LMFDB - Embedded newform 182.2.h.d.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,2,Mod(9,182)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(182, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("182.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.23207289578928.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 3x^{8} + 13x^{7} + x^{6} - 39x^{5} + 3x^{4} + 117x^{3} - 81x^{2} - 162x + 243 $ x^10 - 2x^9 - 3x^8 + 13x^7 + x^6 - 39x^5 + 3x^4 + 117x^3 - 81x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.5
Root			$-1.73100 - 0.0603688i$ of defining polynomial
Character	$\chi$	$=$	182.9
Dual form			182.2.h.d.81.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +2.62644 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.917780 + 1.58964i) q^{5} +(-1.31322 - 2.27456i) q^{6} +(1.05365 - 2.42690i) q^{7} +1.00000 q^{8} +3.89817 q^{9} +1.83556 q^{10} -0.0872528 q^{11} +(-1.31322 + 2.27456i) q^{12} +(3.59786 - 0.235328i) q^{13} +(-2.62858 + 0.300964i) q^{14} +(-2.41049 + 4.17509i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.40546 + 2.43433i) q^{17} +(-1.94908 - 3.37591i) q^{18} -6.97084 q^{19} +(-0.917780 - 1.58964i) q^{20} +(2.76734 - 6.37409i) q^{21} +(0.0436264 + 0.0755631i) q^{22} +(-0.813218 - 1.40854i) q^{23} +2.62644 q^{24} +(0.815359 + 1.41224i) q^{25} +(-2.00273 - 2.99818i) q^{26} +2.35899 q^{27} +(1.57493 + 2.12593i) q^{28} +(-1.05151 + 1.82126i) q^{29} +4.82098 q^{30} +(-3.71080 - 6.42729i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.229164 q^{33} +2.81092 q^{34} +(2.89088 + 3.90228i) q^{35} +(-1.94908 + 3.37591i) q^{36} +(-4.41108 - 7.64022i) q^{37} +(3.48542 + 6.03693i) q^{38} +(9.44956 - 0.618073i) q^{39} +(-0.917780 + 1.58964i) q^{40} +(-5.21139 + 9.02639i) q^{41} +(-6.90379 + 0.790462i) q^{42} +(2.99057 + 5.17982i) q^{43} +(0.0436264 - 0.0755631i) q^{44} +(-3.57766 + 6.19669i) q^{45} +(-0.813218 + 1.40854i) q^{46} +(-4.00059 + 6.92923i) q^{47} +(-1.31322 - 2.27456i) q^{48} +(-4.77966 - 5.11418i) q^{49} +(0.815359 - 1.41224i) q^{50} +(-3.69135 + 6.39360i) q^{51} +(-1.59513 + 3.23350i) q^{52} +(-0.447411 - 0.774938i) q^{53} +(-1.17949 - 2.04294i) q^{54} +(0.0800789 - 0.138701i) q^{55} +(1.05365 - 2.42690i) q^{56} -18.3085 q^{57} +2.10301 q^{58} +(3.41945 - 5.92267i) q^{59} +(-2.41049 - 4.17509i) q^{60} +8.86567 q^{61} +(-3.71080 + 6.42729i) q^{62} +(4.10729 - 9.46046i) q^{63} +1.00000 q^{64} +(-2.92796 + 5.93529i) q^{65} +(0.114582 + 0.198462i) q^{66} +6.60969 q^{67} +(-1.40546 - 2.43433i) q^{68} +(-2.13587 - 3.69943i) q^{69} +(1.93403 - 4.45472i) q^{70} +(-3.79147 - 6.56701i) q^{71} +3.89817 q^{72} +(5.45471 + 9.44783i) q^{73} +(-4.41108 + 7.64022i) q^{74} +(2.14149 + 3.70917i) q^{75} +(3.48542 - 6.03693i) q^{76} +(-0.0919336 + 0.211754i) q^{77} +(-5.26005 - 7.87452i) q^{78} +(4.60897 - 7.98297i) q^{79} +1.83556 q^{80} -5.49878 q^{81} +10.4228 q^{82} +16.8793 q^{83} +(4.13646 + 5.58363i) q^{84} +(-2.57980 - 4.46835i) q^{85} +(2.99057 - 5.17982i) q^{86} +(-2.76171 + 4.78343i) q^{87} -0.0872528 q^{88} +(4.95471 + 8.58181i) q^{89} +7.15533 q^{90} +(3.21976 - 8.97960i) q^{91} +1.62644 q^{92} +(-9.74617 - 16.8809i) q^{93} +8.00118 q^{94} +(6.39770 - 11.0811i) q^{95} +(-1.31322 + 2.27456i) q^{96} +(1.42051 + 2.46040i) q^{97} +(-2.03918 + 6.69640i) q^{98} -0.340126 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + 2 q^{3} - 5 q^{4} - 2 q^{5} - q^{6} + 10 q^{8} + 8 q^{9} + 4 q^{10} + 8 q^{11} - q^{12} - 6 q^{13} - 3 q^{14} + 3 q^{15} - 5 q^{16} - 3 q^{17} - 4 q^{18} + 10 q^{19} - 2 q^{20} - 16 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 - 2 * q^5 - q^6 + 10 * q^8 + 8 * q^9 + 4 * q^10 + 8 * q^11 - q^12 - 6 * q^13 - 3 * q^14 + 3 * q^15 - 5 * q^16 - 3 * q^17 - 4 * q^18 + 10 * q^19 - 2 * q^20 - 16 * q^21 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 3 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + q^29 - 6 * q^30 - 21 * q^31 - 5 * q^32 + 6 * q^34 - 22 * q^35 - 4 * q^36 + 10 * q^37 - 5 * q^38 + 17 * q^39 - 2 * q^40 - 9 * q^41 + 5 * q^42 + 9 * q^43 - 4 * q^44 + 3 * q^45 + 4 * q^46 - 13 * q^47 - q^48 - 8 * q^49 - 3 * q^50 - 6 * q^51 - 15 * q^53 - 4 * q^54 + 7 * q^55 - 26 * q^57 - 2 * q^58 + q^59 + 3 * q^60 + 30 * q^61 - 21 * q^62 + 20 * q^63 + 10 * q^64 - 25 * q^65 - 3 * q^68 - 18 * q^69 + 26 * q^70 - q^71 + 8 * q^72 - 4 * q^73 + 10 * q^74 - 25 * q^75 - 5 * q^76 + 16 * q^77 + 11 * q^78 - q^79 + 4 * q^80 - 46 * q^81 + 18 * q^82 + 96 * q^83 + 11 * q^84 + 12 * q^85 + 9 * q^86 - 27 * q^87 + 8 * q^88 - 9 * q^89 - 6 * q^90 + 10 * q^91 - 8 * q^92 - 2 * q^93 + 26 * q^94 + 6 * q^95 - q^96 - 19 * q^97 - 5 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	2.62644			1.51637			0.758187	−	0.652037i	$-0.226085\pi$
$3$	2.62644			1.51637			0.758187	+	0.652037i	$0.226085\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.917780	+	1.58964i	−0.410444	+	0.710909i	−0.994938	−	0.100488i	$-0.967960\pi$
$5$	−0.917780	+	1.58964i	−0.410444	+	0.710909i	0.584495	+	0.811398i	$0.301293\pi$
$6$	−1.31322	−	2.27456i	−0.536119	−	0.928586i
$7$	1.05365	−	2.42690i	0.398241	−	0.917281i
$7$	1.05365	−	2.42690i	0.398241	−	0.917281i
$8$	1.00000			0.353553
$9$	3.89817			1.29939
$10$	1.83556			0.580455
$11$	−0.0872528			−0.0263077			−0.0131539	−	0.999913i	$-0.504187\pi$
$11$	−0.0872528			−0.0263077			−0.0131539	+	0.999913i	$0.504187\pi$
$12$	−1.31322	+	2.27456i	−0.379093	+	0.656609i
$13$	3.59786	−	0.235328i	0.997868	−	0.0652682i
$13$	3.59786	−	0.235328i	0.997868	−	0.0652682i
$14$	−2.62858	+	0.300964i	−0.702517	+	0.0804359i
$15$	−2.41049	+	4.17509i	−0.622386	+	1.07800i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.40546	+	2.43433i	−0.340874	+	0.590411i	−0.984595	−	0.174849i	$-0.944056\pi$
$17$	−1.40546	+	2.43433i	−0.340874	+	0.590411i	0.643721	+	0.765260i	$0.277390\pi$
$18$	−1.94908	−	3.37591i	−0.459404	−	0.795711i
$19$	−6.97084			−1.59922			−0.799611	−	0.600519i	$-0.794961\pi$
$19$	−6.97084			−1.59922			−0.799611	+	0.600519i	$0.794961\pi$
$20$	−0.917780	−	1.58964i	−0.205222	−	0.355455i
$21$	2.76734	−	6.37409i	0.603882	−	1.39094i
$22$	0.0436264	+	0.0755631i	0.00930118	+	0.0161101i
$23$	−0.813218	−	1.40854i	−0.169568	−	0.293700i	0.768700	−	0.639609i	$-0.220904\pi$
$23$	−0.813218	−	1.40854i	−0.169568	−	0.293700i	−0.938268	+	0.345909i	$0.887570\pi$
$24$	2.62644			0.536119
$25$	0.815359	+	1.41224i	0.163072	+	0.282449i
$26$	−2.00273	−	2.99818i	−0.392768	−	0.587991i
$27$	2.35899			0.453987
$28$	1.57493	+	2.12593i	0.297634	+	0.401764i
$29$	−1.05151	+	1.82126i	−0.195260	+	0.338200i	−0.946986	−	0.321276i	$-0.895888\pi$
$29$	−1.05151	+	1.82126i	−0.195260	+	0.338200i	0.751726	+	0.659476i	$0.229222\pi$
$30$	4.82098			0.880187
$31$	−3.71080	−	6.42729i	−0.666479	−	1.15438i	−0.978882	−	0.204426i	$-0.934467\pi$
$31$	−3.71080	−	6.42729i	−0.666479	−	1.15438i	0.312403	−	0.949950i	$-0.398866\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.229164			−0.0398923
$34$	2.81092			0.482068
$35$	2.89088	+	3.90228i	0.488648	+	0.659605i
$36$	−1.94908	+	3.37591i	−0.324847	+	0.562652i
$37$	−4.41108	−	7.64022i	−0.725177	−	1.25604i	−0.958901	−	0.283741i	$-0.908424\pi$
$37$	−4.41108	−	7.64022i	−0.725177	−	1.25604i	0.233724	−	0.972303i	$-0.424909\pi$
$38$	3.48542	+	6.03693i	0.565410	+	0.979319i
$39$	9.44956	−	0.618073i	1.51314	−	0.0989709i
$40$	−0.917780	+	1.58964i	−0.145114	+	0.251344i
$41$	−5.21139	+	9.02639i	−0.813882	+	1.40969i	0.0962458	+	0.995358i	$0.469317\pi$
$41$	−5.21139	+	9.02639i	−0.813882	+	1.40969i	−0.910128	+	0.414327i	$0.864017\pi$
$42$	−6.90379	+	0.790462i	−1.06528	+	0.121971i
$43$	2.99057	+	5.17982i	0.456058	+	0.789915i	0.998748	−	0.0500176i	$-0.0159277\pi$
$43$	2.99057	+	5.17982i	0.456058	+	0.789915i	−0.542691	+	0.839933i	$0.682594\pi$
$44$	0.0436264	−	0.0755631i	0.00657693	−	0.0113916i
$45$	−3.57766	+	6.19669i	−0.533326	+	0.923748i
$46$	−0.813218	+	1.40854i	−0.119903	+	0.207677i
$47$	−4.00059	+	6.92923i	−0.583546	+	1.01073i	0.411509	+	0.911406i	$0.365002\pi$
$47$	−4.00059	+	6.92923i	−0.583546	+	1.01073i	−0.995055	+	0.0993257i	$0.968331\pi$
$48$	−1.31322	−	2.27456i	−0.189547	−	0.328305i
$49$	−4.77966	−	5.11418i	−0.682808	−	0.730598i
$50$	0.815359	−	1.41224i	0.115309	−	0.199721i
$51$	−3.69135	+	6.39360i	−0.516892	+	0.895283i
$52$	−1.59513	+	3.23350i	−0.221205	+	0.448406i
$53$	−0.447411	−	0.774938i	−0.0614566	−	0.106446i	0.833660	−	0.552278i	$-0.186241\pi$
$53$	−0.447411	−	0.774938i	−0.0614566	−	0.106446i	−0.895117	+	0.445832i	$0.852908\pi$
$54$	−1.17949	−	2.04294i	−0.160509	−	0.278009i
$55$	0.0800789	−	0.138701i	0.0107978	−	0.0187024i
$56$	1.05365	−	2.42690i	0.140799	−	0.324308i
$57$	−18.3085			−2.42502
$58$	2.10301			0.276139
$59$	3.41945	−	5.92267i	0.445175	−	0.771066i	−0.552889	−	0.833255i	$-0.686475\pi$
$59$	3.41945	−	5.92267i	0.445175	−	0.771066i	0.998064	+	0.0621889i	$0.0198081\pi$
$60$	−2.41049	−	4.17509i	−0.311193	−	0.539002i
$61$	8.86567			1.13513			0.567566	−	0.823328i	$-0.307885\pi$
$61$	8.86567			1.13513			0.567566	+	0.823328i	$0.307885\pi$
$62$	−3.71080	+	6.42729i	−0.471272	+	0.816267i
$63$	4.10729	−	9.46046i	0.517470	−	1.19191i
$64$	1.00000			0.125000
$65$	−2.92796	+	5.93529i	−0.363169	+	0.736182i
$66$	0.114582	+	0.198462i	0.0141041	+	0.0244290i
$67$	6.60969			0.807502			0.403751	−	0.914869i	$-0.367706\pi$
$67$	6.60969			0.807502			0.403751	+	0.914869i	$0.367706\pi$
$68$	−1.40546	−	2.43433i	−0.170437	−	0.295205i
$69$	−2.13587	−	3.69943i	−0.257128	−	0.445359i
$70$	1.93403	−	4.45472i	0.231161	−	0.532440i
$71$	−3.79147	−	6.56701i	−0.449964	−	0.779361i	0.548419	−	0.836204i	$-0.315230\pi$
$71$	−3.79147	−	6.56701i	−0.449964	−	0.779361i	−0.998383	+	0.0568427i	$0.981897\pi$
$72$	3.89817			0.459404
$73$	5.45471	+	9.44783i	0.638425	+	1.10579i	0.985778	+	0.168051i	$0.0537472\pi$
$73$	5.45471	+	9.44783i	0.638425	+	1.10579i	−0.347353	+	0.937734i	$0.612919\pi$
$74$	−4.41108	+	7.64022i	−0.512778	+	0.888157i
$75$	2.14149	+	3.70917i	0.247278	+	0.428298i
$76$	3.48542	−	6.03693i	0.399805	−	0.692483i
$77$	−0.0919336	+	0.211754i	−0.0104768	+	0.0241316i
$78$	−5.26005	−	7.87452i	−0.595583	−	0.891614i
$79$	4.60897	−	7.98297i	0.518549	−	0.898154i	−0.481218	−	0.876601i	$-0.659806\pi$
$79$	4.60897	−	7.98297i	0.518549	−	0.898154i	0.999768	−	0.0215530i	$-0.00686108\pi$
$80$	1.83556			0.205222
$81$	−5.49878			−0.610976
$82$	10.4228			1.15100
$83$	16.8793			1.85274			0.926372	−	0.376609i	$-0.122910\pi$
$83$	16.8793			1.85274			0.926372	+	0.376609i	$0.122910\pi$
$84$	4.13646	+	5.58363i	0.451324	+	0.609224i
$85$	−2.57980	−	4.46835i	−0.279819	−	0.484661i
$86$	2.99057	−	5.17982i	0.322481	−	0.558554i
$87$	−2.76171	+	4.78343i	−0.296087	+	0.512837i
$88$	−0.0872528			−0.00930118
$89$	4.95471	+	8.58181i	0.525198	+	0.909670i	0.999569	+	0.0293448i	$0.00934208\pi$
$89$	4.95471	+	8.58181i	0.525198	+	0.909670i	−0.474371	+	0.880325i	$0.657325\pi$
$90$	7.15533			0.754237
$91$	3.21976	−	8.97960i	0.337523	−	0.941317i
$92$	1.62644			0.169568
$93$	−9.74617	−	16.8809i	−1.01063	−	1.75046i
$94$	8.00118			0.825259
$95$	6.39770	−	11.0811i	0.656390	−	1.13690i
$96$	−1.31322	+	2.27456i	−0.134030	+	0.232146i
$97$	1.42051	+	2.46040i	0.144231	+	0.249816i	0.929086	−	0.369864i	$-0.120596\pi$
$97$	1.42051	+	2.46040i	0.144231	+	0.249816i	−0.784855	+	0.619680i	$0.787262\pi$
$98$	−2.03918	+	6.69640i	−0.205989	+	0.676438i
$99$	−0.340126			−0.0341840
$100$	−1.63072			−0.163072
$101$	−3.76600			−0.374731			−0.187366	−	0.982290i	$-0.559995\pi$
$101$	−3.76600			−0.374731			−0.187366	+	0.982290i	$0.559995\pi$
$102$	7.38270			0.730996
$103$	4.72886	−	8.19062i	0.465948	−	0.807046i	−0.533296	−	0.845929i	$-0.679047\pi$
$103$	4.72886	−	8.19062i	0.465948	−	0.807046i	0.999244	+	0.0388831i	$0.0123800\pi$
$104$	3.59786	−	0.235328i	0.352800	−	0.0230758i
$105$	7.59272	+	10.2491i	0.740973	+	1.00021i
$106$	−0.447411	+	0.774938i	−0.0434564	+	0.0752686i
$107$	−3.67949	−	6.37307i	−0.355710	−	0.616108i	0.631529	−	0.775352i	$-0.282428\pi$
$107$	−3.67949	−	6.37307i	−0.355710	−	0.616108i	−0.987239	+	0.159244i	$0.949094\pi$
$108$	−1.17949	+	2.04294i	−0.113497	+	0.196582i
$109$	−1.96249	−	3.39913i	−0.187972	−	0.325578i	0.756602	−	0.653876i	$-0.226858\pi$
$109$	−1.96249	−	3.39913i	−0.187972	−	0.325578i	−0.944574	+	0.328298i	$0.893525\pi$
$110$	−0.160158			−0.0152704
$111$	−11.5854	−	20.0665i	−1.09964	−	1.90463i
$112$	−2.62858	+	0.300964i	−0.248377	+	0.0284384i
$113$	−7.47705	−	12.9506i	−0.703382	−	1.21829i	−0.967272	−	0.253740i	$-0.918339\pi$
$113$	−7.47705	−	12.9506i	−0.703382	−	1.21829i	0.263891	−	0.964553i	$-0.414994\pi$
$114$	9.15424	+	15.8556i	0.857373	+	1.48501i
$115$	2.98542			0.278392
$116$	−1.05151	−	1.82126i	−0.0976298	−	0.169100i
$117$	14.0251	−	0.917347i	1.29662	−	0.0848088i
$118$	−6.83891			−0.629573
$119$	4.42700	+	5.97582i	0.405822	+	0.547803i
$120$	−2.41049	+	4.17509i	−0.220047	+	0.381132i
$121$	−10.9924			−0.999308
$122$	−4.43283	−	7.67789i	−0.401330	−	0.695124i
$123$	−13.6874	+	23.7072i	−1.23415	+	2.13761i
$124$	7.42160			0.666479
$125$	−12.1711			−1.08861
$126$	−10.2466	+	1.17321i	−0.912843	+	0.104518i
$127$	−0.323239	+	0.559866i	−0.0286828	+	0.0496800i	−0.880010	−	0.474954i	$-0.842465\pi$
$127$	−0.323239	+	0.559866i	−0.0286828	+	0.0496800i	0.851328	+	0.524634i	$0.175798\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	7.85454	+	13.6045i	0.691554	+	1.19781i
$130$	6.60409	−	0.431958i	0.579217	−	0.0378852i
$131$	1.39817	−	2.42170i	0.122159	−	0.211585i	−0.798460	−	0.602048i	$-0.794352\pi$
$131$	1.39817	−	2.42170i	0.122159	−	0.211585i	0.920619	+	0.390463i	$0.127685\pi$
$132$	0.114582	−	0.198462i	0.00997308	−	0.0172739i
$133$	−7.34481	+	16.9175i	−0.636876	+	1.46694i
$134$	−3.30485	−	5.72416i	−0.285495	−	0.494492i
$135$	−2.16503	+	3.74994i	−0.186336	+	0.322744i
$136$	−1.40546	+	2.43433i	−0.120517	+	0.208742i
$137$	5.20854	−	9.02146i	0.444996	−	0.770755i	−0.553056	−	0.833144i	$-0.686539\pi$
$137$	5.20854	−	9.02146i	0.444996	−	0.770755i	0.998052	+	0.0623887i	$0.0198719\pi$
$138$	−2.13587	+	3.69943i	−0.181817	+	0.314916i
$139$	6.12235	+	10.6042i	0.519291	+	0.899438i	0.999749	+	0.0224200i	$0.00713711\pi$
$139$	6.12235	+	10.6042i	0.519291	+	0.899438i	−0.480458	+	0.877018i	$0.659530\pi$
$140$	−4.82491	+	0.552437i	−0.407780	+	0.0466895i
$141$	−10.5073	+	18.1992i	−0.884874	+	1.53265i
$142$	−3.79147	+	6.56701i	−0.318173	+	0.551092i
$143$	−0.313924	+	0.0205330i	−0.0262516	+	0.00171706i
$144$	−1.94908	−	3.37591i	−0.162424	−	0.281326i
$145$	−1.93010	−	3.34303i	−0.160286	−	0.277624i
$146$	5.45471	−	9.44783i	0.451435	−	0.781908i
$147$	−12.5535	−	13.4321i	−1.03539	−	1.10786i
$148$	8.82216			0.725177
$149$	22.0024			1.80251			0.901253	−	0.433294i	$-0.142649\pi$
$149$	22.0024			1.80251			0.901253	+	0.433294i	$0.142649\pi$
$150$	2.14149	−	3.70917i	0.174852	−	0.302852i
$151$	5.94347	+	10.2944i	0.483673	+	0.837746i	0.999824	−	0.0187516i	$-0.00596916\pi$
$151$	5.94347	+	10.2944i	0.483673	+	0.837746i	−0.516151	+	0.856497i	$0.672636\pi$
$152$	−6.97084			−0.565410
$153$	−5.47872	+	9.48941i	−0.442928	+	0.767174i
$154$	0.229351	−	0.0262599i	0.0184816	−	0.00211609i
$155$	13.6228			1.09421
$156$	−4.18951	+	8.49260i	−0.335429	+	0.679952i
$157$	0.800191	+	1.38597i	0.0638622	+	0.110613i	0.896189	−	0.443673i	$-0.146325\pi$
$157$	0.800191	+	1.38597i	0.0638622	+	0.110613i	−0.832326	+	0.554286i	$0.812992\pi$
$158$	−9.21793			−0.733339
$159$	−1.17510	−	2.03533i	−0.0931912	−	0.161412i
$160$	−0.917780	−	1.58964i	−0.0725569	−	0.125672i
$161$	−4.27522	+	0.489499i	−0.336934	+	0.0385779i
$162$	2.74939	+	4.76209i	0.216013	+	0.374145i
$163$	−4.60937			−0.361034			−0.180517	−	0.983572i	$-0.557777\pi$
$163$	−4.60937			−0.361034			−0.180517	+	0.983572i	$0.557777\pi$
$164$	−5.21139	−	9.02639i	−0.406941	−	0.704843i
$165$	0.210322	−	0.364289i	0.0163736	−	0.0283598i
$166$	−8.43966	−	14.6179i	−0.655044	−	1.13457i
$167$	−9.67113	+	16.7509i	−0.748374	+	1.29622i	0.200227	+	0.979750i	$0.435832\pi$
$167$	−9.67113	+	16.7509i	−0.748374	+	1.29622i	−0.948602	+	0.316473i	$0.897501\pi$
$168$	2.76734	−	6.37409i	0.213505	−	0.491772i
$169$	12.8892	−	1.69335i	0.991480	−	0.130258i
$170$	−2.57980	+	4.46835i	−0.197862	+	0.342707i
$171$	−27.1735			−2.07801
$172$	−5.98114			−0.456058
$173$	−14.2034			−1.07986			−0.539931	−	0.841710i	$-0.681550\pi$
$173$	−14.2034			−1.07986			−0.539931	+	0.841710i	$0.681550\pi$
$174$	5.52343			0.418730
$175$	4.28647	−	0.490787i	0.324027	−	0.0371000i
$176$	0.0436264	+	0.0755631i	0.00328846	+	0.00569579i
$177$	8.98098	−	15.5555i	0.675052	−	1.16922i
$178$	4.95471	−	8.58181i	0.371371	−	0.643234i
$179$	−10.5355			−0.787463			−0.393731	−	0.919226i	$-0.628816\pi$
$179$	−10.5355			−0.787463			−0.393731	+	0.919226i	$0.628816\pi$
$180$	−3.57766	−	6.19669i	−0.266663	−	0.461874i
$181$	18.5808			1.38110			0.690549	−	0.723285i	$-0.257369\pi$
$181$	18.5808			1.38110			0.690549	+	0.723285i	$0.257369\pi$
$182$	−9.38644	+	1.70140i	−0.695769	+	0.126116i
$183$	23.2851			1.72128
$184$	−0.813218	−	1.40854i	−0.0599513	−	0.103839i
$185$	16.1936			1.19058
$186$	−9.74617	+	16.8809i	−0.714624	+	1.23777i
$187$	0.122630	−	0.212402i	0.00896761	−	0.0155323i
$188$	−4.00059	−	6.92923i	−0.291773	−	0.505366i
$189$	2.48554	−	5.72502i	0.180796	−	0.416434i
$190$	−12.7954			−0.928276
$191$	22.8279			1.65177			0.825886	−	0.563837i	$-0.190675\pi$
$191$	22.8279			1.65177			0.825886	+	0.563837i	$0.190675\pi$
$192$	2.62644			0.189547
$193$	−2.92304			−0.210405			−0.105203	−	0.994451i	$-0.533549\pi$
$193$	−2.92304			−0.210405			−0.105203	+	0.994451i	$0.533549\pi$
$194$	1.42051	−	2.46040i	0.101987	−	0.176646i
$195$	−7.69010	+	15.5887i	−0.550700	+	1.11633i
$196$	6.81884	−	1.58221i	0.487060	−	0.113015i
$197$	2.37415	−	4.11215i	0.169151	−	0.292979i	−0.768970	−	0.639284i	$-0.779231\pi$
$197$	2.37415	−	4.11215i	0.169151	−	0.292979i	0.938122	+	0.346306i	$0.112564\pi$
$198$	0.170063	+	0.294558i	0.0120859	+	0.0209333i
$199$	4.92265	−	8.52628i	0.348958	−	0.604412i	−0.637107	−	0.770775i	$-0.719869\pi$
$199$	4.92265	−	8.52628i	0.348958	−	0.604412i	0.986065	+	0.166363i	$0.0532024\pi$
$200$	0.815359	+	1.41224i	0.0576546	+	0.0998607i
$201$	17.3599			1.22448
$202$	1.88300	+	3.26145i	0.132488	+	0.229475i
$203$	3.31210	+	4.47086i	0.232464	+	0.313793i
$204$	−3.69135	−	6.39360i	−0.258446	−	0.447642i
$205$	−9.56582	−	16.5685i	−0.668106	−	1.15719i
$206$	−9.45771			−0.658950
$207$	−3.17006	−	5.49071i	−0.220335	−	0.381631i
$208$	−2.00273	−	2.99818i	−0.138864	−	0.207886i
$209$	0.608226			0.0420718
$210$	5.07961	−	11.7000i	0.350527	−	0.807379i
$211$	2.18356	−	3.78203i	0.150322	−	0.260366i	−0.781024	−	0.624501i	$-0.785302\pi$
$211$	2.18356	−	3.78203i	0.150322	−	0.260366i	0.931346	+	0.364136i	$0.118636\pi$
$212$	0.894821			0.0614566
$213$	−9.95805	−	17.2478i	−0.682314	−	1.18180i
$214$	−3.67949	+	6.37307i	−0.251525	+	0.435654i
$215$	−10.9787			−0.748744
$216$	2.35899			0.160509
$217$	−19.5082	+	2.23363i	−1.32431	+	0.151629i
$218$	−1.96249	+	3.39913i	−0.132917	+	0.230218i
$219$	14.3264	+	24.8141i	0.968091	+	1.67678i
$220$	0.0800789	+	0.138701i	0.00539892	+	0.00935120i
$221$	−4.48378	+	9.08911i	−0.301612	+	0.611400i
$222$	−11.5854	+	20.0665i	−0.777563	+	1.34678i
$223$	−14.0542	+	24.3427i	−0.941142	+	1.63011i	−0.177844	+	0.984059i	$0.556912\pi$
$223$	−14.0542	+	24.3427i	−0.941142	+	1.63011i	−0.763298	+	0.646047i	$0.776421\pi$
$224$	1.57493	+	2.12593i	0.105230	+	0.142045i
$225$	3.17841	+	5.50517i	0.211894	+	0.367011i
$226$	−7.47705	+	12.9506i	−0.497366	+	0.861463i
$227$	13.3454	−	23.1150i	0.885767	−	1.53419i	0.0409354	−	0.999162i	$-0.486966\pi$
$227$	13.3454	−	23.1150i	0.885767	−	1.53419i	0.844832	−	0.535032i	$-0.179700\pi$
$228$	9.15424	−	15.8556i	0.606254	−	1.05006i
$229$	−4.70473	+	8.14883i	−0.310897	+	0.538490i	−0.978557	−	0.205977i	$-0.933963\pi$
$229$	−4.70473	+	8.14883i	−0.310897	+	0.538490i	0.667660	+	0.744467i	$0.267296\pi$
$230$	−1.49271	−	2.58545i	−0.0984265	−	0.170480i
$231$	−0.241458	+	0.556157i	−0.0158868	+	0.0365925i
$232$	−1.05151	+	1.82126i	−0.0690347	+	0.119572i
$233$	−11.5107	+	19.9372i	−0.754093	+	1.30613i	0.191731	+	0.981448i	$0.438590\pi$
$233$	−11.5107	+	19.9372i	−0.754093	+	1.30613i	−0.945824	+	0.324680i	$0.894743\pi$
$234$	−7.80699	−	11.6874i	−0.510359	−	0.764029i
$235$	−7.34332	−	12.7190i	−0.479026	−	0.829697i
$236$	3.41945	+	5.92267i	0.222588	+	0.385533i
$237$	12.1052	−	20.9668i	0.786315	−	1.36194i
$238$	2.96171	−	6.82181i	0.191979	−	0.442192i
$239$	11.0321			0.713610			0.356805	−	0.934179i	$-0.383866\pi$
$239$	11.0321			0.713610			0.356805	+	0.934179i	$0.383866\pi$
$240$	4.82098			0.311193
$241$	−3.69969	+	6.40806i	−0.238318	+	0.412779i	−0.960232	−	0.279204i	$-0.909929\pi$
$241$	−3.69969	+	6.40806i	−0.238318	+	0.412779i	0.721914	+	0.691983i	$0.243263\pi$
$242$	5.49619	+	9.51969i	0.353309	+	0.611949i
$243$	−21.5192			−1.38045
$244$	−4.43283	+	7.67789i	−0.283783	+	0.491527i
$245$	12.5164	−	2.90425i	0.799643	−	0.185546i
$246$	27.3748			1.74535
$247$	−25.0801	+	1.64043i	−1.59581	+	0.104378i
$248$	−3.71080	−	6.42729i	−0.235636	−	0.408133i
$249$	44.3324			2.80945
$250$	6.08554	+	10.5405i	0.384883	+	0.666638i
$251$	−1.94394	−	3.36700i	−0.122700	−	0.212523i	0.798131	−	0.602483i	$-0.205822\pi$
$251$	−1.94394	−	3.36700i	−0.122700	−	0.212523i	−0.920832	+	0.389960i	$0.872489\pi$
$252$	6.13935	+	8.28725i	0.386743	+	0.522048i
$253$	0.0709556	+	0.122899i	0.00446094	+	0.00772657i
$254$	0.646477			0.0405636
$255$	−6.77569	−	11.7358i	−0.424310	−	0.734927i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.86569	−	13.6238i	−0.490648	−	0.849828i	0.509294	−	0.860593i	$-0.329907\pi$
$257$	−7.86569	−	13.6238i	−0.490648	−	0.849828i	−0.999942	+	0.0107648i	$0.996573\pi$
$258$	7.85454	−	13.6045i	0.489003	−	0.846977i
$259$	−23.1897	+	2.65515i	−1.44094	+	0.164983i
$260$	−3.67613	−	5.50333i	−0.227984	−	0.341302i
$261$	−4.09895	+	7.09958i	−0.253718	+	0.439453i
$262$	−2.79634			−0.172758
$263$	−12.7599			−0.786808			−0.393404	−	0.919366i	$-0.628703\pi$
$263$	−12.7599			−0.786808			−0.393404	+	0.919366i	$0.628703\pi$
$264$	−0.229164			−0.0141041
$265$	1.64250			0.100898
$266$	18.3234	−	2.09797i	1.12348	−	0.128635i
$267$	13.0132	+	22.5396i	0.796397	+	1.37940i
$268$	−3.30485	+	5.72416i	−0.201876	+	0.349659i
$269$	−6.51291	+	11.2807i	−0.397099	+	0.687796i	−0.993367	−	0.114990i	$-0.963316\pi$
$269$	−6.51291	+	11.2807i	−0.397099	+	0.687796i	0.596267	+	0.802786i	$0.296650\pi$
$270$	4.33006			0.263519
$271$	4.68905	+	8.12167i	0.284839	+	0.493356i	0.972570	−	0.232610i	$-0.0747264\pi$
$271$	4.68905	+	8.12167i	0.284839	+	0.493356i	−0.687731	+	0.725966i	$0.741393\pi$
$272$	2.81092			0.170437
$273$	8.45650	−	23.5843i	0.511810	−	1.42739i
$274$	−10.4171			−0.629319
$275$	−0.0711424	−	0.123222i	−0.00429005	−	0.00743058i
$276$	4.27173			0.257128
$277$	8.79375	−	15.2312i	0.528365	−	0.915155i	−0.471088	−	0.882086i	$-0.656139\pi$
$277$	8.79375	−	15.2312i	0.528365	−	0.915155i	0.999453	−	0.0330692i	$-0.0105282\pi$
$278$	6.12235	−	10.6042i	0.367194	−	0.635999i
$279$	−14.4653	−	25.0547i	−0.866016	−	1.49998i
$280$	2.89088	+	3.90228i	0.172763	+	0.233206i
$281$	13.5973			0.811146			0.405573	−	0.914063i	$-0.367072\pi$
$281$	13.5973			0.811146			0.405573	+	0.914063i	$0.367072\pi$
$282$	21.0146			1.25140
$283$	6.44841			0.383318			0.191659	−	0.981462i	$-0.438613\pi$
$283$	6.44841			0.383318			0.191659	+	0.981462i	$0.438613\pi$
$284$	7.58293			0.449964
$285$	16.8032	−	29.1039i	0.995333	−	1.72397i
$286$	0.174744	+	0.261599i	0.0103328	+	0.0154687i
$287$	16.4152	+	22.1581i	0.968956	+	1.30795i
$288$	−1.94908	+	3.37591i	−0.114851	+	0.198928i
$289$	4.54937	+	7.87975i	0.267610	+	0.463514i
$290$	−1.93010	+	3.34303i	−0.113339	+	0.196310i
$291$	3.73088	+	6.46208i	0.218708	+	0.378814i
$292$	−10.9094			−0.638425
$293$	−0.972625	−	1.68464i	−0.0568214	−	0.0984175i	0.836216	−	0.548401i	$-0.184763\pi$
$293$	−0.972625	−	1.68464i	−0.0568214	−	0.0984175i	−0.893037	+	0.449983i	$0.851430\pi$
$294$	−5.35579	+	17.5877i	−0.312356	+	1.02573i
$295$	6.27661	+	10.8714i	0.365439	+	0.632958i
$296$	−4.41108	−	7.64022i	−0.256389	−	0.444079i
$297$	−0.205828			−0.0119434
$298$	−11.0012	−	19.0546i	−0.637282	−	1.10380i
$299$	−3.25732	−	4.87635i	−0.188375	−	0.282006i
$300$	−4.28298			−0.247278
$301$	15.7219	−	1.80011i	0.906195	−	0.103756i
$302$	5.94347	−	10.2944i	0.342008	−	0.592376i
$303$	−9.89117			−0.568233
$304$	3.48542	+	6.03693i	0.199903	+	0.346242i
$305$	−8.13673	+	14.0932i	−0.465908	+	0.806976i
$306$	10.9574			0.626395
$307$	6.07696			0.346830			0.173415	−	0.984849i	$-0.444520\pi$
$307$	6.07696			0.346830			0.173415	+	0.984849i	$0.444520\pi$
$308$	−0.137417	−	0.185494i	−0.00783007	−	0.0105695i
$309$	12.4200	−	21.5121i	0.706552	−	1.22378i
$310$	−6.81139	−	11.7977i	−0.386861	−	0.670063i
$311$	6.12086	+	10.6016i	0.347082	+	0.601164i	0.985730	−	0.168335i	$-0.0538392\pi$
$311$	6.12086	+	10.6016i	0.347082	+	0.601164i	−0.638648	+	0.769499i	$0.720506\pi$
$312$	9.44956	−	0.618073i	0.534976	−	0.0349915i
$313$	−4.69419	+	8.13058i	−0.265332	+	0.459568i	−0.967650	−	0.252295i	$-0.918815\pi$
$313$	−4.69419	+	8.13058i	−0.265332	+	0.459568i	0.702319	+	0.711862i	$0.252148\pi$
$314$	0.800191	−	1.38597i	0.0451574	−	0.0782149i
$315$	11.2691	+	15.2117i	0.634944	+	0.857085i
$316$	4.60897	+	7.98297i	0.259275	+	0.449077i
$317$	1.39828	−	2.42190i	0.0785355	−	0.136027i	−0.824083	−	0.566469i	$-0.808309\pi$
$317$	1.39828	−	2.42190i	0.0785355	−	0.136027i	0.902618	+	0.430442i	$0.141642\pi$
$318$	−1.17510	+	2.03533i	−0.0658961	+	0.114135i
$319$	0.0917468	−	0.158910i	0.00513683	−	0.00889726i
$320$	−0.917780	+	1.58964i	−0.0513055	+	0.0888637i
$321$	−9.66396	−	16.7385i	−0.539389	−	0.934250i
$322$	2.56153	+	3.45770i	0.142748	+	0.192690i
$323$	9.79723	−	16.9693i	0.545133	−	0.944197i
$324$	2.74939	−	4.76209i	0.152744	−	0.264560i
$325$	3.26589	+	4.88918i	0.181159	+	0.271203i
$326$	2.30469	+	3.99183i	0.127645	+	0.221087i
$327$	−5.15436	−	8.92761i	−0.285037	−	0.493698i
$328$	−5.21139	+	9.02639i	−0.287751	+	0.498399i
$329$	12.6013	+	17.0100i	0.694733	+	0.937790i
$330$	−0.420644			−0.0231557
$331$	−25.7164			−1.41350			−0.706752	−	0.707462i	$-0.749840\pi$
$331$	−25.7164			−1.41350			−0.706752	+	0.707462i	$0.749840\pi$
$332$	−8.43966	+	14.6179i	−0.463186	+	0.802262i
$333$	−17.1951	−	29.7829i	−0.942288	−	1.63209i
$334$	19.3423			1.05836
$335$	−6.06624	+	10.5070i	−0.331434	+	0.574061i
$336$	−6.90379	+	0.790462i	−0.376633	+	0.0431233i
$337$	−34.3496			−1.87114			−0.935570	−	0.353141i	$-0.885114\pi$
$337$	−34.3496			−1.87114			−0.935570	+	0.353141i	$0.885114\pi$
$338$	−7.91111	−	10.3157i	−0.430308	−	0.561102i
$339$	−19.6380	−	34.0140i	−1.06659	−	1.84739i
$340$	5.15961			0.279819
$341$	0.323777	+	0.560799i	0.0175335	+	0.0303690i
$342$	13.5868	+	23.5330i	0.734688	+	1.27252i
$343$	−17.4477	+	6.21119i	−0.942085	+	0.335373i
$344$	2.99057	+	5.17982i	0.161241	+	0.279277i
$345$	7.84102			0.422146
$346$	7.10168	+	12.3005i	0.381789	+	0.661277i
$347$	6.46296	−	11.1942i	0.346950	−	0.600935i	−0.638756	−	0.769409i	$-0.720551\pi$
$347$	6.46296	−	11.1942i	0.346950	−	0.600935i	0.985706	+	0.168475i	$0.0538841\pi$
$348$	−2.76171	−	4.78343i	−0.148043	−	0.256419i
$349$	4.74593	−	8.22019i	0.254044	−	0.440017i	−0.710592	−	0.703605i	$-0.751573\pi$
$349$	4.74593	−	8.22019i	0.254044	−	0.440017i	0.964635	+	0.263588i	$0.0849060\pi$
$350$	−2.56827	−	3.46680i	−0.137280	−	0.185308i
$351$	8.48731	−	0.555135i	0.453019	−	0.0296309i
$352$	0.0436264	−	0.0755631i	0.00232529	−	0.00402753i
$353$	−9.16562			−0.487837			−0.243918	−	0.969796i	$-0.578433\pi$
$353$	−9.16562			−0.487837			−0.243918	+	0.969796i	$0.578433\pi$
$354$	−17.9620			−0.954667
$355$	13.9189			0.738740
$356$	−9.90942			−0.525198
$357$	11.6272	+	15.6951i	0.615379	+	0.830674i
$358$	5.26777	+	9.12404i	0.278410	+	0.482220i
$359$	4.07401	−	7.05639i	0.215018	−	0.372422i	−0.738260	−	0.674516i	$-0.764352\pi$
$359$	4.07401	−	7.05639i	0.215018	−	0.372422i	0.953278	+	0.302094i	$0.0976857\pi$
$360$	−3.57766	+	6.19669i	−0.188559	+	0.326594i
$361$	29.5927			1.55751
$362$	−9.29039	−	16.0914i	−0.488292	−	0.845747i
$363$	−28.8708			−1.51532
$364$	6.16668	+	7.27819i	0.323222	+	0.381481i
$365$	−20.0249			−1.04815
$366$	−11.6426	−	20.1655i	−0.608566	−	1.05407i
$367$	−25.5076			−1.33148			−0.665742	−	0.746182i	$-0.731885\pi$
$367$	−25.5076			−1.33148			−0.665742	+	0.746182i	$0.731885\pi$
$368$	−0.813218	+	1.40854i	−0.0423919	+	0.0734250i
$369$	−20.3149	+	35.1864i	−1.05755	+	1.83173i
$370$	−8.09681	−	14.0241i	−0.420933	−	0.729077i
$371$	−2.35211	+	0.269309i	−0.122115	+	0.0139818i
$372$	19.4923			1.01063
$373$	2.83889			0.146992			0.0734961	−	0.997296i	$-0.476584\pi$
$373$	2.83889			0.146992			0.0734961	+	0.997296i	$0.476584\pi$
$374$	−0.245260			−0.0126821
$375$	−31.9666			−1.65075
$376$	−4.00059	+	6.92923i	−0.206315	+	0.357348i
$377$	−3.35458	+	6.80010i	−0.172770	+	0.350223i
$378$	−6.20078	+	0.709969i	−0.318934	+	0.0365169i
$379$	0.804301	−	1.39309i	0.0413142	−	0.0715582i	−0.844629	−	0.535352i	$-0.820179\pi$
$379$	0.804301	−	1.39309i	0.0413142	−	0.0715582i	0.885943	+	0.463794i	$0.153512\pi$
$380$	6.39770	+	11.0811i	0.328195	+	0.568451i
$381$	−0.848966	+	1.47045i	−0.0434938	+	0.0753335i
$382$	−11.4140	−	19.7696i	−0.583990	−	1.01150i
$383$	15.9499			0.814999			0.407500	−	0.913205i	$-0.366401\pi$
$383$	15.9499			0.814999			0.407500	+	0.913205i	$0.366401\pi$
$384$	−1.31322	−	2.27456i	−0.0670149	−	0.116073i
$385$	−0.252237	−	0.340485i	−0.0128552	−	0.0173527i
$386$	1.46152	+	2.53143i	0.0743895	+	0.128846i
$387$	11.6578	+	20.1918i	0.592597	+	1.02641i
$388$	−2.84102			−0.144231
$389$	−2.12674	−	3.68363i	−0.107830	−	0.186767i	0.807061	−	0.590468i	$-0.201057\pi$
$389$	−2.12674	−	3.68363i	−0.107830	−	0.186767i	−0.914891	+	0.403701i	$0.867724\pi$
$390$	17.3452	−	1.13451i	0.878310	−	0.0574482i
$391$	4.57178			0.231205
$392$	−4.77966	−	5.11418i	−0.241409	−	0.258305i
$393$	3.67220	−	6.36044i	0.185238	−	0.320842i
$394$	−4.74831			−0.239216
$395$	8.46004	+	14.6532i	0.425671	+	0.737283i
$396$	0.170063	−	0.294558i	0.00854599	−	0.0148021i
$397$	−1.66111			−0.0833686			−0.0416843	−	0.999131i	$-0.513272\pi$
$397$	−1.66111			−0.0833686			−0.0416843	+	0.999131i	$0.513272\pi$
$398$	−9.84531			−0.493501
$399$	−19.2907	+	44.4328i	−0.965741	+	2.22442i
$400$	0.815359	−	1.41224i	0.0407680	−	0.0706122i
$401$	1.30242	+	2.25586i	0.0650398	+	0.112652i	0.896712	−	0.442615i	$-0.145949\pi$
$401$	1.30242	+	2.25586i	0.0650398	+	0.112652i	−0.831672	+	0.555267i	$0.812616\pi$
$402$	−8.67997	−	15.0341i	−0.432917	−	0.749835i
$403$	−14.8635	−	22.2513i	−0.740402	−	1.10841i
$404$	1.88300	−	3.26145i	0.0936828	−	0.162263i
$405$	5.04667	−	8.74109i	0.250771	−	0.434348i
$406$	2.21583	−	5.10379i	0.109970	−	0.253297i
$407$	0.384879	+	0.666630i	0.0190778	+	0.0330436i
$408$	−3.69135	+	6.39360i	−0.182749	+	0.316530i
$409$	3.17978	−	5.50753i	0.157230	−	0.272330i	−0.776639	−	0.629946i	$-0.783077\pi$
$409$	3.17978	−	5.50753i	0.157230	−	0.272330i	0.933869	+	0.357616i	$0.116410\pi$
$410$	−9.56582	+	16.5685i	−0.472422	+	0.818259i
$411$	13.6799	−	23.6943i	0.674780	−	1.16875i
$412$	4.72886	+	8.19062i	0.232974	+	0.403523i
$413$	−10.7708	−	14.5391i	−0.529997	−	0.715420i
$414$	−3.17006	+	5.49071i	−0.155800	+	0.269854i
$415$	−15.4915	+	26.8321i	−0.760448	+	1.31713i
$416$	−1.59513	+	3.23350i	−0.0782078	+	0.158536i
$417$	16.0800	+	27.8513i	0.787439	+	1.36388i
$418$	−0.304113	−	0.526739i	−0.0148746	−	0.0257636i
$419$	4.71852	−	8.17271i	0.230515	−	0.399263i	−0.727445	−	0.686166i	$-0.759292\pi$
$419$	4.71852	−	8.17271i	0.230515	−	0.399263i	0.957960	+	0.286903i	$0.0926257\pi$
$420$	−12.6723	+	1.45094i	−0.618346	+	0.0707987i
$421$	−30.3009			−1.47677			−0.738387	−	0.674377i	$-0.764412\pi$
$421$	−30.3009			−1.47677			−0.738387	+	0.674377i	$0.764412\pi$
$422$	−4.36711			−0.212588
$423$	−15.5950	+	27.0113i	−0.758254	+	1.31333i
$424$	−0.447411	−	0.774938i	−0.0217282	−	0.0376343i
$425$	−4.58381			−0.222348
$426$	−9.95805	+	17.2478i	−0.482469	+	0.835661i
$427$	9.34128	−	21.5161i	0.452056	−	1.04124i
$428$	7.35899			0.355710
$429$	−0.824500	+	0.0539286i	−0.0398073	+	0.00260370i
$430$	5.48937	+	9.50787i	0.264721	+	0.458510i
$431$	−4.78839			−0.230649			−0.115324	−	0.993328i	$-0.536791\pi$
$431$	−4.78839			−0.230649			−0.115324	+	0.993328i	$0.536791\pi$
$432$	−1.17949	−	2.04294i	−0.0567484	−	0.0982911i
$433$	20.1875	+	34.9658i	0.970151	+	1.68035i	0.695088	+	0.718925i	$0.255365\pi$
$433$	20.1875	+	34.9658i	0.970151	+	1.68035i	0.275063	+	0.961426i	$0.411301\pi$
$434$	11.6885	+	15.7778i	0.561066	+	0.757359i
$435$	−5.06929	−	8.78027i	−0.243054	−	0.420982i
$436$	3.92498			0.187972
$437$	5.66882	+	9.81868i	0.271176	+	0.469691i
$438$	14.3264	−	24.8141i	0.684544	−	1.18567i
$439$	−0.509403	−	0.882313i	−0.0243125	−	0.0421105i	0.853613	−	0.520907i	$-0.174406\pi$
$439$	−0.509403	−	0.882313i	−0.0243125	−	0.0421105i	−0.877926	+	0.478797i	$0.841073\pi$
$440$	0.0800789	−	0.138701i	0.00381761	−	0.00661229i
$441$	−18.6319	−	19.9360i	−0.887234	−	0.949331i
$442$	10.1133	−	0.661487i	0.481040	−	0.0314637i
$443$	13.4582	−	23.3103i	0.639419	−	1.10751i	−0.346141	−	0.938182i	$-0.612508\pi$
$443$	13.4582	−	23.3103i	0.639419	−	1.10751i	0.985560	−	0.169324i	$-0.0541585\pi$
$444$	23.1709			1.09964
$445$	−18.1893			−0.862257
$446$	28.1085			1.33098
$447$	57.7879			2.73327
$448$	1.05365	−	2.42690i	0.0497801	−	0.114660i
$449$	−4.41776	−	7.65179i	−0.208487	−	0.361110i	0.742751	−	0.669568i	$-0.233521\pi$
$449$	−4.41776	−	7.65179i	−0.208487	−	0.361110i	−0.951238	+	0.308457i	$0.900187\pi$
$450$	3.17841	−	5.50517i	0.149832	−	0.259516i
$451$	0.454708	−	0.787578i	0.0214114	−	0.0370856i
$452$	14.9541			0.703382
$453$	15.6101	+	27.0376i	0.733429	+	1.27034i
$454$	−26.6909			−1.25266
$455$	11.3193	+	13.3596i	0.530657	+	0.626306i
$456$	−18.3085			−0.857373
$457$	17.9361	+	31.0662i	0.839014	+	1.45321i	0.890720	+	0.454552i	$0.150201\pi$
$457$	17.9361	+	31.0662i	0.839014	+	1.45321i	−0.0517063	+	0.998662i	$0.516466\pi$
$458$	9.40945			0.439675
$459$	−3.31546	+	5.74254i	−0.154752	+	0.268039i
$460$	−1.49271	+	2.58545i	−0.0695980	+	0.120547i
$461$	−20.6169	−	35.7095i	−0.960224	−	1.66316i	−0.721932	−	0.691964i	$-0.756746\pi$
$461$	−20.6169	−	35.7095i	−0.960224	−	1.66316i	−0.238292	−	0.971193i	$-0.576588\pi$
$462$	0.602375	−	0.0689700i	0.0280250	−	0.00320878i
$463$	21.0313			0.977408			0.488704	−	0.872450i	$-0.337470\pi$
$463$	21.0313			0.977408			0.488704	+	0.872450i	$0.337470\pi$
$464$	2.10301			0.0976298
$465$	35.7794			1.65923
$466$	23.0215			1.06645
$467$	10.2160	−	17.6946i	0.472740	−	0.818809i	−0.526774	−	0.850006i	$-0.676598\pi$
$467$	10.2160	−	17.6946i	0.472740	−	0.818809i	0.999513	+	0.0311965i	$0.00993176\pi$
$468$	−6.21809	+	12.6048i	−0.287432	+	0.582655i
$469$	6.96428	−	16.0410i	0.321581	−	0.740706i
$470$	−7.34332	+	12.7190i	−0.338722	+	0.586684i
$471$	2.10165	+	3.64017i	0.0968390	+	0.167730i
$472$	3.41945	−	5.92267i	0.157393	−	0.272613i
$473$	−0.260936	−	0.451954i	−0.0119978	−	0.0207809i
$474$	−24.2103			−1.11202
$475$	−5.68374	−	9.84453i	−0.260788	−	0.451698i
$476$	−7.38871	+	0.845984i	−0.338661	+	0.0387756i
$477$	−1.74408	−	3.02084i	−0.0798561	−	0.138315i
$478$	−5.51607	−	9.55412i	−0.252299	−	0.436995i
$479$	−39.2000			−1.79109			−0.895547	−	0.444966i	$-0.853216\pi$
$479$	−39.2000			−1.79109			−0.895547	+	0.444966i	$0.853216\pi$
$480$	−2.41049	−	4.17509i	−0.110023	−	0.190566i
$481$	−17.6684	−	26.4504i	−0.805611	−	1.20603i
$482$	7.39939			0.337033
$483$	−11.2286	+	1.28564i	−0.510918	+	0.0584985i
$484$	5.49619	−	9.51969i	0.249827	−	0.432713i
$485$	−5.21487			−0.236795
$486$	10.7596	+	18.6361i	0.488064	+	0.845352i
$487$	5.80410	−	10.0530i	0.263009	−	0.455545i	−0.704031	−	0.710169i	$-0.748618\pi$
$487$	5.80410	−	10.0530i	0.263009	−	0.455545i	0.967040	+	0.254624i	$0.0819518\pi$
$488$	8.86567			0.401330
$489$	−12.1062			−0.547462
$490$	−8.77335	−	9.38739i	−0.396340	−	0.424079i
$491$	11.9193	−	20.6448i	0.537910	−	0.931688i	−0.461106	−	0.887345i	$-0.652547\pi$
$491$	11.9193	−	20.6448i	0.537910	−	0.931688i	0.999016	−	0.0443428i	$-0.0141194\pi$
$492$	−13.6874	−	23.7072i	−0.617075	−	1.06880i
$493$	−2.95569	−	5.11941i	−0.133118	−	0.230567i
$494$	13.9607	+	20.8998i	0.628123	+	0.940328i
$495$	0.312161	−	0.540679i	0.0140306	−	0.0243017i
$496$	−3.71080	+	6.42729i	−0.166620	+	0.288594i
$497$	−19.9323	+	2.28219i	−0.894087	+	0.102370i
$498$	−22.1662	−	38.3930i	−0.993292	−	1.72043i
$499$	−4.09131	+	7.08635i	−0.183152	+	0.317229i	−0.942952	−	0.332928i	$-0.891963\pi$
$499$	−4.09131	+	7.08635i	−0.183152	+	0.317229i	0.759800	+	0.650157i	$0.225297\pi$
$500$	6.08554	−	10.5405i	0.272154	−	0.471384i
$501$	−25.4006	+	43.9951i	−1.13482	+	1.96556i
$502$	−1.94394	+	3.36700i	−0.0867622	+	0.150276i
$503$	−4.28341	−	7.41908i	−0.190988	−	0.330801i	0.754590	−	0.656196i	$-0.227836\pi$
$503$	−4.28341	−	7.41908i	−0.190988	−	0.330801i	−0.945578	+	0.325396i	$0.894502\pi$
$504$	4.10729	−	9.46046i	0.182953	−	0.421402i
$505$	3.45636	−	5.98660i	0.153806	−	0.266400i
$506$	0.0709556	−	0.122899i	0.00315436	−	0.00546351i
$507$	33.8528	−	4.44749i	1.50345	−	0.197520i
$508$	−0.323239	−	0.559866i	−0.0143414	−	0.0248400i
$509$	7.42352	+	12.8579i	0.329042	+	0.569917i	0.982322	−	0.187199i	$-0.0599410\pi$
$509$	7.42352	+	12.8579i	0.329042	+	0.569917i	−0.653280	+	0.757116i	$0.726608\pi$
$510$	−6.77569	+	11.7358i	−0.300033	+	0.519672i
$511$	28.6762	−	3.28334i	1.26856	−	0.145246i
$512$	1.00000			0.0441942
$513$	−16.4441			−0.726026
$514$	−7.86569	+	13.6238i	−0.346941	+	0.600919i
$515$	8.68010	+	15.0344i	0.382491	+	0.662494i
$516$	−15.7091			−0.691554
$517$	0.349063	−	0.604594i	0.0153518	−	0.0265900i
$518$	13.8943	+	18.7553i	0.610480	+	0.824062i
$519$	−37.3042			−1.63747
$520$	−2.92796	+	5.93529i	−0.128400	+	0.260280i
$521$	−9.55852	−	16.5558i	−0.418766	−	0.725325i	0.577049	−	0.816709i	$-0.304204\pi$
$521$	−9.55852	−	16.5558i	−0.418766	−	0.725325i	−0.995816	+	0.0913847i	$0.970871\pi$
$522$	8.19789			0.358812
$523$	4.84605	+	8.39360i	0.211903	+	0.367027i	0.952310	−	0.305132i	$-0.0987006\pi$
$523$	4.84605	+	8.39360i	0.211903	+	0.367027i	−0.740407	+	0.672159i	$0.765367\pi$
$524$	1.39817	+	2.42170i	0.0610793	+	0.105792i
$525$	11.2581	−	1.28902i	0.491346	−	0.0562575i
$526$	6.37994	+	11.0504i	0.278178	+	0.481819i
$527$	20.8615			0.908741
$528$	0.114582	+	0.198462i	0.00498654	+	0.00863694i
$529$	10.1774	−	17.6277i	0.442494	−	0.766421i
$530$	−0.821249	−	1.42245i	−0.0356728	−	0.0617871i
$531$	13.3296	−	23.0876i	0.578456	−	1.00192i
$532$	−10.9786	−	14.8196i	−0.475983	−	0.642509i
$533$	−16.6257	+	33.7021i	−0.720139	+	1.45980i
$534$	13.0132	−	22.5396i	0.563137	−	0.975383i
$535$	13.5079			0.583996
$536$	6.60969			0.285495
$537$	−27.6709			−1.19409
$538$	13.0258			0.561583
$539$	0.417038	+	0.446227i	0.0179631	+	0.0192203i
$540$	−2.16503	−	3.74994i	−0.0931681	−	0.161372i
$541$	2.80233	−	4.85378i	0.120482	−	0.208680i	−0.799476	−	0.600698i	$-0.794889\pi$
$541$	2.80233	−	4.85378i	0.120482	−	0.208680i	0.919958	+	0.392018i	$0.128223\pi$
$542$	4.68905	−	8.12167i	0.201412	−	0.348855i
$543$	48.8013			2.09426
$544$	−1.40546	−	2.43433i	−0.0602585	−	0.104371i
$545$	7.20454			0.308608
$546$	−24.6529	+	4.46863i	−1.05505	+	0.191240i
$547$	−37.1487			−1.58836			−0.794181	−	0.607681i	$-0.792100\pi$
$547$	−37.1487			−1.58836			−0.794181	+	0.607681i	$0.792100\pi$
$548$	5.20854	+	9.02146i	0.222498	+	0.385378i
$549$	34.5599			1.47498
$550$	−0.0711424	+	0.123222i	−0.00303352	+	0.00525421i
$551$	7.32988	−	12.6957i	0.312263	−	0.540856i
$552$	−2.13587	−	3.69943i	−0.0909085	−	0.157458i
$553$	−14.5176	−	19.5967i	−0.617352	−	0.833337i
$554$	−17.5875			−0.747221
$555$	42.5315			1.80536
$556$	−12.2447			−0.519291
$557$	−29.7435			−1.26027			−0.630136	−	0.776485i	$-0.717001\pi$
$557$	−29.7435			−1.26027			−0.630136	+	0.776485i	$0.717001\pi$
$558$	−14.4653	+	25.0547i	−0.612366	+	1.06065i
$559$	11.9786	+	17.9325i	0.506642	+	0.758465i
$560$	1.93403	−	4.45472i	0.0817278	−	0.188246i
$561$	0.322080	−	0.557860i	0.0135982	−	0.0235528i
$562$	−6.79864	−	11.7756i	−0.286783	−	0.496723i
$563$	−4.48827	+	7.77391i	−0.189158	+	0.327631i	−0.944970	−	0.327158i	$-0.893909\pi$
$563$	−4.48827	+	7.77391i	−0.189158	+	0.327631i	0.755812	+	0.654789i	$0.227242\pi$
$564$	−10.5073	−	18.1992i	−0.442437	−	0.766323i
$565$	27.4492			1.15479
$566$	−3.22420	−	5.58448i	−0.135523	−	0.234733i
$567$	−5.79377	+	13.3450i	−0.243316	+	0.560436i
$568$	−3.79147	−	6.56701i	−0.159086	−	0.275546i
$569$	6.68319	+	11.5756i	0.280174	+	0.485276i	0.971427	−	0.237337i	$-0.0762745\pi$
$569$	6.68319	+	11.5756i	0.280174	+	0.485276i	−0.691253	+	0.722612i	$0.742941\pi$
$570$	−33.6063			−1.40761
$571$	16.2327	+	28.1159i	0.679319	+	1.17662i	0.975186	+	0.221386i	$0.0710581\pi$
$571$	16.2327	+	28.1159i	0.679319	+	1.17662i	−0.295867	+	0.955229i	$0.595609\pi$
$572$	0.139180	−	0.282132i	0.00581940	−	0.0117965i
$573$	59.9562			2.50470
$574$	10.9819	−	25.2950i	0.458377	−	1.05579i
$575$	1.32613	−	2.29693i	0.0553035	−	0.0957884i
$576$	3.89817			0.162424
$577$	−6.60186	−	11.4348i	−0.274839	−	0.476035i	0.695256	−	0.718763i	$-0.255291\pi$
$577$	−6.60186	−	11.4348i	−0.274839	−	0.476035i	−0.970094	+	0.242728i	$0.921958\pi$
$578$	4.54937	−	7.87975i	0.189229	−	0.327754i
$579$	−7.67719			−0.319053
$580$	3.86020			0.160286
$581$	17.7848	−	40.9643i	0.737839	−	1.69949i
$582$	3.73088	−	6.46208i	0.154650	−	0.267862i
$583$	0.0390378	+	0.0676155i	0.00161678	+	0.00280035i
$584$	5.45471	+	9.44783i	0.225717	+	0.390954i
$585$	−11.4137	+	23.1368i	−0.471898	+	0.956588i
$586$	−0.972625	+	1.68464i	−0.0401788	+	0.0695917i
$587$	5.18691	−	8.98398i	0.214086	−	0.370809i	−0.738903	−	0.673812i	$-0.764656\pi$
$587$	5.18691	−	8.98398i	0.214086	−	0.370809i	0.952990	+	0.303003i	$0.0979892\pi$
$588$	17.9093	−	4.15558i	0.738565	−	0.171373i
$589$	25.8674	+	44.8036i	1.06585	+	1.84610i
$590$	6.27661	−	10.8714i	0.258404	−	0.447569i
$591$	6.23556	−	10.8003i	0.256497	−	0.444266i
$592$	−4.41108	+	7.64022i	−0.181294	+	0.314011i
$593$	−18.3275	+	31.7441i	−0.752619	+	1.30357i	0.193931	+	0.981015i	$0.437876\pi$
$593$	−18.3275	+	31.7441i	−0.752619	+	1.30357i	−0.946549	+	0.322559i	$0.895457\pi$
$594$	0.102914	+	0.178252i	0.00422261	+	0.00731378i
$595$	−13.5624	+	1.55285i	−0.556005	+	0.0636608i
$596$	−11.0012	+	19.0546i	−0.450626	+	0.780508i
$597$	12.9290	−	22.3937i	0.529150	−	0.916515i
$598$	−2.59438	+	5.25909i	−0.106092	+	0.215060i
$599$	−18.7178	−	32.4202i	−0.764789	−	1.32465i	−0.940358	−	0.340187i	$-0.889510\pi$
$599$	−18.7178	−	32.4202i	−0.764789	−	1.32465i	0.175568	−	0.984467i	$-0.443824\pi$
$600$	2.14149	+	3.70917i	0.0874260	+	0.151426i
$601$	−0.994692	+	1.72286i	−0.0405743	+	0.0702768i	−0.885599	−	0.464450i	$-0.846252\pi$
$601$	−0.994692	+	1.72286i	−0.0405743	+	0.0702768i	0.845025	+	0.534727i	$0.179585\pi$
$602$	−9.41988	−	12.7155i	−0.383926	−	0.518245i
$603$	25.7657			1.04926
$604$	−11.8869			−0.483673
$605$	10.0886	−	17.4740i	0.410160	−	0.710417i
$606$	4.94558	+	8.56600i	0.200901	+	0.347970i
$607$	−5.39853			−0.219119			−0.109560	−	0.993980i	$-0.534944\pi$
$607$	−5.39853			−0.219119			−0.109560	+	0.993980i	$0.534944\pi$
$608$	3.48542	−	6.03693i	0.141353	−	0.244830i
$609$	8.69901	+	11.7424i	0.352502	+	0.475827i
$610$	16.2735			0.658893
$611$	−12.7629	+	25.8719i	−0.516333	+	1.04666i
$612$	−5.47872	−	9.48941i	−0.221464	−	0.383587i
$613$	−4.04069			−0.163202			−0.0816009	−	0.996665i	$-0.526003\pi$
$613$	−4.04069			−0.163202			−0.0816009	+	0.996665i	$0.526003\pi$
$614$	−3.03848	−	5.26280i	−0.122623	−	0.212389i
$615$	−25.1240	−	43.5161i	−1.01310	−	1.75474i
$616$	−0.0919336	+	0.211754i	−0.00370411	+	0.00853179i
$617$	12.1383	+	21.0241i	0.488669	+	0.846400i	0.999915	−	0.0130346i	$-0.00414917\pi$
$617$	12.1383	+	21.0241i	0.488669	+	0.846400i	−0.511246	+	0.859435i	$0.670816\pi$
$618$	−24.8401			−0.999215
$619$	−7.27576	−	12.6020i	−0.292437	−	0.506517i	0.681948	−	0.731401i	$-0.261133\pi$
$619$	−7.27576	−	12.6020i	−0.292437	−	0.506517i	−0.974386	+	0.224884i	$0.927800\pi$
$620$	−6.81139	+	11.7977i	−0.273552	+	0.473806i
$621$	−1.91837	−	3.32272i	−0.0769816	−	0.133336i
$622$	6.12086	−	10.6016i	0.245424	−	0.425087i
$623$	26.0477	−	2.98238i	1.04358	−	0.119486i
$624$	−5.26005	−	7.87452i	−0.210570	−	0.315233i
$625$	7.09358	−	12.2864i	0.283743	−	0.491458i
$626$	9.38839			0.375235
$627$	1.59747			0.0637967
$628$	−1.60038			−0.0638622
$629$	24.7984			0.988776
$630$	7.53918	−	17.3652i	0.300368	−	0.691848i
$631$	4.19668	+	7.26886i	0.167067	+	0.289369i	0.937387	−	0.348288i	$-0.113237\pi$
$631$	4.19668	+	7.26886i	0.167067	+	0.289369i	−0.770320	+	0.637657i	$0.779904\pi$
$632$	4.60897	−	7.98297i	0.183335	−	0.317545i
$633$	5.73497	−	9.93327i	0.227945	−	0.394812i
$634$	−2.79657			−0.111066
$635$	−0.593324	−	1.02767i	−0.0235453	−	0.0407817i
$636$	2.35019			0.0931912
$637$	−18.4001	−	17.2753i	−0.729037	−	0.684474i
$638$	−0.183494			−0.00726458
$639$	−14.7798	−	25.5993i	−0.584679	−	1.01269i
$640$	1.83556			0.0725569
$641$	−0.194764	+	0.337341i	−0.00769272	+	0.0133242i	−0.869846	−	0.493323i	$-0.835782\pi$
$641$	−0.194764	+	0.337341i	−0.00769272	+	0.0133242i	0.862153	+	0.506647i	$0.169115\pi$
$642$	−9.66396	+	16.7385i	−0.381406	+	0.660614i
$643$	−5.93499	−	10.2797i	−0.234053	−	0.405392i	0.724944	−	0.688808i	$-0.241866\pi$
$643$	−5.93499	−	10.2797i	−0.234053	−	0.405392i	−0.958997	+	0.283416i	$0.908532\pi$
$644$	1.71369	−	3.94719i	0.0675288	−	0.155541i
$645$	−28.8350			−1.13538
$646$	−19.5945			−0.770934
$647$	19.8084			0.778750			0.389375	−	0.921079i	$-0.372691\pi$
$647$	19.8084			0.778750			0.389375	+	0.921079i	$0.372691\pi$
$648$	−5.49878			−0.216013
$649$	−0.298357	+	0.516769i	−0.0117115	+	0.0202850i
$650$	2.60121	−	5.27294i	0.102028	−	0.206822i
$651$	−51.2372	+	5.86649i	−2.00814	+	0.229926i
$652$	2.30469	−	3.99183i	0.0902584	−	0.156332i
$653$	2.79653	+	4.84373i	0.109437	+	0.189550i	0.915542	−	0.402222i	$-0.131762\pi$
$653$	2.79653	+	4.84373i	0.109437	+	0.189550i	−0.806106	+	0.591772i	$0.798429\pi$
$654$	−5.15436	+	8.92761i	−0.201551	+	0.349097i
$655$	2.56642	+	4.44518i	0.100279	+	0.173687i
$656$	10.4228			0.406941
$657$	21.2634	+	36.8293i	0.829563	+	1.43685i
$658$	8.43042	−	19.4180i	0.328652	−	0.756994i
$659$	−5.58265	−	9.66943i	−0.217469	−	0.376668i	0.736564	−	0.676367i	$-0.236447\pi$
$659$	−5.58265	−	9.66943i	−0.217469	−	0.376668i	−0.954034	+	0.299700i	$0.903113\pi$
$660$	0.210322	+	0.364289i	0.00818678	+	0.0141799i
$661$	8.22042			0.319737			0.159869	−	0.987138i	$-0.448893\pi$
$661$	8.22042			0.319737			0.159869	+	0.987138i	$0.448893\pi$
$662$	12.8582	+	22.2711i	0.499749	+	0.865590i
$663$	−11.7764	+	23.8720i	−0.457356	+	0.927111i
$664$	16.8793			0.655044
$665$	−20.1519	−	27.2022i	−0.781456	−	1.05486i
$666$	−17.1951	+	29.7829i	−0.666298	+	1.15406i
$667$	3.42041			0.132439
$668$	−9.67113	−	16.7509i	−0.374187	−	0.648111i
$669$	−36.9126	+	63.9345i	−1.42712	+	2.47185i
$670$	12.1325			0.468719
$671$	−0.773554			−0.0298627
$672$	4.13646	+	5.58363i	0.159567	+	0.215393i
$673$	−1.98340	+	3.43536i	−0.0764546	+	0.132423i	−0.901718	−	0.432325i	$-0.857693\pi$
$673$	−1.98340	+	3.43536i	−0.0764546	+	0.132423i	0.825263	+	0.564748i	$0.191027\pi$
$674$	17.1748	+	29.7476i	0.661548	+	1.14583i
$675$	1.92342	+	3.33146i	0.0740325	+	0.128228i
$676$	−4.97813	+	12.0091i	−0.191467	+	0.461888i
$677$	−12.4424	+	21.5509i	−0.478201	+	0.828268i	−0.999688	−	0.0249913i	$-0.992044\pi$
$677$	−12.4424	+	21.5509i	−0.478201	+	0.828268i	0.521487	+	0.853259i	$0.325378\pi$
$678$	−19.6380	+	34.0140i	−0.754193	+	1.30630i
$679$	7.46785	−	0.855045i	0.286590	−	0.0328136i
$680$	−2.57980	−	4.46835i	−0.0989310	−	0.171353i
$681$	35.0509	−	60.7100i	1.34315	−	2.32641i
$682$	0.323777	−	0.560799i	0.0123981	−	0.0214741i
$683$	−25.3588	+	43.9227i	−0.970327	+	1.68066i	−0.275761	+	0.961226i	$0.588930\pi$
$683$	−25.3588	+	43.9227i	−0.970327	+	1.68066i	−0.694566	+	0.719429i	$0.744403\pi$
$684$	13.5868	−	23.5330i	0.519503	−	0.899806i
$685$	9.56059	+	16.5594i	0.365291	+	0.632703i
$686$	14.1029	+	12.0045i	0.538451	+	0.458335i
$687$	−12.3567	+	21.4024i	−0.471436	+	0.816552i
$688$	2.99057	−	5.17982i	0.114014	−	0.197479i
$689$	−1.79209	−	2.68283i	−0.0682731	−	0.102208i
$690$	−3.92051	−	6.79053i	−0.149251	−	0.258511i
$691$	6.05622	+	10.4897i	0.230389	+	0.399046i	0.957923	−	0.287026i	$-0.0926667\pi$
$691$	6.05622	+	10.4897i	0.230389	+	0.399046i	−0.727533	+	0.686072i	$0.759333\pi$
$692$	7.10168	−	12.3005i	0.269965	−	0.467594i
$693$	−0.358373	+	0.825451i	−0.0136135	+	0.0313563i
$694$	−12.9259			−0.490661
$695$	−22.4759			−0.852558
$696$	−2.76171	+	4.78343i	−0.104682	+	0.181315i
$697$	−14.6488	−	25.3724i	−0.554862	−	0.961049i
$698$	−9.49186			−0.359272
$699$	−30.2322	+	52.3637i	−1.14349	+	1.98058i
$700$	−1.71820	+	3.95759i	−0.0649419	+	0.149583i
$701$	2.45486			0.0927186			0.0463593	−	0.998925i	$-0.485238\pi$
$701$	2.45486			0.0927186			0.0463593	+	0.998925i	$0.485238\pi$
$702$	−4.72441	−	7.07266i	−0.178312	−	0.266940i
$703$	30.7490	+	53.2588i	1.15972	+	2.00869i
$704$	−0.0872528			−0.00328846
$705$	−19.2868	−	33.4057i	−0.726382	−	1.25813i
$706$	4.58281	+	7.93766i	0.172476	+	0.298738i
$707$	−3.96804	+	9.13970i	−0.149233	+	0.343734i
$708$	8.98098	+	15.5555i	0.337526	+	0.584612i
$709$	3.63735			0.136603			0.0683017	−	0.997665i	$-0.478242\pi$
$709$	3.63735			0.136603			0.0683017	+	0.997665i	$0.478242\pi$
$710$	−6.95947	−	12.0541i	−0.261184	−	0.452384i
$711$	17.9665	−	31.1190i	0.673798	−	1.16705i
$712$	4.95471	+	8.58181i	0.185686	+	0.321617i
$713$	−6.03538	+	10.4536i	−0.226027	+	0.391490i
$714$	7.77875	−	17.9170i	0.291112	−	0.670528i
$715$	0.255473	−	0.517871i	0.00955414	−	0.0193673i
$716$	5.26777	−	9.12404i	0.196866	−	0.340981i
$717$	28.9752			1.08210
$718$	−8.14802			−0.304081
$719$	−41.2047			−1.53668			−0.768339	−	0.640043i	$-0.778916\pi$
$719$	−41.2047			−1.53668			−0.768339	+	0.640043i	$0.778916\pi$
$720$	7.15533			0.266663
$721$	−14.8952	−	20.1065i	−0.554728	−	0.748804i
$722$	−14.7963	−	25.6280i	−0.550663	−	0.953776i
$723$	−9.71701	+	16.8304i	−0.361380	+	0.625928i
$724$	−9.29039	+	16.0914i	−0.345275	+	0.598033i
$725$	−3.42942			−0.127365
$726$	14.4354	+	25.0029i	0.535748	+	0.927943i
$727$	−24.1162			−0.894422			−0.447211	−	0.894428i	$-0.647583\pi$
$727$	−24.1162			−0.894422			−0.447211	+	0.894428i	$0.647583\pi$
$728$	3.21976	−	8.97960i	0.119332	−	0.332806i
$729$	−40.0224			−1.48231
$730$	10.0124	+	17.3421i	0.370577	+	0.641859i
$731$	−16.8125			−0.621832
$732$	−11.6426	+	20.1655i	−0.430321	+	0.745338i
$733$	−9.37448	+	16.2371i	−0.346254	+	0.599730i	−0.985581	−	0.169205i	$-0.945880\pi$
$733$	−9.37448	+	16.2371i	−0.346254	+	0.599730i	0.639327	+	0.768935i	$0.279213\pi$
$734$	12.7538	+	22.0902i	0.470751	+	0.815364i
$735$	32.8735	−	7.62782i	1.21256	−	0.281356i
$736$	1.62644			0.0599513
$737$	−0.576714			−0.0212435
$738$	40.6297			1.49560
$739$	0.931468			0.0342646			0.0171323	−	0.999853i	$-0.494546\pi$
$739$	0.931468			0.0342646			0.0171323	+	0.999853i	$0.494546\pi$
$740$	−8.09681	+	14.0241i	−0.297645	+	0.515535i
$741$	−65.8714	+	4.30849i	−2.41985	+	0.158276i
$742$	1.40928	+	1.90233i	0.0517364	+	0.0698368i
$743$	14.8945	−	25.7980i	0.546425	−	0.946437i	−0.452090	−	0.891972i	$-0.649322\pi$
$743$	14.8945	−	25.7980i	0.546425	−	0.946437i	0.998516	−	0.0544644i	$-0.0173451\pi$
$744$	−9.74617	−	16.8809i	−0.357312	−	0.618883i
$745$	−20.1933	+	34.9759i	−0.739827	+	1.28142i
$746$	−1.41945	−	2.45855i	−0.0519696	−	0.0900140i
$747$	65.7984			2.40744
$748$	0.122630	+	0.212402i	0.00448380	+	0.00776617i
$749$	−19.3437	+	2.21479i	−0.706802	+	0.0809266i
$750$	15.9833	+	27.6839i	0.583627	+	1.01087i
$751$	6.49099	+	11.2427i	0.236860	+	0.410253i	0.959812	−	0.280645i	$-0.0905485\pi$
$751$	6.49099	+	11.2427i	0.236860	+	0.410253i	−0.722952	+	0.690898i	$0.757215\pi$
$752$	8.00118			0.291773
$753$	−5.10563	−	8.84321i	−0.186059	−	0.322264i
$754$	7.56635	−	0.494897i	0.275550	−	0.0180231i
$755$	−21.8192			−0.794082
$756$	3.71524	+	5.01505i	0.135122	+	0.182395i
$757$	13.6228	−	23.5954i	0.495129	−	0.857589i	−0.504855	−	0.863204i	$-0.668454\pi$
$757$	13.6228	−	23.5954i	0.495129	−	0.857589i	0.999984	+	0.00561523i	$0.00178739\pi$
$758$	−1.60860			−0.0584271
$759$	0.186360	+	0.322786i	0.00676445	+	0.0117164i
$760$	6.39770	−	11.0811i	0.232069	−	0.401955i
$761$	5.78873			0.209841			0.104921	−	0.994481i	$-0.466541\pi$
$761$	5.78873			0.209841			0.104921	+	0.994481i	$0.466541\pi$
$762$	1.69793			0.0615096
$763$	−10.3171	+	1.18128i	−0.373505	+	0.0427651i
$764$	−11.4140	+	19.7696i	−0.412943	+	0.715238i
$765$	−10.0565	−	17.4184i	−0.363594	−	0.629763i
$766$	−7.97493	−	13.8130i	−0.288146	−	0.499083i
$767$	10.9090	−	22.1136i	0.393900	−	0.798477i
$768$	−1.31322	+	2.27456i	−0.0473867	+	0.0820761i
$769$	13.8054	−	23.9117i	0.497836	−	0.862277i	−0.502161	−	0.864774i	$-0.667462\pi$
$769$	13.8054	−	23.9117i	0.497836	−	0.862277i	0.999997	+	0.00249727i	$0.000794907\pi$
$770$	−0.168750	+	0.388686i	−0.00608132	+	0.0140073i
$771$	−20.6587	−	35.7820i	−0.744006	−	1.28866i
$772$	1.46152	−	2.53143i	0.0526013	−	0.0911081i
$773$	−15.7900	+	27.3490i	−0.567926	+	0.983676i	0.428845	+	0.903378i	$0.358921\pi$
$773$	−15.7900	+	27.3490i	−0.567926	+	0.983676i	−0.996771	+	0.0802984i	$0.974413\pi$
$774$	11.6578	−	20.1918i	0.419029	−	0.725780i
$775$	6.05127	−	10.4811i	0.217368	−	0.376492i
$776$	1.42051	+	2.46040i	0.0509934	+	0.0883231i
$777$	−60.9064	+	6.97359i	−2.18500	+	0.250176i
$778$	−2.12674	+	3.68363i	−0.0762474	+	0.132064i
$779$	36.3278	−	62.9216i	1.30158	−	2.25440i
$780$	−9.65513	−	14.4542i	−0.345709	−	0.517542i
$781$	0.330816	+	0.572990i	0.0118375	+	0.0205032i
$782$	−2.28589	−	3.95928i	−0.0817432	−	0.141583i
$783$	−2.48049	+	4.29633i	−0.0886454	+	0.153538i
$784$	−2.03918	+	6.69640i	−0.0728280	+	0.239157i
$785$	−2.93760			−0.104847
$786$	−7.34441			−0.261966
$787$	−10.8572	+	18.8052i	−0.387017	+	0.670333i	−0.992047	−	0.125870i	$-0.959828\pi$
$787$	−10.8572	+	18.8052i	−0.387017	+	0.670333i	0.605030	+	0.796203i	$0.293161\pi$
$788$	2.37415	+	4.11215i	0.0845757	+	0.146489i
$789$	−33.5130			−1.19309
$790$	8.46004	−	14.6532i	0.300995	−	0.521338i
$791$	−39.3080	+	4.50064i	−1.39763	+	0.160024i
$792$	−0.340126			−0.0120859
$793$	31.8975	−	2.08634i	1.13271	−	0.0740880i
$794$	0.830554	+	1.43856i	0.0294752	+	0.0510526i
$795$	4.31392			0.152999
$796$	4.92265	+	8.52628i	0.174479	+	0.302206i
$797$	−22.9458	−	39.7433i	−0.812783	−	1.40778i	−0.910909	−	0.412608i	$-0.864618\pi$
$797$	−22.9458	−	39.7433i	−0.812783	−	1.40778i	0.0981258	−	0.995174i	$-0.468715\pi$
$798$	48.1253	−	5.51019i	1.70362	−	0.195059i
$799$	−11.2453	−	19.4775i	−0.397831	−	0.689064i
$800$	−1.63072			−0.0576546
$801$	19.3143	+	33.4533i	0.682437	+	1.18202i
$802$	1.30242	−	2.25586i	0.0459901	−	0.0796572i
$803$	−0.475938	−	0.824350i	−0.0167955	−	0.0290907i
$804$	−8.67997	+	15.0341i	−0.306119	+	0.530213i
$805$	3.14558	−	7.24531i	0.110867	−	0.255364i
$806$	−11.8384	+	23.9978i	−0.416991	+	0.845285i
$807$	−17.1058	+	29.6280i	−0.602151	+	1.04296i
$808$	−3.76600			−0.132488
$809$	35.7521			1.25698			0.628489	−	0.777818i	$-0.283674\pi$
$809$	35.7521			1.25698			0.628489	+	0.777818i	$0.283674\pi$
$810$	−10.0933			−0.354644
$811$	38.5968			1.35532			0.677658	−	0.735377i	$-0.262995\pi$
$811$	38.5968			1.35532			0.677658	+	0.735377i	$0.262995\pi$
$812$	−5.52793	+	0.632930i	−0.193992	+	0.0222115i
$813$	12.3155	+	21.3310i	0.431923	+	0.748112i
$814$	0.384879	−	0.666630i	0.0134900	−	0.0233654i
$815$	4.23039	−	7.32725i	0.148184	−	0.256662i
$816$	7.38270			0.258446
$817$	−20.8468	−	36.1077i	−0.729337	−	1.26325i
$818$	−6.35955			−0.222357
$819$	12.5512	−	35.0040i	0.438573	−	1.22314i
$820$	19.1316			0.668106
$821$	−11.3932	−	19.7336i	−0.397626	−	0.688708i	0.595807	−	0.803128i	$-0.296832\pi$
$821$	−11.3932	−	19.7336i	−0.397626	−	0.688708i	−0.993433	+	0.114420i	$0.963499\pi$
$822$	−27.3598			−0.954283
$823$	17.7822	−	30.7996i	0.619848	−	1.07361i	−0.369666	−	0.929165i	$-0.620528\pi$
$823$	17.7822	−	30.7996i	0.619848	−	1.07361i	0.989513	−	0.144443i	$-0.0461389\pi$
$824$	4.72886	−	8.19062i	0.164738	−	0.285334i
$825$	−0.186851	−	0.323635i	−0.00650531	−	0.0112675i
$826$	−7.20579	+	16.5973i	−0.250722	+	0.577495i
$827$	−29.9739			−1.04229			−0.521147	−	0.853467i	$-0.674496\pi$
$827$	−29.9739			−1.04229			−0.521147	+	0.853467i	$0.674496\pi$
$828$	6.34013			0.220335
$829$	−24.2760			−0.843141			−0.421571	−	0.906796i	$-0.638521\pi$
$829$	−24.2760			−0.843141			−0.421571	+	0.906796i	$0.638521\pi$
$830$	30.9830			1.07544
$831$	23.0962	−	40.0038i	0.801199	−	1.38772i
$832$	3.59786	−	0.235328i	0.124733	−	0.00815852i
$833$	19.1672	−	4.44747i	0.664104	−	0.154096i
$834$	16.0800	−	27.8513i	0.556803	−	0.964412i
$835$	−17.7519	−	30.7473i	−0.614331	−	1.06405i
$836$	−0.304113	+	0.526739i	−0.0105180	+	0.0182176i
$837$	−8.75372	−	15.1619i	−0.302573	−	0.524071i
$838$	−9.43703			−0.325997
$839$	−11.0416	−	19.1246i	−0.381197	−	0.660253i	0.610037	−	0.792373i	$-0.291155\pi$
$839$	−11.0416	−	19.1246i	−0.381197	−	0.660253i	−0.991234	+	0.132120i	$0.957821\pi$
$840$	7.59272	+	10.2491i	0.261974	+	0.353627i
$841$	12.2887	+	21.2846i	0.423747	+	0.733952i
$842$	15.1504	+	26.2413i	0.522118	+	0.904336i
$843$	35.7124			1.23000
$844$	2.18356	+	3.78203i	0.0751611	+	0.130183i
$845$	−9.13766	+	22.0434i	−0.314345	+	0.758316i
$846$	31.1900			1.07233
$847$	−11.5821	+	26.6774i	−0.397965	+	0.916646i
$848$	−0.447411	+	0.774938i	−0.0153641	+	0.0266115i
$849$	16.9363			0.581253
$850$	2.29191	+	3.96970i	0.0786118	+	0.136160i
$851$	−7.17435	+	12.4263i	−0.245933	+	0.425969i
$852$	19.9161			0.682314
$853$	42.8773			1.46809			0.734045	−	0.679100i	$-0.237630\pi$
$853$	42.8773			1.46809			0.734045	+	0.679100i	$0.237630\pi$
$854$	−23.3041	+	2.66824i	−0.797450	+	0.0913054i
$855$	24.9393	−	43.1962i	0.852907	−	1.47728i
$856$	−3.67949	−	6.37307i	−0.125762	−	0.217827i
$857$	7.91204	+	13.7041i	0.270270	+	0.468122i	0.968931	−	0.247331i	$-0.0795536\pi$
$857$	7.91204	+	13.7041i	0.270270	+	0.468122i	−0.698661	+	0.715453i	$0.746220\pi$
$858$	0.458954	+	0.687074i	0.0156684	+	0.0234563i
$859$	15.7121	−	27.2141i	0.536090	−	0.928535i	−0.463020	−	0.886348i	$-0.653234\pi$
$859$	15.7121	−	27.2141i	0.536090	−	0.928535i	0.999110	−	0.0421868i	$-0.0134325\pi$
$860$	5.48937	−	9.50787i	0.187186	−	0.324216i
$861$	43.1134	+	58.1969i	1.46930	+	1.98335i
$862$	2.39419	+	4.14687i	0.0815466	+	0.141243i
$863$	−25.1722	+	43.5995i	−0.856872	+	1.48415i	0.0180258	+	0.999838i	$0.494262\pi$
$863$	−25.1722	+	43.5995i	−0.856872	+	1.48415i	−0.874898	+	0.484308i	$0.839071\pi$
$864$	−1.17949	+	2.04294i	−0.0401272	+	0.0695023i
$865$	13.0356	−	22.5782i	0.443222	−	0.767684i
$866$	20.1875	−	34.9658i	0.686000	−	1.18819i
$867$	11.9486	+	20.6957i	0.405797	+	0.702861i
$868$	7.81974	−	18.0114i	0.265419	−	0.611348i
$869$	−0.402145	+	0.696536i	−0.0136418	+	0.0236284i
$870$	−5.06929	+	8.78027i	−0.171865	+	0.297679i
$871$	23.7808	−	1.55544i	0.805781	−	0.0527042i
$872$	−1.96249	−	3.39913i	−0.0664583	−	0.115109i
$873$	5.53739	+	9.59105i	0.187412	+	0.324608i
$874$	5.66882	−	9.81868i	0.191751	−	0.332122i
$875$	−12.8240	+	29.5380i	−0.433531	+	0.998565i
$876$	−28.6529			−0.968091
$877$	2.37518			0.0802041			0.0401021	−	0.999196i	$-0.487232\pi$
$877$	2.37518			0.0802041			0.0401021	+	0.999196i	$0.487232\pi$
$878$	−0.509403	+	0.882313i	−0.0171915	+	0.0297766i
$879$	−2.55454	−	4.42459i	−0.0861625	−	0.149238i
$880$	−0.160158			−0.00539892
$881$	−9.38846	+	16.2613i	−0.316305	+	0.547857i	−0.979714	−	0.200400i	$-0.935776\pi$
$881$	−9.38846	+	16.2613i	−0.316305	+	0.547857i	0.663409	+	0.748257i	$0.269109\pi$
$882$	−7.94908	+	26.1037i	−0.267660	+	0.878957i
$883$	16.9385			0.570026			0.285013	−	0.958524i	$-0.408002\pi$
$883$	16.9385			0.570026			0.285013	+	0.958524i	$0.408002\pi$
$884$	−5.62951	−	8.42763i	−0.189341	−	0.283452i
$885$	16.4851	+	28.5531i	0.554142	+	0.959801i
$886$	−26.9164			−0.904275
$887$	9.68429	+	16.7737i	0.325167	+	0.563205i	0.981546	−	0.191226i	$-0.0612463\pi$
$887$	9.68429	+	16.7737i	0.325167	+	0.563205i	−0.656379	+	0.754431i	$0.727913\pi$
$888$	−11.5854	−	20.0665i	−0.388781	−	0.673389i
$889$	1.01816	+	1.37437i	0.0341479	+	0.0460948i
$890$	9.09467	+	15.7524i	0.304854	+	0.528022i
$891$	0.479784			0.0160734
$892$	−14.0542	−	24.3427i	−0.470571	−	0.815053i
$893$	27.8875	−	48.3026i	0.933219	−	1.61638i
$894$	−28.8939	−	50.0458i	−0.966357	−	1.67378i
$895$	9.66930	−	16.7477i	0.323209	−	0.559815i
$896$	−2.62858	+	0.300964i	−0.0878146	+	0.0100545i
$897$	−8.55513	−	12.8074i	−0.285648	−	0.427627i
$898$	−4.41776	+	7.65179i	−0.147423	+	0.255343i
$899$	15.6077			0.520546
$900$	−6.35682			−0.211894
$901$	2.51527			0.0837958
$902$	−0.909416			−0.0302802
$903$	41.2926	−	4.72787i	1.37413	−	0.157334i
$904$	−7.47705	−	12.9506i	−0.248683	−	0.430732i
$905$	−17.0531	+	29.5368i	−0.566863	+	0.981836i
$906$	15.6101	−	27.0376i	0.518612	−	0.898263i
$907$	26.8091			0.890181			0.445090	−	0.895486i	$-0.353172\pi$
$907$	26.8091			0.890181			0.445090	+	0.895486i	$0.353172\pi$
$908$	13.3454	+	23.1150i	0.442884	+	0.767097i
$909$	−14.6805			−0.486922
$910$	5.91006	−	16.4826i	0.195917	−	0.546392i
$911$	0.383210			0.0126963			0.00634816	−	0.999980i	$-0.497979\pi$
$911$	0.383210			0.0126963			0.00634816	+	0.999980i	$0.497979\pi$
$912$	9.15424	+	15.8556i	0.303127	+	0.525032i
$913$	−1.47277			−0.0487415
$914$	17.9361	−	31.0662i	0.593272	−	1.02758i
$915$	−21.3706	+	37.0150i	−0.706491	+	1.22368i
$916$	−4.70473	−	8.14883i	−0.155449	−	0.269245i
$917$	−4.40404	−	5.94483i	−0.145434	−	0.196316i
$918$	6.63091			0.218853
$919$	−37.5792			−1.23962			−0.619812	−	0.784750i	$-0.712791\pi$
$919$	−37.5792			−1.23962			−0.619812	+	0.784750i	$0.712791\pi$
$920$	2.98542			0.0984265
$921$	15.9607			0.525924
$922$	−20.6169	+	35.7095i	−0.678981	+	1.17603i
$923$	−15.1866	−	22.7350i	−0.499872	−	0.748331i
$924$	−0.360917	−	0.487187i	−0.0118733	−	0.0160273i
$925$	7.19323	−	12.4590i	0.236512	−	0.409651i
$926$	−10.5157	−	18.2136i	−0.345566	−	0.598537i
$927$	18.4339	−	31.9284i	0.605448	−	1.04867i
$928$	−1.05151	−	1.82126i	−0.0345174	−	0.0597858i
$929$	11.3793			0.373344			0.186672	−	0.982422i	$-0.440230\pi$
$929$	11.3793			0.373344			0.186672	+	0.982422i	$0.440230\pi$
$930$	−17.8897	−	30.9859i	−0.586626	−	1.01607i
$931$	33.3183	+	35.6502i	1.09196	+	1.16839i
$932$	−11.5107	−	19.9372i	−0.377047	−	0.653064i
$933$	16.0760	+	27.8445i	0.526306	+	0.911589i
$934$	−20.4320			−0.668555
$935$	0.225095	+	0.389876i	0.00736140	+	0.0127503i
$936$	14.0251	−	0.917347i	0.458424	−	0.0299844i
$937$	−3.70274			−0.120963			−0.0604817	−	0.998169i	$-0.519264\pi$
$937$	−3.70274			−0.120963			−0.0604817	+	0.998169i	$0.519264\pi$
$938$	−17.3741	+	1.98928i	−0.567284	+	0.0649522i
$939$	−12.3290	+	21.3545i	−0.402342	+	0.696876i
$940$	14.6866			0.479026
$941$	−26.6167	−	46.1015i	−0.867680	−	1.50287i	−0.864361	−	0.502872i	$-0.832277\pi$
$941$	−26.6167	−	46.1015i	−0.867680	−	1.50287i	−0.00331944	−	0.999994i	$-0.501057\pi$
$942$	2.10165	−	3.64017i	0.0684755	−	0.118603i
$943$	16.9520			0.552033
$944$	−6.83891			−0.222588
$945$	6.81955	+	9.20542i	0.221840	+	0.299452i
$946$	−0.260936	+	0.451954i	−0.00848375	+	0.0146943i
$947$	11.3032	+	19.5778i	0.367306	+	0.636193i	0.989143	−	0.146953i	$-0.0469468\pi$
$947$	11.3032	+	19.5778i	0.367306	+	0.636193i	−0.621837	+	0.783147i	$0.713613\pi$
$948$	12.1052	+	20.9668i	0.393157	+	0.680968i
$949$	21.8486	+	32.7084i	0.709237	+	1.06176i
$950$	−5.68374	+	9.84453i	−0.184405	+	0.319399i
$951$	3.67251	−	6.36097i	0.119089	−	0.206268i
$952$	4.42700	+	5.97582i	0.143480	+	0.193677i
$953$	7.94844	+	13.7671i	0.257475	+	0.445960i	0.965565	−	0.260162i	$-0.0837761\pi$
$953$	7.94844	+	13.7671i	0.257475	+	0.445960i	−0.708090	+	0.706123i	$0.750443\pi$
$954$	−1.74408	+	3.02084i	−0.0564668	+	0.0978033i
$955$	−20.9510	+	36.2883i	−0.677960	+	1.17426i
$956$	−5.51607	+	9.55412i	−0.178403	+	0.309002i
$957$	0.240967	−	0.417367i	0.00778936	−	0.0134916i
$958$	19.6000	+	33.9482i	0.633248	+	1.09682i
$959$	−16.4062	−	22.1460i	−0.529783	−	0.715132i
$960$	−2.41049	+	4.17509i	−0.0777983	+	0.134751i
$961$	−12.0400	+	20.8540i	−0.388388	+	0.672708i
$962$	−14.0725	+	28.5265i	−0.453716	+	0.919732i
$963$	−14.3433	−	24.8433i	−0.462206	−	0.800564i
$964$	−3.69969	−	6.40806i	−0.119159	−	0.206390i
$965$	2.68271	−	4.64659i	0.0863595	−	0.149579i
$966$	6.72769	+	9.08142i	0.216460	+	0.292190i
$967$	−26.3252			−0.846560			−0.423280	−	0.905999i	$-0.639121\pi$
$967$	−26.3252			−0.846560			−0.423280	+	0.905999i	$0.639121\pi$
$968$	−10.9924			−0.353309
$969$	25.7318	−	44.5688i	0.826625	−	1.43176i
$970$	2.60743	+	4.51621i	0.0837197	+	0.145007i
$971$	−18.7368			−0.601294			−0.300647	−	0.953736i	$-0.597203\pi$
$971$	−18.7368			−0.601294			−0.300647	+	0.953736i	$0.597203\pi$
$972$	10.7596	−	18.6361i	0.345114	−	0.597754i
$973$	32.1861	−	3.68521i	1.03184	−	0.118142i
$974$	−11.6082			−0.371951
$975$	8.57766	+	12.8411i	0.274705	+	0.411245i
$976$	−4.43283	−	7.67789i	−0.141892	−	0.245763i
$977$	−32.6941			−1.04598			−0.522989	−	0.852340i	$-0.675183\pi$
$977$	−32.6941			−1.04598			−0.522989	+	0.852340i	$0.675183\pi$
$978$	6.05311	+	10.4843i	0.193557	+	0.335251i
$979$	−0.432312	−	0.748786i	−0.0138168	−	0.0239313i
$980$	−3.74304	+	12.2916i	−0.119567	+	0.392642i
$981$	−7.65012	−	13.2504i	−0.244250	−	0.423053i
$982$	−23.8386			−0.760720
$983$	8.06918	+	13.9762i	0.257367	+	0.445772i	0.965536	−	0.260271i	$-0.0838118\pi$
$983$	8.06918	+	13.9762i	0.257367	+	0.445772i	−0.708169	+	0.706043i	$0.750479\pi$
$984$	−13.6874	+	23.7072i	−0.436338	+	0.755759i
$985$	4.35790	+	7.54811i	0.138854	+	0.240503i
$986$	−2.95569	+	5.11941i	−0.0941285	+	0.163035i
$987$	33.0965	+	44.6756i	1.05347	+	1.42204i
$988$	11.1194	−	22.5403i	0.353756	−	0.717101i
$989$	4.86397	−	8.42465i	0.154665	−	0.267888i
$990$	−0.624322			−0.0198423
$991$	−29.1059			−0.924579			−0.462289	−	0.886729i	$-0.652972\pi$
$991$	−29.1059			−0.924579			−0.462289	+	0.886729i	$0.652972\pi$
$992$	7.42160			0.235636
$993$	−67.5426			−2.14340
$994$	11.9426	+	16.1208i	0.378796	+	0.511321i
$995$	9.03583	+	15.6505i	0.286455	+	0.496154i
$996$	−22.1662	+	38.3930i	−0.702364	+	1.21653i
$997$	−13.6617	+	23.6627i	−0.432670	+	0.749406i	−0.997102	−	0.0760733i	$-0.975762\pi$
$997$	−13.6617	+	23.6627i	−0.432670	+	0.749406i	0.564432	+	0.825479i	$0.309095\pi$
$998$	8.18261			0.259016
$999$	−10.4057	−	18.0232i	−0.329221	−	0.570228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.h.d.9.5	yes	10
3.2	odd	2		1638.2.p.k.919.4		10
7.2	even	3		1274.2.g.p.295.1		10
7.3	odd	6		1274.2.e.s.165.5		10
7.4	even	3		182.2.e.d.165.1	yes	10
7.5	odd	6		1274.2.g.q.295.5		10
7.6	odd	2		1274.2.h.s.373.1		10
13.3	even	3		182.2.e.d.107.1	✓	10
21.11	odd	6		1638.2.m.j.1621.4		10
39.29	odd	6		1638.2.m.j.289.4		10
91.3	odd	6		1274.2.h.s.263.1		10
91.16	even	3		1274.2.g.p.393.1		10
91.55	odd	6		1274.2.e.s.471.5		10
91.68	odd	6		1274.2.g.q.393.5		10
91.81	even	3	inner	182.2.h.d.81.5	yes	10
273.263	odd	6		1638.2.p.k.991.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.e.d.107.1	✓	10	13.3	even	3
182.2.e.d.165.1	yes	10	7.4	even	3
182.2.h.d.9.5	yes	10	1.1	even	1	trivial
182.2.h.d.81.5	yes	10	91.81	even	3	inner
1274.2.e.s.165.5		10	7.3	odd	6
1274.2.e.s.471.5		10	91.55	odd	6
1274.2.g.p.295.1		10	7.2	even	3
1274.2.g.p.393.1		10	91.16	even	3
1274.2.g.q.295.5		10	7.5	odd	6
1274.2.g.q.393.5		10	91.68	odd	6
1274.2.h.s.263.1		10	91.3	odd	6
1274.2.h.s.373.1		10	7.6	odd	2
1638.2.m.j.289.4		10	39.29	odd	6
1638.2.m.j.1621.4		10	21.11	odd	6
1638.2.p.k.919.4		10	3.2	odd	2
1638.2.p.k.991.4		10	273.263	odd	6

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:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +2.62644 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.917780 + 1.58964i) q^{5} +(-1.31322 - 2.27456i) q^{6} +(1.05365 - 2.42690i) q^{7} +1.00000 q^{8} +3.89817 q^{9} +1.83556 q^{10} -0.0872528 q^{11} +(-1.31322 + 2.27456i) q^{12} +(3.59786 - 0.235328i) q^{13} +(-2.62858 + 0.300964i) q^{14} +(-2.41049 + 4.17509i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.40546 + 2.43433i) q^{17} +(-1.94908 - 3.37591i) q^{18} -6.97084 q^{19} +(-0.917780 - 1.58964i) q^{20} +(2.76734 - 6.37409i) q^{21} +(0.0436264 + 0.0755631i) q^{22} +(-0.813218 - 1.40854i) q^{23} +2.62644 q^{24} +(0.815359 + 1.41224i) q^{25} +(-2.00273 - 2.99818i) q^{26} +2.35899 q^{27} +(1.57493 + 2.12593i) q^{28} +(-1.05151 + 1.82126i) q^{29} +4.82098 q^{30} +(-3.71080 - 6.42729i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.229164 q^{33} +2.81092 q^{34} +(2.89088 + 3.90228i) q^{35} +(-1.94908 + 3.37591i) q^{36} +(-4.41108 - 7.64022i) q^{37} +(3.48542 + 6.03693i) q^{38} +(9.44956 - 0.618073i) q^{39} +(-0.917780 + 1.58964i) q^{40} +(-5.21139 + 9.02639i) q^{41} +(-6.90379 + 0.790462i) q^{42} +(2.99057 + 5.17982i) q^{43} +(0.0436264 - 0.0755631i) q^{44} +(-3.57766 + 6.19669i) q^{45} +(-0.813218 + 1.40854i) q^{46} +(-4.00059 + 6.92923i) q^{47} +(-1.31322 - 2.27456i) q^{48} +(-4.77966 - 5.11418i) q^{49} +(0.815359 - 1.41224i) q^{50} +(-3.69135 + 6.39360i) q^{51} +(-1.59513 + 3.23350i) q^{52} +(-0.447411 - 0.774938i) q^{53} +(-1.17949 - 2.04294i) q^{54} +(0.0800789 - 0.138701i) q^{55} +(1.05365 - 2.42690i) q^{56} -18.3085 q^{57} +2.10301 q^{58} +(3.41945 - 5.92267i) q^{59} +(-2.41049 - 4.17509i) q^{60} +8.86567 q^{61} +(-3.71080 + 6.42729i) q^{62} +(4.10729 - 9.46046i) q^{63} +1.00000 q^{64} +(-2.92796 + 5.93529i) q^{65} +(0.114582 + 0.198462i) q^{66} +6.60969 q^{67} +(-1.40546 - 2.43433i) q^{68} +(-2.13587 - 3.69943i) q^{69} +(1.93403 - 4.45472i) q^{70} +(-3.79147 - 6.56701i) q^{71} +3.89817 q^{72} +(5.45471 + 9.44783i) q^{73} +(-4.41108 + 7.64022i) q^{74} +(2.14149 + 3.70917i) q^{75} +(3.48542 - 6.03693i) q^{76} +(-0.0919336 + 0.211754i) q^{77} +(-5.26005 - 7.87452i) q^{78} +(4.60897 - 7.98297i) q^{79} +1.83556 q^{80} -5.49878 q^{81} +10.4228 q^{82} +16.8793 q^{83} +(4.13646 + 5.58363i) q^{84} +(-2.57980 - 4.46835i) q^{85} +(2.99057 - 5.17982i) q^{86} +(-2.76171 + 4.78343i) q^{87} -0.0872528 q^{88} +(4.95471 + 8.58181i) q^{89} +7.15533 q^{90} +(3.21976 - 8.97960i) q^{91} +1.62644 q^{92} +(-9.74617 - 16.8809i) q^{93} +8.00118 q^{94} +(6.39770 - 11.0811i) q^{95} +(-1.31322 + 2.27456i) q^{96} +(1.42051 + 2.46040i) q^{97} +(-2.03918 + 6.69640i) q^{98} -0.340126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + 2 q^{3} - 5 q^{4} - 2 q^{5} - q^{6} + 10 q^{8} + 8 q^{9} + 4 q^{10} + 8 q^{11} - q^{12} - 6 q^{13} - 3 q^{14} + 3 q^{15} - 5 q^{16} - 3 q^{17} - 4 q^{18} + 10 q^{19} - 2 q^{20} - 16 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 - 2 * q^5 - q^6 + 10 * q^8 + 8 * q^9 + 4 * q^10 + 8 * q^11 - q^12 - 6 * q^13 - 3 * q^14 + 3 * q^15 - 5 * q^16 - 3 * q^17 - 4 * q^18 + 10 * q^19 - 2 * q^20 - 16 * q^21 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 3 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + q^29 - 6 * q^30 - 21 * q^31 - 5 * q^32 + 6 * q^34 - 22 * q^35 - 4 * q^36 + 10 * q^37 - 5 * q^38 + 17 * q^39 - 2 * q^40 - 9 * q^41 + 5 * q^42 + 9 * q^43 - 4 * q^44 + 3 * q^45 + 4 * q^46 - 13 * q^47 - q^48 - 8 * q^49 - 3 * q^50 - 6 * q^51 - 15 * q^53 - 4 * q^54 + 7 * q^55 - 26 * q^57 - 2 * q^58 + q^59 + 3 * q^60 + 30 * q^61 - 21 * q^62 + 20 * q^63 + 10 * q^64 - 25 * q^65 - 3 * q^68 - 18 * q^69 + 26 * q^70 - q^71 + 8 * q^72 - 4 * q^73 + 10 * q^74 - 25 * q^75 - 5 * q^76 + 16 * q^77 + 11 * q^78 - q^79 + 4 * q^80 - 46 * q^81 + 18 * q^82 + 96 * q^83 + 11 * q^84 + 12 * q^85 + 9 * q^86 - 27 * q^87 + 8 * q^88 - 9 * q^89 - 6 * q^90 + 10 * q^91 - 8 * q^92 - 2 * q^93 + 26 * q^94 + 6 * q^95 - q^96 - 19 * q^97 - 5 * q^98 + 54 * q^99

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