LMFDB - Embedded newform 231.2.i.d.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.d.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 - 0.358719i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +(1.00000 + 1.73205i) q^{5} +0.414214 q^{6} +(1.00000 + 2.44949i) q^{7} -1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +(1.00000 + 1.73205i) q^{5} +0.414214 q^{6} +(1.00000 + 2.44949i) q^{7} -1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.414214 - 0.717439i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.914214 + 1.58346i) q^{12} +4.82843 q^{13} +(0.671573 - 0.866025i) q^{14} -2.00000 q^{15} +(-1.50000 - 2.59808i) q^{16} +(0.792893 - 1.37333i) q^{17} +(-0.207107 + 0.358719i) q^{18} +(0.621320 + 1.07616i) q^{19} +3.65685 q^{20} +(-2.62132 - 0.358719i) q^{21} +0.414214 q^{22} +(3.50000 + 6.06218i) q^{23} +(0.792893 - 1.37333i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(4.79289 + 0.655892i) q^{28} -5.24264 q^{29} +(0.414214 + 0.717439i) q^{30} +(2.82843 - 4.89898i) q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.500000 - 0.866025i) q^{33} -0.656854 q^{34} +(-3.24264 + 4.18154i) q^{35} -1.82843 q^{36} +(-3.74264 - 6.48244i) q^{37} +(0.257359 - 0.445759i) q^{38} +(-2.41421 + 4.18154i) q^{39} +(-1.58579 - 2.74666i) q^{40} -6.82843 q^{41} +(0.414214 + 1.01461i) q^{42} -11.2426 q^{43} +(0.914214 + 1.58346i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.44975 - 2.51104i) q^{46} +(-2.08579 - 3.61269i) q^{47} +3.00000 q^{48} +(-5.00000 + 4.89898i) q^{49} -0.414214 q^{50} +(0.792893 + 1.37333i) q^{51} +(4.41421 - 7.64564i) q^{52} +(6.41421 - 11.1097i) q^{53} +(-0.207107 - 0.358719i) q^{54} -2.00000 q^{55} +(-1.58579 - 3.88437i) q^{56} -1.24264 q^{57} +(1.08579 + 1.88064i) q^{58} +(-1.32843 + 2.30090i) q^{59} +(-1.82843 + 3.16693i) q^{60} +(2.00000 + 3.46410i) q^{61} -2.34315 q^{62} +(1.62132 - 2.09077i) q^{63} -4.17157 q^{64} +(4.82843 + 8.36308i) q^{65} +(-0.207107 + 0.358719i) q^{66} +(4.41421 - 7.64564i) q^{67} +(-1.44975 - 2.51104i) q^{68} -7.00000 q^{69} +(2.17157 + 0.297173i) q^{70} -9.82843 q^{71} +(0.792893 + 1.37333i) q^{72} +(-5.82843 + 10.0951i) q^{73} +(-1.55025 + 2.68512i) q^{74} +(0.500000 + 0.866025i) q^{75} +2.27208 q^{76} +(-2.62132 - 0.358719i) q^{77} +2.00000 q^{78} +(4.65685 + 8.06591i) q^{79} +(3.00000 - 5.19615i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.41421 + 2.44949i) q^{82} +2.82843 q^{83} +(-2.96447 + 3.82282i) q^{84} +3.17157 q^{85} +(2.32843 + 4.03295i) q^{86} +(2.62132 - 4.54026i) q^{87} +(0.792893 - 1.37333i) q^{88} +(-7.07107 - 12.2474i) q^{89} -0.828427 q^{90} +(4.82843 + 11.8272i) q^{91} +12.7990 q^{92} +(2.82843 + 4.89898i) q^{93} +(-0.863961 + 1.49642i) q^{94} +(-1.24264 + 2.15232i) q^{95} +(-2.20711 - 3.82282i) q^{96} +5.48528 q^{97} +(2.79289 + 0.778985i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 8 q^{13} + 14 q^{14} - 8 q^{15} - 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} - 4 q^{22} + 14 q^{23} + 6 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{27} + 22 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{32} - 2 q^{33} + 20 q^{34} + 4 q^{35} + 4 q^{36} + 2 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 16 q^{41} - 4 q^{42} - 28 q^{43} - 2 q^{44} + 4 q^{45} - 14 q^{46} - 14 q^{47} + 12 q^{48} - 20 q^{49} + 4 q^{50} + 6 q^{51} + 12 q^{52} + 20 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 12 q^{57} + 10 q^{58} + 6 q^{59} + 4 q^{60} + 8 q^{61} - 32 q^{62} - 2 q^{63} - 28 q^{64} + 8 q^{65} + 2 q^{66} + 12 q^{67} + 14 q^{68} - 28 q^{69} + 20 q^{70} - 28 q^{71} + 6 q^{72} - 12 q^{73} - 26 q^{74} + 2 q^{75} + 60 q^{76} - 2 q^{77} + 8 q^{78} - 4 q^{79} + 12 q^{80} - 2 q^{81} - 26 q^{84} + 24 q^{85} - 2 q^{86} + 2 q^{87} + 6 q^{88} + 8 q^{90} + 8 q^{91} - 28 q^{92} + 22 q^{94} + 12 q^{95} - 6 q^{96} - 12 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 8 * q^13 + 14 * q^14 - 8 * q^15 - 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 - 4 * q^22 + 14 * q^23 + 6 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^27 + 22 * q^28 - 4 * q^29 - 4 * q^30 - 6 * q^32 - 2 * q^33 + 20 * q^34 + 4 * q^35 + 4 * q^36 + 2 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 16 * q^41 - 4 * q^42 - 28 * q^43 - 2 * q^44 + 4 * q^45 - 14 * q^46 - 14 * q^47 + 12 * q^48 - 20 * q^49 + 4 * q^50 + 6 * q^51 + 12 * q^52 + 20 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 12 * q^57 + 10 * q^58 + 6 * q^59 + 4 * q^60 + 8 * q^61 - 32 * q^62 - 2 * q^63 - 28 * q^64 + 8 * q^65 + 2 * q^66 + 12 * q^67 + 14 * q^68 - 28 * q^69 + 20 * q^70 - 28 * q^71 + 6 * q^72 - 12 * q^73 - 26 * q^74 + 2 * q^75 + 60 * q^76 - 2 * q^77 + 8 * q^78 - 4 * q^79 + 12 * q^80 - 2 * q^81 - 26 * q^84 + 24 * q^85 - 2 * q^86 + 2 * q^87 + 6 * q^88 + 8 * q^90 + 8 * q^91 - 28 * q^92 + 22 * q^94 + 12 * q^95 - 6 * q^96 - 12 * q^97 + 14 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.207107	−	0.358719i	−0.146447	−	0.253653i	0.783465	−	0.621436i	$-0.213450\pi$
$2$	−0.207107	−	0.358719i	−0.146447	−	0.253653i	−0.929912	+	0.367783i	$0.880117\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	0.414214			0.169102
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$8$	−1.58579			−0.560660
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.414214	−	0.717439i	0.130986	−	0.226874i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	0.914214	+	1.58346i	0.263911	+	0.457107i
$13$	4.82843			1.33916			0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843			1.33916			0.669582	+	0.742738i	$0.266473\pi$
$14$	0.671573	−	0.866025i	0.179485	−	0.231455i
$15$	−2.00000			−0.516398
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	0.792893	−	1.37333i	0.192305	−	0.333082i	−0.753709	−	0.657209i	$-0.771737\pi$
$17$	0.792893	−	1.37333i	0.192305	−	0.333082i	0.946014	+	0.324127i	$0.105070\pi$
$18$	−0.207107	+	0.358719i	−0.0488155	+	0.0845510i
$19$	0.621320	+	1.07616i	0.142541	+	0.246888i	0.928453	−	0.371451i	$-0.121139\pi$
$19$	0.621320	+	1.07616i	0.142541	+	0.246888i	−0.785912	+	0.618338i	$0.787806\pi$
$20$	3.65685			0.817697
$21$	−2.62132	−	0.358719i	−0.572019	−	0.0782790i
$22$	0.414214			0.0883106
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$	0.792893	−	1.37333i	0.161849	−	0.280330i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	1.00000			0.192450
$28$	4.79289	+	0.655892i	0.905772	+	0.123952i
$29$	−5.24264			−0.973534			−0.486767	−	0.873532i	$-0.661824\pi$
$29$	−5.24264			−0.973534			−0.486767	+	0.873532i	$0.661824\pi$
$30$	0.414214	+	0.717439i	0.0756247	+	0.130986i
$31$	2.82843	−	4.89898i	0.508001	−	0.879883i	−0.491957	−	0.870620i	$-0.663718\pi$
$31$	2.82843	−	4.89898i	0.508001	−	0.879883i	0.999957	−	0.00926296i	$-0.00294853\pi$
$32$	−2.20711	+	3.82282i	−0.390165	+	0.675786i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	−0.656854			−0.112650
$35$	−3.24264	+	4.18154i	−0.548106	+	0.706809i
$36$	−1.82843			−0.304738
$37$	−3.74264	−	6.48244i	−0.615286	−	1.06571i	−0.990334	−	0.138702i	$-0.955707\pi$
$37$	−3.74264	−	6.48244i	−0.615286	−	1.06571i	0.375048	−	0.927005i	$-0.377626\pi$
$38$	0.257359	−	0.445759i	0.0417492	−	0.0723117i
$39$	−2.41421	+	4.18154i	−0.386584	+	0.669582i
$40$	−1.58579	−	2.74666i	−0.250735	−	0.434286i
$41$	−6.82843			−1.06642			−0.533211	−	0.845983i	$-0.679015\pi$
$41$	−6.82843			−1.06642			−0.533211	+	0.845983i	$0.679015\pi$
$42$	0.414214	+	1.01461i	0.0639145	+	0.156558i
$43$	−11.2426			−1.71449			−0.857243	−	0.514912i	$-0.827825\pi$
$43$	−11.2426			−1.71449			−0.857243	+	0.514912i	$0.827825\pi$
$44$	0.914214	+	1.58346i	0.137823	+	0.238716i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	1.44975	−	2.51104i	0.213754	−	0.370232i
$47$	−2.08579	−	3.61269i	−0.304243	−	0.526965i	0.672849	−	0.739780i	$-0.265070\pi$
$47$	−2.08579	−	3.61269i	−0.304243	−	0.526965i	−0.977093	+	0.212815i	$0.931737\pi$
$48$	3.00000			0.433013
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$	−0.414214			−0.0585786
$51$	0.792893	+	1.37333i	0.111027	+	0.192305i
$52$	4.41421	−	7.64564i	0.612141	−	1.06026i
$53$	6.41421	−	11.1097i	0.881060	−	1.52604i	0.0308961	−	0.999523i	$-0.490164\pi$
$53$	6.41421	−	11.1097i	0.881060	−	1.52604i	0.850164	−	0.526518i	$-0.176503\pi$
$54$	−0.207107	−	0.358719i	−0.0281837	−	0.0488155i
$55$	−2.00000			−0.269680
$56$	−1.58579	−	3.88437i	−0.211910	−	0.519070i
$57$	−1.24264			−0.164592
$58$	1.08579	+	1.88064i	0.142571	+	0.246940i
$59$	−1.32843	+	2.30090i	−0.172946	+	0.299552i	−0.939449	−	0.342690i	$-0.888662\pi$
$59$	−1.32843	+	2.30090i	−0.172946	+	0.299552i	0.766502	+	0.642242i	$0.221995\pi$
$60$	−1.82843	+	3.16693i	−0.236049	+	0.408849i
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−2.34315			−0.297580
$63$	1.62132	−	2.09077i	0.204267	−	0.263412i
$64$	−4.17157			−0.521447
$65$	4.82843	+	8.36308i	0.598893	+	1.03731i
$66$	−0.207107	+	0.358719i	−0.0254931	+	0.0441553i
$67$	4.41421	−	7.64564i	0.539282	−	0.934064i	−0.459661	−	0.888095i	$-0.652029\pi$
$67$	4.41421	−	7.64564i	0.539282	−	0.934064i	0.998943	−	0.0459693i	$-0.0146376\pi$
$68$	−1.44975	−	2.51104i	−0.175808	−	0.304508i
$69$	−7.00000			−0.842701
$70$	2.17157	+	0.297173i	0.259553	+	0.0355190i
$71$	−9.82843			−1.16642			−0.583210	−	0.812322i	$-0.698203\pi$
$71$	−9.82843			−1.16642			−0.583210	+	0.812322i	$0.698203\pi$
$72$	0.792893	+	1.37333i	0.0934434	+	0.161849i
$73$	−5.82843	+	10.0951i	−0.682166	+	1.18155i	0.292153	+	0.956372i	$0.405628\pi$
$73$	−5.82843	+	10.0951i	−0.682166	+	1.18155i	−0.974319	+	0.225174i	$0.927705\pi$
$74$	−1.55025	+	2.68512i	−0.180213	+	0.312138i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	2.27208			0.260625
$77$	−2.62132	−	0.358719i	−0.298727	−	0.0408799i
$78$	2.00000			0.226455
$79$	4.65685	+	8.06591i	0.523937	+	0.907486i	0.999612	+	0.0278643i	$0.00887063\pi$
$79$	4.65685	+	8.06591i	0.523937	+	0.907486i	−0.475675	+	0.879621i	$0.657796\pi$
$80$	3.00000	−	5.19615i	0.335410	−	0.580948i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.41421	+	2.44949i	0.156174	+	0.270501i
$83$	2.82843			0.310460			0.155230	−	0.987878i	$-0.450388\pi$
$83$	2.82843			0.310460			0.155230	+	0.987878i	$0.450388\pi$
$84$	−2.96447	+	3.82282i	−0.323450	+	0.417104i
$85$	3.17157			0.344005
$86$	2.32843	+	4.03295i	0.251081	+	0.434885i
$87$	2.62132	−	4.54026i	0.281035	−	0.486767i
$88$	0.792893	−	1.37333i	0.0845227	−	0.146398i
$89$	−7.07107	−	12.2474i	−0.749532	−	1.29823i	−0.948047	−	0.318129i	$-0.896945\pi$
$89$	−7.07107	−	12.2474i	−0.749532	−	1.29823i	0.198516	−	0.980098i	$-0.436388\pi$
$90$	−0.828427			−0.0873239
$91$	4.82843	+	11.8272i	0.506157	+	1.23983i
$92$	12.7990			1.33439
$93$	2.82843	+	4.89898i	0.293294	+	0.508001i
$94$	−0.863961	+	1.49642i	−0.0891108	+	0.154344i
$95$	−1.24264	+	2.15232i	−0.127492	+	0.220823i
$96$	−2.20711	−	3.82282i	−0.225262	−	0.390165i
$97$	5.48528			0.556946			0.278473	−	0.960444i	$-0.410172\pi$
$97$	5.48528			0.556946			0.278473	+	0.960444i	$0.410172\pi$
$98$	2.79289	+	0.778985i	0.282125	+	0.0786894i
$99$	1.00000			0.100504
$100$	−0.914214	−	1.58346i	−0.0914214	−	0.158346i
$101$	7.44975	−	12.9033i	0.741278	−	1.28393i	−0.210636	−	0.977565i	$-0.567554\pi$
$101$	7.44975	−	12.9033i	0.741278	−	1.28393i	0.951914	−	0.306366i	$-0.0991131\pi$
$102$	0.328427	−	0.568852i	0.0325191	−	0.0563248i
$103$	2.24264	+	3.88437i	0.220974	+	0.382738i	0.955104	−	0.296271i	$-0.0957431\pi$
$103$	2.24264	+	3.88437i	0.220974	+	0.382738i	−0.734130	+	0.679009i	$0.762410\pi$
$104$	−7.65685			−0.750816
$105$	−2.00000	−	4.89898i	−0.195180	−	0.478091i
$106$	−5.31371			−0.516113
$107$	0.828427	+	1.43488i	0.0800871	+	0.138715i	0.903287	−	0.429036i	$-0.141147\pi$
$107$	0.828427	+	1.43488i	0.0800871	+	0.138715i	−0.823200	+	0.567751i	$0.807813\pi$
$108$	0.914214	−	1.58346i	0.0879702	−	0.152369i
$109$	0.585786	−	1.01461i	0.0561082	−	0.0971822i	−0.836607	−	0.547803i	$-0.815464\pi$
$109$	0.585786	−	1.01461i	0.0561082	−	0.0971822i	0.892715	+	0.450621i	$0.148797\pi$
$110$	0.414214	+	0.717439i	0.0394937	+	0.0684051i
$111$	7.48528			0.710471
$112$	4.86396	−	6.27231i	0.459601	−	0.592678i
$113$	3.65685			0.344008			0.172004	−	0.985096i	$-0.444976\pi$
$113$	3.65685			0.344008			0.172004	+	0.985096i	$0.444976\pi$
$114$	0.257359	+	0.445759i	0.0241039	+	0.0417492i
$115$	−7.00000	+	12.1244i	−0.652753	+	1.13060i
$116$	−4.79289	+	8.30153i	−0.445009	+	0.770778i
$117$	−2.41421	−	4.18154i	−0.223194	−	0.386584i
$118$	1.10051			0.101310
$119$	4.15685	+	0.568852i	0.381058	+	0.0521466i
$120$	3.17157			0.289524
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.828427	−	1.43488i	0.0750023	−	0.129908i
$123$	3.41421	−	5.91359i	0.307849	−	0.533211i
$124$	−5.17157	−	8.95743i	−0.464421	−	0.804401i
$125$	12.0000			1.07331
$126$	−1.08579	−	0.148586i	−0.0967295	−	0.0132371i
$127$	−1.92893			−0.171165			−0.0855825	−	0.996331i	$-0.527275\pi$
$127$	−1.92893			−0.171165			−0.0855825	+	0.996331i	$0.527275\pi$
$128$	5.27817	+	9.14207i	0.466529	+	0.808052i
$129$	5.62132	−	9.73641i	0.494930	−	0.857243i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	5.41421	+	9.37769i	0.473042	+	0.819333i	0.999524	−	0.0308535i	$-0.00982254\pi$
$131$	5.41421	+	9.37769i	0.473042	+	0.819333i	−0.526482	+	0.850186i	$0.676489\pi$
$132$	−1.82843			−0.159144
$133$	−2.01472	+	2.59808i	−0.174698	+	0.225282i
$134$	−3.65685			−0.315904
$135$	1.00000	+	1.73205i	0.0860663	+	0.149071i
$136$	−1.25736	+	2.17781i	−0.107818	+	0.186746i
$137$	8.24264	−	14.2767i	0.704216	−	1.21974i	−0.262757	−	0.964862i	$-0.584632\pi$
$137$	8.24264	−	14.2767i	0.704216	−	1.21974i	0.966974	−	0.254876i	$-0.0820348\pi$
$138$	1.44975	+	2.51104i	0.123411	+	0.213754i
$139$	5.58579			0.473780			0.236890	−	0.971536i	$-0.423872\pi$
$139$	5.58579			0.473780			0.236890	+	0.971536i	$0.423872\pi$
$140$	3.65685	+	8.95743i	0.309061	+	0.757041i
$141$	4.17157			0.351310
$142$	2.03553	+	3.52565i	0.170818	+	0.295866i
$143$	−2.41421	+	4.18154i	−0.201887	+	0.349678i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−5.24264	−	9.08052i	−0.435378	−	0.754096i
$146$	4.82843			0.399603
$147$	−1.74264	−	6.77962i	−0.143731	−	0.559173i
$148$	−13.6863			−1.12501
$149$	−10.1066	−	17.5051i	−0.827965	−	1.43408i	−0.899632	−	0.436649i	$-0.856165\pi$
$149$	−10.1066	−	17.5051i	−0.827965	−	1.43408i	0.0716669	−	0.997429i	$-0.477168\pi$
$150$	0.207107	−	0.358719i	0.0169102	−	0.0292893i
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	−0.883745	−	0.467969i	$-0.844986\pi$
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	0.847145	+	0.531361i	$0.178319\pi$
$152$	−0.985281	−	1.70656i	−0.0799169	−	0.138420i
$153$	−1.58579			−0.128203
$154$	0.414214	+	1.01461i	0.0333783	+	0.0817598i
$155$	11.3137			0.908739
$156$	4.41421	+	7.64564i	0.353420	+	0.612141i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	1.92893	−	3.34101i	0.153458	−	0.265796i
$159$	6.41421	+	11.1097i	0.508680	+	0.881060i
$160$	−8.82843			−0.697948
$161$	−11.3492	+	14.6354i	−0.894446	+	1.15343i
$162$	0.414214			0.0325437
$163$	−6.48528	−	11.2328i	−0.507966	−	0.879824i	−0.999957	−	0.00922341i	$-0.997064\pi$
$163$	−6.48528	−	11.2328i	−0.507966	−	0.879824i	0.491991	−	0.870600i	$-0.336269\pi$
$164$	−6.24264	+	10.8126i	−0.487468	+	0.844320i
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	−0.585786	−	1.01461i	−0.0454658	−	0.0787492i
$167$	10.8284			0.837929			0.418964	−	0.908003i	$-0.362393\pi$
$167$	10.8284			0.837929			0.418964	+	0.908003i	$0.362393\pi$
$168$	4.15685	+	0.568852i	0.320708	+	0.0438879i
$169$	10.3137			0.793362
$170$	−0.656854	−	1.13770i	−0.0503784	−	0.0872580i
$171$	0.621320	−	1.07616i	0.0475136	−	0.0822959i
$172$	−10.2782	+	17.8023i	−0.783703	+	1.35741i
$173$	4.58579	+	7.94282i	0.348651	+	0.603881i	0.986010	−	0.166686i	$-0.0533066\pi$
$173$	4.58579	+	7.94282i	0.348651	+	0.603881i	−0.637359	+	0.770567i	$0.719973\pi$
$174$	−2.17157			−0.164627
$175$	2.62132	+	0.358719i	0.198153	+	0.0271166i
$176$	3.00000			0.226134
$177$	−1.32843	−	2.30090i	−0.0998507	−	0.172946i
$178$	−2.92893	+	5.07306i	−0.219533	+	0.380242i
$179$	−6.08579	+	10.5409i	−0.454873	+	0.787863i	−0.998681	−	0.0513465i	$-0.983649\pi$
$179$	−6.08579	+	10.5409i	−0.454873	+	0.787863i	0.543808	+	0.839210i	$0.316982\pi$
$180$	−1.82843	−	3.16693i	−0.136283	−	0.236049i
$181$	−0.343146			−0.0255058			−0.0127529	−	0.999919i	$-0.504059\pi$
$181$	−0.343146			−0.0255058			−0.0127529	+	0.999919i	$0.504059\pi$
$182$	3.24264	−	4.18154i	0.240361	−	0.309956i
$183$	−4.00000			−0.295689
$184$	−5.55025	−	9.61332i	−0.409170	−	0.708703i
$185$	7.48528	−	12.9649i	0.550329	−	0.953197i
$186$	1.17157	−	2.02922i	0.0859039	−	0.148790i
$187$	0.792893	+	1.37333i	0.0579821	+	0.100428i
$188$	−7.62742			−0.556287
$189$	1.00000	+	2.44949i	0.0727393	+	0.178174i
$190$	1.02944			0.0746832
$191$	5.17157	+	8.95743i	0.374202	+	0.648137i	0.990207	−	0.139605i	$-0.0445834\pi$
$191$	5.17157	+	8.95743i	0.374202	+	0.648137i	−0.616005	+	0.787742i	$0.711250\pi$
$192$	2.08579	−	3.61269i	0.150529	−	0.260723i
$193$	−8.07107	+	13.9795i	−0.580968	+	1.00627i	0.414397	+	0.910096i	$0.363993\pi$
$193$	−8.07107	+	13.9795i	−0.580968	+	1.00627i	−0.995365	+	0.0961701i	$0.969341\pi$
$194$	−1.13604	−	1.96768i	−0.0815628	−	0.141271i
$195$	−9.65685			−0.691542
$196$	3.18629	+	12.3960i	0.227592	+	0.885431i
$197$	−13.5858			−0.967947			−0.483974	−	0.875083i	$-0.660807\pi$
$197$	−13.5858			−0.967947			−0.483974	+	0.875083i	$0.660807\pi$
$198$	−0.207107	−	0.358719i	−0.0147184	−	0.0254931i
$199$	−9.89949	+	17.1464i	−0.701757	+	1.21548i	0.266093	+	0.963947i	$0.414267\pi$
$199$	−9.89949	+	17.1464i	−0.701757	+	1.21548i	−0.967849	+	0.251531i	$0.919066\pi$
$200$	−0.792893	+	1.37333i	−0.0560660	+	0.0971092i
$201$	4.41421	+	7.64564i	0.311355	+	0.539282i
$202$	−6.17157			−0.434230
$203$	−5.24264	−	12.8418i	−0.367961	−	0.901317i
$204$	2.89949			0.203005
$205$	−6.82843	−	11.8272i	−0.476918	−	0.826046i
$206$	0.928932	−	1.60896i	0.0647218	−	0.112101i
$207$	3.50000	−	6.06218i	0.243267	−	0.421350i
$208$	−7.24264	−	12.5446i	−0.502187	−	0.869813i
$209$	−1.24264			−0.0859553
$210$	−1.34315	+	1.73205i	−0.0926859	+	0.119523i
$211$	−18.9706			−1.30599			−0.652994	−	0.757363i	$-0.726487\pi$
$211$	−18.9706			−1.30599			−0.652994	+	0.757363i	$0.726487\pi$
$212$	−11.7279	−	20.3134i	−0.805477	−	1.39513i
$213$	4.91421	−	8.51167i	0.336716	−	0.583210i
$214$	0.343146	−	0.594346i	0.0234570	−	0.0406286i
$215$	−11.2426	−	19.4728i	−0.766742	−	1.32804i
$216$	−1.58579			−0.107899
$217$	14.8284	+	2.02922i	1.00662	+	0.137753i
$218$	−0.485281			−0.0328674
$219$	−5.82843	−	10.0951i	−0.393849	−	0.682166i
$220$	−1.82843	+	3.16693i	−0.123273	+	0.213514i
$221$	3.82843	−	6.63103i	0.257528	−	0.446051i
$222$	−1.55025	−	2.68512i	−0.104046	−	0.180213i
$223$	10.9706			0.734643			0.367322	−	0.930094i	$-0.380275\pi$
$223$	10.9706			0.734643			0.367322	+	0.930094i	$0.380275\pi$
$224$	−11.5711	−	1.58346i	−0.773124	−	0.105800i
$225$	−1.00000			−0.0666667
$226$	−0.757359	−	1.31178i	−0.0503788	−	0.0872586i
$227$	9.48528	−	16.4290i	0.629560	−	1.09043i	−0.358080	−	0.933691i	$-0.616568\pi$
$227$	9.48528	−	16.4290i	0.629560	−	1.09043i	0.987640	−	0.156739i	$-0.0500983\pi$
$228$	−1.13604	+	1.96768i	−0.0752360	+	0.130313i
$229$	2.17157	+	3.76127i	0.143502	+	0.248552i	0.928813	−	0.370549i	$-0.120830\pi$
$229$	2.17157	+	3.76127i	0.143502	+	0.248552i	−0.785311	+	0.619101i	$0.787497\pi$
$230$	5.79899			0.382374
$231$	1.62132	−	2.09077i	0.106675	−	0.137563i
$232$	8.31371			0.545822
$233$	−3.79289	−	6.56948i	−0.248481	−	0.430381i	0.714624	−	0.699509i	$-0.246598\pi$
$233$	−3.79289	−	6.56948i	−0.248481	−	0.430381i	−0.963104	+	0.269128i	$0.913265\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	4.17157	−	7.22538i	0.272123	−	0.471332i
$236$	2.42893	+	4.20703i	0.158110	+	0.273855i
$237$	−9.31371			−0.604990
$238$	−0.656854	−	1.60896i	−0.0425775	−	0.104293i
$239$	10.4853			0.678236			0.339118	−	0.940744i	$-0.389871\pi$
$239$	10.4853			0.678236			0.339118	+	0.940744i	$0.389871\pi$
$240$	3.00000	+	5.19615i	0.193649	+	0.335410i
$241$	7.65685	−	13.2621i	0.493221	−	0.854284i	−0.506748	−	0.862094i	$-0.669153\pi$
$241$	7.65685	−	13.2621i	0.493221	−	0.854284i	0.999970	+	0.00780972i	$0.00248593\pi$
$242$	−0.207107	+	0.358719i	−0.0133133	+	0.0230594i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.31371			0.468212
$245$	−13.4853	−	3.76127i	−0.861543	−	0.240299i
$246$	−2.82843			−0.180334
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$	−4.48528	+	7.76874i	−0.284816	+	0.493315i
$249$	−1.41421	+	2.44949i	−0.0896221	+	0.155230i
$250$	−2.48528	−	4.30463i	−0.157183	−	0.272249i
$251$	−19.4853			−1.22990			−0.614950	−	0.788566i	$-0.710824\pi$
$251$	−19.4853			−1.22990			−0.614950	+	0.788566i	$0.710824\pi$
$252$	−1.82843	−	4.47871i	−0.115180	−	0.282132i
$253$	−7.00000			−0.440086
$254$	0.399495	+	0.691946i	0.0250665	+	0.0434165i
$255$	−1.58579	+	2.74666i	−0.0993058	+	0.172003i
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	14.7279	+	25.5095i	0.918703	+	1.59124i	0.801388	+	0.598145i	$0.204095\pi$
$257$	14.7279	+	25.5095i	0.918703	+	1.59124i	0.117314	+	0.993095i	$0.462571\pi$
$258$	−4.65685			−0.289923
$259$	12.1360	−	15.6500i	0.754097	−	0.972444i
$260$	17.6569			1.09503
$261$	2.62132	+	4.54026i	0.162256	+	0.281035i
$262$	2.24264	−	3.88437i	0.138551	−	0.239977i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	0.792893	+	1.37333i	0.0487992	+	0.0845227i
$265$	25.6569			1.57609
$266$	1.34924	+	0.184640i	0.0827274	+	0.0113210i
$267$	14.1421			0.865485
$268$	−8.07107	−	13.9795i	−0.493019	−	0.853934i
$269$	−5.89949	+	10.2182i	−0.359699	+	0.623016i	−0.987910	−	0.155026i	$-0.950454\pi$
$269$	−5.89949	+	10.2182i	−0.359699	+	0.623016i	0.628212	+	0.778042i	$0.283787\pi$
$270$	0.414214	−	0.717439i	0.0252082	−	0.0436619i
$271$	−5.48528	−	9.50079i	−0.333207	−	0.577132i	0.649932	−	0.759993i	$-0.274798\pi$
$271$	−5.48528	−	9.50079i	−0.333207	−	0.577132i	−0.983139	+	0.182861i	$0.941464\pi$
$272$	−4.75736			−0.288457
$273$	−12.6569	−	1.73205i	−0.766028	−	0.104828i
$274$	−6.82843			−0.412520
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−6.39949	+	11.0843i	−0.385204	+	0.667193i
$277$	7.17157	−	12.4215i	0.430898	−	0.746337i	−0.566053	−	0.824369i	$-0.691530\pi$
$277$	7.17157	−	12.4215i	0.430898	−	0.746337i	0.996951	+	0.0780316i	$0.0248635\pi$
$278$	−1.15685	−	2.00373i	−0.0693835	−	0.120176i
$279$	−5.65685			−0.338667
$280$	5.14214	−	6.63103i	0.307301	−	0.396280i
$281$	11.5858			0.691150			0.345575	−	0.938391i	$-0.387684\pi$
$281$	11.5858			0.691150			0.345575	+	0.938391i	$0.387684\pi$
$282$	−0.863961	−	1.49642i	−0.0514481	−	0.0891108i
$283$	−15.8284	+	27.4156i	−0.940902	+	1.62969i	−0.177147	+	0.984184i	$0.556687\pi$
$283$	−15.8284	+	27.4156i	−0.940902	+	1.62969i	−0.763755	+	0.645506i	$0.776646\pi$
$284$	−8.98528	+	15.5630i	−0.533178	+	0.923492i
$285$	−1.24264	−	2.15232i	−0.0736077	−	0.127492i
$286$	2.00000			0.118262
$287$	−6.82843	−	16.7262i	−0.403069	−	0.987314i
$288$	4.41421			0.260110
$289$	7.24264	+	12.5446i	0.426038	+	0.737919i
$290$	−2.17157	+	3.76127i	−0.127519	+	0.220870i
$291$	−2.74264	+	4.75039i	−0.160776	+	0.278473i
$292$	10.6569	+	18.4582i	0.623645	+	1.08019i
$293$	−19.7279			−1.15252			−0.576259	−	0.817267i	$-0.695488\pi$
$293$	−19.7279			−1.15252			−0.576259	+	0.817267i	$0.695488\pi$
$294$	−2.07107	+	2.02922i	−0.120787	+	0.118347i
$295$	−5.31371			−0.309376
$296$	5.93503	+	10.2798i	0.344967	+	0.597500i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−4.18629	+	7.25087i	−0.242505	+	0.420032i
$299$	16.8995	+	29.2708i	0.977323	+	1.69277i
$300$	1.82843			0.105564
$301$	−11.2426	−	27.5387i	−0.648015	−	1.58731i
$302$	0.372583			0.0214397
$303$	7.44975	+	12.9033i	0.427977	+	0.741278i
$304$	1.86396	−	3.22848i	0.106905	−	0.185166i
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$	0.328427	+	0.568852i	0.0187749	+	0.0325191i
$307$	5.31371			0.303269			0.151635	−	0.988437i	$-0.451546\pi$
$307$	5.31371			0.303269			0.151635	+	0.988437i	$0.451546\pi$
$308$	−2.96447	+	3.82282i	−0.168916	+	0.217825i
$309$	−4.48528			−0.255159
$310$	−2.34315	−	4.05845i	−0.133082	−	0.230504i
$311$	7.81371	−	13.5337i	0.443075	−	0.767428i	−0.554841	−	0.831956i	$-0.687221\pi$
$311$	7.81371	−	13.5337i	0.443075	−	0.767428i	0.997916	+	0.0645283i	$0.0205543\pi$
$312$	3.82843	−	6.63103i	0.216742	−	0.375408i
$313$	17.3995	+	30.1368i	0.983478	+	1.70343i	0.648515	+	0.761202i	$0.275390\pi$
$313$	17.3995	+	30.1368i	0.983478	+	1.70343i	0.334962	+	0.942232i	$0.391276\pi$
$314$	2.89949			0.163628
$315$	5.24264	+	0.717439i	0.295389	+	0.0404231i
$316$	17.0294			0.957981
$317$	1.34315	+	2.32640i	0.0754386	+	0.130663i	0.901277	−	0.433243i	$-0.142631\pi$
$317$	1.34315	+	2.32640i	0.0754386	+	0.130663i	−0.825838	+	0.563907i	$0.809298\pi$
$318$	2.65685	−	4.60181i	0.148989	−	0.258056i
$319$	2.62132	−	4.54026i	0.146766	−	0.254206i
$320$	−4.17157	−	7.22538i	−0.233198	−	0.403911i
$321$	−1.65685			−0.0924766
$322$	7.60051	+	1.04011i	0.423560	+	0.0579628i
$323$	1.97056			0.109645
$324$	0.914214	+	1.58346i	0.0507896	+	0.0879702i
$325$	2.41421	−	4.18154i	0.133916	−	0.231950i
$326$	−2.68629	+	4.65279i	−0.148780	+	0.257694i
$327$	0.585786	+	1.01461i	0.0323941	+	0.0561082i
$328$	10.8284			0.597900
$329$	6.76346	−	8.72180i	0.372881	−	0.480848i
$330$	−0.828427			−0.0456034
$331$	−2.75736	−	4.77589i	−0.151558	−	0.262506i	0.780242	−	0.625477i	$-0.215096\pi$
$331$	−2.75736	−	4.77589i	−0.151558	−	0.262506i	−0.931800	+	0.362971i	$0.881762\pi$
$332$	2.58579	−	4.47871i	0.141913	−	0.245801i
$333$	−3.74264	+	6.48244i	−0.205095	+	0.355236i
$334$	−2.24264	−	3.88437i	−0.122712	−	0.212543i
$335$	17.6569			0.964697
$336$	3.00000	+	7.34847i	0.163663	+	0.400892i
$337$	32.1421			1.75089			0.875447	−	0.483314i	$-0.160567\pi$
$337$	32.1421			1.75089			0.875447	+	0.483314i	$0.160567\pi$
$338$	−2.13604	−	3.69973i	−0.116185	−	0.201239i
$339$	−1.82843	+	3.16693i	−0.0993065	+	0.172004i
$340$	2.89949	−	5.02207i	0.157247	−	0.272360i
$341$	2.82843	+	4.89898i	0.153168	+	0.265295i
$342$	−0.514719			−0.0278328
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	17.8284			0.961244
$345$	−7.00000	−	12.1244i	−0.376867	−	0.652753i
$346$	1.89949	−	3.29002i	0.102117	−	0.176873i
$347$	9.48528	−	16.4290i	0.509197	−	0.881954i	−0.490747	−	0.871302i	$-0.663276\pi$
$347$	9.48528	−	16.4290i	0.509197	−	0.881954i	0.999943	−	0.0106521i	$-0.00339072\pi$
$348$	−4.79289	−	8.30153i	−0.256926	−	0.445009i
$349$	−22.9706			−1.22959			−0.614793	−	0.788688i	$-0.710760\pi$
$349$	−22.9706			−1.22959			−0.614793	+	0.788688i	$0.710760\pi$
$350$	−0.414214	−	1.01461i	−0.0221406	−	0.0542333i
$351$	4.82843			0.257722
$352$	−2.20711	−	3.82282i	−0.117639	−	0.203757i
$353$	4.65685	−	8.06591i	0.247859	−	0.429305i	−0.715072	−	0.699051i	$-0.753606\pi$
$353$	4.65685	−	8.06591i	0.247859	−	0.429305i	0.962932	+	0.269746i	$0.0869396\pi$
$354$	−0.550253	+	0.953065i	−0.0292456	+	0.0506549i
$355$	−9.82843	−	17.0233i	−0.521639	−	0.903505i
$356$	−25.8579			−1.37046
$357$	−2.57107	+	3.31552i	−0.136075	+	0.175476i
$358$	5.04163			0.266458
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	0.952063	−	0.305903i	$-0.0989582\pi$
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	−0.740951	+	0.671559i	$0.765625\pi$
$360$	−1.58579	+	2.74666i	−0.0835783	+	0.144762i
$361$	8.72792	−	15.1172i	0.459364	−	0.795642i
$362$	0.0710678	+	0.123093i	0.00373524	+	0.00646963i
$363$	1.00000			0.0524864
$364$	23.1421	+	3.16693i	1.21298	+	0.165992i
$365$	−23.3137			−1.22030
$366$	0.828427	+	1.43488i	0.0433026	+	0.0750023i
$367$	−12.0711	+	20.9077i	−0.630105	+	1.09137i	0.357425	+	0.933942i	$0.383655\pi$
$367$	−12.0711	+	20.9077i	−0.630105	+	1.09137i	−0.987530	+	0.157431i	$0.949679\pi$
$368$	10.5000	−	18.1865i	0.547350	−	0.948039i
$369$	3.41421	+	5.91359i	0.177737	+	0.307849i
$370$	−6.20101			−0.322375
$371$	33.6274	+	4.60181i	1.74585	+	0.238914i
$372$	10.3431			0.536267
$373$	−4.82843	−	8.36308i	−0.250006	−	0.433024i	0.713521	−	0.700634i	$-0.247099\pi$
$373$	−4.82843	−	8.36308i	−0.250006	−	0.433024i	−0.963527	+	0.267610i	$0.913766\pi$
$374$	0.328427	−	0.568852i	0.0169826	−	0.0294147i
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$	3.30761	+	5.72895i	0.170577	+	0.295448i
$377$	−25.3137			−1.30372
$378$	0.671573	−	0.866025i	0.0345420	−	0.0445435i
$379$	13.1716			0.676578			0.338289	−	0.941042i	$-0.390152\pi$
$379$	13.1716			0.676578			0.338289	+	0.941042i	$0.390152\pi$
$380$	2.27208	+	3.93535i	0.116555	+	0.201879i
$381$	0.964466	−	1.67050i	0.0494111	−	0.0855825i
$382$	2.14214	−	3.71029i	0.109601	−	0.189835i
$383$	10.1569	+	17.5922i	0.518991	+	0.898919i	0.999756	+	0.0220695i	$0.00702553\pi$
$383$	10.1569	+	17.5922i	0.518991	+	0.898919i	−0.480765	+	0.876849i	$0.659641\pi$
$384$	−10.5563			−0.538701
$385$	−2.00000	−	4.89898i	−0.101929	−	0.249675i
$386$	6.68629			0.340323
$387$	5.62132	+	9.73641i	0.285748	+	0.494930i
$388$	5.01472	−	8.68575i	0.254584	−	0.440952i
$389$	−13.8995	+	24.0746i	−0.704732	+	1.22063i	0.262056	+	0.965053i	$0.415600\pi$
$389$	−13.8995	+	24.0746i	−0.704732	+	1.22063i	−0.966788	+	0.255580i	$0.917734\pi$
$390$	2.00000	+	3.46410i	0.101274	+	0.175412i
$391$	11.1005			0.561377
$392$	7.92893	−	7.76874i	0.400472	−	0.392380i
$393$	−10.8284			−0.546222
$394$	2.81371	+	4.87349i	0.141753	+	0.245523i
$395$	−9.31371	+	16.1318i	−0.468624	+	0.811680i
$396$	0.914214	−	1.58346i	0.0459410	−	0.0795721i
$397$	−0.257359	−	0.445759i	−0.0129165	−	0.0223720i	0.859495	−	0.511144i	$-0.170778\pi$
$397$	−0.257359	−	0.445759i	−0.0129165	−	0.0223720i	−0.872411	+	0.488772i	$0.837445\pi$
$398$	8.20101			0.411079
$399$	−1.24264	−	3.04384i	−0.0622098	−	0.152382i
$400$	−3.00000			−0.150000
$401$	−12.2426	−	21.2049i	−0.611368	−	1.05892i	−0.991010	−	0.133787i	$-0.957286\pi$
$401$	−12.2426	−	21.2049i	−0.611368	−	1.05892i	0.379642	−	0.925134i	$-0.376047\pi$
$402$	1.82843	−	3.16693i	0.0911937	−	0.157952i
$403$	13.6569	−	23.6544i	0.680296	−	1.17831i
$404$	−13.6213	−	23.5928i	−0.677686	−	1.17379i
$405$	−2.00000			−0.0993808
$406$	−3.52082	+	4.54026i	−0.174735	+	0.225329i
$407$	7.48528			0.371032
$408$	−1.25736	−	2.17781i	−0.0622486	−	0.107818i
$409$	−15.8995	+	27.5387i	−0.786179	+	1.36170i	0.142113	+	0.989851i	$0.454611\pi$
$409$	−15.8995	+	27.5387i	−0.786179	+	1.36170i	−0.928292	+	0.371852i	$0.878723\pi$
$410$	−2.82843	+	4.89898i	−0.139686	+	0.241943i
$411$	8.24264	+	14.2767i	0.406579	+	0.704216i
$412$	8.20101			0.404035
$413$	−6.96447	−	0.953065i	−0.342699	−	0.0468973i
$414$	−2.89949			−0.142502
$415$	2.82843	+	4.89898i	0.138842	+	0.240481i
$416$	−10.6569	+	18.4582i	−0.522495	+	0.904988i
$417$	−2.79289	+	4.83743i	−0.136769	+	0.236890i
$418$	0.257359	+	0.445759i	0.0125879	+	0.0218028i
$419$	−24.7990			−1.21151			−0.605755	−	0.795651i	$-0.707129\pi$
$419$	−24.7990			−1.21151			−0.605755	+	0.795651i	$0.707129\pi$
$420$	−9.58579	−	1.31178i	−0.467738	−	0.0640085i
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	3.92893	+	6.80511i	0.191257	+	0.331268i
$423$	−2.08579	+	3.61269i	−0.101414	+	0.175655i
$424$	−10.1716	+	17.6177i	−0.493975	+	0.855590i
$425$	−0.792893	−	1.37333i	−0.0384610	−	0.0666164i
$426$	−4.07107			−0.197244
$427$	−6.48528	+	8.36308i	−0.313845	+	0.404718i
$428$	3.02944			0.146433
$429$	−2.41421	−	4.18154i	−0.116559	−	0.201887i
$430$	−4.65685	+	8.06591i	−0.224573	+	0.388973i
$431$	13.4853	−	23.3572i	0.649563	−	1.12508i	−0.333664	−	0.942692i	$-0.608285\pi$
$431$	13.4853	−	23.3572i	0.649563	−	1.12508i	0.983227	−	0.182384i	$-0.0583815\pi$
$432$	−1.50000	−	2.59808i	−0.0721688	−	0.125000i
$433$	29.1421			1.40048			0.700241	−	0.713907i	$-0.253076\pi$
$433$	29.1421			1.40048			0.700241	+	0.713907i	$0.253076\pi$
$434$	−2.34315	−	5.73951i	−0.112475	−	0.275505i
$435$	10.4853			0.502731
$436$	−1.07107	−	1.85514i	−0.0512948	−	0.0888453i
$437$	−4.34924	+	7.53311i	−0.208052	+	0.360357i
$438$	−2.41421	+	4.18154i	−0.115356	+	0.199802i
$439$	−5.55025	−	9.61332i	−0.264899	−	0.458819i	0.702638	−	0.711547i	$-0.252005\pi$
$439$	−5.55025	−	9.61332i	−0.264899	−	0.458819i	−0.967537	+	0.252729i	$0.918672\pi$
$440$	3.17157			0.151199
$441$	6.74264	+	1.88064i	0.321078	+	0.0895542i
$442$	−3.17157			−0.150856
$443$	5.81371	+	10.0696i	0.276218	+	0.478423i	0.970442	−	0.241336i	$-0.0775856\pi$
$443$	5.81371	+	10.0696i	0.276218	+	0.478423i	−0.694224	+	0.719759i	$0.744252\pi$
$444$	6.84315	−	11.8527i	0.324761	−	0.562503i
$445$	14.1421	−	24.4949i	0.670402	−	1.16117i
$446$	−2.27208	−	3.93535i	−0.107586	−	0.186344i
$447$	20.2132			0.956052
$448$	−4.17157	−	10.2182i	−0.197088	−	0.482766i
$449$	−4.00000			−0.188772			−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$	0.207107	+	0.358719i	0.00976311	+	0.0169102i
$451$	3.41421	−	5.91359i	0.160769	−	0.278460i
$452$	3.34315	−	5.79050i	0.157248	−	0.272362i
$453$	−0.449747	−	0.778985i	−0.0211310	−	0.0365999i
$454$	−7.85786			−0.368788
$455$	−15.6569	+	20.1903i	−0.734005	+	0.946534i
$456$	1.97056			0.0922801
$457$	−6.58579	−	11.4069i	−0.308070	−	0.533593i	0.669870	−	0.742478i	$-0.266350\pi$
$457$	−6.58579	−	11.4069i	−0.308070	−	0.533593i	−0.977940	+	0.208885i	$0.933016\pi$
$458$	0.899495	−	1.55797i	0.0420306	−	0.0727992i
$459$	0.792893	−	1.37333i	0.0370091	−	0.0641016i
$460$	12.7990	+	22.1685i	0.596756	+	1.03361i
$461$	15.2426			0.709921			0.354960	−	0.934881i	$-0.384494\pi$
$461$	15.2426			0.709921			0.354960	+	0.934881i	$0.384494\pi$
$462$	−1.08579	−	0.148586i	−0.0505154	−	0.00691287i
$463$	−26.6274			−1.23748			−0.618741	−	0.785595i	$-0.712357\pi$
$463$	−26.6274			−1.23748			−0.618741	+	0.785595i	$0.712357\pi$
$464$	7.86396	+	13.6208i	0.365075	+	0.632329i
$465$	−5.65685	+	9.79796i	−0.262330	+	0.454369i
$466$	−1.57107	+	2.72117i	−0.0727783	+	0.126056i
$467$	−7.15685	−	12.3960i	−0.331180	−	0.573620i	0.651564	−	0.758594i	$-0.274113\pi$
$467$	−7.15685	−	12.3960i	−0.331180	−	0.573620i	−0.982743	+	0.184974i	$0.940780\pi$
$468$	−8.82843			−0.408094
$469$	23.1421	+	3.16693i	1.06860	+	0.146235i
$470$	−3.45584			−0.159406
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	2.10660	−	3.64874i	0.0969642	−	0.167947i
$473$	5.62132	−	9.73641i	0.258469	−	0.447681i
$474$	1.92893	+	3.34101i	0.0885988	+	0.153458i
$475$	1.24264			0.0570163
$476$	4.70101	−	6.06218i	0.215470	−	0.277859i
$477$	−12.8284			−0.587373
$478$	−2.17157	−	3.76127i	−0.0993254	−	0.172037i
$479$	−7.00000	+	12.1244i	−0.319838	+	0.553976i	−0.980454	−	0.196748i	$-0.936962\pi$
$479$	−7.00000	+	12.1244i	−0.319838	+	0.553976i	0.660616	+	0.750724i	$0.270295\pi$
$480$	4.41421	−	7.64564i	0.201480	−	0.348974i
$481$	−18.0711	−	31.3000i	−0.823970	−	1.42716i
$482$	−6.34315			−0.288922
$483$	−7.00000	−	17.1464i	−0.318511	−	0.780189i
$484$	−1.82843			−0.0831103
$485$	5.48528	+	9.50079i	0.249074	+	0.431408i
$486$	−0.207107	+	0.358719i	−0.00939455	+	0.0162718i
$487$	−6.31371	+	10.9357i	−0.286101	+	0.495542i	−0.972876	−	0.231329i	$-0.925693\pi$
$487$	−6.31371	+	10.9357i	−0.286101	+	0.495542i	0.686774	+	0.726871i	$0.259026\pi$
$488$	−3.17157	−	5.49333i	−0.143570	−	0.248671i
$489$	12.9706			0.586549
$490$	1.44365	+	5.61642i	0.0652175	+	0.253724i
$491$	−18.4853			−0.834229			−0.417115	−	0.908854i	$-0.636959\pi$
$491$	−18.4853			−0.834229			−0.417115	+	0.908854i	$0.636959\pi$
$492$	−6.24264	−	10.8126i	−0.281440	−	0.487468i
$493$	−4.15685	+	7.19988i	−0.187215	+	0.324266i
$494$	1.24264	−	2.15232i	0.0559090	−	0.0968373i
$495$	1.00000	+	1.73205i	0.0449467	+	0.0778499i
$496$	−16.9706			−0.762001
$497$	−9.82843	−	24.0746i	−0.440865	−	1.07989i
$498$	1.17157			0.0524994
$499$	−3.89949	−	6.75412i	−0.174565	−	0.302356i	0.765445	−	0.643501i	$-0.222519\pi$
$499$	−3.89949	−	6.75412i	−0.174565	−	0.302356i	−0.940011	+	0.341145i	$0.889185\pi$
$500$	10.9706	−	19.0016i	0.490618	−	0.849776i
$501$	−5.41421	+	9.37769i	−0.241889	+	0.418964i
$502$	4.03553	+	6.98975i	0.180115	+	0.311968i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−2.57107	+	3.31552i	−0.114524	+	0.147685i
$505$	29.7990			1.32604
$506$	1.44975	+	2.51104i	0.0644491	+	0.111629i
$507$	−5.15685	+	8.93193i	−0.229024	+	0.396681i
$508$	−1.76346	+	3.05440i	−0.0782407	+	0.135517i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$	1.31371			0.0581720
$511$	−30.5563	−	4.18154i	−1.35173	−	0.184980i
$512$	22.7574			1.00574
$513$	0.621320	+	1.07616i	0.0274320	+	0.0475136i
$514$	6.10051	−	10.5664i	0.269082	−	0.466063i
$515$	−4.48528	+	7.76874i	−0.197645	+	0.342331i
$516$	−10.2782	−	17.8023i	−0.452471	−	0.783703i
$517$	4.17157			0.183466
$518$	−8.12742	−	1.11221i	−0.357098	−	0.0488678i
$519$	−9.17157			−0.402587
$520$	−7.65685	−	13.2621i	−0.335775	−	0.581580i
$521$	−18.4142	+	31.8944i	−0.806741	+	1.39732i	0.108368	+	0.994111i	$0.465438\pi$
$521$	−18.4142	+	31.8944i	−0.806741	+	1.39732i	−0.915109	+	0.403206i	$0.867896\pi$
$522$	1.08579	−	1.88064i	0.0475236	−	0.0823133i
$523$	−17.1421	−	29.6910i	−0.749573	−	1.29830i	−0.948027	−	0.318189i	$-0.896925\pi$
$523$	−17.1421	−	29.6910i	−0.749573	−	1.29830i	0.198454	−	0.980110i	$-0.436408\pi$
$524$	19.7990			0.864923
$525$	−1.62132	+	2.09077i	−0.0707602	+	0.0912487i
$526$	7.45584			0.325090
$527$	−4.48528	−	7.76874i	−0.195382	−	0.338411i
$528$	−1.50000	+	2.59808i	−0.0652791	+	0.113067i
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$	−5.31371	−	9.20361i	−0.230813	−	0.399779i
$531$	2.65685			0.115298
$532$	2.27208	+	5.56543i	0.0985071	+	0.241292i
$533$	−32.9706			−1.42811
$534$	−2.92893	−	5.07306i	−0.126747	−	0.219533i
$535$	−1.65685	+	2.86976i	−0.0716321	+	0.124070i
$536$	−7.00000	+	12.1244i	−0.302354	+	0.523692i
$537$	−6.08579	−	10.5409i	−0.262621	−	0.454873i
$538$	4.88730			0.210707
$539$	−1.74264	−	6.77962i	−0.0750608	−	0.292019i
$540$	3.65685			0.157366
$541$	−4.17157	−	7.22538i	−0.179350	−	0.310643i	0.762308	−	0.647214i	$-0.224066\pi$
$541$	−4.17157	−	7.22538i	−0.179350	−	0.310643i	−0.941658	+	0.336571i	$0.890733\pi$
$542$	−2.27208	+	3.93535i	−0.0975941	+	0.169038i
$543$	0.171573	−	0.297173i	0.00736290	−	0.0127529i
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$	2.34315			0.100369
$546$	2.00000	+	4.89898i	0.0855921	+	0.209657i
$547$	18.2132			0.778740			0.389370	−	0.921081i	$-0.372693\pi$
$547$	18.2132			0.778740			0.389370	+	0.921081i	$0.372693\pi$
$548$	−15.0711	−	26.1039i	−0.643804	−	1.11510i
$549$	2.00000	−	3.46410i	0.0853579	−	0.147844i
$550$	0.207107	−	0.358719i	0.00883106	−	0.0152958i
$551$	−3.25736	−	5.64191i	−0.138768	−	0.240354i
$552$	11.1005			0.472469
$553$	−15.1005	+	19.4728i	−0.642139	+	0.828069i
$554$	−5.94113			−0.252414
$555$	7.48528	+	12.9649i	0.317732	+	0.550329i
$556$	5.10660	−	8.84489i	0.216568	−	0.375107i
$557$	−11.2782	+	19.5344i	−0.477872	+	0.827698i	−0.999678	−	0.0253659i	$-0.991925\pi$
$557$	−11.2782	+	19.5344i	−0.477872	+	0.827698i	0.521807	+	0.853064i	$0.325258\pi$
$558$	1.17157	+	2.02922i	0.0495966	+	0.0859039i
$559$	−54.2843			−2.29598
$560$	15.7279	+	2.15232i	0.664626	+	0.0909520i
$561$	−1.58579			−0.0669520
$562$	−2.39949	−	4.15605i	−0.101217	−	0.175312i
$563$	−9.58579	+	16.6031i	−0.403993	+	0.699736i	−0.994204	−	0.107513i	$-0.965711\pi$
$563$	−9.58579	+	16.6031i	−0.403993	+	0.699736i	0.590211	+	0.807249i	$0.299045\pi$
$564$	3.81371	−	6.60554i	0.160586	−	0.278143i
$565$	3.65685	+	6.33386i	0.153845	+	0.266467i
$566$	13.1127			0.551168
$567$	−2.62132	−	0.358719i	−0.110085	−	0.0150648i
$568$	15.5858			0.653965
$569$	3.62132	+	6.27231i	0.151814	+	0.262949i	0.931894	−	0.362730i	$-0.118155\pi$
$569$	3.62132	+	6.27231i	0.151814	+	0.262949i	−0.780081	+	0.625679i	$0.784822\pi$
$570$	−0.514719	+	0.891519i	−0.0215592	+	0.0373416i
$571$	9.03553	−	15.6500i	0.378125	−	0.654932i	−0.612664	−	0.790343i	$-0.709902\pi$
$571$	9.03553	−	15.6500i	0.378125	−	0.654932i	0.990790	+	0.135411i	$0.0432355\pi$
$572$	4.41421	+	7.64564i	0.184568	+	0.319680i
$573$	−10.3431			−0.432091
$574$	−4.58579	+	5.91359i	−0.191407	+	0.246829i
$575$	7.00000			0.291920
$576$	2.08579	+	3.61269i	0.0869078	+	0.150529i
$577$	1.82843	−	3.16693i	0.0761184	−	0.131841i	−0.825454	−	0.564470i	$-0.809081\pi$
$577$	1.82843	−	3.16693i	0.0761184	−	0.131841i	0.901572	+	0.432629i	$0.142414\pi$
$578$	3.00000	−	5.19615i	0.124784	−	0.216131i
$579$	−8.07107	−	13.9795i	−0.335422	−	0.580968i
$580$	−19.1716			−0.796056
$581$	2.82843	+	6.92820i	0.117343	+	0.287430i
$582$	2.27208			0.0941807
$583$	6.41421	+	11.1097i	0.265650	+	0.460119i
$584$	9.24264	−	16.0087i	0.382463	−	0.662446i
$585$	4.82843	−	8.36308i	0.199631	−	0.345771i
$586$	4.08579	+	7.07679i	0.168782	+	0.292339i
$587$	31.3137			1.29246			0.646228	−	0.763145i	$-0.276346\pi$
$587$	31.3137			1.29246			0.646228	+	0.763145i	$0.276346\pi$
$588$	−12.3284	−	3.43861i	−0.508416	−	0.141806i
$589$	7.02944			0.289643
$590$	1.10051	+	1.90613i	0.0453071	+	0.0784742i
$591$	6.79289	−	11.7656i	0.279422	−	0.483974i
$592$	−11.2279	+	19.4473i	−0.461465	+	0.799280i
$593$	23.8640	+	41.3336i	0.979975	+	1.69737i	0.662429	+	0.749124i	$0.269525\pi$
$593$	23.8640	+	41.3336i	0.979975	+	1.69737i	0.317546	+	0.948243i	$0.397141\pi$
$594$	0.414214			0.0169954
$595$	3.17157	+	7.76874i	0.130022	+	0.318487i
$596$	−36.9584			−1.51387
$597$	−9.89949	−	17.1464i	−0.405159	−	0.701757i
$598$	7.00000	−	12.1244i	0.286251	−	0.495802i
$599$	23.3137	−	40.3805i	0.952572	−	1.64990i	0.212744	−	0.977108i	$-0.431760\pi$
$599$	23.3137	−	40.3805i	0.952572	−	1.64990i	0.739828	−	0.672796i	$-0.234907\pi$
$600$	−0.792893	−	1.37333i	−0.0323697	−	0.0560660i
$601$	2.48528			0.101377			0.0506884	−	0.998715i	$-0.483858\pi$
$601$	2.48528			0.101377			0.0506884	+	0.998715i	$0.483858\pi$
$602$	−7.55025	+	9.73641i	−0.307725	+	0.396827i
$603$	−8.82843			−0.359521
$604$	0.822330	+	1.42432i	0.0334602	+	0.0579547i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$	3.08579	−	5.34474i	0.125352	−	0.217115i
$607$	20.6569	+	35.7787i	0.838436	+	1.45221i	0.891202	+	0.453607i	$0.149863\pi$
$607$	20.6569	+	35.7787i	0.838436	+	1.45221i	−0.0527662	+	0.998607i	$0.516804\pi$
$608$	−5.48528			−0.222458
$609$	13.7426	+	1.88064i	0.556880	+	0.0762073i
$610$	3.31371			0.134168
$611$	−10.0711	−	17.4436i	−0.407432	−	0.705693i
$612$	−1.44975	+	2.51104i	−0.0586026	+	0.101503i
$613$	−15.4142	+	26.6982i	−0.622574	+	1.07833i	0.366430	+	0.930445i	$0.380580\pi$
$613$	−15.4142	+	26.6982i	−0.622574	+	1.07833i	−0.989005	+	0.147885i	$0.952754\pi$
$614$	−1.10051	−	1.90613i	−0.0444128	−	0.0769252i
$615$	13.6569			0.550698
$616$	4.15685	+	0.568852i	0.167484	+	0.0229197i
$617$	18.8284			0.758004			0.379002	−	0.925396i	$-0.376267\pi$
$617$	18.8284			0.758004			0.379002	+	0.925396i	$0.376267\pi$
$618$	0.928932	+	1.60896i	0.0373671	+	0.0647218i
$619$	5.31371	−	9.20361i	0.213576	−	0.369924i	−0.739255	−	0.673425i	$-0.764822\pi$
$619$	5.31371	−	9.20361i	0.213576	−	0.369924i	0.952831	+	0.303501i	$0.0981556\pi$
$620$	10.3431	−	17.9149i	0.415391	−	0.719478i
$621$	3.50000	+	6.06218i	0.140450	+	0.243267i
$622$	−6.47309			−0.259547
$623$	22.9289	−	29.5680i	0.918628	−	1.18462i
$624$	14.4853			0.579875
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	7.20711	−	12.4831i	0.288054	−	0.498924i
$627$	0.621320	−	1.07616i	0.0248131	−	0.0429776i
$628$	6.39949	+	11.0843i	0.255368	+	0.442310i
$629$	−11.8701			−0.473290
$630$	−0.828427	−	2.02922i	−0.0330053	−	0.0808462i
$631$	−30.2843			−1.20560			−0.602799	−	0.797893i	$-0.705948\pi$
$631$	−30.2843			−1.20560			−0.602799	+	0.797893i	$0.705948\pi$
$632$	−7.38478	−	12.7908i	−0.293751	−	0.508791i
$633$	9.48528	−	16.4290i	0.377006	−	0.652994i
$634$	0.556349	−	0.963625i	0.0220954	−	0.0382704i
$635$	−1.92893	−	3.34101i	−0.0765473	−	0.132584i
$636$	23.4558			0.930085
$637$	−24.1421	+	23.6544i	−0.956546	+	0.937220i
$638$	−2.17157			−0.0859734
$639$	4.91421	+	8.51167i	0.194403	+	0.336716i
$640$	−10.5563	+	18.2841i	−0.417276	+	0.722744i
$641$	−2.24264	+	3.88437i	−0.0885790	+	0.153423i	−0.906911	−	0.421323i	$-0.861566\pi$
$641$	−2.24264	+	3.88437i	−0.0885790	+	0.153423i	0.818332	+	0.574746i	$0.194899\pi$
$642$	0.343146	+	0.594346i	0.0135429	+	0.0234570i
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$	12.7990	+	31.3510i	0.504351	+	1.23540i
$645$	22.4853			0.885357
$646$	−0.408117	−	0.706879i	−0.0160571	−	0.0278118i
$647$	−1.65685	+	2.86976i	−0.0651377	+	0.112822i	−0.896755	−	0.442527i	$-0.854082\pi$
$647$	−1.65685	+	2.86976i	−0.0651377	+	0.112822i	0.831617	+	0.555349i	$0.187415\pi$
$648$	0.792893	−	1.37333i	0.0311478	−	0.0539496i
$649$	−1.32843	−	2.30090i	−0.0521453	−	0.0903184i
$650$	−2.00000			−0.0784465
$651$	−9.17157	+	11.8272i	−0.359462	+	0.463544i
$652$	−23.7157			−0.928780
$653$	15.5563	+	26.9444i	0.608767	+	1.05442i	0.991444	+	0.130533i	$0.0416689\pi$
$653$	15.5563	+	26.9444i	0.608767	+	1.05442i	−0.382677	+	0.923882i	$0.624998\pi$
$654$	0.242641	−	0.420266i	0.00948800	−	0.0164337i
$655$	−10.8284	+	18.7554i	−0.423102	+	0.732834i
$656$	10.2426	+	17.7408i	0.399908	+	0.692661i
$657$	11.6569			0.454777
$658$	−4.52944	−	0.619839i	−0.176576	−	0.0241639i
$659$	17.5147			0.682277			0.341138	−	0.940013i	$-0.389188\pi$
$659$	17.5147			0.682277			0.341138	+	0.940013i	$0.389188\pi$
$660$	−1.82843	−	3.16693i	−0.0711714	−	0.123273i
$661$	10.9853	−	19.0271i	0.427278	−	0.740067i	−0.569352	−	0.822094i	$-0.692806\pi$
$661$	10.9853	−	19.0271i	0.427278	−	0.740067i	0.996630	+	0.0820266i	$0.0261393\pi$
$662$	−1.14214	+	1.97824i	−0.0443904	+	0.0768864i
$663$	3.82843	+	6.63103i	0.148684	+	0.257528i
$664$	−4.48528			−0.174063
$665$	−6.51472	−	0.891519i	−0.252630	−	0.0345716i
$666$	3.10051			0.120142
$667$	−18.3492	−	31.7818i	−0.710486	−	1.23060i
$668$	9.89949	−	17.1464i	0.383023	−	0.663415i
$669$	−5.48528	+	9.50079i	−0.212073	+	0.367322i
$670$	−3.65685	−	6.33386i	−0.141277	−	0.244698i
$671$	−4.00000			−0.154418
$672$	7.15685	−	9.22911i	0.276082	−	0.356021i
$673$	32.8284			1.26544			0.632721	−	0.774379i	$-0.281938\pi$
$673$	32.8284			1.26544			0.632721	+	0.774379i	$0.281938\pi$
$674$	−6.65685	−	11.5300i	−0.256412	−	0.444119i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	9.42893	−	16.3314i	0.362651	−	0.628130i
$677$	−25.0061	−	43.3118i	−0.961062	−	1.66461i	−0.719841	−	0.694139i	$-0.755785\pi$
$677$	−25.0061	−	43.3118i	−0.961062	−	1.66461i	−0.241221	−	0.970470i	$-0.577548\pi$
$678$	1.51472			0.0581724
$679$	5.48528	+	13.4361i	0.210506	+	0.515632i
$680$	−5.02944			−0.192870
$681$	9.48528	+	16.4290i	0.363477	+	0.629560i
$682$	1.17157	−	2.02922i	0.0448618	−	0.0777030i
$683$	−21.3995	+	37.0650i	−0.818829	+	1.41825i	0.0877167	+	0.996145i	$0.472043\pi$
$683$	−21.3995	+	37.0650i	−0.818829	+	1.41825i	−0.906546	+	0.422108i	$0.861290\pi$
$684$	−1.13604	−	1.96768i	−0.0434375	−	0.0752360i
$685$	32.9706			1.25974
$686$	0.884776	+	7.62015i	0.0337809	+	0.290939i
$687$	−4.34315			−0.165701
$688$	16.8640	+	29.2092i	0.642932	+	1.11359i
$689$	30.9706	−	53.6426i	1.17988	−	2.04362i
$690$	−2.89949	+	5.02207i	−0.110382	+	0.191187i
$691$	−19.7279	−	34.1698i	−0.750486	−	1.29988i	−0.947588	−	0.319496i	$-0.896486\pi$
$691$	−19.7279	−	34.1698i	−0.750486	−	1.29988i	0.197102	−	0.980383i	$-0.436847\pi$
$692$	16.7696			0.637483
$693$	1.00000	+	2.44949i	0.0379869	+	0.0930484i
$694$	−7.85786			−0.298280
$695$	5.58579	+	9.67487i	0.211881	+	0.366989i
$696$	−4.15685	+	7.19988i	−0.157565	+	0.272911i
$697$	−5.41421	+	9.37769i	−0.205078	+	0.355205i
$698$	4.75736	+	8.23999i	0.180069	+	0.311888i
$699$	7.58579			0.286921
$700$	2.96447	−	3.82282i	0.112046	−	0.144489i
$701$	16.8995			0.638285			0.319143	−	0.947707i	$-0.396605\pi$
$701$	16.8995			0.638285			0.319143	+	0.947707i	$0.396605\pi$
$702$	−1.00000	−	1.73205i	−0.0377426	−	0.0653720i
$703$	4.65076	−	8.05535i	0.175407	−	0.303813i
$704$	2.08579	−	3.61269i	0.0786110	−	0.136158i
$705$	4.17157	+	7.22538i	0.157111	+	0.272123i
$706$	−3.85786			−0.145193
$707$	39.0563	+	5.34474i	1.46887	+	0.201010i
$708$	−4.85786			−0.182570
$709$	23.8848	+	41.3696i	0.897012	+	1.55367i	0.831295	+	0.555831i	$0.187600\pi$
$709$	23.8848	+	41.3696i	0.897012	+	1.55367i	0.0657165	+	0.997838i	$0.479067\pi$
$710$	−4.07107	+	7.05130i	−0.152784	+	0.264630i
$711$	4.65685	−	8.06591i	0.174646	−	0.302495i
$712$	11.2132	+	19.4218i	0.420233	+	0.727864i
$713$	39.5980			1.48296
$714$	1.72183	+	0.235626i	0.0644377	+	0.00881810i
$715$	−9.65685			−0.361146
$716$	11.1274	+	19.2733i	0.415851	+	0.720275i
$717$	−5.24264	+	9.08052i	−0.195790	+	0.339118i
$718$	1.65685	−	2.86976i	0.0618333	−	0.107098i
$719$	−25.3995	−	43.9932i	−0.947241	−	1.64067i	−0.751200	−	0.660074i	$-0.770525\pi$
$719$	−25.3995	−	43.9932i	−0.947241	−	1.64067i	−0.196041	−	0.980596i	$-0.562809\pi$
$720$	−6.00000			−0.223607
$721$	−7.27208	+	9.37769i	−0.270826	+	0.349244i
$722$	−7.23045			−0.269089
$723$	7.65685	+	13.2621i	0.284761	+	0.493221i
$724$	−0.313708	+	0.543359i	−0.0116589	+	0.0201938i
$725$	−2.62132	+	4.54026i	−0.0973534	+	0.168621i
$726$	−0.207107	−	0.358719i	−0.00768645	−	0.0133133i
$727$	−50.0833			−1.85749			−0.928743	−	0.370725i	$-0.879109\pi$
$727$	−50.0833			−1.85749			−0.928743	+	0.370725i	$0.879109\pi$
$728$	−7.65685	−	18.7554i	−0.283782	−	0.695121i
$729$	1.00000			0.0370370
$730$	4.82843	+	8.36308i	0.178708	+	0.309532i
$731$	−8.91421	+	15.4399i	−0.329704	+	0.571064i
$732$	−3.65685	+	6.33386i	−0.135161	+	0.234106i
$733$	0.828427	+	1.43488i	0.0305987	+	0.0529984i	0.880919	−	0.473267i	$-0.156925\pi$
$733$	0.828427	+	1.43488i	0.0305987	+	0.0529984i	−0.850321	+	0.526265i	$0.823592\pi$
$734$	10.0000			0.369107
$735$	10.0000	−	9.79796i	0.368856	−	0.361403i
$736$	−30.8995			−1.13897
$737$	4.41421	+	7.64564i	0.162600	+	0.281631i
$738$	1.41421	−	2.44949i	0.0520579	−	0.0901670i
$739$	14.1716	−	24.5459i	0.521310	−	0.902935i	−0.478383	−	0.878151i	$-0.658777\pi$
$739$	14.1716	−	24.5459i	0.521310	−	0.902935i	0.999693	−	0.0247837i	$-0.00788971\pi$
$740$	−13.6863	−	23.7054i	−0.503118	−	0.871426i
$741$	−6.00000			−0.220416
$742$	−5.31371	−	13.0159i	−0.195072	−	0.477828i
$743$	−5.79899			−0.212744			−0.106372	−	0.994326i	$-0.533923\pi$
$743$	−5.79899			−0.212744			−0.106372	+	0.994326i	$0.533923\pi$
$744$	−4.48528	−	7.76874i	−0.164438	−	0.284816i
$745$	20.2132	−	35.0103i	0.740554	−	1.28268i
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$	−1.41421	−	2.44949i	−0.0517434	−	0.0896221i
$748$	2.89949			0.106016
$749$	−2.68629	+	3.46410i	−0.0981550	+	0.126576i
$750$	4.97056			0.181499
$751$	3.34315	+	5.79050i	0.121993	+	0.211298i	0.920554	−	0.390616i	$-0.127738\pi$
$751$	3.34315	+	5.79050i	0.121993	+	0.211298i	−0.798560	+	0.601915i	$0.794405\pi$
$752$	−6.25736	+	10.8381i	−0.228182	+	0.395224i
$753$	9.74264	−	16.8747i	0.355042	−	0.614950i
$754$	5.24264	+	9.08052i	0.190926	+	0.330693i
$755$	−1.79899			−0.0654719
$756$	4.79289	+	0.655892i	0.174316	+	0.0238546i
$757$	−30.3137			−1.10177			−0.550885	−	0.834581i	$-0.685710\pi$
$757$	−30.3137			−1.10177			−0.550885	+	0.834581i	$0.685710\pi$
$758$	−2.72792	−	4.72490i	−0.0990826	−	0.171616i
$759$	3.50000	−	6.06218i	0.127042	−	0.220043i
$760$	1.97056	−	3.41311i	0.0714798	−	0.123807i
$761$	19.8995	+	34.4669i	0.721356	+	1.24943i	0.960456	+	0.278431i	$0.0898142\pi$
$761$	19.8995	+	34.4669i	0.721356	+	1.24943i	−0.239100	+	0.970995i	$0.576852\pi$
$762$	−0.798990			−0.0289443
$763$	3.07107	+	0.420266i	0.111180	+	0.0152147i
$764$	18.9117			0.684201
$765$	−1.58579	−	2.74666i	−0.0573342	−	0.0993058i
$766$	4.20711	−	7.28692i	0.152009	−	0.263287i
$767$	−6.41421	+	11.1097i	−0.231604	+	0.401150i
$768$	−1.98528	−	3.43861i	−0.0716377	−	0.124080i
$769$	−5.79899			−0.209117			−0.104558	−	0.994519i	$-0.533343\pi$
$769$	−5.79899			−0.209117			−0.104558	+	0.994519i	$0.533343\pi$
$770$	−1.34315	+	1.73205i	−0.0484036	+	0.0624188i
$771$	−29.4558			−1.06083
$772$	14.7574	+	25.5605i	0.531129	+	0.919942i
$773$	20.1716	−	34.9382i	0.725521	−	1.25664i	−0.233238	−	0.972420i	$-0.574932\pi$
$773$	20.1716	−	34.9382i	0.725521	−	1.25664i	0.958759	−	0.284220i	$-0.0917345\pi$
$774$	2.32843	−	4.03295i	0.0836936	−	0.144962i
$775$	−2.82843	−	4.89898i	−0.101600	−	0.175977i
$776$	−8.69848			−0.312257
$777$	7.48528	+	18.3351i	0.268533	+	0.657769i
$778$	11.5147			0.412823
$779$	−4.24264	−	7.34847i	−0.152008	−	0.263286i
$780$	−8.82843	+	15.2913i	−0.316108	+	0.547516i
$781$	4.91421	−	8.51167i	0.175844	−	0.304571i
$782$	−2.29899	−	3.98197i	−0.0822117	−	0.142395i
$783$	−5.24264			−0.187357
$784$	20.2279	+	5.64191i	0.722426	+	0.201497i
$785$	−14.0000			−0.499681
$786$	2.24264	+	3.88437i	0.0799923	+	0.138551i
$787$	17.7635	−	30.7672i	0.633199	−	1.09673i	−0.353695	−	0.935361i	$-0.615075\pi$
$787$	17.7635	−	30.7672i	0.633199	−	1.09673i	0.986894	−	0.161372i	$-0.0515918\pi$
$788$	−12.4203	+	21.5126i	−0.442455	+	0.766355i
$789$	−9.00000	−	15.5885i	−0.320408	−	0.554964i
$790$	7.71573			0.274513
$791$	3.65685	+	8.95743i	0.130023	+	0.318489i
$792$	−1.58579			−0.0563485
$793$	9.65685	+	16.7262i	0.342925	+	0.593963i
$794$	−0.106602	+	0.184640i	−0.00378315	+	0.00655261i
$795$	−12.8284	+	22.2195i	−0.454977	+	0.788044i
$796$	18.1005	+	31.3510i	0.641555	+	1.11121i
$797$	16.8284			0.596093			0.298047	−	0.954551i	$-0.403665\pi$
$797$	16.8284			0.596093			0.298047	+	0.954551i	$0.403665\pi$
$798$	−0.834524	+	1.07616i	−0.0295418	+	0.0380956i
$799$	−6.61522			−0.234030
$800$	2.20711	+	3.82282i	0.0780330	+	0.135157i
$801$	−7.07107	+	12.2474i	−0.249844	+	0.432742i
$802$	−5.07107	+	8.78335i	−0.179066	+	0.310151i
$803$	−5.82843	−	10.0951i	−0.205681	−	0.356249i
$804$	16.1421			0.569289
$805$	−36.6985	−	5.02207i	−1.29345	−	0.177005i
$806$	−11.3137			−0.398508
$807$	−5.89949	−	10.2182i	−0.207672	−	0.359699i
$808$	−11.8137	+	20.4619i	−0.415605	+	0.719849i
$809$	−2.58579	+	4.47871i	−0.0909114	+	0.157463i	−0.907895	−	0.419198i	$-0.862311\pi$
$809$	−2.58579	+	4.47871i	−0.0909114	+	0.157463i	0.816983	+	0.576661i	$0.195645\pi$
$810$	0.414214	+	0.717439i	0.0145540	+	0.0252082i
$811$	−18.9706			−0.666147			−0.333073	−	0.942901i	$-0.608086\pi$
$811$	−18.9706			−0.666147			−0.333073	+	0.942901i	$0.608086\pi$
$812$	−25.1274	−	3.43861i	−0.881799	−	0.120671i
$813$	10.9706			0.384754
$814$	−1.55025	−	2.68512i	−0.0543363	−	0.0941133i
$815$	12.9706	−	22.4657i	0.454339	−	0.786938i
$816$	2.37868	−	4.11999i	0.0832704	−	0.144229i
$817$	−6.98528	−	12.0989i	−0.244384	−	0.423286i
$818$	13.1716			0.460533
$819$	7.82843	−	10.0951i	0.273547	−	0.352752i
$820$	−24.9706			−0.872010
$821$	−16.5858	−	28.7274i	−0.578848	−	1.00259i	−0.995612	−	0.0935793i	$-0.970169\pi$
$821$	−16.5858	−	28.7274i	−0.578848	−	1.00259i	0.416764	−	0.909015i	$-0.363164\pi$
$822$	3.41421	−	5.91359i	0.119084	−	0.206260i
$823$	19.4142	−	33.6264i	0.676737	−	1.17214i	−0.299221	−	0.954184i	$-0.596727\pi$
$823$	19.4142	−	33.6264i	0.676737	−	1.17214i	0.975958	−	0.217959i	$-0.0699399\pi$
$824$	−3.55635	−	6.15978i	−0.123891	−	0.214586i
$825$	−1.00000			−0.0348155
$826$	1.10051	+	2.69568i	0.0382915	+	0.0937946i
$827$	−14.6863			−0.510692			−0.255346	−	0.966850i	$-0.582189\pi$
$827$	−14.6863			−0.510692			−0.255346	+	0.966850i	$0.582189\pi$
$828$	−6.39949	−	11.0843i	−0.222398	−	0.385204i
$829$	5.91421	−	10.2437i	0.205409	−	0.355779i	−0.744854	−	0.667228i	$-0.767481\pi$
$829$	5.91421	−	10.2437i	0.205409	−	0.355779i	0.950263	+	0.311449i	$0.100814\pi$
$830$	1.17157	−	2.02922i	0.0406659	−	0.0704354i
$831$	7.17157	+	12.4215i	0.248779	+	0.430898i
$832$	−20.1421			−0.698303
$833$	2.76346	+	10.7510i	0.0957481	+	0.372501i
$834$	2.31371			0.0801172
$835$	10.8284	+	18.7554i	0.374733	+	0.649057i
$836$	−1.13604	+	1.96768i	−0.0392907	+	0.0680535i
$837$	2.82843	−	4.89898i	0.0977647	−	0.169334i
$838$	5.13604	+	8.89588i	0.177422	+	0.307303i
$839$	−24.9706			−0.862080			−0.431040	−	0.902333i	$-0.641853\pi$
$839$	−24.9706			−0.862080			−0.431040	+	0.902333i	$0.641853\pi$
$840$	3.17157	+	7.76874i	0.109430	+	0.268047i
$841$	−1.51472			−0.0522317
$842$	1.44975	+	2.51104i	0.0499616	+	0.0865360i
$843$	−5.79289	+	10.0336i	−0.199518	+	0.345575i
$844$	−17.3431	+	30.0392i	−0.596976	+	1.03399i
$845$	10.3137	+	17.8639i	0.354802	+	0.614536i
$846$	1.72792			0.0594072
$847$	1.62132	−	2.09077i	0.0557092	−	0.0718397i
$848$	−38.4853			−1.32159
$849$	−15.8284	−	27.4156i	−0.543230	−	0.940902i
$850$	−0.328427	+	0.568852i	−0.0112650	+	0.0195115i
$851$	26.1985	−	45.3771i	0.898072	−	1.55551i
$852$	−8.98528	−	15.5630i	−0.307831	−	0.533178i
$853$	4.48528			0.153573			0.0767866	−	0.997048i	$-0.475534\pi$
$853$	4.48528			0.153573			0.0767866	+	0.997048i	$0.475534\pi$
$854$	4.34315	+	0.594346i	0.148619	+	0.0203381i
$855$	2.48528			0.0849948
$856$	−1.31371	−	2.27541i	−0.0449016	−	0.0777719i
$857$	−13.1777	+	22.8244i	−0.450141	+	0.779666i	−0.998394	−	0.0566456i	$-0.981959\pi$
$857$	−13.1777	+	22.8244i	−0.450141	+	0.779666i	0.548254	+	0.836312i	$0.315293\pi$
$858$	−1.00000	+	1.73205i	−0.0341394	+	0.0591312i
$859$	3.75736	+	6.50794i	0.128199	+	0.222048i	0.922979	−	0.384850i	$-0.125747\pi$
$859$	3.75736	+	6.50794i	0.128199	+	0.222048i	−0.794780	+	0.606898i	$0.792414\pi$
$860$	−41.1127			−1.40193
$861$	17.8995	+	2.44949i	0.610013	+	0.0834784i
$862$	−11.1716			−0.380505
$863$	21.3137	+	36.9164i	0.725527	+	1.25665i	0.958757	+	0.284228i	$0.0917373\pi$
$863$	21.3137	+	36.9164i	0.725527	+	1.25665i	−0.233230	+	0.972422i	$0.574929\pi$
$864$	−2.20711	+	3.82282i	−0.0750873	+	0.130055i
$865$	−9.17157	+	15.8856i	−0.311843	+	0.540128i
$866$	−6.03553	−	10.4539i	−0.205096	−	0.355236i
$867$	−14.4853			−0.491946
$868$	16.7696	−	21.6251i	0.569196	−	0.734005i
$869$	−9.31371			−0.315946
$870$	−2.17157	−	3.76127i	−0.0736232	−	0.127519i
$871$	21.3137	−	36.9164i	0.722187	−	1.25087i
$872$	−0.928932	+	1.60896i	−0.0314576	+	0.0544862i
$873$	−2.74264	−	4.75039i	−0.0928243	−	0.160776i
$874$	3.60303			0.121874
$875$	12.0000	+	29.3939i	0.405674	+	0.993694i
$876$	−21.3137			−0.720123
$877$	7.24264	+	12.5446i	0.244567	+	0.423602i	0.962010	−	0.273015i	$-0.0880210\pi$
$877$	7.24264	+	12.5446i	0.244567	+	0.423602i	−0.717443	+	0.696617i	$0.754688\pi$
$878$	−2.29899	+	3.98197i	−0.0775872	+	0.134385i
$879$	9.86396	−	17.0849i	0.332703	−	0.576259i
$880$	3.00000	+	5.19615i	0.101130	+	0.175162i
$881$	39.3137			1.32451			0.662256	−	0.749277i	$-0.269599\pi$
$881$	39.3137			1.32451			0.662256	+	0.749277i	$0.269599\pi$
$882$	−0.721825	−	2.80821i	−0.0243051	−	0.0945573i
$883$	28.3431			0.953823			0.476911	−	0.878951i	$-0.341756\pi$
$883$	28.3431			0.953823			0.476911	+	0.878951i	$0.341756\pi$
$884$	−7.00000	−	12.1244i	−0.235435	−	0.407786i
$885$	2.65685	−	4.60181i	0.0893092	−	0.154688i
$886$	2.40812	−	4.17098i	0.0809023	−	0.140127i
$887$	−4.65685	−	8.06591i	−0.156362	−	0.270827i	0.777192	−	0.629263i	$-0.216643\pi$
$887$	−4.65685	−	8.06591i	−0.156362	−	0.270827i	−0.933554	+	0.358437i	$0.883310\pi$
$888$	−11.8701			−0.398333
$889$	−1.92893	−	4.72490i	−0.0646943	−	0.158468i
$890$	−11.7157			−0.392712
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	10.0294	−	17.3715i	0.335810	−	0.581641i
$893$	2.59188	−	4.48927i	0.0867341	−	0.150228i
$894$	−4.18629	−	7.25087i	−0.140011	−	0.242505i
$895$	−24.3431			−0.813702
$896$	−17.1152	+	22.0709i	−0.571779	+	0.737337i
$897$	−33.7990			−1.12852
$898$	0.828427	+	1.43488i	0.0276450	+	0.0478825i
$899$	−14.8284	+	25.6836i	−0.494556	+	0.856596i
$900$	−0.914214	+	1.58346i	−0.0304738	+	0.0527821i
$901$	−10.1716	−	17.6177i	−0.338864	−	0.586930i
$902$	−2.82843			−0.0941763
$903$	29.4706	+	4.03295i	0.980719	+	0.134208i
$904$	−5.79899			−0.192872
$905$	−0.343146	−	0.594346i	−0.0114066	−	0.0197567i
$906$	−0.186292	+	0.322666i	−0.00618912	+	0.0107199i
$907$	17.2426	−	29.8651i	0.572532	−	0.991655i	−0.423772	−	0.905769i	$-0.639294\pi$
$907$	17.2426	−	29.8651i	0.572532	−	0.991655i	0.996305	−	0.0858867i	$-0.0273723\pi$
$908$	−17.3431	−	30.0392i	−0.575553	−	0.996886i
$909$	−14.8995			−0.494185
$910$	10.4853	+	1.43488i	0.347584	+	0.0475657i
$911$	−21.4853			−0.711839			−0.355920	−	0.934517i	$-0.615832\pi$
$911$	−21.4853			−0.711839			−0.355920	+	0.934517i	$0.615832\pi$
$912$	1.86396	+	3.22848i	0.0617219	+	0.106905i
$913$	−1.41421	+	2.44949i	−0.0468036	+	0.0810663i
$914$	−2.72792	+	4.72490i	−0.0902316	+	0.156286i
$915$	−4.00000	−	6.92820i	−0.132236	−	0.229039i
$916$	7.94113			0.262382
$917$	−17.5563	+	22.6398i	−0.579762	+	0.747631i
$918$	−0.656854			−0.0216794
$919$	7.17767	+	12.4321i	0.236769	+	0.410097i	0.959785	−	0.280735i	$-0.0905781\pi$
$919$	7.17767	+	12.4321i	0.236769	+	0.410097i	−0.723016	+	0.690831i	$0.757245\pi$
$920$	11.1005	−	19.2266i	0.365973	−	0.633884i
$921$	−2.65685	+	4.60181i	−0.0875463	+	0.151635i
$922$	−3.15685	−	5.46783i	−0.103965	−	0.180073i
$923$	−47.4558			−1.56203
$924$	−1.82843	−	4.47871i	−0.0601508	−	0.147339i
$925$	−7.48528			−0.246115
$926$	5.51472	+	9.55177i	0.181225	+	0.313891i
$927$	2.24264	−	3.88437i	0.0736580	−	0.127579i
$928$	11.5711	−	20.0417i	0.379839	−	0.657900i
$929$	8.58579	+	14.8710i	0.281691	+	0.487902i	0.971801	−	0.235802i	$-0.0757715\pi$
$929$	8.58579	+	14.8710i	0.281691	+	0.487902i	−0.690111	+	0.723704i	$0.742438\pi$
$930$	4.68629			0.153670
$931$	−8.37868	−	2.33696i	−0.274600	−	0.0765907i
$932$	−13.8701			−0.454329
$933$	7.81371	+	13.5337i	0.255809	+	0.443075i
$934$	−2.96447	+	5.13461i	−0.0970003	+	0.168009i
$935$	−1.58579	+	2.74666i	−0.0518608	+	0.0898255i
$936$	3.82843	+	6.63103i	0.125136	+	0.216742i
$937$	34.1421			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$937$	34.1421			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$938$	−3.65685	−	8.95743i	−0.119401	−	0.292470i
$939$	−34.7990			−1.13562
$940$	−7.62742	−	13.2111i	−0.248779	−	0.430898i
$941$	−1.03553	+	1.79360i	−0.0337574	+	0.0584696i	−0.882411	−	0.470480i	$-0.844081\pi$
$941$	−1.03553	+	1.79360i	−0.0337574	+	0.0584696i	0.848653	+	0.528950i	$0.177414\pi$
$942$	−1.44975	+	2.51104i	−0.0472353	+	0.0818140i
$943$	−23.8995	−	41.3951i	−0.778275	−	1.34801i
$944$	7.97056			0.259420
$945$	−3.24264	+	4.18154i	−0.105483	+	0.136026i
$946$	−4.65685			−0.151407
$947$	−10.2574	−	17.7663i	−0.333319	−	0.577326i	0.649841	−	0.760070i	$-0.274835\pi$
$947$	−10.2574	−	17.7663i	−0.333319	−	0.577326i	−0.983161	+	0.182744i	$0.941502\pi$
$948$	−8.51472	+	14.7479i	−0.276545	+	0.478990i
$949$	−28.1421	+	48.7436i	−0.913532	+	1.58228i
$950$	−0.257359	−	0.445759i	−0.00834984	−	0.0144623i
$951$	−2.68629			−0.0871090
$952$	−6.59188	−	0.902079i	−0.213644	−	0.0292365i
$953$	14.1421			0.458109			0.229054	−	0.973414i	$-0.426437\pi$
$953$	14.1421			0.458109			0.229054	+	0.973414i	$0.426437\pi$
$954$	2.65685	+	4.60181i	0.0860188	+	0.148989i
$955$	−10.3431	+	17.9149i	−0.334696	+	0.579711i
$956$	9.58579	−	16.6031i	0.310026	−	0.536982i
$957$	2.62132	+	4.54026i	0.0847353	+	0.146766i
$958$	5.79899			0.187357
$959$	43.2132	+	5.91359i	1.39543	+	0.190960i
$960$	8.34315			0.269274
$961$	−0.500000	−	0.866025i	−0.0161290	−	0.0279363i
$962$	−7.48528	+	12.9649i	−0.241335	+	0.418005i
$963$	0.828427	−	1.43488i	0.0266957	−	0.0462383i
$964$	−14.0000	−	24.2487i	−0.450910	−	0.780998i
$965$	−32.2843			−1.03927
$966$	−4.70101	+	6.06218i	−0.151253	+	0.195047i
$967$	27.0416			0.869600			0.434800	−	0.900527i	$-0.356819\pi$
$967$	27.0416			0.869600			0.434800	+	0.900527i	$0.356819\pi$
$968$	0.792893	+	1.37333i	0.0254846	+	0.0441405i
$969$	−0.985281	+	1.70656i	−0.0316518	+	0.0548225i
$970$	2.27208	−	3.93535i	0.0729520	−	0.126357i
$971$	14.4853	+	25.0892i	0.464855	+	0.805152i	0.999195	−	0.0401174i	$-0.0127732\pi$
$971$	14.4853	+	25.0892i	0.464855	+	0.805152i	−0.534340	+	0.845270i	$0.679440\pi$
$972$	−1.82843			−0.0586468
$973$	5.58579	+	13.6823i	0.179072	+	0.438635i
$974$	5.23045			0.167594
$975$	2.41421	+	4.18154i	0.0773167	+	0.133916i
$976$	6.00000	−	10.3923i	0.192055	−	0.332650i
$977$	3.58579	−	6.21076i	0.114719	−	0.198700i	−0.802948	−	0.596049i	$-0.796736\pi$
$977$	3.58579	−	6.21076i	0.114719	−	0.198700i	0.917668	+	0.397349i	$0.130070\pi$
$978$	−2.68629	−	4.65279i	−0.0858981	−	0.148780i
$979$	14.1421			0.451985
$980$	−18.2843	+	17.9149i	−0.584070	+	0.572269i
$981$	−1.17157			−0.0374054
$982$	3.82843	+	6.63103i	0.122170	+	0.211605i
$983$	17.9853	−	31.1514i	0.573641	−	0.993576i	−0.422546	−	0.906341i	$-0.638864\pi$
$983$	17.9853	−	31.1514i	0.573641	−	0.993576i	0.996188	−	0.0872347i	$-0.0278030\pi$
$984$	−5.41421	+	9.37769i	−0.172599	+	0.298950i
$985$	−13.5858	−	23.5313i	−0.432879	−	0.749769i
$986$	3.44365			0.109668
$987$	4.17157	+	10.2182i	0.132783	+	0.325250i
$988$	10.9706			0.349020
$989$	−39.3492	−	68.1549i	−1.25123	−	2.16720i
$990$	0.414214	−	0.717439i	0.0131646	−	0.0228017i
$991$	23.6569	−	40.9749i	0.751485	−	1.30161i	−0.195618	−	0.980680i	$-0.562671\pi$
$991$	23.6569	−	40.9749i	0.751485	−	1.30161i	0.947103	−	0.320930i	$-0.103995\pi$
$992$	12.4853	+	21.6251i	0.396408	+	0.686599i
$993$	5.51472			0.175004
$994$	−6.60051	+	8.51167i	−0.209355	+	0.269974i
$995$	−39.5980			−1.25534
$996$	2.58579	+	4.47871i	0.0819338	+	0.141913i
$997$	−19.0711	+	33.0321i	−0.603987	+	1.04614i	0.388224	+	0.921565i	$0.373089\pi$
$997$	−19.0711	+	33.0321i	−0.603987	+	1.04614i	−0.992211	+	0.124571i	$0.960245\pi$
$998$	−1.61522	+	2.79765i	−0.0511290	+	0.0885580i
$999$	−3.74264	−	6.48244i	−0.118412	−	0.205095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.d.67.1	✓	4
3.2	odd	2		693.2.i.f.298.2		4
7.2	even	3	inner	231.2.i.d.100.1	yes	4
7.3	odd	6		1617.2.a.m.1.2		2
7.4	even	3		1617.2.a.n.1.2		2
21.2	odd	6		693.2.i.f.100.2		4
21.11	odd	6		4851.2.a.be.1.1		2
21.17	even	6		4851.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.d.67.1	✓	4	1.1	even	1	trivial
231.2.i.d.100.1	yes	4	7.2	even	3	inner
693.2.i.f.100.2		4	21.2	odd	6
693.2.i.f.298.2		4	3.2	odd	2
1617.2.a.m.1.2		2	7.3	odd	6
1617.2.a.n.1.2		2	7.4	even	3
4851.2.a.bd.1.1		2	21.17	even	6
4851.2.a.be.1.1		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +(1.00000 + 1.73205i) q^{5} +0.414214 q^{6} +(1.00000 + 2.44949i) q^{7} -1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.207107 - 0.358719i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +(1.00000 + 1.73205i) q^{5} +0.414214 q^{6} +(1.00000 + 2.44949i) q^{7} -1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.414214 - 0.717439i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.914214 + 1.58346i) q^{12} +4.82843 q^{13} +(0.671573 - 0.866025i) q^{14} -2.00000 q^{15} +(-1.50000 - 2.59808i) q^{16} +(0.792893 - 1.37333i) q^{17} +(-0.207107 + 0.358719i) q^{18} +(0.621320 + 1.07616i) q^{19} +3.65685 q^{20} +(-2.62132 - 0.358719i) q^{21} +0.414214 q^{22} +(3.50000 + 6.06218i) q^{23} +(0.792893 - 1.37333i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(4.79289 + 0.655892i) q^{28} -5.24264 q^{29} +(0.414214 + 0.717439i) q^{30} +(2.82843 - 4.89898i) q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.500000 - 0.866025i) q^{33} -0.656854 q^{34} +(-3.24264 + 4.18154i) q^{35} -1.82843 q^{36} +(-3.74264 - 6.48244i) q^{37} +(0.257359 - 0.445759i) q^{38} +(-2.41421 + 4.18154i) q^{39} +(-1.58579 - 2.74666i) q^{40} -6.82843 q^{41} +(0.414214 + 1.01461i) q^{42} -11.2426 q^{43} +(0.914214 + 1.58346i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.44975 - 2.51104i) q^{46} +(-2.08579 - 3.61269i) q^{47} +3.00000 q^{48} +(-5.00000 + 4.89898i) q^{49} -0.414214 q^{50} +(0.792893 + 1.37333i) q^{51} +(4.41421 - 7.64564i) q^{52} +(6.41421 - 11.1097i) q^{53} +(-0.207107 - 0.358719i) q^{54} -2.00000 q^{55} +(-1.58579 - 3.88437i) q^{56} -1.24264 q^{57} +(1.08579 + 1.88064i) q^{58} +(-1.32843 + 2.30090i) q^{59} +(-1.82843 + 3.16693i) q^{60} +(2.00000 + 3.46410i) q^{61} -2.34315 q^{62} +(1.62132 - 2.09077i) q^{63} -4.17157 q^{64} +(4.82843 + 8.36308i) q^{65} +(-0.207107 + 0.358719i) q^{66} +(4.41421 - 7.64564i) q^{67} +(-1.44975 - 2.51104i) q^{68} -7.00000 q^{69} +(2.17157 + 0.297173i) q^{70} -9.82843 q^{71} +(0.792893 + 1.37333i) q^{72} +(-5.82843 + 10.0951i) q^{73} +(-1.55025 + 2.68512i) q^{74} +(0.500000 + 0.866025i) q^{75} +2.27208 q^{76} +(-2.62132 - 0.358719i) q^{77} +2.00000 q^{78} +(4.65685 + 8.06591i) q^{79} +(3.00000 - 5.19615i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.41421 + 2.44949i) q^{82} +2.82843 q^{83} +(-2.96447 + 3.82282i) q^{84} +3.17157 q^{85} +(2.32843 + 4.03295i) q^{86} +(2.62132 - 4.54026i) q^{87} +(0.792893 - 1.37333i) q^{88} +(-7.07107 - 12.2474i) q^{89} -0.828427 q^{90} +(4.82843 + 11.8272i) q^{91} +12.7990 q^{92} +(2.82843 + 4.89898i) q^{93} +(-0.863961 + 1.49642i) q^{94} +(-1.24264 + 2.15232i) q^{95} +(-2.20711 - 3.82282i) q^{96} +5.48528 q^{97} +(2.79289 + 0.778985i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 8 q^{13} + 14 q^{14} - 8 q^{15} - 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} - 4 q^{22} + 14 q^{23} + 6 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{27} + 22 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{32} - 2 q^{33} + 20 q^{34} + 4 q^{35} + 4 q^{36} + 2 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 16 q^{41} - 4 q^{42} - 28 q^{43} - 2 q^{44} + 4 q^{45} - 14 q^{46} - 14 q^{47} + 12 q^{48} - 20 q^{49} + 4 q^{50} + 6 q^{51} + 12 q^{52} + 20 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 12 q^{57} + 10 q^{58} + 6 q^{59} + 4 q^{60} + 8 q^{61} - 32 q^{62} - 2 q^{63} - 28 q^{64} + 8 q^{65} + 2 q^{66} + 12 q^{67} + 14 q^{68} - 28 q^{69} + 20 q^{70} - 28 q^{71} + 6 q^{72} - 12 q^{73} - 26 q^{74} + 2 q^{75} + 60 q^{76} - 2 q^{77} + 8 q^{78} - 4 q^{79} + 12 q^{80} - 2 q^{81} - 26 q^{84} + 24 q^{85} - 2 q^{86} + 2 q^{87} + 6 q^{88} + 8 q^{90} + 8 q^{91} - 28 q^{92} + 22 q^{94} + 12 q^{95} - 6 q^{96} - 12 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 8 * q^13 + 14 * q^14 - 8 * q^15 - 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 - 4 * q^22 + 14 * q^23 + 6 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^27 + 22 * q^28 - 4 * q^29 - 4 * q^30 - 6 * q^32 - 2 * q^33 + 20 * q^34 + 4 * q^35 + 4 * q^36 + 2 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 16 * q^41 - 4 * q^42 - 28 * q^43 - 2 * q^44 + 4 * q^45 - 14 * q^46 - 14 * q^47 + 12 * q^48 - 20 * q^49 + 4 * q^50 + 6 * q^51 + 12 * q^52 + 20 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 12 * q^57 + 10 * q^58 + 6 * q^59 + 4 * q^60 + 8 * q^61 - 32 * q^62 - 2 * q^63 - 28 * q^64 + 8 * q^65 + 2 * q^66 + 12 * q^67 + 14 * q^68 - 28 * q^69 + 20 * q^70 - 28 * q^71 + 6 * q^72 - 12 * q^73 - 26 * q^74 + 2 * q^75 + 60 * q^76 - 2 * q^77 + 8 * q^78 - 4 * q^79 + 12 * q^80 - 2 * q^81 - 26 * q^84 + 24 * q^85 - 2 * q^86 + 2 * q^87 + 6 * q^88 + 8 * q^90 + 8 * q^91 - 28 * q^92 + 22 * q^94 + 12 * q^95 - 6 * q^96 - 12 * q^97 + 14 * q^98 + 4 * q^99

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