LMFDB - Embedded newform 210.2.t.e.89.1

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			89.1
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	210.89
Dual form			210.2.t.e.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.72286 + 0.178197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 0.358719i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} +1.00000 q^{8} +(2.93649 - 0.614017i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.72286 + 0.178197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 0.358719i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} +1.00000 q^{8} +(2.93649 - 0.614017i) q^{9} +(-0.792893 + 2.09077i) q^{10} +(0.184829 - 0.106711i) q^{11} +(1.01575 + 1.40294i) q^{12} +6.70141 q^{13} +(2.64360 - 0.106711i) q^{14} +(-3.73861 + 1.01132i) 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} +(4.74264 - 1.58346i) q^{25} +(-3.35071 + 5.80359i) q^{26} +(-4.94975 + 1.58114i) q^{27} +(-1.22938 + 2.34278i) q^{28} -2.02265i q^{29} +(0.993475 - 3.74340i) q^{30} +(-0.261387 + 0.150912i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.299418 + 0.216784i) q^{33} -3.16228i q^{34} +(-3.92344 - 4.42793i) 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} +(2.20711 - 0.358719i) q^{40} -6.70141 q^{41} +(-4.53553 + 0.654929i) q^{42} -2.02265i q^{43} +(-0.184829 - 0.106711i) q^{44} +(6.26089 - 2.40858i) 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} +(2.74514 + 2.73207i) q^{60} +(3.00000 + 1.73205i) q^{61} -0.301824i q^{62} +(-5.52581 - 5.69784i) q^{63} +1.00000 q^{64} +(14.7907 - 2.40393i) 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} +(5.79642 - 1.18383i) q^{70} +2.02265i q^{71} +(2.93649 - 0.614017i) q^{72} +(5.99430 + 10.3824i) q^{73} +(6.17913 - 3.56752i) q^{74} +(-7.88874 + 3.57321i) q^{75} -4.89433i q^{76} +(-0.500000 - 0.262377i) q^{77} +(4.73861 - 10.5959i) q^{78} +(-0.261387 + 0.452736i) q^{79} +(-0.792893 + 2.09077i) 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} +(-1.04456 + 6.62638i) q^{90} +(-9.47723 - 14.9848i) q^{91} -6.47723 q^{92} +(0.423441 - 0.306579i) q^{93} +(-6.71584 + 3.87739i) q^{94} +(10.2329 + 3.88068i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$6$	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
$10$	−0.792893	+	2.09077i	−0.250735	+	0.661160i
$11$	0.184829	−	0.106711i	0.0557279	−	0.0321745i	−0.471877	−	0.881664i	$-0.656423\pi$
$11$	0.184829	−	0.106711i	0.0557279	−	0.0321745i	0.527605	+	0.849490i	$0.323090\pi$
$12$	1.01575	+	1.40294i	0.293223	+	0.404994i
$13$	6.70141			1.85864			0.929318	−	0.369279i	$-0.120395\pi$
$13$	6.70141			1.85864			0.929318	+	0.369279i	$0.120395\pi$
$14$	2.64360	−	0.106711i	0.706531	−	0.0285197i
$15$	−3.73861	+	1.01132i	−0.965306	+	0.261123i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.73861	+	1.58114i	−0.664211	+	0.383482i	−0.793880	−	0.608075i	$-0.791942\pi$
$17$	−2.73861	+	1.58114i	−0.664211	+	0.383482i	0.129668	+	0.991557i	$0.458609\pi$
$18$	−0.936492	+	2.85008i	−0.220733	+	0.671771i
$19$	4.23861	+	2.44716i	0.972404	+	0.561418i	0.899968	−	0.435955i	$-0.143589\pi$
$19$	4.23861	+	2.44716i	0.972404	+	0.561418i	0.0724360	+	0.997373i	$0.476923\pi$
$20$	−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	−0.301084	−	0.953597i	$-0.597349\pi$
$23$	3.23861	−	5.60944i	0.675297	−	1.16965i	0.976382	−	0.216052i	$-0.0693181\pi$
$24$	−1.72286	+	0.178197i	−0.351677	+	0.0363743i
$25$	4.74264	−	1.58346i	0.948528	−	0.316693i
$26$	−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	$-0.939865\pi$
$29$		−	2.02265i		−	0.375596i	0.982208	−	0.187798i	$-0.0601350\pi$
$30$	0.993475	−	3.74340i	0.181383	−	0.683447i
$31$	−0.261387	+	0.150912i	−0.0469465	+	0.0271046i	−0.523290	−	0.852155i	$-0.675295\pi$
$31$	−0.261387	+	0.150912i	−0.0469465	+	0.0271046i	0.476343	+	0.879260i	$0.341962\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.299418	+	0.216784i	−0.0521220	+	0.0377372i
$34$		−	3.16228i		−	0.542326i
$35$	−3.92344	−	4.42793i	−0.663183	−	0.748458i
$36$	−2.00000	−	2.23607i	−0.333333	−	0.372678i
$37$	−6.17913	−	3.56752i	−1.01584	−	0.586497i	−0.102946	−	0.994687i	$-0.532827\pi$
$37$	−6.17913	−	3.56752i	−1.01584	−	0.586497i	−0.912897	+	0.408190i	$0.866160\pi$
$38$	−4.23861	+	2.44716i	−0.687594	+	0.396982i
$39$	−11.5456	+	1.19417i	−1.84877	+	0.191220i
$40$	2.20711	−	0.358719i	0.348974	−	0.0567185i
$41$	−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
$45$	6.26089	−	2.40858i	0.933319	−	0.359050i
$46$	3.23861	+	5.60944i	0.477507	+	0.827067i
$47$	6.71584	+	3.87739i	0.979606	+	0.565576i	0.902151	−	0.431420i	$-0.141987\pi$
$47$	6.71584	+	3.87739i	0.979606	+	0.565576i	0.0774546	+	0.996996i	$0.475321\pi$
$48$	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	$-0.278246\pi$
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	−0.985062	+	0.172200i	$0.944912\pi$
$54$	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	0.660405	−	0.750910i	$-0.270385\pi$
$59$	−2.45877	−	4.25871i	−0.320105	−	0.554437i	−0.980509	+	0.196472i	$0.937051\pi$
$60$	2.74514	+	2.73207i	0.354396	+	0.352709i
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$		−	0.301824i		−	0.0383317i
$63$	−5.52581	−	5.69784i	−0.696187	−	0.717861i
$64$	1.00000			0.125000
$65$	14.7907	−	2.40393i	1.83456	−	0.298170i
$66$	−0.0380311	−	0.367696i	−0.00468131	−	0.0452602i
$67$	−4.61230	+	2.66291i	−0.563482	+	0.325326i	−0.754542	−	0.656252i	$-0.772141\pi$
$67$	−4.61230	+	2.66291i	−0.563482	+	0.325326i	0.191060	+	0.981578i	$0.438808\pi$
$68$	2.73861	+	1.58114i	0.332106	+	0.191741i
$69$	−4.58009	+	10.2414i	−0.551378	+	1.23292i
$70$	5.79642	−	1.18383i	0.692805	−	0.141495i
$71$			2.02265i			0.240044i	0.992771	+	0.120022i	$0.0382965\pi$
$71$			2.02265i			0.240044i	−0.992771	+	0.120022i	$0.961703\pi$
$72$	2.93649	−	0.614017i	0.346069	−	0.0723626i
$73$	5.99430	+	10.3824i	0.701580	+	1.21517i	0.967912	+	0.251291i	$0.0808551\pi$
$73$	5.99430	+	10.3824i	0.701580	+	1.21517i	−0.266331	+	0.963882i	$0.585812\pi$
$74$	6.17913	−	3.56752i	0.718310	−	0.414716i
$75$	−7.88874	+	3.57321i	−0.910913	+	0.412599i
$76$		−	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	−0.880355	−	0.474315i	$-0.842696\pi$
$79$	−0.261387	+	0.452736i	−0.0294084	+	0.0509368i	0.850947	+	0.525252i	$0.176029\pi$
$80$	−0.792893	+	2.09077i	−0.0886482	+	0.233755i
$81$	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	0.437016	+	0.899454i	$0.356035\pi$
$89$	−5.28720	+	9.15769i	−0.560442	+	0.970714i	−0.997458	+	0.0712599i	$0.977298\pi$
$90$	−1.04456	+	6.62638i	−0.110106	+	0.698482i
$91$	−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
$95$	10.2329	+	3.88068i	1.04988	+	0.398149i
$96$	1.01575	+	1.40294i	0.103670	+	0.143187i
$97$	−3.50333			−0.355709			−0.177854	−	0.984057i	$-0.556916\pi$
$97$	−3.50333			−0.355709			−0.177854	+	0.984057i	$0.556916\pi$
$98$	−3.97723	−	5.76035i	−0.401760	−	0.581884i
$99$	0.477226	−	0.426844i	0.0479630	−	0.0428994i
$100$	−3.74264	−	3.31552i	−0.374264	−	0.331552i
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	−0.997244	−	0.0741967i	$-0.976361\pi$
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	0.434366	−	0.900737i	$-0.356973\pi$
$102$	0.563508	+	5.44816i	0.0557956	+	0.539448i
$103$	−5.28720	+	9.15769i	−0.520963	+	0.902334i	0.478740	+	0.877957i	$0.341094\pi$
$103$	−5.28720	+	9.15769i	−0.520963	+	0.902334i	−0.999703	+	0.0243776i	$0.992240\pi$
$104$	6.70141			0.657127
$105$	7.54858	+	6.92957i	0.736666	+	0.676256i
$106$	5.00000			0.485643
$107$	−2.73861	+	4.74342i	−0.264752	+	0.458563i	−0.967499	−	0.252877i	$-0.918623\pi$
$107$	−2.73861	+	4.74342i	−0.264752	+	0.458563i	0.702747	+	0.711440i	$0.251957\pi$
$108$	3.84418	+	3.49604i	0.369906	+	0.336406i
$109$	−6.21584	−	10.7661i	−0.595369	−	1.03121i	−0.993495	−	0.113879i	$-0.963672\pi$
$109$	−6.21584	−	10.7661i	−0.595369	−	1.03121i	0.398125	−	0.917331i	$-0.369661\pi$
$110$	0.0765585	+	0.471045i	0.00729957	+	0.0449123i
$111$	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	$-0.400740\pi$
$113$	6.52277			0.613611			0.306806	+	0.951772i	$0.400740\pi$
$114$	6.86646	−	4.97143i	0.643103	−	0.465617i
$115$	5.13575	−	13.5424i	0.478911	−	1.26283i
$116$	−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
$120$	−3.73861	+	1.01132i	−0.341287	+	0.0923207i
$121$	−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
$130$	−5.31350	+	14.0111i	−0.466025	+	1.22886i
$131$	3.01326	−	5.21911i	0.263269	−	0.455996i	−0.703839	−	0.710359i	$-0.748533\pi$
$131$	3.01326	−	5.21911i	0.263269	−	0.455996i	0.967109	+	0.254363i	$0.0818659\pi$
$132$	0.337449	+	0.150912i	0.0293712	+	0.0131352i
$133$	−0.522278	−	12.9386i	−0.0452873	−	1.12192i
$134$		−	5.32582i		−	0.460081i
$135$	−10.3574	+	5.26531i	−0.891426	+	0.453166i
$136$	−2.73861	+	1.58114i	−0.234834	+	0.135582i
$137$	−3.73861	−	6.47547i	−0.319411	−	0.553237i	0.660954	−	0.750426i	$-0.270152\pi$
$137$	−3.73861	−	6.47547i	−0.319411	−	0.553237i	−0.980365	+	0.197190i	$0.936818\pi$
$138$	−6.57926	−	9.08717i	−0.560064	−	0.773551i
$139$		−	7.53185i		−	0.638843i	−0.947613	−	0.319422i	$-0.896511\pi$
$139$		−	7.53185i		−	0.638843i	0.947613	−	0.319422i	$-0.103489\pi$
$140$	−1.87298	+	5.61177i	−0.158296	+	0.474281i
$141$	−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
$145$	−0.725563	−	4.46420i	−0.0602547	−	0.370731i
$146$	−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	0.584370	−	0.811488i	$-0.301342\pi$
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	−0.410584	+	0.911823i	$0.634675\pi$
$150$	0.849876	−	8.61845i	0.0693921	−	0.703694i
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	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	$-0.0525831\pi$
$157$	4.39526	+	7.61282i	0.350780	+	0.607569i	−0.635606	+	0.772013i	$0.719250\pi$
$158$	−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	$-0.528556\pi$
$163$	−12.7279	−	7.34847i	−0.996928	−	0.575577i	−0.907338	+	0.420402i	$0.861889\pi$
$164$	3.35071	+	5.80359i	0.261646	+	0.453184i
$165$	−0.583084	+	0.585872i	−0.0453930	+	0.0456101i
$166$	−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
$170$	−1.13437	−	6.97948i	−0.0870023	−	0.535302i
$171$	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	$-0.477629\pi$
$173$	−9.97723	−	5.76035i	−0.758554	−	0.437952i	−0.828776	+	0.559580i	$0.810963\pi$
$174$	−3.19808	−	1.43023i	−0.242446	−	0.108425i
$175$	−10.2478	−	8.36551i	−0.774664	−	0.632373i
$176$			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	−0.897752	−	0.440500i	$-0.854801\pi$
$179$	−12.9128	+	7.45518i	−0.965144	+	0.557226i	−0.0673918	+	0.997727i	$0.521468\pi$
$180$	−5.21633	−	4.21780i	−0.388803	−	0.314376i
$181$			3.16228i			0.235050i	0.993070	+	0.117525i	$0.0374961\pi$
$181$			3.16228i			0.235050i	−0.993070	+	0.117525i	$0.962504\pi$
$182$	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
$185$	−14.9177	−	5.65733i	−1.09677	−	0.415935i
$186$	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	0.449167	−	0.893448i	$-0.351721\pi$
$191$	−1.38201	−	0.797901i	−0.0999984	−	0.0577341i	−0.549165	+	0.835714i	$0.685054\pi$
$192$	−1.72286	+	0.178197i	−0.124337	+	0.0128603i
$193$	−6.36396	+	3.67423i	−0.458088	+	0.264477i	−0.711240	−	0.702949i	$-0.751866\pi$
$193$	−6.36396	+	3.67423i	−0.458088	+	0.264477i	0.253152	+	0.967427i	$0.418533\pi$
$194$	1.75166	−	3.03397i	0.125762	−	0.217826i
$195$	−25.0540	+	6.77729i	−1.79415	+	0.485332i
$196$	6.97723	−	0.564201i	0.498373	−	0.0403001i
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$	0.131045	+	0.626711i	0.00931293	+	0.0445384i
$199$	−19.4317	+	11.2189i	−1.37748	+	0.795286i	−0.991855	−	0.127372i	$-0.959346\pi$
$199$	−19.4317	+	11.2189i	−1.37748	+	0.795286i	−0.385620	+	0.922658i	$0.626012\pi$
$200$	4.74264	−	1.58346i	0.335355	−	0.111968i
$201$	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
$205$	−14.7907	+	2.40393i	−1.03303	+	0.167898i
$206$	−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
$210$	−9.77547	+	3.07248i	−0.674572	+	0.212021i
$211$	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
$215$	−0.725563	−	4.46420i	−0.0494830	−	0.304456i
$216$	−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
$220$	−0.446216	−	0.169221i	−0.0300839	−	0.0114089i
$221$	−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	$-0.431299\pi$
$223$	6.39617			0.428319			0.214160	+	0.976799i	$0.431299\pi$
$224$	−1.22938	+	2.34278i	−0.0821417	+	0.156533i
$225$	12.9545	−	7.56189i	0.863630	−	0.504126i
$226$	−3.26139	+	5.64889i	−0.216944	+	0.375758i
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	−0.170648	−	0.985332i	$-0.554586\pi$
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	0.767999	+	0.640451i	$0.221253\pi$
$228$	0.872155	+	8.43224i	0.0577598	+	0.558439i
$229$	−6.26139	−	3.61501i	−0.413764	−	0.238887i	0.278642	−	0.960395i	$-0.410116\pi$
$229$	−6.26139	−	3.61501i	−0.413764	−	0.238887i	−0.692406	+	0.721508i	$0.743449\pi$
$230$	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	$-0.791507\pi$
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	0.924072	+	0.382219i	$0.124840\pi$
$234$	−6.27582	+	19.0996i	−0.410263	+	1.24858i
$235$	16.2135	+	6.14871i	1.05765	+	0.401098i
$236$	−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			$\pi$
$240$	0.993475	−	3.74340i	0.0641285	−	0.241635i
$241$	3.45445	−	1.99443i	0.222521	−	0.128472i	−0.384596	−	0.923085i	$-0.625659\pi$
$241$	3.45445	−	1.99443i	0.222521	−	0.128472i	0.607117	+	0.794613i	$0.292326\pi$
$242$	−5.47723	−	9.48683i	−0.352089	−	0.609837i
$243$	−13.5640	+	7.68223i	−0.870134	+	0.492815i
$244$		−	3.46410i		−	0.221766i
$245$	−4.35258	+	15.0351i	−0.278076	+	0.960559i
$246$	−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
$250$	−0.449747	+	11.1713i	−0.0284445	+	0.706534i
$251$	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
$255$	8.63957	−	8.68089i	0.541031	−	0.543618i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.4772	−	11.8225i	−1.27733	−	0.737469i	−0.300977	−	0.953631i	$-0.597313\pi$
$257$	−20.4772	−	11.8225i	−1.27733	−	0.737469i	−0.976357	+	0.216162i	$0.930646\pi$
$258$	−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	$-0.147026\pi$
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	−0.833546	+	0.552450i	$0.813693\pi$
$264$	−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	0.850373	+	0.526180i	$0.176376\pi$
$269$	14.4474	+	25.0236i	0.880872	+	1.52572i	0.0304992	+	0.999535i	$0.490290\pi$
$270$	0.618823	−	11.6025i	0.0376604	−	0.706103i
$271$	5.47723	+	3.16228i	0.332718	+	0.192095i	0.657047	−	0.753850i	$-0.271805\pi$
$271$	5.47723	+	3.16228i	0.332718	+	0.192095i	−0.324329	+	0.945944i	$0.605139\pi$
$272$		−	3.16228i		−	0.191741i
$273$	18.9982	+	24.1279i	1.14982	+	1.46029i
$274$	7.47723			0.451716
$275$	0.707603	−	0.798761i	0.0426701	−	0.0481671i
$276$	11.1594	−	1.15422i	0.671714	−	0.0694760i
$277$	8.48528	−	4.89898i	0.509831	−	0.294351i	−0.222933	−	0.974834i	$-0.571563\pi$
$277$	8.48528	−	4.89898i	0.509831	−	0.294351i	0.732764	+	0.680483i	$0.238230\pi$
$278$	6.52277	+	3.76593i	0.391210	+	0.225865i
$279$	−0.674899	+	0.603648i	−0.0404051	+	0.0361395i
$280$	−3.92344	−	4.42793i	−0.234470	−	0.264620i
$281$			11.6072i			0.692427i	0.938156	+	0.346213i	$0.112533\pi$
$281$			11.6072i			0.692427i	−0.938156	+	0.346213i	$0.887467\pi$
$282$	10.8795	−	7.87694i	0.647865	−	0.469065i
$283$	−12.3583	−	21.4051i	−0.734623	−	1.27240i	−0.954889	−	0.296964i	$-0.904026\pi$
$283$	−12.3583	−	21.4051i	−0.734623	−	1.27240i	0.220266	−	0.975440i	$-0.429307\pi$
$284$	1.75166	−	1.01132i	0.103942	−	0.0600110i
$285$	−18.3214	−	4.86239i	−1.08527	−	0.288023i
$286$			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
$290$	4.22889	+	1.60374i	0.248329	+	0.0941750i
$291$	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
$300$	7.03886	+	5.04524i	0.406389	+	0.291287i
$301$	−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
$305$	7.24264	+	2.74666i	0.414712	+	0.157273i
$306$	−1.94169	−	9.28600i	−0.110999	−	0.530845i
$307$	3.50333			0.199945			0.0999727	−	0.994990i	$-0.468124\pi$
$307$	3.50333			0.199945			0.0999727	+	0.994990i	$0.468124\pi$
$308$	0.0227744	+	0.564201i	0.00129769	+	0.0321484i
$309$	7.47723	−	16.7196i	0.425365	−	0.951144i
$310$	−0.108270	−	0.666158i	−0.00614933	−	0.0378352i
$311$	14.4474	+	25.0236i	0.819236	+	1.41896i	0.906246	+	0.422750i	$0.138935\pi$
$311$	14.4474	+	25.0236i	0.819236	+	1.41896i	−0.0870106	+	0.996207i	$0.527731\pi$
$312$	−11.5456	+	1.19417i	−0.653640	+	0.0676066i
$313$	11.6190	−	20.1246i	0.656742	−	1.13751i	−0.324712	−	0.945813i	$-0.605267\pi$
$313$	11.6190	−	20.1246i	0.656742	−	1.13751i	0.981454	−	0.191697i	$-0.0613992\pi$
$314$	−8.79052			−0.496078
$315$	−14.2400	−	10.5935i	−0.802332	−	0.596878i
$316$	0.522774			0.0294084
$317$	−16.9545	+	29.3660i	−0.952257	+	1.64936i	−0.211733	+	0.977328i	$0.567911\pi$
$317$	−16.9545	+	29.3660i	−0.952257	+	1.64936i	−0.740524	+	0.672030i	$0.765423\pi$
$318$	−8.61430	+	0.890985i	−0.483066	+	0.0499640i
$319$	−0.215838	−	0.373843i	−0.0120846	−	0.0209312i
$320$	2.20711	−	0.358719i	0.123381	−	0.0200530i
$321$	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
$325$	31.7824	−	10.6114i	1.76297	−	0.588617i
$326$	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
$330$	−0.215838	−	0.797901i	−0.0118815	−	0.0439230i
$331$	5.71584	−	9.90012i	0.314171	−	0.544160i	−0.665090	−	0.746763i	$-0.731607\pi$
$331$	5.71584	−	9.90012i	0.314171	−	0.544160i	0.979261	+	0.202603i	$0.0649402\pi$
$332$	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
$340$	6.61160	+	2.50735i	0.358564	+	0.135980i
$341$	−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
$345$	−6.43496	+	24.2468i	−0.346447	+	1.30540i
$346$	9.97723	−	5.76035i	0.536379	−	0.309679i
$347$	3.26139	+	5.64889i	0.175080	+	0.303248i	0.940189	−	0.340653i	$-0.110648\pi$
$347$	3.26139	+	5.64889i	0.175080	+	0.303248i	−0.765109	+	0.643901i	$0.777315\pi$
$348$	2.83766	−	2.05451i	0.152114	−	0.110133i
$349$		−	32.5282i		−	1.74120i	−0.491994	−	0.870599i	$-0.663732\pi$
$349$		−	32.5282i		−	1.74120i	0.491994	−	0.870599i	$-0.336268\pi$
$350$	12.3687	−	4.69214i	0.661133	−	0.250805i
$351$	−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	$-0.551935\pi$
$353$	11.4772	−	6.62638i	0.610871	−	0.352687i	0.773306	+	0.634033i	$0.218602\pi$
$354$	−8.47223	+	0.876291i	−0.450294	+	0.0465743i
$355$	0.725563	+	4.46420i	0.0385089	+	0.236935i
$356$	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	0.641030	−	0.767516i	$-0.278507\pi$
$359$	5.62465	+	3.24739i	0.296857	+	0.171391i	−0.344173	+	0.938906i	$0.611841\pi$
$360$	6.26089	−	2.40858i	0.329978	−	0.126943i
$361$	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	$-0.234604\pi$
$367$	−4.05781	−	7.02834i	−0.211816	−	0.366876i	−0.952283	+	0.305217i	$0.901271\pi$
$368$	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	$-0.363196\pi$
$373$	−3.13367	−	1.80922i	−0.162255	−	0.0936781i	−0.578929	+	0.815378i	$0.696529\pi$
$374$	−0.337449	−	0.584480i	−0.0174491	−	0.0302227i
$375$	−16.1295	+	10.7163i	−0.832924	+	0.553387i
$376$	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	$0.578649\pi$
$380$	−1.75569	−	10.8023i	−0.0900650	−	0.554147i
$381$	−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	$-0.340056\pi$
$383$	−0.715838	−	0.413289i	−0.0365776	−	0.0211181i	−0.518177	+	0.855273i	$0.673389\pi$
$384$	0.707107	−	1.58114i	0.0360844	−	0.0806872i
$385$	−1.19767	−	0.399735i	−0.0610391	−	0.0203724i
$386$		−	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	−0.652580	−	0.757720i	$-0.726313\pi$
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	0.329914	+	0.944011i	$0.392980\pi$
$390$	6.65768	−	25.0860i	0.337125	−	1.27028i
$391$			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
$395$	−0.414504	+	1.09300i	−0.0208560	+	0.0549949i
$396$	−0.608270	−	0.199868i	−0.0305667	−	0.0100437i
$397$	−15.1867	+	26.3041i	−0.762198	+	1.32017i	0.179517	+	0.983755i	$0.442547\pi$
$397$	−15.1867	+	26.3041i	−0.762198	+	1.32017i	−0.941715	+	0.336411i	$0.890787\pi$
$398$		−	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	−0.330014	−	0.943976i	$-0.607054\pi$
$401$	−26.2834	−	15.1747i	−1.31253	−	0.757789i	−0.982514	+	0.186187i	$0.940387\pi$
$402$	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
$405$	16.9061	−	10.9171i	0.840073	−	0.542473i
$406$	−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	−0.896430	−	0.443186i	$-0.853848\pi$
$409$	−19.4317	+	11.2189i	−0.960835	+	0.554738i	−0.0644048	+	0.997924i	$0.520515\pi$
$410$	5.31350	−	14.0111i	0.262415	−	0.691959i
$411$	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
$415$	5.99666	+	36.8959i	0.294365	+	1.81115i
$416$	−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	$0.632904\pi$
$420$	2.22689	−	10.0020i	0.108661	−	0.488050i
$421$	−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
$425$	−10.4846	+	11.8353i	−0.508577	+	0.574095i
$426$	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
$430$	4.22889	+	1.60374i	0.203935	+	0.0773393i
$431$	32.0928	−	18.5288i	1.54586	−	0.892501i	0.547406	−	0.836867i	$-0.315615\pi$
$431$	32.0928	−	18.5288i	1.54586	−	0.892501i	0.998451	−	0.0556344i	$-0.0177181\pi$
$432$	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
$435$	2.04555	+	7.56189i	0.0980766	+	0.362565i
$436$	−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	0.889929	−	0.456100i	$-0.150754\pi$
$439$	19.6931	+	11.3698i	0.939899	+	0.542651i	0.0499701	+	0.998751i	$0.484087\pi$
$440$	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	0.0242161	−	0.999707i	$-0.492291\pi$
$443$	18.4772	−	32.0035i	0.877879	−	1.52053i	0.853663	−	0.520825i	$-0.174376\pi$
$444$	−1.27144	−	12.2927i	−0.0603401	−	0.583385i
$445$	−8.38437	+	22.1086i	−0.397457	+	1.04805i
$446$	−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	$-0.973556\pi$
$449$		−	3.51660i		−	0.165959i	0.996551	−	0.0829793i	$-0.0264435\pi$
$450$	0.0715641	+	14.9998i	0.00337357	+	0.707099i
$451$	−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
$455$	−26.2926	−	29.6734i	−1.23262	−	1.39111i
$456$	−7.73861	−	3.46081i	−0.362394	−	0.162067i
$457$	−32.8322	−	18.9557i	−1.53582	−	0.886708i	−0.999077	−	0.0429646i	$-0.986320\pi$
$457$	−32.8322	−	18.9557i	−1.53582	−	0.886708i	−0.536747	−	0.843743i	$-0.680347\pi$
$458$	6.26139	−	3.61501i	0.292575	−	0.168918i
$459$	11.0554	−	12.1564i	0.516024	−	0.567411i
$460$	−14.2959	+	2.32351i	−0.666551	+	0.108334i
$461$	−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
$465$	0.824605	−	0.828548i	0.0382401	−	0.0384230i
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−29.7386	−	17.1696i	−1.37614	−	0.794514i	−0.384447	−	0.923147i	$-0.625608\pi$
$467$	−29.7386	−	17.1696i	−1.37614	−	0.794514i	−0.991692	+	0.128633i	$0.958941\pi$
$468$	−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	0.966226	−	0.257698i	$-0.0829639\pi$
$479$	5.68906	+	9.85374i	0.259940	+	0.450229i	−0.706286	+	0.707927i	$0.749631\pi$
$480$	2.74514	+	2.73207i	0.125298	+	0.124701i
$481$	−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
$485$	−7.73221	+	1.25671i	−0.351102	+	0.0570643i
$486$	0.129018	−	15.5879i	0.00585235	−	0.707083i
$487$	−31.7232	+	18.3154i	−1.43751	+	0.829949i	−0.997677	−	0.0681277i	$-0.978297\pi$
$487$	−31.7232	+	18.3154i	−1.43751	+	0.829949i	−0.439838	+	0.898077i	$0.644964\pi$
$488$	3.00000	+	1.73205i	0.135804	+	0.0784063i
$489$	23.2379	+	10.3923i	1.05085	+	0.469956i
$490$	−10.8445	−	11.2870i	−0.489905	−	0.509895i
$491$		−	4.04529i		−	0.182561i	−0.995825	−	0.0912807i	$-0.970904\pi$
$491$		−	4.04529i		−	0.182561i	0.995825	−	0.0912807i	$-0.0290961\pi$
$492$	−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
$495$	0.900171	−	1.11328i	0.0404597	−	0.0500382i
$496$		−	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	0.168947	−	0.985625i	$-0.445963\pi$
$499$	20.9545	−	36.2942i	0.938050	−	1.62475i	0.769103	−	0.639125i	$-0.220703\pi$
$500$	−9.44975	−	5.97514i	−0.422606	−	0.267216i
$501$	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	−0.745517	−	0.666487i	$-0.767797\pi$
$509$	4.61230	−	7.98873i	0.204437	−	0.354094i	0.949953	+	0.312393i	$0.101130\pi$
$510$	3.19808	+	11.8225i	0.141614	+	0.523511i
$511$	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
$515$	−8.38437	+	22.1086i	−0.369459	+	0.974223i
$516$	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
$520$	14.7907	−	2.40393i	0.648616	−	0.105419i
$521$	−9.31280	−	16.1302i	−0.408001	−	0.706679i	0.586664	−	0.809830i	$-0.300441\pi$
$521$	−9.31280	−	16.1302i	−0.408001	−	0.706679i	−0.994666	+	0.103151i	$0.967107\pi$
$522$	5.76471	+	1.89419i	0.252315	+	0.0829065i
$523$	−7.03886	+	12.1917i	−0.307788	+	0.533104i	−0.977878	−	0.209175i	$-0.932922\pi$
$523$	−7.03886	+	12.1917i	−0.307788	+	0.533104i	0.670090	+	0.742280i	$0.266255\pi$
$524$	−6.02651			−0.263269
$525$	19.1463	+	12.5865i	0.835613	+	0.549318i
$526$	−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
$530$	11.0355	−	1.79360i	0.479353	−	0.0779089i
$531$	−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
$535$	−4.34286	+	11.4516i	−0.187758	+	0.495097i
$536$	−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
$540$	9.73861	+	6.33715i	0.419083	+	0.272707i
$541$	−9.73861	+	16.8678i	−0.418696	+	0.725202i	−0.995809	−	0.0914622i	$-0.970846\pi$
$541$	−9.73861	+	16.8678i	−0.418696	+	0.725202i	0.577113	+	0.816664i	$0.304179\pi$
$542$	−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
$550$	0.337946	+	1.01218i	0.0144101	+	0.0431596i
$551$	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
$555$	26.7093	+	7.08849i	1.13375	+	0.300890i
$556$	−6.52277	+	3.76593i	−0.276627	+	0.159711i
$557$	18.9317	+	32.7906i	0.802161	+	1.38938i	0.918191	+	0.396138i	$0.129650\pi$
$557$	18.9317	+	32.7906i	0.802161	+	1.38938i	−0.116030	+	0.993246i	$0.537017\pi$
$558$	−0.185325	−	0.886304i	−0.00784543	−	0.0375202i
$559$		−	13.5546i		−	0.573298i
$560$	5.79642	−	1.18383i	0.244944	−	0.0500261i
$561$	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	$-0.596390\pi$
$563$	9.00000	−	5.19615i	0.379305	−	0.218992i	0.677516	+	0.735508i	$0.263057\pi$
$564$	1.38188	+	13.3604i	0.0581876	+	0.562574i
$565$	14.3965	−	2.33985i	0.605664	−	0.0984381i
$566$	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	0.702283	−	0.711898i	$-0.252164\pi$
$569$	10.4218	+	6.01701i	0.436903	+	0.252246i	−0.265380	+	0.964144i	$0.585497\pi$
$570$	13.3717	−	13.4356i	0.560077	−	0.562756i
$571$	3.47723	+	6.02273i	0.145517	+	0.252043i	0.929566	−	0.368656i	$-0.120182\pi$
$571$	3.47723	+	6.02273i	0.145517	+	0.252043i	−0.784048	+	0.620700i	$0.786849\pi$
$572$	−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	$-0.266467\pi$
$577$	−7.40852	−	12.8319i	−0.308421	−	0.534200i	−0.978017	+	0.208525i	$0.933134\pi$
$578$	−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
$585$	41.9568	−	16.1409i	1.73470	−	0.667343i
$586$	−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
$590$	10.8535	−	1.76402i	0.446833	−	0.0726234i
$591$	−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	$-0.0656818\pi$
$593$	31.4317	+	18.1471i	1.29074	+	0.745212i	0.311958	+	0.950096i	$0.399015\pi$
$594$	−0.337449	−	1.05638i	−0.0138457	−	0.0433440i
$595$	17.7460	+	5.92289i	0.727514	+	0.242815i
$596$		−	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	−0.394756	−	0.918786i	$-0.629171\pi$
$599$	4.98196	−	2.87633i	0.203557	−	0.117524i	0.598314	+	0.801262i	$0.295838\pi$
$600$	−7.88874	+	3.57321i	−0.322056	+	0.145876i
$601$			16.7169i			0.681895i	0.940082	+	0.340947i	$0.110748\pi$
$601$			16.7169i			0.681895i	−0.940082	+	0.340947i	$0.889252\pi$
$602$	−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
$605$	−8.68571	+	22.9032i	−0.353124	+	0.931149i
$606$	−19.4919	+	2.01607i	−0.791806	+	0.0818972i
$607$	13.2180	−	22.8942i	0.536502	−	0.929248i	−0.462587	−	0.886574i	$-0.653079\pi$
$607$	13.2180	−	22.8942i	0.536502	−	0.929248i	0.999089	−	0.0426745i	$-0.0135879\pi$
$608$		−	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	$-0.494842\pi$
$613$	22.0407	−	12.7252i	0.890216	−	0.513967i	0.874013	+	0.485902i	$0.161509\pi$
$614$	−1.75166	+	3.03397i	−0.0706914	+	0.122441i
$615$	25.0540	−	6.77729i	1.01027	−	0.273287i
$616$	−0.500000	−	0.262377i	−0.0201456	−	0.0105715i
$617$	25.4772			1.02567			0.512837	−	0.858486i	$-0.328594\pi$
$617$	25.4772			1.02567			0.512837	+	0.858486i	$0.328594\pi$
$618$	10.7410	+	14.8353i	0.432065	+	0.596762i
$619$	−23.1475	+	13.3642i	−0.930377	+	0.537154i	−0.886931	−	0.461902i	$-0.847167\pi$
$619$	−23.1475	+	13.3642i	−0.930377	+	0.537154i	−0.0434463	+	0.999056i	$0.513834\pi$
$620$	0.631045	+	0.239314i	0.0253434	+	0.00961109i
$621$	−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
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	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
$630$	16.2943	−	7.03542i	0.649179	−	0.280298i
$631$	−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
$635$	4.88929	+	30.0825i	0.194025	+	1.19379i
$636$	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
$640$	−0.792893	+	2.09077i	−0.0313419	+	0.0826450i
$641$	5.43982	−	3.14068i	0.214860	−	0.124049i	−0.388708	−	0.921361i	$-0.627079\pi$
$641$	5.43982	−	3.14068i	0.214860	−	0.124049i	0.603568	+	0.797312i	$0.293745\pi$
$642$	5.56351	+	7.68423i	0.219574	+	0.303272i
$643$	−20.4095			−0.804871			−0.402436	−	0.915448i	$-0.631836\pi$
$643$	−20.4095			−0.804871			−0.402436	+	0.915448i	$0.631836\pi$
$644$	9.16018	+	14.4835i	0.360962	+	0.570731i
$645$	2.04555	+	7.56189i	0.0805434	+	0.297749i
$646$	7.73861	−	13.4037i	0.304472	−	0.527360i
$647$	−20.6703	+	11.9340i	−0.812633	+	0.469174i	−0.847869	−	0.530205i	$-0.822115\pi$
$647$	−20.6703	+	11.9340i	−0.812633	+	0.469174i	0.0352364	+	0.999379i	$0.488782\pi$
$648$	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	−0.493920	−	0.869507i	$-0.664436\pi$
$653$	12.9317	−	22.3983i	0.506056	−	0.876514i	0.999975	−	0.00700659i	$-0.00223029\pi$
$654$	−21.4180	+	2.21529i	−0.837511	+	0.0866246i
$655$	4.77838	−	12.6001i	0.186707	−	0.492325i
$656$	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	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$	0.798922	+	0.212029i	0.0310980	+	0.00825322i
$661$	11.4772	−	6.62638i	0.446412	−	0.257736i	−0.259901	−	0.965635i	$-0.583690\pi$
$661$	11.4772	−	6.62638i	0.446412	−	0.257736i	0.706314	+	0.707899i	$0.250357\pi$
$662$	5.71584	+	9.90012i	0.222152	+	0.384779i
$663$	29.7308	−	21.5256i	1.15465	−	0.835983i
$664$			16.7169i			0.648740i
$665$	−5.79407	−	28.3696i	−0.224684	−	1.10013i
$666$	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
$670$	−1.91048	−	11.7547i	−0.0738081	−	0.454122i
$671$	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
$675$	−20.9712	+	15.3365i	−0.807182	+	0.590303i
$676$	−15.9545	−	27.6339i	−0.613633	−	1.06284i
$677$	−28.5000	−	16.4545i	−1.09534	−	0.632397i	−0.160350	−	0.987060i	$-0.551262\pi$
$677$	−28.5000	−	16.4545i	−1.09534	−	0.632397i	−0.934994	+	0.354663i	$0.884596\pi$
$678$	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	$-0.184669\pi$
$683$	−1.47723	−	2.55863i	−0.0565245	−	0.0979032i	−0.892903	+	0.450249i	$0.851335\pi$
$684$	−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
$690$	−17.7809	−	17.6962i	−0.676906	−	0.673685i
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$			11.5207i			0.437952i
$693$	−1.62935	−	0.463461i	−0.0618939	−	0.0176054i
$694$	−6.52277			−0.247601
$695$	−2.70182	−	16.6236i	−0.102486	−	0.630569i
$696$	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
$700$	−2.12082	+	13.0576i	−0.0801596	+	0.493533i
$701$			7.03320i			0.265640i	0.991140	+	0.132820i	$0.0424033\pi$
$701$			7.03320i			0.265640i	−0.991140	+	0.132820i	$0.957597\pi$
$702$	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
$705$	−29.0292	−	7.70418i	−1.09330	−	0.290156i
$706$			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	−0.947190	−	0.320672i	$-0.896091\pi$
$709$	−5.21584	+	9.03410i	−0.195885	+	0.339283i	0.751305	+	0.659955i	$0.229425\pi$
$710$	−4.22889	−	1.60374i	−0.158707	−	0.0601874i
$711$	−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	−0.0320690	+	0.999486i	$0.510210\pi$
$719$	−23.6398	+	40.9453i	−0.881614	+	1.52700i	−0.849545	+	0.527515i	$0.823124\pi$
$720$	−1.04456	+	6.62638i	−0.0389283	+	0.246951i
$721$	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
$725$	−3.20279	−	9.59268i	−0.118949	−	0.356263i
$726$	11.1270	+	15.3685i	0.412962	+	0.570377i
$727$	−23.6076			−0.875556			−0.437778	−	0.899083i	$-0.644234\pi$
$727$	−23.6076			−0.875556			−0.437778	+	0.899083i	$0.644234\pi$
$728$	−9.47723	−	14.9848i	−0.351249	−	0.555374i
$729$	22.0000	−	15.6525i	0.814815	−	0.579721i
$730$	−26.4601	+	4.30055i	−0.979334	+	0.159170i
$731$	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	−0.306569	−	0.951849i	$-0.599181\pi$
$733$	18.1677	−	31.4674i	0.671041	−	1.16228i	0.977609	−	0.210428i	$-0.0674858\pi$
$734$	8.11562			0.299553
$735$	4.81967	−	26.6790i	0.177776	−	0.984071i
$736$	−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	0.904258	−	0.426986i	$-0.140425\pi$
$739$	2.23861	+	3.87739i	0.0823487	+	0.142632i	−0.821910	+	0.569618i	$0.807091\pi$
$740$	2.55948	+	15.7478i	0.0940884	+	0.578901i
$741$	−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	$-0.616009\pi$
$743$	−19.4317			−0.712879			−0.356440	+	0.934318i	$0.616009\pi$
$744$	0.423441	−	0.306579i	0.0155241	−	0.0112397i
$745$	5.12132	+	1.94218i	0.187631	+	0.0711561i
$746$	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
$750$	−1.21584	−	19.3267i	−0.0443961	−	0.705712i
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−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
$760$	10.2329	+	3.88068i	0.371187	+	0.140767i
$761$	4.76492	−	8.25308i	0.172728	−	0.299174i	−0.766645	−	0.642072i	$-0.778075\pi$
$761$	4.76492	−	8.25308i	0.172728	−	0.299174i	0.939373	+	0.342898i	$0.111408\pi$
$762$	21.5507	+	9.63774i	0.780698	+	0.349139i
$763$	−15.2833	+	29.1247i	−0.553293	+	1.05438i
$764$			1.59580i			0.0577341i
$765$	−13.3379	+	16.4955i	−0.482231	+	0.596396i
$766$	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	$0.174076\pi$
$769$			28.8412i			1.04004i	−0.854154	+	0.520020i	$0.825924\pi$
$770$	0.945018	−	0.837348i	0.0340561	−	0.0301759i
$771$	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	$-0.840241\pi$
$773$	−24.9772	+	14.4206i	−0.898368	+	0.518673i	−0.0216979	+	0.999765i	$0.506907\pi$
$774$	5.76471	+	1.89419i	0.207208	+	0.0680853i
$775$	−1.00070	+	1.12962i	−0.0359463	+	0.0405771i
$776$	−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
$780$	18.3963	+	18.3087i	0.658693	+	0.655558i
$781$	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	0.989830	+	0.142256i	$0.0454356\pi$
$787$	17.3402	+	30.0341i	0.618112	+	1.07060i	−0.371718	+	0.928346i	$0.621231\pi$
$788$	−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
$795$	13.7257	+	13.6604i	0.486800	+	0.484483i
$796$	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
$800$	−3.74264	−	3.31552i	−0.132322	−	0.117221i
$801$	−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
$805$	−37.5448	+	7.66795i	−1.32328	+	0.270260i
$806$		−	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	−0.965429	−	0.260666i	$-0.916058\pi$
$809$	−34.7686	+	20.0737i	−1.22240	+	0.705753i	−0.256971	+	0.966419i	$0.582725\pi$
$810$	1.00138	+	20.0997i	0.0351848	+	0.706231i
$811$			6.70527i			0.235454i	0.993046	+	0.117727i	$0.0375608\pi$
$811$			6.70527i			0.235454i	−0.993046	+	0.117727i	$0.962439\pi$
$812$	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
$815$	−30.7279	−	11.6531i	−1.07635	−	0.408190i
$816$	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	0.998930	+	0.0462557i	$0.0147289\pi$
$821$	44.0814	+	25.4504i	1.53845	+	0.888226i	0.539523	+	0.841971i	$0.318604\pi$
$822$	−12.8822	+	1.33242i	−0.449319	+	0.0464734i
$823$	−28.2199	+	16.2927i	−0.983682	+	0.567929i	−0.903380	−	0.428841i	$-0.858922\pi$
$823$	−28.2199	+	16.2927i	−0.983682	+	0.567929i	−0.0803025	+	0.996771i	$0.525589\pi$
$824$	−5.28720	+	9.15769i	−0.184188	+	0.319023i
$825$	−1.07676	+	1.50225i	−0.0374881	+	0.0523015i
$826$	−6.95445	−	10.9960i	−0.241976	−	0.382598i
$827$	39.9089			1.38777			0.693884	−	0.720087i	$-0.255898\pi$
$827$	39.9089			1.38777			0.693884	+	0.720087i	$0.255898\pi$
$828$	−19.0203	+	3.97713i	−0.661002	+	0.138215i
$829$	−16.3069	+	9.41481i	−0.566363	+	0.326990i	−0.755696	−	0.654923i	$-0.772701\pi$
$829$	−16.3069	+	9.41481i	−0.566363	+	0.326990i	0.189332	+	0.981913i	$0.439368\pi$
$830$	−34.9511	−	13.2547i	−1.21317	−	0.460077i
$831$	−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
$835$	−5.26707	−	32.4069i	−0.182275	−	1.12149i
$836$	−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	$0.722784\pi$
$840$	7.54858	+	6.92957i	0.260451	+	0.239093i
$841$	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
$845$	70.4264	−	11.4463i	2.42274	−	0.393766i
$846$	−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
$850$	−5.00735	−	14.9975i	−0.171751	−	0.514412i
$851$	−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	$-0.125702\pi$
$853$	53.9165			1.84607			0.923033	+	0.384720i	$0.125702\pi$
$854$	8.11562	+	4.25871i	0.277711	+	0.145730i
$855$	32.4317	+	5.11240i	1.10914	+	0.174840i
$856$	−2.73861	+	4.74342i	−0.0936039	+	0.162127i
$857$	34.9545	−	20.1810i	1.19402	−	0.689369i	0.234805	−	0.972042i	$-0.424555\pi$
$857$	34.9545	−	20.1810i	1.19402	−	0.689369i	0.959216	+	0.282674i	$0.0912214\pi$
$858$	−0.254862	−	2.46408i	−0.00870085	−	0.0841223i
$859$	−15.5228	−	8.96208i	−0.529630	−	0.305782i	0.211236	−	0.977435i	$-0.432251\pi$
$859$	−15.5228	−	8.96208i	−0.529630	−	0.305782i	−0.740866	+	0.671653i	$0.765585\pi$
$860$	−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	$-0.748225\pi$
$863$	7.76139	−	13.4431i	0.264201	−	0.457609i	0.967354	+	0.253429i	$0.0815585\pi$
$864$	3.84418	+	3.49604i	0.130782	+	0.118938i
$865$	−24.0872	−	9.13469i	−0.818988	−	0.310589i
$866$		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
$870$	−7.57156	−	2.00945i	−0.256700	−	0.0681267i
$871$	−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
$875$	−25.6190	−	14.7875i	−0.866079	−	0.499908i
$876$	−8.47723	+	18.9557i	−0.286419	+	0.640452i
$877$	36.6169	+	21.1408i	1.23647	+	0.713874i	0.968370	−	0.249518i	$-0.0802723\pi$
$877$	36.6169	+	21.1408i	1.23647	+	0.713874i	0.268096	+	0.963392i	$0.413606\pi$
$878$	−19.6931	+	11.3698i	−0.664609	+	0.383712i
$879$	−0.818370	−	7.91224i	−0.0276029	−	0.266873i
$880$	0.0765585	+	0.471045i	0.00258079	+	0.0158789i
$881$	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
$885$	13.4993	+	13.4351i	0.453775	+	0.451615i
$886$	18.4772	+	32.0035i	0.620755	+	1.07518i
$887$	3.00000	+	1.73205i	0.100730	+	0.0581566i	0.549519	−	0.835481i	$-0.314811\pi$
$887$	3.00000	+	1.73205i	0.100730	+	0.0581566i	−0.448789	+	0.893638i	$0.648144\pi$
$888$	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
$900$	−13.0260	−	7.43794i	−0.434201	−	0.247931i
$901$	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
$905$	1.13437	+	6.97948i	0.0377078	+	0.232006i
$906$	3.44572	−	0.356394i	0.114476	−	0.0118404i
$907$	8.48528	−	4.89898i	0.281749	−	0.162668i	−0.352466	−	0.935825i	$-0.614657\pi$
$907$	8.48528	−	4.89898i	0.281749	−	0.162668i	0.634215	+	0.773157i	$0.281323\pi$
$908$	−9.00000	−	5.19615i	−0.298675	−	0.172440i
$909$	−22.6274	−	25.2982i	−0.750504	−	0.839089i
$910$	38.8442	−	7.93335i	1.28767	−	0.262988i
$911$		−	15.1238i		−	0.501073i	−0.968107	−	0.250537i	$-0.919393\pi$
$911$		−	15.1238i		−	0.501073i	0.968107	−	0.250537i	$-0.0806071\pi$
$912$	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
$915$	−12.9675	−	3.44150i	−0.428692	−	0.113772i
$916$			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	−0.464256	−	0.885701i	$-0.653678\pi$
$919$	16.2158	−	28.0867i	0.534911	−	0.926493i	0.999168	−	0.0407925i	$-0.0129883\pi$
$920$	5.13575	−	13.5424i	0.169321	−	0.446479i
$921$	−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	−0.992225	−	0.124461i	$-0.960280\pi$
$929$	−11.8360	+	20.5005i	−0.388326	+	0.672601i	0.603898	+	0.797061i	$0.293613\pi$
$930$	0.305242	+	1.12840i	0.0100093	+	0.0370018i
$931$	−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
$935$	−0.535123	+	1.41106i	−0.0175004	+	0.0461465i
$936$	19.6786	−	4.11478i	0.643216	−	0.134496i
$937$	22.6918			0.741310			0.370655	−	0.928771i	$-0.379133\pi$
$937$	22.6918			0.741310			0.370655	+	0.928771i	$0.379133\pi$
$938$	−11.9089	+	7.53185i	−0.388839	+	0.245924i
$939$	−16.4317	+	36.7423i	−0.536228	+	1.19904i
$940$	−2.78179	−	17.1156i	−0.0907320	−	0.558250i
$941$	2.49098	+	4.31450i	0.0812036	+	0.140649i	0.903767	−	0.428024i	$-0.140790\pi$
$941$	2.49098	+	4.31450i	0.0812036	+	0.140649i	−0.822564	+	0.568673i	$0.807457\pi$
$942$	15.1448	−	1.56644i	0.493445	−	0.0510375i
$943$	−21.7033	+	37.5912i	−0.706756	+	1.22414i
$944$	4.91754			0.160052
$945$	26.4212	+	15.7137i	0.859482	+	0.511165i
$946$	0.431677			0.0140350
$947$	16.4317	−	28.4605i	0.533958	−	0.924842i	−0.465255	−	0.885177i	$-0.654037\pi$
$947$	16.4317	−	28.4605i	0.533958	−	0.924842i	0.999213	−	0.0396654i	$-0.0126292\pi$
$948$	−0.900667	+	0.0931568i	−0.0292523	+	0.00302559i
$949$	40.1703	+	69.5770i	1.30398	+	2.25856i
$950$	−16.2272	+	18.3177i	−0.526481	+	0.594305i
$951$	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	$-0.367044\pi$
$953$	25.0455			0.811305			0.405652	+	0.914027i	$0.367044\pi$
$954$	14.6825	−	3.07008i	0.475362	−	0.0993976i
$955$	−3.33646	−	1.26530i	−0.107965	−	0.0409442i
$956$		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
$960$	−3.73861	+	1.01132i	−0.120663	+	0.0326403i
$961$	−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
$970$	2.77776	−	7.32465i	0.0891886	−	0.235180i
$971$	−0.490070	+	0.848827i	−0.0157271	+	0.0272401i	−0.873782	−	0.486318i	$-0.838340\pi$
$971$	−0.490070	+	0.848827i	−0.0157271	+	0.0272401i	0.858055	+	0.513558i	$0.171673\pi$
$972$	13.4350	+	7.90569i	0.430929	+	0.253575i
$973$	−16.8417	+	10.6516i	−0.539921	+	0.341476i
$974$		−	36.6308i		−	1.17373i
$975$	−52.8657	+	23.9456i	−1.69306	+	0.766872i
$976$	−3.00000	+	1.73205i	−0.0960277	+	0.0554416i
$977$	19.9545	+	34.5621i	0.638399	+	1.10574i	0.985784	+	0.168018i	$0.0537365\pi$
$977$	19.9545	+	34.5621i	0.638399	+	1.10574i	−0.347385	+	0.937723i	$0.612930\pi$
$978$	−20.6190	+	14.9285i	−0.659321	+	0.477359i
$979$			2.25681i			0.0721278i
$980$	15.1971	−	3.74812i	0.485453	−	0.119729i
$981$	−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	$-0.847961\pi$
$983$	−29.2842	+	16.9072i	−0.934020	+	0.539257i	−0.0459391	+	0.998944i	$0.514628\pi$
$984$	11.5456	−	1.19417i	0.368060	−	0.0380688i
$985$	19.8640	−	3.22848i	0.632918	−	0.102868i
$986$	−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
$990$	0.514043	+	1.33621i	0.0163374	+	0.0424676i
$991$	−10.7386	−	18.5998i	−0.341123	−	0.590843i	0.643518	−	0.765431i	$-0.277474\pi$
$991$	−10.7386	−	18.5998i	−0.341123	−	0.590843i	−0.984642	+	0.174588i	$0.944141\pi$
$992$	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	$-0.0877745\pi$
$997$	7.74597	+	13.4164i	0.245317	+	0.424902i	−0.716904	+	0.697172i	$0.754441\pi$
$998$	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.e.89.1	yes	8
3.2	odd	2		210.2.t.f.89.3	yes	8
5.2	odd	4		1050.2.s.i.551.3		16
5.3	odd	4		1050.2.s.i.551.6		16
5.4	even	2		210.2.t.f.89.4	yes	8
7.2	even	3		1470.2.d.f.1469.5		8
7.3	odd	6	inner	210.2.t.e.59.2	yes	8
7.5	odd	6		1470.2.d.f.1469.4		8
15.2	even	4		1050.2.s.i.551.5		16
15.8	even	4		1050.2.s.i.551.4		16
15.14	odd	2	inner	210.2.t.e.89.2	yes	8
21.2	odd	6		1470.2.d.e.1469.8		8
21.5	even	6		1470.2.d.e.1469.1		8
21.17	even	6		210.2.t.f.59.4	yes	8
35.3	even	12		1050.2.s.i.101.4		16
35.9	even	6		1470.2.d.e.1469.4		8
35.17	even	12		1050.2.s.i.101.5		16
35.19	odd	6		1470.2.d.e.1469.5		8
35.24	odd	6		210.2.t.f.59.3	yes	8
105.17	odd	12		1050.2.s.i.101.3		16
105.38	odd	12		1050.2.s.i.101.6		16
105.44	odd	6		1470.2.d.f.1469.1		8
105.59	even	6	inner	210.2.t.e.59.1	✓	8
105.89	even	6		1470.2.d.f.1469.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.1	✓	8	105.59	even	6	inner
210.2.t.e.59.2	yes	8	7.3	odd	6	inner
210.2.t.e.89.1	yes	8	1.1	even	1	trivial
210.2.t.e.89.2	yes	8	15.14	odd	2	inner
210.2.t.f.59.3	yes	8	35.24	odd	6
210.2.t.f.59.4	yes	8	21.17	even	6
210.2.t.f.89.3	yes	8	3.2	odd	2
210.2.t.f.89.4	yes	8	5.4	even	2
1050.2.s.i.101.3		16	105.17	odd	12
1050.2.s.i.101.4		16	35.3	even	12
1050.2.s.i.101.5		16	35.17	even	12
1050.2.s.i.101.6		16	105.38	odd	12
1050.2.s.i.551.3		16	5.2	odd	4
1050.2.s.i.551.4		16	15.8	even	4
1050.2.s.i.551.5		16	15.2	even	4
1050.2.s.i.551.6		16	5.3	odd	4
1470.2.d.e.1469.1		8	21.5	even	6
1470.2.d.e.1469.4		8	35.9	even	6
1470.2.d.e.1469.5		8	35.19	odd	6
1470.2.d.e.1469.8		8	21.2	odd	6
1470.2.d.f.1469.1		8	105.44	odd	6
1470.2.d.f.1469.4		8	7.5	odd	6
1470.2.d.f.1469.5		8	7.2	even	3
1470.2.d.f.1469.8		8	105.89	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.72286 + 0.178197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 0.358719i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} +1.00000 q^{8} +(2.93649 - 0.614017i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.72286 + 0.178197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 0.358719i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} +1.00000 q^{8} +(2.93649 - 0.614017i) q^{9} +(-0.792893 + 2.09077i) q^{10} +(0.184829 - 0.106711i) q^{11} +(1.01575 + 1.40294i) q^{12} +6.70141 q^{13} +(2.64360 - 0.106711i) q^{14} +(-3.73861 + 1.01132i) 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} +(4.74264 - 1.58346i) q^{25} +(-3.35071 + 5.80359i) q^{26} +(-4.94975 + 1.58114i) q^{27} +(-1.22938 + 2.34278i) q^{28} -2.02265i q^{29} +(0.993475 - 3.74340i) q^{30} +(-0.261387 + 0.150912i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.299418 + 0.216784i) q^{33} -3.16228i q^{34} +(-3.92344 - 4.42793i) 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} +(2.20711 - 0.358719i) q^{40} -6.70141 q^{41} +(-4.53553 + 0.654929i) q^{42} -2.02265i q^{43} +(-0.184829 - 0.106711i) q^{44} +(6.26089 - 2.40858i) 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} +(2.74514 + 2.73207i) q^{60} +(3.00000 + 1.73205i) q^{61} -0.301824i q^{62} +(-5.52581 - 5.69784i) q^{63} +1.00000 q^{64} +(14.7907 - 2.40393i) 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} +(5.79642 - 1.18383i) q^{70} +2.02265i q^{71} +(2.93649 - 0.614017i) q^{72} +(5.99430 + 10.3824i) q^{73} +(6.17913 - 3.56752i) q^{74} +(-7.88874 + 3.57321i) q^{75} -4.89433i q^{76} +(-0.500000 - 0.262377i) q^{77} +(4.73861 - 10.5959i) q^{78} +(-0.261387 + 0.452736i) q^{79} +(-0.792893 + 2.09077i) 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} +(-1.04456 + 6.62638i) q^{90} +(-9.47723 - 14.9848i) q^{91} -6.47723 q^{92} +(0.423441 - 0.306579i) q^{93} +(-6.71584 + 3.87739i) q^{94} +(10.2329 + 3.88068i) 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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