LMFDB - Embedded newform 210.2.j.a.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(113,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("210.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.j (of order $4$, 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 $\Q(i)$
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} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.3
Root			$1.12212i$ of defining polynomial
Character	$\chi$	$=$	210.197
Dual form			210.2.j.a.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.46025 + 0.931481i) q^{3} -1.00000i q^{4} +(-2.16244 + 0.569088i) q^{5} +(-1.69121 + 0.373900i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.26469 + 2.72040i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.46025 + 0.931481i) q^{3} -1.00000i q^{4} +(-2.16244 + 0.569088i) q^{5} +(-1.69121 + 0.373900i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.26469 + 2.72040i) q^{9} +(1.12667 - 1.93148i) q^{10} +6.30293i q^{11} +(0.931481 - 1.46025i) q^{12} +(-0.977522 + 0.977522i) q^{13} -1.00000 q^{14} +(-3.68780 - 1.18326i) q^{15} -1.00000 q^{16} +(4.86992 - 4.86992i) q^{17} +(-2.81788 - 1.02934i) q^{18} +0.285884i q^{19} +(0.569088 + 2.16244i) q^{20} +(0.373900 + 1.69121i) q^{21} +(-4.45685 - 4.45685i) q^{22} +(-4.26030 - 4.26030i) q^{23} +(0.373900 + 1.69121i) q^{24} +(4.35228 - 2.46123i) q^{25} -1.38242i q^{26} +(-0.687232 + 5.15051i) q^{27} +(0.707107 - 0.707107i) q^{28} -3.84102 q^{29} +(3.44436 - 1.77098i) q^{30} +6.64835 q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.87106 + 9.20389i) q^{33} +6.88711i q^{34} +(-1.93148 - 1.12667i) q^{35} +(2.72040 - 1.26469i) q^{36} +(0.317848 + 0.317848i) q^{37} +(-0.202151 - 0.202151i) q^{38} +(-2.33797 + 0.516888i) q^{39} +(-1.93148 - 1.12667i) q^{40} -4.55435i q^{41} +(-1.46025 - 0.931481i) q^{42} +(2.07154 - 2.07154i) q^{43} +6.30293 q^{44} +(-4.28295 - 5.16297i) q^{45} +6.02497 q^{46} +(6.69331 - 6.69331i) q^{47} +(-1.46025 - 0.931481i) q^{48} +1.00000i q^{49} +(-1.33717 + 4.81788i) q^{50} +(11.6476 - 2.57509i) q^{51} +(0.977522 + 0.977522i) q^{52} +(-3.12501 - 3.12501i) q^{53} +(-3.15601 - 4.12790i) q^{54} +(-3.58692 - 13.6297i) q^{55} +1.00000i q^{56} +(-0.266296 + 0.417464i) q^{57} +(2.71601 - 2.71601i) q^{58} +13.0634 q^{59} +(-1.18326 + 3.68780i) q^{60} +1.09215 q^{61} +(-4.70110 + 4.70110i) q^{62} +(-1.02934 + 2.81788i) q^{63} +1.00000i q^{64} +(1.55753 - 2.67013i) q^{65} +(-2.35667 - 10.6596i) q^{66} +(-5.63576 - 5.63576i) q^{67} +(-4.86992 - 4.86992i) q^{68} +(-2.25274 - 10.1895i) q^{69} +(2.16244 - 0.569088i) q^{70} +5.42814i q^{71} +(-1.02934 + 2.81788i) q^{72} +(-3.69101 + 3.69101i) q^{73} -0.449505 q^{74} +(8.64803 + 0.460033i) q^{75} +0.285884 q^{76} +(-4.45685 + 4.45685i) q^{77} +(1.28770 - 2.01869i) q^{78} +4.38280i q^{79} +(2.16244 - 0.569088i) q^{80} +(-5.80113 + 6.88091i) q^{81} +(3.22041 + 3.22041i) q^{82} +(1.52991 + 1.52991i) q^{83} +(1.69121 - 0.373900i) q^{84} +(-7.75949 + 13.3023i) q^{85} +2.92960i q^{86} +(-5.60887 - 3.57783i) q^{87} +(-4.45685 + 4.45685i) q^{88} -8.96370 q^{89} +(6.67928 + 0.622268i) q^{90} -1.38242 q^{91} +(-4.26030 + 4.26030i) q^{92} +(9.70829 + 6.19281i) q^{93} +9.46577i q^{94} +(-0.162693 - 0.618207i) q^{95} +(1.69121 - 0.373900i) q^{96} +(1.50962 + 1.50962i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-17.1465 + 7.97124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^3 - 4 * q^5	$ 12 q + 4 q^{3} - 4 q^{5} - 4 q^{12} - 12 q^{14} + 20 q^{15} - 12 q^{16} + 28 q^{17} - 4 q^{21} + 4 q^{22} - 24 q^{23} - 4 q^{24} + 20 q^{25} - 20 q^{27} + 8 q^{29} + 16 q^{30} - 8 q^{31} + 4 q^{33} - 8 q^{35} + 4 q^{36} - 20 q^{37} - 4 q^{38} - 40 q^{39} - 8 q^{40} - 4 q^{42} + 8 q^{43} + 8 q^{44} + 8 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 16 q^{50} + 8 q^{51} - 24 q^{53} - 4 q^{54} - 16 q^{55} - 12 q^{57} - 8 q^{58} + 32 q^{59} - 4 q^{60} + 28 q^{62} + 8 q^{63} - 8 q^{66} - 28 q^{68} - 32 q^{69} + 4 q^{70} + 8 q^{72} - 24 q^{73} + 8 q^{74} + 36 q^{75} + 4 q^{77} + 4 q^{80} - 36 q^{81} + 32 q^{82} - 24 q^{83} - 36 q^{85} - 64 q^{87} + 4 q^{88} + 48 q^{89} + 48 q^{90} + 24 q^{91} - 24 q^{92} + 76 q^{93} + 8 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 4 * q^5 - 4 * q^12 - 12 * q^14 + 20 * q^15 - 12 * q^16 + 28 * q^17 - 4 * q^21 + 4 * q^22 - 24 * q^23 - 4 * q^24 + 20 * q^25 - 20 * q^27 + 8 * q^29 + 16 * q^30 - 8 * q^31 + 4 * q^33 - 8 * q^35 + 4 * q^36 - 20 * q^37 - 4 * q^38 - 40 * q^39 - 8 * q^40 - 4 * q^42 + 8 * q^43 + 8 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 - 4 * q^48 - 16 * q^50 + 8 * q^51 - 24 * q^53 - 4 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^58 + 32 * q^59 - 4 * q^60 + 28 * q^62 + 8 * q^63 - 8 * q^66 - 28 * q^68 - 32 * q^69 + 4 * q^70 + 8 * q^72 - 24 * q^73 + 8 * q^74 + 36 * q^75 + 4 * q^77 + 4 * q^80 - 36 * q^81 + 32 * q^82 - 24 * q^83 - 36 * q^85 - 64 * q^87 + 4 * q^88 + 48 * q^89 + 48 * q^90 + 24 * q^91 - 24 * q^92 + 76 * q^93 + 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.46025	+	0.931481i	0.843078	+	0.537791i
$3$	1.46025	+	0.931481i	0.843078	+	0.537791i
$4$		−	1.00000i		−	0.500000i
$5$	−2.16244	+	0.569088i	−0.967072	+	0.254504i
$5$	−2.16244	+	0.569088i	−0.967072	+	0.254504i
$6$	−1.69121	+	0.373900i	−0.690435	+	0.152644i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.26469	+	2.72040i	0.421563	+	0.906799i
$10$	1.12667	−	1.93148i	0.356284	−	0.610788i
$11$			6.30293i			1.90041i	0.311631	+	0.950203i	$0.399125\pi$
$11$			6.30293i			1.90041i	−0.311631	+	0.950203i	$0.600875\pi$
$12$	0.931481	−	1.46025i	0.268895	−	0.421539i
$13$	−0.977522	+	0.977522i	−0.271116	+	0.271116i	−0.829549	−	0.558434i	$-0.811403\pi$
$13$	−0.977522	+	0.977522i	−0.271116	+	0.271116i	0.558434	+	0.829549i	$0.311403\pi$
$14$	−1.00000			−0.267261
$15$	−3.68780	−	1.18326i	−0.952187	−	0.305515i
$16$	−1.00000			−0.250000
$17$	4.86992	−	4.86992i	1.18113	−	1.18113i	0.201678	−	0.979452i	$-0.435360\pi$
$17$	4.86992	−	4.86992i	1.18113	−	1.18113i	0.979452	−	0.201678i	$-0.0646395\pi$
$18$	−2.81788	−	1.02934i	−0.664181	−	0.242618i
$19$			0.285884i			0.0655864i	0.999462	+	0.0327932i	$0.0104403\pi$
$19$			0.285884i			0.0655864i	−0.999462	+	0.0327932i	$0.989560\pi$
$20$	0.569088	+	2.16244i	0.127252	+	0.483536i
$21$	0.373900	+	1.69121i	0.0815916	+	0.369053i
$22$	−4.45685	−	4.45685i	−0.950203	−	0.950203i
$23$	−4.26030	−	4.26030i	−0.888334	−	0.888334i	0.106029	−	0.994363i	$-0.466186\pi$
$23$	−4.26030	−	4.26030i	−0.888334	−	0.888334i	−0.994363	+	0.106029i	$0.966186\pi$
$24$	0.373900	+	1.69121i	0.0763220	+	0.345217i
$25$	4.35228	−	2.46123i	0.870456	−	0.492247i
$26$		−	1.38242i		−	0.271116i
$27$	−0.687232	+	5.15051i	−0.132258	+	0.991215i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	−3.84102			−0.713259			−0.356630	−	0.934246i	$-0.616074\pi$
$29$	−3.84102			−0.713259			−0.356630	+	0.934246i	$0.616074\pi$
$30$	3.44436	−	1.77098i	0.628851	−	0.323336i
$31$	6.64835			1.19408			0.597040	−	0.802212i	$-0.296343\pi$
$31$	6.64835			1.19408			0.597040	+	0.802212i	$0.296343\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−5.87106	+	9.20389i	−1.02202	+	1.60219i
$34$			6.88711i			1.18113i
$35$	−1.93148	−	1.12667i	−0.326480	−	0.190442i
$36$	2.72040	−	1.26469i	0.453400	−	0.210781i
$37$	0.317848	+	0.317848i	0.0522539	+	0.0522539i	0.732751	−	0.680497i	$-0.238236\pi$
$37$	0.317848	+	0.317848i	0.0522539	+	0.0522539i	−0.680497	+	0.732751i	$0.738236\pi$
$38$	−0.202151	−	0.202151i	−0.0327932	−	0.0327932i
$39$	−2.33797	+	0.516888i	−0.374375	+	0.0827684i
$40$	−1.93148	−	1.12667i	−0.305394	−	0.178142i
$41$		−	4.55435i		−	0.711270i	−0.934625	−	0.355635i	$-0.884265\pi$
$41$		−	4.55435i		−	0.711270i	0.934625	−	0.355635i	$-0.115735\pi$
$42$	−1.46025	−	0.931481i	−0.225322	−	0.143731i
$43$	2.07154	−	2.07154i	0.315907	−	0.315907i	−0.531286	−	0.847193i	$-0.678291\pi$
$43$	2.07154	−	2.07154i	0.315907	−	0.315907i	0.847193	+	0.531286i	$0.178291\pi$
$44$	6.30293			0.950203
$45$	−4.28295	−	5.16297i	−0.638465	−	0.769651i
$46$	6.02497			0.888334
$47$	6.69331	−	6.69331i	0.976320	−	0.976320i	−0.0234064	−	0.999726i	$-0.507451\pi$
$47$	6.69331	−	6.69331i	0.976320	−	0.976320i	0.999726	+	0.0234064i	$0.00745116\pi$
$48$	−1.46025	−	0.931481i	−0.210770	−	0.134448i
$49$			1.00000i			0.142857i
$50$	−1.33717	+	4.81788i	−0.189104	+	0.681351i
$51$	11.6476	−	2.57509i	1.63099	−	0.360585i
$52$	0.977522	+	0.977522i	0.135558	+	0.135558i
$53$	−3.12501	−	3.12501i	−0.429253	−	0.429253i	0.459121	−	0.888374i	$-0.348164\pi$
$53$	−3.12501	−	3.12501i	−0.429253	−	0.429253i	−0.888374	+	0.459121i	$0.848164\pi$
$54$	−3.15601	−	4.12790i	−0.429479	−	0.561737i
$55$	−3.58692	−	13.6297i	−0.483661	−	1.83783i
$56$			1.00000i			0.133631i
$57$	−0.266296	+	0.417464i	−0.0352717	+	0.0552945i
$58$	2.71601	−	2.71601i	0.356630	−	0.356630i
$59$	13.0634			1.70071			0.850354	−	0.526211i	$-0.176388\pi$
$59$	13.0634			1.70071			0.850354	+	0.526211i	$0.176388\pi$
$60$	−1.18326	+	3.68780i	−0.152758	+	0.476094i
$61$	1.09215			0.139835			0.0699176	−	0.997553i	$-0.477726\pi$
$61$	1.09215			0.139835			0.0699176	+	0.997553i	$0.477726\pi$
$62$	−4.70110	+	4.70110i	−0.597040	+	0.597040i
$63$	−1.02934	+	2.81788i	−0.129685	+	0.355020i
$64$			1.00000i			0.125000i
$65$	1.55753	−	2.67013i	0.193188	−	0.331188i
$66$	−2.35667	−	10.6596i	−0.290085	−	1.31211i
$67$	−5.63576	−	5.63576i	−0.688518	−	0.688518i	0.273386	−	0.961904i	$-0.411856\pi$
$67$	−5.63576	−	5.63576i	−0.688518	−	0.688518i	−0.961904	+	0.273386i	$0.911856\pi$
$68$	−4.86992	−	4.86992i	−0.590565	−	0.590565i
$69$	−2.25274	−	10.1895i	−0.271198	−	1.22667i
$70$	2.16244	−	0.569088i	0.258461	−	0.0680190i
$71$			5.42814i			0.644202i	0.946705	+	0.322101i	$0.104389\pi$
$71$			5.42814i			0.644202i	−0.946705	+	0.322101i	$0.895611\pi$
$72$	−1.02934	+	2.81788i	−0.121309	+	0.332090i
$73$	−3.69101	+	3.69101i	−0.432000	+	0.432000i	−0.889308	−	0.457308i	$-0.848814\pi$
$73$	−3.69101	+	3.69101i	−0.432000	+	0.432000i	0.457308	+	0.889308i	$0.348814\pi$
$74$	−0.449505			−0.0522539
$75$	8.64803	+	0.460033i	0.998588	+	0.0531200i
$76$	0.285884			0.0327932
$77$	−4.45685	+	4.45685i	−0.507905	+	0.507905i
$78$	1.28770	−	2.01869i	0.145804	−	0.228572i
$79$			4.38280i			0.493104i	0.969130	+	0.246552i	$0.0792976\pi$
$79$			4.38280i			0.493104i	−0.969130	+	0.246552i	$0.920702\pi$
$80$	2.16244	−	0.569088i	0.241768	−	0.0636260i
$81$	−5.80113	+	6.88091i	−0.644570	+	0.764545i
$82$	3.22041	+	3.22041i	0.355635	+	0.355635i
$83$	1.52991	+	1.52991i	0.167930	+	0.167930i	0.786069	−	0.618139i	$-0.212113\pi$
$83$	1.52991	+	1.52991i	0.167930	+	0.167930i	−0.618139	+	0.786069i	$0.712113\pi$
$84$	1.69121	−	0.373900i	0.184526	−	0.0407958i
$85$	−7.75949	+	13.3023i	−0.841635	+	1.44284i
$86$			2.92960i			0.315907i
$87$	−5.60887	−	3.57783i	−0.601334	−	0.383584i
$88$	−4.45685	+	4.45685i	−0.475102	+	0.475102i
$89$	−8.96370			−0.950150			−0.475075	−	0.879945i	$-0.657579\pi$
$89$	−8.96370			−0.950150			−0.475075	+	0.879945i	$0.657579\pi$
$90$	6.67928	+	0.622268i	0.704058	+	0.0655928i
$91$	−1.38242			−0.144917
$92$	−4.26030	+	4.26030i	−0.444167	+	0.444167i
$93$	9.70829	+	6.19281i	1.00670	+	0.642165i
$94$			9.46577i			0.976320i
$95$	−0.162693	−	0.618207i	−0.0166920	−	0.0634267i
$96$	1.69121	−	0.373900i	0.172609	−	0.0381610i
$97$	1.50962	+	1.50962i	0.153278	+	0.153278i	0.779580	−	0.626302i	$-0.215432\pi$
$97$	1.50962	+	1.50962i	0.153278	+	0.153278i	−0.626302	+	0.779580i	$0.715432\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−17.1465	+	7.97124i	−1.72329	+	0.801140i
$100$	−2.46123	−	4.35228i	−0.246123	−	0.435228i
$101$		−	1.57944i		−	0.157160i	−0.996908	−	0.0785802i	$-0.974961\pi$
$101$		−	1.57944i		−	0.157160i	0.996908	−	0.0785802i	$-0.0250387\pi$
$102$	−6.41521	+	10.0569i	−0.635201	+	0.995785i
$103$	4.29497	−	4.29497i	0.423196	−	0.423196i	−0.463106	−	0.886303i	$-0.653265\pi$
$103$	4.29497	−	4.29497i	0.423196	−	0.423196i	0.886303	+	0.463106i	$0.153265\pi$
$104$	−1.38242			−0.135558
$105$	−1.77098	−	3.44436i	−0.172830	−	0.336135i
$106$	4.41943			0.429253
$107$	7.11516	−	7.11516i	0.687849	−	0.687849i	−0.273907	−	0.961756i	$-0.588316\pi$
$107$	7.11516	−	7.11516i	0.687849	−	0.687849i	0.961756	+	0.273907i	$0.0883162\pi$
$108$	5.15051	+	0.687232i	0.495608	+	0.0661289i
$109$			4.12915i			0.395501i	0.980252	+	0.197751i	$0.0633636\pi$
$109$			4.12915i			0.395501i	−0.980252	+	0.197751i	$0.936636\pi$
$110$	12.1740	+	7.10132i	1.16074	+	0.677084i
$111$	0.168070	+	0.760209i	0.0159525	+	0.0721559i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	8.20404	+	8.20404i	0.771771	+	0.771771i	0.978416	−	0.206645i	$-0.0662545\pi$
$113$	8.20404	+	8.20404i	0.771771	+	0.771771i	−0.206645	+	0.978416i	$0.566255\pi$
$114$	−0.106892	−	0.483491i	−0.0100114	−	0.0452831i
$115$	11.6371	+	6.78815i	1.08517	+	0.632998i
$116$			3.84102i			0.356630i
$117$	−3.89551	−	1.42299i	−0.360140	−	0.131555i
$118$	−9.23721	+	9.23721i	−0.850354	+	0.850354i
$119$	6.88711			0.631341
$120$	−1.77098	−	3.44436i	−0.161668	−	0.314426i
$121$	−28.7270			−2.61154
$122$	−0.772265	+	0.772265i	−0.0699176	+	0.0699176i
$123$	4.24229	−	6.65051i	0.382514	−	0.599656i
$124$		−	6.64835i		−	0.597040i
$125$	−8.01087	+	7.79910i	−0.716514	+	0.697572i
$126$	−1.26469	−	2.72040i	−0.112667	−	0.242352i
$127$	−6.41439	−	6.41439i	−0.569185	−	0.569185i	0.362715	−	0.931900i	$-0.381850\pi$
$127$	−6.41439	−	6.41439i	−0.569185	−	0.569185i	−0.931900	+	0.362715i	$0.881850\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	4.95457	−	1.09538i	0.436226	−	0.0964425i
$130$	0.786721	+	2.98941i	0.0690000	+	0.262188i
$131$			2.00357i			0.175053i	0.996162	+	0.0875263i	$0.0278962\pi$
$131$			2.00357i			0.175053i	−0.996162	+	0.0875263i	$0.972104\pi$
$132$	9.20389	+	5.87106i	0.801096	+	0.511010i
$133$	−0.202151	+	0.202151i	−0.0175287	+	0.0175287i
$134$	7.97017			0.688518
$135$	−1.44499	−	11.5287i	−0.124365	−	0.992236i
$136$	6.88711			0.590565
$137$	−7.18005	+	7.18005i	−0.613433	+	0.613433i	−0.943839	−	0.330406i	$-0.892814\pi$
$137$	−7.18005	+	7.18005i	−0.613433	+	0.613433i	0.330406	+	0.943839i	$0.392814\pi$
$138$	8.79800	+	5.61215i	0.748935	+	0.477738i
$139$		−	7.92412i		−	0.672115i	−0.941842	−	0.336057i	$-0.890906\pi$
$139$		−	7.92412i		−	0.672115i	0.941842	−	0.336057i	$-0.109094\pi$
$140$	−1.12667	+	1.93148i	−0.0952209	+	0.163240i
$141$	16.0086	−	3.53925i	1.34817	−	0.298059i
$142$	−3.83827	−	3.83827i	−0.322101	−	0.322101i
$143$	−6.16126	−	6.16126i	−0.515230	−	0.515230i
$144$	−1.26469	−	2.72040i	−0.105391	−	0.226700i
$145$	8.30597	−	2.18588i	0.689773	−	0.181527i
$146$		−	5.21988i		−	0.432000i
$147$	−0.931481	+	1.46025i	−0.0768272	+	0.120440i
$148$	0.317848	−	0.317848i	0.0261270	−	0.0261270i
$149$	−4.88159			−0.399916			−0.199958	−	0.979805i	$-0.564081\pi$
$149$	−4.88159			−0.399916			−0.199958	+	0.979805i	$0.564081\pi$
$150$	−6.44037	+	5.78979i	−0.525854	+	0.472734i
$151$	−1.36645			−0.111200			−0.0555999	−	0.998453i	$-0.517707\pi$
$151$	−1.36645			−0.111200			−0.0555999	+	0.998453i	$0.517707\pi$
$152$	−0.202151	+	0.202151i	−0.0163966	+	0.0163966i
$153$	19.4071	+	7.08920i	1.56897	+	0.573128i
$154$		−	6.30293i		−	0.507905i
$155$	−14.3767	+	3.78350i	−1.15476	+	0.303898i
$156$	0.516888	+	2.33797i	0.0413842	+	0.187188i
$157$	−8.22730	−	8.22730i	−0.656610	−	0.656610i	0.297966	−	0.954576i	$-0.403692\pi$
$157$	−8.22730	−	8.22730i	−0.656610	−	0.656610i	−0.954576	+	0.297966i	$0.903692\pi$
$158$	−3.09911	−	3.09911i	−0.246552	−	0.246552i
$159$	−1.65242	−	7.47419i	−0.131046	−	0.592742i
$160$	−1.12667	+	1.93148i	−0.0890710	+	0.152697i
$161$		−	6.02497i		−	0.474834i
$162$	−0.763518	−	8.96755i	−0.0599876	−	0.704558i
$163$	−13.7521	+	13.7521i	−1.07714	+	1.07714i	−0.0803803	+	0.996764i	$0.525613\pi$
$163$	−13.7521	+	13.7521i	−1.07714	+	1.07714i	−0.996764	+	0.0803803i	$0.974387\pi$
$164$	−4.55435			−0.355635
$165$	7.45798	−	23.2440i	0.580603	−	1.80954i
$166$	−2.16362			−0.167930
$167$	10.5146	−	10.5146i	0.813647	−	0.813647i	−0.171532	−	0.985179i	$-0.554872\pi$
$167$	10.5146	−	10.5146i	0.813647	−	0.813647i	0.985179	+	0.171532i	$0.0548716\pi$
$168$	−0.931481	+	1.46025i	−0.0718653	+	0.112661i
$169$			11.0889i			0.852992i
$170$	−3.91937	−	14.8930i	−0.300602	−	1.14224i
$171$	−0.777719	+	0.361554i	−0.0594737	+	0.0276488i
$172$	−2.07154	−	2.07154i	−0.157953	−	0.157953i
$173$	−3.15253	−	3.15253i	−0.239682	−	0.239682i	0.577036	−	0.816719i	$-0.304209\pi$
$173$	−3.15253	−	3.15253i	−0.239682	−	0.239682i	−0.816719	+	0.577036i	$0.804209\pi$
$174$	6.49598	−	1.43616i	0.492459	−	0.108875i
$175$	4.81788	+	1.33717i	0.364198	+	0.101081i
$176$		−	6.30293i		−	0.475102i
$177$	19.0759	+	12.1683i	1.43383	+	0.914625i
$178$	6.33829	−	6.33829i	0.475075	−	0.475075i
$179$	−0.251416			−0.0187917			−0.00939584	−	0.999956i	$-0.502991\pi$
$179$	−0.251416			−0.0187917			−0.00939584	+	0.999956i	$0.502991\pi$
$180$	−5.16297	+	4.28295i	−0.384825	+	0.319233i
$181$	−12.8653			−0.956270			−0.478135	−	0.878286i	$-0.658687\pi$
$181$	−12.8653			−0.956270			−0.478135	+	0.878286i	$0.658687\pi$
$182$	0.977522	−	0.977522i	0.0724587	−	0.0724587i
$183$	1.59481	+	1.01731i	0.117892	+	0.0752020i
$184$		−	6.02497i		−	0.444167i
$185$	−0.868211	−	0.506444i	−0.0638321	−	0.0372345i
$186$	−11.2438	+	2.48582i	−0.824434	+	0.182269i
$187$	30.6948	+	30.6948i	2.24463	+	2.24463i
$188$	−6.69331	−	6.69331i	−0.488160	−	0.488160i
$189$	−4.12790	+	3.15601i	−0.300261	+	0.229566i
$190$	0.552180	+	0.322097i	0.0400594	+	0.0233674i
$191$			16.4695i			1.19169i	0.803100	+	0.595845i	$0.203183\pi$
$191$			16.4695i			1.19169i	−0.803100	+	0.595845i	$0.796817\pi$
$192$	−0.931481	+	1.46025i	−0.0672238	+	0.105385i
$193$	13.9786	−	13.9786i	1.00620	−	1.00620i	0.00621990	−	0.999981i	$-0.498020\pi$
$193$	13.9786	−	13.9786i	1.00620	−	1.00620i	0.999981	−	0.00621990i	$-0.00197987\pi$
$194$	−2.13492			−0.153278
$195$	4.76157	−	2.44825i	0.340983	−	0.175323i
$196$	1.00000			0.0714286
$197$	11.7072	−	11.7072i	0.834104	−	0.834104i	−0.153971	−	0.988075i	$-0.549206\pi$
$197$	11.7072	−	11.7072i	0.834104	−	0.834104i	0.988075	+	0.153971i	$0.0492063\pi$
$198$	6.48788	−	17.7609i	0.461073	−	1.26221i
$199$		−	11.1512i		−	0.790487i	−0.918576	−	0.395243i	$-0.870660\pi$
$199$		−	11.1512i		−	0.790487i	0.918576	−	0.395243i	$-0.129340\pi$
$200$	4.81788	+	1.33717i	0.340676	+	0.0945522i
$201$	−2.98004	−	13.4793i	−0.210196	−	0.950753i
$202$	1.11683	+	1.11683i	0.0785802	+	0.0785802i
$203$	−2.71601	−	2.71601i	−0.190627	−	0.190627i
$204$	−2.57509	−	11.6476i	−0.180292	−	0.815493i
$205$	2.59183	+	9.84850i	0.181021	+	0.687849i
$206$			6.07401i			0.423196i
$207$	6.20176	−	16.9777i	0.431052	−	1.18003i
$208$	0.977522	−	0.977522i	0.0677789	−	0.0677789i
$209$	−1.80191			−0.124641
$210$	3.68780	+	1.18326i	0.254483	+	0.0816524i
$211$	0.766419			0.0527625			0.0263812	−	0.999652i	$-0.491602\pi$
$211$	0.766419			0.0527625			0.0263812	+	0.999652i	$0.491602\pi$
$212$	−3.12501	+	3.12501i	−0.214626	+	0.214626i
$213$	−5.05621	+	7.92647i	−0.346446	+	0.543112i
$214$			10.0624i			0.687849i
$215$	−3.30069	+	5.65846i	−0.225105	+	0.385904i
$216$	−4.12790	+	3.15601i	−0.280868	+	0.214739i
$217$	4.70110	+	4.70110i	0.319131	+	0.319131i
$218$	−2.91975	−	2.91975i	−0.197751	−	0.197751i
$219$	−8.82792	+	1.95171i	−0.596535	+	0.131884i
$220$	−13.6297	+	3.58692i	−0.918915	+	0.241830i
$221$			9.52091i			0.640446i
$222$	−0.656392	−	0.418706i	−0.0440542	−	0.0281017i
$223$	−1.66559	+	1.66559i	−0.111536	+	0.111536i	−0.760672	−	0.649136i	$-0.775131\pi$
$223$	−1.66559	+	1.66559i	−0.111536	+	0.111536i	0.649136	+	0.760672i	$0.275131\pi$
$224$	1.00000			0.0668153
$225$	12.1998	+	8.72723i	0.813321	+	0.581816i
$226$	−11.6023			−0.771771
$227$	−5.55282	+	5.55282i	−0.368554	+	0.368554i	−0.866950	−	0.498396i	$-0.833923\pi$
$227$	−5.55282	+	5.55282i	−0.368554	+	0.368554i	0.498396	+	0.866950i	$0.333923\pi$
$228$	0.417464	+	0.266296i	0.0276472	+	0.0176359i
$229$		−	7.79020i		−	0.514791i	−0.966306	−	0.257396i	$-0.917136\pi$
$229$		−	7.79020i		−	0.514791i	0.966306	−	0.257396i	$-0.0828643\pi$
$230$	−13.0286	+	3.42874i	−0.859083	+	0.226084i
$231$	−10.6596	+	2.35667i	−0.701350	+	0.155057i
$232$	−2.71601	−	2.71601i	−0.178315	−	0.178315i
$233$	−5.53555	−	5.53555i	−0.362646	−	0.362646i	0.502140	−	0.864786i	$-0.332546\pi$
$233$	−5.53555	−	5.53555i	−0.362646	−	0.362646i	−0.864786	+	0.502140i	$0.832546\pi$
$234$	3.76074	−	1.74834i	0.245848	−	0.114292i
$235$	−10.6648	+	18.2830i	−0.695694	+	1.19265i
$236$		−	13.0634i		−	0.850354i
$237$	−4.08250	+	6.40001i	−0.265187	+	0.415725i
$238$	−4.86992	+	4.86992i	−0.315670	+	0.315670i
$239$	25.9459			1.67830			0.839149	−	0.543901i	$-0.183053\pi$
$239$	25.9459			1.67830			0.839149	+	0.543901i	$0.183053\pi$
$240$	3.68780	+	1.18326i	0.238047	+	0.0763788i
$241$	3.35854			0.216342			0.108171	−	0.994132i	$-0.465501\pi$
$241$	3.35854			0.216342			0.108171	+	0.994132i	$0.465501\pi$
$242$	20.3130	−	20.3130i	1.30577	−	1.30577i
$243$	−14.8806	+	4.64424i	−0.954588	+	0.297928i
$244$		−	1.09215i		−	0.0699176i
$245$	−0.569088	−	2.16244i	−0.0363577	−	0.138153i
$246$	1.70287	+	7.70237i	0.108571	+	0.491085i
$247$	−0.279458	−	0.279458i	−0.0177815	−	0.0177815i
$248$	4.70110	+	4.70110i	0.298520	+	0.298520i
$249$	0.808977	+	3.65914i	0.0512669	+	0.231889i
$250$	0.149748	−	11.1793i	0.00947091	−	0.707043i
$251$		−	18.4740i		−	1.16607i	−0.812447	−	0.583035i	$-0.801865\pi$
$251$		−	18.4740i		−	1.16607i	0.812447	−	0.583035i	$-0.198135\pi$
$252$	2.81788	+	1.02934i	0.177510	+	0.0648425i
$253$	26.8524	−	26.8524i	1.68820	−	1.68820i
$254$	9.07132			0.569185
$255$	−23.7217	+	12.1970i	−1.48551	+	0.763803i
$256$	1.00000			0.0625000
$257$	−8.49575	+	8.49575i	−0.529950	+	0.529950i	−0.920557	−	0.390607i	$-0.872265\pi$
$257$	−8.49575	+	8.49575i	−0.529950	+	0.529950i	0.390607	+	0.920557i	$0.372265\pi$
$258$	−2.72886	+	4.27796i	−0.169892	+	0.266334i
$259$			0.449505i			0.0279309i
$260$	−2.67013	−	1.55753i	−0.165594	−	0.0965942i
$261$	−4.85769	−	10.4491i	−0.300683	−	0.646783i
$262$	−1.41674	−	1.41674i	−0.0875263	−	0.0875263i
$263$	−3.09922	−	3.09922i	−0.191106	−	0.191106i	0.605068	−	0.796174i	$-0.293146\pi$
$263$	−3.09922	−	3.09922i	−0.191106	−	0.191106i	−0.796174	+	0.605068i	$0.793146\pi$
$264$	−10.6596	+	2.35667i	−0.656053	+	0.145043i
$265$	8.53604	+	4.97923i	0.524365	+	0.305872i
$266$		−	0.285884i		−	0.0175287i
$267$	−13.0893	−	8.34951i	−0.801051	−	0.510982i
$268$	−5.63576	+	5.63576i	−0.344259	+	0.344259i
$269$	−9.23352			−0.562978			−0.281489	−	0.959564i	$-0.590828\pi$
$269$	−9.23352			−0.562978			−0.281489	+	0.959564i	$0.590828\pi$
$270$	9.17382	+	7.13029i	0.558301	+	0.433936i
$271$	−23.2360			−1.41149			−0.705745	−	0.708466i	$-0.749387\pi$
$271$	−23.2360			−1.41149			−0.705745	+	0.708466i	$0.749387\pi$
$272$	−4.86992	+	4.86992i	−0.295283	+	0.295283i
$273$	−2.01869	−	1.28770i	−0.122177	−	0.0779353i
$274$		−	10.1541i		−	0.613433i
$275$	15.5130	+	27.4321i	0.935469	+	1.65422i
$276$	−10.1895	+	2.25274i	−0.613336	+	0.135599i
$277$	12.1601	+	12.1601i	0.730628	+	0.730628i	0.970744	−	0.240116i	$-0.0771856\pi$
$277$	12.1601	+	12.1601i	0.730628	+	0.730628i	−0.240116	+	0.970744i	$0.577186\pi$
$278$	5.60320	+	5.60320i	0.336057	+	0.336057i
$279$	8.40809	+	18.0862i	0.503379	+	1.08279i
$280$	−0.569088	−	2.16244i	−0.0340095	−	0.129230i
$281$		−	16.0124i		−	0.955220i	−0.878572	−	0.477610i	$-0.841503\pi$
$281$		−	16.0124i		−	0.955220i	0.878572	−	0.477610i	$-0.158497\pi$
$282$	−8.81718	+	13.8224i	−0.525056	+	0.823114i
$283$	19.8944	−	19.8944i	1.18260	−	1.18260i	0.203527	−	0.979069i	$-0.434759\pi$
$283$	19.8944	−	19.8944i	1.18260	−	1.18260i	0.979069	−	0.203527i	$-0.0652406\pi$
$284$	5.42814			0.322101
$285$	0.338274	−	1.05429i	0.0200376	−	0.0624505i
$286$	8.71333			0.515230
$287$	3.22041	−	3.22041i	0.190095	−	0.190095i
$288$	2.81788	+	1.02934i	0.166045	+	0.0606546i
$289$		−	30.4323i		−	1.79014i
$290$	−4.32756	+	7.41885i	−0.254123	+	0.435650i
$291$	0.798246	+	3.61060i	0.0467940	+	0.211657i
$292$	3.69101	+	3.69101i	0.216000	+	0.216000i
$293$	6.63925	+	6.63925i	0.387869	+	0.387869i	0.873927	−	0.486058i	$-0.161566\pi$
$293$	6.63925	+	6.63925i	0.387869	+	0.387869i	−0.486058	+	0.873927i	$0.661566\pi$
$294$	−0.373900	−	1.69121i	−0.0218063	−	0.0986335i
$295$	−28.2488	+	7.43422i	−1.64471	+	0.432837i
$296$			0.449505i			0.0261270i
$297$	−32.4633	−	4.33158i	−1.88371	−	0.251344i
$298$	3.45181	−	3.45181i	0.199958	−	0.199958i
$299$	8.32907			0.481683
$300$	0.460033	−	8.64803i	0.0265600	−	0.499294i
$301$	2.92960			0.168859
$302$	0.966224	−	0.966224i	0.0555999	−	0.0555999i
$303$	1.47122	−	2.30639i	0.0845194	−	0.132499i
$304$		−	0.285884i		−	0.0163966i
$305$	−2.36170	+	0.621528i	−0.135231	+	0.0355886i
$306$	−18.7357	+	8.71005i	−1.07105	+	0.497920i
$307$	3.85359	+	3.85359i	0.219936	+	0.219936i	0.808471	−	0.588536i	$-0.200295\pi$
$307$	3.85359	+	3.85359i	0.219936	+	0.219936i	−0.588536	+	0.808471i	$0.700295\pi$
$308$	4.45685	+	4.45685i	0.253952	+	0.253952i
$309$	10.2724	−	2.27107i	0.584379	−	0.129197i
$310$	7.49049	−	12.8412i	0.425431	−	0.729329i
$311$			28.2254i			1.60052i	0.599655	+	0.800259i	$0.295304\pi$
$311$			28.2254i			1.60052i	−0.599655	+	0.800259i	$0.704696\pi$
$312$	−2.01869	−	1.28770i	−0.114286	−	0.0729018i
$313$	−5.27143	+	5.27143i	−0.297959	+	0.297959i	−0.840214	−	0.542255i	$-0.817571\pi$
$313$	−5.27143	+	5.27143i	−0.297959	+	0.297959i	0.542255	+	0.840214i	$0.317571\pi$
$314$	11.6352			0.656610
$315$	0.622268	−	6.67928i	0.0350608	−	0.376335i
$316$	4.38280			0.246552
$317$	−22.4384	+	22.4384i	−1.26027	+	1.26027i	−0.309306	+	0.950963i	$0.600097\pi$
$317$	−22.4384	+	22.4384i	−1.26027	+	1.26027i	−0.950963	+	0.309306i	$0.899903\pi$
$318$	6.45349	+	4.11661i	0.361894	+	0.230848i
$319$		−	24.2097i		−	1.35548i
$320$	−0.569088	−	2.16244i	−0.0318130	−	0.120884i
$321$	17.0176	−	3.76231i	0.949829	−	0.209992i
$322$	4.26030	+	4.26030i	0.237417	+	0.237417i
$323$	1.39224	+	1.39224i	0.0774660	+	0.0774660i
$324$	6.88091	+	5.80113i	0.382273	+	0.322285i
$325$	−1.84854	+	6.66036i	−0.102538	+	0.369450i
$326$		−	19.4484i		−	1.07714i
$327$	−3.84623	+	6.02961i	−0.212697	+	0.333438i
$328$	3.22041	−	3.22041i	0.177817	−	0.177817i
$329$	9.46577			0.521865
$330$	11.1624	+	21.7096i	0.614469	+	1.19507i
$331$	23.8482			1.31082			0.655409	−	0.755274i	$-0.272496\pi$
$331$	23.8482			1.31082			0.655409	+	0.755274i	$0.272496\pi$
$332$	1.52991	−	1.52991i	0.0839648	−	0.0839648i
$333$	−0.462695	+	1.26665i	−0.0253555	+	0.0694122i
$334$			14.8699i			0.813647i
$335$	15.3942	+	8.97974i	0.841077	+	0.490616i
$336$	−0.373900	−	1.69121i	−0.0203979	−	0.0922632i
$337$	−9.69647	−	9.69647i	−0.528200	−	0.528200i	0.391835	−	0.920035i	$-0.371840\pi$
$337$	−9.69647	−	9.69647i	−0.528200	−	0.528200i	−0.920035	+	0.391835i	$0.871840\pi$
$338$	−7.84104	−	7.84104i	−0.426496	−	0.426496i
$339$	4.33808	+	19.6219i	0.235612	+	1.06571i
$340$	13.3023	+	7.75949i	0.721420	+	0.420818i
$341$			41.9041i			2.26924i
$342$	0.294273	−	0.805588i	0.0159125	−	0.0435612i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	2.92960			0.157953
$345$	10.6701	+	20.7522i	0.574461	+	1.11726i
$346$	4.45835			0.239682
$347$	−2.11053	+	2.11053i	−0.113299	+	0.113299i	−0.761484	−	0.648184i	$-0.775529\pi$
$347$	−2.11053	+	2.11053i	−0.113299	+	0.113299i	0.648184	+	0.761484i	$0.275529\pi$
$348$	−3.57783	+	5.60887i	−0.191792	+	0.300667i
$349$		−	15.3537i		−	0.821863i	−0.911666	−	0.410931i	$-0.865204\pi$
$349$		−	15.3537i		−	0.821863i	0.911666	−	0.410931i	$-0.134796\pi$
$350$	−4.35228	+	2.46123i	−0.232639	+	0.131559i
$351$	−4.36295	−	5.70652i	−0.232877	−	0.304591i
$352$	4.45685	+	4.45685i	0.237551	+	0.237551i
$353$	−3.24802	−	3.24802i	−0.172875	−	0.172875i	0.615366	−	0.788241i	$-0.289008\pi$
$353$	−3.24802	−	3.24802i	−0.172875	−	0.172875i	−0.788241	+	0.615366i	$0.789008\pi$
$354$	−22.0930	+	4.88440i	−1.17423	+	0.259603i
$355$	−3.08909	−	11.7380i	−0.163952	−	0.622989i
$356$			8.96370i			0.475075i
$357$	10.0569	+	6.41521i	0.532270	+	0.339529i
$358$	0.177778	−	0.177778i	0.00939584	−	0.00939584i
$359$	−10.4735			−0.552768			−0.276384	−	0.961047i	$-0.589136\pi$
$359$	−10.4735			−0.552768			−0.276384	+	0.961047i	$0.589136\pi$
$360$	0.622268	−	6.67928i	0.0327964	−	0.352029i
$361$	18.9183			0.995698
$362$	9.09714	−	9.09714i	0.478135	−	0.478135i
$363$	−41.9487	−	26.7586i	−2.20174	−	1.40446i
$364$			1.38242i			0.0724587i
$365$	5.88107	−	10.0821i	0.307829	−	0.527721i
$366$	−1.84705	+	0.408354i	−0.0965470	+	0.0213450i
$367$	1.44611	+	1.44611i	0.0754862	+	0.0754862i	0.743842	−	0.668356i	$-0.233002\pi$
$367$	1.44611	+	1.44611i	0.0754862	+	0.0754862i	−0.668356	+	0.743842i	$0.733002\pi$
$368$	4.26030	+	4.26030i	0.222083	+	0.222083i
$369$	12.3896	−	5.75983i	0.644979	−	0.299845i
$370$	0.972028	−	0.255808i	0.0505333	−	0.0132988i
$371$		−	4.41943i		−	0.229445i
$372$	6.19281	−	9.70829i	0.321082	−	0.503351i
$373$	−16.7299	+	16.7299i	−0.866242	+	0.866242i	−0.992054	−	0.125812i	$-0.959846\pi$
$373$	−16.7299	+	16.7299i	−0.866242	+	0.866242i	0.125812	+	0.992054i	$0.459846\pi$
$374$	−43.4090			−2.24463
$375$	−18.9626	+	3.92670i	−0.979226	+	0.202774i
$376$	9.46577			0.488160
$377$	3.75468	−	3.75468i	0.193376	−	0.193376i
$378$	0.687232	−	5.15051i	0.0353474	−	0.264913i
$379$			28.9831i			1.48876i	0.667756	+	0.744380i	$0.267255\pi$
$379$			28.9831i			1.48876i	−0.667756	+	0.744380i	$0.732745\pi$
$380$	−0.618207	+	0.162693i	−0.0317134	+	0.00834599i
$381$	−3.39176	−	15.3415i	−0.173765	−	0.785970i
$382$	−11.6457	−	11.6457i	−0.595845	−	0.595845i
$383$	−17.6093	−	17.6093i	−0.899792	−	0.899792i	0.0956253	−	0.995417i	$-0.469515\pi$
$383$	−17.6093	−	17.6093i	−0.899792	−	0.899792i	−0.995417	+	0.0956253i	$0.969515\pi$
$384$	−0.373900	−	1.69121i	−0.0190805	−	0.0863043i
$385$	7.10132	−	12.1740i	0.361917	−	0.620444i
$386$			19.7687i			1.00620i
$387$	8.25526	+	3.01556i	0.419638	+	0.153290i
$388$	1.50962	−	1.50962i	0.0766392	−	0.0766392i
$389$	5.90624			0.299458			0.149729	−	0.988727i	$-0.452160\pi$
$389$	5.90624			0.299458			0.149729	+	0.988727i	$0.452160\pi$
$390$	−1.63576	+	5.09811i	−0.0828300	+	0.258153i
$391$	−41.4947			−2.09848
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	−1.86629	+	2.92572i	−0.0941416	+	0.147583i
$394$			16.5565i			0.834104i
$395$	−2.49420	−	9.47754i	−0.125497	−	0.476867i
$396$	7.97124	+	17.1465i	0.400570	+	0.861643i
$397$	−17.8605	−	17.8605i	−0.896395	−	0.896395i	0.0987205	−	0.995115i	$-0.468525\pi$
$397$	−17.8605	−	17.8605i	−0.896395	−	0.896395i	−0.995115	+	0.0987205i	$0.968525\pi$
$398$	7.88508	+	7.88508i	0.395243	+	0.395243i
$399$	−0.483491	+	0.106892i	−0.0242048	+	0.00535130i
$400$	−4.35228	+	2.46123i	−0.217614	+	0.123062i
$401$		−	27.6315i		−	1.37985i	−0.723880	−	0.689926i	$-0.757643\pi$
$401$		−	27.6315i		−	1.37985i	0.723880	−	0.689926i	$-0.242357\pi$
$402$	11.6385	+	7.42406i	0.580475	+	0.370278i
$403$	−6.49891	+	6.49891i	−0.323734	+	0.323734i
$404$	−1.57944			−0.0785802
$405$	8.62874	−	18.1809i	0.428766	−	0.903416i
$406$	3.84102			0.190627
$407$	−2.00338	+	2.00338i	−0.0993037	+	0.0993037i
$408$	10.0569	+	6.41521i	0.497893	+	0.317600i
$409$			9.35480i			0.462565i	0.972887	+	0.231282i	$0.0742921\pi$
$409$			9.35480i			0.462565i	−0.972887	+	0.231282i	$0.925708\pi$
$410$	−8.79664	−	5.13124i	−0.434435	−	0.253414i
$411$	−17.1728	+	3.79663i	−0.847071	+	0.187274i
$412$	−4.29497	−	4.29497i	−0.211598	−	0.211598i
$413$	9.23721	+	9.23721i	0.454533	+	0.454533i
$414$	7.61971	+	16.3903i	0.374488	+	0.805541i
$415$	−4.17899	−	2.43768i	−0.205139	−	0.119661i
$416$			1.38242i			0.0677789i
$417$	7.38116	−	11.5712i	0.361457	−	0.566646i
$418$	1.27414	−	1.27414i	0.0623204	−	0.0623204i
$419$	8.34692			0.407774			0.203887	−	0.978994i	$-0.434643\pi$
$419$	8.34692			0.407774			0.203887	+	0.978994i	$0.434643\pi$
$420$	−3.44436	+	1.77098i	−0.168068	+	0.0864151i
$421$	27.0969			1.32062			0.660312	−	0.750991i	$-0.270424\pi$
$421$	27.0969			1.32062			0.660312	+	0.750991i	$0.270424\pi$
$422$	−0.541940	+	0.541940i	−0.0263812	+	0.0263812i
$423$	26.6734	+	9.74352i	1.29691	+	0.473746i
$424$		−	4.41943i		−	0.214626i
$425$	9.20924	−	33.1813i	0.446714	−	1.60953i
$426$	−2.02958	−	9.18013i	−0.0983335	−	0.444779i
$427$	0.772265	+	0.772265i	0.0373725	+	0.0373725i
$428$	−7.11516	−	7.11516i	−0.343924	−	0.343924i
$429$	−3.25791	−	14.7361i	−0.157293	−	0.711465i
$430$	−1.66720	−	6.33508i	−0.0803995	−	0.305504i
$431$		−	22.0104i		−	1.06020i	−0.847935	−	0.530101i	$-0.822154\pi$
$431$		−	22.0104i		−	1.06020i	0.847935	−	0.530101i	$-0.177846\pi$
$432$	0.687232	−	5.15051i	0.0330645	−	0.247804i
$433$	3.04246	−	3.04246i	0.146211	−	0.146211i	−0.630212	−	0.776423i	$-0.717032\pi$
$433$	3.04246	−	3.04246i	0.146211	−	0.146211i	0.776423	+	0.630212i	$0.217032\pi$
$434$	−6.64835			−0.319131
$435$	14.1649	+	4.54491i	0.679156	+	0.217912i
$436$	4.12915			0.197751
$437$	1.21795	−	1.21795i	0.0582626	−	0.0582626i
$438$	4.86221	−	7.62235i	0.232326	−	0.364210i
$439$		−	3.84848i		−	0.183678i	−0.995774	−	0.0918390i	$-0.970725\pi$
$439$		−	3.84848i		−	0.183678i	0.995774	−	0.0918390i	$-0.0292745\pi$
$440$	7.10132	−	12.1740i	0.338542	−	0.580372i
$441$	−2.72040	+	1.26469i	−0.129543	+	0.0602232i
$442$	−6.73230	−	6.73230i	−0.320223	−	0.320223i
$443$	1.25470	+	1.25470i	0.0596125	+	0.0596125i	0.736285	−	0.676672i	$-0.236579\pi$
$443$	1.25470	+	1.25470i	0.0596125	+	0.0596125i	−0.676672	+	0.736285i	$0.736579\pi$
$444$	0.760209	−	0.168070i	0.0360779	−	0.00797625i
$445$	19.3834	−	5.10113i	0.918863	−	0.241817i
$446$		−	2.35550i		−	0.111536i
$447$	−7.12837	−	4.54711i	−0.337160	−	0.215071i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−36.8518			−1.73914			−0.869571	−	0.493808i	$-0.835605\pi$
$449$	−36.8518			−1.73914			−0.869571	+	0.493808i	$0.835605\pi$
$450$	−14.7977	+	2.45548i	−0.697568	+	0.115753i
$451$	28.7058			1.35170
$452$	8.20404	−	8.20404i	0.385885	−	0.385885i
$453$	−1.99536	−	1.27282i	−0.0937502	−	0.0598022i
$454$		−	7.85287i		−	0.368554i
$455$	2.98941	−	0.786721i	0.140146	−	0.0368821i
$456$	−0.483491	+	0.106892i	−0.0226415	+	0.00500568i
$457$	−17.4336	−	17.4336i	−0.815509	−	0.815509i	0.169945	−	0.985454i	$-0.445641\pi$
$457$	−17.4336	−	17.4336i	−0.815509	−	0.815509i	−0.985454	+	0.169945i	$0.945641\pi$
$458$	5.50851	+	5.50851i	0.257396	+	0.257396i
$459$	21.7358	+	28.4293i	1.01454	+	1.32697i
$460$	6.78815	−	11.6371i	0.316499	−	0.542584i
$461$		−	22.2553i		−	1.03653i	−0.855219	−	0.518267i	$-0.826578\pi$
$461$		−	22.2553i		−	1.03653i	0.855219	−	0.518267i	$-0.173422\pi$
$462$	5.87106	−	9.20389i	0.273146	−	0.428204i
$463$	−11.8397	+	11.8397i	−0.550236	+	0.550236i	−0.926509	−	0.376273i	$-0.877205\pi$
$463$	−11.8397	+	11.8397i	−0.550236	+	0.550236i	0.376273	+	0.926509i	$0.377205\pi$
$464$	3.84102			0.178315
$465$	−24.5178	−	7.86670i	−1.13699	−	0.364810i
$466$	7.82845			0.362646
$467$	−19.7958	+	19.7958i	−0.916038	+	0.916038i	−0.996738	−	0.0807000i	$-0.974284\pi$
$467$	−19.7958	+	19.7958i	−0.916038	+	0.916038i	0.0807000	+	0.996738i	$0.474284\pi$
$468$	−1.42299	+	3.89551i	−0.0657777	+	0.180070i
$469$		−	7.97017i		−	0.368028i
$470$	−5.38686	−	20.4691i	−0.248477	−	0.944171i
$471$	−4.35038	−	19.6775i	−0.200455	−	0.906692i
$472$	9.23721	+	9.23721i	0.425177	+	0.425177i
$473$	13.0568	+	13.0568i	0.600351	+	0.600351i
$474$	−1.63873	−	7.41225i	−0.0752693	−	0.340456i
$475$	0.703629	+	1.24425i	0.0322847	+	0.0570900i
$476$		−	6.88711i		−	0.315670i
$477$	4.54911	−	12.4534i	0.208289	−	0.570203i
$478$	−18.3465	+	18.3465i	−0.839149	+	0.839149i
$479$	−7.58779			−0.346695			−0.173347	−	0.984861i	$-0.555458\pi$
$479$	−7.58779			−0.346695			−0.173347	+	0.984861i	$0.555458\pi$
$480$	−3.44436	+	1.77098i	−0.157213	+	0.0808340i
$481$	−0.621407			−0.0283337
$482$	−2.37484	+	2.37484i	−0.108171	+	0.108171i
$483$	5.61215	−	8.79800i	0.255362	−	0.400323i
$484$			28.7270i			1.30577i
$485$	−4.12356	−	2.40535i	−0.187241	−	0.109221i
$486$	7.23817	−	13.8061i	0.328330	−	0.626258i
$487$	2.74204	+	2.74204i	0.124254	+	0.124254i	0.766499	−	0.642245i	$-0.221997\pi$
$487$	2.74204	+	2.74204i	0.124254	+	0.124254i	−0.642245	+	0.766499i	$0.721997\pi$
$488$	0.772265	+	0.772265i	0.0349588	+	0.0349588i
$489$	−32.8913	+	7.27173i	−1.48740	+	0.328839i
$490$	1.93148	+	1.12667i	0.0872554	+	0.0508977i
$491$		−	41.2178i		−	1.86013i	−0.367390	−	0.930067i	$-0.619749\pi$
$491$		−	41.2178i		−	1.86013i	0.367390	−	0.930067i	$-0.380251\pi$
$492$	−6.65051	−	4.24229i	−0.299828	−	0.191257i
$493$	−18.7055	+	18.7055i	−0.842452	+	0.842452i
$494$	0.395214			0.0177815
$495$	32.5419	−	26.9952i	1.46265	−	1.21334i
$496$	−6.64835			−0.298520
$497$	−3.83827	+	3.83827i	−0.172170	+	0.172170i
$498$	−3.15944	−	2.01537i	−0.141578	−	0.0903109i
$499$		−	16.1619i		−	0.723505i	−0.932274	−	0.361753i	$-0.882179\pi$
$499$		−	16.1619i		−	0.723505i	0.932274	−	0.361753i	$-0.117821\pi$
$500$	7.79910	+	8.01087i	0.348786	+	0.358257i
$501$	25.1482	−	5.55987i	1.12354	−	0.248397i
$502$	13.0631	+	13.0631i	0.583035	+	0.583035i
$503$	21.1438	+	21.1438i	0.942754	+	0.942754i	0.998448	−	0.0556938i	$-0.0177371\pi$
$503$	21.1438	+	21.1438i	0.942754	+	0.942754i	−0.0556938	+	0.998448i	$0.517737\pi$
$504$	−2.72040	+	1.26469i	−0.121176	+	0.0563337i
$505$	0.898842	+	3.41545i	0.0399979	+	0.151985i
$506$			37.9750i			1.68820i
$507$	−10.3291	+	16.1926i	−0.458731	+	0.719140i
$508$	−6.41439	+	6.41439i	−0.284592	+	0.284592i
$509$	31.1749			1.38180			0.690901	−	0.722949i	$-0.257214\pi$
$509$	31.1749			1.38180			0.690901	+	0.722949i	$0.257214\pi$
$510$	8.14922	−	25.3983i	0.360853	−	1.12466i
$511$	−5.21988			−0.230914
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.47245	−	0.196469i	−0.0650102	−	0.00867431i
$514$		−	12.0148i		−	0.529950i
$515$	−6.84340	+	11.7318i	−0.301556	+	0.516966i
$516$	−1.09538	−	4.95457i	−0.0482212	−	0.218113i
$517$	42.1875	+	42.1875i	1.85540	+	1.85540i
$518$	−0.317848	−	0.317848i	−0.0139655	−	0.0139655i
$519$	−1.66697	−	7.54001i	−0.0731721	−	0.330970i
$520$	2.98941	−	0.786721i	0.131094	−	0.0345000i
$521$			25.1391i			1.10136i	0.834715	+	0.550682i	$0.185632\pi$
$521$			25.1391i			1.10136i	−0.834715	+	0.550682i	$0.814368\pi$
$522$	10.8235	+	3.95372i	0.473733	+	0.173050i
$523$	8.35714	−	8.35714i	0.365432	−	0.365432i	−0.500376	−	0.865808i	$-0.666805\pi$
$523$	8.35714	−	8.35714i	0.365432	−	0.365432i	0.865808	+	0.500376i	$0.166805\pi$
$524$	2.00357			0.0875263
$525$	5.78979	+	6.44037i	0.252687	+	0.281081i
$526$	4.38296			0.191106
$527$	32.3770	−	32.3770i	1.41036	−	1.41036i
$528$	5.87106	−	9.20389i	0.255505	−	0.400548i
$529$			13.3003i			0.578275i
$530$	−9.55674	+	2.51504i	−0.415118	+	0.109247i
$531$	16.5211	+	35.5376i	0.716955	+	1.54220i
$532$	0.202151	+	0.202151i	0.00876435	+	0.00876435i
$533$	4.45198	+	4.45198i	0.192836	+	0.192836i
$534$	15.1595	−	3.35152i	0.656016	−	0.145035i
$535$	−11.3369	+	19.4353i	−0.490139	+	0.840259i
$536$		−	7.97017i		−	0.344259i
$537$	−0.367131	−	0.234189i	−0.0158429	−	0.0101060i
$538$	6.52909	−	6.52909i	0.281489	−	0.281489i
$539$	−6.30293			−0.271487
$540$	−11.5287	+	1.44499i	−0.496118	+	0.0621827i
$541$	15.9353			0.685111			0.342555	−	0.939498i	$-0.388708\pi$
$541$	15.9353			0.685111			0.342555	+	0.939498i	$0.388708\pi$
$542$	16.4304	−	16.4304i	0.705745	−	0.705745i
$543$	−18.7866	−	11.9838i	−0.806211	−	0.514273i
$544$		−	6.88711i		−	0.295283i
$545$	−2.34985	−	8.92904i	−0.100657	−	0.382478i
$546$	2.33797	−	0.516888i	0.100056	−	0.0221208i
$547$	−23.5457	−	23.5457i	−1.00674	−	1.00674i	−0.999977	−	0.00676436i	$-0.997847\pi$
$547$	−23.5457	−	23.5457i	−1.00674	−	1.00674i	−0.00676436	−	0.999977i	$-0.502153\pi$
$548$	7.18005	+	7.18005i	0.306717	+	0.306717i
$549$	1.38123	+	2.97108i	0.0589493	+	0.126802i
$550$	−30.3668	−	8.42809i	−1.29484	−	0.359375i
$551$		−	1.09809i		−	0.0467801i
$552$	5.61215	−	8.79800i	0.238869	−	0.374468i
$553$	−3.09911	+	3.09911i	−0.131788	+	0.131788i
$554$	−17.1969			−0.730628
$555$	−0.796067	−	1.54826i	−0.0337912	−	0.0657199i
$556$	−7.92412			−0.336057
$557$	−19.6460	+	19.6460i	−0.832429	+	0.832429i	−0.987849	−	0.155419i	$-0.950327\pi$
$557$	−19.6460	+	19.6460i	−0.832429	+	0.832429i	0.155419	+	0.987849i	$0.450327\pi$
$558$	−18.7343	−	6.84343i	−0.793085	−	0.289706i
$559$			4.04995i			0.171295i
$560$	1.93148	+	1.12667i	0.0816200	+	0.0476104i
$561$	16.2306	+	73.4139i	0.685257	+	3.09954i
$562$	11.3225	+	11.3225i	0.477610	+	0.477610i
$563$	−25.9632	−	25.9632i	−1.09422	−	1.09422i	−0.995073	−	0.0991442i	$-0.968389\pi$
$563$	−25.9632	−	25.9632i	−1.09422	−	1.09422i	−0.0991442	−	0.995073i	$-0.531611\pi$
$564$	−3.53925	−	16.0086i	−0.149029	−	0.674085i
$565$	−22.4095	−	13.0719i	−0.942776	−	0.549939i
$566$			28.1349i			1.18260i
$567$	−8.96755	+	0.763518i	−0.376602	+	0.0320647i
$568$	−3.83827	+	3.83827i	−0.161050	+	0.161050i
$569$	−45.5655			−1.91020			−0.955102	−	0.296277i	$-0.904255\pi$
$569$	−45.5655			−1.91020			−0.955102	+	0.296277i	$0.904255\pi$
$570$	0.506296	+	0.984689i	0.0212064	+	0.0412441i
$571$	−17.3897			−0.727734			−0.363867	−	0.931451i	$-0.618544\pi$
$571$	−17.3897			−0.727734			−0.363867	+	0.931451i	$0.618544\pi$
$572$	−6.16126	+	6.16126i	−0.257615	+	0.257615i
$573$	−15.3410	+	24.0496i	−0.640879	+	1.00469i
$574$			4.55435i			0.190095i
$575$	−29.0276	−	8.05641i	−1.21054	−	0.335976i
$576$	−2.72040	+	1.26469i	−0.113350	+	0.0526953i
$577$	−14.7414	−	14.7414i	−0.613693	−	0.613693i	0.330214	−	0.943906i	$-0.392879\pi$
$577$	−14.7414	−	14.7414i	−0.613693	−	0.613693i	−0.943906	+	0.330214i	$0.892879\pi$
$578$	21.5189	+	21.5189i	0.895068	+	0.895068i
$579$	33.4331	−	7.39151i	1.38943	−	0.307181i
$580$	−2.18588	−	8.30597i	−0.0907636	−	0.344886i
$581$			2.16362i			0.0897621i
$582$	−3.11753	−	1.98864i	−0.129226	−	0.0824317i
$583$	19.6967	−	19.6967i	0.815755	−	0.815755i
$584$	−5.21988			−0.216000
$585$	9.23360	+	0.860238i	0.381762	+	0.0355665i
$586$	−9.38931			−0.387869
$587$	−15.1380	+	15.1380i	−0.624811	+	0.624811i	−0.946758	−	0.321947i	$-0.895663\pi$
$587$	−15.1380	+	15.1380i	−0.624811	+	0.624811i	0.321947	+	0.946758i	$0.395663\pi$
$588$	1.46025	+	0.931481i	0.0602199	+	0.0384136i
$589$			1.90066i			0.0783153i
$590$	14.7181	−	25.2317i	0.605935	−	1.03877i
$591$	28.0005	−	6.19047i	1.15179	−	0.254642i
$592$	−0.317848	−	0.317848i	−0.0130635	−	0.0130635i
$593$	16.1719	+	16.1719i	0.664098	+	0.664098i	0.956343	−	0.292245i	$-0.0944023\pi$
$593$	16.1719	+	16.1719i	0.664098	+	0.664098i	−0.292245	+	0.956343i	$0.594402\pi$
$594$	26.0179	−	19.8921i	1.06753	−	0.816184i
$595$	−14.8930	+	3.91937i	−0.610552	+	0.160679i
$596$			4.88159i			0.199958i
$597$	10.3871	−	16.2836i	0.425116	−	0.666442i
$598$	−5.88954	+	5.88954i	−0.240841	+	0.240841i
$599$	−28.5725			−1.16744			−0.583720	−	0.811955i	$-0.698404\pi$
$599$	−28.5725			−1.16744			−0.583720	+	0.811955i	$0.698404\pi$
$600$	5.78979	+	6.44037i	0.236367	+	0.262927i
$601$	6.29448			0.256757			0.128378	−	0.991725i	$-0.459023\pi$
$601$	6.29448			0.256757			0.128378	+	0.991725i	$0.459023\pi$
$602$	−2.07154	+	2.07154i	−0.0844296	+	0.0844296i
$603$	8.20404	−	22.4590i	0.334094	−	0.914601i
$604$			1.36645i			0.0555999i
$605$	62.1203	−	16.3482i	2.52555	−	0.664648i
$606$	0.590553	+	2.67117i	0.0239896	+	0.108509i
$607$	−0.368490	−	0.368490i	−0.0149566	−	0.0149566i	0.699589	−	0.714546i	$-0.253366\pi$
$607$	−0.368490	−	0.368490i	−0.0149566	−	0.0149566i	−0.714546	+	0.699589i	$0.753366\pi$
$608$	0.202151	+	0.202151i	0.00819830	+	0.00819830i
$609$	−1.43616	−	6.49598i	−0.0581960	−	0.263230i
$610$	1.23049	−	2.10946i	0.0498210	−	0.0854096i
$611$			13.0857i			0.529391i
$612$	7.08920	−	19.4071i	0.286564	−	0.784484i
$613$	−27.1118	+	27.1118i	−1.09504	+	1.09504i	−0.100053	+	0.994982i	$0.531901\pi$
$613$	−27.1118	+	27.1118i	−1.09504	+	1.09504i	−0.994982	+	0.100053i	$0.968099\pi$
$614$	−5.44979			−0.219936
$615$	−5.38896	+	16.7956i	−0.217304	+	0.677262i
$616$	−6.30293			−0.253952
$617$	−18.2218	+	18.2218i	−0.733582	+	0.733582i	−0.971328	−	0.237745i	$-0.923592\pi$
$617$	−18.2218	+	18.2218i	−0.733582	+	0.733582i	0.237745	+	0.971328i	$0.423592\pi$
$618$	−5.65782	+	8.86960i	−0.227591	+	0.356788i
$619$			15.1105i			0.607341i	0.952777	+	0.303670i	$0.0982121\pi$
$619$			15.1105i			0.607341i	−0.952777	+	0.303670i	$0.901788\pi$
$620$	3.78350	+	14.3767i	0.151949	+	0.577380i
$621$	24.8705	−	19.0149i	0.998019	−	0.763041i
$622$	−19.9584	−	19.9584i	−0.800259	−	0.800259i
$623$	−6.33829	−	6.33829i	−0.253938	−	0.253938i
$624$	2.33797	−	0.516888i	0.0935938	−	0.0206921i
$625$	12.8846	−	21.4240i	0.515386	−	0.856958i
$626$		−	7.45493i		−	0.297959i
$627$	−2.63125	−	1.67844i	−0.105082	−	0.0670306i
$628$	−8.22730	+	8.22730i	−0.328305	+	0.328305i
$629$	3.09579			0.123437
$630$	4.28295	+	5.16297i	0.170637	+	0.205698i
$631$	18.7681			0.747148			0.373574	−	0.927600i	$-0.378132\pi$
$631$	18.7681			0.747148			0.373574	+	0.927600i	$0.378132\pi$
$632$	−3.09911	+	3.09911i	−0.123276	+	0.123276i
$633$	1.11917	+	0.713904i	0.0444829	+	0.0283751i
$634$		−	31.7327i		−	1.26027i
$635$	17.5211	+	10.2204i	0.695302	+	0.405583i
$636$	−7.47419	+	1.65242i	−0.296371	+	0.0655229i
$637$	−0.977522	−	0.977522i	−0.0387308	−	0.0387308i
$638$	17.1188	+	17.1188i	0.677741	+	0.677741i
$639$	−14.7667	+	6.86490i	−0.584162	+	0.271571i
$640$	1.93148	+	1.12667i	0.0763485	+	0.0445355i
$641$		−	21.9502i		−	0.866979i	−0.901159	−	0.433489i	$-0.857282\pi$
$641$		−	21.9502i		−	0.866979i	0.901159	−	0.433489i	$-0.142718\pi$
$642$	−9.37289	+	14.6936i	−0.369919	+	0.579910i
$643$	−29.9588	+	29.9588i	−1.18146	+	1.18146i	−0.202091	+	0.979367i	$0.564774\pi$
$643$	−29.9588	+	29.9588i	−1.18146	+	1.18146i	−0.979367	+	0.202091i	$0.935226\pi$
$644$	−6.02497			−0.237417
$645$	−10.0906	+	5.18827i	−0.397317	+	0.204288i
$646$	−1.96892			−0.0774660
$647$	20.4792	−	20.4792i	0.805120	−	0.805120i	−0.178771	−	0.983891i	$-0.557212\pi$
$647$	20.4792	−	20.4792i	0.805120	−	0.805120i	0.983891	+	0.178771i	$0.0572121\pi$
$648$	−8.96755	+	0.763518i	−0.352279	+	0.0299938i
$649$			82.3377i			3.23204i
$650$	−3.40247	−	6.01670i	−0.133456	−	0.235994i
$651$	2.48582	+	11.2438i	0.0974269	+	0.440678i
$652$	13.7521	+	13.7521i	0.538572	+	0.538572i
$653$	16.2736	+	16.2736i	0.636835	+	0.636835i	0.949773	−	0.312939i	$-0.101313\pi$
$653$	16.2736	+	16.2736i	0.636835	+	0.636835i	−0.312939	+	0.949773i	$0.601313\pi$
$654$	−1.54389	−	6.98327i	−0.0603708	−	0.273068i
$655$	−1.14021	−	4.33259i	−0.0445516	−	0.169288i
$656$			4.55435i			0.177817i
$657$	−14.7090	−	5.37304i	−0.573852	−	0.209622i
$658$	−6.69331	+	6.69331i	−0.260932	+	0.260932i
$659$	43.5045			1.69469			0.847347	−	0.531040i	$-0.178199\pi$
$659$	43.5045			1.69469			0.847347	+	0.531040i	$0.178199\pi$
$660$	−23.2440	−	7.45798i	−0.904771	−	0.290302i
$661$	−45.7539			−1.77962			−0.889811	−	0.456330i	$-0.849164\pi$
$661$	−45.7539			−1.77962			−0.889811	+	0.456330i	$0.849164\pi$
$662$	−16.8632	+	16.8632i	−0.655409	+	0.655409i
$663$	−8.86855	+	13.9030i	−0.344426	+	0.539946i
$664$			2.16362i			0.0839648i
$665$	0.322097	−	0.552180i	0.0124904	−	0.0214126i
$666$	−0.568484	−	1.22283i	−0.0220283	−	0.0473838i
$667$	16.3639	+	16.3639i	0.633612	+	0.633612i
$668$	−10.5146	−	10.5146i	−0.406823	−	0.406823i
$669$	−3.98365	+	0.880721i	−0.154017	+	0.0340507i
$670$	−17.2350	+	4.53573i	−0.665846	+	0.175230i
$671$			6.88374i			0.265744i
$672$	1.46025	+	0.931481i	0.0563305	+	0.0359326i
$673$	17.9013	−	17.9013i	0.690044	−	0.690044i	−0.272198	−	0.962241i	$-0.587750\pi$
$673$	17.9013	−	17.9013i	0.690044	−	0.690044i	0.962241	+	0.272198i	$0.0877504\pi$
$674$	13.7129			0.528200
$675$	9.68558	+	24.1079i	0.372798	+	0.927912i
$676$	11.0889			0.426496
$677$	−21.4226	+	21.4226i	−0.823337	+	0.823337i	−0.986585	−	0.163248i	$-0.947803\pi$
$677$	−21.4226	+	21.4226i	−0.823337	+	0.823337i	0.163248	+	0.986585i	$0.447803\pi$
$678$	−16.9423	−	10.8073i	−0.650663	−	0.415051i
$679$			2.13492i			0.0819307i
$680$	−14.8930	+	3.91937i	−0.571119	+	0.150301i
$681$	−13.2809	+	2.93619i	−0.508924	+	0.112515i
$682$	−29.6307	−	29.6307i	−1.13462	−	1.13462i
$683$	16.7015	+	16.7015i	0.639067	+	0.639067i	0.950325	−	0.311258i	$-0.100750\pi$
$683$	16.7015	+	16.7015i	0.639067	+	0.639067i	−0.311258	+	0.950325i	$0.600750\pi$
$684$	0.361554	+	0.777719i	0.0138244	+	0.0297368i
$685$	11.4403	−	19.6125i	0.437113	−	0.749355i
$686$		−	1.00000i		−	0.0381802i
$687$	7.25642	−	11.3757i	0.276850	−	0.434009i
$688$	−2.07154	+	2.07154i	−0.0789767	+	0.0789767i
$689$	6.10953			0.232754
$690$	−22.2189	−	7.12909i	−0.845860	−	0.271400i
$691$	2.98394			0.113514			0.0567572	−	0.998388i	$-0.481924\pi$
$691$	2.98394			0.113514			0.0567572	+	0.998388i	$0.481924\pi$
$692$	−3.15253	+	3.15253i	−0.119841	+	0.119841i
$693$	−17.7609	−	6.48788i	−0.674682	−	0.246454i
$694$		−	2.98474i		−	0.113299i
$695$	4.50952	+	17.1354i	0.171056	+	0.649983i
$696$	−1.43616	−	6.49598i	−0.0544374	−	0.246229i
$697$	−22.1793	−	22.1793i	−0.840102	−	0.840102i
$698$	10.8567	+	10.8567i	0.410931	+	0.410931i
$699$	−2.92706	−	13.2396i	−0.110711	−	0.500767i
$700$	1.33717	−	4.81788i	0.0505403	−	0.182099i
$701$			14.7851i			0.558425i	0.960229	+	0.279213i	$0.0900734\pi$
$701$			14.7851i			0.558425i	−0.960229	+	0.279213i	$0.909927\pi$
$702$	7.12019	+	0.950046i	0.268734	+	0.0358572i
$703$	−0.0908679	+	0.0908679i	−0.00342715	+	0.00342715i
$704$	−6.30293			−0.237551
$705$	−32.6035	+	16.7637i	−1.22792	+	0.631358i
$706$	4.59340			0.172875
$707$	1.11683	−	1.11683i	0.0420029	−	0.0420029i
$708$	12.1683	−	19.0759i	0.457313	−	0.716915i
$709$			30.1615i			1.13274i	0.824152	+	0.566369i	$0.191652\pi$
$709$			30.1615i			1.13274i	−0.824152	+	0.566369i	$0.808348\pi$
$710$	10.4843	+	6.11571i	0.393470	+	0.229519i
$711$	−11.9230	+	5.54288i	−0.447146	+	0.207874i
$712$	−6.33829	−	6.33829i	−0.237538	−	0.237538i
$713$	−28.3240	−	28.3240i	−1.06074	−	1.06074i
$714$	−11.6476	+	2.57509i	−0.435899	+	0.0963703i
$715$	16.8296	+	9.81704i	0.629392	+	0.367136i
$716$			0.251416i			0.00939584i
$717$	37.8876	+	24.1681i	1.41494	+	0.902573i
$718$	7.40585	−	7.40585i	0.276384	−	0.276384i
$719$	0.144200			0.00537777			0.00268888	−	0.999996i	$-0.499144\pi$
$719$	0.144200			0.00537777			0.00268888	+	0.999996i	$0.499144\pi$
$720$	4.28295	+	5.16297i	0.159616	+	0.192413i
$721$	6.07401			0.226208
$722$	−13.3772	+	13.3772i	−0.497849	+	0.497849i
$723$	4.90432	+	3.12841i	0.182394	+	0.116347i
$724$			12.8653i			0.478135i
$725$	−16.7172	+	9.45365i	−0.620861	+	0.351100i
$726$	48.5834	−	10.7410i	1.80310	−	0.398636i
$727$	21.5446	+	21.5446i	0.799045	+	0.799045i	0.982945	−	0.183900i	$-0.0588723\pi$
$727$	21.5446	+	21.5446i	0.799045	+	0.799045i	−0.183900	+	0.982945i	$0.558872\pi$
$728$	−0.977522	−	0.977522i	−0.0362294	−	0.0362294i
$729$	−26.0554	−	7.07918i	−0.965016	−	0.262192i
$730$	2.97057	+	11.2877i	0.109946	+	0.417775i
$731$		−	20.1765i		−	0.746254i
$732$	1.01731	−	1.59481i	0.0376010	−	0.0589460i
$733$	37.1546	−	37.1546i	1.37233	−	1.37233i	0.515362	−	0.856972i	$-0.327657\pi$
$733$	37.1546	−	37.1546i	1.37233	−	1.37233i	0.856972	−	0.515362i	$-0.172343\pi$
$734$	−2.04510			−0.0754862
$735$	1.18326	−	3.68780i	0.0436451	−	0.136027i
$736$	−6.02497			−0.222083
$737$	35.5218	−	35.5218i	1.30846	−	1.30846i
$738$	−4.68799	+	12.8336i	−0.172567	+	0.472412i
$739$			14.3549i			0.528053i	0.964515	+	0.264027i	$0.0850507\pi$
$739$			14.3549i			0.528053i	−0.964515	+	0.264027i	$0.914949\pi$
$740$	−0.506444	+	0.868211i	−0.0186172	+	0.0319161i
$741$	−0.147770	−	0.668390i	−0.00542848	−	0.0245539i
$742$	3.12501	+	3.12501i	0.114723	+	0.114723i
$743$	8.55425	+	8.55425i	0.313825	+	0.313825i	0.846389	−	0.532564i	$-0.178772\pi$
$743$	8.55425	+	8.55425i	0.313825	+	0.313825i	−0.532564	+	0.846389i	$0.678772\pi$
$744$	2.48582	+	11.2438i	0.0911345	+	0.412217i
$745$	10.5561	−	2.77805i	0.386747	−	0.101780i
$746$		−	23.6597i		−	0.866242i
$747$	−2.22711	+	6.09683i	−0.0814856	+	0.223071i
$748$	30.6948	−	30.6948i	1.12231	−	1.12231i
$749$	10.0624			0.367671
$750$	10.6320	−	16.1852i	0.388226	−	0.591000i
$751$	14.1560			0.516561			0.258281	−	0.966070i	$-0.416844\pi$
$751$	14.1560			0.516561			0.258281	+	0.966070i	$0.416844\pi$
$752$	−6.69331	+	6.69331i	−0.244080	+	0.244080i
$753$	17.2082	−	26.9768i	0.627101	−	0.983088i
$754$			5.30992i			0.193376i
$755$	2.95486	−	0.777628i	0.107538	−	0.0283008i
$756$	3.15601	+	4.12790i	0.114783	+	0.150130i
$757$	−20.8958	−	20.8958i	−0.759471	−	0.759471i	0.216755	−	0.976226i	$-0.430453\pi$
$757$	−20.8958	−	20.8958i	−0.759471	−	0.759471i	−0.976226	+	0.216755i	$0.930453\pi$
$758$	−20.4941	−	20.4941i	−0.744380	−	0.744380i
$759$	64.2238	−	14.1988i	2.33118	−	0.515386i
$760$	0.322097	−	0.552180i	0.0116837	−	0.0200297i
$761$		−	40.0280i		−	1.45101i	−0.688214	−	0.725507i	$-0.741605\pi$
$761$		−	40.0280i		−	1.45101i	0.688214	−	0.725507i	$-0.258395\pi$
$762$	13.2464	+	8.44975i	0.479868	+	0.306102i
$763$	−2.91975	+	2.91975i	−0.105702	+	0.105702i
$764$	16.4695			0.595845
$765$	−46.0010	−	4.28563i	−1.66317	−	0.154947i
$766$	24.9033			0.899792
$767$	−12.7697	+	12.7697i	−0.461089	+	0.461089i
$768$	1.46025	+	0.931481i	0.0526924	+	0.0336119i
$769$			42.4533i			1.53090i	0.643493	+	0.765452i	$0.277485\pi$
$769$			42.4533i			1.53090i	−0.643493	+	0.765452i	$0.722515\pi$
$770$	3.58692	+	13.6297i	0.129264	+	0.491180i
$771$	−20.3196	+	4.49233i	−0.731792	+	0.161787i
$772$	−13.9786	−	13.9786i	−0.503100	−	0.503100i
$773$	−16.8991	−	16.8991i	−0.607820	−	0.607820i	0.334556	−	0.942376i	$-0.391414\pi$
$773$	−16.8991	−	16.8991i	−0.607820	−	0.607820i	−0.942376	+	0.334556i	$0.891414\pi$
$774$	−7.96967	+	3.70503i	−0.286464	+	0.133174i
$775$	28.9355	−	16.3632i	1.03939	−	0.587782i
$776$			2.13492i			0.0766392i
$777$	−0.418706	+	0.656392i	−0.0150210	+	0.0235479i
$778$	−4.17634	+	4.17634i	−0.149729	+	0.149729i
$779$	1.30202			0.0466496
$780$	−2.44825	−	4.76157i	−0.0876615	−	0.170491i
$781$	−34.2132			−1.22424
$782$	29.3412	−	29.3412i	1.04924	−	1.04924i
$783$	2.63967	−	19.7832i	0.0943341	−	0.706994i
$784$		−	1.00000i		−	0.0357143i
$785$	22.4731	+	13.1090i	0.802099	+	0.467879i
$786$	−0.749134	−	3.38846i	−0.0267207	−	0.120862i
$787$	8.08931	+	8.08931i	0.288353	+	0.288353i	0.836429	−	0.548076i	$-0.184640\pi$
$787$	8.08931	+	8.08931i	0.288353	+	0.288353i	−0.548076	+	0.836429i	$0.684640\pi$
$788$	−11.7072	−	11.7072i	−0.417052	−	0.417052i
$789$	−1.63879	−	7.41251i	−0.0583424	−	0.263892i
$790$	8.46530	+	4.93797i	0.301182	+	0.175685i
$791$			11.6023i			0.412529i
$792$	−17.7609	−	6.48788i	−0.631107	−	0.230537i
$793$	−1.06760	+	1.06760i	−0.0379115	+	0.0379115i
$794$	25.2586			0.896395
$795$	7.82674	+	15.2221i	0.277586	+	0.539872i
$796$	−11.1512			−0.395243
$797$	−3.04716	+	3.04716i	−0.107936	+	0.107936i	−0.759012	−	0.651076i	$-0.774318\pi$
$797$	−3.04716	+	3.04716i	−0.107936	+	0.107936i	0.651076	+	0.759012i	$0.274318\pi$
$798$	0.266296	−	0.417464i	0.00942677	−	0.0147781i
$799$		−	65.1918i		−	2.30632i
$800$	1.33717	−	4.81788i	0.0472761	−	0.170338i
$801$	−11.3363	−	24.3848i	−0.400548	−	0.861595i
$802$	19.5384	+	19.5384i	0.689926	+	0.689926i
$803$	−23.2642	−	23.2642i	−0.820975	−	0.820975i
$804$	−13.4793	+	2.98004i	−0.475377	+	0.105098i
$805$	3.42874	+	13.0286i	0.120847	+	0.459199i
$806$		−	9.19085i		−	0.323734i
$807$	−13.4833	−	8.60085i	−0.474635	−	0.302764i
$808$	1.11683	−	1.11683i	0.0392901	−	0.0392901i
$809$	10.4944			0.368962			0.184481	−	0.982836i	$-0.440940\pi$
$809$	10.4944			0.368962			0.184481	+	0.982836i	$0.440940\pi$
$810$	6.75439	+	18.9573i	0.237325	+	0.666091i
$811$	10.8699			0.381692			0.190846	−	0.981620i	$-0.438877\pi$
$811$	10.8699			0.381692			0.190846	+	0.981620i	$0.438877\pi$
$812$	−2.71601	+	2.71601i	−0.0953133	+	0.0953133i
$813$	−33.9305	−	21.6439i	−1.19000	−	0.759086i
$814$		−	2.83320i		−	0.0993037i
$815$	21.9119	−	37.5641i	0.767539	−	1.31581i
$816$	−11.6476	+	2.57509i	−0.407746	+	0.0901462i
$817$	0.592221	+	0.592221i	0.0207192	+	0.0207192i
$818$	−6.61484	−	6.61484i	−0.231282	−	0.231282i
$819$	−1.74834	−	3.76074i	−0.0610918	−	0.131411i
$820$	9.84850	−	2.59183i	0.343925	−	0.0905105i
$821$		−	47.8291i		−	1.66925i	−0.550820	−	0.834624i	$-0.685685\pi$
$821$		−	47.8291i		−	1.66925i	0.550820	−	0.834624i	$-0.314315\pi$
$822$	9.45837	−	14.8276i	0.329899	−	0.517172i
$823$	12.5787	−	12.5787i	0.438466	−	0.438466i	−0.453030	−	0.891495i	$-0.649657\pi$
$823$	12.5787	−	12.5787i	0.438466	−	0.438466i	0.891495	+	0.453030i	$0.149657\pi$
$824$	6.07401			0.211598
$825$	−2.89956	+	54.5079i	−0.100950	+	1.89772i
$826$	−13.0634			−0.454533
$827$	−0.598351	+	0.598351i	−0.0208067	+	0.0208067i	−0.717434	−	0.696627i	$-0.754683\pi$
$827$	−0.598351	+	0.598351i	−0.0208067	+	0.0208067i	0.696627	+	0.717434i	$0.254683\pi$
$828$	−16.9777	−	6.20176i	−0.590015	−	0.215526i
$829$		−	32.5297i		−	1.12980i	−0.825159	−	0.564901i	$-0.808914\pi$
$829$		−	32.5297i		−	1.12980i	0.825159	−	0.564901i	$-0.191086\pi$
$830$	4.67870	−	1.23129i	0.162400	−	0.0427387i
$831$	6.42993	+	29.0837i	0.223052	+	1.00890i
$832$	−0.977522	−	0.977522i	−0.0338895	−	0.0338895i
$833$	4.86992	+	4.86992i	0.168733	+	0.168733i
$834$	2.96283	+	13.4014i	0.102594	+	0.464051i
$835$	−16.7535	+	28.7210i	−0.579779	+	0.993931i
$836$			1.80191i			0.0623204i
$837$	−4.56896	+	34.2424i	−0.157926	+	1.18359i
$838$	−5.90217	+	5.90217i	−0.203887	+	0.203887i
$839$	−50.4871			−1.74301			−0.871505	−	0.490387i	$-0.836855\pi$
$839$	−50.4871			−1.74301			−0.871505	+	0.490387i	$0.836855\pi$
$840$	1.18326	−	3.68780i	0.0408262	−	0.127241i
$841$	−14.2466			−0.491261
$842$	−19.1604	+	19.1604i	−0.660312	+	0.660312i
$843$	14.9152	−	23.3822i	0.513708	−	0.805326i
$844$		−	0.766419i		−	0.0263812i
$845$	−6.31056	−	23.9791i	−0.217090	−	0.824905i
$846$	−25.7507	+	11.9712i	−0.885326	+	0.411580i
$847$	−20.3130	−	20.3130i	−0.697964	−	0.697964i
$848$	3.12501	+	3.12501i	0.107313	+	0.107313i
$849$	47.5820	−	10.5196i	1.63301	−	0.361032i
$850$	16.9508	+	29.9746i	0.581408	+	1.02812i
$851$		−	2.70826i		−	0.0928379i
$852$	7.92647	+	5.05621i	0.271556	+	0.173223i
$853$	1.16052	−	1.16052i	0.0397356	−	0.0397356i	−0.686960	−	0.726695i	$-0.741055\pi$
$853$	1.16052	−	1.16052i	0.0397356	−	0.0397356i	0.726695	+	0.686960i	$0.241055\pi$
$854$	−1.09215			−0.0373725
$855$	1.47601	−	1.22443i	0.0504786	−	0.0418746i
$856$	10.0624			0.343924
$857$	24.7253	−	24.7253i	0.844600	−	0.844600i	−0.144853	−	0.989453i	$-0.546271\pi$
$857$	24.7253	−	24.7253i	0.844600	−	0.844600i	0.989453	+	0.144853i	$0.0462710\pi$
$858$	12.7237	+	8.11630i	0.434379	+	0.277086i
$859$		−	48.4452i		−	1.65293i	−0.562989	−	0.826464i	$-0.690349\pi$
$859$		−	48.4452i		−	1.65293i	0.562989	−	0.826464i	$-0.309651\pi$
$860$	5.65846	+	3.30069i	0.192952	+	0.112552i
$861$	7.70237	−	1.70287i	0.262496	−	0.0580337i
$862$	15.5637	+	15.5637i	0.530101	+	0.530101i
$863$	31.1904	+	31.1904i	1.06173	+	1.06173i	0.997965	+	0.0637701i	$0.0203124\pi$
$863$	31.1904	+	31.1904i	1.06173	+	1.06173i	0.0637701	+	0.997965i	$0.479688\pi$
$864$	3.15601	+	4.12790i	0.107370	+	0.140434i
$865$	8.61121	+	5.02308i	0.292790	+	0.170790i
$866$			4.30269i			0.146211i
$867$	28.3471	−	44.4389i	0.962718	−	1.50923i
$868$	4.70110	−	4.70110i	0.159566	−	0.159566i
$869$	−27.6245			−0.937098
$870$	−13.2299	+	6.80238i	−0.448534	+	0.230622i
$871$	11.0182			0.373336
$872$	−2.91975	+	2.91975i	−0.0988753	+	0.0988753i
$873$	−2.19756	+	6.01595i	−0.0743763	+	0.203609i
$874$			1.72245i			0.0582626i
$875$	−11.1793	−	0.149748i	−0.377931	−	0.00506242i
$876$	1.95171	+	8.82792i	0.0659422	+	0.298268i
$877$	8.70402	+	8.70402i	0.293914	+	0.293914i	0.838624	−	0.544710i	$-0.183360\pi$
$877$	8.70402	+	8.70402i	0.293914	+	0.293914i	−0.544710	+	0.838624i	$0.683360\pi$
$878$	2.72129	+	2.72129i	0.0918390	+	0.0918390i
$879$	3.51066	+	15.8793i	0.118412	+	0.535596i
$880$	3.58692	+	13.6297i	0.120915	+	0.459457i
$881$			0.355501i			0.0119771i	0.999982	+	0.00598857i	$0.00190623\pi$
$881$			0.355501i			0.0119771i	−0.999982	+	0.00598857i	$0.998094\pi$
$882$	1.02934	−	2.81788i	0.0346598	−	0.0948830i
$883$	8.48174	−	8.48174i	0.285433	−	0.285433i	−0.549838	−	0.835271i	$-0.685311\pi$
$883$	8.48174	−	8.48174i	0.285433	−	0.285433i	0.835271	+	0.549838i	$0.185311\pi$
$884$	9.52091			0.320223
$885$	−48.1752	−	15.4573i	−1.61939	−	0.519593i
$886$	−1.77441			−0.0596125
$887$	2.65437	−	2.65437i	0.0891249	−	0.0891249i	−0.661139	−	0.750264i	$-0.729927\pi$
$887$	2.65437	−	2.65437i	0.0891249	−	0.0891249i	0.750264	+	0.661139i	$0.229927\pi$
$888$	−0.418706	+	0.656392i	−0.0140508	+	0.0220271i
$889$		−	9.07132i		−	0.304242i
$890$	−10.0991	+	17.3132i	−0.338523	+	0.580340i
$891$	−43.3699	−	36.5641i	−1.45295	−	1.22494i
$892$	1.66559	+	1.66559i	0.0557681	+	0.0557681i
$893$	1.91351	+	1.91351i	0.0640333	+	0.0640333i
$894$	8.25581	−	1.82523i	0.276116	−	0.0610447i
$895$	0.543671	−	0.143078i	0.0181729	−	0.00478256i
$896$		−	1.00000i		−	0.0334077i
$897$	12.1626	+	7.75837i	0.406096	+	0.259044i
$898$	26.0581	−	26.0581i	0.869571	−	0.869571i
$899$	−25.5365			−0.851688
$900$	8.72723	−	12.1998i	0.290908	−	0.406660i
$901$	−30.4371			−1.01401
$902$	−20.2980	+	20.2980i	−0.675851	+	0.675851i
$903$	4.27796	+	2.72886i	0.142362	+	0.0908109i
$904$			11.6023i			0.385885i
$905$	27.8204	−	7.32149i	0.924782	−	0.243374i
$906$	2.31095	−	0.510914i	0.0767762	−	0.0169740i
$907$	−21.5594	−	21.5594i	−0.715870	−	0.715870i	0.251887	−	0.967757i	$-0.418949\pi$
$907$	−21.5594	−	21.5594i	−0.715870	−	0.715870i	−0.967757	+	0.251887i	$0.918949\pi$
$908$	5.55282	+	5.55282i	0.184277	+	0.184277i
$909$	4.29671	−	1.99750i	0.142513	−	0.0662530i
$910$	−1.55753	+	2.67013i	−0.0516318	+	0.0885138i
$911$			18.6500i			0.617902i	0.951078	+	0.308951i	$0.0999778\pi$
$911$			18.6500i			0.617902i	−0.951078	+	0.308951i	$0.900022\pi$
$912$	0.266296	−	0.417464i	0.00881793	−	0.0138236i
$913$	−9.64293	+	9.64293i	−0.319134	+	0.319134i
$914$	24.6548			0.815509
$915$	−4.02763	−	1.29229i	−0.133149	−	0.0427218i
$916$	−7.79020			−0.257396
$917$	−1.41674	+	1.41674i	−0.0467848	+	0.0467848i
$918$	−35.4721	−	4.73304i	−1.17075	−	0.156214i
$919$		−	6.56474i		−	0.216551i	−0.994121	−	0.108275i	$-0.965467\pi$
$919$		−	6.56474i		−	0.216551i	0.994121	−	0.108275i	$-0.0345329\pi$
$920$	3.42874	+	13.0286i	0.113042	+	0.429541i
$921$	2.03768	+	9.21676i	0.0671437	+	0.303702i
$922$	15.7369	+	15.7369i	0.518267	+	0.518267i
$923$	−5.30612	−	5.30612i	−0.174653	−	0.174653i
$924$	2.35667	+	10.6596i	0.0775286	+	0.350675i
$925$	2.16566	+	0.601065i	0.0712066	+	0.0197629i
$926$		−	16.7438i		−	0.550236i
$927$	17.1158	+	6.25224i	0.562158	+	0.205350i
$928$	−2.71601	+	2.71601i	−0.0891574	+	0.0891574i
$929$	9.96590			0.326971			0.163485	−	0.986546i	$-0.447726\pi$
$929$	9.96590			0.326971			0.163485	+	0.986546i	$0.447726\pi$
$930$	22.8993	−	11.7741i	0.750898	−	0.386089i
$931$	−0.285884			−0.00936948
$932$	−5.53555	+	5.53555i	−0.181323	+	0.181323i
$933$	−26.2914	+	41.2163i	−0.860743	+	1.34936i
$934$		−	27.9954i		−	0.916038i
$935$	−83.8437	−	48.9076i	−2.74198	−	1.59945i
$936$	−1.74834	−	3.76074i	−0.0571461	−	0.122924i
$937$	−21.4995	−	21.4995i	−0.702357	−	0.702357i	0.262559	−	0.964916i	$-0.415434\pi$
$937$	−21.4995	−	21.4995i	−0.702357	−	0.702357i	−0.964916	+	0.262559i	$0.915434\pi$
$938$	5.63576	+	5.63576i	0.184014	+	0.184014i
$939$	−12.6079	+	2.78740i	−0.411442	+	0.0909632i
$940$	18.2830	+	10.6648i	0.596324	+	0.347847i
$941$			60.1796i			1.96180i	0.194518	+	0.980899i	$0.437686\pi$
$941$			60.1796i			1.96180i	−0.194518	+	0.980899i	$0.562314\pi$
$942$	16.9903	+	10.8379i	0.553574	+	0.353119i
$943$	−19.4029	+	19.4029i	−0.631845	+	0.631845i
$944$	−13.0634			−0.425177
$945$	7.13029	−	9.17382i	0.231948	−	0.298424i
$946$	−18.4651			−0.600351
$947$	−31.0571	+	31.0571i	−1.00922	+	1.00922i	−0.00926262	+	0.999957i	$0.502948\pi$
$947$	−31.0571	+	31.0571i	−1.00922	+	1.00922i	−0.999957	+	0.00926262i	$0.997052\pi$
$948$	6.40001	+	4.08250i	0.207863	+	0.132593i
$949$		−	7.21608i		−	0.234244i
$950$	−1.37736	−	0.382276i	−0.0446874	−	0.0124027i
$951$	−53.6668	+	11.8649i	−1.74027	+	0.384745i
$952$	4.86992	+	4.86992i	0.157835	+	0.157835i
$953$	−5.02499	−	5.02499i	−0.162775	−	0.162775i	0.621020	−	0.783795i	$-0.286719\pi$
$953$	−5.02499	−	5.02499i	−0.162775	−	0.162775i	−0.783795	+	0.621020i	$0.786719\pi$
$954$	5.58920	+	12.0226i	0.180957	+	0.389246i
$955$	−9.37258	−	35.6142i	−0.303289	−	1.15245i
$956$		−	25.9459i		−	0.839149i
$957$	22.5509	−	35.3523i	0.728966	−	1.14278i
$958$	5.36537	−	5.36537i	0.173347	−	0.173347i
$959$	−10.1541			−0.327894
$960$	1.18326	−	3.68780i	0.0381894	−	0.119023i
$961$	13.2006			0.425826
$962$	0.439401	−	0.439401i	0.0141669	−	0.0141669i
$963$	28.3545	+	10.3576i	0.913712	+	0.333769i
$964$		−	3.35854i		−	0.108171i
$965$	−22.2728	+	38.1829i	−0.716986	+	1.22915i
$966$	2.25274	+	10.1895i	0.0724806	+	0.327842i
$967$	43.4004	+	43.4004i	1.39566	+	1.39566i	0.811984	+	0.583679i	$0.198388\pi$
$967$	43.4004	+	43.4004i	1.39566	+	1.39566i	0.583679	+	0.811984i	$0.301612\pi$
$968$	−20.3130	−	20.3130i	−0.652886	−	0.652886i
$969$	0.736178	+	3.32986i	0.0236494	+	0.106970i
$970$	4.61663	−	1.21496i	0.148231	−	0.0390099i
$971$			18.7579i			0.601969i	0.953629	+	0.300985i	$0.0973153\pi$
$971$			18.7579i			0.601969i	−0.953629	+	0.300985i	$0.902685\pi$
$972$	4.64424	+	14.8806i	0.148964	+	0.477294i
$973$	5.60320	−	5.60320i	0.179630	−	0.179630i
$974$	−3.87783			−0.124254
$975$	−8.90333	+	8.00394i	−0.285135	+	0.256331i
$976$	−1.09215			−0.0349588
$977$	−1.97273	+	1.97273i	−0.0631133	+	0.0631133i	−0.737959	−	0.674846i	$-0.764210\pi$
$977$	−1.97273	+	1.97273i	−0.0631133	+	0.0631133i	0.674846	+	0.737959i	$0.264210\pi$
$978$	18.1158	−	28.3995i	0.579278	−	0.908117i
$979$		−	56.4976i		−	1.80567i
$980$	−2.16244	+	0.569088i	−0.0690766	+	0.0181788i
$981$	−11.2329	+	5.22209i	−0.358640	+	0.166728i
$982$	29.1454	+	29.1454i	0.930067	+	0.930067i
$983$	25.3760	+	25.3760i	0.809369	+	0.809369i	0.984538	−	0.175169i	$-0.0560473\pi$
$983$	25.3760	+	25.3760i	0.809369	+	0.809369i	−0.175169	+	0.984538i	$0.556047\pi$
$984$	7.70237	−	1.70287i	0.245543	−	0.0542855i
$985$	−18.6537	+	31.9785i	−0.594356	+	1.01892i
$986$		−	26.4535i		−	0.842452i
$987$	13.8224	+	8.81718i	0.439973	+	0.280654i
$988$	−0.279458	+	0.279458i	−0.00889075	+	0.00889075i
$989$	−17.6508			−0.561261
$990$	−3.92211	+	42.0991i	−0.124653	+	1.33800i
$991$	38.4444			1.22123			0.610614	−	0.791928i	$-0.290923\pi$
$991$	38.4444			1.22123			0.610614	+	0.791928i	$0.290923\pi$
$992$	4.70110	−	4.70110i	0.149260	−	0.149260i
$993$	34.8245	+	22.2142i	1.10512	+	0.704945i
$994$		−	5.42814i		−	0.172170i
$995$	6.34600	+	24.1137i	0.201182	+	0.764457i
$996$	3.65914	−	0.808977i	0.115944	−	0.0256334i
$997$	−2.86440	−	2.86440i	−0.0907166	−	0.0907166i	0.660292	−	0.751009i	$-0.270432\pi$
$997$	−2.86440	−	2.86440i	−0.0907166	−	0.0907166i	−0.751009	+	0.660292i	$0.770432\pi$
$998$	11.4282	+	11.4282i	0.361753	+	0.361753i
$999$	−1.85552	+	1.41864i	−0.0587059	+	0.0448839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.j.a.197.3	yes	12
3.2	odd	2		210.2.j.b.197.4	yes	12
5.2	odd	4		1050.2.j.d.743.3		12
5.3	odd	4		210.2.j.b.113.4	yes	12
5.4	even	2		1050.2.j.c.407.4		12
15.2	even	4		1050.2.j.c.743.4		12
15.8	even	4	inner	210.2.j.a.113.3	✓	12
15.14	odd	2		1050.2.j.d.407.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.3	✓	12	15.8	even	4	inner
210.2.j.a.197.3	yes	12	1.1	even	1	trivial
210.2.j.b.113.4	yes	12	5.3	odd	4
210.2.j.b.197.4	yes	12	3.2	odd	2
1050.2.j.c.407.4		12	5.4	even	2
1050.2.j.c.743.4		12	15.2	even	4
1050.2.j.d.407.3		12	15.14	odd	2
1050.2.j.d.743.3		12	5.2	odd	4

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.46025 + 0.931481i) q^{3} -1.00000i q^{4} +(-2.16244 + 0.569088i) q^{5} +(-1.69121 + 0.373900i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.26469 + 2.72040i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.46025 + 0.931481i) q^{3} -1.00000i q^{4} +(-2.16244 + 0.569088i) q^{5} +(-1.69121 + 0.373900i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.26469 + 2.72040i) q^{9} +(1.12667 - 1.93148i) q^{10} +6.30293i q^{11} +(0.931481 - 1.46025i) q^{12} +(-0.977522 + 0.977522i) q^{13} -1.00000 q^{14} +(-3.68780 - 1.18326i) q^{15} -1.00000 q^{16} +(4.86992 - 4.86992i) q^{17} +(-2.81788 - 1.02934i) q^{18} +0.285884i q^{19} +(0.569088 + 2.16244i) q^{20} +(0.373900 + 1.69121i) q^{21} +(-4.45685 - 4.45685i) q^{22} +(-4.26030 - 4.26030i) q^{23} +(0.373900 + 1.69121i) q^{24} +(4.35228 - 2.46123i) q^{25} -1.38242i q^{26} +(-0.687232 + 5.15051i) q^{27} +(0.707107 - 0.707107i) q^{28} -3.84102 q^{29} +(3.44436 - 1.77098i) q^{30} +6.64835 q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.87106 + 9.20389i) q^{33} +6.88711i q^{34} +(-1.93148 - 1.12667i) q^{35} +(2.72040 - 1.26469i) q^{36} +(0.317848 + 0.317848i) q^{37} +(-0.202151 - 0.202151i) q^{38} +(-2.33797 + 0.516888i) q^{39} +(-1.93148 - 1.12667i) q^{40} -4.55435i q^{41} +(-1.46025 - 0.931481i) q^{42} +(2.07154 - 2.07154i) q^{43} +6.30293 q^{44} +(-4.28295 - 5.16297i) q^{45} +6.02497 q^{46} +(6.69331 - 6.69331i) q^{47} +(-1.46025 - 0.931481i) q^{48} +1.00000i q^{49} +(-1.33717 + 4.81788i) q^{50} +(11.6476 - 2.57509i) q^{51} +(0.977522 + 0.977522i) q^{52} +(-3.12501 - 3.12501i) q^{53} +(-3.15601 - 4.12790i) q^{54} +(-3.58692 - 13.6297i) q^{55} +1.00000i q^{56} +(-0.266296 + 0.417464i) q^{57} +(2.71601 - 2.71601i) q^{58} +13.0634 q^{59} +(-1.18326 + 3.68780i) q^{60} +1.09215 q^{61} +(-4.70110 + 4.70110i) q^{62} +(-1.02934 + 2.81788i) q^{63} +1.00000i q^{64} +(1.55753 - 2.67013i) q^{65} +(-2.35667 - 10.6596i) q^{66} +(-5.63576 - 5.63576i) q^{67} +(-4.86992 - 4.86992i) q^{68} +(-2.25274 - 10.1895i) q^{69} +(2.16244 - 0.569088i) q^{70} +5.42814i q^{71} +(-1.02934 + 2.81788i) q^{72} +(-3.69101 + 3.69101i) q^{73} -0.449505 q^{74} +(8.64803 + 0.460033i) q^{75} +0.285884 q^{76} +(-4.45685 + 4.45685i) q^{77} +(1.28770 - 2.01869i) q^{78} +4.38280i q^{79} +(2.16244 - 0.569088i) q^{80} +(-5.80113 + 6.88091i) q^{81} +(3.22041 + 3.22041i) q^{82} +(1.52991 + 1.52991i) q^{83} +(1.69121 - 0.373900i) q^{84} +(-7.75949 + 13.3023i) q^{85} +2.92960i q^{86} +(-5.60887 - 3.57783i) q^{87} +(-4.45685 + 4.45685i) q^{88} -8.96370 q^{89} +(6.67928 + 0.622268i) q^{90} -1.38242 q^{91} +(-4.26030 + 4.26030i) q^{92} +(9.70829 + 6.19281i) q^{93} +9.46577i q^{94} +(-0.162693 - 0.618207i) q^{95} +(1.69121 - 0.373900i) q^{96} +(1.50962 + 1.50962i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-17.1465 + 7.97124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^3 - 4 * q^5	\( 12 q + 4 q^{3} - 4 q^{5} - 4 q^{12} - 12 q^{14} + 20 q^{15} - 12 q^{16} + 28 q^{17} - 4 q^{21} + 4 q^{22} - 24 q^{23} - 4 q^{24} + 20 q^{25} - 20 q^{27} + 8 q^{29} + 16 q^{30} - 8 q^{31} + 4 q^{33} - 8 q^{35} + 4 q^{36} - 20 q^{37} - 4 q^{38} - 40 q^{39} - 8 q^{40} - 4 q^{42} + 8 q^{43} + 8 q^{44} + 8 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 16 q^{50} + 8 q^{51} - 24 q^{53} - 4 q^{54} - 16 q^{55} - 12 q^{57} - 8 q^{58} + 32 q^{59} - 4 q^{60} + 28 q^{62} + 8 q^{63} - 8 q^{66} - 28 q^{68} - 32 q^{69} + 4 q^{70} + 8 q^{72} - 24 q^{73} + 8 q^{74} + 36 q^{75} + 4 q^{77} + 4 q^{80} - 36 q^{81} + 32 q^{82} - 24 q^{83} - 36 q^{85} - 64 q^{87} + 4 q^{88} + 48 q^{89} + 48 q^{90} + 24 q^{91} - 24 q^{92} + 76 q^{93} + 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 4 * q^5 - 4 * q^12 - 12 * q^14 + 20 * q^15 - 12 * q^16 + 28 * q^17 - 4 * q^21 + 4 * q^22 - 24 * q^23 - 4 * q^24 + 20 * q^25 - 20 * q^27 + 8 * q^29 + 16 * q^30 - 8 * q^31 + 4 * q^33 - 8 * q^35 + 4 * q^36 - 20 * q^37 - 4 * q^38 - 40 * q^39 - 8 * q^40 - 4 * q^42 + 8 * q^43 + 8 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 - 4 * q^48 - 16 * q^50 + 8 * q^51 - 24 * q^53 - 4 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^58 + 32 * q^59 - 4 * q^60 + 28 * q^62 + 8 * q^63 - 8 * q^66 - 28 * q^68 - 32 * q^69 + 4 * q^70 + 8 * q^72 - 24 * q^73 + 8 * q^74 + 36 * q^75 + 4 * q^77 + 4 * q^80 - 36 * q^81 + 32 * q^82 - 24 * q^83 - 36 * q^85 - 64 * q^87 + 4 * q^88 + 48 * q^89 + 48 * q^90 + 24 * q^91 - 24 * q^92 + 76 * q^93 + 8 * q^97 - 40 * q^99

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