LMFDB - Embedded newform 546.2.bb.a.269.19

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			269.19
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.72167 - 0.189348i) q^{3} -1.00000 q^{4} +(1.42622 + 2.47029i) q^{5} +(-0.189348 - 1.72167i) q^{6} +(-1.89518 + 1.84615i) q^{7} +1.00000i q^{8} +(2.92829 - 0.651988i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.72167 - 0.189348i) q^{3} -1.00000 q^{4} +(1.42622 + 2.47029i) q^{5} +(-0.189348 - 1.72167i) q^{6} +(-1.89518 + 1.84615i) q^{7} +1.00000i q^{8} +(2.92829 - 0.651988i) q^{9} +(2.47029 - 1.42622i) q^{10} +(1.78545 - 1.03083i) q^{11} +(-1.72167 + 0.189348i) q^{12} +(-3.41477 - 1.15729i) q^{13} +(1.84615 + 1.89518i) q^{14} +(2.92323 + 3.98298i) q^{15} +1.00000 q^{16} +4.08561 q^{17} +(-0.651988 - 2.92829i) q^{18} +(3.75913 + 2.17033i) q^{19} +(-1.42622 - 2.47029i) q^{20} +(-2.91332 + 3.53731i) q^{21} +(-1.03083 - 1.78545i) q^{22} +1.37818i q^{23} +(0.189348 + 1.72167i) q^{24} +(-1.56823 + 2.71626i) q^{25} +(-1.15729 + 3.41477i) q^{26} +(4.91811 - 1.67697i) q^{27} +(1.89518 - 1.84615i) q^{28} +(6.75519 + 3.90011i) q^{29} +(3.98298 - 2.92323i) q^{30} +(2.44780 + 1.41324i) q^{31} -1.00000i q^{32} +(2.87877 - 2.11282i) q^{33} -4.08561i q^{34} +(-7.26350 - 2.04863i) q^{35} +(-2.92829 + 0.651988i) q^{36} -6.35706 q^{37} +(2.17033 - 3.75913i) q^{38} +(-6.09824 - 1.34589i) q^{39} +(-2.47029 + 1.42622i) q^{40} +(-3.55429 + 6.15620i) q^{41} +(3.53731 + 2.91332i) q^{42} +(-5.02540 - 8.70425i) q^{43} +(-1.78545 + 1.03083i) q^{44} +(5.78701 + 6.30387i) q^{45} +1.37818 q^{46} +(-3.65196 - 6.32538i) q^{47} +(1.72167 - 0.189348i) q^{48} +(0.183445 - 6.99760i) q^{49} +(2.71626 + 1.56823i) q^{50} +(7.03407 - 0.773601i) q^{51} +(3.41477 + 1.15729i) q^{52} +(-5.80600 - 3.35210i) q^{53} +(-1.67697 - 4.91811i) q^{54} +(5.09290 + 2.94039i) q^{55} +(-1.84615 - 1.89518i) q^{56} +(6.88293 + 3.02482i) q^{57} +(3.90011 - 6.75519i) q^{58} -10.8441 q^{59} +(-2.92323 - 3.98298i) q^{60} +(3.41234 + 1.97012i) q^{61} +(1.41324 - 2.44780i) q^{62} +(-4.34599 + 6.64172i) q^{63} -1.00000 q^{64} +(-2.01139 - 10.0860i) q^{65} +(-2.11282 - 2.87877i) q^{66} +(-6.46495 - 11.1976i) q^{67} -4.08561 q^{68} +(0.260955 + 2.37277i) q^{69} +(-2.04863 + 7.26350i) q^{70} +(-5.66543 + 3.27094i) q^{71} +(0.651988 + 2.92829i) q^{72} +(2.16906 + 1.25231i) q^{73} +6.35706i q^{74} +(-2.18566 + 4.97344i) q^{75} +(-3.75913 - 2.17033i) q^{76} +(-1.48069 + 5.24982i) q^{77} +(-1.34589 + 6.09824i) q^{78} +(-7.08737 - 12.2757i) q^{79} +(1.42622 + 2.47029i) q^{80} +(8.14982 - 3.81843i) q^{81} +(6.15620 + 3.55429i) q^{82} +10.2916 q^{83} +(2.91332 - 3.53731i) q^{84} +(5.82700 + 10.0927i) q^{85} +(-8.70425 + 5.02540i) q^{86} +(12.3687 + 5.43563i) q^{87} +(1.03083 + 1.78545i) q^{88} -6.03095 q^{89} +(6.30387 - 5.78701i) q^{90} +(8.60816 - 4.11091i) q^{91} -1.37818i q^{92} +(4.48190 + 1.96964i) q^{93} +(-6.32538 + 3.65196i) q^{94} +12.3815i q^{95} +(-0.189348 - 1.72167i) q^{96} +(15.8274 - 9.13794i) q^{97} +(-6.99760 - 0.183445i) q^{98} +(4.55623 - 4.18267i) 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
$3$	1.72167	−	0.189348i	0.994007	−	0.109320i
$3$	1.72167	−	0.189348i	0.994007	−	0.109320i
$4$	−1.00000			−0.500000
$5$	1.42622	+	2.47029i	0.637827	+	1.10475i	0.985909	+	0.167285i	$0.0534999\pi$
$5$	1.42622	+	2.47029i	0.637827	+	1.10475i	−0.348082	+	0.937464i	$0.613167\pi$
$6$	−0.189348	−	1.72167i	−0.0773009	−	0.702869i
$7$	−1.89518	+	1.84615i	−0.716312	+	0.697780i
$7$	−1.89518	+	1.84615i	−0.716312	+	0.697780i
$8$			1.00000i			0.353553i
$9$	2.92829	−	0.651988i	0.976098	−	0.217329i
$10$	2.47029	−	1.42622i	0.781175	−	0.451012i
$11$	1.78545	−	1.03083i	0.538333	−	0.310807i	−0.206070	−	0.978537i	$-0.566067\pi$
$11$	1.78545	−	1.03083i	0.538333	−	0.310807i	0.744403	+	0.667730i	$0.232734\pi$
$12$	−1.72167	+	0.189348i	−0.497003	+	0.0546600i
$13$	−3.41477	−	1.15729i	−0.947088	−	0.320975i
$13$	−3.41477	−	1.15729i	−0.947088	−	0.320975i
$14$	1.84615	+	1.89518i	0.493405	+	0.506509i
$15$	2.92323	+	3.98298i	0.754775	+	1.02840i
$16$	1.00000			0.250000
$17$	4.08561			0.990906			0.495453	−	0.868635i	$-0.335002\pi$
$17$	4.08561			0.990906			0.495453	+	0.868635i	$0.335002\pi$
$18$	−0.651988	−	2.92829i	−0.153675	−	0.690206i
$19$	3.75913	+	2.17033i	0.862403	+	0.497909i	0.864816	−	0.502088i	$-0.167435\pi$
$19$	3.75913	+	2.17033i	0.862403	+	0.497909i	−0.00241311	+	0.999997i	$0.500768\pi$
$20$	−1.42622	−	2.47029i	−0.318913	−	0.552374i
$21$	−2.91332	+	3.53731i	−0.635738	+	0.771905i
$22$	−1.03083	−	1.78545i	−0.219774	−	0.380659i
$23$			1.37818i			0.287371i	0.989623	+	0.143685i	$0.0458953\pi$
$23$			1.37818i			0.287371i	−0.989623	+	0.143685i	$0.954105\pi$
$24$	0.189348	+	1.72167i	0.0386504	+	0.351434i
$25$	−1.56823	+	2.71626i	−0.313647	+	0.543252i
$26$	−1.15729	+	3.41477i	−0.226963	+	0.669692i
$27$	4.91811	−	1.67697i	0.946490	−	0.322734i
$28$	1.89518	−	1.84615i	0.358156	−	0.348890i
$29$	6.75519	+	3.90011i	1.25441	+	0.724233i	0.971982	−	0.235056i	$-0.0755275\pi$
$29$	6.75519	+	3.90011i	1.25441	+	0.724233i	0.282426	+	0.959289i	$0.408861\pi$
$30$	3.98298	−	2.92323i	0.727189	−	0.533707i
$31$	2.44780	+	1.41324i	0.439638	+	0.253825i	0.703444	−	0.710751i	$-0.251645\pi$
$31$	2.44780	+	1.41324i	0.439638	+	0.253825i	−0.263806	+	0.964576i	$0.584978\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.87877	−	2.11282i	0.501129	−	0.367795i
$34$		−	4.08561i		−	0.700676i
$35$	−7.26350	−	2.04863i	−1.22775	−	0.346282i
$36$	−2.92829	+	0.651988i	−0.488049	+	0.108665i
$37$	−6.35706			−1.04509			−0.522547	−	0.852610i	$-0.675018\pi$
$37$	−6.35706			−1.04509			−0.522547	+	0.852610i	$0.675018\pi$
$38$	2.17033	−	3.75913i	0.352075	−	0.609811i
$39$	−6.09824	−	1.34589i	−0.976500	−	0.215515i
$40$	−2.47029	+	1.42622i	−0.390588	+	0.225506i
$41$	−3.55429	+	6.15620i	−0.555086	+	0.961438i	0.442811	+	0.896615i	$0.353981\pi$
$41$	−3.55429	+	6.15620i	−0.555086	+	0.961438i	−0.997897	+	0.0648225i	$0.979352\pi$
$42$	3.53731	+	2.91332i	0.545819	+	0.449535i
$43$	−5.02540	−	8.70425i	−0.766367	−	1.32739i	−0.939521	−	0.342491i	$-0.888729\pi$
$43$	−5.02540	−	8.70425i	−0.766367	−	1.32739i	0.173155	−	0.984895i	$-0.444604\pi$
$44$	−1.78545	+	1.03083i	−0.269167	+	0.155403i
$45$	5.78701	+	6.30387i	0.862676	+	0.939725i
$46$	1.37818			0.203202
$47$	−3.65196	−	6.32538i	−0.532693	−	0.922652i	−0.999271	−	0.0381719i	$-0.987847\pi$
$47$	−3.65196	−	6.32538i	−0.532693	−	0.922652i	0.466578	−	0.884480i	$-0.345487\pi$
$48$	1.72167	−	0.189348i	0.248502	−	0.0273300i
$49$	0.183445	−	6.99760i	0.0262064	−	0.999657i
$50$	2.71626	+	1.56823i	0.384137	+	0.221782i
$51$	7.03407	−	0.773601i	0.984967	−	0.108326i
$52$	3.41477	+	1.15729i	0.473544	+	0.160487i
$53$	−5.80600	−	3.35210i	−0.797516	−	0.460446i	0.0450859	−	0.998983i	$-0.485644\pi$
$53$	−5.80600	−	3.35210i	−0.797516	−	0.460446i	−0.842602	+	0.538537i	$0.818977\pi$
$54$	−1.67697	−	4.91811i	−0.228207	−	0.669269i
$55$	5.09290	+	2.94039i	0.686727	+	0.396482i
$56$	−1.84615	−	1.89518i	−0.246702	−	0.253255i
$57$	6.88293	+	3.02482i	0.911666	+	0.400647i
$58$	3.90011	−	6.75519i	0.512110	−	0.887000i
$59$	−10.8441			−1.41178			−0.705888	−	0.708323i	$-0.749452\pi$
$59$	−10.8441			−1.41178			−0.705888	+	0.708323i	$0.749452\pi$
$60$	−2.92323	−	3.98298i	−0.377388	−	0.514200i
$61$	3.41234	+	1.97012i	0.436905	+	0.252247i	0.702284	−	0.711897i	$-0.252164\pi$
$61$	3.41234	+	1.97012i	0.436905	+	0.252247i	−0.265379	+	0.964144i	$0.585497\pi$
$62$	1.41324	−	2.44780i	0.179481	−	0.310871i
$63$	−4.34599	+	6.64172i	−0.547543	+	0.836778i
$64$	−1.00000			−0.125000
$65$	−2.01139	−	10.0860i	−0.249482	−	1.25102i
$66$	−2.11282	−	2.87877i	−0.260070	−	0.354352i
$67$	−6.46495	−	11.1976i	−0.789820	−	1.36801i	−0.926077	−	0.377335i	$-0.876841\pi$
$67$	−6.46495	−	11.1976i	−0.789820	−	1.36801i	0.136257	−	0.990674i	$-0.456493\pi$
$68$	−4.08561			−0.495453
$69$	0.260955	+	2.37277i	0.0314153	+	0.285648i
$70$	−2.04863	+	7.26350i	−0.244858	+	0.868154i
$71$	−5.66543	+	3.27094i	−0.672362	+	0.388189i	−0.796971	−	0.604017i	$-0.793566\pi$
$71$	−5.66543	+	3.27094i	−0.672362	+	0.388189i	0.124609	+	0.992206i	$0.460232\pi$
$72$	0.651988	+	2.92829i	0.0768376	+	0.345103i
$73$	2.16906	+	1.25231i	0.253869	+	0.146571i	0.621535	−	0.783387i	$-0.286510\pi$
$73$	2.16906	+	1.25231i	0.253869	+	0.146571i	−0.367666	+	0.929958i	$0.619843\pi$
$74$			6.35706i			0.738993i
$75$	−2.18566	+	4.97344i	−0.252379	+	0.574284i
$76$	−3.75913	−	2.17033i	−0.431202	−	0.248954i
$77$	−1.48069	+	5.24982i	−0.168740	+	0.598273i
$78$	−1.34589	+	6.09824i	−0.152392	+	0.690490i
$79$	−7.08737	−	12.2757i	−0.797391	−	1.38112i	−0.921310	−	0.388829i	$-0.872880\pi$
$79$	−7.08737	−	12.2757i	−0.797391	−	1.38112i	0.123919	−	0.992292i	$-0.460454\pi$
$80$	1.42622	+	2.47029i	0.159457	+	0.276187i
$81$	8.14982	−	3.81843i	0.905536	−	0.424270i
$82$	6.15620	+	3.55429i	0.679839	+	0.392505i
$83$	10.2916			1.12965			0.564825	−	0.825211i	$-0.308944\pi$
$83$	10.2916			1.12965			0.564825	+	0.825211i	$0.308944\pi$
$84$	2.91332	−	3.53731i	0.317869	−	0.385953i
$85$	5.82700	+	10.0927i	0.632027	+	1.09470i
$86$	−8.70425	+	5.02540i	−0.938603	+	0.541903i
$87$	12.3687	+	5.43563i	1.32606	+	0.582760i
$88$	1.03083	+	1.78545i	0.109887	+	0.190330i
$89$	−6.03095			−0.639279			−0.319639	−	0.947539i	$-0.603562\pi$
$89$	−6.03095			−0.639279			−0.319639	+	0.947539i	$0.603562\pi$
$90$	6.30387	−	5.78701i	0.664486	−	0.610004i
$91$	8.60816	−	4.11091i	0.902380	−	0.430941i
$92$		−	1.37818i		−	0.143685i
$93$	4.48190	+	1.96964i	0.464751	+	0.204243i
$94$	−6.32538	+	3.65196i	−0.652414	+	0.376671i
$95$			12.3815i			1.27032i
$96$	−0.189348	−	1.72167i	−0.0193252	−	0.175717i
$97$	15.8274	−	9.13794i	1.60703	−	0.927817i	0.616995	−	0.786967i	$-0.288350\pi$
$97$	15.8274	−	9.13794i	1.60703	−	0.927817i	0.990031	−	0.140850i	$-0.0449836\pi$
$98$	−6.99760	−	0.183445i	−0.706864	−	0.0185307i
$99$	4.55623	−	4.18267i	0.457919	−	0.420374i
$100$	1.56823	−	2.71626i	0.156823	−	0.271626i
$101$	−5.47293	−	9.47939i	−0.544577	−	0.943235i	−0.998633	−	0.0522619i	$-0.983357\pi$
$101$	−5.47293	−	9.47939i	−0.544577	−	0.943235i	0.454057	−	0.890973i	$-0.349976\pi$
$102$	−0.773601	−	7.03407i	−0.0765979	−	0.696477i
$103$	−2.40226	+	1.38694i	−0.236701	+	0.136660i	−0.613660	−	0.789571i	$-0.710303\pi$
$103$	−2.40226	+	1.38694i	−0.236701	+	0.136660i	0.376958	+	0.926230i	$0.376970\pi$
$104$	1.15729	−	3.41477i	0.113482	−	0.334846i
$105$	−12.8932	−	2.15174i	−1.25825	−	0.209989i
$106$	−3.35210	+	5.80600i	−0.325585	+	0.563929i
$107$		−	0.895779i		−	0.0865982i	−0.999062	−	0.0432991i	$-0.986213\pi$
$107$		−	0.895779i		−	0.0865982i	0.999062	−	0.0432991i	$-0.0137868\pi$
$108$	−4.91811	+	1.67697i	−0.473245	+	0.161367i
$109$	−5.76038	+	9.97726i	−0.551744	+	0.955648i	0.446405	+	0.894831i	$0.352704\pi$
$109$	−5.76038	+	9.97726i	−0.551744	+	0.955648i	−0.998149	+	0.0608174i	$0.980629\pi$
$110$	2.94039	−	5.09290i	0.280355	−	0.485589i
$111$	−10.9448	+	1.20369i	−1.03883	+	0.114250i
$112$	−1.89518	+	1.84615i	−0.179078	+	0.174445i
$113$	−2.96337	+	1.71090i	−0.278771	+	0.160948i	−0.632867	−	0.774261i	$-0.718122\pi$
$113$	−2.96337	+	1.71090i	−0.278771	+	0.160948i	0.354096	+	0.935209i	$0.384789\pi$
$114$	3.02482	−	6.88293i	0.283300	−	0.644645i
$115$	−3.40451	+	1.96560i	−0.317472	+	0.183293i
$116$	−6.75519	−	3.90011i	−0.627204	−	0.362116i
$117$	−10.7540	−	1.16250i	−0.994208	−	0.107473i
$118$			10.8441i			0.998277i
$119$	−7.74298	+	7.54266i	−0.709798	+	0.691434i
$120$	−3.98298	+	2.92323i	−0.363594	+	0.266853i
$121$	−3.37478	+	5.84529i	−0.306798	+	0.531390i
$122$	1.97012	−	3.41234i	0.178366	−	0.308939i
$123$	−4.95365	+	11.2719i	−0.446655	+	1.01636i
$124$	−2.44780	−	1.41324i	−0.219819	−	0.126912i
$125$	5.31564			0.475445
$126$	6.64172	+	4.34599i	0.591691	+	0.387171i
$127$	5.80763	−	10.0591i	0.515343	−	0.892601i	−0.484498	−	0.874792i	$-0.660998\pi$
$127$	5.80763	−	10.0591i	0.515343	−	0.892601i	0.999841	−	0.0178086i	$-0.00566895\pi$
$128$			1.00000i			0.0883883i
$129$	−10.3002	−	14.0343i	−0.906883	−	1.23565i
$130$	−10.0860	+	2.01139i	−0.884605	+	0.176410i
$131$	0.606766	+	1.05095i	0.0530134	+	0.0918218i	0.891314	−	0.453386i	$-0.149784\pi$
$131$	0.606766	+	1.05095i	0.0530134	+	0.0918218i	−0.838301	+	0.545208i	$0.816451\pi$
$132$	−2.87877	+	2.11282i	−0.250565	+	0.183897i
$133$	−11.1310	+	2.82674i	−0.965181	+	0.245110i
$134$	−11.1976	+	6.46495i	−0.967328	+	0.558487i
$135$	11.1569	+	9.75742i	0.960237	+	0.839785i
$136$			4.08561i			0.350338i
$137$		−	9.46777i		−	0.808886i	−0.914563	−	0.404443i	$-0.867465\pi$
$137$		−	9.46777i		−	0.808886i	0.914563	−	0.404443i	$-0.132535\pi$
$138$	2.37277	−	0.260955i	0.201984	−	0.0222140i
$139$	5.66528	−	3.27085i	0.480522	−	0.277430i	−0.240112	−	0.970745i	$-0.577184\pi$
$139$	5.66528	−	3.27085i	0.480522	−	0.277430i	0.720634	+	0.693316i	$0.243851\pi$
$140$	7.26350	+	2.04863i	0.613877	+	0.173141i
$141$	−7.48517	−	10.1987i	−0.630365	−	0.858888i
$142$	3.27094	+	5.66543i	0.274491	+	0.475432i
$143$	−7.28988	+	1.45377i	−0.609610	+	0.121570i
$144$	2.92829	−	0.651988i	0.244025	−	0.0543324i
$145$			22.2497i			1.84774i
$146$	1.25231	−	2.16906i	0.103642	−	0.179513i
$147$	−1.00915	−	12.0823i	−0.0832330	−	0.996530i
$148$	6.35706			0.522547
$149$	17.1055	+	9.87585i	1.40133	+	0.809061i	0.994530	−	0.104454i	$-0.0333094\pi$
$149$	17.1055	+	9.87585i	1.40133	+	0.809061i	0.406805	+	0.913515i	$0.366643\pi$
$150$	4.97344	+	2.18566i	0.406080	+	0.178459i
$151$	−11.0526	+	19.1436i	−0.899444	+	1.55788i	−0.0712375	+	0.997459i	$0.522695\pi$
$151$	−11.0526	+	19.1436i	−0.899444	+	1.55788i	−0.828206	+	0.560423i	$0.810639\pi$
$152$	−2.17033	+	3.75913i	−0.176037	+	0.304906i
$153$	11.9639	−	2.66377i	0.967222	−	0.215353i
$154$	5.24982	+	1.48069i	0.423043	+	0.119317i
$155$			8.06238i			0.647586i
$156$	6.09824	+	1.34589i	0.488250	+	0.107758i
$157$	−13.7392	−	7.93232i	−1.09651	−	0.633068i	−0.161205	−	0.986921i	$-0.551538\pi$
$157$	−13.7392	−	7.93232i	−1.09651	−	0.633068i	−0.935301	+	0.353853i	$0.884871\pi$
$158$	−12.2757	+	7.08737i	−0.976601	+	0.563841i
$159$	−10.6307	−	4.67185i	−0.843072	−	0.370502i
$160$	2.47029	−	1.42622i	0.195294	−	0.112753i
$161$	−2.54433	−	2.61191i	−0.200522	−	0.205847i
$162$	−3.81843	−	8.14982i	−0.300004	−	0.640311i
$163$	−1.86738	+	3.23439i	−0.146264	+	0.253337i	−0.929844	−	0.367954i	$-0.880058\pi$
$163$	−1.86738	+	3.23439i	−0.146264	+	0.253337i	0.783580	+	0.621291i	$0.213392\pi$
$164$	3.55429	−	6.15620i	0.277543	−	0.480719i
$165$	9.32506	+	4.09805i	0.725955	+	0.319033i
$166$		−	10.2916i		−	0.798783i
$167$	7.93312	−	13.7406i	0.613883	−	1.06328i	−0.376696	−	0.926337i	$-0.622940\pi$
$167$	7.93312	−	13.7406i	0.613883	−	1.06328i	0.990579	−	0.136940i	$-0.0437268\pi$
$168$	−3.53731	−	2.91332i	−0.272910	−	0.224767i
$169$	10.3214	+	7.90377i	0.793951	+	0.607982i
$170$	10.0927	−	5.82700i	0.774071	−	0.446910i
$171$	12.4229	+	3.90447i	0.950001	+	0.298582i
$172$	5.02540	+	8.70425i	0.383183	+	0.663693i
$173$	−2.79263	+	4.83698i	−0.212320	+	0.367749i	−0.952440	−	0.304726i	$-0.901435\pi$
$173$	−2.79263	+	4.83698i	−0.212320	+	0.367749i	0.740120	+	0.672474i	$0.234769\pi$
$174$	5.43563	−	12.3687i	0.412074	−	0.937668i
$175$	−2.04254	−	8.04301i	−0.154401	−	0.607994i
$176$	1.78545	−	1.03083i	0.134583	−	0.0777017i
$177$	−18.6699	+	2.05330i	−1.40332	+	0.154335i
$178$			6.03095i			0.452039i
$179$	−0.229448	+	0.132472i	−0.0171497	+	0.00990139i	−0.508550	−	0.861032i	$-0.669818\pi$
$179$	−0.229448	+	0.132472i	−0.0171497	+	0.00990139i	0.491401	+	0.870934i	$0.336485\pi$
$180$	−5.78701	−	6.30387i	−0.431338	−	0.469862i
$181$			2.90040i			0.215585i	0.994173	+	0.107792i	$0.0343782\pi$
$181$			2.90040i			0.215585i	−0.994173	+	0.107792i	$0.965622\pi$
$182$	−4.11091	−	8.60816i	−0.304721	−	0.638079i
$183$	6.24796	+	2.74577i	0.461863	+	0.202973i
$184$	−1.37818			−0.101601
$185$	−9.06660	−	15.7038i	−0.666590	−	1.15457i
$186$	1.96964	−	4.48190i	0.144421	−	0.328629i
$187$	7.29465	−	4.21157i	0.533438	−	0.307980i
$188$	3.65196	+	6.32538i	0.266347	+	0.461326i
$189$	−6.22476	+	12.2577i	−0.452785	+	0.891620i
$190$	12.3815			0.898251
$191$	−0.509369	−	0.294084i	−0.0368566	−	0.0212792i	0.481458	−	0.876469i	$-0.340107\pi$
$191$	−0.509369	−	0.294084i	−0.0368566	−	0.0212792i	−0.518315	+	0.855190i	$0.673441\pi$
$192$	−1.72167	+	0.189348i	−0.124251	+	0.0136650i
$193$	9.34180	+	16.1805i	0.672437	+	1.16470i	0.977211	+	0.212271i	$0.0680859\pi$
$193$	9.34180	+	16.1805i	0.672437	+	1.16470i	−0.304774	+	0.952425i	$0.598581\pi$
$194$	−9.13794	−	15.8274i	−0.656066	−	1.13634i
$195$	−5.37271	−	16.9840i	−0.384748	−	1.21625i
$196$	−0.183445	+	6.99760i	−0.0131032	+	0.499828i
$197$	20.3079	+	11.7248i	1.44688	+	0.835357i	0.998294	−	0.0583826i	$-0.0185943\pi$
$197$	20.3079	+	11.7248i	1.44688	+	0.835357i	0.448586	+	0.893740i	$0.351928\pi$
$198$	−4.18267	−	4.55623i	−0.297249	−	0.323797i
$199$		−	18.7498i		−	1.32913i	−0.747228	−	0.664567i	$-0.768616\pi$
$199$		−	18.7498i		−	1.32913i	0.747228	−	0.664567i	$-0.231384\pi$
$200$	−2.71626	−	1.56823i	−0.192068	−	0.110891i
$201$	−13.2508	−	18.0545i	−0.934637	−	1.27347i
$202$	−9.47939	+	5.47293i	−0.666968	+	0.385074i
$203$	−20.0025	+	5.07968i	−1.40390	+	0.356524i
$204$	−7.03407	+	0.773601i	−0.492484	+	0.0541629i
$205$	−20.2768			−1.41620
$206$	1.38694	+	2.40226i	0.0966330	+	0.167373i
$207$	0.898558	+	4.03572i	0.0624541	+	0.280502i
$208$	−3.41477	−	1.15729i	−0.236772	−	0.0802437i
$209$	8.94898			0.619014
$210$	−2.15174	+	12.8932i	−0.148484	+	0.889718i
$211$	2.78247	−	4.81937i	0.191553	−	0.331779i	−0.754212	−	0.656631i	$-0.771981\pi$
$211$	2.78247	−	4.81937i	0.191553	−	0.331779i	0.945765	+	0.324852i	$0.105314\pi$
$212$	5.80600	+	3.35210i	0.398758	+	0.230223i
$213$	−9.13465	+	6.70421i	−0.625896	+	0.459365i
$214$	−0.895779			−0.0612342
$215$	14.3347	−	24.8284i	0.977618	−	1.69328i
$216$	1.67697	+	4.91811i	0.114104	+	0.334635i
$217$	−7.24808	+	1.84066i	−0.492032	+	0.124952i
$218$	9.97726	+	5.76038i	0.675746	+	0.390142i
$219$	3.97152	+	1.74535i	0.268371	+	0.117940i
$220$	−5.09290	−	2.94039i	−0.343364	−	0.198241i
$221$	−13.9514	−	4.72824i	−0.938475	−	0.318056i
$222$	1.20369	+	10.9448i	0.0807867	+	0.734564i
$223$	−1.62683	−	0.939253i	−0.108941	−	0.0628971i	0.444540	−	0.895759i	$-0.353367\pi$
$223$	−1.62683	−	0.939253i	−0.108941	−	0.0628971i	−0.553480	+	0.832862i	$0.686701\pi$
$224$	1.84615	+	1.89518i	0.123351	+	0.126627i
$225$	−2.82128	+	8.97648i	−0.188085	+	0.598432i
$226$	1.71090	+	2.96337i	0.113808	+	0.197121i
$227$	−10.7630			−0.714368			−0.357184	−	0.934034i	$-0.616263\pi$
$227$	−10.7630			−0.714368			−0.357184	+	0.934034i	$0.616263\pi$
$228$	−6.88293	−	3.02482i	−0.455833	−	0.200323i
$229$	4.85743	−	2.80444i	0.320988	−	0.185323i	−0.330845	−	0.943685i	$-0.607334\pi$
$229$	4.85743	−	2.80444i	0.320988	−	0.185323i	0.651833	+	0.758363i	$0.274000\pi$
$230$	1.96560	+	3.40451i	0.129608	+	0.224487i
$231$	−1.55521	+	9.31883i	−0.102325	+	0.613134i
$232$	−3.90011	+	6.75519i	−0.256055	+	0.443500i
$233$	−12.8530	+	7.42068i	−0.842027	+	0.486145i	−0.857953	−	0.513729i	$-0.828264\pi$
$233$	−12.8530	+	7.42068i	−0.842027	+	0.486145i	0.0159256	+	0.999873i	$0.494931\pi$
$234$	−1.16250	+	10.7540i	−0.0759947	+	0.703011i
$235$	10.4170	−	18.0428i	0.679532	−	1.17698i
$236$	10.8441			0.705888
$237$	−14.5265	−	19.7927i	−0.943596	−	1.28567i
$238$	7.54266	+	7.74298i	0.488918	+	0.501903i
$239$		−	12.7315i		−	0.823530i	−0.911290	−	0.411765i	$-0.864912\pi$
$239$		−	12.7315i		−	0.823530i	0.911290	−	0.411765i	$-0.135088\pi$
$240$	2.92323	+	3.98298i	0.188694	+	0.257100i
$241$		−	3.02382i		−	0.194782i	−0.995246	−	0.0973908i	$-0.968950\pi$
$241$		−	3.02382i		−	0.194782i	0.995246	−	0.0973908i	$-0.0310497\pi$
$242$	5.84529	+	3.37478i	0.375749	+	0.216939i
$243$	13.3083	−	8.11722i	0.853727	−	0.520720i
$244$	−3.41234	−	1.97012i	−0.218453	−	0.126124i
$245$	17.5477	−	9.52698i	1.12108	−	0.608656i
$246$	11.2719	+	4.95365i	0.718673	+	0.315833i
$247$	−10.3249	−	11.7616i	−0.656955	−	0.748373i
$248$	−1.41324	+	2.44780i	−0.0897407	+	0.155435i
$249$	17.7187	−	1.94869i	1.12288	−	0.123493i
$250$		−	5.31564i		−	0.336190i
$251$	11.9432	+	20.6862i	0.753849	+	1.30570i	0.945945	+	0.324328i	$0.105138\pi$
$251$	11.9432	+	20.6862i	0.753849	+	1.30570i	−0.192096	+	0.981376i	$0.561528\pi$
$252$	4.34599	−	6.64172i	0.273772	−	0.418389i
$253$	1.42067	+	2.46067i	0.0893168	+	0.154701i
$254$	−10.0591	−	5.80763i	−0.631164	−	0.364403i
$255$	11.9432	+	16.2729i	0.747911	+	1.01905i
$256$	1.00000			0.0625000
$257$	11.0814			0.691241			0.345620	−	0.938374i	$-0.387669\pi$
$257$	11.0814			0.691241			0.345620	+	0.938374i	$0.387669\pi$
$258$	−14.0343	+	10.3002i	−0.873737	+	0.641263i
$259$	12.0478	−	11.7361i	0.748614	−	0.729246i
$260$	2.01139	+	10.0860i	0.124741	+	0.625510i
$261$	22.3240	+	7.01637i	1.38182	+	0.434303i
$262$	1.05095	−	0.606766i	0.0649278	−	0.0374861i
$263$	−3.54575	+	2.04714i	−0.218641	+	0.126232i	−0.605321	−	0.795982i	$-0.706955\pi$
$263$	−3.54575	+	2.04714i	−0.218641	+	0.126232i	0.386680	+	0.922214i	$0.373622\pi$
$264$	2.11282	+	2.87877i	0.130035	+	0.177176i
$265$		−	19.1234i		−	1.17474i
$266$	2.82674	+	11.1310i	0.173319	+	0.682486i
$267$	−10.3833	+	1.14195i	−0.635448	+	0.0698859i
$268$	6.46495	+	11.1976i	0.394910	+	0.684004i
$269$	18.1762			1.10822			0.554112	−	0.832442i	$-0.313058\pi$
$269$	18.1762			1.10822			0.554112	+	0.832442i	$0.313058\pi$
$270$	9.75742	−	11.1569i	0.593818	−	0.678990i
$271$		−	14.3605i		−	0.872337i	−0.899865	−	0.436169i	$-0.856335\pi$
$271$		−	14.3605i		−	0.872337i	0.899865	−	0.436169i	$-0.143665\pi$
$272$	4.08561			0.247726
$273$	14.0420	−	8.70757i	0.849862	−	0.527006i
$274$	−9.46777			−0.571969
$275$			6.46632i			0.389934i
$276$	−0.260955	−	2.37277i	−0.0157077	−	0.142824i
$277$	5.83961			0.350868			0.175434	−	0.984491i	$-0.443867\pi$
$277$	5.83961			0.350868			0.175434	+	0.984491i	$0.443867\pi$
$278$	−3.27085	−	5.66528i	−0.196172	−	0.339781i
$279$	8.08929	+	2.54244i	0.484293	+	0.152212i
$280$	2.04863	−	7.26350i	0.122429	−	0.434077i
$281$			14.5423i			0.867519i	0.901029	+	0.433760i	$0.142813\pi$
$281$			14.5423i			0.867519i	−0.901029	+	0.433760i	$0.857187\pi$
$282$	−10.1987	+	7.48517i	−0.607326	+	0.445735i
$283$	4.43257	−	2.55915i	0.263489	−	0.152126i	−0.362436	−	0.932009i	$-0.618055\pi$
$283$	4.43257	−	2.55915i	0.263489	−	0.152126i	0.625925	+	0.779883i	$0.284722\pi$
$284$	5.66543	−	3.27094i	0.336181	−	0.194094i
$285$	2.34441	+	21.3169i	0.138871	+	1.26271i
$286$	1.45377	+	7.28988i	0.0859630	+	0.431059i
$287$	−4.62926	−	18.2289i	−0.273257	−	1.07602i
$288$	−0.651988	−	2.92829i	−0.0384188	−	0.172551i
$289$	−0.307794			−0.0181055
$290$	22.2497			1.30655
$291$	25.5193	−	18.7294i	1.49597	−	1.09794i
$292$	−2.16906	−	1.25231i	−0.126935	−	0.0732857i
$293$	15.1987	+	26.3249i	0.887917	+	1.53792i	0.842334	+	0.538957i	$0.181181\pi$
$293$	15.1987	+	26.3249i	0.887917	+	1.53792i	0.0455833	+	0.998961i	$0.485485\pi$
$294$	−12.0823	+	1.00915i	−0.704653	+	0.0588546i
$295$	−15.4661	−	26.7880i	−0.900469	−	1.55966i
$296$		−	6.35706i		−	0.369497i
$297$	7.05235	−	8.06388i	0.409219	−	0.467914i
$298$	9.87585	−	17.1055i	0.572093	−	0.990893i
$299$	1.59496	−	4.70618i	0.0922387	−	0.272165i
$300$	2.18566	−	4.97344i	0.126189	−	0.287142i
$301$	25.5934	+	7.21850i	1.47518	+	0.416067i
$302$	19.1436	+	11.0526i	1.10159	+	0.636003i
$303$	−11.2175	−	15.2841i	−0.644427	−	0.878048i
$304$	3.75913	+	2.17033i	0.215601	+	0.124477i
$305$			11.2393i			0.643561i
$306$	−2.66377	−	11.9639i	−0.152278	−	0.683929i
$307$			1.17043i			0.0667999i	0.999442	+	0.0333999i	$0.0106335\pi$
$307$			1.17043i			0.0667999i	−0.999442	+	0.0333999i	$0.989366\pi$
$308$	1.48069	−	5.24982i	0.0843700	−	0.299136i
$309$	−3.87328	+	2.84272i	−0.220343	+	0.161717i
$310$	8.06238			0.457912
$311$	−1.48661	+	2.57489i	−0.0842980	+	0.146008i	−0.905092	−	0.425216i	$-0.860198\pi$
$311$	−1.48661	+	2.57489i	−0.0842980	+	0.146008i	0.820794	+	0.571225i	$0.193531\pi$
$312$	1.34589	−	6.09824i	0.0761962	−	0.345245i
$313$	−10.5964	+	6.11782i	−0.598942	+	0.345799i	−0.768625	−	0.639699i	$-0.779059\pi$
$313$	−10.5964	+	6.11782i	−0.598942	+	0.345799i	0.169683	+	0.985499i	$0.445726\pi$
$314$	−7.93232	+	13.7392i	−0.447647	+	0.775346i
$315$	−22.6053	−	1.26329i	−1.27367	−	0.0711782i
$316$	7.08737	+	12.2757i	0.398696	+	0.690561i
$317$	−9.60122	+	5.54327i	−0.539258	+	0.311341i	−0.744778	−	0.667312i	$-0.767445\pi$
$317$	−9.60122	+	5.54327i	−0.539258	+	0.311341i	0.205520	+	0.978653i	$0.434111\pi$
$318$	−4.67185	+	10.6307i	−0.261985	+	0.596142i
$319$	16.0814			0.900386
$320$	−1.42622	−	2.47029i	−0.0797284	−	0.138094i
$321$	−0.169614	−	1.54224i	−0.00946691	−	0.0860792i
$322$	−2.61191	+	2.54433i	−0.145556	+	0.141790i
$323$	15.3583	+	8.86714i	0.854560	+	0.493381i
$324$	−8.14982	+	3.81843i	−0.452768	+	0.212135i
$325$	8.49866	−	7.46051i	0.471421	−	0.413834i
$326$	3.23439	+	1.86738i	0.179136	+	0.103424i
$327$	−8.02829	+	18.2683i	−0.443966	+	1.01024i
$328$	−6.15620	−	3.55429i	−0.339920	−	0.196253i
$329$	18.5988	+	5.24569i	1.02538	+	0.289204i
$330$	4.09805	−	9.32506i	0.225590	−	0.513327i
$331$	13.4967	−	23.3769i	0.741844	−	1.28491i	−0.209811	−	0.977742i	$-0.567285\pi$
$331$	13.4967	−	23.3769i	0.741844	−	1.28491i	0.951655	−	0.307169i	$-0.0993818\pi$
$332$	−10.2916			−0.564825
$333$	−18.6154	+	4.14473i	−1.02012	+	0.227130i
$334$	−13.7406	−	7.93312i	−0.751850	−	0.434081i
$335$	18.4410	−	31.9407i	1.00754	−	1.74511i
$336$	−2.91332	+	3.53731i	−0.158934	+	0.192976i
$337$	4.24529			0.231256			0.115628	−	0.993293i	$-0.463112\pi$
$337$	4.24529			0.231256			0.115628	+	0.993293i	$0.463112\pi$
$338$	7.90377	−	10.3214i	0.429908	−	0.561408i
$339$	−4.77799	+	3.50672i	−0.259505	+	0.190459i
$340$	−5.82700	−	10.0927i	−0.316013	−	0.547351i
$341$	5.82723			0.315562
$342$	3.90447	−	12.4229i	0.211130	−	0.671752i
$343$	12.5710	+	13.6004i	0.678768	+	0.734353i
$344$	8.70425	−	5.02540i	0.469302	−	0.270951i
$345$	−5.48927	+	4.02875i	−0.295532	+	0.216900i
$346$	4.83698	+	2.79263i	0.260038	+	0.150133i
$347$		−	7.97045i		−	0.427876i	−0.976847	−	0.213938i	$-0.931371\pi$
$347$		−	7.97045i		−	0.427876i	0.976847	−	0.213938i	$-0.0686291\pi$
$348$	−12.3687	−	5.43563i	−0.663031	−	0.291380i
$349$	−5.06976	−	2.92703i	−0.271378	−	0.156680i	0.358136	−	0.933670i	$-0.383413\pi$
$349$	−5.06976	−	2.92703i	−0.271378	−	0.156680i	−0.629514	+	0.776989i	$0.716746\pi$
$350$	−8.04301	+	2.04254i	−0.429917	+	0.109178i
$351$	−18.7350	+	0.0348107i	−0.999998	+	0.00185806i
$352$	−1.03083	−	1.78545i	−0.0549434	−	0.0951648i
$353$	−7.12956	−	12.3488i	−0.379468	−	0.657258i	0.611517	−	0.791231i	$-0.290560\pi$
$353$	−7.12956	−	12.3488i	−0.379468	−	0.657258i	−0.990985	+	0.133974i	$0.957226\pi$
$354$	2.05330	+	18.6699i	0.109132	+	0.992294i
$355$	−16.1603	−	9.33018i	−0.857702	−	0.495194i
$356$	6.03095			0.319639
$357$	−11.9027	+	14.4521i	−0.629956	+	0.764885i
$358$	0.132472	+	0.229448i	0.00700134	+	0.0121267i
$359$	−7.12892	+	4.11588i	−0.376250	+	0.217228i	−0.676185	−	0.736731i	$-0.736368\pi$
$359$	−7.12892	+	4.11588i	−0.376250	+	0.217228i	0.299935	+	0.953959i	$0.403035\pi$
$360$	−6.30387	+	5.78701i	−0.332243	+	0.305002i
$361$	−0.0793021	−	0.137355i	−0.00417379	−	0.00722922i
$362$	2.90040			0.152442
$363$	−4.70347	+	10.7027i	−0.246868	+	0.561744i
$364$	−8.60816	+	4.11091i	−0.451190	+	0.215470i
$365$			7.14428i			0.373949i
$366$	2.74577	−	6.24796i	0.143524	−	0.326586i
$367$	20.7299	−	11.9684i	1.08209	−	0.624745i	0.150631	−	0.988590i	$-0.451870\pi$
$367$	20.7299	−	11.9684i	1.08209	−	0.624745i	0.931459	+	0.363845i	$0.118536\pi$
$368$			1.37818i			0.0718427i
$369$	−6.39423	+	20.3445i	−0.332870	+	1.05909i
$370$	−15.7038	+	9.06660i	−0.816402	+	0.471350i
$371$	17.1919	−	4.36592i	0.892560	−	0.226667i
$372$	−4.48190	−	1.96964i	−0.232375	−	0.102121i
$373$	−10.6761	+	18.4915i	−0.552786	+	0.957453i	0.445287	+	0.895388i	$0.353102\pi$
$373$	−10.6761	+	18.4915i	−0.552786	+	0.957453i	−0.998072	+	0.0620645i	$0.980232\pi$
$374$	−4.21157	−	7.29465i	−0.217775	−	0.377197i
$375$	9.15177	−	1.00650i	0.472596	−	0.0519756i
$376$	6.32538	−	3.65196i	0.326207	−	0.188336i
$377$	−18.5539	−	21.1357i	−0.955574	−	1.08855i
$378$	12.2577	+	6.22476i	0.630470	+	0.320167i
$379$	−7.80867	+	13.5250i	−0.401104	+	0.694733i	−0.993859	−	0.110650i	$-0.964707\pi$
$379$	−7.80867	+	13.5250i	−0.401104	+	0.694733i	0.592755	+	0.805383i	$0.298040\pi$
$380$		−	12.3815i		−	0.635159i
$381$	8.09415	−	18.4181i	0.414676	−	0.943589i
$382$	−0.294084	+	0.509369i	−0.0150466	+	0.0260616i
$383$	4.82625	−	8.35931i	0.246610	−	0.427141i	−0.715973	−	0.698128i	$-0.754017\pi$
$383$	4.82625	−	8.35931i	0.246610	−	0.427141i	0.962583	+	0.270987i	$0.0873501\pi$
$384$	0.189348	+	1.72167i	0.00966261	+	0.0878586i
$385$	−15.0804	+	3.82970i	−0.768568	+	0.195179i
$386$	16.1805	−	9.34180i	0.823564	−	0.475485i
$387$	−20.3909	−	22.2121i	−1.03653	−	1.12910i
$388$	−15.8274	+	9.13794i	−0.803513	+	0.463909i
$389$	−7.14154	−	4.12317i	−0.362090	−	0.209053i	0.307907	−	0.951416i	$-0.400371\pi$
$389$	−7.14154	−	4.12317i	−0.362090	−	0.209053i	−0.669997	+	0.742364i	$0.733705\pi$
$390$	−16.9840	+	5.37271i	−0.860018	+	0.272058i
$391$			5.63071i			0.284757i
$392$	6.99760	+	0.183445i	0.353432	+	0.00926537i
$393$	1.24364	+	1.69450i	0.0627336	+	0.0854761i
$394$	11.7248	−	20.3079i	0.590687	−	1.02310i
$395$	20.2164	−	35.0157i	1.01720	−	1.76183i
$396$	−4.55623	+	4.18267i	−0.228959	+	0.210187i
$397$	−8.95426	−	5.16974i	−0.449401	−	0.259462i	0.258176	−	0.966098i	$-0.416879\pi$
$397$	−8.95426	−	5.16974i	−0.449401	−	0.259462i	−0.707577	+	0.706636i	$0.750212\pi$
$398$	−18.7498			−0.939840
$399$	−18.6287	+	6.97434i	−0.932601	+	0.349154i
$400$	−1.56823	+	2.71626i	−0.0784116	+	0.135813i
$401$			25.7432i			1.28555i	0.766053	+	0.642777i	$0.222218\pi$
$401$			25.7432i			1.28555i	−0.766053	+	0.642777i	$0.777782\pi$
$402$	−18.0545	+	13.2508i	−0.900477	+	0.660888i
$403$	−6.72315	−	7.65870i	−0.334904	−	0.381507i
$404$	5.47293	+	9.47939i	0.272288	+	0.471617i
$405$	21.0561	+	14.6865i	1.04629	+	0.729779i
$406$	5.07968	+	20.0025i	0.252100	+	0.992709i
$407$	−11.3502	+	6.55305i	−0.562609	+	0.324823i
$408$	0.773601	+	7.03407i	0.0382989	+	0.348238i
$409$			34.6570i			1.71368i	0.515584	+	0.856839i	$0.327575\pi$
$409$			34.6570i			1.71368i	−0.515584	+	0.856839i	$0.672425\pi$
$410$			20.2768i			1.00140i
$411$	−1.79270	−	16.3004i	−0.0884273	−	0.804038i
$412$	2.40226	−	1.38694i	0.118351	−	0.0683298i
$413$	20.5515	−	20.0198i	1.01127	−	0.985109i
$414$	4.03572	−	0.898558i	0.198345	−	0.0441617i
$415$	14.6781	+	25.4233i	0.720521	+	1.24798i
$416$	−1.15729	+	3.41477i	−0.0567408	+	0.167423i
$417$	9.13441	−	6.70403i	0.447314	−	0.328298i
$418$		−	8.94898i		−	0.437709i
$419$	−18.0720	+	31.3016i	−0.882873	+	1.52918i	−0.0347413	+	0.999396i	$0.511061\pi$
$419$	−18.0720	+	31.3016i	−0.882873	+	1.52918i	−0.848132	+	0.529785i	$0.822273\pi$
$420$	12.8932	+	2.15174i	0.629126	+	0.104994i
$421$	−19.0053			−0.926260			−0.463130	−	0.886290i	$-0.653274\pi$
$421$	−19.0053			−0.926260			−0.463130	+	0.886290i	$0.653274\pi$
$422$	−4.81937	−	2.78247i	−0.234603	−	0.135448i
$423$	−14.8181	−	16.1416i	−0.720481	−	0.784829i
$424$	3.35210	−	5.80600i	0.162792	−	0.281964i
$425$	−6.40719	+	11.0976i	−0.310794	+	0.538311i
$426$	6.70421	+	9.13465i	0.324820	+	0.442575i
$427$	−10.1041	+	2.56597i	−0.488974	+	0.124176i
$428$			0.895779i			0.0432991i
$429$	−12.2755	+	3.88323i	−0.592666	+	0.187484i
$430$	−24.8284	−	14.3347i	−1.19733	−	0.691281i
$431$	−31.7678	+	18.3411i	−1.53020	+	0.883461i	−0.530848	+	0.847467i	$0.678126\pi$
$431$	−31.7678	+	18.3411i	−1.53020	+	0.883461i	−0.999352	+	0.0359942i	$0.988540\pi$
$432$	4.91811	−	1.67697i	0.236622	−	0.0806835i
$433$	−4.92583	+	2.84393i	−0.236720	+	0.136670i	−0.613668	−	0.789564i	$-0.710307\pi$
$433$	−4.92583	+	2.84393i	−0.236720	+	0.136670i	0.376948	+	0.926234i	$0.376973\pi$
$434$	1.84066	+	7.24808i	0.0883547	+	0.347919i
$435$	4.21294	+	38.3067i	0.201995	+	1.83667i
$436$	5.76038	−	9.97726i	0.275872	−	0.477824i
$437$	−2.99111	+	5.18076i	−0.143084	+	0.247829i
$438$	1.74535	−	3.97152i	0.0833962	−	0.189767i
$439$			19.8235i			0.946123i	0.881029	+	0.473061i	$0.156851\pi$
$439$			19.8235i			0.946123i	−0.881029	+	0.473061i	$0.843149\pi$
$440$	−2.94039	+	5.09290i	−0.140178	+	0.242795i
$441$	−4.02517	−	20.6106i	−0.191675	−	0.981459i
$442$	−4.72824	+	13.9514i	−0.224899	+	0.663602i
$443$	−0.526014	+	0.303694i	−0.0249917	+	0.0144290i	−0.512444	−	0.858721i	$-0.671260\pi$
$443$	−0.526014	+	0.303694i	−0.0249917	+	0.0144290i	0.487452	+	0.873150i	$0.337926\pi$
$444$	10.9448	−	1.20369i	0.519415	−	0.0571248i
$445$	−8.60148	−	14.8982i	−0.407749	−	0.706243i
$446$	−0.939253	+	1.62683i	−0.0444749	+	0.0770328i
$447$	31.3199	+	13.7641i	1.48138	+	0.651018i
$448$	1.89518	−	1.84615i	0.0895390	−	0.0872225i
$449$	−0.384292	+	0.221871i	−0.0181359	+	0.0104707i	−0.509041	−	0.860743i	$-0.670000\pi$
$449$	−0.384292	+	0.221871i	−0.0181359	+	0.0104707i	0.490905	+	0.871213i	$0.336666\pi$
$450$	8.97648	+	2.82128i	0.423155	+	0.132996i
$451$			14.6555i			0.690099i
$452$	2.96337	−	1.71090i	0.139385	−	0.0804741i
$453$	−15.4041	+	35.0517i	−0.723746	+	1.64687i
$454$			10.7630i			0.505135i
$455$	22.4323	+	15.4016i	1.05164	+	0.722038i
$456$	−3.02482	+	6.88293i	−0.141650	+	0.322323i
$457$	−28.5798			−1.33691			−0.668453	−	0.743754i	$-0.733043\pi$
$457$	−28.5798			−1.33691			−0.668453	+	0.743754i	$0.733043\pi$
$458$	−2.80444	−	4.85743i	−0.131043	−	0.226973i
$459$	20.0935	−	6.85146i	0.937882	−	0.319799i
$460$	3.40451	−	1.96560i	0.158736	−	0.0916464i
$461$	−18.2440	−	31.5996i	−0.849709	−	1.47174i	−0.881468	−	0.472243i	$-0.843444\pi$
$461$	−18.2440	−	31.5996i	−0.849709	−	1.47174i	0.0317595	−	0.999496i	$-0.489889\pi$
$462$	9.31883	+	1.55521i	0.433551	+	0.0723550i
$463$	−38.3097			−1.78040			−0.890201	−	0.455567i	$-0.849436\pi$
$463$	−38.3097			−1.78040			−0.890201	+	0.455567i	$0.849436\pi$
$464$	6.75519	+	3.90011i	0.313602	+	0.181058i
$465$	1.52659	+	13.8808i	0.0707940	+	0.643705i
$466$	7.42068	+	12.8530i	0.343756	+	0.595403i
$467$	−11.2682	−	19.5171i	−0.521431	−	0.903145i	−0.999689	−	0.0249257i	$-0.992065\pi$
$467$	−11.2682	−	19.5171i	−0.521431	−	0.903145i	0.478258	−	0.878219i	$-0.341268\pi$
$468$	10.7540	+	1.16250i	0.497104	+	0.0537364i
$469$	32.9248	+	9.28628i	1.52033	+	0.428801i
$470$	−18.0428	−	10.4170i	−0.832254	−	0.480502i
$471$	−25.1563	−	11.0554i	−1.15914	−	0.509404i
$472$		−	10.8441i		−	0.499138i
$473$	−17.9452	−	10.3607i	−0.825121	−	0.476384i
$474$	−19.7927	+	14.5265i	−0.909108	+	0.667223i
$475$	−11.7904	+	6.80718i	−0.540980	+	0.312335i
$476$	7.74298	−	7.54266i	0.354899	−	0.345717i
$477$	−19.1872	−	6.03048i	−0.878522	−	0.276117i
$478$	−12.7315			−0.582324
$479$	−9.33625	−	16.1709i	−0.426584	−	0.738865i	0.569983	−	0.821657i	$-0.306950\pi$
$479$	−9.33625	−	16.1709i	−0.426584	−	0.738865i	−0.996567	+	0.0827914i	$0.973616\pi$
$480$	3.98298	−	2.92323i	0.181797	−	0.133427i
$481$	21.7079	+	7.35697i	0.989796	+	0.335449i
$482$	−3.02382			−0.137731
$483$	−4.87506	−	4.01508i	−0.221823	−	0.182692i
$484$	3.37478	−	5.84529i	0.153399	−	0.265695i
$485$	45.1468	+	26.0655i	2.05001	+	1.18357i
$486$	−8.11722	−	13.3083i	−0.368205	−	0.603676i
$487$	−1.56070			−0.0707220			−0.0353610	−	0.999375i	$-0.511258\pi$
$487$	−1.56070			−0.0707220			−0.0353610	+	0.999375i	$0.511258\pi$
$488$	−1.97012	+	3.41234i	−0.0891830	+	0.154469i
$489$	−2.60258	+	5.92214i	−0.117693	+	0.267808i
$490$	−9.52698	−	17.5477i	−0.430385	−	0.792726i
$491$	−23.0262	−	13.2942i	−1.03916	−	0.599959i	−0.119564	−	0.992826i	$-0.538150\pi$
$491$	−23.0262	−	13.2942i	−1.03916	−	0.599959i	−0.919595	+	0.392868i	$0.871483\pi$
$492$	4.95365	−	11.2719i	0.223328	−	0.508179i
$493$	27.5991	+	15.9343i	1.24300	+	0.717646i
$494$	−11.7616	+	10.3249i	−0.529180	+	0.464538i
$495$	16.8306	+	5.28981i	0.756480	+	0.237759i
$496$	2.44780	+	1.41324i	0.109909	+	0.0634562i
$497$	4.69838	−	16.6583i	0.210751	−	0.747225i
$498$	−1.94869	−	17.7187i	−0.0873229	−	0.793996i
$499$	−2.95848	−	5.12424i	−0.132440	−	0.229392i	0.792177	−	0.610292i	$-0.208948\pi$
$499$	−2.95848	−	5.12424i	−0.132440	−	0.229392i	−0.924617	+	0.380899i	$0.875614\pi$
$500$	−5.31564			−0.237723
$501$	11.0565	−	25.1588i	0.493967	−	1.12401i
$502$	20.6862	−	11.9432i	0.923272	−	0.533052i
$503$	21.6022	+	37.4160i	0.963193	+	1.66830i	0.714395	+	0.699743i	$0.246702\pi$
$503$	21.6022	+	37.4160i	0.963193	+	1.66830i	0.248798	+	0.968555i	$0.419964\pi$
$504$	−6.64172	−	4.34599i	−0.295846	−	0.193586i
$505$	15.6113	−	27.0395i	0.694692	−	1.20324i
$506$	2.46067	−	1.42067i	0.109390	−	0.0631565i
$507$	19.2665	+	11.6534i	0.855657	+	0.517544i
$508$	−5.80763	+	10.0591i	−0.257672	+	0.446300i
$509$	−33.3363			−1.47761			−0.738803	−	0.673921i	$-0.764609\pi$
$509$	−33.3363			−1.47761			−0.738803	+	0.673921i	$0.764609\pi$
$510$	16.2729	−	11.9432i	0.720576	−	0.528853i
$511$	−6.42271	+	1.63106i	−0.284124	+	0.0721539i
$512$		−	1.00000i		−	0.0441942i
$513$	22.1274	+	4.36997i	0.976948	+	0.192939i
$514$		−	11.0814i		−	0.488781i
$515$	−6.85232	−	3.95619i	−0.301949	−	0.174330i
$516$	10.3002	+	14.0343i	0.453442	+	0.617826i
$517$	−13.0408	−	7.52910i	−0.573533	−	0.331130i
$518$	−11.7361	−	12.0478i	−0.515655	−	0.529350i
$519$	−3.89212	+	8.85646i	−0.170845	+	0.388755i
$520$	10.0860	−	2.01139i	0.442302	−	0.0882051i
$521$	3.50547	−	6.07166i	0.153578	−	0.266004i	−0.778963	−	0.627070i	$-0.784254\pi$
$521$	3.50547	−	6.07166i	0.153578	−	0.266004i	0.932540	+	0.361066i	$0.117587\pi$
$522$	7.01637	−	22.3240i	0.307098	−	0.977096i
$523$		−	18.2581i		−	0.798370i	−0.916870	−	0.399185i	$-0.869293\pi$
$523$		−	18.2581i		−	0.798370i	0.916870	−	0.399185i	$-0.130707\pi$
$524$	−0.606766	−	1.05095i	−0.0265067	−	0.0459109i
$525$	−5.03950	−	13.4607i	−0.219942	−	0.587471i
$526$	2.04714	+	3.54575i	0.0892596	+	0.154602i
$527$	10.0008	+	5.77394i	0.435640	+	0.251517i
$528$	2.87877	−	2.11282i	0.125282	−	0.0919487i
$529$	21.1006			0.917418
$530$	−19.1234			−0.830666
$531$	−31.7546	+	7.07020i	−1.37803	+	0.306821i
$532$	11.1310	−	2.82674i	0.482590	−	0.122555i
$533$	19.2616	−	16.9087i	0.834313	−	0.732397i
$534$	1.14195	+	10.3833i	0.0494168	+	0.449329i
$535$	2.21284	−	1.27758i	0.0956693	−	0.0552347i
$536$	11.1976	−	6.46495i	0.483664	−	0.279244i
$537$	−0.369950	+	0.271518i	−0.0159645	+	0.0117169i
$538$		−	18.1762i		−	0.783632i
$539$	−6.88580	−	12.6830i	−0.296592	−	0.546294i
$540$	−11.1569	−	9.75742i	−0.480118	−	0.419892i
$541$	7.10217	+	12.3013i	0.305346	+	0.528875i	0.977338	−	0.211683i	$-0.0678944\pi$
$541$	7.10217	+	12.3013i	0.305346	+	0.528875i	−0.671992	+	0.740558i	$0.734561\pi$
$542$	−14.3605			−0.616836
$543$	0.549183	+	4.99353i	0.0235677	+	0.214293i
$544$		−	4.08561i		−	0.175169i
$545$	−32.8624			−1.40767
$546$	−8.70757	−	14.0420i	−0.372650	−	0.600943i
$547$	1.17690			0.0503208			0.0251604	−	0.999683i	$-0.491990\pi$
$547$	1.17690			0.0503208			0.0251604	+	0.999683i	$0.491990\pi$
$548$			9.46777i			0.404443i
$549$	11.2768	+	3.54427i	0.481283	+	0.151266i
$550$	6.46632			0.275725
$551$	16.9291	+	29.3220i	0.721204	+	1.24916i
$552$	−2.37277	+	0.260955i	−0.100992	+	0.0111070i
$553$	36.0946	+	10.1803i	1.53490	+	0.432911i
$554$		−	5.83961i		−	0.248101i
$555$	−18.5832	−	25.3200i	−0.788812	−	1.07478i
$556$	−5.66528	+	3.27085i	−0.240261	+	0.138715i
$557$	26.2819	−	15.1739i	1.11360	−	0.642938i	0.173842	−	0.984774i	$-0.444382\pi$
$557$	26.2819	−	15.1739i	1.11360	−	0.642938i	0.939760	+	0.341836i	$0.111049\pi$
$558$	2.54244	−	8.08929i	0.107630	−	0.342447i
$559$	7.08726	+	35.5389i	0.299759	+	1.50314i
$560$	−7.26350	−	2.04863i	−0.306939	−	0.0865705i
$561$	11.7615	−	8.63216i	0.496572	−	0.364450i
$562$	14.5423			0.613429
$563$	−17.4226			−0.734274			−0.367137	−	0.930167i	$-0.619662\pi$
$563$	−17.4226			−0.734274			−0.367137	+	0.930167i	$0.619662\pi$
$564$	7.48517	+	10.1987i	0.315183	+	0.429444i
$565$	−8.45287	−	4.88026i	−0.355615	−	0.205314i
$566$	−2.55915	−	4.43257i	−0.107569	−	0.186315i
$567$	−8.39601	+	22.2824i	−0.352599	+	0.935774i
$568$	−3.27094	−	5.66543i	−0.137245	−	0.237716i
$569$		−	42.0382i		−	1.76233i	−0.472805	−	0.881167i	$-0.656759\pi$
$569$		−	42.0382i		−	1.76233i	0.472805	−	0.881167i	$-0.343241\pi$
$570$	21.3169	−	2.34441i	0.892867	−	0.0981967i
$571$	−17.8452	+	30.9087i	−0.746797	+	1.29349i	0.202553	+	0.979271i	$0.435076\pi$
$571$	−17.8452	+	30.9087i	−0.746797	+	1.29349i	−0.949350	+	0.314219i	$0.898257\pi$
$572$	7.28988	−	1.45377i	0.304805	−	0.0607850i
$573$	−0.932649	−	0.409868i	−0.0389620	−	0.0171225i
$574$	−18.2289	+	4.62926i	−0.760859	+	0.193222i
$575$	−3.74350	−	2.16131i	−0.156115	−	0.0901328i
$576$	−2.92829	+	0.651988i	−0.122012	+	0.0271662i
$577$	−34.3730	−	19.8453i	−1.43097	−	0.826170i	−0.433773	−	0.901022i	$-0.642818\pi$
$577$	−34.3730	−	19.8453i	−1.43097	−	0.826170i	−0.997195	+	0.0748524i	$0.976151\pi$
$578$			0.307794i			0.0128025i
$579$	19.1472	+	26.0886i	0.795732	+	1.08420i
$580$		−	22.2497i		−	0.923870i
$581$	−19.5045	+	18.9999i	−0.809182	+	0.788247i
$582$	−18.7294	−	25.5193i	−0.776358	−	1.05781i
$583$	−13.8218			−0.572439
$584$	−1.25231	+	2.16906i	−0.0518208	+	0.0897563i
$585$	−12.4659	−	28.2235i	−0.515402	−	1.16690i
$586$	26.3249	−	15.1987i	1.08747	−	0.627852i
$587$	5.31225	−	9.20108i	0.219260	−	0.379769i	−0.735322	−	0.677718i	$-0.762969\pi$
$587$	5.31225	−	9.20108i	0.219260	−	0.379769i	0.954582	+	0.297949i	$0.0963024\pi$
$588$	1.00915	+	12.0823i	0.0416165	+	0.498265i
$589$	6.13440	+	10.6251i	0.252763	+	0.437799i
$590$	−26.7880	+	15.4661i	−1.10285	+	0.636728i
$591$	37.1836	+	16.3410i	1.52953	+	0.672177i
$592$	−6.35706			−0.261274
$593$	17.5065	+	30.3222i	0.718907	+	1.24518i	0.961433	+	0.275038i	$0.0886904\pi$
$593$	17.5065	+	30.3222i	0.718907	+	1.24518i	−0.242527	+	0.970145i	$0.577976\pi$
$594$	−8.06388	−	7.05235i	−0.330865	−	0.289362i
$595$	−29.6758	−	8.36992i	−1.21659	−	0.343133i
$596$	−17.1055	−	9.87585i	−0.700667	−	0.404531i
$597$	−3.55022	−	32.2809i	−0.145301	−	1.32117i
$598$	−4.70618	−	1.59496i	−0.192450	−	0.0652226i
$599$	8.65396	+	4.99637i	0.353591	+	0.204146i	0.666266	−	0.745714i	$-0.267892\pi$
$599$	8.65396	+	4.99637i	0.353591	+	0.204146i	−0.312675	+	0.949860i	$0.601225\pi$
$600$	−4.97344	−	2.18566i	−0.203040	−	0.0892293i
$601$	−6.92945	−	4.00072i	−0.282658	−	0.163193i	0.351968	−	0.936012i	$-0.385513\pi$
$601$	−6.92945	−	4.00072i	−0.282658	−	0.163193i	−0.634626	+	0.772819i	$0.718846\pi$
$602$	7.21850	−	25.5934i	0.294204	−	1.04311i
$603$	−26.2320	−	28.5749i	−1.06825	−	1.16366i
$604$	11.0526	−	19.1436i	0.449722	−	0.778941i
$605$	−19.2528			−0.782737
$606$	−15.2841	+	11.2175i	−0.620874	+	0.455679i
$607$	29.7375	+	17.1690i	1.20701	+	0.696866i	0.962105	−	0.272681i	$-0.0879104\pi$
$607$	29.7375	+	17.1690i	1.20701	+	0.696866i	0.244904	+	0.969547i	$0.421244\pi$
$608$	2.17033	−	3.75913i	0.0880187	−	0.152453i
$609$	−33.4759	+	12.5330i	−1.35651	+	0.507862i
$610$	11.2393			0.455066
$611$	5.15032	+	25.8261i	0.208359	+	1.04481i
$612$	−11.9639	+	2.66377i	−0.483611	+	0.107677i
$613$	−14.5821	−	25.2570i	−0.588967	−	1.02012i	−0.994368	−	0.105982i	$-0.966201\pi$
$613$	−14.5821	−	25.2570i	−0.588967	−	1.02012i	0.405401	−	0.914139i	$-0.367132\pi$
$614$	1.17043			0.0472347
$615$	−34.9100	+	3.83937i	−1.40771	+	0.154818i
$616$	−5.24982	−	1.48069i	−0.211521	−	0.0596586i
$617$	13.7657	−	7.94764i	0.554187	−	0.319960i	−0.196622	−	0.980479i	$-0.562997\pi$
$617$	13.7657	−	7.94764i	0.554187	−	0.319960i	0.750809	+	0.660519i	$0.229664\pi$
$618$	2.84272	+	3.87328i	0.114351	+	0.155806i
$619$	−12.0626	−	6.96433i	−0.484835	−	0.279920i	0.237594	−	0.971365i	$-0.423641\pi$
$619$	−12.0626	−	6.96433i	−0.484835	−	0.279920i	−0.722429	+	0.691445i	$0.756975\pi$
$620$		−	8.06238i		−	0.323793i
$621$	2.31118	+	6.77804i	0.0927443	+	0.271993i
$622$	2.57489	+	1.48661i	0.103244	+	0.0596077i
$623$	11.4298	−	11.1340i	0.457923	−	0.446076i
$624$	−6.09824	−	1.34589i	−0.244125	−	0.0538789i
$625$	15.4225	+	26.7125i	0.616898	+	1.06850i
$626$	6.11782	+	10.5964i	0.244517	+	0.423516i
$627$	15.4072	−	1.69447i	0.615304	−	0.0676705i
$628$	13.7392	+	7.93232i	0.548253	+	0.316534i
$629$	−25.9725			−1.03559
$630$	−1.26329	+	22.6053i	−0.0503306	+	0.900618i
$631$	9.83148	+	17.0286i	0.391385	+	0.677899i	0.992633	−	0.121164i	$-0.0386627\pi$
$631$	9.83148	+	17.0286i	0.391385	+	0.677899i	−0.601247	+	0.799063i	$0.705329\pi$
$632$	12.2757	−	7.08737i	0.488300	−	0.281920i
$633$	3.87795	−	8.82422i	0.154135	−	0.350731i
$634$	5.54327	+	9.60122i	0.220151	+	0.381313i
$635$	33.1319			1.31480
$636$	10.6307	+	4.67185i	0.421536	+	0.185251i
$637$	−8.72468	+	23.6829i	−0.345684	+	0.938351i
$638$		−	16.0814i		−	0.636669i
$639$	−14.4574	+	13.2721i	−0.571927	+	0.525034i
$640$	−2.47029	+	1.42622i	−0.0976469	+	0.0563765i
$641$			49.5725i			1.95800i	0.203870	+	0.978998i	$0.434648\pi$
$641$			49.5725i			1.95800i	−0.203870	+	0.978998i	$0.565352\pi$
$642$	−1.54224	+	0.169614i	−0.0608672	+	0.00669412i
$643$	30.8334	−	17.8017i	1.21595	−	0.702030i	0.251902	−	0.967753i	$-0.418944\pi$
$643$	30.8334	−	17.8017i	1.21595	−	0.702030i	0.964049	+	0.265723i	$0.0856106\pi$
$644$	2.54433	+	2.61191i	0.100261	+	0.102924i
$645$	19.9784	−	45.4606i	0.786649	−	1.79001i
$646$	8.86714	−	15.3583i	0.348873	−	0.604265i
$647$	11.9838	+	20.7566i	0.471132	+	0.816024i	0.999455	−	0.0330193i	$-0.0105123\pi$
$647$	11.9838	+	20.7566i	0.471132	+	0.816024i	−0.528323	+	0.849044i	$0.677179\pi$
$648$	3.81843	+	8.14982i	0.150002	+	0.320155i
$649$	−19.3615	+	11.1784i	−0.760006	+	0.438790i
$650$	−7.46051	−	8.49866i	−0.292625	−	0.333345i
$651$	−12.1303	+	4.54142i	−0.475423	+	0.177992i
$652$	1.86738	−	3.23439i	0.0731321	−	0.126669i
$653$		−	0.490762i		−	0.0192050i	−0.999954	−	0.00960251i	$-0.996943\pi$
$653$		−	0.490762i		−	0.0192050i	0.999954	−	0.00960251i	$-0.00305662\pi$
$654$	18.2683	+	8.02829i	0.714346	+	0.313931i
$655$	−1.73077	+	2.99778i	−0.0676267	+	0.117133i
$656$	−3.55429	+	6.15620i	−0.138772	+	0.240359i
$657$	7.16813	+	2.25292i	0.279655	+	0.0878949i
$658$	5.24569	−	18.5988i	0.204498	−	0.725055i
$659$	18.7736	−	10.8389i	0.731314	−	0.422225i	−0.0875884	−	0.996157i	$-0.527916\pi$
$659$	18.7736	−	10.8389i	0.731314	−	0.422225i	0.818903	+	0.573932i	$0.194583\pi$
$660$	−9.32506	−	4.09805i	−0.362977	−	0.159516i
$661$	24.0162	−	13.8657i	0.934121	−	0.539315i	0.0460082	−	0.998941i	$-0.485350\pi$
$661$	24.0162	−	13.8657i	0.934121	−	0.539315i	0.888112	+	0.459626i	$0.152017\pi$
$662$	−23.3769	−	13.4967i	−0.908570	−	0.524563i
$663$	−24.9150	−	5.49879i	−0.967620	−	0.213555i
$664$			10.2916i			0.399392i
$665$	−22.8582	−	23.4653i	−0.886403	−	0.909945i
$666$	4.14473	+	18.6154i	0.160605	+	0.721330i
$667$	−5.37506	+	9.30988i	−0.208123	+	0.360480i
$668$	−7.93312	+	13.7406i	−0.306942	+	0.531638i
$669$	−2.97872	−	1.30905i	−0.115164	−	0.0506107i
$670$	−31.9407	−	18.4410i	−1.23398	−	0.712436i
$671$	8.12342			0.313601
$672$	3.53731	+	2.91332i	0.136455	+	0.112384i
$673$	0.414076	−	0.717200i	0.0159614	−	0.0276460i	−0.857934	−	0.513759i	$-0.828252\pi$
$673$	0.414076	−	0.717200i	0.0159614	−	0.0276460i	0.873896	+	0.486113i	$0.161586\pi$
$674$		−	4.24529i		−	0.163523i
$675$	−3.15764	+	15.9887i	−0.121537	+	0.615407i
$676$	−10.3214	−	7.90377i	−0.396975	−	0.303991i
$677$	10.5010	+	18.1882i	0.403586	+	0.699031i	0.994156	−	0.107955i	$-0.0344303\pi$
$677$	10.5010	+	18.1882i	0.403586	+	0.699031i	−0.590570	+	0.806986i	$0.701097\pi$
$678$	3.50672	+	4.77799i	0.134675	+	0.183498i
$679$	−13.1258	+	46.5378i	−0.503720	+	1.78596i
$680$	−10.0927	+	5.82700i	−0.387036	+	0.223455i
$681$	−18.5304	+	2.03796i	−0.710087	+	0.0780947i
$682$		−	5.82723i		−	0.223136i
$683$		−	2.42833i		−	0.0929174i	−0.998920	−	0.0464587i	$-0.985206\pi$
$683$		−	2.42833i		−	0.0929174i	0.998920	−	0.0464587i	$-0.0147936\pi$
$684$	−12.4229	−	3.90447i	−0.475000	−	0.149291i
$685$	23.3882	−	13.5032i	0.893616	−	0.515929i
$686$	13.6004	−	12.5710i	0.519266	−	0.479962i
$687$	7.83188	−	5.74806i	0.298805	−	0.219302i
$688$	−5.02540	−	8.70425i	−0.191592	−	0.331846i
$689$	15.9468	+	18.1659i	0.607526	+	0.692065i
$690$	4.02875	+	5.48927i	0.153372	+	0.208973i
$691$			9.18162i			0.349285i	0.984632	+	0.174643i	$0.0558770\pi$
$691$			9.18162i			0.349285i	−0.984632	+	0.174643i	$0.944123\pi$
$692$	2.79263	−	4.83698i	0.106160	−	0.183874i
$693$	−0.913065	+	16.3384i	−0.0346845	+	0.620645i
$694$	−7.97045			−0.302554
$695$	16.1599	+	9.32993i	0.612980	+	0.353904i
$696$	−5.43563	+	12.3687i	−0.206037	+	0.468834i
$697$	−14.5214	+	25.1519i	−0.550038	+	0.952694i
$698$	−2.92703	+	5.06976i	−0.110790	+	0.191893i
$699$	−20.7235	+	15.2096i	−0.783835	+	0.575281i
$700$	2.04254	+	8.04301i	0.0772006	+	0.303997i
$701$		−	7.30740i		−	0.275997i	−0.990432	−	0.137998i	$-0.955933\pi$
$701$		−	7.30740i		−	0.275997i	0.990432	−	0.137998i	$-0.0440669\pi$
$702$	0.0348107	+	18.7350i	0.00131384	+	0.707106i
$703$	−23.8970	−	13.7969i	−0.901293	−	0.520362i
$704$	−1.78545	+	1.03083i	−0.0672917	+	0.0388509i
$705$	14.5183	−	33.0362i	0.546792	−	1.24422i
$706$	−12.3488	+	7.12956i	−0.464751	+	0.268324i
$707$	27.8726	+	7.86133i	1.04826	+	0.295656i
$708$	18.6699	−	2.05330i	0.701658	−	0.0771676i
$709$	3.54955	−	6.14800i	0.133306	−	0.230893i	−0.791643	−	0.610984i	$-0.790774\pi$
$709$	3.54955	−	6.14800i	0.133306	−	0.230893i	0.924949	+	0.380091i	$0.124107\pi$
$710$	−9.33018	+	16.1603i	−0.350155	+	0.606487i
$711$	−28.7575	−	31.3259i	−1.07849	−	1.17481i
$712$		−	6.03095i		−	0.226019i
$713$	−1.94770	+	3.37351i	−0.0729419	+	0.126339i
$714$	14.4521	+	11.9027i	0.540856	+	0.445446i
$715$	−13.9882	−	15.9347i	−0.523130	−	0.595925i
$716$	0.229448	−	0.132472i	0.00857486	−	0.00495070i
$717$	−2.41067	−	21.9194i	−0.0900282	−	0.818594i
$718$	4.11588	+	7.12892i	0.153603	+	0.266049i
$719$	−8.22204	+	14.2410i	−0.306630	+	0.531099i	−0.977623	−	0.210365i	$-0.932535\pi$
$719$	−8.22204	+	14.2410i	−0.306630	+	0.531099i	0.670993	+	0.741464i	$0.265868\pi$
$720$	5.78701	+	6.30387i	0.215669	+	0.234931i
$721$	1.99221	−	7.06345i	0.0741938	−	0.263056i
$722$	−0.137355	+	0.0793021i	−0.00511183	+	0.00295132i
$723$	−0.572554	−	5.20602i	−0.0212935	−	0.193614i
$724$		−	2.90040i		−	0.107792i
$725$	−21.1874	+	12.2326i	−0.786881	+	0.454306i
$726$	10.7027	+	4.70347i	0.397213	+	0.174562i
$727$			37.5539i			1.39280i	0.717656	+	0.696398i	$0.245215\pi$
$727$			37.5539i			1.39280i	−0.717656	+	0.696398i	$0.754785\pi$
$728$	4.11091	+	8.60816i	0.152361	+	0.319040i
$729$	21.3755	−	16.4951i	0.791686	−	0.610929i
$730$	7.14428			0.264422
$731$	−20.5318	−	35.5622i	−0.759397	−	1.31531i
$732$	−6.24796	−	2.74577i	−0.230931	−	0.101487i
$733$	3.68363	−	2.12674i	0.136058	−	0.0785531i	−0.430426	−	0.902626i	$-0.641637\pi$
$733$	3.68363	−	2.12674i	0.136058	−	0.0785531i	0.566484	+	0.824073i	$0.308303\pi$
$734$	−11.9684	−	20.7299i	−0.441761	−	0.765153i
$735$	28.4075	−	19.7249i	1.04783	−	0.727565i
$736$	1.37818			0.0508005
$737$	−23.0857	−	13.3285i	−0.850373	−	0.490963i
$738$	20.3445	+	6.39423i	0.748893	+	0.235375i
$739$	−8.37071	−	14.4985i	−0.307921	−	0.533336i	0.669986	−	0.742374i	$-0.266300\pi$
$739$	−8.37071	−	14.4985i	−0.307921	−	0.533336i	−0.977907	+	0.209038i	$0.932967\pi$
$740$	9.06660	+	15.7038i	0.333295	+	0.577283i
$741$	−20.0030	−	18.2946i	−0.734830	−	0.672069i
$742$	−4.36592	−	17.1919i	−0.160278	−	0.631136i
$743$	37.8379	+	21.8457i	1.38814	+	0.801441i	0.993105	−	0.117226i	$-0.0374002\pi$
$743$	37.8379	+	21.8457i	1.38814	+	0.801441i	0.395032	+	0.918667i	$0.370734\pi$
$744$	−1.96964	+	4.48190i	−0.0722107	+	0.164314i
$745$			56.3407i			2.06416i
$746$	18.4915	+	10.6761i	0.677021	+	0.390878i
$747$	30.1368	−	6.71000i	1.10265	−	0.245506i
$748$	−7.29465	+	4.21157i	−0.266719	+	0.153990i
$749$	1.65374	+	1.69767i	0.0604265	+	0.0620314i
$750$	−1.00650	−	9.15177i	−0.0367523	−	0.334176i
$751$	37.0409			1.35164			0.675820	−	0.737066i	$-0.263790\pi$
$751$	37.0409			1.35164			0.675820	+	0.737066i	$0.263790\pi$
$752$	−3.65196	−	6.32538i	−0.133173	−	0.230663i
$753$	24.4792	+	33.3535i	0.892070	+	1.21547i
$754$	−21.1357	+	18.5539i	−0.769718	+	0.675693i
$755$	−63.0537			−2.29476
$756$	6.22476	−	12.2577i	0.226392	−	0.445810i
$757$	11.1135	−	19.2491i	0.403926	−	0.699621i	−0.590269	−	0.807206i	$-0.700979\pi$
$757$	11.1135	−	19.2491i	0.403926	−	0.699621i	0.994196	+	0.107585i	$0.0343119\pi$
$758$	13.5250	+	7.80867i	0.491250	+	0.283624i
$759$	2.91185	+	3.96747i	0.105693	+	0.144010i
$760$	−12.3815			−0.449125
$761$	0.319451	−	0.553305i	0.0115801	−	0.0200573i	−0.860177	−	0.509995i	$-0.829647\pi$
$761$	0.319451	−	0.553305i	0.0115801	−	0.0200573i	0.871757	+	0.489938i	$0.162981\pi$
$762$	−18.4181	−	8.09415i	−0.667218	−	0.293220i
$763$	−7.50257	−	29.5433i	−0.271611	−	1.06954i
$764$	0.509369	+	0.294084i	0.0184283	+	0.0106396i
$765$	23.6435	+	25.7551i	0.854831	+	0.931179i
$766$	−8.35931	−	4.82625i	−0.302034	−	0.174379i
$767$	37.0300	+	12.5497i	1.33708	+	0.453145i
$768$	1.72167	−	0.189348i	0.0621254	−	0.00683249i
$769$	32.7494	+	18.9079i	1.18097	+	0.681835i	0.956239	−	0.292586i	$-0.0945157\pi$
$769$	32.7494	+	18.9079i	1.18097	+	0.681835i	0.224733	+	0.974420i	$0.427849\pi$
$770$	3.82970	+	15.0804i	0.138013	+	0.543460i
$771$	19.0786	−	2.09824i	0.687098	−	0.0755664i
$772$	−9.34180	−	16.1805i	−0.336219	−	0.582348i
$773$	−10.2296			−0.367933			−0.183966	−	0.982933i	$-0.558894\pi$
$773$	−10.2296			−0.367933			−0.183966	+	0.982933i	$0.558894\pi$
$774$	−22.2121	+	20.3909i	−0.798398	+	0.732937i
$775$	−7.67744	+	4.43257i	−0.275782	+	0.159223i
$776$	9.13794	+	15.8274i	0.328033	+	0.568170i
$777$	18.5201	−	22.4869i	0.664406	−	0.806714i
$778$	−4.12317	+	7.14154i	−0.147823	+	0.256036i
$779$	−26.7220	+	15.4280i	−0.957416	+	0.552765i
$780$	5.37271	+	16.9840i	0.192374	+	0.608125i
$781$	−6.74356	+	11.6802i	−0.241303	+	0.417950i
$782$	5.63071			0.201354
$783$	39.7631	+	7.85288i	1.42102	+	0.280639i
$784$	0.183445	−	6.99760i	0.00655161	−	0.249914i
$785$		−	45.2531i		−	1.61515i
$786$	1.69450	−	1.24364i	0.0604407	−	0.0443593i
$787$		−	17.9009i		−	0.638098i	−0.947738	−	0.319049i	$-0.896637\pi$
$787$		−	17.9009i		−	0.638098i	0.947738	−	0.319049i	$-0.103363\pi$
$788$	−20.3079	−	11.7248i	−0.723440	−	0.417678i
$789$	−5.71700	+	4.19588i	−0.203530	+	0.149377i
$790$	−35.0157	−	20.2164i	−1.24580	−	0.719266i
$791$	2.45755	−	8.71331i	0.0873803	−	0.309810i
$792$	4.18267	+	4.55623i	0.148625	+	0.161899i
$793$	−9.37237	−	10.6766i	−0.332823	−	0.379136i
$794$	−5.16974	+	8.95426i	−0.183467	+	0.317775i
$795$	−3.62097	−	32.9241i	−0.128422	−	1.16770i
$796$			18.7498i			0.664567i
$797$	−16.6924	−	28.9121i	−0.591275	−	1.02412i	−0.994061	−	0.108824i	$-0.965292\pi$
$797$	−16.6924	−	28.9121i	−0.591275	−	1.02412i	0.402786	−	0.915294i	$-0.368042\pi$
$798$	6.97434	+	18.6287i	0.246889	+	0.659448i
$799$	−14.9205	−	25.8430i	−0.527849	−	0.914261i
$800$	2.71626	+	1.56823i	0.0960342	+	0.0554454i
$801$	−17.6604	+	3.93211i	−0.623999	+	0.138934i
$802$	25.7432			0.909024
$803$	5.16366			0.182222
$804$	13.2508	+	18.0545i	0.467318	+	0.636733i
$805$	2.82339	−	10.0104i	0.0995114	−	0.352821i
$806$	−7.65870	+	6.72315i	−0.269766	+	0.236813i
$807$	31.2934	−	3.44162i	1.10158	−	0.121151i
$808$	9.47939	−	5.47293i	0.333484	−	0.192537i
$809$	−7.64969	+	4.41655i	−0.268949	+	0.155278i	−0.628410	−	0.777882i	$-0.716294\pi$
$809$	−7.64969	+	4.41655i	−0.268949	+	0.155278i	0.359461	+	0.933160i	$0.382961\pi$
$810$	14.6865	−	21.0561i	0.516032	−	0.739836i
$811$		−	0.491936i		−	0.0172742i	−0.999963	−	0.00863710i	$-0.997251\pi$
$811$		−	0.491936i		−	0.0172742i	0.999963	−	0.00863710i	$-0.00274931\pi$
$812$	20.0025	−	5.07968i	0.701951	−	0.178262i
$813$	−2.71912	−	24.7240i	−0.0953638	−	0.867109i
$814$	6.55305	+	11.3502i	0.229684	+	0.397825i
$815$	−10.6532			−0.373165
$816$	7.03407	−	0.773601i	0.246242	−	0.0270814i
$817$		−	43.6272i		−	1.52632i
$818$	34.6570			1.21175
$819$	22.5270	−	17.6504i	0.787156	−	0.616754i
$820$	20.2768			0.708098
$821$		−	38.6879i		−	1.35022i	−0.737718	−	0.675109i	$-0.764097\pi$
$821$		−	38.6879i		−	1.35022i	0.737718	−	0.675109i	$-0.235903\pi$
$822$	−16.3004	+	1.79270i	−0.568541	+	0.0625276i
$823$	18.7795			0.654613			0.327307	−	0.944918i	$-0.393859\pi$
$823$	18.7795			0.654613			0.327307	+	0.944918i	$0.393859\pi$
$824$	−1.38694	−	2.40226i	−0.0483165	−	0.0836866i
$825$	1.22438	+	11.1329i	0.0426276	+	0.387597i
$826$	−20.0198	−	20.5515i	−0.696577	−	0.715078i
$827$			24.1251i			0.838912i	0.907776	+	0.419456i	$0.137779\pi$
$827$			24.1251i			0.838912i	−0.907776	+	0.419456i	$0.862221\pi$
$828$	−0.898558	−	4.03572i	−0.0312271	−	0.140251i
$829$	2.40289	−	1.38731i	0.0834560	−	0.0481833i	−0.457691	−	0.889111i	$-0.651323\pi$
$829$	2.40289	−	1.38731i	0.0834560	−	0.0481833i	0.541147	+	0.840928i	$0.317990\pi$
$830$	25.4233	−	14.6781i	0.882455	−	0.509485i
$831$	10.0539	−	1.10572i	0.348766	−	0.0383569i
$832$	3.41477	+	1.15729i	0.118386	+	0.0401218i
$833$	0.749485	−	28.5894i	0.0259681	−	0.990566i
$834$	−6.70403	−	9.13441i	−0.232142	−	0.316299i
$835$	45.2576			1.56621
$836$	−8.94898			−0.309507
$837$	14.4085	+	2.84555i	0.498031	+	0.0983568i
$838$	31.3016	+	18.0720i	1.08129	+	0.624286i
$839$	−15.5301	−	26.8988i	−0.536157	−	0.928651i	−0.999106	−	0.0422665i	$-0.986542\pi$
$839$	−15.5301	−	26.8988i	−0.536157	−	0.928651i	0.462949	−	0.886385i	$-0.346791\pi$
$840$	2.15174	−	12.8932i	0.0742422	−	0.444859i
$841$	15.9217	+	27.5773i	0.549026	+	0.950941i
$842$			19.0053i			0.654965i
$843$	2.75354	+	25.0370i	0.0948371	+	0.862320i
$844$	−2.78247	+	4.81937i	−0.0957764	+	0.165890i
$845$	−4.80406	+	36.7693i	−0.165265	+	1.26490i
$846$	−16.1416	+	14.8181i	−0.554958	+	0.509457i
$847$	−4.39547	−	17.3083i	−0.151030	−	0.594719i
$848$	−5.80600	−	3.35210i	−0.199379	−	0.115112i
$849$	7.14686	−	5.24531i	0.245280	−	0.180018i
$850$	11.0976	+	6.40719i	0.380644	+	0.219765i
$851$		−	8.76119i		−	0.300330i
$852$	9.13465	−	6.70421i	0.312948	−	0.229682i
$853$		−	5.16044i		−	0.176690i	−0.996090	−	0.0883451i	$-0.971842\pi$
$853$		−	5.16044i		−	0.176690i	0.996090	−	0.0883451i	$-0.0281578\pi$
$854$	2.56597	+	10.1041i	0.0878056	+	0.345757i
$855$	8.07261	+	36.2568i	0.276078	+	1.23996i
$856$	0.895779			0.0306171
$857$	−0.856918	+	1.48422i	−0.0292717	+	0.0507002i	−0.880290	−	0.474436i	$-0.842652\pi$
$857$	−0.856918	+	1.48422i	−0.0292717	+	0.0507002i	0.851018	+	0.525136i	$0.175985\pi$
$858$	3.88323	+	12.2755i	0.132571	+	0.419078i
$859$	49.7659	−	28.7323i	1.69799	−	0.980335i	0.750324	−	0.661070i	$-0.229897\pi$
$859$	49.7659	−	28.7323i	1.69799	−	0.980335i	0.947665	−	0.319265i	$-0.103436\pi$
$860$	−14.3347	+	24.8284i	−0.488809	+	0.846642i
$861$	−11.4217	−	30.5076i	−0.389249	−	1.03970i
$862$	18.3411	+	31.7678i	0.624701	+	1.08201i
$863$	−35.2165	+	20.3323i	−1.19878	+	0.692118i	−0.960284	−	0.279024i	$-0.909989\pi$
$863$	−35.2165	+	20.3323i	−1.19878	+	0.692118i	−0.238500	+	0.971142i	$0.576656\pi$
$864$	−1.67697	−	4.91811i	−0.0570518	−	0.167317i
$865$	−15.9317			−0.541693
$866$	2.84393	+	4.92583i	0.0966406	+	0.167386i
$867$	−0.529919	+	0.0582800i	−0.0179970	+	0.00197929i
$868$	7.24808	−	1.84066i	0.246016	−	0.0624762i
$869$	−25.3083	−	14.6117i	−0.858524	−	0.495669i
$870$	38.3067	−	4.21294i	1.29872	−	0.142832i
$871$	9.11744	+	45.7192i	0.308933	+	1.54914i
$872$	−9.97726	−	5.76038i	−0.337873	−	0.195071i
$873$	40.3894	−	37.0778i	1.36697	−	1.25489i
$874$	5.18076	+	2.99111i	0.175242	+	0.101176i
$875$	−10.0741	+	9.81348i	−0.340567	+	0.331756i
$876$	−3.97152	−	1.74535i	−0.134185	−	0.0589700i
$877$	−5.97222	+	10.3442i	−0.201668	+	0.349298i	−0.949066	−	0.315078i	$-0.897969\pi$
$877$	−5.97222	+	10.3442i	−0.201668	+	0.349298i	0.747398	+	0.664376i	$0.231303\pi$
$878$	19.8235			0.669010
$879$	31.1517	+	42.4450i	1.05072	+	1.43163i
$880$	5.09290	+	2.94039i	0.171682	+	0.0991205i
$881$	−6.30204	+	10.9155i	−0.212321	+	0.367751i	−0.952441	−	0.304724i	$-0.901436\pi$
$881$	−6.30204	+	10.9155i	−0.212321	+	0.367751i	0.740119	+	0.672475i	$0.234769\pi$
$882$	−20.6106	+	4.02517i	−0.693996	+	0.135535i
$883$	−46.6817			−1.57097			−0.785483	−	0.618884i	$-0.787585\pi$
$883$	−46.6817			−1.57097			−0.785483	+	0.618884i	$0.787585\pi$
$884$	13.9514	+	4.72824i	0.469237	+	0.159028i
$885$	−31.6997	−	43.1917i	−1.06557	−	1.45187i
$886$	0.303694	+	0.526014i	0.0102028	+	0.0176718i
$887$	41.7696			1.40249			0.701243	−	0.712922i	$-0.252629\pi$
$887$	41.7696			1.40249			0.701243	+	0.712922i	$0.252629\pi$
$888$	−1.20369	−	10.9448i	−0.0403933	−	0.367282i
$889$	7.56411	+	29.7856i	0.253692	+	0.998977i
$890$	−14.8982	+	8.60148i	−0.499389	+	0.288322i
$891$	10.6149	−	15.2187i	0.355614	−	0.509845i
$892$	1.62683	+	0.939253i	0.0544704	+	0.0314485i
$893$		−	31.7039i		−	1.06093i
$894$	13.7641	−	31.3199i	0.460339	−	1.04750i
$895$	−0.654487	−	0.377868i	−0.0218771	−	0.0126307i
$896$	−1.84615	−	1.89518i	−0.0616756	−	0.0633137i
$897$	1.85489	−	8.40449i	0.0619328	−	0.280618i
$898$	0.221871	+	0.384292i	0.00740393	+	0.0128240i
$899$	11.0236	+	19.0934i	0.367657	+	0.636800i
$900$	2.82128	−	8.97648i	0.0940426	−	0.299216i
$901$	−23.7211	−	13.6954i	−0.790263	−	0.456259i
$902$	14.6555			0.487973
$903$	45.4302	+	7.58182i	1.51182	+	0.252307i
$904$	−1.71090	−	2.96337i	−0.0569038	−	0.0985603i
$905$	−7.16483	+	4.13662i	−0.238167	+	0.137506i
$906$	35.0517	+	15.4041i	1.16451	+	0.511765i
$907$	14.8290	+	25.6845i	0.492388	+	0.852840i	0.999962	−	0.00876787i	$-0.00279093\pi$
$907$	14.8290	+	25.6845i	0.492388	+	0.852840i	−0.507574	+	0.861608i	$0.669458\pi$
$908$	10.7630			0.357184
$909$	−22.2068	−	24.1902i	−0.736553	−	0.802337i
$910$	15.4016	−	22.4323i	0.510558	−	0.743624i
$911$			37.9318i			1.25674i	0.777916	+	0.628368i	$0.216277\pi$
$911$			37.9318i			1.25674i	−0.777916	+	0.628368i	$0.783723\pi$
$912$	6.88293	+	3.02482i	0.227916	+	0.100162i
$913$	18.3751	−	10.6089i	0.608128	−	0.351103i
$914$			28.5798i			0.945335i
$915$	2.12814	+	19.3504i	0.0703540	+	0.639704i
$916$	−4.85743	+	2.80444i	−0.160494	+	0.0926613i
$917$	−3.09014	−	0.871560i	−0.102046	−	0.0287814i
$918$	−6.85146	−	20.0935i	−0.226132	−	0.663183i
$919$	−8.15257	+	14.1207i	−0.268928	+	0.465798i	−0.968585	−	0.248681i	$-0.920003\pi$
$919$	−8.15257	+	14.1207i	−0.268928	+	0.465798i	0.699657	+	0.714479i	$0.253336\pi$
$920$	−1.96560	−	3.40451i	−0.0648038	−	0.112243i
$921$	0.221618	+	2.01509i	0.00730256	+	0.0663995i
$922$	−31.5996	+	18.2440i	−1.04068	+	0.600835i
$923$	23.1316	−	4.61296i	0.761385	−	0.151837i
$924$	1.55521	−	9.31883i	0.0511627	−	0.306567i
$925$	9.96935	−	17.2674i	0.327790	−	0.567749i
$926$			38.3097i			1.25893i
$927$	−6.13025	+	5.62762i	−0.201344	+	0.184835i
$928$	3.90011	−	6.75519i	0.128027	−	0.221750i
$929$	22.5701	−	39.0925i	0.740500	−	1.28258i	−0.211767	−	0.977320i	$-0.567922\pi$
$929$	22.5701	−	39.0925i	0.740500	−	1.28258i	0.952268	−	0.305264i	$-0.0987447\pi$
$930$	13.8808	−	1.52659i	0.455168	−	0.0500589i
$931$	15.8767	−	25.9067i	0.520338	−	0.849059i
$932$	12.8530	−	7.42068i	0.421014	−	0.243072i
$933$	−2.07191	+	4.71459i	−0.0678311	+	0.154349i
$934$	−19.5171	+	11.2682i	−0.638620	+	0.368707i
$935$	20.8076	+	12.0133i	0.680482	+	0.392876i
$936$	1.16250	−	10.7540i	0.0379974	−	0.351506i
$937$			8.79906i			0.287453i	0.989617	+	0.143726i	$0.0459085\pi$
$937$			8.79906i			0.287453i	−0.989617	+	0.143726i	$0.954091\pi$
$938$	9.28628	−	32.9248i	0.303208	−	1.07503i
$939$	−17.0851	+	12.5393i	−0.557550	+	0.409203i
$940$	−10.4170	+	18.0428i	−0.339766	+	0.588492i
$941$	−29.1636	+	50.5128i	−0.950705	+	1.64667i	−0.206801	+	0.978383i	$0.566305\pi$
$941$	−29.1636	+	50.5128i	−0.950705	+	1.64667i	−0.743904	+	0.668286i	$0.767028\pi$
$942$	−11.0554	+	25.1563i	−0.360203	+	0.819636i
$943$	−8.48437	−	4.89845i	−0.276289	−	0.159516i
$944$	−10.8441			−0.352944
$945$	−39.1581	+	2.10530i	−1.27381	+	0.0684855i
$946$	−10.3607	+	17.9452i	−0.336854	+	0.583449i
$947$		−	16.8822i		−	0.548597i	−0.961645	−	0.274298i	$-0.911554\pi$
$947$		−	16.8822i		−	0.548597i	0.961645	−	0.274298i	$-0.0884456\pi$
$948$	14.5265	+	19.7927i	0.471798	+	0.642837i
$949$	−5.95756	−	6.78657i	−0.193391	−	0.220302i
$950$	6.80718	+	11.7904i	0.220854	+	0.382530i
$951$	−15.4805	+	11.3616i	−0.501990	+	0.368427i
$952$	−7.54266	−	7.74298i	−0.244459	−	0.250951i
$953$	−27.3038	+	15.7639i	−0.884457	+	0.510641i	−0.872125	−	0.489282i	$-0.837259\pi$
$953$	−27.3038	+	15.7639i	−0.884457	+	0.510641i	−0.0123316	+	0.999924i	$0.503925\pi$
$954$	−6.03048	+	19.1872i	−0.195244	+	0.621209i
$955$		−	1.67772i		−	0.0542897i
$956$			12.7315i			0.411765i
$957$	27.6869	−	3.04498i	0.894990	−	0.0984301i
$958$	−16.1709	+	9.33625i	−0.522457	+	0.301640i
$959$	17.4789	+	17.9432i	0.564424	+	0.579415i
$960$	−2.92323	−	3.98298i	−0.0943469	−	0.128550i
$961$	−11.5055	−	19.9281i	−0.371146	−	0.642843i
$962$	7.35697	−	21.7079i	0.237198	−	0.699892i
$963$	−0.584037	−	2.62311i	−0.0188203	−	0.0845284i
$964$			3.02382i			0.0973908i
$965$	−26.6470	+	46.1540i	−0.857797	+	1.48575i
$966$	−4.01508	+	4.87506i	−0.129183	+	0.156853i
$967$	−24.7371			−0.795492			−0.397746	−	0.917496i	$-0.630207\pi$
$967$	−24.7371			−0.795492			−0.397746	+	0.917496i	$0.630207\pi$
$968$	−5.84529	−	3.37478i	−0.187875	−	0.108470i
$969$	28.1209	+	12.3582i	0.903375	+	0.397003i
$970$	26.0655	−	45.1468i	0.836913	−	1.44958i
$971$	−20.7356	+	35.9151i	−0.665436	+	1.15257i	0.313731	+	0.949512i	$0.398421\pi$
$971$	−20.7356	+	35.9151i	−0.665436	+	1.15257i	−0.979167	+	0.203057i	$0.934912\pi$
$972$	−13.3083	+	8.11722i	−0.426864	+	0.260360i
$973$	−4.69826	+	16.6578i	−0.150619	+	0.534025i
$974$			1.56070i			0.0500080i
$975$	13.2193	−	14.4537i	0.423355	−	0.462890i
$976$	3.41234	+	1.97012i	0.109226	+	0.0630619i
$977$	−27.5604	+	15.9120i	−0.881736	+	0.509071i	−0.871230	−	0.490874i	$-0.836677\pi$
$977$	−27.5604	+	15.9120i	−0.881736	+	0.509071i	−0.0105057	+	0.999945i	$0.503344\pi$
$978$	5.92214	+	2.60258i	0.189369	+	0.0832214i
$979$	−10.7679	+	6.21688i	−0.344145	+	0.198692i
$980$	−17.5477	+	9.52698i	−0.560542	+	0.304328i
$981$	−10.3630	+	32.9721i	−0.330866	+	1.05272i
$982$	−13.2942	+	23.0262i	−0.424235	+	0.734797i
$983$	11.3615	−	19.6787i	0.362376	−	0.627653i	−0.625975	−	0.779843i	$-0.715299\pi$
$983$	11.3615	−	19.6787i	0.362376	−	0.627653i	0.988351	+	0.152189i	$0.0486323\pi$
$984$	−11.2719	−	4.95365i	−0.359337	−	0.157916i
$985$			66.8887i			2.13125i
$986$	15.9343	−	27.5991i	0.507453	−	0.878934i
$987$	33.0142	+	5.50971i	1.05085	+	0.175376i
$988$	10.3249	+	11.7616i	0.328478	+	0.374186i
$989$	11.9960	−	6.92592i	0.381452	−	0.220231i
$990$	5.28981	−	16.8306i	0.168121	−	0.534912i
$991$	−25.2957	−	43.8135i	−0.803546	−	1.39178i	−0.917268	−	0.398270i	$-0.869611\pi$
$991$	−25.2957	−	43.8135i	−0.803546	−	1.39178i	0.113723	−	0.993513i	$-0.463722\pi$
$992$	1.41324	−	2.44780i	0.0448703	−	0.0777177i
$993$	18.8104	−	42.8029i	0.596931	−	1.35831i
$994$	−16.6583	−	4.69838i	−0.528368	−	0.149024i
$995$	46.3174	−	26.7414i	1.46836	−	0.847758i
$996$	−17.7187	+	1.94869i	−0.561440	+	0.0617466i
$997$			4.87560i			0.154412i	0.997015	+	0.0772058i	$0.0245999\pi$
$997$			4.87560i			0.154412i	−0.997015	+	0.0772058i	$0.975400\pi$
$998$	−5.12424	+	2.95848i	−0.162205	+	0.0936490i
$999$	−31.2647	+	10.6606i	−0.989171	+	0.337287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.19	yes	76
3.2	odd	2	inner	546.2.bb.a.269.32	yes	76
7.5	odd	6		546.2.u.a.425.12	yes	76
13.3	even	3		546.2.u.a.185.27	yes	76
21.5	even	6		546.2.u.a.425.27	yes	76
39.29	odd	6		546.2.u.a.185.12	✓	76
91.68	odd	6	inner	546.2.bb.a.341.13	yes	76
273.68	even	6	inner	546.2.bb.a.341.38	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.12	✓	76	39.29	odd	6
546.2.u.a.185.27	yes	76	13.3	even	3
546.2.u.a.425.12	yes	76	7.5	odd	6
546.2.u.a.425.27	yes	76	21.5	even	6
546.2.bb.a.269.19	yes	76	1.1	even	1	trivial
546.2.bb.a.269.32	yes	76	3.2	odd	2	inner
546.2.bb.a.341.13	yes	76	91.68	odd	6	inner
546.2.bb.a.341.38	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.72167 - 0.189348i) q^{3} -1.00000 q^{4} +(1.42622 + 2.47029i) q^{5} +(-0.189348 - 1.72167i) q^{6} +(-1.89518 + 1.84615i) q^{7} +1.00000i q^{8} +(2.92829 - 0.651988i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.72167 - 0.189348i) q^{3} -1.00000 q^{4} +(1.42622 + 2.47029i) q^{5} +(-0.189348 - 1.72167i) q^{6} +(-1.89518 + 1.84615i) q^{7} +1.00000i q^{8} +(2.92829 - 0.651988i) q^{9} +(2.47029 - 1.42622i) q^{10} +(1.78545 - 1.03083i) q^{11} +(-1.72167 + 0.189348i) q^{12} +(-3.41477 - 1.15729i) q^{13} +(1.84615 + 1.89518i) q^{14} +(2.92323 + 3.98298i) q^{15} +1.00000 q^{16} +4.08561 q^{17} +(-0.651988 - 2.92829i) q^{18} +(3.75913 + 2.17033i) q^{19} +(-1.42622 - 2.47029i) q^{20} +(-2.91332 + 3.53731i) q^{21} +(-1.03083 - 1.78545i) q^{22} +1.37818i q^{23} +(0.189348 + 1.72167i) q^{24} +(-1.56823 + 2.71626i) q^{25} +(-1.15729 + 3.41477i) q^{26} +(4.91811 - 1.67697i) q^{27} +(1.89518 - 1.84615i) q^{28} +(6.75519 + 3.90011i) q^{29} +(3.98298 - 2.92323i) q^{30} +(2.44780 + 1.41324i) q^{31} -1.00000i q^{32} +(2.87877 - 2.11282i) q^{33} -4.08561i q^{34} +(-7.26350 - 2.04863i) q^{35} +(-2.92829 + 0.651988i) q^{36} -6.35706 q^{37} +(2.17033 - 3.75913i) q^{38} +(-6.09824 - 1.34589i) q^{39} +(-2.47029 + 1.42622i) q^{40} +(-3.55429 + 6.15620i) q^{41} +(3.53731 + 2.91332i) q^{42} +(-5.02540 - 8.70425i) q^{43} +(-1.78545 + 1.03083i) q^{44} +(5.78701 + 6.30387i) q^{45} +1.37818 q^{46} +(-3.65196 - 6.32538i) q^{47} +(1.72167 - 0.189348i) q^{48} +(0.183445 - 6.99760i) q^{49} +(2.71626 + 1.56823i) q^{50} +(7.03407 - 0.773601i) q^{51} +(3.41477 + 1.15729i) q^{52} +(-5.80600 - 3.35210i) q^{53} +(-1.67697 - 4.91811i) q^{54} +(5.09290 + 2.94039i) q^{55} +(-1.84615 - 1.89518i) q^{56} +(6.88293 + 3.02482i) q^{57} +(3.90011 - 6.75519i) q^{58} -10.8441 q^{59} +(-2.92323 - 3.98298i) q^{60} +(3.41234 + 1.97012i) q^{61} +(1.41324 - 2.44780i) q^{62} +(-4.34599 + 6.64172i) q^{63} -1.00000 q^{64} +(-2.01139 - 10.0860i) q^{65} +(-2.11282 - 2.87877i) q^{66} +(-6.46495 - 11.1976i) q^{67} -4.08561 q^{68} +(0.260955 + 2.37277i) q^{69} +(-2.04863 + 7.26350i) q^{70} +(-5.66543 + 3.27094i) q^{71} +(0.651988 + 2.92829i) q^{72} +(2.16906 + 1.25231i) q^{73} +6.35706i q^{74} +(-2.18566 + 4.97344i) q^{75} +(-3.75913 - 2.17033i) q^{76} +(-1.48069 + 5.24982i) q^{77} +(-1.34589 + 6.09824i) q^{78} +(-7.08737 - 12.2757i) q^{79} +(1.42622 + 2.47029i) q^{80} +(8.14982 - 3.81843i) q^{81} +(6.15620 + 3.55429i) q^{82} +10.2916 q^{83} +(2.91332 - 3.53731i) q^{84} +(5.82700 + 10.0927i) q^{85} +(-8.70425 + 5.02540i) q^{86} +(12.3687 + 5.43563i) q^{87} +(1.03083 + 1.78545i) q^{88} -6.03095 q^{89} +(6.30387 - 5.78701i) q^{90} +(8.60816 - 4.11091i) q^{91} -1.37818i q^{92} +(4.48190 + 1.96964i) q^{93} +(-6.32538 + 3.65196i) q^{94} +12.3815i q^{95} +(-0.189348 - 1.72167i) q^{96} +(15.8274 - 9.13794i) q^{97} +(-6.99760 - 0.183445i) q^{98} +(4.55623 - 4.18267i) 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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