LMFDB - Embedded newform 210.2.r.a.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(101,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("210.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.r (of order $6$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$-1.21252 + 1.23685i$ of defining polynomial
Character	$\chi$	$=$	210.101
Dual form			210.2.r.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.23685 + 1.21252i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.67740 + 0.431645i) q^{6} +(-0.311378 + 2.62736i) q^{7} -1.00000i q^{8} +(0.0596020 + 2.99941i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.23685 + 1.21252i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.67740 + 0.431645i) q^{6} +(-0.311378 + 2.62736i) q^{7} -1.00000i q^{8} +(0.0596020 + 2.99941i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-4.44749 - 2.56776i) q^{11} +(1.66850 - 0.464886i) q^{12} -5.00256i q^{13} +(1.04402 + 2.43105i) q^{14} +(-0.431645 + 1.67740i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87973 - 3.25579i) q^{17} +(1.55132 + 2.56776i) q^{18} +(2.33193 - 1.34634i) q^{19} +1.00000 q^{20} +(-3.57085 + 2.87211i) q^{21} -5.13552 q^{22} +(2.15298 - 1.24302i) q^{23} +(1.21252 - 1.23685i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.50128 - 4.33235i) q^{26} +(-3.56312 + 3.78209i) q^{27} +(2.11968 + 1.58334i) q^{28} +6.18694i q^{29} +(0.464886 + 1.66850i) q^{30} +(-4.13446 - 2.38703i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.38743 - 8.56861i) q^{33} -3.75947i q^{34} +(-2.43105 + 1.04402i) q^{35} +(2.62736 + 1.44809i) q^{36} +(-0.0262075 - 0.0453927i) q^{37} +(1.34634 - 2.33193i) q^{38} +(6.06570 - 6.18743i) q^{39} +(0.866025 - 0.500000i) q^{40} +6.55478 q^{41} +(-1.65640 + 4.27275i) q^{42} -9.45088 q^{43} +(-4.44749 + 2.56776i) q^{44} +(-2.56776 + 1.55132i) q^{45} +(1.24302 - 2.15298i) q^{46} +(1.53446 + 2.65776i) q^{47} +(0.431645 - 1.67740i) q^{48} +(-6.80609 - 1.63621i) q^{49} +1.00000i q^{50} +(6.27266 - 1.74772i) q^{51} +(-4.33235 - 2.50128i) q^{52} +(-0.963053 - 0.556019i) q^{53} +(-1.19470 + 5.05694i) q^{54} -5.13552i q^{55} +(2.62736 + 0.311378i) q^{56} +(4.51670 + 1.16228i) q^{57} +(3.09347 + 5.35804i) q^{58} +(-6.63079 + 11.4849i) q^{59} +(1.23685 + 1.21252i) q^{60} +(3.59330 - 2.07459i) q^{61} -4.77406 q^{62} +(-7.89910 - 0.777354i) q^{63} -1.00000 q^{64} +(4.33235 - 2.50128i) q^{65} +(-6.35188 - 6.22691i) q^{66} +(0.448087 - 0.776110i) q^{67} +(-1.87973 - 3.25579i) q^{68} +(4.17010 + 1.07309i) q^{69} +(-1.58334 + 2.11968i) q^{70} +13.4240i q^{71} +(2.99941 - 0.0596020i) q^{72} +(-6.04511 - 3.49014i) q^{73} +(-0.0453927 - 0.0262075i) q^{74} +(-1.66850 + 0.464886i) q^{75} -2.69268i q^{76} +(8.13130 - 10.8856i) q^{77} +(2.15933 - 8.39132i) q^{78} +(8.37381 + 14.5039i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.99290 + 0.357541i) q^{81} +(5.67661 - 3.27739i) q^{82} -1.37724 q^{83} +(0.701891 + 4.52850i) q^{84} +3.75947 q^{85} +(-8.18470 + 4.72544i) q^{86} +(-7.50177 + 7.65232i) q^{87} +(-2.56776 + 4.44749i) q^{88} +(2.67056 + 4.62555i) q^{89} +(-1.44809 + 2.62736i) q^{90} +(13.1436 + 1.55769i) q^{91} -2.48605i q^{92} +(-2.21939 - 7.96551i) q^{93} +(2.65776 + 1.53446i) q^{94} +(2.33193 + 1.34634i) q^{95} +(-0.464886 - 1.66850i) q^{96} +0.633608i q^{97} +(-6.71235 + 1.98605i) q^{98} +(7.43669 - 13.4929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9 - 12 * q^11 + 2 * q^12 + 12 * q^14 - 4 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 12 * q^20 - 18 * q^21 - 24 * q^23 - 4 * q^24 - 6 * q^25 - 4 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 + 12 * q^31 - 22 * q^33 + 4 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 + 30 * q^39 - 4 * q^41 - 20 * q^42 - 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 - 48 * q^53 - 4 * q^54 + 6 * q^56 - 36 * q^57 + 8 * q^58 + 12 * q^59 - 2 * q^60 - 30 * q^61 + 8 * q^62 - 4 * q^63 - 12 * q^64 + 12 * q^65 - 34 * q^66 - 4 * q^67 - 12 * q^68 + 50 * q^69 + 6 * q^70 + 4 * q^72 - 2 * q^75 + 20 * q^77 + 32 * q^78 - 4 * q^79 + 6 * q^80 + 50 * q^81 - 40 * q^83 - 12 * q^84 + 24 * q^85 - 54 * q^86 + 8 * q^87 + 26 * q^89 - 8 * q^90 + 28 * q^91 - 32 * q^93 + 24 * q^94 - 2 * q^96 + 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.23685	+	1.21252i	0.714096	+	0.700047i
$3$	1.23685	+	1.21252i	0.714096	+	0.700047i
$4$	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
$6$	1.67740	+	0.431645i	0.684797	+	0.176219i
$7$	−0.311378	+	2.62736i	−0.117690	+	0.993050i
$7$	−0.311378	+	2.62736i	−0.117690	+	0.993050i
$8$		−	1.00000i		−	0.353553i
$9$	0.0596020	+	2.99941i	0.0198673	+	0.999803i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−4.44749	−	2.56776i	−1.34097	−	0.774210i	−0.354020	−	0.935238i	$-0.615186\pi$
$11$	−4.44749	−	2.56776i	−1.34097	−	0.774210i	−0.986950	+	0.161028i	$0.948519\pi$
$12$	1.66850	−	0.464886i	0.481654	−	0.134201i
$13$		−	5.00256i		−	1.38746i	−0.720234	−	0.693731i	$-0.755966\pi$
$13$		−	5.00256i		−	1.38746i	0.720234	−	0.693731i	$-0.244034\pi$
$14$	1.04402	+	2.43105i	0.279026	+	0.649726i
$15$	−0.431645	+	1.67740i	−0.111450	+	0.433104i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.87973	−	3.25579i	0.455902	−	0.789646i	−0.542837	−	0.839838i	$-0.682650\pi$
$17$	1.87973	−	3.25579i	0.455902	−	0.789646i	0.998740	+	0.0501922i	$0.0159834\pi$
$18$	1.55132	+	2.56776i	0.365650	+	0.605227i
$19$	2.33193	−	1.34634i	0.534981	−	0.308871i	−0.208062	−	0.978116i	$-0.566715\pi$
$19$	2.33193	−	1.34634i	0.534981	−	0.308871i	0.743042	+	0.669245i	$0.233382\pi$
$20$	1.00000			0.223607
$21$	−3.57085	+	2.87211i	−0.779224	+	0.626745i
$22$	−5.13552			−1.09490
$23$	2.15298	−	1.24302i	0.448927	−	0.259188i	−0.258450	−	0.966025i	$-0.583212\pi$
$23$	2.15298	−	1.24302i	0.448927	−	0.259188i	0.707377	+	0.706836i	$0.249878\pi$
$24$	1.21252	−	1.23685i	0.247504	−	0.252471i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.50128	−	4.33235i	−0.490542	−	0.849643i
$27$	−3.56312	+	3.78209i	−0.685722	+	0.727864i
$28$	2.11968	+	1.58334i	0.400581	+	0.299224i
$29$			6.18694i			1.14889i	0.818545	+	0.574443i	$0.194781\pi$
$29$			6.18694i			1.14889i	−0.818545	+	0.574443i	$0.805219\pi$
$30$	0.464886	+	1.66850i	0.0848761	+	0.304624i
$31$	−4.13446	−	2.38703i	−0.742571	−	0.428724i	0.0804322	−	0.996760i	$-0.474370\pi$
$31$	−4.13446	−	2.38703i	−0.742571	−	0.428724i	−0.823003	+	0.568036i	$0.807703\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.38743	−	8.56861i	−0.415599	−	1.49160i
$34$		−	3.75947i		−	0.644743i
$35$	−2.43105	+	1.04402i	−0.410923	+	0.176472i
$36$	2.62736	+	1.44809i	0.437894	+	0.241348i
$37$	−0.0262075	−	0.0453927i	−0.00430849	−	0.00746252i	0.863863	−	0.503727i	$-0.168038\pi$
$37$	−0.0262075	−	0.0453927i	−0.00430849	−	0.00746252i	−0.868172	+	0.496264i	$0.834705\pi$
$38$	1.34634	−	2.33193i	0.218405	−	0.378288i
$39$	6.06570	−	6.18743i	0.971289	−	0.990781i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	6.55478			1.02369			0.511843	−	0.859079i	$-0.328963\pi$
$41$	6.55478			1.02369			0.511843	+	0.859079i	$0.328963\pi$
$42$	−1.65640	+	4.27275i	−0.255588	+	0.659299i
$43$	−9.45088			−1.44125			−0.720623	−	0.693327i	$-0.756144\pi$
$43$	−9.45088			−1.44125			−0.720623	+	0.693327i	$0.756144\pi$
$44$	−4.44749	+	2.56776i	−0.670485	+	0.387105i
$45$	−2.56776	+	1.55132i	−0.382779	+	0.231257i
$46$	1.24302	−	2.15298i	0.183274	−	0.317440i
$47$	1.53446	+	2.65776i	0.223824	+	0.387674i	0.955966	−	0.293478i	$-0.0948127\pi$
$47$	1.53446	+	2.65776i	0.223824	+	0.387674i	−0.732142	+	0.681152i	$0.761479\pi$
$48$	0.431645	−	1.67740i	0.0623027	−	0.242112i
$49$	−6.80609	−	1.63621i	−0.972298	−	0.233744i
$50$			1.00000i			0.141421i
$51$	6.27266	−	1.74772i	0.878347	−	0.244730i
$52$	−4.33235	−	2.50128i	−0.600788	−	0.346865i
$53$	−0.963053	−	0.556019i	−0.132286	−	0.0763751i	0.432397	−	0.901683i	$-0.357668\pi$
$53$	−0.963053	−	0.556019i	−0.132286	−	0.0763751i	−0.564682	+	0.825308i	$0.691001\pi$
$54$	−1.19470	+	5.05694i	−0.162579	+	0.688163i
$55$		−	5.13552i		−	0.692474i
$56$	2.62736	+	0.311378i	0.351096	+	0.0416096i
$57$	4.51670	+	1.16228i	0.598252	+	0.153948i
$58$	3.09347	+	5.35804i	0.406192	+	0.703546i
$59$	−6.63079	+	11.4849i	−0.863255	+	1.49520i	0.00551419	+	0.999985i	$0.498245\pi$
$59$	−6.63079	+	11.4849i	−0.863255	+	1.49520i	−0.868769	+	0.495217i	$0.835089\pi$
$60$	1.23685	+	1.21252i	0.159677	+	0.156535i
$61$	3.59330	−	2.07459i	0.460075	−	0.265624i	−0.252001	−	0.967727i	$-0.581089\pi$
$61$	3.59330	−	2.07459i	0.460075	−	0.265624i	0.712076	+	0.702103i	$0.247755\pi$
$62$	−4.77406			−0.606307
$63$	−7.89910	−	0.777354i	−0.995193	−	0.0979373i
$64$	−1.00000			−0.125000
$65$	4.33235	−	2.50128i	0.537362	−	0.310246i
$66$	−6.35188	−	6.22691i	−0.781862	−	0.766480i
$67$	0.448087	−	0.776110i	0.0547426	−	0.0948169i	−0.837356	−	0.546659i	$-0.815900\pi$
$67$	0.448087	−	0.776110i	0.0547426	−	0.0948169i	0.892098	+	0.451842i	$0.149233\pi$
$68$	−1.87973	−	3.25579i	−0.227951	−	0.394823i
$69$	4.17010	+	1.07309i	0.502021	+	0.129185i
$70$	−1.58334	+	2.11968i	−0.189246	+	0.253350i
$71$			13.4240i			1.59313i	0.604551	+	0.796567i	$0.293353\pi$
$71$			13.4240i			1.59313i	−0.604551	+	0.796567i	$0.706647\pi$
$72$	2.99941	−	0.0596020i	0.353484	−	0.00702416i
$73$	−6.04511	−	3.49014i	−0.707526	−	0.408490i	0.102618	−	0.994721i	$-0.467278\pi$
$73$	−6.04511	−	3.49014i	−0.707526	−	0.408490i	−0.810144	+	0.586230i	$0.800611\pi$
$74$	−0.0453927	−	0.0262075i	−0.00527680	−	0.00304656i
$75$	−1.66850	+	0.464886i	−0.192661	+	0.0536804i
$76$		−	2.69268i		−	0.308871i
$77$	8.13130	−	10.8856i	0.926648	−	1.24053i
$78$	2.15933	−	8.39132i	0.244496	−	0.950130i
$79$	8.37381	+	14.5039i	0.942127	+	1.63181i	0.761403	+	0.648279i	$0.224511\pi$
$79$	8.37381	+	14.5039i	0.942127	+	1.63181i	0.180724	+	0.983534i	$0.442156\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.99290	+	0.357541i	−0.999211	+	0.0397268i
$82$	5.67661	−	3.27739i	0.626877	−	0.361927i
$83$	−1.37724			−0.151172			−0.0755861	−	0.997139i	$-0.524083\pi$
$83$	−1.37724			−0.151172			−0.0755861	+	0.997139i	$0.524083\pi$
$84$	0.701891	+	4.52850i	0.0765826	+	0.494100i
$85$	3.75947			0.407771
$86$	−8.18470	+	4.72544i	−0.882579	+	0.509557i
$87$	−7.50177	+	7.65232i	−0.804274	+	0.820415i
$88$	−2.56776	+	4.44749i	−0.273724	+	0.474105i
$89$	2.67056	+	4.62555i	0.283079	+	0.490307i	0.972142	−	0.234395i	$-0.0753108\pi$
$89$	2.67056	+	4.62555i	0.283079	+	0.490307i	−0.689062	+	0.724702i	$0.741977\pi$
$90$	−1.44809	+	2.62736i	−0.152642	+	0.276949i
$91$	13.1436	+	1.55769i	1.37782	+	0.163290i
$92$		−	2.48605i		−	0.259188i
$93$	−2.21939	−	7.96551i	−0.230141	−	0.825985i
$94$	2.65776	+	1.53446i	0.274127	+	0.158267i
$95$	2.33193	+	1.34634i	0.239251	+	0.138131i
$96$	−0.464886	−	1.66850i	−0.0474472	−	0.170290i
$97$			0.633608i			0.0643331i	0.999483	+	0.0321666i	$0.0102407\pi$
$97$			0.633608i			0.0643331i	−0.999483	+	0.0321666i	$0.989759\pi$
$98$	−6.71235	+	1.98605i	−0.678050	+	0.200621i
$99$	7.43669	−	13.4929i	0.747415	−	1.35609i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	8.81430	−	15.2668i	0.877056	−	1.51910i	0.0224989	−	0.999747i	$-0.492838\pi$
$101$	8.81430	−	15.2668i	0.877056	−	1.51910i	0.854557	−	0.519358i	$-0.173829\pi$
$102$	4.55842	−	4.64990i	0.451351	−	0.460409i
$103$	12.7448	−	7.35823i	1.25579	−	0.725028i	0.283533	−	0.958962i	$-0.408493\pi$
$103$	12.7448	−	7.35823i	1.25579	−	0.725028i	0.972252	+	0.233934i	$0.0751601\pi$
$104$	−5.00256			−0.490542
$105$	−4.27275	−	1.65640i	−0.416977	−	0.161648i
$106$	−1.11204			−0.108011
$107$	4.07900	−	2.35501i	0.394331	−	0.227667i	−0.289704	−	0.957116i	$-0.593557\pi$
$107$	4.07900	−	2.35501i	0.394331	−	0.227667i	0.684035	+	0.729449i	$0.260223\pi$
$108$	1.49383	+	4.97679i	0.143744	+	0.478892i
$109$	−4.31181	+	7.46828i	−0.412997	+	0.715331i	−0.995216	−	0.0977007i	$-0.968851\pi$
$109$	−4.31181	+	7.46828i	−0.412997	+	0.715331i	0.582219	+	0.813032i	$0.302185\pi$
$110$	−2.56776	−	4.44749i	−0.244827	−	0.424052i
$111$	0.0226247	−	0.0879211i	0.00214744	−	0.00834510i
$112$	2.43105	−	1.04402i	0.229713	−	0.0986507i
$113$		−	15.3809i		−	1.44691i	−0.690372	−	0.723455i	$-0.742553\pi$
$113$		−	15.3809i		−	1.44691i	0.690372	−	0.723455i	$-0.257447\pi$
$114$	4.49272	−	1.25179i	0.420782	−	0.117241i
$115$	2.15298	+	1.24302i	0.200766	+	0.115913i
$116$	5.35804	+	3.09347i	0.497482	+	0.287221i
$117$	15.0047	−	0.298163i	1.38719	−	0.0275652i
$118$			13.2616i			1.22083i
$119$	7.96885	+	5.95252i	0.730503	+	0.545667i
$120$	1.67740	+	0.431645i	0.153125	+	0.0394037i
$121$	7.68681	+	13.3139i	0.698801	+	1.21036i
$122$	2.07459	−	3.59330i	0.187825	−	0.325322i
$123$	8.10729	+	7.94779i	0.731010	+	0.716628i
$124$	−4.13446	+	2.38703i	−0.371286	+	0.214362i
$125$	−1.00000			−0.0894427
$126$	−7.22949	+	3.27634i	−0.644055	+	0.291880i
$127$	−1.78518			−0.158409			−0.0792047	−	0.996858i	$-0.525238\pi$
$127$	−1.78518			−0.158409			−0.0792047	+	0.996858i	$0.525238\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−11.6893	−	11.4594i	−1.02919	−	1.00894i
$130$	2.50128	−	4.33235i	0.219377	−	0.379972i
$131$	−1.55132	−	2.68697i	−0.135540	−	0.234761i	0.790264	−	0.612767i	$-0.209943\pi$
$131$	−1.55132	−	2.68697i	−0.135540	−	0.234761i	−0.925803	+	0.378005i	$0.876610\pi$
$132$	−8.61435	−	2.21673i	−0.749783	−	0.192941i
$133$	2.81121	+	6.54604i	0.243763	+	0.567614i
$134$		−	0.896174i		−	0.0774177i
$135$	−5.05694	−	1.19470i	−0.435232	−	0.102824i
$136$	−3.25579	−	1.87973i	−0.279182	−	0.161186i
$137$	−8.44989	−	4.87855i	−0.721923	−	0.416803i	0.0935370	−	0.995616i	$-0.470183\pi$
$137$	−8.44989	−	4.87855i	−0.721923	−	0.416803i	−0.815460	+	0.578813i	$0.803516\pi$
$138$	4.14796	−	1.15573i	0.353098	−	0.0983821i
$139$		−	4.26248i		−	0.361539i	−0.983526	−	0.180769i	$-0.942141\pi$
$139$		−	4.26248i		−	0.361539i	0.983526	−	0.180769i	$-0.0578588\pi$
$140$	−0.311378	+	2.62736i	−0.0263162	+	0.222053i
$141$	−1.32468	+	5.14781i	−0.111558	+	0.433524i
$142$	6.71199	+	11.6255i	0.563258	+	0.975591i
$143$	−12.8454	+	22.2489i	−1.07419	+	1.86054i
$144$	2.56776	−	1.55132i	0.213980	−	0.129277i
$145$	−5.35804	+	3.09347i	−0.444961	+	0.256899i
$146$	−6.98029			−0.577693
$147$	−6.43419	−	10.2762i	−0.530683	−	0.847570i
$148$	−0.0524150			−0.00430849
$149$	7.77014	−	4.48609i	0.636554	−	0.367515i	−0.146732	−	0.989176i	$-0.546875\pi$
$149$	7.77014	−	4.48609i	0.636554	−	0.367515i	0.783286	+	0.621662i	$0.213542\pi$
$150$	−1.21252	+	1.23685i	−0.0990017	+	0.100988i
$151$	−6.61328	+	11.4545i	−0.538181	+	0.932157i	0.460821	+	0.887493i	$0.347555\pi$
$151$	−6.61328	+	11.4545i	−0.538181	+	0.932157i	−0.999002	+	0.0446642i	$0.985778\pi$
$152$	−1.34634	−	2.33193i	−0.109202	−	0.189144i
$153$	9.87748	+	5.44403i	0.798547	+	0.440124i
$154$	1.59909	−	13.4929i	0.128858	−	1.08729i
$155$		−	4.77406i		−	0.383462i
$156$	−2.32562	−	8.34676i	−0.186199	−	0.668276i
$157$	7.41664	+	4.28200i	0.591912	+	0.341741i	0.765853	−	0.643015i	$-0.222317\pi$
$157$	7.41664	+	4.28200i	0.591912	+	0.341741i	−0.173941	+	0.984756i	$0.555650\pi$
$158$	14.5039	+	8.37381i	1.15387	+	0.666185i
$159$	−0.516971	−	1.85543i	−0.0409985	−	0.147145i
$160$		−	1.00000i		−	0.0790569i
$161$	2.59549	+	6.04371i	0.204553	+	0.476311i
$162$	−7.60931	+	4.80609i	−0.597843	+	0.377602i
$163$	−5.53728	−	9.59085i	−0.433713	−	0.751213i	0.563477	−	0.826132i	$-0.309464\pi$
$163$	−5.53728	−	9.59085i	−0.433713	−	0.751213i	−0.997190	+	0.0749190i	$0.976130\pi$
$164$	3.27739	−	5.67661i	0.255921	−	0.443269i
$165$	6.22691	−	6.35188i	0.484765	−	0.494493i
$166$	−1.19273	+	0.688622i	−0.0925737	+	0.0534474i
$167$	2.95799			0.228896			0.114448	−	0.993429i	$-0.463490\pi$
$167$	2.95799			0.228896			0.114448	+	0.993429i	$0.463490\pi$
$168$	2.87211	+	3.57085i	0.221588	+	0.275497i
$169$	−12.0256			−0.925049
$170$	3.25579	−	1.87973i	0.249708	−	0.144169i
$171$	4.17720	+	6.91415i	0.319439	+	0.528738i
$172$	−4.72544	+	8.18470i	−0.360311	+	0.624078i
$173$	10.3708	+	17.9628i	0.788478	+	1.36568i	0.926899	+	0.375311i	$0.122464\pi$
$173$	10.3708	+	17.9628i	0.788478	+	1.36568i	−0.138421	+	0.990374i	$0.544203\pi$
$174$	−2.67056	+	10.3780i	−0.202455	+	0.786753i
$175$	−2.11968	−	1.58334i	−0.160232	−	0.119690i
$176$			5.13552i			0.387105i
$177$	−22.1269	+	6.16512i	−1.66316	+	0.463399i
$178$	4.62555	+	2.67056i	0.346700	+	0.200167i
$179$	−21.2335	−	12.2592i	−1.58707	−	0.916294i	−0.993787	−	0.111298i	$-0.964499\pi$
$179$	−21.2335	−	12.2592i	−1.58707	−	0.916294i	−0.593281	−	0.804996i	$-0.702168\pi$
$180$	0.0596020	+	2.99941i	0.00444247	+	0.223563i
$181$		−	18.6533i		−	1.38649i	−0.720704	−	0.693243i	$-0.756181\pi$
$181$		−	18.6533i		−	1.38649i	0.720704	−	0.693243i	$-0.243819\pi$
$182$	12.1615	−	5.22278i	0.901470	−	0.387138i
$183$	6.95985	+	1.79098i	0.514487	+	0.132393i
$184$	−1.24302	−	2.15298i	−0.0916369	−	0.158720i
$185$	0.0262075	−	0.0453927i	0.00192681	−	0.00333734i
$186$	−5.90481	−	5.78864i	−0.432962	−	0.424444i
$187$	−16.7202	+	9.65341i	−1.22270	+	0.705927i
$188$	3.06892			0.223824
$189$	−8.82745	−	10.5393i	−0.642103	−	0.766619i
$190$	2.69268			0.195347
$191$	−6.29976	+	3.63717i	−0.455835	+	0.263176i	−0.710291	−	0.703908i	$-0.751437\pi$
$191$	−6.29976	+	3.63717i	−0.455835	+	0.263176i	0.254457	+	0.967084i	$0.418103\pi$
$192$	−1.23685	−	1.21252i	−0.0892620	−	0.0875059i
$193$	5.53208	−	9.58185i	0.398208	−	0.689716i	−0.595297	−	0.803506i	$-0.702966\pi$
$193$	5.53208	−	9.58185i	0.398208	−	0.689716i	0.993505	+	0.113789i	$0.0362989\pi$
$194$	0.316804	+	0.548721i	0.0227452	+	0.0393958i
$195$	8.39132	+	2.15933i	0.600915	+	0.154633i
$196$	−4.82004	+	5.07614i	−0.344289	+	0.362582i
$197$		−	8.86701i		−	0.631748i	−0.948801	−	0.315874i	$-0.897702\pi$
$197$		−	8.86701i		−	0.631748i	0.948801	−	0.315874i	$-0.102298\pi$
$198$	−0.306087	−	15.4035i	−0.0217527	−	1.09468i
$199$	16.0911	+	9.29018i	1.14066	+	0.658563i	0.946595	−	0.322425i	$-0.104498\pi$
$199$	16.0911	+	9.29018i	1.14066	+	0.658563i	0.194070	+	0.980988i	$0.437831\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	1.49526	−	0.416619i	0.105468	−	0.0293860i
$202$		−	17.6286i		−	1.24034i
$203$	−16.2553	−	1.92648i	−1.14090	−	0.135212i
$204$	1.62276	−	6.30614i	0.113616	−	0.441518i
$205$	3.27739	+	5.67661i	0.228903	+	0.396472i
$206$	7.35823	−	12.7448i	0.512672	−	0.887974i
$207$	3.85666	+	6.38358i	0.268056	+	0.443689i
$208$	−4.33235	+	2.50128i	−0.300394	+	0.173433i
$209$	−13.8283			−0.956524
$210$	−4.52850	+	0.701891i	−0.312496	+	0.0484351i
$211$	−7.36879			−0.507288			−0.253644	−	0.967298i	$-0.581629\pi$
$211$	−7.36879			−0.507288			−0.253644	+	0.967298i	$0.581629\pi$
$212$	−0.963053	+	0.556019i	−0.0661428	+	0.0381876i
$213$	−16.2768	+	16.6035i	−1.11527	+	1.13765i
$214$	2.35501	−	4.07900i	0.160985	−	0.278834i
$215$	−4.72544	−	8.18470i	−0.322272	−	0.558192i
$216$	3.78209	+	3.56312i	0.257339	+	0.242439i
$217$	7.55898	−	10.1195i	0.513137	−	0.686954i
$218$			8.62362i			0.584065i
$219$	−3.24504	−	11.6466i	−0.219279	−	0.787003i
$220$	−4.44749	−	2.56776i	−0.299850	−	0.173119i
$221$	−16.2873	−	9.40348i	−1.09560	−	0.632547i
$222$	−0.0243670	−	0.0874543i	−0.00163541	−	0.00586955i
$223$		−	5.79472i		−	0.388043i	−0.980997	−	0.194021i	$-0.937847\pi$
$223$		−	5.79472i		−	0.388043i	0.980997	−	0.194021i	$-0.0621531\pi$
$224$	1.58334	−	2.11968i	0.105792	−	0.141627i
$225$	−2.62736	−	1.44809i	−0.175158	−	0.0965391i
$226$	−7.69043	−	13.3202i	−0.511560	−	0.886047i
$227$	5.33902	−	9.24746i	0.354363	−	0.613775i	−0.632645	−	0.774442i	$-0.718031\pi$
$227$	5.33902	−	9.24746i	0.354363	−	0.613775i	0.987009	+	0.160666i	$0.0513643\pi$
$228$	3.26492	−	3.33044i	0.216224	−	0.220564i
$229$	−7.46827	+	4.31181i	−0.493517	+	0.284932i	−0.726032	−	0.687661i	$-0.758638\pi$
$229$	−7.46827	+	4.31181i	−0.493517	+	0.284932i	0.232515	+	0.972593i	$0.425304\pi$
$230$	2.48605			0.163925
$231$	23.2562	−	3.60458i	1.53015	−	0.237164i
$232$	6.18694			0.406192
$233$	−13.9131	+	8.03272i	−0.911476	+	0.526241i	−0.880906	−	0.473292i	$-0.843066\pi$
$233$	−13.9131	+	8.03272i	−0.911476	+	0.526241i	−0.0305704	+	0.999533i	$0.509732\pi$
$234$	12.8454	−	7.76058i	0.839730	−	0.507325i
$235$	−1.53446	+	2.65776i	−0.100097	+	0.173373i
$236$	6.63079	+	11.4849i	0.431628	+	0.747601i
$237$	−7.22904	+	28.0925i	−0.469576	+	1.82481i
$238$	9.87748	+	1.17061i	0.640262	+	0.0758797i
$239$		−	11.0070i		−	0.711981i	−0.934490	−	0.355990i	$-0.884144\pi$
$239$		−	11.0070i		−	0.711981i	0.934490	−	0.355990i	$-0.115856\pi$
$240$	1.66850	−	0.464886i	0.107701	−	0.0300082i
$241$	8.40789	+	4.85430i	0.541600	+	0.312693i	0.745727	−	0.666252i	$-0.232102\pi$
$241$	8.40789	+	4.85430i	0.541600	+	0.312693i	−0.204127	+	0.978944i	$0.565436\pi$
$242$	13.3139	+	7.68681i	0.855853	+	0.494127i
$243$	−11.5564	−	10.4618i	−0.741343	−	0.671126i
$244$		−	4.14918i		−	0.265624i
$245$	−1.98605	−	6.71235i	−0.126884	−	0.428836i
$246$	10.9950	+	2.82934i	0.701017	+	0.180392i
$247$	−6.73514	−	11.6656i	−0.428547	−	0.742265i
$248$	−2.38703	+	4.13446i	−0.151577	+	0.262539i
$249$	−1.70345	−	1.66993i	−0.107951	−	0.105828i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−4.59082			−0.289770			−0.144885	−	0.989449i	$-0.546281\pi$
$251$	−4.59082			−0.289770			−0.144885	+	0.989449i	$0.546281\pi$
$252$	−4.62276	+	6.45214i	−0.291206	+	0.406447i
$253$	−12.7672			−0.802664
$254$	−1.54601	+	0.892591i	−0.0970055	+	0.0560062i
$255$	4.64990	+	4.55842i	0.291188	+	0.285459i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.87132	+	10.1694i	0.366243	+	0.634352i	0.988975	−	0.148084i	$-0.0473105\pi$
$257$	5.87132	+	10.1694i	0.366243	+	0.634352i	−0.622732	+	0.782435i	$0.713977\pi$
$258$	−15.8529	−	4.07943i	−0.986961	−	0.253974i
$259$	0.127424	−	0.0547224i	0.00791772	−	0.00340028i
$260$		−	5.00256i		−	0.310246i
$261$	−18.5571	+	0.368754i	−1.14866	+	0.0228253i
$262$	−2.68697	−	1.55132i	−0.166001	−	0.0958409i
$263$	19.8431	+	11.4564i	1.22358	+	0.706432i	0.965679	−	0.259740i	$-0.0836368\pi$
$263$	19.8431	+	11.4564i	1.22358	+	0.706432i	0.257898	+	0.966172i	$0.416970\pi$
$264$	−8.56861	+	2.38743i	−0.527361	+	0.146936i
$265$		−	1.11204i		−	0.0683120i
$266$	5.70760	+	4.26343i	0.349955	+	0.261408i
$267$	−2.30547	+	8.95922i	−0.141093	+	0.548295i
$268$	−0.448087	−	0.776110i	−0.0273713	−	0.0474084i
$269$	4.06200	−	7.03559i	0.247665	−	0.428968i	−0.715213	−	0.698907i	$-0.753670\pi$
$269$	4.06200	−	7.03559i	0.247665	−	0.428968i	0.962877	+	0.269939i	$0.0870036\pi$
$270$	−4.97679	+	1.49383i	−0.302878	+	0.0909115i
$271$	−9.47446	+	5.47008i	−0.575533	+	0.332284i	−0.759356	−	0.650675i	$-0.774486\pi$
$271$	−9.47446	+	5.47008i	−0.575533	+	0.332284i	0.183823	+	0.982959i	$0.441153\pi$
$272$	−3.75947			−0.227951
$273$	14.3679	+	17.8634i	0.869585	+	1.08114i
$274$	−9.75710			−0.589448
$275$	4.44749	−	2.56776i	0.268194	−	0.154842i
$276$	3.01438	−	3.07487i	0.181444	−	0.185085i
$277$	−2.39144	+	4.14209i	−0.143688	+	0.248874i	−0.928883	−	0.370374i	$-0.879229\pi$
$277$	−2.39144	+	4.14209i	−0.143688	+	0.248874i	0.785195	+	0.619249i	$0.212563\pi$
$278$	−2.13124	−	3.69142i	−0.127823	−	0.221396i
$279$	6.91326	−	12.5432i	0.413886	−	0.750942i
$280$	1.04402	+	2.43105i	0.0623922	+	0.145283i
$281$			21.1040i			1.25896i	0.777018	+	0.629479i	$0.216732\pi$
$281$			21.1040i			1.25896i	−0.777018	+	0.629479i	$0.783268\pi$
$282$	1.42670	+	5.12048i	0.0849585	+	0.304920i
$283$	19.0570	+	11.0026i	1.13282	+	0.654035i	0.944643	−	0.328100i	$-0.106408\pi$
$283$	19.0570	+	11.0026i	1.13282	+	0.654035i	0.188178	+	0.982135i	$0.439742\pi$
$284$	11.6255	+	6.71199i	0.689847	+	0.398283i
$285$	1.25179	+	4.49272i	0.0741495	+	0.266126i
$286$			25.6908i			1.51913i
$287$	−2.04102	+	17.2218i	−0.120477	+	1.01657i
$288$	1.44809	−	2.62736i	0.0853294	−	0.154819i
$289$	1.43321	+	2.48239i	0.0843065	+	0.146023i
$290$	−3.09347	+	5.35804i	−0.181655	+	0.314635i
$291$	−0.768261	+	0.783679i	−0.0450362	+	0.0459401i
$292$	−6.04511	+	3.49014i	−0.353763	+	0.204245i
$293$	11.2905			0.659598			0.329799	−	0.944051i	$-0.393019\pi$
$293$	11.2905			0.659598			0.329799	+	0.944051i	$0.393019\pi$
$294$	−10.7103	−	5.68240i	−0.624637	−	0.331404i
$295$	−13.2616			−0.772119
$296$	−0.0453927	+	0.0262075i	−0.00263840	+	0.00152328i
$297$	25.5584	−	7.67159i	1.48305	−	0.445151i
$298$	4.48609	−	7.77014i	0.259872	−	0.450112i
$299$	−6.21830	−	10.7704i	−0.359614	−	0.622869i
$300$	−0.431645	+	1.67740i	−0.0249211	+	0.0968449i
$301$	2.94280	−	24.8309i	0.169620	−	1.43123i
$302$			13.2266i			0.761103i
$303$	29.4133	−	8.19529i	1.68975	−	0.470807i
$304$	−2.33193	−	1.34634i	−0.133745	−	0.0772178i
$305$	3.59330	+	2.07459i	0.205752	+	0.118791i
$306$	11.2762	−	0.224072i	0.644616	−	0.0128093i
$307$			2.12162i			0.121087i	0.998166	+	0.0605436i	$0.0192834\pi$
$307$			2.12162i			0.121087i	−0.998166	+	0.0605436i	$0.980717\pi$
$308$	−5.36160	−	12.4847i	−0.305505	−	0.711384i
$309$	24.6854	+	6.35229i	1.40431	+	0.361369i
$310$	−2.38703	−	4.13446i	−0.135574	−	0.234822i
$311$	5.50229	−	9.53025i	0.312006	−	0.540411i	−0.666790	−	0.745245i	$-0.732332\pi$
$311$	5.50229	−	9.53025i	0.312006	−	0.540411i	0.978797	+	0.204835i	$0.0656656\pi$
$312$	−6.18743	−	6.06570i	−0.350294	−	0.343402i
$313$	−6.43835	+	3.71718i	−0.363917	+	0.210108i	−0.670798	−	0.741640i	$-0.734048\pi$
$313$	−6.43835	+	3.71718i	−0.363917	+	0.210108i	0.306881	+	0.951748i	$0.400715\pi$
$314$	8.56400			0.483294
$315$	−3.27634	−	7.22949i	−0.184601	−	0.407336i
$316$	16.7476			0.942127
$317$	−3.87512	+	2.23730i	−0.217648	+	0.125659i	−0.604861	−	0.796331i	$-0.706771\pi$
$317$	−3.87512	+	2.23730i	−0.217648	+	0.125659i	0.387213	+	0.921990i	$0.373438\pi$
$318$	−1.37543	−	1.34837i	−0.0771301	−	0.0756126i
$319$	15.8866	−	27.5164i	0.889478	−	1.54062i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	7.90060	+	2.03306i	0.440969	+	0.113474i
$322$	5.26961	+	3.93627i	0.293664	+	0.219360i
$323$		−	10.1230i		−	0.563260i
$324$	−4.18681	+	7.96685i	−0.232600	+	0.442603i
$325$	4.33235	+	2.50128i	0.240315	+	0.138746i
$326$	−9.59085	−	5.53728i	−0.531188	−	0.306681i
$327$	−14.3885	+	4.00900i	−0.795685	+	0.221698i
$328$		−	6.55478i		−	0.361927i
$329$	−7.46070	+	3.20401i	−0.411322	+	0.176643i
$330$	2.21673	−	8.61435i	0.122027	−	0.474204i
$331$	−8.48598	−	14.6981i	−0.466432	−	0.807883i	0.532833	−	0.846220i	$-0.321127\pi$
$331$	−8.48598	−	14.6981i	−0.466432	−	0.807883i	−0.999265	+	0.0383371i	$0.987794\pi$
$332$	−0.688622	+	1.19273i	−0.0377930	+	0.0654595i
$333$	0.134589	−	0.0813125i	0.00737545	−	0.00445590i
$334$	2.56169	−	1.47899i	0.140169	−	0.0809269i
$335$	0.896174			0.0489632
$336$	4.27275	+	1.65640i	0.233097	+	0.0903638i
$337$	30.7045			1.67258			0.836290	−	0.548287i	$-0.184720\pi$
$337$	30.7045			1.67258			0.836290	+	0.548287i	$0.184720\pi$
$338$	−10.4145	+	6.01282i	−0.566475	+	0.327054i
$339$	18.6496	−	19.0238i	1.01291	−	1.03323i
$340$	1.87973	−	3.25579i	0.101943	−	0.176570i
$341$	12.2587	+	21.2326i	0.663844	+	1.14981i
$342$	7.07464	+	3.89923i	0.382553	+	0.210846i
$343$	6.41818	−	17.3726i	0.346549	−	0.938032i
$344$			9.45088i			0.509557i
$345$	1.15573	+	4.14796i	0.0622223	+	0.223319i
$346$	17.9628	+	10.3708i	0.965685	+	0.557538i
$347$	−28.7525	−	16.6003i	−1.54352	−	0.891149i	−0.998613	−	0.0526494i	$-0.983233\pi$
$347$	−28.7525	−	16.6003i	−1.54352	−	0.891149i	−0.544902	−	0.838500i	$-0.683433\pi$
$348$	2.87622	+	10.3229i	0.154181	+	0.553365i
$349$			21.5465i			1.15336i	0.816972	+	0.576678i	$0.195651\pi$
$349$			21.5465i			1.15336i	−0.816972	+	0.576678i	$0.804349\pi$
$350$	−2.62736	−	0.311378i	−0.140439	−	0.0166439i
$351$	18.9201	+	17.8247i	1.00988	+	0.951413i
$352$	2.56776	+	4.44749i	0.136862	+	0.237052i
$353$	−2.75846	+	4.77779i	−0.146818	+	0.254296i	−0.930050	−	0.367434i	$-0.880237\pi$
$353$	−2.75846	+	4.77779i	−0.146818	+	0.254296i	0.783232	+	0.621730i	$0.213570\pi$
$354$	−16.0799	+	16.4026i	−0.854637	+	0.871788i
$355$	−11.6255	+	6.71199i	−0.617018	+	0.356235i
$356$	5.34113			0.283079
$357$	2.63874	+	17.0248i	0.139657	+	0.901045i
$358$	−24.5184			−1.29584
$359$	16.7632	−	9.67826i	0.884730	−	0.510799i	0.0125151	−	0.999922i	$-0.496016\pi$
$359$	16.7632	−	9.67826i	0.884730	−	0.510799i	0.872215	+	0.489122i	$0.162683\pi$
$360$	1.55132	+	2.56776i	0.0817618	+	0.135333i
$361$	−5.87475	+	10.1754i	−0.309197	+	0.535545i
$362$	−9.32664	−	16.1542i	−0.490197	−	0.849046i
$363$	−6.63595	+	25.7878i	−0.348297	+	1.35351i
$364$	7.92078	−	10.6038i	0.415161	−	0.555791i
$365$		−	6.98029i		−	0.365365i
$366$	6.92290	−	1.92890i	0.361866	−	0.100825i
$367$	−12.1526	−	7.01628i	−0.634358	−	0.366247i	0.148080	−	0.988975i	$-0.452691\pi$
$367$	−12.1526	−	7.01628i	−0.634358	−	0.366247i	−0.782438	+	0.622728i	$0.786024\pi$
$368$	−2.15298	−	1.24302i	−0.112232	−	0.0647971i
$369$	0.390678	+	19.6605i	0.0203379	+	1.02348i
$370$		−	0.0524150i		−	0.00272493i
$371$	1.76074	−	2.35716i	0.0914130	−	0.122378i
$372$	−8.00803	−	2.06070i	−0.415197	−	0.106842i
$373$	0.669190	+	1.15907i	0.0346493	+	0.0600144i	0.882830	−	0.469693i	$-0.155635\pi$
$373$	0.669190	+	1.15907i	0.0346493	+	0.0600144i	−0.848181	+	0.529707i	$0.822302\pi$
$374$	−9.65341	+	16.7202i	−0.499166	+	0.864581i
$375$	−1.23685	−	1.21252i	−0.0638707	−	0.0626141i
$376$	2.65776	−	1.53446i	0.137063	−	0.0791336i
$377$	30.9505			1.59403
$378$	−12.9144	−	4.71354i	−0.664247	−	0.242439i
$379$	8.07964			0.415023			0.207512	−	0.978233i	$-0.433464\pi$
$379$	8.07964			0.415023			0.207512	+	0.978233i	$0.433464\pi$
$380$	2.33193	−	1.34634i	0.119625	−	0.0690657i
$381$	−2.20801	−	2.16457i	−0.113120	−	0.110894i
$382$	−3.63717	+	6.29976i	−0.186094	+	0.322324i
$383$	−11.6471	−	20.1734i	−0.595141	−	1.03081i	−0.993527	−	0.113596i	$-0.963763\pi$
$383$	−11.6471	−	20.1734i	−0.595141	−	1.03081i	0.398386	−	0.917218i	$-0.369570\pi$
$384$	−1.67740	−	0.431645i	−0.0855996	−	0.0220273i
$385$	13.4929	+	1.59909i	0.687662	+	0.0814971i
$386$		−	11.0642i		−	0.563151i
$387$	−0.563291	−	28.3470i	−0.0286337	−	1.44096i
$388$	0.548721	+	0.316804i	0.0278571	+	0.0160833i
$389$	10.1748	+	5.87442i	0.515882	+	0.297845i	0.735248	−	0.677798i	$-0.237066\pi$
$389$	10.1748	+	5.87442i	0.515882	+	0.297845i	−0.219366	+	0.975643i	$0.570399\pi$
$390$	8.34676	−	2.32562i	0.422655	−	0.117762i
$391$		−	9.34621i		−	0.472658i
$392$	−1.63621	+	6.80609i	−0.0826409	+	0.343759i
$393$	1.33924	−	5.20438i	0.0675558	−	0.262526i
$394$	−4.43350	−	7.67905i	−0.223357	−	0.386865i
$395$	−8.37381	+	14.5039i	−0.421332	+	0.729769i
$396$	−7.96685	−	13.1868i	−0.400349	−	0.662662i
$397$	14.9142	−	8.61072i	0.748522	−	0.432160i	−0.0766373	−	0.997059i	$-0.524418\pi$
$397$	14.9142	−	8.61072i	0.748522	−	0.432160i	0.825160	+	0.564899i	$0.191085\pi$
$398$	18.5804			0.931349
$399$	−4.46014	+	11.5051i	−0.223286	+	0.575976i
$400$	1.00000			0.0500000
$401$	−7.31712	+	4.22454i	−0.365400	+	0.210964i	−0.671447	−	0.741053i	$-0.734327\pi$
$401$	−7.31712	+	4.22454i	−0.365400	+	0.210964i	0.306047	+	0.952016i	$0.400993\pi$
$402$	1.08663	−	1.10843i	0.0541960	−	0.0552837i
$403$	−11.9413	+	20.6829i	−0.594838	+	1.03029i
$404$	−8.81430	−	15.2668i	−0.438528	−	0.759552i
$405$	−4.80609	−	7.60931i	−0.238816	−	0.378109i
$406$	−15.0408	+	6.45929i	−0.746461	+	0.320569i
$407$			0.269179i			0.0133427i
$408$	−1.74772	−	6.27266i	−0.0865251	−	0.310543i
$409$	−25.2043	−	14.5517i	−1.24627	−	0.719535i	−0.275908	−	0.961184i	$-0.588979\pi$
$409$	−25.2043	−	14.5517i	−1.24627	−	0.719535i	−0.970364	+	0.241649i	$0.922312\pi$
$410$	5.67661	+	3.27739i	0.280348	+	0.161859i
$411$	−4.53594	−	16.2797i	−0.223741	−	0.803018i
$412$		−	14.7165i		−	0.725028i
$413$	−28.1102	−	20.9976i	−1.38321	−	1.03323i
$414$	6.53175	+	3.60001i	0.321018	+	0.176931i
$415$	−0.688622	−	1.19273i	−0.0338031	−	0.0585487i
$416$	−2.50128	+	4.33235i	−0.122635	+	0.212411i
$417$	5.16833	−	5.27205i	0.253094	−	0.258174i
$418$	−11.9757	+	6.91415i	−0.585749	+	0.338182i
$419$	2.07947			0.101589			0.0507944	−	0.998709i	$-0.483825\pi$
$419$	2.07947			0.101589			0.0507944	+	0.998709i	$0.483825\pi$
$420$	−3.57085	+	2.87211i	−0.174240	+	0.140145i
$421$	−32.8371			−1.60038			−0.800190	−	0.599746i	$-0.795268\pi$
$421$	−32.8371			−1.60038			−0.800190	+	0.599746i	$0.795268\pi$
$422$	−6.38156	+	3.68439i	−0.310649	+	0.179354i
$423$	−7.88025	+	4.76087i	−0.383151	+	0.231482i
$424$	−0.556019	+	0.963053i	−0.0270027	+	0.0467700i
$425$	1.87973	+	3.25579i	0.0911804	+	0.157929i
$426$	−5.79440	+	22.5174i	−0.280740	+	1.09097i
$427$	4.33183	+	10.0869i	0.209632	+	0.488138i
$428$		−	4.71002i		−	0.227667i
$429$	−42.8650	+	11.9433i	−2.06954	+	0.576627i
$430$	−8.18470	−	4.72544i	−0.394701	−	0.227881i
$431$	7.57956	+	4.37606i	0.365094	+	0.210787i	0.671313	−	0.741174i	$-0.265731\pi$
$431$	7.57956	+	4.37606i	0.365094	+	0.210787i	−0.306219	+	0.951961i	$0.599064\pi$
$432$	5.05694	+	1.19470i	0.243302	+	0.0574802i
$433$		−	12.3440i		−	0.593214i	−0.955000	−	0.296607i	$-0.904145\pi$
$433$		−	12.3440i		−	0.593214i	0.955000	−	0.296607i	$-0.0958552\pi$
$434$	1.48654	−	12.5432i	0.0713561	−	0.602093i
$435$	−10.3780	−	2.67056i	−0.497586	−	0.128044i
$436$	4.31181	+	7.46828i	0.206498	+	0.357666i
$437$	3.34706	−	5.79728i	0.160112	−	0.277321i
$438$	−8.63358	−	8.46372i	−0.412528	−	0.404412i
$439$	−9.72433	+	5.61435i	−0.464117	+	0.267958i	−0.713774	−	0.700376i	$-0.753016\pi$
$439$	−9.72433	+	5.61435i	−0.464117	+	0.267958i	0.249657	+	0.968334i	$0.419682\pi$
$440$	−5.13552			−0.244827
$441$	4.50200	−	20.5118i	0.214381	−	0.976750i
$442$	−18.8070			−0.894556
$443$	28.9532	−	16.7161i	1.37561	−	0.794208i	0.383981	−	0.923341i	$-0.374553\pi$
$443$	28.9532	−	16.7161i	1.37561	−	0.794208i	0.991627	+	0.129133i	$0.0412195\pi$
$444$	−0.0648296	−	0.0635541i	−0.00307667	−	0.00301614i
$445$	−2.67056	+	4.62555i	−0.126597	+	0.219272i
$446$	−2.89736	−	5.01837i	−0.137194	−	0.237627i
$447$	15.0500	+	3.87280i	0.711839	+	0.183177i
$448$	0.311378	−	2.62736i	0.0147112	−	0.124131i
$449$			27.8343i			1.31358i	0.754073	+	0.656791i	$0.228086\pi$
$449$			27.8343i			1.31358i	−0.754073	+	0.656791i	$0.771914\pi$
$450$	−2.99941	+	0.0596020i	−0.141393	+	0.00280966i
$451$	−29.1524	−	16.8311i	−1.37273	−	0.792547i
$452$	−13.3202	−	7.69043i	−0.626530	−	0.361727i
$453$	−22.0685	+	6.14884i	−1.03687	+	0.288898i
$454$		−	10.6780i		−	0.501146i
$455$	5.22278	+	12.1615i	0.244848	+	0.570140i
$456$	1.16228	−	4.51670i	0.0544288	−	0.211514i
$457$	−14.1611	−	24.5277i	−0.662427	−	1.14736i	−0.979976	−	0.199115i	$-0.936193\pi$
$457$	−14.1611	−	24.5277i	−0.662427	−	1.14736i	0.317550	−	0.948242i	$-0.397140\pi$
$458$	−4.31181	+	7.46827i	−0.201477	+	0.348969i
$459$	5.61599	+	18.7101i	0.262132	+	0.873312i
$460$	2.15298	−	1.24302i	0.100383	−	0.0579563i
$461$	−35.5758			−1.65693			−0.828466	−	0.560040i	$-0.810786\pi$
$461$	−35.5758			−1.65693			−0.828466	+	0.560040i	$0.810786\pi$
$462$	18.3382	−	14.7498i	0.853171	−	0.686222i
$463$	18.8371			0.875434			0.437717	−	0.899113i	$-0.355787\pi$
$463$	18.8371			0.875434			0.437717	+	0.899113i	$0.355787\pi$
$464$	5.35804	−	3.09347i	0.248741	−	0.143611i
$465$	5.78864	−	5.90481i	0.268442	−	0.273829i
$466$	−8.03272	+	13.9131i	−0.372109	+	0.644511i
$467$	6.28462	+	10.8853i	0.290818	+	0.503711i	0.974003	−	0.226534i	$-0.0727394\pi$
$467$	6.28462	+	10.8853i	0.290818	+	0.503711i	−0.683186	+	0.730245i	$0.739406\pi$
$468$	7.24415	−	13.1436i	0.334861	−	0.607561i
$469$	1.89960	+	1.41895i	0.0877153	+	0.0655211i
$470$			3.06892i			0.141559i
$471$	3.98128	+	14.2890i	0.183448	+	0.658403i
$472$	11.4849	+	6.63079i	0.528634	+	0.305207i
$473$	42.0327	+	24.2676i	1.93267	+	1.11583i
$474$	7.78573	+	27.9434i	0.357611	+	1.28348i
$475$			2.69268i			0.123548i
$476$	9.13946	−	3.92496i	0.418906	−	0.179900i
$477$	1.61033	−	2.92173i	0.0737319	−	0.133777i
$478$	−5.50348	−	9.53230i	−0.251723	−	0.435997i
$479$	−10.7038	+	18.5395i	−0.489069	+	0.847093i	−0.999921	−	0.0125762i	$-0.995997\pi$
$479$	−10.7038	+	18.5395i	−0.489069	+	0.847093i	0.510852	+	0.859669i	$0.329330\pi$
$480$	1.21252	−	1.23685i	0.0553436	−	0.0564543i
$481$	−0.227080	+	0.131105i	−0.0103540	+	0.00597786i
$482$	9.70859			0.442214
$483$	−4.11788	+	10.6222i	−0.187370	+	0.483329i
$484$	15.3736			0.698801
$485$	−0.548721	+	0.316804i	−0.0249161	+	0.0143853i
$486$	−15.2390	−	3.28200i	−0.691257	−	0.148875i
$487$	−1.25796	+	2.17886i	−0.0570038	+	0.0987335i	−0.893119	−	0.449820i	$-0.851488\pi$
$487$	−1.25796	+	2.17886i	−0.0570038	+	0.0987335i	0.836115	+	0.548554i	$0.184821\pi$
$488$	−2.07459	−	3.59330i	−0.0939123	−	0.162661i
$489$	4.78028	−	18.5765i	0.216172	−	0.840058i
$490$	−5.07614	−	4.82004i	−0.229317	−	0.217747i
$491$		−	34.7105i		−	1.56646i	−0.621729	−	0.783232i	$-0.713570\pi$
$491$		−	34.7105i		−	1.56646i	0.621729	−	0.783232i	$-0.286430\pi$
$492$	10.9366	−	3.04723i	0.493062	−	0.137380i
$493$	20.1434	+	11.6298i	0.907212	+	0.523779i
$494$	−11.6656	−	6.73514i	−0.524861	−	0.303028i
$495$	15.4035	−	0.306087i	0.692337	−	0.0137576i
$496$			4.77406i			0.214362i
$497$	−35.2697	−	4.17993i	−1.58206	−	0.187496i
$498$	−2.31019	−	0.594481i	−0.103522	−	0.0266393i
$499$	3.07500	+	5.32606i	0.137656	+	0.238427i	0.926609	−	0.376026i	$-0.122710\pi$
$499$	3.07500	+	5.32606i	0.137656	+	0.238427i	−0.788953	+	0.614454i	$0.789376\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	3.65859	+	3.58661i	0.163454	+	0.160238i
$502$	−3.97576	+	2.29541i	−0.177447	+	0.102449i
$503$	5.99378			0.267249			0.133625	−	0.991032i	$-0.457338\pi$
$503$	5.99378			0.267249			0.133625	+	0.991032i	$0.457338\pi$
$504$	−0.777354	+	7.89910i	−0.0346261	+	0.351854i
$505$	17.6286			0.784462
$506$	−11.0567	+	6.38358i	−0.491529	+	0.283785i
$507$	−14.8739	−	14.5813i	−0.660574	−	0.647578i
$508$	−0.892591	+	1.54601i	−0.0396023	+	0.0685933i
$509$	−7.71953	−	13.3706i	−0.342162	−	0.592642i	0.642672	−	0.766142i	$-0.277826\pi$
$509$	−7.71953	−	13.3706i	−0.342162	−	0.592642i	−0.984834	+	0.173499i	$0.944493\pi$
$510$	6.30614	+	1.62276i	0.279241	+	0.0718568i
$511$	11.0522	−	14.7959i	0.488920	−	0.654534i
$512$			1.00000i			0.0441942i
$513$	−3.21695	+	13.6167i	−0.142032	+	0.601193i
$514$	10.1694	+	5.87132i	0.448554	+	0.258973i
$515$	12.7448	+	7.35823i	0.561604	+	0.324242i
$516$	−15.7688	+	4.39358i	−0.694181	+	0.193417i
$517$		−	15.7605i		−	0.693146i
$518$	0.0829910	−	0.111103i	0.00364641	−	0.00488158i
$519$	−8.95303	+	34.7921i	−0.392994	+	1.52720i
$520$	−2.50128	−	4.33235i	−0.109688	−	0.189986i
$521$	21.0358	−	36.4350i	0.921594	−	1.59625i	0.124646	−	0.992201i	$-0.460221\pi$
$521$	21.0358	−	36.4350i	0.921594	−	1.59625i	0.796949	−	0.604047i	$-0.206446\pi$
$522$	−15.8866	+	9.59792i	−0.695337	+	0.420090i
$523$	15.4383	−	8.91333i	0.675071	−	0.389753i	−0.122924	−	0.992416i	$-0.539227\pi$
$523$	15.4383	−	8.91333i	0.675071	−	0.389753i	0.797996	+	0.602663i	$0.205894\pi$
$524$	−3.10264			−0.135540
$525$	−0.701891	−	4.52850i	−0.0306330	−	0.197640i
$526$	22.9128			0.999046
$527$	−15.5434	+	8.97396i	−0.677080	+	0.390912i
$528$	−6.22691	+	6.35188i	−0.270992	+	0.276430i
$529$	−8.40979	+	14.5662i	−0.365643	+	0.633312i
$530$	−0.556019	−	0.963053i	−0.0241519	−	0.0418324i
$531$	−34.8430	−	19.2039i	−1.51206	−	0.833379i
$532$	7.07464	+	0.838440i	0.306725	+	0.0363510i
$533$		−	32.7907i		−	1.42032i
$534$	2.48301	+	8.91165i	0.107450	+	0.385645i
$535$	4.07900	+	2.35501i	0.176350	+	0.101816i
$536$	−0.776110	−	0.448087i	−0.0335228	−	0.0193544i
$537$	−11.3982	−	40.9088i	−0.491870	−	1.76534i
$538$		−	8.12400i		−	0.350251i
$539$	26.0686	+	24.7534i	1.12286	+	1.06621i
$540$	−3.56312	+	3.78209i	−0.153332	+	0.162755i
$541$	17.7195	+	30.6912i	0.761823	+	1.31952i	0.941910	+	0.335865i	$0.109029\pi$
$541$	17.7195	+	30.6912i	0.761823	+	1.31952i	−0.180087	+	0.983651i	$0.557638\pi$
$542$	−5.47008	+	9.47446i	−0.234960	+	0.406963i
$543$	22.6174	−	23.0713i	0.970606	−	0.990085i
$544$	−3.25579	+	1.87973i	−0.139591	+	0.0805929i
$545$	−8.62362			−0.369395
$546$	21.3747	+	8.28623i	0.914752	+	0.354618i
$547$	33.9313			1.45080			0.725399	−	0.688329i	$-0.241655\pi$
$547$	33.9313			1.45080			0.725399	+	0.688329i	$0.241655\pi$
$548$	−8.44989	+	4.87855i	−0.360962	+	0.208401i
$549$	6.43671	+	10.6541i	0.274712	+	0.454706i
$550$	2.56776	−	4.44749i	0.109490	−	0.189642i
$551$	8.32971	+	14.4275i	0.354857	+	0.614631i
$552$	1.07309	−	4.17010i	0.0456738	−	0.177491i
$553$	−40.7144	+	17.4849i	−1.73135	+	0.743532i
$554$			4.78288i			0.203205i
$555$	0.0874543	−	0.0243670i	0.00371223	−	0.00103432i
$556$	−3.69142	−	2.13124i	−0.156551	−	0.0903847i
$557$	5.87408	+	3.39140i	0.248893	+	0.143698i	0.619257	−	0.785188i	$-0.287434\pi$
$557$	5.87408	+	3.39140i	0.248893	+	0.143698i	−0.370364	+	0.928887i	$0.620767\pi$
$558$	−0.284544	−	14.3194i	−0.0120457	−	0.606187i
$559$			47.2786i			1.99967i
$560$	2.11968	+	1.58334i	0.0895726	+	0.0669085i
$561$	−32.3853	−	8.33370i	−1.36731	−	0.351849i
$562$	10.5520	+	18.2766i	0.445109	+	0.770951i
$563$	9.74586	−	16.8803i	0.410739	−	0.711421i	−0.584232	−	0.811587i	$-0.698604\pi$
$563$	9.74586	−	16.8803i	0.410739	−	0.711421i	0.994971	+	0.100166i	$0.0319374\pi$
$564$	3.79579	+	3.72111i	0.159832	+	0.156687i
$565$	13.3202	−	7.69043i	0.560386	−	0.323539i
$566$	22.0051			0.924944
$567$	1.86080	−	23.7389i	0.0781462	−	0.996942i
$568$	13.4240			0.563258
$569$	24.4915	−	14.1402i	1.02674	−	0.592788i	0.110690	−	0.993855i	$-0.464694\pi$
$569$	24.4915	−	14.1402i	1.02674	−	0.592788i	0.916049	+	0.401067i	$0.131361\pi$
$570$	3.33044	+	3.26492i	0.139497	+	0.136752i
$571$	9.87150	−	17.0979i	0.413110	−	0.715527i	−0.582118	−	0.813104i	$-0.697776\pi$
$571$	9.87150	−	17.0979i	0.413110	−	0.715527i	0.995228	+	0.0975773i	$0.0311093\pi$
$572$	12.8454	+	22.2489i	0.537093	+	0.930272i
$573$	−12.2020	−	3.13993i	−0.509746	−	0.131173i
$574$	6.84333	+	15.9350i	0.285635	+	0.665115i
$575$			2.48605i			0.103675i
$576$	−0.0596020	−	2.99941i	−0.00248342	−	0.124975i
$577$	−17.3952	−	10.0431i	−0.724172	−	0.418101i	0.0921142	−	0.995748i	$-0.470638\pi$
$577$	−17.3952	−	10.0431i	−0.724172	−	0.418101i	−0.816286	+	0.577647i	$0.803971\pi$
$578$	2.48239	+	1.43321i	0.103254	+	0.0596137i
$579$	18.4605	−	5.14357i	0.767193	−	0.213760i
$580$			6.18694i			0.256899i
$581$	0.428843	−	3.61852i	0.0177914	−	0.150122i
$582$	−0.273494	+	1.06282i	−0.0113367	+	0.0440551i
$583$	2.85545	+	4.94579i	0.118261	+	0.204833i
$584$	−3.49014	+	6.04511i	−0.144423	+	0.250148i
$585$	7.76058	+	12.8454i	0.320861	+	0.531092i
$586$	9.77786	−	5.64525i	0.403920	−	0.233203i
$587$	−31.1052			−1.28385			−0.641925	−	0.766767i	$-0.721864\pi$
$587$	−31.1052			−1.28385			−0.641925	+	0.766767i	$0.721864\pi$
$588$	−12.1166	+	0.434047i	−0.499679	+	0.0178998i
$589$	−12.8550			−0.529681
$590$	−11.4849	+	6.63079i	−0.472824	+	0.272985i
$591$	10.7514	−	10.9672i	0.442254	−	0.451129i
$592$	−0.0262075	+	0.0453927i	−0.00107712	+	0.00186563i
$593$	4.46332	+	7.73070i	0.183287	+	0.317462i	0.942998	−	0.332799i	$-0.107993\pi$
$593$	4.46332	+	7.73070i	0.183287	+	0.317462i	−0.759711	+	0.650261i	$0.774660\pi$
$594$	18.2985	−	19.4230i	0.750795	−	0.796936i
$595$	−1.17061	+	9.87748i	−0.0479905	+	0.404937i
$596$		−	8.97218i		−	0.367515i
$597$	8.63774	+	31.0013i	0.353519	+	1.26880i
$598$	−10.7704	−	6.21830i	−0.440435	−	0.254285i
$599$	−4.30419	−	2.48502i	−0.175864	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$599$	−4.30419	−	2.48502i	−0.175864	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$600$	0.464886	+	1.66850i	0.0189789	+	0.0681161i
$601$			25.0660i			1.02246i	0.859442	+	0.511232i	$0.170811\pi$
$601$			25.0660i			1.02246i	−0.859442	+	0.511232i	$0.829189\pi$
$602$	−9.86692	−	22.9756i	−0.402146	−	0.936415i
$603$	2.35458	+	1.29774i	0.0958858	+	0.0528480i
$604$	6.61328	+	11.4545i	0.269091	+	0.466079i
$605$	−7.68681	+	13.3139i	−0.312513	+	0.541289i
$606$	21.3750	−	21.8040i	0.868300	−	0.885725i
$607$	−20.0866	+	11.5970i	−0.815291	+	0.470709i	−0.848790	−	0.528730i	$-0.822668\pi$
$607$	−20.0866	+	11.5970i	−0.815291	+	0.470709i	0.0334986	+	0.999439i	$0.489335\pi$
$608$	−2.69268			−0.109202
$609$	−17.7695	−	22.0926i	−0.720058	−	0.895239i
$610$	4.14918			0.167995
$611$	13.2956	−	7.67622i	0.537883	−	0.310547i
$612$	9.65341	−	5.83214i	0.390216	−	0.235750i
$613$	−2.15278	+	3.72873i	−0.0869500	+	0.150602i	−0.906221	−	0.422805i	$-0.861045\pi$
$613$	−2.15278	+	3.72873i	−0.0869500	+	0.150602i	0.819270	+	0.573407i	$0.194379\pi$
$614$	1.06081	+	1.83737i	0.0428108	+	0.0741504i
$615$	−2.82934	+	10.9950i	−0.114090	+	0.443362i
$616$	−10.8856	−	8.13130i	−0.438595	−	0.327619i
$617$			36.2107i			1.45779i	0.684626	+	0.728895i	$0.259966\pi$
$617$			36.2107i			1.45779i	−0.684626	+	0.728895i	$0.740034\pi$
$618$	24.5544	−	6.84147i	0.987722	−	0.275204i
$619$	17.5269	+	10.1191i	0.704464	+	0.406723i	0.809008	−	0.587798i	$-0.200005\pi$
$619$	17.5269	+	10.1191i	0.704464	+	0.406723i	−0.104544	+	0.994520i	$0.533338\pi$
$620$	−4.13446	−	2.38703i	−0.166044	−	0.0958655i
$621$	−2.97009	+	12.5718i	−0.119186	+	0.504489i
$622$		−	11.0046i		−	0.441244i
$623$	−12.9846	+	5.57625i	−0.520215	+	0.223408i
$624$	−8.39132	−	2.15933i	−0.335922	−	0.0864425i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.71718	+	6.43835i	−0.148569	+	0.257328i
$627$	−17.1036	−	16.7671i	−0.683050	−	0.669612i
$628$	7.41664	−	4.28200i	0.295956	−	0.170870i
$629$	−0.197052			−0.00785699
$630$	−6.45214	−	4.62276i	−0.257059	−	0.184175i
$631$	−16.1847			−0.644304			−0.322152	−	0.946688i	$-0.604406\pi$
$631$	−16.1847			−0.644304			−0.322152	+	0.946688i	$0.604406\pi$
$632$	14.5039	−	8.37381i	0.576933	−	0.333092i
$633$	−9.11410	−	8.93479i	−0.362253	−	0.355126i
$634$	−2.23730	+	3.87512i	−0.0888545	+	0.153901i
$635$	−0.892591	−	1.54601i	−0.0354214	−	0.0613517i
$636$	−1.86534	−	0.480006i	−0.0739654	−	0.0190335i
$637$	−8.18523	+	34.0479i	−0.324311	+	1.34903i
$638$		−	31.7732i		−	1.25791i
$639$	−40.2640	+	0.800096i	−1.59282	+	0.0316513i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−5.57645	−	3.21957i	−0.220257	−	0.127165i	0.385812	−	0.922577i	$-0.373921\pi$
$641$	−5.57645	−	3.21957i	−0.220257	−	0.127165i	−0.606069	+	0.795412i	$0.707255\pi$
$642$	7.85865	−	2.18962i	0.310156	−	0.0864174i
$643$			35.5764i			1.40299i	0.712672	+	0.701497i	$0.247485\pi$
$643$			35.5764i			1.40299i	−0.712672	+	0.701497i	$0.752515\pi$
$644$	6.53175	+	0.774100i	0.257387	+	0.0305038i
$645$	4.07943	−	15.8529i	0.160627	−	0.624209i
$646$	−5.06151	−	8.76679i	−0.199142	−	0.344925i
$647$	−6.85590	+	11.8748i	−0.269533	+	0.466845i	−0.968741	−	0.248073i	$-0.920203\pi$
$647$	−6.85590	+	11.8748i	−0.269533	+	0.466845i	0.699208	+	0.714918i	$0.253536\pi$
$648$	0.357541	+	8.99290i	0.0140455	+	0.353274i
$649$	58.9808	−	34.0526i	2.31520	−	1.33668i
$650$	5.00256			0.196217
$651$	21.6194	−	3.35087i	0.847330	−	0.131331i
$652$	−11.0746			−0.433713
$653$	−1.61145	+	0.930370i	−0.0630608	+	0.0364082i	−0.531199	−	0.847247i	$-0.678258\pi$
$653$	−1.61145	+	0.930370i	−0.0630608	+	0.0364082i	0.468138	+	0.883655i	$0.344925\pi$
$654$	−10.4563	+	10.6661i	−0.408873	+	0.417079i
$655$	1.55132	−	2.68697i	0.0606151	−	0.104988i
$656$	−3.27739	−	5.67661i	−0.127961	−	0.221634i
$657$	10.1081	−	18.3398i	0.394353	−	0.715502i
$658$	−4.85915	+	6.50511i	−0.189429	+	0.253595i
$659$			13.8786i			0.540633i	0.962771	+	0.270317i	$0.0871284\pi$
$659$			13.8786i			0.540633i	−0.962771	+	0.270317i	$0.912872\pi$
$660$	−2.38743	−	8.56861i	−0.0929307	−	0.333533i
$661$	19.0521	+	10.9997i	0.741041	+	0.427840i	0.822448	−	0.568841i	$-0.192608\pi$
$661$	19.0521	+	10.9997i	0.741041	+	0.427840i	−0.0814067	+	0.996681i	$0.525941\pi$
$662$	−14.6981	−	8.48598i	−0.571260	−	0.329817i
$663$	−8.74309	−	31.3794i	−0.339553	−	1.21867i
$664$			1.37724i			0.0534474i
$665$	−4.26343	+	5.70760i	−0.165329	+	0.221331i
$666$	0.0759015	−	0.137713i	0.00294112	−	0.00533628i
$667$	7.69051	+	13.3203i	0.297778	+	0.515766i
$668$	1.47899	−	2.56169i	0.0572240	−	0.0991148i
$669$	7.02620	−	7.16720i	0.271648	−	0.277100i
$670$	0.776110	−	0.448087i	0.0299837	−	0.0173111i
$671$	−21.3082			−0.822595
$672$	4.52850	−	0.701891i	0.174691	−	0.0270760i
$673$	13.4735			0.519366			0.259683	−	0.965694i	$-0.416382\pi$
$673$	13.4735			0.519366			0.259683	+	0.965694i	$0.416382\pi$
$674$	26.5909	−	15.3523i	1.02424	−	0.591347i
$675$	−1.49383	−	4.97679i	−0.0574975	−	0.191557i
$676$	−6.01282	+	10.4145i	−0.231262	+	0.400558i
$677$	−0.639271	−	1.10725i	−0.0245692	−	0.0425551i	0.853479	−	0.521127i	$-0.174488\pi$
$677$	−0.639271	−	1.10725i	−0.0245692	−	0.0425551i	−0.878049	+	0.478572i	$0.841155\pi$
$678$	6.63908	−	25.7999i	0.254972	−	0.990839i
$679$	−1.66472	−	0.197292i	−0.0638860	−	0.00757136i
$680$		−	3.75947i		−	0.144169i
$681$	17.8163	−	4.96407i	0.682721	−	0.190224i
$682$	21.2326	+	12.2587i	0.813039	+	0.469409i
$683$	−34.6622	−	20.0122i	−1.32631	−	0.765747i	−0.341585	−	0.939851i	$-0.610964\pi$
$683$	−34.6622	−	20.0122i	−1.32631	−	0.765747i	−0.984727	+	0.174104i	$0.944297\pi$
$684$	8.07643	−	0.160489i	0.308810	−	0.00613644i
$685$		−	9.75710i		−	0.372799i
$686$	−3.12799	−	18.2542i	−0.119427	−	0.696948i
$687$	−14.4653	−	3.72234i	−0.551885	−	0.142016i
$688$	4.72544	+	8.18470i	0.180156	+	0.312039i
$689$	−2.78152	+	4.81774i	−0.105968	+	0.183541i
$690$	3.07487	+	3.01438i	0.117058	+	0.114755i
$691$	21.6787	−	12.5162i	0.824696	−	0.476138i	−0.0273375	−	0.999626i	$-0.508703\pi$
$691$	21.6787	−	12.5162i	0.824696	−	0.476138i	0.852033	+	0.523488i	$0.175370\pi$
$692$	20.7416			0.788478
$693$	33.1351	+	23.7403i	1.25870	+	0.901819i
$694$	−33.2005			−1.26027
$695$	3.69142	−	2.13124i	0.140023	−	0.0808425i
$696$	7.65232	+	7.50177i	0.290060	+	0.284354i
$697$	12.3212	−	21.3410i	0.466700	−	0.808348i
$698$	10.7732	+	18.6598i	0.407773	+	0.706283i
$699$	−26.9482	−	6.93458i	−1.01928	−	0.262290i
$700$	−2.43105	+	1.04402i	−0.0918852	+	0.0394603i
$701$		−	7.09535i		−	0.267988i	−0.990982	−	0.133994i	$-0.957220\pi$
$701$		−	7.09535i		−	0.267988i	0.990982	−	0.133994i	$-0.0427802\pi$
$702$	25.2977	+	5.97658i	0.954800	+	0.225572i
$703$	−0.122228	−	0.0705683i	−0.00460991	−	0.00266153i
$704$	4.44749	+	2.56776i	0.167621	+	0.0967762i
$705$	−5.12048	+	1.42670i	−0.192848	+	0.0537325i
$706$			5.51692i			0.207632i
$707$	37.3669	+	27.9121i	1.40533	+	1.04974i
$708$	−5.72430	+	22.2450i	−0.215132	+	0.836019i
$709$	−13.9611	−	24.1814i	−0.524320	−	0.908150i	−0.999599	−	0.0283143i	$-0.990986\pi$
$709$	−13.9611	−	24.1814i	−0.524320	−	0.908150i	0.475279	−	0.879835i	$-0.342347\pi$
$710$	−6.71199	+	11.6255i	−0.251896	+	0.436298i
$711$	−43.0039	+	25.9809i	−1.61277	+	0.974361i
$712$	4.62555	−	2.67056i	0.173350	−	0.100084i
$713$	−11.8685			−0.444481
$714$	10.7976	+	13.4245i	0.404090	+	0.502399i
$715$	−25.6908			−0.960781
$716$	−21.2335	+	12.2592i	−0.793534	+	0.458147i
$717$	13.3461	−	13.6140i	0.498420	−	0.508423i
$718$	9.67826	−	16.7632i	0.361190	−	0.625599i
$719$	−12.0025	−	20.7889i	−0.447618	−	0.775296i	0.550613	−	0.834761i	$-0.314394\pi$
$719$	−12.0025	−	20.7889i	−0.447618	−	0.775296i	−0.998230	+	0.0594644i	$0.981061\pi$
$720$	2.62736	+	1.44809i	0.0979161	+	0.0539670i
$721$	15.3643	+	35.7765i	0.572196	+	1.33239i
$722$			11.7495i			0.437271i
$723$	4.51339	+	16.1988i	0.167855	+	0.602438i
$724$	−16.1542	−	9.32664i	−0.600366	−	0.346622i
$725$	−5.35804	−	3.09347i	−0.198993	−	0.114889i
$726$	7.14698	+	25.6508i	0.265249	+	0.951991i
$727$			12.3007i			0.456206i	0.973637	+	0.228103i	$0.0732523\pi$
$727$			12.3007i			0.456206i	−0.973637	+	0.228103i	$0.926748\pi$
$728$	1.55769	−	13.1436i	0.0577318	−	0.487133i
$729$	−1.60841	−	26.9521i	−0.0595706	−	0.998224i
$730$	−3.49014	−	6.04511i	−0.129176	−	0.223739i
$731$	−17.7651	+	30.7701i	−0.657067	+	1.13807i
$732$	5.03096	−	5.13192i	0.185949	−	0.189681i
$733$	−18.6720	+	10.7803i	−0.689665	+	0.398178i	−0.803486	−	0.595323i	$-0.797024\pi$
$733$	−18.6720	+	10.7803i	−0.689665	+	0.398178i	0.113822	+	0.993501i	$0.463691\pi$
$734$	−14.0326			−0.517951
$735$	5.68240	−	10.7103i	0.209598	−	0.395055i
$736$	−2.48605			−0.0916369
$737$	−3.98573	+	2.30116i	−0.146816	+	0.0847644i
$738$	10.1686	+	16.8311i	0.374310	+	0.619562i
$739$	−0.411063	+	0.711982i	−0.0151212	+	0.0261907i	−0.873487	−	0.486847i	$-0.838147\pi$
$739$	−0.411063	+	0.711982i	−0.0151212	+	0.0261907i	0.858366	+	0.513038i	$0.171480\pi$
$740$	−0.0262075	−	0.0453927i	−0.000963407	−	0.00166867i
$741$	5.81439	−	22.5951i	0.213597	−	0.830052i
$742$	0.346264	−	2.92173i	0.0127118	−	0.107260i
$743$		−	10.6722i		−	0.391526i	−0.980651	−	0.195763i	$-0.937282\pi$
$743$		−	10.6722i		−	0.391526i	0.980651	−	0.195763i	$-0.0627184\pi$
$744$	−7.96551	+	2.21939i	−0.292030	+	0.0813670i
$745$	7.77014	+	4.48609i	0.284676	+	0.164358i
$746$	1.15907	+	0.669190i	0.0424366	+	0.0245008i
$747$	−0.0820865	−	4.13092i	−0.00300339	−	0.151142i
$748$			19.3068i			0.705927i
$749$	4.91736	+	11.4503i	0.179676	+	0.418385i
$750$	−1.67740	−	0.431645i	−0.0612501	−	0.0157615i
$751$	13.4066	+	23.2209i	0.489213	+	0.847342i	0.999923	−	0.0124115i	$-0.00395079\pi$
$751$	13.4066	+	23.2209i	0.489213	+	0.847342i	−0.510710	+	0.859753i	$0.670617\pi$
$752$	1.53446	−	2.65776i	0.0559559	−	0.0969185i
$753$	−5.67816	−	5.56644i	−0.206923	−	0.202853i
$754$	26.8040	−	15.4753i	0.976142	−	0.563576i
$755$	−13.2266			−0.481364
$756$	−13.5410	+	2.37517i	−0.492481	+	0.0863839i
$757$	−14.2502			−0.517934			−0.258967	−	0.965886i	$-0.583382\pi$
$757$	−14.2502			−0.517934			−0.258967	+	0.965886i	$0.583382\pi$
$758$	6.99717	−	4.03982i	0.254149	−	0.146733i
$759$	−15.7911	−	15.4804i	−0.573180	−	0.561903i
$760$	1.34634	−	2.33193i	0.0488368	−	0.0845878i
$761$	13.6118	+	23.5763i	0.493428	+	0.854642i	0.999971	−	0.00757262i	$-0.00241046\pi$
$761$	13.6118	+	23.5763i	0.493428	+	0.854642i	−0.506544	+	0.862214i	$0.669077\pi$
$762$	−2.99447	−	0.770566i	−0.108478	−	0.0279147i
$763$	−18.2793	−	13.6542i	−0.661754	−	0.494314i
$764$			7.27434i			0.263176i
$765$	0.224072	+	11.2762i	0.00810133	+	0.407691i
$766$	−20.1734	−	11.6471i	−0.728896	−	0.420828i
$767$	57.4538	+	33.1709i	2.07453	+	1.19773i
$768$	−1.66850	+	0.464886i	−0.0602067	+	0.0167751i
$769$		−	6.31431i		−	0.227700i	−0.993498	−	0.113850i	$-0.963682\pi$
$769$		−	6.31431i		−	0.227700i	0.993498	−	0.113850i	$-0.0363183\pi$
$770$	12.4847	−	5.36160i	0.449919	−	0.193218i
$771$	−5.06866	+	19.6972i	−0.182543	+	0.709376i
$772$	−5.53208	−	9.58185i	−0.199104	−	0.344858i
$773$	21.2084	−	36.7341i	0.762814	−	1.32123i	−0.178580	−	0.983925i	$-0.557150\pi$
$773$	21.2084	−	36.7341i	0.762814	−	1.32123i	0.941395	−	0.337308i	$-0.109516\pi$
$774$	−14.6613	−	24.2676i	−0.526991	−	0.872282i
$775$	4.13446	−	2.38703i	0.148514	−	0.0857447i
$776$	0.633608			0.0227452
$777$	0.223956	+	0.0868200i	0.00803437	+	0.00311465i
$778$	11.7488			0.421216
$779$	15.2853	−	8.82495i	0.547652	−	0.316187i
$780$	6.06570	−	6.18743i	0.217187	−	0.221545i
$781$	34.4696	−	59.7031i	1.23342	−	2.13634i
$782$	−4.67310	−	8.09405i	−0.167110	−	0.289443i
$783$	−23.3995	−	22.0448i	−0.836232	−	0.787816i
$784$	1.98605	+	6.71235i	0.0709302	+	0.239727i
$785$			8.56400i			0.305662i
$786$	−1.44237	−	5.17675i	−0.0514478	−	0.184648i
$787$	−34.5667	−	19.9571i	−1.23217	−	0.711393i	−0.264687	−	0.964334i	$-0.585269\pi$
$787$	−34.5667	−	19.9571i	−1.23217	−	0.711393i	−0.967482	+	0.252941i	$0.918602\pi$
$788$	−7.67905	−	4.43350i	−0.273555	−	0.157937i
$789$	10.6518	+	38.2300i	0.379216	+	1.36102i
$790$			16.7476i			0.595854i
$791$	40.4111	+	4.78926i	1.43685	+	0.170287i
$792$	−13.4929	−	7.43669i	−0.479449	−	0.264251i
$793$	−10.3783	−	17.9757i	−0.368543	−	0.638336i
$794$	8.61072	−	14.9142i	0.305583	−	0.529285i
$795$	1.34837	−	1.37543i	0.0478216	−	0.0487813i
$796$	16.0911	−	9.29018i	0.570332	−	0.329282i
$797$	−17.5658			−0.622211			−0.311105	−	0.950375i	$-0.600699\pi$
$797$	−17.5658			−0.622211			−0.311105	+	0.950375i	$0.600699\pi$
$798$	1.88997	+	12.1938i	0.0669041	+	0.431656i
$799$	11.5375			0.408167
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−13.7147	+	8.28580i	−0.484587	+	0.292764i
$802$	−4.22454	+	7.31712i	−0.149174	+	0.258377i
$803$	17.9237	+	31.0448i	0.632514	+	1.09555i
$804$	0.386830	−	1.50325i	0.0136424	−	0.0530154i
$805$	−3.93627	+	5.26961i	−0.138735	+	0.185729i
$806$			23.8826i			0.841227i
$807$	13.5549	−	3.77673i	0.477154	−	0.132947i
$808$	−15.2668	−	8.81430i	−0.537085	−	0.310086i
$809$	16.6120	+	9.59095i	0.584047	+	0.337200i	0.762740	−	0.646705i	$-0.223854\pi$
$809$	16.6120	+	9.59095i	0.584047	+	0.337200i	−0.178693	+	0.983905i	$0.557187\pi$
$810$	−7.96685	−	4.18681i	−0.279926	−	0.147109i
$811$		−	45.4972i		−	1.59762i	−0.601582	−	0.798811i	$-0.705463\pi$
$811$		−	45.4972i		−	1.59762i	0.601582	−	0.798811i	$-0.294537\pi$
$812$	−9.79604	+	13.1143i	−0.343774	+	0.460222i
$813$	−18.3511	−	4.72227i	−0.643600	−	0.165617i
$814$	0.134589	+	0.233115i	0.00471735	+	0.00817069i
$815$	5.53728	−	9.59085i	0.193962	−	0.335953i
$816$	−4.64990	−	4.55842i	−0.162779	−	0.159577i
$817$	−22.0388	+	12.7241i	−0.771038	+	0.445159i
$818$	−29.1034			−1.01758
$819$	−3.88876	+	39.5157i	−0.135884	+	1.38079i
$820$	6.55478			0.228903
$821$	−2.21615	+	1.27949i	−0.0773441	+	0.0446546i	−0.538173	−	0.842834i	$-0.680885\pi$
$821$	−2.21615	+	1.27949i	−0.0773441	+	0.0446546i	0.460829	+	0.887489i	$0.347552\pi$
$822$	−12.0681	−	11.8307i	−0.420923	−	0.412641i
$823$	17.7673	−	30.7738i	0.619328	−	1.07271i	−0.370281	−	0.928920i	$-0.620739\pi$
$823$	17.7673	−	30.7738i	0.619328	−	1.07271i	0.989609	−	0.143787i	$-0.0459281\pi$
$824$	−7.35823	−	12.7448i	−0.256336	−	0.443987i
$825$	8.61435	+	2.21673i	0.299913	+	0.0771765i
$826$	−34.8430	−	4.12936i	−1.21234	−	0.143679i
$827$			1.85721i			0.0645814i	0.999479	+	0.0322907i	$0.0102802\pi$
$827$			1.85721i			0.0645814i	−0.999479	+	0.0322907i	$0.989720\pi$
$828$	7.45667	−	0.148173i	0.259137	−	0.00514938i
$829$	−46.4027	−	26.7906i	−1.61163	−	0.930477i	−0.988992	−	0.147970i	$-0.952726\pi$
$829$	−46.4027	−	26.7906i	−1.61163	−	0.930477i	−0.622641	−	0.782507i	$-0.713940\pi$
$830$	−1.19273	−	0.688622i	−0.0414002	−	0.0239024i
$831$	−7.98021	+	2.22349i	−0.276831	+	0.0771320i
$832$			5.00256i			0.173433i
$833$	−18.1208	+	19.0836i	−0.627848	+	0.661207i
$834$	1.83988	−	7.14990i	0.0637098	−	0.247581i
$835$	1.47899	+	2.56169i	0.0511827	+	0.0886510i
$836$	−6.91415	+	11.9757i	−0.239131	+	0.414187i
$837$	23.7595	−	7.13163i	0.821250	−	0.246505i
$838$	1.80088	−	1.03974i	0.0622102	−	0.0359171i
$839$	6.41502			0.221471			0.110736	−	0.993850i	$-0.464679\pi$
$839$	6.41502			0.221471			0.110736	+	0.993850i	$0.464679\pi$
$840$	−1.65640	+	4.27275i	−0.0571511	+	0.147424i
$841$	−9.27817			−0.319937
$842$	−28.4377	+	16.4185i	−0.980029	+	0.565820i
$843$	−25.5889	+	26.1025i	−0.881330	+	0.899017i
$844$	−3.68439	+	6.38156i	−0.126822	+	0.219662i
$845$	−6.01282	−	10.4145i	−0.206847	−	0.358270i
$846$	−4.44406	+	8.06316i	−0.152790	+	0.277217i
$847$	−37.3741	+	16.0504i	−1.28419	+	0.551497i
$848$			1.11204i			0.0381876i
$849$	10.2299	+	36.7155i	0.351088	+	1.26007i
$850$	3.25579	+	1.87973i	0.111673	+	0.0644743i
$851$	−0.112848	−	0.0651531i	−0.00386839	−	0.00223342i
$852$	6.24062	+	22.3979i	0.213800	+	0.767338i
$853$		−	40.7419i		−	1.39498i	−0.716596	−	0.697488i	$-0.754301\pi$
$853$		−	40.7419i		−	1.39498i	0.716596	−	0.697488i	$-0.245699\pi$
$854$	8.79492	+	6.56958i	0.300956	+	0.224806i
$855$	−3.89923	+	7.07464i	−0.133351	+	0.241948i
$856$	−2.35501	−	4.07900i	−0.0804926	−	0.139417i
$857$	−4.03870	+	6.99524i	−0.137959	+	0.238953i	−0.926724	−	0.375743i	$-0.877388\pi$
$857$	−4.03870	+	6.99524i	−0.137959	+	0.238953i	0.788765	+	0.614695i	$0.210721\pi$
$858$	−31.1505	+	31.7757i	−1.06346	+	1.08480i
$859$	−11.3048	+	6.52683i	−0.385715	+	0.222693i	−0.680302	−	0.732932i	$-0.738151\pi$
$859$	−11.3048	+	6.52683i	−0.385715	+	0.222693i	0.294587	+	0.955625i	$0.404818\pi$
$860$	−9.45088			−0.322272
$861$	−23.4062	+	18.8260i	−0.797680	+	0.641590i
$862$	8.75212			0.298098
$863$	−46.9292	+	27.0946i	−1.59749	+	0.922310i	−0.605518	+	0.795831i	$0.707034\pi$
$863$	−46.9292	+	27.0946i	−1.59749	+	0.922310i	−0.991969	+	0.126479i	$0.959632\pi$
$864$	4.97679	−	1.49383i	0.169314	−	0.0508211i
$865$	−10.3708	+	17.9628i	−0.352618	+	0.610753i
$866$	−6.17199	−	10.6902i	−0.209733	−	0.363268i
$867$	−1.23728	+	4.80815i	−0.0420202	+	0.163293i
$868$	−4.98422	−	11.6060i	−0.169176	−	0.393934i
$869$		−	86.0078i		−	2.91762i
$870$	−10.3229	+	2.87622i	−0.349978	+	0.0975129i
$871$	−3.88254	−	2.24158i	−0.131555	−	0.0759532i
$872$	7.46828	+	4.31181i	0.252908	+	0.146016i
$873$	−1.90045	+	0.0377643i	−0.0643204	+	0.00127813i
$874$		−	6.69412i		−	0.226432i
$875$	0.311378	−	2.62736i	0.0105265	−	0.0888211i
$876$	−11.7088	−	3.01301i	−0.395602	−	0.101800i
$877$	9.37226	+	16.2332i	0.316479	+	0.548157i	0.979751	−	0.200221i	$-0.0641661\pi$
$877$	9.37226	+	16.2332i	0.316479	+	0.548157i	−0.663272	+	0.748378i	$0.730833\pi$
$878$	−5.61435	+	9.72433i	−0.189475	+	0.328180i
$879$	13.9647	+	13.6899i	0.471017	+	0.461750i
$880$	−4.44749	+	2.56776i	−0.149925	+	0.0865593i
$881$	36.3542			1.22480			0.612402	−	0.790546i	$-0.290203\pi$
$881$	36.3542			1.22480			0.612402	+	0.790546i	$0.290203\pi$
$882$	−6.35703	−	20.0147i	−0.214052	−	0.673930i
$883$	−22.9059			−0.770845			−0.385422	−	0.922740i	$-0.625944\pi$
$883$	−22.9059			−0.770845			−0.385422	+	0.922740i	$0.625944\pi$
$884$	−16.2873	+	9.40348i	−0.547801	+	0.316273i
$885$	−16.4026	−	16.0799i	−0.551367	−	0.540520i
$886$	16.7161	−	28.9532i	0.561590	−	0.972702i
$887$	−25.9727	−	44.9860i	−0.872077	−	1.51048i	−0.859844	−	0.510557i	$-0.829439\pi$
$887$	−25.9727	−	44.9860i	−0.872077	−	1.51048i	−0.0122334	−	0.999925i	$-0.503894\pi$
$888$	−0.0879211	−	0.0226247i	−0.00295044	−	0.000759235i
$889$	0.555867	−	4.69033i	0.0186432	−	0.157308i
$890$			5.34113i			0.179035i
$891$	40.9139	+	21.5015i	1.37067	+	0.720326i
$892$	−5.01837	−	2.89736i	−0.168028	−	0.0970107i
$893$	7.15648	+	4.13180i	0.239483	+	0.138265i
$894$	14.9701	−	4.17104i	0.500673	−	0.139500i
$895$		−	24.5184i		−	0.819558i
$896$	−1.04402	−	2.43105i	−0.0348783	−	0.0812158i
$897$	5.36821	−	20.8612i	0.179239	−	0.696535i
$898$	13.9171	+	24.1052i	0.464421	+	0.804401i
$899$	14.7684	−	25.5796i	0.492554	−	0.853129i
$900$	−2.56776	+	1.55132i	−0.0855921	+	0.0517107i
$901$	−3.62057	+	2.09033i	−0.120619	+	0.0696391i
$902$	−33.6622			−1.12083
$903$	33.7477	−	27.1439i	1.12305	−	0.903294i
$904$	−15.3809			−0.511560
$905$	16.1542	−	9.32664i	0.536984	−	0.310028i
$906$	−16.0374	+	16.3593i	−0.532808	+	0.543501i
$907$	1.66199	−	2.87864i	0.0551853	−	0.0955838i	−0.837113	−	0.547030i	$-0.815758\pi$
$907$	1.66199	−	2.87864i	0.0551853	−	0.0955838i	0.892298	+	0.451446i	$0.149092\pi$
$908$	−5.33902	−	9.24746i	−0.177182	−	0.306888i
$909$	46.3168	+	25.5277i	1.53623	+	0.846702i
$910$	10.6038	+	7.92078i	0.351513	+	0.262571i
$911$		−	0.497610i		−	0.0164866i	−0.999966	−	0.00824328i	$-0.997376\pi$
$911$		−	0.497610i		−	0.0164866i	0.999966	−	0.00824328i	$-0.00262395\pi$
$912$	−1.25179	−	4.49272i	−0.0414508	−	0.148769i
$913$	6.12529	+	3.53644i	0.202717	+	0.117039i
$914$	−24.5277	−	14.1611i	−0.811304	−	0.468406i
$915$	1.92890	+	6.92290i	0.0637673	+	0.228864i
$916$			8.62361i			0.284932i
$917$	7.54269	−	3.23922i	0.249081	−	0.106969i
$918$	14.2186	+	13.3954i	0.469285	+	0.442114i
$919$	−24.7546	−	42.8762i	−0.816579	−	1.41436i	−0.908189	−	0.418561i	$-0.862535\pi$
$919$	−24.7546	−	42.8762i	−0.816579	−	1.41436i	0.0916101	−	0.995795i	$-0.470799\pi$
$920$	1.24302	−	2.15298i	0.0409813	−	0.0709816i
$921$	−2.57250	+	2.62413i	−0.0847667	+	0.0864679i
$922$	−30.8096	+	17.7879i	−1.01466	+	0.585814i
$923$	67.1543			2.21041
$924$	8.50647	−	21.9428i	0.279842	−	0.721865i
$925$	0.0524150			0.00172339
$926$	16.3134	−	9.41855i	0.536092	−	0.309513i
$927$	22.8300	+	37.7884i	0.749834	+	1.24113i
$928$	3.09347	−	5.35804i	0.101548	−	0.175886i
$929$	−26.4197	−	45.7602i	−0.866802	−	1.50134i	−0.865247	−	0.501346i	$-0.832838\pi$
$929$	−26.4197	−	45.7602i	−0.866802	−	1.50134i	−0.00155503	−	0.999999i	$-0.500495\pi$
$930$	2.06070	−	8.00803i	0.0675731	−	0.262594i
$931$	−18.0742	+	5.34778i	−0.592357	+	0.175266i
$932$			16.0654i			0.526241i
$933$	18.3611	−	5.11587i	0.601116	−	0.167486i
$934$	10.8853	+	6.28462i	0.356177	+	0.205639i
$935$	−16.7202	−	9.65341i	−0.546809	−	0.315700i
$936$	−0.298163	−	15.0047i	−0.00974575	−	0.490445i
$937$			55.7017i			1.81970i	0.414941	+	0.909848i	$0.363802\pi$
$937$			55.7017i			1.81970i	−0.414941	+	0.909848i	$0.636198\pi$
$938$	2.35458	+	0.279049i	0.0768796	+	0.00911127i
$939$	−12.4704	−	3.20901i	−0.406957	−	0.104722i
$940$	1.53446	+	2.65776i	0.0500485	+	0.0866865i
$941$	−0.110773	+	0.191865i	−0.00361110	+	0.00625461i	−0.867825	−	0.496869i	$-0.834483\pi$
$941$	−0.110773	+	0.191865i	−0.00361110	+	0.00625461i	0.864214	+	0.503124i	$0.167816\pi$
$942$	10.5924	+	10.3840i	0.345119	+	0.338329i
$943$	14.1123	−	8.14775i	0.459560	−	0.265327i
$944$	13.2616			0.431628
$945$	4.71354	−	12.9144i	0.153332	−	0.420106i
$946$	48.5352			1.57802
$947$	−15.0194	+	8.67143i	−0.488064	+	0.281784i	−0.723771	−	0.690041i	$-0.757593\pi$
$947$	−15.0194	+	8.67143i	−0.488064	+	0.281784i	0.235707	+	0.971824i	$0.424259\pi$
$948$	20.7143	+	20.3068i	0.672770	+	0.659534i
$949$	−17.4597	+	30.2410i	−0.566765	+	0.981665i
$950$	1.34634	+	2.33193i	0.0436810	+	0.0756577i
$951$	−7.50571	−	1.93144i	−0.243389	−	0.0626312i
$952$	5.95252	−	7.96885i	0.192922	−	0.258272i
$953$			47.2619i			1.53096i	0.643458	+	0.765482i	$0.277499\pi$
$953$			47.2619i			1.53096i	−0.643458	+	0.765482i	$0.722501\pi$
$954$	−0.0662797	−	3.33546i	−0.00214588	−	0.107989i
$955$	−6.29976	−	3.63717i	−0.203855	−	0.117696i
$956$	−9.53230	−	5.50348i	−0.308297	−	0.177995i
$957$	53.0134	−	14.7709i	1.71368	−	0.477475i
$958$			21.4076i			0.691648i
$959$	15.4488	−	20.6819i	0.498869	−	0.667853i
$960$	0.431645	−	1.67740i	0.0139313	−	0.0541380i
$961$	−4.10415	−	7.10860i	−0.132392	−	0.229310i
$962$	−0.131105	+	0.227080i	−0.00422698	+	0.00732135i
$963$	7.30675	+	12.0942i	0.235457	+	0.389730i
$964$	8.40789	−	4.85430i	0.270800	−	0.156346i
$965$	11.0642			0.356168
$966$	1.74493	+	11.2581i	0.0561423	+	0.362223i
$967$	56.9397			1.83106			0.915528	−	0.402254i	$-0.131773\pi$
$967$	56.9397			1.83106			0.915528	+	0.402254i	$0.131773\pi$
$968$	13.3139	−	7.68681i	0.427926	−	0.247063i
$969$	12.2743	−	12.5207i	0.394309	−	0.402222i
$970$	−0.316804	+	0.548721i	−0.0101720	+	0.0176184i
$971$	−0.585122	−	1.01346i	−0.0187775	−	0.0325235i	0.856484	−	0.516174i	$-0.172644\pi$
$971$	−0.585122	−	1.01346i	−0.0187775	−	0.0325235i	−0.875261	+	0.483650i	$0.839311\pi$
$972$	−14.8384	+	4.77723i	−0.475942	+	0.153230i
$973$	11.1991	+	1.32724i	0.359026	+	0.0425494i
$974$			2.51593i			0.0806155i
$975$	2.32562	+	8.34676i	0.0744795	+	0.267310i
$976$	−3.59330	−	2.07459i	−0.115019	−	0.0664060i
$977$	−28.1359	−	16.2443i	−0.900146	−	0.519700i	−0.0228986	−	0.999738i	$-0.507289\pi$
$977$	−28.1359	−	16.2443i	−0.900146	−	0.519700i	−0.877248	+	0.480038i	$0.840623\pi$
$978$	−5.14840	−	18.4779i	−0.164628	−	0.590857i
$979$		−	27.4295i		−	0.876650i
$980$	−6.80609	−	1.63621i	−0.217412	−	0.0522667i
$981$	−22.6574	−	12.4878i	−0.723395	−	0.398703i
$982$	−17.3553	−	30.0602i	−0.553829	−	0.959260i
$983$	12.3949	−	21.4685i	0.395335	−	0.684740i	−0.597809	−	0.801638i	$-0.703962\pi$
$983$	12.3949	−	21.4685i	0.395335	−	0.684740i	0.993144	+	0.116899i	$0.0372953\pi$
$984$	7.94779	−	8.10729i	0.253366	−	0.258451i
$985$	7.67905	−	4.43350i	0.244675	−	0.141263i
$986$	23.2596			0.740736
$987$	−13.1127	−	5.08334i	−0.417382	−	0.161805i
$988$	−13.4703			−0.428547
$989$	−20.3476	+	11.7477i	−0.647015	+	0.373554i
$990$	13.1868	−	7.96685i	0.419104	−	0.253203i
$991$	−17.7444	+	30.7343i	−0.563671	+	0.976307i	0.433501	+	0.901153i	$0.357278\pi$
$991$	−17.7444	+	30.7343i	−0.563671	+	0.976307i	−0.997172	+	0.0751537i	$0.976055\pi$
$992$	2.38703	+	4.13446i	0.0757884	+	0.131269i
$993$	7.32587	−	28.4688i	0.232479	−	0.903431i
$994$	−32.6344	+	14.0149i	−1.03510	+	0.444526i
$995$			18.5804i			0.589037i
$996$	−2.29793	+	0.640261i	−0.0728126	+	0.0202875i
$997$	−33.6474	−	19.4263i	−1.06562	−	0.615238i	−0.138641	−	0.990343i	$-0.544273\pi$
$997$	−33.6474	−	19.4263i	−1.06562	−	0.615238i	−0.926982	+	0.375105i	$0.877607\pi$
$998$	5.32606	+	3.07500i	0.168593	+	0.0973375i
$999$	0.265060	+	0.0626204i	0.00838612	+	0.00198122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.r.a.101.6	✓	12
3.2	odd	2		210.2.r.b.101.3	yes	12
5.2	odd	4		1050.2.u.g.899.6		12
5.3	odd	4		1050.2.u.f.899.1		12
5.4	even	2		1050.2.s.g.101.1		12
7.3	odd	6		1470.2.b.a.881.10		12
7.4	even	3		1470.2.b.b.881.9		12
7.5	odd	6		210.2.r.b.131.3	yes	12
15.2	even	4		1050.2.u.e.899.3		12
15.8	even	4		1050.2.u.h.899.4		12
15.14	odd	2		1050.2.s.f.101.4		12
21.5	even	6	inner	210.2.r.a.131.6	yes	12
21.11	odd	6		1470.2.b.a.881.4		12
21.17	even	6		1470.2.b.b.881.3		12
35.12	even	12		1050.2.u.h.299.4		12
35.19	odd	6		1050.2.s.f.551.4		12
35.33	even	12		1050.2.u.e.299.3		12
105.47	odd	12		1050.2.u.f.299.1		12
105.68	odd	12		1050.2.u.g.299.6		12
105.89	even	6		1050.2.s.g.551.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.6	✓	12	1.1	even	1	trivial
210.2.r.a.131.6	yes	12	21.5	even	6	inner
210.2.r.b.101.3	yes	12	3.2	odd	2
210.2.r.b.131.3	yes	12	7.5	odd	6
1050.2.s.f.101.4		12	15.14	odd	2
1050.2.s.f.551.4		12	35.19	odd	6
1050.2.s.g.101.1		12	5.4	even	2
1050.2.s.g.551.1		12	105.89	even	6
1050.2.u.e.299.3		12	35.33	even	12
1050.2.u.e.899.3		12	15.2	even	4
1050.2.u.f.299.1		12	105.47	odd	12
1050.2.u.f.899.1		12	5.3	odd	4
1050.2.u.g.299.6		12	105.68	odd	12
1050.2.u.g.899.6		12	5.2	odd	4
1050.2.u.h.299.4		12	35.12	even	12
1050.2.u.h.899.4		12	15.8	even	4
1470.2.b.a.881.4		12	21.11	odd	6
1470.2.b.a.881.10		12	7.3	odd	6
1470.2.b.b.881.3		12	21.17	even	6
1470.2.b.b.881.9		12	7.4	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.23685 + 1.21252i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.67740 + 0.431645i) q^{6} +(-0.311378 + 2.62736i) q^{7} -1.00000i q^{8} +(0.0596020 + 2.99941i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.23685 + 1.21252i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.67740 + 0.431645i) q^{6} +(-0.311378 + 2.62736i) q^{7} -1.00000i q^{8} +(0.0596020 + 2.99941i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-4.44749 - 2.56776i) q^{11} +(1.66850 - 0.464886i) q^{12} -5.00256i q^{13} +(1.04402 + 2.43105i) q^{14} +(-0.431645 + 1.67740i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87973 - 3.25579i) q^{17} +(1.55132 + 2.56776i) q^{18} +(2.33193 - 1.34634i) q^{19} +1.00000 q^{20} +(-3.57085 + 2.87211i) q^{21} -5.13552 q^{22} +(2.15298 - 1.24302i) q^{23} +(1.21252 - 1.23685i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.50128 - 4.33235i) q^{26} +(-3.56312 + 3.78209i) q^{27} +(2.11968 + 1.58334i) q^{28} +6.18694i q^{29} +(0.464886 + 1.66850i) q^{30} +(-4.13446 - 2.38703i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.38743 - 8.56861i) q^{33} -3.75947i q^{34} +(-2.43105 + 1.04402i) q^{35} +(2.62736 + 1.44809i) q^{36} +(-0.0262075 - 0.0453927i) q^{37} +(1.34634 - 2.33193i) q^{38} +(6.06570 - 6.18743i) q^{39} +(0.866025 - 0.500000i) q^{40} +6.55478 q^{41} +(-1.65640 + 4.27275i) q^{42} -9.45088 q^{43} +(-4.44749 + 2.56776i) q^{44} +(-2.56776 + 1.55132i) q^{45} +(1.24302 - 2.15298i) q^{46} +(1.53446 + 2.65776i) q^{47} +(0.431645 - 1.67740i) q^{48} +(-6.80609 - 1.63621i) q^{49} +1.00000i q^{50} +(6.27266 - 1.74772i) q^{51} +(-4.33235 - 2.50128i) q^{52} +(-0.963053 - 0.556019i) q^{53} +(-1.19470 + 5.05694i) q^{54} -5.13552i q^{55} +(2.62736 + 0.311378i) q^{56} +(4.51670 + 1.16228i) q^{57} +(3.09347 + 5.35804i) q^{58} +(-6.63079 + 11.4849i) q^{59} +(1.23685 + 1.21252i) q^{60} +(3.59330 - 2.07459i) q^{61} -4.77406 q^{62} +(-7.89910 - 0.777354i) q^{63} -1.00000 q^{64} +(4.33235 - 2.50128i) q^{65} +(-6.35188 - 6.22691i) q^{66} +(0.448087 - 0.776110i) q^{67} +(-1.87973 - 3.25579i) q^{68} +(4.17010 + 1.07309i) q^{69} +(-1.58334 + 2.11968i) q^{70} +13.4240i q^{71} +(2.99941 - 0.0596020i) q^{72} +(-6.04511 - 3.49014i) q^{73} +(-0.0453927 - 0.0262075i) q^{74} +(-1.66850 + 0.464886i) q^{75} -2.69268i q^{76} +(8.13130 - 10.8856i) q^{77} +(2.15933 - 8.39132i) q^{78} +(8.37381 + 14.5039i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.99290 + 0.357541i) q^{81} +(5.67661 - 3.27739i) q^{82} -1.37724 q^{83} +(0.701891 + 4.52850i) q^{84} +3.75947 q^{85} +(-8.18470 + 4.72544i) q^{86} +(-7.50177 + 7.65232i) q^{87} +(-2.56776 + 4.44749i) q^{88} +(2.67056 + 4.62555i) q^{89} +(-1.44809 + 2.62736i) q^{90} +(13.1436 + 1.55769i) q^{91} -2.48605i q^{92} +(-2.21939 - 7.96551i) q^{93} +(2.65776 + 1.53446i) q^{94} +(2.33193 + 1.34634i) q^{95} +(-0.464886 - 1.66850i) q^{96} +0.633608i q^{97} +(-6.71235 + 1.98605i) q^{98} +(7.43669 - 13.4929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9 - 12 * q^11 + 2 * q^12 + 12 * q^14 - 4 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 12 * q^20 - 18 * q^21 - 24 * q^23 - 4 * q^24 - 6 * q^25 - 4 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 + 12 * q^31 - 22 * q^33 + 4 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 + 30 * q^39 - 4 * q^41 - 20 * q^42 - 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 - 48 * q^53 - 4 * q^54 + 6 * q^56 - 36 * q^57 + 8 * q^58 + 12 * q^59 - 2 * q^60 - 30 * q^61 + 8 * q^62 - 4 * q^63 - 12 * q^64 + 12 * q^65 - 34 * q^66 - 4 * q^67 - 12 * q^68 + 50 * q^69 + 6 * q^70 + 4 * q^72 - 2 * q^75 + 20 * q^77 + 32 * q^78 - 4 * q^79 + 6 * q^80 + 50 * q^81 - 40 * q^83 - 12 * q^84 + 24 * q^85 - 54 * q^86 + 8 * q^87 + 26 * q^89 - 8 * q^90 + 28 * q^91 - 32 * q^93 + 24 * q^94 - 2 * q^96 + 16 * q^98 + 48 * q^99

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