LMFDB - Embedded newform 210.2.t.f.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(59,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("210.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	210.59
Dual form			210.2.t.f.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.792893 + 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.792893 + 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(-2.20711 + 0.358719i) q^{10} +(0.184829 + 0.106711i) q^{11} +(-1.01575 + 1.40294i) q^{12} -6.70141 q^{13} +(2.64360 + 0.106711i) q^{14} +(-1.73861 + 3.46081i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73861 + 1.58114i) q^{17} +(0.936492 + 2.85008i) q^{18} +(4.23861 - 2.44716i) q^{19} +(-1.41421 - 1.73205i) q^{20} +(2.83495 - 3.60042i) q^{21} +0.213422i q^{22} +(-3.23861 - 5.60944i) q^{23} +(-1.72286 - 0.178197i) q^{24} +(-3.74264 - 3.31552i) q^{25} +(-3.35071 - 5.80359i) q^{26} +(4.94975 + 1.58114i) q^{27} +(1.22938 + 2.34278i) q^{28} +2.02265i q^{29} +(-3.86646 + 0.224724i) q^{30} +(-0.261387 - 0.150912i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.299418 + 0.216784i) q^{33} +3.16228i q^{34} +(3.55378 + 4.72976i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(6.17913 - 3.56752i) q^{37} +(4.23861 + 2.44716i) q^{38} +(-11.5456 - 1.19417i) q^{39} +(0.792893 - 2.09077i) q^{40} -6.70141 q^{41} +(4.53553 + 0.654929i) q^{42} -2.02265i q^{43} +(-0.184829 + 0.106711i) q^{44} +(-3.61209 + 5.65268i) q^{45} +(3.23861 - 5.60944i) q^{46} +(-6.71584 + 3.87739i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 - 6.32456i) q^{49} +(1.00000 - 4.89898i) q^{50} +(4.43649 + 3.21209i) q^{51} +(3.35071 - 5.80359i) q^{52} +(2.50000 - 4.33013i) q^{53} +(1.10557 + 5.07718i) q^{54} +(-0.369657 + 0.301824i) q^{55} +(-1.41421 + 2.23607i) q^{56} +(7.73861 - 3.46081i) q^{57} +(-1.75166 + 1.01132i) q^{58} +(-2.45877 + 4.25871i) q^{59} +(-2.12785 - 3.23609i) q^{60} +(3.00000 - 1.73205i) q^{61} -0.301824i q^{62} +(5.52581 - 5.69784i) q^{63} +1.00000 q^{64} +(5.31350 - 14.0111i) q^{65} +(-0.0380311 + 0.367696i) q^{66} +(4.61230 + 2.66291i) q^{67} +(-2.73861 + 1.58114i) q^{68} +(-4.58009 - 10.2414i) q^{69} +(-2.31920 + 5.44255i) q^{70} -2.02265i q^{71} +(-2.93649 - 0.614017i) q^{72} +(-5.99430 + 10.3824i) q^{73} +(6.17913 + 3.56752i) q^{74} +(-5.85723 - 6.37909i) q^{75} +4.89433i q^{76} +(0.500000 - 0.262377i) q^{77} +(-4.73861 - 10.5959i) q^{78} +(-0.261387 - 0.452736i) q^{79} +(2.20711 - 0.358719i) q^{80} +(8.24597 + 3.60611i) q^{81} +(-3.35071 - 5.80359i) q^{82} +16.7169i q^{83} +(1.70058 + 4.25535i) q^{84} +(-5.47723 + 4.47214i) q^{85} +(1.75166 - 1.01132i) q^{86} +(-0.360429 + 3.48474i) q^{87} +(-0.184829 - 0.106711i) q^{88} +(-5.28720 - 9.15769i) q^{89} +(-6.70141 - 0.301824i) q^{90} +(-9.47723 + 14.9848i) q^{91} +6.47723 q^{92} +(-0.423441 - 0.306579i) q^{93} +(-6.71584 - 3.87739i) q^{94} +(1.75569 + 10.8023i) q^{95} +(1.01575 - 1.40294i) q^{96} +3.50333 q^{97} +(3.97723 - 5.76035i) q^{98} +(0.477226 + 0.426844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9	$ 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9} - 12 q^{10} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 12 q^{19} + 4 q^{21} - 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} + 4 q^{32} + 12 q^{33} + 8 q^{35} - 16 q^{36} + 12 q^{38} - 8 q^{39} + 12 q^{40} + 8 q^{42} - 24 q^{45} + 4 q^{46} + 12 q^{47} - 24 q^{49} + 8 q^{50} + 20 q^{51} + 20 q^{53} + 40 q^{57} - 4 q^{60} + 24 q^{61} - 20 q^{63} + 8 q^{64} - 16 q^{65} + 12 q^{66} - 8 q^{70} - 8 q^{72} - 24 q^{75} + 4 q^{77} - 16 q^{78} - 24 q^{79} + 12 q^{80} + 4 q^{81} + 4 q^{84} - 12 q^{87} - 32 q^{91} + 8 q^{92} + 20 q^{93} + 12 q^{94} - 12 q^{95} - 12 q^{98} - 40 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9 - 12 * q^10 + 8 * q^15 - 4 * q^16 - 8 * q^18 + 12 * q^19 + 4 * q^21 - 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 + 4 * q^32 + 12 * q^33 + 8 * q^35 - 16 * q^36 + 12 * q^38 - 8 * q^39 + 12 * q^40 + 8 * q^42 - 24 * q^45 + 4 * q^46 + 12 * q^47 - 24 * q^49 + 8 * q^50 + 20 * q^51 + 20 * q^53 + 40 * q^57 - 4 * q^60 + 24 * q^61 - 20 * q^63 + 8 * q^64 - 16 * q^65 + 12 * q^66 - 8 * q^70 - 8 * q^72 - 24 * q^75 + 4 * q^77 - 16 * q^78 - 24 * q^79 + 12 * q^80 + 4 * q^81 + 4 * q^84 - 12 * q^87 - 32 * q^91 + 8 * q^92 + 20 * q^93 + 12 * q^94 - 12 * q^95 - 12 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.792893	+	2.09077i	−0.354593	+	0.935021i
$5$	−0.792893	+	2.09077i	−0.354593	+	0.935021i
$6$	0.707107	+	1.58114i	0.288675	+	0.645497i
$7$	1.41421	−	2.23607i	0.534522	−	0.845154i
$7$	1.41421	−	2.23607i	0.534522	−	0.845154i
$8$	−1.00000			−0.353553
$9$	2.93649	+	0.614017i	0.978831	+	0.204672i
$10$	−2.20711	+	0.358719i	−0.697948	+	0.113437i
$11$	0.184829	+	0.106711i	0.0557279	+	0.0321745i	0.527605	−	0.849490i	$-0.323090\pi$
$11$	0.184829	+	0.106711i	0.0557279	+	0.0321745i	−0.471877	+	0.881664i	$0.656423\pi$
$12$	−1.01575	+	1.40294i	−0.293223	+	0.404994i
$13$	−6.70141			−1.85864			−0.929318	−	0.369279i	$-0.879605\pi$
$13$	−6.70141			−1.85864			−0.929318	+	0.369279i	$0.879605\pi$
$14$	2.64360	+	0.106711i	0.706531	+	0.0285197i
$15$	−1.73861	+	3.46081i	−0.448908	+	0.893578i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.73861	+	1.58114i	0.664211	+	0.383482i	0.793880	−	0.608075i	$-0.208058\pi$
$17$	2.73861	+	1.58114i	0.664211	+	0.383482i	−0.129668	+	0.991557i	$0.541391\pi$
$18$	0.936492	+	2.85008i	0.220733	+	0.671771i
$19$	4.23861	−	2.44716i	0.972404	−	0.561418i	0.0724360	−	0.997373i	$-0.476923\pi$
$19$	4.23861	−	2.44716i	0.972404	−	0.561418i	0.899968	+	0.435955i	$0.143589\pi$
$20$	−1.41421	−	1.73205i	−0.316228	−	0.387298i
$21$	2.83495	−	3.60042i	0.618637	−	0.785677i
$22$			0.213422i			0.0455017i
$23$	−3.23861	−	5.60944i	−0.675297	−	1.16965i	−0.976382	−	0.216052i	$-0.930682\pi$
$23$	−3.23861	−	5.60944i	−0.675297	−	1.16965i	0.301084	−	0.953597i	$-0.402651\pi$
$24$	−1.72286	−	0.178197i	−0.351677	−	0.0363743i
$25$	−3.74264	−	3.31552i	−0.748528	−	0.663103i
$26$	−3.35071	−	5.80359i	−0.657127	−	1.13818i
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$	1.22938	+	2.34278i	0.232332	+	0.442744i
$29$			2.02265i			0.375596i	0.982208	+	0.187798i	$0.0601350\pi$
$29$			2.02265i			0.375596i	−0.982208	+	0.187798i	$0.939865\pi$
$30$	−3.86646	+	0.224724i	−0.705915	+	0.0410287i
$31$	−0.261387	−	0.150912i	−0.0469465	−	0.0271046i	0.476343	−	0.879260i	$-0.341962\pi$
$31$	−0.261387	−	0.150912i	−0.0469465	−	0.0271046i	−0.523290	+	0.852155i	$0.675295\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.299418	+	0.216784i	0.0521220	+	0.0377372i
$34$			3.16228i			0.542326i
$35$	3.55378	+	4.72976i	0.600699	+	0.799475i
$36$	−2.00000	+	2.23607i	−0.333333	+	0.372678i
$37$	6.17913	−	3.56752i	1.01584	−	0.586497i	0.102946	−	0.994687i	$-0.467173\pi$
$37$	6.17913	−	3.56752i	1.01584	−	0.586497i	0.912897	+	0.408190i	$0.133840\pi$
$38$	4.23861	+	2.44716i	0.687594	+	0.396982i
$39$	−11.5456	−	1.19417i	−1.84877	−	0.191220i
$40$	0.792893	−	2.09077i	0.125367	−	0.330580i
$41$	−6.70141			−1.04658			−0.523292	−	0.852153i	$-0.675296\pi$
$41$	−6.70141			−1.04658			−0.523292	+	0.852153i	$0.675296\pi$
$42$	4.53553	+	0.654929i	0.699848	+	0.101058i
$43$		−	2.02265i		−	0.308451i	−0.988036	−	0.154225i	$-0.950712\pi$
$43$		−	2.02265i		−	0.308451i	0.988036	−	0.154225i	$-0.0492882\pi$
$44$	−0.184829	+	0.106711i	−0.0278640	+	0.0160873i
$45$	−3.61209	+	5.65268i	−0.538459	+	0.842652i
$46$	3.23861	−	5.60944i	0.477507	−	0.827067i
$47$	−6.71584	+	3.87739i	−0.979606	+	0.565576i	−0.902151	−	0.431420i	$-0.858013\pi$
$47$	−6.71584	+	3.87739i	−0.979606	+	0.565576i	−0.0774546	+	0.996996i	$0.524679\pi$
$48$	−0.707107	−	1.58114i	−0.102062	−	0.228218i
$49$	−3.00000	−	6.32456i	−0.428571	−	0.903508i
$50$	1.00000	−	4.89898i	0.141421	−	0.692820i
$51$	4.43649	+	3.21209i	0.621233	+	0.449783i
$52$	3.35071	−	5.80359i	0.464659	−	0.804813i
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	−0.641661	−	0.766989i	$-0.721754\pi$
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	0.985062	+	0.172200i	$0.0550875\pi$
$54$	1.10557	+	5.07718i	0.150449	+	0.690916i
$55$	−0.369657	+	0.301824i	−0.0498446	+	0.0406979i
$56$	−1.41421	+	2.23607i	−0.188982	+	0.298807i
$57$	7.73861	−	3.46081i	1.02500	−	0.458396i
$58$	−1.75166	+	1.01132i	−0.230005	+	0.132793i
$59$	−2.45877	+	4.25871i	−0.320105	+	0.554437i	−0.980509	−	0.196472i	$-0.937051\pi$
$59$	−2.45877	+	4.25871i	−0.320105	+	0.554437i	0.660405	+	0.750910i	$0.270385\pi$
$60$	−2.12785	−	3.23609i	−0.274704	−	0.417777i
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	−0.295495	−	0.955344i	$-0.595484\pi$
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	0.679605	+	0.733578i	$0.262151\pi$
$62$		−	0.301824i		−	0.0383317i
$63$	5.52581	−	5.69784i	0.696187	−	0.717861i
$64$	1.00000			0.125000
$65$	5.31350	−	14.0111i	0.659059	−	1.73786i
$66$	−0.0380311	+	0.367696i	−0.00468131	+	0.0452602i
$67$	4.61230	+	2.66291i	0.563482	+	0.325326i	0.754542	−	0.656252i	$-0.227859\pi$
$67$	4.61230	+	2.66291i	0.563482	+	0.325326i	−0.191060	+	0.981578i	$0.561192\pi$
$68$	−2.73861	+	1.58114i	−0.332106	+	0.191741i
$69$	−4.58009	−	10.2414i	−0.551378	−	1.23292i
$70$	−2.31920	+	5.44255i	−0.277197	+	0.650509i
$71$		−	2.02265i		−	0.240044i	−0.992771	−	0.120022i	$-0.961703\pi$
$71$		−	2.02265i		−	0.240044i	0.992771	−	0.120022i	$-0.0382965\pi$
$72$	−2.93649	−	0.614017i	−0.346069	−	0.0723626i
$73$	−5.99430	+	10.3824i	−0.701580	+	1.21517i	0.266331	+	0.963882i	$0.414188\pi$
$73$	−5.99430	+	10.3824i	−0.701580	+	1.21517i	−0.967912	+	0.251291i	$0.919145\pi$
$74$	6.17913	+	3.56752i	0.718310	+	0.414716i
$75$	−5.85723	−	6.37909i	−0.676335	−	0.736594i
$76$			4.89433i			0.561418i
$77$	0.500000	−	0.262377i	0.0569803	−	0.0299007i
$78$	−4.73861	−	10.5959i	−0.536542	−	1.19974i
$79$	−0.261387	−	0.452736i	−0.0294084	−	0.0509368i	0.850947	−	0.525252i	$-0.176029\pi$
$79$	−0.261387	−	0.452736i	−0.0294084	−	0.0509368i	−0.880355	+	0.474315i	$0.842696\pi$
$80$	2.20711	−	0.358719i	0.246762	−	0.0401061i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	−3.35071	−	5.80359i	−0.370023	−	0.640899i
$83$			16.7169i			1.83491i	0.397835	+	0.917457i	$0.369762\pi$
$83$			16.7169i			1.83491i	−0.397835	+	0.917457i	$0.630238\pi$
$84$	1.70058	+	4.25535i	0.185549	+	0.464297i
$85$	−5.47723	+	4.47214i	−0.594089	+	0.485071i
$86$	1.75166	−	1.01132i	0.188887	−	0.109054i
$87$	−0.360429	+	3.48474i	−0.0386421	+	0.373603i
$88$	−0.184829	−	0.106711i	−0.0197028	−	0.0113754i
$89$	−5.28720	−	9.15769i	−0.560442	−	0.970714i	−0.997458	−	0.0712599i	$-0.977298\pi$
$89$	−5.28720	−	9.15769i	−0.560442	−	0.970714i	0.437016	−	0.899454i	$-0.356035\pi$
$90$	−6.70141	−	0.301824i	−0.706391	−	0.0318150i
$91$	−9.47723	+	14.9848i	−0.993483	+	1.57083i
$92$	6.47723			0.675297
$93$	−0.423441	−	0.306579i	−0.0439088	−	0.0317907i
$94$	−6.71584	−	3.87739i	−0.692686	−	0.399922i
$95$	1.75569	+	10.8023i	0.180130	+	1.10829i
$96$	1.01575	−	1.40294i	0.103670	−	0.143187i
$97$	3.50333			0.355709			0.177854	−	0.984057i	$-0.443084\pi$
$97$	3.50333			0.355709			0.177854	+	0.984057i	$0.443084\pi$
$98$	3.97723	−	5.76035i	0.401760	−	0.581884i
$99$	0.477226	+	0.426844i	0.0479630	+	0.0428994i
$100$	4.74264	−	1.58346i	0.474264	−	0.158346i
$101$	−5.65685	+	9.79796i	−0.562878	+	0.974933i	0.434366	+	0.900737i	$0.356973\pi$
$101$	−5.65685	+	9.79796i	−0.562878	+	0.974933i	−0.997244	+	0.0741967i	$0.976361\pi$
$102$	−0.563508	+	5.44816i	−0.0557956	+	0.539448i
$103$	5.28720	+	9.15769i	0.520963	+	0.902334i	0.999703	+	0.0243776i	$0.00776038\pi$
$103$	5.28720	+	9.15769i	0.520963	+	0.902334i	−0.478740	+	0.877957i	$0.658906\pi$
$104$	6.70141			0.657127
$105$	5.27984	+	8.78198i	0.515260	+	0.857034i
$106$	5.00000			0.485643
$107$	2.73861	+	4.74342i	0.264752	+	0.458563i	0.967499	−	0.252877i	$-0.0813767\pi$
$107$	2.73861	+	4.74342i	0.264752	+	0.458563i	−0.702747	+	0.711440i	$0.748043\pi$
$108$	−3.84418	+	3.49604i	−0.369906	+	0.336406i
$109$	−6.21584	+	10.7661i	−0.595369	+	1.03121i	0.398125	+	0.917331i	$0.369661\pi$
$109$	−6.21584	+	10.7661i	−0.595369	+	1.03121i	−0.993495	+	0.113879i	$0.963672\pi$
$110$	−0.446216	−	0.169221i	−0.0425450	−	0.0161346i
$111$	11.2815	−	5.04524i	1.07079	−	0.478873i
$112$	−2.64360	−	0.106711i	−0.249797	−	0.0100832i
$113$	−6.52277			−0.613611			−0.306806	−	0.951772i	$-0.599260\pi$
$113$	−6.52277			−0.613611			−0.306806	+	0.951772i	$0.599260\pi$
$114$	6.86646	+	4.97143i	0.643103	+	0.465617i
$115$	14.2959	−	2.32351i	1.33310	−	0.216668i
$116$	−1.75166	−	1.01132i	−0.162638	−	0.0938990i
$117$	−19.6786	−	4.11478i	−1.81929	−	0.380411i
$118$	−4.91754			−0.452696
$119$	7.40852	−	3.88766i	0.679138	−	0.356381i
$120$	1.73861	−	3.46081i	0.158713	−	0.315928i
$121$	−5.47723	−	9.48683i	−0.497930	−	0.862439i
$122$	3.00000	+	1.73205i	0.271607	+	0.156813i
$123$	−11.5456	−	1.19417i	−1.04103	−	0.107675i
$124$	0.261387	−	0.150912i	0.0234733	−	0.0135523i
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$	7.69738	+	1.93657i	0.685737	+	0.172523i
$127$			13.6298i			1.20945i	0.796434	+	0.604726i	$0.206717\pi$
$127$			13.6298i			1.20945i	−0.796434	+	0.604726i	$0.793283\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.360429	−	3.48474i	0.0317340	−	0.306814i
$130$	14.7907	−	2.40393i	1.29723	−	0.210838i
$131$	3.01326	+	5.21911i	0.263269	+	0.455996i	0.967109	−	0.254363i	$-0.0818659\pi$
$131$	3.01326	+	5.21911i	0.263269	+	0.455996i	−0.703839	+	0.710359i	$0.748533\pi$
$132$	−0.337449	+	0.150912i	−0.0293712	+	0.0131352i
$133$	0.522278	−	12.9386i	0.0452873	−	1.12192i
$134$			5.32582i			0.460081i
$135$	−7.23042	+	9.09511i	−0.622295	+	0.782782i
$136$	−2.73861	−	1.58114i	−0.234834	−	0.135582i
$137$	3.73861	−	6.47547i	0.319411	−	0.553237i	−0.660954	−	0.750426i	$-0.729848\pi$
$137$	3.73861	−	6.47547i	0.319411	−	0.553237i	0.980365	+	0.197190i	$0.0631815\pi$
$138$	6.57926	−	9.08717i	0.560064	−	0.773551i
$139$			7.53185i			0.638843i	0.947613	+	0.319422i	$0.103489\pi$
$139$			7.53185i			0.638843i	−0.947613	+	0.319422i	$0.896511\pi$
$140$	−5.87298	+	0.712788i	−0.496358	+	0.0602416i
$141$	−12.2614	+	5.48346i	−1.03260	+	0.461791i
$142$	1.75166	−	1.01132i	0.146996	−	0.0848683i
$143$	−1.23861	−	0.715113i	−0.103578	−	0.0598008i
$144$	−0.936492	−	2.85008i	−0.0780410	−	0.237507i
$145$	−4.22889	−	1.60374i	−0.351190	−	0.133184i
$146$	−11.9886			−0.992184
$147$	−4.04156	−	11.4309i	−0.333342	−	0.942806i
$148$			7.13505i			0.586497i
$149$	2.12132	−	1.22474i	0.173785	−	0.100335i	−0.410584	−	0.911823i	$-0.634675\pi$
$149$	2.12132	−	1.22474i	0.173785	−	0.100335i	0.584370	+	0.811488i	$0.301342\pi$
$150$	2.59584	−	8.26206i	0.211950	−	0.674594i
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−4.23861	+	2.44716i	−0.343797	+	0.198491i
$153$	7.07107	+	6.32456i	0.571662	+	0.511310i
$154$	0.477226	+	0.301824i	0.0384559	+	0.0243217i
$155$	0.522774	−	0.426844i	0.0419903	−	0.0342849i
$156$	6.80698	−	9.40169i	0.544994	−	0.752738i
$157$	−4.39526	+	7.61282i	−0.350780	+	0.607569i	−0.986386	−	0.164445i	$-0.947417\pi$
$157$	−4.39526	+	7.61282i	−0.350780	+	0.607569i	0.635606	+	0.772013i	$0.280750\pi$
$158$	0.261387	−	0.452736i	0.0207949	−	0.0360177i
$159$	5.07877	−	7.01471i	0.402772	−	0.556303i
$160$	1.41421	+	1.73205i	0.111803	+	0.136931i
$161$	−17.1232	−	0.691190i	−1.34950	−	0.0544734i
$162$	1.00000	+	8.94427i	0.0785674	+	0.702728i
$163$	12.7279	−	7.34847i	0.996928	−	0.575577i	0.0895899	−	0.995979i	$-0.471444\pi$
$163$	12.7279	−	7.34847i	0.996928	−	0.575577i	0.907338	+	0.420402i	$0.138111\pi$
$164$	3.35071	−	5.80359i	0.261646	−	0.453184i
$165$	−0.690652	+	0.454129i	−0.0537672	+	0.0353539i
$166$	−14.4772	+	8.35843i	−1.12365	+	0.648740i
$167$		−	14.6830i		−	1.13620i	−0.822958	−	0.568102i	$-0.807678\pi$
$167$		−	14.6830i		−	1.13620i	0.822958	−	0.568102i	$-0.192322\pi$
$168$	−2.83495	+	3.60042i	−0.218721	+	0.277779i
$169$	31.9089			2.45453
$170$	−6.61160	−	2.50735i	−0.507086	−	0.192305i
$171$	13.9493	−	4.58350i	1.06673	−	0.350509i
$172$	1.75166	+	1.01132i	0.133563	+	0.0771127i
$173$	9.97723	−	5.76035i	0.758554	−	0.437952i	−0.0702221	−	0.997531i	$-0.522371\pi$
$173$	9.97723	−	5.76035i	0.758554	−	0.437952i	0.828776	+	0.559580i	$0.189037\pi$
$174$	−3.19808	+	1.43023i	−0.242446	+	0.108425i
$175$	−12.7066	+	3.67995i	−0.960529	+	0.278178i
$176$		−	0.213422i		−	0.0160873i
$177$	−4.99501	+	6.89902i	−0.375448	+	0.518562i
$178$	5.28720	−	9.15769i	0.396292	−	0.686398i
$179$	−12.9128	−	7.45518i	−0.965144	−	0.557226i	−0.0673918	−	0.997727i	$-0.521468\pi$
$179$	−12.9128	−	7.45518i	−0.965144	−	0.557226i	−0.897752	+	0.440500i	$0.854801\pi$
$180$	−3.08932	−	5.95450i	−0.230264	−	0.443823i
$181$		−	3.16228i		−	0.235050i	−0.993070	−	0.117525i	$-0.962504\pi$
$181$		−	3.16228i		−	0.235050i	0.993070	−	0.117525i	$-0.0374961\pi$
$182$	−17.7158	−	0.715113i	−1.31319	−	0.0530077i
$183$	5.47723	−	2.44949i	0.404888	−	0.181071i
$184$	3.23861	+	5.60944i	0.238754	+	0.413534i
$185$	2.55948	+	15.7478i	0.188177	+	1.15780i
$186$	0.0537841	−	0.520000i	0.00394364	−	0.0381283i
$187$	0.337449	+	0.584480i	0.0246767	+	0.0427414i
$188$		−	7.75478i		−	0.565576i
$189$	10.5355	−	8.83190i	0.766347	−	0.642426i
$190$	−8.47723	+	6.92163i	−0.615003	+	0.502148i
$191$	−1.38201	+	0.797901i	−0.0999984	+	0.0577341i	−0.549165	−	0.835714i	$-0.685054\pi$
$191$	−1.38201	+	0.797901i	−0.0999984	+	0.0577341i	0.449167	+	0.893448i	$0.351721\pi$
$192$	1.72286	+	0.178197i	0.124337	+	0.0128603i
$193$	6.36396	+	3.67423i	0.458088	+	0.264477i	0.711240	−	0.702949i	$-0.248134\pi$
$193$	6.36396	+	3.67423i	0.458088	+	0.264477i	−0.253152	+	0.967427i	$0.581467\pi$
$194$	1.75166	+	3.03397i	0.125762	+	0.217826i
$195$	11.6512	−	23.1923i	0.834357	−	1.66084i
$196$	6.97723	+	0.564201i	0.498373	+	0.0403001i
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$	−0.131045	+	0.626711i	−0.00931293	+	0.0445384i
$199$	−19.4317	−	11.2189i	−1.37748	−	0.795286i	−0.385620	−	0.922658i	$-0.626012\pi$
$199$	−19.4317	−	11.2189i	−1.37748	−	0.795286i	−0.991855	+	0.127372i	$0.959346\pi$
$200$	3.74264	+	3.31552i	0.264645	+	0.234442i
$201$	7.47182	+	5.40972i	0.527022	+	0.381572i
$202$	−11.3137			−0.796030
$203$	4.52277	+	2.86045i	0.317437	+	0.200764i
$204$	−5.00000	+	2.23607i	−0.350070	+	0.156556i
$205$	5.31350	−	14.0111i	0.371111	−	0.978578i
$206$	−5.28720	+	9.15769i	−0.368376	+	0.638047i
$207$	−6.06587	−	18.4606i	−0.421607	−	1.28310i
$208$	3.35071	+	5.80359i	0.232330	+	0.402407i
$209$	1.04456			0.0722535
$210$	−4.96550	+	8.96347i	−0.342652	+	0.618538i
$211$	13.5228			0.930946			0.465473	−	0.885062i	$-0.345884\pi$
$211$	13.5228			0.930946			0.465473	+	0.885062i	$0.345884\pi$
$212$	2.50000	+	4.33013i	0.171701	+	0.297394i
$213$	0.360429	−	3.48474i	0.0246962	−	0.238770i
$214$	−2.73861	+	4.74342i	−0.187208	+	0.324253i
$215$	4.22889	+	1.60374i	0.288408	+	0.109374i
$216$	−4.94975	−	1.58114i	−0.336788	−	0.107583i
$217$	−0.707107	+	0.371058i	−0.0480015	+	0.0251890i
$218$	−12.4317			−0.841979
$219$	−12.1775	+	16.8193i	−0.822877	+	1.13654i
$220$	−0.0765585	−	0.471045i	−0.00516158	−	0.0317578i
$221$	−18.3526	−	10.5959i	−1.23453	−	0.712755i
$222$	10.0101	+	7.24745i	0.671831	+	0.486417i
$223$	−6.39617			−0.428319			−0.214160	−	0.976799i	$-0.568701\pi$
$223$	−6.39617			−0.428319			−0.214160	+	0.976799i	$0.568701\pi$
$224$	−1.22938	−	2.34278i	−0.0821417	−	0.156533i
$225$	−8.95445	−	12.0340i	−0.596963	−	0.802268i
$226$	−3.26139	−	5.64889i	−0.216944	−	0.375758i
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	0.170648	−	0.985332i	$-0.445414\pi$
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	−0.767999	+	0.640451i	$0.778747\pi$
$228$	−0.872155	+	8.43224i	−0.0577598	+	0.558439i
$229$	−6.26139	+	3.61501i	−0.413764	+	0.238887i	−0.692406	−	0.721508i	$-0.743449\pi$
$229$	−6.26139	+	3.61501i	−0.413764	+	0.238887i	0.278642	+	0.960395i	$0.410116\pi$
$230$	9.16018	+	11.2189i	0.604004	+	0.739751i
$231$	0.908185	−	0.362941i	0.0597542	−	0.0238798i
$232$		−	2.02265i		−	0.132793i
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	0.793047	−	0.609160i	$-0.208493\pi$
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	−0.924072	+	0.382219i	$0.875160\pi$
$234$	−6.27582	−	19.0996i	−0.410263	−	1.24858i
$235$	−2.78179	−	17.1156i	−0.181464	−	1.11650i
$236$	−2.45877	−	4.25871i	−0.160052	−	0.277219i
$237$	−0.369657	−	0.826579i	−0.0240118	−	0.0536921i
$238$	7.07107	+	4.47214i	0.458349	+	0.289886i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	3.86646	−	0.224724i	0.249579	−	0.0145058i
$241$	3.45445	+	1.99443i	0.222521	+	0.128472i	0.607117	−	0.794613i	$-0.292326\pi$
$241$	3.45445	+	1.99443i	0.222521	+	0.128472i	−0.384596	+	0.923085i	$0.625659\pi$
$242$	5.47723	−	9.48683i	0.352089	−	0.609837i
$243$	13.5640	+	7.68223i	0.870134	+	0.492815i
$244$			3.46410i			0.221766i
$245$	15.6019	−	1.25761i	0.996767	−	0.0803460i
$246$	−4.73861	−	10.5959i	−0.302123	−	0.675567i
$247$	−28.4047	+	16.3995i	−1.80735	+	1.04347i
$248$	0.261387	+	0.150912i	0.0165981	+	0.00958292i
$249$	−2.97889	+	28.8008i	−0.188780	+	1.82518i
$250$	9.44975	+	5.97514i	0.597655	+	0.377901i
$251$	16.6009			1.04784			0.523920	−	0.851768i	$-0.324469\pi$
$251$	16.6009			1.04784			0.523920	+	0.851768i	$0.324469\pi$
$252$	2.17157	+	7.63441i	0.136796	+	0.480923i
$253$		−	1.38238i		−	0.0869095i
$254$	−11.8038	+	6.81491i	−0.740635	+	0.427606i
$255$	−10.2334	+	6.72884i	−0.640841	+	0.421376i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	20.4772	−	11.8225i	1.27733	−	0.737469i	0.300977	−	0.953631i	$-0.402687\pi$
$257$	20.4772	−	11.8225i	1.27733	−	0.737469i	0.976357	+	0.216162i	$0.0693540\pi$
$258$	3.19808	−	1.43023i	0.199104	−	0.0890420i
$259$	0.761387	−	18.8622i	0.0473103	−	1.17204i
$260$	9.47723	+	11.6072i	0.587753	+	0.719847i
$261$	−1.24194	+	5.93948i	−0.0768741	+	0.367645i
$262$	−3.01326	+	5.21911i	−0.186160	+	0.322438i
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$	−0.299418	−	0.216784i	−0.0184279	−	0.0133421i
$265$	7.07107	+	8.66025i	0.434372	+	0.531995i
$266$	11.4663	−	6.01701i	0.703046	−	0.368927i
$267$	−7.47723	−	16.7196i	−0.457599	−	1.02322i
$268$	−4.61230	+	2.66291i	−0.281741	+	0.162663i
$269$	14.4474	−	25.0236i	0.880872	−	1.52572i	0.0304992	−	0.999535i	$-0.490290\pi$
$269$	14.4474	−	25.0236i	0.880872	−	1.52572i	0.850373	−	0.526180i	$-0.176376\pi$
$270$	−11.4918	−	1.71417i	−0.699369	−	0.104321i
$271$	5.47723	−	3.16228i	0.332718	−	0.192095i	−0.324329	−	0.945944i	$-0.605139\pi$
$271$	5.47723	−	3.16228i	0.332718	−	0.192095i	0.657047	+	0.753850i	$0.271805\pi$
$272$		−	3.16228i		−	0.191741i
$273$	−18.9982	+	24.1279i	−1.14982	+	1.46029i
$274$	7.47723			0.451716
$275$	−0.337946	−	1.01218i	−0.0203789	−	0.0610369i
$276$	11.1594	+	1.15422i	0.671714	+	0.0694760i
$277$	−8.48528	−	4.89898i	−0.509831	−	0.294351i	0.222933	−	0.974834i	$-0.428437\pi$
$277$	−8.48528	−	4.89898i	−0.509831	−	0.294351i	−0.732764	+	0.680483i	$0.761770\pi$
$278$	−6.52277	+	3.76593i	−0.391210	+	0.225865i
$279$	−0.674899	−	0.603648i	−0.0404051	−	0.0361395i
$280$	−3.55378	−	4.72976i	−0.212379	−	0.282657i
$281$		−	11.6072i		−	0.692427i	−0.938156	−	0.346213i	$-0.887467\pi$
$281$		−	11.6072i		−	0.692427i	0.938156	−	0.346213i	$-0.112533\pi$
$282$	−10.8795	−	7.87694i	−0.647865	−	0.469065i
$283$	12.3583	−	21.4051i	0.734623	−	1.27240i	−0.220266	−	0.975440i	$-0.570693\pi$
$283$	12.3583	−	21.4051i	0.734623	−	1.27240i	0.954889	−	0.296964i	$-0.0959741\pi$
$284$	1.75166	+	1.01132i	0.103942	+	0.0600110i
$285$	1.09987	+	18.9237i	0.0651507	+	1.12094i
$286$		−	1.43023i		−	0.0845711i
$287$	−9.47723	+	14.9848i	−0.559423	+	0.884525i
$288$	2.00000	−	2.23607i	0.117851	−	0.131762i
$289$	−3.50000	−	6.06218i	−0.205882	−	0.356599i
$290$	−0.725563	−	4.46420i	−0.0426065	−	0.262147i
$291$	6.03574	+	0.624282i	0.353821	+	0.0365961i
$292$	−5.99430	−	10.3824i	−0.350790	−	0.607586i
$293$			4.59250i			0.268297i	0.990961	+	0.134148i	$0.0428299\pi$
$293$			4.59250i			0.268297i	−0.990961	+	0.134148i	$0.957170\pi$
$294$	7.87868	−	9.21555i	0.459494	−	0.537462i
$295$	−6.95445	−	8.51743i	−0.404904	−	0.495904i
$296$	−6.17913	+	3.56752i	−0.359155	+	0.207358i
$297$	0.746131	+	0.820432i	0.0432949	+	0.0476063i
$298$	2.12132	+	1.22474i	0.122885	+	0.0709476i
$299$	21.7033	+	37.5912i	1.25513	+	2.17395i
$300$	8.45307	−	1.88296i	0.488038	−	0.108713i
$301$	−4.52277	−	2.86045i	−0.260688	−	0.164874i
$302$	2.00000			0.115087
$303$	−11.4919	+	15.8725i	−0.660194	+	0.911850i
$304$	−4.23861	−	2.44716i	−0.243101	−	0.140354i
$305$	1.24264	+	7.64564i	0.0711534	+	0.437788i
$306$	−1.94169	+	9.28600i	−0.110999	+	0.530845i
$307$	−3.50333			−0.199945			−0.0999727	−	0.994990i	$-0.531876\pi$
$307$	−3.50333			−0.199945			−0.0999727	+	0.994990i	$0.531876\pi$
$308$	−0.0227744	+	0.564201i	−0.00129769	+	0.0321484i
$309$	7.47723	+	16.7196i	0.425365	+	0.951144i
$310$	0.631045	+	0.239314i	0.0358409	+	0.0135921i
$311$	14.4474	−	25.0236i	0.819236	−	1.41896i	−0.0870106	−	0.996207i	$-0.527731\pi$
$311$	14.4474	−	25.0236i	0.819236	−	1.41896i	0.906246	−	0.422750i	$-0.138935\pi$
$312$	11.5456	+	1.19417i	0.653640	+	0.0676066i
$313$	−11.6190	−	20.1246i	−0.656742	−	1.13751i	−0.981454	−	0.191697i	$-0.938601\pi$
$313$	−11.6190	−	20.1246i	−0.656742	−	1.13751i	0.324712	−	0.945813i	$-0.394733\pi$
$314$	−8.79052			−0.496078
$315$	7.53151	+	16.0710i	0.424352	+	0.905497i
$316$	0.522774			0.0294084
$317$	16.9545	+	29.3660i	0.952257	+	1.64936i	0.740524	+	0.672030i	$0.234577\pi$
$317$	16.9545	+	29.3660i	0.952257	+	1.64936i	0.211733	+	0.977328i	$0.432089\pi$
$318$	8.61430	+	0.890985i	0.483066	+	0.0499640i
$319$	−0.215838	+	0.373843i	−0.0120846	+	0.0209312i
$320$	−0.792893	+	2.09077i	−0.0443241	+	0.116878i
$321$	3.87298	+	8.66025i	0.216169	+	0.483368i
$322$	−7.96300	−	15.1747i	−0.443761	−	0.845653i
$323$	15.4772			0.861176
$324$	−7.24597	+	5.33816i	−0.402554	+	0.296565i
$325$	25.0810	+	22.2186i	1.39124	+	1.23247i
$326$	12.7279	+	7.34847i	0.704934	+	0.406994i
$327$	−12.6275	+	17.4409i	−0.698303	+	0.964485i
$328$	6.70141			0.370023
$329$	−0.827520	+	20.5005i	−0.0456226	+	1.13023i
$330$	−0.738613	−	0.371058i	−0.0406593	−	0.0204261i
$331$	5.71584	+	9.90012i	0.314171	+	0.544160i	0.979261	−	0.202603i	$-0.0649402\pi$
$331$	5.71584	+	9.90012i	0.314171	+	0.544160i	−0.665090	+	0.746763i	$0.731607\pi$
$332$	−14.4772	−	8.35843i	−0.794541	−	0.458728i
$333$	20.3355	−	6.68191i	1.11438	−	0.366167i
$334$	12.7158	−	7.34149i	0.695780	−	0.401709i
$335$	−9.22460	+	7.53185i	−0.503994	+	0.411509i
$336$	−4.53553	−	0.654929i	−0.247434	−	0.0357293i
$337$			17.1464i			0.934025i	0.884251	+	0.467013i	$0.154670\pi$
$337$			17.1464i			0.934025i	−0.884251	+	0.467013i	$0.845330\pi$
$338$	15.9545	+	27.6339i	0.867808	+	1.50309i
$339$	−11.2378	−	1.16234i	−0.610355	−	0.0631296i
$340$	−1.13437	−	6.97948i	−0.0615199	−	0.378516i
$341$	−0.0322079	−	0.0557857i	−0.00174416	−	0.00302097i
$342$	10.9441	+	9.78866i	0.591787	+	0.529310i
$343$	−18.3848	−	2.23607i	−0.992685	−	0.120736i
$344$			2.02265i			0.109054i
$345$	25.0439	−	1.45559i	1.34832	−	0.0783661i
$346$	9.97723	+	5.76035i	0.536379	+	0.309679i
$347$	−3.26139	+	5.64889i	−0.175080	+	0.303248i	−0.940189	−	0.340653i	$-0.889352\pi$
$347$	−3.26139	+	5.64889i	−0.175080	+	0.303248i	0.765109	+	0.643901i	$0.222685\pi$
$348$	−2.83766	−	2.05451i	−0.152114	−	0.110133i
$349$			32.5282i			1.74120i	0.491994	+	0.870599i	$0.336268\pi$
$349$			32.5282i			1.74120i	−0.491994	+	0.870599i	$0.663732\pi$
$350$	−9.54024	−	9.16427i	−0.509947	−	0.489851i
$351$	−33.1703	−	10.5959i	−1.77050	−	0.565565i
$352$	0.184829	−	0.106711i	0.00985140	−	0.00568771i
$353$	−11.4772	−	6.62638i	−0.610871	−	0.352687i	0.162435	−	0.986719i	$-0.448065\pi$
$353$	−11.4772	−	6.62638i	−0.610871	−	0.352687i	−0.773306	+	0.634033i	$0.781398\pi$
$354$	−8.47223	−	0.876291i	−0.450294	−	0.0465743i
$355$	4.22889	+	1.60374i	0.224446	+	0.0851178i
$356$	10.5744			0.560442
$357$	13.4566	−	5.37771i	0.712199	−	0.284619i
$358$		−	14.9104i		−	0.788037i
$359$	5.62465	−	3.24739i	0.296857	−	0.171391i	−0.344173	−	0.938906i	$-0.611841\pi$
$359$	5.62465	−	3.24739i	0.296857	−	0.171391i	0.641030	+	0.767516i	$0.278507\pi$
$360$	3.61209	−	5.65268i	0.190374	−	0.297922i
$361$	2.47723	−	4.29068i	0.130380	−	0.225825i
$362$	2.73861	−	1.58114i	0.143938	−	0.0831028i
$363$	−7.74597	−	17.3205i	−0.406558	−	0.909091i
$364$	−8.23861	−	15.6999i	−0.431821	−	0.822900i
$365$	−16.9545	−	20.7649i	−0.887437	−	1.08688i
$366$	4.85993	+	3.51867i	0.254033	+	0.183924i
$367$	4.05781	−	7.02834i	0.211816	−	0.366876i	−0.740467	−	0.672093i	$-0.765396\pi$
$367$	4.05781	−	7.02834i	0.211816	−	0.366876i	0.952283	+	0.305217i	$0.0987289\pi$
$368$	−3.23861	+	5.60944i	−0.168824	+	0.292412i
$369$	−19.6786	−	4.11478i	−1.02443	−	0.214207i
$370$	−12.3583	+	10.0905i	−0.642476	+	0.524579i
$371$	−6.14692	−	11.7139i	−0.319132	−	0.608155i
$372$	0.477226	−	0.213422i	0.0247430	−	0.0110654i
$373$	3.13367	−	1.80922i	0.162255	−	0.0936781i	−0.416674	−	0.909056i	$-0.636804\pi$
$373$	3.13367	−	1.80922i	0.162255	−	0.0936781i	0.578929	+	0.815378i	$0.303471\pi$
$374$	−0.337449	+	0.584480i	−0.0174491	+	0.0302227i
$375$	17.9814	−	7.18818i	0.928554	−	0.371196i
$376$	6.71584	−	3.87739i	0.346343	−	0.199961i
$377$		−	13.5546i		−	0.698097i
$378$	12.9164	+	4.70809i	0.664349	+	0.242158i
$379$	−9.52277			−0.489152			−0.244576	−	0.969630i	$-0.578649\pi$
$379$	−9.52277			−0.489152			−0.244576	+	0.969630i	$0.578649\pi$
$380$	−10.2329	−	3.88068i	−0.524938	−	0.199075i
$381$	−2.42879	+	23.4823i	−0.124431	+	1.20303i
$382$	−1.38201	−	0.797901i	−0.0707096	−	0.0408242i
$383$	0.715838	−	0.413289i	0.0365776	−	0.0211181i	−0.481600	−	0.876391i	$-0.659944\pi$
$383$	0.715838	−	0.413289i	0.0365776	−	0.0211181i	0.518177	+	0.855273i	$0.326611\pi$
$384$	0.707107	+	1.58114i	0.0360844	+	0.0806872i
$385$	0.152124	+	1.25342i	0.00775298	+	0.0638803i
$386$			7.34847i			0.374027i
$387$	1.24194	−	5.93948i	0.0631313	−	0.301921i
$388$	−1.75166	+	3.03397i	−0.0889272	+	0.154026i
$389$	−6.36396	−	3.67423i	−0.322666	−	0.186291i	0.329914	−	0.944011i	$-0.392980\pi$
$389$	−6.36396	−	3.67423i	−0.322666	−	0.186291i	−0.652580	+	0.757720i	$0.726313\pi$
$390$	25.9107	−	1.50596i	1.31204	−	0.0762575i
$391$		−	20.4828i		−	1.03586i
$392$	3.00000	+	6.32456i	0.151523	+	0.319438i
$393$	4.26139	+	9.52875i	0.214959	+	0.480662i
$394$	−4.50000	−	7.79423i	−0.226707	−	0.392668i
$395$	1.15382	−	0.187529i	0.0580549	−	0.00943563i
$396$	−0.608270	+	0.199868i	−0.0305667	+	0.0100437i
$397$	15.1867	+	26.3041i	0.762198	+	1.32017i	0.941715	+	0.336411i	$0.109213\pi$
$397$	15.1867	+	26.3041i	0.762198	+	1.32017i	−0.179517	+	0.983755i	$0.557453\pi$
$398$		−	22.4378i		−	1.12470i
$399$	3.20544	−	22.1984i	0.160473	−	1.11131i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$	−26.2834	+	15.1747i	−1.31253	+	0.757789i	−0.982514	−	0.186187i	$-0.940387\pi$
$401$	−26.2834	+	15.1747i	−1.31253	+	0.757789i	−0.330014	+	0.943976i	$0.607054\pi$
$402$	−0.949046	+	9.17565i	−0.0473341	+	0.457640i
$403$	1.75166	+	1.01132i	0.0872565	+	0.0503776i
$404$	−5.65685	−	9.79796i	−0.281439	−	0.487467i
$405$	−14.0777	+	14.3812i	−0.699528	+	0.714606i
$406$	−0.215838	+	5.34706i	−0.0107119	+	0.265370i
$407$	1.52277			0.0754811
$408$	−4.43649	−	3.21209i	−0.219639	−	0.159022i
$409$	−19.4317	−	11.2189i	−0.960835	−	0.554738i	−0.0644048	−	0.997924i	$-0.520515\pi$
$409$	−19.4317	−	11.2189i	−0.960835	−	0.554738i	−0.896430	+	0.443186i	$0.853848\pi$
$410$	14.7907	−	2.40393i	0.730462	−	0.118721i
$411$	7.59501	−	10.4901i	0.374634	−	0.517439i
$412$	−10.5744			−0.520963
$413$	6.04555	+	11.5207i	0.297482	+	0.566897i
$414$	12.9545	−	14.4835i	0.636677	−	0.711826i
$415$	−34.9511	−	13.2547i	−1.71568	−	0.650647i
$416$	−3.35071	+	5.80359i	−0.164282	+	0.284544i
$417$	−1.34215	+	12.9763i	−0.0657255	+	0.635453i
$418$	0.522278	+	0.904612i	0.0255455	+	0.0442460i
$419$	−16.6009			−0.811007			−0.405504	−	0.914093i	$-0.632904\pi$
$419$	−16.6009			−0.811007			−0.405504	+	0.914093i	$0.632904\pi$
$420$	−10.2453	+	0.181486i	−0.499922	+	0.00885560i
$421$	−2.95445			−0.143991			−0.0719956	−	0.997405i	$-0.522937\pi$
$421$	−2.95445			−0.143991			−0.0719956	+	0.997405i	$0.522937\pi$
$422$	6.76139	+	11.7111i	0.329139	+	0.570086i
$423$	−22.1018	+	7.26229i	−1.07463	+	0.353105i
$424$	−2.50000	+	4.33013i	−0.121411	+	0.210290i
$425$	−5.00735	−	14.9975i	−0.242892	−	0.727488i
$426$	3.19808	−	1.43023i	0.154948	−	0.0692947i
$427$	0.369657	−	9.15769i	0.0178890	−	0.443172i
$428$	−5.47723			−0.264752
$429$	−2.00653	−	1.45276i	−0.0968759	−	0.0701398i
$430$	0.725563	+	4.46420i	0.0349897	+	0.215283i
$431$	32.0928	+	18.5288i	1.54586	+	0.892501i	0.998451	+	0.0556344i	$0.0177181\pi$
$431$	32.0928	+	18.5288i	1.54586	+	0.892501i	0.547406	+	0.836867i	$0.315615\pi$
$432$	−1.10557	−	5.07718i	−0.0531916	−	0.244276i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	−0.674899	−	0.426844i	−0.0323962	−	0.0204891i
$435$	−7.00000	−	3.51660i	−0.335624	−	0.168608i
$436$	−6.21584	−	10.7661i	−0.297685	−	0.515605i
$437$	−27.4545	−	15.8508i	−1.31332	−	0.758248i
$438$	−20.6547	−	2.13633i	−0.986919	−	0.102078i
$439$	19.6931	−	11.3698i	0.939899	−	0.542651i	0.0499701	−	0.998751i	$-0.484087\pi$
$439$	19.6931	−	11.3698i	0.939899	−	0.542651i	0.889929	+	0.456100i	$0.150754\pi$
$440$	0.369657	−	0.301824i	0.0176227	−	0.0143889i
$441$	−4.92609	−	20.4141i	−0.234576	−	0.972098i
$442$		−	21.1917i		−	1.00799i
$443$	−18.4772	−	32.0035i	−0.877879	−	1.52053i	−0.853663	−	0.520825i	$-0.825624\pi$
$443$	−18.4772	−	32.0035i	−0.877879	−	1.52053i	−0.0242161	−	0.999707i	$-0.507709\pi$
$444$	−1.27144	+	12.2927i	−0.0603401	+	0.583385i
$445$	23.3388	−	3.79324i	1.10637	−	0.179817i
$446$	−3.19808	−	5.53924i	−0.151434	−	0.262291i
$447$	3.87298	−	1.73205i	0.183186	−	0.0819232i
$448$	1.41421	−	2.23607i	0.0668153	−	0.105644i
$449$			3.51660i			0.165959i	0.996551	+	0.0829793i	$0.0264435\pi$
$449$			3.51660i			0.165959i	−0.996551	+	0.0829793i	$0.973556\pi$
$450$	5.94455	−	13.7718i	0.280229	−	0.649209i
$451$	−1.23861	−	0.715113i	−0.0583240	−	0.0336734i
$452$	3.26139	−	5.64889i	0.153403	−	0.265701i
$453$	2.03151	−	2.80588i	0.0954485	−	0.131832i
$454$		−	10.3923i		−	0.487735i
$455$	−23.8154	−	31.6961i	−1.11648	−	1.48593i
$456$	−7.73861	+	3.46081i	−0.362394	+	0.162067i
$457$	32.8322	−	18.9557i	1.53582	−	0.886708i	0.536747	−	0.843743i	$-0.319653\pi$
$457$	32.8322	−	18.9557i	1.53582	−	0.886708i	0.999077	−	0.0429646i	$-0.0136803\pi$
$458$	−6.26139	−	3.61501i	−0.292575	−	0.168918i
$459$	11.0554	+	12.1564i	0.516024	+	0.567411i
$460$	−5.13575	+	13.5424i	−0.239455	+	0.631417i
$461$	−16.2957			−0.758965			−0.379482	−	0.925199i	$-0.623898\pi$
$461$	−16.2957			−0.758965			−0.379482	+	0.925199i	$0.623898\pi$
$462$	0.768409	+	0.605041i	0.0357496	+	0.0281490i
$463$			17.6751i			0.821433i	0.911763	+	0.410716i	$0.134721\pi$
$463$			17.6751i			0.821433i	−0.911763	+	0.410716i	$0.865279\pi$
$464$	1.75166	−	1.01132i	0.0813189	−	0.0469495i
$465$	0.976729	−	0.642235i	0.0452947	−	0.0297829i
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	29.7386	−	17.1696i	1.37614	−	0.794514i	0.384447	−	0.923147i	$-0.374392\pi$
$467$	29.7386	−	17.1696i	1.37614	−	0.794514i	0.991692	+	0.128633i	$0.0410589\pi$
$468$	13.4028	−	14.9848i	0.619546	−	0.692673i
$469$	12.4772	−	6.54749i	0.576145	−	0.302335i
$470$	13.4317	−	10.9669i	0.619557	−	0.505866i
$471$	−8.92900	+	12.3326i	−0.411427	+	0.568256i
$472$	2.45877	−	4.25871i	0.113174	−	0.196023i
$473$	0.215838	−	0.373843i	0.00992426	−	0.0171893i
$474$	0.531010	−	0.733422i	0.0243901	−	0.0336872i
$475$	−23.9772	−	4.89433i	−1.10015	−	0.224567i
$476$	−0.337449	+	8.35979i	−0.0154670	+	0.383170i
$477$	10.0000	−	11.1803i	0.457869	−	0.511913i
$478$		0			0
$479$	5.68906	−	9.85374i	0.259940	−	0.450229i	−0.706286	−	0.707927i	$-0.749631\pi$
$479$	5.68906	−	9.85374i	0.259940	−	0.450229i	0.966226	+	0.257698i	$0.0829639\pi$
$480$	2.12785	+	3.23609i	0.0971224	+	0.147707i
$481$	−41.4089	+	23.9074i	−1.88808	+	1.09009i
$482$			3.98886i			0.181687i
$483$	−29.3777	−	4.24212i	−1.33673	−	0.193023i
$484$	10.9545			0.497930
$485$	−2.77776	+	7.32465i	−0.126132	+	0.332595i
$486$	0.129018	+	15.5879i	0.00585235	+	0.707083i
$487$	31.7232	+	18.3154i	1.43751	+	0.829949i	0.997677	−	0.0681277i	$-0.0217025\pi$
$487$	31.7232	+	18.3154i	1.43751	+	0.829949i	0.439838	+	0.898077i	$0.355036\pi$
$488$	−3.00000	+	1.73205i	−0.135804	+	0.0784063i
$489$	23.2379	−	10.3923i	1.05085	−	0.469956i
$490$	8.89006	+	12.8828i	0.401612	+	0.581986i
$491$			4.04529i			0.182561i	0.995825	+	0.0912807i	$0.0290961\pi$
$491$			4.04529i			0.182561i	−0.995825	+	0.0912807i	$0.970904\pi$
$492$	6.80698	−	9.40169i	0.306882	−	0.423861i
$493$	−3.19808	+	5.53924i	−0.144034	+	0.249475i
$494$	−28.4047	−	16.3995i	−1.27799	−	0.737846i
$495$	−1.27082	+	0.659328i	−0.0571191	+	0.0296346i
$496$			0.301824i			0.0135523i
$497$	−4.52277	−	2.86045i	−0.202874	−	0.128309i
$498$	−26.4317	+	11.8206i	−1.18443	+	0.529694i
$499$	20.9545	+	36.2942i	0.938050	+	1.62475i	0.769103	+	0.639125i	$0.220703\pi$
$499$	20.9545	+	36.2942i	0.938050	+	1.62475i	0.168947	+	0.985625i	$0.445963\pi$
$500$	−0.449747	+	11.1713i	−0.0201133	+	0.499595i
$501$	2.61646	−	25.2967i	0.116895	−	1.13017i
$502$	8.30045	+	14.3768i	0.370467	+	0.641668i
$503$			22.4378i			1.00045i	0.865895	+	0.500225i	$0.166749\pi$
$503$			22.4378i			1.00045i	−0.865895	+	0.500225i	$0.833251\pi$
$504$	−5.52581	+	5.69784i	−0.246139	+	0.253802i
$505$	−16.0000	−	19.5959i	−0.711991	−	0.872007i
$506$	1.19718	−	0.691190i	0.0532210	−	0.0307272i
$507$	54.9746	+	5.68607i	2.44151	+	0.252527i
$508$	−11.8038	−	6.81491i	−0.523708	−	0.302363i
$509$	4.61230	+	7.98873i	0.204437	+	0.354094i	0.949953	−	0.312393i	$-0.101130\pi$
$509$	4.61230	+	7.98873i	0.204437	+	0.354094i	−0.745517	+	0.666487i	$0.767797\pi$
$510$	−10.9441	−	5.49798i	−0.484611	−	0.243454i
$511$	14.7386	+	28.0867i	0.651998	+	1.24248i
$512$	−1.00000			−0.0441942
$513$	24.8494	−	5.41101i	1.09713	−	0.238902i
$514$	20.4772	+	11.8225i	0.903212	+	0.521470i
$515$	−23.3388	+	3.79324i	−1.02843	+	0.167150i
$516$	2.83766	+	2.05451i	0.124921	+	0.0904447i
$517$	−1.65504			−0.0727885
$518$	16.7158	−	8.77172i	0.734452	−	0.385407i
$519$	18.2158	−	8.14637i	0.799587	−	0.357586i
$520$	−5.31350	+	14.0111i	−0.233013	+	0.614428i
$521$	−9.31280	+	16.1302i	−0.408001	+	0.706679i	−0.994666	−	0.103151i	$-0.967107\pi$
$521$	−9.31280	+	16.1302i	−0.408001	+	0.706679i	0.586664	+	0.809830i	$0.300441\pi$
$522$	−5.76471	+	1.89419i	−0.252315	+	0.0829065i
$523$	7.03886	+	12.1917i	0.307788	+	0.533104i	0.977878	−	0.209175i	$-0.0670780\pi$
$523$	7.03886	+	12.1917i	0.307788	+	0.533104i	−0.670090	+	0.742280i	$0.733745\pi$
$524$	−6.02651			−0.263269
$525$	−22.5475	+	4.07576i	−0.984052	+	0.177881i
$526$	−2.00000			−0.0872041
$527$	−0.477226	−	0.826579i	−0.0207883	−	0.0360063i
$528$	0.0380311	−	0.367696i	0.00165509	−	0.0160019i
$529$	−9.47723	+	16.4150i	−0.412053	+	0.713697i
$530$	−3.96447	+	10.4539i	−0.172205	+	0.454086i
$531$	−9.83508	+	10.9960i	−0.426806	+	0.477184i
$532$	10.9441	+	6.92163i	0.474485	+	0.300091i
$533$	44.9089			1.94522
$534$	10.7410	−	14.8353i	0.464807	−	0.641984i
$535$	−12.0888	+	1.96479i	−0.522645	+	0.0849452i
$536$	−4.61230	−	2.66291i	−0.199221	−	0.115020i
$537$	−20.9184	−	15.1452i	−0.902694	−	0.653565i
$538$	28.8948			1.24574
$539$	0.120413	−	1.48909i	0.00518655	−	0.0641397i
$540$	−4.26139	−	10.8093i	−0.183381	−	0.465157i
$541$	−9.73861	−	16.8678i	−0.418696	−	0.725202i	0.577113	−	0.816664i	$-0.304179\pi$
$541$	−9.73861	−	16.8678i	−0.418696	−	0.725202i	−0.995809	+	0.0914622i	$0.970846\pi$
$542$	5.47723	+	3.16228i	0.235267	+	0.135831i
$543$	0.563508	−	5.44816i	0.0241825	−	0.233803i
$544$	2.73861	−	1.58114i	0.117417	−	0.0677908i
$545$	−17.5810	−	21.5323i	−0.753089	−	0.922342i
$546$	−30.3945	−	4.38895i	−1.30076	−	0.187830i
$547$		−	23.2144i		−	0.992575i	−0.868158	−	0.496287i	$-0.834696\pi$
$547$		−	23.2144i		−	0.992575i	0.868158	−	0.496287i	$-0.165304\pi$
$548$	3.73861	+	6.47547i	0.159706	+	0.276618i
$549$	9.87298	−	3.24410i	0.421369	−	0.138455i
$550$	0.707603	−	0.798761i	0.0301723	−	0.0340593i
$551$	4.94975	+	8.57321i	0.210866	+	0.365231i
$552$	4.58009	+	10.2414i	0.194942	+	0.435903i
$553$	−1.38201	−	0.0557857i	−0.0587689	−	0.00237225i
$554$		−	9.79796i		−	0.416275i
$555$	1.60341	+	27.5874i	0.0680611	+	1.17102i
$556$	−6.52277	−	3.76593i	−0.276627	−	0.159711i
$557$	−18.9317	+	32.7906i	−0.802161	+	1.38938i	0.116030	+	0.993246i	$0.462983\pi$
$557$	−18.9317	+	32.7906i	−0.802161	+	1.38938i	−0.918191	+	0.396138i	$0.870350\pi$
$558$	0.185325	−	0.886304i	0.00784543	−	0.0375202i
$559$			13.5546i			0.573298i
$560$	2.31920	−	5.44255i	0.0980041	−	0.229990i
$561$	0.477226	+	1.06711i	0.0201485	+	0.0450534i
$562$	10.0521	−	5.80359i	0.424023	−	0.244810i
$563$	−9.00000	−	5.19615i	−0.379305	−	0.218992i	0.298211	−	0.954500i	$-0.403610\pi$
$563$	−9.00000	−	5.19615i	−0.379305	−	0.218992i	−0.677516	+	0.735508i	$0.736943\pi$
$564$	1.38188	−	13.3604i	0.0581876	−	0.562574i
$565$	5.17186	−	13.6376i	0.217582	−	0.573739i
$566$	24.7165			1.03891
$567$	19.7251	−	13.3387i	0.828375	−	0.560174i
$568$			2.02265i			0.0848683i
$569$	10.4218	−	6.01701i	0.436903	−	0.252246i	−0.265380	−	0.964144i	$-0.585497\pi$
$569$	10.4218	−	6.01701i	0.436903	−	0.252246i	0.702283	+	0.711898i	$0.252164\pi$
$570$	−15.8385	+	10.4144i	−0.663401	+	0.436210i
$571$	3.47723	−	6.02273i	0.145517	−	0.252043i	−0.784048	−	0.620700i	$-0.786849\pi$
$571$	3.47723	−	6.02273i	0.145517	−	0.252043i	0.929566	+	0.368656i	$0.120182\pi$
$572$	1.23861	−	0.715113i	0.0517890	−	0.0299004i
$573$	−2.52319	+	1.12840i	−0.105408	+	0.0471397i
$574$	−17.7158	−	0.715113i	−0.739445	−	0.0298483i
$575$	−6.47723	+	31.7318i	−0.270119	+	1.32331i
$576$	2.93649	+	0.614017i	0.122354	+	0.0255840i
$577$	7.40852	−	12.8319i	0.308421	−	0.534200i	−0.669596	−	0.742725i	$-0.733533\pi$
$577$	7.40852	−	12.8319i	0.308421	−	0.534200i	0.978017	+	0.208525i	$0.0668663\pi$
$578$	3.50000	−	6.06218i	0.145581	−	0.252153i
$579$	10.3095	+	7.46423i	0.428447	+	0.310203i
$580$	3.50333	−	2.86045i	0.145468	−	0.118774i
$581$	37.3800	+	23.6412i	1.55079	+	0.980803i
$582$	2.47723	+	5.53924i	0.102684	+	0.229609i
$583$	0.924143	−	0.533554i	0.0382741	−	0.0220976i
$584$	5.99430	−	10.3824i	0.248046	−	0.429628i
$585$	24.2061	−	37.8809i	1.00080	−	1.56618i
$586$	−3.97723	+	2.29625i	−0.164298	+	0.0948573i
$587$			27.4110i			1.13137i	0.824621	+	0.565686i	$0.191389\pi$
$587$			27.4110i			1.13137i	−0.824621	+	0.565686i	$0.808611\pi$
$588$	11.9202	+	2.21536i	0.491583	+	0.0913599i
$589$	−1.47723			−0.0608680
$590$	3.89908	−	10.2814i	0.160523	−	0.423280i
$591$	−15.5057	−	1.60377i	−0.637821	−	0.0659704i
$592$	−6.17913	−	3.56752i	−0.253961	−	0.146624i
$593$	−31.4317	+	18.1471i	−1.29074	+	0.745212i	−0.978786	−	0.204884i	$-0.934318\pi$
$593$	−31.4317	+	18.1471i	−1.29074	+	0.745212i	−0.311958	+	0.950096i	$0.600985\pi$
$594$	−0.337449	+	1.05638i	−0.0138457	+	0.0433440i
$595$	2.25403	+	18.5720i	0.0924064	+	0.761378i
$596$			2.44949i			0.100335i
$597$	−31.4789	−	22.7912i	−1.28834	−	0.932783i
$598$	−21.7033	+	37.5912i	−0.887513	+	1.53722i
$599$	4.98196	+	2.87633i	0.203557	+	0.117524i	0.598314	−	0.801262i	$-0.295838\pi$
$599$	4.98196	+	2.87633i	0.203557	+	0.117524i	−0.394756	+	0.918786i	$0.629171\pi$
$600$	5.85723	+	6.37909i	0.239120	+	0.260425i
$601$		−	16.7169i		−	0.681895i	−0.940082	−	0.340947i	$-0.889252\pi$
$601$		−	16.7169i		−	0.681895i	0.940082	−	0.340947i	$-0.110748\pi$
$602$	0.215838	−	5.34706i	0.00879691	−	0.217930i
$603$	11.9089	+	10.6516i	0.484968	+	0.433769i
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$	24.1776	−	3.92957i	0.982961	−	0.159760i
$606$	−19.4919	−	2.01607i	−0.791806	−	0.0818972i
$607$	−13.2180	−	22.8942i	−0.536502	−	0.929248i	−0.999089	−	0.0426745i	$-0.986412\pi$
$607$	−13.2180	−	22.8942i	−0.536502	−	0.929248i	0.462587	−	0.886574i	$-0.346921\pi$
$608$		−	4.89433i		−	0.198491i
$609$	7.28238	+	5.73411i	0.295097	+	0.232358i
$610$	−6.00000	+	4.89898i	−0.242933	+	0.198354i
$611$	45.0056	−	25.9840i	1.82073	−	1.05120i
$612$	−9.01276	+	2.96145i	−0.364319	+	0.119709i
$613$	−22.0407	−	12.7252i	−0.890216	−	0.513967i	−0.0162031	−	0.999869i	$-0.505158\pi$
$613$	−22.0407	−	12.7252i	−0.890216	−	0.513967i	−0.874013	+	0.485902i	$0.838491\pi$
$614$	−1.75166	−	3.03397i	−0.0706914	−	0.122441i
$615$	11.6512	−	23.1923i	0.469820	−	0.935205i
$616$	−0.500000	+	0.262377i	−0.0201456	+	0.0105715i
$617$	−25.4772			−1.02567			−0.512837	−	0.858486i	$-0.671406\pi$
$617$	−25.4772			−1.02567			−0.512837	+	0.858486i	$0.671406\pi$
$618$	−10.7410	+	14.8353i	−0.432065	+	0.596762i
$619$	−23.1475	−	13.3642i	−0.930377	−	0.537154i	−0.0434463	−	0.999056i	$-0.513834\pi$
$619$	−23.1475	−	13.3642i	−0.930377	−	0.537154i	−0.886931	+	0.461902i	$0.847167\pi$
$620$	0.108270	+	0.666158i	0.00434823	+	0.0267535i
$621$	−7.16101	−	32.8860i	−0.287361	−	1.31967i
$622$	28.8948			1.15857
$623$	−27.9545	−	1.12840i	−1.11997	−	0.0452085i
$624$	4.73861	+	10.5959i	0.189696	+	0.424174i
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	11.6190	−	20.1246i	0.464387	−	0.804341i
$627$	1.79962	+	0.186137i	0.0718701	+	0.00743359i
$628$	−4.39526	−	7.61282i	−0.175390	−	0.303784i
$629$	22.5630			0.899646
$630$	−10.1521	+	14.5580i	−0.404470	+	0.580003i
$631$	−7.47723			−0.297664			−0.148832	−	0.988863i	$-0.547551\pi$
$631$	−7.47723			−0.297664			−0.148832	+	0.988863i	$0.547551\pi$
$632$	0.261387	+	0.452736i	0.0103974	+	0.0180089i
$633$	23.2978	+	2.40972i	0.926006	+	0.0957777i
$634$	−16.9545	+	29.3660i	−0.673347	+	1.16627i
$635$	−28.4968	−	10.8070i	−1.13086	−	0.428863i
$636$	3.53553	+	7.90569i	0.140193	+	0.313481i
$637$	20.1042	+	42.3834i	0.796559	+	1.67929i
$638$	−0.431677			−0.0170902
$639$	1.24194	−	5.93948i	0.0491303	−	0.234962i
$640$	−2.20711	+	0.358719i	−0.0872436	+	0.0141796i
$641$	5.43982	+	3.14068i	0.214860	+	0.124049i	0.603568	−	0.797312i	$-0.293745\pi$
$641$	5.43982	+	3.14068i	0.214860	+	0.124049i	−0.388708	+	0.921361i	$0.627079\pi$
$642$	−5.56351	+	7.68423i	−0.219574	+	0.303272i
$643$	20.4095			0.804871			0.402436	−	0.915448i	$-0.368164\pi$
$643$	20.4095			0.804871			0.402436	+	0.915448i	$0.368164\pi$
$644$	9.16018	−	14.4835i	0.360962	−	0.570731i
$645$	7.00000	+	3.51660i	0.275625	+	0.138466i
$646$	7.73861	+	13.4037i	0.304472	+	0.527360i
$647$	20.6703	+	11.9340i	0.812633	+	0.469174i	0.847869	−	0.530205i	$-0.177885\pi$
$647$	20.6703	+	11.9340i	0.812633	+	0.469174i	−0.0352364	+	0.999379i	$0.511218\pi$
$648$	−8.24597	−	3.60611i	−0.323932	−	0.141661i
$649$	−0.908902	+	0.524755i	−0.0356775	+	0.0205984i
$650$	−6.70141	+	32.8301i	−0.262851	+	1.28770i
$651$	−1.28437	+	0.513276i	−0.0503383	+	0.0201169i
$652$			14.6969i			0.575577i
$653$	−12.9317	−	22.3983i	−0.506056	−	0.876514i	−0.999975	−	0.00700659i	$-0.997770\pi$
$653$	−12.9317	−	22.3983i	−0.506056	−	0.876514i	0.493920	−	0.869507i	$-0.335564\pi$
$654$	−21.4180	−	2.21529i	−0.837511	−	0.0866246i
$655$	−13.3012	+	2.16183i	−0.519719	+	0.0844696i
$656$	3.35071	+	5.80359i	0.130823	+	0.226592i
$657$	−23.9772	+	26.8073i	−0.935440	+	1.04585i
$658$	−18.1677	+	9.53361i	−0.708252	+	0.371659i
$659$			34.2929i			1.33586i	0.744224	+	0.667930i	$0.232819\pi$
$659$			34.2929i			1.33586i	−0.744224	+	0.667930i	$0.767181\pi$
$660$	−0.0479609	−	0.825186i	−0.00186688	−	0.0321203i
$661$	11.4772	+	6.62638i	0.446412	+	0.257736i	0.706314	−	0.707899i	$-0.250357\pi$
$661$	11.4772	+	6.62638i	0.446412	+	0.257736i	−0.259901	+	0.965635i	$0.583690\pi$
$662$	−5.71584	+	9.90012i	−0.222152	+	0.384779i
$663$	−29.7308	−	21.5256i	−1.15465	−	0.835983i
$664$		−	16.7169i		−	0.648740i
$665$	26.6376	+	11.3509i	1.03296	+	0.440170i
$666$	15.9545	+	14.2701i	0.618222	+	0.552955i
$667$	11.3459	−	6.55057i	0.439316	−	0.253639i
$668$	12.7158	+	7.34149i	0.491991	+	0.284051i
$669$	−11.0197	−	1.13978i	−0.426046	−	0.0440664i
$670$	−11.1351	−	4.22281i	−0.430185	−	0.163141i
$671$	0.739315			0.0285409
$672$	−1.70058	−	4.25535i	−0.0656014	−	0.164154i
$673$			48.4514i			1.86766i	0.357713	+	0.933832i	$0.383557\pi$
$673$			48.4514i			1.86766i	−0.357713	+	0.933832i	$0.616443\pi$
$674$	−14.8492	+	8.57321i	−0.571971	+	0.330228i
$675$	−13.2828	−	22.3286i	−0.511257	−	0.859428i
$676$	−15.9545	+	27.6339i	−0.613633	+	1.06284i
$677$	28.5000	−	16.4545i	1.09534	−	0.632397i	0.160350	−	0.987060i	$-0.448738\pi$
$677$	28.5000	−	16.4545i	1.09534	−	0.632397i	0.934994	+	0.354663i	$0.115404\pi$
$678$	−4.61230	−	10.3134i	−0.177134	−	0.396084i
$679$	4.95445	−	7.83368i	0.190134	−	0.300629i
$680$	5.47723	−	4.47214i	0.210042	−	0.171499i
$681$	−14.5798	−	10.5560i	−0.558699	−	0.404507i
$682$	0.0322079	−	0.0557857i	0.00123330	−	0.00213615i
$683$	1.47723	−	2.55863i	0.0565245	−	0.0979032i	−0.836379	−	0.548152i	$-0.815331\pi$
$683$	1.47723	−	2.55863i	0.0565245	−	0.0979032i	0.892903	+	0.450249i	$0.148665\pi$
$684$	−3.00520	+	14.3722i	−0.114907	+	0.549533i
$685$	10.5744	+	12.9509i	0.404027	+	0.494830i
$686$	−7.25590	−	17.0397i	−0.277031	−	0.650579i
$687$	−11.4317	+	5.11240i	−0.436146	+	0.195050i
$688$	−1.75166	+	1.01132i	−0.0667815	+	0.0385563i
$689$	−16.7535	+	29.0180i	−0.638259	+	1.10550i
$690$	13.7825	+	20.9609i	0.524692	+	0.797967i
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$			11.5207i			0.437952i
$693$	1.62935	−	0.463461i	0.0618939	−	0.0176054i
$694$	−6.52277			−0.247601
$695$	−15.7474	−	5.97195i	−0.597332	−	0.226529i
$696$	0.360429	−	3.48474i	0.0136620	−	0.132089i
$697$	−18.3526	−	10.5959i	−0.695153	−	0.401347i
$698$	−28.1703	+	16.2641i	−1.06626	+	0.615606i
$699$	−2.82843	−	6.32456i	−0.106981	−	0.239217i
$700$	3.16637	−	12.8442i	0.119678	−	0.485466i
$701$		−	7.03320i		−	0.265640i	−0.991140	−	0.132820i	$-0.957597\pi$
$701$		−	7.03320i		−	0.265640i	0.991140	−	0.132820i	$-0.0424033\pi$
$702$	−7.40886	−	34.0242i	−0.279629	−	1.28416i
$703$	17.4606	−	30.2427i	0.658540	−	1.14063i
$704$	0.184829	+	0.106711i	0.00696599	+	0.00402182i
$705$	−1.74268	−	29.9835i	−0.0656332	−	1.12925i
$706$		−	13.2528i		−	0.498774i
$707$	13.9089	+	26.5055i	0.523098	+	0.996843i
$708$	−3.47723	−	7.77531i	−0.130682	−	0.292214i
$709$	−5.21584	−	9.03410i	−0.195885	−	0.339283i	0.751305	−	0.659955i	$-0.229425\pi$
$709$	−5.21584	−	9.03410i	−0.195885	−	0.339283i	−0.947190	+	0.320672i	$0.896091\pi$
$710$	0.725563	+	4.46420i	0.0272299	+	0.167538i
$711$	−0.489574	−	1.48995i	−0.0183605	−	0.0558775i
$712$	5.28720	+	9.15769i	0.198146	+	0.343199i
$713$			1.95498i			0.0732146i
$714$	11.3855	+	8.96491i	0.426093	+	0.335503i
$715$	2.47723	−	2.02265i	0.0926430	−	0.0756427i
$716$	12.9128	−	7.45518i	0.482572	−	0.278613i
$717$		0			0
$718$	5.62465	+	3.24739i	0.209910	+	0.121192i
$719$	−23.6398	−	40.9453i	−0.881614	−	1.52700i	−0.849545	−	0.527515i	$-0.823124\pi$
$719$	−23.6398	−	40.9453i	−0.881614	−	1.52700i	−0.0320690	−	0.999486i	$-0.510210\pi$
$720$	6.70141	+	0.301824i	0.249747	+	0.0112483i
$721$	27.9545	+	1.12840i	1.04108	+	0.0420239i
$722$	4.95445			0.184386
$723$	5.59613	+	4.05169i	0.208122	+	0.150684i
$724$	2.73861	+	1.58114i	0.101780	+	0.0587626i
$725$	6.70611	−	7.57004i	0.249059	−	0.281144i
$726$	11.1270	−	15.3685i	0.412962	−	0.570377i
$727$	23.6076			0.875556			0.437778	−	0.899083i	$-0.355766\pi$
$727$	23.6076			0.875556			0.437778	+	0.899083i	$0.355766\pi$
$728$	9.47723	−	14.9848i	0.351249	−	0.555374i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	9.50569	−	25.0654i	0.351821	−	0.927713i
$731$	3.19808	−	5.53924i	0.118285	−	0.204876i
$732$	−0.617292	+	5.96816i	−0.0228158	+	0.220590i
$733$	−18.1677	−	31.4674i	−0.671041	−	1.16228i	−0.977609	−	0.210428i	$-0.932514\pi$
$733$	−18.1677	−	31.4674i	−0.671041	−	1.16228i	0.306569	−	0.951849i	$-0.400819\pi$
$734$	8.11562			0.299553
$735$	27.1039	+	0.613514i	0.999744	+	0.0226298i
$736$	−6.47723			−0.238754
$737$	0.568323	+	0.984365i	0.0209345	+	0.0362595i
$738$	−6.27582	−	19.0996i	−0.231016	−	0.703066i
$739$	2.23861	−	3.87739i	0.0823487	−	0.142632i	−0.821910	−	0.569618i	$-0.807091\pi$
$739$	2.23861	−	3.87739i	0.0823487	−	0.142632i	0.904258	+	0.426986i	$0.140425\pi$
$740$	−14.9177	−	5.65733i	−0.548387	−	0.207968i
$741$	−51.8596	+	23.1923i	−1.90511	+	0.851991i
$742$	7.07107	−	11.1803i	0.259587	−	0.410443i
$743$	19.4317			0.712879			0.356440	−	0.934318i	$-0.383991\pi$
$743$	19.4317			0.712879			0.356440	+	0.934318i	$0.383991\pi$
$744$	0.423441	+	0.306579i	0.0155241	+	0.0112397i
$745$	0.878680	+	5.40629i	0.0321923	+	0.198071i
$746$	3.13367	+	1.80922i	0.114732	+	0.0662404i
$747$	−10.2644	+	49.0889i	−0.375556	+	1.79607i
$748$	−0.674899			−0.0246767
$749$	14.4796	+	0.584480i	0.529073	+	0.0213564i
$750$	15.2158	+	11.9782i	0.555604	+	0.437384i
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	6.71584	+	3.87739i	0.244901	+	0.141394i
$753$	28.6010	+	2.95823i	1.04228	+	0.107804i
$754$	11.7386	−	6.77729i	0.427495	−	0.246814i
$755$	2.82843	+	3.46410i	0.102937	+	0.126072i
$756$	2.38089	+	13.5400i	0.0865920	+	0.492445i
$757$		−	30.2476i		−	1.09937i	−0.835373	−	0.549683i	$-0.814748\pi$
$757$		−	30.2476i		−	1.09937i	0.835373	−	0.549683i	$-0.185252\pi$
$758$	−4.76139	−	8.24696i	−0.172941	−	0.299543i
$759$	0.246336	−	2.38165i	0.00894143	−	0.0864484i
$760$	−1.75569	−	10.8023i	−0.0636856	−	0.391841i
$761$	4.76492	+	8.25308i	0.172728	+	0.299174i	0.939373	−	0.342898i	$-0.111408\pi$
$761$	4.76492	+	8.25308i	0.172728	+	0.299174i	−0.766645	+	0.642072i	$0.778075\pi$
$762$	−21.5507	+	9.63774i	−0.780698	+	0.349139i
$763$	15.2833	+	29.1247i	0.553293	+	1.05438i
$764$		−	1.59580i		−	0.0577341i
$765$	−18.8298	+	9.76928i	−0.680793	+	0.353209i
$766$	0.715838	+	0.413289i	0.0258643	+	0.0149328i
$767$	16.4772	−	28.5394i	0.594958	−	1.03050i
$768$	−1.01575	+	1.40294i	−0.0366528	+	0.0506243i
$769$		−	28.8412i		−	1.04004i	−0.854154	−	0.520020i	$-0.825924\pi$
$769$		−	28.8412i		−	1.04004i	0.854154	−	0.520020i	$-0.174076\pi$
$770$	−1.00943	+	0.758455i	−0.0363775	+	0.0273328i
$771$	37.3861	−	16.7196i	1.34643	−	0.602141i
$772$	−6.36396	+	3.67423i	−0.229044	+	0.132239i
$773$	24.9772	+	14.4206i	0.898368	+	0.518673i	0.876670	−	0.481091i	$-0.159759\pi$
$773$	24.9772	+	14.4206i	0.898368	+	0.518673i	0.0216979	+	0.999765i	$0.493093\pi$
$774$	5.76471	−	1.89419i	0.207208	−	0.0680853i
$775$	0.477927	+	1.43144i	0.0171677	+	0.0514189i
$776$	−3.50333			−0.125762
$777$	4.67295	−	32.3612i	0.167641	−	1.16095i
$778$		−	7.34847i		−	0.263455i
$779$	−28.4047	+	16.3995i	−1.01770	+	0.587571i
$780$	14.2596	+	21.6864i	0.510574	+	0.776496i
$781$	0.215838	−	0.373843i	0.00772330	−	0.0133772i
$782$	17.7386	−	10.2414i	0.634331	−	0.366231i
$783$	−3.19808	+	10.0116i	−0.114290	+	0.357785i
$784$	−3.97723	+	5.76035i	−0.142044	+	0.205727i
$785$	−12.4317	−	15.2256i	−0.443706	−	0.543426i
$786$	−6.12145	+	8.45485i	−0.218345	+	0.301574i
$787$	−17.3402	+	30.0341i	−0.618112	+	1.07060i	0.371718	+	0.928346i	$0.378769\pi$
$787$	−17.3402	+	30.0341i	−0.618112	+	1.07060i	−0.989830	+	0.142256i	$0.954564\pi$
$788$	4.50000	−	7.79423i	0.160306	−	0.277658i
$789$	−2.03151	+	2.80588i	−0.0723235	+	0.0998921i
$790$	0.739315	+	0.905472i	0.0263036	+	0.0322152i
$791$	−9.22460	+	14.5854i	−0.327989	+	0.518596i
$792$	−0.477226	−	0.426844i	−0.0169575	−	0.0151672i
$793$	−20.1042	+	11.6072i	−0.713922	+	0.412183i
$794$	−15.1867	+	26.3041i	−0.538956	+	0.933498i
$795$	10.6392	+	16.1804i	0.377335	+	0.573861i
$796$	19.4317	−	11.2189i	0.688738	−	0.397643i
$797$		−	28.9201i		−	1.02440i	−0.858865	−	0.512201i	$-0.828830\pi$
$797$		−	28.9201i		−	1.02440i	0.858865	−	0.512201i	$-0.171170\pi$
$798$	20.8271	−	8.32321i	0.737271	−	0.294638i
$799$	−24.5228			−0.867553
$800$	−4.74264	+	1.58346i	−0.167678	+	0.0559839i
$801$	−9.90283	−	30.1379i	−0.349899	−	1.06487i
$802$	−26.2834	−	15.1747i	−0.928098	−	0.535838i
$803$	−2.21584	+	1.27931i	−0.0781952	+	0.0451460i
$804$	−8.42087	+	3.76593i	−0.296981	+	0.132814i
$805$	15.0220	−	35.2526i	0.529455	−	1.24249i
$806$			2.02265i			0.0712447i
$807$	29.3499	−	40.5377i	1.03317	−	1.42699i
$808$	5.65685	−	9.79796i	0.199007	−	0.344691i
$809$	−34.7686	−	20.0737i	−1.22240	−	0.705753i	−0.256971	−	0.966419i	$-0.582725\pi$
$809$	−34.7686	−	20.0737i	−1.22240	−	0.705753i	−0.965429	+	0.260666i	$0.916058\pi$
$810$	−19.4933	−	5.00108i	−0.684925	−	0.175720i
$811$		−	6.70527i		−	0.235454i	−0.993046	−	0.117727i	$-0.962439\pi$
$811$		−	6.70527i		−	0.235454i	0.993046	−	0.117727i	$-0.0375608\pi$
$812$	−4.73861	+	2.48661i	−0.166293	+	0.0872629i
$813$	10.0000	−	4.47214i	0.350715	−	0.156845i
$814$	0.761387	+	1.31876i	0.0266866	+	0.0462226i
$815$	5.27208	+	32.4377i	0.184673	+	1.13624i
$816$	0.563508	−	5.44816i	0.0197267	−	0.190724i
$817$	−4.94975	−	8.57321i	−0.173170	−	0.299939i
$818$		−	22.4378i		−	0.784518i
$819$	−37.0307	+	38.1836i	−1.29396	+	1.33424i
$820$	9.47723	+	11.6072i	0.330959	+	0.405340i
$821$	44.0814	−	25.4504i	1.53845	−	0.888226i	0.539523	−	0.841971i	$-0.318604\pi$
$821$	44.0814	−	25.4504i	1.53845	−	0.888226i	0.998930	−	0.0462557i	$-0.0147289\pi$
$822$	12.8822	+	1.33242i	0.449319	+	0.0464734i
$823$	28.2199	+	16.2927i	0.983682	+	0.567929i	0.903380	−	0.428841i	$-0.141078\pi$
$823$	28.2199	+	16.2927i	0.983682	+	0.567929i	0.0803025	+	0.996771i	$0.474411\pi$
$824$	−5.28720	−	9.15769i	−0.184188	−	0.319023i
$825$	−0.401865	−	1.80407i	−0.0139912	−	0.0628097i
$826$	−6.95445	+	10.9960i	−0.241976	+	0.382598i
$827$	−39.9089			−1.38777			−0.693884	−	0.720087i	$-0.744102\pi$
$827$	−39.9089			−1.38777			−0.693884	+	0.720087i	$0.744102\pi$
$828$	19.0203	+	3.97713i	0.661002	+	0.138215i
$829$	−16.3069	−	9.41481i	−0.566363	−	0.326990i	0.189332	−	0.981913i	$-0.439368\pi$
$829$	−16.3069	−	9.41481i	−0.566363	−	0.326990i	−0.755696	+	0.654923i	$0.772701\pi$
$830$	−5.99666	−	36.8959i	−0.208147	−	1.28068i
$831$	−13.7460	−	9.95231i	−0.476842	−	0.345242i
$832$	−6.70141			−0.232330
$833$	1.78416	−	22.0639i	0.0618175	−	0.764470i
$834$	−11.9089	+	5.32582i	−0.412372	+	0.184418i
$835$	30.6987	+	11.6420i	1.06237	+	0.402889i
$836$	−0.522278	+	0.904612i	−0.0180634	+	0.0312867i
$837$	−1.05519	−	1.16027i	−0.0364726	−	0.0401046i
$838$	−8.30045	−	14.3768i	−0.286734	−	0.496639i
$839$	−37.3156			−1.28828			−0.644139	−	0.764908i	$-0.722784\pi$
$839$	−37.3156			−1.28828			−0.644139	+	0.764908i	$0.722784\pi$
$840$	−5.27984	−	8.78198i	−0.182172	−	0.303007i
$841$	24.9089			0.858928
$842$	−1.47723	−	2.55863i	−0.0509086	−	0.0881762i
$843$	2.06837	−	19.9975i	0.0712383	−	0.688752i
$844$	−6.76139	+	11.7111i	−0.232737	+	0.403112i
$845$	−25.3004	+	66.7142i	−0.870359	+	2.29504i
$846$	−17.3402	−	15.5096i	−0.596169	−	0.533230i
$847$	−28.9592	−	1.16896i	−0.995049	−	0.0401659i
$848$	−5.00000			−0.171701
$849$	25.1059	−	34.6759i	0.861632	−	1.19007i
$850$	10.4846	−	11.8353i	0.359618	−	0.405946i
$851$	−40.0236	−	23.1077i	−1.37199	−	0.792120i
$852$	2.83766	+	2.05451i	0.0972165	+	0.0703863i
$853$	−53.9165			−1.84607			−0.923033	−	0.384720i	$-0.874298\pi$
$853$	−53.9165			−1.84607			−0.923033	+	0.384720i	$0.874298\pi$
$854$	8.11562	−	4.25871i	0.277711	−	0.145730i
$855$	−1.47723	+	32.7989i	−0.0505200	+	1.12170i
$856$	−2.73861	−	4.74342i	−0.0936039	−	0.162127i
$857$	−34.9545	−	20.1810i	−1.19402	−	0.689369i	−0.234805	−	0.972042i	$-0.575445\pi$
$857$	−34.9545	−	20.1810i	−1.19402	−	0.689369i	−0.959216	+	0.282674i	$0.908779\pi$
$858$	0.254862	−	2.46408i	0.00870085	−	0.0841223i
$859$	−15.5228	+	8.96208i	−0.529630	+	0.305782i	−0.740866	−	0.671653i	$-0.765585\pi$
$859$	−15.5228	+	8.96208i	−0.529630	+	0.305782i	0.211236	+	0.977435i	$0.432251\pi$
$860$	−3.50333	+	2.86045i	−0.119462	+	0.0975407i
$861$	−18.9982	+	24.1279i	−0.647456	+	0.822277i
$862$			37.0576i			1.26219i
$863$	−7.76139	−	13.4431i	−0.264201	−	0.457609i	0.703153	−	0.711038i	$-0.251775\pi$
$863$	−7.76139	−	13.4431i	−0.264201	−	0.457609i	−0.967354	+	0.253429i	$0.918441\pi$
$864$	3.84418	−	3.49604i	0.130782	−	0.118938i
$865$	4.13270	+	25.4274i	0.140516	+	0.864559i
$866$		0			0
$867$	−4.94975	−	11.0680i	−0.168102	−	0.375888i
$868$	0.0322079	−	0.797901i	0.00109321	−	0.0270825i
$869$		−	0.111571i		−	0.00378480i
$870$	−0.454536	−	7.82048i	−0.0154102	−	0.265139i
$871$	−30.9089	−	17.8453i	−1.04731	−	0.604664i
$872$	6.21584	−	10.7661i	0.210495	−	0.364588i
$873$	10.2875	+	2.15110i	0.348179	+	0.0728037i
$874$		−	31.7017i		−	1.07232i
$875$	2.38105	−	29.4844i	0.0804942	−	0.996755i
$876$	−8.47723	−	18.9557i	−0.286419	−	0.640452i
$877$	−36.6169	+	21.1408i	−1.23647	+	0.713874i	−0.968370	−	0.249518i	$-0.919728\pi$
$877$	−36.6169	+	21.1408i	−1.23647	+	0.713874i	−0.268096	+	0.963392i	$0.586394\pi$
$878$	19.6931	+	11.3698i	0.664609	+	0.383712i
$879$	−0.818370	+	7.91224i	−0.0276029	+	0.266873i
$880$	0.446216	+	0.169221i	0.0150419	+	0.00570443i
$881$	26.5004			0.892821			0.446411	−	0.894828i	$-0.352702\pi$
$881$	26.5004			0.892821			0.446411	+	0.894828i	$0.352702\pi$
$882$	15.2160	−	14.4731i	0.512351	−	0.487336i
$883$		−	29.2823i		−	0.985428i	−0.870191	−	0.492714i	$-0.836005\pi$
$883$		−	29.2823i		−	0.985428i	0.870191	−	0.492714i	$-0.163995\pi$
$884$	18.3526	−	10.5959i	0.617264	−	0.356377i
$885$	−10.4638	−	15.9136i	−0.351736	−	0.534930i
$886$	18.4772	−	32.0035i	0.620755	−	1.07518i
$887$	−3.00000	+	1.73205i	−0.100730	+	0.0581566i	−0.549519	−	0.835481i	$-0.685189\pi$
$887$	−3.00000	+	1.73205i	−0.100730	+	0.0581566i	0.448789	+	0.893638i	$0.351856\pi$
$888$	−11.2815	+	5.04524i	−0.378582	+	0.169307i
$889$	30.4772	+	19.2755i	1.02217	+	0.646479i
$890$	14.9545	+	18.3154i	0.501274	+	0.613933i
$891$	1.13928	+	1.54645i	0.0381673	+	0.0518079i
$892$	3.19808	−	5.53924i	0.107080	−	0.185468i
$893$	−18.9772	+	32.8695i	−0.635049	+	1.09994i
$894$	3.43649	+	2.48808i	0.114933	+	0.0832137i
$895$	25.8255	−	21.0864i	0.863251	−	0.704842i
$896$	2.64360	+	0.106711i	0.0883164	+	0.00356496i
$897$	30.6931	+	68.6318i	1.02481	+	2.29155i
$898$	−3.04546	+	1.75830i	−0.101628	+	0.0586752i
$899$	0.305242	−	0.528694i	0.0101804	−	0.0176329i
$900$	14.8990	−	1.73777i	0.496633	−	0.0579256i
$901$	13.6931	−	7.90569i	0.456182	−	0.263377i
$902$		−	1.43023i		−	0.0476213i
$903$	−7.28238	−	5.73411i	−0.242342	−	0.190819i
$904$	6.52277			0.216944
$905$	6.61160	+	2.50735i	0.219777	+	0.0833471i
$906$	3.44572	+	0.356394i	0.114476	+	0.0118404i
$907$	−8.48528	−	4.89898i	−0.281749	−	0.162668i	0.352466	−	0.935825i	$-0.385343\pi$
$907$	−8.48528	−	4.89898i	−0.281749	−	0.162668i	−0.634215	+	0.773157i	$0.718677\pi$
$908$	9.00000	−	5.19615i	0.298675	−	0.172440i
$909$	−22.6274	+	25.2982i	−0.750504	+	0.839089i
$910$	15.5419	−	36.4727i	0.515209	−	1.20906i
$911$			15.1238i			0.501073i	0.968107	+	0.250537i	$0.0806071\pi$
$911$			15.1238i			0.501073i	−0.968107	+	0.250537i	$0.919393\pi$
$912$	−6.86646	−	4.97143i	−0.227371	−	0.164620i
$913$	−1.78387	+	3.08976i	−0.0590375	+	0.102256i
$914$	32.8322	+	18.9557i	1.08599	+	0.626997i
$915$	0.778465	+	13.3938i	0.0257353	+	0.442786i
$916$		−	7.23003i		−	0.238887i
$917$	15.9317	+	0.643094i	0.526110	+	0.0212368i
$918$	−5.00000	+	15.6525i	−0.165025	+	0.516609i
$919$	16.2158	+	28.0867i	0.534911	+	0.926493i	0.999168	+	0.0407925i	$0.0129883\pi$
$919$	16.2158	+	28.0867i	0.534911	+	0.926493i	−0.464256	+	0.885701i	$0.653678\pi$
$920$	−14.2959	+	2.32351i	−0.471323	+	0.0766038i
$921$	−6.03574	−	0.624282i	−0.198884	−	0.0205708i
$922$	−8.14783	−	14.1125i	−0.268335	−	0.464769i
$923$			13.5546i			0.446155i
$924$	−0.139776	+	0.967982i	−0.00459830	+	0.0318443i
$925$	−34.9545	−	7.13505i	−1.14930	−	0.234599i
$926$	−15.3071	+	8.83756i	−0.503023	+	0.290420i
$927$	9.90283	+	30.1379i	0.325252	+	0.989859i
$928$	1.75166	+	1.01132i	0.0575012	+	0.0331983i
$929$	−11.8360	−	20.5005i	−0.388326	−	0.672601i	0.603898	−	0.797061i	$-0.293613\pi$
$929$	−11.8360	−	20.5005i	−0.388326	−	0.672601i	−0.992225	+	0.124461i	$0.960280\pi$
$930$	1.04456	+	0.524755i	0.0342523	+	0.0172074i
$931$	−28.1931	−	19.4658i	−0.923990	−	0.637967i
$932$	4.00000			0.131024
$933$	29.3499	−	40.5377i	0.960874	−	1.32714i
$934$	29.7386	+	17.1696i	0.973077	+	0.561806i
$935$	−1.48957	+	0.242099i	−0.0487143	+	0.00791750i
$936$	19.6786	+	4.11478i	0.643216	+	0.134496i
$937$	−22.6918			−0.741310			−0.370655	−	0.928771i	$-0.620867\pi$
$937$	−22.6918			−0.741310			−0.370655	+	0.928771i	$0.620867\pi$
$938$	11.9089	+	7.53185i	0.388839	+	0.245924i
$939$	−16.4317	−	36.7423i	−0.536228	−	1.19904i
$940$	16.2135	+	6.14871i	0.528825	+	0.200549i
$941$	2.49098	−	4.31450i	0.0812036	−	0.140649i	−0.822564	−	0.568673i	$-0.807457\pi$
$941$	2.49098	−	4.31450i	0.0812036	−	0.140649i	0.903767	+	0.428024i	$0.140790\pi$
$942$	−15.1448	−	1.56644i	−0.493445	−	0.0510375i
$943$	21.7033	+	37.5912i	0.706756	+	1.22414i
$944$	4.91754			0.160052
$945$	10.1119	+	29.0301i	0.328941	+	0.944350i
$946$	0.431677			0.0140350
$947$	−16.4317	−	28.4605i	−0.533958	−	0.924842i	−0.999213	−	0.0396654i	$-0.987371\pi$
$947$	−16.4317	−	28.4605i	−0.533958	−	0.924842i	0.465255	−	0.885177i	$-0.345963\pi$
$948$	0.900667	+	0.0931568i	0.0292523	+	0.00302559i
$949$	40.1703	−	69.5770i	1.30398	−	2.25856i
$950$	−7.74999	−	23.2120i	−0.251443	−	0.753098i
$951$	23.9772	+	53.6147i	0.777514	+	1.73858i
$952$	−7.40852	+	3.88766i	−0.240111	+	0.126000i
$953$	−25.0455			−0.811305			−0.405652	−	0.914027i	$-0.632956\pi$
$953$	−25.0455			−0.811305			−0.405652	+	0.914027i	$0.632956\pi$
$954$	14.6825	+	3.07008i	0.475362	+	0.0993976i
$955$	−0.572445	−	3.52211i	−0.0185239	−	0.113973i
$956$		0			0
$957$	−0.438477	+	0.605617i	−0.0141739	+	0.0195768i
$958$	11.3781			0.367611
$959$	−9.19239	−	17.5175i	−0.296838	−	0.565669i
$960$	−1.73861	+	3.46081i	−0.0561135	+	0.111697i
$961$	−15.4545	−	26.7679i	−0.498531	−	0.863480i
$962$	−41.4089	−	23.9074i	−1.33508	−	0.770807i
$963$	5.12938	+	15.6106i	0.165292	+	0.503043i
$964$	−3.45445	+	1.99443i	−0.111260	+	0.0642362i
$965$	−12.7279	+	10.3923i	−0.409726	+	0.334540i
$966$	−11.0151	−	27.5629i	−0.354403	−	0.886821i
$967$		−	46.4287i		−	1.49305i	−0.665359	−	0.746524i	$-0.731721\pi$
$967$		−	46.4287i		−	1.49305i	0.665359	−	0.746524i	$-0.268279\pi$
$968$	5.47723	+	9.48683i	0.176045	+	0.304918i
$969$	26.6651	+	2.75799i	0.856606	+	0.0885996i
$970$	−7.73221	+	1.25671i	−0.248266	+	0.0403506i
$971$	−0.490070	−	0.848827i	−0.0157271	−	0.0272401i	0.858055	−	0.513558i	$-0.171673\pi$
$971$	−0.490070	−	0.848827i	−0.0157271	−	0.0272401i	−0.873782	+	0.486318i	$0.838340\pi$
$972$	−13.4350	+	7.90569i	−0.430929	+	0.253575i
$973$	16.8417	+	10.6516i	0.539921	+	0.341476i
$974$			36.6308i			1.17373i
$975$	39.2517	+	42.7489i	1.25706	+	1.36906i
$976$	−3.00000	−	1.73205i	−0.0960277	−	0.0554416i
$977$	−19.9545	+	34.5621i	−0.638399	+	1.10574i	0.347385	+	0.937723i	$0.387070\pi$
$977$	−19.9545	+	34.5621i	−0.638399	+	1.10574i	−0.985784	+	0.168018i	$0.946263\pi$
$978$	20.6190	+	14.9285i	0.659321	+	0.477359i
$979$		−	2.25681i		−	0.0721278i
$980$	−6.71181	+	14.1404i	−0.214401	+	0.451699i
$981$	−24.8634	+	27.7981i	−0.793826	+	0.887524i
$982$	−3.50333	+	2.02265i	−0.111796	+	0.0645452i
$983$	29.2842	+	16.9072i	0.934020	+	0.539257i	0.888081	−	0.459688i	$-0.152039\pi$
$983$	29.2842	+	16.9072i	0.934020	+	0.539257i	0.0459391	+	0.998944i	$0.485372\pi$
$984$	11.5456	+	1.19417i	0.368060	+	0.0380688i
$985$	7.13604	−	18.8169i	0.227373	−	0.599557i
$986$	−6.39617			−0.203696
$987$	−5.07883	+	35.1721i	−0.161661	+	1.11954i
$988$		−	32.7989i		−	1.04347i
$989$	−11.3459	+	6.55057i	−0.360779	+	0.208296i
$990$	−1.20640	−	0.770899i	−0.0383421	−	0.0245008i
$991$	−10.7386	+	18.5998i	−0.341123	+	0.590843i	−0.984642	−	0.174588i	$-0.944141\pi$
$991$	−10.7386	+	18.5998i	−0.341123	+	0.590843i	0.643518	+	0.765431i	$0.277474\pi$
$992$	−0.261387	+	0.150912i	−0.00829905	+	0.00479146i
$993$	8.08342	+	18.0751i	0.256519	+	0.573595i
$994$	0.215838	−	5.34706i	0.00684598	−	0.169599i
$995$	38.8634	−	31.7318i	1.23205	−	1.00597i
$996$	−23.4528	−	16.9802i	−0.743130	−	0.538038i
$997$	−7.74597	+	13.4164i	−0.245317	+	0.424902i	−0.962221	−	0.272270i	$-0.912225\pi$
$997$	−7.74597	+	13.4164i	−0.245317	+	0.424902i	0.716904	+	0.697172i	$0.245559\pi$
$998$	−20.9545	+	36.2942i	−0.663302	+	1.14887i
$999$	36.2259	−	7.88828i	1.14614	−	0.249574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.t.f.59.4	yes	8
3.2	odd	2		210.2.t.e.59.2	yes	8
5.2	odd	4		1050.2.s.i.101.3		16
5.3	odd	4		1050.2.s.i.101.6		16
5.4	even	2		210.2.t.e.59.1	✓	8
7.3	odd	6		1470.2.d.e.1469.8		8
7.4	even	3		1470.2.d.e.1469.1		8
7.5	odd	6	inner	210.2.t.f.89.3	yes	8
15.2	even	4		1050.2.s.i.101.5		16
15.8	even	4		1050.2.s.i.101.4		16
15.14	odd	2	inner	210.2.t.f.59.3	yes	8
21.5	even	6		210.2.t.e.89.1	yes	8
21.11	odd	6		1470.2.d.f.1469.4		8
21.17	even	6		1470.2.d.f.1469.5		8
35.4	even	6		1470.2.d.f.1469.8		8
35.12	even	12		1050.2.s.i.551.5		16
35.19	odd	6		210.2.t.e.89.2	yes	8
35.24	odd	6		1470.2.d.f.1469.1		8
35.33	even	12		1050.2.s.i.551.4		16
105.47	odd	12		1050.2.s.i.551.3		16
105.59	even	6		1470.2.d.e.1469.4		8
105.68	odd	12		1050.2.s.i.551.6		16
105.74	odd	6		1470.2.d.e.1469.5		8
105.89	even	6	inner	210.2.t.f.89.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.1	✓	8	5.4	even	2
210.2.t.e.59.2	yes	8	3.2	odd	2
210.2.t.e.89.1	yes	8	21.5	even	6
210.2.t.e.89.2	yes	8	35.19	odd	6
210.2.t.f.59.3	yes	8	15.14	odd	2	inner
210.2.t.f.59.4	yes	8	1.1	even	1	trivial
210.2.t.f.89.3	yes	8	7.5	odd	6	inner
210.2.t.f.89.4	yes	8	105.89	even	6	inner
1050.2.s.i.101.3		16	5.2	odd	4
1050.2.s.i.101.4		16	15.8	even	4
1050.2.s.i.101.5		16	15.2	even	4
1050.2.s.i.101.6		16	5.3	odd	4
1050.2.s.i.551.3		16	105.47	odd	12
1050.2.s.i.551.4		16	35.33	even	12
1050.2.s.i.551.5		16	35.12	even	12
1050.2.s.i.551.6		16	105.68	odd	12
1470.2.d.e.1469.1		8	7.4	even	3
1470.2.d.e.1469.4		8	105.59	even	6
1470.2.d.e.1469.5		8	105.74	odd	6
1470.2.d.e.1469.8		8	7.3	odd	6
1470.2.d.f.1469.1		8	35.24	odd	6
1470.2.d.f.1469.4		8	21.11	odd	6
1470.2.d.f.1469.5		8	21.17	even	6
1470.2.d.f.1469.8		8	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.792893 + 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.792893 + 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(-2.20711 + 0.358719i) q^{10} +(0.184829 + 0.106711i) q^{11} +(-1.01575 + 1.40294i) q^{12} -6.70141 q^{13} +(2.64360 + 0.106711i) q^{14} +(-1.73861 + 3.46081i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73861 + 1.58114i) q^{17} +(0.936492 + 2.85008i) q^{18} +(4.23861 - 2.44716i) q^{19} +(-1.41421 - 1.73205i) q^{20} +(2.83495 - 3.60042i) q^{21} +0.213422i q^{22} +(-3.23861 - 5.60944i) q^{23} +(-1.72286 - 0.178197i) q^{24} +(-3.74264 - 3.31552i) q^{25} +(-3.35071 - 5.80359i) q^{26} +(4.94975 + 1.58114i) q^{27} +(1.22938 + 2.34278i) q^{28} +2.02265i q^{29} +(-3.86646 + 0.224724i) q^{30} +(-0.261387 - 0.150912i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.299418 + 0.216784i) q^{33} +3.16228i q^{34} +(3.55378 + 4.72976i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(6.17913 - 3.56752i) q^{37} +(4.23861 + 2.44716i) q^{38} +(-11.5456 - 1.19417i) q^{39} +(0.792893 - 2.09077i) q^{40} -6.70141 q^{41} +(4.53553 + 0.654929i) q^{42} -2.02265i q^{43} +(-0.184829 + 0.106711i) q^{44} +(-3.61209 + 5.65268i) q^{45} +(3.23861 - 5.60944i) q^{46} +(-6.71584 + 3.87739i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 - 6.32456i) q^{49} +(1.00000 - 4.89898i) q^{50} +(4.43649 + 3.21209i) q^{51} +(3.35071 - 5.80359i) q^{52} +(2.50000 - 4.33013i) q^{53} +(1.10557 + 5.07718i) q^{54} +(-0.369657 + 0.301824i) q^{55} +(-1.41421 + 2.23607i) q^{56} +(7.73861 - 3.46081i) q^{57} +(-1.75166 + 1.01132i) q^{58} +(-2.45877 + 4.25871i) q^{59} +(-2.12785 - 3.23609i) q^{60} +(3.00000 - 1.73205i) q^{61} -0.301824i q^{62} +(5.52581 - 5.69784i) q^{63} +1.00000 q^{64} +(5.31350 - 14.0111i) q^{65} +(-0.0380311 + 0.367696i) q^{66} +(4.61230 + 2.66291i) q^{67} +(-2.73861 + 1.58114i) q^{68} +(-4.58009 - 10.2414i) q^{69} +(-2.31920 + 5.44255i) q^{70} -2.02265i q^{71} +(-2.93649 - 0.614017i) q^{72} +(-5.99430 + 10.3824i) q^{73} +(6.17913 + 3.56752i) q^{74} +(-5.85723 - 6.37909i) q^{75} +4.89433i q^{76} +(0.500000 - 0.262377i) q^{77} +(-4.73861 - 10.5959i) q^{78} +(-0.261387 - 0.452736i) q^{79} +(2.20711 - 0.358719i) q^{80} +(8.24597 + 3.60611i) q^{81} +(-3.35071 - 5.80359i) q^{82} +16.7169i q^{83} +(1.70058 + 4.25535i) q^{84} +(-5.47723 + 4.47214i) q^{85} +(1.75166 - 1.01132i) q^{86} +(-0.360429 + 3.48474i) q^{87} +(-0.184829 - 0.106711i) q^{88} +(-5.28720 - 9.15769i) q^{89} +(-6.70141 - 0.301824i) q^{90} +(-9.47723 + 14.9848i) q^{91} +6.47723 q^{92} +(-0.423441 - 0.306579i) q^{93} +(-6.71584 - 3.87739i) q^{94} +(1.75569 + 10.8023i) q^{95} +(1.01575 - 1.40294i) q^{96} +3.50333 q^{97} +(3.97723 - 5.76035i) q^{98} +(0.477226 + 0.426844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9	\( 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9} - 12 q^{10} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 12 q^{19} + 4 q^{21} - 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} + 4 q^{32} + 12 q^{33} + 8 q^{35} - 16 q^{36} + 12 q^{38} - 8 q^{39} + 12 q^{40} + 8 q^{42} - 24 q^{45} + 4 q^{46} + 12 q^{47} - 24 q^{49} + 8 q^{50} + 20 q^{51} + 20 q^{53} + 40 q^{57} - 4 q^{60} + 24 q^{61} - 20 q^{63} + 8 q^{64} - 16 q^{65} + 12 q^{66} - 8 q^{70} - 8 q^{72} - 24 q^{75} + 4 q^{77} - 16 q^{78} - 24 q^{79} + 12 q^{80} + 4 q^{81} + 4 q^{84} - 12 q^{87} - 32 q^{91} + 8 q^{92} + 20 q^{93} + 12 q^{94} - 12 q^{95} - 12 q^{98} - 40 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9 - 12 * q^10 + 8 * q^15 - 4 * q^16 - 8 * q^18 + 12 * q^19 + 4 * q^21 - 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 + 4 * q^32 + 12 * q^33 + 8 * q^35 - 16 * q^36 + 12 * q^38 - 8 * q^39 + 12 * q^40 + 8 * q^42 - 24 * q^45 + 4 * q^46 + 12 * q^47 - 24 * q^49 + 8 * q^50 + 20 * q^51 + 20 * q^53 + 40 * q^57 - 4 * q^60 + 24 * q^61 - 20 * q^63 + 8 * q^64 - 16 * q^65 + 12 * q^66 - 8 * q^70 - 8 * q^72 - 24 * q^75 + 4 * q^77 - 16 * q^78 - 24 * q^79 + 12 * q^80 + 4 * q^81 + 4 * q^84 - 12 * q^87 - 32 * q^91 + 8 * q^92 + 20 * q^93 + 12 * q^94 - 12 * q^95 - 12 * q^98 - 40 * q^99

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