LMFDB - Embedded newform 546.2.bb.a.269.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (of order $6$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.5
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.42260 - 0.988029i) q^{3} -1.00000 q^{4} +(1.41378 + 2.44875i) q^{5} +(-0.988029 + 1.42260i) q^{6} +(0.383892 - 2.61775i) q^{7} +1.00000i q^{8} +(1.04760 + 2.81115i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.42260 - 0.988029i) q^{3} -1.00000 q^{4} +(1.41378 + 2.44875i) q^{5} +(-0.988029 + 1.42260i) q^{6} +(0.383892 - 2.61775i) q^{7} +1.00000i q^{8} +(1.04760 + 2.81115i) q^{9} +(2.44875 - 1.41378i) q^{10} +(-4.64708 + 2.68299i) q^{11} +(1.42260 + 0.988029i) q^{12} +(-2.04050 + 2.97260i) q^{13} +(-2.61775 - 0.383892i) q^{14} +(0.408180 - 4.88045i) q^{15} +1.00000 q^{16} -7.32456 q^{17} +(2.81115 - 1.04760i) q^{18} +(2.17739 + 1.25712i) q^{19} +(-1.41378 - 2.44875i) q^{20} +(-3.13254 + 3.34472i) q^{21} +(2.68299 + 4.64708i) q^{22} +4.84619i q^{23} +(0.988029 - 1.42260i) q^{24} +(-1.49757 + 2.59386i) q^{25} +(2.97260 + 2.04050i) q^{26} +(1.28718 - 5.03420i) q^{27} +(-0.383892 + 2.61775i) q^{28} +(5.21665 + 3.01183i) q^{29} +(-4.88045 - 0.408180i) q^{30} +(1.76151 + 1.01701i) q^{31} -1.00000i q^{32} +(9.26182 + 0.774619i) q^{33} +7.32456i q^{34} +(6.95295 - 2.76088i) q^{35} +(-1.04760 - 2.81115i) q^{36} +0.639208 q^{37} +(1.25712 - 2.17739i) q^{38} +(5.83984 - 2.21276i) q^{39} +(-2.44875 + 1.41378i) q^{40} +(-5.97580 + 10.3504i) q^{41} +(3.34472 + 3.13254i) q^{42} +(-0.836889 - 1.44953i) q^{43} +(4.64708 - 2.68299i) q^{44} +(-5.40271 + 6.53965i) q^{45} +4.84619 q^{46} +(-2.48934 - 4.31167i) q^{47} +(-1.42260 - 0.988029i) q^{48} +(-6.70525 - 2.00987i) q^{49} +(2.59386 + 1.49757i) q^{50} +(10.4199 + 7.23689i) q^{51} +(2.04050 - 2.97260i) q^{52} +(2.82599 + 1.63159i) q^{53} +(-5.03420 - 1.28718i) q^{54} +(-13.1399 - 7.58634i) q^{55} +(2.61775 + 0.383892i) q^{56} +(-1.85549 - 3.93970i) q^{57} +(3.01183 - 5.21665i) q^{58} +4.67055 q^{59} +(-0.408180 + 4.88045i) q^{60} +(4.84184 + 2.79544i) q^{61} +(1.01701 - 1.76151i) q^{62} +(7.76105 - 1.66317i) q^{63} -1.00000 q^{64} +(-10.1640 - 0.794034i) q^{65} +(0.774619 - 9.26182i) q^{66} +(-2.19314 - 3.79862i) q^{67} +7.32456 q^{68} +(4.78818 - 6.89421i) q^{69} +(-2.76088 - 6.95295i) q^{70} +(7.14590 - 4.12569i) q^{71} +(-2.81115 + 1.04760i) q^{72} +(1.55287 + 0.896552i) q^{73} -0.639208i q^{74} +(4.69326 - 2.21040i) q^{75} +(-2.17739 - 1.25712i) q^{76} +(5.23943 + 13.1949i) q^{77} +(-2.21276 - 5.83984i) q^{78} +(2.02845 + 3.51337i) q^{79} +(1.41378 + 2.44875i) q^{80} +(-6.80509 + 5.88989i) q^{81} +(10.3504 + 5.97580i) q^{82} -12.1228 q^{83} +(3.13254 - 3.34472i) q^{84} +(-10.3553 - 17.9360i) q^{85} +(-1.44953 + 0.836889i) q^{86} +(-4.44544 - 9.43884i) q^{87} +(-2.68299 - 4.64708i) q^{88} -16.2075 q^{89} +(6.53965 + 5.40271i) q^{90} +(6.99821 + 6.48267i) q^{91} -4.84619i q^{92} +(-1.50109 - 3.18722i) q^{93} +(-4.31167 + 2.48934i) q^{94} +7.10916i q^{95} +(-0.988029 + 1.42260i) q^{96} +(-4.57690 + 2.64248i) q^{97} +(-2.00987 + 6.70525i) q^{98} +(-12.4105 - 10.2529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.42260	−	0.988029i	−0.821340	−	0.570439i
$3$	−1.42260	−	0.988029i	−0.821340	−	0.570439i
$4$	−1.00000			−0.500000
$5$	1.41378	+	2.44875i	0.632263	+	1.09511i	0.987088	+	0.160179i	$0.0512072\pi$
$5$	1.41378	+	2.44875i	0.632263	+	1.09511i	−0.354825	+	0.934933i	$0.615459\pi$
$6$	−0.988029	+	1.42260i	−0.403361	+	0.580775i
$7$	0.383892	−	2.61775i	0.145098	−	0.989417i
$7$	0.383892	−	2.61775i	0.145098	−	0.989417i
$8$			1.00000i			0.353553i
$9$	1.04760	+	2.81115i	0.349198	+	0.937049i
$10$	2.44875	−	1.41378i	0.774361	−	0.447078i
$11$	−4.64708	+	2.68299i	−1.40115	+	0.808952i	−0.994510	−	0.104638i	$-0.966632\pi$
$11$	−4.64708	+	2.68299i	−1.40115	+	0.808952i	−0.406636	+	0.913590i	$0.633298\pi$
$12$	1.42260	+	0.988029i	0.410670	+	0.285220i
$13$	−2.04050	+	2.97260i	−0.565932	+	0.824452i
$13$	−2.04050	+	2.97260i	−0.565932	+	0.824452i
$14$	−2.61775	−	0.383892i	−0.699624	−	0.102599i
$15$	0.408180	−	4.88045i	0.105392	−	1.26013i
$16$	1.00000			0.250000
$17$	−7.32456			−1.77647			−0.888234	−	0.459392i	$-0.848067\pi$
$17$	−7.32456			−1.77647			−0.888234	+	0.459392i	$0.848067\pi$
$18$	2.81115	−	1.04760i	0.662594	−	0.246921i
$19$	2.17739	+	1.25712i	0.499528	+	0.288402i	0.728518	−	0.685026i	$-0.240209\pi$
$19$	2.17739	+	1.25712i	0.499528	+	0.288402i	−0.228991	+	0.973429i	$0.573543\pi$
$20$	−1.41378	−	2.44875i	−0.316132	−	0.547556i
$21$	−3.13254	+	3.34472i	−0.683577	+	0.729879i
$22$	2.68299	+	4.64708i	0.572016	+	0.990760i
$23$			4.84619i			1.01050i	0.862973	+	0.505251i	$0.168600\pi$
$23$			4.84619i			1.01050i	−0.862973	+	0.505251i	$0.831400\pi$
$24$	0.988029	−	1.42260i	0.201681	−	0.290388i
$25$	−1.49757	+	2.59386i	−0.299514	+	0.518773i
$26$	2.97260	+	2.04050i	0.582976	+	0.400174i
$27$	1.28718	−	5.03420i	0.247719	−	0.968832i
$28$	−0.383892	+	2.61775i	−0.0725488	+	0.494709i
$29$	5.21665	+	3.01183i	0.968707	+	0.559283i	0.898842	−	0.438273i	$-0.144410\pi$
$29$	5.21665	+	3.01183i	0.968707	+	0.559283i	0.0698653	+	0.997556i	$0.477743\pi$
$30$	−4.88045	−	0.408180i	−0.891044	−	0.0745232i
$31$	1.76151	+	1.01701i	0.316376	+	0.182660i	0.649776	−	0.760126i	$-0.274863\pi$
$31$	1.76151	+	1.01701i	0.316376	+	0.182660i	−0.333400	+	0.942785i	$0.608196\pi$
$32$		−	1.00000i		−	0.176777i
$33$	9.26182	+	0.774619i	1.61228	+	0.134844i
$34$			7.32456i			1.25615i
$35$	6.95295	−	2.76088i	1.17526	−	0.466674i
$36$	−1.04760	−	2.81115i	−0.174599	−	0.468524i
$37$	0.639208			0.105085			0.0525426	−	0.998619i	$-0.483267\pi$
$37$	0.639208			0.105085			0.0525426	+	0.998619i	$0.483267\pi$
$38$	1.25712	−	2.17739i	0.203931	−	0.353219i
$39$	5.83984	−	2.21276i	0.935122	−	0.354326i
$40$	−2.44875	+	1.41378i	−0.387181	+	0.223539i
$41$	−5.97580	+	10.3504i	−0.933263	+	1.61646i	−0.155560	+	0.987826i	$0.549718\pi$
$41$	−5.97580	+	10.3504i	−0.933263	+	1.61646i	−0.777703	+	0.628632i	$0.783615\pi$
$42$	3.34472	+	3.13254i	0.516102	+	0.483362i
$43$	−0.836889	−	1.44953i	−0.127624	−	0.221052i	0.795131	−	0.606437i	$-0.207402\pi$
$43$	−0.836889	−	1.44953i	−0.127624	−	0.221052i	−0.922756	+	0.385385i	$0.874069\pi$
$44$	4.64708	−	2.68299i	0.700573	−	0.404476i
$45$	−5.40271	+	6.53965i	−0.805388	+	0.974873i
$46$	4.84619			0.714532
$47$	−2.48934	−	4.31167i	−0.363108	−	0.628922i	0.625362	−	0.780334i	$-0.284951\pi$
$47$	−2.48934	−	4.31167i	−0.363108	−	0.628922i	−0.988471	+	0.151413i	$0.951618\pi$
$48$	−1.42260	−	0.988029i	−0.205335	−	0.142610i
$49$	−6.70525	−	2.00987i	−0.957893	−	0.287124i
$50$	2.59386	+	1.49757i	0.366828	+	0.211788i
$51$	10.4199	+	7.23689i	1.45908	+	1.01337i
$52$	2.04050	−	2.97260i	0.282966	−	0.412226i
$53$	2.82599	+	1.63159i	0.388179	+	0.224115i	0.681371	−	0.731938i	$-0.261384\pi$
$53$	2.82599	+	1.63159i	0.388179	+	0.224115i	−0.293192	+	0.956054i	$0.594717\pi$
$54$	−5.03420	−	1.28718i	−0.685068	−	0.175164i
$55$	−13.1399	−	7.58634i	−1.77179	−	1.02294i
$56$	2.61775	+	0.383892i	0.349812	+	0.0512997i
$57$	−1.85549	−	3.93970i	−0.245766	−	0.521826i
$58$	3.01183	−	5.21665i	0.395473	−	0.684979i
$59$	4.67055			0.608054			0.304027	−	0.952663i	$-0.401669\pi$
$59$	4.67055			0.608054			0.304027	+	0.952663i	$0.401669\pi$
$60$	−0.408180	+	4.88045i	−0.0526958	+	0.630063i
$61$	4.84184	+	2.79544i	0.619934	+	0.357919i	0.776843	−	0.629694i	$-0.216820\pi$
$61$	4.84184	+	2.79544i	0.619934	+	0.357919i	−0.156909	+	0.987613i	$0.550153\pi$
$62$	1.01701	−	1.76151i	0.129160	−	0.223712i
$63$	7.76105	−	1.66317i	0.977800	−	0.209540i
$64$	−1.00000			−0.125000
$65$	−10.1640	−	0.794034i	−1.26069	−	0.0984878i
$66$	0.774619	−	9.26182i	0.0953491	−	1.14005i
$67$	−2.19314	−	3.79862i	−0.267934	−	0.464076i	0.700394	−	0.713756i	$-0.253008\pi$
$67$	−2.19314	−	3.79862i	−0.267934	−	0.464076i	−0.968328	+	0.249681i	$0.919674\pi$
$68$	7.32456			0.888234
$69$	4.78818	−	6.89421i	0.576429	−	0.829965i
$70$	−2.76088	−	6.95295i	−0.329988	−	0.831036i
$71$	7.14590	−	4.12569i	0.848062	−	0.489629i	−0.0119346	−	0.999929i	$-0.503799\pi$
$71$	7.14590	−	4.12569i	0.848062	−	0.489629i	0.859996	+	0.510300i	$0.170466\pi$
$72$	−2.81115	+	1.04760i	−0.331297	+	0.123460i
$73$	1.55287	+	0.896552i	0.181750	+	0.104934i	0.588115	−	0.808778i	$-0.299870\pi$
$73$	1.55287	+	0.896552i	0.181750	+	0.104934i	−0.406365	+	0.913711i	$0.633204\pi$
$74$		−	0.639208i		−	0.0743065i
$75$	4.69326	−	2.21040i	0.541931	−	0.255235i
$76$	−2.17739	−	1.25712i	−0.249764	−	0.144201i
$77$	5.23943	+	13.1949i	0.597088	+	1.50370i
$78$	−2.21276	−	5.83984i	−0.250546	−	0.661231i
$79$	2.02845	+	3.51337i	0.228218	+	0.395285i	0.957280	−	0.289162i	$-0.0933767\pi$
$79$	2.02845	+	3.51337i	0.228218	+	0.395285i	−0.729062	+	0.684448i	$0.760043\pi$
$80$	1.41378	+	2.44875i	0.158066	+	0.273778i
$81$	−6.80509	+	5.88989i	−0.756121	+	0.654432i
$82$	10.3504	+	5.97580i	1.14301	+	0.659916i
$83$	−12.1228			−1.33065			−0.665327	−	0.746552i	$-0.731708\pi$
$83$	−12.1228			−1.33065			−0.665327	+	0.746552i	$0.731708\pi$
$84$	3.13254	−	3.34472i	0.341788	−	0.364939i
$85$	−10.3553	−	17.9360i	−1.12320	−	1.94543i
$86$	−1.44953	+	0.836889i	−0.156307	+	0.0902441i
$87$	−4.44544	−	9.43884i	−0.476601	−	1.01195i
$88$	−2.68299	−	4.64708i	−0.286008	−	0.495380i
$89$	−16.2075			−1.71800			−0.858998	−	0.511978i	$-0.828913\pi$
$89$	−16.2075			−1.71800			−0.858998	+	0.511978i	$0.828913\pi$
$90$	6.53965	+	5.40271i	0.689339	+	0.569495i
$91$	6.99821	+	6.48267i	0.733612	+	0.679569i
$92$		−	4.84619i		−	0.505251i
$93$	−1.50109	−	3.18722i	−0.155656	−	0.330499i
$94$	−4.31167	+	2.48934i	−0.444715	+	0.256756i
$95$			7.10916i			0.729385i
$96$	−0.988029	+	1.42260i	−0.100840	+	0.145194i
$97$	−4.57690	+	2.64248i	−0.464714	+	0.268303i	−0.714024	−	0.700121i	$-0.753129\pi$
$97$	−4.57690	+	2.64248i	−0.464714	+	0.268303i	0.249310	+	0.968424i	$0.419796\pi$
$98$	−2.00987	+	6.70525i	−0.203027	+	0.677333i
$99$	−12.4105	−	10.2529i	−1.24731	−	1.03046i
$100$	1.49757	−	2.59386i	0.149757	−	0.259386i
$101$	0.0181979	+	0.0315196i	0.00181076	+	0.00313632i	0.866929	−	0.498431i	$-0.166090\pi$
$101$	0.0181979	+	0.0315196i	0.00181076	+	0.00313632i	−0.865119	+	0.501567i	$0.832757\pi$
$102$	7.23689	−	10.4199i	0.716558	−	1.03173i
$103$	−15.9496	+	9.20853i	−1.57156	+	0.907343i	−0.575587	+	0.817741i	$0.695226\pi$
$103$	−15.9496	+	9.20853i	−1.57156	+	0.907343i	−0.995978	+	0.0896026i	$0.971440\pi$
$104$	−2.97260	−	2.04050i	−0.291488	−	0.200087i
$105$	−12.6191	−	2.94208i	−1.23150	−	0.287118i
$106$	1.63159	−	2.82599i	0.158474	−	0.274484i
$107$		−	5.56596i		−	0.538082i	−0.963129	−	0.269041i	$-0.913293\pi$
$107$		−	5.56596i		−	0.538082i	0.963129	−	0.269041i	$-0.0867067\pi$
$108$	−1.28718	+	5.03420i	−0.123859	+	0.484416i
$109$	2.93599	−	5.08529i	0.281217	−	0.487082i	−0.690468	−	0.723363i	$-0.742595\pi$
$109$	2.93599	−	5.08529i	0.281217	−	0.487082i	0.971685	+	0.236281i	$0.0759285\pi$
$110$	−7.58634	+	13.1399i	−0.723329	+	1.25284i
$111$	−0.909340	−	0.631557i	−0.0863107	−	0.0599447i
$112$	0.383892	−	2.61775i	0.0362744	−	0.247354i
$113$	−0.869871	+	0.502220i	−0.0818306	+	0.0472449i	−0.540357	−	0.841436i	$-0.681711\pi$
$113$	−0.869871	+	0.502220i	−0.0818306	+	0.0472449i	0.458526	+	0.888681i	$0.348377\pi$
$114$	−3.93970	+	1.85549i	−0.368987	+	0.173783i
$115$	−11.8671	+	6.85147i	−1.10661	+	0.638903i
$116$	−5.21665	−	3.01183i	−0.484354	−	0.279642i
$117$	−10.4940	−	2.62205i	−0.970174	−	0.242408i
$118$		−	4.67055i		−	0.429959i
$119$	−2.81184	+	19.1739i	−0.257761	+	1.75767i
$120$	4.88045	+	0.408180i	0.445522	+	0.0372616i
$121$	8.89688	−	15.4099i	0.808808	−	1.40090i
$122$	2.79544	−	4.84184i	0.253087	−	0.438360i
$123$	18.7277	−	8.82022i	1.68862	−	0.795292i
$124$	−1.76151	−	1.01701i	−0.158188	−	0.0913299i
$125$	5.66889			0.507041
$126$	−1.66317	−	7.76105i	−0.148167	−	0.691409i
$127$	5.94284	−	10.2933i	0.527341	−	0.913382i	−0.472151	−	0.881518i	$-0.656522\pi$
$127$	5.94284	−	10.2933i	0.527341	−	0.913382i	0.999492	−	0.0318643i	$-0.0101444\pi$
$128$			1.00000i			0.0883883i
$129$	−0.241622	+	2.88898i	−0.0212737	+	0.254361i
$130$	−0.794034	+	10.1640i	−0.0696414	+	0.891439i
$131$	3.27806	+	5.67776i	0.286405	+	0.496068i	0.972949	−	0.231020i	$-0.0742063\pi$
$131$	3.27806	+	5.67776i	0.286405	+	0.496068i	−0.686544	+	0.727088i	$0.740873\pi$
$132$	−9.26182	−	0.774619i	−0.806138	−	0.0674220i
$133$	4.12670	−	5.21727i	0.357831	−	0.452395i
$134$	−3.79862	+	2.19314i	−0.328151	+	0.189458i
$135$	14.1473	−	3.96528i	1.21760	−	0.341277i
$136$		−	7.32456i		−	0.628076i
$137$		−	15.0048i		−	1.28194i	−0.767564	−	0.640972i	$-0.778532\pi$
$137$		−	15.0048i		−	1.28194i	0.767564	−	0.640972i	$-0.221468\pi$
$138$	−6.89421	−	4.78818i	−0.586874	−	0.407597i
$139$	−14.8457	+	8.57114i	−1.25919	+	0.726995i	−0.972917	−	0.231153i	$-0.925750\pi$
$139$	−14.8457	+	8.57114i	−1.25919	+	0.726995i	−0.286274	+	0.958148i	$0.592417\pi$
$140$	−6.95295	+	2.76088i	−0.587631	+	0.233337i
$141$	−0.718711	+	8.59334i	−0.0605264	+	0.723690i
$142$	−4.12569	−	7.14590i	−0.346220	−	0.599670i
$143$	1.50687	−	19.2886i	0.126011	−	1.61299i
$144$	1.04760	+	2.81115i	0.0872996	+	0.234262i
$145$			17.0323i			1.41446i
$146$	0.896552	−	1.55287i	0.0741992	−	0.128517i
$147$	7.55310	+	9.48423i	0.622969	+	0.782246i
$148$	−0.639208			−0.0525426
$149$	9.92624	+	5.73092i	0.813190	+	0.469495i	0.848062	−	0.529897i	$-0.177769\pi$
$149$	9.92624	+	5.73092i	0.813190	+	0.469495i	−0.0348727	+	0.999392i	$0.511103\pi$
$150$	−2.21040	−	4.69326i	−0.180478	−	0.383203i
$151$	−6.15167	+	10.6550i	−0.500616	+	0.867092i	0.499384	+	0.866381i	$0.333560\pi$
$151$	−6.15167	+	10.6550i	−0.500616	+	0.867092i	−1.00000		0.000710935i	$0.999774\pi$
$152$	−1.25712	+	2.17739i	−0.101966	+	0.176610i
$153$	−7.67318	−	20.5904i	−0.620340	−	1.66464i
$154$	13.1949	−	5.23943i	1.06327	−	0.422205i
$155$			5.75131i			0.461956i
$156$	−5.83984	+	2.21276i	−0.467561	+	0.177163i
$157$	14.2430	+	8.22323i	1.13672	+	0.656285i	0.945616	−	0.325285i	$-0.105460\pi$
$157$	14.2430	+	8.22323i	1.13672	+	0.656285i	0.191103	+	0.981570i	$0.438794\pi$
$158$	3.51337	−	2.02845i	0.279509	−	0.161375i
$159$	−2.40820	−	5.11326i	−0.190983	−	0.405508i
$160$	2.44875	−	1.41378i	0.193590	−	0.111769i
$161$	12.6861	+	1.86042i	0.999807	+	0.146621i
$162$	5.88989	+	6.80509i	0.462753	+	0.534658i
$163$	−3.00753	+	5.20920i	−0.235568	+	0.408016i	−0.959438	−	0.281921i	$-0.909028\pi$
$163$	−3.00753	+	5.20920i	−0.235568	+	0.408016i	0.723869	+	0.689937i	$0.242362\pi$
$164$	5.97580	−	10.3504i	0.466631	−	0.808229i
$165$	11.1974	+	23.7750i	0.871713	+	1.85088i
$166$			12.1228i			0.940914i
$167$	3.93039	−	6.80763i	0.304142	−	0.526790i	−0.672928	−	0.739708i	$-0.734963\pi$
$167$	3.93039	−	6.80763i	0.304142	−	0.526790i	0.977070	+	0.212918i	$0.0682968\pi$
$168$	−3.34472	−	3.13254i	−0.258051	−	0.241681i
$169$	−4.67275	−	12.1312i	−0.359443	−	0.933167i
$170$	−17.9360	+	10.3553i	−1.37563	+	0.794219i
$171$	−1.25292	+	7.43791i	−0.0958128	+	0.568791i
$172$	0.836889	+	1.44953i	0.0638122	+	0.110526i
$173$	8.14791	−	14.1126i	0.619474	−	1.07296i	−0.370108	−	0.928989i	$-0.620679\pi$
$173$	8.14791	−	14.1126i	0.619474	−	1.07296i	0.989582	−	0.143972i	$-0.0459874\pi$
$174$	−9.43884	+	4.44544i	−0.715557	+	0.337008i
$175$	6.21519	+	4.91603i	0.469824	+	0.371617i
$176$	−4.64708	+	2.68299i	−0.350287	+	0.202238i
$177$	−6.64434	−	4.61464i	−0.499419	−	0.346858i
$178$			16.2075i			1.21481i
$179$	9.54740	−	5.51220i	0.713606	−	0.412001i	−0.0987885	−	0.995108i	$-0.531497\pi$
$179$	9.54740	−	5.51220i	0.713606	−	0.412001i	0.812395	+	0.583108i	$0.198163\pi$
$180$	5.40271	−	6.53965i	0.402694	−	0.487436i
$181$		−	3.78477i		−	0.281320i	−0.990058	−	0.140660i	$-0.955078\pi$
$181$		−	3.78477i		−	0.281320i	0.990058	−	0.140660i	$-0.0449224\pi$
$182$	6.48267	−	6.99821i	0.480528	−	0.518742i
$183$	−4.12604	−	8.76068i	−0.305006	−	0.647608i
$184$	−4.84619			−0.357266
$185$	0.903702	+	1.56526i	0.0664415	+	0.115080i
$186$	−3.18722	+	1.50109i	−0.233698	+	0.110065i
$187$	34.0378	−	19.6517i	2.48909	−	1.43708i
$188$	2.48934	+	4.31167i	0.181554	+	0.314461i
$189$	−12.6841	−	5.30212i	−0.922636	−	0.385672i
$190$	7.10916			0.515753
$191$	6.98367	+	4.03202i	0.505321	+	0.291747i	0.730908	−	0.682476i	$-0.239097\pi$
$191$	6.98367	+	4.03202i	0.505321	+	0.291747i	−0.225587	+	0.974223i	$0.572430\pi$
$192$	1.42260	+	0.988029i	0.102667	+	0.0713049i
$193$	5.50345	+	9.53225i	0.396147	+	0.686146i	0.993247	−	0.116021i	$-0.0370138\pi$
$193$	5.50345	+	9.53225i	0.396147	+	0.686146i	−0.597100	+	0.802167i	$0.703681\pi$
$194$	2.64248	+	4.57690i	0.189719	+	0.328602i
$195$	13.6748	+	11.1719i	0.979270	+	0.800036i
$196$	6.70525	+	2.00987i	0.478947	+	0.143562i
$197$	1.95410	+	1.12820i	0.139224	+	0.0803808i	0.567994	−	0.823033i	$-0.307720\pi$
$197$	1.95410	+	1.12820i	0.139224	+	0.0803808i	−0.428770	+	0.903414i	$0.641053\pi$
$198$	−10.2529	+	12.4105i	−0.728644	+	0.881979i
$199$		−	7.25276i		−	0.514134i	−0.966394	−	0.257067i	$-0.917244\pi$
$199$		−	7.25276i		−	0.514134i	0.966394	−	0.257067i	$-0.0827561\pi$
$200$	−2.59386	−	1.49757i	−0.183414	−	0.105894i
$201$	−0.633191	+	7.57082i	−0.0446619	+	0.534004i
$202$	0.0315196	−	0.0181979i	0.00221771	−	0.00128040i
$203$	9.88686	−	12.4997i	0.693922	−	0.877305i
$204$	−10.4199	−	7.23689i	−0.729542	−	0.506683i
$205$	−33.7939			−2.36027
$206$	9.20853	+	15.9496i	0.641589	+	1.11126i
$207$	−13.6234	+	5.07685i	−0.946889	+	0.352866i
$208$	−2.04050	+	2.97260i	−0.141483	+	0.206113i
$209$	−13.4913			−0.933215
$210$	−2.94208	+	12.6191i	−0.203023	+	0.870802i
$211$	2.35068	−	4.07150i	0.161827	−	0.280293i	−0.773697	−	0.633556i	$-0.781595\pi$
$211$	2.35068	−	4.07150i	0.161827	−	0.280293i	0.935524	+	0.353263i	$0.114928\pi$
$212$	−2.82599	−	1.63159i	−0.194090	−	0.112058i
$213$	−14.2421	−	1.19115i	−0.975850	−	0.0816160i
$214$	−5.56596			−0.380481
$215$	2.36636	−	4.09866i	0.161384	−	0.279526i
$216$	5.03420	+	1.28718i	0.342534	+	0.0875818i
$217$	3.33850	−	4.22077i	0.226632	−	0.286524i
$218$	−5.08529	−	2.93599i	−0.344419	−	0.198851i
$219$	−1.32330	−	2.80972i	−0.0894205	−	0.189863i
$220$	13.1399	+	7.58634i	0.885893	+	0.511471i
$221$	14.9457	−	21.7730i	1.00536	−	1.46461i
$222$	−0.631557	+	0.909340i	−0.0423873	+	0.0610309i
$223$	18.5099	+	10.6867i	1.23951	+	0.715634i	0.968995	−	0.247081i	$-0.0794713\pi$
$223$	18.5099	+	10.6867i	1.23951	+	0.715634i	0.270519	+	0.962715i	$0.412805\pi$
$224$	−2.61775	−	0.383892i	−0.174906	−	0.0256499i
$225$	−8.86058	−	1.49256i	−0.590705	−	0.0995042i
$226$	0.502220	+	0.869871i	0.0334072	+	0.0578630i
$227$	−12.4663			−0.827417			−0.413708	−	0.910410i	$-0.635767\pi$
$227$	−12.4663			−0.827417			−0.413708	+	0.910410i	$0.635767\pi$
$228$	1.85549	+	3.93970i	0.122883	+	0.260913i
$229$	−9.09478	+	5.25087i	−0.601000	+	0.346987i	−0.769435	−	0.638725i	$-0.779462\pi$
$229$	−9.09478	+	5.25087i	−0.601000	+	0.346987i	0.168435	+	0.985713i	$0.446129\pi$
$230$	6.85147	+	11.8671i	0.451773	+	0.782493i
$231$	5.58330	−	23.9478i	0.367354	−	1.57565i
$232$	−3.01183	+	5.21665i	−0.197737	+	0.342490i
$233$	−2.78543	+	1.60817i	−0.182480	+	0.105355i	−0.588457	−	0.808528i	$-0.700264\pi$
$233$	−2.78543	+	1.60817i	−0.182480	+	0.105355i	0.405977	+	0.913883i	$0.366931\pi$
$234$	−2.62205	+	10.4940i	−0.171408	+	0.686017i
$235$	7.03879	−	12.1915i	0.459160	−	0.795288i
$236$	−4.67055			−0.304027
$237$	0.585643	−	7.00230i	0.0380416	−	0.454848i
$238$	19.1739	+	2.81184i	1.24286	+	0.182265i
$239$			11.9941i			0.775834i	0.921694	+	0.387917i	$0.126805\pi$
$239$			11.9941i			0.775834i	−0.921694	+	0.387917i	$0.873195\pi$
$240$	0.408180	−	4.88045i	0.0263479	−	0.315032i
$241$			18.3905i			1.18464i	0.805703	+	0.592319i	$0.201788\pi$
$241$			18.3905i			1.18464i	−0.805703	+	0.592319i	$0.798212\pi$
$242$	−15.4099	−	8.89688i	−0.990583	−	0.571913i
$243$	15.5003	−	1.65534i	0.994346	−	0.106190i
$244$	−4.84184	−	2.79544i	−0.309967	−	0.178960i
$245$	−4.55812	−	19.2610i	−0.291208	−	1.23054i
$246$	−8.82022	−	18.7277i	−0.562357	−	1.19403i
$247$	−8.17987	+	3.90738i	−0.520472	+	0.248621i
$248$	−1.01701	+	1.76151i	−0.0645800	+	0.111856i
$249$	17.2460	+	11.9777i	1.09292	+	0.759057i
$250$		−	5.66889i		−	0.358532i
$251$	−5.22792	−	9.05503i	−0.329983	−	0.571548i	0.652525	−	0.757767i	$-0.273710\pi$
$251$	−5.22792	−	9.05503i	−0.329983	−	0.571548i	−0.982508	+	0.186219i	$0.940377\pi$
$252$	−7.76105	+	1.66317i	−0.488900	+	0.104770i
$253$	−13.0023	−	22.5206i	−0.817447	−	1.41586i
$254$	−10.2933	−	5.94284i	−0.645859	−	0.372887i
$255$	−2.98974	+	35.7472i	−0.187225	+	2.23857i
$256$	1.00000			0.0625000
$257$	1.76706			0.110226			0.0551131	−	0.998480i	$-0.482448\pi$
$257$	1.76706			0.110226			0.0551131	+	0.998480i	$0.482448\pi$
$258$	2.88898	+	0.241622i	0.179860	+	0.0150427i
$259$	0.245387	−	1.67329i	0.0152476	−	0.103973i
$260$	10.1640	+	0.794034i	0.630343	+	0.0492439i
$261$	−3.00177	+	17.8199i	−0.185805	+	1.10303i
$262$	5.67776	−	3.27806i	0.350773	−	0.202519i
$263$	−18.1822	+	10.4975i	−1.12116	+	0.647303i	−0.941697	−	0.336461i	$-0.890770\pi$
$263$	−18.1822	+	10.4975i	−1.12116	+	0.647303i	−0.179465	+	0.983764i	$0.557437\pi$
$264$	−0.774619	+	9.26182i	−0.0476745	+	0.570025i
$265$			9.22683i			0.566800i
$266$	−5.21727	−	4.12670i	−0.319891	−	0.253024i
$267$	23.0569	+	16.0135i	1.41106	+	0.980012i
$268$	2.19314	+	3.79862i	0.133967	+	0.232038i
$269$	−17.5469			−1.06985			−0.534925	−	0.844899i	$-0.679660\pi$
$269$	−17.5469			−1.06985			−0.534925	+	0.844899i	$0.679660\pi$
$270$	−3.96528	−	14.1473i	−0.241319	−	0.860975i
$271$		−	22.1933i		−	1.34814i	−0.738665	−	0.674072i	$-0.764544\pi$
$271$		−	22.1933i		−	1.34814i	0.738665	−	0.674072i	$-0.235456\pi$
$272$	−7.32456			−0.444117
$273$	−3.55060	−	16.1367i	−0.214892	−	0.976638i
$274$	−15.0048			−0.906471
$275$		−	16.0719i		−	0.969169i
$276$	−4.78818	+	6.89421i	−0.288215	+	0.414983i
$277$	12.8518			0.772190			0.386095	−	0.922459i	$-0.373824\pi$
$277$	12.8518			0.772190			0.386095	+	0.922459i	$0.373824\pi$
$278$	8.57114	+	14.8457i	0.514063	+	0.890383i
$279$	−1.01361	+	6.01726i	−0.0606831	+	0.360244i
$280$	2.76088	+	6.95295i	0.164994	+	0.415518i
$281$			26.5541i			1.58408i	0.610467	+	0.792042i	$0.290982\pi$
$281$			26.5541i			1.58408i	−0.610467	+	0.792042i	$0.709018\pi$
$282$	8.59334	+	0.718711i	0.511726	+	0.0427986i
$283$	1.33293	−	0.769566i	0.0792343	−	0.0457460i	−0.459859	−	0.887992i	$-0.652100\pi$
$283$	1.33293	−	0.769566i	0.0792343	−	0.0457460i	0.539094	+	0.842246i	$0.318767\pi$
$284$	−7.14590	+	4.12569i	−0.424031	+	0.244814i
$285$	7.02406	−	10.1135i	0.416070	−	0.599073i
$286$	−19.2886	−	1.50687i	−1.14056	−	0.0891031i
$287$	24.8007	+	19.6166i	1.46394	+	1.15793i
$288$	2.81115	−	1.04760i	0.165648	−	0.0617302i
$289$	36.6492			2.15584
$290$	17.0323			1.00017
$291$	9.12196	+	0.762922i	0.534738	+	0.0447233i
$292$	−1.55287	−	0.896552i	−0.0908751	−	0.0524668i
$293$	−3.32608	−	5.76094i	−0.194312	−	0.336557i	0.752363	−	0.658749i	$-0.228914\pi$
$293$	−3.32608	−	5.76094i	−0.194312	−	0.336557i	−0.946675	+	0.322191i	$0.895581\pi$
$294$	9.48423	−	7.55310i	0.553132	−	0.440506i
$295$	6.60315	+	11.4370i	0.384450	+	0.665888i
$296$			0.639208i			0.0371532i
$297$	7.52507	+	26.8478i	0.436649	+	1.55787i
$298$	5.73092	−	9.92624i	0.331983	−	0.575012i
$299$	−14.4058	−	9.88864i	−0.833110	−	0.571875i
$300$	−4.69326	+	2.21040i	−0.270965	+	0.127617i
$301$	−4.11580	+	1.63430i	−0.237231	+	0.0941997i
$302$	10.6550	+	6.15167i	0.613126	+	0.353989i
$303$	0.00525400	−	0.0628200i	0.000301834	−	0.00360891i
$304$	2.17739	+	1.25712i	0.124882	+	0.0721006i
$305$			15.8086i			0.905197i
$306$	−20.5904	+	7.67318i	−1.17708	+	0.438647i
$307$			24.3883i			1.39191i	0.718085	+	0.695956i	$0.245019\pi$
$307$			24.3883i			1.39191i	−0.718085	+	0.695956i	$0.754981\pi$
$308$	−5.23943	−	13.1949i	−0.298544	−	0.751848i
$309$	31.7883	+	2.65864i	1.80837	+	0.151245i
$310$	5.75131			0.326652
$311$	16.4246	−	28.4483i	0.931355	−	1.61315i	0.150346	−	0.988633i	$-0.451961\pi$
$311$	16.4246	−	28.4483i	0.931355	−	1.61315i	0.781009	−	0.624520i	$-0.214705\pi$
$312$	2.21276	+	5.83984i	0.125273	+	0.330616i
$313$	11.3671	−	6.56281i	0.642508	−	0.370952i	−0.143072	−	0.989712i	$-0.545698\pi$
$313$	11.3671	−	6.56281i	0.642508	−	0.370952i	0.785580	+	0.618760i	$0.212365\pi$
$314$	8.22323	−	14.2430i	0.464064	−	0.803782i
$315$	15.0451	+	16.6535i	0.847696	+	0.938317i
$316$	−2.02845	−	3.51337i	−0.114109	−	0.197643i
$317$	19.0370	−	10.9910i	1.06922	−	0.617317i	0.141254	−	0.989973i	$-0.454886\pi$
$317$	19.0370	−	10.9910i	1.06922	−	0.617317i	0.927969	+	0.372657i	$0.121553\pi$
$318$	−5.11326	+	2.40820i	−0.286737	+	0.135045i
$319$	−32.3229			−1.80973
$320$	−1.41378	−	2.44875i	−0.0790329	−	0.136889i
$321$	−5.49934	+	7.91815i	−0.306943	+	0.441948i
$322$	1.86042	−	12.6861i	0.103677	−	0.706971i
$323$	−15.9484	−	9.20783i	−0.887395	−	0.512338i
$324$	6.80509	−	5.88989i	0.378060	−	0.327216i
$325$	−4.65475	−	9.74445i	−0.258199	−	0.540525i
$326$	5.20920	+	3.00753i	0.288511	+	0.166572i
$327$	−9.20117	+	4.33350i	−0.508826	+	0.239643i
$328$	−10.3504	−	5.97580i	−0.571504	−	0.329958i
$329$	−12.2425	+	4.86127i	−0.674952	+	0.268011i
$330$	23.7750	−	11.1974i	1.30877	−	0.616394i
$331$	−6.48561	+	11.2334i	−0.356481	+	0.617444i	−0.987370	−	0.158429i	$-0.949357\pi$
$331$	−6.48561	+	11.2334i	−0.356481	+	0.617444i	0.630889	+	0.775873i	$0.282690\pi$
$332$	12.1228			0.665327
$333$	0.669632	+	1.79691i	0.0366956	+	0.0984700i
$334$	−6.80763	−	3.93039i	−0.372497	−	0.215061i
$335$	6.20124	−	10.7409i	0.338810	−	0.586836i
$336$	−3.13254	+	3.34472i	−0.170894	+	0.182470i
$337$	27.9808			1.52421			0.762107	−	0.647451i	$-0.224165\pi$
$337$	27.9808			1.52421			0.762107	+	0.647451i	$0.224165\pi$
$338$	−12.1312	+	4.67275i	−0.659849	+	0.254164i
$339$	1.73369	+	0.144998i	0.0941611	+	0.00787523i
$340$	10.3553	+	17.9360i	0.561598	+	0.972716i
$341$	−10.9145			−0.591052
$342$	7.43791	+	1.25292i	0.402196	+	0.0677499i
$343$	−7.83543	+	16.7811i	−0.423074	+	0.906095i
$344$	1.44953	−	0.836889i	0.0781536	−	0.0451220i
$345$	23.6516	+	1.97812i	1.27336	+	0.106498i
$346$	−14.1126	−	8.14791i	−0.758698	−	0.438034i
$347$		−	12.7624i		−	0.685124i	−0.939495	−	0.342562i	$-0.888705\pi$
$347$		−	12.7624i		−	0.685124i	0.939495	−	0.342562i	$-0.111295\pi$
$348$	4.44544	+	9.43884i	0.238300	+	0.505975i
$349$	12.8171	+	7.39994i	0.686082	+	0.396110i	0.802143	−	0.597133i	$-0.203693\pi$
$349$	12.8171	+	7.39994i	0.686082	+	0.396110i	−0.116061	+	0.993242i	$0.537027\pi$
$350$	4.91603	−	6.21519i	0.262773	−	0.332216i
$351$	12.3382	+	14.0985i	0.658564	+	0.752525i
$352$	2.68299	+	4.64708i	0.143004	+	0.247690i
$353$	8.65493	+	14.9908i	0.460656	+	0.797879i	0.998994	−	0.0448501i	$-0.0142810\pi$
$353$	8.65493	+	14.9908i	0.460656	+	0.797879i	−0.538338	+	0.842729i	$0.680948\pi$
$354$	−4.61464	+	6.64434i	−0.245266	+	0.353143i
$355$	20.2055	+	11.6657i	1.07240	+	0.619149i
$356$	16.2075			0.858998
$357$	22.9445	−	24.4986i	1.21435	−	1.29661i
$358$	−5.51220	−	9.54740i	−0.291329	−	0.504596i
$359$	5.42394	−	3.13151i	0.286264	−	0.165275i	−0.349992	−	0.936753i	$-0.613816\pi$
$359$	5.42394	−	3.13151i	0.286264	−	0.165275i	0.636256	+	0.771478i	$0.280482\pi$
$360$	−6.53965	−	5.40271i	−0.344670	−	0.284748i
$361$	−6.33931	−	10.9800i	−0.333648	−	0.577896i
$362$	−3.78477			−0.198923
$363$	−27.8821	+	13.1317i	−1.46343	+	0.689236i
$364$	−6.99821	−	6.48267i	−0.366806	−	0.339784i
$365$			5.07012i			0.265382i
$366$	−8.76068	+	4.12604i	−0.457928	+	0.215672i
$367$	−23.3199	+	13.4638i	−1.21729	+	0.702803i	−0.964338	−	0.264675i	$-0.914735\pi$
$367$	−23.3199	+	13.4638i	−1.21729	+	0.702803i	−0.252953	+	0.967478i	$0.581402\pi$
$368$			4.84619i			0.252625i
$369$	−35.3567	−	5.95583i	−1.84059	−	0.310048i
$370$	1.56526	−	0.903702i	0.0813739	−	0.0469813i
$371$	5.35596	−	6.77138i	0.278068	−	0.351553i
$372$	1.50109	+	3.18722i	0.0778280	+	0.165249i
$373$	−7.77432	+	13.4655i	−0.402539	+	0.697218i	−0.994032	−	0.109093i	$-0.965205\pi$
$373$	−7.77432	+	13.4655i	−0.402539	+	0.697218i	0.591493	+	0.806310i	$0.298539\pi$
$374$	−19.6517	−	34.0378i	−1.01617	−	1.76005i
$375$	−8.06457	−	5.60103i	−0.416453	−	0.289236i
$376$	4.31167	−	2.48934i	0.222357	−	0.128378i
$377$	−19.5975	+	9.36140i	−1.00932	+	0.482137i
$378$	−5.30212	+	12.6841i	−0.272711	+	0.652402i
$379$	−18.5733	+	32.1700i	−0.954049	+	1.65246i	−0.217519	+	0.976056i	$0.569796\pi$
$379$	−18.5733	+	32.1700i	−0.954049	+	1.65246i	−0.736530	+	0.676405i	$0.763537\pi$
$380$		−	7.10916i		−	0.364692i
$381$	−18.6244	+	8.77157i	−0.954155	+	0.449381i
$382$	4.03202	−	6.98367i	0.206296	−	0.357316i
$383$	−15.6693	+	27.1401i	−0.800666	+	1.38679i	0.118513	+	0.992953i	$0.462187\pi$
$383$	−15.6693	+	27.1401i	−0.800666	+	1.38679i	−0.919179	+	0.393841i	$0.871146\pi$
$384$	0.988029	−	1.42260i	0.0504202	−	0.0725969i
$385$	−24.9035	+	31.4847i	−1.26920	+	1.60461i
$386$	9.53225	−	5.50345i	0.485179	−	0.280118i
$387$	3.19813	−	3.87114i	0.162570	−	0.196781i
$388$	4.57690	−	2.64248i	0.232357	−	0.134151i
$389$	−18.2426	−	10.5324i	−0.924939	−	0.534014i	−0.0397316	−	0.999210i	$-0.512650\pi$
$389$	−18.2426	−	10.5324i	−0.924939	−	0.534014i	−0.885207	+	0.465197i	$0.845984\pi$
$390$	11.1719	−	13.6748i	0.565711	−	0.692448i
$391$		−	35.4963i		−	1.79512i
$392$	2.00987	−	6.70525i	0.101514	−	0.338666i
$393$	0.946424	−	11.3160i	0.0477408	−	0.570817i
$394$	1.12820	−	1.95410i	0.0568378	−	0.0984459i
$395$	−5.73557	+	9.93430i	−0.288588	+	0.499849i
$396$	12.4105	+	10.2529i	0.623653	+	0.515229i
$397$	14.0444	+	8.10856i	0.704870	+	0.406957i	0.809159	−	0.587590i	$-0.199923\pi$
$397$	14.0444	+	8.10856i	0.704870	+	0.406957i	−0.104289	+	0.994547i	$0.533257\pi$
$398$	−7.25276			−0.363548
$399$	−11.0255	+	3.34480i	−0.551964	+	0.167449i
$400$	−1.49757	+	2.59386i	−0.0748784	+	0.129693i
$401$			18.6153i			0.929604i	0.885415	+	0.464802i	$0.153874\pi$
$401$			18.6153i			0.929604i	−0.885415	+	0.464802i	$0.846126\pi$
$402$	7.57082	+	0.633191i	0.377598	+	0.0315807i
$403$	−6.61750	+	3.16107i	−0.329641	+	0.157464i
$404$	−0.0181979	−	0.0315196i	−0.000905378	−	0.00156816i
$405$	−24.0438	−	8.33690i	−1.19474	−	0.414264i
$406$	−12.4997	−	9.88686i	−0.620348	−	0.490677i
$407$	−2.97045	+	1.71499i	−0.147240	+	0.0850089i
$408$	−7.23689	+	10.4199i	−0.358279	+	0.515864i
$409$			9.43206i			0.466385i	0.972431	+	0.233193i	$0.0749173\pi$
$409$			9.43206i			0.466385i	−0.972431	+	0.233193i	$0.925083\pi$
$410$			33.7939i			1.66896i
$411$	−14.8251	+	21.3458i	−0.731271	+	1.05291i
$412$	15.9496	−	9.20853i	0.785782	−	0.453672i
$413$	1.79299	−	12.2264i	0.0882272	−	0.601619i
$414$	5.07685	+	13.6234i	0.249514	+	0.669552i
$415$	−17.1391	−	29.6857i	−0.841323	−	1.45721i
$416$	2.97260	+	2.04050i	0.145744	+	0.100044i
$417$	29.5880	+	2.47462i	1.44893	+	0.121182i
$418$			13.4913i			0.659883i
$419$	15.5700	−	26.9681i	0.760646	−	1.31748i	−0.181873	−	0.983322i	$-0.558216\pi$
$419$	15.5700	−	26.9681i	0.760646	−	1.31748i	0.942518	−	0.334155i	$-0.108451\pi$
$420$	12.6191	+	2.94208i	0.615750	+	0.143559i
$421$	1.34712			0.0656545			0.0328272	−	0.999461i	$-0.489549\pi$
$421$	1.34712			0.0656545			0.0328272	+	0.999461i	$0.489549\pi$
$422$	−4.07150	−	2.35068i	−0.198197	−	0.114429i
$423$	9.51291	−	11.5148i	0.462534	−	0.559869i
$424$	−1.63159	+	2.82599i	−0.0792368	+	0.137242i
$425$	10.9690	−	18.9989i	0.532076	−	0.921583i
$426$	−1.19115	+	14.2421i	−0.0577112	+	0.690030i
$427$	9.17651	−	11.6016i	0.444082	−	0.561441i
$428$			5.56596i			0.269041i
$429$	−21.2013	+	25.9511i	−1.02361	+	1.25293i
$430$	−4.09866	−	2.36636i	−0.197655	−	0.114116i
$431$	−1.40088	+	0.808798i	−0.0674780	+	0.0389584i	−0.533359	−	0.845889i	$-0.679071\pi$
$431$	−1.40088	+	0.808798i	−0.0674780	+	0.0389584i	0.465881	+	0.884847i	$0.345737\pi$
$432$	1.28718	−	5.03420i	0.0619297	−	0.242208i
$433$	−2.72492	+	1.57323i	−0.130951	+	0.0756048i	−0.564045	−	0.825744i	$-0.690755\pi$
$433$	−2.72492	+	1.57323i	−0.130951	+	0.0756048i	0.433093	+	0.901349i	$0.357422\pi$
$434$	−4.22077	−	3.33850i	−0.202603	−	0.160253i
$435$	16.8284	−	24.2302i	0.806862	−	1.16175i
$436$	−2.93599	+	5.08529i	−0.140609	+	0.243541i
$437$	−6.09223	+	10.5521i	−0.291431	+	0.504773i
$438$	−2.80972	+	1.32330i	−0.134254	+	0.0632298i
$439$			1.66372i			0.0794050i	0.999212	+	0.0397025i	$0.0126410\pi$
$439$			1.66372i			0.0794050i	−0.999212	+	0.0397025i	$0.987359\pi$
$440$	7.58634	−	13.1399i	0.361664	−	0.626421i
$441$	−1.37436	−	20.9550i	−0.0654456	−	0.997856i
$442$	−21.7730	−	14.9457i	−1.03564	−	0.710896i
$443$	12.6887	−	7.32582i	0.602858	−	0.348060i	−0.167307	−	0.985905i	$-0.553507\pi$
$443$	12.6887	−	7.32582i	0.602858	−	0.348060i	0.770165	+	0.637844i	$0.220174\pi$
$444$	0.909340	+	0.631557i	0.0431553	+	0.0299724i
$445$	−22.9140	−	39.6882i	−1.08623	−	1.88140i
$446$	10.6867	−	18.5099i	0.506030	−	0.876469i
$447$	−8.45878	−	17.9602i	−0.400087	−	0.849490i
$448$	−0.383892	+	2.61775i	−0.0181372	+	0.123677i
$449$	−4.85551	+	2.80333i	−0.229146	+	0.132297i	−0.610178	−	0.792264i	$-0.708902\pi$
$449$	−4.85551	+	2.80333i	−0.229146	+	0.132297i	0.381032	+	0.924562i	$0.375569\pi$
$450$	−1.49256	+	8.86058i	−0.0703601	+	0.417692i
$451$		−	64.1321i		−	3.01986i
$452$	0.869871	−	0.502220i	0.0409153	−	0.0236225i
$453$	19.2788	−	9.07980i	0.905798	−	0.426606i
$454$			12.4663i			0.585072i
$455$	−5.98045	+	26.3019i	−0.280368	+	1.23305i
$456$	3.93970	−	1.85549i	0.184494	−	0.0868914i
$457$	41.7616			1.95353			0.976763	−	0.214324i	$-0.0687548\pi$
$457$	41.7616			1.95353			0.976763	+	0.214324i	$0.0687548\pi$
$458$	5.25087	+	9.09478i	0.245357	+	0.424971i
$459$	−9.42806	+	36.8733i	−0.440064	+	1.72110i
$460$	11.8671	−	6.85147i	0.553306	−	0.319451i
$461$	10.8220	+	18.7442i	0.504030	+	0.873005i	0.999989	+	0.00465958i	$0.00148320\pi$
$461$	10.8220	+	18.7442i	0.504030	+	0.873005i	−0.495959	+	0.868346i	$0.665183\pi$
$462$	−23.9478	−	5.58330i	−1.11415	−	0.259759i
$463$	−0.578725			−0.0268956			−0.0134478	−	0.999910i	$-0.504281\pi$
$463$	−0.578725			−0.0268956			−0.0134478	+	0.999910i	$0.504281\pi$
$464$	5.21665	+	3.01183i	0.242177	+	0.139821i
$465$	5.68246	−	8.18182i	0.263518	−	0.379423i
$466$	1.60817	+	2.78543i	0.0744971	+	0.129033i
$467$	10.1683	+	17.6119i	0.470531	+	0.814983i	0.999432	−	0.0337004i	$-0.0107292\pi$
$467$	10.1683	+	17.6119i	0.470531	+	0.814983i	−0.528901	+	0.848683i	$0.677396\pi$
$468$	10.4940	+	2.62205i	0.485087	+	0.121204i
$469$	−10.7858	+	4.28283i	−0.498041	+	0.197763i
$470$	−12.1915	−	7.03879i	−0.562354	−	0.324675i
$471$	−12.1374	−	25.7709i	−0.559262	−	1.18746i
$472$			4.67055i			0.214980i
$473$	7.77818	+	4.49073i	0.357641	+	0.206484i
$474$	−7.00230	−	0.585643i	−0.321626	−	0.0268995i
$475$	−6.52158	+	3.76524i	−0.299231	+	0.172761i
$476$	2.81184	−	19.1739i	0.128881	−	0.878834i
$477$	−1.62613	+	9.65351i	−0.0744555	+	0.442004i
$478$	11.9941			0.548597
$479$	−7.80327	−	13.5157i	−0.356540	−	0.617546i	0.630840	−	0.775913i	$-0.282710\pi$
$479$	−7.80327	−	13.5157i	−0.356540	−	0.617546i	−0.987380	+	0.158367i	$0.949377\pi$
$480$	−4.88045	−	0.408180i	−0.222761	−	0.0186308i
$481$	−1.30430	+	1.90011i	−0.0594711	+	0.0866377i
$482$	18.3905			0.837666
$483$	−16.2092	−	15.1809i	−0.737543	−	0.690755i
$484$	−8.89688	+	15.4099i	−0.404404	+	0.700448i
$485$	−12.9415	−	7.47178i	−0.587643	−	0.339276i
$486$	−1.65534	−	15.5003i	−0.0750879	−	0.703109i
$487$	22.4792			1.01863			0.509315	−	0.860580i	$-0.329899\pi$
$487$	22.4792			1.01863			0.509315	+	0.860580i	$0.329899\pi$
$488$	−2.79544	+	4.84184i	−0.126544	+	0.219180i
$489$	9.42537	−	4.43909i	0.426230	−	0.200743i
$490$	−19.2610	+	4.55812i	−0.870122	+	0.205915i
$491$	28.7412	+	16.5938i	1.29707	+	0.748866i	0.979898	−	0.199501i	$-0.0639321\pi$
$491$	28.7412	+	16.5938i	1.29707	+	0.748866i	0.317176	+	0.948367i	$0.397265\pi$
$492$	−18.7277	+	8.82022i	−0.844309	+	0.397646i
$493$	−38.2097	−	22.0604i	−1.72088	−	0.993549i
$494$	3.90738	+	8.17987i	0.175801	+	0.368030i
$495$	7.56098	−	44.8857i	0.339841	−	2.01746i
$496$	1.76151	+	1.01701i	0.0790940	+	0.0456649i
$497$	−8.05677	−	20.2900i	−0.361395	−	0.910131i
$498$	11.9777	−	17.2460i	0.536734	−	0.772810i
$499$	−13.3645	−	23.1479i	−0.598276	−	1.03624i	−0.993076	−	0.117477i	$-0.962519\pi$
$499$	−13.3645	−	23.1479i	−0.598276	−	1.03624i	0.394800	−	0.918767i	$-0.370814\pi$
$500$	−5.66889			−0.253520
$501$	−12.3175	+	5.80121i	−0.550306	+	0.259179i
$502$	−9.05503	+	5.22792i	−0.404146	+	0.233334i
$503$	1.69136	+	2.92951i	0.0754138	+	0.130621i	0.901266	−	0.433266i	$-0.142639\pi$
$503$	1.69136	+	2.92951i	0.0754138	+	0.130621i	−0.825852	+	0.563886i	$0.809306\pi$
$504$	1.66317	+	7.76105i	0.0740834	+	0.345705i
$505$	−0.0514557	+	0.0891239i	−0.00228975	+	0.00396596i
$506$	−22.5206	+	13.0023i	−1.00116	+	0.578023i
$507$	−5.33849	+	21.8747i	−0.237090	+	0.971488i
$508$	−5.94284	+	10.2933i	−0.263671	+	0.456691i
$509$	31.3346			1.38888			0.694441	−	0.719550i	$-0.255652\pi$
$509$	31.3346			1.38888			0.694441	+	0.719550i	$0.255652\pi$
$510$	35.7472	+	2.98974i	1.58291	+	0.132388i
$511$	2.94309	−	3.72086i	0.130195	−	0.164601i
$512$		−	1.00000i		−	0.0441942i
$513$	9.13128	−	9.34328i	0.403156	−	0.412516i
$514$		−	1.76706i		−	0.0779416i
$515$	−45.0987	−	26.0377i	−1.98729	−	1.14736i
$516$	0.241622	−	2.88898i	0.0106368	−	0.127180i
$517$	23.1364	+	13.3578i	1.01754	+	0.587474i
$518$	−1.67329	−	0.245387i	−0.0735201	−	0.0107817i
$519$	−25.5349	+	12.0262i	−1.12086	+	0.527893i
$520$	0.794034	−	10.1640i	0.0348207	−	0.445720i
$521$	9.29916	−	16.1066i	0.407403	−	0.705644i	−0.587194	−	0.809446i	$-0.699768\pi$
$521$	9.29916	−	16.1066i	0.407403	−	0.705644i	0.994598	+	0.103802i	$0.0331009\pi$
$522$	17.8199	+	3.00177i	0.779958	+	0.131384i
$523$			3.78482i			0.165499i	0.996570	+	0.0827493i	$0.0263701\pi$
$523$			3.78482i			0.165499i	−0.996570	+	0.0827493i	$0.973630\pi$
$524$	−3.27806	−	5.67776i	−0.143203	−	0.248034i
$525$	−3.98456	−	13.1343i	−0.173901	−	0.573230i
$526$	10.4975	+	18.1822i	0.457712	+	0.792781i
$527$	−12.9023	−	7.44913i	−0.562032	−	0.324489i
$528$	9.26182	+	0.774619i	0.403069	+	0.0337110i
$529$	−0.485594			−0.0211128
$530$	9.22683			0.400788
$531$	4.89285	+	13.1296i	0.212332	+	0.569776i
$532$	−4.12670	+	5.21727i	−0.178915	+	0.226197i
$533$	−18.5740	−	38.8836i	−0.804530	−	1.68424i
$534$	16.0135	−	23.0569i	0.692973	−	0.997770i
$535$	13.6296	−	7.86907i	0.589260	−	0.340209i
$536$	3.79862	−	2.19314i	0.164076	−	0.0947291i
$537$	−19.0284	−	1.59145i	−0.821135	−	0.0686762i
$538$			17.5469i			0.756499i
$539$	36.5523	−	8.65012i	1.57442	−	0.372587i
$540$	−14.1473	+	3.96528i	−0.608802	+	0.170639i
$541$	12.8908	+	22.3276i	0.554221	+	0.959938i	0.997964	+	0.0637841i	$0.0203169\pi$
$541$	12.8908	+	22.3276i	0.554221	+	0.959938i	−0.443743	+	0.896154i	$0.646350\pi$
$542$	−22.1933			−0.953282
$543$	−3.73946	+	5.38422i	−0.160476	+	0.231059i
$544$			7.32456i			0.314038i
$545$	16.6034			0.711213
$546$	−16.1367	+	3.55060i	−0.690587	+	0.151952i
$547$	−17.2559			−0.737809			−0.368905	−	0.929467i	$-0.620267\pi$
$547$	−17.2559			−0.737809			−0.368905	+	0.929467i	$0.620267\pi$
$548$			15.0048i			0.640972i
$549$	−2.78610	+	16.5396i	−0.118908	+	0.705894i
$550$	−16.0719			−0.685306
$551$	7.57245	+	13.1159i	0.322597	+	0.558755i
$552$	6.89421	+	4.78818i	0.293437	+	0.203799i
$553$	9.97585	−	3.96122i	0.424216	−	0.168448i
$554$		−	12.8518i		−	0.546021i
$555$	0.260912	−	3.11963i	0.0110751	−	0.132421i
$556$	14.8457	−	8.57114i	0.629596	−	0.363497i
$557$	−34.8056	+	20.0950i	−1.47476	+	0.851454i	−0.999595	−	0.0284423i	$-0.990945\pi$
$557$	−34.8056	+	20.0950i	−1.47476	+	0.851454i	−0.475166	+	0.879896i	$0.657612\pi$
$558$	6.01726	+	1.01361i	0.254731	+	0.0429094i
$559$	6.01656	+	0.470029i	0.254473	+	0.0198801i
$560$	6.95295	−	2.76088i	0.293816	−	0.116669i
$561$	−67.8388	−	5.67375i	−2.86416	−	0.239546i
$562$	26.5541			1.12012
$563$	36.7290			1.54794			0.773971	−	0.633221i	$-0.218268\pi$
$563$	36.7290			1.54794			0.773971	+	0.633221i	$0.218268\pi$
$564$	0.718711	−	8.59334i	0.0302632	−	0.361845i
$565$	−2.45962	−	1.42006i	−0.103477	−	0.0597424i
$566$	−0.769566	−	1.33293i	−0.0323473	−	0.0560271i
$567$	12.8058	+	20.0751i	0.537795	+	0.843076i
$568$	4.12569	+	7.14590i	0.173110	+	0.299835i
$569$			11.6897i			0.490058i	0.969516	+	0.245029i	$0.0787975\pi$
$569$			11.6897i			0.490058i	−0.969516	+	0.245029i	$0.921203\pi$
$570$	−10.1135	−	7.02406i	−0.423609	−	0.294206i
$571$	−3.35122	+	5.80449i	−0.140244	+	0.242910i	−0.927589	−	0.373603i	$-0.878122\pi$
$571$	−3.35122	+	5.80449i	−0.140244	+	0.242910i	0.787344	+	0.616514i	$0.211455\pi$
$572$	−1.50687	+	19.2886i	−0.0630054	+	0.806495i
$573$	−5.95123	−	12.6360i	−0.248616	−	0.527878i
$574$	19.6166	−	24.8007i	0.818781	−	1.03516i
$575$	−12.5704	−	7.25751i	−0.524221	−	0.302659i
$576$	−1.04760	−	2.81115i	−0.0436498	−	0.117131i
$577$	−11.0699	−	6.39122i	−0.460847	−	0.266070i	0.251553	−	0.967843i	$-0.419059\pi$
$577$	−11.0699	−	6.39122i	−0.460847	−	0.266070i	−0.712400	+	0.701773i	$0.752392\pi$
$578$		−	36.6492i		−	1.52441i
$579$	1.58893	−	18.9982i	0.0660335	−	0.789537i
$580$		−	17.0323i		−	0.707229i
$581$	−4.65386	+	31.7346i	−0.193075	+	1.31657i
$582$	0.762922	−	9.12196i	0.0316241	−	0.378117i
$583$	−17.5101			−0.725195
$584$	−0.896552	+	1.55287i	−0.0370996	+	0.0642584i
$585$	−8.41558	−	29.4042i	−0.347941	−	1.21572i
$586$	−5.76094	+	3.32608i	−0.237982	+	0.137399i
$587$	9.01119	−	15.6078i	0.371932	−	0.644204i	−0.617931	−	0.786232i	$-0.712029\pi$
$587$	9.01119	−	15.6078i	0.371932	−	0.644204i	0.989863	+	0.142028i	$0.0453623\pi$
$588$	−7.55310	−	9.48423i	−0.311485	−	0.391123i
$589$	2.55699	+	4.42884i	0.105359	+	0.182487i
$590$	11.4370	−	6.60315i	0.470854	−	0.271847i
$591$	−1.66521	−	3.53568i	−0.0684975	−	0.145439i
$592$	0.639208			0.0262713
$593$	−6.20188	−	10.7420i	−0.254681	−	0.441120i	0.710128	−	0.704073i	$-0.248637\pi$
$593$	−6.20188	−	10.7420i	−0.254681	−	0.441120i	−0.964809	+	0.262953i	$0.915304\pi$
$594$	26.8478	−	7.52507i	1.10158	−	0.308757i
$595$	−50.9273	+	20.2223i	−2.08782	+	0.829032i
$596$	−9.92624	−	5.73092i	−0.406595	−	0.234748i
$597$	−7.16594	+	10.3178i	−0.293282	+	0.422279i
$598$	−9.88864	+	14.4058i	−0.404376	+	0.589098i
$599$	−20.8366	−	12.0300i	−0.851359	−	0.491532i	0.00974999	−	0.999952i	$-0.496896\pi$
$599$	−20.8366	−	12.0300i	−0.851359	−	0.491532i	−0.861109	+	0.508420i	$0.830230\pi$
$600$	2.21040	+	4.69326i	0.0902390	+	0.191601i
$601$	−38.2975	−	22.1111i	−1.56219	−	0.901930i	−0.997036	−	0.0769429i	$-0.975484\pi$
$601$	−38.2975	−	22.1111i	−1.56219	−	0.901930i	−0.565152	−	0.824987i	$-0.691183\pi$
$602$	1.63430	+	4.11580i	0.0666092	+	0.167747i
$603$	8.38097	−	10.1446i	0.341299	−	0.413122i
$604$	6.15167	−	10.6550i	0.250308	−	0.433546i
$605$	50.3131			2.04552
$606$	−0.0628200	−	0.00525400i	−0.00255189	−	0.000213429i
$607$	−2.02607	−	1.16975i	−0.0822358	−	0.0474789i	0.458318	−	0.888788i	$-0.348452\pi$
$607$	−2.02607	−	1.16975i	−0.0822358	−	0.0474789i	−0.540554	+	0.841309i	$0.681785\pi$
$608$	1.25712	−	2.17739i	0.0509828	−	0.0883048i
$609$	−26.4151	+	8.01355i	−1.07039	+	0.324726i
$610$	15.8086			0.640071
$611$	17.8964	+	1.39811i	0.724010	+	0.0565615i
$612$	7.67318	+	20.5904i	0.310170	+	0.832318i
$613$	20.8792	+	36.1638i	0.843302	+	1.46064i	0.887088	+	0.461601i	$0.152725\pi$
$613$	20.8792	+	36.1638i	0.843302	+	1.46064i	−0.0437858	+	0.999041i	$0.513942\pi$
$614$	24.3883			0.984230
$615$	48.0753	+	33.3894i	1.93858	+	1.34639i
$616$	−13.1949	+	5.23943i	−0.531637	+	0.211103i
$617$	−21.2369	+	12.2611i	−0.854965	+	0.493614i	−0.862323	−	0.506359i	$-0.830991\pi$
$617$	−21.2369	+	12.2611i	−0.854965	+	0.493614i	0.00735804	+	0.999973i	$0.497658\pi$
$618$	2.65864	−	31.7883i	0.106946	−	1.27871i
$619$	−6.74880	−	3.89642i	−0.271257	−	0.156610i	0.358202	−	0.933644i	$-0.383390\pi$
$619$	−6.74880	−	3.89642i	−0.271257	−	0.156610i	−0.629459	+	0.777034i	$0.716723\pi$
$620$		−	5.75131i		−	0.230978i
$621$	24.3967	+	6.23794i	0.979006	+	0.250320i
$622$	−28.4483	−	16.4246i	−1.14067	−	0.658567i
$623$	−6.22195	+	42.4273i	−0.249277	+	1.69982i
$624$	5.83984	−	2.21276i	0.233781	−	0.0885815i
$625$	15.5024	+	26.8510i	0.620097	+	1.07404i
$626$	−6.56281	−	11.3671i	−0.262303	−	0.454322i
$627$	19.1928	+	13.3298i	0.766487	+	0.532342i
$628$	−14.2430	−	8.22323i	−0.568360	−	0.328143i
$629$	−4.68192			−0.186681
$630$	16.6535	−	15.0451i	0.663490	−	0.599412i
$631$	10.1378	+	17.5592i	0.403580	+	0.699021i	0.994155	−	0.107961i	$-0.0344323\pi$
$631$	10.1378	+	17.5592i	0.403580	+	0.699021i	−0.590575	+	0.806983i	$0.701099\pi$
$632$	−3.51337	+	2.02845i	−0.139755	+	0.0806873i
$633$	−7.36684	+	3.46958i	−0.292806	+	0.137903i
$634$	−10.9910	−	19.0370i	−0.436509	−	0.756055i
$635$	33.6075			1.33367
$636$	2.40820	+	5.11326i	0.0954915	+	0.202754i
$637$	19.6566	−	15.8309i	0.778822	−	0.627245i
$638$			32.3229i			1.27968i
$639$	19.0839	+	15.7661i	0.754948	+	0.623698i
$640$	−2.44875	+	1.41378i	−0.0967951	+	0.0558847i
$641$		−	41.3155i		−	1.63186i	−0.578149	−	0.815931i	$-0.696225\pi$
$641$		−	41.3155i		−	1.63186i	0.578149	−	0.815931i	$-0.303775\pi$
$642$	7.91815	+	5.49934i	0.312505	+	0.217041i
$643$	29.2874	−	16.9091i	1.15498	−	0.666828i	0.204884	−	0.978786i	$-0.434318\pi$
$643$	29.2874	−	16.9091i	1.15498	−	0.666828i	0.950096	+	0.311958i	$0.100985\pi$
$644$	−12.6861	−	1.86042i	−0.499904	−	0.0733106i
$645$	−7.41598	+	3.49272i	−0.292004	+	0.137526i
$646$	−9.20783	+	15.9484i	−0.362277	+	0.627483i
$647$	12.4285	+	21.5268i	0.488615	+	0.846306i	0.999914	−	0.0130964i	$-0.00416885\pi$
$647$	12.4285	+	21.5268i	0.488615	+	0.846306i	−0.511299	+	0.859403i	$0.670836\pi$
$648$	−5.88989	−	6.80509i	−0.231377	−	0.267329i
$649$	−21.7044	+	12.5311i	−0.851973	+	0.491887i
$650$	−9.74445	+	4.65475i	−0.382209	+	0.182574i
$651$	−8.91960	+	2.70594i	−0.349587	+	0.106054i
$652$	3.00753	−	5.20920i	0.117784	−	0.204008i
$653$		−	9.90848i		−	0.387749i	−0.981026	−	0.193874i	$-0.937895\pi$
$653$		−	9.90848i		−	0.387749i	0.981026	−	0.193874i	$-0.0621054\pi$
$654$	4.33350	+	9.20117i	0.169453	+	0.359794i
$655$	−9.26893	+	16.0542i	−0.362167	+	0.627291i
$656$	−5.97580	+	10.3504i	−0.233316	+	0.404115i
$657$	−0.893556	+	5.30458i	−0.0348609	+	0.206951i
$658$	4.86127	+	12.2425i	0.189512	+	0.477263i
$659$	14.5005	−	8.37187i	0.564859	−	0.326122i	−0.190234	−	0.981739i	$-0.560925\pi$
$659$	14.5005	−	8.37187i	0.564859	−	0.326122i	0.755094	+	0.655617i	$0.227591\pi$
$660$	−11.1974	−	23.7750i	−0.435857	−	0.925440i
$661$	4.25236	−	2.45510i	0.165398	−	0.0954923i	−0.415016	−	0.909814i	$-0.636224\pi$
$661$	4.25236	−	2.45510i	0.165398	−	0.0954923i	0.580414	+	0.814322i	$0.302891\pi$
$662$	11.2334	+	6.48561i	0.436599	+	0.252070i
$663$	−42.7742	+	16.2075i	−1.66121	+	0.629448i
$664$		−	12.1228i		−	0.470457i
$665$	18.6100	+	2.72915i	0.721666	+	0.105832i
$666$	1.79691	−	0.669632i	0.0696288	−	0.0259477i
$667$	−14.5959	+	25.2809i	−0.565157	+	0.978880i
$668$	−3.93039	+	6.80763i	−0.152071	+	0.263395i
$669$	−15.7735	−	33.4912i	−0.609837	−	1.29485i
$670$	−10.7409	−	6.20124i	−0.414956	−	0.239575i
$671$	−30.0005			−1.15816
$672$	3.34472	+	3.13254i	0.129026	+	0.120840i
$673$	8.86744	−	15.3589i	0.341815	−	0.592040i	−0.642955	−	0.765904i	$-0.722292\pi$
$673$	8.86744	−	15.3589i	0.341815	−	0.592040i	0.984770	+	0.173863i	$0.0556251\pi$
$674$		−	27.9808i		−	1.07778i
$675$	11.1304	+	10.8778i	0.428409	+	0.418688i
$676$	4.67275	+	12.1312i	0.179721	+	0.466584i
$677$	−23.2931	−	40.3449i	−0.895228	−	1.55058i	−0.833522	−	0.552486i	$-0.813679\pi$
$677$	−23.2931	−	40.3449i	−0.895228	−	1.55058i	−0.0617058	−	0.998094i	$-0.519654\pi$
$678$	0.144998	−	1.73369i	0.00556863	−	0.0665819i
$679$	5.16031	+	12.9956i	0.198035	+	0.498726i
$680$	17.9360	−	10.3553i	0.687814	−	0.397110i
$681$	17.7346	+	12.3171i	0.679590	+	0.471991i
$682$			10.9145i			0.417937i
$683$		−	24.3511i		−	0.931770i	−0.884845	−	0.465885i	$-0.845736\pi$
$683$		−	24.3511i		−	0.931770i	0.884845	−	0.465885i	$-0.154264\pi$
$684$	1.25292	−	7.43791i	0.0479064	−	0.284396i
$685$	36.7428	−	21.2135i	1.40387	−	0.810526i
$686$	16.7811	+	7.83543i	0.640706	+	0.299158i
$687$	18.1263	+	1.51600i	0.691560	+	0.0578392i
$688$	−0.836889	−	1.44953i	−0.0319061	−	0.0552630i
$689$	−10.6165	+	5.07130i	−0.404455	+	0.193201i
$690$	1.97812	−	23.6516i	0.0753058	−	0.900401i
$691$		−	16.4387i		−	0.625359i	−0.949859	−	0.312680i	$-0.898773\pi$
$691$		−	16.4387i		−	0.625359i	0.949859	−	0.312680i	$-0.101227\pi$
$692$	−8.14791	+	14.1126i	−0.309737	+	0.536480i
$693$	−31.6039	+	28.5517i	−1.20053	+	1.08459i
$694$	−12.7624			−0.484456
$695$	−41.9771	−	24.2355i	−1.59228	−	0.919304i
$696$	9.43884	−	4.44544i	0.357778	−	0.168504i
$697$	43.7701	−	75.8121i	1.65791	−	2.87159i
$698$	7.39994	−	12.8171i	0.280092	−	0.485133i
$699$	5.55148	+	0.464303i	0.209976	+	0.0175615i
$700$	−6.21519	−	4.91603i	−0.234912	−	0.185808i
$701$			39.4946i			1.49169i	0.666120	+	0.745844i	$0.267954\pi$
$701$			39.4946i			1.49169i	−0.666120	+	0.745844i	$0.732046\pi$
$702$	14.0985	−	12.3382i	0.532115	−	0.465675i
$703$	1.39181	+	0.803560i	0.0524930	+	0.0303068i
$704$	4.64708	−	2.68299i	0.175143	−	0.101119i
$705$	−22.0590	+	10.3892i	−0.830790	+	0.391279i
$706$	14.9908	−	8.65493i	0.564186	−	0.325733i
$707$	0.0894966	−	0.0355374i	0.00336587	−	0.00133652i
$708$	6.64434	+	4.61464i	0.249710	+	0.173429i
$709$	5.92435	−	10.2613i	0.222493	−	0.385370i	−0.733071	−	0.680152i	$-0.761914\pi$
$709$	5.92435	−	10.2613i	0.222493	−	0.385370i	0.955564	+	0.294782i	$0.0952471\pi$
$710$	11.6657	−	20.2055i	0.437804	−	0.758299i
$711$	−7.75162	+	9.38286i	−0.290708	+	0.351885i
$712$		−	16.2075i		−	0.607404i
$713$	−4.92861	+	8.53660i	−0.184578	+	0.319698i
$714$	−24.4986	−	22.9445i	−0.916839	−	0.858677i
$715$	49.3631	−	23.5799i	1.84608	−	0.881838i
$716$	−9.54740	+	5.51220i	−0.356803	+	0.206000i
$717$	11.8505	−	17.0628i	0.442566	−	0.637223i
$718$	−3.13151	−	5.42394i	−0.116867	−	0.202419i
$719$	−18.6611	+	32.3220i	−0.695942	+	1.20541i	0.273920	+	0.961753i	$0.411680\pi$
$719$	−18.6611	+	32.3220i	−0.695942	+	1.20541i	−0.969862	+	0.243655i	$0.921654\pi$
$720$	−5.40271	+	6.53965i	−0.201347	+	0.243718i
$721$	17.9827	+	45.2873i	0.669711	+	1.68659i
$722$	−10.9800	+	6.33931i	−0.408634	+	0.235925i
$723$	18.1704	−	26.1624i	0.675764	−	0.972991i
$724$			3.78477i			0.140660i
$725$	−15.6246	+	9.02085i	−0.580282	+	0.335026i
$726$	13.1317	+	27.8821i	0.487364	+	1.03480i
$727$		−	42.1110i		−	1.56181i	−0.624650	−	0.780905i	$-0.714758\pi$
$727$		−	42.1110i		−	1.56181i	0.624650	−	0.780905i	$-0.285242\pi$
$728$	−6.48267	+	6.99821i	−0.240264	+	0.259371i
$729$	−23.6863	−	12.9599i	−0.877271	−	0.479995i
$730$	5.07012			0.187654
$731$	6.12985	+	10.6172i	0.226721	+	0.392692i
$732$	4.12604	+	8.76068i	0.152503	+	0.323804i
$733$	33.9637	−	19.6090i	1.25448	−	0.724274i	0.282484	−	0.959272i	$-0.408842\pi$
$733$	33.9637	−	19.6090i	1.25448	−	0.724274i	0.971996	+	0.234998i	$0.0755084\pi$
$734$	13.4638	+	23.3199i	0.496957	+	0.860755i
$735$	−12.5460	+	31.9043i	−0.462767	+	1.17681i
$736$	4.84619			0.178633
$737$	20.3834	+	11.7683i	0.750830	+	0.433492i
$738$	−5.95583	+	35.3567i	−0.219237	+	1.30150i
$739$	−6.88122	−	11.9186i	−0.253130	−	0.438433i	0.711256	−	0.702933i	$-0.248127\pi$
$739$	−6.88122	−	11.9186i	−0.253130	−	0.438433i	−0.964386	+	0.264499i	$0.914793\pi$
$740$	−0.903702	−	1.56526i	−0.0332208	−	0.0575401i
$741$	15.4973	+	2.52330i	0.569308	+	0.0926959i
$742$	−6.77138	−	5.35596i	−0.248585	−	0.196623i
$743$	−35.2355	−	20.3432i	−1.29266	−	0.746320i	−0.313538	−	0.949576i	$-0.601514\pi$
$743$	−35.2355	−	20.3432i	−1.29266	−	0.746320i	−0.979126	+	0.203256i	$0.934848\pi$
$744$	3.18722	−	1.50109i	0.116849	−	0.0550327i
$745$			32.4091i			1.18738i
$746$	13.4655	+	7.77432i	0.493007	+	0.284638i
$747$	−12.6998	−	34.0791i	−0.464662	−	1.24689i
$748$	−34.0378	+	19.6517i	−1.24455	+	0.718539i
$749$	−14.5703	−	2.13673i	−0.532388	−	0.0780744i
$750$	−5.60103	+	8.06457i	−0.204521	+	0.294477i
$751$	19.4558			0.709952			0.354976	−	0.934875i	$-0.384489\pi$
$751$	19.4558			0.709952			0.354976	+	0.934875i	$0.384489\pi$
$752$	−2.48934	−	4.31167i	−0.0907770	−	0.157230i
$753$	−1.50938	+	18.0470i	−0.0550048	+	0.657671i
$754$	9.36140	+	19.5975i	0.340922	+	0.713700i
$755$	−34.7885			−1.26608
$756$	12.6841	+	5.30212i	0.461318	+	0.192836i
$757$	−9.52424	+	16.4965i	−0.346164	+	0.599574i	−0.985565	−	0.169300i	$-0.945849\pi$
$757$	−9.52424	+	16.4965i	−0.346164	+	0.599574i	0.639400	+	0.768874i	$0.279183\pi$
$758$	32.1700	+	18.5733i	1.16847	+	0.674614i
$759$	−3.75396	+	44.8846i	−0.136260	+	1.62921i
$760$	−7.10916			−0.257877
$761$	−21.8081	+	37.7727i	−0.790543	+	1.36926i	0.135088	+	0.990834i	$0.456868\pi$
$761$	−21.8081	+	37.7727i	−0.790543	+	1.36926i	−0.925631	+	0.378427i	$0.876465\pi$
$762$	8.77157	+	18.6244i	0.317760	+	0.674690i
$763$	−12.1849	−	9.63791i	−0.441124	−	0.348916i
$764$	−6.98367	−	4.03202i	−0.252660	−	0.145874i
$765$	39.5725	−	47.9001i	1.43075	−	1.73183i
$766$	27.1401	+	15.6693i	0.980611	+	0.566156i
$767$	−9.53024	+	13.8837i	−0.344117	+	0.501312i
$768$	−1.42260	−	0.988029i	−0.0513337	−	0.0356524i
$769$	10.8919	+	6.28847i	0.392774	+	0.226768i	0.683361	−	0.730080i	$-0.260517\pi$
$769$	10.8919	+	6.28847i	0.392774	+	0.226768i	−0.290588	+	0.956848i	$0.593851\pi$
$770$	31.4847	+	24.9035i	1.13463	+	0.897459i
$771$	−2.51382	−	1.74591i	−0.0905331	−	0.0628773i
$772$	−5.50345	−	9.53225i	−0.198073	−	0.343073i
$773$	15.9038			0.572018			0.286009	−	0.958227i	$-0.407671\pi$
$773$	15.9038			0.572018			0.286009	+	0.958227i	$0.407671\pi$
$774$	−3.87114	−	3.19813i	−0.139145	−	0.114954i
$775$	−5.27595	+	3.04607i	−0.189518	+	0.109418i
$776$	−2.64248	−	4.57690i	−0.0948593	−	0.164301i
$777$	−2.00235	+	2.13798i	−0.0718338	+	0.0766995i
$778$	−10.5324	+	18.2426i	−0.377605	+	0.654031i
$779$	−26.0233	+	15.0246i	−0.932381	+	0.538310i
$780$	−13.6748	−	11.1719i	−0.489635	−	0.400018i
$781$	−22.1384	+	38.3448i	−0.792173	+	1.37208i
$782$	−35.4963			−1.26934
$783$	21.8769	−	22.3849i	0.781818	−	0.799970i
$784$	−6.70525	−	2.00987i	−0.239473	−	0.0717810i
$785$			46.5035i			1.65978i
$786$	−11.3160	−	0.946424i	−0.403629	−	0.0337578i
$787$			30.6180i			1.09142i	0.837976	+	0.545708i	$0.183739\pi$
$787$			30.6180i			1.09142i	−0.837976	+	0.545708i	$0.816261\pi$
$788$	−1.95410	−	1.12820i	−0.0696118	−	0.0401904i
$789$	36.2379	+	3.03078i	1.29010	+	0.107899i
$790$	9.93430	+	5.73557i	0.353447	+	0.204062i
$791$	0.980752	+	2.46991i	0.0348715	+	0.0878197i
$792$	10.2529	−	12.4105i	0.364322	−	0.440989i
$793$	−18.1895	+	8.68880i	−0.645928	+	0.308548i
$794$	8.10856	−	14.0444i	0.287762	−	0.498418i
$795$	9.11638	−	13.1261i	0.323325	−	0.465535i
$796$			7.25276i			0.257067i
$797$	23.5838	+	40.8483i	0.835381	+	1.44692i	0.893720	+	0.448626i	$0.148086\pi$
$797$	23.5838	+	40.8483i	0.835381	+	1.44692i	−0.0583386	+	0.998297i	$0.518580\pi$
$798$	3.34480	+	11.0255i	0.118405	+	0.390298i
$799$	18.2334	+	31.5811i	0.645050	+	1.11726i
$800$	2.59386	+	1.49757i	0.0917070	+	0.0529470i
$801$	−16.9790	−	45.5618i	−0.599922	−	1.60985i
$802$	18.6153			0.657329
$803$	−9.62177			−0.339545
$804$	0.633191	−	7.57082i	0.0223309	−	0.267002i
$805$	13.3798	+	33.6953i	0.471575	+	1.18760i
$806$	3.16107	+	6.61750i	0.111344	+	0.233092i
$807$	24.9622	+	17.3368i	0.878711	+	0.610285i
$808$	−0.0315196	+	0.0181979i	−0.00110886	+	0.000640199i
$809$	3.88186	−	2.24119i	0.136479	−	0.0787961i	−0.430206	−	0.902731i	$-0.641559\pi$
$809$	3.88186	−	2.24119i	0.136479	−	0.0787961i	0.566685	+	0.823935i	$0.308226\pi$
$810$	−8.33690	+	24.0438i	−0.292929	+	0.844811i
$811$			27.3659i			0.960948i	0.877009	+	0.480474i	$0.159535\pi$
$811$			27.3659i			0.960948i	−0.877009	+	0.480474i	$0.840465\pi$
$812$	−9.88686	+	12.4997i	−0.346961	+	0.438652i
$813$	−21.9276	+	31.5722i	−0.769034	+	1.10728i
$814$	1.71499	+	2.97045i	0.0601104	+	0.104114i
$815$	−17.0080			−0.595765
$816$	10.4199	+	7.23689i	0.364771	+	0.253342i
$817$		−	4.20827i		−	0.147229i
$818$	9.43206			0.329784
$819$	−10.8924	+	26.4642i	−0.380613	+	0.924735i
$820$	33.7939			1.18014
$821$			27.5238i			0.960588i	0.877108	+	0.480294i	$0.159470\pi$
$821$			27.5238i			0.960588i	−0.877108	+	0.480294i	$0.840530\pi$
$822$	21.3458	+	14.8251i	0.744521	+	0.517086i
$823$	−36.4824			−1.27170			−0.635848	−	0.771814i	$-0.719350\pi$
$823$	−36.4824			−1.27170			−0.635848	+	0.771814i	$0.719350\pi$
$824$	−9.20853	−	15.9496i	−0.320794	−	0.555632i
$825$	−15.8795	+	22.8639i	−0.552852	+	0.796017i
$826$	−12.2264	−	1.79299i	−0.425409	−	0.0623861i
$827$			47.0909i			1.63751i	0.574142	+	0.818755i	$0.305336\pi$
$827$			47.0909i			1.63751i	−0.574142	+	0.818755i	$0.694664\pi$
$828$	13.6234	−	5.07685i	0.473444	−	0.176433i
$829$	29.6783	−	17.1348i	1.03077	−	0.595115i	0.113564	−	0.993531i	$-0.463773\pi$
$829$	29.6783	−	17.1348i	1.03077	−	0.595115i	0.917205	+	0.398416i	$0.130440\pi$
$830$	−29.6857	+	17.1391i	−1.03041	+	0.594905i
$831$	−18.2830	−	12.6980i	−0.634231	−	0.440487i
$832$	2.04050	−	2.97260i	0.0707415	−	0.103057i
$833$	49.1131	+	14.7214i	1.70167	+	0.510067i
$834$	2.47462	−	29.5880i	0.0856889	−	1.02455i
$835$	22.2269			0.769192
$836$	13.4913			0.466608
$837$	7.38719	−	7.55870i	0.255339	−	0.261267i
$838$	−26.9681	−	15.5700i	−0.931597	−	0.537858i
$839$	−7.26358	−	12.5809i	−0.250767	−	0.434340i	0.712971	−	0.701194i	$-0.247349\pi$
$839$	−7.26358	−	12.5809i	−0.250767	−	0.434340i	−0.963737	+	0.266854i	$0.914016\pi$
$840$	2.94208	−	12.6191i	0.101511	−	0.435401i
$841$	3.64227	+	6.30861i	0.125596	+	0.217538i
$842$		−	1.34712i		−	0.0464247i
$843$	26.2362	−	37.7759i	0.903623	−	1.30107i
$844$	−2.35068	+	4.07150i	−0.0809137	+	0.140147i
$845$	23.0999	−	28.5932i	0.794660	−	0.983637i
$846$	−11.5148	−	9.51291i	−0.395887	−	0.327061i
$847$	−36.9237	−	29.2056i	−1.26871	−	1.00352i
$848$	2.82599	+	1.63159i	0.0970448	+	0.0560289i
$849$	−2.65658	−	0.222185i	−0.0911736	−	0.00762537i
$850$	−18.9989	−	10.9690i	−0.651658	−	0.376235i
$851$			3.09773i			0.106189i
$852$	14.2421	+	1.19115i	0.487925	+	0.0408080i
$853$			43.2554i			1.48104i	0.672036	+	0.740518i	$0.265420\pi$
$853$			43.2554i			1.48104i	−0.672036	+	0.740518i	$0.734580\pi$
$854$	−11.6016	−	9.17651i	−0.396998	−	0.314014i
$855$	−19.9849	+	7.44753i	−0.683469	+	0.254700i
$856$	5.56596			0.190241
$857$	10.9150	−	18.9053i	0.372850	−	0.645794i	−0.617153	−	0.786843i	$-0.711714\pi$
$857$	10.9150	−	18.9053i	0.372850	−	0.645794i	0.990003	+	0.141049i	$0.0450474\pi$
$858$	25.9511	+	21.2013i	0.885956	+	0.723802i
$859$	−10.7860	+	6.22730i	−0.368014	+	0.212473i	−0.672590	−	0.740015i	$-0.734818\pi$
$859$	−10.7860	+	6.22730i	−0.368014	+	0.212473i	0.304577	+	0.952488i	$0.401485\pi$
$860$	−2.36636	+	4.09866i	−0.0806922	+	0.139763i
$861$	−15.8997	−	52.4104i	−0.541862	−	1.78614i
$862$	0.808798	+	1.40088i	0.0275478	+	0.0477141i
$863$	−32.8756	+	18.9807i	−1.11910	+	0.646112i	−0.941171	−	0.337932i	$-0.890273\pi$
$863$	−32.8756	+	18.9807i	−1.11910	+	0.646112i	−0.177928	+	0.984044i	$0.556939\pi$
$864$	−5.03420	−	1.28718i	−0.171267	−	0.0437909i
$865$	46.0775			1.56668
$866$	1.57323	+	2.72492i	0.0534606	+	0.0925965i
$867$	−52.1373	−	36.2105i	−1.77068	−	1.22977i
$868$	−3.33850	+	4.22077i	−0.113316	+	0.143262i
$869$	−18.8527	−	10.8846i	−0.639534	−	0.369235i
$870$	−24.2302	−	16.8284i	−0.821481	−	0.570537i
$871$	15.7669	+	1.23175i	0.534241	+	0.0417362i
$872$	5.08529	+	2.93599i	0.172210	+	0.0994253i
$873$	−12.2231	−	10.0981i	−0.413690	−	0.341769i
$874$	10.5521	+	6.09223i	0.356929	+	0.206073i
$875$	2.17624	−	14.8397i	0.0735704	−	0.501675i
$876$	1.32330	+	2.80972i	0.0447102	+	0.0949317i
$877$	15.2719	−	26.4518i	0.515697	−	0.893213i	−0.484137	−	0.874992i	$-0.660867\pi$
$877$	15.2719	−	26.4518i	0.515697	−	0.893213i	0.999834	−	0.0182207i	$-0.00580014\pi$
$878$	1.66372			0.0561478
$879$	−0.960288	+	11.4818i	−0.0323897	+	0.387271i
$880$	−13.1399	−	7.58634i	−0.442947	−	0.255735i
$881$	1.78267	−	3.08767i	0.0600596	−	0.104026i	−0.834432	−	0.551111i	$-0.814204\pi$
$881$	1.78267	−	3.08767i	0.0600596	−	0.104026i	0.894492	+	0.447084i	$0.147538\pi$
$882$	−20.9550	+	1.37436i	−0.705591	+	0.0462770i
$883$	21.6463			0.728455			0.364228	−	0.931310i	$-0.381333\pi$
$883$	21.6463			0.728455			0.364228	+	0.931310i	$0.381333\pi$
$884$	−14.9457	+	21.7730i	−0.502680	+	0.732306i
$885$	1.90643	−	22.7944i	0.0640839	−	0.766226i
$886$	−7.32582	−	12.6887i	−0.246116	−	0.426285i
$887$	−5.03734			−0.169137			−0.0845686	−	0.996418i	$-0.526951\pi$
$887$	−5.03734			−0.169137			−0.0845686	+	0.996418i	$0.526951\pi$
$888$	0.631557	−	0.909340i	0.0211937	−	0.0305154i
$889$	−24.6639	−	19.5084i	−0.827200	−	0.654290i
$890$	−39.6882	+	22.9140i	−1.33035	+	0.768078i
$891$	15.8212	−	45.6288i	0.530032	−	1.52862i
$892$	−18.5099	−	10.6867i	−0.619757	−	0.357817i
$893$		−	12.5176i		−	0.418885i
$894$	−17.9602	+	8.45878i	−0.600680	+	0.282904i
$895$	26.9959	+	15.5861i	0.902374	+	0.520986i
$896$	2.61775	+	0.383892i	0.0874530	+	0.0128249i
$897$	10.7235	+	28.3010i	0.358047	+	0.944942i
$898$	2.80333	+	4.85551i	0.0935483	+	0.162030i
$899$	6.12611	+	10.6107i	0.204317	+	0.353888i
$900$	8.86058	+	1.49256i	0.295353	+	0.0497521i
$901$	−20.6991	−	11.9507i	−0.689588	−	0.398134i
$902$	−64.1321			−2.13536
$903$	7.46988	+	1.74156i	0.248582	+	0.0579556i
$904$	−0.502220	−	0.869871i	−0.0167036	−	0.0289315i
$905$	9.26793	−	5.35084i	0.308077	−	0.177868i
$906$	−9.07980	−	19.2788i	−0.301656	−	0.640496i
$907$	−3.24512	−	5.62071i	−0.107752	−	0.186632i	0.807107	−	0.590405i	$-0.201032\pi$
$907$	−3.24512	−	5.62071i	−0.107752	−	0.186632i	−0.914859	+	0.403773i	$0.867699\pi$
$908$	12.4663			0.413708
$909$	−0.0695423	+	0.0841767i	−0.00230657	+	0.00279197i
$910$	26.3019	+	5.98045i	0.871901	+	0.198250i
$911$			10.4476i			0.346145i	0.984909	+	0.173072i	$0.0553694\pi$
$911$			10.4476i			0.346145i	−0.984909	+	0.173072i	$0.944631\pi$
$912$	−1.85549	−	3.93970i	−0.0614415	−	0.130457i
$913$	56.3357	−	32.5254i	1.86444	−	1.07644i
$914$		−	41.7616i		−	1.38135i
$915$	15.6193	−	22.4893i	0.516360	−	0.743474i
$916$	9.09478	−	5.25087i	0.300500	−	0.173494i
$917$	16.1214	−	6.40149i	0.532375	−	0.211396i
$918$	36.8733	+	9.42806i	1.21700	+	0.311172i
$919$	−22.0869	+	38.2556i	−0.728578	+	1.26193i	0.228906	+	0.973449i	$0.426485\pi$
$919$	−22.0869	+	38.2556i	−0.728578	+	1.26193i	−0.957484	+	0.288486i	$0.906848\pi$
$920$	−6.85147	−	11.8671i	−0.225886	−	0.391246i
$921$	24.0963	−	34.6948i	0.794001	−	1.14323i
$922$	18.7442	−	10.8220i	0.617308	−	0.356403i
$923$	−2.31714	+	29.6604i	−0.0762696	+	0.976283i
$924$	−5.58330	+	23.9478i	−0.183677	+	0.787824i
$925$	−0.957258	+	1.65802i	−0.0314745	+	0.0545154i
$926$			0.578725i			0.0190181i
$927$	−42.5953	−	35.1900i	−1.39901	−	1.15579i
$928$	3.01183	−	5.21665i	0.0988683	−	0.171245i
$929$	8.11177	−	14.0500i	0.266139	−	0.460966i	−0.701723	−	0.712450i	$-0.747585\pi$
$929$	8.11177	−	14.0500i	0.266139	−	0.460966i	0.967861	+	0.251485i	$0.0809188\pi$
$930$	−8.18182	−	5.68246i	−0.268293	−	0.186335i
$931$	−12.0733	−	12.8056i	−0.395687	−	0.419685i
$932$	2.78543	−	1.60817i	0.0912399	−	0.0526774i
$933$	−51.4734	+	24.2426i	−1.68516	+	0.793666i
$934$	17.6119	−	10.1683i	0.576280	−	0.332715i
$935$	96.2442	+	55.5666i	3.14752	+	1.81722i
$936$	2.62205	−	10.4940i	0.0857042	−	0.343008i
$937$			6.64803i			0.217182i	0.994087	+	0.108591i	$0.0346338\pi$
$937$			6.64803i			0.217182i	−0.994087	+	0.108591i	$0.965366\pi$
$938$	4.28283	+	10.7858i	0.139839	+	0.352168i
$939$	−22.6551	−	1.89478i	−0.739323	−	0.0618338i
$940$	−7.03879	+	12.1915i	−0.229580	+	0.397644i
$941$	−6.62704	+	11.4784i	−0.216035	+	0.374184i	−0.953592	−	0.301101i	$-0.902646\pi$
$941$	−6.62704	+	11.4784i	−0.216035	+	0.374184i	0.737557	+	0.675285i	$0.235979\pi$
$942$	−25.7709	+	12.1374i	−0.839662	+	0.395458i
$943$	−50.1600	−	28.9599i	−1.63343	−	0.943063i
$944$	4.67055			0.152014
$945$	−4.94910	−	38.5563i	−0.160994	−	1.25424i
$946$	4.49073	−	7.77818i	0.146006	−	0.252890i
$947$			7.98486i			0.259473i	0.991548	+	0.129737i	$0.0414132\pi$
$947$			7.98486i			0.259473i	−0.991548	+	0.129737i	$0.958587\pi$
$948$	−0.585643	+	7.00230i	−0.0190208	+	0.227424i
$949$	−5.83373	+	2.78667i	−0.189371	+	0.0904591i
$950$	3.76524	+	6.52158i	0.122160	+	0.211588i
$951$	−37.9415	−	3.17327i	−1.23034	−	0.102900i
$952$	−19.1739	−	2.81184i	−0.621429	−	0.0911323i
$953$	26.3580	−	15.2178i	0.853819	−	0.492953i	−0.00811831	−	0.999967i	$-0.502584\pi$
$953$	26.3580	−	15.2178i	0.853819	−	0.492953i	0.861938	+	0.507014i	$0.169251\pi$
$954$	9.65351	+	1.62613i	0.312544	+	0.0526480i
$955$			22.8016i			0.737844i
$956$		−	11.9941i		−	0.387917i
$957$	45.9826	+	31.9360i	1.48641	+	1.03234i
$958$	−13.5157	+	7.80327i	−0.436671	+	0.252112i
$959$	−39.2788	−	5.76021i	−1.26838	−	0.186007i
$960$	−0.408180	+	4.88045i	−0.0131740	+	0.157516i
$961$	−13.4314	−	23.2639i	−0.433271	−	0.750447i
$962$	1.90011	+	1.30430i	0.0612621	+	0.0420524i
$963$	15.6467	−	5.83088i	0.504209	−	0.187897i
$964$		−	18.3905i		−	0.592319i
$965$	−15.5614	+	26.9531i	−0.500938	+	0.867650i
$966$	−15.1809	+	16.2092i	−0.488438	+	0.521522i
$967$	−11.9638			−0.384731			−0.192365	−	0.981323i	$-0.561616\pi$
$967$	−11.9638			−0.384731			−0.192365	+	0.981323i	$0.561616\pi$
$968$	15.4099	+	8.89688i	0.495292	+	0.285957i
$969$	13.5907	+	28.8566i	0.436595	+	0.927008i
$970$	−7.47178	+	12.9415i	−0.239904	+	0.415526i
$971$	9.54617	−	16.5345i	0.306351	−	0.530616i	−0.671210	−	0.741267i	$-0.734225\pi$
$971$	9.54617	−	16.5345i	0.306351	−	0.530616i	0.977561	+	0.210651i	$0.0675585\pi$
$972$	−15.5003	+	1.65534i	−0.497173	+	0.0530951i
$973$	16.7380	+	42.1526i	0.536595	+	1.35135i
$974$		−	22.4792i		−	0.720280i
$975$	−3.00594	+	18.4615i	−0.0962672	+	0.591241i
$976$	4.84184	+	2.79544i	0.154984	+	0.0894798i
$977$	23.8427	−	13.7656i	0.762796	−	0.440400i	−0.0675028	−	0.997719i	$-0.521503\pi$
$977$	23.8427	−	13.7656i	0.762796	−	0.440400i	0.830299	+	0.557319i	$0.188170\pi$
$978$	−4.43909	−	9.42537i	−0.141946	−	0.301390i
$979$	75.3177	−	43.4847i	2.40717	−	1.38978i
$980$	4.55812	+	19.2610i	0.145604	+	0.615269i
$981$	17.3712	+	2.92618i	0.554621	+	0.0934258i
$982$	16.5938	−	28.7412i	0.529528	−	0.917169i
$983$	−2.40101	+	4.15868i	−0.0765804	+	0.132641i	−0.901772	−	0.432211i	$-0.857734\pi$
$983$	−2.40101	+	4.15868i	−0.0765804	+	0.132641i	0.825192	+	0.564852i	$0.191067\pi$
$984$	8.82022	+	18.7277i	0.281178	+	0.597016i
$985$			6.38011i			0.203287i
$986$	−22.0604	+	38.2097i	−0.702545	+	1.21684i
$987$	22.2193	+	5.18032i	0.707249	+	0.164891i
$988$	8.17987	−	3.90738i	0.260236	−	0.124310i
$989$	7.02472	−	4.05573i	0.223373	−	0.128965i
$990$	−44.8857	−	7.56098i	−1.42656	−	0.240304i
$991$	21.1265	+	36.5922i	0.671107	+	1.16239i	0.977591	+	0.210515i	$0.0675141\pi$
$991$	21.1265	+	36.5922i	0.671107	+	1.16239i	−0.306484	+	0.951876i	$0.599153\pi$
$992$	1.01701	−	1.76151i	0.0322900	−	0.0559279i
$993$	20.3254	−	9.57270i	0.645007	−	0.303780i
$994$	−20.2900	+	8.05677i	−0.643560	+	0.255545i
$995$	17.7601	−	10.2538i	0.563035	−	0.325068i
$996$	−17.2460	−	11.9777i	−0.546459	−	0.379528i
$997$			29.8309i			0.944754i	0.881397	+	0.472377i	$0.156604\pi$
$997$			29.8309i			0.944754i	−0.881397	+	0.472377i	$0.843396\pi$
$998$	−23.1479	+	13.3645i	−0.732735	+	0.423045i
$999$	0.822779	−	3.21790i	0.0260316	−	0.101810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.5	yes	76
3.2	odd	2	inner	546.2.bb.a.269.30	yes	76
7.5	odd	6		546.2.u.a.425.3	yes	76
13.3	even	3		546.2.u.a.185.36	yes	76
21.5	even	6		546.2.u.a.425.36	yes	76
39.29	odd	6		546.2.u.a.185.3	✓	76
91.68	odd	6	inner	546.2.bb.a.341.11	yes	76
273.68	even	6	inner	546.2.bb.a.341.24	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.3	✓	76	39.29	odd	6
546.2.u.a.185.36	yes	76	13.3	even	3
546.2.u.a.425.3	yes	76	7.5	odd	6
546.2.u.a.425.36	yes	76	21.5	even	6
546.2.bb.a.269.5	yes	76	1.1	even	1	trivial
546.2.bb.a.269.30	yes	76	3.2	odd	2	inner
546.2.bb.a.341.11	yes	76	91.68	odd	6	inner
546.2.bb.a.341.24	yes	76	273.68	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.42260 - 0.988029i) q^{3} -1.00000 q^{4} +(1.41378 + 2.44875i) q^{5} +(-0.988029 + 1.42260i) q^{6} +(0.383892 - 2.61775i) q^{7} +1.00000i q^{8} +(1.04760 + 2.81115i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.42260 - 0.988029i) q^{3} -1.00000 q^{4} +(1.41378 + 2.44875i) q^{5} +(-0.988029 + 1.42260i) q^{6} +(0.383892 - 2.61775i) q^{7} +1.00000i q^{8} +(1.04760 + 2.81115i) q^{9} +(2.44875 - 1.41378i) q^{10} +(-4.64708 + 2.68299i) q^{11} +(1.42260 + 0.988029i) q^{12} +(-2.04050 + 2.97260i) q^{13} +(-2.61775 - 0.383892i) q^{14} +(0.408180 - 4.88045i) q^{15} +1.00000 q^{16} -7.32456 q^{17} +(2.81115 - 1.04760i) q^{18} +(2.17739 + 1.25712i) q^{19} +(-1.41378 - 2.44875i) q^{20} +(-3.13254 + 3.34472i) q^{21} +(2.68299 + 4.64708i) q^{22} +4.84619i q^{23} +(0.988029 - 1.42260i) q^{24} +(-1.49757 + 2.59386i) q^{25} +(2.97260 + 2.04050i) q^{26} +(1.28718 - 5.03420i) q^{27} +(-0.383892 + 2.61775i) q^{28} +(5.21665 + 3.01183i) q^{29} +(-4.88045 - 0.408180i) q^{30} +(1.76151 + 1.01701i) q^{31} -1.00000i q^{32} +(9.26182 + 0.774619i) q^{33} +7.32456i q^{34} +(6.95295 - 2.76088i) q^{35} +(-1.04760 - 2.81115i) q^{36} +0.639208 q^{37} +(1.25712 - 2.17739i) q^{38} +(5.83984 - 2.21276i) q^{39} +(-2.44875 + 1.41378i) q^{40} +(-5.97580 + 10.3504i) q^{41} +(3.34472 + 3.13254i) q^{42} +(-0.836889 - 1.44953i) q^{43} +(4.64708 - 2.68299i) q^{44} +(-5.40271 + 6.53965i) q^{45} +4.84619 q^{46} +(-2.48934 - 4.31167i) q^{47} +(-1.42260 - 0.988029i) q^{48} +(-6.70525 - 2.00987i) q^{49} +(2.59386 + 1.49757i) q^{50} +(10.4199 + 7.23689i) q^{51} +(2.04050 - 2.97260i) q^{52} +(2.82599 + 1.63159i) q^{53} +(-5.03420 - 1.28718i) q^{54} +(-13.1399 - 7.58634i) q^{55} +(2.61775 + 0.383892i) q^{56} +(-1.85549 - 3.93970i) q^{57} +(3.01183 - 5.21665i) q^{58} +4.67055 q^{59} +(-0.408180 + 4.88045i) q^{60} +(4.84184 + 2.79544i) q^{61} +(1.01701 - 1.76151i) q^{62} +(7.76105 - 1.66317i) q^{63} -1.00000 q^{64} +(-10.1640 - 0.794034i) q^{65} +(0.774619 - 9.26182i) q^{66} +(-2.19314 - 3.79862i) q^{67} +7.32456 q^{68} +(4.78818 - 6.89421i) q^{69} +(-2.76088 - 6.95295i) q^{70} +(7.14590 - 4.12569i) q^{71} +(-2.81115 + 1.04760i) q^{72} +(1.55287 + 0.896552i) q^{73} -0.639208i q^{74} +(4.69326 - 2.21040i) q^{75} +(-2.17739 - 1.25712i) q^{76} +(5.23943 + 13.1949i) q^{77} +(-2.21276 - 5.83984i) q^{78} +(2.02845 + 3.51337i) q^{79} +(1.41378 + 2.44875i) q^{80} +(-6.80509 + 5.88989i) q^{81} +(10.3504 + 5.97580i) q^{82} -12.1228 q^{83} +(3.13254 - 3.34472i) q^{84} +(-10.3553 - 17.9360i) q^{85} +(-1.44953 + 0.836889i) q^{86} +(-4.44544 - 9.43884i) q^{87} +(-2.68299 - 4.64708i) q^{88} -16.2075 q^{89} +(6.53965 + 5.40271i) q^{90} +(6.99821 + 6.48267i) q^{91} -4.84619i q^{92} +(-1.50109 - 3.18722i) q^{93} +(-4.31167 + 2.48934i) q^{94} +7.10916i q^{95} +(-0.988029 + 1.42260i) q^{96} +(-4.57690 + 2.64248i) q^{97} +(-2.00987 + 6.70525i) q^{98} +(-12.4105 - 10.2529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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