LMFDB - Embedded newform 403.2.f.c.94.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.5
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.944860 - 1.63655i) q^{2} +(0.990948 + 1.71637i) q^{3} +(-0.785520 + 1.36056i) q^{4} -1.89350 q^{5} +(1.87261 - 3.24346i) q^{6} +(-0.456547 + 0.790763i) q^{7} -0.810613 q^{8} +(-0.463958 + 0.803598i) q^{9} +O(q^{10})$	\(q+(-0.944860 - 1.63655i) q^{2} +(0.990948 + 1.71637i) q^{3} +(-0.785520 + 1.36056i) q^{4} -1.89350 q^{5} +(1.87261 - 3.24346i) q^{6} +(-0.456547 + 0.790763i) q^{7} -0.810613 q^{8} +(-0.463958 + 0.803598i) q^{9} +(1.78910 + 3.09881i) q^{10} +(-2.50063 - 4.33122i) q^{11} -3.11364 q^{12} +(-2.31073 - 2.76777i) q^{13} +1.72549 q^{14} +(-1.87637 - 3.24996i) q^{15} +(2.33696 + 4.04773i) q^{16} +(2.80290 - 4.85477i) q^{17} +1.75350 q^{18} +(1.51562 - 2.62513i) q^{19} +(1.48739 - 2.57623i) q^{20} -1.80966 q^{21} +(-4.72549 + 8.18480i) q^{22} +(-1.32115 - 2.28830i) q^{23} +(-0.803276 - 1.39131i) q^{24} -1.41464 q^{25} +(-2.34627 + 6.39676i) q^{26} +4.10666 q^{27} +(-0.717254 - 1.24232i) q^{28} +(-2.45469 - 4.25165i) q^{29} +(-3.54580 + 6.14151i) q^{30} +1.00000 q^{31} +(3.60558 - 6.24505i) q^{32} +(4.95600 - 8.58404i) q^{33} -10.5934 q^{34} +(0.864474 - 1.49731i) q^{35} +(-0.728896 - 1.26249i) q^{36} +(-2.22147 - 3.84770i) q^{37} -5.72819 q^{38} +(2.46072 - 6.70878i) q^{39} +1.53490 q^{40} +(4.95269 + 8.57831i) q^{41} +(1.70987 + 2.96159i) q^{42} +(-4.24153 + 7.34655i) q^{43} +7.85719 q^{44} +(0.878506 - 1.52162i) q^{45} +(-2.49660 + 4.32424i) q^{46} -7.40533 q^{47} +(-4.63161 + 8.02218i) q^{48} +(3.08313 + 5.34014i) q^{49} +(1.33664 + 2.31512i) q^{50} +11.1101 q^{51} +(5.58084 - 0.969744i) q^{52} -7.22516 q^{53} +(-3.88022 - 6.72073i) q^{54} +(4.73496 + 8.20119i) q^{55} +(0.370083 - 0.641002i) q^{56} +6.00761 q^{57} +(-4.63868 + 8.03442i) q^{58} +(-0.903999 + 1.56577i) q^{59} +5.89569 q^{60} +(-2.83472 + 4.90987i) q^{61} +(-0.944860 - 1.63655i) q^{62} +(-0.423637 - 0.733761i) q^{63} -4.27924 q^{64} +(4.37537 + 5.24078i) q^{65} -18.7309 q^{66} +(-2.96679 - 5.13863i) q^{67} +(4.40347 + 7.62704i) q^{68} +(2.61838 - 4.53517i) q^{69} -3.26723 q^{70} +(-2.39626 + 4.15044i) q^{71} +(0.376090 - 0.651407i) q^{72} -9.42665 q^{73} +(-4.19796 + 7.27108i) q^{74} +(-1.40184 - 2.42805i) q^{75} +(2.38110 + 4.12419i) q^{76} +4.56663 q^{77} +(-13.3043 + 2.31179i) q^{78} +13.4790 q^{79} +(-4.42504 - 7.66439i) q^{80} +(5.46136 + 9.45935i) q^{81} +(9.35920 - 16.2106i) q^{82} +14.1994 q^{83} +(1.42152 - 2.46215i) q^{84} +(-5.30730 + 9.19252i) q^{85} +16.0306 q^{86} +(4.86494 - 8.42633i) q^{87} +(2.02704 + 3.51094i) q^{88} +(-8.55597 - 14.8194i) q^{89} -3.32026 q^{90} +(3.24360 - 0.563619i) q^{91} +4.15116 q^{92} +(0.990948 + 1.71637i) q^{93} +(6.99700 + 12.1192i) q^{94} +(-2.86983 + 4.97070i) q^{95} +14.2918 q^{96} +(5.49074 - 9.51025i) q^{97} +(5.82625 - 10.0914i) q^{98} +4.64075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.944860	−	1.63655i	−0.668117	−	1.15721i	−0.978430	−	0.206578i	$-0.933767\pi$
$2$	−0.944860	−	1.63655i	−0.668117	−	1.15721i	0.310313	−	0.950634i	$-0.399566\pi$
$3$	0.990948	+	1.71637i	0.572124	+	0.990948i	0.996348	+	0.0853908i	$0.0272139\pi$
$3$	0.990948	+	1.71637i	0.572124	+	0.990948i	−0.424223	+	0.905558i	$0.639453\pi$
$4$	−0.785520	+	1.36056i	−0.392760	+	0.680281i
$5$	−1.89350			−0.846801			−0.423400	−	0.905943i	$-0.639164\pi$
$5$	−1.89350			−0.846801			−0.423400	+	0.905943i	$0.639164\pi$
$6$	1.87261	−	3.24346i	0.764492	−	1.32414i
$7$	−0.456547	+	0.790763i	−0.172559	+	0.298880i	−0.939314	−	0.343060i	$-0.888537\pi$
$7$	−0.456547	+	0.790763i	−0.172559	+	0.298880i	0.766755	+	0.641940i	$0.221870\pi$
$8$	−0.810613			−0.286595
$9$	−0.463958	+	0.803598i	−0.154653	+	0.267866i
$10$	1.78910	+	3.09881i	0.565762	+	0.979928i
$11$	−2.50063	−	4.33122i	−0.753969	−	1.30591i	−0.945885	−	0.324501i	$-0.894803\pi$
$11$	−2.50063	−	4.33122i	−0.753969	−	1.30591i	0.191916	−	0.981411i	$-0.438530\pi$
$12$	−3.11364			−0.898831
$13$	−2.31073	−	2.76777i	−0.640880	−	0.767641i
$13$	−2.31073	−	2.76777i	−0.640880	−	0.767641i
$14$	1.72549			0.461157
$15$	−1.87637	−	3.24996i	−0.484475	−	0.839136i
$16$	2.33696	+	4.04773i	0.584239	+	1.01193i
$17$	2.80290	−	4.85477i	0.679803	−	1.17745i	−0.295237	−	0.955424i	$-0.595399\pi$
$17$	2.80290	−	4.85477i	0.679803	−	1.17745i	0.975040	−	0.222030i	$-0.0712682\pi$
$18$	1.75350			0.413304
$19$	1.51562	−	2.62513i	0.347707	−	0.602246i	−0.638135	−	0.769925i	$-0.720294\pi$
$19$	1.51562	−	2.62513i	0.347707	−	0.602246i	0.985842	+	0.167678i	$0.0536270\pi$
$20$	1.48739	−	2.57623i	0.332590	−	0.576062i
$21$	−1.80966			−0.394900
$22$	−4.72549	+	8.18480i	−1.00748	+	1.74500i
$23$	−1.32115	−	2.28830i	−0.275479	−	0.477143i	0.694777	−	0.719225i	$-0.255503\pi$
$23$	−1.32115	−	2.28830i	−0.275479	−	0.477143i	−0.970256	+	0.242082i	$0.922170\pi$
$24$	−0.803276	−	1.39131i	−0.163968	−	0.284001i
$25$	−1.41464			−0.282928
$26$	−2.34627	+	6.39676i	−0.460141	+	1.25451i
$27$	4.10666			0.790327
$28$	−0.717254	−	1.24232i	−0.135548	−	0.234777i
$29$	−2.45469	−	4.25165i	−0.455824	−	0.789511i	0.542911	−	0.839790i	$-0.317322\pi$
$29$	−2.45469	−	4.25165i	−0.455824	−	0.789511i	−0.998735	+	0.0502793i	$0.983989\pi$
$30$	−3.54580	+	6.14151i	−0.647372	+	1.12128i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	3.60558	−	6.24505i	0.637382	−	1.10398i
$33$	4.95600	−	8.58404i	0.862728	−	1.49429i
$34$	−10.5934			−1.81675
$35$	0.864474	−	1.49731i	0.146123	−	0.253092i
$36$	−0.728896	−	1.26249i	−0.121483	−	0.210414i
$37$	−2.22147	−	3.84770i	−0.365208	−	0.632558i	0.623602	−	0.781742i	$-0.285669\pi$
$37$	−2.22147	−	3.84770i	−0.365208	−	0.632558i	−0.988809	+	0.149184i	$0.952335\pi$
$38$	−5.72819			−0.929236
$39$	2.46072	−	6.70878i	0.394030	−	1.07427i
$40$	1.53490			0.242689
$41$	4.95269	+	8.57831i	0.773480	+	1.33971i	0.935645	+	0.352943i	$0.114819\pi$
$41$	4.95269	+	8.57831i	0.773480	+	1.33971i	−0.162165	+	0.986764i	$0.551848\pi$
$42$	1.70987	+	2.96159i	0.263839	+	0.456983i
$43$	−4.24153	+	7.34655i	−0.646828	+	1.12034i	0.337048	+	0.941487i	$0.390571\pi$
$43$	−4.24153	+	7.34655i	−0.646828	+	1.12034i	−0.983876	+	0.178851i	$0.942762\pi$
$44$	7.85719			1.18452
$45$	0.878506	−	1.52162i	0.130960	−	0.226829i
$46$	−2.49660	+	4.32424i	−0.368104	+	0.637574i
$47$	−7.40533			−1.08018			−0.540090	−	0.841608i	$-0.681610\pi$
$47$	−7.40533			−1.08018			−0.540090	+	0.841608i	$0.681610\pi$
$48$	−4.63161	+	8.02218i	−0.668515	+	1.15790i
$49$	3.08313	+	5.34014i	0.440447	+	0.762877i
$50$	1.33664	+	2.31512i	0.189029	+	0.327408i
$51$	11.1101			1.55573
$52$	5.58084	−	0.969744i	0.773923	−	0.134479i
$53$	−7.22516			−0.992451			−0.496226	−	0.868194i	$-0.665281\pi$
$53$	−7.22516			−0.992451			−0.496226	+	0.868194i	$0.665281\pi$
$54$	−3.88022	−	6.72073i	−0.528031	−	0.914576i
$55$	4.73496	+	8.20119i	0.638462	+	1.10585i
$56$	0.370083	−	0.641002i	0.0494544	−	0.0856576i
$57$	6.00761			0.795727
$58$	−4.63868	+	8.03442i	−0.609088	+	1.05497i
$59$	−0.903999	+	1.56577i	−0.117691	+	0.203846i	−0.918852	−	0.394602i	$-0.870882\pi$
$59$	−0.903999	+	1.56577i	−0.117691	+	0.203846i	0.801161	+	0.598448i	$0.204216\pi$
$60$	5.89569			0.761131
$61$	−2.83472	+	4.90987i	−0.362948	+	0.628645i	−0.988445	−	0.151582i	$-0.951563\pi$
$61$	−2.83472	+	4.90987i	−0.362948	+	0.628645i	0.625496	+	0.780227i	$0.284896\pi$
$62$	−0.944860	−	1.63655i	−0.119997	−	0.207841i
$63$	−0.423637	−	0.733761i	−0.0533732	−	0.0924452i
$64$	−4.27924			−0.534906
$65$	4.37537	+	5.24078i	0.542698	+	0.650039i
$66$	−18.7309			−2.30561
$67$	−2.96679	−	5.13863i	−0.362451	−	0.627784i	0.625912	−	0.779893i	$-0.284727\pi$
$67$	−2.96679	−	5.13863i	−0.362451	−	0.627784i	−0.988364	+	0.152109i	$0.951393\pi$
$68$	4.40347	+	7.62704i	0.533999	+	0.924914i
$69$	2.61838	−	4.53517i	0.315216	−	0.545970i
$70$	−3.26723			−0.390508
$71$	−2.39626	+	4.15044i	−0.284384	+	0.492567i	−0.972460	−	0.233072i	$-0.925122\pi$
$71$	−2.39626	+	4.15044i	−0.284384	+	0.492567i	0.688076	+	0.725639i	$0.258456\pi$
$72$	0.376090	−	0.651407i	0.0443226	−	0.0767690i
$73$	−9.42665			−1.10331			−0.551653	−	0.834074i	$-0.686003\pi$
$73$	−9.42665			−1.10331			−0.551653	+	0.834074i	$0.686003\pi$
$74$	−4.19796	+	7.27108i	−0.488003	+	0.845245i
$75$	−1.40184	−	2.42805i	−0.161870	−	0.280367i
$76$	2.38110	+	4.12419i	0.273131	+	0.473077i
$77$	4.56663			0.520415
$78$	−13.3043	+	2.31179i	−1.50641	+	0.261758i
$79$	13.4790			1.51651			0.758254	−	0.651959i	$-0.226052\pi$
$79$	13.4790			1.51651			0.758254	+	0.651959i	$0.226052\pi$
$80$	−4.42504	−	7.66439i	−0.494734	−	0.856905i
$81$	5.46136	+	9.45935i	0.606818	+	1.05104i
$82$	9.35920	−	16.2106i	1.03355	−	1.79016i
$83$	14.1994			1.55859			0.779295	−	0.626658i	$-0.215577\pi$
$83$	14.1994			1.55859			0.779295	+	0.626658i	$0.215577\pi$
$84$	1.42152	−	2.46215i	0.155101	−	0.268643i
$85$	−5.30730	+	9.19252i	−0.575658	+	0.997069i
$86$	16.0306			1.72863
$87$	4.86494	−	8.42633i	0.521577	−	0.903397i
$88$	2.02704	+	3.51094i	0.216084	+	0.374268i
$89$	−8.55597	−	14.8194i	−0.906931	−	1.57085i	−0.818304	−	0.574786i	$-0.805085\pi$
$89$	−8.55597	−	14.8194i	−0.906931	−	1.57085i	−0.0886275	−	0.996065i	$-0.528248\pi$
$90$	−3.32026			−0.349986
$91$	3.24360	−	0.563619i	0.340022	−	0.0590833i
$92$	4.15116			0.432788
$93$	0.990948	+	1.71637i	0.102757	+	0.177980i
$94$	6.99700	+	12.1192i	0.721686	+	1.25000i
$95$	−2.86983	+	4.97070i	−0.294439	+	0.509983i
$96$	14.2918			1.45865
$97$	5.49074	−	9.51025i	0.557501	−	0.965619i	−0.440204	−	0.897898i	$-0.645094\pi$
$97$	5.49074	−	9.51025i	0.557501	−	0.965619i	0.997704	−	0.0677215i	$-0.0215729\pi$
$98$	5.82625	−	10.0914i	0.588540	−	1.01938i
$99$	4.64075			0.466413
$100$	1.11123	−	1.92471i	0.111123	−	0.192471i
$101$	−6.60114	−	11.4335i	−0.656838	−	1.13768i	−0.981430	−	0.191823i	$-0.938560\pi$
$101$	−6.60114	−	11.4335i	−0.656838	−	1.13768i	0.324591	−	0.945854i	$-0.394773\pi$
$102$	−10.4975	−	18.1822i	−1.03941	−	1.80031i
$103$	6.66912			0.657128			0.328564	−	0.944482i	$-0.393435\pi$
$103$	6.66912			0.657128			0.328564	+	0.944482i	$0.393435\pi$
$104$	1.87310	+	2.24359i	0.183673	+	0.220002i
$105$	3.42660			0.334402
$106$	6.82676	+	11.8243i	0.663074	+	1.14848i
$107$	−3.39824	−	5.88593i	−0.328521	−	0.569014i	0.653698	−	0.756756i	$-0.273217\pi$
$107$	−3.39824	−	5.88593i	−0.328521	−	0.569014i	−0.982219	+	0.187741i	$0.939883\pi$
$108$	−3.22586	+	5.58736i	−0.310409	+	0.537644i
$109$	2.83658			0.271696			0.135848	−	0.990730i	$-0.456624\pi$
$109$	2.83658			0.271696			0.135848	+	0.990730i	$0.456624\pi$
$110$	8.94775	−	15.4979i	0.853134	−	1.47767i
$111$	4.40273	−	7.62575i	0.417888	−	0.723804i
$112$	−4.26772			−0.403262
$113$	3.39116	−	5.87366i	0.319014	−	0.552548i	−0.661269	−	0.750149i	$-0.729982\pi$
$113$	3.39116	−	5.87366i	0.319014	−	0.552548i	0.980282	+	0.197601i	$0.0633151\pi$
$114$	−5.67635	−	9.83172i	−0.531638	−	0.920825i
$115$	2.50160	+	4.33290i	0.233276	+	0.404045i
$116$	7.71283			0.716119
$117$	3.29625	−	0.572767i	0.304739	−	0.0529523i
$118$	3.41661			0.314524
$119$	2.55931	+	4.43286i	0.234612	+	0.406360i
$120$	1.52101	+	2.63446i	0.138848	+	0.240492i
$121$	−7.00633	+	12.1353i	−0.636939	+	1.10321i
$122$	10.7136			0.969967
$123$	−9.81572	+	17.0013i	−0.885054	+	1.53296i
$124$	−0.785520	+	1.36056i	−0.0705418	+	0.122182i
$125$	12.1462			1.08638
$126$	−0.800555	+	1.38660i	−0.0713191	+	0.123528i
$127$	−5.19550	−	8.99887i	−0.461026	−	0.798521i	0.537986	−	0.842954i	$-0.319185\pi$
$127$	−5.19550	−	8.99887i	−0.461026	−	0.798521i	−0.999012	+	0.0444329i	$0.985852\pi$
$128$	−3.16787	−	5.48692i	−0.280003	−	0.484979i
$129$	−16.8126			−1.48026
$130$	4.44267	−	12.1123i	0.389648	−	1.06232i
$131$	17.7850			1.55388			0.776942	−	0.629573i	$-0.216770\pi$
$131$	17.7850			1.55388			0.776942	+	0.629573i	$0.216770\pi$
$132$	7.78607	+	13.4859i	0.677691	+	1.17379i
$133$	1.38390	+	2.39699i	0.120000	+	0.207846i
$134$	−5.60641	+	9.71058i	−0.484320	+	0.838866i
$135$	−7.77598			−0.669249
$136$	−2.27207	+	3.93534i	−0.194828	+	0.337452i
$137$	−3.89485	+	6.74607i	−0.332759	+	0.576356i	−0.983052	−	0.183328i	$-0.941313\pi$
$137$	−3.89485	+	6.74607i	−0.332759	+	0.576356i	0.650292	+	0.759684i	$0.274646\pi$
$138$	−9.89601			−0.842404
$139$	7.51101	−	13.0094i	0.637075	−	1.10345i	−0.348996	−	0.937124i	$-0.613477\pi$
$139$	7.51101	−	13.0094i	0.637075	−	1.10345i	0.986071	−	0.166323i	$-0.0531893\pi$
$140$	1.35812	+	2.35234i	0.114782	+	0.198809i
$141$	−7.33830	−	12.7103i	−0.617997	−	1.07040i
$142$	9.05652			0.760006
$143$	−6.20955	+	16.9294i	−0.519269	+	1.41571i
$144$	−4.33699			−0.361416
$145$	4.64797	+	8.05051i	0.385993	+	0.668559i
$146$	8.90686	+	15.4271i	0.737137	+	1.27676i
$147$	−6.11044	+	10.5836i	−0.503981	+	0.872921i
$148$	6.98004			0.573756
$149$	2.00322	−	3.46968i	0.164110	−	0.284247i	−0.772229	−	0.635345i	$-0.780858\pi$
$149$	2.00322	−	3.46968i	0.164110	−	0.284247i	0.936339	+	0.351098i	$0.114191\pi$
$150$	−2.64908	+	4.58834i	−0.216296	+	0.374636i
$151$	17.5701			1.42984			0.714919	−	0.699207i	$-0.246464\pi$
$151$	17.5701			1.42984			0.714919	+	0.699207i	$0.246464\pi$
$152$	−1.22858	+	2.12796i	−0.0996511	+	0.172601i
$153$	2.60085	+	4.50481i	0.210267	+	0.364192i
$154$	−4.31482	−	7.47349i	−0.347698	−	0.602231i
$155$	−1.89350			−0.152090
$156$	7.19477	+	8.61784i	0.576042	+	0.689979i
$157$	−4.05318			−0.323479			−0.161740	−	0.986833i	$-0.551710\pi$
$157$	−4.05318			−0.323479			−0.161740	+	0.986833i	$0.551710\pi$
$158$	−12.7358	−	22.0590i	−1.01321	−	1.75492i
$159$	−7.15976	−	12.4011i	−0.567806	−	0.983468i
$160$	−6.82718	+	11.8250i	−0.539736	+	0.934850i
$161$	2.41267			0.190145
$162$	10.3204	−	17.8755i	0.810850	−	1.40443i
$163$	−2.59070	+	4.48723i	−0.202919	+	0.351467i	−0.949468	−	0.313864i	$-0.898376\pi$
$163$	−2.59070	+	4.48723i	−0.202919	+	0.351467i	0.746548	+	0.665331i	$0.231710\pi$
$164$	−15.5618			−1.21517
$165$	−9.38420	+	16.2539i	−0.730559	+	1.26537i
$166$	−13.4165	−	23.2380i	−1.04132	−	1.80362i
$167$	2.51705	+	4.35965i	0.194775	+	0.337360i	0.946827	−	0.321744i	$-0.104269\pi$
$167$	2.51705	+	4.35965i	0.194775	+	0.337360i	−0.752052	+	0.659104i	$0.770936\pi$
$168$	1.46693			0.113176
$169$	−2.32110	+	12.7911i	−0.178546	+	0.983932i
$170$	20.0586			1.53843
$171$	1.40637	+	2.43590i	0.107548	+	0.186278i
$172$	−6.66362	−	11.5417i	−0.508097	−	0.880049i
$173$	−6.97791	+	12.0861i	−0.530521	+	0.918889i	0.468845	+	0.883280i	$0.344670\pi$
$173$	−6.97791	+	12.0861i	−0.530521	+	0.918889i	−0.999366	+	0.0356083i	$0.988663\pi$
$174$	−18.3868			−1.39390
$175$	0.645850	−	1.11865i	0.0488217	−	0.0845616i
$176$	11.6877	−	20.2438i	0.880996	−	1.52593i
$177$	−3.58327			−0.269335
$178$	−16.1684	+	28.0045i	−1.21187	+	2.09902i
$179$	−9.45931	−	16.3840i	−0.707022	−	1.22460i	−0.965957	−	0.258703i	$-0.916705\pi$
$179$	−9.45931	−	16.3840i	−0.707022	−	1.22460i	0.258935	−	0.965895i	$-0.416629\pi$
$180$	1.38017	+	2.39052i	0.102872	+	0.178179i
$181$	−13.6951			−1.01795			−0.508973	−	0.860783i	$-0.669975\pi$
$181$	−13.6951			−1.01795			−0.508973	+	0.860783i	$0.669975\pi$
$182$	−3.98714	−	4.77576i	−0.295546	−	0.354003i
$183$	−11.2362			−0.830606
$184$	1.07094	+	1.85492i	0.0789508	+	0.136747i
$185$	4.20637	+	7.28564i	0.309258	+	0.535651i
$186$	1.87261	−	3.24346i	0.137307	−	0.237822i
$187$	−28.0361			−2.05020
$188$	5.81704	−	10.0754i	0.424251	−	0.734825i
$189$	−1.87488	+	3.24739i	−0.136378	+	0.236213i
$190$	10.8464			0.786878
$191$	0.383270	−	0.663842i	0.0277324	−	0.0480339i	−0.851826	−	0.523825i	$-0.824505\pi$
$191$	0.383270	−	0.663842i	0.0277324	−	0.0480339i	0.879559	+	0.475791i	$0.157838\pi$
$192$	−4.24051	−	7.34478i	−0.306032	−	0.530064i
$193$	4.17709	+	7.23493i	0.300674	+	0.520782i	0.976289	−	0.216473i	$-0.0694552\pi$
$193$	4.17709	+	7.23493i	0.300674	+	0.520782i	−0.675615	+	0.737254i	$0.736122\pi$
$194$	−20.7519			−1.48990
$195$	−4.65938	+	12.7031i	−0.333665	+	0.909689i
$196$	−9.68744			−0.691960
$197$	9.99892	+	17.3186i	0.712393	+	1.23390i	0.963956	+	0.266060i	$0.0857221\pi$
$197$	9.99892	+	17.3186i	0.712393	+	1.23390i	−0.251563	+	0.967841i	$0.580945\pi$
$198$	−4.38486	−	7.59480i	−0.311618	−	0.539739i
$199$	0.122137	−	0.211548i	0.00865809	−	0.0149963i	−0.861664	−	0.507479i	$-0.830577\pi$
$199$	0.122137	−	0.211548i	0.00865809	−	0.0149963i	0.870322	+	0.492483i	$0.163911\pi$
$200$	1.14673			0.0810858
$201$	5.87988	−	10.1842i	0.414734	−	0.718341i
$202$	−12.4743	+	21.6061i	−0.877689	+	1.52020i
$203$	4.48273			0.314626
$204$	−8.72722	+	15.1160i	−0.611028	+	1.05833i
$205$	−9.37794	−	16.2431i	−0.654984	−	1.13447i
$206$	−6.30139	−	10.9143i	−0.439038	−	0.760437i
$207$	2.45183			0.170414
$208$	5.80311	−	15.8213i	0.402373	−	1.09701i
$209$	−15.1600			−1.04864
$210$	−3.23765	−	5.60778i	−0.223419	−	0.386974i
$211$	−1.21094	−	2.09740i	−0.0833643	−	0.144391i	0.821329	−	0.570455i	$-0.193233\pi$
$211$	−1.21094	−	2.09740i	−0.0833643	−	0.144391i	−0.904693	+	0.426064i	$0.859900\pi$
$212$	5.67551	−	9.83027i	0.389795	−	0.675145i
$213$	−9.49828			−0.650811
$214$	−6.42173	+	11.1228i	−0.438980	+	0.760336i
$215$	8.03136	−	13.9107i	0.547735	−	0.948704i
$216$	−3.32891			−0.226504
$217$	−0.456547	+	0.790763i	−0.0309924	+	0.0536805i
$218$	−2.68018	−	4.64220i	−0.181524	−	0.314409i
$219$	−9.34132	−	16.1796i	−0.631228	−	1.09332i
$220$	−14.8776			−1.00305
$221$	−19.9136	+	3.46025i	−1.33953	+	0.232762i
$222$	−16.6398			−1.11679
$223$	−1.66164	−	2.87804i	−0.111272	−	0.192728i	0.805012	−	0.593259i	$-0.202159\pi$
$223$	−1.66164	−	2.87804i	−0.111272	−	0.192728i	−0.916283	+	0.400531i	$0.868826\pi$
$224$	3.29223	+	5.70232i	0.219972	+	0.381002i
$225$	0.656333	−	1.13680i	0.0437556	−	0.0757868i
$226$	−12.8167			−0.852553
$227$	−2.52004	+	4.36484i	−0.167261	+	0.289705i	−0.937456	−	0.348104i	$-0.886826\pi$
$227$	−2.52004	+	4.36484i	−0.167261	+	0.289705i	0.770195	+	0.637809i	$0.220159\pi$
$228$	−4.71910	+	8.17371i	−0.312530	+	0.541317i
$229$	25.0893			1.65795			0.828973	−	0.559289i	$-0.188926\pi$
$229$	25.0893			1.65795			0.828973	+	0.559289i	$0.188926\pi$
$230$	4.72733	−	8.18797i	0.311711	−	0.539899i
$231$	4.52529	+	7.83803i	0.297742	+	0.515705i
$232$	1.98980	+	3.44644i	0.130637	+	0.226270i
$233$	11.3187			0.741513			0.370756	−	0.928730i	$-0.379098\pi$
$233$	11.3187			0.741513			0.370756	+	0.928730i	$0.379098\pi$
$234$	−4.05186	−	4.85328i	−0.264878	−	0.317269i
$235$	14.0220			0.914697
$236$	−1.42022	−	2.45989i	−0.0924484	−	0.160125i
$237$	13.3570	+	23.1350i	0.867632	+	1.50278i
$238$	4.83638	−	8.37686i	0.313496	−	0.542991i
$239$	5.71189			0.369472			0.184736	−	0.982788i	$-0.440857\pi$
$239$	5.71189			0.369472			0.184736	+	0.982788i	$0.440857\pi$
$240$	8.76997	−	15.1900i	0.566099	−	0.980512i
$241$	5.67097	−	9.82241i	0.365299	−	0.632717i	−0.623525	−	0.781804i	$-0.714300\pi$
$241$	5.67097	−	9.82241i	0.365299	−	0.632717i	0.988824	+	0.149087i	$0.0476333\pi$
$242$	26.4800			1.70220
$243$	−4.66386	+	8.07805i	−0.299187	+	0.518207i
$244$	−4.45345	−	7.71361i	−0.285103	−	0.493813i
$245$	−5.83792	−	10.1116i	−0.372971	−	0.646005i
$246$	37.0979			2.36528
$247$	−10.7679	+	1.87107i	−0.685148	+	0.119053i
$248$	−0.810613			−0.0514740
$249$	14.0709	+	24.3715i	0.891707	+	1.54448i
$250$	−11.4764	−	19.8777i	−0.725832	−	1.25718i
$251$	6.05081	−	10.4803i	0.381924	−	0.661511i	−0.609414	−	0.792852i	$-0.708595\pi$
$251$	6.05081	−	10.4803i	0.381924	−	0.661511i	0.991337	+	0.131341i	$0.0419284\pi$
$252$	1.33110			0.0838515
$253$	−6.60742	+	11.4444i	−0.415405	+	0.719502i
$254$	−9.81804	+	17.0053i	−0.616039	+	1.06701i
$255$	−21.0371			−1.31739
$256$	−10.2656	+	17.7806i	−0.641602	+	1.11129i
$257$	14.1936	+	24.5841i	0.885373	+	1.53351i	0.845285	+	0.534316i	$0.179431\pi$
$257$	14.1936	+	24.5841i	0.885373	+	1.53351i	0.0400884	+	0.999196i	$0.487236\pi$
$258$	15.8855	+	27.5145i	0.988989	+	1.71298i
$259$	4.05683			0.252079
$260$	−10.5673	+	1.83621i	−0.655359	+	0.113877i
$261$	4.55549			0.281978
$262$	−16.8043	−	29.1060i	−1.03818	−	1.79817i
$263$	−9.33728	−	16.1726i	−0.575761	−	0.997247i	−0.995958	−	0.0898147i	$-0.971373\pi$
$263$	−9.33728	−	16.1726i	−0.575761	−	0.997247i	0.420197	−	0.907433i	$-0.361961\pi$
$264$	−4.01739	+	6.95833i	−0.247254	+	0.428256i
$265$	13.6809			0.840409
$266$	2.61519	−	4.52964i	0.160348	−	0.277730i
$267$	16.9571	−	29.3705i	1.03775	−	1.79744i
$268$	9.32190			0.569426
$269$	1.48634	−	2.57441i	0.0906235	−	0.156964i	−0.817150	−	0.576425i	$-0.804447\pi$
$269$	1.48634	−	2.57441i	0.0906235	−	0.156964i	0.907774	+	0.419460i	$0.137781\pi$
$270$	7.34721	+	12.7257i	0.447137	+	0.774464i
$271$	−4.12470	−	7.14418i	−0.250557	−	0.433978i	0.713122	−	0.701040i	$-0.247281\pi$
$271$	−4.12470	−	7.14418i	−0.250557	−	0.433978i	−0.963679	+	0.267062i	$0.913947\pi$
$272$	26.2010			1.58867
$273$	4.18162	+	5.00872i	0.253083	+	0.303141i
$274$	14.7203			0.889288
$275$	3.53750	+	6.12712i	0.213319	+	0.369480i
$276$	4.11358	+	7.12493i	0.247609	+	0.428871i
$277$	−0.528398	+	0.915211i	−0.0317483	+	0.0549897i	−0.881463	−	0.472253i	$-0.843441\pi$
$277$	−0.528398	+	0.915211i	−0.0317483	+	0.0549897i	0.849715	+	0.527243i	$0.176774\pi$
$278$	−28.3874			−1.70256
$279$	−0.463958	+	0.803598i	−0.0277764	+	0.0481102i
$280$	−0.700754	+	1.21374i	−0.0418780	+	0.0725349i
$281$	19.3020			1.15146			0.575732	−	0.817639i	$-0.304717\pi$
$281$	19.3020			1.15146			0.575732	+	0.817639i	$0.304717\pi$
$282$	−13.8673	+	24.0189i	−0.825788	+	1.43031i
$283$	−15.1924	−	26.3140i	−0.903096	−	1.56421i	−0.823453	−	0.567384i	$-0.807956\pi$
$283$	−15.1924	−	26.3140i	−0.903096	−	1.56421i	−0.0796420	−	0.996824i	$-0.525378\pi$
$284$	−3.76462	−	6.52052i	−0.223389	−	0.386921i
$285$	−11.3754			−0.673822
$286$	33.5730	−	5.83374i	1.98521	−	0.344956i
$287$	−9.04454			−0.533883
$288$	3.34567	+	5.79487i	0.197146	+	0.341466i
$289$	−7.21250	−	12.4924i	−0.424265	−	0.734848i
$290$	8.78335	−	15.2132i	0.515776	−	0.893351i
$291$	21.7642			1.27584
$292$	7.40482	−	12.8255i	0.433335	−	0.750557i
$293$	−15.6791	+	27.1570i	−0.915984	+	1.58653i	−0.110529	+	0.993873i	$0.535254\pi$
$293$	−15.6791	+	27.1570i	−0.915984	+	1.58653i	−0.805455	+	0.592657i	$0.798079\pi$
$294$	23.0941			1.34687
$295$	1.71173	−	2.96480i	0.0996605	−	0.172617i
$296$	1.80075	+	3.11900i	0.104667	+	0.181288i
$297$	−10.2692	−	17.7869i	−0.595882	−	1.03210i
$298$	−7.57104			−0.438579
$299$	−3.28067	+	8.94426i	−0.189726	+	0.517260i
$300$	4.40468			0.254305
$301$	−3.87292	−	6.70810i	−0.223231	−	0.386648i
$302$	−16.6013	−	28.7543i	−0.955299	−	1.65463i
$303$	13.0828	−	22.6600i	0.751586	−	1.30179i
$304$	14.1678			0.812576
$305$	5.36755	−	9.29687i	0.307345	−	0.532337i
$306$	4.91488	−	8.51283i	0.280965	−	0.486646i
$307$	9.36676			0.534589			0.267295	−	0.963615i	$-0.413870\pi$
$307$	9.36676			0.534589			0.267295	+	0.963615i	$0.413870\pi$
$308$	−3.58718	+	6.21317i	−0.204398	+	0.354028i
$309$	6.60876	+	11.4467i	0.375959	+	0.651180i
$310$	1.78910	+	3.09881i	0.101614	+	0.176000i
$311$	−5.57366			−0.316053			−0.158027	−	0.987435i	$-0.550513\pi$
$311$	−5.57366			−0.316053			−0.158027	+	0.987435i	$0.550513\pi$
$312$	−1.99469	+	5.43823i	−0.112927	+	0.307879i
$313$	2.18060			0.123255			0.0616274	−	0.998099i	$-0.480371\pi$
$313$	2.18060			0.123255			0.0616274	+	0.998099i	$0.480371\pi$
$314$	3.82969	+	6.63322i	0.216122	+	0.374334i
$315$	0.802158	+	1.38938i	0.0451965	+	0.0782826i
$316$	−10.5880	+	18.3390i	−0.595624	+	1.03165i
$317$	−13.4942			−0.757910			−0.378955	−	0.925415i	$-0.623716\pi$
$317$	−13.4942			−0.757910			−0.378955	+	0.925415i	$0.623716\pi$
$318$	−13.5299	+	23.4345i	−0.758721	+	1.31414i
$319$	−12.2766	+	21.2636i	−0.687355	+	1.19053i
$320$	8.10277			0.452959
$321$	6.73497	−	11.6653i	0.375909	−	0.651094i
$322$	−2.27963	−	3.94844i	−0.127039	−	0.220038i
$323$	−8.49626	−	14.7160i	−0.472745	−	0.818818i
$324$	−17.1600			−0.953335
$325$	3.26885	+	3.91540i	0.181323	+	0.217187i
$326$	9.79140			0.542295
$327$	2.81091	+	4.86864i	0.155444	+	0.269236i
$328$	−4.01471	−	6.95369i	−0.221675	−	0.383953i
$329$	3.38088	−	5.85586i	0.186394	−	0.322844i
$330$	35.4670			1.95240
$331$	10.7864	−	18.6825i	0.592873	−	1.02689i	−0.400971	−	0.916091i	$-0.631327\pi$
$331$	10.7864	−	18.6825i	0.592873	−	1.02689i	0.993843	−	0.110795i	$-0.0353396\pi$
$332$	−11.1539	+	19.3192i	−0.612152	+	1.06028i
$333$	4.12267			0.225921
$334$	4.75651	−	8.23852i	0.260265	−	0.450792i
$335$	5.61763	+	9.73003i	0.306924	+	0.531608i
$336$	−4.22909	−	7.32500i	−0.230716	−	0.399612i
$337$	10.8227			0.589549			0.294774	−	0.955567i	$-0.404755\pi$
$337$	10.8227			0.589549			0.294774	+	0.955567i	$0.404755\pi$
$338$	23.1263	−	8.28723i	1.25791	−	0.450766i
$339$	13.4419			0.730062
$340$	−8.33799	−	14.4418i	−0.452191	−	0.783218i
$341$	−2.50063	−	4.33122i	−0.135417	−	0.234549i
$342$	2.65764	−	4.60317i	0.143709	−	0.248911i
$343$	−12.0220			−0.649129
$344$	3.43824	−	5.95521i	0.185378	−	0.321083i
$345$	−4.95792	+	8.58736i	−0.266925	+	0.462328i
$346$	26.3726			1.41780
$347$	7.05045	−	12.2117i	0.378488	−	0.655560i	−0.612355	−	0.790583i	$-0.709777\pi$
$347$	7.05045	−	12.2117i	0.378488	−	0.655560i	0.990842	+	0.135023i	$0.0431108\pi$
$348$	7.64302	+	13.2381i	0.409709	+	0.709637i
$349$	−0.984722	−	1.70559i	−0.0527110	−	0.0912981i	0.838466	−	0.544954i	$-0.183453\pi$
$349$	−0.984722	−	1.70559i	−0.0527110	−	0.0912981i	−0.891177	+	0.453656i	$0.850120\pi$
$350$	−2.44095			−0.130474
$351$	−9.48936	−	11.3663i	−0.506505	−	0.606687i
$352$	−36.0649			−1.92227
$353$	−15.5255	−	26.8910i	−0.826341	−	1.43126i	−0.900890	−	0.434047i	$-0.857085\pi$
$353$	−15.5255	−	26.8910i	−0.826341	−	1.43126i	0.0745498	−	0.997217i	$-0.476248\pi$
$354$	3.38568	+	5.86418i	0.179947	+	0.311677i
$355$	4.53733	−	7.85888i	0.240816	−	0.417106i
$356$	26.8836			1.42483
$357$	−5.07229	+	8.78547i	−0.268454	+	0.464976i
$358$	−17.8754	+	30.9612i	−0.944747	+	1.63635i
$359$	3.85313			0.203361			0.101680	−	0.994817i	$-0.467578\pi$
$359$	3.85313			0.203361			0.101680	+	0.994817i	$0.467578\pi$
$360$	−0.712128	+	1.23344i	−0.0375324	+	0.0650081i
$361$	4.90579	+	8.49708i	0.258200	+	0.447215i
$362$	12.9399	+	22.4126i	0.680107	+	1.17798i
$363$	−27.7716			−1.45763
$364$	−1.78108	+	4.85586i	−0.0933539	+	0.254516i
$365$	17.8494			0.934280
$366$	10.6167	+	18.3886i	0.554942	+	0.961188i
$367$	−7.75756	−	13.4365i	−0.404941	−	0.701379i	0.589373	−	0.807861i	$-0.299375\pi$
$367$	−7.75756	−	13.4365i	−0.404941	−	0.701379i	−0.994315	+	0.106482i	$0.966041\pi$
$368$	6.17493	−	10.6953i	0.321891	−	0.557531i
$369$	−9.19135			−0.478483
$370$	7.94885	−	13.7678i	0.413241	−	0.715755i
$371$	3.29862	−	5.71338i	0.171256	−	0.296624i
$372$	−3.11364			−0.161435
$373$	14.1023	−	24.4259i	0.730190	−	1.26473i	−0.226611	−	0.973985i	$-0.572765\pi$
$373$	14.1023	−	24.4259i	0.730190	−	1.26473i	0.956802	−	0.290742i	$-0.0939020\pi$
$374$	26.4902	+	45.8823i	1.36977	+	2.37252i
$375$	12.0362	+	20.8473i	0.621547	+	1.07655i
$376$	6.00286			0.309574
$377$	−6.09547	+	16.6184i	−0.313932	+	0.855891i
$378$	7.08601			0.364465
$379$	0.555362	+	0.961914i	0.0285270	+	0.0494102i	0.879936	−	0.475091i	$-0.157585\pi$
$379$	0.555362	+	0.961914i	0.0285270	+	0.0494102i	−0.851409	+	0.524502i	$0.824252\pi$
$380$	−4.50863	−	7.80917i	−0.231288	−	0.400602i
$381$	10.2969	−	17.8348i	0.527529	−	0.913706i
$382$	−1.44854			−0.0741140
$383$	−15.4154	+	26.7003i	−0.787691	+	1.36432i	0.139687	+	0.990196i	$0.455390\pi$
$383$	−15.4154	+	26.7003i	−0.787691	+	1.36432i	−0.927378	+	0.374126i	$0.877943\pi$
$384$	6.27840	−	10.8745i	0.320393	−	0.554937i
$385$	−8.64693			−0.440688
$386$	7.89353	−	13.6720i	0.401770	−	0.695886i
$387$	−3.93578	−	6.81698i	−0.200067	−	0.346526i
$388$	8.62618	+	14.9410i	0.437928	+	0.758514i
$389$	−22.0467			−1.11781			−0.558907	−	0.829230i	$-0.688779\pi$
$389$	−22.0467			−1.11781			−0.558907	+	0.829230i	$0.688779\pi$
$390$	25.1917	−	4.37738i	1.27563	−	0.221657i
$391$	−14.8122			−0.749085
$392$	−2.49922	−	4.32878i	−0.126230	−	0.218637i
$393$	17.6240	+	30.5257i	0.889015	+	1.53982i
$394$	18.8951	−	32.7274i	0.951924	−	1.64878i
$395$	−25.5226			−1.28418
$396$	−3.64540	+	6.31402i	−0.183188	+	0.317292i
$397$	12.8357	−	22.2320i	0.644204	−	1.11579i	−0.340281	−	0.940324i	$-0.610522\pi$
$397$	12.8357	−	22.2320i	0.644204	−	1.11579i	0.984485	−	0.175470i	$-0.0561446\pi$
$398$	−0.461611			−0.0231385
$399$	−2.74275	+	4.75059i	−0.137309	+	0.237827i
$400$	−3.30595	−	5.72608i	−0.165298	−	0.286304i
$401$	11.8726	+	20.5640i	0.592891	+	1.02692i	0.993841	+	0.110818i	$0.0353470\pi$
$401$	11.8726	+	20.5640i	0.592891	+	1.02692i	−0.400949	+	0.916100i	$0.631320\pi$
$402$	−22.2226			−1.10836
$403$	−2.31073	−	2.76777i	−0.115105	−	0.137872i
$404$	20.7413			1.03192
$405$	−10.3411	−	17.9113i	−0.513854	−	0.890021i
$406$	−4.23555	−	7.33618i	−0.210207	−	0.364089i
$407$	−11.1102	+	19.2434i	−0.550711	+	0.953859i
$408$	−9.00601			−0.445864
$409$	−12.8723	+	22.2955i	−0.636495	+	1.10244i	0.349701	+	0.936861i	$0.386283\pi$
$409$	−12.8723	+	22.2955i	−0.636495	+	1.10244i	−0.986196	+	0.165581i	$0.947050\pi$
$410$	−17.7217	+	30.6948i	−0.875211	+	1.51591i
$411$	−15.4384			−0.761519
$412$	−5.23873	+	9.07375i	−0.258094	+	0.447032i
$413$	−0.825436	−	1.42970i	−0.0406171	−	0.0703508i
$414$	−2.31663	−	4.01253i	−0.113856	−	0.197205i
$415$	−26.8867			−1.31982
$416$	−25.6164	+	4.45118i	−1.25595	+	0.218237i
$417$	29.7721			1.45795
$418$	14.3241	+	24.8101i	0.700615	+	1.21350i
$419$	4.91077	+	8.50570i	0.239907	+	0.415531i	0.960687	−	0.277633i	$-0.0895498\pi$
$419$	4.91077	+	8.50570i	0.239907	+	0.415531i	−0.720781	+	0.693163i	$0.756216\pi$
$420$	−2.69166	+	4.66209i	−0.131340	+	0.227487i
$421$	−0.785293			−0.0382728			−0.0191364	−	0.999817i	$-0.506092\pi$
$421$	−0.785293			−0.0382728			−0.0191364	+	0.999817i	$0.506092\pi$
$422$	−2.28833	+	3.96351i	−0.111394	+	0.192940i
$423$	3.43576	−	5.95091i	0.167052	−	0.289343i
$424$	5.85680			0.284432
$425$	−3.96510	+	6.86775i	−0.192335	+	0.333135i
$426$	8.97454	+	15.5444i	0.434818	+	0.753127i
$427$	−2.58836	−	4.48318i	−0.125260	−	0.216956i
$428$	10.6776			0.516119
$429$	−35.2106	+	6.11830i	−1.69998	+	0.295394i
$430$	−30.3541			−1.46380
$431$	5.56663	+	9.64168i	0.268135	+	0.464423i	0.968380	−	0.249479i	$-0.0802594\pi$
$431$	5.56663	+	9.64168i	0.268135	+	0.464423i	−0.700245	+	0.713902i	$0.746926\pi$
$432$	9.59708	+	16.6226i	0.461740	+	0.799757i
$433$	1.98890	−	3.44487i	0.0955803	−	0.165550i	−0.814270	−	0.580486i	$-0.802863\pi$
$433$	1.98890	−	3.44487i	0.0955803	−	0.165550i	0.909851	+	0.414936i	$0.136196\pi$
$434$	1.72549			0.0828263
$435$	−9.21179	+	15.9553i	−0.441671	+	0.764997i
$436$	−2.22820	+	3.85935i	−0.106711	+	0.184829i
$437$	−8.00944			−0.383143
$438$	−17.6525	+	30.5750i	−0.843468	+	1.46093i
$439$	−12.6790	−	21.9606i	−0.605135	−	1.04812i	−0.992030	−	0.126001i	$-0.959786\pi$
$439$	−12.6790	−	21.9606i	−0.605135	−	1.04812i	0.386895	−	0.922124i	$-0.373547\pi$
$440$	−3.83822	−	6.64799i	−0.182980	−	0.316930i
$441$	−5.72176			−0.272465
$442$	24.4784	+	29.3201i	1.16432	+	1.39461i
$443$	−24.7280			−1.17486			−0.587432	−	0.809274i	$-0.699861\pi$
$443$	−24.7280			−1.17486			−0.587432	+	0.809274i	$0.699861\pi$
$444$	6.91686	+	11.9804i	0.328260	+	0.568563i
$445$	16.2008	+	28.0606i	0.767990	+	1.33020i
$446$	−3.14003	+	5.43869i	−0.148685	+	0.257530i
$447$	7.94035			0.375566
$448$	1.95368	−	3.38387i	0.0923026	−	0.159873i
$449$	−16.1093	+	27.9021i	−0.760244	+	1.31678i	0.182481	+	0.983209i	$0.441587\pi$
$449$	−16.1093	+	27.9021i	−0.760244	+	1.31678i	−0.942725	+	0.333572i	$0.891746\pi$
$450$	−2.48057			−0.116935
$451$	24.7697	−	42.9024i	1.16636	−	2.02020i
$452$	5.32765	+	9.22776i	0.250592	+	0.434037i
$453$	17.4111	+	30.1569i	0.818045	+	1.41690i
$454$	9.52435			0.447000
$455$	−6.14178	+	1.06721i	−0.287931	+	0.0500318i
$456$	−4.86984			−0.228051
$457$	6.57821	+	11.3938i	0.307716	+	0.532979i	0.977862	−	0.209250i	$-0.0671022\pi$
$457$	6.57821	+	11.3938i	0.307716	+	0.532979i	−0.670147	+	0.742229i	$0.733769\pi$
$458$	−23.7058	−	41.0597i	−1.10770	−	1.91859i
$459$	11.5106	−	19.9369i	0.537267	−	0.930573i
$460$	−7.86023			−0.366485
$461$	6.79018	−	11.7609i	0.316250	−	0.547761i	−0.663452	−	0.748219i	$-0.730909\pi$
$461$	6.79018	−	11.7609i	0.316250	−	0.547761i	0.979702	+	0.200457i	$0.0642428\pi$
$462$	8.55153	−	14.8117i	0.397853	−	0.689102i
$463$	−8.31656			−0.386503			−0.193252	−	0.981149i	$-0.561903\pi$
$463$	−8.31656			−0.386503			−0.193252	+	0.981149i	$0.561903\pi$
$464$	11.4730	−	19.8718i	0.532621	−	0.922526i
$465$	−1.87637	−	3.24996i	−0.0870144	−	0.150713i
$466$	−10.6946	−	18.5236i	−0.495417	−	0.858088i
$467$	12.6227			0.584110			0.292055	−	0.956401i	$-0.405661\pi$
$467$	12.6227			0.584110			0.292055	+	0.956401i	$0.405661\pi$
$468$	−1.80999	+	4.93467i	−0.0836668	+	0.228105i
$469$	5.41792			0.250176
$470$	−13.2489	−	22.9477i	−0.611124	−	1.05850i
$471$	−4.01650	−	6.95678i	−0.185070	−	0.320551i
$472$	0.732793	−	1.26923i	0.0337295	−	0.0584213i
$473$	42.4261			1.95075
$474$	25.2410	−	43.7187i	1.15936	−	2.00807i
$475$	−2.14406	+	3.71362i	−0.0983761	+	0.170392i
$476$	−8.04157			−0.368585
$477$	3.35217	−	5.80612i	0.153485	−	0.265844i
$478$	−5.39694	−	9.34777i	−0.246850	−	0.427557i
$479$	3.10427	+	5.37675i	0.141838	+	0.245670i	0.928189	−	0.372110i	$-0.121366\pi$
$479$	3.10427	+	5.37675i	0.141838	+	0.245670i	−0.786351	+	0.617780i	$0.788032\pi$
$480$	−27.0615			−1.23518
$481$	−5.51634	+	15.0395i	−0.251523	+	0.685742i
$482$	−21.4331			−0.976251
$483$	2.39083	+	4.14104i	0.108786	+	0.188424i
$484$	−11.0072	−	19.0651i	−0.500328	−	0.866594i
$485$	−10.3967	+	18.0077i	−0.472092	+	0.817687i
$486$	17.6268			0.799567
$487$	−0.0747352	+	0.129445i	−0.00338658	+	0.00586572i	−0.867714	−	0.497064i	$-0.834411\pi$
$487$	−0.0747352	+	0.129445i	−0.00338658	+	0.00586572i	0.864327	+	0.502930i	$0.167745\pi$
$488$	2.29786	−	3.98001i	0.104019	−	0.180166i
$489$	−10.2690			−0.464381
$490$	−11.0320	+	19.1080i	−0.498376	+	0.863213i
$491$	9.21118	+	15.9542i	0.415695	+	0.720004i	0.995501	−	0.0947499i	$-0.0302051\pi$
$491$	9.21118	+	15.9542i	0.415695	+	0.720004i	−0.579806	+	0.814754i	$0.696872\pi$
$492$	−15.4209	−	26.7098i	−0.695228	−	1.20417i
$493$	−27.5210			−1.23948
$494$	13.2363	+	15.8543i	0.595529	+	0.713320i
$495$	−8.78728			−0.394959
$496$	2.33696	+	4.04773i	0.104932	+	0.181748i
$497$	−2.18801	−	3.78975i	−0.0981457	−	0.169993i
$498$	26.5901	−	46.0553i	1.19153	−	2.06379i
$499$	11.4628			0.513145			0.256572	−	0.966525i	$-0.417407\pi$
$499$	11.4628			0.513145			0.256572	+	0.966525i	$0.417407\pi$
$500$	−9.54105	+	16.5256i	−0.426689	+	0.739046i
$501$	−4.98853	+	8.64038i	−0.222871	+	0.386024i
$502$	−22.8687			−1.02068
$503$	6.98507	−	12.0985i	0.311449	−	0.539445i	−0.667228	−	0.744854i	$-0.732519\pi$
$503$	6.98507	−	12.0985i	0.311449	−	0.539445i	0.978676	+	0.205409i	$0.0658525\pi$
$504$	0.343406	+	0.594796i	0.0152965	+	0.0264943i
$505$	12.4993	+	21.6494i	0.556211	+	0.963386i
$506$	24.9723			1.11016
$507$	−24.2544	+	8.69146i	−1.07718	+	0.386001i
$508$	16.3247			0.724291
$509$	−13.6447	−	23.6332i	−0.604789	−	1.04753i	−0.992085	−	0.125570i	$-0.959924\pi$
$509$	−13.6447	−	23.6332i	−0.604789	−	1.04753i	0.387296	−	0.921956i	$-0.373409\pi$
$510$	19.8771	+	34.4281i	0.880172	+	1.52450i
$511$	4.30371	−	7.45424i	0.190385	−	0.329756i
$512$	26.1269			1.15465
$513$	6.22413	−	10.7805i	0.274802	−	0.475971i
$514$	26.8220	−	46.4570i	1.18307	−	2.04913i
$515$	−12.6280			−0.556457
$516$	13.2066	−	22.8745i	0.581389	−	1.00699i
$517$	18.5180	+	32.0742i	0.814422	+	1.41062i
$518$	−3.83313	−	6.63918i	−0.168418	−	0.291709i
$519$	−27.6590			−1.21410
$520$	−3.54673	−	4.24825i	−0.155534	−	0.186298i
$521$	−31.5523			−1.38233			−0.691166	−	0.722696i	$-0.742903\pi$
$521$	−31.5523			−1.38233			−0.691166	+	0.722696i	$0.742903\pi$
$522$	−4.30430	−	7.45526i	−0.188394	−	0.326308i
$523$	14.7755	+	25.5919i	0.646087	+	1.11906i	0.984049	+	0.177896i	$0.0569291\pi$
$523$	14.7755	+	25.5919i	0.646087	+	1.11906i	−0.337962	+	0.941160i	$0.609738\pi$
$524$	−13.9705	+	24.1976i	−0.610304	+	1.05708i
$525$	2.56002			0.111728
$526$	−17.6448	+	30.5617i	−0.769351	+	1.33256i
$527$	2.80290	−	4.85477i	0.122096	−	0.211477i
$528$	46.3278			2.01616
$529$	8.00913	−	13.8722i	0.348223	−	0.603140i
$530$	−12.9265	−	22.3894i	−0.561491	−	0.972531i
$531$	−0.838834	−	1.45290i	−0.0364023	−	0.0630506i
$532$	−4.34834			−0.188524
$533$	12.2985	−	33.5300i	0.532706	−	1.45235i
$534$	−64.0882			−2.77337
$535$	6.43459	+	11.1450i	0.278191	+	0.481842i
$536$	2.40492	+	4.16544i	0.103877	+	0.179920i
$537$	18.7474	−	32.4714i	0.809009	−	1.40124i
$538$	−5.61752			−0.242188
$539$	15.4195	−	26.7074i	0.664167	−	1.15037i
$540$	6.10819	−	10.5797i	0.262855	−	0.455277i
$541$	27.6468			1.18863			0.594314	−	0.804233i	$-0.297424\pi$
$541$	27.6468			1.18863			0.594314	+	0.804233i	$0.297424\pi$
$542$	−7.79452	+	13.5005i	−0.334803	+	0.579896i
$543$	−13.5711	−	23.5058i	−0.582392	−	1.00873i
$544$	−20.2122	−	35.0085i	−0.866589	−	1.50098i
$545$	−5.37109			−0.230072
$546$	4.24594	−	11.5760i	0.181710	−	0.495405i
$547$	11.6311			0.497311			0.248655	−	0.968592i	$-0.420011\pi$
$547$	11.6311			0.497311			0.248655	+	0.968592i	$0.420011\pi$
$548$	−6.11897	−	10.5984i	−0.261389	−	0.452739i
$549$	−2.63038	−	4.55594i	−0.112262	−	0.194443i
$550$	6.68488	−	11.5785i	0.285044	−	0.493711i
$551$	−14.8815			−0.633974
$552$	−2.12249	+	3.67627i	−0.0903393	+	0.156472i
$553$	−6.15381	+	10.6587i	−0.261687	+	0.453255i
$554$	1.99705			0.0848464
$555$	−8.33658	+	14.4394i	−0.353868	+	0.612918i
$556$	11.8001	+	20.4384i	0.500436	+	0.866780i
$557$	−1.67094	−	2.89415i	−0.0707999	−	0.122629i	0.828452	−	0.560060i	$-0.189222\pi$
$557$	−1.67094	−	2.89415i	−0.0707999	−	0.122629i	−0.899252	+	0.437431i	$0.855889\pi$
$558$	1.75350			0.0742315
$559$	30.1346	−	5.23628i	1.27456	−	0.221471i
$560$	8.08095			0.341483
$561$	−27.7823	−	48.1204i	−1.17297	−	2.03164i
$562$	−18.2377	−	31.5887i	−0.769312	−	1.33249i
$563$	13.2238	−	22.9043i	0.557317	−	0.965301i	−0.440403	−	0.897800i	$-0.645164\pi$
$563$	13.2238	−	22.9043i	0.557317	−	0.965301i	0.997719	−	0.0675004i	$-0.0215024\pi$
$564$	23.0575			0.970898
$565$	−6.42118	+	11.1218i	−0.270141	+	0.467898i
$566$	−28.7094	+	49.7262i	−1.20675	+	2.09015i
$567$	−9.97347			−0.418846
$568$	1.94244	−	3.36440i	0.0815029	−	0.141167i
$569$	18.0218	+	31.2147i	0.755514	+	1.30859i	0.945118	+	0.326728i	$0.105946\pi$
$569$	18.0218	+	31.2147i	0.755514	+	1.30859i	−0.189604	+	0.981861i	$0.560721\pi$
$570$	10.7482	+	18.6164i	0.450192	+	0.779755i
$571$	31.2601			1.30819			0.654096	−	0.756411i	$-0.273049\pi$
$571$	31.2601			1.30819			0.654096	+	0.756411i	$0.273049\pi$
$572$	−18.1558	−	21.7469i	−0.759133	−	0.909283i
$573$	1.51920			0.0634656
$574$	8.54583	+	14.8018i	0.356696	+	0.617815i
$575$	1.86895	+	3.23712i	0.0779406	+	0.134997i
$576$	1.98539	−	3.43879i	0.0827245	−	0.143283i
$577$	−15.6857			−0.653006			−0.326503	−	0.945196i	$-0.605870\pi$
$577$	−15.6857			−0.653006			−0.326503	+	0.945196i	$0.605870\pi$
$578$	−13.6296	+	23.6072i	−0.566917	+	0.981929i
$579$	−8.27856	+	14.3389i	−0.344045	+	0.595904i
$580$	−14.6043			−0.606410
$581$	−6.48271	+	11.2284i	−0.268948	+	0.465832i
$582$	−20.5641	−	35.6181i	−0.852409	−	1.47642i
$583$	18.0675	+	31.2938i	0.748278	+	1.29606i
$584$	7.64136			0.316202
$585$	−6.24147	+	1.08454i	−0.258053	+	0.0448401i
$586$	59.2583			2.44794
$587$	8.22612	+	14.2481i	0.339528	+	0.588080i	0.984344	−	0.176258i	$-0.0563992\pi$
$587$	8.22612	+	14.2481i	0.339528	+	0.588080i	−0.644816	+	0.764338i	$0.723066\pi$
$588$	−9.59976	−	16.6273i	−0.395887	−	0.685697i
$589$	1.51562	−	2.62513i	0.0624500	−	0.108167i
$590$	−6.46936			−0.266340
$591$	−19.8168	+	34.3237i	−0.815155	+	1.41189i
$592$	10.3830	−	17.9838i	0.426737	−	0.739130i
$593$	−17.1073			−0.702514			−0.351257	−	0.936279i	$-0.614246\pi$
$593$	−17.1073			−0.702514			−0.351257	+	0.936279i	$0.614246\pi$
$594$	−19.4060	+	33.6122i	−0.796238	+	1.37912i
$595$	−4.84607	−	8.39364i	−0.198669	−	0.344106i
$596$	3.14714	+	5.45100i	0.128912	+	0.223282i
$597$	0.484128			0.0198140
$598$	17.7375	−	3.08211i	0.725339	−	0.126037i
$599$	22.9308			0.936926			0.468463	−	0.883483i	$-0.344808\pi$
$599$	22.9308			0.936926			0.468463	+	0.883483i	$0.344808\pi$
$600$	1.13635	+	1.96821i	0.0463911	+	0.0803518i
$601$	15.1934	+	26.3157i	0.619751	+	1.07344i	0.989531	+	0.144320i	$0.0460996\pi$
$601$	15.1934	+	26.3157i	0.619751	+	1.07344i	−0.369780	+	0.929119i	$0.620567\pi$
$602$	−7.31873	+	12.6764i	−0.298289	+	0.516652i
$603$	5.50586			0.224216
$604$	−13.8017	+	23.9053i	−0.561583	+	0.972691i
$605$	13.2665	−	22.9783i	0.539360	−	0.934200i
$606$	−49.4456			−2.00859
$607$	−13.2355	+	22.9245i	−0.537212	+	0.930478i	0.461841	+	0.886963i	$0.347189\pi$
$607$	−13.2355	+	22.9245i	−0.537212	+	0.930478i	−0.999053	+	0.0435155i	$0.986144\pi$
$608$	−10.9294	−	18.9302i	−0.443245	−	0.767722i
$609$	4.44215	+	7.69403i	0.180005	+	0.311778i
$610$	−20.2863			−0.821369
$611$	17.1117	+	20.4963i	0.692265	+	0.829190i
$612$	−8.17209			−0.330337
$613$	3.73700	+	6.47268i	0.150936	+	0.261429i	0.931572	−	0.363557i	$-0.118438\pi$
$613$	3.73700	+	6.47268i	0.150936	+	0.261429i	−0.780636	+	0.624986i	$0.785105\pi$
$614$	−8.85028	−	15.3291i	−0.357168	−	0.618633i
$615$	18.5861	−	32.1921i	0.749464	−	1.29811i
$616$	−3.70177			−0.149148
$617$	−7.22025	+	12.5058i	−0.290676	+	0.503466i	−0.973970	−	0.226678i	$-0.927214\pi$
$617$	−7.22025	+	12.5058i	−0.290676	+	0.503466i	0.683294	+	0.730144i	$0.260547\pi$
$618$	12.4887	−	21.6311i	0.502369	−	0.870129i
$619$	15.6513			0.629080			0.314540	−	0.949244i	$-0.398150\pi$
$619$	15.6513			0.629080			0.314540	+	0.949244i	$0.398150\pi$
$620$	1.48739	−	2.57623i	0.0597349	−	0.103464i
$621$	−5.42551	−	9.39725i	−0.217718	−	0.377099i
$622$	5.26633	+	9.12154i	0.211160	+	0.365741i
$623$	15.6248			0.625995
$624$	32.9059	−	5.71783i	1.31729	−	0.228896i
$625$	−15.9256			−0.637023
$626$	−2.06036	−	3.56865i	−0.0823485	−	0.142632i
$627$	−15.0228	−	26.0203i	−0.599953	−	1.03915i
$628$	3.18386	−	5.51461i	0.127050	−	0.220057i
$629$	−24.9063			−0.993077
$630$	1.51585	−	2.62554i	0.0603931	−	0.104604i
$631$	22.8692	−	39.6107i	0.910410	−	1.57688i	0.0969250	−	0.995292i	$-0.469099\pi$
$631$	22.8692	−	39.6107i	0.910410	−	1.57688i	0.813485	−	0.581585i	$-0.197567\pi$
$632$	−10.9263			−0.434624
$633$	2.39995	−	4.15684i	0.0953895	−	0.165220i
$634$	12.7501	+	22.0839i	0.506372	+	0.877062i
$635$	9.83770	+	17.0394i	0.390397	+	0.676188i
$636$	22.4965			0.892046
$637$	7.65600	−	20.8730i	0.303342	−	0.827018i
$638$	46.3985			1.83693
$639$	−2.22353	−	3.85126i	−0.0879613	−	0.152353i
$640$	5.99838	+	10.3895i	0.237107	+	0.410681i
$641$	12.6909	−	21.9813i	0.501262	−	0.868211i	−0.498737	−	0.866753i	$-0.666203\pi$
$641$	12.6909	−	21.9813i	0.501262	−	0.868211i	0.999999	−	0.00145772i	$-0.000464006\pi$
$642$	−25.4544			−1.00460
$643$	12.1752	−	21.0881i	0.480144	−	0.831634i	−0.519596	−	0.854412i	$-0.673918\pi$
$643$	12.1752	−	21.0881i	0.480144	−	0.831634i	0.999741	+	0.0227778i	$0.00725102\pi$
$644$	−1.89520	+	3.28258i	−0.0746813	+	0.129352i
$645$	31.8347			1.25349
$646$	−16.0556	+	27.8090i	−0.631698	+	1.09413i
$647$	−4.04509	−	7.00631i	−0.159029	−	0.275446i	0.775490	−	0.631360i	$-0.217503\pi$
$647$	−4.04509	−	7.00631i	−0.159029	−	0.275446i	−0.934519	+	0.355914i	$0.884170\pi$
$648$	−4.42705	−	7.66787i	−0.173911	−	0.301222i
$649$	9.04228			0.354940
$650$	3.31913	−	9.04912i	0.130187	−	0.354936i
$651$	−1.80966			−0.0709261
$652$	−4.07010	−	7.04962i	−0.159397	−	0.276084i
$653$	−12.4918	−	21.6364i	−0.488842	−	0.846699i	0.511076	−	0.859536i	$-0.329247\pi$
$653$	−12.4918	−	21.6364i	−0.488842	−	0.846699i	−0.999918	+	0.0128368i	$0.995914\pi$
$654$	5.31183	−	9.20036i	0.207709	−	0.359763i
$655$	−33.6760			−1.31583
$656$	−23.1484	+	40.0943i	−0.903795	+	1.56542i
$657$	4.37356	−	7.57524i	0.170629	−	0.295538i
$658$	−12.7778			−0.498132
$659$	14.8913	−	25.7925i	0.580083	−	1.00473i	−0.415386	−	0.909645i	$-0.636354\pi$
$659$	14.8913	−	25.7925i	0.580083	−	1.00473i	0.995469	−	0.0950877i	$-0.0303131\pi$
$660$	−14.7430	−	25.5356i	−0.573869	−	0.993970i
$661$	−16.5705	−	28.7010i	−0.644519	−	1.11634i	−0.984412	−	0.175875i	$-0.943724\pi$
$661$	−16.5705	−	28.7010i	−0.644519	−	1.11634i	0.339894	−	0.940464i	$-0.389609\pi$
$662$	−40.7664			−1.58443
$663$	−25.6724	−	30.7502i	−0.997035	−	1.19424i
$664$	−11.5102			−0.446684
$665$	−2.62043	−	4.53872i	−0.101616	−	0.176004i
$666$	−3.89535	−	6.74694i	−0.150942	−	0.261439i
$667$	−6.48602	+	11.2341i	−0.251140	+	0.434987i
$668$	−7.90876			−0.305999
$669$	3.29320	−	5.70398i	0.127322	−	0.220529i
$670$	10.6158	−	18.3870i	0.410122	−	0.710353i
$671$	28.3543			1.09461
$672$	−6.52487	+	11.3014i	−0.251702	+	0.435961i
$673$	−15.6667	−	27.1355i	−0.603906	−	1.04600i	−0.992223	−	0.124470i	$-0.960277\pi$
$673$	−15.6667	−	27.1355i	−0.603906	−	1.04600i	0.388318	−	0.921525i	$-0.373056\pi$
$674$	−10.2259	−	17.7118i	−0.393888	−	0.682233i
$675$	−5.80945			−0.223606
$676$	−15.5798	−	13.2057i	−0.599224	−	0.507910i
$677$	−38.8697			−1.49388			−0.746942	−	0.664889i	$-0.768479\pi$
$677$	−38.8697			−1.49388			−0.746942	+	0.664889i	$0.768479\pi$
$678$	−12.7007	−	21.9982i	−0.487766	−	0.844836i
$679$	5.01357	+	8.68375i	0.192403	+	0.333252i
$680$	4.30217	−	7.45158i	0.164981	−	0.285755i
$681$	−9.98893			−0.382777
$682$	−4.72549	+	8.18480i	−0.180949	+	0.313412i
$683$	−10.7692	+	18.6527i	−0.412070	+	0.713727i	−0.995116	−	0.0987126i	$-0.968528\pi$
$683$	−10.7692	+	18.6527i	−0.412070	+	0.713727i	0.583046	+	0.812439i	$0.301861\pi$
$684$	−4.41892			−0.168962
$685$	7.37491	−	12.7737i	0.281781	−	0.488059i
$686$	11.3591	+	19.6746i	0.433694	+	0.751180i
$687$	24.8622	+	43.0625i	0.948551	+	1.64294i
$688$	−39.6491			−1.51161
$689$	16.6954	+	19.9976i	0.636042	+	0.761847i
$690$	18.7381			0.713349
$691$	−16.2666	−	28.1745i	−0.618809	−	1.07181i	−0.989703	−	0.143134i	$-0.954282\pi$
$691$	−16.2666	−	28.1745i	−0.618809	−	1.07181i	0.370894	−	0.928675i	$-0.379051\pi$
$692$	−10.9626	−	18.9877i	−0.416735	−	0.721806i
$693$	−2.11872	+	3.66973i	−0.0804835	+	0.139402i
$694$	−26.6467			−1.01150
$695$	−14.2221	+	24.6334i	−0.539476	+	0.934400i
$696$	−3.94358	+	6.83049i	−0.149481	+	0.258909i
$697$	55.5276			2.10326
$698$	−1.86085	+	3.22308i	−0.0704342	+	0.121996i
$699$	11.2162	+	19.4271i	0.424238	+	0.734801i
$700$	1.01466	+	1.75744i	0.0383504	+	0.0664249i
$701$	−21.1049			−0.797122			−0.398561	−	0.917142i	$-0.630490\pi$
$701$	−21.1049			−0.797122			−0.398561	+	0.917142i	$0.630490\pi$
$702$	−9.63532	+	26.2693i	−0.363662	+	0.991471i
$703$	−13.4676			−0.507941
$704$	10.7008	+	18.5344i	0.403302	+	0.698540i
$705$	13.8951	+	24.0670i	0.523320	+	0.906417i
$706$	−29.3389	+	50.8165i	−1.10418	+	1.91250i
$707$	12.0549			0.453372
$708$	2.81473	−	4.87525i	0.105784	−	0.183223i
$709$	−21.8596	+	37.8619i	−0.820953	+	1.42193i	0.0840200	+	0.996464i	$0.473224\pi$
$709$	−21.8596	+	37.8619i	−0.820953	+	1.42193i	−0.904973	+	0.425469i	$0.860109\pi$
$710$	−17.1486			−0.643574
$711$	−6.25370	+	10.8317i	−0.234532	+	0.406221i
$712$	6.93558	+	12.0128i	0.259922	+	0.450198i
$713$	−1.32115	−	2.28830i	−0.0494774	−	0.0856974i
$714$	19.1704			0.717435
$715$	11.7578	−	32.0560i	0.439717	−	1.19883i
$716$	29.7219			1.11076
$717$	5.66019	+	9.80374i	0.211384	+	0.366127i
$718$	−3.64067	−	6.30583i	−0.135869	−	0.235331i
$719$	−7.58979	+	13.1459i	−0.283051	+	0.490260i	−0.972135	−	0.234423i	$-0.924680\pi$
$719$	−7.58979	+	13.1459i	−0.283051	+	0.490260i	0.689083	+	0.724682i	$0.258013\pi$
$720$	8.21212			0.306048
$721$	−3.04477	+	5.27369i	−0.113393	+	0.196403i
$722$	9.27057	−	16.0571i	0.345015	−	0.597583i
$723$	22.4786			0.835987
$724$	10.7577	−	18.6330i	0.399809	−	0.692489i
$725$	3.47250	+	6.01455i	0.128966	+	0.223375i
$726$	26.2403	+	45.4495i	0.973869	+	1.68679i
$727$	−14.2907			−0.530011			−0.265006	−	0.964247i	$-0.585374\pi$
$727$	−14.2907			−0.530011			−0.265006	+	0.964247i	$0.585374\pi$
$728$	−2.62931	+	0.456876i	−0.0974486	+	0.0169330i
$729$	14.2816			0.528947
$730$	−16.8652	−	29.2114i	−0.624208	−	1.08116i
$731$	23.7772	+	41.1833i	0.879431	+	1.52322i
$732$	8.82629	−	15.2876i	0.326229	−	0.565045i
$733$	−26.7298			−0.987286			−0.493643	−	0.869665i	$-0.664335\pi$
$733$	−26.7298			−0.987286			−0.493643	+	0.869665i	$0.664335\pi$
$734$	−14.6596	+	25.3912i	−0.541096	+	0.937206i
$735$	11.5702	−	20.0401i	0.426772	−	0.739190i
$736$	−19.0540			−0.702341
$737$	−14.8377	+	25.6997i	−0.546554	+	0.946660i
$738$	8.68454	+	15.0421i	0.319682	+	0.553706i
$739$	−20.5578	−	35.6072i	−0.756231	−	1.30983i	−0.944760	−	0.327763i	$-0.893705\pi$
$739$	−20.5578	−	35.6072i	−0.756231	−	1.30983i	0.188529	−	0.982068i	$-0.439628\pi$
$740$	−13.2167			−0.485857
$741$	−13.8819	−	16.6277i	−0.509965	−	0.610833i
$742$	−12.4669			−0.457676
$743$	−6.48600	−	11.2341i	−0.237948	−	0.412138i	0.722177	−	0.691708i	$-0.243142\pi$
$743$	−6.48600	−	11.2341i	−0.237948	−	0.412138i	−0.960125	+	0.279570i	$0.909808\pi$
$744$	−0.803276	−	1.39131i	−0.0294495	−	0.0510080i
$745$	−3.79310	+	6.56985i	−0.138969	+	0.240701i
$746$	−53.2989			−1.95141
$747$	−6.58793	+	11.4106i	−0.241040	+	0.417493i
$748$	22.0229	−	38.1448i	0.805238	−	1.39471i
$749$	6.20583			0.226756
$750$	22.7451	−	39.3956i	0.830532	−	1.43852i
$751$	4.40816	+	7.63515i	0.160856	+	0.278611i	0.935176	−	0.354184i	$-0.115241\pi$
$751$	4.40816	+	7.63515i	0.160856	+	0.278611i	−0.774320	+	0.632794i	$0.781908\pi$
$752$	−17.3059	−	29.9748i	−0.631083	−	1.09307i
$753$	23.9842			0.874031
$754$	32.9561	−	5.72656i	1.20019	−	0.208549i
$755$	−33.2691			−1.21079
$756$	−2.94552	−	5.10179i	−0.107127	−	0.185550i
$757$	14.1530	+	24.5138i	0.514400	+	0.890968i	0.999860	+	0.0167089i	$0.00531884\pi$
$757$	14.1530	+	24.5138i	0.514400	+	0.890968i	−0.485460	+	0.874259i	$0.661348\pi$
$758$	1.04948	−	1.81775i	0.0381187	−	0.0660236i
$759$	−26.1904			−0.950652
$760$	2.32632	−	4.02931i	0.0843846	−	0.146158i
$761$	−5.78332	+	10.0170i	−0.209645	+	0.363116i	−0.951603	−	0.307331i	$-0.900564\pi$
$761$	−5.78332	+	10.0170i	−0.209645	+	0.363116i	0.741958	+	0.670447i	$0.233898\pi$
$762$	−38.9167			−1.40980
$763$	−1.29503	+	2.24307i	−0.0468834	+	0.0812044i
$764$	0.602132	+	1.04292i	0.0217844	+	0.0377316i
$765$	−4.92473	−	8.52988i	−0.178054	−	0.308398i
$766$	58.2617			2.10508
$767$	6.42259	−	1.11601i	0.231906	−	0.0402967i
$768$	−40.6909			−1.46831
$769$	5.40990	+	9.37022i	0.195086	+	0.337899i	0.946929	−	0.321444i	$-0.104168\pi$
$769$	5.40990	+	9.37022i	0.195086	+	0.337899i	−0.751843	+	0.659343i	$0.770835\pi$
$770$	8.17013	+	14.1511i	0.294431	+	0.509970i
$771$	−28.1303	+	48.7231i	−1.01309	+	1.75472i
$772$	−13.1248			−0.472370
$773$	7.69962	−	13.3361i	0.276936	−	0.479667i	−0.693686	−	0.720278i	$-0.744014\pi$
$773$	7.69962	−	13.3361i	0.276936	−	0.479667i	0.970622	+	0.240611i	$0.0773477\pi$
$774$	−7.43753	+	12.8822i	−0.267336	+	0.463040i
$775$	−1.41464			−0.0508154
$776$	−4.45087	+	7.70913i	−0.159777	+	0.276742i
$777$	4.02010	+	6.96303i	0.144220	+	0.249797i
$778$	20.8311	+	36.0805i	0.746830	+	1.29355i
$779$	30.0256			1.07578
$780$	−13.6233	−	16.3179i	−0.487793	−	0.584275i
$781$	23.9687			0.857666
$782$	13.9954	+	24.2408i	0.500476	+	0.866850i
$783$	−10.0806	−	17.4601i	−0.360250	−	0.623972i
$784$	−14.4103	+	24.9593i	−0.514653	+	0.891405i
$785$	7.67472			0.273923
$786$	33.3045	−	57.6850i	1.18793	−	2.05756i
$787$	23.2679	−	40.3012i	0.829411	−	1.43658i	−0.0690901	−	0.997610i	$-0.522010\pi$
$787$	23.2679	−	40.3012i	0.829411	−	1.43658i	0.898501	−	0.438971i	$-0.144657\pi$
$788$	−31.4174			−1.11920
$789$	18.5055	−	32.0525i	0.658814	−	1.14110i
$790$	24.1153	+	41.7689i	0.857983	+	1.48607i
$791$	3.09645	+	5.36321i	0.110097	+	0.190694i
$792$	−3.76185			−0.133672
$793$	20.1396	−	3.49953i	0.715180	−	0.124272i
$794$	−48.5117			−1.72161
$795$	13.5570	+	23.4815i	0.480818	+	0.832802i
$796$	0.191883	+	0.332351i	0.00680111	+	0.0117799i
$797$	−6.50509	+	11.2672i	−0.230422	+	0.399103i	−0.957932	−	0.286994i	$-0.907344\pi$
$797$	−6.50509	+	11.2672i	−0.230422	+	0.399103i	0.727510	+	0.686097i	$0.240677\pi$
$798$	10.3661			0.366955
$799$	−20.7564	+	35.9512i	−0.734309	+	1.27186i
$800$	−5.10060	+	8.83450i	−0.180333	+	0.312347i
$801$	15.8784			0.561037
$802$	22.4360	−	38.8602i	0.792241	−	1.37220i
$803$	23.5726	+	40.8289i	0.831858	+	1.44082i
$804$	9.23752	+	15.9999i	0.325782	+	0.564272i
$805$	−4.56840			−0.161015
$806$	−2.34627	+	6.39676i	−0.0826438	+	0.225316i
$807$	5.89153			0.207392
$808$	5.35097	+	9.26815i	0.188247	+	0.326053i
$809$	5.35529	+	9.27563i	0.188282	+	0.326114i	0.944678	−	0.328001i	$-0.106375\pi$
$809$	5.35529	+	9.27563i	0.188282	+	0.326114i	−0.756396	+	0.654114i	$0.773041\pi$
$810$	−19.5418	+	33.8474i	−0.686629	+	1.18928i
$811$	−33.2055			−1.16600			−0.583002	−	0.812471i	$-0.698122\pi$
$811$	−33.2055			−1.16600			−0.583002	+	0.812471i	$0.698122\pi$
$812$	−3.52127	+	6.09902i	−0.123572	+	0.214034i
$813$	8.17472	−	14.1590i	0.286700	−	0.496579i
$814$	41.9902			1.47176
$815$	4.90550	−	8.49658i	0.171832	−	0.297622i
$816$	25.9639	+	44.9707i	0.908917	+	1.57429i
$817$	12.8571	+	22.2692i	0.449813	+	0.779100i
$818$	48.6501			1.70101
$819$	−1.05197	+	2.86805i	−0.0367589	+	0.100218i
$820$	29.4663			1.02901
$821$	−16.2401	−	28.1286i	−0.566782	−	0.981695i	−0.996881	−	0.0789134i	$-0.974855\pi$
$821$	−16.2401	−	28.1286i	−0.566782	−	0.981695i	0.430100	−	0.902781i	$-0.358478\pi$
$822$	14.5871	+	25.2656i	0.508784	+	0.881239i
$823$	−10.3277	+	17.8881i	−0.360000	+	0.623539i	−0.987960	−	0.154707i	$-0.950557\pi$
$823$	−10.3277	+	17.8881i	−0.360000	+	0.623539i	0.627960	+	0.778246i	$0.283890\pi$
$824$	−5.40608			−0.188330
$825$	−7.01095	+	12.1433i	−0.244090	+	0.422776i
$826$	−1.55984	+	2.70173i	−0.0542739	+	0.0940051i
$827$	−32.8182			−1.14120			−0.570601	−	0.821227i	$-0.693290\pi$
$827$	−32.8182			−1.14120			−0.570601	+	0.821227i	$0.693290\pi$
$828$	−1.92596	+	3.33586i	−0.0669318	+	0.115929i
$829$	−14.5330	−	25.1720i	−0.504754	−	0.874259i	−0.999985	−	0.00549762i	$-0.998250\pi$
$829$	−14.5330	−	25.1720i	−0.504754	−	0.874259i	0.495231	−	0.868761i	$-0.335083\pi$
$830$	25.4041	+	44.0013i	0.881791	+	1.52731i
$831$	−2.09446			−0.0726560
$832$	9.88816	+	11.8440i	0.342810	+	0.410616i
$833$	34.5668			1.19767
$834$	−28.1304	−	48.7234i	−0.974078	−	1.68715i
$835$	−4.76604	−	8.25502i	−0.164936	−	0.285677i
$836$	11.9085	−	20.6262i	0.411865	−	0.713371i
$837$	4.10666			0.141947
$838$	9.27998	−	16.0734i	0.320572	−	0.555246i
$839$	−18.5026	+	32.0474i	−0.638779	+	1.10640i	0.346922	+	0.937894i	$0.387227\pi$
$839$	−18.5026	+	32.0474i	−0.638779	+	1.10640i	−0.985701	+	0.168504i	$0.946106\pi$
$840$	−2.77764			−0.0958378
$841$	2.44900	−	4.24179i	0.0844482	−	0.146269i
$842$	0.741992	+	1.28517i	0.0255707	+	0.0442898i
$843$	19.1273	+	33.1295i	0.658780	+	1.14104i
$844$	3.80486			0.130969
$845$	4.39501	−	24.2200i	0.151193	−	0.833194i
$846$	−12.9852			−0.446442
$847$	−6.39744	−	11.0807i	−0.219819	−	0.380737i
$848$	−16.8849	−	29.2455i	−0.579829	−	1.00429i
$849$	30.1098	−	52.1517i	1.03337	−	1.78984i
$850$	14.9858			0.514010
$851$	−5.86979	+	10.1668i	−0.201214	+	0.348512i
$852$	7.46109	−	12.9230i	0.255613	−	0.442734i
$853$	21.9781			0.752517			0.376259	−	0.926515i	$-0.377210\pi$
$853$	21.9781			0.752517			0.376259	+	0.926515i	$0.377210\pi$
$854$	−4.89128	+	8.47195i	−0.167376	+	0.289904i
$855$	−2.66296	−	4.61238i	−0.0910714	−	0.157740i
$856$	2.75466	+	4.77121i	0.0941523	+	0.163077i
$857$	−42.5595			−1.45380			−0.726902	−	0.686741i	$-0.759041\pi$
$857$	−42.5595			−1.45380			−0.726902	+	0.686741i	$0.759041\pi$
$858$	43.2819	+	51.8428i	1.47762	+	1.76988i
$859$	−52.5951			−1.79452			−0.897261	−	0.441501i	$-0.854446\pi$
$859$	−52.5951			−1.79452			−0.897261	+	0.441501i	$0.854446\pi$
$860$	12.6176	+	21.8543i	0.430257	+	0.745226i
$861$	−8.96268	−	15.5238i	−0.305447	−	0.529050i
$862$	10.5194	−	18.2201i	0.358291	−	0.620578i
$863$	50.7294			1.72685			0.863424	−	0.504479i	$-0.168315\pi$
$863$	50.7294			1.72685			0.863424	+	0.504479i	$0.168315\pi$
$864$	14.8069	−	25.6463i	0.503740	−	0.872504i
$865$	13.2127	−	22.8851i	0.449245	−	0.778116i
$866$	−7.51692			−0.255435
$867$	14.2944	−	24.7587i	0.485465	−	0.840849i
$868$	−0.717254	−	1.24232i	−0.0243452	−	0.0421671i
$869$	−33.7061	−	58.3807i	−1.14340	−	1.98043i
$870$	34.8154			1.18035
$871$	−7.36711	+	20.0854i	−0.249625	+	0.680567i
$872$	−2.29937			−0.0778666
$873$	5.09494	+	8.82470i	0.172438	+	0.298671i
$874$	7.56780	+	13.1078i	0.255985	+	0.443378i
$875$	−5.54529	+	9.60472i	−0.187465	+	0.324699i
$876$	29.3512			0.991685
$877$	−2.19042	+	3.79392i	−0.0739653	+	0.128112i	−0.900636	−	0.434575i	$-0.856899\pi$
$877$	−2.19042	+	3.79392i	−0.0739653	+	0.128112i	0.826671	+	0.562686i	$0.190232\pi$
$878$	−23.9597	+	41.4995i	−0.808601	+	1.40054i
$879$	−62.1488			−2.09623
$880$	−22.1308	+	38.3316i	−0.746029	+	1.29216i
$881$	−18.8420	−	32.6352i	−0.634802	−	1.09951i	−0.986557	−	0.163417i	$-0.947748\pi$
$881$	−18.8420	−	32.6352i	−0.634802	−	1.09951i	0.351755	−	0.936092i	$-0.385585\pi$
$882$	5.40627	+	9.36393i	0.182038	+	0.315300i
$883$	52.7331			1.77461			0.887305	−	0.461183i	$-0.152575\pi$
$883$	52.7331			1.77461			0.887305	+	0.461183i	$0.152575\pi$
$884$	10.9347	−	29.8118i	0.367773	−	1.00268i
$885$	6.78493			0.228073
$886$	23.3645	+	40.4685i	0.784946	+	1.35957i
$887$	4.32393	+	7.48927i	0.145183	+	0.251465i	0.929441	−	0.368970i	$-0.120289\pi$
$887$	4.32393	+	7.48927i	0.145183	+	0.251465i	−0.784258	+	0.620435i	$0.786956\pi$
$888$	−3.56891	+	6.18153i	−0.119765	+	0.207439i
$889$	9.48796			0.318216
$890$	30.6149	−	53.0266i	1.02621	−	1.77746i
$891$	27.3137	−	47.3087i	0.915044	−	1.58490i
$892$	5.22100			0.174812
$893$	−11.2237	+	19.4400i	−0.375586	+	0.650534i
$894$	−7.50252	−	12.9947i	−0.250922	−	0.434609i
$895$	17.9112	+	31.0232i	0.598707	+	1.03699i
$896$	5.78513			0.193268
$897$	−18.6027	+	3.23245i	−0.621125	+	0.107929i
$898$	60.8841			2.03173
$899$	−2.45469	−	4.25165i	−0.0818685	−	0.141800i
$900$	1.03113	+	1.78596i	0.0343709	+	0.0595321i
$901$	−20.2514	+	35.0764i	−0.674672	+	1.16857i
$902$	−93.6156			−3.11706
$903$	7.67573	−	13.2948i	0.255432	−	0.442422i
$904$	−2.74892	+	4.76127i	−0.0914277	+	0.158357i
$905$	25.9317			0.861998
$906$	32.9021	−	56.9881i	1.09310	−	1.89330i
$907$	−23.5706	−	40.8254i	−0.782647	−	1.35559i	−0.930394	−	0.366560i	$-0.880535\pi$
$907$	−23.5706	−	40.8254i	−0.782647	−	1.35559i	0.147747	−	0.989025i	$-0.452798\pi$
$908$	−3.95909	−	6.85735i	−0.131387	−	0.227569i
$909$	12.2506			0.406327
$910$	7.54966	+	9.04293i	0.250269	+	0.299770i
$911$	30.4168			1.00775			0.503876	−	0.863776i	$-0.331907\pi$
$911$	30.4168			1.00775			0.503876	+	0.863776i	$0.331907\pi$
$912$	14.0395	+	24.3171i	0.464895	+	0.805221i
$913$	−35.5075	−	61.5009i	−1.17513	−	2.03538i
$914$	12.4310	−	21.5311i	0.411180	−	0.712184i
$915$	21.2759			0.703358
$916$	−19.7081	+	34.1355i	−0.651175	+	1.12787i
$917$	−8.11969	+	14.0637i	−0.268136	+	0.464425i
$918$	−43.5034			−1.43583
$919$	−0.492393	+	0.852850i	−0.0162425	+	0.0281329i	−0.874032	−	0.485868i	$-0.838504\pi$
$919$	−0.492393	+	0.852850i	−0.0162425	+	0.0281329i	0.857790	+	0.514000i	$0.171837\pi$
$920$	−2.02783	−	3.51230i	−0.0668556	−	0.115797i
$921$	9.28198	+	16.0769i	0.305852	+	0.529751i
$922$	−25.6631			−0.845168
$923$	17.0246	−	2.95824i	0.560371	−	0.0973717i
$924$	−14.2188			−0.467765
$925$	3.14258	+	5.44312i	0.103328	+	0.178969i
$926$	7.85798	+	13.6104i	0.258229	+	0.447266i
$927$	−3.09419	+	5.35929i	−0.101627	+	0.176022i
$928$	−35.4023			−1.16214
$929$	−0.236692	+	0.409962i	−0.00776560	+	0.0134504i	−0.869882	−	0.493260i	$-0.835805\pi$
$929$	−0.236692	+	0.409962i	−0.00776560	+	0.0134504i	0.862116	+	0.506710i	$0.169139\pi$
$930$	−3.54580	+	6.14151i	−0.116272	+	0.201388i
$931$	18.6914			0.612586
$932$	−8.89107	+	15.3998i	−0.291237	+	0.504437i
$933$	−5.52321	−	9.56648i	−0.180822	−	0.313192i
$934$	−11.9267	−	20.6577i	−0.390254	−	0.675940i
$935$	53.0865			1.73611
$936$	−2.67198	+	0.464292i	−0.0873366	+	0.0151759i
$937$	0.933257			0.0304882			0.0152441	−	0.999884i	$-0.495147\pi$
$937$	0.933257			0.0304882			0.0152441	+	0.999884i	$0.495147\pi$
$938$	−5.11918	−	8.86667i	−0.167147	−	0.289507i
$939$	2.16086	+	3.74272i	0.0705170	+	0.122139i
$940$	−11.0146	+	19.0778i	−0.359256	+	0.622250i
$941$	52.9082			1.72476			0.862380	−	0.506262i	$-0.168973\pi$
$941$	52.9082			1.72476			0.862380	+	0.506262i	$0.168973\pi$
$942$	−7.59005	+	13.1464i	−0.247297	+	0.428331i
$943$	13.0865	−	22.6664i	0.426154	−	0.738121i
$944$	−8.45042			−0.275038
$945$	3.55010	−	6.14895i	0.115485	−	0.200025i
$946$	−40.0867	−	69.4322i	−1.30333	−	2.25744i
$947$	−21.9980	−	38.1016i	−0.714838	−	1.23814i	−0.963022	−	0.269423i	$-0.913167\pi$
$947$	−21.9980	−	38.1016i	−0.714838	−	1.23814i	0.248183	−	0.968713i	$-0.420166\pi$
$948$	−41.9688			−1.36308
$949$	21.7824	+	26.0908i	0.707087	+	0.846943i
$950$	8.10334			0.262907
$951$	−13.3721	−	23.1611i	−0.433619	−	0.751049i
$952$	−2.07461	−	3.59333i	−0.0672385	−	0.116461i
$953$	−16.6932	+	28.9135i	−0.540746	+	0.936600i	0.458115	+	0.888893i	$0.348525\pi$
$953$	−16.6932	+	28.9135i	−0.540746	+	0.936600i	−0.998861	+	0.0477072i	$0.984809\pi$
$954$	−12.6693			−0.410184
$955$	−0.725723	+	1.25699i	−0.0234838	+	0.0406752i
$956$	−4.48681	+	7.77138i	−0.145114	+	0.251344i
$957$	−48.6617			−1.57301
$958$	5.86619	−	10.1605i	0.189528	−	0.328272i
$959$	−3.55636	−	6.15980i	−0.114841	−	0.198910i
$960$	8.02943	+	13.9074i	0.259149	+	0.448859i
$961$	1.00000			0.0322581
$962$	29.8250	−	5.18248i	0.961596	−	0.167090i
$963$	6.30656			0.203226
$964$	8.90933	+	15.4314i	0.286950	+	0.497012i
$965$	−7.90934	−	13.6994i	−0.254611	−	0.440999i
$966$	4.51800	−	7.82540i	0.145364	−	0.251778i
$967$	−26.7757			−0.861048			−0.430524	−	0.902579i	$-0.641671\pi$
$967$	−26.7757			−0.861048			−0.430524	+	0.902579i	$0.641671\pi$
$968$	5.67942	−	9.83704i	0.182543	−	0.316174i
$969$	16.8387	−	29.1655i	0.540938	−	0.936931i
$970$	39.2939			1.26165
$971$	0.0936504	−	0.162207i	0.00300538	−	0.00520548i	−0.864519	−	0.502600i	$-0.832377\pi$
$971$	0.0936504	−	0.162207i	0.00300538	−	0.00520548i	0.867524	+	0.497395i	$0.165710\pi$
$972$	−7.32712	−	12.6909i	−0.235017	−	0.407062i
$973$	6.85826	+	11.8789i	0.219866	+	0.380818i
$974$	0.282457			0.00905051
$975$	−3.48103	+	9.49052i	−0.111482	+	0.303940i
$976$	−26.4984			−0.848194
$977$	4.23656	+	7.33793i	0.135539	+	0.234761i	0.925803	−	0.378005i	$-0.123390\pi$
$977$	4.23656	+	7.33793i	0.135539	+	0.234761i	−0.790264	+	0.612767i	$0.790057\pi$
$978$	9.70277	+	16.8057i	0.310260	+	0.537387i
$979$	−42.7907	+	74.1156i	−1.36760	+	2.36875i
$980$	18.3432			0.585953
$981$	−1.31605	+	2.27947i	−0.0420184	+	0.0727780i
$982$	17.4065	−	30.1490i	0.555465	−	0.962094i
$983$	47.9679			1.52994			0.764969	−	0.644067i	$-0.222754\pi$
$983$	47.9679			1.52994			0.764969	+	0.644067i	$0.222754\pi$
$984$	7.95675	−	13.7815i	0.253652	−	0.439338i
$985$	−18.9330	−	32.7929i	−0.603255	−	1.04487i
$986$	26.0035	+	45.0394i	0.828120	+	1.43435i
$987$	13.4011			0.426563
$988$	5.91273	−	16.1202i	0.188109	−	0.512852i
$989$	22.4148			0.712749
$990$	8.30275	+	14.3808i	0.263879	+	0.457051i
$991$	17.7543	+	30.7513i	0.563984	+	0.976849i	0.997143	+	0.0755314i	$0.0240653\pi$
$991$	17.7543	+	30.7513i	0.563984	+	0.976849i	−0.433160	+	0.901317i	$0.642601\pi$
$992$	3.60558	−	6.24505i	0.114477	−	0.198280i
$993$	42.7550			1.35679
$994$	−4.13473	+	7.16156i	−0.131146	+	0.227151i
$995$	−0.231268	+	0.400567i	−0.00733168	+	0.0126988i
$996$	−44.2119			−1.40091
$997$	0.721968	−	1.25049i	0.0228650	−	0.0396033i	−0.854367	−	0.519671i	$-0.826055\pi$
$997$	0.721968	−	1.25049i	0.0228650	−	0.0396033i	0.877231	+	0.480068i	$0.159388\pi$
$998$	−10.8307	−	18.7594i	−0.342841	−	0.593817i
$999$	−9.12282	−	15.8012i	−0.288633	−	0.499928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.5	✓	36
13.3	even	3		5239.2.a.p.1.14		18
13.9	even	3	inner	403.2.f.c.373.5	yes	36
13.10	even	6		5239.2.a.o.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.5	✓	36	1.1	even	1	trivial
403.2.f.c.373.5	yes	36	13.9	even	3	inner
5239.2.a.o.1.5		18	13.10	even	6
5239.2.a.p.1.14		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.944860 - 1.63655i) q^{2} +(0.990948 + 1.71637i) q^{3} +(-0.785520 + 1.36056i) q^{4} -1.89350 q^{5} +(1.87261 - 3.24346i) q^{6} +(-0.456547 + 0.790763i) q^{7} -0.810613 q^{8} +(-0.463958 + 0.803598i) q^{9} +O(q^{10})\)	\(q+(-0.944860 - 1.63655i) q^{2} +(0.990948 + 1.71637i) q^{3} +(-0.785520 + 1.36056i) q^{4} -1.89350 q^{5} +(1.87261 - 3.24346i) q^{6} +(-0.456547 + 0.790763i) q^{7} -0.810613 q^{8} +(-0.463958 + 0.803598i) q^{9} +(1.78910 + 3.09881i) q^{10} +(-2.50063 - 4.33122i) q^{11} -3.11364 q^{12} +(-2.31073 - 2.76777i) q^{13} +1.72549 q^{14} +(-1.87637 - 3.24996i) q^{15} +(2.33696 + 4.04773i) q^{16} +(2.80290 - 4.85477i) q^{17} +1.75350 q^{18} +(1.51562 - 2.62513i) q^{19} +(1.48739 - 2.57623i) q^{20} -1.80966 q^{21} +(-4.72549 + 8.18480i) q^{22} +(-1.32115 - 2.28830i) q^{23} +(-0.803276 - 1.39131i) q^{24} -1.41464 q^{25} +(-2.34627 + 6.39676i) q^{26} +4.10666 q^{27} +(-0.717254 - 1.24232i) q^{28} +(-2.45469 - 4.25165i) q^{29} +(-3.54580 + 6.14151i) q^{30} +1.00000 q^{31} +(3.60558 - 6.24505i) q^{32} +(4.95600 - 8.58404i) q^{33} -10.5934 q^{34} +(0.864474 - 1.49731i) q^{35} +(-0.728896 - 1.26249i) q^{36} +(-2.22147 - 3.84770i) q^{37} -5.72819 q^{38} +(2.46072 - 6.70878i) q^{39} +1.53490 q^{40} +(4.95269 + 8.57831i) q^{41} +(1.70987 + 2.96159i) q^{42} +(-4.24153 + 7.34655i) q^{43} +7.85719 q^{44} +(0.878506 - 1.52162i) q^{45} +(-2.49660 + 4.32424i) q^{46} -7.40533 q^{47} +(-4.63161 + 8.02218i) q^{48} +(3.08313 + 5.34014i) q^{49} +(1.33664 + 2.31512i) q^{50} +11.1101 q^{51} +(5.58084 - 0.969744i) q^{52} -7.22516 q^{53} +(-3.88022 - 6.72073i) q^{54} +(4.73496 + 8.20119i) q^{55} +(0.370083 - 0.641002i) q^{56} +6.00761 q^{57} +(-4.63868 + 8.03442i) q^{58} +(-0.903999 + 1.56577i) q^{59} +5.89569 q^{60} +(-2.83472 + 4.90987i) q^{61} +(-0.944860 - 1.63655i) q^{62} +(-0.423637 - 0.733761i) q^{63} -4.27924 q^{64} +(4.37537 + 5.24078i) q^{65} -18.7309 q^{66} +(-2.96679 - 5.13863i) q^{67} +(4.40347 + 7.62704i) q^{68} +(2.61838 - 4.53517i) q^{69} -3.26723 q^{70} +(-2.39626 + 4.15044i) q^{71} +(0.376090 - 0.651407i) q^{72} -9.42665 q^{73} +(-4.19796 + 7.27108i) q^{74} +(-1.40184 - 2.42805i) q^{75} +(2.38110 + 4.12419i) q^{76} +4.56663 q^{77} +(-13.3043 + 2.31179i) q^{78} +13.4790 q^{79} +(-4.42504 - 7.66439i) q^{80} +(5.46136 + 9.45935i) q^{81} +(9.35920 - 16.2106i) q^{82} +14.1994 q^{83} +(1.42152 - 2.46215i) q^{84} +(-5.30730 + 9.19252i) q^{85} +16.0306 q^{86} +(4.86494 - 8.42633i) q^{87} +(2.02704 + 3.51094i) q^{88} +(-8.55597 - 14.8194i) q^{89} -3.32026 q^{90} +(3.24360 - 0.563619i) q^{91} +4.15116 q^{92} +(0.990948 + 1.71637i) q^{93} +(6.99700 + 12.1192i) q^{94} +(-2.86983 + 4.97070i) q^{95} +14.2918 q^{96} +(5.49074 - 9.51025i) q^{97} +(5.82625 - 10.0914i) q^{98} +4.64075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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