LMFDB - Embedded newform 210.2.r.a.101.5

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			101.5
Root			$1.73138 - 0.0481063i$ of defining polynomial
Character	$\chi$	$=$	210.101
Dual form			210.2.r.a.131.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.0481063 - 1.73138i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.907353 - 1.47537i) q^{6} +(2.27338 - 1.35342i) q^{7} -1.00000i q^{8} +(-2.99537 + 0.166581i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.0481063 - 1.73138i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.907353 - 1.47537i) q^{6} +(2.27338 - 1.35342i) q^{7} -1.00000i q^{8} +(-2.99537 + 0.166581i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-2.84394 - 1.64195i) q^{11} +(-1.52347 - 0.824030i) q^{12} +5.91369i q^{13} +(1.29209 - 2.30879i) q^{14} +(1.47537 - 0.907353i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.20199 - 2.08191i) q^{17} +(-2.51078 + 1.64195i) q^{18} +(4.77563 - 2.75721i) q^{19} +1.00000 q^{20} +(-2.45266 - 3.87098i) q^{21} -3.28390 q^{22} +(-5.62699 + 3.24875i) q^{23} +(-1.73138 + 0.0481063i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.95685 + 5.12141i) q^{26} +(0.432512 + 5.17812i) q^{27} +(-0.0354092 - 2.64551i) q^{28} +3.80949i q^{29} +(0.824030 - 1.52347i) q^{30} +(4.50485 + 2.60088i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.70603 + 5.00294i) q^{33} -2.40398i q^{34} +(2.30879 + 1.29209i) q^{35} +(-1.35342 + 2.67736i) q^{36} +(0.940152 + 1.62839i) q^{37} +(2.75721 - 4.77563i) q^{38} +(10.2389 - 0.284486i) q^{39} +(0.866025 - 0.500000i) q^{40} -0.103155 q^{41} +(-4.05955 - 2.12604i) q^{42} -1.48931 q^{43} +(-2.84394 + 1.64195i) q^{44} +(-1.64195 - 2.51078i) q^{45} +(-3.24875 + 5.62699i) q^{46} +(6.23353 + 10.7968i) q^{47} +(-1.47537 + 0.907353i) q^{48} +(3.33650 - 6.15368i) q^{49} +1.00000i q^{50} +(-3.66240 - 1.98095i) q^{51} +(5.12141 + 2.95685i) q^{52} +(-2.11123 - 1.21892i) q^{53} +(2.96363 + 4.26813i) q^{54} -3.28390i q^{55} +(-1.35342 - 2.27338i) q^{56} +(-5.00352 - 8.13580i) q^{57} +(1.90474 + 3.29911i) q^{58} +(1.82693 - 3.16433i) q^{59} +(-0.0481063 - 1.73138i) q^{60} +(-12.3257 + 7.11625i) q^{61} +5.20176 q^{62} +(-6.58416 + 4.43270i) q^{63} -1.00000 q^{64} +(-5.12141 + 2.95685i) q^{65} +(0.157976 + 5.68568i) q^{66} +(1.67736 - 2.90527i) q^{67} +(-1.20199 - 2.08191i) q^{68} +(5.89552 + 9.58619i) q^{69} +(2.64551 - 0.0354092i) q^{70} -13.9116i q^{71} +(0.166581 + 2.99537i) q^{72} +(-7.02609 - 4.05651i) q^{73} +(1.62839 + 0.940152i) q^{74} +(1.52347 + 0.824030i) q^{75} -5.51442i q^{76} +(-8.68760 + 0.116280i) q^{77} +(8.72488 - 5.36581i) q^{78} +(-4.57567 - 7.92530i) q^{79} +(0.500000 - 0.866025i) q^{80} +(8.94450 - 0.997943i) q^{81} +(-0.0893347 + 0.0515774i) q^{82} -6.54676 q^{83} +(-4.57869 + 0.188573i) q^{84} +2.40398 q^{85} +(-1.28978 + 0.744654i) q^{86} +(6.59568 - 0.183260i) q^{87} +(-1.64195 + 2.84394i) q^{88} +(-5.62039 - 9.73481i) q^{89} +(-2.67736 - 1.35342i) q^{90} +(8.00373 + 13.4441i) q^{91} +6.49749i q^{92} +(4.28640 - 7.92475i) q^{93} +(10.7968 + 6.23353i) q^{94} +(4.77563 + 2.75721i) q^{95} +(-0.824030 + 1.52347i) q^{96} -7.90564i q^{97} +(-0.187351 - 6.99749i) q^{98} +(8.79217 + 4.44450i) 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
$3$	−0.0481063	−	1.73138i	−0.0277742	−	0.999614i
$3$	−0.0481063	−	1.73138i	−0.0277742	−	0.999614i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.907353	−	1.47537i	−0.370425	−	0.602317i
$7$	2.27338	−	1.35342i	0.859256	−	0.511546i
$7$	2.27338	−	1.35342i	0.859256	−	0.511546i
$8$		−	1.00000i		−	0.353553i
$9$	−2.99537	+	0.166581i	−0.998457	+	0.0555270i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−2.84394	−	1.64195i	−0.857480	−	0.495066i	0.00568763	−	0.999984i	$-0.498190\pi$
$11$	−2.84394	−	1.64195i	−0.857480	−	0.495066i	−0.863168	+	0.504918i	$0.831523\pi$
$12$	−1.52347	−	0.824030i	−0.439789	−	0.237877i
$13$			5.91369i			1.64016i	0.572246	+	0.820082i	$0.306072\pi$
$13$			5.91369i			1.64016i	−0.572246	+	0.820082i	$0.693928\pi$
$14$	1.29209	−	2.30879i	0.345326	−	0.617049i
$15$	1.47537	−	0.907353i	0.380938	−	0.234277i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.20199	−	2.08191i	0.291525	−	0.504937i	−0.682645	−	0.730750i	$-0.739171\pi$
$17$	1.20199	−	2.08191i	0.291525	−	0.504937i	0.974171	+	0.225813i	$0.0725039\pi$
$18$	−2.51078	+	1.64195i	−0.591796	+	0.387011i
$19$	4.77563	−	2.75721i	1.09560	−	0.632547i	0.160541	−	0.987029i	$-0.448676\pi$
$19$	4.77563	−	2.75721i	1.09560	−	0.632547i	0.935063	+	0.354482i	$0.115343\pi$
$20$	1.00000			0.223607
$21$	−2.45266	−	3.87098i	−0.535213	−	0.844717i
$22$	−3.28390			−0.700129
$23$	−5.62699	+	3.24875i	−1.17331	+	0.677410i	−0.954457	−	0.298348i	$-0.903565\pi$
$23$	−5.62699	+	3.24875i	−1.17331	+	0.677410i	−0.218852	+	0.975758i	$0.570231\pi$
$24$	−1.73138	+	0.0481063i	−0.353417	+	0.00981966i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.95685	+	5.12141i	0.579885	+	1.00439i
$27$	0.432512	+	5.17812i	0.0832369	+	0.996530i
$28$	−0.0354092	−	2.64551i	−0.00669172	−	0.499955i
$29$			3.80949i			0.707404i	0.935358	+	0.353702i	$0.115077\pi$
$29$			3.80949i			0.707404i	−0.935358	+	0.353702i	$0.884923\pi$
$30$	0.824030	−	1.52347i	0.150447	−	0.278147i
$31$	4.50485	+	2.60088i	0.809096	+	0.467132i	0.846642	−	0.532163i	$-0.178621\pi$
$31$	4.50485	+	2.60088i	0.809096	+	0.467132i	−0.0375460	+	0.999295i	$0.511954\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.70603	+	5.00294i	−0.471059	+	0.870899i
$34$		−	2.40398i		−	0.412279i
$35$	2.30879	+	1.29209i	0.390256	+	0.218403i
$36$	−1.35342	+	2.67736i	−0.225570	+	0.446226i
$37$	0.940152	+	1.62839i	0.154560	+	0.267706i	0.932899	−	0.360139i	$-0.117271\pi$
$37$	0.940152	+	1.62839i	0.154560	+	0.267706i	−0.778339	+	0.627845i	$0.783937\pi$
$38$	2.75721	−	4.77563i	0.447278	−	0.774709i
$39$	10.2389	−	0.284486i	1.63953	−	0.0455542i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−0.103155			−0.0161101			−0.00805504	−	0.999968i	$-0.502564\pi$
$41$	−0.103155			−0.0161101			−0.00805504	+	0.999968i	$0.502564\pi$
$42$	−4.05955	−	2.12604i	−0.626402	−	0.328055i
$43$	−1.48931			−0.227117			−0.113559	−	0.993531i	$-0.536225\pi$
$43$	−1.48931			−0.227117			−0.113559	+	0.993531i	$0.536225\pi$
$44$	−2.84394	+	1.64195i	−0.428740	+	0.247533i
$45$	−1.64195	−	2.51078i	−0.244767	−	0.374285i
$46$	−3.24875	+	5.62699i	−0.479001	+	0.829655i
$47$	6.23353	+	10.7968i	0.909254	+	1.57487i	0.815103	+	0.579317i	$0.196681\pi$
$47$	6.23353	+	10.7968i	0.909254	+	1.57487i	0.0941518	+	0.995558i	$0.469986\pi$
$48$	−1.47537	+	0.907353i	−0.212951	+	0.130965i
$49$	3.33650	−	6.15368i	0.476642	−	0.879097i
$50$			1.00000i			0.141421i
$51$	−3.66240	−	1.98095i	−0.512839	−	0.277389i
$52$	5.12141	+	2.95685i	0.710212	+	0.410041i
$53$	−2.11123	−	1.21892i	−0.290000	−	0.167432i	0.347942	−	0.937516i	$-0.386881\pi$
$53$	−2.11123	−	1.21892i	−0.290000	−	0.167432i	−0.637942	+	0.770085i	$0.720214\pi$
$54$	2.96363	+	4.26813i	0.403298	+	0.580819i
$55$		−	3.28390i		−	0.442801i
$56$	−1.35342	−	2.27338i	−0.180859	−	0.303793i
$57$	−5.00352	−	8.13580i	−0.662733	−	1.07761i
$58$	1.90474	+	3.29911i	0.250105	+	0.433195i
$59$	1.82693	−	3.16433i	0.237846	−	0.411961i	−0.722250	−	0.691632i	$-0.756892\pi$
$59$	1.82693	−	3.16433i	0.237846	−	0.411961i	0.960096	+	0.279671i	$0.0902254\pi$
$60$	−0.0481063	−	1.73138i	−0.00621050	−	0.223521i
$61$	−12.3257	+	7.11625i	−1.57815	+	0.911143i	−0.583028	+	0.812452i	$0.698132\pi$
$61$	−12.3257	+	7.11625i	−1.57815	+	0.911143i	−0.995118	+	0.0986907i	$0.968535\pi$
$62$	5.20176			0.660624
$63$	−6.58416	+	4.43270i	−0.829526	+	0.558468i
$64$	−1.00000			−0.125000
$65$	−5.12141	+	2.95685i	−0.635233	+	0.366752i
$66$	0.157976	+	5.68568i	0.0194455	+	0.699859i
$67$	1.67736	−	2.90527i	0.204922	−	0.354935i	−0.745186	−	0.666857i	$-0.767639\pi$
$67$	1.67736	−	2.90527i	0.204922	−	0.354935i	0.950108	+	0.311922i	$0.100973\pi$
$68$	−1.20199	−	2.08191i	−0.145763	−	0.252468i
$69$	5.89552	+	9.58619i	0.709737	+	1.15404i
$70$	2.64551	−	0.0354092i	0.316199	−	0.00423221i
$71$		−	13.9116i		−	1.65100i	−0.564403	−	0.825500i	$-0.690893\pi$
$71$		−	13.9116i		−	1.65100i	0.564403	−	0.825500i	$-0.309107\pi$
$72$	0.166581	+	2.99537i	0.0196317	+	0.353008i
$73$	−7.02609	−	4.05651i	−0.822341	−	0.474779i	0.0288818	−	0.999583i	$-0.490805\pi$
$73$	−7.02609	−	4.05651i	−0.822341	−	0.474779i	−0.851223	+	0.524804i	$0.824139\pi$
$74$	1.62839	+	0.940152i	0.189297	+	0.109290i
$75$	1.52347	+	0.824030i	0.175916	+	0.0951508i
$76$		−	5.51442i		−	0.632547i
$77$	−8.68760	+	0.116280i	−0.990044	+	0.0132514i
$78$	8.72488	−	5.36581i	0.987898	−	0.607558i
$79$	−4.57567	−	7.92530i	−0.514803	−	0.891666i	−0.999852	−	0.0171788i	$-0.994532\pi$
$79$	−4.57567	−	7.92530i	−0.514803	−	0.891666i	0.485049	−	0.874487i	$-0.338802\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	8.94450	−	0.997943i	0.993834	−	0.110883i
$82$	−0.0893347	+	0.0515774i	−0.00986537	+	0.00569577i
$83$	−6.54676			−0.718600			−0.359300	−	0.933222i	$-0.616984\pi$
$83$	−6.54676			−0.718600			−0.359300	+	0.933222i	$0.616984\pi$
$84$	−4.57869	+	0.188573i	−0.499576	+	0.0205750i
$85$	2.40398			0.260748
$86$	−1.28978	+	0.744654i	−0.139080	+	0.0802981i
$87$	6.59568	−	0.183260i	0.707131	−	0.0196476i
$88$	−1.64195	+	2.84394i	−0.175032	+	0.303165i
$89$	−5.62039	−	9.73481i	−0.595761	−	1.03189i	−0.993439	−	0.114363i	$-0.963517\pi$
$89$	−5.62039	−	9.73481i	−0.595761	−	1.03189i	0.397679	−	0.917525i	$-0.369816\pi$
$90$	−2.67736	−	1.35342i	−0.282218	−	0.142663i
$91$	8.00373	+	13.4441i	0.839019	+	1.40932i
$92$			6.49749i			0.677410i
$93$	4.28640	−	7.92475i	0.444479	−	0.821758i
$94$	10.7968	+	6.23353i	1.11360	+	0.642940i
$95$	4.77563	+	2.75721i	0.489969	+	0.282884i
$96$	−0.824030	+	1.52347i	−0.0841022	+	0.155489i
$97$		−	7.90564i		−	0.802696i	−0.915926	−	0.401348i	$-0.868542\pi$
$97$		−	7.90564i		−	0.802696i	0.915926	−	0.401348i	$-0.131458\pi$
$98$	−0.187351	−	6.99749i	−0.0189253	−	0.706853i
$99$	8.79217	+	4.44450i	0.883647	+	0.446689i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.45606	−	4.25403i	0.244387	−	0.423291i	−0.717572	−	0.696485i	$-0.754746\pi$
$101$	2.45606	−	4.25403i	0.244387	−	0.423291i	0.961959	+	0.273193i	$0.0880798\pi$
$102$	−4.16221	+	0.115647i	−0.412120	+	0.0114507i
$103$	−3.96330	+	2.28821i	−0.390515	+	0.225464i	−0.682383	−	0.730995i	$-0.739056\pi$
$103$	−3.96330	+	2.28821i	−0.390515	+	0.225464i	0.291868	+	0.956459i	$0.405723\pi$
$104$	5.91369			0.579885
$105$	2.12604	−	4.05955i	0.207480	−	0.396172i
$106$	−2.43784			−0.236784
$107$	−4.27148	+	2.46614i	−0.412940	+	0.238411i	−0.692052	−	0.721848i	$-0.743293\pi$
$107$	−4.27148	+	2.46614i	−0.412940	+	0.238411i	0.279112	+	0.960258i	$0.409960\pi$
$108$	4.70064	+	2.21449i	0.452319	+	0.213090i
$109$	−3.80083	+	6.58323i	−0.364053	+	0.630559i	−0.988624	−	0.150410i	$-0.951941\pi$
$109$	−3.80083	+	6.58323i	−0.364053	+	0.630559i	0.624570	+	0.780969i	$0.285274\pi$
$110$	−1.64195	−	2.84394i	−0.156554	−	0.271159i
$111$	2.77414	−	1.70610i	0.263310	−	0.161936i
$112$	−2.30879	−	1.29209i	−0.218160	−	0.122091i
$113$			3.88234i			0.365220i	0.983185	+	0.182610i	$0.0584546\pi$
$113$			3.88234i			0.365220i	−0.983185	+	0.182610i	$0.941545\pi$
$114$	−8.40108	−	4.54405i	−0.786833	−	0.425589i
$115$	−5.62699	−	3.24875i	−0.524720	−	0.302947i
$116$	3.29911	+	1.90474i	0.306315	+	0.176851i
$117$	−0.985109	−	17.7137i	−0.0910733	−	1.63763i
$118$		−	3.65385i		−	0.336365i
$119$	−0.0851231	−	6.35976i	−0.00780322	−	0.582999i
$120$	−0.907353	−	1.47537i	−0.0828296	−	0.134682i
$121$	−0.108006	−	0.187073i	−0.00981876	−	0.0170066i
$122$	−7.11625	+	12.3257i	−0.644275	+	1.11592i
$123$	0.00496240	+	0.178601i	0.000447445	+	0.0161039i
$124$	4.50485	−	2.60088i	0.404548	−	0.233566i
$125$	−1.00000			−0.0894427
$126$	−3.48570	+	7.13091i	−0.310530	+	0.635272i
$127$	−14.1380			−1.25455			−0.627273	−	0.778799i	$-0.715829\pi$
$127$	−14.1380			−1.25455			−0.627273	+	0.778799i	$0.715829\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	0.0716451	+	2.57856i	0.00630800	+	0.227030i
$130$	−2.95685	+	5.12141i	−0.259333	+	0.449177i
$131$	2.51078	+	4.34879i	0.219368	+	0.379956i	0.954615	−	0.297843i	$-0.0962673\pi$
$131$	2.51078	+	4.34879i	0.219368	+	0.379956i	−0.735247	+	0.677799i	$0.762934\pi$
$132$	2.97965	+	4.84496i	0.259346	+	0.421700i
$133$	7.12514	−	12.7316i	0.617828	−	1.10397i
$134$		−	3.35472i		−	0.289803i
$135$	−4.26813	+	2.96363i	−0.367342	+	0.255068i
$136$	−2.08191	−	1.20199i	−0.178522	−	0.103070i
$137$	2.53719	+	1.46485i	0.216767	+	0.125150i	0.604452	−	0.796641i	$-0.293392\pi$
$137$	2.53719	+	1.46485i	0.216767	+	0.125150i	−0.387685	+	0.921792i	$0.626725\pi$
$138$	9.89876	+	5.35413i	0.842639	+	0.455774i
$139$			3.36557i			0.285464i	0.989761	+	0.142732i	$0.0455887\pi$
$139$			3.36557i			0.285464i	−0.989761	+	0.142732i	$0.954411\pi$
$140$	2.27338	−	1.35342i	0.192136	−	0.114385i
$141$	18.3935	−	11.3120i	1.54901	−	0.952644i
$142$	−6.95578	−	12.0478i	−0.583716	−	1.01103i
$143$	9.70999	−	16.8182i	0.811990	−	1.40641i
$144$	1.64195	+	2.51078i	0.136829	+	0.209231i
$145$	−3.29911	+	1.90474i	−0.273976	+	0.158180i
$146$	−8.11303			−0.671439
$147$	−10.8149	−	5.48072i	−0.891997	−	0.452042i
$148$	1.88030			0.154560
$149$	8.34064	−	4.81547i	0.683292	−	0.394499i	−0.117802	−	0.993037i	$-0.537585\pi$
$149$	8.34064	−	4.81547i	0.683292	−	0.394499i	0.801094	+	0.598538i	$0.204252\pi$
$150$	1.73138	−	0.0481063i	0.141367	−	0.00392787i
$151$	11.7684	−	20.3835i	0.957699	−	1.65878i	0.229633	−	0.973277i	$-0.426247\pi$
$151$	11.7684	−	20.3835i	0.957699	−	1.65878i	0.728066	−	0.685507i	$-0.240419\pi$
$152$	−2.75721	−	4.77563i	−0.223639	−	0.387355i
$153$	−3.25360	+	6.43632i	−0.263038	+	0.520345i
$154$	−7.46554	+	4.44450i	−0.601591	+	0.358148i
$155$			5.20176i			0.417815i
$156$	4.87306	−	9.00936i	0.390157	−	0.721326i
$157$	3.70963	+	2.14176i	0.296061	+	0.170931i	0.640672	−	0.767815i	$-0.278656\pi$
$157$	3.70963	+	2.14176i	0.296061	+	0.170931i	−0.344611	+	0.938746i	$0.611989\pi$
$158$	−7.92530	−	4.57567i	−0.630503	−	0.364021i
$159$	−2.00885	+	3.71399i	−0.159313	+	0.294539i
$160$		−	1.00000i		−	0.0790569i
$161$	−8.39536	+	15.0013i	−0.661647	+	1.18227i
$162$	7.24719	−	5.33650i	0.569393	−	0.419275i
$163$	11.0446	+	19.1299i	0.865083	+	1.49837i	0.866965	+	0.498369i	$0.166067\pi$
$163$	11.0446	+	19.1299i	0.865083	+	1.49837i	−0.00188269	+	0.999998i	$0.500599\pi$
$164$	−0.0515774	+	0.0893347i	−0.00402752	+	0.00697587i
$165$	−5.68568	+	0.157976i	−0.442630	+	0.0122984i
$166$	−5.66966	+	3.27338i	−0.440051	+	0.254063i
$167$	12.9338			1.00085			0.500424	−	0.865780i	$-0.333177\pi$
$167$	12.9338			1.00085			0.500424	+	0.865780i	$0.333177\pi$
$168$	−3.87098	+	2.45266i	−0.298653	+	0.189227i
$169$	−21.9718			−1.69014
$170$	2.08191	−	1.20199i	0.159675	−	0.0921884i
$171$	−13.8455	+	9.05440i	−1.05879	+	0.692407i
$172$	−0.744654	+	1.28978i	−0.0567793	+	0.0983447i
$173$	11.6298	+	20.1433i	0.884195	+	1.53147i	0.846634	+	0.532176i	$0.178625\pi$
$173$	11.6298	+	20.1433i	0.884195	+	1.53147i	0.0375608	+	0.999294i	$0.488041\pi$
$174$	5.62039	−	3.45655i	0.426081	−	0.262040i
$175$	0.0354092	+	2.64551i	0.00267669	+	0.199982i
$176$			3.28390i			0.247533i
$177$	−5.56655	−	3.01089i	−0.418408	−	0.226312i
$178$	−9.73481	−	5.62039i	−0.729655	−	0.421266i
$179$	−8.18788	−	4.72728i	−0.611991	−	0.353333i	0.161753	−	0.986831i	$-0.448285\pi$
$179$	−8.18788	−	4.72728i	−0.611991	−	0.353333i	−0.773744	+	0.633498i	$0.781618\pi$
$180$	−2.99537	+	0.166581i	−0.223262	+	0.0124162i
$181$		−	8.42502i		−	0.626227i	−0.949716	−	0.313113i	$-0.898628\pi$
$181$		−	8.42502i		−	0.626227i	0.949716	−	0.313113i	$-0.101372\pi$
$182$	13.6535	+	7.64104i	1.01206	+	0.566391i
$183$	12.9139	+	20.9982i	0.954623	+	1.55223i
$184$	3.24875	+	5.62699i	0.239501	+	0.414827i
$185$	−0.940152	+	1.62839i	−0.0691213	+	0.119722i
$186$	−0.250237	−	9.00623i	−0.0183483	−	0.660369i
$187$	−6.83677	+	3.94721i	−0.499954	+	0.288649i
$188$	12.4671			0.909254
$189$	7.99145	+	11.1865i	0.581292	+	0.813695i
$190$	5.51442			0.400058
$191$	4.44301	−	2.56517i	0.321485	−	0.185609i	−0.330569	−	0.943782i	$-0.607241\pi$
$191$	4.44301	−	2.56517i	0.321485	−	0.185609i	0.652054	+	0.758172i	$0.273907\pi$
$192$	0.0481063	+	1.73138i	0.00347178	+	0.124952i
$193$	−7.63955	+	13.2321i	−0.549907	+	0.952467i	0.448374	+	0.893846i	$0.352003\pi$
$193$	−7.63955	+	13.2321i	−0.549907	+	0.952467i	−0.998280	+	0.0586203i	$0.981330\pi$
$194$	−3.95282	−	6.84648i	−0.283796	−	0.491549i
$195$	5.36581	+	8.72488i	0.384253	+	0.624801i
$196$	−3.66100	−	5.96633i	−0.261500	−	0.426166i
$197$			16.0694i			1.14489i	0.819942	+	0.572447i	$0.194006\pi$
$197$			16.0694i			1.14489i	−0.819942	+	0.572447i	$0.805994\pi$
$198$	9.83650	−	0.547035i	0.699049	−	0.0388761i
$199$	−5.74190	−	3.31509i	−0.407032	−	0.235000i	0.282481	−	0.959273i	$-0.408842\pi$
$199$	−5.74190	−	3.31509i	−0.407032	−	0.235000i	−0.689514	+	0.724273i	$0.742176\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	−5.11083	−	2.76439i	−0.360490	−	0.194985i
$202$		−	4.91213i		−	0.345616i
$203$	5.15584	+	8.66040i	0.361869	+	0.607841i
$204$	−3.54676	+	2.18126i	−0.248323	+	0.152719i
$205$	−0.0515774	−	0.0893347i	−0.00360232	−	0.00623941i
$206$	−2.28821	+	3.96330i	−0.159427	+	0.276136i
$207$	16.3138	−	10.6686i	1.13388	−	0.741516i
$208$	5.12141	−	2.95685i	0.355106	−	0.205020i
$209$	−18.1088			−1.25261
$210$	−0.188573	−	4.57869i	−0.0130128	−	0.315960i
$211$	−10.9980			−0.757135			−0.378568	−	0.925574i	$-0.623583\pi$
$211$	−10.9980			−0.757135			−0.378568	+	0.925574i	$0.623583\pi$
$212$	−2.11123	+	1.21892i	−0.145000	+	0.0837158i
$213$	−24.0862	+	0.669234i	−1.65036	+	0.0458552i
$214$	−2.46614	+	4.27148i	−0.168582	+	0.291993i
$215$	−0.744654	−	1.28978i	−0.0507850	−	0.0879621i
$216$	5.17812	−	0.432512i	0.352326	−	0.0294287i
$217$	13.7613	−	0.184190i	0.934180	−	0.0125037i
$218$			7.60166i			0.514849i
$219$	−6.68538	+	12.3600i	−0.451756	+	0.835211i
$220$	−2.84394	−	1.64195i	−0.191738	−	0.110700i
$221$	12.3118	+	7.10820i	0.828179	+	0.478149i
$222$	1.54943	−	2.86459i	0.103991	−	0.192259i
$223$		−	22.0431i		−	1.47612i	−0.674737	−	0.738058i	$-0.735743\pi$
$223$		−	22.0431i		−	1.47612i	0.674737	−	0.738058i	$-0.264257\pi$
$224$	−2.64551	+	0.0354092i	−0.176761	+	0.00236588i
$225$	1.35342	−	2.67736i	0.0902282	−	0.178491i
$226$	1.94117	+	3.36221i	0.129125	+	0.223651i
$227$	3.12420	−	5.41126i	0.207360	−	0.359158i	−0.743522	−	0.668711i	$-0.766846\pi$
$227$	3.12420	−	5.41126i	0.207360	−	0.359158i	0.950882	+	0.309553i	$0.100179\pi$
$228$	−9.54757	+	0.265278i	−0.632303	+	0.0175685i
$229$	−10.5527	+	6.09261i	−0.697342	+	0.402611i	−0.806357	−	0.591429i	$-0.798564\pi$
$229$	−10.5527	+	6.09261i	−0.697342	+	0.402611i	0.109015	+	0.994040i	$0.465230\pi$
$230$	−6.49749			−0.428432
$231$	0.619254	+	15.0360i	0.0407439	+	0.989294i
$232$	3.80949			0.250105
$233$	13.9997	−	8.08273i	0.917151	−	0.529517i	0.0344258	−	0.999407i	$-0.489040\pi$
$233$	13.9997	−	8.08273i	0.917151	−	0.529517i	0.882725	+	0.469890i	$0.155706\pi$
$234$	−9.70999	−	14.8480i	−0.634762	−	0.970642i
$235$	−6.23353	+	10.7968i	−0.406631	+	0.704305i
$236$	−1.82693	−	3.16433i	−0.118923	−	0.205980i
$237$	−13.5016	+	8.30350i	−0.877024	+	0.539370i
$238$	−3.25360	−	5.46516i	−0.210900	−	0.354253i
$239$		−	5.36347i		−	0.346934i	−0.984840	−	0.173467i	$-0.944503\pi$
$239$		−	5.36347i		−	0.346934i	0.984840	−	0.173467i	$-0.0554970\pi$
$240$	−1.52347	−	0.824030i	−0.0983399	−	0.0531909i
$241$	13.9360	+	8.04597i	0.897698	+	0.518286i	0.876453	−	0.481488i	$-0.159903\pi$
$241$	13.9360	+	8.04597i	0.897698	+	0.518286i	0.0212455	+	0.999774i	$0.493237\pi$
$242$	−0.187073	−	0.108006i	−0.0120255	−	0.00694291i
$243$	−2.15811	−	15.4383i	−0.138443	−	0.990370i
$244$			14.2325i			0.911143i
$245$	6.99749	−	0.187351i	0.447053	−	0.0119694i
$246$	0.0935978	+	0.152191i	0.00596758	+	0.00970337i
$247$	16.3053	+	28.2416i	1.03748	+	1.79697i
$248$	2.60088	−	4.50485i	0.165156	−	0.286059i
$249$	0.314940	+	11.3349i	0.0199585	+	0.718323i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−1.05846			−0.0668093			−0.0334047	−	0.999442i	$-0.510635\pi$
$251$	−1.05846			−0.0668093			−0.0334047	+	0.999442i	$0.510635\pi$
$252$	0.546756	+	7.91840i	0.0344424	+	0.498812i
$253$	21.3371			1.34145
$254$	−12.2439	+	7.06901i	−0.768250	+	0.443549i
$255$	−0.115647	−	4.16221i	−0.00724207	−	0.260648i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.23091	−	2.13199i	−0.0767819	−	0.132990i	0.825078	−	0.565019i	$-0.191131\pi$
$257$	−1.23091	−	2.13199i	−0.0767819	−	0.132990i	−0.901860	+	0.432029i	$0.857798\pi$
$258$	1.35133	+	2.19728i	0.0841299	+	0.136796i
$259$	4.34122	+	2.42953i	0.269750	+	0.150963i
$260$			5.91369i			0.366752i
$261$	−0.634588	−	11.4108i	−0.0392800	−	0.706312i
$262$	4.34879	+	2.51078i	0.268669	+	0.155116i
$263$	−26.5856	−	15.3492i	−1.63934	−	0.946471i	−0.981062	−	0.193692i	$-0.937954\pi$
$263$	−26.5856	−	15.3492i	−1.63934	−	0.946471i	−0.658273	−	0.752779i	$-0.728713\pi$
$264$	5.00294	+	2.70603i	0.307909	+	0.166545i
$265$		−	2.43784i		−	0.149755i
$266$	−0.195261	−	14.5885i	−0.0119722	−	0.894477i
$267$	−16.5843	+	10.1994i	−1.01494	+	0.624191i
$268$	−1.67736	−	2.90527i	−0.102461	−	0.177468i
$269$	−8.37650	+	14.5085i	−0.510724	+	0.884601i	0.489198	+	0.872173i	$0.337289\pi$
$269$	−8.37650	+	14.5085i	−0.510724	+	0.884601i	−0.999923	+	0.0124280i	$0.996044\pi$
$270$	−2.21449	+	4.70064i	−0.134770	+	0.286072i
$271$	13.2178	−	7.63132i	0.802926	−	0.463570i	−0.0415670	−	0.999136i	$-0.513235\pi$
$271$	13.2178	−	7.63132i	0.802926	−	0.463570i	0.844493	+	0.535566i	$0.179902\pi$
$272$	−2.40398			−0.145763
$273$	22.8918	−	14.5043i	1.38547	−	0.877838i
$274$	2.92970			0.176989
$275$	2.84394	−	1.64195i	0.171496	−	0.0990133i
$276$	11.2496	−	0.312570i	0.677149	−	0.0188145i
$277$	1.75611	−	3.04167i	0.105514	−	0.182756i	−0.808434	−	0.588587i	$-0.799684\pi$
$277$	1.75611	−	3.04167i	0.105514	−	0.182756i	0.913948	+	0.405831i	$0.133018\pi$
$278$	1.68279	+	2.91467i	0.100927	+	0.174810i
$279$	−13.9270	−	7.04018i	−0.833786	−	0.421484i
$280$	1.29209	−	2.30879i	0.0772173	−	0.137976i
$281$		−	4.15840i		−	0.248069i	−0.992278	−	0.124035i	$-0.960417\pi$
$281$		−	4.15840i		−	0.248069i	0.992278	−	0.124035i	$-0.0395834\pi$
$282$	10.2732	−	18.9933i	0.611762	−	1.13103i
$283$	0.149485	+	0.0863055i	0.00888599	+	0.00513033i	0.504436	−	0.863449i	$-0.331700\pi$
$283$	0.149485	+	0.0863055i	0.00888599	+	0.00513033i	−0.495550	+	0.868579i	$0.665034\pi$
$284$	−12.0478	−	6.95578i	−0.714904	−	0.412750i
$285$	4.54405	−	8.40108i	0.269166	−	0.497637i
$286$		−	19.4200i		−	1.14833i
$287$	−0.234510	+	0.139612i	−0.0138427	+	0.00824104i
$288$	2.67736	+	1.35342i	0.157765	+	0.0797512i
$289$	5.61044	+	9.71757i	0.330026	+	0.571622i
$290$	−1.90474	+	3.29911i	−0.111850	+	0.193730i
$291$	−13.6877	+	0.380311i	−0.802386	+	0.0222942i
$292$	−7.02609	+	4.05651i	−0.411171	+	0.237390i
$293$	−4.38021			−0.255895			−0.127947	−	0.991781i	$-0.540839\pi$
$293$	−4.38021			−0.255895			−0.127947	+	0.991781i	$0.540839\pi$
$294$	−12.1063	+	0.661000i	−0.706055	+	0.0385503i
$295$	3.65385			0.212736
$296$	1.62839	−	0.940152i	0.0946483	−	0.0546452i
$297$	7.27217	−	15.4364i	0.421974	−	0.895712i
$298$	4.81547	−	8.34064i	0.278953	−	0.483160i
$299$	−19.2121	−	33.2763i	−1.11106	−	1.92442i
$300$	1.47537	−	0.907353i	0.0851804	−	0.0523860i
$301$	−3.38576	+	2.01566i	−0.195152	+	0.116181i
$302$		−	23.5368i		−	1.35439i
$303$	−7.48350	−	4.04774i	−0.429916	−	0.232537i
$304$	−4.77563	−	2.75721i	−0.273901	−	0.158137i
$305$	−12.3257	−	7.11625i	−0.705768	−	0.407476i
$306$	0.400457	+	7.20081i	0.0228926	+	0.411643i
$307$		−	4.76658i		−	0.272043i	−0.990706	−	0.136022i	$-0.956568\pi$
$307$		−	4.76658i		−	0.272043i	0.990706	−	0.136022i	$-0.0434316\pi$
$308$	−4.24310	+	7.58182i	−0.241773	+	0.432014i
$309$	4.15243	+	6.75190i	0.236223	+	0.384102i
$310$	2.60088	+	4.50485i	0.147720	+	0.255859i
$311$	−2.98511	+	5.17035i	−0.169270	+	0.293184i	−0.938163	−	0.346193i	$-0.887474\pi$
$311$	−2.98511	+	5.17035i	−0.169270	+	0.293184i	0.768894	+	0.639377i	$0.220808\pi$
$312$	−0.284486	−	10.2389i	−0.0161059	−	0.579662i
$313$	23.1417	−	13.3609i	1.30805	−	0.755201i	0.326277	−	0.945274i	$-0.394206\pi$
$313$	23.1417	−	13.3609i	1.30805	−	0.755201i	0.981770	+	0.190073i	$0.0608726\pi$
$314$	4.28351			0.241733
$315$	−7.13091	−	3.48570i	−0.401781	−	0.196397i
$316$	−9.15135			−0.514803
$317$	20.5873	−	11.8861i	1.15630	−	0.667588i	0.205883	−	0.978577i	$-0.433993\pi$
$317$	20.5873	−	11.8861i	1.15630	−	0.667588i	0.950414	+	0.310988i	$0.100660\pi$
$318$	0.117276	+	4.22084i	0.00657649	+	0.236693i
$319$	6.25498	−	10.8339i	0.350212	−	0.606584i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	4.47532	+	7.27694i	0.249788	+	0.406159i
$322$	0.230071	+	17.1892i	0.0128214	+	0.957917i
$323$		−	13.2566i		−	0.737615i
$324$	3.60801	−	8.24514i	0.200445	−	0.458063i
$325$	−5.12141	−	2.95685i	−0.284085	−	0.164016i
$326$	19.1299	+	11.0446i	1.05951	+	0.611706i
$327$	11.5809	+	6.26399i	0.640427	+	0.346400i
$328$			0.103155i			0.00569577i
$329$	28.7838	+	16.1086i	1.58690	+	0.888096i
$330$	−4.84496	+	2.97965i	−0.266706	+	0.164025i
$331$	−2.27966	−	3.94849i	−0.125301	−	0.217028i	0.796549	−	0.604574i	$-0.206656\pi$
$331$	−2.27966	−	3.94849i	−0.125301	−	0.217028i	−0.921851	+	0.387545i	$0.873323\pi$
$332$	−3.27338	+	5.66966i	−0.179650	+	0.311163i
$333$	−3.08736	−	4.72102i	−0.169186	−	0.258711i
$334$	11.2010	−	6.46690i	0.612892	−	0.353853i
$335$	3.35472			0.183288
$336$	−2.12604	+	4.05955i	−0.115985	+	0.221467i
$337$	12.8779			0.701503			0.350751	−	0.936469i	$-0.385926\pi$
$337$	12.8779			0.701503			0.350751	+	0.936469i	$0.385926\pi$
$338$	−19.0281	+	10.9859i	−1.03499	+	0.597554i
$339$	6.72182	−	0.186765i	0.365079	−	0.0101437i
$340$	1.20199	−	2.08191i	0.0651871	−	0.112907i
$341$	−8.54102	−	14.7935i	−0.462522	−	0.801112i
$342$	−7.46334	+	14.7641i	−0.403571	+	0.798350i
$343$	−0.743416	−	18.5053i	−0.0401407	−	0.999194i
$344$			1.48931i			0.0802981i
$345$	−5.35413	+	9.89876i	−0.288257	+	0.532932i
$346$	20.1433	+	11.6298i	1.08291	+	0.625220i
$347$	16.2720	+	9.39464i	0.873526	+	0.504331i	0.868518	−	0.495657i	$-0.165073\pi$
$347$	16.2720	+	9.39464i	0.873526	+	0.504331i	0.00500776	+	0.999987i	$0.498406\pi$
$348$	3.13913	−	5.80365i	0.168275	−	0.311108i
$349$		−	8.52974i		−	0.456586i	−0.973592	−	0.228293i	$-0.926686\pi$
$349$		−	8.52974i		−	0.456586i	0.973592	−	0.228293i	$-0.0733145\pi$
$350$	1.35342	+	2.27338i	0.0723435	+	0.121517i
$351$	−30.6218	+	2.55774i	−1.63447	+	0.136522i
$352$	1.64195	+	2.84394i	0.0875162	+	0.151582i
$353$	−2.80987	+	4.86684i	−0.149554	+	0.259036i	−0.931063	−	0.364859i	$-0.881117\pi$
$353$	−2.80987	+	4.86684i	−0.149554	+	0.259036i	0.781508	+	0.623895i	$0.214451\pi$
$354$	−6.32622	+	0.175774i	−0.336235	+	0.00934226i
$355$	12.0478	−	6.95578i	0.639429	−	0.369175i
$356$	−11.2408			−0.595761
$357$	−11.0071	+	0.453326i	−0.582557	+	0.0239925i
$358$	−9.45455			−0.499689
$359$	23.4396	−	13.5328i	1.23709	−	0.714236i	0.268594	−	0.963254i	$-0.413441\pi$
$359$	23.4396	−	13.5328i	1.23709	−	0.714236i	0.968499	+	0.249018i	$0.0801077\pi$
$360$	−2.51078	+	1.64195i	−0.132330	+	0.0865383i
$361$	5.70441	−	9.88033i	0.300232	−	0.520017i
$362$	−4.21251	−	7.29628i	−0.221405	−	0.383484i
$363$	−0.318698	+	0.196000i	−0.0167273	+	0.0102873i
$364$	15.6448	−	0.209399i	0.820008	−	0.0109755i
$365$		−	8.11303i		−	0.424655i
$366$	21.6829	+	11.7280i	1.13338	+	0.613033i
$367$	−16.2700	−	9.39351i	−0.849289	−	0.490337i	0.0111216	−	0.999938i	$-0.496460\pi$
$367$	−16.2700	−	9.39351i	−0.849289	−	0.490337i	−0.860411	+	0.509601i	$0.829793\pi$
$368$	5.62699	+	3.24875i	0.293327	+	0.169353i
$369$	0.308987	−	0.0171836i	0.0160852	−	0.000894544i
$370$			1.88030i			0.0977523i
$371$	−6.44934	+	0.0863221i	−0.334833	+	0.00448162i
$372$	−4.71983	−	7.67451i	−0.244712	−	0.397905i
$373$	6.66836	+	11.5499i	0.345275	+	0.598033i	0.985404	−	0.170234i	$-0.0544524\pi$
$373$	6.66836	+	11.5499i	0.345275	+	0.598033i	−0.640129	+	0.768268i	$0.721119\pi$
$374$	−3.94721	+	6.83677i	−0.204106	+	0.353521i
$375$	0.0481063	+	1.73138i	0.00248420	+	0.0894082i
$376$	10.7968	−	6.23353i	0.556802	−	0.321470i
$377$	−22.5281			−1.16026
$378$	12.5140	+	5.69203i	0.643652	+	0.292766i
$379$	−33.4683			−1.71915			−0.859576	−	0.511008i	$-0.829272\pi$
$379$	−33.4683			−1.71915			−0.859576	+	0.511008i	$0.829272\pi$
$380$	4.77563	−	2.75721i	0.244985	−	0.141442i
$381$	0.680128	+	24.4783i	0.0348440	+	1.25406i
$382$	2.56517	−	4.44301i	0.131246	−	0.227324i
$383$	4.64240	+	8.04088i	0.237216	+	0.410870i	0.959914	−	0.280294i	$-0.0904319\pi$
$383$	4.64240	+	8.04088i	0.237216	+	0.410870i	−0.722699	+	0.691163i	$0.757099\pi$
$384$	0.907353	+	1.47537i	0.0463031	+	0.0752896i
$385$	−4.44450	−	7.46554i	−0.226513	−	0.380479i
$386$			15.2791i			0.777686i
$387$	4.46103	−	0.248090i	0.226767	−	0.0126111i
$388$	−6.84648	−	3.95282i	−0.347578	−	0.200674i
$389$	16.8511	+	9.72899i	0.854385	+	0.493279i	0.862128	−	0.506691i	$-0.169131\pi$
$389$	16.8511	+	9.72899i	0.854385	+	0.493279i	−0.00774302	+	0.999970i	$0.502465\pi$
$390$	9.00936	+	4.87306i	0.456207	+	0.246757i
$391$			15.6198i			0.789929i
$392$	−6.15368	−	3.33650i	−0.310808	−	0.168518i
$393$	7.40864	−	4.55632i	0.373717	−	0.229836i
$394$	8.03468	+	13.9165i	0.404781	+	0.701102i
$395$	4.57567	−	7.92530i	0.230227	−	0.398765i
$396$	8.24514	−	5.39199i	0.414334	−	0.270958i
$397$	1.98370	−	1.14529i	0.0995589	−	0.0574804i	−0.449394	−	0.893334i	$-0.648360\pi$
$397$	1.98370	−	1.14529i	0.0995589	−	0.0574804i	0.548953	+	0.835853i	$0.315027\pi$
$398$	−6.63017			−0.332341
$399$	−22.3861	−	11.7239i	−1.12071	−	0.586927i
$400$	1.00000			0.0500000
$401$	−1.30687	+	0.754520i	−0.0652618	+	0.0376789i	−0.532276	−	0.846571i	$-0.678663\pi$
$401$	−1.30687	+	0.754520i	−0.0652618	+	0.0376789i	0.467014	+	0.884250i	$0.345330\pi$
$402$	−5.80830	+	0.161383i	−0.289692	+	0.00804906i
$403$	−15.3808	+	26.6403i	−0.766172	+	1.32705i
$404$	−2.45606	−	4.25403i	−0.122194	−	0.211646i
$405$	5.33650	+	7.24719i	0.265173	+	0.360116i
$406$	8.79529	+	4.92221i	0.436503	+	0.244285i
$407$		−	6.17473i		−	0.306070i
$408$	−1.98095	+	3.66240i	−0.0980717	+	0.181316i
$409$	16.6655	+	9.62186i	0.824058	+	0.475770i	0.851814	−	0.523845i	$-0.175503\pi$
$409$	16.6655	+	9.62186i	0.824058	+	0.475770i	−0.0277558	+	0.999615i	$0.508836\pi$
$410$	−0.0893347	−	0.0515774i	−0.00441193	−	0.00254723i
$411$	2.41416	−	4.46332i	0.119082	−	0.220159i
$412$			4.57642i			0.225464i
$413$	−0.129380	−	9.66632i	−0.00636638	−	0.475649i
$414$	8.79385	−	17.3961i	0.432194	−	0.854972i
$415$	−3.27338	−	5.66966i	−0.160684	−	0.278313i
$416$	2.95685	−	5.12141i	0.144971	−	0.251098i
$417$	5.82710	−	0.161905i	0.285354	−	0.00792854i
$418$	−15.6827	+	9.05440i	−0.767065	+	0.442865i
$419$	−1.34919			−0.0659121			−0.0329560	−	0.999457i	$-0.510492\pi$
$419$	−1.34919			−0.0659121			−0.0329560	+	0.999457i	$0.510492\pi$
$420$	−2.45266	−	3.87098i	−0.119677	−	0.188884i
$421$	−23.3783			−1.13939			−0.569695	−	0.821856i	$-0.692939\pi$
$421$	−23.3783			−1.13939			−0.569695	+	0.821856i	$0.692939\pi$
$422$	−9.52457	+	5.49901i	−0.463649	+	0.267688i
$423$	−20.4703	−	31.3020i	−0.995299	−	1.52196i
$424$	−1.21892	+	2.11123i	−0.0591960	+	0.102531i
$425$	1.20199	+	2.08191i	0.0583051	+	0.100987i
$426$	−20.5247	+	12.6227i	−0.994424	+	0.611572i
$427$	−18.3897	+	32.8598i	−0.889940	+	1.59020i
$428$			4.93228i			0.238411i
$429$	−29.5858	−	16.0026i	−1.42842	−	0.772615i
$430$	−1.28978	−	0.744654i	−0.0621986	−	0.0359104i
$431$	6.72021	+	3.87992i	0.323701	+	0.186889i	0.653041	−	0.757322i	$-0.273493\pi$
$431$	6.72021	+	3.87992i	0.323701	+	0.186889i	−0.329340	+	0.944211i	$0.606826\pi$
$432$	4.26813	−	2.96363i	0.205350	−	0.142588i
$433$			34.0914i			1.63833i	0.573560	+	0.819164i	$0.305562\pi$
$433$			34.0914i			1.63833i	−0.573560	+	0.819164i	$0.694438\pi$
$434$	11.8256	−	7.04018i	0.567645	−	0.337939i
$435$	3.45655	+	5.62039i	0.165729	+	0.269477i
$436$	3.80083	+	6.58323i	0.182027	+	0.315279i
$437$	−17.9149	+	31.0296i	−0.856988	+	1.48435i
$438$	0.390288	+	14.0468i	0.0186487	+	0.671180i
$439$	10.3571	−	5.97965i	0.494316	−	0.285393i	−0.232047	−	0.972704i	$-0.574542\pi$
$439$	10.3571	−	5.97965i	0.494316	−	0.285393i	0.726363	+	0.687311i	$0.241209\pi$
$440$	−3.28390			−0.156554
$441$	−8.96896	+	18.9884i	−0.427093	+	0.904208i
$442$	14.2164			0.676205
$443$	−3.12301	+	1.80307i	−0.148378	+	0.0856663i	−0.572351	−	0.820009i	$-0.693969\pi$
$443$	−3.12301	+	1.80307i	−0.148378	+	0.0856663i	0.423973	+	0.905675i	$0.360635\pi$
$444$	−0.0904545	−	3.25553i	−0.00429278	−	0.154500i
$445$	5.62039	−	9.73481i	0.266432	−	0.461474i
$446$	−11.0216	−	19.0899i	−0.521886	−	0.903933i
$447$	−8.73866	−	14.2092i	−0.413325	−	0.672072i
$448$	−2.27338	+	1.35342i	−0.107407	+	0.0639432i
$449$			19.0134i			0.897296i	0.893708	+	0.448648i	$0.148094\pi$
$449$			19.0134i			0.897296i	−0.893708	+	0.448648i	$0.851906\pi$
$450$	−0.166581	−	2.99537i	−0.00785270	−	0.141203i
$451$	0.293366	+	0.169375i	0.0138141	+	0.00797556i
$452$	3.36221	+	1.94117i	0.158145	+	0.0913050i
$453$	−35.8577	−	19.3950i	−1.68474	−	0.911258i
$454$		−	6.24839i		−	0.293251i
$455$	−7.64104	+	13.6535i	−0.358217	+	0.640084i
$456$	−8.13580	+	5.00352i	−0.380994	+	0.234311i
$457$	−18.9452	−	32.8141i	−0.886219	−	1.53498i	−0.844310	−	0.535856i	$-0.819989\pi$
$457$	−18.9452	−	32.8141i	−0.886219	−	1.53498i	−0.0419097	−	0.999121i	$-0.513344\pi$
$458$	−6.09261	+	10.5527i	−0.284689	+	0.493095i
$459$	11.3002	+	5.32360i	0.527450	+	0.248484i
$460$	−5.62699	+	3.24875i	−0.262360	+	0.151474i
$461$	32.6110			1.51884			0.759422	−	0.650598i	$-0.225482\pi$
$461$	32.6110			1.51884			0.759422	+	0.650598i	$0.225482\pi$
$462$	8.05427	+	12.7119i	0.374719	+	0.591411i
$463$	5.80289			0.269683			0.134841	−	0.990867i	$-0.456947\pi$
$463$	5.80289			0.269683			0.134841	+	0.990867i	$0.456947\pi$
$464$	3.29911	−	1.90474i	0.153157	−	0.0884255i
$465$	9.00623	−	0.250237i	0.417654	−	0.0116045i
$466$	8.08273	−	13.9997i	0.374425	−	0.648524i
$467$	11.1463	+	19.3060i	0.515790	+	0.893375i	0.999832	+	0.0183299i	$0.00583491\pi$
$467$	11.1463	+	19.3060i	0.515790	+	0.893375i	−0.484042	+	0.875045i	$0.660832\pi$
$468$	−15.8331	−	8.00373i	−0.731884	−	0.369972i
$469$	−0.118788	−	8.87495i	−0.00548512	−	0.409807i
$470$			12.4671i			0.575063i
$471$	3.52974	−	6.52582i	0.162642	−	0.300694i
$472$	−3.16433	−	1.82693i	−0.145650	−	0.0840911i
$473$	4.23550	+	2.44537i	0.194748	+	0.112438i
$474$	−7.54098	+	13.9418i	−0.346369	+	0.640370i
$475$			5.51442i			0.253019i
$476$	−5.55028	−	3.10616i	−0.254397	−	0.142371i
$477$	6.52697	+	3.29943i	0.298850	+	0.151070i
$478$	−2.68173	−	4.64490i	−0.122660	−	0.212453i
$479$	−21.1941	+	36.7093i	−0.968385	+	1.67729i	−0.268154	+	0.963376i	$0.586414\pi$
$479$	−21.1941	+	36.7093i	−0.968385	+	1.67729i	−0.700231	+	0.713916i	$0.746920\pi$
$480$	−1.73138	+	0.0481063i	−0.0790264	+	0.00219574i
$481$	−9.62981	+	5.55977i	−0.439081	+	0.253504i
$482$	16.0919			0.732968
$483$	26.3769	+	13.8139i	1.20019	+	0.628555i
$484$	−0.216013			−0.00981876
$485$	6.84648	−	3.95282i	0.310883	−	0.179488i
$486$	−9.58815	−	12.2909i	−0.434927	−	0.557529i
$487$	−8.77524	+	15.1992i	−0.397644	+	0.688740i	−0.993435	−	0.114400i	$-0.963506\pi$
$487$	−8.77524	+	15.1992i	−0.397644	+	0.688740i	0.595790	+	0.803140i	$0.296839\pi$
$488$	7.11625	+	12.3257i	0.322138	+	0.557959i
$489$	32.5898	−	20.0428i	1.47376	−	0.906365i
$490$	5.96633	−	3.66100i	0.269531	−	0.165387i
$491$		−	31.2732i		−	1.41134i	−0.708542	−	0.705669i	$-0.750647\pi$
$491$		−	31.2732i		−	1.41134i	0.708542	−	0.705669i	$-0.249353\pi$
$492$	0.157154	+	0.0850027i	0.00708504	+	0.00383222i
$493$	7.93100	+	4.57896i	0.357194	+	0.206226i
$494$	28.2416	+	16.3053i	1.27065	+	0.733610i
$495$	0.547035	+	9.83650i	0.0245874	+	0.442118i
$496$		−	5.20176i		−	0.233566i
$497$	−18.8282	−	31.6263i	−0.844561	−	1.41863i
$498$	5.94022	+	9.65888i	0.266187	+	0.432825i
$499$	2.68212	+	4.64557i	0.120068	+	0.207964i	0.919794	−	0.392401i	$-0.128355\pi$
$499$	2.68212	+	4.64557i	0.120068	+	0.207964i	−0.799726	+	0.600365i	$0.795022\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−0.622198	−	22.3934i	−0.0277978	−	1.00046i
$502$	−0.916652	+	0.529229i	−0.0409122	+	0.0236207i
$503$	21.3393			0.951470			0.475735	−	0.879589i	$-0.342182\pi$
$503$	21.3393			0.951470			0.475735	+	0.879589i	$0.342182\pi$
$504$	4.43270	+	6.58416i	0.197448	+	0.293282i
$505$	4.91213			0.218587
$506$	18.4785	−	10.6686i	0.821468	−	0.474275i
$507$	1.05698	+	38.0416i	0.0469422	+	1.68949i
$508$	−7.06901	+	12.2439i	−0.313637	+	0.543234i
$509$	16.1907	+	28.0432i	0.717642	+	1.24299i	0.961932	+	0.273290i	$0.0881118\pi$
$509$	16.1907	+	28.0432i	0.717642	+	1.24299i	−0.244290	+	0.969702i	$0.578555\pi$
$510$	−2.18126	−	3.54676i	−0.0965877	−	0.157053i
$511$	−21.4631	+	0.287276i	−0.949473	+	0.0127083i
$512$			1.00000i			0.0441942i
$513$	16.3427	+	23.5363i	0.721547	+	1.03915i
$514$	−2.13199	−	1.23091i	−0.0940382	−	0.0542930i
$515$	−3.96330	−	2.28821i	−0.174644	−	0.100831i
$516$	2.26892	+	1.22723i	0.0998837	+	0.0540260i
$517$		−	40.9406i		−	1.80056i
$518$	4.97437	−	0.0665801i	0.218561	−	0.00292536i
$519$	34.3164	−	21.1046i	1.50632	−	0.926389i
$520$	2.95685	+	5.12141i	0.129666	+	0.224589i
$521$	−13.0323	+	22.5726i	−0.570955	+	0.988923i	0.425514	+	0.904952i	$0.360093\pi$
$521$	−13.0323	+	22.5726i	−0.570955	+	0.988923i	−0.996468	+	0.0839705i	$0.973240\pi$
$522$	−6.25498	−	9.56477i	−0.273773	−	0.418639i
$523$	11.2502	−	6.49533i	0.491939	−	0.284021i	−0.233440	−	0.972371i	$-0.574998\pi$
$523$	11.2502	−	6.49533i	0.491939	−	0.284021i	0.725379	+	0.688350i	$0.241665\pi$
$524$	5.02155			0.219368
$525$	4.57869	−	0.188573i	0.199831	−	0.00823000i
$526$	−30.6984			−1.33851
$527$	10.8296	−	6.25246i	0.471744	−	0.272362i
$528$	5.68568	−	0.157976i	0.247438	−	0.00687504i
$529$	9.60870	−	16.6428i	0.417770	−	0.723598i
$530$	−1.21892	−	2.11123i	−0.0529465	−	0.0917061i
$531$	−4.94521	+	9.78268i	−0.214604	+	0.424532i
$532$	−7.46334	−	12.5364i	−0.323577	−	0.543520i
$533$		−	0.610026i		−	0.0264232i
$534$	−9.26275	+	17.1251i	−0.400838	+	0.741073i
$535$	−4.27148	−	2.46614i	−0.184672	−	0.106621i
$536$	−2.90527	−	1.67736i	−0.125489	−	0.0724508i
$537$	−7.79083	+	14.4038i	−0.336199	+	0.621569i
$538$			16.7530i			0.722273i
$539$	−19.5928	+	12.0223i	−0.843923	+	0.517839i
$540$	0.432512	+	5.17812i	0.0186123	+	0.222831i
$541$	−10.6231	−	18.3998i	−0.456724	−	0.791069i	0.542062	−	0.840339i	$-0.317644\pi$
$541$	−10.6231	−	18.3998i	−0.456724	−	0.791069i	−0.998786	+	0.0492698i	$0.984311\pi$
$542$	7.63132	−	13.2178i	0.327793	−	0.567755i
$543$	−14.5869	+	0.405297i	−0.625985	+	0.0173930i
$544$	−2.08191	+	1.20199i	−0.0892611	+	0.0515349i
$545$	−7.60166			−0.325619
$546$	12.5727	−	24.0070i	0.538064	−	1.02740i
$547$	5.49150			0.234800			0.117400	−	0.993085i	$-0.462544\pi$
$547$	5.49150			0.234800			0.117400	+	0.993085i	$0.462544\pi$
$548$	2.53719	−	1.46485i	0.108383	−	0.0625752i
$549$	35.7347	−	23.3691i	1.52512	−	0.997367i
$550$	1.64195	−	2.84394i	0.0700129	−	0.121266i
$551$	10.5036	+	18.1927i	0.447466	+	0.775034i
$552$	9.58619	−	5.89552i	0.408015	−	0.250930i
$553$	−21.1285	−	11.8244i	−0.898476	−	0.502824i
$554$		−	3.51222i		−	0.149220i
$555$	2.86459	+	1.54943i	0.121595	+	0.0657695i
$556$	2.91467	+	1.68279i	0.123610	+	0.0713661i
$557$	−30.7037	−	17.7268i	−1.30096	−	0.751109i	−0.320390	−	0.947286i	$-0.603814\pi$
$557$	−30.7037	−	17.7268i	−1.30096	−	0.751109i	−0.980568	+	0.196177i	$0.937147\pi$
$558$	−15.5812	+	0.866514i	−0.659605	+	0.0366824i
$559$		−	8.80731i		−	0.372509i
$560$	−0.0354092	−	2.64551i	−0.00149631	−	0.111793i
$561$	7.16303	+	11.6472i	0.302423	+	0.491745i
$562$	−2.07920	−	3.60128i	−0.0877058	−	0.151911i
$563$	19.5733	−	33.9020i	0.824916	−	1.42880i	−0.0770670	−	0.997026i	$-0.524556\pi$
$563$	19.5733	−	33.9020i	0.824916	−	1.42880i	0.901983	−	0.431771i	$-0.142111\pi$
$564$	−0.599745	−	21.5853i	−0.0252538	−	0.908904i
$565$	−3.36221	+	1.94117i	−0.141449	+	0.0816657i
$566$	0.172611			0.00725538
$567$	18.9836	−	14.3744i	0.797236	−	0.603668i
$568$	−13.9116			−0.583716
$569$	36.3773	−	21.0025i	1.52502	−	0.880469i	0.525457	−	0.850820i	$-0.323894\pi$
$569$	36.3773	−	21.0025i	1.52502	−	0.880469i	0.999560	−	0.0296490i	$-0.00943896\pi$
$570$	−0.265278	−	9.54757i	−0.0111113	−	0.399904i
$571$	9.84182	−	17.0465i	0.411867	−	0.713375i	−0.583227	−	0.812310i	$-0.698210\pi$
$571$	9.84182	−	17.0465i	0.411867	−	0.713375i	0.995094	+	0.0989342i	$0.0315433\pi$
$572$	−9.70999	−	16.8182i	−0.405995	−	0.703204i
$573$	−4.65503	−	7.56915i	−0.194467	−	0.316206i
$574$	−0.133286	+	0.238163i	−0.00556323	+	0.00994072i
$575$		−	6.49749i		−	0.270964i
$576$	2.99537	−	0.166581i	0.124807	−	0.00694087i
$577$	21.9785	+	12.6893i	0.914976	+	0.528261i	0.882029	−	0.471196i	$-0.156177\pi$
$577$	21.9785	+	12.6893i	0.914976	+	0.528261i	0.0329469	+	0.999457i	$0.489511\pi$
$578$	9.71757	+	5.61044i	0.404197	+	0.233364i
$579$	23.2773	+	12.5904i	0.967372	+	0.523241i
$580$			3.80949i			0.158180i
$581$	−14.8833	+	8.86053i	−0.617461	+	0.367597i
$582$	−11.6637	+	7.17320i	−0.483477	+	0.297339i
$583$	4.00281	+	6.93307i	0.165780	+	0.287139i
$584$	−4.05651	+	7.02609i	−0.167860	+	0.290742i
$585$	14.8480	−	9.70999i	0.613888	−	0.401458i
$586$	−3.79338	+	2.19011i	−0.156703	+	0.0904725i
$587$	−30.1344			−1.24378			−0.621889	−	0.783105i	$-0.713635\pi$
$587$	−30.1344			−1.24378			−0.621889	+	0.783105i	$0.713635\pi$
$588$	−10.1539	+	6.62561i	−0.418739	+	0.273235i
$589$	28.6847			1.18193
$590$	3.16433	−	1.82693i	0.130273	−	0.0752134i
$591$	27.8222	−	0.773038i	1.14445	−	0.0317985i
$592$	0.940152	−	1.62839i	0.0386400	−	0.0669265i
$593$	−0.505610	−	0.875743i	−0.0207629	−	0.0359625i	0.855457	−	0.517873i	$-0.173276\pi$
$593$	−0.505610	−	0.875743i	−0.0207629	−	0.0359625i	−0.876220	+	0.481911i	$0.839943\pi$
$594$	−1.42032	−	17.0044i	−0.0582766	−	0.697700i
$595$	5.46516	−	3.25360i	0.224050	−	0.133385i
$596$		−	9.63094i		−	0.394499i
$597$	−5.46346	+	10.1009i	−0.223605	+	0.413402i
$598$	−33.2763	−	19.2121i	−1.36077	−	0.785641i
$599$	−17.7082	−	10.2239i	−0.723539	−	0.417735i	0.0925150	−	0.995711i	$-0.470509\pi$
$599$	−17.7082	−	10.2239i	−0.723539	−	0.417735i	−0.816054	+	0.577976i	$0.803843\pi$
$600$	0.824030	−	1.52347i	0.0336409	−	0.0621956i
$601$			43.8623i			1.78918i	0.446886	+	0.894591i	$0.352533\pi$
$601$			43.8623i			1.78918i	−0.446886	+	0.894591i	$0.647467\pi$
$602$	−1.92432	+	3.43849i	−0.0784295	+	0.140143i
$603$	−4.54035	+	8.98178i	−0.184897	+	0.365766i
$604$	−11.7684	−	20.3835i	−0.478850	−	0.829392i
$605$	0.108006	−	0.187073i	0.00439108	−	0.00760558i
$606$	−8.50477	+	0.236304i	−0.345483	+	0.00959921i
$607$	−32.5289	+	18.7806i	−1.32031	+	0.762280i	−0.983777	−	0.179393i	$-0.942587\pi$
$607$	−32.5289	+	18.7806i	−1.32031	+	0.762280i	−0.336530	+	0.941673i	$0.609253\pi$
$608$	−5.51442			−0.223639
$609$	14.7464	−	9.34336i	0.597556	−	0.378612i
$610$	−14.2325			−0.576257
$611$	−63.8490	+	36.8632i	−2.58305	+	1.49133i
$612$	3.94721	+	6.03586i	0.159557	+	0.243985i
$613$	−22.6557	+	39.2409i	−0.915057	+	1.58492i	−0.108238	+	0.994125i	$0.534521\pi$
$613$	−22.6557	+	39.2409i	−0.915057	+	1.58492i	−0.806818	+	0.590800i	$0.798812\pi$
$614$	−2.38329	−	4.12798i	−0.0961818	−	0.166592i
$615$	−0.152191	+	0.0935978i	−0.00613695	+	0.00377423i
$616$	0.116280	+	8.68760i	0.00468507	+	0.350033i
$617$		−	28.3334i		−	1.14066i	−0.821416	−	0.570329i	$-0.806816\pi$
$617$		−	28.3334i		−	1.14066i	0.821416	−	0.570329i	$-0.193184\pi$
$618$	6.97206	+	3.77111i	0.280457	+	0.151696i
$619$	−13.6375	−	7.87364i	−0.548139	−	0.316468i	0.200232	−	0.979749i	$-0.435830\pi$
$619$	−13.6375	−	7.87364i	−0.548139	−	0.316468i	−0.748371	+	0.663280i	$0.769164\pi$
$620$	4.50485	+	2.60088i	0.180919	+	0.104454i
$621$	−19.2561	−	27.7321i	−0.772722	−	1.11285i
$622$			5.97021i			0.239384i
$623$	−25.9526	−	14.5241i	−1.03977	−	0.581897i
$624$	−5.36581	−	8.72488i	−0.214804	−	0.349275i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.3609	−	23.1417i	0.534008	−	0.924929i
$627$	0.871147	+	31.3532i	0.0347903	+	1.25213i
$628$	3.70963	−	2.14176i	0.148030	−	0.0854654i
$629$	4.52021			0.180233
$630$	−7.91840	+	0.546756i	−0.315477	+	0.0217833i
$631$	18.3939			0.732252			0.366126	−	0.930565i	$-0.380684\pi$
$631$	18.3939			0.732252			0.366126	+	0.930565i	$0.380684\pi$
$632$	−7.92530	+	4.57567i	−0.315251	+	0.182011i
$633$	0.529075	+	19.0418i	0.0210288	+	0.756843i
$634$	11.8861	−	20.5873i	0.472056	−	0.817625i
$635$	−7.06901	−	12.2439i	−0.280525	−	0.485884i
$636$	2.21198	+	3.59671i	0.0877108	+	0.142619i
$637$	36.3910	+	19.7310i	1.44186	+	0.781771i
$638$		−	12.5100i		−	0.495274i
$639$	2.31740	+	41.6703i	0.0916750	+	1.64845i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−19.8217	−	11.4441i	−0.782909	−	0.452013i	0.0545511	−	0.998511i	$-0.482627\pi$
$641$	−19.8217	−	11.4441i	−0.782909	−	0.452013i	−0.837460	+	0.546498i	$0.815961\pi$
$642$	7.51421	+	4.06435i	0.296562	+	0.160407i
$643$		−	10.5338i		−	0.415411i	−0.978191	−	0.207705i	$-0.933400\pi$
$643$		−	10.5338i		−	0.415411i	0.978191	−	0.207705i	$-0.0665995\pi$
$644$	8.79385	+	14.7713i	0.346526	+	0.582069i
$645$	−2.19728	+	1.35133i	−0.0865177	+	0.0532084i
$646$	−6.62828	−	11.4805i	−0.260786	−	0.451695i
$647$	12.4473	−	21.5593i	0.489352	−	0.847582i	−0.510573	−	0.859834i	$-0.670567\pi$
$647$	12.4473	−	21.5593i	0.489352	−	0.847582i	0.999925	+	0.0122519i	$0.00390001\pi$
$648$	−0.997943	−	8.94450i	−0.0392029	−	0.351373i
$649$	−10.3913	+	5.99944i	−0.407896	+	0.235499i
$650$	−5.91369			−0.231954
$651$	−0.980911	−	23.8173i	−0.0384449	−	0.933472i
$652$	22.0893			0.865083
$653$	−35.9305	+	20.7445i	−1.40607	+	0.811795i	−0.995006	−	0.0998116i	$-0.968176\pi$
$653$	−35.9305	+	20.7445i	−1.40607	+	0.811795i	−0.411064	+	0.911607i	$0.634843\pi$
$654$	13.1614	−	0.365688i	0.514651	−	0.0142995i
$655$	−2.51078	+	4.34879i	−0.0981042	+	0.169921i
$656$	0.0515774	+	0.0893347i	0.00201376	+	0.00348794i
$657$	21.7215	+	10.9804i	0.847436	+	0.428384i
$658$	32.9818	−	0.441449i	1.28576	−	0.0172095i
$659$			2.65098i			0.103268i	0.998666	+	0.0516338i	$0.0164429\pi$
$659$			2.65098i			0.103268i	−0.998666	+	0.0516338i	$0.983557\pi$
$660$	−2.70603	+	5.00294i	−0.105332	+	0.194739i
$661$	−11.4271	−	6.59741i	−0.444461	−	0.256610i	0.261027	−	0.965331i	$-0.415939\pi$
$661$	−11.4271	−	6.59741i	−0.444461	−	0.256610i	−0.705488	+	0.708722i	$0.749272\pi$
$662$	−3.94849	−	2.27966i	−0.153462	−	0.0886015i
$663$	11.7147	−	21.6583i	0.454963	−	0.841140i
$664$			6.54676i			0.254063i
$665$	14.5885	−	0.195261i	0.565717	−	0.00757191i
$666$	−5.03425	−	2.54485i	−0.195073	−	0.0986108i
$667$	−12.3761	−	21.4359i	−0.479203	−	0.830003i
$668$	6.46690	−	11.2010i	0.250212	−	0.433380i
$669$	−38.1651	+	1.06041i	−1.47555	+	0.0409979i
$670$	2.90527	−	1.67736i	0.112240	−	0.0648020i
$671$	46.7381			1.80430
$672$	0.188573	+	4.57869i	0.00727436	+	0.176627i
$673$	−2.26483			−0.0873027			−0.0436514	−	0.999047i	$-0.513899\pi$
$673$	−2.26483			−0.0873027			−0.0436514	+	0.999047i	$0.513899\pi$
$674$	11.1526	−	6.43894i	0.429581	−	0.248019i
$675$	−4.70064	−	2.21449i	−0.180928	−	0.0852359i
$676$	−10.9859	+	19.0281i	−0.422534	+	0.731851i
$677$	−5.90532	−	10.2283i	−0.226960	−	0.393106i	0.729946	−	0.683505i	$-0.239545\pi$
$677$	−5.90532	−	10.2283i	−0.226960	−	0.393106i	−0.956906	+	0.290399i	$0.906212\pi$
$678$	5.72789	−	3.52265i	0.219978	−	0.135287i
$679$	−10.6997	−	17.9725i	−0.410616	−	0.689721i
$680$		−	2.40398i		−	0.0921884i
$681$	−9.51926	−	5.14886i	−0.364779	−	0.197305i
$682$	−14.7935	−	8.54102i	−0.566472	−	0.327053i
$683$	3.86454	+	2.23119i	0.147872	+	0.0853742i	0.572111	−	0.820176i	$-0.306125\pi$
$683$	3.86454	+	2.23119i	0.147872	+	0.0853742i	−0.424238	+	0.905551i	$0.639458\pi$
$684$	0.918597	+	16.5177i	0.0351234	+	0.631571i
$685$			2.92970i			0.111938i
$686$	−9.89648	−	15.6544i	−0.377850	−	0.597687i
$687$	11.0563	+	17.9777i	0.421823	+	0.685891i
$688$	0.744654	+	1.28978i	0.0283897	+	0.0491723i
$689$	7.20832	−	12.4852i	0.274615	−	0.475648i
$690$	0.312570	+	11.2496i	0.0118994	+	0.428267i
$691$	23.6406	−	13.6489i	0.899332	−	0.519230i	0.0223487	−	0.999750i	$-0.492886\pi$
$691$	23.6406	−	13.6489i	0.899332	−	0.519230i	0.876983	+	0.480521i	$0.159552\pi$
$692$	23.2595			0.884195
$693$	26.0032	−	1.79549i	0.987781	−	0.0682051i
$694$	18.7893			0.713231
$695$	−2.91467	+	1.68279i	−0.110560	+	0.0638318i
$696$	−0.183260	−	6.59568i	−0.00694647	−	0.250008i
$697$	−0.123991	+	0.214759i	−0.00469650	+	0.00813457i
$698$	−4.26487	−	7.38697i	−0.161428	−	0.279601i
$699$	−14.6678	−	23.8500i	−0.554786	−	0.902090i
$700$	2.30879	+	1.29209i	0.0872640	+	0.0488365i
$701$			23.5071i			0.887851i	0.896064	+	0.443926i	$0.146415\pi$
$701$			23.5071i			0.887851i	−0.896064	+	0.443926i	$0.853585\pi$
$702$	−25.2404	+	17.5260i	−0.952638	+	0.661476i
$703$	8.97963	+	5.18439i	0.338673	+	0.195533i
$704$	2.84394	+	1.64195i	0.107185	+	0.0618833i
$705$	18.9933	+	10.2732i	0.715327	+	0.386912i
$706$			5.61974i			0.211502i
$707$	−0.173935	−	12.9951i	−0.00654149	−	0.488731i
$708$	−5.39078	+	3.31533i	−0.202598	+	0.124598i
$709$	−13.5095	−	23.3991i	−0.507360	−	0.878773i	−0.999964	−	0.00851903i	$-0.997288\pi$
$709$	−13.5095	−	23.3991i	−0.507360	−	0.878773i	0.492604	−	0.870253i	$-0.336045\pi$
$710$	6.95578	−	12.0478i	0.261046	−	0.452145i
$711$	15.0260	+	22.9770i	0.563521	+	0.861705i
$712$	−9.73481	+	5.62039i	−0.364827	+	0.210633i
$713$	−33.7984			−1.26576
$714$	−9.30576	+	5.89614i	−0.348259	+	0.220657i
$715$	19.4200			0.726266
$716$	−8.18788	+	4.72728i	−0.305996	+	0.176667i
$717$	−9.28621	+	0.258017i	−0.346800	+	0.00963581i
$718$	13.5328	−	23.4396i	0.505041	−	0.874757i
$719$	17.3360	+	30.0268i	0.646524	+	1.11981i	0.983947	+	0.178459i	$0.0571112\pi$
$719$	17.3360	+	30.0268i	0.646524	+	1.11981i	−0.337424	+	0.941353i	$0.609555\pi$
$720$	−1.35342	+	2.67736i	−0.0504391	+	0.0997793i
$721$	−5.91315	+	10.5660i	−0.220217	+	0.393498i
$722$		−	11.4088i		−	0.424592i
$723$	13.2602	−	24.5157i	0.493154	−	0.911747i
$724$	−7.29628	−	4.21251i	−0.271164	−	0.156557i
$725$	−3.29911	−	1.90474i	−0.122526	−	0.0707404i
$726$	−0.178001	+	0.329090i	−0.00660624	+	0.0122137i
$727$		−	16.8936i		−	0.626549i	−0.949663	−	0.313274i	$-0.898574\pi$
$727$		−	16.8936i		−	0.626549i	0.949663	−	0.313274i	$-0.101426\pi$
$728$	13.4441	−	8.00373i	0.498270	−	0.296638i
$729$	−26.6259	+	4.47919i	−0.986143	+	0.165896i
$730$	−4.05651	−	7.02609i	−0.150138	−	0.260047i
$731$	−1.79013	+	3.10060i	−0.0662105	+	0.114680i
$732$	24.6419	−	0.684674i	0.910791	−	0.0253063i
$733$	−15.6317	+	9.02495i	−0.577369	+	0.333344i	−0.760087	−	0.649821i	$-0.774844\pi$
$733$	−15.6317	+	9.02495i	−0.577369	+	0.333344i	0.182718	+	0.983165i	$0.441510\pi$
$734$	−18.7870			−0.693442
$735$	−0.661000	−	12.1063i	−0.0243814	−	0.446548i
$736$	6.49749			0.239501
$737$	−9.54061	+	5.50827i	−0.351433	+	0.202900i
$738$	0.258999	−	0.169375i	0.00953388	−	0.00623478i
$739$	−13.2235	+	22.9037i	−0.486433	+	0.842527i	−0.999878	−	0.0155954i	$-0.995036\pi$
$739$	−13.2235	+	22.9037i	−0.486433	+	0.842527i	0.513445	+	0.858122i	$0.328369\pi$
$740$	0.940152	+	1.62839i	0.0345607	+	0.0598608i
$741$	48.1126	−	29.5893i	1.76746	−	1.08699i
$742$	−5.54214	+	3.29943i	−0.203458	+	0.121126i
$743$			48.5084i			1.77960i	0.456350	+	0.889801i	$0.349157\pi$
$743$			48.5084i			1.77960i	−0.456350	+	0.889801i	$0.650843\pi$
$744$	−7.92475	−	4.28640i	−0.290535	−	0.157147i
$745$	8.34064	+	4.81547i	0.305577	+	0.176425i
$746$	11.5499	+	6.66836i	0.422873	+	0.244146i
$747$	19.6100	−	1.09056i	0.717491	−	0.0399017i
$748$			7.89443i			0.288649i
$749$	−6.37296	+	11.3876i	−0.232863	+	0.416094i
$750$	0.907353	+	1.47537i	0.0331318	+	0.0538728i
$751$	7.85169	+	13.5995i	0.286512	+	0.496254i	0.972975	−	0.230911i	$-0.0741707\pi$
$751$	7.85169	+	13.5995i	0.286512	+	0.496254i	−0.686462	+	0.727165i	$0.740837\pi$
$752$	6.23353	−	10.7968i	0.227314	−	0.393719i
$753$	0.0509186	+	1.83260i	0.00185558	+	0.0667836i
$754$	−19.5099	+	11.2641i	−0.710510	+	0.410213i
$755$	23.5368			0.856592
$756$	13.6835	−	1.32757i	0.497663	−	0.0482832i
$757$	5.53921			0.201326			0.100663	−	0.994921i	$-0.467904\pi$
$757$	5.53921			0.201326			0.100663	+	0.994921i	$0.467904\pi$
$758$	−28.9844	+	16.7342i	−1.05276	+	0.607812i
$759$	−1.02645	−	36.9427i	−0.0372578	−	1.34093i
$760$	2.75721	−	4.77563i	0.100015	−	0.173230i
$761$	6.87928	+	11.9153i	0.249374	+	0.431928i	0.963352	−	0.268240i	$-0.0864419\pi$
$761$	6.87928	+	11.9153i	0.249374	+	0.431928i	−0.713978	+	0.700168i	$0.753109\pi$
$762$	12.8282	+	20.8588i	0.464715	+	0.755634i
$763$	0.269169	+	20.1103i	0.00974457	+	0.728042i
$764$		−	5.13035i		−	0.185609i
$765$	−7.20081	+	0.400457i	−0.260346	+	0.0144786i
$766$	8.04088	+	4.64240i	0.290529	+	0.167737i
$767$	18.7129	+	10.8039i	0.675683	+	0.390106i
$768$	1.52347	+	0.824030i	0.0549737	+	0.0297346i
$769$			11.0157i			0.397238i	0.980077	+	0.198619i	$0.0636455\pi$
$769$			11.0157i			0.397238i	−0.980077	+	0.198619i	$0.936354\pi$
$770$	−7.58182	−	4.24310i	−0.273230	−	0.152911i
$771$	−3.63208	+	2.23373i	−0.130806	+	0.0804460i
$772$	7.63955	+	13.2321i	0.274953	+	0.476233i
$773$	17.5720	−	30.4356i	0.632022	−	1.09469i	−0.355116	−	0.934822i	$-0.615559\pi$
$773$	17.5720	−	30.4356i	0.632022	−	1.09469i	0.987138	−	0.159872i	$-0.0511080\pi$
$774$	3.73932	−	2.44537i	0.134407	−	0.0878969i
$775$	−4.50485	+	2.60088i	−0.161819	+	0.0934263i
$776$	−7.90564			−0.283796
$777$	3.99760	−	7.63319i	0.143413	−	0.273839i
$778$	19.4580			0.697602
$779$	−0.492629	+	0.284420i	−0.0176503	+	0.0101904i
$780$	10.2389	−	0.284486i	0.366610	−	0.0101862i
$781$	−22.8421	+	39.5637i	−0.817354	+	1.41570i
$782$	7.80992	+	13.5272i	0.279282	+	0.483731i
$783$	−19.7260	+	1.64765i	−0.704949	+	0.0588821i
$784$	−6.99749	+	0.187351i	−0.249910	+	0.00669112i
$785$			4.28351i			0.152885i
$786$	4.13791	−	7.65021i	0.147594	−	0.272874i
$787$	−6.04499	−	3.49008i	−0.215481	−	0.124408i	0.388375	−	0.921501i	$-0.373036\pi$
$787$	−6.04499	−	3.49008i	−0.215481	−	0.124408i	−0.603856	+	0.797093i	$0.706370\pi$
$788$	13.9165	+	8.03468i	0.495754	+	0.286224i
$789$	−25.2964	+	46.7682i	−0.900575	+	1.66499i
$790$		−	9.15135i		−	0.325590i
$791$	5.25445	+	8.82603i	0.186827	+	0.313818i
$792$	4.44450	−	8.79217i	0.157928	−	0.312416i
$793$	−42.0834	−	72.8905i	−1.49442	−	2.58842i
$794$	1.14529	−	1.98370i	0.0406447	−	0.0703988i
$795$	−4.22084	+	0.117276i	−0.149698	+	0.00415934i
$796$	−5.74190	+	3.31509i	−0.203516	+	0.117500i
$797$	−0.975566			−0.0345563			−0.0172782	−	0.999851i	$-0.505500\pi$
$797$	−0.975566			−0.0345563			−0.0172782	+	0.999851i	$0.505500\pi$
$798$	−25.2488	+	1.03987i	−0.893799	+	0.0368110i
$799$	29.9706			1.06028
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	18.4568	+	28.2231i	0.652139	+	0.997215i
$802$	−0.754520	+	1.30687i	−0.0266430	+	0.0461471i
$803$	13.3212	+	23.0730i	0.470094	+	0.814227i
$804$	−4.94944	+	3.04391i	−0.174553	+	0.107350i
$805$	−17.1892	+	0.230071i	−0.605840	+	0.00810895i
$806$			30.7616i			1.08353i
$807$	25.5228	+	13.8050i	0.898444	+	0.485958i
$808$	−4.25403	−	2.45606i	−0.149656	−	0.0864040i
$809$	−25.3918	−	14.6599i	−0.892727	−	0.515416i	−0.0178934	−	0.999840i	$-0.505696\pi$
$809$	−25.3918	−	14.6599i	−0.892727	−	0.515416i	−0.874833	+	0.484424i	$0.839029\pi$
$810$	8.24514	+	3.60801i	0.289705	+	0.126772i
$811$		−	1.54090i		−	0.0541084i	−0.999634	−	0.0270542i	$-0.991387\pi$
$811$		−	1.54090i		−	0.0541084i	0.999634	−	0.0270542i	$-0.00861267\pi$
$812$	10.0780	−	0.134891i	0.353670	−	0.00473375i
$813$	−13.8486	−	22.5180i	−0.485692	−	0.789741i
$814$	−3.08736	−	5.34747i	−0.108212	−	0.187429i
$815$	−11.0446	+	19.1299i	−0.386877	+	0.670090i
$816$	0.115647	+	4.16221i	0.00404844	+	0.145706i
$817$	−7.11238	+	4.10633i	−0.248831	+	0.143662i
$818$	19.2437			0.672841
$819$	−26.2137	−	38.9367i	−0.915979	−	1.36056i
$820$	−0.103155			−0.00360232
$821$	27.2749	−	15.7472i	0.951899	−	0.549579i	0.0582289	−	0.998303i	$-0.481455\pi$
$821$	27.2749	−	15.7472i	0.951899	−	0.549579i	0.893670	+	0.448724i	$0.148121\pi$
$822$	−0.140937	−	5.07242i	−0.00491574	−	0.176921i
$823$	23.4689	−	40.6493i	0.818074	−	1.41695i	−0.0890256	−	0.996029i	$-0.528375\pi$
$823$	23.4689	−	40.6493i	0.818074	−	1.41695i	0.907099	−	0.420916i	$-0.138291\pi$
$824$	2.28821	+	3.96330i	0.0797136	+	0.138068i
$825$	−2.97965	−	4.84496i	−0.103738	−	0.168680i
$826$	−4.94521	−	8.30659i	−0.172066	−	0.289023i
$827$			7.83421i			0.272422i	0.990680	+	0.136211i	$0.0434925\pi$
$827$			7.83421i			0.272422i	−0.990680	+	0.136211i	$0.956507\pi$
$828$	−1.08236	−	19.4624i	−0.0376145	−	0.676365i
$829$	10.4939	+	6.05866i	0.364468	+	0.210426i	0.671039	−	0.741422i	$-0.265848\pi$
$829$	10.4939	+	6.05866i	0.364468	+	0.210426i	−0.306571	+	0.951848i	$0.599182\pi$
$830$	−5.66966	−	3.27338i	−0.196797	−	0.113621i
$831$	−5.35077	−	2.89417i	−0.185616	−	0.100398i
$832$		−	5.91369i		−	0.205020i
$833$	−8.80097	−	14.3429i	−0.304935	−	0.496953i
$834$	4.96546	−	3.05376i	0.171940	−	0.105743i
$835$	6.46690	+	11.2010i	0.223796	+	0.387627i
$836$	−9.05440	+	15.6827i	−0.313153	+	0.542397i
$837$	−11.5193	+	24.4516i	−0.398164	+	0.845171i
$838$	−1.16843	+	0.674593i	−0.0403627	+	0.0233034i
$839$	−12.4633			−0.430279			−0.215140	−	0.976583i	$-0.569021\pi$
$839$	−12.4633			−0.430279			−0.215140	+	0.976583i	$0.569021\pi$
$840$	−4.05955	−	2.12604i	−0.140068	−	0.0733553i
$841$	14.4878			0.499580
$842$	−20.2462	+	11.6892i	−0.697732	+	0.402835i
$843$	−7.19978	+	0.200045i	−0.247974	+	0.00688993i
$844$	−5.49901	+	9.52457i	−0.189284	+	0.327849i
$845$	−10.9859	−	19.0281i	−0.377926	−	0.654587i
$846$	−33.3788	−	16.8732i	−1.14759	−	0.580113i
$847$	−0.498728	−	0.279108i	−0.0171365	−	0.00959028i
$848$			2.43784i			0.0837158i
$849$	0.142237	−	0.262968i	0.00488155	−	0.00902505i
$850$	2.08191	+	1.20199i	0.0714089	+	0.0412279i
$851$	−10.5805	−	6.10863i	−0.362693	−	0.209401i
$852$	−11.4635	+	21.1939i	−0.392735	+	0.726092i
$853$		−	21.5297i		−	0.737162i	−0.929596	−	0.368581i	$-0.879844\pi$
$853$		−	21.5297i		−	0.737162i	0.929596	−	0.368581i	$-0.120156\pi$
$854$	0.503962	+	37.6523i	0.0172452	+	1.28844i
$855$	−14.7641	−	7.46334i	−0.504921	−	0.255241i
$856$	2.46614	+	4.27148i	0.0842910	+	0.145996i
$857$	25.1782	−	43.6098i	0.860069	−	1.48968i	−0.0117917	−	0.999930i	$-0.503754\pi$
$857$	25.1782	−	43.6098i	0.860069	−	1.48968i	0.871861	−	0.489753i	$-0.162913\pi$
$858$	−33.6234	+	0.934223i	−1.14788	+	0.0318939i
$859$	10.3726	−	5.98863i	0.353909	−	0.204329i	−0.312497	−	0.949919i	$-0.601165\pi$
$859$	10.3726	−	5.98863i	0.353909	−	0.204329i	0.666405	+	0.745590i	$0.267832\pi$
$860$	−1.48931			−0.0507850
$861$	0.253003	+	0.399310i	0.00862233	+	0.0136085i
$862$	7.75984			0.264301
$863$	−44.9466	+	25.9499i	−1.53000	+	0.883346i	−0.530639	+	0.847598i	$0.678048\pi$
$863$	−44.9466	+	25.9499i	−1.53000	+	0.883346i	−0.999361	+	0.0357482i	$0.988619\pi$
$864$	2.21449	−	4.70064i	0.0753386	−	0.159919i
$865$	−11.6298	+	20.1433i	−0.395424	+	0.684894i
$866$	17.0457	+	29.5240i	0.579236	+	1.00327i
$867$	16.5549	−	10.1813i	0.562235	−	0.345775i
$868$	6.72115	−	12.0098i	0.228131	−	0.407638i
$869$			30.0521i			1.01945i
$870$	5.80365	+	3.13913i	0.196762	+	0.106426i
$871$	17.1809	+	9.91938i	0.582152	+	0.336106i
$872$	6.58323	+	3.80083i	0.222936	+	0.128712i
$873$	1.31693	+	23.6803i	0.0445713	+	0.801458i
$874$			35.8299i			1.21196i
$875$	−2.27338	+	1.35342i	−0.0768542	+	0.0457540i
$876$	7.36138	+	11.9697i	0.248718	+	0.404419i
$877$	4.30976	+	7.46473i	0.145530	+	0.252066i	0.929571	−	0.368644i	$-0.120178\pi$
$877$	4.30976	+	7.46473i	0.145530	+	0.252066i	−0.784040	+	0.620710i	$0.786844\pi$
$878$	5.97965	−	10.3571i	0.201804	−	0.349534i
$879$	0.210716	+	7.58383i	0.00710728	+	0.255796i
$880$	−2.84394	+	1.64195i	−0.0958692	+	0.0553501i
$881$	−21.7764			−0.733667			−0.366833	−	0.930287i	$-0.619558\pi$
$881$	−21.7764			−0.733667			−0.366833	+	0.930287i	$0.619558\pi$
$882$	1.72684	+	20.9289i	0.0581456	+	0.704712i
$883$	24.1748			0.813546			0.406773	−	0.913529i	$-0.366654\pi$
$883$	24.1748			0.813546			0.406773	+	0.913529i	$0.366654\pi$
$884$	12.3118	−	7.10820i	0.414090	−	0.239075i
$885$	−0.175774	−	6.32622i	−0.00590856	−	0.212654i
$886$	−1.80307	+	3.12301i	−0.0605753	+	0.104919i
$887$	−9.87147	−	17.0979i	−0.331452	−	0.574091i	0.651345	−	0.758782i	$-0.274205\pi$
$887$	−9.87147	−	17.0979i	−0.331452	−	0.574091i	−0.982797	+	0.184691i	$0.940872\pi$
$888$	−1.70610	−	2.77414i	−0.0572529	−	0.0930941i
$889$	−32.1411	+	19.1347i	−1.07798	+	0.641758i
$890$		−	11.2408i		−	0.376792i
$891$	−27.0762	−	11.8483i	−0.907087	−	0.396934i
$892$	−19.0899	−	11.0216i	−0.639177	−	0.369029i
$893$	59.5381	+	34.3743i	1.99237	+	1.15029i
$894$	−14.6725	−	7.93619i	−0.490722	−	0.265426i
$895$		−	9.45455i		−	0.316031i
$896$	−1.29209	+	2.30879i	−0.0431658	+	0.0771312i
$897$	−56.6898	+	34.8643i	−1.89282	+	1.16408i
$898$	9.50668	+	16.4661i	0.317242	+	0.549480i
$899$	−9.90801	+	17.1612i	−0.330451	+	0.572357i
$900$	−1.64195	−	2.51078i	−0.0547316	−	0.0836926i
$901$	−5.07536	+	2.93026i	−0.169085	+	0.0976212i
$902$	0.338750			0.0112791
$903$	3.65276	+	5.76508i	0.121556	+	0.191850i
$904$	3.88234			0.129125
$905$	7.29628	−	4.21251i	0.242537	−	0.140029i
$906$	−40.7512	+	1.13227i	−1.35387	+	0.0376171i
$907$	10.5712	−	18.3098i	0.351010	−	0.607967i	−0.635417	−	0.772169i	$-0.719172\pi$
$907$	10.5712	−	18.3098i	0.351010	−	0.607967i	0.986427	+	0.164203i	$0.0525051\pi$
$908$	−3.12420	−	5.41126i	−0.103680	−	0.179579i
$909$	−6.64818	+	13.1515i	−0.220506	+	0.436208i
$910$	0.209399	+	15.6448i	0.00694152	+	0.518619i
$911$		−	48.9326i		−	1.62121i	−0.585594	−	0.810604i	$-0.699139\pi$
$911$		−	48.9326i		−	1.62121i	0.585594	−	0.810604i	$-0.300861\pi$
$912$	−4.54405	+	8.40108i	−0.150468	+	0.278187i
$913$	18.6186	+	10.7494i	0.616185	+	0.355755i
$914$	−32.8141	−	18.9452i	−1.08539	−	0.626652i
$915$	−11.7280	+	21.6829i	−0.387716	+	0.716813i
$916$			12.1852i			0.402611i
$917$	11.5937	+	6.48831i	0.382858	+	0.214263i
$918$	12.4481	−	1.03975i	0.410849	−	0.0343168i
$919$	11.2203	+	19.4341i	0.370123	+	0.641071i	0.989584	−	0.143956i	$-0.0459824\pi$
$919$	11.2203	+	19.4341i	0.370123	+	0.641071i	−0.619462	+	0.785027i	$0.712649\pi$
$920$	−3.24875	+	5.62699i	−0.107108	+	0.185516i
$921$	−8.25277	+	0.229303i	−0.271938	+	0.00755578i
$922$	28.2419	−	16.3055i	0.930098	−	0.536993i
$923$	82.2688			2.70791
$924$	13.3312	+	6.98169i	0.438563	+	0.229681i
$925$	−1.88030			−0.0618240
$926$	5.02545	−	2.90144i	0.165146	−	0.0953473i
$927$	11.4904	−	7.51425i	0.377393	−	0.246800i
$928$	1.90474	−	3.29911i	0.0625262	−	0.108299i
$929$	−8.52306	−	14.7624i	−0.279632	−	0.484338i	0.691661	−	0.722222i	$-0.256879\pi$
$929$	−8.52306	−	14.7624i	−0.279632	−	0.484338i	−0.971293	+	0.237885i	$0.923546\pi$
$930$	7.67451	−	4.71983i	0.251657	−	0.154769i
$931$	−1.03313	−	38.5871i	−0.0338596	−	1.26464i
$932$		−	16.1655i		−	0.529517i
$933$	9.09546	+	4.91963i	0.297772	+	0.161062i
$934$	19.3060	+	11.1463i	0.631711	+	0.364719i
$935$	−6.83677	−	3.94721i	−0.223586	−	0.129088i
$936$	−17.7137	+	0.985109i	−0.578991	+	0.0321993i
$937$			38.9259i			1.27165i	0.771832	+	0.635827i	$0.219341\pi$
$937$			38.9259i			1.27165i	−0.771832	+	0.635827i	$0.780659\pi$
$938$	−4.54035	−	7.62654i	−0.148248	−	0.249015i
$939$	−24.2460	−	39.4244i	−0.791240	−	1.28657i
$940$	6.23353	+	10.7968i	0.203315	+	0.352153i
$941$	18.0677	−	31.2943i	0.588992	−	1.02016i	−0.405373	−	0.914151i	$-0.632858\pi$
$941$	18.0677	−	31.2943i	0.588992	−	1.02016i	0.994365	−	0.106012i	$-0.0338083\pi$
$942$	−0.206064	−	7.41640i	−0.00671393	−	0.241639i
$943$	0.580452	−	0.335124i	0.0189021	−	0.0109131i
$944$	−3.65385			−0.118923
$945$	−5.69203	+	12.5140i	−0.185162	+	0.407081i
$946$	4.89073			0.159011
$947$	−7.84276	+	4.52802i	−0.254855	+	0.147141i	−0.621986	−	0.783029i	$-0.713674\pi$
$947$	−7.84276	+	4.52802i	−0.254855	+	0.147141i	0.367130	+	0.930170i	$0.380340\pi$
$948$	0.440238	+	15.8445i	0.0142983	+	0.514605i
$949$	23.9890	−	41.5501i	0.778715	−	1.34877i
$950$	2.75721	+	4.77563i	0.0894557	+	0.154942i
$951$	−21.5697	−	35.0727i	−0.699446	−	1.13731i
$952$	−6.35976	+	0.0851231i	−0.206121	+	0.00275886i
$953$		−	45.8921i		−	1.48659i	−0.668963	−	0.743296i	$-0.733261\pi$
$953$		−	45.8921i		−	1.48659i	0.668963	−	0.743296i	$-0.266739\pi$
$954$	7.30224	−	0.406098i	0.236419	−	0.0131479i
$955$	4.44301	+	2.56517i	0.143772	+	0.0830071i
$956$	−4.64490	−	2.68173i	−0.150227	−	0.0867334i
$957$	−19.0586	−	10.3086i	−0.616077	−	0.333229i
$958$			42.3883i			1.36950i
$959$	7.75055	−	0.103738i	0.250278	−	0.00334988i
$960$	−1.47537	+	0.907353i	−0.0476173	+	0.0292847i
$961$	−1.97086	−	3.41362i	−0.0635760	−	0.110117i
$962$	−5.55977	+	9.62981i	−0.179254	+	0.310477i
$963$	12.3839	−	8.09856i	0.399065	−	0.260972i
$964$	13.9360	−	8.04597i	0.448849	−	0.259143i
$965$	−15.2791			−0.491852
$966$	29.7500	−	1.22525i	0.957192	−	0.0394218i
$967$	−13.6246			−0.438137			−0.219068	−	0.975710i	$-0.570302\pi$
$967$	−13.6246			−0.438137			−0.219068	+	0.975710i	$0.570302\pi$
$968$	−0.187073	+	0.108006i	−0.00601274	+	0.00347146i
$969$	−22.9522	+	0.637724i	−0.737330	+	0.0204867i
$970$	3.95282	−	6.84648i	0.126917	−	0.219827i
$971$	17.2371	+	29.8556i	0.553166	+	0.958112i	0.998044	+	0.0625206i	$0.0199139\pi$
$971$	17.2371	+	29.8556i	0.553166	+	0.958112i	−0.444877	+	0.895591i	$0.646753\pi$
$972$	−14.4491	−	5.85020i	−0.463454	−	0.187645i
$973$	4.55504	+	7.65122i	0.146028	+	0.245287i
$974$			17.5505i			0.562354i
$975$	−4.87306	+	9.00936i	−0.156063	+	0.288531i
$976$	12.3257	+	7.11625i	0.394536	+	0.227786i
$977$	6.10133	+	3.52260i	0.195199	+	0.112698i	0.594414	−	0.804159i	$-0.297384\pi$
$977$	6.10133	+	3.52260i	0.195199	+	0.112698i	−0.399215	+	0.916857i	$0.630717\pi$
$978$	18.2022	−	33.6524i	0.582043	−	1.07609i
$979$			36.9136i			1.17976i
$980$	3.33650	−	6.15368i	0.106580	−	0.196572i
$981$	10.2883	−	20.3524i	0.328479	−	0.649801i
$982$	−15.6366	−	27.0834i	−0.498983	−	0.864265i
$983$	−26.4833	+	45.8704i	−0.844685	+	1.46304i	0.0412090	+	0.999151i	$0.486879\pi$
$983$	−26.4833	+	45.8704i	−0.844685	+	1.46304i	−0.885894	+	0.463887i	$0.846454\pi$
$984$	0.178601	−	0.00496240i	0.00569358	−	0.000158196i
$985$	−13.9165	+	8.03468i	−0.443416	+	0.256006i
$986$	9.15793			0.291648
$987$	26.5055	−	50.6107i	0.843678	−	1.61096i
$988$	32.6106			1.03748
$989$	8.38032	−	4.83838i	0.266479	−	0.153852i
$990$	5.39199	+	8.24514i	0.171369	+	0.262048i
$991$	15.4388	−	26.7408i	0.490429	−	0.849449i	−0.509510	−	0.860465i	$-0.670173\pi$
$991$	15.4388	−	26.7408i	0.490429	−	0.849449i	0.999939	+	0.0110161i	$0.00350662\pi$
$992$	−2.60088	−	4.50485i	−0.0825780	−	0.143029i
$993$	−6.72668	+	4.13691i	−0.213465	+	0.131281i
$994$	−32.1189	−	17.9750i	−1.01875	−	0.570133i
$995$		−	6.63017i		−	0.210191i
$996$	9.97382	+	5.39472i	0.316032	+	0.170938i
$997$	21.5634	+	12.4497i	0.682921	+	0.394285i	0.800955	−	0.598725i	$-0.204326\pi$
$997$	21.5634	+	12.4497i	0.682921	+	0.394285i	−0.118034	+	0.993010i	$0.537659\pi$
$998$	4.64557	+	2.68212i	0.147053	+	0.0849010i
$999$	−8.02538	+	5.57252i	−0.253912	+	0.176307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.r.a.101.5	✓	12
3.2	odd	2		210.2.r.b.101.1	yes	12
5.2	odd	4		1050.2.u.g.899.1		12
5.3	odd	4		1050.2.u.f.899.6		12
5.4	even	2		1050.2.s.g.101.2		12
7.3	odd	6		1470.2.b.a.881.12		12
7.4	even	3		1470.2.b.b.881.7		12
7.5	odd	6		210.2.r.b.131.1	yes	12
15.2	even	4		1050.2.u.e.899.4		12
15.8	even	4		1050.2.u.h.899.3		12
15.14	odd	2		1050.2.s.f.101.6		12
21.5	even	6	inner	210.2.r.a.131.5	yes	12
21.11	odd	6		1470.2.b.a.881.6		12
21.17	even	6		1470.2.b.b.881.1		12
35.12	even	12		1050.2.u.h.299.3		12
35.19	odd	6		1050.2.s.f.551.6		12
35.33	even	12		1050.2.u.e.299.4		12
105.47	odd	12		1050.2.u.f.299.6		12
105.68	odd	12		1050.2.u.g.299.1		12
105.89	even	6		1050.2.s.g.551.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.5	✓	12	1.1	even	1	trivial
210.2.r.a.131.5	yes	12	21.5	even	6	inner
210.2.r.b.101.1	yes	12	3.2	odd	2
210.2.r.b.131.1	yes	12	7.5	odd	6
1050.2.s.f.101.6		12	15.14	odd	2
1050.2.s.f.551.6		12	35.19	odd	6
1050.2.s.g.101.2		12	5.4	even	2
1050.2.s.g.551.2		12	105.89	even	6
1050.2.u.e.299.4		12	35.33	even	12
1050.2.u.e.899.4		12	15.2	even	4
1050.2.u.f.299.6		12	105.47	odd	12
1050.2.u.f.899.6		12	5.3	odd	4
1050.2.u.g.299.1		12	105.68	odd	12
1050.2.u.g.899.1		12	5.2	odd	4
1050.2.u.h.299.3		12	35.12	even	12
1050.2.u.h.899.3		12	15.8	even	4
1470.2.b.a.881.6		12	21.11	odd	6
1470.2.b.a.881.12		12	7.3	odd	6
1470.2.b.b.881.1		12	21.17	even	6
1470.2.b.b.881.7		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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.0481063 - 1.73138i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.907353 - 1.47537i) q^{6} +(2.27338 - 1.35342i) q^{7} -1.00000i q^{8} +(-2.99537 + 0.166581i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.0481063 - 1.73138i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.907353 - 1.47537i) q^{6} +(2.27338 - 1.35342i) q^{7} -1.00000i q^{8} +(-2.99537 + 0.166581i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-2.84394 - 1.64195i) q^{11} +(-1.52347 - 0.824030i) q^{12} +5.91369i q^{13} +(1.29209 - 2.30879i) q^{14} +(1.47537 - 0.907353i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.20199 - 2.08191i) q^{17} +(-2.51078 + 1.64195i) q^{18} +(4.77563 - 2.75721i) q^{19} +1.00000 q^{20} +(-2.45266 - 3.87098i) q^{21} -3.28390 q^{22} +(-5.62699 + 3.24875i) q^{23} +(-1.73138 + 0.0481063i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.95685 + 5.12141i) q^{26} +(0.432512 + 5.17812i) q^{27} +(-0.0354092 - 2.64551i) q^{28} +3.80949i q^{29} +(0.824030 - 1.52347i) q^{30} +(4.50485 + 2.60088i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.70603 + 5.00294i) q^{33} -2.40398i q^{34} +(2.30879 + 1.29209i) q^{35} +(-1.35342 + 2.67736i) q^{36} +(0.940152 + 1.62839i) q^{37} +(2.75721 - 4.77563i) q^{38} +(10.2389 - 0.284486i) q^{39} +(0.866025 - 0.500000i) q^{40} -0.103155 q^{41} +(-4.05955 - 2.12604i) q^{42} -1.48931 q^{43} +(-2.84394 + 1.64195i) q^{44} +(-1.64195 - 2.51078i) q^{45} +(-3.24875 + 5.62699i) q^{46} +(6.23353 + 10.7968i) q^{47} +(-1.47537 + 0.907353i) q^{48} +(3.33650 - 6.15368i) q^{49} +1.00000i q^{50} +(-3.66240 - 1.98095i) q^{51} +(5.12141 + 2.95685i) q^{52} +(-2.11123 - 1.21892i) q^{53} +(2.96363 + 4.26813i) q^{54} -3.28390i q^{55} +(-1.35342 - 2.27338i) q^{56} +(-5.00352 - 8.13580i) q^{57} +(1.90474 + 3.29911i) q^{58} +(1.82693 - 3.16433i) q^{59} +(-0.0481063 - 1.73138i) q^{60} +(-12.3257 + 7.11625i) q^{61} +5.20176 q^{62} +(-6.58416 + 4.43270i) q^{63} -1.00000 q^{64} +(-5.12141 + 2.95685i) q^{65} +(0.157976 + 5.68568i) q^{66} +(1.67736 - 2.90527i) q^{67} +(-1.20199 - 2.08191i) q^{68} +(5.89552 + 9.58619i) q^{69} +(2.64551 - 0.0354092i) q^{70} -13.9116i q^{71} +(0.166581 + 2.99537i) q^{72} +(-7.02609 - 4.05651i) q^{73} +(1.62839 + 0.940152i) q^{74} +(1.52347 + 0.824030i) q^{75} -5.51442i q^{76} +(-8.68760 + 0.116280i) q^{77} +(8.72488 - 5.36581i) q^{78} +(-4.57567 - 7.92530i) q^{79} +(0.500000 - 0.866025i) q^{80} +(8.94450 - 0.997943i) q^{81} +(-0.0893347 + 0.0515774i) q^{82} -6.54676 q^{83} +(-4.57869 + 0.188573i) q^{84} +2.40398 q^{85} +(-1.28978 + 0.744654i) q^{86} +(6.59568 - 0.183260i) q^{87} +(-1.64195 + 2.84394i) q^{88} +(-5.62039 - 9.73481i) q^{89} +(-2.67736 - 1.35342i) q^{90} +(8.00373 + 13.4441i) q^{91} +6.49749i q^{92} +(4.28640 - 7.92475i) q^{93} +(10.7968 + 6.23353i) q^{94} +(4.77563 + 2.75721i) q^{95} +(-0.824030 + 1.52347i) q^{96} -7.90564i q^{97} +(-0.187351 - 6.99749i) q^{98} +(8.79217 + 4.44450i) 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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