LMFDB - Embedded newform 287.2.h.d.57.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (of order $5$, degree $4$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.9
Character	$\chi$	$=$	287.57
Dual form			287.2.h.d.141.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.718417 - 2.21106i) q^{2} +0.707185 q^{3} +(-2.75463 - 2.00136i) q^{4} +(3.19921 + 2.32437i) q^{5} +(0.508054 - 1.56363i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.64242 + 1.91983i) q^{8} -2.49989 q^{9} +O(q^{10})$	\(q+(0.718417 - 2.21106i) q^{2} +0.707185 q^{3} +(-2.75463 - 2.00136i) q^{4} +(3.19921 + 2.32437i) q^{5} +(0.508054 - 1.56363i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.64242 + 1.91983i) q^{8} -2.49989 q^{9} +(7.43769 - 5.40380i) q^{10} +(0.354186 - 0.257331i) q^{11} +(-1.94804 - 1.41533i) q^{12} +(1.94294 - 5.97974i) q^{13} -2.32485 q^{14} +(2.26244 + 1.64376i) q^{15} +(0.242152 + 0.745267i) q^{16} +(-2.54585 + 1.84967i) q^{17} +(-1.79596 + 5.52741i) q^{18} +(1.48742 + 4.57781i) q^{19} +(-4.16078 - 12.8056i) q^{20} +(-0.218532 - 0.672573i) q^{21} +(-0.314522 - 0.967999i) q^{22} +(-1.66392 + 5.12101i) q^{23} +(-1.86868 + 1.35768i) q^{24} +(3.28722 + 10.1170i) q^{25} +(-11.8257 - 8.59190i) q^{26} -3.88944 q^{27} +(-1.05218 + 3.23827i) q^{28} +(1.48766 + 1.08085i) q^{29} +(5.25982 - 3.82148i) q^{30} +(-1.97296 + 1.43344i) q^{31} -4.71063 q^{32} +(0.250475 - 0.181981i) q^{33} +(2.26075 + 6.95786i) q^{34} +(1.22199 - 3.76090i) q^{35} +(6.88628 + 5.00318i) q^{36} +(-2.74620 - 1.99523i) q^{37} +11.1904 q^{38} +(1.37402 - 4.22878i) q^{39} -12.9161 q^{40} +(6.33974 - 0.898713i) q^{41} -1.64410 q^{42} +(-0.457574 + 1.40827i) q^{43} -1.49067 q^{44} +(-7.99768 - 5.81066i) q^{45} +(10.1275 + 7.35805i) q^{46} +(-3.34471 + 10.2940i) q^{47} +(0.171246 + 0.527042i) q^{48} +(-0.809017 + 0.587785i) q^{49} +24.7309 q^{50} +(-1.80039 + 1.30806i) q^{51} +(-17.3197 + 12.5835i) q^{52} +(-4.30909 - 3.13074i) q^{53} +(-2.79424 + 8.59979i) q^{54} +1.73125 q^{55} +(2.64242 + 1.91983i) q^{56} +(1.05188 + 3.23736i) q^{57} +(3.45858 - 2.51281i) q^{58} +(-1.37367 + 4.22773i) q^{59} +(-2.94244 - 9.05590i) q^{60} +(-3.61745 - 11.1334i) q^{61} +(1.75201 + 5.39214i) q^{62} +(0.772508 + 2.37754i) q^{63} +(-3.86850 + 11.9060i) q^{64} +(20.1150 - 14.6144i) q^{65} +(-0.222425 - 0.684554i) q^{66} +(0.599123 + 0.435288i) q^{67} +10.7147 q^{68} +(-1.17670 + 3.62150i) q^{69} +(-7.43769 - 5.40380i) q^{70} +(12.0808 - 8.77719i) q^{71} +(6.60577 - 4.79937i) q^{72} +6.87223 q^{73} +(-6.38449 + 4.63861i) q^{74} +(2.32467 + 7.15460i) q^{75} +(5.06454 - 15.5871i) q^{76} +(-0.354186 - 0.257331i) q^{77} +(-8.36298 - 6.07606i) q^{78} -6.98492 q^{79} +(-0.957577 + 2.94712i) q^{80} +4.74912 q^{81} +(2.56747 - 14.6632i) q^{82} -8.01007 q^{83} +(-0.744084 + 2.29005i) q^{84} -12.4440 q^{85} +(2.78504 + 2.02345i) q^{86} +(1.05205 + 0.764360i) q^{87} +(-0.441877 + 1.35996i) q^{88} +(-4.77167 - 14.6857i) q^{89} +(-18.5934 + 13.5089i) q^{90} -6.28747 q^{91} +(14.8325 - 10.7764i) q^{92} +(-1.39525 + 1.01371i) q^{93} +(20.3577 + 14.7907i) q^{94} +(-5.88193 + 18.1027i) q^{95} -3.33129 q^{96} +(1.19788 + 0.870311i) q^{97} +(0.718417 + 2.21106i) q^{98} +(-0.885427 + 0.643300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.718417	−	2.21106i	0.507998	−	1.56346i	−0.287674	−	0.957728i	$-0.592882\pi$
$2$	0.718417	−	2.21106i	0.507998	−	1.56346i	0.795672	−	0.605728i	$-0.207118\pi$
$3$	0.707185			0.408293			0.204147	−	0.978940i	$-0.434558\pi$
$3$	0.707185			0.408293			0.204147	+	0.978940i	$0.434558\pi$
$4$	−2.75463	−	2.00136i	−1.37732	−	1.00068i
$5$	3.19921	+	2.32437i	1.43073	+	1.03949i	0.989880	+	0.141908i	$0.0453239\pi$
$5$	3.19921	+	2.32437i	1.43073	+	1.03949i	0.440853	+	0.897580i	$0.354676\pi$
$6$	0.508054	−	1.56363i	0.207412	−	0.638349i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−2.64242	+	1.91983i	−0.934238	+	0.678763i
$9$	−2.49989			−0.833296
$10$	7.43769	−	5.40380i	2.35200	−	1.70883i
$11$	0.354186	−	0.257331i	0.106791	−	0.0775883i	−0.533108	−	0.846047i	$-0.678976\pi$
$11$	0.354186	−	0.257331i	0.106791	−	0.0775883i	0.639899	+	0.768459i	$0.278976\pi$
$12$	−1.94804	−	1.41533i	−0.562350	−	0.408571i
$13$	1.94294	−	5.97974i	0.538874	−	1.65848i	−0.196254	−	0.980553i	$-0.562878\pi$
$13$	1.94294	−	5.97974i	0.538874	−	1.65848i	0.735127	−	0.677929i	$-0.237122\pi$
$14$	−2.32485			−0.621342
$15$	2.26244	+	1.64376i	0.584159	+	0.424416i
$16$	0.242152	+	0.745267i	0.0605380	+	0.186317i
$17$	−2.54585	+	1.84967i	−0.617459	+	0.448610i	−0.852033	−	0.523488i	$-0.824630\pi$
$17$	−2.54585	+	1.84967i	−0.617459	+	0.448610i	0.234574	+	0.972098i	$0.424630\pi$
$18$	−1.79596	+	5.52741i	−0.423313	+	1.30282i
$19$	1.48742	+	4.57781i	0.341238	+	1.05022i	0.963567	+	0.267466i	$0.0861865\pi$
$19$	1.48742	+	4.57781i	0.341238	+	1.05022i	−0.622329	+	0.782755i	$0.713814\pi$
$20$	−4.16078	−	12.8056i	−0.930378	−	2.86341i
$21$	−0.218532	−	0.672573i	−0.0476876	−	0.146767i
$22$	−0.314522	−	0.967999i	−0.0670563	−	0.206378i
$23$	−1.66392	+	5.12101i	−0.346951	+	1.06780i	0.613580	+	0.789632i	$0.289729\pi$
$23$	−1.66392	+	5.12101i	−0.346951	+	1.06780i	−0.960531	+	0.278172i	$0.910271\pi$
$24$	−1.86868	+	1.35768i	−0.381443	+	0.277135i
$25$	3.28722	+	10.1170i	0.657443	+	2.02340i
$26$	−11.8257	−	8.59190i	−2.31922	−	1.68501i
$27$	−3.88944			−0.748523
$28$	−1.05218	+	3.23827i	−0.198843	+	0.611975i
$29$	1.48766	+	1.08085i	0.276252	+	0.200708i	0.717281	−	0.696784i	$-0.245387\pi$
$29$	1.48766	+	1.08085i	0.276252	+	0.200708i	−0.441029	+	0.897493i	$0.645387\pi$
$30$	5.25982	−	3.82148i	0.960307	−	0.697704i
$31$	−1.97296	+	1.43344i	−0.354354	+	0.257453i	−0.750693	−	0.660651i	$-0.770280\pi$
$31$	−1.97296	+	1.43344i	−0.354354	+	0.257453i	0.396339	+	0.918104i	$0.370280\pi$
$32$	−4.71063			−0.832730
$33$	0.250475	−	0.181981i	0.0436021	−	0.0316788i
$34$	2.26075	+	6.95786i	0.387715	+	1.19326i
$35$	1.22199	−	3.76090i	0.206554	−	0.635709i
$36$	6.88628	+	5.00318i	1.14771	+	0.833863i
$37$	−2.74620	−	1.99523i	−0.451472	−	0.328014i	0.338705	−	0.940893i	$-0.390011\pi$
$37$	−2.74620	−	1.99523i	−0.451472	−	0.328014i	−0.790177	+	0.612879i	$0.790011\pi$
$38$	11.1904			1.81532
$39$	1.37402	−	4.22878i	0.220019	−	0.677147i
$40$	−12.9161			−2.04221
$41$	6.33974	−	0.898713i	0.990101	−	0.140355i
$41$	6.33974	−	0.898713i	0.990101	−	0.140355i
$42$	−1.64410			−0.253690
$43$	−0.457574	+	1.40827i	−0.0697793	+	0.214759i	−0.979865	−	0.199662i	$-0.936016\pi$
$43$	−0.457574	+	1.40827i	−0.0697793	+	0.214759i	0.910086	+	0.414420i	$0.136016\pi$
$44$	−1.49067			−0.224726
$45$	−7.99768	−	5.81066i	−1.19222	−	0.866202i
$46$	10.1275	+	7.35805i	1.49322	+	1.08488i
$47$	−3.34471	+	10.2940i	−0.487877	+	1.50153i	0.339894	+	0.940464i	$0.389609\pi$
$47$	−3.34471	+	10.2940i	−0.487877	+	1.50153i	−0.827771	+	0.561066i	$0.810391\pi$
$48$	0.171246	+	0.527042i	0.0247173	+	0.0760719i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	24.7309			3.49748
$51$	−1.80039	+	1.30806i	−0.252104	+	0.183165i
$52$	−17.3197	+	12.5835i	−2.40181	+	1.74502i
$53$	−4.30909	−	3.13074i	−0.591899	−	0.430040i	0.251095	−	0.967962i	$-0.419209\pi$
$53$	−4.30909	−	3.13074i	−0.591899	−	0.430040i	−0.842994	+	0.537923i	$0.819209\pi$
$54$	−2.79424	+	8.59979i	−0.380248	+	1.17028i
$55$	1.73125			0.233442
$56$	2.64242	+	1.91983i	0.353109	+	0.256548i
$57$	1.05188	+	3.23736i	0.139325	+	0.428799i
$58$	3.45858	−	2.51281i	0.454134	−	0.329948i
$59$	−1.37367	+	4.22773i	−0.178837	+	0.550404i	−0.999788	−	0.0205949i	$-0.993444\pi$
$59$	−1.37367	+	4.22773i	−0.178837	+	0.550404i	0.820951	+	0.570999i	$0.193444\pi$
$60$	−2.94244	−	9.05590i	−0.379867	−	1.16911i
$61$	−3.61745	−	11.1334i	−0.463166	−	1.42548i	−0.861274	−	0.508141i	$-0.830333\pi$
$61$	−3.61745	−	11.1334i	−0.463166	−	1.42548i	0.398108	−	0.917339i	$-0.369667\pi$
$62$	1.75201	+	5.39214i	0.222506	+	0.684802i
$63$	0.772508	+	2.37754i	0.0973269	+	0.299541i
$64$	−3.86850	+	11.9060i	−0.483563	+	1.48825i
$65$	20.1150	−	14.6144i	2.49496	−	1.81269i
$66$	−0.222425	−	0.684554i	−0.0273786	−	0.0842628i
$67$	0.599123	+	0.435288i	0.0731945	+	0.0531789i	0.623781	−	0.781599i	$-0.285596\pi$
$67$	0.599123	+	0.435288i	0.0731945	+	0.0531789i	−0.550586	+	0.834778i	$0.685596\pi$
$68$	10.7147			1.29935
$69$	−1.17670	+	3.62150i	−0.141658	+	0.435978i
$70$	−7.43769	−	5.40380i	−0.888974	−	0.645877i
$71$	12.0808	−	8.77719i	1.43372	−	1.04166i	0.444416	−	0.895821i	$-0.353411\pi$
$71$	12.0808	−	8.77719i	1.43372	−	1.04166i	0.989308	−	0.145841i	$-0.0465887\pi$
$72$	6.60577	−	4.79937i	0.778497	−	0.565611i
$73$	6.87223			0.804334			0.402167	−	0.915566i	$-0.368257\pi$
$73$	6.87223			0.804334			0.402167	+	0.915566i	$0.368257\pi$
$74$	−6.38449	+	4.63861i	−0.742182	+	0.539227i
$75$	2.32467	+	7.15460i	0.268430	+	0.826142i
$76$	5.06454	−	15.5871i	0.580943	−	1.78796i
$77$	−0.354186	−	0.257331i	−0.0403633	−	0.0293256i
$78$	−8.36298	−	6.07606i	−0.946922	−	0.687979i
$79$	−6.98492			−0.785865			−0.392932	−	0.919567i	$-0.628539\pi$
$79$	−6.98492			−0.785865			−0.392932	+	0.919567i	$0.628539\pi$
$80$	−0.957577	+	2.94712i	−0.107060	+	0.329498i
$81$	4.74912			0.527679
$82$	2.56747	−	14.6632i	0.283530	−	1.61928i
$83$	−8.01007			−0.879219			−0.439610	−	0.898189i	$-0.644883\pi$
$83$	−8.01007			−0.879219			−0.439610	+	0.898189i	$0.644883\pi$
$84$	−0.744084	+	2.29005i	−0.0811862	+	0.249865i
$85$	−12.4440			−1.34974
$86$	2.78504	+	2.02345i	0.300318	+	0.218194i
$87$	1.05205	+	0.764360i	0.112792	+	0.0819479i
$88$	−0.441877	+	1.35996i	−0.0471042	+	0.144972i
$89$	−4.77167	−	14.6857i	−0.505796	−	1.55668i	−0.799428	−	0.600762i	$-0.794864\pi$
$89$	−4.77167	−	14.6857i	−0.505796	−	1.55668i	0.293632	−	0.955918i	$-0.405136\pi$
$90$	−18.5934	+	13.5089i	−1.95992	+	1.42396i
$91$	−6.28747			−0.659106
$92$	14.8325	−	10.7764i	1.54639	−	1.12352i
$93$	−1.39525	+	1.01371i	−0.144680	+	0.105116i
$94$	20.3577	+	14.7907i	2.09974	+	1.52555i
$95$	−5.88193	+	18.1027i	−0.603473	+	1.85730i
$96$	−3.33129			−0.339998
$97$	1.19788	+	0.870311i	0.121626	+	0.0883667i	0.646935	−	0.762545i	$-0.276050\pi$
$97$	1.19788	+	0.870311i	0.121626	+	0.0883667i	−0.525309	+	0.850911i	$0.676050\pi$
$98$	0.718417	+	2.21106i	0.0725711	+	0.223351i
$99$	−0.885427	+	0.643300i	−0.0889887	+	0.0646541i
$100$	11.1927	−	34.4476i	1.11927	−	3.44476i
$101$	0.410385	+	1.26303i	0.0408348	+	0.125677i	0.969396	−	0.245503i	$-0.0789533\pi$
$101$	0.410385	+	1.26303i	0.0408348	+	0.125677i	−0.928561	+	0.371180i	$0.878953\pi$
$102$	1.59877	+	4.92049i	0.158301	+	0.487202i
$103$	−0.722300	−	2.22301i	−0.0711704	−	0.219040i	0.909144	−	0.416481i	$-0.136737\pi$
$103$	−0.722300	−	2.22301i	−0.0711704	−	0.219040i	−0.980315	+	0.197441i	$0.936737\pi$
$104$	6.34605	+	19.5311i	0.622281	+	1.91518i
$105$	0.864174	−	2.65965i	0.0843347	−	0.259556i
$106$	−10.0180	+	7.27849i	−0.973032	+	0.706949i
$107$	4.13859	+	12.7373i	0.400093	+	1.23136i	0.924924	+	0.380153i	$0.124129\pi$
$107$	4.13859	+	12.7373i	0.400093	+	1.23136i	−0.524831	+	0.851206i	$0.675871\pi$
$108$	10.7140	+	7.78417i	1.03095	+	0.749032i
$109$	11.1234			1.06543			0.532713	−	0.846296i	$-0.321173\pi$
$109$	11.1234			1.06543			0.532713	+	0.846296i	$0.321173\pi$
$110$	1.24376	−	3.82790i	0.118588	−	0.364976i
$111$	−1.94207	−	1.41100i	−0.184333	−	0.133926i
$112$	0.633962	−	0.460600i	0.0599038	−	0.0435226i
$113$	−0.963394	+	0.699947i	−0.0906285	+	0.0658454i	−0.632177	−	0.774824i	$-0.717838\pi$
$113$	−0.963394	+	0.699947i	−0.0906285	+	0.0658454i	0.541548	+	0.840670i	$0.317838\pi$
$114$	7.91369			0.741185
$115$	−17.2263	+	12.5157i	−1.60636	+	1.16709i
$116$	−1.93479	−	5.95468i	−0.179641	−	0.552879i
$117$	−4.85713	+	14.9487i	−0.449041	+	1.38201i
$118$	8.36091	+	6.07455i	0.769684	+	0.559208i
$119$	2.54585	+	1.84967i	0.233378	+	0.169559i
$120$	−9.13405			−0.833821
$121$	−3.33996	+	10.2793i	−0.303633	+	0.934485i
$122$	−27.2154			−2.46396
$123$	4.48337	−	0.635557i	0.404252	−	0.0573062i
$124$	8.30360			0.745686
$125$	−6.88916	+	21.2027i	−0.616185	+	1.89642i
$126$	5.81186			0.517762
$127$	−16.5061	−	11.9924i	−1.46468	−	1.06415i	−0.982113	−	0.188292i	$-0.939705\pi$
$127$	−16.5061	−	11.9924i	−1.46468	−	1.06415i	−0.482566	−	0.875860i	$-0.660295\pi$
$128$	15.9238	+	11.5693i	1.40748	+	1.02259i
$129$	−0.323589	+	0.995905i	−0.0284904	+	0.0876845i
$130$	−17.8624	−	54.9747i	−1.56663	−	4.82160i
$131$	14.2630	−	10.3627i	1.24617	−	0.905394i	0.248175	−	0.968715i	$-0.420169\pi$
$131$	14.2630	−	10.3627i	1.24617	−	0.905394i	0.997993	+	0.0633208i	$0.0201691\pi$
$132$	−1.05418			−0.0917543
$133$	3.89412	−	2.82924i	0.337663	−	0.245326i
$134$	1.39287	−	1.01198i	0.120326	−	0.0874217i
$135$	−12.4432	−	9.04048i	−1.07094	−	0.778081i
$136$	3.17616	−	9.77521i	0.272353	−	0.838217i
$137$	−2.49005			−0.212739			−0.106370	−	0.994327i	$-0.533923\pi$
$137$	−2.49005			−0.212739			−0.106370	+	0.994327i	$0.533923\pi$
$138$	7.16200	+	5.20350i	0.609670	+	0.442951i
$139$	−5.38015	−	16.5584i	−0.456339	−	1.40447i	−0.869556	−	0.493834i	$-0.835595\pi$
$139$	−5.38015	−	16.5584i	−0.456339	−	1.40447i	0.413218	−	0.910632i	$-0.364405\pi$
$140$	−10.8931	+	7.91427i	−0.920631	+	0.668878i
$141$	−2.36533	+	7.27974i	−0.199197	+	0.613065i
$142$	−10.7279	−	33.0170i	−0.900264	−	2.77073i
$143$	−0.850614	−	2.61792i	−0.0711319	−	0.218922i
$144$	−0.605353	−	1.86308i	−0.0504461	−	0.155257i
$145$	2.24706	+	6.91573i	0.186608	+	0.574320i
$146$	4.93713	−	15.1949i	0.408600	−	1.25754i
$147$	−0.572125	+	0.415673i	−0.0471880	+	0.0342841i
$148$	3.57160	+	10.9923i	0.293584	+	0.903558i
$149$	11.2476	+	8.17189i	0.921443	+	0.669467i	0.943883	−	0.330281i	$-0.107143\pi$
$149$	11.2476	+	8.17189i	0.921443	+	0.669467i	−0.0224399	+	0.999748i	$0.507143\pi$
$150$	17.4893			1.42800
$151$	1.58095	−	4.86567i	0.128656	−	0.395962i	−0.865893	−	0.500229i	$-0.833249\pi$
$151$	1.58095	−	4.86567i	0.128656	−	0.395962i	0.994549	+	0.104266i	$0.0332493\pi$
$152$	−12.7190	−	9.24092i	−1.03165	−	0.749537i
$153$	6.36434	−	4.62396i	0.514526	−	0.373825i
$154$	−0.823429	+	0.598256i	−0.0663538	+	0.0482089i
$155$	−9.64375			−0.774605
$156$	−12.2482	+	8.89886i	−0.980643	+	0.712479i
$157$	−2.83499	−	8.72521i	−0.226257	−	0.696348i	−0.998162	−	0.0606091i	$-0.980696\pi$
$157$	−2.83499	−	8.72521i	−0.226257	−	0.696348i	0.771905	−	0.635738i	$-0.219304\pi$
$158$	−5.01809	+	15.4441i	−0.399218	+	1.22867i
$159$	−3.04732	−	2.21401i	−0.241668	−	0.175582i
$160$	−15.0703	−	10.9492i	−1.19141	−	0.865613i
$161$	5.38455			0.424362
$162$	3.41185	−	10.5006i	0.268060	−	0.825004i
$163$	−11.5984			−0.908454			−0.454227	−	0.890886i	$-0.650084\pi$
$163$	−11.5984			−0.908454			−0.454227	+	0.890886i	$0.650084\pi$
$164$	−19.2623	−	10.2125i	−1.50413	−	0.797460i
$165$	1.22431			0.0953127
$166$	−5.75457	+	17.7108i	−0.446641	+	1.37462i
$167$	18.5726			1.43719			0.718597	−	0.695427i	$-0.244785\pi$
$167$	18.5726			1.43719			0.718597	+	0.695427i	$0.244785\pi$
$168$	1.86868	+	1.35768i	0.144172	+	0.104747i
$169$	−21.4651	−	15.5953i	−1.65116	−	1.19964i
$170$	−8.94000	+	27.5145i	−0.685667	+	2.11027i
$171$	−3.71839	−	11.4440i	−0.284352	−	0.875146i
$172$	4.07890	−	2.96349i	0.311013	−	0.225964i
$173$	−17.6998			−1.34569			−0.672847	−	0.739781i	$-0.734929\pi$
$173$	−17.6998			−1.34569			−0.672847	+	0.739781i	$0.734929\pi$
$174$	2.44586	−	1.77702i	0.185420	−	0.134715i
$175$	8.60604	−	6.25266i	0.650556	−	0.472656i
$176$	0.277547	+	0.201650i	0.0209209	+	0.0151999i
$177$	−0.971442	+	2.98979i	−0.0730180	+	0.224726i
$178$	−35.8990			−2.69074
$179$	6.22367	+	4.52176i	0.465179	+	0.337972i	0.795559	−	0.605876i	$-0.207177\pi$
$179$	6.22367	+	4.52176i	0.465179	+	0.337972i	−0.330381	+	0.943848i	$0.607177\pi$
$180$	10.4015	+	32.0125i	0.775281	+	2.38607i
$181$	6.58001	−	4.78066i	0.489089	−	0.355344i	−0.315745	−	0.948844i	$-0.602254\pi$
$181$	6.58001	−	4.78066i	0.489089	−	0.355344i	0.804834	+	0.593500i	$0.202254\pi$
$182$	−4.51703	+	13.9020i	−0.334825	+	1.03048i
$183$	−2.55820	−	7.87334i	−0.189108	−	0.582014i
$184$	−5.43471	−	16.7263i	−0.400652	−	1.23308i
$185$	−4.14803	−	12.7663i	−0.304970	−	0.938600i
$186$	1.23900	+	3.81324i	0.0908476	+	0.279600i
$187$	−0.425727	+	1.31025i	−0.0311323	+	0.0958152i
$188$	29.8154	−	21.6622i	2.17451	−	1.57988i
$189$	1.20190	+	3.69908i	0.0874256	+	0.269068i
$190$	35.8005	+	26.0106i	2.59724	+	1.88701i
$191$	−1.34712			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$191$	−1.34712			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$192$	−2.73575	+	8.41977i	−0.197436	+	0.607644i
$193$	11.9939	+	8.71404i	0.863336	+	0.627251i	0.928791	−	0.370605i	$-0.120850\pi$
$193$	11.9939	+	8.71404i	0.863336	+	0.627251i	−0.0654542	+	0.997856i	$0.520850\pi$
$194$	2.78489	−	2.02334i	0.199943	−	0.145267i
$195$	14.2250	−	10.3351i	1.01867	−	0.740110i
$196$	3.40492			0.243208
$197$	14.9000	−	10.8255i	1.06158	−	0.771285i	0.0872022	−	0.996191i	$-0.472207\pi$
$197$	14.9000	−	10.8255i	1.06158	−	0.771285i	0.974381	+	0.224906i	$0.0722074\pi$
$198$	0.786270	+	2.41989i	0.0558778	+	0.171974i
$199$	−2.51308	+	7.73446i	−0.178147	+	0.548281i	−0.999763	−	0.0217603i	$-0.993073\pi$
$199$	−2.51308	+	7.73446i	−0.178147	+	0.548281i	0.821616	+	0.570042i	$0.193073\pi$
$200$	−28.1092	−	20.4225i	−1.98762	−	1.44409i
$201$	0.423691	+	0.307829i	0.0298848	+	0.0217126i
$202$	3.08747			0.217234
$203$	0.568236	−	1.74885i	0.0398823	−	0.122745i
$204$	7.57730			0.530517
$205$	22.3711	+	11.8607i	1.56247	+	0.828387i
$206$	−5.43413			−0.378614
$207$	4.15961	−	12.8020i	0.289113	−	0.889798i
$208$	4.92699			0.341625
$209$	1.70484	+	1.23864i	0.117926	+	0.0856784i
$210$	−5.25982	−	3.82148i	−0.362962	−	0.263707i
$211$	−0.581736	+	1.79040i	−0.0400484	+	0.123256i	−0.969082	−	0.246739i	$-0.920641\pi$
$211$	−0.581736	+	1.79040i	−0.0400484	+	0.123256i	0.929033	+	0.369996i	$0.120641\pi$
$212$	5.60424	+	17.2481i	0.384901	+	1.18460i
$213$	8.54334	−	6.20710i	0.585380	−	0.425303i
$214$	31.1361			2.12842
$215$	−4.73720	+	3.44178i	−0.323075	+	0.234727i
$216$	10.2775	−	7.46707i	0.699298	−	0.508070i
$217$	1.97296	+	1.43344i	0.133933	+	0.0973081i
$218$	7.99122	−	24.5945i	0.541234	−	1.66575i
$219$	4.85994			0.328404
$220$	−4.76896	−	3.46485i	−0.321523	−	0.233600i
$221$	6.11411	+	18.8173i	0.411280	+	1.26579i
$222$	−4.51502	+	3.28035i	−0.303028	+	0.220163i
$223$	0.498361	−	1.53380i	0.0333727	−	0.102711i	−0.932983	−	0.359921i	$-0.882803\pi$
$223$	0.498361	−	1.53380i	0.0333727	−	0.102711i	0.966355	+	0.257211i	$0.0828035\pi$
$224$	1.45567	+	4.48008i	0.0972607	+	0.299338i
$225$	−8.21767	−	25.2914i	−0.547845	−	1.68609i
$226$	0.855506	+	2.63298i	0.0569074	+	0.175143i
$227$	−5.32970	−	16.4031i	−0.353744	−	1.08871i	−0.956734	−	0.290964i	$-0.906024\pi$
$227$	−5.32970	−	16.4031i	−0.353744	−	1.08871i	0.602989	−	0.797749i	$-0.293976\pi$
$228$	3.58157	−	11.0229i	0.237195	−	0.730012i
$229$	1.00976	−	0.733630i	0.0667265	−	0.0484796i	−0.553922	−	0.832569i	$-0.686869\pi$
$229$	1.00976	−	0.733630i	0.0667265	−	0.0484796i	0.620648	+	0.784089i	$0.286869\pi$
$230$	15.2972	+	47.0799i	1.00867	+	3.10436i
$231$	−0.250475	−	0.181981i	−0.0164801	−	0.0119735i
$232$	−6.00608			−0.394318
$233$	5.80181	−	17.8561i	0.380089	−	1.16979i	−0.559891	−	0.828566i	$-0.689157\pi$
$233$	5.80181	−	17.8561i	0.380089	−	1.16979i	0.939981	−	0.341228i	$-0.110843\pi$
$234$	29.5630	+	21.4788i	1.93260	+	1.40411i
$235$	−34.6274	+	25.1583i	−2.25884	+	1.64115i
$236$	12.2452	−	8.89665i	0.797094	−	0.579122i
$237$	−4.93963			−0.320864
$238$	5.91871	−	4.30019i	0.383653	−	0.278740i
$239$	4.36255	+	13.4265i	0.282190	+	0.868491i	0.987227	+	0.159321i	$0.0509303\pi$
$239$	4.36255	+	13.4265i	0.282190	+	0.868491i	−0.705037	+	0.709170i	$0.749070\pi$
$240$	−0.677184	+	2.08416i	−0.0437120	+	0.134532i
$241$	16.3210	+	11.8579i	1.05133	+	0.763833i	0.972464	−	0.233053i	$-0.0748716\pi$
$241$	16.3210	+	11.8579i	1.05133	+	0.763833i	0.0788613	+	0.996886i	$0.474872\pi$
$242$	20.3288	+	14.7697i	1.30678	+	0.949433i
$243$	15.0268			0.963971
$244$	−12.3171	+	37.9081i	−0.788521	+	2.42682i
$245$	−3.95445			−0.252640
$246$	1.81568	−	10.3696i	0.115763	−	0.661142i
$247$	30.2641			1.92566
$248$	2.46143	−	7.57550i	0.156301	−	0.481045i
$249$	−5.66460			−0.358979
$250$	41.9311	+	30.4647i	2.65196	+	1.92676i
$251$	−13.0922	−	9.51207i	−0.826375	−	0.600397i	0.0921565	−	0.995745i	$-0.470624\pi$
$251$	−13.0922	−	9.51207i	−0.826375	−	0.600397i	−0.918531	+	0.395348i	$0.870624\pi$
$252$	2.63033	−	8.09531i	0.165695	−	0.509957i
$253$	0.728460	+	2.24197i	0.0457979	+	0.140951i
$254$	−38.3742	+	27.8805i	−2.40781	+	1.74938i
$255$	−8.80022			−0.551091
$256$	16.7647	−	12.1802i	1.04779	−	0.761265i
$257$	10.2666	−	7.45915i	0.640416	−	0.465289i	−0.219577	−	0.975595i	$-0.570468\pi$
$257$	10.2666	−	7.45915i	0.640416	−	0.465289i	0.859993	+	0.510306i	$0.170468\pi$
$258$	1.96953	+	1.43095i	0.122618	+	0.0890871i
$259$	−1.04895	+	3.22835i	−0.0651789	+	0.200600i
$260$	−84.6581			−5.25027
$261$	−3.71899	−	2.70200i	−0.230199	−	0.167250i
$262$	−12.6658	−	38.9812i	−0.782494	−	2.40827i
$263$	−11.4250	+	8.30078i	−0.704498	+	0.511848i	−0.881394	−	0.472382i	$-0.843394\pi$
$263$	−11.4250	+	8.30078i	−0.704498	+	0.511848i	0.176896	+	0.984230i	$0.443394\pi$
$264$	−0.312489	+	0.961741i	−0.0192323	+	0.0591911i
$265$	−6.50873	−	20.0318i	−0.399828	−	1.23054i
$266$	−3.45803	−	10.6427i	−0.212025	−	0.652547i
$267$	−3.37445	−	10.3855i	−0.206513	−	0.635582i
$268$	−0.779197	−	2.39812i	−0.0475970	−	0.146489i
$269$	2.93036	−	9.01871i	0.178667	−	0.549880i	−0.821115	−	0.570763i	$-0.806648\pi$
$269$	2.93036	−	9.01871i	0.178667	−	0.549880i	0.999782	+	0.0208825i	$0.00664760\pi$
$270$	−28.9284	+	21.0177i	−1.76053	+	1.27910i
$271$	3.26968	+	10.0631i	0.198619	+	0.611287i	0.999915	+	0.0130189i	$0.00414416\pi$
$271$	3.26968	+	10.0631i	0.198619	+	0.611287i	−0.801296	+	0.598268i	$0.795856\pi$
$272$	−1.99498	−	1.44944i	−0.120963	−	0.0878850i
$273$	−4.44641			−0.269109
$274$	−1.78890	+	5.50565i	−0.108071	+	0.332609i
$275$	3.76771	+	2.73740i	0.227202	+	0.165072i
$276$	10.4893	−	7.62092i	0.631382	−	0.458726i
$277$	−26.7252	+	19.4170i	−1.60576	+	1.16665i	−0.730614	+	0.682790i	$0.760766\pi$
$277$	−26.7252	+	19.4170i	−1.60576	+	1.16665i	−0.875144	+	0.483862i	$0.839234\pi$
$278$	−40.4769			−2.42764
$279$	4.93218	−	3.58344i	0.295282	−	0.214535i
$280$	3.99129	+	12.2839i	0.238525	+	0.734104i
$281$	−4.92276	+	15.1507i	−0.293667	+	0.903814i	0.689999	+	0.723811i	$0.257611\pi$
$281$	−4.92276	+	15.1507i	−0.293667	+	0.903814i	−0.983666	+	0.180004i	$0.942389\pi$
$282$	14.3967	+	10.4598i	0.857309	+	0.622871i
$283$	−11.5815	−	8.41442i	−0.688446	−	0.500185i	0.187703	−	0.982226i	$-0.439896\pi$
$283$	−11.5815	−	8.41442i	−0.688446	−	0.500185i	−0.876149	+	0.482041i	$0.839896\pi$
$284$	−50.8444			−3.01706
$285$	−4.15961	+	12.8020i	−0.246394	+	0.758323i
$286$	−6.39948			−0.378409
$287$	−2.81381	−	5.75173i	−0.166094	−	0.339514i
$288$	11.7761			0.693911
$289$	−2.19321	+	6.75001i	−0.129012	+	0.397060i
$290$	16.9054			0.992721
$291$	0.847123	+	0.615471i	0.0496592	+	0.0360795i
$292$	−18.9305	−	13.7538i	−1.10782	−	0.804881i
$293$	9.17617	−	28.2414i	0.536078	−	1.64988i	−0.205231	−	0.978714i	$-0.565795\pi$
$293$	9.17617	−	28.2414i	0.536078	−	1.64988i	0.741309	−	0.671164i	$-0.234205\pi$
$294$	0.508054	+	1.56363i	0.0296303	+	0.0911927i
$295$	−14.2215	+	10.3325i	−0.828006	+	0.601582i
$296$	11.0871			0.644426
$297$	−1.37759	+	1.00087i	−0.0799357	+	0.0580767i
$298$	26.1491	−	18.9984i	1.51477	−	1.10055i
$299$	27.3894	+	19.8996i	1.58397	+	1.15082i
$300$	7.91530	−	24.3608i	0.456990	−	1.40647i
$301$	1.48074			0.0853484
$302$	−9.62251	−	6.99116i	−0.553713	−	0.402296i
$303$	0.290218	+	0.893199i	0.0166726	+	0.0513129i
$304$	−3.05151	+	2.21705i	−0.175016	+	0.127157i
$305$	14.3050	−	44.0263i	0.819102	−	2.52094i
$306$	−5.65162	−	17.3939i	−0.323081	−	0.994342i
$307$	1.22109	+	3.75814i	0.0696915	+	0.214488i	0.979836	−	0.199802i	$-0.0640299\pi$
$307$	1.22109	+	3.75814i	0.0696915	+	0.214488i	−0.910145	+	0.414290i	$0.864030\pi$
$308$	0.460641	+	1.41771i	0.0262475	+	0.0807814i
$309$	−0.510800	−	1.57208i	−0.0290584	−	0.0894325i
$310$	−6.92824	+	21.3229i	−0.393498	+	1.21106i
$311$	9.29513	−	6.75331i	0.527079	−	0.382945i	−0.292185	−	0.956362i	$-0.594382\pi$
$311$	9.29513	−	6.75331i	0.527079	−	0.382945i	0.819264	+	0.573417i	$0.194382\pi$
$312$	4.48783	+	13.8121i	0.254073	+	0.781957i
$313$	2.70173	+	1.96292i	0.152711	+	0.110951i	0.661517	−	0.749930i	$-0.269913\pi$
$313$	2.70173	+	1.96292i	0.152711	+	0.110951i	−0.508806	+	0.860881i	$0.669913\pi$
$314$	−21.3287			−1.20365
$315$	−3.05484	+	9.40184i	−0.172121	+	0.529734i
$316$	19.2409	+	13.9793i	1.08239	+	0.786399i
$317$	13.0134	−	9.45476i	0.730904	−	0.531033i	−0.158946	−	0.987287i	$-0.550809\pi$
$317$	13.0134	−	9.45476i	0.730904	−	0.531033i	0.889849	+	0.456255i	$0.150809\pi$
$318$	−7.08456	+	5.14724i	−0.397282	+	0.288643i
$319$	0.805045			0.0450739
$320$	−40.0501	+	29.0981i	−2.23887	+	1.62664i
$321$	2.92675	+	9.00761i	0.163355	+	0.502756i
$322$	3.86835	−	11.9056i	0.215575	−	0.663471i
$323$	−12.2542	−	8.90318i	−0.681841	−	0.495386i
$324$	−13.0821	−	9.50469i	−0.726782	−	0.528038i
$325$	66.8840			3.71005
$326$	−8.33247	+	25.6447i	−0.461493	+	1.42033i
$327$	7.86628			0.435006
$328$	−15.0269	+	14.5460i	−0.829722	+	0.803170i
$329$	10.8237			0.596731
$330$	0.879569	−	2.70703i	0.0484187	−	0.149017i
$331$	5.16968			0.284151			0.142076	−	0.989856i	$-0.454622\pi$
$331$	5.16968			0.284151			0.142076	+	0.989856i	$0.454622\pi$
$332$	22.0648	+	16.0310i	1.21096	+	0.879817i
$333$	6.86519	+	4.98785i	0.376210	+	0.273333i
$334$	13.3429	−	41.0652i	0.730091	−	2.24699i
$335$	0.904954	+	2.78516i	0.0494429	+	0.152170i
$336$	0.448328	−	0.325730i	0.0244583	−	0.0177700i
$337$	−28.7815			−1.56783			−0.783914	−	0.620869i	$-0.786780\pi$
$337$	−28.7815			−1.56783			−0.783914	+	0.620869i	$0.786780\pi$
$338$	−49.9031	+	36.2567i	−2.71437	+	1.97211i
$339$	−0.681298	+	0.494992i	−0.0370030	+	0.0268843i
$340$	34.2787	+	24.9050i	1.85903	+	1.35066i
$341$	−0.329926	+	1.01541i	−0.0178665	+	0.0549874i
$342$	−27.9748			−1.51270
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−1.49453	−	4.59970i	−0.0805799	−	0.247999i
$345$	−12.1822	+	8.85089i	−0.655868	+	0.476516i
$346$	−12.7159	+	39.1355i	−0.683610	+	2.10393i
$347$	−2.28131	−	7.02114i	−0.122467	−	0.376914i	0.870964	−	0.491347i	$-0.163495\pi$
$347$	−2.28131	−	7.02114i	−0.122467	−	0.376914i	−0.993431	+	0.114432i	$0.963495\pi$
$348$	−1.36826	−	4.21106i	−0.0733463	−	0.225737i
$349$	7.06666	+	21.7489i	0.378269	+	1.16419i	0.941246	+	0.337721i	$0.109656\pi$
$349$	7.06666	+	21.7489i	0.378269	+	1.16419i	−0.562977	+	0.826473i	$0.690344\pi$
$350$	−7.64227	−	23.5205i	−0.408497	−	1.25722i
$351$	−7.55693	+	23.2578i	−0.403359	+	1.24141i
$352$	−1.66844	+	1.21219i	−0.0889282	+	0.0646101i
$353$	−3.10322	−	9.55074i	−0.165168	−	0.508334i	0.833881	−	0.551945i	$-0.186114\pi$
$353$	−3.10322	−	9.55074i	−0.165168	−	0.508334i	−0.999049	+	0.0436102i	$0.986114\pi$
$354$	5.91271	+	4.29583i	0.314257	+	0.228321i
$355$	59.0504			3.13407
$356$	−16.2471	+	50.0035i	−0.861096	+	2.65018i
$357$	1.80039	+	1.30806i	0.0952865	+	0.0692297i
$358$	14.4691	−	10.5124i	0.764714	−	0.555598i
$359$	5.24308	−	3.80932i	0.276719	−	0.201048i	−0.440766	−	0.897622i	$-0.645293\pi$
$359$	5.24308	−	3.80932i	0.276719	−	0.201048i	0.717485	+	0.696574i	$0.245293\pi$
$360$	32.2888			1.70177
$361$	−3.37261	+	2.45035i	−0.177506	+	0.128966i
$362$	−5.84314	−	17.9833i	−0.307108	−	0.945182i
$363$	−2.36197	+	7.26939i	−0.123971	+	0.381544i
$364$	17.3197	+	12.5835i	0.907799	+	0.659554i
$365$	21.9858	+	15.9736i	1.15079	+	0.836096i
$366$	−19.2463			−1.00602
$367$	−1.28997	+	3.97012i	−0.0673359	+	0.207239i	−0.979063	−	0.203558i	$-0.934749\pi$
$367$	−1.28997	+	3.97012i	−0.0673359	+	0.207239i	0.911727	+	0.410797i	$0.134749\pi$
$368$	−4.21944			−0.219954
$369$	−15.8487	+	2.24668i	−0.825048	+	0.116958i
$370$	−31.2072			−1.62238
$371$	−1.64593	+	5.06564i	−0.0854522	+	0.262995i
$372$	5.87218			0.304459
$373$	−1.31438	−	0.954950i	−0.0680558	−	0.0494455i	0.553237	−	0.833024i	$-0.313392\pi$
$373$	−1.31438	−	0.954950i	−0.0680558	−	0.0494455i	−0.621293	+	0.783578i	$0.713392\pi$
$374$	2.59120	+	1.88262i	0.133988	+	0.0973479i
$375$	−4.87191	+	14.9942i	−0.251584	+	0.774297i
$376$	−10.9246	−	33.6223i	−0.563391	−	1.73394i
$377$	9.35362	−	6.79580i	0.481736	−	0.350002i
$378$	9.04235			0.465088
$379$	−0.369691	+	0.268597i	−0.0189898	+	0.0137969i	−0.597240	−	0.802063i	$-0.703736\pi$
$379$	−0.369691	+	0.268597i	−0.0189898	+	0.0137969i	0.578250	+	0.815860i	$0.303736\pi$
$380$	52.4326	−	38.0945i	2.68974	−	1.95421i
$381$	−11.6729	−	8.48083i	−0.598019	−	0.434486i
$382$	−0.967792	+	2.97856i	−0.0495166	+	0.152396i
$383$	24.2167			1.23742			0.618709	−	0.785620i	$-0.287656\pi$
$383$	24.2167			1.23742			0.618709	+	0.785620i	$0.287656\pi$
$384$	11.2611	+	8.18165i	0.574664	+	0.417518i
$385$	−0.534986	−	1.64652i	−0.0272654	−	0.0839143i
$386$	27.8839	−	20.2588i	1.41925	−	1.03115i
$387$	1.14388	−	3.52051i	0.0581469	−	0.178958i
$388$	−1.55792	−	4.79478i	−0.0790913	−	0.243418i
$389$	−6.11955	−	18.8340i	−0.310274	−	0.954924i	−0.977656	−	0.210209i	$-0.932586\pi$
$389$	−6.11955	−	18.8340i	−0.310274	−	0.954924i	0.667383	−	0.744715i	$-0.267414\pi$
$390$	−12.6320	−	38.8773i	−0.639646	−	1.96863i
$391$	−5.23609	−	16.1150i	−0.264800	−	0.814971i
$392$	1.00932	−	3.10636i	0.0509782	−	0.156895i
$393$	10.0866	−	7.32835i	0.508802	−	0.369667i
$394$	−13.2314	−	40.7221i	−0.666589	−	2.05155i
$395$	−22.3463	−	16.2355i	−1.12436	−	0.816897i
$396$	3.72650			0.187264
$397$	4.77100	−	14.6836i	0.239449	−	0.736950i	−0.757051	−	0.653356i	$-0.773360\pi$
$397$	4.77100	−	14.6836i	0.239449	−	0.736950i	0.996500	−	0.0835932i	$-0.0266396\pi$
$398$	15.2959	+	11.1131i	0.766716	+	0.557051i
$399$	2.75386	−	2.00080i	0.137866	−	0.100165i
$400$	−6.74387	+	4.89971i	−0.337193	+	0.244985i
$401$	4.37570			0.218512			0.109256	−	0.994014i	$-0.465153\pi$
$401$	4.37570			0.218512			0.109256	+	0.994014i	$0.465153\pi$
$402$	0.985017	−	0.715656i	0.0491282	−	0.0356937i
$403$	4.73826	+	14.5829i	0.236029	+	0.726424i
$404$	1.39733	−	4.30053i	0.0695195	−	0.213959i
$405$	15.1934	+	11.0387i	0.754968	+	0.548516i
$406$	−3.45858	−	2.51281i	−0.171647	−	0.124709i
$407$	−1.48610			−0.0736633
$408$	2.24613	−	6.91288i	0.111200	−	0.342239i
$409$	−11.4428			−0.565809			−0.282904	−	0.959148i	$-0.591298\pi$
$409$	−11.4428			−0.565809			−0.282904	+	0.959148i	$0.591298\pi$
$410$	42.2965	−	40.9430i	2.08888	−	2.02203i
$411$	−1.76093			−0.0868601
$412$	−2.45937	+	7.56917i	−0.121165	+	0.372906i
$413$	4.44530			0.218739
$414$	−25.3176	−	18.3943i	−1.24429	−	0.904031i
$415$	−25.6259	−	18.6183i	−1.25793	−	0.913938i
$416$	−9.15246	+	28.1684i	−0.448736	+	1.38107i
$417$	−3.80476	−	11.7099i	−0.186320	−	0.573434i
$418$	3.96349	−	2.87964i	0.193861	−	0.140848i
$419$	−28.6885			−1.40152			−0.700762	−	0.713395i	$-0.747156\pi$
$419$	−28.6885			−1.40152			−0.700762	+	0.713395i	$0.747156\pi$
$420$	−7.70341	+	5.59685i	−0.375888	+	0.273098i
$421$	−9.90562	+	7.19685i	−0.482770	+	0.350753i	−0.802397	−	0.596790i	$-0.796442\pi$
$421$	−9.90562	+	7.19685i	−0.482770	+	0.350753i	0.319627	+	0.947543i	$0.396442\pi$
$422$	3.54075	+	2.57251i	0.172361	+	0.125228i
$423$	8.36142	−	25.7338i	0.406546	−	1.25122i
$424$	17.3969			0.844870
$425$	−27.0819	−	19.6761i	−1.31366	−	0.954432i
$426$	−7.58659	−	23.3491i	−0.367572	−	1.13127i
$427$	−9.47060	+	6.88079i	−0.458314	+	0.332985i
$428$	14.0916	−	43.3694i	0.681141	−	2.09634i
$429$	−0.601542	−	1.85135i	−0.0290427	−	0.0893842i
$430$	4.20670	+	12.9469i	0.202865	+	0.624354i
$431$	11.4942	+	35.3755i	0.553657	+	1.70398i	0.699465	+	0.714667i	$0.253422\pi$
$431$	11.4942	+	35.3755i	0.553657	+	1.70398i	−0.145808	+	0.989313i	$0.546578\pi$
$432$	−0.941835	−	2.89867i	−0.0453141	−	0.139462i
$433$	−1.22305	+	3.76415i	−0.0587758	+	0.180893i	−0.976134	−	0.217170i	$-0.930317\pi$
$433$	−1.22305	+	3.76415i	−0.0587758	+	0.180893i	0.917358	+	0.398063i	$0.130317\pi$
$434$	4.58683	−	3.33252i	0.220175	−	0.159966i
$435$	1.58909	+	4.89070i	0.0761908	+	0.234491i
$436$	−30.6408	−	22.2619i	−1.46743	−	1.06615i
$437$	−25.9180			−1.23982
$438$	3.49147	−	10.7456i	0.166829	−	0.513446i
$439$	−10.8264	−	7.86583i	−0.516715	−	0.375416i	0.298650	−	0.954363i	$-0.403464\pi$
$439$	−10.8264	−	7.86583i	−0.516715	−	0.375416i	−0.815365	+	0.578947i	$0.803464\pi$
$440$	−4.57470	+	3.32371i	−0.218090	+	0.158452i
$441$	2.02245	−	1.46940i	0.0963073	−	0.0699713i
$442$	45.9987			2.18794
$443$	−33.2522	+	24.1591i	−1.57986	+	1.14784i	−0.663006	+	0.748614i	$0.730719\pi$
$443$	−33.2522	+	24.1591i	−1.57986	+	1.14784i	−0.916855	+	0.399221i	$0.869281\pi$
$444$	2.52578	+	7.77356i	0.119868	+	0.368917i
$445$	18.8693	−	58.0738i	0.894491	−	2.75296i
$446$	−3.03329	−	2.20381i	−0.143630	−	0.104354i
$447$	7.95416	+	5.77904i	0.376219	+	0.273339i
$448$	12.5187			0.591455
$449$	−7.14626	+	21.9939i	−0.337253	+	1.03796i	0.628349	+	0.777932i	$0.283731\pi$
$449$	−7.14626	+	21.9939i	−0.337253	+	1.03796i	−0.965602	+	0.260026i	$0.916269\pi$
$450$	−61.8246			−2.91444
$451$	2.01418	−	1.94973i	0.0948441	−	0.0918090i
$452$	4.05464			0.190714
$453$	1.11803	−	3.44093i	0.0525294	−	0.161669i
$454$	−40.0973			−1.88186
$455$	−20.1150	−	14.6144i	−0.943005	−	0.685133i
$456$	−8.99471	−	6.53504i	−0.421216	−	0.306031i
$457$	−6.46841	+	19.9077i	−0.302579	+	0.931243i	0.677990	+	0.735071i	$0.262851\pi$
$457$	−6.46841	+	19.9077i	−0.302579	+	0.931243i	−0.980569	+	0.196172i	$0.937149\pi$
$458$	−0.896675	−	2.75968i	−0.0418989	−	0.128952i
$459$	9.90192	−	7.19417i	0.462182	−	0.335795i
$460$	72.5006			3.38036
$461$	−2.15084	+	1.56268i	−0.100175	+	0.0727812i	−0.636745	−	0.771074i	$-0.719720\pi$
$461$	−2.15084	+	1.56268i	−0.100175	+	0.0727812i	0.536570	+	0.843856i	$0.319720\pi$
$462$	−0.582317	+	0.423078i	−0.0270918	+	0.0196834i
$463$	12.7098	+	9.23421i	0.590674	+	0.429150i	0.842557	−	0.538608i	$-0.181050\pi$
$463$	12.7098	+	9.23421i	0.590674	+	0.429150i	−0.251882	+	0.967758i	$0.581050\pi$
$464$	−0.445281	+	1.37043i	−0.0206716	+	0.0636208i
$465$	−6.81992			−0.316266
$466$	−35.3129	−	25.6563i	−1.63584	−	1.18851i
$467$	1.06292	+	3.27132i	0.0491859	+	0.151379i	0.972633	−	0.232347i	$-0.0746406\pi$
$467$	1.06292	+	3.27132i	0.0491859	+	0.151379i	−0.923447	+	0.383726i	$0.874641\pi$
$468$	43.2973	−	31.4573i	2.00142	−	1.45412i
$469$	0.228845	−	0.704311i	0.0105671	−	0.0325221i
$470$	30.7496	+	94.6375i	1.41837	+	4.36530i
$471$	−2.00486	−	6.17034i	−0.0923793	−	0.284314i
$472$	−4.48671	−	13.8087i	−0.206518	−	0.635596i
$473$	0.200325	+	0.616537i	0.00921095	+	0.0283484i
$474$	−3.54872	+	10.9218i	−0.162998	+	0.501656i
$475$	−41.4243	+	30.0965i	−1.90068	+	1.38092i
$476$	−3.31103	−	10.1903i	−0.151761	−	0.467072i
$477$	10.7722	+	7.82650i	0.493227	+	0.358351i
$478$	32.8210			1.50120
$479$	−10.9069	+	33.5679i	−0.498348	+	1.53376i	0.313325	+	0.949646i	$0.398557\pi$
$479$	−10.9069	+	33.5679i	−0.498348	+	1.53376i	−0.811673	+	0.584112i	$0.801443\pi$
$480$	−10.6575	−	7.74313i	−0.486446	−	0.353424i
$481$	−17.2666	+	12.5450i	−0.787291	+	0.572001i
$482$	37.9437	−	27.5677i	1.72829	−	1.25568i
$483$	3.80787			0.173264
$484$	29.7730	−	21.6314i	1.35332	−	0.983243i
$485$	1.80936	+	5.56862i	0.0821586	+	0.252858i
$486$	10.7955	−	33.2252i	0.489695	−	1.50713i
$487$	−14.8433	−	10.7843i	−0.672612	−	0.488681i	0.198287	−	0.980144i	$-0.436462\pi$
$487$	−14.8433	−	10.7843i	−0.672612	−	0.488681i	−0.870899	+	0.491463i	$0.836462\pi$
$488$	30.9330	+	22.4741i	1.40027	+	1.01736i
$489$	−8.20219			−0.370916
$490$	−2.84094	+	8.74353i	−0.128341	+	0.394992i
$491$	15.9588			0.720211			0.360105	−	0.932912i	$-0.382741\pi$
$491$	15.9588			0.720211			0.360105	+	0.932912i	$0.382741\pi$
$492$	−13.6220	−	7.22211i	−0.614128	−	0.325598i
$493$	−5.78657			−0.260614
$494$	21.7423	−	66.9158i	0.978230	−	3.01068i
$495$	−4.32793			−0.194526
$496$	−1.54605	−	1.12327i	−0.0694197	−	0.0504363i
$497$	−12.0808	−	8.77719i	−0.541897	−	0.393711i
$498$	−4.06955	+	12.5248i	−0.182361	+	0.561249i
$499$	−0.741166	−	2.28108i	−0.0331792	−	0.102115i	0.933095	−	0.359629i	$-0.117097\pi$
$499$	−0.741166	−	2.28108i	−0.0331792	−	0.102115i	−0.966275	+	0.257514i	$0.917097\pi$
$500$	61.4113	−	44.6179i	2.74640	−	1.99537i
$501$	13.1343			0.586797
$502$	−30.4375	+	22.1141i	−1.35849	+	0.987001i
$503$	−1.72190	+	1.25103i	−0.0767756	+	0.0557807i	−0.625511	−	0.780215i	$-0.715109\pi$
$503$	−1.72190	+	1.25103i	−0.0767756	+	0.0557807i	0.548735	+	0.835996i	$0.315109\pi$
$504$	−6.60577	−	4.79937i	−0.294244	−	0.213781i
$505$	−1.62284	+	4.99460i	−0.0722156	+	0.222257i
$506$	5.48047			0.243637
$507$	−15.1798	−	11.0288i	−0.674158	−	0.489805i
$508$	21.4672	+	66.0693i	0.952453	+	2.93135i
$509$	19.3452	−	14.0551i	0.857463	−	0.622983i	−0.0697306	−	0.997566i	$-0.522214\pi$
$509$	19.3452	−	14.0551i	0.857463	−	0.622983i	0.927194	+	0.374583i	$0.122214\pi$
$510$	−6.32223	+	19.4578i	−0.279953	+	0.861608i
$511$	−2.12364	−	6.53588i	−0.0939442	−	0.289130i
$512$	−2.72253	−	8.37908i	−0.120320	−	0.370307i
$513$	−5.78523	−	17.8051i	−0.255424	−	0.786115i
$514$	−9.11691	−	28.0590i	−0.402130	−	1.23763i
$515$	2.85630	−	8.79078i	0.125864	−	0.387368i
$516$	2.88453	−	2.09574i	0.126985	−	0.0922596i
$517$	1.46431	+	4.50668i	0.0644003	+	0.198204i
$518$	6.38449	+	4.63861i	0.280518	+	0.203809i
$519$	−12.5171			−0.549438
$520$	−25.0951	+	77.2348i	−1.10049	+	3.38697i
$521$	23.2947	+	16.9246i	1.02056	+	0.741480i	0.966397	−	0.257053i	$-0.0827514\pi$
$521$	23.2947	+	16.9246i	1.02056	+	0.741480i	0.0541616	+	0.998532i	$0.482751\pi$
$522$	−8.64607	+	6.28174i	−0.378428	+	0.274944i
$523$	−3.52497	+	2.56104i	−0.154136	+	0.111986i	−0.662180	−	0.749345i	$-0.730369\pi$
$523$	−3.52497	+	2.56104i	−0.154136	+	0.111986i	0.508044	+	0.861331i	$0.330369\pi$
$524$	−60.0290			−2.62238
$525$	6.08606	−	4.42178i	0.265618	−	0.192982i
$526$	10.1456	+	31.2249i	0.442368	+	1.36147i
$527$	2.37147	−	7.29863i	0.103303	−	0.317933i
$528$	0.196277	+	0.142604i	0.00854188	+	0.00620604i
$529$	−4.84874	−	3.52282i	−0.210815	−	0.153166i
$530$	−48.9675			−2.12701
$531$	3.43403	−	10.5689i	0.149024	−	0.458650i
$532$	−16.3892			−0.710562
$533$	6.94364	−	39.6562i	0.300762	−	1.71770i
$534$	−25.3872			−1.09861
$535$	−16.3658	+	50.3689i	−0.707557	+	2.17764i
$536$	−2.41882			−0.104477
$537$	4.40128	+	3.19772i	0.189929	+	0.137992i
$538$	−17.8357	−	12.9584i	−0.768951	−	0.558676i
$539$	−0.135287	+	0.416371i	−0.00582723	+	0.0179344i
$540$	16.1831	+	49.8064i	0.696409	+	2.14333i
$541$	37.1360	−	26.9809i	1.59660	−	1.16000i	0.702949	−	0.711240i	$-0.251866\pi$
$541$	37.1360	−	26.9809i	1.59660	−	1.16000i	0.893653	−	0.448759i	$-0.148134\pi$
$542$	24.5990			1.05662
$543$	4.65329	−	3.38081i	0.199692	−	0.145084i
$544$	11.9926	−	8.71310i	0.514177	−	0.373571i
$545$	35.5861	+	25.8548i	1.52434	+	1.10750i
$546$	−3.19438	+	9.83128i	−0.136707	+	0.420740i
$547$	33.1993			1.41950			0.709749	−	0.704454i	$-0.248808\pi$
$547$	33.1993			1.41950			0.709749	+	0.704454i	$0.248808\pi$
$548$	6.85918	+	4.98348i	0.293010	+	0.212884i
$549$	9.04321	+	27.8321i	0.385955	+	1.18785i
$550$	8.75935	−	6.36404i	0.373500	−	0.271364i
$551$	−2.73514	+	8.41790i	−0.116521	+	0.358615i
$552$	−3.84335	−	11.8286i	−0.163584	−	0.503459i
$553$	2.15846	+	6.64305i	0.0917870	+	0.282491i
$554$	23.7323	+	73.0404i	1.00829	+	3.10319i
$555$	−2.93343	−	9.02816i	−0.124517	−	0.383224i
$556$	−18.3190	+	56.3800i	−0.776897	+	2.39104i
$557$	−7.53135	+	5.47185i	−0.319114	+	0.231850i	−0.735797	−	0.677202i	$-0.763192\pi$
$557$	−7.53135	+	5.47185i	−0.319114	+	0.231850i	0.416684	+	0.909052i	$0.363192\pi$
$558$	−4.37984	−	13.4798i	−0.185413	−	0.570643i
$559$	7.53204	+	5.47234i	0.318571	+	0.231455i
$560$	3.09878			0.130948
$561$	−0.301068	+	0.926592i	−0.0127111	+	0.0391207i
$562$	29.9625	+	21.7690i	1.26389	+	0.918271i
$563$	9.79590	−	7.11714i	0.412848	−	0.299952i	−0.361906	−	0.932215i	$-0.617874\pi$
$563$	9.79590	−	7.11714i	0.412848	−	0.299952i	0.774754	+	0.632263i	$0.217874\pi$
$564$	21.0850	−	15.3192i	0.887839	−	0.645053i
$565$	−4.70904			−0.198111
$566$	−26.9251	+	19.5622i	−1.13175	+	0.822262i
$567$	−1.46756	−	4.51668i	−0.0616316	−	0.189683i
$568$	−15.0718	+	46.3861i	−0.632397	+	1.94632i
$569$	−21.2928	−	15.4701i	−0.892640	−	0.648541i	0.0439247	−	0.999035i	$-0.486014\pi$
$569$	−21.2928	−	15.4701i	−0.892640	−	0.648541i	−0.936565	+	0.350494i	$0.886014\pi$
$570$	25.3176	+	18.3943i	1.06044	+	0.770453i
$571$	−43.5777			−1.82367			−0.911836	−	0.410555i	$-0.865335\pi$
$571$	−43.5777			−1.82367			−0.911836	+	0.410555i	$0.865335\pi$
$572$	−2.89627	+	8.91380i	−0.121099	+	0.372705i
$573$	−0.952661			−0.0397980
$574$	−14.7389	+	2.08937i	−0.615191	+	0.0872087i
$575$	−57.2790			−2.38870
$576$	9.67083	−	29.7638i	0.402951	−	1.24016i
$577$	5.81372			0.242028			0.121014	−	0.992651i	$-0.461385\pi$
$577$	5.81372			0.242028			0.121014	+	0.992651i	$0.461385\pi$
$578$	13.3491	+	9.69865i	0.555247	+	0.403411i
$579$	8.48187	+	6.16244i	0.352495	+	0.256102i
$580$	7.65104	−	23.5475i	0.317692	−	0.977756i
$581$	2.47525	+	7.61803i	0.102691	+	0.316049i
$582$	1.96943	−	1.43088i	0.0816356	−	0.0593117i
$583$	−2.33186			−0.0965757
$584$	−18.1594	+	13.1935i	−0.751439	+	0.545953i
$585$	−50.2852	+	36.5344i	−2.07904	+	1.51051i
$586$	−55.8511	−	40.5782i	−2.30719	−	1.67627i
$587$	−3.08323	+	9.48921i	−0.127259	+	0.391662i	−0.994306	−	0.106564i	$-0.966015\pi$
$587$	−3.08323	+	9.48921i	−0.127259	+	0.391662i	0.867047	+	0.498226i	$0.166015\pi$
$588$	2.40791			0.0993003
$589$	−9.49663	−	6.89970i	−0.391302	−	0.284297i
$590$	12.6289	+	38.8676i	0.519922	+	1.60015i
$591$	10.5371	−	7.65563i	0.433437	−	0.314911i
$592$	0.821982	−	2.52980i	0.0337832	−	0.103974i
$593$	−2.97353	−	9.15159i	−0.122108	−	0.375811i	0.871255	−	0.490831i	$-0.163307\pi$
$593$	−2.97353	−	9.15159i	−0.122108	−	0.375811i	−0.993363	+	0.115020i	$0.963307\pi$
$594$	1.22331	+	3.76497i	0.0501932	+	0.154479i
$595$	3.84541	+	11.8350i	0.157647	+	0.485186i
$596$	−14.6283	−	45.0211i	−0.599197	−	1.84414i
$597$	−1.77721	+	5.46969i	−0.0727364	+	0.223860i
$598$	63.6763	−	46.2635i	2.60392	−	1.89186i
$599$	−1.25932	−	3.87578i	−0.0514544	−	0.158360i	0.922028	−	0.387124i	$-0.126532\pi$
$599$	−1.25932	−	3.87578i	−0.0514544	−	0.158360i	−0.973482	+	0.228764i	$0.926532\pi$
$600$	−19.8784	−	14.4425i	−0.811532	−	0.589612i
$601$	−11.2882			−0.460454			−0.230227	−	0.973137i	$-0.573947\pi$
$601$	−11.2882			−0.460454			−0.230227	+	0.973137i	$0.573947\pi$
$602$	1.06379	−	3.27401i	0.0433568	−	0.133438i
$603$	−1.49774	−	1.08817i	−0.0609927	−	0.0443138i
$604$	−14.0929	+	10.2391i	−0.573432	+	0.416623i
$605$	−34.5782	+	25.1225i	−1.40580	+	1.02138i
$606$	2.18342			0.0886952
$607$	−5.13577	+	3.73136i	−0.208454	+	0.151451i	−0.687114	−	0.726549i	$-0.741123\pi$
$607$	−5.13577	+	3.73136i	−0.208454	+	0.151451i	0.478660	+	0.878001i	$0.341123\pi$
$608$	−7.00669	−	21.5644i	−0.284159	−	0.874551i
$609$	0.401848	−	1.23676i	0.0162837	−	0.0501160i
$610$	−87.0678	−	63.2584i	−3.52527	−	2.56126i
$611$	55.0567	+	40.0011i	2.22736	+	1.61827i
$612$	−26.7856			−1.08275
$613$	4.06952	−	12.5247i	0.164366	−	0.505868i	−0.834623	−	0.550822i	$-0.814314\pi$
$613$	4.06952	−	12.5247i	0.164366	−	0.505868i	0.998989	+	0.0449544i	$0.0143143\pi$
$614$	9.18673			0.370746
$615$	15.8205	+	8.38771i	0.637945	+	0.338225i
$616$	1.42994			0.0576141
$617$	−4.53723	+	13.9641i	−0.182662	+	0.562175i	−0.999900	−	0.0141244i	$-0.995504\pi$
$617$	−4.53723	+	13.9641i	−0.182662	+	0.562175i	0.817238	+	0.576300i	$0.195504\pi$
$618$	−3.84293			−0.154585
$619$	−3.47410	−	2.52408i	−0.139636	−	0.101451i	0.515774	−	0.856724i	$-0.327504\pi$
$619$	−3.47410	−	2.52408i	−0.139636	−	0.101451i	−0.655410	+	0.755273i	$0.727504\pi$
$620$	26.5650	+	19.3006i	1.06688	+	0.775131i
$621$	6.47171	−	19.9179i	0.259701	−	0.799276i
$622$	−8.25420	−	25.4038i	−0.330963	−	1.01860i
$623$	−12.4924	+	9.07626i	−0.500497	+	0.363632i
$624$	3.48429			0.139483
$625$	−28.2924	+	20.5557i	−1.13170	+	0.822226i
$626$	6.28111	−	4.56349i	0.251044	−	0.182394i
$627$	1.20564	+	0.875946i	0.0481485	+	0.0349819i
$628$	−9.65291	+	29.7086i	−0.385193	+	1.18550i
$629$	10.6819			0.425916
$630$	18.5934	+	13.5089i	0.740779	+	0.538207i
$631$	2.77823	+	8.55052i	0.110600	+	0.340391i	0.991004	−	0.133833i	$-0.0427287\pi$
$631$	2.77823	+	8.55052i	0.110600	+	0.340391i	−0.880404	+	0.474224i	$0.842729\pi$
$632$	18.4571	−	13.4099i	0.734185	−	0.533416i
$633$	−0.411395	+	1.26614i	−0.0163515	+	0.0503247i
$634$	−11.5560	−	35.5658i	−0.458949	−	1.41250i
$635$	−24.9319	−	76.7324i	−0.989391	−	3.04503i
$636$	3.96323	+	12.1976i	0.157152	+	0.483665i
$637$	1.94294	+	5.97974i	0.0769819	+	0.236926i
$638$	0.578358	−	1.78000i	0.0228974	−	0.0704710i
$639$	−30.2006	+	21.9420i	−1.19472	+	0.868013i
$640$	24.0523	+	74.0255i	0.950752	+	2.92611i
$641$	−2.53724	−	1.84341i	−0.100215	−	0.0728103i	0.536549	−	0.843869i	$-0.319728\pi$
$641$	−2.53724	−	1.84341i	−0.100215	−	0.0728103i	−0.636764	+	0.771059i	$0.719728\pi$
$642$	22.0190			0.869021
$643$	−6.10165	+	18.7790i	−0.240626	+	0.740570i	0.755699	+	0.654919i	$0.227297\pi$
$643$	−6.10165	+	18.7790i	−0.240626	+	0.740570i	−0.996325	+	0.0856513i	$0.972703\pi$
$644$	−14.8325	−	10.7764i	−0.584481	−	0.424650i
$645$	−3.35008	+	2.43397i	−0.131909	+	0.0958377i
$646$	−28.4891	+	20.6985i	−1.12089	+	0.814373i
$647$	47.1220			1.85256			0.926278	−	0.376840i	$-0.122989\pi$
$647$	47.1220			1.85256			0.926278	+	0.376840i	$0.122989\pi$
$648$	−12.5492	+	9.11751i	−0.492978	+	0.358170i
$649$	0.601392	+	1.85089i	0.0236067	+	0.0726540i
$650$	48.0506	−	147.885i	1.88470	−	5.80051i
$651$	1.39525	+	1.01371i	0.0546840	+	0.0397303i
$652$	31.9493	+	23.2125i	1.25123	+	0.909071i
$653$	6.44792			0.252327			0.126163	−	0.992009i	$-0.459734\pi$
$653$	6.44792			0.252327			0.126163	+	0.992009i	$0.459734\pi$
$654$	5.65127	−	17.3928i	0.220982	−	0.680113i
$655$	69.7173			2.72408
$656$	2.20496	+	4.50717i	0.0860893	+	0.175976i
$657$	−17.1798			−0.670249
$658$	7.77595	−	23.9319i	0.303138	−	0.932963i
$659$	26.2912			1.02416			0.512080	−	0.858938i	$-0.328875\pi$
$659$	26.2912			1.02416			0.512080	+	0.858938i	$0.328875\pi$
$660$	−3.37254	−	2.45029i	−0.131276	−	0.0953775i
$661$	16.1653	+	11.7448i	0.628758	+	0.456820i	0.855970	−	0.517026i	$-0.172961\pi$
$661$	16.1653	+	11.7448i	0.628758	+	0.456820i	−0.227212	+	0.973845i	$0.572961\pi$
$662$	3.71398	−	11.4305i	0.144348	−	0.444258i
$663$	4.32381	+	13.3073i	0.167923	+	0.516813i
$664$	21.1660	−	15.3780i	0.821400	−	0.596782i
$665$	19.0343			0.738119
$666$	15.9605	−	11.5960i	0.618458	−	0.449336i
$667$	−8.01038	+	5.81988i	−0.310163	+	0.225347i
$668$	−51.1608	−	37.1705i	−1.97947	−	1.43817i
$669$	0.352433	−	1.08468i	0.0136259	−	0.0419361i
$670$	6.80830			0.263028
$671$	−4.14621	−	3.01240i	−0.160063	−	0.116292i
$672$	1.02942	+	3.16824i	0.0397109	+	0.122218i
$673$	−27.1029	+	19.6914i	−1.04474	+	0.759047i	−0.971205	−	0.238246i	$-0.923428\pi$
$673$	−27.1029	+	19.6914i	−1.04474	+	0.759047i	−0.0735333	+	0.997293i	$0.523428\pi$
$674$	−20.6771	+	63.6377i	−0.796453	+	2.45123i
$675$	−12.7854	−	39.3495i	−0.492111	−	1.51456i
$676$	27.9167	+	85.9188i	1.07372	+	3.30457i
$677$	10.5752	+	32.5470i	0.406436	+	1.25088i	0.919690	+	0.392645i	$0.128440\pi$
$677$	10.5752	+	32.5470i	0.406436	+	1.25088i	−0.513254	+	0.858237i	$0.671560\pi$
$678$	0.605001	+	1.86200i	0.0232349	+	0.0715097i
$679$	0.457550	−	1.40819i	0.0175591	−	0.0540415i
$680$	32.8824	−	23.8904i	1.26098	−	0.916157i
$681$	−3.76908	−	11.6000i	−0.144432	−	0.444515i
$682$	2.00811	+	1.45897i	0.0768943	+	0.0558670i
$683$	−44.3897			−1.69852			−0.849262	−	0.527972i	$-0.822953\pi$
$683$	−44.3897			−1.69852			−0.849262	+	0.527972i	$0.822953\pi$
$684$	−12.6608	+	38.9659i	−0.484098	+	1.48990i
$685$	−7.96620	−	5.78779i	−0.304373	−	0.221140i
$686$	1.88084	−	1.36651i	0.0718108	−	0.0521736i
$687$	0.714084	−	0.518812i	0.0272440	−	0.0197939i
$688$	−1.16034			−0.0442374
$689$	−27.0933	+	19.6844i	−1.03217	+	0.749917i
$690$	10.8180	+	33.2942i	0.411832	+	1.26749i
$691$	−10.1955	+	31.3785i	−0.387854	+	1.19369i	0.546534	+	0.837437i	$0.315947\pi$
$691$	−10.1955	+	31.3785i	−0.387854	+	1.19369i	−0.934388	+	0.356256i	$0.884053\pi$
$692$	48.7566	+	35.4238i	1.85345	+	1.34661i
$693$	0.885427	+	0.643300i	0.0336346	+	0.0244369i
$694$	−17.1631			−0.651502
$695$	21.2755	−	65.4794i	0.807027	−	2.48377i
$696$	−4.24741			−0.160998
$697$	−14.4777	+	14.0144i	−0.548382	+	0.530833i
$698$	53.1650			2.01233
$699$	4.10295	−	12.6276i	0.155188	−	0.477619i
$700$	−36.2203			−1.36900
$701$	9.66925	+	7.02512i	0.365202	+	0.265335i	0.755219	−	0.655473i	$-0.227531\pi$
$701$	9.66925	+	7.02512i	0.365202	+	0.265335i	−0.390016	+	0.920808i	$0.627531\pi$
$702$	45.9955	+	33.4177i	1.73599	+	1.26127i
$703$	5.04903	−	15.5393i	0.190428	−	0.586077i
$704$	1.69362	+	5.21244i	0.0638309	+	0.196451i
$705$	−24.4880	+	17.7916i	−0.922271	+	0.670069i
$706$	−23.3467			−0.878664
$707$	1.07440	−	0.780598i	0.0404070	−	0.0293574i
$708$	8.65961	−	6.29157i	0.325448	−	0.236452i
$709$	−39.3991	−	28.6251i	−1.47966	−	1.07504i	−0.977665	−	0.210169i	$-0.932599\pi$
$709$	−39.3991	−	28.6251i	−1.47966	−	1.07504i	−0.501997	−	0.864869i	$-0.667401\pi$
$710$	42.4228	−	130.564i	1.59210	−	4.89998i
$711$	17.4615			0.654859
$712$	40.8028	+	29.6450i	1.52915	+	1.11099i
$713$	−4.05781	−	12.4887i	−0.151966	−	0.467704i
$714$	4.18562	−	3.04103i	0.156643	−	0.113808i
$715$	3.36371	−	10.3524i	0.125796	−	0.387159i
$716$	−8.09427	−	24.9116i	−0.302497	−	0.930990i
$717$	3.08513	+	9.49505i	0.115216	+	0.354599i
$718$	−4.65592	−	14.3295i	−0.173758	−	0.534771i
$719$	−6.76697	−	20.8266i	−0.252366	−	0.776701i	−0.994337	−	0.106270i	$-0.966109\pi$
$719$	−6.76697	−	20.8266i	−0.252366	−	0.776701i	0.741972	−	0.670431i	$-0.233891\pi$
$720$	2.39384	−	7.36747i	0.0892130	−	0.274569i
$721$	−1.89101	+	1.37390i	−0.0704248	+	0.0511666i
$722$	2.99492	+	9.21742i	0.111459	+	0.343037i
$723$	11.5419	+	8.38571i	0.429249	+	0.311868i
$724$	−27.6933			−1.02922
$725$	−6.04469	+	18.6036i	−0.224494	+	0.690922i
$726$	14.3762	+	10.4449i	0.533550	+	0.387647i
$727$	2.42552	−	1.76224i	0.0899576	−	0.0653580i	−0.541897	−	0.840445i	$-0.682294\pi$
$727$	2.42552	−	1.76224i	0.0899576	−	0.0653580i	0.631855	+	0.775087i	$0.282294\pi$
$728$	16.6142	−	12.0709i	0.615762	−	0.447377i
$729$	−3.62060			−0.134096
$730$	51.1135	−	37.1361i	1.89180	−	1.37447i
$731$	−1.43991	−	4.43159i	−0.0532571	−	0.163908i
$732$	−8.71047	+	26.8081i	−0.321948	+	0.990854i
$733$	24.6046	+	17.8763i	0.908790	+	0.660275i	0.940709	−	0.339216i	$-0.110162\pi$
$733$	24.6046	+	17.8763i	0.908790	+	0.660275i	−0.0319182	+	0.999490i	$0.510162\pi$
$734$	7.85144	+	5.70441i	0.289802	+	0.210553i
$735$	−2.79653			−0.103151
$736$	7.83810	−	24.1232i	0.288916	−	0.889193i
$737$	0.324215			0.0119426
$738$	−6.41839	+	36.6564i	−0.236264	+	1.34934i
$739$	43.5715			1.60280			0.801402	−	0.598126i	$-0.204088\pi$
$739$	43.5715			1.60280			0.801402	+	0.598126i	$0.204088\pi$
$740$	−14.1237	+	43.4683i	−0.519198	+	1.59793i
$741$	21.4023			0.786234
$742$	10.0180	+	7.27849i	0.367771	+	0.267202i
$743$	−2.80769	−	2.03991i	−0.103004	−	0.0748369i	0.535091	−	0.844794i	$-0.320277\pi$
$743$	−2.80769	−	2.03991i	−0.103004	−	0.0748369i	−0.638095	+	0.769958i	$0.720277\pi$
$744$	1.74069	−	5.35728i	0.0638166	−	0.196407i
$745$	16.9892	+	52.2873i	0.622435	+	1.91566i
$746$	−3.05573	+	2.22011i	−0.111878	+	0.0812842i
$747$	20.0243			0.732650
$748$	3.79501	−	2.75724i	0.138759	−	0.100815i
$749$	10.8350	−	7.87207i	0.395901	−	0.287639i
$750$	29.6530	+	21.5442i	1.08278	+	0.786683i
$751$	−2.29854	+	7.07416i	−0.0838748	+	0.258140i	−0.984195	−	0.177088i	$-0.943332\pi$
$751$	−2.29854	+	7.07416i	−0.0838748	+	0.258140i	0.900320	+	0.435228i	$0.143332\pi$
$752$	−8.48169			−0.309295
$753$	−9.25864	−	6.72679i	−0.337403	−	0.245138i
$754$	−8.30614	−	25.5637i	−0.302492	−	0.930973i
$755$	16.3674	−	11.8916i	0.595671	−	0.432780i
$756$	4.09238	−	12.5950i	0.148838	−	0.458077i
$757$	3.18894	+	9.81456i	0.115904	+	0.356716i	0.992135	−	0.125176i	$-0.0399496\pi$
$757$	3.18894	+	9.81456i	0.115904	+	0.356716i	−0.876230	+	0.481892i	$0.839950\pi$
$758$	0.328291	+	1.01037i	0.0119241	+	0.0366985i
$759$	0.515156	+	1.58549i	0.0186990	+	0.0575496i
$760$	−19.2116	−	59.1274i	−0.696879	−	2.14477i
$761$	−10.2000	+	31.3924i	−0.369750	+	1.13797i	0.577203	+	0.816601i	$0.304144\pi$
$761$	−10.2000	+	31.3924i	−0.369750	+	1.13797i	−0.946953	+	0.321373i	$0.895856\pi$
$762$	−27.1376	+	19.7166i	−0.983092	+	0.714258i
$763$	−3.43731	−	10.5790i	−0.124439	−	0.382984i
$764$	3.71082	+	2.69607i	0.134253	+	0.0975402i
$765$	31.1087			1.12474
$766$	17.3977	−	53.5447i	0.628605	−	1.93465i
$767$	22.6118	+	16.4284i	0.816465	+	0.593196i
$768$	11.8557	−	8.61368i	0.427806	−	0.310819i
$769$	26.5941	−	19.3217i	0.959007	−	0.696759i	0.00608715	−	0.999981i	$-0.498062\pi$
$769$	26.5941	−	19.3217i	0.959007	−	0.696759i	0.952920	+	0.303222i	$0.0980624\pi$
$770$	−4.02489			−0.145047
$771$	7.26042	−	5.27500i	0.261478	−	0.189975i
$772$	−15.5987	−	48.0080i	−0.561411	−	1.72785i
$773$	−6.19879	+	19.0779i	−0.222955	+	0.686185i	0.775538	+	0.631301i	$0.217479\pi$
$773$	−6.19879	+	19.0779i	−0.222955	+	0.686185i	−0.998493	+	0.0548836i	$0.982521\pi$
$774$	−6.96228	−	5.05839i	−0.250254	−	0.181820i
$775$	−20.9876	−	15.2484i	−0.753898	−	0.547739i
$776$	−4.83616			−0.173608
$777$	−0.741805	+	2.28304i	−0.0266121	+	0.0819036i
$778$	−46.0396			−1.65060
$779$	13.5440	+	27.6854i	0.485264	+	0.991931i
$780$	−59.8689			−2.14365
$781$	2.02020	−	6.21752i	0.0722883	−	0.222480i
$782$	−39.3930			−1.40869
$783$	−5.78616	−	4.20389i	−0.206781	−	0.150235i
$784$	−0.633962	−	0.460600i	−0.0226415	−	0.0164500i
$785$	11.2108	−	34.5034i	0.400132	−	1.23148i
$786$	−8.95704	−	27.5669i	−0.319487	−	0.983280i
$787$	5.13724	−	3.73242i	0.183123	−	0.133047i	−0.492447	−	0.870342i	$-0.663898\pi$
$787$	5.13724	−	3.73242i	0.183123	−	0.133047i	0.675570	+	0.737296i	$0.263898\pi$
$788$	−62.7098			−2.23395
$789$	−8.07962	+	5.87019i	−0.287642	+	0.208984i
$790$	−51.9517	+	37.7451i	−1.84836	+	1.34291i
$791$	0.963394	+	0.699947i	0.0342543	+	0.0248872i
$792$	1.10464	−	3.39974i	0.0392518	−	0.120805i
$793$	−73.6030			−2.61372
$794$	−29.0388	−	21.0979i	−1.03055	−	0.748737i
$795$	−4.60287	−	14.1662i	−0.163247	−	0.502423i
$796$	22.4020	−	16.2760i	0.794020	−	0.576889i
$797$	−9.13418	+	28.1121i	−0.323549	+	0.995782i	0.648542	+	0.761179i	$0.275379\pi$
$797$	−9.13418	+	28.1121i	−0.323549	+	0.995782i	−0.972091	+	0.234603i	$0.924621\pi$
$798$	−2.44546	−	7.52637i	−0.0865685	−	0.266430i
$799$	−10.5253	−	32.3935i	−0.372358	−	1.14600i
$800$	−15.4849	−	47.6575i	−0.547473	−	1.68495i
$801$	11.9286	+	36.7126i	0.421478	+	1.29718i
$802$	3.14358	−	9.67495i	0.111004	−	0.341634i
$803$	2.43405	−	1.76844i	0.0858958	−	0.0624070i
$804$	−0.551036	−	1.69592i	−0.0194335	−	0.0598103i
$805$	17.2263	+	12.5157i	0.607148	+	0.441119i
$806$	35.6476			1.25563
$807$	2.07230	−	6.37789i	0.0729485	−	0.224512i
$808$	−3.50923	−	2.54960i	−0.123454	−	0.0896947i
$809$	−3.25728	+	2.36655i	−0.114520	+	0.0832035i	−0.643571	−	0.765386i	$-0.722548\pi$
$809$	−3.25728	+	2.36655i	−0.114520	+	0.0832035i	0.529051	+	0.848590i	$0.322548\pi$
$810$	35.3224	−	25.6632i	1.24110	−	0.901715i
$811$	29.3350			1.03009			0.515046	−	0.857162i	$-0.327775\pi$
$811$	29.3350			1.03009			0.515046	+	0.857162i	$0.327775\pi$
$812$	−5.06536	+	3.68020i	−0.177759	+	0.129150i
$813$	2.31227	+	7.11644i	0.0810949	+	0.249584i
$814$	−1.06764	+	3.28586i	−0.0374208	+	0.115169i
$815$	−37.1057	−	26.9588i	−1.29975	−	0.944327i
$816$	−1.41082	−	1.02502i	−0.0493885	−	0.0358829i
$817$	−7.12738			−0.249356
$818$	−8.22069	+	25.3007i	−0.287430	+	0.884617i
$819$	15.7180			0.549231
$820$	−37.8868	−	77.4446i	−1.32306	−	2.70448i
$821$	−16.5069			−0.576094			−0.288047	−	0.957616i	$-0.593006\pi$
$821$	−16.5069			−0.576094			−0.288047	+	0.957616i	$0.593006\pi$
$822$	−1.26508	+	3.89352i	−0.0441247	+	0.135802i
$823$	43.9083			1.53055			0.765274	−	0.643705i	$-0.222603\pi$
$823$	43.9083			1.53055			0.765274	+	0.643705i	$0.222603\pi$
$824$	6.17643	+	4.48744i	0.215166	+	0.156327i
$825$	2.66447	+	1.93585i	0.0927649	+	0.0673976i
$826$	3.19358	−	9.82884i	0.111119	−	0.341989i
$827$	14.8305	+	45.6435i	0.515706	+	1.58718i	0.781993	+	0.623287i	$0.214203\pi$
$827$	14.8305	+	45.6435i	0.515706	+	1.58718i	−0.266286	+	0.963894i	$0.585797\pi$
$828$	−37.0795	+	26.9399i	−1.28860	+	0.936225i
$829$	10.3496			0.359456			0.179728	−	0.983716i	$-0.442478\pi$
$829$	10.3496			0.359456			0.179728	+	0.983716i	$0.442478\pi$
$830$	−59.5764	+	43.2848i	−2.06793	+	1.50244i
$831$	−18.8996	+	13.7314i	−0.655621	+	0.476336i
$832$	63.6788	+	46.2653i	2.20766	+	1.60396i
$833$	0.972428	−	2.99282i	0.0336926	−	0.103695i
$834$	−28.6246			−0.991190
$835$	59.4178	+	43.1696i	2.05624	+	1.49394i
$836$	−2.21725	−	6.82399i	−0.0766852	−	0.236013i
$837$	7.67370	−	5.57527i	0.265242	−	0.192710i
$838$	−20.6103	+	63.4320i	−0.711971	+	2.19122i
$839$	8.51292	+	26.2001i	0.293898	+	0.904526i	0.983589	+	0.180422i	$0.0577465\pi$
$839$	8.51292	+	26.2001i	0.293898	+	0.904526i	−0.689691	+	0.724104i	$0.742254\pi$
$840$	2.82258	+	8.68700i	0.0973882	+	0.299730i
$841$	−7.91659	−	24.3648i	−0.272986	−	0.840164i
$842$	8.79631	+	27.0723i	0.303141	+	0.932972i
$843$	−3.48130	+	10.7143i	−0.119902	+	0.369021i
$844$	5.18570	−	3.76763i	0.178499	−	0.129687i
$845$	−32.4223	−	99.7855i	−1.11536	−	3.43272i
$846$	−50.8920	−	36.9752i	−1.74970	−	1.27123i
$847$	10.8083			0.371379
$848$	1.28978	−	3.96954i	0.0442912	−	0.136314i
$849$	−8.19023	−	5.95055i	−0.281088	−	0.204222i
$850$	−62.9612	+	45.7440i	−2.15955	+	1.56901i
$851$	14.7870	−	10.7434i	0.506893	−	0.368279i
$852$	−35.9564			−1.23185
$853$	15.7171	−	11.4192i	0.538145	−	0.390985i	−0.285251	−	0.958453i	$-0.592077\pi$
$853$	15.7171	−	11.4192i	0.538145	−	0.390985i	0.823396	+	0.567468i	$0.192077\pi$
$854$	8.41001	+	25.8833i	0.287785	+	0.885710i
$855$	14.7042	−	45.2548i	0.502872	−	1.54768i
$856$	−35.3894	−	25.7119i	−1.20958	−	0.878814i
$857$	−38.0877	−	27.6723i	−1.30105	−	0.945268i	−0.301085	−	0.953597i	$-0.597349\pi$
$857$	−38.0877	−	27.6723i	−1.30105	−	0.945268i	−0.999965	+	0.00832924i	$0.997349\pi$
$858$	−4.52562			−0.154502
$859$	12.9743	−	39.9307i	0.442676	−	1.36242i	−0.442336	−	0.896849i	$-0.645850\pi$
$859$	12.9743	−	39.9307i	0.442676	−	1.36242i	0.885012	−	0.465568i	$-0.154150\pi$
$860$	19.9375			0.679863
$861$	−1.98989	−	4.06754i	−0.0678152	−	0.138621i
$862$	86.4751			2.94535
$863$	12.1311	−	37.3357i	0.412947	−	1.27092i	−0.501127	−	0.865374i	$-0.667081\pi$
$863$	12.1311	−	37.3357i	0.412947	−	1.27092i	0.914074	−	0.405547i	$-0.132919\pi$
$864$	18.3217			0.623318
$865$	−56.6256	−	41.1409i	−1.92533	−	1.39883i
$866$	7.44410	+	5.40846i	0.252961	+	0.183787i
$867$	−1.55101	+	4.77351i	−0.0526749	+	0.162117i
$868$	−2.56595	−	7.89720i	−0.0870942	−	0.268048i
$869$	−2.47396	+	1.79744i	−0.0839235	+	0.0609740i
$870$	11.9553			0.405321
$871$	3.76697	−	2.73686i	0.127639	−	0.0927351i
$872$	−29.3927	+	21.3550i	−0.995361	+	0.723172i
$873$	−2.99457	−	2.17568i	−0.101351	−	0.0736356i
$874$	−18.6199	+	57.3062i	−0.629828	+	1.93841i
$875$	22.2938			0.753668
$876$	−13.3874	−	9.72649i	−0.452317	−	0.328628i
$877$	10.2019	+	31.3984i	0.344495	+	1.06025i	0.961854	+	0.273565i	$0.0882029\pi$
$877$	10.2019	+	31.3984i	0.344495	+	1.06025i	−0.617358	+	0.786682i	$0.711797\pi$
$878$	−25.1697	+	18.2869i	−0.849436	+	0.617151i
$879$	6.48925	−	19.9719i	0.218877	−	0.673634i
$880$	0.419226	+	1.29024i	0.0141321	+	0.0434941i
$881$	10.4067	+	32.0284i	0.350610	+	1.07907i	0.958512	+	0.285053i	$0.0920114\pi$
$881$	10.4067	+	32.0284i	0.350610	+	1.07907i	−0.607902	+	0.794012i	$0.707989\pi$
$882$	−1.79596	−	5.52741i	−0.0604733	−	0.186118i
$883$	−11.6137	−	35.7434i	−0.390833	−	1.20286i	−0.932160	−	0.362048i	$-0.882078\pi$
$883$	−11.6137	−	35.7434i	−0.390833	−	1.20286i	0.541327	−	0.840812i	$-0.317922\pi$
$884$	20.8180	−	64.0713i	0.700187	−	2.15495i
$885$	−10.0572	+	7.30699i	−0.338070	+	0.245622i
$886$	29.5284	+	90.8790i	0.992026	+	3.05314i
$887$	−0.911311	−	0.662107i	−0.0305988	−	0.0222314i	0.572381	−	0.819988i	$-0.306020\pi$
$887$	−0.911311	−	0.662107i	−0.0305988	−	0.0222314i	−0.602980	+	0.797757i	$0.706020\pi$
$888$	7.84065			0.263115
$889$	−6.30477	+	19.4041i	−0.211455	+	0.650792i
$890$	−114.849	−	83.4424i	−3.84974	−	2.79700i
$891$	1.68207	−	1.22210i	0.0563515	−	0.0409418i
$892$	−4.44248	+	3.22765i	−0.148745	+	0.108070i
$893$	−52.0989			−1.74342
$894$	18.4922	−	13.4354i	0.618472	−	0.449346i
$895$	9.40063	+	28.9322i	0.314228	+	0.967095i
$896$	6.08235	−	18.7196i	0.203197	−	0.625376i
$897$	19.3694	+	14.0727i	0.646725	+	0.469874i
$898$	43.4959	+	31.6017i	1.45148	+	1.05456i
$899$	−4.48442			−0.149564
$900$	−27.9805	+	86.1151i	−0.932683	+	2.87050i
$901$	16.7611			0.558394
$902$	−2.86394	−	5.85420i	−0.0953588	−	0.194923i
$903$	1.04716			0.0348472
$904$	1.20191	−	3.69911i	0.0399751	−	0.123031i
$905$	32.1629			1.06913
$906$	−6.80489	−	4.94404i	−0.226077	−	0.164255i
$907$	−2.99317	−	2.17466i	−0.0993865	−	0.0722085i	0.536982	−	0.843594i	$-0.319564\pi$
$907$	−2.99317	−	2.17466i	−0.0993865	−	0.0722085i	−0.636369	+	0.771385i	$0.719564\pi$
$908$	−18.1472	+	55.8513i	−0.602235	+	1.85349i
$909$	−1.02592	−	3.15745i	−0.0340275	−	0.104726i
$910$	−46.7643	+	33.9762i	−1.55022	+	1.12630i
$911$	46.0206			1.52473			0.762365	−	0.647147i	$-0.224038\pi$
$911$	46.0206			1.52473			0.762365	+	0.647147i	$0.224038\pi$
$912$	−2.15798	+	1.56787i	−0.0714579	+	0.0519172i
$913$	−2.83706	+	2.06124i	−0.0938929	+	0.0682172i
$914$	39.3702	+	28.6041i	1.30225	+	0.946139i
$915$	10.1163	−	31.1347i	0.334434	−	1.02928i
$916$	−4.24976			−0.140416
$917$	−14.2630	−	10.3627i	−0.471007	−	0.342207i
$918$	−8.79303	−	27.0622i	−0.290213	−	0.893185i
$919$	−39.3562	+	28.5939i	−1.29824	+	0.943226i	−0.999937	−	0.0112448i	$-0.996421\pi$
$919$	−39.3562	+	28.5939i	−1.29824	+	0.943226i	−0.298303	+	0.954471i	$0.596421\pi$
$920$	21.4913	−	66.1434i	0.708547	−	2.18068i
$921$	0.863539	+	2.65770i	0.0284546	+	0.0875742i
$922$	1.90998	+	5.87830i	0.0629017	+	0.193592i
$923$	−29.0132	−	89.2934i	−0.954981	−	2.93913i
$924$	0.325759	+	1.00258i	0.0107167	+	0.0329825i
$925$	11.1584	−	34.3421i	0.366886	−	1.12916i
$926$	29.5483	−	21.4681i	0.971019	−	0.705486i
$927$	1.80567	+	5.55728i	0.0593060	+	0.182525i
$928$	−7.00782	−	5.09148i	−0.230043	−	0.167136i
$929$	−33.3285			−1.09347			−0.546737	−	0.837304i	$-0.684130\pi$
$929$	−33.3285			−1.09347			−0.546737	+	0.837304i	$0.684130\pi$
$930$	−4.89955	+	15.0793i	−0.160662	+	0.494468i
$931$	−3.89412	−	2.82924i	−0.127625	−	0.0927247i
$932$	−51.7184	+	37.5756i	−1.69409	+	1.23083i
$933$	6.57338	−	4.77584i	0.215203	−	0.156354i
$934$	7.99671			0.261660
$935$	−4.40750	+	3.20224i	−0.144141	+	0.104724i
$936$	−15.8644	−	48.8257i	−0.518545	−	1.59592i
$937$	0.697330	−	2.14616i	0.0227808	−	0.0701120i	−0.939020	−	0.343863i	$-0.888264\pi$
$937$	0.697330	−	2.14616i	0.0227808	−	0.0701120i	0.961801	+	0.273751i	$0.0882644\pi$
$938$	−1.39287	−	1.01198i	−0.0454788	−	0.0330423i
$939$	1.91062	+	1.38815i	0.0623508	+	0.0453005i
$940$	145.737			4.75341
$941$	7.83960	−	24.1278i	0.255564	−	0.786544i	−0.738155	−	0.674632i	$-0.764302\pi$
$941$	7.83960	−	24.1278i	0.255564	−	0.786544i	0.993718	−	0.111912i	$-0.0356975\pi$
$942$	−15.0833			−0.491441
$943$	−5.94648	+	33.9613i	−0.193644	+	1.10593i
$944$	−3.48343			−0.113376
$945$	−4.75286	+	14.6278i	−0.154611	+	0.475842i
$946$	1.50712			0.0490006
$947$	14.0980	+	10.2428i	0.458124	+	0.332846i	0.792795	−	0.609489i	$-0.208625\pi$
$947$	14.0980	+	10.2428i	0.458124	+	0.332846i	−0.334671	+	0.942335i	$0.608625\pi$
$948$	13.6069	+	9.88598i	0.441931	+	0.321082i
$949$	13.3523	−	41.0942i	0.433434	−	1.33397i
$950$	36.7853	+	113.213i	1.19347	+	3.67313i
$951$	9.20286	−	6.68627i	0.298423	−	0.216817i
$952$	−10.2783			−0.333120
$953$	−16.9807	+	12.3372i	−0.550059	+	0.399641i	−0.827807	−	0.561013i	$-0.810412\pi$
$953$	−16.9807	+	12.3372i	−0.550059	+	0.399641i	0.277748	+	0.960654i	$0.410412\pi$
$954$	25.0438	−	18.1954i	0.810824	−	0.589098i
$955$	−4.30972	−	3.13119i	−0.139459	−	0.101323i
$956$	14.8541	−	45.7163i	0.480416	−	1.47857i
$957$	0.569316			0.0184034
$958$	66.3851	+	48.2316i	2.14480	+	1.55829i
$959$	0.769468	+	2.36818i	0.0248474	+	0.0764725i
$960$	−28.3229	+	20.5778i	−0.914117	+	0.664145i
$961$	−7.74171	+	23.8265i	−0.249732	+	0.768598i
$962$	15.3330	+	47.1901i	0.494356	+	1.52147i
$963$	−10.3460	−	31.8418i	−0.333396	−	1.02609i
$964$	−21.2264	−	65.3282i	−0.683657	−	2.10408i
$965$	18.1163	+	55.7562i	0.583184	+	1.79486i
$966$	2.73564	−	8.41944i	0.0880178	−	0.270891i
$967$	−37.4528	+	27.2111i	−1.20440	+	0.875049i	−0.994710	−	0.102718i	$-0.967246\pi$
$967$	−37.4528	+	27.2111i	−1.20440	+	0.875049i	−0.209692	+	0.977768i	$0.567246\pi$
$968$	−10.9090	−	33.5745i	−0.350629	−	1.07913i
$969$	−8.66597	−	6.29620i	−0.278391	−	0.202263i
$970$	13.6124			0.437069
$971$	−2.91444	+	8.96972i	−0.0935288	+	0.287852i	−0.986867	−	0.161532i	$-0.948357\pi$
$971$	−2.91444	+	8.96972i	−0.0935288	+	0.287852i	0.893339	+	0.449384i	$0.148357\pi$
$972$	−41.3934	−	30.0741i	−1.32769	−	0.964626i
$973$	−14.0854	+	10.2337i	−0.451558	+	0.328076i
$974$	−34.5083	+	25.0717i	−1.10572	+	0.803351i
$975$	47.2993			1.51479
$976$	7.42135	−	5.39192i	0.237552	−	0.172591i
$977$	−1.77745	−	5.47042i	−0.0568656	−	0.175014i	0.918589	−	0.395213i	$-0.129329\pi$
$977$	−1.77745	−	5.47042i	−0.0568656	−	0.175014i	−0.975455	+	0.220199i	$0.929329\pi$
$978$	−5.89259	+	18.1355i	−0.188424	+	0.579911i
$979$	−5.46915	−	3.97357i	−0.174795	−	0.126996i
$980$	10.8931	+	7.91427i	0.347966	+	0.252812i
$981$	−27.8072			−0.887815
$982$	11.4651	−	35.2859i	0.365865	−	1.12602i
$983$	35.1989			1.12267			0.561336	−	0.827588i	$-0.310288\pi$
$983$	35.1989			1.12267			0.561336	+	0.827588i	$0.310288\pi$
$984$	−10.6268	+	10.2867i	−0.338770	+	0.327929i
$985$	72.8308			2.32058
$986$	−4.15717	+	12.7945i	−0.132391	+	0.407458i
$987$	7.65437			0.243641
$988$	−83.3665	−	60.5693i	−2.65224	−	1.92697i
$989$	−6.45038	−	4.68648i	−0.205110	−	0.149021i
$990$	−3.10926	+	9.56933i	−0.0988189	+	0.304133i
$991$	−8.20117	−	25.2406i	−0.260519	−	0.801795i	−0.992692	−	0.120676i	$-0.961494\pi$
$991$	−8.20117	−	25.2406i	−0.260519	−	0.801795i	0.732173	−	0.681119i	$-0.238506\pi$
$992$	9.29388	−	6.75240i	0.295081	−	0.214389i
$993$	3.65592			0.116017
$994$	−28.0860	+	20.4056i	−0.890832	+	0.647228i
$995$	−26.0176	+	18.9029i	−0.824813	+	0.599262i
$996$	15.6039	+	11.3369i	0.494429	+	0.359223i
$997$	5.18822	−	15.9677i	0.164313	−	0.505702i	−0.834672	−	0.550747i	$-0.814343\pi$
$997$	5.18822	−	15.9677i	0.164313	−	0.505702i	0.998985	+	0.0450447i	$0.0143430\pi$
$998$	−5.57606			−0.176507
$999$	10.6812	+	7.76033i	0.337937	+	0.245526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.d.57.9	✓	40
41.18	even	5	inner	287.2.h.d.141.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.d.57.9	✓	40	1.1	even	1	trivial
287.2.h.d.141.9	yes	40	41.18	even	5	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.718417 - 2.21106i) q^{2} +0.707185 q^{3} +(-2.75463 - 2.00136i) q^{4} +(3.19921 + 2.32437i) q^{5} +(0.508054 - 1.56363i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.64242 + 1.91983i) q^{8} -2.49989 q^{9} +O(q^{10})\)	\(q+(0.718417 - 2.21106i) q^{2} +0.707185 q^{3} +(-2.75463 - 2.00136i) q^{4} +(3.19921 + 2.32437i) q^{5} +(0.508054 - 1.56363i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.64242 + 1.91983i) q^{8} -2.49989 q^{9} +(7.43769 - 5.40380i) q^{10} +(0.354186 - 0.257331i) q^{11} +(-1.94804 - 1.41533i) q^{12} +(1.94294 - 5.97974i) q^{13} -2.32485 q^{14} +(2.26244 + 1.64376i) q^{15} +(0.242152 + 0.745267i) q^{16} +(-2.54585 + 1.84967i) q^{17} +(-1.79596 + 5.52741i) q^{18} +(1.48742 + 4.57781i) q^{19} +(-4.16078 - 12.8056i) q^{20} +(-0.218532 - 0.672573i) q^{21} +(-0.314522 - 0.967999i) q^{22} +(-1.66392 + 5.12101i) q^{23} +(-1.86868 + 1.35768i) q^{24} +(3.28722 + 10.1170i) q^{25} +(-11.8257 - 8.59190i) q^{26} -3.88944 q^{27} +(-1.05218 + 3.23827i) q^{28} +(1.48766 + 1.08085i) q^{29} +(5.25982 - 3.82148i) q^{30} +(-1.97296 + 1.43344i) q^{31} -4.71063 q^{32} +(0.250475 - 0.181981i) q^{33} +(2.26075 + 6.95786i) q^{34} +(1.22199 - 3.76090i) q^{35} +(6.88628 + 5.00318i) q^{36} +(-2.74620 - 1.99523i) q^{37} +11.1904 q^{38} +(1.37402 - 4.22878i) q^{39} -12.9161 q^{40} +(6.33974 - 0.898713i) q^{41} -1.64410 q^{42} +(-0.457574 + 1.40827i) q^{43} -1.49067 q^{44} +(-7.99768 - 5.81066i) q^{45} +(10.1275 + 7.35805i) q^{46} +(-3.34471 + 10.2940i) q^{47} +(0.171246 + 0.527042i) q^{48} +(-0.809017 + 0.587785i) q^{49} +24.7309 q^{50} +(-1.80039 + 1.30806i) q^{51} +(-17.3197 + 12.5835i) q^{52} +(-4.30909 - 3.13074i) q^{53} +(-2.79424 + 8.59979i) q^{54} +1.73125 q^{55} +(2.64242 + 1.91983i) q^{56} +(1.05188 + 3.23736i) q^{57} +(3.45858 - 2.51281i) q^{58} +(-1.37367 + 4.22773i) q^{59} +(-2.94244 - 9.05590i) q^{60} +(-3.61745 - 11.1334i) q^{61} +(1.75201 + 5.39214i) q^{62} +(0.772508 + 2.37754i) q^{63} +(-3.86850 + 11.9060i) q^{64} +(20.1150 - 14.6144i) q^{65} +(-0.222425 - 0.684554i) q^{66} +(0.599123 + 0.435288i) q^{67} +10.7147 q^{68} +(-1.17670 + 3.62150i) q^{69} +(-7.43769 - 5.40380i) q^{70} +(12.0808 - 8.77719i) q^{71} +(6.60577 - 4.79937i) q^{72} +6.87223 q^{73} +(-6.38449 + 4.63861i) q^{74} +(2.32467 + 7.15460i) q^{75} +(5.06454 - 15.5871i) q^{76} +(-0.354186 - 0.257331i) q^{77} +(-8.36298 - 6.07606i) q^{78} -6.98492 q^{79} +(-0.957577 + 2.94712i) q^{80} +4.74912 q^{81} +(2.56747 - 14.6632i) q^{82} -8.01007 q^{83} +(-0.744084 + 2.29005i) q^{84} -12.4440 q^{85} +(2.78504 + 2.02345i) q^{86} +(1.05205 + 0.764360i) q^{87} +(-0.441877 + 1.35996i) q^{88} +(-4.77167 - 14.6857i) q^{89} +(-18.5934 + 13.5089i) q^{90} -6.28747 q^{91} +(14.8325 - 10.7764i) q^{92} +(-1.39525 + 1.01371i) q^{93} +(20.3577 + 14.7907i) q^{94} +(-5.88193 + 18.1027i) q^{95} -3.33129 q^{96} +(1.19788 + 0.870311i) q^{97} +(0.718417 + 2.21106i) q^{98} +(-0.885427 + 0.643300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

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