LMFDB - Embedded newform 50.2.d.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,2,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.399252010106$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	50.11
Dual form			50.2.d.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 - 2.12663i) q^{5} +(0.809017 + 2.48990i) q^{6} -3.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-3.11803 - 2.26538i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 - 2.12663i) q^{5} +(0.809017 + 2.48990i) q^{6} -3.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-3.11803 - 2.26538i) q^{9} +(-0.690983 - 2.12663i) q^{10} +(0.190983 - 0.138757i) q^{11} +(2.11803 + 1.53884i) q^{12} +(-0.809017 - 0.587785i) q^{13} +(-2.42705 + 1.76336i) q^{14} +(4.73607 + 3.44095i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.42705 + 7.46969i) q^{17} -3.85410 q^{18} +(-0.263932 - 0.812299i) q^{19} +(-1.80902 - 1.31433i) q^{20} +(2.42705 - 7.46969i) q^{21} +(0.0729490 - 0.224514i) q^{22} +(5.04508 - 3.66547i) q^{23} +2.61803 q^{24} +(-4.04508 - 2.93893i) q^{25} -1.00000 q^{26} +(1.80902 - 1.31433i) q^{27} +(-0.927051 + 2.85317i) q^{28} +(-0.163119 + 0.502029i) q^{29} +5.85410 q^{30} +(1.30902 + 4.02874i) q^{31} -1.00000 q^{32} +(0.190983 + 0.587785i) q^{33} +(6.35410 + 4.61653i) q^{34} +(-2.07295 + 6.37988i) q^{35} +(-3.11803 + 2.26538i) q^{36} +(-5.92705 - 4.30625i) q^{37} +(-0.690983 - 0.502029i) q^{38} +(2.11803 - 1.53884i) q^{39} -2.23607 q^{40} +(6.04508 + 4.39201i) q^{41} +(-2.42705 - 7.46969i) q^{42} -1.76393 q^{43} +(-0.0729490 - 0.224514i) q^{44} +(-6.97214 + 5.06555i) q^{45} +(1.92705 - 5.93085i) q^{46} +(1.83688 - 5.65334i) q^{47} +(2.11803 - 1.53884i) q^{48} +2.00000 q^{49} -5.00000 q^{50} -20.5623 q^{51} +(-0.809017 + 0.587785i) q^{52} +(0.472136 - 1.45309i) q^{53} +(0.690983 - 2.12663i) q^{54} +(-0.163119 - 0.502029i) q^{55} +(0.927051 + 2.85317i) q^{56} +2.23607 q^{57} +(0.163119 + 0.502029i) q^{58} +(-3.61803 - 2.62866i) q^{59} +(4.73607 - 3.44095i) q^{60} +(1.73607 - 1.26133i) q^{61} +(3.42705 + 2.48990i) q^{62} +(9.35410 + 6.79615i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.80902 + 1.31433i) q^{65} +(0.500000 + 0.363271i) q^{66} +(-1.78115 - 5.48183i) q^{67} +7.85410 q^{68} +(5.04508 + 15.5272i) q^{69} +(2.07295 + 6.37988i) q^{70} +(-0.927051 + 2.85317i) q^{71} +(-1.19098 + 3.66547i) q^{72} +(4.61803 - 3.35520i) q^{73} -7.32624 q^{74} +(10.5902 - 7.69421i) q^{75} -0.854102 q^{76} +(-0.572949 + 0.416272i) q^{77} +(0.809017 - 2.48990i) q^{78} +(-0.854102 + 2.62866i) q^{79} +(-1.80902 + 1.31433i) q^{80} +(-1.76393 - 5.42882i) q^{81} +7.47214 q^{82} +(-4.16312 - 12.8128i) q^{83} +(-6.35410 - 4.61653i) q^{84} +17.5623 q^{85} +(-1.42705 + 1.03681i) q^{86} +(-1.11803 - 0.812299i) q^{87} +(-0.190983 - 0.138757i) q^{88} +(3.61803 - 2.62866i) q^{89} +(-2.66312 + 8.19624i) q^{90} +(2.42705 + 1.76336i) q^{91} +(-1.92705 - 5.93085i) q^{92} -11.0902 q^{93} +(-1.83688 - 5.65334i) q^{94} -1.90983 q^{95} +(0.809017 - 2.48990i) q^{96} +(-3.26393 + 10.0453i) q^{97} +(1.61803 - 1.17557i) q^{98} -0.909830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9} - 5 q^{10} + 3 q^{11} + 4 q^{12} - q^{13} - 3 q^{14} + 10 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 7 q^{22} + 9 q^{23} + 6 q^{24} - 5 q^{25} - 4 q^{26} + 5 q^{27} + 3 q^{28} + 15 q^{29} + 10 q^{30} + 3 q^{31} - 4 q^{32} + 3 q^{33} + 12 q^{34} - 15 q^{35} - 8 q^{36} - 17 q^{37} - 5 q^{38} + 4 q^{39} + 13 q^{41} - 3 q^{42} - 16 q^{43} - 7 q^{44} - 10 q^{45} + q^{46} + 23 q^{47} + 4 q^{48} + 8 q^{49} - 20 q^{50} - 42 q^{51} - q^{52} - 16 q^{53} + 5 q^{54} + 15 q^{55} - 3 q^{56} - 15 q^{58} - 10 q^{59} + 10 q^{60} - 2 q^{61} + 7 q^{62} + 24 q^{63} - q^{64} - 5 q^{65} + 2 q^{66} + 13 q^{67} + 18 q^{68} + 9 q^{69} + 15 q^{70} + 3 q^{71} - 7 q^{72} + 14 q^{73} + 2 q^{74} + 20 q^{75} + 10 q^{76} - 9 q^{77} + q^{78} + 10 q^{79} - 5 q^{80} - 16 q^{81} + 12 q^{82} - q^{83} - 12 q^{84} + 30 q^{85} + q^{86} - 3 q^{88} + 10 q^{89} + 5 q^{90} + 3 q^{91} - q^{92} - 22 q^{93} - 23 q^{94} - 30 q^{95} + q^{96} - 22 q^{97} + 2 q^{98} - 26 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9 - 5 * q^10 + 3 * q^11 + 4 * q^12 - q^13 - 3 * q^14 + 10 * q^15 - q^16 + 3 * q^17 - 2 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 7 * q^22 + 9 * q^23 + 6 * q^24 - 5 * q^25 - 4 * q^26 + 5 * q^27 + 3 * q^28 + 15 * q^29 + 10 * q^30 + 3 * q^31 - 4 * q^32 + 3 * q^33 + 12 * q^34 - 15 * q^35 - 8 * q^36 - 17 * q^37 - 5 * q^38 + 4 * q^39 + 13 * q^41 - 3 * q^42 - 16 * q^43 - 7 * q^44 - 10 * q^45 + q^46 + 23 * q^47 + 4 * q^48 + 8 * q^49 - 20 * q^50 - 42 * q^51 - q^52 - 16 * q^53 + 5 * q^54 + 15 * q^55 - 3 * q^56 - 15 * q^58 - 10 * q^59 + 10 * q^60 - 2 * q^61 + 7 * q^62 + 24 * q^63 - q^64 - 5 * q^65 + 2 * q^66 + 13 * q^67 + 18 * q^68 + 9 * q^69 + 15 * q^70 + 3 * q^71 - 7 * q^72 + 14 * q^73 + 2 * q^74 + 20 * q^75 + 10 * q^76 - 9 * q^77 + q^78 + 10 * q^79 - 5 * q^80 - 16 * q^81 + 12 * q^82 - q^83 - 12 * q^84 + 30 * q^85 + q^86 - 3 * q^88 + 10 * q^89 + 5 * q^90 + 3 * q^91 - q^92 - 22 * q^93 - 23 * q^94 - 30 * q^95 + q^96 - 22 * q^97 + 2 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.809017	+	2.48990i	−0.467086	+	1.43754i	0.389254	+	0.921131i	$0.372733\pi$
$3$	−0.809017	+	2.48990i	−0.467086	+	1.43754i	−0.856340	+	0.516413i	$0.827267\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$6$	0.809017	+	2.48990i	0.330280	+	1.01650i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−3.11803	−	2.26538i	−1.03934	−	0.755128i
$10$	−0.690983	−	2.12663i	−0.218508	−	0.672499i
$11$	0.190983	−	0.138757i	0.0575835	−	0.0418369i	−0.558621	−	0.829423i	$-0.688669\pi$
$11$	0.190983	−	0.138757i	0.0575835	−	0.0418369i	0.616205	+	0.787586i	$0.288669\pi$
$12$	2.11803	+	1.53884i	0.611424	+	0.444225i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i	0.469916	−	0.882711i	$-0.344284\pi$
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i	−0.694297	+	0.719689i	$0.744284\pi$
$14$	−2.42705	+	1.76336i	−0.648657	+	0.471277i
$15$	4.73607	+	3.44095i	1.22285	+	0.888451i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.42705	+	7.46969i	0.588646	+	1.81167i	0.584106	+	0.811677i	$0.301445\pi$
$17$	2.42705	+	7.46969i	0.588646	+	1.81167i	0.00454037	+	0.999990i	$0.498555\pi$
$18$	−3.85410			−0.908421
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	0.916206	−	0.400707i	$-0.131236\pi$
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	−0.976756	+	0.214353i	$0.931236\pi$
$20$	−1.80902	−	1.31433i	−0.404508	−	0.293893i
$21$	2.42705	−	7.46969i	0.529626	−	1.63002i
$22$	0.0729490	−	0.224514i	0.0155528	−	0.0478665i
$23$	5.04508	−	3.66547i	1.05197	−	0.764303i	0.0793863	−	0.996844i	$-0.474704\pi$
$23$	5.04508	−	3.66547i	1.05197	−	0.764303i	0.972587	+	0.232541i	$0.0747039\pi$
$24$	2.61803			0.534404
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	−1.00000			−0.196116
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$	−0.927051	+	2.85317i	−0.175196	+	0.539198i
$29$	−0.163119	+	0.502029i	−0.0302904	+	0.0932244i	−0.965059	−	0.262033i	$-0.915607\pi$
$29$	−0.163119	+	0.502029i	−0.0302904	+	0.0932244i	0.934768	+	0.355258i	$0.115607\pi$
$30$	5.85410			1.06881
$31$	1.30902	+	4.02874i	0.235106	+	0.723583i	0.997107	+	0.0760071i	$0.0242172\pi$
$31$	1.30902	+	4.02874i	0.235106	+	0.723583i	−0.762001	+	0.647576i	$0.775783\pi$
$32$	−1.00000			−0.176777
$33$	0.190983	+	0.587785i	0.0332459	+	0.102320i
$34$	6.35410	+	4.61653i	1.08972	+	0.791728i
$35$	−2.07295	+	6.37988i	−0.350392	+	1.07840i
$36$	−3.11803	+	2.26538i	−0.519672	+	0.377564i
$37$	−5.92705	−	4.30625i	−0.974401	−	0.707944i	−0.0179508	−	0.999839i	$-0.505714\pi$
$37$	−5.92705	−	4.30625i	−0.974401	−	0.707944i	−0.956450	+	0.291895i	$0.905714\pi$
$38$	−0.690983	−	0.502029i	−0.112092	−	0.0814398i
$39$	2.11803	−	1.53884i	0.339157	−	0.246412i
$40$	−2.23607			−0.353553
$41$	6.04508	+	4.39201i	0.944084	+	0.685917i	0.949400	−	0.314069i	$-0.101692\pi$
$41$	6.04508	+	4.39201i	0.944084	+	0.685917i	−0.00531652	+	0.999986i	$0.501692\pi$
$42$	−2.42705	−	7.46969i	−0.374502	−	1.15260i
$43$	−1.76393			−0.268997			−0.134499	−	0.990914i	$-0.542942\pi$
$43$	−1.76393			−0.268997			−0.134499	+	0.990914i	$0.542942\pi$
$44$	−0.0729490	−	0.224514i	−0.0109975	−	0.0338468i
$45$	−6.97214	+	5.06555i	−1.03934	+	0.755128i
$46$	1.92705	−	5.93085i	0.284128	−	0.874457i
$47$	1.83688	−	5.65334i	0.267937	−	0.824624i	−0.723066	−	0.690779i	$-0.757268\pi$
$47$	1.83688	−	5.65334i	0.267937	−	0.824624i	0.991002	−	0.133845i	$-0.0427324\pi$
$48$	2.11803	−	1.53884i	0.305712	−	0.222113i
$49$	2.00000			0.285714
$50$	−5.00000			−0.707107
$51$	−20.5623			−2.87930
$52$	−0.809017	+	0.587785i	−0.112190	+	0.0815111i
$53$	0.472136	−	1.45309i	0.0648529	−	0.199597i	−0.913379	−	0.407109i	$-0.866537\pi$
$53$	0.472136	−	1.45309i	0.0648529	−	0.199597i	0.978232	+	0.207513i	$0.0665368\pi$
$54$	0.690983	−	2.12663i	0.0940309	−	0.289397i
$55$	−0.163119	−	0.502029i	−0.0219950	−	0.0676935i
$56$	0.927051	+	2.85317i	0.123882	+	0.381271i
$57$	2.23607			0.296174
$58$	0.163119	+	0.502029i	0.0214186	+	0.0659196i
$59$	−3.61803	−	2.62866i	−0.471028	−	0.342222i	0.326814	−	0.945089i	$-0.394025\pi$
$59$	−3.61803	−	2.62866i	−0.471028	−	0.342222i	−0.797842	+	0.602867i	$0.794025\pi$
$60$	4.73607	−	3.44095i	0.611424	−	0.444225i
$61$	1.73607	−	1.26133i	0.222281	−	0.161496i	−0.471072	−	0.882095i	$-0.656133\pi$
$61$	1.73607	−	1.26133i	0.222281	−	0.161496i	0.693353	+	0.720598i	$0.256133\pi$
$62$	3.42705	+	2.48990i	0.435236	+	0.316217i
$63$	9.35410	+	6.79615i	1.17851	+	0.856235i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.80902	+	1.31433i	−0.224381	+	0.163022i
$66$	0.500000	+	0.363271i	0.0615457	+	0.0447156i
$67$	−1.78115	−	5.48183i	−0.217602	−	0.669712i	−0.998959	−	0.0456261i	$-0.985472\pi$
$67$	−1.78115	−	5.48183i	−0.217602	−	0.669712i	0.781356	−	0.624085i	$-0.214528\pi$
$68$	7.85410			0.952450
$69$	5.04508	+	15.5272i	0.607357	+	1.86925i
$70$	2.07295	+	6.37988i	0.247765	+	0.762542i
$71$	−0.927051	+	2.85317i	−0.110021	+	0.338609i	−0.990876	−	0.134777i	$-0.956968\pi$
$71$	−0.927051	+	2.85317i	−0.110021	+	0.338609i	0.880855	+	0.473386i	$0.156968\pi$
$72$	−1.19098	+	3.66547i	−0.140359	+	0.431980i
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	−0.283771	−	0.958892i	$-0.591585\pi$
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	0.824271	+	0.566196i	$0.191585\pi$
$74$	−7.32624			−0.851658
$75$	10.5902	−	7.69421i	1.22285	−	0.888451i
$76$	−0.854102			−0.0979722
$77$	−0.572949	+	0.416272i	−0.0652936	+	0.0474386i
$78$	0.809017	−	2.48990i	0.0916031	−	0.281925i
$79$	−0.854102	+	2.62866i	−0.0960940	+	0.295747i	−0.987537	−	0.157385i	$-0.949693\pi$
$79$	−0.854102	+	2.62866i	−0.0960940	+	0.295747i	0.891443	+	0.453132i	$0.149693\pi$
$80$	−1.80902	+	1.31433i	−0.202254	+	0.146946i
$81$	−1.76393	−	5.42882i	−0.195992	−	0.603203i
$82$	7.47214			0.825159
$83$	−4.16312	−	12.8128i	−0.456962	−	1.40638i	−0.868817	−	0.495134i	$-0.835119\pi$
$83$	−4.16312	−	12.8128i	−0.456962	−	1.40638i	0.411855	−	0.911249i	$-0.364881\pi$
$84$	−6.35410	−	4.61653i	−0.693289	−	0.503704i
$85$	17.5623			1.90490
$86$	−1.42705	+	1.03681i	−0.153883	+	0.111802i
$87$	−1.11803	−	0.812299i	−0.119866	−	0.0870876i
$88$	−0.190983	−	0.138757i	−0.0203589	−	0.0147916i
$89$	3.61803	−	2.62866i	0.383511	−	0.278637i	−0.379280	−	0.925282i	$-0.623828\pi$
$89$	3.61803	−	2.62866i	0.383511	−	0.278637i	0.762791	+	0.646645i	$0.223828\pi$
$90$	−2.66312	+	8.19624i	−0.280717	+	0.863959i
$91$	2.42705	+	1.76336i	0.254424	+	0.184850i
$92$	−1.92705	−	5.93085i	−0.200909	−	0.618334i
$93$	−11.0902			−1.15000
$94$	−1.83688	−	5.65334i	−0.189460	−	0.583097i
$95$	−1.90983			−0.195944
$96$	0.809017	−	2.48990i	0.0825700	−	0.254124i
$97$	−3.26393	+	10.0453i	−0.331402	+	1.01995i	0.637065	+	0.770810i	$0.280148\pi$
$97$	−3.26393	+	10.0453i	−0.331402	+	1.01995i	−0.968467	+	0.249141i	$0.919852\pi$
$98$	1.61803	−	1.17557i	0.163446	−	0.118751i
$99$	−0.909830			−0.0914414
$100$	−4.04508	+	2.93893i	−0.404508	+	0.293893i
$101$	−1.61803			−0.161000			−0.0805002	−	0.996755i	$-0.525652\pi$
$101$	−1.61803			−0.161000			−0.0805002	+	0.996755i	$0.525652\pi$
$102$	−16.6353	+	12.0862i	−1.64714	+	1.19671i
$103$	−6.13525	+	18.8824i	−0.604525	+	1.86054i	−0.104499	+	0.994525i	$0.533324\pi$
$103$	−6.13525	+	18.8824i	−0.604525	+	1.86054i	−0.500026	+	0.866010i	$0.666676\pi$
$104$	−0.309017	+	0.951057i	−0.0303016	+	0.0932588i
$105$	−14.2082	−	10.3229i	−1.38658	−	1.00741i
$106$	−0.472136	−	1.45309i	−0.0458579	−	0.141136i
$107$	10.0902			0.975454			0.487727	−	0.872996i	$-0.337826\pi$
$107$	10.0902			0.975454			0.487727	+	0.872996i	$0.337826\pi$
$108$	−0.690983	−	2.12663i	−0.0664899	−	0.204635i
$109$	12.1353	+	8.81678i	1.16235	+	0.844494i	0.990073	−	0.140555i	$-0.0448886\pi$
$109$	12.1353	+	8.81678i	1.16235	+	0.844494i	0.172274	+	0.985049i	$0.444889\pi$
$110$	−0.427051	−	0.310271i	−0.0407177	−	0.0295832i
$111$	15.5172	−	11.2739i	1.47283	−	1.07007i
$112$	2.42705	+	1.76336i	0.229335	+	0.166621i
$113$	−6.66312	−	4.84104i	−0.626814	−	0.455407i	0.228481	−	0.973548i	$-0.426624\pi$
$113$	−6.66312	−	4.84104i	−0.626814	−	0.455407i	−0.855295	+	0.518142i	$0.826624\pi$
$114$	1.80902	−	1.31433i	0.169430	−	0.123098i
$115$	−4.30902	−	13.2618i	−0.401818	−	1.23667i
$116$	0.427051	+	0.310271i	0.0396507	+	0.0288079i
$117$	1.19098	+	3.66547i	0.110106	+	0.338873i
$118$	−4.47214			−0.411693
$119$	−7.28115	−	22.4091i	−0.667462	−	2.05424i
$120$	1.80902	−	5.56758i	0.165140	−	0.508248i
$121$	−3.38197	+	10.4086i	−0.307451	+	0.946238i
$122$	0.663119	−	2.04087i	0.0600360	−	0.184772i
$123$	−15.8262	+	11.4984i	−1.42700	+	1.03678i
$124$	4.23607			0.380410
$125$	−9.04508	+	6.57164i	−0.809017	+	0.587785i
$126$	11.5623			1.03005
$127$	10.0902	−	7.33094i	0.895358	−	0.650516i	−0.0419116	−	0.999121i	$-0.513345\pi$
$127$	10.0902	−	7.33094i	0.895358	−	0.650516i	0.937269	+	0.348606i	$0.113345\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	1.42705	−	4.39201i	0.125645	−	0.386695i
$130$	−0.690983	+	2.12663i	−0.0606032	+	0.186518i
$131$	3.21885	+	9.90659i	0.281232	+	0.865543i	0.987503	+	0.157601i	$0.0503761\pi$
$131$	3.21885	+	9.90659i	0.281232	+	0.865543i	−0.706271	+	0.707942i	$0.749624\pi$
$132$	0.618034			0.0537930
$133$	0.791796	+	2.43690i	0.0686574	+	0.211306i
$134$	−4.66312	−	3.38795i	−0.402832	−	0.292675i
$135$	−1.54508	−	4.75528i	−0.132980	−	0.409270i
$136$	6.35410	−	4.61653i	0.544860	−	0.395864i
$137$	4.92705	+	3.57971i	0.420946	+	0.305835i	0.778018	−	0.628241i	$-0.216225\pi$
$137$	4.92705	+	3.57971i	0.420946	+	0.305835i	−0.357072	+	0.934077i	$0.616225\pi$
$138$	13.2082	+	9.59632i	1.12436	+	0.816893i
$139$	−8.35410	+	6.06961i	−0.708586	+	0.514818i	−0.882717	−	0.469905i	$-0.844288\pi$
$139$	−8.35410	+	6.06961i	−0.708586	+	0.514818i	0.174131	+	0.984722i	$0.444288\pi$
$140$	5.42705	+	3.94298i	0.458670	+	0.333243i
$141$	12.5902	+	9.14729i	1.06028	+	0.770341i
$142$	0.927051	+	2.85317i	0.0777964	+	0.239433i
$143$	−0.236068			−0.0197410
$144$	1.19098	+	3.66547i	0.0992486	+	0.305456i
$145$	0.954915	+	0.693786i	0.0793014	+	0.0576158i
$146$	1.76393	−	5.42882i	0.145984	−	0.449293i
$147$	−1.61803	+	4.97980i	−0.133453	+	0.410727i
$148$	−5.92705	+	4.30625i	−0.487201	+	0.353972i
$149$	−2.23607			−0.183186			−0.0915929	−	0.995797i	$-0.529196\pi$
$149$	−2.23607			−0.183186			−0.0915929	+	0.995797i	$0.529196\pi$
$150$	4.04508	−	12.4495i	0.330280	−	1.01650i
$151$	3.70820			0.301769			0.150885	−	0.988551i	$-0.451788\pi$
$151$	3.70820			0.301769			0.150885	+	0.988551i	$0.451788\pi$
$152$	−0.690983	+	0.502029i	−0.0560461	+	0.0407199i
$153$	9.35410	−	28.7890i	0.756234	−	2.32745i
$154$	−0.218847	+	0.673542i	−0.0176352	+	0.0542756i
$155$	9.47214			0.760820
$156$	−0.809017	−	2.48990i	−0.0647732	−	0.199351i
$157$	−15.5623			−1.24201			−0.621004	−	0.783808i	$-0.713275\pi$
$157$	−15.5623			−1.24201			−0.621004	+	0.783808i	$0.713275\pi$
$158$	0.854102	+	2.62866i	0.0679487	+	0.209125i
$159$	3.23607	+	2.35114i	0.256637	+	0.186458i
$160$	−0.690983	+	2.12663i	−0.0546270	+	0.168125i
$161$	−15.1353	+	10.9964i	−1.19283	+	0.866638i
$162$	−4.61803	−	3.35520i	−0.362827	−	0.263609i
$163$	3.92705	+	2.85317i	0.307590	+	0.223477i	0.730862	−	0.682525i	$-0.239118\pi$
$163$	3.92705	+	2.85317i	0.307590	+	0.223477i	−0.423271	+	0.906003i	$0.639118\pi$
$164$	6.04508	−	4.39201i	0.472042	−	0.342958i
$165$	1.38197			0.107586
$166$	−10.8992	−	7.91872i	−0.845941	−	0.614612i
$167$	4.82624	+	14.8536i	0.373466	+	1.14941i	0.944508	+	0.328488i	$0.106539\pi$
$167$	4.82624	+	14.8536i	0.373466	+	1.14941i	−0.571043	+	0.820920i	$0.693461\pi$
$168$	−7.85410			−0.605957
$169$	−3.70820	−	11.4127i	−0.285246	−	0.877898i
$170$	14.2082	−	10.3229i	1.08972	−	0.791728i
$171$	−1.01722	+	3.13068i	−0.0777888	+	0.239409i
$172$	−0.545085	+	1.67760i	−0.0415623	+	0.127916i
$173$	−2.61803	+	1.90211i	−0.199045	+	0.144615i	−0.682843	−	0.730565i	$-0.739257\pi$
$173$	−2.61803	+	1.90211i	−0.199045	+	0.144615i	0.483798	+	0.875180i	$0.339257\pi$
$174$	−1.38197			−0.104767
$175$	12.1353	+	8.81678i	0.917339	+	0.666486i
$176$	−0.236068			−0.0177943
$177$	9.47214	−	6.88191i	0.711969	−	0.517276i
$178$	1.38197	−	4.25325i	0.103583	−	0.318795i
$179$	−3.45492	+	10.6331i	−0.258232	+	0.794758i	0.734943	+	0.678129i	$0.237209\pi$
$179$	−3.45492	+	10.6331i	−0.258232	+	0.794758i	−0.993176	+	0.116629i	$0.962791\pi$
$180$	2.66312	+	8.19624i	0.198497	+	0.610911i
$181$	−6.61803	−	20.3682i	−0.491915	−	1.51396i	−0.821710	−	0.569905i	$-0.806980\pi$
$181$	−6.61803	−	20.3682i	−0.491915	−	1.51396i	0.329796	−	0.944052i	$-0.393020\pi$
$182$	3.00000			0.222375
$183$	1.73607	+	5.34307i	0.128334	+	0.394971i
$184$	−5.04508	−	3.66547i	−0.371929	−	0.270222i
$185$	−13.2533	+	9.62908i	−0.974401	+	0.707944i
$186$	−8.97214	+	6.51864i	−0.657869	+	0.477970i
$187$	1.50000	+	1.08981i	0.109691	+	0.0796951i
$188$	−4.80902	−	3.49396i	−0.350734	−	0.254823i
$189$	−5.42705	+	3.94298i	−0.394760	+	0.286810i
$190$	−1.54508	+	1.12257i	−0.112092	+	0.0814398i
$191$	−14.2812	−	10.3759i	−1.03335	−	0.750771i	−0.0643719	−	0.997926i	$-0.520504\pi$
$191$	−14.2812	−	10.3759i	−1.03335	−	0.750771i	−0.968976	+	0.247155i	$0.920504\pi$
$192$	−0.809017	−	2.48990i	−0.0583858	−	0.179693i
$193$	16.6525			1.19867			0.599336	−	0.800498i	$-0.295431\pi$
$193$	16.6525			1.19867			0.599336	+	0.800498i	$0.295431\pi$
$194$	3.26393	+	10.0453i	0.234337	+	0.721214i
$195$	−1.80902	−	5.56758i	−0.129546	−	0.398703i
$196$	0.618034	−	1.90211i	0.0441453	−	0.135865i
$197$	3.70820	−	11.4127i	0.264199	−	0.813120i	−0.727678	−	0.685919i	$-0.759401\pi$
$197$	3.70820	−	11.4127i	0.264199	−	0.813120i	0.991877	−	0.127201i	$-0.0405994\pi$
$198$	−0.736068	+	0.534785i	−0.0523101	+	0.0380055i
$199$	−17.5623			−1.24496			−0.622479	−	0.782636i	$-0.713875\pi$
$199$	−17.5623			−1.24496			−0.622479	+	0.782636i	$0.713875\pi$
$200$	−1.54508	+	4.75528i	−0.109254	+	0.336249i
$201$	15.0902			1.06438
$202$	−1.30902	+	0.951057i	−0.0921021	+	0.0669161i
$203$	0.489357	−	1.50609i	0.0343461	−	0.105706i
$204$	−6.35410	+	19.5559i	−0.444876	+	1.36919i
$205$	13.5172	−	9.82084i	0.944084	−	0.685917i
$206$	6.13525	+	18.8824i	0.427463	+	1.31560i
$207$	−24.0344			−1.67051
$208$	0.309017	+	0.951057i	0.0214265	+	0.0659439i
$209$	−0.163119	−	0.118513i	−0.0112832	−	0.00819771i
$210$	−17.5623			−1.21191
$211$	−9.11803	+	6.62464i	−0.627711	+	0.456059i	−0.855607	−	0.517627i	$-0.826816\pi$
$211$	−9.11803	+	6.62464i	−0.627711	+	0.456059i	0.227895	+	0.973686i	$0.426816\pi$
$212$	−1.23607	−	0.898056i	−0.0848935	−	0.0616787i
$213$	−6.35410	−	4.61653i	−0.435376	−	0.316319i
$214$	8.16312	−	5.93085i	0.558019	−	0.405425i
$215$	−1.21885	+	3.75123i	−0.0831247	+	0.255831i
$216$	−1.80902	−	1.31433i	−0.123088	−	0.0894287i
$217$	−3.92705	−	12.0862i	−0.266586	−	0.820466i
$218$	15.0000			1.01593
$219$	4.61803	+	14.2128i	0.312058	+	0.960415i
$220$	−0.527864			−0.0355886
$221$	2.42705	−	7.46969i	0.163261	−	0.502466i
$222$	5.92705	−	18.2416i	0.397798	−	1.22430i
$223$	7.28115	−	5.29007i	0.487582	−	0.354249i	−0.316672	−	0.948535i	$-0.602565\pi$
$223$	7.28115	−	5.29007i	0.487582	−	0.354249i	0.804254	+	0.594286i	$0.202565\pi$
$224$	3.00000			0.200446
$225$	5.95492	+	18.3273i	0.396994	+	1.22182i
$226$	−8.23607			−0.547855
$227$	12.4271	−	9.02878i	0.824812	−	0.599261i	−0.0932746	−	0.995640i	$-0.529733\pi$
$227$	12.4271	−	9.02878i	0.824812	−	0.599261i	0.918087	+	0.396379i	$0.129733\pi$
$228$	0.690983	−	2.12663i	0.0457615	−	0.140839i
$229$	5.42705	−	16.7027i	0.358630	−	1.10375i	−0.595245	−	0.803544i	$-0.702945\pi$
$229$	5.42705	−	16.7027i	0.358630	−	1.10375i	0.953875	−	0.300204i	$-0.0970549\pi$
$230$	−11.2812	−	8.19624i	−0.743857	−	0.540444i
$231$	−0.572949	−	1.76336i	−0.0376973	−	0.116020i
$232$	0.527864			0.0346560
$233$	8.56231	+	26.3521i	0.560935	+	1.72638i	0.679730	+	0.733463i	$0.262097\pi$
$233$	8.56231	+	26.3521i	0.560935	+	1.72638i	−0.118795	+	0.992919i	$0.537903\pi$
$234$	3.11803	+	2.26538i	0.203832	+	0.148093i
$235$	−10.7533	−	7.81272i	−0.701467	−	0.509646i
$236$	−3.61803	+	2.62866i	−0.235514	+	0.171111i
$237$	−5.85410	−	4.25325i	−0.380265	−	0.276279i
$238$	−19.0623	−	13.8496i	−1.23563	−	0.897735i
$239$	14.6353	−	10.6331i	0.946676	−	0.687800i	−0.00334240	−	0.999994i	$-0.501064\pi$
$239$	14.6353	−	10.6331i	0.946676	−	0.687800i	0.950018	+	0.312194i	$0.101064\pi$
$240$	−1.80902	−	5.56758i	−0.116772	−	0.359386i
$241$	−10.8262	−	7.86572i	−0.697379	−	0.506676i	0.181698	−	0.983354i	$-0.441841\pi$
$241$	−10.8262	−	7.86572i	−0.697379	−	0.506676i	−0.879078	+	0.476679i	$0.841841\pi$
$242$	3.38197	+	10.4086i	0.217401	+	0.669092i
$243$	21.6525			1.38901
$244$	−0.663119	−	2.04087i	−0.0424518	−	0.130653i
$245$	1.38197	−	4.25325i	0.0882906	−	0.271730i
$246$	−6.04508	+	18.6049i	−0.385421	+	1.18620i
$247$	−0.263932	+	0.812299i	−0.0167936	+	0.0516854i
$248$	3.42705	−	2.48990i	0.217618	−	0.158109i
$249$	35.2705			2.23518
$250$	−3.45492	+	10.6331i	−0.218508	+	0.672499i
$251$	23.1803			1.46313			0.731565	−	0.681772i	$-0.238790\pi$
$251$	23.1803			1.46313			0.731565	+	0.681772i	$0.238790\pi$
$252$	9.35410	−	6.79615i	0.589253	−	0.428117i
$253$	0.454915	−	1.40008i	0.0286003	−	0.0880226i
$254$	3.85410	−	11.8617i	0.241828	−	0.744270i
$255$	−14.2082	+	43.7284i	−0.889752	+	2.73838i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−16.7426			−1.04438			−0.522189	−	0.852830i	$-0.674884\pi$
$257$	−16.7426			−1.04438			−0.522189	+	0.852830i	$0.674884\pi$
$258$	−1.42705	−	4.39201i	−0.0888443	−	0.273435i
$259$	17.7812	+	12.9188i	1.10487	+	0.802733i
$260$	0.690983	+	2.12663i	0.0428529	+	0.131888i
$261$	1.64590	−	1.19581i	0.101879	−	0.0740191i
$262$	8.42705	+	6.12261i	0.520625	+	0.378256i
$263$	−1.92705	−	1.40008i	−0.118827	−	0.0863329i	0.526785	−	0.849999i	$-0.323397\pi$
$263$	−1.92705	−	1.40008i	−0.118827	−	0.0863329i	−0.645612	+	0.763666i	$0.723397\pi$
$264$	0.500000	−	0.363271i	0.0307729	−	0.0223578i
$265$	−2.76393	−	2.00811i	−0.169787	−	0.123357i
$266$	2.07295	+	1.50609i	0.127101	+	0.0923440i
$267$	3.61803	+	11.1352i	0.221420	+	0.681461i
$268$	−5.76393			−0.352088
$269$	4.04508	+	12.4495i	0.246633	+	0.759059i	0.995364	+	0.0961842i	$0.0306638\pi$
$269$	4.04508	+	12.4495i	0.246633	+	0.759059i	−0.748730	+	0.662875i	$0.769336\pi$
$270$	−4.04508	−	2.93893i	−0.246176	−	0.178857i
$271$	−2.93769	+	9.04129i	−0.178452	+	0.549219i	−0.999774	−	0.0212453i	$-0.993237\pi$
$271$	−2.93769	+	9.04129i	−0.178452	+	0.549219i	0.821322	+	0.570465i	$0.193237\pi$
$272$	2.42705	−	7.46969i	0.147162	−	0.452917i
$273$	−6.35410	+	4.61653i	−0.384568	+	0.279405i
$274$	6.09017			0.367921
$275$	−1.18034			−0.0711772
$276$	16.3262			0.982724
$277$	−11.0902	+	8.05748i	−0.666344	+	0.484127i	−0.868799	−	0.495164i	$-0.835108\pi$
$277$	−11.0902	+	8.05748i	−0.666344	+	0.484127i	0.202456	+	0.979291i	$0.435108\pi$
$278$	−3.19098	+	9.82084i	−0.191382	+	0.589015i
$279$	5.04508	−	15.5272i	0.302041	−	0.929588i
$280$	6.70820			0.400892
$281$	−5.92705	−	18.2416i	−0.353578	−	1.08820i	−0.956829	−	0.290651i	$-0.906128\pi$
$281$	−5.92705	−	18.2416i	−0.353578	−	1.08820i	0.603251	−	0.797551i	$-0.293872\pi$
$282$	15.5623			0.926722
$283$	−7.94427	−	24.4500i	−0.472238	−	1.45340i	−0.849647	−	0.527352i	$-0.823185\pi$
$283$	−7.94427	−	24.4500i	−0.472238	−	1.45340i	0.377409	−	0.926047i	$-0.376815\pi$
$284$	2.42705	+	1.76336i	0.144019	+	0.104636i
$285$	1.54508	−	4.75528i	0.0915229	−	0.281679i
$286$	−0.190983	+	0.138757i	−0.0112931	+	0.00820489i
$287$	−18.1353	−	13.1760i	−1.07049	−	0.777757i
$288$	3.11803	+	2.26538i	0.183732	+	0.133489i
$289$	−36.1525	+	26.2663i	−2.12662	+	1.54508i
$290$	1.18034			0.0693119
$291$	−22.3713	−	16.2537i	−1.31143	−	0.952810i
$292$	−1.76393	−	5.42882i	−0.103226	−	0.317698i
$293$	−11.5623			−0.675477			−0.337739	−	0.941240i	$-0.609662\pi$
$293$	−11.5623			−0.675477			−0.337739	+	0.941240i	$0.609662\pi$
$294$	1.61803	+	4.97980i	0.0943657	+	0.290428i
$295$	−8.09017	+	5.87785i	−0.471028	+	0.342222i
$296$	−2.26393	+	6.96767i	−0.131588	+	0.404987i
$297$	0.163119	−	0.502029i	0.00946512	−	0.0291307i
$298$	−1.80902	+	1.31433i	−0.104794	+	0.0761370i
$299$	−6.23607			−0.360641
$300$	−4.04508	−	12.4495i	−0.233543	−	0.718772i
$301$	5.29180			0.305014
$302$	3.00000	−	2.17963i	0.172631	−	0.125423i
$303$	1.30902	−	4.02874i	0.0752011	−	0.231445i
$304$	−0.263932	+	0.812299i	−0.0151375	+	0.0465886i
$305$	−1.48278	−	4.56352i	−0.0849037	−	0.261307i
$306$	−9.35410	−	28.7890i	−0.534738	−	1.64576i
$307$	17.1246			0.977353			0.488677	−	0.872465i	$-0.337480\pi$
$307$	17.1246			0.977353			0.488677	+	0.872465i	$0.337480\pi$
$308$	0.218847	+	0.673542i	0.0124700	+	0.0383786i
$309$	−42.0517	−	30.5523i	−2.39224	−	1.73806i
$310$	7.66312	−	5.56758i	0.435236	−	0.316217i
$311$	17.0623	−	12.3965i	0.967515	−	0.702941i	0.0126308	−	0.999920i	$-0.495979\pi$
$311$	17.0623	−	12.3965i	0.967515	−	0.702941i	0.954884	+	0.296980i	$0.0959794\pi$
$312$	−2.11803	−	1.53884i	−0.119910	−	0.0871198i
$313$	−2.88197	−	2.09387i	−0.162898	−	0.118353i	0.503350	−	0.864083i	$-0.332101\pi$
$313$	−2.88197	−	2.09387i	−0.162898	−	0.118353i	−0.666248	+	0.745730i	$0.732101\pi$
$314$	−12.5902	+	9.14729i	−0.710504	+	0.516212i
$315$	20.9164	−	15.1967i	1.17851	−	0.856235i
$316$	2.23607	+	1.62460i	0.125789	+	0.0913908i
$317$	3.28115	+	10.0984i	0.184288	+	0.567180i	0.999935	−	0.0113694i	$-0.00361906\pi$
$317$	3.28115	+	10.0984i	0.184288	+	0.567180i	−0.815647	+	0.578549i	$0.803619\pi$
$318$	4.00000			0.224309
$319$	0.0385072	+	0.118513i	0.00215599	+	0.00663545i
$320$	0.690983	+	2.12663i	0.0386271	+	0.118882i
$321$	−8.16312	+	25.1235i	−0.455621	+	1.40226i
$322$	−5.78115	+	17.7926i	−0.322171	+	0.991541i
$323$	5.42705	−	3.94298i	0.301969	−	0.219393i
$324$	−5.70820			−0.317122
$325$	1.54508	+	4.75528i	0.0857059	+	0.263776i
$326$	4.85410			0.268844
$327$	−31.7705	+	23.0826i	−1.75691	+	1.27647i
$328$	2.30902	−	7.10642i	0.127494	−	0.392387i
$329$	−5.51064	+	16.9600i	−0.303812	+	0.935036i
$330$	1.11803	−	0.812299i	0.0615457	−	0.0447156i
$331$	1.40983	+	4.33901i	0.0774913	+	0.238494i	0.982297	−	0.187332i	$-0.0599839\pi$
$331$	1.40983	+	4.33901i	0.0774913	+	0.238494i	−0.904805	+	0.425825i	$0.859984\pi$
$332$	−13.4721			−0.739380
$333$	8.72542	+	26.8541i	0.478150	+	1.47160i
$334$	12.6353	+	9.18005i	0.691370	+	0.502310i
$335$	−12.8885			−0.704176
$336$	−6.35410	+	4.61653i	−0.346645	+	0.251852i
$337$	25.4164	+	18.4661i	1.38452	+	1.00591i	0.996442	+	0.0842863i	$0.0268610\pi$
$337$	25.4164	+	18.4661i	1.38452	+	1.00591i	0.388078	+	0.921626i	$0.373139\pi$
$338$	−9.70820	−	7.05342i	−0.528057	−	0.383656i
$339$	17.4443	−	12.6740i	0.947443	−	0.688357i
$340$	5.42705	−	16.7027i	0.294323	−	0.905834i
$341$	0.809017	+	0.587785i	0.0438107	+	0.0318304i
$342$	1.01722	+	3.13068i	0.0550050	+	0.169288i
$343$	15.0000			0.809924
$344$	0.545085	+	1.67760i	0.0293890	+	0.0904501i
$345$	36.5066			1.96545
$346$	−1.00000	+	3.07768i	−0.0537603	+	0.165457i
$347$	−3.06231	+	9.42481i	−0.164393	+	0.505950i	−0.998991	−	0.0449095i	$-0.985700\pi$
$347$	−3.06231	+	9.42481i	−0.164393	+	0.505950i	0.834598	+	0.550860i	$0.185700\pi$
$348$	−1.11803	+	0.812299i	−0.0599329	+	0.0435438i
$349$	−22.2361			−1.19027			−0.595135	−	0.803626i	$-0.702901\pi$
$349$	−22.2361			−1.19027			−0.595135	+	0.803626i	$0.702901\pi$
$350$	15.0000			0.801784
$351$	−2.23607			−0.119352
$352$	−0.190983	+	0.138757i	−0.0101794	+	0.00739579i
$353$	−5.18034	+	15.9434i	−0.275722	+	0.848584i	0.713306	+	0.700853i	$0.247197\pi$
$353$	−5.18034	+	15.9434i	−0.275722	+	0.848584i	−0.989028	+	0.147731i	$0.952803\pi$
$354$	3.61803	−	11.1352i	0.192296	−	0.591827i
$355$	5.42705	+	3.94298i	0.288038	+	0.209272i
$356$	−1.38197	−	4.25325i	−0.0732441	−	0.225422i
$357$	61.6869			3.26482
$358$	3.45492	+	10.6331i	0.182598	+	0.561979i
$359$	−2.50000	−	1.81636i	−0.131945	−	0.0958636i	0.519855	−	0.854254i	$-0.325986\pi$
$359$	−2.50000	−	1.81636i	−0.131945	−	0.0958636i	−0.651800	+	0.758391i	$0.725986\pi$
$360$	6.97214	+	5.06555i	0.367464	+	0.266978i
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	−17.3262	−	12.5882i	−0.910647	−	0.661624i
$363$	−23.1803	−	16.8415i	−1.21665	−	0.883950i
$364$	2.42705	−	1.76336i	0.127212	−	0.0924250i
$365$	−3.94427	−	12.1392i	−0.206453	−	0.635396i
$366$	4.54508	+	3.30220i	0.237575	+	0.172609i
$367$	−9.74671	−	29.9973i	−0.508774	−	1.56585i	−0.794332	−	0.607484i	$-0.792179\pi$
$367$	−9.74671	−	29.9973i	−0.508774	−	1.56585i	0.285557	−	0.958362i	$-0.407821\pi$
$368$	−6.23607			−0.325078
$369$	−8.89919	−	27.3889i	−0.463273	−	1.42581i
$370$	−5.06231	+	15.5802i	−0.263177	+	0.809975i
$371$	−1.41641	+	4.35926i	−0.0735362	+	0.226321i
$372$	−3.42705	+	10.5474i	−0.177684	+	0.546856i
$373$	13.1353	−	9.54332i	0.680118	−	0.494134i	−0.193279	−	0.981144i	$-0.561912\pi$
$373$	13.1353	−	9.54332i	0.680118	−	0.494134i	0.873397	+	0.487009i	$0.161912\pi$
$374$	1.85410			0.0958733
$375$	−9.04508	−	27.8379i	−0.467086	−	1.43754i
$376$	−5.94427			−0.306552
$377$	0.427051	−	0.310271i	0.0219942	−	0.0159798i
$378$	−2.07295	+	6.37988i	−0.106621	+	0.328146i
$379$	0.163119	−	0.502029i	0.00837886	−	0.0257875i	−0.946780	−	0.321882i	$-0.895684\pi$
$379$	0.163119	−	0.502029i	0.00837886	−	0.0257875i	0.955159	+	0.296095i	$0.0956845\pi$
$380$	−0.590170	+	1.81636i	−0.0302751	+	0.0931771i
$381$	10.0902	+	31.0543i	0.516935	+	1.59096i
$382$	−17.6525			−0.903179
$383$	−1.33688	−	4.11450i	−0.0683114	−	0.210241i	0.911073	−	0.412244i	$-0.135255\pi$
$383$	−1.33688	−	4.11450i	−0.0683114	−	0.210241i	−0.979385	+	0.202003i	$0.935255\pi$
$384$	−2.11803	−	1.53884i	−0.108085	−	0.0785287i
$385$	0.489357	+	1.50609i	0.0249399	+	0.0767572i
$386$	13.4721	−	9.78808i	0.685714	−	0.498200i
$387$	5.50000	+	3.99598i	0.279581	+	0.203127i
$388$	8.54508	+	6.20837i	0.433811	+	0.315182i
$389$	26.8713	−	19.5232i	1.36243	−	0.989863i	0.364144	−	0.931343i	$-0.381362\pi$
$389$	26.8713	−	19.5232i	1.36243	−	0.989863i	0.998286	−	0.0585208i	$-0.0186384\pi$
$390$	−4.73607	−	3.44095i	−0.239820	−	0.174240i
$391$	39.6246	+	28.7890i	2.00390	+	1.45592i
$392$	−0.618034	−	1.90211i	−0.0312154	−	0.0960712i
$393$	−27.2705			−1.37562
$394$	−3.70820	−	11.4127i	−0.186817	−	0.574962i
$395$	5.00000	+	3.63271i	0.251577	+	0.182782i
$396$	−0.281153	+	0.865300i	−0.0141285	+	0.0434830i
$397$	−1.78115	+	5.48183i	−0.0893935	+	0.275125i	−0.985752	−	0.168205i	$-0.946203\pi$
$397$	−1.78115	+	5.48183i	−0.0893935	+	0.275125i	0.896359	+	0.443330i	$0.146203\pi$
$398$	−14.2082	+	10.3229i	−0.712193	+	0.517438i
$399$	−6.70820			−0.335830
$400$	1.54508	+	4.75528i	0.0772542	+	0.237764i
$401$	8.18034			0.408507			0.204253	−	0.978918i	$-0.434523\pi$
$401$	8.18034			0.408507			0.204253	+	0.978918i	$0.434523\pi$
$402$	12.2082	−	8.86978i	0.608890	−	0.442384i
$403$	1.30902	−	4.02874i	0.0652068	−	0.200686i
$404$	−0.500000	+	1.53884i	−0.0248759	+	0.0765602i
$405$	−12.7639			−0.634245
$406$	−0.489357	−	1.50609i	−0.0242864	−	0.0747458i
$407$	−1.72949			−0.0857276
$408$	6.35410	+	19.5559i	0.314575	+	0.968162i
$409$	−5.42705	−	3.94298i	−0.268350	−	0.194968i	0.445470	−	0.895297i	$-0.353037\pi$
$409$	−5.42705	−	3.94298i	−0.268350	−	0.194968i	−0.713820	+	0.700329i	$0.753037\pi$
$410$	5.16312	−	15.8904i	0.254988	−	0.784773i
$411$	−12.8992	+	9.37181i	−0.636270	+	0.462277i
$412$	16.0623	+	11.6699i	0.791333	+	0.574937i
$413$	10.8541	+	7.88597i	0.534095	+	0.388043i
$414$	−19.4443	+	14.1271i	−0.955634	+	0.694309i
$415$	−30.1246			−1.47876
$416$	0.809017	+	0.587785i	0.0396653	+	0.0288185i
$417$	−8.35410	−	25.7113i	−0.409102	−	1.25909i
$418$	−0.201626			−0.00986186
$419$	8.41641	+	25.9030i	0.411168	+	1.26545i	0.915633	+	0.402014i	$0.131690\pi$
$419$	8.41641	+	25.9030i	0.411168	+	1.26545i	−0.504465	+	0.863432i	$0.668310\pi$
$420$	−14.2082	+	10.3229i	−0.693289	+	0.503704i
$421$	−3.79180	+	11.6699i	−0.184801	+	0.568758i	−0.999945	−	0.0104998i	$-0.996658\pi$
$421$	−3.79180	+	11.6699i	−0.184801	+	0.568758i	0.815144	+	0.579258i	$0.196658\pi$
$422$	−3.48278	+	10.7189i	−0.169539	+	0.521787i
$423$	−18.5344	+	13.4661i	−0.901175	+	0.654742i
$424$	−1.52786			−0.0741996
$425$	12.1353	−	37.3485i	0.588646	−	1.81167i
$426$	−7.85410			−0.380532
$427$	−5.20820	+	3.78398i	−0.252043	+	0.183120i
$428$	3.11803	−	9.59632i	0.150716	−	0.463856i
$429$	0.190983	−	0.587785i	0.00922075	−	0.0283785i
$430$	1.21885	+	3.75123i	0.0587780	+	0.180900i
$431$	−9.90983	−	30.4993i	−0.477340	−	1.46910i	−0.842776	−	0.538264i	$-0.819080\pi$
$431$	−9.90983	−	30.4993i	−0.477340	−	1.46910i	0.365436	−	0.930836i	$-0.380920\pi$
$432$	−2.23607			−0.107583
$433$	7.21885	+	22.2173i	0.346916	+	1.06770i	0.960550	+	0.278106i	$0.0897068\pi$
$433$	7.21885	+	22.2173i	0.346916	+	1.06770i	−0.613635	+	0.789590i	$0.710293\pi$
$434$	−10.2812	−	7.46969i	−0.493511	−	0.358557i
$435$	−2.50000	+	1.81636i	−0.119866	+	0.0870876i
$436$	12.1353	−	8.81678i	0.581173	−	0.422247i
$437$	−4.30902	−	3.13068i	−0.206128	−	0.149761i
$438$	12.0902	+	8.78402i	0.577691	+	0.419717i
$439$	4.57295	−	3.32244i	0.218255	−	0.158572i	−0.473286	−	0.880909i	$-0.656932\pi$
$439$	4.57295	−	3.32244i	0.218255	−	0.158572i	0.691541	+	0.722337i	$0.256932\pi$
$440$	−0.427051	+	0.310271i	−0.0203589	+	0.0147916i
$441$	−6.23607	−	4.53077i	−0.296956	−	0.215751i
$442$	−2.42705	−	7.46969i	−0.115443	−	0.355297i
$443$	−7.41641			−0.352364			−0.176182	−	0.984358i	$-0.556375\pi$
$443$	−7.41641			−0.352364			−0.176182	+	0.984358i	$0.556375\pi$
$444$	−5.92705	−	18.2416i	−0.281285	−	0.865707i
$445$	−3.09017	−	9.51057i	−0.146488	−	0.450844i
$446$	2.78115	−	8.55951i	0.131691	−	0.405304i
$447$	1.80902	−	5.56758i	0.0855636	−	0.263338i
$448$	2.42705	−	1.76336i	0.114667	−	0.0833107i
$449$	13.9443			0.658071			0.329035	−	0.944318i	$-0.393276\pi$
$449$	13.9443			0.658071			0.329035	+	0.944318i	$0.393276\pi$
$450$	15.5902	+	11.3269i	0.734928	+	0.533956i
$451$	1.76393			0.0830603
$452$	−6.66312	+	4.84104i	−0.313407	+	0.227703i
$453$	−3.00000	+	9.23305i	−0.140952	+	0.433807i
$454$	4.74671	−	14.6089i	0.222774	−	0.685628i
$455$	5.42705	−	3.94298i	0.254424	−	0.184850i
$456$	−0.690983	−	2.12663i	−0.0323582	−	0.0995884i
$457$	−11.2148			−0.524605			−0.262303	−	0.964986i	$-0.584482\pi$
$457$	−11.2148			−0.524605			−0.262303	+	0.964986i	$0.584482\pi$
$458$	−5.42705	−	16.7027i	−0.253589	−	0.780468i
$459$	14.2082	+	10.3229i	0.663182	+	0.481830i
$460$	−13.9443			−0.650155
$461$	−22.7984	+	16.5640i	−1.06183	+	0.771462i	−0.974425	−	0.224711i	$-0.927856\pi$
$461$	−22.7984	+	16.5640i	−1.06183	+	0.771462i	−0.0874008	+	0.996173i	$0.527856\pi$
$462$	−1.50000	−	1.08981i	−0.0697863	−	0.0507027i
$463$	−9.69098	−	7.04091i	−0.450378	−	0.327219i	0.339367	−	0.940654i	$-0.389787\pi$
$463$	−9.69098	−	7.04091i	−0.450378	−	0.327219i	−0.789745	+	0.613435i	$0.789787\pi$
$464$	0.427051	−	0.310271i	0.0198253	−	0.0144040i
$465$	−7.66312	+	23.5847i	−0.355369	+	1.09371i
$466$	22.4164	+	16.2865i	1.03842	+	0.754456i
$467$	0.982779	+	3.02468i	0.0454776	+	0.139966i	0.971217	−	0.238196i	$-0.0765562\pi$
$467$	0.982779	+	3.02468i	0.0454776	+	0.139966i	−0.925739	+	0.378162i	$0.876556\pi$
$468$	3.85410			0.178156
$469$	5.34346	+	16.4455i	0.246738	+	0.759381i
$470$	−13.2918			−0.613105
$471$	12.5902	−	38.7486i	0.580124	−	1.78544i
$472$	−1.38197	+	4.25325i	−0.0636101	+	0.195772i
$473$	−0.336881	+	0.244758i	−0.0154898	+	0.0112540i
$474$	−7.23607			−0.332364
$475$	−1.31966	+	4.06150i	−0.0605502	+	0.186354i
$476$	−23.5623			−1.07998
$477$	−4.76393	+	3.46120i	−0.218125	+	0.158477i
$478$	5.59017	−	17.2048i	0.255688	−	0.786928i
$479$	−12.2984	+	37.8505i	−0.561927	+	1.72943i	0.114983	+	0.993368i	$0.463319\pi$
$479$	−12.2984	+	37.8505i	−0.561927	+	1.72943i	−0.676910	+	0.736066i	$0.736681\pi$
$480$	−4.73607	−	3.44095i	−0.216171	−	0.157057i
$481$	2.26393	+	6.96767i	0.103226	+	0.317698i
$482$	−13.3820			−0.609532
$483$	−15.1353	−	46.5815i	−0.688678	−	2.11953i
$484$	8.85410	+	6.43288i	0.402459	+	0.292404i
$485$	19.1074	+	13.8823i	0.867622	+	0.630364i
$486$	17.5172	−	12.7270i	0.794597	−	0.577309i
$487$	14.6631	+	10.6534i	0.664449	+	0.482751i	0.868163	−	0.496280i	$-0.165301\pi$
$487$	14.6631	+	10.6534i	0.664449	+	0.482751i	−0.203713	+	0.979031i	$0.565301\pi$
$488$	−1.73607	−	1.26133i	−0.0785881	−	0.0570976i
$489$	−10.2812	+	7.46969i	−0.464930	+	0.337791i
$490$	−1.38197	−	4.25325i	−0.0624309	−	0.192142i
$491$	−11.9443	−	8.67802i	−0.539037	−	0.391634i	0.284690	−	0.958620i	$-0.408109\pi$
$491$	−11.9443	−	8.67802i	−0.539037	−	0.391634i	−0.823727	+	0.566986i	$0.808109\pi$
$492$	6.04508	+	18.6049i	0.272533	+	0.838772i
$493$	−4.14590			−0.186722
$494$	0.263932	+	0.812299i	0.0118749	+	0.0365471i
$495$	−0.628677	+	1.93487i	−0.0282569	+	0.0869659i
$496$	1.30902	−	4.02874i	0.0587766	−	0.180896i
$497$	2.78115	−	8.55951i	0.124752	−	0.383946i
$498$	28.5344	−	20.7315i	1.27866	−	0.929000i
$499$	40.8541			1.82888			0.914440	−	0.404721i	$-0.132631\pi$
$499$	40.8541			1.82888			0.914440	+	0.404721i	$0.132631\pi$
$500$	3.45492	+	10.6331i	0.154508	+	0.475528i
$501$	−40.8885			−1.82677
$502$	18.7533	−	13.6251i	0.837000	−	0.608116i
$503$	2.31966	−	7.13918i	0.103429	−	0.318320i	−0.885930	−	0.463819i	$-0.846479\pi$
$503$	2.31966	−	7.13918i	0.103429	−	0.318320i	0.989358	+	0.145499i	$0.0464787\pi$
$504$	3.57295	−	10.9964i	0.159152	−	0.489819i
$505$	−1.11803	+	3.44095i	−0.0497519	+	0.153120i
$506$	−0.454915	−	1.40008i	−0.0202234	−	0.0622413i
$507$	31.4164			1.39525
$508$	−3.85410	−	11.8617i	−0.170998	−	0.526278i
$509$	10.5902	+	7.69421i	0.469401	+	0.341040i	0.797208	−	0.603705i	$-0.206310\pi$
$509$	10.5902	+	7.69421i	0.469401	+	0.341040i	−0.327807	+	0.944745i	$0.606310\pi$
$510$	14.2082	+	43.7284i	0.629150	+	1.93632i
$511$	−13.8541	+	10.0656i	−0.612869	+	0.445276i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−1.54508	−	1.12257i	−0.0682172	−	0.0495627i
$514$	−13.5451	+	9.84108i	−0.597448	+	0.434071i
$515$	35.9164	+	26.0948i	1.58267	+	1.14987i
$516$	−3.73607	−	2.71441i	−0.164471	−	0.119495i
$517$	−0.433629	−	1.33457i	−0.0190710	−	0.0586944i
$518$	21.9787			0.965689
$519$	−2.61803	−	8.05748i	−0.114919	−	0.353684i
$520$	1.80902	+	1.31433i	0.0793306	+	0.0576371i
$521$	10.0279	−	30.8626i	0.439329	−	1.35211i	−0.449256	−	0.893403i	$-0.648311\pi$
$521$	10.0279	−	30.8626i	0.439329	−	1.35211i	0.888585	−	0.458712i	$-0.151689\pi$
$522$	0.628677	−	1.93487i	0.0275164	−	0.0846869i
$523$	−21.5623	+	15.6659i	−0.942854	+	0.685023i	−0.949106	−	0.314957i	$-0.898010\pi$
$523$	−21.5623	+	15.6659i	−0.942854	+	0.685023i	0.00625211	+	0.999980i	$0.498010\pi$
$524$	10.4164			0.455043
$525$	−31.7705	+	23.0826i	−1.38658	+	1.00741i
$526$	−2.38197			−0.103859
$527$	−26.9164	+	19.5559i	−1.17250	+	0.851869i
$528$	0.190983	−	0.587785i	0.00831147	−	0.0255801i
$529$	4.90983	−	15.1109i	0.213471	−	0.656996i
$530$	−3.41641			−0.148399
$531$	5.32624	+	16.3925i	0.231139	+	0.711373i
$532$	2.56231			0.111090
$533$	−2.30902	−	7.10642i	−0.100015	−	0.307813i
$534$	9.47214	+	6.88191i	0.409899	+	0.297809i
$535$	6.97214	−	21.4580i	0.301432	−	0.927711i
$536$	−4.66312	+	3.38795i	−0.201416	+	0.146337i
$537$	−23.6803	−	17.2048i	−1.02188	−	0.742441i
$538$	10.5902	+	7.69421i	0.456575	+	0.331721i
$539$	0.381966	−	0.277515i	0.0164524	−	0.0119534i
$540$	−5.00000			−0.215166
$541$	−23.2254	−	16.8743i	−0.998539	−	0.725481i	−0.0367646	−	0.999324i	$-0.511705\pi$
$541$	−23.2254	−	16.8743i	−0.998539	−	0.725481i	−0.961774	+	0.273843i	$0.911705\pi$
$542$	2.93769	+	9.04129i	0.126185	+	0.388357i
$543$	56.0689			2.40615
$544$	−2.42705	−	7.46969i	−0.104059	−	0.320261i
$545$	27.1353	−	19.7149i	1.16235	−	0.844494i
$546$	−2.42705	+	7.46969i	−0.103868	+	0.319673i
$547$	3.28115	−	10.0984i	0.140292	−	0.431774i	−0.856084	−	0.516837i	$-0.827109\pi$
$547$	3.28115	−	10.0984i	0.140292	−	0.431774i	0.996376	+	0.0850631i	$0.0271092\pi$
$548$	4.92705	−	3.57971i	0.210473	−	0.152918i
$549$	−8.27051			−0.352977
$550$	−0.954915	+	0.693786i	−0.0407177	+	0.0295832i
$551$	0.450850			0.0192068
$552$	13.2082	−	9.59632i	0.562178	−	0.408447i
$553$	2.56231	−	7.88597i	0.108960	−	0.335345i
$554$	−4.23607	+	13.0373i	−0.179973	+	0.553901i
$555$	−13.2533	−	40.7894i	−0.562571	−	1.73141i
$556$	3.19098	+	9.82084i	0.135328	+	0.416496i
$557$	−10.8885			−0.461362			−0.230681	−	0.973029i	$-0.574095\pi$
$557$	−10.8885			−0.461362			−0.230681	+	0.973029i	$0.574095\pi$
$558$	−5.04508	−	15.5272i	−0.213575	−	0.657318i
$559$	1.42705	+	1.03681i	0.0603578	+	0.0438525i
$560$	5.42705	−	3.94298i	0.229335	−	0.166621i
$561$	−3.92705	+	2.85317i	−0.165800	+	0.120461i
$562$	−15.5172	−	11.2739i	−0.654554	−	0.475562i
$563$	28.1976	+	20.4867i	1.18839	+	0.863413i	0.993093	−	0.117332i	$-0.0374343\pi$
$563$	28.1976	+	20.4867i	1.18839	+	0.863413i	0.195293	+	0.980745i	$0.437434\pi$
$564$	12.5902	−	9.14729i	0.530142	−	0.385171i
$565$	−14.8992	+	10.8249i	−0.626814	+	0.455407i
$566$	−20.7984	−	15.1109i	−0.874221	−	0.635159i
$567$	5.29180	+	16.2865i	0.222235	+	0.683968i
$568$	3.00000			0.125877
$569$	6.87132	+	21.1478i	0.288061	+	0.886560i	0.985464	+	0.169882i	$0.0543385\pi$
$569$	6.87132	+	21.1478i	0.288061	+	0.886560i	−0.697404	+	0.716679i	$0.745661\pi$
$570$	−1.54508	−	4.75528i	−0.0647165	−	0.199177i
$571$	0.517221	−	1.59184i	0.0216450	−	0.0666165i	−0.939651	−	0.342136i	$-0.888850\pi$
$571$	0.517221	−	1.59184i	0.0216450	−	0.0666165i	0.961296	+	0.275519i	$0.0888497\pi$
$572$	−0.0729490	+	0.224514i	−0.00305015	+	0.00938740i
$573$	37.3885	−	27.1644i	1.56193	−	1.13481i
$574$	−22.4164			−0.935643
$575$	−31.1803			−1.30031
$576$	3.85410			0.160588
$577$	34.7877	−	25.2748i	1.44823	−	1.05220i	0.461992	−	0.886884i	$-0.347135\pi$
$577$	34.7877	−	25.2748i	1.44823	−	1.05220i	0.986240	−	0.165318i	$-0.0528651\pi$
$578$	−13.8090	+	42.4998i	−0.574379	+	1.76776i
$579$	−13.4721	+	41.4630i	−0.559883	+	1.72314i
$580$	0.954915	−	0.693786i	0.0396507	−	0.0288079i
$581$	12.4894	+	38.4383i	0.518146	+	1.59469i
$582$	−27.6525			−1.14623
$583$	−0.111456	−	0.343027i	−0.00461604	−	0.0142067i
$584$	−4.61803	−	3.35520i	−0.191096	−	0.138839i
$585$	8.61803			0.356312
$586$	−9.35410	+	6.79615i	−0.386414	+	0.280746i
$587$	9.56231	+	6.94742i	0.394679	+	0.286751i	0.767370	−	0.641205i	$-0.221565\pi$
$587$	9.56231	+	6.94742i	0.394679	+	0.286751i	−0.372691	+	0.927955i	$0.621565\pi$
$588$	4.23607	+	3.07768i	0.174692	+	0.126922i
$589$	2.92705	−	2.12663i	0.120607	−	0.0876261i
$590$	−3.09017	+	9.51057i	−0.127220	+	0.391544i
$591$	25.4164	+	18.4661i	1.04549	+	0.759594i
$592$	2.26393	+	6.96767i	0.0930470	+	0.286369i
$593$	−47.0132			−1.93060			−0.965299	−	0.261145i	$-0.915900\pi$
$593$	−47.0132			−1.93060			−0.965299	+	0.261145i	$0.915900\pi$
$594$	−0.163119	−	0.502029i	−0.00669285	−	0.0205985i
$595$	−52.6869			−2.15995
$596$	−0.690983	+	2.12663i	−0.0283038	+	0.0871100i
$597$	14.2082	−	43.7284i	0.581503	−	1.78968i
$598$	−5.04508	+	3.66547i	−0.206309	+	0.149892i
$599$	−8.94427			−0.365453			−0.182727	−	0.983164i	$-0.558492\pi$
$599$	−8.94427			−0.365453			−0.182727	+	0.983164i	$0.558492\pi$
$600$	−10.5902	−	7.69421i	−0.432342	−	0.314115i
$601$	−14.8328			−0.605043			−0.302522	−	0.953143i	$-0.597828\pi$
$601$	−14.8328			−0.605043			−0.302522	+	0.953143i	$0.597828\pi$
$602$	4.28115	−	3.11044i	0.174487	−	0.126772i
$603$	−6.86475	+	21.1275i	−0.279554	+	0.860379i
$604$	1.14590	−	3.52671i	0.0466259	−	0.143500i
$605$	19.7984	+	14.3844i	0.804918	+	0.584807i
$606$	−1.30902	−	4.02874i	−0.0531752	−	0.163656i
$607$	−27.1459			−1.10182			−0.550909	−	0.834565i	$-0.685719\pi$
$607$	−27.1459			−1.10182			−0.550909	+	0.834565i	$0.685719\pi$
$608$	0.263932	+	0.812299i	0.0107039	+	0.0329431i
$609$	3.35410	+	2.43690i	0.135915	+	0.0987481i
$610$	−3.88197	−	2.82041i	−0.157176	−	0.114195i
$611$	−4.80902	+	3.49396i	−0.194552	+	0.141350i
$612$	−24.4894	−	17.7926i	−0.989924	−	0.719222i
$613$	33.6246	+	24.4297i	1.35809	+	0.986707i	0.998564	+	0.0535698i	$0.0170600\pi$
$613$	33.6246	+	24.4297i	1.35809	+	0.986707i	0.359521	+	0.933137i	$0.382940\pi$
$614$	13.8541	−	10.0656i	0.559106	−	0.406214i
$615$	13.5172	+	41.6017i	0.545067	+	1.67754i
$616$	0.572949	+	0.416272i	0.0230848	+	0.0167721i
$617$	−9.38197	−	28.8747i	−0.377704	−	1.16245i	−0.941636	−	0.336632i	$-0.890712\pi$
$617$	−9.38197	−	28.8747i	−0.377704	−	1.16245i	0.563933	−	0.825821i	$-0.309288\pi$
$618$	−51.9787			−2.09089
$619$	−14.5106	−	44.6592i	−0.583232	−	1.79500i	−0.606257	−	0.795269i	$-0.707330\pi$
$619$	−14.5106	−	44.6592i	−0.583232	−	1.79500i	0.0230252	−	0.999735i	$-0.492670\pi$
$620$	2.92705	−	9.00854i	0.117553	−	0.361792i
$621$	4.30902	−	13.2618i	0.172915	−	0.532177i
$622$	6.51722	−	20.0579i	0.261317	−	0.804250i
$623$	−10.8541	+	7.88597i	−0.434860	+	0.315945i
$624$	−2.61803			−0.104805
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	−3.56231			−0.142378
$627$	0.427051	−	0.310271i	0.0170548	−	0.0123910i
$628$	−4.80902	+	14.8006i	−0.191901	+	0.590610i
$629$	17.7812	−	54.7248i	0.708981	−	2.18202i
$630$	7.98936	−	24.5887i	0.318304	−	0.979638i
$631$	2.72949	+	8.40051i	0.108659	+	0.334419i	0.990572	−	0.136994i	$-0.0437441\pi$
$631$	2.72949	+	8.40051i	0.108659	+	0.334419i	−0.881913	+	0.471413i	$0.843744\pi$
$632$	2.76393			0.109943
$633$	−9.11803	−	28.0624i	−0.362409	−	1.11538i
$634$	8.59017	+	6.24112i	0.341159	+	0.247867i
$635$	−8.61803	−	26.5236i	−0.341996	−	1.05256i
$636$	3.23607	−	2.35114i	0.128318	−	0.0932288i
$637$	−1.61803	−	1.17557i	−0.0641088	−	0.0465778i
$638$	0.100813	+	0.0732450i	0.00399123	+	0.00289980i
$639$	9.35410	−	6.79615i	0.370043	−	0.268852i
$640$	1.80902	+	1.31433i	0.0715077	+	0.0519534i
$641$	−11.6180	−	8.44100i	−0.458885	−	0.333399i	0.334209	−	0.942499i	$-0.391531\pi$
$641$	−11.6180	−	8.44100i	−0.458885	−	0.333399i	−0.793094	+	0.609100i	$0.791531\pi$
$642$	8.16312	+	25.1235i	0.322173	+	0.991545i
$643$	−36.2361			−1.42901			−0.714506	−	0.699630i	$-0.753348\pi$
$643$	−36.2361			−1.42901			−0.714506	+	0.699630i	$0.753348\pi$
$644$	5.78115	+	17.7926i	0.227809	+	0.701125i
$645$	−8.35410	−	6.06961i	−0.328942	−	0.238991i
$646$	2.07295	−	6.37988i	0.0815591	−	0.251013i
$647$	2.36475	−	7.27794i	0.0929677	−	0.286125i	−0.893751	−	0.448563i	$-0.851936\pi$
$647$	2.36475	−	7.27794i	0.0929677	−	0.286125i	0.986719	+	0.162438i	$0.0519358\pi$
$648$	−4.61803	+	3.35520i	−0.181414	+	0.131805i
$649$	−1.05573			−0.0414410
$650$	4.04508	+	2.93893i	0.158661	+	0.115274i
$651$	33.2705			1.30397
$652$	3.92705	−	2.85317i	0.153795	−	0.111739i
$653$	12.5451	−	38.6098i	0.490927	−	1.51092i	−0.332282	−	0.943180i	$-0.607819\pi$
$653$	12.5451	−	38.6098i	0.490927	−	1.51092i	0.823209	−	0.567738i	$-0.192181\pi$
$654$	−12.1353	+	37.3485i	−0.474526	+	1.46044i
$655$	23.2918			0.910086
$656$	−2.30902	−	7.10642i	−0.0901520	−	0.277459i
$657$	−22.0000			−0.858302
$658$	5.51064	+	16.9600i	0.214827	+	0.661170i
$659$	−4.57295	−	3.32244i	−0.178137	−	0.129424i	0.495144	−	0.868811i	$-0.335115\pi$
$659$	−4.57295	−	3.32244i	−0.178137	−	0.129424i	−0.673281	+	0.739387i	$0.735115\pi$
$660$	0.427051	−	1.31433i	0.0166229	−	0.0511601i
$661$	−5.07295	+	3.68571i	−0.197315	+	0.143358i	−0.682056	−	0.731300i	$-0.738914\pi$
$661$	−5.07295	+	3.68571i	−0.197315	+	0.143358i	0.484741	+	0.874658i	$0.338914\pi$
$662$	3.69098	+	2.68166i	0.143454	+	0.104226i
$663$	16.6353	+	12.0862i	0.646060	+	0.469390i
$664$	−10.8992	+	7.91872i	−0.422970	+	0.307306i
$665$	5.72949			0.222180
$666$	22.8435	+	16.5967i	0.885166	+	0.643111i
$667$	1.01722	+	3.13068i	0.0393870	+	0.121221i
$668$	15.6180			0.604280
$669$	7.28115	+	22.4091i	0.281506	+	0.866385i
$670$	−10.4271	+	7.57570i	−0.402832	+	0.292675i
$671$	0.156541	−	0.481784i	0.00604320	−	0.0185991i
$672$	−2.42705	+	7.46969i	−0.0936255	+	0.288150i
$673$	1.00000	−	0.726543i	0.0385472	−	0.0280062i	−0.568345	−	0.822790i	$-0.692416\pi$
$673$	1.00000	−	0.726543i	0.0385472	−	0.0280062i	0.606892	+	0.794784i	$0.292416\pi$
$674$	31.4164			1.21011
$675$	−11.1803			−0.430331
$676$	−12.0000			−0.461538
$677$	−8.59017	+	6.24112i	−0.330147	+	0.239866i	−0.740493	−	0.672064i	$-0.765408\pi$
$677$	−8.59017	+	6.24112i	−0.330147	+	0.239866i	0.410346	+	0.911930i	$0.365408\pi$
$678$	6.66312	−	20.5070i	0.255896	−	0.787565i
$679$	9.79180	−	30.1360i	0.375775	−	1.15652i
$680$	−5.42705	−	16.7027i	−0.208118	−	0.640521i
$681$	12.4271	+	38.2465i	0.476206	+	1.46561i
$682$	1.00000			0.0382920
$683$	10.3090	+	31.7279i	0.394464	+	1.21403i	0.929379	+	0.369128i	$0.120344\pi$
$683$	10.3090	+	31.7279i	0.394464	+	1.21403i	−0.534915	+	0.844906i	$0.679656\pi$
$684$	2.66312	+	1.93487i	0.101827	+	0.0739816i
$685$	11.0172	−	8.00448i	0.420946	−	0.305835i
$686$	12.1353	−	8.81678i	0.463326	−	0.336626i
$687$	37.1976	+	27.0256i	1.41918	+	1.03109i
$688$	1.42705	+	1.03681i	0.0544058	+	0.0395281i
$689$	−1.23607	+	0.898056i	−0.0470904	+	0.0342132i
$690$	29.5344	−	21.4580i	1.12436	−	0.816893i
$691$	−1.02786	−	0.746787i	−0.0391018	−	0.0284091i	0.568063	−	0.822985i	$-0.307693\pi$
$691$	−1.02786	−	0.746787i	−0.0391018	−	0.0284091i	−0.607164	+	0.794576i	$0.707693\pi$
$692$	1.00000	+	3.07768i	0.0380143	+	0.116996i
$693$	2.72949			0.103685
$694$	3.06231	+	9.42481i	0.116244	+	0.357761i
$695$	7.13525	+	21.9601i	0.270656	+	0.832992i
$696$	−0.427051	+	1.31433i	−0.0161873	+	0.0498195i
$697$	−18.1353	+	55.8146i	−0.686922	+	2.11413i
$698$	−17.9894	+	13.0700i	−0.680907	+	0.494708i
$699$	−72.5410			−2.74375
$700$	12.1353	−	8.81678i	0.458670	−	0.333243i
$701$	−4.18034			−0.157889			−0.0789446	−	0.996879i	$-0.525155\pi$
$701$	−4.18034			−0.157889			−0.0789446	+	0.996879i	$0.525155\pi$
$702$	−1.80902	+	1.31433i	−0.0682769	+	0.0496061i
$703$	−1.93363	+	5.95110i	−0.0729282	+	0.224450i
$704$	−0.0729490	+	0.224514i	−0.00274937	+	0.00846169i
$705$	28.1525	−	20.4540i	1.06028	−	0.770341i
$706$	5.18034	+	15.9434i	0.194965	+	0.600040i
$707$	4.85410			0.182557
$708$	−3.61803	−	11.1352i	−0.135974	−	0.418485i
$709$	−6.28115	−	4.56352i	−0.235894	−	0.171387i	0.463558	−	0.886066i	$-0.346572\pi$
$709$	−6.28115	−	4.56352i	−0.235894	−	0.171387i	−0.699452	+	0.714680i	$0.746572\pi$
$710$	6.70820			0.251754
$711$	8.61803	−	6.26137i	0.323202	−	0.234820i
$712$	−3.61803	−	2.62866i	−0.135592	−	0.0985130i
$713$	21.3713	+	15.5272i	0.800362	+	0.581497i
$714$	49.9058	−	36.2587i	1.86768	−	1.35695i
$715$	−0.163119	+	0.502029i	−0.00610030	+	0.0187748i
$716$	9.04508	+	6.57164i	0.338031	+	0.245594i
$717$	14.6353	+	45.0427i	0.546564	+	1.68215i
$718$	−3.09017			−0.115324
$719$	−8.19098	−	25.2093i	−0.305472	−	0.940147i	−0.979501	−	0.201441i	$-0.935438\pi$
$719$	−8.19098	−	25.2093i	−0.305472	−	0.940147i	0.674028	−	0.738705i	$-0.264562\pi$
$720$	8.61803			0.321175
$721$	18.4058	−	56.6471i	0.685466	−	2.10965i
$722$	5.64590	−	17.3763i	0.210119	−	0.646678i
$723$	28.3435	−	20.5927i	1.05410	−	0.765852i
$724$	−21.4164			−0.795935
$725$	2.13525	−	1.55135i	0.0793014	−	0.0576158i
$726$	−28.6525			−1.06339
$727$	23.1803	−	16.8415i	0.859711	−	0.624617i	−0.0680952	−	0.997679i	$-0.521692\pi$
$727$	23.1803	−	16.8415i	0.859711	−	0.624617i	0.927806	+	0.373062i	$0.121692\pi$
$728$	0.927051	−	2.85317i	0.0343588	−	0.105745i
$729$	−12.2254	+	37.6260i	−0.452794	+	1.39356i
$730$	−10.3262	−	7.50245i	−0.382191	−	0.277678i
$731$	−4.28115	−	13.1760i	−0.158344	−	0.487333i
$732$	5.61803			0.207649
$733$	−12.2918	−	37.8303i	−0.454008	−	1.39729i	−0.872296	−	0.488978i	$-0.837370\pi$
$733$	−12.2918	−	37.8303i	−0.454008	−	1.39729i	0.418288	−	0.908314i	$-0.362630\pi$
$734$	−25.5172	−	18.5393i	−0.941858	−	0.684300i
$735$	9.47214	+	6.88191i	0.349385	+	0.253843i
$736$	−5.04508	+	3.66547i	−0.185964	+	0.135111i
$737$	−1.10081	−	0.799788i	−0.0405490	−	0.0294606i
$738$	−23.2984	−	16.9273i	−0.857625	−	0.623101i
$739$	−24.2705	+	17.6336i	−0.892805	+	0.648661i	−0.936608	−	0.350379i	$-0.886053\pi$
$739$	−24.2705	+	17.6336i	−0.892805	+	0.648661i	0.0438028	+	0.999040i	$0.486053\pi$
$740$	5.06231	+	15.5802i	0.186094	+	0.572739i
$741$	−1.80902	−	1.31433i	−0.0664559	−	0.0482830i
$742$	1.41641	+	4.35926i	0.0519980	+	0.160033i
$743$	−18.2705			−0.670280			−0.335140	−	0.942168i	$-0.608784\pi$
$743$	−18.2705			−0.670280			−0.335140	+	0.942168i	$0.608784\pi$
$744$	3.42705	+	10.5474i	0.125642	+	0.386686i
$745$	−1.54508	+	4.75528i	−0.0566075	+	0.174220i
$746$	5.01722	−	15.4414i	0.183694	−	0.565350i
$747$	−16.0451	+	49.3817i	−0.587059	+	1.80678i
$748$	1.50000	−	1.08981i	0.0548454	−	0.0398475i
$749$	−30.2705			−1.10606
$750$	−23.6803	−	17.2048i	−0.864684	−	0.628230i
$751$	1.14590			0.0418144			0.0209072	−	0.999781i	$-0.493345\pi$
$751$	1.14590			0.0418144			0.0209072	+	0.999781i	$0.493345\pi$
$752$	−4.80902	+	3.49396i	−0.175367	+	0.127411i
$753$	−18.7533	+	57.7167i	−0.683408	+	2.10331i
$754$	0.163119	−	0.502029i	0.00594044	−	0.0182828i
$755$	2.56231	−	7.88597i	0.0932519	−	0.287000i
$756$	2.07295	+	6.37988i	0.0753924	+	0.232034i
$757$	10.4164			0.378591			0.189295	−	0.981920i	$-0.439380\pi$
$757$	10.4164			0.378591			0.189295	+	0.981920i	$0.439380\pi$
$758$	−0.163119	−	0.502029i	−0.00592475	−	0.0182345i
$759$	3.11803	+	2.26538i	0.113177	+	0.0822282i
$760$	0.590170	+	1.81636i	0.0214077	+	0.0658862i
$761$	30.6803	−	22.2906i	1.11216	−	0.808033i	0.129159	−	0.991624i	$-0.458772\pi$
$761$	30.6803	−	22.2906i	1.11216	−	0.808033i	0.983003	+	0.183591i	$0.0587723\pi$
$762$	26.4164	+	19.1926i	0.956965	+	0.695276i
$763$	−36.4058	−	26.4503i	−1.31798	−	0.957566i
$764$	−14.2812	+	10.3759i	−0.516674	+	0.375386i
$765$	−54.7599	−	39.7854i	−1.97985	−	1.43844i
$766$	−3.50000	−	2.54290i	−0.126460	−	0.0918787i
$767$	1.38197	+	4.25325i	0.0498999	+	0.153576i
$768$	−2.61803			−0.0944702
$769$	−7.23607	−	22.2703i	−0.260939	−	0.803089i	−0.992601	−	0.121421i	$-0.961255\pi$
$769$	−7.23607	−	22.2703i	−0.260939	−	0.803089i	0.731662	−	0.681668i	$-0.238745\pi$
$770$	1.28115	+	0.930812i	0.0461695	+	0.0335441i
$771$	13.5451	−	41.6875i	0.487814	−	1.50134i
$772$	5.14590	−	15.8374i	0.185205	−	0.570002i
$773$	−5.01722	+	3.64522i	−0.180457	+	0.131110i	−0.674347	−	0.738415i	$-0.735575\pi$
$773$	−5.01722	+	3.64522i	−0.180457	+	0.131110i	0.493890	+	0.869525i	$0.335575\pi$
$774$	6.79837			0.244363
$775$	6.54508	−	20.1437i	0.235106	−	0.723583i
$776$	10.5623			0.379165
$777$	−46.5517	+	33.8218i	−1.67003	+	1.21335i
$778$	10.2639	−	31.5891i	0.367980	−	1.13253i
$779$	1.97214	−	6.06961i	0.0706591	−	0.217466i
$780$	−5.85410			−0.209610
$781$	0.218847	+	0.673542i	0.00783096	+	0.0241012i
$782$	48.9787			1.75148
$783$	0.364745	+	1.12257i	0.0130349	+	0.0401174i
$784$	−1.61803	−	1.17557i	−0.0577869	−	0.0419847i
$785$	−10.7533	+	33.0952i	−0.383801	+	1.18122i
$786$	−22.0623	+	16.0292i	−0.786936	+	0.571743i
$787$	−12.4721	−	9.06154i	−0.444584	−	0.323009i	0.342870	−	0.939383i	$-0.388601\pi$
$787$	−12.4721	−	9.06154i	−0.444584	−	0.323009i	−0.787454	+	0.616374i	$0.788601\pi$
$788$	−9.70820	−	7.05342i	−0.345840	−	0.251268i
$789$	5.04508	−	3.66547i	0.179610	−	0.130494i
$790$	6.18034			0.219887
$791$	19.9894	+	14.5231i	0.710740	+	0.516383i
$792$	0.281153	+	0.865300i	0.00999034	+	0.0307471i
$793$	−2.14590			−0.0762031
$794$	1.78115	+	5.48183i	0.0632108	+	0.194543i
$795$	7.23607	−	5.25731i	0.256637	−	0.186458i
$796$	−5.42705	+	16.7027i	−0.192357	+	0.592013i
$797$	1.04508	−	3.21644i	0.0370188	−	0.113932i	−0.930840	−	0.365428i	$-0.880923\pi$
$797$	1.04508	−	3.21644i	0.0370188	−	0.113932i	0.967858	+	0.251496i	$0.0809226\pi$
$798$	−5.42705	+	3.94298i	−0.192116	+	0.139580i
$799$	46.6869			1.65166
$800$	4.04508	+	2.93893i	0.143015	+	0.103907i
$801$	−17.2361			−0.609007
$802$	6.61803	−	4.80828i	0.233691	−	0.169786i
$803$	0.416408	−	1.28157i	0.0146947	−	0.0452257i
$804$	4.66312	−	14.3516i	0.164456	−	0.506142i
$805$	12.9271	+	39.7854i	0.455619	+	1.40225i
$806$	−1.30902	−	4.02874i	−0.0461082	−	0.141906i
$807$	−34.2705			−1.20638
$808$	0.500000	+	1.53884i	0.0175899	+	0.0541363i
$809$	−1.80902	−	1.31433i	−0.0636017	−	0.0462093i	0.555530	−	0.831496i	$-0.312515\pi$
$809$	−1.80902	−	1.31433i	−0.0636017	−	0.0462093i	−0.619132	+	0.785287i	$0.712515\pi$
$810$	−10.3262	+	7.50245i	−0.362827	+	0.263609i
$811$	−18.6525	+	13.5518i	−0.654977	+	0.475869i	−0.864963	−	0.501836i	$-0.832658\pi$
$811$	−18.6525	+	13.5518i	−0.654977	+	0.475869i	0.209986	+	0.977704i	$0.432658\pi$
$812$	−1.28115	−	0.930812i	−0.0449597	−	0.0326651i
$813$	−20.1353	−	14.6291i	−0.706174	−	0.513066i
$814$	−1.39919	+	1.01657i	−0.0490415	+	0.0356307i
$815$	8.78115	−	6.37988i	0.307590	−	0.223477i
$816$	16.6353	+	12.0862i	0.582350	+	0.423102i
$817$	0.465558	+	1.43284i	0.0162878	+	0.0501287i
$818$	−6.70820			−0.234547
$819$	−3.57295	−	10.9964i	−0.124849	−	0.384246i
$820$	−5.16312	−	15.8904i	−0.180304	−	0.554918i
$821$	−9.31966	+	28.6830i	−0.325258	+	1.00104i	0.646065	+	0.763282i	$0.276413\pi$
$821$	−9.31966	+	28.6830i	−0.325258	+	1.00104i	−0.971324	+	0.237760i	$0.923587\pi$
$822$	−4.92705	+	15.1639i	−0.171851	+	0.528902i
$823$	−26.5623	+	19.2986i	−0.925904	+	0.672708i	−0.944986	−	0.327109i	$-0.893925\pi$
$823$	−26.5623	+	19.2986i	−0.925904	+	0.672708i	0.0190827	+	0.999818i	$0.493925\pi$
$824$	19.8541			0.691650
$825$	0.954915	−	2.93893i	0.0332459	−	0.102320i
$826$	13.4164			0.466817
$827$	−19.4443	+	14.1271i	−0.676144	+	0.491247i	−0.872076	−	0.489370i	$-0.837227\pi$
$827$	−19.4443	+	14.1271i	−0.676144	+	0.491247i	0.195932	+	0.980617i	$0.437227\pi$
$828$	−7.42705	+	22.8581i	−0.258108	+	0.794374i
$829$	8.21478	−	25.2825i	0.285311	−	0.878097i	−0.700994	−	0.713167i	$-0.747260\pi$
$829$	8.21478	−	25.2825i	0.285311	−	0.878097i	0.986305	−	0.164930i	$-0.0527399\pi$
$830$	−24.3713	+	17.7068i	−0.845941	+	0.614612i
$831$	−11.0902	−	34.1320i	−0.384714	−	1.18403i
$832$	1.00000			0.0346688
$833$	4.85410	+	14.9394i	0.168185	+	0.517619i
$834$	−21.8713	−	15.8904i	−0.757342	−	0.550241i
$835$	34.9230			1.20856
$836$	−0.163119	+	0.118513i	−0.00564159	+	0.00409885i
$837$	7.66312	+	5.56758i	0.264876	+	0.192444i
$838$	22.0344	+	16.0090i	0.761167	+	0.553020i
$839$	−20.4271	+	14.8411i	−0.705220	+	0.512372i	−0.881628	−	0.471945i	$-0.843552\pi$
$839$	−20.4271	+	14.8411i	−0.705220	+	0.512372i	0.176408	+	0.984317i	$0.443552\pi$
$840$	−5.42705	+	16.7027i	−0.187251	+	0.576299i
$841$	23.2361	+	16.8820i	0.801244	+	0.582138i
$842$	3.79180	+	11.6699i	0.130674	+	0.402173i
$843$	50.2148			1.72949
$844$	3.48278	+	10.7189i	0.119882	+	0.368959i
$845$	−26.8328			−0.923077
$846$	−7.07953	+	21.7885i	−0.243399	+	0.749106i
$847$	10.1459	−	31.2259i	0.348617	−	1.07293i
$848$	−1.23607	+	0.898056i	−0.0424467	+	0.0308394i
$849$	67.3050			2.30990
$850$	−12.1353	−	37.3485i	−0.416236	−	1.28104i
$851$	−45.6869			−1.56613
$852$	−6.35410	+	4.61653i	−0.217688	+	0.158160i
$853$	−7.68034	+	23.6377i	−0.262970	+	0.809338i	0.729184	+	0.684317i	$0.239900\pi$
$853$	−7.68034	+	23.6377i	−0.262970	+	0.809338i	−0.992154	+	0.125021i	$0.960100\pi$
$854$	−1.98936	+	6.12261i	−0.0680744	+	0.209511i
$855$	5.95492	+	4.32650i	0.203654	+	0.147963i
$856$	−3.11803	−	9.59632i	−0.106572	−	0.327996i
$857$	35.3394			1.20717			0.603585	−	0.797298i	$-0.293738\pi$
$857$	35.3394			1.20717			0.603585	+	0.797298i	$0.293738\pi$
$858$	−0.190983	−	0.587785i	−0.00652005	−	0.0200667i
$859$	31.8713	+	23.1559i	1.08744	+	0.790068i	0.978964	−	0.204031i	$-0.0654045\pi$
$859$	31.8713	+	23.1559i	1.08744	+	0.790068i	0.108471	+	0.994100i	$0.465404\pi$
$860$	3.19098	+	2.31838i	0.108812	+	0.0790563i
$861$	47.4787	−	34.4953i	1.61807	−	1.17560i
$862$	−25.9443	−	18.8496i	−0.883665	−	0.642020i
$863$	5.47214	+	3.97574i	0.186274	+	0.135336i	0.677014	−	0.735970i	$-0.263274\pi$
$863$	5.47214	+	3.97574i	0.186274	+	0.135336i	−0.490740	+	0.871306i	$0.663274\pi$
$864$	−1.80902	+	1.31433i	−0.0615440	+	0.0447143i
$865$	2.23607	+	6.88191i	0.0760286	+	0.233992i
$866$	18.8992	+	13.7311i	0.642221	+	0.466601i
$867$	−36.1525	−	111.266i	−1.22780	−	3.77879i
$868$	−12.7082			−0.431345
$869$	0.201626	+	0.620541i	0.00683970	+	0.0210504i
$870$	−0.954915	+	2.93893i	−0.0323747	+	0.0996389i
$871$	−1.78115	+	5.48183i	−0.0603521	+	0.185745i
$872$	4.63525	−	14.2658i	0.156970	−	0.483103i
$873$	32.9336	−	23.9277i	1.11463	−	0.809829i
$874$	−5.32624			−0.180163
$875$	27.1353	−	19.7149i	0.917339	−	0.666486i
$876$	14.9443			0.504920
$877$	−19.8713	+	14.4374i	−0.671007	+	0.487515i	−0.870362	−	0.492412i	$-0.836115\pi$
$877$	−19.8713	+	14.4374i	−0.671007	+	0.487515i	0.199355	+	0.979927i	$0.436115\pi$
$878$	1.74671	−	5.37582i	0.0589486	−	0.181425i
$879$	9.35410	−	28.7890i	0.315506	−	0.971028i
$880$	−0.163119	+	0.502029i	−0.00549874	+	0.0169234i
$881$	4.88854	+	15.0454i	0.164699	+	0.506892i	0.999014	−	0.0443963i	$-0.0141364\pi$
$881$	4.88854	+	15.0454i	0.164699	+	0.506892i	−0.834315	+	0.551288i	$0.814136\pi$
$882$	−7.70820			−0.259549
$883$	5.77458	+	17.7723i	0.194330	+	0.598086i	0.999984	+	0.00569940i	$0.00181418\pi$
$883$	5.77458	+	17.7723i	0.194330	+	0.598086i	−0.805654	+	0.592387i	$0.798186\pi$
$884$	−6.35410	−	4.61653i	−0.213712	−	0.155271i
$885$	−8.09017	−	24.8990i	−0.271948	−	0.836970i
$886$	−6.00000	+	4.35926i	−0.201574	+	0.146452i
$887$	−8.75329	−	6.35964i	−0.293907	−	0.213536i	0.431054	−	0.902326i	$-0.358142\pi$
$887$	−8.75329	−	6.35964i	−0.293907	−	0.213536i	−0.724960	+	0.688791i	$0.758142\pi$
$888$	−15.5172	−	11.2739i	−0.520724	−	0.378328i
$889$	−30.2705	+	21.9928i	−1.01524	+	0.737615i
$890$	−8.09017	−	5.87785i	−0.271183	−	0.197026i
$891$	−1.09017	−	0.792055i	−0.0365221	−	0.0265348i
$892$	−2.78115	−	8.55951i	−0.0931199	−	0.286594i
$893$	−5.07701			−0.169896
$894$	−1.80902	−	5.56758i	−0.0605026	−	0.186208i
$895$	20.2254	+	14.6946i	0.676061	+	0.491187i
$896$	0.927051	−	2.85317i	0.0309706	−	0.0953177i
$897$	5.04508	−	15.5272i	0.168450	−	0.518437i
$898$	11.2812	−	8.19624i	0.376457	−	0.273512i
$899$	−2.23607			−0.0745770
$900$	19.2705			0.642350
$901$	12.0000			0.399778
$902$	1.42705	−	1.03681i	0.0475156	−	0.0345221i
$903$	−4.28115	+	13.1760i	−0.142468	+	0.438471i
$904$	−2.54508	+	7.83297i	−0.0846483	+	0.260521i
$905$	−47.8885			−1.59187
$906$	3.00000	+	9.23305i	0.0996683	+	0.306748i
$907$	23.3820			0.776385			0.388193	−	0.921578i	$-0.373099\pi$
$907$	23.3820			0.776385			0.388193	+	0.921578i	$0.373099\pi$
$908$	−4.74671	−	14.6089i	−0.157525	−	0.484813i
$909$	5.04508	+	3.66547i	0.167335	+	0.121576i
$910$	2.07295	−	6.37988i	0.0687176	−	0.211491i
$911$	−8.42705	+	6.12261i	−0.279201	+	0.202851i	−0.718569	−	0.695456i	$-0.755202\pi$
$911$	−8.42705	+	6.12261i	−0.279201	+	0.202851i	0.439368	+	0.898307i	$0.355202\pi$
$912$	−1.80902	−	1.31433i	−0.0599025	−	0.0435217i
$913$	−2.57295	−	1.86936i	−0.0851522	−	0.0618667i
$914$	−9.07295	+	6.59188i	−0.300106	+	0.218040i
$915$	12.5623			0.415297
$916$	−14.2082	−	10.3229i	−0.469452	−	0.341077i
$917$	−9.65654	−	29.7198i	−0.318887	−	0.981434i
$918$	17.5623			0.579642
$919$	7.92705	+	24.3970i	0.261489	+	0.804781i	0.992481	+	0.122395i	$0.0390576\pi$
$919$	7.92705	+	24.3970i	0.261489	+	0.804781i	−0.730992	+	0.682386i	$0.760942\pi$
$920$	−11.2812	+	8.19624i	−0.371929	+	0.270222i
$921$	−13.8541	+	42.6385i	−0.456508	+	1.40499i
$922$	−8.70820	+	26.8011i	−0.286789	+	0.882647i
$923$	2.42705	−	1.76336i	0.0798874	−	0.0580416i
$924$	−1.85410			−0.0609955
$925$	11.3197	+	34.8383i	0.372188	+	1.14548i
$926$	−11.9787			−0.393645
$927$	61.9058	−	44.9772i	2.03325	−	1.47724i
$928$	0.163119	−	0.502029i	0.00535464	−	0.0164799i
$929$	−5.28773	+	16.2740i	−0.173485	+	0.533931i	−0.999561	−	0.0296271i	$-0.990568\pi$
$929$	−5.28773	+	16.2740i	−0.173485	+	0.533931i	0.826076	+	0.563558i	$0.190568\pi$
$930$	7.66312	+	23.5847i	0.251284	+	0.773371i
$931$	−0.527864	−	1.62460i	−0.0173000	−	0.0532441i
$932$	27.7082			0.907612
$933$	17.0623	+	52.5124i	0.558595	+	1.71918i
$934$	2.57295	+	1.86936i	0.0841895	+	0.0611672i
$935$	3.35410	−	2.43690i	0.109691	−	0.0796951i
$936$	3.11803	−	2.26538i	0.101916	−	0.0740464i
$937$	18.5451	+	13.4738i	0.605842	+	0.440170i	0.847948	−	0.530080i	$-0.177838\pi$
$937$	18.5451	+	13.4738i	0.605842	+	0.440170i	−0.242106	+	0.970250i	$0.577838\pi$
$938$	13.9894	+	10.1639i	0.456769	+	0.331862i
$939$	7.54508	−	5.48183i	0.246225	−	0.178893i
$940$	−10.7533	+	7.81272i	−0.350734	+	0.254823i
$941$	9.39919	+	6.82891i	0.306405	+	0.222616i	0.730352	−	0.683071i	$-0.239356\pi$
$941$	9.39919	+	6.82891i	0.306405	+	0.222616i	−0.423948	+	0.905687i	$0.639356\pi$
$942$	−12.5902	−	38.7486i	−0.410210	−	1.26250i
$943$	46.5967			1.51740
$944$	1.38197	+	4.25325i	0.0449792	+	0.138432i
$945$	4.63525	+	14.2658i	0.150785	+	0.464068i
$946$	−0.128677	+	0.396027i	−0.00418365	+	0.0128760i
$947$	−12.8607	+	39.5811i	−0.417916	+	1.28621i	0.491701	+	0.870764i	$0.336375\pi$
$947$	−12.8607	+	39.5811i	−0.417916	+	1.28621i	−0.909617	+	0.415449i	$0.863625\pi$
$948$	−5.85410	+	4.25325i	−0.190132	+	0.138139i
$949$	−5.70820			−0.185296
$950$	1.31966	+	4.06150i	0.0428154	+	0.131772i
$951$	−27.7984			−0.901424
$952$	−19.0623	+	13.8496i	−0.617813	+	0.448867i
$953$	13.0967	−	40.3076i	0.424245	−	1.30569i	−0.479470	−	0.877558i	$-0.659171\pi$
$953$	13.0967	−	40.3076i	0.424245	−	1.30569i	0.903715	−	0.428134i	$-0.140829\pi$
$954$	−1.81966	+	5.60034i	−0.0589137	+	0.181318i
$955$	−31.9336	+	23.2011i	−1.03335	+	0.750771i
$956$	−5.59017	−	17.2048i	−0.180799	−	0.556442i
$957$	−0.326238			−0.0105458
$958$	12.2984	+	37.8505i	0.397342	+	1.22289i
$959$	−14.7812	−	10.7391i	−0.477308	−	0.346785i
$960$	−5.85410			−0.188940
$961$	10.5623	−	7.67396i	0.340720	−	0.247547i
$962$	5.92705	+	4.30625i	0.191096	+	0.138839i
$963$	−31.4615	−	22.8581i	−1.01383	−	0.736592i
$964$	−10.8262	+	7.86572i	−0.348690	+	0.253338i
$965$	11.5066	−	35.4136i	0.370410	−	1.14000i
$966$	−39.6246	−	28.7890i	−1.27490	−	0.926270i
$967$	8.38197	+	25.7970i	0.269546	+	0.829577i	0.990611	+	0.136710i	$0.0436528\pi$
$967$	8.38197	+	25.7970i	0.269546	+	0.829577i	−0.721065	+	0.692867i	$0.756347\pi$
$968$	10.9443			0.351762
$969$	5.42705	+	16.7027i	0.174342	+	0.536569i
$970$	23.6180			0.758329
$971$	−16.0902	+	49.5205i	−0.516358	+	1.58919i	0.264439	+	0.964402i	$0.414813\pi$
$971$	−16.0902	+	49.5205i	−0.516358	+	1.58919i	−0.780797	+	0.624785i	$0.785187\pi$
$972$	6.69098	−	20.5927i	0.214613	−	0.660512i
$973$	25.0623	−	18.2088i	0.803461	−	0.583748i
$974$	18.1246			0.580750
$975$	−13.0902			−0.419221
$976$	−2.14590			−0.0686885
$977$	21.0451	−	15.2901i	0.673292	−	0.489175i	−0.197834	−	0.980236i	$-0.563391\pi$
$977$	21.0451	−	15.2901i	0.673292	−	0.489175i	0.871126	+	0.491060i	$0.163391\pi$
$978$	−3.92705	+	12.0862i	−0.125573	+	0.386475i
$979$	0.326238	−	1.00406i	0.0104266	−	0.0320898i
$980$	−3.61803	−	2.62866i	−0.115574	−	0.0839693i
$981$	−17.8647	−	54.9820i	−0.570377	−	1.75544i
$982$	−14.7639			−0.471136
$983$	−14.3647	−	44.2101i	−0.458164	−	1.41008i	−0.867380	−	0.497647i	$-0.834198\pi$
$983$	−14.3647	−	44.2101i	−0.458164	−	1.41008i	0.409216	−	0.912438i	$-0.365802\pi$
$984$	15.8262	+	11.4984i	0.504522	+	0.366557i
$985$	−21.7082	−	15.7719i	−0.691681	−	0.502536i
$986$	−3.35410	+	2.43690i	−0.106816	+	0.0776066i
$987$	−37.7705	−	27.4419i	−1.20225	−	0.873485i
$988$	0.690983	+	0.502029i	0.0219831	+	0.0159717i
$989$	−8.89919	+	6.46564i	−0.282978	+	0.205595i
$990$	0.628677	+	1.93487i	0.0199807	+	0.0614942i
$991$	−42.4336	−	30.8298i	−1.34795	−	0.979342i	−0.999111	−	0.0421589i	$-0.986576\pi$
$991$	−42.4336	−	30.8298i	−1.34795	−	0.979342i	−0.348838	−	0.937183i	$-0.613424\pi$
$992$	−1.30902	−	4.02874i	−0.0415613	−	0.127913i
$993$	−11.9443			−0.379040
$994$	−2.78115	−	8.55951i	−0.0882128	−	0.271491i
$995$	−12.1353	+	37.3485i	−0.384713	+	1.18403i
$996$	10.8992	−	33.5442i	0.345354	−	1.06289i
$997$	−16.4549	+	50.6430i	−0.521132	+	1.60388i	0.250707	+	0.968063i	$0.419337\pi$
$997$	−16.4549	+	50.6430i	−0.521132	+	1.60388i	−0.771839	+	0.635818i	$0.780663\pi$
$998$	33.0517	−	24.0134i	1.04623	−	0.760132i
$999$	−16.3820			−0.518302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.2.d.a.11.1	✓	4
3.2	odd	2		450.2.h.a.361.1		4
4.3	odd	2		400.2.u.c.161.1		4
5.2	odd	4		250.2.e.b.199.2		8
5.3	odd	4		250.2.e.b.199.1		8
5.4	even	2		250.2.d.a.51.1		4
25.3	odd	20		1250.2.b.b.1249.3		4
25.4	even	10		1250.2.a.d.1.2		2
25.9	even	10		250.2.d.a.201.1		4
25.12	odd	20		250.2.e.b.49.1		8
25.13	odd	20		250.2.e.b.49.2		8
25.16	even	5	inner	50.2.d.a.41.1	yes	4
25.21	even	5		1250.2.a.a.1.1		2
25.22	odd	20		1250.2.b.b.1249.2		4
75.41	odd	10		450.2.h.a.91.1		4
100.71	odd	10		10000.2.a.n.1.2		2
100.79	odd	10		10000.2.a.a.1.1		2
100.91	odd	10		400.2.u.c.241.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.11.1	✓	4	1.1	even	1	trivial
50.2.d.a.41.1	yes	4	25.16	even	5	inner
250.2.d.a.51.1		4	5.4	even	2
250.2.d.a.201.1		4	25.9	even	10
250.2.e.b.49.1		8	25.12	odd	20
250.2.e.b.49.2		8	25.13	odd	20
250.2.e.b.199.1		8	5.3	odd	4
250.2.e.b.199.2		8	5.2	odd	4
400.2.u.c.161.1		4	4.3	odd	2
400.2.u.c.241.1		4	100.91	odd	10
450.2.h.a.91.1		4	75.41	odd	10
450.2.h.a.361.1		4	3.2	odd	2
1250.2.a.a.1.1		2	25.21	even	5
1250.2.a.d.1.2		2	25.4	even	10
1250.2.b.b.1249.2		4	25.22	odd	20
1250.2.b.b.1249.3		4	25.3	odd	20
10000.2.a.a.1.1		2	100.79	odd	10
10000.2.a.n.1.2		2	100.71	odd	10

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 - 2.12663i) q^{5} +(0.809017 + 2.48990i) q^{6} -3.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-3.11803 - 2.26538i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 - 2.12663i) q^{5} +(0.809017 + 2.48990i) q^{6} -3.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-3.11803 - 2.26538i) q^{9} +(-0.690983 - 2.12663i) q^{10} +(0.190983 - 0.138757i) q^{11} +(2.11803 + 1.53884i) q^{12} +(-0.809017 - 0.587785i) q^{13} +(-2.42705 + 1.76336i) q^{14} +(4.73607 + 3.44095i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.42705 + 7.46969i) q^{17} -3.85410 q^{18} +(-0.263932 - 0.812299i) q^{19} +(-1.80902 - 1.31433i) q^{20} +(2.42705 - 7.46969i) q^{21} +(0.0729490 - 0.224514i) q^{22} +(5.04508 - 3.66547i) q^{23} +2.61803 q^{24} +(-4.04508 - 2.93893i) q^{25} -1.00000 q^{26} +(1.80902 - 1.31433i) q^{27} +(-0.927051 + 2.85317i) q^{28} +(-0.163119 + 0.502029i) q^{29} +5.85410 q^{30} +(1.30902 + 4.02874i) q^{31} -1.00000 q^{32} +(0.190983 + 0.587785i) q^{33} +(6.35410 + 4.61653i) q^{34} +(-2.07295 + 6.37988i) q^{35} +(-3.11803 + 2.26538i) q^{36} +(-5.92705 - 4.30625i) q^{37} +(-0.690983 - 0.502029i) q^{38} +(2.11803 - 1.53884i) q^{39} -2.23607 q^{40} +(6.04508 + 4.39201i) q^{41} +(-2.42705 - 7.46969i) q^{42} -1.76393 q^{43} +(-0.0729490 - 0.224514i) q^{44} +(-6.97214 + 5.06555i) q^{45} +(1.92705 - 5.93085i) q^{46} +(1.83688 - 5.65334i) q^{47} +(2.11803 - 1.53884i) q^{48} +2.00000 q^{49} -5.00000 q^{50} -20.5623 q^{51} +(-0.809017 + 0.587785i) q^{52} +(0.472136 - 1.45309i) q^{53} +(0.690983 - 2.12663i) q^{54} +(-0.163119 - 0.502029i) q^{55} +(0.927051 + 2.85317i) q^{56} +2.23607 q^{57} +(0.163119 + 0.502029i) q^{58} +(-3.61803 - 2.62866i) q^{59} +(4.73607 - 3.44095i) q^{60} +(1.73607 - 1.26133i) q^{61} +(3.42705 + 2.48990i) q^{62} +(9.35410 + 6.79615i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.80902 + 1.31433i) q^{65} +(0.500000 + 0.363271i) q^{66} +(-1.78115 - 5.48183i) q^{67} +7.85410 q^{68} +(5.04508 + 15.5272i) q^{69} +(2.07295 + 6.37988i) q^{70} +(-0.927051 + 2.85317i) q^{71} +(-1.19098 + 3.66547i) q^{72} +(4.61803 - 3.35520i) q^{73} -7.32624 q^{74} +(10.5902 - 7.69421i) q^{75} -0.854102 q^{76} +(-0.572949 + 0.416272i) q^{77} +(0.809017 - 2.48990i) q^{78} +(-0.854102 + 2.62866i) q^{79} +(-1.80902 + 1.31433i) q^{80} +(-1.76393 - 5.42882i) q^{81} +7.47214 q^{82} +(-4.16312 - 12.8128i) q^{83} +(-6.35410 - 4.61653i) q^{84} +17.5623 q^{85} +(-1.42705 + 1.03681i) q^{86} +(-1.11803 - 0.812299i) q^{87} +(-0.190983 - 0.138757i) q^{88} +(3.61803 - 2.62866i) q^{89} +(-2.66312 + 8.19624i) q^{90} +(2.42705 + 1.76336i) q^{91} +(-1.92705 - 5.93085i) q^{92} -11.0902 q^{93} +(-1.83688 - 5.65334i) q^{94} -1.90983 q^{95} +(0.809017 - 2.48990i) q^{96} +(-3.26393 + 10.0453i) q^{97} +(1.61803 - 1.17557i) q^{98} -0.909830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9} - 5 q^{10} + 3 q^{11} + 4 q^{12} - q^{13} - 3 q^{14} + 10 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 7 q^{22} + 9 q^{23} + 6 q^{24} - 5 q^{25} - 4 q^{26} + 5 q^{27} + 3 q^{28} + 15 q^{29} + 10 q^{30} + 3 q^{31} - 4 q^{32} + 3 q^{33} + 12 q^{34} - 15 q^{35} - 8 q^{36} - 17 q^{37} - 5 q^{38} + 4 q^{39} + 13 q^{41} - 3 q^{42} - 16 q^{43} - 7 q^{44} - 10 q^{45} + q^{46} + 23 q^{47} + 4 q^{48} + 8 q^{49} - 20 q^{50} - 42 q^{51} - q^{52} - 16 q^{53} + 5 q^{54} + 15 q^{55} - 3 q^{56} - 15 q^{58} - 10 q^{59} + 10 q^{60} - 2 q^{61} + 7 q^{62} + 24 q^{63} - q^{64} - 5 q^{65} + 2 q^{66} + 13 q^{67} + 18 q^{68} + 9 q^{69} + 15 q^{70} + 3 q^{71} - 7 q^{72} + 14 q^{73} + 2 q^{74} + 20 q^{75} + 10 q^{76} - 9 q^{77} + q^{78} + 10 q^{79} - 5 q^{80} - 16 q^{81} + 12 q^{82} - q^{83} - 12 q^{84} + 30 q^{85} + q^{86} - 3 q^{88} + 10 q^{89} + 5 q^{90} + 3 q^{91} - q^{92} - 22 q^{93} - 23 q^{94} - 30 q^{95} + q^{96} - 22 q^{97} + 2 q^{98} - 26 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9 - 5 * q^10 + 3 * q^11 + 4 * q^12 - q^13 - 3 * q^14 + 10 * q^15 - q^16 + 3 * q^17 - 2 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 7 * q^22 + 9 * q^23 + 6 * q^24 - 5 * q^25 - 4 * q^26 + 5 * q^27 + 3 * q^28 + 15 * q^29 + 10 * q^30 + 3 * q^31 - 4 * q^32 + 3 * q^33 + 12 * q^34 - 15 * q^35 - 8 * q^36 - 17 * q^37 - 5 * q^38 + 4 * q^39 + 13 * q^41 - 3 * q^42 - 16 * q^43 - 7 * q^44 - 10 * q^45 + q^46 + 23 * q^47 + 4 * q^48 + 8 * q^49 - 20 * q^50 - 42 * q^51 - q^52 - 16 * q^53 + 5 * q^54 + 15 * q^55 - 3 * q^56 - 15 * q^58 - 10 * q^59 + 10 * q^60 - 2 * q^61 + 7 * q^62 + 24 * q^63 - q^64 - 5 * q^65 + 2 * q^66 + 13 * q^67 + 18 * q^68 + 9 * q^69 + 15 * q^70 + 3 * q^71 - 7 * q^72 + 14 * q^73 + 2 * q^74 + 20 * q^75 + 10 * q^76 - 9 * q^77 + q^78 + 10 * q^79 - 5 * q^80 - 16 * q^81 + 12 * q^82 - q^83 - 12 * q^84 + 30 * q^85 + q^86 - 3 * q^88 + 10 * q^89 + 5 * q^90 + 3 * q^91 - q^92 - 22 * q^93 - 23 * q^94 - 30 * q^95 + q^96 - 22 * q^97 + 2 * q^98 - 26 * q^99

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