LMFDB - Embedded newform 61.2.g.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.2
Root			$-0.776536i$ of defining polynomial
Character	$\chi$	$=$	61.3
Dual form			61.2.g.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.738530 - 0.239963i) q^{2} +(0.554995 - 1.70810i) q^{3} +(-1.13019 - 0.821131i) q^{4} +(-0.515969 - 0.374873i) q^{5} +(-0.819760 + 1.12830i) q^{6} +(1.31473 - 0.427183i) q^{7} +(1.55051 + 2.13410i) q^{8} +(-0.182527 - 0.132614i) q^{9} +O(q^{10})$	\(q+(-0.738530 - 0.239963i) q^{2} +(0.554995 - 1.70810i) q^{3} +(-1.13019 - 0.821131i) q^{4} +(-0.515969 - 0.374873i) q^{5} +(-0.819760 + 1.12830i) q^{6} +(1.31473 - 0.427183i) q^{7} +(1.55051 + 2.13410i) q^{8} +(-0.182527 - 0.132614i) q^{9} +(0.291103 + 0.400668i) q^{10} +0.172452i q^{11} +(-2.02982 + 1.47475i) q^{12} +2.97038 q^{13} -1.07348 q^{14} +(-0.926680 + 0.673273i) q^{15} +(0.230394 + 0.709079i) q^{16} +(-4.72228 + 6.49966i) q^{17} +(0.102979 + 0.141739i) q^{18} +(0.512304 - 1.57671i) q^{19} +(0.275323 + 0.847356i) q^{20} -2.48278i q^{21} +(0.0413820 - 0.127361i) q^{22} +(-0.377428 + 0.519485i) q^{23} +(4.50577 - 1.46401i) q^{24} +(-1.41939 - 4.36844i) q^{25} +(-2.19372 - 0.712782i) q^{26} +(4.03116 - 2.92881i) q^{27} +(-1.83667 - 0.596771i) q^{28} +0.820197i q^{29} +(0.845941 - 0.274863i) q^{30} +(4.24726 - 1.38002i) q^{31} -5.85473i q^{32} +(0.294565 + 0.0957098i) q^{33} +(5.04722 - 3.66702i) q^{34} +(-0.838501 - 0.272446i) q^{35} +(0.0973970 + 0.299757i) q^{36} +(-10.3995 + 3.37901i) q^{37} +(-0.756704 + 1.04151i) q^{38} +(1.64855 - 5.07371i) q^{39} -1.68237i q^{40} +(0.807618 + 2.48559i) q^{41} +(-0.595774 + 1.83360i) q^{42} +(5.75786 + 7.92501i) q^{43} +(0.141606 - 0.194903i) q^{44} +(0.0444649 + 0.136849i) q^{45} +(0.403399 - 0.293086i) q^{46} -10.4380 q^{47} +1.33904 q^{48} +(-4.11708 + 2.99123i) q^{49} +3.56682i q^{50} +(8.48122 + 11.6734i) q^{51} +(-3.35710 - 2.43908i) q^{52} +(-2.67554 - 3.68256i) q^{53} +(-3.67994 + 1.19569i) q^{54} +(0.0646476 - 0.0889798i) q^{55} +(2.95016 + 2.14341i) q^{56} +(-2.40885 - 1.75013i) q^{57} +(0.196817 - 0.605740i) q^{58} +(7.74387 + 2.51614i) q^{59} +1.60017 q^{60} +(4.77527 - 6.18036i) q^{61} -3.46788 q^{62} +(-0.296625 - 0.0963792i) q^{63} +(-0.944131 + 2.90574i) q^{64} +(-1.53263 - 1.11352i) q^{65} +(-0.194578 - 0.141369i) q^{66} +(-2.71616 + 3.73847i) q^{67} +(10.6741 - 3.46824i) q^{68} +(0.677861 + 0.932995i) q^{69} +(0.553881 + 0.402418i) q^{70} +(-3.82926 - 5.27053i) q^{71} -0.595149i q^{72} +(-10.0925 + 7.33262i) q^{73} +8.49119 q^{74} -8.24947 q^{75} +(-1.87369 + 1.36131i) q^{76} +(0.0736685 + 0.226728i) q^{77} +(-2.43500 + 3.35149i) q^{78} +(-1.32326 - 1.82132i) q^{79} +(0.146939 - 0.452231i) q^{80} +(-2.97458 - 9.15482i) q^{81} -2.02948i q^{82} +(1.38191 - 4.25308i) q^{83} +(-2.03869 + 2.80601i) q^{84} +(4.87310 - 1.58337i) q^{85} +(-2.35064 - 7.23453i) q^{86} +(1.40098 + 0.455205i) q^{87} +(-0.368029 + 0.267388i) q^{88} +(10.1803 + 3.30777i) q^{89} -0.111737i q^{90} +(3.90526 - 1.26890i) q^{91} +(0.853131 - 0.277199i) q^{92} -8.02064i q^{93} +(7.70876 + 2.50473i) q^{94} +(-0.855400 + 0.621484i) q^{95} +(-10.0005 - 3.24935i) q^{96} +(3.79290 + 11.6733i) q^{97} +(3.75837 - 1.22117i) q^{98} +(0.0228695 - 0.0314771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.738530	−	0.239963i	−0.522219	−	0.169679i	0.0360329	−	0.999351i	$-0.488528\pi$
$2$	−0.738530	−	0.239963i	−0.522219	−	0.169679i	−0.558252	+	0.829671i	$0.688528\pi$
$3$	0.554995	−	1.70810i	0.320426	−	0.986171i	−0.653037	−	0.757326i	$-0.726505\pi$
$3$	0.554995	−	1.70810i	0.320426	−	0.986171i	0.973463	−	0.228844i	$-0.0734947\pi$
$4$	−1.13019	−	0.821131i	−0.565095	−	0.410566i
$5$	−0.515969	−	0.374873i	−0.230748	−	0.167648i	0.466403	−	0.884572i	$-0.345550\pi$
$5$	−0.515969	−	0.374873i	−0.230748	−	0.167648i	−0.697152	+	0.716924i	$0.745550\pi$
$6$	−0.819760	+	1.12830i	−0.334666	+	0.460628i
$7$	1.31473	−	0.427183i	0.496923	−	0.161460i	−0.0498241	−	0.998758i	$-0.515866\pi$
$7$	1.31473	−	0.427183i	0.496923	−	0.161460i	0.546747	+	0.837298i	$0.315866\pi$
$8$	1.55051	+	2.13410i	0.548188	+	0.754517i
$9$	−0.182527	−	0.132614i	−0.0608423	−	0.0442045i
$10$	0.291103	+	0.400668i	0.0920547	+	0.126702i
$11$			0.172452i			0.0519962i	0.999662	+	0.0259981i	$0.00827638\pi$
$11$			0.172452i			0.0519962i	−0.999662	+	0.0259981i	$0.991724\pi$
$12$	−2.02982	+	1.47475i	−0.585959	+	0.425724i
$13$	2.97038			0.823836			0.411918	−	0.911221i	$-0.364859\pi$
$13$	2.97038			0.823836			0.411918	+	0.911221i	$0.364859\pi$
$14$	−1.07348			−0.286899
$15$	−0.926680	+	0.673273i	−0.239268	+	0.173838i
$16$	0.230394	+	0.709079i	0.0575984	+	0.177270i
$17$	−4.72228	+	6.49966i	−1.14532	+	1.57640i	−0.390316	+	0.920681i	$0.627634\pi$
$17$	−4.72228	+	6.49966i	−1.14532	+	1.57640i	−0.755005	+	0.655719i	$0.772366\pi$
$18$	0.102979	+	0.141739i	0.0242724	+	0.0334081i
$19$	0.512304	−	1.57671i	0.117531	−	0.361722i	−0.874936	−	0.484239i	$-0.839097\pi$
$19$	0.512304	−	1.57671i	0.117531	−	0.361722i	0.992466	+	0.122517i	$0.0390965\pi$
$20$	0.275323	+	0.847356i	0.0615640	+	0.189475i
$21$		−	2.48278i		−	0.541786i
$22$	0.0413820	−	0.127361i	0.00882268	−	0.0271534i
$23$	−0.377428	+	0.519485i	−0.0786992	+	0.108320i	−0.846552	−	0.532307i	$-0.821325\pi$
$23$	−0.377428	+	0.519485i	−0.0786992	+	0.108320i	0.767852	+	0.640627i	$0.221325\pi$
$24$	4.50577	−	1.46401i	0.919736	−	0.298840i
$25$	−1.41939	−	4.36844i	−0.283878	−	0.873687i
$26$	−2.19372	−	0.712782i	−0.430223	−	0.139788i
$27$	4.03116	−	2.92881i	0.775798	−	0.563650i
$28$	−1.83667	−	0.596771i	−0.347098	−	0.112779i
$29$			0.820197i			0.152307i	0.997096	+	0.0761534i	$0.0242639\pi$
$29$			0.820197i			0.152307i	−0.997096	+	0.0761534i	$0.975736\pi$
$30$	0.845941	−	0.274863i	0.154447	−	0.0501829i
$31$	4.24726	−	1.38002i	0.762831	−	0.247859i	0.0983375	−	0.995153i	$-0.468648\pi$
$31$	4.24726	−	1.38002i	0.762831	−	0.247859i	0.664493	+	0.747294i	$0.268648\pi$
$32$		−	5.85473i		−	1.03498i
$33$	0.294565	+	0.0957098i	0.0512771	+	0.0166609i
$34$	5.04722	−	3.66702i	0.865591	−	0.628889i
$35$	−0.838501	−	0.272446i	−0.141733	−	0.0460517i
$36$	0.0973970	+	0.299757i	0.0162328	+	0.0499595i
$37$	−10.3995	+	3.37901i	−1.70967	+	0.555506i	−0.990279	−	0.139099i	$-0.955579\pi$
$37$	−10.3995	+	3.37901i	−1.70967	+	0.555506i	−0.719392	+	0.694604i	$0.755579\pi$
$38$	−0.756704	+	1.04151i	−0.122754	+	0.168956i
$39$	1.64855	−	5.07371i	0.263979	−	0.812443i
$40$		−	1.68237i		−	0.266006i
$41$	0.807618	+	2.48559i	0.126129	+	0.388184i	0.994105	−	0.108421i	$-0.0345795\pi$
$41$	0.807618	+	2.48559i	0.126129	+	0.388184i	−0.867976	+	0.496606i	$0.834580\pi$
$42$	−0.595774	+	1.83360i	−0.0919300	+	0.282931i
$43$	5.75786	+	7.92501i	0.878065	+	1.20855i	0.976953	+	0.213454i	$0.0684715\pi$
$43$	5.75786	+	7.92501i	0.878065	+	1.20855i	−0.0988878	+	0.995099i	$0.531529\pi$
$44$	0.141606	−	0.194903i	0.0213478	−	0.0293828i
$45$	0.0444649	+	0.136849i	0.00662844	+	0.0204002i
$46$	0.403399	−	0.293086i	0.0594779	−	0.0432132i
$47$	−10.4380			−1.52254			−0.761268	−	0.648438i	$-0.775423\pi$
$47$	−10.4380			−1.52254			−0.761268	+	0.648438i	$0.775423\pi$
$48$	1.33904			0.193274
$49$	−4.11708	+	2.99123i	−0.588154	+	0.427319i
$50$			3.56682i			0.504425i
$51$	8.48122	+	11.6734i	1.18761	+	1.63460i
$52$	−3.35710	−	2.43908i	−0.465546	−	0.338239i
$53$	−2.67554	−	3.68256i	−0.367513	−	0.505839i	0.584709	−	0.811243i	$-0.301209\pi$
$53$	−2.67554	−	3.68256i	−0.367513	−	0.505839i	−0.952223	+	0.305404i	$0.901209\pi$
$54$	−3.67994	+	1.19569i	−0.500777	+	0.162712i
$55$	0.0646476	−	0.0889798i	0.00871708	−	0.0119980i
$56$	2.95016	+	2.14341i	0.394231	+	0.286426i
$57$	−2.40885	−	1.75013i	−0.319060	−	0.231811i
$58$	0.196817	−	0.605740i	0.0258433	−	0.0795375i
$59$	7.74387	+	2.51614i	1.00817	+	0.327573i	0.766124	−	0.642693i	$-0.222183\pi$
$59$	7.74387	+	2.51614i	1.00817	+	0.327573i	0.242042	+	0.970266i	$0.422183\pi$
$60$	1.60017			0.206581
$61$	4.77527	−	6.18036i	0.611411	−	0.791313i
$61$	4.77527	−	6.18036i	0.611411	−	0.791313i
$62$	−3.46788			−0.440421
$63$	−0.296625	−	0.0963792i	−0.0373712	−	0.0121426i
$64$	−0.944131	+	2.90574i	−0.118016	+	0.363217i
$65$	−1.53263	−	1.11352i	−0.190099	−	0.138115i
$66$	−0.194578	−	0.141369i	−0.0239509	−	0.0174013i
$67$	−2.71616	+	3.73847i	−0.331831	+	0.456726i	−0.942033	−	0.335519i	$-0.891088\pi$
$67$	−2.71616	+	3.73847i	−0.331831	+	0.456726i	0.610202	+	0.792246i	$0.291088\pi$
$68$	10.6741	−	3.46824i	1.29443	−	0.420586i
$69$	0.677861	+	0.932995i	0.0816048	+	0.112319i
$70$	0.553881	+	0.402418i	0.0662015	+	0.0480982i
$71$	−3.82926	−	5.27053i	−0.454450	−	0.625497i	0.518896	−	0.854837i	$-0.326343\pi$
$71$	−3.82926	−	5.27053i	−0.454450	−	0.625497i	−0.973346	+	0.229340i	$0.926343\pi$
$72$		−	0.595149i		−	0.0701390i
$73$	−10.0925	+	7.33262i	−1.18124	+	0.858218i	−0.992310	−	0.123774i	$-0.960500\pi$
$73$	−10.0925	+	7.33262i	−1.18124	+	0.858218i	−0.188925	+	0.981991i	$0.560500\pi$
$74$	8.49119			0.987081
$75$	−8.24947			−0.952567
$76$	−1.87369	+	1.36131i	−0.214927	+	0.156153i
$77$	0.0736685	+	0.226728i	0.00839530	+	0.0258381i
$78$	−2.43500	+	3.35149i	−0.275710	+	0.379482i
$79$	−1.32326	−	1.82132i	−0.148879	−	0.204914i	0.728064	−	0.685510i	$-0.240421\pi$
$79$	−1.32326	−	1.82132i	−0.148879	−	0.204914i	−0.876942	+	0.480595i	$0.840421\pi$
$80$	0.146939	−	0.452231i	0.0164283	−	0.0505610i
$81$	−2.97458	−	9.15482i	−0.330509	−	1.01720i
$82$		−	2.02948i		−	0.224119i
$83$	1.38191	−	4.25308i	0.151684	−	0.466837i	−0.846125	−	0.532984i	$-0.821071\pi$
$83$	1.38191	−	4.25308i	0.151684	−	0.466837i	0.997810	+	0.0661472i	$0.0210707\pi$
$84$	−2.03869	+	2.80601i	−0.222439	+	0.306161i
$85$	4.87310	−	1.58337i	0.528562	−	0.171740i
$86$	−2.35064	−	7.23453i	−0.253476	−	0.780119i
$87$	1.40098	+	0.455205i	0.150200	+	0.0488031i
$88$	−0.368029	+	0.267388i	−0.0392320	+	0.0285037i
$89$	10.1803	+	3.30777i	1.07911	+	0.350622i	0.794027	−	0.607882i	$-0.207981\pi$
$89$	10.1803	+	3.30777i	1.07911	+	0.350622i	0.285078	+	0.958504i	$0.407981\pi$
$90$		−	0.111737i		−	0.0117781i
$91$	3.90526	−	1.26890i	0.409383	−	0.133017i
$92$	0.853131	−	0.277199i	0.0889450	−	0.0289000i
$93$		−	8.02064i		−	0.831701i
$94$	7.70876	+	2.50473i	0.795098	+	0.258343i
$95$	−0.855400	+	0.621484i	−0.0877622	+	0.0637630i
$96$	−10.0005	−	3.24935i	−1.02067	−	0.331635i
$97$	3.79290	+	11.6733i	0.385111	+	1.18525i	0.936400	+	0.350935i	$0.114136\pi$
$97$	3.79290	+	11.6733i	0.385111	+	1.18525i	−0.551289	+	0.834314i	$0.685864\pi$
$98$	3.75837	−	1.22117i	0.379653	−	0.123357i
$99$	0.0228695	−	0.0314771i	0.00229847	−	0.00316357i
$100$	−1.98288	+	6.10267i	−0.198288	+	0.610267i
$101$		−	11.9559i		−	1.18966i	−0.803853	−	0.594828i	$-0.797220\pi$
$101$		−	11.9559i		−	1.18966i	0.803853	−	0.594828i	$-0.202780\pi$
$102$	−3.46245	−	10.6563i	−0.342834	−	1.05513i
$103$	3.21348	−	9.89006i	0.316633	−	0.974496i	−0.658444	−	0.752630i	$-0.728785\pi$
$103$	3.21348	−	9.89006i	0.316633	−	0.974496i	0.975077	−	0.221867i	$-0.0712150\pi$
$104$	4.60561	+	6.33908i	0.451618	+	0.621598i
$105$	−0.930727	+	1.28104i	−0.0908296	+	0.125016i
$106$	1.09229	+	3.36171i	0.106092	+	0.326518i
$107$	11.3846	−	8.27143i	1.10059	−	0.799629i	0.119438	−	0.992842i	$-0.461891\pi$
$107$	11.3846	−	8.27143i	1.10059	−	0.799629i	0.981157	+	0.193213i	$0.0618907\pi$
$108$	−6.96092			−0.669815
$109$	−8.99979			−0.862023			−0.431012	−	0.902346i	$-0.641843\pi$
$109$	−8.99979			−0.862023			−0.431012	+	0.902346i	$0.641843\pi$
$110$	−0.0690960	+	0.0502012i	−0.00658805	+	0.00478650i
$111$			19.6387i			1.86403i
$112$	0.605813	+	0.833829i	0.0572439	+	0.0787895i
$113$	−3.98317	−	2.89394i	−0.374705	−	0.272239i	0.384454	−	0.923144i	$-0.374390\pi$
$113$	−3.98317	−	2.89394i	−0.374705	−	0.272239i	−0.759159	+	0.650905i	$0.774390\pi$
$114$	1.35904	+	1.87056i	0.127286	+	0.175194i
$115$	0.389482	−	0.126550i	0.0363194	−	0.0118009i
$116$	0.673489	−	0.926979i	0.0625319	−	0.0860678i
$117$	−0.542175	−	0.393913i	−0.0501241	−	0.0364173i
$118$	−5.11530	−	3.71648i	−0.470901	−	0.342130i
$119$	−3.43200	+	10.5626i	−0.314611	+	0.968272i
$120$	−2.87366	−	0.933707i	−0.262328	−	0.0852354i
$121$	10.9703			0.997296
$122$	−5.00973	+	3.41849i	−0.453560	+	0.309495i
$123$	4.69386			0.423231
$124$	−5.93339	−	1.92787i	−0.532834	−	0.173128i
$125$	−1.89066	+	5.81886i	−0.169106	+	0.520455i
$126$	0.195939	+	0.142358i	0.0174556	+	0.0126822i
$127$	−5.67893	−	4.12598i	−0.503923	−	0.366122i	0.306590	−	0.951842i	$-0.400812\pi$
$127$	−5.67893	−	4.12598i	−0.503923	−	0.366122i	−0.810514	+	0.585720i	$0.800812\pi$
$128$	−5.48812	+	7.55374i	−0.485085	+	0.667663i
$129$	16.7323	−	5.43665i	1.47319	−	0.478670i
$130$	0.864687	+	1.19014i	0.0758380	+	0.104382i
$131$	−0.458499	−	0.333119i	−0.0400592	−	0.0291047i	0.567575	−	0.823321i	$-0.307882\pi$
$131$	−0.458499	−	0.333119i	−0.0400592	−	0.0291047i	−0.607635	+	0.794217i	$0.707882\pi$
$132$	−0.254324	−	0.350046i	−0.0221360	−	0.0304676i
$133$		−	2.29180i		−	0.198724i
$134$	2.90305	−	2.10919i	0.250786	−	0.182206i
$135$	−3.17789			−0.273509
$136$	−21.1928			−1.81727
$137$	−9.76837	+	7.09713i	−0.834568	+	0.606349i	−0.920848	−	0.389922i	$-0.872502\pi$
$137$	−9.76837	+	7.09713i	−0.834568	+	0.606349i	0.0862801	+	0.996271i	$0.472502\pi$
$138$	−0.276736	−	0.851706i	−0.0235573	−	0.0725020i
$139$	−2.10140	+	2.89233i	−0.178238	+	0.245324i	−0.888783	−	0.458328i	$-0.848449\pi$
$139$	−2.10140	+	2.89233i	−0.178238	+	0.245324i	0.710545	+	0.703652i	$0.248449\pi$
$140$	0.723952	+	0.996435i	0.0611851	+	0.0842141i
$141$	−5.79302	+	17.8291i	−0.487860	+	1.50148i
$142$	1.56329	+	4.81132i	0.131189	+	0.403757i
$143$			0.512248i			0.0428363i
$144$	0.0519804	−	0.159979i	0.00433170	−	0.0133316i
$145$	0.307470	−	0.423196i	0.0255340	−	0.0351445i
$146$	9.21315	−	2.99353i	0.762486	−	0.247747i
$147$	2.82436	+	8.69249i	0.232949	+	0.716945i
$148$	14.5280	+	4.72045i	1.19420	+	0.388018i
$149$	10.2709	−	7.46225i	0.841425	−	0.611331i	−0.0813431	−	0.996686i	$-0.525921\pi$
$149$	10.2709	−	7.46225i	0.841425	−	0.611331i	0.922768	+	0.385355i	$0.125921\pi$
$150$	6.09248	+	1.97957i	0.497449	+	0.161631i
$151$		−	18.2540i		−	1.48549i	−0.669574	−	0.742745i	$-0.733523\pi$
$151$		−	18.2540i		−	1.48549i	0.669574	−	0.742745i	$-0.266477\pi$
$152$	4.15918	−	1.35140i	0.337354	−	0.109613i
$153$	1.72389	−	0.560125i	0.139368	−	0.0452834i
$154$		−	0.185123i		−	0.0149177i
$155$	−2.70879	−	0.880138i	−0.217575	−	0.0706944i
$156$	−6.02935	+	4.38058i	−0.482734	+	0.350727i
$157$	15.7204	+	5.10787i	1.25463	+	0.407653i	0.859576	−	0.511007i	$-0.170727\pi$
$157$	15.7204	+	5.10787i	1.25463	+	0.407653i	0.395050	+	0.918660i	$0.370727\pi$
$158$	0.540221	+	1.66263i	0.0429777	+	0.132272i
$159$	−7.77509	+	2.52628i	−0.616604	+	0.200347i
$160$	−2.19478	+	3.02086i	−0.173513	+	0.238820i
$161$	−0.274302	+	0.844215i	−0.0216180	+	0.0665335i
$162$			7.47489i			0.587283i
$163$	−1.38525	−	4.26337i	−0.108501	−	0.333933i	0.882035	−	0.471184i	$-0.156173\pi$
$163$	−1.38525	−	4.26337i	−0.108501	−	0.333933i	−0.990536	+	0.137251i	$0.956173\pi$
$164$	1.12824	−	3.47235i	0.0881004	−	0.271145i
$165$	−0.116107	−	0.159808i	−0.00903892	−	0.0124410i
$166$	−2.04116	+	2.80942i	−0.158425	+	0.218053i
$167$	−4.64043	−	14.2818i	−0.359087	−	1.10516i	−0.953601	−	0.301072i	$-0.902656\pi$
$167$	−4.64043	−	14.2818i	−0.359087	−	1.10516i	0.594514	−	0.804085i	$-0.297344\pi$
$168$	5.29848	−	3.84957i	0.408787	−	0.297001i
$169$	−4.17682			−0.321294
$170$	−3.97888			−0.305166
$171$	−0.302603	+	0.219854i	−0.0231406	+	0.0168126i
$172$		−	13.6847i		−	1.04345i
$173$	6.89937	+	9.49617i	0.524549	+	0.721980i	0.986288	−	0.165036i	$-0.0527740\pi$
$173$	6.89937	+	9.49617i	0.524549	+	0.721980i	−0.461738	+	0.887016i	$0.652774\pi$
$174$	−0.925431	−	0.672365i	−0.0701567	−	0.0509718i
$175$	−3.73224	−	5.13699i	−0.282131	−	0.388320i
$176$	−0.122282	+	0.0397318i	−0.00921735	+	0.00299490i
$177$	8.59561	−	11.8308i	0.646085	−	0.889260i
$178$	−6.72468	−	4.88577i	−0.504036	−	0.366204i
$179$	−13.9563	−	10.1399i	−1.04314	−	0.757889i	−0.0722473	−	0.997387i	$-0.523017\pi$
$179$	−13.9563	−	10.1399i	−1.04314	−	0.757889i	−0.970897	+	0.239498i	$0.923017\pi$
$180$	0.0621172	−	0.191177i	0.00462994	−	0.0142495i
$181$	−1.97264	−	0.640949i	−0.146625	−	0.0476414i	0.234785	−	0.972047i	$-0.424561\pi$
$181$	−1.97264	−	0.640949i	−0.146625	−	0.0476414i	−0.381410	+	0.924406i	$0.624561\pi$
$182$	−3.18864			−0.236358
$183$	−7.90640	−	11.5867i	−0.584458	−	0.856513i
$184$	−1.69384			−0.124871
$185$	6.63253	+	2.15504i	0.487633	+	0.158442i
$186$	−1.92466	+	5.92348i	−0.141123	+	0.434331i
$187$	−1.12088	−	0.814366i	−0.0819668	−	0.0595523i
$188$	11.7969	+	8.57095i	0.860377	+	0.625101i
$189$	4.04877	−	5.57265i	0.294505	−	0.405351i
$190$	0.780871	−	0.253721i	0.0566504	−	0.0184068i
$191$	−12.5735	−	17.3060i	−0.909788	−	1.25222i	−0.967239	−	0.253868i	$-0.918297\pi$
$191$	−12.5735	−	17.3060i	−0.909788	−	1.25222i	0.0574509	−	0.998348i	$-0.481703\pi$
$192$	4.43930	+	3.22534i	0.320379	+	0.232769i
$193$	−8.23230	−	11.3308i	−0.592574	−	0.815608i	0.402429	−	0.915451i	$-0.368166\pi$
$193$	−8.23230	−	11.3308i	−0.592574	−	0.815608i	−0.995003	+	0.0998429i	$0.968166\pi$
$194$		−	9.53127i		−	0.684305i
$195$	−2.75260	+	1.99988i	−0.197118	+	0.143214i
$196$	7.10928			0.507806
$197$	10.7214			0.763867			0.381933	−	0.924190i	$-0.375258\pi$
$197$	10.7214			0.763867			0.381933	+	0.924190i	$0.375258\pi$
$198$	−0.0244431	+	0.0177590i	−0.00173710	+	0.00126207i
$199$	6.13292	+	18.8752i	0.434751	+	1.33803i	0.893341	+	0.449379i	$0.148355\pi$
$199$	6.13292	+	18.8752i	0.434751	+	1.33803i	−0.458590	+	0.888648i	$0.651645\pi$
$200$	7.12188	−	9.80242i	0.503593	−	0.693136i
$201$	4.87821	+	6.71429i	0.344083	+	0.473589i
$202$	−2.86897	+	8.82978i	−0.201860	+	0.621261i
$203$	0.350374	+	1.07834i	0.0245914	+	0.0756847i
$204$		−	20.1573i		−	1.41130i
$205$	0.515077	−	1.58524i	0.0359745	−	0.110718i
$206$	−4.74649	+	6.53299i	−0.330704	+	0.455175i
$207$	0.137782	−	0.0447680i	0.00957648	−	0.00311159i
$208$	0.684358	+	2.10624i	0.0474517	+	0.146041i
$209$	0.271907	+	0.0883478i	0.0188082	+	0.00611115i
$210$	0.994770	−	0.722743i	0.0686457	−	0.0498740i
$211$	14.0230	+	4.55633i	0.965380	+	0.313671i	0.748950	−	0.662627i	$-0.230559\pi$
$211$	14.0230	+	4.55633i	0.965380	+	0.313671i	0.216430	+	0.976298i	$0.430559\pi$
$212$			6.35896i			0.436735i
$213$	−11.1278	+	3.61564i	−0.762464	+	0.247740i
$214$	−10.3927	+	3.37680i	−0.710432	+	0.230833i
$215$		−	6.24753i		−	0.426078i
$216$	12.5007	+	4.06173i	0.850567	+	0.276366i
$217$	4.99450	−	3.62871i	0.339048	−	0.246333i
$218$	6.64661	+	2.15961i	0.450165	+	0.146268i
$219$	6.92355	+	21.3085i	0.467850	+	1.43990i
$220$	−0.146128	+	0.0474799i	−0.00985196	+	0.00320110i
$221$	−14.0270	+	19.3065i	−0.943557	+	1.29870i
$222$	4.71256	−	14.5038i	0.316287	−	0.973430i
$223$			17.4934i			1.17145i	0.810511	+	0.585723i	$0.199189\pi$
$223$			17.4934i			1.17145i	−0.810511	+	0.585723i	$0.800811\pi$
$224$	−2.50104	−	7.69742i	−0.167108	−	0.514305i
$225$	−0.320237	+	0.985588i	−0.0213491	+	0.0657059i
$226$	2.24725	+	3.09307i	0.149485	+	0.205748i
$227$	−16.4800	+	22.6828i	−1.09382	+	1.50551i	−0.250484	+	0.968121i	$0.580590\pi$
$227$	−16.4800	+	22.6828i	−1.09382	+	1.50551i	−0.843334	+	0.537390i	$0.819410\pi$
$228$	1.28537	+	3.95596i	0.0851257	+	0.261990i
$229$	0.838247	−	0.609022i	0.0553929	−	0.0402453i	−0.559744	−	0.828665i	$-0.689101\pi$
$229$	0.838247	−	0.609022i	0.0553929	−	0.0402453i	0.615137	+	0.788420i	$0.289101\pi$
$230$	−0.318012			−0.0209691
$231$	0.428159			0.0281708
$232$	−1.75038	+	1.27172i	−0.114918	+	0.0834928i
$233$			7.36539i			0.482523i	0.970460	+	0.241261i	$0.0775611\pi$
$233$			7.36539i			0.482523i	−0.970460	+	0.241261i	$0.922439\pi$
$234$	0.305888	+	0.421019i	0.0199965	+	0.0275228i
$235$	5.38567	+	3.91292i	0.351323	+	0.255251i
$236$	−6.68597	−	9.20244i	−0.435219	−	0.599028i
$237$	−3.84539	+	1.24944i	−0.249785	+	0.0811601i
$238$	5.06926	−	6.97724i	0.328592	−	0.452267i
$239$	−14.1537	−	10.2833i	−0.915527	−	0.665169i	0.0268798	−	0.999639i	$-0.491443\pi$
$239$	−14.1537	−	10.2833i	−0.915527	−	0.665169i	−0.942407	+	0.334470i	$0.891443\pi$
$240$	−0.690905	−	0.501972i	−0.0445977	−	0.0324021i
$241$	−2.05299	+	6.31847i	−0.132245	+	0.407008i	−0.995151	−	0.0983556i	$-0.968642\pi$
$241$	−2.05299	+	6.31847i	−0.132245	+	0.407008i	0.862906	+	0.505364i	$0.168642\pi$
$242$	−8.10186	−	2.63245i	−0.520807	−	0.169221i
$243$	−2.33981			−0.150099
$244$	−10.4718	+	3.06385i	−0.670391	+	0.196143i
$245$	3.24562			0.207355
$246$	−3.46655	−	1.12635i	−0.221019	−	0.0718136i
$247$	1.52174	−	4.68344i	0.0968261	−	0.298000i
$248$	9.53052	+	6.92432i	0.605188	+	0.439695i
$249$	−6.49773	−	4.72088i	−0.411777	−	0.299173i
$250$	2.79262	−	3.84371i	0.176621	−	0.243098i
$251$	−12.8737	+	4.18293i	−0.812583	+	0.264024i	−0.685691	−	0.727892i	$-0.740500\pi$
$251$	−12.8737	+	4.18293i	−0.812583	+	0.264024i	−0.126892	+	0.991917i	$0.540500\pi$
$252$	0.256102	+	0.352494i	0.0161329	+	0.0222051i
$253$	−0.0895862	−	0.0650882i	−0.00563223	−	0.00409206i
$254$	3.20397	+	4.40989i	0.201035	+	0.276701i
$255$		−	9.20249i		−	0.576282i
$256$	10.8093	−	7.85341i	0.675581	−	0.490838i
$257$	21.2807			1.32745			0.663726	−	0.747976i	$-0.268974\pi$
$257$	21.2807			1.32745			0.663726	+	0.747976i	$0.268974\pi$
$258$	−13.6619			−0.850551
$259$	−12.2291	+	8.88499i	−0.759882	+	0.552087i
$260$	0.817814	+	2.51697i	0.0507187	+	0.156096i
$261$	0.108769	−	0.149708i	0.00673265	−	0.00926670i
$262$	0.258679	+	0.356041i	0.0159812	+	0.0219963i
$263$	−4.05985	+	12.4949i	−0.250341	+	0.770471i	0.744371	+	0.667767i	$0.232750\pi$
$263$	−4.05985	+	12.4949i	−0.250341	+	0.770471i	−0.994712	+	0.102705i	$0.967250\pi$
$264$	0.252472	+	0.777028i	0.0155386	+	0.0478228i
$265$			2.90308i			0.178335i
$266$	−0.549947	+	1.69256i	−0.0337194	+	0.103778i
$267$	11.3000	−	15.5531i	0.691547	−	0.951833i
$268$	6.13954	−	1.99486i	0.375032	−	0.121855i
$269$	4.18822	+	12.8900i	0.255360	+	0.785918i	0.993758	+	0.111553i	$0.0355826\pi$
$269$	4.18822	+	12.8900i	0.255360	+	0.785918i	−0.738398	+	0.674365i	$0.764417\pi$
$270$	2.34697	+	0.762575i	0.142832	+	0.0464089i
$271$	−13.7878	+	10.0174i	−0.837549	+	0.608515i	−0.921685	−	0.387939i	$-0.873187\pi$
$271$	−13.7878	+	10.0174i	−0.837549	+	0.608515i	0.0841357	+	0.996454i	$0.473187\pi$
$272$	−5.69676	−	1.85099i	−0.345417	−	0.112233i
$273$		−	7.37480i		−	0.446343i
$274$	8.91728	−	2.89740i	0.538712	−	0.175038i
$275$	0.753345	−	0.244777i	0.0454284	−	0.0147606i
$276$		−	1.61107i		−	0.0969753i
$277$	7.47382	+	2.42839i	0.449059	+	0.145908i	0.524811	−	0.851219i	$-0.324136\pi$
$277$	7.47382	+	2.42839i	0.449059	+	0.145908i	−0.0757526	+	0.997127i	$0.524136\pi$
$278$	2.24600	−	1.63181i	0.134706	−	0.0978696i
$279$	−0.958249	−	0.311354i	−0.0573689	−	0.0186403i
$280$	−0.718680	−	2.21187i	−0.0429494	−	0.132185i
$281$	13.9690	−	4.53881i	0.833321	−	0.270762i	0.138878	−	0.990310i	$-0.455651\pi$
$281$	13.9690	−	4.53881i	0.833321	−	0.270762i	0.694444	+	0.719547i	$0.255651\pi$
$282$	8.55663	−	11.7772i	0.509540	−	0.701322i
$283$	4.84506	−	14.9116i	0.288009	−	0.886401i	−0.697472	−	0.716613i	$-0.745692\pi$
$283$	4.84506	−	14.9116i	0.288009	−	0.886401i	0.985481	−	0.169788i	$-0.0543084\pi$
$284$			9.10103i			0.540047i
$285$	0.586814	+	1.80603i	0.0347598	+	0.106980i
$286$	0.122921	−	0.378311i	0.00726844	−	0.0223700i
$287$	2.12360	+	2.92289i	0.125352	+	0.172533i
$288$	−0.776418	+	1.06865i	−0.0457508	+	0.0629706i
$289$	−14.6924	−	45.2185i	−0.864258	−	2.65991i
$290$	−0.328627	+	0.238762i	−0.0192976	+	0.0140206i
$291$	22.0443			1.29226
$292$	17.4275			1.01987
$293$	0.384893	−	0.279641i	0.0224857	−	0.0163368i	−0.576486	−	0.817107i	$-0.695576\pi$
$293$	0.384893	−	0.279641i	0.0224857	−	0.0163368i	0.598971	+	0.800770i	$0.295576\pi$
$294$		−	7.09741i		−	0.413929i
$295$	−3.05236	−	4.20122i	−0.177715	−	0.244604i
$296$	−23.3357	−	16.9544i	−1.35636	−	0.985453i
$297$	0.505079	+	0.695182i	0.0293077	+	0.0403385i
$298$	−9.37603	+	3.04646i	−0.543139	+	0.176477i
$299$	−1.12111	+	1.54307i	−0.0648353	+	0.0892381i
$300$	9.32347	+	6.77390i	0.538291	+	0.391091i
$301$	10.9555	+	7.95962i	0.631463	+	0.458785i
$302$	−4.38028	+	13.4811i	−0.252057	+	0.775752i
$303$	−20.4218	−	6.63545i	−1.17320	−	0.381197i
$304$	1.23604			0.0708920
$305$	−4.78074	+	1.39875i	−0.273744	+	0.0800922i
$306$	−1.40755			−0.0804643
$307$	7.34978	+	2.38809i	0.419474	+	0.136295i	0.511146	−	0.859494i	$-0.329221\pi$
$307$	7.34978	+	2.38809i	0.419474	+	0.136295i	−0.0916720	+	0.995789i	$0.529221\pi$
$308$	0.102914	−	0.316737i	0.00586408	−	0.0180478i
$309$	−15.1097	−	10.9779i	−0.859562	−	0.624508i
$310$	1.78932	+	1.30002i	0.101626	+	0.0738360i
$311$	1.94581	−	2.67818i	0.110337	−	0.151866i	−0.750277	−	0.661123i	$-0.770080\pi$
$311$	1.94581	−	2.67818i	0.110337	−	0.151866i	0.860614	+	0.509258i	$0.170080\pi$
$312$	13.3839	−	4.34868i	0.757712	−	0.246196i
$313$	2.22806	+	3.06667i	0.125938	+	0.173338i	0.867330	−	0.497734i	$-0.165834\pi$
$313$	2.22806	+	3.06667i	0.125938	+	0.173338i	−0.741392	+	0.671072i	$0.765834\pi$
$314$	−10.3843	−	7.54463i	−0.586020	−	0.425768i
$315$	0.116919	+	0.160925i	0.00658764	+	0.00906711i
$316$			3.14501i			0.176921i
$317$	1.65683	−	1.20376i	0.0930568	−	0.0676097i	−0.540284	−	0.841483i	$-0.681683\pi$
$317$	1.65683	−	1.20376i	0.0930568	−	0.0676097i	0.633341	+	0.773873i	$0.281683\pi$
$318$	6.34834			0.355997
$319$	−0.141444			−0.00791937
$320$	1.57643	−	1.14534i	0.0881249	−	0.0640265i
$321$	−7.80999	−	24.0367i	−0.435911	−	1.34160i
$322$	0.405161	−	0.557656i	0.0225787	−	0.0310769i
$323$	7.82884	+	10.7755i	0.435608	+	0.599564i
$324$	−4.15546	+	12.7892i	−0.230859	+	0.710511i
$325$	−4.21614	−	12.9759i	−0.233869	−	0.719775i
$326$			3.48103i			0.192796i
$327$	−4.99483	+	15.3725i	−0.276215	+	0.850102i
$328$	−4.05227	+	5.57747i	−0.223749	+	0.307964i
$329$	−13.7232	+	4.45892i	−0.756582	+	0.245828i
$330$	0.0474006	+	0.145884i	0.00260932	+	0.00803066i
$331$	20.0131	+	6.50266i	1.10002	+	0.357418i	0.802111	−	0.597176i	$-0.203710\pi$
$331$	20.0131	+	6.50266i	1.10002	+	0.357418i	0.297910	+	0.954594i	$0.403710\pi$
$332$	−5.05416	+	3.67206i	−0.277383	+	0.201531i
$333$	2.34630	+	0.762358i	0.128576	+	0.0417769i
$334$			11.6610i			0.638064i
$335$	2.80290	−	0.910718i	0.153139	−	0.0497579i
$336$	1.76048	−	0.572016i	0.0960423	−	0.0312060i
$337$		−	4.44526i		−	0.242149i	−0.992643	−	0.121074i	$-0.961366\pi$
$337$		−	4.44526i		−	0.242149i	0.992643	−	0.121074i	$-0.0386340\pi$
$338$	3.08470	+	1.00228i	0.167786	+	0.0545169i
$339$	−7.15376	+	5.19751i	−0.388539	+	0.282290i
$340$	−6.80768	−	2.21195i	−0.369198	−	0.119960i
$341$	0.237987	+	0.732448i	0.0128877	+	0.0396643i
$342$	0.276238	−	0.0897551i	0.0149372	−	0.00485340i
$343$	−9.82291	+	13.5201i	−0.530387	+	0.730015i
$344$	−7.98511	+	24.5756i	−0.430528	+	1.32503i
$345$		−	0.735508i		−	0.0395984i
$346$	−2.81666	−	8.66879i	−0.151425	−	0.466037i
$347$	6.00280	−	18.4747i	0.322247	−	0.991774i	−0.650421	−	0.759574i	$-0.725407\pi$
$347$	6.00280	−	18.4747i	0.322247	−	0.991774i	0.972668	−	0.232200i	$-0.0745925\pi$
$348$	−1.20959	−	1.66485i	−0.0648407	−	0.0892455i
$349$	8.09416	−	11.1407i	0.433270	−	0.596346i	−0.535430	−	0.844580i	$-0.679850\pi$
$349$	8.09416	−	11.1407i	0.433270	−	0.596346i	0.968700	+	0.248234i	$0.0798503\pi$
$350$	1.52368	+	4.68942i	0.0814444	+	0.250660i
$351$	11.9741	−	8.69970i	0.639131	−	0.464356i
$352$	1.00966			0.0538150
$353$	−11.1114			−0.591400			−0.295700	−	0.955281i	$-0.595553\pi$
$353$	−11.1114			−0.591400			−0.295700	+	0.955281i	$0.595553\pi$
$354$	−9.18707	+	6.67480i	−0.488287	+	0.354762i
$355$			4.15492i			0.220520i
$356$	−8.78952	−	12.0977i	−0.465843	−	0.641178i
$357$	16.1372	+	11.7244i	0.854072	+	0.620519i
$358$	7.87396	+	10.8376i	0.416152	+	0.572784i
$359$	12.8376	−	4.17121i	0.677545	−	0.220148i	0.0500249	−	0.998748i	$-0.484070\pi$
$359$	12.8376	−	4.17121i	0.677545	−	0.220148i	0.627520	+	0.778600i	$0.284070\pi$
$360$	−0.223105	+	0.307078i	−0.0117587	+	0.0161844i
$361$	13.1478	+	9.55241i	0.691987	+	0.502758i
$362$	1.30305	+	0.946719i	0.0684867	+	0.0497585i
$363$	6.08843	−	18.7383i	0.319560	−	0.983504i
$364$	−5.45562	−	1.77264i	−0.285952	−	0.0929115i
$365$	7.95621			0.416447
$366$	3.05874	+	10.4544i	0.159883	+	0.546458i
$367$	28.8255			1.50468			0.752340	−	0.658775i	$-0.228925\pi$
$367$	28.8255			1.50468			0.752340	+	0.658775i	$0.228925\pi$
$368$	−0.455313	−	0.147940i	−0.0237348	−	0.00771191i
$369$	0.182211	−	0.560789i	0.00948554	−	0.0291935i
$370$	−4.38119	−	3.18312i	−0.227767	−	0.165483i
$371$	−5.09075	−	3.69864i	−0.264298	−	0.192024i
$372$	−6.58600	+	9.06485i	−0.341468	+	0.469990i
$373$	−30.6128	+	9.94669i	−1.58507	+	0.515020i	−0.963356	−	0.268225i	$-0.913563\pi$
$373$	−30.6128	+	9.94669i	−1.58507	+	0.515020i	−0.621713	+	0.783245i	$0.713563\pi$
$374$	0.632385	+	0.870403i	0.0326998	+	0.0450074i
$375$	8.88987	+	6.45887i	0.459071	+	0.333535i
$376$	−16.1842	−	22.2756i	−0.834636	−	1.14878i
$377$			2.43630i			0.125476i
$378$	−4.32737	+	3.14401i	−0.222576	+	0.161711i
$379$	−12.1417			−0.623677			−0.311838	−	0.950135i	$-0.600945\pi$
$379$	−12.1417			−0.623677			−0.311838	+	0.950135i	$0.600945\pi$
$380$	1.47708			0.0757729
$381$	−10.1994	+	7.41026i	−0.522529	+	0.379639i
$382$	5.13313	+	15.7981i	0.262634	+	0.808304i
$383$	−8.78082	+	12.0858i	−0.448679	+	0.617553i	−0.972113	−	0.234513i	$-0.924651\pi$
$383$	−8.78082	+	12.0858i	−0.448679	+	0.617553i	0.523434	+	0.852066i	$0.324651\pi$
$384$	9.85665	+	13.5665i	0.502995	+	0.692314i
$385$	0.0469837	−	0.144601i	0.00239451	−	0.00736955i
$386$	3.36083	+	10.3436i	0.171062	+	0.526474i
$387$		−	2.21010i		−	0.112346i
$388$	5.29865	−	16.3076i	0.268998	−	0.827892i
$389$	8.45984	−	11.6440i	0.428931	−	0.590373i	−0.538777	−	0.842449i	$-0.681113\pi$
$389$	8.45984	−	11.6440i	0.428931	−	0.590373i	0.967707	+	0.252076i	$0.0811133\pi$
$390$	2.51277	−	0.816449i	0.127239	−	0.0413425i
$391$	−1.59416	−	4.90631i	−0.0806200	−	0.248123i
$392$	−12.7672	−	4.14830i	−0.644839	−	0.209521i
$393$	−0.823464	+	0.598281i	−0.0415382	+	0.0301793i
$394$	−7.91806	−	2.57273i	−0.398906	−	0.129612i
$395$			1.43580i			0.0722429i
$396$	−0.0516937	+	0.0167963i	−0.00259770	+	0.000844045i
$397$	−7.56030	+	2.45649i	−0.379441	+	0.123288i	−0.492527	−	0.870297i	$-0.663927\pi$
$397$	−7.56030	+	2.45649i	−0.379441	+	0.123288i	0.113086	+	0.993585i	$0.463927\pi$
$398$		−	15.4116i		−	0.772512i
$399$	−3.91462	−	1.27194i	−0.195976	−	0.0636765i
$400$	2.77055	−	2.01292i	0.138527	−	0.100646i
$401$	2.43793	+	0.792132i	0.121745	+	0.0395572i	0.369256	−	0.929328i	$-0.379613\pi$
$401$	2.43793	+	0.792132i	0.121745	+	0.0395572i	−0.247511	+	0.968885i	$0.579613\pi$
$402$	−1.99153	−	6.12929i	−0.0993283	−	0.305701i
$403$	12.6160	−	4.09919i	0.628448	−	0.204195i
$404$	−9.81736	+	13.5124i	−0.488432	+	0.672269i
$405$	−1.89711	+	5.83869i	−0.0942680	+	0.290127i
$406$		−	0.880463i		−	0.0436967i
$407$	−0.582716	−	1.79342i	−0.0288842	−	0.0888963i
$408$	−11.7619	+	36.1994i	−0.582301	+	1.79214i
$409$	−4.60227	−	6.33448i	−0.227568	−	0.313220i	0.679930	−	0.733277i	$-0.262010\pi$
$409$	−4.60227	−	6.33448i	−0.227568	−	0.313220i	−0.907498	+	0.420057i	$0.862010\pi$
$410$	−0.760799	+	1.04715i	−0.0375732	+	0.0517150i
$411$	6.70121	+	20.6242i	0.330546	+	1.01732i
$412$	−11.7529	+	8.53896i	−0.579023	+	0.420684i
$413$	11.2560			0.553870
$414$	−0.112498			−0.00552900
$415$	−2.30739	+	1.67642i	−0.113265	+	0.0822921i
$416$		−	17.3908i		−	0.852655i
$417$	3.77411	+	5.19462i	0.184819	+	0.254382i
$418$	−0.179611	−	0.130495i	−0.00878506	−	0.00638272i
$419$	−12.2558	−	16.8686i	−0.598734	−	0.824086i	0.396858	−	0.917880i	$-0.370101\pi$
$419$	−12.2558	−	16.8686i	−0.598734	−	0.824086i	−0.995592	+	0.0937938i	$0.970101\pi$
$420$	2.10380	−	0.683565i	0.102655	−	0.0333546i
$421$	−9.32480	+	12.8345i	−0.454463	+	0.625515i	−0.973349	−	0.229329i	$-0.926347\pi$
$421$	−9.32480	+	12.8345i	−0.454463	+	0.625515i	0.518886	+	0.854843i	$0.326347\pi$
$422$	−9.26302	−	6.72998i	−0.450917	−	0.327610i
$423$	1.90521	+	1.38422i	0.0926346	+	0.0673030i
$424$	3.71049	−	11.4197i	0.180197	−	0.554590i
$425$	35.0961	+	11.4034i	1.70241	+	0.553147i
$426$	9.08583			0.440210
$427$	3.63807	−	10.1654i	0.176058	−	0.491940i
$428$	−19.6587			−0.950241
$429$	0.874970	+	0.284295i	0.0422439	+	0.0137259i
$430$	−1.49917	+	4.61398i	−0.0722966	+	0.222506i
$431$	24.0040	+	17.4399i	1.15623	+	0.840052i	0.989297	−	0.145916i	$-0.0466131\pi$
$431$	24.0040	+	17.4399i	1.15623	+	0.840052i	0.166935	+	0.985968i	$0.446613\pi$
$432$	3.00551	+	2.18363i	0.144603	+	0.105060i
$433$	−5.42306	+	7.46421i	−0.260616	+	0.358707i	−0.919194	−	0.393806i	$-0.871158\pi$
$433$	−5.42306	+	7.46421i	−0.260616	+	0.358707i	0.658578	+	0.752513i	$0.271158\pi$
$434$	−4.55934	+	1.48142i	−0.218855	+	0.0711104i
$435$	−0.552216	−	0.760060i	−0.0264767	−	0.0364421i
$436$	10.1715	+	7.39000i	0.487125	+	0.353917i
$437$	0.625720	+	0.861229i	0.0299322	+	0.0411982i
$438$		−	17.3984i		−	0.831326i
$439$	10.7221	−	7.79005i	0.511737	−	0.371799i	−0.301745	−	0.953389i	$-0.597569\pi$
$439$	10.7221	−	7.79005i	0.511737	−	0.371799i	0.813482	+	0.581590i	$0.197569\pi$
$440$	0.290128			0.0138313
$441$	1.14816			0.0546741
$442$	14.9922	−	10.8925i	0.713106	−	0.518102i
$443$	−11.4041	−	35.0981i	−0.541823	−	1.66756i	−0.728426	−	0.685124i	$-0.759748\pi$
$443$	−11.4041	−	35.0981i	−0.541823	−	1.66756i	0.186603	−	0.982435i	$-0.440252\pi$
$444$	16.1260	−	22.1955i	0.765305	−	1.05335i
$445$	−4.01270	−	5.52301i	−0.190220	−	0.261816i
$446$	4.19777	−	12.9194i	0.198770	−	0.611752i
$447$	−7.04595	−	21.6852i	−0.333262	−	1.02568i
$448$			4.22359i			0.199546i
$449$	−4.09238	+	12.5951i	−0.193131	+	0.594398i	0.806862	+	0.590740i	$0.201164\pi$
$449$	−4.09238	+	12.5951i	−0.193131	+	0.594398i	−0.999993	+	0.00365737i	$0.998836\pi$
$450$	0.473009	−	0.651041i	0.0222979	−	0.0306904i
$451$	−0.428645	+	0.139275i	−0.0201841	+	0.00655821i
$452$	2.12543	+	6.54140i	0.0999718	+	0.307682i
$453$	−31.1796	−	10.1309i	−1.46495	−	0.475990i
$454$	17.6140	−	12.7973i	0.826667	−	0.600609i
$455$	−2.49067	−	0.809268i	−0.116764	−	0.0379391i
$456$		−	7.85431i		−	0.367812i
$457$	3.77018	−	1.22500i	0.176361	−	0.0573033i	−0.219505	−	0.975611i	$-0.570444\pi$
$457$	3.77018	−	1.22500i	0.176361	−	0.0573033i	0.395867	+	0.918308i	$0.370444\pi$
$458$	−0.765213	+	0.248633i	−0.0357561	+	0.0116179i
$459$			40.0319i			1.86853i
$460$	−0.544104	−	0.176790i	−0.0253690	−	0.00824287i
$461$	18.2107	−	13.2308i	0.848155	−	0.616221i	−0.0764816	−	0.997071i	$-0.524369\pi$
$461$	18.2107	−	13.2308i	0.848155	−	0.616221i	0.924637	+	0.380850i	$0.124369\pi$
$462$	−0.316208	−	0.102742i	−0.0147113	−	0.00478001i
$463$	−9.23620	−	28.4261i	−0.429243	−	1.32107i	−0.898873	−	0.438210i	$-0.855613\pi$
$463$	−9.23620	−	28.4261i	−0.429243	−	1.32107i	0.469630	−	0.882863i	$-0.344387\pi$
$464$	−0.581584	+	0.188968i	−0.0269994	+	0.00877263i
$465$	−3.00672	+	4.13840i	−0.139433	+	0.191914i
$466$	1.76742	−	5.43956i	0.0818742	−	0.251983i
$467$		−	20.5522i		−	0.951044i	−0.879704	−	0.475522i	$-0.842259\pi$
$467$		−	20.5522i		−	0.951044i	0.879704	−	0.475522i	$-0.157741\pi$
$468$	0.289307	+	0.890394i	0.0133732	+	0.0411585i
$469$	−1.97401	+	6.07538i	−0.0911514	+	0.280535i
$470$	−3.03852	−	4.18217i	−0.140157	−	0.192909i
$471$	17.4495	−	24.0172i	0.804030	−	1.10665i
$472$	6.63728	+	20.4274i	0.305506	+	0.940249i
$473$	−1.36668	+	0.992953i	−0.0628401	+	0.0456560i
$474$	3.13976			0.144214
$475$	−7.61492			−0.349397
$476$	12.5521	−	9.11963i	0.575324	−	0.417997i
$477$			1.02698i			0.0470222i
$478$	7.98533	+	10.9909i	0.365240	+	0.502710i
$479$	14.8959	+	10.8225i	0.680613	+	0.494494i	0.873561	−	0.486715i	$-0.161805\pi$
$479$	14.8959	+	10.8225i	0.680613	+	0.494494i	−0.192948	+	0.981209i	$0.561805\pi$
$480$	3.94183	+	5.42547i	0.179919	+	0.247638i
$481$	−30.8906	+	10.0370i	−1.40849	+	0.457646i
$482$	3.03239	−	4.17373i	0.138122	−	0.190108i
$483$	1.28977	+	0.937070i	0.0586864	+	0.0426381i
$484$	−12.3985	−	9.00802i	−0.563567	−	0.409456i
$485$	2.41901	−	7.44494i	0.109842	−	0.338057i
$486$	1.72802	+	0.561468i	0.0783847	+	0.0254687i
$487$	−22.6094			−1.02453			−0.512264	−	0.858828i	$-0.671193\pi$
$487$	−22.6094			−1.02453			−0.512264	+	0.858828i	$0.671193\pi$
$488$	20.5936	+	0.608174i	0.932227	+	0.0275307i
$489$	−8.05105			−0.364081
$490$	−2.39699	−	0.778828i	−0.108285	−	0.0351839i
$491$	−2.66932	+	8.21531i	−0.120465	+	0.370752i	−0.993048	−	0.117714i	$-0.962443\pi$
$491$	−2.66932	+	8.21531i	−0.120465	+	0.370752i	0.872583	+	0.488466i	$0.162443\pi$
$492$	−5.30495	−	3.85427i	−0.239166	−	0.173764i
$493$	−5.33100	−	3.87320i	−0.240096	−	0.174440i
$494$	−2.24770	+	3.09370i	−0.101129	+	0.139192i
$495$	−0.0235999	+	0.00766806i	−0.00106073	+	0.000344654i
$496$	1.95708	+	2.69370i	0.0878757	+	0.120950i
$497$	−7.28594	−	5.29355i	−0.326819	−	0.237448i
$498$	3.66593	+	5.04572i	0.164274	+	0.226104i
$499$			33.7367i			1.51026i	0.655573	+	0.755132i	$0.272427\pi$
$499$			33.7367i			1.51026i	−0.655573	+	0.755132i	$0.727573\pi$
$500$	6.91485	−	5.02394i	0.309242	−	0.224677i
$501$	−26.9701			−1.20493
$502$	10.5114			0.469146
$503$	19.4766	−	14.1506i	0.868420	−	0.630944i	−0.0617425	−	0.998092i	$-0.519666\pi$
$503$	19.4766	−	14.1506i	0.868420	−	0.630944i	0.930163	+	0.367148i	$0.119666\pi$
$504$	−0.254237	−	0.782462i	−0.0113246	−	0.0348536i
$505$	−4.48195	+	6.16887i	−0.199444	+	0.274511i
$506$	0.0505433	+	0.0695669i	0.00224692	+	0.00309263i
$507$	−2.31811	+	7.13441i	−0.102951	+	0.316850i
$508$	3.03029	+	9.32629i	0.134448	+	0.413787i
$509$			3.20965i			0.142265i	0.997467	+	0.0711326i	$0.0226614\pi$
$509$			3.20965i			0.142265i	−0.997467	+	0.0711326i	$0.977339\pi$
$510$	−2.20826	+	6.79631i	−0.0977832	+	0.300946i
$511$	−10.1366	+	13.9518i	−0.448415	+	0.617190i
$512$	7.89241	−	2.56440i	0.348798	−	0.113331i
$513$	−2.55271	−	7.85643i	−0.112705	−	0.346870i
$514$	−15.7164	−	5.10657i	−0.693221	−	0.225241i
$515$	−5.36557	+	3.89832i	−0.236435	+	0.171780i
$516$	−23.3748	−	7.59495i	−1.02902	−	0.334349i
$517$		−	1.80005i		−	0.0791660i
$518$	11.1637	−	3.62729i	0.490503	−	0.159374i
$519$	20.0495	−	6.51448i	0.880075	−	0.285954i
$520$		−	4.99729i		−	0.219146i
$521$	−9.78041	−	3.17785i	−0.428488	−	0.139224i	0.0868304	−	0.996223i	$-0.472326\pi$
$521$	−9.78041	−	3.17785i	−0.428488	−	0.139224i	−0.515318	+	0.856999i	$0.672326\pi$
$522$	−0.116254	+	0.0844633i	−0.00508829	+	0.00369686i
$523$	8.93207	+	2.90221i	0.390572	+	0.126905i	0.497718	−	0.867339i	$-0.334171\pi$
$523$	8.93207	+	2.90221i	0.390572	+	0.126905i	−0.107146	+	0.994243i	$0.534171\pi$
$524$	0.244656	+	0.752975i	0.0106879	+	0.0328939i
$525$	−10.8459	+	3.52403i	−0.473352	+	0.153801i
$526$	5.99664	−	8.25367i	0.261466	−	0.359877i
$527$	−11.0871	+	34.1226i	−0.482962	+	1.48640i
$528$			0.230920i			0.0100495i
$529$	6.97998	+	21.4822i	0.303477	+	0.934007i
$530$	0.696630	−	2.14401i	0.0302597	−	0.0931297i
$531$	−1.07979	−	1.48620i	−0.0468589	−	0.0644958i
$532$	−1.88187	+	2.59017i	−0.0815894	+	0.112298i
$533$	2.39894	+	7.38317i	0.103909	+	0.319800i
$534$	−12.0775	+	8.77484i	−0.522646	+	0.379724i
$535$	−8.97486			−0.388017
$536$	−12.1897			−0.526514
$537$	−25.0655	+	18.2112i	−1.08166	+	0.785871i
$538$		−	10.5247i		−	0.453751i
$539$	−0.515844	−	0.709998i	−0.0222190	−	0.0305818i
$540$	3.59162	+	2.60946i	0.154559	+	0.112293i
$541$	5.82174	+	8.01294i	0.250296	+	0.344503i	0.915615	−	0.402056i	$-0.131704\pi$
$541$	5.82174	+	8.01294i	0.250296	+	0.344503i	−0.665319	+	0.746559i	$0.731704\pi$
$542$	12.5865	−	4.08960i	0.540637	−	0.175664i
$543$	−2.18961	+	3.01373i	−0.0939650	+	0.129332i
$544$	38.0538	+	27.6477i	1.63154	+	1.18539i
$545$	4.64361	+	3.37378i	0.198910	+	0.144517i
$546$	−1.76968	+	5.44651i	−0.0757352	+	0.233089i
$547$	−13.7001	−	4.45143i	−0.585773	−	0.190329i	0.00111214	−	0.999999i	$-0.499646\pi$
$547$	−13.7001	−	4.45143i	−0.585773	−	0.190329i	−0.586885	+	0.809670i	$0.699646\pi$
$548$	16.8678			0.720556
$549$	−1.69121	+	0.494816i	−0.0721793	+	0.0211182i
$550$	−0.615105			−0.0262282
$551$	1.29321	+	0.420191i	0.0550928	+	0.0179007i
$552$	−0.940070	+	2.89324i	−0.0400120	+	0.123144i
$553$	−2.51777	−	1.82927i	−0.107067	−	0.0777885i
$554$	−4.93692	−	3.58688i	−0.209750	−	0.152392i
$555$	7.36203	−	10.1330i	0.312501	−	0.430121i
$556$	4.74996	−	1.54336i	0.201443	−	0.0654529i
$557$	11.3283	+	15.5920i	0.479993	+	0.660654i	0.978504	−	0.206230i	$-0.0661194\pi$
$557$	11.3283	+	15.5920i	0.479993	+	0.660654i	−0.498510	+	0.866884i	$0.666119\pi$
$558$	0.632982	+	0.459888i	0.0267963	+	0.0194686i
$559$	17.1031	+	23.5403i	0.723382	+	0.995650i
$560$		−	0.657333i		−	0.0277774i
$561$	−2.01310	+	1.46260i	−0.0849931	+	0.0617511i
$562$	−11.4057			−0.481119
$563$	40.1372			1.69158			0.845790	−	0.533516i	$-0.179130\pi$
$563$	40.1372			1.69158			0.845790	+	0.533516i	$0.179130\pi$
$564$	21.1872	−	15.3934i	0.892143	−	0.648180i
$565$	0.970329	+	2.98637i	0.0408220	+	0.125637i
$566$	−7.15644	+	9.85000i	−0.300808	+	0.414026i
$567$	−7.82156	−	10.7655i	−0.328475	−	0.452107i
$568$	5.31050	−	16.3440i	0.222824	−	0.685780i
$569$	2.35176	+	7.23797i	0.0985909	+	0.303432i	0.988173	−	0.153344i	$-0.0490042\pi$
$569$	2.35176	+	7.23797i	0.0985909	+	0.303432i	−0.889582	+	0.456776i	$0.849004\pi$
$570$		−	1.47462i		−	0.0617650i
$571$	1.35899	−	4.18253i	0.0568718	−	0.175033i	−0.918585	−	0.395223i	$-0.870667\pi$
$571$	1.35899	−	4.18253i	0.0568718	−	0.175033i	0.975457	+	0.220189i	$0.0706675\pi$
$572$	0.420623	−	0.578938i	0.0175871	−	0.0242066i
$573$	−36.5385	+	11.8721i	−1.52642	+	0.495963i
$574$	−0.866960	−	2.66823i	−0.0361862	−	0.111370i
$575$	2.80506	+	0.911418i	0.116979	+	0.0380088i
$576$	0.557670	−	0.405171i	0.0232362	−	0.0168821i
$577$	−5.60010	−	1.81958i	−0.233135	−	0.0757502i	0.190120	−	0.981761i	$-0.439112\pi$
$577$	−5.60010	−	1.81958i	−0.233135	−	0.0757502i	−0.423255	+	0.906011i	$0.639112\pi$
$578$			36.9208i			1.53570i
$579$	−23.9230	+	7.77305i	−0.994205	+	0.323037i
$580$	−0.694999	+	0.225819i	−0.0288583	+	0.00937662i
$581$		−	6.18200i		−	0.256473i
$582$	−16.2803	−	5.28980i	−0.674842	−	0.219269i
$583$	0.635065	−	0.461402i	0.0263017	−	0.0191093i
$584$	−31.2970	−	10.1690i	−1.29508	−	0.420797i
$585$	0.132078	+	0.406494i	0.00546075	+	0.0168065i
$586$	−0.351358	+	0.114163i	−0.0145145	+	0.00471604i
$587$	23.9389	−	32.9490i	0.988063	−	1.35995i	0.0556927	−	0.998448i	$-0.482263\pi$
$587$	23.9389	−	32.9490i	0.988063	−	1.35995i	0.932370	−	0.361504i	$-0.117737\pi$
$588$	3.94561	−	12.1433i	0.162714	−	0.500783i
$589$		−	7.40369i		−	0.305064i
$590$	1.24612	+	3.83518i	0.0513021	+	0.157892i
$591$	5.95031	−	18.3132i	0.244763	−	0.753303i
$592$	−4.79197	−	6.59558i	−0.196949	−	0.271077i
$593$	12.7809	−	17.5914i	0.524848	−	0.722392i	−0.461486	−	0.887147i	$-0.652684\pi$
$593$	12.7809	−	17.5914i	0.524848	−	0.722392i	0.986334	+	0.164756i	$0.0526836\pi$
$594$	−0.206198	−	0.634613i	−0.00846041	−	0.0260385i
$595$	5.73044	−	4.16341i	0.234925	−	0.170683i
$596$	−17.7356			−0.726477
$597$	35.6444			1.45883
$598$	1.19825	−	0.870579i	0.0490001	−	0.0356006i
$599$			25.8881i			1.05776i	0.848697	+	0.528880i	$0.177388\pi$
$599$			25.8881i			1.05776i	−0.848697	+	0.528880i	$0.822612\pi$
$600$	−12.7909	−	17.6052i	−0.522186	−	0.718727i
$601$	21.2933	+	15.4705i	0.868571	+	0.631054i	0.930203	−	0.367045i	$-0.119631\pi$
$601$	21.2933	+	15.4705i	0.868571	+	0.631054i	−0.0616322	+	0.998099i	$0.519631\pi$
$602$	−6.18093	−	8.50732i	−0.251916	−	0.346733i
$603$	0.991543	−	0.322172i	0.0403788	−	0.0131199i
$604$	−14.9889	+	20.6305i	−0.609891	+	0.839443i
$605$	−5.66031	−	4.11246i	−0.230124	−	0.167195i
$606$	13.4899	+	9.80096i	0.547988	+	0.398137i
$607$	5.10162	−	15.7012i	0.207068	−	0.637291i	−0.792554	−	0.609802i	$-0.791249\pi$
$607$	5.10162	−	15.7012i	0.207068	−	0.637291i	0.999622	−	0.0274888i	$-0.00875107\pi$
$608$	−9.23122	−	2.99941i	−0.374376	−	0.121642i
$609$	2.03637			0.0825177
$610$	3.86637	+	0.114182i	0.156545	+	0.00462311i
$611$	−31.0048			−1.25432
$612$	−2.40826	−	0.782490i	−0.0973480	−	0.0316303i
$613$	8.48796	−	26.1232i	0.342825	−	1.05511i	−0.619912	−	0.784671i	$-0.712832\pi$
$613$	8.48796	−	26.1232i	0.342825	−	1.05511i	0.962738	−	0.270437i	$-0.0871682\pi$
$614$	−4.85498	−	3.52735i	−0.195931	−	0.142352i
$615$	−2.42188	−	1.75960i	−0.0976598	−	0.0709540i
$616$	−0.369636	+	0.508760i	−0.0148930	+	0.0204985i
$617$	−27.9087	+	9.06810i	−1.12356	+	0.365068i	−0.811127	−	0.584871i	$-0.801145\pi$
$617$	−27.9087	+	9.06810i	−1.12356	+	0.365068i	−0.312437	+	0.949938i	$0.601145\pi$
$618$	8.52470	+	11.7332i	0.342914	+	0.471980i
$619$	−16.8658	−	12.2537i	−0.677892	−	0.492517i	0.194766	−	0.980850i	$-0.437605\pi$
$619$	−16.8658	−	12.2537i	−0.677892	−	0.492517i	−0.872658	+	0.488333i	$0.837605\pi$
$620$	2.33874	+	3.21899i	0.0939259	+	0.129278i
$621$			3.19955i			0.128393i
$622$	−2.07971	+	1.51099i	−0.0833886	+	0.0605854i
$623$	14.7973			0.592843
$624$	3.97747			0.159226
$625$	−15.4232	+	11.2056i	−0.616929	+	0.448225i
$626$	−0.909605	−	2.79948i	−0.0363551	−	0.111890i
$627$	0.301813	−	0.415411i	0.0120533	−	0.0165899i
$628$	−13.5728	−	18.6814i	−0.541615	−	0.745469i
$629$	27.1470	−	83.5500i	1.08242	−	3.33136i
$630$	−0.0477321	−	0.146904i	−0.00190169	−	0.00585281i
$631$			24.7125i			0.983789i	0.870655	+	0.491894i	$0.163695\pi$
$631$			24.7125i			0.983789i	−0.870655	+	0.491894i	$0.836305\pi$
$632$	1.83513	−	5.64794i	0.0729975	−	0.224663i
$633$	15.5653	−	21.4238i	0.618666	−	0.851521i
$634$	−1.51248	+	0.491433i	−0.0600681	+	0.0195173i
$635$	1.38343	+	4.25776i	0.0548997	+	0.168964i
$636$	10.8617	+	3.52919i	0.430696	+	0.139941i
$637$	−12.2293	+	8.88511i	−0.484543	+	0.352041i
$638$	0.104461	+	0.0339414i	0.00413565	+	0.00134375i
$639$			1.46983i			0.0581454i
$640$	5.66339	−	1.84015i	0.223865	−	0.0727382i
$641$	9.02491	−	2.93237i	0.356463	−	0.115822i	−0.125311	−	0.992118i	$-0.539993\pi$
$641$	9.02491	−	2.93237i	0.356463	−	0.115822i	0.481773	+	0.876296i	$0.339993\pi$
$642$			19.6259i			0.774573i
$643$	−25.8225	−	8.39025i	−1.01834	−	0.330879i	−0.248170	−	0.968716i	$-0.579829\pi$
$643$	−25.8225	−	8.39025i	−1.01834	−	0.330879i	−0.770171	+	0.637837i	$0.779829\pi$
$644$	1.00322	−	0.728886i	0.0395326	−	0.0287221i
$645$	−10.6714	−	3.46734i	−0.420185	−	0.136527i
$646$	−3.19612	−	9.83664i	−0.125750	−	0.387017i
$647$	27.6368	−	8.97976i	1.08652	−	0.353031i	0.289617	−	0.957143i	$-0.406472\pi$
$647$	27.6368	−	8.97976i	1.08652	−	0.353031i	0.796899	+	0.604112i	$0.206472\pi$
$648$	14.9251	−	20.5427i	0.586315	−	0.806993i
$649$	−0.433912	+	1.33544i	−0.0170325	+	0.0524208i
$650$			10.5948i			0.415563i
$651$	−3.42628	−	10.5450i	−0.134286	−	0.413291i
$652$	−1.93519	+	5.95589i	−0.0757877	+	0.233251i
$653$	1.93157	+	2.65857i	0.0755881	+	0.104038i	0.845137	−	0.534550i	$-0.179519\pi$
$653$	1.93157	+	2.65857i	0.0755881	+	0.104038i	−0.769549	+	0.638588i	$0.779519\pi$
$654$	7.37766	−	10.1545i	0.288489	−	0.397072i
$655$	0.111694	+	0.343758i	0.00436423	+	0.0134317i
$656$	−1.57641	+	1.14533i	−0.0615485	+	0.0447176i
$657$	2.81456			0.109806
$658$	11.2049			0.436814
$659$	39.8078	−	28.9220i	1.55069	−	1.12664i	0.607533	−	0.794294i	$-0.292159\pi$
$659$	39.8078	−	28.9220i	1.55069	−	1.12664i	0.943157	−	0.332348i	$-0.107841\pi$
$660$			0.275952i			0.0107414i
$661$	−20.0713	−	27.6258i	−0.780685	−	1.07452i	−0.995206	−	0.0978010i	$-0.968819\pi$
$661$	−20.0713	−	27.6258i	−0.780685	−	1.07452i	0.214521	−	0.976719i	$-0.431181\pi$
$662$	−13.2199	−	9.60481i	−0.513806	−	0.373302i
$663$	25.1925	+	34.6745i	0.978394	+	1.34664i
$664$	11.2192	−	3.64532i	0.435388	−	0.141466i
$665$	−0.859136	+	1.18250i	−0.0333158	+	0.0458553i
$666$	−1.54987	−	1.12605i	−0.0600563	−	0.0436335i
$667$	−0.426080	−	0.309565i	−0.0164979	−	0.0119864i
$668$	−6.48264	+	19.9515i	−0.250821	+	0.771948i
$669$	29.8805	+	9.70876i	1.15525	+	0.375362i
$670$	−2.28857			−0.0884150
$671$	1.06581	+	0.823504i	0.0411453	+	0.0317910i
$672$	−14.5360			−0.560738
$673$	−12.7939	−	4.15700i	−0.493169	−	0.160240i	0.0518651	−	0.998654i	$-0.483483\pi$
$673$	−12.7939	−	4.15700i	−0.493169	−	0.160240i	−0.545034	+	0.838414i	$0.683483\pi$
$674$	−1.06670	+	3.28296i	−0.0410877	+	0.126455i
$675$	−18.5161	−	13.4528i	−0.712686	−	0.517797i
$676$	4.72060	+	3.42971i	0.181561	+	0.131912i
$677$	−12.8995	+	17.7546i	−0.495767	+	0.682365i	−0.981439	−	0.191777i	$-0.938575\pi$
$677$	−12.8995	+	17.7546i	−0.495767	+	0.682365i	0.485672	+	0.874141i	$0.338575\pi$
$678$	6.53048	−	2.12188i	0.250801	−	0.0814903i
$679$	9.97331	+	13.7271i	0.382740	+	0.526797i
$680$	10.9348	+	7.94463i	0.419332	+	0.304663i
$681$	29.5981	+	40.7383i	1.13420	+	1.56110i
$682$		−	0.598043i		−	0.0229002i
$683$	−27.3564	+	19.8756i	−1.04676	+	0.760519i	−0.971594	−	0.236652i	$-0.923950\pi$
$683$	−27.3564	+	19.8756i	−1.04676	+	0.760519i	−0.0751698	+	0.997171i	$0.523950\pi$
$684$	0.522527			0.0199793
$685$	7.70070			0.294229
$686$	10.4988	−	7.62784i	0.400847	−	0.291232i
$687$	−0.575047	−	1.76981i	−0.0219394	−	0.0675225i
$688$	−4.29288	+	5.90865i	−0.163665	+	0.225265i
$689$	−7.94738	−	10.9386i	−0.302771	−	0.416728i
$690$	−0.176495	+	0.543195i	−0.00671904	+	0.0206791i
$691$	10.0282	+	30.8637i	0.381491	+	1.17411i	0.938994	+	0.343935i	$0.111760\pi$
$691$	10.0282	+	30.8637i	0.381491	+	1.17411i	−0.557502	+	0.830175i	$0.688240\pi$
$692$		−	16.3978i		−	0.623349i
$693$	0.0166208	−	0.0511535i	0.000631371	−	0.00194316i
$694$	−8.86649	+	12.2037i	−0.336567	+	0.463245i
$695$	2.16851	−	0.704593i	0.0822564	−	0.0267267i
$696$	1.20078	+	3.69562i	0.0455154	+	0.140082i
$697$	−19.9693	−	6.48842i	−0.756392	−	0.245767i
$698$	−8.65112	+	6.28541i	−0.327450	+	0.237906i
$699$	12.5808	+	4.08775i	0.475850	+	0.154613i
$700$			8.87044i			0.335271i
$701$	−17.4925	+	5.68367i	−0.660684	+	0.214669i	−0.620119	−	0.784508i	$-0.712916\pi$
$701$	−17.4925	+	5.68367i	−0.660684	+	0.214669i	−0.0405648	+	0.999177i	$0.512916\pi$
$702$	−10.9308	+	3.55164i	−0.412558	+	0.134048i
$703$			18.1281i			0.683715i
$704$	−0.501100	−	0.162817i	−0.0188859	−	0.00613640i
$705$	9.67267	−	7.02760i	0.364294	−	0.264675i
$706$	8.20609	+	2.66632i	0.308840	+	0.100348i
$707$	−5.10735	−	15.7188i	−0.192082	−	0.591167i
$708$	−19.4293	+	6.31298i	−0.730199	+	0.237256i
$709$	15.8430	−	21.8060i	0.594996	−	0.818942i	−0.400242	−	0.916409i	$-0.631074\pi$
$709$	15.8430	−	21.8060i	0.594996	−	0.818942i	0.995239	+	0.0974671i	$0.0310741\pi$
$710$	0.997026	−	3.06853i	0.0374177	−	0.115160i
$711$			0.507922i			0.0190486i
$712$	8.72551	+	26.8544i	0.327002	+	1.00641i
$713$	−0.886136	+	2.72725i	−0.0331861	+	0.102136i
$714$	−9.10440	−	12.5311i	−0.340723	−	0.468966i
$715$	0.192028	−	0.264304i	0.00718145	−	0.00988442i
$716$	7.44714	+	22.9199i	0.278313	+	0.856558i
$717$	−25.4200	+	18.4687i	−0.949329	+	0.689728i
$718$	−10.4819			−0.391182
$719$	−25.6949			−0.958259			−0.479129	−	0.877744i	$-0.659048\pi$
$719$	−25.6949			−0.958259			−0.479129	+	0.877744i	$0.659048\pi$
$720$	−0.0867923	+	0.0630583i	−0.00323456	+	0.00235004i
$721$		−	14.3755i		−	0.535373i
$722$	−7.41779	−	10.2097i	−0.276062	−	0.379966i
$723$	9.65316	+	7.01343i	0.359005	+	0.260832i
$724$	1.70315	+	2.34419i	0.0632972	+	0.0871211i
$725$	3.58298	−	1.16418i	0.133069	−	0.0432366i
$726$	−8.99298	+	12.3778i	−0.333761	+	0.459382i
$727$	6.93366	+	5.03760i	0.257155	+	0.186834i	0.708892	−	0.705317i	$-0.249195\pi$
$727$	6.93366	+	5.03760i	0.257155	+	0.186834i	−0.451737	+	0.892151i	$0.649195\pi$
$728$	8.76310	+	6.36676i	0.324782	+	0.235968i
$729$	7.62516	−	23.4678i	0.282413	−	0.869179i
$730$	−5.87590	−	1.90919i	−0.217477	−	0.0706625i
$731$	−78.7001			−2.91083
$732$	−0.578458	+	19.5874i	−0.0213804	+	0.723969i
$733$	33.5419			1.23890			0.619450	−	0.785036i	$-0.287356\pi$
$733$	33.5419			1.23890			0.619450	+	0.785036i	$0.287356\pi$
$734$	−21.2885	−	6.91705i	−0.785773	−	0.255313i
$735$	1.80130	−	5.54383i	0.0664420	−	0.204487i
$736$	3.04145	+	2.20974i	0.112109	+	0.0814521i
$737$	−0.644705	−	0.468406i	−0.0237480	−	0.0172540i
$738$	−0.269137	+	0.370435i	−0.00990707	+	0.0136359i
$739$	26.6079	−	8.64542i	0.978787	−	0.318027i	0.224429	−	0.974491i	$-0.427948\pi$
$739$	26.6079	−	8.64542i	0.978787	−	0.318027i	0.754358	+	0.656463i	$0.227948\pi$
$740$	−5.72645	−	7.88178i	−0.210508	−	0.289740i
$741$	−7.15521	−	5.19856i	−0.262853	−	0.190974i
$742$	2.87213	+	3.95315i	0.105439	+	0.145125i
$743$			36.3522i			1.33363i	0.745223	+	0.666816i	$0.232343\pi$
$743$			36.3522i			1.33363i	−0.745223	+	0.666816i	$0.767657\pi$
$744$	17.1168	−	12.4361i	0.627533	−	0.455929i
$745$	−8.09687			−0.296646
$746$	24.9953			0.915142
$747$	−0.816253	+	0.593042i	−0.0298651	+	0.0216983i
$748$	0.598105	+	1.84078i	0.0218689	+	0.0673055i
$749$	11.4344	−	15.7380i	0.417802	−	0.575056i
$750$	−5.01554	−	6.90330i	−0.183142	−	0.252073i
$751$	3.11364	−	9.58279i	0.113618	−	0.349681i	−0.878038	−	0.478591i	$-0.841148\pi$
$751$	3.11364	−	9.58279i	0.113618	−	0.349681i	0.991656	+	0.128910i	$0.0411477\pi$
$752$	−2.40484	−	7.40135i	−0.0876956	−	0.269899i
$753$			24.3111i			0.885946i
$754$	0.584622	−	1.79928i	0.0212907	−	0.0655259i
$755$	−6.84294	+	9.41850i	−0.249040	+	0.342774i
$756$	−9.15176	+	2.97359i	−0.332846	+	0.108148i
$757$	−12.8136	−	39.4361i	−0.465717	−	1.43333i	−0.858079	−	0.513518i	$-0.828342\pi$
$757$	−12.8136	−	39.4361i	−0.465717	−	1.43333i	0.392363	−	0.919811i	$-0.371658\pi$
$758$	8.96700	+	2.91355i	0.325696	+	0.105825i
$759$	−0.160897	+	0.116898i	−0.00584018	+	0.00424314i
$760$	−2.65261	−	0.861887i	−0.0962204	−	0.0312639i
$761$			6.71167i			0.243298i	0.992573	+	0.121649i	$0.0388182\pi$
$761$			6.71167i			0.243298i	−0.992573	+	0.121649i	$0.961182\pi$
$762$	9.31071	−	3.02523i	0.337292	−	0.109593i
$763$	−11.8323	+	3.84455i	−0.428359	+	0.139182i
$764$			29.8835i			1.08115i
$765$	−1.09945	−	0.357232i	−0.0397506	−	0.0129158i
$766$	9.38503	−	6.81862i	0.339095	−	0.246367i
$767$	23.0023	+	7.47389i	0.830564	+	0.269866i
$768$	−7.41529	−	22.8219i	−0.267576	−	0.823515i
$769$	−20.3129	+	6.60005i	−0.732501	+	0.238004i	−0.651435	−	0.758705i	$-0.725832\pi$
$769$	−20.3129	+	6.60005i	−0.732501	+	0.238004i	−0.0810661	+	0.996709i	$0.525832\pi$
$770$	−0.0693978	+	0.0955178i	−0.00250092	+	0.00344222i
$771$	11.8107	−	36.3495i	0.425350	−	1.30909i
$772$			19.5657i			0.704187i
$773$	8.76293	+	26.9695i	0.315181	+	0.970026i	0.975680	+	0.219200i	$0.0703446\pi$
$773$	8.76293	+	26.9695i	0.315181	+	0.970026i	−0.660499	+	0.750827i	$0.729655\pi$
$774$	−0.530342	+	1.63222i	−0.0190627	+	0.0586691i
$775$	−12.0570	−	16.5951i	−0.433102	−	0.596114i
$776$	−19.0311	+	26.1941i	−0.683177	+	0.940312i
$777$	8.38933	+	25.8197i	0.300965	+	0.926276i
$778$	−9.04196	+	6.56937i	−0.324170	+	0.235523i
$779$	4.33281			0.155239
$780$	4.75312			0.170189
$781$	0.908913	−	0.660364i	0.0325235	−	0.0236297i
$782$			4.00599i			0.143254i
$783$	2.40220	+	3.30635i	0.0858478	+	0.118159i
$784$	−3.06957	−	2.23017i	−0.109627	−	0.0796490i
$785$	−6.19644	−	8.52867i	−0.221160	−	0.304401i
$786$	0.751718	−	0.244248i	0.0268129	−	0.00871203i
$787$	−7.98752	+	10.9939i	−0.284724	+	0.391890i	−0.927292	−	0.374340i	$-0.877869\pi$
$787$	−7.98752	+	10.9939i	−0.284724	+	0.391890i	0.642567	+	0.766229i	$0.277869\pi$
$788$	−12.1172	−	8.80366i	−0.431657	−	0.313617i
$789$	19.0894	+	13.8693i	0.679600	+	0.493758i
$790$	0.344538	−	1.06038i	0.0122581	−	0.0377266i
$791$	−6.47304	−	2.10322i	−0.230155	−	0.0747819i
$792$	0.102634			0.00364696
$793$	14.1844	−	18.3580i	0.503702	−	0.651913i
$794$	6.17298			0.219071
$795$	4.95874	+	1.61119i	0.175868	+	0.0571431i
$796$	8.56764	−	26.3685i	0.303672	−	0.934606i
$797$	14.3322	+	10.4129i	0.507672	+	0.368845i	0.811940	−	0.583741i	$-0.198412\pi$
$797$	14.3322	+	10.4129i	0.507672	+	0.368845i	−0.304268	+	0.952587i	$0.598412\pi$
$798$	2.58585	+	1.87873i	0.0915380	+	0.0665062i
$799$	49.2911	−	67.8433i	1.74379	−	2.40012i
$800$	−25.5760	+	8.31016i	−0.904249	+	0.293808i
$801$	−1.41952	−	1.95380i	−0.0501562	−	0.0690340i
$802$	−1.61040	−	1.17003i	−0.0568653	−	0.0413151i
$803$	−1.26452	−	1.74047i	−0.0446241	−	0.0614197i
$804$		−	11.5941i		−	0.408891i
$805$	0.458005	−	0.332760i	0.0161426	−	0.0117283i
$806$	−10.3009			−0.362835
$807$	24.3419			0.856874
$808$	25.5150	−	18.5377i	0.897615	−	0.652155i
$809$	14.7450	+	45.3803i	0.518405	+	1.59549i	0.777000	+	0.629501i	$0.216741\pi$
$809$	14.7450	+	45.3803i	0.518405	+	1.59549i	−0.258595	+	0.965986i	$0.583259\pi$
$810$	2.80214	−	3.85681i	0.0984571	−	0.135515i
$811$	1.00717	+	1.38625i	0.0353664	+	0.0486777i	0.826334	−	0.563180i	$-0.190422\pi$
$811$	1.00717	+	1.38625i	0.0353664	+	0.0486777i	−0.790968	+	0.611858i	$0.790422\pi$
$812$	0.489470	−	1.50643i	0.0171770	−	0.0528654i
$813$	9.45858	+	29.1105i	0.331727	+	1.02095i
$814$			1.46432i			0.0513244i
$815$	−0.883476	+	2.71906i	−0.0309468	+	0.0952445i
$816$	−6.32334	+	8.70333i	−0.221361	+	0.304677i
$817$	15.4452	−	5.01846i	0.540360	−	0.175574i
$818$	1.87887	+	5.78258i	0.0656933	+	0.202183i
$819$	−0.881089	−	0.286283i	−0.0307877	−	0.0100035i
$820$	−1.88383	+	1.36868i	−0.0657861	+	0.0477964i
$821$	−38.1418	−	12.3930i	−1.33116	−	0.432519i	−0.444845	−	0.895607i	$-0.646741\pi$
$821$	−38.1418	−	12.3930i	−1.33116	−	0.432519i	−0.886312	+	0.463088i	$0.846741\pi$
$822$		−	16.8396i		−	0.587349i
$823$	−26.1407	+	8.49361i	−0.911206	+	0.296069i	−0.726854	−	0.686792i	$-0.759019\pi$
$823$	−26.1407	+	8.49361i	−0.911206	+	0.296069i	−0.184352	+	0.982860i	$0.559019\pi$
$824$	26.0889	−	8.47678i	0.908848	−	0.295303i
$825$		−	1.42264i		−	0.0495298i
$826$	−8.31287	−	2.70101i	−0.289242	−	0.0939803i
$827$	−36.1037	+	26.2309i	−1.25545	+	0.912138i	−0.998525	−	0.0542934i	$-0.982709\pi$
$827$	−36.1037	+	26.2309i	−1.25545	+	0.912138i	−0.256925	+	0.966431i	$0.582709\pi$
$828$	−0.192480	−	0.0625405i	−0.00668913	−	0.00217343i
$829$	−4.56698	−	14.0557i	−0.158618	−	0.488176i	0.839892	−	0.542754i	$-0.182618\pi$
$829$	−4.56698	−	14.0557i	−0.158618	−	0.488176i	−0.998509	+	0.0545786i	$0.982618\pi$
$830$	2.10635	−	0.684396i	0.0731126	−	0.0237557i
$831$	8.29586	−	11.4183i	0.287780	−	0.396096i
$832$	−2.80443	+	8.63116i	−0.0972262	+	0.299232i
$833$		−	40.8851i		−	1.41658i
$834$	−1.54078	−	4.74203i	−0.0533528	−	0.164203i
$835$	−2.95954	+	9.10853i	−0.102419	+	0.315214i
$836$	−0.234761	−	0.323121i	−0.00811938	−	0.0111754i
$837$	13.0796	−	18.0025i	0.452097	−	0.622258i
$838$	5.00341	+	15.3989i	0.172840	+	0.531947i
$839$	−38.5315	+	27.9948i	−1.33026	+	0.966487i	−0.330513	+	0.943801i	$0.607222\pi$
$839$	−38.5315	+	27.9948i	−1.33026	+	0.966487i	−0.999743	+	0.0226857i	$0.992778\pi$
$840$	−4.17695			−0.144119
$841$	28.3273			0.976803
$842$	9.96644	−	7.24104i	0.343466	−	0.249543i
$843$		−	26.3794i		−	0.908556i
$844$	−12.1073	−	16.6642i	−0.416749	−	0.573606i
$845$	2.15511	+	1.56578i	0.0741380	+	0.0538644i
$846$	−1.07490	−	1.47947i	−0.0369557	−	0.0508651i
$847$	14.4230	−	4.68631i	0.495579	−	0.161023i
$848$	1.99480	−	2.74561i	0.0685017	−	0.0942845i
$849$	−22.7814	−	16.5517i	−0.781857	−	0.568052i
$850$	−23.1831	−	16.8435i	−0.795175	−	0.577728i
$851$	2.16973	−	6.67773i	0.0743772	−	0.228910i
$852$	15.5454	+	5.05102i	0.532578	+	0.173045i
$853$	21.8547			0.748289			0.374145	−	0.927370i	$-0.377936\pi$
$853$	21.8547			0.748289			0.374145	+	0.927370i	$0.377936\pi$
$854$	−5.12615	+	6.63447i	−0.175413	+	0.227027i
$855$	0.238551			0.00815827
$856$	35.3040	+	11.4710i	1.20667	+	0.392070i
$857$	−10.4831	+	32.2636i	−0.358095	+	1.10210i	0.596099	+	0.802911i	$0.296717\pi$
$857$	−10.4831	+	32.2636i	−0.358095	+	1.10210i	−0.954193	+	0.299191i	$0.903283\pi$
$858$	−0.577971	−	0.419920i	−0.0197316	−	0.0143358i
$859$	7.30168	+	5.30498i	0.249130	+	0.181004i	0.705341	−	0.708868i	$-0.250794\pi$
$859$	7.30168	+	5.30498i	0.249130	+	0.181004i	−0.456211	+	0.889872i	$0.650794\pi$
$860$	−5.13004	+	7.06089i	−0.174933	+	0.240774i
$861$	6.17117	−	2.00514i	0.210313	−	0.0683348i
$862$	−13.5427	−	18.6400i	−0.461267	−	0.634880i
$863$	20.4669	+	14.8701i	0.696701	+	0.506183i	0.878856	−	0.477087i	$-0.158307\pi$
$863$	20.4669	+	14.8701i	0.696701	+	0.506183i	−0.182155	+	0.983270i	$0.558307\pi$
$864$	−17.1474	−	23.6014i	−0.583367	−	0.802936i
$865$		−	7.48612i		−	0.254536i
$866$	5.79623	−	4.21120i	0.196964	−	0.143103i
$867$	−85.3918			−2.90006
$868$	−8.62438			−0.292731
$869$	0.314089	−	0.228199i	0.0106548	−	0.00774113i
$870$	0.225442	+	0.693838i	0.00764319	+	0.0235233i
$871$	−8.06802	+	11.1047i	−0.273375	+	0.376268i
$872$	−13.9543	−	19.2064i	−0.472551	−	0.650411i
$873$	0.855738	−	2.63369i	0.0289624	−	0.0891369i
$874$	−0.255450	−	0.786193i	−0.00864071	−	0.0265934i
$875$			8.45791i			0.285929i
$876$	9.67215	−	29.7678i	0.326792	−	1.00576i
$877$	14.9531	−	20.5812i	0.504930	−	0.694976i	−0.478124	−	0.878292i	$-0.658683\pi$
$877$	14.9531	−	20.5812i	0.504930	−	0.694976i	0.983054	+	0.183316i	$0.0586832\pi$
$878$	−9.78790	+	3.18028i	−0.330326	+	0.107329i
$879$	−0.264041	−	0.812634i	−0.00890587	−	0.0274095i
$880$	0.0779881	+	0.0253399i	0.00262898	+	0.000854207i
$881$	39.2646	−	28.5274i	1.32286	−	0.961112i	0.322965	−	0.946411i	$-0.395320\pi$
$881$	39.2646	−	28.5274i	1.32286	−	0.961112i	0.999892	−	0.0147008i	$-0.00467958\pi$
$882$	−0.847948	−	0.275515i	−0.0285519	−	0.00927707i
$883$		−	16.6730i		−	0.561092i	−0.959841	−	0.280546i	$-0.909484\pi$
$883$		−	16.6730i		−	0.561092i	0.959841	−	0.280546i	$-0.0905155\pi$
$884$	31.7063	−	10.3020i	1.06640	−	0.346494i
$885$	−8.87013	+	2.88208i	−0.298166	+	0.0968801i
$886$			28.6575i			0.962768i
$887$	−46.6089	−	15.1442i	−1.56498	−	0.508491i	−0.606844	−	0.794821i	$-0.707565\pi$
$887$	−46.6089	−	15.1442i	−1.56498	−	0.508491i	−0.958131	+	0.286330i	$0.907565\pi$
$888$	−41.9109	+	30.4501i	−1.40644	+	1.02184i
$889$	−9.22882	−	2.99863i	−0.309525	−	0.100571i
$890$	1.63818	+	5.04181i	0.0549120	+	0.169002i
$891$	1.57877	−	0.512972i	0.0528906	−	0.0171852i
$892$	14.3644	−	19.7709i	0.480956	−	0.661979i
$893$	−5.34742	+	16.4577i	−0.178945	+	0.550735i
$894$			17.7059i			0.592175i
$895$	3.39986	+	10.4637i	0.113645	+	0.349763i
$896$	−3.98858	+	12.2756i	−0.133249	+	0.410099i
$897$	2.01351	+	2.77135i	0.0672290	+	0.0925328i
$898$	6.04469	−	8.31980i	0.201714	−	0.277635i
$899$	1.13189	+	3.48359i	0.0377506	+	0.116184i
$900$	1.17123	−	0.850945i	0.0390409	−	0.0283648i
$901$	36.5701			1.21833
$902$	0.349988			0.0116533
$903$	19.6760	−	14.2955i	0.654778	−	0.475724i
$904$		−	12.9875i		−	0.431959i
$905$	0.777545	+	1.07020i	0.0258465	+	0.0355746i
$906$	20.5960	+	14.9639i	0.684258	+	0.497142i
$907$	−8.52225	−	11.7299i	−0.282977	−	0.389484i	0.643740	−	0.765244i	$-0.277382\pi$
$907$	−8.52225	−	11.7299i	−0.282977	−	0.389484i	−0.926717	+	0.375760i	$0.877382\pi$
$908$	37.2511	−	12.1036i	1.23622	−	0.401673i
$909$	−1.58551	+	2.18227i	−0.0525882	+	0.0723814i
$910$	1.64524	+	1.19534i	0.0545392	+	0.0396250i
$911$	31.3498	+	22.7769i	1.03866	+	0.754634i	0.970024	−	0.243008i	$-0.0781340\pi$
$911$	31.3498	+	22.7769i	1.03866	+	0.754634i	0.0686400	+	0.997641i	$0.478134\pi$
$912$	0.685998	−	2.11128i	0.0227157	−	0.0699116i
$913$	0.733452	+	0.238313i	0.0242737	+	0.00788701i
$914$	−3.07834			−0.101823
$915$	−0.264085	+	8.94227i	−0.00873038	+	0.295622i
$916$	−1.44747			−0.0478256
$917$	−0.745106	−	0.242100i	−0.0246056	−	0.00799483i
$918$	9.60616	−	29.5647i	0.317051	−	0.975782i
$919$	36.4508	+	26.4831i	1.20240	+	0.873596i	0.994519	−	0.104557i	$-0.0333426\pi$
$919$	36.4508	+	26.4831i	1.20240	+	0.873596i	0.207883	+	0.978154i	$0.433343\pi$
$920$	0.873967	+	0.634974i	0.0288138	+	0.0209345i
$921$	8.15817	−	11.2288i	0.268821	−	0.370000i
$922$	−16.6240	+	5.40147i	−0.547483	+	0.177888i
$923$	−11.3744	−	15.6555i	−0.374393	−	0.515307i
$924$	−0.483902	−	0.351575i	−0.0159192	−	0.0115660i
$925$	29.5220	+	40.6335i	0.970676	+	1.33602i
$926$			23.2099i			0.762724i
$927$	−1.89810	+	1.37905i	−0.0623419	+	0.0452940i
$928$	4.80204			0.157635
$929$	−18.4731			−0.606084			−0.303042	−	0.952977i	$-0.598002\pi$
$929$	−18.4731			−0.606084			−0.303042	+	0.952977i	$0.598002\pi$
$930$	3.21362	−	2.33483i	0.105379	−	0.0765621i
$931$	2.60711	+	8.02387i	0.0854447	+	0.262972i
$932$	6.04795	−	8.32430i	0.198107	−	0.272671i
$933$	−3.49468	−	4.81002i	−0.114411	−	0.157473i
$934$	−4.93177	+	15.1784i	−0.161372	+	0.496653i
$935$	0.273054	+	0.840375i	0.00892983	+	0.0274832i
$936$		−	1.76782i		−	0.0577830i
$937$	−7.27600	+	22.3932i	−0.237697	+	0.731555i	0.759056	+	0.651026i	$0.225661\pi$
$937$	−7.27600	+	22.3932i	−0.237697	+	0.731555i	−0.996752	+	0.0805293i	$0.974339\pi$
$938$	2.91573	−	4.01316i	0.0952020	−	0.131034i
$939$	6.47473	−	2.10377i	0.211295	−	0.0686538i
$940$	−2.87381	−	8.84469i	−0.0937334	−	0.288482i
$941$	−16.9496	−	5.50727i	−0.552542	−	0.179532i	0.0194207	−	0.999811i	$-0.493818\pi$
$941$	−16.9496	−	5.50727i	−0.552542	−	0.179532i	−0.571963	+	0.820280i	$0.693818\pi$
$942$	−18.6502	+	13.5502i	−0.607656	+	0.441488i
$943$	−1.59605	−	0.518587i	−0.0519744	−	0.0168875i
$944$			6.07071i			0.197585i
$945$	−4.17808	+	1.35754i	−0.135913	+	0.0441608i
$946$	1.24761	−	0.405372i	0.0405632	−	0.0131798i
$947$		−	49.6515i		−	1.61346i	−0.590922	−	0.806729i	$-0.701236\pi$
$947$		−	49.6515i		−	1.61346i	0.590922	−	0.806729i	$-0.298764\pi$
$948$	5.37198	+	1.74546i	0.174474	+	0.0566900i
$949$	−29.9786	+	21.7807i	−0.973145	+	0.707031i
$950$	5.62385	+	1.82730i	0.182462	+	0.0592854i
$951$	−1.13660	−	3.49811i	−0.0368569	−	0.113434i
$952$	−27.8629	+	9.05322i	−0.903043	+	0.293416i
$953$	−32.2472	+	44.3845i	−1.04459	+	1.43776i	−0.151185	+	0.988506i	$0.548309\pi$
$953$	−32.2472	+	44.3845i	−1.04459	+	1.43776i	−0.893406	+	0.449250i	$0.851691\pi$
$954$	0.246437	−	0.758455i	0.00797869	−	0.0245559i
$955$			13.6428i			0.441471i
$956$	7.55246	+	23.2441i	0.244264	+	0.751768i
$957$	−0.0785009	+	0.241601i	−0.00253757	+	0.00780985i
$958$	−8.40408	−	11.5672i	−0.271524	−	0.373720i
$959$	−9.81102	+	13.5037i	−0.316814	+	0.436058i
$960$	−1.08145	−	3.32835i	−0.0349035	−	0.107422i
$961$	−8.94475	+	6.49874i	−0.288540	+	0.209637i
$962$	25.2221			0.813193
$963$	−3.17491			−0.102310
$964$	7.50856	−	5.45529i	0.241835	−	0.175703i
$965$			8.93241i			0.287544i
$966$	−0.727668	−	1.00155i	−0.0234123	−	0.0322243i
$967$	−42.7297	−	31.0449i	−1.37409	−	0.998337i	−0.997405	−	0.0719975i	$-0.977063\pi$
$967$	−42.7297	−	31.0449i	−1.37409	−	0.998337i	−0.376689	−	0.926340i	$-0.622937\pi$
$968$	17.0095	+	23.4116i	0.546706	+	0.752477i
$969$	22.7505	−	7.39209i	0.730852	−	0.237468i
$970$	−3.57302	+	4.91784i	−0.114723	+	0.157902i
$971$	−42.0930	−	30.5824i	−1.35083	−	0.981435i	−0.998970	−	0.0453825i	$-0.985549\pi$
$971$	−42.0930	−	30.5824i	−1.35083	−	0.981435i	−0.351860	−	0.936053i	$-0.614451\pi$
$972$	2.64444	+	1.92129i	0.0848203	+	0.0616256i
$973$	−1.52723	+	4.70032i	−0.0489607	+	0.150685i
$974$	16.6977	+	5.42541i	0.535029	+	0.173841i
$975$	−24.5041			−0.784759
$976$	5.48255	+	1.96213i	0.175492	+	0.0628062i
$977$	0.851462			0.0272407			0.0136203	−	0.999907i	$-0.495664\pi$
$977$	0.851462			0.0272407			0.0136203	+	0.999907i	$0.495664\pi$
$978$	5.94594	+	1.93195i	0.190130	+	0.0617770i
$979$	−0.570430	+	1.75560i	−0.0182310	+	0.0561093i
$980$	−3.66817	−	2.66508i	−0.117175	−	0.0851328i
$981$	1.64270	+	1.19349i	0.0524475	+	0.0381053i
$982$	3.94274	−	5.42671i	0.125818	−	0.173173i
$983$	−17.0607	+	5.54336i	−0.544152	+	0.176806i	−0.568178	−	0.822906i	$-0.692351\pi$
$983$	−17.0607	+	5.54336i	−0.544152	+	0.176806i	0.0240262	+	0.999711i	$0.492351\pi$
$984$	7.27788	+	10.0171i	0.232010	+	0.319335i
$985$	−5.53190	−	4.01916i	−0.176261	−	0.128061i
$986$	3.00768	+	4.13972i	0.0957841	+	0.131835i
$987$			25.9152i			0.824889i
$988$	−5.56557	+	4.04363i	−0.177064	+	0.128645i
$989$	−6.29010			−0.200014
$990$	0.0192692			0.000612417
$991$	−3.18954	+	2.31734i	−0.101319	+	0.0736127i	−0.637291	−	0.770623i	$-0.719945\pi$
$991$	−3.18954	+	2.31734i	−0.101319	+	0.0736127i	0.535972	+	0.844236i	$0.319945\pi$
$992$	−8.07964	−	24.8666i	−0.256529	−	0.789515i
$993$	22.2143	−	30.5754i	0.704951	−	0.970282i
$994$	4.11063	+	5.65780i	0.130381	+	0.179454i
$995$	3.91141	−	12.0381i	0.124000	−	0.381633i
$996$	3.46721	+	10.6710i	0.109863	+	0.338123i
$997$			48.7837i			1.54500i	0.635017	+	0.772498i	$0.280993\pi$
$997$			48.7837i			1.54500i	−0.635017	+	0.772498i	$0.719007\pi$
$998$	8.09556	−	24.9156i	0.256261	−	0.788689i
$999$	−32.0257	+	44.0796i	−1.01325	+	1.39462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.3.2	✓	16
3.2	odd	2		549.2.y.b.64.3		16
4.3	odd	2		976.2.bd.b.369.1		16
61.23	odd	20		3721.2.a.k.1.6		16
61.38	odd	20		3721.2.a.k.1.11		16
61.41	even	10	inner	61.2.g.a.41.2	yes	16
183.41	odd	10		549.2.y.b.163.3		16
244.163	odd	10		976.2.bd.b.529.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.3.2	✓	16	1.1	even	1	trivial
61.2.g.a.41.2	yes	16	61.41	even	10	inner
549.2.y.b.64.3		16	3.2	odd	2
549.2.y.b.163.3		16	183.41	odd	10
976.2.bd.b.369.1		16	4.3	odd	2
976.2.bd.b.529.1		16	244.163	odd	10
3721.2.a.k.1.6		16	61.23	odd	20
3721.2.a.k.1.11		16	61.38	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.738530 - 0.239963i) q^{2} +(0.554995 - 1.70810i) q^{3} +(-1.13019 - 0.821131i) q^{4} +(-0.515969 - 0.374873i) q^{5} +(-0.819760 + 1.12830i) q^{6} +(1.31473 - 0.427183i) q^{7} +(1.55051 + 2.13410i) q^{8} +(-0.182527 - 0.132614i) q^{9} +O(q^{10})\)	\(q+(-0.738530 - 0.239963i) q^{2} +(0.554995 - 1.70810i) q^{3} +(-1.13019 - 0.821131i) q^{4} +(-0.515969 - 0.374873i) q^{5} +(-0.819760 + 1.12830i) q^{6} +(1.31473 - 0.427183i) q^{7} +(1.55051 + 2.13410i) q^{8} +(-0.182527 - 0.132614i) q^{9} +(0.291103 + 0.400668i) q^{10} +0.172452i q^{11} +(-2.02982 + 1.47475i) q^{12} +2.97038 q^{13} -1.07348 q^{14} +(-0.926680 + 0.673273i) q^{15} +(0.230394 + 0.709079i) q^{16} +(-4.72228 + 6.49966i) q^{17} +(0.102979 + 0.141739i) q^{18} +(0.512304 - 1.57671i) q^{19} +(0.275323 + 0.847356i) q^{20} -2.48278i q^{21} +(0.0413820 - 0.127361i) q^{22} +(-0.377428 + 0.519485i) q^{23} +(4.50577 - 1.46401i) q^{24} +(-1.41939 - 4.36844i) q^{25} +(-2.19372 - 0.712782i) q^{26} +(4.03116 - 2.92881i) q^{27} +(-1.83667 - 0.596771i) q^{28} +0.820197i q^{29} +(0.845941 - 0.274863i) q^{30} +(4.24726 - 1.38002i) q^{31} -5.85473i q^{32} +(0.294565 + 0.0957098i) q^{33} +(5.04722 - 3.66702i) q^{34} +(-0.838501 - 0.272446i) q^{35} +(0.0973970 + 0.299757i) q^{36} +(-10.3995 + 3.37901i) q^{37} +(-0.756704 + 1.04151i) q^{38} +(1.64855 - 5.07371i) q^{39} -1.68237i q^{40} +(0.807618 + 2.48559i) q^{41} +(-0.595774 + 1.83360i) q^{42} +(5.75786 + 7.92501i) q^{43} +(0.141606 - 0.194903i) q^{44} +(0.0444649 + 0.136849i) q^{45} +(0.403399 - 0.293086i) q^{46} -10.4380 q^{47} +1.33904 q^{48} +(-4.11708 + 2.99123i) q^{49} +3.56682i q^{50} +(8.48122 + 11.6734i) q^{51} +(-3.35710 - 2.43908i) q^{52} +(-2.67554 - 3.68256i) q^{53} +(-3.67994 + 1.19569i) q^{54} +(0.0646476 - 0.0889798i) q^{55} +(2.95016 + 2.14341i) q^{56} +(-2.40885 - 1.75013i) q^{57} +(0.196817 - 0.605740i) q^{58} +(7.74387 + 2.51614i) q^{59} +1.60017 q^{60} +(4.77527 - 6.18036i) q^{61} -3.46788 q^{62} +(-0.296625 - 0.0963792i) q^{63} +(-0.944131 + 2.90574i) q^{64} +(-1.53263 - 1.11352i) q^{65} +(-0.194578 - 0.141369i) q^{66} +(-2.71616 + 3.73847i) q^{67} +(10.6741 - 3.46824i) q^{68} +(0.677861 + 0.932995i) q^{69} +(0.553881 + 0.402418i) q^{70} +(-3.82926 - 5.27053i) q^{71} -0.595149i q^{72} +(-10.0925 + 7.33262i) q^{73} +8.49119 q^{74} -8.24947 q^{75} +(-1.87369 + 1.36131i) q^{76} +(0.0736685 + 0.226728i) q^{77} +(-2.43500 + 3.35149i) q^{78} +(-1.32326 - 1.82132i) q^{79} +(0.146939 - 0.452231i) q^{80} +(-2.97458 - 9.15482i) q^{81} -2.02948i q^{82} +(1.38191 - 4.25308i) q^{83} +(-2.03869 + 2.80601i) q^{84} +(4.87310 - 1.58337i) q^{85} +(-2.35064 - 7.23453i) q^{86} +(1.40098 + 0.455205i) q^{87} +(-0.368029 + 0.267388i) q^{88} +(10.1803 + 3.30777i) q^{89} -0.111737i q^{90} +(3.90526 - 1.26890i) q^{91} +(0.853131 - 0.277199i) q^{92} -8.02064i q^{93} +(7.70876 + 2.50473i) q^{94} +(-0.855400 + 0.621484i) q^{95} +(-10.0005 - 3.24935i) q^{96} +(3.79290 + 11.6733i) q^{97} +(3.75837 - 1.22117i) q^{98} +(0.0228695 - 0.0314771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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