LMFDB - Embedded newform 1190.2.i.k.851.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(681,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.681"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,2,-4,4,-4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.10423593216.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			851.2
Root			$-0.758290 + 1.31340i$ of defining polynomial
Character	$\chi$	$=$	1190.851
Dual form			1190.2.i.k.681.2

$q$-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} +(-0.408297 + 0.707191i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.816594 q^{6} +(2.28580 - 1.33233i) q^{7} +1.00000 q^{8} +(1.16659 + 2.02059i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.92488 + 5.06604i) q^{11} +(-0.408297 - 0.707191i) q^{12} -4.53844 q^{13} +(-2.29673 - 1.31340i) q^{14} -0.816594 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(1.16659 - 2.02059i) q^{18} +(2.51658 + 4.35884i) q^{19} -1.00000 q^{20} +(0.00892731 + 2.16049i) q^{21} +5.84975 q^{22} +(-3.28580 - 5.69118i) q^{23} +(-0.408297 + 0.707191i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.26922 + 3.93041i) q^{26} -4.35504 q^{27} +(0.0109324 + 2.64573i) q^{28} -5.96636 q^{29} +(0.408297 + 0.707191i) q^{30} +(3.04737 - 5.27820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.38844 - 4.13689i) q^{33} +1.00000 q^{34} +(2.29673 + 1.31340i) q^{35} -2.33317 q^{36} +(1.62814 + 2.82003i) q^{37} +(2.51658 - 4.35884i) q^{38} +(1.85303 - 3.20955i) q^{39} +(0.500000 + 0.866025i) q^{40} -5.07689 q^{41} +(1.86657 - 1.08797i) q^{42} -4.20479 q^{43} +(-2.92488 - 5.06604i) q^{44} +(-1.16659 + 2.02059i) q^{45} +(-3.28580 + 5.69118i) q^{46} +(1.97814 + 3.42623i) q^{47} +0.816594 q^{48} +(3.44978 - 6.09089i) q^{49} +1.00000 q^{50} +(-0.408297 - 0.707191i) q^{51} +(2.26922 - 3.93041i) q^{52} +(6.95239 - 12.0419i) q^{53} +(2.17752 + 3.77157i) q^{54} -5.84975 q^{55} +(2.28580 - 1.33233i) q^{56} -4.11005 q^{57} +(2.98318 + 5.16702i) q^{58} +(-5.34083 + 9.25058i) q^{59} +(0.408297 - 0.707191i) q^{60} +(-0.0218647 - 0.0378709i) q^{61} -6.09474 q^{62} +(5.35868 + 3.06438i) q^{63} +1.00000 q^{64} +(-2.26922 - 3.93041i) q^{65} +(-2.38844 + 4.13689i) q^{66} +(-6.01129 + 10.4119i) q^{67} +(-0.500000 - 0.866025i) q^{68} +5.36633 q^{69} +(-0.0109324 - 2.64573i) q^{70} -4.49873 q^{71} +(1.16659 + 2.02059i) q^{72} +(-3.86657 + 6.69710i) q^{73} +(1.62814 - 2.82003i) q^{74} +(-0.408297 - 0.707191i) q^{75} -5.03316 q^{76} +(0.0639517 + 15.4769i) q^{77} -3.70607 q^{78} +(3.83518 + 6.64272i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-1.72161 + 2.98192i) q^{81} +(2.53844 + 4.39671i) q^{82} -13.7943 q^{83} +(-1.87550 - 1.07251i) q^{84} -1.00000 q^{85} +(2.10240 + 3.64146i) q^{86} +(2.43605 - 4.21936i) q^{87} +(-2.92488 + 5.06604i) q^{88} +(3.92688 + 6.80156i) q^{89} +2.33317 q^{90} +(-10.3740 + 6.04672i) q^{91} +6.57160 q^{92} +(2.48847 + 4.31015i) q^{93} +(1.97814 - 3.42623i) q^{94} +(-2.51658 + 4.35884i) q^{95} +(-0.408297 - 0.707191i) q^{96} +3.51002 q^{97} +(-6.99976 + 0.0578482i) q^{98} -13.6485 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} - 28 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20}+ \cdots - 52 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 2 * q^11 + 2 * q^12 - 28 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 2 * q^21 + 4 * q^22 - 6 * q^23 + 2 * q^24 - 4 * q^25 + 14 * q^26 - 16 * q^27 + 4 * q^28 - 2 * q^30 + 18 * q^31 - 4 * q^32 - 8 * q^33 + 8 * q^34 + 2 * q^35 + 8 * q^36 + 8 * q^37 + 4 * q^38 - 6 * q^39 + 4 * q^40 - 24 * q^41 - 4 * q^42 + 28 * q^43 - 2 * q^44 + 4 * q^45 - 6 * q^46 + 8 * q^47 - 4 * q^48 - 4 * q^49 + 8 * q^50 + 2 * q^51 + 14 * q^52 + 22 * q^53 + 8 * q^54 - 4 * q^55 - 2 * q^56 + 16 * q^57 + 2 * q^59 - 2 * q^60 - 8 * q^61 - 36 * q^62 + 2 * q^63 + 8 * q^64 - 14 * q^65 - 8 * q^66 - 8 * q^67 - 4 * q^68 - 16 * q^69 - 4 * q^70 - 16 * q^71 - 4 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 - 8 * q^76 - 22 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 + 24 * q^81 + 12 * q^82 - 12 * q^83 + 2 * q^84 - 8 * q^85 - 14 * q^86 + 42 * q^87 - 2 * q^88 + 12 * q^89 - 8 * q^90 - 6 * q^91 + 12 * q^92 + 20 * q^93 + 8 * q^94 - 4 * q^95 + 2 * q^96 - 32 * q^97 - 16 * q^98 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1190\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.408297	+	0.707191i	−0.235730	+	0.408297i	−0.959485	−	0.281761i	$-0.909082\pi$
$3$	−0.408297	+	0.707191i	−0.235730	+	0.408297i	0.723754	+	0.690058i	$0.242415\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.816594			0.333373
$7$	2.28580	−	1.33233i	0.863952	−	0.503574i
$7$	2.28580	−	1.33233i	0.863952	−	0.503574i
$8$	1.00000			0.353553
$9$	1.16659	+	2.02059i	0.388862	+	0.673529i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.92488	+	5.06604i	−0.881884	+	1.52747i	−0.0326392	+	0.999467i	$0.510391\pi$
$11$	−2.92488	+	5.06604i	−0.881884	+	1.52747i	−0.849244	+	0.528000i	$0.822942\pi$
$12$	−0.408297	−	0.707191i	−0.117865	−	0.204149i
$13$	−4.53844			−1.25874			−0.629369	−	0.777107i	$-0.716687\pi$
$13$	−4.53844			−1.25874			−0.629369	+	0.777107i	$0.716687\pi$
$14$	−2.29673	−	1.31340i	−0.613828	−	0.351020i
$15$	−0.816594			−0.210844
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$	1.16659	−	2.02059i	0.274967	−	0.476257i
$19$	2.51658	+	4.35884i	0.577343	+	0.999987i	0.995783	+	0.0917429i	$0.0292438\pi$
$19$	2.51658	+	4.35884i	0.577343	+	0.999987i	−0.418440	+	0.908245i	$0.637423\pi$
$20$	−1.00000			−0.223607
$21$	0.00892731	+	2.16049i	0.00194810	+	0.471457i
$22$	5.84975			1.24717
$23$	−3.28580	−	5.69118i	−0.685137	−	1.18669i	−0.973394	−	0.229139i	$-0.926409\pi$
$23$	−3.28580	−	5.69118i	−0.685137	−	1.18669i	0.288257	−	0.957553i	$-0.406924\pi$
$24$	−0.408297	+	0.707191i	−0.0833433	+	0.144355i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.26922	+	3.93041i	0.445031	+	0.770816i
$27$	−4.35504			−0.838128
$28$	0.0109324	+	2.64573i	0.00206602	+	0.499996i
$29$	−5.96636			−1.10793			−0.553963	−	0.832541i	$-0.686885\pi$
$29$	−5.96636			−1.10793			−0.553963	+	0.832541i	$0.686885\pi$
$30$	0.408297	+	0.707191i	0.0745445	+	0.129115i
$31$	3.04737	−	5.27820i	0.547324	−	0.947993i	−0.451133	−	0.892457i	$-0.648980\pi$
$31$	3.04737	−	5.27820i	0.547324	−	0.947993i	0.998457	−	0.0555363i	$-0.0176868\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.38844	−	4.13689i	−0.415774	−	0.720141i
$34$	1.00000			0.171499
$35$	2.29673	+	1.31340i	0.388219	+	0.222005i
$36$	−2.33317			−0.388862
$37$	1.62814	+	2.82003i	0.267665	+	0.463609i	0.968258	−	0.249951i	$-0.0804146\pi$
$37$	1.62814	+	2.82003i	0.267665	+	0.463609i	−0.700593	+	0.713561i	$0.747081\pi$
$38$	2.51658	−	4.35884i	0.408243	−	0.707098i
$39$	1.85303	−	3.20955i	0.296723	−	0.513939i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.07689			−0.792877			−0.396438	−	0.918061i	$-0.629754\pi$
$41$	−5.07689			−0.792877			−0.396438	+	0.918061i	$0.629754\pi$
$42$	1.86657	−	1.08797i	0.288018	−	0.167878i
$43$	−4.20479			−0.641225			−0.320612	−	0.947210i	$-0.603889\pi$
$43$	−4.20479			−0.641225			−0.320612	+	0.947210i	$0.603889\pi$
$44$	−2.92488	−	5.06604i	−0.440942	−	0.763734i
$45$	−1.16659	+	2.02059i	−0.173905	+	0.301211i
$46$	−3.28580	+	5.69118i	−0.484465	+	0.839118i
$47$	1.97814	+	3.42623i	0.288541	+	0.499767i	0.973462	−	0.228850i	$-0.0734966\pi$
$47$	1.97814	+	3.42623i	0.288541	+	0.499767i	−0.684921	+	0.728617i	$0.740163\pi$
$48$	0.816594			0.117865
$49$	3.44978	−	6.09089i	0.492826	−	0.870128i
$50$	1.00000			0.141421
$51$	−0.408297	−	0.707191i	−0.0571730	−	0.0990266i
$52$	2.26922	−	3.93041i	0.314685	−	0.545050i
$53$	6.95239	−	12.0419i	0.954984	−	1.65408i	0.220580	−	0.975369i	$-0.429205\pi$
$53$	6.95239	−	12.0419i	0.954984	−	1.65408i	0.734405	−	0.678712i	$-0.237462\pi$
$54$	2.17752	+	3.77157i	0.296323	+	0.513246i
$55$	−5.84975			−0.788781
$56$	2.28580	−	1.33233i	0.305453	−	0.178040i
$57$	−4.11005			−0.544389
$58$	2.98318	+	5.16702i	0.391711	+	0.678463i
$59$	−5.34083	+	9.25058i	−0.695316	+	1.20432i	0.274758	+	0.961514i	$0.411402\pi$
$59$	−5.34083	+	9.25058i	−0.695316	+	1.20432i	−0.970074	+	0.242810i	$0.921931\pi$
$60$	0.408297	−	0.707191i	0.0527109	−	0.0912980i
$61$	−0.0218647	−	0.0378709i	−0.00279949	−	0.00484887i	0.864622	−	0.502422i	$-0.167558\pi$
$61$	−0.0218647	−	0.0378709i	−0.00279949	−	0.00484887i	−0.867422	+	0.497574i	$0.834224\pi$
$62$	−6.09474			−0.774033
$63$	5.35868	+	3.06438i	0.675130	+	0.386076i
$64$	1.00000			0.125000
$65$	−2.26922	−	3.93041i	−0.281462	−	0.487507i
$66$	−2.38844	+	4.13689i	−0.293996	+	0.509217i
$67$	−6.01129	+	10.4119i	−0.734397	+	1.27201i	0.220591	+	0.975366i	$0.429201\pi$
$67$	−6.01129	+	10.4119i	−0.734397	+	1.27201i	−0.954988	+	0.296646i	$0.904132\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	5.36633			0.646031
$70$	−0.0109324	−	2.64573i	−0.00130667	−	0.316225i
$71$	−4.49873			−0.533900			−0.266950	−	0.963710i	$-0.586016\pi$
$71$	−4.49873			−0.533900			−0.266950	+	0.963710i	$0.586016\pi$
$72$	1.16659	+	2.02059i	0.137484	+	0.238129i
$73$	−3.86657	+	6.69710i	−0.452548	+	0.783836i	−0.998544	−	0.0539518i	$-0.982818\pi$
$73$	−3.86657	+	6.69710i	−0.452548	+	0.783836i	0.545995	+	0.837788i	$0.316152\pi$
$74$	1.62814	−	2.82003i	0.189268	−	0.327821i
$75$	−0.408297	−	0.707191i	−0.0471461	−	0.0816594i
$76$	−5.03316			−0.577343
$77$	0.0639517	+	15.4769i	0.00728797	+	1.76375i
$78$	−3.70607			−0.419629
$79$	3.83518	+	6.64272i	0.431491	+	0.747365i	0.997002	−	0.0773761i	$-0.0246542\pi$
$79$	3.83518	+	6.64272i	0.431491	+	0.747365i	−0.565511	+	0.824741i	$0.691321\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−1.72161	+	2.98192i	−0.191290	+	0.331324i
$82$	2.53844	+	4.39671i	0.280324	+	0.485536i
$83$	−13.7943			−1.51412			−0.757058	−	0.653348i	$-0.773364\pi$
$83$	−13.7943			−1.51412			−0.757058	+	0.653348i	$0.773364\pi$
$84$	−1.87550	−	1.07251i	−0.204634	−	0.117021i
$85$	−1.00000			−0.108465
$86$	2.10240	+	3.64146i	0.226707	+	0.392668i
$87$	2.43605	−	4.21936i	0.261172	−	0.452363i
$88$	−2.92488	+	5.06604i	−0.311793	+	0.540041i
$89$	3.92688	+	6.80156i	0.416249	+	0.720964i	0.995559	−	0.0941435i	$-0.0300113\pi$
$89$	3.92688	+	6.80156i	0.416249	+	0.720964i	−0.579310	+	0.815107i	$0.696678\pi$
$90$	2.33317			0.245938
$91$	−10.3740	+	6.04672i	−1.08749	+	0.633868i
$92$	6.57160			0.685137
$93$	2.48847	+	4.31015i	0.258042	+	0.446942i
$94$	1.97814	−	3.42623i	0.204029	−	0.353389i
$95$	−2.51658	+	4.35884i	−0.258196	+	0.447208i
$96$	−0.408297	−	0.707191i	−0.0416716	−	0.0721774i
$97$	3.51002			0.356389			0.178194	−	0.983995i	$-0.442974\pi$
$97$	3.51002			0.356389			0.178194	+	0.983995i	$0.442974\pi$
$98$	−6.99976	+	0.0578482i	−0.707083	+	0.00584355i
$99$	−13.6485			−1.37173
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.54974	+	9.61243i	−0.552220	+	0.956473i	0.445894	+	0.895086i	$0.352886\pi$
$101$	−5.54974	+	9.61243i	−0.552220	+	0.956473i	−0.998114	+	0.0613870i	$0.980448\pi$
$102$	−0.408297	+	0.707191i	−0.0404274	+	0.0700224i
$103$	−0.325521	−	0.563820i	−0.0320746	−	0.0555548i	0.849543	−	0.527520i	$-0.176878\pi$
$103$	−0.325521	−	0.563820i	−0.0320746	−	0.0555548i	−0.881617	+	0.471965i	$0.843545\pi$
$104$	−4.53844			−0.445031
$105$	−1.86657	+	1.08797i	−0.182159	+	0.106175i
$106$	−13.9048			−1.35055
$107$	7.12967	+	12.3489i	0.689251	+	1.19382i	0.972080	+	0.234648i	$0.0753937\pi$
$107$	7.12967	+	12.3489i	0.689251	+	1.19382i	−0.282829	+	0.959170i	$0.591273\pi$
$108$	2.17752	−	3.77157i	0.209532	−	0.362920i
$109$	2.19975	−	3.81007i	0.210698	−	0.364939i	−0.741236	−	0.671245i	$-0.765760\pi$
$109$	2.19975	−	3.81007i	0.210698	−	0.364939i	0.951933	+	0.306306i	$0.0990932\pi$
$110$	2.92488	+	5.06604i	0.278876	+	0.483028i
$111$	−2.65906			−0.252387
$112$	−2.29673	−	1.31340i	−0.217021	−	0.124104i
$113$	7.45379			0.701194			0.350597	−	0.936526i	$-0.385979\pi$
$113$	7.45379			0.701194			0.350597	+	0.936526i	$0.385979\pi$
$114$	2.05502	+	3.55941i	0.192471	+	0.333369i
$115$	3.28580	−	5.69118i	0.306403	−	0.530705i
$116$	2.98318	−	5.16702i	0.276981	−	0.479746i
$117$	−5.29449	−	9.17033i	−0.489476	−	0.847797i
$118$	10.6817			0.983326
$119$	0.0109324	+	2.64573i	0.00100217	+	0.242534i
$120$	−0.816594			−0.0745445
$121$	−11.6098	−	20.1088i	−1.05544	−	1.82807i
$122$	−0.0218647	+	0.0378709i	−0.00197954	+	0.00342867i
$123$	2.07288	−	3.59033i	0.186905	−	0.323729i
$124$	3.04737	+	5.27820i	0.273662	+	0.473997i
$125$	−1.00000			−0.0894427
$126$	−0.0255071	−	6.17295i	−0.00227236	−	0.549930i
$127$	20.4249			1.81242			0.906208	−	0.422832i	$-0.138964\pi$
$127$	20.4249			1.81242			0.906208	+	0.422832i	$0.138964\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.71680	−	2.97359i	0.151156	−	0.261810i
$130$	−2.26922	+	3.93041i	−0.199024	+	0.344720i
$131$	−2.86397	−	4.96053i	−0.250226	−	0.433404i	0.713362	−	0.700796i	$-0.247172\pi$
$131$	−2.86397	−	4.96053i	−0.250226	−	0.433404i	−0.963588	+	0.267392i	$0.913838\pi$
$132$	4.77687			0.415774
$133$	11.5598	+	6.61053i	1.00236	+	0.573206i
$134$	12.0226			1.03859
$135$	−2.17752	−	3.77157i	−0.187411	−	0.324605i
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	3.55502	−	6.15748i	0.303726	−	0.526069i	−0.673251	−	0.739414i	$-0.735103\pi$
$137$	3.55502	−	6.15748i	0.303726	−	0.526069i	0.976977	+	0.213345i	$0.0684358\pi$
$138$	−2.68317	−	4.64738i	−0.228406	−	0.395611i
$139$	3.89348			0.330241			0.165120	−	0.986273i	$-0.447199\pi$
$139$	3.89348			0.330241			0.165120	+	0.986273i	$0.447199\pi$
$140$	−2.28580	+	1.33233i	−0.193186	+	0.112603i
$141$	−3.23067			−0.272071
$142$	2.24936	+	3.89601i	0.188762	+	0.326946i
$143$	13.2744	−	22.9919i	1.11006	−	1.92268i
$144$	1.16659	−	2.02059i	0.0972156	−	0.168382i
$145$	−2.98318	−	5.16702i	−0.247740	−	0.429098i
$146$	7.73315			0.640000
$147$	2.89889	+	4.92655i	0.239097	+	0.406335i
$148$	−3.25628			−0.267665
$149$	3.43076	+	5.94226i	0.281059	+	0.486809i	0.971646	−	0.236441i	$-0.0759810\pi$
$149$	3.43076	+	5.94226i	0.281059	+	0.486809i	−0.690587	+	0.723250i	$0.742648\pi$
$150$	−0.408297	+	0.707191i	−0.0333373	+	0.0577419i
$151$	−2.03560	+	3.52576i	−0.165655	+	0.286922i	−0.936888	−	0.349631i	$-0.886307\pi$
$151$	−2.03560	+	3.52576i	−0.165655	+	0.286922i	0.771233	+	0.636553i	$0.219640\pi$
$152$	2.51658	+	4.35884i	0.204122	+	0.353549i
$153$	−2.33317			−0.188626
$154$	13.3714	−	7.79381i	1.07750	−	0.628043i
$155$	6.09474			0.489542
$156$	1.85303	+	3.20955i	0.148361	+	0.256970i
$157$	4.10264	−	7.10597i	0.327426	−	0.567118i	−0.654574	−	0.755998i	$-0.727152\pi$
$157$	4.10264	−	7.10597i	0.327426	−	0.567118i	0.982000	+	0.188879i	$0.0604855\pi$
$158$	3.83518	−	6.64272i	0.305110	−	0.528467i
$159$	5.67728	+	9.83334i	0.450238	+	0.779834i
$160$	−1.00000			−0.0790569
$161$	−15.0932	−	8.63112i	−1.18951	−	0.680228i
$162$	3.44322			0.270525
$163$	8.97401	+	15.5434i	0.702899	+	1.21746i	0.967444	+	0.253084i	$0.0814448\pi$
$163$	8.97401	+	15.5434i	0.702899	+	1.21746i	−0.264545	+	0.964373i	$0.585222\pi$
$164$	2.53844	−	4.39671i	0.198219	−	0.343326i
$165$	2.38844	−	4.13689i	0.185940	−	0.322057i
$166$	6.89713	+	11.9462i	0.535321	+	0.927203i
$167$	−22.4978			−1.74093			−0.870465	−	0.492231i	$-0.836182\pi$
$167$	−22.4978			−1.74093			−0.870465	+	0.492231i	$0.836182\pi$
$168$	0.00892731	+	2.16049i	0.000688757	+	0.166685i
$169$	7.59748			0.584421
$170$	0.500000	+	0.866025i	0.0383482	+	0.0664211i
$171$	−5.87162	+	10.1699i	−0.449014	+	0.777715i
$172$	2.10240	−	3.64146i	0.160306	−	0.277659i
$173$	1.60628	+	2.78215i	0.122123	+	0.211523i	0.920605	−	0.390496i	$-0.127696\pi$
$173$	1.60628	+	2.78215i	0.122123	+	0.211523i	−0.798482	+	0.602019i	$0.794363\pi$
$174$	−4.87210			−0.369353
$175$	0.0109324	+	2.64573i	0.000826410	+	0.199998i
$176$	5.84975			0.440942
$177$	−4.36129	−	7.55397i	−0.327814	−	0.567791i
$178$	3.92688	−	6.80156i	0.294332	−	0.509798i
$179$	−4.41772	+	7.65171i	−0.330196	+	0.571915i	−0.982550	−	0.185999i	$-0.940448\pi$
$179$	−4.41772	+	7.65171i	−0.330196	+	0.571915i	0.652354	+	0.757914i	$0.273781\pi$
$180$	−1.16659	−	2.02059i	−0.0869523	−	0.150606i
$181$	−8.18949			−0.608720			−0.304360	−	0.952557i	$-0.598443\pi$
$181$	−8.18949			−0.608720			−0.304360	+	0.952557i	$0.598443\pi$
$182$	10.4236	+	5.96078i	0.772649	+	0.441842i
$183$	0.0357093			0.00263970
$184$	−3.28580	−	5.69118i	−0.242233	−	0.419559i
$185$	−1.62814	+	2.82003i	−0.119703	+	0.207332i
$186$	2.48847	−	4.31015i	0.182463	−	0.316036i
$187$	−2.92488	−	5.06604i	−0.213888	−	0.370465i
$188$	−3.95627			−0.288541
$189$	−9.95476	+	5.80236i	−0.724102	+	0.422059i
$190$	5.03316			0.365144
$191$	11.9995	+	20.7838i	0.868255	+	1.50386i	0.863779	+	0.503872i	$0.168092\pi$
$191$	11.9995	+	20.7838i	0.868255	+	1.50386i	0.00447642	+	0.999990i	$0.498575\pi$
$192$	−0.408297	+	0.707191i	−0.0294663	+	0.0510371i
$193$	7.69847	−	13.3341i	0.554148	−	0.959813i	−0.443821	−	0.896115i	$-0.646377\pi$
$193$	7.69847	−	13.3341i	0.554148	−	0.959813i	0.997969	−	0.0636973i	$-0.0202892\pi$
$194$	−1.75501	−	3.03977i	−0.126002	−	0.218243i
$195$	3.70607			0.265397
$196$	3.54998	+	6.03305i	0.253570	+	0.430932i
$197$	24.6654			1.75734			0.878668	−	0.477433i	$-0.158433\pi$
$197$	24.6654			1.75734			0.878668	+	0.477433i	$0.158433\pi$
$198$	6.82425	+	11.8199i	0.484978	+	0.840007i
$199$	12.4465	−	21.5580i	0.882309	−	1.52820i	0.0335422	−	0.999437i	$-0.489321\pi$
$199$	12.4465	−	21.5580i	0.882309	−	1.52820i	0.848767	−	0.528767i	$-0.177345\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−4.90879	−	8.50227i	−0.346239	−	0.599704i
$202$	11.0995			0.780957
$203$	−13.6379	+	7.94918i	−0.957195	+	0.557923i
$204$	0.816594			0.0571730
$205$	−2.53844	−	4.39671i	−0.177293	−	0.307080i
$206$	−0.325521	+	0.563820i	−0.0226802	+	0.0392832i
$207$	7.66635	−	13.2785i	0.532848	−	0.922920i
$208$	2.26922	+	3.93041i	0.157342	+	0.272525i
$209$	−29.4427			−2.03660
$210$	1.87550	+	1.07251i	0.129422	+	0.0740104i
$211$	22.8711			1.57451			0.787257	−	0.616625i	$-0.211500\pi$
$211$	22.8711			1.57451			0.787257	+	0.616625i	$0.211500\pi$
$212$	6.95239	+	12.0419i	0.477492	+	0.827040i
$213$	1.83682	−	3.18146i	0.125857	−	0.217990i
$214$	7.12967	−	12.3489i	0.487374	−	0.844157i
$215$	−2.10240	−	3.64146i	−0.143382	−	0.248345i
$216$	−4.35504			−0.296323
$217$	−0.0666300	−	16.1250i	−0.00452314	−	1.09464i
$218$	−4.39949			−0.297971
$219$	−3.15742	−	5.46881i	−0.213359	−	0.369548i
$220$	2.92488	−	5.06604i	0.197195	−	0.341552i
$221$	2.26922	−	3.93041i	0.152644	−	0.264388i
$222$	1.32953	+	2.30282i	0.0892323	+	0.154555i
$223$	−26.0275			−1.74293			−0.871464	−	0.490459i	$-0.836829\pi$
$223$	−26.0275			−1.74293			−0.871464	+	0.490459i	$0.836829\pi$
$224$	0.0109324	+	2.64573i	0.000730450	+	0.176775i
$225$	−2.33317			−0.155545
$226$	−3.72690	−	6.45517i	−0.247909	−	0.429392i
$227$	1.55563	−	2.69442i	0.103251	−	0.178835i	−0.809772	−	0.586745i	$-0.800409\pi$
$227$	1.55563	−	2.69442i	0.103251	−	0.178835i	0.913022	+	0.407910i	$0.133742\pi$
$228$	2.05502	−	3.55941i	0.136097	−	0.235727i
$229$	−3.31131	−	5.73536i	−0.218817	−	0.379003i	0.735629	−	0.677384i	$-0.236887\pi$
$229$	−3.31131	−	5.73536i	−0.218817	−	0.379003i	−0.954447	+	0.298381i	$0.903553\pi$
$230$	−6.57160			−0.433319
$231$	−10.9712	−	6.27393i	−0.721853	−	0.412794i
$232$	−5.96636			−0.391711
$233$	13.8442	+	23.9789i	0.906966	+	1.57091i	0.818257	+	0.574853i	$0.194941\pi$
$233$	13.8442	+	23.9789i	0.906966	+	1.57091i	0.0887090	+	0.996058i	$0.471726\pi$
$234$	−5.29449	+	9.17033i	−0.346112	+	0.599483i
$235$	−1.97814	+	3.42623i	−0.129039	+	0.223503i
$236$	−5.34083	−	9.25058i	−0.347658	−	0.602162i
$237$	−6.26357			−0.406863
$238$	2.28580	−	1.33233i	0.148167	−	0.0863623i
$239$	−13.7717			−0.890815			−0.445407	−	0.895328i	$-0.646941\pi$
$239$	−13.7717			−0.890815			−0.445407	+	0.895328i	$0.646941\pi$
$240$	0.408297	+	0.707191i	0.0263555	+	0.0456490i
$241$	−2.18444	+	3.78356i	−0.140712	+	0.243721i	−0.927765	−	0.373165i	$-0.878273\pi$
$241$	−2.18444	+	3.78356i	−0.140712	+	0.243721i	0.787053	+	0.616886i	$0.211606\pi$
$242$	−11.6098	+	20.1088i	−0.746307	+	1.29264i
$243$	−7.93842	−	13.7497i	−0.509250	−	0.882046i
$244$	0.0437295			0.00279949
$245$	6.99976	−	0.0578482i	0.447198	−	0.00369579i
$246$	−4.14576			−0.264324
$247$	−11.4214	−	19.7824i	−0.726724	−	1.25872i
$248$	3.04737	−	5.27820i	0.193508	−	0.335166i
$249$	5.63215	−	9.75517i	0.356923	−	0.618209i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−28.5196			−1.80014			−0.900072	−	0.435742i	$-0.856486\pi$
$251$	−28.5196			−1.80014			−0.900072	+	0.435742i	$0.856486\pi$
$252$	−5.33317	+	3.10856i	−0.335958	+	0.195821i
$253$	38.4423			2.41684
$254$	−10.2124	−	17.6885i	−0.640786	−	1.10987i
$255$	0.408297	−	0.707191i	0.0255686	−	0.0442860i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.371619	−	0.643662i	−0.0231809	−	0.0401505i	0.854202	−	0.519941i	$-0.174046\pi$
$257$	−0.371619	−	0.643662i	−0.0231809	−	0.0401505i	−0.877383	+	0.479790i	$0.840713\pi$
$258$	−3.43361			−0.213767
$259$	7.47882	+	4.27679i	0.464711	+	0.265747i
$260$	4.53844			0.281462
$261$	−6.96028	−	12.0556i	−0.430831	−	0.746220i
$262$	−2.86397	+	4.96053i	−0.176936	+	0.306463i
$263$	−2.18293	+	3.78094i	−0.134605	+	0.233143i	−0.925447	−	0.378878i	$-0.876310\pi$
$263$	−2.18293	+	3.78094i	−0.134605	+	0.233143i	0.790841	+	0.612021i	$0.209643\pi$
$264$	−2.38844	−	4.13689i	−0.146998	−	0.254608i
$265$	13.9048			0.854164
$266$	−0.0550244	−	13.3164i	−0.00337376	−	0.816479i
$267$	−6.41334			−0.392490
$268$	−6.01129	−	10.4119i	−0.367198	−	0.636006i
$269$	7.57160	−	13.1144i	0.461649	−	0.799599i	−0.537394	−	0.843331i	$-0.680591\pi$
$269$	7.57160	−	13.1144i	0.461649	−	0.799599i	0.999043	+	0.0437317i	$0.0139247\pi$
$270$	−2.17752	+	3.77157i	−0.132520	+	0.229531i
$271$	1.30001	+	2.25169i	0.0789702	+	0.136780i	0.902806	−	0.430048i	$-0.141503\pi$
$271$	1.30001	+	2.25169i	0.0789702	+	0.136780i	−0.823836	+	0.566829i	$0.808170\pi$
$272$	1.00000			0.0606339
$273$	−0.0405161	−	9.80525i	−0.00245215	−	0.593441i
$274$	−7.11005			−0.429534
$275$	−2.92488	−	5.06604i	−0.176377	−	0.305493i
$276$	−2.68317	+	4.64738i	−0.161508	+	0.279739i
$277$	7.93945	−	13.7515i	0.477035	−	0.826250i	−0.522618	−	0.852567i	$-0.675045\pi$
$277$	7.93945	−	13.7515i	0.477035	−	0.826250i	0.999654	+	0.0263172i	$0.00837801\pi$
$278$	−1.94674	−	3.37186i	−0.116758	−	0.202230i
$279$	14.2201			0.851335
$280$	2.29673	+	1.31340i	0.137256	+	0.0784905i
$281$	16.2226			0.967762			0.483881	−	0.875134i	$-0.339227\pi$
$281$	16.2226			0.967762			0.483881	+	0.875134i	$0.339227\pi$
$282$	1.61533	+	2.79784i	0.0961917	+	0.166609i
$283$	1.08521	−	1.87965i	0.0645093	−	0.111733i	−0.831967	−	0.554825i	$-0.812785\pi$
$283$	1.08521	−	1.87965i	0.0645093	−	0.111733i	0.896476	+	0.443092i	$0.146118\pi$
$284$	2.24936	−	3.89601i	0.133475	−	0.231186i
$285$	−2.05502	−	3.55941i	−0.121729	−	0.210841i
$286$	−26.5488			−1.56986
$287$	−11.6048	+	6.76410i	−0.685008	+	0.399272i
$288$	−2.33317			−0.137484
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−2.98318	+	5.16702i	−0.175178	+	0.303418i
$291$	−1.43313	+	2.48226i	−0.0840116	+	0.145512i
$292$	−3.86657	−	6.69710i	−0.226274	−	0.391918i
$293$	15.0043			0.876558			0.438279	−	0.898839i	$-0.355588\pi$
$293$	15.0043			0.876558			0.438279	+	0.898839i	$0.355588\pi$
$294$	2.81707	−	4.97379i	0.164295	−	0.290077i
$295$	−10.6817			−0.621910
$296$	1.62814	+	2.82003i	0.0946339	+	0.163911i
$297$	12.7380	−	22.0628i	0.739131	−	1.28021i
$298$	3.43076	−	5.94226i	0.198739	−	0.344226i
$299$	14.9124	+	25.8291i	0.862408	+	1.49373i
$300$	0.816594			0.0471461
$301$	−9.61132	+	5.60218i	−0.553987	+	0.322904i
$302$	4.07120			0.234271
$303$	−4.53188	−	7.84945i	−0.260350	−	0.450939i
$304$	2.51658	−	4.35884i	0.144336	−	0.249997i
$305$	0.0218647	−	0.0378709i	0.00125197	−	0.00216848i
$306$	1.16659	+	2.02059i	0.0666893	+	0.115509i
$307$	27.9407			1.59466			0.797331	−	0.603542i	$-0.206244\pi$
$307$	27.9407			1.59466			0.797331	+	0.603542i	$0.206244\pi$
$308$	−13.4353	−	7.68305i	−0.765549	−	0.437782i
$309$	0.531638			0.0302438
$310$	−3.04737	−	5.27820i	−0.173079	−	0.299782i
$311$	−11.1760	+	19.3574i	−0.633733	+	1.09766i	0.353049	+	0.935605i	$0.385145\pi$
$311$	−11.1760	+	19.3574i	−0.633733	+	1.09766i	−0.986782	+	0.162053i	$0.948188\pi$
$312$	1.85303	−	3.20955i	0.104907	−	0.181705i
$313$	6.47566	+	11.2162i	0.366026	+	0.633975i	0.988940	−	0.148315i	$-0.0473849\pi$
$313$	6.47566	+	11.2162i	0.366026	+	0.633975i	−0.622914	+	0.782290i	$0.714052\pi$
$314$	−8.20527			−0.463050
$315$	0.0255071	+	6.17295i	0.00143716	+	0.347806i
$316$	−7.67036			−0.431491
$317$	−9.11108	−	15.7809i	−0.511729	−	0.886341i	−0.999908	−	0.0135974i	$-0.995672\pi$
$317$	−9.11108	−	15.7809i	−0.511729	−	0.886341i	0.488178	−	0.872744i	$-0.337662\pi$
$318$	5.67728	−	9.83334i	0.318366	−	0.551426i
$319$	17.4509	−	30.2258i	0.977061	−	1.69232i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−11.6441			−0.649910
$322$	0.0718432	+	17.3867i	0.00400367	+	0.968922i
$323$	−5.03316			−0.280052
$324$	−1.72161	−	2.98192i	−0.0956451	−	0.165662i
$325$	2.26922	−	3.93041i	0.125874	−	0.218020i
$326$	8.97401	−	15.5434i	0.497025	−	0.860872i
$327$	1.79630	+	3.11128i	0.0993356	+	0.172054i
$328$	−5.07689			−0.280324
$329$	9.08650	+	5.19615i	0.500955	+	0.286473i
$330$	−4.77687			−0.262958
$331$	5.91535	+	10.2457i	0.325137	+	0.563154i	0.981540	−	0.191257i	$-0.0612563\pi$
$331$	5.91535	+	10.2457i	0.325137	+	0.563154i	−0.656403	+	0.754410i	$0.727923\pi$
$332$	6.89713	−	11.9462i	0.378529	−	0.655631i
$333$	−3.79874	+	6.57961i	−0.208170	+	0.360560i
$334$	11.2489	+	19.4836i	0.615512	+	1.06610i
$335$	−12.0226			−0.656864
$336$	1.86657	−	1.08797i	0.101830	−	0.0593539i
$337$	−1.49993			−0.0817063			−0.0408532	−	0.999165i	$-0.513008\pi$
$337$	−1.49993			−0.0817063			−0.0408532	+	0.999165i	$0.513008\pi$
$338$	−3.79874	−	6.57961i	−0.206624	−	0.357884i
$339$	−3.04336	+	5.27126i	−0.165293	+	0.286295i
$340$	0.500000	−	0.866025i	0.0271163	−	0.0469668i
$341$	17.8264	+	30.8762i	0.965352	+	1.67204i
$342$	11.7432			0.635002
$343$	−0.229575	−	18.5188i	−0.0123959	−	0.999923i
$344$	−4.20479			−0.226707
$345$	2.68317	+	4.64738i	0.144457	+	0.250207i
$346$	1.60628	−	2.78215i	0.0863540	−	0.149570i
$347$	−3.99187	+	6.91412i	−0.214295	+	0.371169i	−0.953054	−	0.302800i	$-0.902079\pi$
$347$	−3.99187	+	6.91412i	−0.214295	+	0.371169i	0.738759	+	0.673969i	$0.235412\pi$
$348$	2.43605	+	4.21936i	0.130586	+	0.226181i
$349$	−0.190444			−0.0101942			−0.00509711	−	0.999987i	$-0.501622\pi$
$349$	−0.190444			−0.0101942			−0.00509711	+	0.999987i	$0.501622\pi$
$350$	2.28580	−	1.33233i	0.122181	−	0.0712161i
$351$	19.7651			1.05498
$352$	−2.92488	−	5.06604i	−0.155896	−	0.270021i
$353$	−4.06656	+	7.04349i	−0.216441	+	0.374887i	−0.953717	−	0.300704i	$-0.902778\pi$
$353$	−4.06656	+	7.04349i	−0.216441	+	0.374887i	0.737276	+	0.675591i	$0.236112\pi$
$354$	−4.36129	+	7.55397i	−0.231800	+	0.401489i
$355$	−2.24936	−	3.89601i	−0.119384	−	0.206779i
$356$	−7.85376			−0.416249
$357$	−1.87550	−	1.07251i	−0.0992620	−	0.0567634i
$358$	8.83543			0.466967
$359$	16.3379	+	28.2981i	0.862282	+	1.49352i	0.869721	+	0.493544i	$0.164299\pi$
$359$	16.3379	+	28.2981i	0.862282	+	1.49352i	−0.00743915	+	0.999972i	$0.502368\pi$
$360$	−1.16659	+	2.02059i	−0.0614845	+	0.106494i
$361$	−3.16635	+	5.48428i	−0.166650	+	0.288646i
$362$	4.09474	+	7.09230i	0.215215	+	0.372763i
$363$	18.9610			0.995195
$364$	−0.0496160	−	12.0075i	−0.00260058	−	0.629364i
$365$	−7.73315			−0.404771
$366$	−0.0178546	−	0.0309251i	−0.000933276	−	0.00161648i
$367$	−1.94414	+	3.36734i	−0.101483	+	0.175774i	−0.912296	−	0.409532i	$-0.865692\pi$
$367$	−1.94414	+	3.36734i	−0.101483	+	0.175774i	0.810813	+	0.585306i	$0.199025\pi$
$368$	−3.28580	+	5.69118i	−0.171284	+	0.296673i
$369$	−5.92263	−	10.2583i	−0.308320	−	0.534026i
$370$	3.25628			0.169286
$371$	−0.152012	−	36.7883i	−0.00789208	−	1.90995i
$372$	−4.97693			−0.258042
$373$	−12.9635	−	22.4535i	−0.671225	−	1.16260i	−0.977557	−	0.210672i	$-0.932435\pi$
$373$	−12.9635	−	22.4535i	−0.671225	−	1.16260i	0.306331	−	0.951925i	$-0.400898\pi$
$374$	−2.92488	+	5.06604i	−0.151242	+	0.261958i
$375$	0.408297	−	0.707191i	0.0210844	−	0.0365192i
$376$	1.97814	+	3.42623i	0.102015	+	0.176694i
$377$	27.0780			1.39459
$378$	10.0024	+	5.71989i	0.514466	+	0.294200i
$379$	−28.1128			−1.44406			−0.722030	−	0.691862i	$-0.756791\pi$
$379$	−28.1128			−1.44406			−0.722030	+	0.691862i	$0.756791\pi$
$380$	−2.51658	−	4.35884i	−0.129098	−	0.223604i
$381$	−8.33942	+	14.4443i	−0.427242	+	0.740004i
$382$	11.9995	−	20.7838i	0.613949	−	1.06339i
$383$	−5.26795	−	9.12435i	−0.269180	−	0.466233i	0.699471	−	0.714661i	$-0.253419\pi$
$383$	−5.26795	−	9.12435i	−0.269180	−	0.466233i	−0.968650	+	0.248429i	$0.920086\pi$
$384$	0.816594			0.0416716
$385$	−13.3714	+	7.79381i	−0.681469	+	0.397210i
$386$	−15.3969			−0.783684
$387$	−4.90526	−	8.49615i	−0.249348	−	0.431884i
$388$	−1.75501	+	3.03977i	−0.0890971	+	0.154321i
$389$	10.5026	−	18.1910i	0.532503	−	0.922323i	−0.466776	−	0.884375i	$-0.654585\pi$
$389$	10.5026	−	18.1910i	0.532503	−	0.922323i	0.999280	−	0.0379474i	$-0.0120819\pi$
$390$	−1.85303	−	3.20955i	−0.0938320	−	0.162522i
$391$	6.57160			0.332340
$392$	3.44978	−	6.09089i	0.174240	−	0.307637i
$393$	4.67740			0.235943
$394$	−12.3327	−	21.3609i	−0.621312	−	1.07614i
$395$	−3.83518	+	6.64272i	−0.192969	+	0.334232i
$396$	6.82425	−	11.8199i	0.342931	−	0.593974i
$397$	−5.53188	−	9.58151i	−0.277637	−	0.480882i	0.693160	−	0.720784i	$-0.256218\pi$
$397$	−5.53188	−	9.58151i	−0.277637	−	0.480882i	−0.970797	+	0.239902i	$0.922885\pi$
$398$	−24.8930			−1.24777
$399$	−9.39476	+	5.47595i	−0.470326	+	0.274140i
$400$	1.00000			0.0500000
$401$	−1.54957	−	2.68394i	−0.0773819	−	0.134029i	0.824738	−	0.565515i	$-0.191323\pi$
$401$	−1.54957	−	2.68394i	−0.0773819	−	0.134029i	−0.902120	+	0.431486i	$0.857989\pi$
$402$	−4.90879	+	8.50227i	−0.244828	+	0.424055i
$403$	−13.8303	+	23.9548i	−0.688938	+	1.19328i
$404$	−5.54974	−	9.61243i	−0.276110	−	0.478236i
$405$	−3.44322			−0.171095
$406$	13.7031	+	7.83620i	0.680076	+	0.388904i
$407$	−19.0485			−0.944197
$408$	−0.408297	−	0.707191i	−0.0202137	−	0.0350112i
$409$	−8.78824	+	15.2217i	−0.434551	+	0.752664i	−0.997259	−	0.0739919i	$-0.976426\pi$
$409$	−8.78824	+	15.2217i	−0.434551	+	0.752664i	0.562708	+	0.826656i	$0.309759\pi$
$410$	−2.53844	+	4.39671i	−0.125365	+	0.217138i
$411$	2.90301	+	5.02816i	0.143195	+	0.248021i
$412$	0.651043			0.0320746
$413$	0.116776	+	28.2608i	0.00574616	+	1.39062i
$414$	−15.3327			−0.753561
$415$	−6.89713	−	11.9462i	−0.338567	−	0.586415i
$416$	2.26922	−	3.93041i	0.111258	−	0.192704i
$417$	−1.58970	+	2.75344i	−0.0778478	+	0.134836i
$418$	14.7214	+	25.4982i	0.720046	+	1.24716i
$419$	26.3257			1.28609			0.643046	−	0.765827i	$-0.277670\pi$
$419$	26.3257			1.28609			0.643046	+	0.765827i	$0.277670\pi$
$420$	−0.00892731	−	2.16049i	−0.000435608	−	0.105421i
$421$	14.5206			0.707690			0.353845	−	0.935304i	$-0.384874\pi$
$421$	14.5206			0.707690			0.353845	+	0.935304i	$0.384874\pi$
$422$	−11.4356	−	19.8070i	−0.556675	−	0.964189i
$423$	−4.61533	+	7.99399i	−0.224405	+	0.388681i
$424$	6.95239	−	12.0419i	0.337638	−	0.584806i
$425$	−0.500000	−	0.866025i	−0.0242536	−	0.0420084i
$426$	−3.67363			−0.177988
$427$	−0.100435	−	0.0574342i	−0.00486039	−	0.00277943i
$428$	−14.2593			−0.689251
$429$	10.8398	+	18.7751i	0.523350	+	0.906469i
$430$	−2.10240	+	3.64146i	−0.101387	+	0.175607i
$431$	−2.25945	+	3.91349i	−0.108834	+	0.188506i	−0.915298	−	0.402777i	$-0.868045\pi$
$431$	−2.25945	+	3.91349i	−0.108834	+	0.188506i	0.806464	+	0.591283i	$0.201378\pi$
$432$	2.17752	+	3.77157i	0.104766	+	0.181460i
$433$	21.5608			1.03615			0.518073	−	0.855336i	$-0.326649\pi$
$433$	21.5608			1.03615			0.518073	+	0.855336i	$0.326649\pi$
$434$	−13.9314	+	8.12022i	−0.668728	+	0.389783i
$435$	4.87210			0.233599
$436$	2.19975	+	3.81007i	0.105349	+	0.182469i
$437$	16.5380	−	28.6446i	0.791118	−	1.37026i
$438$	−3.15742	+	5.46881i	−0.150867	+	0.261310i
$439$	8.36196	+	14.4833i	0.399095	+	0.691252i	0.993614	−	0.112829i	$-0.0359912\pi$
$439$	8.36196	+	14.4833i	0.399095	+	0.691252i	−0.594520	+	0.804081i	$0.702658\pi$
$440$	−5.84975			−0.278876
$441$	16.3317	−	0.134970i	0.777698	−	0.00642714i
$442$	−4.53844			−0.215872
$443$	−12.4871	−	21.6282i	−0.593278	−	1.02759i	−0.993787	−	0.111295i	$-0.964500\pi$
$443$	−12.4871	−	21.6282i	−0.593278	−	1.02759i	0.400509	−	0.916293i	$-0.368833\pi$
$444$	1.32953	−	2.30282i	0.0630968	−	0.109287i
$445$	−3.92688	+	6.80156i	−0.186152	+	0.322425i
$446$	13.0137	+	22.5404i	0.616218	+	1.06732i
$447$	−5.60308			−0.265017
$448$	2.28580	−	1.33233i	0.107994	−	0.0629468i
$449$	30.0889			1.41998			0.709992	−	0.704210i	$-0.248699\pi$
$449$	30.0889			1.41998			0.709992	+	0.704210i	$0.248699\pi$
$450$	1.16659	+	2.02059i	0.0549934	+	0.0952514i
$451$	14.8493	−	25.7197i	0.699225	−	1.21109i
$452$	−3.72690	+	6.45517i	−0.175298	+	0.303626i
$453$	−1.66226	−	2.87912i	−0.0780997	−	0.135273i
$454$	−3.11125			−0.146018
$455$	−10.4236	−	5.96078i	−0.488666	−	0.279446i
$456$	−4.11005			−0.192471
$457$	−3.07288	−	5.32238i	−0.143743	−	0.248971i	0.785160	−	0.619293i	$-0.212581\pi$
$457$	−3.07288	−	5.32238i	−0.143743	−	0.248971i	−0.928903	+	0.370322i	$0.879247\pi$
$458$	−3.31131	+	5.73536i	−0.154727	+	0.267996i
$459$	2.17752	−	3.77157i	0.101638	−	0.176042i
$460$	3.28580	+	5.69118i	0.153201	+	0.265352i
$461$	−23.4047			−1.09007			−0.545033	−	0.838415i	$-0.683483\pi$
$461$	−23.4047			−1.09007			−0.545033	+	0.838415i	$0.683483\pi$
$462$	0.0522226	+	12.6383i	0.00242961	+	0.587988i
$463$	3.32782			0.154657			0.0773284	−	0.997006i	$-0.475361\pi$
$463$	3.32782			0.154657			0.0773284	+	0.997006i	$0.475361\pi$
$464$	2.98318	+	5.16702i	0.138491	+	0.239873i
$465$	−2.48847	+	4.31015i	−0.115400	+	0.199878i
$466$	13.8442	−	23.9789i	0.641322	−	1.11080i
$467$	10.1035	+	17.4998i	0.467534	+	0.809792i	0.999312	−	0.0370915i	$-0.0118093\pi$
$467$	10.1035	+	17.4998i	0.467534	+	0.809792i	−0.531778	+	0.846884i	$0.678476\pi$
$468$	10.5890			0.489476
$469$	0.131435	+	31.8085i	0.00606912	+	1.46878i
$470$	3.95627			0.182489
$471$	3.35019	+	5.80270i	0.154369	+	0.267374i
$472$	−5.34083	+	9.25058i	−0.245831	+	0.425793i
$473$	12.2985	−	21.3016i	0.565486	−	0.979450i
$474$	3.13178	+	5.42441i	0.143848	+	0.249151i
$475$	−5.03316			−0.230937
$476$	−2.29673	−	1.31340i	−0.105271	−	0.0601994i
$477$	32.4423			1.48543
$478$	6.88583	+	11.9266i	0.314951	+	0.545510i
$479$	3.43677	−	5.95267i	0.157030	−	0.271984i	−0.776766	−	0.629789i	$-0.783141\pi$
$479$	3.43677	−	5.95267i	0.157030	−	0.271984i	0.933796	+	0.357805i	$0.116475\pi$
$480$	0.408297	−	0.707191i	0.0186361	−	0.0322787i
$481$	−7.38923	−	12.7985i	−0.336920	−	0.583563i
$482$	4.36888			0.198997
$483$	12.2664	−	7.14974i	0.558139	−	0.325324i
$484$	23.2196			1.05544
$485$	1.75501	+	3.03977i	0.0796909	+	0.138029i
$486$	−7.93842	+	13.7497i	−0.360094	+	0.623701i
$487$	−5.68785	+	9.85165i	−0.257741	+	0.446421i	−0.965636	−	0.259897i	$-0.916311\pi$
$487$	−5.68785	+	9.85165i	−0.257741	+	0.446421i	0.707895	+	0.706317i	$0.249645\pi$
$488$	−0.0218647	−	0.0378709i	−0.000989771	−	0.00171433i
$489$	−14.6563			−0.662779
$490$	−3.54998	−	6.03305i	−0.160372	−	0.272545i
$491$	−13.2890			−0.599723			−0.299861	−	0.953983i	$-0.596940\pi$
$491$	−13.2890			−0.599723			−0.299861	+	0.953983i	$0.596940\pi$
$492$	2.07288	+	3.59033i	0.0934526	+	0.161865i
$493$	2.98318	−	5.16702i	0.134356	−	0.232711i
$494$	−11.4214	+	19.7824i	−0.513871	+	0.890051i
$495$	−6.82425	−	11.8199i	−0.306727	−	0.531267i
$496$	−6.09474			−0.273662
$497$	−10.2832	+	5.99380i	−0.461264	+	0.268858i
$498$	−11.2643			−0.504766
$499$	10.2556	+	17.7632i	0.459104	+	0.795192i	0.998914	−	0.0465953i	$-0.0148371\pi$
$499$	10.2556	+	17.7632i	0.459104	+	0.795192i	−0.539810	+	0.841787i	$0.681504\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	9.18577	−	15.9102i	0.410390	−	0.710816i
$502$	14.2598	+	24.6987i	0.636447	+	1.10236i
$503$	−30.2906			−1.35059			−0.675295	−	0.737548i	$-0.735984\pi$
$503$	−30.2906			−1.35059			−0.675295	+	0.737548i	$0.735984\pi$
$504$	5.35868	+	3.06438i	0.238695	+	0.136498i
$505$	−11.0995			−0.493920
$506$	−19.2211	−	33.2920i	−0.854484	−	1.48001i
$507$	−3.10203	+	5.37287i	−0.137766	+	0.238618i
$508$	−10.2124	+	17.6885i	−0.453104	+	0.784799i
$509$	−9.57160	−	16.5785i	−0.424254	−	0.734829i	0.572097	−	0.820186i	$-0.306130\pi$
$509$	−9.57160	−	16.5785i	−0.424254	−	0.734829i	−0.996350	+	0.0853570i	$0.972797\pi$
$510$	−0.816594			−0.0361594
$511$	0.0845416	+	20.4598i	0.00373990	+	0.905088i
$512$	1.00000			0.0441942
$513$	−10.9598	−	18.9829i	−0.483887	−	0.838117i
$514$	−0.371619	+	0.643662i	−0.0163914	+	0.0283907i
$515$	0.325521	−	0.563820i	0.0143442	−	0.0248449i
$516$	1.71680	+	2.97359i	0.0755781	+	0.130905i
$517$	−23.1432			−1.01784
$518$	−0.0355989	−	8.61525i	−0.00156413	−	0.378532i
$519$	−2.62335			−0.115152
$520$	−2.26922	−	3.93041i	−0.0995120	−	0.172360i
$521$	12.7814	−	22.1381i	0.559965	−	0.969888i	−0.437533	−	0.899202i	$-0.644148\pi$
$521$	12.7814	−	22.1381i	0.559965	−	0.969888i	0.997499	−	0.0706860i	$-0.0225188\pi$
$522$	−6.96028	+	12.0556i	−0.304643	+	0.527658i
$523$	16.5172	+	28.6086i	0.722246	+	1.25097i	0.960097	+	0.279666i	$0.0902237\pi$
$523$	16.5172	+	28.6086i	0.722246	+	1.25097i	−0.237851	+	0.971302i	$0.576443\pi$
$524$	5.72793			0.250226
$525$	−1.87550	−	1.07251i	−0.0818535	−	0.0468083i
$526$	4.36586			0.190360
$527$	3.04737	+	5.27820i	0.132746	+	0.229922i
$528$	−2.38844	+	4.13689i	−0.103943	+	0.180035i
$529$	−10.0930	+	17.4816i	−0.438826	+	0.760068i
$530$	−6.95239	−	12.0419i	−0.301992	−	0.523066i
$531$	−24.9222			−1.08153
$532$	−11.5048	+	6.70584i	−0.498797	+	0.290735i
$533$	23.0412			0.998024
$534$	3.20667	+	5.55411i	0.138766	+	0.240350i
$535$	−7.12967	+	12.3489i	−0.308242	+	0.533892i
$536$	−6.01129	+	10.4119i	−0.259648	+	0.449724i
$537$	−3.60748	−	6.24834i	−0.155674	−	0.269636i
$538$	−15.1432			−0.652870
$539$	20.7665	+	35.2918i	0.894476	+	1.52013i
$540$	4.35504			0.187411
$541$	−5.82060	−	10.0816i	−0.250247	−	0.433441i	0.713346	−	0.700812i	$-0.247179\pi$
$541$	−5.82060	−	10.0816i	−0.250247	−	0.433441i	−0.963594	+	0.267370i	$0.913845\pi$
$542$	1.30001	−	2.25169i	0.0558404	−	0.0967184i
$543$	3.34374	−	5.79153i	0.143494	−	0.248539i
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	4.39949			0.188454
$546$	−8.47134	+	4.93771i	−0.362540	+	0.211315i
$547$	7.14696			0.305582			0.152791	−	0.988259i	$-0.451174\pi$
$547$	7.14696			0.305582			0.152791	+	0.988259i	$0.451174\pi$
$548$	3.55502	+	6.15748i	0.151863	+	0.263035i
$549$	0.0510143	−	0.0883593i	0.00217724	−	0.00377108i
$550$	−2.92488	+	5.06604i	−0.124717	+	0.216016i
$551$	−15.0148	−	26.0064i	−0.639653	−	1.10791i
$552$	5.36633			0.228406
$553$	17.6168	+	10.0742i	0.749142	+	0.428400i
$554$	−15.8789			−0.674630
$555$	−1.32953	−	2.30282i	−0.0564355	−	0.0977491i
$556$	−1.94674	+	3.37186i	−0.0825602	+	0.142999i
$557$	0.742551	−	1.28614i	0.0314629	−	0.0544953i	−0.849865	−	0.527000i	$-0.823317\pi$
$557$	0.742551	−	1.28614i	0.0314629	−	0.0544953i	0.881328	+	0.472505i	$0.156650\pi$
$558$	−7.11005	−	12.3150i	−0.300992	−	0.521334i
$559$	19.0832			0.807134
$560$	−0.0109324	−	2.64573i	−0.000461977	−	0.111802i
$561$	4.77687			0.201680
$562$	−8.11132	−	14.0492i	−0.342156	−	0.592631i
$563$	−20.1739	+	34.9423i	−0.850230	+	1.47264i	0.0307712	+	0.999526i	$0.490204\pi$
$563$	−20.1739	+	34.9423i	−0.850230	+	1.47264i	−0.881001	+	0.473115i	$0.843130\pi$
$564$	1.61533	−	2.79784i	0.0680178	−	0.117810i
$565$	3.72690	+	6.45517i	0.156792	+	0.271571i
$566$	−2.17043			−0.0912300
$567$	0.0376426	+	9.10983i	0.00158084	+	0.382577i
$568$	−4.49873			−0.188762
$569$	2.22706	+	3.85739i	0.0933634	+	0.161710i	0.908924	−	0.416961i	$-0.136905\pi$
$569$	2.22706	+	3.85739i	0.0933634	+	0.161710i	−0.815561	+	0.578671i	$0.803572\pi$
$570$	−2.05502	+	3.55941i	−0.0860755	+	0.149087i
$571$	9.10240	−	15.7658i	0.380923	−	0.659779i	−0.610271	−	0.792193i	$-0.708939\pi$
$571$	9.10240	−	15.7658i	0.380923	−	0.659779i	0.991195	+	0.132414i	$0.0422728\pi$
$572$	13.2744	+	22.9919i	0.555030	+	0.961341i
$573$	−19.5975			−0.818696
$574$	11.6603	+	6.66797i	0.486690	+	0.278316i
$575$	6.57160			0.274055
$576$	1.16659	+	2.02059i	0.0486078	+	0.0841912i
$577$	13.2000	−	22.8630i	0.549523	−	0.951801i	−0.448785	−	0.893640i	$-0.648143\pi$
$577$	13.2000	−	22.8630i	0.549523	−	0.951801i	0.998307	−	0.0581611i	$-0.0185237\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	6.28653	+	10.8886i	0.261259	+	0.452514i
$580$	5.96636			0.247740
$581$	−31.5309	+	18.3785i	−1.30812	+	0.762470i
$582$	2.86626			0.118810
$583$	40.6698	+	70.4421i	1.68437	+	2.91741i
$584$	−3.86657	+	6.69710i	−0.160000	+	0.277128i
$585$	5.29449	−	9.17033i	0.218900	−	0.379146i
$586$	−7.50213	−	12.9941i	−0.309910	−	0.536780i
$587$	20.2638			0.836378			0.418189	−	0.908360i	$-0.362665\pi$
$587$	20.2638			0.836378			0.418189	+	0.908360i	$0.362665\pi$
$588$	−5.71596	+	0.0472385i	−0.235722	+	0.00194808i
$589$	30.6758			1.26398
$590$	5.34083	+	9.25058i	0.219878	+	0.380840i
$591$	−10.0708	+	17.4432i	−0.414258	+	0.717515i
$592$	1.62814	−	2.82003i	0.0669162	−	0.115902i
$593$	7.33293	+	12.7010i	0.301128	+	0.521568i	0.976392	−	0.216008i	$-0.0693037\pi$
$593$	7.33293	+	12.7010i	0.301128	+	0.521568i	−0.675264	+	0.737576i	$0.735970\pi$
$594$	−25.4759			−1.04529
$595$	−2.28580	+	1.33233i	−0.0937087	+	0.0546203i
$596$	−6.86153			−0.281059
$597$	10.1637	+	17.6041i	0.415974	+	0.720489i
$598$	14.9124	−	25.8291i	0.609815	−	1.05623i
$599$	18.0036	−	31.1832i	0.735609	−	1.27411i	−0.218847	−	0.975759i	$-0.570229\pi$
$599$	18.0036	−	31.1832i	0.735609	−	1.27411i	0.954456	−	0.298353i	$-0.0964372\pi$
$600$	−0.408297	−	0.707191i	−0.0166687	−	0.0288710i
$601$	37.4519			1.52769			0.763847	−	0.645397i	$-0.223308\pi$
$601$	37.4519			1.52769			0.763847	+	0.645397i	$0.223308\pi$
$602$	9.65729	+	5.52256i	0.393602	+	0.225083i
$603$	−28.0508			−1.14232
$604$	−2.03560	−	3.52576i	−0.0828273	−	0.143461i
$605$	11.6098	−	20.1088i	0.472006	−	0.817538i
$606$	−4.53188	+	7.84945i	−0.184095	+	0.318862i
$607$	1.31871	+	2.28407i	0.0535248	+	0.0927076i	0.891546	−	0.452929i	$-0.149621\pi$
$607$	1.31871	+	2.28407i	0.0535248	+	0.0927076i	−0.838022	+	0.545637i	$0.816288\pi$
$608$	−5.03316			−0.204122
$609$	−0.0532636	−	12.8902i	−0.00215835	−	0.522339i
$610$	−0.0437295			−0.00177056
$611$	−8.97766	−	15.5498i	−0.363197	−	0.629076i
$612$	1.16659	−	2.02059i	0.0471565	−	0.0816774i
$613$	−20.4944	+	35.4973i	−0.827760	+	1.43372i	0.0720322	+	0.997402i	$0.477052\pi$
$613$	−20.4944	+	35.4973i	−0.827760	+	1.43372i	−0.899792	+	0.436319i	$0.856282\pi$
$614$	−13.9704	−	24.1974i	−0.563798	−	0.976527i
$615$	4.14576			0.167173
$616$	0.0639517	+	15.4769i	0.00257669	+	0.623581i
$617$	−30.6838			−1.23528			−0.617642	−	0.786459i	$-0.711912\pi$
$617$	−30.6838			−1.23528			−0.617642	+	0.786459i	$0.711912\pi$
$618$	−0.265819	−	0.460412i	−0.0106928	−	0.0185205i
$619$	3.39408	−	5.87873i	0.136420	−	0.236286i	−0.789719	−	0.613469i	$-0.789774\pi$
$619$	3.39408	−	5.87873i	0.136420	−	0.236286i	0.926139	+	0.377183i	$0.123107\pi$
$620$	−3.04737	+	5.27820i	−0.122385	+	0.211978i
$621$	14.3098	+	24.7853i	0.574232	+	0.994600i
$622$	22.3520			0.896234
$623$	18.0380	+	10.3151i	0.722678	+	0.413266i
$624$	−3.70607			−0.148361
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.47566	−	11.2162i	0.258819	−	0.448288i
$627$	12.0214	−	20.8217i	0.480088	−	0.831537i
$628$	4.10264	+	7.10597i	0.163713	+	0.283559i
$629$	−3.25628			−0.129837
$630$	5.33317	−	3.10856i	0.212479	−	0.123848i
$631$	−13.4306			−0.534663			−0.267332	−	0.963605i	$-0.586142\pi$
$631$	−13.4306			−0.534663			−0.267332	+	0.963605i	$0.586142\pi$
$632$	3.83518	+	6.64272i	0.152555	+	0.264233i
$633$	−9.33822	+	16.1743i	−0.371161	+	0.642870i
$634$	−9.11108	+	15.7809i	−0.361847	+	0.626738i
$635$	10.2124	+	17.6885i	0.405269	+	0.701946i
$636$	−11.3546			−0.450238
$637$	−15.6566	+	27.6432i	−0.620339	+	1.09526i
$638$	−34.9018			−1.38177
$639$	−5.24815	−	9.09007i	−0.207614	−	0.359598i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	7.76527	−	13.4498i	0.306710	−	0.531237i	−0.670931	−	0.741520i	$-0.734105\pi$
$641$	7.76527	−	13.4498i	0.306710	−	0.531237i	0.977641	+	0.210283i	$0.0674386\pi$
$642$	5.82205	+	10.0841i	0.229778	+	0.397987i
$643$	−11.8772			−0.468392			−0.234196	−	0.972189i	$-0.575246\pi$
$643$	−11.8772			−0.468392			−0.234196	+	0.972189i	$0.575246\pi$
$644$	15.0214	−	8.75556i	0.591926	−	0.345017i
$645$	3.43361			0.135198
$646$	2.51658	+	4.35884i	0.0990135	+	0.171496i
$647$	−21.0622	+	36.4808i	−0.828040	+	1.43421i	0.0715328	+	0.997438i	$0.477211\pi$
$647$	−21.0622	+	36.4808i	−0.828040	+	1.43421i	−0.899573	+	0.436770i	$0.856122\pi$
$648$	−1.72161	+	2.98192i	−0.0676313	+	0.117141i
$649$	−31.2425	−	54.1136i	−1.22638	−	2.12415i
$650$	−4.53844			−0.178012
$651$	11.4307	+	6.53669i	0.448004	+	0.256193i
$652$	−17.9480			−0.702899
$653$	−10.6008	−	18.3610i	−0.414840	−	0.718523i	0.580572	−	0.814209i	$-0.302829\pi$
$653$	−10.6008	−	18.3610i	−0.414840	−	0.718523i	−0.995412	+	0.0956857i	$0.969496\pi$
$654$	1.79630	−	3.11128i	0.0702409	−	0.121661i
$655$	2.86397	−	4.96053i	0.111904	−	0.193824i
$656$	2.53844	+	4.39671i	0.0991096	+	0.171663i
$657$	−18.0428			−0.703916
$658$	−0.0432514	−	10.4672i	−0.00168612	−	0.408055i
$659$	41.7673			1.62702			0.813511	−	0.581549i	$-0.197553\pi$
$659$	41.7673			1.62702			0.813511	+	0.581549i	$0.197553\pi$
$660$	2.38844	+	4.13689i	0.0929698	+	0.161028i
$661$	−18.6266	+	32.2623i	−0.724492	+	1.25486i	0.234691	+	0.972070i	$0.424592\pi$
$661$	−18.6266	+	32.2623i	−0.724492	+	1.25486i	−0.959183	+	0.282787i	$0.908741\pi$
$662$	5.91535	−	10.2457i	0.229907	−	0.398210i
$663$	1.85303	+	3.20955i	0.0719659	+	0.124649i
$664$	−13.7943			−0.535321
$665$	0.0550244	+	13.3164i	0.00213375	+	0.516387i
$666$	7.59748			0.294396
$667$	19.6043	+	33.9556i	0.759081	+	1.31477i
$668$	11.2489	−	19.4836i	0.435232	−	0.753845i
$669$	10.6269	−	18.4064i	0.410861	−	0.711632i
$670$	6.01129	+	10.4119i	0.232237	+	0.402246i
$671$	0.255807			0.00987531
$672$	−1.87550	−	1.07251i	−0.0723490	−	0.0413730i
$673$	37.5956			1.44920			0.724601	−	0.689168i	$-0.242024\pi$
$673$	37.5956			1.44920			0.724601	+	0.689168i	$0.242024\pi$
$674$	0.749964	+	1.29898i	0.0288875	+	0.0500347i
$675$	2.17752	−	3.77157i	0.0838128	−	0.145168i
$676$	−3.79874	+	6.57961i	−0.146105	+	0.253062i
$677$	−5.05455	−	8.75473i	−0.194262	−	0.336472i	0.752396	−	0.658711i	$-0.228898\pi$
$677$	−5.05455	−	8.75473i	−0.194262	−	0.336472i	−0.946658	+	0.322239i	$0.895565\pi$
$678$	6.08672			0.233759
$679$	8.02321	−	4.67651i	0.307903	−	0.179468i
$680$	−1.00000			−0.0383482
$681$	1.27032	+	2.20025i	0.0486786	+	0.0843138i
$682$	17.8264	−	30.8762i	0.682607	−	1.18231i
$683$	−9.47097	+	16.4042i	−0.362397	+	0.627690i	−0.988355	−	0.152167i	$-0.951375\pi$
$683$	−9.47097	+	16.4042i	−0.362397	+	0.627690i	0.625958	+	0.779857i	$0.284708\pi$
$684$	−5.87162	−	10.1699i	−0.224507	−	0.388857i
$685$	7.11005			0.271661
$686$	−15.9230	+	9.45824i	−0.607943	+	0.361117i
$687$	5.40799			0.206328
$688$	2.10240	+	3.64146i	0.0801531	+	0.138829i
$689$	−31.5530	+	54.6515i	−1.20207	+	2.08205i
$690$	2.68317	−	4.64738i	0.102146	−	0.176923i
$691$	3.52824	+	6.11110i	0.134221	+	0.232477i	0.925299	−	0.379237i	$-0.123814\pi$
$691$	3.52824	+	6.11110i	0.134221	+	0.232477i	−0.791079	+	0.611714i	$0.790480\pi$
$692$	−3.21256			−0.122123
$693$	−31.1978	+	18.1843i	−1.18510	+	0.690765i
$694$	7.98374			0.303059
$695$	1.94674	+	3.37186i	0.0738441	+	0.127902i
$696$	2.43605	−	4.21936i	0.0923382	−	0.159934i
$697$	2.53844	−	4.39671i	0.0961504	−	0.166537i
$698$	0.0952218	+	0.164929i	0.00360420	+	0.00624266i
$699$	−22.6102			−0.855198
$700$	−2.29673	−	1.31340i	−0.0868084	−	0.0496417i
$701$	−1.81491			−0.0685483			−0.0342742	−	0.999412i	$-0.510912\pi$
$701$	−1.81491			−0.0685483			−0.0342742	+	0.999412i	$0.510912\pi$
$702$	−9.88255	−	17.1171i	−0.372993	−	0.646043i
$703$	−8.19470	+	14.1936i	−0.309069	+	0.535323i
$704$	−2.92488	+	5.06604i	−0.110235	+	0.190933i
$705$	−1.61533	−	2.79784i	−0.0608370	−	0.105373i
$706$	8.13312			0.306094
$707$	0.121344	+	29.3662i	0.00456360	+	1.10443i
$708$	8.72258			0.327814
$709$	−5.22385	−	9.04797i	−0.196186	−	0.339804i	0.751103	−	0.660185i	$-0.229522\pi$
$709$	−5.22385	−	9.04797i	−0.196186	−	0.339804i	−0.947289	+	0.320381i	$0.896189\pi$
$710$	−2.24936	+	3.89601i	−0.0844171	+	0.146215i
$711$	−8.94814	+	15.4986i	−0.335581	+	0.581244i
$712$	3.92688	+	6.80156i	0.147166	+	0.254899i
$713$	−40.0522			−1.49997
$714$	0.00892731	+	2.16049i	0.000334096	+	0.0808542i
$715$	26.5488			0.992868
$716$	−4.41772	−	7.65171i	−0.165098	−	0.285958i
$717$	5.62293	−	9.73920i	0.209992	−	0.363717i
$718$	16.3379	−	28.2981i	0.609725	−	1.05608i
$719$	−13.8709	−	24.0251i	−0.517297	−	0.895984i	−0.999798	−	0.0200892i	$-0.993605\pi$
$719$	−13.8709	−	24.0251i	−0.517297	−	0.895984i	0.482501	−	0.875895i	$-0.339728\pi$
$720$	2.33317			0.0869523
$721$	−1.49527	−	0.855078i	−0.0556869	−	0.0318448i
$722$	6.33270			0.235679
$723$	−1.78380	−	3.08964i	−0.0663403	−	0.114905i
$724$	4.09474	−	7.09230i	0.152180	−	0.263583i
$725$	2.98318	−	5.16702i	0.110793	−	0.191898i
$726$	−9.48050	−	16.4207i	−0.351854	−	0.609430i
$727$	41.2137			1.52853			0.764265	−	0.644902i	$-0.223102\pi$
$727$	41.2137			1.52853			0.764265	+	0.644902i	$0.223102\pi$
$728$	−10.3740	+	6.04672i	−0.384486	+	0.224106i
$729$	2.63526			0.0976022
$730$	3.86657	+	6.69710i	0.143108	+	0.247871i
$731$	2.10240	−	3.64146i	0.0777599	−	0.134684i
$732$	−0.0178546	+	0.0309251i	−0.000659926	+	0.00114303i
$733$	−16.1200	−	27.9207i	−0.595406	−	1.03127i	−0.993489	−	0.113925i	$-0.963658\pi$
$733$	−16.1200	−	27.9207i	−0.595406	−	1.03127i	0.398083	−	0.917349i	$-0.369676\pi$
$734$	3.88827			0.143519
$735$	−2.81707	+	4.97379i	−0.103909	+	0.183461i
$736$	6.57160			0.242233
$737$	−35.1646	−	60.9069i	−1.29530	−	2.24353i
$738$	−5.92263	+	10.2583i	−0.218015	+	0.377613i
$739$	−16.7533	+	29.0176i	−0.616281	+	1.06743i	0.373877	+	0.927478i	$0.378028\pi$
$739$	−16.7533	+	29.0176i	−0.616281	+	1.06743i	−0.990158	+	0.139952i	$0.955305\pi$
$740$	−1.62814	−	2.82003i	−0.0598517	−	0.103666i
$741$	18.6532			0.685243
$742$	−31.7836	+	18.5258i	−1.16681	+	0.680103i
$743$	10.8697			0.398770			0.199385	−	0.979921i	$-0.436106\pi$
$743$	10.8697			0.398770			0.199385	+	0.979921i	$0.436106\pi$
$744$	2.48847	+	4.31015i	0.0912316	+	0.158018i
$745$	−3.43076	+	5.94226i	−0.125693	+	0.217707i
$746$	−12.9635	+	22.4535i	−0.474628	+	0.822080i
$747$	−16.0922	−	27.8725i	−0.588783	−	1.01980i
$748$	5.84975			0.213888
$749$	32.7499	+	18.7282i	1.19666	+	0.684312i
$750$	−0.816594			−0.0298178
$751$	−9.08855	−	15.7418i	−0.331646	−	0.574427i	0.651189	−	0.758916i	$-0.274271\pi$
$751$	−9.08855	−	15.7418i	−0.331646	−	0.574427i	−0.982835	+	0.184488i	$0.940937\pi$
$752$	1.97814	−	3.42623i	0.0721352	−	0.124942i
$753$	11.6445	−	20.1688i	0.424349	−	0.734993i
$754$	−13.5390	−	23.4502i	−0.493061	−	0.854007i
$755$	−4.07120			−0.148166
$756$	−0.0476109	−	11.5223i	−0.00173159	−	0.419060i
$757$	−37.9958			−1.38098			−0.690490	−	0.723342i	$-0.742605\pi$
$757$	−37.9958			−1.38098			−0.690490	+	0.723342i	$0.742605\pi$
$758$	14.0564	+	24.3464i	0.510552	+	0.884302i
$759$	−15.6959	+	27.1860i	−0.569724	+	0.986791i
$760$	−2.51658	+	4.35884i	−0.0912859	+	0.158112i
$761$	22.8657	+	39.6045i	0.828881	+	1.43566i	0.898917	+	0.438119i	$0.144355\pi$
$761$	22.8657	+	39.6045i	0.828881	+	1.43566i	−0.0700365	+	0.997544i	$0.522312\pi$
$762$	16.6788			0.604211
$763$	−0.0480969	−	11.6399i	−0.00174122	−	0.421391i
$764$	−23.9990			−0.868255
$765$	−1.16659	−	2.02059i	−0.0421780	−	0.0730545i
$766$	−5.26795	+	9.12435i	−0.190339	+	0.329676i
$767$	24.2390	−	41.9833i	0.875221	−	1.51593i
$768$	−0.408297	−	0.707191i	−0.0147332	−	0.0255186i
$769$	37.2625			1.34372			0.671861	−	0.740678i	$-0.265495\pi$
$769$	37.2625			1.34372			0.671861	+	0.740678i	$0.265495\pi$
$770$	13.4353	+	7.68305i	0.484176	+	0.276878i
$771$	0.606923			0.0218578
$772$	7.69847	+	13.3341i	0.277074	+	0.479906i
$773$	−13.9011	+	24.0773i	−0.499987	+	0.866002i	−1.00000		1.55616e-5i	$-0.999995\pi$
$773$	−13.9011	+	24.0773i	−0.499987	+	0.866002i	0.500013	+	0.866018i	$0.333328\pi$
$774$	−4.90526	+	8.49615i	−0.176316	+	0.305388i
$775$	3.04737	+	5.27820i	0.109465	+	0.189599i
$776$	3.51002			0.126002
$777$	−6.07809	+	3.54276i	−0.218050	+	0.127096i
$778$	−21.0052			−0.753073
$779$	−12.7764	−	22.1294i	−0.457762	−	0.792867i
$780$	−1.85303	+	3.20955i	−0.0663492	+	0.114920i
$781$	13.1582	−	22.7907i	0.470838	−	0.815515i
$782$	−3.28580	−	5.69118i	−0.117500	−	0.203516i
$783$	25.9837			0.928583
$784$	−6.99976	+	0.0578482i	−0.249991	+	0.00206601i
$785$	8.20527			0.292859
$786$	−2.33870	−	4.05074i	−0.0834186	−	0.144485i
$787$	7.06355	−	12.2344i	0.251788	−	0.436110i	−0.712230	−	0.701946i	$-0.752315\pi$
$787$	7.06355	−	12.2344i	0.251788	−	0.436110i	0.964018	+	0.265836i	$0.0856480\pi$
$788$	−12.3327	+	21.3609i	−0.439334	+	0.760949i
$789$	−1.78257	−	3.08750i	−0.0634610	−	0.109918i
$790$	7.67036			0.272899
$791$	17.0379	−	9.93093i	0.605798	−	0.353103i
$792$	−13.6485			−0.484978
$793$	0.0992319	+	0.171875i	0.00352383	+	0.00610345i
$794$	−5.53188	+	9.58151i	−0.196319	+	0.340035i
$795$	−5.67728	+	9.83334i	−0.201352	+	0.348753i
$796$	12.4465	+	21.5580i	0.441155	+	0.764102i
$797$	22.6562			0.802523			0.401262	−	0.915964i	$-0.368572\pi$
$797$	22.6562			0.802523			0.401262	+	0.915964i	$0.368572\pi$
$798$	9.43969	+	5.39812i	0.334161	+	0.191092i
$799$	−3.95627			−0.139963
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−9.16210	+	15.8692i	−0.323727	+	0.560711i
$802$	−1.54957	+	2.68394i	−0.0547173	+	0.0947731i
$803$	−22.6185	−	39.1764i	−0.798189	−	1.38250i
$804$	9.81758			0.346239
$805$	−0.0718432	−	17.3867i	−0.00253214	−	0.612800i
$806$	27.6607			0.974305
$807$	6.18293	+	10.7091i	0.217649	+	0.376980i
$808$	−5.54974	+	9.61243i	−0.195239	+	0.338164i
$809$	−11.4239	+	19.7867i	−0.401641	+	0.695663i	−0.993924	−	0.110067i	$-0.964893\pi$
$809$	−11.4239	+	19.7867i	−0.401641	+	0.695663i	0.592283	+	0.805730i	$0.298227\pi$
$810$	1.72161	+	2.98192i	0.0604913	+	0.104774i
$811$	30.9767			1.08774			0.543870	−	0.839170i	$-0.316959\pi$
$811$	30.9767			1.08774			0.543870	+	0.839170i	$0.316959\pi$
$812$	−0.0652265	−	15.7854i	−0.00228900	−	0.553958i
$813$	−2.12317			−0.0744628
$814$	9.52423	+	16.4965i	0.333824	+	0.578200i
$815$	−8.97401	+	15.5434i	−0.314346	+	0.544463i
$816$	−0.408297	+	0.707191i	−0.0142933	+	0.0247566i
$817$	−10.5817	−	18.3280i	−0.370207	−	0.641217i
$818$	17.5765			0.614547
$819$	−24.3201	−	13.9075i	−0.849812	−	0.485968i
$820$	5.07689			0.177293
$821$	−1.91703	−	3.32039i	−0.0669048	−	0.115882i	0.830633	−	0.556821i	$-0.187979\pi$
$821$	−1.91703	−	3.32039i	−0.0669048	−	0.115882i	−0.897537	+	0.440938i	$0.854646\pi$
$822$	2.90301	−	5.02816i	0.101254	−	0.175377i
$823$	2.78624	−	4.82590i	0.0971221	−	0.168220i	−0.813370	−	0.581746i	$-0.802370\pi$
$823$	2.78624	−	4.82590i	0.0971221	−	0.168220i	0.910492	+	0.413526i	$0.135703\pi$
$824$	−0.325521	−	0.563820i	−0.0113401	−	0.0196416i
$825$	4.77687			0.166309
$826$	24.4161	−	14.2315i	0.849546	−	0.495178i
$827$	2.74540			0.0954668			0.0477334	−	0.998860i	$-0.484800\pi$
$827$	2.74540			0.0954668			0.0477334	+	0.998860i	$0.484800\pi$
$828$	7.66635	+	13.2785i	0.266424	+	0.461460i
$829$	−6.11945	+	10.5992i	−0.212537	+	0.368126i	−0.952508	−	0.304514i	$-0.901506\pi$
$829$	−6.11945	+	10.5992i	−0.212537	+	0.368126i	0.739971	+	0.672639i	$0.234839\pi$
$830$	−6.89713	+	11.9462i	−0.239403	+	0.414658i
$831$	6.48331	+	11.2294i	0.224904	+	0.389544i
$832$	−4.53844			−0.157342
$833$	3.54998	+	6.03305i	0.122999	+	0.209033i
$834$	3.17940			0.110093
$835$	−11.2489	−	19.4836i	−0.389284	−	0.674259i
$836$	14.7214	−	25.4982i	0.509149	−	0.881872i
$837$	−13.2714	+	22.9868i	−0.458727	+	0.794539i
$838$	−13.1628	−	22.7987i	−0.454702	−	0.787568i
$839$	−10.1766			−0.351335			−0.175667	−	0.984450i	$-0.556208\pi$
$839$	−10.1766			−0.351335			−0.175667	+	0.984450i	$0.556208\pi$
$840$	−1.86657	+	1.08797i	−0.0644029	+	0.0375387i
$841$	6.59748			0.227499
$842$	−7.26029	−	12.5752i	−0.250206	−	0.433370i
$843$	−6.62366	+	11.4725i	−0.228131	+	0.395134i
$844$	−11.4356	+	19.8070i	−0.393629	+	0.681785i
$845$	3.79874	+	6.57961i	0.130681	+	0.226345i
$846$	9.23067			0.317357
$847$	−53.3293	−	30.4966i	−1.83242	−	1.04787i
$848$	−13.9048			−0.477492
$849$	0.886180	+	1.53491i	0.0304136	+	0.0526779i
$850$	−0.500000	+	0.866025i	−0.0171499	+	0.0297044i
$851$	10.6995	−	18.5321i	0.366774	−	0.635272i
$852$	1.83682	+	3.18146i	0.0629283	+	0.108995i
$853$	−27.3969			−0.938053			−0.469027	−	0.883184i	$-0.655395\pi$
$853$	−27.3969			−0.938053			−0.469027	+	0.883184i	$0.655395\pi$
$854$	0.000478067		0.115696i	1.63591e−5		0.00395905i
$855$	−11.7432			−0.401610
$856$	7.12967	+	12.3489i	0.243687	+	0.422078i
$857$	−9.02307	+	15.6284i	−0.308222	+	0.533856i	−0.977974	−	0.208729i	$-0.933067\pi$
$857$	−9.02307	+	15.6284i	−0.308222	+	0.533856i	0.669751	+	0.742585i	$0.266401\pi$
$858$	10.8398	−	18.7751i	0.370064	−	0.640970i
$859$	−8.11125	−	14.0491i	−0.276752	−	0.479349i	0.693823	−	0.720145i	$-0.255925\pi$
$859$	−8.11125	−	14.0491i	−0.276752	−	0.479349i	−0.970576	+	0.240796i	$0.922591\pi$
$860$	4.20479			0.143382
$861$	−0.0453230	−	10.9686i	−0.00154460	−	0.373807i
$862$	4.51891			0.153915
$863$	8.28168	+	14.3443i	0.281912	+	0.488285i	0.971856	−	0.235577i	$-0.0756981\pi$
$863$	8.28168	+	14.3443i	0.281912	+	0.488285i	−0.689944	+	0.723863i	$0.742365\pi$
$864$	2.17752	−	3.77157i	0.0740807	−	0.128312i
$865$	−1.60628	+	2.78215i	−0.0546151	+	0.0945961i
$866$	−10.7804	−	18.6722i	−0.366333	−	0.634508i
$867$	0.816594			0.0277330
$868$	13.9980	+	8.00482i	0.475123	+	0.271701i
$869$	−44.8697			−1.52210
$870$	−2.43605	−	4.21936i	−0.0825898	−	0.143050i
$871$	27.2819	−	47.2537i	0.924413	−	1.60113i
$872$	2.19975	−	3.81007i	0.0744928	−	0.129025i
$873$	4.09474	+	7.09230i	0.138586	+	0.240038i
$874$	−33.0759			−1.11881
$875$	−2.28580	+	1.33233i	−0.0772742	+	0.0450410i
$876$	6.31484			0.213359
$877$	11.7545	+	20.3594i	0.396922	+	0.687490i	0.993344	−	0.115181i	$-0.0367449\pi$
$877$	11.7545	+	20.3594i	0.396922	+	0.687490i	−0.596422	+	0.802671i	$0.703412\pi$
$878$	8.36196	−	14.4833i	0.282203	−	0.488789i
$879$	−6.12619	+	10.6109i	−0.206631	+	0.357896i
$880$	2.92488	+	5.06604i	0.0985976	+	0.170776i
$881$	−39.7518			−1.33927			−0.669635	−	0.742690i	$-0.733550\pi$
$881$	−39.7518			−1.33927			−0.669635	+	0.742690i	$0.733550\pi$
$882$	−8.28272	−	14.0761i	−0.278894	−	0.473969i
$883$	−12.6768			−0.426607			−0.213304	−	0.976986i	$-0.568422\pi$
$883$	−12.6768			−0.426607			−0.213304	+	0.976986i	$0.568422\pi$
$884$	2.26922	+	3.93041i	0.0763222	+	0.132194i
$885$	4.36129	−	7.55397i	0.146603	−	0.253924i
$886$	−12.4871	+	21.6282i	−0.419511	+	0.726614i
$887$	2.01615	+	3.49207i	0.0676955	+	0.117252i	0.897887	−	0.440227i	$-0.145102\pi$
$887$	2.01615	+	3.49207i	0.0676955	+	0.117252i	−0.830191	+	0.557479i	$0.811769\pi$
$888$	−2.65906			−0.0892323
$889$	46.6873	−	27.2127i	1.56584	−	0.912686i
$890$	7.85376			0.263259
$891$	−10.0710	−	17.4435i	−0.337391	−	0.584379i
$892$	13.0137	−	22.5404i	0.435732	−	0.754710i
$893$	−9.95627	+	17.2448i	−0.333174	+	0.577074i
$894$	2.80154	+	4.85241i	0.0936976	+	0.162289i
$895$	−8.83543			−0.295336
$896$	−2.29673	−	1.31340i	−0.0767285	−	0.0438775i
$897$	−24.3548			−0.813183
$898$	−15.0445	−	26.0578i	−0.502040	−	0.869559i
$899$	−18.1817	+	31.4917i	−0.606394	+	1.05031i
$900$	1.16659	−	2.02059i	0.0388862	−	0.0673529i
$901$	6.95239	+	12.0419i	0.231618	+	0.401174i
$902$	−29.6986			−0.988854
$903$	−0.0375375	−	9.08440i	−0.00124917	−	0.302310i
$904$	7.45379			0.247909
$905$	−4.09474	−	7.09230i	−0.136114	−	0.235756i
$906$	−1.66226	+	2.87912i	−0.0552248	+	0.0956522i
$907$	23.6989	−	41.0477i	0.786910	−	1.36297i	−0.140942	−	0.990018i	$-0.545013\pi$
$907$	23.6989	−	41.0477i	0.786910	−	1.36297i	0.927852	−	0.372950i	$-0.121654\pi$
$908$	1.55563	+	2.69442i	0.0516253	+	0.0894176i
$909$	−25.8970			−0.858950
$910$	0.0496160	+	12.0075i	0.00164475	+	0.398045i
$911$	27.8023			0.921130			0.460565	−	0.887626i	$-0.347647\pi$
$911$	27.8023			0.921130			0.460565	+	0.887626i	$0.347647\pi$
$912$	2.05502	+	3.55941i	0.0680487	+	0.117864i
$913$	40.3465	−	69.8822i	1.33527	−	2.31276i
$914$	−3.07288	+	5.32238i	−0.101642	+	0.176049i
$915$	0.0178546	+	0.0309251i	0.000590256	+	0.00102235i
$916$	6.62262			0.218817
$917$	−13.1555	−	7.52305i	−0.434434	−	0.248433i
$918$	−4.35504			−0.143738
$919$	17.9582	+	31.1046i	0.592387	+	1.02605i	0.993910	+	0.110196i	$0.0351478\pi$
$919$	17.9582	+	31.1046i	0.592387	+	1.02605i	−0.401522	+	0.915849i	$0.631519\pi$
$920$	3.28580	−	5.69118i	0.108330	−	0.187633i
$921$	−11.4081	+	19.7595i	−0.375910	+	0.651096i
$922$	11.7024	+	20.2691i	0.385396	+	0.667526i
$923$	20.4172			0.672041
$924$	10.9190	−	6.36438i	0.359208	−	0.209373i
$925$	−3.25628			−0.107066
$926$	−1.66391	−	2.88197i	−0.0546794	−	0.0947076i
$927$	0.759498	−	1.31549i	0.0249452	−	0.0432063i
$928$	2.98318	−	5.16702i	0.0979277	−	0.169616i
$929$	−9.78817	−	16.9536i	−0.321139	−	0.556230i	0.659584	−	0.751631i	$-0.270732\pi$
$929$	−9.78817	−	16.9536i	−0.321139	−	0.556230i	−0.980723	+	0.195401i	$0.937399\pi$
$930$	4.97693			0.163200
$931$	35.2309	−	0.291159i	1.15465	−	0.00954236i
$932$	−27.6885			−0.906966
$933$	−9.12626	−	15.8071i	−0.298780	−	0.517503i
$934$	10.1035	−	17.4998i	0.330596	−	0.572610i
$935$	2.92488	−	5.06604i	0.0956537	−	0.165677i
$936$	−5.29449	−	9.17033i	−0.173056	−	0.299741i
$937$	−50.2723			−1.64233			−0.821163	−	0.570694i	$-0.806674\pi$
$937$	−50.2723			−1.64233			−0.821163	+	0.570694i	$0.806674\pi$
$938$	27.4813	−	16.0181i	0.897295	−	0.523009i
$939$	−10.5760			−0.345134
$940$	−1.97814	−	3.42623i	−0.0645197	−	0.111751i
$941$	9.41984	−	16.3156i	0.307078	−	0.531875i	−0.670644	−	0.741780i	$-0.733982\pi$
$941$	9.41984	−	16.3156i	0.307078	−	0.531875i	0.977722	+	0.209905i	$0.0673154\pi$
$942$	3.35019	−	5.80270i	0.109155	−	0.189062i
$943$	16.6817	+	28.8935i	0.543229	+	0.940901i
$944$	10.6817			0.347658
$945$	−10.0024	−	5.71989i	−0.325377	−	0.186068i
$946$	−24.5970			−0.799717
$947$	−27.2952	−	47.2767i	−0.886975	−	1.53629i	−0.843433	−	0.537235i	$-0.819469\pi$
$947$	−27.2952	−	47.2767i	−0.886975	−	1.53629i	−0.0435429	−	0.999052i	$-0.513865\pi$
$948$	3.13178	−	5.42441i	0.101716	−	0.176177i
$949$	17.5482	−	30.3944i	0.569640	−	0.986645i
$950$	2.51658	+	4.35884i	0.0816486	+	0.141420i
$951$	14.8801			0.482521
$952$	0.0109324	+	2.64573i	0.000354320	+	0.0857486i
$953$	13.0559			0.422922			0.211461	−	0.977386i	$-0.432178\pi$
$953$	13.0559			0.422922			0.211461	+	0.977386i	$0.432178\pi$
$954$	−16.2211	−	28.0958i	−0.525179	−	0.909636i
$955$	−11.9995	+	20.7838i	−0.388295	+	0.672547i
$956$	6.88583	−	11.9266i	0.222704	−	0.385734i
$957$	14.2503	+	24.6822i	0.460646	+	0.797863i
$958$	−6.87355			−0.222074
$959$	−0.0777297	−	18.8113i	−0.00251002	−	0.607447i
$960$	−0.816594			−0.0263555
$961$	−3.07295	−	5.32251i	−0.0991274	−	0.171694i
$962$	−7.38923	+	12.7985i	−0.238238	+	0.412641i
$963$	−16.6348	+	28.8122i	−0.536048	+	0.928462i
$964$	−2.18444	−	3.78356i	−0.0703561	−	0.121860i
$965$	15.3969			0.495645
$966$	−12.3250	−	7.04812i	−0.396552	−	0.226770i
$967$	−23.6607			−0.760875			−0.380438	−	0.924807i	$-0.624227\pi$
$967$	−23.6607			−0.760875			−0.380438	+	0.924807i	$0.624227\pi$
$968$	−11.6098	−	20.1088i	−0.373153	−	0.646321i
$969$	2.05502	−	3.55941i	0.0660169	−	0.114345i
$970$	1.75501	−	3.03977i	0.0563500	−	0.0976010i
$971$	−22.4540	−	38.8915i	−0.720584	−	1.24809i	−0.960766	−	0.277361i	$-0.910540\pi$
$971$	−22.4540	−	38.8915i	−0.720584	−	1.24809i	0.240181	−	0.970728i	$-0.422793\pi$
$972$	15.8768			0.509250
$973$	8.89973	−	5.18741i	0.285312	−	0.166301i
$974$	11.3757			0.364501
$975$	1.85303	+	3.20955i	0.0593446	+	0.102788i
$976$	−0.0218647	+	0.0378709i	−0.000699874	+	0.00121222i
$977$	−24.2859	+	42.0645i	−0.776976	+	1.34576i	0.156701	+	0.987646i	$0.449914\pi$
$977$	−24.2859	+	42.0645i	−0.776976	+	1.34576i	−0.933677	+	0.358116i	$0.883419\pi$
$978$	7.32813	+	12.6927i	0.234328	+	0.405867i
$979$	−45.9426			−1.46833
$980$	−3.44978	+	6.09089i	−0.110199	+	0.194567i
$981$	10.2648			0.327729
$982$	6.64448	+	11.5086i	0.212034	+	0.367254i
$983$	17.9593	−	31.1065i	0.572814	−	0.992142i	−0.423462	−	0.905914i	$-0.639185\pi$
$983$	17.9593	−	31.1065i	0.572814	−	0.992142i	0.996275	−	0.0862284i	$-0.0274815\pi$
$984$	2.07288	−	3.59033i	0.0660810	−	0.114456i
$985$	12.3327	+	21.3609i	0.392952	+	0.680613i
$986$	−5.96636			−0.190008
$987$	−7.38467	+	4.30432i	−0.235057	+	0.137008i
$988$	22.8427			0.726724
$989$	13.8161	+	23.9302i	0.439327	+	0.760937i
$990$	−6.82425	+	11.8199i	−0.216889	+	0.375662i
$991$	−14.6020	+	25.2913i	−0.463847	+	0.803406i	−0.999149	−	0.0412548i	$-0.986864\pi$
$991$	−14.6020	+	25.2913i	−0.463847	+	0.803406i	0.535302	+	0.844661i	$0.320198\pi$
$992$	3.04737	+	5.27820i	0.0967542	+	0.167583i
$993$	−9.66088			−0.306579
$994$	10.3324	+	5.90861i	0.327723	+	0.187410i
$995$	24.8930			0.789161
$996$	5.63215	+	9.75517i	0.178462	+	0.309105i
$997$	−8.64698	+	14.9770i	−0.273853	+	0.474327i	−0.969845	−	0.243723i	$-0.921631\pi$
$997$	−8.64698	+	14.9770i	−0.273853	+	0.474327i	0.695992	+	0.718049i	$0.254965\pi$
$998$	10.2556	−	17.7632i	0.324636	−	0.562286i
$999$	−7.09062	−	12.2813i	−0.224337	−	0.388564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.i.k.851.2	yes	8
7.2	even	3	inner	1190.2.i.k.681.2	✓	8
7.3	odd	6		8330.2.a.cl.1.2		4
7.4	even	3		8330.2.a.cd.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.i.k.681.2	✓	8	7.2	even	3	inner
1190.2.i.k.851.2	yes	8	1.1	even	1	trivial
8330.2.a.cd.1.3		4	7.4	even	3
8330.2.a.cl.1.2		4	7.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.408297 + 0.707191i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.816594 q^{6} +(2.28580 - 1.33233i) q^{7} +1.00000 q^{8} +(1.16659 + 2.02059i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.92488 + 5.06604i) q^{11} +(-0.408297 - 0.707191i) q^{12} -4.53844 q^{13} +(-2.29673 - 1.31340i) q^{14} -0.816594 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(1.16659 - 2.02059i) q^{18} +(2.51658 + 4.35884i) q^{19} -1.00000 q^{20} +(0.00892731 + 2.16049i) q^{21} +5.84975 q^{22} +(-3.28580 - 5.69118i) q^{23} +(-0.408297 + 0.707191i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.26922 + 3.93041i) q^{26} -4.35504 q^{27} +(0.0109324 + 2.64573i) q^{28} -5.96636 q^{29} +(0.408297 + 0.707191i) q^{30} +(3.04737 - 5.27820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.38844 - 4.13689i) q^{33} +1.00000 q^{34} +(2.29673 + 1.31340i) q^{35} -2.33317 q^{36} +(1.62814 + 2.82003i) q^{37} +(2.51658 - 4.35884i) q^{38} +(1.85303 - 3.20955i) q^{39} +(0.500000 + 0.866025i) q^{40} -5.07689 q^{41} +(1.86657 - 1.08797i) q^{42} -4.20479 q^{43} +(-2.92488 - 5.06604i) q^{44} +(-1.16659 + 2.02059i) q^{45} +(-3.28580 + 5.69118i) q^{46} +(1.97814 + 3.42623i) q^{47} +0.816594 q^{48} +(3.44978 - 6.09089i) q^{49} +1.00000 q^{50} +(-0.408297 - 0.707191i) q^{51} +(2.26922 - 3.93041i) q^{52} +(6.95239 - 12.0419i) q^{53} +(2.17752 + 3.77157i) q^{54} -5.84975 q^{55} +(2.28580 - 1.33233i) q^{56} -4.11005 q^{57} +(2.98318 + 5.16702i) q^{58} +(-5.34083 + 9.25058i) q^{59} +(0.408297 - 0.707191i) q^{60} +(-0.0218647 - 0.0378709i) q^{61} -6.09474 q^{62} +(5.35868 + 3.06438i) q^{63} +1.00000 q^{64} +(-2.26922 - 3.93041i) q^{65} +(-2.38844 + 4.13689i) q^{66} +(-6.01129 + 10.4119i) q^{67} +(-0.500000 - 0.866025i) q^{68} +5.36633 q^{69} +(-0.0109324 - 2.64573i) q^{70} -4.49873 q^{71} +(1.16659 + 2.02059i) q^{72} +(-3.86657 + 6.69710i) q^{73} +(1.62814 - 2.82003i) q^{74} +(-0.408297 - 0.707191i) q^{75} -5.03316 q^{76} +(0.0639517 + 15.4769i) q^{77} -3.70607 q^{78} +(3.83518 + 6.64272i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-1.72161 + 2.98192i) q^{81} +(2.53844 + 4.39671i) q^{82} -13.7943 q^{83} +(-1.87550 - 1.07251i) q^{84} -1.00000 q^{85} +(2.10240 + 3.64146i) q^{86} +(2.43605 - 4.21936i) q^{87} +(-2.92488 + 5.06604i) q^{88} +(3.92688 + 6.80156i) q^{89} +2.33317 q^{90} +(-10.3740 + 6.04672i) q^{91} +6.57160 q^{92} +(2.48847 + 4.31015i) q^{93} +(1.97814 - 3.42623i) q^{94} +(-2.51658 + 4.35884i) q^{95} +(-0.408297 - 0.707191i) q^{96} +3.51002 q^{97} +(-6.99976 + 0.0578482i) q^{98} -13.6485 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} - 28 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20}+ \cdots - 52 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 2 * q^11 + 2 * q^12 - 28 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 2 * q^21 + 4 * q^22 - 6 * q^23 + 2 * q^24 - 4 * q^25 + 14 * q^26 - 16 * q^27 + 4 * q^28 - 2 * q^30 + 18 * q^31 - 4 * q^32 - 8 * q^33 + 8 * q^34 + 2 * q^35 + 8 * q^36 + 8 * q^37 + 4 * q^38 - 6 * q^39 + 4 * q^40 - 24 * q^41 - 4 * q^42 + 28 * q^43 - 2 * q^44 + 4 * q^45 - 6 * q^46 + 8 * q^47 - 4 * q^48 - 4 * q^49 + 8 * q^50 + 2 * q^51 + 14 * q^52 + 22 * q^53 + 8 * q^54 - 4 * q^55 - 2 * q^56 + 16 * q^57 + 2 * q^59 - 2 * q^60 - 8 * q^61 - 36 * q^62 + 2 * q^63 + 8 * q^64 - 14 * q^65 - 8 * q^66 - 8 * q^67 - 4 * q^68 - 16 * q^69 - 4 * q^70 - 16 * q^71 - 4 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 - 8 * q^76 - 22 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 + 24 * q^81 + 12 * q^82 - 12 * q^83 + 2 * q^84 - 8 * q^85 - 14 * q^86 + 42 * q^87 - 2 * q^88 + 12 * q^89 - 8 * q^90 - 6 * q^91 + 12 * q^92 + 20 * q^93 + 8 * q^94 - 4 * q^95 + 2 * q^96 - 32 * q^97 - 16 * q^98 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more