LMFDB - Embedded newform 930.2.j.c.497.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.1
Root			$2.16053i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.c.683.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(1.41421 - 1.00000i) q^{6} +(0.218591 + 0.218591i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(1.41421 - 1.00000i) q^{6} +(0.218591 + 0.218591i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +(1.52773 - 1.63280i) q^{10} +0.894921i q^{11} +(-0.292893 + 1.70711i) q^{12} +(3.57474 - 3.57474i) q^{13} -0.309135 q^{14} +(3.83686 + 0.527726i) q^{15} -1.00000 q^{16} +(-4.36459 + 4.36459i) q^{17} +(-2.70711 + 1.29289i) q^{18} +6.55178i q^{19} +(0.0743018 + 2.23483i) q^{20} +(-0.309135 - 0.437183i) q^{21} +(-0.632805 - 0.632805i) q^{22} +(-3.19562 - 3.19562i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(4.98896 - 0.332104i) q^{25} +5.05545i q^{26} +(-4.53553 - 2.53553i) q^{27} +(0.218591 - 0.218591i) q^{28} +2.39124 q^{29} +(-3.08623 + 2.33991i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.262116 - 1.52773i) q^{33} -6.17246i q^{34} +(-0.504757 - 0.472274i) q^{35} +(1.00000 - 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(-4.63280 - 4.63280i) q^{38} +(-7.14949 + 5.05545i) q^{39} +(-1.63280 - 1.52773i) q^{40} -4.71231i q^{41} +(0.527726 + 0.0905435i) q^{42} +(-3.37912 + 3.37912i) q^{43} +0.894921 q^{44} +(-6.39536 - 2.02468i) q^{45} +4.51929 q^{46} +(8.98896 - 8.98896i) q^{47} +(1.70711 + 0.292893i) q^{48} -6.90444i q^{49} +(-3.29289 + 3.76256i) q^{50} +(8.72918 - 6.17246i) q^{51} +(-3.57474 - 3.57474i) q^{52} +(-10.1579 - 10.1579i) q^{53} +(5.00000 - 1.41421i) q^{54} +(-0.0664943 - 2.00000i) q^{55} +0.309135i q^{56} +(1.91897 - 11.1846i) q^{57} +(-1.69087 + 1.69087i) q^{58} -6.79073 q^{59} +(0.527726 - 3.83686i) q^{60} -5.61916 q^{61} +(-0.707107 + 0.707107i) q^{62} +(0.399678 + 0.836861i) q^{63} +1.00000i q^{64} +(-7.72335 + 8.25457i) q^{65} +(0.894921 + 1.26561i) q^{66} +(-9.52512 - 9.52512i) q^{67} +(4.36459 + 4.36459i) q^{68} +(4.51929 + 6.39124i) q^{69} +(0.690865 - 0.0229693i) q^{70} +12.5518i q^{71} +(1.29289 + 2.70711i) q^{72} +(-7.83686 + 7.83686i) q^{73} +2.82843 q^{74} +(-8.61396 - 0.894295i) q^{75} +6.55178 q^{76} +(-0.195622 + 0.195622i) q^{77} +(1.48071 - 8.63020i) q^{78} -13.0830i q^{79} +(2.23483 - 0.0743018i) q^{80} +(7.00000 + 5.65685i) q^{81} +(3.33210 + 3.33210i) q^{82} +(-1.55913 - 1.55913i) q^{83} +(-0.437183 + 0.309135i) q^{84} +(9.42983 - 10.0784i) q^{85} -4.77880i q^{86} +(-4.08211 - 0.700379i) q^{87} +(-0.632805 + 0.632805i) q^{88} +1.83947 q^{89} +(5.95387 - 3.09054i) q^{90} +1.56282 q^{91} +(-3.19562 + 3.19562i) q^{92} +(-1.70711 - 0.292893i) q^{93} +12.7123i q^{94} +(-0.486809 - 14.6421i) q^{95} +(-1.41421 + 1.00000i) q^{96} +(-6.81739 - 6.81739i) q^{97} +(4.88217 + 4.88217i) q^{98} +(-0.894921 + 2.53122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^3 + 4 * q^7	$ 8 q - 8 q^{3} + 4 q^{7} - 8 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{15} - 8 q^{16} + 4 q^{17} - 16 q^{18} + 4 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 q^{45} + 28 q^{46} + 28 q^{47} + 8 q^{48} - 32 q^{50} - 8 q^{51} + 4 q^{52} - 12 q^{53} + 40 q^{54} - 20 q^{55} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 q^{63} - 36 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} + 12 q^{77} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 q^{90} + 8 q^{91} - 12 q^{92} - 8 q^{93} - 36 q^{95} + 12 q^{97} + 32 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 4 * q^7 - 8 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^15 - 8 * q^16 + 4 * q^17 - 16 * q^18 + 4 * q^20 + 12 * q^21 + 4 * q^22 - 12 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^33 + 24 * q^35 + 8 * q^36 - 16 * q^37 - 28 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^42 - 8 * q^43 + 4 * q^44 - 12 * q^45 + 28 * q^46 + 28 * q^47 + 8 * q^48 - 32 * q^50 - 8 * q^51 + 4 * q^52 - 12 * q^53 + 40 * q^54 - 20 * q^55 - 24 * q^57 - 28 * q^58 + 24 * q^59 - 8 * q^60 + 56 * q^61 - 28 * q^63 - 36 * q^65 + 4 * q^66 - 16 * q^67 - 4 * q^68 + 28 * q^69 + 20 * q^70 + 16 * q^72 - 36 * q^73 - 32 * q^75 + 4 * q^76 + 12 * q^77 + 20 * q^78 + 56 * q^81 + 28 * q^82 - 12 * q^83 - 8 * q^84 + 32 * q^85 - 20 * q^87 + 4 * q^88 + 36 * q^89 - 4 * q^90 + 8 * q^91 - 12 * q^92 - 8 * q^93 - 36 * q^95 + 12 * q^97 + 32 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.70711	−	0.292893i	−0.985599	−	0.169102i
$3$	−1.70711	−	0.292893i	−0.985599	−	0.169102i
$4$		−	1.00000i		−	0.500000i
$5$	−2.23483	+	0.0743018i	−0.999448	+	0.0332288i
$5$	−2.23483	+	0.0743018i	−0.999448	+	0.0332288i
$6$	1.41421	−	1.00000i	0.577350	−	0.408248i
$7$	0.218591	+	0.218591i	0.0826198	+	0.0826198i	0.747209	−	0.664589i	$-0.231393\pi$
$7$	0.218591	+	0.218591i	0.0826198	+	0.0826198i	−0.664589	+	0.747209i	$0.731393\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.82843	+	1.00000i	0.942809	+	0.333333i
$10$	1.52773	−	1.63280i	0.483109	−	0.516338i
$11$			0.894921i			0.269829i	0.990857	+	0.134914i	$0.0430760\pi$
$11$			0.894921i			0.269829i	−0.990857	+	0.134914i	$0.956924\pi$
$12$	−0.292893	+	1.70711i	−0.0845510	+	0.492799i
$13$	3.57474	−	3.57474i	0.991456	−	0.991456i	−0.00850795	−	0.999964i	$-0.502708\pi$
$13$	3.57474	−	3.57474i	0.991456	−	0.991456i	0.999964	+	0.00850795i	$0.00270820\pi$
$14$	−0.309135			−0.0826198
$15$	3.83686	+	0.527726i	0.990673	+	0.136258i
$16$	−1.00000			−0.250000
$17$	−4.36459	+	4.36459i	−1.05857	+	1.05857i	−0.0603934	+	0.998175i	$0.519236\pi$
$17$	−4.36459	+	4.36459i	−1.05857	+	1.05857i	−0.998175	+	0.0603934i	$0.980764\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$			6.55178i			1.50308i	0.659687	+	0.751540i	$0.270689\pi$
$19$			6.55178i			1.50308i	−0.659687	+	0.751540i	$0.729311\pi$
$20$	0.0743018	+	2.23483i	0.0166144	+	0.499724i
$21$	−0.309135	−	0.437183i	−0.0674588	−	0.0954011i
$22$	−0.632805	−	0.632805i	−0.134914	−	0.134914i
$23$	−3.19562	−	3.19562i	−0.666333	−	0.666333i	0.290532	−	0.956865i	$-0.406168\pi$
$23$	−3.19562	−	3.19562i	−0.666333	−	0.666333i	−0.956865	+	0.290532i	$0.906168\pi$
$24$	−1.00000	−	1.41421i	−0.204124	−	0.288675i
$25$	4.98896	−	0.332104i	0.997792	−	0.0664208i
$26$			5.05545i			0.991456i
$27$	−4.53553	−	2.53553i	−0.872864	−	0.487964i
$28$	0.218591	−	0.218591i	0.0413099	−	0.0413099i
$29$	2.39124			0.444043			0.222021	−	0.975042i	$-0.428734\pi$
$29$	2.39124			0.444043			0.222021	+	0.975042i	$0.428734\pi$
$30$	−3.08623	+	2.33991i	−0.563466	+	0.427207i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.262116	−	1.52773i	0.0456286	−	0.265943i
$34$		−	6.17246i		−	1.05857i
$35$	−0.504757	−	0.472274i	−0.0853195	−	0.0798288i
$36$	1.00000	−	2.82843i	0.166667	−	0.471405i
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$	−4.63280	−	4.63280i	−0.751540	−	0.751540i
$39$	−7.14949	+	5.05545i	−1.14483	+	0.809520i
$40$	−1.63280	−	1.52773i	−0.258169	−	0.241555i
$41$		−	4.71231i		−	0.735939i	−0.929838	−	0.367969i	$-0.880053\pi$
$41$		−	4.71231i		−	0.735939i	0.929838	−	0.367969i	$-0.119947\pi$
$42$	0.527726	+	0.0905435i	0.0814299	+	0.0139712i
$43$	−3.37912	+	3.37912i	−0.515311	+	0.515311i	−0.916149	−	0.400838i	$-0.868719\pi$
$43$	−3.37912	+	3.37912i	−0.515311	+	0.515311i	0.400838	+	0.916149i	$0.368719\pi$
$44$	0.894921			0.134914
$45$	−6.39536	−	2.02468i	−0.953365	−	0.301821i
$46$	4.51929			0.666333
$47$	8.98896	−	8.98896i	1.31117	−	1.31117i	0.390624	−	0.920550i	$-0.372259\pi$
$47$	8.98896	−	8.98896i	1.31117	−	1.31117i	0.920550	−	0.390624i	$-0.127741\pi$
$48$	1.70711	+	0.292893i	0.246400	+	0.0422755i
$49$		−	6.90444i		−	0.986348i
$50$	−3.29289	+	3.76256i	−0.465685	+	0.532106i
$51$	8.72918	−	6.17246i	1.22233	−	0.864317i
$52$	−3.57474	−	3.57474i	−0.495728	−	0.495728i
$53$	−10.1579	−	10.1579i	−1.39530	−	1.39530i	−0.812913	−	0.582385i	$-0.802120\pi$
$53$	−10.1579	−	10.1579i	−1.39530	−	1.39530i	−0.582385	−	0.812913i	$-0.697880\pi$
$54$	5.00000	−	1.41421i	0.680414	−	0.192450i
$55$	−0.0664943	−	2.00000i	−0.00896609	−	0.269680i
$56$			0.309135i			0.0413099i
$57$	1.91897	−	11.1846i	0.254174	−	1.48143i
$58$	−1.69087	+	1.69087i	−0.222021	+	0.222021i
$59$	−6.79073			−0.884078			−0.442039	−	0.896996i	$-0.645745\pi$
$59$	−6.79073			−0.884078			−0.442039	+	0.896996i	$0.645745\pi$
$60$	0.527726	−	3.83686i	0.0681292	−	0.495337i
$61$	−5.61916			−0.719459			−0.359730	−	0.933057i	$-0.617131\pi$
$61$	−5.61916			−0.719459			−0.359730	+	0.933057i	$0.617131\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	0.399678	+	0.836861i	0.0503548	+	0.105435i
$64$			1.00000i			0.125000i
$65$	−7.72335	+	8.25457i	−0.957963	+	1.02385i
$66$	0.894921	+	1.26561i	0.110157	+	0.155786i
$67$	−9.52512	−	9.52512i	−1.16368	−	1.16368i	−0.983664	−	0.180015i	$-0.942386\pi$
$67$	−9.52512	−	9.52512i	−1.16368	−	1.16368i	−0.180015	−	0.983664i	$-0.557614\pi$
$68$	4.36459	+	4.36459i	0.529284	+	0.529284i
$69$	4.51929	+	6.39124i	0.544059	+	0.769415i
$70$	0.690865	−	0.0229693i	0.0825742	−	0.00274535i
$71$			12.5518i			1.48962i	0.667276	+	0.744811i	$0.267460\pi$
$71$			12.5518i			1.48962i	−0.667276	+	0.744811i	$0.732540\pi$
$72$	1.29289	+	2.70711i	0.152369	+	0.319036i
$73$	−7.83686	+	7.83686i	−0.917235	+	0.917235i	−0.996828	−	0.0795923i	$-0.974638\pi$
$73$	−7.83686	+	7.83686i	−0.917235	+	0.917235i	0.0795923	+	0.996828i	$0.474638\pi$
$74$	2.82843			0.328798
$75$	−8.61396	−	0.894295i	−0.994654	−	0.103264i
$76$	6.55178			0.751540
$77$	−0.195622	+	0.195622i	−0.0222932	+	0.0222932i
$78$	1.48071	−	8.63020i	0.167657	−	0.977177i
$79$		−	13.0830i		−	1.47195i	−0.677008	−	0.735976i	$-0.736724\pi$
$79$		−	13.0830i		−	1.47195i	0.677008	−	0.735976i	$-0.263276\pi$
$80$	2.23483	−	0.0743018i	0.249862	−	0.00830719i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	3.33210	+	3.33210i	0.367969	+	0.367969i
$83$	−1.55913	−	1.55913i	−0.171137	−	0.171137i	0.616342	−	0.787479i	$-0.288614\pi$
$83$	−1.55913	−	1.55913i	−0.171137	−	0.171137i	−0.787479	+	0.616342i	$0.788614\pi$
$84$	−0.437183	+	0.309135i	−0.0477006	+	0.0337294i
$85$	9.42983	−	10.0784i	1.02281	−	1.09316i
$86$		−	4.77880i		−	0.515311i
$87$	−4.08211	−	0.700379i	−0.437648	−	0.0750885i
$88$	−0.632805	+	0.632805i	−0.0674572	+	0.0674572i
$89$	1.83947			0.194983			0.0974916	−	0.995236i	$-0.468918\pi$
$89$	1.83947			0.194983			0.0974916	+	0.995236i	$0.468918\pi$
$90$	5.95387	−	3.09054i	0.627593	−	0.325772i
$91$	1.56282			0.163828
$92$	−3.19562	+	3.19562i	−0.333167	+	0.333167i
$93$	−1.70711	−	0.292893i	−0.177019	−	0.0303716i
$94$			12.7123i			1.31117i
$95$	−0.486809	−	14.6421i	−0.0499455	−	1.50225i
$96$	−1.41421	+	1.00000i	−0.144338	+	0.102062i
$97$	−6.81739	−	6.81739i	−0.692201	−	0.692201i	0.270515	−	0.962716i	$-0.412806\pi$
$97$	−6.81739	−	6.81739i	−0.692201	−	0.692201i	−0.962716	+	0.270515i	$0.912806\pi$
$98$	4.88217	+	4.88217i	0.493174	+	0.493174i
$99$	−0.894921	+	2.53122i	−0.0899430	+	0.254397i
$100$	−0.332104	−	4.98896i	−0.0332104	−	0.498896i
$101$		−	9.43477i		−	0.938795i	−0.882987	−	0.469397i	$-0.844471\pi$
$101$		−	9.43477i		−	0.938795i	0.882987	−	0.469397i	$-0.155529\pi$
$102$	−1.80787	+	10.5370i	−0.179006	+	1.04332i
$103$	−5.08211	+	5.08211i	−0.500755	+	0.500755i	−0.911673	−	0.410917i	$-0.865208\pi$
$103$	−5.08211	+	5.08211i	−0.500755	+	0.500755i	0.410917	+	0.911673i	$0.365208\pi$
$104$	5.05545			0.495728
$105$	0.723349	+	0.954061i	0.0705916	+	0.0931069i
$106$	14.3655			1.39530
$107$	−3.16897	+	3.16897i	−0.306355	+	0.306355i	−0.843494	−	0.537139i	$-0.819505\pi$
$107$	−3.16897	+	3.16897i	−0.306355	+	0.306355i	0.537139	+	0.843494i	$0.319505\pi$
$108$	−2.53553	+	4.53553i	−0.243982	+	0.436432i
$109$		−	17.8618i		−	1.71085i	−0.517927	−	0.855425i	$-0.673296\pi$
$109$		−	17.8618i		−	1.71085i	0.517927	−	0.855425i	$-0.326704\pi$
$110$	1.46123	+	1.36720i	0.139323	+	0.130357i
$111$	2.82843	+	4.00000i	0.268462	+	0.379663i
$112$	−0.218591	−	0.218591i	−0.0206549	−	0.0206549i
$113$	0.0470185	+	0.0470185i	0.00442313	+	0.00442313i	0.709315	−	0.704892i	$-0.249004\pi$
$113$	0.0470185	+	0.0470185i	0.00442313	+	0.00442313i	−0.704892	+	0.709315i	$0.749004\pi$
$114$	6.55178	+	9.26561i	0.613630	+	0.867804i
$115$	7.37912	+	6.90424i	0.688107	+	0.643824i
$116$		−	2.39124i		−	0.222021i
$117$	13.6857	−	6.53616i	1.26524	−	0.604268i
$118$	4.80177	−	4.80177i	0.442039	−	0.442039i
$119$	−1.90812			−0.174917
$120$	2.33991	+	3.08623i	0.213604	+	0.281733i
$121$	10.1991			0.927192
$122$	3.97334	−	3.97334i	0.359730	−	0.359730i
$123$	−1.38020	+	8.04441i	−0.124449	+	0.725340i
$124$		−	1.00000i		−	0.0898027i
$125$	−11.1248	+	1.11289i	−0.995034	+	0.0995396i
$126$	−0.874366	−	0.309135i	−0.0778947	−	0.0275399i
$127$	6.40811	+	6.40811i	0.568628	+	0.568628i	0.931744	−	0.363116i	$-0.118287\pi$
$127$	6.40811	+	6.40811i	0.568628	+	0.568628i	−0.363116	+	0.931744i	$0.618287\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	6.75825	−	4.77880i	0.595030	−	0.420750i
$130$	−0.375629	−	11.2981i	−0.0329449	−	0.990908i
$131$			13.7521i			1.20153i	0.799426	+	0.600765i	$0.205137\pi$
$131$			13.7521i			1.20153i	−0.799426	+	0.600765i	$0.794863\pi$
$132$	−1.52773	−	0.262116i	−0.132972	−	0.0228143i
$133$	−1.43216	+	1.43216i	−0.124184	+	0.124184i
$134$	13.4706			1.16368
$135$	10.3246	+	5.32950i	0.888596	+	0.458690i
$136$	−6.17246			−0.529284
$137$	3.81650	−	3.81650i	0.326066	−	0.326066i	−0.525023	−	0.851088i	$-0.675943\pi$
$137$	3.81650	−	3.81650i	0.326066	−	0.326066i	0.851088	+	0.525023i	$0.175943\pi$
$138$	−7.71491	−	1.32367i	−0.656737	−	0.112678i
$139$			11.2279i			0.952339i	0.879354	+	0.476170i	$0.157975\pi$
$139$			11.2279i			0.952339i	−0.879354	+	0.476170i	$0.842025\pi$
$140$	−0.472274	+	0.504757i	−0.0399144	+	0.0426598i
$141$	−17.9779	+	12.7123i	−1.51401	+	1.07057i
$142$	−8.87545	−	8.87545i	−0.744811	−	0.744811i
$143$	3.19912	+	3.19912i	0.267523	+	0.267523i
$144$	−2.82843	−	1.00000i	−0.235702	−	0.0833333i
$145$	−5.34403	+	0.177674i	−0.443798	+	0.0147550i
$146$		−	11.0830i		−	0.917235i
$147$	−2.02226	+	11.7866i	−0.166793	+	0.972143i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	17.1853			1.40787			0.703936	−	0.710263i	$-0.251424\pi$
$149$	17.1853			1.40787			0.703936	+	0.710263i	$0.251424\pi$
$150$	6.72335	−	5.45862i	0.548959	−	0.445695i
$151$	−19.3474			−1.57447			−0.787236	−	0.616651i	$-0.788489\pi$
$151$	−19.3474			−1.57447			−0.787236	+	0.616651i	$0.788489\pi$
$152$	−4.63280	+	4.63280i	−0.375770	+	0.375770i
$153$	−16.7095	+	7.98033i	−1.35088	+	0.645171i
$154$		−	0.276651i		−	0.0222932i
$155$	−2.23483	+	0.0743018i	−0.179506	+	0.00596806i
$156$	5.05545	+	7.14949i	0.404760	+	0.572417i
$157$	−12.6276	−	12.6276i	−1.00779	−	1.00779i	−0.999969	−	0.00782202i	$-0.997510\pi$
$157$	−12.6276	−	12.6276i	−1.00779	−	1.00779i	−0.00782202	−	0.999969i	$-0.502490\pi$
$158$	9.25107	+	9.25107i	0.735976	+	0.735976i
$159$	14.3655	+	20.3158i	1.13926	+	1.61115i
$160$	−1.52773	+	1.63280i	−0.120777	+	0.129085i
$161$		−	1.39707i		−	0.110105i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	−2.30913	+	2.30913i	−0.180865	+	0.180865i	−0.791733	−	0.610867i	$-0.790821\pi$
$163$	−2.30913	+	2.30913i	−0.180865	+	0.180865i	0.610867	+	0.791733i	$0.290821\pi$
$164$	−4.71231			−0.367969
$165$	−0.472274	+	3.43369i	−0.0367665	+	0.267312i
$166$	2.20494			0.171137
$167$	5.07950	−	5.07950i	0.393064	−	0.393064i	−0.482714	−	0.875778i	$-0.660349\pi$
$167$	5.07950	−	5.07950i	0.393064	−	0.393064i	0.875778	+	0.482714i	$0.160349\pi$
$168$	0.0905435	−	0.527726i	0.00698559	−	0.0407150i
$169$		−	12.5576i		−	0.965969i
$170$	0.458625	+	13.7944i	0.0351749	+	1.05798i
$171$	−6.55178	+	18.5312i	−0.501027	+	1.41712i
$172$	3.37912	+	3.37912i	0.257656	+	0.257656i
$173$	11.9402	+	11.9402i	0.907798	+	0.907798i	0.996094	−	0.0882962i	$-0.0281422\pi$
$173$	11.9402	+	11.9402i	0.907798	+	0.907798i	−0.0882962	+	0.996094i	$0.528142\pi$
$174$	3.38173	−	2.39124i	0.256368	−	0.181280i
$175$	1.16314	+	1.01795i	0.0879250	+	0.0769497i
$176$		−	0.894921i		−	0.0674572i
$177$	11.5925	+	1.98896i	0.871346	+	0.149499i
$178$	−1.30070	+	1.30070i	−0.0974916	+	0.0974916i
$179$	−9.77996			−0.730989			−0.365494	−	0.930814i	$-0.619100\pi$
$179$	−9.77996			−0.730989			−0.365494	+	0.930814i	$0.619100\pi$
$180$	−2.02468	+	6.39536i	−0.150910	+	0.476682i
$181$	−17.2485			−1.28207			−0.641034	−	0.767512i	$-0.721494\pi$
$181$	−17.2485			−1.28207			−0.641034	+	0.767512i	$0.721494\pi$
$182$	−1.10508	+	1.10508i	−0.0819139	+	0.0819139i
$183$	9.59250	+	1.64581i	0.709098	+	0.121662i
$184$		−	4.51929i		−	0.333167i
$185$	4.61827	+	4.32106i	0.339542	+	0.317691i
$186$	1.41421	−	1.00000i	0.103695	−	0.0733236i
$187$	−3.90596	−	3.90596i	−0.285632	−	0.285632i
$188$	−8.98896	−	8.98896i	−0.655587	−	0.655587i
$189$	−0.437183	−	1.54567i	−0.0318004	−	0.112431i
$190$	10.6978	+	10.0093i	0.776098	+	0.726152i
$191$		−	24.0429i		−	1.73968i	−0.493332	−	0.869841i	$-0.664221\pi$
$191$		−	24.0429i		−	1.73968i	0.493332	−	0.869841i	$-0.335779\pi$
$192$	0.292893	−	1.70711i	0.0211377	−	0.123200i
$193$	6.53705	−	6.53705i	0.470547	−	0.470547i	−0.431545	−	0.902092i	$-0.642031\pi$
$193$	6.53705	−	6.53705i	0.470547	−	0.470547i	0.902092	+	0.431545i	$0.142031\pi$
$194$	9.64124			0.692201
$195$	15.6023	−	11.8293i	1.11730	−	0.847115i
$196$	−6.90444			−0.493174
$197$	6.26650	−	6.26650i	0.446469	−	0.446469i	−0.447710	−	0.894179i	$-0.647760\pi$
$197$	6.26650	−	6.26650i	0.446469	−	0.446469i	0.894179	+	0.447710i	$0.147760\pi$
$198$	−1.15704	−	2.42265i	−0.0822271	−	0.172170i
$199$			10.7497i			0.762028i	0.924569	+	0.381014i	$0.124425\pi$
$199$			10.7497i			0.762028i	−0.924569	+	0.381014i	$0.875575\pi$
$200$	3.76256	+	3.29289i	0.266053	+	0.232843i
$201$	13.4706	+	19.0502i	0.950140	+	1.34370i
$202$	6.67139	+	6.67139i	0.469397	+	0.469397i
$203$	0.522705	+	0.522705i	0.0366867	+	0.0366867i
$204$	−6.17246	−	8.72918i	−0.432159	−	0.611165i
$205$	0.350133	+	10.5312i	0.0244543	+	0.735532i
$206$		−	7.18719i		−	0.500755i
$207$	−5.84296	−	12.2342i	−0.406114	−	0.850336i
$208$	−3.57474	+	3.57474i	−0.247864	+	0.247864i
$209$	−5.86332			−0.405575
$210$	−1.18611	−	0.163139i	−0.0818492	−	0.0112576i
$211$	−2.91700			−0.200815			−0.100407	−	0.994946i	$-0.532015\pi$
$211$	−2.91700			−0.200815			−0.100407	+	0.994946i	$0.532015\pi$
$212$	−10.1579	+	10.1579i	−0.697649	+	0.697649i
$213$	3.67633	−	21.4272i	0.251898	−	1.46817i
$214$		−	4.48159i		−	0.306355i
$215$	7.30070	−	7.80285i	0.497904	−	0.532150i
$216$	−1.41421	−	5.00000i	−0.0962250	−	0.340207i
$217$	0.218591	+	0.218591i	0.0148390	+	0.0148390i
$218$	12.6302	+	12.6302i	0.855425	+	0.855425i
$219$	15.6737	−	11.0830i	1.05913	−	0.748919i
$220$	−2.00000	+	0.0664943i	−0.134840	+	0.00448304i
$221$			31.2046i			2.09905i
$222$	−4.82843	−	0.828427i	−0.324063	−	0.0556004i
$223$	−13.7181	+	13.7181i	−0.918634	+	0.918634i	−0.996930	−	0.0782960i	$-0.975052\pi$
$223$	−13.7181	+	13.7181i	−0.918634	+	0.918634i	0.0782960	+	0.996930i	$0.475052\pi$
$224$	0.309135			0.0206549
$225$	14.4430	+	4.04963i	0.962867	+	0.269975i
$226$	−0.0664943			−0.00442313
$227$	−7.35704	+	7.35704i	−0.488304	+	0.488304i	−0.907771	−	0.419467i	$-0.862217\pi$
$227$	−7.35704	+	7.35704i	−0.488304	+	0.488304i	0.419467	+	0.907771i	$0.362217\pi$
$228$	−11.1846	−	1.91897i	−0.740717	−	0.127087i
$229$		−	15.6228i		−	1.03239i	−0.856472	−	0.516193i	$-0.827349\pi$
$229$		−	15.6228i		−	1.03239i	0.856472	−	0.516193i	$-0.172651\pi$
$230$	−10.0999	+	0.335792i	−0.665965	+	0.0221414i
$231$	0.391244	−	0.276651i	0.0257420	−	0.0182023i
$232$	1.69087	+	1.69087i	0.111011	+	0.111011i
$233$	1.35857	+	1.35857i	0.0890027	+	0.0890027i	0.750206	−	0.661204i	$-0.229954\pi$
$233$	1.35857	+	1.35857i	0.0890027	+	0.0890027i	−0.661204	+	0.750206i	$0.729954\pi$
$234$	−5.05545	+	14.2990i	−0.330485	+	0.934754i
$235$	−19.4209	+	20.7567i	−1.26688	+	1.35402i
$236$			6.79073i			0.442039i
$237$	−3.83192	+	22.3341i	−0.248910	+	1.45075i
$238$	1.34925	−	1.34925i	0.0874587	−	0.0874587i
$239$	4.09226			0.264707			0.132353	−	0.991203i	$-0.457747\pi$
$239$	4.09226			0.264707			0.132353	+	0.991203i	$0.457747\pi$
$240$	−3.83686	−	0.527726i	−0.247668	−	0.0340646i
$241$	−2.94455			−0.189675			−0.0948375	−	0.995493i	$-0.530233\pi$
$241$	−2.94455			−0.189675			−0.0948375	+	0.995493i	$0.530233\pi$
$242$	−7.21186	+	7.21186i	−0.463596	+	0.463596i
$243$	−10.2929	−	11.7071i	−0.660289	−	0.751011i
$244$			5.61916i			0.359730i
$245$	0.513012	+	15.4303i	0.0327751	+	0.985803i
$246$	−4.71231	−	6.66421i	−0.300446	−	0.424894i
$247$	23.4209	+	23.4209i	1.49024	+	1.49024i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	2.20494	+	3.11826i	0.139733	+	0.197612i
$250$	7.07950	−	8.65336i	0.447747	−	0.547287i
$251$		−	20.9870i		−	1.32469i	−0.749199	−	0.662345i	$-0.769561\pi$
$251$		−	20.9870i		−	1.32469i	0.749199	−	0.662345i	$-0.230439\pi$
$252$	0.836861	−	0.399678i	0.0527173	−	0.0251774i
$253$	2.85983	−	2.85983i	0.179796	−	0.179796i
$254$	−9.06244			−0.568628
$255$	−19.0496	+	14.4430i	−1.19293	+	0.904456i
$256$	1.00000			0.0625000
$257$	8.75234	−	8.75234i	0.545956	−	0.545956i	−0.379313	−	0.925269i	$-0.623840\pi$
$257$	8.75234	−	8.75234i	0.545956	−	0.545956i	0.925269	+	0.379313i	$0.123840\pi$
$258$	−1.39968	+	8.15792i	−0.0871402	+	0.507890i
$259$		−	0.874366i		−	0.0543304i
$260$	8.25457	+	7.72335i	0.511927	+	0.478982i
$261$	6.76346	+	2.39124i	0.418648	+	0.148014i
$262$	−9.72423	−	9.72423i	−0.600765	−	0.600765i
$263$	7.25457	+	7.25457i	0.447336	+	0.447336i	0.894468	−	0.447132i	$-0.147555\pi$
$263$	7.25457	+	7.25457i	0.447336	+	0.447336i	−0.447132	+	0.894468i	$0.647555\pi$
$264$	1.26561	−	0.894921i	0.0778929	−	0.0550786i
$265$	23.4560	+	21.9465i	1.44089	+	1.34816i
$266$		−	2.02538i		−	0.124184i
$267$	−3.14017	−	0.538768i	−0.192175	−	0.0329721i
$268$	−9.52512	+	9.52512i	−0.581839	+	0.581839i
$269$	−23.1274			−1.41010			−0.705051	−	0.709156i	$-0.749076\pi$
$269$	−23.1274			−1.41010			−0.705051	+	0.709156i	$0.749076\pi$
$270$	−11.0691	+	3.53204i	−0.673643	+	0.214953i
$271$	12.0132			0.729749			0.364874	−	0.931057i	$-0.381112\pi$
$271$	12.0132			0.729749			0.364874	+	0.931057i	$0.381112\pi$
$272$	4.36459	−	4.36459i	0.264642	−	0.264642i
$273$	−2.66790	−	0.457739i	−0.161468	−	0.0277036i
$274$			5.39735i			0.326066i
$275$	0.297207	+	4.46473i	0.0179223	+	0.269233i
$276$	6.39124	−	4.51929i	0.384708	−	0.272029i
$277$	−8.31612	−	8.31612i	−0.499667	−	0.499667i	0.411667	−	0.911334i	$-0.364947\pi$
$277$	−8.31612	−	8.31612i	−0.499667	−	0.499667i	−0.911334	+	0.411667i	$0.864947\pi$
$278$	−7.93933	−	7.93933i	−0.476170	−	0.476170i
$279$	2.82843	+	1.00000i	0.169334	+	0.0598684i
$280$	−0.0229693	−	0.690865i	−0.00137268	−	0.0412871i
$281$		−	18.1759i		−	1.08428i	−0.840288	−	0.542141i	$-0.817614\pi$
$281$		−	18.1759i		−	1.08428i	0.840288	−	0.542141i	$-0.182386\pi$
$282$	3.72335	−	21.7013i	0.221722	−	1.29229i
$283$	−2.79442	+	2.79442i	−0.166111	+	0.166111i	−0.785267	−	0.619157i	$-0.787475\pi$
$283$	−2.79442	+	2.79442i	−0.166111	+	0.166111i	0.619157	+	0.785267i	$0.287475\pi$
$284$	12.5518			0.744811
$285$	−3.45754	+	25.1383i	−0.204807	+	1.48906i
$286$	−4.52423			−0.267523
$287$	1.03007	−	1.03007i	0.0608031	−	0.0608031i
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$		−	21.0993i		−	1.24113i
$290$	3.65317	−	3.90444i	0.214521	−	0.229276i
$291$	9.64124	+	13.6348i	0.565179	+	0.799284i
$292$	7.83686	+	7.83686i	0.458618	+	0.458618i
$293$	−8.65774	−	8.65774i	−0.505791	−	0.505791i	0.407441	−	0.913232i	$-0.366421\pi$
$293$	−8.65774	−	8.65774i	−0.505791	−	0.505791i	−0.913232	+	0.407441i	$0.866421\pi$
$294$	−6.90444	−	9.76435i	−0.402675	−	0.569468i
$295$	15.1761	−	0.504563i	0.883589	−	0.0293768i
$296$		−	2.82843i		−	0.164399i
$297$	2.26910	−	4.05895i	0.131667	−	0.235524i
$298$	−12.1518	+	12.1518i	−0.703936	+	0.703936i
$299$	−22.8471			−1.32128
$300$	−0.894295	+	8.61396i	−0.0516321	+	0.497327i
$301$	−1.47729			−0.0851498
$302$	13.6807	−	13.6807i	0.787236	−	0.787236i
$303$	−2.76338	+	16.1062i	−0.158752	+	0.925275i
$304$		−	6.55178i		−	0.375770i
$305$	12.5579	−	0.417513i	0.719062	−	0.0239067i
$306$	6.17246	−	17.4584i	0.352856	−	0.998027i
$307$	−9.70621	−	9.70621i	−0.553962	−	0.553962i	0.373620	−	0.927582i	$-0.378117\pi$
$307$	−9.70621	−	9.70621i	−0.553962	−	0.553962i	−0.927582	+	0.373620i	$0.878117\pi$
$308$	0.195622	+	0.195622i	0.0111466	+	0.0111466i
$309$	10.1642	−	7.18719i	0.578222	−	0.408865i
$310$	1.52773	−	1.63280i	0.0867690	−	0.0927371i
$311$			26.1226i			1.48127i	0.671905	+	0.740637i	$0.265476\pi$
$311$			26.1226i			1.48127i	−0.671905	+	0.740637i	$0.734524\pi$
$312$	−8.63020	−	1.48071i	−0.488589	−	0.0838286i
$313$	6.78374	−	6.78374i	0.383440	−	0.383440i	−0.488900	−	0.872340i	$-0.662602\pi$
$313$	6.78374	−	6.78374i	0.383440	−	0.383440i	0.872340	+	0.488900i	$0.162602\pi$
$314$	17.8581			1.00779
$315$	−0.955395	−	1.84055i	−0.0538304	−	0.103703i
$316$	−13.0830			−0.735976
$317$	12.3863	−	12.3863i	0.695684	−	0.695684i	−0.267792	−	0.963477i	$-0.586294\pi$
$317$	12.3863	−	12.3863i	0.695684	−	0.695684i	0.963477	+	0.267792i	$0.0862942\pi$
$318$	−24.5234	−	4.20755i	−1.37520	−	0.235948i
$319$			2.13998i			0.119816i
$320$	−0.0743018	−	2.23483i	−0.00415360	−	0.124931i
$321$	6.33793	−	4.48159i	0.353749	−	0.250138i
$322$	0.987879	+	0.987879i	0.0550523	+	0.0550523i
$323$	−28.5958	−	28.5958i	−1.59111	−	1.59111i
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	16.6471	−	19.0214i	0.923413	−	1.05512i
$326$		−	3.26561i		−	0.180865i
$327$	−5.23160	+	30.4920i	−0.289308	+	1.68621i
$328$	3.33210	−	3.33210i	0.183985	−	0.183985i
$329$	3.92982			0.216658
$330$	−2.09404	−	2.76193i	−0.115273	−	0.152039i
$331$	7.16510			0.393830			0.196915	−	0.980421i	$-0.436908\pi$
$331$	7.16510			0.393830			0.196915	+	0.980421i	$0.436908\pi$
$332$	−1.55913	+	1.55913i	−0.0855684	+	0.0855684i
$333$	−3.65685	−	7.65685i	−0.200394	−	0.419593i
$334$			7.18350i			0.393064i
$335$	21.9948	+	20.5793i	1.20170	+	1.12437i
$336$	0.309135	+	0.437183i	0.0168647	+	0.0238503i
$337$	19.8293	+	19.8293i	1.08017	+	1.08017i	0.996493	+	0.0836787i	$0.0266670\pi$
$337$	19.8293	+	19.8293i	1.08017	+	1.08017i	0.0836787	+	0.996493i	$0.473333\pi$
$338$	8.87957	+	8.87957i	0.482985	+	0.482985i
$339$	−0.0664943	−	0.0940371i	−0.00361147	−	0.00510739i
$340$	−10.0784	−	9.42983i	−0.546579	−	0.511404i
$341$			0.894921i			0.0484627i
$342$	−8.47075	−	17.7364i	−0.458046	−	0.959072i
$343$	3.03939	−	3.03939i	0.164112	−	0.164112i
$344$	−4.77880			−0.257656
$345$	−10.5747	−	13.9476i	−0.569325	−	0.750912i
$346$	−16.8860			−0.907798
$347$	2.61458	−	2.61458i	0.140358	−	0.140358i	−0.633437	−	0.773795i	$-0.718356\pi$
$347$	2.61458	−	2.61458i	0.140358	−	0.140358i	0.773795	+	0.633437i	$0.218356\pi$
$348$	−0.700379	+	4.08211i	−0.0375443	+	0.218824i
$349$			5.15937i			0.276175i	0.990420	+	0.138087i	$0.0440955\pi$
$349$			5.15937i			0.276175i	−0.990420	+	0.138087i	$0.955905\pi$
$350$	−1.54226	+	0.102665i	−0.0824373	+	0.00548768i
$351$	−25.2773	+	7.14949i	−1.34920	+	0.381612i
$352$	0.632805	+	0.632805i	0.0337286	+	0.0337286i
$353$	−5.67982	−	5.67982i	−0.302307	−	0.302307i	0.539609	−	0.841916i	$-0.318572\pi$
$353$	−5.67982	−	5.67982i	−0.302307	−	0.302307i	−0.841916	+	0.539609i	$0.818572\pi$
$354$	−9.60354	+	6.79073i	−0.510422	+	0.360923i
$355$	−0.932619	−	28.0511i	−0.0494983	−	1.48880i
$356$		−	1.83947i		−	0.0974916i
$357$	3.25737	+	0.558876i	0.172398	+	0.0295789i
$358$	6.91548	−	6.91548i	0.365494	−	0.365494i
$359$	−8.87284			−0.468290			−0.234145	−	0.972202i	$-0.575229\pi$
$359$	−8.87284			−0.468290			−0.234145	+	0.972202i	$0.575229\pi$
$360$	−3.09054	−	5.95387i	−0.162886	−	0.313796i
$361$	−23.9258			−1.25925
$362$	12.1965	−	12.1965i	0.641034	−	0.641034i
$363$	−17.4110	−	2.98725i	−0.913839	−	0.156790i
$364$		−	1.56282i		−	0.0819139i
$365$	16.9318	−	18.0964i	0.886250	−	0.947207i
$366$	−7.94669	+	5.61916i	−0.415380	+	0.293718i
$367$	7.33579	+	7.33579i	0.382925	+	0.382925i	0.872155	−	0.489230i	$-0.162722\pi$
$367$	7.33579	+	7.33579i	0.382925	+	0.382925i	−0.489230	+	0.872155i	$0.662722\pi$
$368$	3.19562	+	3.19562i	0.166583	+	0.166583i
$369$	4.71231	−	13.3284i	0.245313	−	0.693850i
$370$	−6.32106	+	0.210157i	−0.328616	+	0.0109256i
$371$		−	4.44087i		−	0.230558i
$372$	−0.292893	+	1.70711i	−0.0151858	+	0.0885094i
$373$	−11.2342	+	11.2342i	−0.581685	+	0.581685i	−0.935366	−	0.353681i	$-0.884930\pi$
$373$	−11.2342	+	11.2342i	−0.581685	+	0.581685i	0.353681	+	0.935366i	$0.384930\pi$
$374$	5.52387			0.285632
$375$	19.3172	+	1.35857i	0.997536	+	0.0701561i
$376$	12.7123			0.655587
$377$	8.54809	−	8.54809i	0.440249	−	0.440249i
$378$	1.40209	+	0.783822i	0.0721158	+	0.0403155i
$379$		−	16.6939i		−	0.857509i	−0.903421	−	0.428754i	$-0.858953\pi$
$379$		−	16.6939i		−	0.857509i	0.903421	−	0.428754i	$-0.141047\pi$
$380$	−14.6421	+	0.486809i	−0.751125	+	0.0249728i
$381$	−9.06244	−	12.8162i	−0.464283	−	0.656595i
$382$	17.0009	+	17.0009i	0.869841	+	0.869841i
$383$	−4.38542	−	4.38542i	−0.224084	−	0.224084i	0.586132	−	0.810216i	$-0.300650\pi$
$383$	−4.38542	−	4.38542i	−0.224084	−	0.224084i	−0.810216	+	0.586132i	$0.800650\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$	0.422648	−	0.451718i	0.0215401	−	0.0230217i
$386$			9.24478i			0.470547i
$387$	−12.9367	+	6.17848i	−0.657611	+	0.314070i
$388$	−6.81739	+	6.81739i	−0.346100	+	0.346100i
$389$	0.173712			0.00880757			0.00440379	−	0.999990i	$-0.498598\pi$
$389$	0.173712			0.00880757			0.00440379	+	0.999990i	$0.498598\pi$
$390$	−2.66790	+	19.3971i	−0.135094	+	0.982209i
$391$	27.8951			1.41072
$392$	4.88217	−	4.88217i	0.246587	−	0.246587i
$393$	4.02791	−	23.4764i	0.203181	−	1.18423i
$394$			8.86216i			0.446469i
$395$	0.972090	+	29.2383i	0.0489112	+	1.47114i
$396$	2.53122	+	0.894921i	0.127199	+	0.0449715i
$397$	10.7268	+	10.7268i	0.538365	+	0.538365i	0.923048	−	0.384684i	$-0.125689\pi$
$397$	10.7268	+	10.7268i	0.538365	+	0.538365i	−0.384684	+	0.923048i	$0.625689\pi$
$398$	−7.60121	−	7.60121i	−0.381014	−	0.381014i
$399$	2.86432	−	2.02538i	0.143396	−	0.101396i
$400$	−4.98896	+	0.332104i	−0.249448	+	0.0166052i
$401$			6.81309i			0.340229i	0.985424	+	0.170115i	$0.0544138\pi$
$401$			6.81309i			0.340229i	−0.985424	+	0.170115i	$0.945586\pi$
$402$	−22.9957	−	3.94543i	−1.14692	−	0.196780i
$403$	3.57474	−	3.57474i	0.178071	−	0.178071i
$404$	−9.43477			−0.469397
$405$	−16.0641	−	12.1220i	−0.798234	−	0.602348i
$406$	−0.739217			−0.0366867
$407$	1.78984	−	1.78984i	0.0887192	−	0.0887192i
$408$	10.5370	+	1.80787i	0.521662	+	0.0895030i
$409$		−	13.8327i		−	0.683984i	−0.939703	−	0.341992i	$-0.888898\pi$
$409$		−	13.8327i		−	0.683984i	0.939703	−	0.341992i	$-0.111102\pi$
$410$	−7.69428	−	7.19912i	−0.379993	−	0.355539i
$411$	−7.63300	+	5.39735i	−0.376508	+	0.266231i
$412$	5.08211	+	5.08211i	0.250378	+	0.250378i
$413$	−1.48440	−	1.48440i	−0.0730423	−	0.0730423i
$414$	12.7825	+	4.51929i	0.628225	+	0.222111i
$415$	3.60024	+	3.36855i	0.176729	+	0.165356i
$416$		−	5.05545i		−	0.247864i
$417$	3.28858	−	19.1672i	0.161042	−	0.938624i
$418$	4.14600	−	4.14600i	0.202787	−	0.202787i
$419$	−14.3518			−0.701130			−0.350565	−	0.936538i	$-0.614010\pi$
$419$	−14.3518			−0.701130			−0.350565	+	0.936538i	$0.614010\pi$
$420$	0.954061	−	0.723349i	0.0465534	−	0.0352958i
$421$	23.1036			1.12600			0.562999	−	0.826458i	$-0.309647\pi$
$421$	23.1036			1.12600			0.562999	+	0.826458i	$0.309647\pi$
$422$	2.06263	−	2.06263i	0.100407	−	0.100407i
$423$	34.4136	−	16.4357i	1.67325	−	0.799129i
$424$		−	14.3655i		−	0.697649i
$425$	−20.3252	+	23.2242i	−0.985919	+	1.12654i
$426$	12.5518	+	17.7509i	0.608136	+	0.860033i
$427$	−1.22830	−	1.22830i	−0.0594416	−	0.0594416i
$428$	3.16897	+	3.16897i	0.153178	+	0.153178i
$429$	−4.52423	−	6.39823i	−0.218432	−	0.308910i
$430$	0.355074	+	10.6798i	0.0171232	+	0.515027i
$431$			15.4008i			0.741828i	0.928667	+	0.370914i	$0.120956\pi$
$431$			15.4008i			0.741828i	−0.928667	+	0.370914i	$0.879044\pi$
$432$	4.53553	+	2.53553i	0.218216	+	0.121991i
$433$	5.07340	−	5.07340i	0.243812	−	0.243812i	−0.574613	−	0.818425i	$-0.694847\pi$
$433$	5.07340	−	5.07340i	0.243812	−	0.243812i	0.818425	+	0.574613i	$0.194847\pi$
$434$	−0.309135			−0.0148390
$435$	9.17487	+	1.26192i	0.439901	+	0.0605046i
$436$	−17.8618			−0.855425
$437$	20.9370	−	20.9370i	1.00155	−	1.00155i
$438$	−3.24613	+	18.9199i	−0.155106	+	0.904026i
$439$			8.76562i			0.418360i	0.977877	+	0.209180i	$0.0670795\pi$
$439$			8.76562i			0.418360i	−0.977877	+	0.209180i	$0.932921\pi$
$440$	1.36720	−	1.46123i	0.0651785	−	0.0696615i
$441$	6.90444	−	19.5287i	0.328783	−	0.929938i
$442$	−22.0650	−	22.0650i	−1.04952	−	1.04952i
$443$	−21.1417	−	21.1417i	−1.00447	−	1.00447i	−0.999990	−	0.00448100i	$-0.998574\pi$
$443$	−21.1417	−	21.1417i	−1.00447	−	1.00447i	−0.00448100	−	0.999990i	$-0.501426\pi$
$444$	4.00000	−	2.82843i	0.189832	−	0.134231i
$445$	−4.11091	+	0.136676i	−0.194876	+	0.00647906i
$446$		−	19.4004i		−	0.918634i
$447$	−29.3371	−	5.03345i	−1.38760	−	0.238074i
$448$	−0.218591	+	0.218591i	−0.0103275	+	0.0103275i
$449$	9.58146			0.452177			0.226088	−	0.974107i	$-0.427406\pi$
$449$	9.58146			0.452177			0.226088	+	0.974107i	$0.427406\pi$
$450$	−13.0763	+	7.34923i	−0.616421	+	0.346446i
$451$	4.21714			0.198578
$452$	0.0470185	−	0.0470185i	0.00221157	−	0.00221157i
$453$	33.0282	+	5.66674i	1.55180	+	0.266246i
$454$		−	10.4044i		−	0.488304i
$455$	−3.49264	+	0.116120i	−0.163737	+	0.00544380i
$456$	9.26561	−	6.55178i	0.433902	−	0.306815i
$457$	−8.63350	−	8.63350i	−0.403858	−	0.403858i	0.475732	−	0.879590i	$-0.342183\pi$
$457$	−8.63350	−	8.63350i	−0.403858	−	0.403858i	−0.879590	+	0.475732i	$0.842183\pi$
$458$	11.0470	+	11.0470i	0.516193	+	0.516193i
$459$	30.8623	−	8.72918i	1.44053	−	0.407443i
$460$	6.90424	−	7.37912i	0.321912	−	0.344053i
$461$			7.85481i			0.365835i	0.983128	+	0.182917i	$0.0585541\pi$
$461$			7.85481i			0.365835i	−0.983128	+	0.182917i	$0.941446\pi$
$462$	−0.0810293	+	0.472274i	−0.00376983	+	0.0219722i
$463$	21.6311	−	21.6311i	1.00528	−	1.00528i	0.00529575	−	0.999986i	$-0.498314\pi$
$463$	21.6311	−	21.6311i	1.00528	−	1.00528i	0.999986	−	0.00529575i	$-0.00168570\pi$
$464$	−2.39124			−0.111011
$465$	3.83686	+	0.527726i	0.177930	+	0.0244727i
$466$	−1.92130			−0.0890027
$467$	2.83706	−	2.83706i	0.131283	−	0.131283i	−0.638412	−	0.769695i	$-0.720408\pi$
$467$	2.83706	−	2.83706i	0.131283	−	0.131283i	0.769695	+	0.638412i	$0.220408\pi$
$468$	−6.53616	−	13.6857i	−0.302134	−	0.632619i
$469$		−	4.16422i		−	0.192286i
$470$	−0.944547	−	28.4099i	−0.0435687	−	1.31045i
$471$	17.8581	+	25.2552i	0.822858	+	1.16370i
$472$	−4.80177	−	4.80177i	−0.221019	−	0.221019i
$473$	−3.02405	−	3.02405i	−0.139046	−	0.139046i
$474$	−13.0830	−	18.5021i	−0.600922	−	0.849832i
$475$	2.17587	+	32.6865i	0.0998359	+	1.49976i
$476$			1.90812i			0.0874587i
$477$	−18.5730	−	38.8889i	−0.850400	−	1.78060i
$478$	−2.89367	+	2.89367i	−0.132353	+	0.132353i
$479$	−32.7974			−1.49855			−0.749277	−	0.662257i	$-0.769599\pi$
$479$	−32.7974			−1.49855			−0.749277	+	0.662257i	$0.769599\pi$
$480$	3.08623	−	2.33991i	0.140866	−	0.106802i
$481$	−14.2990			−0.651977
$482$	2.08211	−	2.08211i	0.0948375	−	0.0948375i
$483$	−0.409193	+	2.38495i	−0.0186189	+	0.108519i
$484$		−	10.1991i		−	0.463596i
$485$	15.7423	+	14.7292i	0.714819	+	0.668817i
$486$	15.5563	+	1.00000i	0.705650	+	0.0453609i
$487$	5.36953	+	5.36953i	0.243317	+	0.243317i	0.818221	−	0.574904i	$-0.194961\pi$
$487$	5.36953	+	5.36953i	0.243317	+	0.243317i	−0.574904	+	0.818221i	$0.694961\pi$
$488$	−3.97334	−	3.97334i	−0.179865	−	0.179865i
$489$	4.61827	−	3.26561i	0.208845	−	0.147676i
$490$	−11.2736	−	10.5481i	−0.509289	−	0.476514i
$491$		−	16.7932i		−	0.757865i	−0.925424	−	0.378932i	$-0.876291\pi$
$491$		−	16.7932i		−	0.757865i	0.925424	−	0.378932i	$-0.123709\pi$
$492$	8.04441	+	1.38020i	0.362670	+	0.0622243i
$493$	−10.4368	+	10.4368i	−0.470050	+	0.470050i
$494$	−33.1222			−1.49024
$495$	1.81193	−	5.72335i	0.0814400	−	0.257245i
$496$	−1.00000			−0.0449013
$497$	−2.74371	+	2.74371i	−0.123072	+	0.123072i
$498$	−3.76407	−	0.645813i	−0.168672	−	0.0289396i
$499$		−	40.3002i		−	1.80409i	−0.431646	−	0.902043i	$-0.642067\pi$
$499$		−	40.3002i		−	1.80409i	0.431646	−	0.902043i	$-0.357933\pi$
$500$	1.11289	+	11.1248i	0.0497698	+	0.497517i
$501$	−10.1590	+	7.18350i	−0.453871	+	0.320935i
$502$	14.8401	+	14.8401i	0.662345	+	0.662345i
$503$	14.5686	+	14.5686i	0.649584	+	0.649584i	0.952892	−	0.303309i	$-0.0980913\pi$
$503$	14.5686	+	14.5686i	0.649584	+	0.649584i	−0.303309	+	0.952892i	$0.598091\pi$
$504$	−0.309135	+	0.874366i	−0.0137700	+	0.0389473i
$505$	0.701020	+	21.0851i	0.0311950	+	0.938276i
$506$			4.04441i			0.179796i
$507$	−3.67804	+	21.4372i	−0.163347	+	0.952058i
$508$	6.40811	−	6.40811i	0.284314	−	0.284314i
$509$	−27.4584			−1.21707			−0.608535	−	0.793527i	$-0.708242\pi$
$509$	−27.4584			−1.21707			−0.608535	+	0.793527i	$0.708242\pi$
$510$	3.25737	−	23.6829i	0.144239	−	1.04870i
$511$	−3.42614			−0.151564
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	16.6122	−	29.7158i	0.733449	−	1.31198i
$514$			12.3777i			0.545956i
$515$	10.9801	−	11.7353i	0.483839	−	0.517118i
$516$	−4.77880	−	6.75825i	−0.210375	−	0.297515i
$517$	8.04441	+	8.04441i	0.353793	+	0.353793i
$518$	0.618270	+	0.618270i	0.0271652	+	0.0271652i
$519$	−16.8860	−	23.8804i	−0.741214	−	1.04823i
$520$	−11.2981	+	0.375629i	−0.495454	+	0.0164724i
$521$		−	1.83617i		−	0.0804440i	−0.999191	−	0.0402220i	$-0.987193\pi$
$521$		−	1.83617i		−	0.0804440i	0.999191	−	0.0402220i	$-0.0128065\pi$
$522$	−6.47335	+	3.09162i	−0.283331	+	0.135317i
$523$	−20.3678	+	20.3678i	−0.890622	+	0.890622i	−0.994582	−	0.103960i	$-0.966849\pi$
$523$	−20.3678	+	20.3678i	−0.890622	+	0.890622i	0.103960	+	0.994582i	$0.466849\pi$
$524$	13.7521			0.600765
$525$	−1.68745	−	2.07842i	−0.0736464	−	0.0907098i
$526$	−10.2595			−0.447336
$527$	−4.36459	+	4.36459i	−0.190124	+	0.190124i
$528$	−0.262116	+	1.52773i	−0.0114072	+	0.0664858i
$529$		−	2.57600i		−	0.112000i
$530$	−32.1044	+	1.06738i	−1.39453	+	0.0463640i
$531$	−19.2071	−	6.79073i	−0.833516	−	0.294693i
$532$	1.43216	+	1.43216i	0.0620921	+	0.0620921i
$533$	−16.8453	−	16.8453i	−0.729651	−	0.729651i
$534$	2.60140	−	1.83947i	0.112574	−	0.0796016i
$535$	6.84665	−	7.31757i	0.296006	−	0.316366i
$536$		−	13.4706i		−	0.581839i
$537$	16.6954	+	2.86448i	0.720461	+	0.123612i
$538$	16.3535	−	16.3535i	0.705051	−	0.705051i
$539$	6.17893			0.266145
$540$	5.32950	−	10.3246i	0.229345	−	0.444298i
$541$	14.4899			0.622972			0.311486	−	0.950251i	$-0.399173\pi$
$541$	14.4899			0.622972			0.311486	+	0.950251i	$0.399173\pi$
$542$	−8.49460	+	8.49460i	−0.364874	+	0.364874i
$543$	29.4450	+	5.05196i	1.26360	+	0.216800i
$544$			6.17246i			0.264642i
$545$	1.32716	+	39.9181i	0.0568494	+	1.70991i
$546$	2.21016	−	1.56282i	0.0945860	−	0.0668824i
$547$	5.73896	+	5.73896i	0.245380	+	0.245380i	0.819072	−	0.573691i	$-0.194489\pi$
$547$	5.73896	+	5.73896i	0.245380	+	0.245380i	−0.573691	+	0.819072i	$0.694489\pi$
$548$	−3.81650	−	3.81650i	−0.163033	−	0.163033i
$549$	−15.8934	−	5.61916i	−0.678313	−	0.239820i
$550$	−3.36720	−	2.94688i	−0.143578	−	0.125655i
$551$			15.6669i			0.667432i
$552$	−1.32367	+	7.71491i	−0.0563391	+	0.328369i
$553$	2.85983	−	2.85983i	0.121612	−	0.121612i
$554$	11.7608			0.499667
$555$	−6.61827	−	8.72918i	−0.280930	−	0.370533i
$556$	11.2279			0.476170
$557$	−0.0691016	+	0.0691016i	−0.00292793	+	0.00292793i	−0.708569	−	0.705641i	$-0.750659\pi$
$557$	−0.0691016	+	0.0691016i	−0.00292793	+	0.00292793i	0.705641	+	0.708569i	$0.250659\pi$
$558$	−2.70711	+	1.29289i	−0.114601	+	0.0547325i
$559$			24.1590i			1.02182i
$560$	0.504757	+	0.472274i	0.0213299	+	0.0199572i
$561$	5.52387	+	7.81193i	0.233218	+	0.329820i
$562$	12.8523	+	12.8523i	0.542141	+	0.542141i
$563$	24.3232	+	24.3232i	1.02510	+	1.02510i	0.999677	+	0.0254249i	$0.00809386\pi$
$563$	24.3232	+	24.3232i	1.02510	+	1.02510i	0.0254249	+	0.999677i	$0.491906\pi$
$564$	12.7123	+	17.9779i	0.535285	+	0.757007i
$565$	−0.108572	−	0.101585i	−0.00456767	−	0.00427371i
$566$		−	3.95190i		−	0.166111i
$567$	0.293600	+	2.76668i	0.0123300	+	0.116190i
$568$	−8.87545	+	8.87545i	−0.372405	+	0.372405i
$569$	−35.1115			−1.47195			−0.735976	−	0.677008i	$-0.763276\pi$
$569$	−35.1115			−1.47195			−0.735976	+	0.677008i	$0.763276\pi$
$570$	−15.3306	−	20.2203i	−0.642127	−	0.846934i
$571$	6.21180			0.259956			0.129978	−	0.991517i	$-0.458509\pi$
$571$	6.21180			0.259956			0.129978	+	0.991517i	$0.458509\pi$
$572$	3.19912	−	3.19912i	0.133762	−	0.133762i
$573$	−7.04200	+	41.0438i	−0.294184	+	1.71463i
$574$			1.45674i			0.0608031i
$575$	−17.0041	−	14.8815i	−0.709120	−	0.620603i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	23.7019	+	23.7019i	0.986722	+	0.986722i	0.999913	−	0.0131909i	$-0.00419892\pi$
$577$	23.7019	+	23.7019i	0.986722	+	0.986722i	−0.0131909	+	0.999913i	$0.504199\pi$
$578$	14.9194	+	14.9194i	0.620566	+	0.620566i
$579$	−13.0741	+	9.24478i	−0.543341	+	0.384200i
$580$	0.177674	+	5.34403i	0.00737750	+	0.221899i
$581$		−	0.681625i		−	0.0282786i
$582$	−16.4586	−	2.82385i	−0.682232	−	0.117052i
$583$	9.09054	−	9.09054i	0.376492	−	0.376492i
$584$	−11.0830			−0.458618
$585$	−30.0995	+	15.6241i	−1.24446	+	0.645977i
$586$	12.2439			0.505791
$587$	16.7138	−	16.7138i	0.689854	−	0.689854i	−0.272346	−	0.962199i	$-0.587799\pi$
$587$	16.7138	−	16.7138i	0.689854	−	0.689854i	0.962199	+	0.272346i	$0.0877994\pi$
$588$	11.7866	+	2.02226i	0.486072	+	0.0833967i
$589$			6.55178i			0.269961i
$590$	−10.3744	+	11.0879i	−0.427106	+	0.456483i
$591$	−12.5330	+	8.86216i	−0.515538	+	0.364541i
$592$	2.00000	+	2.00000i	0.0821995	+	0.0821995i
$593$	23.3939	+	23.3939i	0.960672	+	0.960672i	0.999255	−	0.0385829i	$-0.0122844\pi$
$593$	23.3939	+	23.3939i	0.960672	+	0.960672i	−0.0385829	+	0.999255i	$0.512284\pi$
$594$	1.26561	+	4.47461i	0.0519286	+	0.183595i
$595$	4.26434	−	0.141777i	0.174821	−	0.00581229i
$596$		−	17.1853i		−	0.703936i
$597$	3.14852	−	18.3509i	0.128860	−	0.751054i
$598$	16.1553	−	16.1553i	0.660640	−	0.660640i
$599$	−21.9457			−0.896677			−0.448339	−	0.893864i	$-0.647984\pi$
$599$	−21.9457			−0.896677			−0.448339	+	0.893864i	$0.647984\pi$
$600$	−5.45862	−	6.72335i	−0.222847	−	0.274480i
$601$	12.5120			0.510376			0.255188	−	0.966891i	$-0.417863\pi$
$601$	12.5120			0.510376			0.255188	+	0.966891i	$0.417863\pi$
$602$	1.04460	−	1.04460i	0.0425749	−	0.0425749i
$603$	−17.4160	−	36.4662i	−0.709234	−	1.48502i
$604$			19.3474i			0.787236i
$605$	−22.7933	+	0.757813i	−0.926680	+	0.0308095i
$606$	−9.43477	−	13.3428i	−0.383261	−	0.542013i
$607$	0.824660	+	0.824660i	0.0334719	+	0.0334719i	0.723645	−	0.690173i	$-0.242465\pi$
$607$	0.824660	+	0.824660i	0.0334719	+	0.0334719i	−0.690173	+	0.723645i	$0.742465\pi$
$608$	4.63280	+	4.63280i	0.187885	+	0.187885i
$609$	−0.739217	−	1.04541i	−0.0299546	−	0.0423622i
$610$	−8.58453	+	9.17499i	−0.347578	+	0.371484i
$611$		−	64.2665i		−	2.59994i
$612$	7.98033	+	16.7095i	0.322586	+	0.675442i
$613$	−30.7528	+	30.7528i	−1.24209	+	1.24209i	−0.282961	+	0.959132i	$0.591317\pi$
$613$	−30.7528	+	30.7528i	−1.24209	+	1.24209i	−0.959132	+	0.282961i	$0.908683\pi$
$614$	13.7266			0.553962
$615$	2.48681	−	18.0805i	0.100278	−	0.729075i
$616$	−0.276651			−0.0111466
$617$	7.17227	−	7.17227i	0.288745	−	0.288745i	−0.547839	−	0.836584i	$-0.684549\pi$
$617$	7.17227	−	7.17227i	0.288745	−	0.288745i	0.836584	+	0.547839i	$0.184549\pi$
$618$	−2.10508	+	12.2693i	−0.0846787	+	0.493544i
$619$			29.0416i			1.16728i	0.812012	+	0.583640i	$0.198372\pi$
$619$			29.0416i			1.16728i	−0.812012	+	0.583640i	$0.801628\pi$
$620$	0.0743018	+	2.23483i	0.00298403	+	0.0897531i
$621$	6.39124	+	22.5965i	0.256472	+	0.906765i
$622$	−18.4714	−	18.4714i	−0.740637	−	0.740637i
$623$	0.402092	+	0.402092i	0.0161095	+	0.0161095i
$624$	7.14949	−	5.05545i	0.286209	−	0.202380i
$625$	24.7794	−	3.31371i	0.991177	−	0.132548i
$626$			9.59366i			0.383440i
$627$	10.0093	+	1.71733i	0.399734	+	0.0685835i
$628$	−12.6276	+	12.6276i	−0.503896	+	0.503896i
$629$	17.4584			0.696110
$630$	1.97703	+	0.625898i	0.0787668	+	0.0249364i
$631$	−29.2810			−1.16566			−0.582828	−	0.812595i	$-0.698054\pi$
$631$	−29.2810			−1.16566			−0.582828	+	0.812595i	$0.698054\pi$
$632$	9.25107	−	9.25107i	0.367988	−	0.367988i
$633$	4.97964	+	0.854371i	0.197923	+	0.0339582i
$634$			17.5169i			0.695684i
$635$	−14.7972	−	13.8449i	−0.587209	−	0.549419i
$636$	20.3158	−	14.3655i	0.805576	−	0.569628i
$637$	−24.6816	−	24.6816i	−0.977920	−	0.977920i
$638$	−1.51319	−	1.51319i	−0.0599078	−	0.0599078i
$639$	−12.5518	+	35.5018i	−0.496541	+	1.40443i
$640$	1.63280	+	1.52773i	0.0645423	+	0.0603887i
$641$		−	48.2990i		−	1.90770i	−0.300291	−	0.953848i	$-0.597084\pi$
$641$		−	48.2990i		−	1.90770i	0.300291	−	0.953848i	$-0.402916\pi$
$642$	−1.31263	+	7.65056i	−0.0518053	+	0.301944i
$643$	−12.7695	+	12.7695i	−0.503579	+	0.503579i	−0.912548	−	0.408969i	$-0.865888\pi$
$643$	−12.7695	+	12.7695i	−0.503579	+	0.503579i	0.408969	+	0.912548i	$0.365888\pi$
$644$	−1.39707			−0.0550523
$645$	−14.7485	+	11.1820i	−0.580721	+	0.440290i
$646$	40.4406			1.59111
$647$	5.60373	−	5.60373i	0.220306	−	0.220306i	−0.588322	−	0.808627i	$-0.700211\pi$
$647$	5.60373	−	5.60373i	0.220306	−	0.220306i	0.808627	+	0.588322i	$0.200211\pi$
$648$	0.949747	+	8.94975i	0.0373096	+	0.351579i
$649$		−	6.07717i		−	0.238550i
$650$	1.67894	+	25.2214i	0.0658533	+	0.989266i
$651$	−0.309135	−	0.437183i	−0.0121160	−	0.0171345i
$652$	2.30913	+	2.30913i	0.0904327	+	0.0904327i
$653$	−5.29935	−	5.29935i	−0.207379	−	0.207379i	0.595773	−	0.803153i	$-0.296846\pi$
$653$	−5.29935	−	5.29935i	−0.207379	−	0.207379i	−0.803153	+	0.595773i	$0.796846\pi$
$654$	−17.8618	−	25.2604i	−0.698452	−	0.987760i
$655$	−1.02181	−	30.7337i	−0.0399254	−	1.20087i
$656$			4.71231i			0.183985i
$657$	−30.0029	+	14.3291i	−1.17052	+	0.559033i
$658$	−2.77880	+	2.77880i	−0.108329	+	0.108329i
$659$	40.4185			1.57448			0.787241	−	0.616646i	$-0.211509\pi$
$659$	40.4185			1.57448			0.787241	+	0.616646i	$0.211509\pi$
$660$	3.43369	+	0.472274i	0.133656	+	0.0183832i
$661$	8.54986			0.332551			0.166276	−	0.986079i	$-0.446826\pi$
$661$	8.54986			0.332551			0.166276	+	0.986079i	$0.446826\pi$
$662$	−5.06649	+	5.06649i	−0.196915	+	0.196915i
$663$	9.13961	−	53.2695i	0.354953	−	2.06882i
$664$		−	2.20494i		−	0.0855684i
$665$	3.09423	−	3.30706i	0.119989	−	0.128242i
$666$	8.00000	+	2.82843i	0.309994	+	0.109599i
$667$	−7.64151	−	7.64151i	−0.295881	−	0.295881i
$668$	−5.07950	−	5.07950i	−0.196532	−	0.196532i
$669$	27.4363	−	19.4004i	1.06075	−	0.750062i
$670$	−30.1044	+	1.00089i	−1.16304	+	0.0386676i
$671$		−	5.02870i		−	0.194131i
$672$	−0.527726	−	0.0905435i	−0.0203575	−	0.00349279i
$673$	−25.2231	+	25.2231i	−0.972278	+	0.972278i	−0.999626	−	0.0273475i	$-0.991294\pi$
$673$	−25.2231	+	25.2231i	−0.972278	+	0.972278i	0.0273475	+	0.999626i	$0.491294\pi$
$674$	−28.0429			−1.08017
$675$	−23.4697	−	11.1434i	−0.903347	−	0.428910i
$676$	−12.5576			−0.482985
$677$	−32.2155	+	32.2155i	−1.23814	+	1.23814i	−0.277384	+	0.960759i	$0.589467\pi$
$677$	−32.2155	+	32.2155i	−1.23814	+	1.23814i	−0.960759	+	0.277384i	$0.910533\pi$
$678$	0.113513	+	0.0194757i	0.00435943	+	0.000747961i
$679$		−	2.98044i		−	0.114379i
$680$	13.7944	−	0.458625i	0.528992	−	0.0175875i
$681$	14.7141	−	10.4044i	0.563845	−	0.398698i
$682$	−0.632805	−	0.632805i	−0.0242314	−	0.0242314i
$683$	6.13560	+	6.13560i	0.234772	+	0.234772i	0.814681	−	0.579909i	$-0.196912\pi$
$683$	6.13560	+	6.13560i	0.234772	+	0.234772i	−0.579909	+	0.814681i	$0.696912\pi$
$684$	18.5312	+	6.55178i	0.708559	+	0.250513i
$685$	−8.24567	+	8.81281i	−0.315051	+	0.336720i
$686$			4.29835i			0.164112i
$687$	−4.57582	+	26.6699i	−0.174579	+	1.01752i
$688$	3.37912	−	3.37912i	0.128828	−	0.128828i
$689$	−72.6240			−2.76675
$690$	17.3399	+	2.38495i	0.660119	+	0.0907935i
$691$	−26.6510			−1.01385			−0.506926	−	0.861989i	$-0.669218\pi$
$691$	−26.6510			−1.01385			−0.506926	+	0.861989i	$0.669218\pi$
$692$	11.9402	−	11.9402i	0.453899	−	0.453899i
$693$	−0.748925	+	0.357681i	−0.0284493	+	0.0135872i
$694$			3.69758i			0.140358i
$695$	−0.834254	−	25.0925i	−0.0316451	−	0.951813i
$696$	−2.39124	−	3.38173i	−0.0906399	−	0.128184i
$697$	20.5673	+	20.5673i	0.779041	+	0.779041i
$698$	−3.64823	−	3.64823i	−0.138087	−	0.138087i
$699$	−1.92130	−	2.71713i	−0.0726704	−	0.102771i
$700$	1.01795	−	1.16314i	0.0384748	−	0.0439625i
$701$			50.7429i			1.91653i	0.285878	+	0.958266i	$0.407715\pi$
$701$			50.7429i			1.91653i	−0.285878	+	0.958266i	$0.592285\pi$
$702$	12.8183	−	22.9292i	0.483794	−	0.865406i
$703$	13.1036	−	13.1036i	0.494210	−	0.494210i
$704$	−0.894921			−0.0337286
$705$	39.2331	−	29.7457i	1.47760	−	1.12029i
$706$	8.03248			0.302307
$707$	2.06236	−	2.06236i	0.0775630	−	0.0775630i
$708$	1.98896	−	11.5925i	0.0747496	−	0.435673i
$709$			12.7840i			0.480113i	0.970759	+	0.240056i	$0.0771659\pi$
$709$			12.7840i			0.480113i	−0.970759	+	0.240056i	$0.922834\pi$
$710$	20.4946	+	19.1757i	0.769149	+	0.719650i
$711$	13.0830	−	37.0043i	0.490651	−	1.38777i
$712$	1.30070	+	1.30070i	0.0487458	+	0.0487458i
$713$	−3.19562	−	3.19562i	−0.119677	−	0.119677i
$714$	−2.69849	+	1.90812i	−0.100989	+	0.0714097i
$715$	−7.38719	−	6.91179i	−0.276265	−	0.258486i
$716$			9.77996i			0.365494i
$717$	−6.98593	−	1.19860i	−0.260894	−	0.0447624i
$718$	6.27404	−	6.27404i	0.234145	−	0.234145i
$719$	37.4700			1.39740			0.698698	−	0.715417i	$-0.253763\pi$
$719$	37.4700			1.39740			0.698698	+	0.715417i	$0.253763\pi$
$720$	6.39536	+	2.02468i	0.238341	+	0.0754552i
$721$	−2.22181			−0.0827446
$722$	16.9181	−	16.9181i	0.629625	−	0.629625i
$723$	5.02666	+	0.862438i	0.186943	+	0.0320744i
$724$			17.2485i			0.641034i
$725$	11.9298	−	0.794142i	0.443062	−	0.0294937i
$726$	14.4237	−	10.1991i	0.535315	−	0.378525i
$727$	14.9790	+	14.9790i	0.555540	+	0.555540i	0.928034	−	0.372494i	$-0.121497\pi$
$727$	14.9790	+	14.9790i	0.555540	+	0.555540i	−0.372494	+	0.928034i	$0.621497\pi$
$728$	1.10508	+	1.10508i	0.0409569	+	0.0409569i
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$	0.823486	+	24.7686i	0.0304786	+	0.916729i
$731$		−	29.4970i		−	1.09098i
$732$	1.64581	−	9.59250i	0.0608310	−	0.354549i
$733$	12.0888	−	12.0888i	0.446511	−	0.446511i	−0.447682	−	0.894193i	$-0.647750\pi$
$733$	12.0888	−	12.0888i	0.446511	−	0.446511i	0.894193	+	0.447682i	$0.147750\pi$
$734$	−10.3744			−0.382925
$735$	3.64365	−	26.4914i	0.134398	−	0.977149i
$736$	−4.51929			−0.166583
$737$	8.52423	−	8.52423i	0.313994	−	0.313994i
$738$	6.09251	+	12.7567i	0.224268	+	0.469581i
$739$			6.73275i			0.247668i	0.992303	+	0.123834i	$0.0395191\pi$
$739$			6.73275i			0.247668i	−0.992303	+	0.123834i	$0.960481\pi$
$740$	4.32106	−	4.61827i	0.158845	−	0.169771i
$741$	−33.1222	−	46.8419i	−1.21677	−	1.72078i
$742$	3.14017	+	3.14017i	0.115279	+	0.115279i
$743$	−15.0314	−	15.0314i	−0.551449	−	0.551449i	0.375410	−	0.926859i	$-0.377502\pi$
$743$	−15.0314	−	15.0314i	−0.551449	−	0.551449i	−0.926859	+	0.375410i	$0.877502\pi$
$744$	−1.00000	−	1.41421i	−0.0366618	−	0.0518476i
$745$	−38.4062	+	1.27690i	−1.40709	+	0.0467819i
$746$		−	15.8876i		−	0.581685i
$747$	−2.85076	−	5.96902i	−0.104304	−	0.218395i
$748$	−3.90596	+	3.90596i	−0.142816	+	0.142816i
$749$	−1.38542			−0.0506220
$750$	−14.6200	+	12.6987i	−0.533846	+	0.463690i
$751$	34.0716			1.24329			0.621645	−	0.783299i	$-0.286465\pi$
$751$	34.0716			1.24329			0.621645	+	0.783299i	$0.286465\pi$
$752$	−8.98896	+	8.98896i	−0.327794	+	0.327794i
$753$	−6.14696	+	35.8271i	−0.224008	+	1.30561i
$754$			12.0888i			0.440249i
$755$	43.2383	−	1.43755i	1.57360	−	0.0523178i
$756$	−1.54567	+	0.437183i	−0.0562156	+	0.0159002i
$757$	−13.4109	−	13.4109i	−0.487428	−	0.487428i	0.420066	−	0.907494i	$-0.362007\pi$
$757$	−13.4109	−	13.4109i	−0.487428	−	0.487428i	−0.907494	+	0.420066i	$0.862007\pi$
$758$	11.8044	+	11.8044i	0.428754	+	0.428754i
$759$	−5.71966	+	4.04441i	−0.207611	+	0.146803i
$760$	10.0093	−	10.6978i	0.363076	−	0.388049i
$761$			51.2537i			1.85794i	0.370151	+	0.928972i	$0.379306\pi$
$761$			51.2537i			1.85794i	−0.370151	+	0.928972i	$0.620694\pi$
$762$	15.4706	+	2.65433i	0.560439	+	0.0961561i
$763$	3.90444	−	3.90444i	0.141350	−	0.141350i
$764$	−24.0429			−0.869841
$765$	36.7500	−	19.0763i	1.32870	−	0.689703i
$766$	6.20192			0.224084
$767$	−24.2751	+	24.2751i	−0.876524	+	0.876524i
$768$	−1.70711	−	0.292893i	−0.0615999	−	0.0105689i
$769$			21.1359i			0.762181i	0.924538	+	0.381090i	$0.124451\pi$
$769$			21.1359i			0.762181i	−0.924538	+	0.381090i	$0.875549\pi$
$770$	0.0205557	+	0.618270i	0.000740776	+	0.0222809i
$771$	−17.5047	+	12.3777i	−0.630416	+	0.445771i
$772$	−6.53705	−	6.53705i	−0.235273	−	0.235273i
$773$	−5.10946	−	5.10946i	−0.183774	−	0.183774i	0.609224	−	0.792998i	$-0.291481\pi$
$773$	−5.10946	−	5.10946i	−0.183774	−	0.183774i	−0.792998	+	0.609224i	$0.791481\pi$
$774$	4.77880	−	13.5165i	0.171770	−	0.485840i
$775$	4.98896	−	0.332104i	0.179209	−	0.0119295i
$776$		−	9.64124i		−	0.346100i
$777$	−0.256096	+	1.49264i	−0.00918738	+	0.0535480i
$778$	−0.122833	+	0.122833i	−0.00440379	+	0.00440379i
$779$	30.8740			1.10618
$780$	−11.8293	−	15.6023i	−0.423557	−	0.558652i
$781$	−11.2329			−0.401943
$782$	−19.7248	+	19.7248i	−0.705359	+	0.705359i
$783$	−10.8456	−	6.06308i	−0.387589	−	0.216677i
$784$			6.90444i			0.246587i
$785$	29.1588	+	27.2823i	1.04072	+	0.973747i
$786$	13.7521	+	19.4485i	0.490523	+	0.693704i
$787$	5.33840	+	5.33840i	0.190293	+	0.190293i	0.795823	−	0.605529i	$-0.207039\pi$
$787$	5.33840	+	5.33840i	0.190293	+	0.190293i	−0.605529	+	0.795823i	$0.707039\pi$
$788$	−6.26650	−	6.26650i	−0.223235	−	0.223235i
$789$	−10.2595	−	14.5091i	−0.365248	−	0.516539i
$790$	−21.3620	−	19.9872i	−0.760025	−	0.711114i
$791$			0.0205557i			0.000730877i
$792$	−2.42265	+	1.15704i	−0.0860850	+	0.0411135i
$793$	−20.0870	+	20.0870i	−0.713312	+	0.713312i
$794$	−15.1700			−0.538365
$795$	−33.6139	−	44.3352i	−1.19216	−	1.57241i
$796$	10.7497			0.381014
$797$	−2.18933	+	2.18933i	−0.0775500	+	0.0775500i	−0.744818	−	0.667268i	$-0.767464\pi$
$797$	−2.18933	+	2.18933i	−0.0775500	+	0.0775500i	0.667268	+	0.744818i	$0.267464\pi$
$798$	−0.593221	+	3.45754i	−0.0209998	+	0.122396i
$799$			78.4662i			2.77593i
$800$	3.29289	−	3.76256i	0.116421	−	0.133027i
$801$	5.20280	+	1.83947i	0.183832	+	0.0649944i
$802$	−4.81758	−	4.81758i	−0.170115	−	0.170115i
$803$	−7.01337	−	7.01337i	−0.247497	−	0.247497i
$804$	19.0502	−	13.4706i	0.671850	−	0.475070i
$805$	0.103805	+	3.12222i	0.00365864	+	0.110044i
$806$			5.05545i			0.178071i
$807$	39.4810	+	6.77386i	1.38980	+	0.238451i
$808$	6.67139	−	6.67139i	0.234699	−	0.234699i
$809$	2.54711			0.0895516			0.0447758	−	0.998997i	$-0.485743\pi$
$809$	2.54711			0.0895516			0.0447758	+	0.998997i	$0.485743\pi$
$810$	19.9306	−	2.78751i	0.700291	−	0.0979431i
$811$	−5.43529			−0.190859			−0.0954294	−	0.995436i	$-0.530422\pi$
$811$	−5.43529			−0.190859			−0.0954294	+	0.995436i	$0.530422\pi$
$812$	0.522705	−	0.522705i	0.0183434	−	0.0183434i
$813$	−20.5078	−	3.51858i	−0.719239	−	0.123402i
$814$			2.53122i			0.0887192i
$815$	4.98896	−	5.33210i	0.174756	−	0.186775i
$816$	−8.72918	+	6.17246i	−0.305582	+	0.216079i
$817$	−22.1393	−	22.1393i	−0.774554	−	0.774554i
$818$	9.78121	+	9.78121i	0.341992	+	0.341992i
$819$	4.42031	+	1.56282i	0.154458	+	0.0546093i
$820$	10.5312	−	0.350133i	0.367766	−	0.0122272i
$821$			15.6179i			0.545069i	0.962146	+	0.272534i	$0.0878618\pi$
$821$			15.6179i			0.545069i	−0.962146	+	0.272534i	$0.912138\pi$
$822$	1.58085	−	9.21384i	0.0551383	−	0.321370i
$823$	24.6369	−	24.6369i	0.858789	−	0.858789i	−0.132407	−	0.991195i	$-0.542271\pi$
$823$	24.6369	−	24.6369i	0.858789	−	0.858789i	0.991195	+	0.132407i	$0.0422705\pi$
$824$	−7.18719			−0.250378
$825$	0.800323	−	7.70881i	0.0278637	−	0.268386i
$826$	2.09925			0.0730423
$827$	−16.9360	+	16.9360i	−0.588924	+	0.588924i	−0.937340	−	0.348416i	$-0.886720\pi$
$827$	−16.9360	+	16.9360i	−0.588924	+	0.588924i	0.348416	+	0.937340i	$0.386720\pi$
$828$	−12.2342	+	5.84296i	−0.425168	+	0.203057i
$829$			16.4317i			0.570696i	0.958424	+	0.285348i	$0.0921092\pi$
$829$			16.4317i			0.570696i	−0.958424	+	0.285348i	$0.907891\pi$
$830$	−4.92768	+	0.163831i	−0.171042	+	0.00568666i
$831$	11.7608	+	16.6322i	0.407977	+	0.576966i
$832$	3.57474	+	3.57474i	0.123932	+	0.123932i
$833$	30.1350	+	30.1350i	1.04412	+	1.04412i
$834$	11.2279	+	15.8787i	0.388791	+	0.549833i
$835$	−10.9744	+	11.7293i	−0.379786	+	0.405908i
$836$			5.86332i			0.202787i
$837$	−4.53553	−	2.53553i	−0.156771	−	0.0876409i
$838$	10.1482	−	10.1482i	0.350565	−	0.350565i
$839$	−35.2129			−1.21569			−0.607843	−	0.794057i	$-0.707965\pi$
$839$	−35.2129			−1.21569			−0.607843	+	0.794057i	$0.707965\pi$
$840$	−0.163139	+	1.18611i	−0.00562882	+	0.0409246i
$841$	−23.2820			−0.802826
$842$	−16.3367	+	16.3367i	−0.562999	+	0.562999i
$843$	−5.32359	+	31.0282i	−0.183354	+	1.06867i
$844$			2.91700i			0.100407i
$845$	0.933052	+	28.0641i	0.0320980	+	0.965436i
$846$	−12.7123	+	35.9558i	−0.437058	+	1.23619i
$847$	2.22944	+	2.22944i	0.0766044	+	0.0766044i
$848$	10.1579	+	10.1579i	0.348825	+	0.348825i
$849$	5.58883	−	3.95190i	0.191808	−	0.135629i
$850$	−2.04990	−	30.7941i	−0.0703110	−	1.05623i
$851$			12.7825i			0.438178i
$852$	−21.4272	−	3.67633i	−0.734085	−	0.125949i
$853$	14.1055	−	14.1055i	0.482964	−	0.482964i	−0.423113	−	0.906077i	$-0.639063\pi$
$853$	14.1055	−	14.1055i	0.482964	−	0.482964i	0.906077	+	0.423113i	$0.139063\pi$
$854$	1.73708			0.0594416
$855$	13.2652	−	41.9010i	0.453661	−	1.43298i
$856$	−4.48159			−0.153178
$857$	−34.6304	+	34.6304i	−1.18295	+	1.18295i	−0.203978	+	0.978975i	$0.565387\pi$
$857$	−34.6304	+	34.6304i	−1.18295	+	1.18295i	−0.978975	+	0.203978i	$0.934613\pi$
$858$	7.72335	+	1.32512i	0.263671	+	0.0452388i
$859$		−	11.2737i		−	0.384653i	−0.981331	−	0.192327i	$-0.938397\pi$
$859$		−	11.2737i		−	0.384653i	0.981331	−	0.192327i	$-0.0616033\pi$
$860$	−7.80285	−	7.30070i	−0.266075	−	0.248952i
$861$	−2.06014	+	1.45674i	−0.0702094	+	0.0496455i
$862$	−10.8900	−	10.8900i	−0.370914	−	0.370914i
$863$	24.7143	+	24.7143i	0.841284	+	0.841284i	0.989026	−	0.147742i	$-0.0472006\pi$
$863$	24.7143	+	24.7143i	0.841284	+	0.841284i	−0.147742	+	0.989026i	$0.547201\pi$
$864$	−5.00000	+	1.41421i	−0.170103	+	0.0481125i
$865$	−27.5716	−	25.7972i	−0.937462	−	0.877132i
$866$			7.17487i			0.243812i
$867$	−6.17983	+	36.0187i	−0.209878	+	1.22326i
$868$	0.218591	−	0.218591i	0.00741948	−	0.00741948i
$869$	11.7083			0.397175
$870$	−7.37993	+	5.59530i	−0.250203	+	0.189698i
$871$	−68.0997			−2.30747
$872$	12.6302	−	12.6302i	0.427712	−	0.427712i
$873$	−12.4651	−	26.0999i	−0.421879	−	0.883347i
$874$			29.6094i			1.00155i
$875$	−2.67506	−	2.18852i	−0.0904334	−	0.0739855i
$876$	−11.0830	−	15.6737i	−0.374460	−	0.529566i
$877$	−21.9874	−	21.9874i	−0.742462	−	0.742462i	0.230589	−	0.973051i	$-0.425935\pi$
$877$	−21.9874	−	21.9874i	−0.742462	−	0.742462i	−0.973051	+	0.230589i	$0.925935\pi$
$878$	−6.19823	−	6.19823i	−0.209180	−	0.209180i
$879$	12.2439	+	17.3155i	0.412976	+	0.584037i
$880$	0.0664943	+	2.00000i	0.00224152	+	0.0674200i
$881$		−	50.8515i		−	1.71323i	−0.515954	−	0.856616i	$-0.672563\pi$
$881$		−	50.8515i		−	1.71323i	0.515954	−	0.856616i	$-0.327437\pi$
$882$	8.92670	+	18.6910i	0.300578	+	0.629360i
$883$	−18.7011	+	18.7011i	−0.629341	+	0.629341i	−0.947902	−	0.318561i	$-0.896800\pi$
$883$	−18.7011	+	18.7011i	−0.629341	+	0.629341i	0.318561	+	0.947902i	$0.396800\pi$
$884$	31.2046			1.04952
$885$	−26.0551	−	3.58365i	−0.875832	−	0.120463i
$886$	29.8988			1.00447
$887$	−14.9041	+	14.9041i	−0.500430	+	0.500430i	−0.911571	−	0.411142i	$-0.865130\pi$
$887$	−14.9041	+	14.9041i	−0.500430	+	0.500430i	0.411142	+	0.911571i	$0.365130\pi$
$888$	−0.828427	+	4.82843i	−0.0278002	+	0.162031i
$889$			2.80152i			0.0939599i
$890$	2.81020	−	3.00349i	0.0941983	−	0.100677i
$891$	−5.06244	+	6.26445i	−0.169598	+	0.209867i
$892$	13.7181	+	13.7181i	0.459317	+	0.459317i
$893$	58.8936	+	58.8936i	1.97080	+	1.97080i
$894$	24.3036	−	17.1853i	0.812836	−	0.574762i
$895$	21.8566	−	0.726669i	0.730585	−	0.0242899i
$896$		−	0.309135i		−	0.0103275i
$897$	39.0024	+	6.69175i	1.30225	+	0.223431i
$898$	−6.77511	+	6.77511i	−0.226088	+	0.226088i
$899$	2.39124			0.0797525
$900$	4.04963	−	14.4430i	0.134988	−	0.481434i
$901$	88.6703			2.95404
$902$	−2.98197	+	2.98197i	−0.0992888	+	0.0992888i
$903$	2.52190	+	0.432690i	0.0839236	+	0.0143990i
$904$			0.0664943i			0.00221157i
$905$	38.5474	−	1.28159i	1.28136	−	0.0426016i
$906$	−27.3614	+	19.3474i	−0.909022	+	0.642776i
$907$	28.6764	+	28.6764i	0.952184	+	0.952184i	0.998908	−	0.0467242i	$-0.0148782\pi$
$907$	28.6764	+	28.6764i	0.952184	+	0.952184i	−0.0467242	+	0.998908i	$0.514878\pi$
$908$	7.35704	+	7.35704i	0.244152	+	0.244152i
$909$	9.43477	−	26.6856i	0.312932	−	0.885104i
$910$	2.38756	−	2.55178i	0.0791467	−	0.0845905i
$911$			31.2435i			1.03514i	0.855640	+	0.517572i	$0.173164\pi$
$911$			31.2435i			1.03514i	−0.855640	+	0.517572i	$0.826836\pi$
$912$	−1.91897	+	11.1846i	−0.0635435	+	0.370358i
$913$	1.39530	−	1.39530i	0.0461776	−	0.0461776i
$914$	12.2096			0.403858
$915$	−21.5599	−	2.96538i	−0.712749	−	0.0980323i
$916$	−15.6228			−0.516193
$917$	−3.00610	+	3.00610i	−0.0992702	+	0.0992702i
$918$	−15.6505	+	27.9954i	−0.516543	+	0.923986i
$919$		−	35.4719i		−	1.17011i	−0.810993	−	0.585056i	$-0.801073\pi$
$919$		−	35.4719i		−	1.17011i	0.810993	−	0.585056i	$-0.198927\pi$
$920$	0.335792	+	10.0999i	0.0110707	+	0.332983i
$921$	13.7266	+	19.4124i	0.452308	+	0.639661i
$922$	−5.55419	−	5.55419i	−0.182917	−	0.182917i
$923$	44.8694	+	44.8694i	1.47689	+	1.47689i
$924$	−0.276651	−	0.391244i	−0.00910117	−	0.0128710i
$925$	−10.6421	−	9.31371i	−0.349911	−	0.306233i
$926$			30.5910i			1.00528i
$927$	−19.4565	+	9.29227i	−0.639035	+	0.305198i
$928$	1.69087	−	1.69087i	0.0555054	−	0.0555054i
$929$	−12.0618			−0.395736			−0.197868	−	0.980229i	$-0.563402\pi$
$929$	−12.0618			−0.395736			−0.197868	+	0.980229i	$0.563402\pi$
$930$	−3.08623	+	2.33991i	−0.101201	+	0.0767287i
$931$	45.2363			1.48256
$932$	1.35857	−	1.35857i	0.0445013	−	0.0445013i
$933$	7.65112	−	44.5940i	0.250486	−	1.45994i
$934$			4.01220i			0.131283i
$935$	9.01940	+	8.43896i	0.294966	+	0.275983i
$936$	14.2990	+	5.05545i	0.467377	+	0.165243i
$937$	29.9584	+	29.9584i	0.978697	+	0.978697i	0.999778	−	0.0210808i	$-0.00671072\pi$
$937$	29.9584	+	29.9584i	0.978697	+	0.978697i	−0.0210808	+	0.999778i	$0.506711\pi$
$938$	2.94455	+	2.94455i	0.0961429	+	0.0961429i
$939$	−13.5675	+	9.59366i	−0.442758	+	0.313077i
$940$	20.7567	+	19.4209i	0.677010	+	0.633441i
$941$		−	19.1066i		−	0.622858i	−0.950269	−	0.311429i	$-0.899192\pi$
$941$		−	19.1066i		−	0.622858i	0.950269	−	0.311429i	$-0.100808\pi$
$942$	−30.4857	−	5.23052i	−0.993278	−	0.170420i
$943$	−15.0588	+	15.0588i	−0.490380	+	0.490380i
$944$	6.79073			0.221019
$945$	1.09188	+	3.42184i	0.0355188	+	0.111313i
$946$	4.27665			0.139046
$947$	−5.88211	+	5.88211i	−0.191143	+	0.191143i	−0.796190	−	0.605047i	$-0.793154\pi$
$947$	−5.88211	+	5.88211i	−0.191143	+	0.191143i	0.605047	+	0.796190i	$0.293154\pi$
$948$	22.3341	+	3.83192i	0.725377	+	0.124455i
$949$			56.0296i			1.81880i
$950$	−24.6514	−	21.5743i	−0.799799	−	0.699963i
$951$	−24.7726	+	17.5169i	−0.803307	+	0.568024i
$952$	−1.34925	−	1.34925i	−0.0437293	−	0.0437293i
$953$	−5.01193	−	5.01193i	−0.162352	−	0.162352i	0.621256	−	0.783608i	$-0.286623\pi$
$953$	−5.01193	−	5.01193i	−0.162352	−	0.162352i	−0.783608	+	0.621256i	$0.786623\pi$
$954$	40.6317	+	14.3655i	1.31550	+	0.465099i
$955$	1.78643	+	53.7318i	0.0578075	+	1.73872i
$956$		−	4.09226i		−	0.132353i
$957$	0.626784	−	3.65317i	0.0202611	−	0.118090i
$958$	23.1913	−	23.1913i	0.749277	−	0.749277i
$959$	1.66851			0.0538789
$960$	−0.527726	+	3.83686i	−0.0170323	+	0.123834i
$961$	1.00000			0.0322581
$962$	10.1109	−	10.1109i	0.325989	−	0.325989i
$963$	−12.1322	+	5.79422i	−0.390953	+	0.186716i
$964$			2.94455i			0.0948375i
$965$	−14.1235	+	15.0949i	−0.454651	+	0.485923i
$966$	−1.39707	−	1.97576i	−0.0449500	−	0.0635689i
$967$	−17.6499	−	17.6499i	−0.567581	−	0.567581i	0.363869	−	0.931450i	$-0.381456\pi$
$967$	−17.6499	−	17.6499i	−0.567581	−	0.567581i	−0.931450	+	0.363869i	$0.881456\pi$
$968$	7.21186	+	7.21186i	0.231798	+	0.231798i
$969$	40.4406	+	57.1916i	1.29914	+	1.83726i
$970$	−21.5466	+	0.716361i	−0.691818	+	0.0230010i
$971$			8.99838i			0.288772i	0.989521	+	0.144386i	$0.0461207\pi$
$971$			8.99838i			0.288772i	−0.989521	+	0.144386i	$0.953879\pi$
$972$	−11.7071	+	10.2929i	−0.375506	+	0.330145i
$973$	−2.45433	+	2.45433i	−0.0786821	+	0.0786821i
$974$	−7.59366			−0.243317
$975$	−33.9896	+	27.5958i	−1.08854	+	0.883774i
$976$	5.61916			0.179865
$977$	10.3778	−	10.3778i	0.332015	−	0.332015i	−0.521336	−	0.853351i	$-0.674566\pi$
$977$	10.3778	−	10.3778i	0.332015	−	0.332015i	0.853351	+	0.521336i	$0.174566\pi$
$978$	−0.956475	+	5.57474i	−0.0305847	+	0.178261i
$979$			1.64618i			0.0526121i
$980$	15.4303	−	0.513012i	0.492902	−	0.0163876i
$981$	17.8618	−	50.5208i	0.570283	−	1.61300i
$982$	11.8746	+	11.8746i	0.378932	+	0.378932i
$983$	−28.4058	−	28.4058i	−0.906005	−	0.906005i	0.0899417	−	0.995947i	$-0.471332\pi$
$983$	−28.4058	−	28.4058i	−0.906005	−	0.906005i	−0.995947	+	0.0899417i	$0.971332\pi$
$984$	−6.66421	+	4.71231i	−0.212447	+	0.150223i
$985$	−13.5390	+	14.4702i	−0.431387	+	0.461058i
$986$		−	14.7599i		−	0.470050i
$987$	−6.70862	−	1.15102i	−0.213538	−	0.0366373i
$988$	23.4209	−	23.4209i	0.745119	−	0.745119i
$989$	21.5968			0.686738
$990$	2.76579	+	5.32824i	0.0879027	+	0.169343i
$991$	−22.2759			−0.707618			−0.353809	−	0.935318i	$-0.615114\pi$
$991$	−22.2759			−0.707618			−0.353809	+	0.935318i	$0.615114\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−12.2316	−	2.09861i	−0.388158	−	0.0665974i
$994$		−	3.88019i		−	0.123072i
$995$	−0.798724	−	24.0239i	−0.0253213	−	0.761607i
$996$	3.11826	−	2.20494i	0.0988058	−	0.0698663i
$997$	24.3930	+	24.3930i	0.772535	+	0.772535i	0.978549	−	0.206014i	$-0.0660494\pi$
$997$	24.3930	+	24.3930i	0.772535	+	0.772535i	−0.206014	+	0.978549i	$0.566049\pi$
$998$	28.4966	+	28.4966i	0.902043	+	0.902043i
$999$	4.00000	+	14.1421i	0.126554	+	0.447437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.c.497.1	✓	8
3.2	odd	2		930.2.j.f.497.4	yes	8
5.3	odd	4		930.2.j.f.683.4	yes	8
15.8	even	4	inner	930.2.j.c.683.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.1	✓	8	1.1	even	1	trivial
930.2.j.c.683.1	yes	8	15.8	even	4	inner
930.2.j.f.497.4	yes	8	3.2	odd	2
930.2.j.f.683.4	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(1.41421 - 1.00000i) q^{6} +(0.218591 + 0.218591i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(1.41421 - 1.00000i) q^{6} +(0.218591 + 0.218591i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +(1.52773 - 1.63280i) q^{10} +0.894921i q^{11} +(-0.292893 + 1.70711i) q^{12} +(3.57474 - 3.57474i) q^{13} -0.309135 q^{14} +(3.83686 + 0.527726i) q^{15} -1.00000 q^{16} +(-4.36459 + 4.36459i) q^{17} +(-2.70711 + 1.29289i) q^{18} +6.55178i q^{19} +(0.0743018 + 2.23483i) q^{20} +(-0.309135 - 0.437183i) q^{21} +(-0.632805 - 0.632805i) q^{22} +(-3.19562 - 3.19562i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(4.98896 - 0.332104i) q^{25} +5.05545i q^{26} +(-4.53553 - 2.53553i) q^{27} +(0.218591 - 0.218591i) q^{28} +2.39124 q^{29} +(-3.08623 + 2.33991i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.262116 - 1.52773i) q^{33} -6.17246i q^{34} +(-0.504757 - 0.472274i) q^{35} +(1.00000 - 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(-4.63280 - 4.63280i) q^{38} +(-7.14949 + 5.05545i) q^{39} +(-1.63280 - 1.52773i) q^{40} -4.71231i q^{41} +(0.527726 + 0.0905435i) q^{42} +(-3.37912 + 3.37912i) q^{43} +0.894921 q^{44} +(-6.39536 - 2.02468i) q^{45} +4.51929 q^{46} +(8.98896 - 8.98896i) q^{47} +(1.70711 + 0.292893i) q^{48} -6.90444i q^{49} +(-3.29289 + 3.76256i) q^{50} +(8.72918 - 6.17246i) q^{51} +(-3.57474 - 3.57474i) q^{52} +(-10.1579 - 10.1579i) q^{53} +(5.00000 - 1.41421i) q^{54} +(-0.0664943 - 2.00000i) q^{55} +0.309135i q^{56} +(1.91897 - 11.1846i) q^{57} +(-1.69087 + 1.69087i) q^{58} -6.79073 q^{59} +(0.527726 - 3.83686i) q^{60} -5.61916 q^{61} +(-0.707107 + 0.707107i) q^{62} +(0.399678 + 0.836861i) q^{63} +1.00000i q^{64} +(-7.72335 + 8.25457i) q^{65} +(0.894921 + 1.26561i) q^{66} +(-9.52512 - 9.52512i) q^{67} +(4.36459 + 4.36459i) q^{68} +(4.51929 + 6.39124i) q^{69} +(0.690865 - 0.0229693i) q^{70} +12.5518i q^{71} +(1.29289 + 2.70711i) q^{72} +(-7.83686 + 7.83686i) q^{73} +2.82843 q^{74} +(-8.61396 - 0.894295i) q^{75} +6.55178 q^{76} +(-0.195622 + 0.195622i) q^{77} +(1.48071 - 8.63020i) q^{78} -13.0830i q^{79} +(2.23483 - 0.0743018i) q^{80} +(7.00000 + 5.65685i) q^{81} +(3.33210 + 3.33210i) q^{82} +(-1.55913 - 1.55913i) q^{83} +(-0.437183 + 0.309135i) q^{84} +(9.42983 - 10.0784i) q^{85} -4.77880i q^{86} +(-4.08211 - 0.700379i) q^{87} +(-0.632805 + 0.632805i) q^{88} +1.83947 q^{89} +(5.95387 - 3.09054i) q^{90} +1.56282 q^{91} +(-3.19562 + 3.19562i) q^{92} +(-1.70711 - 0.292893i) q^{93} +12.7123i q^{94} +(-0.486809 - 14.6421i) q^{95} +(-1.41421 + 1.00000i) q^{96} +(-6.81739 - 6.81739i) q^{97} +(4.88217 + 4.88217i) q^{98} +(-0.894921 + 2.53122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^3 + 4 * q^7	\( 8 q - 8 q^{3} + 4 q^{7} - 8 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{15} - 8 q^{16} + 4 q^{17} - 16 q^{18} + 4 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 q^{45} + 28 q^{46} + 28 q^{47} + 8 q^{48} - 32 q^{50} - 8 q^{51} + 4 q^{52} - 12 q^{53} + 40 q^{54} - 20 q^{55} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 q^{63} - 36 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} + 12 q^{77} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 q^{90} + 8 q^{91} - 12 q^{92} - 8 q^{93} - 36 q^{95} + 12 q^{97} + 32 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 4 * q^7 - 8 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^15 - 8 * q^16 + 4 * q^17 - 16 * q^18 + 4 * q^20 + 12 * q^21 + 4 * q^22 - 12 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^33 + 24 * q^35 + 8 * q^36 - 16 * q^37 - 28 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^42 - 8 * q^43 + 4 * q^44 - 12 * q^45 + 28 * q^46 + 28 * q^47 + 8 * q^48 - 32 * q^50 - 8 * q^51 + 4 * q^52 - 12 * q^53 + 40 * q^54 - 20 * q^55 - 24 * q^57 - 28 * q^58 + 24 * q^59 - 8 * q^60 + 56 * q^61 - 28 * q^63 - 36 * q^65 + 4 * q^66 - 16 * q^67 - 4 * q^68 + 28 * q^69 + 20 * q^70 + 16 * q^72 - 36 * q^73 - 32 * q^75 + 4 * q^76 + 12 * q^77 + 20 * q^78 + 56 * q^81 + 28 * q^82 - 12 * q^83 - 8 * q^84 + 32 * q^85 - 20 * q^87 + 4 * q^88 + 36 * q^89 - 4 * q^90 + 8 * q^91 - 12 * q^92 - 8 * q^93 - 36 * q^95 + 12 * q^97 + 32 * q^98 - 4 * q^99

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