LMFDB - Embedded newform 570.2.k.b.77.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.12
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.581841 + 1.63140i) q^{3} -1.00000i q^{4} +(1.36872 - 1.76822i) q^{5} +(0.742149 + 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.32292 - 1.89843i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.581841 + 1.63140i) q^{3} -1.00000i q^{4} +(1.36872 - 1.76822i) q^{5} +(0.742149 + 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.32292 - 1.89843i) q^{9} +(-0.282491 - 2.21815i) q^{10} -6.12593i q^{11} +(1.63140 + 0.581841i) q^{12} +(-0.754312 + 0.754312i) q^{13} +0.145422 q^{14} +(2.08830 + 3.26175i) q^{15} -1.00000 q^{16} +(2.33294 - 2.33294i) q^{17} +(-2.98495 + 0.300162i) q^{18} -1.00000i q^{19} +(-1.76822 - 1.36872i) q^{20} +(-0.227584 + 0.107925i) q^{21} +(-4.33169 - 4.33169i) q^{22} +(6.21428 + 6.21428i) q^{23} +(1.56500 - 0.742149i) q^{24} +(-1.25322 - 4.84040i) q^{25} +1.06676i q^{26} +(4.44866 - 2.68503i) q^{27} +(0.102829 - 0.102829i) q^{28} -2.40803 q^{29} +(3.78306 + 0.829756i) q^{30} +3.69470 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.99383 + 3.56432i) q^{33} -3.29927i q^{34} +(0.322567 - 0.0410804i) q^{35} +(-1.89843 + 2.32292i) q^{36} +(-3.66137 - 3.66137i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-0.791694 - 1.66947i) q^{39} +(-2.21815 + 0.282491i) q^{40} +10.3063i q^{41} +(-0.0846123 + 0.237241i) q^{42} +(-0.994803 + 0.994803i) q^{43} -6.12593 q^{44} +(-6.53627 + 1.50903i) q^{45} +8.78832 q^{46} +(4.88564 - 4.88564i) q^{47} +(0.581841 - 1.63140i) q^{48} -6.97885i q^{49} +(-4.30884 - 2.53652i) q^{50} +(2.44855 + 5.16335i) q^{51} +(0.754312 + 0.754312i) q^{52} +(-2.86461 - 2.86461i) q^{53} +(1.24708 - 5.04428i) q^{54} +(-10.8320 - 8.38468i) q^{55} -0.145422i q^{56} +(1.63140 + 0.581841i) q^{57} +(-1.70274 + 1.70274i) q^{58} +7.12402 q^{59} +(3.26175 - 2.08830i) q^{60} -10.3444 q^{61} +(2.61255 - 2.61255i) q^{62} +(-0.0436501 - 0.434076i) q^{63} +1.00000i q^{64} +(0.301350 + 2.36623i) q^{65} +(9.58706 - 4.54636i) q^{66} +(4.37645 + 4.37645i) q^{67} +(-2.33294 - 2.33294i) q^{68} +(-13.7537 + 6.52225i) q^{69} +(0.199041 - 0.257138i) q^{70} -0.311021i q^{71} +(0.300162 + 2.98495i) q^{72} +(0.755853 - 0.755853i) q^{73} -5.17797 q^{74} +(8.62579 + 0.771844i) q^{75} -1.00000 q^{76} +(0.629921 - 0.629921i) q^{77} +(-1.74031 - 0.620684i) q^{78} +14.3107i q^{79} +(-1.36872 + 1.76822i) q^{80} +(1.79194 + 8.81981i) q^{81} +(7.28768 + 7.28768i) q^{82} +(11.1880 + 11.1880i) q^{83} +(0.107925 + 0.227584i) q^{84} +(-0.932016 - 7.31829i) q^{85} +1.40686i q^{86} +(1.40109 - 3.92846i) q^{87} +(-4.33169 + 4.33169i) q^{88} -2.30981 q^{89} +(-3.55480 + 5.68888i) q^{90} -0.155130 q^{91} +(6.21428 - 6.21428i) q^{92} +(-2.14973 + 6.02753i) q^{93} -6.90934i q^{94} +(-1.76822 - 1.36872i) q^{95} +(-0.742149 - 1.56500i) q^{96} +(-0.595441 - 0.595441i) q^{97} +(-4.93479 - 4.93479i) q^{98} +(-11.6296 + 14.2301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.581841	+	1.63140i	−0.335926	+	0.941888i
$3$	−0.581841	+	1.63140i	−0.335926	+	0.941888i
$4$		−	1.00000i		−	0.500000i
$5$	1.36872	−	1.76822i	0.612110	−	0.790773i
$5$	1.36872	−	1.76822i	0.612110	−	0.790773i
$6$	0.742149	+	1.56500i	0.302981	+	0.638907i
$7$	0.102829	+	0.102829i	0.0388656	+	0.0388656i	0.726272	−	0.687407i	$-0.241251\pi$
$7$	0.102829	+	0.102829i	0.0388656	+	0.0388656i	−0.687407	+	0.726272i	$0.741251\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.32292	−	1.89843i	−0.774307	−	0.632810i
$10$	−0.282491	−	2.21815i	−0.0893316	−	0.701441i
$11$		−	6.12593i		−	1.84704i	−0.383553	−	0.923519i	$-0.625300\pi$
$11$		−	6.12593i		−	1.84704i	0.383553	−	0.923519i	$-0.374700\pi$
$12$	1.63140	+	0.581841i	0.470944	+	0.167963i
$13$	−0.754312	+	0.754312i	−0.209209	+	0.209209i	−0.803931	−	0.594722i	$-0.797262\pi$
$13$	−0.754312	+	0.754312i	−0.209209	+	0.209209i	0.594722	+	0.803931i	$0.297262\pi$
$14$	0.145422			0.0388656
$15$	2.08830	+	3.26175i	0.539196	+	0.842180i
$16$	−1.00000			−0.250000
$17$	2.33294	−	2.33294i	0.565820	−	0.565820i	−0.365134	−	0.930955i	$-0.618977\pi$
$17$	2.33294	−	2.33294i	0.565820	−	0.565820i	0.930955	+	0.365134i	$0.118977\pi$
$18$	−2.98495	+	0.300162i	−0.703559	+	0.0707490i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−1.76822	−	1.36872i	−0.395386	−	0.306055i
$21$	−0.227584	+	0.107925i	−0.0496630	+	0.0235511i
$22$	−4.33169	−	4.33169i	−0.923519	−	0.923519i
$23$	6.21428	+	6.21428i	1.29577	+	1.29577i	0.931163	+	0.364604i	$0.118796\pi$
$23$	6.21428	+	6.21428i	1.29577	+	1.29577i	0.364604	+	0.931163i	$0.381204\pi$
$24$	1.56500	−	0.742149i	0.319454	−	0.151491i
$25$	−1.25322	−	4.84040i	−0.250644	−	0.968079i
$26$			1.06676i			0.209209i
$27$	4.44866	−	2.68503i	0.856146	−	0.516734i
$28$	0.102829	−	0.102829i	0.0194328	−	0.0194328i
$29$	−2.40803			−0.447160			−0.223580	−	0.974686i	$-0.571774\pi$
$29$	−2.40803			−0.447160			−0.223580	+	0.974686i	$0.571774\pi$
$30$	3.78306	+	0.829756i	0.690688	+	0.151492i
$31$	3.69470			0.663588			0.331794	−	0.943352i	$-0.392346\pi$
$31$	3.69470			0.663588			0.331794	+	0.943352i	$0.392346\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	9.99383	+	3.56432i	1.73970	+	0.620468i
$34$		−	3.29927i		−	0.565820i
$35$	0.322567	−	0.0410804i	0.0545238	−	0.00694385i
$36$	−1.89843	+	2.32292i	−0.316405	+	0.387154i
$37$	−3.66137	−	3.66137i	−0.601926	−	0.601926i	0.338897	−	0.940823i	$-0.389946\pi$
$37$	−3.66137	−	3.66137i	−0.601926	−	0.601926i	−0.940823	+	0.338897i	$0.889946\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$	−0.791694	−	1.66947i	−0.126773	−	0.267330i
$40$	−2.21815	+	0.282491i	−0.350721	+	0.0446658i
$41$			10.3063i			1.60958i	0.593561	+	0.804789i	$0.297722\pi$
$41$			10.3063i			1.60958i	−0.593561	+	0.804789i	$0.702278\pi$
$42$	−0.0846123	+	0.237241i	−0.0130560	+	0.0366070i
$43$	−0.994803	+	0.994803i	−0.151706	+	0.151706i	−0.778880	−	0.627174i	$-0.784212\pi$
$43$	−0.994803	+	0.994803i	−0.151706	+	0.151706i	0.627174	+	0.778880i	$0.284212\pi$
$44$	−6.12593			−0.923519
$45$	−6.53627	+	1.50903i	−0.974370	+	0.224952i
$46$	8.78832			1.29577
$47$	4.88564	−	4.88564i	0.712645	−	0.712645i	−0.254443	−	0.967088i	$-0.581892\pi$
$47$	4.88564	−	4.88564i	0.712645	−	0.712645i	0.967088	+	0.254443i	$0.0818922\pi$
$48$	0.581841	−	1.63140i	0.0839815	−	0.235472i
$49$		−	6.97885i		−	0.996979i
$50$	−4.30884	−	2.53652i	−0.609361	−	0.358718i
$51$	2.44855	+	5.16335i	0.342866	+	0.723014i
$52$	0.754312	+	0.754312i	0.104604	+	0.104604i
$53$	−2.86461	−	2.86461i	−0.393484	−	0.393484i	0.482443	−	0.875927i	$-0.339749\pi$
$53$	−2.86461	−	2.86461i	−0.393484	−	0.393484i	−0.875927	+	0.482443i	$0.839749\pi$
$54$	1.24708	−	5.04428i	0.169706	−	0.686440i
$55$	−10.8320	−	8.38468i	−1.46059	−	1.13059i
$56$		−	0.145422i		−	0.0194328i
$57$	1.63140	+	0.581841i	0.216084	+	0.0770667i
$58$	−1.70274	+	1.70274i	−0.223580	+	0.223580i
$59$	7.12402			0.927469			0.463734	−	0.885974i	$-0.346509\pi$
$59$	7.12402			0.927469			0.463734	+	0.885974i	$0.346509\pi$
$60$	3.26175	−	2.08830i	0.421090	−	0.269598i
$61$	−10.3444			−1.32446			−0.662230	−	0.749301i	$-0.730390\pi$
$61$	−10.3444			−1.32446			−0.662230	+	0.749301i	$0.730390\pi$
$62$	2.61255	−	2.61255i	0.331794	−	0.331794i
$63$	−0.0436501	−	0.434076i	−0.00549940	−	0.0546884i
$64$			1.00000i			0.125000i
$65$	0.301350	+	2.36623i	0.0373779	+	0.293495i
$66$	9.58706	−	4.54636i	1.18009	−	0.559618i
$67$	4.37645	+	4.37645i	0.534669	+	0.534669i	0.921958	−	0.387289i	$-0.126589\pi$
$67$	4.37645	+	4.37645i	0.534669	+	0.534669i	−0.387289	+	0.921958i	$0.626589\pi$
$68$	−2.33294	−	2.33294i	−0.282910	−	0.282910i
$69$	−13.7537	+	6.52225i	−1.65575	+	0.785186i
$70$	0.199041	−	0.257138i	0.0237900	−	0.0307338i
$71$		−	0.311021i		−	0.0369114i	−0.999830	−	0.0184557i	$-0.994125\pi$
$71$		−	0.311021i		−	0.0369114i	0.999830	−	0.0184557i	$-0.00587497\pi$
$72$	0.300162	+	2.98495i	0.0353745	+	0.351779i
$73$	0.755853	−	0.755853i	0.0884659	−	0.0884659i	−0.661489	−	0.749955i	$-0.730075\pi$
$73$	0.755853	−	0.755853i	0.0884659	−	0.0884659i	0.749955	+	0.661489i	$0.230075\pi$
$74$	−5.17797			−0.601926
$75$	8.62579	+	0.771844i	0.996020	+	0.0891248i
$76$	−1.00000			−0.114708
$77$	0.629921	−	0.629921i	0.0717862	−	0.0717862i
$78$	−1.74031	−	0.620684i	−0.197051	−	0.0702786i
$79$			14.3107i			1.61008i	0.593218	+	0.805042i	$0.297857\pi$
$79$			14.3107i			1.61008i	−0.593218	+	0.805042i	$0.702143\pi$
$80$	−1.36872	+	1.76822i	−0.153027	+	0.197693i
$81$	1.79194	+	8.81981i	0.199104	+	0.979978i
$82$	7.28768	+	7.28768i	0.804789	+	0.804789i
$83$	11.1880	+	11.1880i	1.22804	+	1.22804i	0.964704	+	0.263337i	$0.0848230\pi$
$83$	11.1880	+	11.1880i	1.22804	+	1.22804i	0.263337	+	0.964704i	$0.415177\pi$
$84$	0.107925	+	0.227584i	0.0117755	+	0.0248315i
$85$	−0.932016	−	7.31829i	−0.101091	−	0.793780i
$86$			1.40686i			0.151706i
$87$	1.40109	−	3.92846i	0.150213	−	0.421175i
$88$	−4.33169	+	4.33169i	−0.461759	+	0.461759i
$89$	−2.30981			−0.244840			−0.122420	−	0.992478i	$-0.539065\pi$
$89$	−2.30981			−0.244840			−0.122420	+	0.992478i	$0.539065\pi$
$90$	−3.55480	+	5.68888i	−0.374709	+	0.599661i
$91$	−0.155130			−0.0162620
$92$	6.21428	−	6.21428i	0.647883	−	0.647883i
$93$	−2.14973	+	6.02753i	−0.222917	+	0.625026i
$94$		−	6.90934i		−	0.712645i
$95$	−1.76822	−	1.36872i	−0.181416	−	0.140428i
$96$	−0.742149	−	1.56500i	−0.0757453	−	0.159727i
$97$	−0.595441	−	0.595441i	−0.0604579	−	0.0604579i	0.676231	−	0.736689i	$-0.263612\pi$
$97$	−0.595441	−	0.595441i	−0.0604579	−	0.0604579i	−0.736689	+	0.676231i	$0.763612\pi$
$98$	−4.93479	−	4.93479i	−0.498489	−	0.498489i
$99$	−11.6296	+	14.2301i	−1.16882	+	1.43018i
$100$	−4.84040	+	1.25322i	−0.484040	+	0.125322i
$101$			7.75006i			0.771160i	0.922674	+	0.385580i	$0.125999\pi$
$101$			7.75006i			0.771160i	−0.922674	+	0.385580i	$0.874001\pi$
$102$	5.38243	+	1.91965i	0.532940	+	0.190074i
$103$	−11.2131	+	11.2131i	−1.10486	+	1.10486i	−0.111042	+	0.993816i	$0.535419\pi$
$103$	−11.2131	+	11.2131i	−1.10486	+	1.10486i	−0.993816	+	0.111042i	$0.964581\pi$
$104$	1.06676			0.104604
$105$	−0.120664	+	0.550138i	−0.0117756	+	0.0536880i
$106$	−4.05117			−0.393484
$107$	−10.9025	+	10.9025i	−1.05399	+	1.05399i	−0.0555308	+	0.998457i	$0.517685\pi$
$107$	−10.9025	+	10.9025i	−1.05399	+	1.05399i	−0.998457	+	0.0555308i	$0.982315\pi$
$108$	−2.68503	−	4.44866i	−0.258367	−	0.428073i
$109$			0.958181i			0.0917771i	0.998947	+	0.0458886i	$0.0146119\pi$
$109$			0.958181i			0.0917771i	−0.998947	+	0.0458886i	$0.985388\pi$
$110$	−13.5882	+	1.73052i	−1.29559	+	0.164999i
$111$	8.10350	−	3.84282i	0.769150	−	0.364745i
$112$	−0.102829	−	0.102829i	−0.00971639	−	0.00971639i
$113$	−4.94211	−	4.94211i	−0.464915	−	0.464915i	0.435348	−	0.900262i	$-0.356625\pi$
$113$	−4.94211	−	4.94211i	−0.464915	−	0.464915i	−0.900262	+	0.435348i	$0.856625\pi$
$114$	1.56500	−	0.742149i	0.146575	−	0.0695087i
$115$	19.4938	−	2.48262i	1.81781	−	0.231506i
$116$			2.40803i			0.223580i
$117$	3.18422	−	0.320201i	0.294381	−	0.0296026i
$118$	5.03744	−	5.03744i	0.463734	−	0.463734i
$119$	0.479786			0.0439819
$120$	0.829756	−	3.78306i	0.0757460	−	0.345344i
$121$	−26.5270			−2.41155
$122$	−7.31457	+	7.31457i	−0.662230	+	0.662230i
$123$	−16.8137	−	5.99664i	−1.51604	−	0.540699i
$124$		−	3.69470i		−	0.331794i
$125$	−10.2742	−	4.40918i	−0.918952	−	0.394369i
$126$	−0.337803	−	0.276073i	−0.0300939	−	0.0245945i
$127$	8.80226	+	8.80226i	0.781074	+	0.781074i	0.980012	−	0.198938i	$-0.0637492\pi$
$127$	8.80226	+	8.80226i	0.781074	+	0.781074i	−0.198938	+	0.980012i	$0.563749\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−1.04410	−	2.20174i	−0.0919281	−	0.193852i
$130$	1.88627	+	1.46009i	0.165436	+	0.128059i
$131$		−	22.1054i		−	1.93136i	−0.259735	−	0.965680i	$-0.583635\pi$
$131$		−	22.1054i		−	1.93136i	0.259735	−	0.965680i	$-0.416365\pi$
$132$	3.56432	−	9.99383i	0.310234	−	0.869852i
$133$	0.102829	−	0.102829i	0.00891637	−	0.00891637i
$134$	6.18924			0.534669
$135$	1.34124	−	11.5413i	0.115436	−	0.993315i
$136$	−3.29927			−0.282910
$137$	1.58617	−	1.58617i	0.135516	−	0.135516i	−0.636095	−	0.771611i	$-0.719451\pi$
$137$	1.58617	−	1.58617i	0.135516	−	0.135516i	0.771611	+	0.636095i	$0.219451\pi$
$138$	−5.11340	+	14.3373i	−0.435282	+	1.22047i
$139$			11.1773i			0.948045i	0.880513	+	0.474022i	$0.157198\pi$
$139$			11.1773i			0.948045i	−0.880513	+	0.474022i	$0.842802\pi$
$140$	−0.0410804	−	0.322567i	−0.00347192	−	0.0272619i
$141$	5.12777	+	10.8131i	0.431836	+	0.910627i
$142$	−0.219925	−	0.219925i	−0.0184557	−	0.0184557i
$143$	4.62086	+	4.62086i	0.386416	+	0.386416i
$144$	2.32292	+	1.89843i	0.193577	+	0.158202i
$145$	−3.29592	+	4.25793i	−0.273711	+	0.353602i
$146$		−	1.06894i		−	0.0884659i
$147$	11.3853	+	4.06058i	0.939043	+	0.334911i
$148$	−3.66137	+	3.66137i	−0.300963	+	0.300963i
$149$	9.86195			0.807922			0.403961	−	0.914776i	$-0.367633\pi$
$149$	9.86195			0.807922			0.403961	+	0.914776i	$0.367633\pi$
$150$	6.64513	−	5.55358i	0.542573	−	0.453448i
$151$	−7.90117			−0.642988			−0.321494	−	0.946912i	$-0.604185\pi$
$151$	−7.90117			−0.642988			−0.321494	+	0.946912i	$0.604185\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$	−9.84815	+	0.990317i	−0.796176	+	0.0800624i
$154$		−	0.890843i		−	0.0717862i
$155$	5.05701	−	6.53306i	0.406189	−	0.524748i
$156$	−1.66947	+	0.791694i	−0.133665	+	0.0633863i
$157$	3.96376	+	3.96376i	0.316342	+	0.316342i	0.847360	−	0.531018i	$-0.178190\pi$
$157$	3.96376	+	3.96376i	0.316342	+	0.316342i	−0.531018	+	0.847360i	$0.678190\pi$
$158$	10.1192	+	10.1192i	0.805042	+	0.805042i
$159$	6.34006	−	3.00657i	0.502800	−	0.238437i
$160$	0.282491	+	2.21815i	0.0223329	+	0.175360i
$161$			1.27801i			0.100721i
$162$	7.50363	+	4.96945i	0.589541	+	0.390437i
$163$	6.35109	−	6.35109i	0.497456	−	0.497456i	−0.413189	−	0.910645i	$-0.635585\pi$
$163$	6.35109	−	6.35109i	0.497456	−	0.497456i	0.910645	+	0.413189i	$0.135585\pi$
$164$	10.3063			0.804789
$165$	19.9813	−	12.7928i	1.55554	−	0.995916i
$166$	15.8222			1.22804
$167$	14.9173	−	14.9173i	1.15434	−	1.15434i	0.168664	−	0.985674i	$-0.446055\pi$
$167$	14.9173	−	14.9173i	1.15434	−	1.15434i	0.985674	−	0.168664i	$-0.0539453\pi$
$168$	0.237241	+	0.0846123i	0.0183035	+	0.00652798i
$169$			11.8620i			0.912464i
$170$	−5.83385	−	4.51578i	−0.447435	−	0.346344i
$171$	−1.89843	+	2.32292i	−0.145176	+	0.177638i
$172$	0.994803	+	0.994803i	0.0758530	+	0.0758530i
$173$	6.19199	+	6.19199i	0.470769	+	0.470769i	0.902163	−	0.431395i	$-0.141978\pi$
$173$	6.19199	+	6.19199i	0.470769	+	0.470769i	−0.431395	+	0.902163i	$0.641978\pi$
$174$	−1.78712	−	3.76856i	−0.135481	−	0.285694i
$175$	0.368865	−	0.626598i	0.0278836	−	0.0473664i
$176$			6.12593i			0.461759i
$177$	−4.14505	+	11.6221i	−0.311561	+	0.873572i
$178$	−1.63328	+	1.63328i	−0.122420	+	0.122420i
$179$	−8.96071			−0.669755			−0.334877	−	0.942262i	$-0.608695\pi$
$179$	−8.96071			−0.669755			−0.334877	+	0.942262i	$0.608695\pi$
$180$	1.50903	+	6.53627i	0.112476	+	0.487185i
$181$	8.58326			0.637989			0.318994	−	0.947757i	$-0.396655\pi$
$181$	8.58326			0.637989			0.318994	+	0.947757i	$0.396655\pi$
$182$	−0.109693	+	0.109693i	−0.00813101	+	0.00813101i
$183$	6.01877	−	16.8758i	0.444920	−	1.24749i
$184$		−	8.78832i		−	0.647883i
$185$	−11.4855	+	1.46273i	−0.844432	+	0.107542i
$186$	2.74202	+	5.78220i	0.201055	+	0.423971i
$187$	−14.2914	−	14.2914i	−1.04509	−	1.04509i
$188$	−4.88564	−	4.88564i	−0.356322	−	0.356322i
$189$	0.733548	+	0.181352i	0.0533578	+	0.0131914i
$190$	−2.21815	+	0.282491i	−0.160922	+	0.0204941i
$191$			15.3727i			1.11233i	0.831073	+	0.556164i	$0.187727\pi$
$191$			15.3727i			1.11233i	−0.831073	+	0.556164i	$0.812273\pi$
$192$	−1.63140	−	0.581841i	−0.117736	−	0.0419907i
$193$	16.5440	−	16.5440i	1.19087	−	1.19087i	0.214042	−	0.976824i	$-0.431337\pi$
$193$	16.5440	−	16.5440i	1.19087	−	1.19087i	0.976824	−	0.214042i	$-0.0686629\pi$
$194$	−0.842081			−0.0604579
$195$	−4.03561	−	0.885149i	−0.288996	−	0.0633868i
$196$	−6.97885			−0.498489
$197$	3.02772	−	3.02772i	0.215716	−	0.215716i	−0.590974	−	0.806690i	$-0.701257\pi$
$197$	3.02772	−	3.02772i	0.215716	−	0.215716i	0.806690	+	0.590974i	$0.201257\pi$
$198$	1.83877	+	18.2856i	0.130676	+	1.29950i
$199$		−	8.01713i		−	0.568319i	−0.958777	−	0.284160i	$-0.908285\pi$
$199$		−	8.01713i		−	0.568319i	0.958777	−	0.284160i	$-0.0917146\pi$
$200$	−2.53652	+	4.30884i	−0.179359	+	0.304681i
$201$	−9.68614	+	4.59334i	−0.683208	+	0.323989i
$202$	5.48012	+	5.48012i	0.385580	+	0.385580i
$203$	−0.247615	−	0.247615i	−0.0173791	−	0.0173791i
$204$	5.16335	−	2.44855i	0.361507	−	0.171433i
$205$	18.2239	+	14.1065i	1.27281	+	0.985238i
$206$			15.8577i			1.10486i
$207$	−2.63792	−	26.2327i	−0.183348	−	1.82330i
$208$	0.754312	−	0.754312i	0.0523021	−	0.0523021i
$209$	−6.12593			−0.423740
$210$	0.303684	+	0.474329i	0.0209562	+	0.0327318i
$211$	−4.50891			−0.310406			−0.155203	−	0.987883i	$-0.549603\pi$
$211$	−4.50891			−0.310406			−0.155203	+	0.987883i	$0.549603\pi$
$212$	−2.86461	+	2.86461i	−0.196742	+	0.196742i
$213$	0.507400	+	0.180965i	0.0347664	+	0.0123995i
$214$			15.4185i			1.05399i
$215$	0.397427	+	3.12064i	0.0271043	+	0.212826i
$216$	−5.04428	−	1.24708i	−0.343220	−	0.0848530i
$217$	0.379921	+	0.379921i	0.0257907	+	0.0257907i
$218$	0.677536	+	0.677536i	0.0458886	+	0.0458886i
$219$	0.793312	+	1.67288i	0.0536070	+	0.113043i
$220$	−8.38468	+	10.8320i	−0.565295	+	0.730294i
$221$			3.51953i			0.236749i
$222$	3.01275	−	8.44733i	0.202203	−	0.566947i
$223$	8.46796	−	8.46796i	0.567057	−	0.567057i	−0.364246	−	0.931303i	$-0.618673\pi$
$223$	8.46796	−	8.46796i	0.567057	−	0.567057i	0.931303	+	0.364246i	$0.118673\pi$
$224$	−0.145422			−0.00971639
$225$	−6.27802	+	13.6230i	−0.418535	+	0.908201i
$226$	−6.98920			−0.464915
$227$	6.20188	−	6.20188i	0.411633	−	0.411633i	−0.470674	−	0.882307i	$-0.655989\pi$
$227$	6.20188	−	6.20188i	0.411633	−	0.411633i	0.882307	+	0.470674i	$0.155989\pi$
$228$	0.581841	−	1.63140i	0.0385334	−	0.108042i
$229$		−	11.8117i		−	0.780536i	−0.920701	−	0.390268i	$-0.872382\pi$
$229$		−	11.8117i		−	0.780536i	0.920701	−	0.390268i	$-0.127618\pi$
$230$	12.0287	−	15.5397i	0.793151	−	1.02466i
$231$	0.661138	+	1.39417i	0.0434997	+	0.0917294i
$232$	1.70274	+	1.70274i	0.111790	+	0.111790i
$233$	10.5412	+	10.5412i	0.690575	+	0.690575i	0.962358	−	0.271783i	$-0.0876134\pi$
$233$	10.5412	+	10.5412i	0.690575	+	0.690575i	−0.271783	+	0.962358i	$0.587613\pi$
$234$	2.02517	−	2.47800i	0.132389	−	0.161992i
$235$	−1.95183	−	15.3260i	−0.127323	−	0.999757i
$236$		−	7.12402i		−	0.463734i
$237$	−23.3465	−	8.32658i	−1.51652	−	0.540869i
$238$	0.339260	−	0.339260i	0.0219909	−	0.0219909i
$239$	6.27313			0.405775			0.202887	−	0.979202i	$-0.434967\pi$
$239$	6.27313			0.405775			0.202887	+	0.979202i	$0.434967\pi$
$240$	−2.08830	−	3.26175i	−0.134799	−	0.210545i
$241$	13.3425			0.859466			0.429733	−	0.902956i	$-0.358608\pi$
$241$	13.3425			0.859466			0.429733	+	0.902956i	$0.358608\pi$
$242$	−18.7574	+	18.7574i	−1.20577	+	1.20577i
$243$	−15.4312	−	2.20836i	−0.989914	−	0.141666i
$244$			10.3444i			0.662230i
$245$	−12.3402	−	9.55209i	−0.788384	−	0.610260i
$246$	−16.1294	+	7.64884i	−1.02837	+	0.487672i
$247$	0.754312	+	0.754312i	0.0479957	+	0.0479957i
$248$	−2.61255	−	2.61255i	−0.165897	−	0.165897i
$249$	−24.7617	+	11.7424i	−1.56921	+	0.744146i
$250$	−10.3827	+	4.14720i	−0.656661	+	0.262292i
$251$		−	26.7821i		−	1.69047i	−0.534392	−	0.845237i	$-0.679459\pi$
$251$		−	26.7821i		−	1.69047i	0.534392	−	0.845237i	$-0.320541\pi$
$252$	−0.434076	+	0.0436501i	−0.0273442	+	0.00274970i
$253$	38.0682	−	38.0682i	2.39333	−	2.39333i
$254$	12.4483			0.781074
$255$	12.4813	+	2.73759i	0.781611	+	0.171434i
$256$	1.00000			0.0625000
$257$	6.20250	−	6.20250i	0.386901	−	0.386901i	−0.486679	−	0.873581i	$-0.661792\pi$
$257$	6.20250	−	6.20250i	0.386901	−	0.386901i	0.873581	+	0.486679i	$0.161792\pi$
$258$	−2.29516	−	0.818571i	−0.142890	−	0.0509620i
$259$		−	0.752988i		−	0.0467884i
$260$	2.36623	−	0.301350i	0.146748	−	0.0186889i
$261$	5.59367	+	4.57148i	0.346239	+	0.282967i
$262$	−15.6309	−	15.6309i	−0.965680	−	0.965680i
$263$	10.7076	+	10.7076i	0.660261	+	0.660261i	0.955442	−	0.295181i	$-0.0953798\pi$
$263$	10.7076	+	10.7076i	0.660261	+	0.660261i	−0.295181	+	0.955442i	$0.595380\pi$
$264$	−4.54636	−	9.58706i	−0.279809	−	0.590043i
$265$	−8.98610	+	1.14442i	−0.552012	+	0.0703011i
$266$		−	0.145422i		−	0.00891637i
$267$	1.34394	−	3.76823i	0.0822480	−	0.230612i
$268$	4.37645	−	4.37645i	0.267335	−	0.267335i
$269$	7.39882			0.451114			0.225557	−	0.974230i	$-0.427580\pi$
$269$	7.39882			0.451114			0.225557	+	0.974230i	$0.427580\pi$
$270$	−7.21251	−	9.10932i	−0.438939	−	0.554375i
$271$	−32.2520			−1.95917			−0.979585	−	0.201030i	$-0.935571\pi$
$271$	−32.2520			−1.95917			−0.979585	+	0.201030i	$0.935571\pi$
$272$	−2.33294	+	2.33294i	−0.141455	+	0.141455i
$273$	0.0902608	−	0.253078i	0.00546283	−	0.0153170i
$274$		−	2.24319i		−	0.135516i
$275$	−29.6519	+	7.67712i	−1.78808	+	0.462948i
$276$	6.52225	+	13.7537i	0.392593	+	0.827875i
$277$	0.315711	+	0.315711i	0.0189693	+	0.0189693i	0.716528	−	0.697559i	$-0.245730\pi$
$277$	0.315711	+	0.315711i	0.0189693	+	0.0189693i	−0.697559	+	0.716528i	$0.745730\pi$
$278$	7.90353	+	7.90353i	0.474022	+	0.474022i
$279$	−8.58251	−	7.01413i	−0.513821	−	0.419925i
$280$	−0.257138	−	0.199041i	−0.0153669	−	0.0118950i
$281$		−	2.25919i		−	0.134772i	−0.997727	−	0.0673860i	$-0.978534\pi$
$281$		−	2.25919i		−	0.134772i	0.997727	−	0.0673860i	$-0.0214659\pi$
$282$	11.2719	+	4.02014i	0.671232	+	0.239396i
$283$	−17.3455	+	17.3455i	−1.03109	+	1.03109i	−0.0315844	+	0.999501i	$0.510055\pi$
$283$	−17.3455	+	17.3455i	−1.03109	+	1.03109i	−0.999501	+	0.0315844i	$0.989945\pi$
$284$	−0.311021			−0.0184557
$285$	3.26175	−	2.08830i	0.193209	−	0.123700i
$286$	6.53489			0.386416
$287$	−1.05979	+	1.05979i	−0.0625572	+	0.0625572i
$288$	2.98495	−	0.300162i	0.175890	−	0.0176872i
$289$			6.11480i			0.359694i
$290$	0.680248	+	5.34138i	0.0399455	+	0.313657i
$291$	1.31785	−	0.624950i	0.0772539	−	0.0366352i
$292$	−0.755853	−	0.755853i	−0.0442330	−	0.0442330i
$293$	−1.37475	−	1.37475i	−0.0803135	−	0.0803135i	0.665809	−	0.746122i	$-0.268087\pi$
$293$	−1.37475	−	1.37475i	−0.0803135	−	0.0803135i	−0.746122	+	0.665809i	$0.768087\pi$
$294$	10.9219	−	5.17935i	0.636977	−	0.302066i
$295$	9.75078	−	12.5969i	0.567712	−	0.733417i
$296$			5.17797i			0.300963i
$297$	−16.4483	−	27.2522i	−0.954427	−	1.58133i
$298$	6.97345	−	6.97345i	0.403961	−	0.403961i
$299$	−9.37501			−0.542171
$300$	0.771844	−	8.62579i	0.0445624	−	0.498010i
$301$	−0.204588			−0.0117923
$302$	−5.58697	+	5.58697i	−0.321494	+	0.321494i
$303$	−12.6434	−	4.50930i	−0.726346	−	0.259053i
$304$			1.00000i			0.0573539i
$305$	−14.1585	+	18.2911i	−0.810715	+	1.04735i
$306$	−6.26343	+	7.66395i	−0.358057	+	0.438119i
$307$	2.48065	+	2.48065i	0.141578	+	0.141578i	0.774343	−	0.632765i	$-0.218080\pi$
$307$	2.48065	+	2.48065i	0.141578	+	0.141578i	−0.632765	+	0.774343i	$0.718080\pi$
$308$	−0.629921	−	0.629921i	−0.0358931	−	0.0358931i
$309$	−11.7688	−	24.8172i	−0.669502	−	1.41180i
$310$	−1.04372	−	8.19542i	−0.0592794	−	0.465468i
$311$			1.76203i			0.0999158i	0.998751	+	0.0499579i	$0.0159087\pi$
$311$			1.76203i			0.0999158i	−0.998751	+	0.0499579i	$0.984091\pi$
$312$	−0.620684	+	1.74031i	−0.0351393	+	0.0985256i
$313$	−9.58013	+	9.58013i	−0.541501	+	0.541501i	−0.923969	−	0.382468i	$-0.875074\pi$
$313$	−9.58013	+	9.58013i	−0.541501	+	0.541501i	0.382468	+	0.923969i	$0.375074\pi$
$314$	5.60560			0.316342
$315$	−0.827287	−	0.516945i	−0.0466123	−	0.0291265i
$316$	14.3107			0.805042
$317$	−7.82453	+	7.82453i	−0.439469	+	0.439469i	−0.891833	−	0.452364i	$-0.850581\pi$
$317$	−7.82453	+	7.82453i	−0.439469	+	0.439469i	0.452364	+	0.891833i	$0.350581\pi$
$318$	2.35713	−	6.60907i	0.132182	−	0.370618i
$319$			14.7514i			0.825922i
$320$	1.76822	+	1.36872i	0.0988466	+	0.0765137i
$321$	−11.4428	−	24.1299i	−0.638677	−	1.34680i
$322$	0.903691	+	0.903691i	0.0503607	+	0.0503607i
$323$	−2.33294	−	2.33294i	−0.129808	−	0.129808i
$324$	8.81981	−	1.79194i	0.489989	−	0.0995521i
$325$	4.59649	+	2.70585i	0.254967	+	0.150094i
$326$		−	8.98180i		−	0.497456i
$327$	−1.56318	−	0.557509i	−0.0864438	−	0.0308303i
$328$	7.28768	−	7.28768i	0.402395	−	0.402395i
$329$	1.00477			0.0553947
$330$	5.08303	−	23.1747i	0.279811	−	1.27573i
$331$	−10.1328			−0.556947			−0.278473	−	0.960444i	$-0.589828\pi$
$331$	−10.1328			−0.556947			−0.278473	+	0.960444i	$0.589828\pi$
$332$	11.1880	−	11.1880i	0.614020	−	0.614020i
$333$	1.55423	+	15.4559i	0.0851713	+	0.846981i
$334$		−	21.0963i		−	1.15434i
$335$	13.7287	−	1.74841i	0.750078	−	0.0955257i
$336$	0.227584	−	0.107925i	0.0124157	−	0.00588777i
$337$	8.59971	+	8.59971i	0.468456	+	0.468456i	0.901414	−	0.432958i	$-0.142530\pi$
$337$	8.59971	+	8.59971i	0.468456	+	0.468456i	−0.432958	+	0.901414i	$0.642530\pi$
$338$	8.38772	+	8.38772i	0.456232	+	0.456232i
$339$	10.9381	−	5.18703i	0.594075	−	0.281721i
$340$	−7.31829	+	0.932016i	−0.396890	+	0.0505457i
$341$		−	22.6335i		−	1.22567i
$342$	0.300162	+	2.98495i	0.0162309	+	0.161407i
$343$	1.43743	−	1.43743i	0.0776137	−	0.0776137i
$344$	1.40686			0.0758530
$345$	−7.29216	+	33.2467i	−0.392597	+	1.78994i
$346$	8.75680			0.470769
$347$	−7.91015	+	7.91015i	−0.424639	+	0.424639i	−0.886797	−	0.462158i	$-0.847075\pi$
$347$	−7.91015	+	7.91015i	−0.424639	+	0.424639i	0.462158	+	0.886797i	$0.347075\pi$
$348$	−3.92846	−	1.40109i	−0.210587	−	0.0751064i
$349$			18.5835i			0.994752i	0.867535	+	0.497376i	$0.165703\pi$
$349$			18.5835i			0.994752i	−0.867535	+	0.497376i	$0.834297\pi$
$350$	−0.182245	−	0.703899i	−0.00974140	−	0.0376250i
$351$	−1.33033	+	5.38103i	−0.0710079	+	0.287218i
$352$	4.33169	+	4.33169i	0.230880	+	0.230880i
$353$	3.74671	+	3.74671i	0.199417	+	0.199417i	0.799750	−	0.600333i	$-0.204965\pi$
$353$	3.74671	+	3.74671i	0.199417	+	0.199417i	−0.600333	+	0.799750i	$0.704965\pi$
$354$	5.28709	+	11.1491i	0.281006	+	0.592566i
$355$	−0.549955	−	0.425701i	−0.0291886	−	0.0225938i
$356$			2.30981i			0.122420i
$357$	−0.279159	+	0.782721i	−0.0147747	+	0.0414260i
$358$	−6.33618	+	6.33618i	−0.334877	+	0.334877i
$359$	17.1601			0.905676			0.452838	−	0.891593i	$-0.350412\pi$
$359$	17.1601			0.905676			0.452838	+	0.891593i	$0.350412\pi$
$360$	5.68888	+	3.55480i	0.299831	+	0.187354i
$361$	−1.00000			−0.0526316
$362$	6.06928	−	6.06928i	0.318994	−	0.318994i
$363$	15.4345	−	43.2762i	0.810102	−	2.27141i
$364$			0.155130i			0.00813101i
$365$	−0.301966	−	2.37107i	−0.0158056	−	0.124107i
$366$	−7.67706	−	16.1889i	−0.401286	−	0.846207i
$367$	24.6532	+	24.6532i	1.28689	+	1.28689i	0.936668	+	0.350218i	$0.113892\pi$
$367$	24.6532	+	24.6532i	1.28689	+	1.28689i	0.350218	+	0.936668i	$0.386108\pi$
$368$	−6.21428	−	6.21428i	−0.323942	−	0.323942i
$369$	19.5658	−	23.9408i	1.01856	−	1.24631i
$370$	−7.08718	+	9.15579i	−0.368445	+	0.475987i
$371$		−	0.589127i		−	0.0305860i
$372$	6.02753	+	2.14973i	0.312513	+	0.111458i
$373$	−10.9785	+	10.9785i	−0.568446	+	0.568446i	−0.931693	−	0.363247i	$-0.881668\pi$
$373$	−10.9785	+	10.9785i	−0.568446	+	0.568446i	0.363247	+	0.931693i	$0.381668\pi$
$374$	−20.2111			−1.04509
$375$	13.1711	−	14.1959i	0.680151	−	0.733072i
$376$	−6.90934			−0.356322
$377$	1.81641	−	1.81641i	0.0935497	−	0.0935497i
$378$	0.646932	−	0.390461i	0.0332746	−	0.0200832i
$379$		−	31.8871i		−	1.63793i	−0.573843	−	0.818966i	$-0.694548\pi$
$379$		−	31.8871i		−	1.63793i	0.573843	−	0.818966i	$-0.305452\pi$
$380$	−1.36872	+	1.76822i	−0.0702138	+	0.0907079i
$381$	−19.4815	+	9.23848i	−0.998068	+	0.473302i
$382$	10.8701	+	10.8701i	0.556164	+	0.556164i
$383$	3.71847	+	3.71847i	0.190005	+	0.190005i	0.795698	−	0.605693i	$-0.207104\pi$
$383$	3.71847	+	3.71847i	0.190005	+	0.190005i	−0.605693	+	0.795698i	$0.707104\pi$
$384$	−1.56500	+	0.742149i	−0.0798634	+	0.0378727i
$385$	−0.251655	−	1.97603i	−0.0128255	−	0.100708i
$386$		−	23.3968i		−	1.19087i
$387$	4.19941	−	0.422288i	0.213468	−	0.0214661i
$388$	−0.595441	+	0.595441i	−0.0302289	+	0.0302289i
$389$	27.6876			1.40382			0.701908	−	0.712268i	$-0.252332\pi$
$389$	27.6876			1.40382			0.701908	+	0.712268i	$0.252332\pi$
$390$	−3.47950	+	2.22771i	−0.176191	+	0.112804i
$391$	28.9951			1.46634
$392$	−4.93479	+	4.93479i	−0.249245	+	0.249245i
$393$	36.0628	+	12.8618i	1.81913	+	0.648794i
$394$		−	4.28184i		−	0.215716i
$395$	25.3046	+	19.5874i	1.27321	+	0.985548i
$396$	14.2301	+	11.6296i	0.715088	+	0.584412i
$397$	−0.647982	−	0.647982i	−0.0325213	−	0.0325213i	0.690659	−	0.723180i	$-0.257321\pi$
$397$	−0.647982	−	0.647982i	−0.0325213	−	0.0325213i	−0.723180	+	0.690659i	$0.757321\pi$
$398$	−5.66897	−	5.66897i	−0.284160	−	0.284160i
$399$	0.107925	+	0.227584i	0.00540299	+	0.0113935i
$400$	1.25322	+	4.84040i	0.0626609	+	0.242020i
$401$		−	28.9315i		−	1.44477i	−0.691491	−	0.722385i	$-0.743046\pi$
$401$		−	28.9315i		−	1.44477i	0.691491	−	0.722385i	$-0.256954\pi$
$402$	−3.60115	+	10.0971i	−0.179609	+	0.503599i
$403$	−2.78696	+	2.78696i	−0.138828	+	0.138828i
$404$	7.75006			0.385580
$405$	18.0480	+	8.90329i	0.896814	+	0.442408i
$406$	−0.350180			−0.0173791
$407$	−22.4293	+	22.4293i	−1.11178	+	1.11178i
$408$	1.91965	−	5.38243i	0.0950369	−	0.266470i
$409$		−	15.5261i		−	0.767717i	−0.923392	−	0.383859i	$-0.874595\pi$
$409$		−	15.5261i		−	0.767717i	0.923392	−	0.383859i	$-0.125405\pi$
$410$	22.8610	−	2.91145i	1.12902	−	0.143786i
$411$	1.66478	+	3.51058i	0.0821176	+	0.173164i
$412$	11.2131	+	11.2131i	0.552429	+	0.552429i
$413$	0.732553	+	0.732553i	0.0360466	+	0.0360466i
$414$	−20.4146	−	16.6840i	−1.00332	−	0.819974i
$415$	35.0960	−	4.46963i	1.72280	−	0.219406i
$416$		−	1.06676i		−	0.0523021i
$417$	−18.2346	−	6.50340i	−0.892953	−	0.318473i
$418$	−4.33169	+	4.33169i	−0.211870	+	0.211870i
$419$	6.96160			0.340096			0.170048	−	0.985436i	$-0.445608\pi$
$419$	6.96160			0.340096			0.170048	+	0.985436i	$0.445608\pi$
$420$	0.550138	+	0.120664i	0.0268440	+	0.00588782i
$421$	−29.4232			−1.43400			−0.717000	−	0.697073i	$-0.754485\pi$
$421$	−29.4232			−1.43400			−0.717000	+	0.697073i	$0.754485\pi$
$422$	−3.18828	+	3.18828i	−0.155203	+	0.155203i
$423$	−20.6240	+	2.07393i	−1.00277	+	0.100838i
$424$			4.05117i			0.196742i
$425$	−14.2160	−	8.36867i	−0.689578	−	0.405940i
$426$	0.486747	−	0.230824i	0.0235830	−	0.0111835i
$427$	−1.06370	−	1.06370i	−0.0514759	−	0.0514759i
$428$	10.9025	+	10.9025i	0.526994	+	0.526994i
$429$	−10.2271	+	4.84986i	−0.493768	+	0.234154i
$430$	2.48765	+	1.92560i	0.119965	+	0.0928607i
$431$			19.6775i			0.947834i	0.880570	+	0.473917i	$0.157160\pi$
$431$			19.6775i			0.947834i	−0.880570	+	0.473917i	$0.842840\pi$
$432$	−4.44866	+	2.68503i	−0.214036	+	0.129184i
$433$	−22.2656	+	22.2656i	−1.07002	+	1.07002i	−0.0726615	+	0.997357i	$0.523149\pi$
$433$	−22.2656	+	22.2656i	−1.07002	+	1.07002i	−0.997357	+	0.0726615i	$0.976851\pi$
$434$	0.537290			0.0257907
$435$	−5.02869	−	7.85439i	−0.241107	−	0.376589i
$436$	0.958181			0.0458886
$437$	6.21428	−	6.21428i	0.297269	−	0.297269i
$438$	1.74386	+	0.621952i	0.0833250	+	0.0297180i
$439$			1.96512i			0.0937899i	0.998900	+	0.0468950i	$0.0149326\pi$
$439$			1.96512i			0.0937899i	−0.998900	+	0.0468950i	$0.985067\pi$
$440$	1.73052	+	13.5882i	0.0824994	+	0.647794i
$441$	−13.2489	+	16.2113i	−0.630898	+	0.771968i
$442$	2.48868	+	2.48868i	0.118374	+	0.118374i
$443$	−10.2690	−	10.2690i	−0.487896	−	0.487896i	0.419746	−	0.907642i	$-0.362119\pi$
$443$	−10.2690	−	10.2690i	−0.487896	−	0.487896i	−0.907642	+	0.419746i	$0.862119\pi$
$444$	−3.84282	−	8.10350i	−0.182372	−	0.384575i
$445$	−3.16148	+	4.08426i	−0.149869	+	0.193613i
$446$		−	11.9755i		−	0.567057i
$447$	−5.73809	+	16.0888i	−0.271402	+	0.760973i
$448$	−0.102829	+	0.102829i	−0.00485820	+	0.00485820i
$449$	−28.7172			−1.35525			−0.677623	−	0.735409i	$-0.736990\pi$
$449$	−28.7172			−1.35525			−0.677623	+	0.735409i	$0.736990\pi$
$450$	5.19369	+	14.0722i	0.244833	+	0.663368i
$451$	63.1359			2.97295
$452$	−4.94211	+	4.94211i	−0.232457	+	0.232457i
$453$	4.59722	−	12.8900i	0.215996	−	0.605623i
$454$		−	8.77078i		−	0.411633i
$455$	−0.212329	+	0.274304i	−0.00995414	+	0.0128596i
$456$	−0.742149	−	1.56500i	−0.0347543	−	0.0732877i
$457$	13.0668	+	13.0668i	0.611239	+	0.611239i	0.943269	−	0.332030i	$-0.107733\pi$
$457$	13.0668	+	13.0668i	0.611239	+	0.611239i	−0.332030	+	0.943269i	$0.607733\pi$
$458$	−8.35210	−	8.35210i	−0.390268	−	0.390268i
$459$	4.11445	−	16.6425i	0.192046	−	0.776804i
$460$	−2.48262	−	19.4938i	−0.115753	−	0.908904i
$461$		−	35.6982i		−	1.66263i	−0.555800	−	0.831316i	$-0.687588\pi$
$461$		−	35.6982i		−	1.66263i	0.555800	−	0.831316i	$-0.312412\pi$
$462$	1.45332	+	0.518329i	0.0676146	+	0.0241148i
$463$	−18.7714	+	18.7714i	−0.872381	+	0.872381i	−0.992731	−	0.120350i	$-0.961598\pi$
$463$	−18.7714	+	18.7714i	−0.872381	+	0.872381i	0.120350	+	0.992731i	$0.461598\pi$
$464$	2.40803			0.111790
$465$	7.71564	+	12.0512i	0.357804	+	0.558861i
$466$	14.9075			0.690575
$467$	5.01672	−	5.01672i	0.232146	−	0.232146i	−0.581442	−	0.813588i	$-0.697511\pi$
$467$	5.01672	−	5.01672i	0.232146	−	0.232146i	0.813588	+	0.581442i	$0.197511\pi$
$468$	−0.320201	−	3.18422i	−0.0148013	−	0.147190i
$469$			0.900050i			0.0415604i
$470$	−12.2173	−	9.45695i	−0.563540	−	0.436217i
$471$	−8.77274	+	4.16019i	−0.404227	+	0.191692i
$472$	−5.03744	−	5.03744i	−0.231867	−	0.231867i
$473$	6.09409	+	6.09409i	0.280207	+	0.280207i
$474$	−22.3963	+	10.6207i	−1.02869	+	0.487825i
$475$	−4.84040	+	1.25322i	−0.222093	+	0.0575016i
$476$		−	0.479786i		−	0.0219909i
$477$	1.21601	+	12.0925i	0.0556772	+	0.553678i
$478$	4.43577	−	4.43577i	0.202887	−	0.202887i
$479$	−6.25041			−0.285589			−0.142794	−	0.989752i	$-0.545609\pi$
$479$	−6.25041			−0.285589			−0.142794	+	0.989752i	$0.545609\pi$
$480$	−3.78306	−	0.829756i	−0.172672	−	0.0378730i
$481$	5.52364			0.251856
$482$	9.43457	−	9.43457i	0.429733	−	0.429733i
$483$	−2.08495	−	0.743599i	−0.0948683	−	0.0338349i
$484$			26.5270i			1.20577i
$485$	−1.86786	+	0.237880i	−0.0848153	+	0.0108016i
$486$	−12.4731	+	9.34999i	−0.565790	+	0.424124i
$487$	−11.4086	−	11.4086i	−0.516973	−	0.516973i	0.399681	−	0.916654i	$-0.369121\pi$
$487$	−11.4086	−	11.4086i	−0.516973	−	0.516973i	−0.916654	+	0.399681i	$0.869121\pi$
$488$	7.31457	+	7.31457i	0.331115	+	0.331115i
$489$	6.66584	+	14.0565i	0.301439	+	0.635656i
$490$	−15.4802	+	1.97147i	−0.699322	+	0.0890617i
$491$		−	10.2744i		−	0.463675i	−0.972754	−	0.231838i	$-0.925526\pi$
$491$		−	10.2744i		−	0.463675i	0.972754	−	0.231838i	$-0.0744738\pi$
$492$	−5.99664	+	16.8137i	−0.270350	+	0.758022i
$493$	−5.61779	+	5.61779i	−0.253012	+	0.253012i
$494$	1.06676			0.0479957
$495$	9.24420	+	40.0407i	0.415496	+	1.79970i
$496$	−3.69470			−0.165897
$497$	0.0319819	−	0.0319819i	0.00143458	−	0.00143458i
$498$	−9.20600	+	25.8123i	−0.412531	+	1.15668i
$499$			26.3326i			1.17881i	0.807839	+	0.589404i	$0.200637\pi$
$499$			26.3326i			1.17881i	−0.807839	+	0.589404i	$0.799363\pi$
$500$	−4.40918	+	10.2742i	−0.197184	+	0.459476i
$501$	15.6566	+	33.0156i	0.699485	+	1.47503i
$502$	−18.9378	−	18.9378i	−0.845237	−	0.845237i
$503$	−18.5070	−	18.5070i	−0.825188	−	0.825188i	0.161658	−	0.986847i	$-0.448316\pi$
$503$	−18.5070	−	18.5070i	−0.825188	−	0.825188i	−0.986847	+	0.161658i	$0.948316\pi$
$504$	−0.276073	+	0.337803i	−0.0122973	+	0.0150469i
$505$	13.7038	+	10.6077i	0.609812	+	0.472034i
$506$		−	53.8366i		−	2.39333i
$507$	−19.3517	−	6.90181i	−0.859439	−	0.306520i
$508$	8.80226	−	8.80226i	0.390537	−	0.390537i
$509$	40.9795			1.81638			0.908191	−	0.418555i	$-0.137463\pi$
$509$	40.9795			1.81638			0.908191	+	0.418555i	$0.137463\pi$
$510$	10.7614	−	6.88986i	0.476523	−	0.305088i
$511$	0.155447			0.00687656
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.68503	−	4.44866i	−0.118547	−	0.196413i
$514$		−	8.77166i		−	0.386901i
$515$	4.47966	+	35.1748i	0.197397	+	1.54999i
$516$	−2.20174	+	1.04410i	−0.0969261	+	0.0459641i
$517$	−29.9291	−	29.9291i	−1.31628	−	1.31628i
$518$	−0.532443	−	0.532443i	−0.0233942	−	0.0233942i
$519$	−13.7044	+	6.49886i	−0.601555	+	0.285268i
$520$	1.46009	−	1.88627i	0.0640293	−	0.0827182i
$521$		−	26.2549i		−	1.15025i	−0.818066	−	0.575125i	$-0.804954\pi$
$521$		−	26.2549i		−	1.15025i	0.818066	−	0.575125i	$-0.195046\pi$
$522$	7.18784	−	0.722800i	0.314603	−	0.0316361i
$523$	12.9426	−	12.9426i	0.565942	−	0.565942i	−0.365047	−	0.930989i	$-0.618947\pi$
$523$	12.9426	−	12.9426i	0.565942	−	0.565942i	0.930989	+	0.365047i	$0.118947\pi$
$524$	−22.1054			−0.965680
$525$	0.807611	+	0.966346i	0.0352470	+	0.0421748i
$526$	15.1429			0.660261
$527$	8.61951	−	8.61951i	0.375472	−	0.375472i
$528$	−9.99383	−	3.56432i	−0.434926	−	0.155117i
$529$			54.2345i			2.35802i
$530$	−5.54491	+	7.16336i	−0.240855	+	0.311156i
$531$	−16.5485	−	13.5244i	−0.718146	−	0.586911i
$532$	−0.102829	−	0.102829i	−0.00445819	−	0.00445819i
$533$	−7.77419	−	7.77419i	−0.336738	−	0.336738i
$534$	−1.71423	−	3.61485i	−0.0741818	−	0.156430i
$535$	4.35560	+	34.2006i	0.188309	+	1.47862i
$536$		−	6.18924i		−	0.267335i
$537$	5.21371	−	14.6185i	0.224988	−	0.630834i
$538$	5.23176	−	5.23176i	0.225557	−	0.225557i
$539$	−42.7520			−1.84146
$540$	−11.5413	−	1.34124i	−0.496657	−	0.0577180i
$541$	17.1469			0.737202			0.368601	−	0.929588i	$-0.379837\pi$
$541$	17.1469			0.737202			0.368601	+	0.929588i	$0.379837\pi$
$542$	−22.8056	+	22.8056i	−0.979585	+	0.979585i
$543$	−4.99409	+	14.0027i	−0.214317	+	0.600914i
$544$			3.29927i			0.141455i
$545$	1.69428	+	1.31148i	0.0725749	+	0.0561777i
$546$	−0.115129	−	0.242778i	−0.00492709	−	0.0103899i
$547$	0.690907	+	0.690907i	0.0295410	+	0.0295410i	0.721723	−	0.692182i	$-0.243350\pi$
$547$	0.690907	+	0.690907i	0.0295410	+	0.0295410i	−0.692182	+	0.721723i	$0.743350\pi$
$548$	−1.58617	−	1.58617i	−0.0677580	−	0.0677580i
$549$	24.0292	+	19.6380i	1.02554	+	0.838131i
$550$	−15.5385	+	26.3956i	−0.662566	+	1.12551i
$551$			2.40803i			0.102586i
$552$	14.3373	+	5.11340i	0.610234	+	0.217641i
$553$	−1.47155	+	1.47155i	−0.0625768	+	0.0625768i
$554$	0.446483			0.0189693
$555$	4.29645	−	19.5885i	0.182374	−	0.831487i
$556$	11.1773			0.474022
$557$	17.1913	−	17.1913i	0.728419	−	0.728419i	−0.241886	−	0.970305i	$-0.577766\pi$
$557$	17.1913	−	17.1913i	0.728419	−	0.728419i	0.970305	+	0.241886i	$0.0777660\pi$
$558$	−11.0285	+	1.10901i	−0.466873	+	0.0469482i
$559$		−	1.50078i		−	0.0634764i
$560$	−0.322567	+	0.0410804i	−0.0136310	+	0.00173596i
$561$	31.6303	−	14.9997i	1.33543	−	0.633286i
$562$	−1.59749	−	1.59749i	−0.0673860	−	0.0673860i
$563$	−14.9893	−	14.9893i	−0.631723	−	0.631723i	0.316777	−	0.948500i	$-0.397399\pi$
$563$	−14.9893	−	14.9893i	−0.631723	−	0.631723i	−0.948500	+	0.316777i	$0.897399\pi$
$564$	10.8131	−	5.12777i	0.455314	−	0.215918i
$565$	−15.5031	+	1.97439i	−0.652221	+	0.0830632i
$566$			24.5303i			1.03109i
$567$	−0.722666	+	1.09119i	−0.0303491	+	0.0458257i
$568$	−0.219925	+	0.219925i	−0.00922786	+	0.00922786i
$569$	−35.8239			−1.50181			−0.750907	−	0.660408i	$-0.770383\pi$
$569$	−35.8239			−1.50181			−0.750907	+	0.660408i	$0.770383\pi$
$570$	0.829756	−	3.78306i	0.0347546	−	0.158455i
$571$	−5.53111			−0.231470			−0.115735	−	0.993280i	$-0.536922\pi$
$571$	−5.53111			−0.231470			−0.115735	+	0.993280i	$0.536922\pi$
$572$	4.62086	−	4.62086i	0.193208	−	0.193208i
$573$	−25.0790	−	8.94445i	−1.04769	−	0.373660i
$574$			1.49876i			0.0625572i
$575$	22.2917	−	37.8674i	0.929630	−	1.57918i
$576$	1.89843	−	2.32292i	0.0791012	−	0.0967884i
$577$	7.04676	+	7.04676i	0.293360	+	0.293360i	0.838406	−	0.545046i	$-0.183488\pi$
$577$	7.04676	+	7.04676i	0.293360	+	0.293360i	−0.545046	+	0.838406i	$0.683488\pi$
$578$	4.32382	+	4.32382i	0.179847	+	0.179847i
$579$	17.3639	+	36.6159i	0.721620	+	1.52171i
$580$	4.25793	+	3.29592i	0.176801	+	0.136856i
$581$			2.30089i			0.0954570i
$582$	0.489957	−	1.37377i	0.0203094	−	0.0569446i
$583$	−17.5484	+	17.5484i	−0.726780	+	0.726780i
$584$	−1.06894			−0.0442330
$585$	3.79211	−	6.06867i	0.156785	−	0.250908i
$586$	−1.94418			−0.0803135
$587$	−26.9429	+	26.9429i	−1.11205	+	1.11205i	−0.119179	+	0.992873i	$0.538026\pi$
$587$	−26.9429	+	26.9429i	−1.11205	+	1.11205i	−0.992873	+	0.119179i	$0.961974\pi$
$588$	4.06058	−	11.3853i	0.167456	−	0.469521i
$589$		−	3.69470i		−	0.152238i
$590$	−2.01247	−	15.8022i	−0.0828523	−	0.650565i
$591$	3.17776	+	6.70106i	0.130716	+	0.275645i
$592$	3.66137	+	3.66137i	0.150482	+	0.150482i
$593$	20.6797	+	20.6797i	0.849213	+	0.849213i	0.990035	−	0.140822i	$-0.0449744\pi$
$593$	20.6797	+	20.6797i	0.849213	+	0.849213i	−0.140822	+	0.990035i	$0.544974\pi$
$594$	−30.9009	−	7.63952i	−1.26788	−	0.313453i
$595$	0.656692	−	0.848367i	0.0269217	−	0.0347797i
$596$		−	9.86195i		−	0.403961i
$597$	13.0791	+	4.66470i	0.535293	+	0.190913i
$598$	−6.62914	+	6.62914i	−0.271086	+	0.271086i
$599$	43.6578			1.78381			0.891904	−	0.452225i	$-0.149369\pi$
$599$	43.6578			1.78381			0.891904	+	0.452225i	$0.149369\pi$
$600$	−5.55358	−	6.64513i	−0.226724	−	0.271286i
$601$	−34.9857			−1.42710			−0.713548	−	0.700606i	$-0.752913\pi$
$601$	−34.9857			−1.42710			−0.713548	+	0.700606i	$0.752913\pi$
$602$	−0.144666	+	0.144666i	−0.00589614	+	0.00589614i
$603$	−1.85778	−	18.4746i	−0.0756546	−	0.752342i
$604$			7.90117i			0.321494i
$605$	−36.3080	+	46.9057i	−1.47613	+	1.90699i
$606$	−12.1288	+	5.75170i	−0.492699	+	0.233647i
$607$	17.1411	+	17.1411i	0.695736	+	0.695736i	0.963488	−	0.267752i	$-0.0862806\pi$
$607$	17.1411	+	17.1411i	0.695736	+	0.695736i	−0.267752	+	0.963488i	$0.586281\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$	0.548030	−	0.259886i	0.0222073	−	0.0105311i
$610$	2.92219	+	22.9454i	0.118316	+	0.929031i
$611$			7.37060i			0.298183i
$612$	0.990317	+	9.84815i	0.0400312	+	0.398088i
$613$	11.6759	−	11.6759i	0.471584	−	0.471584i	−0.430843	−	0.902427i	$-0.641784\pi$
$613$	11.6759	−	11.6759i	0.471584	−	0.471584i	0.902427	+	0.430843i	$0.141784\pi$
$614$	3.50817			0.141578
$615$	−33.6167	+	21.5227i	−1.35555	+	0.867879i
$616$	−0.890843			−0.0358931
$617$	−26.0987	+	26.0987i	−1.05069	+	1.05069i	−0.0520498	+	0.998644i	$0.516575\pi$
$617$	−26.0987	+	26.0987i	−1.05069	+	1.05069i	−0.998644	+	0.0520498i	$0.983425\pi$
$618$	−25.8702	−	9.22665i	−1.04065	−	0.371150i
$619$		−	23.5922i		−	0.948249i	−0.880458	−	0.474124i	$-0.842765\pi$
$619$		−	23.5922i		−	0.948249i	0.880458	−	0.474124i	$-0.157235\pi$
$620$	−6.53306	−	5.05701i	−0.262374	−	0.203094i
$621$	44.3308	+	10.9597i	1.77893	+	0.439799i
$622$	1.24595	+	1.24595i	0.0499579	+	0.0499579i
$623$	−0.237515	−	0.237515i	−0.00951583	−	0.00951583i
$624$	0.791694	+	1.66947i	0.0316931	+	0.0668324i
$625$	−21.8589	+	12.1321i	−0.874356	+	0.485286i
$626$			13.5483i			0.541501i
$627$	3.56432	−	9.99383i	0.142345	−	0.399115i
$628$	3.96376	−	3.96376i	0.158171	−	0.158171i
$629$	−17.0835			−0.681164
$630$	−0.950515	+	0.219445i	−0.0378694	+	0.00874291i
$631$	33.3627			1.32815			0.664075	−	0.747666i	$-0.268826\pi$
$631$	33.3627			1.32815			0.664075	+	0.747666i	$0.268826\pi$
$632$	10.1192	−	10.1192i	0.402521	−	0.402521i
$633$	2.62347	−	7.35584i	0.104274	−	0.292368i
$634$			11.0656i			0.439469i
$635$	27.6122	−	3.51653i	1.09576	−	0.139549i
$636$	−3.00657	−	6.34006i	−0.119218	−	0.251400i
$637$	5.26423	+	5.26423i	0.208577	+	0.208577i
$638$	10.4308	+	10.4308i	0.412961	+	0.412961i
$639$	−0.590452	+	0.722478i	−0.0233579	+	0.0285808i
$640$	2.21815	−	0.282491i	0.0876802	−	0.0111665i
$641$			3.43192i			0.135553i	0.997701	+	0.0677764i	$0.0215904\pi$
$641$			3.43192i			0.135553i	−0.997701	+	0.0677764i	$0.978410\pi$
$642$	−25.1537	−	8.97112i	−0.992739	−	0.354062i
$643$	14.6003	−	14.6003i	0.575778	−	0.575778i	−0.357959	−	0.933737i	$-0.616527\pi$
$643$	14.6003	−	14.6003i	0.575778	−	0.575778i	0.933737	+	0.357959i	$0.116527\pi$
$644$	1.27801			0.0503607
$645$	−5.32224	−	1.16735i	−0.209563	−	0.0459645i
$646$	−3.29927			−0.129808
$647$	−32.0282	+	32.0282i	−1.25916	+	1.25916i	−0.307662	+	0.951496i	$0.599547\pi$
$647$	−32.0282	+	32.0282i	−1.25916	+	1.25916i	−0.951496	+	0.307662i	$0.900453\pi$
$648$	4.96945	−	7.50363i	0.195219	−	0.294771i
$649$		−	43.6413i		−	1.71307i
$650$	5.16354	−	1.33688i	0.202531	−	0.0524368i
$651$	−0.840857	+	0.398749i	−0.0329558	+	0.0156282i
$652$	−6.35109	−	6.35109i	−0.248728	−	0.248728i
$653$	−21.8830	−	21.8830i	−0.856346	−	0.856346i	0.134559	−	0.990906i	$-0.457038\pi$
$653$	−21.8830	−	21.8830i	−0.856346	−	0.856346i	−0.990906	+	0.134559i	$0.957038\pi$
$654$	−1.49955	+	0.711114i	−0.0586371	+	0.0278067i
$655$	−39.0873	−	30.2561i	−1.52727	−	1.18220i
$656$		−	10.3063i		−	0.402395i
$657$	−3.19072	+	0.320855i	−0.124482	+	0.0125177i
$658$	0.710478	−	0.710478i	0.0276973	−	0.0276973i
$659$	9.03239			0.351852			0.175926	−	0.984403i	$-0.443708\pi$
$659$	9.03239			0.351852			0.175926	+	0.984403i	$0.443708\pi$
$660$	−12.7928	−	19.9813i	−0.497958	−	0.777769i
$661$	−29.1658			−1.13442			−0.567210	−	0.823573i	$-0.691977\pi$
$661$	−29.1658			−1.13442			−0.567210	+	0.823573i	$0.691977\pi$
$662$	−7.16494	+	7.16494i	−0.278473	+	0.278473i
$663$	−5.74175	−	2.04780i	−0.222991	−	0.0795301i
$664$		−	15.8222i		−	0.614020i
$665$	−0.0410804	−	0.322567i	−0.00159303	−	0.0125086i
$666$	12.0280	+	9.83000i	0.466076	+	0.380905i
$667$	−14.9642	−	14.9642i	−0.579415	−	0.579415i
$668$	−14.9173	−	14.9173i	−0.577169	−	0.577169i
$669$	8.88761	+	18.7416i	0.343615	+	0.724593i
$670$	8.47133	−	10.9440i	0.327276	−	0.422802i
$671$			63.3688i			2.44633i
$672$	0.0846123	−	0.237241i	0.00326399	−	0.00915176i
$673$	13.7053	−	13.7053i	0.528300	−	0.528300i	−0.391765	−	0.920065i	$-0.628135\pi$
$673$	13.7053	−	13.7053i	0.528300	−	0.528300i	0.920065	+	0.391765i	$0.128135\pi$
$674$	12.1618			0.468456
$675$	−18.5718	−	18.1684i	−0.714827	−	0.699301i
$676$	11.8620			0.456232
$677$	0.194042	−	0.194042i	0.00745766	−	0.00745766i	−0.703368	−	0.710826i	$-0.748321\pi$
$677$	0.194042	−	0.194042i	0.00745766	−	0.00745766i	0.710826	+	0.703368i	$0.248321\pi$
$678$	4.06660	−	11.4022i	0.156177	−	0.437898i
$679$		−	0.122457i		−	0.00469946i
$680$	−4.51578	+	5.83385i	−0.173172	+	0.223718i
$681$	6.50923	+	13.7262i	0.249434	+	0.525991i
$682$	−16.0043	−	16.0043i	−0.612836	−	0.612836i
$683$	−8.50150	−	8.50150i	−0.325301	−	0.325301i	0.525495	−	0.850796i	$-0.323880\pi$
$683$	−8.50150	−	8.50150i	−0.325301	−	0.325301i	−0.850796	+	0.525495i	$0.823880\pi$
$684$	2.32292	+	1.89843i	0.0888192	+	0.0725882i
$685$	−0.633682	−	4.97574i	−0.0242117	−	0.190113i
$686$		−	2.03283i		−	0.0776137i
$687$	19.2695	+	6.87251i	0.735178	+	0.262202i
$688$	0.994803	−	0.994803i	0.0379265	−	0.0379265i
$689$	4.32162			0.164640
$690$	18.3526	+	28.6653i	0.698673	+	1.09127i
$691$	−34.6840			−1.31944			−0.659721	−	0.751511i	$-0.729325\pi$
$691$	−34.6840			−1.31944			−0.659721	+	0.751511i	$0.729325\pi$
$692$	6.19199	−	6.19199i	0.235384	−	0.235384i
$693$	−2.65912	+	0.267398i	−0.101012	+	0.0101576i
$694$			11.1866i			0.424639i
$695$	19.7639	+	15.2986i	0.749688	+	0.580307i
$696$	−3.76856	+	1.78712i	−0.142847	+	0.0677406i
$697$	24.0440	+	24.0440i	0.910732	+	0.910732i
$698$	13.1405	+	13.1405i	0.497376	+	0.497376i
$699$	−23.3301	+	11.0636i	−0.882427	+	0.418462i
$700$	−0.626598	−	0.368865i	−0.0236832	−	0.0139418i
$701$		−	6.61547i		−	0.249863i	−0.992165	−	0.124931i	$-0.960129\pi$
$701$		−	6.61547i		−	0.249863i	0.992165	−	0.124931i	$-0.0398711\pi$
$702$	2.86428	+	4.74565i	0.108105	+	0.179113i
$703$	−3.66137	+	3.66137i	−0.138091	+	0.138091i
$704$	6.12593			0.230880
$705$	26.1384	+	5.73307i	0.984430	+	0.215920i
$706$	5.29865			0.199417
$707$	−0.796928	+	0.796928i	−0.0299716	+	0.0299716i
$708$	11.6221	+	4.14505i	0.436786	+	0.155780i
$709$		−	17.2370i		−	0.647351i	−0.946168	−	0.323675i	$-0.895081\pi$
$709$		−	17.2370i		−	0.647351i	0.946168	−	0.323675i	$-0.104919\pi$
$710$	−0.689892	+	0.0878608i	−0.0258912	+	0.00329736i
$711$	27.1679	−	33.2427i	1.01888	−	1.24670i
$712$	1.63328	+	1.63328i	0.0612099	+	0.0612099i
$713$	22.9599	+	22.9599i	0.859856	+	0.859856i
$714$	0.356073	+	0.750863i	0.0133257	+	0.0281003i
$715$	14.4954	−	1.84605i	0.542096	−	0.0690383i
$716$			8.96071i			0.334877i
$717$	−3.64996	+	10.2340i	−0.136310	+	0.382195i
$718$	12.1340	−	12.1340i	0.452838	−	0.452838i
$719$	−16.3498			−0.609746			−0.304873	−	0.952393i	$-0.598614\pi$
$719$	−16.3498			−0.609746			−0.304873	+	0.952393i	$0.598614\pi$
$720$	6.53627	−	1.50903i	0.243592	−	0.0562381i
$721$	−2.30605			−0.0858819
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	−7.76321	+	21.7669i	−0.288717	+	0.809521i
$724$		−	8.58326i		−	0.318994i
$725$	3.01779	+	11.6558i	0.112078	+	0.432887i
$726$	−19.6870	−	41.5147i	−0.730654	−	1.54076i
$727$	−33.8444	−	33.8444i	−1.25522	−	1.25522i	−0.953349	−	0.301871i	$-0.902389\pi$
$727$	−33.8444	−	33.8444i	−1.25522	−	1.25522i	−0.301871	−	0.953349i	$-0.597611\pi$
$728$	0.109693	+	0.109693i	0.00406550	+	0.00406550i
$729$	12.5812	−	23.8896i	0.465972	−	0.884800i
$730$	−1.89012	−	1.46308i	−0.0699565	−	0.0541509i
$731$			4.64163i			0.171677i
$732$	−16.8758	−	6.01877i	−0.623747	−	0.222460i
$733$	−8.42136	+	8.42136i	−0.311050	+	0.311050i	−0.845316	−	0.534266i	$-0.820588\pi$
$733$	−8.42136	+	8.42136i	−0.311050	+	0.311050i	0.534266	+	0.845316i	$0.320588\pi$
$734$	34.8649			1.28689
$735$	22.7633	−	14.5739i	0.839636	−	0.537567i
$736$	−8.78832			−0.323942
$737$	26.8099	−	26.8099i	0.987554	−	0.987554i
$738$	−3.09357	−	30.7638i	−0.113876	−	1.13243i
$739$			18.4254i			0.677788i	0.940825	+	0.338894i	$0.110053\pi$
$739$			18.4254i			0.677788i	−0.940825	+	0.338894i	$0.889947\pi$
$740$	1.46273	+	11.4855i	0.0537710	+	0.422216i
$741$	−1.66947	+	0.791694i	−0.0613296	+	0.0290836i
$742$	−0.416576	−	0.416576i	−0.0152930	−	0.0152930i
$743$	27.2664	+	27.2664i	1.00031	+	1.00031i	1.00000		0.000307644i	$9.79262e-5\pi$
$743$	27.2664	+	27.2664i	1.00031	+	1.00031i	0.000307644		1.00000i	$0.499902\pi$
$744$	5.78220	−	2.74202i	0.211986	−	0.100527i
$745$	13.4982	−	17.4381i	0.494537	−	0.638883i
$746$			15.5260i			0.568446i
$747$	−4.74923	−	47.2284i	−0.173765	−	1.72800i
$748$	−14.2914	+	14.2914i	−0.522546	+	0.522546i
$749$	−2.24219			−0.0819277
$750$	−0.724644	−	19.3514i	−0.0264603	−	0.706612i
$751$	29.9776			1.09390			0.546949	−	0.837166i	$-0.315789\pi$
$751$	29.9776			1.09390			0.546949	+	0.837166i	$0.315789\pi$
$752$	−4.88564	+	4.88564i	−0.178161	+	0.178161i
$753$	43.6923	+	15.5829i	1.59224	+	0.567874i
$754$		−	2.56879i		−	0.0935497i
$755$	−10.8145	+	13.9710i	−0.393579	+	0.508458i
$756$	0.181352	−	0.733548i	0.00659572	−	0.0266789i
$757$	14.2204	+	14.2204i	0.516851	+	0.516851i	0.916617	−	0.399766i	$-0.130909\pi$
$757$	14.2204	+	14.2204i	0.516851	+	0.516851i	−0.399766	+	0.916617i	$0.630909\pi$
$758$	−22.5476	−	22.5476i	−0.818966	−	0.818966i
$759$	39.9548	+	84.2541i	1.45027	+	3.05823i
$760$	0.282491	+	2.21815i	0.0102470	+	0.0804608i
$761$		−	25.8646i		−	0.937590i	−0.883307	−	0.468795i	$-0.844688\pi$
$761$		−	25.8646i		−	0.937590i	0.883307	−	0.468795i	$-0.155312\pi$
$762$	−7.24291	+	20.3081i	−0.262383	+	0.735685i
$763$	−0.0985285	+	0.0985285i	−0.00356697	+	0.00356697i
$764$	15.3727			0.556164
$765$	−11.7282	+	18.7692i	−0.424036	+	0.678601i
$766$	5.25871			0.190005
$767$	−5.37374	+	5.37374i	−0.194034	+	0.194034i
$768$	−0.581841	+	1.63140i	−0.0209954	+	0.0588680i
$769$		−	3.81692i		−	0.137642i	−0.997629	−	0.0688208i	$-0.978076\pi$
$769$		−	3.81692i		−	0.137642i	0.997629	−	0.0688208i	$-0.0219237\pi$
$770$	−1.57521	−	1.21931i	−0.0567666	−	0.0439410i
$771$	6.50988	+	13.7276i	0.234448	+	0.494388i
$772$	−16.5440	−	16.5440i	−0.595433	−	0.595433i
$773$	−13.3692	−	13.3692i	−0.480857	−	0.480857i	0.424549	−	0.905405i	$-0.360433\pi$
$773$	−13.3692	−	13.3692i	−0.480857	−	0.480857i	−0.905405	+	0.424549i	$0.860433\pi$
$774$	2.67083	−	3.26804i	0.0960010	−	0.117467i
$775$	−4.63027	−	17.8838i	−0.166324	−	0.642406i
$776$			0.842081i			0.0302289i
$777$	1.22842	+	0.438119i	0.0440695	+	0.0157174i
$778$	19.5781	−	19.5781i	0.701908	−	0.701908i
$779$	10.3063			0.369263
$780$	−0.885149	+	4.03561i	−0.0316934	+	0.144498i
$781$	−1.90529			−0.0681768
$782$	20.5026	−	20.5026i	0.733171	−	0.733171i
$783$	−10.7125	+	6.46563i	−0.382834	+	0.231063i
$784$			6.97885i			0.249245i
$785$	12.4341	−	1.58353i	0.443791	−	0.0565187i
$786$	34.5949	−	16.4055i	1.23396	−	0.585166i
$787$	−22.7110	−	22.7110i	−0.809561	−	0.809561i	0.175006	−	0.984567i	$-0.444005\pi$
$787$	−22.7110	−	22.7110i	−0.809561	−	0.809561i	−0.984567	+	0.175006i	$0.944005\pi$
$788$	−3.02772	−	3.02772i	−0.107858	−	0.107858i
$789$	−23.6986	+	11.2383i	−0.843691	+	0.400093i
$790$	31.7434	−	4.04266i	1.12938	−	0.143831i
$791$		−	1.01638i		−	0.0361384i
$792$	18.2856	−	1.83877i	0.649750	−	0.0653380i
$793$	7.80288	−	7.80288i	0.277088	−	0.277088i
$794$	−0.916384			−0.0325213
$795$	3.36148	−	15.3258i	0.119219	−	0.543550i
$796$	−8.01713			−0.284160
$797$	−3.31221	+	3.31221i	−0.117325	+	0.117325i	−0.763332	−	0.646007i	$-0.776438\pi$
$797$	−3.31221	+	3.31221i	−0.117325	+	0.117325i	0.646007	+	0.763332i	$0.276438\pi$
$798$	0.237241	+	0.0846123i	0.00839823	+	0.00299524i
$799$		−	22.7958i		−	0.806458i
$800$	4.30884	+	2.53652i	0.152340	+	0.0896795i
$801$	5.36552	+	4.38502i	0.189581	+	0.154937i
$802$	−20.4577	−	20.4577i	−0.722385	−	0.722385i
$803$	−4.63031	−	4.63031i	−0.163400	−	0.163400i
$804$	4.59334	+	9.68614i	0.161995	+	0.341604i
$805$	2.25981	+	1.74924i	0.0796478	+	0.0616526i
$806$			3.94136i			0.138828i
$807$	−4.30494	+	12.0704i	−0.151541	+	0.424899i
$808$	5.48012	−	5.48012i	0.192790	−	0.192790i
$809$	−7.82368			−0.275066			−0.137533	−	0.990497i	$-0.543917\pi$
$809$	−7.82368			−0.275066			−0.137533	+	0.990497i	$0.543917\pi$
$810$	19.0575	−	6.46631i	0.669611	−	0.227203i
$811$	0.275979			0.00969094			0.00484547	−	0.999988i	$-0.498458\pi$
$811$	0.275979			0.00969094			0.00484547	+	0.999988i	$0.498458\pi$
$812$	−0.247615	+	0.247615i	−0.00868957	+	0.00868957i
$813$	18.7655	−	52.6159i	0.658136	−	1.84532i
$814$			31.7199i			1.11178i
$815$	−2.53728	−	19.9230i	−0.0888770	−	0.697872i
$816$	−2.44855	−	5.16335i	−0.0857165	−	0.180753i
$817$	0.994803	+	0.994803i	0.0348037	+	0.0348037i
$818$	−10.9786	−	10.9786i	−0.383859	−	0.383859i
$819$	0.360354	+	0.294503i	0.0125918	+	0.0102908i
$820$	14.1065	−	18.2239i	0.492619	−	0.636405i
$821$		−	19.8023i		−	0.691106i	−0.938399	−	0.345553i	$-0.887691\pi$
$821$		−	19.8023i		−	0.691106i	0.938399	−	0.345553i	$-0.112309\pi$
$822$	3.65954	+	1.30518i	0.127641	+	0.0455234i
$823$	−26.0210	+	26.0210i	−0.907036	+	0.907036i	−0.996032	−	0.0889960i	$-0.971634\pi$
$823$	−26.0210	+	26.0210i	−0.907036	+	0.907036i	0.0889960	+	0.996032i	$0.471634\pi$
$824$	15.8577			0.552429
$825$	4.72826	−	52.8410i	0.164617	−	1.83969i
$826$	1.03599			0.0360466
$827$	−7.10260	+	7.10260i	−0.246982	+	0.246982i	−0.819731	−	0.572749i	$-0.805877\pi$
$827$	−7.10260	+	7.10260i	−0.246982	+	0.246982i	0.572749	+	0.819731i	$0.305877\pi$
$828$	−26.2327	+	2.63792i	−0.911648	+	0.0916742i
$829$		−	40.2350i		−	1.39742i	−0.715406	−	0.698709i	$-0.753758\pi$
$829$		−	40.2350i		−	1.39742i	0.715406	−	0.698709i	$-0.246242\pi$
$830$	21.6561	−	27.9772i	0.751696	−	0.971101i
$831$	−0.698745	+	0.331357i	−0.0242392	+	0.0114947i
$832$	−0.754312	−	0.754312i	−0.0261511	−	0.0261511i
$833$	−16.2812	−	16.2812i	−0.564111	−	0.564111i
$834$	−17.4924	+	8.29521i	−0.605713	+	0.287240i
$835$	−5.95952	−	46.7948i	−0.206238	−	1.61940i
$836$			6.12593i			0.211870i
$837$	16.4365	−	9.92039i	0.568129	−	0.342899i
$838$	4.92259	−	4.92259i	0.170048	−	0.170048i
$839$	7.79127			0.268984			0.134492	−	0.990915i	$-0.457060\pi$
$839$	7.79127			0.268984			0.134492	+	0.990915i	$0.457060\pi$
$840$	0.474329	−	0.303684i	0.0163659	−	0.0104781i
$841$	−23.2014			−0.800048
$842$	−20.8054	+	20.8054i	−0.717000	+	0.717000i
$843$	3.68564	+	1.31449i	0.126940	+	0.0452734i
$844$			4.50891i			0.155203i
$845$	20.9747	+	16.2358i	0.721551	+	0.558528i
$846$	−13.1169	+	16.0499i	−0.450968	+	0.551806i
$847$	−2.72774	−	2.72774i	−0.0937262	−	0.0937262i
$848$	2.86461	+	2.86461i	0.0983710	+	0.0983710i
$849$	−18.2051	−	38.3898i	−0.624799	−	1.31754i
$850$	−15.9698	+	4.13471i	−0.547759	+	0.141819i
$851$		−	45.5056i		−	1.55991i
$852$	0.180965	−	0.507400i	0.00619975	−	0.0173832i
$853$	−27.5401	+	27.5401i	−0.942956	+	0.942956i	−0.998459	−	0.0555025i	$-0.982324\pi$
$853$	−27.5401	+	27.5401i	−0.942956	+	0.942956i	0.0555025	+	0.998459i	$0.482324\pi$
$854$	−1.50429			−0.0514759
$855$	1.50903	+	6.53627i	0.0516076	+	0.223536i
$856$	15.4185			0.526994
$857$	−12.3126	+	12.3126i	−0.420590	+	0.420590i	−0.885407	−	0.464817i	$-0.846120\pi$
$857$	−12.3126	+	12.3126i	−0.420590	+	0.420590i	0.464817	+	0.885407i	$0.346120\pi$
$858$	−3.80227	+	10.6610i	−0.129807	+	0.363961i
$859$			6.21722i			0.212129i	0.994359	+	0.106064i	$0.0338250\pi$
$859$			6.21722i			0.212129i	−0.994359	+	0.106064i	$0.966175\pi$
$860$	3.12064	−	0.397427i	0.106413	−	0.0135521i
$861$	−1.11231	−	2.34556i	−0.0379073	−	0.0799365i
$862$	13.9141	+	13.9141i	0.473917	+	0.473917i
$863$	31.4921	+	31.4921i	1.07200	+	1.07200i	0.997198	+	0.0748042i	$0.0238332\pi$
$863$	31.4921	+	31.4921i	1.07200	+	1.07200i	0.0748042	+	0.997198i	$0.476167\pi$
$864$	−1.24708	+	5.04428i	−0.0424265	+	0.171610i
$865$	19.4239	−	2.47372i	0.660433	−	0.0841090i
$866$			31.4884i			1.07002i
$867$	−9.97568	−	3.55784i	−0.338792	−	0.120831i
$868$	0.379921	−	0.379921i	0.0128954	−	0.0128954i
$869$	87.6666			2.97389
$870$	−9.10971	−	1.99808i	−0.308848	−	0.0677412i
$871$	−6.60243			−0.223715
$872$	0.677536	−	0.677536i	0.0229443	−	0.0229443i
$873$	0.252761	+	2.51357i	0.00855466	+	0.0850713i
$874$		−	8.78832i		−	0.297269i
$875$	−0.603092	−	1.50987i	−0.0203882	−	0.0510430i
$876$	1.67288	−	0.793312i	0.0565215	−	0.0268035i
$877$	−18.1228	−	18.1228i	−0.611965	−	0.611965i	0.331493	−	0.943458i	$-0.392448\pi$
$877$	−18.1228	−	18.1228i	−0.611965	−	0.611965i	−0.943458	+	0.331493i	$0.892448\pi$
$878$	1.38955	+	1.38955i	0.0468950	+	0.0468950i
$879$	3.04264	−	1.44287i	0.102626	−	0.0486670i
$880$	10.8320	+	8.38468i	0.365147	+	0.282647i
$881$		−	11.5979i		−	0.390744i	−0.980729	−	0.195372i	$-0.937409\pi$
$881$		−	11.5979i		−	0.390744i	0.980729	−	0.195372i	$-0.0625915\pi$
$882$	2.09479	+	20.8315i	0.0705352	+	0.701433i
$883$	−9.62477	+	9.62477i	−0.323899	+	0.323899i	−0.850261	−	0.526362i	$-0.823556\pi$
$883$	−9.62477	+	9.62477i	−0.323899	+	0.323899i	0.526362	+	0.850261i	$0.323556\pi$
$884$	3.51953			0.118374
$885$	14.8771	+	23.2368i	0.500088	+	0.781096i
$886$	−14.5226			−0.487896
$887$	−28.5533	+	28.5533i	−0.958726	+	0.958726i	−0.999181	−	0.0404558i	$-0.987119\pi$
$887$	−28.5533	+	28.5533i	−0.958726	+	0.958726i	0.0404558	+	0.999181i	$0.487119\pi$
$888$	−8.44733	−	3.01275i	−0.283474	−	0.101101i
$889$			1.81025i			0.0607138i
$890$	0.652502	+	5.12352i	0.0218719	+	0.171741i
$891$	54.0295	−	10.9773i	1.81006	−	0.367753i
$892$	−8.46796	−	8.46796i	−0.283528	−	0.283528i
$893$	−4.88564	−	4.88564i	−0.163492	−	0.163492i
$894$	7.31904	+	15.4339i	0.244785	+	0.516187i
$895$	−12.2647	+	15.8445i	−0.409963	+	0.529624i
$896$			0.145422i			0.00485820i
$897$	5.45477	−	15.2944i	0.182129	−	0.510665i
$898$	−20.3061	+	20.3061i	−0.677623	+	0.677623i
$899$	−8.89696			−0.296730
$900$	13.6230	+	6.27802i	0.454100	+	0.209267i
$901$	−13.3659			−0.445283
$902$	44.6438	−	44.6438i	1.48648	−	1.48648i
$903$	0.119038	−	0.333765i	0.00396133	−	0.0111070i
$904$			6.98920i			0.232457i
$905$	11.7481	−	15.1771i	0.390519	−	0.504504i
$906$	−5.86385	−	12.3653i	−0.194813	−	0.410810i
$907$	34.8096	+	34.8096i	1.15583	+	1.15583i	0.985363	+	0.170470i	$0.0545287\pi$
$907$	34.8096	+	34.8096i	1.15583	+	1.15583i	0.170470	+	0.985363i	$0.445471\pi$
$908$	−6.20188	−	6.20188i	−0.205817	−	0.205817i
$909$	14.7129	−	18.0028i	0.487997	−	0.597115i
$910$	0.0438228	+	0.344101i	0.00145271	+	0.0114069i
$911$			39.4916i			1.30842i	0.756315	+	0.654208i	$0.226998\pi$
$911$			39.4916i			1.30842i	−0.756315	+	0.654208i	$0.773002\pi$
$912$	−1.63140	−	0.581841i	−0.0540210	−	0.0192667i
$913$	68.5368	−	68.5368i	2.26824	−	2.26824i
$914$	18.4793			0.611239
$915$	−21.6021	−	33.7407i	−0.714144	−	1.11543i
$916$	−11.8117			−0.390268
$917$	2.27307	−	2.27307i	0.0750634	−	0.0750634i
$918$	−8.85864	−	14.6774i	−0.292379	−	0.484425i
$919$		−	42.8370i		−	1.41306i	−0.707683	−	0.706530i	$-0.750259\pi$
$919$		−	42.8370i		−	1.41306i	0.707683	−	0.706530i	$-0.249741\pi$
$920$	−15.5397	−	12.0287i	−0.512329	−	0.396576i
$921$	−5.49027	+	2.60358i	−0.180910	+	0.0857910i
$922$	−25.2425	−	25.2425i	−0.831316	−	0.831316i
$923$	0.234607	+	0.234607i	0.00772219	+	0.00772219i
$924$	1.39417	−	0.661138i	0.0458647	−	0.0217499i
$925$	−13.1340	+	22.3110i	−0.431844	+	0.733581i
$926$			26.5468i			0.872381i
$927$	47.3344	−	4.75988i	1.55466	−	0.156335i
$928$	1.70274	−	1.70274i	0.0558950	−	0.0558950i
$929$	15.7833			0.517832			0.258916	−	0.965900i	$-0.416635\pi$
$929$	15.7833			0.517832			0.258916	+	0.965900i	$0.416635\pi$
$930$	13.9773	+	3.06570i	0.458333	+	0.100528i
$931$	−6.97885			−0.228723
$932$	10.5412	−	10.5412i	0.345287	−	0.345287i
$933$	−2.87458	−	1.02522i	−0.0941095	−	0.0335643i
$934$		−	7.09471i		−	0.232146i
$935$	−44.8313	+	5.70946i	−1.46614	+	0.186719i
$936$	−2.47800	−	2.02517i	−0.0809959	−	0.0661946i
$937$	−35.2671	−	35.2671i	−1.15213	−	1.15213i	−0.986126	−	0.166000i	$-0.946915\pi$
$937$	−35.2671	−	35.2671i	−1.15213	−	1.15213i	−0.166000	−	0.986126i	$-0.553085\pi$
$938$	0.636431	+	0.636431i	0.0207802	+	0.0207802i
$939$	−10.0549	−	21.2031i	−0.328129	−	0.691938i
$940$	−15.3260	+	1.95183i	−0.499878	+	0.0636617i
$941$		−	20.0837i		−	0.654710i	−0.944901	−	0.327355i	$-0.893843\pi$
$941$		−	20.0837i		−	0.654710i	0.944901	−	0.327355i	$-0.106157\pi$
$942$	−3.26157	+	9.14497i	−0.106268	+	0.297959i
$943$	−64.0464	+	64.0464i	−2.08564	+	2.08564i
$944$	−7.12402			−0.231867
$945$	1.32469	−	1.04886i	0.0430922	−	0.0341193i
$946$	8.61835			0.280207
$947$	−9.64395	+	9.64395i	−0.313386	+	0.313386i	−0.846220	−	0.532834i	$-0.821127\pi$
$947$	−9.64395	+	9.64395i	−0.313386	+	0.313386i	0.532834	+	0.846220i	$0.321127\pi$
$948$	−8.32658	+	23.3465i	−0.270435	+	0.758260i
$949$			1.14030i			0.0370157i
$950$	−2.53652	+	4.30884i	−0.0822955	+	0.139797i
$951$	−8.21229	−	17.3176i	−0.266302	−	0.561560i
$952$	−0.339260	−	0.339260i	−0.0109955	−	0.0109955i
$953$	−38.7018	−	38.7018i	−1.25368	−	1.25368i	−0.954060	−	0.299616i	$-0.903142\pi$
$953$	−38.7018	−	38.7018i	−1.25368	−	1.25368i	−0.299616	−	0.954060i	$-0.596858\pi$
$954$	9.41054	+	7.69085i	0.304678	+	0.249000i
$955$	27.1823	+	21.0409i	0.879599	+	0.680867i
$956$		−	6.27313i		−	0.202887i
$957$	−24.0655	−	8.58299i	−0.777926	−	0.277449i
$958$	−4.41971	+	4.41971i	−0.142794	+	0.142794i
$959$	0.326208			0.0105338
$960$	−3.26175	+	2.08830i	−0.105273	+	0.0673995i
$961$	−17.3492			−0.559650
$962$	3.90580	−	3.90580i	0.125928	−	0.125928i
$963$	46.0234	−	4.62806i	1.48308	−	0.149137i
$964$		−	13.3425i		−	0.429733i
$965$	−6.60940	−	51.8977i	−0.212764	−	1.67065i
$966$	−2.00008	+	0.948476i	−0.0643516	+	0.0305167i
$967$	−16.1280	−	16.1280i	−0.518642	−	0.518642i	0.398519	−	0.917160i	$-0.369524\pi$
$967$	−16.1280	−	16.1280i	−0.518642	−	0.518642i	−0.917160	+	0.398519i	$0.869524\pi$
$968$	18.7574	+	18.7574i	0.602887	+	0.602887i
$969$	5.16335	−	2.44855i	0.165871	−	0.0786588i
$970$	−1.15257	+	1.48899i	−0.0370068	+	0.0478084i
$971$			33.4314i			1.07286i	0.843943	+	0.536432i	$0.180228\pi$
$971$			33.4314i			1.07286i	−0.843943	+	0.536432i	$0.819772\pi$
$972$	−2.20836	+	15.4312i	−0.0708332	+	0.494957i
$973$	−1.14934	+	1.14934i	−0.0368463	+	0.0368463i
$974$	−16.1342			−0.516973
$975$	−7.08875	+	5.92433i	−0.227022	+	0.189730i
$976$	10.3444			0.331115
$977$	−28.5627	+	28.5627i	−0.913800	+	0.913800i	−0.996569	−	0.0827686i	$-0.973624\pi$
$977$	−28.5627	+	28.5627i	−0.913800	+	0.913800i	0.0827686	+	0.996569i	$0.473624\pi$
$978$	14.6529	+	5.22598i	0.468548	+	0.167108i
$979$			14.1498i			0.452228i
$980$	−9.55209	+	12.3402i	−0.305130	+	0.394192i
$981$	1.81904	−	2.22578i	0.0580774	−	0.0710637i
$982$	−7.26507	−	7.26507i	−0.231838	−	0.231838i
$983$	−23.2189	−	23.2189i	−0.740569	−	0.740569i	0.232119	−	0.972687i	$-0.425434\pi$
$983$	−23.2189	−	23.2189i	−0.740569	−	0.740569i	−0.972687	+	0.232119i	$0.925434\pi$
$984$	7.64884	+	16.1294i	0.243836	+	0.514186i
$985$	−1.20958	−	9.49777i	−0.0385405	−	0.302624i
$986$			7.94475i			0.253012i
$987$	−0.584615	+	1.63918i	−0.0186085	+	0.0521756i
$988$	0.754312	−	0.754312i	0.0239979	−	0.0239979i
$989$	−12.3640			−0.393151
$990$	34.8497	+	21.7764i	1.10760	+	0.692101i
$991$	−8.55119			−0.271638			−0.135819	−	0.990734i	$-0.543366\pi$
$991$	−8.55119			−0.271638			−0.135819	+	0.990734i	$0.543366\pi$
$992$	−2.61255	+	2.61255i	−0.0829486	+	0.0829486i
$993$	5.89565	−	16.5306i	0.187093	−	0.524582i
$994$		−	0.0452292i		−	0.00143458i
$995$	−14.1761	−	10.9732i	−0.449412	−	0.347874i
$996$	11.7424	+	24.7617i	0.372073	+	0.784604i
$997$	13.6217	+	13.6217i	0.431402	+	0.431402i	0.889105	−	0.457703i	$-0.151328\pi$
$997$	13.6217	+	13.6217i	0.431402	+	0.431402i	−0.457703	+	0.889105i	$0.651328\pi$
$998$	18.6199	+	18.6199i	0.589404	+	0.589404i
$999$	−26.1191	−	6.45733i	−0.826373	−	0.204301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.12	yes	36
3.2	odd	2	inner	570.2.k.b.77.2	✓	36
5.3	odd	4	inner	570.2.k.b.533.2	yes	36
15.8	even	4	inner	570.2.k.b.533.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.2	✓	36	3.2	odd	2	inner
570.2.k.b.77.12	yes	36	1.1	even	1	trivial
570.2.k.b.533.2	yes	36	5.3	odd	4	inner
570.2.k.b.533.12	yes	36	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.581841 + 1.63140i) q^{3} -1.00000i q^{4} +(1.36872 - 1.76822i) q^{5} +(0.742149 + 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.32292 - 1.89843i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.581841 + 1.63140i) q^{3} -1.00000i q^{4} +(1.36872 - 1.76822i) q^{5} +(0.742149 + 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.32292 - 1.89843i) q^{9} +(-0.282491 - 2.21815i) q^{10} -6.12593i q^{11} +(1.63140 + 0.581841i) q^{12} +(-0.754312 + 0.754312i) q^{13} +0.145422 q^{14} +(2.08830 + 3.26175i) q^{15} -1.00000 q^{16} +(2.33294 - 2.33294i) q^{17} +(-2.98495 + 0.300162i) q^{18} -1.00000i q^{19} +(-1.76822 - 1.36872i) q^{20} +(-0.227584 + 0.107925i) q^{21} +(-4.33169 - 4.33169i) q^{22} +(6.21428 + 6.21428i) q^{23} +(1.56500 - 0.742149i) q^{24} +(-1.25322 - 4.84040i) q^{25} +1.06676i q^{26} +(4.44866 - 2.68503i) q^{27} +(0.102829 - 0.102829i) q^{28} -2.40803 q^{29} +(3.78306 + 0.829756i) q^{30} +3.69470 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.99383 + 3.56432i) q^{33} -3.29927i q^{34} +(0.322567 - 0.0410804i) q^{35} +(-1.89843 + 2.32292i) q^{36} +(-3.66137 - 3.66137i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-0.791694 - 1.66947i) q^{39} +(-2.21815 + 0.282491i) q^{40} +10.3063i q^{41} +(-0.0846123 + 0.237241i) q^{42} +(-0.994803 + 0.994803i) q^{43} -6.12593 q^{44} +(-6.53627 + 1.50903i) q^{45} +8.78832 q^{46} +(4.88564 - 4.88564i) q^{47} +(0.581841 - 1.63140i) q^{48} -6.97885i q^{49} +(-4.30884 - 2.53652i) q^{50} +(2.44855 + 5.16335i) q^{51} +(0.754312 + 0.754312i) q^{52} +(-2.86461 - 2.86461i) q^{53} +(1.24708 - 5.04428i) q^{54} +(-10.8320 - 8.38468i) q^{55} -0.145422i q^{56} +(1.63140 + 0.581841i) q^{57} +(-1.70274 + 1.70274i) q^{58} +7.12402 q^{59} +(3.26175 - 2.08830i) q^{60} -10.3444 q^{61} +(2.61255 - 2.61255i) q^{62} +(-0.0436501 - 0.434076i) q^{63} +1.00000i q^{64} +(0.301350 + 2.36623i) q^{65} +(9.58706 - 4.54636i) q^{66} +(4.37645 + 4.37645i) q^{67} +(-2.33294 - 2.33294i) q^{68} +(-13.7537 + 6.52225i) q^{69} +(0.199041 - 0.257138i) q^{70} -0.311021i q^{71} +(0.300162 + 2.98495i) q^{72} +(0.755853 - 0.755853i) q^{73} -5.17797 q^{74} +(8.62579 + 0.771844i) q^{75} -1.00000 q^{76} +(0.629921 - 0.629921i) q^{77} +(-1.74031 - 0.620684i) q^{78} +14.3107i q^{79} +(-1.36872 + 1.76822i) q^{80} +(1.79194 + 8.81981i) q^{81} +(7.28768 + 7.28768i) q^{82} +(11.1880 + 11.1880i) q^{83} +(0.107925 + 0.227584i) q^{84} +(-0.932016 - 7.31829i) q^{85} +1.40686i q^{86} +(1.40109 - 3.92846i) q^{87} +(-4.33169 + 4.33169i) q^{88} -2.30981 q^{89} +(-3.55480 + 5.68888i) q^{90} -0.155130 q^{91} +(6.21428 - 6.21428i) q^{92} +(-2.14973 + 6.02753i) q^{93} -6.90934i q^{94} +(-1.76822 - 1.36872i) q^{95} +(-0.742149 - 1.56500i) q^{96} +(-0.595441 - 0.595441i) q^{97} +(-4.93479 - 4.93479i) q^{98} +(-11.6296 + 14.2301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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