	$0.658379\pi$
$578$	38.9931	+	67.5380i	1.62190	+	2.80921i
$579$	0.0911383	−	0.157856i	0.00378758	−	0.00656028i
$580$	18.6658			0.775056
$581$	−31.9328	+	2.77974i	−1.32479	+	0.115323i
$582$	−1.17315			−0.0486285
$583$	5.99360	−	10.3812i	0.248229	−	0.429946i
$584$	−9.09335	−	15.7502i	−0.376286	−	0.651746i
$585$	−4.91411	−	8.51148i	−0.203173	−	0.351907i
$586$	−16.7714	+	29.0488i	−0.692818	+	1.20000i
$587$	3.62632			0.149674			0.0748371	−	0.997196i	$-0.476156\pi$
$587$	3.62632			0.149674			0.0748371	+	0.997196i	$0.476156\pi$
$588$	0.151641	−	0.415505i	0.00625359	−	0.0171351i
$589$	−31.6553			−1.30434
$590$	27.1878	−	47.0906i	1.11930	−	1.93869i
$591$	0.614777	+	1.06483i	0.0252886	+	0.0438011i
$592$	5.28630	+	9.15615i	0.217266	+	0.376315i
$593$	−3.85161	+	6.67118i	−0.158167	+	0.273953i	−0.934208	−	0.356730i	$-0.883892\pi$
$593$	−3.85161	+	6.67118i	−0.158167	+	0.273953i	0.776041	+	0.630683i	$0.217225\pi$
$594$	−0.657996			−0.0269979
$595$	68.1106	−	5.92902i	2.79226	−	0.243066i
$596$	−2.52803			−0.103552
$597$	−0.265751	+	0.460294i	−0.0108765	+	0.0188386i
$598$	−7.02286	−	12.1639i	−0.287186	−	0.497421i
$599$	−13.8244	−	23.9446i	−0.564850	−	0.978349i	−0.997064	−	0.0765776i	$-0.975601\pi$
$599$	−13.8244	−	23.9446i	−0.564850	−	0.978349i	0.432214	−	0.901771i	$-0.357733\pi$
$600$	0.317152	−	0.549323i	0.0129477	−	0.0224260i
$601$	8.33880			0.340147			0.170073	−	0.985431i	$-0.445600\pi$
$601$	8.33880			0.340147			0.170073	+	0.985431i	$0.445600\pi$
$602$	2.80738	−	6.01362i	0.114420	−	0.245097i
$603$	8.41034			0.342496
$604$	7.65807	−	13.2642i	0.311602	−	0.539711i
$605$	−1.64023	−	2.84097i	−0.0666850	−	0.115502i
$606$	−0.596399	−	1.03299i	−0.0242270	−	0.0419625i
$607$	−3.35483	+	5.81073i	−0.136168	+	0.235850i	−0.926043	−	0.377418i	$-0.876812\pi$
$607$	−3.35483	+	5.81073i	−0.136168	+	0.235850i	0.789875	+	0.613268i	$0.210145\pi$
$608$	40.1147			1.62687
$609$	−0.548812	−	0.784512i	−0.0222390	−	0.0317900i
$610$	54.5450			2.20846
$611$	2.32254	−	4.02275i	0.0939598	−	0.162743i
$612$	−11.7618	−	20.3720i	−0.475441	−	0.823488i
$613$	−2.28689	−	3.96101i	−0.0923665	−	0.159984i	0.816140	−	0.577854i	$-0.196110\pi$
$613$	−2.28689	−	3.96101i	−0.0923665	−	0.159984i	−0.908506	+	0.417871i	$0.862776\pi$
$614$	1.97160	−	3.41490i	0.0795671	−	0.137814i
$615$	0.827654			0.0333742
$616$	2.63389	+	3.76508i	0.106123	+	0.151699i
$617$	−23.6560			−0.952355			−0.476178	−	0.879349i	$-0.657978\pi$
$617$	−23.6560			−0.952355			−0.476178	+	0.879349i	$0.657978\pi$
$618$	−0.324433	+	0.561934i	−0.0130506	+	0.0226043i
$619$	−5.98855	−	10.3725i	−0.240700	−	0.416905i	0.720214	−	0.693752i	$-0.244044\pi$
$619$	−5.98855	−	10.3725i	−0.240700	−	0.416905i	−0.960914	+	0.276847i	$0.910710\pi$
$620$	6.68578	+	11.5801i	0.268508	+	0.465069i
$621$	−1.54200	+	2.67082i	−0.0618783	+	0.107176i
$622$	9.61292			0.385443
$623$	−14.8896	+	31.8947i	−0.596541	+	1.27783i
$624$	−0.316961			−0.0126886
$625$	10.3064	−	17.8513i	0.412258	−	0.714052i
$626$	23.5705	+	40.8254i	0.942068	+	1.63171i
$627$	0.245358	+	0.424973i	0.00979866	+	0.0169718i
$628$	−1.67681	+	2.90432i	−0.0669120	+	0.115895i
$629$	−16.6565			−0.664136
$630$	−44.8447	+	3.90372i	−1.78665	+	0.155528i
$631$	−6.39411			−0.254545			−0.127273	−	0.991868i	$-0.540622\pi$
$631$	−6.39411			−0.254545			−0.127273	+	0.991868i	$0.540622\pi$
$632$	−5.56615	+	9.64085i	−0.221409	+	0.383492i
$633$	−0.206158	−	0.357075i	−0.00819403	−	0.0141925i
$634$	4.71385	+	8.16462i	0.187211	+	0.324259i
$635$	−19.9282	+	34.5166i	−0.790826	+	1.36975i
$636$	0.757439			0.0300344
$637$	−6.89471	+	1.20953i	−0.273178	+	0.0479234i
$638$	−9.88198			−0.391231
$639$	−9.87494	+	17.1039i	−0.390647	+	0.676620i
$640$	19.9219	+	34.5057i	0.787480	+	1.36396i
$641$	19.7869	+	34.2720i	0.781537	+	1.35366i	0.931046	+	0.364901i	$0.118897\pi$
$641$	19.7869	+	34.2720i	0.781537	+	1.35366i	−0.149509	+	0.988760i	$0.547769\pi$
$642$	0.108377	−	0.187714i	0.00427730	−	0.00740850i
$643$	32.7481			1.29146			0.645730	−	0.763566i	$-0.276553\pi$
$643$	32.7481			1.29146			0.645730	+	0.763566i	$0.276553\pi$
$644$	−21.3167	+	1.85562i	−0.839998	+	0.0731216i
$645$	0.301332			0.0118649
$646$	−52.7789	+	91.4157i	−2.07656	+	3.59670i
$647$	−14.4256	−	24.9859i	−0.567129	−	0.982295i	−0.996848	−	0.0793330i	$-0.974721\pi$
$647$	−14.4256	−	24.9859i	−0.567129	−	0.982295i	0.429720	−	0.902962i	$-0.358612\pi$
$648$	−7.78382	−	13.4820i	−0.305777	−	0.529622i
$649$	−4.78753	+	8.29225i	−0.187927	+	0.325499i
$650$	9.97376			0.391203
$651$	0.290130	−	0.621478i	0.0113711	−	0.0243576i
$652$	−2.23298			−0.0874502
$653$	17.0670	−	29.5609i	0.667882	−	1.15681i	−0.310613	−	0.950536i	$-0.600534\pi$
$653$	17.0670	−	29.5609i	0.667882	−	1.15681i	0.978495	−	0.206269i	$-0.0661323\pi$
$654$	−0.279543	−	0.484183i	−0.0109310	−	0.0189330i
$655$	−23.1027	−	40.0151i	−0.902699	−	1.56352i
$656$	−9.94984	+	17.2336i	−0.388476	+	0.672860i
$657$	−31.3737			−1.22400
$658$	−12.1952	−	17.4327i	−0.475419	−	0.679598i
$659$	−24.5588			−0.956677			−0.478338	−	0.878176i	$-0.658761\pi$
$659$	−24.5588			−0.956677			−0.478338	+	0.878176i	$0.658761\pi$
$660$	0.103642	−	0.179513i	0.00403426	−	0.00698754i
$661$	−4.53830	−	7.86057i	−0.176520	−	0.305741i	0.764167	−	0.645019i	$-0.223151\pi$
$661$	−4.53830	−	7.86057i	−0.176520	−	0.305741i	−0.940686	+	0.339278i	$0.889817\pi$
$662$	14.2676	+	24.7122i	0.554526	+	0.960467i
$663$	0.249675	−	0.432451i	0.00969659	−	0.0167950i
$664$	21.0404			0.816528
$665$	38.5123	+	55.0523i	1.49344	+	2.13484i
$666$	10.9668			0.424954
$667$	−23.1582	+	40.1112i	−0.896689	+	1.55311i
$668$	−8.75550	−	15.1650i	−0.338761	−	0.586750i
$669$	0.263808	+	0.456929i	0.0101994	+	0.0176659i
$670$	−7.97089	+	13.8060i	−0.307942	+	0.533372i
$671$	−9.60490			−0.370793
$672$	−0.367662	+	0.787557i	−0.0141829	+	0.0303807i
$673$	32.1241			1.23829			0.619147	−	0.785275i	$-0.287479\pi$
$673$	32.1241			1.23829			0.619147	+	0.785275i	$0.287479\pi$
$674$	27.1886	−	47.0921i	1.04727	−	1.81392i
$675$	−1.09496	−	1.89653i	−0.0421451	−	0.0729975i
$676$	−0.498384	−	0.863226i	−0.0191686	−	0.0332010i
$677$	−9.62746	+	16.6753i	−0.370013	+	0.640882i	−0.989567	−	0.144072i	$-0.953980\pi$
$677$	−9.62746	+	16.6753i	−0.370013	+	0.640882i	0.619554	+	0.784954i	$0.287314\pi$
$678$	0.939149			0.0360678
$679$	28.1773	−	2.45283i	1.08134	−	0.0941309i
$680$	−44.8780			−1.72099
$681$	−0.0551591	+	0.0955383i	−0.00211370	+	0.00366104i
$682$	−3.53956	−	6.13070i	−0.135537	−	0.234757i
$683$	−1.58896	−	2.75216i	−0.0607998	−	0.105308i	0.834023	−	0.551729i	$-0.186032\pi$
$683$	−1.58896	−	2.75216i	−0.0607998	−	0.105308i	−0.894823	+	0.446421i	$0.852698\pi$
$684$	11.5584	−	20.0197i	0.441946	−	0.765473i
$685$	25.1292			0.960138
$686$	−8.33839	+	30.9574i	−0.318361	+	1.18196i
$687$	0.611412			0.0233268
$688$	−3.62253	+	6.27440i	−0.138108	+	0.239209i
$689$	−5.99360	−	10.3812i	−0.228338	−	0.395493i
$690$	−1.46045	−	2.52957i	−0.0555983	−	0.0962990i
$691$	−18.5098	+	32.0599i	−0.704145	+	1.21961i	0.262854	+	0.964835i	$0.415336\pi$
$691$	−18.5098	+	32.0599i	−0.704145	+	1.21961i	−0.966999	+	0.254779i	$0.917997\pi$
$692$	−2.55419			−0.0970958
$693$	7.89676	−	0.687411i	0.299973	−	0.0261126i
$694$	−30.1198			−1.14333
$695$	−19.4344	+	33.6614i	−0.737190	+	1.27685i
$696$	0.314233	+	0.544268i	0.0119110	+	0.0206304i
$697$	−15.6753	−	27.1504i	−0.593745	−	1.02840i
$698$	26.3137	−	45.5767i	0.995989	−	1.72510i
$699$	1.20003			0.0453892
$700$	6.42731	−	13.7677i	0.242929	−	0.520372i
$701$	35.8261			1.35313			0.676566	−	0.736382i	$-0.263467\pi$
$701$	35.8261			1.35313			0.676566	+	0.736382i	$0.263467\pi$
$702$	−0.328998	+	0.569841i	−0.0124172	+	0.0215073i
$703$	−8.18421	−	14.1755i	−0.308674	−	0.534638i
$704$	−0.514541	−	0.891211i	−0.0193925	−	0.0335888i
$705$	0.482986	−	0.836556i	0.0181903	−	0.0315065i
$706$	−38.9351			−1.46534
$707$	16.4844	+	23.5640i	0.619961	+	0.886217i
$708$	−0.605023			−0.0227382
$709$	−7.22996	+	12.5227i	−0.271527	+	0.470298i	−0.969253	−	0.246066i	$-0.920862\pi$
$709$	−7.22996	+	12.5227i	−0.271527	+	0.470298i	0.697726	+	0.716365i	$0.254195\pi$
$710$	−18.7179	−	32.4204i	−0.702471	−	1.21672i
$711$	9.60209	+	16.6313i	0.360106	+	0.623723i
$712$	11.5526	−	20.0097i	0.432952	−	0.749894i
$713$	−33.1795			−1.24258
$714$	−1.31100	−	1.87404i	−0.0490629	−	0.0701341i
$715$	−3.28047			−0.122682
$716$	0.156513	−	0.271088i	0.00584916	−	0.0101310i
$717$	0.00671812	+	0.0116361i	0.000250893	+	0.000434559i
$718$	−2.96929	−	5.14297i	−0.110813	−	0.191934i
$719$	10.5789	−	18.3233i	0.394528	−	0.683342i	−0.598513	−	0.801113i	$-0.704241\pi$
$719$	10.5789	−	18.3233i	0.394528	−	0.683342i	0.993041	+	0.117771i	$0.0375748\pi$
$720$	49.1410			1.83138
$721$	6.61751	−	14.1752i	0.246449	−	0.527911i
$722$	−70.8412			−2.63644
$723$	−0.804381	+	1.39323i	−0.0299153	+	0.0518148i
$724$	8.81833	+	15.2738i	0.327731	+	0.567646i
$725$	−16.4445	−	28.4827i	−0.610732	−	1.05782i
$726$	−0.0548697	+	0.0950372i	−0.00203641	+	0.00352716i
$727$	−25.7051			−0.953349			−0.476674	−	0.879080i	$-0.658158\pi$
$727$	−25.7051			−0.953349			−0.476674	+	0.879080i	$0.658158\pi$
$728$	4.57760	−	0.398479i	0.169657	−	0.0147686i
$729$	−26.7832			−0.991972
$730$	29.7343	−	51.5014i	1.10052	−	1.90615i
$731$	−5.70706	−	9.88491i	−0.211083	−	0.365607i
$732$	−0.303454	−	0.525598i	−0.0112160	−	0.0194267i
$733$	19.3146	−	33.4538i	0.713400	−	1.23565i	−0.250173	−	0.968201i	$-0.580488\pi$
$733$	19.3146	−	33.4538i	0.713400	−	1.23565i	0.963573	−	0.267444i	$-0.0861791\pi$
$734$	51.1958			1.88967
$735$	−1.43380	+	0.251530i	−0.0528864	+	0.00927781i
$736$	42.0462			1.54984
$737$	1.40360	−	2.43111i	0.0517024	−	0.0895512i
$738$	10.3208	+	17.8761i	0.379913	+	0.658029i
$739$	−11.7211	−	20.3015i	−0.431167	−	0.746803i	0.565807	−	0.824538i	$-0.308565\pi$
$739$	−11.7211	−	20.3015i	−0.431167	−	0.746803i	−0.996974	+	0.0777347i	$0.975231\pi$
$740$	−3.45710	+	5.98788i	−0.127086	+	0.220119i
$741$	0.490716			0.0180269
$742$	−54.6958	+	4.76126i	−2.00795	+	0.174791i
$743$	43.6871			1.60272			0.801362	−	0.598180i	$-0.204109\pi$
$743$	43.6871			1.60272			0.801362	+	0.598180i	$0.204109\pi$
$744$	−0.225106	+	0.389895i	−0.00825279	+	0.0142943i
$745$	4.16001	+	7.20534i	0.152411	+	0.263983i
$746$	18.0263	+	31.2224i	0.659989	+	1.14313i
$747$	18.1483	−	31.4338i	0.664011	−	1.15010i
$748$	−7.85169			−0.287086
$749$	−2.21058	+	4.73522i	−0.0807729	+	0.173021i
$750$	0.274122			0.0100095
$751$	−23.1335	+	40.0684i	−0.844153	+	1.46212i	0.0422019	+	0.999109i	$0.486563\pi$
$751$	−23.1335	+	40.0684i	−0.844153	+	1.46212i	−0.886355	+	0.463007i	$0.846771\pi$
$752$	11.6127	+	20.1137i	0.423470	+	0.733472i
$753$	0.558095	+	0.966649i	0.0203381	+	0.0352267i
$754$	−4.94099	+	8.55805i	−0.179940	+	0.311666i
$755$	−50.4070			−1.83450
$756$	0.574593	+	0.821366i	0.0208978	+	0.0298728i
$757$	17.8028			0.647055			0.323527	−	0.946219i	$-0.395131\pi$
$757$	17.8028			0.647055			0.323527	+	0.946219i	$0.395131\pi$
$758$	−6.93178	+	12.0062i	−0.251773	+	0.436084i
$759$	0.257172	+	0.445435i	0.00933475	+	0.0161683i
$760$	−22.0510	−	38.1934i	−0.799873	−	1.38542i
$761$	1.16063	−	2.01028i	0.0420730	−	0.0728725i	−0.844222	−	0.535994i	$-0.819937\pi$
$761$	1.16063	−	2.01028i	0.0420730	−	0.0728725i	0.886295	+	0.463121i	$0.153270\pi$
$762$	1.33329			0.0483001
$763$	7.72655	+	11.0449i	0.279720	+	0.399852i
$764$	10.2739			0.371695
$765$	−38.7092	+	67.0463i	−1.39953	+	2.42406i
$766$	−15.3700	−	26.6216i	−0.555341	−	0.961879i
$767$	4.78753	+	8.29225i	0.172868	+	0.299416i
$768$	0.601198	−	1.04131i	0.0216939	−	0.0375749i
$769$	23.7710			0.857206			0.428603	−	0.903493i	$-0.359006\pi$
$769$	23.7710			0.857206			0.428603	+	0.903493i	$0.359006\pi$
$770$	−6.35572	+	13.6144i	−0.229044	+	0.490629i
$771$	−0.130347			−0.00469435
$772$	−1.43304	+	2.48210i	−0.0515763	+	0.0893327i
$773$	4.77041	+	8.26259i	0.171580	+	0.297185i	0.938972	−	0.343993i	$-0.111780\pi$
$773$	4.77041	+	8.26259i	0.171580	+	0.297185i	−0.767393	+	0.641177i	$0.778446\pi$
$774$	3.75758	+	6.50832i	0.135063	+	0.233937i
$775$	11.7803	−	20.4040i	0.423160	−	0.732934i
$776$	−18.5660			−0.666479
$777$	0.353313	−	0.0307558i	0.0126750	−	0.00110336i
$778$	−48.0308			−1.72199
$779$	15.4043	−	26.6810i	0.551915	−	0.955945i
$780$	−0.103642	−	0.179513i	−0.00371098	−	0.00642760i
$781$	3.29606	+	5.70895i	0.117942	+	0.204282i
$782$	−55.3201	+	95.8173i	−1.97824	+	3.42642i
$783$	2.16977			0.0775413
$784$	11.9993	−	32.8787i	0.428547	−	1.17424i
$785$	11.0371			0.393932
$786$	−0.772842	+	1.33860i	−0.0275664	+	0.0477464i
$787$	10.0957	+	17.4863i	0.359874	+	0.623320i	0.987939	−	0.154841i	$-0.0494864\pi$
$787$	10.0957	+	17.4863i	0.359874	+	0.623320i	−0.628066	+	0.778160i	$0.716153\pi$
$788$	−9.66663	−	16.7431i	−0.344360	−	0.596448i
$789$	0.341920	−	0.592222i	0.0121727	−	0.0210837i
$790$	−36.4014			−1.29511
$791$	−22.5570	+	1.96358i	−0.802035	+	0.0698170i
$792$	−5.20316			−0.184886
$793$	−4.80245	+	8.31809i	−0.170540	+	0.295384i
$794$	−7.72366	−	13.3778i	−0.274102	−	0.474759i
$795$	−1.24641	−	2.15884i	−0.0442055	−	0.0765661i
$796$	4.17861	−	7.23757i	0.148107	−	0.256529i
$797$	−6.08025			−0.215374			−0.107687	−	0.994185i	$-0.534344\pi$
$797$	−6.08025			−0.215374			−0.107687	+	0.994185i	$0.534344\pi$
$798$	0.950735	−	2.03654i	0.0336557	−	0.0720928i
$799$	−36.5900			−1.29446
$800$	−14.9283	+	25.8567i	−0.527797	+	0.914171i
$801$	−19.9292	−	34.5184i	−0.704165	−	1.21965i
$802$	2.24314	+	3.88523i	0.0792079	+	0.137192i
$803$	−5.23596	+	9.06894i	−0.184773	+	0.320036i
$804$	0.177380			0.00625571
$805$	40.3667	+	57.7030i	1.42274	+	2.03377i
$806$	−7.07912			−0.249351
$807$	0.487218	−	0.843886i	0.0171509	−	0.0297062i
$808$	−9.43848	−	16.3479i	−0.332044	−	0.575118i
$809$	11.7745	+	20.3941i	0.413971	+	0.717018i	0.995320	−	0.0966361i	$-0.0308083\pi$
$809$	11.7745	+	20.3941i	0.413971	+	0.717018i	−0.581349	+	0.813654i	$0.697475\pi$
$810$	25.4523	−	44.0846i	0.894302	−	1.54898i
$811$	−11.3445			−0.398358			−0.199179	−	0.979963i	$-0.563827\pi$
$811$	−11.3445			−0.398358			−0.199179	+	0.979963i	$0.563827\pi$
$812$	8.62942	+	12.3355i	0.302833	+	0.432892i
$813$	−0.106330			−0.00372915
$814$	1.83025	−	3.17008i	0.0641501	−	0.111111i
$815$	3.67448	+	6.36439i	0.128712	+	0.222935i
$816$	1.24837	+	2.16225i	0.0437019	+	0.0756938i
$817$	5.60837	−	9.71398i	0.196212	−	0.339849i
$818$	4.82423			0.168675
$819$	3.35306	−	7.18250i	0.117166	−	0.250977i
$820$	−13.0139			−0.454464
$821$	1.03612	−	1.79461i	0.0361608	−	0.0626324i	−0.847379	−	0.530989i	$-0.821820\pi$
$821$	1.03612	−	1.79461i	0.0361608	−	0.0626324i	0.883539	+	0.468357i	$0.155154\pi$
$822$	−0.420316	−	0.728009i	−0.0146602	−	0.0253922i
$823$	6.99904	+	12.1227i	0.243971	+	0.422571i	0.961842	−	0.273606i	$-0.0882164\pi$
$823$	6.99904	+	12.1227i	0.243971	+	0.422571i	−0.717871	+	0.696177i	$0.754883\pi$
$824$	−5.13440	+	8.89304i	−0.178865	+	0.309804i
$825$	−0.365232			−0.0127157
$826$	43.6896	−	3.80317i	1.52015	−	0.132329i
$827$	44.0449			1.53159			0.765796	−	0.643084i	$-0.222345\pi$
$827$	44.0449			1.53159			0.765796	+	0.643084i	$0.222345\pi$
$828$	12.1149	−	20.9836i	0.421022	−	0.729232i
$829$	8.93892	+	15.4827i	0.310461	+	0.537735i	0.978462	−	0.206426i	$-0.0661831\pi$
$829$	8.93892	+	15.4827i	0.310461	+	0.537735i	−0.668001	+	0.744160i	$0.732850\pi$
$830$	34.4000	+	59.5826i	1.19404	+	2.06814i
$831$	−0.825805	+	1.43034i	−0.0286468	+	0.0496178i
$832$	−1.02908			−0.0356770
$833$	35.4066	+	42.2706i	1.22676	+	1.46459i
$834$	1.30026			0.0450242
$835$	−28.8153	+	49.9095i	−0.997194	+	1.72719i
$836$	−3.85796	−	6.68219i	−0.133430	−	0.231108i
$837$	0.777176	+	1.34611i	0.0268631	+	0.0465283i
$838$	−4.02293	+	6.96793i	−0.138970	+	0.240703i
$839$	−44.1847			−1.52543			−0.762713	−	0.646737i	$-0.776133\pi$
$839$	−44.1847			−1.52543			−0.762713	+	0.646737i	$0.776133\pi$
$840$	0.951940	−	0.0828662i	0.0328451	−	0.00285916i
$841$	3.58629			0.123665
$842$	3.43187	−	5.94418i	0.118270	−	0.204850i
$843$	−0.0603242	−	0.104485i	−0.00207768	−	0.00359864i
$844$	3.24158	+	5.61458i	0.111580	+	0.193262i
$845$	−1.64023	+	2.84097i	−0.0564257	+	0.0977322i
$846$	24.0912			0.828272
$847$	1.11919	−	2.39738i	0.0384557	−	0.0823749i
$848$	59.9359			2.05821
$849$	0.416385	−	0.721201i	0.0142903	−	0.0247515i
$850$	−39.2824	−	68.0392i	−1.34738	−	2.33372i
$851$	−8.57828	−	14.8580i	−0.294060	−	0.509326i
$852$	−0.208269	+	0.360733i	−0.00713519	+	0.0123585i
$853$	39.6185			1.35651			0.678255	−	0.734826i	$-0.262736\pi$
$853$	39.6185			1.35651			0.678255	+	0.734826i	$0.262736\pi$
$854$	25.2168	+	36.0467i	0.862900	+	1.23349i
$855$	−76.0797			−2.60187
$856$	1.71515	−	2.97073i	0.0586226	−	0.101537i
$857$	15.4613	+	26.7798i	0.528150	+	0.914782i	0.999461	+	0.0328152i	$0.0104473\pi$
$857$	15.4613	+	26.7798i	0.528150	+	0.914782i	−0.471312	+	0.881967i	$0.656219\pi$
$858$	0.0548697	+	0.0950372i	0.00187322	+	0.00324452i
$859$	26.0267	−	45.0796i	0.888019	−	1.53809i	0.0458057	−	0.998950i	$-0.485415\pi$
$859$	26.0267	−	45.0796i	0.888019	−	1.53809i	0.842214	−	0.539144i	$-0.181252\pi$
$860$	−4.73808			−0.161567
$861$	0.382634	+	0.546964i	0.0130401	+	0.0186405i
$862$	13.9999			0.476837
$863$	−13.8300	+	23.9542i	−0.470778	+	0.815412i	−0.999441	−	0.0334198i	$-0.989360\pi$
$863$	−13.8300	+	23.9542i	−0.470778	+	0.815412i	0.528663	+	0.848832i	$0.322693\pi$
$864$	−0.984863	−	1.70583i	−0.0335057	−	0.0580336i
$865$	4.20306	+	7.27991i	0.142908	+	0.247524i
$866$	−8.41121	+	14.5686i	−0.285824	+	0.495063i
$867$	−2.85580			−0.0969879
$868$	−4.56194	+	9.77200i	−0.154842	+	0.331683i
$869$	6.40998			0.217444
$870$	−1.02751	+	1.77970i	−0.0348358	+	0.0603374i
$871$	−1.40360	−	2.43111i	−0.0475593	−	0.0823751i
$872$	−4.42399	−	7.66257i	−0.149815	−	0.259487i
$873$	−16.0140	+	27.7370i	−0.541990	+	0.938754i
$874$	−108.727			−3.67775
$875$	−6.58402	+	0.573137i	−0.222580	+	0.0193756i
$876$	−0.661693			−0.0223565
$877$	−22.5105	+	38.9894i	−0.760126	+	1.31658i	0.182659	+	0.983176i	$0.441529\pi$
$877$	−22.5105	+	38.9894i	−0.760126	+	1.31658i	−0.942785	+	0.333401i	$0.891804\pi$
$878$	0.315181	+	0.545909i	0.0106368	+	0.0184235i
$879$	−0.614155	−	1.06375i	−0.0207149	−	0.0358793i
$880$	8.20115	−	14.2048i	0.276461	−	0.478844i
$881$	15.3813			0.518209			0.259105	−	0.965849i	$-0.416573\pi$
$881$	15.3813			0.518209			0.259105	+	0.965849i	$0.416573\pi$
$882$	−23.3120	−	27.8314i	−0.784957	−	0.937131i
$883$	−16.7702			−0.564363			−0.282182	−	0.959361i	$-0.591058\pi$
$883$	−16.7702			−0.564363			−0.282182	+	0.959361i	$0.591058\pi$
$884$	−3.92585	+	6.79977i	−0.132041	+	0.228701i
$885$	0.995597	+	1.72442i	0.0334666	+	0.0579659i
$886$	−28.2412	−	48.9152i	−0.948781	−	1.64334i
$887$	−13.2246	+	22.9057i	−0.444039	+	0.769098i	−0.997985	−	0.0634548i	$-0.979788\pi$
$887$	−13.2246	+	22.9057i	−0.444039	+	0.769098i	0.553946	+	0.832553i	$0.313121\pi$
$888$	−0.232797			−0.00781216
$889$	−32.0237	+	2.78766i	−1.07404	+	0.0934951i
$890$	75.5516			2.53249
$891$	−4.48192	+	7.76292i	−0.150150	+	0.260068i
$892$	−4.14807	−	7.18466i	−0.138888	−	0.240560i
$893$	−17.9786	−	31.1399i	−0.601632	−	1.04206i
$894$	0.139162	−	0.241036i	0.00465428	−	0.00806145i
$895$	−1.03020			−0.0344358
$896$	−13.5934	+	29.1179i	−0.454122	+	0.972762i
$897$	0.514344			0.0171734
$898$	5.97046	−	10.3411i	0.199237	−	0.345089i
$899$	11.6719	+	20.2163i	0.389279	+	0.674250i
$900$	8.60271	+	14.9003i	0.286757	+	0.496678i
$901$	−47.2125	+	81.7745i	−1.57288	+	2.72430i
$902$	6.88975			0.229404
$903$	0.139309	+	0.199138i	0.00463591	+	0.00662691i
$904$	14.8628			0.494328
$905$	29.0221	−	50.2677i	0.964726	−	1.67095i
$906$	0.843118	+	1.46032i	0.0280107	+	0.0485160i
$907$	−27.3026	−	47.2895i	−0.906567	−	1.57022i	−0.818799	−	0.574080i	$-0.805360\pi$
$907$	−27.3026	−	47.2895i	−0.906567	−	1.57022i	−0.0877682	−	0.996141i	$-0.527973\pi$
$908$	0.867310	−	1.50223i	0.0287827	−	0.0498531i
$909$	−32.5644			−1.08009
$910$	8.61256	+	12.3114i	0.285503	+	0.408119i
$911$	2.69389			0.0892525			0.0446263	−	0.999004i	$-0.485790\pi$
$911$	2.69389			0.0892525			0.0446263	+	0.999004i	$0.485790\pi$
$912$	−1.22679	+	2.12486i	−0.0406230	+	0.0703611i
$913$	−6.05755	−	10.4920i	−0.200476	−	0.347234i
$914$	13.2245	+	22.9054i	0.437426	+	0.757644i
$915$	−0.998699	+	1.72980i	−0.0330160	+	0.0571854i
$916$	−9.61371			−0.317646
$917$	15.7638	−	33.7672i	0.520566	−	1.11509i
$918$	5.18314			0.171069
$919$	0.181450	−	0.314280i	0.00598548	−	0.0103672i	−0.863017	−	0.505175i	$-0.831428\pi$
$919$	0.181450	−	0.314280i	0.00598548	−	0.0103672i	0.869003	+	0.494807i	$0.164761\pi$
$920$	−23.1127	−	40.0324i	−0.762004	−	1.31983i
$921$	0.0721984	+	0.125051i	0.00237902	+	0.00412058i
$922$	6.00347	−	10.3983i	0.197714	−	0.342451i
$923$	6.59212			0.216982
$924$	0.166548	−	0.0144980i	0.00547903	−	0.000476949i
$925$	12.1827			0.400566
$926$	−6.80902	+	11.7936i	−0.223758	+	0.387561i
$927$	8.85729	+	15.3413i	0.290911	+	0.503873i
$928$	−14.7910	−	25.6187i	−0.485538	−	0.840976i
$929$	2.31268	−	4.00568i	0.0758765	−	0.131422i	−0.825591	−	0.564270i	$-0.809158\pi$
$929$	2.31268	−	4.00568i	0.0758765	−	0.131422i	0.901467	+	0.432848i	$0.142491\pi$
$930$	−1.47215			−0.0482736
$931$	−18.5773	+	50.9026i	−0.608845	+	1.66827i
$932$	−18.8690			−0.618075
$933$	−0.176009	+	0.304857i	−0.00576228	+	0.00998056i
$934$	−8.07457	−	13.9856i	−0.264208	−	0.457622i
$935$	12.9204	+	22.3787i	0.422541	+	0.731863i
$936$	−2.60158	+	4.50607i	−0.0850353	+	0.147285i
$937$	−25.9933			−0.849164			−0.424582	−	0.905390i	$-0.639579\pi$
$937$	−25.9933			−0.849164			−0.424582	+	0.905390i	$0.639579\pi$
$938$	−12.8089	+	1.11501i	−0.418225	+	0.0364064i
$939$	−1.72627			−0.0563348
$940$	−7.59437	+	13.1538i	−0.247701	+	0.429031i
$941$	−12.8996	−	22.3427i	−0.420515	−	0.728353i	0.575475	−	0.817819i	$-0.304817\pi$
$941$	−12.8996	−	22.3427i	−0.420515	−	0.728353i	−0.995990	+	0.0894664i	$0.971484\pi$
$942$	−0.184609	−	0.319752i	−0.00601489	−	0.0104181i
$943$	16.1460	−	27.9656i	0.525785	−	0.910687i
$944$	−47.8752			−1.55821
$945$	1.39552	−	2.98929i	0.0453961	−	0.0972417i
$946$	2.50841			0.0815556
$947$	19.4767	−	33.7346i	0.632908	−	1.09623i	−0.354047	−	0.935228i	$-0.615195\pi$
$947$	19.4767	−	33.7346i	0.632908	−	1.09623i	0.986954	−	0.161001i	$-0.0514721\pi$
$948$	0.202515	+	0.350766i	0.00657737	+	0.0113923i
$949$	5.23596	+	9.06894i	0.169966	+	0.294390i
$950$	38.6032	−	66.8626i	1.25245	−	2.16931i
$951$	−0.345235			−0.0111950
$952$	−20.7476	−	29.6581i	−0.672433	−	0.961225i
$953$	53.5731			1.73540			0.867702	−	0.497085i	$-0.165596\pi$
$953$	53.5731			1.73540			0.867702	+	0.497085i	$0.165596\pi$
$954$	31.0852	−	53.8411i	1.00642	−	1.74317i
$955$	−16.9062	−	29.2823i	−0.547071	−	0.947554i
$956$	−0.105634	−	0.182964i	−0.00341646	−	0.00591748i
$957$	0.180936	−	0.313390i	0.00584882	−	0.0101304i
$958$	39.0737			1.26242
$959$	11.6175	+	16.6069i	0.375149	+	0.536266i
$960$	−0.214004			−0.00690695
$961$	7.13866	−	12.3645i	0.230279	−	0.398856i
$962$	−1.83025	−	3.17008i	−0.0590095	−	0.102207i
$963$	−2.95878	−	5.12476i	−0.0953455	−	0.165143i
$964$	12.6479	−	21.9069i	0.407362	−	0.705573i
$965$	9.43257			0.303645
$966$	0.996513	−	2.13460i	0.0320623	−	0.0686797i
$967$	26.3420			0.847103			0.423551	−	0.905872i	$-0.360783\pi$
$967$	26.3420			0.847103			0.423551	+	0.905872i	$0.360783\pi$
$968$	−0.868357	+	1.50404i	−0.0279100	+	0.0483416i
$969$	−1.93272	−	3.34758i	−0.0620880	−	0.107540i
$970$	−30.3544	−	52.5753i	−0.974621	−	1.68809i
$971$	8.15027	−	14.1167i	0.261555	−	0.453026i	−0.705101	−	0.709107i	$-0.749098\pi$
$971$	8.15027	−	14.1167i	0.261555	−	0.453026i	0.966655	+	0.256081i	$0.0824315\pi$
$972$	−1.70301			−0.0546242
$973$	−31.2303	+	2.71859i	−1.00120	+	0.0871540i
$974$	20.4514			0.655304
$975$	−0.182616	+	0.316300i	−0.00584839	+	0.0101297i
$976$	−24.0122	−	41.5904i	−0.768612	−	1.33127i
$977$	5.96885	+	10.3383i	0.190960	+	0.330753i	0.945569	−	0.325422i	$-0.105506\pi$
$977$	5.96885	+	10.3383i	0.190960	+	0.330753i	−0.754608	+	0.656175i	$0.772173\pi$
$978$	0.122920	−	0.212904i	0.00393056	−	0.00680793i
$979$	−13.3040			−0.425197
$980$	22.5448	−	3.95500i	0.720166	−	0.126338i
$981$	−15.2635			−0.487327
$982$	23.7537	−	41.1425i	0.758009	−	1.31291i
$983$	−3.90552	−	6.76457i	−0.124567	−	0.215756i	0.796997	−	0.603984i	$-0.206421\pi$
$983$	−3.90552	−	6.76457i	−0.124567	−	0.215756i	−0.921564	+	0.388228i	$0.873087\pi$
$984$	−0.219084	−	0.379465i	−0.00698415	−	0.0120969i
$985$	−31.8139	+	55.1033i	−1.01368	+	1.75574i
$986$	77.8419			2.47899
$987$	0.776137	−	0.0675626i	0.0247047	−	0.00215054i
$988$	−7.71592			−0.245476
$989$	5.87841	−	10.1817i	0.186923	−	0.323759i
$990$	−8.50690	−	14.7344i	−0.270367	−	0.468289i
$991$	−12.0761	−	20.9165i	−0.383611	−	0.664433i	0.607965	−	0.793964i	$-0.291986\pi$
$991$	−12.0761	−	20.9165i	−0.383611	−	0.664433i	−0.991575	+	0.129531i	$0.958653\pi$
$992$	10.5958	−	18.3524i	0.336416	−	0.582689i
$993$	−1.04494			−0.0331601
$994$	12.7719	−	27.3583i	0.405099	−	0.867751i
$995$	−27.5045			−0.871952
$996$	0.382760	−	0.662961i	0.0121282	−	0.0210067i
$997$	−18.8180	−	32.5937i	−0.595972	−	1.03225i	−0.993409	−	0.114624i	$-0.963434\pi$
$997$	−18.8180	−	32.5937i	−0.595972	−	1.03225i	0.397437	−	0.917629i	$-0.369900\pi$
$998$	19.7820	+	34.2634i	0.626188	+	1.08459i
$999$	−0.401864	+	0.696050i	−0.0127144	+	0.0220220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.716.21	yes	50
7.2	even	3		7007.2.a.bh.1.5		25
7.4	even	3	inner	1001.2.i.d.144.21	✓	50
7.5	odd	6		7007.2.a.bi.1.5		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.21	✓	50	7.4	even	3	inner
1001.2.i.d.716.21	yes	50	1.1	even	1	trivial
7007.2.a.bh.1.5		25	7.2	even	3
7007.2.a.bi.1.5		25	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.865559 - 1.49919i) q^{2} +(0.0316961 + 0.0548993i) q^{3} +(-0.498384 - 0.863226i) q^{4} +(-1.64023 + 2.84097i) q^{5} +0.109739 q^{6} +(-2.63578 + 0.229444i) q^{7} +1.73671 q^{8} +(1.49799 - 2.59460i) q^{9} +O(q^{10})\)	\(q+(0.865559 - 1.49919i) q^{2} +(0.0316961 + 0.0548993i) q^{3} +(-0.498384 - 0.863226i) q^{4} +(-1.64023 + 2.84097i) q^{5} +0.109739 q^{6} +(-2.63578 + 0.229444i) q^{7} +1.73671 q^{8} +(1.49799 - 2.59460i) q^{9} +(2.83944 + 4.91805i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.0315937 - 0.0547219i) q^{12} -1.00000 q^{13} +(-1.93744 + 4.15014i) q^{14} -0.207956 q^{15} +(2.49999 - 4.33012i) q^{16} +(3.93858 + 6.82182i) q^{17} +(-2.59320 - 4.49155i) q^{18} +(-3.87047 + 6.70386i) q^{19} +3.26986 q^{20} +(-0.0961405 - 0.137430i) q^{21} -1.73112 q^{22} +(-4.05683 + 7.02664i) q^{23} +(0.0550471 + 0.0953444i) q^{24} +(-2.88073 - 4.98957i) q^{25} +(-0.865559 + 1.49919i) q^{26} +0.380099 q^{27} +(1.51169 + 2.16093i) q^{28} +5.70844 q^{29} +(-0.179998 + 0.311766i) q^{30} +(2.04467 + 3.54147i) q^{31} +(-2.59107 - 4.48787i) q^{32} +(0.0316961 - 0.0548993i) q^{33} +13.6363 q^{34} +(3.67146 - 7.86452i) q^{35} -2.98630 q^{36} +(-1.05726 + 1.83123i) q^{37} +(6.70024 + 11.6052i) q^{38} +(-0.0316961 - 0.0548993i) q^{39} +(-2.84861 + 4.93394i) q^{40} -3.97994 q^{41} +(-0.289250 + 0.0251791i) q^{42} -1.44901 q^{43} +(-0.498384 + 0.863226i) q^{44} +(4.91411 + 8.51148i) q^{45} +(7.02286 + 12.1639i) q^{46} +(-2.32254 + 4.02275i) q^{47} +0.316961 q^{48} +(6.89471 - 1.20953i) q^{49} -9.97376 q^{50} +(-0.249675 + 0.432451i) q^{51} +(0.498384 + 0.863226i) q^{52} +(5.99360 + 10.3812i) q^{53} +(0.328998 - 0.569841i) q^{54} +3.28047 q^{55} +(-4.57760 + 0.398479i) q^{56} -0.490716 q^{57} +(4.94099 - 8.55805i) q^{58} +(-4.78753 - 8.29225i) q^{59} +(0.103642 + 0.179513i) q^{60} +(4.80245 - 8.31809i) q^{61} +7.07912 q^{62} +(-3.35306 + 7.18250i) q^{63} +1.02908 q^{64} +(1.64023 - 2.84097i) q^{65} +(-0.0548697 - 0.0950372i) q^{66} +(1.40360 + 2.43111i) q^{67} +(3.92585 - 6.79977i) q^{68} -0.514344 q^{69} +(-8.61256 - 12.3114i) q^{70} -6.59212 q^{71} +(2.60158 - 4.50607i) q^{72} +(-5.23596 - 9.06894i) q^{73} +(1.83025 + 3.17008i) q^{74} +(0.182616 - 0.316300i) q^{75} +7.71592 q^{76} +(1.51660 + 2.16793i) q^{77} -0.109739 q^{78} +(-3.20499 + 5.55120i) q^{79} +(8.20115 + 14.2048i) q^{80} +(-4.48192 - 7.76292i) q^{81} +(-3.44487 + 5.96670i) q^{82} +12.1151 q^{83} +(-0.0707185 + 0.151484i) q^{84} -25.8407 q^{85} +(-1.25421 + 2.17235i) q^{86} +(0.180936 + 0.313390i) q^{87} +(-0.868357 - 1.50404i) q^{88} +(6.65199 - 11.5216i) q^{89} +17.0138 q^{90} +(2.63578 - 0.229444i) q^{91} +8.08744 q^{92} +(-0.129616 + 0.224502i) q^{93} +(4.02058 + 6.96385i) q^{94} +(-12.6970 - 21.9918i) q^{95} +(0.164254 - 0.284496i) q^{96} -10.6903 q^{97} +(4.15446 - 11.3834i) q^{98} -2.99598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

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