LMFDB - Embedded newform 847.2.f.j.148.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.j.372.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 2.48990i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})$	\(q+(0.809017 + 2.48990i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(-0.809017 - 2.48990i) q^{9} +2.61803 q^{10} +3.00000 q^{12} +(-1.00000 - 3.07768i) q^{13} +(2.11803 + 1.53884i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(3.04508 - 9.37181i) q^{16} +(2.50000 - 7.69421i) q^{17} +(5.54508 - 4.02874i) q^{18} +(-5.04508 - 3.66547i) q^{19} +(1.50000 + 4.61653i) q^{20} -0.618034 q^{21} -6.09017 q^{23} +(1.42705 + 4.39201i) q^{24} +(3.23607 + 2.35114i) q^{25} +(6.85410 - 4.97980i) q^{26} +(-1.07295 + 3.30220i) q^{27} +(-1.50000 + 4.61653i) q^{28} +(-1.92705 + 1.40008i) q^{29} +(-1.30902 - 0.951057i) q^{30} +(0.0729490 + 0.224514i) q^{31} +10.8541 q^{32} +21.1803 q^{34} +(-0.309017 - 0.951057i) q^{35} +(10.2812 + 7.46969i) q^{36} +(2.00000 - 1.45309i) q^{37} +(5.04508 - 15.5272i) q^{38} +(-0.618034 + 1.90211i) q^{39} +(-6.04508 + 4.39201i) q^{40} +(9.04508 + 6.57164i) q^{41} +(-0.500000 - 1.53884i) q^{42} -7.56231 q^{43} -2.61803 q^{45} +(-4.92705 - 15.1639i) q^{46} +(3.54508 + 2.57565i) q^{47} +(-4.92705 + 3.57971i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.23607 + 9.95959i) q^{50} +(-4.04508 + 2.93893i) q^{51} +(12.7082 + 9.23305i) q^{52} +(-1.42705 - 4.39201i) q^{53} -9.09017 q^{54} -7.47214 q^{56} +(1.19098 + 3.66547i) q^{57} +(-5.04508 - 3.66547i) q^{58} +(0.0729490 - 0.0530006i) q^{59} +(0.927051 - 2.85317i) q^{60} +(1.66312 - 5.11855i) q^{61} +(-0.500000 + 0.363271i) q^{62} +(-2.11803 - 1.53884i) q^{63} +(2.69098 + 8.28199i) q^{64} -3.23607 q^{65} +7.32624 q^{67} +(12.1353 + 37.3485i) q^{68} +(3.04508 + 2.21238i) q^{69} +(2.11803 - 1.53884i) q^{70} +(-1.51722 + 4.66953i) q^{71} +(-6.04508 + 18.6049i) q^{72} +(-7.89919 + 5.73910i) q^{73} +(5.23607 + 3.80423i) q^{74} +(-0.763932 - 2.35114i) q^{75} +30.2705 q^{76} -5.23607 q^{78} +(-2.66312 - 8.19624i) q^{79} +(-7.97214 - 5.79210i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(-9.04508 + 27.8379i) q^{82} +(3.30902 - 10.1841i) q^{83} +(2.42705 - 1.76336i) q^{84} +(-6.54508 - 4.75528i) q^{85} +(-6.11803 - 18.8294i) q^{86} +1.47214 q^{87} +0.145898 q^{89} +(-2.11803 - 6.51864i) q^{90} +(-2.61803 - 1.90211i) q^{91} +(23.9164 - 17.3763i) q^{92} +(0.0450850 - 0.138757i) q^{93} +(-3.54508 + 10.9106i) q^{94} +(-5.04508 + 3.66547i) q^{95} +(-5.42705 - 3.94298i) q^{96} +(2.16312 + 6.65740i) q^{97} +2.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - 9 q^{4} - q^{5} + 2 q^{6} + q^{7} - 13 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 - 9 * q^4 - q^5 + 2 * q^6 + q^7 - 13 * q^8 - q^9	$ 4 q + q^{2} - 2 q^{3} - 9 q^{4} - q^{5} + 2 q^{6} + q^{7} - 13 q^{8} - q^{9} + 6 q^{10} + 12 q^{12} - 4 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} + 10 q^{17} + 11 q^{18} - 9 q^{19} + 6 q^{20} + 2 q^{21} - 2 q^{23} - q^{24} + 4 q^{25} + 14 q^{26} - 11 q^{27} - 6 q^{28} - q^{29} - 3 q^{30} + 7 q^{31} + 30 q^{32} + 40 q^{34} + q^{35} + 21 q^{36} + 8 q^{37} + 9 q^{38} + 2 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{45} - 13 q^{46} + 3 q^{47} - 13 q^{48} - q^{49} - 4 q^{50} - 5 q^{51} + 24 q^{52} + q^{53} - 14 q^{54} - 12 q^{56} + 7 q^{57} - 9 q^{58} + 7 q^{59} - 3 q^{60} - 9 q^{61} - 2 q^{62} - 4 q^{63} + 13 q^{64} - 4 q^{65} - 2 q^{67} + 15 q^{68} + q^{69} + 4 q^{70} + 23 q^{71} - 13 q^{72} - 7 q^{73} + 12 q^{74} - 12 q^{75} + 54 q^{76} - 12 q^{78} + 5 q^{79} - 14 q^{80} - 14 q^{81} - 25 q^{82} + 11 q^{83} + 3 q^{84} - 15 q^{85} - 20 q^{86} - 12 q^{87} + 14 q^{89} - 4 q^{90} - 6 q^{91} + 42 q^{92} - 11 q^{93} - 3 q^{94} - 9 q^{95} - 15 q^{96} - 7 q^{97} + 6 q^{98}+O(q^{100}) $ 4 * q + q^2 - 2 * q^3 - 9 * q^4 - q^5 + 2 * q^6 + q^7 - 13 * q^8 - q^9 + 6 * q^10 + 12 * q^12 - 4 * q^13 + 4 * q^14 - 2 * q^15 + q^16 + 10 * q^17 + 11 * q^18 - 9 * q^19 + 6 * q^20 + 2 * q^21 - 2 * q^23 - q^24 + 4 * q^25 + 14 * q^26 - 11 * q^27 - 6 * q^28 - q^29 - 3 * q^30 + 7 * q^31 + 30 * q^32 + 40 * q^34 + q^35 + 21 * q^36 + 8 * q^37 + 9 * q^38 + 2 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^45 - 13 * q^46 + 3 * q^47 - 13 * q^48 - q^49 - 4 * q^50 - 5 * q^51 + 24 * q^52 + q^53 - 14 * q^54 - 12 * q^56 + 7 * q^57 - 9 * q^58 + 7 * q^59 - 3 * q^60 - 9 * q^61 - 2 * q^62 - 4 * q^63 + 13 * q^64 - 4 * q^65 - 2 * q^67 + 15 * q^68 + q^69 + 4 * q^70 + 23 * q^71 - 13 * q^72 - 7 * q^73 + 12 * q^74 - 12 * q^75 + 54 * q^76 - 12 * q^78 + 5 * q^79 - 14 * q^80 - 14 * q^81 - 25 * q^82 + 11 * q^83 + 3 * q^84 - 15 * q^85 - 20 * q^86 - 12 * q^87 + 14 * q^89 - 4 * q^90 - 6 * q^91 + 42 * q^92 - 11 * q^93 - 3 * q^94 - 9 * q^95 - 15 * q^96 - 7 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	0.645974	+	0.763359i	$0.276451\pi$
$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	−0.0739128	+	0.997265i	$0.523549\pi$
$3$	−0.500000	−	0.363271i	−0.288675	−	0.209735i	0.434017	−	0.900905i	$-0.357096\pi$
$3$	−0.500000	−	0.363271i	−0.288675	−	0.209735i	−0.722692	+	0.691170i	$0.757096\pi$
$4$	−3.92705	+	2.85317i	−1.96353	+	1.42658i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i	−0.857877	−	0.513855i	$-0.828217\pi$
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i	0.996074	+	0.0885298i	$0.0282169\pi$
$6$	0.500000	−	1.53884i	0.204124	−	0.628230i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−6.04508	−	4.39201i	−2.13726	−	1.55281i
$9$	−0.809017	−	2.48990i	−0.269672	−	0.829966i
$10$	2.61803			0.827895
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	−0.988588	−	0.150644i	$-0.951865\pi$
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	0.711238	−	0.702951i	$-0.248135\pi$
$14$	2.11803	+	1.53884i	0.566068	+	0.411273i
$15$	−0.500000	+	0.363271i	−0.129099	+	0.0937962i
$16$	3.04508	−	9.37181i	0.761271	−	2.34295i
$17$	2.50000	−	7.69421i	0.606339	−	1.86612i	0.119029	−	0.992891i	$-0.462022\pi$
$17$	2.50000	−	7.69421i	0.606339	−	1.86612i	0.487310	−	0.873229i	$-0.337978\pi$
$18$	5.54508	−	4.02874i	1.30699	−	0.949583i
$19$	−5.04508	−	3.66547i	−1.15742	−	0.840916i	−0.167972	−	0.985792i	$-0.553722\pi$
$19$	−5.04508	−	3.66547i	−1.15742	−	0.840916i	−0.989450	+	0.144876i	$0.953722\pi$
$20$	1.50000	+	4.61653i	0.335410	+	1.03229i
$21$	−0.618034			−0.134866
$22$		0			0
$23$	−6.09017			−1.26989			−0.634944	−	0.772558i	$-0.718977\pi$
$23$	−6.09017			−1.26989			−0.634944	+	0.772558i	$0.718977\pi$
$24$	1.42705	+	4.39201i	0.291296	+	0.896516i
$25$	3.23607	+	2.35114i	0.647214	+	0.470228i
$26$	6.85410	−	4.97980i	1.34420	−	0.976618i
$27$	−1.07295	+	3.30220i	−0.206489	+	0.635508i
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	−1.92705	+	1.40008i	−0.357844	+	0.259989i	−0.752152	−	0.658989i	$-0.770984\pi$
$29$	−1.92705	+	1.40008i	−0.357844	+	0.259989i	0.394308	+	0.918978i	$0.370984\pi$
$30$	−1.30902	−	0.951057i	−0.238993	−	0.173638i
$31$	0.0729490	+	0.224514i	0.0131020	+	0.0403239i	0.957394	−	0.288786i	$-0.0932515\pi$
$31$	0.0729490	+	0.224514i	0.0131020	+	0.0403239i	−0.944292	+	0.329109i	$0.893251\pi$
$32$	10.8541			1.91875
$33$		0			0
$34$	21.1803			3.63240
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	10.2812	+	7.46969i	1.71353	+	1.24495i
$37$	2.00000	−	1.45309i	0.328798	−	0.238886i	−0.411122	−	0.911580i	$-0.634863\pi$
$37$	2.00000	−	1.45309i	0.328798	−	0.238886i	0.739920	+	0.672694i	$0.234863\pi$
$38$	5.04508	−	15.5272i	0.818421	−	2.51884i
$39$	−0.618034	+	1.90211i	−0.0989646	+	0.304582i
$40$	−6.04508	+	4.39201i	−0.955812	+	0.694438i
$41$	9.04508	+	6.57164i	1.41260	+	1.02632i	0.992937	+	0.118640i	$0.0378533\pi$
$41$	9.04508	+	6.57164i	1.41260	+	1.02632i	0.419668	+	0.907678i	$0.362147\pi$
$42$	−0.500000	−	1.53884i	−0.0771517	−	0.237448i
$43$	−7.56231			−1.15324			−0.576620	−	0.817012i	$-0.695629\pi$
$43$	−7.56231			−1.15324			−0.576620	+	0.817012i	$0.695629\pi$
$44$		0			0
$45$	−2.61803			−0.390273
$46$	−4.92705	−	15.1639i	−0.726454	−	2.23580i
$47$	3.54508	+	2.57565i	0.517104	+	0.375698i	0.815512	−	0.578741i	$-0.196456\pi$
$47$	3.54508	+	2.57565i	0.517104	+	0.375698i	−0.298408	+	0.954438i	$0.596456\pi$
$48$	−4.92705	+	3.57971i	−0.711159	+	0.516687i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.23607	+	9.95959i	−0.457649	+	1.40850i
$51$	−4.04508	+	2.93893i	−0.566425	+	0.411532i
$52$	12.7082	+	9.23305i	1.76231	+	1.28039i
$53$	−1.42705	−	4.39201i	−0.196021	−	0.603289i	−0.999963	−	0.00858231i	$-0.997268\pi$
$53$	−1.42705	−	4.39201i	−0.196021	−	0.603289i	0.803943	−	0.594707i	$-0.202732\pi$
$54$	−9.09017			−1.23702
$55$		0			0
$56$	−7.47214			−0.998506
$57$	1.19098	+	3.66547i	0.157750	+	0.485503i
$58$	−5.04508	−	3.66547i	−0.662452	−	0.481300i
$59$	0.0729490	−	0.0530006i	0.00949715	−	0.00690009i	−0.583027	−	0.812453i	$-0.698132\pi$
$59$	0.0729490	−	0.0530006i	0.00949715	−	0.00690009i	0.592524	+	0.805553i	$0.298132\pi$
$60$	0.927051	−	2.85317i	0.119682	−	0.368343i
$61$	1.66312	−	5.11855i	0.212941	−	0.655364i	−0.786353	−	0.617778i	$-0.788033\pi$
$61$	1.66312	−	5.11855i	0.212941	−	0.655364i	0.999293	−	0.0375860i	$-0.0119668\pi$
$62$	−0.500000	+	0.363271i	−0.0635001	+	0.0461355i
$63$	−2.11803	−	1.53884i	−0.266847	−	0.193876i
$64$	2.69098	+	8.28199i	0.336373	+	1.03525i
$65$	−3.23607			−0.401385
$66$		0			0
$67$	7.32624			0.895042			0.447521	−	0.894273i	$-0.352307\pi$
$67$	7.32624			0.895042			0.447521	+	0.894273i	$0.352307\pi$
$68$	12.1353	+	37.3485i	1.47162	+	4.52917i
$69$	3.04508	+	2.21238i	0.366585	+	0.266340i
$70$	2.11803	−	1.53884i	0.253153	−	0.183927i
$71$	−1.51722	+	4.66953i	−0.180061	+	0.554171i	−0.999828	−	0.0185259i	$-0.994103\pi$
$71$	−1.51722	+	4.66953i	−0.180061	+	0.554171i	0.819767	+	0.572697i	$0.194103\pi$
$72$	−6.04508	+	18.6049i	−0.712420	+	2.19260i
$73$	−7.89919	+	5.73910i	−0.924530	+	0.671710i	−0.944647	−	0.328087i	$-0.893596\pi$
$73$	−7.89919	+	5.73910i	−0.924530	+	0.671710i	0.0201175	+	0.999798i	$0.493596\pi$
$74$	5.23607	+	3.80423i	0.608681	+	0.442232i
$75$	−0.763932	−	2.35114i	−0.0882113	−	0.271486i
$76$	30.2705			3.47227
$77$		0			0
$78$	−5.23607			−0.592868
$79$	−2.66312	−	8.19624i	−0.299624	−	0.922149i	−0.981629	−	0.190801i	$-0.938892\pi$
$79$	−2.66312	−	8.19624i	−0.299624	−	0.922149i	0.682004	−	0.731348i	$-0.261108\pi$
$80$	−7.97214	−	5.79210i	−0.891312	−	0.647576i
$81$	−4.61803	+	3.35520i	−0.513115	+	0.372800i
$82$	−9.04508	+	27.8379i	−0.998863	+	3.07418i
$83$	3.30902	−	10.1841i	0.363212	−	1.11785i	−0.587881	−	0.808947i	$-0.700038\pi$
$83$	3.30902	−	10.1841i	0.363212	−	1.11785i	0.951093	−	0.308904i	$-0.0999621\pi$
$84$	2.42705	−	1.76336i	0.264813	−	0.192398i
$85$	−6.54508	−	4.75528i	−0.709914	−	0.515783i
$86$	−6.11803	−	18.8294i	−0.659725	−	2.03042i
$87$	1.47214			0.157830
$88$		0			0
$89$	0.145898			0.0154652			0.00773258	−	0.999970i	$-0.497539\pi$
$89$	0.145898			0.0154652			0.00773258	+	0.999970i	$0.497539\pi$
$90$	−2.11803	−	6.51864i	−0.223260	−	0.687125i
$91$	−2.61803	−	1.90211i	−0.274445	−	0.199396i
$92$	23.9164	−	17.3763i	2.49346	−	1.81160i
$93$	0.0450850	−	0.138757i	0.00467509	−	0.0143885i
$94$	−3.54508	+	10.9106i	−0.365648	+	1.12535i
$95$	−5.04508	+	3.66547i	−0.517615	+	0.376069i
$96$	−5.42705	−	3.94298i	−0.553896	−	0.402429i
$97$	2.16312	+	6.65740i	0.219631	+	0.675956i	0.998792	+	0.0491321i	$0.0156455\pi$
$97$	2.16312	+	6.65740i	0.219631	+	0.675956i	−0.779161	+	0.626824i	$0.784354\pi$
$98$	2.61803			0.264461
$99$		0			0
$100$	−19.4164			−1.94164
$101$	−3.02786	−	9.31881i	−0.301284	−	0.927256i	−0.981038	−	0.193816i	$-0.937914\pi$
$101$	−3.02786	−	9.31881i	−0.301284	−	0.927256i	0.679754	−	0.733440i	$-0.262086\pi$
$102$	−10.5902	−	7.69421i	−1.04858	−	0.761840i
$103$	−1.73607	+	1.26133i	−0.171060	+	0.124282i	−0.670021	−	0.742342i	$-0.733715\pi$
$103$	−1.73607	+	1.26133i	−0.171060	+	0.124282i	0.498961	+	0.866624i	$0.333715\pi$
$104$	−7.47214	+	22.9969i	−0.732703	+	2.25503i
$105$	−0.190983	+	0.587785i	−0.0186380	+	0.0573620i
$106$	9.78115	−	7.10642i	0.950030	−	0.690237i
$107$	−8.66312	−	6.29412i	−0.837495	−	0.608476i	0.0841746	−	0.996451i	$-0.473175\pi$
$107$	−8.66312	−	6.29412i	−0.837495	−	0.608476i	−0.921670	+	0.387975i	$0.873175\pi$
$108$	−5.20820	−	16.0292i	−0.501160	−	1.54241i
$109$	10.4721			1.00305			0.501524	−	0.865144i	$-0.332773\pi$
$109$	10.4721			1.00305			0.501524	+	0.865144i	$0.332773\pi$
$110$		0			0
$111$	−1.52786			−0.145018
$112$	−3.04508	−	9.37181i	−0.287733	−	0.885553i
$113$	−5.54508	−	4.02874i	−0.521638	−	0.378992i	0.295583	−	0.955317i	$-0.404486\pi$
$113$	−5.54508	−	4.02874i	−0.521638	−	0.378992i	−0.817220	+	0.576325i	$0.804486\pi$
$114$	−8.16312	+	5.93085i	−0.764546	+	0.555475i
$115$	−1.88197	+	5.79210i	−0.175494	+	0.540116i
$116$	3.57295	−	10.9964i	0.331740	−	1.02099i
$117$	−6.85410	+	4.97980i	−0.633662	+	0.460382i
$118$	0.190983	+	0.138757i	0.0175814	+	0.0127736i
$119$	−2.50000	−	7.69421i	−0.229175	−	0.705327i
$120$	4.61803			0.421567
$121$		0			0
$122$	14.0902			1.27566
$123$	−2.13525	−	6.57164i	−0.192529	−	0.592545i
$124$	−0.927051	−	0.673542i	−0.0832516	−	0.0604859i
$125$	7.28115	−	5.29007i	0.651246	−	0.473158i
$126$	2.11803	−	6.51864i	0.188689	−	0.580726i
$127$	4.61803	−	14.2128i	0.409784	−	1.26119i	−0.507049	−	0.861917i	$-0.669264\pi$
$127$	4.61803	−	14.2128i	0.409784	−	1.26119i	0.916834	−	0.399269i	$-0.130736\pi$
$128$	−0.881966	+	0.640786i	−0.0779555	+	0.0566380i
$129$	3.78115	+	2.74717i	0.332912	+	0.241875i
$130$	−2.61803	−	8.05748i	−0.229617	−	0.706688i
$131$	−1.05573			−0.0922394			−0.0461197	−	0.998936i	$-0.514686\pi$
$131$	−1.05573			−0.0922394			−0.0461197	+	0.998936i	$0.514686\pi$
$132$		0			0
$133$	−6.23607			−0.540736
$134$	5.92705	+	18.2416i	0.512019	+	1.57583i
$135$	2.80902	+	2.04087i	0.241762	+	0.175650i
$136$	−48.9058	+	35.5321i	−4.19363	+	3.04685i
$137$	0.100813	−	0.310271i	0.00861304	−	0.0265082i	−0.946658	−	0.322241i	$-0.895564\pi$
$137$	0.100813	−	0.310271i	0.00861304	−	0.0265082i	0.955271	+	0.295733i	$0.0955638\pi$
$138$	−3.04508	+	9.37181i	−0.259215	+	0.797781i
$139$	−4.80902	+	3.49396i	−0.407895	+	0.296353i	−0.772749	−	0.634711i	$-0.781119\pi$
$139$	−4.80902	+	3.49396i	−0.407895	+	0.296353i	0.364854	+	0.931065i	$0.381119\pi$
$140$	3.92705	+	2.85317i	0.331896	+	0.241137i
$141$	−0.836881	−	2.57565i	−0.0704781	−	0.216909i
$142$	−12.8541			−1.07869
$143$		0			0
$144$	−25.7984			−2.14986
$145$	0.736068	+	2.26538i	0.0611271	+	0.188130i
$146$	−20.6803	−	15.0251i	−1.71152	−	1.24349i
$147$	−0.500000	+	0.363271i	−0.0412393	+	0.0299621i
$148$	−3.70820	+	11.4127i	−0.304812	+	0.938116i
$149$	0.663119	−	2.04087i	0.0543248	−	0.167195i	−0.920213	−	0.391418i	$-0.871985\pi$
$149$	0.663119	−	2.04087i	0.0543248	−	0.167195i	0.974538	+	0.224224i	$0.0719846\pi$
$150$	5.23607	−	3.80423i	0.427523	−	0.310614i
$151$	14.5172	+	10.5474i	1.18139	+	0.858333i	0.992328	−	0.123631i	$-0.0394539\pi$
$151$	14.5172	+	10.5474i	1.18139	+	0.858333i	0.189066	+	0.981964i	$0.439454\pi$
$152$	14.3992	+	44.3161i	1.16793	+	3.59451i
$153$	−21.1803			−1.71233
$154$		0			0
$155$	0.236068			0.0189614
$156$	−3.00000	−	9.23305i	−0.240192	−	0.739236i
$157$	12.8541	+	9.33905i	1.02587	+	0.745337i	0.967478	−	0.252956i	$-0.0814029\pi$
$157$	12.8541	+	9.33905i	1.02587	+	0.745337i	0.0583913	+	0.998294i	$0.481403\pi$
$158$	18.2533	−	13.2618i	1.45215	−	1.05505i
$159$	−0.881966	+	2.71441i	−0.0699445	+	0.215267i
$160$	3.35410	−	10.3229i	0.265165	−	0.816094i
$161$	−4.92705	+	3.57971i	−0.388306	+	0.282121i
$162$	−12.0902	−	8.78402i	−0.949893	−	0.690138i
$163$	1.45492	+	4.47777i	0.113958	+	0.350726i	0.991728	−	0.128356i	$-0.0409699\pi$
$163$	1.45492	+	4.47777i	0.113958	+	0.350726i	−0.877770	+	0.479081i	$0.840970\pi$
$164$	−54.2705			−4.23781
$165$		0			0
$166$	28.0344			2.17589
$167$	0.763932	+	2.35114i	0.0591148	+	0.181937i	0.976253	−	0.216632i	$-0.0695071\pi$
$167$	0.763932	+	2.35114i	0.0591148	+	0.181937i	−0.917139	+	0.398569i	$0.869507\pi$
$168$	3.73607	+	2.71441i	0.288244	+	0.209421i
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	6.54508	−	20.1437i	0.501985	−	1.54495i
$171$	−5.04508	+	15.5272i	−0.385807	+	1.18739i
$172$	29.6976	−	21.5765i	2.26442	−	1.64520i
$173$	−14.2533	−	10.3556i	−1.08366	−	0.787323i	−0.105340	−	0.994436i	$-0.533593\pi$
$173$	−14.2533	−	10.3556i	−1.08366	−	0.787323i	−0.978317	+	0.207113i	$0.933593\pi$
$174$	1.19098	+	3.66547i	0.0902882	+	0.277878i
$175$	4.00000			0.302372
$176$		0			0
$177$	−0.0557281			−0.00418878
$178$	0.118034	+	0.363271i	0.00884702	+	0.0272283i
$179$	6.66312	+	4.84104i	0.498025	+	0.361836i	0.808262	−	0.588823i	$-0.200408\pi$
$179$	6.66312	+	4.84104i	0.498025	+	0.361836i	−0.310237	+	0.950659i	$0.600408\pi$
$180$	10.2812	−	7.46969i	0.766312	−	0.556758i
$181$	6.00000	−	18.4661i	0.445976	−	1.37257i	−0.435433	−	0.900221i	$-0.643405\pi$
$181$	6.00000	−	18.4661i	0.445976	−	1.37257i	0.881409	−	0.472353i	$-0.156595\pi$
$182$	2.61803	−	8.05748i	0.194062	−	0.597260i
$183$	−2.69098	+	1.95511i	−0.198923	+	0.144526i
$184$	36.8156	+	26.7481i	2.71408	+	1.97190i
$185$	−0.763932	−	2.35114i	−0.0561654	−	0.172859i
$186$	0.381966			0.0280071
$187$		0			0
$188$	−21.2705			−1.55131
$189$	1.07295	+	3.30220i	0.0780456	+	0.240200i
$190$	−13.2082	−	9.59632i	−0.958224	−	0.696190i
$191$	−16.3713	+	11.8945i	−1.18459	+	0.860653i	−0.992682	−	0.120760i	$-0.961467\pi$
$191$	−16.3713	+	11.8945i	−1.18459	+	0.860653i	−0.191906	+	0.981413i	$0.561467\pi$
$192$	1.66312	−	5.11855i	0.120025	−	0.369400i
$193$	−0.100813	+	0.310271i	−0.00725668	+	0.0223338i	−0.954619	−	0.297829i	$-0.903738\pi$
$193$	−0.100813	+	0.310271i	−0.00725668	+	0.0223338i	0.947363	+	0.320163i	$0.103738\pi$
$194$	−14.8262	+	10.7719i	−1.06446	+	0.773377i
$195$	1.61803	+	1.17557i	0.115870	+	0.0841844i
$196$	1.50000	+	4.61653i	0.107143	+	0.329752i
$197$	17.7082			1.26166			0.630829	−	0.775922i	$-0.282715\pi$
$197$	17.7082			1.26166			0.630829	+	0.775922i	$0.282715\pi$
$198$		0			0
$199$	−3.76393			−0.266818			−0.133409	−	0.991061i	$-0.542592\pi$
$199$	−3.76393			−0.266818			−0.133409	+	0.991061i	$0.542592\pi$
$200$	−9.23607	−	28.4257i	−0.653089	−	2.01000i
$201$	−3.66312	−	2.66141i	−0.258376	−	0.187722i
$202$	20.7533	−	15.0781i	1.46020	−	1.06089i
$203$	−0.736068	+	2.26538i	−0.0516618	+	0.158999i
$204$	7.50000	−	23.0826i	0.525105	−	1.61611i
$205$	9.04508	−	6.57164i	0.631736	−	0.458983i
$206$	−4.54508	−	3.30220i	−0.316671	−	0.230075i
$207$	4.92705	+	15.1639i	0.342454	+	1.05396i
$208$	−31.8885			−2.21107
$209$		0			0
$210$	−1.61803			−0.111655
$211$	−4.13525	−	12.7270i	−0.284683	−	0.876163i	−0.986494	−	0.163800i	$-0.947625\pi$
$211$	−4.13525	−	12.7270i	−0.284683	−	0.876163i	0.701811	−	0.712363i	$-0.252375\pi$
$212$	18.1353	+	13.1760i	1.24553	+	0.904934i
$213$	2.45492	−	1.78360i	0.168208	−	0.122210i
$214$	8.66312	−	26.6623i	0.592199	−	1.82260i
$215$	−2.33688	+	7.19218i	−0.159374	+	0.490503i
$216$	20.9894	−	15.2497i	1.42814	−	1.03761i
$217$	0.190983	+	0.138757i	0.0129648	+	0.00941946i
$218$	8.47214	+	26.0746i	0.573805	+	1.76599i
$219$	6.03444			0.407770
$220$		0			0
$221$	−26.1803			−1.76108
$222$	−1.23607	−	3.80423i	−0.0829595	−	0.255323i
$223$	21.8713	+	15.8904i	1.46461	+	1.06410i	0.982131	+	0.188196i	$0.0602641\pi$
$223$	21.8713	+	15.8904i	1.46461	+	1.06410i	0.482481	+	0.875907i	$0.339736\pi$
$224$	8.78115	−	6.37988i	0.586715	−	0.426274i
$225$	3.23607	−	9.95959i	0.215738	−	0.663973i
$226$	5.54508	−	17.0660i	0.368854	−	1.13521i
$227$	10.5451	−	7.66145i	0.699902	−	0.508508i	−0.179998	−	0.983667i	$-0.557609\pi$
$227$	10.5451	−	7.66145i	0.699902	−	0.508508i	0.879900	+	0.475158i	$0.157609\pi$
$228$	−15.1353	−	10.9964i	−1.00236	−	0.728255i
$229$	3.47214	+	10.6861i	0.229445	+	0.706160i	0.997810	+	0.0661474i	$0.0210708\pi$
$229$	3.47214	+	10.6861i	0.229445	+	0.706160i	−0.768365	+	0.640012i	$0.778929\pi$
$230$	−15.9443			−1.05133
$231$		0			0
$232$	17.7984			1.16852
$233$	0.798374	+	2.45714i	0.0523032	+	0.160973i	0.973796	−	0.227422i	$-0.0730297\pi$
$233$	0.798374	+	2.45714i	0.0523032	+	0.160973i	−0.921493	+	0.388395i	$0.873030\pi$
$234$	−17.9443	−	13.0373i	−1.17305	−	0.852273i
$235$	3.54508	−	2.57565i	0.231256	−	0.168017i
$236$	−0.135255	+	0.416272i	−0.00880435	+	0.0270970i
$237$	−1.64590	+	5.06555i	−0.106913	+	0.329043i
$238$	17.1353	−	12.4495i	1.11071	−	0.806981i
$239$	−4.78115	−	3.47371i	−0.309267	−	0.224696i	0.422315	−	0.906449i	$-0.361218\pi$
$239$	−4.78115	−	3.47371i	−0.309267	−	0.224696i	−0.731582	+	0.681754i	$0.761218\pi$
$240$	1.88197	+	5.79210i	0.121480	+	0.373878i
$241$	17.2705			1.11249			0.556246	−	0.831018i	$-0.312241\pi$
$241$	17.2705			1.11249			0.556246	+	0.831018i	$0.312241\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$	8.07295	+	24.8460i	0.516818	+	1.59060i
$245$	−0.809017	−	0.587785i	−0.0516862	−	0.0375522i
$246$	14.6353	−	10.6331i	0.933110	−	0.677944i
$247$	−6.23607	+	19.1926i	−0.396792	+	1.22120i
$248$	0.545085	−	1.67760i	0.0346129	−	0.106528i
$249$	−5.35410	+	3.88998i	−0.339302	+	0.246518i
$250$	19.0623	+	13.8496i	1.20561	+	0.875924i
$251$	7.10739	+	21.8743i	0.448615	+	1.38069i	0.878471	+	0.477796i	$0.158564\pi$
$251$	7.10739	+	21.8743i	0.448615	+	1.38069i	−0.429856	+	0.902897i	$0.641436\pi$
$252$	12.7082			0.800542
$253$		0			0
$254$	39.1246			2.45490
$255$	1.54508	+	4.75528i	0.0967570	+	0.297787i
$256$	11.7812	+	8.55951i	0.736322	+	0.534969i
$257$	−9.35410	+	6.79615i	−0.583493	+	0.423932i	−0.839982	−	0.542615i	$-0.817434\pi$
$257$	−9.35410	+	6.79615i	−0.583493	+	0.423932i	0.256489	+	0.966547i	$0.417434\pi$
$258$	−3.78115	+	11.6372i	−0.235404	+	0.724500i
$259$	0.763932	−	2.35114i	0.0474684	−	0.146093i
$260$	12.7082	−	9.23305i	0.788129	−	0.572609i
$261$	5.04508	+	3.66547i	0.312283	+	0.226887i
$262$	−0.854102	−	2.62866i	−0.0527666	−	0.162399i
$263$	−23.1246			−1.42592			−0.712962	−	0.701202i	$-0.752647\pi$
$263$	−23.1246			−1.42592			−0.712962	+	0.701202i	$0.752647\pi$
$264$		0			0
$265$	−4.61803			−0.283684
$266$	−5.04508	−	15.5272i	−0.309334	−	0.952032i
$267$	−0.0729490	−	0.0530006i	−0.00446441	−	0.00324358i
$268$	−28.7705	+	20.9030i	−1.75744	+	1.27685i
$269$	3.13525	−	9.64932i	0.191160	−	0.588330i	−0.808840	−	0.588029i	$-0.799904\pi$
$269$	3.13525	−	9.64932i	0.191160	−	0.588330i	1.00000		0.000300908i	$-9.57819e-5\pi$
$270$	−2.80902	+	8.64527i	−0.170951	+	0.526134i
$271$	16.0172	−	11.6372i	0.972977	−	0.706909i	0.0168488	−	0.999858i	$-0.494637\pi$
$271$	16.0172	−	11.6372i	0.972977	−	0.706909i	0.956128	+	0.292949i	$0.0946366\pi$
$272$	−64.4959	−	46.8590i	−3.91064	−	2.84125i
$273$	0.618034	+	1.90211i	0.0374051	+	0.115121i
$274$	0.854102			0.0515982
$275$		0			0
$276$	−18.2705			−1.09976
$277$	1.86475	+	5.73910i	0.112042	+	0.344829i	0.991319	−	0.131482i	$-0.0419736\pi$
$277$	1.86475	+	5.73910i	0.112042	+	0.344829i	−0.879277	+	0.476311i	$0.841974\pi$
$278$	−12.5902	−	9.14729i	−0.755108	−	0.548618i
$279$	0.500000	−	0.363271i	0.0299342	−	0.0217485i
$280$	−2.30902	+	7.10642i	−0.137990	+	0.424690i
$281$	0.871323	−	2.68166i	0.0519788	−	0.159974i	−0.921698	−	0.387909i	$-0.873197\pi$
$281$	0.871323	−	2.68166i	0.0519788	−	0.159974i	0.973676	+	0.227935i	$0.0731974\pi$
$282$	5.73607	−	4.16750i	0.341578	−	0.248171i
$283$	−4.80902	−	3.49396i	−0.285866	−	0.207694i	0.435606	−	0.900138i	$-0.356534\pi$
$283$	−4.80902	−	3.49396i	−0.285866	−	0.207694i	−0.721472	+	0.692443i	$0.756534\pi$
$284$	−7.36475	−	22.6664i	−0.437017	−	1.34500i
$285$	3.85410			0.228297
$286$		0			0
$287$	11.1803			0.659955
$288$	−8.78115	−	27.0256i	−0.517434	−	1.59250i
$289$	−39.1976	−	28.4787i	−2.30574	−	1.67522i
$290$	−5.04508	+	3.66547i	−0.296258	+	0.215244i
$291$	1.33688	−	4.11450i	0.0783694	−	0.241196i
$292$	14.6459	−	45.0754i	0.857086	−	2.63784i
$293$	−8.89919	+	6.46564i	−0.519896	+	0.377727i	−0.816565	−	0.577254i	$-0.804124\pi$
$293$	−8.89919	+	6.46564i	−0.519896	+	0.377727i	0.296669	+	0.954980i	$0.404124\pi$
$294$	−1.30902	−	0.951057i	−0.0763434	−	0.0554667i
$295$	−0.0278640	−	0.0857567i	−0.00162231	−	0.00499295i
$296$	−18.4721			−1.07367
$297$		0			0
$298$	5.61803			0.325444
$299$	6.09017	+	18.7436i	0.352204	+	1.08397i
$300$	9.70820	+	7.05342i	0.560503	+	0.407230i
$301$	−6.11803	+	4.44501i	−0.352638	+	0.256206i
$302$	−14.5172	+	44.6794i	−0.835372	+	2.57101i
$303$	−1.87132	+	5.75934i	−0.107505	+	0.330865i
$304$	−49.7148	+	36.1199i	−2.85134	+	2.07162i
$305$	−4.35410	−	3.16344i	−0.249315	−	0.181138i
$306$	−17.1353	−	52.7369i	−0.979557	−	3.01477i
$307$	0.819660			0.0467805			0.0233902	−	0.999726i	$-0.492554\pi$
$307$	0.819660			0.0467805			0.0233902	+	0.999726i	$0.492554\pi$
$308$		0			0
$309$	1.32624			0.0754470
$310$	0.190983	+	0.587785i	0.0108471	+	0.0333840i
$311$	−7.28115	−	5.29007i	−0.412876	−	0.299972i	0.361889	−	0.932221i	$-0.382132\pi$
$311$	−7.28115	−	5.29007i	−0.412876	−	0.299972i	−0.774765	+	0.632249i	$0.782132\pi$
$312$	12.0902	−	8.78402i	0.684471	−	0.497297i
$313$	0.826238	−	2.54290i	0.0467017	−	0.143733i	−0.924986	−	0.380000i	$-0.875924\pi$
$313$	0.826238	−	2.54290i	0.0467017	−	0.143733i	0.971688	+	0.236267i	$0.0759240\pi$
$314$	−12.8541	+	39.5609i	−0.725399	+	2.23255i
$315$	−2.11803	+	1.53884i	−0.119338	+	0.0867039i
$316$	33.8435	+	24.5887i	1.90384	+	1.38322i
$317$	−7.59017	−	23.3601i	−0.426306	−	1.31204i	−0.901738	−	0.432283i	$-0.857708\pi$
$317$	−7.59017	−	23.3601i	−0.426306	−	1.31204i	0.475431	−	0.879753i	$-0.342292\pi$
$318$	−7.47214			−0.419017
$319$		0			0
$320$	8.70820			0.486803
$321$	2.04508	+	6.29412i	0.114146	+	0.351304i
$322$	−12.8992	−	9.37181i	−0.718844	−	0.522270i
$323$	−40.8156	+	29.6543i	−2.27104	+	1.65001i
$324$	8.56231	−	26.3521i	0.475684	−	1.46400i
$325$	4.00000	−	12.3107i	0.221880	−	0.682877i
$326$	−9.97214	+	7.24518i	−0.552306	+	0.401273i
$327$	−5.23607	−	3.80423i	−0.289555	−	0.210374i
$328$	−25.8156	−	79.4522i	−1.42543	−	4.38702i
$329$	4.38197			0.241586
$330$		0			0
$331$	−16.1803			−0.889352			−0.444676	−	0.895692i	$-0.646681\pi$
$331$	−16.1803			−0.889352			−0.444676	+	0.895692i	$0.646681\pi$
$332$	16.0623	+	49.4347i	0.881534	+	2.71308i
$333$	−5.23607	−	3.80423i	−0.286935	−	0.208470i
$334$	−5.23607	+	3.80423i	−0.286505	+	0.208158i
$335$	2.26393	−	6.96767i	0.123692	−	0.380684i
$336$	−1.88197	+	5.79210i	−0.102670	+	0.315985i
$337$	6.51722	−	4.73504i	0.355016	−	0.257934i	−0.395954	−	0.918270i	$-0.629586\pi$
$337$	6.51722	−	4.73504i	0.355016	−	0.257934i	0.750970	+	0.660336i	$0.229586\pi$
$338$	5.35410	+	3.88998i	0.291225	+	0.211587i
$339$	1.30902	+	4.02874i	0.0710960	+	0.218811i
$340$	39.2705			2.12974
$341$		0			0
$342$	−42.7426			−2.31126
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	45.7148	+	33.2137i	2.46478	+	1.79076i
$345$	3.04508	−	2.21238i	0.163942	−	0.119111i
$346$	14.2533	−	43.8671i	0.766262	−	2.35831i
$347$	−10.3992	+	32.0054i	−0.558258	+	1.71814i	0.128924	+	0.991654i	$0.458848\pi$
$347$	−10.3992	+	32.0054i	−0.558258	+	1.71814i	−0.687182	+	0.726486i	$0.741152\pi$
$348$	−5.78115	+	4.20025i	−0.309902	+	0.225157i
$349$	6.63525	+	4.82079i	0.355177	+	0.258051i	0.751038	−	0.660259i	$-0.229554\pi$
$349$	6.63525	+	4.82079i	0.355177	+	0.258051i	−0.395861	+	0.918311i	$0.629554\pi$
$350$	3.23607	+	9.95959i	0.172975	+	0.532363i
$351$	11.2361			0.599737
$352$		0			0
$353$	12.9098			0.687121			0.343560	−	0.939131i	$-0.388367\pi$
$353$	12.9098			0.687121			0.343560	+	0.939131i	$0.388367\pi$
$354$	−0.0450850	−	0.138757i	−0.00239624	−	0.00737487i
$355$	3.97214	+	2.88593i	0.210819	+	0.153169i
$356$	−0.572949	+	0.416272i	−0.0303662	+	0.0220624i
$357$	−1.54508	+	4.75528i	−0.0817746	+	0.251676i
$358$	−6.66312	+	20.5070i	−0.352157	+	1.08383i
$359$	−10.8262	+	7.86572i	−0.571387	+	0.415137i	−0.835609	−	0.549325i	$-0.814885\pi$
$359$	−10.8262	+	7.86572i	−0.571387	+	0.415137i	0.264222	+	0.964462i	$0.414885\pi$
$360$	15.8262	+	11.4984i	0.834116	+	0.606021i
$361$	6.14590	+	18.9151i	0.323468	+	0.995533i
$362$	50.8328			2.67171
$363$		0			0
$364$	15.7082			0.823334
$365$	3.01722	+	9.28605i	0.157929	+	0.486054i
$366$	−7.04508	−	5.11855i	−0.368252	−	0.267551i
$367$	16.8541	−	12.2452i	0.879777	−	0.639195i	−0.0534155	−	0.998572i	$-0.517011\pi$
$367$	16.8541	−	12.2452i	0.879777	−	0.639195i	0.933192	+	0.359377i	$0.117011\pi$
$368$	−18.5451	+	57.0759i	−0.966729	+	2.97529i
$369$	9.04508	−	27.8379i	0.470868	−	1.44918i
$370$	5.23607	−	3.80423i	0.272210	−	0.197772i
$371$	−3.73607	−	2.71441i	−0.193967	−	0.140925i
$372$	0.218847	+	0.673542i	0.0113467	+	0.0349215i
$373$	35.5623			1.84135			0.920673	−	0.390334i	$-0.127641\pi$
$373$	35.5623			1.84135			0.920673	+	0.390334i	$0.127641\pi$
$374$		0			0
$375$	−5.56231			−0.287236
$376$	−10.1180	−	31.1401i	−0.521798	−	1.60593i
$377$	6.23607	+	4.53077i	0.321174	+	0.233346i
$378$	−7.35410	+	5.34307i	−0.378254	+	0.274818i
$379$	−8.05573	+	24.7930i	−0.413795	+	1.27353i	0.499529	+	0.866297i	$0.333506\pi$
$379$	−8.05573	+	24.7930i	−0.413795	+	1.27353i	−0.913324	+	0.407233i	$0.866494\pi$
$380$	9.35410	−	28.7890i	0.479855	−	1.47684i
$381$	−7.47214	+	5.42882i	−0.382809	+	0.278127i
$382$	−42.8607	−	31.1401i	−2.19294	−	1.59327i
$383$	4.51064	+	13.8823i	0.230483	+	0.709354i	0.997689	+	0.0679526i	$0.0216467\pi$
$383$	4.51064	+	13.8823i	0.230483	+	0.709354i	−0.767205	+	0.641401i	$0.778353\pi$
$384$	0.673762			0.0343828
$385$		0			0
$386$	−0.854102			−0.0434726
$387$	6.11803	+	18.8294i	0.310997	+	0.957151i
$388$	−27.4894	−	19.9722i	−1.39556	−	1.01393i
$389$	9.56231	−	6.94742i	0.484828	−	0.352248i	−0.318364	−	0.947969i	$-0.603133\pi$
$389$	9.56231	−	6.94742i	0.484828	−	0.352248i	0.803192	+	0.595720i	$0.203133\pi$
$390$	−1.61803	+	4.97980i	−0.0819323	+	0.252162i
$391$	−15.2254	+	46.8590i	−0.769983	+	2.36976i
$392$	−6.04508	+	4.39201i	−0.305323	+	0.221830i
$393$	0.527864	+	0.383516i	0.0266272	+	0.0193458i
$394$	14.3262	+	44.0916i	0.721745	+	2.22130i
$395$	−8.61803			−0.433620
$396$		0			0
$397$	−23.1803			−1.16339			−0.581694	−	0.813408i	$-0.697610\pi$
$397$	−23.1803			−1.16339			−0.581694	+	0.813408i	$0.697610\pi$
$398$	−3.04508	−	9.37181i	−0.152636	−	0.469766i
$399$	3.11803	+	2.26538i	0.156097	+	0.113411i
$400$	31.8885	−	23.1684i	1.59443	−	1.15842i
$401$	−8.18034	+	25.1765i	−0.408507	+	1.25725i	0.509425	+	0.860515i	$0.329858\pi$
$401$	−8.18034	+	25.1765i	−0.408507	+	1.25725i	−0.917931	+	0.396739i	$0.870142\pi$
$402$	3.66312	−	11.2739i	0.182700	−	0.562292i
$403$	0.618034	−	0.449028i	0.0307865	−	0.0223677i
$404$	38.4787	+	27.9564i	1.91439	+	1.39088i
$405$	1.76393	+	5.42882i	0.0876505	+	0.269760i
$406$	−6.23607			−0.309491
$407$		0			0
$408$	37.3607			1.84963
$409$	1.32624	+	4.08174i	0.0655782	+	0.201829i	0.978477	−	0.206358i	$-0.0661611\pi$
$409$	1.32624	+	4.08174i	0.0655782	+	0.201829i	−0.912898	+	0.408187i	$0.866161\pi$
$410$	23.6803	+	17.2048i	1.16949	+	0.849683i
$411$	−0.163119	+	0.118513i	−0.00804606	+	0.00584581i
$412$	3.21885	−	9.90659i	0.158581	−	0.488063i
$413$	0.0278640	−	0.0857567i	0.00137110	−	0.00421981i
$414$	−33.7705	+	24.5357i	−1.65973	+	1.20586i
$415$	−8.66312	−	6.29412i	−0.425256	−	0.308966i
$416$	−10.8541	−	33.4055i	−0.532166	−	1.63784i
$417$	3.67376			0.179905
$418$		0			0
$419$	−5.88854			−0.287674			−0.143837	−	0.989601i	$-0.545944\pi$
$419$	−5.88854			−0.287674			−0.143837	+	0.989601i	$0.545944\pi$
$420$	−0.927051	−	2.85317i	−0.0452355	−	0.139220i
$421$	−4.23607	−	3.07768i	−0.206453	−	0.149997i	0.479754	−	0.877403i	$-0.340726\pi$
$421$	−4.23607	−	3.07768i	−0.206453	−	0.149997i	−0.686208	+	0.727406i	$0.740726\pi$
$422$	28.3435	−	20.5927i	1.37974	−	1.00244i
$423$	3.54508	−	10.9106i	0.172368	−	0.530494i
$424$	−10.6631	+	32.8177i	−0.517847	+	1.59377i
$425$	26.1803	−	19.0211i	1.26993	−	0.922660i
$426$	6.42705	+	4.66953i	0.311392	+	0.226239i
$427$	−1.66312	−	5.11855i	−0.0804840	−	0.247704i
$428$	51.9787			2.51249
$429$		0			0
$430$	−19.7984			−0.954762
$431$	2.20820	+	6.79615i	0.106365	+	0.327359i	0.990049	−	0.140727i	$-0.0449438\pi$
$431$	2.20820	+	6.79615i	0.106365	+	0.327359i	−0.883683	+	0.468086i	$0.844944\pi$
$432$	27.6803	+	20.1109i	1.33177	+	0.967588i
$433$	30.7705	−	22.3561i	1.47874	−	1.07436i	0.500775	−	0.865577i	$-0.333048\pi$
$433$	30.7705	−	22.3561i	1.47874	−	1.07436i	0.977961	−	0.208788i	$-0.0669517\pi$
$434$	−0.190983	+	0.587785i	−0.00916748	+	0.0282146i
$435$	0.454915	−	1.40008i	0.0218115	−	0.0671289i
$436$	−41.1246	+	29.8788i	−1.96951	+	1.43093i
$437$	30.7254	+	22.3233i	1.46980	+	1.06787i
$438$	4.88197	+	15.0251i	0.233269	+	0.717929i
$439$	−5.61803			−0.268134			−0.134067	−	0.990972i	$-0.542804\pi$
$439$	−5.61803			−0.268134			−0.134067	+	0.990972i	$0.542804\pi$
$440$		0			0
$441$	−2.61803			−0.124668
$442$	−21.1803	−	65.1864i	−1.00745	−	3.10060i
$443$	6.54508	+	4.75528i	0.310966	+	0.225930i	0.732311	−	0.680970i	$-0.238442\pi$
$443$	6.54508	+	4.75528i	0.310966	+	0.225930i	−0.421345	+	0.906901i	$0.638442\pi$
$444$	6.00000	−	4.35926i	0.284747	−	0.206881i
$445$	0.0450850	−	0.138757i	0.00213723	−	0.00657773i
$446$	−21.8713	+	67.3130i	−1.03564	+	3.18736i
$447$	−1.07295	+	0.779543i	−0.0507487	+	0.0368711i
$448$	7.04508	+	5.11855i	0.332849	+	0.241829i
$449$	−1.02786	−	3.16344i	−0.0485079	−	0.149292i	0.923869	−	0.382710i	$-0.125009\pi$
$449$	−1.02786	−	3.16344i	−0.0485079	−	0.149292i	−0.972377	+	0.233418i	$0.925009\pi$
$450$	27.4164			1.29242
$451$		0			0
$452$	33.2705			1.56491
$453$	−3.42705	−	10.5474i	−0.161017	−	0.495559i
$454$	27.6074	+	20.0579i	1.29568	+	0.941366i
$455$	−2.61803	+	1.90211i	−0.122735	+	0.0891724i
$456$	8.89919	−	27.3889i	0.416743	−	1.28260i
$457$	2.11803	−	6.51864i	0.0990775	−	0.304929i	−0.889217	−	0.457485i	$-0.848750\pi$
$457$	2.11803	−	6.51864i	0.0990775	−	0.304929i	0.988295	+	0.152556i	$0.0487504\pi$
$458$	−23.7984	+	17.2905i	−1.11202	+	0.807933i
$459$	22.7254	+	16.5110i	1.06073	+	0.770667i
$460$	−9.13525	−	28.1154i	−0.425933	−	1.31089i
$461$	−19.5066			−0.908512			−0.454256	−	0.890871i	$-0.650095\pi$
$461$	−19.5066			−0.908512			−0.454256	+	0.890871i	$0.650095\pi$
$462$		0			0
$463$	17.7639			0.825560			0.412780	−	0.910831i	$-0.364558\pi$
$463$	17.7639			0.825560			0.412780	+	0.910831i	$0.364558\pi$
$464$	7.25329	+	22.3233i	0.336725	+	1.03633i
$465$	−0.118034	−	0.0857567i	−0.00547370	−	0.00397687i
$466$	−5.47214	+	3.97574i	−0.253492	+	0.184173i
$467$	10.3541	−	31.8666i	0.479131	−	1.47461i	−0.361174	−	0.932498i	$-0.617624\pi$
$467$	10.3541	−	31.8666i	0.479131	−	1.47461i	0.840305	−	0.542114i	$-0.182376\pi$
$468$	12.7082	−	39.1118i	0.587437	−	1.80794i
$469$	5.92705	−	4.30625i	0.273686	−	0.198844i
$470$	9.28115	+	6.74315i	0.428108	+	0.311038i
$471$	−3.03444	−	9.33905i	−0.139820	−	0.430321i
$472$	−0.673762			−0.0310124
$473$		0			0
$474$	−13.9443			−0.640482
$475$	−7.70820	−	23.7234i	−0.353677	−	1.08850i
$476$	31.7705	+	23.0826i	1.45620	+	1.05799i
$477$	−9.78115	+	7.10642i	−0.447848	+	0.325381i
$478$	4.78115	−	14.7149i	0.218685	−	0.673043i
$479$	−8.10739	+	24.9520i	−0.370436	+	1.14009i	0.576070	+	0.817400i	$0.304585\pi$
$479$	−8.10739	+	24.9520i	−0.370436	+	1.14009i	−0.946506	+	0.322685i	$0.895415\pi$
$480$	−5.42705	+	3.94298i	−0.247710	+	0.179972i
$481$	−6.47214	−	4.70228i	−0.295104	−	0.214406i
$482$	13.9721	+	43.0018i	0.636413	+	1.95868i
$483$	3.76393			0.171265
$484$		0			0
$485$	7.00000			0.317854
$486$	11.2812	+	34.7198i	0.511723	+	1.57492i
$487$	−13.4271	−	9.75532i	−0.608438	−	0.442056i	0.240426	−	0.970667i	$-0.422713\pi$
$487$	−13.4271	−	9.75532i	−0.608438	−	0.442056i	−0.848864	+	0.528612i	$0.822713\pi$
$488$	−32.5344	+	23.6377i	−1.47276	+	1.07003i
$489$	0.899187	−	2.76741i	0.0406626	−	0.125147i
$490$	0.809017	−	2.48990i	0.0365477	−	0.112482i
$491$	23.3435	−	16.9600i	1.05348	−	0.765395i	0.0806053	−	0.996746i	$-0.474315\pi$
$491$	23.3435	−	16.9600i	1.05348	−	0.765395i	0.972870	+	0.231351i	$0.0743147\pi$
$492$	27.1353	+	19.7149i	1.22335	+	0.888817i
$493$	5.95492	+	18.3273i	0.268196	+	0.825422i
$494$	−52.8328			−2.37706
$495$		0			0
$496$	2.32624			0.104451
$497$	1.51722	+	4.66953i	0.0680567	+	0.209457i
$498$	−14.0172	−	10.1841i	−0.628127	−	0.456361i
$499$	−0.881966	+	0.640786i	−0.0394822	+	0.0286855i	−0.607351	−	0.794433i	$-0.707768\pi$
$499$	−0.881966	+	0.640786i	−0.0394822	+	0.0286855i	0.567869	+	0.823119i	$0.307768\pi$
$500$	−13.5000	+	41.5487i	−0.603738	+	1.85812i
$501$	0.472136	−	1.45309i	0.0210935	−	0.0649191i
$502$	−48.7148	+	35.3934i	−2.17425	+	1.57968i
$503$	15.2361	+	11.0697i	0.679343	+	0.493571i	0.873140	−	0.487470i	$-0.162080\pi$
$503$	15.2361	+	11.0697i	0.679343	+	0.493571i	−0.193797	+	0.981042i	$0.562080\pi$
$504$	6.04508	+	18.6049i	0.269269	+	0.828726i
$505$	−9.79837			−0.436022
$506$		0			0
$507$	−1.56231			−0.0693844
$508$	22.4164	+	68.9906i	0.994567	+	3.06096i
$509$	−25.6803	−	18.6579i	−1.13826	−	0.826995i	−0.151385	−	0.988475i	$-0.548373\pi$
$509$	−25.6803	−	18.6579i	−1.13826	−	0.826995i	−0.986876	+	0.161480i	$0.948373\pi$
$510$	−10.5902	+	7.69421i	−0.468941	+	0.340705i
$511$	−3.01722	+	9.28605i	−0.133474	+	0.410791i
$512$	−12.4549	+	38.3323i	−0.550435	+	1.69406i
$513$	17.5172	−	12.7270i	0.773404	−	0.561911i
$514$	−24.4894	−	17.7926i	−1.08018	−	0.784796i
$515$	0.663119	+	2.04087i	0.0292205	+	0.0899315i
$516$	−22.6869			−0.998736
$517$		0			0
$518$	6.47214			0.284369
$519$	3.36475	+	10.3556i	0.147696	+	0.454561i
$520$	19.5623	+	14.2128i	0.857864	+	0.623275i
$521$	6.28115	−	4.56352i	0.275182	−	0.199932i	−0.441631	−	0.897197i	$-0.645600\pi$
$521$	6.28115	−	4.56352i	0.275182	−	0.199932i	0.716813	+	0.697265i	$0.245600\pi$
$522$	−5.04508	+	15.5272i	−0.220817	+	0.679606i
$523$	1.10081	−	3.38795i	0.0481352	−	0.148145i	−0.924100	−	0.382151i	$-0.875183\pi$
$523$	1.10081	−	3.38795i	0.0481352	−	0.148145i	0.972235	+	0.234006i	$0.0751835\pi$
$524$	4.14590	−	3.01217i	0.181114	−	0.131587i
$525$	−2.00000	−	1.45309i	−0.0872872	−	0.0634178i
$526$	−18.7082	−	57.5779i	−0.815716	−	2.51052i
$527$	1.90983			0.0831935
$528$		0			0
$529$	14.0902			0.612616
$530$	−3.73607	−	11.4984i	−0.162284	−	0.499460i
$531$	−0.190983	−	0.138757i	−0.00828796	−	0.00602155i
$532$	24.4894	−	17.7926i	1.06175	−	0.771405i
$533$	11.1803	−	34.4095i	0.484274	−	1.49044i
$534$	0.0729490	−	0.224514i	0.00315681	−	0.00971567i
$535$	−8.66312	+	6.29412i	−0.374539	+	0.272119i
$536$	−44.2877	−	32.1769i	−1.91294	−	1.38983i
$537$	−1.57295	−	4.84104i	−0.0678778	−	0.208906i
$538$	26.5623			1.14518
$539$		0			0
$540$	−16.8541			−0.725285
$541$	3.92705	+	12.0862i	0.168837	+	0.519627i	0.999299	−	0.0374489i	$-0.0119232\pi$
$541$	3.92705	+	12.0862i	0.168837	+	0.519627i	−0.830461	+	0.557076i	$0.811923\pi$
$542$	41.9336	+	30.4666i	1.80120	+	1.30865i
$543$	−9.70820	+	7.05342i	−0.416619	+	0.302691i
$544$	27.1353	−	83.5137i	1.16341	−	3.58062i
$545$	3.23607	−	9.95959i	0.138618	−	0.426622i
$546$	−4.23607	+	3.07768i	−0.181287	+	0.131713i
$547$	−28.5344	−	20.7315i	−1.22004	−	0.886414i	−0.223941	−	0.974603i	$-0.571892\pi$
$547$	−28.5344	−	20.7315i	−1.22004	−	0.886414i	−0.996104	+	0.0881884i	$0.971892\pi$
$548$	0.489357	+	1.50609i	0.0209043	+	0.0643368i
$549$	−14.0902			−0.601354
$550$		0			0
$551$	14.8541			0.632806
$552$	−8.69098	−	26.7481i	−0.369913	−	1.13847i
$553$	−6.97214	−	5.06555i	−0.296485	−	0.215409i
$554$	−12.7812	+	9.28605i	−0.543019	+	0.394527i
$555$	−0.472136	+	1.45309i	−0.0200411	+	0.0616800i
$556$	8.91641	−	27.4419i	0.378140	−	1.16380i
$557$	−11.5172	+	8.36775i	−0.488000	+	0.354553i	−0.804415	−	0.594068i	$-0.797521\pi$
$557$	−11.5172	+	8.36775i	−0.488000	+	0.354553i	0.316414	+	0.948621i	$0.397521\pi$
$558$	1.30902	+	0.951057i	0.0554151	+	0.0402614i
$559$	7.56231	+	23.2744i	0.319851	+	0.984402i
$560$	−9.85410			−0.416412
$561$		0			0
$562$	7.38197			0.311389
$563$	−4.62868	−	14.2456i	−0.195075	−	0.600381i	−0.999976	−	0.00697043i	$-0.997781\pi$
$563$	−4.62868	−	14.2456i	−0.195075	−	0.600381i	0.804900	−	0.593410i	$-0.202219\pi$
$564$	10.6353	+	7.72696i	0.447825	+	0.325364i
$565$	−5.54508	+	4.02874i	−0.233283	+	0.169490i
$566$	4.80902	−	14.8006i	0.202138	−	0.622117i
$567$	−1.76393	+	5.42882i	−0.0740782	+	0.227989i
$568$	29.6803	−	21.5640i	1.24536	−	0.904807i
$569$	−20.4721	−	14.8739i	−0.858237	−	0.623545i	0.0691681	−	0.997605i	$-0.477966\pi$
$569$	−20.4721	−	14.8739i	−0.858237	−	0.623545i	−0.927405	+	0.374060i	$0.877966\pi$
$570$	3.11803	+	9.59632i	0.130600	+	0.401946i
$571$	28.3050			1.18453			0.592263	−	0.805745i	$-0.298235\pi$
$571$	28.3050			1.18453			0.592263	+	0.805745i	$0.298235\pi$
$572$		0			0
$573$	12.5066			0.522470
$574$	9.04508	+	27.8379i	0.377535	+	1.16193i
$575$	−19.7082	−	14.3188i	−0.821889	−	0.597137i
$576$	18.4443	−	13.4005i	0.768511	−	0.558356i
$577$	−6.69098	+	20.5927i	−0.278549	+	0.857286i	0.709709	+	0.704495i	$0.248826\pi$
$577$	−6.69098	+	20.5927i	−0.278549	+	0.857286i	−0.988258	+	0.152792i	$0.951174\pi$
$578$	39.1976	−	120.638i	1.63040	−	5.01787i
$579$	0.163119	−	0.118513i	0.00677899	−	0.00492523i
$580$	−9.35410	−	6.79615i	−0.388408	−	0.282195i
$581$	−3.30902	−	10.1841i	−0.137281	−	0.422508i
$582$	11.3262			0.469488
$583$		0			0
$584$	72.9574			3.01900
$585$	2.61803	+	8.05748i	0.108242	+	0.333136i
$586$	−23.2984	−	16.9273i	−0.962447	−	0.699259i
$587$	−0.809017	+	0.587785i	−0.0333917	+	0.0242605i	−0.604356	−	0.796714i	$-0.706569\pi$
$587$	−0.809017	+	0.587785i	−0.0333917	+	0.0242605i	0.570964	+	0.820975i	$0.306569\pi$
$588$	0.927051	−	2.85317i	0.0382309	−	0.117663i
$589$	0.454915	−	1.40008i	0.0187444	−	0.0576895i
$590$	0.190983	−	0.138757i	0.00786265	−	0.00571255i
$591$	−8.85410	−	6.43288i	−0.364209	−	0.264613i
$592$	−7.52786	−	23.1684i	−0.309393	−	0.952215i
$593$	29.1246			1.19600			0.598002	−	0.801494i	$-0.295961\pi$
$593$	29.1246			1.19600			0.598002	+	0.801494i	$0.295961\pi$
$594$		0			0
$595$	−8.09017			−0.331665
$596$	3.21885	+	9.90659i	0.131849	+	0.405790i
$597$	1.88197	+	1.36733i	0.0770237	+	0.0559610i
$598$	−41.7426	+	30.3278i	−1.70698	+	1.24020i
$599$	−4.94427	+	15.2169i	−0.202017	+	0.621746i	0.797805	+	0.602915i	$0.205994\pi$
$599$	−4.94427	+	15.2169i	−0.202017	+	0.621746i	−0.999823	+	0.0188306i	$0.994006\pi$
$600$	−5.70820	+	17.5680i	−0.233036	+	0.717212i
$601$	0.236068	−	0.171513i	0.00962941	−	0.00699618i	−0.582960	−	0.812501i	$-0.698106\pi$
$601$	0.236068	−	0.171513i	0.00962941	−	0.00699618i	0.592590	+	0.805505i	$0.298106\pi$
$602$	−16.0172	−	11.6372i	−0.652813	−	0.474297i
$603$	−5.92705	−	18.2416i	−0.241368	−	0.742855i
$604$	−87.1033			−3.54418
$605$		0			0
$606$	−15.8541			−0.644029
$607$	−13.8435	−	42.6058i	−0.561889	−	1.72932i	−0.677019	−	0.735965i	$-0.736729\pi$
$607$	−13.8435	−	42.6058i	−0.561889	−	1.72932i	0.115131	−	0.993350i	$-0.463271\pi$
$608$	−54.7599	−	39.7854i	−2.22081	−	1.61351i
$609$	1.19098	−	0.865300i	0.0482611	−	0.0350637i
$610$	4.35410	−	13.4005i	0.176292	−	0.542572i
$611$	4.38197	−	13.4863i	0.177275	−	0.545597i
$612$	83.1763	−	60.4311i	3.36220	−	2.44278i
$613$	28.2254	+	20.5070i	1.14001	+	0.828269i	0.987121	−	0.159974i	$-0.0511410\pi$
$613$	28.2254	+	20.5070i	1.14001	+	0.828269i	0.152893	+	0.988243i	$0.451141\pi$
$614$	0.663119	+	2.04087i	0.0267613	+	0.0823628i
$615$	−6.90983			−0.278631
$616$		0			0
$617$	−17.4164			−0.701158			−0.350579	−	0.936533i	$-0.614015\pi$
$617$	−17.4164			−0.701158			−0.350579	+	0.936533i	$0.614015\pi$
$618$	1.07295	+	3.30220i	0.0431603	+	0.132834i
$619$	21.2705	+	15.4539i	0.854934	+	0.621146i	0.926502	−	0.376290i	$-0.122800\pi$
$619$	21.2705	+	15.4539i	0.854934	+	0.621146i	−0.0715680	+	0.997436i	$0.522800\pi$
$620$	−0.927051	+	0.673542i	−0.0372313	+	0.0270501i
$621$	6.53444	−	20.1109i	0.262218	−	0.807024i
$622$	7.28115	−	22.4091i	0.291948	−	0.898522i
$623$	0.118034	−	0.0857567i	0.00472893	−	0.00343577i
$624$	15.9443	+	11.5842i	0.638282	+	0.463739i
$625$	3.39919	+	10.4616i	0.135967	+	0.418465i
$626$	7.00000			0.279776
$627$		0			0
$628$	−77.1246			−3.07761
$629$	−6.18034	−	19.0211i	−0.246426	−	0.758422i
$630$	−5.54508	−	4.02874i	−0.220921	−	0.160509i
$631$	28.9894	−	21.0620i	1.15405	−	0.838465i	0.165034	−	0.986288i	$-0.447227\pi$
$631$	28.9894	−	21.0620i	1.15405	−	0.838465i	0.989014	+	0.147823i	$0.0472265\pi$
$632$	−19.8992	+	61.2434i	−0.791547	+	2.43613i
$633$	−2.55573	+	7.86572i	−0.101581	+	0.312634i
$634$	52.0238	−	37.7975i	2.06613	−	1.50113i
$635$	−12.0902	−	8.78402i	−0.479784	−	0.348583i
$636$	−4.28115	−	13.1760i	−0.169759	−	0.522464i
$637$	−3.23607			−0.128218
$638$		0			0
$639$	12.8541			0.508500
$640$	0.336881	+	1.03681i	0.0133164	+	0.0409836i
$641$	−0.281153	−	0.204270i	−0.0111049	−	0.00806816i	0.582219	−	0.813032i	$-0.302185\pi$
$641$	−0.281153	−	0.204270i	−0.0111049	−	0.00806816i	−0.593324	+	0.804964i	$0.702185\pi$
$642$	−14.0172	+	10.1841i	−0.553216	+	0.401935i
$643$	8.78115	−	27.0256i	0.346295	−	1.06579i	−0.614592	−	0.788845i	$-0.710679\pi$
$643$	8.78115	−	27.0256i	0.346295	−	1.06579i	0.960887	−	0.276941i	$-0.0893206\pi$
$644$	9.13525	−	28.1154i	0.359979	−	1.10790i
$645$	3.78115	−	2.74717i	0.148883	−	0.108170i
$646$	−106.857	−	77.6359i	−4.20422	−	3.05454i
$647$	−5.00000	−	15.3884i	−0.196570	−	0.604981i	−0.999955	−	0.00952037i	$-0.996970\pi$
$647$	−5.00000	−	15.3884i	−0.196570	−	0.604981i	0.803384	−	0.595461i	$-0.203030\pi$
$648$	42.6525			1.67555
$649$		0			0
$650$	33.8885			1.32922
$651$	−0.0450850	−	0.138757i	−0.00176702	−	0.00543833i
$652$	−18.4894	−	13.4333i	−0.724099	−	0.526089i
$653$	−11.1353	+	8.09024i	−0.435756	+	0.316595i	−0.783946	−	0.620828i	$-0.786796\pi$
$653$	−11.1353	+	8.09024i	−0.435756	+	0.316595i	0.348190	+	0.937424i	$0.386796\pi$
$654$	5.23607	−	16.1150i	0.204746	−	0.630145i
$655$	−0.326238	+	1.00406i	−0.0127472	+	0.0392318i
$656$	89.1312	−	64.7576i	3.47999	−	2.52836i
$657$	20.6803	+	15.0251i	0.806817	+	0.586187i
$658$	3.54508	+	10.9106i	0.138202	+	0.425341i
$659$	−22.5279			−0.877561			−0.438780	−	0.898594i	$-0.644589\pi$
$659$	−22.5279			−0.877561			−0.438780	+	0.898594i	$0.644589\pi$
$660$		0			0
$661$	−14.4377			−0.561561			−0.280781	−	0.959772i	$-0.590593\pi$
$661$	−14.4377			−0.561561			−0.280781	+	0.959772i	$0.590593\pi$
$662$	−13.0902	−	40.2874i	−0.508764	−	1.56581i
$663$	13.0902	+	9.51057i	0.508380	+	0.369360i
$664$	−64.7320	+	47.0306i	−2.51209	+	1.82514i
$665$	−1.92705	+	5.93085i	−0.0747278	+	0.229989i
$666$	5.23607	−	16.1150i	0.202894	−	0.624442i
$667$	11.7361	−	8.52675i	0.454422	−	0.330157i
$668$	−9.70820	−	7.05342i	−0.375622	−	0.272905i
$669$	−5.16312	−	15.8904i	−0.199618	−	0.614360i
$670$	19.1803			0.741001
$671$		0			0
$672$	−6.70820			−0.258775
$673$	10.3262	+	31.7809i	0.398047	+	1.22506i	0.926563	+	0.376140i	$0.122749\pi$
$673$	10.3262	+	31.7809i	0.398047	+	1.22506i	−0.528516	+	0.848924i	$0.677251\pi$
$674$	17.0623	+	12.3965i	0.657215	+	0.477495i
$675$	−11.2361	+	8.16348i	−0.432476	+	0.314213i
$676$	−3.79180	+	11.6699i	−0.145838	+	0.448844i
$677$	0.843459	−	2.59590i	0.0324168	−	0.0997685i	−0.933539	−	0.358476i	$-0.883297\pi$
$677$	0.843459	−	2.59590i	0.0324168	−	0.0997685i	0.965956	+	0.258707i	$0.0832965\pi$
$678$	−8.97214	+	6.51864i	−0.344573	+	0.250347i
$679$	5.66312	+	4.11450i	0.217331	+	0.157900i
$680$	18.6803	+	57.4922i	0.716358	+	2.20472i
$681$	−8.05573			−0.308696
$682$		0			0
$683$	38.5066			1.47341			0.736707	−	0.676213i	$-0.236380\pi$
$683$	38.5066			1.47341			0.736707	+	0.676213i	$0.236380\pi$
$684$	−24.4894	−	75.3705i	−0.936374	−	2.88186i
$685$	−0.263932	−	0.191758i	−0.0100843	−	0.00732669i
$686$	2.11803	−	1.53884i	0.0808669	−	0.0587533i
$687$	2.14590	−	6.60440i	0.0818711	−	0.251973i
$688$	−23.0279	+	70.8725i	−0.877929	+	2.70199i
$689$	−12.0902	+	8.78402i	−0.460599	+	0.334645i
$690$	7.97214	+	5.79210i	0.303494	+	0.220501i
$691$	−15.0000	−	46.1653i	−0.570627	−	1.75621i	−0.650609	−	0.759413i	$-0.725486\pi$
$691$	−15.0000	−	46.1653i	−0.570627	−	1.75621i	0.0799823	−	0.996796i	$-0.474514\pi$
$692$	85.5197			3.25097
$693$		0			0
$694$	−88.1033			−3.34436
$695$	1.83688	+	5.65334i	0.0696769	+	0.214443i
$696$	−8.89919	−	6.46564i	−0.337323	−	0.245079i
$697$	73.1763	−	53.1657i	2.77175	−	2.01379i
$698$	−6.63525	+	20.4212i	−0.251148	+	0.772954i
$699$	0.493422	−	1.51860i	0.0186629	−	0.0574386i
$700$	−15.7082	+	11.4127i	−0.593714	+	0.431359i
$701$	−15.7812	−	11.4657i	−0.596046	−	0.433053i	0.248427	−	0.968651i	$-0.420086\pi$
$701$	−15.7812	−	11.4657i	−0.596046	−	0.433053i	−0.844473	+	0.535598i	$0.820086\pi$
$702$	9.09017	+	27.9767i	0.343086	+	1.05591i
$703$	−15.4164			−0.581441
$704$		0			0
$705$	−2.70820			−0.101997
$706$	10.4443	+	32.1442i	0.393075	+	1.20976i
$707$	−7.92705	−	5.75934i	−0.298127	−	0.216602i
$708$	0.218847	−	0.159002i	0.00822478	−	0.00597565i
$709$	6.80902	−	20.9560i	0.255718	−	0.787019i	−0.737969	−	0.674834i	$-0.764215\pi$
$709$	6.80902	−	20.9560i	0.255718	−	0.787019i	0.993687	−	0.112185i	$-0.0357849\pi$
$710$	−3.97214	+	12.2250i	−0.149072	+	0.458795i
$711$	−18.2533	+	13.2618i	−0.684552	+	0.497356i
$712$	−0.881966	−	0.640786i	−0.0330531	−	0.0240145i
$713$	−0.444272	−	1.36733i	−0.0166381	−	0.0512068i
$714$	−13.0902			−0.489887
$715$		0			0
$716$	−39.9787			−1.49407
$717$	1.12868	+	3.47371i	0.0421512	+	0.129728i
$718$	−28.3435	−	20.5927i	−1.05777	−	0.768514i
$719$	−26.6074	+	19.3314i	−0.992288	+	0.720940i	−0.960421	−	0.278553i	$-0.910145\pi$
$719$	−26.6074	+	19.3314i	−0.992288	+	0.720940i	−0.0318672	+	0.999492i	$0.510145\pi$
$720$	−7.97214	+	24.5357i	−0.297104	+	0.914392i
$721$	−0.663119	+	2.04087i	−0.0246958	+	0.0760060i
$722$	−42.1246	+	30.6053i	−1.56772	+	1.13901i
$723$	−8.63525	−	6.27388i	−0.321149	−	0.233328i
$724$	29.1246	+	89.6363i	1.08241	+	3.33131i
$725$	−9.52786			−0.353856
$726$		0			0
$727$	43.4508			1.61150			0.805751	−	0.592254i	$-0.201762\pi$
$727$	43.4508			1.61150			0.805751	+	0.592254i	$0.201762\pi$
$728$	7.47214	+	22.9969i	0.276936	+	0.852321i
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	−20.6803	+	15.0251i	−0.765414	+	0.556106i
$731$	−18.9058	+	58.1860i	−0.699255	+	2.15209i
$732$	4.98936	−	15.3557i	0.184412	−	0.567562i
$733$	28.3607	−	20.6052i	1.04753	−	0.761072i	0.0757852	−	0.997124i	$-0.475854\pi$
$733$	28.3607	−	20.6052i	1.04753	−	0.761072i	0.971740	+	0.236052i	$0.0758537\pi$
$734$	44.1246	+	32.0584i	1.62867	+	1.18330i
$735$	0.190983	+	0.587785i	0.00704451	+	0.0216808i
$736$	−66.1033			−2.43660
$737$		0			0
$738$	76.6312			2.82083
$739$	4.20820	+	12.9515i	0.154801	+	0.476429i	0.998141	−	0.0609519i	$-0.0194136\pi$
$739$	4.20820	+	12.9515i	0.154801	+	0.476429i	−0.843339	+	0.537381i	$0.819414\pi$
$740$	9.70820	+	7.05342i	0.356881	+	0.259289i
$741$	10.0902	−	7.33094i	0.370672	−	0.269309i
$742$	3.73607	−	11.4984i	0.137155	−	0.422121i
$743$	8.06231	−	24.8132i	0.295777	−	0.910309i	−0.687182	−	0.726485i	$-0.741152\pi$
$743$	8.06231	−	24.8132i	0.295777	−	0.910309i	0.982959	−	0.183824i	$-0.0588475\pi$
$744$	−0.881966	+	0.640786i	−0.0323344	+	0.0234923i
$745$	−1.73607	−	1.26133i	−0.0636046	−	0.0462115i
$746$	28.7705	+	88.5465i	1.05336	+	3.24192i
$747$	−28.0344			−1.02573
$748$		0			0
$749$	−10.7082			−0.391269
$750$	−4.50000	−	13.8496i	−0.164317	−	0.505715i
$751$	17.2361	+	12.5227i	0.628953	+	0.456961i	0.856037	−	0.516914i	$-0.172919\pi$
$751$	17.2361	+	12.5227i	0.628953	+	0.456961i	−0.227084	+	0.973875i	$0.572919\pi$
$752$	34.9336	−	25.3808i	1.27390	−	0.925541i
$753$	4.39261	−	13.5191i	0.160076	−	0.492662i
$754$	−6.23607	+	19.1926i	−0.227104	+	0.698955i
$755$	14.5172	−	10.5474i	0.528336	−	0.383858i
$756$	−13.6353	−	9.90659i	−0.495909	−	0.360299i
$757$	−5.94427	−	18.2946i	−0.216048	−	0.664928i	−0.999078	−	0.0429433i	$-0.986327\pi$
$757$	−5.94427	−	18.2946i	−0.216048	−	0.664928i	0.783029	−	0.621985i	$-0.213673\pi$
$758$	−68.2492			−2.47892
$759$		0			0
$760$	46.5967			1.69024
$761$	14.6180	+	44.9897i	0.529903	+	1.63087i	0.754411	+	0.656402i	$0.227923\pi$
$761$	14.6180	+	44.9897i	0.529903	+	1.63087i	−0.224508	+	0.974472i	$0.572077\pi$
$762$	−19.5623	−	14.2128i	−0.708668	−	0.514877i
$763$	8.47214	−	6.15537i	0.306712	−	0.222839i
$764$	30.3541	−	93.4203i	1.09817	−	3.37983i
$765$	−6.54508	+	20.1437i	−0.236638	+	0.728297i
$766$	−30.9164	+	22.4621i	−1.11706	+	0.811588i
$767$	−0.236068	−	0.171513i	−0.00852392	−	0.00619299i
$768$	−2.78115	−	8.55951i	−0.100356	−	0.308865i
$769$	−28.4377			−1.02549			−0.512745	−	0.858541i	$-0.671371\pi$
$769$	−28.4377			−1.02549			−0.512745	+	0.858541i	$0.671371\pi$
$770$		0			0
$771$	7.14590			0.257353
$772$	−0.489357	−	1.50609i	−0.0176123	−	0.0542052i
$773$	−28.9336	−	21.0215i	−1.04067	−	0.756091i	−0.0702540	−	0.997529i	$-0.522381\pi$
$773$	−28.9336	−	21.0215i	−1.04067	−	0.756091i	−0.970416	+	0.241438i	$0.922381\pi$
$774$	−41.9336	+	30.4666i	−1.50727	+	1.09510i
$775$	−0.291796	+	0.898056i	−0.0104816	+	0.0322591i
$776$	16.1631	−	49.7450i	0.580222	−	1.78574i
$777$	−1.23607	+	0.898056i	−0.0443437	+	0.0322176i
$778$	25.0344	+	18.1886i	0.897528	+	0.652092i
$779$	−21.5451	−	66.3090i	−0.771933	−	2.37576i
$780$	−9.70820			−0.347609
$781$		0			0
$782$	−128.992			−4.61274
$783$	−2.55573	−	7.86572i	−0.0913343	−	0.281098i
$784$	−7.97214	−	5.79210i	−0.284719	−	0.206861i
$785$	12.8541	−	9.33905i	0.458783	−	0.333325i
$786$	−0.527864	+	1.62460i	−0.0188283	+	0.0579475i
$787$	−0.135255	+	0.416272i	−0.00482132	+	0.0148385i	−0.953438	−	0.301588i	$-0.902483\pi$
$787$	−0.135255	+	0.416272i	−0.00482132	+	0.0148385i	0.948617	+	0.316427i	$0.102483\pi$
$788$	−69.5410	+	50.5245i	−2.47730	+	1.79986i
$789$	11.5623	+	8.40051i	0.411629	+	0.299066i
$790$	−6.97214	−	21.4580i	−0.248057	−	0.763442i
$791$	−6.85410			−0.243704
$792$		0			0
$793$	−17.4164			−0.618475
$794$	−18.7533	−	57.7167i	−0.665529	−	2.04829i
$795$	2.30902	+	1.67760i	0.0818924	+	0.0594983i
$796$	14.7812	−	10.7391i	0.523904	−	0.380639i
$797$	8.57953	−	26.4051i	0.303902	−	0.935316i	−0.676182	−	0.736735i	$-0.736367\pi$
$797$	8.57953	−	26.4051i	0.303902	−	0.935316i	0.980084	−	0.198581i	$-0.0636333\pi$
$798$	−3.11803	+	9.59632i	−0.110377	+	0.339706i
$799$	28.6803	−	20.8375i	1.01464	−	0.737177i
$800$	35.1246	+	25.5195i	1.24184	+	0.902251i
$801$	−0.118034	−	0.363271i	−0.00417053	−	0.0128356i
$802$	−69.3050			−2.44724
$803$		0			0
$804$	21.9787			0.775129
$805$	1.88197	+	5.79210i	0.0663306	+	0.204145i
$806$	1.61803	+	1.17557i	0.0569928	+	0.0414077i
$807$	−5.07295	+	3.68571i	−0.178576	+	0.129743i
$808$	−22.6246	+	69.6314i	−0.795931	+	2.44962i
$809$	1.70163	−	5.23707i	0.0598260	−	0.184125i	−0.916677	−	0.399629i	$-0.869139\pi$
$809$	1.70163	−	5.23707i	0.0598260	−	0.184125i	0.976503	+	0.215503i	$0.0691391\pi$
$810$	−12.0902	+	8.78402i	−0.424805	+	0.308639i
$811$	44.3607	+	32.2299i	1.55771	+	1.13175i	0.937852	+	0.347035i	$0.112811\pi$
$811$	44.3607	+	32.2299i	1.55771	+	1.13175i	0.619862	+	0.784711i	$0.287189\pi$
$812$	−3.57295	−	10.9964i	−0.125386	−	0.385898i
$813$	−12.2361			−0.429138
$814$		0			0
$815$	4.70820			0.164921
$816$	15.2254	+	46.8590i	0.532996	+	1.64039i
$817$	38.1525	+	27.7194i	1.33479	+	0.969779i
$818$	−9.09017	+	6.60440i	−0.317830	+	0.230917i
$819$	−2.61803	+	8.05748i	−0.0914815	+	0.281551i
$820$	−16.7705	+	51.6143i	−0.585652	+	1.80245i
$821$	−40.9894	+	29.7805i	−1.43054	+	1.03935i	−0.440622	+	0.897693i	$0.645242\pi$
$821$	−40.9894	+	29.7805i	−1.43054	+	1.03935i	−0.989916	+	0.141654i	$0.954758\pi$
$822$	−0.427051	−	0.310271i	−0.0148951	−	0.0108219i
$823$	1.20163	+	3.69822i	0.0418861	+	0.128912i	0.969813	−	0.243850i	$-0.0784106\pi$
$823$	1.20163	+	3.69822i	0.0418861	+	0.128912i	−0.927927	+	0.372762i	$0.878411\pi$
$824$	16.0344			0.558586
$825$		0			0
$826$	0.236068			0.00821386
$827$	−9.14590	−	28.1482i	−0.318034	−	0.978808i	−0.974488	−	0.224442i	$-0.927944\pi$
$827$	−9.14590	−	28.1482i	−0.318034	−	0.978808i	0.656453	−	0.754366i	$-0.272056\pi$
$828$	−62.6140	−	45.4917i	−2.17599	−	1.58095i
$829$	0.826238	−	0.600297i	0.0286964	−	0.0208492i	−0.573345	−	0.819314i	$-0.694354\pi$
$829$	0.826238	−	0.600297i	0.0286964	−	0.0208492i	0.602041	+	0.798465i	$0.294354\pi$
$830$	8.66312	−	26.6623i	0.300701	−	0.925463i
$831$	1.15248	−	3.54696i	0.0399789	−	0.123043i
$832$	22.7984	−	16.5640i	0.790391	−	0.574253i
$833$	−6.54508	−	4.75528i	−0.226774	−	0.164761i
$834$	2.97214	+	9.14729i	0.102917	+	0.316745i
$835$	2.47214			0.0855518
$836$		0			0
$837$	−0.819660			−0.0283316
$838$	−4.76393	−	14.6619i	−0.164567	−	0.506486i
$839$	15.0451	+	10.9309i	0.519414	+	0.377376i	0.816383	−	0.577511i	$-0.195976\pi$
$839$	15.0451	+	10.9309i	0.519414	+	0.377376i	−0.296969	+	0.954887i	$0.595976\pi$
$840$	3.73607	−	2.71441i	0.128907	−	0.0936561i
$841$	−7.20820	+	22.1846i	−0.248559	+	0.764985i
$842$	4.23607	−	13.0373i	0.145985	−	0.449294i
$843$	−1.40983	+	1.02430i	−0.0485571	+	0.0352788i
$844$	52.5517	+	38.1810i	1.80890	+	1.31424i
$845$	−0.781153	−	2.40414i	−0.0268725	−	0.0827050i
$846$	30.0344			1.03261
$847$		0			0
$848$	−45.5066			−1.56270
$849$	1.13525	+	3.49396i	0.0389618	+	0.119912i
$850$	68.5410	+	49.7980i	2.35094	+	1.70806i
$851$	−12.1803	+	8.84953i	−0.417537	+	0.303358i
$852$	−4.55166	+	14.0086i	−0.155937	+	0.479926i
$853$	14.2426	−	43.8344i	0.487659	−	1.50086i	−0.340434	−	0.940269i	$-0.610574\pi$
$853$	14.2426	−	43.8344i	0.487659	−	1.50086i	0.828093	−	0.560591i	$-0.189426\pi$
$854$	11.3992	−	8.28199i	0.390072	−	0.283404i
$855$	13.2082	+	9.59632i	0.451711	+	0.328187i
$856$	24.7254	+	76.0970i	0.845098	+	2.60094i
$857$	3.90983			0.133557			0.0667786	−	0.997768i	$-0.478728\pi$
$857$	3.90983			0.133557			0.0667786	+	0.997768i	$0.478728\pi$
$858$		0			0
$859$	1.43769			0.0490535			0.0245267	−	0.999699i	$-0.492192\pi$
$859$	1.43769			0.0490535			0.0245267	+	0.999699i	$0.492192\pi$
$860$	−11.3435	−	34.9116i	−0.386809	−	1.19047i
$861$	−5.59017	−	4.06150i	−0.190512	−	0.138415i
$862$	−15.1353	+	10.9964i	−0.515509	+	0.374539i
$863$	−9.28773	+	28.5847i	−0.316158	+	0.973034i	0.659117	+	0.752040i	$0.270930\pi$
$863$	−9.28773	+	28.5847i	−0.316158	+	0.973034i	−0.975275	+	0.220994i	$0.929070\pi$
$864$	−11.6459	+	35.8424i	−0.396201	+	1.21938i
$865$	−14.2533	+	10.3556i	−0.484626	+	0.352102i
$866$	80.5582	+	58.5290i	2.73748	+	1.98890i
$867$	9.25329	+	28.4787i	0.314258	+	0.967187i
$868$	−1.14590			−0.0388943
$869$		0			0
$870$	3.85410			0.130666
$871$	−7.32624	−	22.5478i	−0.248240	−	0.764004i
$872$	−63.3050	−	45.9937i	−2.14378	−	1.55754i
$873$	14.8262	−	10.7719i	0.501792	−	0.364573i
$874$	−30.7254	+	94.5631i	−1.03930	+	3.19865i
$875$	2.78115	−	8.55951i	0.0940201	−	0.289364i
$876$	−23.6976	+	17.2173i	−0.800666	+	0.581718i
$877$	10.5172	+	7.64121i	0.355141	+	0.258025i	0.751023	−	0.660276i	$-0.229561\pi$
$877$	10.5172	+	7.64121i	0.355141	+	0.258025i	−0.395881	+	0.918302i	$0.629561\pi$
$878$	−4.54508	−	13.9883i	−0.153389	−	0.472083i
$879$	6.79837			0.229303
$880$		0			0
$881$	20.8541			0.702593			0.351296	−	0.936264i	$-0.385741\pi$
$881$	20.8541			0.702593			0.351296	+	0.936264i	$0.385741\pi$
$882$	−2.11803	−	6.51864i	−0.0713179	−	0.219494i
$883$	37.7254	+	27.4091i	1.26956	+	0.922391i	0.999185	−	0.0403641i	$-0.0128518\pi$
$883$	37.7254	+	27.4091i	1.26956	+	0.922391i	0.270377	+	0.962755i	$0.412852\pi$
$884$	102.812	−	74.6969i	3.45793	−	2.51233i
$885$	−0.0172209	+	0.0530006i	−0.000578875	+	0.00178159i
$886$	−6.54508	+	20.1437i	−0.219886	+	0.676741i
$887$	4.68034	−	3.40047i	0.157150	−	0.114176i	−0.506431	−	0.862280i	$-0.669036\pi$
$887$	4.68034	−	3.40047i	0.157150	−	0.114176i	0.663582	+	0.748104i	$0.269036\pi$
$888$	9.23607	+	6.71040i	0.309942	+	0.225186i
$889$	−4.61803	−	14.2128i	−0.154884	−	0.476684i
$890$	0.381966			0.0128035
$891$		0			0
$892$	−131.228			−4.39384
$893$	−8.44427	−	25.9888i	−0.282577	−	0.869682i
$894$	−2.80902	−	2.04087i	−0.0939476	−	0.0682569i
$895$	6.66312	−	4.84104i	0.222724	−	0.161818i
$896$	−0.336881	+	1.03681i	−0.0112544	+	0.0346375i
$897$	3.76393	−	11.5842i	0.125674	−	0.386785i
$898$	7.04508	−	5.11855i	0.235098	−	0.170808i
$899$	−0.454915	−	0.330515i	−0.0151723	−	0.0110233i
$900$	15.7082	+	48.3449i	0.523607	+	1.61150i
$901$	−37.3607			−1.24466
$902$		0			0
$903$	4.67376			0.155533
$904$	15.8262	+	48.7082i	0.526373	+	1.62001i
$905$	−15.7082	−	11.4127i	−0.522158	−	0.379370i
$906$	23.4894	−	17.0660i	0.780382	−	0.566980i
$907$	−6.25329	+	19.2456i	−0.207637	+	0.639041i	0.791958	+	0.610576i	$0.209062\pi$
$907$	−6.25329	+	19.2456i	−0.207637	+	0.639041i	−0.999595	+	0.0284652i	$0.990938\pi$
$908$	−19.5517	+	60.1738i	−0.648845	+	1.99694i
$909$	−20.7533	+	15.0781i	−0.688343	+	0.500111i
$910$	−6.85410	−	4.97980i	−0.227211	−	0.165079i
$911$	−7.05166	−	21.7028i	−0.233632	−	0.719045i	−0.997300	−	0.0734361i	$-0.976603\pi$
$911$	−7.05166	−	21.7028i	−0.233632	−	0.719045i	0.763668	−	0.645609i	$-0.223397\pi$
$912$	37.9787			1.25760
$913$		0			0
$914$	17.9443			0.593544
$915$	1.02786	+	3.16344i	0.0339801	+	0.104580i
$916$	−44.1246	−	32.0584i	−1.45792	−	1.05924i
$917$	−0.854102	+	0.620541i	−0.0282049	+	0.0204921i
$918$	−22.7254	+	69.9417i	−0.750051	+	2.30842i
$919$	−6.45492	+	19.8662i	−0.212928	+	0.655325i	0.786366	+	0.617761i	$0.211960\pi$
$919$	−6.45492	+	19.8662i	−0.212928	+	0.655325i	−0.999294	+	0.0375644i	$0.988040\pi$
$920$	36.8156	−	26.7481i	1.21377	−	0.881859i
$921$	−0.409830	−	0.297759i	−0.0135044	−	0.00981149i
$922$	−15.7812	−	48.5694i	−0.519725	−	1.59955i
$923$	15.8885			0.522978
$924$		0			0
$925$	9.88854			0.325133
$926$	14.3713	+	44.2304i	0.472271	+	1.45350i
$927$	4.54508	+	3.30220i	0.149280	+	0.108458i
$928$	−20.9164	+	15.1967i	−0.686615	+	0.498855i
$929$	7.41641	−	22.8254i	0.243324	−	0.748876i	−0.752583	−	0.658497i	$-0.771192\pi$
$929$	7.41641	−	22.8254i	0.243324	−	0.748876i	0.995908	−	0.0903783i	$-0.0288076\pi$
$930$	0.118034	−	0.363271i	0.00387049	−	0.0119121i
$931$	−5.04508	+	3.66547i	−0.165346	+	0.120131i
$932$	−10.1459	−	7.37143i	−0.332340	−	0.241459i
$933$	1.71885	+	5.29007i	0.0562725	+	0.173189i
$934$	87.7214			2.87033
$935$		0			0
$936$	63.3050			2.06919
$937$	−11.6565	−	35.8751i	−0.380803	−	1.17199i	−0.939480	−	0.342605i	$-0.888691\pi$
$937$	−11.6565	−	35.8751i	−0.380803	−	1.17199i	0.558677	−	0.829385i	$-0.311309\pi$
$938$	15.5172	+	11.2739i	0.506655	+	0.368107i
$939$	−1.33688	+	0.971301i	−0.0436275	+	0.0316972i
$940$	−6.57295	+	20.2295i	−0.214386	+	0.659812i
$941$	9.60081	−	29.5483i	0.312978	−	0.963246i	−0.663601	−	0.748086i	$-0.730973\pi$
$941$	9.60081	−	29.5483i	0.312978	−	0.963246i	0.976579	−	0.215160i	$-0.0690271\pi$
$942$	20.7984	−	15.1109i	0.677648	−	0.492340i
$943$	−55.0861	−	40.0224i	−1.79385	−	1.30331i
$944$	−0.274575	−	0.845055i	−0.00893666	−	0.0275042i
$945$	3.47214			0.112949
$946$		0			0
$947$	19.7082			0.640431			0.320215	−	0.947345i	$-0.396245\pi$
$947$	19.7082			0.640431			0.320215	+	0.947345i	$0.396245\pi$
$948$	−7.98936	−	24.5887i	−0.259482	−	0.798604i
$949$	25.5623	+	18.5721i	0.829788	+	0.602876i
$950$	52.8328	−	38.3853i	1.71412	−	1.24538i
$951$	−4.69098	+	14.4374i	−0.152116	+	0.468164i
$952$	−18.6803	+	57.4922i	−0.605433	+	1.86333i
$953$	−1.42705	+	1.03681i	−0.0462267	+	0.0335857i	−0.610659	−	0.791894i	$-0.709095\pi$
$953$	−1.42705	+	1.03681i	−0.0462267	+	0.0335857i	0.564432	+	0.825480i	$0.309095\pi$
$954$	−25.6074	−	18.6049i	−0.829070	−	0.602355i
$955$	6.25329	+	19.2456i	0.202352	+	0.622774i
$956$	28.6869			0.927801
$957$		0			0
$958$	−68.6869			−2.21917
$959$	−0.100813	−	0.310271i	−0.00325542	−	0.0100192i
$960$	−4.35410	−	3.16344i	−0.140528	−	0.102100i
$961$	25.0344	−	18.1886i	0.807563	−	0.586729i
$962$	6.47214	−	19.9192i	0.208670	−	0.642220i
$963$	−8.66312	+	26.6623i	−0.279165	+	0.859182i
$964$	−67.8222	+	49.2757i	−2.18441	+	1.58706i
$965$	0.263932	+	0.191758i	0.00849627	+	0.00617290i
$966$	3.04508	+	9.37181i	0.0979740	+	0.301533i
$967$	28.4508			0.914918			0.457459	−	0.889231i	$-0.348760\pi$
$967$	28.4508			0.914918			0.457459	+	0.889231i	$0.348760\pi$
$968$		0			0
$969$	31.1803			1.00166
$970$	5.66312	+	17.4293i	0.181832	+	0.559621i
$971$	−42.2705	−	30.7113i	−1.35653	−	0.985573i	−0.998657	−	0.0518010i	$-0.983504\pi$
$971$	−42.2705	−	30.7113i	−1.35653	−	0.985573i	−0.357868	−	0.933772i	$-0.616496\pi$
$972$	−54.7599	+	39.7854i	−1.75642	+	1.27612i
$973$	−1.83688	+	5.65334i	−0.0588877	+	0.181238i
$974$	13.4271	−	41.3242i	0.430230	−	1.32411i
$975$	−6.47214	+	4.70228i	−0.207274	+	0.150594i
$976$	−42.9058	−	31.1729i	−1.37338	−	0.997819i
$977$	−10.2533	−	31.5564i	−0.328032	−	1.00958i	−0.970053	−	0.242892i	$-0.921904\pi$
$977$	−10.2533	−	31.5564i	−0.328032	−	1.00958i	0.642022	−	0.766686i	$-0.278096\pi$
$978$	7.61803			0.243598
$979$		0			0
$980$	4.85410			0.155059
$981$	−8.47214	−	26.0746i	−0.270494	−	0.832496i
$982$	61.1140	+	44.4019i	1.95023	+	1.41692i
$983$	11.8262	−	8.59226i	0.377198	−	0.274051i	−0.382991	−	0.923752i	$-0.625106\pi$
$983$	11.8262	−	8.59226i	0.377198	−	0.274051i	0.760190	+	0.649701i	$0.225106\pi$
$984$	−15.9549	+	49.1042i	−0.508624	+	1.56538i
$985$	5.47214	−	16.8415i	0.174357	−	0.536615i
$986$	−40.8156	+	29.6543i	−1.29983	+	0.944384i
$987$	−2.19098	−	1.59184i	−0.0697398	−	0.0506689i
$988$	−30.2705	−	93.1630i	−0.963033	−	2.96391i
$989$	46.0557			1.46449
$990$		0			0
$991$	−34.2705			−1.08864			−0.544319	−	0.838878i	$-0.683212\pi$
$991$	−34.2705			−1.08864			−0.544319	+	0.838878i	$0.683212\pi$
$992$	0.791796	+	2.43690i	0.0251396	+	0.0773716i
$993$	8.09017	+	5.87785i	0.256734	+	0.186528i
$994$	−10.3992	+	7.55545i	−0.329842	+	0.239644i
$995$	−1.16312	+	3.57971i	−0.0368733	+	0.113485i
$996$	9.92705	−	30.5523i	0.314551	−	0.968087i
$997$	21.7361	−	15.7922i	0.688388	−	0.500143i	−0.187742	−	0.982218i	$-0.560117\pi$
$997$	21.7361	−	15.7922i	0.688388	−	0.500143i	0.876130	+	0.482075i	$0.160117\pi$
$998$	−2.30902	−	1.67760i	−0.0730907	−	0.0531035i
$999$	2.65248	+	8.16348i	0.0839206	+	0.258281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.j.148.1		4
11.2	odd	10		847.2.f.d.372.1		4
11.3	even	5		847.2.a.h.1.2	yes	2
11.4	even	5		847.2.f.c.729.1		4
11.5	even	5		847.2.f.c.323.1		4
11.6	odd	10		847.2.f.l.323.1		4
11.7	odd	10		847.2.f.l.729.1		4
11.8	odd	10		847.2.a.d.1.1	✓	2
11.9	even	5	inner	847.2.f.j.372.1		4
11.10	odd	2		847.2.f.d.148.1		4
33.8	even	10		7623.2.a.bx.1.2		2
33.14	odd	10		7623.2.a.t.1.1		2
77.41	even	10		5929.2.a.i.1.1		2
77.69	odd	10		5929.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.d.1.1	✓	2	11.8	odd	10
847.2.a.h.1.2	yes	2	11.3	even	5
847.2.f.c.323.1		4	11.5	even	5
847.2.f.c.729.1		4	11.4	even	5
847.2.f.d.148.1		4	11.10	odd	2
847.2.f.d.372.1		4	11.2	odd	10
847.2.f.j.148.1		4	1.1	even	1	trivial
847.2.f.j.372.1		4	11.9	even	5	inner
847.2.f.l.323.1		4	11.6	odd	10
847.2.f.l.729.1		4	11.7	odd	10
5929.2.a.i.1.1		2	77.41	even	10
5929.2.a.s.1.2		2	77.69	odd	10
7623.2.a.t.1.1		2	33.14	odd	10
7623.2.a.bx.1.2		2	33.8	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 2.48990i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 2.48990i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(-0.809017 - 2.48990i) q^{9} +2.61803 q^{10} +3.00000 q^{12} +(-1.00000 - 3.07768i) q^{13} +(2.11803 + 1.53884i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(3.04508 - 9.37181i) q^{16} +(2.50000 - 7.69421i) q^{17} +(5.54508 - 4.02874i) q^{18} +(-5.04508 - 3.66547i) q^{19} +(1.50000 + 4.61653i) q^{20} -0.618034 q^{21} -6.09017 q^{23} +(1.42705 + 4.39201i) q^{24} +(3.23607 + 2.35114i) q^{25} +(6.85410 - 4.97980i) q^{26} +(-1.07295 + 3.30220i) q^{27} +(-1.50000 + 4.61653i) q^{28} +(-1.92705 + 1.40008i) q^{29} +(-1.30902 - 0.951057i) q^{30} +(0.0729490 + 0.224514i) q^{31} +10.8541 q^{32} +21.1803 q^{34} +(-0.309017 - 0.951057i) q^{35} +(10.2812 + 7.46969i) q^{36} +(2.00000 - 1.45309i) q^{37} +(5.04508 - 15.5272i) q^{38} +(-0.618034 + 1.90211i) q^{39} +(-6.04508 + 4.39201i) q^{40} +(9.04508 + 6.57164i) q^{41} +(-0.500000 - 1.53884i) q^{42} -7.56231 q^{43} -2.61803 q^{45} +(-4.92705 - 15.1639i) q^{46} +(3.54508 + 2.57565i) q^{47} +(-4.92705 + 3.57971i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.23607 + 9.95959i) q^{50} +(-4.04508 + 2.93893i) q^{51} +(12.7082 + 9.23305i) q^{52} +(-1.42705 - 4.39201i) q^{53} -9.09017 q^{54} -7.47214 q^{56} +(1.19098 + 3.66547i) q^{57} +(-5.04508 - 3.66547i) q^{58} +(0.0729490 - 0.0530006i) q^{59} +(0.927051 - 2.85317i) q^{60} +(1.66312 - 5.11855i) q^{61} +(-0.500000 + 0.363271i) q^{62} +(-2.11803 - 1.53884i) q^{63} +(2.69098 + 8.28199i) q^{64} -3.23607 q^{65} +7.32624 q^{67} +(12.1353 + 37.3485i) q^{68} +(3.04508 + 2.21238i) q^{69} +(2.11803 - 1.53884i) q^{70} +(-1.51722 + 4.66953i) q^{71} +(-6.04508 + 18.6049i) q^{72} +(-7.89919 + 5.73910i) q^{73} +(5.23607 + 3.80423i) q^{74} +(-0.763932 - 2.35114i) q^{75} +30.2705 q^{76} -5.23607 q^{78} +(-2.66312 - 8.19624i) q^{79} +(-7.97214 - 5.79210i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(-9.04508 + 27.8379i) q^{82} +(3.30902 - 10.1841i) q^{83} +(2.42705 - 1.76336i) q^{84} +(-6.54508 - 4.75528i) q^{85} +(-6.11803 - 18.8294i) q^{86} +1.47214 q^{87} +0.145898 q^{89} +(-2.11803 - 6.51864i) q^{90} +(-2.61803 - 1.90211i) q^{91} +(23.9164 - 17.3763i) q^{92} +(0.0450850 - 0.138757i) q^{93} +(-3.54508 + 10.9106i) q^{94} +(-5.04508 + 3.66547i) q^{95} +(-5.42705 - 3.94298i) q^{96} +(2.16312 + 6.65740i) q^{97} +2.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - 9 q^{4} - q^{5} + 2 q^{6} + q^{7} - 13 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 - 9 * q^4 - q^5 + 2 * q^6 + q^7 - 13 * q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - 9 q^{4} - q^{5} + 2 q^{6} + q^{7} - 13 q^{8} - q^{9} + 6 q^{10} + 12 q^{12} - 4 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} + 10 q^{17} + 11 q^{18} - 9 q^{19} + 6 q^{20} + 2 q^{21} - 2 q^{23} - q^{24} + 4 q^{25} + 14 q^{26} - 11 q^{27} - 6 q^{28} - q^{29} - 3 q^{30} + 7 q^{31} + 30 q^{32} + 40 q^{34} + q^{35} + 21 q^{36} + 8 q^{37} + 9 q^{38} + 2 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{45} - 13 q^{46} + 3 q^{47} - 13 q^{48} - q^{49} - 4 q^{50} - 5 q^{51} + 24 q^{52} + q^{53} - 14 q^{54} - 12 q^{56} + 7 q^{57} - 9 q^{58} + 7 q^{59} - 3 q^{60} - 9 q^{61} - 2 q^{62} - 4 q^{63} + 13 q^{64} - 4 q^{65} - 2 q^{67} + 15 q^{68} + q^{69} + 4 q^{70} + 23 q^{71} - 13 q^{72} - 7 q^{73} + 12 q^{74} - 12 q^{75} + 54 q^{76} - 12 q^{78} + 5 q^{79} - 14 q^{80} - 14 q^{81} - 25 q^{82} + 11 q^{83} + 3 q^{84} - 15 q^{85} - 20 q^{86} - 12 q^{87} + 14 q^{89} - 4 q^{90} - 6 q^{91} + 42 q^{92} - 11 q^{93} - 3 q^{94} - 9 q^{95} - 15 q^{96} - 7 q^{97} + 6 q^{98}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - 9 * q^4 - q^5 + 2 * q^6 + q^7 - 13 * q^8 - q^9 + 6 * q^10 + 12 * q^12 - 4 * q^13 + 4 * q^14 - 2 * q^15 + q^16 + 10 * q^17 + 11 * q^18 - 9 * q^19 + 6 * q^20 + 2 * q^21 - 2 * q^23 - q^24 + 4 * q^25 + 14 * q^26 - 11 * q^27 - 6 * q^28 - q^29 - 3 * q^30 + 7 * q^31 + 30 * q^32 + 40 * q^34 + q^35 + 21 * q^36 + 8 * q^37 + 9 * q^38 + 2 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^45 - 13 * q^46 + 3 * q^47 - 13 * q^48 - q^49 - 4 * q^50 - 5 * q^51 + 24 * q^52 + q^53 - 14 * q^54 - 12 * q^56 + 7 * q^57 - 9 * q^58 + 7 * q^59 - 3 * q^60 - 9 * q^61 - 2 * q^62 - 4 * q^63 + 13 * q^64 - 4 * q^65 - 2 * q^67 + 15 * q^68 + q^69 + 4 * q^70 + 23 * q^71 - 13 * q^72 - 7 * q^73 + 12 * q^74 - 12 * q^75 + 54 * q^76 - 12 * q^78 + 5 * q^79 - 14 * q^80 - 14 * q^81 - 25 * q^82 + 11 * q^83 + 3 * q^84 - 15 * q^85 - 20 * q^86 - 12 * q^87 + 14 * q^89 - 4 * q^90 - 6 * q^91 + 42 * q^92 - 11 * q^93 - 3 * q^94 - 9 * q^95 - 15 * q^96 - 7 * q^97 + 6 * q^98

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