LMFDB - Embedded newform 210.2.r.b.131.1

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			131.1
Root			$1.73138 + 0.0481063i$ of defining polynomial
Character	$\chi$	$=$	210.131
Dual form			210.2.r.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.52347 - 0.824030i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.907353 + 1.47537i) q^{6} +(2.27338 + 1.35342i) q^{7} -1.00000i q^{8} +(1.64195 + 2.51078i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.52347 - 0.824030i) 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} +(1.64195 + 2.51078i) q^{9} +(0.866025 - 0.500000i) q^{10} +(2.84394 - 1.64195i) q^{11} +(-0.0481063 - 1.73138i) 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} +(-0.166581 - 2.99537i) q^{18} +(4.77563 + 2.75721i) q^{19} -1.00000 q^{20} +(-2.34817 - 3.93524i) q^{21} -3.28390 q^{22} +(5.62699 + 3.24875i) q^{23} +(-0.824030 + 1.52347i) 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} +(-1.73138 + 0.0481063i) q^{30} +(4.50485 - 2.60088i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.68568 + 0.157976i) 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} +(-4.87306 + 9.00936i) q^{39} +(0.866025 + 0.500000i) q^{40} +0.103155 q^{41} +(0.0659590 + 4.58210i) q^{42} -1.48931 q^{43} +(2.84394 + 1.64195i) q^{44} +(-2.99537 + 0.166581i) 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} +(0.115647 + 4.16221i) q^{51} +(5.12141 - 2.95685i) q^{52} +(2.11123 - 1.21892i) q^{53} +(-2.21449 + 4.70064i) 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} +(1.52347 + 0.824030i) q^{60} +(-12.3257 - 7.11625i) q^{61} -5.20176 q^{62} +(0.334628 + 7.93020i) q^{63} -1.00000 q^{64} +(5.12141 + 2.95685i) q^{65} +(5.00294 + 2.70603i) 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} +(2.51078 - 1.64195i) q^{72} +(-7.02609 + 4.05651i) q^{73} +(-1.62839 + 0.940152i) q^{74} +(0.0481063 + 1.73138i) 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} +(-3.60801 + 8.24514i) q^{81} +(-0.0893347 - 0.0515774i) q^{82} +6.54676 q^{83} +(2.23393 - 4.00120i) q^{84} +2.40398 q^{85} +(1.28978 + 0.744654i) q^{86} +(3.13913 - 5.80365i) 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} +(-9.00623 + 0.250237i) q^{93} +(10.7968 - 6.23353i) q^{94} +(-4.77563 + 2.75721i) q^{95} +(-1.73138 + 0.0481063i) 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}+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
$3$	−1.52347	−	0.824030i	−0.879578	−	0.475754i
$3$	−1.52347	−	0.824030i	−0.879578	−	0.475754i
$4$	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
$9$	1.64195	+	2.51078i	0.547316	+	0.836926i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	2.84394	−	1.64195i	0.857480	−	0.495066i	−0.00568763	−	0.999984i	$-0.501810\pi$
$11$	2.84394	−	1.64195i	0.857480	−	0.495066i	0.863168	+	0.504918i	$0.168477\pi$
$12$	−0.0481063	−	1.73138i	−0.0138871	−	0.499807i
$13$		−	5.91369i		−	1.64016i	−0.572246	−	0.820082i	$-0.693928\pi$
$13$		−	5.91369i		−	1.64016i	0.572246	−	0.820082i	$-0.306072\pi$
$14$	−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	$-0.260829\pi$
$17$	−1.20199	−	2.08191i	−0.291525	−	0.504937i	−0.974171	+	0.225813i	$0.927496\pi$
$18$	−0.166581	−	2.99537i	−0.0392635	−	0.706016i
$19$	4.77563	+	2.75721i	1.09560	+	0.632547i	0.935063	−	0.354482i	$-0.115343\pi$
$19$	4.77563	+	2.75721i	1.09560	+	0.632547i	0.160541	+	0.987029i	$0.448676\pi$
$20$	−1.00000			−0.223607
$21$	−2.34817	−	3.93524i	−0.512413	−	0.858739i
$22$	−3.28390			−0.700129
$23$	5.62699	+	3.24875i	1.17331	+	0.677410i	0.954457	−	0.298348i	$-0.0964355\pi$
$23$	5.62699	+	3.24875i	1.17331	+	0.677410i	0.218852	+	0.975758i	$0.429769\pi$
$24$	−0.824030	+	1.52347i	−0.168204	+	0.310978i
$25$	−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	$0.884923\pi$
$30$	−1.73138	+	0.0481063i	−0.316106	+	0.00878297i
$31$	4.50485	−	2.60088i	0.809096	−	0.467132i	−0.0375460	−	0.999295i	$-0.511954\pi$
$31$	4.50485	−	2.60088i	0.809096	−	0.467132i	0.846642	+	0.532163i	$0.178621\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.68568	+	0.157976i	−0.989751	+	0.0275001i
$34$			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	−0.778339	−	0.627845i	$-0.783937\pi$
$37$	0.940152	−	1.62839i	0.154560	−	0.267706i	0.932899	+	0.360139i	$0.117271\pi$
$38$	−2.75721	−	4.77563i	−0.447278	−	0.774709i
$39$	−4.87306	+	9.00936i	−0.780314	+	1.44265i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	0.103155			0.0161101			0.00805504	−	0.999968i	$-0.497436\pi$
$41$	0.103155			0.0161101			0.00805504	+	0.999968i	$0.497436\pi$
$42$	0.0659590	+	4.58210i	0.0101777	+	0.707034i
$43$	−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
$45$	−2.99537	+	0.166581i	−0.446524	+	0.0248324i
$46$	−3.24875	−	5.62699i	−0.479001	−	0.829655i
$47$	−6.23353	+	10.7968i	−0.909254	+	1.57487i	−0.0941518	+	0.995558i	$0.530014\pi$
$47$	−6.23353	+	10.7968i	−0.909254	+	1.57487i	−0.815103	+	0.579317i	$0.803319\pi$
$48$	1.47537	−	0.907353i	0.212951	−	0.130965i
$49$	3.33650	+	6.15368i	0.476642	+	0.879097i
$50$			1.00000i			0.141421i
$51$	0.115647	+	4.16221i	0.0161938	+	0.582826i
$52$	5.12141	−	2.95685i	0.710212	−	0.410041i
$53$	2.11123	−	1.21892i	0.290000	−	0.167432i	−0.347942	−	0.937516i	$-0.613119\pi$
$53$	2.11123	−	1.21892i	0.290000	−	0.167432i	0.637942	+	0.770085i	$0.279786\pi$
$54$	−2.21449	+	4.70064i	−0.301355	+	0.639676i
$55$			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	$-0.243108\pi$
$59$	−1.82693	−	3.16433i	−0.237846	−	0.411961i	−0.960096	+	0.279671i	$0.909775\pi$
$60$	1.52347	+	0.824030i	0.196680	+	0.106382i
$61$	−12.3257	−	7.11625i	−1.57815	−	0.911143i	−0.995118	−	0.0986907i	$-0.968535\pi$
$61$	−12.3257	−	7.11625i	−1.57815	−	0.911143i	−0.583028	−	0.812452i	$-0.698132\pi$
$62$	−5.20176			−0.660624
$63$	0.334628	+	7.93020i	0.0421592	+	0.999111i
$64$	−1.00000			−0.125000
$65$	5.12141	+	2.95685i	0.635233	+	0.366752i
$66$	5.00294	+	2.70603i	0.615819	+	0.333089i
$67$	1.67736	+	2.90527i	0.204922	+	0.354935i	0.950108	−	0.311922i	$-0.100973\pi$
$67$	1.67736	+	2.90527i	0.204922	+	0.354935i	−0.745186	+	0.666857i	$0.767639\pi$
$68$	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	$-0.309107\pi$
$72$	2.51078	−	1.64195i	0.295898	−	0.193506i
$73$	−7.02609	+	4.05651i	−0.822341	+	0.474779i	−0.851223	−	0.524804i	$-0.824139\pi$
$73$	−7.02609	+	4.05651i	−0.822341	+	0.474779i	0.0288818	+	0.999583i	$0.490805\pi$
$74$	−1.62839	+	0.940152i	−0.189297	+	0.109290i
$75$	0.0481063	+	1.73138i	0.00555484	+	0.199923i
$76$			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	0.485049	+	0.874487i	$0.338802\pi$
$79$	−4.57567	+	7.92530i	−0.514803	+	0.891666i	−0.999852	+	0.0171788i	$0.994532\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−3.60801	+	8.24514i	−0.400890	+	0.916126i
$82$	−0.0893347	−	0.0515774i	−0.00986537	−	0.00569577i
$83$	6.54676			0.718600			0.359300	−	0.933222i	$-0.383016\pi$
$83$	6.54676			0.718600			0.359300	+	0.933222i	$0.383016\pi$
$84$	2.23393	−	4.00120i	0.243742	−	0.436566i
$85$	2.40398			0.260748
$86$	1.28978	+	0.744654i	0.139080	+	0.0802981i
$87$	3.13913	−	5.80365i	0.336550	−	0.622217i
$88$	−1.64195	−	2.84394i	−0.175032	−	0.303165i
$89$	5.62039	−	9.73481i	0.595761	−	1.03189i	−0.397679	−	0.917525i	$-0.630184\pi$
$89$	5.62039	−	9.73481i	0.595761	−	1.03189i	0.993439	−	0.114363i	$-0.0364826\pi$
$90$	2.67736	+	1.35342i	0.282218	+	0.142663i
$91$	8.00373	−	13.4441i	0.839019	−	1.40932i
$92$			6.49749i			0.677410i
$93$	−9.00623	+	0.250237i	−0.933903	+	0.0259484i
$94$	10.7968	−	6.23353i	1.11360	−	0.642940i
$95$	−4.77563	+	2.75721i	−0.489969	+	0.282884i
$96$	−1.73138	+	0.0481063i	−0.176708	+	0.00490983i
$97$			7.90564i			0.802696i	0.915926	+	0.401348i	$0.131458\pi$
$97$			7.90564i			0.802696i	−0.915926	+	0.401348i	$0.868542\pi$
$98$	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	$-0.245254\pi$
$101$	−2.45606	−	4.25403i	−0.244387	−	0.423291i	−0.961959	+	0.273193i	$0.911920\pi$
$102$	1.98095	−	3.66240i	0.196143	−	0.362632i
$103$	−3.96330	−	2.28821i	−0.390515	−	0.225464i	0.291868	−	0.956459i	$-0.405723\pi$
$103$	−3.96330	−	2.28821i	−0.390515	−	0.225464i	−0.682383	+	0.730995i	$0.739056\pi$
$104$	−5.91369			−0.579885
$105$	4.58210	−	0.0659590i	0.447167	−	0.00643694i
$106$	−2.43784			−0.236784
$107$	4.27148	+	2.46614i	0.412940	+	0.238411i	0.692052	−	0.721848i	$-0.256707\pi$
$107$	4.27148	+	2.46614i	0.412940	+	0.238411i	−0.279112	+	0.960258i	$0.590040\pi$
$108$	4.26813	−	2.96363i	0.410701	−	0.285175i
$109$	−3.80083	−	6.58323i	−0.364053	−	0.630559i	0.624570	−	0.780969i	$-0.285274\pi$
$109$	−3.80083	−	6.58323i	−0.364053	−	0.630559i	−0.988624	+	0.150410i	$0.951941\pi$
$110$	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	$0.941545\pi$
$114$	0.265278	+	9.54757i	0.0248456	+	0.894212i
$115$	−5.62699	+	3.24875i	−0.524720	+	0.302947i
$116$	−3.29911	+	1.90474i	−0.306315	+	0.176851i
$117$	14.8480	−	9.70999i	1.37270	−	0.897688i
$118$			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
$123$	−0.157154	−	0.0850027i	−0.0141701	−	0.00766444i
$124$	4.50485	+	2.60088i	0.404548	+	0.233566i
$125$	1.00000			0.0894427
$126$	3.67530	−	7.03507i	0.327422	−	0.626734i
$127$	−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
$129$	2.26892	+	1.22723i	0.199767	+	0.108052i
$130$	−2.95685	−	5.12141i	−0.259333	−	0.449177i
$131$	−2.51078	+	4.34879i	−0.219368	+	0.379956i	−0.954615	−	0.297843i	$-0.903733\pi$
$131$	−2.51078	+	4.34879i	−0.219368	+	0.379956i	0.735247	+	0.677799i	$0.237066\pi$
$132$	−2.97965	−	4.84496i	−0.259346	−	0.421700i
$133$	7.12514	+	12.7316i	0.617828	+	1.10397i
$134$		−	3.35472i		−	0.289803i
$135$	4.70064	+	2.21449i	0.404567	+	0.190593i
$136$	−2.08191	+	1.20199i	−0.178522	+	0.103070i
$137$	−2.53719	+	1.46485i	−0.216767	+	0.125150i	−0.604452	−	0.796641i	$-0.706608\pi$
$137$	−2.53719	+	1.46485i	−0.216767	+	0.125150i	0.387685	+	0.921792i	$0.373275\pi$
$138$	0.312570	+	11.2496i	0.0266078	+	0.957633i
$139$		−	3.36557i		−	0.285464i	−0.989761	−	0.142732i	$-0.954411\pi$
$139$		−	3.36557i		−	0.285464i	0.989761	−	0.142732i	$-0.0455887\pi$
$140$	−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
$144$	−2.99537	+	0.166581i	−0.249614	+	0.0138817i
$145$	−3.29911	−	1.90474i	−0.273976	−	0.158180i
$146$	8.11303			0.671439
$147$	−0.0122469	−	12.1243i	−0.00101011	−	0.999999i
$148$	1.88030			0.154560
$149$	−8.34064	−	4.81547i	−0.683292	−	0.394499i	0.117802	−	0.993037i	$-0.462415\pi$
$149$	−8.34064	−	4.81547i	−0.683292	−	0.394499i	−0.801094	+	0.598538i	$0.795748\pi$
$150$	0.824030	−	1.52347i	0.0672818	−	0.124391i
$151$	11.7684	+	20.3835i	0.957699	+	1.65878i	0.728066	+	0.685507i	$0.240419\pi$
$151$	11.7684	+	20.3835i	0.957699	+	1.65878i	0.229633	+	0.973277i	$0.426247\pi$
$152$	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
$156$	−10.2389	+	0.284486i	−0.819766	+	0.0227771i
$157$	3.70963	−	2.14176i	0.296061	−	0.170931i	−0.344611	−	0.938746i	$-0.611989\pi$
$157$	3.70963	−	2.14176i	0.296061	−	0.170931i	0.640672	+	0.767815i	$0.278656\pi$
$158$	7.92530	−	4.57567i	0.630503	−	0.364021i
$159$	−4.22084	+	0.117276i	−0.334734	+	0.00930056i
$160$			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	−0.00188269	−	0.999998i	$-0.500599\pi$
$163$	11.0446	−	19.1299i	0.865083	−	1.49837i	0.866965	−	0.498369i	$-0.166067\pi$
$164$	0.0515774	+	0.0893347i	0.00402752	+	0.00697587i
$165$	2.70603	−	5.00294i	0.210664	−	0.389478i
$166$	−5.66966	−	3.27338i	−0.440051	−	0.254063i
$167$	−12.9338			−1.00085			−0.500424	−	0.865780i	$-0.666823\pi$
$167$	−12.9338			−1.00085			−0.500424	+	0.865780i	$0.666823\pi$
$168$	−3.93524	+	2.34817i	−0.303610	+	0.181165i
$169$	−21.9718			−1.69014
$170$	−2.08191	−	1.20199i	−0.159675	−	0.0921884i
$171$	0.918597	+	16.5177i	0.0702469	+	1.26314i
$172$	−0.744654	−	1.28978i	−0.0567793	−	0.0983447i
$173$	−11.6298	+	20.1433i	−0.884195	+	1.53147i	−0.0375608	+	0.999294i	$0.511959\pi$
$173$	−11.6298	+	20.1433i	−0.884195	+	1.53147i	−0.846634	+	0.532176i	$0.821375\pi$
$174$	−5.62039	+	3.45655i	−0.426081	+	0.262040i
$175$	0.0354092	−	2.64551i	0.00267669	−	0.199982i
$176$			3.28390i			0.247533i
$177$	0.175774	+	6.32622i	0.0132119	+	0.475508i
$178$	−9.73481	+	5.62039i	−0.729655	+	0.421266i
$179$	8.18788	−	4.72728i	0.611991	−	0.353333i	−0.161753	−	0.986831i	$-0.551715\pi$
$179$	8.18788	−	4.72728i	0.611991	−	0.353333i	0.773744	+	0.633498i	$0.218382\pi$
$180$	−1.64195	−	2.51078i	−0.122384	−	0.187142i
$181$			8.42502i			0.626227i	0.949716	+	0.313113i	$0.101372\pi$
$181$			8.42502i			0.626227i	−0.949716	+	0.313113i	$0.898628\pi$
$182$	−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
$186$	7.92475	+	4.28640i	0.581071	+	0.314294i
$187$	−6.83677	−	3.94721i	−0.499954	−	0.288649i
$188$	−12.4671			−0.909254
$189$	6.02492	−	12.3572i	0.438249	−	0.898854i
$190$	5.51442			0.400058
$191$	−4.44301	−	2.56517i	−0.321485	−	0.185609i	0.330569	−	0.943782i	$-0.392759\pi$
$191$	−4.44301	−	2.56517i	−0.321485	−	0.185609i	−0.652054	+	0.758172i	$0.726093\pi$
$192$	1.52347	+	0.824030i	0.109947	+	0.0594692i
$193$	−7.63955	−	13.2321i	−0.549907	−	0.952467i	−0.998280	−	0.0586203i	$-0.981330\pi$
$193$	−7.63955	−	13.2321i	−0.549907	−	0.952467i	0.448374	−	0.893846i	$-0.352003\pi$
$194$	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	$0.805994\pi$
$198$	−5.39199	−	8.24514i	−0.383192	−	0.585956i
$199$	−5.74190	+	3.31509i	−0.407032	+	0.235000i	−0.689514	−	0.724273i	$-0.742176\pi$
$199$	−5.74190	+	3.31509i	−0.407032	+	0.235000i	0.282481	+	0.959273i	$0.408842\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−0.161383	−	5.80830i	−0.0113831	−	0.409686i
$202$			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
$207$	1.08236	+	19.4624i	0.0752291	+	1.35273i
$208$	5.12141	+	2.95685i	0.355106	+	0.205020i
$209$	18.1088			1.25261
$210$	−4.00120	−	2.23393i	−0.276109	−	0.154156i
$211$	−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
$213$	−11.4635	+	21.1939i	−0.785469	+	1.45218i
$214$	−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
$219$	14.0468	−	0.390288i	0.949192	−	0.0263732i
$220$	−2.84394	+	1.64195i	−0.191738	+	0.110700i
$221$	−12.3118	+	7.10820i	−0.828179	+	0.478149i
$222$	3.25553	−	0.0904545i	0.218497	−	0.00607091i
$223$			22.0431i			1.47612i	0.674737	+	0.738058i	$0.264257\pi$
$223$			22.0431i			1.47612i	−0.674737	+	0.738058i	$0.735743\pi$
$224$	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	$-0.233154\pi$
$227$	−3.12420	−	5.41126i	−0.207360	−	0.359158i	−0.950882	+	0.309553i	$0.899821\pi$
$228$	4.54405	−	8.40108i	0.300937	−	0.556375i
$229$	−10.5527	−	6.09261i	−0.697342	−	0.402611i	0.109015	−	0.994040i	$-0.465230\pi$
$229$	−10.5527	−	6.09261i	−0.697342	−	0.402611i	−0.806357	+	0.591429i	$0.798564\pi$
$230$	6.49749			0.428432
$231$	−13.1395	−	7.33599i	−0.864517	−	0.482673i
$232$	3.80949			0.250105
$233$	−13.9997	−	8.08273i	−0.917151	−	0.529517i	−0.0344258	−	0.999407i	$-0.510960\pi$
$233$	−13.9997	−	8.08273i	−0.917151	−	0.529517i	−0.882725	+	0.469890i	$0.844294\pi$
$234$	−17.7137	+	0.985109i	−1.15798	+	0.0643986i
$235$	−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	$-0.0554970\pi$
$240$	0.0481063	+	1.73138i	0.00310525	+	0.111760i
$241$	13.9360	−	8.04597i	0.897698	−	0.518286i	0.0212455	−	0.999774i	$-0.493237\pi$
$241$	13.9360	−	8.04597i	0.897698	−	0.518286i	0.876453	+	0.481488i	$0.159903\pi$
$242$	0.187073	−	0.108006i	0.0120255	−	0.00694291i
$243$	12.2909	−	9.58815i	0.788465	−	0.615080i
$244$		−	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
$249$	−9.97382	−	5.39472i	−0.632065	−	0.341877i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	1.05846			0.0668093			0.0334047	−	0.999442i	$-0.489365\pi$
$251$	1.05846			0.0668093			0.0334047	+	0.999442i	$0.489365\pi$
$252$	−6.70044	+	4.25490i	−0.422088	+	0.268033i
$253$	21.3371			1.34145
$254$	12.2439	+	7.06901i	0.768250	+	0.443549i
$255$	−3.66240	−	1.98095i	−0.229349	−	0.124052i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.23091	−	2.13199i	0.0767819	−	0.132990i	−0.825078	−	0.565019i	$-0.808869\pi$
$257$	1.23091	−	2.13199i	0.0767819	−	0.132990i	0.901860	+	0.432029i	$0.142202\pi$
$258$	−1.35133	−	2.19728i	−0.0841299	−	0.136796i
$259$	4.34122	−	2.42953i	0.269750	−	0.150963i
$260$			5.91369i			0.366752i
$261$	−9.56477	+	6.25498i	−0.592044	+	0.387174i
$262$	4.34879	−	2.51078i	0.268669	−	0.155116i
$263$	26.5856	−	15.3492i	1.63934	−	0.946471i	0.658273	−	0.752779i	$-0.271287\pi$
$263$	26.5856	−	15.3492i	1.63934	−	0.946471i	0.981062	−	0.193692i	$-0.0620462\pi$
$264$	0.157976	+	5.68568i	0.00972277	+	0.349930i
$265$			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	0.999923	+	0.0124280i	$0.00395605\pi$
$269$	8.37650	+	14.5085i	0.510724	+	0.884601i	−0.489198	+	0.872173i	$0.662711\pi$
$270$	−2.96363	−	4.26813i	−0.180361	−	0.259750i
$271$	13.2178	+	7.63132i	0.802926	+	0.463570i	0.844493	−	0.535566i	$-0.179902\pi$
$271$	13.2178	+	7.63132i	0.802926	+	0.463570i	−0.0415670	+	0.999136i	$0.513235\pi$
$272$	2.40398			0.145763
$273$	−23.2718	+	13.8864i	−1.40847	+	0.840442i
$274$	2.92970			0.176989
$275$	−2.84394	−	1.64195i	−0.171496	−	0.0990133i
$276$	5.35413	−	9.89876i	0.322281	−	0.595836i
$277$	1.75611	+	3.04167i	0.105514	+	0.182756i	0.913948	−	0.405831i	$-0.133018\pi$
$277$	1.75611	+	3.04167i	0.105514	+	0.182756i	−0.808434	+	0.588587i	$0.799684\pi$
$278$	−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	$-0.0395834\pi$
$282$	−21.5853	+	0.599745i	−1.28538	+	0.0357143i
$283$	0.149485	−	0.0863055i	0.00888599	−	0.00513033i	−0.495550	−	0.868579i	$-0.665034\pi$
$283$	0.149485	−	0.0863055i	0.00888599	−	0.00513033i	0.504436	+	0.863449i	$0.331700\pi$
$284$	12.0478	−	6.95578i	0.714904	−	0.412750i
$285$	9.54757	−	0.265278i	0.565549	−	0.0157137i
$286$			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
$291$	6.51448	−	12.0440i	0.381886	−	0.706034i
$292$	−7.02609	−	4.05651i	−0.411171	−	0.237390i
$293$	4.38021			0.255895			0.127947	−	0.991781i	$-0.459161\pi$
$293$	4.38021			0.255895			0.127947	+	0.991781i	$0.459161\pi$
$294$	−6.05157	+	10.5061i	−0.352935	+	0.612729i
$295$	3.65385			0.212736
$296$	−1.62839	−	0.940152i	−0.0946483	−	0.0546452i
$297$	−9.73225	−	14.0161i	−0.564722	−	0.813297i
$298$	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
$303$	0.236304	+	8.50477i	0.0135753	+	0.488586i
$304$	−4.77563	+	2.75721i	−0.273901	+	0.158137i
$305$	12.3257	−	7.11625i	0.705768	−	0.407476i
$306$	−6.03586	+	3.94721i	−0.345047	+	0.225647i
$307$			4.76658i			0.272043i	0.990706	+	0.136022i	$0.0434316\pi$
$307$			4.76658i			0.272043i	−0.990706	+	0.136022i	$0.956568\pi$
$308$	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	$-0.112526\pi$
$311$	2.98511	+	5.17035i	0.169270	+	0.293184i	−0.768894	+	0.639377i	$0.779192\pi$
$312$	9.00936	+	4.87306i	0.510055	+	0.275883i
$313$	23.1417	+	13.3609i	1.30805	+	0.755201i	0.981770	−	0.190073i	$-0.0608726\pi$
$313$	23.1417	+	13.3609i	1.30805	+	0.755201i	0.326277	+	0.945274i	$0.394206\pi$
$314$	−4.28351			−0.241733
$315$	−7.03507	−	3.67530i	−0.396381	−	0.207080i
$316$	−9.15135			−0.514803
$317$	−20.5873	−	11.8861i	−1.15630	−	0.667588i	−0.205883	−	0.978577i	$-0.566007\pi$
$317$	−20.5873	−	11.8861i	−1.15630	−	0.667588i	−0.950414	+	0.310988i	$0.899340\pi$
$318$	3.71399	+	2.00885i	0.208270	+	0.112651i
$319$	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
$324$	−8.94450	+	0.997943i	−0.496917	+	0.0554413i
$325$	−5.12141	+	2.95685i	−0.284085	+	0.164016i
$326$	−19.1299	+	11.0446i	−1.05951	+	0.611706i
$327$	0.365688	+	13.1614i	0.0202226	+	0.727826i
$328$		−	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	−0.921851	−	0.387545i	$-0.873323\pi$
$331$	−2.27966	+	3.94849i	−0.125301	+	0.217028i	0.796549	+	0.604574i	$0.206656\pi$
$332$	3.27338	+	5.66966i	0.179650	+	0.311163i
$333$	5.63221	−	0.313223i	0.308643	−	0.0171645i
$334$	11.2010	+	6.46690i	0.612892	+	0.353853i
$335$	−3.35472			−0.183288
$336$	4.58210	−	0.0659590i	0.249974	−	0.00359836i
$337$	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
$339$	3.19917	−	5.91465i	0.173755	−	0.321240i
$340$	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
$345$	11.2496	−	0.312570i	0.605661	−	0.0168282i
$346$	20.1433	−	11.6298i	1.08291	−	0.625220i
$347$	−16.2720	+	9.39464i	−0.873526	+	0.504331i	−0.868518	−	0.495657i	$-0.834927\pi$
$347$	−16.2720	+	9.39464i	−0.873526	+	0.504331i	−0.00500776	+	0.999987i	$0.501594\pi$
$348$	6.59568	−	0.183260i	0.353565	−	0.00982379i
$349$			8.52974i			0.456586i	0.973592	+	0.228293i	$0.0733145\pi$
$349$			8.52974i			0.456586i	−0.973592	+	0.228293i	$0.926686\pi$
$350$	−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	$-0.118883\pi$
$353$	2.80987	+	4.86684i	0.149554	+	0.259036i	−0.781508	+	0.623895i	$0.785549\pi$
$354$	3.01089	−	5.56655i	0.160027	−	0.295859i
$355$	12.0478	+	6.95578i	0.639429	+	0.369175i
$356$	11.2408			0.595761
$357$	−5.37032	+	9.61879i	−0.284227	+	0.509081i
$358$	−9.45455			−0.499689
$359$	−23.4396	−	13.5328i	−1.23709	−	0.714236i	−0.268594	−	0.963254i	$-0.586559\pi$
$359$	−23.4396	−	13.5328i	−1.23709	−	0.714236i	−0.968499	+	0.249018i	$0.919892\pi$
$360$	0.166581	+	2.99537i	0.00877959	+	0.157870i
$361$	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
$366$	−0.684674	−	24.6419i	−0.0357885	−	1.28805i
$367$	−16.2700	+	9.39351i	−0.849289	+	0.490337i	−0.860411	−	0.509601i	$-0.829793\pi$
$367$	−16.2700	+	9.39351i	−0.849289	+	0.490337i	0.0111216	+	0.999938i	$0.496460\pi$
$368$	−5.62699	+	3.24875i	−0.293327	+	0.169353i
$369$	0.169375	+	0.258999i	0.00881731	+	0.0134829i
$370$		−	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	−0.640129	−	0.768268i	$-0.721119\pi$
$373$	6.66836	−	11.5499i	0.345275	−	0.598033i	0.985404	+	0.170234i	$0.0544524\pi$
$374$	3.94721	+	6.83677i	0.204106	+	0.353521i
$375$	−1.52347	−	0.824030i	−0.0786719	−	0.0425527i
$376$	10.7968	+	6.23353i	0.556802	+	0.321470i
$377$	22.5281			1.16026
$378$	−11.3963	+	7.68918i	−0.586164	+	0.395489i
$379$	−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
$381$	21.5389	+	11.6502i	1.10347	+	0.596855i
$382$	2.56517	+	4.44301i	0.131246	+	0.227324i
$383$	−4.64240	+	8.04088i	−0.237216	+	0.410870i	−0.959914	−	0.280294i	$-0.909568\pi$
$383$	−4.64240	+	8.04088i	−0.237216	+	0.410870i	0.722699	+	0.691163i	$0.242901\pi$
$384$	−0.907353	−	1.47537i	−0.0463031	−	0.0752896i
$385$	−4.44450	+	7.46554i	−0.226513	+	0.380479i
$386$			15.2791i			0.777686i
$387$	−2.44537	−	3.73932i	−0.124305	−	0.190080i
$388$	−6.84648	+	3.95282i	−0.347578	+	0.200674i
$389$	−16.8511	+	9.72899i	−0.854385	+	0.493279i	−0.862128	−	0.506691i	$-0.830869\pi$
$389$	−16.8511	+	9.72899i	−0.854385	+	0.493279i	0.00774302	+	0.999970i	$0.497535\pi$
$390$	0.284486	+	10.2389i	0.0144055	+	0.518465i
$391$		−	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
$396$	0.547035	+	9.83650i	0.0274895	+	0.494302i
$397$	1.98370	+	1.14529i	0.0995589	+	0.0574804i	0.548953	−	0.835853i	$-0.315027\pi$
$397$	1.98370	+	1.14529i	0.0995589	+	0.0574804i	−0.449394	+	0.893334i	$0.648360\pi$
$398$	6.63017			0.332341
$399$	−0.363726	−	25.2676i	−0.0182091	−	1.26496i
$400$	1.00000			0.0500000
$401$	1.30687	+	0.754520i	0.0652618	+	0.0376789i	0.532276	−	0.846571i	$-0.321337\pi$
$401$	1.30687	+	0.754520i	0.0652618	+	0.0376789i	−0.467014	+	0.884250i	$0.654670\pi$
$402$	−2.76439	+	5.11083i	−0.137875	+	0.254905i
$403$	−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
$408$	4.16221	−	0.115647i	0.206060	−	0.00572536i
$409$	16.6655	−	9.62186i	0.824058	−	0.475770i	−0.0277558	−	0.999615i	$-0.508836\pi$
$409$	16.6655	−	9.62186i	0.824058	−	0.475770i	0.851814	+	0.523845i	$0.175503\pi$
$410$	0.0893347	−	0.0515774i	0.00441193	−	0.00254723i
$411$	5.07242	−	0.140937i	0.250204	−	0.00695191i
$412$		−	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
$417$	−2.77333	+	5.12737i	−0.135811	+	0.251088i
$418$	−15.6827	−	9.05440i	−0.767065	−	0.442865i
$419$	1.34919			0.0659121			0.0329560	−	0.999457i	$-0.489508\pi$
$419$	1.34919			0.0659121			0.0329560	+	0.999457i	$0.489508\pi$
$420$	2.34817	+	3.93524i	0.114579	+	0.192020i
$421$	−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
$423$	−37.3435	+	2.07678i	−1.81570	+	0.100976i
$424$	−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
$429$	0.934223	+	33.6234i	0.0451047	+	1.62335i
$430$	−1.28978	+	0.744654i	−0.0621986	+	0.0359104i
$431$	−6.72021	+	3.87992i	−0.323701	+	0.186889i	−0.653041	−	0.757322i	$-0.726507\pi$
$431$	−6.72021	+	3.87992i	−0.323701	+	0.186889i	0.329340	+	0.944211i	$0.393174\pi$
$432$	4.70064	+	2.21449i	0.226160	+	0.106545i
$433$		−	34.0914i		−	1.63833i	−0.573560	−	0.819164i	$-0.694438\pi$
$433$		−	34.0914i		−	1.63833i	0.573560	−	0.819164i	$-0.305562\pi$
$434$	−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
$438$	−12.3600	−	6.68538i	−0.590583	−	0.319440i
$439$	10.3571	+	5.97965i	0.494316	+	0.285393i	0.726363	−	0.687311i	$-0.241209\pi$
$439$	10.3571	+	5.97965i	0.494316	+	0.285393i	−0.232047	+	0.972704i	$0.574542\pi$
$440$	3.28390			0.156554
$441$	−9.97217	+	18.4812i	−0.474865	+	0.880059i
$442$	14.2164			0.676205
$443$	3.12301	+	1.80307i	0.148378	+	0.0856663i	0.572351	−	0.820009i	$-0.306031\pi$
$443$	3.12301	+	1.80307i	0.148378	+	0.0856663i	−0.423973	+	0.905675i	$0.639365\pi$
$444$	−2.86459	−	1.54943i	−0.135948	−	0.0735325i
$445$	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	$0.851906\pi$
$450$	−2.51078	+	1.64195i	−0.118359	+	0.0774022i
$451$	0.293366	−	0.169375i	0.0138141	−	0.00797556i
$452$	−3.36221	+	1.94117i	−0.158145	+	0.0913050i
$453$	−1.13227	−	40.7512i	−0.0531987	−	1.91466i
$454$			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	−0.0419097	+	0.999121i	$0.513344\pi$
$457$	−18.9452	+	32.8141i	−0.886219	+	1.53498i	−0.844310	+	0.535856i	$0.819989\pi$
$458$	6.09261	+	10.5527i	0.284689	+	0.493095i
$459$	−10.2605	+	7.12450i	−0.478919	+	0.332543i
$460$	−5.62699	−	3.24875i	−0.262360	−	0.151474i
$461$	−32.6110			−1.51884			−0.759422	−	0.650598i	$-0.774518\pi$
$461$	−32.6110			−1.51884			−0.759422	+	0.650598i	$0.774518\pi$
$462$	7.71116	+	12.9229i	0.358756	+	0.601228i
$463$	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
$465$	4.28640	−	7.92475i	0.198777	−	0.367501i
$466$	8.08273	+	13.9997i	0.374425	+	0.648524i
$467$	−11.1463	+	19.3060i	−0.515790	+	0.893375i	0.484042	+	0.875045i	$0.339168\pi$
$467$	−11.1463	+	19.3060i	−0.515790	+	0.893375i	−0.999832	+	0.0183299i	$0.994165\pi$
$468$	15.8331	+	8.00373i	0.731884	+	0.369972i
$469$	−0.118788	+	8.87495i	−0.00548512	+	0.409807i
$470$			12.4671i			0.575063i
$471$	−7.41640	+	0.206064i	−0.341730	+	0.00949493i
$472$	−3.16433	+	1.82693i	−0.145650	+	0.0840911i
$473$	−4.23550	+	2.44537i	−0.194748	+	0.112438i
$474$	−15.8445	+	0.440238i	−0.727761	+	0.0202208i
$475$		−	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	0.700231	+	0.713916i	$0.253080\pi$
$479$	21.1941	+	36.7093i	0.968385	+	1.67729i	0.268154	+	0.963376i	$0.413586\pi$
$480$	0.824030	−	1.52347i	0.0376117	−	0.0695368i
$481$	−9.62981	−	5.55977i	−0.439081	−	0.253504i
$482$	−16.0919			−0.732968
$483$	−0.428568	−	29.7722i	−0.0195005	−	1.35468i
$484$	−0.216013			−0.00981876
$485$	−6.84648	−	3.95282i	−0.310883	−	0.179488i
$486$	−15.4383	+	2.15811i	−0.700298	+	0.0978938i
$487$	−8.77524	−	15.1992i	−0.397644	−	0.688740i	0.595790	−	0.803140i	$-0.296839\pi$
$487$	−8.77524	−	15.1992i	−0.397644	−	0.688740i	−0.993435	+	0.114400i	$0.963506\pi$
$488$	−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	$-0.249353\pi$
$492$	−0.00496240	−	0.178601i	−0.000223722	−	0.00805193i
$493$	7.93100	−	4.57896i	0.357194	−	0.206226i
$494$	−28.2416	+	16.3053i	−1.27065	+	0.733610i
$495$	−8.24514	+	5.39199i	−0.370591	+	0.242352i
$496$			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	−0.799726	−	0.600365i	$-0.795022\pi$
$499$	2.68212	−	4.64557i	0.120068	−	0.207964i	0.919794	+	0.392401i	$0.128355\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	19.7043	+	10.6578i	0.880324	+	0.476157i
$502$	−0.916652	−	0.529229i	−0.0409122	−	0.0236207i
$503$	−21.3393			−0.951470			−0.475735	−	0.879589i	$-0.657818\pi$
$503$	−21.3393			−0.951470			−0.475735	+	0.879589i	$0.657818\pi$
$504$	7.93020	−	0.334628i	0.353239	−	0.0149055i
$505$	4.91213			0.218587
$506$	−18.4785	−	10.6686i	−0.821468	−	0.474275i
$507$	33.4735	+	18.1054i	1.48661	+	0.804089i
$508$	−7.06901	−	12.2439i	−0.313637	−	0.543234i
$509$	−16.1907	+	28.0432i	−0.717642	+	1.24299i	0.244290	+	0.969702i	$0.421445\pi$
$509$	−16.1907	+	28.0432i	−0.717642	+	1.24299i	−0.961932	+	0.273290i	$0.911888\pi$
$510$	2.18126	+	3.54676i	0.0965877	+	0.157053i
$511$	−21.4631	−	0.287276i	−0.949473	−	0.0127083i
$512$			1.00000i			0.0441942i
$513$	12.2117	−	25.9213i	0.539158	−	1.14445i
$514$	−2.13199	+	1.23091i	−0.0940382	+	0.0542930i
$515$	3.96330	−	2.28821i	0.174644	−	0.100831i
$516$	0.0716451	+	2.57856i	0.00315400	+	0.113515i
$517$			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	0.996468	+	0.0839705i	$0.0267602\pi$
$521$	13.0323	+	22.5726i	0.570955	+	0.988923i	−0.425514	+	0.904952i	$0.639907\pi$
$522$	11.4108	−	0.634588i	0.499438	−	0.0277751i
$523$	11.2502	+	6.49533i	0.491939	+	0.284021i	0.725379	−	0.688350i	$-0.241665\pi$
$523$	11.2502	+	6.49533i	0.491939	+	0.284021i	−0.233440	+	0.972371i	$0.574998\pi$
$524$	−5.02155			−0.219368
$525$	−2.23393	+	4.00120i	−0.0974966	+	0.174626i
$526$	−30.6984			−1.33851
$527$	−10.8296	−	6.25246i	−0.471744	−	0.272362i
$528$	2.70603	−	5.00294i	0.117765	−	0.217725i
$529$	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
$534$	19.4621	−	0.540753i	0.842208	−	0.0234007i
$535$	−4.27148	+	2.46614i	−0.184672	+	0.106621i
$536$	2.90527	−	1.67736i	0.125489	−	0.0724508i
$537$	−16.3694	+	0.454824i	−0.706394	+	0.0196271i
$538$		−	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	−0.998786	−	0.0492698i	$-0.984311\pi$
$541$	−10.6231	+	18.3998i	−0.456724	+	0.791069i	0.542062	+	0.840339i	$0.317644\pi$
$542$	−7.63132	−	13.2178i	−0.327793	−	0.567755i
$543$	6.94247	−	12.8353i	0.297930	−	0.550816i
$544$	−2.08191	−	1.20199i	−0.0892611	−	0.0515349i
$545$	7.60166			0.325619
$546$	27.0971	−	0.390062i	1.15965	−	0.0166931i
$547$	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
$549$	−2.37086	−	42.6317i	−0.101186	−	1.81947i
$550$	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
$555$	−0.0904545	−	3.25553i	−0.00383958	−	0.138189i
$556$	2.91467	−	1.68279i	0.123610	−	0.0713661i
$557$	30.7037	−	17.7268i	1.30096	−	0.751109i	0.320390	−	0.947286i	$-0.396186\pi$
$557$	30.7037	−	17.7268i	1.30096	−	0.751109i	0.980568	+	0.196177i	$0.0628528\pi$
$558$	−8.54102	−	13.0605i	−0.361570	−	0.552893i
$559$			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	−0.901983	−	0.431771i	$-0.857889\pi$
$563$	−19.5733	−	33.9020i	−0.824916	−	1.42880i	0.0770670	−	0.997026i	$-0.475444\pi$
$564$	18.9933	+	10.2732i	0.799760	+	0.432581i
$565$	−3.36221	−	1.94117i	−0.141449	−	0.0816657i
$566$	−0.172611			−0.00725538
$567$	−19.3615	+	13.8612i	−0.813107	+	0.582114i
$568$	−13.9116			−0.583716
$569$	−36.3773	−	21.0025i	−1.52502	−	0.880469i	−0.999560	−	0.0296490i	$-0.990561\pi$
$569$	−36.3773	−	21.0025i	−1.52502	−	0.880469i	−0.525457	−	0.850820i	$-0.676106\pi$
$570$	−8.40108	−	4.54405i	−0.351882	−	0.190329i
$571$	9.84182	+	17.0465i	0.411867	+	0.713375i	0.995094	−	0.0989342i	$-0.0315433\pi$
$571$	9.84182	+	17.0465i	0.411867	+	0.713375i	−0.583227	+	0.812310i	$0.698210\pi$
$572$	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
$576$	−1.64195	−	2.51078i	−0.0684145	−	0.104616i
$577$	21.9785	−	12.6893i	0.914976	−	0.528261i	0.0329469	−	0.999457i	$-0.489511\pi$
$577$	21.9785	−	12.6893i	0.914976	−	0.528261i	0.882029	+	0.471196i	$0.156177\pi$
$578$	−9.71757	+	5.61044i	−0.404197	+	0.233364i
$579$	0.735021	+	26.4540i	0.0305464	+	1.09939i
$580$		−	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
$585$	0.985109	+	17.7137i	0.0407292	+	0.732372i
$586$	−3.79338	−	2.19011i	−0.156703	−	0.0904725i
$587$	30.1344			1.24378			0.621889	−	0.783105i	$-0.286365\pi$
$587$	30.1344			1.24378			0.621889	+	0.783105i	$0.286365\pi$
$588$	10.4939	−	6.07278i	0.432760	−	0.250437i
$589$	28.6847			1.18193
$590$	−3.16433	−	1.82693i	−0.130273	−	0.0752134i
$591$	13.2416	−	24.4813i	0.544688	−	1.00702i
$592$	0.940152	+	1.62839i	0.0386400	+	0.0669265i
$593$	0.505610	−	0.875743i	0.0207629	−	0.0359625i	−0.855457	−	0.517873i	$-0.826724\pi$
$593$	0.505610	−	0.875743i	0.0207629	−	0.0359625i	0.876220	+	0.481911i	$0.160057\pi$
$594$	1.42032	+	17.0044i	0.0582766	+	0.697700i
$595$	5.46516	+	3.25360i	0.224050	+	0.133385i
$596$		−	9.63094i		−	0.394499i
$597$	11.4794	−	0.318953i	0.469819	−	0.0130539i
$598$	−33.2763	+	19.2121i	−1.36077	+	0.785641i
$599$	17.7082	−	10.2239i	0.723539	−	0.417735i	−0.0925150	−	0.995711i	$-0.529491\pi$
$599$	17.7082	−	10.2239i	0.723539	−	0.417735i	0.816054	+	0.577976i	$0.196157\pi$
$600$	1.73138	−	0.0481063i	0.0706834	−	0.00196393i
$601$		−	43.8623i		−	1.78918i	−0.446886	−	0.894591i	$-0.647467\pi$
$601$		−	43.8623i		−	1.78918i	0.446886	−	0.894591i	$-0.352533\pi$
$602$	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
$606$	4.04774	−	7.48350i	0.164428	−	0.303996i
$607$	−32.5289	−	18.7806i	−1.32031	−	0.762280i	−0.336530	−	0.941673i	$-0.609253\pi$
$607$	−32.5289	−	18.7806i	−1.32031	−	0.762280i	−0.983777	+	0.179393i	$0.942587\pi$
$608$	5.51442			0.223639
$609$	14.9912	−	8.94533i	0.607475	−	0.362483i
$610$	−14.2325			−0.576257
$611$	63.8490	+	36.8632i	2.58305	+	1.49133i
$612$	7.20081	−	0.400457i	0.291076	−	0.0161875i
$613$	−22.6557	−	39.2409i	−0.915057	−	1.58492i	−0.806818	−	0.590800i	$-0.798812\pi$
$613$	−22.6557	−	39.2409i	−0.915057	−	1.58492i	−0.108238	−	0.994125i	$-0.534521\pi$
$614$	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	$-0.193184\pi$
$618$	−0.220155	−	7.92353i	−0.00885592	−	0.318731i
$619$	−13.6375	+	7.87364i	−0.548139	+	0.316468i	−0.748371	−	0.663280i	$-0.769164\pi$
$619$	−13.6375	+	7.87364i	−0.548139	+	0.316468i	0.200232	+	0.979749i	$0.435830\pi$
$620$	−4.50485	+	2.60088i	−0.180919	+	0.104454i
$621$	14.3887	−	30.5424i	0.577397	−	1.22562i
$622$		−	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
$627$	−27.5883	−	14.9222i	−1.10177	−	0.595935i
$628$	3.70963	+	2.14176i	0.148030	+	0.0854654i
$629$	−4.52021			−0.180233
$630$	4.25490	+	6.70044i	0.169519	+	0.266952i
$631$	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
$633$	16.7552	+	9.06270i	0.665960	+	0.360210i
$634$	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
$639$	34.9289	−	22.8421i	1.38176	−	0.903619i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	19.8217	−	11.4441i	0.782909	−	0.452013i	−0.0545511	−	0.998511i	$-0.517373\pi$
$641$	19.8217	−	11.4441i	0.782909	−	0.452013i	0.837460	+	0.546498i	$0.184039\pi$
$642$	0.237274	+	8.53967i	0.00936446	+	0.337034i
$643$			10.5338i			0.415411i	0.978191	+	0.207705i	$0.0665995\pi$
$643$			10.5338i			0.415411i	−0.978191	+	0.207705i	$0.933400\pi$
$644$	−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	$-0.329433\pi$
$647$	−12.4473	−	21.5593i	−0.489352	−	0.847582i	−0.999925	+	0.0122519i	$0.996100\pi$
$648$	8.24514	+	3.60801i	0.323900	+	0.141736i
$649$	−10.3913	−	5.99944i	−0.407896	−	0.235499i
$650$	5.91369			0.231954
$651$	−20.8133	−	11.6204i	−0.815736	−	0.455438i
$652$	22.0893			0.865083
$653$	35.9305	+	20.7445i	1.40607	+	0.811795i	0.995006	−	0.0998116i	$-0.0318240\pi$
$653$	35.9305	+	20.7445i	1.40607	+	0.811795i	0.411064	+	0.911607i	$0.365157\pi$
$654$	6.26399	−	11.5809i	0.244942	−	0.452850i
$655$	−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	$0.983557\pi$
$660$	5.68568	−	0.157976i	0.221315	−	0.00614922i
$661$	−11.4271	+	6.59741i	−0.444461	+	0.256610i	−0.705488	−	0.708722i	$-0.749272\pi$
$661$	−11.4271	+	6.59741i	−0.444461	+	0.256610i	0.261027	+	0.965331i	$0.415939\pi$
$662$	3.94849	−	2.27966i	0.153462	−	0.0886015i
$663$	24.6140	−	0.683899i	0.955930	−	0.0265604i
$664$		−	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
$669$	18.1642	−	33.5821i	0.702268	−	1.29836i
$670$	2.90527	+	1.67736i	0.112240	+	0.0648020i
$671$	−46.7381			−1.80430
$672$	−4.00120	−	2.23393i	−0.154349	−	0.0861757i
$673$	−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
$675$	−4.26813	+	2.96363i	−0.164280	+	0.114070i
$676$	−10.9859	−	19.0281i	−0.422534	−	0.731851i
$677$	5.90532	−	10.2283i	0.226960	−	0.393106i	−0.729946	−	0.683505i	$-0.760455\pi$
$677$	5.90532	−	10.2283i	0.226960	−	0.393106i	0.956906	+	0.290399i	$0.0937881\pi$
$678$	−5.72789	+	3.52265i	−0.219978	+	0.135287i
$679$	−10.6997	+	17.9725i	−0.410616	+	0.689721i
$680$		−	2.40398i		−	0.0921884i
$681$	0.300587	+	10.8184i	0.0115185	+	0.414560i
$682$	−14.7935	+	8.54102i	−0.566472	+	0.327053i
$683$	−3.86454	+	2.23119i	−0.147872	+	0.0853742i	−0.572111	−	0.820176i	$-0.693875\pi$
$683$	−3.86454	+	2.23119i	−0.147872	+	0.0853742i	0.424238	+	0.905551i	$0.360542\pi$
$684$	−13.8455	+	9.05440i	−0.529395	+	0.346203i
$685$		−	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
$690$	−9.89876	−	5.35413i	−0.376840	−	0.203828i
$691$	23.6406	+	13.6489i	0.899332	+	0.519230i	0.876983	−	0.480521i	$-0.159552\pi$
$691$	23.6406	+	13.6489i	0.899332	+	0.519230i	0.0223487	+	0.999750i	$0.492886\pi$
$692$	−23.2595			−0.884195
$693$	13.9726	+	22.0036i	0.530777	+	0.835846i
$694$	18.7893			0.713231
$695$	2.91467	+	1.68279i	0.110560	+	0.0638318i
$696$	−5.80365	−	3.13913i	−0.219987	−	0.118988i
$697$	−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	$0.853585\pi$
$702$	27.7981	+	13.0958i	1.04917	+	0.494271i
$703$	8.97963	−	5.18439i	0.338673	−	0.195533i
$704$	−2.84394	+	1.64195i	−0.107185	+	0.0618833i
$705$	0.599745	+	21.5853i	0.0225877	+	0.812948i
$706$		−	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	0.492604	+	0.870253i	$0.336045\pi$
$709$	−13.5095	+	23.3991i	−0.507360	+	0.878773i	−0.999964	+	0.00851903i	$0.997288\pi$
$710$	−6.95578	−	12.0478i	−0.261046	−	0.452145i
$711$	−27.4117	+	1.52444i	−1.02802	+	0.0571710i
$712$	−9.73481	−	5.62039i	−0.364827	−	0.210633i
$713$	33.7984			1.26576
$714$	9.46023	−	5.64496i	0.354040	−	0.211257i
$715$	19.4200			0.726266
$716$	8.18788	+	4.72728i	0.305996	+	0.176667i
$717$	−4.41966	+	8.17110i	−0.165055	+	0.305155i
$718$	13.5328	+	23.4396i	0.505041	+	0.874757i
$719$	−17.3360	+	30.0268i	−0.646524	+	1.11981i	0.337424	+	0.941353i	$0.390445\pi$
$719$	−17.3360	+	30.0268i	−0.646524	+	1.11981i	−0.983947	+	0.178459i	$0.942889\pi$
$720$	1.35342	−	2.67736i	0.0504391	−	0.0997793i
$721$	−5.91315	−	10.5660i	−0.220217	−	0.393498i
$722$		−	11.4088i		−	0.424592i
$723$	−27.8613	+	0.774124i	−1.03617	+	0.0287900i
$724$	−7.29628	+	4.21251i	−0.271164	+	0.156557i
$725$	3.29911	−	1.90474i	0.122526	−	0.0707404i
$726$	−0.374001	+	0.0103916i	−0.0138805	+	0.000385668i
$727$			16.8936i			0.626549i	0.949663	+	0.313274i	$0.101426\pi$
$727$			16.8936i			0.626549i	−0.949663	+	0.313274i	$0.898574\pi$
$728$	−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
$732$	−11.7280	+	21.6829i	−0.433480	+	0.801422i
$733$	−15.6317	−	9.02495i	−0.577369	−	0.333344i	0.182718	−	0.983165i	$-0.441510\pi$
$733$	−15.6317	−	9.02495i	−0.577369	−	0.333344i	−0.760087	+	0.649821i	$0.774844\pi$
$734$	18.7870			0.693442
$735$	10.5061	+	6.05157i	0.387524	+	0.223215i
$736$	6.49749			0.239501
$737$	9.54061	+	5.50827i	0.351433	+	0.202900i
$738$	−0.0171836	−	0.308987i	−0.000632538	−	0.0113740i
$739$	−13.2235	−	22.9037i	−0.486433	−	0.842527i	0.513445	−	0.858122i	$-0.328369\pi$
$739$	−13.2235	−	22.9037i	−0.486433	−	0.842527i	−0.999878	+	0.0155954i	$0.995036\pi$
$740$	−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	$0.650843\pi$
$744$	0.250237	+	9.00623i	0.00917415	+	0.330185i
$745$	8.34064	−	4.81547i	0.305577	−	0.176425i
$746$	−11.5499	+	6.66836i	−0.422873	+	0.244146i
$747$	10.7494	+	16.4374i	0.393301	+	0.601415i
$748$		−	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	−0.686462	−	0.727165i	$-0.740837\pi$
$751$	7.85169	−	13.5995i	0.286512	−	0.496254i	0.972975	+	0.230911i	$0.0741707\pi$
$752$	−6.23353	−	10.7968i	−0.227314	−	0.393719i
$753$	−1.61253	−	0.872202i	−0.0587640	−	0.0317848i
$754$	−19.5099	−	11.2641i	−0.710510	−	0.410213i
$755$	−23.5368			−0.856592
$756$	13.7141	−	0.960862i	0.498777	−	0.0349462i
$757$	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
$759$	−32.5065	−	17.5824i	−1.17991	−	0.638201i
$760$	2.75721	+	4.77563i	0.100015	+	0.173230i
$761$	−6.87928	+	11.9153i	−0.249374	+	0.431928i	−0.963352	−	0.268240i	$-0.913558\pi$
$761$	−6.87928	+	11.9153i	−0.249374	+	0.431928i	0.713978	+	0.700168i	$0.246891\pi$
$762$	−12.8282	−	20.8588i	−0.464715	−	0.755634i
$763$	0.269169	−	20.1103i	0.00974457	−	0.728042i
$764$		−	5.13035i		−	0.185609i
$765$	3.94721	+	6.03586i	0.142712	+	0.218227i
$766$	8.04088	−	4.64240i	0.290529	−	0.167737i
$767$	−18.7129	+	10.8039i	−0.675683	+	0.390106i
$768$	0.0481063	+	1.73138i	0.00173589	+	0.0624759i
$769$		−	11.0157i		−	0.397238i	−0.980077	−	0.198619i	$-0.936354\pi$
$769$		−	11.0157i		−	0.397238i	0.980077	−	0.198619i	$-0.0636455\pi$
$770$	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	−0.987138	−	0.159872i	$-0.948892\pi$
$773$	−17.5720	−	30.4356i	−0.632022	−	1.09469i	0.355116	−	0.934822i	$-0.384441\pi$
$774$	0.248090	+	4.46103i	0.00891742	+	0.160348i
$775$	−4.50485	−	2.60088i	−0.161819	−	0.0934263i
$776$	7.90564			0.283796
$777$	−8.61574	+	0.124023i	−0.309088	+	0.00444930i
$778$	19.4580			0.697602
$779$	0.492629	+	0.284420i	0.0176503	+	0.0101904i
$780$	4.87306	−	9.00936i	0.174484	−	0.322587i
$781$	−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
$786$	−8.69423	+	0.241569i	−0.310113	+	0.00861647i
$787$	−6.04499	+	3.49008i	−0.215481	+	0.124408i	−0.603856	−	0.797093i	$-0.706370\pi$
$787$	−6.04499	+	3.49008i	−0.215481	+	0.124408i	0.388375	+	0.921501i	$0.373036\pi$
$788$	−13.9165	+	8.03468i	−0.495754	+	0.286224i
$789$	−53.1506	+	1.47679i	−1.89221	+	0.0525749i
$790$			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
$795$	2.00885	−	3.71399i	0.0712467	−	0.131722i
$796$	−5.74190	−	3.31509i	−0.203516	−	0.117500i
$797$	0.975566			0.0345563			0.0172782	−	0.999851i	$-0.494500\pi$
$797$	0.975566			0.0345563			0.0172782	+	0.999851i	$0.494500\pi$
$798$	−12.3188	+	22.0643i	−0.436081	+	0.781067i
$799$	29.9706			1.06028
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	33.6703	−	1.87250i	1.18968	−	0.0661616i
$802$	−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
$807$	−0.805925	−	29.0059i	−0.0283699	−	1.02105i
$808$	−4.25403	+	2.45606i	−0.149656	+	0.0864040i
$809$	25.3918	−	14.6599i	0.892727	−	0.515416i	0.0178934	−	0.999840i	$-0.494304\pi$
$809$	25.3918	−	14.6599i	0.892727	−	0.515416i	0.874833	+	0.484424i	$0.160971\pi$
$810$	0.997943	+	8.94450i	0.0350642	+	0.314278i
$811$			1.54090i			0.0541084i	0.999634	+	0.0270542i	$0.00861267\pi$
$811$			1.54090i			0.0541084i	−0.999634	+	0.0270542i	$0.991387\pi$
$812$	−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
$816$	−3.66240	−	1.98095i	−0.128210	−	0.0693472i
$817$	−7.11238	−	4.10633i	−0.248831	−	0.143662i
$818$	−19.2437			−0.672841
$819$	46.8968	−	1.97889i	1.63871	−	0.0691480i
$820$	−0.103155			−0.00360232
$821$	−27.2749	−	15.7472i	−0.951899	−	0.549579i	−0.0582289	−	0.998303i	$-0.518545\pi$
$821$	−27.2749	−	15.7472i	−0.951899	−	0.549579i	−0.893670	+	0.448724i	$0.851879\pi$
$822$	−4.46332	−	2.41416i	−0.155676	−	0.0842034i
$823$	23.4689	+	40.6493i	0.818074	+	1.41695i	0.907099	+	0.420916i	$0.138291\pi$
$823$	23.4689	+	40.6493i	0.818074	+	1.41695i	−0.0890256	+	0.996029i	$0.528375\pi$
$824$	−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	$0.956507\pi$
$828$	−16.3138	+	10.6686i	−0.566942	+	0.370758i
$829$	10.4939	−	6.05866i	0.364468	−	0.210426i	−0.306571	−	0.951848i	$-0.599182\pi$
$829$	10.4939	−	6.05866i	0.364468	−	0.210426i	0.671039	+	0.741422i	$0.265848\pi$
$830$	5.66966	−	3.27338i	0.196797	−	0.113621i
$831$	−0.168960	−	6.08099i	−0.00586115	−	0.210947i
$832$			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
$837$	−15.4161	−	22.2018i	−0.532857	−	0.767405i
$838$	−1.16843	−	0.674593i	−0.0403627	−	0.0233034i
$839$	12.4633			0.430279			0.215140	−	0.976583i	$-0.430979\pi$
$839$	12.4633			0.430279			0.215140	+	0.976583i	$0.430979\pi$
$840$	−0.0659590	−	4.58210i	−0.00227580	−	0.158098i
$841$	14.4878			0.499580
$842$	20.2462	+	11.6892i	0.697732	+	0.402835i
$843$	−3.42665	+	6.33522i	−0.118020	+	0.218196i
$844$	−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
$849$	−0.298856	+	0.00830368i	−0.0102567	+	0.000284981i
$850$	2.08191	−	1.20199i	0.0714089	−	0.0412279i
$851$	10.5805	−	6.10863i	0.362693	−	0.209401i
$852$	−24.0862	+	0.669234i	−0.825181	+	0.0229276i
$853$			21.5297i			0.737162i	0.929596	+	0.368581i	$0.120156\pi$
$853$			21.5297i			0.737162i	−0.929596	+	0.368581i	$0.879844\pi$
$854$	−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	−0.871861	−	0.489753i	$-0.837087\pi$
$857$	−25.1782	−	43.6098i	−0.860069	−	1.48968i	0.0117917	−	0.999930i	$-0.496246\pi$
$858$	16.0026	−	29.5858i	0.546321	−	1.01004i
$859$	10.3726	+	5.98863i	0.353909	+	0.204329i	0.666405	−	0.745590i	$-0.267832\pi$
$859$	10.3726	+	5.98863i	0.353909	+	0.204329i	−0.312497	+	0.949919i	$0.601165\pi$
$860$	1.48931			0.0507850
$861$	−0.242225	−	0.405939i	−0.00825502	−	0.0138344i
$862$	7.75984			0.264301
$863$	44.9466	+	25.9499i	1.53000	+	0.883346i	0.999361	+	0.0357482i	$0.0113814\pi$
$863$	44.9466	+	25.9499i	1.53000	+	0.883346i	0.530639	+	0.847598i	$0.321952\pi$
$864$	−2.96363	−	4.26813i	−0.100825	−	0.145205i
$865$	−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
$870$	−0.183260	−	6.59568i	−0.00621311	−	0.223614i
$871$	17.1809	−	9.91938i	0.582152	−	0.336106i
$872$	−6.58323	+	3.80083i	−0.222936	+	0.128712i
$873$	−19.8493	+	12.9807i	−0.671797	+	0.439329i
$874$		−	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	−0.784040	−	0.620710i	$-0.786844\pi$
$877$	4.30976	−	7.46473i	0.145530	−	0.252066i	0.929571	+	0.368644i	$0.120178\pi$
$878$	−5.97965	−	10.3571i	−0.201804	−	0.349534i
$879$	−6.67315	−	3.60943i	−0.225080	−	0.121743i
$880$	−2.84394	−	1.64195i	−0.0958692	−	0.0553501i
$881$	21.7764			0.733667			0.366833	−	0.930287i	$-0.380442\pi$
$881$	21.7764			0.733667			0.366833	+	0.930287i	$0.380442\pi$
$882$	17.8768	−	11.0191i	0.601942	−	0.371033i
$883$	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
$885$	−5.56655	−	3.01089i	−0.187118	−	0.101210i
$886$	−1.80307	−	3.12301i	−0.0605753	−	0.104919i
$887$	9.87147	−	17.0979i	0.331452	−	0.574091i	−0.651345	−	0.758782i	$-0.725795\pi$
$887$	9.87147	−	17.0979i	0.331452	−	0.574091i	0.982797	+	0.184691i	$0.0591283\pi$
$888$	1.70610	+	2.77414i	0.0572529	+	0.0930941i
$889$	−32.1411	−	19.1347i	−1.07798	−	0.641758i
$890$		−	11.2408i		−	0.376792i
$891$	3.27714	+	29.3728i	0.109788	+	0.984027i
$892$	−19.0899	+	11.0216i	−0.639177	+	0.369029i
$893$	−59.5381	+	34.3743i	−1.99237	+	1.15029i
$894$	−0.463309	−	16.6748i	−0.0154954	−	0.557690i
$895$			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
$900$	2.99537	−	0.166581i	0.0998457	−	0.00555270i
$901$	−5.07536	−	2.93026i	−0.169085	−	0.0976212i
$902$	−0.338750			−0.0112791
$903$	3.49715	+	5.86078i	0.116378	+	0.195034i
$904$	3.88234			0.129125
$905$	−7.29628	−	4.21251i	−0.242537	−	0.140029i
$906$	−19.3950	+	35.8577i	−0.644357	+	1.19129i
$907$	10.5712	+	18.3098i	0.351010	+	0.607967i	0.986427	−	0.164203i	$-0.0525051\pi$
$907$	10.5712	+	18.3098i	0.351010	+	0.607967i	−0.635417	+	0.772169i	$0.719172\pi$
$908$	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	$-0.300861\pi$
$912$	9.54757	−	0.265278i	0.316152	−	0.00878425i
$913$	18.6186	−	10.7494i	0.616185	−	0.355755i
$914$	32.8141	−	18.9452i	1.08539	−	0.626652i
$915$	−24.6419	+	0.684674i	−0.814637	+	0.0226346i
$916$		−	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	−0.619462	−	0.785027i	$-0.712649\pi$
$919$	11.2203	−	19.4341i	0.370123	−	0.641071i	0.989584	+	0.143956i	$0.0459824\pi$
$920$	3.24875	+	5.62699i	0.107108	+	0.185516i
$921$	3.92781	−	7.26176i	0.129426	−	0.239283i
$922$	28.2419	+	16.3055i	0.930098	+	0.536993i
$923$	−82.2688			−2.70791
$924$	−0.216603	−	15.0472i	−0.00712571	−	0.495015i
$925$	−1.88030			−0.0618240
$926$	−5.02545	−	2.90144i	−0.165146	−	0.0953473i
$927$	−0.762344	−	13.7081i	−0.0250387	−	0.450232i
$928$	1.90474	+	3.29911i	0.0625262	+	0.108299i
$929$	8.52306	−	14.7624i	0.279632	−	0.484338i	−0.691661	−	0.722222i	$-0.743121\pi$
$929$	8.52306	−	14.7624i	0.279632	−	0.484338i	0.971293	+	0.237885i	$0.0764541\pi$
$930$	−7.67451	+	4.71983i	−0.251657	+	0.154769i
$931$	−1.03313	+	38.5871i	−0.0338596	+	1.26464i
$932$		−	16.1655i		−	0.529517i
$933$	−0.287205	−	10.3367i	−0.00940267	−	0.338409i
$934$	19.3060	−	11.1463i	0.631711	−	0.364719i
$935$	6.83677	−	3.94721i	0.223586	−	0.129088i
$936$	−9.70999	−	14.8480i	−0.317381	−	0.485321i
$937$		−	38.9259i		−	1.27165i	−0.771832	−	0.635827i	$-0.780659\pi$
$937$		−	38.9259i		−	1.27165i	0.771832	−	0.635827i	$-0.219341\pi$
$938$	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	−0.994365	−	0.106012i	$-0.966192\pi$
$941$	−18.0677	−	31.2943i	−0.588992	−	1.02016i	0.405373	−	0.914151i	$-0.367142\pi$
$942$	6.52582	+	3.52974i	0.212623	+	0.115005i
$943$	0.580452	+	0.335124i	0.0189021	+	0.0109131i
$944$	3.65385			0.118923
$945$	7.68918	+	11.3963i	0.250129	+	0.370723i
$946$	4.89073			0.159011
$947$	7.84276	+	4.52802i	0.254855	+	0.147141i	0.621986	−	0.783029i	$-0.286326\pi$
$947$	7.84276	+	4.52802i	0.254855	+	0.147141i	−0.367130	+	0.930170i	$0.619660\pi$
$948$	13.9418	+	7.54098i	0.452810	+	0.244920i
$949$	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	$-0.266739\pi$
$954$	−4.00281	−	6.12088i	−0.129596	−	0.198171i
$955$	4.44301	−	2.56517i	0.143772	−	0.0830071i
$956$	4.64490	−	2.68173i	0.150227	−	0.0867334i
$957$	−0.601808	−	21.6595i	−0.0194537	−	0.700153i
$958$		−	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
$963$	0.821624	+	14.7740i	0.0264765	+	0.476086i
$964$	13.9360	+	8.04597i	0.448849	+	0.259143i
$965$	15.2791			0.491852
$966$	−14.5149	+	25.9977i	−0.467010	+	0.836463i
$967$	−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
$969$	−10.9238	+	20.1960i	−0.350923	+	0.648790i
$970$	3.95282	+	6.84648i	0.126917	+	0.219827i
$971$	−17.2371	+	29.8556i	−0.553166	+	0.958112i	0.444877	+	0.895591i	$0.353247\pi$
$971$	−17.2371	+	29.8556i	−0.553166	+	0.958112i	−0.998044	+	0.0625206i	$0.980086\pi$
$972$	14.4491	+	5.85020i	0.463454	+	0.187645i
$973$	4.55504	−	7.65122i	0.146028	−	0.245287i
$974$			17.5505i			0.562354i
$975$	10.2389	−	0.284486i	0.327906	−	0.00911085i
$976$	12.3257	−	7.11625i	0.394536	−	0.227786i
$977$	−6.10133	+	3.52260i	−0.195199	+	0.112698i	−0.594414	−	0.804159i	$-0.702616\pi$
$977$	−6.10133	+	3.52260i	−0.195199	+	0.112698i	0.399215	+	0.916857i	$0.369283\pi$
$978$	38.2450	−	1.06263i	1.22294	−	0.0339793i
$979$		−	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	0.885894	+	0.463887i	$0.153546\pi$
$983$	26.4833	+	45.8704i	0.844685	+	1.46304i	−0.0412090	+	0.999151i	$0.513121\pi$
$984$	−0.0850027	+	0.157154i	−0.00270979	+	0.00500988i
$985$	−13.9165	−	8.03468i	−0.443416	−	0.256006i
$986$	−9.15793			−0.291648
$987$	57.1254	−	0.822316i	1.81832	−	0.0261746i
$988$	32.6106			1.03748
$989$	−8.38032	−	4.83838i	−0.266479	−	0.153852i
$990$	9.83650	−	0.547035i	0.312624	−	0.0173859i
$991$	15.4388	+	26.7408i	0.490429	+	0.849449i	0.999939	−	0.0110161i	$-0.00350662\pi$
$991$	15.4388	+	26.7408i	0.490429	+	0.849449i	−0.509510	+	0.860465i	$0.670173\pi$
$992$	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
$996$	−0.314940	−	11.3349i	−0.00997927	−	0.359161i
$997$	21.5634	−	12.4497i	0.682921	−	0.394285i	−0.118034	−	0.993010i	$-0.537659\pi$
$997$	21.5634	−	12.4497i	0.682921	−	0.394285i	0.800955	+	0.598725i	$0.204326\pi$
$998$	−4.64557	+	2.68212i	−0.147053	+	0.0849010i
$999$	−8.83863	−	4.16392i	−0.279642	−	0.131741i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.5	✓	12	7.3	odd	6
210.2.r.a.131.5	yes	12	3.2	odd	2
210.2.r.b.101.1	yes	12	21.17	even	6	inner
210.2.r.b.131.1	yes	12	1.1	even	1	trivial
1050.2.s.f.101.6		12	105.59	even	6
1050.2.s.f.551.6		12	5.4	even	2
1050.2.s.g.101.2		12	35.24	odd	6
1050.2.s.g.551.2		12	15.14	odd	2
1050.2.u.e.299.4		12	5.3	odd	4
1050.2.u.e.899.4		12	105.17	odd	12
1050.2.u.f.299.6		12	15.2	even	4
1050.2.u.f.899.6		12	35.3	even	12
1050.2.u.g.299.1		12	15.8	even	4
1050.2.u.g.899.1		12	35.17	even	12
1050.2.u.h.299.3		12	5.2	odd	4
1050.2.u.h.899.3		12	105.38	odd	12
1470.2.b.a.881.6		12	21.5	even	6
1470.2.b.a.881.12		12	7.2	even	3
1470.2.b.b.881.1		12	21.2	odd	6
1470.2.b.b.881.7		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.52347 - 0.824030i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.907353 + 1.47537i) q^{6} +(2.27338 + 1.35342i) q^{7} -1.00000i q^{8} +(1.64195 + 2.51078i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.52347 - 0.824030i) 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} +(1.64195 + 2.51078i) q^{9} +(0.866025 - 0.500000i) q^{10} +(2.84394 - 1.64195i) q^{11} +(-0.0481063 - 1.73138i) 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} +(-0.166581 - 2.99537i) q^{18} +(4.77563 + 2.75721i) q^{19} -1.00000 q^{20} +(-2.34817 - 3.93524i) q^{21} -3.28390 q^{22} +(5.62699 + 3.24875i) q^{23} +(-0.824030 + 1.52347i) 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} +(-1.73138 + 0.0481063i) q^{30} +(4.50485 - 2.60088i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.68568 + 0.157976i) 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} +(-4.87306 + 9.00936i) q^{39} +(0.866025 + 0.500000i) q^{40} +0.103155 q^{41} +(0.0659590 + 4.58210i) q^{42} -1.48931 q^{43} +(2.84394 + 1.64195i) q^{44} +(-2.99537 + 0.166581i) 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} +(0.115647 + 4.16221i) q^{51} +(5.12141 - 2.95685i) q^{52} +(2.11123 - 1.21892i) q^{53} +(-2.21449 + 4.70064i) 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} +(1.52347 + 0.824030i) q^{60} +(-12.3257 - 7.11625i) q^{61} -5.20176 q^{62} +(0.334628 + 7.93020i) q^{63} -1.00000 q^{64} +(5.12141 + 2.95685i) q^{65} +(5.00294 + 2.70603i) 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} +(2.51078 - 1.64195i) q^{72} +(-7.02609 + 4.05651i) q^{73} +(-1.62839 + 0.940152i) q^{74} +(0.0481063 + 1.73138i) 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} +(-3.60801 + 8.24514i) q^{81} +(-0.0893347 - 0.0515774i) q^{82} +6.54676 q^{83} +(2.23393 - 4.00120i) q^{84} +2.40398 q^{85} +(1.28978 + 0.744654i) q^{86} +(3.13913 - 5.80365i) 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} +(-9.00623 + 0.250237i) q^{93} +(10.7968 - 6.23353i) q^{94} +(-4.77563 + 2.75721i) q^{95} +(-1.73138 + 0.0481063i) q^{96} +7.90564i q^{97} +(0.187351 - 6.99749i) q^{98} +(8.79217 + 4.44450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7}+O(q^{10}) \) 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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