LMFDB - Embedded newform 570.2.x.a.103.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.5
Character	$\chi$	$=$	570.103
Dual form			570.2.x.a.487.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.19635 - 0.419581i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.57035 + 2.57035i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.19635 - 0.419581i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.57035 + 2.57035i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.01292 + 0.973741i) q^{10} -5.12724 q^{11} +(0.707107 + 0.707107i) q^{12} +(-4.44516 - 1.19108i) q^{13} +(1.81751 - 3.14802i) q^{14} +(0.973741 + 2.01292i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.673352 + 2.51298i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.94198 - 1.86031i) q^{19} +(1.69230 - 1.46154i) q^{20} +(-3.14802 - 1.81751i) q^{21} +(4.95253 - 1.32703i) q^{22} +(-1.45325 + 5.42359i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.64790 - 1.84309i) q^{25} +4.60197 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.940813 + 3.51116i) q^{28} +(4.79881 + 8.31179i) q^{29} +(-1.46154 - 1.69230i) q^{30} -6.03555i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.32703 - 4.95253i) q^{33} +(-1.30082 - 2.25308i) q^{34} +(-4.56692 + 6.72385i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.87870 + 4.87870i) q^{37} +(4.28915 + 0.776664i) q^{38} -4.60197i q^{39} +(-1.25637 + 1.84974i) q^{40} +(-5.16438 - 2.98166i) q^{41} +(3.51116 + 0.940813i) q^{42} +(-0.264867 + 0.0709708i) q^{43} +(-4.44032 + 2.56362i) q^{44} +(-1.69230 + 1.46154i) q^{45} -5.61492i q^{46} +(-6.50508 - 1.74303i) q^{47} +(0.965926 + 0.258819i) q^{48} -6.21339i q^{49} +(-4.01250 + 2.98326i) q^{50} +(-2.25308 + 1.30082i) q^{51} +(-4.44516 + 1.19108i) q^{52} +(9.48221 + 2.54075i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-11.2612 + 2.15129i) q^{55} -3.63502i q^{56} +(0.776664 - 4.28915i) q^{57} +(-6.78655 - 6.78655i) q^{58} +(-3.25228 + 5.63312i) q^{59} +(1.84974 + 1.25637i) q^{60} +(-5.80839 - 10.0604i) q^{61} +(1.56211 + 5.82989i) q^{62} +(0.940813 - 3.51116i) q^{63} -1.00000i q^{64} +(-10.2629 - 0.750918i) q^{65} +(2.56362 + 4.44032i) q^{66} +(-1.78386 + 6.65746i) q^{67} +(1.83963 + 1.83963i) q^{68} -5.61492 q^{69} +(2.67104 - 7.67675i) q^{70} +(5.61576 + 3.24226i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-6.48755 + 1.73833i) q^{73} +(-5.97517 - 3.44976i) q^{74} +(2.98326 + 4.01250i) q^{75} +(-4.34401 + 0.359913i) q^{76} +(13.1788 - 13.1788i) q^{77} +(1.19108 + 4.44516i) q^{78} +(4.09212 - 7.08776i) q^{79} +(0.734807 - 2.11188i) q^{80} +(0.500000 - 0.866025i) q^{81} +(5.76012 + 1.54342i) q^{82} +(-1.64176 - 1.64176i) q^{83} -3.63502 q^{84} +(2.53332 + 5.23686i) q^{85} +(0.237473 - 0.137105i) q^{86} +(-6.78655 + 6.78655i) q^{87} +(3.62551 - 3.62551i) q^{88} +(7.97739 + 13.8172i) q^{89} +(1.25637 - 1.84974i) q^{90} +(14.4871 - 8.36413i) q^{91} +(1.45325 + 5.42359i) q^{92} +(5.82989 - 1.56211i) q^{93} +6.73455 q^{94} +(-9.43853 - 2.43192i) q^{95} -1.00000 q^{96} +(-1.01062 + 0.270794i) q^{97} +(1.60814 + 6.00167i) q^{98} +(4.44032 - 2.56362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.19635	−	0.419581i	0.982237	−	0.187642i
$5$	2.19635	−	0.419581i	0.982237	−	0.187642i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.57035	+	2.57035i	−0.971501	+	0.971501i	−0.999605	−	0.0281044i	$-0.991053\pi$
$7$	−2.57035	+	2.57035i	−0.971501	+	0.971501i	0.0281044	+	0.999605i	$0.491053\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−2.01292	+	0.973741i	−0.636540	+	0.307924i
$11$	−5.12724			−1.54592			−0.772961	−	0.634454i	$-0.781225\pi$
$11$	−5.12724			−1.54592			−0.772961	+	0.634454i	$0.781225\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−4.44516	−	1.19108i	−1.23287	−	0.330345i	−0.417171	−	0.908828i	$-0.636978\pi$
$13$	−4.44516	−	1.19108i	−1.23287	−	0.330345i	−0.815694	+	0.578483i	$0.803645\pi$
$14$	1.81751	−	3.14802i	0.485750	−	0.841344i
$15$	0.973741	+	2.01292i	0.251419	+	0.519733i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.673352	+	2.51298i	0.163312	+	0.609488i	0.998249	+	0.0591435i	$0.0188369\pi$
$17$	0.673352	+	2.51298i	0.163312	+	0.609488i	−0.834938	+	0.550345i	$0.814496\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−3.94198	−	1.86031i	−0.904353	−	0.426785i
$19$	−3.94198	−	1.86031i	−0.904353	−	0.426785i
$20$	1.69230	−	1.46154i	0.378411	−	0.326811i
$21$	−3.14802	−	1.81751i	−0.686955	−	0.396613i
$22$	4.95253	−	1.32703i	1.05588	−	0.282923i
$23$	−1.45325	+	5.42359i	−0.303023	+	1.13090i	0.631611	+	0.775286i	$0.282394\pi$
$23$	−1.45325	+	5.42359i	−0.303023	+	1.13090i	−0.934634	+	0.355612i	$0.884273\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.64790	−	1.84309i	0.929581	−	0.368618i
$26$	4.60197			0.902520
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.940813	+	3.51116i	−0.177797	+	0.663547i
$29$	4.79881	+	8.31179i	0.891117	+	1.54346i	0.838537	+	0.544844i	$0.183411\pi$
$29$	4.79881	+	8.31179i	0.891117	+	1.54346i	0.0525800	+	0.998617i	$0.483256\pi$
$30$	−1.46154	−	1.69230i	−0.266840	−	0.308971i
$31$		−	6.03555i		−	1.08402i	−0.840373	−	0.542008i	$-0.817664\pi$
$31$		−	6.03555i		−	1.08402i	0.840373	−	0.542008i	$-0.182336\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−1.32703	−	4.95253i	−0.231006	−	0.862126i
$34$	−1.30082	−	2.25308i	−0.223088	−	0.386400i
$35$	−4.56692	+	6.72385i	−0.771950	+	1.13654i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.87870	+	4.87870i	0.802054	+	0.802054i	0.983416	−	0.181363i	$-0.0580507\pi$
$37$	4.87870	+	4.87870i	0.802054	+	0.802054i	−0.181363	+	0.983416i	$0.558051\pi$
$38$	4.28915	+	0.776664i	0.695792	+	0.125992i
$39$		−	4.60197i		−	0.736904i
$40$	−1.25637	+	1.84974i	−0.198649	+	0.292470i
$41$	−5.16438	−	2.98166i	−0.806541	−	0.465657i	0.0392122	−	0.999231i	$-0.487515\pi$
$41$	−5.16438	−	2.98166i	−0.806541	−	0.465657i	−0.845753	+	0.533574i	$0.820848\pi$
$42$	3.51116	+	0.940813i	0.541784	+	0.145171i
$43$	−0.264867	+	0.0709708i	−0.0403918	+	0.0108229i	−0.278958	−	0.960303i	$-0.589989\pi$
$43$	−0.264867	+	0.0709708i	−0.0403918	+	0.0108229i	0.238567	+	0.971126i	$0.423322\pi$
$44$	−4.44032	+	2.56362i	−0.669404	+	0.386480i
$45$	−1.69230	+	1.46154i	−0.252274	+	0.217874i
$46$		−	5.61492i		−	0.827874i
$47$	−6.50508	−	1.74303i	−0.948863	−	0.254247i	−0.248983	−	0.968508i	$-0.580096\pi$
$47$	−6.50508	−	1.74303i	−0.948863	−	0.254247i	−0.699880	+	0.714261i	$0.746763\pi$
$48$	0.965926	+	0.258819i	0.139419	+	0.0373573i
$49$		−	6.21339i		−	0.887627i
$50$	−4.01250	+	2.98326i	−0.567454	+	0.421896i
$51$	−2.25308	+	1.30082i	−0.315494	+	0.182151i
$52$	−4.44516	+	1.19108i	−0.616433	+	0.165173i
$53$	9.48221	+	2.54075i	1.30248	+	0.348999i	0.842388	−	0.538871i	$-0.181149\pi$
$53$	9.48221	+	2.54075i	1.30248	+	0.348999i	0.460094	+	0.887870i	$0.347816\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−11.2612	+	2.15129i	−1.51846	+	0.290080i
$56$		−	3.63502i		−	0.485750i
$57$	0.776664	−	4.28915i	0.102872	−	0.568112i
$58$	−6.78655	−	6.78655i	−0.891117	−	0.891117i
$59$	−3.25228	+	5.63312i	−0.423411	+	0.733370i	−0.996271	−	0.0862841i	$-0.972501\pi$
$59$	−3.25228	+	5.63312i	−0.423411	+	0.733370i	0.572859	+	0.819654i	$0.305834\pi$
$60$	1.84974	+	1.25637i	0.238801	+	0.162196i
$61$	−5.80839	−	10.0604i	−0.743688	−	1.28811i	−0.950805	−	0.309789i	$-0.899741\pi$
$61$	−5.80839	−	10.0604i	−0.743688	−	1.28811i	0.207117	−	0.978316i	$-0.433592\pi$
$62$	1.56211	+	5.82989i	0.198389	+	0.740397i
$63$	0.940813	−	3.51116i	0.118531	−	0.442365i
$64$		−	1.00000i		−	0.125000i
$65$	−10.2629	−	0.750918i	−1.27295	−	0.0931400i
$66$	2.56362	+	4.44032i	0.315560	+	0.546566i
$67$	−1.78386	+	6.65746i	−0.217933	+	0.813339i	0.767180	+	0.641432i	$0.221659\pi$
$67$	−1.78386	+	6.65746i	−0.217933	+	0.813339i	−0.985113	+	0.171907i	$0.945007\pi$
$68$	1.83963	+	1.83963i	0.223088	+	0.223088i
$69$	−5.61492			−0.675956
$70$	2.67104	−	7.67675i	0.319250	−	0.917547i
$71$	5.61576	+	3.24226i	0.666468	+	0.384785i	0.794737	−	0.606954i	$-0.207609\pi$
$71$	5.61576	+	3.24226i	0.666468	+	0.384785i	−0.128269	+	0.991739i	$0.540942\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−6.48755	+	1.73833i	−0.759310	+	0.203456i	−0.617644	−	0.786458i	$-0.711913\pi$
$73$	−6.48755	+	1.73833i	−0.759310	+	0.203456i	−0.141666	+	0.989914i	$0.545246\pi$
$74$	−5.97517	−	3.44976i	−0.694599	−	0.401027i
$75$	2.98326	+	4.01250i	0.344477	+	0.463324i
$76$	−4.34401	+	0.359913i	−0.498293	+	0.0412849i
$77$	13.1788	−	13.1788i	1.50186	−	1.50186i
$78$	1.19108	+	4.44516i	0.134863	+	0.503315i
$79$	4.09212	−	7.08776i	0.460399	−	0.797435i	−0.538581	−	0.842574i	$-0.681040\pi$
$79$	4.09212	−	7.08776i	0.460399	−	0.797435i	0.998981	+	0.0451384i	$0.0143729\pi$
$80$	0.734807	−	2.11188i	0.0821540	−	0.236116i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	5.76012	+	1.54342i	0.636099	+	0.170442i
$83$	−1.64176	−	1.64176i	−0.180206	−	0.180206i	0.611239	−	0.791446i	$-0.290671\pi$
$83$	−1.64176	−	1.64176i	−0.180206	−	0.180206i	−0.791446	+	0.611239i	$0.790671\pi$
$84$	−3.63502			−0.396613
$85$	2.53332	+	5.23686i	0.274777	+	0.568018i
$86$	0.237473	−	0.137105i	0.0256074	−	0.0147844i
$87$	−6.78655	+	6.78655i	−0.727594	+	0.727594i
$88$	3.62551	−	3.62551i	0.386480	−	0.386480i
$89$	7.97739	+	13.8172i	0.845602	+	1.46463i	0.885098	+	0.465405i	$0.154091\pi$
$89$	7.97739	+	13.8172i	0.845602	+	1.46463i	−0.0394960	+	0.999220i	$0.512575\pi$
$90$	1.25637	−	1.84974i	0.132433	−	0.194980i
$91$	14.4871	−	8.36413i	1.51866	−	0.876799i
$92$	1.45325	+	5.42359i	0.151511	+	0.565449i
$93$	5.82989	−	1.56211i	0.604532	−	0.161984i
$94$	6.73455			0.694616
$95$	−9.43853	−	2.43192i	−0.968372	−	0.249510i
$96$	−1.00000			−0.102062
$97$	−1.01062	+	0.270794i	−0.102612	+	0.0274949i	−0.309760	−	0.950815i	$-0.600249\pi$
$97$	−1.01062	+	0.270794i	−0.102612	+	0.0274949i	0.207147	+	0.978310i	$0.433582\pi$
$98$	1.60814	+	6.00167i	0.162447	+	0.606260i
$99$	4.44032	−	2.56362i	0.446269	−	0.257654i
$100$	3.10366	−	3.92012i	0.310366	−	0.392012i
$101$	1.52782	+	2.64626i	0.152024	+	0.263313i	0.931971	−	0.362532i	$-0.118088\pi$
$101$	1.52782	+	2.64626i	0.152024	+	0.263313i	−0.779948	+	0.625845i	$0.784754\pi$
$102$	1.83963	−	1.83963i	0.182151	−	0.182151i
$103$	−5.18209	+	5.18209i	−0.510606	+	0.510606i	−0.914712	−	0.404106i	$-0.867583\pi$
$103$	−5.18209	+	5.18209i	−0.510606	+	0.510606i	0.404106	+	0.914712i	$0.367583\pi$
$104$	3.98542	−	2.30098i	0.390803	−	0.225630i
$105$	−7.67675	−	2.67104i	−0.749174	−	0.260667i
$106$	−9.81671			−0.953483
$107$	11.4351	+	11.4351i	1.10547	+	1.10547i	0.993738	+	0.111733i	$0.0356402\pi$
$107$	11.4351	+	11.4351i	1.10547	+	1.10547i	0.111733	+	0.993738i	$0.464360\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−8.56203	+	14.8299i	−0.820094	+	1.42044i	0.0855176	+	0.996337i	$0.472746\pi$
$109$	−8.56203	+	14.8299i	−0.820094	+	1.42044i	−0.905612	+	0.424108i	$0.860588\pi$
$110$	10.3207	−	4.99260i	0.984040	−	0.476026i
$111$	−3.44976	+	5.97517i	−0.327437	+	0.567138i
$112$	0.940813	+	3.51116i	0.0888985	+	0.331774i
$113$	3.74127	−	3.74127i	0.351949	−	0.351949i	−0.508886	−	0.860834i	$-0.669942\pi$
$113$	3.74127	−	3.74127i	0.351949	−	0.351949i	0.860834	+	0.508886i	$0.169942\pi$
$114$	0.359913	+	4.34401i	0.0337090	+	0.406854i
$115$	−0.916205	+	12.5219i	−0.0854365	+	1.16767i
$116$	8.31179	+	4.79881i	0.771730	+	0.445559i
$117$	4.44516	−	1.19108i	0.410955	−	0.110115i
$118$	1.68351	−	6.28293i	0.154979	−	0.578390i
$119$	−8.18999	−	4.72850i	−0.750775	−	0.433460i
$120$	−2.11188	−	0.734807i	−0.192788	−	0.0670784i
$121$	15.2886			1.38987
$122$	8.21430	+	8.21430i	0.743688	+	0.743688i
$123$	1.54342	−	5.76012i	0.139165	−	0.519373i
$124$	−3.01777	−	5.22694i	−0.271004	−	0.469393i
$125$	9.43510	−	5.99824i	0.843901	−	0.536499i
$126$			3.63502i			0.323834i
$127$	2.98266	−	11.1314i	0.264668	−	0.987756i	−0.697785	−	0.716308i	$-0.745831\pi$
$127$	2.98266	−	11.1314i	0.264668	−	0.987756i	0.962453	−	0.271448i	$-0.0875026\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−0.137105	−	0.237473i	−0.0120714	−	0.0209083i
$130$	10.1075	−	1.93090i	0.886489	−	0.169351i
$131$	5.69642	−	9.86649i	0.497699	−	0.862040i	−0.502298	−	0.864695i	$-0.667512\pi$
$131$	5.69642	−	9.86649i	0.497699	−	0.862040i	0.999996	+	0.00265521i	$0.000845179\pi$
$132$	−3.62551	−	3.62551i	−0.315560	−	0.315560i
$133$	14.9139	−	5.35062i	1.29320	−	0.463958i
$134$		−	6.89231i		−	0.595405i
$135$	−1.84974	−	1.25637i	−0.159200	−	0.108131i
$136$	−2.25308	−	1.30082i	−0.193200	−	0.111544i
$137$	−7.11512	−	1.90649i	−0.607886	−	0.162883i	−0.0582711	−	0.998301i	$-0.518559\pi$
$137$	−7.11512	−	1.90649i	−0.607886	−	0.162883i	−0.549615	+	0.835418i	$0.685225\pi$
$138$	5.42359	−	1.45325i	0.461687	−	0.123709i
$139$	4.47391	−	2.58301i	0.379472	−	0.219088i	−0.298117	−	0.954529i	$-0.596358\pi$
$139$	4.47391	−	2.58301i	0.379472	−	0.219088i	0.677589	+	0.735441i	$0.263025\pi$
$140$	−0.593139	+	8.10649i	−0.0501294	+	0.685123i
$141$		−	6.73455i		−	0.567152i
$142$	−6.26356	−	1.67832i	−0.525627	−	0.140841i
$143$	22.7914	+	6.10694i	1.90591	+	0.510688i
$144$			1.00000i			0.0833333i
$145$	14.0273	+	16.2421i	1.16491	+	1.34883i
$146$	5.81657	−	3.35820i	0.481383	−	0.277927i
$147$	6.00167	−	1.60814i	0.495010	−	0.132637i
$148$	6.66443	+	1.78573i	0.547813	+	0.146786i
$149$	−14.0120	−	8.08986i	−1.14791	−	0.662747i	−0.199534	−	0.979891i	$-0.563943\pi$
$149$	−14.0120	−	8.08986i	−1.14791	−	0.662747i	−0.948377	+	0.317144i	$0.897276\pi$
$150$	−3.92012	−	3.10366i	−0.320076	−	0.253413i
$151$			0.724606i			0.0589676i	0.999565	+	0.0294838i	$0.00938634\pi$
$151$			0.724606i			0.0589676i	−0.999565	+	0.0294838i	$0.990614\pi$
$152$	4.10284	−	1.47196i	0.332785	−	0.119392i
$153$	−1.83963	−	1.83963i	−0.148725	−	0.148725i
$154$	−9.31882	+	16.1407i	−0.750932	+	1.30065i
$155$	−2.53240	−	13.2562i	−0.203407	−	1.06476i
$156$	−2.30098	−	3.98542i	−0.184226	−	0.319089i
$157$	2.41313	+	9.00592i	0.192589	+	0.718751i	0.992878	+	0.119137i	$0.0380127\pi$
$157$	2.41313	+	9.00592i	0.192589	+	0.718751i	−0.800289	+	0.599614i	$0.795321\pi$
$158$	−2.11824	+	7.90537i	−0.168518	+	0.628917i
$159$			9.81671i			0.778516i
$160$	−0.163173	+	2.23011i	−0.0129000	+	0.176305i
$161$	−10.2052	−	17.6759i	−0.804280	−	1.39305i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	11.3357	+	11.3357i	0.887877	+	0.887877i	0.994319	−	0.106442i	$-0.0339459\pi$
$163$	11.3357	+	11.3357i	0.887877	+	0.887877i	−0.106442	+	0.994319i	$0.533946\pi$
$164$	−5.96331			−0.465657
$165$	−4.99260	−	10.3207i	−0.388674	−	0.803466i
$166$	2.01074	+	1.16090i	0.156063	+	0.0901032i
$167$	2.58064	−	9.63108i	0.199696	−	0.745275i	−0.791305	−	0.611421i	$-0.790598\pi$
$167$	2.58064	−	9.63108i	0.199696	−	0.745275i	0.991001	−	0.133854i	$-0.0427353\pi$
$168$	3.51116	−	0.940813i	0.270892	−	0.0725853i
$169$	7.08244	+	4.08905i	0.544803	+	0.314542i
$170$	−3.80240	−	4.40275i	−0.291630	−	0.337676i
$171$	4.34401	−	0.359913i	0.332195	−	0.0275233i
$172$	−0.193896	+	0.193896i	−0.0147844	+	0.0147844i
$173$	−2.99740	−	11.1865i	−0.227888	−	0.850491i	−0.981227	−	0.192858i	$-0.938224\pi$
$173$	−2.99740	−	11.1865i	−0.227888	−	0.850491i	0.753338	−	0.657633i	$-0.228442\pi$
$174$	4.79881	−	8.31179i	0.363797	−	0.630115i
$175$	−7.20935	+	16.6841i	−0.544975	+	1.26120i
$176$	−2.56362	+	4.44032i	−0.193240	+	0.334702i
$177$	−6.28293	−	1.68351i	−0.472254	−	0.126540i
$178$	−11.2817	−	11.2817i	−0.845602	−	0.845602i
$179$	−1.34728			−0.100700			−0.0503502	−	0.998732i	$-0.516034\pi$
$179$	−1.34728			−0.100700			−0.0503502	+	0.998732i	$0.516034\pi$
$180$	−0.734807	+	2.11188i	−0.0547693	+	0.157411i
$181$	−5.86002	+	3.38328i	−0.435572	+	0.251478i	−0.701718	−	0.712455i	$-0.747583\pi$
$181$	−5.86002	+	3.38328i	−0.435572	+	0.251478i	0.266146	+	0.963933i	$0.414250\pi$
$182$	−11.8287	+	11.8287i	−0.876799	+	0.876799i
$183$	8.21430	−	8.21430i	0.607219	−	0.607219i
$184$	−2.80746	−	4.86266i	−0.206969	−	0.358480i
$185$	12.7623	+	8.66833i	0.938306	+	0.637308i
$186$	−5.22694	+	3.01777i	−0.383258	+	0.221274i
$187$	−3.45244	−	12.8847i	−0.252467	−	0.942220i
$188$	−6.50508	+	1.74303i	−0.474432	+	0.127124i
$189$	3.63502			0.264409
$190$	9.74634	−	0.0938174i	0.707074	−	0.00680623i
$191$	11.6122			0.840231			0.420115	−	0.907471i	$-0.361990\pi$
$191$	11.6122			0.840231			0.420115	+	0.907471i	$0.361990\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	−2.60451	−	9.72017i	−0.187477	−	0.699674i	−0.994087	−	0.108589i	$-0.965367\pi$
$193$	−2.60451	−	9.72017i	−0.187477	−	0.699674i	0.806610	−	0.591084i	$-0.201300\pi$
$194$	0.906093	−	0.523133i	0.0650537	−	0.0375588i
$195$	−1.93090	−	10.1075i	−0.138274	−	0.723815i
$196$	−3.10669	−	5.38095i	−0.221907	−	0.384354i
$197$	−16.8782	+	16.8782i	−1.20252	+	1.20252i	−0.229123	+	0.973397i	$0.573586\pi$
$197$	−16.8782	+	16.8782i	−1.20252	+	1.20252i	−0.973397	+	0.229123i	$0.926414\pi$
$198$	−3.62551	+	3.62551i	−0.257654	+	0.257654i
$199$	−8.69939	+	5.02260i	−0.616684	+	0.356042i	−0.775577	−	0.631253i	$-0.782541\pi$
$199$	−8.69939	+	5.02260i	−0.616684	+	0.356042i	0.158893	+	0.987296i	$0.449207\pi$
$200$	−1.98330	+	4.58983i	−0.140241	+	0.324550i
$201$	−6.89231			−0.486146
$202$	−2.16066	−	2.16066i	−0.152024	−	0.152024i
$203$	−33.6988	−	9.02957i	−2.36519	−	0.633752i
$204$	−1.30082	+	2.25308i	−0.0910753	+	0.157747i
$205$	−12.5938	−	4.38189i	−0.879592	−	0.306044i
$206$	3.66429	−	6.34673i	0.255303	−	0.442198i
$207$	−1.45325	−	5.42359i	−0.101008	−	0.376966i
$208$	−3.25408	+	3.25408i	−0.225630	+	0.225630i
$209$	20.2115	+	9.53827i	1.39806	+	0.659776i
$210$	8.10649	+	0.593139i	0.559401	+	0.0409305i
$211$	15.0391	+	8.68285i	1.03534	+	0.597752i	0.918509	−	0.395400i	$-0.129394\pi$
$211$	15.0391	+	8.68285i	1.03534	+	0.597752i	0.116828	+	0.993152i	$0.462727\pi$
$212$	9.48221	−	2.54075i	0.651241	−	0.174500i
$213$	−1.67832	+	6.26356i	−0.114996	+	0.429172i
$214$	−14.0051	−	8.08583i	−0.957366	−	0.552736i
$215$	−0.551962	+	0.267010i	−0.0376435	+	0.0182099i
$216$	1.00000			0.0680414
$217$	15.5135	+	15.5135i	1.05312	+	1.05312i
$218$	4.43203	−	16.5406i	0.300175	−	1.12027i
$219$	−3.35820	−	5.81657i	−0.226926	−	0.393048i
$220$	−8.67685	+	7.49368i	−0.584993	+	0.505224i
$221$		−	11.9726i		−	0.805366i
$222$	1.78573	−	6.66443i	0.119850	−	0.447287i
$223$	2.54671	+	9.50446i	0.170540	+	0.636466i	0.997268	+	0.0738637i	$0.0235330\pi$
$223$	2.54671	+	9.50446i	0.170540	+	0.636466i	−0.826728	+	0.562602i	$0.809800\pi$
$224$	−1.81751	−	3.14802i	−0.121438	−	0.210336i
$225$	−3.10366	+	3.92012i	−0.206910	+	0.261341i
$226$	−2.64547	+	4.58210i	−0.175974	+	0.304796i
$227$	15.8834	+	15.8834i	1.05422	+	1.05422i	0.998443	+	0.0557783i	$0.0177640\pi$
$227$	15.8834	+	15.8834i	1.05422	+	1.05422i	0.0557783	+	0.998443i	$0.482236\pi$
$228$	−1.47196	−	4.10284i	−0.0974831	−	0.271717i
$229$		−	13.2874i		−	0.878056i	−0.898473	−	0.439028i	$-0.855323\pi$
$229$		−	13.2874i		−	0.878056i	0.898473	−	0.439028i	$-0.144677\pi$
$230$	−2.35591	−	12.3323i	−0.155344	−	0.813169i
$231$	16.1407	+	9.31882i	1.06198	+	0.613133i
$232$	−9.27060	−	2.48405i	−0.608645	−	0.163086i
$233$	−19.3392	+	5.18192i	−1.26695	+	0.339479i	−0.828863	−	0.559452i	$-0.811012\pi$
$233$	−19.3392	+	5.18192i	−1.26695	+	0.339479i	−0.438090	+	0.898931i	$0.644345\pi$
$234$	−3.98542	+	2.30098i	−0.260535	+	0.150420i
$235$	−15.0188	−	1.09890i	−0.979716	−	0.0716843i
$236$			6.50456i			0.423411i
$237$	7.90537	+	2.11824i	0.513509	+	0.137594i
$238$	9.13475	+	2.44765i	0.592118	+	0.158658i
$239$			16.8119i			1.08747i	0.839257	+	0.543734i	$0.182990\pi$
$239$			16.8119i			1.08747i	−0.839257	+	0.543734i	$0.817010\pi$
$240$	2.23011	+	0.163173i	0.143953	+	0.0105328i
$241$	20.0115	−	11.5537i	1.28906	−	0.744237i	0.310570	−	0.950551i	$-0.399480\pi$
$241$	20.0115	−	11.5537i	1.28906	−	0.744237i	0.978486	+	0.206314i	$0.0661468\pi$
$242$	−14.7676	+	3.95698i	−0.949300	+	0.254364i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−10.0604	−	5.80839i	−0.644053	−	0.371844i
$245$	−2.60702	−	13.6468i	−0.166556	−	0.871860i
$246$			5.96331i			0.380207i
$247$	15.3070	+	12.9646i	0.973959	+	0.824917i
$248$	4.26778	+	4.26778i	0.271004	+	0.271004i
$249$	1.16090	−	2.01074i	0.0735690	−	0.127425i
$250$	−7.56114	+	8.23584i	−0.478209	+	0.520880i
$251$	5.12674	+	8.87978i	0.323597	+	0.560487i	0.981227	−	0.192854i	$-0.0617744\pi$
$251$	5.12674	+	8.87978i	0.323597	+	0.560487i	−0.657630	+	0.753341i	$0.728441\pi$
$252$	−0.940813	−	3.51116i	−0.0592657	−	0.221182i
$253$	7.45115	−	27.8081i	0.468450	−	1.74828i
$254$			11.5241i			0.723087i
$255$	−4.40275	+	3.80240i	−0.275711	+	0.238115i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.52147	−	5.67821i	0.0949067	−	0.354197i	−0.902099	−	0.431530i	$-0.857974\pi$
$257$	1.52147	−	5.67821i	0.0949067	−	0.354197i	0.997005	+	0.0773333i	$0.0246406\pi$
$258$	0.193896	+	0.193896i	0.0120714	+	0.0120714i
$259$	−25.0799			−1.55839
$260$	−9.26337	+	4.48112i	−0.574490	+	0.277907i
$261$	−8.31179	−	4.79881i	−0.514487	−	0.297039i
$262$	−2.94869	+	11.0046i	−0.182170	+	0.679869i
$263$	2.73024	−	0.731565i	0.168354	−	0.0451102i	−0.173658	−	0.984806i	$-0.555559\pi$
$263$	2.73024	−	0.731565i	0.168354	−	0.0451102i	0.342011	+	0.939696i	$0.388892\pi$
$264$	4.44032	+	2.56362i	0.273283	+	0.157780i
$265$	21.8923	+	1.60183i	1.34483	+	0.0983994i
$266$	−13.0209	+	9.02831i	−0.798363	+	0.553561i
$267$	−11.2817	+	11.2817i	−0.690431	+	0.690431i
$268$	1.78386	+	6.65746i	0.108967	+	0.406669i
$269$	3.71545	−	6.43535i	0.226535	−	0.392370i	−0.730244	−	0.683187i	$-0.760594\pi$
$269$	3.71545	−	6.43535i	0.226535	−	0.392370i	0.956779	+	0.290816i	$0.0939269\pi$
$270$	2.11188	+	0.734807i	0.128525	+	0.0447190i
$271$	5.36930	−	9.29991i	0.326162	−	0.564929i	−0.655585	−	0.755122i	$-0.727578\pi$
$271$	5.36930	−	9.29991i	0.326162	−	0.564929i	0.981747	+	0.190192i	$0.0609112\pi$
$272$	2.51298	+	0.673352i	0.152372	+	0.0408280i
$273$	11.8287	+	11.8287i	0.715903	+	0.715903i
$274$	7.36612			0.445003
$275$	−23.8309	+	9.44997i	−1.43706	+	0.569855i
$276$	−4.86266	+	2.80746i	−0.292698	+	0.168989i
$277$	6.32607	−	6.32607i	0.380097	−	0.380097i	−0.491040	−	0.871137i	$-0.663383\pi$
$277$	6.32607	−	6.32607i	0.380097	−	0.380097i	0.871137	+	0.491040i	$0.163383\pi$
$278$	−3.65293	+	3.65293i	−0.219088	+	0.219088i
$279$	3.01777	+	5.22694i	0.180669	+	0.312929i
$280$	−1.52519	−	7.98378i	−0.0911472	−	0.477122i
$281$	−19.1049	+	11.0302i	−1.13970	+	0.658009i	−0.946357	−	0.323122i	$-0.895268\pi$
$281$	−19.1049	+	11.0302i	−1.13970	+	0.658009i	−0.193347	+	0.981130i	$0.561934\pi$
$282$	1.74303	+	6.50508i	0.103796	+	0.387372i
$283$	−27.2573	+	7.30357i	−1.62028	+	0.434152i	−0.951083	−	0.308934i	$-0.900028\pi$
$283$	−27.2573	+	7.30357i	−1.62028	+	0.434152i	−0.669195	+	0.743086i	$0.733361\pi$
$284$	6.48452			0.384785
$285$	−0.0938174	−	9.74634i	−0.00555726	−	0.577324i
$286$	−23.5954			−1.39522
$287$	20.9382	−	5.61036i	1.23594	−	0.331169i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	8.86075	−	5.11576i	0.521221	−	0.300927i
$290$	−17.7531	−	12.0581i	−1.04250	−	0.708078i
$291$	−0.523133	−	0.906093i	−0.0306666	−	0.0531161i
$292$	−4.74921	+	4.74921i	−0.277927	+	0.277927i
$293$	−6.05702	+	6.05702i	−0.353855	+	0.353855i	−0.861542	−	0.507687i	$-0.830501\pi$
$293$	−6.05702	+	6.05702i	−0.353855	+	0.353855i	0.507687	+	0.861542i	$0.330501\pi$
$294$	−5.38095	+	3.10669i	−0.313824	+	0.181186i
$295$	−4.77960	+	13.7369i	−0.278279	+	0.799793i
$296$	−6.89953			−0.401027
$297$	3.62551	+	3.62551i	0.210373	+	0.210373i
$298$	15.6284	+	4.18762i	0.905329	+	0.242582i
$299$	12.9198	−	22.3778i	0.747173	−	1.29414i
$300$	4.58983	+	1.98330i	0.264994	+	0.114506i
$301$	0.498380	−	0.863220i	0.0287261	−	0.0497552i
$302$	−0.187542	−	0.699916i	−0.0107918	−	0.0402756i
$303$	−2.16066	+	2.16066i	−0.124127	+	0.124127i
$304$	−3.58207	+	2.48370i	−0.205446	+	0.142450i
$305$	−16.9784	−	19.6591i	−0.972181	−	1.12568i
$306$	2.25308	+	1.30082i	0.128800	+	0.0743627i
$307$	−10.2908	+	2.75742i	−0.587328	+	0.157374i	−0.540232	−	0.841516i	$-0.681663\pi$
$307$	−10.2908	+	2.75742i	−0.587328	+	0.157374i	−0.0470964	+	0.998890i	$0.514997\pi$
$308$	4.82377	−	18.0026i	0.274860	−	1.02579i
$309$	−6.34673	−	3.66429i	−0.361053	−	0.208454i
$310$	5.87706	+	12.1490i	0.333795	+	0.690019i
$311$	−19.7234			−1.11841			−0.559206	−	0.829029i	$-0.688894\pi$
$311$	−19.7234			−1.11841			−0.559206	+	0.829029i	$0.688894\pi$
$312$	3.25408	+	3.25408i	0.184226	+	0.184226i
$313$	−0.857522	+	3.20032i	−0.0484700	+	0.180893i	−0.985917	−	0.167236i	$-0.946516\pi$
$313$	−0.857522	+	3.20032i	−0.0484700	+	0.180893i	0.937447	+	0.348128i	$0.113183\pi$
$314$	−4.66181	−	8.07449i	−0.263081	−	0.455670i
$315$	0.593139	−	8.10649i	0.0334196	−	0.456749i
$316$		−	8.18424i		−	0.460399i
$317$	2.96046	−	11.0486i	0.166276	−	0.620551i	−0.831598	−	0.555378i	$-0.812573\pi$
$317$	2.96046	−	11.0486i	0.166276	−	0.620551i	0.997874	−	0.0651728i	$-0.0207599\pi$
$318$	−2.54075	−	9.48221i	−0.142478	−	0.531736i
$319$	−24.6047	−	42.6165i	−1.37760	−	2.38607i
$320$	−0.419581	−	2.19635i	−0.0234553	−	0.122780i
$321$	−8.08583	+	14.0051i	−0.451307	+	0.781686i
$322$	14.4323	+	14.4323i	0.804280	+	0.804280i
$323$	2.02059	−	11.1588i	0.112429	−	0.620891i
$324$		−	1.00000i		−	0.0555556i
$325$	−22.8559	+	2.65682i	−1.26782	+	0.147374i
$326$	−13.8833	−	8.01552i	−0.768924	−	0.443938i
$327$	−16.5406	−	4.43203i	−0.914696	−	0.245092i
$328$	5.76012	−	1.54342i	0.318049	−	0.0852211i
$329$	21.2005	−	12.2401i	1.16882	−	0.674820i
$330$	7.49368	+	8.67685i	0.412513	+	0.477645i
$331$			2.47839i			0.136224i	0.997678	+	0.0681122i	$0.0216976\pi$
$331$			2.47839i			0.136224i	−0.997678	+	0.0681122i	$0.978302\pi$
$332$	−2.24268	−	0.600925i	−0.123083	−	0.0329801i
$333$	−6.66443	−	1.78573i	−0.365209	−	0.0978574i
$334$			9.97083i			0.545579i
$335$	−1.12464	+	15.3706i	−0.0614458	+	0.839785i
$336$	−3.14802	+	1.81751i	−0.171739	+	0.0991534i
$337$	−24.5995	+	6.59141i	−1.34002	+	0.359057i	−0.856442	−	0.516244i	$-0.827330\pi$
$337$	−24.5995	+	6.59141i	−1.34002	+	0.359057i	−0.483578	+	0.875301i	$0.660663\pi$
$338$	−7.89943	−	2.11665i	−0.429672	−	0.115130i
$339$	4.58210	+	2.64547i	0.248865	+	0.143682i
$340$	4.81235	+	3.26860i	0.260986	+	0.177265i
$341$			30.9457i			1.67580i
$342$	−4.10284	+	1.47196i	−0.221856	+	0.0795947i
$343$	−2.02187	−	2.02187i	−0.109171	−	0.109171i
$344$	0.137105	−	0.237473i	0.00739221	−	0.0128037i
$345$	−12.3323	+	2.35591i	−0.663950	+	0.126838i
$346$	5.79054	+	10.0295i	0.311301	+	0.539190i
$347$	2.64029	+	9.85368i	0.141738	+	0.528973i	0.999879	+	0.0155593i	$0.00495287\pi$
$347$	2.64029	+	9.85368i	0.141738	+	0.528973i	−0.858141	+	0.513414i	$0.828380\pi$
$348$	−2.48405	+	9.27060i	−0.133159	+	0.496956i
$349$			36.6572i			1.96222i	0.193462	+	0.981108i	$0.438028\pi$
$349$			36.6572i			1.96222i	−0.193462	+	0.981108i	$0.561972\pi$
$350$	2.64553	−	17.9815i	0.141409	−	0.961154i
$351$	2.30098	+	3.98542i	0.122817	+	0.212726i
$352$	1.32703	−	4.95253i	0.0707308	−	0.263971i
$353$	−4.26327	−	4.26327i	−0.226911	−	0.226911i	0.584490	−	0.811401i	$-0.301295\pi$
$353$	−4.26327	−	4.26327i	−0.226911	−	0.226911i	−0.811401	+	0.584490i	$0.801295\pi$
$354$	6.50456			0.345714
$355$	13.6946	+	4.76487i	0.726832	+	0.252893i
$356$	13.8172	+	7.97739i	0.732313	+	0.422801i
$357$	2.44765	−	9.13475i	0.129543	−	0.483462i
$358$	1.30137	−	0.348701i	0.0687796	−	0.0184294i
$359$	19.3115	+	11.1495i	1.01922	+	0.588447i	0.913878	−	0.405989i	$-0.133073\pi$
$359$	19.3115	+	11.1495i	1.01922	+	0.588447i	0.105343	+	0.994436i	$0.466406\pi$
$360$	0.163173	−	2.23011i	0.00859999	−	0.117537i
$361$	12.0785	+	14.6666i	0.635709	+	0.771929i
$362$	4.78469	−	4.78469i	0.251478	−	0.251478i
$363$	3.95698	+	14.7676i	0.207688	+	0.775101i
$364$	8.36413	−	14.4871i	0.438399	−	0.759330i
$365$	−13.5195	+	6.54004i	−0.707646	+	0.342321i
$366$	−5.80839	+	10.0604i	−0.303609	+	0.525867i
$367$	−32.3164	−	8.65914i	−1.68690	−	0.452004i	−0.717314	−	0.696751i	$-0.754628\pi$
$367$	−32.3164	−	8.65914i	−1.68690	−	0.452004i	−0.969587	+	0.244747i	$0.921295\pi$
$368$	3.97034	+	3.97034i	0.206969	+	0.206969i
$369$	5.96331			0.310438
$370$	−14.5710	−	5.06982i	−0.757511	−	0.263568i
$371$	−30.9032	+	17.8420i	−1.60442	+	0.926310i
$372$	4.26778	−	4.26778i	0.221274	−	0.221274i
$373$	5.23496	−	5.23496i	0.271056	−	0.271056i	−0.558469	−	0.829525i	$-0.688611\pi$
$373$	5.23496	−	5.23496i	0.271056	−	0.271056i	0.829525	+	0.558469i	$0.188611\pi$
$374$	6.66960	+	11.5521i	0.344877	+	0.597344i
$375$	8.23584	+	7.56114i	0.425297	+	0.390456i
$376$	5.83229	−	3.36728i	0.300778	−	0.173654i
$377$	−11.4315	−	42.6630i	−0.588753	−	2.19726i
$378$	−3.51116	+	0.940813i	−0.180595	+	0.0483902i
$379$	14.5298			0.746348			0.373174	−	0.927761i	$-0.378270\pi$
$379$	14.5298			0.746348			0.373174	+	0.927761i	$0.378270\pi$
$380$	−9.38996	+	2.61316i	−0.481695	+	0.134052i
$381$	11.5241			0.590398
$382$	−11.2165	+	3.00546i	−0.573888	+	0.153773i
$383$	0.346985	+	1.29496i	0.0177301	+	0.0661696i	0.974224	−	0.225582i	$-0.0724285\pi$
$383$	0.346985	+	1.29496i	0.0177301	+	0.0661696i	−0.956494	+	0.291752i	$0.905762\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	23.4157	−	34.4748i	1.19337	−	1.75700i
$386$	5.03153	+	8.71487i	0.256098	+	0.443575i
$387$	0.193896	−	0.193896i	0.00985628	−	0.00985628i
$388$	−0.739822	+	0.739822i	−0.0375588	+	0.0375588i
$389$	21.1987	−	12.2391i	1.07482	−	0.620547i	0.145324	−	0.989384i	$-0.453577\pi$
$389$	21.1987	−	12.2391i	1.07482	−	0.620547i	0.929494	+	0.368838i	$0.120244\pi$
$390$	4.48112	+	9.26337i	0.226910	+	0.469069i
$391$	−14.6079			−0.738755
$392$	4.39353	+	4.39353i	0.221907	+	0.221907i
$393$	11.0046	+	2.94869i	0.555111	+	0.148742i
$394$	11.9347	−	20.6715i	0.601260	−	1.04141i
$395$	6.01384	−	17.2842i	0.302589	−	0.869661i
$396$	2.56362	−	4.44032i	0.128827	−	0.223135i
$397$	−7.65950	−	28.5856i	−0.384419	−	1.43467i	−0.839080	−	0.544007i	$-0.816906\pi$
$397$	−7.65950	−	28.5856i	−0.384419	−	1.43467i	0.454661	−	0.890664i	$-0.349760\pi$
$398$	7.10302	−	7.10302i	0.356042	−	0.356042i
$399$	9.02831	+	13.0209i	0.451981	+	0.651861i
$400$	0.727788	−	4.94675i	0.0363894	−	0.247337i
$401$	−15.6465	−	9.03350i	−0.781348	−	0.451111i	0.0555599	−	0.998455i	$-0.482306\pi$
$401$	−15.6465	−	9.03350i	−0.781348	−	0.451111i	−0.836908	+	0.547344i	$0.815639\pi$
$402$	6.65746	−	1.78386i	0.332044	−	0.0889710i
$403$	−7.18880	+	26.8290i	−0.358100	+	1.33645i
$404$	2.64626	+	1.52782i	0.131656	+	0.0760118i
$405$	0.734807	−	2.11188i	0.0365129	−	0.104940i
$406$	34.8876			1.73144
$407$	−25.0143	−	25.0143i	−1.23991	−	1.23991i
$408$	0.673352	−	2.51298i	0.0333359	−	0.124411i
$409$	11.0562	+	19.1499i	0.546693	+	0.946900i	0.998498	+	0.0547834i	$0.0174468\pi$
$409$	11.0562	+	19.1499i	0.546693	+	0.946900i	−0.451805	+	0.892117i	$0.649220\pi$
$410$	13.2988	+	0.973054i	0.656782	+	0.0480557i
$411$		−	7.36612i		−	0.363344i
$412$	−1.89678	+	7.07886i	−0.0934474	+	0.348751i
$413$	−6.11958	−	22.8386i	−0.301125	−	1.12381i
$414$	2.80746	+	4.86266i	0.137979	+	0.238987i
$415$	−4.29473	−	2.91703i	−0.210820	−	0.143191i
$416$	2.30098	−	3.98542i	0.112815	−	0.195401i
$417$	3.65293	+	3.65293i	0.178885	+	0.178885i
$418$	−21.9915	−	3.98214i	−1.07564	−	0.194773i
$419$			14.5035i			0.708544i	0.935142	+	0.354272i	$0.115271\pi$
$419$			14.5035i			0.708544i	−0.935142	+	0.354272i	$0.884729\pi$
$420$	−7.98378	+	1.52519i	−0.389569	+	0.0744214i
$421$	3.29924	+	1.90482i	0.160795	+	0.0928352i	0.578238	−	0.815868i	$-0.303740\pi$
$421$	3.29924	+	1.90482i	0.160795	+	0.0928352i	−0.417443	+	0.908703i	$0.637074\pi$
$422$	−16.7740	−	4.49457i	−0.816544	−	0.218792i
$423$	6.50508	−	1.74303i	0.316288	−	0.0847490i
$424$	−8.50152	+	4.90836i	−0.412870	+	0.238371i
$425$	7.76133	+	10.4391i	0.376480	+	0.506369i
$426$		−	6.48452i		−	0.314176i
$427$	40.7884	+	10.9292i	1.97389	+	0.528902i
$428$	15.6206	+	4.18553i	0.755051	+	0.202315i
$429$			23.5954i			1.13920i
$430$	0.464047	−	0.400770i	0.0223783	−	0.0193268i
$431$	28.2021	−	16.2825i	1.35845	−	0.784300i	0.369032	−	0.929417i	$-0.379689\pi$
$431$	28.2021	−	16.2825i	1.35845	−	0.784300i	0.989415	+	0.145117i	$0.0463558\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	−9.10491	−	2.43965i	−0.437554	−	0.117242i	0.0333160	−	0.999445i	$-0.489393\pi$
$433$	−9.10491	−	2.43965i	−0.437554	−	0.117242i	−0.470870	+	0.882203i	$0.656060\pi$
$434$	−19.0000	−	10.9697i	−0.912031	−	0.526561i
$435$	−12.0581	+	17.7531i	−0.578143	+	0.851198i
$436$			17.1241i			0.820094i
$437$	15.8183	−	18.6762i	0.756690	−	0.893405i
$438$	4.74921	+	4.74921i	0.226926	+	0.226926i
$439$	0.594852	−	1.03031i	0.0283907	−	0.0491742i	−0.851481	−	0.524386i	$-0.824295\pi$
$439$	0.594852	−	1.03031i	0.0283907	−	0.0491742i	0.879872	+	0.475211i	$0.157628\pi$
$440$	6.44169	−	9.48407i	0.307095	−	0.452135i
$441$	3.10669	+	5.38095i	0.147938	+	0.256236i
$442$	3.09874	+	11.5647i	0.147392	+	0.550075i
$443$	−1.01552	+	3.78996i	−0.0482487	+	0.180067i	−0.985845	−	0.167659i	$-0.946379\pi$
$443$	−1.01552	+	3.78996i	−0.0482487	+	0.180067i	0.937596	+	0.347726i	$0.113046\pi$
$444$			6.89953i			0.327437i
$445$	23.3186	+	27.0003i	1.10541	+	1.27994i
$446$	−4.91987	−	8.52146i	−0.232963	−	0.403503i
$447$	4.18762	−	15.6284i	0.198068	−	0.739198i
$448$	2.57035	+	2.57035i	0.121438	+	0.121438i
$449$	11.9732			0.565052			0.282526	−	0.959260i	$-0.408828\pi$
$449$	11.9732			0.565052			0.282526	+	0.959260i	$0.408828\pi$
$450$	1.98330	−	4.58983i	0.0934938	−	0.216367i
$451$	26.4790	+	15.2877i	1.24685	+	0.719868i
$452$	1.36940	−	5.11066i	0.0644111	−	0.240385i
$453$	−0.699916	+	0.187542i	−0.0328849	+	0.00881148i
$454$	−19.4532	−	11.2313i	−0.912983	−	0.527111i
$455$	28.3093	−	24.4490i	1.32716	−	1.14619i
$456$	2.48370	+	3.58207i	0.116310	+	0.167746i
$457$	17.6876	−	17.6876i	0.827392	−	0.827392i	−0.159763	−	0.987155i	$-0.551073\pi$
$457$	17.6876	−	17.6876i	0.827392	−	0.827392i	0.987155	+	0.159763i	$0.0510731\pi$
$458$	3.43903	+	12.8346i	0.160695	+	0.599724i
$459$	1.30082	−	2.25308i	0.0607169	−	0.105165i
$460$	5.46747	+	11.3024i	0.254922	+	0.526975i
$461$	−2.96390	+	5.13363i	−0.138043	+	0.239097i	−0.926756	−	0.375665i	$-0.877414\pi$
$461$	−2.96390	+	5.13363i	−0.138043	+	0.239097i	0.788713	+	0.614762i	$0.210748\pi$
$462$	−18.0026	−	4.82377i	−0.837555	−	0.224422i
$463$	2.44769	+	2.44769i	0.113754	+	0.113754i	0.761692	−	0.647939i	$-0.224369\pi$
$463$	2.44769	+	2.44769i	0.113754	+	0.113754i	−0.647939	+	0.761692i	$0.724369\pi$
$464$	9.59763			0.445559
$465$	12.1490	−	5.87706i	0.563399	−	0.272542i
$466$	17.3391	−	10.0107i	0.803216	−	0.463737i
$467$	−3.62793	+	3.62793i	−0.167880	+	0.167880i	−0.786047	−	0.618167i	$-0.787876\pi$
$467$	−3.62793	+	3.62793i	−0.167880	+	0.167880i	0.618167	+	0.786047i	$0.287876\pi$
$468$	3.25408	−	3.25408i	0.150420	−	0.150420i
$469$	−12.5269	−	21.6972i	−0.578437	−	1.00188i
$470$	14.7914	−	2.82569i	0.682278	−	0.130339i
$471$	−8.07449	+	4.66181i	−0.372053	+	0.214805i
$472$	−1.68351	−	6.28293i	−0.0774896	−	0.289195i
$473$	1.35804	−	0.363884i	0.0624425	−	0.0167314i
$474$	−8.18424			−0.375915
$475$	−21.7507	−	1.38112i	−0.997990	−	0.0633702i
$476$	−9.45699			−0.433460
$477$	−9.48221	+	2.54075i	−0.434161	+	0.116333i
$478$	−4.35123	−	16.2390i	−0.199021	−	0.742755i
$479$	7.89795	−	4.55988i	0.360867	−	0.208346i	−0.308594	−	0.951194i	$-0.599859\pi$
$479$	7.89795	−	4.55988i	0.360867	−	0.208346i	0.669461	+	0.742847i	$0.266525\pi$
$480$	−2.19635	+	0.419581i	−0.100249	+	0.0191511i
$481$	−15.8757	−	27.4975i	−0.723869	−	1.25378i
$482$	−16.3393	+	16.3393i	−0.744237	+	0.744237i
$483$	14.4323	−	14.4323i	0.656692	−	0.656692i
$484$	13.2403	−	7.64430i	0.601832	−	0.347468i
$485$	−2.10605	+	1.01879i	−0.0956306	+	0.0462610i
$486$	−1.00000			−0.0453609
$487$	−28.5135	−	28.5135i	−1.29207	−	1.29207i	−0.933505	−	0.358565i	$-0.883266\pi$
$487$	−28.5135	−	28.5135i	−1.29207	−	1.29207i	−0.358565	−	0.933505i	$-0.616734\pi$
$488$	11.2209	+	3.00664i	0.507948	+	0.136104i
$489$	−8.01552	+	13.8833i	−0.362474	+	0.627824i
$490$	6.05023	+	12.5070i	0.273322	+	0.565010i
$491$	−5.74523	+	9.95103i	−0.259279	+	0.449084i	−0.966049	−	0.258360i	$-0.916818\pi$
$491$	−5.74523	+	9.95103i	−0.259279	+	0.449084i	0.706770	+	0.707443i	$0.250151\pi$
$492$	−1.54342	−	5.76012i	−0.0695827	−	0.259686i
$493$	−17.6561	+	17.6561i	−0.795191	+	0.795191i
$494$	−18.1409	−	8.56110i	−0.816197	−	0.385182i
$495$	8.67685	−	7.49368i	0.389995	−	0.336816i
$496$	−5.22694	−	3.01777i	−0.234696	−	0.135502i
$497$	−22.7682	+	6.10072i	−1.02129	+	0.273655i
$498$	−0.600925	+	2.24268i	−0.0269281	+	0.100497i
$499$	30.8531	+	17.8130i	1.38117	+	0.797421i	0.992298	−	0.123870i	$-0.0395305\pi$
$499$	30.8531	+	17.8130i	1.38117	+	0.797421i	0.388875	+	0.921291i	$0.372864\pi$
$500$	5.17191	−	9.91218i	0.231295	−	0.443286i
$501$	9.97083			0.445464
$502$	−7.25031	−	7.25031i	−0.323597	−	0.323597i
$503$	−1.55869	+	5.81713i	−0.0694988	+	0.259373i	−0.991930	−	0.126789i	$-0.959533\pi$
$503$	−1.55869	+	5.81713i	−0.0694988	+	0.259373i	0.922431	+	0.386162i	$0.126199\pi$
$504$	1.81751	+	3.14802i	0.0809584	+	0.140224i
$505$	4.46594	+	5.17107i	0.198732	+	0.230110i
$506$			28.7890i			1.27983i
$507$	−2.11665	+	7.89943i	−0.0940036	+	0.350826i
$508$	−2.98266	−	11.1314i	−0.132334	−	0.493878i
$509$	−2.60304	−	4.50860i	−0.115378	−	0.199840i	0.802553	−	0.596581i	$-0.203475\pi$
$509$	−2.60304	−	4.50860i	−0.115378	−	0.199840i	−0.917931	+	0.396741i	$0.870141\pi$
$510$	3.26860	−	4.81235i	0.144736	−	0.213094i
$511$	12.2071	−	21.1434i	0.540012	−	0.935328i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.47196	+	4.10284i	0.0649888	+	0.181145i
$514$			5.87851i			0.259290i
$515$	−9.20737	+	13.5560i	−0.405725	+	0.597348i
$516$	−0.237473	−	0.137105i	−0.0104542	−	0.00603571i
$517$	33.3531	+	8.93694i	1.46687	+	0.393046i
$518$	24.2254	−	6.49117i	1.06440	−	0.285205i
$519$	10.0295	−	5.79054i	0.440246	−	0.254176i
$520$	7.78793	−	6.72597i	0.341523	−	0.294953i
$521$			15.6957i			0.687642i	0.939035	+	0.343821i	$0.111721\pi$
$521$			15.6957i			0.687642i	−0.939035	+	0.343821i	$0.888279\pi$
$522$	9.27060	+	2.48405i	0.405763	+	0.108724i
$523$	−10.6468	−	2.85281i	−0.465553	−	0.124745i	0.0184146	−	0.999830i	$-0.494138\pi$
$523$	−10.6468	−	2.85281i	−0.465553	−	0.124745i	−0.483968	+	0.875086i	$0.660805\pi$
$524$		−	11.3928i		−	0.497699i
$525$	−17.9815	−	2.64553i	−0.784779	−	0.115460i
$526$	−2.44786	+	1.41328i	−0.106732	+	0.0616217i
$527$	15.1672	−	4.06405i	0.660695	−	0.177033i
$528$	−4.95253	−	1.32703i	−0.215531	−	0.0577515i
$529$	−7.38484	−	4.26364i	−0.321080	−	0.185376i
$530$	−21.5609	+	4.11890i	−0.936547	+	0.178914i
$531$		−	6.50456i		−	0.282274i
$532$	10.2405	−	12.0907i	0.443983	−	0.524200i
$533$	19.4051	+	19.4051i	0.840529	+	0.840529i
$534$	7.97739	−	13.8172i	0.345215	−	0.597931i
$535$	29.9134	+	20.3175i	1.29327	+	0.878402i
$536$	−3.44616	−	5.96892i	−0.148851	−	0.257818i
$537$	−0.348701	−	1.30137i	−0.0150476	−	0.0561583i
$538$	−1.92326	+	7.17770i	−0.0829176	+	0.309453i
$539$			31.8575i			1.37220i
$540$	−2.23011	−	0.163173i	−0.0959685	−	0.00702186i
$541$	−13.9935	−	24.2374i	−0.601626	−	1.04205i	−0.992575	−	0.121634i	$-0.961186\pi$
$541$	−13.9935	−	24.2374i	−0.601626	−	1.04205i	0.390949	−	0.920412i	$-0.372147\pi$
$542$	−2.77936	+	10.3727i	−0.119384	+	0.445546i
$543$	−4.78469	−	4.78469i	−0.205331	−	0.205331i
$544$	−2.60163			−0.111544
$545$	−12.5829	+	36.1641i	−0.538992	+	1.54910i
$546$	−14.4871	−	8.36413i	−0.619990	−	0.357952i
$547$	−6.93049	+	25.8650i	−0.296327	+	1.10591i	0.643832	+	0.765167i	$0.277344\pi$
$547$	−6.93049	+	25.8650i	−0.296327	+	1.10591i	−0.940158	+	0.340738i	$0.889323\pi$
$548$	−7.11512	+	1.90649i	−0.303943	+	0.0814413i
$549$	10.0604	+	5.80839i	0.429368	+	0.247896i
$550$	20.5731	−	15.2959i	0.877239	−	0.652218i
$551$	−3.45431	−	41.6922i	−0.147159	−	1.77615i
$552$	3.97034	−	3.97034i	0.168989	−	0.168989i
$553$	7.69984	+	28.7362i	0.327430	+	1.22199i
$554$	−4.47321	+	7.74783i	−0.190048	+	0.329174i
$555$	−5.06982	+	14.5710i	−0.215202	+	0.618505i
$556$	2.58301	−	4.47391i	0.109544	−	0.189736i
$557$	−0.198481	−	0.0531828i	−0.00840990	−	0.00225343i	0.254612	−	0.967043i	$-0.418052\pi$
$557$	−0.198481	−	0.0531828i	−0.00840990	−	0.00225343i	−0.263022	+	0.964790i	$0.584719\pi$
$558$	−4.26778	−	4.26778i	−0.180669	−	0.180669i
$559$	1.26191			0.0533729
$560$	3.53957	+	7.31699i	0.149574	+	0.309199i
$561$	11.5521	−	6.66960i	0.487729	−	0.281591i
$562$	15.5991	−	15.5991i	0.658009	−	0.658009i
$563$	5.07047	−	5.07047i	0.213695	−	0.213695i	−0.592140	−	0.805835i	$-0.701717\pi$
$563$	5.07047	−	5.07047i	0.213695	−	0.213695i	0.805835	+	0.592140i	$0.201717\pi$
$564$	−3.36728	−	5.83229i	−0.141788	−	0.245584i
$565$	6.64737	−	9.78689i	0.279657	−	0.411738i
$566$	24.4382	−	14.1094i	1.02722	−	0.593063i
$567$	0.940813	+	3.51116i	0.0395104	+	0.147455i
$568$	−6.26356	+	1.67832i	−0.262813	+	0.0704206i
$569$	3.13492			0.131423			0.0657114	−	0.997839i	$-0.479068\pi$
$569$	3.13492			0.131423			0.0657114	+	0.997839i	$0.479068\pi$
$570$	2.61316	+	9.38996i	0.109453	+	0.393302i
$571$	3.51729			0.147194			0.0735971	−	0.997288i	$-0.476552\pi$
$571$	3.51729			0.147194			0.0735971	+	0.997288i	$0.476552\pi$
$572$	22.7914	−	6.10694i	0.952956	−	0.255344i
$573$	3.00546	+	11.2165i	0.125555	+	0.468578i
$574$	−18.7726	+	10.8384i	−0.783555	+	0.452386i
$575$	3.24162	+	27.8868i	0.135185	+	1.16296i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−14.3508	+	14.3508i	−0.597430	+	0.597430i	−0.939628	−	0.342198i	$-0.888829\pi$
$577$	−14.3508	+	14.3508i	−0.597430	+	0.597430i	0.342198	+	0.939628i	$0.388829\pi$
$578$	−7.23477	+	7.23477i	−0.300927	+	0.300927i
$579$	8.71487	−	5.03153i	0.362178	−	0.209103i
$580$	20.2691	+	7.05241i	0.841628	+	0.292835i
$581$	8.43979			0.350141
$582$	0.739822	+	0.739822i	0.0306666	+	0.0306666i
$583$	−48.6176	−	13.0270i	−2.01354	−	0.539525i
$584$	3.35820	−	5.81657i	0.138963	−	0.240692i
$585$	9.26337	−	4.48112i	0.382993	−	0.185272i
$586$	4.28296	−	7.41831i	0.176928	−	0.306448i
$587$	−2.83524	−	10.5812i	−0.117023	−	0.436735i	0.882408	−	0.470486i	$-0.155921\pi$
$587$	−2.83524	−	10.5812i	−0.117023	−	0.436735i	−0.999430	+	0.0337510i	$0.989255\pi$
$588$	4.39353	−	4.39353i	0.181186	−	0.181186i
$589$	−11.2280	+	23.7920i	−0.462642	+	0.980333i
$590$	1.06137	−	14.5059i	0.0436960	−	0.597197i
$591$	−20.6715	−	11.9347i	−0.850310	−	0.490927i
$592$	6.66443	−	1.78573i	0.273906	−	0.0733930i
$593$	−10.0228	+	37.4056i	−0.411588	+	1.53607i	0.379986	+	0.924992i	$0.375929\pi$
$593$	−10.0228	+	37.4056i	−0.411588	+	1.53607i	−0.791574	+	0.611074i	$0.790738\pi$
$594$	−4.44032	−	2.56362i	−0.182189	−	0.105187i
$595$	−19.9721	−	6.94907i	−0.818775	−	0.284884i
$596$	−16.1797			−0.662747
$597$	−7.10302	−	7.10302i	−0.290707	−	0.290707i
$598$	−6.68779	+	24.9592i	−0.273484	+	1.02066i
$599$	−9.52480	−	16.4974i	−0.389173	−	0.674067i	0.603166	−	0.797616i	$-0.293906\pi$
$599$	−9.52480	−	16.4974i	−0.389173	−	0.674067i	−0.992338	+	0.123549i	$0.960572\pi$
$600$	−4.94675	−	0.727788i	−0.201950	−	0.0297118i
$601$			3.96685i			0.161811i	0.996722	+	0.0809055i	$0.0257812\pi$
$601$			3.96685i			0.161811i	−0.996722	+	0.0809055i	$0.974219\pi$
$602$	−0.257981	+	0.962796i	−0.0105145	+	0.0392407i
$603$	−1.78386	−	6.65746i	−0.0726445	−	0.271113i
$604$	0.362303	+	0.627527i	0.0147419	+	0.0255337i
$605$	33.5791	−	6.41480i	1.36518	−	0.260799i
$606$	1.52782	−	2.64626i	0.0620634	−	0.107497i
$607$	2.07297	+	2.07297i	0.0841392	+	0.0841392i	0.747924	−	0.663785i	$-0.231051\pi$
$607$	2.07297	+	2.07297i	0.0841392	+	0.0841392i	−0.663785	+	0.747924i	$0.731051\pi$
$608$	2.81719	−	3.32618i	0.114252	−	0.134894i
$609$		−	34.8876i		−	1.41372i
$610$	21.4880	+	14.5949i	0.870025	+	0.590931i
$611$	26.8400	+	15.4961i	1.08583	+	0.626905i
$612$	−2.51298	−	0.673352i	−0.101581	−	0.0272186i
$613$	6.59830	−	1.76801i	0.266503	−	0.0714093i	−0.123093	−	0.992395i	$-0.539281\pi$
$613$	6.59830	−	1.76801i	0.266503	−	0.0714093i	0.389596	+	0.920986i	$0.372615\pi$
$614$	9.22650	−	5.32692i	0.372351	−	0.214977i
$615$	0.973054	−	13.2988i	0.0392373	−	0.536260i
$616$			18.6376i			0.750932i
$617$	−30.1791	−	8.08647i	−1.21497	−	0.325549i	−0.406257	−	0.913759i	$-0.633166\pi$
$617$	−30.1791	−	8.08647i	−1.21497	−	0.325549i	−0.808708	+	0.588210i	$0.799833\pi$
$618$	7.07886	+	1.89678i	0.284754	+	0.0762995i
$619$			10.4321i			0.419303i	0.977776	+	0.209652i	$0.0672330\pi$
$619$			10.4321i			0.419303i	−0.977776	+	0.209652i	$0.932767\pi$
$620$	−8.82121	−	10.2140i	−0.354268	−	0.410203i
$621$	4.86266	−	2.80746i	0.195132	−	0.112659i
$622$	19.0514	−	5.10479i	0.763890	−	0.204684i
$623$	−56.0198	−	15.0105i	−2.24439	−	0.601382i
$624$	−3.98542	−	2.30098i	−0.159544	−	0.0921130i
$625$	18.2060	−	17.1330i	0.728241	−	0.685321i
$626$		−	3.31321i		−	0.132423i
$627$	−3.98214	+	21.9915i	−0.159032	+	0.878256i
$628$	6.59279	+	6.59279i	0.263081	+	0.263081i
$629$	−8.97502	+	15.5452i	−0.357857	+	0.619827i
$630$	1.52519	+	7.98378i	0.0607648	+	0.318081i
$631$	−7.98788	−	13.8354i	−0.317993	−	0.550779i	0.662076	−	0.749436i	$-0.269675\pi$
$631$	−7.98788	−	13.8354i	−0.317993	−	0.550779i	−0.980069	+	0.198657i	$0.936342\pi$
$632$	2.11824	+	7.90537i	0.0842589	+	0.314459i
$633$	−4.49457	+	16.7740i	−0.178643	+	0.666706i
$634$			11.4384i			0.454275i
$635$	1.88043	−	25.7000i	0.0746225	−	1.01987i
$636$	4.90836	+	8.50152i	0.194629	+	0.337107i
$637$	−7.40062	+	27.6195i	−0.293223	+	1.09432i
$638$	34.7963	+	34.7963i	1.37760	+	1.37760i
$639$	−6.48452			−0.256524
$640$	0.973741	+	2.01292i	0.0384905	+	0.0795675i
$641$	−25.4746	−	14.7078i	−1.00619	−	0.580922i	−0.0961135	−	0.995370i	$-0.530641\pi$
$641$	−25.4746	−	14.7078i	−1.00619	−	0.580922i	−0.910073	+	0.414448i	$0.863975\pi$
$642$	4.18553	−	15.6206i	0.165190	−	0.616497i
$643$	20.5552	−	5.50775i	0.810618	−	0.217204i	0.170377	−	0.985379i	$-0.445501\pi$
$643$	20.5552	−	5.50775i	0.810618	−	0.217204i	0.640240	+	0.768175i	$0.278835\pi$
$644$	−17.6759	−	10.2052i	−0.696527	−	0.402140i
$645$	−0.400770	−	0.464047i	−0.0157803	−	0.0182718i
$646$	0.936362	+	11.3015i	0.0368407	+	0.444653i
$647$	−10.2133	+	10.2133i	−0.401526	+	0.401526i	−0.878771	−	0.477244i	$-0.841636\pi$
$647$	−10.2133	+	10.2133i	−0.401526	+	0.401526i	0.477244	+	0.878771i	$0.341636\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	16.6752	−	28.8824i	0.654560	−	1.13373i
$650$	21.3895	−	8.48185i	0.838965	−	0.332685i
$651$	−10.9697	+	19.0000i	−0.429935	+	0.744670i
$652$	15.4848	+	4.14914i	0.606431	+	0.162493i
$653$	−8.99938	−	8.99938i	−0.352173	−	0.352173i	0.508745	−	0.860917i	$-0.330110\pi$
$653$	−8.99938	−	8.99938i	−0.352173	−	0.352173i	−0.860917	+	0.508745i	$0.830110\pi$
$654$	17.1241			0.669604
$655$	8.37155	−	24.0604i	0.327103	−	0.940117i
$656$	−5.16438	+	2.98166i	−0.201635	+	0.116414i
$657$	4.74921	−	4.74921i	0.185284	−	0.185284i
$658$	−17.3101	+	17.3101i	−0.674820	+	0.674820i
$659$	16.1241	+	27.9278i	0.628108	+	1.08791i	0.987931	+	0.154894i	$0.0495035\pi$
$659$	16.1241	+	27.9278i	0.628108	+	1.08791i	−0.359824	+	0.933020i	$0.617163\pi$
$660$	−9.48407	−	6.44169i	−0.369167	−	0.250742i
$661$	−22.5741	+	13.0331i	−0.878029	+	0.506930i	−0.870008	−	0.493038i	$-0.835887\pi$
$661$	−22.5741	+	13.0331i	−0.878029	+	0.506930i	−0.00802100	+	0.999968i	$0.502553\pi$
$662$	−0.641454	−	2.39394i	−0.0249308	−	0.0930431i
$663$	11.5647	−	3.09874i	0.449134	−	0.120345i
$664$	2.32180			0.0901032
$665$	30.5112	−	18.0094i	1.18317	−	0.698376i
$666$	6.89953			0.267351
$667$	−52.0536	+	13.9477i	−2.01552	+	0.540058i
$668$	−2.58064	−	9.63108i	−0.0998479	−	0.372638i
$669$	−8.52146	+	4.91987i	−0.329459	+	0.190213i
$670$	−2.89188	−	15.1379i	−0.111723	−	0.584829i
$671$	29.7810	+	51.5822i	1.14968	+	1.99131i
$672$	2.57035	−	2.57035i	0.0991534	−	0.0991534i
$673$	−7.03254	+	7.03254i	−0.271085	+	0.271085i	−0.829537	−	0.558452i	$-0.811395\pi$
$673$	−7.03254	+	7.03254i	−0.271085	+	0.271085i	0.558452	+	0.829537i	$0.311395\pi$
$674$	22.0553	−	12.7336i	0.849538	−	0.490481i
$675$	−4.58983	−	1.98330i	−0.176663	−	0.0763373i
$676$	8.17809			0.314542
$677$	−4.59971	−	4.59971i	−0.176781	−	0.176781i	0.613170	−	0.789951i	$-0.289894\pi$
$677$	−4.59971	−	4.59971i	−0.176781	−	0.176781i	−0.789951	+	0.613170i	$0.789894\pi$
$678$	−5.11066	−	1.36940i	−0.196274	−	0.0525914i
$679$	1.90160	−	3.29367i	0.0729767	−	0.126399i
$680$	−5.49435	−	1.91170i	−0.210699	−	0.0733103i
$681$	−11.2313	+	19.4532i	−0.430384	+	0.745447i
$682$	−8.00934	−	29.8913i	−0.306693	−	1.14460i
$683$	5.58601	−	5.58601i	0.213743	−	0.213743i	−0.592113	−	0.805855i	$-0.701706\pi$
$683$	5.58601	−	5.58601i	0.213743	−	0.213743i	0.805855	+	0.592113i	$0.201706\pi$
$684$	3.58207	−	2.48370i	0.136964	−	0.0949667i
$685$	−16.4272	−	1.20195i	−0.627652	−	0.0459243i
$686$	2.47627	+	1.42968i	0.0945445	+	0.0545853i
$687$	12.8346	−	3.43903i	0.489672	−	0.131207i
$688$	−0.0709708	+	0.264867i	−0.00270574	+	0.0100979i
$689$	−39.1237	−	22.5881i	−1.49049	−	0.860538i
$690$	11.3024	−	5.46747i	0.430273	−	0.208143i
$691$	−2.97150			−0.113041			−0.0565205	−	0.998401i	$-0.518001\pi$
$691$	−2.97150			−0.113041			−0.0565205	+	0.998401i	$0.518001\pi$
$692$	−8.18906	−	8.18906i	−0.311301	−	0.311301i
$693$	−4.82377	+	18.0026i	−0.183240	+	0.683861i
$694$	−5.10064	−	8.83457i	−0.193618	−	0.335356i
$695$	8.74249	−	7.55036i	0.331621	−	0.286402i
$696$		−	9.59763i		−	0.363797i
$697$	4.01541	−	14.9857i	0.152094	−	0.567624i
$698$	−9.48758	−	35.4081i	−0.359110	−	1.34022i
$699$	−10.0107	−	17.3391i	−0.378640	−	0.655823i
$700$	2.09858	+	18.0535i	0.0793190	+	0.682360i
$701$	−14.9367	+	25.8712i	−0.564153	+	0.977141i	0.432975	+	0.901406i	$0.357464\pi$
$701$	−14.9367	+	25.8712i	−0.564153	+	0.977141i	−0.997128	+	0.0757352i	$0.975870\pi$
$702$	−3.25408	−	3.25408i	−0.122817	−	0.122817i
$703$	−10.1559	−	28.3077i	−0.383035	−	1.06764i
$704$			5.12724i			0.193240i
$705$	−2.82569	−	14.7914i	−0.106422	−	0.557078i
$706$	5.22141	+	3.01458i	0.196510	+	0.113455i
$707$	−10.7288	−	2.87478i	−0.403499	−	0.108117i
$708$	−6.28293	+	1.68351i	−0.236127	+	0.0632700i
$709$	−36.1011	+	20.8430i	−1.35580	+	0.782774i	−0.989055	−	0.147545i	$-0.952863\pi$
$709$	−36.1011	+	20.8430i	−1.35580	+	0.782774i	−0.366750	+	0.930320i	$0.619529\pi$
$710$	−14.4612	−	1.05810i	−0.542718	−	0.0397098i
$711$			8.18424i			0.306933i
$712$	−15.4111	−	4.12940i	−0.577557	−	0.154756i
$713$	32.7343	+	8.77114i	1.22591	+	0.328482i
$714$			9.45699i			0.353919i
$715$	52.6202	+	3.85014i	1.96788	+	0.143987i
$716$	−1.16678	+	0.673639i	−0.0436045	+	0.0251751i
$717$	−16.2390	+	4.35123i	−0.606457	+	0.162500i
$718$	−21.5392	−	5.77140i	−0.803834	−	0.215387i
$719$	−42.3357	−	24.4425i	−1.57885	−	0.911552i	−0.995020	−	0.0996785i	$-0.968219\pi$
$719$	−42.3357	−	24.4425i	−1.57885	−	0.911552i	−0.583834	−	0.811873i	$-0.698448\pi$
$720$	0.419581	+	2.19635i	0.0156368	+	0.0818531i
$721$		−	26.6395i		−	0.992109i
$722$	−15.4629	−	11.0408i	−0.575470	−	0.410894i
$723$	16.3393	+	16.3393i	0.607667	+	0.607667i
$724$	−3.38328	+	5.86002i	−0.125739	+	0.217786i
$725$	37.6238	+	29.7878i	1.39731	+	1.10629i
$726$	−7.64430	−	13.2403i	−0.283706	−	0.491394i
$727$	−4.49639	−	16.7808i	−0.166762	−	0.622364i	−0.997809	−	0.0661619i	$-0.978925\pi$
$727$	−4.49639	−	16.7808i	−0.166762	−	0.622364i	0.831047	−	0.556202i	$-0.187742\pi$
$728$	−4.32959	+	16.1582i	−0.160465	+	0.598865i
$729$			1.00000i			0.0370370i
$730$	11.3662	−	9.81631i	0.420682	−	0.363318i
$731$	−0.356697	−	0.617817i	−0.0131929	−	0.0228508i
$732$	3.00664	−	11.2209i	0.111129	−	0.414738i
$733$	−13.3218	−	13.3218i	−0.492053	−	0.492053i	0.416899	−	0.908953i	$-0.363117\pi$
$733$	−13.3218	−	13.3218i	−0.492053	−	0.492053i	−0.908953	+	0.416899i	$0.863117\pi$
$734$	33.4564			1.23490
$735$	12.5070	−	6.05023i	0.461329	−	0.223166i
$736$	−4.86266	−	2.80746i	−0.179240	−	0.103484i
$737$	9.14629	−	34.1344i	0.336908	−	1.25736i
$738$	−5.76012	+	1.54342i	−0.212033	+	0.0568141i
$739$	−7.63744	−	4.40948i	−0.280948	−	0.162205i	0.352905	−	0.935659i	$-0.385194\pi$
$739$	−7.63744	−	4.40948i	−0.280948	−	0.162205i	−0.633852	+	0.773454i	$0.718527\pi$
$740$	15.3867	+	1.12582i	0.565626	+	0.0413859i
$741$	−8.56110	+	18.1409i	−0.314500	+	0.666422i
$742$	25.2324	−	25.2324i	0.926310	−	0.926310i
$743$	7.95355	+	29.6830i	0.291787	+	1.08897i	0.943735	+	0.330702i	$0.107285\pi$
$743$	7.95355	+	29.6830i	0.291787	+	1.08897i	−0.651948	+	0.758264i	$0.726048\pi$
$744$	−3.01777	+	5.22694i	−0.110637	+	0.191629i
$745$	−34.1697	−	11.8890i	−1.25188	−	0.435578i
$746$	−3.70168	+	6.41149i	−0.135528	+	0.234741i
$747$	2.24268	+	0.600925i	0.0820555	+	0.0219867i
$748$	−9.43223	−	9.43223i	−0.344877	−	0.344877i
$749$	−58.7843			−2.14793
$750$	−9.91218	−	5.17191i	−0.361942	−	0.188852i
$751$	34.8932	−	20.1456i	1.27327	−	0.735124i	0.297669	−	0.954669i	$-0.403791\pi$
$751$	34.8932	−	20.1456i	1.27327	−	0.735124i	0.975602	+	0.219545i	$0.0704574\pi$
$752$	−4.76205	+	4.76205i	−0.173654	+	0.173654i
$753$	−7.25031	+	7.25031i	−0.264216	+	0.264216i
$754$	22.0840	+	38.2506i	0.804251	+	1.39300i
$755$	0.304031	+	1.59149i	0.0110648	+	0.0579202i
$756$	3.14802	−	1.81751i	0.114492	−	0.0661022i
$757$	8.34746	+	31.1531i	0.303393	+	1.13228i	0.934319	+	0.356437i	$0.116008\pi$
$757$	8.34746	+	31.1531i	0.303393	+	1.13228i	−0.630926	+	0.775843i	$0.717325\pi$
$758$	−14.0347	+	3.76060i	−0.509765	+	0.136591i
$759$	28.7890			1.04498
$760$	8.39367	−	4.95442i	0.304470	−	0.179716i
$761$	37.4969			1.35926			0.679631	−	0.733554i	$-0.262140\pi$
$761$	37.4969			1.35926			0.679631	+	0.733554i	$0.262140\pi$
$762$	−11.1314	+	2.98266i	−0.403250	+	0.108050i
$763$	−16.1105	−	60.1254i	−0.583241	−	2.17668i
$764$	10.0565	−	5.80611i	0.363831	−	0.210058i
$765$	−4.81235	−	3.26860i	−0.173991	−	0.118176i
$766$	−0.670323	−	1.16103i	−0.0242197	−	0.0419498i
$767$	21.1664	−	21.1664i	0.764274	−	0.764274i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	37.6656	−	21.7462i	1.35825	−	0.784189i	0.368866	−	0.929483i	$-0.379746\pi$
$769$	37.6656	−	21.7462i	1.35825	−	0.784189i	0.989389	+	0.145294i	$0.0464128\pi$
$770$	−13.6951	+	39.3605i	−0.493536	+	1.41846i
$771$	5.87851			0.211709
$772$	−7.11566	−	7.11566i	−0.256098	−	0.256098i
$773$	−51.6108	−	13.8291i	−1.85631	−	0.497397i	−0.856486	−	0.516170i	$-0.827357\pi$
$773$	−51.6108	−	13.8291i	−1.85631	−	0.497397i	−0.999824	+	0.0187728i	$0.994024\pi$
$774$	−0.137105	+	0.237473i	−0.00492814	+	0.00853579i
$775$	−11.1241	−	28.0526i	−0.399588	−	1.00768i
$776$	0.523133	−	0.906093i	0.0187794	−	0.0325268i
$777$	−6.49117	−	24.2254i	−0.232869	−	0.869080i
$778$	−17.3087	+	17.3087i	−0.620547	+	0.620547i
$779$	14.8111	+	21.3610i	0.530662	+	0.765338i
$780$	−6.72597	−	7.78793i	−0.240828	−	0.278853i
$781$	−28.7933	−	16.6238i	−1.03031	−	0.594848i
$782$	14.1102	−	3.78081i	0.504579	−	0.135202i
$783$	2.48405	−	9.27060i	0.0887727	−	0.331304i
$784$	−5.38095	−	3.10669i	−0.192177	−	0.110953i
$785$	9.07879	+	18.7677i	0.324036	+	0.669846i
$786$	−11.3928			−0.406369
$787$	−5.95943	−	5.95943i	−0.212431	−	0.212431i	0.592868	−	0.805299i	$-0.297995\pi$
$787$	−5.95943	−	5.95943i	−0.212431	−	0.212431i	−0.805299	+	0.592868i	$0.797995\pi$
$788$	−6.17784	+	23.0560i	−0.220077	+	0.821337i
$789$	1.41328	+	2.44786i	0.0503139	+	0.0871463i
$790$	−1.33545	+	18.2517i	−0.0475132	+	0.649367i
$791$			19.2327i			0.683837i
$792$	−1.32703	+	4.95253i	−0.0471539	+	0.175981i
$793$	13.8365	+	51.6384i	0.491348	+	1.83373i
$794$	14.7970	+	25.6292i	0.525126	+	0.909545i
$795$	4.11890	+	21.5609i	0.146082	+	0.764687i
$796$	−5.02260	+	8.69939i	−0.178021	+	0.308342i
$797$	27.2295	+	27.2295i	0.964520	+	0.964520i	0.999392	−	0.0348720i	$-0.0111024\pi$
$797$	27.2295	+	27.2295i	0.964520	+	0.964520i	−0.0348720	+	0.999392i	$0.511102\pi$
$798$	−12.0907	−	10.2405i	−0.428007	−	0.362511i
$799$		−	17.5208i		−	0.619842i
$800$	0.577324	+	4.96656i	0.0204115	+	0.175594i
$801$	−13.8172	−	7.97739i	−0.488208	−	0.281867i
$802$	17.4514	+	4.67608i	0.616230	+	0.165118i
$803$	33.2632	−	8.91285i	1.17383	−	0.314528i
$804$	−5.96892	+	3.44616i	−0.210508	+	0.121537i
$805$	−29.8306	−	34.5405i	−1.05139	−	1.21739i
$806$		−	27.7754i		−	0.978346i
$807$	7.17770	+	1.92326i	0.252667	+	0.0677019i
$808$	−2.95152	−	0.790857i	−0.103834	−	0.0278223i
$809$			47.3921i			1.66622i	0.553110	+	0.833108i	$0.313441\pi$
$809$			47.3921i			1.66622i	−0.553110	+	0.833108i	$0.686559\pi$
$810$	−0.163173	+	2.23011i	−0.00573333	+	0.0783580i
$811$	−14.8782	+	8.58992i	−0.522444	+	0.301633i	−0.737934	−	0.674873i	$-0.764198\pi$
$811$	−14.8782	+	8.58992i	−0.522444	+	0.301633i	0.215490	+	0.976506i	$0.430865\pi$
$812$	−33.6988	+	9.02957i	−1.18260	+	0.316876i
$813$	10.3727	+	2.77936i	0.363786	+	0.0974763i
$814$	30.6361	+	17.6878i	1.07380	+	0.619956i
$815$	29.6533	+	20.1408i	1.03871	+	0.705503i
$816$			2.60163i			0.0910753i
$817$	1.17613	+	0.212969i	0.0411475	+	0.00745085i
$818$	−15.6358	−	15.6358i	−0.546693	−	0.546693i
$819$	−8.36413	+	14.4871i	−0.292266	+	0.506220i
$820$	−13.0975	+	2.50209i	−0.457385	+	0.0873768i
$821$	−18.2809	−	31.6635i	−0.638009	−	1.10506i	−0.985869	−	0.167517i	$-0.946425\pi$
$821$	−18.2809	−	31.6635i	−0.638009	−	1.10506i	0.347861	−	0.937546i	$-0.386908\pi$
$822$	1.90649	+	7.11512i	0.0664965	+	0.248168i
$823$	0.282278	−	1.05347i	0.00983958	−	0.0367218i	−0.960832	−	0.277133i	$-0.910616\pi$
$823$	0.282278	−	1.05347i	0.00983958	−	0.0367218i	0.970671	+	0.240411i	$0.0772823\pi$
$824$		−	7.32858i		−	0.255303i
$825$	−15.2959	−	20.5731i	−0.532534	−	0.716262i
$826$	11.8221	+	20.4765i	0.411344	+	0.712469i
$827$	−1.39467	+	5.20496i	−0.0484973	+	0.180994i	−0.985926	−	0.167184i	$-0.946533\pi$
$827$	−1.39467	+	5.20496i	−0.0484973	+	0.180994i	0.937429	+	0.348178i	$0.113199\pi$
$828$	−3.97034	−	3.97034i	−0.137979	−	0.137979i
$829$	32.4709			1.12776			0.563880	−	0.825857i	$-0.309308\pi$
$829$	32.4709			1.12776			0.563880	+	0.825857i	$0.309308\pi$
$830$	4.90337	+	1.70607i	0.170198	+	0.0592187i
$831$	7.74783	+	4.47321i	0.268769	+	0.155174i
$832$	−1.19108	+	4.44516i	−0.0412931	+	0.154108i
$833$	15.6141	−	4.18380i	0.540998	−	0.144960i
$834$	−4.47391	−	2.58301i	−0.154919	−	0.0894424i
$835$	1.62697	−	22.2360i	0.0563037	−	0.769509i
$836$	22.2728	−	1.84536i	0.770321	−	0.0638232i
$837$	−4.26778	+	4.26778i	−0.147516	+	0.147516i
$838$	−3.75379	−	14.0093i	−0.129673	−	0.483945i
$839$	−1.11929	+	1.93867i	−0.0386423	+	0.0669304i	−0.884700	−	0.466161i	$-0.845637\pi$
$839$	−1.11929	+	1.93867i	−0.0386423	+	0.0669304i	0.846057	+	0.533092i	$0.178970\pi$
$840$	7.31699	−	3.53957i	0.252460	−	0.122127i
$841$	−31.5572	+	54.6587i	−1.08818	+	1.88478i
$842$	−3.67983	−	0.986007i	−0.126815	−	0.0339801i
$843$	−15.5991	−	15.5991i	−0.537262	−	0.537262i
$844$	17.3657			0.597752
$845$	17.2712	+	6.00932i	0.594147	+	0.206727i
$846$	−5.83229	+	3.36728i	−0.200518	+	0.115769i
$847$	−39.2970	+	39.2970i	−1.35026	+	1.35026i
$848$	6.94146	−	6.94146i	0.238371	−	0.238371i
$849$	−14.1094	−	24.4382i	−0.484234	−	0.838718i
$850$	−10.1987	−	8.07457i	−0.349813	−	0.276956i
$851$	−33.5501	+	19.3701i	−1.15008	+	0.664000i
$852$	1.67832	+	6.26356i	0.0574982	+	0.214586i
$853$	5.00563	−	1.34126i	0.171390	−	0.0459237i	−0.172104	−	0.985079i	$-0.555056\pi$
$853$	5.00563	−	1.34126i	0.171390	−	0.0459237i	0.343493	+	0.939155i	$0.388390\pi$
$854$	−42.2273			−1.44499
$855$	9.38996	−	2.61316i	0.321130	−	0.0893682i
$856$	−16.1717			−0.552736
$857$	22.8284	−	6.11685i	0.779803	−	0.208948i	0.153105	−	0.988210i	$-0.451073\pi$
$857$	22.8284	−	6.11685i	0.779803	−	0.208948i	0.626698	+	0.779262i	$0.284406\pi$
$858$	−6.10694	−	22.7914i	−0.208487	−	0.778085i
$859$	−29.2548	+	16.8903i	−0.998161	+	0.576289i	−0.907704	−	0.419612i	$-0.862166\pi$
$859$	−29.2548	+	16.8903i	−0.998161	+	0.576289i	−0.0904577	+	0.995900i	$0.528833\pi$
$860$	−0.344508	+	0.507218i	−0.0117476	+	0.0172960i
$861$	10.8384	+	18.7726i	0.369371	+	0.639770i
$862$	−23.0269	+	23.0269i	−0.784300	+	0.784300i
$863$	31.2056	−	31.2056i	1.06225	−	1.06225i	0.0643208	−	0.997929i	$-0.479512\pi$
$863$	31.2056	−	31.2056i	1.06225	−	1.06225i	0.997929	−	0.0643208i	$-0.0204881\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−11.2770	−	23.3117i	−0.383428	−	0.792622i
$866$	9.42609			0.320312
$867$	7.23477	+	7.23477i	0.245706	+	0.245706i
$868$	21.1918	+	5.67832i	0.719296	+	0.192735i
$869$	−20.9813	+	36.3406i	−0.711741	+	1.23277i
$870$	7.05241	−	20.2691i	0.239099	−	0.687186i
$871$	15.8591	−	27.4688i	0.537365	−	0.930744i
$872$	−4.43203	−	16.5406i	−0.150088	−	0.560135i
$873$	0.739822	−	0.739822i	0.0250392	−	0.0250392i
$874$	−10.4455	+	22.1339i	−0.353324	+	0.748690i
$875$	−8.83391	+	39.6691i	−0.298641	+	1.34106i
$876$	−5.81657	−	3.35820i	−0.196524	−	0.113463i
$877$	−19.3453	+	5.18355i	−0.653244	+	0.175036i	−0.570195	−	0.821509i	$-0.693132\pi$
$877$	−19.3453	+	5.18355i	−0.653244	+	0.175036i	−0.0830486	+	0.996545i	$0.526466\pi$
$878$	−0.307918	+	1.14917i	−0.0103917	+	0.0387825i
$879$	−7.41831	−	4.28296i	−0.250213	−	0.144461i
$880$	−3.76753	+	10.8281i	−0.127004	+	0.365017i
$881$	4.02295			0.135537			0.0677683	−	0.997701i	$-0.478412\pi$
$881$	4.02295			0.135537			0.0677683	+	0.997701i	$0.478412\pi$
$882$	−4.39353	−	4.39353i	−0.147938	−	0.147938i
$883$	−5.30011	+	19.7803i	−0.178363	+	0.665660i	0.817591	+	0.575799i	$0.195309\pi$
$883$	−5.30011	+	19.7803i	−0.178363	+	0.665660i	−0.995954	+	0.0898609i	$0.971358\pi$
$884$	−5.98631	−	10.3686i	−0.201341	−	0.348734i
$885$	−14.5059	−	1.06137i	−0.487610	−	0.0356776i
$886$		−	3.92366i		−	0.131818i
$887$	0.775106	−	2.89274i	0.0260255	−	0.0971286i	−0.951691	−	0.307056i	$-0.900656\pi$
$887$	0.775106	−	2.89274i	0.0260255	−	0.0971286i	0.977717	+	0.209927i	$0.0673228\pi$
$888$	−1.78573	−	6.66443i	−0.0599251	−	0.223644i
$889$	20.9452	+	36.2782i	0.702480	+	1.21673i
$890$	−29.5122	−	20.0450i	−0.989252	−	0.671911i
$891$	−2.56362	+	4.44032i	−0.0858845	+	0.148756i
$892$	6.95775	+	6.95775i	0.232963	+	0.232963i
$893$	22.4003	+	18.9725i	0.749598	+	0.634890i
$894$			16.1797i			0.541131i
$895$	−2.95909	+	0.565292i	−0.0989116	+	0.0188956i
$896$	−3.14802	−	1.81751i	−0.105168	−	0.0607188i
$897$	24.9592	+	6.68779i	0.833363	+	0.223299i
$898$	−11.5653	+	3.09890i	−0.385938	+	0.103412i
$899$	50.1662	−	28.9635i	1.67314	−	0.965986i
$900$	−0.727788	+	4.94675i	−0.0242596	+	0.164892i
$901$			25.5395i			0.850843i
$902$	−29.5335	−	7.91348i	−0.983359	−	0.263490i
$903$	0.962796	+	0.257981i	0.0320399	+	0.00858505i
$904$			5.29095i			0.175974i
$905$	−11.4511	+	9.88963i	−0.380647	+	0.328742i
$906$	0.627527	−	0.362303i	0.0208482	−	0.0120367i
$907$	−27.7443	+	7.43406i	−0.921234	+	0.246844i	−0.688113	−	0.725604i	$-0.741561\pi$
$907$	−27.7443	+	7.43406i	−0.921234	+	0.246844i	−0.233122	+	0.972448i	$0.574894\pi$
$908$	21.6972	+	5.81375i	0.720047	+	0.192936i
$909$	−2.64626	−	1.52782i	−0.0877709	−	0.0506745i
$910$	−21.0168	+	30.9429i	−0.696700	+	1.02575i
$911$		−	44.4605i		−	1.47304i	−0.676415	−	0.736520i	$-0.736467\pi$
$911$		−	44.4605i		−	1.47304i	0.676415	−	0.736520i	$-0.263533\pi$
$912$	−3.32618	−	2.81719i	−0.110141	−	0.0932863i
$913$	8.41769	+	8.41769i	0.278585	+	0.278585i
$914$	−12.5070	+	21.6628i	−0.413696	+	0.716542i
$915$	14.5949	−	21.4880i	0.482493	−	0.710373i
$916$	−6.64370	−	11.5072i	−0.219514	−	0.380210i
$917$	10.7185	+	40.0021i	0.353957	+	1.32099i
$918$	−0.673352	+	2.51298i	−0.0222239	+	0.0829408i
$919$		−	35.2612i		−	1.16316i	−0.813490	−	0.581579i	$-0.802435\pi$
$919$		−	35.2612i		−	1.16316i	0.813490	−	0.581579i	$-0.197565\pi$
$920$	−8.20644	−	9.50215i	−0.270558	−	0.313276i
$921$	−5.32692	−	9.22650i	−0.175528	−	0.304023i
$922$	1.53423	−	5.72582i	0.0505271	−	0.188570i
$923$	−21.1011	−	21.1011i	−0.694553	−	0.694553i
$924$	18.6376			0.613133
$925$	31.6676	+	13.6838i	1.04123	+	0.449922i
$926$	−2.99779	−	1.73078i	−0.0985136	−	0.0568769i
$927$	1.89678	−	7.07886i	0.0622983	−	0.232500i
$928$	−9.27060	+	2.48405i	−0.304322	+	0.0815429i
$929$	−43.5689	−	25.1545i	−1.42945	−	0.825294i	−0.432374	−	0.901695i	$-0.642324\pi$
$929$	−43.5689	−	25.1545i	−1.42945	−	0.825294i	−0.997077	+	0.0764008i	$0.975657\pi$
$930$	−10.2140	+	8.82121i	−0.334930	+	0.289259i
$931$	−11.5588	+	24.4931i	−0.378826	+	0.802728i
$932$	−14.1573	+	14.1573i	−0.463737	+	0.463737i
$933$	−5.10479	−	19.0514i	−0.167123	−	0.623713i
$934$	2.56533	−	4.44328i	0.0839402	−	0.145389i
$935$	−12.9889	−	26.8507i	−0.424783	−	0.878111i
$936$	−2.30098	+	3.98542i	−0.0752100	+	0.130268i
$937$	51.5077	+	13.8015i	1.68268	+	0.450874i	0.968486	−	0.249069i	$-0.0801246\pi$
$937$	51.5077	+	13.8015i	1.68268	+	0.450874i	0.714199	+	0.699943i	$0.246791\pi$
$938$	17.7157	+	17.7157i	0.578437	+	0.578437i
$939$	−3.31321			−0.108123
$940$	−13.5561	+	6.55771i	−0.442151	+	0.213889i
$941$	−29.9062	+	17.2663i	−0.974914	+	0.562867i	−0.900731	−	0.434378i	$-0.856968\pi$
$941$	−29.9062	+	17.2663i	−0.974914	+	0.562867i	−0.0741830	+	0.997245i	$0.523635\pi$
$942$	6.59279	−	6.59279i	0.214805	−	0.214805i
$943$	23.6764	−	23.6764i	0.771010	−	0.771010i
$944$	3.25228	+	5.63312i	0.105853	+	0.183342i
$945$	7.98378	−	1.52519i	0.259712	−	0.0496143i
$946$	−1.21758	+	0.702971i	−0.0395870	+	0.0228556i
$947$	−7.69812	−	28.7298i	−0.250155	−	0.933592i	−0.970722	−	0.240206i	$-0.922785\pi$
$947$	−7.69812	−	28.7298i	−0.250155	−	0.933592i	0.720567	−	0.693386i	$-0.243882\pi$
$948$	7.90537	−	2.11824i	0.256754	−	0.0687971i
$949$	30.9087			1.00334
$950$	21.3670	−	4.29543i	0.693237	−	0.139362i
$951$	11.4384			0.370914
$952$	9.13475	−	2.44765i	0.296059	−	0.0793288i
$953$	−1.43547	−	5.35726i	−0.0464996	−	0.173539i	0.938771	−	0.344542i	$-0.111966\pi$
$953$	−1.43547	−	5.35726i	−0.0464996	−	0.173539i	−0.985270	+	0.171003i	$0.945299\pi$
$954$	8.50152	−	4.90836i	0.275247	−	0.158914i
$955$	25.5045	−	4.87226i	0.825306	−	0.157663i
$956$	8.40593	+	14.5595i	0.271867	+	0.470888i
$957$	34.7963	−	34.7963i	1.12480	−	1.12480i
$958$	−6.44865	+	6.44865i	−0.208346	+	0.208346i
$959$	23.1887	−	13.3880i	0.748802	−	0.432321i
$960$	2.01292	−	0.973741i	0.0649666	−	0.0314274i
$961$	−5.42783			−0.175091
$962$	22.4516	+	22.4516i	0.723869	+	0.723869i
$963$	−15.6206	−	4.18553i	−0.503367	−	0.134877i
$964$	11.5537	−	20.0115i	0.372118	−	0.644528i
$965$	−9.79882	−	20.2561i	−0.315435	−	0.652067i
$966$	−10.2052	+	17.6759i	−0.328346	+	0.568712i
$967$	−2.21986	−	8.28464i	−0.0713859	−	0.266416i	0.921004	−	0.389554i	$-0.127371\pi$
$967$	−2.21986	−	8.28464i	−0.0713859	−	0.266416i	−0.992390	+	0.123138i	$0.960704\pi$
$968$	−10.8107	+	10.8107i	−0.347468	+	0.347468i
$969$	11.3015	−	0.936362i	0.363057	−	0.0300803i
$970$	1.77060	−	1.52916i	0.0568506	−	0.0490984i
$971$	33.6610	+	19.4342i	1.08023	+	0.623672i	0.930959	−	0.365124i	$-0.118973\pi$
$971$	33.6610	+	19.4342i	1.08023	+	0.623672i	0.149273	+	0.988796i	$0.452307\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	−4.86026	+	18.1388i	−0.155813	+	0.581502i
$974$	34.9218	+	20.1621i	1.11897	+	0.646035i
$975$	−8.48185	−	21.3895i	−0.271636	−	0.685012i
$976$	−11.6168			−0.371844
$977$	3.97300	+	3.97300i	0.127108	+	0.127108i	0.767799	−	0.640691i	$-0.221352\pi$
$977$	3.97300	+	3.97300i	0.127108	+	0.127108i	−0.640691	+	0.767799i	$0.721352\pi$
$978$	4.14914	−	15.4848i	0.132675	−	0.495149i
$979$	−40.9020	−	70.8443i	−1.30723	−	2.26419i
$980$	−9.08113	−	10.5149i	−0.290086	−	0.335888i
$981$		−	17.1241i		−	0.546729i
$982$	2.97395	−	11.0989i	0.0949025	−	0.354181i
$983$	5.07918	+	18.9558i	0.162001	+	0.604595i	0.998404	+	0.0564802i	$0.0179878\pi$
$983$	5.07918	+	18.9558i	0.162001	+	0.604595i	−0.836403	+	0.548115i	$0.815346\pi$
$984$	2.98166	+	5.16438i	0.0950518	+	0.164634i
$985$	−29.9886	+	44.1521i	−0.955517	+	1.40680i
$986$	12.4847	−	21.6242i	0.397595	−	0.688655i
$987$	17.3101	+	17.3101i	0.550988	+	0.550988i
$988$	19.7385	+	3.57418i	0.627966	+	0.113710i
$989$		−	1.53967i		−	0.0489586i
$990$	−6.44169	+	9.48407i	−0.204730	+	0.301424i
$991$	28.0186	+	16.1765i	0.890039	+	0.513865i	0.873955	−	0.486006i	$-0.161547\pi$
$991$	28.0186	+	16.1765i	0.890039	+	0.513865i	0.0160841	+	0.999871i	$0.494880\pi$
$992$	5.82989	+	1.56211i	0.185099	+	0.0495972i
$993$	−2.39394	+	0.641454i	−0.0759693	+	0.0203559i
$994$	20.4134	−	11.7857i	0.647474	−	0.373819i
$995$	−16.9995	+	14.6815i	−0.538921	+	0.465434i
$996$		−	2.32180i		−	0.0735690i
$997$	48.7306	+	13.0573i	1.54331	+	0.413530i	0.927335	−	0.374233i	$-0.122094\pi$
$997$	48.7306	+	13.0573i	1.54331	+	0.413530i	0.615979	+	0.787763i	$0.288761\pi$
$998$	−34.4121	−	9.22070i	−1.08930	−	0.291876i
$999$		−	6.89953i		−	0.218291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.a.103.5	✓	40
5.2	odd	4	inner	570.2.x.a.217.3	yes	40
19.12	odd	6	inner	570.2.x.a.373.3	yes	40
95.12	even	12	inner	570.2.x.a.487.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.5	✓	40	1.1	even	1	trivial
570.2.x.a.217.3	yes	40	5.2	odd	4	inner
570.2.x.a.373.3	yes	40	19.12	odd	6	inner
570.2.x.a.487.5	yes	40	95.12	even	12	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.19635 - 0.419581i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.57035 + 2.57035i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.19635 - 0.419581i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.57035 + 2.57035i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.01292 + 0.973741i) q^{10} -5.12724 q^{11} +(0.707107 + 0.707107i) q^{12} +(-4.44516 - 1.19108i) q^{13} +(1.81751 - 3.14802i) q^{14} +(0.973741 + 2.01292i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.673352 + 2.51298i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.94198 - 1.86031i) q^{19} +(1.69230 - 1.46154i) q^{20} +(-3.14802 - 1.81751i) q^{21} +(4.95253 - 1.32703i) q^{22} +(-1.45325 + 5.42359i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.64790 - 1.84309i) q^{25} +4.60197 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.940813 + 3.51116i) q^{28} +(4.79881 + 8.31179i) q^{29} +(-1.46154 - 1.69230i) q^{30} -6.03555i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.32703 - 4.95253i) q^{33} +(-1.30082 - 2.25308i) q^{34} +(-4.56692 + 6.72385i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.87870 + 4.87870i) q^{37} +(4.28915 + 0.776664i) q^{38} -4.60197i q^{39} +(-1.25637 + 1.84974i) q^{40} +(-5.16438 - 2.98166i) q^{41} +(3.51116 + 0.940813i) q^{42} +(-0.264867 + 0.0709708i) q^{43} +(-4.44032 + 2.56362i) q^{44} +(-1.69230 + 1.46154i) q^{45} -5.61492i q^{46} +(-6.50508 - 1.74303i) q^{47} +(0.965926 + 0.258819i) q^{48} -6.21339i q^{49} +(-4.01250 + 2.98326i) q^{50} +(-2.25308 + 1.30082i) q^{51} +(-4.44516 + 1.19108i) q^{52} +(9.48221 + 2.54075i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-11.2612 + 2.15129i) q^{55} -3.63502i q^{56} +(0.776664 - 4.28915i) q^{57} +(-6.78655 - 6.78655i) q^{58} +(-3.25228 + 5.63312i) q^{59} +(1.84974 + 1.25637i) q^{60} +(-5.80839 - 10.0604i) q^{61} +(1.56211 + 5.82989i) q^{62} +(0.940813 - 3.51116i) q^{63} -1.00000i q^{64} +(-10.2629 - 0.750918i) q^{65} +(2.56362 + 4.44032i) q^{66} +(-1.78386 + 6.65746i) q^{67} +(1.83963 + 1.83963i) q^{68} -5.61492 q^{69} +(2.67104 - 7.67675i) q^{70} +(5.61576 + 3.24226i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-6.48755 + 1.73833i) q^{73} +(-5.97517 - 3.44976i) q^{74} +(2.98326 + 4.01250i) q^{75} +(-4.34401 + 0.359913i) q^{76} +(13.1788 - 13.1788i) q^{77} +(1.19108 + 4.44516i) q^{78} +(4.09212 - 7.08776i) q^{79} +(0.734807 - 2.11188i) q^{80} +(0.500000 - 0.866025i) q^{81} +(5.76012 + 1.54342i) q^{82} +(-1.64176 - 1.64176i) q^{83} -3.63502 q^{84} +(2.53332 + 5.23686i) q^{85} +(0.237473 - 0.137105i) q^{86} +(-6.78655 + 6.78655i) q^{87} +(3.62551 - 3.62551i) q^{88} +(7.97739 + 13.8172i) q^{89} +(1.25637 - 1.84974i) q^{90} +(14.4871 - 8.36413i) q^{91} +(1.45325 + 5.42359i) q^{92} +(5.82989 - 1.56211i) q^{93} +6.73455 q^{94} +(-9.43853 - 2.43192i) q^{95} -1.00000 q^{96} +(-1.01062 + 0.270794i) q^{97} +(1.60814 + 6.00167i) q^{98} +(4.44032 - 2.56362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more