LMFDB - Embedded newform 231.2.i.e.67.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
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			67.4
Root			$-0.758290 - 1.31340i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.e.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.758290 + 1.31340i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.150007 + 0.259820i) q^{4} +(1.16659 + 2.02059i) q^{5} -1.51658 q^{6} +(-2.28580 + 1.33233i) q^{7} +2.57816 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.758290 + 1.31340i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.150007 + 0.259820i) q^{4} +(1.16659 + 2.02059i) q^{5} -1.51658 q^{6} +(-2.28580 + 1.33233i) q^{7} +2.57816 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.76922 + 3.06438i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.150007 - 0.259820i) q^{12} -1.53844 q^{13} +(-3.48318 - 1.99187i) q^{14} -2.33317 q^{15} +(2.25501 + 3.90579i) q^{16} +(0.0583043 - 0.100986i) q^{17} +(0.758290 - 1.31340i) q^{18} +(1.80566 + 3.12750i) q^{19} -0.699986 q^{20} +(-0.0109324 - 2.64573i) q^{21} +1.51658 q^{22} +(-3.55502 - 6.15748i) q^{23} +(-1.28908 + 2.23276i) q^{24} +(-0.221850 + 0.384256i) q^{25} +(-1.16659 - 2.02059i) q^{26} +1.00000 q^{27} +(-0.00327987 - 0.793757i) q^{28} +5.05502 q^{29} +(-1.76922 - 3.06438i) q^{30} +(2.18845 - 3.79051i) q^{31} +(-0.841739 + 1.45793i) q^{32} +(0.500000 + 0.866025i) q^{33} +0.176846 q^{34} +(-5.35868 - 3.06438i) q^{35} +0.300014 q^{36} +(0.150007 + 0.259820i) q^{37} +(-2.73843 + 4.74310i) q^{38} +(0.769222 - 1.33233i) q^{39} +(3.00765 + 5.20941i) q^{40} +8.20479 q^{41} +(3.46660 - 2.02059i) q^{42} -4.18293 q^{43} +(0.150007 + 0.259820i) q^{44} +(1.16659 - 2.02059i) q^{45} +(5.39148 - 9.33831i) q^{46} +(-1.15001 - 1.99187i) q^{47} -4.51002 q^{48} +(3.44978 - 6.09089i) q^{49} -0.672908 q^{50} +(0.0583043 + 0.100986i) q^{51} +(0.230778 - 0.399719i) q^{52} +(5.94346 - 10.2944i) q^{53} +(0.758290 + 1.31340i) q^{54} +2.33317 q^{55} +(-5.89317 + 3.43497i) q^{56} -3.61132 q^{57} +(3.83317 + 6.63925i) q^{58} +(-2.47814 + 4.29226i) q^{59} +(0.349993 - 0.606205i) q^{60} +(2.28580 + 3.95913i) q^{61} +6.63792 q^{62} +(2.29673 + 1.31340i) q^{63} +6.46691 q^{64} +(-1.79473 - 3.10856i) q^{65} +(-0.758290 + 1.31340i) q^{66} +(-6.14472 + 10.6430i) q^{67} +(0.0174921 + 0.0302972i) q^{68} +7.11005 q^{69} +(-0.0386836 - 9.36176i) q^{70} +4.25628 q^{71} +(-1.28908 - 2.23276i) q^{72} +(-5.21900 + 9.03958i) q^{73} +(-0.227498 + 0.394038i) q^{74} +(-0.221850 - 0.384256i) q^{75} -1.08345 q^{76} +(0.0109324 + 2.64573i) q^{77} +2.33317 q^{78} +(-7.15742 - 12.3970i) q^{79} +(-5.26133 + 9.11289i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.22161 + 10.7761i) q^{82} -11.1869 q^{83} +(0.689053 + 0.394038i) q^{84} +0.272068 q^{85} +(-3.17187 - 5.49384i) q^{86} +(-2.52751 + 4.37778i) q^{87} +(1.28908 - 2.23276i) q^{88} +(-6.96636 - 12.0661i) q^{89} +3.53844 q^{90} +(3.51658 - 2.04972i) q^{91} +2.13312 q^{92} +(2.18845 + 3.79051i) q^{93} +(1.74408 - 3.02083i) q^{94} +(-4.21292 + 7.29700i) q^{95} +(-0.841739 - 1.45793i) q^{96} -16.4101 q^{97} +(10.6157 - 0.0877314i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9} - 10 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 8 q^{15} - 12 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{24} - 4 q^{25} + 4 q^{26} + 8 q^{27} - 22 q^{28} + 16 q^{29} - 10 q^{30} + 12 q^{31} - 26 q^{32} + 4 q^{33} - 32 q^{34} - 2 q^{35} + 8 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} + 4 q^{41} + 20 q^{42} + 36 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} - 12 q^{47} + 24 q^{48} - 4 q^{49} + 4 q^{50} - 2 q^{51} + 6 q^{52} + 12 q^{53} - 2 q^{54} - 8 q^{55} + 48 q^{56} + 4 q^{58} - 12 q^{59} - 2 q^{61} - 52 q^{62} + 2 q^{63} + 112 q^{64} + 4 q^{65} + 2 q^{66} - 28 q^{67} + 48 q^{68} + 8 q^{69} - 32 q^{70} + 24 q^{71} - 12 q^{72} - 6 q^{73} + 16 q^{74} - 4 q^{75} - 36 q^{76} + 4 q^{77} - 8 q^{78} - 2 q^{79} - 16 q^{80} - 4 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{85} - 36 q^{86} - 8 q^{87} + 12 q^{88} - 8 q^{89} + 20 q^{90} + 12 q^{91} - 32 q^{92} + 12 q^{93} - 20 q^{94} - 34 q^{95} - 26 q^{96} - 88 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9 - 10 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^24 - 4 * q^25 + 4 * q^26 + 8 * q^27 - 22 * q^28 + 16 * q^29 - 10 * q^30 + 12 * q^31 - 26 * q^32 + 4 * q^33 - 32 * q^34 - 2 * q^35 + 8 * q^36 + 4 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 + 4 * q^41 + 20 * q^42 + 36 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 - 12 * q^47 + 24 * q^48 - 4 * q^49 + 4 * q^50 - 2 * q^51 + 6 * q^52 + 12 * q^53 - 2 * q^54 - 8 * q^55 + 48 * q^56 + 4 * q^58 - 12 * q^59 - 2 * q^61 - 52 * q^62 + 2 * q^63 + 112 * q^64 + 4 * q^65 + 2 * q^66 - 28 * q^67 + 48 * q^68 + 8 * q^69 - 32 * q^70 + 24 * q^71 - 12 * q^72 - 6 * q^73 + 16 * q^74 - 4 * q^75 - 36 * q^76 + 4 * q^77 - 8 * q^78 - 2 * q^79 - 16 * q^80 - 4 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^85 - 36 * q^86 - 8 * q^87 + 12 * q^88 - 8 * q^89 + 20 * q^90 + 12 * q^91 - 32 * q^92 + 12 * q^93 - 20 * q^94 - 34 * q^95 - 26 * q^96 - 88 * q^97 + 16 * q^98 - 8 * 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 $

$2$	0.758290	+	1.31340i	0.536192	+	0.928712i	0.999105	+	0.0423078i	$0.0134710\pi$
$2$	0.758290	+	1.31340i	0.536192	+	0.928712i	−0.462913	+	0.886404i	$0.653196\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.150007	+	0.259820i	−0.0750036	+	0.129910i
$5$	1.16659	+	2.02059i	0.521714	+	0.903634i	0.999681	+	0.0252568i	$0.00804036\pi$
$5$	1.16659	+	2.02059i	0.521714	+	0.903634i	−0.477967	+	0.878378i	$0.658626\pi$
$6$	−1.51658			−0.619141
$7$	−2.28580	+	1.33233i	−0.863952	+	0.503574i
$7$	−2.28580	+	1.33233i	−0.863952	+	0.503574i
$8$	2.57816			0.911519
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.76922	+	3.06438i	−0.559477	+	0.969043i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−0.150007	−	0.259820i	−0.0433033	−	0.0750036i
$13$	−1.53844			−0.426688			−0.213344	−	0.976977i	$-0.568435\pi$
$13$	−1.53844			−0.426688			−0.213344	+	0.976977i	$0.568435\pi$
$14$	−3.48318	−	1.99187i	−0.930919	−	0.532350i
$15$	−2.33317			−0.602423
$16$	2.25501	+	3.90579i	0.563753	+	0.976448i
$17$	0.0583043	−	0.100986i	0.0141409	−	0.0244927i	−0.858868	−	0.512196i	$-0.828832\pi$
$17$	0.0583043	−	0.100986i	0.0141409	−	0.0244927i	0.873009	+	0.487704i	$0.162165\pi$
$18$	0.758290	−	1.31340i	0.178731	−	0.309571i
$19$	1.80566	+	3.12750i	0.414247	+	0.717497i	0.995349	−	0.0963336i	$-0.0307116\pi$
$19$	1.80566	+	3.12750i	0.414247	+	0.717497i	−0.581102	+	0.813831i	$0.697378\pi$
$20$	−0.699986			−0.156522
$21$	−0.0109324	−	2.64573i	−0.00238564	−	0.577345i
$22$	1.51658			0.323336
$23$	−3.55502	−	6.15748i	−0.741274	−	1.28392i	−0.951916	−	0.306361i	$-0.900889\pi$
$23$	−3.55502	−	6.15748i	−0.741274	−	1.28392i	0.210642	−	0.977563i	$-0.432445\pi$
$24$	−1.28908	+	2.23276i	−0.263133	+	0.455759i
$25$	−0.221850	+	0.384256i	−0.0443701	+	0.0768512i
$26$	−1.16659	−	2.02059i	−0.228787	−	0.396270i
$27$	1.00000			0.192450
$28$	−0.00327987	−	0.793757i	−0.000619837	−	0.150006i
$29$	5.05502			0.938694			0.469347	−	0.883014i	$-0.344489\pi$
$29$	5.05502			0.938694			0.469347	+	0.883014i	$0.344489\pi$
$30$	−1.76922	−	3.06438i	−0.323014	−	0.559477i
$31$	2.18845	−	3.79051i	0.393058	−	0.680796i	−0.599794	−	0.800155i	$-0.704751\pi$
$31$	2.18845	−	3.79051i	0.393058	−	0.680796i	0.992851	+	0.119359i	$0.0380840\pi$
$32$	−0.841739	+	1.45793i	−0.148800	+	0.257729i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	0.176846			0.0303289
$35$	−5.35868	−	3.06438i	−0.905782	−	0.517975i
$36$	0.300014			0.0500024
$37$	0.150007	+	0.259820i	0.0246610	+	0.0427142i	0.878093	−	0.478491i	$-0.158816\pi$
$37$	0.150007	+	0.259820i	0.0246610	+	0.0427142i	−0.853432	+	0.521205i	$0.825483\pi$
$38$	−2.73843	+	4.74310i	−0.444232	+	0.769432i
$39$	0.769222	−	1.33233i	0.123174	−	0.213344i
$40$	3.00765	+	5.20941i	0.475552	+	0.823680i
$41$	8.20479			1.28137			0.640687	−	0.767802i	$-0.278650\pi$
$41$	8.20479			1.28137			0.640687	+	0.767802i	$0.278650\pi$
$42$	3.46660	−	2.02059i	0.534908	−	0.311783i
$43$	−4.18293			−0.637891			−0.318945	−	0.947773i	$-0.603329\pi$
$43$	−4.18293			−0.637891			−0.318945	+	0.947773i	$0.603329\pi$
$44$	0.150007	+	0.259820i	0.0226144	+	0.0391693i
$45$	1.16659	−	2.02059i	0.173905	−	0.301211i
$46$	5.39148	−	9.33831i	0.794930	−	1.37686i
$47$	−1.15001	−	1.99187i	−0.167746	−	0.290544i	0.769881	−	0.638187i	$-0.220315\pi$
$47$	−1.15001	−	1.99187i	−0.167746	−	0.290544i	−0.937627	+	0.347643i	$0.886982\pi$
$48$	−4.51002			−0.650965
$49$	3.44978	−	6.09089i	0.492826	−	0.870128i
$50$	−0.672908			−0.0951635
$51$	0.0583043	+	0.100986i	0.00816423	+	0.0141409i
$52$	0.230778	−	0.399719i	0.0320031	−	0.0554310i
$53$	5.94346	−	10.2944i	0.816397	−	1.41404i	−0.0919230	−	0.995766i	$-0.529301\pi$
$53$	5.94346	−	10.2944i	0.816397	−	1.41404i	0.908320	−	0.418275i	$-0.137365\pi$
$54$	0.758290	+	1.31340i	0.103190	+	0.178731i
$55$	2.33317			0.314605
$56$	−5.89317	+	3.43497i	−0.787508	+	0.459017i
$57$	−3.61132			−0.478331
$58$	3.83317	+	6.63925i	0.503320	+	0.871777i
$59$	−2.47814	+	4.29226i	−0.322626	+	0.558804i	−0.981029	−	0.193861i	$-0.937899\pi$
$59$	−2.47814	+	4.29226i	−0.322626	+	0.558804i	0.658403	+	0.752665i	$0.271232\pi$
$60$	0.349993	−	0.606205i	0.0451839	−	0.0782608i
$61$	2.28580	+	3.95913i	0.292667	+	0.506914i	0.974439	−	0.224650i	$-0.0721239\pi$
$61$	2.28580	+	3.95913i	0.292667	+	0.506914i	−0.681773	+	0.731564i	$0.738791\pi$
$62$	6.63792			0.843017
$63$	2.29673	+	1.31340i	0.289361	+	0.165472i
$64$	6.46691			0.808364
$65$	−1.79473	−	3.10856i	−0.222609	−	0.385570i
$66$	−0.758290	+	1.31340i	−0.0933390	+	0.161668i
$67$	−6.14472	+	10.6430i	−0.750697	+	1.30025i	0.196788	+	0.980446i	$0.436949\pi$
$67$	−6.14472	+	10.6430i	−0.750697	+	1.30025i	−0.947485	+	0.319800i	$0.896384\pi$
$68$	0.0174921	+	0.0302972i	0.00212123	+	0.00367408i
$69$	7.11005			0.855949
$70$	−0.0386836	−	9.36176i	−0.00462357	−	1.11894i
$71$	4.25628			0.505128			0.252564	−	0.967580i	$-0.418726\pi$
$71$	4.25628			0.505128			0.252564	+	0.967580i	$0.418726\pi$
$72$	−1.28908	−	2.23276i	−0.151920	−	0.263133i
$73$	−5.21900	+	9.03958i	−0.610838	+	1.05800i	0.380261	+	0.924879i	$0.375834\pi$
$73$	−5.21900	+	9.03958i	−0.610838	+	1.05800i	−0.991099	+	0.133124i	$0.957499\pi$
$74$	−0.227498	+	0.394038i	−0.0264461	+	0.0458060i
$75$	−0.221850	−	0.384256i	−0.0256171	−	0.0443701i
$76$	−1.08345			−0.124280
$77$	0.0109324	+	2.64573i	0.00124586	+	0.301509i
$78$	2.33317			0.264180
$79$	−7.15742	−	12.3970i	−0.805273	−	1.39477i	−0.916107	−	0.400934i	$-0.868686\pi$
$79$	−7.15742	−	12.3970i	−0.805273	−	1.39477i	0.110834	−	0.993839i	$-0.464648\pi$
$80$	−5.26133	+	9.11289i	−0.588235	+	1.01885i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.22161	+	10.7761i	0.687062	+	1.19003i
$83$	−11.1869			−1.22793			−0.613963	−	0.789335i	$-0.710426\pi$
$83$	−11.1869			−1.22793			−0.613963	+	0.789335i	$0.710426\pi$
$84$	0.689053	+	0.394038i	0.0751819	+	0.0429931i
$85$	0.272068			0.0295099
$86$	−3.17187	−	5.49384i	−0.342032	−	0.592416i
$87$	−2.52751	+	4.37778i	−0.270978	+	0.469347i
$88$	1.28908	−	2.23276i	0.137417	−	0.238013i
$89$	−6.96636	−	12.0661i	−0.738433	−	1.27900i	−0.953201	−	0.302338i	$-0.902233\pi$
$89$	−6.96636	−	12.0661i	−0.738433	−	1.27900i	0.214768	−	0.976665i	$-0.431101\pi$
$90$	3.53844			0.372985
$91$	3.51658	−	2.04972i	0.368638	−	0.214869i
$92$	2.13312			0.222393
$93$	2.18845	+	3.79051i	0.226932	+	0.393058i
$94$	1.74408	−	3.02083i	0.179888	−	0.311575i
$95$	−4.21292	+	7.29700i	−0.432237	+	0.748656i
$96$	−0.841739	−	1.45793i	−0.0859096	−	0.148800i
$97$	−16.4101			−1.66619			−0.833095	−	0.553130i	$-0.813433\pi$
$97$	−16.4101			−1.66619			−0.833095	+	0.553130i	$0.813433\pi$
$98$	10.6157	−	0.0877314i	1.07235	−	0.00886221i
$99$	−1.00000			−0.100504
$100$	−0.0665583	−	0.115282i	−0.00665583	−	0.0115282i
$101$	−4.82753	+	8.36152i	−0.480357	+	0.832002i	−0.999746	−	0.0225353i	$-0.992826\pi$
$101$	−4.82753	+	8.36152i	−0.480357	+	0.832002i	0.519389	+	0.854538i	$0.326160\pi$
$102$	−0.0884231	+	0.153153i	−0.00875519	+	0.0151644i
$103$	−4.41006	−	7.63845i	−0.434536	−	0.752639i	0.562721	−	0.826647i	$-0.309754\pi$
$103$	−4.41006	−	7.63845i	−0.434536	−	0.752639i	−0.997258	+	0.0740075i	$0.976421\pi$
$104$	−3.96636			−0.388934
$105$	5.33317	−	3.10856i	0.520464	−	0.303365i
$106$	18.0275			1.75098
$107$	−5.24207	−	9.07954i	−0.506770	−	0.877752i	−0.999969	−	0.00783538i	$-0.997506\pi$
$107$	−5.24207	−	9.07954i	−0.506770	−	0.877752i	0.493199	−	0.869917i	$-0.335827\pi$
$108$	−0.150007	+	0.259820i	−0.0144344	+	0.0250012i
$109$	−5.26394	+	9.11741i	−0.504194	+	0.873289i	0.495794	+	0.868440i	$0.334877\pi$
$109$	−5.26394	+	9.11741i	−0.504194	+	0.873289i	−0.999988	+	0.00484932i	$0.998456\pi$
$110$	1.76922	+	3.06438i	0.168689	+	0.292177i
$111$	−0.300014			−0.0284761
$112$	−10.3583	−	5.92345i	−0.978769	−	0.559713i
$113$	11.4327			1.07549			0.537747	−	0.843106i	$-0.319276\pi$
$113$	11.4327			1.07549			0.537747	+	0.843106i	$0.319276\pi$
$114$	−2.73843	−	4.74310i	−0.256477	−	0.444232i
$115$	8.29449	−	14.3665i	0.773465	−	1.33968i
$116$	−0.758290	+	1.31340i	−0.0704055	+	0.121946i
$117$	0.769222	+	1.33233i	0.0711146	+	0.123174i
$118$	−7.51658			−0.691957
$119$	0.00127481	+	0.308514i	0.000116861	+	0.0282815i
$120$	−6.01531			−0.549120
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−3.46660	+	6.00433i	−0.313851	+	0.543606i
$123$	−4.10240	+	7.10556i	−0.369901	+	0.640687i
$124$	0.656567	+	1.13721i	0.0589614	+	0.102124i
$125$	10.6306			0.950833
$126$	0.0165798	+	4.01246i	0.00147705	+	0.357458i
$127$	0.234898			0.0208438			0.0104219	−	0.999946i	$-0.496683\pi$
$127$	0.234898			0.0208438			0.0104219	+	0.999946i	$0.496683\pi$
$128$	6.58727	+	11.4095i	0.582238	+	1.00847i
$129$	2.09146	−	3.62252i	0.184143	−	0.318945i
$130$	2.72185	−	4.71438i	0.238722	−	0.413479i
$131$	2.87927	+	4.98704i	0.251563	+	0.435720i	0.963956	−	0.266060i	$-0.0857221\pi$
$131$	2.87927	+	4.98704i	0.251563	+	0.435720i	−0.712393	+	0.701780i	$0.752389\pi$
$132$	−0.300014			−0.0261129
$133$	−8.29425	−	4.74310i	−0.719203	−	0.411279i
$134$	−18.6379			−1.61007
$135$	1.16659	+	2.02059i	0.100404	+	0.173905i
$136$	0.150318	−	0.260358i	0.0128897	−	0.0223255i
$137$	−8.04325	+	13.9313i	−0.687181	+	1.19023i	0.285565	+	0.958359i	$0.407819\pi$
$137$	−8.04325	+	13.9313i	−0.687181	+	1.19023i	−0.972746	+	0.231874i	$0.925514\pi$
$138$	5.39148	+	9.33831i	0.458953	+	0.794930i
$139$	−14.2930			−1.21231			−0.606157	−	0.795345i	$-0.707290\pi$
$139$	−14.2930			−1.21231			−0.606157	+	0.795345i	$0.707290\pi$
$140$	1.60003	−	0.932613i	0.135227	−	0.0788202i
$141$	2.30001			0.193696
$142$	3.22750	+	5.59019i	0.270846	+	0.469118i
$143$	−0.769222	+	1.33233i	−0.0643256	+	0.111415i
$144$	2.25501	−	3.90579i	0.187918	−	0.325483i
$145$	5.89713	+	10.2141i	0.489730	+	0.848237i
$146$	−15.8301			−1.31011
$147$	3.54998	+	6.03305i	0.292797	+	0.497597i
$148$	−0.0900086			−0.00739866
$149$	0.336454	+	0.582755i	0.0275634	+	0.0477412i	0.879478	−	0.475939i	$-0.157892\pi$
$149$	0.336454	+	0.582755i	0.0275634	+	0.0477412i	−0.851915	+	0.523681i	$0.824559\pi$
$150$	0.336454	−	0.582755i	0.0274713	−	0.0475818i
$151$	−11.8862	+	20.5875i	−0.967285	+	1.67539i	−0.263937	+	0.964540i	$0.585021\pi$
$151$	−11.8862	+	20.5875i	−0.967285	+	1.67539i	−0.703347	+	0.710846i	$0.748312\pi$
$152$	4.65529	+	8.06320i	0.377594	+	0.654012i
$153$	−0.116609			−0.00942724
$154$	−3.46660	+	2.02059i	−0.279347	+	0.162824i
$155$	10.2121			0.820254
$156$	0.230778	+	0.399719i	0.0184770	+	0.0320031i
$157$	7.62790	−	13.2119i	0.608773	−	1.05443i	−0.382670	−	0.923885i	$-0.624995\pi$
$157$	7.62790	−	13.2119i	0.608773	−	1.05443i	0.991443	−	0.130541i	$-0.0416713\pi$
$158$	10.8548	−	18.8011i	0.863561	−	1.49573i
$159$	5.94346	+	10.2944i	0.471347	+	0.816397i
$160$	−3.92785			−0.310523
$161$	16.3299	+	9.33831i	1.28698	+	0.735962i
$162$	−1.51658			−0.119154
$163$	−0.210316	−	0.364279i	−0.0164733	−	0.0285325i	0.857671	−	0.514198i	$-0.171911\pi$
$163$	−0.210316	−	0.364279i	−0.0164733	−	0.0285325i	−0.874145	+	0.485666i	$0.838577\pi$
$164$	−1.23078	+	2.13177i	−0.0961076	+	0.166463i
$165$	−1.16659	+	2.02059i	−0.0908187	+	0.157303i
$166$	−8.48294	−	14.6929i	−0.658404	−	1.14039i
$167$	16.4331			1.27163			0.635817	−	0.771840i	$-0.280663\pi$
$167$	16.4331			1.27163			0.635817	+	0.771840i	$0.280663\pi$
$168$	−0.0281855	−	6.82112i	−0.00217455	−	0.526261i
$169$	−10.6332			−0.817938
$170$	0.206306	+	0.357333i	0.0158230	+	0.0274062i
$171$	1.80566	−	3.12750i	0.138082	−	0.239166i
$172$	0.627469	−	1.08681i	0.0478441	−	0.0828684i
$173$	−1.93076	−	3.34418i	−0.146793	−	0.254253i	0.783247	−	0.621710i	$-0.213562\pi$
$173$	−1.93076	−	3.34418i	−0.146793	−	0.254253i	−0.930041	+	0.367457i	$0.880229\pi$
$174$	−7.66635			−0.581184
$175$	−0.00485070	−	1.17391i	−0.000366679	−	0.0887394i
$176$	4.51002			0.339956
$177$	−2.47814	−	4.29226i	−0.186268	−	0.322626i
$178$	10.5650	−	18.2992i	0.791884	−	1.37158i
$179$	6.35480	−	11.0068i	0.474980	−	0.822690i	−0.524609	−	0.851343i	$-0.675789\pi$
$179$	6.35480	−	11.0068i	0.474980	−	0.822690i	0.999589	+	0.0286535i	$0.00912195\pi$
$180$	0.349993	+	0.606205i	0.0260869	+	0.0451839i
$181$	16.5196			1.22789			0.613947	−	0.789347i	$-0.289581\pi$
$181$	16.5196			1.22789			0.613947	+	0.789347i	$0.289581\pi$
$182$	5.35868	+	3.06438i	0.397212	+	0.227147i
$183$	−4.57160			−0.337943
$184$	−9.16544	−	15.8750i	−0.675685	−	1.17032i
$185$	−0.349993	+	0.606205i	−0.0257320	+	0.0445691i
$186$	−3.31896	+	5.74861i	−0.243358	+	0.421509i
$187$	−0.0583043	−	0.100986i	−0.00426363	−	0.00738482i
$188$	0.690037			0.0503261
$189$	−2.28580	+	1.33233i	−0.166268	+	0.0969129i
$190$	−12.7785			−0.927048
$191$	8.20479	+	14.2111i	0.593678	+	1.02828i	0.993732	+	0.111789i	$0.0356580\pi$
$191$	8.20479	+	14.2111i	0.593678	+	1.02828i	−0.400054	+	0.916492i	$0.631009\pi$
$192$	−3.23346	+	5.60051i	−0.233355	+	0.404182i
$193$	−10.3266	+	17.8862i	−0.743326	+	1.28748i	0.207647	+	0.978204i	$0.433420\pi$
$193$	−10.3266	+	17.8862i	−0.743326	+	1.28748i	−0.950973	+	0.309274i	$0.899914\pi$
$194$	−12.4436	−	21.5529i	−0.893397	−	1.54741i
$195$	3.58946			0.257046
$196$	1.06504	+	1.81000i	0.0760746	+	0.129286i
$197$	26.3132			1.87474			0.937368	−	0.348342i	$-0.113255\pi$
$197$	26.3132			1.87474			0.937368	+	0.348342i	$0.113255\pi$
$198$	−0.758290	−	1.31340i	−0.0538893	−	0.0933390i
$199$	5.50528	−	9.53543i	0.390259	−	0.675949i	−0.602224	−	0.798327i	$-0.705719\pi$
$199$	5.50528	−	9.53543i	0.390259	−	0.675949i	0.992484	+	0.122378i	$0.0390520\pi$
$200$	−0.571967	+	0.990675i	−0.0404442	+	0.0700513i
$201$	−6.14472	−	10.6430i	−0.433415	−	0.750697i
$202$	−14.6427			−1.03025
$203$	−11.5548	+	6.73497i	−0.810987	+	0.472702i
$204$	−0.0349842			−0.00244939
$205$	9.57160	+	16.5785i	0.668510	+	1.15789i
$206$	6.68821	−	11.5843i	0.465990	−	0.807118i
$207$	−3.55502	+	6.15748i	−0.247091	+	0.427975i
$208$	−3.46921	−	6.00884i	−0.240546	−	0.416638i
$209$	3.61132			0.249800
$210$	8.12687	+	4.64738i	0.560807	+	0.320700i
$211$	22.2476			1.53159			0.765793	−	0.643087i	$-0.222347\pi$
$211$	22.2476			1.53159			0.765793	+	0.643087i	$0.222347\pi$
$212$	1.78312	+	3.08846i	0.122465	+	0.212116i
$213$	−2.12814	+	3.68605i	−0.145818	+	0.252564i
$214$	7.95002	−	13.7698i	0.543452	−	0.941287i
$215$	−4.87975	−	8.45197i	−0.332796	−	0.576420i
$216$	2.57816			0.175422
$217$	0.0478499	+	11.5801i	0.00324827	+	0.786108i
$218$	−15.9664			−1.08138
$219$	−5.21900	−	9.03958i	−0.352668	−	0.610838i
$220$	−0.349993	+	0.606205i	−0.0235965	+	0.0408704i
$221$	−0.0896979	+	0.155361i	−0.00603373	+	0.0104507i
$222$	−0.227498	−	0.394038i	−0.0152687	−	0.0264461i
$223$	−16.8020			−1.12515			−0.562573	−	0.826748i	$-0.690188\pi$
$223$	−16.8020			−1.12515			−0.562573	+	0.826748i	$0.690188\pi$
$224$	−0.0184044	−	4.45402i	−0.00122970	−	0.297597i
$225$	0.443701			0.0295801
$226$	8.66927	+	15.0156i	0.576671	+	0.998823i
$227$	−2.71008	+	4.69399i	−0.179874	+	0.311551i	−0.941837	−	0.336069i	$-0.890902\pi$
$227$	−2.71008	+	4.69399i	−0.179874	+	0.311551i	0.761963	+	0.647620i	$0.224236\pi$
$228$	0.541724	−	0.938294i	0.0358766	−	0.0621401i
$229$	−14.1161	−	24.4499i	−0.932820	−	1.61569i	−0.778476	−	0.627675i	$-0.784007\pi$
$229$	−14.1161	−	24.4499i	−0.932820	−	1.61569i	−0.154345	−	0.988017i	$-0.549327\pi$
$230$	25.1585			1.65890
$231$	−2.29673	−	1.31340i	−0.151114	−	0.0864152i
$232$	13.0327			0.855637
$233$	−2.80566	−	4.85955i	−0.183805	−	0.318360i	0.759368	−	0.650661i	$-0.225508\pi$
$233$	−2.80566	−	4.85955i	−0.183805	−	0.318360i	−0.943173	+	0.332302i	$0.892175\pi$
$234$	−1.16659	+	2.02059i	−0.0762622	+	0.132090i
$235$	2.68317	−	4.64738i	0.175031	−	0.303162i
$236$	−0.743476	−	1.28774i	−0.0483962	−	0.0838246i
$237$	14.3148			0.929849
$238$	−0.404235	+	0.235618i	−0.0262027	+	0.0152728i
$239$	12.0153			0.777205			0.388603	−	0.921405i	$-0.372958\pi$
$239$	12.0153			0.777205			0.388603	+	0.921405i	$0.372958\pi$
$240$	−5.26133	−	9.11289i	−0.339617	−	0.588235i
$241$	10.3663	−	17.9550i	0.667754	−	1.15658i	−0.310776	−	0.950483i	$-0.600589\pi$
$241$	10.3663	−	17.9550i	0.667754	−	1.15658i	0.978531	−	0.206101i	$-0.0660776\pi$
$242$	0.758290	−	1.31340i	0.0487447	−	0.0844283i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.37155			−0.0878043
$245$	16.3317	−	0.134970i	1.04339	−	0.00862291i
$246$	−12.4432			−0.793351
$247$	−2.77791	−	4.81148i	−0.176754	−	0.306147i
$248$	5.64219	−	9.77256i	0.358279	−	0.620558i
$249$	5.59347	−	9.68817i	0.354472	−	0.613963i
$250$	8.06111	+	13.9622i	0.509829	+	0.883050i
$251$	−27.2885			−1.72243			−0.861217	−	0.508237i	$-0.830297\pi$
$251$	−27.2885			−1.72243			−0.861217	+	0.508237i	$0.830297\pi$
$252$	−0.685773	+	0.399719i	−0.0431997	+	0.0251799i
$253$	−7.11005			−0.447005
$254$	0.178121	+	0.308514i	0.0111763	+	0.0193579i
$255$	−0.136034	+	0.235618i	−0.00851878	+	0.0147550i
$256$	−3.52321	+	6.10238i	−0.220201	+	0.381399i
$257$	−4.45099	−	7.70933i	−0.277645	−	0.480895i	0.693154	−	0.720789i	$-0.256221\pi$
$257$	−4.45099	−	7.70933i	−0.277645	−	0.480895i	−0.970799	+	0.239894i	$0.922887\pi$
$258$	6.34374			0.394944
$259$	−0.689053	−	0.394038i	−0.0428157	−	0.0244843i
$260$	1.07689			0.0667858
$261$	−2.52751	−	4.37778i	−0.156449	−	0.270978i
$262$	−4.36664	+	7.56325i	−0.269772	+	0.467259i
$263$	1.12790	−	1.95359i	0.0695495	−	0.120463i	−0.829154	−	0.559021i	$-0.811177\pi$
$263$	1.12790	−	1.95359i	0.0695495	−	0.120463i	0.898703	+	0.438558i	$0.144510\pi$
$264$	1.28908	+	2.23276i	0.0793375	+	0.137417i
$265$	27.7343			1.70370
$266$	−0.0598751	−	14.4903i	−0.00367118	−	0.888456i
$267$	13.9327			0.852669
$268$	−1.84350	−	3.19304i	−0.112610	−	0.195046i
$269$	−4.18444	+	7.24767i	−0.255130	+	0.441898i	−0.964931	−	0.262504i	$-0.915452\pi$
$269$	−4.18444	+	7.24767i	−0.255130	+	0.441898i	0.709801	+	0.704402i	$0.248785\pi$
$270$	−1.76922	+	3.06438i	−0.107671	+	0.186492i
$271$	−4.44734	−	7.70302i	−0.270157	−	0.467925i	0.698745	−	0.715371i	$-0.253742\pi$
$271$	−4.44734	−	7.70302i	−0.270157	−	0.467925i	−0.968902	+	0.247445i	$0.920409\pi$
$272$	0.525907			0.0318878
$273$	0.0168189	+	4.07031i	0.00101792	+	0.246346i
$274$	−24.3965			−1.47384
$275$	0.221850	+	0.384256i	0.0133781	+	0.0231715i
$276$	−1.06656	+	1.84733i	−0.0641993	+	0.111196i
$277$	2.69999	−	4.67651i	0.162226	−	0.280984i	−0.773440	−	0.633869i	$-0.781466\pi$
$277$	2.69999	−	4.67651i	0.162226	−	0.280984i	0.935667	+	0.352885i	$0.114799\pi$
$278$	−10.8382	−	18.7723i	−0.650033	−	1.12589i
$279$	−4.37690			−0.262038
$280$	−13.8156	−	7.90048i	−0.825638	−	0.472144i
$281$	−19.7416			−1.17768			−0.588841	−	0.808249i	$-0.700416\pi$
$281$	−19.7416			−1.17768			−0.588841	+	0.808249i	$0.700416\pi$
$282$	1.74408	+	3.02083i	0.103858	+	0.179888i
$283$	5.05259	−	8.75133i	0.300345	−	0.520213i	−0.675869	−	0.737022i	$-0.736232\pi$
$283$	5.05259	−	8.75133i	0.300345	−	0.520213i	0.976214	+	0.216809i	$0.0695649\pi$
$284$	−0.638473	+	1.10587i	−0.0378864	+	0.0656212i
$285$	−4.21292	−	7.29700i	−0.249552	−	0.432237i
$286$	−2.33317			−0.137963
$287$	−18.7545	+	10.9315i	−1.10705	+	0.645267i
$288$	1.68348			0.0991999
$289$	8.49320	+	14.7107i	0.499600	+	0.865333i
$290$	−8.94346	+	15.4905i	−0.525178	+	0.909635i
$291$	8.20503	−	14.2115i	0.480987	−	0.833095i
$292$	−1.56578	−	2.71200i	−0.0916301	−	0.158708i
$293$	−16.1108			−0.941201			−0.470601	−	0.882346i	$-0.655963\pi$
$293$	−16.1108			−0.941201			−0.470601	+	0.882346i	$0.655963\pi$
$294$	−5.23187	+	9.23733i	−0.305129	+	0.538732i
$295$	−11.5638			−0.673273
$296$	0.386743	+	0.669859i	0.0224790	+	0.0389347i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−0.510259	+	0.883795i	−0.0295585	+	0.0511969i
$299$	5.46921	+	9.47295i	0.316292	+	0.547835i
$300$	0.133117			0.00768549
$301$	9.56135	−	5.57305i	0.551107	−	0.321225i
$302$	−36.0527			−2.07460
$303$	−4.82753	−	8.36152i	−0.277334	−	0.480357i
$304$	−8.14357	+	14.1051i	−0.467066	+	0.808982i
$305$	−5.33317	+	9.23733i	−0.305377	+	0.528928i
$306$	−0.0884231	−	0.153153i	−0.00505481	−	0.00875519i
$307$	27.8168			1.58759			0.793795	−	0.608185i	$-0.208102\pi$
$307$	27.8168			1.58759			0.793795	+	0.608185i	$0.208102\pi$
$308$	−0.689053	−	0.394038i	−0.0392625	−	0.0224524i
$309$	8.82013			0.501759
$310$	7.74372	+	13.4125i	0.439813	+	0.761779i
$311$	−4.52139	+	7.83127i	−0.256384	+	0.444071i	−0.965271	−	0.261252i	$-0.915865\pi$
$311$	−4.52139	+	7.83127i	−0.256384	+	0.444071i	0.708886	+	0.705323i	$0.249198\pi$
$312$	1.98318	−	3.43497i	0.112276	−	0.194467i
$313$	8.08842	+	14.0096i	0.457185	+	0.791867i	0.998811	−	0.0487523i	$-0.0155245\pi$
$313$	8.08842	+	14.0096i	0.457185	+	0.791867i	−0.541626	+	0.840619i	$0.682191\pi$
$314$	23.1366			1.30568
$315$	0.0255071	+	6.17295i	0.00143716	+	0.347806i
$316$	4.29466			0.241593
$317$	2.61685	+	4.53251i	0.146977	+	0.254571i	0.930109	−	0.367284i	$-0.119712\pi$
$317$	2.61685	+	4.53251i	0.146977	+	0.254571i	−0.783132	+	0.621856i	$0.786379\pi$
$318$	−9.01373	+	15.6122i	−0.505465	+	0.875491i
$319$	2.52751	−	4.37778i	0.141514	−	0.245109i
$320$	7.54422	+	13.0670i	0.421734	+	0.730466i
$321$	10.4841			0.585168
$322$	0.117883	+	28.5288i	0.00656938	+	1.58985i
$323$	0.421111			0.0234312
$324$	−0.150007	−	0.259820i	−0.00833373	−	0.0144344i
$325$	0.341305	−	0.591157i	0.0189322	−	0.0327915i
$326$	0.318962	−	0.552458i	0.0176657	−	0.0305978i
$327$	−5.26394	−	9.11741i	−0.291096	−	0.504194i
$328$	21.1533			1.16800
$329$	5.28252	+	3.02083i	0.291235	+	0.166544i
$330$	−3.53844			−0.194785
$331$	9.76510	+	16.9137i	0.536739	+	0.929658i	0.999077	+	0.0429549i	$0.0136772\pi$
$331$	9.76510	+	16.9137i	0.536739	+	0.929658i	−0.462338	+	0.886704i	$0.652989\pi$
$332$	1.67812	−	2.90659i	0.0920988	−	0.159520i
$333$	0.150007	−	0.259820i	0.00822034	−	0.0142381i
$334$	12.4611	+	21.5832i	0.681840	+	1.18098i
$335$	−28.6734			−1.56660
$336$	10.3090	−	6.00884i	0.562403	−	0.327809i
$337$	−0.243643			−0.0132721			−0.00663605	−	0.999978i	$-0.502112\pi$
$337$	−0.243643			−0.0132721			−0.00663605	+	0.999978i	$0.502112\pi$
$338$	−8.06304	−	13.9656i	−0.438572	−	0.759628i
$339$	−5.71633	+	9.90097i	−0.310468	+	0.537747i
$340$	−0.0408121	+	0.0706887i	−0.00221335	+	0.00383363i
$341$	−2.18845	−	3.79051i	−0.118511	−	0.205268i
$342$	5.47686			0.296155
$343$	0.229575	+	18.5188i	0.0123959	+	0.999923i
$344$	−10.7843			−0.581449
$345$	8.29449	+	14.3665i	0.446560	+	0.773465i
$346$	2.92816	−	5.07172i	0.157419	−	0.272657i
$347$	−11.0805	+	19.1920i	−0.594834	+	1.03028i	0.398736	+	0.917066i	$0.369449\pi$
$347$	−11.0805	+	19.1920i	−0.594834	+	1.03028i	−0.993570	+	0.113217i	$0.963884\pi$
$348$	−0.758290	−	1.31340i	−0.0406486	−	0.0704055i
$349$	−16.1822			−0.866213			−0.433107	−	0.901343i	$-0.642583\pi$
$349$	−16.1822			−0.866213			−0.433107	+	0.901343i	$0.642583\pi$
$350$	1.53813	−	0.896537i	0.0822167	−	0.0479219i
$351$	−1.53844			−0.0821161
$352$	0.841739	+	1.45793i	0.0448648	+	0.0777082i
$353$	3.88844	−	6.73497i	0.206961	−	0.358466i	−0.743795	−	0.668408i	$-0.766976\pi$
$353$	3.88844	−	6.73497i	0.206961	−	0.358466i	0.950756	+	0.309941i	$0.100309\pi$
$354$	3.75829	−	6.50955i	0.199751	−	0.345979i
$355$	4.96533	+	8.60020i	0.263532	+	0.456451i
$356$	4.18002			0.221540
$357$	−0.267819	−	0.153153i	−0.0141745	−	0.00810573i
$358$	19.2751			1.01872
$359$	−5.40642	−	9.36420i	−0.285340	−	0.494223i	0.687352	−	0.726325i	$-0.258773\pi$
$359$	−5.40642	−	9.36420i	−0.285340	−	0.494223i	−0.972692	+	0.232102i	$0.925440\pi$
$360$	3.00765	−	5.20941i	0.158517	−	0.274560i
$361$	2.97917	−	5.16008i	0.156798	−	0.271583i
$362$	12.5267	+	21.6968i	0.658387	+	1.14036i
$363$	1.00000			0.0524864
$364$	0.00504590	+	1.22115i	0.000264477	+	0.0640057i
$365$	−24.3537			−1.27473
$366$	−3.46660	−	6.00433i	−0.181202	−	0.313851i
$367$	0.878346	−	1.52134i	0.0458493	−	0.0794133i	−0.842190	−	0.539181i	$-0.818734\pi$
$367$	0.878346	−	1.52134i	0.0458493	−	0.0794133i	0.888039	+	0.459768i	$0.152067\pi$
$368$	16.0332	−	27.7704i	0.835790	−	1.44763i
$369$	−4.10240	−	7.10556i	−0.213562	−	0.369901i
$370$	−1.06158			−0.0551891
$371$	0.129952	+	31.4496i	0.00674679	+	1.63278i
$372$	−1.31313			−0.0680828
$373$	4.63683	+	8.03123i	0.240086	+	0.415841i	0.960739	−	0.277455i	$-0.0894910\pi$
$373$	4.63683	+	8.03123i	0.240086	+	0.415841i	−0.720653	+	0.693296i	$0.756158\pi$
$374$	0.0884231	−	0.153153i	0.00457225	−	0.00791936i
$375$	−5.31532	+	9.20640i	−0.274482	+	0.475417i
$376$	−2.96491	−	5.13537i	−0.152903	−	0.264836i
$377$	−7.77687			−0.400529
$378$	−3.48318	−	1.99187i	−0.179156	−	0.102451i
$379$	−11.5130			−0.591386			−0.295693	−	0.955283i	$-0.595550\pi$
$379$	−11.5130			−0.591386			−0.295693	+	0.955283i	$0.595550\pi$
$380$	−1.26394	−	2.18920i	−0.0648386	−	0.112304i
$381$	−0.117449	+	0.203428i	−0.00601710	+	0.0104219i
$382$	−12.4432	+	21.5523i	−0.636651	+	1.10271i
$383$	11.2392	+	19.4669i	0.574298	+	0.994713i	0.996118	+	0.0880331i	$0.0280581\pi$
$383$	11.2392	+	19.4669i	0.574298	+	0.994713i	−0.421820	+	0.906680i	$0.638609\pi$
$384$	−13.1745			−0.672311
$385$	−5.33317	+	3.10856i	−0.271804	+	0.158427i
$386$	−31.3223			−1.59426
$387$	2.09146	+	3.62252i	0.106315	+	0.184143i
$388$	2.46163	−	4.26366i	0.124970	−	0.216455i
$389$	17.1663	−	29.7329i	0.870365	−	1.50752i	0.00874493	−	0.999962i	$-0.497216\pi$
$389$	17.1663	−	29.7329i	0.870365	−	1.50752i	0.861620	−	0.507554i	$-0.169450\pi$
$390$	2.72185	+	4.71438i	0.137826	+	0.238722i
$391$	−0.829092			−0.0419290
$392$	8.89410	−	15.7033i	0.449220	−	0.793138i
$393$	−5.75854			−0.290480
$394$	19.9530	+	34.5596i	1.00522	+	1.74109i
$395$	16.6995	−	28.9244i	0.840243	−	1.45534i
$396$	0.150007	−	0.259820i	0.00753814	−	0.0130564i
$397$	4.89980	+	8.48671i	0.245914	+	0.425936i	0.962388	−	0.271678i	$-0.0875785\pi$
$397$	4.89980	+	8.48671i	0.245914	+	0.425936i	−0.716474	+	0.697614i	$0.754245\pi$
$398$	16.6984			0.837016
$399$	8.25477	−	4.81148i	0.413255	−	0.240875i
$400$	−2.00110			−0.100055
$401$	−1.73819	−	3.01064i	−0.0868011	−	0.150344i	0.819356	−	0.573285i	$-0.194331\pi$
$401$	−1.73819	−	3.01064i	−0.0868011	−	0.150344i	−0.906157	+	0.422941i	$0.860998\pi$
$402$	9.31896	−	16.1409i	0.464788	−	0.805036i
$403$	−3.36681	+	5.83149i	−0.167713	+	0.290487i
$404$	−1.44833	−	2.50858i	−0.0720570	−	0.124806i
$405$	−2.33317			−0.115936
$406$	−17.6076	−	10.0690i	−0.873849	−	0.499714i
$407$	0.300014			0.0148712
$408$	0.150318	+	0.260358i	0.00744185	+	0.0128897i
$409$	−17.5609	+	30.4164i	−0.868332	+	1.50399i	−0.00463138	+	0.999989i	$0.501474\pi$
$409$	−17.5609	+	30.4164i	−0.868332	+	1.50399i	−0.863700	+	0.504006i	$0.831859\pi$
$410$	−14.5161	+	25.1426i	−0.716899	+	1.24171i
$411$	−8.04325	−	13.9313i	−0.396744	−	0.687181i
$412$	2.64616			0.130367
$413$	−0.0541838	−	13.1129i	−0.00266621	−	0.645246i
$414$	−10.7830			−0.529953
$415$	−13.0505	−	22.6042i	−0.640626	−	1.10960i
$416$	1.29497	−	2.24295i	0.0634911	−	0.109970i
$417$	7.14649	−	12.3781i	0.349965	−	0.606157i
$418$	2.73843	+	4.74310i	0.133941	+	0.231993i
$419$	13.8100			0.674664			0.337332	−	0.941386i	$-0.390475\pi$
$419$	13.8100			0.674664			0.337332	+	0.941386i	$0.390475\pi$
$420$	0.00765250	+	1.85197i	0.000373404	+	0.0903670i
$421$	9.72050			0.473748			0.236874	−	0.971540i	$-0.423877\pi$
$421$	9.72050			0.473748			0.236874	+	0.971540i	$0.423877\pi$
$422$	16.8701	+	29.2199i	0.821224	+	1.42240i
$423$	−1.15001	+	1.99187i	−0.0559153	+	0.0968481i
$424$	15.3232	−	26.5406i	0.744161	−	1.28893i
$425$	0.0258696	+	0.0448075i	0.00125486	+	0.00217348i
$426$	−6.45500			−0.312746
$427$	−10.4998	−	6.00433i	−0.508119	−	0.290570i
$428$	3.14539			0.152038
$429$	−0.769222	−	1.33233i	−0.0371384	−	0.0643256i
$430$	7.40053	−	12.8181i	0.356885	−	0.618143i
$431$	5.09584	−	8.82625i	0.245458	−	0.425145i	−0.716802	−	0.697276i	$-0.754395\pi$
$431$	5.09584	−	8.82625i	0.245458	−	0.425145i	0.962260	+	0.272131i	$0.0877284\pi$
$432$	2.25501	+	3.90579i	0.108494	+	0.187918i
$433$	−21.0101			−1.00968			−0.504840	−	0.863213i	$-0.668449\pi$
$433$	−21.0101			−1.00968			−0.504840	+	0.863213i	$0.668449\pi$
$434$	−15.1730	+	8.84392i	−0.728326	+	0.424522i
$435$	−11.7943			−0.565491
$436$	−1.57926	−	2.73535i	−0.0756327	−	0.131000i
$437$	12.8383	−	22.2367i	0.614141	−	1.06372i
$438$	7.91504	−	13.7092i	0.378195	−	0.655053i
$439$	−4.92336	−	8.52751i	−0.234979	−	0.406996i	0.724287	−	0.689498i	$-0.242169\pi$
$439$	−4.92336	−	8.52751i	−0.234979	−	0.406996i	−0.959267	+	0.282502i	$0.908836\pi$
$440$	6.01531			0.286768
$441$	−6.99976	+	0.0578482i	−0.333322	+	0.00275468i
$442$	−0.272068			−0.0129410
$443$	−7.77560	−	13.4677i	−0.369430	−	0.639871i	0.620047	−	0.784565i	$-0.287114\pi$
$443$	−7.77560	−	13.4677i	−0.369430	−	0.639871i	−0.989477	+	0.144694i	$0.953780\pi$
$444$	0.0450043	−	0.0779497i	0.00213581	−	0.00369933i
$445$	16.2537	−	28.1523i	0.770501	−	1.33455i
$446$	−12.7408	−	22.0677i	−0.603294	−	1.04494i
$447$	−0.672908			−0.0318274
$448$	−14.7821	+	8.61607i	−0.698388	+	0.407071i
$449$	2.62021			0.123655			0.0618277	−	0.998087i	$-0.480307\pi$
$449$	2.62021			0.123655			0.0618277	+	0.998087i	$0.480307\pi$
$450$	0.336454	+	0.582755i	0.0158606	+	0.0274713i
$451$	4.10240	−	7.10556i	0.193174	−	0.334588i
$452$	−1.71498	+	2.97043i	−0.0806659	+	0.139717i
$453$	−11.8862	−	20.5875i	−0.558462	−	0.967285i
$454$	−8.22010			−0.385788
$455$	8.24403	+	4.71438i	0.386486	+	0.221014i
$456$	−9.31058			−0.436008
$457$	−3.81295	−	6.60423i	−0.178362	−	0.308933i	0.762957	−	0.646449i	$-0.223747\pi$
$457$	−3.81295	−	6.60423i	−0.178362	−	0.308933i	−0.941320	+	0.337516i	$0.890413\pi$
$458$	21.4082	−	37.0802i	1.00034	−	1.73264i
$459$	0.0583043	−	0.100986i	0.00272141	−	0.00471362i
$460$	2.48847	+	4.31015i	0.116025	+	0.200962i
$461$	−12.7392			−0.593325			−0.296662	−	0.954982i	$-0.595874\pi$
$461$	−12.7392			−0.593325			−0.296662	+	0.954982i	$0.595874\pi$
$462$	−0.0165798	−	4.01246i	−0.000771363	−	0.186676i
$463$	−8.76838			−0.407501			−0.203751	−	0.979023i	$-0.565313\pi$
$463$	−8.76838			−0.407501			−0.203751	+	0.979023i	$0.565313\pi$
$464$	11.3991	+	19.7439i	0.529191	+	0.916586i
$465$	−5.10604	+	8.84392i	−0.236787	+	0.410127i
$466$	4.25501	−	7.36989i	0.197110	−	0.341404i
$467$	9.68413	+	16.7734i	0.448128	+	0.776181i	0.998264	−	0.0588943i	$-0.0187575\pi$
$467$	9.68413	+	16.7734i	0.448128	+	0.776181i	−0.550136	+	0.835075i	$0.685424\pi$
$468$	−0.461555			−0.0213354
$469$	−0.134353	−	32.5145i	−0.00620384	−	1.50138i
$470$	8.13847			0.375400
$471$	7.62790	+	13.2119i	0.351475	+	0.608773i
$472$	−6.38904	+	11.0661i	−0.294079	+	0.509360i
$473$	−2.09146	+	3.62252i	−0.0961656	+	0.166564i
$474$	10.8548	+	18.8011i	0.498577	+	0.863561i
$475$	−1.60235			−0.0735207
$476$	−0.0803495	−	0.0459482i	−0.00368281	−	0.00210603i
$477$	−11.8869			−0.544265
$478$	9.11108	+	15.7809i	0.416731	+	0.721800i
$479$	−12.0995	+	20.9569i	−0.552839	+	0.957546i	0.445229	+	0.895417i	$0.353122\pi$
$479$	−12.0995	+	20.9569i	−0.552839	+	0.957546i	−0.998068	+	0.0621289i	$0.980211\pi$
$480$	1.96392	−	3.40161i	0.0896404	−	0.155262i
$481$	−0.230778	−	0.399719i	−0.0105226	−	0.0182256i
$482$	31.4427			1.43218
$483$	−16.2522	+	9.47295i	−0.739499	+	0.431034i
$484$	0.300014			0.0136370
$485$	−19.1438	−	33.1580i	−0.869274	−	1.50563i
$486$	0.758290	−	1.31340i	0.0343967	−	0.0595769i
$487$	10.6093	−	18.3759i	0.480755	−	0.832692i	−0.519001	−	0.854773i	$-0.673696\pi$
$487$	10.6093	−	18.3759i	0.480755	−	0.832692i	0.999756	+	0.0220818i	$0.00702942\pi$
$488$	5.89317	+	10.2073i	0.266771	+	0.462062i
$489$	0.420633			0.0190217
$490$	12.5614	+	21.3476i	0.567466	+	0.964386i
$491$	−28.2038			−1.27282			−0.636411	−	0.771350i	$-0.719582\pi$
$491$	−28.2038			−1.27282			−0.636411	+	0.771350i	$0.719582\pi$
$492$	−1.23078	−	2.13177i	−0.0554877	−	0.0961076i
$493$	0.294729	−	0.510486i	0.0132739	−	0.0229911i
$494$	4.21292	−	7.29700i	0.189548	−	0.328307i
$495$	−1.16659	−	2.02059i	−0.0524342	−	0.0908187i
$496$	19.7399			0.886349
$497$	−9.72902	+	5.67078i	−0.436406	+	0.254369i
$498$	16.9659			0.760259
$499$	17.7490	+	30.7422i	0.794555	+	1.37621i	0.923122	+	0.384508i	$0.125629\pi$
$499$	17.7490	+	30.7422i	0.794555	+	1.37621i	−0.128567	+	0.991701i	$0.541038\pi$
$500$	−1.59467	+	2.76205i	−0.0713159	+	0.123523i
$501$	−8.21657	+	14.2315i	−0.367089	+	0.635817i
$502$	−20.6926	−	35.8406i	−0.923555	−	1.59964i
$503$	16.0477			0.715529			0.357765	−	0.933812i	$-0.383539\pi$
$503$	16.0477			0.715529			0.357765	+	0.933812i	$0.383539\pi$
$504$	5.92136	+	3.38615i	0.263758	+	0.150831i
$505$	−22.5269			−1.00243
$506$	−5.39148	−	9.33831i	−0.239680	−	0.415139i
$507$	5.31659	−	9.20861i	0.236118	−	0.408969i
$508$	−0.0352364	+	0.0610313i	−0.00156336	+	0.00270782i
$509$	−4.10652	−	7.11270i	−0.182018	−	0.315265i	0.760550	−	0.649280i	$-0.224930\pi$
$509$	−4.10652	−	7.11270i	−0.182018	−	0.315265i	−0.942568	+	0.334015i	$0.891596\pi$
$510$	−0.412613			−0.0182708
$511$	−0.114112	−	27.6161i	−0.00504803	−	1.22167i
$512$	15.6626			0.692197
$513$	1.80566	+	3.12750i	0.0797219	+	0.138082i
$514$	6.75027	−	11.6918i	0.297742	−	0.515704i
$515$	10.2894	−	17.8218i	0.453407	−	0.785324i
$516$	0.627469	+	1.08681i	0.0276228	+	0.0478441i
$517$	−2.30001			−0.101155
$518$	−0.00497418	−	1.20380i	−0.000218553	−	0.0528917i
$519$	3.86153			0.169502
$520$	−4.62711	−	8.01438i	−0.202912	−	0.351454i
$521$	4.27767	−	7.40914i	0.187408	−	0.324601i	−0.756977	−	0.653441i	$-0.773325\pi$
$521$	4.27767	−	7.40914i	0.187408	−	0.324601i	0.944385	+	0.328841i	$0.106658\pi$
$522$	3.83317	−	6.63925i	0.167773	−	0.290592i
$523$	−15.0185	−	26.0128i	−0.656712	−	1.13746i	−0.981462	−	0.191658i	$-0.938613\pi$
$523$	−15.0185	−	26.0128i	−0.656712	−	1.13746i	0.324750	−	0.945800i	$-0.394720\pi$
$524$	−1.72765			−0.0754725
$525$	1.01906	+	0.582755i	0.0444756	+	0.0254335i
$526$	3.42111			0.149168
$527$	−0.255192	−	0.442006i	−0.0111163	−	0.0192541i
$528$	−2.25501	+	3.90579i	−0.0981367	+	0.169978i
$529$	−13.7764	+	23.8614i	−0.598974	+	1.03745i
$530$	21.0306	+	36.4261i	0.913511	+	1.58225i
$531$	4.95627			0.215084
$532$	2.47655	−	1.44351i	0.107372	−	0.0625843i
$533$	−12.6226			−0.546746
$534$	10.5650	+	18.2992i	0.457194	+	0.791884i
$535$	12.2307	−	21.1841i	0.528778	−	0.915870i
$536$	−15.8421	+	27.4393i	−0.684275	+	1.18520i
$537$	6.35480	+	11.0068i	0.274230	+	0.474980i
$538$	−12.6921			−0.547194
$539$	−3.54998	−	6.03305i	−0.152908	−	0.259862i
$540$	−0.699986			−0.0301226
$541$	−9.50845	−	16.4691i	−0.408800	−	0.708063i	0.585955	−	0.810343i	$-0.300719\pi$
$541$	−9.50845	−	16.4691i	−0.408800	−	0.708063i	−0.994756	+	0.102281i	$0.967386\pi$
$542$	6.74475	−	11.6823i	0.289712	−	0.501796i
$543$	−8.25982	+	14.3064i	−0.354463	+	0.613947i
$544$	0.0981539	+	0.170008i	0.00420831	+	0.00728901i
$545$	−24.5634			−1.05218
$546$	−5.33317	+	3.10856i	−0.228239	+	0.133034i
$547$	34.4968			1.47498			0.737489	−	0.675360i	$-0.236012\pi$
$547$	34.4968			1.47498			0.737489	+	0.675360i	$0.236012\pi$
$548$	−2.41309	−	4.17960i	−0.103082	−	0.178543i
$549$	2.28580	−	3.95913i	0.0975557	−	0.168971i
$550$	−0.336454	+	0.582755i	−0.0143464	+	0.0248488i
$551$	9.12766	+	15.8096i	0.388852	+	0.673511i
$552$	18.3309			0.780214
$553$	32.8774	+	18.8011i	1.39809	+	0.799503i
$554$	8.18949			0.347938
$555$	−0.349993	−	0.606205i	−0.0148564	−	0.0257320i
$556$	2.14405	−	3.71360i	0.0909279	−	0.157492i
$557$	−2.71456	+	4.70176i	−0.115020	+	0.199220i	−0.917788	−	0.397072i	$-0.870026\pi$
$557$	−2.71456	+	4.70176i	−0.115020	+	0.199220i	0.802768	+	0.596292i	$0.203360\pi$
$558$	−3.31896	−	5.74861i	−0.140503	−	0.243358i
$559$	6.43520			0.272180
$560$	−0.115038	−	27.8401i	−0.00486123	−	1.17646i
$561$	0.116609			0.00492321
$562$	−14.9698	−	25.9285i	−0.631464	−	1.09373i
$563$	17.0841	−	29.5905i	0.720007	−	1.24709i	−0.240989	−	0.970528i	$-0.577472\pi$
$563$	17.0841	−	29.5905i	0.720007	−	1.24709i	0.960996	−	0.276562i	$-0.0891950\pi$
$564$	−0.345019	+	0.597590i	−0.0145279	+	0.0251631i
$565$	13.3372	+	23.1007i	0.561100	+	0.971853i
$566$	15.3253			0.644170
$567$	−0.0109324	−	2.64573i	−0.000459117	−	0.111110i
$568$	10.9734			0.460434
$569$	8.29626	+	14.3695i	0.347797	+	0.602402i	0.985858	−	0.167584i	$-0.0535965\pi$
$569$	8.29626	+	14.3695i	0.347797	+	0.602402i	−0.638061	+	0.769986i	$0.720263\pi$
$570$	6.38923	−	11.0665i	0.267616	−	0.463524i
$571$	−6.96720	+	12.0675i	−0.291568	+	0.505011i	−0.974181	−	0.225769i	$-0.927510\pi$
$571$	−6.96720	+	12.0675i	−0.291568	+	0.505011i	0.682612	+	0.730781i	$0.260844\pi$
$572$	−0.230778	−	0.399719i	−0.00964930	−	0.0167131i
$573$	−16.4096			−0.685520
$574$	−28.5788	−	16.3429i	−1.19286	−	0.682139i
$575$	3.15473			0.131562
$576$	−3.23346	−	5.60051i	−0.134727	−	0.233355i
$577$	−22.8387	+	39.5578i	−0.950788	+	1.64681i	−0.207062	+	0.978328i	$0.566390\pi$
$577$	−22.8387	+	39.5578i	−0.950788	+	1.64681i	−0.743726	+	0.668485i	$0.766943\pi$
$578$	−12.8806	+	22.3099i	−0.535763	+	0.927969i
$579$	−10.3266	−	17.8862i	−0.429159	−	0.743326i
$580$	−3.53844			−0.146926
$581$	25.5711	−	14.9047i	1.06087	−	0.618352i
$582$	24.8872			1.03161
$583$	−5.94346	−	10.2944i	−0.246153	−	0.426350i
$584$	−13.4554	+	23.3055i	−0.556790	+	0.964389i
$585$	−1.79473	+	3.10856i	−0.0742029	+	0.128523i
$586$	−12.2166	−	21.1598i	−0.504665	−	0.874105i
$587$	29.3966			1.21333			0.606664	−	0.794958i	$-0.292507\pi$
$587$	29.3966			1.21333			0.606664	+	0.794958i	$0.292507\pi$
$588$	−2.10003	+	0.0173553i	−0.0866037	+	0.000715720i
$589$	15.8064			0.651292
$590$	−8.76874	−	15.1879i	−0.361003	−	0.625276i
$591$	−13.1566	+	22.7879i	−0.541189	+	0.937368i
$592$	−0.676535	+	1.17179i	−0.0278054	+	0.0481604i
$593$	0.912178	+	1.57994i	0.0374587	+	0.0648803i	0.884147	−	0.467209i	$-0.154740\pi$
$593$	0.912178	+	1.57994i	0.0374587	+	0.0648803i	−0.846688	+	0.532089i	$0.821407\pi$
$594$	1.51658			0.0622260
$595$	−0.621893	+	0.362485i	−0.0254951	+	0.0148604i
$596$	−0.201882			−0.00826941
$597$	5.50528	+	9.53543i	0.225316	+	0.390259i
$598$	−8.29449	+	14.3665i	−0.339187	+	0.587489i
$599$	11.2497	−	19.4851i	0.459651	−	0.796139i	−0.539291	−	0.842119i	$-0.681308\pi$
$599$	11.2497	−	19.4851i	0.459651	−	0.796139i	0.998942	+	0.0459800i	$0.0146411\pi$
$600$	−0.571967	−	0.990675i	−0.0233504	−	0.0404442i
$601$	−10.3352			−0.421583			−0.210792	−	0.977531i	$-0.567604\pi$
$601$	−10.3352			−0.421583			−0.210792	+	0.977531i	$0.567604\pi$
$602$	14.5699	+	8.33185i	0.593825	+	0.339581i
$603$	12.2894			0.500465
$604$	−3.56603	−	6.17654i	−0.145100	−	0.251320i
$605$	1.16659	−	2.02059i	0.0474285	−	0.0821486i
$606$	7.32133	−	12.6809i	0.297409	−	0.515127i
$607$	16.3137	+	28.2562i	0.662155	+	1.14689i	0.980048	+	0.198759i	$0.0636911\pi$
$607$	16.3137	+	28.2562i	0.662155	+	1.14689i	−0.317894	+	0.948126i	$0.602976\pi$
$608$	−6.07958			−0.246560
$609$	−0.0552634	−	13.3742i	−0.00223939	−	0.541951i
$610$	−16.1764			−0.654962
$611$	1.76922	+	3.06438i	0.0715751	+	0.123972i
$612$	0.0174921	−	0.0302972i	0.000707077	−	0.00122469i
$613$	3.19350	−	5.53130i	0.128984	−	0.223407i	−0.794299	−	0.607527i	$-0.792162\pi$
$613$	3.19350	−	5.53130i	0.128984	−	0.223407i	0.923283	+	0.384120i	$0.125495\pi$
$614$	21.0932	+	36.5345i	0.851253	+	1.47441i
$615$	−19.1432			−0.771929
$616$	0.0281855	+	6.82112i	0.00113562	+	0.274831i
$617$	4.14609			0.166915			0.0834577	−	0.996511i	$-0.473404\pi$
$617$	4.14609			0.166915			0.0834577	+	0.996511i	$0.473404\pi$
$618$	6.68821	+	11.5843i	0.269039	+	0.465990i
$619$	19.2980	−	33.4252i	0.775653	−	1.34347i	−0.158774	−	0.987315i	$-0.550754\pi$
$619$	19.2980	−	33.4252i	0.775653	−	1.34347i	0.934427	−	0.356155i	$-0.115913\pi$
$620$	−1.53188	+	2.65330i	−0.0615220	+	0.106559i
$621$	−3.55502	−	6.15748i	−0.142658	−	0.247091i
$622$	−13.7141			−0.549885
$623$	31.9998	+	18.2992i	1.28204	+	0.733142i
$624$	6.93842			0.277759
$625$	13.5108	+	23.4014i	0.540433	+	0.936057i
$626$	−12.2667	+	21.2466i	−0.490278	+	0.849186i
$627$	−1.80566	+	3.12750i	−0.0721112	+	0.124900i
$628$	2.28848	+	3.96376i	0.0913203	+	0.158171i
$629$	0.0349842			0.00139491
$630$	−8.08818	+	4.71438i	−0.322241	+	0.187826i
$631$	−8.89990			−0.354299			−0.177150	−	0.984184i	$-0.556688\pi$
$631$	−8.89990			−0.354299			−0.177150	+	0.984184i	$0.556688\pi$
$632$	−18.4530	−	31.9615i	−0.734021	−	1.27136i
$633$	−11.1238	+	19.2670i	−0.442131	+	0.765793i
$634$	−3.96866	+	6.87392i	−0.157616	+	0.272998i
$635$	0.274029	+	0.474632i	0.0108745	+	0.0188352i
$636$	−3.56625			−0.141411
$637$	−5.30730	+	9.37050i	−0.210283	+	0.371273i
$638$	7.66635			0.303514
$639$	−2.12814	−	3.68605i	−0.0841880	−	0.145818i
$640$	−15.3693	+	26.6203i	−0.607523	+	1.05226i
$641$	−18.6648	+	32.3284i	−0.737217	+	1.27690i	0.216527	+	0.976277i	$0.430527\pi$
$641$	−18.6648	+	32.3284i	−0.737217	+	1.27690i	−0.953744	+	0.300620i	$0.902806\pi$
$642$	7.95002	+	13.7698i	0.313762	+	0.543452i
$643$	15.9206			0.627846			0.313923	−	0.949449i	$-0.398357\pi$
$643$	15.9206			0.627846			0.313923	+	0.949449i	$0.398357\pi$
$644$	−4.87588	+	2.84202i	−0.192137	+	0.111991i
$645$	9.75950			0.384280
$646$	0.319324	+	0.553086i	0.0125636	+	0.0217609i
$647$	−8.77640	+	15.2012i	−0.345036	+	0.597619i	−0.985360	−	0.170485i	$-0.945467\pi$
$647$	−8.77640	+	15.2012i	−0.345036	+	0.597619i	0.640325	+	0.768105i	$0.278800\pi$
$648$	−1.28908	+	2.23276i	−0.0506399	+	0.0877109i
$649$	2.47814	+	4.29226i	0.0972753	+	0.168486i
$650$	1.03523			0.0406051
$651$	−10.0526	−	5.74861i	−0.393992	−	0.225306i
$652$	0.126196			0.00494221
$653$	11.9829	+	20.7549i	0.468926	+	0.812204i	0.999369	−	0.0355170i	$-0.0113078\pi$
$653$	11.9829	+	20.7549i	0.468926	+	0.812204i	−0.530443	+	0.847721i	$0.677974\pi$
$654$	7.98318	−	13.8273i	0.312167	−	0.540689i
$655$	−6.71784	+	11.6356i	−0.262488	+	0.454642i
$656$	18.5019	+	32.0462i	0.722377	+	1.25119i
$657$	10.4380			0.407226
$658$	0.0381338	+	9.22871i	0.00148661	+	0.359773i
$659$	−38.6166			−1.50429			−0.752144	−	0.658999i	$-0.770980\pi$
$659$	−38.6166			−1.50429			−0.752144	+	0.658999i	$0.770980\pi$
$660$	−0.349993	−	0.606205i	−0.0136235	−	0.0235965i
$661$	−5.18942	+	8.98833i	−0.201845	+	0.349606i	−0.949123	−	0.314906i	$-0.898027\pi$
$661$	−5.18942	+	8.98833i	−0.201845	+	0.349606i	0.747278	+	0.664512i	$0.231360\pi$
$662$	−14.8096	+	25.6509i	−0.575590	+	0.996951i
$663$	−0.0896979	−	0.155361i	−0.00348358	−	0.00603373i
$664$	−28.8418			−1.11928
$665$	−0.0921145	−	22.2925i	−0.00357205	−	0.864466i
$666$	0.454996			0.0176307
$667$	−17.9707	−	31.1262i	−0.695830	−	1.20521i
$668$	−2.46509	+	4.26966i	−0.0953771	+	0.165198i
$669$	8.40101	−	14.5510i	0.324802	−	0.562573i
$670$	−21.7428	−	37.6596i	−0.839996	−	1.45492i
$671$	4.57160			0.176485
$672$	3.86650	+	2.21107i	0.149154	+	0.0852940i
$673$	−11.8103			−0.455253			−0.227627	−	0.973748i	$-0.573097\pi$
$673$	−11.8103			−0.455253			−0.227627	+	0.973748i	$0.573097\pi$
$674$	−0.184752	−	0.320000i	−0.00711640	−	0.0123260i
$675$	−0.221850	+	0.384256i	−0.00853903	+	0.0147900i
$676$	1.59505	−	2.76272i	0.0613483	−	0.106258i
$677$	−20.9845	−	36.3462i	−0.806499	−	1.39690i	−0.915275	−	0.402830i	$-0.868026\pi$
$677$	−20.9845	−	36.3462i	−0.806499	−	1.39690i	0.108776	−	0.994066i	$-0.465307\pi$
$678$	−17.3385			−0.665882
$679$	37.5102	−	21.8637i	1.43951	−	0.839050i
$680$	0.701436			0.0268988
$681$	−2.71008	−	4.69399i	−0.103850	−	0.179874i
$682$	3.31896	−	5.74861i	0.127090	−	0.220126i
$683$	−12.0767	+	20.9174i	−0.462100	+	0.800381i	−0.999065	−	0.0432234i	$-0.986237\pi$
$683$	−12.0767	+	20.9174i	−0.462100	+	0.800381i	0.536965	+	0.843604i	$0.319571\pi$
$684$	0.541724	+	0.938294i	0.0207134	+	0.0358766i
$685$	−37.5326			−1.43405
$686$	−24.1485	+	14.3442i	−0.921994	+	0.547663i
$687$	28.2323			1.07713
$688$	−9.43254	−	16.3376i	−0.359612	−	0.622867i
$689$	−9.14369	+	15.8373i	−0.348347	+	0.603354i
$690$	−12.5793	+	21.7879i	−0.478884	+	0.829452i
$691$	2.63720	+	4.56776i	0.100324	+	0.173766i	0.911818	−	0.410595i	$-0.134679\pi$
$691$	2.63720	+	4.56776i	0.100324	+	0.173766i	−0.811494	+	0.584360i	$0.801345\pi$
$692$	1.15851			0.0440401
$693$	2.28580	−	1.33233i	0.0868304	−	0.0506111i
$694$	−33.6090			−1.27578
$695$	−16.6740	−	28.8802i	−0.632481	−	1.09549i
$696$	−6.51634	+	11.2866i	−0.247001	+	0.427819i
$697$	0.478374	−	0.828569i	0.0181197	−	0.0313843i
$698$	−12.2708	−	21.2537i	−0.464457	−	0.804463i
$699$	5.61132			0.212240
$700$	0.305733	+	0.174835i	0.0115556	+	0.00660814i
$701$	26.9166			1.01662			0.508312	−	0.861173i	$-0.330270\pi$
$701$	26.9166			1.01662			0.508312	+	0.861173i	$0.330270\pi$
$702$	−1.16659	−	2.02059i	−0.0440300	−	0.0762622i
$703$	−0.541724	+	0.938294i	−0.0204315	+	0.0353884i
$704$	3.23346	−	5.60051i	0.121865	−	0.211077i
$705$	2.68317	+	4.64738i	0.101054	+	0.175031i
$706$	11.7943			0.443883
$707$	−0.105553	−	25.5447i	−0.00396972	−	0.960705i
$708$	1.48695			0.0558831
$709$	−5.87138	−	10.1695i	−0.220504	−	0.381925i	0.734457	−	0.678655i	$-0.237437\pi$
$709$	−5.87138	−	10.1695i	−0.220504	−	0.381925i	−0.954961	+	0.296731i	$0.904104\pi$
$710$	−7.53031	+	13.0429i	−0.282608	+	0.489491i
$711$	−7.15742	+	12.3970i	−0.268424	+	0.464924i
$712$	−17.9604	−	31.1084i	−0.673095	−	1.16584i
$713$	−31.1200			−1.16545
$714$	−0.00193335	−	0.467887i	−7.23537e−5	−	0.0175102i
$715$	−3.58946			−0.134238
$716$	1.90653	+	3.30221i	0.0712504	+	0.123409i
$717$	−6.00765	+	10.4056i	−0.224360	+	0.388603i
$718$	8.19927	−	14.2015i	0.305994	−	0.529997i
$719$	−14.0839	−	24.3941i	−0.525242	−	0.909746i	−0.999568	−	0.0293966i	$-0.990641\pi$
$719$	−14.0839	−	24.3941i	−0.525242	−	0.909746i	0.474326	−	0.880349i	$-0.342692\pi$
$720$	10.5227			0.392156
$721$	20.2575	+	11.5843i	0.754428	+	0.431423i
$722$	9.03630			0.336296
$723$	10.3663	+	17.9550i	0.385528	+	0.667754i
$724$	−2.47806	+	4.29213i	−0.0920965	+	0.159516i
$725$	−1.12146	+	1.94242i	−0.0416499	+	0.0721398i
$726$	0.758290	+	1.31340i	0.0281428	+	0.0487447i
$727$	32.9885			1.22347			0.611737	−	0.791061i	$-0.290471\pi$
$727$	32.9885			1.22347			0.611737	+	0.791061i	$0.290471\pi$
$728$	9.06632	−	5.28451i	0.336020	−	0.195857i
$729$	1.00000			0.0370370
$730$	−18.4672	−	31.9861i	−0.683500	−	1.18386i
$731$	−0.243882	+	0.422417i	−0.00902032	+	0.0156237i
$732$	0.685773	−	1.18779i	0.0253469	−	0.0439021i
$733$	−0.953106	−	1.65083i	−0.0352038	−	0.0609747i	0.847887	−	0.530177i	$-0.177875\pi$
$733$	−0.953106	−	1.65083i	−0.0352038	−	0.0609747i	−0.883090	+	0.469203i	$0.844541\pi$
$734$	2.66416			0.0983360
$735$	−8.04894	+	14.2111i	−0.296890	+	0.524185i
$736$	11.9696			0.441206
$737$	6.14472	+	10.6430i	0.226344	+	0.392039i
$738$	6.22161	−	10.7761i	0.229021	−	0.396675i
$739$	18.9136	−	32.7594i	0.695749	−	1.20507i	−0.274178	−	0.961679i	$-0.588406\pi$
$739$	18.9136	−	32.7594i	0.695749	−	1.20507i	0.969927	−	0.243394i	$-0.0782609\pi$
$740$	−0.105003	−	0.181870i	−0.00385998	−	0.00668569i
$741$	5.55582			0.204098
$742$	−41.2072	+	24.0186i	−1.51276	+	0.881750i
$743$	46.4995			1.70590			0.852950	−	0.521993i	$-0.174811\pi$
$743$	46.4995			1.70590			0.852950	+	0.521993i	$0.174811\pi$
$744$	5.64219	+	9.77256i	0.206853	+	0.358279i
$745$	−0.785005	+	1.35967i	−0.0287604	+	0.0498144i
$746$	−7.03212	+	12.1800i	−0.257464	+	0.445941i
$747$	5.59347	+	9.68817i	0.204654	+	0.354472i
$748$	0.0349842			0.00127915
$749$	24.0793	+	13.7698i	0.879838	+	0.503139i
$750$	−16.1222			−0.588700
$751$	−2.07408	−	3.59242i	−0.0756843	−	0.131089i	0.825699	−	0.564110i	$-0.190781\pi$
$751$	−2.07408	−	3.59242i	−0.0756843	−	0.131089i	−0.901384	+	0.433021i	$0.857447\pi$
$752$	5.18656	−	8.98338i	0.189134	−	0.327590i
$753$	13.6442	−	23.6325i	0.497224	−	0.861217i
$754$	−5.89713	−	10.2141i	−0.214761	−	0.371976i
$755$	−55.4651			−2.01858
$756$	−0.00327987	−	0.793757i	−0.000119288	−	0.0288686i
$757$	4.56418			0.165888			0.0829439	−	0.996554i	$-0.473568\pi$
$757$	4.56418			0.165888			0.0829439	+	0.996554i	$0.473568\pi$
$758$	−8.73023	−	15.1212i	−0.317096	−	0.549227i
$759$	3.55502	−	6.15748i	0.129039	−	0.223502i
$760$	−10.8616	+	18.8129i	−0.393992	+	0.682414i
$761$	6.52544	+	11.3024i	0.236547	+	0.409711i	0.959721	−	0.280954i	$-0.0906510\pi$
$761$	6.52544	+	11.3024i	0.236547	+	0.409711i	−0.723174	+	0.690666i	$0.757318\pi$
$762$	−0.356242			−0.0129053
$763$	−0.115095	−	27.8539i	−0.00416671	−	1.00838i
$764$	−4.92311			−0.178112
$765$	−0.136034	−	0.235618i	−0.00491832	−	0.00851878i
$766$	−17.0452	+	29.5231i	−0.615868	+	1.06671i
$767$	3.81247	−	6.60340i	0.137660	−	0.238435i
$768$	−3.52321	−	6.10238i	−0.127133	−	0.220201i
$769$	−4.40156			−0.158724			−0.0793622	−	0.996846i	$-0.525288\pi$
$769$	−4.40156			−0.158724			−0.0793622	+	0.996846i	$0.525288\pi$
$770$	−8.12687	−	4.64738i	−0.292872	−	0.167480i
$771$	8.90197			0.320597
$772$	−3.09813	−	5.36612i	−0.111504	−	0.193131i
$773$	−11.2048	+	19.4073i	−0.403008	+	0.698031i	−0.994087	−	0.108583i	$-0.965369\pi$
$773$	−11.2048	+	19.4073i	−0.403008	+	0.698031i	0.591079	+	0.806614i	$0.298702\pi$
$774$	−3.17187	+	5.49384i	−0.114011	+	0.197472i
$775$	0.971018	+	1.68185i	0.0348800	+	0.0604139i
$776$	−42.3078			−1.51876
$777$	0.685773	−	0.399719i	0.0246020	−	0.0143398i
$778$	52.0681			1.86673
$779$	14.8151	+	25.6605i	0.530805	+	0.919382i
$780$	−0.538445	+	0.932613i	−0.0192794	+	0.0333929i
$781$	2.12814	−	3.68605i	0.0761509	−	0.131897i
$782$	−0.628692	−	1.08893i	−0.0224820	−	0.0389399i
$783$	5.05502			0.180652
$784$	31.5691	−	0.260897i	1.12747	−	0.00931773i
$785$	35.5945			1.27042
$786$	−4.36664	−	7.56325i	−0.155753	−	0.269772i
$787$	3.28143	−	5.68360i	0.116970	−	0.202599i	−0.801595	−	0.597867i	$-0.796015\pi$
$787$	3.28143	−	5.68360i	0.116970	−	0.202599i	0.918566	+	0.395268i	$0.129348\pi$
$788$	−3.94716	+	6.83669i	−0.140612	+	0.243547i
$789$	1.12790	+	1.95359i	0.0401544	+	0.0695495i
$790$	50.6523			1.80213
$791$	−26.1328	+	15.2321i	−0.929175	+	0.541591i
$792$	−2.57816			−0.0916111
$793$	−3.51658	−	6.09089i	−0.124877	−	0.216294i
$794$	−7.43094	+	12.8708i	−0.263714	+	0.456767i
$795$	−13.8671	+	24.0186i	−0.491816	+	0.851851i
$796$	1.65166	+	2.86077i	0.0585417	+	0.101397i
$797$	23.7974			0.842947			0.421473	−	0.906841i	$-0.361513\pi$
$797$	23.7974			0.842947			0.421473	+	0.906841i	$0.361513\pi$
$798$	12.5789	+	7.19329i	0.445288	+	0.254640i
$799$	−0.268201			−0.00948828
$800$	−0.373480	−	0.646887i	−0.0132045	−	0.0228709i
$801$	−6.96636	+	12.0661i	−0.246144	+	0.426334i
$802$	2.63611	−	4.56587i	0.0930841	−	0.161226i
$803$	5.21900	+	9.03958i	0.184175	+	0.319000i
$804$	3.68701			0.130031
$805$	0.181357	+	43.8899i	0.00639199	+	1.54692i
$806$	−10.2121			−0.359705
$807$	−4.18444	−	7.24767i	−0.147299	−	0.255130i
$808$	−12.4462	+	21.5574i	−0.437854	+	0.758386i
$809$	5.79765	−	10.0418i	0.203834	−	0.353052i	−0.745926	−	0.666028i	$-0.767993\pi$
$809$	5.79765	−	10.0418i	0.203834	−	0.353052i	0.949761	+	0.312977i	$0.101326\pi$
$810$	−1.76922	−	3.06438i	−0.0621641	−	0.107671i
$811$	39.5907			1.39022			0.695109	−	0.718905i	$-0.255356\pi$
$811$	39.5907			1.39022			0.695109	+	0.718905i	$0.255356\pi$
$812$	−0.0165798	−	4.01246i	−0.000581838	−	0.140810i
$813$	8.89469			0.311950
$814$	0.227498	+	0.394038i	0.00797380	+	0.0138110i
$815$	0.490705	−	0.849926i	0.0171886	−	0.0297716i
$816$	−0.262953	+	0.455449i	−0.00920521	+	0.0159439i
$817$	−7.55295	−	13.0821i	−0.264244	−	0.457685i
$818$	−53.2651			−1.86237
$819$	−3.53340	−	2.02059i	−0.123467	−	0.0706051i
$820$	−5.74324			−0.200563
$821$	2.57404	+	4.45837i	0.0898347	+	0.155598i	0.907441	−	0.420179i	$-0.138033\pi$
$821$	2.57404	+	4.45837i	0.0898347	+	0.155598i	−0.817606	+	0.575778i	$0.804699\pi$
$822$	12.1982	−	21.1280i	0.425462	−	0.736922i
$823$	−11.0892	+	19.2071i	−0.386546	+	0.669517i	−0.991982	−	0.126377i	$-0.959665\pi$
$823$	−11.0892	+	19.2071i	−0.386546	+	0.669517i	0.605436	+	0.795894i	$0.292999\pi$
$824$	−11.3699	−	19.6932i	−0.396088	−	0.686045i
$825$	−0.443701			−0.0154477
$826$	17.1814	−	10.0146i	0.597818	−	0.348452i
$827$	−24.8915			−0.865564			−0.432782	−	0.901499i	$-0.642468\pi$
$827$	−24.8915			−0.865564			−0.432782	+	0.901499i	$0.642468\pi$
$828$	−1.06656	−	1.84733i	−0.0370655	−	0.0641993i
$829$	−16.0767	+	27.8456i	−0.558365	+	0.967117i	0.439268	+	0.898356i	$0.355238\pi$
$829$	−16.0767	+	27.8456i	−0.558365	+	0.967117i	−0.997633	+	0.0687607i	$0.978095\pi$
$830$	19.7922	−	34.2811i	0.686997	−	1.18991i
$831$	2.69999	+	4.67651i	0.0936615	+	0.162226i
$832$	−9.94899			−0.344919
$833$	−0.413958	−	0.703505i	−0.0143428	−	0.0243750i
$834$	21.6764			0.750594
$835$	19.1707	+	33.2046i	0.663429	+	1.14909i
$836$	−0.541724	+	0.938294i	−0.0187359	+	0.0324516i
$837$	2.18845	−	3.79051i	0.0756440	−	0.131019i
$838$	10.4720	+	18.1381i	0.361750	+	0.626569i
$839$	23.6483			0.816429			0.408215	−	0.912886i	$-0.366152\pi$
$839$	23.6483			0.816429			0.408215	+	0.912886i	$0.366152\pi$
$840$	13.7498	−	8.01438i	0.474413	−	0.276523i
$841$	−3.44673			−0.118853
$842$	7.37096	+	12.7669i	0.254020	+	0.439976i
$843$	9.87078	−	17.0967i	0.339968	−	0.588841i
$844$	−3.33729	+	5.78036i	−0.114874	+	0.198968i
$845$	−12.4045	−	21.4853i	−0.426729	−	0.739117i
$846$	−3.48816			−0.119925
$847$	2.29673	+	1.31340i	0.0789167	+	0.0451288i
$848$	53.6103			1.84098
$849$	5.05259	+	8.75133i	0.173404	+	0.300345i
$850$	−0.0392334	+	0.0679542i	−0.00134569	+	0.00233081i
$851$	1.06656	−	1.84733i	0.0365611	−	0.0633258i
$852$	−0.638473	−	1.10587i	−0.0218737	−	0.0378864i
$853$	−27.0742			−0.927003			−0.463501	−	0.886096i	$-0.653407\pi$
$853$	−27.0742			−0.927003			−0.463501	+	0.886096i	$0.653407\pi$
$854$	−0.0757964	−	18.3434i	−0.00259370	−	0.627697i
$855$	8.42585			0.288158
$856$	−13.5149	−	23.4085i	−0.461931	−	0.800087i
$857$	16.6489	−	28.8367i	0.568714	−	0.985042i	−0.427979	−	0.903788i	$-0.640774\pi$
$857$	16.6489	−	28.8367i	0.568714	−	0.985042i	0.996693	−	0.0812532i	$-0.0258922\pi$
$858$	1.16659	−	2.02059i	0.0398266	−	0.0689817i
$859$	11.0153	+	19.0791i	0.375837	+	0.650969i	0.990452	−	0.137858i	$-0.0440218\pi$
$859$	11.0153	+	19.0791i	0.375837	+	0.650969i	−0.614615	+	0.788828i	$0.710688\pi$
$860$	2.92799			0.0998436
$861$	−0.0896979	−	21.7077i	−0.00305689	−	0.739795i
$862$	15.4565			0.526450
$863$	15.8925	+	27.5267i	0.540988	+	0.937019i	0.998848	+	0.0479941i	$0.0152829\pi$
$863$	15.8925	+	27.5267i	0.540988	+	0.937019i	−0.457860	+	0.889024i	$0.651384\pi$
$864$	−0.841739	+	1.45793i	−0.0286365	+	0.0495999i
$865$	4.50481	−	7.80255i	0.153168	−	0.265295i
$866$	−15.9317	−	27.5946i	−0.541383	−	0.937702i
$867$	−16.9864			−0.576888
$868$	−3.01592	−	1.72467i	−0.102367	−	0.0585390i
$869$	−14.3148			−0.485598
$870$	−8.94346	−	15.4905i	−0.303212	−	0.525178i
$871$	9.45331	−	16.3736i	0.320313	−	0.554799i
$872$	−13.5713	+	23.5062i	−0.459582	+	0.796019i
$873$	8.20503	+	14.2115i	0.277698	+	0.480987i
$874$	38.9407			1.31719
$875$	−24.2995	+	14.1635i	−0.821474	+	0.478815i
$876$	3.13155			0.105805
$877$	−14.6740	−	25.4161i	−0.495506	−	0.858241i	0.504481	−	0.863423i	$-0.331684\pi$
$877$	−14.6740	−	25.4161i	−0.495506	−	0.858241i	−0.999987	+	0.00518172i	$0.998351\pi$
$878$	7.46667	−	12.9327i	0.251988	−	0.436456i
$879$	8.05539	−	13.9523i	0.271701	−	0.470601i
$880$	5.26133	+	9.11289i	0.177359	+	0.307196i
$881$	−43.4442			−1.46367			−0.731836	−	0.681481i	$-0.761336\pi$
$881$	−43.4442			−1.46367			−0.731836	+	0.681481i	$0.761336\pi$
$882$	−5.38383	−	9.14960i	−0.181283	−	0.308083i
$883$	26.4200			0.889104			0.444552	−	0.895753i	$-0.353363\pi$
$883$	26.4200			0.889104			0.444552	+	0.895753i	$0.353363\pi$
$884$	−0.0269106	−	0.0466106i	−0.000905103	−	0.00156768i
$885$	5.78192	−	10.0146i	0.194357	−	0.336636i
$886$	11.7923	−	20.4249i	0.396171	−	0.686188i
$887$	6.41163	+	11.1053i	0.215282	+	0.372879i	0.953360	−	0.301837i	$-0.0975997\pi$
$887$	6.41163	+	11.1053i	0.215282	+	0.372879i	−0.738078	+	0.674715i	$0.764266\pi$
$888$	−0.773486			−0.0259565
$889$	−0.536931	+	0.312962i	−0.0180081	+	0.0104964i
$890$	49.3002			1.65255
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	2.52042	−	4.36550i	0.0843900	−	0.146168i
$893$	4.15305	−	7.19329i	0.138976	−	0.240714i
$894$	−0.510259	−	0.883795i	−0.0170656	−	0.0295585i
$895$	29.6537			0.991214
$896$	−30.2584	−	17.3034i	−1.01086	−	0.578066i
$897$	−10.9384			−0.365223
$898$	1.98688	+	3.44138i	0.0663031	+	0.114840i
$899$	11.0627	−	19.1611i	0.368961	−	0.639059i
$900$	−0.0665583	+	0.115282i	−0.00221861	+	0.00384275i
$901$	−0.693058	−	1.20041i	−0.0230891	−	0.0399915i
$902$	12.4432			0.414314
$903$	0.0457293	+	11.0669i	0.00152178	+	0.368283i
$904$	29.4753			0.980332
$905$	19.2716	+	33.3794i	0.640609	+	1.10957i
$906$	18.0264	−	31.2226i	0.598886	−	1.03730i
$907$	−26.7692	+	46.3656i	−0.888856	+	1.53954i	−0.0476276	+	0.998865i	$0.515166\pi$
$907$	−26.7692	+	46.3656i	−0.888856	+	1.53954i	−0.841229	+	0.540679i	$0.818167\pi$
$908$	−0.813062	−	1.40826i	−0.0269824	−	0.0467349i
$909$	9.65505			0.320238
$910$	0.0595126	+	14.4026i	0.00197282	+	0.477440i
$911$	28.4552			0.942764			0.471382	−	0.881929i	$-0.343755\pi$
$911$	28.4552			0.942764			0.471382	+	0.881929i	$0.343755\pi$
$912$	−8.14357	−	14.1051i	−0.269661	−	0.467066i
$913$	−5.59347	+	9.68817i	−0.185117	+	0.320632i
$914$	5.78265	−	10.0158i	0.191273	−	0.331294i
$915$	−5.33317	−	9.23733i	−0.176309	−	0.305377i
$916$	8.47008			0.279859
$917$	−13.2258	−	7.56325i	−0.436756	−	0.249761i
$918$	0.176846			0.00583679
$919$	−26.0926	−	45.1936i	−0.860714	−	1.49080i	−0.871241	−	0.490856i	$-0.836684\pi$
$919$	−26.0926	−	45.1936i	−0.860714	−	1.49080i	0.0105268	−	0.999945i	$-0.496649\pi$
$920$	21.3846	−	37.0391i	0.705028	−	1.22114i
$921$	−13.9084	+	24.0901i	−0.458298	+	0.793795i
$922$	−9.66003	−	16.7317i	−0.318136	−	0.551028i
$923$	−6.54806			−0.215532
$924$	0.685773	−	0.399719i	0.0225603	−	0.0131498i
$925$	−0.133117			−0.00437685
$926$	−6.64897	−	11.5164i	−0.218499	−	0.378451i
$927$	−4.41006	+	7.63845i	−0.144845	+	0.250880i
$928$	−4.25501	+	7.36989i	−0.139678	+	0.241929i
$929$	17.8753	+	30.9610i	0.586470	+	1.01580i	0.994690	+	0.102913i	$0.0328162\pi$
$929$	17.8753	+	30.9610i	0.586470	+	1.01580i	−0.408220	+	0.912883i	$0.633850\pi$
$930$	−15.4874			−0.507853
$931$	25.2784	−	0.208909i	0.828466	−	0.00684670i
$932$	1.68348			0.0551441
$933$	−4.52139	−	7.83127i	−0.148024	−	0.256384i
$934$	−14.6868	+	25.4382i	−0.480565	+	0.832364i
$935$	0.136034	−	0.235618i	0.00444879	−	0.00770552i
$936$	1.98318	+	3.43497i	0.0648223	+	0.112276i
$937$	−43.8725			−1.43325			−0.716626	−	0.697457i	$-0.754315\pi$
$937$	−43.8725			−1.43325			−0.716626	+	0.697457i	$0.754315\pi$
$938$	42.6026	−	24.8319i	1.39102	−	0.810790i
$939$	−16.1768			−0.527911
$940$	0.804989	+	1.39428i	0.0262558	+	0.0454764i
$941$	−14.4501	+	25.0284i	−0.471061	+	0.815902i	−0.999452	−	0.0330992i	$-0.989462\pi$
$941$	−14.4501	+	25.0284i	−0.471061	+	0.815902i	0.528391	+	0.849001i	$0.322796\pi$
$942$	−11.5683	+	20.0369i	−0.376916	+	0.652838i
$943$	−29.1682	−	50.5209i	−0.949848	−	1.64519i
$944$	−22.3529			−0.727524
$945$	−5.35868	−	3.06438i	−0.174318	−	0.0996844i
$946$	−6.34374			−0.206253
$947$	−1.49022	−	2.58113i	−0.0484256	−	0.0838756i	0.840797	−	0.541351i	$-0.182087\pi$
$947$	−1.49022	−	2.58113i	−0.0484256	−	0.0838756i	−0.889222	+	0.457476i	$0.848754\pi$
$948$	−2.14733	+	3.71928i	−0.0697420	+	0.120797i
$949$	8.02915	−	13.9069i	0.260637	−	0.451437i
$950$	−1.21504	−	2.10452i	−0.0394212	−	0.0682796i
$951$	−5.23370			−0.169714
$952$	0.00328666	+	0.795401i	0.000106521	+	0.0257791i
$953$	−31.6198			−1.02427			−0.512134	−	0.858906i	$-0.671145\pi$
$953$	−31.6198			−1.02427			−0.512134	+	0.858906i	$0.671145\pi$
$954$	−9.01373	−	15.6122i	−0.291830	−	0.505465i
$955$	−19.1432	+	33.1570i	−0.619460	+	1.07294i
$956$	−1.80238	+	3.12182i	−0.0582932	+	0.100967i
$957$	2.52751	+	4.37778i	0.0817029	+	0.141514i
$958$	−36.6997			−1.18571
$959$	−0.175864	−	42.5605i	−0.00567893	−	1.37435i
$960$	−15.0884			−0.486977
$961$	5.92136	+	10.2561i	0.191012	+	0.330842i
$962$	0.349993	−	0.606205i	0.0112842	−	0.0195448i
$963$	−5.24207	+	9.07954i	−0.168923	+	0.292584i
$964$	3.11005	+	5.38676i	0.100168	+	0.173496i
$965$	−48.1876			−1.55121
$966$	−24.7656	−	14.1623i	−0.796820	−	0.455664i
$967$	24.3425			0.782803			0.391402	−	0.920220i	$-0.371990\pi$
$967$	24.3425			0.782803			0.391402	+	0.920220i	$0.371990\pi$
$968$	−1.28908	−	2.23276i	−0.0414327	−	0.0717635i
$969$	−0.210556	+	0.364693i	−0.00676402	+	0.0117156i
$970$	29.0330	−	50.2867i	0.932195	−	1.61461i
$971$	−2.10349	−	3.64335i	−0.0675042	−	0.116921i	0.830298	−	0.557320i	$-0.188170\pi$
$971$	−2.10349	−	3.64335i	−0.0675042	−	0.116921i	−0.897802	+	0.440399i	$0.854837\pi$
$972$	0.300014			0.00962296
$973$	32.6709	−	19.0430i	1.04738	−	0.610490i
$974$	32.1798			1.03111
$975$	0.341305	+	0.591157i	0.0109305	+	0.0189322i
$976$	−10.3090	+	17.8557i	−0.329983	+	0.571548i
$977$	3.41912	−	5.92209i	0.109387	−	0.189464i	−0.806135	−	0.591732i	$-0.798444\pi$
$977$	3.41912	−	5.92209i	0.109387	−	0.189464i	0.915522	+	0.402267i	$0.131778\pi$
$978$	0.318962	+	0.552458i	0.0101993	+	0.0176657i
$979$	−13.9327			−0.445292
$980$	−2.41480	+	4.26354i	−0.0771379	+	0.136194i
$981$	10.5279			0.336129
$982$	−21.3867	−	37.0428i	−0.682477	−	1.18208i
$983$	−8.72313	+	15.1089i	−0.278224	+	0.481899i	−0.970944	−	0.239309i	$-0.923079\pi$
$983$	−8.72313	+	15.1089i	−0.278224	+	0.481899i	0.692719	+	0.721208i	$0.256413\pi$
$984$	−10.5767	+	18.3193i	−0.337171	+	0.583998i
$985$	30.6966	+	53.1681i	0.978075	+	1.69408i
$986$	0.893961			0.0284695
$987$	−5.25738	+	3.06438i	−0.167344	+	0.0975404i
$988$	1.66683			0.0530288
$989$	14.8704	+	25.7563i	0.472852	+	0.819003i
$990$	1.76922	−	3.06438i	0.0562296	−	0.0973925i
$991$	−13.6551	+	23.6512i	−0.433767	+	0.751307i	−0.997194	−	0.0748592i	$-0.976149\pi$
$991$	−13.6551	+	23.6512i	−0.433767	+	0.751307i	0.563427	+	0.826166i	$0.309483\pi$
$992$	3.68421	+	6.38124i	0.116974	+	0.202605i
$993$	−19.5302			−0.619772
$994$	−14.8254	−	8.47797i	−0.470233	−	0.268905i
$995$	25.6896			0.814414
$996$	1.67812	+	2.90659i	0.0531733	+	0.0920988i
$997$	15.2156	−	26.3542i	0.481883	−	0.834646i	−0.517901	−	0.855441i	$-0.673286\pi$
$997$	15.2156	−	26.3542i	0.481883	−	0.834646i	0.999784	+	0.0207947i	$0.00661962\pi$
$998$	−26.9178	+	46.6230i	−0.852068	+	1.47582i
$999$	0.150007	+	0.259820i	0.00474602	+	0.00822034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.e.67.4	✓	8
3.2	odd	2		693.2.i.i.298.1		8
7.2	even	3	inner	231.2.i.e.100.4	yes	8
7.3	odd	6		1617.2.a.x.1.1		4
7.4	even	3		1617.2.a.z.1.1		4
21.2	odd	6		693.2.i.i.100.1		8
21.11	odd	6		4851.2.a.bt.1.4		4
21.17	even	6		4851.2.a.bu.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.4	✓	8	1.1	even	1	trivial
231.2.i.e.100.4	yes	8	7.2	even	3	inner
693.2.i.i.100.1		8	21.2	odd	6
693.2.i.i.298.1		8	3.2	odd	2
1617.2.a.x.1.1		4	7.3	odd	6
1617.2.a.z.1.1		4	7.4	even	3
4851.2.a.bt.1.4		4	21.11	odd	6
4851.2.a.bu.1.4		4	21.17	even	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)

\(f(q)\)	\(=\)	\(q+(0.758290 + 1.31340i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.150007 + 0.259820i) q^{4} +(1.16659 + 2.02059i) q^{5} -1.51658 q^{6} +(-2.28580 + 1.33233i) q^{7} +2.57816 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.758290 + 1.31340i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.150007 + 0.259820i) q^{4} +(1.16659 + 2.02059i) q^{5} -1.51658 q^{6} +(-2.28580 + 1.33233i) q^{7} +2.57816 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.76922 + 3.06438i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.150007 - 0.259820i) q^{12} -1.53844 q^{13} +(-3.48318 - 1.99187i) q^{14} -2.33317 q^{15} +(2.25501 + 3.90579i) q^{16} +(0.0583043 - 0.100986i) q^{17} +(0.758290 - 1.31340i) q^{18} +(1.80566 + 3.12750i) q^{19} -0.699986 q^{20} +(-0.0109324 - 2.64573i) q^{21} +1.51658 q^{22} +(-3.55502 - 6.15748i) q^{23} +(-1.28908 + 2.23276i) q^{24} +(-0.221850 + 0.384256i) q^{25} +(-1.16659 - 2.02059i) q^{26} +1.00000 q^{27} +(-0.00327987 - 0.793757i) q^{28} +5.05502 q^{29} +(-1.76922 - 3.06438i) q^{30} +(2.18845 - 3.79051i) q^{31} +(-0.841739 + 1.45793i) q^{32} +(0.500000 + 0.866025i) q^{33} +0.176846 q^{34} +(-5.35868 - 3.06438i) q^{35} +0.300014 q^{36} +(0.150007 + 0.259820i) q^{37} +(-2.73843 + 4.74310i) q^{38} +(0.769222 - 1.33233i) q^{39} +(3.00765 + 5.20941i) q^{40} +8.20479 q^{41} +(3.46660 - 2.02059i) q^{42} -4.18293 q^{43} +(0.150007 + 0.259820i) q^{44} +(1.16659 - 2.02059i) q^{45} +(5.39148 - 9.33831i) q^{46} +(-1.15001 - 1.99187i) q^{47} -4.51002 q^{48} +(3.44978 - 6.09089i) q^{49} -0.672908 q^{50} +(0.0583043 + 0.100986i) q^{51} +(0.230778 - 0.399719i) q^{52} +(5.94346 - 10.2944i) q^{53} +(0.758290 + 1.31340i) q^{54} +2.33317 q^{55} +(-5.89317 + 3.43497i) q^{56} -3.61132 q^{57} +(3.83317 + 6.63925i) q^{58} +(-2.47814 + 4.29226i) q^{59} +(0.349993 - 0.606205i) q^{60} +(2.28580 + 3.95913i) q^{61} +6.63792 q^{62} +(2.29673 + 1.31340i) q^{63} +6.46691 q^{64} +(-1.79473 - 3.10856i) q^{65} +(-0.758290 + 1.31340i) q^{66} +(-6.14472 + 10.6430i) q^{67} +(0.0174921 + 0.0302972i) q^{68} +7.11005 q^{69} +(-0.0386836 - 9.36176i) q^{70} +4.25628 q^{71} +(-1.28908 - 2.23276i) q^{72} +(-5.21900 + 9.03958i) q^{73} +(-0.227498 + 0.394038i) q^{74} +(-0.221850 - 0.384256i) q^{75} -1.08345 q^{76} +(0.0109324 + 2.64573i) q^{77} +2.33317 q^{78} +(-7.15742 - 12.3970i) q^{79} +(-5.26133 + 9.11289i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.22161 + 10.7761i) q^{82} -11.1869 q^{83} +(0.689053 + 0.394038i) q^{84} +0.272068 q^{85} +(-3.17187 - 5.49384i) q^{86} +(-2.52751 + 4.37778i) q^{87} +(1.28908 - 2.23276i) q^{88} +(-6.96636 - 12.0661i) q^{89} +3.53844 q^{90} +(3.51658 - 2.04972i) q^{91} +2.13312 q^{92} +(2.18845 + 3.79051i) q^{93} +(1.74408 - 3.02083i) q^{94} +(-4.21292 + 7.29700i) q^{95} +(-0.841739 - 1.45793i) q^{96} -16.4101 q^{97} +(10.6157 - 0.0877314i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9} - 10 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 8 q^{15} - 12 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{24} - 4 q^{25} + 4 q^{26} + 8 q^{27} - 22 q^{28} + 16 q^{29} - 10 q^{30} + 12 q^{31} - 26 q^{32} + 4 q^{33} - 32 q^{34} - 2 q^{35} + 8 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} + 4 q^{41} + 20 q^{42} + 36 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} - 12 q^{47} + 24 q^{48} - 4 q^{49} + 4 q^{50} - 2 q^{51} + 6 q^{52} + 12 q^{53} - 2 q^{54} - 8 q^{55} + 48 q^{56} + 4 q^{58} - 12 q^{59} - 2 q^{61} - 52 q^{62} + 2 q^{63} + 112 q^{64} + 4 q^{65} + 2 q^{66} - 28 q^{67} + 48 q^{68} + 8 q^{69} - 32 q^{70} + 24 q^{71} - 12 q^{72} - 6 q^{73} + 16 q^{74} - 4 q^{75} - 36 q^{76} + 4 q^{77} - 8 q^{78} - 2 q^{79} - 16 q^{80} - 4 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{85} - 36 q^{86} - 8 q^{87} + 12 q^{88} - 8 q^{89} + 20 q^{90} + 12 q^{91} - 32 q^{92} + 12 q^{93} - 20 q^{94} - 34 q^{95} - 26 q^{96} - 88 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9 - 10 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^24 - 4 * q^25 + 4 * q^26 + 8 * q^27 - 22 * q^28 + 16 * q^29 - 10 * q^30 + 12 * q^31 - 26 * q^32 + 4 * q^33 - 32 * q^34 - 2 * q^35 + 8 * q^36 + 4 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 + 4 * q^41 + 20 * q^42 + 36 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 - 12 * q^47 + 24 * q^48 - 4 * q^49 + 4 * q^50 - 2 * q^51 + 6 * q^52 + 12 * q^53 - 2 * q^54 - 8 * q^55 + 48 * q^56 + 4 * q^58 - 12 * q^59 - 2 * q^61 - 52 * q^62 + 2 * q^63 + 112 * q^64 + 4 * q^65 + 2 * q^66 - 28 * q^67 + 48 * q^68 + 8 * q^69 - 32 * q^70 + 24 * q^71 - 12 * q^72 - 6 * q^73 + 16 * q^74 - 4 * q^75 - 36 * q^76 + 4 * q^77 - 8 * q^78 - 2 * q^79 - 16 * q^80 - 4 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^85 - 36 * q^86 - 8 * q^87 + 12 * q^88 - 8 * q^89 + 20 * q^90 + 12 * q^91 - 32 * q^92 + 12 * q^93 - 20 * q^94 - 34 * q^95 - 26 * q^96 - 88 * q^97 + 16 * q^98 - 8 * q^99

Introduction

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