LMFDB - Embedded newform 210.2.j.b.113.4

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			113.4
Root			$1.12212i$ of defining polynomial
Character	$\chi$	$=$	210.113
Dual form			210.2.j.b.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.931481 + 1.46025i) q^{3} +1.00000i q^{4} +(2.16244 + 0.569088i) q^{5} +(-1.69121 + 0.373900i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.26469 - 2.72040i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.931481 + 1.46025i) 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} +(-1.46025 - 0.931481i) q^{12} +(-0.977522 - 0.977522i) q^{13} +1.00000 q^{14} +(-2.84528 + 2.62762i) q^{15} -1.00000 q^{16} +(-4.86992 - 4.86992i) q^{17} +(1.02934 - 2.81788i) 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} +(5.15051 + 0.687232i) q^{27} +(0.707107 + 0.707107i) q^{28} +3.84102 q^{29} +(-3.86992 - 0.153913i) q^{30} +6.64835 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-9.20389 - 5.87106i) 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} +(-0.931481 + 1.46025i) q^{42} +(2.07154 + 2.07154i) q^{43} -6.30293 q^{44} +(-1.18666 - 6.60241i) q^{45} +6.02497 q^{46} +(-6.69331 - 6.69331i) q^{47} +(0.931481 - 1.46025i) 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} +(0.417464 + 0.266296i) q^{57} +(2.71601 + 2.71601i) q^{58} -13.0634 q^{59} +(-2.62762 - 2.84528i) q^{60} +1.09215 q^{61} +(4.70110 + 4.70110i) q^{62} +(-2.81788 - 1.02934i) 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} +(2.81788 + 1.02934i) q^{72} +(-3.69101 - 3.69101i) q^{73} +0.449505 q^{74} +(-7.64809 + 4.06284i) q^{75} +0.285884 q^{76} +(4.45685 + 4.45685i) q^{77} +(2.01869 + 1.28770i) 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} +(-3.57783 + 5.60887i) q^{87} +(-4.45685 - 4.45685i) q^{88} +8.96370 q^{89} +(3.82951 - 5.50771i) q^{90} -1.38242 q^{91} +(4.26030 + 4.26030i) q^{92} +(-6.19281 + 9.70829i) 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} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 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} - 48 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} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 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 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * 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 - 48 * 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 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.931481	+	1.46025i	−0.537791	+	0.843078i
$3$	−0.931481	+	1.46025i	−0.537791	+	0.843078i
$4$			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	$0.600875\pi$
$12$	−1.46025	−	0.931481i	−0.421539	−	0.268895i
$13$	−0.977522	−	0.977522i	−0.271116	−	0.271116i	0.558434	−	0.829549i	$-0.311403\pi$
$13$	−0.977522	−	0.977522i	−0.271116	−	0.271116i	−0.829549	+	0.558434i	$0.811403\pi$
$14$	1.00000			0.267261
$15$	−2.84528	+	2.62762i	−0.734649	+	0.678448i
$16$	−1.00000			−0.250000
$17$	−4.86992	−	4.86992i	−1.18113	−	1.18113i	−0.979452	−	0.201678i	$-0.935360\pi$
$17$	−4.86992	−	4.86992i	−1.18113	−	1.18113i	−0.201678	−	0.979452i	$-0.564640\pi$
$18$	1.02934	−	2.81788i	0.242618	−	0.664181i
$19$		−	0.285884i		−	0.0655864i	−0.999462	−	0.0327932i	$-0.989560\pi$
$19$		−	0.285884i		−	0.0655864i	0.999462	−	0.0327932i	$-0.0104403\pi$
$20$	−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	$-0.533814\pi$
$23$	4.26030	−	4.26030i	0.888334	−	0.888334i	0.994363	+	0.106029i	$0.0338136\pi$
$24$	−0.373900	−	1.69121i	−0.0763220	−	0.345217i
$25$	4.35228	+	2.46123i	0.870456	+	0.492247i
$26$		−	1.38242i		−	0.271116i
$27$	5.15051	+	0.687232i	0.991215	+	0.132258i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	3.84102			0.713259			0.356630	−	0.934246i	$-0.383926\pi$
$29$	3.84102			0.713259			0.356630	+	0.934246i	$0.383926\pi$
$30$	−3.86992	−	0.153913i	−0.706548	−	0.0281006i
$31$	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
$33$	−9.20389	−	5.87106i	−1.60219	−	1.02202i
$34$		−	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	−0.680497	−	0.732751i	$-0.738236\pi$
$37$	0.317848	−	0.317848i	0.0522539	−	0.0522539i	0.732751	+	0.680497i	$0.238236\pi$
$38$	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	$-0.115735\pi$
$42$	−0.931481	+	1.46025i	−0.143731	+	0.225322i
$43$	2.07154	+	2.07154i	0.315907	+	0.315907i	0.847193	−	0.531286i	$-0.178291\pi$
$43$	2.07154	+	2.07154i	0.315907	+	0.315907i	−0.531286	+	0.847193i	$0.678291\pi$
$44$	−6.30293			−0.950203
$45$	−1.18666	−	6.60241i	−0.176897	−	0.984229i
$46$	6.02497			0.888334
$47$	−6.69331	−	6.69331i	−0.976320	−	0.976320i	0.0234064	−	0.999726i	$-0.492549\pi$
$47$	−6.69331	−	6.69331i	−0.976320	−	0.976320i	−0.999726	+	0.0234064i	$0.992549\pi$
$48$	0.931481	−	1.46025i	0.134448	−	0.210770i
$49$		−	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	$-0.651836\pi$
$53$	3.12501	−	3.12501i	0.429253	−	0.429253i	0.888374	+	0.459121i	$0.151836\pi$
$54$	3.15601	+	4.12790i	0.429479	+	0.561737i
$55$	−3.58692	+	13.6297i	−0.483661	+	1.83783i
$56$			1.00000i			0.133631i
$57$	0.417464	+	0.266296i	0.0552945	+	0.0352717i
$58$	2.71601	+	2.71601i	0.356630	+	0.356630i
$59$	−13.0634			−1.70071			−0.850354	−	0.526211i	$-0.823612\pi$
$59$	−13.0634			−1.70071			−0.850354	+	0.526211i	$0.823612\pi$
$60$	−2.62762	−	2.84528i	−0.339224	−	0.367324i
$61$	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
$63$	−2.81788	−	1.02934i	−0.355020	−	0.129685i
$64$		−	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	−0.961904	−	0.273386i	$-0.911856\pi$
$67$	−5.63576	+	5.63576i	−0.688518	+	0.688518i	0.273386	+	0.961904i	$0.411856\pi$
$68$	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	$0.895611\pi$
$72$	2.81788	+	1.02934i	0.332090	+	0.121309i
$73$	−3.69101	−	3.69101i	−0.432000	−	0.432000i	0.457308	−	0.889308i	$-0.348814\pi$
$73$	−3.69101	−	3.69101i	−0.432000	−	0.432000i	−0.889308	+	0.457308i	$0.848814\pi$
$74$	0.449505			0.0522539
$75$	−7.64809	+	4.06284i	−0.883126	+	0.469137i
$76$	0.285884			0.0327932
$77$	4.45685	+	4.45685i	0.507905	+	0.507905i
$78$	2.01869	+	1.28770i	0.228572	+	0.145804i
$79$		−	4.38280i		−	0.493104i	−0.969130	−	0.246552i	$-0.920702\pi$
$79$		−	4.38280i		−	0.493104i	0.969130	−	0.246552i	$-0.0792976\pi$
$80$	−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	$-0.787887\pi$
$83$	−1.52991	+	1.52991i	−0.167930	+	0.167930i	0.618139	+	0.786069i	$0.287887\pi$
$84$	−1.69121	+	0.373900i	−0.184526	+	0.0407958i
$85$	−7.75949	−	13.3023i	−0.841635	−	1.44284i
$86$			2.92960i			0.315907i
$87$	−3.57783	+	5.60887i	−0.383584	+	0.601334i
$88$	−4.45685	−	4.45685i	−0.475102	−	0.475102i
$89$	8.96370			0.950150			0.475075	−	0.879945i	$-0.342421\pi$
$89$	8.96370			0.950150			0.475075	+	0.879945i	$0.342421\pi$
$90$	3.82951	−	5.50771i	0.403666	−	0.580563i
$91$	−1.38242			−0.144917
$92$	4.26030	+	4.26030i	0.444167	+	0.444167i
$93$	−6.19281	+	9.70829i	−0.642165	+	1.00670i
$94$		−	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	−0.626302	−	0.779580i	$-0.715432\pi$
$97$	1.50962	−	1.50962i	0.153278	−	0.153278i	0.779580	+	0.626302i	$0.215432\pi$
$98$	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	$-0.0250387\pi$
$102$	10.0569	+	6.41521i	0.995785	+	0.635201i
$103$	4.29497	+	4.29497i	0.423196	+	0.423196i	0.886303	−	0.463106i	$-0.153265\pi$
$103$	4.29497	+	4.29497i	0.423196	+	0.423196i	−0.463106	+	0.886303i	$0.653265\pi$
$104$	1.38242			0.135558
$105$	−0.153913	+	3.86992i	−0.0150204	+	0.377666i
$106$	4.41943			0.429253
$107$	−7.11516	−	7.11516i	−0.687849	−	0.687849i	0.273907	−	0.961756i	$-0.411684\pi$
$107$	−7.11516	−	7.11516i	−0.687849	−	0.687849i	−0.961756	+	0.273907i	$0.911684\pi$
$108$	−0.687232	+	5.15051i	−0.0661289	+	0.495608i
$109$		−	4.12915i		−	0.395501i	−0.980252	−	0.197751i	$-0.936636\pi$
$109$		−	4.12915i		−	0.395501i	0.980252	−	0.197751i	$-0.0633636\pi$
$110$	−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	$-0.933745\pi$
$113$	−8.20404	+	8.20404i	−0.771771	+	0.771771i	0.206645	+	0.978416i	$0.433745\pi$
$114$	0.106892	+	0.483491i	0.0100114	+	0.0452831i
$115$	11.6371	−	6.78815i	1.08517	−	0.632998i
$116$			3.84102i			0.356630i
$117$	−1.42299	+	3.89551i	−0.131555	+	0.360140i
$118$	−9.23721	−	9.23721i	−0.850354	−	0.850354i
$119$	−6.88711			−0.631341
$120$	0.153913	−	3.86992i	0.0140503	−	0.353274i
$121$	−28.7270			−2.61154
$122$	0.772265	+	0.772265i	0.0699176	+	0.0699176i
$123$	6.65051	+	4.24229i	0.599656	+	0.382514i
$124$			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	−0.931900	−	0.362715i	$-0.881850\pi$
$127$	−6.41439	+	6.41439i	−0.569185	+	0.569185i	0.362715	+	0.931900i	$0.381850\pi$
$128$	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	$0.972104\pi$
$132$	5.87106	−	9.20389i	0.511010	−	0.801096i
$133$	−0.202151	−	0.202151i	−0.0175287	−	0.0175287i
$134$	−7.97017			−0.688518
$135$	10.7466	+	4.41719i	0.924916	+	0.380171i
$136$	6.88711			0.590565
$137$	7.18005	+	7.18005i	0.613433	+	0.613433i	0.943839	−	0.330406i	$-0.107186\pi$
$137$	7.18005	+	7.18005i	0.613433	+	0.613433i	−0.330406	+	0.943839i	$0.607186\pi$
$138$	−5.61215	+	8.79800i	−0.477738	+	0.748935i
$139$			7.92412i			0.672115i	0.941842	+	0.336057i	$0.109094\pi$
$139$			7.92412i			0.672115i	−0.941842	+	0.336057i	$0.890906\pi$
$140$	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
$147$	1.46025	+	0.931481i	0.120440	+	0.0768272i
$148$	0.317848	+	0.317848i	0.0261270	+	0.0261270i
$149$	4.88159			0.399916			0.199958	−	0.979805i	$-0.435919\pi$
$149$	4.88159			0.399916			0.199958	+	0.979805i	$0.435919\pi$
$150$	−8.28088	−	2.53516i	−0.676131	−	0.206995i
$151$	−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
$153$	−7.08920	+	19.4071i	−0.573128	+	1.56897i
$154$			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	−0.954576	−	0.297966i	$-0.903692\pi$
$157$	−8.22730	+	8.22730i	−0.656610	+	0.656610i	0.297966	+	0.954576i	$0.403692\pi$
$158$	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
$162$	−8.96755	+	0.763518i	−0.704558	+	0.0599876i
$163$	−13.7521	−	13.7521i	−1.07714	−	1.07714i	−0.996764	−	0.0803803i	$-0.974387\pi$
$163$	−13.7521	−	13.7521i	−1.07714	−	1.07714i	−0.0803803	−	0.996764i	$-0.525613\pi$
$164$	4.55435			0.355635
$165$	−16.5617	−	17.9336i	−1.28933	−	1.39613i
$166$	−2.16362			−0.167930
$167$	−10.5146	−	10.5146i	−0.813647	−	0.813647i	0.171532	−	0.985179i	$-0.445128\pi$
$167$	−10.5146	−	10.5146i	−0.813647	−	0.813647i	−0.985179	+	0.171532i	$0.945128\pi$
$168$	−1.46025	−	0.931481i	−0.112661	−	0.0718653i
$169$		−	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	$-0.695791\pi$
$173$	3.15253	−	3.15253i	0.239682	−	0.239682i	0.816719	+	0.577036i	$0.195791\pi$
$174$	−6.49598	+	1.43616i	−0.492459	+	0.108875i
$175$	4.81788	−	1.33717i	0.364198	−	0.101081i
$176$		−	6.30293i		−	0.475102i
$177$	12.1683	−	19.0759i	0.914625	−	1.43383i
$178$	6.33829	+	6.33829i	0.475075	+	0.475075i
$179$	0.251416			0.0187917			0.00939584	−	0.999956i	$-0.497009\pi$
$179$	0.251416			0.0187917			0.00939584	+	0.999956i	$0.497009\pi$
$180$	6.60241	−	1.18666i	0.492115	−	0.0884487i
$181$	−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
$183$	−1.01731	+	1.59481i	−0.0752020	+	0.117892i
$184$			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	$0.796817\pi$
$192$	1.46025	+	0.931481i	0.105385	+	0.0672238i
$193$	13.9786	+	13.9786i	1.00620	+	1.00620i	0.999981	+	0.00621990i	$0.00197987\pi$
$193$	13.9786	+	13.9786i	1.00620	+	1.00620i	0.00621990	+	0.999981i	$0.498020\pi$
$194$	2.13492			0.153278
$195$	5.34988	+	0.212774i	0.383113	+	0.0152370i
$196$	1.00000			0.0714286
$197$	−11.7072	−	11.7072i	−0.834104	−	0.834104i	0.153971	−	0.988075i	$-0.450794\pi$
$197$	−11.7072	−	11.7072i	−0.834104	−	0.834104i	−0.988075	+	0.153971i	$0.950794\pi$
$198$	17.7609	+	6.48788i	1.26221	+	0.461073i
$199$			11.1512i			0.790487i	0.918576	+	0.395243i	$0.129340\pi$
$199$			11.1512i			0.790487i	−0.918576	+	0.395243i	$0.870660\pi$
$200$	−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
$207$	−16.9777	−	6.20176i	−1.18003	−	0.431052i
$208$	0.977522	+	0.977522i	0.0677789	+	0.0677789i
$209$	1.80191			0.124641
$210$	−2.84528	+	2.62762i	−0.196343	+	0.181323i
$211$	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
$213$	−7.92647	−	5.05621i	−0.543112	−	0.346446i
$214$		−	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
$222$	−0.418706	+	0.656392i	−0.0281017	+	0.0440542i
$223$	−1.66559	−	1.66559i	−0.111536	−	0.111536i	0.649136	−	0.760672i	$-0.275131\pi$
$223$	−1.66559	−	1.66559i	−0.111536	−	0.111536i	−0.760672	+	0.649136i	$0.775131\pi$
$224$	−1.00000			−0.0668153
$225$	1.19127	−	14.9526i	0.0794177	−	0.996841i
$226$	−11.6023			−0.771771
$227$	5.55282	+	5.55282i	0.368554	+	0.368554i	0.866950	−	0.498396i	$-0.166077\pi$
$227$	5.55282	+	5.55282i	0.368554	+	0.368554i	−0.498396	+	0.866950i	$0.666077\pi$
$228$	−0.266296	+	0.417464i	−0.0176359	+	0.0276472i
$229$			7.79020i			0.514791i	0.966306	+	0.257396i	$0.0828643\pi$
$229$			7.79020i			0.514791i	−0.966306	+	0.257396i	$0.917136\pi$
$230$	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	$-0.667454\pi$
$233$	5.53555	−	5.53555i	0.362646	−	0.362646i	0.864786	+	0.502140i	$0.167454\pi$
$234$	−3.76074	+	1.74834i	−0.245848	+	0.114292i
$235$	−10.6648	−	18.2830i	−0.695694	−	1.19265i
$236$		−	13.0634i		−	0.850354i
$237$	6.40001	+	4.08250i	0.415725	+	0.265187i
$238$	−4.86992	−	4.86992i	−0.315670	−	0.315670i
$239$	−25.9459			−1.67830			−0.839149	−	0.543901i	$-0.816947\pi$
$239$	−25.9459			−1.67830			−0.839149	+	0.543901i	$0.816947\pi$
$240$	2.84528	−	2.62762i	0.183662	−	0.169612i
$241$	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
$243$	−4.64424	−	14.8806i	−0.297928	−	0.954588i
$244$			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	$-0.198135\pi$
$252$	1.02934	−	2.81788i	0.0648425	−	0.177510i
$253$	26.8524	+	26.8524i	1.68820	+	1.68820i
$254$	−9.07132			−0.569185
$255$	26.6526	+	1.06002i	1.66905	+	0.0663809i
$256$	1.00000			0.0625000
$257$	8.49575	+	8.49575i	0.529950	+	0.529950i	0.920557	−	0.390607i	$-0.127735\pi$
$257$	8.49575	+	8.49575i	0.529950	+	0.529950i	−0.390607	+	0.920557i	$0.627735\pi$
$258$	−4.27796	−	2.72886i	−0.266334	−	0.169892i
$259$		−	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	$-0.706854\pi$
$263$	3.09922	−	3.09922i	0.191106	−	0.191106i	0.796174	+	0.605068i	$0.206854\pi$
$264$	10.6596	−	2.35667i	0.656053	−	0.145043i
$265$	8.53604	−	4.97923i	0.524365	−	0.305872i
$266$		−	0.285884i		−	0.0175287i
$267$	−8.34951	+	13.0893i	−0.510982	+	0.801051i
$268$	−5.63576	−	5.63576i	−0.344259	−	0.344259i
$269$	9.23352			0.562978			0.281489	−	0.959564i	$-0.409172\pi$
$269$	9.23352			0.562978			0.281489	+	0.959564i	$0.409172\pi$
$270$	4.47554	+	10.7224i	0.272373	+	0.652544i
$271$	−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
$273$	1.28770	−	2.01869i	0.0779353	−	0.122177i
$274$			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	−0.240116	−	0.970744i	$-0.577186\pi$
$277$	12.1601	−	12.1601i	0.730628	−	0.730628i	0.970744	+	0.240116i	$0.0771856\pi$
$278$	−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	$-0.158497\pi$
$282$	13.8224	+	8.81718i	0.823114	+	0.525056i
$283$	19.8944	+	19.8944i	1.18260	+	1.18260i	0.979069	+	0.203527i	$0.0652406\pi$
$283$	19.8944	+	19.8944i	1.18260	+	1.18260i	0.203527	+	0.979069i	$0.434759\pi$
$284$	−5.42814			−0.322101
$285$	0.751194	+	0.813422i	0.0444969	+	0.0481829i
$286$	8.71333			0.515230
$287$	−3.22041	−	3.22041i	−0.190095	−	0.190095i
$288$	−1.02934	+	2.81788i	−0.0606546	+	0.166045i
$289$			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	$-0.838434\pi$
$293$	−6.63925	+	6.63925i	−0.387869	+	0.387869i	0.486058	+	0.873927i	$0.338434\pi$
$294$	0.373900	+	1.69121i	0.0218063	+	0.0986335i
$295$	−28.2488	−	7.43422i	−1.64471	−	0.432837i
$296$			0.449505i			0.0261270i
$297$	−4.33158	+	32.4633i	−0.251344	+	1.88371i
$298$	3.45181	+	3.45181i	0.199958	+	0.199958i
$299$	−8.32907			−0.481683
$300$	−4.06284	−	7.64809i	−0.234568	−	0.441563i
$301$	2.92960			0.168859
$302$	−0.966224	−	0.966224i	−0.0555999	−	0.0555999i
$303$	2.30639	+	1.47122i	0.132499	+	0.0845194i
$304$			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	−0.588536	−	0.808471i	$-0.700295\pi$
$307$	3.85359	−	3.85359i	0.219936	−	0.219936i	0.808471	+	0.588536i	$0.200295\pi$
$308$	−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	$0.704696\pi$
$312$	−1.28770	+	2.01869i	−0.0729018	+	0.114286i
$313$	−5.27143	−	5.27143i	−0.297959	−	0.297959i	0.542255	−	0.840214i	$-0.317571\pi$
$313$	−5.27143	−	5.27143i	−0.297959	−	0.297959i	−0.840214	+	0.542255i	$0.817571\pi$
$314$	−11.6352			−0.656610
$315$	−5.50771	−	3.82951i	−0.310324	−	0.215769i
$316$	4.38280			0.246552
$317$	22.4384	+	22.4384i	1.26027	+	1.26027i	0.950963	+	0.309306i	$0.100097\pi$
$317$	22.4384	+	22.4384i	1.26027	+	1.26027i	0.309306	+	0.950963i	$0.399903\pi$
$318$	−4.11661	+	6.45349i	−0.230848	+	0.361894i
$319$			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
$327$	6.02961	+	3.84623i	0.333438	+	0.212697i
$328$	3.22041	+	3.22041i	0.177817	+	0.177817i
$329$	−9.46577			−0.521865
$330$	0.970106	−	24.3919i	0.0534026	−	1.34273i
$331$	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
$333$	−1.26665	−	0.462695i	−0.0694122	−	0.0253555i
$334$		−	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	−0.920035	−	0.391835i	$-0.871840\pi$
$337$	−9.69647	+	9.69647i	−0.528200	+	0.528200i	0.391835	+	0.920035i	$0.371840\pi$
$338$	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
$342$	−0.805588	−	0.294273i	−0.0435612	−	0.0159125i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−2.92960			−0.157953
$345$	−0.927324	+	23.3162i	−0.0499255	+	1.25530i
$346$	4.45835			0.239682
$347$	2.11053	+	2.11053i	0.113299	+	0.113299i	0.761484	−	0.648184i	$-0.224471\pi$
$347$	2.11053	+	2.11053i	0.113299	+	0.113299i	−0.648184	+	0.761484i	$0.724471\pi$
$348$	−5.60887	−	3.57783i	−0.300667	−	0.191792i
$349$			15.3537i			0.821863i	0.911666	+	0.410931i	$0.134796\pi$
$349$			15.3537i			0.821863i	−0.911666	+	0.410931i	$0.865204\pi$
$350$	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	$-0.710992\pi$
$353$	3.24802	−	3.24802i	0.172875	−	0.172875i	0.788241	+	0.615366i	$0.210992\pi$
$354$	22.0930	−	4.88440i	1.17423	−	0.259603i
$355$	−3.08909	+	11.7380i	−0.163952	+	0.622989i
$356$			8.96370i			0.475075i
$357$	6.41521	−	10.0569i	0.339529	−	0.532270i
$358$	0.177778	+	0.177778i	0.00939584	+	0.00939584i
$359$	10.4735			0.552768			0.276384	−	0.961047i	$-0.410864\pi$
$359$	10.4735			0.552768			0.276384	+	0.961047i	$0.410864\pi$
$360$	5.50771	+	3.82951i	0.290282	+	0.201833i
$361$	18.9183			0.995698
$362$	−9.09714	−	9.09714i	−0.478135	−	0.478135i
$363$	26.7586	−	41.9487i	1.40446	−	2.20174i
$364$		−	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	−0.668356	−	0.743842i	$-0.733002\pi$
$367$	1.44611	−	1.44611i	0.0754862	−	0.0754862i	0.743842	+	0.668356i	$0.233002\pi$
$368$	−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
$372$	−9.70829	−	6.19281i	−0.503351	−	0.321082i
$373$	−16.7299	−	16.7299i	−0.866242	−	0.866242i	0.125812	−	0.992054i	$-0.459846\pi$
$373$	−16.7299	−	16.7299i	−0.866242	−	0.866242i	−0.992054	+	0.125812i	$0.959846\pi$
$374$	43.4090			2.24463
$375$	−18.8506	+	4.43321i	−0.973443	+	0.228930i
$376$	9.46577			0.488160
$377$	−3.75468	−	3.75468i	−0.193376	−	0.193376i
$378$	5.15051	+	0.687232i	0.264913	+	0.0353474i
$379$		−	28.9831i		−	1.48876i	−0.667756	−	0.744380i	$-0.732745\pi$
$379$		−	28.9831i		−	1.48876i	0.667756	−	0.744380i	$-0.267255\pi$
$380$	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	$-0.530485\pi$
$383$	17.6093	−	17.6093i	0.899792	−	0.899792i	0.995417	+	0.0956253i	$0.0304850\pi$
$384$	0.373900	+	1.69121i	0.0190805	+	0.0863043i
$385$	7.10132	+	12.1740i	0.361917	+	0.620444i
$386$			19.7687i			1.00620i
$387$	3.01556	−	8.25526i	0.153290	−	0.419638i
$388$	1.50962	+	1.50962i	0.0766392	+	0.0766392i
$389$	−5.90624			−0.299458			−0.149729	−	0.988727i	$-0.547840\pi$
$389$	−5.90624			−0.299458			−0.149729	+	0.988727i	$0.547840\pi$
$390$	3.63248	+	3.93339i	0.183938	+	0.199175i
$391$	−41.4947			−2.09848
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−2.92572	−	1.86629i	−0.147583	−	0.0941416i
$394$		−	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	−0.995115	−	0.0987205i	$-0.968525\pi$
$397$	−17.8605	+	17.8605i	−0.896395	+	0.896395i	0.0987205	+	0.995115i	$0.468525\pi$
$398$	−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	$-0.242357\pi$
$402$	7.42406	−	11.6385i	0.370278	−	0.580475i
$403$	−6.49891	−	6.49891i	−0.323734	−	0.323734i
$404$	1.57944			0.0785802
$405$	−16.4604	+	11.5782i	−0.817925	+	0.575325i
$406$	3.84102			0.190627
$407$	2.00338	+	2.00338i	0.0993037	+	0.0993037i
$408$	−6.41521	+	10.0569i	−0.317600	+	0.497893i
$409$		−	9.35480i		−	0.462565i	−0.972887	−	0.231282i	$-0.925708\pi$
$409$		−	9.35480i		−	0.462565i	0.972887	−	0.231282i	$-0.0742921\pi$
$410$	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
$417$	−11.5712	−	7.38116i	−0.566646	−	0.361457i
$418$	1.27414	+	1.27414i	0.0623204	+	0.0623204i
$419$	−8.34692			−0.407774			−0.203887	−	0.978994i	$-0.565357\pi$
$419$	−8.34692			−0.407774			−0.203887	+	0.978994i	$0.565357\pi$
$420$	−3.86992	−	0.153913i	−0.188833	−	0.00751020i
$421$	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
$423$	−9.74352	+	26.6734i	−0.473746	+	1.29691i
$424$			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	$-0.177846\pi$
$432$	−5.15051	−	0.687232i	−0.247804	−	0.0330645i
$433$	3.04246	+	3.04246i	0.146211	+	0.146211i	0.776423	−	0.630212i	$-0.217032\pi$
$433$	3.04246	+	3.04246i	0.146211	+	0.146211i	−0.630212	+	0.776423i	$0.717032\pi$
$434$	6.64835			0.319131
$435$	−10.9288	+	10.0927i	−0.523995	+	0.483909i
$436$	4.12915			0.197751
$437$	−1.21795	−	1.21795i	−0.0582626	−	0.0582626i
$438$	7.62235	+	4.86221i	0.364210	+	0.232326i
$439$			3.84848i			0.183678i	0.995774	+	0.0918390i	$0.0292745\pi$
$439$			3.84848i			0.183678i	−0.995774	+	0.0918390i	$0.970725\pi$
$440$	−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	$-0.763421\pi$
$443$	−1.25470	+	1.25470i	−0.0596125	+	0.0596125i	0.676672	+	0.736285i	$0.263421\pi$
$444$	−0.760209	+	0.168070i	−0.0360779	+	0.00797625i
$445$	19.3834	+	5.10113i	0.918863	+	0.241817i
$446$		−	2.35550i		−	0.111536i
$447$	−4.54711	+	7.12837i	−0.215071	+	0.337160i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	36.8518			1.73914			0.869571	−	0.493808i	$-0.164395\pi$
$449$	36.8518			1.73914			0.869571	+	0.493808i	$0.164395\pi$
$450$	11.4155	−	9.73075i	0.538130	−	0.458712i
$451$	28.7058			1.35170
$452$	−8.20404	−	8.20404i	−0.385885	−	0.385885i
$453$	1.27282	−	1.99536i	0.0598022	−	0.0937502i
$454$			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	−0.985454	−	0.169945i	$-0.945641\pi$
$457$	−17.4336	+	17.4336i	−0.815509	+	0.815509i	0.169945	+	0.985454i	$0.445641\pi$
$458$	−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	$-0.173422\pi$
$462$	−9.20389	−	5.87106i	−0.428204	−	0.273146i
$463$	−11.8397	−	11.8397i	−0.550236	−	0.550236i	0.376273	−	0.926509i	$-0.377205\pi$
$463$	−11.8397	−	11.8397i	−0.550236	−	0.550236i	−0.926509	+	0.376273i	$0.877205\pi$
$464$	−3.84102			−0.178315
$465$	−18.9164	+	17.4693i	−0.877229	+	0.810120i
$466$	7.82845			0.362646
$467$	19.7958	+	19.7958i	0.916038	+	0.916038i	0.996738	−	0.0807000i	$-0.0257156\pi$
$467$	19.7958	+	19.7958i	0.916038	+	0.916038i	−0.0807000	+	0.996738i	$0.525716\pi$
$468$	−3.89551	−	1.42299i	−0.180070	−	0.0657777i
$469$			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
$477$	−12.4534	−	4.54911i	−0.570203	−	0.208289i
$478$	−18.3465	−	18.3465i	−0.839149	−	0.839149i
$479$	7.58779			0.346695			0.173347	−	0.984861i	$-0.444542\pi$
$479$	7.58779			0.346695			0.173347	+	0.984861i	$0.444542\pi$
$480$	3.86992	+	0.153913i	0.176637	+	0.00702515i
$481$	−0.621407			−0.0283337
$482$	2.37484	+	2.37484i	0.108171	+	0.108171i
$483$	8.79800	+	5.61215i	0.400323	+	0.255362i
$484$		−	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	−0.642245	−	0.766499i	$-0.721997\pi$
$487$	2.74204	−	2.74204i	0.124254	−	0.124254i	0.766499	+	0.642245i	$0.221997\pi$
$488$	−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	$-0.380251\pi$
$492$	−4.24229	+	6.65051i	−0.191257	+	0.299828i
$493$	−18.7055	−	18.7055i	−0.842452	−	0.842452i
$494$	−0.395214			−0.0177815
$495$	41.6146	−	7.47946i	1.87044	−	0.336177i
$496$	−6.64835			−0.298520
$497$	3.83827	+	3.83827i	0.172170	+	0.172170i
$498$	2.01537	−	3.15944i	0.0903109	−	0.141578i
$499$			16.1619i			0.723505i	0.932274	+	0.361753i	$0.117821\pi$
$499$			16.1619i			0.723505i	−0.932274	+	0.361753i	$0.882179\pi$
$500$	−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	$-0.982263\pi$
$503$	−21.1438	+	21.1438i	−0.942754	+	0.942754i	0.0556938	+	0.998448i	$0.482263\pi$
$504$	2.72040	−	1.26469i	0.121176	−	0.0563337i
$505$	0.898842	−	3.41545i	0.0399979	−	0.151985i
$506$			37.9750i			1.68820i
$507$	16.1926	+	10.3291i	0.719140	+	0.458731i
$508$	−6.41439	−	6.41439i	−0.284592	−	0.284592i
$509$	−31.1749			−1.38180			−0.690901	−	0.722949i	$-0.742786\pi$
$509$	−31.1749			−1.38180			−0.690901	+	0.722949i	$0.742786\pi$
$510$	18.0967	+	19.5958i	0.801335	+	0.867716i
$511$	−5.21988			−0.230914
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.196469	−	1.47245i	0.00867431	−	0.0650102i
$514$			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	$0.814368\pi$
$522$	3.95372	−	10.8235i	0.173050	−	0.473733i
$523$	8.35714	+	8.35714i	0.365432	+	0.365432i	0.865808	−	0.500376i	$-0.166805\pi$
$523$	8.35714	+	8.35714i	0.365432	+	0.365432i	−0.500376	+	0.865808i	$0.666805\pi$
$524$	−2.00357			−0.0875263
$525$	−2.53516	+	8.28088i	−0.110643	+	0.361407i
$526$	4.38296			0.191106
$527$	−32.3770	−	32.3770i	−1.41036	−	1.41036i
$528$	9.20389	+	5.87106i	0.400548	+	0.255505i
$529$		−	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
$537$	−0.234189	+	0.367131i	−0.0101060	+	0.0158429i
$538$	6.52909	+	6.52909i	0.281489	+	0.281489i
$539$	6.30293			0.271487
$540$	−4.41719	+	10.7466i	−0.190085	+	0.462458i
$541$	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
$543$	11.9838	−	18.7866i	0.514273	−	0.806211i
$544$			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	−0.00676436	+	0.999977i	$0.502153\pi$
$547$	−23.5457	+	23.5457i	−1.00674	+	1.00674i	−0.999977	+	0.00676436i	$0.997847\pi$
$548$	−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
$552$	−8.79800	−	5.61215i	−0.374468	−	0.238869i
$553$	−3.09911	−	3.09911i	−0.131788	−	0.131788i
$554$	17.1969			0.730628
$555$	−0.0691849	+	1.73955i	−0.00293674	+	0.0738399i
$556$	−7.92412			−0.336057
$557$	19.6460	+	19.6460i	0.832429	+	0.832429i	0.987849	−	0.155419i	$-0.0496729\pi$
$557$	19.6460	+	19.6460i	0.832429	+	0.832429i	−0.155419	+	0.987849i	$0.549673\pi$
$558$	6.84343	−	18.7343i	0.289706	−	0.793085i
$559$		−	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	0.0991442	−	0.995073i	$-0.468389\pi$
$563$	25.9632	−	25.9632i	1.09422	−	1.09422i	0.995073	−	0.0991442i	$-0.0316105\pi$
$564$	3.53925	+	16.0086i	0.149029	+	0.674085i
$565$	−22.4095	+	13.0719i	−0.942776	+	0.549939i
$566$			28.1349i			1.18260i
$567$	0.763518	+	8.96755i	0.0320647	+	0.376602i
$568$	−3.83827	−	3.83827i	−0.161050	−	0.161050i
$569$	45.5655			1.91020			0.955102	−	0.296277i	$-0.0957453\pi$
$569$	45.5655			1.91020			0.955102	+	0.296277i	$0.0957453\pi$
$570$	−0.0440014	+	1.10635i	−0.00184302	+	0.0463399i
$571$	−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
$573$	−24.0496	−	15.3410i	−1.00469	−	0.640879i
$574$		−	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	−0.943906	−	0.330214i	$-0.892879\pi$
$577$	−14.7414	+	14.7414i	−0.613693	+	0.613693i	0.330214	+	0.943906i	$0.392879\pi$
$578$	−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
$582$	−1.98864	+	3.11753i	−0.0824317	+	0.129226i
$583$	19.6967	+	19.6967i	0.815755	+	0.815755i
$584$	5.21988			0.216000
$585$	−5.29401	+	7.61399i	−0.218880	+	0.314800i
$586$	−9.38931			−0.387869
$587$	15.1380	+	15.1380i	0.624811	+	0.624811i	0.946758	−	0.321947i	$-0.104337\pi$
$587$	15.1380	+	15.1380i	0.624811	+	0.624811i	−0.321947	+	0.946758i	$0.604337\pi$
$588$	−0.931481	+	1.46025i	−0.0384136	+	0.0602199i
$589$		−	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	$-0.905598\pi$
$593$	−16.1719	+	16.1719i	−0.664098	+	0.664098i	0.292245	+	0.956343i	$0.405598\pi$
$594$	−26.0179	+	19.8921i	−1.06753	+	0.816184i
$595$	−14.8930	−	3.91937i	−0.610552	−	0.160679i
$596$			4.88159i			0.199958i
$597$	−16.2836	−	10.3871i	−0.666442	−	0.425116i
$598$	−5.88954	−	5.88954i	−0.240841	−	0.240841i
$599$	28.5725			1.16744			0.583720	−	0.811955i	$-0.301596\pi$
$599$	28.5725			1.16744			0.583720	+	0.811955i	$0.301596\pi$
$600$	2.53516	−	8.28088i	0.103497	−	0.338066i
$601$	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
$603$	22.4590	+	8.20404i	0.914601	+	0.334094i
$604$		−	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	−0.714546	−	0.699589i	$-0.753366\pi$
$607$	−0.368490	+	0.368490i	−0.0149566	+	0.0149566i	0.699589	+	0.714546i	$0.253366\pi$
$608$	−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
$612$	−19.4071	−	7.08920i	−0.784484	−	0.286564i
$613$	−27.1118	−	27.1118i	−1.09504	−	1.09504i	−0.994982	−	0.100053i	$-0.968099\pi$
$613$	−27.1118	−	27.1118i	−1.09504	−	1.09504i	−0.100053	−	0.994982i	$-0.531901\pi$
$614$	5.44979			0.219936
$615$	11.9671	+	12.9584i	0.482559	+	0.522534i
$616$	−6.30293			−0.253952
$617$	18.2218	+	18.2218i	0.733582	+	0.733582i	0.971328	−	0.237745i	$-0.0764083\pi$
$617$	18.2218	+	18.2218i	0.733582	+	0.733582i	−0.237745	+	0.971328i	$0.576408\pi$
$618$	−8.86960	−	5.65782i	−0.356788	−	0.227591i
$619$		−	15.1105i		−	0.607341i	−0.952777	−	0.303670i	$-0.901788\pi$
$619$		−	15.1105i		−	0.607341i	0.952777	−	0.303670i	$-0.0982121\pi$
$620$	−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
$627$	−1.67844	+	2.63125i	−0.0670306	+	0.105082i
$628$	−8.22730	−	8.22730i	−0.328305	−	0.328305i
$629$	−3.09579			−0.123437
$630$	−1.18666	−	6.60241i	−0.0472778	−	0.263046i
$631$	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
$633$	−0.713904	+	1.11917i	−0.0283751	+	0.0444829i
$634$			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	$-0.142718\pi$
$642$	14.6936	+	9.37289i	0.579910	+	0.369919i
$643$	−29.9588	−	29.9588i	−1.18146	−	1.18146i	−0.979367	−	0.202091i	$-0.935226\pi$
$643$	−29.9588	−	29.9588i	−1.18146	−	1.18146i	−0.202091	−	0.979367i	$-0.564774\pi$
$644$	6.02497			0.237417
$645$	−11.3373	−	0.450904i	−0.446407	−	0.0177543i
$646$	−1.96892			−0.0774660
$647$	−20.4792	−	20.4792i	−0.805120	−	0.805120i	0.178771	−	0.983891i	$-0.442788\pi$
$647$	−20.4792	−	20.4792i	−0.805120	−	0.805120i	−0.983891	+	0.178771i	$0.942788\pi$
$648$	−0.763518	−	8.96755i	−0.0299938	−	0.352279i
$649$		−	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	$-0.898687\pi$
$653$	−16.2736	+	16.2736i	−0.636835	+	0.636835i	0.312939	+	0.949773i	$0.398687\pi$
$654$	1.54389	+	6.98327i	0.0603708	+	0.273068i
$655$	−1.14021	+	4.33259i	−0.0445516	+	0.169288i
$656$			4.55435i			0.177817i
$657$	−5.37304	+	14.7090i	−0.209622	+	0.573852i
$658$	−6.69331	−	6.69331i	−0.260932	−	0.260932i
$659$	−43.5045			−1.69469			−0.847347	−	0.531040i	$-0.821801\pi$
$659$	−43.5045			−1.69469			−0.847347	+	0.531040i	$0.821801\pi$
$660$	17.9336	−	16.5617i	0.698066	−	0.644663i
$661$	−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
$663$	−13.9030	−	8.86855i	−0.539946	−	0.344426i
$664$		−	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
$672$	0.931481	−	1.46025i	0.0359326	−	0.0563305i
$673$	17.9013	+	17.9013i	0.690044	+	0.690044i	0.962241	−	0.272198i	$-0.0877504\pi$
$673$	17.9013	+	17.9013i	0.690044	+	0.690044i	−0.272198	+	0.962241i	$0.587750\pi$
$674$	−13.7129			−0.528200
$675$	20.7250	+	15.6676i	0.797705	+	0.603047i
$676$	11.0889			0.426496
$677$	21.4226	+	21.4226i	0.823337	+	0.823337i	0.986585	−	0.163248i	$-0.0521971\pi$
$677$	21.4226	+	21.4226i	0.823337	+	0.823337i	−0.163248	+	0.986585i	$0.552197\pi$
$678$	10.8073	−	16.9423i	0.415051	−	0.650663i
$679$		−	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	$-0.899250\pi$
$683$	−16.7015	+	16.7015i	−0.639067	+	0.639067i	0.311258	+	0.950325i	$0.399250\pi$
$684$	−0.361554	−	0.777719i	−0.0138244	−	0.0297368i
$685$	11.4403	+	19.6125i	0.437113	+	0.749355i
$686$		−	1.00000i		−	0.0381802i
$687$	−11.3757	−	7.25642i	−0.434009	−	0.276850i
$688$	−2.07154	−	2.07154i	−0.0789767	−	0.0789767i
$689$	−6.10953			−0.232754
$690$	−17.1428	+	15.8313i	−0.652614	+	0.602688i
$691$	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
$693$	6.48788	−	17.7609i	0.246454	−	0.674682i
$694$			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	$0.909927\pi$
$702$	0.950046	−	7.12019i	0.0358572	−	0.268734i
$703$	−0.0908679	−	0.0908679i	−0.00342715	−	0.00342715i
$704$	6.30293			0.237551
$705$	36.6318	+	1.45691i	1.37963	+	0.0548704i
$706$	4.59340			0.172875
$707$	−1.11683	−	1.11683i	−0.0420029	−	0.0420029i
$708$	19.0759	+	12.1683i	0.716915	+	0.457313i
$709$		−	30.1615i		−	1.13274i	−0.824152	−	0.566369i	$-0.808348\pi$
$709$		−	30.1615i		−	1.13274i	0.824152	−	0.566369i	$-0.191652\pi$
$710$	−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
$717$	24.1681	−	37.8876i	0.902573	−	1.41494i
$718$	7.40585	+	7.40585i	0.276384	+	0.276384i
$719$	−0.144200			−0.00537777			−0.00268888	−	0.999996i	$-0.500856\pi$
$719$	−0.144200			−0.00537777			−0.00268888	+	0.999996i	$0.500856\pi$
$720$	1.18666	+	6.60241i	0.0442243	+	0.246057i
$721$	6.07401			0.226208
$722$	13.3772	+	13.3772i	0.497849	+	0.497849i
$723$	−3.12841	+	4.90432i	−0.116347	+	0.182394i
$724$		−	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	−0.183900	−	0.982945i	$-0.558872\pi$
$727$	21.5446	−	21.5446i	0.799045	−	0.799045i	0.982945	+	0.183900i	$0.0588723\pi$
$728$	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
$732$	−1.59481	−	1.01731i	−0.0589460	−	0.0376010i
$733$	37.1546	+	37.1546i	1.37233	+	1.37233i	0.856972	+	0.515362i	$0.172343\pi$
$733$	37.1546	+	37.1546i	1.37233	+	1.37233i	0.515362	+	0.856972i	$0.327657\pi$
$734$	2.04510			0.0754862
$735$	2.62762	+	2.84528i	0.0969211	+	0.104950i
$736$	−6.02497			−0.222083
$737$	−35.5218	−	35.5218i	−1.30846	−	1.30846i
$738$	−12.8336	−	4.68799i	−0.472412	−	0.172567i
$739$		−	14.3549i		−	0.528053i	−0.964515	−	0.264027i	$-0.914949\pi$
$739$		−	14.3549i		−	0.528053i	0.964515	−	0.264027i	$-0.0850507\pi$
$740$	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	$-0.821228\pi$
$743$	−8.55425	+	8.55425i	−0.313825	+	0.313825i	0.532564	+	0.846389i	$0.321228\pi$
$744$	−2.48582	−	11.2438i	−0.0911345	−	0.412217i
$745$	10.5561	+	2.77805i	0.386747	+	0.101780i
$746$		−	23.6597i		−	0.866242i
$747$	6.09683	+	2.22711i	0.223071	+	0.0814856i
$748$	30.6948	+	30.6948i	1.12231	+	1.12231i
$749$	−10.0624			−0.367671
$750$	−16.4642	−	10.1947i	−0.601186	−	0.372257i
$751$	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
$753$	26.9768	+	17.2082i	0.983088	+	0.627101i
$754$		−	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	−0.976226	−	0.216755i	$-0.930453\pi$
$757$	−20.8958	+	20.8958i	−0.759471	+	0.759471i	0.216755	+	0.976226i	$0.430453\pi$
$758$	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	$-0.258395\pi$
$762$	8.44975	−	13.2464i	0.306102	−	0.479868i
$763$	−2.91975	−	2.91975i	−0.105702	−	0.105702i
$764$	−16.4695			−0.595845
$765$	−26.3743	+	37.9322i	−0.953564	+	1.37144i
$766$	24.9033			0.899792
$767$	12.7697	+	12.7697i	0.461089	+	0.461089i
$768$	−0.931481	+	1.46025i	−0.0336119	+	0.0526924i
$769$		−	42.4533i		−	1.53090i	−0.643493	−	0.765452i	$-0.722515\pi$
$769$		−	42.4533i		−	1.53090i	0.643493	−	0.765452i	$-0.277485\pi$
$770$	−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	$-0.608586\pi$
$773$	16.8991	−	16.8991i	0.607820	−	0.607820i	0.942376	+	0.334556i	$0.108586\pi$
$774$	7.96967	−	3.70503i	0.286464	−	0.133174i
$775$	28.9355	+	16.3632i	1.03939	+	0.587782i
$776$			2.13492i			0.0766392i
$777$	0.656392	+	0.418706i	0.0235479	+	0.0150210i
$778$	−4.17634	−	4.17634i	−0.149729	−	0.149729i
$779$	−1.30202			−0.0466496
$780$	−0.212774	+	5.34988i	−0.00761852	+	0.191556i
$781$	−34.2132			−1.22424
$782$	−29.3412	−	29.3412i	−1.04924	−	1.04924i
$783$	19.7832	+	2.63967i	0.706994	+	0.0943341i
$784$			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	−0.548076	−	0.836429i	$-0.684640\pi$
$787$	8.08931	−	8.08931i	0.288353	−	0.288353i	0.836429	+	0.548076i	$0.184640\pi$
$788$	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
$792$	−6.48788	+	17.7609i	−0.230537	+	0.631107i
$793$	−1.06760	−	1.06760i	−0.0379115	−	0.0379115i
$794$	−25.2586			−0.896395
$795$	−0.680209	+	17.1029i	−0.0241245	+	0.606576i
$796$	−11.1512			−0.395243
$797$	3.04716	+	3.04716i	0.107936	+	0.107936i	0.759012	−	0.651076i	$-0.225682\pi$
$797$	3.04716	+	3.04716i	0.107936	+	0.107936i	−0.651076	+	0.759012i	$0.725682\pi$
$798$	0.417464	+	0.266296i	0.0147781	+	0.00942677i
$799$			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
$807$	−8.60085	+	13.4833i	−0.302764	+	0.474635i
$808$	1.11683	+	1.11683i	0.0392901	+	0.0392901i
$809$	−10.4944			−0.368962			−0.184481	−	0.982836i	$-0.559060\pi$
$809$	−10.4944			−0.368962			−0.184481	+	0.982836i	$0.559060\pi$
$810$	−19.8263	−	3.45227i	−0.696625	−	0.121300i
$811$	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
$813$	21.6439	−	33.9305i	0.759086	−	1.19000i
$814$			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	$-0.314315\pi$
$822$	−14.8276	−	9.45837i	−0.517172	−	0.329899i
$823$	12.5787	+	12.5787i	0.438466	+	0.438466i	0.891495	−	0.453030i	$-0.149657\pi$
$823$	12.5787	+	12.5787i	0.438466	+	0.438466i	−0.453030	+	0.891495i	$0.649657\pi$
$824$	−6.07401			−0.211598
$825$	−25.6078	−	48.2054i	−0.891550	−	1.67830i
$826$	−13.0634			−0.454533
$827$	0.598351	+	0.598351i	0.0208067	+	0.0208067i	0.717434	−	0.696627i	$-0.245317\pi$
$827$	0.598351	+	0.598351i	0.0208067	+	0.0208067i	−0.696627	+	0.717434i	$0.745317\pi$
$828$	6.20176	−	16.9777i	0.215526	−	0.590015i
$829$			32.5297i			1.12980i	0.825159	+	0.564901i	$0.191086\pi$
$829$			32.5297i			1.12980i	−0.825159	+	0.564901i	$0.808914\pi$
$830$	−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
$837$	34.2424	+	4.56896i	1.18359	+	0.157926i
$838$	−5.90217	−	5.90217i	−0.203887	−	0.203887i
$839$	50.4871			1.74301			0.871505	−	0.490387i	$-0.163145\pi$
$839$	50.4871			1.74301			0.871505	+	0.490387i	$0.163145\pi$
$840$	−2.62762	−	2.84528i	−0.0906614	−	0.0981716i
$841$	−14.2466			−0.491261
$842$	19.1604	+	19.1604i	0.660312	+	0.660312i
$843$	23.3822	+	14.9152i	0.805326	+	0.513708i
$844$			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
$852$	5.05621	−	7.92647i	0.173223	−	0.271556i
$853$	1.16052	+	1.16052i	0.0397356	+	0.0397356i	0.726695	−	0.686960i	$-0.241055\pi$
$853$	1.16052	+	1.16052i	0.0397356	+	0.0397356i	−0.686960	+	0.726695i	$0.741055\pi$
$854$	1.09215			0.0373725
$855$	−1.88753	+	0.339248i	−0.0645520	+	0.0116021i
$856$	10.0624			0.343924
$857$	−24.7253	−	24.7253i	−0.844600	−	0.844600i	0.144853	−	0.989453i	$-0.453729\pi$
$857$	−24.7253	−	24.7253i	−0.844600	−	0.844600i	−0.989453	+	0.144853i	$0.953729\pi$
$858$	−8.11630	+	12.7237i	−0.277086	+	0.434379i
$859$			48.4452i			1.65293i	0.562989	+	0.826464i	$0.309651\pi$
$859$			48.4452i			1.65293i	−0.562989	+	0.826464i	$0.690349\pi$
$860$	−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	−0.0637701	+	0.997965i	$0.520312\pi$
$863$	−31.1904	+	31.1904i	−1.06173	+	1.06173i	−0.997965	+	0.0637701i	$0.979688\pi$
$864$	−3.15601	−	4.12790i	−0.107370	−	0.140434i
$865$	8.61121	−	5.02308i	0.292790	−	0.170790i
$866$			4.30269i			0.146211i
$867$	−44.4389	−	28.3471i	−1.50923	−	0.962718i
$868$	4.70110	+	4.70110i	0.159566	+	0.159566i
$869$	27.6245			0.937098
$870$	−14.8645	−	0.591184i	−0.503952	−	0.0200430i
$871$	11.0182			0.373336
$872$	2.91975	+	2.91975i	0.0988753	+	0.0988753i
$873$	−6.01595	−	2.19756i	−0.203609	−	0.0743763i
$874$		−	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	−0.544710	−	0.838624i	$-0.683360\pi$
$877$	8.70402	−	8.70402i	0.293914	−	0.293914i	0.838624	+	0.544710i	$0.183360\pi$
$878$	−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	$0.998094\pi$
$882$	−2.81788	−	1.02934i	−0.0948830	−	0.0346598i
$883$	8.48174	+	8.48174i	0.285433	+	0.285433i	0.835271	−	0.549838i	$-0.185311\pi$
$883$	8.48174	+	8.48174i	0.285433	+	0.285433i	−0.549838	+	0.835271i	$0.685311\pi$
$884$	−9.52091			−0.320223
$885$	37.1690	−	34.3256i	1.24942	−	1.15384i
$886$	−1.77441			−0.0596125
$887$	−2.65437	−	2.65437i	−0.0891249	−	0.0891249i	0.661139	−	0.750264i	$-0.270073\pi$
$887$	−2.65437	−	2.65437i	−0.0891249	−	0.0891249i	−0.750264	+	0.661139i	$0.770073\pi$
$888$	−0.656392	−	0.418706i	−0.0220271	−	0.0140508i
$889$			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
$897$	7.75837	−	12.1626i	0.259044	−	0.406096i
$898$	26.0581	+	26.0581i	0.869571	+	0.869571i
$899$	25.5365			0.851688
$900$	14.9526	+	1.19127i	0.498421	+	0.0397089i
$901$	−30.4371			−1.01401
$902$	20.2980	+	20.2980i	0.675851	+	0.675851i
$903$	−2.72886	+	4.27796i	−0.0908109	+	0.142362i
$904$		−	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	−0.967757	−	0.251887i	$-0.918949\pi$
$907$	−21.5594	+	21.5594i	−0.715870	+	0.715870i	0.251887	+	0.967757i	$0.418949\pi$
$908$	−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	$0.900022\pi$
$912$	−0.417464	−	0.266296i	−0.0138236	−	0.00881793i
$913$	−9.64293	−	9.64293i	−0.319134	−	0.319134i
$914$	−24.6548			−0.815509
$915$	−3.10747	+	2.86975i	−0.102730	+	0.0948708i
$916$	−7.79020			−0.257396
$917$	1.41674	+	1.41674i	0.0467848	+	0.0467848i
$918$	4.73304	−	35.4721i	0.156214	−	1.17075i
$919$			6.56474i			0.216551i	0.994121	+	0.108275i	$0.0345329\pi$
$919$			6.56474i			0.216551i	−0.994121	+	0.108275i	$0.965467\pi$
$920$	−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
$927$	6.25224	−	17.1158i	0.205350	−	0.562158i
$928$	−2.71601	−	2.71601i	−0.0891574	−	0.0891574i
$929$	−9.96590			−0.326971			−0.163485	−	0.986546i	$-0.552274\pi$
$929$	−9.96590			−0.326971			−0.163485	+	0.986546i	$0.552274\pi$
$930$	−25.7286	−	1.02327i	−0.843675	−	0.0335544i
$931$	−0.285884			−0.00936948
$932$	5.53555	+	5.53555i	0.181323	+	0.181323i
$933$	−41.2163	−	26.2914i	−1.34936	−	0.860743i
$934$			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	−0.964916	−	0.262559i	$-0.915434\pi$
$937$	−21.4995	+	21.4995i	−0.702357	+	0.702357i	0.262559	+	0.964916i	$0.415434\pi$
$938$	−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	$0.562314\pi$
$942$	10.8379	−	16.9903i	0.353119	−	0.553574i
$943$	−19.4029	−	19.4029i	−0.631845	−	0.631845i
$944$	13.0634			0.425177
$945$	10.7224	−	4.47554i	0.348799	−	0.145589i
$946$	−18.4651			−0.600351
$947$	31.0571	+	31.0571i	1.00922	+	1.00922i	0.999957	+	0.00926262i	$0.00294843\pi$
$947$	31.0571	+	31.0571i	1.00922	+	1.00922i	0.00926262	+	0.999957i	$0.497052\pi$
$948$	−4.08250	+	6.40001i	−0.132593	+	0.207863i
$949$			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	$-0.713281\pi$
$953$	5.02499	−	5.02499i	0.162775	−	0.162775i	0.783795	+	0.621020i	$0.213281\pi$
$954$	−5.58920	−	12.0226i	−0.180957	−	0.389246i
$955$	−9.37258	+	35.6142i	−0.303289	+	1.15245i
$956$		−	25.9459i		−	0.839149i
$957$	−35.3523	−	22.5509i	−1.14278	−	0.728966i
$958$	5.36537	+	5.36537i	0.173347	+	0.173347i
$959$	10.1541			0.327894
$960$	2.62762	+	2.84528i	0.0848059	+	0.0918311i
$961$	13.2006			0.425826
$962$	−0.439401	−	0.439401i	−0.0141669	−	0.0141669i
$963$	−10.3576	+	28.3545i	−0.333769	+	0.913712i
$964$			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	0.583679	−	0.811984i	$-0.301612\pi$
$967$	43.4004	−	43.4004i	1.39566	−	1.39566i	0.811984	−	0.583679i	$-0.198388\pi$
$968$	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	$0.902685\pi$
$972$	14.8806	−	4.64424i	0.477294	−	0.148964i
$973$	5.60320	+	5.60320i	0.179630	+	0.179630i
$974$	3.87783			0.124254
$975$	11.4477	+	3.50466i	0.366620	+	0.112239i
$976$	−1.09215			−0.0349588
$977$	1.97273	+	1.97273i	0.0631133	+	0.0631133i	0.737959	−	0.674846i	$-0.235790\pi$
$977$	1.97273	+	1.97273i	0.0631133	+	0.0631133i	−0.674846	+	0.737959i	$0.735790\pi$
$978$	28.3995	+	18.1158i	0.908117	+	0.579278i
$979$			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	$-0.943953\pi$
$983$	−25.3760	+	25.3760i	−0.809369	+	0.809369i	0.175169	+	0.984538i	$0.443953\pi$
$984$	−7.70237	+	1.70287i	−0.245543	+	0.0542855i
$985$	−18.6537	−	31.9785i	−0.594356	−	1.01892i
$986$		−	26.4535i		−	0.842452i
$987$	8.81718	−	13.8224i	0.280654	−	0.439973i
$988$	−0.279458	−	0.279458i	−0.00889075	−	0.00889075i
$989$	17.6508			0.561261
$990$	34.7147	+	24.1372i	1.10331	+	0.767129i
$991$	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
$993$	−22.2142	+	34.8245i	−0.704945	+	1.10512i
$994$			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	−0.751009	−	0.660292i	$-0.770432\pi$
$997$	−2.86440	+	2.86440i	−0.0907166	+	0.0907166i	0.660292	+	0.751009i	$0.270432\pi$
$998$	−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.b.113.4	yes	12
3.2	odd	2		210.2.j.a.113.3	✓	12
5.2	odd	4		210.2.j.a.197.3	yes	12
5.3	odd	4		1050.2.j.c.407.4		12
5.4	even	2		1050.2.j.d.743.3		12
15.2	even	4	inner	210.2.j.b.197.4	yes	12
15.8	even	4		1050.2.j.d.407.3		12
15.14	odd	2		1050.2.j.c.743.4		12

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

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.931481 + 1.46025i) q^{3} +1.00000i q^{4} +(2.16244 + 0.569088i) q^{5} +(-1.69121 + 0.373900i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.26469 - 2.72040i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.931481 + 1.46025i) 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} +(-1.46025 - 0.931481i) q^{12} +(-0.977522 - 0.977522i) q^{13} +1.00000 q^{14} +(-2.84528 + 2.62762i) q^{15} -1.00000 q^{16} +(-4.86992 - 4.86992i) q^{17} +(1.02934 - 2.81788i) 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} +(5.15051 + 0.687232i) q^{27} +(0.707107 + 0.707107i) q^{28} +3.84102 q^{29} +(-3.86992 - 0.153913i) q^{30} +6.64835 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-9.20389 - 5.87106i) 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} +(-0.931481 + 1.46025i) q^{42} +(2.07154 + 2.07154i) q^{43} -6.30293 q^{44} +(-1.18666 - 6.60241i) q^{45} +6.02497 q^{46} +(-6.69331 - 6.69331i) q^{47} +(0.931481 - 1.46025i) 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} +(0.417464 + 0.266296i) q^{57} +(2.71601 + 2.71601i) q^{58} -13.0634 q^{59} +(-2.62762 - 2.84528i) q^{60} +1.09215 q^{61} +(4.70110 + 4.70110i) q^{62} +(-2.81788 - 1.02934i) 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} +(2.81788 + 1.02934i) q^{72} +(-3.69101 - 3.69101i) q^{73} +0.449505 q^{74} +(-7.64809 + 4.06284i) q^{75} +0.285884 q^{76} +(4.45685 + 4.45685i) q^{77} +(2.01869 + 1.28770i) 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} +(-3.57783 + 5.60887i) q^{87} +(-4.45685 - 4.45685i) q^{88} +8.96370 q^{89} +(3.82951 - 5.50771i) q^{90} -1.38242 q^{91} +(4.26030 + 4.26030i) q^{92} +(-6.19281 + 9.70829i) 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	\( 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * 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 - 48 * 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 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

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