LMFDB - Embedded newform 847.2.f.w.148.3

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.3
Root			$0.901622 - 0.655067i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.w.372.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.344389 + 1.05992i) q^{2} +(2.31283 + 1.68037i) q^{3} +(0.613206 - 0.445520i) q^{4} +(1.06799 - 3.28693i) q^{5} +(-0.984546 + 3.03012i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(2.48664 + 1.80665i) q^{8} +(1.59850 + 4.91966i) q^{9} +O(q^{10})$	\(q+(0.344389 + 1.05992i) q^{2} +(2.31283 + 1.68037i) q^{3} +(0.613206 - 0.445520i) q^{4} +(1.06799 - 3.28693i) q^{5} +(-0.984546 + 3.03012i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(2.48664 + 1.80665i) q^{8} +(1.59850 + 4.91966i) q^{9} +3.85168 q^{10} +2.16688 q^{12} +(-0.636468 - 1.95885i) q^{13} +(-0.901622 - 0.655067i) q^{14} +(7.99333 - 5.80749i) q^{15} +(-0.590087 + 1.81610i) q^{16} +(0.597555 - 1.83909i) q^{17} +(-4.66395 + 3.38856i) q^{18} +(-1.31300 - 0.953952i) q^{19} +(-0.809496 - 2.49137i) q^{20} -2.85882 q^{21} -0.807136 q^{23} +(2.71534 + 8.35696i) q^{24} +(-5.61820 - 4.08186i) q^{25} +(1.85703 - 1.34921i) q^{26} +(-1.91954 + 5.90773i) q^{27} +(-0.234224 + 0.720867i) q^{28} +(-6.45084 + 4.68681i) q^{29} +(8.90830 + 6.47226i) q^{30} +(0.243635 + 0.749832i) q^{31} +4.01918 q^{32} +2.15508 q^{34} +(1.06799 + 3.28693i) q^{35} +(3.17202 + 2.30461i) q^{36} +(-8.14014 + 5.91416i) q^{37} +(0.558930 - 1.72021i) q^{38} +(1.81955 - 5.59998i) q^{39} +(8.59403 - 6.24393i) q^{40} +(1.72008 + 1.24971i) q^{41} +(-0.984546 - 3.03012i) q^{42} +3.08043 q^{43} +17.8777 q^{45} +(-0.277969 - 0.855500i) q^{46} +(-6.12128 - 4.44737i) q^{47} +(-4.41650 + 3.20877i) q^{48} +(0.309017 - 0.951057i) q^{49} +(2.39160 - 7.36059i) q^{50} +(4.47239 - 3.24938i) q^{51} +(-1.26299 - 0.917617i) q^{52} +(3.34432 + 10.2928i) q^{53} -6.92280 q^{54} -3.07366 q^{56} +(-1.43376 - 4.41266i) q^{57} +(-7.18925 - 5.22329i) q^{58} +(2.66704 - 1.93771i) q^{59} +(2.31420 - 7.12238i) q^{60} +(-0.332696 + 1.02393i) q^{61} +(-0.710857 + 0.516468i) q^{62} +(-4.18492 - 3.04052i) q^{63} +(2.56433 + 7.89221i) q^{64} -7.11832 q^{65} +2.40314 q^{67} +(-0.452925 - 1.39396i) q^{68} +(-1.86677 - 1.35629i) q^{69} +(-3.11608 + 2.26396i) q^{70} +(-0.985330 + 3.03253i) q^{71} +(-4.91323 + 15.1214i) q^{72} +(-0.992078 + 0.720787i) q^{73} +(-9.07192 - 6.59113i) q^{74} +(-6.13491 - 18.8813i) q^{75} -1.23015 q^{76} +6.56217 q^{78} +(-2.93004 - 9.01775i) q^{79} +(5.33918 + 3.87914i) q^{80} +(-1.81200 + 1.31650i) q^{81} +(-0.732217 + 2.25353i) q^{82} +(-4.96572 + 15.2829i) q^{83} +(-1.75304 + 1.27366i) q^{84} +(-5.40676 - 3.92824i) q^{85} +(1.06087 + 3.26501i) q^{86} -22.7953 q^{87} -4.43830 q^{89} +(6.15690 + 18.9490i) q^{90} +(1.66629 + 1.21063i) q^{91} +(-0.494940 + 0.359595i) q^{92} +(-0.696508 + 2.14363i) q^{93} +(2.60576 - 8.01970i) q^{94} +(-4.53784 + 3.29693i) q^{95} +(9.29568 + 6.75371i) q^{96} +(1.99874 + 6.15150i) q^{97} +1.11447 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * 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 $

$2$	0.344389	+	1.05992i	0.243520	+	0.749477i	0.995876	+	0.0907209i	$0.0289171\pi$
$2$	0.344389	+	1.05992i	0.243520	+	0.749477i	−0.752356	+	0.658756i	$0.771083\pi$
$3$	2.31283	+	1.68037i	1.33531	+	0.970163i	0.999602	+	0.0281981i	$0.00897692\pi$
$3$	2.31283	+	1.68037i	1.33531	+	0.970163i	0.335712	+	0.941965i	$0.391023\pi$
$4$	0.613206	−	0.445520i	0.306603	−	0.222760i
$5$	1.06799	−	3.28693i	0.477618	−	1.46996i	−0.364776	−	0.931095i	$-0.618854\pi$
$5$	1.06799	−	3.28693i	0.477618	−	1.46996i	0.842394	−	0.538862i	$-0.181146\pi$
$6$	−0.984546	+	3.03012i	−0.401939	+	1.23704i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	2.48664	+	1.80665i	0.879161	+	0.638748i
$9$	1.59850	+	4.91966i	0.532832	+	1.63989i
$10$	3.85168			1.21801
$11$		0			0
$11$		0			0
$12$	2.16688			0.625525
$13$	−0.636468	−	1.95885i	−0.176524	−	0.543286i	0.823175	−	0.567787i	$-0.192200\pi$
$13$	−0.636468	−	1.95885i	−0.176524	−	0.543286i	−0.999700	+	0.0245009i	$0.992200\pi$
$14$	−0.901622	−	0.655067i	−0.240969	−	0.175074i
$15$	7.99333	−	5.80749i	2.06387	−	1.49949i
$16$	−0.590087	+	1.81610i	−0.147522	+	0.454025i
$17$	0.597555	−	1.83909i	0.144928	−	0.446044i	−0.852073	−	0.523422i	$-0.824655\pi$
$17$	0.597555	−	1.83909i	0.144928	−	0.446044i	0.997002	+	0.0773786i	$0.0246550\pi$
$18$	−4.66395	+	3.38856i	−1.09930	+	0.798691i
$19$	−1.31300	−	0.953952i	−0.301223	−	0.218852i	0.426898	−	0.904300i	$-0.359606\pi$
$19$	−1.31300	−	0.953952i	−0.301223	−	0.218852i	−0.728121	+	0.685448i	$0.759606\pi$
$20$	−0.809496	−	2.49137i	−0.181009	−	0.557088i
$21$	−2.85882			−0.623845
$22$		0			0
$23$	−0.807136			−0.168299			−0.0841497	−	0.996453i	$-0.526817\pi$
$23$	−0.807136			−0.168299			−0.0841497	+	0.996453i	$0.526817\pi$
$24$	2.71534	+	8.35696i	0.554267	+	1.70586i
$25$	−5.61820	−	4.08186i	−1.12364	−	0.816372i
$26$	1.85703	−	1.34921i	0.364193	−	0.264602i
$27$	−1.91954	+	5.90773i	−0.369415	+	1.13694i
$28$	−0.234224	+	0.720867i	−0.0442641	+	0.136231i
$29$	−6.45084	+	4.68681i	−1.19789	+	0.870319i	−0.994076	−	0.108690i	$-0.965334\pi$
$29$	−6.45084	+	4.68681i	−1.19789	+	0.870319i	−0.203815	+	0.979009i	$0.565334\pi$
$30$	8.90830	+	6.47226i	1.62643	+	1.18167i
$31$	0.243635	+	0.749832i	0.0437582	+	0.134674i	0.970549	−	0.240905i	$-0.0774441\pi$
$31$	0.243635	+	0.749832i	0.0437582	+	0.134674i	−0.926791	+	0.375578i	$0.877444\pi$
$32$	4.01918			0.710497
$33$		0			0
$34$	2.15508			0.369592
$35$	1.06799	+	3.28693i	0.180523	+	0.555592i
$36$	3.17202	+	2.30461i	0.528669	+	0.384101i
$37$	−8.14014	+	5.91416i	−1.33823	+	0.972282i	−0.338724	+	0.940886i	$0.609995\pi$
$37$	−8.14014	+	5.91416i	−1.33823	+	0.972282i	−0.999507	+	0.0313960i	$0.990005\pi$
$38$	0.558930	−	1.72021i	0.0906704	−	0.279055i
$39$	1.81955	−	5.59998i	0.291360	−	0.896715i
$40$	8.59403	−	6.24393i	1.35884	−	0.987252i
$41$	1.72008	+	1.24971i	0.268631	+	0.195172i	0.713943	−	0.700203i	$-0.246907\pi$
$41$	1.72008	+	1.24971i	0.268631	+	0.195172i	−0.445312	+	0.895375i	$0.646907\pi$
$42$	−0.984546	−	3.03012i	−0.151919	−	0.467558i
$43$	3.08043			0.469761			0.234880	−	0.972024i	$-0.424530\pi$
$43$	3.08043			0.469761			0.234880	+	0.972024i	$0.424530\pi$
$44$		0			0
$45$	17.8777			2.66506
$46$	−0.277969	−	0.855500i	−0.0409842	−	0.126137i
$47$	−6.12128	−	4.44737i	−0.892881	−	0.648716i	0.0437469	−	0.999043i	$-0.486070\pi$
$47$	−6.12128	−	4.44737i	−0.892881	−	0.648716i	−0.936627	+	0.350327i	$0.886070\pi$
$48$	−4.41650	+	3.20877i	−0.637466	+	0.463146i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	2.39160	−	7.36059i	0.338224	−	1.04094i
$51$	4.47239	−	3.24938i	0.626260	−	0.455004i
$52$	−1.26299	−	0.917617i	−0.175145	−	0.127251i
$53$	3.34432	+	10.2928i	0.459378	+	1.41382i	0.865918	+	0.500186i	$0.166735\pi$
$53$	3.34432	+	10.2928i	0.459378	+	1.41382i	−0.406540	+	0.913633i	$0.633265\pi$
$54$	−6.92280			−0.942073
$55$		0			0
$56$	−3.07366			−0.410735
$57$	−1.43376	−	4.41266i	−0.189906	−	0.584471i
$58$	−7.18925	−	5.22329i	−0.943994	−	0.685852i
$59$	2.66704	−	1.93771i	0.347218	−	0.252269i	−0.400483	−	0.916304i	$-0.631158\pi$
$59$	2.66704	−	1.93771i	0.347218	−	0.252269i	0.747701	+	0.664035i	$0.231158\pi$
$60$	2.31420	−	7.12238i	0.298762	−	0.919495i
$61$	−0.332696	+	1.02393i	−0.0425974	+	0.131101i	−0.970094	−	0.242731i	$-0.921957\pi$
$61$	−0.332696	+	1.02393i	−0.0425974	+	0.131101i	0.927496	+	0.373833i	$0.121957\pi$
$62$	−0.710857	+	0.516468i	−0.0902789	+	0.0655915i
$63$	−4.18492	−	3.04052i	−0.527250	−	0.383069i
$64$	2.56433	+	7.89221i	0.320542	+	0.986526i
$65$	−7.11832			−0.882919
$66$		0			0
$67$	2.40314			0.293590			0.146795	−	0.989167i	$-0.453104\pi$
$67$	2.40314			0.293590			0.146795	+	0.989167i	$0.453104\pi$
$68$	−0.452925	−	1.39396i	−0.0549253	−	0.169043i
$69$	−1.86677	−	1.35629i	−0.224733	−	0.163278i
$70$	−3.11608	+	2.26396i	−0.372442	+	0.270595i
$71$	−0.985330	+	3.03253i	−0.116937	+	0.359896i	−0.992346	−	0.123487i	$-0.960592\pi$
$71$	−0.985330	+	3.03253i	−0.116937	+	0.359896i	0.875409	+	0.483383i	$0.160592\pi$
$72$	−4.91323	+	15.1214i	−0.579030	+	1.78207i
$73$	−0.992078	+	0.720787i	−0.116114	+	0.0843617i	−0.644327	−	0.764750i	$-0.722862\pi$
$73$	−0.992078	+	0.720787i	−0.116114	+	0.0843617i	0.528213	+	0.849112i	$0.322862\pi$
$74$	−9.07192	−	6.59113i	−1.05459	−	0.766204i
$75$	−6.13491	−	18.8813i	−0.708399	−	2.18023i
$76$	−1.23015			−0.141107
$77$		0			0
$78$	6.56217			0.743020
$79$	−2.93004	−	9.01775i	−0.329656	−	1.01458i	−0.969295	−	0.245901i	$-0.920916\pi$
$79$	−2.93004	−	9.01775i	−0.329656	−	1.01458i	0.639639	−	0.768675i	$-0.279084\pi$
$80$	5.33918	+	3.87914i	0.596939	+	0.433701i
$81$	−1.81200	+	1.31650i	−0.201334	+	0.146278i
$82$	−0.732217	+	2.25353i	−0.0808599	+	0.248861i
$83$	−4.96572	+	15.2829i	−0.545058	+	1.67752i	0.175793	+	0.984427i	$0.443751\pi$
$83$	−4.96572	+	15.2829i	−0.545058	+	1.67752i	−0.720851	+	0.693090i	$0.756249\pi$
$84$	−1.75304	+	1.27366i	−0.191273	+	0.138968i
$85$	−5.40676	−	3.92824i	−0.586445	−	0.426077i
$86$	1.06087	+	3.26501i	0.114396	+	0.352075i
$87$	−22.7953			−2.44391
$88$		0			0
$89$	−4.43830			−0.470459			−0.235230	−	0.971940i	$-0.575584\pi$
$89$	−4.43830			−0.470459			−0.235230	+	0.971940i	$0.575584\pi$
$90$	6.15690	+	18.9490i	0.648994	+	1.99740i
$91$	1.66629	+	1.21063i	0.174675	+	0.126909i
$92$	−0.494940	+	0.359595i	−0.0516011	+	0.0374904i
$93$	−0.696508	+	2.14363i	−0.0722246	+	0.222284i
$94$	2.60576	−	8.01970i	0.268763	−	0.827169i
$95$	−4.53784	+	3.29693i	−0.465572	+	0.338258i
$96$	9.29568	+	6.75371i	0.948736	+	0.689297i
$97$	1.99874	+	6.15150i	0.202942	+	0.624590i	0.999792	+	0.0204129i	$0.00649807\pi$
$97$	1.99874	+	6.15150i	0.202942	+	0.624590i	−0.796850	+	0.604177i	$0.793502\pi$
$98$	1.11447			0.112578
$99$		0			0
$100$	−5.26366			−0.526366
$101$	−4.77274	−	14.6890i	−0.474905	−	1.46161i	−0.846086	−	0.533047i	$-0.821047\pi$
$101$	−4.77274	−	14.6890i	−0.474905	−	1.46161i	0.371181	−	0.928561i	$-0.378953\pi$
$102$	4.98433	+	3.62133i	0.493522	+	0.358565i
$103$	−7.20682	+	5.23606i	−0.710109	+	0.515925i	−0.883209	−	0.468980i	$-0.844622\pi$
$103$	−7.20682	+	5.23606i	−0.710109	+	0.515925i	0.173100	+	0.984904i	$0.444622\pi$
$104$	1.95628	−	6.02083i	0.191829	−	0.590390i
$105$	−3.05318	+	9.39672i	−0.297960	+	0.917026i
$106$	−9.75776	+	7.08943i	−0.947757	+	0.688586i
$107$	−2.84142	−	2.06441i	−0.274691	−	0.199574i	0.441908	−	0.897061i	$-0.354302\pi$
$107$	−2.84142	−	2.06441i	−0.274691	−	0.199574i	−0.716598	+	0.697486i	$0.754302\pi$
$108$	1.45494	+	4.47785i	0.140002	+	0.430881i
$109$	3.87655			0.371306			0.185653	−	0.982615i	$-0.440560\pi$
$109$	3.87655			0.371306			0.185653	+	0.982615i	$0.440560\pi$
$110$		0			0
$111$	−28.7648			−2.73023
$112$	−0.590087	−	1.81610i	−0.0557580	−	0.171605i
$113$	−8.61920	−	6.26221i	−0.810826	−	0.589099i	0.103244	−	0.994656i	$-0.467078\pi$
$113$	−8.61920	−	6.26221i	−0.810826	−	0.589099i	−0.914070	+	0.405557i	$0.867078\pi$
$114$	4.18330	−	3.03935i	0.391802	−	0.284661i
$115$	−0.862010	+	2.65299i	−0.0803829	+	0.247393i
$116$	−1.86763	+	5.74796i	−0.173405	+	0.533685i
$117$	8.61947	−	6.26241i	0.796871	−	0.578960i
$118$	2.97232	+	2.15952i	0.273624	+	0.198800i
$119$	0.597555	+	1.83909i	0.0547778	+	0.168589i
$120$	30.3687			2.77227
$121$		0			0
$122$	−1.19987			−0.108631
$123$	1.87828	+	5.78074i	0.169358	+	0.521232i
$124$	0.483464	+	0.351257i	0.0434163	+	0.0315438i
$125$	−5.43680	+	3.95007i	−0.486282	+	0.353305i
$126$	1.78147	−	5.48280i	0.158706	−	0.488447i
$127$	6.01066	−	18.4989i	0.533360	−	1.64151i	−0.213807	−	0.976876i	$-0.568586\pi$
$127$	6.01066	−	18.4989i	0.533360	−	1.64151i	0.747167	−	0.664637i	$-0.231414\pi$
$128$	−0.978825	+	0.711158i	−0.0865167	+	0.0628581i
$129$	7.12451	+	5.17626i	0.627278	+	0.455744i
$130$	−2.45147	−	7.54486i	−0.215008	−	0.661728i
$131$	5.11284			0.446711			0.223355	−	0.974737i	$-0.428299\pi$
$131$	5.11284			0.446711			0.223355	+	0.974737i	$0.428299\pi$
$132$		0			0
$133$	1.62296			0.140728
$134$	0.827615	+	2.54714i	0.0714951	+	0.220039i
$135$	17.3682	+	12.6188i	1.49482	+	1.08605i
$136$	4.80849	−	3.49357i	0.412325	−	0.299571i
$137$	2.81221	−	8.65511i	0.240264	−	0.739456i	−0.756116	−	0.654438i	$-0.772905\pi$
$137$	2.81221	−	8.65511i	0.240264	−	0.739456i	0.996379	−	0.0850177i	$-0.0270947\pi$
$138$	0.794662	−	2.44572i	0.0676461	−	0.208193i
$139$	10.5306	−	7.65095i	0.893197	−	0.648945i	−0.0435129	−	0.999053i	$-0.513855\pi$
$139$	10.5306	−	7.65095i	0.893197	−	0.648945i	0.936710	+	0.350108i	$0.113855\pi$
$140$	2.11929	+	1.53975i	0.179112	+	0.130133i
$141$	−6.68426	−	20.5720i	−0.562916	−	1.73248i
$142$	−3.55358			−0.298210
$143$		0			0
$144$	−9.87786			−0.823155
$145$	8.51578	+	26.2089i	0.707197	+	2.17653i
$146$	−1.10564	−	0.803293i	−0.0915032	−	0.0664810i
$147$	2.31283	−	1.68037i	0.190759	−	0.138595i
$148$	−2.35671	+	7.25320i	−0.193720	+	0.596209i
$149$	−0.972321	+	2.99250i	−0.0796557	+	0.245155i	−0.982952	−	0.183862i	$-0.941140\pi$
$149$	−0.972321	+	2.99250i	−0.0796557	+	0.245155i	0.903296	+	0.429017i	$0.141140\pi$
$150$	17.8999	−	13.0050i	1.46152	−	1.06186i
$151$	−2.31942	−	1.68516i	−0.188752	−	0.137136i	0.489396	−	0.872062i	$-0.337217\pi$
$151$	−2.31942	−	1.68516i	−0.188752	−	0.137136i	−0.678148	+	0.734925i	$0.737217\pi$
$152$	−1.54151	−	4.74427i	−0.125033	−	0.384811i
$153$	10.0029			0.808684
$154$		0			0
$155$	2.72484			0.218864
$156$	−1.37915	−	4.24459i	−0.110420	−	0.339839i
$157$	17.3854	+	12.6312i	1.38750	+	1.00808i	0.996134	+	0.0878468i	$0.0279986\pi$
$157$	17.3854	+	12.6312i	1.38750	+	1.00808i	0.391370	+	0.920234i	$0.372001\pi$
$158$	8.54902	−	6.21123i	0.680124	−	0.494139i
$159$	−9.56080	+	29.4251i	−0.758221	+	2.33356i
$160$	4.29243	−	13.2107i	0.339346	−	1.04440i
$161$	0.652986	−	0.474422i	0.0514625	−	0.0373897i
$162$	−2.01942	−	1.46719i	−0.158661	−	0.115274i
$163$	−2.54088	−	7.82002i	−0.199017	−	0.612511i	−0.999906	−	0.0136985i	$-0.995639\pi$
$163$	−2.54088	−	7.82002i	−0.199017	−	0.612511i	0.800889	−	0.598812i	$-0.204361\pi$
$164$	1.61153			0.125840
$165$		0			0
$166$	−17.9088			−1.38999
$167$	−6.70832	−	20.6461i	−0.519105	−	1.59764i	−0.775686	−	0.631119i	$-0.782596\pi$
$167$	−6.70832	−	20.6461i	−0.519105	−	1.59764i	0.256581	−	0.966523i	$-0.417404\pi$
$168$	−7.10886	−	5.16489i	−0.548460	−	0.398480i
$169$	7.08523	−	5.14772i	0.545018	−	0.395979i
$170$	2.30159	−	7.08357i	0.176524	−	0.543285i
$171$	2.59429	−	7.98442i	0.198391	−	0.610584i
$172$	1.88894	−	1.37239i	0.144030	−	0.104644i
$173$	6.50905	+	4.72910i	0.494874	+	0.359547i	0.807056	−	0.590475i	$-0.201060\pi$
$173$	6.50905	+	4.72910i	0.494874	+	0.359547i	−0.312181	+	0.950022i	$0.601060\pi$
$174$	−7.85045	−	24.1612i	−0.595141	−	1.83166i
$175$	6.94447			0.524953
$176$		0			0
$177$	9.42449			0.708388
$178$	−1.52850	−	4.70425i	−0.114566	−	0.352598i
$179$	2.92938	+	2.12832i	0.218952	+	0.159078i	0.691855	−	0.722037i	$-0.256794\pi$
$179$	2.92938	+	2.12832i	0.218952	+	0.159078i	−0.472903	+	0.881115i	$0.656794\pi$
$180$	10.9627	−	7.96490i	0.817114	−	0.593668i
$181$	4.88800	−	15.0437i	0.363322	−	1.11819i	−0.587703	−	0.809077i	$-0.699967\pi$
$181$	4.88800	−	15.0437i	0.363322	−	1.11819i	0.951025	−	0.309114i	$-0.100033\pi$
$182$	−0.709322	+	2.18307i	−0.0525784	+	0.161820i
$183$	−2.49006	+	1.80913i	−0.184070	+	0.133735i
$184$	−2.00706	−	1.45821i	−0.147962	−	0.107501i
$185$	10.7458	+	33.0723i	0.790050	+	2.43152i
$186$	−2.51195			−0.184185
$187$		0			0
$188$	−5.73500			−0.418268
$189$	−1.91954	−	5.90773i	−0.139626	−	0.429724i
$190$	−5.05727	−	3.67432i	−0.366893	−	0.266563i
$191$	−0.347134	+	0.252207i	−0.0251177	+	0.0182491i	−0.600273	−	0.799795i	$-0.704942\pi$
$191$	−0.347134	+	0.252207i	−0.0251177	+	0.0182491i	0.575156	+	0.818044i	$0.304942\pi$
$192$	−7.33097	+	22.5624i	−0.529067	+	1.62830i
$193$	−4.68928	+	14.4321i	−0.337542	+	1.03885i	0.627915	+	0.778282i	$0.283909\pi$
$193$	−4.68928	+	14.4321i	−0.337542	+	1.03885i	−0.965456	+	0.260564i	$0.916091\pi$
$194$	−5.83176	+	4.23702i	−0.418696	+	0.304200i
$195$	−16.4635	−	11.9614i	−1.17897	−	0.856575i
$196$	−0.234224	−	0.720867i	−0.0167303	−	0.0514905i
$197$	−20.8082			−1.48252			−0.741262	−	0.671216i	$-0.765772\pi$
$197$	−20.8082			−1.48252			−0.741262	+	0.671216i	$0.765772\pi$
$198$		0			0
$199$	8.44567			0.598698			0.299349	−	0.954144i	$-0.403231\pi$
$199$	8.44567			0.598698			0.299349	+	0.954144i	$0.403231\pi$
$200$	−6.59595	−	20.3003i	−0.466404	−	1.43544i
$201$	5.55806	+	4.03817i	0.392035	+	0.284830i
$202$	13.9255	−	10.1174i	0.979792	−	0.711861i
$203$	2.46400	−	7.58342i	0.172939	−	0.532252i
$204$	1.29483	−	3.98508i	0.0906563	−	0.279011i
$205$	5.94472	−	4.31910i	0.415198	−	0.301659i
$206$	−8.03176	−	5.83542i	−0.559599	−	0.406573i
$207$	−1.29020	−	3.97084i	−0.0896753	−	0.275992i
$208$	3.93303			0.272707
$209$		0			0
$210$	−11.0113			−0.759849
$211$	−3.04668	−	9.37672i	−0.209742	−	0.645520i	−0.999485	−	0.0320823i	$-0.989786\pi$
$211$	−3.04668	−	9.37672i	−0.209742	−	0.645520i	0.789743	−	0.613438i	$-0.210214\pi$
$212$	6.63639	+	4.82162i	0.455789	+	0.331150i
$213$	−7.37469	+	5.35802i	−0.505305	+	0.367126i
$214$	1.20956	−	3.72264i	0.0826838	−	0.254475i
$215$	3.28986	−	10.1251i	0.224366	−	0.690528i
$216$	−15.4464	+	11.2225i	−1.05100	+	0.763593i
$217$	−0.637845	−	0.463421i	−0.0432997	−	0.0314591i
$218$	1.33504	+	4.10883i	0.0904204	+	0.278285i
$219$	−3.50570			−0.236893
$220$		0			0
$221$	−3.98281			−0.267913
$222$	−9.90627	−	30.4884i	−0.664865	−	2.04625i
$223$	−14.0736	−	10.2250i	−0.942436	−	0.684720i	0.00656992	−	0.999978i	$-0.497909\pi$
$223$	−14.0736	−	10.2250i	−0.942436	−	0.684720i	−0.949006	+	0.315259i	$0.897909\pi$
$224$	−3.25158	+	2.36241i	−0.217255	+	0.157845i
$225$	11.1007	−	34.1645i	0.740048	−	2.27763i
$226$	3.66909	−	11.2923i	0.244064	−	0.751153i
$227$	10.2191	−	7.42460i	0.678264	−	0.492788i	−0.194517	−	0.980899i	$-0.562314\pi$
$227$	10.2191	−	7.42460i	0.678264	−	0.492788i	0.872781	+	0.488111i	$0.162314\pi$
$228$	−2.84512	−	2.06710i	−0.188423	−	0.136897i
$229$	1.41326	+	4.34958i	0.0933910	+	0.287428i	0.986831	−	0.161755i	$-0.0517153\pi$
$229$	1.41326	+	4.34958i	0.0933910	+	0.287428i	−0.893440	+	0.449183i	$0.851715\pi$
$230$	−3.10883			−0.204990
$231$		0			0
$232$	−24.5084			−1.60905
$233$	7.37218	+	22.6893i	0.482968	+	1.48642i	0.834903	+	0.550398i	$0.185524\pi$
$233$	7.37218	+	22.6893i	0.482968	+	1.48642i	−0.351935	+	0.936025i	$0.614476\pi$
$234$	9.60612	+	6.97925i	0.627971	+	0.456248i
$235$	−21.1556	+	15.3705i	−1.38004	+	1.00266i
$236$	0.772151	−	2.37644i	0.0502628	−	0.154693i
$237$	8.37646	−	25.7801i	0.544110	−	1.67460i
$238$	−1.74349	+	1.26672i	−0.113014	+	0.0821094i
$239$	−7.15021	−	5.19493i	−0.462509	−	0.336032i	0.332006	−	0.943277i	$-0.392275\pi$
$239$	−7.15021	−	5.19493i	−0.462509	−	0.336032i	−0.794515	+	0.607245i	$0.792275\pi$
$240$	5.83024	+	17.9436i	0.376340	+	1.15826i
$241$	18.9464			1.22045			0.610224	−	0.792229i	$-0.291079\pi$
$241$	18.9464			1.22045			0.610224	+	0.792229i	$0.291079\pi$
$242$		0			0
$243$	12.2322			0.784696
$244$	0.252172	+	0.776105i	0.0161436	+	0.0496850i
$245$	−2.79603	−	2.03143i	−0.178632	−	0.129783i
$246$	−5.48027	+	3.98165i	−0.349409	+	0.253861i
$247$	−1.03296	+	3.17913i	−0.0657258	+	0.202283i
$248$	−0.748851	+	2.30473i	−0.0475521	+	0.146350i
$249$	−37.1658	+	27.0026i	−2.35529	+	1.71122i
$250$	−6.05913	−	4.40222i	−0.383213	−	0.278421i
$251$	−0.885925	−	2.72660i	−0.0559191	−	0.172101i	0.919196	−	0.393800i	$-0.128840\pi$
$251$	−0.885925	−	2.72660i	−0.0559191	−	0.172101i	−0.975115	+	0.221699i	$0.928840\pi$
$252$	−3.92083			−0.246989
$253$		0			0
$254$	21.6774			1.36016
$255$	−5.90402	−	18.1707i	−0.369724	−	1.13789i
$256$	12.3362	+	8.96275i	0.771010	+	0.560172i
$257$	−18.1348	+	13.1757i	−1.13122	+	0.821879i	−0.985872	−	0.167502i	$-0.946430\pi$
$257$	−18.1348	+	13.1757i	−1.13122	+	0.821879i	−0.145347	+	0.989381i	$0.546430\pi$
$258$	−3.03282	+	9.33406i	−0.188815	+	0.581113i
$259$	3.10926	−	9.56931i	0.193200	−	0.594608i
$260$	−4.36500	+	3.17136i	−0.270706	+	0.196679i
$261$	−33.3692	−	24.2441i	−2.06550	−	1.50067i
$262$	1.76080	+	5.41920i	0.108783	+	0.334799i
$263$	0.990706			0.0610895			0.0305448	−	0.999533i	$-0.490276\pi$
$263$	0.990706			0.0610895			0.0305448	+	0.999533i	$0.490276\pi$
$264$		0			0
$265$	37.4032			2.29766
$266$	0.558930	+	1.72021i	0.0342702	+	0.105473i
$267$	−10.2650	−	7.45800i	−0.628211	−	0.456422i
$268$	1.47362	−	1.07065i	0.0900156	−	0.0654002i
$269$	−2.22194	+	6.83844i	−0.135474	+	0.416947i	−0.995664	−	0.0930279i	$-0.970345\pi$
$269$	−2.22194	+	6.83844i	−0.135474	+	0.416947i	0.860189	+	0.509975i	$0.170345\pi$
$270$	−7.39345	+	22.7547i	−0.449951	+	1.38481i
$271$	21.9764	−	15.9668i	1.33497	−	0.969912i	0.335356	−	0.942091i	$-0.391143\pi$
$271$	21.9764	−	15.9668i	1.33497	−	0.969912i	0.999613	−	0.0278207i	$-0.00885676\pi$
$272$	2.98736	+	2.17044i	0.181135	+	0.131602i
$273$	1.81955	+	5.59998i	0.110124	+	0.338927i
$274$	10.1422			0.612714
$275$		0			0
$276$	−1.74897			−0.105275
$277$	6.48491	+	19.9585i	0.389640	+	1.19919i	0.933058	+	0.359727i	$0.117130\pi$
$277$	6.48491	+	19.9585i	0.389640	+	1.19919i	−0.543417	+	0.839463i	$0.682870\pi$
$278$	11.7360	+	8.52673i	0.703881	+	0.511399i
$279$	−3.29947	+	2.39721i	−0.197534	+	0.143517i
$280$	−3.28263	+	10.1029i	−0.196174	+	0.603763i
$281$	−8.70130	+	26.7798i	−0.519076	+	1.59755i	0.256665	+	0.966500i	$0.417376\pi$
$281$	−8.70130	+	26.7798i	−0.519076	+	1.59755i	−0.775741	+	0.631051i	$0.782624\pi$
$282$	19.5027	−	14.1696i	1.16137	−	0.843786i
$283$	21.1896	+	15.3951i	1.25959	+	0.915145i	0.998737	−	0.0502344i	$-0.0159969\pi$
$283$	21.1896	+	15.3951i	1.25959	+	0.915145i	0.260851	+	0.965379i	$0.415997\pi$
$284$	0.746845	+	2.29855i	0.0443171	+	0.136394i
$285$	−16.0353			−0.949851
$286$		0			0
$287$	−2.12613			−0.125502
$288$	6.42463	+	19.7730i	0.378575	+	1.16513i
$289$	10.7281	+	7.79444i	0.631066	+	0.458496i
$290$	−24.8466	+	18.0521i	−1.45904	+	1.06006i
$291$	−5.71404	+	17.5860i	−0.334963	+	1.03091i
$292$	−0.287223	+	0.883981i	−0.0168085	+	0.0517311i
$293$	3.61133	−	2.62379i	0.210976	−	0.153283i	−0.477279	−	0.878752i	$-0.658377\pi$
$293$	3.61133	−	2.62379i	0.210976	−	0.153283i	0.688255	+	0.725469i	$0.258377\pi$
$294$	2.57757	+	1.87272i	0.150327	+	0.109219i
$295$	−3.52077	−	10.8358i	−0.204987	−	0.630885i
$296$	−30.9264			−1.79756
$297$		0			0
$298$	−3.50667			−0.203136
$299$	0.513716	+	1.58105i	0.0297089	+	0.0914347i
$300$	−12.1740	−	8.84491i	−0.702865	−	0.510661i
$301$	−2.49212	+	1.81063i	−0.143643	+	0.104363i
$302$	0.987351	−	3.03875i	0.0568157	−	0.174861i
$303$	13.6444	−	41.9931i	0.783849	−	2.41244i
$304$	2.50726	−	1.82163i	0.143801	−	0.104478i
$305$	3.01028	+	2.18710i	0.172368	+	0.125233i
$306$	3.44488	+	10.6023i	0.196931	+	0.606090i
$307$	12.8841			0.735334			0.367667	−	0.929957i	$-0.380157\pi$
$307$	12.8841			0.735334			0.367667	+	0.929957i	$0.380157\pi$
$308$		0			0
$309$	−25.4667			−1.44875
$310$	0.938405	+	2.88811i	0.0532978	+	0.164034i
$311$	−21.6977	−	15.7643i	−1.23036	−	0.893912i	−0.233447	−	0.972370i	$-0.575001\pi$
$311$	−21.6977	−	15.7643i	−1.23036	−	0.893912i	−0.996917	+	0.0784574i	$0.975001\pi$
$312$	14.6418	−	10.6379i	0.828928	−	0.602251i
$313$	1.10896	−	3.41304i	0.0626824	−	0.192917i	−0.914811	−	0.403882i	$-0.867661\pi$
$313$	1.10896	−	3.41304i	0.0626824	−	0.192917i	0.977494	+	0.210965i	$0.0676607\pi$
$314$	−7.40075	+	22.7772i	−0.417648	+	1.28539i
$315$	−14.4634	+	10.5083i	−0.814920	+	0.592074i
$316$	−5.81431	−	4.22434i	−0.327081	−	0.237638i
$317$	−5.22797	−	16.0900i	−0.293632	−	0.903706i	−0.983678	−	0.179940i	$-0.942410\pi$
$317$	−5.22797	−	16.0900i	−0.293632	−	0.903706i	0.690046	−	0.723766i	$-0.257590\pi$
$318$	−34.4809			−1.93359
$319$		0			0
$320$	28.6798			1.60325
$321$	−3.10275	−	9.54929i	−0.173179	−	0.532989i
$322$	0.727732	+	0.528728i	0.0405549	+	0.0294649i
$323$	−2.53899	+	1.84468i	−0.141273	+	0.102641i
$324$	−0.524605	+	1.61457i	−0.0291447	+	0.0896983i
$325$	−4.41993	+	13.6032i	−0.245174	+	0.754567i
$326$	7.41355	−	5.38626i	0.410598	−	0.298317i
$327$	8.96581	+	6.51404i	0.495810	+	0.360227i
$328$	2.01943	+	6.21516i	0.111504	+	0.343175i
$329$	7.56632			0.417145
$330$		0			0
$331$	−1.23826			−0.0680610			−0.0340305	−	0.999421i	$-0.510834\pi$
$331$	−1.23826			−0.0680610			−0.0340305	+	0.999421i	$0.510834\pi$
$332$	3.76384	+	11.5839i	0.206567	+	0.635749i
$333$	−42.1077	−	30.5930i	−2.30749	−	1.67649i
$334$	19.5729	−	14.2206i	1.07098	−	0.778115i
$335$	2.56652	−	7.89894i	0.140224	−	0.431565i
$336$	1.68695	−	5.19190i	0.0920307	−	0.283242i
$337$	16.5691	−	12.0382i	0.902579	−	0.655762i	−0.0365484	−	0.999332i	$-0.511636\pi$
$337$	16.5691	−	12.0382i	0.902579	−	0.655762i	0.939127	+	0.343570i	$0.111636\pi$
$338$	7.89626	+	5.73697i	0.429500	+	0.312050i
$339$	−9.41192	−	28.9669i	−0.511185	−	1.57327i
$340$	−5.06556			−0.274719
$341$		0			0
$342$	9.35630			0.505931
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	7.65992	+	5.56526i	0.412995	+	0.300059i
$345$	−6.45170	+	4.68743i	−0.347348	+	0.252363i
$346$	−2.77083	+	8.52773i	−0.148961	+	0.458454i
$347$	8.42685	−	25.9352i	0.452377	−	1.39227i	−0.421810	−	0.906684i	$-0.638605\pi$
$347$	8.42685	−	25.9352i	0.452377	−	1.39227i	0.874187	−	0.485589i	$-0.161395\pi$
$348$	−13.9782	+	10.1558i	−0.749311	+	0.544406i
$349$	−6.45947	−	4.69308i	−0.345767	−	0.251215i	0.401324	−	0.915936i	$-0.368550\pi$
$349$	−6.45947	−	4.69308i	−0.345767	−	0.251215i	−0.747091	+	0.664721i	$0.768550\pi$
$350$	2.39160	+	7.36059i	0.127836	+	0.393440i
$351$	12.7941			0.682897
$352$		0			0
$353$	5.93472			0.315873			0.157937	−	0.987449i	$-0.449516\pi$
$353$	5.93472			0.315873			0.157937	+	0.987449i	$0.449516\pi$
$354$	3.24569	+	9.98921i	0.172507	+	0.530920i
$355$	8.91539	+	6.47741i	0.473180	+	0.343785i
$356$	−2.72159	+	1.97735i	−0.144244	+	0.104800i
$357$	−1.70830	+	5.25761i	−0.0904129	+	0.278262i
$358$	−1.24700	+	3.83788i	−0.0659061	+	0.202838i
$359$	−22.9925	+	16.7050i	−1.21350	+	0.881657i	−0.995544	−	0.0943020i	$-0.969938\pi$
$359$	−22.9925	+	16.7050i	−1.21350	+	0.881657i	−0.217953	+	0.975959i	$0.569938\pi$
$360$	44.4555	+	32.2988i	2.34301	+	1.70230i
$361$	−5.05737	−	15.5650i	−0.266178	−	0.819210i
$362$	17.6285			0.926535
$363$		0			0
$364$	1.56114			0.0818261
$365$	1.30965	+	4.03068i	0.0685500	+	0.210975i
$366$	−2.77509	−	2.01622i	−0.145056	−	0.105389i
$367$	24.5953	−	17.8695i	1.28386	−	0.932781i	0.284200	−	0.958765i	$-0.408272\pi$
$367$	24.5953	−	17.8695i	1.28386	−	0.932781i	0.999662	+	0.0259840i	$0.00827188\pi$
$368$	0.476280	−	1.46584i	0.0248278	−	0.0764122i
$369$	−3.39862	+	10.4599i	−0.176925	+	0.544519i
$370$	−31.3532	+	22.7795i	−1.62998	+	1.18425i
$371$	−8.75554	−	6.36127i	−0.454565	−	0.330261i
$372$	0.527928	+	1.62480i	0.0273718	+	0.0842418i
$373$	14.4226			0.746772			0.373386	−	0.927676i	$-0.378197\pi$
$373$	14.4226			0.746772			0.373386	+	0.927676i	$0.378197\pi$
$374$		0			0
$375$	−19.2120			−0.992103
$376$	−7.18659	−	22.1180i	−0.370620	−	1.14065i
$377$	13.2865	+	9.65320i	0.684289	+	0.497165i
$378$	5.60066	−	4.06912i	0.288067	−	0.209293i
$379$	−6.92421	+	21.3105i	−0.355673	+	1.09465i	0.599946	+	0.800041i	$0.295189\pi$
$379$	−6.92421	+	21.3105i	−0.355673	+	1.09465i	−0.955618	+	0.294607i	$0.904811\pi$
$380$	−1.31378	+	4.04340i	−0.0673955	+	0.207422i
$381$	44.9867	−	32.6847i	2.30474	−	1.67449i
$382$	−0.386869	−	0.281077i	−0.0197939	−	0.0143811i
$383$	10.4072	+	32.0302i	0.531785	+	1.63667i	0.750495	+	0.660876i	$0.229815\pi$
$383$	10.4072	+	32.0302i	0.531785	+	1.63667i	−0.218710	+	0.975790i	$0.570185\pi$
$384$	−3.45887			−0.176510
$385$		0			0
$386$	−16.9118			−0.860790
$387$	4.92405	+	15.1547i	0.250304	+	0.770355i
$388$	3.96626	+	2.88166i	0.201356	+	0.146294i
$389$	−1.96416	+	1.42704i	−0.0995866	+	0.0723539i	−0.636464	−	0.771306i	$-0.719604\pi$
$389$	−1.96416	+	1.42704i	−0.0995866	+	0.0723539i	0.536878	+	0.843660i	$0.319604\pi$
$390$	7.00831	−	21.5694i	0.354880	−	1.09221i
$391$	−0.482308	+	1.48439i	−0.0243914	+	0.0750689i
$392$	2.48664	−	1.80665i	0.125594	−	0.0912497i
$393$	11.8251	+	8.59146i	0.596499	+	0.433382i
$394$	−7.16612	−	22.0550i	−0.361024	−	1.11112i
$395$	−32.7699			−1.64883
$396$		0			0
$397$	−5.89696			−0.295960			−0.147980	−	0.988990i	$-0.547277\pi$
$397$	−5.89696			−0.295960			−0.147980	+	0.988990i	$0.547277\pi$
$398$	2.90860	+	8.95175i	0.145795	+	0.448710i
$399$	3.75363	+	2.72717i	0.187917	+	0.136530i
$400$	10.7283	−	7.79456i	0.536415	−	0.389728i
$401$	3.47322	−	10.6895i	0.173445	−	0.533807i	−0.826114	−	0.563502i	$-0.809454\pi$
$401$	3.47322	−	10.6895i	0.173445	−	0.533807i	0.999559	+	0.0296950i	$0.00945359\pi$
$402$	−2.36600	+	7.28180i	−0.118005	+	0.363183i
$403$	1.31374	−	0.954487i	0.0654420	−	0.0475464i
$404$	−9.47090	−	6.88102i	−0.471195	−	0.342343i
$405$	2.39204	+	7.36193i	0.118861	+	0.365817i
$406$	8.88640			0.441025
$407$		0			0
$408$	16.9917			0.841216
$409$	9.06482	+	27.8987i	0.448227	+	1.37950i	0.878906	+	0.476995i	$0.158274\pi$
$409$	9.06482	+	27.8987i	0.448227	+	1.37950i	−0.430679	+	0.902505i	$0.641726\pi$
$410$	6.62520	+	4.81349i	0.327195	+	0.237721i
$411$	21.0480	−	15.2922i	1.03822	−	0.754311i
$412$	−2.08649	+	6.42157i	−0.102794	+	0.316368i
$413$	−1.01872	+	3.13529i	−0.0501278	+	0.154277i
$414$	3.76444	−	2.73503i	0.185012	−	0.134419i
$415$	44.9305	+	32.6439i	2.20555	+	1.60243i
$416$	−2.55808	−	7.87295i	−0.125420	−	0.386003i
$417$	37.2120			1.82228
$418$		0			0
$419$	−20.2858			−0.991027			−0.495514	−	0.868600i	$-0.665020\pi$
$419$	−20.2858			−0.991027			−0.495514	+	0.868600i	$0.665020\pi$
$420$	2.31420	+	7.12238i	0.112921	+	0.347537i
$421$	2.47561	+	1.79864i	0.120654	+	0.0876603i	0.646476	−	0.762934i	$-0.276242\pi$
$421$	2.47561	+	1.79864i	0.120654	+	0.0876603i	−0.525822	+	0.850595i	$0.676242\pi$
$422$	8.88934	−	6.45848i	0.432726	−	0.314394i
$423$	12.0947	−	37.2237i	0.588066	−	1.80988i
$424$	−10.2793	+	31.6364i	−0.499207	+	1.53640i
$425$	−10.8641	+	7.89321i	−0.526985	+	0.382877i
$426$	−8.21884	−	5.97134i	−0.398204	−	0.289312i
$427$	−0.332696	−	1.02393i	−0.0161003	−	0.0495516i
$428$	−2.66211			−0.128678
$429$		0			0
$430$	11.8648			0.572173
$431$	2.33060	+	7.17284i	0.112261	+	0.345503i	0.991366	−	0.131125i	$-0.0418588\pi$
$431$	2.33060	+	7.17284i	0.112261	+	0.345503i	−0.879105	+	0.476628i	$0.841859\pi$
$432$	−9.59634	−	6.97215i	−0.461704	−	0.335448i
$433$	26.0193	−	18.9041i	1.25041	−	0.908474i	0.252161	−	0.967685i	$-0.418859\pi$
$433$	26.0193	−	18.9041i	1.25041	−	0.908474i	0.998245	+	0.0592114i	$0.0188586\pi$
$434$	0.271523	−	0.835662i	0.0130335	−	0.0401131i
$435$	−24.3451	+	74.9264i	−1.16726	+	3.59245i
$436$	2.37712	−	1.72708i	0.113844	−	0.0827122i
$437$	1.05977	+	0.769968i	0.0506957	+	0.0368326i
$438$	−1.20732	−	3.71576i	−0.0576882	−	0.177546i
$439$	−4.66725			−0.222756			−0.111378	−	0.993778i	$-0.535526\pi$
$439$	−4.66725			−0.222756			−0.111378	+	0.993778i	$0.535526\pi$
$440$		0			0
$441$	5.17284			0.246326
$442$	−1.37164	−	4.22146i	−0.0652421	−	0.200794i
$443$	−13.9775	−	10.1553i	−0.664091	−	0.482491i	0.203951	−	0.978981i	$-0.434622\pi$
$443$	−13.9775	−	10.1553i	−0.664091	−	0.482491i	−0.868042	+	0.496490i	$0.834622\pi$
$444$	−17.6387	+	12.8153i	−0.837097	+	0.608187i
$445$	−4.74005	+	14.5884i	−0.224700	+	0.691555i
$446$	5.99095	−	18.4383i	0.283680	−	0.873077i
$447$	−7.27732	+	5.28728i	−0.344206	+	0.250080i
$448$	−6.71351	−	4.87765i	−0.317184	−	0.230447i
$449$	−5.17297	−	15.9208i	−0.244128	−	0.751347i	−0.995779	−	0.0917865i	$-0.970742\pi$
$449$	−5.17297	−	15.9208i	−0.244128	−	0.751347i	0.751651	−	0.659561i	$-0.229258\pi$
$450$	40.0346			1.88725
$451$		0			0
$452$	−8.07529			−0.379829
$453$	−2.53274	−	7.79498i	−0.118999	−	0.366240i
$454$	11.3888	+	8.27447i	0.534504	+	0.388340i
$455$	5.75884	−	4.18404i	0.269979	−	0.196151i
$456$	4.40689	−	13.5630i	0.206372	−	0.635146i
$457$	−6.70487	+	20.6355i	−0.313640	+	0.965286i	0.662670	+	0.748912i	$0.269423\pi$
$457$	−6.70487	+	20.6355i	−0.313640	+	0.965286i	−0.976310	+	0.216375i	$0.930577\pi$
$458$	−4.12349	+	2.99589i	−0.192678	+	0.139989i
$459$	9.71779	+	7.06039i	0.453588	+	0.329551i
$460$	0.653373	+	2.01087i	0.0304637	+	0.0937575i
$461$	−6.07778			−0.283070			−0.141535	−	0.989933i	$-0.545204\pi$
$461$	−6.07778			−0.283070			−0.141535	+	0.989933i	$0.545204\pi$
$462$		0			0
$463$	−5.14719			−0.239210			−0.119605	−	0.992822i	$-0.538163\pi$
$463$	−5.14719			−0.239210			−0.119605	+	0.992822i	$0.538163\pi$
$464$	−4.70516	−	14.4810i	−0.218432	−	0.672264i
$465$	6.30210	+	4.57874i	0.292253	+	0.212334i
$466$	−21.5099	+	15.6279i	−0.996427	+	0.723947i
$467$	−1.21112	+	3.72745i	−0.0560441	+	0.172486i	−0.975160	−	0.221501i	$-0.928904\pi$
$467$	−1.21112	+	3.72745i	−0.0560441	+	0.172486i	0.919116	+	0.393987i	$0.128904\pi$
$468$	2.49548	−	7.68030i	0.115354	−	0.355022i
$469$	−1.94418	+	1.41253i	−0.0897739	+	0.0652246i
$470$	−23.5772	−	17.1299i	−1.08754	−	0.790142i
$471$	18.9843	+	58.4277i	0.874752	+	2.69221i
$472$	10.1327			0.466397
$473$		0			0
$474$	30.2096			1.38757
$475$	3.48281	+	10.7190i	0.159802	+	0.491821i
$476$	1.18577	+	0.861515i	0.0543499	+	0.0394875i
$477$	−45.2910	+	32.9059i	−2.07373	+	1.50666i
$478$	3.04376	−	9.36773i	0.139218	−	0.428470i
$479$	−4.67015	+	14.3732i	−0.213385	+	0.656730i	0.785880	+	0.618379i	$0.212210\pi$
$479$	−4.67015	+	14.3732i	−0.213385	+	0.656730i	−0.999264	+	0.0383508i	$0.987790\pi$
$480$	32.1266	−	23.3413i	1.46637	−	1.06538i
$481$	16.7659	+	12.1811i	0.764458	+	0.555411i
$482$	6.52495	+	20.0817i	0.297203	+	0.914698i
$483$	2.30745			0.104993
$484$		0			0
$485$	22.3541			1.01505
$486$	4.21264	+	12.9652i	0.191089	+	0.588112i
$487$	−20.2876	−	14.7398i	−0.919317	−	0.667923i	0.0240370	−	0.999711i	$-0.492348\pi$
$487$	−20.2876	−	14.7398i	−0.919317	−	0.667923i	−0.943354	+	0.331788i	$0.892348\pi$
$488$	−2.67719	+	1.94509i	−0.121191	+	0.0880501i
$489$	7.26391	−	22.3560i	0.328485	−	1.01097i
$490$	1.19024	−	3.66317i	0.0537694	−	0.165485i
$491$	−30.1122	+	21.8778i	−1.35895	+	0.987332i	−0.360435	+	0.932784i	$0.617372\pi$
$491$	−30.1122	+	21.8778i	−1.35895	+	0.987332i	−0.998511	+	0.0545479i	$0.982628\pi$
$492$	3.72721	+	2.70797i	0.168035	+	0.122085i
$493$	4.76471	+	14.6643i	0.214592	+	0.660446i
$494$	−3.72536			−0.167612
$495$		0			0
$496$	−1.50554			−0.0676006
$497$	−0.985330	−	3.03253i	−0.0441981	−	0.136028i
$498$	−41.4201	−	30.0934i	−1.85608	−	1.34852i
$499$	25.7375	−	18.6994i	1.15217	−	0.837101i	0.163403	−	0.986559i	$-0.447753\pi$
$499$	25.7375	−	18.6994i	1.15217	−	0.837101i	0.988768	+	0.149458i	$0.0477530\pi$
$500$	−1.57404	+	4.84441i	−0.0703934	+	0.216649i
$501$	19.1779	−	59.0234i	0.856804	−	2.63697i
$502$	2.58487	−	1.87802i	0.115369	−	0.0838201i
$503$	15.5379	+	11.2889i	0.692799	+	0.503348i	0.877579	−	0.479432i	$-0.159157\pi$
$503$	15.5379	+	11.2889i	0.692799	+	0.503348i	−0.184780	+	0.982780i	$0.559157\pi$
$504$	−4.91323	−	15.1214i	−0.218853	−	0.673559i
$505$	−53.3788			−2.37532
$506$		0			0
$507$	25.0370			1.11193
$508$	−4.55587	−	14.0215i	−0.202134	−	0.622104i
$509$	−2.03507	−	1.47857i	−0.0902029	−	0.0655363i	0.541770	−	0.840527i	$-0.317754\pi$
$509$	−2.03507	−	1.47857i	−0.0902029	−	0.0655363i	−0.631973	+	0.774991i	$0.717754\pi$
$510$	17.2262	−	12.5156i	0.762790	−	0.554200i
$511$	0.378940	−	1.16626i	0.0167633	−	0.0515922i
$512$	−5.99912	+	18.4634i	−0.265126	+	0.815974i
$513$	8.15605	−	5.92572i	0.360098	−	0.261627i
$514$	−20.2107	−	14.6839i	−0.891454	−	0.647679i
$515$	9.51376	+	29.2803i	0.419226	+	1.29025i
$516$	6.67492			0.293847
$517$		0			0
$518$	11.2135			0.492693
$519$	7.10770	+	21.8753i	0.311993	+	0.960217i
$520$	−17.7007	−	12.8603i	−0.776228	−	0.563962i
$521$	−12.0517	+	8.75610i	−0.527996	+	0.383612i	−0.819608	−	0.572925i	$-0.805809\pi$
$521$	−12.0517	+	8.75610i	−0.527996	+	0.383612i	0.291612	+	0.956537i	$0.405809\pi$
$522$	14.2049	−	43.7181i	0.621730	−	1.91349i
$523$	−3.06082	+	9.42024i	−0.133840	+	0.411918i	−0.995408	−	0.0957248i	$-0.969483\pi$
$523$	−3.06082	+	9.42024i	−0.133840	+	0.411918i	0.861567	+	0.507643i	$0.169483\pi$
$524$	3.13522	−	2.27787i	0.136963	−	0.0995093i
$525$	16.0614	+	11.6693i	0.700977	+	0.509290i
$526$	0.341188	+	1.05007i	0.0148765	+	0.0457852i
$527$	1.52459			0.0664122
$528$		0			0
$529$	−22.3485			−0.971675
$530$	12.8813	+	39.6444i	0.559526	+	1.72204i
$531$	13.7962	+	10.0235i	0.598702	+	0.434982i
$532$	0.995209	−	0.723061i	0.0431478	−	0.0313487i
$533$	1.35322	−	4.16477i	0.0586143	−	0.180396i
$534$	4.36971	−	13.4486i	0.189096	−	0.581977i
$535$	−9.82017	+	7.13477i	−0.424563	+	0.308463i
$536$	5.97575	+	4.34164i	0.258113	+	0.187530i
$537$	3.19880	+	9.84488i	0.138038	+	0.424838i
$538$	−8.01342			−0.345483
$539$		0			0
$540$	16.2722			0.700245
$541$	−6.80096	−	20.9312i	−0.292396	−	0.899903i	−0.984084	−	0.177706i	$-0.943132\pi$
$541$	−6.80096	−	20.9312i	−0.292396	−	0.899903i	0.691687	−	0.722197i	$-0.256868\pi$
$542$	24.4919	+	17.7944i	1.05202	+	0.764336i
$543$	36.5842	−	26.5800i	1.56998	−	1.14066i
$544$	2.40168	−	7.39161i	0.102971	−	0.316912i
$545$	4.14010	−	12.7419i	0.177342	−	0.545804i
$546$	−5.30891	+	3.85715i	−0.227200	+	0.165071i
$547$	8.78938	+	6.38586i	0.375807	+	0.273040i	0.759615	−	0.650373i	$-0.225388\pi$
$547$	8.78938	+	6.38586i	0.375807	+	0.273040i	−0.383808	+	0.923413i	$0.625388\pi$
$548$	−2.13156	−	6.56026i	−0.0910557	−	0.280240i
$549$	−5.56922			−0.237689
$550$		0			0
$551$	12.9410			0.551303
$552$	−2.19165	−	6.74520i	−0.0932828	−	0.287095i
$553$	7.67096	+	5.57328i	0.326202	+	0.237000i
$554$	−18.9211	+	13.7470i	−0.803880	+	0.584053i
$555$	−30.7204	+	94.5476i	−1.30401	+	4.01332i
$556$	3.04879	−	9.38322i	0.129298	−	0.397937i
$557$	−27.1932	+	19.7570i	−1.15221	+	0.837130i	−0.988773	−	0.149423i	$-0.952258\pi$
$557$	−27.1932	+	19.7570i	−1.15221	+	0.837130i	−0.163438	+	0.986554i	$0.552258\pi$
$558$	−3.67715	−	2.67161i	−0.155666	−	0.113098i
$559$	−1.96059	−	6.03408i	−0.0829242	−	0.255214i
$560$	−6.59959			−0.278884
$561$		0			0
$562$	−31.3811			−1.32373
$563$	−0.634561	−	1.95298i	−0.0267436	−	0.0823082i	0.936794	−	0.349882i	$-0.113778\pi$
$563$	−0.634561	−	1.95298i	−0.0267436	−	0.0823082i	−0.963537	+	0.267573i	$0.913778\pi$
$564$	−13.2641	−	9.63693i	−0.558519	−	0.405788i
$565$	−29.7886	+	21.6427i	−1.25322	+	0.910515i
$566$	−9.02015	+	27.7612i	−0.379145	+	1.16689i
$567$	0.692124	−	2.13014i	0.0290665	−	0.0894575i
$568$	−7.92890	+	5.76068i	−0.332689	+	0.241713i
$569$	−2.64885	−	1.92450i	−0.111046	−	0.0806793i	0.530877	−	0.847449i	$-0.321863\pi$
$569$	−2.64885	−	1.92450i	−0.111046	−	0.0806793i	−0.641922	+	0.766770i	$0.721863\pi$
$570$	−5.52239	−	16.9962i	−0.231308	−	0.711891i
$571$	−43.8897			−1.83673			−0.918363	−	0.395738i	$-0.870489\pi$
$571$	−43.8897			−1.83673			−0.918363	+	0.395738i	$0.870489\pi$
$572$		0			0
$573$	−1.22666			−0.0512446
$574$	−0.732217	−	2.25353i	−0.0305622	−	0.0940607i
$575$	4.53465	+	3.29461i	0.189108	+	0.137395i
$576$	−34.7279	+	25.2313i	−1.44700	+	1.05131i
$577$	−13.5629	+	41.7422i	−0.564630	+	1.73775i	0.104418	+	0.994533i	$0.466702\pi$
$577$	−13.5629	+	41.7422i	−0.564630	+	1.73775i	−0.669048	+	0.743219i	$0.733298\pi$
$578$	−4.56684	+	14.0553i	−0.189955	+	0.584623i
$579$	−35.0968	+	25.4993i	−1.45857	+	1.05972i
$580$	16.8985	+	12.2775i	0.701673	+	0.509795i
$581$	−4.96572	−	15.2829i	−0.206013	−	0.634042i
$582$	−20.6076			−0.854214
$583$		0			0
$584$	−3.76915			−0.155969
$585$	−11.3786	−	35.0197i	−0.470447	−	1.44789i
$586$	4.02471	+	2.92412i	0.166259	+	0.120794i
$587$	−2.25850	+	1.64090i	−0.0932183	+	0.0677271i	−0.633418	−	0.773810i	$-0.718349\pi$
$587$	−2.25850	+	1.64090i	−0.0932183	+	0.0677271i	0.540200	+	0.841537i	$0.318349\pi$
$588$	0.669603	−	2.06083i	0.0276140	−	0.0849871i
$589$	0.395410	−	1.21695i	0.0162926	−	0.0501434i
$590$	10.2726	−	7.46346i	0.422915	−	0.307266i
$591$	−48.1259	−	34.9655i	−1.97963	−	1.43829i
$592$	−5.93732	−	18.2732i	−0.244022	−	0.751023i
$593$	23.2526			0.954871			0.477435	−	0.878667i	$-0.341566\pi$
$593$	23.2526			0.954871			0.477435	+	0.878667i	$0.341566\pi$
$594$		0			0
$595$	6.68312			0.273981
$596$	0.736985	+	2.26821i	0.0301881	+	0.0929093i
$597$	19.5334	+	14.1919i	0.799450	+	0.580835i
$598$	−1.49887	+	1.08900i	−0.0612935	+	0.0445324i
$599$	3.23215	−	9.94753i	0.132062	−	0.406445i	−0.863059	−	0.505102i	$-0.831455\pi$
$599$	3.23215	−	9.94753i	0.132062	−	0.406445i	0.995121	+	0.0986573i	$0.0314547\pi$
$600$	18.8566	−	58.0347i	0.769818	−	2.36926i
$601$	−18.0489	+	13.1133i	−0.736229	+	0.534902i	−0.891528	−	0.452966i	$-0.850366\pi$
$601$	−18.0489	+	13.1133i	−0.736229	+	0.534902i	0.155299	+	0.987868i	$0.450366\pi$
$602$	−2.77738	−	2.01789i	−0.113198	−	0.0822429i
$603$	3.84141	+	11.8226i	0.156434	+	0.481455i
$604$	−2.17306			−0.0884204
$605$		0			0
$606$	49.2083			1.99895
$607$	5.86774	+	18.0591i	0.238164	+	0.732994i	0.996686	+	0.0813464i	$0.0259220\pi$
$607$	5.86774	+	18.0591i	0.238164	+	0.732994i	−0.758522	+	0.651648i	$0.774078\pi$
$608$	−5.27719	−	3.83410i	−0.214018	−	0.155493i
$609$	18.4418	−	13.3987i	0.747299	−	0.542944i
$610$	−1.28144	+	3.94387i	−0.0518840	+	0.159683i
$611$	−4.81572	+	14.8213i	−0.194823	+	0.599604i
$612$	6.13382	−	4.45648i	0.247945	−	0.180143i
$613$	−16.3111	−	11.8507i	−0.658801	−	0.478647i	0.207457	−	0.978244i	$-0.433481\pi$
$613$	−16.3111	−	11.8507i	−0.658801	−	0.478647i	−0.866258	+	0.499597i	$0.833481\pi$
$614$	4.43714	+	13.6561i	0.179068	+	0.551116i
$615$	21.0068			0.847077
$616$		0			0
$617$	7.03919			0.283387			0.141694	−	0.989911i	$-0.454745\pi$
$617$	7.03919			0.283387			0.141694	+	0.989911i	$0.454745\pi$
$618$	−8.77046	−	26.9927i	−0.352799	−	1.08581i
$619$	25.1467	+	18.2702i	1.01073	+	0.734340i	0.964363	−	0.264584i	$-0.0852346\pi$
$619$	25.1467	+	18.2702i	1.01073	+	0.734340i	0.0463701	+	0.998924i	$0.485235\pi$
$620$	1.67089	−	1.21397i	0.0671045	−	0.0487543i
$621$	1.54933	−	4.76834i	0.0621724	−	0.191347i
$622$	9.23646	−	28.4269i	0.370348	−	1.13982i
$623$	3.59066	−	2.60877i	0.143857	−	0.104518i
$624$	9.09645	+	6.60896i	0.364149	+	0.264570i
$625$	−3.55266	−	10.9340i	−0.142106	−	0.437358i
$626$	3.99947			0.159851
$627$		0			0
$628$	16.2883			0.649973
$629$	6.01246	+	18.5045i	0.239733	+	0.737821i
$630$	−16.1190	−	11.7111i	−0.642195	−	0.466582i
$631$	−17.7757	+	12.9148i	−0.707639	+	0.514130i	−0.882411	−	0.470479i	$-0.844081\pi$
$631$	−17.7757	+	12.9148i	−0.707639	+	0.514130i	0.174772	+	0.984609i	$0.444081\pi$
$632$	9.00596	−	27.7175i	0.358238	−	1.10254i
$633$	8.70991	−	26.8063i	0.346188	−	1.06546i
$634$	15.2537	−	11.0825i	0.605802	−	0.440141i
$635$	−54.3852	−	39.5132i	−2.15821	−	1.56803i
$636$	7.24675	+	22.3032i	0.287352	+	0.884379i
$637$	−2.05965			−0.0816064
$638$		0			0
$639$	−16.4941			−0.652496
$640$	1.29215	+	3.97683i	0.0510768	+	0.157198i
$641$	10.7526	+	7.81222i	0.424702	+	0.308564i	0.779527	−	0.626369i	$-0.215460\pi$
$641$	10.7526	+	7.81222i	0.424702	+	0.308564i	−0.354825	+	0.934933i	$0.615460\pi$
$642$	9.05293	−	6.57734i	0.357291	−	0.259587i
$643$	4.53958	−	13.9714i	0.179024	−	0.550978i	−0.820771	−	0.571258i	$-0.806456\pi$
$643$	4.53958	−	13.9714i	0.179024	−	0.550978i	0.999794	+	0.0202797i	$0.00645568\pi$
$644$	0.189050	−	0.581837i	0.00744963	−	0.0229276i
$645$	24.6229	−	17.8896i	0.969524	−	0.704401i
$646$	−2.82962	−	2.05584i	−0.111330	−	0.0808859i
$647$	−1.89898	−	5.84446i	−0.0746566	−	0.229770i	0.906764	−	0.421639i	$-0.138545\pi$
$647$	−1.89898	−	5.84446i	−0.0746566	−	0.229770i	−0.981420	+	0.191869i	$0.938545\pi$
$648$	−6.88426			−0.270439
$649$		0			0
$650$	−15.9404			−0.625236
$651$	−0.696508	−	2.14363i	−0.0272983	−	0.0840156i
$652$	−5.04206	−	3.66327i	−0.197462	−	0.143465i
$653$	32.9020	−	23.9047i	1.28755	−	0.935463i	0.287802	−	0.957690i	$-0.407076\pi$
$653$	32.9020	−	23.9047i	1.28755	−	0.935463i	0.999753	+	0.0222266i	$0.00707554\pi$
$654$	−3.81664	+	11.7464i	−0.149242	+	0.459321i
$655$	5.46044	−	16.8055i	0.213357	−	0.656646i
$656$	−3.28460	+	2.38640i	−0.128242	+	0.0931732i
$657$	−5.13186	−	3.72852i	−0.200213	−	0.145463i
$658$	2.60576	+	8.01970i	0.101583	+	0.312640i
$659$	18.0090			0.701531			0.350765	−	0.936463i	$-0.385921\pi$
$659$	18.0090			0.701531			0.350765	+	0.936463i	$0.385921\pi$
$660$		0			0
$661$	−17.1420			−0.666745			−0.333373	−	0.942795i	$-0.608187\pi$
$661$	−17.1420			−0.666745			−0.333373	+	0.942795i	$0.608187\pi$
$662$	−0.426444	−	1.31246i	−0.0165742	−	0.0510102i
$663$	−9.21157	−	6.69260i	−0.357748	−	0.259919i
$664$	−39.9588	+	29.0318i	−1.55070	+	1.12665i
$665$	1.73330	−	5.33455i	0.0672145	−	0.206865i
$666$	17.9247	−	55.1667i	0.694570	−	2.13767i
$667$	5.20670	−	3.78289i	0.201604	−	0.146474i
$668$	−13.3118	−	9.67161i	−0.515050	−	0.374206i
$669$	−15.3679	−	47.2976i	−0.594159	−	1.82863i
$670$	9.25613			0.357596
$671$		0			0
$672$	−11.4901			−0.443240
$673$	−7.16690	−	22.0574i	−0.276264	−	0.850252i	−0.988882	−	0.148700i	$-0.952491\pi$
$673$	−7.16690	−	22.0574i	−0.276264	−	0.850252i	0.712619	−	0.701552i	$-0.247509\pi$
$674$	18.4658	+	13.4162i	0.711274	+	0.516771i
$675$	34.8989	−	25.3555i	1.34326	−	0.975934i
$676$	2.05129	−	6.31323i	0.0788959	−	0.242817i
$677$	−8.51976	+	26.2211i	−0.327441	+	1.00776i	0.642886	+	0.765962i	$0.277737\pi$
$677$	−8.51976	+	26.2211i	−0.327441	+	1.00776i	−0.970327	+	0.241798i	$0.922263\pi$
$678$	27.4613	−	19.9518i	1.05464	−	0.766243i
$679$	−5.23278	−	3.80184i	−0.200816	−	0.145901i
$680$	−6.34771	−	19.5362i	−0.243424	−	0.749181i
$681$	36.1111			1.38378
$682$		0			0
$683$	21.9351			0.839322			0.419661	−	0.907681i	$-0.362149\pi$
$683$	21.9351			0.839322			0.419661	+	0.907681i	$0.362149\pi$
$684$	−1.96638	−	6.05190i	−0.0751865	−	0.231400i
$685$	−25.4453	−	18.4871i	−0.972214	−	0.706355i
$686$	−0.901622	+	0.655067i	−0.0344241	+	0.0250106i
$687$	−4.04026	+	12.4346i	−0.154146	+	0.474411i
$688$	−1.81772	+	5.59437i	−0.0692999	+	0.213283i
$689$	18.0334	−	13.1020i	0.687017	−	0.499147i
$690$	−7.19020	−	5.22399i	−0.273726	−	0.198874i
$691$	−7.93142	−	24.4104i	−0.301726	−	0.928616i	−0.980879	−	0.194619i	$-0.937653\pi$
$691$	−7.93142	−	24.4104i	−0.301726	−	0.928616i	0.679153	−	0.733996i	$-0.262347\pi$
$692$	6.09830			0.231823
$693$		0			0
$694$	30.3913			1.15364
$695$	−13.9015	−	42.7845i	−0.527315	−	1.62291i
$696$	−56.6837	−	41.1832i	−2.14859	−	1.56104i
$697$	3.32616	−	2.41660i	0.125987	−	0.0915353i
$698$	2.74972	−	8.46277i	0.104078	−	0.320321i
$699$	−21.0757	+	64.8644i	−0.797157	+	2.45340i
$700$	4.25839	−	3.09390i	0.160952	−	0.116939i
$701$	14.8968	+	10.8232i	0.562644	+	0.408785i	0.832426	−	0.554137i	$-0.186951\pi$
$701$	14.8968	+	10.8232i	0.562644	+	0.408785i	−0.269781	+	0.962922i	$0.586951\pi$
$702$	4.40614	+	13.5607i	0.166299	+	0.511815i
$703$	16.3298			0.615892
$704$		0			0
$705$	−74.7575			−2.81553
$706$	2.04385	+	6.29033i	0.0769214	+	0.236740i
$707$	12.4952	+	9.07828i	0.469930	+	0.341424i
$708$	5.77915	−	4.19880i	0.217194	−	0.157801i
$709$	7.31198	−	22.5039i	0.274607	−	0.845153i	−0.714716	−	0.699415i	$-0.753444\pi$
$709$	7.31198	−	22.5039i	0.274607	−	0.845153i	0.989323	−	0.145739i	$-0.0465559\pi$
$710$	−3.79518	+	11.6804i	−0.142431	+	0.438356i
$711$	39.6806	−	28.8297i	1.48814	−	1.08120i
$712$	−11.0365	−	8.01847i	−0.413609	−	0.300505i
$713$	−0.196647	−	0.605216i	−0.00736447	−	0.0226655i
$714$	−6.16097			−0.230569
$715$		0			0
$716$	2.74452			0.102568
$717$	−7.80782	−	24.0300i	−0.291589	−	0.897417i
$718$	−25.6244	−	18.6172i	−0.956293	−	0.694787i
$719$	−8.99808	+	6.53749i	−0.335572	+	0.243807i	−0.742791	−	0.669523i	$-0.766498\pi$
$719$	−8.99808	+	6.53749i	−0.335572	+	0.243807i	0.407219	+	0.913330i	$0.366498\pi$
$720$	−10.5494	+	32.4678i	−0.393154	+	1.21000i
$721$	2.75276	−	8.47213i	0.102518	−	0.315519i
$722$	14.7560	−	10.7208i	0.549160	−	0.398988i
$723$	43.8200	+	31.8371i	1.62968	+	1.18403i
$724$	−3.70493	−	11.4026i	−0.137693	−	0.423775i
$725$	55.3730			2.05650
$726$		0			0
$727$	42.4803			1.57551			0.787753	−	0.615991i	$-0.211244\pi$
$727$	42.4803			1.57551			0.787753	+	0.615991i	$0.211244\pi$
$728$	1.95628	+	6.02083i	0.0725047	+	0.223147i
$729$	33.7270	+	24.5041i	1.24915	+	0.907561i
$730$	−3.82117	+	2.77624i	−0.141428	+	0.102753i
$731$	1.84072	−	5.66517i	0.0680817	−	0.209534i
$732$	−0.720913	+	2.21874i	−0.0266457	+	0.0820071i
$733$	−17.9508	+	13.0420i	−0.663029	+	0.481719i	−0.867684	−	0.497116i	$-0.834393\pi$
$733$	−17.9508	+	13.0420i	−0.663029	+	0.481719i	0.204656	+	0.978834i	$0.434393\pi$
$734$	27.4106	+	19.9150i	1.01174	+	0.735075i
$735$	−3.05318	−	9.39672i	−0.112618	−	0.346603i
$736$	−3.24402			−0.119576
$737$		0			0
$738$	−12.2571			−0.451189
$739$	9.09997	+	28.0068i	0.334748	+	1.03025i	0.966846	+	0.255359i	$0.0821938\pi$
$739$	9.09997	+	28.0068i	0.334748	+	1.03025i	−0.632098	+	0.774888i	$0.717806\pi$
$740$	21.3238	+	15.4926i	0.783878	+	0.569521i
$741$	−7.73118	+	5.61703i	−0.284012	+	0.206347i
$742$	3.72713	−	11.4709i	0.136827	−	0.421111i
$743$	5.22421	−	16.0785i	0.191658	−	0.589862i	−0.808342	−	0.588714i	$-0.799635\pi$
$743$	5.22421	−	16.0785i	0.191658	−	0.589862i	0.999999	−	0.00114815i	$-0.000365467\pi$
$744$	−5.60476	+	4.07210i	−0.205481	+	0.149290i
$745$	8.79769	+	6.39190i	0.322322	+	0.234181i
$746$	4.96697	+	15.2868i	0.181854	+	0.559688i
$747$	−83.1244			−3.04136
$748$		0			0
$749$	3.51219			0.128333
$750$	−6.61640	−	20.3632i	−0.241597	−	0.743558i
$751$	1.25516	+	0.911929i	0.0458015	+	0.0332767i	0.610450	−	0.792054i	$-0.290988\pi$
$751$	1.25516	+	0.911929i	0.0458015	+	0.0332767i	−0.564649	+	0.825331i	$0.690988\pi$
$752$	11.6890	−	8.49253i	0.426253	−	0.309691i
$753$	2.53270	−	7.79484i	0.0922966	−	0.284060i
$754$	−5.65591	+	17.4071i	−0.205976	+	0.633929i
$755$	−8.01610	+	5.82404i	−0.291736	+	0.211958i
$756$	−3.80909	−	2.76746i	−0.138535	−	0.100652i
$757$	3.87713	+	11.9326i	0.140917	+	0.433697i	0.996463	−	0.0840286i	$-0.0267787\pi$
$757$	3.87713	+	11.9326i	0.140917	+	0.433697i	−0.855547	+	0.517726i	$0.826779\pi$
$758$	−24.9721			−0.907027
$759$		0			0
$760$	−17.2404			−0.625375
$761$	−2.79177	−	8.59218i	−0.101202	−	0.311466i	0.887619	−	0.460579i	$-0.152358\pi$
$761$	−2.79177	−	8.59218i	−0.101202	−	0.311466i	−0.988820	+	0.149113i	$0.952358\pi$
$762$	50.1362	+	36.4260i	1.81624	+	1.31958i
$763$	−3.13619	+	2.27858i	−0.113538	+	0.0824901i
$764$	−0.100501	+	0.309310i	−0.00363600	+	0.0111904i
$765$	10.6829	−	32.8787i	0.386242	−	1.18873i
$766$	−30.3653	+	22.0617i	−1.09714	+	0.797122i
$767$	−5.49317	−	3.99102i	−0.198347	−	0.144107i
$768$	13.4707	+	41.4587i	0.486083	+	1.49601i
$769$	−16.1383			−0.581963			−0.290981	−	0.956729i	$-0.593982\pi$
$769$	−16.1383			−0.581963			−0.290981	+	0.956729i	$0.593982\pi$
$770$		0			0
$771$	−64.0829			−2.30789
$772$	3.55431	+	10.9390i	0.127922	+	0.393704i
$773$	14.8968	+	10.8231i	0.535800	+	0.389282i	0.822523	−	0.568732i	$-0.192566\pi$
$773$	14.8968	+	10.8231i	0.535800	+	0.389282i	−0.286723	+	0.958014i	$0.592566\pi$
$774$	−14.3670	+	10.4382i	−0.516410	+	0.375193i
$775$	1.69192	−	5.20719i	0.0607755	−	0.187048i
$776$	−6.14345	+	18.9076i	−0.220537	+	0.678744i
$777$	23.2712	−	16.9075i	0.834849	−	0.606553i
$778$	−2.18899	−	1.59039i	−0.0784789	−	0.0570183i
$779$	−1.06630	−	3.28174i	−0.0382043	−	0.117581i
$780$	−15.4246			−0.552288
$781$		0			0
$782$	−1.73944			−0.0622022
$783$	−15.3058	−	47.1064i	−0.546984	−	1.68344i
$784$	1.54487	+	1.12241i	0.0551739	+	0.0400861i
$785$	60.0852	−	43.6544i	2.14453	−	1.55809i
$786$	−5.03382	+	15.4925i	−0.179550	+	0.552599i
$787$	14.5198	−	44.6873i	0.517575	−	1.59293i	−0.260973	−	0.965346i	$-0.584043\pi$
$787$	14.5198	−	44.6873i	0.517575	−	1.59293i	0.778548	−	0.627585i	$-0.215957\pi$
$788$	−12.7597	+	9.27048i	−0.454546	+	0.330247i
$789$	2.29134	+	1.66475i	0.0815737	+	0.0592668i
$790$	−11.2856	−	34.7335i	−0.401524	−	1.23576i
$791$	10.6539			0.378810
$792$		0			0
$793$	2.21748			0.0787450
$794$	−2.03085	−	6.25031i	−0.0720722	−	0.221815i
$795$	86.5074	+	62.8513i	3.06810	+	2.22911i
$796$	5.17894	−	3.76272i	0.183563	−	0.133366i
$797$	−0.965537	+	2.97162i	−0.0342011	+	0.105260i	−0.966700	−	0.255913i	$-0.917624\pi$
$797$	−0.965537	+	2.97162i	−0.0342011	+	0.105260i	0.932499	+	0.361173i	$0.117624\pi$
$798$	−1.59788	+	4.91776i	−0.0565643	+	0.174087i
$799$	−11.8369	+	8.60001i	−0.418759	+	0.304246i
$800$	−22.5805	−	16.4057i	−0.798342	−	0.580029i
$801$	−7.09461	−	21.8350i	−0.250676	−	0.771500i
$802$	12.5261			0.442314
$803$		0			0
$804$	5.20732			0.183648
$805$	−0.862010	−	2.65299i	−0.0303819	−	0.0935058i
$806$	1.46412	+	1.06374i	0.0515714	+	0.0374688i
$807$	−16.6301	+	12.0825i	−0.585408	+	0.425323i
$808$	14.6698	−	45.1489i	0.516081	−	1.58833i
$809$	−10.1128	+	31.1240i	−0.355547	+	1.09426i	0.600145	+	0.799891i	$0.295109\pi$
$809$	−10.1128	+	31.1240i	−0.355547	+	1.09426i	−0.955692	+	0.294369i	$0.904891\pi$
$810$	−6.97927	+	5.07074i	−0.245227	+	0.178167i
$811$	−26.4236	−	19.1978i	−0.927856	−	0.674127i	0.0176106	−	0.999845i	$-0.494394\pi$
$811$	−26.4236	−	19.1978i	−0.927856	−	0.674127i	−0.945467	+	0.325718i	$0.894394\pi$
$812$	−1.86763	−	5.74796i	−0.0655408	−	0.201714i
$813$	77.6578			2.72358
$814$		0			0
$815$	−28.4174			−0.995419
$816$	3.26211	+	10.0397i	0.114197	+	0.351461i
$817$	−4.04461	−	2.93858i	−0.141503	−	0.102808i
$818$	−26.4485	+	19.2160i	−0.924751	+	0.671871i
$819$	−3.29235	+	10.1328i	−0.115044	+	0.354069i
$820$	1.72110	−	5.29699i	0.0601033	−	0.184979i
$821$	6.01215	−	4.36808i	0.209825	−	0.152447i	−0.477909	−	0.878409i	$-0.658605\pi$
$821$	6.01215	−	4.36808i	0.209825	−	0.152447i	0.687735	+	0.725962i	$0.258605\pi$
$822$	23.4573	+	17.0427i	0.818166	+	0.594432i
$823$	2.02674	+	6.23766i	0.0706477	+	0.217431i	0.980146	−	0.198276i	$-0.0635342\pi$
$823$	2.02674	+	6.23766i	0.0706477	+	0.217431i	−0.909499	+	0.415707i	$0.863534\pi$
$824$	−27.3805			−0.953846
$825$		0			0
$826$	−3.67399			−0.127835
$827$	7.37124	+	22.6863i	0.256323	+	0.788881i	0.993566	+	0.113254i	$0.0361273\pi$
$827$	7.37124	+	22.6863i	0.256323	+	0.788881i	−0.737243	+	0.675628i	$0.763873\pi$
$828$	−2.56025	−	1.86013i	−0.0889748	−	0.0646439i
$829$	21.1502	−	15.3666i	0.734578	−	0.533702i	−0.156430	−	0.987689i	$-0.549999\pi$
$829$	21.1502	−	15.3666i	0.734578	−	0.533702i	0.891008	+	0.453987i	$0.149999\pi$
$830$	−19.1264	+	58.8649i	−0.663886	+	2.04323i
$831$	−18.5392	+	57.0577i	−0.643117	+	1.97931i
$832$	13.8275	−	10.0463i	0.479383	−	0.348292i
$833$	−1.56442	−	1.13662i	−0.0542039	−	0.0393815i
$834$	12.8154	+	39.4418i	0.443762	+	1.36576i
$835$	−75.0265			−2.59640
$836$		0			0
$837$	−4.89747			−0.169281
$838$	−6.98622	−	21.5014i	−0.241335	−	0.742752i
$839$	−27.7404	−	20.1545i	−0.957703	−	0.695812i	−0.00508714	−	0.999987i	$-0.501619\pi$
$839$	−27.7404	−	20.1545i	−0.957703	−	0.695812i	−0.952616	+	0.304175i	$0.901619\pi$
$840$	−24.5688	+	17.8503i	−0.847703	+	0.615892i
$841$	10.6857	−	32.8871i	0.368471	−	1.13404i
$842$	−1.05384	+	3.24339i	−0.0363177	+	0.111774i
$843$	−65.1247	+	47.3159i	−2.24301	+	1.62965i
$844$	−6.04576	−	4.39250i	−0.208104	−	0.151196i
$845$	−9.35325	−	28.7863i	−0.321761	−	0.990280i
$846$	43.6195			1.49967
$847$		0			0
$848$	−20.6661			−0.709678
$849$	23.1384	+	71.2126i	0.794108	+	2.44401i
$850$	−12.1076	−	8.79672i	−0.415289	−	0.301725i
$851$	6.57020	−	4.77353i	0.225223	−	0.163634i
$852$	−2.13509	+	6.57114i	−0.0731471	+	0.225124i
$853$	6.60808	−	20.3376i	0.226256	−	0.696345i	−0.771905	−	0.635737i	$-0.780696\pi$
$853$	6.60808	−	20.3376i	0.226256	−	0.696345i	0.998162	−	0.0606079i	$-0.0193039\pi$
$854$	0.970711	−	0.705263i	0.0332171	−	0.0241336i
$855$	−23.4735	−	17.0545i	−0.802777	−	0.583252i
$856$	−3.33592	−	10.2669i	−0.114020	−	0.350916i
$857$	42.8697			1.46440			0.732200	−	0.681090i	$-0.238494\pi$
$857$	42.8697			1.46440			0.732200	+	0.681090i	$0.238494\pi$
$858$		0			0
$859$	−30.3915			−1.03695			−0.518473	−	0.855094i	$-0.673499\pi$
$859$	−30.3915			−1.03695			−0.518473	+	0.855094i	$0.673499\pi$
$860$	−2.49359	−	7.67449i	−0.0850308	−	0.261698i
$861$	−4.91739	−	3.57269i	−0.167584	−	0.121757i
$862$	−6.80001	+	4.94049i	−0.231609	+	0.168274i
$863$	3.65209	−	11.2400i	0.124319	−	0.382614i	−0.869458	−	0.494008i	$-0.835532\pi$
$863$	3.65209	−	11.2400i	0.124319	−	0.382614i	0.993776	+	0.111394i	$0.0355315\pi$
$864$	−7.71496	+	23.7442i	−0.262468	+	0.807794i
$865$	22.4958	−	16.3442i	0.764880	−	0.555718i
$866$	28.9976	+	21.0680i	0.985379	+	0.715920i
$867$	11.7148	+	36.0545i	0.397856	+	1.22447i
$868$	−0.597594			−0.0202837
$869$		0			0
$870$	−87.8003			−2.97671
$871$	−1.52952	−	4.70738i	−0.0518258	−	0.159503i
$872$	9.63959	+	7.00357i	0.326438	+	0.237171i
$873$	−27.0683	+	19.6663i	−0.916124	+	0.665603i
$874$	−0.451132	+	1.38844i	−0.0152598	+	0.0469647i
$875$	2.07667	−	6.39134i	0.0702044	−	0.216067i
$876$	−2.14972	+	1.56186i	−0.0726322	+	0.0527703i
$877$	7.44690	+	5.41049i	0.251464	+	0.182699i	0.706375	−	0.707837i	$-0.250329\pi$
$877$	7.44690	+	5.41049i	0.251464	+	0.182699i	−0.454911	+	0.890537i	$0.650329\pi$
$878$	−1.60735	−	4.94692i	−0.0542454	−	0.166950i
$879$	12.7613			0.430429
$880$		0			0
$881$	−41.9030			−1.41175			−0.705874	−	0.708338i	$-0.749445\pi$
$881$	−41.9030			−1.41175			−0.705874	+	0.708338i	$0.749445\pi$
$882$	1.78147	+	5.48280i	0.0599852	+	0.184616i
$883$	12.9830	+	9.43269i	0.436912	+	0.317435i	0.784407	−	0.620247i	$-0.212968\pi$
$883$	12.9830	+	9.43269i	0.436912	+	0.317435i	−0.347495	+	0.937682i	$0.612968\pi$
$884$	−2.44228	+	1.77442i	−0.0821429	+	0.0596803i
$885$	10.0652	−	30.9776i	0.338339	−	1.04130i
$886$	5.95006	−	18.3124i	0.199896	−	0.615217i
$887$	27.3839	−	19.8956i	0.919461	−	0.668027i	−0.0239289	−	0.999714i	$-0.507618\pi$
$887$	27.3839	−	19.8956i	0.919461	−	0.668027i	0.943390	+	0.331686i	$0.107618\pi$
$888$	−71.5277	−	51.9679i	−2.40031	−	1.74393i
$889$	6.01066	+	18.4989i	0.201591	+	0.620433i
$890$	−17.0949			−0.573024
$891$		0			0
$892$	−13.1855			−0.441482
$893$	3.79468	+	11.6788i	0.126984	+	0.390817i
$894$	−8.11033	−	5.89250i	−0.271250	−	0.197075i
$895$	10.1242	−	7.35563i	0.338413	−	0.245872i
$896$	0.373878	−	1.15068i	0.0124904	−	0.0384414i
$897$	−1.46862	+	4.51995i	−0.0490358	+	0.150917i
$898$	15.0932	−	10.9659i	0.503668	−	0.365936i
$899$	−5.08597	−	3.69517i	−0.169627	−	0.123241i
$900$	−8.41394	−	25.8955i	−0.280465	−	0.863182i
$901$	20.9277			0.697202
$902$		0			0
$903$	−8.80638			−0.293058
$904$	−10.1192	−	31.1438i	−0.336560	−	1.03583i
$905$	−44.2273	−	32.1330i	−1.47016	−	1.06814i
$906$	7.38981	−	5.36901i	0.245510	−	0.178373i
$907$	−13.6281	+	41.9429i	−0.452512	+	1.39269i	0.421518	+	0.906820i	$0.361497\pi$
$907$	−13.6281	+	41.9429i	−0.452512	+	1.39269i	−0.874031	+	0.485870i	$0.838503\pi$
$908$	2.95859	−	9.10562i	0.0981844	−	0.302181i
$909$	64.6356	−	46.9605i	2.14383	−	1.55758i
$910$	6.41804	+	4.66298i	0.212756	+	0.154576i
$911$	15.3197	+	47.1492i	0.507565	+	1.56212i	0.796416	+	0.604750i	$0.206727\pi$
$911$	15.3197	+	47.1492i	0.507565	+	1.56212i	−0.288851	+	0.957374i	$0.593273\pi$
$912$	8.85988			0.293380
$913$		0			0
$914$	−24.1810			−0.799837
$915$	3.28714	+	10.1168i	0.108669	+	0.334450i
$916$	2.80445	+	2.03755i	0.0926615	+	0.0673225i
$917$	−4.13637	+	3.00525i	−0.136595	+	0.0992421i
$918$	−4.13675	+	12.7316i	−0.136533	+	0.420206i
$919$	−12.6056	+	38.7961i	−0.415821	+	1.27977i	0.495693	+	0.868498i	$0.334914\pi$
$919$	−12.6056	+	38.7961i	−0.415821	+	1.27977i	−0.911514	+	0.411268i	$0.865086\pi$
$920$	−6.93655	+	5.03970i	−0.228691	+	0.166154i
$921$	29.7988	+	21.6501i	0.981902	+	0.713394i
$922$	−2.09312	−	6.44197i	−0.0689333	−	0.212155i
$923$	6.56740			0.216169
$924$		0			0
$925$	69.8737			2.29743
$926$	−1.77264	−	5.45561i	−0.0582525	−	0.179283i
$927$	−37.2798	−	27.0853i	−1.22443	−	0.889599i
$928$	−25.9271	+	18.8371i	−0.851097	+	0.618359i
$929$	12.7911	−	39.3670i	0.419663	−	1.29159i	−0.488350	−	0.872648i	$-0.662401\pi$
$929$	12.7911	−	39.3670i	0.419663	−	1.29159i	0.908013	−	0.418942i	$-0.137599\pi$
$930$	−2.68273	+	8.25659i	−0.0879702	+	0.270744i
$931$	−1.31300	+	0.953952i	−0.0430319	+	0.0312645i
$932$	14.6292	+	10.6287i	0.479195	+	0.348156i
$933$	−23.6933	−	72.9204i	−0.775683	−	2.38731i
$934$	−4.36790			−0.142922
$935$		0			0
$936$	32.7476			1.07039
$937$	0.493327	+	1.51831i	0.0161163	+	0.0496009i	0.958791	−	0.284111i	$-0.0916986\pi$
$937$	0.493327	+	1.51831i	0.0161163	+	0.0496009i	−0.942675	+	0.333712i	$0.891699\pi$
$938$	−2.16672	−	1.57422i	−0.0707461	−	0.0514000i
$939$	8.30003	−	6.03032i	0.270861	−	0.196792i
$940$	−6.12490	+	18.8505i	−0.199772	+	0.614836i
$941$	2.19645	−	6.75998i	0.0716023	−	0.220369i	−0.908851	−	0.417121i	$-0.863039\pi$
$941$	2.19645	−	6.75998i	0.0716023	−	0.220369i	0.980453	+	0.196752i	$0.0630392\pi$
$942$	−55.3908	+	40.2438i	−1.80473	+	1.31121i
$943$	−1.38834	−	1.00869i	−0.0452105	−	0.0328473i
$944$	1.94530	+	5.98703i	0.0633142	+	0.194861i
$945$	−21.4683			−0.698364
$946$		0			0
$947$	−2.45986			−0.0799347			−0.0399674	−	0.999201i	$-0.512725\pi$
$947$	−2.45986			−0.0799347			−0.0399674	+	0.999201i	$0.512725\pi$
$948$	−6.34906	−	19.5404i	−0.206208	−	0.634643i
$949$	2.04334	+	1.48457i	0.0663295	+	0.0481912i
$950$	−10.1618	+	7.38300i	−0.329693	+	0.239536i
$951$	14.9458	−	45.9985i	0.484651	−	1.49160i
$952$	−1.83668	+	5.65272i	−0.0595272	+	0.183206i
$953$	23.1379	−	16.8107i	0.749511	−	0.544551i	−0.146164	−	0.989260i	$-0.546693\pi$
$953$	23.1379	−	16.8107i	0.749511	−	0.544551i	0.895675	+	0.444709i	$0.146693\pi$
$954$	−50.4753	−	36.6725i	−1.63420	−	1.18732i
$955$	0.458253	+	1.41036i	0.0148287	+	0.0456381i
$956$	−6.69900			−0.216661
$957$		0			0
$958$	−16.8428			−0.544168
$959$	2.81221	+	8.65511i	0.0908111	+	0.279488i
$960$	66.3315	+	48.1927i	2.14084	+	1.55541i
$961$	24.5766	−	17.8560i	0.792795	−	0.575999i
$962$	−7.13703	+	21.9655i	−0.230107	+	0.708197i
$963$	5.61422	−	17.2788i	0.180916	−	0.556801i
$964$	11.6181	−	8.44103i	0.374193	−	0.271867i
$965$	42.4292	+	30.8266i	1.36584	+	0.992344i
$966$	0.794662	+	2.44572i	0.0255678	+	0.0786897i
$967$	−0.213338			−0.00686047			−0.00343024	−	0.999994i	$-0.501092\pi$
$967$	−0.213338			−0.00686047			−0.00343024	+	0.999994i	$0.501092\pi$
$968$		0			0
$969$	−8.97201			−0.288223
$970$	7.69852	+	23.6936i	0.247185	+	0.760756i
$971$	0.670027	+	0.486803i	0.0215022	+	0.0156222i	0.598484	−	0.801134i	$-0.295770\pi$
$971$	0.670027	+	0.486803i	0.0215022	+	0.0156222i	−0.576982	+	0.816757i	$0.695770\pi$
$972$	7.50086	−	5.44969i	0.240590	−	0.174799i
$973$	−4.02234	+	12.3795i	−0.128950	+	0.396869i
$974$	8.63618	−	26.5794i	0.276721	−	0.851659i
$975$	−33.0809	+	24.0347i	−1.05944	+	0.769726i
$976$	−1.66325	−	1.20842i	−0.0532392	−	0.0386806i
$977$	3.01512	+	9.27959i	0.0964623	+	0.296880i	0.987632	−	0.156790i	$-0.0501145\pi$
$977$	3.01512	+	9.27959i	0.0964623	+	0.296880i	−0.891170	+	0.453670i	$0.850114\pi$
$978$	26.1972			0.837694
$979$		0			0
$980$	−2.61958			−0.0836795
$981$	6.19665	+	19.0713i	0.197844	+	0.608900i
$982$	−33.5591	−	24.3821i	−1.07091	−	0.778064i
$983$	−36.5027	+	26.5207i	−1.16425	+	0.845880i	−0.990310	−	0.138876i	$-0.955651\pi$
$983$	−36.5027	+	26.5207i	−1.16425	+	0.845880i	−0.173944	+	0.984756i	$0.555651\pi$
$984$	−5.77318	+	17.7680i	−0.184042	+	0.566424i
$985$	−22.2229	+	68.3950i	−0.708080	+	2.17925i
$986$	−13.9021	+	10.1004i	−0.442732	+	0.321663i
$987$	17.4996	+	12.7142i	0.557019	+	0.404698i
$988$	0.782948	+	2.40967i	0.0249089	+	0.0766617i
$989$	−2.48632			−0.0790604
$990$		0			0
$991$	53.5405			1.70077			0.850384	−	0.526162i	$-0.176369\pi$
$991$	53.5405			1.70077			0.850384	+	0.526162i	$0.176369\pi$
$992$	0.979212	+	3.01370i	0.0310900	+	0.0956852i
$993$	−2.86389	−	2.08074i	−0.0908829	−	0.0660303i
$994$	2.87491	−	2.08874i	0.0911866	−	0.0662509i
$995$	9.01987	−	27.7603i	0.285949	−	0.880061i
$996$	−10.7601	+	33.1163i	−0.340948	+	1.04933i
$997$	25.2095	−	18.3158i	0.798394	−	0.580067i	−0.112049	−	0.993703i	$-0.535741\pi$
$997$	25.2095	−	18.3158i	0.798394	−	0.580067i	0.910443	+	0.413636i	$0.135741\pi$
$998$	28.6836	+	20.8399i	0.907965	+	0.659675i
$999$	−19.3140	−	59.4422i	−0.611066	−	1.88067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.w.148.3		16
11.2	odd	10		847.2.f.v.372.2		16
11.3	even	5		847.2.a.p.1.6		8
11.4	even	5		77.2.f.b.36.2	yes	16
11.5	even	5		77.2.f.b.15.2	✓	16
11.6	odd	10		847.2.f.x.323.3		16
11.7	odd	10		847.2.f.x.729.3		16
11.8	odd	10		847.2.a.o.1.3		8
11.9	even	5	inner	847.2.f.w.372.3		16
11.10	odd	2		847.2.f.v.148.2		16
33.5	odd	10		693.2.m.i.631.3		16
33.8	even	10		7623.2.a.cw.1.6		8
33.14	odd	10		7623.2.a.ct.1.3		8
33.26	odd	10		693.2.m.i.190.3		16
77.4	even	15		539.2.q.g.520.2		32
77.5	odd	30		539.2.q.f.312.2		32
77.16	even	15		539.2.q.g.312.2		32
77.26	odd	30		539.2.q.f.410.3		32
77.27	odd	10		539.2.f.e.246.2		16
77.37	even	15		539.2.q.g.410.3		32
77.38	odd	30		539.2.q.f.422.3		32
77.41	even	10		5929.2.a.bs.1.3		8
77.48	odd	10		539.2.f.e.344.2		16
77.59	odd	30		539.2.q.f.520.2		32
77.60	even	15		539.2.q.g.422.3		32
77.69	odd	10		5929.2.a.bt.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	11.5	even	5
77.2.f.b.36.2	yes	16	11.4	even	5
539.2.f.e.246.2		16	77.27	odd	10
539.2.f.e.344.2		16	77.48	odd	10
539.2.q.f.312.2		32	77.5	odd	30
539.2.q.f.410.3		32	77.26	odd	30
539.2.q.f.422.3		32	77.38	odd	30
539.2.q.f.520.2		32	77.59	odd	30
539.2.q.g.312.2		32	77.16	even	15
539.2.q.g.410.3		32	77.37	even	15
539.2.q.g.422.3		32	77.60	even	15
539.2.q.g.520.2		32	77.4	even	15
693.2.m.i.190.3		16	33.26	odd	10
693.2.m.i.631.3		16	33.5	odd	10
847.2.a.o.1.3		8	11.8	odd	10
847.2.a.p.1.6		8	11.3	even	5
847.2.f.v.148.2		16	11.10	odd	2
847.2.f.v.372.2		16	11.2	odd	10
847.2.f.w.148.3		16	1.1	even	1	trivial
847.2.f.w.372.3		16	11.9	even	5	inner
847.2.f.x.323.3		16	11.6	odd	10
847.2.f.x.729.3		16	11.7	odd	10
5929.2.a.bs.1.3		8	77.41	even	10
5929.2.a.bt.1.6		8	77.69	odd	10
7623.2.a.ct.1.3		8	33.14	odd	10
7623.2.a.cw.1.6		8	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)

\(f(q)\)	\(=\)	\(q+(0.344389 + 1.05992i) q^{2} +(2.31283 + 1.68037i) q^{3} +(0.613206 - 0.445520i) q^{4} +(1.06799 - 3.28693i) q^{5} +(-0.984546 + 3.03012i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(2.48664 + 1.80665i) q^{8} +(1.59850 + 4.91966i) q^{9} +O(q^{10})\)	\(q+(0.344389 + 1.05992i) q^{2} +(2.31283 + 1.68037i) q^{3} +(0.613206 - 0.445520i) q^{4} +(1.06799 - 3.28693i) q^{5} +(-0.984546 + 3.03012i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(2.48664 + 1.80665i) q^{8} +(1.59850 + 4.91966i) q^{9} +3.85168 q^{10} +2.16688 q^{12} +(-0.636468 - 1.95885i) q^{13} +(-0.901622 - 0.655067i) q^{14} +(7.99333 - 5.80749i) q^{15} +(-0.590087 + 1.81610i) q^{16} +(0.597555 - 1.83909i) q^{17} +(-4.66395 + 3.38856i) q^{18} +(-1.31300 - 0.953952i) q^{19} +(-0.809496 - 2.49137i) q^{20} -2.85882 q^{21} -0.807136 q^{23} +(2.71534 + 8.35696i) q^{24} +(-5.61820 - 4.08186i) q^{25} +(1.85703 - 1.34921i) q^{26} +(-1.91954 + 5.90773i) q^{27} +(-0.234224 + 0.720867i) q^{28} +(-6.45084 + 4.68681i) q^{29} +(8.90830 + 6.47226i) q^{30} +(0.243635 + 0.749832i) q^{31} +4.01918 q^{32} +2.15508 q^{34} +(1.06799 + 3.28693i) q^{35} +(3.17202 + 2.30461i) q^{36} +(-8.14014 + 5.91416i) q^{37} +(0.558930 - 1.72021i) q^{38} +(1.81955 - 5.59998i) q^{39} +(8.59403 - 6.24393i) q^{40} +(1.72008 + 1.24971i) q^{41} +(-0.984546 - 3.03012i) q^{42} +3.08043 q^{43} +17.8777 q^{45} +(-0.277969 - 0.855500i) q^{46} +(-6.12128 - 4.44737i) q^{47} +(-4.41650 + 3.20877i) q^{48} +(0.309017 - 0.951057i) q^{49} +(2.39160 - 7.36059i) q^{50} +(4.47239 - 3.24938i) q^{51} +(-1.26299 - 0.917617i) q^{52} +(3.34432 + 10.2928i) q^{53} -6.92280 q^{54} -3.07366 q^{56} +(-1.43376 - 4.41266i) q^{57} +(-7.18925 - 5.22329i) q^{58} +(2.66704 - 1.93771i) q^{59} +(2.31420 - 7.12238i) q^{60} +(-0.332696 + 1.02393i) q^{61} +(-0.710857 + 0.516468i) q^{62} +(-4.18492 - 3.04052i) q^{63} +(2.56433 + 7.89221i) q^{64} -7.11832 q^{65} +2.40314 q^{67} +(-0.452925 - 1.39396i) q^{68} +(-1.86677 - 1.35629i) q^{69} +(-3.11608 + 2.26396i) q^{70} +(-0.985330 + 3.03253i) q^{71} +(-4.91323 + 15.1214i) q^{72} +(-0.992078 + 0.720787i) q^{73} +(-9.07192 - 6.59113i) q^{74} +(-6.13491 - 18.8813i) q^{75} -1.23015 q^{76} +6.56217 q^{78} +(-2.93004 - 9.01775i) q^{79} +(5.33918 + 3.87914i) q^{80} +(-1.81200 + 1.31650i) q^{81} +(-0.732217 + 2.25353i) q^{82} +(-4.96572 + 15.2829i) q^{83} +(-1.75304 + 1.27366i) q^{84} +(-5.40676 - 3.92824i) q^{85} +(1.06087 + 3.26501i) q^{86} -22.7953 q^{87} -4.43830 q^{89} +(6.15690 + 18.9490i) q^{90} +(1.66629 + 1.21063i) q^{91} +(-0.494940 + 0.359595i) q^{92} +(-0.696508 + 2.14363i) q^{93} +(2.60576 - 8.01970i) q^{94} +(-4.53784 + 3.29693i) q^{95} +(9.29568 + 6.75371i) q^{96} +(1.99874 + 6.15150i) q^{97} +1.11447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more