LMFDB - Embedded newform 350.2.m.b.169.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.10
Character	$\chi$	$=$	350.169
Dual form			350.2.m.b.29.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(1.91132 + 2.63070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.23309 + 0.115392i) q^{5} +(2.63070 + 1.91132i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.34041 + 7.20305i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(1.91132 + 2.63070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.23309 + 0.115392i) q^{5} +(2.63070 + 1.91132i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.34041 + 7.20305i) q^{9} +(-2.08814 + 0.799807i) q^{10} +(1.35392 + 4.16695i) q^{11} +(3.09258 + 1.00484i) q^{12} +(0.626642 + 0.203608i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-4.57171 - 5.65404i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.67804 - 6.43877i) q^{17} +7.57374i q^{18} +(-2.64889 - 1.92453i) q^{19} +(-1.73878 + 1.40593i) q^{20} +(2.63070 - 1.91132i) q^{21} +(2.57532 + 3.54462i) q^{22} +(1.08442 - 0.352350i) q^{23} +3.25173 q^{24} +(4.97337 - 0.515363i) q^{25} +0.658890 q^{26} +(-14.1446 + 4.59587i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(4.10797 - 2.98461i) q^{29} +(-6.09515 - 3.96458i) q^{30} +(-8.14782 - 5.91974i) q^{31} -1.00000i q^{32} +(-8.37423 + 11.5261i) q^{33} +(2.45939 - 7.56923i) q^{34} +(0.115392 + 2.23309i) q^{35} +(2.34041 + 7.20305i) q^{36} +(-4.08838 - 1.32840i) q^{37} +(-3.11396 - 1.01179i) q^{38} +(0.662079 + 2.03767i) q^{39} +(-1.21922 + 1.87443i) q^{40} +(1.48075 - 4.55728i) q^{41} +(1.91132 - 2.63070i) q^{42} +5.18419i q^{43} +(3.54462 + 2.57532i) q^{44} +(4.39517 - 16.3551i) q^{45} +(0.922463 - 0.670209i) q^{46} +(1.71563 + 2.36136i) q^{47} +(3.09258 - 1.00484i) q^{48} -1.00000 q^{49} +(4.57070 - 2.02699i) q^{50} +25.8797 q^{51} +(0.626642 - 0.203608i) q^{52} +(0.275357 + 0.378996i) q^{53} +(-12.0322 + 8.74187i) q^{54} +(-3.50427 - 9.14893i) q^{55} +(-0.809017 - 0.587785i) q^{56} -10.6468i q^{57} +(2.98461 - 4.10797i) q^{58} +(1.34725 - 4.14642i) q^{59} +(-7.02195 - 1.88704i) q^{60} +(-0.519272 - 1.59815i) q^{61} +(-9.57834 - 3.11219i) q^{62} +(7.20305 + 2.34041i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.42284 - 0.382365i) q^{65} +(-4.40259 + 13.5498i) q^{66} +(-6.81177 + 9.37559i) q^{67} -7.95876i q^{68} +(2.99960 + 2.17934i) q^{69} +(0.799807 + 2.08814i) q^{70} +(10.4563 - 7.59697i) q^{71} +(4.45173 + 6.12728i) q^{72} +(0.370532 - 0.120393i) q^{73} -4.29878 q^{74} +(10.8615 + 12.0984i) q^{75} -3.27421 q^{76} +(4.16695 - 1.35392i) q^{77} +(1.25935 + 1.73334i) q^{78} +(-6.04840 + 4.39442i) q^{79} +(-0.580318 + 2.15945i) q^{80} +(-20.7434 - 15.0710i) q^{81} -4.79181i q^{82} +(-5.15210 + 7.09126i) q^{83} +(1.00484 - 3.09258i) q^{84} +(-9.70349 + 14.9182i) q^{85} +(1.60200 + 4.93046i) q^{86} +(15.7033 + 5.10230i) q^{87} +(4.16695 + 1.35392i) q^{88} +(0.369773 + 1.13804i) q^{89} +(-0.873952 - 16.9128i) q^{90} +(0.203608 - 0.626642i) q^{91} +(0.670209 - 0.922463i) q^{92} -32.7490i q^{93} +(2.36136 + 1.71563i) q^{94} +(6.13728 + 3.99199i) q^{95} +(2.63070 - 1.91132i) q^{96} +(9.86047 + 13.5718i) q^{97} +(-0.951057 + 0.309017i) q^{98} -33.1835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	1.91132	+	2.63070i	1.10350	+	1.51884i	0.830662	+	0.556778i	$0.187962\pi$
$3$	1.91132	+	2.63070i	1.10350	+	1.51884i	0.272839	+	0.962060i	$0.412038\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.23309	+	0.115392i	−0.998668	+	0.0516050i
$5$	−2.23309	+	0.115392i	−0.998668	+	0.0516050i
$6$	2.63070	+	1.91132i	1.07398	+	0.780292i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−2.34041	+	7.20305i	−0.780138	+	2.40102i
$10$	−2.08814	+	0.799807i	−0.660326	+	0.252921i
$11$	1.35392	+	4.16695i	0.408223	+	1.25638i	0.918174	+	0.396178i	$0.129664\pi$
$11$	1.35392	+	4.16695i	0.408223	+	1.25638i	−0.509950	+	0.860204i	$0.670336\pi$
$12$	3.09258	+	1.00484i	0.892750	+	0.290072i
$13$	0.626642	+	0.203608i	0.173799	+	0.0564708i	0.394624	−	0.918843i	$-0.370875\pi$
$13$	0.626642	+	0.203608i	0.173799	+	0.0564708i	−0.220825	+	0.975313i	$0.570875\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−4.57171	−	5.65404i	−1.18041	−	1.45987i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.67804	−	6.43877i	1.13459	−	1.56163i	0.355552	−	0.934657i	$-0.384293\pi$
$17$	4.67804	−	6.43877i	1.13459	−	1.56163i	0.779040	−	0.626975i	$-0.215707\pi$
$18$			7.57374i			1.78515i
$19$	−2.64889	−	1.92453i	−0.607697	−	0.441518i	0.240905	−	0.970549i	$-0.422556\pi$
$19$	−2.64889	−	1.92453i	−0.607697	−	0.441518i	−0.848603	+	0.529031i	$0.822556\pi$
$20$	−1.73878	+	1.40593i	−0.388803	+	0.314376i
$21$	2.63070	−	1.91132i	0.574067	−	0.417084i
$22$	2.57532	+	3.54462i	0.549059	+	0.755715i
$23$	1.08442	−	0.352350i	0.226117	−	0.0734700i	−0.193767	−	0.981048i	$-0.562071\pi$
$23$	1.08442	−	0.352350i	0.226117	−	0.0734700i	0.419884	+	0.907578i	$0.362071\pi$
$24$	3.25173			0.663756
$25$	4.97337	−	0.515363i	0.994674	−	0.103073i
$26$	0.658890			0.129219
$27$	−14.1446	+	4.59587i	−2.72214	+	0.884476i
$28$	−0.587785	−	0.809017i	−0.111081	−	0.152890i
$29$	4.10797	−	2.98461i	0.762830	−	0.554229i	−0.136947	−	0.990578i	$-0.543729\pi$
$29$	4.10797	−	2.98461i	0.762830	−	0.554229i	0.899777	+	0.436350i	$0.143729\pi$
$30$	−6.09515	−	3.96458i	−1.11282	−	0.723830i
$31$	−8.14782	−	5.91974i	−1.46339	−	1.06322i	−0.982463	−	0.186456i	$-0.940300\pi$
$31$	−8.14782	−	5.91974i	−1.46339	−	1.06322i	−0.480928	−	0.876760i	$-0.659700\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−8.37423	+	11.5261i	−1.45777	+	2.00644i
$34$	2.45939	−	7.56923i	0.421782	−	1.29811i
$35$	0.115392	+	2.23309i	0.0195049	+	0.377461i
$36$	2.34041	+	7.20305i	0.390069	+	1.20051i
$37$	−4.08838	−	1.32840i	−0.672125	−	0.218387i	−0.0469809	−	0.998896i	$-0.514960\pi$
$37$	−4.08838	−	1.32840i	−0.672125	−	0.218387i	−0.625145	+	0.780509i	$0.714960\pi$
$38$	−3.11396	−	1.01179i	−0.505151	−	0.164133i
$39$	0.662079	+	2.03767i	0.106017	+	0.326288i
$40$	−1.21922	+	1.87443i	−0.192776	+	0.296374i
$41$	1.48075	−	4.55728i	0.231254	−	0.711727i	−0.766342	−	0.642433i	$-0.777925\pi$
$41$	1.48075	−	4.55728i	0.231254	−	0.711727i	0.997596	−	0.0692945i	$-0.0220748\pi$
$42$	1.91132	−	2.63070i	0.294923	−	0.405926i
$43$			5.18419i			0.790582i	0.918556	+	0.395291i	$0.129356\pi$
$43$			5.18419i			0.790582i	−0.918556	+	0.395291i	$0.870644\pi$
$44$	3.54462	+	2.57532i	0.534371	+	0.388244i
$45$	4.39517	−	16.3551i	0.655194	−	2.43808i
$46$	0.922463	−	0.670209i	0.136010	−	0.0988169i
$47$	1.71563	+	2.36136i	0.250250	+	0.344439i	0.915599	−	0.402093i	$-0.131717\pi$
$47$	1.71563	+	2.36136i	0.250250	+	0.344439i	−0.665349	+	0.746533i	$0.731717\pi$
$48$	3.09258	−	1.00484i	0.446375	−	0.145036i
$49$	−1.00000			−0.142857
$50$	4.57070	−	2.02699i	0.646395	−	0.286660i
$51$	25.8797			3.62389
$52$	0.626642	−	0.203608i	0.0868996	−	0.0282354i
$53$	0.275357	+	0.378996i	0.0378232	+	0.0520591i	0.827510	−	0.561451i	$-0.189757\pi$
$53$	0.275357	+	0.378996i	0.0378232	+	0.0520591i	−0.789687	+	0.613510i	$0.789757\pi$
$54$	−12.0322	+	8.74187i	−1.63737	+	1.18962i
$55$	−3.50427	−	9.14893i	−0.472515	−	1.23364i
$56$	−0.809017	−	0.587785i	−0.108109	−	0.0785461i
$57$		−	10.6468i		−	1.41021i
$58$	2.98461	−	4.10797i	0.391899	−	0.539403i
$59$	1.34725	−	4.14642i	0.175397	−	0.539817i	−0.824254	−	0.566220i	$-0.808405\pi$
$59$	1.34725	−	4.14642i	0.175397	−	0.539817i	0.999651	+	0.0264027i	$0.00840522\pi$
$60$	−7.02195	−	1.88704i	−0.906530	−	0.243615i
$61$	−0.519272	−	1.59815i	−0.0664860	−	0.204623i	0.912294	−	0.409535i	$-0.134309\pi$
$61$	−0.519272	−	1.59815i	−0.0664860	−	0.204623i	−0.978780	+	0.204912i	$0.934309\pi$
$62$	−9.57834	−	3.11219i	−1.21645	−	0.395248i
$63$	7.20305	+	2.34041i	0.907500	+	0.294864i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.42284	−	0.382365i	−0.176482	−	0.0474266i
$66$	−4.40259	+	13.5498i	−0.541922	+	1.66786i
$67$	−6.81177	+	9.37559i	−0.832190	+	1.14541i	0.155322	+	0.987864i	$0.450359\pi$
$67$	−6.81177	+	9.37559i	−0.832190	+	1.14541i	−0.987511	+	0.157547i	$0.949641\pi$
$68$		−	7.95876i		−	0.965141i
$69$	2.99960	+	2.17934i	0.361110	+	0.262361i
$70$	0.799807	+	2.08814i	0.0955952	+	0.249580i
$71$	10.4563	−	7.59697i	1.24094	−	0.901594i	0.243278	−	0.969957i	$-0.421777\pi$
$71$	10.4563	−	7.59697i	1.24094	−	0.901594i	0.997661	+	0.0683624i	$0.0217774\pi$
$72$	4.45173	+	6.12728i	0.524642	+	0.722107i
$73$	0.370532	−	0.120393i	0.0433675	−	0.0140910i	−0.287253	−	0.957855i	$-0.592742\pi$
$73$	0.370532	−	0.120393i	0.0433675	−	0.0140910i	0.330620	+	0.943764i	$0.392742\pi$
$74$	−4.29878			−0.499723
$75$	10.8615	+	12.0984i	1.25417	+	1.39701i
$76$	−3.27421			−0.375578
$77$	4.16695	−	1.35392i	0.474868	−	0.154294i
$78$	1.25935	+	1.73334i	0.142593	+	0.196263i
$79$	−6.04840	+	4.39442i	−0.680498	+	0.494411i	−0.873523	−	0.486783i	$-0.838170\pi$
$79$	−6.04840	+	4.39442i	−0.680498	+	0.494411i	0.193025	+	0.981194i	$0.438170\pi$
$80$	−0.580318	+	2.15945i	−0.0648815	+	0.241434i
$81$	−20.7434	−	15.0710i	−2.30483	−	1.67456i
$82$		−	4.79181i		−	0.529166i
$83$	−5.15210	+	7.09126i	−0.565516	+	0.778367i	−0.992015	−	0.126122i	$-0.959747\pi$
$83$	−5.15210	+	7.09126i	−0.565516	+	0.778367i	0.426498	+	0.904488i	$0.359747\pi$
$84$	1.00484	−	3.09258i	0.109637	−	0.337428i
$85$	−9.70349	+	14.9182i	−1.05249	+	1.61810i
$86$	1.60200	+	4.93046i	0.172749	+	0.531665i
$87$	15.7033	+	5.10230i	1.68357	+	0.547024i
$88$	4.16695	+	1.35392i	0.444198	+	0.144329i
$89$	0.369773	+	1.13804i	0.0391959	+	0.120632i	0.968740	−	0.248079i	$-0.0797991\pi$
$89$	0.369773	+	1.13804i	0.0391959	+	0.120632i	−0.929544	+	0.368711i	$0.879799\pi$
$90$	−0.873952	−	16.9128i	−0.0921226	−	1.78277i
$91$	0.203608	−	0.626642i	0.0213439	−	0.0656899i
$92$	0.670209	−	0.922463i	0.0698741	−	0.0961735i
$93$		−	32.7490i		−	3.39591i
$94$	2.36136	+	1.71563i	0.243555	+	0.176953i
$95$	6.13728	+	3.99199i	0.629672	+	0.409569i
$96$	2.63070	−	1.91132i	0.268495	−	0.195073i
$97$	9.86047	+	13.5718i	1.00118	+	1.37800i	0.924599	+	0.380941i	$0.124400\pi$
$97$	9.86047	+	13.5718i	1.00118	+	1.37800i	0.0765800	+	0.997063i	$0.475600\pi$
$98$	−0.951057	+	0.309017i	−0.0960712	+	0.0312154i
$99$	−33.1835			−3.33507
$100$	3.72062	−	3.34021i	0.372062	−	0.334021i
$101$	−3.38271			−0.336592			−0.168296	−	0.985737i	$-0.553826\pi$
$101$	−3.38271			−0.336592			−0.168296	+	0.985737i	$0.553826\pi$
$102$	24.6131	−	7.99727i	2.43706	−	0.791848i
$103$	−5.41360	−	7.45119i	−0.533418	−	0.734187i	0.454228	−	0.890885i	$-0.349915\pi$
$103$	−5.41360	−	7.45119i	−0.533418	−	0.734187i	−0.987647	+	0.156698i	$0.949915\pi$
$104$	0.533053	−	0.387286i	0.0522702	−	0.0379765i
$105$	−5.65404	+	4.57171i	−0.551778	+	0.446153i
$106$	0.378996	+	0.275357i	0.0368114	+	0.0267450i
$107$			11.0793i			1.07108i	0.844511	+	0.535538i	$0.179891\pi$
$107$			11.0793i			1.07108i	−0.844511	+	0.535538i	$0.820109\pi$
$108$	−8.74187	+	12.0322i	−0.841187	+	1.15779i
$109$	−0.737638	+	2.27022i	−0.0706529	+	0.217447i	−0.980148	−	0.198267i	$-0.936469\pi$
$109$	−0.737638	+	2.27022i	−0.0706529	+	0.217447i	0.909495	+	0.415715i	$0.136469\pi$
$110$	−6.15993	−	7.61828i	−0.587326	−	0.726374i
$111$	−4.31958	−	13.2943i	−0.409996	−	1.26184i
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	−11.6528	−	3.78623i	−1.09620	−	0.356178i	−0.295563	−	0.955323i	$-0.595507\pi$
$113$	−11.6528	−	3.78623i	−1.09620	−	0.356178i	−0.800640	+	0.599145i	$0.795507\pi$
$114$	−3.29005	−	10.1257i	−0.308142	−	0.948363i
$115$	−2.38095	+	0.911962i	−0.222025	+	0.0850409i
$116$	1.56910	−	4.82921i	0.145688	−	0.448380i
$117$	−2.93320	+	4.03721i	−0.271175	+	0.373240i
$118$		−	4.35980i		−	0.401352i
$119$	−6.43877	−	4.67804i	−0.590241	−	0.428835i
$120$	−7.26140	+	0.375225i	−0.662872	+	0.0342532i
$121$	−6.63117	+	4.81783i	−0.602834	+	0.437984i
$122$	−0.987714	−	1.35947i	−0.0894234	−	0.123081i
$123$	14.8190	−	4.81500i	1.33619	−	0.434153i
$124$	−10.0713			−0.904426
$125$	−11.0465	+	1.72474i	−0.988029	+	0.154265i
$126$	7.57374			0.674722
$127$	7.40657	−	2.40654i	0.657227	−	0.213546i	0.0386291	−	0.999254i	$-0.487701\pi$
$127$	7.40657	−	2.40654i	0.657227	−	0.213546i	0.618598	+	0.785708i	$0.287701\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−13.6381	+	9.90864i	−1.20077	+	0.872407i
$130$	−1.47136	+	0.0760309i	−0.129047	+	0.00666835i
$131$	−4.49298	−	3.26434i	−0.392554	−	0.285207i	0.373948	−	0.927450i	$-0.378004\pi$
$131$	−4.49298	−	3.26434i	−0.392554	−	0.285207i	−0.766501	+	0.642243i	$0.778004\pi$
$132$			14.2471i			1.24005i
$133$	−1.92453	+	2.64889i	−0.166878	+	0.229688i
$134$	−3.58116	+	11.0217i	−0.309365	+	0.952127i
$135$	31.0559	−	11.8952i	2.67287	−	1.02377i
$136$	−2.45939	−	7.56923i	−0.210891	−	0.649056i
$137$	−3.96048	−	1.28684i	−0.338367	−	0.109942i	0.134905	−	0.990859i	$-0.456927\pi$
$137$	−3.96048	−	1.28684i	−0.338367	−	0.109942i	−0.473272	+	0.880917i	$0.656927\pi$
$138$	3.52624	+	1.14575i	0.300174	+	0.0975323i
$139$	1.68753	+	5.19367i	0.143134	+	0.440522i	0.996766	−	0.0803546i	$-0.0256053\pi$
$139$	1.68753	+	5.19367i	0.143134	+	0.440522i	−0.853632	+	0.520876i	$0.825605\pi$
$140$	1.40593	+	1.73878i	0.118823	+	0.146954i
$141$	−2.93292	+	9.02661i	−0.246997	+	0.760178i
$142$	7.59697	−	10.4563i	0.637523	−	0.877476i
$143$			2.88685i			0.241411i
$144$	6.12728	+	4.45173i	0.510607	+	0.370978i
$145$	−8.82905	+	7.13893i	−0.733213	+	0.592856i
$146$	0.315194	−	0.229002i	0.0260856	−	0.0189523i
$147$	−1.91132	−	2.63070i	−0.157643	−	0.216977i
$148$	−4.08838	+	1.32840i	−0.336063	+	0.109193i
$149$	−0.382162			−0.0313079			−0.0156540	−	0.999877i	$-0.504983\pi$
$149$	−0.382162			−0.0313079			−0.0156540	+	0.999877i	$0.504983\pi$
$150$	14.0685	+	8.14992i	1.14869	+	0.665439i
$151$	7.02172			0.571419			0.285710	−	0.958316i	$-0.407771\pi$
$151$	7.02172			0.571419			0.285710	+	0.958316i	$0.407771\pi$
$152$	−3.11396	+	1.01179i	−0.252575	+	0.0820667i
$153$	35.4303	+	48.7656i	2.86437	+	3.94246i
$154$	3.54462	−	2.57532i	0.285634	−	0.207525i
$155$	18.8779	+	12.2791i	1.51631	+	0.986281i
$156$	1.73334	+	1.25935i	0.138779	+	0.100829i
$157$			7.19715i			0.574395i	0.957871	+	0.287198i	$0.0927237\pi$
$157$			7.19715i			0.574395i	−0.957871	+	0.287198i	$0.907276\pi$
$158$	−4.39442	+	6.04840i	−0.349601	+	0.481185i
$159$	−0.470732	+	1.44876i	−0.0373315	+	0.114894i
$160$	0.115392	+	2.23309i	0.00912257	+	0.176541i
$161$	−0.352350	−	1.08442i	−0.0277690	−	0.0854643i
$162$	−24.3854	−	7.92329i	−1.91590	−	0.622513i
$163$	−12.4884	−	4.05771i	−0.978164	−	0.317825i	−0.224057	−	0.974576i	$-0.571930\pi$
$163$	−12.4884	−	4.05771i	−0.978164	−	0.317825i	−0.754107	+	0.656751i	$0.771930\pi$
$164$	−1.48075	−	4.55728i	−0.115627	−	0.355864i
$165$	17.3704	−	26.7052i	1.35228	−	2.07900i
$166$	−2.70862	+	8.33627i	−0.210230	+	0.647020i
$167$	−10.3355	+	14.2256i	−0.799783	+	1.10081i	0.193038	+	0.981191i	$0.438166\pi$
$167$	−10.3355	+	14.2256i	−0.799783	+	1.10081i	−0.992820	+	0.119615i	$0.961834\pi$
$168$		−	3.25173i		−	0.250876i
$169$	−10.1660	−	7.38603i	−0.782000	−	0.568156i
$170$	−4.61861	+	17.1866i	−0.354231	+	1.31815i
$171$	20.0620	−	14.5759i	1.53418	−	1.11465i
$172$	3.04719	+	4.19410i	0.232346	+	0.319797i
$173$	4.87643	−	1.58445i	0.370748	−	0.120463i	−0.117716	−	0.993047i	$-0.537557\pi$
$173$	4.87643	−	1.58445i	0.370748	−	0.120463i	0.488464	+	0.872584i	$0.337557\pi$
$174$	16.5114			1.25173
$175$	−0.515363	−	4.97337i	−0.0389578	−	0.375951i
$176$	4.38139			0.330260
$177$	13.4830	−	4.38090i	1.01345	−	0.329289i
$178$	0.703350	+	0.968079i	0.0527183	+	0.0725606i
$179$	11.6729	−	8.48087i	0.872474	−	0.633890i	−0.0587754	−	0.998271i	$-0.518720\pi$
$179$	11.6729	−	8.48087i	0.872474	−	0.633890i	0.931250	+	0.364381i	$0.118720\pi$
$180$	−6.05753	−	15.8150i	−0.451502	−	1.17878i
$181$	−9.80269	−	7.12207i	−0.728628	−	0.529380i	0.160501	−	0.987036i	$-0.448689\pi$
$181$	−9.80269	−	7.12207i	−0.728628	−	0.529380i	−0.889129	+	0.457656i	$0.848689\pi$
$182$		−	0.658890i		−	0.0488402i
$183$	3.21178	−	4.42063i	0.237421	−	0.326783i
$184$	0.352350	−	1.08442i	0.0259756	−	0.0799446i
$185$	9.28300	+	2.49466i	0.682500	+	0.183411i
$186$	−10.1200	−	31.1461i	−0.742034	−	2.28375i
$187$	33.1637	+	10.7756i	2.42517	+	0.787986i
$188$	2.77594	+	0.901958i	0.202456	+	0.0657821i
$189$	4.59587	+	14.1446i	0.334301	+	1.02887i
$190$	7.07050	+	1.90008i	0.512948	+	0.137846i
$191$	0.608053	−	1.87139i	0.0439972	−	0.135409i	−0.926645	−	0.375938i	$-0.877321\pi$
$191$	0.608053	−	1.87139i	0.0439972	−	0.135409i	0.970642	+	0.240528i	$0.0773207\pi$
$192$	1.91132	−	2.63070i	0.137938	−	0.189855i
$193$		−	11.0945i		−	0.798598i	−0.916821	−	0.399299i	$-0.869254\pi$
$193$		−	11.0945i		−	0.798598i	0.916821	−	0.399299i	$-0.130746\pi$
$194$	13.5718	+	9.86047i	0.974397	+	0.707941i
$195$	−1.71361	−	4.47390i	−0.122714	−	0.320382i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	4.01899	+	5.53166i	0.286341	+	0.394114i	0.927821	−	0.373025i	$-0.121679\pi$
$197$	4.01899	+	5.53166i	0.286341	+	0.394114i	−0.641480	+	0.767139i	$0.721679\pi$
$198$	−31.5594	+	10.2543i	−2.24283	+	0.728739i
$199$	17.0534			1.20889			0.604443	−	0.796649i	$-0.293396\pi$
$199$	17.0534			1.20889			0.604443	+	0.796649i	$0.293396\pi$
$200$	2.50634	−	4.32646i	0.177225	−	0.305927i
$201$	−37.6839			−2.65801
$202$	−3.21714	+	1.04531i	−0.226357	+	0.0735480i
$203$	−2.98461	−	4.10797i	−0.209479	−	0.288323i
$204$	20.9371	−	15.2117i	1.46589	−	1.06503i
$205$	−2.78077	+	10.3477i	−0.194217	+	0.722713i
$206$	−7.45119	−	5.41360i	−0.519149	−	0.377184i
$207$			8.63579i			0.600229i
$208$	0.387286	−	0.533053i	0.0268534	−	0.0369606i
$209$	4.43303	−	13.6435i	0.306639	−	0.943738i
$210$	−3.96458	+	6.09515i	−0.273582	+	0.420605i
$211$	5.02868	+	15.4767i	0.346189	+	1.06546i	0.960944	+	0.276742i	$0.0892547\pi$
$211$	5.02868	+	15.4767i	0.346189	+	1.06546i	−0.614756	+	0.788718i	$0.710745\pi$
$212$	0.445537	+	0.144764i	0.0305996	+	0.00994241i
$213$	39.9707	+	12.9873i	2.73875	+	0.889874i
$214$	3.42369	+	10.5370i	0.234039	+	0.720297i
$215$	−0.598216	−	11.5768i	−0.0407980	−	0.789529i
$216$	−4.59587	+	14.1446i	−0.312710	+	0.962421i
$217$	−5.91974	+	8.14782i	−0.401858	+	0.553110i
$218$			2.38705i			0.161671i
$219$	1.02492	+	0.744651i	0.0692580	+	0.0503189i
$220$	−8.21262	−	5.34189i	−0.553695	−	0.360150i
$221$	4.24244	−	3.08231i	0.285377	−	0.207339i
$222$	−8.21633	−	11.3088i	−0.551444	−	0.758998i
$223$	−22.2434	+	7.22731i	−1.48953	+	0.483977i	−0.936943	−	0.349481i	$-0.886358\pi$
$223$	−22.2434	+	7.22731i	−1.48953	+	0.483977i	−0.552583	+	0.833458i	$0.686358\pi$
$224$	−1.00000			−0.0668153
$225$	−7.92756	+	37.0296i	−0.528504	+	2.46864i
$226$	−12.2525			−0.815023
$227$	−1.05073	+	0.341403i	−0.0697394	+	0.0226597i	−0.343679	−	0.939087i	$-0.611673\pi$
$227$	−1.05073	+	0.341403i	−0.0697394	+	0.0226597i	0.273940	+	0.961747i	$0.411673\pi$
$228$	−6.25806	−	8.61347i	−0.414450	−	0.570441i
$229$	−11.9438	+	8.67766i	−0.789267	+	0.573436i	−0.907746	−	0.419520i	$-0.862198\pi$
$229$	−11.9438	+	8.67766i	−0.789267	+	0.573436i	0.118479	+	0.992957i	$0.462198\pi$
$230$	−1.98261	+	1.60308i	−0.130729	+	0.105704i
$231$	11.5261	+	8.37423i	0.758364	+	0.550984i
$232$		−	5.07773i		−	0.333369i
$233$	−4.37873	+	6.02680i	−0.286860	+	0.394829i	−0.927991	−	0.372603i	$-0.878465\pi$
$233$	−4.37873	+	6.02680i	−0.286860	+	0.394829i	0.641131	+	0.767431i	$0.278465\pi$
$234$	−1.54208	+	4.74602i	−0.100809	+	0.310257i
$235$	−4.10363	−	5.07515i	−0.267691	−	0.331066i
$236$	−1.34725	−	4.14642i	−0.0876987	−	0.269909i
$237$	−23.1208	−	7.51241i	−1.50186	−	0.487984i
$238$	−7.56923	−	2.45939i	−0.490640	−	0.159419i
$239$	−0.950118	−	2.92416i	−0.0614580	−	0.189148i	0.915614	−	0.402059i	$-0.131705\pi$
$239$	−0.950118	−	2.92416i	−0.0614580	−	0.189148i	−0.977072	+	0.212911i	$0.931705\pi$
$240$	−6.79005	+	2.60076i	−0.438296	+	0.167878i
$241$	1.91384	−	5.89019i	0.123281	−	0.379421i	−0.870303	−	0.492517i	$-0.836077\pi$
$241$	1.91384	−	5.89019i	0.123281	−	0.379421i	0.993584	+	0.113096i	$0.0360769\pi$
$242$	−4.81783	+	6.63117i	−0.309702	+	0.426268i
$243$		−	38.7577i		−	2.48631i
$244$	−1.35947	−	0.987714i	−0.0870313	−	0.0632319i
$245$	2.23309	−	0.115392i	0.142667	−	0.00737215i
$246$	12.6058	−	9.15866i	0.803718	−	0.583935i
$247$	−1.26805	−	1.74533i	−0.0806844	−	0.111053i
$248$	−9.57834	+	3.11219i	−0.608225	+	0.197624i
$249$	−28.5023			−1.80626
$250$	−9.97288	+	5.05388i	−0.630740	+	0.319636i
$251$	7.71705			0.487096			0.243548	−	0.969889i	$-0.421689\pi$
$251$	7.71705			0.487096			0.243548	+	0.969889i	$0.421689\pi$
$252$	7.20305	−	2.34041i	0.453750	−	0.147432i
$253$	2.93645	+	4.04167i	0.184613	+	0.254098i
$254$	6.30041	−	4.57751i	0.395323	−	0.287219i
$255$	−57.7917	+	2.98632i	−3.61906	+	0.187011i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$		−	19.3066i		−	1.20431i	−0.798379	−	0.602155i	$-0.794309\pi$
$257$		−	19.3066i		−	1.20431i	0.798379	−	0.602155i	$-0.205691\pi$
$258$	−9.90864	+	13.6381i	−0.616885	+	0.849070i
$259$	−1.32840	+	4.08838i	−0.0825425	+	0.254040i
$260$	−1.37585	+	0.526985i	−0.0853267	+	0.0326822i
$261$	11.8840	+	36.5751i	0.735600	+	2.26394i
$262$	−5.28182	−	1.71617i	−0.326312	−	0.106025i
$263$	2.36640	+	0.768891i	0.145919	+	0.0474119i	0.381066	−	0.924548i	$-0.375557\pi$
$263$	2.36640	+	0.768891i	0.145919	+	0.0474119i	−0.235147	+	0.971960i	$0.575557\pi$
$264$	4.40259	+	13.5498i	0.270961	+	0.833932i
$265$	−0.658629	−	0.814558i	−0.0404593	−	0.0500379i
$266$	−1.01179	+	3.11396i	−0.0620366	+	0.190929i
$267$	−2.28710	+	3.14793i	−0.139969	+	0.192650i
$268$			11.5889i			0.707903i
$269$	18.2828	+	13.2832i	1.11472	+	0.809892i	0.983401	−	0.181448i	$-0.0580783\pi$
$269$	18.2828	+	13.2832i	1.11472	+	0.809892i	0.131321	+	0.991340i	$0.458078\pi$
$270$	25.8601	−	20.9098i	1.57380	−	1.27253i
$271$	3.40219	−	2.47184i	0.206668	−	0.150153i	−0.479637	−	0.877467i	$-0.659232\pi$
$271$	3.40219	−	2.47184i	0.206668	−	0.150153i	0.686305	+	0.727314i	$0.259232\pi$
$272$	−4.67804	−	6.43877i	−0.283648	−	0.390408i
$273$	2.03767	−	0.662079i	0.123325	−	0.0400708i
$274$	−4.16429			−0.251574
$275$	8.88105	+	20.0260i	0.535548	+	1.20761i
$276$	3.70771			0.223178
$277$	−8.83200	+	2.86969i	−0.530663	+	0.172423i	−0.562079	−	0.827083i	$-0.689998\pi$
$277$	−8.83200	+	2.86969i	−0.530663	+	0.172423i	0.0314159	+	0.999506i	$0.489998\pi$
$278$	3.20987	+	4.41800i	0.192515	+	0.264974i
$279$	61.7095	−	44.8345i	3.69445	−	2.68417i
$280$	1.87443	+	1.21922i	0.112019	+	0.0728625i
$281$	−4.07694	−	2.96207i	−0.243210	−	0.176702i	0.459502	−	0.888177i	$-0.348028\pi$
$281$	−4.07694	−	2.96207i	−0.243210	−	0.176702i	−0.702712	+	0.711474i	$0.748028\pi$
$282$			9.49114i			0.565189i
$283$	13.2955	−	18.2996i	0.790333	−	1.08780i	−0.203734	−	0.979026i	$-0.565308\pi$
$283$	13.2955	−	18.2996i	0.790333	−	1.08780i	0.994067	−	0.108773i	$-0.0346922\pi$
$284$	3.99396	−	12.2922i	0.236998	−	0.729405i
$285$	1.22856	+	23.7753i	0.0727739	+	1.40833i
$286$	0.892087	+	2.74556i	0.0527502	+	0.162348i
$287$	−4.55728	−	1.48075i	−0.269008	−	0.0874059i
$288$	7.20305	+	2.34041i	0.424444	+	0.137910i
$289$	−14.3204	−	44.0737i	−0.842377	−	2.59257i
$290$	−6.19088	+	9.51786i	−0.363541	+	0.558908i
$291$	−16.8568	+	51.8800i	−0.988164	+	3.04126i
$292$	0.229002	−	0.315194i	0.0134013	−	0.0184453i
$293$		−	7.99697i		−	0.467188i	−0.972334	−	0.233594i	$-0.924951\pi$
$293$		−	7.99697i		−	0.467188i	0.972334	−	0.233594i	$-0.0750486\pi$
$294$	−2.63070	−	1.91132i	−0.153426	−	0.111470i
$295$	−2.53007	+	9.41478i	−0.147306	+	0.548150i
$296$	−3.47778	+	2.52676i	−0.202142	+	0.146865i
$297$	−38.3015	−	52.7176i	−2.22248	−	3.05898i
$298$	−0.363458	+	0.118095i	−0.0210545	+	0.00684103i
$299$	0.751284			0.0434479
$300$	15.8984	+	3.40364i	0.917894	+	0.196509i
$301$	5.18419			0.298812
$302$	6.67805	−	2.16983i	0.384279	−	0.124860i
$303$	−6.46543	−	8.89890i	−0.371429	−	0.511228i
$304$	−2.64889	+	1.92453i	−0.151924	+	0.110379i
$305$	1.34400	+	3.50890i	0.0769569	+	0.200919i
$306$	48.7656	+	35.4303i	2.78774	+	2.02541i
$307$		−	17.0859i		−	0.975144i	−0.873083	−	0.487572i	$-0.837883\pi$
$307$		−	17.0859i		−	0.975144i	0.873083	−	0.487572i	$-0.162117\pi$
$308$	2.57532	−	3.54462i	0.146742	−	0.201973i
$309$	9.25474	−	28.4832i	0.526484	−	1.62035i
$310$	21.7484	+	5.84453i	1.23523	+	0.331947i
$311$	7.47310	+	22.9999i	0.423761	+	1.30420i	0.904176	+	0.427161i	$0.140486\pi$
$311$	7.47310	+	22.9999i	0.423761	+	1.30420i	−0.480415	+	0.877041i	$0.659514\pi$
$312$	2.03767	+	0.662079i	0.115360	+	0.0374828i
$313$	−19.3857	−	6.29880i	−1.09574	−	0.356029i	−0.295281	−	0.955410i	$-0.595413\pi$
$313$	−19.3857	−	6.29880i	−1.09574	−	0.356029i	−0.800464	+	0.599381i	$0.795413\pi$
$314$	2.22404	+	6.84490i	0.125510	+	0.386280i
$315$	−16.3551	−	4.39517i	−0.921507	−	0.247640i
$316$	−2.31028	+	7.11032i	−0.129964	+	0.399987i
$317$	17.0313	−	23.4416i	0.956575	−	1.31661i	0.00803033	−	0.999968i	$-0.497444\pi$
$317$	17.0313	−	23.4416i	0.956575	−	1.31661i	0.948544	−	0.316644i	$-0.102556\pi$
$318$			1.52332i			0.0854236i
$319$	17.9986	+	13.0768i	1.00773	+	0.732158i
$320$	0.799807	+	2.08814i	0.0447106	+	0.116730i
$321$	−29.1464	+	21.1761i	−1.62679	+	1.18193i
$322$	−0.670209	−	0.922463i	−0.0373493	−	0.0514069i
$323$	−24.7832	+	8.05256i	−1.37898	+	0.448057i
$324$	−25.6403			−1.42446
$325$	3.22145	+	0.689671i	0.178694	+	0.0382561i
$326$	−13.1310			−0.727261
$327$	−7.38213	+	2.39860i	−0.408233	+	0.132643i
$328$	−2.81655	−	3.87665i	−0.155518	−	0.214052i
$329$	2.36136	−	1.71563i	0.130186	−	0.0945856i
$330$	8.26784	−	30.7659i	0.455130	−	1.69361i
$331$	−20.9436	−	15.2164i	−1.15117	−	0.836372i	−0.162531	−	0.986703i	$-0.551966\pi$
$331$	−20.9436	−	15.2164i	−1.15117	−	0.836372i	−0.988636	+	0.150332i	$0.951966\pi$
$332$			8.76528i			0.481057i
$333$	19.1370	−	26.3398i	1.04870	−	1.44341i
$334$	−5.43368	+	16.7231i	−0.297318	+	0.915050i
$335$	14.1294	−	21.7226i	0.771972	−	1.18683i
$336$	−1.00484	−	3.09258i	−0.0548185	−	0.168714i
$337$	20.9732	+	6.81459i	1.14248	+	0.371214i	0.818306	−	0.574783i	$-0.194913\pi$
$337$	20.9732	+	6.81459i	1.14248	+	0.371214i	0.324175	+	0.945997i	$0.394913\pi$
$338$	−11.9508	−	3.88307i	−0.650040	−	0.211211i
$339$	−12.3118	−	37.8918i	−0.668684	−	2.05800i
$340$	0.918380	+	17.7726i	0.0498061	+	0.963855i
$341$	13.6357	−	41.9664i	0.738415	−	2.27261i
$342$	14.5759	−	20.0620i	0.788175	−	1.08483i
$343$			1.00000i			0.0539949i
$344$	4.19410	+	3.04719i	0.226131	+	0.164294i
$345$	−6.94985	−	4.52052i	−0.374168	−	0.243377i
$346$	4.14814	−	3.01380i	0.223006	−	0.162023i
$347$	20.2673	+	27.8956i	1.08801	+	1.49751i	0.850389	+	0.526154i	$0.176367\pi$
$347$	20.2673	+	27.8956i	1.08801	+	1.49751i	0.237618	+	0.971359i	$0.423633\pi$
$348$	15.7033	−	5.10230i	0.841783	−	0.273512i
$349$	−25.9573			−1.38946			−0.694731	−	0.719269i	$-0.744477\pi$
$349$	−25.9573			−1.38946			−0.694731	+	0.719269i	$0.744477\pi$
$350$	−2.02699	−	4.57070i	−0.108347	−	0.244314i
$351$	−9.79938			−0.523052
$352$	4.16695	−	1.35392i	0.222099	−	0.0721644i
$353$	8.21005	+	11.3002i	0.436977	+	0.601447i	0.969537	−	0.244945i	$-0.0787699\pi$
$353$	8.21005	+	11.3002i	0.436977	+	0.601447i	−0.532560	+	0.846392i	$0.678770\pi$
$354$	11.4693	−	8.33296i	0.609589	−	0.442892i
$355$	−22.4733	+	18.1713i	−1.19276	+	0.964432i
$356$	0.968079	+	0.703350i	0.0513081	+	0.0372775i
$357$		−	25.8797i		−	1.36970i
$358$	8.48087	−	11.6729i	0.448228	−	0.616933i
$359$	−0.142946	+	0.439944i	−0.00754442	+	0.0232193i	−0.954758	−	0.297384i	$-0.903886\pi$
$359$	−0.142946	+	0.439944i	−0.00754442	+	0.0232193i	0.947213	+	0.320604i	$0.103886\pi$
$360$	−10.6482	−	13.1691i	−0.561207	−	0.694071i
$361$	−2.55852	−	7.87432i	−0.134659	−	0.414438i
$362$	−11.5238	−	3.74430i	−0.605675	−	0.196796i
$363$	−25.3485	−	8.23624i	−1.33045	−	0.432291i
$364$	−0.203608	−	0.626642i	−0.0106720	−	0.0328449i
$365$	−0.813539	+	0.311605i	−0.0425826	+	0.0163102i
$366$	1.68853	−	5.19677i	0.0882610	−	0.271639i
$367$	−22.0547	+	30.3557i	−1.15125	+	1.58455i	−0.411897	+	0.911231i	$0.635133\pi$
$367$	−22.0547	+	30.3557i	−1.15125	+	1.58455i	−0.739349	+	0.673323i	$0.764867\pi$
$368$		−	1.14023i		−	0.0594385i
$369$	29.3608	+	21.3318i	1.52846	+	1.11049i
$370$	9.59955	−	0.496046i	0.499057	−	0.0257882i
$371$	0.378996	−	0.275357i	0.0196765	−	0.0142958i
$372$	−19.2494	−	26.4945i	−0.998034	−	1.37368i
$373$	−4.09692	+	1.33117i	−0.212130	+	0.0689253i	−0.413154	−	0.910661i	$-0.635573\pi$
$373$	−4.09692	+	1.33117i	−0.212130	+	0.0689253i	0.201024	+	0.979586i	$0.435573\pi$
$374$	34.8704			1.80311
$375$	−25.6507	−	25.7636i	−1.32459	−	1.33042i
$376$	2.91880			0.150526
$377$	3.18191	−	1.03387i	0.163877	−	0.0532468i
$378$	8.74187	+	12.0322i	0.449633	+	0.618867i
$379$	−6.41735	+	4.66248i	−0.329637	+	0.239495i	−0.740277	−	0.672302i	$-0.765305\pi$
$379$	−6.41735	+	4.66248i	−0.329637	+	0.239495i	0.410639	+	0.911798i	$0.365305\pi$
$380$	7.31160	−	0.377819i	0.375077	−	0.0193817i
$381$	20.4872	+	14.8848i	1.04959	+	0.762573i
$382$		−	1.96770i		−	0.100676i
$383$	−12.4930	+	17.1951i	−0.638362	+	0.878629i	−0.998527	−	0.0542591i	$-0.982720\pi$
$383$	−12.4930	+	17.1951i	−0.638362	+	0.878629i	0.360165	+	0.932889i	$0.382720\pi$
$384$	1.00484	−	3.09258i	0.0512780	−	0.157817i
$385$	−9.14893	+	3.50427i	−0.466273	+	0.178594i
$386$	−3.42838	−	10.5515i	−0.174500	−	0.537056i
$387$	−37.3420	−	12.1332i	−1.89820	−	0.616763i
$388$	15.9546	+	5.18396i	0.809971	+	0.263176i
$389$	9.96900	+	30.6814i	0.505449	+	1.55561i	0.800015	+	0.599980i	$0.204825\pi$
$389$	9.96900	+	30.6814i	0.505449	+	1.55561i	−0.294566	+	0.955631i	$0.595175\pi$
$390$	−3.01225	−	3.72539i	−0.152531	−	0.188643i
$391$	2.80427	−	8.63064i	0.141818	−	0.436470i
$392$	−0.587785	+	0.809017i	−0.0296876	+	0.0408615i
$393$		−	18.0589i		−	0.910951i
$394$	5.53166	+	4.01899i	0.278681	+	0.202474i
$395$	12.9995	−	10.5111i	0.654077	−	0.528869i
$396$	−26.8460	+	19.5048i	−1.34906	+	0.980152i
$397$	1.82047	+	2.50566i	0.0913668	+	0.125756i	0.852253	−	0.523129i	$-0.175236\pi$
$397$	1.82047	+	2.50566i	0.0913668	+	0.125756i	−0.760886	+	0.648885i	$0.775236\pi$
$398$	16.2188	−	5.26980i	0.812974	−	0.264151i
$399$	−10.6468			−0.533009
$400$	1.04672	−	4.88921i	0.0523358	−	0.244461i
$401$	7.59895			0.379474			0.189737	−	0.981835i	$-0.439237\pi$
$401$	7.59895			0.379474			0.189737	+	0.981835i	$0.439237\pi$
$402$	−35.8395	+	11.6450i	−1.78751	+	0.580798i
$403$	−3.90046	−	5.36852i	−0.194296	−	0.267425i
$404$	−2.73667	+	1.98830i	−0.136154	+	0.0989218i
$405$	48.0610	+	31.2612i	2.38817	+	1.55338i
$406$	−4.10797	−	2.98461i	−0.203875	−	0.148124i
$407$		−	18.8346i		−	0.933597i
$408$	15.2117	−	20.9371i	0.753092	−	1.03654i
$409$	5.56677	−	17.1328i	0.275259	−	0.847160i	−0.713892	−	0.700256i	$-0.753069\pi$
$409$	5.56677	−	17.1328i	0.275259	−	0.847160i	0.989151	−	0.146904i	$-0.0469308\pi$
$410$	0.552938	+	10.7005i	0.0273076	+	0.528461i
$411$	−4.18445	−	12.8784i	−0.206404	−	0.635245i
$412$	−8.75939	−	2.84610i	−0.431544	−	0.140217i
$413$	−4.14642	−	1.34725i	−0.204032	−	0.0662940i
$414$	2.66860	+	8.21312i	0.131155	+	0.403653i
$415$	10.6868	−	16.4299i	0.524595	−	0.806513i
$416$	0.203608	−	0.626642i	0.00998271	−	0.0307236i
$417$	−10.4376	+	14.3661i	−0.511132	+	0.703513i
$418$		−	14.3456i		−	0.701666i
$419$	29.5393	+	21.4615i	1.44309	+	1.04847i	0.987386	+	0.158333i	$0.0506119\pi$
$419$	29.5393	+	21.4615i	1.44309	+	1.04847i	0.455702	+	0.890132i	$0.349388\pi$
$420$	−1.88704	+	7.02195i	−0.0920779	+	0.342636i
$421$	−2.79172	+	2.02830i	−0.136060	+	0.0988534i	−0.653733	−	0.756725i	$-0.726798\pi$
$421$	−2.79172	+	2.02830i	−0.136060	+	0.0988534i	0.517673	+	0.855578i	$0.326798\pi$
$422$	9.56512	+	13.1653i	0.465623	+	0.640875i
$423$	−21.0243	+	6.83120i	−1.02223	+	0.332144i
$424$	0.468465			0.0227507
$425$	19.9473	−	34.4333i	0.967587	−	1.67026i
$426$	42.0277			2.03625
$427$	−1.59815	+	0.519272i	−0.0773401	+	0.0251293i
$428$	6.51225	+	8.96334i	0.314781	+	0.433259i
$429$	−7.59446	+	5.51770i	−0.366664	+	0.266397i
$430$	−4.14635	−	10.8253i	−0.199955	−	0.522042i
$431$	−6.81684	−	4.95273i	−0.328356	−	0.238564i	0.411377	−	0.911465i	$-0.365048\pi$
$431$	−6.81684	−	4.95273i	−0.328356	−	0.238564i	−0.739733	+	0.672901i	$0.765048\pi$
$432$			14.8726i			0.715556i
$433$	13.6083	−	18.7302i	0.653973	−	0.900116i	−0.345290	−	0.938496i	$-0.612220\pi$
$433$	13.6083	−	18.7302i	0.653973	−	0.900116i	0.999263	+	0.0383795i	$0.0122196\pi$
$434$	−3.11219	+	9.57834i	−0.149390	+	0.459775i
$435$	−35.6555	−	9.58185i	−1.70955	−	0.459415i
$436$	0.737638	+	2.27022i	0.0353264	+	0.108724i
$437$	−3.55062	−	1.15367i	−0.169849	−	0.0551874i
$438$	1.20487	+	0.391486i	0.0575710	+	0.0187059i
$439$	−9.45103	−	29.0873i	−0.451073	−	1.38826i	−0.875684	−	0.482884i	$-0.839589\pi$
$439$	−9.45103	−	29.0873i	−0.451073	−	1.38826i	0.424611	−	0.905376i	$-0.360411\pi$
$440$	−9.46140	−	2.54260i	−0.451055	−	0.121214i
$441$	2.34041	−	7.20305i	0.111448	−	0.343003i
$442$	3.08231	−	4.24244i	0.146611	−	0.201792i
$443$			17.9444i			0.852564i	0.904590	+	0.426282i	$0.140177\pi$
$443$			17.9444i			0.852564i	−0.904590	+	0.426282i	$0.859823\pi$
$444$	−11.3088	−	8.21633i	−0.536692	−	0.389930i
$445$	−0.957058	−	2.49869i	−0.0453689	−	0.118449i
$446$	−18.9213	+	13.7472i	−0.895952	+	0.650947i
$447$	−0.730433	−	1.00536i	−0.0345483	−	0.0475517i
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	17.1723			0.810409			0.405204	−	0.914226i	$-0.367200\pi$
$449$	17.1723			0.810409			0.405204	+	0.914226i	$0.367200\pi$
$450$	3.90322	+	37.6670i	0.184000	+	1.77564i
$451$	20.9948			0.988605
$452$	−11.6528	+	3.78623i	−0.548102	+	0.178089i
$453$	13.4207	+	18.4721i	0.630561	+	0.867893i
$454$	−0.893804	+	0.649387i	−0.0419483	+	0.0304772i
$455$	−0.382365	+	1.42284i	−0.0179256	+	0.0667038i
$456$	−8.61347	−	6.25806i	−0.403363	−	0.293060i
$457$			17.5523i			0.821064i	0.911846	+	0.410532i	$0.134657\pi$
$457$			17.5523i			0.821064i	−0.911846	+	0.410532i	$0.865343\pi$
$458$	−8.67766	+	11.9438i	−0.405481	+	0.558096i
$459$	−36.5774	+	112.574i	−1.70729	+	5.25450i
$460$	−1.39019	+	2.13728i	−0.0648180	+	0.0996512i
$461$	−2.25058	−	6.92656i	−0.104820	−	0.322602i	0.884868	−	0.465841i	$-0.154248\pi$
$461$	−2.25058	−	6.92656i	−0.104820	−	0.322602i	−0.989688	+	0.143239i	$0.954248\pi$
$462$	13.5498	+	4.40259i	0.630393	+	0.204827i
$463$	40.4619	+	13.1469i	1.88042	+	0.610986i	0.986745	+	0.162276i	$0.0518836\pi$
$463$	40.4619	+	13.1469i	1.88042	+	0.610986i	0.893677	+	0.448710i	$0.148116\pi$
$464$	−1.56910	−	4.82921i	−0.0728438	−	0.224190i
$465$	3.77898	+	73.1314i	0.175246	+	3.39139i
$466$	−2.30203	+	7.08493i	−0.106640	+	0.328203i
$467$	4.29161	−	5.90689i	0.198592	−	0.273338i	−0.698094	−	0.716007i	$-0.745968\pi$
$467$	4.29161	−	5.90689i	0.198592	−	0.273338i	0.896685	+	0.442668i	$0.145968\pi$
$468$			4.99026i			0.230675i
$469$	9.37559	+	6.81177i	0.432925	+	0.314538i
$470$	−5.47109	−	3.55866i	−0.252363	−	0.164149i
$471$	−18.9336	+	13.7561i	−0.872413	+	0.633845i
$472$	−2.56263	−	3.52715i	−0.117954	−	0.162350i
$473$	−21.6023	+	7.01900i	−0.993273	+	0.322734i
$474$	−24.3107			−1.11663
$475$	−14.1657	−	8.20627i	−0.649969	−	0.376529i
$476$	−7.95876			−0.364789
$477$	−3.37438	+	1.09640i	−0.154502	+	0.0502008i
$478$	−1.80723	−	2.48744i	−0.0826608	−	0.113773i
$479$	−25.3484	+	18.4167i	−1.15820	+	0.841481i	−0.989549	−	0.144195i	$-0.953941\pi$
$479$	−25.3484	+	18.4167i	−1.15820	+	0.841481i	−0.168650	+	0.985676i	$0.553941\pi$
$480$	−5.65404	+	4.57171i	−0.258071	+	0.208669i
$481$	−2.29148	−	1.66486i	−0.104482	−	0.0759109i
$482$		−	6.19331i		−	0.282098i
$483$	2.17934	−	2.99960i	0.0991633	−	0.136487i
$484$	−2.53288	+	7.79541i	−0.115131	+	0.354337i
$485$	−23.5854	−	29.1692i	−1.07096	−	1.32450i
$486$	−11.9768	−	36.8607i	−0.543278	−	1.67204i
$487$	27.2701	+	8.86060i	1.23573	+	0.401512i	0.852786	−	0.522260i	$-0.174911\pi$
$487$	27.2701	+	8.86060i	1.23573	+	0.401512i	0.382942	+	0.923773i	$0.374911\pi$
$488$	−1.59815	−	0.519272i	−0.0723451	−	0.0235063i
$489$	−13.1946	−	40.6088i	−0.596680	−	1.83639i
$490$	2.08814	−	0.799807i	0.0943323	−	0.0361316i
$491$	10.3418	−	31.8288i	0.466720	−	1.43642i	−0.390087	−	0.920778i	$-0.627555\pi$
$491$	10.3418	−	31.8288i	0.466720	−	1.43642i	0.856807	−	0.515637i	$-0.172445\pi$
$492$	9.15866	−	12.6058i	0.412904	−	0.568314i
$493$		−	40.4124i		−	1.82008i
$494$	−1.74533	−	1.26805i	−0.0785260	−	0.0570525i
$495$	74.1017	−	3.82912i	3.33062	−	0.172106i
$496$	−8.14782	+	5.91974i	−0.365848	+	0.265804i
$497$	−7.59697	−	10.4563i	−0.340771	−	0.469031i
$498$	−27.1073	+	8.80770i	−1.21471	+	0.394682i
$499$	11.1077			0.497251			0.248625	−	0.968600i	$-0.420021\pi$
$499$	11.1077			0.497251			0.248625	+	0.968600i	$0.420021\pi$
$500$	−7.92303	+	7.88832i	−0.354329	+	0.352776i
$501$	−57.1776			−2.55451
$502$	7.33935	−	2.38470i	0.327571	−	0.106434i
$503$	−4.82664	−	6.64330i	−0.215209	−	0.296210i	0.687740	−	0.725957i	$-0.258603\pi$
$503$	−4.82664	−	6.64330i	−0.215209	−	0.296210i	−0.902949	+	0.429747i	$0.858603\pi$
$504$	6.12728	−	4.45173i	0.272931	−	0.198296i
$505$	7.55388	−	0.390338i	0.336143	−	0.0173698i
$506$	4.04167	+	2.93645i	0.179674	+	0.130541i
$507$		−	40.8608i		−	1.81469i
$508$	4.57751	−	6.30041i	0.203094	−	0.279535i
$509$	−0.147906	+	0.455207i	−0.00655581	+	0.0201767i	−0.954281	−	0.298911i	$-0.903377\pi$
$509$	−0.147906	+	0.455207i	−0.00655581	+	0.0201767i	0.947725	+	0.319088i	$0.103377\pi$
$510$	−54.0404	+	20.6988i	−2.39295	+	0.916557i
$511$	−0.120393	−	0.370532i	−0.00532589	−	0.0163914i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	46.3125	+	15.0479i	2.04475	+	0.664379i
$514$	−5.96606	−	18.3616i	−0.263151	−	0.809897i
$515$	12.9489	+	16.0145i	0.570595	+	0.705682i
$516$	−5.20928	+	16.0325i	−0.229326	+	0.705792i
$517$	−7.51683	+	10.3460i	−0.330590	+	0.455018i
$518$			4.29878i			0.188877i
$519$	13.4886	+	9.80007i	0.592085	+	0.430175i
$520$	−1.14567	+	0.926354i	−0.0502407	+	0.0406233i
$521$	7.25669	−	5.27229i	0.317921	−	0.230983i	−0.417367	−	0.908738i	$-0.637047\pi$
$521$	7.25669	−	5.27229i	0.317921	−	0.230983i	0.735288	+	0.677755i	$0.237047\pi$
$522$	22.6047	+	31.1127i	0.989380	+	1.36176i
$523$	28.4478	−	9.24325i	1.24394	−	0.404179i	0.388192	−	0.921579i	$-0.373100\pi$
$523$	28.4478	−	9.24325i	1.24394	−	0.404179i	0.855744	+	0.517400i	$0.173100\pi$
$524$	−5.55363			−0.242611
$525$	12.0984	−	10.8615i	0.528019	−	0.474033i
$526$	2.48818			0.108490
$527$	−76.2317	+	24.7692i	−3.32070	+	1.07896i
$528$	8.37423	+	11.5261i	0.364442	+	0.501611i
$529$	−17.5556	+	12.7549i	−0.763286	+	0.554560i
$530$	−0.878106	−	0.571163i	−0.0381425	−	0.0248097i
$531$	26.7137	+	19.4087i	1.15928	+	0.842264i
$532$			3.27421i			0.141955i
$533$	1.85580	−	2.55429i	0.0803835	−	0.110638i
$534$	−1.20240	+	3.70061i	−0.0520330	+	0.160141i
$535$	−1.27847	−	24.7411i	−0.0552729	−	1.06965i
$536$	3.58116	+	11.0217i	0.154682	+	0.476064i
$537$	44.6213	+	14.4983i	1.92555	+	0.625649i
$538$	21.4927	+	6.98340i	0.926616	+	0.301076i
$539$	−1.35392	−	4.16695i	−0.0583176	−	0.179483i
$540$	18.1330	−	27.8776i	0.780318	−	1.19966i
$541$	5.90960	−	18.1879i	0.254074	−	0.781959i	−0.739937	−	0.672676i	$-0.765145\pi$
$541$	5.90960	−	18.1879i	0.254074	−	0.781959i	0.994011	−	0.109282i	$-0.0348553\pi$
$542$	2.47184	−	3.40219i	0.106174	−	0.146137i
$543$		−	39.4005i		−	1.69084i
$544$	−6.43877	−	4.67804i	−0.276060	−	0.200569i
$545$	1.38525	−	5.15471i	0.0593374	−	0.220804i
$546$	1.73334	−	1.25935i	0.0741803	−	0.0538951i
$547$	20.2550	+	27.8786i	0.866040	+	1.19200i	0.980095	+	0.198528i	$0.0636160\pi$
$547$	20.2550	+	27.8786i	0.866040	+	1.19200i	−0.114055	+	0.993474i	$0.536384\pi$
$548$	−3.96048	+	1.28684i	−0.169183	+	0.0549710i
$549$	12.7269			0.543171
$550$	14.6348	+	16.3015i	0.624028	+	0.695097i
$551$	−16.6255			−0.708272
$552$	3.52624	−	1.14575i	0.150087	−	0.0487662i
$553$	4.39442	+	6.04840i	0.186870	+	0.257204i
$554$	−7.51295	+	5.45847i	−0.319194	+	0.231908i
$555$	11.1801	+	29.1889i	0.474567	+	1.23900i
$556$	4.41800	+	3.20987i	0.187365	+	0.136129i
$557$		−	36.8184i		−	1.56004i	−0.625752	−	0.780022i	$-0.715208\pi$
$557$		−	36.8184i		−	1.56004i	0.625752	−	0.780022i	$-0.284792\pi$
$558$	44.8345	−	61.7095i	1.89800	−	2.61237i
$559$	−1.05554	+	3.24863i	−0.0446448	+	0.137402i
$560$	2.15945	+	0.580318i	0.0912535	+	0.0245229i
$561$	35.0392	+	107.839i	1.47936	+	4.55299i
$562$	−4.79273	−	1.55725i	−0.202169	−	0.0656888i
$563$	12.3452	+	4.01121i	0.520290	+	0.169052i	0.557377	−	0.830260i	$-0.311808\pi$
$563$	12.3452	+	4.01121i	0.520290	+	0.169052i	−0.0370870	+	0.999312i	$0.511808\pi$
$564$	2.93292	+	9.02661i	0.123498	+	0.380089i
$565$	26.4586	+	7.11033i	1.11312	+	0.299134i
$566$	6.98983	−	21.5125i	0.293805	−	0.904238i
$567$	−15.0710	+	20.7434i	−0.632922	+	0.871143i
$568$		−	12.9247i		−	0.542310i
$569$	0.351477	+	0.255363i	0.0147347	+	0.0107054i	0.595128	−	0.803631i	$-0.297101\pi$
$569$	0.351477	+	0.255363i	0.0147347	+	0.0107054i	−0.580394	+	0.814336i	$0.697101\pi$
$570$	8.51542	+	22.2320i	0.356672	+	0.931198i
$571$	3.66177	−	2.66043i	0.153240	−	0.111335i	−0.508523	−	0.861048i	$-0.669808\pi$
$571$	3.66177	−	2.66043i	0.153240	−	0.111335i	0.661763	+	0.749713i	$0.269808\pi$
$572$	1.69685	+	2.33551i	0.0709489	+	0.0976527i
$573$	6.08527	−	1.97722i	0.254216	−	0.0825997i
$574$	−4.79181			−0.200006
$575$	5.21164	−	2.31124i	0.217340	−	0.0963852i
$576$	7.57374			0.315572
$577$	−1.09818	+	0.356819i	−0.0457177	+	0.0148546i	−0.331787	−	0.943354i	$-0.607651\pi$
$577$	−1.09818	+	0.356819i	−0.0457177	+	0.0148546i	0.286069	+	0.958209i	$0.407651\pi$
$578$	−27.2390	−	37.4913i	−1.13299	−	1.55943i
$579$	29.1863	−	21.2051i	1.21294	−	0.881252i
$580$	−2.94669	+	10.9651i	−0.122355	+	0.455301i
$581$	7.09126	+	5.15210i	0.294195	+	0.213745i
$582$			54.5498i			2.26116i
$583$	−1.20645	+	1.66053i	−0.0499659	+	0.0687721i
$584$	0.120393	−	0.370532i	0.00498191	−	0.0153327i
$585$	6.08424	−	9.35391i	0.251552	−	0.386736i
$586$	−2.47120	−	7.60557i	−0.102084	−	0.314183i
$587$	−40.9152	−	13.2942i	−1.68875	−	0.548709i	−0.702175	−	0.712005i	$-0.747787\pi$
$587$	−40.9152	−	13.2942i	−1.68875	−	0.548709i	−0.986577	+	0.163296i	$0.947787\pi$
$588$	−3.09258	−	1.00484i	−0.127536	−	0.0414389i
$589$	10.1900	+	31.3615i	0.419870	+	1.29223i
$590$	0.503088	+	9.73582i	0.0207118	+	0.400817i
$591$	−6.87060	+	21.1455i	−0.282619	+	0.869810i
$592$	−2.52676	+	3.47778i	−0.103849	+	0.142936i
$593$			43.5188i			1.78710i	0.448960	+	0.893552i	$0.351795\pi$
$593$			43.5188i			1.78710i	−0.448960	+	0.893552i	$0.648205\pi$
$594$	−52.7176	−	38.3015i	−2.16303	−	1.57153i
$595$	14.9182	+	9.70349i	0.611585	+	0.397804i
$596$	−0.309176	+	0.224629i	−0.0126643	+	0.00920117i
$597$	32.5945	+	44.8625i	1.33401	+	1.83610i
$598$	0.714514	−	0.232160i	0.0292186	−	0.00949371i
$599$	3.17926			0.129901			0.0649505	−	0.997888i	$-0.479311\pi$
$599$	3.17926			0.129901			0.0649505	+	0.997888i	$0.479311\pi$
$600$	16.1720	−	1.67582i	0.660221	−	0.0684151i
$601$	18.9056			0.771177			0.385588	−	0.922671i	$-0.373998\pi$
$601$	18.9056			0.771177			0.385588	+	0.922671i	$0.373998\pi$
$602$	4.93046	−	1.60200i	0.200951	−	0.0652928i
$603$	−51.5906	−	71.0083i	−2.10093	−	2.89168i
$604$	5.68069	−	4.12726i	0.231144	−	0.167936i
$605$	14.2520	−	11.5238i	0.579428	−	0.468510i
$606$	−8.89890	−	6.46543i	−0.361493	−	0.262640i
$607$			21.6029i			0.876833i	0.898772	+	0.438417i	$0.144461\pi$
$607$			21.6029i			0.876833i	−0.898772	+	0.438417i	$0.855539\pi$
$608$	−1.92453	+	2.64889i	−0.0780501	+	0.107427i
$609$	5.10230	−	15.7033i	0.206756	−	0.636328i
$610$	2.36253	+	2.92185i	0.0956559	+	0.118302i
$611$	0.594291	+	1.82904i	0.0240424	+	0.0739951i
$612$	57.3274	+	18.6268i	2.31732	+	0.752943i
$613$	−25.4666	−	8.27461i	−1.02859	−	0.334208i	−0.254356	−	0.967111i	$-0.581863\pi$
$613$	−25.4666	−	8.27461i	−1.02859	−	0.334208i	−0.774232	+	0.632902i	$0.781863\pi$
$614$	−5.27984	−	16.2497i	−0.213077	−	0.655783i
$615$	−32.5366	+	12.4623i	−1.31200	+	0.502529i
$616$	1.35392	−	4.16695i	0.0545511	−	0.167891i
$617$	11.4362	−	15.7405i	0.460403	−	0.633691i	−0.514189	−	0.857677i	$-0.671907\pi$
$617$	11.4362	−	15.7405i	0.460403	−	0.633691i	0.974592	+	0.223986i	$0.0719070\pi$
$618$		−	29.9490i		−	1.20472i
$619$	−2.15443	−	1.56529i	−0.0865940	−	0.0629142i	0.543646	−	0.839315i	$-0.317043\pi$
$619$	−2.15443	−	1.56529i	−0.0865940	−	0.0629142i	−0.630240	+	0.776400i	$0.717043\pi$
$620$	22.4900	−	1.16215i	0.903221	−	0.0466729i
$621$	−13.7194	+	9.96772i	−0.550540	+	0.399991i
$622$	14.2147	+	19.5648i	0.569957	+	0.784479i
$623$	1.13804	−	0.369773i	0.0455948	−	0.0148146i
$624$	2.14253			0.0857699
$625$	24.4688	−	5.12618i	0.978752	−	0.205047i
$626$	−20.3833			−0.814682
$627$	44.3648	−	14.4150i	1.77176	−	0.575680i
$628$	4.23038	+	5.82262i	0.168811	+	0.232348i
$629$	−27.6788	+	20.1099i	−1.10363	+	0.801832i
$630$	−16.9128	+	0.873952i	−0.673823	+	0.0348191i
$631$	−8.68740	−	6.31176i	−0.345840	−	0.251267i	0.401282	−	0.915955i	$-0.368565\pi$
$631$	−8.68740	−	6.31176i	−0.345840	−	0.251267i	−0.747122	+	0.664687i	$0.768565\pi$
$632$			7.47623i			0.297389i
$633$	−31.1032	+	42.8099i	−1.23624	+	1.70154i
$634$	8.95390	−	27.5573i	0.355605	−	1.09444i
$635$	−16.2618	+	6.22868i	−0.645331	+	0.247178i
$636$	0.470732	+	1.44876i	0.0186657	+	0.0574472i
$637$	−0.626642	−	0.203608i	−0.0248284	−	0.00806725i
$638$	21.1586	+	6.87486i	0.837678	+	0.272178i
$639$	30.2492	+	93.0976i	1.19664	+	3.68288i
$640$	1.40593	+	1.73878i	0.0555743	+	0.0687313i
$641$	5.55911	−	17.1092i	0.219572	−	0.675772i	−0.779226	−	0.626743i	$-0.784388\pi$
$641$	5.55911	−	17.1092i	0.219572	−	0.675772i	0.998797	−	0.0490284i	$-0.0156125\pi$
$642$	−21.1761	+	29.1464i	−0.835753	+	1.15031i
$643$			19.0997i			0.753220i	0.926372	+	0.376610i	$0.122910\pi$
$643$			19.0997i			0.753220i	−0.926372	+	0.376610i	$0.877090\pi$
$644$	−0.922463	−	0.670209i	−0.0363502	−	0.0264099i
$645$	29.3117	−	23.7006i	1.15415	−	0.933210i
$646$	−21.0819	+	15.3169i	−0.829456	+	0.602635i
$647$	−0.551203	−	0.758667i	−0.0216700	−	0.0298263i	0.798045	−	0.602599i	$-0.205868\pi$
$647$	−0.551203	−	0.758667i	−0.0216700	−	0.0298263i	−0.819715	+	0.572772i	$0.805868\pi$
$648$	−24.3854	+	7.92329i	−0.957948	+	0.311256i
$649$	19.1020			0.749818
$650$	3.27690	−	0.339567i	0.128531	−	0.0133189i
$651$	−32.7490			−1.28353
$652$	−12.4884	+	4.05771i	−0.489082	+	0.158912i
$653$	−12.7760	−	17.5847i	−0.499964	−	0.688141i	0.482223	−	0.876049i	$-0.339830\pi$
$653$	−12.7760	−	17.5847i	−0.499964	−	0.688141i	−0.982187	+	0.187907i	$0.939830\pi$
$654$	−6.27961	+	4.56241i	−0.245552	+	0.178404i
$655$	10.4099	+	6.77111i	0.406749	+	0.264569i
$656$	−3.87665	−	2.81655i	−0.151358	−	0.109968i
$657$			2.95074i			0.115119i
$658$	1.71563	−	2.36136i	0.0668821	−	0.0920553i
$659$	11.7939	−	36.2978i	0.459424	−	1.41396i	−0.406437	−	0.913679i	$-0.633229\pi$
$659$	11.7939	−	36.2978i	0.459424	−	1.41396i	0.865861	−	0.500284i	$-0.166771\pi$
$660$	−1.64401	−	31.8150i	−0.0639928	−	1.23840i
$661$	−12.9408	−	39.8275i	−0.503337	−	1.54911i	−0.803548	−	0.595239i	$-0.797057\pi$
$661$	−12.9408	−	39.8275i	−0.503337	−	1.54911i	0.300211	−	0.953873i	$-0.402943\pi$
$662$	−24.6207	−	7.99976i	−0.956912	−	0.310919i
$663$	16.2173	+	5.26932i	0.629828	+	0.204644i
$664$	2.70862	+	8.33627i	0.105115	+	0.323510i
$665$	3.99199	−	6.13728i	0.154803	−	0.237994i
$666$	10.0609	−	30.9643i	0.389853	−	1.19984i
$667$	3.40314	−	4.68402i	0.131770	−	0.181366i
$668$			17.5838i			0.680336i
$669$	−61.5271	−	44.7020i	−2.37877	−	1.72828i
$670$	6.72523	−	25.0256i	0.259818	−	0.966824i
$671$	5.95637	−	4.32756i	0.229943	−	0.167064i
$672$	−1.91132	−	2.63070i	−0.0737307	−	0.101482i
$673$	−26.1874	+	8.50879i	−1.00945	+	0.327990i	−0.766635	−	0.642083i	$-0.778070\pi$
$673$	−26.1874	+	8.50879i	−1.00945	+	0.327990i	−0.242814	+	0.970073i	$0.578070\pi$
$674$	22.0525			0.849430
$675$	−67.9780	+	30.1466i	−2.61647	+	1.16034i
$676$	−12.5659			−0.483302
$677$	24.3865	−	7.92367i	0.937251	−	0.304531i	0.199726	−	0.979852i	$-0.435995\pi$
$677$	24.3865	−	7.92367i	0.937251	−	0.304531i	0.737524	+	0.675320i	$0.235995\pi$
$678$	−23.4184	−	32.2327i	−0.899378	−	1.23789i
$679$	13.5718	−	9.86047i	0.520837	−	0.378410i
$680$	6.36547	+	16.6190i	0.244105	+	0.637308i
$681$	−2.90641	−	2.11163i	−0.111374	−	0.0809178i
$682$		−	44.1261i		−	1.68968i
$683$	0.150951	−	0.207766i	0.00577598	−	0.00794995i	−0.806119	−	0.591753i	$-0.798436\pi$
$683$	0.150951	−	0.207766i	0.00577598	−	0.00794995i	0.811895	+	0.583803i	$0.198436\pi$
$684$	7.66301	−	23.5843i	0.293002	−	0.901769i
$685$	8.99259	+	2.41661i	0.343589	+	0.0923340i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−45.6567	−	14.8348i	−1.74191	−	0.565982i
$688$	4.93046	+	1.60200i	0.187972	+	0.0610758i
$689$	0.0953833	+	0.293560i	0.00363381	+	0.0111837i
$690$	−8.00662	−	2.15165i	−0.304807	−	0.0819119i
$691$	7.62967	−	23.4817i	0.290246	−	0.893286i	−0.694531	−	0.719463i	$-0.744388\pi$
$691$	7.62967	−	23.4817i	0.290246	−	0.893286i	0.984777	−	0.173823i	$-0.0556121\pi$
$692$	3.01380	−	4.14814i	0.114568	−	0.157689i
$693$			33.1835i			1.26054i
$694$	27.8956	+	20.2673i	1.05890	+	0.769337i
$695$	−4.36771	−	11.4032i	−0.165677	−	0.432548i
$696$	13.3580	−	9.70515i	0.506333	−	0.367873i
$697$	−22.4163	−	30.8533i	−0.849076	−	1.16865i
$698$	−24.6869	+	8.02125i	−0.934412	+	0.303609i
$699$	−24.2239			−0.916231
$700$	−3.34021	−	3.72062i	−0.126248	−	0.140626i
$701$	−8.99367			−0.339686			−0.169843	−	0.985471i	$-0.554326\pi$
$701$	−8.99367			−0.339686			−0.169843	+	0.985471i	$0.554326\pi$
$702$	−9.31976	+	3.02818i	−0.351752	+	0.114291i
$703$	8.27313	+	11.3870i	0.312027	+	0.429469i
$704$	3.54462	−	2.57532i	0.133593	−	0.0970609i
$705$	5.50788	−	20.4957i	0.207439	−	0.771911i
$706$	11.3002	+	8.21005i	0.425287	+	0.308989i
$707$			3.38271i			0.127220i
$708$	8.33296	−	11.4693i	0.313172	−	0.431044i
$709$	2.70498	−	8.32508i	0.101588	−	0.312655i	−0.887327	−	0.461141i	$-0.847440\pi$
$709$	2.70498	−	8.32508i	0.101588	−	0.312655i	0.988914	+	0.148486i	$0.0474401\pi$
$710$	−15.7581	+	24.2265i	−0.591392	+	0.909206i
$711$	−17.4975	−	53.8517i	−0.656207	−	2.01960i
$712$	1.13804	+	0.369773i	0.0426500	+	0.0138578i
$713$	−10.9215	−	3.54860i	−0.409013	−	0.132896i
$714$	−7.99727	−	24.6131i	−0.299290	−	0.921121i
$715$	−0.333121	−	6.44660i	−0.0124580	−	0.241089i
$716$	4.45866	−	13.7223i	0.166628	−	0.512828i
$717$	5.87663	−	8.08848i	0.219467	−	0.302070i
$718$			0.462584i			0.0172635i
$719$	−9.01887	−	6.55259i	−0.336347	−	0.244371i	0.406772	−	0.913530i	$-0.366654\pi$
$719$	−9.01887	−	6.55259i	−0.336347	−	0.244371i	−0.743119	+	0.669159i	$0.766654\pi$
$720$	−14.1965	−	9.23407i	−0.529071	−	0.344134i
$721$	−7.45119	+	5.41360i	−0.277497	+	0.201613i
$722$	−4.86660	−	6.69830i	−0.181116	−	0.249285i
$723$	19.1533	−	6.22329i	0.712319	−	0.231447i
$724$	−12.1168			−0.450317
$725$	18.8923	−	16.9607i	0.701642	−	0.629904i
$726$	−26.6530			−0.989187
$727$	−2.19118	+	0.711959i	−0.0812665	+	0.0264051i	−0.349368	−	0.936986i	$-0.613604\pi$
$727$	−2.19118	+	0.711959i	−0.0812665	+	0.0264051i	0.268102	+	0.963391i	$0.413604\pi$
$728$	−0.387286	−	0.533053i	−0.0143538	−	0.0197563i
$729$	39.7296	−	28.8652i	1.47147	−	1.06908i
$730$	−0.677430	+	0.547752i	−0.0250728	+	0.0202732i
$731$	33.3798	+	24.2519i	1.23460	+	0.896988i
$732$		−	5.46420i		−	0.201963i
$733$	−15.8141	+	21.7663i	−0.584108	+	0.803956i	−0.994138	−	0.108116i	$-0.965518\pi$
$733$	−15.8141	+	21.7663i	−0.584108	+	0.803956i	0.410030	+	0.912072i	$0.365518\pi$
$734$	−11.5948	+	35.6852i	−0.427973	+	1.31717i
$735$	4.57171	+	5.65404i	0.168630	+	0.208553i
$736$	−0.352350	−	1.08442i	−0.0129878	−	0.0399723i
$737$	−48.2902	−	15.6904i	−1.77879	−	0.577965i
$738$	34.5156	+	11.2148i	1.27054	+	0.412823i
$739$	−8.66698	−	26.6742i	−0.318820	−	0.981227i	−0.974153	−	0.225887i	$-0.927472\pi$
$739$	−8.66698	−	26.6742i	−0.318820	−	0.981227i	0.655334	−	0.755340i	$-0.272528\pi$
$740$	8.97643	−	3.43819i	0.329980	−	0.126390i
$741$	2.16778	−	6.67175i	0.0796355	−	0.245093i
$742$	0.275357	−	0.378996i	0.0101087	−	0.0139134i
$743$			44.6732i			1.63890i	0.573149	+	0.819451i	$0.305722\pi$
$743$			44.6732i			1.63890i	−0.573149	+	0.819451i	$0.694278\pi$
$744$	−26.4945	−	19.2494i	−0.971335	−	0.705716i
$745$	0.853402	−	0.0440986i	0.0312662	−	0.00161565i
$746$	−3.48504	+	2.53203i	−0.127597	+	0.0927043i
$747$	−39.0207	−	53.7073i	−1.42769	−	1.96505i
$748$	33.1637	−	10.7756i	1.21259	−	0.393993i
$749$	11.0793			0.404829
$750$	−32.3566	−	16.5761i	−1.18150	−	0.605274i
$751$	−22.1784			−0.809303			−0.404651	−	0.914471i	$-0.632607\pi$
$751$	−22.1784			−0.809303			−0.404651	+	0.914471i	$0.632607\pi$
$752$	2.77594	−	0.901958i	0.101228	−	0.0328910i
$753$	14.7497	+	20.3013i	0.537510	+	0.739819i
$754$	2.70670	−	1.96653i	0.0985721	−	0.0716169i
$755$	−15.6801	+	0.810252i	−0.570658	+	0.0294881i
$756$	12.0322	+	8.74187i	0.437605	+	0.317939i
$757$		−	13.2148i		−	0.480298i	−0.970736	−	0.240149i	$-0.922804\pi$
$757$		−	13.2148i		−	0.480298i	0.970736	−	0.240149i	$-0.0771964\pi$
$758$	−4.66248	+	6.41735i	−0.169349	+	0.233089i
$759$	−5.01996	+	15.4498i	−0.182213	+	0.560794i
$760$	6.83699	−	2.61874i	0.248004	−	0.0949915i
$761$	−8.54647	−	26.3033i	−0.309809	−	0.953495i	−0.977839	−	0.209360i	$-0.932862\pi$
$761$	−8.54647	−	26.3033i	−0.309809	−	0.953495i	0.668029	−	0.744135i	$-0.267138\pi$
$762$	24.0842	+	7.82542i	0.872477	+	0.283485i
$763$	2.27022	+	0.737638i	0.0821873	+	0.0267043i
$764$	−0.608053	−	1.87139i	−0.0219986	−	0.0677047i
$765$	−84.7461	−	104.809i	−3.06400	−	3.78939i
$766$	−6.56795	+	20.2141i	−0.237310	+	0.730364i
$767$	1.68849	−	2.32401i	0.0609678	−	0.0839150i
$768$		−	3.25173i		−	0.117337i
$769$	30.3959	+	22.0839i	1.09611	+	0.796368i	0.980420	−	0.196918i	$-0.0630934\pi$
$769$	30.3959	+	22.0839i	1.09611	+	0.796368i	0.115686	+	0.993286i	$0.463093\pi$
$770$	−7.61828	+	6.15993i	−0.274544	+	0.221989i
$771$	50.7899	−	36.9010i	1.82915	−	1.32896i
$772$	−6.52117	−	8.97562i	−0.234702	−	0.323039i
$773$	−39.3480	+	12.7849i	−1.41525	+	0.459842i	−0.914090	−	0.405512i	$-0.867093\pi$
$773$	−39.3480	+	12.7849i	−1.41525	+	0.459842i	−0.501160	+	0.865355i	$0.667093\pi$
$774$	−39.2637			−1.41131
$775$	−43.5729	−	25.2420i	−1.56519	−	0.906718i
$776$	16.7756			0.602210
$777$	−13.2943	+	4.31958i	−0.476930	+	0.154964i
$778$	18.9622	+	26.0992i	0.679827	+	0.935701i
$779$	−12.6930	+	9.22198i	−0.454773	+	0.330412i
$780$	−4.01603	−	2.61222i	−0.143797	−	0.0935325i
$781$	45.8133	+	33.2853i	1.63933	+	1.19104i
$782$		−	9.07479i		−	0.324514i
$783$	−44.3888	+	61.0960i	−1.58633	+	2.18339i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	−0.830497	−	16.0719i	−0.0296417	−	0.573630i
$786$	−5.58051	−	17.1750i	−0.199050	−	0.612613i
$787$	5.30638	+	1.72415i	0.189152	+	0.0614592i	0.402061	−	0.915613i	$-0.368294\pi$
$787$	5.30638	+	1.72415i	0.189152	+	0.0614592i	−0.212909	+	0.977072i	$0.568294\pi$
$788$	6.50285	+	2.11291i	0.231655	+	0.0752691i
$789$	2.50023	+	7.69490i	0.0890104	+	0.273946i
$790$	9.11519	−	14.0137i	0.324304	−	0.498585i
$791$	−3.78623	+	11.6528i	−0.134623	+	0.414326i
$792$	−19.5048	+	26.8460i	−0.693072	+	0.953932i
$793$		−	1.10720i		−	0.0393178i
$794$	2.50566	+	1.82047i	0.0889226	+	0.0646061i
$795$	0.884010	−	3.28954i	0.0313526	−	0.116668i
$796$	13.7965	−	10.0238i	0.489004	−	0.355283i
$797$	−5.26985	−	7.25333i	−0.186668	−	0.256926i	0.705419	−	0.708791i	$-0.250759\pi$
$797$	−5.26985	−	7.25333i	−0.186668	−	0.256926i	−0.892086	+	0.451865i	$0.850759\pi$
$798$	−10.1257	+	3.29005i	−0.358448	+	0.116467i
$799$	23.2300			0.821819
$800$	−0.515363	−	4.97337i	−0.0182208	−	0.175835i
$801$	−9.06282			−0.320219
$802$	7.22703	−	2.34821i	0.255195	−	0.0829180i
$803$	1.00335	+	1.38099i	0.0354073	+	0.0487340i
$804$	−30.4869	+	22.1500i	−1.07519	+	0.781171i
$805$	0.911962	+	2.38095i	0.0321424	+	0.0839174i
$806$	−5.36852	−	3.90046i	−0.189098	−	0.137388i
$807$			73.4851i			2.58680i
$808$	−1.98830	+	2.73667i	−0.0699483	+	0.0962756i
$809$	−9.76640	+	30.0579i	−0.343368	+	1.05678i	0.619083	+	0.785325i	$0.287504\pi$
$809$	−9.76640	+	30.0579i	−0.343368	+	1.05678i	−0.962452	+	0.271453i	$0.912496\pi$
$810$	55.3690	+	14.8795i	1.94547	+	0.522813i
$811$	12.5539	+	38.6370i	0.440828	+	1.35673i	0.886995	+	0.461779i	$0.152789\pi$
$811$	12.5539	+	38.6370i	0.440828	+	1.35673i	−0.446167	+	0.894950i	$0.647211\pi$
$812$	−4.82921	−	1.56910i	−0.169472	−	0.0550648i
$813$	13.0053	+	4.22569i	0.456117	+	0.148201i
$814$	−5.82022	−	17.9128i	−0.203998	−	0.627843i
$815$	28.3558	+	7.62017i	0.993262	+	0.266923i
$816$	7.99727	−	24.6131i	0.279961	−	0.861630i
$817$	9.97715	−	13.7324i	0.349056	−	0.480435i
$818$		−	18.0144i		−	0.629860i
$819$	4.03721	+	2.93320i	0.141071	+	0.102494i
$820$	3.83252	+	10.0059i	0.133837	+	0.349423i
$821$	−9.49166	+	6.89610i	−0.331261	+	0.240675i	−0.740966	−	0.671543i	$-0.765632\pi$
$821$	−9.49166	+	6.89610i	−0.331261	+	0.240675i	0.409704	+	0.912218i	$0.365632\pi$
$822$	−7.95929	−	10.9550i	−0.277612	−	0.382100i
$823$	12.8239	−	4.16674i	0.447014	−	0.145244i	−0.0768556	−	0.997042i	$-0.524488\pi$
$823$	12.8239	−	4.16674i	0.447014	−	0.145244i	0.523869	+	0.851799i	$0.324488\pi$
$824$	−9.21017			−0.320852
$825$	−35.7080	+	61.6395i	−1.24319	+	2.14601i
$826$	−4.35980			−0.151697
$827$	28.8743	−	9.38182i	1.00406	−	0.326238i	0.239571	−	0.970879i	$-0.422993\pi$
$827$	28.8743	−	9.38182i	1.00406	−	0.326238i	0.764485	+	0.644641i	$0.222993\pi$
$828$	5.07599	+	6.98650i	0.176403	+	0.242798i
$829$	44.5429	−	32.3623i	1.54704	−	1.12399i	0.601321	−	0.799008i	$-0.294641\pi$
$829$	44.5429	−	32.3623i	1.54704	−	1.12399i	0.945720	−	0.324983i	$-0.105359\pi$
$830$	5.08664	−	18.9282i	0.176560	−	0.657007i
$831$	−24.4301	−	17.7495i	−0.847469	−	0.615723i
$832$		−	0.658890i		−	0.0228429i
$833$	−4.67804	+	6.43877i	−0.162085	+	0.223090i
$834$	−5.48738	+	16.8884i	−0.190012	+	0.584798i
$835$	21.4385	−	32.9596i	0.741910	−	1.14061i
$836$	−4.43303	−	13.6435i	−0.153320	−	0.471869i
$837$	142.454	+	46.2862i	4.92394	+	1.59989i
$838$	34.7255	+	11.2830i	1.19957	+	0.389765i
$839$	0.842399	+	2.59264i	0.0290828	+	0.0895078i	0.964544	−	0.263921i	$-0.0850157\pi$
$839$	0.842399	+	2.59264i	0.0290828	+	0.0895078i	−0.935462	+	0.353429i	$0.885016\pi$
$840$	0.375225	+	7.26140i	0.0129465	+	0.250542i
$841$	−0.994012	+	3.05926i	−0.0342763	+	0.105492i
$842$	−2.02830	+	2.79172i	−0.0698999	+	0.0962090i
$843$		−	16.3867i		−	0.564388i
$844$	13.1653	+	9.56512i	0.453167	+	0.329245i
$845$	23.5539	+	15.3206i	0.810278	+	0.527044i
$846$	−17.8843	+	12.9937i	−0.614875	+	0.446733i
$847$	4.81783	+	6.63117i	0.165542	+	0.227850i
$848$	0.445537	−	0.144764i	0.0152998	−	0.00497120i
$849$	73.5527			2.52432
$850$	8.33056	−	38.9120i	0.285736	−	1.33467i
$851$	−4.90158			−0.168024
$852$	39.9707	−	12.9873i	1.36938	−	0.444937i
$853$	22.8999	+	31.5191i	0.784079	+	1.07919i	0.994820	+	0.101650i	$0.0324123\pi$
$853$	22.8999	+	31.5191i	0.784079	+	1.07919i	−0.210741	+	0.977542i	$0.567588\pi$
$854$	−1.35947	+	0.987714i	−0.0465202	+	0.0337989i
$855$	−43.1183	+	34.8643i	−1.47461	+	1.19233i
$856$	8.96334	+	6.51225i	0.306361	+	0.222584i
$857$			35.4048i			1.20941i	0.796451	+	0.604703i	$0.206708\pi$
$857$			35.4048i			1.20941i	−0.796451	+	0.604703i	$0.793292\pi$
$858$	−5.51770	+	7.59446i	−0.188371	+	0.259270i
$859$	−0.707245	+	2.17668i	−0.0241309	+	0.0742673i	−0.962397	−	0.271648i	$-0.912431\pi$
$859$	−0.707245	+	2.17668i	−0.0241309	+	0.0742673i	0.938266	+	0.345915i	$0.112431\pi$
$860$	−7.28862	−	9.01418i	−0.248540	−	0.307381i
$861$	−4.81500	−	14.8190i	−0.164095	−	0.505031i
$862$	−8.01368	−	2.60380i	−0.272947	−	0.0886859i
$863$	43.6005	+	14.1666i	1.48418	+	0.482238i	0.935358	−	0.353703i	$-0.115078\pi$
$863$	43.6005	+	14.1666i	1.48418	+	0.482238i	0.548819	+	0.835941i	$0.315078\pi$
$864$	4.59587	+	14.1446i	0.156355	+	0.481211i
$865$	−10.7067	+	4.10092i	−0.364038	+	0.139435i
$866$	7.15430	−	22.0187i	0.243113	−	0.748225i
$867$	88.5740	−	121.912i	3.00813	−	4.14034i
$868$			10.0713i			0.341841i
$869$	−26.5004	−	19.2537i	−0.898964	−	0.653136i
$870$	−36.8714	+	1.90529i	−1.25006	+	0.0645953i
$871$	−6.17748	+	4.48821i	−0.209316	+	0.152077i
$872$	1.40307	+	1.93116i	0.0475140	+	0.0653974i
$873$	−120.836	+	39.2619i	−4.08967	+	1.32882i
$874$	−3.73334			−0.126282
$875$	1.72474	+	11.0465i	0.0583068	+	0.373440i
$876$	1.26688			0.0428038
$877$	36.2294	−	11.7717i	1.22338	−	0.397501i	0.375069	−	0.926997i	$-0.377619\pi$
$877$	36.2294	−	11.7717i	1.22338	−	0.397501i	0.848312	+	0.529496i	$0.177619\pi$
$878$	−17.9769	−	24.7431i	−0.606692	−	0.835040i
$879$	21.0377	−	15.2848i	0.709582	−	0.515542i
$880$	−9.78403	+	0.505579i	−0.329820	+	0.0170431i
$881$	34.7644	+	25.2578i	1.17124	+	0.850956i	0.991157	−	0.132695i	$-0.0423630\pi$
$881$	34.7644	+	25.2578i	1.17124	+	0.850956i	0.180084	+	0.983651i	$0.442363\pi$
$882$		−	7.57374i		−	0.255021i
$883$	9.70679	−	13.3602i	0.326659	−	0.449608i	−0.613826	−	0.789441i	$-0.710371\pi$
$883$	9.70679	−	13.3602i	0.326659	−	0.449608i	0.940486	+	0.339833i	$0.110371\pi$
$884$	1.62047	−	4.98729i	0.0545022	−	0.167741i
$885$	−29.6033	+	11.3388i	−0.995103	+	0.381149i
$886$	5.54512	+	17.0661i	0.186292	+	0.573348i
$887$	15.5188	+	5.04238i	0.521072	+	0.169307i	0.557732	−	0.830021i	$-0.311672\pi$
$887$	15.5188	+	5.04238i	0.521072	+	0.169307i	−0.0366598	+	0.999328i	$0.511672\pi$
$888$	−13.2943	−	4.31958i	−0.446128	−	0.144956i
$889$	−2.40654	−	7.40657i	−0.0807128	−	0.248409i
$890$	−1.68235	−	2.08064i	−0.0563926	−	0.0697433i
$891$	34.7150	−	106.842i	1.16300	−	3.57934i
$892$	−13.7472	+	18.9213i	−0.460289	+	0.633534i
$893$		−	9.55676i		−	0.319805i
$894$	−1.00536	−	0.730433i	−0.0336241	−	0.0244293i
$895$	−25.0880	+	20.2855i	−0.838600	+	0.678069i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	1.43594	+	1.97641i	0.0479448	+	0.0659903i
$898$	16.3318	−	5.30652i	0.544999	−	0.177081i
$899$	−51.1391			−1.70558
$900$	15.3519	+	34.6173i	0.511731	+	1.15391i
$901$	3.72840			0.124211
$902$	19.9672	−	6.48774i	0.664835	−	0.216018i
$903$	9.90864	+	13.6381i	0.329739	+	0.453847i
$904$	−9.91247	+	7.20183i	−0.329684	+	0.239529i
$905$	22.7121	+	14.7731i	0.754976	+	0.491073i
$906$	18.4721	+	13.4207i	0.613693	+	0.445874i
$907$			7.71028i			0.256016i	0.991773	+	0.128008i	$0.0408583\pi$
$907$			7.71028i			0.256016i	−0.991773	+	0.128008i	$0.959142\pi$
$908$	−0.649387	+	0.893804i	−0.0215507	+	0.0296619i
$909$	7.91693	−	24.3658i	0.262588	−	0.808163i
$910$	0.0760309	+	1.47136i	0.00252040	+	0.0487751i
$911$	−17.6953	−	54.4606i	−0.586272	−	1.80436i	−0.594101	−	0.804391i	$-0.702492\pi$
$911$	−17.6953	−	54.4606i	−0.586272	−	1.80436i	0.00782858	−	0.999969i	$-0.497508\pi$
$912$	−10.1257	−	3.29005i	−0.335297	−	0.108945i
$913$	−36.5245	−	11.8675i	−1.20878	−	0.392757i
$914$	5.42397	+	16.6933i	0.179409	+	0.552164i
$915$	−6.66208	+	10.2423i	−0.220241	+	0.338599i
$916$	−4.56212	+	14.0408i	−0.150737	+	0.463920i
$917$	−3.26434	+	4.49298i	−0.107798	+	0.148371i
$918$			118.367i			3.90670i
$919$	−26.0367	−	18.9168i	−0.858872	−	0.624007i	0.0687057	−	0.997637i	$-0.478113\pi$
$919$	−26.0367	−	18.9168i	−0.858872	−	0.624007i	−0.927578	+	0.373630i	$0.878113\pi$
$920$	−0.661694	+	2.46227i	−0.0218154	+	0.0811785i
$921$	44.9480	−	32.6566i	1.48109	−	1.07607i
$922$	−4.28085	−	5.89208i	−0.140982	−	0.194045i
$923$	8.09918	−	2.63158i	0.266588	−	0.0866196i
$924$	14.2471			0.468695
$925$	−21.0176	−	4.49960i	−0.691055	−	0.147946i
$926$	42.5441			1.39809
$927$	66.3414	−	21.5556i	2.17894	−	0.707979i
$928$	−2.98461	−	4.10797i	−0.0979747	−	0.134851i
$929$	−44.6782	+	32.4606i	−1.46585	+	1.06500i	−0.484054	+	0.875038i	$0.660836\pi$
$929$	−44.6782	+	32.4606i	−1.46585	+	1.06500i	−0.981792	+	0.189961i	$0.939164\pi$
$930$	26.1929	+	68.3843i	0.858898	+	2.24241i
$931$	2.64889	+	1.92453i	0.0868139	+	0.0630740i
$932$			7.44953i			0.244018i
$933$	−46.2223	+	63.6196i	−1.51325	+	2.08281i
$934$	2.25623	−	6.94397i	0.0738261	−	0.227213i
$935$	−75.3010	−	20.2359i	−2.46261	−	0.661785i
$936$	1.54208	+	4.74602i	0.0504043	+	0.155129i
$937$	−9.25256	−	3.00634i	−0.302268	−	0.0982129i	0.153956	−	0.988078i	$-0.450799\pi$
$937$	−9.25256	−	3.00634i	−0.302268	−	0.0982129i	−0.456224	+	0.889865i	$0.650799\pi$
$938$	11.0217	+	3.58116i	0.359870	+	0.116929i
$939$	−20.4820	−	63.0370i	−0.668404	−	2.05714i
$940$	−6.30300	−	1.69383i	−0.205581	−	0.0552466i
$941$	−17.6438	+	54.3020i	−0.575171	+	1.77019i	0.0604249	+	0.998173i	$0.480754\pi$
$941$	−17.6438	+	54.3020i	−0.575171	+	1.77019i	−0.635596	+	0.772022i	$0.719246\pi$
$942$	−13.7561	+	18.9336i	−0.448196	+	0.616889i
$943$		−	5.46375i		−	0.177924i
$944$	−3.52715	−	2.56263i	−0.114799	−	0.0834064i
$945$	−11.8952	−	31.0559i	−0.386950	−	1.01025i
$946$	−18.3760	+	13.3509i	−0.597455	+	0.434076i
$947$	−4.70578	−	6.47695i	−0.152917	−	0.210473i	0.725685	−	0.688027i	$-0.241523\pi$
$947$	−4.70578	−	6.47695i	−0.152917	−	0.210473i	−0.878602	+	0.477555i	$0.841523\pi$
$948$	−23.1208	+	7.51241i	−0.750930	+	0.243992i
$949$	0.256704			0.00833297
$950$	−16.0083	−	3.42717i	−0.519378	−	0.111192i
$951$	94.2202			3.05530
$952$	−7.56923	+	2.45939i	−0.245320	+	0.0797093i
$953$	22.7336	+	31.2901i	0.736413	+	1.01359i	0.998817	+	0.0486278i	$0.0154848\pi$
$953$	22.7336	+	31.2901i	0.736413	+	1.01359i	−0.262404	+	0.964958i	$0.584515\pi$
$954$	−2.87042	+	2.08548i	−0.0929332	+	0.0675199i
$955$	−1.14189	+	4.24915i	−0.0369507	+	0.137499i
$956$	−2.48744	−	1.80723i	−0.0804496	−	0.0584500i
$957$			72.3428i			2.33851i
$958$	−18.4167	+	25.3484i	−0.595017	+	0.818971i
$959$	−1.28684	+	3.96048i	−0.0415542	+	0.127891i
$960$	−3.96458	+	6.09515i	−0.127956	+	0.196720i
$961$	21.7641	+	66.9831i	0.702069	+	2.16075i
$962$	−2.69379	−	0.875266i	−0.0868513	−	0.0282197i
$963$	−79.8048	−	25.9301i	−2.57167	−	0.835587i
$964$	−1.91384	−	5.89019i	−0.0616406	−	0.189710i
$965$	1.28022	+	24.7749i	0.0412117	+	0.797533i
$966$	1.14575	−	3.52624i	0.0368638	−	0.113455i
$967$	5.29357	−	7.28598i	0.170230	−	0.234301i	−0.715375	−	0.698741i	$-0.753744\pi$
$967$	5.29357	−	7.28598i	0.170230	−	0.234301i	0.885605	+	0.464439i	$0.153744\pi$
$968$			8.19658i			0.263448i
$969$	−68.5526	−	49.8064i	−2.20223	−	1.60001i
$970$	−31.4448	−	20.4532i	−1.00963	−	0.656714i
$971$	−21.2547	+	15.4424i	−0.682095	+	0.495571i	−0.874052	−	0.485832i	$-0.838517\pi$
$971$	−21.2547	+	15.4424i	−0.682095	+	0.495571i	0.191957	+	0.981403i	$0.438517\pi$
$972$	−22.7812	−	31.3556i	−0.730707	−	1.00573i
$973$	5.19367	−	1.68753i	0.166502	−	0.0540996i
$974$	28.6735			0.918759
$975$	4.34290	+	9.79287i	0.139084	+	0.313623i
$976$	−1.68040			−0.0537883
$977$	−33.7544	+	10.9675i	−1.07990	+	0.350881i	−0.794336	−	0.607479i	$-0.792181\pi$
$977$	−33.7544	+	10.9675i	−1.07990	+	0.350881i	−0.285564	+	0.958360i	$0.592181\pi$
$978$	−25.0976	−	34.5439i	−0.802533	−	1.10459i
$979$	−4.24153	+	3.08165i	−0.135560	+	0.0984900i
$980$	1.73878	−	1.40593i	0.0555433	−	0.0449108i
$981$	−14.6261	−	10.6265i	−0.466976	−	0.339278i
$982$		−	33.4668i		−	1.06797i
$983$	6.30489	−	8.67794i	0.201095	−	0.276783i	−0.696545	−	0.717513i	$-0.745280\pi$
$983$	6.30489	−	8.67794i	0.201095	−	0.276783i	0.897640	+	0.440730i	$0.145280\pi$
$984$	4.81500	−	14.8190i	0.153496	−	0.472413i
$985$	−9.61306	−	11.8889i	−0.306298	−	0.378813i
$986$	−12.4881	−	38.4345i	−0.397703	−	1.22400i
$987$	9.02661	+	2.93292i	0.287320	+	0.0933560i
$988$	−2.05176	−	0.666656i	−0.0652750	−	0.0212091i
$989$	1.82665	+	5.62185i	0.0580841	+	0.178764i
$990$	69.2916	−	26.5404i	2.20223	−	0.843509i
$991$	−13.9016	+	42.7847i	−0.441599	+	1.35910i	0.444573	+	0.895743i	$0.353356\pi$
$991$	−13.9016	+	42.7847i	−0.441599	+	1.35910i	−0.886171	+	0.463358i	$0.846644\pi$
$992$	−5.91974	+	8.14782i	−0.187952	+	0.258693i
$993$		−	84.1800i		−	2.67137i
$994$	−10.4563	−	7.59697i	−0.331655	−	0.240961i
$995$	−38.0818	+	1.96784i	−1.20727	+	0.0623846i
$996$	−23.0588	+	16.7532i	−0.730647	+	0.530846i
$997$	18.8482	+	25.9423i	0.596928	+	0.821600i	0.995423	−	0.0955700i	$-0.0304674\pi$
$997$	18.8482	+	25.9423i	0.596928	+	0.821600i	−0.398495	+	0.917170i	$0.630467\pi$
$998$	10.5641	−	3.43248i	0.334400	−	0.108653i
$999$	63.9338			2.02278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.169.10	yes	40
25.2	odd	20		8750.2.a.bf.1.1		20
25.4	even	10	inner	350.2.m.b.29.10	✓	40
25.23	odd	20		8750.2.a.be.1.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.10	✓	40	25.4	even	10	inner
350.2.m.b.169.10	yes	40	1.1	even	1	trivial
8750.2.a.be.1.20		20	25.23	odd	20
8750.2.a.bf.1.1		20	25.2	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.91132 + 2.63070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.23309 + 0.115392i) q^{5} +(2.63070 + 1.91132i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.34041 + 7.20305i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.91132 + 2.63070i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.23309 + 0.115392i) q^{5} +(2.63070 + 1.91132i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.34041 + 7.20305i) q^{9} +(-2.08814 + 0.799807i) q^{10} +(1.35392 + 4.16695i) q^{11} +(3.09258 + 1.00484i) q^{12} +(0.626642 + 0.203608i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-4.57171 - 5.65404i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.67804 - 6.43877i) q^{17} +7.57374i q^{18} +(-2.64889 - 1.92453i) q^{19} +(-1.73878 + 1.40593i) q^{20} +(2.63070 - 1.91132i) q^{21} +(2.57532 + 3.54462i) q^{22} +(1.08442 - 0.352350i) q^{23} +3.25173 q^{24} +(4.97337 - 0.515363i) q^{25} +0.658890 q^{26} +(-14.1446 + 4.59587i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(4.10797 - 2.98461i) q^{29} +(-6.09515 - 3.96458i) q^{30} +(-8.14782 - 5.91974i) q^{31} -1.00000i q^{32} +(-8.37423 + 11.5261i) q^{33} +(2.45939 - 7.56923i) q^{34} +(0.115392 + 2.23309i) q^{35} +(2.34041 + 7.20305i) q^{36} +(-4.08838 - 1.32840i) q^{37} +(-3.11396 - 1.01179i) q^{38} +(0.662079 + 2.03767i) q^{39} +(-1.21922 + 1.87443i) q^{40} +(1.48075 - 4.55728i) q^{41} +(1.91132 - 2.63070i) q^{42} +5.18419i q^{43} +(3.54462 + 2.57532i) q^{44} +(4.39517 - 16.3551i) q^{45} +(0.922463 - 0.670209i) q^{46} +(1.71563 + 2.36136i) q^{47} +(3.09258 - 1.00484i) q^{48} -1.00000 q^{49} +(4.57070 - 2.02699i) q^{50} +25.8797 q^{51} +(0.626642 - 0.203608i) q^{52} +(0.275357 + 0.378996i) q^{53} +(-12.0322 + 8.74187i) q^{54} +(-3.50427 - 9.14893i) q^{55} +(-0.809017 - 0.587785i) q^{56} -10.6468i q^{57} +(2.98461 - 4.10797i) q^{58} +(1.34725 - 4.14642i) q^{59} +(-7.02195 - 1.88704i) q^{60} +(-0.519272 - 1.59815i) q^{61} +(-9.57834 - 3.11219i) q^{62} +(7.20305 + 2.34041i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.42284 - 0.382365i) q^{65} +(-4.40259 + 13.5498i) q^{66} +(-6.81177 + 9.37559i) q^{67} -7.95876i q^{68} +(2.99960 + 2.17934i) q^{69} +(0.799807 + 2.08814i) q^{70} +(10.4563 - 7.59697i) q^{71} +(4.45173 + 6.12728i) q^{72} +(0.370532 - 0.120393i) q^{73} -4.29878 q^{74} +(10.8615 + 12.0984i) q^{75} -3.27421 q^{76} +(4.16695 - 1.35392i) q^{77} +(1.25935 + 1.73334i) q^{78} +(-6.04840 + 4.39442i) q^{79} +(-0.580318 + 2.15945i) q^{80} +(-20.7434 - 15.0710i) q^{81} -4.79181i q^{82} +(-5.15210 + 7.09126i) q^{83} +(1.00484 - 3.09258i) q^{84} +(-9.70349 + 14.9182i) q^{85} +(1.60200 + 4.93046i) q^{86} +(15.7033 + 5.10230i) q^{87} +(4.16695 + 1.35392i) q^{88} +(0.369773 + 1.13804i) q^{89} +(-0.873952 - 16.9128i) q^{90} +(0.203608 - 0.626642i) q^{91} +(0.670209 - 0.922463i) q^{92} -32.7490i q^{93} +(2.36136 + 1.71563i) q^{94} +(6.13728 + 3.99199i) q^{95} +(2.63070 - 1.91132i) q^{96} +(9.86047 + 13.5718i) q^{97} +(-0.951057 + 0.309017i) q^{98} -33.1835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

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