LMFDB - Embedded newform 322.2.e.b.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, 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("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.1
Root			$0.373419 + 0.0835272i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.b.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.685837 - 1.18790i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57146 - 2.72186i) q^{5} +1.37167 q^{6} +(-1.66774 + 2.05393i) q^{7} +1.00000 q^{8} +(0.559256 - 0.968659i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.685837 - 1.18790i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57146 - 2.72186i) q^{5} +1.37167 q^{6} +(-1.66774 + 2.05393i) q^{7} +1.00000 q^{8} +(0.559256 - 0.968659i) q^{9} +(1.57146 + 2.72186i) q^{10} +(0.126581 + 0.219245i) q^{11} +(-0.685837 + 1.18790i) q^{12} -4.85358 q^{13} +(-0.944883 - 2.47127i) q^{14} -4.31107 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.69630 - 6.40218i) q^{17} +(0.559256 + 0.968659i) q^{18} +(2.80021 - 4.85011i) q^{19} -3.14293 q^{20} +(3.58367 + 0.572461i) q^{21} -0.253163 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.685837 - 1.18790i) q^{24} +(-2.43900 - 4.22447i) q^{25} +(2.42679 - 4.20333i) q^{26} -5.64925 q^{27} +(2.61263 + 0.417345i) q^{28} +5.22526 q^{29} +(2.15554 - 3.73350i) q^{30} +(2.35533 + 4.07955i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.173628 - 0.300733i) q^{33} +7.39260 q^{34} +(2.96970 + 7.76704i) q^{35} -1.11851 q^{36} +(2.73921 - 4.74445i) q^{37} +(2.80021 + 4.85011i) q^{38} +(3.32877 + 5.76559i) q^{39} +(1.57146 - 2.72186i) q^{40} -5.88977 q^{41} +(-2.28760 + 2.81732i) q^{42} -5.71065 q^{43} +(0.126581 - 0.219245i) q^{44} +(-1.75770 - 3.04443i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(6.06972 - 10.5131i) q^{47} +1.37167 q^{48} +(-1.43725 - 6.85086i) q^{49} +4.87800 q^{50} +(-5.07012 + 8.78170i) q^{51} +(2.42679 + 4.20333i) q^{52} +(6.20044 + 10.7395i) q^{53} +(2.82463 - 4.89240i) q^{54} +0.795672 q^{55} +(-1.66774 + 2.05393i) q^{56} -7.68195 q^{57} +(-2.61263 + 4.52520i) q^{58} +(5.46207 + 9.46058i) q^{59} +(2.15554 + 3.73350i) q^{60} +(1.56514 - 2.71090i) q^{61} -4.71065 q^{62} +(1.05686 + 2.76415i) q^{63} +1.00000 q^{64} +(-7.62723 + 13.2107i) q^{65} +(0.173628 + 0.300733i) q^{66} +(1.29607 + 2.24486i) q^{67} +(-3.69630 + 6.40218i) q^{68} +1.37167 q^{69} +(-8.21130 - 1.31168i) q^{70} +4.78121 q^{71} +(0.559256 - 0.968659i) q^{72} +(-3.20891 - 5.55799i) q^{73} +(2.73921 + 4.74445i) q^{74} +(-3.34551 + 5.79460i) q^{75} -5.60042 q^{76} +(-0.661420 - 0.105656i) q^{77} -6.65753 q^{78} +(-1.81830 + 3.14939i) q^{79} +(1.57146 + 2.72186i) q^{80} +(2.19670 + 3.80480i) q^{81} +(2.94488 - 5.10069i) q^{82} +11.8962 q^{83} +(-1.29607 - 3.38978i) q^{84} -23.2344 q^{85} +(2.85533 - 4.94557i) q^{86} +(-3.58367 - 6.20710i) q^{87} +(0.126581 + 0.219245i) q^{88} +(-2.68998 + 4.65917i) q^{89} +3.51540 q^{90} +(8.09454 - 9.96892i) q^{91} +1.00000 q^{92} +(3.23074 - 5.59581i) q^{93} +(6.06972 + 10.5131i) q^{94} +(-8.80086 - 15.2435i) q^{95} +(-0.685837 + 1.18790i) q^{96} +9.98823 q^{97} +(6.65165 + 2.18073i) q^{98} +0.283165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9} + 5 q^{10} + 2 q^{11} + 5 q^{12} - 14 q^{13} + q^{14} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{18} + 9 q^{19} - 10 q^{20} + 25 q^{21} - 4 q^{22} - 4 q^{23} + 5 q^{24} - 11 q^{25} + 7 q^{26} - 34 q^{27} - 2 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} - 4 q^{32} - 13 q^{33} + 6 q^{34} + 16 q^{35} + 14 q^{36} + 9 q^{38} + q^{39} + 5 q^{40} - 30 q^{41} - 8 q^{42} - 36 q^{43} + 2 q^{44} + 11 q^{45} - 4 q^{46} + 21 q^{47} - 10 q^{48} + 17 q^{49} + 22 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} + 17 q^{54} + 20 q^{55} + q^{56} - 18 q^{57} + 2 q^{58} + 16 q^{59} - q^{60} + q^{61} - 28 q^{62} + 37 q^{63} + 8 q^{64} - 2 q^{65} - 13 q^{66} + 17 q^{67} - 3 q^{68} - 10 q^{69} + 4 q^{70} - 2 q^{71} - 7 q^{72} + 4 q^{73} + 22 q^{75} - 18 q^{76} + 13 q^{77} - 2 q^{78} - 5 q^{79} + 5 q^{80} - 16 q^{81} + 15 q^{82} - 8 q^{83} - 17 q^{84} - 108 q^{85} + 18 q^{86} - 25 q^{87} + 2 q^{88} + 9 q^{89} - 22 q^{90} + 38 q^{91} + 8 q^{92} - 13 q^{93} + 21 q^{94} + 3 q^{95} + 5 q^{96} + 80 q^{97} + 2 q^{98} - 82 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9 + 5 * q^10 + 2 * q^11 + 5 * q^12 - 14 * q^13 + q^14 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^18 + 9 * q^19 - 10 * q^20 + 25 * q^21 - 4 * q^22 - 4 * q^23 + 5 * q^24 - 11 * q^25 + 7 * q^26 - 34 * q^27 - 2 * q^28 - 4 * q^29 - q^30 + 14 * q^31 - 4 * q^32 - 13 * q^33 + 6 * q^34 + 16 * q^35 + 14 * q^36 + 9 * q^38 + q^39 + 5 * q^40 - 30 * q^41 - 8 * q^42 - 36 * q^43 + 2 * q^44 + 11 * q^45 - 4 * q^46 + 21 * q^47 - 10 * q^48 + 17 * q^49 + 22 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 + 17 * q^54 + 20 * q^55 + q^56 - 18 * q^57 + 2 * q^58 + 16 * q^59 - q^60 + q^61 - 28 * q^62 + 37 * q^63 + 8 * q^64 - 2 * q^65 - 13 * q^66 + 17 * q^67 - 3 * q^68 - 10 * q^69 + 4 * q^70 - 2 * q^71 - 7 * q^72 + 4 * q^73 + 22 * q^75 - 18 * q^76 + 13 * q^77 - 2 * q^78 - 5 * q^79 + 5 * q^80 - 16 * q^81 + 15 * q^82 - 8 * q^83 - 17 * q^84 - 108 * q^85 + 18 * q^86 - 25 * q^87 + 2 * q^88 + 9 * q^89 - 22 * q^90 + 38 * q^91 + 8 * q^92 - 13 * q^93 + 21 * q^94 + 3 * q^95 + 5 * q^96 + 80 * q^97 + 2 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.685837	−	1.18790i	−0.395968	−	0.685837i	0.597256	−	0.802051i	$-0.296258\pi$
$3$	−0.685837	−	1.18790i	−0.395968	−	0.685837i	−0.993224	+	0.116214i	$0.962924\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.57146	−	2.72186i	0.702780	−	1.21725i	−0.264707	−	0.964329i	$-0.585275\pi$
$5$	1.57146	−	2.72186i	0.702780	−	1.21725i	0.967487	−	0.252922i	$-0.0813916\pi$
$6$	1.37167			0.559983
$7$	−1.66774	+	2.05393i	−0.630348	+	0.776312i
$7$	−1.66774	+	2.05393i	−0.630348	+	0.776312i
$8$	1.00000			0.353553
$9$	0.559256	−	0.968659i	0.186419	−	0.322886i
$10$	1.57146	+	2.72186i	0.496941	+	0.860726i
$11$	0.126581	+	0.219245i	0.0381657	+	0.0661049i	0.884477	−	0.466583i	$-0.154515\pi$
$11$	0.126581	+	0.219245i	0.0381657	+	0.0661049i	−0.846312	+	0.532688i	$0.821182\pi$
$12$	−0.685837	+	1.18790i	−0.197984	+	0.342918i
$13$	−4.85358			−1.34614			−0.673071	−	0.739578i	$-0.735025\pi$
$13$	−4.85358			−1.34614			−0.673071	+	0.739578i	$0.735025\pi$
$14$	−0.944883	−	2.47127i	−0.252531	−	0.660476i
$15$	−4.31107			−1.11311
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.69630	−	6.40218i	−0.896485	−	1.55276i	−0.831956	−	0.554841i	$-0.812779\pi$
$17$	−3.69630	−	6.40218i	−0.896485	−	1.55276i	−0.0645281	−	0.997916i	$-0.520554\pi$
$18$	0.559256	+	0.968659i	0.131818	+	0.228315i
$19$	2.80021	−	4.85011i	0.642412	−	1.11269i	−0.342481	−	0.939525i	$-0.611267\pi$
$19$	2.80021	−	4.85011i	0.642412	−	1.11269i	0.984893	−	0.173166i	$-0.0553996\pi$
$20$	−3.14293			−0.702780
$21$	3.58367	+	0.572461i	0.782022	+	0.124921i
$22$	−0.253163			−0.0539744
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−0.685837	−	1.18790i	−0.139996	−	0.242480i
$25$	−2.43900	−	4.22447i	−0.487800	−	0.844894i
$26$	2.42679	−	4.20333i	0.475933	−	0.824340i
$27$	−5.64925			−1.08720
$28$	2.61263	+	0.417345i	0.493740	+	0.0788707i
$29$	5.22526			0.970306			0.485153	−	0.874429i	$-0.338764\pi$
$29$	5.22526			0.970306			0.485153	+	0.874429i	$0.338764\pi$
$30$	2.15554	−	3.73350i	0.393545	−	0.681640i
$31$	2.35533	+	4.07955i	0.423029	+	0.732708i	0.996234	−	0.0867040i	$-0.0276335\pi$
$31$	2.35533	+	4.07955i	0.423029	+	0.732708i	−0.573205	+	0.819412i	$0.694300\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.173628	−	0.300733i	0.0302248	−	0.0523509i
$34$	7.39260			1.26782
$35$	2.96970	+	7.76704i	0.501971	+	1.31287i
$36$	−1.11851			−0.186419
$37$	2.73921	−	4.74445i	0.450323	−	0.779983i	−0.548083	−	0.836424i	$-0.684642\pi$
$37$	2.73921	−	4.74445i	0.450323	−	0.779983i	0.998406	+	0.0564415i	$0.0179754\pi$
$38$	2.80021	+	4.85011i	0.454254	+	0.786791i
$39$	3.32877	+	5.76559i	0.533029	+	0.923233i
$40$	1.57146	−	2.72186i	0.248470	−	0.430363i
$41$	−5.88977			−0.919827			−0.459913	−	0.887964i	$-0.652120\pi$
$41$	−5.88977			−0.919827			−0.459913	+	0.887964i	$0.652120\pi$
$42$	−2.28760	+	2.81732i	−0.352985	+	0.434722i
$43$	−5.71065			−0.870866			−0.435433	−	0.900221i	$-0.643405\pi$
$43$	−5.71065			−0.870866			−0.435433	+	0.900221i	$0.643405\pi$
$44$	0.126581	−	0.219245i	0.0190828	−	0.0330525i
$45$	−1.75770	−	3.04443i	−0.262022	−	0.453836i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	6.06972	−	10.5131i	0.885360	−	1.53349i	0.0400585	−	0.999197i	$-0.487246\pi$
$47$	6.06972	−	10.5131i	0.885360	−	1.53349i	0.845301	−	0.534290i	$-0.179421\pi$
$48$	1.37167			0.197984
$49$	−1.43725	−	6.85086i	−0.205322	−	0.978694i
$50$	4.87800			0.689853
$51$	−5.07012	+	8.78170i	−0.709959	+	1.22968i
$52$	2.42679	+	4.20333i	0.336535	+	0.582896i
$53$	6.20044	+	10.7395i	0.851696	+	1.47518i	0.879677	+	0.475572i	$0.157759\pi$
$53$	6.20044	+	10.7395i	0.851696	+	1.47518i	−0.0279810	+	0.999608i	$0.508908\pi$
$54$	2.82463	−	4.89240i	0.384383	−	0.665771i
$55$	0.795672			0.107288
$56$	−1.66774	+	2.05393i	−0.222862	+	0.274468i
$57$	−7.68195			−1.01750
$58$	−2.61263	+	4.52520i	−0.343055	+	0.594188i
$59$	5.46207	+	9.46058i	0.711101	+	1.23166i	0.964444	+	0.264287i	$0.0851365\pi$
$59$	5.46207	+	9.46058i	0.711101	+	1.23166i	−0.253343	+	0.967376i	$0.581530\pi$
$60$	2.15554	+	3.73350i	0.278279	+	0.481993i
$61$	1.56514	−	2.71090i	0.200396	−	0.347095i	−0.748260	−	0.663405i	$-0.769111\pi$
$61$	1.56514	−	2.71090i	0.200396	−	0.347095i	0.948656	+	0.316310i	$0.102444\pi$
$62$	−4.71065			−0.598254
$63$	1.05686	+	2.76415i	0.133152	+	0.348250i
$64$	1.00000			0.125000
$65$	−7.62723	+	13.2107i	−0.946041	+	1.63859i
$66$	0.173628	+	0.300733i	0.0213722	+	0.0370177i
$67$	1.29607	+	2.24486i	0.158340	+	0.274253i	0.934270	−	0.356566i	$-0.116052\pi$
$67$	1.29607	+	2.24486i	0.158340	+	0.274253i	−0.775930	+	0.630819i	$0.782719\pi$
$68$	−3.69630	+	6.40218i	−0.448242	+	0.776378i
$69$	1.37167			0.165130
$70$	−8.21130	−	1.31168i	−0.981438	−	0.156776i
$71$	4.78121			0.567426			0.283713	−	0.958909i	$-0.408434\pi$
$71$	4.78121			0.567426			0.283713	+	0.958909i	$0.408434\pi$
$72$	0.559256	−	0.968659i	0.0659089	−	0.114158i
$73$	−3.20891	−	5.55799i	−0.375574	−	0.650514i	0.614839	−	0.788653i	$-0.289221\pi$
$73$	−3.20891	−	5.55799i	−0.375574	−	0.650514i	−0.990413	+	0.138139i	$0.955888\pi$
$74$	2.73921	+	4.74445i	0.318427	+	0.551531i
$75$	−3.34551	+	5.79460i	−0.386306	+	0.669102i
$76$	−5.60042			−0.642412
$77$	−0.661420	−	0.105656i	−0.0753758	−	0.0120406i
$78$	−6.65753			−0.753817
$79$	−1.81830	+	3.14939i	−0.204575	+	0.354334i	−0.949997	−	0.312258i	$-0.898915\pi$
$79$	−1.81830	+	3.14939i	−0.204575	+	0.354334i	0.745422	+	0.666593i	$0.232248\pi$
$80$	1.57146	+	2.72186i	0.175695	+	0.304313i
$81$	2.19670	+	3.80480i	0.244078	+	0.422755i
$82$	2.94488	−	5.10069i	0.325208	−	0.563277i
$83$	11.8962			1.30578			0.652891	−	0.757452i	$-0.273556\pi$
$83$	11.8962			1.30578			0.652891	+	0.757452i	$0.273556\pi$
$84$	−1.29607	−	3.38978i	−0.141413	−	0.369856i
$85$	−23.2344			−2.52013
$86$	2.85533	−	4.94557i	0.307898	−	0.533295i
$87$	−3.58367	−	6.20710i	−0.384210	−	0.665471i
$88$	0.126581	+	0.219245i	0.0134936	+	0.0233716i
$89$	−2.68998	+	4.65917i	−0.285137	+	0.493871i	−0.972642	−	0.232308i	$-0.925372\pi$
$89$	−2.68998	+	4.65917i	−0.285137	+	0.493871i	0.687506	+	0.726179i	$0.258706\pi$
$90$	3.51540			0.370556
$91$	8.09454	−	9.96892i	0.848538	−	1.04503i
$92$	1.00000			0.104257
$93$	3.23074	−	5.59581i	0.335012	−	0.580258i
$94$	6.06972	+	10.5131i	0.626044	+	1.08434i
$95$	−8.80086	−	15.2435i	−0.902949	−	1.56395i
$96$	−0.685837	+	1.18790i	−0.0699979	+	0.121240i
$97$	9.98823			1.01415			0.507076	−	0.861902i	$-0.330726\pi$
$97$	9.98823			1.01415			0.507076	+	0.861902i	$0.330726\pi$
$98$	6.65165	+	2.18073i	0.671918	+	0.220287i
$99$	0.283165			0.0284592
$100$	−2.43900	+	4.22447i	−0.243900	+	0.422447i
$101$	9.13984	+	15.8307i	0.909448	+	1.57521i	0.814833	+	0.579696i	$0.196829\pi$
$101$	9.13984	+	15.8307i	0.909448	+	1.57521i	0.0946149	+	0.995514i	$0.469838\pi$
$102$	−5.07012	−	8.78170i	−0.502017	−	0.869518i
$103$	0.254908	−	0.441513i	0.0251168	−	0.0435036i	−0.853194	−	0.521594i	$-0.825338\pi$
$103$	0.254908	−	0.441513i	0.0251168	−	0.0435036i	0.878311	+	0.478090i	$0.158671\pi$
$104$	−4.85358			−0.475933
$105$	7.18977	−	8.85464i	0.701650	−	0.864124i
$106$	−12.4009			−1.20448
$107$	−4.86579	+	8.42780i	−0.470394	+	0.814746i	−0.999427	−	0.0338554i	$-0.989221\pi$
$107$	−4.86579	+	8.42780i	−0.470394	+	0.814746i	0.529033	+	0.848601i	$0.322555\pi$
$108$	2.82463	+	4.89240i	0.271800	+	0.470771i
$109$	−5.20716	−	9.01907i	−0.498756	−	0.863870i	0.501243	−	0.865306i	$-0.332876\pi$
$109$	−5.20716	−	9.01907i	−0.498756	−	0.863870i	−0.999999	+	0.00143609i	$0.999543\pi$
$110$	−0.397836	+	0.689072i	−0.0379322	+	0.0657004i
$111$	−7.51460			−0.713254
$112$	−0.944883	−	2.47127i	−0.0892830	−	0.233513i
$113$	8.50762			0.800330			0.400165	−	0.916443i	$-0.368953\pi$
$113$	8.50762			0.800330			0.400165	+	0.916443i	$0.368953\pi$
$114$	3.84097	−	6.65276i	0.359740	−	0.623088i
$115$	1.57146	+	2.72186i	0.146540	+	0.253814i
$116$	−2.61263	−	4.52520i	−0.242576	−	0.420155i
$117$	−2.71439	+	4.70147i	−0.250946	+	0.434651i
$118$	−10.9241			−1.00565
$119$	19.3141	+	3.08526i	1.77052	+	0.282825i
$120$	−4.31107			−0.393545
$121$	5.46795	−	9.47077i	0.497087	−	0.860980i
$122$	1.56514	+	2.71090i	0.141701	+	0.245433i
$123$	4.03942	+	6.99648i	0.364222	+	0.630851i
$124$	2.35533	−	4.07955i	0.211515	−	0.366354i
$125$	0.383441			0.0342960
$126$	−2.92225	−	0.466804i	−0.260335	−	0.0415862i
$127$	10.2671			0.911059			0.455529	−	0.890221i	$-0.349450\pi$
$127$	10.2671			0.911059			0.455529	+	0.890221i	$0.349450\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.91658	+	6.78371i	0.344835	+	0.597272i
$130$	−7.62723	−	13.2107i	−0.668952	−	1.15866i
$131$	−2.20044	+	3.81127i	−0.192253	+	0.332992i	−0.945997	−	0.324176i	$-0.894913\pi$
$131$	−2.20044	+	3.81127i	−0.192253	+	0.332992i	0.753743	+	0.657169i	$0.228246\pi$
$132$	−0.347256			−0.0302248
$133$	5.29174	+	13.8402i	0.458852	+	1.20010i
$134$	−2.59214			−0.223927
$135$	−8.87760	+	15.3765i	−0.764062	+	1.32339i
$136$	−3.69630	−	6.40218i	−0.316955	−	0.548982i
$137$	−2.69042	−	4.65994i	−0.229858	−	0.398125i	0.727908	−	0.685675i	$-0.240493\pi$
$137$	−2.69042	−	4.65994i	−0.229858	−	0.398125i	−0.957766	+	0.287549i	$0.907159\pi$
$138$	−0.685837	+	1.18790i	−0.0583823	+	0.101121i
$139$	7.75511			0.657780			0.328890	−	0.944368i	$-0.393325\pi$
$139$	7.75511			0.657780			0.328890	+	0.944368i	$0.393325\pi$
$140$	5.24160	−	6.45535i	0.442996	−	0.545577i
$141$	−16.6513			−1.40230
$142$	−2.39061	+	4.14065i	−0.200615	+	0.347476i
$143$	−0.614373	−	1.06412i	−0.0513764	−	0.0889866i
$144$	0.559256	+	0.968659i	0.0466046	+	0.0807216i
$145$	8.21130	−	14.2224i	0.681912	−	1.18111i
$146$	6.41782			0.531142
$147$	−7.15245	+	6.40589i	−0.589924	+	0.528349i
$148$	−5.47842			−0.450323
$149$	3.35991	−	5.81953i	0.275254	−	0.476754i	−0.694945	−	0.719063i	$-0.744571\pi$
$149$	3.35991	−	5.81953i	0.275254	−	0.476754i	0.970199	+	0.242309i	$0.0779046\pi$
$150$	−3.34551	−	5.79460i	−0.273160	−	0.473127i
$151$	−5.53269	−	9.58291i	−0.450244	−	0.779846i	0.548157	−	0.836376i	$-0.315330\pi$
$151$	−5.53269	−	9.58291i	−0.450244	−	0.779846i	−0.998401	+	0.0565297i	$0.981996\pi$
$152$	2.80021	−	4.85011i	0.227127	−	0.393395i
$153$	−8.26871			−0.668485
$154$	0.422211	−	0.519978i	0.0340227	−	0.0419010i
$155$	14.8052			1.18919
$156$	3.32877	−	5.76559i	0.266515	−	0.461617i
$157$	−3.26816	−	5.66063i	−0.260828	−	0.451767i	0.705634	−	0.708576i	$-0.250662\pi$
$157$	−3.26816	−	5.66063i	−0.260828	−	0.451767i	−0.966462	+	0.256809i	$0.917329\pi$
$158$	−1.81830	−	3.14939i	−0.144656	−	0.250552i
$159$	8.50498	−	14.7311i	0.674489	−	1.16825i
$160$	−3.14293			−0.248470
$161$	−0.944883	−	2.47127i	−0.0744672	−	0.194764i
$162$	−4.39340			−0.345178
$163$	−4.99153	+	8.64558i	−0.390967	+	0.677174i	−0.992577	−	0.121615i	$-0.961193\pi$
$163$	−4.99153	+	8.64558i	−0.390967	+	0.677174i	0.601610	+	0.798790i	$0.294526\pi$
$164$	2.94488	+	5.10069i	0.229957	+	0.398297i
$165$	−0.545701	−	0.945182i	−0.0424828	−	0.0735823i
$166$	−5.94812	+	10.3024i	−0.461663	+	0.799625i
$167$	−14.7364			−1.14033			−0.570167	−	0.821529i	$-0.693122\pi$
$167$	−14.7364			−1.14033			−0.570167	+	0.821529i	$0.693122\pi$
$168$	3.58367	+	0.572461i	0.276486	+	0.0441663i
$169$	10.5573			0.812097
$170$	11.6172	−	20.1216i	0.890999	−	1.54326i
$171$	−3.13207	−	5.42490i	−0.239515	−	0.414852i
$172$	2.85533	+	4.94557i	0.217717	+	0.377096i
$173$	6.22311	−	10.7787i	0.473134	−	0.819493i	−0.526393	−	0.850242i	$-0.676456\pi$
$173$	6.22311	−	10.7787i	0.473134	−	0.819493i	0.999527	+	0.0307487i	$0.00978917\pi$
$174$	7.16735			0.543355
$175$	12.7444	+	2.03581i	0.963386	+	0.153892i
$176$	−0.253163			−0.0190828
$177$	7.49218	−	12.9768i	0.563147	−	0.975399i
$178$	−2.68998	−	4.65917i	−0.201622	−	0.349220i
$179$	−2.16600	−	3.75162i	−0.161894	−	0.280409i	0.773654	−	0.633609i	$-0.218427\pi$
$179$	−2.16600	−	3.75162i	−0.161894	−	0.280409i	−0.935548	+	0.353199i	$0.885094\pi$
$180$	−1.75770	+	3.04443i	−0.131011	+	0.226918i
$181$	23.9272			1.77850			0.889249	−	0.457423i	$-0.151228\pi$
$181$	23.9272			1.77850			0.889249	+	0.457423i	$0.151228\pi$
$182$	4.58607	+	11.9945i	0.339942	+	0.889094i
$183$	−4.29372			−0.317401
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−8.60914	−	14.9115i	−0.632956	−	1.09631i
$186$	3.23074	+	5.59581i	0.236889	+	0.410304i
$187$	0.935765	−	1.62079i	0.0684299	−	0.118524i
$188$	−12.1394			−0.885360
$189$	9.42151	−	11.6032i	0.685314	−	0.844006i
$190$	17.6017			1.27696
$191$	3.71523	−	6.43497i	0.268825	−	0.465618i	−0.699734	−	0.714404i	$-0.746698\pi$
$191$	3.71523	−	6.43497i	0.268825	−	0.465618i	0.968559	+	0.248785i	$0.0800314\pi$
$192$	−0.685837	−	1.18790i	−0.0494960	−	0.0857296i
$193$	−1.23637	−	2.14146i	−0.0889961	−	0.154146i	0.818091	−	0.575089i	$-0.195033\pi$
$193$	−1.23637	−	2.14146i	−0.0889961	−	0.154146i	−0.907087	+	0.420943i	$0.861699\pi$
$194$	−4.99412	+	8.65006i	−0.358557	+	0.621038i
$195$	20.9241			1.49841
$196$	−5.21439	+	4.67013i	−0.372457	+	0.333581i
$197$	−6.41702			−0.457194			−0.228597	−	0.973521i	$-0.573414\pi$
$197$	−6.41702			−0.457194			−0.228597	+	0.973521i	$0.573414\pi$
$198$	−0.141583	+	0.245228i	−0.0100618	+	0.0174276i
$199$	−10.8732	−	18.8329i	−0.770778	−	1.33503i	−0.937137	−	0.348962i	$-0.886534\pi$
$199$	−10.8732	−	18.8329i	−0.770778	−	1.33503i	0.166359	−	0.986065i	$-0.446799\pi$
$200$	−2.43900	−	4.22447i	−0.172463	−	0.298715i
$201$	1.77779	−	3.07922i	0.125395	−	0.217191i
$202$	−18.2797			−1.28615
$203$	−8.71439	+	10.7323i	−0.611630	+	0.753260i
$204$	10.1402			0.709959
$205$	−9.25556	+	16.0311i	−0.646436	+	1.11966i
$206$	0.254908	+	0.441513i	0.0177603	+	0.0307617i
$207$	0.559256	+	0.968659i	0.0388709	+	0.0673265i
$208$	2.42679	−	4.20333i	0.168268	−	0.291448i
$209$	1.41782			0.0980724
$210$	4.07346	+	10.6538i	0.281095	+	0.735185i
$211$	−23.0544			−1.58713			−0.793566	−	0.608484i	$-0.791778\pi$
$211$	−23.0544			−1.58713			−0.793566	+	0.608484i	$0.791778\pi$
$212$	6.20044	−	10.7395i	0.425848	−	0.737590i
$213$	−3.27913	−	5.67962i	−0.224682	−	0.389161i
$214$	−4.86579	−	8.42780i	−0.332619	−	0.576112i
$215$	−8.97409	+	15.5436i	−0.612028	+	1.06006i
$216$	−5.64925			−0.384383
$217$	−12.3072	−	1.96597i	−0.835466	−	0.133458i
$218$	10.4143			0.705347
$219$	−4.40158	+	7.62375i	−0.297431	+	0.515165i
$220$	−0.397836	−	0.689072i	−0.0268221	−	0.0464572i
$221$	17.9403	+	31.0735i	1.20679	+	2.09023i
$222$	3.75730	−	6.50784i	0.252174	−	0.436777i
$223$	−12.6471			−0.846910			−0.423455	−	0.905917i	$-0.639183\pi$
$223$	−12.6471			−0.846910			−0.423455	+	0.905917i	$0.639183\pi$
$224$	2.61263	+	0.417345i	0.174564	+	0.0278850i
$225$	−5.45610			−0.363740
$226$	−4.25381	+	7.36782i	−0.282959	+	0.490100i
$227$	1.24927	+	2.16381i	0.0829172	+	0.143617i	0.904502	−	0.426470i	$-0.140243\pi$
$227$	1.24927	+	2.16381i	0.0829172	+	0.143617i	−0.821585	+	0.570087i	$0.806910\pi$
$228$	3.84097	+	6.65276i	0.254375	+	0.440590i
$229$	−0.0727674	+	0.126037i	−0.00480861	+	0.00832875i	−0.868420	−	0.495830i	$-0.834864\pi$
$229$	−0.0727674	+	0.126037i	−0.00480861	+	0.00832875i	0.863611	+	0.504159i	$0.168197\pi$
$230$	−3.14293			−0.207239
$231$	0.328117	+	0.858166i	0.0215885	+	0.0564632i
$232$	5.22526			0.343055
$233$	2.80784	−	4.86332i	0.183948	−	0.318607i	−0.759274	−	0.650771i	$-0.774446\pi$
$233$	2.80784	−	4.86332i	0.183948	−	0.318607i	0.943221	+	0.332165i	$0.107779\pi$
$234$	−2.71439	−	4.70147i	−0.177445	−	0.307344i
$235$	−19.0767	−	33.0418i	−1.24443	−	2.15541i
$236$	5.46207	−	9.46058i	0.355551	−	0.615832i
$237$	4.98823			0.324021
$238$	−12.3290	+	15.1839i	−0.799169	+	0.984225i
$239$	−6.34297			−0.410293			−0.205146	−	0.978731i	$-0.565767\pi$
$239$	−6.34297			−0.410293			−0.205146	+	0.978731i	$0.565767\pi$
$240$	2.15554	−	3.73350i	0.139139	−	0.240996i
$241$	12.4815	+	21.6185i	0.804002	+	1.39257i	0.916963	+	0.398972i	$0.130633\pi$
$241$	12.4815	+	21.6185i	0.804002	+	1.39257i	−0.112962	+	0.993599i	$0.536034\pi$
$242$	5.46795	+	9.47077i	0.351493	+	0.608804i
$243$	−5.46073	+	9.45825i	−0.350306	+	0.606747i
$244$	−3.13028			−0.200396
$245$	−20.9057	−	6.85388i	−1.33561	−	0.437879i
$246$	−8.07884			−0.515088
$247$	−13.5910	+	23.5404i	−0.864778	+	1.49784i
$248$	2.35533	+	4.07955i	0.149563	+	0.259051i
$249$	−8.15888	−	14.1316i	−0.517048	−	0.895553i
$250$	−0.191720	+	0.332069i	−0.0121255	+	0.0210019i
$251$	−12.1922			−0.769563			−0.384782	−	0.923008i	$-0.625723\pi$
$251$	−12.1922			−0.769563			−0.384782	+	0.923008i	$0.625723\pi$
$252$	1.86539	−	2.29734i	0.117509	−	0.144719i
$253$	−0.253163			−0.0159162
$254$	−5.13356	+	8.89158i	−0.322108	+	0.557907i
$255$	15.9350	+	27.6003i	0.997890	+	1.72840i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.0631873	+	0.109444i	−0.00394151	+	0.00682690i	−0.867989	−	0.496583i	$-0.834588\pi$
$257$	−0.0631873	+	0.109444i	−0.00394151	+	0.00682690i	0.864048	+	0.503410i	$0.167921\pi$
$258$	−7.83315			−0.487671
$259$	5.17646	+	13.5387i	0.321650	+	0.841252i
$260$	15.2545			0.946041
$261$	2.92225	−	5.06149i	0.180883	−	0.313298i
$262$	−2.20044	−	3.81127i	−0.135944	−	0.235461i
$263$	3.99691	+	6.92285i	0.246460	+	0.426881i	0.962541	−	0.271136i	$-0.0873993\pi$
$263$	3.99691	+	6.92285i	0.246460	+	0.426881i	−0.716081	+	0.698017i	$0.754066\pi$
$264$	0.173628	−	0.300733i	0.0106861	−	0.0185088i
$265$	38.9751			2.39422
$266$	−14.6318	−	2.33730i	−0.897134	−	0.143309i
$267$	7.37954			0.451620
$268$	1.29607	−	2.24486i	0.0791701	−	0.137127i
$269$	−15.9424	−	27.6131i	−0.972028	−	1.68360i	−0.689414	−	0.724368i	$-0.742132\pi$
$269$	−15.9424	−	27.6131i	−0.972028	−	1.68360i	−0.282614	−	0.959234i	$-0.591202\pi$
$270$	−8.87760	−	15.3765i	−0.540274	−	0.935781i
$271$	−9.55486	+	16.5495i	−0.580417	+	1.00531i	0.415013	+	0.909815i	$0.363777\pi$
$271$	−9.55486	+	16.5495i	−0.580417	+	1.00531i	−0.995430	+	0.0954956i	$0.969556\pi$
$272$	7.39260			0.448242
$273$	−17.3936	−	2.77848i	−1.05271	−	0.168161i
$274$	5.38083			0.325068
$275$	0.617463	−	1.06948i	0.0372344	−	0.0644920i
$276$	−0.685837	−	1.18790i	−0.0412825	−	0.0715034i
$277$	14.3671	+	24.8845i	0.863235	+	1.49517i	0.868789	+	0.495182i	$0.164898\pi$
$277$	14.3671	+	24.8845i	0.863235	+	1.49517i	−0.00555484	+	0.999985i	$0.501768\pi$
$278$	−3.87756	+	6.71613i	−0.232560	+	0.402806i
$279$	5.26892			0.315442
$280$	2.96970	+	7.76704i	0.177473	+	0.464169i
$281$	7.32721			0.437105			0.218552	−	0.975825i	$-0.429867\pi$
$281$	7.32721			0.437105			0.218552	+	0.975825i	$0.429867\pi$
$282$	8.32567	−	14.4205i	0.495787	−	0.858728i
$283$	0.461422	+	0.799207i	0.0274287	+	0.0475079i	0.879414	−	0.476058i	$-0.157935\pi$
$283$	0.461422	+	0.799207i	0.0274287	+	0.0475079i	−0.851985	+	0.523566i	$0.824601\pi$
$284$	−2.39061	−	4.14065i	−0.141856	−	0.245703i
$285$	−12.0719	+	20.9092i	−0.715078	+	1.23855i
$286$	1.22875			0.0726572
$287$	9.82263	−	12.0972i	0.579811	−	0.714073i
$288$	−1.11851			−0.0659089
$289$	−18.8253	+	32.6063i	−1.10737	+	1.91802i
$290$	8.21130	+	14.2224i	0.482184	+	0.835168i
$291$	−6.85030	−	11.8651i	−0.401572	−	0.695542i
$292$	−3.20891	+	5.55799i	−0.187787	+	0.325257i
$293$	−2.65005			−0.154818			−0.0774088	−	0.996999i	$-0.524665\pi$
$293$	−2.65005			−0.154818			−0.0774088	+	0.996999i	$0.524665\pi$
$294$	−1.97144	−	9.39715i	−0.114977	−	0.548053i
$295$	34.3338			1.99899
$296$	2.73921	−	4.74445i	0.159213	−	0.275766i
$297$	−0.715090	−	1.23857i	−0.0414937	−	0.0718692i
$298$	3.35991	+	5.81953i	0.194634	+	0.337116i
$299$	2.42679	−	4.20333i	0.140345	−	0.243085i
$300$	6.69102			0.386306
$301$	9.52391	−	11.7293i	0.548949	−	0.676064i
$302$	11.0654			0.636742
$303$	12.5369	−	21.7145i	0.720225	−	1.24747i
$304$	2.80021	+	4.85011i	0.160603	+	0.278173i
$305$	−4.91912	−	8.52017i	−0.281668	−	0.487863i
$306$	4.13435	−	7.16091i	0.236345	−	0.409362i
$307$	−15.9965			−0.912969			−0.456485	−	0.889731i	$-0.650892\pi$
$307$	−15.9965			−0.912969			−0.456485	+	0.889731i	$0.650892\pi$
$308$	0.239209	+	0.625634i	0.0136302	+	0.0356488i
$309$	−0.699300			−0.0397818
$310$	−7.40262	+	12.8217i	−0.420441	+	0.728225i
$311$	−6.75879	−	11.7066i	−0.383256	−	0.663819i	0.608270	−	0.793730i	$-0.291864\pi$
$311$	−6.75879	−	11.7066i	−0.383256	−	0.663819i	−0.991526	+	0.129912i	$0.958531\pi$
$312$	3.32877	+	5.76559i	0.188454	+	0.326412i
$313$	−4.70941	+	8.15694i	−0.266192	+	0.461058i	−0.967875	−	0.251431i	$-0.919099\pi$
$313$	−4.70941	+	8.15694i	−0.266192	+	0.461058i	0.701683	+	0.712489i	$0.252432\pi$
$314$	6.53633			0.368866
$315$	9.18443	+	1.46713i	0.517484	+	0.0826636i
$316$	3.63660			0.204575
$317$	9.93921	−	17.2152i	0.558241	−	0.966903i	−0.439402	−	0.898291i	$-0.644810\pi$
$317$	9.93921	−	17.2152i	0.558241	−	0.966903i	0.997643	−	0.0686120i	$-0.0218570\pi$
$318$	8.50498	+	14.7311i	0.476936	+	0.826077i
$319$	0.661420	+	1.14561i	0.0370324	+	0.0641420i
$320$	1.57146	−	2.72186i	0.0878475	−	0.152156i
$321$	13.3486			0.745044
$322$	2.61263	+	0.417345i	0.145596	+	0.0232577i
$323$	−41.4017			−2.30365
$324$	2.19670	−	3.80480i	0.122039	−	0.211378i
$325$	11.8379	+	20.5038i	0.656648	+	1.13735i
$326$	−4.99153	−	8.64558i	−0.276455	−	0.478835i
$327$	−7.14253	+	12.3712i	−0.394983	+	0.684130i
$328$	−5.88977			−0.325208
$329$	11.4703	+	29.9999i	0.632381	+	1.65395i
$330$	1.09140			0.0600797
$331$	−0.226096	+	0.391610i	−0.0124274	+	0.0215249i	−0.872172	−	0.489199i	$-0.837289\pi$
$331$	−0.226096	+	0.391610i	−0.0124274	+	0.0215249i	0.859745	+	0.510724i	$0.170623\pi$
$332$	−5.94812	−	10.3024i	−0.326445	−	0.565420i
$333$	−3.06384	−	5.30672i	−0.167897	−	0.290806i
$334$	7.36818	−	12.7621i	0.403169	−	0.698309i
$335$	8.14692			0.445114
$336$	−2.28760	+	2.81732i	−0.124799	+	0.153697i
$337$	−7.37734			−0.401870			−0.200935	−	0.979605i	$-0.564398\pi$
$337$	−7.37734			−0.401870			−0.200935	+	0.979605i	$0.564398\pi$
$338$	−5.27863	+	9.14285i	−0.287119	+	0.497306i
$339$	−5.83484	−	10.1062i	−0.316905	−	0.548896i
$340$	11.6172	+	20.1216i	0.630032	+	1.09125i
$341$	−0.596281	+	1.03279i	−0.0322904	+	0.0559286i
$342$	6.26413			0.338725
$343$	16.4682	+	8.47347i	0.889197	+	0.457524i
$344$	−5.71065			−0.307898
$345$	2.15554	−	3.73350i	0.116050	−	0.201005i
$346$	6.22311	+	10.7787i	0.334557	+	0.579469i
$347$	12.5259	+	21.6955i	0.672426	+	1.16468i	0.977214	+	0.212256i	$0.0680810\pi$
$347$	12.5259	+	21.6955i	0.672426	+	1.16468i	−0.304788	+	0.952420i	$0.598586\pi$
$348$	−3.58367	+	6.20710i	−0.192105	+	0.332736i
$349$	3.03698			0.162566			0.0812830	−	0.996691i	$-0.474098\pi$
$349$	3.03698			0.162566			0.0812830	+	0.996691i	$0.474098\pi$
$350$	−8.13526	+	10.0191i	−0.434848	+	0.535542i
$351$	27.4191			1.46352
$352$	0.126581	−	0.219245i	0.00674681	−	0.0116858i
$353$	2.17756	+	3.77164i	0.115900	+	0.200744i	0.918139	−	0.396258i	$-0.129692\pi$
$353$	2.17756	+	3.77164i	0.115900	+	0.200744i	−0.802239	+	0.597003i	$0.796358\pi$
$354$	7.49218	+	12.9768i	0.398205	+	0.689711i
$355$	7.51351	−	13.0138i	0.398775	−	0.690699i
$356$	5.37995			0.285137
$357$	−9.58134	−	25.0593i	−0.507098	−	1.32628i
$358$	4.33200			0.228953
$359$	13.5980	−	23.5525i	0.717676	−	1.24305i	−0.244242	−	0.969714i	$-0.578539\pi$
$359$	13.5980	−	23.5525i	0.717676	−	1.24305i	0.961918	−	0.273337i	$-0.0881274\pi$
$360$	−1.75770	−	3.04443i	−0.0926389	−	0.160455i
$361$	−6.18235	−	10.7081i	−0.325387	−	0.563586i
$362$	−11.9636	+	20.7216i	−0.628794	+	1.08910i
$363$	−15.0005			−0.787322
$364$	−12.6806	−	2.02562i	−0.664644	−	0.106171i
$365$	−20.1707			−1.05578
$366$	2.14686	−	3.71847i	0.112218	−	0.194368i
$367$	−6.02049	−	10.4278i	−0.314267	−	0.544326i	0.665015	−	0.746830i	$-0.268425\pi$
$367$	−6.02049	−	10.4278i	−0.314267	−	0.544326i	−0.979281	+	0.202504i	$0.935092\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	−3.29388	+	5.70518i	−0.171473	+	0.297000i
$370$	17.2183			0.895136
$371$	−32.3989	−	5.17544i	−1.68207	−	0.268695i
$372$	−6.46148			−0.335012
$373$	2.22326	−	3.85080i	0.115116	−	0.199387i	−0.802710	−	0.596369i	$-0.796609\pi$
$373$	2.22326	−	3.85080i	0.115116	−	0.199387i	0.917826	+	0.396983i	$0.129943\pi$
$374$	0.935765	+	1.62079i	0.0483873	+	0.0838092i
$375$	−0.262978	−	0.455491i	−0.0135801	−	0.0235214i
$376$	6.06972	−	10.5131i	0.313022	−	0.542170i
$377$	−25.3612			−1.30617
$378$	5.33788	+	13.9609i	0.274551	+	0.718069i
$379$	8.44622			0.433853			0.216927	−	0.976188i	$-0.430397\pi$
$379$	8.44622			0.433853			0.216927	+	0.976188i	$0.430397\pi$
$380$	−8.80086	+	15.2435i	−0.451474	+	0.781977i
$381$	−7.04156	−	12.1963i	−0.360750	−	0.624838i
$382$	3.71523	+	6.43497i	0.190088	+	0.329242i
$383$	14.3621	−	24.8759i	0.733869	−	1.27110i	−0.221348	−	0.975195i	$-0.571046\pi$
$383$	14.3621	−	24.8759i	0.733869	−	1.27110i	0.955218	−	0.295904i	$-0.0956210\pi$
$384$	1.37167			0.0699979
$385$	−1.32698	+	1.63425i	−0.0676290	+	0.0832893i
$386$	2.47275			0.125860
$387$	−3.19371	+	5.53168i	−0.162346	+	0.281191i
$388$	−4.99412	−	8.65006i	−0.253538	−	0.439140i
$389$	14.6133	+	25.3109i	0.740923	+	1.28332i	0.952076	+	0.305862i	$0.0989448\pi$
$389$	14.6133	+	25.3109i	0.740923	+	1.28332i	−0.211153	+	0.977453i	$0.567722\pi$
$390$	−10.4621	+	18.1208i	−0.529768	+	0.917584i
$391$	7.39260			0.373860
$392$	−1.43725	−	6.85086i	−0.0725923	−	0.346021i
$393$	6.03657			0.304505
$394$	3.20851	−	5.55730i	0.161642	−	0.279973i
$395$	5.71479	+	9.89831i	0.287542	+	0.498038i
$396$	−0.141583	−	0.245228i	−0.00711479	−	0.0123232i
$397$	−3.60132	+	6.23767i	−0.180745	+	0.313060i	−0.942135	−	0.335235i	$-0.891184\pi$
$397$	−3.60132	+	6.23767i	−0.180745	+	0.313060i	0.761389	+	0.648295i	$0.224518\pi$
$398$	21.7463			1.09004
$399$	12.8115	−	15.7782i	0.641379	−	0.789897i
$400$	4.87800			0.243900
$401$	−3.91019	+	6.77264i	−0.195265	+	0.338210i	−0.946988	−	0.321270i	$-0.895890\pi$
$401$	−3.91019	+	6.77264i	−0.195265	+	0.338210i	0.751722	+	0.659480i	$0.229224\pi$
$402$	1.77779	+	3.07922i	0.0886679	+	0.153577i
$403$	−11.4318	−	19.8004i	−0.569457	−	0.986329i
$404$	9.13984	−	15.8307i	0.454724	−	0.787605i
$405$	13.8081			0.686132
$406$	−4.93725	−	12.9130i	−0.245032	−	0.640863i
$407$	1.38693			0.0687476
$408$	−5.07012	+	8.78170i	−0.251008	+	0.434759i
$409$	−14.2185	−	24.6272i	−0.703061	−	1.21774i	−0.967387	−	0.253304i	$-0.918483\pi$
$409$	−14.2185	−	24.6272i	−0.703061	−	1.21774i	0.264326	−	0.964434i	$-0.414851\pi$
$410$	−9.25556	−	16.0311i	−0.457099	−	0.791719i
$411$	−3.69037	+	6.39192i	−0.182033	+	0.315290i
$412$	−0.509815			−0.0251168
$413$	−28.5407	−	4.55913i	−1.40440	−	0.224340i
$414$	−1.11851			−0.0549718
$415$	18.6945	−	32.3798i	0.917677	−	1.58946i
$416$	2.42679	+	4.20333i	0.118983	+	0.206085i
$417$	−5.31874	−	9.21233i	−0.260460	−	0.451130i
$418$	−0.708908	+	1.22787i	−0.0346738	+	0.0600569i
$419$	−1.45090			−0.0708809			−0.0354404	−	0.999372i	$-0.511283\pi$
$419$	−1.45090			−0.0708809			−0.0354404	+	0.999372i	$0.511283\pi$
$420$	−11.2632	−	1.79920i	−0.549589	−	0.0877921i
$421$	−21.2780			−1.03703			−0.518513	−	0.855070i	$-0.673514\pi$
$421$	−21.2780			−1.03703			−0.518513	+	0.855070i	$0.673514\pi$
$422$	11.5272	−	19.9657i	0.561136	−	0.971916i
$423$	−6.78905	−	11.7590i	−0.330095	−	0.571741i
$424$	6.20044	+	10.7395i	0.301120	+	0.521555i
$425$	−18.0306	+	31.2298i	−0.874610	+	1.51487i
$426$	6.55826			0.317749
$427$	2.95775	+	7.73578i	0.143135	+	0.374360i
$428$	9.73158			0.470394
$429$	−0.842719	+	1.45963i	−0.0406868	+	0.0704717i
$430$	−8.97409	−	15.5436i	−0.432769	−	0.749578i
$431$	15.6251	+	27.0634i	0.752634	+	1.30360i	0.946542	+	0.322580i	$0.104550\pi$
$431$	15.6251	+	27.0634i	0.752634	+	1.30360i	−0.193908	+	0.981020i	$0.562116\pi$
$432$	2.82463	−	4.89240i	0.135900	−	0.235386i
$433$	21.2327			1.02038			0.510190	−	0.860062i	$-0.329575\pi$
$433$	21.2327			1.02038			0.510190	+	0.860062i	$0.329575\pi$
$434$	7.85617	−	9.67535i	0.377108	−	0.464432i
$435$	−22.5265			−1.08006
$436$	−5.20716	+	9.01907i	−0.249378	+	0.431935i
$437$	2.80021	+	4.85011i	0.133952	+	0.232012i
$438$	−4.40158	−	7.62375i	−0.210315	−	0.364277i
$439$	9.38472	−	16.2548i	0.447908	−	0.775800i	−0.550341	−	0.834940i	$-0.685502\pi$
$439$	9.38472	−	16.2548i	0.447908	−	0.775800i	0.998250	+	0.0591397i	$0.0188357\pi$
$440$	0.795672			0.0379322
$441$	−7.43994	−	2.43917i	−0.354283	−	0.116151i
$442$	−35.8806			−1.70667
$443$	−1.09105	+	1.88975i	−0.0518371	+	0.0897846i	−0.890780	−	0.454435i	$-0.849841\pi$
$443$	−1.09105	+	1.88975i	−0.0518371	+	0.0897846i	0.838943	+	0.544220i	$0.183174\pi$
$444$	3.75730	+	6.50784i	0.178314	+	0.308848i
$445$	8.45440	+	14.6435i	0.400777	+	0.694166i
$446$	6.32353	−	10.9527i	0.299428	−	0.518624i
$447$	−9.21739			−0.435968
$448$	−1.66774	+	2.05393i	−0.0787935	+	0.0970391i
$449$	12.4496			0.587534			0.293767	−	0.955877i	$-0.405091\pi$
$449$	12.4496			0.587534			0.293767	+	0.955877i	$0.405091\pi$
$450$	2.72805	−	4.72512i	0.128601	−	0.222744i
$451$	−0.745534	−	1.29130i	−0.0351058	−	0.0608051i
$452$	−4.25381	−	7.36782i	−0.200082	−	0.346553i
$453$	−7.58905	+	13.1446i	−0.356565	+	0.617588i
$454$	−2.49855			−0.117263
$455$	−14.4137	−	37.6980i	−0.675724	−	1.76731i
$456$	−7.68195			−0.359740
$457$	4.88911	−	8.46819i	0.228703	−	0.396125i	−0.728721	−	0.684811i	$-0.759885\pi$
$457$	4.88911	−	8.46819i	0.228703	−	0.396125i	0.957424	+	0.288686i	$0.0932182\pi$
$458$	−0.0727674	−	0.126037i	−0.00340020	−	0.00588931i
$459$	20.8813	+	36.1675i	0.974657	+	1.68816i
$460$	1.57146	−	2.72186i	0.0732699	−	0.126907i
$461$	−30.4387			−1.41767			−0.708837	−	0.705372i	$-0.750780\pi$
$461$	−30.4387			−1.41767			−0.708837	+	0.705372i	$0.750780\pi$
$462$	−0.907252	−	0.144926i	−0.0422092	−	0.00674255i
$463$	−28.6101			−1.32962			−0.664812	−	0.747011i	$-0.731488\pi$
$463$	−28.6101			−1.32962			−0.664812	+	0.747011i	$0.731488\pi$
$464$	−2.61263	+	4.52520i	−0.121288	+	0.210077i
$465$	−10.1540	−	17.5872i	−0.470880	−	0.815588i
$466$	2.80784	+	4.86332i	0.130071	+	0.225289i
$467$	−0.106744	+	0.184887i	−0.00493954	+	0.00855553i	−0.868485	−	0.495716i	$-0.834906\pi$
$467$	−0.106744	+	0.184887i	−0.00493954	+	0.00855553i	0.863545	+	0.504272i	$0.168239\pi$
$468$	5.42879			0.250946
$469$	−6.77230	−	1.08182i	−0.312716	−	0.0499536i
$470$	38.1534			1.75988
$471$	−4.48285	+	7.76453i	−0.206559	+	0.357771i
$472$	5.46207	+	9.46058i	0.251412	+	0.435459i
$473$	−0.722862	−	1.25203i	−0.0332372	−	0.0575686i
$474$	−2.49412	+	4.31994i	−0.114559	+	0.198421i
$475$	−27.3188			−1.25347
$476$	−6.98514	−	18.2691i	−0.320163	−	0.837365i
$477$	13.8705			0.635087
$478$	3.17148	−	5.49317i	0.145060	−	0.251252i
$479$	9.01570	+	15.6156i	0.411938	+	0.713497i	0.995102	−	0.0988574i	$-0.0315188\pi$
$479$	9.01570	+	15.6156i	0.411938	+	0.713497i	−0.583164	+	0.812355i	$0.698185\pi$
$480$	2.15554	+	3.73350i	0.0983863	+	0.170410i
$481$	−13.2950	+	23.0276i	−0.606199	+	1.04997i
$482$	−24.9629			−1.13703
$483$	−2.28760	+	2.81732i	−0.104089	+	0.128193i
$484$	−10.9359			−0.497087
$485$	15.6962	−	27.1865i	0.712725	−	1.23448i
$486$	−5.46073	−	9.45825i	−0.247704	−	0.429035i
$487$	10.5061	+	18.1972i	0.476078	+	0.824592i	0.999624	−	0.0274055i	$-0.00872454\pi$
$487$	10.5061	+	18.1972i	0.476078	+	0.824592i	−0.523546	+	0.851997i	$0.675391\pi$
$488$	1.56514	−	2.71090i	0.0708505	−	0.122717i
$489$	13.6935			0.619242
$490$	16.3885	−	14.6779i	0.740355	−	0.663079i
$491$	−10.7952			−0.487179			−0.243589	−	0.969878i	$-0.578325\pi$
$491$	−10.7952			−0.487179			−0.243589	+	0.969878i	$0.578325\pi$
$492$	4.03942	−	6.99648i	0.182111	−	0.315426i
$493$	−19.3141	−	33.4530i	−0.869864	−	1.50665i
$494$	−13.5910	−	23.5404i	−0.611490	−	1.05913i
$495$	0.444984	−	0.770735i	0.0200005	−	0.0346420i
$496$	−4.71065			−0.211515
$497$	−7.97384	+	9.82028i	−0.357676	+	0.440500i
$498$	16.3178			0.731216
$499$	16.2477	−	28.1419i	0.727349	−	1.25980i	−0.230651	−	0.973036i	$-0.574086\pi$
$499$	16.2477	−	28.1419i	0.727349	−	1.25980i	0.958000	−	0.286768i	$-0.0925809\pi$
$500$	−0.191720	−	0.332069i	−0.00857399	−	0.0148506i
$501$	10.1067	+	17.5054i	0.451536	+	0.782083i
$502$	6.09609	−	10.5587i	0.272082	−	0.471259i
$503$	34.8801			1.55523			0.777613	−	0.628743i	$-0.216430\pi$
$503$	34.8801			1.55523			0.777613	+	0.628743i	$0.216430\pi$
$504$	1.05686	+	2.76415i	0.0470764	+	0.123125i
$505$	57.4517			2.55657
$506$	0.126581	−	0.219245i	0.00562723	−	0.00974664i
$507$	−7.24055	−	12.5410i	−0.321564	−	0.556966i
$508$	−5.13356	−	8.89158i	−0.227765	−	0.394500i
$509$	6.23339	−	10.7965i	0.276290	−	0.478548i	−0.694170	−	0.719811i	$-0.744228\pi$
$509$	6.23339	−	10.7965i	0.276290	−	0.478548i	0.970460	+	0.241263i	$0.0775616\pi$
$510$	−31.8700			−1.41123
$511$	16.7674	+	2.67844i	0.741745	+	0.118487i
$512$	1.00000			0.0441942
$513$	−15.8191	+	27.3995i	−0.698430	+	1.20972i
$514$	−0.0631873	−	0.109444i	−0.00278707	−	0.00482735i
$515$	−0.801156	−	1.38764i	−0.0353032	−	0.0611469i
$516$	3.91658	−	6.78371i	0.172418	−	0.298636i
$517$	3.07325			0.135161
$518$	−14.3131	−	2.28639i	−0.628880	−	0.100458i
$519$	−17.0722			−0.749385
$520$	−7.62723	+	13.2107i	−0.334476	+	0.579330i
$521$	19.1124	+	33.1036i	0.837328	+	1.45030i	0.892121	+	0.451797i	$0.149217\pi$
$521$	19.1124	+	33.1036i	0.837328	+	1.45030i	−0.0547924	+	0.998498i	$0.517450\pi$
$522$	2.92225	+	5.06149i	0.127904	+	0.221535i
$523$	−9.65205	+	16.7178i	−0.422055	+	0.731020i	−0.996140	−	0.0877753i	$-0.972024\pi$
$523$	−9.65205	+	16.7178i	−0.422055	+	0.731020i	0.574086	+	0.818795i	$0.305358\pi$
$524$	4.40088			0.192253
$525$	−6.32223	−	16.5354i	−0.275925	−	0.721662i
$526$	−7.99382			−0.348547
$527$	17.4120	−	30.1585i	0.758478	−	1.31372i
$528$	0.173628	+	0.300733i	0.00755620	+	0.0130877i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−19.4875	+	33.7534i	−0.846484	+	1.46615i
$531$	12.2188			0.530250
$532$	9.34007	−	11.5029i	0.404943	−	0.498713i
$533$	28.5865			1.23822
$534$	−3.68977	+	6.39087i	−0.159672	+	0.276560i
$535$	15.2928	+	26.4880i	0.661167	+	1.14517i
$536$	1.29607	+	2.24486i	0.0559817	+	0.0969632i
$537$	−2.97105	+	5.14600i	−0.128210	+	0.222066i
$538$	31.8849			1.37465
$539$	1.32009	−	1.18230i	0.0568603	−	0.0509254i
$540$	17.7552			0.764062
$541$	−11.4144	+	19.7703i	−0.490743	+	0.849992i	−0.999943	−	0.0106563i	$-0.996608\pi$
$541$	−11.4144	+	19.7703i	−0.490743	+	0.849992i	0.509200	+	0.860648i	$0.329941\pi$
$542$	−9.55486	−	16.5495i	−0.410416	−	0.710862i
$543$	−16.4102	−	28.4233i	−0.704229	−	1.21976i
$544$	−3.69630	+	6.40218i	−0.158478	+	0.274491i
$545$	−32.7315			−1.40206
$546$	11.1031	−	13.6741i	0.475167	−	0.585197i
$547$	−17.0235			−0.727873			−0.363937	−	0.931424i	$-0.618568\pi$
$547$	−17.0235			−0.727873			−0.363937	+	0.931424i	$0.618568\pi$
$548$	−2.69042	+	4.65994i	−0.114929	+	0.199063i
$549$	−1.75063	−	3.03217i	−0.0747149	−	0.129410i
$550$	0.617463	+	1.06948i	0.0263287	+	0.0456027i
$551$	14.6318	−	25.3430i	0.623336	−	1.07965i
$552$	1.37167			0.0583823
$553$	−3.43616	−	8.98704i	−0.146121	−	0.382168i
$554$	−28.7342			−1.22080
$555$	−11.8089	+	20.4537i	−0.501261	+	0.868210i
$556$	−3.87756	−	6.71613i	−0.164445	−	0.284827i
$557$	10.5739	+	18.3145i	0.448029	+	0.776009i	0.998258	−	0.0590053i	$-0.0187929\pi$
$557$	10.5739	+	18.3145i	0.448029	+	0.776009i	−0.550229	+	0.835014i	$0.685460\pi$
$558$	−2.63446	+	4.56302i	−0.111526	+	0.193168i
$559$	27.7171			1.17231
$560$	−8.21130	−	1.31168i	−0.346991	−	0.0554288i
$561$	−2.56713			−0.108384
$562$	−3.66361	+	6.34555i	−0.154540	+	0.267671i
$563$	−5.32248	−	9.21881i	−0.224316	−	0.388527i	0.731798	−	0.681522i	$-0.238681\pi$
$563$	−5.32248	−	9.21881i	−0.224316	−	0.388527i	−0.956114	+	0.292995i	$0.905348\pi$
$564$	8.32567	+	14.4205i	0.350574	+	0.607212i
$565$	13.3694	−	23.1565i	0.562456	−	0.974202i
$566$	−0.922845			−0.0387901
$567$	−11.4783	−	1.83356i	−0.482044	−	0.0770023i
$568$	4.78121			0.200615
$569$	16.2731	−	28.1859i	0.682206	−	1.18161i	−0.292101	−	0.956388i	$-0.594354\pi$
$569$	16.2731	−	28.1859i	0.682206	−	1.18161i	0.974306	−	0.225227i	$-0.0723125\pi$
$570$	−12.0719	−	20.9092i	−0.505636	−	0.875788i
$571$	−15.9348	−	27.5999i	−0.666851	−	1.15502i	−0.978780	−	0.204915i	$-0.934308\pi$
$571$	−15.9348	−	27.5999i	−0.666851	−	1.15502i	0.311929	−	0.950106i	$-0.399025\pi$
$572$	−0.614373	+	1.06412i	−0.0256882	+	0.0444933i
$573$	−10.1922			−0.425784
$574$	5.56514	+	14.5552i	0.232284	+	0.607523i
$575$	4.87800			0.203427
$576$	0.559256	−	0.968659i	0.0233023	−	0.0403608i
$577$	−3.86968	−	6.70248i	−0.161097	−	0.279028i	0.774165	−	0.632983i	$-0.218170\pi$
$577$	−3.86968	−	6.70248i	−0.161097	−	0.279028i	−0.935262	+	0.353955i	$0.884836\pi$
$578$	−18.8253	−	32.6063i	−0.783028	−	1.35624i
$579$	−1.69590	+	2.93739i	−0.0704793	+	0.122074i
$580$	−16.4226			−0.681912
$581$	−19.8399	+	24.4340i	−0.823097	+	1.01369i
$582$	13.7006			0.567908
$583$	−1.56972	+	2.71883i	−0.0650111	+	0.112603i
$584$	−3.20891	−	5.55799i	−0.132786	−	0.229991i
$585$	8.53114	+	14.7764i	0.352719	+	0.610928i
$586$	1.32503	−	2.29501i	0.0547363	−	0.0948061i
$587$	6.74604			0.278439			0.139219	−	0.990262i	$-0.455541\pi$
$587$	6.74604			0.278439			0.139219	+	0.990262i	$0.455541\pi$
$588$	9.12389	+	2.99125i	0.376263	+	0.123357i
$589$	26.3816			1.08704
$590$	−17.1669	+	29.7339i	−0.706750	+	1.22413i
$591$	4.40103	+	7.62280i	0.181034	+	0.313560i
$592$	2.73921	+	4.74445i	0.112581	+	0.194996i
$593$	−15.2109	+	26.3460i	−0.624635	+	1.08190i	0.363976	+	0.931408i	$0.381419\pi$
$593$	−15.2109	+	26.3460i	−0.624635	+	1.08190i	−0.988611	+	0.150492i	$0.951914\pi$
$594$	1.43018			0.0586810
$595$	38.7491	−	47.7219i	1.58856	−	1.95641i
$596$	−6.71981			−0.275254
$597$	−14.9144	+	25.8326i	−0.610407	+	1.05726i
$598$	2.42679	+	4.20333i	0.0992389	+	0.171887i
$599$	4.68285	+	8.11094i	0.191336	+	0.331404i	0.945693	−	0.325060i	$-0.105385\pi$
$599$	4.68285	+	8.11094i	0.191336	+	0.331404i	−0.754357	+	0.656464i	$0.772051\pi$
$600$	−3.34551	+	5.79460i	−0.136580	+	0.236563i
$601$	−14.6070			−0.595833			−0.297916	−	0.954592i	$-0.596292\pi$
$601$	−14.6070			−0.595833			−0.297916	+	0.954592i	$0.596292\pi$
$602$	5.39590	+	14.1126i	0.219920	+	0.575186i
$603$	2.89934			0.118070
$604$	−5.53269	+	9.58291i	−0.225122	+	0.389923i
$605$	−17.1854	−	29.7660i	−0.698685	−	1.21016i
$606$	12.5369	+	21.7145i	0.509276	+	0.882091i
$607$	−5.44354	+	9.42848i	−0.220946	+	0.382690i	−0.955096	−	0.296298i	$-0.904248\pi$
$607$	−5.44354	+	9.42848i	−0.220946	+	0.382690i	0.734149	+	0.678988i	$0.237581\pi$
$608$	−5.60042			−0.227127
$609$	18.7256	+	2.99125i	0.758800	+	0.121212i
$610$	9.83824			0.398339
$611$	−29.4599	+	51.0260i	−1.19182	+	2.06429i
$612$	4.13435	+	7.16091i	0.167121	+	0.289463i
$613$	7.72526	+	13.3805i	0.312020	+	0.540435i	0.978800	−	0.204820i	$-0.0656610\pi$
$613$	7.72526	+	13.3805i	0.312020	+	0.540435i	−0.666779	+	0.745255i	$0.732328\pi$
$614$	7.99826	−	13.8534i	0.322783	−	0.559077i
$615$	25.3912			1.02387
$616$	−0.661420	−	0.105656i	−0.0266494	−	0.00425700i
$617$	27.4815			1.10636			0.553182	−	0.833060i	$-0.313413\pi$
$617$	27.4815			1.10636			0.553182	+	0.833060i	$0.313413\pi$
$618$	0.349650	−	0.605612i	0.0140650	−	0.0243613i
$619$	−10.4893	−	18.1680i	−0.421600	−	0.730232i	0.574496	−	0.818507i	$-0.305198\pi$
$619$	−10.4893	−	18.1680i	−0.421600	−	0.730232i	−0.996096	+	0.0882749i	$0.971865\pi$
$620$	−7.40262	−	12.8217i	−0.297296	−	0.514933i
$621$	2.82463	−	4.89240i	0.113348	−	0.196325i
$622$	13.5176			0.542006
$623$	−5.08342	−	13.2953i	−0.203663	−	0.532666i
$624$	−6.65753			−0.266515
$625$	12.7976	−	22.1660i	0.511902	−	0.886641i
$626$	−4.70941	−	8.15694i	−0.188226	−	0.326017i
$627$	−0.972391	−	1.68423i	−0.0388336	−	0.0672617i
$628$	−3.26816	+	5.66063i	−0.130414	+	0.225884i
$629$	−40.4998			−1.61483
$630$	−5.86279	+	7.22039i	−0.233579	+	0.287667i
$631$	22.4950			0.895511			0.447755	−	0.894156i	$-0.352224\pi$
$631$	22.4950			0.895511			0.447755	+	0.894156i	$0.352224\pi$
$632$	−1.81830	+	3.14939i	−0.0723282	+	0.125276i
$633$	15.8116	+	27.3864i	0.628454	+	1.08851i
$634$	9.93921	+	17.2152i	0.394736	+	0.683703i
$635$	16.1344	−	27.9456i	0.640274	−	1.10899i
$636$	−17.0100			−0.674489
$637$	6.97583	+	33.2512i	0.276393	+	1.31746i
$638$	−1.32284			−0.0523717
$639$	2.67392	−	4.63137i	0.105779	−	0.183214i
$640$	1.57146	+	2.72186i	0.0621176	+	0.107591i
$641$	−5.26518	−	9.11956i	−0.207962	−	0.360201i	0.743110	−	0.669169i	$-0.233350\pi$
$641$	−5.26518	−	9.11956i	−0.207962	−	0.360201i	−0.951072	+	0.308968i	$0.900016\pi$
$642$	−6.67428	+	11.5602i	−0.263413	+	0.456244i
$643$	−15.5655			−0.613845			−0.306922	−	0.951735i	$-0.599299\pi$
$643$	−15.5655			−0.613845			−0.306922	+	0.951735i	$0.599299\pi$
$644$	−1.66774	+	2.05393i	−0.0657184	+	0.0809362i
$645$	24.6190			0.969374
$646$	20.7008	−	35.8549i	0.814463	−	1.41069i
$647$	10.4508	+	18.1013i	0.410862	+	0.711634i	0.994984	−	0.100032i	$-0.0318945\pi$
$647$	10.4508	+	18.1013i	0.410862	+	0.711634i	−0.584122	+	0.811666i	$0.698561\pi$
$648$	2.19670	+	3.80480i	0.0862945	+	0.149466i
$649$	−1.38279	+	2.39507i	−0.0542793	+	0.0940146i
$650$	−23.6758			−0.928640
$651$	6.10534	+	15.9681i	0.239287	+	0.625839i
$652$	9.98306			0.390967
$653$	1.85384	−	3.21094i	0.0725463	−	0.125654i	−0.827470	−	0.561509i	$-0.810221\pi$
$653$	1.85384	−	3.21094i	0.0725463	−	0.125654i	0.900017	+	0.435856i	$0.143554\pi$
$654$	−7.14253	−	12.3712i	−0.279295	−	0.483753i
$655$	6.91582	+	11.9786i	0.270224	+	0.468041i
$656$	2.94488	−	5.10069i	0.114978	−	0.199148i
$657$	−7.17840			−0.280056
$658$	−31.7158	−	5.06633i	−1.23641	−	0.197506i
$659$	34.8418			1.35724			0.678622	−	0.734488i	$-0.262577\pi$
$659$	34.8418			1.35724			0.678622	+	0.734488i	$0.262577\pi$
$660$	−0.545701	+	0.945182i	−0.0212414	+	0.0367912i
$661$	−2.33730	−	4.04832i	−0.0909103	−	0.157461i	0.816984	−	0.576660i	$-0.195644\pi$
$661$	−2.33730	−	4.04832i	−0.0909103	−	0.157461i	−0.907894	+	0.419199i	$0.862311\pi$
$662$	−0.226096	−	0.391610i	−0.00878748	−	0.0152204i
$663$	24.6082	−	42.6227i	0.955705	−	1.65533i
$664$	11.8962			0.461663
$665$	45.9867	+	7.34598i	1.78329	+	0.284865i
$666$	6.12767			0.237442
$667$	−2.61263	+	4.52520i	−0.101161	+	0.175217i
$668$	7.36818	+	12.7621i	0.285084	+	0.493779i
$669$	8.67382	+	15.0235i	0.335349	+	0.580842i
$670$	−4.07346	+	7.05544i	−0.157371	+	0.272575i
$671$	0.792469			0.0305929
$672$	−1.29607	−	3.38978i	−0.0499970	−	0.130764i
$673$	8.58209			0.330815			0.165408	−	0.986225i	$-0.447106\pi$
$673$	8.58209			0.330815			0.165408	+	0.986225i	$0.447106\pi$
$674$	3.68867	−	6.38897i	0.142082	−	0.246094i
$675$	13.7785	+	23.8651i	0.530336	+	0.918568i
$676$	−5.27863	−	9.14285i	−0.203024	−	0.351648i
$677$	−14.0475	+	24.3310i	−0.539889	+	0.935115i	0.459021	+	0.888426i	$0.348200\pi$
$677$	−14.0475	+	24.3310i	−0.539889	+	0.935115i	−0.998909	+	0.0466893i	$0.985133\pi$
$678$	11.6697			0.448171
$679$	−16.6578	+	20.5151i	−0.639269	+	0.787298i
$680$	−23.2344			−0.890999
$681$	1.71360	−	2.96803i	0.0656651	−	0.113735i
$682$	−0.596281	−	1.03279i	−0.0228328	−	0.0395475i
$683$	−17.9615	−	31.1102i	−0.687277	−	1.19040i	−0.972715	−	0.232002i	$-0.925473\pi$
$683$	−17.9615	−	31.1102i	−0.687277	−	1.19040i	0.285439	−	0.958397i	$-0.407861\pi$
$684$	−3.13207	+	5.42490i	−0.119758	+	0.207426i
$685$	−16.9116			−0.646158
$686$	−15.5723	+	10.0251i	−0.594554	+	0.382761i
$687$	0.199626			0.00761622
$688$	2.85533	−	4.94557i	0.108858	−	0.188548i
$689$	−30.0943	−	52.1249i	−1.14650	−	1.98580i
$690$	2.15554	+	3.73350i	0.0820599	+	0.142132i
$691$	−10.5868	+	18.3368i	−0.402739	+	0.697565i	−0.994055	−	0.108875i	$-0.965275\pi$
$691$	−10.5868	+	18.3368i	−0.402739	+	0.697565i	0.591316	+	0.806440i	$0.298609\pi$
$692$	−12.4462			−0.473134
$693$	−0.472247	+	0.581601i	−0.0179392	+	0.0220932i
$694$	−25.0518			−0.950954
$695$	12.1869	−	21.1083i	0.462275	−	0.800684i
$696$	−3.58367	−	6.20710i	−0.135839	−	0.235280i
$697$	21.7703	+	37.7073i	0.824611	+	1.42827i
$698$	−1.51849	+	2.63010i	−0.0574757	+	0.0995509i
$699$	−7.70288			−0.291349
$700$	−4.60914	−	12.0549i	−0.174209	−	0.455631i
$701$	34.5711			1.30573			0.652867	−	0.757473i	$-0.273566\pi$
$701$	34.5711			1.30573			0.652867	+	0.757473i	$0.273566\pi$
$702$	−13.7096	+	23.7456i	−0.517434	+	0.896222i
$703$	−15.3407	−	26.5709i	−0.578586	−	1.00214i
$704$	0.126581	+	0.219245i	0.00477071	+	0.00826312i
$705$	−26.1670	+	45.3226i	−0.985506	+	1.70695i
$706$	−4.35512			−0.163907
$707$	−47.7580	−	7.62892i	−1.79612	−	0.286915i
$708$	−14.9844			−0.563147
$709$	7.23114	−	12.5247i	0.271571	−	0.470375i	−0.697693	−	0.716397i	$-0.745790\pi$
$709$	7.23114	−	12.5247i	0.271571	−	0.470375i	0.969264	+	0.246022i	$0.0791234\pi$
$710$	7.51351	+	13.0138i	0.281977	+	0.488398i
$711$	2.03379	+	3.52263i	0.0762731	+	0.132109i
$712$	−2.68998	+	4.65917i	−0.100811	+	0.174610i
$713$	−4.71065			−0.176415
$714$	26.4927	+	4.23197i	0.991463	+	0.158378i
$715$	−3.86186			−0.144425
$716$	−2.16600	+	3.75162i	−0.0809472	+	0.140205i
$717$	4.35024	+	7.53484i	0.162463	+	0.281394i
$718$	13.5980	+	23.5525i	0.507474	+	0.878970i
$719$	−19.2684	+	33.3738i	−0.718588	+	1.24463i	0.242971	+	0.970034i	$0.421878\pi$
$719$	−19.2684	+	33.3738i	−0.718588	+	1.24463i	−0.961559	+	0.274598i	$0.911455\pi$
$720$	3.51540			0.131011
$721$	0.481716	+	1.25989i	0.0179400	+	0.0469209i
$722$	12.3647			0.460166
$723$	17.1205	−	29.6536i	0.636718	−	1.10283i
$724$	−11.9636	−	20.7216i	−0.444625	−	0.770112i
$725$	−12.7444	−	22.0739i	−0.473315	−	0.819806i
$726$	7.50025	−	12.9908i	0.278360	−	0.482134i
$727$	−46.3429			−1.71876			−0.859381	−	0.511336i	$-0.829151\pi$
$727$	−46.3429			−1.71876			−0.859381	+	0.511336i	$0.829151\pi$
$728$	8.09454	−	9.96892i	0.300003	−	0.369473i
$729$	28.1609			1.04299
$730$	10.0854	−	17.4684i	0.373276	−	0.646533i
$731$	21.1083	+	36.5606i	0.780718	+	1.35224i
$732$	2.14686	+	3.71847i	0.0793502	+	0.137439i
$733$	−6.10759	+	10.5786i	−0.225589	+	0.390731i	−0.956496	−	0.291746i	$-0.905764\pi$
$733$	−6.10759	+	10.5786i	−0.225589	+	0.390731i	0.730907	+	0.682477i	$0.239097\pi$
$734$	12.0410			0.444440
$735$	6.19611	+	29.5346i	0.228547	+	1.08940i
$736$	1.00000			0.0368605
$737$	−0.328117	+	0.568315i	−0.0120863	+	0.0209341i
$738$	−3.29388	−	5.70518i	−0.121250	−	0.210010i
$739$	5.10918	+	8.84936i	0.187944	+	0.325529i	0.944565	−	0.328325i	$-0.106484\pi$
$739$	5.10918	+	8.84936i	0.187944	+	0.325529i	−0.756620	+	0.653854i	$0.773151\pi$
$740$	−8.60914	+	14.9115i	−0.316478	+	0.548156i
$741$	37.2850			1.36970
$742$	20.6815	−	25.4705i	0.759242	−	0.935053i
$743$	−1.64539			−0.0603635			−0.0301818	−	0.999544i	$-0.509609\pi$
$743$	−1.64539			−0.0603635			−0.0301818	+	0.999544i	$0.509609\pi$
$744$	3.23074	−	5.59581i	0.118445	−	0.205152i
$745$	−10.5599	−	18.2904i	−0.386887	−	0.670107i
$746$	2.22326	+	3.85080i	0.0813994	+	0.140988i
$747$	6.65304	−	11.5234i	0.243422	−	0.421619i
$748$	−1.87153			−0.0684299
$749$	−9.19520	−	24.0494i	−0.335985	−	0.878746i
$750$	0.525955			0.0192052
$751$	−15.4150	+	26.6995i	−0.562500	+	0.974279i	0.434777	+	0.900538i	$0.356827\pi$
$751$	−15.4150	+	26.6995i	−0.562500	+	0.974279i	−0.997277	+	0.0737412i	$0.976506\pi$
$752$	6.06972	+	10.5131i	0.221340	+	0.383372i
$753$	8.36184	+	14.4831i	0.304723	+	0.527795i
$754$	12.6806	−	21.9634i	0.461800	−	0.799862i
$755$	−34.7777			−1.26569
$756$	−14.7594	−	2.35769i	−0.536794	−	0.0857482i
$757$	40.6131			1.47611			0.738053	−	0.674742i	$-0.235745\pi$
$757$	40.6131			1.47611			0.738053	+	0.674742i	$0.235745\pi$
$758$	−4.22311	+	7.31464i	−0.153390	+	0.265680i
$759$	0.173628	+	0.300733i	0.00630231	+	0.0109159i
$760$	−8.80086	−	15.2435i	−0.319241	−	0.552941i
$761$	−10.9370	+	18.9434i	−0.396466	+	0.686699i	−0.993287	−	0.115675i	$-0.963097\pi$
$761$	−10.9370	+	18.9434i	−0.396466	+	0.686699i	0.596821	+	0.802374i	$0.296430\pi$
$762$	14.0831			0.510178
$763$	27.2088	+	4.34636i	0.985023	+	0.157349i
$764$	−7.43047			−0.268825
$765$	−12.9940	+	22.5062i	−0.469798	+	0.813714i
$766$	14.3621	+	24.8759i	0.518924	+	0.898803i
$767$	−26.5106	−	45.9177i	−0.957243	−	1.65799i
$768$	−0.685837	+	1.18790i	−0.0247480	+	0.0428648i
$769$	−2.39428			−0.0863400			−0.0431700	−	0.999068i	$-0.513746\pi$
$769$	−2.39428			−0.0863400			−0.0431700	+	0.999068i	$0.513746\pi$
$770$	−0.751817	−	1.96632i	−0.0270936	−	0.0708614i
$771$	0.173345			0.00624285
$772$	−1.23637	+	2.14146i	−0.0444981	+	0.0770729i
$773$	25.7751	+	44.6438i	0.927066	+	1.60572i	0.788205	+	0.615413i	$0.211011\pi$
$773$	25.7751	+	44.6438i	0.927066	+	1.60572i	0.138861	+	0.990312i	$0.455656\pi$
$774$	−3.19371	−	5.53168i	−0.114796	−	0.198832i
$775$	11.4893	−	19.9000i	0.412707	−	0.714830i
$776$	9.98823			0.358557
$777$	12.5324	−	15.4345i	0.449599	−	0.553708i
$778$	−29.2266			−1.04782
$779$	−16.4926	+	28.5660i	−0.590908	+	1.02348i
$780$	−10.4621	−	18.1208i	−0.374602	−	0.648830i
$781$	0.605212	+	1.04826i	0.0216562	+	0.0375096i
$782$	−3.69630	+	6.40218i	−0.132179	+	0.228942i
$783$	−29.5188			−1.05492
$784$	6.65165	+	2.18073i	0.237559	+	0.0778833i
$785$	−20.5432			−0.733219
$786$	−3.01828	+	5.22782i	−0.107659	+	0.186470i
$787$	21.8195	+	37.7925i	0.777782	+	1.34716i	0.933217	+	0.359313i	$0.116989\pi$
$787$	21.8195	+	37.7925i	0.777782	+	1.34716i	−0.155435	+	0.987846i	$0.549678\pi$
$788$	3.20851	+	5.55730i	0.114298	+	0.197971i
$789$	5.48246	−	9.49589i	0.195181	−	0.338063i
$790$	−11.4296			−0.406646
$791$	−14.1885	+	17.4741i	−0.504487	+	0.621306i
$792$	0.283165			0.0100618
$793$	−7.59653	+	13.1576i	−0.269761	+	0.467239i
$794$	−3.60132	−	6.23767i	−0.127806	−	0.221367i
$795$	−26.7305	−	46.2987i	−0.948035	−	1.64204i
$796$	−10.8732	+	18.8329i	−0.385389	+	0.667513i
$797$	46.5734			1.64971			0.824857	−	0.565342i	$-0.191256\pi$
$797$	46.5734			1.64971			0.824857	+	0.565342i	$0.191256\pi$
$798$	7.25854	+	18.9842i	0.256950	+	0.672033i
$799$	−89.7420			−3.17484
$800$	−2.43900	+	4.22447i	−0.0862317	+	0.149358i
$801$	3.00877	+	5.21134i	0.106310	+	0.184134i
$802$	−3.91019	−	6.77264i	−0.138074	−	0.239150i
$803$	0.812376	−	1.40708i	0.0286681	−	0.0496546i
$804$	−3.55557			−0.125395
$805$	−8.21130	−	1.31168i	−0.289410	−	0.0462308i
$806$	22.8635			0.805334
$807$	−21.8678	+	37.8762i	−0.769784	+	1.33330i
$808$	9.13984	+	15.8307i	0.321538	+	0.556921i
$809$	−20.2689	−	35.1067i	−0.712615	−	1.23429i	−0.963872	−	0.266365i	$-0.914177\pi$
$809$	−20.2689	−	35.1067i	−0.712615	−	1.23429i	0.251257	−	0.967920i	$-0.419156\pi$
$810$	−6.90407	+	11.9582i	−0.242584	+	0.420168i
$811$	7.36250			0.258532			0.129266	−	0.991610i	$-0.458738\pi$
$811$	7.36250			0.258532			0.129266	+	0.991610i	$0.458738\pi$
$812$	13.6516	+	2.18073i	0.479079	+	0.0765287i
$813$	26.2123			0.919306
$814$	−0.693465	+	1.20112i	−0.0243059	+	0.0420991i
$815$	15.6880	+	27.1725i	0.549527	+	0.951810i
$816$	−5.07012	−	8.78170i	−0.177490	−	0.307421i
$817$	−15.9910	+	27.6973i	−0.559455	+	0.969005i
$818$	28.4371			0.994279
$819$	−5.12957	−	13.4160i	−0.179242	−	0.468794i
$820$	18.5111			0.646436
$821$	−23.6087	+	40.8915i	−0.823950	+	1.42712i	0.0787683	+	0.996893i	$0.474901\pi$
$821$	−23.6087	+	40.8915i	−0.823950	+	1.42712i	−0.902719	+	0.430231i	$0.858432\pi$
$822$	−3.69037	−	6.39192i	−0.128717	−	0.222944i
$823$	1.67567	+	2.90234i	0.0584100	+	0.101169i	0.893752	−	0.448562i	$-0.148064\pi$
$823$	1.67567	+	2.90234i	0.0584100	+	0.101169i	−0.835342	+	0.549731i	$0.814730\pi$
$824$	0.254908	−	0.441513i	0.00888013	−	0.0153808i
$825$	−1.69392			−0.0589746
$826$	18.2187	−	22.4374i	0.633909	−	0.780698i
$827$	40.5429			1.40981			0.704907	−	0.709300i	$-0.250989\pi$
$827$	40.5429			1.40981			0.704907	+	0.709300i	$0.250989\pi$
$828$	0.559256	−	0.968659i	0.0194355	−	0.0336632i
$829$	22.1802	+	38.4172i	0.770349	+	1.33428i	0.937372	+	0.348330i	$0.113251\pi$
$829$	22.1802	+	38.4172i	0.770349	+	1.33428i	−0.167023	+	0.985953i	$0.553416\pi$
$830$	18.6945	+	32.3798i	0.648896	+	1.12392i
$831$	19.7070	−	34.1335i	0.683627	−	1.18408i
$832$	−4.85358			−0.168268
$833$	−38.5479	+	34.5244i	−1.33561	+	1.19620i
$834$	10.6375			0.368346
$835$	−23.1577	+	40.1103i	−0.801404	+	1.38807i
$836$	−0.708908	−	1.22787i	−0.0245181	−	0.0424666i
$837$	−13.3058	−	23.0464i	−0.459917	−	0.796600i
$838$	0.725448	−	1.25651i	0.0250602	−	0.0434055i
$839$	8.44186			0.291445			0.145723	−	0.989325i	$-0.453449\pi$
$839$	8.44186			0.291445			0.145723	+	0.989325i	$0.453449\pi$
$840$	7.18977	−	8.85464i	0.248071	−	0.305514i
$841$	−1.69671			−0.0585071
$842$	10.6390	−	18.4273i	0.366644	−	0.635046i
$843$	−5.02527	−	8.70403i	−0.173080	−	0.299783i
$844$	11.5272	+	19.9657i	0.396783	+	0.687248i
$845$	16.5903	−	28.7353i	0.570725	−	0.988525i
$846$	13.5781			0.466825
$847$	10.3332	+	27.0256i	0.355051	+	0.928612i
$848$	−12.4009			−0.425848
$849$	0.632921	−	1.09625i	0.0217218	−	0.0376232i
$850$	−18.0306	−	31.2298i	−0.618443	−	1.07117i
$851$	2.73921	+	4.74445i	0.0938989	+	0.162638i
$852$	−3.27913	+	5.67962i	−0.112341	+	0.194581i
$853$	26.6940			0.913985			0.456993	−	0.889470i	$-0.348927\pi$
$853$	26.6940			0.913985			0.456993	+	0.889470i	$0.348927\pi$
$854$	−8.17825	−	1.30640i	−0.279854	−	0.0447042i
$855$	−19.6877			−0.673306
$856$	−4.86579	+	8.42780i	−0.166309	+	0.288056i
$857$	5.37607	+	9.31162i	0.183643	+	0.318079i	0.943118	−	0.332457i	$-0.107878\pi$
$857$	5.37607	+	9.31162i	0.183643	+	0.318079i	−0.759475	+	0.650536i	$0.774544\pi$
$858$	−0.842719	−	1.45963i	−0.0287699	−	0.0498310i
$859$	5.37712	−	9.31344i	0.183465	−	0.317770i	−0.759593	−	0.650398i	$-0.774602\pi$
$859$	5.37712	−	9.31344i	0.183465	−	0.317770i	0.943058	+	0.332628i	$0.107935\pi$
$860$	17.9482			0.612028
$861$	−21.1070	−	3.37166i	−0.719324	−	0.114906i
$862$	−31.2502			−1.06439
$863$	10.9258	−	18.9241i	0.371920	−	0.644184i	−0.617941	−	0.786225i	$-0.712033\pi$
$863$	10.9258	−	18.9241i	0.371920	−	0.644184i	0.989861	+	0.142040i	$0.0453662\pi$
$864$	2.82463	+	4.89240i	0.0960958	+	0.166443i
$865$	−19.5588	−	33.8768i	−0.665019	−	1.15185i
$866$	−10.6164	+	18.3881i	−0.360759	+	0.624853i
$867$	51.6443			1.75393
$868$	4.45102	+	11.6413i	0.151077	+	0.395132i
$869$	−0.920652			−0.0312310
$870$	11.2632	−	19.5085i	0.381859	−	0.661399i
$871$	−6.29059	−	10.8956i	−0.213148	−	0.369184i
$872$	−5.20716	−	9.01907i	−0.176337	−	0.305424i
$873$	5.58598	−	9.67519i	0.189057	−	0.327456i
$874$	−5.60042			−0.189437
$875$	−0.639481	+	0.787560i	−0.0216184	+	0.0266244i
$876$	8.80315			0.297431
$877$	17.8074	−	30.8434i	0.601314	−	1.04151i	−0.391308	−	0.920260i	$-0.627977\pi$
$877$	17.8074	−	30.8434i	0.601314	−	1.04151i	0.992622	−	0.121247i	$-0.0386894\pi$
$878$	9.38472	+	16.2548i	0.316719	+	0.548574i
$879$	1.81750	+	3.14801i	0.0613029	+	0.106180i
$880$	−0.397836	+	0.689072i	−0.0134110	+	0.0232286i
$881$	−48.0977			−1.62045			−0.810226	−	0.586118i	$-0.800655\pi$
$881$	−48.0977			−1.62045			−0.810226	+	0.586118i	$0.800655\pi$
$882$	5.83236	−	5.22359i	0.196386	−	0.175887i
$883$	−6.18248			−0.208057			−0.104028	−	0.994574i	$-0.533173\pi$
$883$	−6.18248			−0.208057			−0.104028	+	0.994574i	$0.533173\pi$
$884$	17.9403	−	31.0735i	0.603397	−	1.04512i
$885$	−23.5474	−	40.7853i	−0.791537	−	1.37098i
$886$	−1.09105	−	1.88975i	−0.0366544	−	0.0634873i
$887$	20.1427	−	34.8882i	0.676327	−	1.17143i	−0.299752	−	0.954017i	$-0.596904\pi$
$887$	20.1427	−	34.8882i	0.676327	−	1.17143i	0.976079	−	0.217415i	$-0.0697626\pi$
$888$	−7.51460			−0.252174
$889$	−17.1229	+	21.0879i	−0.574284	+	0.707266i
$890$	−16.9088			−0.566784
$891$	−0.556122	+	0.963232i	−0.0186308	+	0.0322695i
$892$	6.32353	+	10.9527i	0.211727	+	0.366723i
$893$	−33.9930	−	58.8776i	−1.13753	−	1.97026i
$894$	4.60870	−	7.98250i	0.154138	−	0.266975i
$895$	−13.6152			−0.455105
$896$	−0.944883	−	2.47127i	−0.0315663	−	0.0825595i
$897$	−6.65753			−0.222288
$898$	−6.22481	+	10.7817i	−0.207725	+	0.359790i
$899$	12.3072	+	21.3167i	0.410468	+	0.710951i
$900$	2.72805	+	4.72512i	0.0909349	+	0.157504i
$901$	45.8374	−	79.3927i	1.52706	−	2.64495i
$902$	1.49107			0.0496471
$903$	−20.4651	−	3.26912i	−0.681036	−	0.108790i
$904$	8.50762			0.282959
$905$	37.6008	−	65.1265i	1.24989	−	2.16488i
$906$	−7.58905	−	13.1446i	−0.252129	−	0.436701i
$907$	−2.15856	−	3.73874i	−0.0716739	−	0.124143i	0.827961	−	0.560786i	$-0.189501\pi$
$907$	−2.15856	−	3.73874i	−0.0716739	−	0.124143i	−0.899635	+	0.436643i	$0.856167\pi$
$908$	1.24927	−	2.16381i	0.0414586	−	0.0718084i
$909$	20.4460			0.678152
$910$	39.8542	+	6.36637i	1.32115	+	0.211043i
$911$	25.1067			0.831821			0.415910	−	0.909406i	$-0.363463\pi$
$911$	25.1067			0.831821			0.415910	+	0.909406i	$0.363463\pi$
$912$	3.84097	−	6.65276i	0.127187	−	0.220295i
$913$	1.50584	+	2.60819i	0.0498361	+	0.0863186i
$914$	4.88911	+	8.46819i	0.161717	+	0.280103i
$915$	−6.74743	+	11.6869i	−0.223063	+	0.386357i
$916$	0.145535			0.00480861
$917$	−4.15831	−	10.8758i	−0.137320	−	0.359150i
$918$	−41.7627			−1.37837
$919$	18.5329	−	32.0999i	0.611343	−	1.05888i	−0.379671	−	0.925122i	$-0.623963\pi$
$919$	18.5329	−	32.0999i	0.611343	−	1.05888i	0.991014	−	0.133756i	$-0.0427039\pi$
$920$	1.57146	+	2.72186i	0.0518096	+	0.0897369i
$921$	10.9710	+	19.0023i	0.361507	+	0.626148i
$922$	15.2194	−	26.3607i	0.501223	−	0.868144i
$923$	−23.2060			−0.763835
$924$	0.579135	−	0.713240i	0.0190521	−	0.0234639i
$925$	−26.7237			−0.878670
$926$	14.3050	−	24.7771i	0.470093	−	0.814225i
$927$	−0.285117	−	0.493837i	−0.00936447	−	0.0162197i
$928$	−2.61263	−	4.52520i	−0.0857637	−	0.148547i
$929$	0.802795	−	1.39048i	0.0263389	−	0.0456202i	−0.852556	−	0.522637i	$-0.824948\pi$
$929$	0.802795	−	1.39048i	0.0263389	−	0.0456202i	0.878894	+	0.477016i	$0.158282\pi$
$930$	20.3080			0.665924
$931$	−37.2520	−	12.2130i	−1.22089	−	0.400265i
$932$	−5.61568			−0.183948
$933$	−9.27086	+	16.0576i	−0.303514	+	0.525702i
$934$	−0.106744	−	0.184887i	−0.00349278	−	0.00604967i
$935$	−2.94104	−	5.09404i	−0.0961824	−	0.166593i
$936$	−2.71439	+	4.70147i	−0.0887227	+	0.153672i
$937$	15.0044			0.490172			0.245086	−	0.969501i	$-0.421184\pi$
$937$	15.0044			0.490172			0.245086	+	0.969501i	$0.421184\pi$
$938$	4.32303	−	5.32408i	0.141152	−	0.173837i
$939$	12.9196			0.421614
$940$	−19.0767	+	33.0418i	−0.622213	+	1.07770i
$941$	−9.17711	−	15.8952i	−0.299165	−	0.518170i	0.676780	−	0.736185i	$-0.263375\pi$
$941$	−9.17711	−	15.8952i	−0.299165	−	0.518170i	−0.975945	+	0.218016i	$0.930042\pi$
$942$	−4.48285	−	7.76453i	−0.146059	−	0.252982i
$943$	2.94488	−	5.10069i	0.0958986	−	0.166101i
$944$	−10.9241			−0.355551
$945$	−16.7766	−	43.8780i	−0.545742	−	1.42735i
$946$	1.44572			0.0470045
$947$	−5.93074	+	10.2723i	−0.192723	+	0.333806i	−0.946152	−	0.323724i	$-0.895065\pi$
$947$	−5.93074	+	10.2723i	−0.192723	+	0.333806i	0.753429	+	0.657530i	$0.228399\pi$
$948$	−2.49412	−	4.31994i	−0.0810051	−	0.140305i
$949$	15.5747	+	26.9762i	0.505576	+	0.875684i
$950$	13.6594	−	23.6588i	0.443170	−	0.767593i
$951$	−27.2667			−0.884183
$952$	19.3141	+	3.08526i	0.625974	+	0.0999939i
$953$	−37.7445			−1.22266			−0.611332	−	0.791374i	$-0.709366\pi$
$953$	−37.7445			−1.22266			−0.611332	+	0.791374i	$0.709366\pi$
$954$	−6.93526	+	12.0122i	−0.224537	+	0.388910i
$955$	−11.6767	−	20.2247i	−0.377850	−	0.654455i
$956$	3.17148	+	5.49317i	0.102573	+	0.177662i
$957$	0.907252	−	1.57141i	0.0293273	−	0.0507964i
$958$	−18.0314			−0.582568
$959$	14.0581	+	2.24566i	0.453960	+	0.0725162i
$960$	−4.31107			−0.139139
$961$	4.40487	−	7.62946i	0.142093	−	0.246112i
$962$	−13.2950	−	23.0276i	−0.428647	−	0.742439i
$963$	5.44244	+	9.42658i	0.175380	+	0.303767i
$964$	12.4815	−	21.6185i	0.402001	−	0.696286i
$965$	−7.77167			−0.250179
$966$	−1.29607	−	3.38978i	−0.0417004	−	0.109064i
$967$	−45.6475			−1.46792			−0.733962	−	0.679191i	$-0.762331\pi$
$967$	−45.6475			−1.46792			−0.733962	+	0.679191i	$0.762331\pi$
$968$	5.46795	−	9.47077i	0.175747	−	0.304402i
$969$	28.3948	+	49.1812i	0.912172	+	1.57993i
$970$	15.6962	+	27.1865i	0.503973	+	0.872907i
$971$	20.7096	−	35.8701i	0.664603	−	1.15113i	−0.314790	−	0.949161i	$-0.601934\pi$
$971$	20.7096	−	35.8701i	0.664603	−	1.15113i	0.979393	−	0.201964i	$-0.0647325\pi$
$972$	10.9215			0.350306
$973$	−12.9336	+	15.9285i	−0.414631	+	0.510643i
$974$	−21.0123			−0.673276
$975$	16.2377	−	28.1245i	0.520023	−	0.900706i
$976$	1.56514	+	2.71090i	0.0500989	+	0.0867738i
$977$	8.94971	+	15.5014i	0.286327	+	0.495932i	0.972930	−	0.231100i	$-0.0742324\pi$
$977$	8.94971	+	15.5014i	0.286327	+	0.495932i	−0.686603	+	0.727032i	$0.740899\pi$
$978$	−6.84675	+	11.8589i	−0.218935	+	0.379206i
$979$	−1.36200			−0.0435298
$980$	4.51719	+	21.5318i	0.144296	+	0.687807i
$981$	−11.6485			−0.371909
$982$	5.39758	−	9.34888i	0.172244	−	0.298335i
$983$	3.77630	+	6.54074i	0.120445	+	0.208617i	0.919943	−	0.392051i	$-0.128234\pi$
$983$	3.77630	+	6.54074i	0.120445	+	0.208617i	−0.799498	+	0.600669i	$0.794901\pi$
$984$	4.03942	+	6.99648i	0.128772	+	0.223040i
$985$	−10.0841	+	17.4662i	−0.321307	+	0.556519i
$986$	38.6282			1.23017
$987$	27.7702	−	34.2007i	0.883935	−	1.08862i
$988$	27.1821			0.864778
$989$	2.85533	−	4.94557i	0.0907941	−	0.157260i
$990$	0.444984	+	0.770735i	0.0141425	+	0.0244956i
$991$	−10.1640	−	17.6046i	−0.322872	−	0.559230i	0.658208	−	0.752836i	$-0.271315\pi$
$991$	−10.1640	−	17.6046i	−0.322872	−	0.559230i	−0.981079	+	0.193606i	$0.937982\pi$
$992$	2.35533	−	4.07955i	0.0747817	−	0.129526i
$993$	0.620261			0.0196834
$994$	−4.51769	−	11.8157i	−0.143292	−	0.374771i
$995$	−68.3471			−2.16675
$996$	−8.15888	+	14.1316i	−0.258524	+	0.447777i
$997$	0.332405	+	0.575742i	0.0105274	+	0.0182339i	0.871241	−	0.490855i	$-0.163316\pi$
$997$	0.332405	+	0.575742i	0.0105274	+	0.0182339i	−0.860714	+	0.509089i	$0.829982\pi$
$998$	16.2477	+	28.1419i	0.514313	+	0.890816i
$999$	−15.4745	+	26.8026i	−0.489591	+	0.847997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.b.93.1	✓	8
7.2	even	3		2254.2.a.w.1.4		4
7.4	even	3	inner	322.2.e.b.277.1	yes	8
7.5	odd	6		2254.2.a.ba.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.b.93.1	✓	8	1.1	even	1	trivial
322.2.e.b.277.1	yes	8	7.4	even	3	inner
2254.2.a.w.1.4		4	7.2	even	3
2254.2.a.ba.1.1		4	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.685837 - 1.18790i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57146 - 2.72186i) q^{5} +1.37167 q^{6} +(-1.66774 + 2.05393i) q^{7} +1.00000 q^{8} +(0.559256 - 0.968659i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.685837 - 1.18790i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57146 - 2.72186i) q^{5} +1.37167 q^{6} +(-1.66774 + 2.05393i) q^{7} +1.00000 q^{8} +(0.559256 - 0.968659i) q^{9} +(1.57146 + 2.72186i) q^{10} +(0.126581 + 0.219245i) q^{11} +(-0.685837 + 1.18790i) q^{12} -4.85358 q^{13} +(-0.944883 - 2.47127i) q^{14} -4.31107 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.69630 - 6.40218i) q^{17} +(0.559256 + 0.968659i) q^{18} +(2.80021 - 4.85011i) q^{19} -3.14293 q^{20} +(3.58367 + 0.572461i) q^{21} -0.253163 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.685837 - 1.18790i) q^{24} +(-2.43900 - 4.22447i) q^{25} +(2.42679 - 4.20333i) q^{26} -5.64925 q^{27} +(2.61263 + 0.417345i) q^{28} +5.22526 q^{29} +(2.15554 - 3.73350i) q^{30} +(2.35533 + 4.07955i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.173628 - 0.300733i) q^{33} +7.39260 q^{34} +(2.96970 + 7.76704i) q^{35} -1.11851 q^{36} +(2.73921 - 4.74445i) q^{37} +(2.80021 + 4.85011i) q^{38} +(3.32877 + 5.76559i) q^{39} +(1.57146 - 2.72186i) q^{40} -5.88977 q^{41} +(-2.28760 + 2.81732i) q^{42} -5.71065 q^{43} +(0.126581 - 0.219245i) q^{44} +(-1.75770 - 3.04443i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(6.06972 - 10.5131i) q^{47} +1.37167 q^{48} +(-1.43725 - 6.85086i) q^{49} +4.87800 q^{50} +(-5.07012 + 8.78170i) q^{51} +(2.42679 + 4.20333i) q^{52} +(6.20044 + 10.7395i) q^{53} +(2.82463 - 4.89240i) q^{54} +0.795672 q^{55} +(-1.66774 + 2.05393i) q^{56} -7.68195 q^{57} +(-2.61263 + 4.52520i) q^{58} +(5.46207 + 9.46058i) q^{59} +(2.15554 + 3.73350i) q^{60} +(1.56514 - 2.71090i) q^{61} -4.71065 q^{62} +(1.05686 + 2.76415i) q^{63} +1.00000 q^{64} +(-7.62723 + 13.2107i) q^{65} +(0.173628 + 0.300733i) q^{66} +(1.29607 + 2.24486i) q^{67} +(-3.69630 + 6.40218i) q^{68} +1.37167 q^{69} +(-8.21130 - 1.31168i) q^{70} +4.78121 q^{71} +(0.559256 - 0.968659i) q^{72} +(-3.20891 - 5.55799i) q^{73} +(2.73921 + 4.74445i) q^{74} +(-3.34551 + 5.79460i) q^{75} -5.60042 q^{76} +(-0.661420 - 0.105656i) q^{77} -6.65753 q^{78} +(-1.81830 + 3.14939i) q^{79} +(1.57146 + 2.72186i) q^{80} +(2.19670 + 3.80480i) q^{81} +(2.94488 - 5.10069i) q^{82} +11.8962 q^{83} +(-1.29607 - 3.38978i) q^{84} -23.2344 q^{85} +(2.85533 - 4.94557i) q^{86} +(-3.58367 - 6.20710i) q^{87} +(0.126581 + 0.219245i) q^{88} +(-2.68998 + 4.65917i) q^{89} +3.51540 q^{90} +(8.09454 - 9.96892i) q^{91} +1.00000 q^{92} +(3.23074 - 5.59581i) q^{93} +(6.06972 + 10.5131i) q^{94} +(-8.80086 - 15.2435i) q^{95} +(-0.685837 + 1.18790i) q^{96} +9.98823 q^{97} +(6.65165 + 2.18073i) q^{98} +0.283165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9} + 5 q^{10} + 2 q^{11} + 5 q^{12} - 14 q^{13} + q^{14} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{18} + 9 q^{19} - 10 q^{20} + 25 q^{21} - 4 q^{22} - 4 q^{23} + 5 q^{24} - 11 q^{25} + 7 q^{26} - 34 q^{27} - 2 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} - 4 q^{32} - 13 q^{33} + 6 q^{34} + 16 q^{35} + 14 q^{36} + 9 q^{38} + q^{39} + 5 q^{40} - 30 q^{41} - 8 q^{42} - 36 q^{43} + 2 q^{44} + 11 q^{45} - 4 q^{46} + 21 q^{47} - 10 q^{48} + 17 q^{49} + 22 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} + 17 q^{54} + 20 q^{55} + q^{56} - 18 q^{57} + 2 q^{58} + 16 q^{59} - q^{60} + q^{61} - 28 q^{62} + 37 q^{63} + 8 q^{64} - 2 q^{65} - 13 q^{66} + 17 q^{67} - 3 q^{68} - 10 q^{69} + 4 q^{70} - 2 q^{71} - 7 q^{72} + 4 q^{73} + 22 q^{75} - 18 q^{76} + 13 q^{77} - 2 q^{78} - 5 q^{79} + 5 q^{80} - 16 q^{81} + 15 q^{82} - 8 q^{83} - 17 q^{84} - 108 q^{85} + 18 q^{86} - 25 q^{87} + 2 q^{88} + 9 q^{89} - 22 q^{90} + 38 q^{91} + 8 q^{92} - 13 q^{93} + 21 q^{94} + 3 q^{95} + 5 q^{96} + 80 q^{97} + 2 q^{98} - 82 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9 + 5 * q^10 + 2 * q^11 + 5 * q^12 - 14 * q^13 + q^14 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^18 + 9 * q^19 - 10 * q^20 + 25 * q^21 - 4 * q^22 - 4 * q^23 + 5 * q^24 - 11 * q^25 + 7 * q^26 - 34 * q^27 - 2 * q^28 - 4 * q^29 - q^30 + 14 * q^31 - 4 * q^32 - 13 * q^33 + 6 * q^34 + 16 * q^35 + 14 * q^36 + 9 * q^38 + q^39 + 5 * q^40 - 30 * q^41 - 8 * q^42 - 36 * q^43 + 2 * q^44 + 11 * q^45 - 4 * q^46 + 21 * q^47 - 10 * q^48 + 17 * q^49 + 22 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 + 17 * q^54 + 20 * q^55 + q^56 - 18 * q^57 + 2 * q^58 + 16 * q^59 - q^60 + q^61 - 28 * q^62 + 37 * q^63 + 8 * q^64 - 2 * q^65 - 13 * q^66 + 17 * q^67 - 3 * q^68 - 10 * q^69 + 4 * q^70 - 2 * q^71 - 7 * q^72 + 4 * q^73 + 22 * q^75 - 18 * q^76 + 13 * q^77 - 2 * q^78 - 5 * q^79 + 5 * q^80 - 16 * q^81 + 15 * q^82 - 8 * q^83 - 17 * q^84 - 108 * q^85 + 18 * q^86 - 25 * q^87 + 2 * q^88 + 9 * q^89 - 22 * q^90 + 38 * q^91 + 8 * q^92 - 13 * q^93 + 21 * q^94 + 3 * q^95 + 5 * q^96 + 80 * q^97 + 2 * q^98 - 82 * q^99

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