LMFDB - Embedded newform 210.2.r.b.131.3

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			131.3
Root			$-1.21252 - 1.23685i$ of defining polynomial
Character	$\chi$	$=$	210.131
Dual form			210.2.r.b.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.66850 - 0.464886i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.67740 - 0.431645i) q^{6} +(-0.311378 - 2.62736i) q^{7} -1.00000i q^{8} +(2.56776 - 1.55132i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.66850 - 0.464886i) 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} +(2.56776 - 1.55132i) q^{9} +(0.866025 - 0.500000i) q^{10} +(4.44749 - 2.56776i) q^{11} +(1.23685 + 1.21252i) 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} +(-2.99941 + 0.0596020i) q^{18} +(2.33193 + 1.34634i) q^{19} -1.00000 q^{20} +(-1.74096 - 4.23899i) q^{21} -5.13552 q^{22} +(-2.15298 - 1.24302i) q^{23} +(-0.464886 - 1.66850i) 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} +(1.21252 - 1.23685i) q^{30} +(-4.13446 + 2.38703i) q^{31} +(0.866025 - 0.500000i) q^{32} +(6.22691 - 6.35188i) 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} +(2.32562 + 8.34676i) q^{39} +(0.866025 + 0.500000i) q^{40} -6.55478 q^{41} +(-0.611783 + 4.54155i) q^{42} -9.45088 q^{43} +(4.44749 + 2.56776i) q^{44} +(0.0596020 + 2.99941i) 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} +(-4.64990 - 4.55842i) q^{51} +(-4.33235 + 2.50128i) q^{52} +(0.963053 - 0.556019i) q^{53} +(-4.97679 + 1.49383i) 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} +(-1.66850 + 0.464886i) q^{60} +(3.59330 + 2.07459i) q^{61} +4.77406 q^{62} +(-4.87543 - 6.26340i) q^{63} -1.00000 q^{64} +(-4.33235 - 2.50128i) q^{65} +(-8.56861 + 2.38743i) 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} +(-1.55132 - 2.56776i) q^{72} +(-6.04511 + 3.49014i) q^{73} +(0.0453927 - 0.0262075i) q^{74} +(-1.23685 - 1.21252i) 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} +(4.18681 - 7.96685i) q^{81} +(5.67661 + 3.27739i) q^{82} +1.37724 q^{83} +(2.80060 - 3.62721i) q^{84} +3.75947 q^{85} +(8.18470 + 4.72544i) q^{86} +(2.87622 + 10.3229i) 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} +(-5.78864 + 5.90481i) q^{93} +(2.65776 - 1.53446i) q^{94} +(-2.33193 + 1.34634i) q^{95} +(1.21252 - 1.23685i) 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}+O(q^{10}) $ 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7	$ 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{11} - 2 q^{12} - 12 q^{14} - 4 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 12 q^{20} + 4 q^{21} + 24 q^{23} - 2 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{30} + 12 q^{31} - 2 q^{33} - 4 q^{35} + 6 q^{36} - 8 q^{37} - 8 q^{38} - 42 q^{39} + 4 q^{41} + 24 q^{42} + 12 q^{44} + 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{51} - 12 q^{52} + 48 q^{53} - 32 q^{54} - 6 q^{56} - 36 q^{57} + 8 q^{58} - 12 q^{59} - 2 q^{60} - 30 q^{61} - 8 q^{62} + 20 q^{63} - 12 q^{64} - 12 q^{65} - 14 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} - 40 q^{81} + 40 q^{83} + 20 q^{84} + 24 q^{85} + 54 q^{86} + 64 q^{87} - 26 q^{89} + 8 q^{90} + 28 q^{91} + 4 q^{93} + 24 q^{94} - 4 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 + 12 * q^11 - 2 * q^12 - 12 * q^14 - 4 * q^15 - 6 * q^16 - 12 * q^17 - 4 * q^18 - 12 * q^20 + 4 * q^21 + 24 * q^23 - 2 * q^24 - 6 * q^25 + 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^30 + 12 * q^31 - 2 * q^33 - 4 * q^35 + 6 * q^36 - 8 * q^37 - 8 * q^38 - 42 * q^39 + 4 * q^41 + 24 * q^42 + 12 * q^44 + 6 * q^45 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 14 * q^49 - 8 * q^51 - 12 * q^52 + 48 * q^53 - 32 * q^54 - 6 * q^56 - 36 * q^57 + 8 * q^58 - 12 * q^59 - 2 * q^60 - 30 * q^61 - 8 * q^62 + 20 * q^63 - 12 * q^64 - 12 * q^65 - 14 * 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 - 40 * q^81 + 40 * q^83 + 20 * q^84 + 24 * q^85 + 54 * q^86 + 64 * q^87 - 26 * q^89 + 8 * q^90 + 28 * q^91 + 4 * q^93 + 24 * q^94 - 4 * q^96 - 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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
$3$	1.66850	−	0.464886i	0.963307	−	0.268402i
$3$	1.66850	−	0.464886i	0.963307	−	0.268402i
$4$	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
$9$	2.56776	−	1.55132i	0.855921	−	0.517107i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	4.44749	−	2.56776i	1.34097	−	0.774210i	0.354020	−	0.935238i	$-0.384814\pi$
$11$	4.44749	−	2.56776i	1.34097	−	0.774210i	0.986950	+	0.161028i	$0.0514810\pi$
$12$	1.23685	+	1.21252i	0.357048	+	0.350024i
$13$			5.00256i			1.38746i	0.720234	+	0.693731i	$0.244034\pi$
$13$			5.00256i			1.38746i	−0.720234	+	0.693731i	$0.755966\pi$
$14$	−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	$-0.317350\pi$
$17$	−1.87973	−	3.25579i	−0.455902	−	0.789646i	−0.998740	+	0.0501922i	$0.984017\pi$
$18$	−2.99941	+	0.0596020i	−0.706967	+	0.0140483i
$19$	2.33193	+	1.34634i	0.534981	+	0.308871i	0.743042	−	0.669245i	$-0.233382\pi$
$19$	2.33193	+	1.34634i	0.534981	+	0.308871i	−0.208062	+	0.978116i	$0.566715\pi$
$20$	−1.00000			−0.223607
$21$	−1.74096	−	4.23899i	−0.379908	−	0.925024i
$22$	−5.13552			−1.09490
$23$	−2.15298	−	1.24302i	−0.448927	−	0.259188i	0.258450	−	0.966025i	$-0.416788\pi$
$23$	−2.15298	−	1.24302i	−0.448927	−	0.259188i	−0.707377	+	0.706836i	$0.750122\pi$
$24$	−0.464886	−	1.66850i	−0.0948944	−	0.340580i
$25$	−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	$0.805219\pi$
$30$	1.21252	−	1.23685i	0.221374	−	0.225817i
$31$	−4.13446	+	2.38703i	−0.742571	+	0.428724i	−0.823003	−	0.568036i	$-0.807703\pi$
$31$	−4.13446	+	2.38703i	−0.742571	+	0.428724i	0.0804322	+	0.996760i	$0.474370\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	6.22691	−	6.35188i	1.08397	−	1.10572i
$34$			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	−0.868172	−	0.496264i	$-0.834705\pi$
$37$	−0.0262075	+	0.0453927i	−0.00430849	+	0.00746252i	0.863863	+	0.503727i	$0.168038\pi$
$38$	−1.34634	−	2.33193i	−0.218405	−	0.378288i
$39$	2.32562	+	8.34676i	0.372397	+	1.33655i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−6.55478			−1.02369			−0.511843	−	0.859079i	$-0.671037\pi$
$41$	−6.55478			−1.02369			−0.511843	+	0.859079i	$0.671037\pi$
$42$	−0.611783	+	4.54155i	−0.0944002	+	0.700777i
$43$	−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
$45$	0.0596020	+	2.99941i	0.00888494	+	0.447125i
$46$	1.24302	+	2.15298i	0.183274	+	0.317440i
$47$	−1.53446	+	2.65776i	−0.223824	+	0.387674i	−0.955966	−	0.293478i	$-0.905187\pi$
$47$	−1.53446	+	2.65776i	−0.223824	+	0.387674i	0.732142	+	0.681152i	$0.238521\pi$
$48$	−0.431645	+	1.67740i	−0.0623027	+	0.242112i
$49$	−6.80609	+	1.63621i	−0.972298	+	0.233744i
$50$			1.00000i			0.141421i
$51$	−4.64990	−	4.55842i	−0.651116	−	0.638306i
$52$	−4.33235	+	2.50128i	−0.600788	+	0.346865i
$53$	0.963053	−	0.556019i	0.132286	−	0.0763751i	−0.432397	−	0.901683i	$-0.642332\pi$
$53$	0.963053	−	0.556019i	0.132286	−	0.0763751i	0.564682	+	0.825308i	$0.308999\pi$
$54$	−4.97679	+	1.49383i	−0.677256	+	0.203284i
$55$			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	0.868769	+	0.495217i	$0.164911\pi$
$59$	6.63079	+	11.4849i	0.863255	+	1.49520i	−0.00551419	+	0.999985i	$0.501755\pi$
$60$	−1.66850	+	0.464886i	−0.215402	+	0.0600165i
$61$	3.59330	+	2.07459i	0.460075	+	0.265624i	0.712076	−	0.702103i	$-0.247755\pi$
$61$	3.59330	+	2.07459i	0.460075	+	0.265624i	−0.252001	+	0.967727i	$0.581089\pi$
$62$	4.77406			0.606307
$63$	−4.87543	−	6.26340i	−0.614246	−	0.789114i
$64$	−1.00000			−0.125000
$65$	−4.33235	−	2.50128i	−0.537362	−	0.310246i
$66$	−8.56861	+	2.38743i	−1.05472	+	0.293873i
$67$	0.448087	+	0.776110i	0.0547426	+	0.0948169i	0.892098	−	0.451842i	$-0.149233\pi$
$67$	0.448087	+	0.776110i	0.0547426	+	0.0948169i	−0.837356	+	0.546659i	$0.815900\pi$
$68$	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	$0.706647\pi$
$72$	−1.55132	−	2.56776i	−0.182825	−	0.302614i
$73$	−6.04511	+	3.49014i	−0.707526	+	0.408490i	−0.810144	−	0.586230i	$-0.800611\pi$
$73$	−6.04511	+	3.49014i	−0.707526	+	0.408490i	0.102618	+	0.994721i	$0.467278\pi$
$74$	0.0453927	−	0.0262075i	0.00527680	−	0.00304656i
$75$	−1.23685	−	1.21252i	−0.142819	−	0.140009i
$76$			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	0.180724	−	0.983534i	$-0.442156\pi$
$79$	8.37381	−	14.5039i	0.942127	−	1.63181i	0.761403	−	0.648279i	$-0.224511\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	4.18681	−	7.96685i	0.465201	−	0.885205i
$82$	5.67661	+	3.27739i	0.626877	+	0.361927i
$83$	1.37724			0.151172			0.0755861	−	0.997139i	$-0.475917\pi$
$83$	1.37724			0.151172			0.0755861	+	0.997139i	$0.475917\pi$
$84$	2.80060	−	3.62721i	0.305570	−	0.395761i
$85$	3.75947			0.407771
$86$	8.18470	+	4.72544i	0.882579	+	0.509557i
$87$	2.87622	+	10.3229i	0.308363	+	1.10673i
$88$	−2.56776	−	4.44749i	−0.273724	−	0.474105i
$89$	−2.67056	+	4.62555i	−0.283079	+	0.490307i	−0.972142	−	0.234395i	$-0.924689\pi$
$89$	−2.67056	+	4.62555i	−0.283079	+	0.490307i	0.689062	+	0.724702i	$0.258023\pi$
$90$	1.44809	−	2.62736i	0.152642	−	0.276949i
$91$	13.1436	−	1.55769i	1.37782	−	0.163290i
$92$		−	2.48605i		−	0.259188i
$93$	−5.78864	+	5.90481i	−0.600254	+	0.612300i
$94$	2.65776	−	1.53446i	0.274127	−	0.158267i
$95$	−2.33193	+	1.34634i	−0.239251	+	0.138131i
$96$	1.21252	−	1.23685i	0.123752	−	0.126236i
$97$		−	0.633608i		−	0.0643331i	−0.999483	−	0.0321666i	$-0.989759\pi$
$97$		−	0.633608i		−	0.0643331i	0.999483	−	0.0321666i	$-0.0102407\pi$
$98$	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	−0.854557	−	0.519358i	$-0.826171\pi$
$101$	−8.81430	−	15.2668i	−0.877056	−	1.51910i	−0.0224989	−	0.999747i	$-0.507162\pi$
$102$	1.74772	+	6.27266i	0.173050	+	0.621085i
$103$	12.7448	+	7.35823i	1.25579	+	0.725028i	0.972252	−	0.233934i	$-0.0751601\pi$
$103$	12.7448	+	7.35823i	1.25579	+	0.725028i	0.283533	+	0.958962i	$0.408493\pi$
$104$	5.00256			0.490542
$105$	4.54155	+	0.611783i	0.443210	+	0.0597039i
$106$	−1.11204			−0.108011
$107$	−4.07900	−	2.35501i	−0.394331	−	0.227667i	0.289704	−	0.957116i	$-0.406443\pi$
$107$	−4.07900	−	2.35501i	−0.394331	−	0.227667i	−0.684035	+	0.729449i	$0.739777\pi$
$108$	5.05694	+	1.19470i	0.486605	+	0.114960i
$109$	−4.31181	−	7.46828i	−0.412997	−	0.715331i	0.582219	−	0.813032i	$-0.302185\pi$
$109$	−4.31181	−	7.46828i	−0.412997	−	0.715331i	−0.995216	+	0.0977007i	$0.968851\pi$
$110$	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	$-0.257447\pi$
$114$	−3.33044	−	3.26492i	−0.311924	−	0.305788i
$115$	2.15298	−	1.24302i	0.200766	−	0.115913i
$116$	−5.35804	+	3.09347i	−0.497482	+	0.287221i
$117$	7.76058	+	12.8454i	0.717466	+	1.18756i
$118$		−	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
$123$	−10.9366	+	3.04723i	−0.986123	+	0.274759i
$124$	−4.13446	−	2.38703i	−0.371286	−	0.214362i
$125$	1.00000			0.0894427
$126$	1.09055	+	7.86198i	0.0971535	+	0.700401i
$127$	−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
$129$	−15.7688	+	4.39358i	−1.38836	+	0.386833i
$130$	2.50128	+	4.33235i	0.219377	+	0.379972i
$131$	1.55132	−	2.68697i	0.135540	−	0.234761i	−0.790264	−	0.612767i	$-0.790057\pi$
$131$	1.55132	−	2.68697i	0.135540	−	0.234761i	0.925803	+	0.378005i	$0.123390\pi$
$132$	8.61435	+	2.21673i	0.749783	+	0.192941i
$133$	2.81121	−	6.54604i	0.243763	−	0.567614i
$134$		−	0.896174i		−	0.0774177i
$135$	1.49383	+	4.97679i	0.128568	+	0.428334i
$136$	−3.25579	+	1.87973i	−0.279182	+	0.161186i
$137$	8.44989	−	4.87855i	0.721923	−	0.416803i	−0.0935370	−	0.995616i	$-0.529817\pi$
$137$	8.44989	−	4.87855i	0.721923	−	0.416803i	0.815460	+	0.578813i	$0.196484\pi$
$138$	3.07487	+	3.01438i	0.261750	+	0.256601i
$139$			4.26248i			0.361539i	0.983526	+	0.180769i	$0.0578588\pi$
$139$			4.26248i			0.361539i	−0.983526	+	0.180769i	$0.942141\pi$
$140$	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
$144$	0.0596020	+	2.99941i	0.00496683	+	0.249951i
$145$	−5.35804	−	3.09347i	−0.444961	−	0.256899i
$146$	6.98029			0.577693
$147$	−10.5953	+	5.89406i	−0.873884	+	0.486134i
$148$	−0.0524150			−0.00430849
$149$	−7.77014	−	4.48609i	−0.636554	−	0.367515i	0.146732	−	0.989176i	$-0.453125\pi$
$149$	−7.77014	−	4.48609i	−0.636554	−	0.367515i	−0.783286	+	0.621662i	$0.786458\pi$
$150$	0.464886	+	1.66850i	0.0379578	+	0.136232i
$151$	−6.61328	−	11.4545i	−0.538181	−	0.932157i	−0.999002	−	0.0446642i	$-0.985778\pi$
$151$	−6.61328	−	11.4545i	−0.538181	−	0.932157i	0.460821	−	0.887493i	$-0.347555\pi$
$152$	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
$156$	−6.06570	+	6.18743i	−0.485644	+	0.495391i
$157$	7.41664	−	4.28200i	0.591912	−	0.341741i	−0.173941	−	0.984756i	$-0.555650\pi$
$157$	7.41664	−	4.28200i	0.591912	−	0.341741i	0.765853	+	0.643015i	$0.222317\pi$
$158$	−14.5039	+	8.37381i	−1.15387	+	0.666185i
$159$	1.34837	−	1.37543i	0.106932	−	0.109078i
$160$			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	−0.997190	−	0.0749190i	$-0.976130\pi$
$163$	−5.53728	+	9.59085i	−0.433713	+	0.751213i	0.563477	+	0.826132i	$0.309464\pi$
$164$	−3.27739	−	5.67661i	−0.255921	−	0.443269i
$165$	2.38743	+	8.56861i	0.185861	+	0.667065i
$166$	−1.19273	−	0.688622i	−0.0925737	−	0.0534474i
$167$	−2.95799			−0.228896			−0.114448	−	0.993429i	$-0.536510\pi$
$167$	−2.95799			−0.228896			−0.114448	+	0.993429i	$0.536510\pi$
$168$	−4.23899	+	1.74096i	−0.327045	+	0.134318i
$169$	−12.0256			−0.925049
$170$	−3.25579	−	1.87973i	−0.249708	−	0.144169i
$171$	8.07643	−	0.160489i	0.617620	−	0.0122729i
$172$	−4.72544	−	8.18470i	−0.360311	−	0.624078i
$173$	−10.3708	+	17.9628i	−0.788478	+	1.36568i	0.138421	+	0.990374i	$0.455797\pi$
$173$	−10.3708	+	17.9628i	−0.788478	+	1.36568i	−0.926899	+	0.375311i	$0.877536\pi$
$174$	2.67056	−	10.3780i	0.202455	−	0.786753i
$175$	−2.11968	+	1.58334i	−0.160232	+	0.119690i
$176$			5.13552i			0.387105i
$177$	16.4026	+	16.0799i	1.23289	+	1.20864i
$178$	4.62555	−	2.67056i	0.346700	−	0.200167i
$179$	21.2335	−	12.2592i	1.58707	−	0.916294i	0.593281	−	0.804996i	$-0.297832\pi$
$179$	21.2335	−	12.2592i	1.58707	−	0.916294i	0.993787	−	0.111298i	$-0.0355009\pi$
$180$	−2.56776	+	1.55132i	−0.191390	+	0.115629i
$181$			18.6533i			1.38649i	0.720704	+	0.693243i	$0.243819\pi$
$181$			18.6533i			1.38649i	−0.720704	+	0.693243i	$0.756181\pi$
$182$	−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
$186$	7.96551	−	2.21939i	0.584060	−	0.162734i
$187$	−16.7202	−	9.65341i	−1.22270	−	0.705927i
$188$	−3.06892			−0.223824
$189$	−11.0464	−	8.18394i	−0.803508	−	0.595294i
$190$	2.69268			0.195347
$191$	6.29976	+	3.63717i	0.455835	+	0.263176i	0.710291	−	0.703908i	$-0.248563\pi$
$191$	6.29976	+	3.63717i	0.455835	+	0.263176i	−0.254457	+	0.967084i	$0.581897\pi$
$192$	−1.66850	+	0.464886i	−0.120413	+	0.0335502i
$193$	5.53208	+	9.58185i	0.398208	+	0.689716i	0.993505	−	0.113789i	$-0.0362989\pi$
$193$	5.53208	+	9.58185i	0.398208	+	0.689716i	−0.595297	+	0.803506i	$0.702966\pi$
$194$	−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	$-0.102298\pi$
$198$	−13.1868	+	7.96685i	−0.937146	+	0.566179i
$199$	16.0911	−	9.29018i	1.14066	−	0.658563i	0.194070	−	0.980988i	$-0.437831\pi$
$199$	16.0911	−	9.29018i	1.14066	−	0.658563i	0.946595	+	0.322425i	$0.104498\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	1.10843	+	1.08663i	0.0781829	+	0.0766448i
$202$			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
$207$	−7.45667	+	0.148173i	−0.518274	+	0.0102988i
$208$	−4.33235	−	2.50128i	−0.300394	−	0.173433i
$209$	13.8283			0.956524
$210$	−3.62721	−	2.80060i	−0.250301	−	0.193260i
$211$	−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
$213$	6.24062	+	22.3979i	0.427600	+	1.53468i
$214$	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
$219$	−8.46372	+	8.63358i	−0.571925	+	0.583403i
$220$	−4.44749	+	2.56776i	−0.299850	+	0.173119i
$221$	16.2873	−	9.40348i	1.09560	−	0.632547i
$222$	0.0635541	−	0.0648296i	0.00426547	−	0.00435108i
$223$			5.79472i			0.388043i	0.980997	+	0.194021i	$0.0621531\pi$
$223$			5.79472i			0.388043i	−0.980997	+	0.194021i	$0.937847\pi$
$224$	−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	$-0.281969\pi$
$227$	−5.33902	−	9.24746i	−0.354363	−	0.613775i	−0.987009	+	0.160666i	$0.948636\pi$
$228$	1.25179	+	4.49272i	0.0829016	+	0.297538i
$229$	−7.46827	−	4.31181i	−0.493517	−	0.284932i	0.232515	−	0.972593i	$-0.425304\pi$
$229$	−7.46827	−	4.31181i	−0.493517	−	0.284932i	−0.726032	+	0.687661i	$0.758638\pi$
$230$	−2.48605			−0.163925
$231$	−18.6276	−	14.3825i	−1.22561	−	0.946301i
$232$	6.18694			0.406192
$233$	13.9131	+	8.03272i	0.911476	+	0.526241i	0.880906	−	0.473292i	$-0.156934\pi$
$233$	13.9131	+	8.03272i	0.911476	+	0.526241i	0.0305704	+	0.999533i	$0.490268\pi$
$234$	−0.298163	−	15.0047i	−0.0194915	−	0.980890i
$235$	−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	$-0.115856\pi$
$240$	−1.23685	−	1.21252i	−0.0798384	−	0.0782677i
$241$	8.40789	−	4.85430i	0.541600	−	0.312693i	−0.204127	−	0.978944i	$-0.565436\pi$
$241$	8.40789	−	4.85430i	0.541600	−	0.312693i	0.745727	+	0.666252i	$0.232102\pi$
$242$	−13.3139	+	7.68681i	−0.855853	+	0.494127i
$243$	3.28200	−	15.2390i	0.210540	−	0.977585i
$244$			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
$249$	2.29793	−	0.640261i	0.145625	−	0.0405749i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	4.59082			0.289770			0.144885	−	0.989449i	$-0.453719\pi$
$251$	4.59082			0.289770			0.144885	+	0.989449i	$0.453719\pi$
$252$	2.98655	−	7.35395i	0.188135	−	0.463255i
$253$	−12.7672			−0.802664
$254$	1.54601	+	0.892591i	0.0970055	+	0.0560062i
$255$	6.27266	−	1.74772i	0.392809	−	0.109447i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.87132	+	10.1694i	−0.366243	+	0.634352i	−0.988975	−	0.148084i	$-0.952689\pi$
$257$	−5.87132	+	10.1694i	−0.366243	+	0.634352i	0.622732	+	0.782435i	$0.286023\pi$
$258$	15.8529	+	4.07943i	0.986961	+	0.253974i
$259$	0.127424	+	0.0547224i	0.00791772	+	0.00340028i
$260$		−	5.00256i		−	0.310246i
$261$	9.59792	+	15.8866i	0.594096	+	0.983355i
$262$	−2.68697	+	1.55132i	−0.166001	+	0.0958409i
$263$	−19.8431	+	11.4564i	−1.22358	+	0.706432i	−0.965679	−	0.259740i	$-0.916363\pi$
$263$	−19.8431	+	11.4564i	−1.22358	+	0.706432i	−0.257898	+	0.966172i	$0.583030\pi$
$264$	−6.35188	−	6.22691i	−0.390931	−	0.383240i
$265$			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	$-0.246330\pi$
$269$	−4.06200	−	7.03559i	−0.247665	−	0.428968i	−0.962877	+	0.269939i	$0.912996\pi$
$270$	1.19470	−	5.05694i	0.0727074	−	0.307756i
$271$	−9.47446	−	5.47008i	−0.575533	−	0.332284i	0.183823	−	0.982959i	$-0.441153\pi$
$271$	−9.47446	−	5.47008i	−0.575533	−	0.332284i	−0.759356	+	0.650675i	$0.774486\pi$
$272$	3.75947			0.227951
$273$	21.2058	−	8.70925i	1.28344	−	0.527108i
$274$	−9.75710			−0.589448
$275$	−4.44749	−	2.56776i	−0.268194	−	0.154842i
$276$	−1.15573	−	4.14796i	−0.0695666	−	0.249678i
$277$	−2.39144	−	4.14209i	−0.143688	−	0.248874i	0.785195	−	0.619249i	$-0.212563\pi$
$277$	−2.39144	−	4.14209i	−0.143688	−	0.248874i	−0.928883	+	0.370374i	$0.879229\pi$
$278$	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	$0.783268\pi$
$282$	3.72111	−	3.79579i	0.221589	−	0.226036i
$283$	19.0570	−	11.0026i	1.13282	−	0.654035i	0.188178	−	0.982135i	$-0.439742\pi$
$283$	19.0570	−	11.0026i	1.13282	−	0.654035i	0.944643	+	0.328100i	$0.106408\pi$
$284$	−11.6255	+	6.71199i	−0.689847	+	0.398283i
$285$	−3.26492	+	3.33044i	−0.193397	+	0.197278i
$286$		−	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
$291$	−0.294555	−	1.05717i	−0.0172671	−	0.0619726i
$292$	−6.04511	−	3.49014i	−0.353763	−	0.204245i
$293$	−11.2905			−0.659598			−0.329799	−	0.944051i	$-0.606981\pi$
$293$	−11.2905			−0.659598			−0.329799	+	0.944051i	$0.606981\pi$
$294$	12.1228	+	0.193238i	0.707017	+	0.0112698i
$295$	−13.2616			−0.772119
$296$	0.0453927	+	0.0262075i	0.00263840	+	0.00152328i
$297$	6.13543	−	25.9701i	0.356014	−	1.50694i
$298$	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
$303$	−21.8040	−	21.3750i	−1.25260	−	1.22796i
$304$	−2.33193	+	1.34634i	−0.133745	+	0.0772178i
$305$	−3.59330	+	2.07459i	−0.205752	+	0.118791i
$306$	5.83214	+	9.65341i	0.333401	+	0.551849i
$307$		−	2.12162i		−	0.121087i	−0.998166	−	0.0605436i	$-0.980717\pi$
$307$		−	2.12162i		−	0.121087i	0.998166	−	0.0605436i	$-0.0192834\pi$
$308$	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	$-0.267668\pi$
$311$	−5.50229	−	9.53025i	−0.312006	−	0.540411i	−0.978797	+	0.204835i	$0.934334\pi$
$312$	8.34676	−	2.32562i	0.472542	−	0.131662i
$313$	−6.43835	−	3.71718i	−0.363917	−	0.210108i	0.306881	−	0.951748i	$-0.400715\pi$
$313$	−6.43835	−	3.71718i	−0.363917	−	0.210108i	−0.670798	+	0.741640i	$0.734048\pi$
$314$	−8.56400			−0.483294
$315$	7.86198	−	1.09055i	0.442972	−	0.0614453i
$316$	16.7476			0.942127
$317$	3.87512	+	2.23730i	0.217648	+	0.125659i	0.604861	−	0.796331i	$-0.293229\pi$
$317$	3.87512	+	2.23730i	0.217648	+	0.125659i	−0.387213	+	0.921990i	$0.626562\pi$
$318$	−1.85543	+	0.516971i	−0.104047	+	0.0289903i
$319$	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
$324$	8.99290	−	0.357541i	0.499605	−	0.0198634i
$325$	4.33235	−	2.50128i	0.240315	−	0.138746i
$326$	9.59085	−	5.53728i	0.531188	−	0.306681i
$327$	−10.6661	−	10.4563i	−0.589839	−	0.578234i
$328$			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	−0.999265	−	0.0383371i	$-0.987794\pi$
$331$	−8.48598	+	14.6981i	−0.466432	+	0.807883i	0.532833	+	0.846220i	$0.321127\pi$
$332$	0.688622	+	1.19273i	0.0377930	+	0.0654595i
$333$	0.00312404	+	0.157214i	0.000171196	+	0.00861527i
$334$	2.56169	+	1.47899i	0.140169	+	0.0809269i
$335$	−0.896174			−0.0489632
$336$	4.54155	+	0.611783i	0.247762	+	0.0333755i
$337$	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
$339$	−7.15034	−	25.6629i	−0.388353	−	1.39382i
$340$	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
$345$	3.01438	−	3.07487i	0.162289	−	0.165545i
$346$	17.9628	−	10.3708i	0.965685	−	0.557538i
$347$	28.7525	−	16.6003i	1.54352	−	0.891149i	0.544902	−	0.838500i	$-0.316567\pi$
$347$	28.7525	−	16.6003i	1.54352	−	0.891149i	0.998613	−	0.0526494i	$-0.0167666\pi$
$348$	−7.50177	+	7.65232i	−0.402137	+	0.410207i
$349$		−	21.5465i		−	1.15336i	−0.816972	−	0.576678i	$-0.804349\pi$
$349$		−	21.5465i		−	1.15336i	0.816972	−	0.576678i	$-0.195651\pi$
$350$	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	$-0.119763\pi$
$353$	2.75846	+	4.77779i	0.146818	+	0.254296i	−0.783232	+	0.621730i	$0.786430\pi$
$354$	−6.16512	−	22.1269i	−0.327672	−	1.17603i
$355$	−11.6255	−	6.71199i	−0.617018	−	0.356235i
$356$	−5.34113			−0.283079
$357$	−10.5287	+	13.6364i	−0.557240	+	0.721713i
$358$	−24.5184			−1.29584
$359$	−16.7632	−	9.67826i	−0.884730	−	0.510799i	−0.0125151	−	0.999922i	$-0.503984\pi$
$359$	−16.7632	−	9.67826i	−0.884730	−	0.510799i	−0.872215	+	0.489122i	$0.837317\pi$
$360$	2.99941	−	0.0596020i	0.158083	−	0.00314130i
$361$	−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
$366$	−5.13192	−	5.03096i	−0.268250	−	0.262972i
$367$	−12.1526	+	7.01628i	−0.634358	+	0.366247i	−0.782438	−	0.622728i	$-0.786024\pi$
$367$	−12.1526	+	7.01628i	−0.634358	+	0.366247i	0.148080	+	0.988975i	$0.452691\pi$
$368$	2.15298	−	1.24302i	0.112232	−	0.0647971i
$369$	−16.8311	+	10.1686i	−0.876193	+	0.529355i
$370$			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	−0.848181	−	0.529707i	$-0.822302\pi$
$373$	0.669190	−	1.15907i	0.0346493	−	0.0600144i	0.882830	+	0.469693i	$0.155635\pi$
$374$	9.65341	+	16.7202i	0.499166	+	0.864581i
$375$	1.66850	−	0.464886i	0.0861608	−	0.0240066i
$376$	2.65776	+	1.53446i	0.137063	+	0.0791336i
$377$	−30.9505			−1.59403
$378$	5.47449	+	12.6107i	0.281578	+	0.648625i
$379$	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
$381$	−2.97857	+	0.829906i	−0.152597	+	0.0425174i
$382$	−3.63717	−	6.29976i	−0.186094	−	0.322324i
$383$	11.6471	−	20.1734i	0.595141	−	1.03081i	−0.398386	−	0.917218i	$-0.630430\pi$
$383$	11.6471	−	20.1734i	0.595141	−	1.03081i	0.993527	−	0.113596i	$-0.0362371\pi$
$384$	1.67740	+	0.431645i	0.0855996	+	0.0220273i
$385$	13.4929	−	1.59909i	0.687662	−	0.0814971i
$386$		−	11.0642i		−	0.563151i
$387$	−24.2676	+	14.6613i	−1.23359	+	0.745278i
$388$	0.548721	−	0.316804i	0.0278571	−	0.0160833i
$389$	−10.1748	+	5.87442i	−0.515882	+	0.297845i	−0.735248	−	0.677798i	$-0.762934\pi$
$389$	−10.1748	+	5.87442i	−0.515882	+	0.297845i	0.219366	+	0.975643i	$0.429601\pi$
$390$	6.18743	+	6.06570i	0.313313	+	0.307148i
$391$			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
$396$	15.4035	−	0.306087i	0.774057	−	0.0153815i
$397$	14.9142	+	8.61072i	0.748522	+	0.432160i	0.825160	−	0.564899i	$-0.191085\pi$
$397$	14.9142	+	8.61072i	0.748522	+	0.432160i	−0.0766373	+	0.997059i	$0.524418\pi$
$398$	−18.5804			−0.931349
$399$	1.64733	−	12.2289i	0.0824699	−	0.612213i
$400$	1.00000			0.0500000
$401$	7.31712	+	4.22454i	0.365400	+	0.210964i	0.671447	−	0.741053i	$-0.265673\pi$
$401$	7.31712	+	4.22454i	0.365400	+	0.210964i	−0.306047	+	0.952016i	$0.599007\pi$
$402$	−0.416619	−	1.49526i	−0.0207790	−	0.0745770i
$403$	−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
$408$	−4.55842	+	4.64990i	−0.225675	+	0.230204i
$409$	−25.2043	+	14.5517i	−1.24627	+	0.719535i	−0.970364	−	0.241649i	$-0.922312\pi$
$409$	−25.2043	+	14.5517i	−1.24627	+	0.719535i	−0.275908	+	0.961184i	$0.588979\pi$
$410$	−5.67661	+	3.27739i	−0.280348	+	0.161859i
$411$	11.8307	−	12.0681i	0.583563	−	0.595274i
$412$			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
$417$	1.98157	+	7.11193i	0.0970377	+	0.348273i
$418$	−11.9757	−	6.91415i	−0.585749	−	0.338182i
$419$	−2.07947			−0.101589			−0.0507944	−	0.998709i	$-0.516175\pi$
$419$	−2.07947			−0.101589			−0.0507944	+	0.998709i	$0.516175\pi$
$420$	1.74096	+	4.23899i	0.0849500	+	0.206842i
$421$	−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
$423$	0.182913	+	9.20493i	0.00889356	+	0.447559i
$424$	−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
$429$	31.7757	+	31.1505i	1.53414	+	1.50396i
$430$	−8.18470	+	4.72544i	−0.394701	+	0.227881i
$431$	−7.57956	+	4.37606i	−0.365094	+	0.210787i	−0.671313	−	0.741174i	$-0.734269\pi$
$431$	−7.57956	+	4.37606i	−0.365094	+	0.210787i	0.306219	+	0.951961i	$0.400936\pi$
$432$	1.49383	+	4.97679i	0.0718718	+	0.239446i
$433$			12.3440i			0.593214i	0.955000	+	0.296607i	$0.0958552\pi$
$433$			12.3440i			0.593214i	−0.955000	+	0.296607i	$0.904145\pi$
$434$	−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
$438$	11.6466	−	3.24504i	0.556495	−	0.155054i
$439$	−9.72433	−	5.61435i	−0.464117	−	0.267958i	0.249657	−	0.968334i	$-0.419682\pi$
$439$	−9.72433	−	5.61435i	−0.464117	−	0.267958i	−0.713774	+	0.700376i	$0.753016\pi$
$440$	5.13552			0.244827
$441$	−14.9381	+	14.7598i	−0.711340	+	0.702848i
$442$	−18.8070			−0.894556
$443$	−28.9532	−	16.7161i	−1.37561	−	0.794208i	−0.383981	−	0.923341i	$-0.625447\pi$
$443$	−28.9532	−	16.7161i	−1.37561	−	0.794208i	−0.991627	+	0.129133i	$0.958780\pi$
$444$	−0.0874543	+	0.0243670i	−0.00415040	+	0.00115641i
$445$	−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	$0.771914\pi$
$450$	1.55132	+	2.56776i	0.0731300	+	0.121045i
$451$	−29.1524	+	16.8311i	−1.37273	+	0.792547i
$452$	13.3202	−	7.69043i	0.626530	−	0.361727i
$453$	−16.3593	−	16.0374i	−0.768627	−	0.753505i
$454$			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	0.317550	+	0.948242i	$0.397140\pi$
$457$	−14.1611	+	24.5277i	−0.662427	+	1.14736i	−0.979976	+	0.199115i	$0.936193\pi$
$458$	4.31181	+	7.46827i	0.201477	+	0.348969i
$459$	−19.0114	−	4.49145i	−0.887376	−	0.209643i
$460$	2.15298	+	1.24302i	0.100383	+	0.0579563i
$461$	35.5758			1.65693			0.828466	−	0.560040i	$-0.189214\pi$
$461$	35.5758			1.65693			0.828466	+	0.560040i	$0.189214\pi$
$462$	8.94073	+	21.7695i	0.415960	+	1.01281i
$463$	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
$465$	−2.21939	−	7.96551i	−0.102922	−	0.369392i
$466$	−8.03272	−	13.9131i	−0.372109	−	0.644511i
$467$	−6.28462	+	10.8853i	−0.290818	+	0.503711i	−0.974003	−	0.226534i	$-0.927261\pi$
$467$	−6.28462	+	10.8853i	−0.290818	+	0.503711i	0.683186	+	0.730245i	$0.260594\pi$
$468$	−7.24415	+	13.1436i	−0.334861	+	0.607561i
$469$	1.89960	−	1.41895i	0.0877153	−	0.0655211i
$470$			3.06892i			0.141559i
$471$	10.3840	−	10.5924i	0.478469	−	0.488072i
$472$	11.4849	−	6.63079i	0.528634	−	0.305207i
$473$	−42.0327	+	24.2676i	−1.93267	+	1.11583i
$474$	−20.3068	+	20.7143i	−0.932722	+	0.951440i
$475$		−	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	$-0.00400322\pi$
$479$	10.7038	+	18.5395i	0.489069	+	0.847093i	−0.510852	+	0.859669i	$0.670670\pi$
$480$	0.464886	+	1.66850i	0.0212190	+	0.0761561i
$481$	−0.227080	−	0.131105i	−0.0103540	−	0.00597786i
$482$	−9.70859			−0.442214
$483$	−1.52092	+	11.2905i	−0.0692044	+	0.513736i
$484$	15.3736			0.698801
$485$	0.548721	+	0.316804i	0.0249161	+	0.0143853i
$486$	−10.4618	+	11.5564i	−0.474558	+	0.524209i
$487$	−1.25796	−	2.17886i	−0.0570038	−	0.0987335i	0.836115	−	0.548554i	$-0.184821\pi$
$487$	−1.25796	−	2.17886i	−0.0570038	−	0.0987335i	−0.893119	+	0.449820i	$0.851488\pi$
$488$	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	$-0.286430\pi$
$492$	−8.10729	−	7.94779i	−0.365505	−	0.358314i
$493$	20.1434	−	11.6298i	0.907212	−	0.523779i
$494$	11.6656	−	6.73514i	0.524861	−	0.303028i
$495$	7.96685	+	13.1868i	0.358083	+	0.592703i
$496$		−	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	−0.788953	−	0.614454i	$-0.789376\pi$
$499$	3.07500	−	5.32606i	0.137656	−	0.238427i	0.926609	+	0.376026i	$0.122710\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−4.93539	+	1.37513i	−0.220497	+	0.0614361i
$502$	−3.97576	−	2.29541i	−0.177447	−	0.102449i
$503$	−5.99378			−0.267249			−0.133625	−	0.991032i	$-0.542662\pi$
$503$	−5.99378			−0.267249			−0.133625	+	0.991032i	$0.542662\pi$
$504$	−6.26340	+	4.87543i	−0.278994	+	0.217169i
$505$	17.6286			0.784462
$506$	11.0567	+	6.38358i	0.491529	+	0.283785i
$507$	−20.0647	+	5.59055i	−0.891107	+	0.248285i
$508$	−0.892591	−	1.54601i	−0.0396023	−	0.0685933i
$509$	7.71953	−	13.3706i	0.342162	−	0.592642i	−0.642672	−	0.766142i	$-0.722174\pi$
$509$	7.71953	−	13.3706i	0.342162	−	0.592642i	0.984834	+	0.173499i	$0.0555075\pi$
$510$	−6.30614	−	1.62276i	−0.279241	−	0.0718568i
$511$	11.0522	+	14.7959i	0.488920	+	0.654534i
$512$			1.00000i			0.0441942i
$513$	13.4009	−	4.02239i	0.591664	−	0.177593i
$514$	10.1694	−	5.87132i	0.448554	−	0.258973i
$515$	−12.7448	+	7.35823i	−0.561604	+	0.324242i
$516$	−11.6893	−	11.4594i	−0.514594	−	0.504470i
$517$			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	−0.796949	−	0.604047i	$-0.793554\pi$
$521$	−21.0358	−	36.4350i	−0.921594	−	1.59625i	−0.124646	−	0.992201i	$-0.539779\pi$
$522$	−0.368754	−	18.5571i	−0.0161399	−	0.812224i
$523$	15.4383	+	8.91333i	0.675071	+	0.389753i	0.797996	−	0.602663i	$-0.205894\pi$
$523$	15.4383	+	8.91333i	0.675071	+	0.389753i	−0.122924	+	0.992416i	$0.539227\pi$
$524$	3.10264			0.135540
$525$	−2.80060	+	3.62721i	−0.122228	+	0.158304i
$526$	22.9128			0.999046
$527$	15.5434	+	8.97396i	0.677080	+	0.390912i
$528$	2.38743	+	8.56861i	0.103900	+	0.372901i
$529$	−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
$534$	6.47621	−	6.60618i	0.280253	−	0.285877i
$535$	4.07900	−	2.35501i	0.176350	−	0.101816i
$536$	0.776110	−	0.448087i	0.0335228	−	0.0193544i
$537$	29.7289	−	30.3256i	1.28290	−	1.30864i
$538$			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	−0.180087	−	0.983651i	$-0.557638\pi$
$541$	17.7195	−	30.6912i	0.761823	−	1.31952i	0.941910	−	0.335865i	$-0.109029\pi$
$542$	5.47008	+	9.47446i	0.234960	+	0.406963i
$543$	8.67164	+	31.1229i	0.372136	+	1.33561i
$544$	−3.25579	−	1.87973i	−0.139591	−	0.0805929i
$545$	8.62362			0.369395
$546$	−22.7194	−	3.06049i	−0.972301	−	0.130977i
$547$	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
$549$	12.4451	−	0.247299i	0.531143	−	0.0105545i
$550$	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
$555$	−0.0648296	−	0.0635541i	−0.00275186	−	0.00269772i
$556$	−3.69142	+	2.13124i	−0.156551	+	0.0903847i
$557$	−5.87408	+	3.39140i	−0.248893	+	0.143698i	−0.619257	−	0.785188i	$-0.712566\pi$
$557$	−5.87408	+	3.39140i	−0.248893	+	0.143698i	0.370364	+	0.928887i	$0.379233\pi$
$558$	12.2587	−	7.40611i	0.518951	−	0.313525i
$559$		−	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	$-0.301396\pi$
$563$	−9.74586	−	16.8803i	−0.410739	−	0.711421i	−0.994971	+	0.100166i	$0.968063\pi$
$564$	−5.12048	+	1.42670i	−0.215611	+	0.0600747i
$565$	13.3202	+	7.69043i	0.560386	+	0.323539i
$566$	−22.0051			−0.924944
$567$	−22.2355	−	8.51957i	−0.933803	−	0.357788i
$568$	13.4240			0.563258
$569$	−24.4915	−	14.1402i	−1.02674	−	0.592788i	−0.110690	−	0.993855i	$-0.535306\pi$
$569$	−24.4915	−	14.1402i	−1.02674	−	0.592788i	−0.916049	+	0.401067i	$0.868639\pi$
$570$	4.49272	−	1.25179i	0.188179	−	0.0524316i
$571$	9.87150	+	17.0979i	0.413110	+	0.715527i	0.995228	−	0.0975773i	$-0.0311093\pi$
$571$	9.87150	+	17.0979i	0.413110	+	0.715527i	−0.582118	+	0.813104i	$0.697776\pi$
$572$	−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
$576$	−2.56776	+	1.55132i	−0.106990	+	0.0646384i
$577$	−17.3952	+	10.0431i	−0.724172	+	0.418101i	−0.816286	−	0.577647i	$-0.803971\pi$
$577$	−17.3952	+	10.0431i	−0.724172	+	0.418101i	0.0921142	+	0.995748i	$0.470638\pi$
$578$	−2.48239	+	1.43321i	−0.103254	+	0.0596137i
$579$	13.6847	+	13.4155i	0.568718	+	0.557529i
$580$		−	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
$585$	−15.0047	+	0.298163i	−0.620369	+	0.0123275i
$586$	9.77786	+	5.64525i	0.403920	+	0.233203i
$587$	31.1052			1.28385			0.641925	−	0.766767i	$-0.278136\pi$
$587$	31.1052			1.28385			0.641925	+	0.766767i	$0.278136\pi$
$588$	−10.4020	−	6.22876i	−0.428973	−	0.256870i
$589$	−12.8550			−0.529681
$590$	11.4849	+	6.63079i	0.472824	+	0.272985i
$591$	−4.12215	−	14.7946i	−0.169562	−	0.608567i
$592$	−0.0262075	−	0.0453927i	−0.00107712	−	0.00186563i
$593$	−4.46332	+	7.73070i	−0.183287	+	0.317462i	−0.942998	−	0.332799i	$-0.892007\pi$
$593$	−4.46332	+	7.73070i	−0.183287	+	0.317462i	0.759711	+	0.650261i	$0.225340\pi$
$594$	−18.2985	+	19.4230i	−0.750795	+	0.796936i
$595$	−1.17061	−	9.87748i	−0.0479905	−	0.404937i
$596$		−	8.97218i		−	0.367515i
$597$	22.5290	−	22.9811i	0.922051	−	0.940555i
$598$	−10.7704	+	6.21830i	−0.440435	+	0.254285i
$599$	4.30419	−	2.48502i	0.175864	−	0.101535i	−0.409484	−	0.912317i	$-0.634291\pi$
$599$	4.30419	−	2.48502i	0.175864	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$600$	−1.21252	+	1.23685i	−0.0495008	+	0.0504942i
$601$		−	25.0660i		−	1.02246i	−0.859442	−	0.511232i	$-0.829189\pi$
$601$		−	25.0660i		−	1.02246i	0.859442	−	0.511232i	$-0.170811\pi$
$602$	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
$606$	8.19529	+	29.4133i	0.332911	+	1.19483i
$607$	−20.0866	−	11.5970i	−0.815291	−	0.470709i	0.0334986	−	0.999439i	$-0.489335\pi$
$607$	−20.0866	−	11.5970i	−0.815291	−	0.470709i	−0.848790	+	0.528730i	$0.822668\pi$
$608$	2.69268			0.109202
$609$	26.2264	−	10.7712i	1.06275	−	0.436471i
$610$	4.14918			0.167995
$611$	−13.2956	−	7.67622i	−0.537883	−	0.310547i
$612$	−0.224072	−	11.2762i	−0.00905756	−	0.455812i
$613$	−2.15278	−	3.72873i	−0.0869500	−	0.150602i	0.819270	−	0.573407i	$-0.194379\pi$
$613$	−2.15278	−	3.72873i	−0.0869500	−	0.150602i	−0.906221	+	0.422805i	$0.861045\pi$
$614$	−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	$0.740034\pi$
$618$	−18.2021	−	17.8440i	−0.732195	−	0.717790i
$619$	17.5269	−	10.1191i	0.704464	−	0.406723i	−0.104544	−	0.994520i	$-0.533338\pi$
$619$	17.5269	−	10.1191i	0.704464	−	0.406723i	0.809008	+	0.587798i	$0.200005\pi$
$620$	4.13446	−	2.38703i	0.166044	−	0.0958655i
$621$	−12.3725	+	3.71373i	−0.496493	+	0.149027i
$622$			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
$627$	23.0725	−	6.42858i	0.921426	−	0.256733i
$628$	7.41664	+	4.28200i	0.295956	+	0.170870i
$629$	0.197052			0.00785699
$630$	−7.35395	−	2.98655i	−0.292988	−	0.118987i
$631$	−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
$633$	−12.2948	+	3.42565i	−0.488674	+	0.136157i
$634$	−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
$639$	20.8249	+	34.4696i	0.823820	+	1.36360i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	5.57645	−	3.21957i	0.220257	−	0.127165i	−0.385812	−	0.922577i	$-0.626079\pi$
$641$	5.57645	−	3.21957i	0.220257	−	0.127165i	0.606069	+	0.795412i	$0.292745\pi$
$642$	5.82559	+	5.71098i	0.229918	+	0.225394i
$643$		−	35.5764i		−	1.40299i	−0.712672	−	0.701497i	$-0.752515\pi$
$643$		−	35.5764i		−	1.40299i	0.712672	−	0.701497i	$-0.247485\pi$
$644$	−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	$-0.0797973\pi$
$647$	6.85590	+	11.8748i	0.269533	+	0.466845i	−0.699208	+	0.714918i	$0.746464\pi$
$648$	−7.96685	−	4.18681i	−0.312967	−	0.164473i
$649$	58.9808	+	34.0526i	2.31520	+	1.33668i
$650$	−5.00256			−0.196217
$651$	17.3165	+	13.3702i	0.678689	+	0.524021i
$652$	−11.0746			−0.433713
$653$	1.61145	+	0.930370i	0.0630608	+	0.0364082i	0.531199	−	0.847247i	$-0.321742\pi$
$653$	1.61145	+	0.930370i	0.0630608	+	0.0364082i	−0.468138	+	0.883655i	$0.655075\pi$
$654$	4.00900	+	14.3885i	0.156764	+	0.562634i
$655$	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	$0.912872\pi$
$660$	−6.22691	+	6.35188i	−0.242382	+	0.247247i
$661$	19.0521	−	10.9997i	0.741041	−	0.427840i	−0.0814067	−	0.996681i	$-0.525941\pi$
$661$	19.0521	−	10.9997i	0.741041	−	0.427840i	0.822448	+	0.568841i	$0.192608\pi$
$662$	14.6981	−	8.48598i	0.571260	−	0.329817i
$663$	22.8038	−	23.2614i	0.885625	−	0.903399i
$664$		−	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
$669$	2.69388	+	9.66847i	0.104151	+	0.373804i
$670$	0.776110	+	0.448087i	0.0299837	+	0.0173111i
$671$	21.3082			0.822595
$672$	−3.62721	−	2.80060i	−0.139923	−	0.108035i
$673$	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
$675$	−5.05694	−	1.19470i	−0.194642	−	0.0459842i
$676$	−6.01282	−	10.4145i	−0.231262	−	0.400558i
$677$	0.639271	−	1.10725i	0.0245692	−	0.0425551i	−0.853479	−	0.521127i	$-0.825512\pi$
$677$	0.639271	−	1.10725i	0.0245692	−	0.0425551i	0.878049	+	0.478572i	$0.158845\pi$
$678$	−6.63908	+	25.7999i	−0.254972	+	0.990839i
$679$	−1.66472	+	0.197292i	−0.0638860	+	0.00757136i
$680$		−	3.75947i		−	0.144169i
$681$	−13.2072	−	12.9473i	−0.506099	−	0.496142i
$682$	21.2326	−	12.2587i	0.813039	−	0.469409i
$683$	34.6622	−	20.0122i	1.32631	−	0.765747i	0.341585	−	0.939851i	$-0.389036\pi$
$683$	34.6622	−	20.0122i	1.32631	−	0.765747i	0.984727	+	0.174104i	$0.0557028\pi$
$684$	4.17720	+	6.91415i	0.159719	+	0.264369i
$685$			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
$690$	−4.14796	+	1.15573i	−0.157910	+	0.0439978i
$691$	21.6787	+	12.5162i	0.824696	+	0.476138i	0.852033	−	0.523488i	$-0.175370\pi$
$691$	21.6787	+	12.5162i	0.824696	+	0.476138i	−0.0273375	+	0.999626i	$0.508703\pi$
$692$	−20.7416			−0.788478
$693$	−37.7664	−	15.3375i	−1.43463	−	0.582623i
$694$	−33.2005			−1.26027
$695$	−3.69142	−	2.13124i	−0.140023	−	0.0808425i
$696$	10.3229	−	2.87622i	0.391288	−	0.109023i
$697$	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	$-0.0427802\pi$
$702$	−7.47297	−	24.8967i	−0.282049	−	0.939666i
$703$	−0.122228	+	0.0705683i	−0.00460991	+	0.00266153i
$704$	−4.44749	+	2.56776i	−0.167621	+	0.0967762i
$705$	−3.79579	−	3.72111i	−0.142958	−	0.140145i
$706$		−	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	0.475279	+	0.879835i	$0.342347\pi$
$709$	−13.9611	+	24.1814i	−0.524320	+	0.908150i	−0.999599	+	0.0283143i	$0.990986\pi$
$710$	6.71199	+	11.6255i	0.251896	+	0.436298i
$711$	−0.998192	−	50.2330i	−0.0374351	−	1.88388i
$712$	4.62555	+	2.67056i	0.173350	+	0.100084i
$713$	11.8685			0.444481
$714$	15.9363	−	6.54507i	0.596403	−	0.244943i
$715$	−25.6908			−0.960781
$716$	21.2335	+	12.2592i	0.793534	+	0.458147i
$717$	−5.11698	−	18.3651i	−0.191097	−	0.685856i
$718$	9.67826	+	16.7632i	0.361190	+	0.625599i
$719$	12.0025	−	20.7889i	0.447618	−	0.775296i	−0.550613	−	0.834761i	$-0.685606\pi$
$719$	12.0025	−	20.7889i	0.447618	−	0.775296i	0.998230	+	0.0594644i	$0.0189393\pi$
$720$	−2.62736	−	1.44809i	−0.0979161	−	0.0539670i
$721$	15.3643	−	35.7765i	0.572196	−	1.33239i
$722$			11.7495i			0.437271i
$723$	11.7718	−	12.0081i	0.437799	−	0.446585i
$724$	−16.1542	+	9.32664i	−0.600366	+	0.346622i
$725$	5.35804	−	3.09347i	0.198993	−	0.114889i
$726$	−18.6408	+	19.0149i	−0.691824	+	0.705708i
$727$		−	12.3007i		−	0.456206i	−0.973637	−	0.228103i	$-0.926748\pi$
$727$		−	12.3007i		−	0.456206i	0.973637	−	0.228103i	$-0.0732523\pi$
$728$	−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
$732$	1.92890	+	6.92290i	0.0712940	+	0.255878i
$733$	−18.6720	−	10.7803i	−0.689665	−	0.398178i	0.113822	−	0.993501i	$-0.463691\pi$
$733$	−18.6720	−	10.7803i	−0.689665	−	0.398178i	−0.803486	+	0.595323i	$0.797024\pi$
$734$	14.0326			0.517951
$735$	0.193238	−	12.1228i	0.00712767	−	0.447157i
$736$	−2.48605			−0.0916369
$737$	3.98573	+	2.30116i	0.146816	+	0.0847644i
$738$	19.6605	−	0.390678i	0.723712	−	0.0143811i
$739$	−0.411063	−	0.711982i	−0.0151212	−	0.0261907i	0.858366	−	0.513038i	$-0.171480\pi$
$739$	−0.411063	−	0.711982i	−0.0151212	−	0.0261907i	−0.873487	+	0.486847i	$0.838147\pi$
$740$	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	$-0.0627184\pi$
$744$	5.90481	+	5.78864i	0.216481	+	0.212222i
$745$	7.77014	−	4.48609i	0.284676	−	0.164358i
$746$	−1.15907	+	0.669190i	−0.0424366	+	0.0245008i
$747$	3.53644	−	2.13655i	0.129391	−	0.0781722i
$748$		−	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	−0.510710	−	0.859753i	$-0.670617\pi$
$751$	13.4066	−	23.2209i	0.489213	−	0.847342i	0.999923	+	0.0124115i	$0.00395079\pi$
$752$	−1.53446	−	2.65776i	−0.0559559	−	0.0969185i
$753$	7.65976	−	2.13420i	0.279137	−	0.0777747i
$754$	26.8040	+	15.4753i	0.976142	+	0.563576i
$755$	13.2266			0.481364
$756$	1.56430	−	13.6584i	0.0568931	−	0.496753i
$757$	−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
$759$	−21.3020	+	5.93527i	−0.773212	+	0.215437i
$760$	1.34634	+	2.33193i	0.0488368	+	0.0845878i
$761$	−13.6118	+	23.5763i	−0.493428	+	0.854642i	−0.999971	−	0.00757262i	$-0.997590\pi$
$761$	−13.6118	+	23.5763i	−0.493428	+	0.854642i	0.506544	+	0.862214i	$0.330923\pi$
$762$	2.99447	+	0.770566i	0.108478	+	0.0279147i
$763$	−18.2793	+	13.6542i	−0.661754	+	0.494314i
$764$			7.27434i			0.263176i
$765$	9.65341	−	5.83214i	0.349020	−	0.210861i
$766$	−20.1734	+	11.6471i	−0.728896	+	0.420828i
$767$	−57.4538	+	33.1709i	−2.07453	+	1.19773i
$768$	−1.23685	−	1.21252i	−0.0446310	−	0.0437530i
$769$			6.31431i			0.227700i	0.993498	+	0.113850i	$0.0363183\pi$
$769$			6.31431i			0.227700i	−0.993498	+	0.113850i	$0.963682\pi$
$770$	−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	−0.941395	−	0.337308i	$-0.890484\pi$
$773$	−21.2084	−	36.7341i	−0.762814	−	1.32123i	0.178580	−	0.983925i	$-0.442850\pi$
$774$	28.3470	−	0.563291i	1.01891	−	0.0202471i
$775$	4.13446	+	2.38703i	0.148514	+	0.0857447i
$776$	−0.633608			−0.0227452
$777$	0.238046	+	0.0320666i	0.00853984	+	0.00115038i
$778$	11.7488			0.421216
$779$	−15.2853	−	8.82495i	−0.547652	−	0.316187i
$780$	−2.32562	−	8.34676i	−0.0832706	−	0.298862i
$781$	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
$786$	−3.76201	+	3.83751i	−0.134186	+	0.136879i
$787$	−34.5667	+	19.9571i	−1.23217	+	0.711393i	−0.967482	−	0.252941i	$-0.918602\pi$
$787$	−34.5667	+	19.9571i	−1.23217	+	0.711393i	−0.264687	+	0.964334i	$0.585269\pi$
$788$	7.67905	−	4.43350i	0.273555	−	0.157937i
$789$	−27.7822	+	28.3397i	−0.989072	+	1.00892i
$790$		−	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
$795$	0.516971	+	1.85543i	0.0183351	+	0.0658054i
$796$	16.0911	+	9.29018i	0.570332	+	0.329282i
$797$	17.5658			0.622211			0.311105	−	0.950375i	$-0.399301\pi$
$797$	17.5658			0.622211			0.311105	+	0.950375i	$0.399301\pi$
$798$	−7.54110	+	9.76690i	−0.266952	+	0.345745i
$799$	11.5375			0.408167
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	0.318342	+	16.0202i	0.0112480	+	0.566046i
$802$	−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
$807$	−10.0482	−	9.85049i	−0.353713	−	0.346754i
$808$	−15.2668	+	8.81430i	−0.537085	+	0.310086i
$809$	−16.6120	+	9.59095i	−0.584047	+	0.337200i	−0.762740	−	0.646705i	$-0.776146\pi$
$809$	−16.6120	+	9.59095i	−0.584047	+	0.337200i	0.178693	+	0.983905i	$0.442813\pi$
$810$	−0.357541	−	8.99290i	−0.0125627	−	0.315978i
$811$			45.4972i			1.59762i	0.601582	+	0.798811i	$0.294537\pi$
$811$			45.4972i			1.59762i	−0.601582	+	0.798811i	$0.705463\pi$
$812$	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
$816$	6.27266	−	1.74772i	0.219587	−	0.0611825i
$817$	−22.0388	−	12.7241i	−0.771038	−	0.445159i
$818$	29.1034			1.01758
$819$	31.3331	−	24.3896i	1.09487	−	0.852243i
$820$	6.55478			0.228903
$821$	2.21615	+	1.27949i	0.0773441	+	0.0446546i	0.538173	−	0.842834i	$-0.319115\pi$
$821$	2.21615	+	1.27949i	0.0773441	+	0.0446546i	−0.460829	+	0.887489i	$0.652448\pi$
$822$	−16.2797	+	4.53594i	−0.567819	+	0.158209i
$823$	17.7673	+	30.7738i	0.619328	+	1.07271i	0.989609	+	0.143787i	$0.0459281\pi$
$823$	17.7673	+	30.7738i	0.619328	+	1.07271i	−0.370281	+	0.928920i	$0.620739\pi$
$824$	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	$0.989720\pi$
$828$	−3.85666	−	6.38358i	−0.134028	−	0.221845i
$829$	−46.4027	+	26.7906i	−1.61163	+	0.930477i	−0.622641	+	0.782507i	$0.713940\pi$
$829$	−46.4027	+	26.7906i	−1.61163	+	0.930477i	−0.988992	+	0.147970i	$0.952726\pi$
$830$	1.19273	−	0.688622i	0.0414002	−	0.0239024i
$831$	−5.91571	−	5.79932i	−0.205214	−	0.201176i
$832$		−	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
$837$	−5.70360	+	24.1422i	−0.197145	+	0.834476i
$838$	1.80088	+	1.03974i	0.0622102	+	0.0359171i
$839$	−6.41502			−0.221471			−0.110736	−	0.993850i	$-0.535321\pi$
$839$	−6.41502			−0.221471			−0.110736	+	0.993850i	$0.535321\pi$
$840$	0.611783	−	4.54155i	0.0211085	−	0.156699i
$841$	−9.27817			−0.319937
$842$	28.4377	+	16.4185i	0.980029	+	0.565820i
$843$	9.81094	+	35.2119i	0.337907	+	1.21276i
$844$	−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
$849$	26.6816	−	27.2171i	0.915710	−	0.934087i
$850$	3.25579	−	1.87973i	0.111673	−	0.0644743i
$851$	0.112848	−	0.0651531i	0.00386839	−	0.00223342i
$852$	−16.2768	+	16.6035i	−0.557634	+	0.568825i
$853$			40.7419i			1.39498i	0.716596	+	0.697488i	$0.245699\pi$
$853$			40.7419i			1.39498i	−0.716596	+	0.697488i	$0.754301\pi$
$854$	−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	$-0.122612\pi$
$857$	4.03870	+	6.99524i	0.137959	+	0.238953i	−0.788765	+	0.614695i	$0.789279\pi$
$858$	−11.9433	−	42.8650i	−0.407737	−	1.46339i
$859$	−11.3048	−	6.52683i	−0.385715	−	0.222693i	0.294587	−	0.955625i	$-0.404818\pi$
$859$	−11.3048	−	6.52683i	−0.385715	−	0.222693i	−0.680302	+	0.732932i	$0.738151\pi$
$860$	9.45088			0.322272
$861$	11.4116	+	27.7857i	0.388906	+	0.946934i
$862$	8.75212			0.298098
$863$	46.9292	+	27.0946i	1.59749	+	0.922310i	0.991969	+	0.126479i	$0.0403676\pi$
$863$	46.9292	+	27.0946i	1.59749	+	0.922310i	0.605518	+	0.795831i	$0.292966\pi$
$864$	1.19470	−	5.05694i	0.0406447	−	0.172041i
$865$	−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
$870$	7.65232	+	7.50177i	0.259438	+	0.254334i
$871$	−3.88254	+	2.24158i	−0.131555	+	0.0759532i
$872$	−7.46828	+	4.31181i	−0.252908	+	0.146016i
$873$	−0.982929	−	1.62695i	−0.0332671	−	0.0550641i
$874$			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	−0.663272	−	0.748378i	$-0.730833\pi$
$877$	9.37226	−	16.2332i	0.316479	−	0.548157i	0.979751	+	0.200221i	$0.0641661\pi$
$878$	5.61435	+	9.72433i	0.189475	+	0.328180i
$879$	−18.8382	+	5.24880i	−0.635396	+	0.177037i
$880$	−4.44749	−	2.56776i	−0.149925	−	0.0865593i
$881$	−36.3542			−1.22480			−0.612402	−	0.790546i	$-0.709797\pi$
$881$	−36.3542			−1.22480			−0.612402	+	0.790546i	$0.709797\pi$
$882$	20.3167	−	5.31331i	0.684099	−	0.178908i
$883$	−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
$885$	−22.1269	+	6.16512i	−0.743788	+	0.207238i
$886$	16.7161	+	28.9532i	0.561590	+	0.972702i
$887$	25.9727	−	44.9860i	0.872077	−	1.51048i	0.0122334	−	0.999925i	$-0.496106\pi$
$887$	25.9727	−	44.9860i	0.872077	−	1.51048i	0.859844	−	0.510557i	$-0.170561\pi$
$888$	0.0879211	+	0.0226247i	0.00295044	+	0.000759235i
$889$	0.555867	+	4.69033i	0.0186432	+	0.157308i
$890$			5.34113i			0.179035i
$891$	−1.83616	−	46.1832i	−0.0615138	−	1.54720i
$892$	−5.01837	+	2.89736i	−0.168028	+	0.0970107i
$893$	−7.15648	+	4.13180i	−0.239483	+	0.138265i
$894$	11.0973	+	10.8789i	0.371148	+	0.363846i
$895$			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
$900$	−0.0596020	−	2.99941i	−0.00198673	−	0.0999803i
$901$	−3.62057	−	2.09033i	−0.120619	−	0.0696391i
$902$	33.6622			1.12083
$903$	16.4536	+	40.0622i	0.547541	+	1.33319i
$904$	−15.3809			−0.511560
$905$	−16.1542	−	9.32664i	−0.536984	−	0.310028i
$906$	6.14884	+	22.0685i	0.204282	+	0.733176i
$907$	1.66199	+	2.87864i	0.0551853	+	0.0955838i	0.892298	−	0.451446i	$-0.149092\pi$
$907$	1.66199	+	2.87864i	0.0551853	+	0.0955838i	−0.837113	+	0.547030i	$0.815758\pi$
$908$	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	$-0.00262395\pi$
$912$	−3.26492	+	3.33044i	−0.108112	+	0.110282i
$913$	6.12529	−	3.53644i	0.202717	−	0.117039i
$914$	24.5277	−	14.1611i	0.811304	−	0.468406i
$915$	−5.03096	+	5.13192i	−0.166318	+	0.169656i
$916$		−	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	0.0916101	+	0.995795i	$0.470799\pi$
$919$	−24.7546	+	42.8762i	−0.816579	+	1.41436i	−0.908189	+	0.418561i	$0.862535\pi$
$920$	−1.24302	−	2.15298i	−0.0409813	−	0.0709816i
$921$	−0.986310	−	3.53991i	−0.0325000	−	0.116644i
$922$	−30.8096	−	17.7879i	−1.01466	−	0.585814i
$923$	−67.1543			−2.21041
$924$	3.14183	−	23.3233i	0.103359	−	0.767279i
$925$	0.0524150			0.00172339
$926$	−16.3134	−	9.41855i	−0.536092	−	0.309513i
$927$	44.1407	−	0.877130i	1.44977	−	0.0288087i
$928$	3.09347	+	5.35804i	0.101548	+	0.175886i
$929$	26.4197	−	45.7602i	0.866802	−	1.50134i	0.00155503	−	0.999999i	$-0.499505\pi$
$929$	26.4197	−	45.7602i	0.866802	−	1.50134i	0.865247	−	0.501346i	$-0.167162\pi$
$930$	−2.06070	+	8.00803i	−0.0675731	+	0.262594i
$931$	−18.0742	−	5.34778i	−0.592357	−	0.175266i
$932$			16.0654i			0.526241i
$933$	−13.6110	−	13.3433i	−0.445605	−	0.436838i
$934$	10.8853	−	6.28462i	0.356177	−	0.205639i
$935$	16.7202	−	9.65341i	0.546809	−	0.315700i
$936$	12.8454	−	7.76058i	0.419865	−	0.253663i
$937$		−	55.7017i		−	1.81970i	−0.414941	−	0.909848i	$-0.636198\pi$
$937$		−	55.7017i		−	1.81970i	0.414941	−	0.909848i	$-0.363802\pi$
$938$	−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	$-0.165517\pi$
$941$	0.110773	+	0.191865i	0.00361110	+	0.00625461i	−0.864214	+	0.503124i	$0.832184\pi$
$942$	−14.2890	+	3.98128i	−0.465561	+	0.129717i
$943$	14.1123	+	8.14775i	0.459560	+	0.265327i
$944$	−13.2616			−0.431628
$945$	12.6107	−	5.47449i	0.410226	−	0.178085i
$946$	48.5352			1.57802
$947$	15.0194	+	8.67143i	0.488064	+	0.281784i	0.723771	−	0.690041i	$-0.242407\pi$
$947$	15.0194	+	8.67143i	0.488064	+	0.281784i	−0.235707	+	0.971824i	$0.575741\pi$
$948$	27.9434	−	7.78573i	0.907558	−	0.252869i
$949$	−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	$0.722501\pi$
$954$	−2.85545	+	1.72513i	−0.0924486	+	0.0558531i
$955$	−6.29976	+	3.63717i	−0.203855	+	0.117696i
$956$	9.53230	−	5.50348i	0.308297	−	0.177995i
$957$	39.2987	+	38.5255i	1.27035	+	1.24535i
$958$		−	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
$963$	−14.1273	+	0.280727i	−0.455245	+	0.00904629i
$964$	8.40789	+	4.85430i	0.270800	+	0.156346i
$965$	−11.0642			−0.356168
$966$	6.96242	−	9.01741i	0.224012	−	0.290131i
$967$	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
$969$	−4.70605	−	16.8902i	−0.151180	−	0.542592i
$970$	−0.316804	−	0.548721i	−0.0101720	−	0.0176184i
$971$	0.585122	−	1.01346i	0.0187775	−	0.0325235i	−0.856484	−	0.516174i	$-0.827356\pi$
$971$	0.585122	−	1.01346i	0.0187775	−	0.0325235i	0.875261	+	0.483650i	$0.160689\pi$
$972$	14.8384	−	4.77723i	0.475942	−	0.153230i
$973$	11.1991	−	1.32724i	0.359026	−	0.0425494i
$974$			2.51593i			0.0806155i
$975$	6.06570	−	6.18743i	0.194258	−	0.198156i
$976$	−3.59330	+	2.07459i	−0.115019	+	0.0664060i
$977$	28.1359	−	16.2443i	0.900146	−	0.519700i	0.0228986	−	0.999738i	$-0.492711\pi$
$977$	28.1359	−	16.2443i	0.900146	−	0.519700i	0.877248	+	0.480038i	$0.159377\pi$
$978$	13.4281	−	13.6976i	0.429383	−	0.438000i
$979$			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	$-0.296038\pi$
$983$	−12.3949	−	21.4685i	−0.395335	−	0.684740i	−0.993144	+	0.116899i	$0.962705\pi$
$984$	3.04723	+	10.9366i	0.0971420	+	0.348647i
$985$	7.67905	+	4.43350i	0.244675	+	0.141263i
$986$	−23.2596			−0.740736
$987$	13.9377	+	1.87751i	0.443640	+	0.0597619i
$988$	−13.4703			−0.428547
$989$	20.3476	+	11.7477i	0.647015	+	0.373554i
$990$	−0.306087	−	15.4035i	−0.00972810	−	0.489556i
$991$	−17.7444	−	30.7343i	−0.563671	−	0.976307i	−0.997172	−	0.0751537i	$-0.976055\pi$
$991$	−17.7444	−	30.7343i	−0.563671	−	0.976307i	0.433501	−	0.901153i	$-0.357278\pi$
$992$	−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
$996$	1.70345	+	1.66993i	0.0539757	+	0.0529138i
$997$	−33.6474	+	19.4263i	−1.06562	+	0.615238i	−0.926982	−	0.375105i	$-0.877607\pi$
$997$	−33.6474	+	19.4263i	−1.06562	+	0.615238i	−0.138641	+	0.990343i	$0.544273\pi$
$998$	−5.32606	+	3.07500i	−0.168593	+	0.0973375i
$999$	0.0782990	+	0.260859i	0.00247727	+	0.00825320i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.6	✓	12	7.3	odd	6
210.2.r.a.131.6	yes	12	3.2	odd	2
210.2.r.b.101.3	yes	12	21.17	even	6	inner
210.2.r.b.131.3	yes	12	1.1	even	1	trivial
1050.2.s.f.101.4		12	105.59	even	6
1050.2.s.f.551.4		12	5.4	even	2
1050.2.s.g.101.1		12	35.24	odd	6
1050.2.s.g.551.1		12	15.14	odd	2
1050.2.u.e.299.3		12	5.3	odd	4
1050.2.u.e.899.3		12	105.17	odd	12
1050.2.u.f.299.1		12	15.2	even	4
1050.2.u.f.899.1		12	35.3	even	12
1050.2.u.g.299.6		12	15.8	even	4
1050.2.u.g.899.6		12	35.17	even	12
1050.2.u.h.299.4		12	5.2	odd	4
1050.2.u.h.899.4		12	105.38	odd	12
1470.2.b.a.881.4		12	21.5	even	6
1470.2.b.a.881.10		12	7.2	even	3
1470.2.b.b.881.3		12	21.2	odd	6
1470.2.b.b.881.9		12	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.66850 - 0.464886i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.67740 - 0.431645i) q^{6} +(-0.311378 - 2.62736i) q^{7} -1.00000i q^{8} +(2.56776 - 1.55132i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.66850 - 0.464886i) 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} +(2.56776 - 1.55132i) q^{9} +(0.866025 - 0.500000i) q^{10} +(4.44749 - 2.56776i) q^{11} +(1.23685 + 1.21252i) 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} +(-2.99941 + 0.0596020i) q^{18} +(2.33193 + 1.34634i) q^{19} -1.00000 q^{20} +(-1.74096 - 4.23899i) q^{21} -5.13552 q^{22} +(-2.15298 - 1.24302i) q^{23} +(-0.464886 - 1.66850i) 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} +(1.21252 - 1.23685i) q^{30} +(-4.13446 + 2.38703i) q^{31} +(0.866025 - 0.500000i) q^{32} +(6.22691 - 6.35188i) 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} +(2.32562 + 8.34676i) q^{39} +(0.866025 + 0.500000i) q^{40} -6.55478 q^{41} +(-0.611783 + 4.54155i) q^{42} -9.45088 q^{43} +(4.44749 + 2.56776i) q^{44} +(0.0596020 + 2.99941i) 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} +(-4.64990 - 4.55842i) q^{51} +(-4.33235 + 2.50128i) q^{52} +(0.963053 - 0.556019i) q^{53} +(-4.97679 + 1.49383i) 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} +(-1.66850 + 0.464886i) q^{60} +(3.59330 + 2.07459i) q^{61} +4.77406 q^{62} +(-4.87543 - 6.26340i) q^{63} -1.00000 q^{64} +(-4.33235 - 2.50128i) q^{65} +(-8.56861 + 2.38743i) 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} +(-1.55132 - 2.56776i) q^{72} +(-6.04511 + 3.49014i) q^{73} +(0.0453927 - 0.0262075i) q^{74} +(-1.23685 - 1.21252i) 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} +(4.18681 - 7.96685i) q^{81} +(5.67661 + 3.27739i) q^{82} +1.37724 q^{83} +(2.80060 - 3.62721i) q^{84} +3.75947 q^{85} +(8.18470 + 4.72544i) q^{86} +(2.87622 + 10.3229i) 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} +(-5.78864 + 5.90481i) q^{93} +(2.65776 - 1.53446i) q^{94} +(-2.33193 + 1.34634i) q^{95} +(1.21252 - 1.23685i) q^{96} -0.633608i q^{97} +(6.71235 + 1.98605i) q^{98} +(7.43669 - 13.4929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7}+O(q^{10}) \) 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{11} - 2 q^{12} - 12 q^{14} - 4 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 12 q^{20} + 4 q^{21} + 24 q^{23} - 2 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{30} + 12 q^{31} - 2 q^{33} - 4 q^{35} + 6 q^{36} - 8 q^{37} - 8 q^{38} - 42 q^{39} + 4 q^{41} + 24 q^{42} + 12 q^{44} + 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{51} - 12 q^{52} + 48 q^{53} - 32 q^{54} - 6 q^{56} - 36 q^{57} + 8 q^{58} - 12 q^{59} - 2 q^{60} - 30 q^{61} - 8 q^{62} + 20 q^{63} - 12 q^{64} - 12 q^{65} - 14 q^{66} - 4 q^{67} + 12 q^{68} - 50 q^{69} + 6 q^{70} + 4 q^{72} + 2 q^{75} - 20 q^{77} + 32 q^{78} - 4 q^{79} - 6 q^{80} - 40 q^{81} + 40 q^{83} + 20 q^{84} + 24 q^{85} + 54 q^{86} + 64 q^{87} - 26 q^{89} + 8 q^{90} + 28 q^{91} + 4 q^{93} + 24 q^{94} - 4 q^{96} - 16 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^11 - 2 * q^12 - 12 * q^14 - 4 * q^15 - 6 * q^16 - 12 * q^17 - 4 * q^18 - 12 * q^20 + 4 * q^21 + 24 * q^23 - 2 * q^24 - 6 * q^25 + 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^30 + 12 * q^31 - 2 * q^33 - 4 * q^35 + 6 * q^36 - 8 * q^37 - 8 * q^38 - 42 * q^39 + 4 * q^41 + 24 * q^42 + 12 * q^44 + 6 * q^45 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 14 * q^49 - 8 * q^51 - 12 * q^52 + 48 * q^53 - 32 * q^54 - 6 * q^56 - 36 * q^57 + 8 * q^58 - 12 * q^59 - 2 * q^60 - 30 * q^61 - 8 * q^62 + 20 * q^63 - 12 * q^64 - 12 * q^65 - 14 * 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 - 40 * q^81 + 40 * q^83 + 20 * q^84 + 24 * q^85 + 54 * q^86 + 64 * q^87 - 26 * q^89 + 8 * q^90 + 28 * q^91 + 4 * q^93 + 24 * q^94 - 4 * q^96 - 16 * q^98 + 48 * q^99

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