LMFDB - Embedded newform 1155.2.q.j.331.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.4
Root			$-0.428252 - 0.741755i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.j.991.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.428252 + 0.741755i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.633200 + 1.09673i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.856504 q^{6} +(-1.20148 - 2.35721i) q^{7} -2.79769 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.428252 + 0.741755i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.633200 + 1.09673i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.856504 q^{6} +(-1.20148 - 2.35721i) q^{7} -2.79769 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.428252 + 0.741755i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.633200 - 1.09673i) q^{12} +0.00203140 q^{13} +(2.26301 + 0.118273i) q^{14} -1.00000 q^{15} +(-0.0682849 + 0.118273i) q^{16} +(2.26640 + 3.92552i) q^{17} +(-0.428252 - 0.741755i) q^{18} +(0.807926 - 1.39937i) q^{19} +1.26640 q^{20} +(-1.44066 + 2.21912i) q^{21} -0.856504 q^{22} +(2.47548 - 4.28766i) q^{23} +(1.39884 + 2.42287i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.000869950 + 0.00150680i) q^{26} +1.00000 q^{27} +(1.82445 - 2.81030i) q^{28} +6.32416 q^{29} +(0.428252 - 0.741755i) q^{30} +(-3.33950 - 5.78419i) q^{31} +(-2.85617 - 4.94704i) q^{32} +(0.500000 - 0.866025i) q^{33} -3.88236 q^{34} +(-2.64215 - 0.138088i) q^{35} -1.26640 q^{36} +(5.72820 - 9.92153i) q^{37} +(0.691993 + 1.19857i) q^{38} +(-0.00101570 - 0.00175924i) q^{39} +(-1.39884 + 2.42287i) q^{40} +9.43955 q^{41} +(-1.02908 - 2.01896i) q^{42} -3.08417 q^{43} +(-0.633200 + 1.09673i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.12026 + 3.67240i) q^{46} +(1.73875 - 3.01160i) q^{47} +0.136570 q^{48} +(-4.11287 + 5.66430i) q^{49} +0.856504 q^{50} +(2.26640 - 3.92552i) q^{51} +(0.00128628 + 0.00222790i) q^{52} +(-4.90692 - 8.49903i) q^{53} +(-0.428252 + 0.741755i) q^{54} +1.00000 q^{55} +(3.36138 + 6.59473i) q^{56} -1.61585 q^{57} +(-2.70833 + 4.69097i) q^{58} +(4.02073 + 6.96411i) q^{59} +(-0.633200 - 1.09673i) q^{60} +(2.48428 - 4.30290i) q^{61} +5.72060 q^{62} +(2.64215 + 0.138088i) q^{63} +4.61951 q^{64} +(0.00101570 - 0.00175924i) q^{65} +(0.428252 + 0.741755i) q^{66} +(-7.55136 - 13.0793i) q^{67} +(-2.87017 + 4.97128i) q^{68} -4.95097 q^{69} +(1.23393 - 1.90069i) q^{70} -6.69420 q^{71} +(1.39884 - 2.42287i) q^{72} +(1.36370 + 2.36199i) q^{73} +(4.90623 + 8.49783i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.04632 q^{76} +(1.44066 - 2.21912i) q^{77} +0.00173990 q^{78} +(2.09778 - 3.63345i) q^{79} +(0.0682849 + 0.118273i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.04251 + 7.00183i) q^{82} +4.95556 q^{83} +(-3.34601 - 0.174875i) q^{84} +4.53280 q^{85} +(1.32080 - 2.28770i) q^{86} +(-3.16208 - 5.47688i) q^{87} +(-1.39884 - 2.42287i) q^{88} +(1.20900 - 2.09405i) q^{89} -0.856504 q^{90} +(-0.00244069 - 0.00478842i) q^{91} +6.26990 q^{92} +(-3.33950 + 5.78419i) q^{93} +(1.48925 + 2.57945i) q^{94} +(-0.807926 - 1.39937i) q^{95} +(-2.85617 + 4.94704i) q^{96} +11.0874 q^{97} +(-2.44018 - 5.47649i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.428252	+	0.741755i	−0.302820	+	0.524500i	−0.976774	−	0.214274i	$-0.931261\pi$
$2$	−0.428252	+	0.741755i	−0.302820	+	0.524500i	0.673954	+	0.738774i	$0.264595\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.633200	+	1.09673i	0.316600	+	0.548367i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.856504			0.349666
$7$	−1.20148	−	2.35721i	−0.454119	−	0.890941i
$7$	−1.20148	−	2.35721i	−0.454119	−	0.890941i
$8$	−2.79769			−0.989131
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.428252	+	0.741755i	0.135425	+	0.234563i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.633200	−	1.09673i	0.182789	−	0.316600i
$13$	0.00203140			0.000563408			0.000281704	−	1.00000i	$-0.499910\pi$
$13$	0.00203140			0.000563408			0.000281704		1.00000i	$0.499910\pi$
$14$	2.26301	+	0.118273i	0.604815	+	0.0316098i
$15$	−1.00000			−0.258199
$16$	−0.0682849	+	0.118273i	−0.0170712	+	0.0295682i
$17$	2.26640	+	3.92552i	0.549683	+	0.952079i	0.998296	+	0.0583525i	$0.0185847\pi$
$17$	2.26640	+	3.92552i	0.549683	+	0.952079i	−0.448613	+	0.893726i	$0.648082\pi$
$18$	−0.428252	−	0.741755i	−0.100940	−	0.174833i
$19$	0.807926	−	1.39937i	0.185351	−	0.321037i	−0.758344	−	0.651855i	$-0.773991\pi$
$19$	0.807926	−	1.39937i	0.185351	−	0.321037i	0.943695	+	0.330817i	$0.107324\pi$
$20$	1.26640			0.283176
$21$	−1.44066	+	2.21912i	−0.314378	+	0.484252i
$22$	−0.856504			−0.182607
$23$	2.47548	−	4.28766i	0.516174	−	0.894039i	−0.483650	−	0.875262i	$-0.660689\pi$
$23$	2.47548	−	4.28766i	0.516174	−	0.894039i	0.999824	−	0.0187777i	$-0.00597748\pi$
$24$	1.39884	+	2.42287i	0.285538	+	0.494566i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.000869950		0.00150680i	−0.000170611		0.000295507i
$27$	1.00000			0.192450
$28$	1.82445	−	2.81030i	0.344789	−	0.531096i
$29$	6.32416			1.17437			0.587183	−	0.809454i	$-0.300237\pi$
$29$	6.32416			1.17437			0.587183	+	0.809454i	$0.300237\pi$
$30$	0.428252	−	0.741755i	0.0781878	−	0.135425i
$31$	−3.33950	−	5.78419i	−0.599793	−	1.03887i	−0.992851	−	0.119358i	$-0.961916\pi$
$31$	−3.33950	−	5.78419i	−0.599793	−	1.03887i	0.393059	−	0.919513i	$-0.371417\pi$
$32$	−2.85617	−	4.94704i	−0.504905	−	0.874521i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−3.88236			−0.665820
$35$	−2.64215	−	0.138088i	−0.446604	−	0.0233411i
$36$	−1.26640			−0.211067
$37$	5.72820	−	9.92153i	0.941710	−	1.63109i	0.179501	−	0.983758i	$-0.442552\pi$
$37$	5.72820	−	9.92153i	0.941710	−	1.63109i	0.762209	−	0.647331i	$-0.224115\pi$
$38$	0.691993	+	1.19857i	0.112256	+	0.194433i
$39$	−0.00101570	−	0.00175924i	−0.000162642	−	0.000281704i
$40$	−1.39884	+	2.42287i	−0.221177	+	0.383089i
$41$	9.43955			1.47421			0.737105	−	0.675778i	$-0.236192\pi$
$41$	9.43955			1.47421			0.737105	+	0.675778i	$0.236192\pi$
$42$	−1.02908	−	2.01896i	−0.158790	−	0.311532i
$43$	−3.08417			−0.470332			−0.235166	−	0.971955i	$-0.575563\pi$
$43$	−3.08417			−0.470332			−0.235166	+	0.971955i	$0.575563\pi$
$44$	−0.633200	+	1.09673i	−0.0954585	+	0.165339i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	2.12026	+	3.67240i	0.312616	+	0.541466i
$47$	1.73875	−	3.01160i	0.253623	−	0.439288i	−0.710898	−	0.703295i	$-0.751711\pi$
$47$	1.73875	−	3.01160i	0.253623	−	0.439288i	0.964521	+	0.264008i	$0.0850445\pi$
$48$	0.136570			0.0197122
$49$	−4.11287	+	5.66430i	−0.587553	+	0.809186i
$50$	0.856504			0.121128
$51$	2.26640	−	3.92552i	0.317360	−	0.549683i
$52$	0.00128628	+	0.00222790i	0.000178375	+	0.000308954i
$53$	−4.90692	−	8.49903i	−0.674017	−	1.16743i	−0.976755	−	0.214358i	$-0.931234\pi$
$53$	−4.90692	−	8.49903i	−0.674017	−	1.16743i	0.302738	−	0.953074i	$-0.402099\pi$
$54$	−0.428252	+	0.741755i	−0.0582777	+	0.100940i
$55$	1.00000			0.134840
$56$	3.36138	+	6.59473i	0.449183	+	0.881258i
$57$	−1.61585			−0.214025
$58$	−2.70833	+	4.69097i	−0.355622	+	0.615955i
$59$	4.02073	+	6.96411i	0.523455	+	0.906650i	0.999627	+	0.0272983i	$0.00869041\pi$
$59$	4.02073	+	6.96411i	0.523455	+	0.906650i	−0.476173	+	0.879352i	$0.657976\pi$
$60$	−0.633200	−	1.09673i	−0.0817458	−	0.141588i
$61$	2.48428	−	4.30290i	0.318080	−	0.550930i	−0.662008	−	0.749497i	$-0.730295\pi$
$61$	2.48428	−	4.30290i	0.318080	−	0.550930i	0.980087	+	0.198567i	$0.0636287\pi$
$62$	5.72060			0.726517
$63$	2.64215	+	0.138088i	0.332879	+	0.0173974i
$64$	4.61951			0.577439
$65$	0.00101570	−	0.00175924i	0.000125982	−	0.000218207i
$66$	0.428252	+	0.741755i	0.0527142	+	0.0913037i
$67$	−7.55136	−	13.0793i	−0.922546	−	1.59790i	−0.795461	−	0.606004i	$-0.792771\pi$
$67$	−7.55136	−	13.0793i	−0.922546	−	1.59790i	−0.127084	−	0.991892i	$-0.540562\pi$
$68$	−2.87017	+	4.97128i	−0.348059	+	0.602856i
$69$	−4.95097			−0.596026
$70$	1.23393	−	1.90069i	0.147483	−	0.227176i
$71$	−6.69420			−0.794456			−0.397228	−	0.917720i	$-0.630028\pi$
$71$	−6.69420			−0.794456			−0.397228	+	0.917720i	$0.630028\pi$
$72$	1.39884	−	2.42287i	0.164855	−	0.285538i
$73$	1.36370	+	2.36199i	0.159609	+	0.276451i	0.934728	−	0.355365i	$-0.115643\pi$
$73$	1.36370	+	2.36199i	0.159609	+	0.276451i	−0.775119	+	0.631815i	$0.782310\pi$
$74$	4.90623	+	8.49783i	0.570337	+	0.987853i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	2.04632			0.234729
$77$	1.44066	−	2.21912i	0.164178	−	0.252892i
$78$	0.00173990			0.000197005
$79$	2.09778	−	3.63345i	0.236018	−	0.408795i	−0.723550	−	0.690272i	$-0.757491\pi$
$79$	2.09778	−	3.63345i	0.236018	−	0.408795i	0.959568	+	0.281477i	$0.0908242\pi$
$80$	0.0682849	+	0.118273i	0.00763448	+	0.0132233i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.04251	+	7.00183i	−0.446421	+	0.773223i
$83$	4.95556			0.543944			0.271972	−	0.962305i	$-0.412324\pi$
$83$	4.95556			0.543944			0.271972	+	0.962305i	$0.412324\pi$
$84$	−3.34601	−	0.174875i	−0.365080	−	0.0190804i
$85$	4.53280			0.491651
$86$	1.32080	−	2.28770i	0.142426	−	0.246689i
$87$	−3.16208	−	5.47688i	−0.339010	−	0.587183i
$88$	−1.39884	−	2.42287i	−0.149117	−	0.258279i
$89$	1.20900	−	2.09405i	0.128154	−	0.221969i	−0.794807	−	0.606862i	$-0.792428\pi$
$89$	1.20900	−	2.09405i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$90$	−0.856504			−0.0902835
$91$	−0.00244069	−	0.00478842i	−0.000255854	−	0.000501963i
$92$	6.26990			0.653683
$93$	−3.33950	+	5.78419i	−0.346290	+	0.599793i
$94$	1.48925	+	2.57945i	0.153604	+	0.266050i
$95$	−0.807926	−	1.39937i	−0.0828915	−	0.143572i
$96$	−2.85617	+	4.94704i	−0.291507	+	0.504905i
$97$	11.0874			1.12576			0.562879	−	0.826540i	$-0.309694\pi$
$97$	11.0874			1.12576			0.562879	+	0.826540i	$0.309694\pi$
$98$	−2.44018	−	5.47649i	−0.246495	−	0.553209i
$99$	−1.00000			−0.100504
$100$	0.633200	−	1.09673i	0.0633200	−	0.109673i
$101$	4.10027	+	7.10188i	0.407993	+	0.706664i	0.994665	−	0.103161i	$-0.0328956\pi$
$101$	4.10027	+	7.10188i	0.407993	+	0.706664i	−0.586672	+	0.809825i	$0.699562\pi$
$102$	1.94118	+	3.36223i	0.192206	+	0.332910i
$103$	−5.96091	+	10.3246i	−0.587346	+	1.01731i	0.407232	+	0.913325i	$0.366494\pi$
$103$	−5.96091	+	10.3246i	−0.587346	+	1.01731i	−0.994578	+	0.103989i	$0.966839\pi$
$104$	−0.00568321			−0.000557284
$105$	1.20148	+	2.35721i	0.117253	+	0.230040i
$106$	8.40559			0.816424
$107$	2.95839	−	5.12409i	0.285999	−	0.495364i	−0.686852	−	0.726797i	$-0.741008\pi$
$107$	2.95839	−	5.12409i	0.285999	−	0.495364i	0.972851	+	0.231433i	$0.0743414\pi$
$108$	0.633200	+	1.09673i	0.0609297	+	0.105533i
$109$	−2.09810	−	3.63401i	−0.200961	−	0.348075i	0.747877	−	0.663837i	$-0.231073\pi$
$109$	−2.09810	−	3.63401i	−0.200961	−	0.348075i	−0.948838	+	0.315762i	$0.897740\pi$
$110$	−0.428252	+	0.741755i	−0.0408322	+	0.0707235i
$111$	−11.4564			−1.08739
$112$	0.360837	+	0.0188586i	0.0340959	+	0.00178197i
$113$	16.2876			1.53220			0.766102	−	0.642718i	$-0.222193\pi$
$113$	16.2876			1.53220			0.766102	+	0.642718i	$0.222193\pi$
$114$	0.691993	−	1.19857i	0.0648110	−	0.112256i
$115$	−2.47548	−	4.28766i	−0.230840	−	0.399827i
$116$	4.00446	+	6.93592i	0.371805	+	0.643984i
$117$	−0.00101570	+	0.00175924i	−9.39013e−5	+	0.000162642i
$118$	−6.88755			−0.634050
$119$	6.53023	−	10.0588i	0.598625	−	0.922092i
$120$	2.79769			0.255393
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.12780	+	3.68546i	0.192642	+	0.333666i
$123$	−4.71978	−	8.17489i	−0.425568	−	0.737105i
$124$	4.22915	−	7.32510i	0.379789	−	0.657813i
$125$	−1.00000			−0.0894427
$126$	−1.23393	+	1.90069i	−0.109927	+	0.169327i
$127$	12.1648			1.07945			0.539725	−	0.841841i	$-0.318528\pi$
$127$	12.1648			1.07945			0.539725	+	0.841841i	$0.318528\pi$
$128$	3.73403	−	6.46753i	0.330045	−	0.571654i
$129$	1.54209	+	2.67097i	0.135773	+	0.235166i
$130$	0.000869950		0.00150680i	7.62996e−5		0.000132155i
$131$	−10.1129	+	17.5160i	−0.883566	+	1.53038i	−0.0362176	+	0.999344i	$0.511531\pi$
$131$	−10.1129	+	17.5160i	−0.883566	+	1.53038i	−0.847348	+	0.531037i	$0.821802\pi$
$132$	1.26640			0.110226
$133$	−4.26932	−	0.223130i	−0.370197	−	0.0193478i
$134$	12.9356			1.11746
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−6.34068	−	10.9824i	−0.543709	−	0.941731i
$137$	1.71327	+	2.96747i	0.146375	+	0.253528i	0.929885	−	0.367851i	$-0.119906\pi$
$137$	1.71327	+	2.96747i	0.146375	+	0.253528i	−0.783510	+	0.621379i	$0.786573\pi$
$138$	2.12026	−	3.67240i	0.180489	−	0.312616i
$139$	16.0857			1.36437			0.682185	−	0.731180i	$-0.261030\pi$
$139$	16.0857			1.36437			0.682185	+	0.731180i	$0.261030\pi$
$140$	−1.52156	−	2.98517i	−0.128595	−	0.252293i
$141$	−3.47750			−0.292858
$142$	2.86681	−	4.96545i	0.240577	−	0.416692i
$143$	0.00101570	+	0.00175924i	8.49369e−5	+	0.000147115i
$144$	−0.0682849	−	0.118273i	−0.00569041	−	0.00985608i
$145$	3.16208	−	5.47688i	0.262596	−	0.454830i
$146$	−2.33603			−0.193331
$147$	6.96186	+	0.729697i	0.574205	+	0.0601844i
$148$	14.5084			1.19258
$149$	0.120465	−	0.208652i	0.00986888	−	0.0170934i	−0.861049	−	0.508522i	$-0.830192\pi$
$149$	0.120465	−	0.208652i	0.00986888	−	0.0170934i	0.870918	+	0.491429i	$0.163525\pi$
$150$	−0.428252	−	0.741755i	−0.0349666	−	0.0605640i
$151$	−6.17352	−	10.6929i	−0.502394	−	0.870172i	−0.999996	−	0.00276665i	$-0.999119\pi$
$151$	−6.17352	−	10.6929i	−0.502394	−	0.870172i	0.497602	−	0.867405i	$-0.334214\pi$
$152$	−2.26032	+	3.91500i	−0.183337	+	0.317548i
$153$	−4.53280			−0.366455
$154$	1.02908	+	2.01896i	0.0829254	+	0.162692i
$155$	−6.67901			−0.536471
$156$	0.00128628	−	0.00222790i	0.000102985	−	0.000178375i
$157$	−10.2826	−	17.8100i	−0.820639	−	1.42139i	−0.905207	−	0.424971i	$-0.860284\pi$
$157$	−10.2826	−	17.8100i	−0.820639	−	1.42139i	0.0845677	−	0.996418i	$-0.473049\pi$
$158$	1.79675	+	3.11207i	0.142942	+	0.247583i
$159$	−4.90692	+	8.49903i	−0.389144	+	0.674017i
$160$	−5.71235			−0.451601
$161$	−13.0812	−	0.683669i	−1.03094	−	0.0538806i
$162$	0.856504			0.0672933
$163$	−8.05837	+	13.9575i	−0.631180	+	1.09324i	0.356131	+	0.934436i	$0.384096\pi$
$163$	−8.05837	+	13.9575i	−0.631180	+	1.09324i	−0.987311	+	0.158800i	$0.949238\pi$
$164$	5.97713	+	10.3527i	0.466735	+	0.808409i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	−2.12223	+	3.67581i	−0.164717	+	0.285298i
$167$	5.29444			0.409696			0.204848	−	0.978794i	$-0.434330\pi$
$167$	5.29444			0.409696			0.204848	+	0.978794i	$0.434330\pi$
$168$	4.03052	−	6.20840i	0.310961	−	0.478989i
$169$	−13.0000			−1.00000
$170$	−1.94118	+	3.36223i	−0.148882	+	0.257871i
$171$	0.807926	+	1.39937i	0.0617837	+	0.107012i
$172$	−1.95290	−	3.38252i	−0.148907	−	0.257914i
$173$	−10.4808	+	18.1533i	−0.796842	+	1.38017i	0.124821	+	0.992179i	$0.460164\pi$
$173$	−10.4808	+	18.1533i	−0.796842	+	1.38017i	−0.921663	+	0.387992i	$0.873169\pi$
$174$	5.41667			0.410637
$175$	−1.44066	+	2.21912i	−0.108904	+	0.167750i
$176$	−0.136570			−0.0102943
$177$	4.02073	−	6.96411i	0.302217	−	0.523455i
$178$	1.03552	+	1.79356i	0.0776151	+	0.134433i
$179$	8.82441	+	15.2843i	0.659567	+	1.14240i	0.980728	+	0.195380i	$0.0625939\pi$
$179$	8.82441	+	15.2843i	0.659567	+	1.14240i	−0.321160	+	0.947025i	$0.604073\pi$
$180$	−0.633200	+	1.09673i	−0.0471959	+	0.0817458i
$181$	−13.6214			−1.01247			−0.506237	−	0.862394i	$-0.668964\pi$
$181$	−13.6214			−1.01247			−0.506237	+	0.862394i	$0.668964\pi$
$182$	0.00459707		0.000240259i	0.000340757		1.78092e-5i
$183$	−4.96857			−0.367287
$184$	−6.92562	+	11.9955i	−0.510564	+	0.884322i
$185$	−5.72820	−	9.92153i	−0.421145	−	0.729445i
$186$	−2.86030	−	4.95418i	−0.209727	−	0.363258i
$187$	−2.26640	+	3.92552i	−0.165736	+	0.287062i
$188$	4.40391			0.321188
$189$	−1.20148	−	2.35721i	−0.0873952	−	0.171462i
$190$	1.38399			0.100405
$191$	6.31896	−	10.9448i	0.457224	−	0.791935i	−0.541589	−	0.840643i	$-0.682177\pi$
$191$	6.31896	−	10.9448i	0.457224	−	0.791935i	0.998813	+	0.0487086i	$0.0155106\pi$
$192$	−2.30975	−	4.00061i	−0.166692	−	0.288719i
$193$	7.43052	+	12.8700i	0.534860	+	0.926405i	0.999170	+	0.0407325i	$0.0129691\pi$
$193$	7.43052	+	12.8700i	0.534860	+	0.926405i	−0.464310	+	0.885673i	$0.653698\pi$
$194$	−4.74821	+	8.22415i	−0.340902	+	0.590459i
$195$	−0.00203140			−0.000145471
$196$	−8.81651	−	0.924088i	−0.629750	−	0.0660063i
$197$	−3.49977			−0.249348			−0.124674	−	0.992198i	$-0.539789\pi$
$197$	−3.49977			−0.249348			−0.124674	+	0.992198i	$0.539789\pi$
$198$	0.428252	−	0.741755i	0.0304346	−	0.0527142i
$199$	−11.5304	−	19.9713i	−0.817369	−	1.41573i	−0.907614	−	0.419806i	$-0.862098\pi$
$199$	−11.5304	−	19.9713i	−0.817369	−	1.41573i	0.0902448	−	0.995920i	$-0.471235\pi$
$200$	1.39884	+	2.42287i	0.0989131	+	0.171323i
$201$	−7.55136	+	13.0793i	−0.532632	+	0.922546i
$202$	−7.02381			−0.494193
$203$	−7.59838	−	14.9074i	−0.533302	−	1.04629i
$204$	5.74034			0.401904
$205$	4.71978	−	8.17489i	0.329644	−	0.570959i
$206$	−5.10555	−	8.84307i	−0.355721	−	0.616126i
$207$	2.47548	+	4.28766i	0.172058	+	0.298013i
$208$	−0.000138714	0	0.000240259i	−9.61806e−6	0	1.66590e-5i
$209$	1.61585			0.111771
$210$	−2.26301	−	0.118273i	−0.156162	−	0.00816161i
$211$	−2.26357			−0.155831			−0.0779153	−	0.996960i	$-0.524826\pi$
$211$	−2.26357			−0.155831			−0.0779153	+	0.996960i	$0.524826\pi$
$212$	6.21412	−	10.7632i	0.426788	−	0.739218i
$213$	3.34710	+	5.79735i	0.229340	+	0.397228i
$214$	2.53388	+	4.38880i	0.173212	+	0.300012i
$215$	−1.54209	+	2.67097i	−0.105169	+	0.182159i
$216$	−2.79769			−0.190358
$217$	−9.62218	+	14.8215i	−0.653196	+	1.00615i
$218$	3.59406			0.243420
$219$	1.36370	−	2.36199i	0.0921502	−	0.159609i
$220$	0.633200	+	1.09673i	0.0426903	+	0.0739418i
$221$	0.00460396	+	0.00797429i	0.000309696	+	0.000536408i
$222$	4.90623	−	8.49783i	0.329284	−	0.570337i
$223$	2.45353			0.164300			0.0821501	−	0.996620i	$-0.473821\pi$
$223$	2.45353			0.164300			0.0821501	+	0.996620i	$0.473821\pi$
$224$	−8.22955	+	12.6764i	−0.549860	+	0.846977i
$225$	1.00000			0.0666667
$226$	−6.97518	+	12.0814i	−0.463982	+	0.803641i
$227$	0.261640	+	0.453174i	0.0173657	+	0.0300782i	0.874578	−	0.484886i	$-0.161139\pi$
$227$	0.261640	+	0.453174i	0.0173657	+	0.0300782i	−0.857212	+	0.514964i	$0.827805\pi$
$228$	−1.02316	−	1.77216i	−0.0677603	−	0.117364i
$229$	−8.68605	+	15.0447i	−0.573990	+	0.994181i	0.422160	+	0.906521i	$0.361272\pi$
$229$	−8.68605	+	15.0447i	−0.573990	+	0.994181i	−0.996151	+	0.0876594i	$0.972061\pi$
$230$	4.24052			0.279612
$231$	−2.64215	−	0.138088i	−0.173840	−	0.00908552i
$232$	−17.6930			−1.16160
$233$	−12.5955	+	21.8160i	−0.825158	+	1.42921i	0.0766413	+	0.997059i	$0.475580\pi$
$233$	−12.5955	+	21.8160i	−0.825158	+	1.42921i	−0.901799	+	0.432156i	$0.857753\pi$
$234$	−0.000869950	−	0.00150680i	−5.68704e−5	−	9.85024e-5i
$235$	−1.73875	−	3.01160i	−0.113424	−	0.196455i
$236$	−5.09186	+	8.81935i	−0.331452	+	0.574091i
$237$	−4.19555			−0.272530
$238$	4.66460	+	9.15154i	0.302361	+	0.593206i
$239$	−27.7599			−1.79564			−0.897820	−	0.440364i	$-0.854850\pi$
$239$	−27.7599			−1.79564			−0.897820	+	0.440364i	$0.854850\pi$
$240$	0.0682849	−	0.118273i	0.00440777	−	0.00763448i
$241$	−0.448019	−	0.775991i	−0.0288594	−	0.0499860i	0.851235	−	0.524785i	$-0.175854\pi$
$241$	−0.448019	−	0.775991i	−0.0288594	−	0.0499860i	−0.880094	+	0.474799i	$0.842521\pi$
$242$	−0.428252	−	0.741755i	−0.0275291	−	0.0476818i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	6.29219			0.402816
$245$	2.84900	+	6.39400i	0.182016	+	0.408498i
$246$	8.08502			0.515482
$247$	0.00164122	−	0.00284267i	0.000104428	−	0.000180875i
$248$	9.34288	+	16.1823i	0.593274	+	1.02758i
$249$	−2.47778	−	4.29164i	−0.157023	−	0.271972i
$250$	0.428252	−	0.741755i	0.0270850	−	0.0469127i
$251$	17.5716			1.10911			0.554556	−	0.832146i	$-0.312888\pi$
$251$	17.5716			1.10911			0.554556	+	0.832146i	$0.312888\pi$
$252$	1.52156	+	2.98517i	0.0958493	+	0.188048i
$253$	4.95097			0.311265
$254$	−5.20960	+	9.02328i	−0.326879	+	0.566171i
$255$	−2.26640	−	3.92552i	−0.141927	−	0.245826i
$256$	7.81772	+	13.5407i	0.488608	+	0.846293i
$257$	−6.83087	+	11.8314i	−0.426098	+	0.738023i	−0.996522	−	0.0833270i	$-0.973445\pi$
$257$	−6.83087	+	11.8314i	−0.426098	+	0.738023i	0.570424	+	0.821350i	$0.306779\pi$
$258$	−2.64161			−0.164459
$259$	−30.2695	−	1.58199i	−1.88085	−	0.0983000i
$260$	0.00257256			0.000159543
$261$	−3.16208	+	5.47688i	−0.195728	+	0.339010i
$262$	−8.66172	−	15.0025i	−0.535123	−	0.926860i
$263$	−2.70402	−	4.68351i	−0.166737	−	0.288797i	0.770534	−	0.637399i	$-0.219990\pi$
$263$	−2.70402	−	4.68351i	−0.166737	−	0.288797i	−0.937271	+	0.348602i	$0.886656\pi$
$264$	−1.39884	+	2.42287i	−0.0860928	+	0.149117i
$265$	−9.81384			−0.602859
$266$	1.99385	−	3.07123i	0.122251	−	0.188309i
$267$	−2.41800			−0.147979
$268$	9.56305	−	16.5637i	0.584156	−	1.01179i
$269$	5.95101	+	10.3075i	0.362840	+	0.628457i	0.988427	−	0.151698i	$-0.0484740\pi$
$269$	5.95101	+	10.3075i	0.362840	+	0.628457i	−0.625587	+	0.780154i	$0.715141\pi$
$270$	0.428252	+	0.741755i	0.0260626	+	0.0451417i
$271$	6.98707	−	12.1020i	0.424434	−	0.735141i	−0.571933	−	0.820300i	$-0.693806\pi$
$271$	6.98707	−	12.1020i	0.424434	−	0.735141i	0.996367	+	0.0851587i	$0.0271397\pi$
$272$	−0.619044			−0.0375350
$273$	−0.00292655	+	0.00450791i	−0.000177123	+	0.000272831i
$274$	−2.93485			−0.177301
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−3.13495	−	5.42990i	−0.188702	−	0.326841i
$277$	10.4089	+	18.0287i	0.625410	+	1.08324i	0.988462	+	0.151472i	$0.0484014\pi$
$277$	10.4089	+	18.0287i	0.625410	+	1.08324i	−0.363052	+	0.931769i	$0.618265\pi$
$278$	−6.88873	+	11.9316i	−0.413158	+	0.715611i
$279$	6.67901			0.399862
$280$	7.39189	+	0.386327i	0.441750	+	0.0230874i
$281$	11.6968			0.697771			0.348886	−	0.937165i	$-0.386560\pi$
$281$	11.6968			0.697771			0.348886	+	0.937165i	$0.386560\pi$
$282$	1.48925	−	2.57945i	0.0886834	−	0.153604i
$283$	0.619189	+	1.07247i	0.0368070	+	0.0637516i	0.883842	−	0.467785i	$-0.154948\pi$
$283$	0.619189	+	1.07247i	0.0368070	+	0.0637516i	−0.847035	+	0.531537i	$0.821615\pi$
$284$	−4.23877	−	7.34176i	−0.251525	−	0.435654i
$285$	−0.807926	+	1.39937i	−0.0478574	+	0.0828915i
$286$	−0.00173990			−0.000102882
$287$	−11.3415	−	22.2510i	−0.669467	−	1.31344i
$288$	5.71235			0.336603
$289$	−1.77314	+	3.07117i	−0.104302	+	0.180657i
$290$	2.70833	+	4.69097i	0.159039	+	0.275463i
$291$	−5.54371	−	9.60199i	−0.324978	−	0.562879i
$292$	−1.72699	+	2.99123i	−0.101064	+	0.175049i
$293$	−21.3052			−1.24466			−0.622331	−	0.782754i	$-0.713814\pi$
$293$	−21.3052			−1.24466			−0.622331	+	0.782754i	$0.713814\pi$
$294$	−3.52269	+	4.85150i	−0.205447	+	0.282945i
$295$	8.04146			0.468192
$296$	−16.0257	+	27.7573i	−0.931475	+	1.61336i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	0.103179	+	0.178711i	0.00597699	+	0.0103524i
$299$	0.00502868	−	0.00870994i	0.000290816	−	0.000503709i
$300$	−1.26640			−0.0731156
$301$	3.70558	+	7.27003i	0.213586	+	0.419038i
$302$	10.5753			0.608540
$303$	4.10027	−	7.10188i	0.235555	−	0.407993i
$304$	0.110338	+	0.191112i	0.00632834	+	0.0109610i
$305$	−2.48428	−	4.30290i	−0.142250	−	0.246384i
$306$	1.94118	−	3.36223i	0.110970	−	0.192206i
$307$	5.68382			0.324393			0.162196	−	0.986758i	$-0.448142\pi$
$307$	5.68382			0.324393			0.162196	+	0.986758i	$0.448142\pi$
$308$	3.34601	+	0.174875i	0.190657	+	0.00996440i
$309$	11.9218			0.678209
$310$	2.86030	−	4.95418i	0.162454	−	0.281379i
$311$	0.0836645	+	0.144911i	0.00474418	+	0.00821715i	0.868388	−	0.495886i	$-0.165157\pi$
$311$	0.0836645	+	0.144911i	0.00474418	+	0.00821715i	−0.863644	+	0.504103i	$0.831823\pi$
$312$	0.00284160	+	0.00492180i	0.000160874	+	0.000278642i
$313$	−0.385134	+	0.667071i	−0.0217690	+	0.0377051i	−0.876705	−	0.481029i	$-0.840263\pi$
$313$	−0.385134	+	0.667071i	−0.0217690	+	0.0377051i	0.854936	+	0.518734i	$0.173597\pi$
$314$	17.6142			0.994024
$315$	1.44066	−	2.21912i	0.0811720	−	0.125033i
$316$	5.31325			0.298893
$317$	14.8380	−	25.7001i	0.833382	−	1.44346i	−0.0619585	−	0.998079i	$-0.519735\pi$
$317$	14.8380	−	25.7001i	0.833382	−	1.44346i	0.895341	−	0.445382i	$-0.146932\pi$
$318$	−4.20280	−	7.27946i	−0.235681	−	0.408212i
$319$	3.16208	+	5.47688i	0.177042	+	0.306646i
$320$	2.30975	−	4.00061i	0.129119	−	0.223641i
$321$	−5.91679			−0.330243
$322$	6.10915	−	9.41023i	0.340450	−	0.524412i
$323$	7.32434			0.407537
$324$	0.633200	−	1.09673i	0.0351778	−	0.0609297i
$325$	−0.00101570	−	0.00175924i	−5.63408e−5	−	9.75851e-5i
$326$	−6.90203	−	11.9547i	−0.382268	−	0.662108i
$327$	−2.09810	+	3.63401i	−0.116025	+	0.200961i
$328$	−26.4089			−1.45819
$329$	−9.18806	−	0.480201i	−0.506554	−	0.0264743i
$330$	0.856504			0.0471490
$331$	5.93376	−	10.2776i	0.326149	−	0.564906i	−0.655595	−	0.755112i	$-0.727582\pi$
$331$	5.93376	−	10.2776i	0.326149	−	0.564906i	0.981744	+	0.190206i	$0.0609156\pi$
$332$	3.13786	+	5.43494i	0.172213	+	0.298281i
$333$	5.72820	+	9.92153i	0.313903	+	0.543696i
$334$	−2.26735	+	3.92717i	−0.124064	+	0.214885i
$335$	−15.1027			−0.825150
$336$	−0.164087	−	0.321924i	−0.00895166	−	0.0175624i
$337$	−23.7030			−1.29118			−0.645592	−	0.763682i	$-0.723390\pi$
$337$	−23.7030			−1.29118			−0.645592	+	0.763682i	$0.723390\pi$
$338$	5.56728	−	9.64281i	0.302820	−	0.524500i
$339$	−8.14378	−	14.1054i	−0.442309	−	0.766102i
$340$	2.87017	+	4.97128i	0.155657	+	0.269605i
$341$	3.33950	−	5.78419i	0.180844	−	0.313231i
$342$	−1.38399			−0.0748373
$343$	18.2935	+	2.88931i	0.987756	+	0.156008i
$344$	8.62854			0.465220
$345$	−2.47548	+	4.28766i	−0.133276	+	0.230840i
$346$	−8.97687	−	15.5484i	−0.482599	−	0.835887i
$347$	−12.7872	−	22.1481i	−0.686455	−	1.18897i	−0.972977	−	0.230901i	$-0.925833\pi$
$347$	−12.7872	−	22.1481i	−0.686455	−	1.18897i	0.286523	−	0.958073i	$-0.407501\pi$
$348$	4.00446	−	6.93592i	0.214661	−	0.371805i
$349$	11.4538			0.613108			0.306554	−	0.951853i	$-0.400824\pi$
$349$	11.4538			0.613108			0.306554	+	0.951853i	$0.400824\pi$
$350$	−1.02908	−	2.01896i	−0.0550065	−	0.107918i
$351$	0.00203140			0.000108428
$352$	2.85617	−	4.94704i	0.152235	−	0.263678i
$353$	−14.8893	−	25.7890i	−0.792477	−	1.37261i	−0.924429	−	0.381354i	$-0.875458\pi$
$353$	−14.8893	−	25.7890i	−0.792477	−	1.37261i	0.131952	−	0.991256i	$-0.457875\pi$
$354$	3.44377	+	5.96479i	0.183035	+	0.317025i
$355$	−3.34710	+	5.79735i	−0.177646	+	0.307691i
$356$	3.06216			0.162294
$357$	−11.9763	−	0.625925i	−0.633854	−	0.0331275i
$358$	−15.1163			−0.798921
$359$	−0.379677	+	0.657619i	−0.0200386	+	0.0347078i	−0.875871	−	0.482546i	$-0.839712\pi$
$359$	−0.379677	+	0.657619i	−0.0200386	+	0.0347078i	0.855832	+	0.517254i	$0.173046\pi$
$360$	−1.39884	−	2.42287i	−0.0737255	−	0.127696i
$361$	8.19451	+	14.1933i	0.431290	+	0.747016i
$362$	5.83342	−	10.1038i	0.306598	−	0.531043i
$363$	1.00000			0.0524864
$364$	0.00370618	−	0.00570882i	0.000194257	−	0.000299224i
$365$	2.72740			0.142758
$366$	2.12780	−	3.68546i	0.111222	−	0.192642i
$367$	−15.7840	−	27.3386i	−0.823916	−	1.42706i	−0.902745	−	0.430176i	$-0.858452\pi$
$367$	−15.7840	−	27.3386i	−0.823916	−	1.42706i	0.0788296	−	0.996888i	$-0.474882\pi$
$368$	0.338076	+	0.585565i	0.0176234	+	0.0305247i
$369$	−4.71978	+	8.17489i	−0.245702	+	0.425568i
$370$	9.81245			0.510125
$371$	−14.1384	+	21.7781i	−0.734029	+	1.13066i
$372$	−8.45830			−0.438542
$373$	−13.8062	+	23.9130i	−0.714858	+	1.23817i	0.248156	+	0.968720i	$0.420175\pi$
$373$	−13.8062	+	23.9130i	−0.714858	+	1.23817i	−0.963014	+	0.269451i	$0.913158\pi$
$374$	−1.94118	−	3.36223i	−0.100376	−	0.173857i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−4.86448	+	8.42552i	−0.250866	+	0.434513i
$377$	0.0128469			0.000661647
$378$	2.26301	+	0.118273i	0.116397	+	0.00608330i
$379$	−9.22242			−0.473724			−0.236862	−	0.971543i	$-0.576119\pi$
$379$	−9.22242			−0.473724			−0.236862	+	0.971543i	$0.576119\pi$
$380$	1.02316	−	1.77216i	0.0524869	−	0.0909100i
$381$	−6.08239	−	10.5350i	−0.311610	−	0.539725i
$382$	5.41221	+	9.37423i	0.276913	+	0.479627i
$383$	−14.1363	+	24.4849i	−0.722333	+	1.25112i	0.237729	+	0.971331i	$0.423597\pi$
$383$	−14.1363	+	24.4849i	−0.722333	+	1.25112i	−0.960062	+	0.279786i	$0.909736\pi$
$384$	−7.46806			−0.381103
$385$	−1.20148	−	2.35721i	−0.0612333	−	0.120134i
$386$	−12.7285			−0.647866
$387$	1.54209	−	2.67097i	0.0783886	−	0.135773i
$388$	7.02056	+	12.1600i	0.356415	+	0.617329i
$389$	−9.74645	−	16.8813i	−0.494165	−	0.855918i	0.505813	−	0.862643i	$-0.331193\pi$
$389$	−9.74645	−	16.8813i	−0.494165	−	0.855918i	−0.999977	+	0.00672494i	$0.997859\pi$
$390$	0.000869950	−	0.00150680i	4.40516e−5	−	7.62996e-5i
$391$	22.4417			1.13493
$392$	11.5065	−	15.8469i	0.581167	−	0.800391i
$393$	20.2258			1.02025
$394$	1.49878	−	2.59597i	0.0755076	−	0.130783i
$395$	−2.09778	−	3.63345i	−0.105551	−	0.182819i
$396$	−0.633200	−	1.09673i	−0.0318195	−	0.0551130i
$397$	−5.68614	+	9.84868i	−0.285379	+	0.494291i	−0.972701	−	0.232062i	$-0.925453\pi$
$397$	−5.68614	+	9.84868i	−0.285379	+	0.494291i	0.687322	+	0.726353i	$0.258786\pi$
$398$	19.7517			0.990063
$399$	1.94142	+	3.80890i	0.0971927	+	0.190684i
$400$	0.136570			0.00682849
$401$	11.6970	−	20.2599i	0.584122	−	1.01173i	−0.410862	−	0.911698i	$-0.634772\pi$
$401$	11.6970	−	20.2599i	0.584122	−	1.01173i	0.994984	−	0.100032i	$-0.0318945\pi$
$402$	−6.46778	−	11.2025i	−0.322583	−	0.558731i
$403$	−0.00678385	−	0.0117500i	−0.000337928	−	0.000585308i
$404$	−5.19259	+	8.99383i	−0.258341	+	0.447460i
$405$	−1.00000			−0.0496904
$406$	14.3116	+	0.747977i	0.710274	+	0.0371215i
$407$	11.4564			0.567872
$408$	−6.34068	+	10.9824i	−0.313910	+	0.543709i
$409$	5.86748	+	10.1628i	0.290128	+	0.502517i	0.973840	−	0.227236i	$-0.0729688\pi$
$409$	5.86748	+	10.1628i	0.290128	+	0.502517i	−0.683712	+	0.729752i	$0.739635\pi$
$410$	4.04251	+	7.00183i	0.199645	+	0.345796i
$411$	1.71327	−	2.96747i	0.0845094	−	0.146375i
$412$	−15.0978			−0.743816
$413$	11.5850	−	17.8450i	0.570061	−	0.878094i
$414$	−4.24052			−0.208410
$415$	2.47778	−	4.29164i	0.121630	−	0.210668i
$416$	−0.00580202	−	0.0100494i	−0.000284467	−	0.000492712i
$417$	−8.04284	−	13.9306i	−0.393860	−	0.682185i
$418$	−0.691993	+	1.19857i	−0.0338465	+	0.0586238i
$419$	−7.27990			−0.355647			−0.177823	−	0.984062i	$-0.556906\pi$
$419$	−7.27990			−0.355647			−0.177823	+	0.984062i	$0.556906\pi$
$420$	−1.82445	+	2.81030i	−0.0890242	+	0.137128i
$421$	38.1812			1.86084			0.930420	−	0.366496i	$-0.119443\pi$
$421$	38.1812			1.86084			0.930420	+	0.366496i	$0.119443\pi$
$422$	0.969379	−	1.67901i	0.0471886	−	0.0817331i
$423$	1.73875	+	3.01160i	0.0845409	+	0.146429i
$424$	13.7280	+	23.7776i	0.666691	+	1.15474i
$425$	2.26640	−	3.92552i	0.109937	−	0.190416i
$426$	−5.73361			−0.277794
$427$	−13.1277	−	0.686099i	−0.635293	−	0.0332027i
$428$	7.49302			0.362189
$429$	0.00101570	−	0.00175924i	4.90384e−5	−	8.49369e-5i
$430$	−1.32080	−	2.28770i	−0.0636948	−	0.110323i
$431$	−6.51873	−	11.2908i	−0.313996	−	0.543857i	0.665228	−	0.746641i	$-0.268335\pi$
$431$	−6.51873	−	11.2908i	−0.313996	−	0.543857i	−0.979224	+	0.202784i	$0.935001\pi$
$432$	−0.0682849	+	0.118273i	−0.00328536	+	0.00569041i
$433$	24.0687			1.15667			0.578335	−	0.815799i	$-0.303703\pi$
$433$	24.0687			1.15667			0.578335	+	0.815799i	$0.303703\pi$
$434$	−6.87321	−	13.4846i	−0.329925	−	0.647284i
$435$	−6.32416			−0.303220
$436$	2.65703	−	4.60211i	0.127249	−	0.220401i
$437$	−4.00002	−	6.92823i	−0.191347	−	0.331422i
$438$	1.16801	+	2.02306i	0.0558098	+	0.0966655i
$439$	−4.95951	+	8.59012i	−0.236704	+	0.409984i	−0.959767	−	0.280799i	$-0.909401\pi$
$439$	−4.95951	+	8.59012i	−0.236704	+	0.409984i	0.723062	+	0.690783i	$0.242734\pi$
$440$	−2.79769			−0.133374
$441$	−2.84900	−	6.39400i	−0.135666	−	0.304476i
$442$	−0.00788662			−0.000375128
$443$	1.68210	−	2.91349i	0.0799191	−	0.138424i	−0.823296	−	0.567613i	$-0.807867\pi$
$443$	1.68210	−	2.91349i	0.0799191	−	0.138424i	0.903215	+	0.429189i	$0.141200\pi$
$444$	−7.25419	−	12.5646i	−0.344269	−	0.596291i
$445$	−1.20900	−	2.09405i	−0.0573122	−	0.0992676i
$446$	−1.05073	+	1.81991i	−0.0497534	+	0.0861754i
$447$	−0.240930			−0.0113956
$448$	−5.55027	−	10.8891i	−0.262226	−	0.514464i
$449$	−10.8815			−0.513528			−0.256764	−	0.966474i	$-0.582656\pi$
$449$	−10.8815			−0.513528			−0.256764	+	0.966474i	$0.582656\pi$
$450$	−0.428252	+	0.741755i	−0.0201880	+	0.0349666i
$451$	4.71978	+	8.17489i	0.222246	+	0.384941i
$452$	10.3133	+	17.8631i	0.485096	+	0.840211i
$453$	−6.17352	+	10.6929i	−0.290057	+	0.502394i
$454$	−0.448192			−0.0210347
$455$	−0.00536724		0.000280511i	−0.000251620		1.31506e-5i
$456$	4.52065			0.211699
$457$	−19.3887	+	33.5822i	−0.906965	+	1.57091i	−0.0887085	+	0.996058i	$0.528274\pi$
$457$	−19.3887	+	33.5822i	−0.906965	+	1.57091i	−0.818257	+	0.574853i	$0.805059\pi$
$458$	−7.43964	−	12.8858i	−0.347632	−	0.602116i
$459$	2.26640	+	3.92552i	0.105787	+	0.183228i
$460$	3.13495	−	5.42990i	0.146168	−	0.253170i
$461$	23.1184			1.07673			0.538366	−	0.842711i	$-0.319042\pi$
$461$	23.1184			1.07673			0.538366	+	0.842711i	$0.319042\pi$
$462$	1.23393	−	1.90069i	0.0574077	−	0.0884280i
$463$	−9.96947			−0.463321			−0.231660	−	0.972797i	$-0.574416\pi$
$463$	−9.96947			−0.463321			−0.231660	+	0.972797i	$0.574416\pi$
$464$	−0.431844	+	0.747977i	−0.0200479	+	0.0347239i
$465$	3.33950	+	5.78419i	0.154866	+	0.268235i
$466$	−10.7881	−	18.6855i	−0.499748	−	0.865590i
$467$	6.70215	−	11.6085i	0.310139	−	0.537176i	−0.668253	−	0.743934i	$-0.732958\pi$
$467$	6.70215	−	11.6085i	0.310139	−	0.537176i	0.978392	+	0.206758i	$0.0662912\pi$
$468$	−0.00257256			−0.000118917
$469$	−21.7579	+	33.5148i	−1.00469	+	1.54757i
$470$	2.97849			0.137388
$471$	−10.2826	+	17.8100i	−0.473796	+	0.820639i
$472$	−11.2487	−	19.4834i	−0.517766	−	0.896796i
$473$	−1.54209	−	2.67097i	−0.0709051	−	0.122811i
$474$	1.79675	−	3.11207i	0.0825276	−	0.142942i
$475$	−1.61585			−0.0741404
$476$	15.1668	+	0.792672i	0.695170	+	0.0363320i
$477$	9.81384			0.449345
$478$	11.8882	−	20.5910i	0.543756	−	0.941812i
$479$	14.6477	+	25.3706i	0.669270	+	1.15921i	0.978108	+	0.208096i	$0.0667265\pi$
$479$	14.6477	+	25.3706i	0.669270	+	1.15921i	−0.308838	+	0.951115i	$0.599940\pi$
$480$	2.85617	+	4.94704i	0.130366	+	0.225800i
$481$	0.0116362	−	0.0201545i	0.000530567	−	0.000918968i
$482$	0.767460			0.0349568
$483$	5.94851	+	11.6705i	0.270667	+	0.531024i
$484$	−1.26640			−0.0575636
$485$	5.54371	−	9.60199i	0.251727	−	0.436004i
$486$	−0.428252	−	0.741755i	−0.0194259	−	0.0336467i
$487$	2.62841	+	4.55254i	0.119105	+	0.206295i	0.919413	−	0.393293i	$-0.128664\pi$
$487$	2.62841	+	4.55254i	0.119105	+	0.206295i	−0.800308	+	0.599589i	$0.795331\pi$
$488$	−6.95024	+	12.0382i	−0.314623	+	0.544943i
$489$	16.1167			0.728824
$490$	−5.96287	−	0.624988i	−0.269375	−	0.0282341i
$491$	−14.2665			−0.643837			−0.321918	−	0.946767i	$-0.604328\pi$
$491$	−14.2665			−0.643837			−0.321918	+	0.946767i	$0.604328\pi$
$492$	5.97713	−	10.3527i	0.269470	−	0.466735i
$493$	14.3331	+	24.8256i	0.645529	+	1.11809i
$494$	0.00140571	+	0.00243476i	6.32459e−5	+	0.000109545i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	0.912151			0.0409568
$497$	8.04298	+	15.7796i	0.360777	+	0.707813i
$498$	4.24446			0.190199
$499$	−0.319801	+	0.553912i	−0.0143163	+	0.0247965i	−0.873095	−	0.487550i	$-0.837891\pi$
$499$	−0.319801	+	0.553912i	−0.0143163	+	0.0247965i	0.858779	+	0.512347i	$0.171224\pi$
$500$	−0.633200	−	1.09673i	−0.0283176	−	0.0490475i
$501$	−2.64722	−	4.58512i	−0.118269	−	0.204848i
$502$	−7.52509	+	13.0338i	−0.335861	+	0.581729i
$503$	16.4756			0.734609			0.367305	−	0.930101i	$-0.380281\pi$
$503$	16.4756			0.734609			0.367305	+	0.930101i	$0.380281\pi$
$504$	−7.39189	−	0.386327i	−0.329261	−	0.0172084i
$505$	8.20055			0.364920
$506$	−2.12026	+	3.67240i	−0.0942571	+	0.163258i
$507$	6.50000	+	11.2583i	0.288675	+	0.500000i
$508$	7.70274	+	13.3415i	0.341754	+	0.591935i
$509$	19.3982	−	33.5988i	0.859812	−	1.48924i	−0.0122955	−	0.999924i	$-0.503914\pi$
$509$	19.3982	−	33.5988i	0.859812	−	1.48924i	0.872108	−	0.489314i	$-0.162753\pi$
$510$	3.88236			0.171914
$511$	3.92925	−	6.05242i	0.173820	−	0.267743i
$512$	1.54429			0.0682487
$513$	0.807926	−	1.39937i	0.0356708	−	0.0617837i
$514$	−5.85067	−	10.1337i	−0.258062	−	0.446976i
$515$	5.96091	+	10.3246i	0.262669	+	0.454957i
$516$	−1.95290	+	3.38252i	−0.0859715	+	0.148907i
$517$	3.47750			0.152940
$518$	14.1364	−	21.7750i	0.621118	−	0.956739i
$519$	20.9616			0.920114
$520$	−0.00284160	+	0.00492180i	−0.000124613	+	0.000215835i
$521$	−2.19247	−	3.79747i	−0.0960540	−	0.166370i	0.813994	−	0.580873i	$-0.197289\pi$
$521$	−2.19247	−	3.79747i	−0.0960540	−	0.166370i	−0.910048	+	0.414503i	$0.863955\pi$
$522$	−2.70833	−	4.69097i	−0.118541	−	0.205318i
$523$	2.33815	−	4.04980i	0.102240	−	0.177085i	−0.810367	−	0.585923i	$-0.800732\pi$
$523$	2.33815	−	4.04980i	0.102240	−	0.177085i	0.912607	+	0.408837i	$0.134066\pi$
$524$	−25.6139			−1.11895
$525$	2.64215	+	0.138088i	0.115313	+	0.00602665i
$526$	4.63202			0.201966
$527$	15.1373	−	26.2186i	0.659391	−	1.14210i
$528$	0.0682849	+	0.118273i	0.00297172	+	0.00514717i
$529$	−0.756028	−	1.30948i	−0.0328708	−	0.0569339i
$530$	4.20280	−	7.27946i	0.182558	−	0.316199i
$531$	−8.04146			−0.348970
$532$	−2.45862	−	4.82360i	−0.106595	−	0.209129i
$533$	0.0191755			0.000830582
$534$	1.03552	−	1.79356i	0.0448111	−	0.0776151i
$535$	−2.95839	−	5.12409i	−0.127902	−	0.221534i
$536$	21.1263	+	36.5919i	0.912519	+	1.58053i
$537$	8.82441	−	15.2843i	0.380801	−	0.659567i
$538$	−10.1941			−0.439500
$539$	−6.96186	−	0.729697i	−0.299869	−	0.0314303i
$540$	1.26640			0.0544972
$541$	6.12151	−	10.6028i	0.263184	−	0.455849i	−0.703902	−	0.710297i	$-0.748561\pi$
$541$	6.12151	−	10.6028i	0.263184	−	0.455849i	0.967086	+	0.254448i	$0.0818939\pi$
$542$	5.98445	+	10.3654i	0.257054	+	0.445231i
$543$	6.81072	+	11.7965i	0.292276	+	0.506237i
$544$	12.9465	−	22.4239i	0.555075	−	0.961418i
$545$	−4.19619			−0.179745
$546$	−0.00209046	−	0.00410131i	−8.94636e−5	−	0.000175520i
$547$	23.7781			1.01668			0.508338	−	0.861157i	$-0.330260\pi$
$547$	23.7781			1.01668			0.508338	+	0.861157i	$0.330260\pi$
$548$	−2.16969	+	3.75801i	−0.0926844	+	0.160534i
$549$	2.48428	+	4.30290i	0.106027	+	0.183643i
$550$	0.428252	+	0.741755i	0.0182607	+	0.0316285i
$551$	5.10945	−	8.84983i	0.217670	−	0.377016i
$552$	13.8512			0.589548
$553$	−11.0853	−	0.579355i	−0.471393	−	0.0246367i
$554$	−17.8305			−0.757546
$555$	−5.72820	+	9.92153i	−0.243148	+	0.421145i
$556$	10.1855	+	17.6417i	0.431959	+	0.748176i
$557$	−0.625443	−	1.08330i	−0.0265009	−	0.0459009i	0.852471	−	0.522775i	$-0.175103\pi$
$557$	−0.625443	−	1.08330i	−0.0265009	−	0.0459009i	−0.878972	+	0.476874i	$0.841770\pi$
$558$	−2.86030	+	4.95418i	−0.121086	+	0.209727i
$559$	−0.00626517			−0.000264988
$560$	0.196751	−	0.303065i	0.00831423	−	0.0128068i
$561$	4.53280			0.191375
$562$	−5.00917	+	8.67614i	−0.211299	+	0.365981i
$563$	−9.71565	−	16.8280i	−0.409466	−	0.709215i	0.585364	−	0.810770i	$-0.300952\pi$
$563$	−9.71565	−	16.8280i	−0.409466	−	0.709215i	−0.994830	+	0.101555i	$0.967618\pi$
$564$	−2.20195	−	3.81390i	−0.0927190	−	0.160594i
$565$	8.14378	−	14.1054i	0.342611	−	0.593420i
$566$	−1.06068			−0.0445836
$567$	−1.44066	+	2.21912i	−0.0605020	+	0.0931943i
$568$	18.7283			0.785821
$569$	−5.00946	+	8.67663i	−0.210007	+	0.363743i	−0.951717	−	0.306978i	$-0.900682\pi$
$569$	−5.00946	+	8.67663i	−0.210007	+	0.363743i	0.741709	+	0.670722i	$0.234015\pi$
$570$	−0.691993	−	1.19857i	−0.0289844	−	0.0502024i
$571$	−1.81887	−	3.15037i	−0.0761172	−	0.131839i	0.825454	−	0.564469i	$-0.190919\pi$
$571$	−1.81887	−	3.15037i	−0.0761172	−	0.131839i	−0.901572	+	0.432630i	$0.857586\pi$
$572$	−0.00128628	+	0.00222790i	−5.37821e−5	+	9.31533e-5i
$573$	−12.6379			−0.527956
$574$	21.3618	+	1.11644i	0.891624	+	0.0465995i
$575$	−4.95097			−0.206470
$576$	−2.30975	+	4.00061i	−0.0962398	+	0.166692i
$577$	17.5754	+	30.4415i	0.731675	+	1.26730i	0.956167	+	0.292822i	$0.0945944\pi$
$577$	17.5754	+	30.4415i	0.731675	+	1.26730i	−0.224492	+	0.974476i	$0.572072\pi$
$578$	−1.51870	−	2.63047i	−0.0631697	−	0.109413i
$579$	7.43052	−	12.8700i	0.308802	−	0.534860i
$580$	8.00891			0.332552
$581$	−5.95403	−	11.6813i	−0.247015	−	0.484622i
$582$	9.49643			0.393640
$583$	4.90692	−	8.49903i	0.203224	−	0.351994i
$584$	−3.81520	−	6.60812i	−0.157874	−	0.273446i
$585$	0.00101570	+	0.00175924i	4.19939e−5	+	7.27356e-5i
$586$	9.12399	−	15.8032i	0.376909	−	0.652825i
$587$	30.0581			1.24063			0.620315	−	0.784353i	$-0.287005\pi$
$587$	30.0581			1.24063			0.620315	+	0.784353i	$0.287005\pi$
$588$	3.60797	+	8.09736i	0.148790	+	0.333930i
$589$	−10.7923			−0.444689
$590$	−3.44377	+	5.96479i	−0.141778	+	0.245567i
$591$	1.74988	+	3.03089i	0.0719806	+	0.124674i
$592$	0.782299	+	1.35498i	0.0321523	+	0.0556894i
$593$	8.38111	−	14.5165i	0.344171	−	0.596122i	−0.641032	−	0.767514i	$-0.721493\pi$
$593$	8.38111	−	14.5165i	0.344171	−	0.596122i	0.985203	+	0.171393i	$0.0548267\pi$
$594$	−0.856504			−0.0351428
$595$	−5.44609	−	10.6848i	−0.223268	−	0.438032i
$596$	0.305114			0.0124980
$597$	−11.5304	+	19.9713i	−0.471908	+	0.817369i
$598$	0.00430709	+	0.00746010i	0.000176130	+	0.000305066i
$599$	10.8784	+	18.8419i	0.444478	+	0.769859i	0.998016	−	0.0629654i	$-0.0200558\pi$
$599$	10.8784	+	18.8419i	0.444478	+	0.769859i	−0.553537	+	0.832824i	$0.686722\pi$
$600$	1.39884	−	2.42287i	0.0571075	−	0.0989131i
$601$	37.5408			1.53132			0.765660	−	0.643245i	$-0.222413\pi$
$601$	37.5408			1.53132			0.765660	+	0.643245i	$0.222413\pi$
$602$	−6.97951	−	0.364774i	−0.284463	−	0.0148671i
$603$	15.1027			0.615030
$604$	7.81815	−	13.5414i	0.318116	−	0.550993i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	3.51190	+	6.08280i	0.142661	+	0.247097i
$607$	−5.43233	+	9.40907i	−0.220491	+	0.381902i	−0.954957	−	0.296743i	$-0.904099\pi$
$607$	−5.43233	+	9.40907i	−0.220491	+	0.381902i	0.734466	+	0.678646i	$0.237433\pi$
$608$	−9.23031			−0.374338
$609$	−9.11096	+	14.0341i	−0.369195	+	0.568689i
$610$	4.25560			0.172304
$611$	0.00353209	−	0.00611776i	0.000142893	−	0.000247498i
$612$	−2.87017	−	4.97128i	−0.116020	−	0.200952i
$613$	−17.1492	−	29.7033i	−0.692649	−	1.19970i	−0.970967	−	0.239214i	$-0.923110\pi$
$613$	−17.1492	−	29.7033i	−0.692649	−	1.19970i	0.278318	−	0.960489i	$-0.410223\pi$
$614$	−2.43411	+	4.21600i	−0.0982327	+	0.170144i
$615$	−9.43955			−0.380640
$616$	−4.03052	+	6.20840i	−0.162394	+	0.250144i
$617$	−28.0304			−1.12846			−0.564231	−	0.825617i	$-0.690827\pi$
$617$	−28.0304			−1.12846			−0.564231	+	0.825617i	$0.690827\pi$
$618$	−5.10555	+	8.84307i	−0.205375	+	0.355721i
$619$	0.550997	+	0.954355i	0.0221465	+	0.0383588i	0.876886	−	0.480698i	$-0.159617\pi$
$619$	0.550997	+	0.954355i	0.0221465	+	0.0383588i	−0.854740	+	0.519057i	$0.826283\pi$
$620$	−4.22915	−	7.32510i	−0.169847	−	0.294183i
$621$	2.47548	−	4.28766i	0.0993377	−	0.172058i
$622$	−0.143318			−0.00574653
$623$	−6.38871	−	0.333897i	−0.255958	−	0.0133773i
$624$	0.000277427	0		1.11060e−5	0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−0.329869	−	0.571349i	−0.0131842	−	0.0228357i
$627$	−0.807926	−	1.39937i	−0.0322655	−	0.0558854i
$628$	13.0219	−	22.5545i	0.519629	−	0.900024i
$629$	51.9295			2.07057
$630$	1.02908	+	2.01896i	0.0409994	+	0.0804373i
$631$	15.4626			0.615555			0.307777	−	0.951458i	$-0.400415\pi$
$631$	15.4626			0.615555			0.307777	+	0.951458i	$0.400415\pi$
$632$	−5.86892	+	10.1653i	−0.233453	+	0.404352i
$633$	1.13179	+	1.96031i	0.0449844	+	0.0779153i
$634$	12.7088	+	22.0122i	0.504730	+	0.874218i
$635$	6.08239	−	10.5350i	0.241372	−	0.418069i
$636$	−12.4282			−0.492812
$637$	−0.00835486	+	0.0115064i	−0.000331032	+	0.000455902i
$638$	−5.41667			−0.214448
$639$	3.34710	−	5.79735i	0.132409	−	0.229340i
$640$	−3.73403	−	6.46753i	−0.147600	−	0.255652i
$641$	13.6267	+	23.6021i	0.538222	+	0.932228i	0.999000	+	0.0447122i	$0.0142371\pi$
$641$	13.6267	+	23.6021i	0.538222	+	0.932228i	−0.460778	+	0.887515i	$0.652430\pi$
$642$	2.53388	−	4.38880i	0.100004	−	0.173212i
$643$	10.3727			0.409061			0.204530	−	0.978860i	$-0.434433\pi$
$643$	10.3727			0.409061			0.204530	+	0.978860i	$0.434433\pi$
$644$	−7.53319	−	14.7795i	−0.296849	−	0.582393i
$645$	3.08417			0.121439
$646$	−3.13666	+	5.43286i	−0.123410	+	0.213753i
$647$	0.818679	+	1.41799i	0.0321856	+	0.0557471i	0.881670	−	0.471867i	$-0.156420\pi$
$647$	0.818679	+	1.41799i	0.0321856	+	0.0557471i	−0.849484	+	0.527614i	$0.823087\pi$
$648$	1.39884	+	2.42287i	0.0549517	+	0.0951792i
$649$	−4.02073	+	6.96411i	−0.157828	+	0.273365i
$650$	0.00173990			6.82445e−5
$651$	17.6469	+	0.922290i	0.691637	+	0.0361474i
$652$	−20.4102			−0.799327
$653$	−23.7575	+	41.1492i	−0.929702	+	1.61029i	−0.145883	+	0.989302i	$0.546602\pi$
$653$	−23.7575	+	41.1492i	−0.929702	+	1.61029i	−0.783819	+	0.620989i	$0.786731\pi$
$654$	−1.79703	−	3.11254i	−0.0702694	−	0.121710i
$655$	10.1129	+	17.5160i	0.395143	+	0.684407i
$656$	−0.644579	+	1.11644i	−0.0251666	+	0.0435898i
$657$	−2.72740			−0.106406
$658$	4.29100	−	6.60964i	0.167281	−	0.257671i
$659$	−39.6789			−1.54567			−0.772836	−	0.634606i	$-0.781162\pi$
$659$	−39.6789			−1.54567			−0.772836	+	0.634606i	$0.781162\pi$
$660$	0.633200	−	1.09673i	0.0246473	−	0.0426903i
$661$	−12.8370	−	22.2344i	−0.499303	−	0.864818i	0.500697	−	0.865623i	$-0.333077\pi$
$661$	−12.8370	−	22.2344i	−0.499303	−	0.864818i	−1.00000		0.000804918i	$0.999744\pi$
$662$	5.08229	+	8.80278i	0.197529	+	0.342130i
$663$	0.00460396	−	0.00797429i	0.000178803	−	0.000309696i
$664$	−13.8641			−0.538032
$665$	−2.32790	+	3.58577i	−0.0902719	+	0.139050i
$666$	−9.81245			−0.380225
$667$	15.6553	−	27.1158i	0.606177	−	1.04993i
$668$	3.35244	+	5.80659i	0.129710	+	0.224664i
$669$	−1.22676	−	2.12482i	−0.0474294	−	0.0821501i
$670$	6.46778	−	11.2025i	0.249872	−	0.432791i
$671$	4.96857			0.191809
$672$	15.0928	+	0.788806i	0.582219	+	0.0304288i
$673$	24.4678			0.943163			0.471582	−	0.881822i	$-0.343683\pi$
$673$	24.4678			0.943163			0.471582	+	0.881822i	$0.343683\pi$
$674$	10.1509	−	17.5818i	0.390997	−	0.677226i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−8.23160	−	14.2575i	−0.316600	−	0.548367i
$677$	3.78680	−	6.55893i	0.145538	−	0.252080i	−0.784035	−	0.620716i	$-0.786842\pi$
$677$	3.78680	−	6.55893i	0.145538	−	0.252080i	0.929574	+	0.368636i	$0.120175\pi$
$678$	13.9504			0.535761
$679$	−13.3214	−	26.1354i	−0.511227	−	1.00298i
$680$	−12.6814			−0.486308
$681$	0.261640	−	0.453174i	0.0100261	−	0.0173657i
$682$	2.86030	+	4.95418i	0.109527	+	0.189706i
$683$	1.65633	+	2.86884i	0.0633776	+	0.109773i	0.895973	−	0.444108i	$-0.146479\pi$
$683$	1.65633	+	2.86884i	0.0633776	+	0.109773i	−0.832596	+	0.553881i	$0.813146\pi$
$684$	−1.02316	+	1.77216i	−0.0391214	+	0.0677603i
$685$	3.42654			0.130921
$686$	−9.97739	+	12.3319i	−0.380939	+	0.470835i
$687$	17.3721			0.662787
$688$	0.210602	−	0.364774i	0.00802914	−	0.0139069i
$689$	−0.00996789	−	0.0172649i	−0.000379746	−	0.000657740i
$690$	−2.12026	−	3.67240i	−0.0807170	−	0.139806i
$691$	−9.17916	+	15.8988i	−0.349192	+	0.604818i	−0.986106	−	0.166117i	$-0.946877\pi$
$691$	−9.17916	+	15.8988i	−0.349192	+	0.604818i	0.636914	+	0.770935i	$0.280210\pi$
$692$	−26.5458			−1.00912
$693$	1.20148	+	2.35721i	0.0456406	+	0.0895430i
$694$	21.9046			0.831489
$695$	8.04284	−	13.9306i	0.305082	−	0.528418i
$696$	8.84650	+	15.3226i	0.335326	+	0.580801i
$697$	21.3938	+	37.0552i	0.810348	+	1.40356i
$698$	−4.90511	+	8.49590i	−0.185661	+	0.321575i
$699$	25.1910			0.952810
$700$	−3.34601	−	0.174875i	−0.126467	−	0.00660964i
$701$	40.6699			1.53608			0.768041	−	0.640400i	$-0.221232\pi$
$701$	40.6699			1.53608			0.768041	+	0.640400i	$0.221232\pi$
$702$	−0.000869950		0.00150680i	−3.28341e−5		5.68704e-5i
$703$	−9.25592	−	16.0317i	−0.349094	−	0.604648i
$704$	2.30975	+	4.00061i	0.0870522	+	0.150779i
$705$	−1.73875	+	3.01160i	−0.0654851	+	0.113424i
$706$	25.5055			0.959912
$707$	11.8142	−	18.1980i	0.444319	−	0.684407i
$708$	10.1837			0.382727
$709$	−4.12136	+	7.13841i	−0.154781	+	0.268088i	−0.932979	−	0.359930i	$-0.882801\pi$
$709$	−4.12136	+	7.13841i	−0.154781	+	0.268088i	0.778198	+	0.628019i	$0.216134\pi$
$710$	−2.86681	−	4.96545i	−0.107589	−	0.186350i
$711$	2.09778	+	3.63345i	0.0786727	+	0.136265i
$712$	−3.38241	+	5.85850i	−0.126761	+	0.219557i
$713$	−33.0675			−1.23839
$714$	5.59317	−	8.61543i	0.209319	−	0.322425i
$715$	0.00203140			7.59699e−5
$716$	−11.1752	+	19.3561i	−0.417638	+	0.723371i
$717$	13.8800	+	24.0408i	0.518356	+	0.897820i
$718$	−0.325195	−	0.563254i	−0.0121362	−	0.0210204i
$719$	−8.07341	+	13.9836i	−0.301087	+	0.521499i	−0.976383	−	0.216049i	$-0.930683\pi$
$719$	−8.07341	+	13.9836i	−0.301087	+	0.521499i	0.675295	+	0.737548i	$0.264016\pi$
$720$	−0.136570			−0.00508966
$721$	31.4992	+	1.64626i	1.17309	+	0.0613100i
$722$	−14.0373			−0.522413
$723$	−0.448019	+	0.775991i	−0.0166620	+	0.0288594i
$724$	−8.62510	−	14.9391i	−0.320549	−	0.555208i
$725$	−3.16208	−	5.47688i	−0.117437	−	0.203406i
$726$	−0.428252	+	0.741755i	−0.0158939	+	0.0275291i
$727$	−39.2754			−1.45665			−0.728323	−	0.685234i	$-0.759700\pi$
$727$	−39.2754			−1.45665			−0.728323	+	0.685234i	$0.759700\pi$
$728$	0.00682829	+	0.0133965i	0.000253073	+	0.000496508i
$729$	1.00000			0.0370370
$730$	−1.16801	+	2.02306i	−0.0432301	+	0.0748768i
$731$	−6.98996	−	12.1070i	−0.258533	−	0.447793i
$732$	−3.14610	−	5.44920i	−0.116283	−	0.201408i
$733$	−12.0195	+	20.8184i	−0.443950	+	0.768944i	−0.997978	−	0.0635539i	$-0.979757\pi$
$733$	−12.0195	+	20.8184i	−0.443950	+	0.768944i	0.554029	+	0.832498i	$0.313090\pi$
$734$	27.0381			0.997993
$735$	4.11287	−	5.66430i	0.151705	−	0.208931i
$736$	−28.2816			−1.04247
$737$	7.55136	−	13.0793i	0.278158	−	0.481784i
$738$	−4.04251	−	7.00183i	−0.148807	−	0.257741i
$739$	5.48118	+	9.49368i	0.201629	+	0.349231i	0.949053	−	0.315116i	$-0.102043\pi$
$739$	5.48118	+	9.49368i	0.201629	+	0.349231i	−0.747425	+	0.664346i	$0.768710\pi$
$740$	7.25419	−	12.5646i	0.266669	−	0.461885i
$741$	−0.00328244			−0.000120583
$742$	−10.0992	−	19.8137i	−0.370753	−	0.727385i
$743$	−24.5343			−0.900076			−0.450038	−	0.893009i	$-0.648590\pi$
$743$	−24.5343			−0.900076			−0.450038	+	0.893009i	$0.648590\pi$
$744$	9.34288	−	16.1823i	0.342527	−	0.593274i
$745$	−0.120465	−	0.208652i	−0.00441350	−	0.00764440i
$746$	−11.8251	−	20.4816i	−0.432947	−	0.749886i
$747$	−2.47778	+	4.29164i	−0.0906573	+	0.157023i
$748$	−5.74034			−0.209888
$749$	−15.6330	−	0.817037i	−0.571218	−	0.0298539i
$750$	−0.856504			−0.0312751
$751$	13.6994	−	23.7281i	0.499898	−	0.865849i	−0.500102	−	0.865967i	$-0.666704\pi$
$751$	13.6994	−	23.7281i	0.499898	−	0.865849i	1.00000		0.000117481i	$3.73954e-5\pi$
$752$	0.237461	+	0.411294i	0.00865930	+	0.0149984i
$753$	−8.78582	−	15.2175i	−0.320173	−	0.554556i
$754$	−0.00550170	+	0.00952922i	−0.000200360	+	0.000347034i
$755$	−12.3470			−0.449355
$756$	1.82445	−	2.81030i	0.0663547	−	0.102209i
$757$	−29.2641			−1.06362			−0.531811	−	0.846863i	$-0.678488\pi$
$757$	−29.2641			−1.06362			−0.531811	+	0.846863i	$0.678488\pi$
$758$	3.94952	−	6.84077i	0.143453	−	0.248468i
$759$	−2.47548	−	4.28766i	−0.0898543	−	0.155632i
$760$	2.26032	+	3.91500i	0.0819906	+	0.142012i
$761$	−22.4994	+	38.9702i	−0.815604	+	1.41267i	0.0932894	+	0.995639i	$0.470262\pi$
$761$	−22.4994	+	38.9702i	−0.815604	+	1.41267i	−0.908893	+	0.417029i	$0.863072\pi$
$762$	10.4192			0.377447
$763$	−6.04529	+	9.31186i	−0.218854	+	0.337112i
$764$	16.0047			0.579028
$765$	−2.26640	+	3.92552i	−0.0819419	+	0.141927i
$766$	−12.1078	−	20.9714i	−0.437474	−	0.757727i
$767$	0.00816770	+	0.0141469i	0.000294918	+	0.000510814i
$768$	7.81772	−	13.5407i	0.282098	−	0.488608i
$769$	−27.3452			−0.986092			−0.493046	−	0.870003i	$-0.664117\pi$
$769$	−27.3452			−0.986092			−0.493046	+	0.870003i	$0.664117\pi$
$770$	2.26301	+	0.118273i	0.0815532	+	0.00426226i
$771$	13.6617			0.492015
$772$	−9.41001	+	16.2986i	−0.338674	+	0.586600i
$773$	9.07317	+	15.7152i	0.326339	+	0.565236i	0.981782	−	0.190008i	$-0.0608515\pi$
$773$	9.07317	+	15.7152i	0.326339	+	0.565236i	−0.655443	+	0.755244i	$0.727518\pi$
$774$	1.32080	+	2.28770i	0.0474753	+	0.0822296i
$775$	−3.33950	+	5.78419i	−0.119959	+	0.207774i
$776$	−31.0191			−1.11352
$777$	13.7647	+	27.0051i	0.493805	+	0.968803i
$778$	16.6958			0.598572
$779$	7.62647	−	13.2094i	0.273246	−	0.473277i
$780$	−0.00128628	−	0.00222790i	−4.60562e−5	−	7.97717e-5i
$781$	−3.34710	−	5.79735i	−0.119769	−	0.207445i
$782$	−9.61072	+	16.6463i	−0.343679	+	0.595269i
$783$	6.32416			0.226007
$784$	−0.389087	−	0.873227i	−0.0138960	−	0.0311867i
$785$	−20.5652			−0.734002
$786$	−8.66172	+	15.0025i	−0.308953	+	0.535123i
$787$	1.50729	+	2.61071i	0.0537292	+	0.0930617i	0.891639	−	0.452747i	$-0.149556\pi$
$787$	1.50729	+	2.61071i	0.0537292	+	0.0930617i	−0.837910	+	0.545809i	$0.816223\pi$
$788$	−2.21605	−	3.83832i	−0.0789437	−	0.136734i
$789$	−2.70402	+	4.68351i	−0.0962658	+	0.166737i
$790$	3.59351			0.127851
$791$	−19.5693	−	38.3932i	−0.695803	−	1.36510i
$792$	2.79769			0.0994114
$793$	0.00504656	−	0.00874090i	0.000179209	−	0.000310398i
$794$	−4.87020	−	8.43544i	−0.172837	−	0.299363i
$795$	4.90692	+	8.49903i	0.174030	+	0.301430i
$796$	14.6021	−	25.2916i	0.517558	−	0.896437i
$797$	−50.6995			−1.79587			−0.897934	−	0.440131i	$-0.854932\pi$
$797$	−50.6995			−1.79587			−0.897934	+	0.440131i	$0.854932\pi$
$798$	−3.65669	−	0.191112i	−0.129445	−	0.00676528i
$799$	15.7628			0.557648
$800$	−2.85617	+	4.94704i	−0.100981	+	0.174904i
$801$	1.20900	+	2.09405i	0.0427180	+	0.0739897i
$802$	10.0186	+	17.3527i	0.353768	+	0.612744i
$803$	−1.36370	+	2.36199i	−0.0481239	+	0.0833530i
$804$	−19.1261			−0.674525
$805$	−7.13266	+	10.9868i	−0.251393	+	0.387233i
$806$	0.0116208			0.000409325
$807$	5.95101	−	10.3075i	0.209486	−	0.362840i
$808$	−11.4713	−	19.8688i	−0.403558	−	0.698984i
$809$	−1.46493	−	2.53733i	−0.0515042	−	0.0892078i	0.839124	−	0.543940i	$-0.183068\pi$
$809$	−1.46493	−	2.53733i	−0.0515042	−	0.0892078i	−0.890628	+	0.454732i	$0.849735\pi$
$810$	0.428252	−	0.741755i	0.0150472	−	0.0260626i
$811$	52.9881			1.86066			0.930332	−	0.366719i	$-0.119519\pi$
$811$	52.9881			1.86066			0.930332	+	0.366719i	$0.119519\pi$
$812$	11.5381	−	17.7728i	0.404909	−	0.623701i
$813$	−13.9741			−0.490094
$814$	−4.90623	+	8.49783i	−0.171963	+	0.297849i
$815$	8.05837	+	13.9575i	0.282272	+	0.488910i
$816$	0.309522	+	0.536108i	0.0108354	+	0.0187675i
$817$	−2.49178	+	4.31589i	−0.0871764	+	0.150994i
$818$	−10.0510			−0.351426
$819$	0.00536724		0.000280511i	0.000187547		9.80186e-6i
$820$	11.9543			0.417461
$821$	23.7894	−	41.2045i	0.830257	−	1.43805i	−0.0675777	−	0.997714i	$-0.521527\pi$
$821$	23.7894	−	41.2045i	0.830257	−	1.43805i	0.897835	−	0.440333i	$-0.145140\pi$
$822$	1.46742	+	2.54165i	0.0511823	+	0.0886503i
$823$	0.145131	+	0.251374i	0.00505894	+	0.00876234i	0.868544	−	0.495612i	$-0.165056\pi$
$823$	0.145131	+	0.251374i	0.00505894	+	0.00876234i	−0.863485	+	0.504375i	$0.831723\pi$
$824$	16.6768	−	28.8850i	0.580963	−	1.00626i
$825$	−1.00000			−0.0348155
$826$	8.27529	+	16.2354i	0.287934	+	0.564902i
$827$	−9.84138			−0.342218			−0.171109	−	0.985252i	$-0.554735\pi$
$827$	−9.84138			−0.342218			−0.171109	+	0.985252i	$0.554735\pi$
$828$	−3.13495	+	5.42990i	−0.108947	+	0.188702i
$829$	11.7523	+	20.3556i	0.408176	+	0.706981i	0.994685	−	0.102961i	$-0.0328318\pi$
$829$	11.7523	+	20.3556i	0.408176	+	0.706981i	−0.586510	+	0.809942i	$0.699498\pi$
$830$	2.12223	+	3.67581i	0.0736637	+	0.127589i
$831$	10.4089	−	18.0287i	0.361080	−	0.625410i
$832$	0.00938405			0.000325333
$833$	−31.5567	−	3.30757i	−1.09338	−	0.114600i
$834$	13.7775			0.477074
$835$	2.64722	−	4.58512i	0.0916108	−	0.158675i
$836$	1.02316	+	1.77216i	0.0353867	+	0.0612915i
$837$	−3.33950	−	5.78419i	−0.115430	−	0.199931i
$838$	3.11763	−	5.39990i	0.107697	−	0.186537i
$839$	7.22057			0.249282			0.124641	−	0.992202i	$-0.460222\pi$
$839$	7.22057			0.249282			0.124641	+	0.992202i	$0.460222\pi$
$840$	−3.36138	−	6.59473i	−0.115979	−	0.227540i
$841$	10.9950			0.379137
$842$	−16.3512	+	28.3211i	−0.563500	+	0.976010i
$843$	−5.84839	−	10.1297i	−0.201429	−	0.348886i
$844$	−1.43329	−	2.48254i	−0.0493360	−	0.0854524i
$845$	−6.50000	+	11.2583i	−0.223607	+	0.387298i
$846$	−2.97849			−0.102403
$847$	2.64215	+	0.138088i	0.0907852	+	0.00474476i
$848$	1.34027			0.0460252
$849$	0.619189	−	1.07247i	0.0212505	−	0.0368070i
$850$	1.94118	+	3.36223i	0.0665820	+	0.115323i
$851$	−28.3601	−	49.1211i	−0.972172	−	1.68385i
$852$	−4.23877	+	7.34176i	−0.145218	+	0.251525i
$853$	−8.96332			−0.306898			−0.153449	−	0.988157i	$-0.549038\pi$
$853$	−8.96332			−0.306898			−0.153449	+	0.988157i	$0.549038\pi$
$854$	6.13087	−	9.44369i	0.209794	−	0.323156i
$855$	1.61585			0.0552610
$856$	−8.27665	+	14.3356i	−0.282890	+	0.489980i
$857$	16.3694	+	28.3526i	0.559167	+	0.968506i	0.997566	+	0.0697253i	$0.0222123\pi$
$857$	16.3694	+	28.3526i	0.559167	+	0.968506i	−0.438399	+	0.898780i	$0.644454\pi$
$858$	0.000869950		0.00150680i	2.96996e−5		5.14412e-5i
$859$	17.6577	−	30.5840i	0.602473	−	1.04351i	−0.389973	−	0.920826i	$-0.627516\pi$
$859$	17.6577	−	30.5840i	0.602473	−	1.04351i	0.992445	−	0.122687i	$-0.0391511\pi$
$860$	−3.90579			−0.133186
$861$	−13.5992	+	20.9475i	−0.463459	+	0.713889i
$862$	11.1666			0.380337
$863$	−5.02855	+	8.70970i	−0.171174	+	0.296482i	−0.938831	−	0.344380i	$-0.888089\pi$
$863$	−5.02855	+	8.70970i	−0.171174	+	0.296482i	0.767657	+	0.640861i	$0.221423\pi$
$864$	−2.85617	−	4.94704i	−0.0971690	−	0.168302i
$865$	10.4808	+	18.1533i	0.356359	+	0.617231i
$866$	−10.3075	+	17.8531i	−0.350263	+	0.606673i
$867$	3.54628			0.120438
$868$	−22.3480	−	1.16799i	−0.758542	−	0.0396441i
$869$	4.19555			0.142324
$870$	2.70833	−	4.69097i	0.0918211	−	0.159039i
$871$	−0.0153398	−	0.0265693i	−0.000519769	−	0.000900267i
$872$	5.86981	+	10.1668i	0.198777	+	0.344292i
$873$	−5.54371	+	9.60199i	−0.187626	+	0.324978i
$874$	6.85206			0.231774
$875$	1.20148	+	2.35721i	0.0406176	+	0.0796882i
$876$	3.45398			0.116699
$877$	24.5613	−	42.5415i	0.829378	−	1.43652i	−0.0691497	−	0.997606i	$-0.522029\pi$
$877$	24.5613	−	42.5415i	0.829378	−	1.43652i	0.898527	−	0.438918i	$-0.144638\pi$
$878$	−4.24784	−	7.35747i	−0.143358	−	0.248303i
$879$	10.6526	+	18.4508i	0.359303	+	0.622331i
$880$	−0.0682849	+	0.118273i	−0.00230188	+	0.00398698i
$881$	−2.15913			−0.0727430			−0.0363715	−	0.999338i	$-0.511580\pi$
$881$	−2.15913			−0.0727430			−0.0363715	+	0.999338i	$0.511580\pi$
$882$	5.96287	+	0.624988i	0.200780	+	0.0210445i
$883$	34.3745			1.15679			0.578397	−	0.815755i	$-0.303679\pi$
$883$	34.3745			1.15679			0.578397	+	0.815755i	$0.303679\pi$
$884$	−0.00583045	+	0.0100986i	−0.000196099	+	0.000339654i
$885$	−4.02073	−	6.96411i	−0.135155	−	0.234096i
$886$	1.44073	+	2.49542i	0.0484022	+	0.0838351i
$887$	−28.2436	+	48.9193i	−0.948326	+	1.64255i	−0.199377	+	0.979923i	$0.563892\pi$
$887$	−28.2436	+	48.9193i	−0.948326	+	1.64255i	−0.748950	+	0.662627i	$0.769442\pi$
$888$	32.0514			1.07557
$889$	−14.6158	−	28.6749i	−0.490198	−	0.961727i
$890$	2.07103			0.0694211
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	1.55357	+	2.69087i	0.0520175	+	0.0900969i
$893$	−2.80956	−	4.86631i	−0.0940185	−	0.162845i
$894$	0.103179	−	0.178711i	0.00345082	−	0.00597699i
$895$	17.6488			0.589935
$896$	−19.7317	−	1.03125i	−0.659190	−	0.0344516i
$897$	−0.0100574			−0.000335806
$898$	4.66001	−	8.07138i	0.155507	−	0.269345i
$899$	−21.1195	−	36.5801i	−0.704376	−	1.22002i
$900$	0.633200	+	1.09673i	0.0211067	+	0.0365578i
$901$	22.2421	−	38.5244i	0.740991	−	1.28343i
$902$	−8.08502			−0.269202
$903$	4.44324	−	6.84415i	0.147862	−	0.227759i
$904$	−45.5675			−1.51555
$905$	−6.81072	+	11.7965i	−0.226396	+	0.392130i
$906$	−5.28765	−	9.15848i	−0.175670	−	0.304270i
$907$	−12.4307	−	21.5307i	−0.412756	−	0.714914i	0.582434	−	0.812878i	$-0.302100\pi$
$907$	−12.4307	−	21.5307i	−0.412756	−	0.714914i	−0.995190	+	0.0979636i	$0.968767\pi$
$908$	−0.331341	+	0.573899i	−0.0109959	+	0.0190455i
$909$	−8.20055			−0.271995
$910$	0.00250660	−	0.00386105i	8.30931e−5	−	0.000127992i
$911$	−0.300338			−0.00995063			−0.00497531	−	0.999988i	$-0.501584\pi$
$911$	−0.300338			−0.00995063			−0.00497531	+	0.999988i	$0.501584\pi$
$912$	0.110338	−	0.191112i	0.00365367	−	0.00632834i
$913$	2.47778	+	4.29164i	0.0820026	+	0.142033i
$914$	−16.6065	−	28.7633i	−0.549295	−	0.951406i
$915$	−2.48428	+	4.30290i	−0.0821278	+	0.142250i
$916$	−22.0000			−0.726902
$917$	53.4394	+	2.79293i	1.76472	+	0.0922307i
$918$	−3.88236			−0.128137
$919$	−2.26420	+	3.92172i	−0.0746892	+	0.129366i	−0.900951	−	0.433921i	$-0.857130\pi$
$919$	−2.26420	+	3.92172i	−0.0746892	+	0.129366i	0.826262	+	0.563286i	$0.190463\pi$
$920$	6.92562	+	11.9955i	0.228331	+	0.395481i
$921$	−2.84191	−	4.92234i	−0.0936442	−	0.162196i
$922$	−9.90051	+	17.1482i	−0.326056	+	0.564745i
$923$	−0.0135986			−0.000447602
$924$	−1.52156	−	2.98517i	−0.0500557	−	0.0982049i
$925$	−11.4564			−0.376684
$926$	4.26945	−	7.39490i	0.140303	−	0.243012i
$927$	−5.96091	−	10.3246i	−0.195782	−	0.339105i
$928$	−18.0629	−	31.2858i	−0.592943	−	1.02701i
$929$	6.46532	−	11.1983i	0.212120	−	0.367403i	−0.740258	−	0.672323i	$-0.765296\pi$
$929$	6.46532	−	11.1983i	0.212120	−	0.367403i	0.952378	+	0.304920i	$0.0986298\pi$
$930$	−5.72060			−0.187586
$931$	4.60356	+	10.3318i	0.150876	+	0.338610i
$932$	−31.9018			−1.04498
$933$	0.0836645	−	0.144911i	0.00273905	−	0.00474418i
$934$	5.74042	+	9.94271i	0.187832	+	0.325335i
$935$	2.26640	+	3.92552i	0.0741192	+	0.128378i
$936$	0.00284160	−	0.00492180i	9.28807e−5	−	0.000160874i
$937$	4.53819			0.148256			0.0741281	−	0.997249i	$-0.476383\pi$
$937$	4.53819			0.148256			0.0741281	+	0.997249i	$0.476383\pi$
$938$	−15.5419	−	30.4918i	−0.507460	−	0.995592i
$939$	0.770267			0.0251367
$940$	2.20195	−	3.81390i	0.0718198	−	0.124396i
$941$	3.26761	+	5.65966i	0.106521	+	0.184500i	0.914359	−	0.404905i	$-0.132696\pi$
$941$	3.26761	+	5.65966i	0.106521	+	0.184500i	−0.807838	+	0.589405i	$0.799362\pi$
$942$	−8.80708	−	15.2543i	−0.286950	−	0.497012i
$943$	23.3675	−	40.4736i	0.760949	−	1.31800i
$944$	−1.09822			−0.0357441
$945$	−2.64215	−	0.138088i	−0.0859490	−	0.00449200i
$946$	2.64161			0.0858860
$947$	21.9497	−	38.0180i	0.713269	−	1.23542i	−0.250355	−	0.968154i	$-0.580547\pi$
$947$	21.9497	−	38.0180i	0.713269	−	1.23542i	0.963623	−	0.267264i	$-0.0861195\pi$
$948$	−2.65662	−	4.60141i	−0.0862831	−	0.149447i
$949$	0.00277021	+	0.00479815i	8.99248e−5	+	0.000155754i
$950$	0.691993	−	1.19857i	0.0224512	−	0.0388866i
$951$	−29.6759			−0.962307
$952$	−18.2695	+	28.1415i	−0.592119	+	0.912070i
$953$	−0.277234			−0.00898048			−0.00449024	−	0.999990i	$-0.501429\pi$
$953$	−0.277234			−0.00898048			−0.00449024	+	0.999990i	$0.501429\pi$
$954$	−4.20280	+	7.27946i	−0.136071	+	0.235681i
$955$	−6.31896	−	10.9448i	−0.204477	−	0.354164i
$956$	−17.5776	−	30.4453i	−0.568499	−	0.984670i
$957$	3.16208	−	5.47688i	0.102215	−	0.177042i
$958$	−25.0916			−0.810674
$959$	4.93648	−	7.60391i	0.159407	−	0.245543i
$960$	−4.61951			−0.149094
$961$	−6.80457	+	11.7859i	−0.219502	+	0.380189i
$962$	0.00996649	+	0.0172625i	0.000321332	+	0.000556564i
$963$	2.95839	+	5.12409i	0.0953329	+	0.165121i
$964$	0.567371	−	0.982715i	0.0182738	−	0.0316511i
$965$	14.8610			0.478394
$966$	−11.2041	−	0.585565i	−0.360485	−	0.0188402i
$967$	25.0202			0.804595			0.402298	−	0.915509i	$-0.368212\pi$
$967$	25.0202			0.804595			0.402298	+	0.915509i	$0.368212\pi$
$968$	1.39884	−	2.42287i	0.0449605	−	0.0778739i
$969$	−3.66217	−	6.34306i	−0.117646	−	0.203769i
$970$	4.74821	+	8.22415i	0.152456	+	0.264061i
$971$	−18.6947	+	32.3802i	−0.599942	+	1.03913i	0.392886	+	0.919587i	$0.371477\pi$
$971$	−18.6947	+	32.3802i	−0.599942	+	1.03913i	−0.992829	+	0.119544i	$0.961857\pi$
$972$	−1.26640			−0.0406198
$973$	−19.3267	−	37.9173i	−0.619586	−	1.21557i
$974$	−4.50249			−0.144269
$975$	−0.00101570	+	0.00175924i	−3.25284e−5	+	5.63408e-5i
$976$	0.339278	+	0.587647i	0.0108600	+	0.0188101i
$977$	7.41631	+	12.8454i	0.237269	+	0.410962i	0.959930	−	0.280241i	$-0.0904145\pi$
$977$	7.41631	+	12.8454i	0.237269	+	0.410962i	−0.722661	+	0.691203i	$0.757081\pi$
$978$	−6.90203	+	11.9547i	−0.220703	+	0.382268i
$979$	2.41800			0.0772797
$980$	−5.20854	+	7.17327i	−0.166381	+	0.229142i
$981$	4.19619			0.133974
$982$	6.10965	−	10.5822i	0.194967	−	0.337692i
$983$	15.5746	+	26.9760i	0.496753	+	0.860401i	0.999993	−	0.00374560i	$-0.00119226\pi$
$983$	15.5746	+	26.9760i	0.496753	+	0.860401i	−0.503240	+	0.864147i	$0.667859\pi$
$984$	13.2045	+	22.8708i	0.420943	+	0.729094i
$985$	−1.74988	+	3.03089i	−0.0557560	+	0.0965721i
$986$	−24.5527			−0.781917
$987$	4.17816	+	8.19719i	0.132992	+	0.260920i
$988$	0.00415688			0.000132248
$989$	−7.63481	+	13.2239i	−0.242773	+	0.420495i
$990$	−0.428252	−	0.741755i	−0.0136107	−	0.0235745i
$991$	12.0770	+	20.9179i	0.383637	+	0.664479i	0.991579	−	0.129502i	$-0.0413380\pi$
$991$	12.0770	+	20.9179i	0.383637	+	0.664479i	−0.607942	+	0.793982i	$0.708005\pi$
$992$	−19.0764	+	33.0413i	−0.605676	+	1.04906i
$993$	−11.8675			−0.376604
$994$	−15.1490	−	0.791743i	−0.480498	−	0.0251126i
$995$	−23.0608			−0.731077
$996$	3.13786	−	5.43494i	0.0994270	−	0.172213i
$997$	15.0967	+	26.1482i	0.478117	+	0.828122i	0.999685	−	0.0250870i	$-0.00798628\pi$
$997$	15.0967	+	26.1482i	0.478117	+	0.828122i	−0.521569	+	0.853209i	$0.674653\pi$
$998$	−0.273911	−	0.474428i	−0.00867051	−	0.0150178i
$999$	5.72820	−	9.92153i	0.181232	−	0.313903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.331.4	✓	16
7.2	even	3		8085.2.a.cf.1.5		8
7.4	even	3	inner	1155.2.q.j.991.4	yes	16
7.5	odd	6		8085.2.a.ce.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.4	✓	16	1.1	even	1	trivial
1155.2.q.j.991.4	yes	16	7.4	even	3	inner
8085.2.a.ce.1.5		8	7.5	odd	6
8085.2.a.cf.1.5		8	7.2	even	3

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.428252 + 0.741755i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.633200 + 1.09673i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.856504 q^{6} +(-1.20148 - 2.35721i) q^{7} -2.79769 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.428252 + 0.741755i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.633200 + 1.09673i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.856504 q^{6} +(-1.20148 - 2.35721i) q^{7} -2.79769 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.428252 + 0.741755i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.633200 - 1.09673i) q^{12} +0.00203140 q^{13} +(2.26301 + 0.118273i) q^{14} -1.00000 q^{15} +(-0.0682849 + 0.118273i) q^{16} +(2.26640 + 3.92552i) q^{17} +(-0.428252 - 0.741755i) q^{18} +(0.807926 - 1.39937i) q^{19} +1.26640 q^{20} +(-1.44066 + 2.21912i) q^{21} -0.856504 q^{22} +(2.47548 - 4.28766i) q^{23} +(1.39884 + 2.42287i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.000869950 + 0.00150680i) q^{26} +1.00000 q^{27} +(1.82445 - 2.81030i) q^{28} +6.32416 q^{29} +(0.428252 - 0.741755i) q^{30} +(-3.33950 - 5.78419i) q^{31} +(-2.85617 - 4.94704i) q^{32} +(0.500000 - 0.866025i) q^{33} -3.88236 q^{34} +(-2.64215 - 0.138088i) q^{35} -1.26640 q^{36} +(5.72820 - 9.92153i) q^{37} +(0.691993 + 1.19857i) q^{38} +(-0.00101570 - 0.00175924i) q^{39} +(-1.39884 + 2.42287i) q^{40} +9.43955 q^{41} +(-1.02908 - 2.01896i) q^{42} -3.08417 q^{43} +(-0.633200 + 1.09673i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.12026 + 3.67240i) q^{46} +(1.73875 - 3.01160i) q^{47} +0.136570 q^{48} +(-4.11287 + 5.66430i) q^{49} +0.856504 q^{50} +(2.26640 - 3.92552i) q^{51} +(0.00128628 + 0.00222790i) q^{52} +(-4.90692 - 8.49903i) q^{53} +(-0.428252 + 0.741755i) q^{54} +1.00000 q^{55} +(3.36138 + 6.59473i) q^{56} -1.61585 q^{57} +(-2.70833 + 4.69097i) q^{58} +(4.02073 + 6.96411i) q^{59} +(-0.633200 - 1.09673i) q^{60} +(2.48428 - 4.30290i) q^{61} +5.72060 q^{62} +(2.64215 + 0.138088i) q^{63} +4.61951 q^{64} +(0.00101570 - 0.00175924i) q^{65} +(0.428252 + 0.741755i) q^{66} +(-7.55136 - 13.0793i) q^{67} +(-2.87017 + 4.97128i) q^{68} -4.95097 q^{69} +(1.23393 - 1.90069i) q^{70} -6.69420 q^{71} +(1.39884 - 2.42287i) q^{72} +(1.36370 + 2.36199i) q^{73} +(4.90623 + 8.49783i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.04632 q^{76} +(1.44066 - 2.21912i) q^{77} +0.00173990 q^{78} +(2.09778 - 3.63345i) q^{79} +(0.0682849 + 0.118273i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.04251 + 7.00183i) q^{82} +4.95556 q^{83} +(-3.34601 - 0.174875i) q^{84} +4.53280 q^{85} +(1.32080 - 2.28770i) q^{86} +(-3.16208 - 5.47688i) q^{87} +(-1.39884 - 2.42287i) q^{88} +(1.20900 - 2.09405i) q^{89} -0.856504 q^{90} +(-0.00244069 - 0.00478842i) q^{91} +6.26990 q^{92} +(-3.33950 + 5.78419i) q^{93} +(1.48925 + 2.57945i) q^{94} +(-0.807926 - 1.39937i) q^{95} +(-2.85617 + 4.94704i) q^{96} +11.0874 q^{97} +(-2.44018 - 5.47649i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

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