LMFDB - Embedded newform 507.2.k.i.188.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	507.188
Dual form			507.2.k.i.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.12132 - 2.12132i) q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.12132 - 2.12132i) q^{8} +(2.94949 - 0.548188i) q^{9} +(1.73205 + 1.00000i) q^{10} +(-1.03528 - 3.86370i) q^{11} +(-1.41421 + 1.00000i) q^{12} -1.41421i q^{14} +(-2.66390 - 2.21441i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.70711 + 1.29289i) q^{18} +(1.36603 + 0.366025i) q^{19} +(1.93185 + 0.517638i) q^{20} +(-0.414214 + 2.41421i) q^{21} +(2.00000 + 3.46410i) q^{22} +(4.24264 - 7.34847i) q^{23} +(3.32162 - 3.99585i) q^{24} -1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(-0.366025 - 1.36603i) q^{28} +(-2.44949 - 1.41421i) q^{29} +(3.14626 + 1.44949i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-1.29410 + 4.82963i) q^{32} +(-2.39960 - 6.49938i) q^{33} +(2.44949 - 1.41421i) q^{35} +(-2.28024 + 1.94949i) q^{36} +(1.36603 - 0.366025i) q^{37} -1.41421 q^{38} -6.00000 q^{40} +(1.93185 - 0.517638i) q^{41} +(-0.224745 - 2.43916i) q^{42} +(-5.19615 + 3.00000i) q^{43} +(2.82843 + 2.82843i) q^{44} +(-4.94646 - 3.39595i) q^{45} +(-2.19615 + 8.19615i) q^{46} +(-2.82843 + 2.82843i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(4.33013 + 2.50000i) q^{49} +(0.258819 + 0.965926i) q^{50} -5.65685i q^{53} +(-4.46360 + 2.66012i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(2.12132 + 3.67423i) q^{56} +(2.41421 + 0.414214i) q^{57} +(2.73205 + 0.732051i) q^{58} +(3.86370 + 1.03528i) q^{59} +(3.41421 + 0.585786i) q^{60} +(-4.00000 - 6.92820i) q^{61} +(-3.53553 + 6.12372i) q^{62} +(-0.330749 + 4.22973i) q^{63} -7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(1.83013 + 6.83013i) q^{67} +(6.14966 - 13.3485i) q^{69} +(-2.00000 + 2.00000i) q^{70} +(1.03528 - 3.86370i) q^{71} +(5.09393 - 7.41970i) q^{72} +(-1.00000 - 1.00000i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(-0.158919 - 1.72474i) q^{75} +(-1.36603 + 0.366025i) q^{76} +5.65685 q^{77} -10.0000 q^{79} +(1.93185 - 0.517638i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-1.73205 + 1.00000i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(-0.848387 - 2.29788i) q^{84} +(4.24264 - 4.24264i) q^{86} +(-4.44949 - 2.04989i) q^{87} +(-10.3923 - 6.00000i) q^{88} +(3.62347 + 13.5230i) q^{89} +(5.65685 + 2.00000i) q^{90} +8.48528i q^{92} +(7.82913 - 9.41832i) q^{93} +(2.00000 - 3.46410i) q^{94} +(-1.41421 - 2.44949i) q^{95} +(-1.46447 + 8.53553i) q^{96} +(9.56218 + 2.56218i) q^{97} +(-4.82963 - 1.29410i) q^{98} +(-5.17157 - 10.8284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 16 q^{22} + 12 q^{24} + 40 q^{27} + 4 q^{28} + 40 q^{31} - 16 q^{33} + 4 q^{37} - 48 q^{40} + 8 q^{42} - 16 q^{45} + 24 q^{46} + 4 q^{48} - 4 q^{54} - 32 q^{55} + 8 q^{57} + 8 q^{58} + 16 q^{60} - 32 q^{61} - 4 q^{63} + 32 q^{66} - 20 q^{67} - 16 q^{70} - 24 q^{72} - 8 q^{73} - 4 q^{76} - 80 q^{79} + 28 q^{81} - 4 q^{84} - 16 q^{87} + 20 q^{93} + 16 q^{94} - 40 q^{96} + 28 q^{97} - 64 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9 + 8 * q^15 - 4 * q^16 - 16 * q^18 + 4 * q^19 + 8 * q^21 + 16 * q^22 + 12 * q^24 + 40 * q^27 + 4 * q^28 + 40 * q^31 - 16 * q^33 + 4 * q^37 - 48 * q^40 + 8 * q^42 - 16 * q^45 + 24 * q^46 + 4 * q^48 - 4 * q^54 - 32 * q^55 + 8 * q^57 + 8 * q^58 + 16 * q^60 - 32 * q^61 - 4 * q^63 + 32 * q^66 - 20 * q^67 - 16 * q^70 - 24 * q^72 - 8 * q^73 - 4 * q^76 - 80 * q^79 + 28 * q^81 - 4 * q^84 - 16 * q^87 + 20 * q^93 + 16 * q^94 - 40 * q^96 + 28 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i	−0.583609	−	0.812035i	$-0.698360\pi$
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i	−0.0994033	+	0.995047i	$0.531693\pi$
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	0.316228	−	0.948683i	$-0.397584\pi$
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$	−1.62484	+	0.599900i	−0.663340	+	0.244908i
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	0.861617	+	0.507559i	$0.169452\pi$
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	−0.999962	+	0.00875026i	$0.997215\pi$
$8$	2.12132	−	2.12132i	0.750000	−	0.750000i
$9$	2.94949	−	0.548188i	0.983163	−	0.182729i
$10$	1.73205	+	1.00000i	0.547723	+	0.316228i
$11$	−1.03528	−	3.86370i	−0.312148	−	1.16495i	−0.926616	−	0.376009i	$-0.877296\pi$
$11$	−1.03528	−	3.86370i	−0.312148	−	1.16495i	0.614468	−	0.788941i	$-0.289370\pi$
$12$	−1.41421	+	1.00000i	−0.408248	+	0.288675i
$13$		0			0
$13$		0			0
$14$		−	1.41421i		−	0.377964i
$15$	−2.66390	−	2.21441i	−0.687817	−	0.571759i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$	1.36603	+	0.366025i	0.313388	+	0.0839720i	0.412085	−	0.911146i	$-0.364801\pi$
$19$	1.36603	+	0.366025i	0.313388	+	0.0839720i	−0.0986970	+	0.995118i	$0.531467\pi$
$20$	1.93185	+	0.517638i	0.431975	+	0.115747i
$21$	−0.414214	+	2.41421i	−0.0903888	+	0.526825i
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$	4.24264	−	7.34847i	0.884652	−	1.53226i	0.0385394	−	0.999257i	$-0.487729\pi$
$23$	4.24264	−	7.34847i	0.884652	−	1.53226i	0.846112	−	0.533005i	$-0.178937\pi$
$24$	3.32162	−	3.99585i	0.678023	−	0.815650i
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	−0.366025	−	1.36603i	−0.0691723	−	0.258155i
$29$	−2.44949	−	1.41421i	−0.454859	−	0.262613i	0.255021	−	0.966935i	$-0.417918\pi$
$29$	−2.44949	−	1.41421i	−0.454859	−	0.262613i	−0.709880	+	0.704323i	$0.751251\pi$
$30$	3.14626	+	1.44949i	0.574427	+	0.264639i
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	−0.0972349	−	0.995261i	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$	−1.29410	+	4.82963i	−0.228766	+	0.853766i
$33$	−2.39960	−	6.49938i	−0.417717	−	1.13140i
$34$		0			0
$35$	2.44949	−	1.41421i	0.414039	−	0.239046i
$36$	−2.28024	+	1.94949i	−0.380040	+	0.324915i
$37$	1.36603	−	0.366025i	0.224573	−	0.0601742i	−0.144778	−	0.989464i	$-0.546247\pi$
$37$	1.36603	−	0.366025i	0.224573	−	0.0601742i	0.369351	+	0.929290i	$0.379580\pi$
$38$	−1.41421			−0.229416
$39$		0			0
$40$	−6.00000			−0.948683
$41$	1.93185	−	0.517638i	0.301705	−	0.0808415i	−0.104791	−	0.994494i	$-0.533417\pi$
$41$	1.93185	−	0.517638i	0.301705	−	0.0808415i	0.406496	+	0.913653i	$0.366751\pi$
$42$	−0.224745	−	2.43916i	−0.0346789	−	0.376370i
$43$	−5.19615	+	3.00000i	−0.792406	+	0.457496i	−0.840809	−	0.541332i	$-0.817920\pi$
$43$	−5.19615	+	3.00000i	−0.792406	+	0.457496i	0.0484030	+	0.998828i	$0.484587\pi$
$44$	2.82843	+	2.82843i	0.426401	+	0.426401i
$45$	−4.94646	−	3.39595i	−0.737375	−	0.506239i
$46$	−2.19615	+	8.19615i	−0.323805	+	1.20846i
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	−0.882632	−	0.470064i	$-0.844231\pi$
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	0.470064	+	0.882632i	$0.344231\pi$
$48$	−0.724745	+	1.57313i	−0.104608	+	0.227062i
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$	0.258819	+	0.965926i	0.0366025	+	0.136603i
$51$		0			0
$52$		0			0
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$	−4.46360	+	2.66012i	−0.607420	+	0.361997i
$55$	−4.00000	+	6.92820i	−0.539360	+	0.934199i
$56$	2.12132	+	3.67423i	0.283473	+	0.490990i
$57$	2.41421	+	0.414214i	0.319770	+	0.0548639i
$58$	2.73205	+	0.732051i	0.358736	+	0.0961230i
$59$	3.86370	+	1.03528i	0.503011	+	0.134781i	0.501397	−	0.865217i	$-0.332820\pi$
$59$	3.86370	+	1.03528i	0.503011	+	0.134781i	0.00161411	+	0.999999i	$0.499486\pi$
$60$	3.41421	+	0.585786i	0.440773	+	0.0756247i
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−3.53553	+	6.12372i	−0.449013	+	0.777714i
$63$	−0.330749	+	4.22973i	−0.0416705	+	0.532896i
$64$		−	7.00000i		−	0.875000i
$65$		0			0
$66$	4.00000	+	5.65685i	0.492366	+	0.696311i
$67$	1.83013	+	6.83013i	0.223586	+	0.834433i	0.982966	+	0.183786i	$0.0588354\pi$
$67$	1.83013	+	6.83013i	0.223586	+	0.834433i	−0.759381	+	0.650647i	$0.774498\pi$
$68$		0			0
$69$	6.14966	−	13.3485i	0.740333	−	1.60697i
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$	1.03528	−	3.86370i	0.122865	−	0.458537i	−0.876890	−	0.480691i	$-0.840386\pi$
$71$	1.03528	−	3.86370i	0.122865	−	0.458537i	0.999755	+	0.0221541i	$0.00705244\pi$
$72$	5.09393	−	7.41970i	0.600325	−	0.874419i
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	−1.22474	+	0.707107i	−0.142374	+	0.0821995i
$75$	−0.158919	−	1.72474i	−0.0183503	−	0.199156i
$76$	−1.36603	+	0.366025i	−0.156694	+	0.0419860i
$77$	5.65685			0.644658
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	1.93185	−	0.517638i	0.215988	−	0.0578737i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	−1.73205	+	1.00000i	−0.191273	+	0.110432i
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$	−0.848387	−	2.29788i	−0.0925666	−	0.250719i
$85$		0			0
$86$	4.24264	−	4.24264i	0.457496	−	0.457496i
$87$	−4.44949	−	2.04989i	−0.477035	−	0.219771i
$88$	−10.3923	−	6.00000i	−1.10782	−	0.639602i
$89$	3.62347	+	13.5230i	0.384087	+	1.43343i	0.839601	+	0.543203i	$0.182789\pi$
$89$	3.62347	+	13.5230i	0.384087	+	1.43343i	−0.455515	+	0.890228i	$0.650545\pi$
$90$	5.65685	+	2.00000i	0.596285	+	0.210819i
$91$		0			0
$92$			8.48528i			0.884652i
$93$	7.82913	−	9.41832i	0.811843	−	0.976634i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$	−1.41421	−	2.44949i	−0.145095	−	0.251312i
$96$	−1.46447	+	8.53553i	−0.149466	+	0.871154i
$97$	9.56218	+	2.56218i	0.970892	+	0.260150i	0.709204	−	0.705003i	$-0.249054\pi$
$97$	9.56218	+	2.56218i	0.970892	+	0.260150i	0.261688	+	0.965153i	$0.415721\pi$
$98$	−4.82963	−	1.29410i	−0.487866	−	0.130723i
$99$	−5.17157	−	10.8284i	−0.519763	−	1.08830i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−4.24264	+	7.34847i	−0.422159	+	0.731200i	−0.996150	−	0.0876610i	$-0.972061\pi$
$101$	−4.24264	+	7.34847i	−0.422159	+	0.731200i	0.573992	+	0.818861i	$0.305394\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		0			0
$105$	4.00000	−	2.82843i	0.390360	−	0.276026i
$106$	1.46410	+	5.46410i	0.142206	+	0.530720i
$107$	4.89898	+	2.82843i	0.473602	+	0.273434i	0.717746	−	0.696305i	$-0.245174\pi$
$107$	4.89898	+	2.82843i	0.473602	+	0.273434i	−0.244144	+	0.969739i	$0.578507\pi$
$108$	−3.62302	+	3.72474i	−0.348625	+	0.358414i
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	−0.753374	−	0.657592i	$-0.771575\pi$
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	0.657592	+	0.753374i	$0.271575\pi$
$110$	2.07055	−	7.72741i	0.197419	−	0.736779i
$111$	2.29788	−	0.848387i	0.218105	−	0.0805254i
$112$	−1.00000	−	1.00000i	−0.0944911	−	0.0944911i
$113$	−12.2474	+	7.07107i	−1.15214	+	0.665190i	−0.949409	−	0.314044i	$-0.898316\pi$
$113$	−12.2474	+	7.07107i	−1.15214	+	0.665190i	−0.202735	+	0.979234i	$0.564983\pi$
$114$	−2.43916	+	0.224745i	−0.228448	+	0.0210493i
$115$	−16.3923	+	4.39230i	−1.52859	+	0.409585i
$116$	2.82843			0.262613
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−10.3485	+	0.953512i	−0.944682	+	0.0870433i
$121$	−4.33013	+	2.50000i	−0.393648	+	0.227273i
$122$	5.65685	+	5.65685i	0.512148	+	0.512148i
$123$	3.24969	−	1.19980i	0.293015	−	0.108182i
$124$	−1.83013	+	6.83013i	−0.164350	+	0.613364i
$125$	−8.48528	+	8.48528i	−0.758947	+	0.758947i
$126$	−0.775255	−	4.17121i	−0.0690652	−	0.371601i
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	−0.776457	−	2.89778i	−0.0686298	−	0.256130i
$129$	−8.48528	+	6.00000i	−0.747087	+	0.528271i
$130$		0			0
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$	5.32780	+	4.42883i	0.463726	+	0.385480i
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$	−3.53553	−	6.12372i	−0.305424	−	0.529009i
$135$	−9.07107	−	5.07107i	−0.780713	−	0.436448i
$136$		0			0
$137$	−13.5230	−	3.62347i	−1.15534	−	0.309574i	−0.370240	−	0.928936i	$-0.620724\pi$
$137$	−13.5230	−	3.62347i	−1.15534	−	0.309574i	−0.785105	+	0.619363i	$0.787391\pi$
$138$	−2.48528	+	14.4853i	−0.211561	+	1.23307i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	−1.41421	+	2.44949i	−0.119523	+	0.207020i
$141$	−4.42883	+	5.32780i	−0.372974	+	0.448682i
$142$			4.00000i			0.335673i
$143$		0			0
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	1.46410	+	5.46410i	0.121587	+	0.453769i
$146$	1.22474	+	0.707107i	0.101361	+	0.0585206i
$147$	7.86566	+	3.62372i	0.648749	+	0.298880i
$148$	−1.00000	+	1.00000i	−0.0821995	+	0.0821995i
$149$	−0.517638	+	1.93185i	−0.0424066	+	0.158263i	−0.983882	−	0.178817i	$-0.942773\pi$
$149$	−0.517638	+	1.93185i	−0.0424066	+	0.158263i	0.941476	+	0.337081i	$0.109440\pi$
$150$	0.599900	+	1.62484i	0.0489817	+	0.132668i
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	0.665246	−	0.746625i	$-0.268327\pi$
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	−0.746625	+	0.665246i	$0.768327\pi$
$152$	3.67423	−	2.12132i	0.298020	−	0.172062i
$153$		0			0
$154$	−5.46410	+	1.46410i	−0.440310	+	0.117981i
$155$	−14.1421			−1.13592
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	9.65926	−	2.58819i	0.768449	−	0.205905i
$159$	−0.898979	−	9.75663i	−0.0712937	−	0.773751i
$160$	8.66025	−	5.00000i	0.684653	−	0.395285i
$161$	8.48528	+	8.48528i	0.668734	+	0.668734i
$162$	−7.27583	+	5.29738i	−0.571644	+	0.416201i
$163$	−0.366025	+	1.36603i	−0.0286693	+	0.106995i	−0.978778	−	0.204924i	$-0.934305\pi$
$163$	−0.366025	+	1.36603i	−0.0286693	+	0.106995i	0.950109	+	0.311919i	$0.100972\pi$
$164$	−1.41421	+	1.41421i	−0.110432	+	0.110432i
$165$	−5.79796	+	12.5851i	−0.451370	+	0.979745i
$166$	6.92820	+	4.00000i	0.537733	+	0.310460i
$167$	−1.03528	−	3.86370i	−0.0801121	−	0.298982i	0.914232	−	0.405192i	$-0.132795\pi$
$167$	−1.03528	−	3.86370i	−0.0801121	−	0.298982i	−0.994344	+	0.106209i	$0.966129\pi$
$168$	4.24264	+	6.00000i	0.327327	+	0.462910i
$169$		0			0
$170$		0			0
$171$	4.22973	+	0.330749i	0.323455	+	0.0252930i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	−4.24264	−	7.34847i	−0.322562	−	0.558694i	0.658454	−	0.752621i	$-0.271211\pi$
$173$	−4.24264	−	7.34847i	−0.322562	−	0.558694i	−0.981016	+	0.193927i	$0.937877\pi$
$174$	4.82843	+	0.828427i	0.366042	+	0.0628029i
$175$	1.36603	+	0.366025i	0.103262	+	0.0276689i
$176$	3.86370	+	1.03528i	0.291238	+	0.0780369i
$177$	6.82843	+	1.17157i	0.513256	+	0.0880608i
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	5.98174	+	0.467750i	0.445853	+	0.0348640i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−8.00000	−	11.3137i	−0.591377	−	0.836333i
$184$	−6.58846	−	24.5885i	−0.485708	−	1.81269i
$185$	−2.44949	−	1.41421i	−0.180090	−	0.103975i
$186$	−5.12472	+	11.1237i	−0.375763	+	0.815631i
$187$		0			0
$188$	1.03528	−	3.86370i	0.0755053	−	0.281790i
$189$	0.101725	+	7.34777i	0.00739938	+	0.534471i
$190$	2.00000	+	2.00000i	0.145095	+	0.145095i
$191$	2.44949	−	1.41421i	0.177239	−	0.102329i	−0.408756	−	0.912644i	$-0.634037\pi$
$191$	2.44949	−	1.41421i	0.177239	−	0.102329i	0.585995	+	0.810315i	$0.300704\pi$
$192$	−1.11243	−	12.0732i	−0.0802827	−	0.871309i
$193$	25.9545	−	6.95448i	1.86824	−	0.500595i	0.868255	−	0.496119i	$-0.165242\pi$
$193$	25.9545	−	6.95448i	1.86824	−	0.500595i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−9.89949			−0.710742
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−21.2504	+	5.69402i	−1.51403	+	0.405682i	−0.917770	−	0.397112i	$-0.870012\pi$
$197$	−21.2504	+	5.69402i	−1.51403	+	0.405682i	−0.596256	+	0.802794i	$0.703346\pi$
$198$	7.79796	+	9.12096i	0.554177	+	0.648198i
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	−2.12132	−	2.12132i	−0.150000	−	0.150000i
$201$	4.24194	+	11.4894i	0.299203	+	0.810399i
$202$	2.19615	−	8.19615i	0.154521	−	0.576679i
$203$	2.82843	−	2.82843i	0.198517	−	0.198517i
$204$		0			0
$205$	−3.46410	−	2.00000i	−0.241943	−	0.139686i
$206$	−1.55291	−	5.79555i	−0.108197	−	0.403795i
$207$	8.48528	−	24.0000i	0.589768	−	1.66812i
$208$		0			0
$209$		−	5.65685i		−	0.391293i
$210$	−3.13165	+	3.76733i	−0.216105	+	0.259970i
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	2.82843	+	4.89898i	0.194257	+	0.336463i
$213$	1.17157	−	6.82843i	0.0802749	−	0.467876i
$214$	−5.46410	−	1.46410i	−0.373518	−	0.100084i
$215$	11.5911	+	3.10583i	0.790507	+	0.211816i
$216$	7.60660	−	13.6066i	0.517564	−	0.925812i
$217$	5.00000	+	8.66025i	0.339422	+	0.587896i
$218$	0.707107	−	1.22474i	0.0478913	−	0.0829502i
$219$	−1.88366	−	1.56583i	−0.127286	−	0.105809i
$220$		−	8.00000i		−	0.539360i
$221$		0			0
$222$	−2.00000	+	1.41421i	−0.134231	+	0.0949158i
$223$	4.02628	+	15.0263i	0.269620	+	1.00623i	0.959362	+	0.282179i	$0.0910572\pi$
$223$	4.02628	+	15.0263i	0.269620	+	1.00623i	−0.689742	+	0.724055i	$0.742276\pi$
$224$	−6.12372	−	3.53553i	−0.409159	−	0.236228i
$225$	−0.548188	−	2.94949i	−0.0365459	−	0.196633i
$226$	10.0000	−	10.0000i	0.665190	−	0.665190i
$227$	−2.07055	+	7.72741i	−0.137427	+	0.512886i	0.862549	+	0.505974i	$0.168867\pi$
$227$	−2.07055	+	7.72741i	−0.137427	+	0.512886i	−0.999976	+	0.00691198i	$0.997800\pi$
$228$	−2.29788	+	0.848387i	−0.152181	+	0.0561858i
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	0.673293	−	0.739375i	$-0.264879\pi$
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	−0.739375	+	0.673293i	$0.764879\pi$
$230$	14.6969	−	8.48528i	0.969087	−	0.559503i
$231$	9.75663	−	0.898979i	0.641939	−	0.0591485i
$232$	−8.19615	+	2.19615i	−0.538104	+	0.144184i
$233$	25.4558			1.66767			0.833834	−	0.552015i	$-0.186141\pi$
$233$	25.4558			1.66767			0.833834	+	0.552015i	$0.186141\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	−3.86370	+	1.03528i	−0.251506	+	0.0673907i
$237$	−17.2474	+	1.58919i	−1.12034	+	0.103229i
$238$		0			0
$239$	−14.1421	−	14.1421i	−0.914779	−	0.914779i	0.0818647	−	0.996643i	$-0.473912\pi$
$239$	−14.1421	−	14.1421i	−0.914779	−	0.914779i	−0.996643	+	0.0818647i	$0.973912\pi$
$240$	3.24969	−	1.19980i	0.209767	−	0.0774468i
$241$	6.22243	−	23.2224i	0.400822	−	1.49589i	−0.410811	−	0.911721i	$-0.634754\pi$
$241$	6.22243	−	23.2224i	0.400822	−	1.49589i	0.811633	−	0.584168i	$-0.198579\pi$
$242$	3.53553	−	3.53553i	0.227273	−	0.227273i
$243$	13.9722	−	6.91215i	0.896317	−	0.443415i
$244$	6.92820	+	4.00000i	0.443533	+	0.256074i
$245$	−2.58819	−	9.65926i	−0.165353	−	0.617107i
$246$	−2.82843	+	2.00000i	−0.180334	+	0.127515i
$247$		0			0
$248$		−	21.2132i		−	1.34704i
$249$	−10.6556	−	8.85765i	−0.675272	−	0.561331i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	12.7279	+	22.0454i	0.803379	+	1.39149i	0.917380	+	0.398013i	$0.130300\pi$
$251$	12.7279	+	22.0454i	0.803379	+	1.39149i	−0.114000	+	0.993481i	$0.536367\pi$
$252$	−1.82843	−	3.82843i	−0.115180	−	0.241168i
$253$	−32.7846	−	8.78461i	−2.06115	−	0.552284i
$254$		0			0
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	4.24264	−	7.34847i	0.264649	−	0.458385i	−0.702823	−	0.711365i	$-0.748077\pi$
$257$	4.24264	−	7.34847i	0.264649	−	0.458385i	0.967472	+	0.252980i	$0.0814107\pi$
$258$	6.64324	−	7.99171i	0.413590	−	0.497542i
$259$			2.00000i			0.124274i
$260$		0			0
$261$	−8.00000	−	2.82843i	−0.495188	−	0.175075i
$262$	−2.92820	−	10.9282i	−0.180905	−	0.675147i
$263$	19.5959	+	11.3137i	1.20834	+	0.697633i	0.962396	−	0.271652i	$-0.0875699\pi$
$263$	19.5959	+	11.3137i	1.20834	+	0.697633i	0.245940	+	0.969285i	$0.420903\pi$
$264$	−18.8776	−	8.69694i	−1.16184	−	0.535260i
$265$	−8.00000	+	8.00000i	−0.491436	+	0.491436i
$266$	0.517638	−	1.93185i	0.0317384	−	0.118449i
$267$	8.39861	+	22.7478i	0.513986	+	1.39214i
$268$	−5.00000	−	5.00000i	−0.305424	−	0.305424i
$269$	17.1464	−	9.89949i	1.04544	−	0.603583i	0.124068	−	0.992274i	$-0.460406\pi$
$269$	17.1464	−	9.89949i	1.04544	−	0.603583i	0.921368	+	0.388691i	$0.127073\pi$
$270$	10.0745	+	2.55051i	0.613113	+	0.155219i
$271$	25.9545	−	6.95448i	1.57662	−	0.422455i	0.638744	−	0.769419i	$-0.279454\pi$
$271$	25.9545	−	6.95448i	1.57662	−	0.422455i	0.937878	+	0.346964i	$0.112788\pi$
$272$		0			0
$273$		0			0
$274$	14.0000			0.845771
$275$	−3.86370	+	1.03528i	−0.232990	+	0.0624295i
$276$	1.34847	+	14.6349i	0.0811683	+	0.880920i
$277$	10.3923	−	6.00000i	0.624413	−	0.360505i	−0.154172	−	0.988044i	$-0.549271\pi$
$277$	10.3923	−	6.00000i	0.624413	−	0.360505i	0.778585	+	0.627539i	$0.215938\pi$
$278$	−2.82843	−	2.82843i	−0.169638	−	0.169638i
$279$	12.0065	−	17.4884i	0.718811	−	1.04700i
$280$	2.19615	−	8.19615i	0.131245	−	0.489814i
$281$	9.89949	−	9.89949i	0.590554	−	0.590554i	−0.347227	−	0.937781i	$-0.612877\pi$
$281$	9.89949	−	9.89949i	0.590554	−	0.590554i	0.937781	+	0.347227i	$0.112877\pi$
$282$	2.89898	−	6.29253i	0.172632	−	0.374715i
$283$	10.3923	+	6.00000i	0.617758	+	0.356663i	0.775996	−	0.630738i	$-0.217248\pi$
$283$	10.3923	+	6.00000i	0.617758	+	0.356663i	−0.158237	+	0.987401i	$0.550581\pi$
$284$	1.03528	+	3.86370i	0.0614323	+	0.229269i
$285$	−2.82843	−	4.00000i	−0.167542	−	0.236940i
$286$		0			0
$287$			2.82843i			0.166957i
$288$	−1.16938	+	14.9543i	−0.0689061	+	0.881193i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−2.82843	−	4.89898i	−0.166091	−	0.287678i
$291$	16.8995	+	2.89949i	0.990666	+	0.169971i
$292$	1.36603	+	0.366025i	0.0799406	+	0.0214200i
$293$	−13.5230	−	3.62347i	−0.790020	−	0.211685i	−0.158822	−	0.987307i	$-0.550770\pi$
$293$	−13.5230	−	3.62347i	−0.790020	−	0.211685i	−0.631198	+	0.775622i	$0.717436\pi$
$294$	−8.53553	−	1.46447i	−0.497802	−	0.0854094i
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$	2.12132	−	3.67423i	0.123299	−	0.213561i
$297$	−10.6405	−	17.8544i	−0.617423	−	1.03602i
$298$		−	2.00000i		−	0.115857i
$299$		0			0
$300$	1.00000	+	1.41421i	0.0577350	+	0.0816497i
$301$	−2.19615	−	8.19615i	−0.126584	−	0.472418i
$302$	1.22474	+	0.707107i	0.0704761	+	0.0406894i
$303$	−6.14966	+	13.3485i	−0.353289	+	0.766850i
$304$	−1.00000	+	1.00000i	−0.0573539	+	0.0573539i
$305$	−4.14110	+	15.4548i	−0.237119	+	0.884940i
$306$		0			0
$307$	17.0000	+	17.0000i	0.970241	+	0.970241i	0.999570	−	0.0293286i	$-0.00933691\pi$
$307$	17.0000	+	17.0000i	0.970241	+	0.970241i	−0.0293286	+	0.999570i	$0.509337\pi$
$308$	−4.89898	+	2.82843i	−0.279145	+	0.161165i
$309$	0.953512	+	10.3485i	0.0542434	+	0.588704i
$310$	13.6603	−	3.66025i	0.775850	−	0.207888i
$311$	−8.48528			−0.481156			−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$		0			0
$313$	8.00000			0.452187			0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000			0.452187			0.226093	+	0.974106i	$0.427405\pi$
$314$	−13.5230	+	3.62347i	−0.763145	+	0.204484i
$315$	6.44949	−	5.51399i	0.363388	−	0.310678i
$316$	8.66025	−	5.00000i	0.487177	−	0.281272i
$317$	7.07107	+	7.07107i	0.397151	+	0.397151i	0.877227	−	0.480076i	$-0.159391\pi$
$317$	7.07107	+	7.07107i	0.397151	+	0.397151i	−0.480076	+	0.877227i	$0.659391\pi$
$318$	3.39355	+	9.19151i	0.190301	+	0.515434i
$319$	−2.92820	+	10.9282i	−0.163948	+	0.611862i
$320$	−9.89949	+	9.89949i	−0.553399	+	0.553399i
$321$	8.89898	+	4.09978i	0.496693	+	0.228827i
$322$	−10.3923	−	6.00000i	−0.579141	−	0.334367i
$323$		0			0
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$		0			0
$326$		−	1.41421i		−	0.0783260i
$327$	−1.56583	+	1.88366i	−0.0865904	+	0.104167i
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	−2.82843	−	4.89898i	−0.155936	−	0.270089i
$330$	2.34315	−	13.6569i	0.128986	−	0.751785i
$331$	9.56218	+	2.56218i	0.525585	+	0.140830i	0.511849	−	0.859076i	$-0.328961\pi$
$331$	9.56218	+	2.56218i	0.525585	+	0.140830i	0.0137361	+	0.999906i	$0.495628\pi$
$332$	7.72741	+	2.07055i	0.424097	+	0.113636i
$333$	3.82843	−	1.82843i	0.209797	−	0.100197i
$334$	2.00000	+	3.46410i	0.109435	+	0.189547i
$335$	7.07107	−	12.2474i	0.386334	−	0.669150i
$336$	−1.88366	−	1.56583i	−0.102762	−	0.0854228i
$337$			6.00000i			0.326841i	0.986557	+	0.163420i	$0.0522527\pi$
$337$			6.00000i			0.326841i	−0.986557	+	0.163420i	$0.947747\pi$
$338$		0			0
$339$	−20.0000	+	14.1421i	−1.08625	+	0.768095i
$340$		0			0
$341$	−24.4949	−	14.1421i	−1.32647	−	0.765840i
$342$	−4.17121	+	0.775255i	−0.225553	+	0.0419210i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−4.65874	+	17.3867i	−0.251183	+	0.937426i
$345$	−27.5745	+	10.1806i	−1.48456	+	0.548108i
$346$	6.00000	+	6.00000i	0.322562	+	0.322562i
$347$	−12.2474	+	7.07107i	−0.657477	+	0.379595i	−0.791315	−	0.611408i	$-0.790603\pi$
$347$	−12.2474	+	7.07107i	−0.657477	+	0.379595i	0.133838	+	0.991003i	$0.457270\pi$
$348$	4.87832	−	0.449490i	0.261505	−	0.0240952i
$349$	−23.2224	+	6.22243i	−1.24307	+	0.333079i	−0.819655	−	0.572857i	$-0.805835\pi$
$349$	−23.2224	+	6.22243i	−1.24307	+	0.333079i	−0.423413	+	0.905937i	$0.639168\pi$
$350$	−1.41421			−0.0755929
$351$		0			0
$352$	20.0000			1.06600
$353$	25.1141	−	6.72930i	1.33669	−	0.358164i	0.481483	−	0.876455i	$-0.340098\pi$
$353$	25.1141	−	6.72930i	1.33669	−	0.358164i	0.855204	+	0.518291i	$0.173432\pi$
$354$	−6.89898	+	0.635674i	−0.366677	+	0.0337857i
$355$	−6.92820	+	4.00000i	−0.367711	+	0.212298i
$356$	−9.89949	−	9.89949i	−0.524672	−	0.524672i
$357$		0			0
$358$		0			0
$359$	−2.82843	+	2.82843i	−0.149279	+	0.149279i	−0.777796	−	0.628517i	$-0.783662\pi$
$359$	−2.82843	+	2.82843i	−0.149279	+	0.149279i	0.628517	+	0.777796i	$0.283662\pi$
$360$	−17.6969	+	3.28913i	−0.932711	+	0.173352i
$361$	−14.7224	−	8.50000i	−0.774865	−	0.447368i
$362$		0			0
$363$	−7.07107	+	5.00000i	−0.371135	+	0.262432i
$364$		0			0
$365$			2.82843i			0.148047i
$366$	10.6556	+	8.85765i	0.556978	+	0.462997i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	4.24264	+	7.34847i	0.221163	+	0.383065i
$369$	5.41421	−	2.58579i	0.281853	−	0.134611i
$370$	2.73205	+	0.732051i	0.142033	+	0.0380575i
$371$	7.72741	+	2.07055i	0.401187	+	0.107498i
$372$	−2.07107	+	12.0711i	−0.107380	+	0.625856i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	−13.2865	+	15.9834i	−0.686111	+	0.825380i
$376$			12.0000i			0.618853i
$377$		0			0
$378$	−2.00000	−	7.07107i	−0.102869	−	0.363696i
$379$	−6.95448	−	25.9545i	−0.357228	−	1.33319i	−0.877658	−	0.479288i	$-0.840895\pi$
$379$	−6.95448	−	25.9545i	−0.357228	−	1.33319i	0.520430	−	0.853904i	$-0.325772\pi$
$380$	2.44949	+	1.41421i	0.125656	+	0.0725476i
$381$		0			0
$382$	−2.00000	+	2.00000i	−0.102329	+	0.102329i
$383$	4.14110	−	15.4548i	0.211601	−	0.789704i	−0.775735	−	0.631059i	$-0.782621\pi$
$383$	4.14110	−	15.4548i	0.211601	−	0.789704i	0.987336	−	0.158645i	$-0.0507126\pi$
$384$	−1.79970	−	4.87453i	−0.0918406	−	0.248752i
$385$	−8.00000	−	8.00000i	−0.407718	−	0.407718i
$386$	−23.2702	+	13.4350i	−1.18442	+	0.683825i
$387$	−13.6814	+	11.6969i	−0.695466	+	0.594589i
$388$	−9.56218	+	2.56218i	−0.485446	+	0.130075i
$389$	−16.9706			−0.860442			−0.430221	−	0.902724i	$-0.641564\pi$
$389$	−16.9706			−0.860442			−0.430221	+	0.902724i	$0.641564\pi$
$390$		0			0
$391$		0			0
$392$	14.4889	−	3.88229i	0.731799	−	0.196085i
$393$	1.79796	+	19.5133i	0.0906950	+	0.984314i
$394$	19.0526	−	11.0000i	0.959854	−	0.554172i
$395$	14.1421	+	14.1421i	0.711568	+	0.711568i
$396$	9.89293	+	6.79191i	0.497138	+	0.341306i
$397$	6.22243	−	23.2224i	0.312295	−	1.16550i	−0.614187	−	0.789161i	$-0.710516\pi$
$397$	6.22243	−	23.2224i	0.312295	−	1.16550i	0.926482	−	0.376340i	$-0.122817\pi$
$398$		0			0
$399$	−1.44949	+	3.14626i	−0.0725653	+	0.157510i
$400$	0.866025	+	0.500000i	0.0433013	+	0.0250000i
$401$	−5.69402	−	21.2504i	−0.284346	−	1.06119i	−0.949316	−	0.314323i	$-0.898223\pi$
$401$	−5.69402	−	21.2504i	−0.284346	−	1.06119i	0.664970	−	0.746870i	$-0.268444\pi$
$402$	−7.07107	−	10.0000i	−0.352673	−	0.498755i
$403$		0			0
$404$		−	8.48528i		−	0.422159i
$405$	−16.4512	−	7.30474i	−0.817465	−	0.362975i
$406$	−2.00000	+	3.46410i	−0.0992583	+	0.171920i
$407$	−2.82843	−	4.89898i	−0.140200	−	0.242833i
$408$		0			0
$409$	−31.4186	−	8.41858i	−1.55355	−	0.416272i	−0.622935	−	0.782274i	$-0.714060\pi$
$409$	−31.4186	−	8.41858i	−1.55355	−	0.416272i	−0.930614	+	0.366002i	$0.880726\pi$
$410$	3.86370	+	1.03528i	0.190815	+	0.0511286i
$411$	−23.8995	−	4.10051i	−1.17888	−	0.202263i
$412$	−3.00000	−	5.19615i	−0.147799	−	0.255996i
$413$	−2.82843	+	4.89898i	−0.139178	+	0.241063i
$414$	−1.98450	+	25.3784i	−0.0975326	+	1.24728i
$415$			16.0000i			0.785409i
$416$		0			0
$417$	4.00000	+	5.65685i	0.195881	+	0.277017i
$418$	1.46410	+	5.46410i	0.0716116	+	0.267258i
$419$	−9.79796	−	5.65685i	−0.478662	−	0.276355i	0.241197	−	0.970476i	$-0.422460\pi$
$419$	−9.79796	−	5.65685i	−0.478662	−	0.276355i	−0.719859	+	0.694121i	$0.755793\pi$
$420$	−2.04989	+	4.44949i	−0.100024	+	0.217113i
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.250242	+	0.968183i	$0.580510\pi$
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.968183	+	0.250242i	$0.919490\pi$
$422$	3.62347	−	13.5230i	0.176388	−	0.658287i
$423$	−6.79191	+	9.89293i	−0.330234	+	0.481011i
$424$	−12.0000	−	12.0000i	−0.582772	−	0.582772i
$425$		0			0
$426$	0.635674	+	6.89898i	0.0307985	+	0.334257i
$427$	10.9282	−	2.92820i	0.528853	−	0.141706i
$428$	−5.65685			−0.273434
$429$		0			0
$430$	−12.0000			−0.578691
$431$	30.9096	−	8.28221i	1.48886	−	0.398940i	0.579511	−	0.814964i	$-0.303244\pi$
$431$	30.9096	−	8.28221i	1.48886	−	0.398940i	0.909353	+	0.416024i	$0.136577\pi$
$432$	−1.27526	+	5.03723i	−0.0613557	+	0.242354i
$433$	−15.5885	+	9.00000i	−0.749133	+	0.432512i	−0.825381	−	0.564577i	$-0.809039\pi$
$433$	−15.5885	+	9.00000i	−0.749133	+	0.432512i	0.0762473	+	0.997089i	$0.475706\pi$
$434$	−7.07107	−	7.07107i	−0.339422	−	0.339422i
$435$	3.39355	+	9.19151i	0.162708	+	0.440699i
$436$	0.366025	−	1.36603i	0.0175294	−	0.0654208i
$437$	8.48528	−	8.48528i	0.405906	−	0.405906i
$438$	2.22474	+	1.02494i	0.106302	+	0.0489737i
$439$	−25.9808	−	15.0000i	−1.23999	−	0.715911i	−0.270901	−	0.962607i	$-0.587322\pi$
$439$	−25.9808	−	15.0000i	−1.23999	−	0.715911i	−0.969093	+	0.246696i	$0.920655\pi$
$440$	6.21166	+	23.1822i	0.296129	+	1.10517i
$441$	14.1421	+	5.00000i	0.673435	+	0.238095i
$442$		0			0
$443$			28.2843i			1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$			28.2843i			1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$	−1.56583	+	1.88366i	−0.0743108	+	0.0893947i
$445$	14.0000	−	24.2487i	0.663664	−	1.14950i
$446$	−7.77817	−	13.4722i	−0.368307	−	0.637927i
$447$	−0.585786	+	3.41421i	−0.0277067	+	0.161487i
$448$	9.56218	+	2.56218i	0.451770	+	0.121052i
$449$	21.2504	+	5.69402i	1.00287	+	0.268717i	0.722646	−	0.691218i	$-0.242926\pi$
$449$	21.2504	+	5.69402i	1.00287	+	0.268717i	0.280221	+	0.959936i	$0.409592\pi$
$450$	1.29289	+	2.70711i	0.0609476	+	0.127614i
$451$	−4.00000	−	6.92820i	−0.188353	−	0.326236i
$452$	7.07107	−	12.2474i	0.332595	−	0.576072i
$453$	−1.88366	−	1.56583i	−0.0885022	−	0.0735689i
$454$		−	8.00000i		−	0.375459i
$455$		0			0
$456$	6.00000	−	4.24264i	0.280976	−	0.198680i
$457$	10.6147	+	39.6147i	0.496536	+	1.85310i	0.521249	+	0.853405i	$0.325466\pi$
$457$	10.6147	+	39.6147i	0.496536	+	1.85310i	−0.0247126	+	0.999695i	$0.507867\pi$
$458$	1.22474	+	0.707107i	0.0572286	+	0.0330409i
$459$		0			0
$460$	12.0000	−	12.0000i	0.559503	−	0.559503i
$461$	2.58819	−	9.65926i	0.120544	−	0.449877i	−0.879098	−	0.476642i	$-0.841854\pi$
$461$	2.58819	−	9.65926i	0.120544	−	0.449877i	0.999642	+	0.0267651i	$0.00852062\pi$
$462$	−9.19151	+	3.39355i	−0.427628	+	0.157882i
$463$	17.0000	+	17.0000i	0.790057	+	0.790057i	0.981503	−	0.191446i	$-0.0613177\pi$
$463$	17.0000	+	17.0000i	0.790057	+	0.790057i	−0.191446	+	0.981503i	$0.561318\pi$
$464$	2.44949	−	1.41421i	0.113715	−	0.0656532i
$465$	−24.3916	+	2.24745i	−1.13113	+	0.104223i
$466$	−24.5885	+	6.58846i	−1.13904	+	0.305204i
$467$	25.4558			1.17796			0.588978	−	0.808149i	$-0.299530\pi$
$467$	25.4558			1.17796			0.588978	+	0.808149i	$0.299530\pi$
$468$		0			0
$469$	−10.0000			−0.461757
$470$	−7.72741	+	2.07055i	−0.356439	+	0.0955075i
$471$	24.1464	−	2.22486i	1.11261	−	0.102516i
$472$	10.3923	−	6.00000i	0.478345	−	0.276172i
$473$	16.9706	+	16.9706i	0.780307	+	0.780307i
$474$	16.2484	−	5.99900i	0.746316	−	0.275543i
$475$	0.366025	−	1.36603i	0.0167944	−	0.0626775i
$476$		0			0
$477$	−3.10102	−	16.6848i	−0.141986	−	0.763946i
$478$	17.3205	+	10.0000i	0.792222	+	0.457389i
$479$	8.28221	+	30.9096i	0.378424	+	1.41230i	0.848277	+	0.529552i	$0.177640\pi$
$479$	8.28221	+	30.9096i	0.378424	+	1.41230i	−0.469853	+	0.882744i	$0.655693\pi$
$480$	14.1421	−	10.0000i	0.645497	−	0.456435i
$481$		0			0
$482$			24.0416i			1.09507i
$483$	15.9834	+	13.2865i	0.727271	+	0.604556i
$484$	2.50000	−	4.33013i	0.113636	−	0.196824i
$485$	−9.89949	−	17.1464i	−0.449513	−	0.778579i
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	25.9545	+	6.95448i	1.17611	+	0.315138i	0.793382	−	0.608724i	$-0.208318\pi$
$487$	25.9545	+	6.95448i	1.17611	+	0.315138i	0.382727	+	0.923861i	$0.374985\pi$
$488$	−23.1822	−	6.21166i	−1.04941	−	0.281189i
$489$	−0.414214	+	2.41421i	−0.0187314	+	0.109175i
$490$	5.00000	+	8.66025i	0.225877	+	0.391230i
$491$	−21.2132	+	36.7423i	−0.957338	+	1.65816i	−0.228415	+	0.973564i	$0.573354\pi$
$491$	−21.2132	+	36.7423i	−0.957338	+	1.65816i	−0.728924	+	0.684595i	$0.759979\pi$
$492$	−2.21441	+	2.66390i	−0.0998334	+	0.120098i
$493$		0			0
$494$		0			0
$495$	−8.00000	+	22.6274i	−0.359573	+	1.01703i
$496$	1.83013	+	6.83013i	0.0821751	+	0.306682i
$497$	4.89898	+	2.82843i	0.219749	+	0.126872i
$498$	12.5851	+	5.79796i	0.563950	+	0.259813i
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$	3.10583	−	11.5911i	0.138897	−	0.518370i
$501$	−2.39960	−	6.49938i	−0.107206	−	0.290371i
$502$	−18.0000	−	18.0000i	−0.803379	−	0.803379i
$503$	−4.89898	+	2.82843i	−0.218435	+	0.126113i	−0.605225	−	0.796054i	$-0.706917\pi$
$503$	−4.89898	+	2.82843i	−0.218435	+	0.126113i	0.386791	+	0.922168i	$0.373584\pi$
$504$	8.27098	+	9.67423i	0.368419	+	0.430925i
$505$	16.3923	−	4.39230i	0.729448	−	0.195455i
$506$	33.9411			1.50887
$507$		0			0
$508$		0			0
$509$	−32.8415	+	8.79985i	−1.45567	+	0.390046i	−0.897993	−	0.440010i	$-0.854975\pi$
$509$	−32.8415	+	8.79985i	−1.45567	+	0.390046i	−0.557680	+	0.830056i	$0.688308\pi$
$510$		0			0
$511$	1.73205	−	1.00000i	0.0766214	−	0.0442374i
$512$	−7.77817	−	7.77817i	−0.343750	−	0.343750i
$513$	7.34777	−	0.101725i	0.324412	−	0.00449125i
$514$	−2.19615	+	8.19615i	−0.0968681	+	0.361517i
$515$	8.48528	−	8.48528i	0.373906	−	0.373906i
$516$	4.34847	−	9.43879i	0.191431	−	0.415520i
$517$	13.8564	+	8.00000i	0.609404	+	0.351840i
$518$	−0.517638	−	1.93185i	−0.0227437	−	0.0848807i
$519$	−8.48528	−	12.0000i	−0.372463	−	0.526742i
$520$		0			0
$521$		−	31.1127i		−	1.36307i	−0.731785	−	0.681536i	$-0.761312\pi$
$521$		−	31.1127i		−	1.36307i	0.731785	−	0.681536i	$-0.238688\pi$
$522$	8.45946	+	0.661498i	0.370260	+	0.0289530i
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−5.65685	−	9.79796i	−0.247121	−	0.428026i
$525$	2.41421	+	0.414214i	0.105365	+	0.0180778i
$526$	−21.8564	−	5.85641i	−0.952985	−	0.255351i
$527$		0			0
$528$	6.82843	+	1.17157i	0.297169	+	0.0509862i
$529$	−24.5000	−	42.4352i	−1.06522	−	1.84501i
$530$	5.65685	−	9.79796i	0.245718	−	0.425596i
$531$	11.9635	+	0.935500i	0.519171	+	0.0405972i
$532$		−	2.00000i		−	0.0867110i
$533$		0			0
$534$	−14.0000	−	19.7990i	−0.605839	−	0.856786i
$535$	−2.92820	−	10.9282i	−0.126597	−	0.472467i
$536$	18.3712	+	10.6066i	0.793514	+	0.458135i
$537$		0			0
$538$	−14.0000	+	14.0000i	−0.603583	+	0.603583i
$539$	5.17638	−	19.3185i	0.222963	−	0.832107i
$540$	10.3913	−	0.143860i	0.447171	−	0.00619076i
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	0.685283	−	0.728277i	$-0.259678\pi$
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	−0.728277	+	0.685283i	$0.759678\pi$
$542$	−23.2702	+	13.4350i	−0.999539	+	0.577084i
$543$		0			0
$544$		0			0
$545$	2.82843			0.121157
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	13.5230	−	3.62347i	0.577672	−	0.154787i
$549$	−15.5959	−	18.2419i	−0.665618	−	0.778546i
$550$	3.46410	−	2.00000i	0.147710	−	0.0852803i
$551$	−2.82843	−	2.82843i	−0.120495	−	0.120495i
$552$	−15.2710	−	41.3618i	−0.649976	−	1.76047i
$553$	3.66025	−	13.6603i	0.155650	−	0.580893i
$554$	−8.48528	+	8.48528i	−0.360505	+	0.360505i
$555$	−4.44949	−	2.04989i	−0.188870	−	0.0870129i
$556$	−3.46410	−	2.00000i	−0.146911	−	0.0848189i
$557$	3.62347	+	13.5230i	0.153531	+	0.572986i	0.999227	+	0.0393204i	$0.0125193\pi$
$557$	3.62347	+	13.5230i	0.153531	+	0.572986i	−0.845695	+	0.533666i	$0.820814\pi$
$558$	−7.07107	+	20.0000i	−0.299342	+	0.846668i
$559$		0			0
$560$			2.82843i			0.119523i
$561$		0			0
$562$	−7.00000	+	12.1244i	−0.295277	+	0.511435i
$563$	16.9706	+	29.3939i	0.715224	+	1.23880i	0.962873	+	0.269954i	$0.0870086\pi$
$563$	16.9706	+	29.3939i	0.715224	+	1.23880i	−0.247649	+	0.968850i	$0.579658\pi$
$564$	1.17157	−	6.82843i	0.0493321	−	0.287529i
$565$	27.3205	+	7.32051i	1.14938	+	0.307976i
$566$	−11.5911	−	3.10583i	−0.487211	−	0.130548i
$567$	1.34315	+	12.6569i	0.0564068	+	0.531538i
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	−4.24264	+	7.34847i	−0.177861	+	0.308064i	−0.941148	−	0.337996i	$-0.890251\pi$
$569$	−4.24264	+	7.34847i	−0.177861	+	0.308064i	0.763287	+	0.646060i	$0.223584\pi$
$570$	3.76733	+	3.13165i	0.157796	+	0.131170i
$571$		−	12.0000i		−	0.502184i	−0.967963	−	0.251092i	$-0.919210\pi$
$571$		−	12.0000i		−	0.502184i	0.967963	−	0.251092i	$-0.0807897\pi$
$572$		0			0
$573$	4.00000	−	2.82843i	0.167102	−	0.118159i
$574$	−0.732051	−	2.73205i	−0.0305552	−	0.114034i
$575$	−7.34847	−	4.24264i	−0.306452	−	0.176930i
$576$	−3.83732	−	20.6464i	−0.159888	−	0.860268i
$577$	−1.00000	+	1.00000i	−0.0416305	+	0.0416305i	−0.727616	−	0.685985i	$-0.759372\pi$
$577$	−1.00000	+	1.00000i	−0.0416305	+	0.0416305i	0.685985	+	0.727616i	$0.259372\pi$
$578$	−4.39992	+	16.4207i	−0.183013	+	0.683013i
$579$	43.6597	−	16.1194i	1.81443	−	0.669898i
$580$	−4.00000	−	4.00000i	−0.166091	−	0.166091i
$581$	9.79796	−	5.65685i	0.406488	−	0.234686i
$582$	−17.0741	+	1.57321i	−0.707744	+	0.0652118i
$583$	−21.8564	+	5.85641i	−0.905200	+	0.242548i
$584$	−4.24264			−0.175562
$585$		0			0
$586$	14.0000			0.578335
$587$	7.72741	−	2.07055i	0.318944	−	0.0854608i	−0.0957952	−	0.995401i	$-0.530539\pi$
$587$	7.72741	−	2.07055i	0.318944	−	0.0854608i	0.414739	+	0.909940i	$0.363873\pi$
$588$	−8.62372	+	0.794593i	−0.355636	+	0.0327685i
$589$	8.66025	−	5.00000i	0.356840	−	0.206021i
$590$	5.65685	+	5.65685i	0.232889	+	0.232889i
$591$	−35.7466	+	13.1978i	−1.47042	+	0.542885i
$592$	−0.366025	+	1.36603i	−0.0150436	+	0.0561433i
$593$	9.89949	−	9.89949i	0.406524	−	0.406524i	−0.474001	−	0.880524i	$-0.657191\pi$
$593$	9.89949	−	9.89949i	0.406524	−	0.406524i	0.880524	+	0.474001i	$0.157191\pi$
$594$	14.8990	+	14.4921i	0.611313	+	0.594617i
$595$		0			0
$596$	−0.517638	−	1.93185i	−0.0212033	−	0.0791317i
$597$		0			0
$598$		0			0
$599$			11.3137i			0.462266i	0.972922	+	0.231133i	$0.0742432\pi$
$599$			11.3137i			0.462266i	−0.972922	+	0.231133i	$0.925757\pi$
$600$	−3.99585	−	3.32162i	−0.163130	−	0.135605i
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	−0.936002	−	0.351996i	$-0.885503\pi$
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	0.772838	+	0.634603i	$0.218836\pi$
$602$	4.24264	+	7.34847i	0.172917	+	0.299501i
$603$	9.14214	+	19.1421i	0.372297	+	0.779528i
$604$	1.36603	+	0.366025i	0.0555828	+	0.0148934i
$605$	9.65926	+	2.58819i	0.392705	+	0.105225i
$606$	2.48528	−	14.4853i	0.100958	−	0.588424i
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	0.911621	+	0.411033i	$0.134832\pi$
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	−0.0998457	+	0.995003i	$0.531835\pi$
$608$	−3.53553	+	6.12372i	−0.143385	+	0.248350i
$609$	4.42883	−	5.32780i	0.179465	−	0.215894i
$610$		−	16.0000i		−	0.647821i
$611$		0			0
$612$		0			0
$613$	−0.366025	−	1.36603i	−0.0147836	−	0.0551732i	0.958140	−	0.286300i	$-0.0924254\pi$
$613$	−0.366025	−	1.36603i	−0.0147836	−	0.0551732i	−0.972924	+	0.231127i	$0.925759\pi$
$614$	−20.8207	−	12.0208i	−0.840254	−	0.485121i
$615$	−6.29253	−	2.89898i	−0.253739	−	0.116898i
$616$	12.0000	−	12.0000i	0.483494	−	0.483494i
$617$	−9.83512	+	36.7052i	−0.395947	+	1.47769i	0.424214	+	0.905562i	$0.360551\pi$
$617$	−9.83512	+	36.7052i	−0.395947	+	1.47769i	−0.820161	+	0.572133i	$0.806116\pi$
$618$	−3.59940	−	9.74907i	−0.144789	−	0.392165i
$619$	−1.00000	−	1.00000i	−0.0401934	−	0.0401934i	0.686724	−	0.726918i	$-0.259048\pi$
$619$	−1.00000	−	1.00000i	−0.0401934	−	0.0401934i	−0.726918	+	0.686724i	$0.759048\pi$
$620$	12.2474	−	7.07107i	0.491869	−	0.283981i
$621$	10.8209	−	42.7423i	0.434228	−	1.71519i
$622$	8.19615	−	2.19615i	0.328636	−	0.0880577i
$623$	−19.7990			−0.793230
$624$		0			0
$625$	19.0000			0.760000
$626$	−7.72741	+	2.07055i	−0.308849	+	0.0827559i
$627$	−0.898979	−	9.75663i	−0.0359018	−	0.389642i
$628$	−12.1244	+	7.00000i	−0.483814	+	0.279330i
$629$		0			0
$630$	−4.80260	+	6.99536i	−0.191340	+	0.278702i
$631$	−6.95448	+	25.9545i	−0.276854	+	1.03323i	0.677735	+	0.735306i	$0.262961\pi$
$631$	−6.95448	+	25.9545i	−0.276854	+	1.03323i	−0.954589	+	0.297926i	$0.903705\pi$
$632$	−21.2132	+	21.2132i	−0.843816	+	0.843816i
$633$	−10.1464	+	22.0239i	−0.403284	+	0.875369i
$634$	−8.66025	−	5.00000i	−0.343943	−	0.198575i
$635$		0			0
$636$	5.65685	+	8.00000i	0.224309	+	0.317221i
$637$		0			0
$638$		−	11.3137i		−	0.447914i
$639$	0.935500	−	11.9635i	0.0370078	−	0.473268i
$640$	−3.00000	+	5.19615i	−0.118585	+	0.205396i
$641$	8.48528	+	14.6969i	0.335148	+	0.580494i	0.983513	−	0.180836i	$-0.0578802\pi$
$641$	8.48528	+	14.6969i	0.335148	+	0.580494i	−0.648365	+	0.761330i	$0.724547\pi$
$642$	−9.65685	−	1.65685i	−0.381126	−	0.0653908i
$643$	−6.83013	−	1.83013i	−0.269354	−	0.0721732i	0.121614	−	0.992577i	$-0.461193\pi$
$643$	−6.83013	−	1.83013i	−0.269354	−	0.0721732i	−0.390968	+	0.920404i	$0.627860\pi$
$644$	−11.5911	−	3.10583i	−0.456754	−	0.122387i
$645$	20.4853	+	3.51472i	0.806607	+	0.138392i
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	10.9571	−	24.6767i	0.430436	−	0.969394i
$649$		−	16.0000i		−	0.628055i
$650$		0			0
$651$	10.0000	+	14.1421i	0.391931	+	0.554274i
$652$	−0.366025	−	1.36603i	−0.0143347	−	0.0534977i
$653$	12.2474	+	7.07107i	0.479280	+	0.276712i	0.720116	−	0.693853i	$-0.244088\pi$
$653$	12.2474	+	7.07107i	0.479280	+	0.276712i	−0.240837	+	0.970566i	$0.577422\pi$
$654$	1.02494	−	2.22474i	0.0400785	−	0.0869944i
$655$	16.0000	−	16.0000i	0.625172	−	0.625172i
$656$	−0.517638	+	1.93185i	−0.0202104	+	0.0754261i
$657$	−3.49768	−	2.40130i	−0.136457	−	0.0936837i
$658$	4.00000	+	4.00000i	0.155936	+	0.155936i
$659$	2.44949	−	1.41421i	0.0954186	−	0.0550899i	−0.451531	−	0.892255i	$-0.649122\pi$
$659$	2.44949	−	1.41421i	0.0954186	−	0.0550899i	0.546950	+	0.837165i	$0.315789\pi$
$660$	−1.27135	−	13.7980i	−0.0494872	−	0.537085i
$661$	1.36603	−	0.366025i	0.0531322	−	0.0142367i	−0.232155	−	0.972679i	$-0.574578\pi$
$661$	1.36603	−	0.366025i	0.0531322	−	0.0142367i	0.285287	+	0.958442i	$0.407911\pi$
$662$	−9.89949			−0.384755
$663$		0			0
$664$	−24.0000			−0.931381
$665$	3.86370	−	1.03528i	0.149828	−	0.0401463i
$666$	−3.22474	+	2.75699i	−0.124956	+	0.106831i
$667$	−20.7846	+	12.0000i	−0.804783	+	0.464642i
$668$	2.82843	+	2.82843i	0.109435	+	0.109435i
$669$	9.33226	+	25.2766i	0.360806	+	0.977252i
$670$	−3.66025	+	13.6603i	−0.141408	+	0.527742i
$671$	−22.6274	+	22.6274i	−0.873522	+	0.873522i
$672$	−11.1237	−	5.12472i	−0.429107	−	0.197690i
$673$	−10.3923	−	6.00000i	−0.400594	−	0.231283i	0.286146	−	0.958186i	$-0.407626\pi$
$673$	−10.3923	−	6.00000i	−0.400594	−	0.231283i	−0.686740	+	0.726903i	$0.740959\pi$
$674$	−1.55291	−	5.79555i	−0.0598160	−	0.223236i
$675$	−1.41421	−	5.00000i	−0.0544331	−	0.192450i
$676$		0			0
$677$		−	22.6274i		−	0.869642i	−0.900517	−	0.434821i	$-0.856812\pi$
$677$		−	22.6274i		−	0.869642i	0.900517	−	0.434821i	$-0.143188\pi$
$678$	15.6583	−	18.8366i	0.601352	−	0.723417i
$679$	−7.00000	+	12.1244i	−0.268635	+	0.465290i
$680$		0			0
$681$	−2.34315	+	13.6569i	−0.0897895	+	0.523332i
$682$	27.3205	+	7.32051i	1.04616	+	0.280317i
$683$	3.86370	+	1.03528i	0.147840	+	0.0396137i	0.331980	−	0.943286i	$-0.392283\pi$
$683$	3.86370	+	1.03528i	0.147840	+	0.0396137i	−0.184140	+	0.982900i	$0.558950\pi$
$684$	−3.82843	+	1.82843i	−0.146384	+	0.0699117i
$685$	14.0000	+	24.2487i	0.534913	+	0.926496i
$686$	8.48528	−	14.6969i	0.323970	−	0.561132i
$687$	−1.88366	−	1.56583i	−0.0718662	−	0.0597400i
$688$		−	6.00000i		−	0.228748i
$689$		0			0
$690$	24.0000	−	16.9706i	0.913664	−	0.646058i
$691$	4.02628	+	15.0263i	0.153167	+	0.571627i	0.999255	+	0.0385841i	$0.0122848\pi$
$691$	4.02628	+	15.0263i	0.153167	+	0.571627i	−0.846088	+	0.533042i	$0.821049\pi$
$692$	7.34847	+	4.24264i	0.279347	+	0.161281i
$693$	16.6848	−	3.10102i	0.633804	−	0.117798i
$694$	10.0000	−	10.0000i	0.379595	−	0.379595i
$695$	2.07055	−	7.72741i	0.0785405	−	0.293117i
$696$	−13.7873	+	5.09032i	−0.522605	+	0.192948i
$697$		0			0
$698$	20.8207	−	12.0208i	0.788074	−	0.454995i
$699$	43.9048	−	4.04541i	1.66063	−	0.153011i
$700$	−1.36603	+	0.366025i	−0.0516309	+	0.0138345i
$701$	−50.9117			−1.92291			−0.961454	−	0.274966i	$-0.911333\pi$
$701$	−50.9117			−1.92291			−0.961454	+	0.274966i	$0.911333\pi$
$702$		0			0
$703$	2.00000			0.0754314
$704$	−27.0459	+	7.24693i	−1.01933	+	0.273129i
$705$	13.7980	−	1.27135i	0.519661	−	0.0478818i
$706$	−22.5167	+	13.0000i	−0.847426	+	0.489261i
$707$	−8.48528	−	8.48528i	−0.319122	−	0.319122i
$708$	−6.49938	+	2.39960i	−0.244262	+	0.0901826i
$709$	−6.95448	+	25.9545i	−0.261181	+	0.974741i	0.703365	+	0.710828i	$0.251680\pi$
$709$	−6.95448	+	25.9545i	−0.261181	+	0.974741i	−0.964547	+	0.263913i	$0.914987\pi$
$710$	5.65685	−	5.65685i	0.212298	−	0.212298i
$711$	−29.4949	+	5.48188i	−1.10615	+	0.205587i
$712$	36.3731	+	21.0000i	1.36314	+	0.787008i
$713$	−15.5291	−	57.9555i	−0.581571	−	2.17045i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−26.6390	−	22.1441i	−0.994853	−	0.826988i
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	−12.7279	−	22.0454i	−0.474671	−	0.822155i	0.524908	−	0.851159i	$-0.324100\pi$
$719$	−12.7279	−	22.0454i	−0.474671	−	0.822155i	−0.999579	+	0.0290041i	$0.990766\pi$
$720$	5.41421	−	2.58579i	0.201776	−	0.0963666i
$721$	−8.19615	−	2.19615i	−0.305241	−	0.0817890i
$722$	16.4207	+	4.39992i	0.611117	+	0.163748i
$723$	7.04163	−	41.0416i	0.261881	−	1.52635i
$724$		0			0
$725$	−1.41421	+	2.44949i	−0.0525226	+	0.0909718i
$726$	5.53603	−	6.65976i	0.205461	−	0.247167i
$727$			48.0000i			1.78022i	0.455744	+	0.890111i	$0.349373\pi$
$727$			48.0000i			1.78022i	−0.455744	+	0.890111i	$0.650627\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	−0.732051	−	2.73205i	−0.0270944	−	0.101118i
$731$		0			0
$732$	12.5851	+	5.79796i	0.465157	+	0.214299i
$733$	5.00000	−	5.00000i	0.184679	−	0.184679i	−0.608712	−	0.793391i	$-0.708314\pi$
$733$	5.00000	−	5.00000i	0.184679	−	0.184679i	0.793391	+	0.608712i	$0.208314\pi$
$734$	2.07055	−	7.72741i	0.0764255	−	0.285224i
$735$	−5.99900	−	16.2484i	−0.221277	−	0.599333i
$736$	30.0000	+	30.0000i	1.10581	+	1.10581i
$737$	24.4949	−	14.1421i	0.902281	−	0.520932i
$738$	−4.56048	+	3.89898i	−0.167874	+	0.143523i
$739$	1.36603	−	0.366025i	0.0502501	−	0.0134645i	−0.233606	−	0.972331i	$-0.575053\pi$
$739$	1.36603	−	0.366025i	0.0502501	−	0.0134645i	0.283857	+	0.958867i	$0.408386\pi$
$740$	2.82843			0.103975
$741$		0			0
$742$	−8.00000			−0.293689
$743$	−15.4548	+	4.14110i	−0.566982	+	0.151922i	−0.530912	−	0.847427i	$-0.678151\pi$
$743$	−15.4548	+	4.14110i	−0.566982	+	0.151922i	−0.0360700	+	0.999349i	$0.511484\pi$
$744$	−3.37117	−	36.5874i	−0.123593	−	1.34136i
$745$	3.46410	−	2.00000i	0.126915	−	0.0732743i
$746$	−2.82843	−	2.82843i	−0.103556	−	0.103556i
$747$	−19.7859	−	13.5838i	−0.723927	−	0.497006i
$748$		0			0
$749$	−5.65685	+	5.65685i	−0.206697	+	0.206697i
$750$	8.69694	−	18.8776i	0.317567	−	0.689312i
$751$	25.9808	+	15.0000i	0.948051	+	0.547358i	0.892475	−	0.451097i	$-0.148967\pi$
$751$	25.9808	+	15.0000i	0.948051	+	0.547358i	0.0555764	+	0.998454i	$0.482300\pi$
$752$	−1.03528	−	3.86370i	−0.0377526	−	0.140895i
$753$	25.4558	+	36.0000i	0.927663	+	1.31191i
$754$		0			0
$755$			2.82843i			0.102937i
$756$	−3.76198	−	6.31249i	−0.136822	−	0.229583i
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	0.973991	+	0.226587i	$0.0727569\pi$
$758$	13.4350	+	23.2702i	0.487982	+	0.845210i
$759$	−57.9411	−	9.94113i	−2.10313	−	0.360840i
$760$	−8.19615	−	2.19615i	−0.297306	−	0.0796628i
$761$	−48.2963	−	12.9410i	−1.75074	−	0.469109i	−0.765955	−	0.642894i	$-0.777734\pi$
$761$	−48.2963	−	12.9410i	−1.75074	−	0.469109i	−0.984784	+	0.173784i	$0.944400\pi$
$762$		0			0
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$	−1.41421	+	2.44949i	−0.0511645	+	0.0886194i
$765$		0			0
$766$			16.0000i			0.578103i
$767$		0			0
$768$	17.0000	+	24.0416i	0.613435	+	0.867528i
$769$	−4.75833	−	17.7583i	−0.171590	−	0.640382i	−0.997107	−	0.0760054i	$-0.975783\pi$
$769$	−4.75833	−	17.7583i	−0.171590	−	0.640382i	0.825518	−	0.564376i	$-0.190883\pi$
$770$	9.79796	+	5.65685i	0.353094	+	0.203859i
$771$	6.14966	−	13.3485i	0.221475	−	0.480733i
$772$	−19.0000	+	19.0000i	−0.683825	+	0.683825i
$773$	−3.62347	+	13.5230i	−0.130327	+	0.486387i	−0.999973	−	0.00728800i	$-0.997680\pi$
$773$	−3.62347	+	13.5230i	−0.130327	+	0.486387i	0.869646	+	0.493675i	$0.164347\pi$
$774$	10.1879	−	14.8394i	0.366195	−	0.533391i
$775$	−5.00000	−	5.00000i	−0.179605	−	0.179605i
$776$	25.7196	−	14.8492i	0.923281	−	0.533057i
$777$	0.317837	+	3.44949i	0.0114023	+	0.123750i
$778$	16.3923	−	4.39230i	0.587693	−	0.157472i
$779$	2.82843			0.101339
$780$		0			0
$781$	−16.0000			−0.572525
$782$		0			0
$783$	−14.2474	−	3.60697i	−0.509162	−	0.128902i
$784$	−4.33013	+	2.50000i	−0.154647	+	0.0892857i
$785$	−19.7990	−	19.7990i	−0.706656	−	0.706656i
$786$	−6.78710	−	18.3830i	−0.242088	−	0.655700i
$787$	−6.95448	+	25.9545i	−0.247901	+	0.925177i	0.724003	+	0.689797i	$0.242300\pi$
$787$	−6.95448	+	25.9545i	−0.247901	+	0.925177i	−0.971903	+	0.235380i	$0.924366\pi$
$788$	15.5563	−	15.5563i	0.554172	−	0.554172i
$789$	35.5959	+	16.3991i	1.26725	+	0.583824i
$790$	−17.3205	−	10.0000i	−0.616236	−	0.355784i
$791$	−5.17638	−	19.3185i	−0.184051	−	0.686887i
$792$	−33.9411	−	12.0000i	−1.20605	−	0.426401i
$793$		0			0
$794$			24.0416i			0.853206i
$795$	−12.5266	+	15.0693i	−0.444273	+	0.534453i
$796$		0			0
$797$	−8.48528	−	14.6969i	−0.300564	−	0.520592i	0.675700	−	0.737177i	$-0.263842\pi$
$797$	−8.48528	−	14.6969i	−0.300564	−	0.520592i	−0.976264	+	0.216585i	$0.930508\pi$
$798$	0.585786	−	3.41421i	0.0207366	−	0.120862i
$799$		0			0
$800$	4.82963	+	1.29410i	0.170753	+	0.0457532i
$801$	18.1005	+	37.8995i	0.639550	+	1.33911i
$802$	11.0000	+	19.0526i	0.388424	+	0.672769i
$803$	−2.82843	+	4.89898i	−0.0998130	+	0.172881i
$804$	−9.41832	−	7.82913i	−0.332158	−	0.276112i
$805$		−	24.0000i		−	0.845889i
$806$		0			0
$807$	28.0000	−	19.7990i	0.985647	−	0.696957i
$808$	6.58846	+	24.5885i	0.231781	+	0.865019i
$809$	26.9444	+	15.5563i	0.947314	+	0.546932i	0.892246	−	0.451550i	$-0.149129\pi$
$809$	26.9444	+	15.5563i	0.947314	+	0.546932i	0.0550686	+	0.998483i	$0.482462\pi$
$810$	17.7812	+	2.79796i	0.624768	+	0.0983103i
$811$	−1.00000	+	1.00000i	−0.0351147	+	0.0351147i	−0.724446	−	0.689331i	$-0.757904\pi$
$811$	−1.00000	+	1.00000i	−0.0351147	+	0.0351147i	0.689331	+	0.724446i	$0.257904\pi$
$812$	−1.03528	+	3.86370i	−0.0363311	+	0.135589i
$813$	43.6597	−	16.1194i	1.53121	−	0.565331i
$814$	4.00000	+	4.00000i	0.140200	+	0.140200i
$815$	2.44949	−	1.41421i	0.0858019	−	0.0495377i
$816$		0			0
$817$	−8.19615	+	2.19615i	−0.286747	+	0.0768336i
$818$	32.5269			1.13728
$819$		0			0
$820$	4.00000			0.139686
$821$	−9.65926	+	2.58819i	−0.337110	+	0.0903285i	−0.423403	−	0.905941i	$-0.639165\pi$
$821$	−9.65926	+	2.58819i	−0.337110	+	0.0903285i	0.0862928	+	0.996270i	$0.472498\pi$
$822$	24.1464	−	2.22486i	0.842203	−	0.0776009i
$823$	−25.9808	+	15.0000i	−0.905632	+	0.522867i	−0.879023	−	0.476779i	$-0.841804\pi$
$823$	−25.9808	+	15.0000i	−0.905632	+	0.522867i	−0.0266091	+	0.999646i	$0.508471\pi$
$824$	12.7279	+	12.7279i	0.443398	+	0.443398i
$825$	−6.49938	+	2.39960i	−0.226279	+	0.0835434i
$826$	1.46410	−	5.46410i	0.0509426	−	0.190120i
$827$	22.6274	−	22.6274i	0.786832	−	0.786832i	−0.194141	−	0.980974i	$-0.562192\pi$
$827$	22.6274	−	22.6274i	0.786832	−	0.786832i	0.980974	+	0.194141i	$0.0621920\pi$
$828$	4.65153	+	25.0273i	0.161652	+	0.869757i
$829$	15.5885	+	9.00000i	0.541409	+	0.312583i	0.745650	−	0.666338i	$-0.232139\pi$
$829$	15.5885	+	9.00000i	0.541409	+	0.312583i	−0.204240	+	0.978921i	$0.565472\pi$
$830$	−4.14110	−	15.4548i	−0.143740	−	0.536444i
$831$	16.9706	−	12.0000i	0.588702	−	0.416275i
$832$		0			0
$833$		0			0
$834$	−5.32780	−	4.42883i	−0.184487	−	0.153358i
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	2.82843	+	4.89898i	0.0978232	+	0.169435i
$837$	17.9289	−	32.0711i	0.619715	−	1.10854i
$838$	10.9282	+	2.92820i	0.377509	+	0.101153i
$839$	3.86370	+	1.03528i	0.133390	+	0.0357417i	0.324896	−	0.945750i	$-0.394671\pi$
$839$	3.86370	+	1.03528i	0.133390	+	0.0357417i	−0.191506	+	0.981491i	$0.561337\pi$
$840$	2.48528	−	14.4853i	0.0857504	−	0.499790i
$841$	−10.5000	−	18.1865i	−0.362069	−	0.627122i
$842$	17.6777	−	30.6186i	0.609213	−	1.05519i
$843$	15.5009	−	18.6473i	0.533879	−	0.642248i
$844$		−	14.0000i		−	0.481900i
$845$		0			0
$846$	4.00000	−	11.3137i	0.137523	−	0.388973i
$847$	−1.83013	−	6.83013i	−0.0628839	−	0.234686i
$848$	4.89898	+	2.82843i	0.168232	+	0.0971286i
$849$	18.8776	+	8.69694i	0.647877	+	0.298478i
$850$		0			0
$851$	3.10583	−	11.5911i	0.106466	−	0.397338i
$852$	2.39960	+	6.49938i	0.0822090	+	0.222665i
$853$	−37.0000	−	37.0000i	−1.26686	−	1.26686i	−0.947703	−	0.319152i	$-0.896602\pi$
$853$	−37.0000	−	37.0000i	−1.26686	−	1.26686i	−0.319152	−	0.947703i	$-0.603398\pi$
$854$	−9.79796	+	5.65685i	−0.335279	+	0.193574i
$855$	−5.51399	−	6.44949i	−0.188574	−	0.220568i
$856$	16.3923	−	4.39230i	0.560277	−	0.150126i
$857$	8.48528			0.289852			0.144926	−	0.989443i	$-0.453706\pi$
$857$	8.48528			0.289852			0.144926	+	0.989443i	$0.453706\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−11.5911	+	3.10583i	−0.395254	+	0.105908i
$861$	0.449490	+	4.87832i	0.0153186	+	0.166253i
$862$	−27.7128	+	16.0000i	−0.943902	+	0.544962i
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	0.753607	−	0.657326i	$-0.228312\pi$
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	−0.657326	+	0.753607i	$0.728312\pi$
$864$	0.359651	+	25.9783i	0.0122356	+	0.883799i
$865$	−4.39230	+	16.3923i	−0.149343	+	0.557355i
$866$	12.7279	−	12.7279i	0.432512	−	0.432512i
$867$	12.3207	−	26.7432i	0.418432	−	0.908248i
$868$	−8.66025	−	5.00000i	−0.293948	−	0.169711i
$869$	10.3528	+	38.6370i	0.351193	+	1.31067i
$870$	−5.65685	−	8.00000i	−0.191785	−	0.271225i
$871$		0			0
$872$			4.24264i			0.143674i
$873$	29.6081	+	2.31524i	1.00208	+	0.0783592i
$874$	−6.00000	+	10.3923i	−0.202953	+	0.351525i
$875$	−8.48528	−	14.6969i	−0.286855	−	0.496847i
$876$	2.41421	+	0.414214i	0.0815687	+	0.0139950i
$877$	17.7583	+	4.75833i	0.599656	+	0.160677i	0.545863	−	0.837875i	$-0.316202\pi$
$877$	17.7583	+	4.75833i	0.599656	+	0.160677i	0.0537936	+	0.998552i	$0.482869\pi$
$878$	28.9778	+	7.76457i	0.977953	+	0.262042i
$879$	−23.8995	−	4.10051i	−0.806110	−	0.138307i
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	12.7279	−	22.0454i	0.428815	−	0.742729i	−0.567954	−	0.823061i	$-0.692265\pi$
$881$	12.7279	−	22.0454i	0.428815	−	0.742729i	0.996768	+	0.0803319i	$0.0255980\pi$
$882$	−14.9543	−	1.16938i	−0.503539	−	0.0393749i
$883$		−	36.0000i		−	1.21150i	−0.795656	−	0.605748i	$-0.792874\pi$
$883$		−	36.0000i		−	1.21150i	0.795656	−	0.605748i	$-0.207126\pi$
$884$		0			0
$885$	−8.00000	−	11.3137i	−0.268917	−	0.380306i
$886$	−7.32051	−	27.3205i	−0.245937	−	0.917850i
$887$	12.2474	+	7.07107i	0.411229	+	0.237423i	0.691318	−	0.722551i	$-0.257031\pi$
$887$	12.2474	+	7.07107i	0.411229	+	0.237423i	−0.280089	+	0.959974i	$0.590364\pi$
$888$	3.07483	−	6.67423i	0.103185	−	0.223973i
$889$		0			0
$890$	−7.24693	+	27.0459i	−0.242918	+	0.906581i
$891$	−21.1895	−	29.1033i	−0.709876	−	0.974999i
$892$	−11.0000	−	11.0000i	−0.368307	−	0.368307i
$893$	−4.89898	+	2.82843i	−0.163938	+	0.0946497i
$894$	−0.317837	−	3.44949i	−0.0106301	−	0.115368i
$895$		0			0
$896$	4.24264			0.141737
$897$		0			0
$898$	−22.0000			−0.734150
$899$	−19.3185	+	5.17638i	−0.644309	+	0.172642i
$900$	1.94949	+	2.28024i	0.0649830	+	0.0760080i
$901$		0			0
$902$	5.65685	+	5.65685i	0.188353	+	0.188353i
$903$	−5.09032	−	13.7873i	−0.169395	−	0.458811i
$904$	−10.9808	+	40.9808i	−0.365215	+	1.36300i
$905$		0			0
$906$	2.22474	+	1.02494i	0.0739122	+	0.0340515i
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	0.317441	−	0.948278i	$-0.397176\pi$
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	−0.662512	+	0.749051i	$0.730510\pi$
$908$	−2.07055	−	7.72741i	−0.0687137	−	0.256443i
$909$	−8.48528	+	24.0000i	−0.281439	+	0.796030i
$910$		0			0
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$	−1.56583	+	1.88366i	−0.0518497	+	0.0623743i
$913$	−16.0000	+	27.7128i	−0.529523	+	0.917160i
$914$	−20.5061	−	35.5176i	−0.678281	−	1.17482i
$915$	−4.68629	+	27.3137i	−0.154924	+	0.902963i
$916$	1.36603	+	0.366025i	0.0451347	+	0.0120938i
$917$	−15.4548	−	4.14110i	−0.510363	−	0.136751i
$918$		0			0
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$	−25.4558	+	44.0908i	−0.839254	+	1.45363i
$921$	32.0223	+	26.6190i	1.05517	+	0.877127i
$922$			10.0000i			0.329332i
$923$		0			0
$924$	−8.00000	+	5.65685i	−0.263181	+	0.186097i
$925$	−0.366025	−	1.36603i	−0.0120348	−	0.0449146i
$926$	−20.8207	−	12.0208i	−0.684209	−	0.395029i
$927$	3.28913	+	17.6969i	0.108029	+	0.581244i
$928$	10.0000	−	10.0000i	0.328266	−	0.328266i
$929$	11.9057	−	44.4326i	0.390613	−	1.45779i	−0.438514	−	0.898725i	$-0.644495\pi$
$929$	11.9057	−	44.4326i	0.390613	−	1.45779i	0.829126	−	0.559061i	$-0.188838\pi$
$930$	22.9788	−	8.48387i	0.753504	−	0.278197i
$931$	5.00000	+	5.00000i	0.163868	+	0.163868i
$932$	−22.0454	+	12.7279i	−0.722121	+	0.416917i
$933$	−14.6349	+	1.34847i	−0.479127	+	0.0441469i
$934$	−24.5885	+	6.58846i	−0.804559	+	0.215581i
$935$		0			0
$936$		0			0
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	9.65926	−	2.58819i	0.315386	−	0.0845074i
$939$	13.7980	−	1.27135i	0.450279	−	0.0414889i
$940$	−6.92820	+	4.00000i	−0.225973	+	0.130466i
$941$	−26.8701	−	26.8701i	−0.875939	−	0.875939i	0.117173	−	0.993112i	$-0.462617\pi$
$941$	−26.8701	−	26.8701i	−0.875939	−	0.875939i	−0.993112	+	0.117173i	$0.962617\pi$
$942$	−22.7478	+	8.39861i	−0.741164	+	0.273641i
$943$	4.39230	−	16.3923i	0.143033	−	0.533807i
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$	10.2474	−	10.5352i	0.333350	−	0.342709i
$946$	−20.7846	−	12.0000i	−0.675766	−	0.390154i
$947$	8.28221	+	30.9096i	0.269136	+	1.00443i	0.959670	+	0.281128i	$0.0907087\pi$
$947$	8.28221	+	30.9096i	0.269136	+	1.00443i	−0.690535	+	0.723299i	$0.742625\pi$
$948$	14.1421	−	10.0000i	0.459315	−	0.324785i
$949$		0			0
$950$			1.41421i			0.0458831i
$951$	13.3195	+	11.0721i	0.431915	+	0.359036i
$952$		0			0
$953$	12.7279	+	22.0454i	0.412298	+	0.714121i	0.995141	−	0.0984642i	$-0.0313930\pi$
$953$	12.7279	+	22.0454i	0.412298	+	0.714121i	−0.582843	+	0.812585i	$0.698060\pi$
$954$	7.31371	+	15.3137i	0.236790	+	0.495800i
$955$	−5.46410	−	1.46410i	−0.176814	−	0.0473772i
$956$	19.3185	+	5.17638i	0.624805	+	0.167416i
$957$	−3.31371	+	19.3137i	−0.107117	+	0.624324i
$958$	−16.0000	−	27.7128i	−0.516937	−	0.895360i
$959$	9.89949	−	17.1464i	0.319671	−	0.553687i
$960$	−15.5009	+	18.6473i	−0.500289	+	0.601840i
$961$		−	19.0000i		−	0.612903i
$962$		0			0
$963$	16.0000	+	5.65685i	0.515593	+	0.182290i
$964$	6.22243	+	23.2224i	0.200411	+	0.747944i
$965$	−46.5403	−	26.8701i	−1.49819	−	0.864978i
$966$	−18.8776	−	8.69694i	−0.607376	−	0.279819i
$967$	23.0000	−	23.0000i	0.739630	−	0.739630i	−0.232876	−	0.972506i	$-0.574814\pi$
$967$	23.0000	−	23.0000i	0.739630	−	0.739630i	0.972506	+	0.232876i	$0.0748137\pi$
$968$	−3.88229	+	14.4889i	−0.124781	+	0.465690i
$969$		0			0
$970$	14.0000	+	14.0000i	0.449513	+	0.449513i
$971$	−26.9444	+	15.5563i	−0.864687	+	0.499227i	−0.865579	−	0.500773i	$-0.833049\pi$
$971$	−26.9444	+	15.5563i	−0.864687	+	0.499227i	0.000892350		1.00000i	$0.499716\pi$
$972$	−8.64420	+	12.9722i	−0.277263	+	0.416083i
$973$	−5.46410	+	1.46410i	−0.175171	+	0.0469369i
$974$	−26.8701			−0.860972
$975$		0			0
$976$	8.00000			0.256074
$977$	36.7052	−	9.83512i	1.17430	−	0.314653i	0.381638	−	0.924312i	$-0.375360\pi$
$977$	36.7052	−	9.83512i	1.17430	−	0.314653i	0.792664	+	0.609658i	$0.208693\pi$
$978$	−0.224745	−	2.43916i	−0.00718655	−	0.0779957i
$979$	48.4974	−	28.0000i	1.54998	−	0.894884i
$980$	7.07107	+	7.07107i	0.225877	+	0.225877i
$981$	−2.40130	+	3.49768i	−0.0766677	+	0.111672i
$982$	10.9808	−	40.9808i	0.350410	−	1.30775i
$983$	−2.82843	+	2.82843i	−0.0902128	+	0.0902128i	−0.750773	−	0.660560i	$-0.770319\pi$
$983$	−2.82843	+	2.82843i	−0.0902128	+	0.0902128i	0.660560	+	0.750773i	$0.270319\pi$
$984$	4.34847	−	9.43879i	0.138624	−	0.300898i
$985$	38.1051	+	22.0000i	1.21413	+	0.700978i
$986$		0			0
$987$	−5.65685	−	8.00000i	−0.180060	−	0.254643i
$988$		0			0
$989$			50.9117i			1.61890i
$990$	1.87100	−	23.9270i	0.0594643	−	0.760449i
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	17.6777	+	30.6186i	0.561267	+	0.972142i
$993$	16.8995	+	2.89949i	0.536289	+	0.0920127i
$994$	−5.46410	−	1.46410i	−0.173311	−	0.0464385i
$995$		0			0
$996$	13.6569	+	2.34315i	0.432734	+	0.0742454i
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−16.2635	+	28.1691i	−0.514811	+	0.891678i
$999$	6.31249	−	3.76198i	0.199718	−	0.119024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.i.188.1		8
3.2	odd	2	inner	507.2.k.i.188.2		8
13.2	odd	12		507.2.k.j.89.1		8
13.3	even	3	inner	507.2.k.i.80.2		8
13.4	even	6		39.2.f.a.5.1	✓	4
13.5	odd	4		507.2.k.j.488.2		8
13.6	odd	12		39.2.f.a.8.2	yes	4
13.7	odd	12		507.2.f.a.437.1		4
13.8	odd	4	inner	507.2.k.i.488.1		8
13.9	even	3		507.2.f.a.239.2		4
13.10	even	6		507.2.k.j.80.1		8
13.11	odd	12	inner	507.2.k.i.89.2		8
13.12	even	2		507.2.k.j.188.2		8
39.2	even	12		507.2.k.j.89.2		8
39.5	even	4		507.2.k.j.488.1		8
39.8	even	4	inner	507.2.k.i.488.2		8
39.11	even	12	inner	507.2.k.i.89.1		8
39.17	odd	6		39.2.f.a.5.2	yes	4
39.20	even	12		507.2.f.a.437.2		4
39.23	odd	6		507.2.k.j.80.2		8
39.29	odd	6	inner	507.2.k.i.80.1		8
39.32	even	12		39.2.f.a.8.1	yes	4
39.35	odd	6		507.2.f.a.239.1		4
39.38	odd	2		507.2.k.j.188.1		8
52.19	even	12		624.2.bf.d.593.2		4
52.43	odd	6		624.2.bf.d.161.2		4
65.4	even	6		975.2.o.j.551.2		4
65.17	odd	12		975.2.n.c.824.2		4
65.19	odd	12		975.2.o.j.476.1		4
65.32	even	12		975.2.n.d.749.2		4
65.43	odd	12		975.2.n.d.824.1		4
65.58	even	12		975.2.n.c.749.1		4
156.71	odd	12		624.2.bf.d.593.1		4
156.95	even	6		624.2.bf.d.161.1		4
195.17	even	12		975.2.n.c.824.1		4
195.32	odd	12		975.2.n.d.749.1		4
195.134	odd	6		975.2.o.j.551.1		4
195.149	even	12		975.2.o.j.476.2		4
195.173	even	12		975.2.n.d.824.2		4
195.188	odd	12		975.2.n.c.749.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.f.a.5.1	✓	4	13.4	even	6
39.2.f.a.5.2	yes	4	39.17	odd	6
39.2.f.a.8.1	yes	4	39.32	even	12
39.2.f.a.8.2	yes	4	13.6	odd	12
507.2.f.a.239.1		4	39.35	odd	6
507.2.f.a.239.2		4	13.9	even	3
507.2.f.a.437.1		4	13.7	odd	12
507.2.f.a.437.2		4	39.20	even	12
507.2.k.i.80.1		8	39.29	odd	6	inner
507.2.k.i.80.2		8	13.3	even	3	inner
507.2.k.i.89.1		8	39.11	even	12	inner
507.2.k.i.89.2		8	13.11	odd	12	inner
507.2.k.i.188.1		8	1.1	even	1	trivial
507.2.k.i.188.2		8	3.2	odd	2	inner
507.2.k.i.488.1		8	13.8	odd	4	inner
507.2.k.i.488.2		8	39.8	even	4	inner
507.2.k.j.80.1		8	13.10	even	6
507.2.k.j.80.2		8	39.23	odd	6
507.2.k.j.89.1		8	13.2	odd	12
507.2.k.j.89.2		8	39.2	even	12
507.2.k.j.188.1		8	39.38	odd	2
507.2.k.j.188.2		8	13.12	even	2
507.2.k.j.488.1		8	39.5	even	4
507.2.k.j.488.2		8	13.5	odd	4
624.2.bf.d.161.1		4	156.95	even	6
624.2.bf.d.161.2		4	52.43	odd	6
624.2.bf.d.593.1		4	156.71	odd	12
624.2.bf.d.593.2		4	52.19	even	12
975.2.n.c.749.1		4	65.58	even	12
975.2.n.c.749.2		4	195.188	odd	12
975.2.n.c.824.1		4	195.17	even	12
975.2.n.c.824.2		4	65.17	odd	12
975.2.n.d.749.1		4	195.32	odd	12
975.2.n.d.749.2		4	65.32	even	12
975.2.n.d.824.1		4	65.43	odd	12
975.2.n.d.824.2		4	195.173	even	12
975.2.o.j.476.1		4	65.19	odd	12
975.2.o.j.476.2		4	195.149	even	12
975.2.o.j.551.1		4	195.134	odd	6
975.2.o.j.551.2		4	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.12132 - 2.12132i) q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(2.12132 - 2.12132i) q^{8} +(2.94949 - 0.548188i) q^{9} +(1.73205 + 1.00000i) q^{10} +(-1.03528 - 3.86370i) q^{11} +(-1.41421 + 1.00000i) q^{12} -1.41421i q^{14} +(-2.66390 - 2.21441i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.70711 + 1.29289i) q^{18} +(1.36603 + 0.366025i) q^{19} +(1.93185 + 0.517638i) q^{20} +(-0.414214 + 2.41421i) q^{21} +(2.00000 + 3.46410i) q^{22} +(4.24264 - 7.34847i) q^{23} +(3.32162 - 3.99585i) q^{24} -1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(-0.366025 - 1.36603i) q^{28} +(-2.44949 - 1.41421i) q^{29} +(3.14626 + 1.44949i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-1.29410 + 4.82963i) q^{32} +(-2.39960 - 6.49938i) q^{33} +(2.44949 - 1.41421i) q^{35} +(-2.28024 + 1.94949i) q^{36} +(1.36603 - 0.366025i) q^{37} -1.41421 q^{38} -6.00000 q^{40} +(1.93185 - 0.517638i) q^{41} +(-0.224745 - 2.43916i) q^{42} +(-5.19615 + 3.00000i) q^{43} +(2.82843 + 2.82843i) q^{44} +(-4.94646 - 3.39595i) q^{45} +(-2.19615 + 8.19615i) q^{46} +(-2.82843 + 2.82843i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(4.33013 + 2.50000i) q^{49} +(0.258819 + 0.965926i) q^{50} -5.65685i q^{53} +(-4.46360 + 2.66012i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(2.12132 + 3.67423i) q^{56} +(2.41421 + 0.414214i) q^{57} +(2.73205 + 0.732051i) q^{58} +(3.86370 + 1.03528i) q^{59} +(3.41421 + 0.585786i) q^{60} +(-4.00000 - 6.92820i) q^{61} +(-3.53553 + 6.12372i) q^{62} +(-0.330749 + 4.22973i) q^{63} -7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(1.83013 + 6.83013i) q^{67} +(6.14966 - 13.3485i) q^{69} +(-2.00000 + 2.00000i) q^{70} +(1.03528 - 3.86370i) q^{71} +(5.09393 - 7.41970i) q^{72} +(-1.00000 - 1.00000i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(-0.158919 - 1.72474i) q^{75} +(-1.36603 + 0.366025i) q^{76} +5.65685 q^{77} -10.0000 q^{79} +(1.93185 - 0.517638i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-1.73205 + 1.00000i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(-0.848387 - 2.29788i) q^{84} +(4.24264 - 4.24264i) q^{86} +(-4.44949 - 2.04989i) q^{87} +(-10.3923 - 6.00000i) q^{88} +(3.62347 + 13.5230i) q^{89} +(5.65685 + 2.00000i) q^{90} +8.48528i q^{92} +(7.82913 - 9.41832i) q^{93} +(2.00000 - 3.46410i) q^{94} +(-1.41421 - 2.44949i) q^{95} +(-1.46447 + 8.53553i) q^{96} +(9.56218 + 2.56218i) q^{97} +(-4.82963 - 1.29410i) q^{98} +(-5.17157 - 10.8284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 16 q^{22} + 12 q^{24} + 40 q^{27} + 4 q^{28} + 40 q^{31} - 16 q^{33} + 4 q^{37} - 48 q^{40} + 8 q^{42} - 16 q^{45} + 24 q^{46} + 4 q^{48} - 4 q^{54} - 32 q^{55} + 8 q^{57} + 8 q^{58} + 16 q^{60} - 32 q^{61} - 4 q^{63} + 32 q^{66} - 20 q^{67} - 16 q^{70} - 24 q^{72} - 8 q^{73} - 4 q^{76} - 80 q^{79} + 28 q^{81} - 4 q^{84} - 16 q^{87} + 20 q^{93} + 16 q^{94} - 40 q^{96} + 28 q^{97} - 64 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9 + 8 * q^15 - 4 * q^16 - 16 * q^18 + 4 * q^19 + 8 * q^21 + 16 * q^22 + 12 * q^24 + 40 * q^27 + 4 * q^28 + 40 * q^31 - 16 * q^33 + 4 * q^37 - 48 * q^40 + 8 * q^42 - 16 * q^45 + 24 * q^46 + 4 * q^48 - 4 * q^54 - 32 * q^55 + 8 * q^57 + 8 * q^58 + 16 * q^60 - 32 * q^61 - 4 * q^63 + 32 * q^66 - 20 * q^67 - 16 * q^70 - 24 * q^72 - 8 * q^73 - 4 * q^76 - 80 * q^79 + 28 * q^81 - 4 * q^84 - 16 * q^87 + 20 * q^93 + 16 * q^94 - 40 * q^96 + 28 * q^97 - 64 * q^99

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