LMFDB - Embedded newform 546.2.bb.a.269.30

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			269.30
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.144357 + 1.72602i) q^{3} -1.00000 q^{4} +(-1.41378 - 2.44875i) q^{5} +(-1.72602 + 0.144357i) q^{6} +(0.383892 - 2.61775i) q^{7} -1.00000i q^{8} +(-2.95832 + 0.498329i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.144357 + 1.72602i) q^{3} -1.00000 q^{4} +(-1.41378 - 2.44875i) q^{5} +(-1.72602 + 0.144357i) q^{6} +(0.383892 - 2.61775i) q^{7} -1.00000i q^{8} +(-2.95832 + 0.498329i) q^{9} +(2.44875 - 1.41378i) q^{10} +(4.64708 - 2.68299i) q^{11} +(-0.144357 - 1.72602i) q^{12} +(-2.04050 + 2.97260i) q^{13} +(2.61775 + 0.383892i) q^{14} +(4.02250 - 2.79372i) q^{15} +1.00000 q^{16} +7.32456 q^{17} +(-0.498329 - 2.95832i) q^{18} +(2.17739 + 1.25712i) q^{19} +(1.41378 + 2.44875i) q^{20} +(4.57372 + 0.284715i) q^{21} +(2.68299 + 4.64708i) q^{22} -4.84619i q^{23} +(1.72602 - 0.144357i) 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} +(2.79372 + 4.02250i) q^{30} +(1.76151 + 1.01701i) q^{31} +1.00000i q^{32} +(5.30175 + 7.63366i) q^{33} +7.32456i q^{34} +(-6.95295 + 2.76088i) q^{35} +(2.95832 - 0.498329i) q^{36} +0.639208 q^{37} +(-1.25712 + 2.17739i) q^{38} +(-5.42535 - 3.09283i) q^{39} +(-2.44875 + 1.41378i) q^{40} +(5.97580 - 10.3504i) q^{41} +(-0.284715 + 4.57372i) 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} +(0.144357 + 1.72602i) q^{48} +(-6.70525 - 2.00987i) q^{49} +(-2.59386 - 1.49757i) q^{50} +(1.05736 + 12.6424i) 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} +(-4.02250 + 2.79372i) q^{60} +(4.84184 + 2.79544i) q^{61} +(-1.01701 + 1.76151i) q^{62} +(0.168825 + 7.93546i) q^{63} -1.00000 q^{64} +(10.1640 + 0.794034i) q^{65} +(-7.63366 + 5.30175i) q^{66} +(-2.19314 - 3.79862i) q^{67} -7.32456 q^{68} +(8.36465 - 0.699584i) q^{69} +(-2.76088 - 6.95295i) q^{70} +(-7.14590 + 4.12569i) q^{71} +(0.498329 + 2.95832i) 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} +(3.09283 - 5.42535i) q^{78} +(2.02845 + 3.51337i) q^{79} +(-1.41378 - 2.44875i) q^{80} +(8.50334 - 2.94843i) q^{81} +(10.3504 + 5.97580i) q^{82} +12.1228 q^{83} +(-4.57372 - 0.284715i) 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} +(-1.72602 + 0.144357i) 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
$3$	0.144357	+	1.72602i	0.0833448	+	0.996521i
$3$	0.144357	+	1.72602i	0.0833448	+	0.996521i
$4$	−1.00000			−0.500000
$5$	−1.41378	−	2.44875i	−0.632263	−	1.09511i	−0.987088	−	0.160179i	$-0.948793\pi$
$5$	−1.41378	−	2.44875i	−0.632263	−	1.09511i	0.354825	−	0.934933i	$-0.384541\pi$
$6$	−1.72602	+	0.144357i	−0.704647	+	0.0589337i
$7$	0.383892	−	2.61775i	0.145098	−	0.989417i
$7$	0.383892	−	2.61775i	0.145098	−	0.989417i
$8$		−	1.00000i		−	0.353553i
$9$	−2.95832	+	0.498329i	−0.986107	+	0.166110i
$10$	2.44875	−	1.41378i	0.774361	−	0.447078i
$11$	4.64708	−	2.68299i	1.40115	−	0.808952i	0.406636	−	0.913590i	$-0.366702\pi$
$11$	4.64708	−	2.68299i	1.40115	−	0.808952i	0.994510	+	0.104638i	$0.0333684\pi$
$12$	−0.144357	−	1.72602i	−0.0416724	−	0.498260i
$13$	−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
$15$	4.02250	−	2.79372i	1.03861	−	0.721335i
$16$	1.00000			0.250000
$17$	7.32456			1.77647			0.888234	−	0.459392i	$-0.151933\pi$
$17$	7.32456			1.77647			0.888234	+	0.459392i	$0.151933\pi$
$18$	−0.498329	−	2.95832i	−0.117457	−	0.697283i
$19$	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
$21$	4.57372	+	0.284715i	0.998068	+	0.0621300i
$22$	2.68299	+	4.64708i	0.572016	+	0.990760i
$23$		−	4.84619i		−	1.01050i	−0.862973	−	0.505251i	$-0.831400\pi$
$23$		−	4.84619i		−	1.01050i	0.862973	−	0.505251i	$-0.168600\pi$
$24$	1.72602	−	0.144357i	0.352323	−	0.0294668i
$25$	−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	−0.0698653	−	0.997556i	$-0.522257\pi$
$29$	−5.21665	−	3.01183i	−0.968707	−	0.559283i	−0.898842	+	0.438273i	$0.855590\pi$
$30$	2.79372	+	4.02250i	0.510061	+	0.734405i
$31$	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
$33$	5.30175	+	7.63366i	0.922916	+	1.32885i
$34$			7.32456i			1.25615i
$35$	−6.95295	+	2.76088i	−1.17526	+	0.466674i
$36$	2.95832	−	0.498329i	0.493054	−	0.0830548i
$37$	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
$39$	−5.42535	−	3.09283i	−0.868751	−	0.495249i
$40$	−2.44875	+	1.41378i	−0.387181	+	0.223539i
$41$	5.97580	−	10.3504i	0.933263	−	1.61646i	0.155560	−	0.987826i	$-0.450282\pi$
$41$	5.97580	−	10.3504i	0.933263	−	1.61646i	0.777703	−	0.628632i	$-0.216385\pi$
$42$	−0.284715	+	4.57372i	−0.0439325	+	0.705741i
$43$	−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	0.988471	−	0.151413i	$-0.0483822\pi$
$47$	2.48934	+	4.31167i	0.363108	+	0.628922i	−0.625362	+	0.780334i	$0.715049\pi$
$48$	0.144357	+	1.72602i	0.0208362	+	0.249130i
$49$	−6.70525	−	2.00987i	−0.957893	−	0.287124i
$50$	−2.59386	−	1.49757i	−0.366828	−	0.211788i
$51$	1.05736	+	12.6424i	0.148059	+	1.77029i
$52$	2.04050	−	2.97260i	0.282966	−	0.412226i
$53$	−2.82599	−	1.63159i	−0.388179	−	0.224115i	0.293192	−	0.956054i	$-0.405283\pi$
$53$	−2.82599	−	1.63159i	−0.388179	−	0.224115i	−0.681371	+	0.731938i	$0.738616\pi$
$54$	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	$-0.598331\pi$
$59$	−4.67055			−0.608054			−0.304027	+	0.952663i	$0.598331\pi$
$60$	−4.02250	+	2.79372i	−0.519303	+	0.360668i
$61$	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
$63$	0.168825	+	7.93546i	0.0212700	+	0.999774i
$64$	−1.00000			−0.125000
$65$	10.1640	+	0.794034i	1.26069	+	0.0984878i
$66$	−7.63366	+	5.30175i	−0.939639	+	0.652600i
$67$	−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
$69$	8.36465	−	0.699584i	1.00699	−	0.0842200i
$70$	−2.76088	−	6.95295i	−0.329988	−	0.831036i
$71$	−7.14590	+	4.12569i	−0.848062	+	0.489629i	−0.859996	−	0.510300i	$-0.829534\pi$
$71$	−7.14590	+	4.12569i	−0.848062	+	0.489629i	0.0119346	+	0.999929i	$0.496201\pi$
$72$	0.498329	+	2.95832i	0.0587286	+	0.348642i
$73$	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
$78$	3.09283	−	5.42535i	0.350194	−	0.614300i
$79$	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
$81$	8.50334	−	2.94843i	0.944815	−	0.327604i
$82$	10.3504	+	5.97580i	1.14301	+	0.659916i
$83$	12.1228			1.33065			0.665327	−	0.746552i	$-0.268292\pi$
$83$	12.1228			1.33065			0.665327	+	0.746552i	$0.268292\pi$
$84$	−4.57372	−	0.284715i	−0.499034	−	0.0310650i
$85$	−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	$-0.171087\pi$
$89$	16.2075			1.71800			0.858998	+	0.511978i	$0.171087\pi$
$90$	−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
$96$	−1.72602	+	0.144357i	−0.176162	+	0.0147334i
$97$	−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	0.865119	−	0.501567i	$-0.167243\pi$
$101$	−0.0181979	−	0.0315196i	−0.00181076	−	0.00313632i	−0.866929	+	0.498431i	$0.833910\pi$
$102$	−12.6424	+	1.05736i	−1.25178	+	0.104694i
$103$	−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
$105$	−5.76906	−	11.6024i	−0.563002	−	1.13228i
$106$	1.63159	−	2.82599i	0.158474	−	0.274484i
$107$			5.56596i			0.538082i	0.963129	+	0.269041i	$0.0867067\pi$
$107$			5.56596i			0.538082i	−0.963129	+	0.269041i	$0.913293\pi$
$108$	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
$111$	0.0922745	+	1.10329i	0.00875831	+	0.104720i
$112$	0.383892	−	2.61775i	0.0362744	−	0.247354i
$113$	0.869871	−	0.502220i	0.0818306	−	0.0472449i	−0.458526	−	0.888681i	$-0.651623\pi$
$113$	0.869871	−	0.502220i	0.0818306	−	0.0472449i	0.540357	+	0.841436i	$0.318289\pi$
$114$	−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
$117$	4.55511	−	9.81076i	0.421120	−	0.907005i
$118$		−	4.67055i		−	0.429959i
$119$	2.81184	−	19.1739i	0.257761	−	1.75767i
$120$	−2.79372	−	4.02250i	−0.255031	−	0.367203i
$121$	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
$126$	−7.93546	+	0.168825i	−0.706947	+	0.0150401i
$127$	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
$129$	2.38112	−	1.65374i	0.209646	−	0.145604i
$130$	−0.794034	+	10.1640i	−0.0696414	+	0.891439i
$131$	−3.27806	−	5.67776i	−0.286405	−	0.496068i	0.686544	−	0.727088i	$-0.259127\pi$
$131$	−3.27806	−	5.67776i	−0.286405	−	0.496068i	−0.972949	+	0.231020i	$0.925794\pi$
$132$	−5.30175	−	7.63366i	−0.461458	−	0.664425i
$133$	4.12670	−	5.21727i	0.357831	−	0.452395i
$134$	3.79862	−	2.19314i	0.328151	−	0.189458i
$135$	−10.5077	+	10.2693i	−0.904356	+	0.883837i
$136$		−	7.32456i		−	0.628076i
$137$			15.0048i			1.28194i	0.767564	+	0.640972i	$0.221468\pi$
$137$			15.0048i			1.28194i	−0.767564	+	0.640972i	$0.778532\pi$
$138$	0.699584	+	8.36465i	0.0595525	+	0.712046i
$139$	−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
$141$	−7.08269	+	4.91909i	−0.596470	+	0.414262i
$142$	−4.12569	−	7.14590i	−0.346220	−	0.599670i
$143$	−1.50687	+	19.2886i	−0.126011	+	1.61299i
$144$	−2.95832	+	0.498329i	−0.246527	+	0.0415274i
$145$			17.0323i			1.41446i
$146$	−0.896552	+	1.55287i	−0.0741992	+	0.128517i
$147$	2.50113	−	11.8636i	0.206290	−	0.978491i
$148$	−0.639208			−0.0525426
$149$	−9.92624	−	5.73092i	−0.813190	−	0.469495i	0.0348727	−	0.999392i	$-0.488897\pi$
$149$	−9.92624	−	5.73092i	−0.813190	−	0.469495i	−0.848062	+	0.529897i	$0.822231\pi$
$150$	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
$153$	−21.6684	+	3.65004i	−1.75179	+	0.295088i
$154$	13.1949	−	5.23943i	1.06327	−	0.422205i
$155$		−	5.75131i		−	0.461956i
$156$	5.42535	+	3.09283i	0.434376	+	0.247624i
$157$	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
$162$	2.94843	+	8.50334i	0.231651	+	0.668085i
$163$	−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	−0.977070	−	0.212918i	$-0.931703\pi$
$167$	−3.93039	+	6.80763i	−0.304142	+	0.526790i	0.672928	+	0.739708i	$0.265037\pi$
$168$	0.284715	−	4.57372i	0.0219663	−	0.352870i
$169$	−4.67275	−	12.1312i	−0.359443	−	0.933167i
$170$	17.9360	−	10.3553i	1.37563	−	0.794219i
$171$	−7.06788	−	2.63390i	−0.540494	−	0.201419i
$172$	0.836889	+	1.44953i	0.0638122	+	0.110526i
$173$	−8.14791	+	14.1126i	−0.619474	+	1.07296i	0.370108	+	0.928989i	$0.379321\pi$
$173$	−8.14791	+	14.1126i	−0.619474	+	1.07296i	−0.989582	+	0.143972i	$0.954013\pi$
$174$	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
$177$	−0.674229	−	8.06149i	−0.0506782	−	0.605939i
$178$			16.2075i			1.21481i
$179$	−9.54740	+	5.51220i	−0.713606	+	0.412001i	−0.812395	−	0.583108i	$-0.801837\pi$
$179$	−9.54740	+	5.51220i	−0.713606	+	0.412001i	0.0987885	+	0.995108i	$0.468503\pi$
$180$	−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
$189$	−13.6724	+	1.43694i	−0.994523	+	0.104522i
$190$	7.10916			0.515753
$191$	−6.98367	−	4.03202i	−0.505321	−	0.291747i	0.225587	−	0.974223i	$-0.427570\pi$
$191$	−6.98367	−	4.03202i	−0.505321	−	0.291747i	−0.730908	+	0.682476i	$0.760903\pi$
$192$	−0.144357	−	1.72602i	−0.0104181	−	0.124565i
$193$	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
$195$	0.0967215	+	17.6579i	0.00692637	+	1.26451i
$196$	6.70525	+	2.00987i	0.478947	+	0.143562i
$197$	−1.95410	−	1.12820i	−0.139224	−	0.0803808i	0.428770	−	0.903414i	$-0.358947\pi$
$197$	−1.95410	−	1.12820i	−0.139224	−	0.0803808i	−0.567994	+	0.823033i	$0.692280\pi$
$198$	−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
$201$	6.23992	−	4.33377i	0.440130	−	0.305680i
$202$	0.0315196	−	0.0181979i	0.00221771	−	0.00128040i
$203$	−9.88686	+	12.4997i	−0.693922	+	0.877305i
$204$	−1.05736	−	12.6424i	−0.0740297	−	0.885144i
$205$	−33.7939			−2.36027
$206$	−9.20853	−	15.9496i	−0.641589	−	1.11126i
$207$	2.41500	+	14.3366i	0.167854	+	0.996463i
$208$	−2.04050	+	2.97260i	−0.141483	+	0.206113i
$209$	13.4913			0.933215
$210$	11.6024	−	5.76906i	0.800642	−	0.398103i
$211$	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
$213$	−8.15260	−	11.7384i	−0.558607	−	0.804303i
$214$	−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
$222$	−1.10329	+	0.0922745i	−0.0740479	+	0.00619306i
$223$	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
$225$	3.13769	−	8.41977i	0.209179	−	0.561318i
$226$	0.502220	+	0.869871i	0.0334072	+	0.0578630i
$227$	12.4663			0.827417			0.413708	−	0.910410i	$-0.364233\pi$
$227$	12.4663			0.827417			0.413708	+	0.910410i	$0.364233\pi$
$228$	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
$231$	22.0183	−	10.9482i	1.44870	−	0.720336i
$232$	−3.01183	+	5.21665i	−0.197737	+	0.342490i
$233$	2.78543	−	1.60817i	0.182480	−	0.105355i	−0.405977	−	0.913883i	$-0.633069\pi$
$233$	2.78543	−	1.60817i	0.182480	−	0.105355i	0.588457	+	0.808528i	$0.299736\pi$
$234$	9.81076	+	4.55511i	0.641349	+	0.297777i
$235$	7.03879	−	12.1915i	0.459160	−	0.795288i
$236$	4.67055			0.304027
$237$	−5.77135	+	4.00833i	−0.374889	+	0.260369i
$238$	19.1739	+	2.81184i	1.24286	+	0.182265i
$239$		−	11.9941i		−	0.775834i	−0.921694	−	0.387917i	$-0.873195\pi$
$239$		−	11.9941i		−	0.775834i	0.921694	−	0.387917i	$-0.126805\pi$
$240$	4.02250	−	2.79372i	0.259652	−	0.180334i
$241$			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
$243$	6.31659	+	14.2513i	0.405209	+	0.914224i
$244$	−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
$249$	1.75002	+	20.9243i	0.110903	+	1.32602i
$250$		−	5.66889i		−	0.358532i
$251$	5.22792	+	9.05503i	0.329983	+	0.571548i	0.982508	−	0.186219i	$-0.0596235\pi$
$251$	5.22792	+	9.05503i	0.329983	+	0.571548i	−0.652525	+	0.757767i	$0.726290\pi$
$252$	−0.168825	−	7.93546i	−0.0106350	−	0.499887i
$253$	−13.0023	−	22.5206i	−0.817447	−	1.41586i
$254$	10.2933	+	5.94284i	0.645859	+	0.372887i
$255$	29.4631	−	20.4628i	1.84505	−	1.28143i
$256$	1.00000			0.0625000
$257$	−1.76706			−0.110226			−0.0551131	−	0.998480i	$-0.517552\pi$
$257$	−1.76706			−0.110226			−0.0551131	+	0.998480i	$0.517552\pi$
$258$	1.65374	+	2.38112i	0.102957	+	0.148242i
$259$	0.245387	−	1.67329i	0.0152476	−	0.103973i
$260$	−10.1640	−	0.794034i	−0.630343	−	0.0492439i
$261$	16.9334	+	6.31036i	1.04815	+	0.390602i
$262$	5.67776	−	3.27806i	0.350773	−	0.202519i
$263$	18.1822	−	10.4975i	1.12116	−	0.647303i	0.179465	−	0.983764i	$-0.442563\pi$
$263$	18.1822	−	10.4975i	1.12116	−	0.647303i	0.941697	+	0.336461i	$0.109230\pi$
$264$	7.63366	−	5.30175i	0.469819	−	0.326300i
$265$			9.22683i			0.566800i
$266$	5.21727	+	4.12670i	0.319891	+	0.253024i
$267$	2.33968	+	27.9746i	0.143186	+	1.71202i
$268$	2.19314	+	3.79862i	0.133967	+	0.232038i
$269$	17.5469			1.06985			0.534925	−	0.844899i	$-0.320340\pi$
$269$	17.5469			1.06985			0.534925	+	0.844899i	$0.320340\pi$
$270$	−10.2693	−	10.5077i	−0.624967	−	0.639476i
$271$		−	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
$273$	−10.1790	+	13.0149i	−0.616062	+	0.787698i
$274$	−15.0048			−0.906471
$275$			16.0719i			0.969169i
$276$	−8.36465	+	0.699584i	−0.503493	+	0.0421100i
$277$	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
$279$	−5.71791	−	2.13082i	−0.342322	−	0.127569i
$280$	2.76088	+	6.95295i	0.164994	+	0.415518i
$281$		−	26.5541i		−	1.58408i	−0.610467	−	0.792042i	$-0.709018\pi$
$281$		−	26.5541i		−	1.58408i	0.610467	−	0.792042i	$-0.290982\pi$
$282$	−4.91909	−	7.08269i	−0.292928	−	0.421768i
$283$	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
$285$	12.2706	−	1.02626i	0.726847	−	0.0607904i
$286$	−19.2886	−	1.50687i	−1.14056	−	0.0891031i
$287$	−24.8007	−	19.6166i	−1.46394	−	1.15793i
$288$	−0.498329	−	2.95832i	−0.0293643	−	0.174321i
$289$	36.6492			2.15584
$290$	−17.0323			−1.00017
$291$	−5.22169	−	7.51838i	−0.306101	−	0.440735i
$292$	−1.55287	−	0.896552i	−0.0908751	−	0.0524668i
$293$	3.32608	+	5.76094i	0.194312	+	0.336557i	0.946675	−	0.322191i	$-0.104419\pi$
$293$	3.32608	+	5.76094i	0.194312	+	0.336557i	−0.752363	+	0.658749i	$0.771086\pi$
$294$	11.8636	+	2.50113i	0.691898	+	0.145869i
$295$	6.60315	+	11.4370i	0.384450	+	0.665888i
$296$		−	0.639208i		−	0.0371532i
$297$	−19.4884	−	19.9408i	−1.13083	−	1.15708i
$298$	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
$303$	0.0517767	−	0.0359601i	0.00297449	−	0.00206585i
$304$	2.17739	+	1.25712i	0.124882	+	0.0721006i
$305$		−	15.8086i		−	0.905197i
$306$	−3.65004	−	21.6684i	−0.208659	−	1.23870i
$307$			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
$309$	−18.1966	−	26.2001i	−1.03517	−	1.49047i
$310$	5.75131			0.326652
$311$	−16.4246	+	28.4483i	−0.931355	+	1.61315i	−0.150346	+	0.988633i	$0.548039\pi$
$311$	−16.4246	+	28.4483i	−0.931355	+	1.61315i	−0.781009	+	0.624520i	$0.785295\pi$
$312$	−3.09283	+	5.42535i	−0.175097	+	0.307150i
$313$	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
$315$	19.1932	−	11.6324i	1.08142	−	0.655413i
$316$	−2.02845	−	3.51337i	−0.114109	−	0.197643i
$317$	−19.0370	+	10.9910i	−1.06922	+	0.617317i	−0.927969	−	0.372657i	$-0.878447\pi$
$317$	−19.0370	+	10.9910i	−1.06922	+	0.617317i	−0.141254	+	0.989973i	$0.545114\pi$
$318$	5.11326	+	2.40820i	0.286737	+	0.135045i
$319$	−32.3229			−1.80973
$320$	1.41378	+	2.44875i	0.0790329	+	0.136889i
$321$	−9.60699	+	0.803488i	−0.536210	+	0.0448463i
$322$	1.86042	−	12.6861i	0.103677	−	0.706971i
$323$	15.9484	+	9.20783i	0.887395	+	0.512338i
$324$	−8.50334	+	2.94843i	−0.472408	+	0.163802i
$325$	−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
$333$	−1.89098	+	0.318536i	−0.103625	+	0.0174557i
$334$	−6.80763	−	3.93039i	−0.372497	−	0.215061i
$335$	−6.20124	+	10.7409i	−0.338810	+	0.586836i
$336$	4.57372	+	0.284715i	0.249517	+	0.0155325i
$337$	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
$339$	0.992417	+	1.42892i	0.0539007	+	0.0776083i
$340$	10.3553	+	17.9360i	0.561598	+	0.972716i
$341$	10.9145			0.591052
$342$	2.63390	−	7.06788i	0.142425	−	0.382187i
$343$	−7.83543	+	16.7811i	−0.423074	+	0.906095i
$344$	−1.44953	+	0.836889i	−0.0781536	+	0.0451220i
$345$	−13.5389	−	19.4938i	−0.728910	−	1.04951i
$346$	−14.1126	−	8.14791i	−0.758698	−	0.438034i
$347$			12.7624i			0.685124i	0.939495	+	0.342562i	$0.111295\pi$
$347$			12.7624i			0.685124i	−0.939495	+	0.342562i	$0.888705\pi$
$348$	−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
$351$	17.5912	+	6.44597i	0.938947	+	0.344061i
$352$	2.68299	+	4.64708i	0.143004	+	0.247690i
$353$	−8.65493	−	14.9908i	−0.460656	−	0.797879i	0.538338	−	0.842729i	$-0.319052\pi$
$353$	−8.65493	−	14.9908i	−0.460656	−	0.797879i	−0.998994	+	0.0448501i	$0.985719\pi$
$354$	8.06149	−	0.674229i	0.428463	−	0.0358349i
$355$	20.2055	+	11.6657i	1.07240	+	0.619149i
$356$	−16.2075			−0.858998
$357$	33.5005	+	2.08542i	1.77304	+	0.110372i
$358$	−5.51220	−	9.54740i	−0.291329	−	0.504596i
$359$	−5.42394	+	3.13151i	−0.286264	+	0.165275i	−0.636256	−	0.771478i	$-0.719518\pi$
$359$	−5.42394	+	3.13151i	−0.286264	+	0.165275i	0.349992	+	0.936753i	$0.386184\pi$
$360$	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
$369$	−12.5204	+	33.5977i	−0.651788	+	1.74903i
$370$	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
$375$	−0.818346	−	9.78464i	−0.0422592	−	0.505276i
$376$	4.31167	−	2.48934i	0.222357	−	0.128378i
$377$	19.5975	−	9.36140i	1.00932	−	0.482137i
$378$	−1.43694	−	13.6724i	−0.0739081	−	0.703234i
$379$	−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	$-0.537813\pi$
$383$	15.6693	−	27.1401i	0.800666	−	1.38679i	0.919179	−	0.393841i	$-0.128854\pi$
$384$	1.72602	−	0.144357i	0.0880808	−	0.00736671i
$385$	−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	0.885207	−	0.465197i	$-0.154016\pi$
$389$	18.2426	+	10.5324i	0.924939	+	0.534014i	0.0397316	+	0.999210i	$0.487350\pi$
$390$	−17.6579	+	0.0967215i	−0.894142	+	0.00489768i
$391$		−	35.4963i		−	1.79512i
$392$	−2.00987	+	6.70525i	−0.101514	+	0.338666i
$393$	9.32674	−	6.47763i	0.470472	−	0.326753i
$394$	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
$399$	9.60086	+	6.36964i	0.480644	+	0.318881i
$400$	−1.49757	+	2.59386i	−0.0748784	+	0.129693i
$401$		−	18.6153i		−	0.929604i	−0.885415	−	0.464802i	$-0.846126\pi$
$401$		−	18.6153i		−	0.929604i	0.885415	−	0.464802i	$-0.153874\pi$
$402$	4.33377	+	6.23992i	0.216149	+	0.311219i
$403$	−6.61750	+	3.16107i	−0.329641	+	0.157464i
$404$	0.0181979	+	0.0315196i	0.000905378	+	0.00156816i
$405$	−19.2418	−	16.6541i	−0.956135	−	0.827547i
$406$	−12.4997	−	9.88686i	−0.620348	−	0.490677i
$407$	2.97045	−	1.71499i	0.147240	−	0.0850089i
$408$	12.6424	−	1.05736i	0.625891	−	0.0523469i
$409$			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
$411$	−25.8986	+	2.16605i	−1.27748	+	0.106843i
$412$	15.9496	−	9.20853i	0.785782	−	0.453672i
$413$	−1.79299	+	12.2264i	−0.0882272	+	0.601619i
$414$	−14.3366	+	2.41500i	−0.704606	+	0.118691i
$415$	−17.1391	−	29.6857i	−0.841323	−	1.45721i
$416$	−2.97260	−	2.04050i	−0.145744	−	0.100044i
$417$	−16.9371	−	24.3867i	−0.829412	−	1.19422i
$418$			13.4913i			0.659883i
$419$	−15.5700	+	26.9681i	−0.760646	+	1.31748i	0.181873	+	0.983322i	$0.441784\pi$
$419$	−15.5700	+	26.9681i	−0.760646	+	1.31748i	−0.942518	+	0.334155i	$0.891549\pi$
$420$	5.76906	+	11.6024i	0.281501	+	0.566139i
$421$	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
$426$	11.7384	−	8.15260i	0.568728	−	0.394995i
$427$	9.17651	−	11.6016i	0.444082	−	0.561441i
$428$		−	5.56596i		−	0.269041i
$429$	−33.5100	+	0.183552i	−1.61788	+	0.00886198i
$430$	−4.09866	−	2.36636i	−0.197655	−	0.114116i
$431$	1.40088	−	0.808798i	0.0674780	−	0.0389584i	−0.465881	−	0.884847i	$-0.654263\pi$
$431$	1.40088	−	0.808798i	0.0674780	−	0.0389584i	0.533359	+	0.845889i	$0.320929\pi$
$432$	−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
$435$	−29.3982	+	2.45874i	−1.40954	+	0.117888i
$436$	−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
$441$	20.8379	+	2.60442i	0.992280	+	0.124020i
$442$	−21.7730	−	14.9457i	−1.03564	−	0.710896i
$443$	−12.6887	+	7.32582i	−0.602858	+	0.348060i	−0.770165	−	0.637844i	$-0.779826\pi$
$443$	−12.6887	+	7.32582i	−0.602858	+	0.348060i	0.167307	+	0.985905i	$0.446493\pi$
$444$	−0.0922745	−	1.10329i	−0.00437915	−	0.0523598i
$445$	−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	−0.381032	−	0.924562i	$-0.624431\pi$
$449$	4.85551	−	2.80333i	0.229146	−	0.132297i	0.610178	+	0.792264i	$0.291098\pi$
$450$	8.41977	+	3.13769i	0.396912	+	0.147912i
$451$		−	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	$-0.998517\pi$
$461$	−10.8220	−	18.7442i	−0.504030	−	0.873005i	0.495959	−	0.868346i	$-0.334817\pi$
$462$	10.9482	+	22.0183i	0.509355	+	1.02439i
$463$	−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
$465$	9.92690	−	0.830244i	0.460349	−	0.0385016i
$466$	1.60817	+	2.78543i	0.0744971	+	0.129033i
$467$	−10.1683	−	17.6119i	−0.470531	−	0.814983i	0.528901	−	0.848683i	$-0.322604\pi$
$467$	−10.1683	−	17.6119i	−0.470531	−	0.814983i	−0.999432	+	0.0337004i	$0.989271\pi$
$468$	−4.55511	+	9.81076i	−0.210560	+	0.453502i
$469$	−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
$474$	−4.00833	−	5.77135i	−0.184109	−	0.265087i
$475$	−6.52158	+	3.76524i	−0.299231	+	0.172761i
$476$	−2.81184	+	19.1739i	−0.128881	+	0.878834i
$477$	9.17325	+	3.41848i	0.420014	+	0.156522i
$478$	11.9941			0.548597
$479$	7.80327	+	13.5157i	0.356540	+	0.617546i	0.987380	−	0.158367i	$-0.0506229\pi$
$479$	7.80327	+	13.5157i	0.356540	+	0.617546i	−0.630840	+	0.775913i	$0.717290\pi$
$480$	2.79372	+	4.02250i	0.127515	+	0.183601i
$481$	−1.30430	+	1.90011i	−0.0594711	+	0.0866377i
$482$	−18.3905			−0.837666
$483$	1.37979	−	22.1651i	0.0627824	−	1.00855i
$484$	−8.89688	+	15.4099i	−0.404404	+	0.700448i
$485$	12.9415	+	7.47178i	0.587643	+	0.339276i
$486$	−14.2513	+	6.31659i	−0.646454	+	0.286526i
$487$	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	−0.317176	−	0.948367i	$-0.602735\pi$
$491$	−28.7412	−	16.5938i	−1.29707	−	0.748866i	−0.979898	+	0.199501i	$0.936068\pi$
$492$	−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
$495$	42.6526	+	15.8948i	1.91709	+	0.714419i
$496$	1.76151	+	1.01701i	0.0790940	+	0.0456649i
$497$	8.05677	+	20.2900i	0.361395	+	0.910131i
$498$	−20.9243	+	1.75002i	−0.937640	+	0.0784203i
$499$	−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	0.825852	−	0.563886i	$-0.190694\pi$
$503$	−1.69136	−	2.92951i	−0.0754138	−	0.130621i	−0.901266	+	0.433266i	$0.857361\pi$
$504$	7.93546	−	0.168825i	0.353473	−	0.00752007i
$505$	−0.0514557	+	0.0891239i	−0.00228975	+	0.00396596i
$506$	22.5206	−	13.0023i	1.00116	−	0.578023i
$507$	20.2642	−	9.81651i	0.899963	−	0.435967i
$508$	−5.94284	+	10.2933i	−0.263671	+	0.456691i
$509$	−31.3346			−1.38888			−0.694441	−	0.719550i	$-0.744348\pi$
$509$	−31.3346			−1.38888			−0.694441	+	0.719550i	$0.744348\pi$
$510$	20.4628	+	29.4631i	0.906107	+	1.30465i
$511$	2.94309	−	3.72086i	0.130195	−	0.164601i
$512$			1.00000i			0.0441942i
$513$	3.52588	−	12.5796i	0.155671	−	0.555401i
$514$		−	1.76706i		−	0.0779416i
$515$	45.0987	+	26.0377i	1.98729	+	1.14736i
$516$	−2.38112	+	1.65374i	−0.104823	+	0.0728019i
$517$	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	−0.994598	−	0.103802i	$-0.966899\pi$
$521$	−9.29916	+	16.1066i	−0.407403	+	0.705644i	0.587194	+	0.809446i	$0.300232\pi$
$522$	−6.31036	+	16.9334i	−0.276197	+	0.741155i
$523$			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
$525$	−7.58797	+	11.4372i	−0.331166	+	0.499162i
$526$	10.4975	+	18.1822i	0.457712	+	0.792781i
$527$	12.9023	+	7.44913i	0.562032	+	0.324489i
$528$	5.30175	+	7.63366i	0.230729	+	0.332212i
$529$	−0.485594			−0.0211128
$530$	−9.22683			−0.400788
$531$	13.8170	−	2.32747i	0.599607	−	0.101004i
$532$	−4.12670	+	5.21727i	−0.178915	+	0.226197i
$533$	18.5740	+	38.8836i	0.804530	+	1.68424i
$534$	−27.9746	+	2.33968i	−1.21058	+	0.101248i
$535$	13.6296	−	7.86907i	0.589260	−	0.340209i
$536$	−3.79862	+	2.19314i	−0.164076	+	0.0947291i
$537$	−10.8924	−	15.6833i	−0.470043	−	0.676785i
$538$			17.5469i			0.756499i
$539$	−36.5523	+	8.65012i	−1.57442	+	0.372587i
$540$	10.5077	−	10.2693i	0.452178	−	0.441918i
$541$	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
$543$	6.53260	−	0.546359i	0.280341	−	0.0234465i
$544$			7.32456i			0.314038i
$545$	−16.6034			−0.711213
$546$	−13.0149	−	10.1790i	−0.556987	−	0.435621i
$547$	−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
$549$	−15.7168	−	5.85698i	−0.670776	−	0.249970i
$550$	−16.0719			−0.685306
$551$	−7.57245	−	13.1159i	−0.322597	−	0.558755i
$552$	−0.699584	−	8.36465i	−0.0297763	−	0.356023i
$553$	9.97585	−	3.96122i	0.424216	−	0.168448i
$554$			12.8518i			0.546021i
$555$	2.57122	−	1.78577i	0.109142	−	0.0758017i
$556$	14.8457	−	8.57114i	0.629596	−	0.363497i
$557$	34.8056	−	20.0950i	1.47476	−	0.851454i	0.475166	−	0.879896i	$-0.342388\pi$
$557$	34.8056	−	20.0950i	1.47476	−	0.851454i	0.999595	+	0.0284423i	$0.00905468\pi$
$558$	2.13082	−	5.71791i	0.0902049	−	0.242058i
$559$	6.01656	+	0.470029i	0.254473	+	0.0198801i
$560$	−6.95295	+	2.76088i	−0.293816	+	0.116669i
$561$	38.8330	+	55.9132i	1.63953	+	2.36066i
$562$	26.5541			1.12012
$563$	−36.7290			−1.54794			−0.773971	−	0.633221i	$-0.781732\pi$
$563$	−36.7290			−1.54794			−0.773971	+	0.633221i	$0.781732\pi$
$564$	7.08269	−	4.91909i	0.298235	−	0.207131i
$565$	−2.45962	−	1.42006i	−0.103477	−	0.0597424i
$566$	0.769566	+	1.33293i	0.0323473	+	0.0560271i
$567$	−4.45391	−	23.3915i	−0.187047	−	0.982351i
$568$	4.12569	+	7.14590i	0.173110	+	0.299835i
$569$		−	11.6897i		−	0.490058i	−0.969516	−	0.245029i	$-0.921203\pi$
$569$		−	11.6897i		−	0.490058i	0.969516	−	0.245029i	$-0.0787975\pi$
$570$	1.02626	+	12.2706i	0.0429853	+	0.513959i
$571$	−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
$576$	2.95832	−	0.498329i	0.123263	−	0.0207637i
$577$	−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
$579$	−15.6584	+	10.8751i	−0.650742	+	0.451955i
$580$		−	17.0323i		−	0.707229i
$581$	4.65386	−	31.7346i	0.193075	−	1.31657i
$582$	7.51838	−	5.22169i	0.311647	−	0.216446i
$583$	−17.5101			−0.725195
$584$	0.896552	−	1.55287i	0.0370996	−	0.0642584i
$585$	−30.4640	+	2.71599i	−1.25953	+	0.112292i
$586$	−5.76094	+	3.32608i	−0.237982	+	0.137399i
$587$	−9.01119	+	15.6078i	−0.371932	+	0.644204i	−0.989863	−	0.142028i	$-0.954638\pi$
$587$	−9.01119	+	15.6078i	−0.371932	+	0.644204i	0.617931	+	0.786232i	$0.287971\pi$
$588$	−2.50113	+	11.8636i	−0.103145	+	0.489245i
$589$	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	0.964809	−	0.262953i	$-0.0846963\pi$
$593$	6.20188	+	10.7420i	0.254681	+	0.441120i	−0.710128	+	0.704073i	$0.751363\pi$
$594$	19.9408	−	19.4884i	0.818181	−	0.799617i
$595$	−50.9273	+	20.2223i	−2.08782	+	0.829032i
$596$	9.92624	+	5.73092i	0.406595	+	0.234748i
$597$	12.5184	−	1.04699i	0.512345	−	0.0428504i
$598$	−9.88864	+	14.4058i	−0.404376	+	0.589098i
$599$	20.8366	+	12.0300i	0.851359	+	0.491532i	0.861109	−	0.508420i	$-0.169770\pi$
$599$	20.8366	+	12.0300i	0.851359	+	0.491532i	−0.00974999	+	0.999952i	$0.503104\pi$
$600$	−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
$606$	0.0359601	+	0.0517767i	0.00146078	+	0.00210328i
$607$	−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
$609$	−23.0020	−	15.2605i	−0.932087	−	0.618389i
$610$	15.8086			0.640071
$611$	−17.8964	−	1.39811i	−0.724010	−	0.0565615i
$612$	21.6684	−	3.65004i	0.875894	−	0.147544i
$613$	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
$615$	−4.87841	−	58.3292i	−0.196716	−	2.35206i
$616$	−13.1949	+	5.23943i	−0.531637	+	0.211103i
$617$	21.2369	−	12.2611i	0.854965	−	0.493614i	−0.00735804	−	0.999973i	$-0.502342\pi$
$617$	21.2369	−	12.2611i	0.854965	−	0.493614i	0.862323	+	0.506359i	$0.169009\pi$
$618$	26.2001	−	18.1966i	1.05392	−	0.731974i
$619$	−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
$624$	−5.42535	−	3.09283i	−0.217188	−	0.123812i
$625$	15.5024	+	26.8510i	0.620097	+	1.07404i
$626$	6.56281	+	11.3671i	0.262303	+	0.454322i
$627$	1.94757	+	23.2864i	0.0777786	+	0.929968i
$628$	−14.2430	−	8.22323i	−0.568360	−	0.328143i
$629$	4.68192			0.186681
$630$	11.6324	+	19.1932i	0.463447	+	0.764677i
$631$	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	$0.303775\pi$
$641$			41.3155i			1.63186i	−0.578149	+	0.815931i	$0.696225\pi$
$642$	−0.803488	−	9.60699i	−0.0317111	−	0.379158i
$643$	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	0.511299	−	0.859403i	$-0.329164\pi$
$647$	−12.4285	−	21.5268i	−0.488615	−	0.846306i	−0.999914	+	0.0130964i	$0.995831\pi$
$648$	−2.94843	−	8.50334i	−0.115825	−	0.334043i
$649$	−21.7044	+	12.5311i	−0.851973	+	0.491887i
$650$	9.74445	−	4.65475i	0.382209	−	0.182574i
$651$	7.76709	+	5.15303i	0.304416	+	0.201963i
$652$	3.00753	−	5.20920i	0.117784	−	0.204008i
$653$			9.90848i			0.387749i	0.981026	+	0.193874i	$0.0621054\pi$
$653$			9.90848i			0.387749i	−0.981026	+	0.193874i	$0.937895\pi$
$654$	−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
$657$	−5.04068	−	1.87845i	−0.196656	−	0.0732852i
$658$	4.86127	+	12.2425i	0.189512	+	0.477263i
$659$	−14.5005	+	8.37187i	−0.564859	+	0.326122i	−0.755094	−	0.655617i	$-0.772409\pi$
$659$	−14.5005	+	8.37187i	−0.564859	+	0.326122i	0.190234	+	0.981739i	$0.439075\pi$
$660$	−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
$663$	−39.7383	−	22.6536i	−1.54331	−	0.879794i
$664$		−	12.1228i		−	0.470457i
$665$	−18.6100	−	2.72915i	−0.721666	−	0.105832i
$666$	−0.318536	−	1.89098i	−0.0123430	−	0.0732742i
$667$	−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
$672$	−0.284715	+	4.57372i	−0.0109831	+	0.176435i
$673$	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
$675$	14.9857	+	4.20028i	0.576799	+	0.161669i
$676$	4.67275	+	12.1312i	0.179721	+	0.466584i
$677$	23.2931	+	40.3449i	0.895228	+	1.55058i	0.833522	+	0.552486i	$0.186321\pi$
$677$	23.2931	+	40.3449i	0.895228	+	1.55058i	0.0617058	+	0.998094i	$0.480346\pi$
$678$	−1.42892	+	0.992417i	−0.0548773	+	0.0381135i
$679$	5.16031	+	12.9956i	0.198035	+	0.498726i
$680$	−17.9360	+	10.3553i	−0.687814	+	0.397110i
$681$	1.79960	+	21.5171i	0.0689609	+	0.824538i
$682$			10.9145i			0.417937i
$683$			24.3511i			0.931770i	0.884845	+	0.465885i	$0.154264\pi$
$683$			24.3511i			0.931770i	−0.884845	+	0.465885i	$0.845736\pi$
$684$	7.06788	+	2.63390i	0.270247	+	0.100710i
$685$	36.7428	−	21.2135i	1.40387	−	0.810526i
$686$	−16.7811	−	7.83543i	−0.640706	−	0.299158i
$687$	−10.3760	−	14.9398i	−0.395870	−	0.569989i
$688$	−0.836889	−	1.44953i	−0.0319061	−	0.0552630i
$689$	10.6165	−	5.07130i	0.404455	−	0.193201i
$690$	19.4938	−	13.5389i	0.742118	−	0.515417i
$691$		−	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
$693$	22.0753	+	36.4237i	0.838572	+	1.38362i
$694$	−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
$699$	3.17784	+	4.57558i	0.120197	+	0.173064i
$700$	−6.21519	−	4.91603i	−0.234912	−	0.185808i
$701$		−	39.4946i		−	1.49169i	−0.666120	−	0.745844i	$-0.732046\pi$
$701$		−	39.4946i		−	1.49169i	0.666120	−	0.745844i	$-0.267954\pi$
$702$	−6.44597	+	17.5912i	−0.243288	+	0.663936i
$703$	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
$708$	0.674229	+	8.06149i	0.0253391	+	0.302969i
$709$	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
$714$	−2.08542	+	33.5005i	−0.0780447	+	1.25373i
$715$	49.3631	−	23.5799i	1.84608	−	0.881838i
$716$	9.54740	−	5.51220i	0.356803	−	0.206000i
$717$	20.7021	−	1.73144i	0.773135	−	0.0646617i
$718$	−3.13151	−	5.42394i	−0.116867	−	0.202419i
$719$	18.6611	−	32.3220i	0.695942	−	1.20541i	−0.273920	−	0.961753i	$-0.588320\pi$
$719$	18.6611	−	32.3220i	0.695942	−	1.20541i	0.969862	−	0.243655i	$-0.0783464\pi$
$720$	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
$723$	−31.7425	+	2.65481i	−1.18052	+	0.0987334i
$724$			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
$735$	−32.5869	+	10.6479i	−1.20199	+	0.392754i
$736$	4.84619			0.178633
$737$	−20.3834	−	11.7683i	−0.750830	−	0.433492i
$738$	−33.5977	−	12.5204i	−1.23675	−	0.460884i
$739$	−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
$741$	−7.92506	−	13.5546i	−0.291134	−	0.497940i
$742$	−6.77138	−	5.35596i	−0.248585	−	0.196623i
$743$	35.2355	+	20.3432i	1.29266	+	0.746320i	0.979126	−	0.203256i	$-0.0651522\pi$
$743$	35.2355	+	20.3432i	1.29266	+	0.746320i	0.313538	+	0.949576i	$0.398486\pi$
$744$	3.18722	+	1.50109i	0.116849	+	0.0550327i
$745$			32.4091i			1.18738i
$746$	−13.4655	−	7.77432i	−0.493007	−	0.284638i
$747$	−35.8632	+	6.04116i	−1.31217	+	0.221034i
$748$	−34.0378	+	19.6517i	−1.24455	+	0.718539i
$749$	14.5703	+	2.13673i	0.532388	+	0.0780744i
$750$	9.78464	−	0.818346i	0.357284	−	0.0298818i
$751$	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
$753$	−14.8745	+	10.3307i	−0.542057	+	0.376471i
$754$	9.36140	+	19.5975i	0.340922	+	0.713700i
$755$	34.7885			1.26608
$756$	13.6724	−	1.43694i	0.497261	−	0.0522610i
$757$	−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
$759$	36.9942	−	25.6933i	1.34280	−	0.932608i
$760$	−7.10916			−0.257877
$761$	21.8081	−	37.7727i	0.790543	−	1.36926i	−0.135088	−	0.990834i	$-0.543132\pi$
$761$	21.8081	−	37.7727i	0.790543	−	1.36926i	0.925631	−	0.378427i	$-0.123535\pi$
$762$	−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
$768$	0.144357	+	1.72602i	0.00520905	+	0.0622825i
$769$	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
$771$	−0.255088	−	3.04999i	−0.00918677	−	0.109843i
$772$	−5.50345	−	9.53225i	−0.198073	−	0.343073i
$773$	−15.9038			−0.572018			−0.286009	−	0.958227i	$-0.592329\pi$
$773$	−15.9038			−0.572018			−0.286009	+	0.958227i	$0.592329\pi$
$774$	−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
$777$	2.92356	+	0.181992i	0.104882	+	0.00652894i
$778$	−10.5324	+	18.2426i	−0.377605	+	0.654031i
$779$	26.0233	−	15.0246i	0.932381	−	0.538310i
$780$	−0.0967215	−	17.6579i	−0.00346318	−	0.632254i
$781$	−22.1384	+	38.3448i	−0.792173	+	1.37208i
$782$	35.4963			1.26934
$783$	−8.44738	+	30.1384i	−0.301885	+	1.07706i
$784$	−6.70525	−	2.00987i	−0.239473	−	0.0717810i
$785$		−	46.5035i		−	1.65978i
$786$	6.47763	+	9.32674i	0.231050	+	0.332674i
$787$			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
$789$	20.7437	+	29.8675i	0.738494	+	1.06331i
$790$	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
$795$	−15.9257	+	1.33196i	−0.564828	+	0.0472398i
$796$			7.25276i			0.257067i
$797$	−23.5838	−	40.8483i	−0.835381	−	1.44692i	−0.893720	−	0.448626i	$-0.851914\pi$
$797$	−23.5838	−	40.8483i	−0.835381	−	1.44692i	0.0583386	−	0.998297i	$-0.481420\pi$
$798$	−6.36964	+	9.60086i	−0.225483	+	0.339867i
$799$	18.2334	+	31.5811i	0.645050	+	1.11726i
$800$	−2.59386	−	1.49757i	−0.0917070	−	0.0529470i
$801$	−47.9471	+	8.07669i	−1.69413	+	0.285376i
$802$	18.6153			0.657329
$803$	9.62177			0.339545
$804$	−6.23992	+	4.33377i	−0.220065	+	0.152840i
$805$	13.3798	+	33.6953i	0.471575	+	1.18760i
$806$	−3.16107	−	6.61750i	−0.111344	−	0.233092i
$807$	2.53302	+	30.2863i	0.0891665	+	1.06613i
$808$	−0.0315196	+	0.0181979i	−0.00110886	+	0.000640199i
$809$	−3.88186	+	2.24119i	−0.136479	+	0.0787961i	−0.566685	−	0.823935i	$-0.691774\pi$
$809$	−3.88186	+	2.24119i	−0.136479	+	0.0787961i	0.430206	+	0.902731i	$0.358441\pi$
$810$	16.6541	−	19.2418i	0.585164	−	0.676089i
$811$			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
$813$	38.3061	−	3.20376i	1.34345	−	0.112361i
$814$	1.71499	+	2.97045i	0.0601104	+	0.104114i
$815$	17.0080			0.595765
$816$	1.05736	+	12.6424i	0.0370148	+	0.442572i
$817$		−	4.20827i		−	0.147229i
$818$	−9.43206			−0.329784
$819$	−23.9335	−	15.6904i	−0.836303	−	0.548268i
$820$	33.7939			1.18014
$821$		−	27.5238i		−	0.960588i	−0.877108	−	0.480294i	$-0.840530\pi$
$821$		−	27.5238i		−	0.960588i	0.877108	−	0.480294i	$-0.159470\pi$
$822$	−2.16605	−	25.8986i	−0.0755496	−	0.903317i
$823$	−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
$825$	−27.7404	+	2.32009i	−0.965797	+	0.0807752i
$826$	−12.2264	−	1.79299i	−0.425409	−	0.0623861i
$827$		−	47.0909i		−	1.63751i	−0.574142	−	0.818755i	$-0.694664\pi$
$827$		−	47.0909i		−	1.63751i	0.574142	−	0.818755i	$-0.305336\pi$
$828$	−2.41500	−	14.3366i	−0.0839270	−	0.498231i
$829$	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
$831$	1.85525	+	22.1825i	0.0643580	+	0.769504i
$832$	2.04050	−	2.97260i	0.0707415	−	0.103057i
$833$	−49.1131	−	14.7214i	−1.70167	−	0.510067i
$834$	24.3867	−	16.9371i	0.844441	−	0.586483i
$835$	22.2269			0.769192
$836$	−13.4913			−0.466608
$837$	2.85243	−	10.1768i	0.0985944	−	0.351763i
$838$	−26.9681	−	15.5700i	−0.931597	−	0.537858i
$839$	7.26358	+	12.5809i	0.250767	+	0.434340i	0.963737	−	0.266854i	$-0.0859840\pi$
$839$	7.26358	+	12.5809i	0.250767	+	0.434340i	−0.712971	+	0.701194i	$0.752651\pi$
$840$	−11.6024	+	5.76906i	−0.400321	+	0.199051i
$841$	3.64227	+	6.30861i	0.125596	+	0.217538i
$842$			1.34712i			0.0464247i
$843$	45.8330	−	3.83328i	1.57857	−	0.132025i
$844$	−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
$849$	1.52071	+	2.18957i	0.0521906	+	0.0751460i
$850$	−18.9989	−	10.9690i	−0.651658	−	0.376235i
$851$		−	3.09773i		−	0.106189i
$852$	8.15260	+	11.7384i	0.279303	+	0.402152i
$853$			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
$855$	3.54270	+	21.0312i	0.121158	+	0.719252i
$856$	5.56596			0.190241
$857$	−10.9150	+	18.9053i	−0.372850	+	0.645794i	−0.990003	−	0.141049i	$-0.954953\pi$
$857$	−10.9150	+	18.9053i	−0.372850	+	0.645794i	0.617153	+	0.786843i	$0.288286\pi$
$858$	−0.183552	−	33.5100i	−0.00626636	−	1.14401i
$859$	−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
$861$	30.2786	−	45.6384i	1.03189	−	1.55535i
$862$	0.808798	+	1.40088i	0.0275478	+	0.0477141i
$863$	32.8756	−	18.9807i	1.11910	−	0.646112i	0.177928	−	0.984044i	$-0.443061\pi$
$863$	32.8756	−	18.9807i	1.11910	−	0.646112i	0.941171	+	0.337932i	$0.109727\pi$
$864$	5.03420	−	1.28718i	0.171267	−	0.0437909i
$865$	46.0775			1.56668
$866$	−1.57323	−	2.72492i	−0.0534606	−	0.0925965i
$867$	5.29059	+	63.2575i	0.179678	+	2.14834i
$868$	−3.33850	+	4.22077i	−0.113316	+	0.143262i
$869$	18.8527	+	10.8846i	0.639534	+	0.369235i
$870$	−2.45874	−	29.3982i	−0.0833591	−	0.996692i
$871$	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
$879$	−9.46337	+	6.57253i	−0.319192	+	0.221686i
$880$	−13.1399	−	7.58634i	−0.442947	−	0.255735i
$881$	−1.78267	+	3.08767i	−0.0600596	+	0.104026i	−0.894492	−	0.447084i	$-0.852462\pi$
$881$	−1.78267	+	3.08767i	−0.0600596	+	0.104026i	0.834432	+	0.551111i	$0.185796\pi$
$882$	−2.60442	+	20.8379i	−0.0876953	+	0.701648i
$883$	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
$885$	−18.7873	+	13.0482i	−0.631529	+	0.438611i
$886$	−7.32582	−	12.6887i	−0.246116	−	0.426285i
$887$	5.03734			0.169137			0.0845686	−	0.996418i	$-0.473049\pi$
$887$	5.03734			0.169137			0.0845686	+	0.996418i	$0.473049\pi$
$888$	1.10329	−	0.0922745i	0.0370240	−	0.00309653i
$889$	−24.6639	−	19.5084i	−0.827200	−	0.654290i
$890$	39.6882	−	22.9140i	1.33035	−	0.768078i
$891$	31.6050	−	36.5160i	1.05881	−	1.22333i
$892$	−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
$897$	−14.9884	+	26.2923i	−0.500450	+	0.877874i
$898$	2.80333	+	4.85551i	0.0935483	+	0.162030i
$899$	−6.12611	−	10.6107i	−0.204317	−	0.353888i
$900$	−3.13769	+	8.41977i	−0.104590	+	0.280659i
$901$	−20.6991	−	11.9507i	−0.689588	−	0.398134i
$902$	64.1321			2.13536
$903$	−3.41499	−	6.86804i	−0.113644	−	0.228554i
$904$	−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	$-0.944631\pi$
$911$		−	10.4476i		−	0.346145i	0.984909	−	0.173072i	$-0.0553694\pi$
$912$	−1.85549	+	3.93970i	−0.0614415	+	0.130457i
$913$	56.3357	−	32.5254i	1.86444	−	1.07644i
$914$			41.7616i			1.38135i
$915$	27.2860	−	2.28209i	0.902047	−	0.0754434i
$916$	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
$921$	−42.0947	+	3.52063i	−1.38707	+	0.116009i
$922$	18.7442	−	10.8220i	0.617308	−	0.356403i
$923$	2.31714	−	29.6604i	0.0762696	−	0.976283i
$924$	−22.0183	+	10.9482i	−0.724350	+	0.360168i
$925$	−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	−0.967861	−	0.251485i	$-0.919081\pi$
$929$	−8.11177	+	14.0500i	−0.266139	+	0.460966i	0.701723	+	0.712450i	$0.252415\pi$
$930$	0.830244	+	9.92690i	0.0272248	+	0.325516i
$931$	−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
$936$	−9.81076	−	4.55511i	−0.320675	−	0.148888i
$937$			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
$939$	12.9685	+	18.6725i	0.423211	+	0.609355i
$940$	−7.03879	+	12.1915i	−0.229580	+	0.397644i
$941$	6.62704	−	11.4784i	0.216035	−	0.374184i	−0.737557	−	0.675285i	$-0.764021\pi$
$941$	6.62704	−	11.4784i	0.216035	−	0.374184i	0.953592	+	0.301101i	$0.0973540\pi$
$942$	−25.7709	−	12.1374i	−0.839662	−	0.395458i
$943$	−50.1600	−	28.9599i	−1.63343	−	0.943063i
$944$	−4.67055			−0.152014
$945$	22.8485	+	31.4488i	0.743263	+	1.02303i
$946$	4.49073	−	7.77818i	0.146006	−	0.252890i
$947$		−	7.98486i		−	0.259473i	−0.991548	−	0.129737i	$-0.958587\pi$
$947$		−	7.98486i		−	0.259473i	0.991548	−	0.129737i	$-0.0414132\pi$
$948$	5.77135	−	4.00833i	0.187445	−	0.130185i
$949$	−5.83373	+	2.78667i	−0.189371	+	0.0904591i
$950$	−3.76524	−	6.52158i	−0.122160	−	0.211588i
$951$	−21.7189	−	31.2717i	−0.704283	−	1.01405i
$952$	−19.1739	−	2.81184i	−0.621429	−	0.0911323i
$953$	−26.3580	+	15.2178i	−0.853819	+	0.492953i	−0.861938	−	0.507014i	$-0.830749\pi$
$953$	−26.3580	+	15.2178i	−0.853819	+	0.492953i	0.00811831	+	0.999967i	$0.497416\pi$
$954$	−3.41848	+	9.17325i	−0.110677	+	0.296995i
$955$			22.8016i			0.737844i
$956$			11.9941i			0.387917i
$957$	−4.66605	−	55.7901i	−0.150832	−	1.80344i
$958$	−13.5157	+	7.80327i	−0.436671	+	0.252112i
$959$	39.2788	+	5.76021i	1.26838	+	0.186007i
$960$	−4.02250	+	2.79372i	−0.129826	+	0.0901669i
$961$	−13.4314	−	23.2639i	−0.433271	−	0.750447i
$962$	−1.90011	−	1.30430i	−0.0612621	−	0.0420524i
$963$	−2.77368	−	16.4659i	−0.0893806	−	0.530607i
$964$		−	18.3905i		−	0.592319i
$965$	15.5614	−	26.9531i	0.500938	−	0.867650i
$966$	22.1651	+	1.37979i	0.713152	+	0.0443939i
$967$	−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	−0.977561	−	0.210651i	$-0.932442\pi$
$971$	−9.54617	+	16.5345i	−0.306351	+	0.530616i	0.671210	+	0.741267i	$0.265775\pi$
$972$	−6.31659	−	14.2513i	−0.202605	−	0.457112i
$973$	16.7380	+	42.1526i	0.536595	+	1.35135i
$974$			22.4792i			0.720280i
$975$	16.1472	−	9.44090i	0.517125	−	0.302351i
$976$	4.84184	+	2.79544i	0.154984	+	0.0894798i
$977$	−23.8427	+	13.7656i	−0.762796	+	0.440400i	−0.830299	−	0.557319i	$-0.811830\pi$
$977$	−23.8427	+	13.7656i	−0.762796	+	0.440400i	0.0675028	+	0.997719i	$0.478497\pi$
$978$	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
$981$	−6.15147	+	16.5070i	−0.196401	+	0.527028i
$982$	16.5938	−	28.7412i	0.529528	−	0.917169i
$983$	2.40101	−	4.15868i	0.0765804	−	0.132641i	−0.825192	−	0.564852i	$-0.808933\pi$
$983$	2.40101	−	4.15868i	0.0765804	−	0.132641i	0.901772	+	0.432211i	$0.142266\pi$
$984$	8.82022	−	18.7277i	0.281178	−	0.597016i
$985$			6.38011i			0.203287i
$986$	22.0604	−	38.2097i	0.702545	−	1.21684i
$987$	10.1580	+	20.4291i	0.323332	+	0.650267i
$988$	8.17987	−	3.90738i	0.260236	−	0.124310i
$989$	−7.02472	+	4.05573i	−0.223373	+	0.128965i
$990$	−15.8948	+	42.6526i	−0.505171	+	1.35559i
$991$	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
$996$	−1.75002	−	20.9243i	−0.0554515	−	0.663012i
$997$			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.269.30	yes	76
3.2	odd	2	inner	546.2.bb.a.269.5	yes	76
7.5	odd	6		546.2.u.a.425.36	yes	76
13.3	even	3		546.2.u.a.185.3	✓	76
21.5	even	6		546.2.u.a.425.3	yes	76
39.29	odd	6		546.2.u.a.185.36	yes	76
91.68	odd	6	inner	546.2.bb.a.341.24	yes	76
273.68	even	6	inner	546.2.bb.a.341.11	yes	76

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.144357 + 1.72602i) q^{3} -1.00000 q^{4} +(-1.41378 - 2.44875i) q^{5} +(-1.72602 + 0.144357i) q^{6} +(0.383892 - 2.61775i) q^{7} -1.00000i q^{8} +(-2.95832 + 0.498329i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.144357 + 1.72602i) q^{3} -1.00000 q^{4} +(-1.41378 - 2.44875i) q^{5} +(-1.72602 + 0.144357i) q^{6} +(0.383892 - 2.61775i) q^{7} -1.00000i q^{8} +(-2.95832 + 0.498329i) q^{9} +(2.44875 - 1.41378i) q^{10} +(4.64708 - 2.68299i) q^{11} +(-0.144357 - 1.72602i) q^{12} +(-2.04050 + 2.97260i) q^{13} +(2.61775 + 0.383892i) q^{14} +(4.02250 - 2.79372i) q^{15} +1.00000 q^{16} +7.32456 q^{17} +(-0.498329 - 2.95832i) q^{18} +(2.17739 + 1.25712i) q^{19} +(1.41378 + 2.44875i) q^{20} +(4.57372 + 0.284715i) q^{21} +(2.68299 + 4.64708i) q^{22} -4.84619i q^{23} +(1.72602 - 0.144357i) 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} +(2.79372 + 4.02250i) q^{30} +(1.76151 + 1.01701i) q^{31} +1.00000i q^{32} +(5.30175 + 7.63366i) q^{33} +7.32456i q^{34} +(-6.95295 + 2.76088i) q^{35} +(2.95832 - 0.498329i) q^{36} +0.639208 q^{37} +(-1.25712 + 2.17739i) q^{38} +(-5.42535 - 3.09283i) q^{39} +(-2.44875 + 1.41378i) q^{40} +(5.97580 - 10.3504i) q^{41} +(-0.284715 + 4.57372i) 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} +(0.144357 + 1.72602i) q^{48} +(-6.70525 - 2.00987i) q^{49} +(-2.59386 - 1.49757i) q^{50} +(1.05736 + 12.6424i) 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} +(-4.02250 + 2.79372i) q^{60} +(4.84184 + 2.79544i) q^{61} +(-1.01701 + 1.76151i) q^{62} +(0.168825 + 7.93546i) q^{63} -1.00000 q^{64} +(10.1640 + 0.794034i) q^{65} +(-7.63366 + 5.30175i) q^{66} +(-2.19314 - 3.79862i) q^{67} -7.32456 q^{68} +(8.36465 - 0.699584i) q^{69} +(-2.76088 - 6.95295i) q^{70} +(-7.14590 + 4.12569i) q^{71} +(0.498329 + 2.95832i) 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} +(3.09283 - 5.42535i) q^{78} +(2.02845 + 3.51337i) q^{79} +(-1.41378 - 2.44875i) q^{80} +(8.50334 - 2.94843i) q^{81} +(10.3504 + 5.97580i) q^{82} +12.1228 q^{83} +(-4.57372 - 0.284715i) 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} +(-1.72602 + 0.144357i) 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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