LMFDB - Embedded newform 570.2.k.b.77.5

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			77.5
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.492817 + 1.66046i) q^{3} -1.00000i q^{4} +(-1.86278 + 1.23695i) q^{5} +(-1.52260 - 0.825649i) q^{6} +(-3.33681 - 3.33681i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.51426 + 1.63661i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.492817 + 1.66046i) q^{3} -1.00000i q^{4} +(-1.86278 + 1.23695i) q^{5} +(-1.52260 - 0.825649i) q^{6} +(-3.33681 - 3.33681i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.51426 + 1.63661i) q^{9} +(0.442526 - 2.19184i) q^{10} -0.00329918i q^{11} +(1.66046 - 0.492817i) q^{12} +(1.14909 - 1.14909i) q^{13} +4.71896 q^{14} +(-2.97192 - 2.48348i) q^{15} -1.00000 q^{16} +(4.95340 - 4.95340i) q^{17} +(0.620596 - 2.93511i) q^{18} -1.00000i q^{19} +(1.23695 + 1.86278i) q^{20} +(3.89620 - 7.18507i) q^{21} +(0.00233287 + 0.00233287i) q^{22} +(1.28904 + 1.28904i) q^{23} +(-0.825649 + 1.52260i) q^{24} +(1.93989 - 4.60834i) q^{25} +1.62506i q^{26} +(-3.95659 - 3.36829i) q^{27} +(-3.33681 + 3.33681i) q^{28} -1.91798 q^{29} +(3.85755 - 0.345380i) q^{30} -3.49143 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.00547816 - 0.00162589i) q^{33} +7.00516i q^{34} +(10.3432 + 2.08826i) q^{35} +(1.63661 + 2.51426i) q^{36} +(-6.71219 - 6.71219i) q^{37} +(0.707107 + 0.707107i) q^{38} +(2.47431 + 1.34173i) q^{39} +(-2.19184 - 0.442526i) q^{40} +3.63777i q^{41} +(2.32558 + 7.83564i) q^{42} +(1.52133 - 1.52133i) q^{43} -0.00329918 q^{44} +(2.65911 - 6.15866i) q^{45} -1.82298 q^{46} +(2.07305 - 2.07305i) q^{47} +(-0.492817 - 1.66046i) q^{48} +15.2685i q^{49} +(1.88688 + 4.63030i) q^{50} +(10.6660 + 5.78381i) q^{51} +(-1.14909 - 1.14909i) q^{52} +(-5.97702 - 5.97702i) q^{53} +(5.17947 - 0.415995i) q^{54} +(0.00408093 + 0.00614564i) q^{55} -4.71896i q^{56} +(1.66046 - 0.492817i) q^{57} +(1.35622 - 1.35622i) q^{58} -11.8886 q^{59} +(-2.48348 + 2.97192i) q^{60} -1.95331 q^{61} +(2.46881 - 2.46881i) q^{62} +(13.8506 + 2.92857i) q^{63} +1.00000i q^{64} +(-0.719129 + 3.56186i) q^{65} +(-0.00272396 + 0.00502332i) q^{66} +(-5.56623 - 5.56623i) q^{67} +(-4.95340 - 4.95340i) q^{68} +(-1.50514 + 2.77566i) q^{69} +(-8.79037 + 5.83713i) q^{70} +3.22989i q^{71} +(-2.93511 - 0.620596i) q^{72} +(10.3760 - 10.3760i) q^{73} +9.49246 q^{74} +(8.60799 + 0.950048i) q^{75} -1.00000 q^{76} +(-0.0110087 + 0.0110087i) q^{77} +(-2.69834 + 0.800855i) q^{78} -12.5069i q^{79} +(1.86278 - 1.23695i) q^{80} +(3.64303 - 8.22972i) q^{81} +(-2.57229 - 2.57229i) q^{82} +(-9.29959 - 9.29959i) q^{83} +(-7.18507 - 3.89620i) q^{84} +(-3.09997 + 15.3542i) q^{85} +2.15149i q^{86} +(-0.945213 - 3.18473i) q^{87} +(0.00233287 - 0.00233287i) q^{88} +6.59825 q^{89} +(2.47456 + 6.23511i) q^{90} -7.66856 q^{91} +(1.28904 - 1.28904i) q^{92} +(-1.72063 - 5.79738i) q^{93} +2.93174i q^{94} +(1.23695 + 1.86278i) q^{95} +(1.52260 + 0.825649i) q^{96} +(7.72270 + 7.72270i) q^{97} +(-10.7965 - 10.7965i) q^{98} +(0.00539946 + 0.00829500i) 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
$3$	0.492817	+	1.66046i	0.284528	+	0.958668i
$3$	0.492817	+	1.66046i	0.284528	+	0.958668i
$4$		−	1.00000i		−	0.500000i
$5$	−1.86278	+	1.23695i	−0.833060	+	0.553182i
$5$	−1.86278	+	1.23695i	−0.833060	+	0.553182i
$6$	−1.52260	−	0.825649i	−0.621598	−	0.337070i
$7$	−3.33681	−	3.33681i	−1.26119	−	1.26119i	−0.950515	−	0.310679i	$-0.899444\pi$
$7$	−3.33681	−	3.33681i	−1.26119	−	1.26119i	−0.310679	−	0.950515i	$-0.600556\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.51426	+	1.63661i	−0.838088	+	0.545536i
$10$	0.442526	−	2.19184i	0.139939	−	0.693121i
$11$		−	0.00329918i		−	0.000994740i	−1.00000		0.000497370i	$-0.999842\pi$
$11$		−	0.00329918i		−	0.000994740i	1.00000		0.000497370i	$-0.000158318\pi$
$12$	1.66046	−	0.492817i	0.479334	−	0.142264i
$13$	1.14909	−	1.14909i	0.318700	−	0.318700i	−0.529568	−	0.848268i	$-0.677646\pi$
$13$	1.14909	−	1.14909i	0.318700	−	0.318700i	0.848268	+	0.529568i	$0.177646\pi$
$14$	4.71896			1.26119
$15$	−2.97192	−	2.48348i	−0.767347	−	0.641232i
$16$	−1.00000			−0.250000
$17$	4.95340	−	4.95340i	1.20138	−	1.20138i	0.227627	−	0.973748i	$-0.426903\pi$
$17$	4.95340	−	4.95340i	1.20138	−	1.20138i	0.973748	−	0.227627i	$-0.0730967\pi$
$18$	0.620596	−	2.93511i	0.146276	−	0.691812i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	1.23695	+	1.86278i	0.276591	+	0.416530i
$21$	3.89620	−	7.18507i	0.850221	−	1.56791i
$22$	0.00233287	+	0.00233287i	0.000497370	+	0.000497370i
$23$	1.28904	+	1.28904i	0.268783	+	0.268783i	0.828610	−	0.559826i	$-0.189132\pi$
$23$	1.28904	+	1.28904i	0.268783	+	0.268783i	−0.559826	+	0.828610i	$0.689132\pi$
$24$	−0.825649	+	1.52260i	−0.168535	+	0.310799i
$25$	1.93989	−	4.60834i	0.387979	−	0.921668i
$26$			1.62506i			0.318700i
$27$	−3.95659	−	3.36829i	−0.761447	−	0.648227i
$28$	−3.33681	+	3.33681i	−0.630597	+	0.630597i
$29$	−1.91798			−0.356160			−0.178080	−	0.984016i	$-0.556989\pi$
$29$	−1.91798			−0.356160			−0.178080	+	0.984016i	$0.556989\pi$
$30$	3.85755	−	0.345380i	0.704290	−	0.0630575i
$31$	−3.49143			−0.627079			−0.313539	−	0.949575i	$-0.601515\pi$
$31$	−3.49143			−0.627079			−0.313539	+	0.949575i	$0.601515\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.00547816	−	0.00162589i	0.000953625	−	0.000283031i
$34$			7.00516i			1.20138i
$35$	10.3432	+	2.08826i	1.74832	+	0.352980i
$36$	1.63661	+	2.51426i	0.272768	+	0.419044i
$37$	−6.71219	−	6.71219i	−1.10348	−	1.10348i	−0.993988	−	0.109488i	$-0.965079\pi$
$37$	−6.71219	−	6.71219i	−1.10348	−	1.10348i	−0.109488	−	0.993988i	$-0.534921\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$	2.47431	+	1.34173i	0.396206	+	0.214848i
$40$	−2.19184	−	0.442526i	−0.346561	−	0.0699695i
$41$			3.63777i			0.568125i	0.958806	+	0.284062i	$0.0916823\pi$
$41$			3.63777i			0.568125i	−0.958806	+	0.284062i	$0.908318\pi$
$42$	2.32558	+	7.83564i	0.358845	+	1.20907i
$43$	1.52133	−	1.52133i	0.232001	−	0.232001i	−0.581526	−	0.813528i	$-0.697544\pi$
$43$	1.52133	−	1.52133i	0.232001	−	0.232001i	0.813528	+	0.581526i	$0.197544\pi$
$44$	−0.00329918			−0.000497370
$45$	2.65911	−	6.15866i	0.396397	−	0.918079i
$46$	−1.82298			−0.268783
$47$	2.07305	−	2.07305i	0.302386	−	0.302386i	−0.539561	−	0.841947i	$-0.681410\pi$
$47$	2.07305	−	2.07305i	0.302386	−	0.302386i	0.841947	+	0.539561i	$0.181410\pi$
$48$	−0.492817	−	1.66046i	−0.0711320	−	0.239667i
$49$			15.2685i			2.18122i
$50$	1.88688	+	4.63030i	0.266845	+	0.654824i
$51$	10.6660	+	5.78381i	1.49354	+	0.809895i
$52$	−1.14909	−	1.14909i	−0.159350	−	0.159350i
$53$	−5.97702	−	5.97702i	−0.821007	−	0.821007i	0.165245	−	0.986252i	$-0.447158\pi$
$53$	−5.97702	−	5.97702i	−0.821007	−	0.821007i	−0.986252	+	0.165245i	$0.947158\pi$
$54$	5.17947	−	0.415995i	0.704837	−	0.0566098i
$55$	0.00408093	+	0.00614564i	0.000550272	+	0.000828678i
$56$		−	4.71896i		−	0.630597i
$57$	1.66046	−	0.492817i	0.219933	−	0.0652752i
$58$	1.35622	−	1.35622i	0.178080	−	0.178080i
$59$	−11.8886			−1.54776			−0.773882	−	0.633330i	$-0.781688\pi$
$59$	−11.8886			−1.54776			−0.773882	+	0.633330i	$0.781688\pi$
$60$	−2.48348	+	2.97192i	−0.320616	+	0.383674i
$61$	−1.95331			−0.250096			−0.125048	−	0.992151i	$-0.539908\pi$
$61$	−1.95331			−0.250096			−0.125048	+	0.992151i	$0.539908\pi$
$62$	2.46881	−	2.46881i	0.313539	−	0.313539i
$63$	13.8506	+	2.92857i	1.74502	+	0.368965i
$64$			1.00000i			0.125000i
$65$	−0.719129	+	3.56186i	−0.0891970	+	0.441795i
$66$	−0.00272396	+	0.00502332i	−0.000335297	+	0.000618328i
$67$	−5.56623	−	5.56623i	−0.680024	−	0.680024i	0.279982	−	0.960005i	$-0.409672\pi$
$67$	−5.56623	−	5.56623i	−0.680024	−	0.680024i	−0.960005	+	0.279982i	$0.909672\pi$
$68$	−4.95340	−	4.95340i	−0.600688	−	0.600688i
$69$	−1.50514	+	2.77566i	−0.181198	+	0.334150i
$70$	−8.79037	+	5.83713i	−1.05065	+	0.697670i
$71$			3.22989i			0.383318i	0.981462	+	0.191659i	$0.0613867\pi$
$71$			3.22989i			0.383318i	−0.981462	+	0.191659i	$0.938613\pi$
$72$	−2.93511	−	0.620596i	−0.345906	−	0.0731380i
$73$	10.3760	−	10.3760i	1.21442	−	1.21442i	0.244868	−	0.969556i	$-0.421255\pi$
$73$	10.3760	−	10.3760i	1.21442	−	1.21442i	0.969556	−	0.244868i	$-0.0787447\pi$
$74$	9.49246			1.10348
$75$	8.60799	+	0.950048i	0.993965	+	0.109702i
$76$	−1.00000			−0.114708
$77$	−0.0110087	+	0.0110087i	−0.00125456	+	0.00125456i
$78$	−2.69834	+	0.800855i	−0.305527	+	0.0906790i
$79$		−	12.5069i		−	1.40714i	−0.710625	−	0.703570i	$-0.751588\pi$
$79$		−	12.5069i		−	1.40714i	0.710625	−	0.703570i	$-0.248412\pi$
$80$	1.86278	−	1.23695i	0.208265	−	0.138296i
$81$	3.64303	−	8.22972i	0.404782	−	0.914413i
$82$	−2.57229	−	2.57229i	−0.284062	−	0.284062i
$83$	−9.29959	−	9.29959i	−1.02076	−	1.02076i	−0.999780	−	0.0209831i	$-0.993320\pi$
$83$	−9.29959	−	9.29959i	−1.02076	−	1.02076i	−0.0209831	−	0.999780i	$-0.506680\pi$
$84$	−7.18507	−	3.89620i	−0.783955	−	0.425110i
$85$	−3.09997	+	15.3542i	−0.336238	+	1.66540i
$86$			2.15149i			0.232001i
$87$	−0.945213	−	3.18473i	−0.101338	−	0.341439i
$88$	0.00233287	−	0.00233287i	0.000248685	−	0.000248685i
$89$	6.59825			0.699413			0.349706	−	0.936859i	$-0.386281\pi$
$89$	6.59825			0.699413			0.349706	+	0.936859i	$0.386281\pi$
$90$	2.47456	+	6.23511i	0.260841	+	0.657238i
$91$	−7.66856			−0.803884
$92$	1.28904	−	1.28904i	0.134392	−	0.134392i
$93$	−1.72063	−	5.79738i	−0.178421	−	0.601160i
$94$			2.93174i			0.302386i
$95$	1.23695	+	1.86278i	0.126909	+	0.191117i
$96$	1.52260	+	0.825649i	0.155399	+	0.0842675i
$97$	7.72270	+	7.72270i	0.784121	+	0.784121i	0.980523	−	0.196402i	$-0.0629258\pi$
$97$	7.72270	+	7.72270i	0.784121	+	0.784121i	−0.196402	+	0.980523i	$0.562926\pi$
$98$	−10.7965	−	10.7965i	−1.09061	−	1.09061i
$99$	0.00539946	+	0.00829500i	0.000542666	+	0.000833679i
$100$	−4.60834	−	1.93989i	−0.460834	−	0.193989i
$101$			16.1869i			1.61066i	0.592826	+	0.805330i	$0.298012\pi$
$101$			16.1869i			1.61066i	−0.592826	+	0.805330i	$0.701988\pi$
$102$	−11.6318	+	3.45226i	−1.15172	+	0.341825i
$103$	0.233618	−	0.233618i	0.0230191	−	0.0230191i	−0.695504	−	0.718523i	$-0.744819\pi$
$103$	0.233618	−	0.233618i	0.0230191	−	0.0230191i	0.718523	+	0.695504i	$0.244819\pi$
$104$	1.62506			0.159350
$105$	1.62983	+	18.2036i	0.159055	+	1.77649i
$106$	8.45278			0.821007
$107$	−13.2302	+	13.2302i	−1.27901	+	1.27901i	−0.337791	+	0.941221i	$0.609680\pi$
$107$	−13.2302	+	13.2302i	−1.27901	+	1.27901i	−0.941221	+	0.337791i	$0.890320\pi$
$108$	−3.36829	+	3.95659i	−0.324114	+	0.380723i
$109$		−	15.5455i		−	1.48899i	−0.667628	−	0.744495i	$-0.732690\pi$
$109$		−	15.5455i		−	1.48899i	0.667628	−	0.744495i	$-0.267310\pi$
$110$	−0.00723128	−	0.00145997i	−0.000689475	−	0.000139203i
$111$	7.83744	−	14.4532i	0.743897	−	1.37184i
$112$	3.33681	+	3.33681i	0.315298	+	0.315298i
$113$	−0.674324	−	0.674324i	−0.0634351	−	0.0634351i	0.674678	−	0.738113i	$-0.264283\pi$
$113$	−0.674324	−	0.674324i	−0.0634351	−	0.0634351i	−0.738113	+	0.674678i	$0.764283\pi$
$114$	−0.825649	+	1.52260i	−0.0773291	+	0.142604i
$115$	−3.99568	−	0.806715i	−0.372599	−	0.0752265i
$116$			1.91798i			0.178080i
$117$	−1.00850	+	4.76971i	−0.0932362	+	0.440960i
$118$	8.40651	−	8.40651i	0.773882	−	0.773882i
$119$	−33.0570			−3.03033
$120$	−0.345380	−	3.85755i	−0.0315287	−	0.352145i
$121$	11.0000			0.999999
$122$	1.38120	−	1.38120i	0.125048	−	0.125048i
$123$	−6.04038	+	1.79276i	−0.544643	+	0.161647i
$124$			3.49143i			0.313539i
$125$	2.08671	+	10.9839i	0.186641	+	0.982428i
$126$	−11.8647	+	7.72308i	−1.05699	+	0.688026i
$127$	0.324072	+	0.324072i	0.0287567	+	0.0287567i	0.721339	−	0.692582i	$-0.243527\pi$
$127$	0.324072	+	0.324072i	0.0287567	+	0.0287567i	−0.692582	+	0.721339i	$0.743527\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.27586	+	1.77638i	0.288423	+	0.156401i
$130$	−2.01012	−	3.02712i	−0.176299	−	0.265496i
$131$		−	15.9941i		−	1.39741i	−0.715409	−	0.698706i	$-0.753760\pi$
$131$		−	15.9941i		−	1.39741i	0.715409	−	0.698706i	$-0.246240\pi$
$132$	−0.00162589	−	0.00547816i	−0.000141516	−	0.000476812i
$133$	−3.33681	+	3.33681i	−0.289338	+	0.289338i
$134$	7.87184			0.680024
$135$	11.5367	+	1.38026i	0.992919	+	0.118793i
$136$	7.00516			0.600688
$137$	−4.73854	+	4.73854i	−0.404841	+	0.404841i	−0.879935	−	0.475094i	$-0.842414\pi$
$137$	−4.73854	+	4.73854i	−0.404841	+	0.404841i	0.475094	+	0.879935i	$0.342414\pi$
$138$	−0.898394	−	3.02698i	−0.0764764	−	0.257674i
$139$			21.0400i			1.78459i	0.451454	+	0.892294i	$0.350905\pi$
$139$			21.0400i			1.78459i	−0.451454	+	0.892294i	$0.649095\pi$
$140$	2.08826	−	10.3432i	0.176490	−	0.874160i
$141$	4.46386	+	2.42059i	0.375925	+	0.203850i
$142$	−2.28388	−	2.28388i	−0.191659	−	0.191659i
$143$	−0.00379104	−	0.00379104i	−0.000317023	−	0.000317023i
$144$	2.51426	−	1.63661i	0.209522	−	0.136384i
$145$	3.57277	−	2.37245i	0.296703	−	0.197021i
$146$			14.6739i			1.21442i
$147$	−25.3528	+	7.52460i	−2.09107	+	0.620618i
$148$	−6.71219	+	6.71219i	−0.551738	+	0.551738i
$149$	−9.46498			−0.775402			−0.387701	−	0.921785i	$-0.626731\pi$
$149$	−9.46498			−0.775402			−0.387701	+	0.921785i	$0.626731\pi$
$150$	−6.75855	+	5.41498i	−0.551833	+	0.442131i
$151$	−11.5421			−0.939279			−0.469639	−	0.882858i	$-0.655616\pi$
$151$	−11.5421			−0.939279			−0.469639	+	0.882858i	$0.655616\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$	−4.34738	+	20.5609i	−0.351465	+	1.66225i
$154$		−	0.0155687i		−	0.00125456i
$155$	6.50376	−	4.31873i	0.522394	−	0.346889i
$156$	1.34173	−	2.47431i	0.107424	−	0.198103i
$157$	−8.81673	−	8.81673i	−0.703651	−	0.703651i	0.261541	−	0.965192i	$-0.415769\pi$
$157$	−8.81673	−	8.81673i	−0.703651	−	0.703651i	−0.965192	+	0.261541i	$0.915769\pi$
$158$	8.84374	+	8.84374i	0.703570	+	0.703570i
$159$	6.97903	−	12.8702i	0.553473	−	1.02067i
$160$	−0.442526	+	2.19184i	−0.0349847	+	0.173280i
$161$		−	8.60255i		−	0.677976i
$162$	3.24328	+	8.39531i	0.254816	+	0.659597i
$163$	1.80955	−	1.80955i	0.141735	−	0.141735i	−0.632679	−	0.774414i	$-0.718045\pi$
$163$	1.80955	−	1.80955i	0.141735	−	0.141735i	0.774414	+	0.632679i	$0.218045\pi$
$164$	3.63777			0.284062
$165$	−0.00819345	+	0.00980490i	−0.000637859	+	0.000763311i
$166$	13.1516			1.02076
$167$	−10.1823	+	10.1823i	−0.787928	+	0.787928i	−0.981154	−	0.193226i	$-0.938105\pi$
$167$	−10.1823	+	10.1823i	−0.787928	+	0.787928i	0.193226	+	0.981154i	$0.438105\pi$
$168$	7.83564	−	2.32558i	0.604533	−	0.179423i
$169$			10.3592i			0.796861i
$170$	−8.66506	−	13.0491i	−0.664580	−	1.00082i
$171$	1.63661	+	2.51426i	0.125154	+	0.192270i
$172$	−1.52133	−	1.52133i	−0.116001	−	0.116001i
$173$	4.12383	+	4.12383i	0.313529	+	0.313529i	0.846275	−	0.532746i	$-0.178840\pi$
$173$	4.12383	+	4.12383i	0.313529	+	0.313529i	−0.532746	+	0.846275i	$0.678840\pi$
$174$	2.92031	+	1.58358i	0.221388	+	0.120051i
$175$	−21.8502	+	8.90409i	−1.65172	+	0.673086i
$176$			0.00329918i			0.000248685i
$177$	−5.85890	−	19.7406i	−0.440382	−	1.48379i
$178$	−4.66567	+	4.66567i	−0.349706	+	0.349706i
$179$	1.74920			0.130741			0.0653706	−	0.997861i	$-0.479177\pi$
$179$	1.74920			0.130741			0.0653706	+	0.997861i	$0.479177\pi$
$180$	−6.15866	−	2.65911i	−0.459040	−	0.198198i
$181$	−16.8570			−1.25297			−0.626485	−	0.779434i	$-0.715507\pi$
$181$	−16.8570			−1.25297			−0.626485	+	0.779434i	$0.715507\pi$
$182$	5.42249	−	5.42249i	0.401942	−	0.401942i
$183$	−0.962624	−	3.24339i	−0.0711592	−	0.239759i
$184$			1.82298i			0.134392i
$185$	20.8060	+	4.20066i	1.52969	+	0.308839i
$186$	5.31604	+	2.88269i	0.389791	+	0.211369i
$187$	−0.0163421	−	0.0163421i	−0.00119506	−	0.00119506i
$188$	−2.07305	−	2.07305i	−0.151193	−	0.151193i
$189$	1.96306	+	24.4417i	0.142792	+	1.77787i
$190$	−2.19184	−	0.442526i	−0.159013	−	0.0321042i
$191$			2.59256i			0.187591i	0.995591	+	0.0937954i	$0.0299000\pi$
$191$			2.59256i			0.187591i	−0.995591	+	0.0937954i	$0.970100\pi$
$192$	−1.66046	+	0.492817i	−0.119833	+	0.0355660i
$193$	−1.18301	+	1.18301i	−0.0851547	+	0.0851547i	−0.748401	−	0.663246i	$-0.769178\pi$
$193$	−1.18301	+	1.18301i	−0.0851547	+	0.0851547i	0.663246	+	0.748401i	$0.269178\pi$
$194$	−10.9215			−0.784121
$195$	−6.26874	+	0.561262i	−0.448913	+	0.0401928i
$196$	15.2685			1.09061
$197$	7.67888	−	7.67888i	0.547097	−	0.547097i	−0.378503	−	0.925600i	$-0.623561\pi$
$197$	7.67888	−	7.67888i	0.547097	−	0.547097i	0.925600	+	0.378503i	$0.123561\pi$
$198$	−0.00968345	−	0.00204746i	−0.000688173	−	0.000145506i
$199$		−	8.22358i		−	0.582954i	−0.956578	−	0.291477i	$-0.905853\pi$
$199$		−	8.22358i		−	0.582954i	0.956578	−	0.291477i	$-0.0941467\pi$
$200$	4.63030	−	1.88688i	0.327412	−	0.133422i
$201$	6.49938	−	11.9857i	0.458431	−	0.845403i
$202$	−11.4459	−	11.4459i	−0.805330	−	0.805330i
$203$	6.39993	+	6.39993i	0.449187	+	0.449187i
$204$	5.78381	−	10.6660i	0.404947	−	0.746772i
$205$	−4.49975	−	6.77637i	−0.314276	−	0.473282i
$206$			0.330386i			0.0230191i
$207$	−5.35064	−	1.13133i	−0.371895	−	0.0786331i
$208$	−1.14909	+	1.14909i	−0.0796749	+	0.0796749i
$209$	−0.00329918			−0.000228209
$210$	−14.0244	−	11.7194i	−0.967773	−	0.808718i
$211$	14.8721			1.02384			0.511920	−	0.859033i	$-0.328934\pi$
$211$	14.8721			1.02384			0.511920	+	0.859033i	$0.328934\pi$
$212$	−5.97702	+	5.97702i	−0.410503	+	0.410503i
$213$	−5.36311	+	1.59175i	−0.367474	+	0.109065i
$214$		−	18.7103i		−	1.27901i
$215$	−0.952091	+	4.71573i	−0.0649320	+	0.321610i
$216$	−0.415995	−	5.17947i	−0.0283049	−	0.352419i
$217$	11.6502	+	11.6502i	0.790868	+	0.790868i
$218$	10.9923	+	10.9923i	0.744495	+	0.744495i
$219$	22.3425	+	12.1155i	1.50977	+	0.818692i
$220$	0.00614564	−	0.00408093i	0.000414339	−	0.000275136i
$221$		−	11.3838i		−	0.765756i
$222$	4.67805	+	15.7619i	0.313970	+	1.05787i
$223$	−4.56460	+	4.56460i	−0.305668	+	0.305668i	−0.843227	−	0.537558i	$-0.819347\pi$
$223$	−4.56460	+	4.56460i	−0.305668	+	0.305668i	0.537558	+	0.843227i	$0.319347\pi$
$224$	−4.71896			−0.315298
$225$	2.66464	+	14.7614i	0.177643	+	0.984095i
$226$	0.953638			0.0634351
$227$	8.94878	−	8.94878i	0.593952	−	0.593952i	−0.344745	−	0.938696i	$-0.612035\pi$
$227$	8.94878	−	8.94878i	0.593952	−	0.593952i	0.938696	+	0.344745i	$0.112035\pi$
$228$	−0.492817	−	1.66046i	−0.0326376	−	0.109967i
$229$		−	15.6381i		−	1.03339i	−0.856169	−	0.516696i	$-0.827162\pi$
$229$		−	15.6381i		−	1.03339i	0.856169	−	0.516696i	$-0.172838\pi$
$230$	3.39580	−	2.25494i	0.223913	−	0.148686i
$231$	−0.0237048	−	0.0128543i	−0.00155966	−	0.000845748i
$232$	−1.35622	−	1.35622i	−0.0890400	−	0.0890400i
$233$	11.5507	+	11.5507i	0.756711	+	0.756711i	0.975722	−	0.219012i	$-0.0702833\pi$
$233$	11.5507	+	11.5507i	0.756711	+	0.756711i	−0.219012	+	0.975722i	$0.570283\pi$
$234$	−2.65958	−	4.08582i	−0.173862	−	0.267098i
$235$	−1.29737	+	6.42592i	−0.0846312	+	0.419181i
$236$			11.8886i			0.773882i
$237$	20.7673	−	6.16363i	1.34898	−	0.400371i
$238$	23.3749	−	23.3749i	1.51517	−	1.51517i
$239$	10.3774			0.671261			0.335631	−	0.941994i	$-0.391051\pi$
$239$	10.3774			0.671261			0.335631	+	0.941994i	$0.391051\pi$
$240$	2.97192	+	2.48348i	0.191837	+	0.160308i
$241$	14.4062			0.927988			0.463994	−	0.885838i	$-0.346416\pi$
$241$	14.4062			0.927988			0.463994	+	0.885838i	$0.346416\pi$
$242$	−7.77817	+	7.77817i	−0.500000	+	0.500000i
$243$	15.4605	+	1.99337i	0.991790	+	0.127875i
$244$			1.95331i			0.125048i
$245$	−18.8865	−	28.4419i	−1.20661	−	1.81709i
$246$	3.00352	−	5.53886i	0.191498	−	0.353145i
$247$	−1.14909	−	1.14909i	−0.0731147	−	0.0731147i
$248$	−2.46881	−	2.46881i	−0.156770	−	0.156770i
$249$	10.8586	−	20.0246i	0.688137	−	1.26901i
$250$	−9.24230	−	6.29125i	−0.584535	−	0.397894i
$251$		−	20.7089i		−	1.30713i	−0.756869	−	0.653567i	$-0.773272\pi$
$251$		−	20.7089i		−	1.30713i	0.756869	−	0.653567i	$-0.226728\pi$
$252$	2.92857	−	13.8506i	0.184482	−	0.872509i
$253$	0.00425277	−	0.00425277i	0.000267370	−	0.000267370i
$254$	−0.458306			−0.0287567
$255$	−27.0228	+	2.41944i	−1.69223	+	0.151511i
$256$	1.00000			0.0625000
$257$	−7.24360	+	7.24360i	−0.451843	+	0.451843i	−0.895966	−	0.444123i	$-0.853515\pi$
$257$	−7.24360	+	7.24360i	−0.451843	+	0.451843i	0.444123	+	0.895966i	$0.353515\pi$
$258$	−3.57247	+	1.06029i	−0.222412	+	0.0660109i
$259$			44.7945i			2.78340i
$260$	3.56186	+	0.719129i	0.220897	+	0.0445985i
$261$	4.82231	−	3.13898i	0.298493	−	0.194298i
$262$	11.3095	+	11.3095i	0.698706	+	0.698706i
$263$	−1.90123	−	1.90123i	−0.117235	−	0.117235i	0.646056	−	0.763290i	$-0.276417\pi$
$263$	−1.90123	−	1.90123i	−0.117235	−	0.117235i	−0.763290	+	0.646056i	$0.776417\pi$
$264$	0.00502332	+	0.00272396i	0.000309164	+	0.000167648i
$265$	18.5272	+	3.74058i	1.13811	+	0.229782i
$266$		−	4.71896i		−	0.289338i
$267$	3.25173	+	10.9561i	0.199003	+	0.670505i
$268$	−5.56623	+	5.56623i	−0.340012	+	0.340012i
$269$	21.4029			1.30496			0.652480	−	0.757806i	$-0.273729\pi$
$269$	21.4029			1.30496			0.652480	+	0.757806i	$0.273729\pi$
$270$	−9.13365	+	7.18167i	−0.555856	+	0.437063i
$271$	4.88606			0.296807			0.148404	−	0.988927i	$-0.452587\pi$
$271$	4.88606			0.296807			0.148404	+	0.988927i	$0.452587\pi$
$272$	−4.95340	+	4.95340i	−0.300344	+	0.300344i
$273$	−3.77920	−	12.7334i	−0.228727	−	0.770657i
$274$		−	6.70131i		−	0.404841i
$275$	−0.0152037	−	0.00640005i	−0.000916820	−	0.000385938i
$276$	2.77566	+	1.50514i	0.167075	+	0.0905988i
$277$	16.6272	+	16.6272i	0.999031	+	0.999031i	1.00000		0.000968978i	$-0.000308435\pi$
$277$	16.6272	+	16.6272i	0.999031	+	0.999031i	−0.000968978		1.00000i	$0.500308\pi$
$278$	−14.8775	−	14.8775i	−0.892294	−	0.892294i
$279$	8.77836	−	5.71409i	0.525547	−	0.342094i
$280$	5.83713	+	8.79037i	0.348835	+	0.525325i
$281$			7.94326i			0.473855i	0.971527	+	0.236928i	$0.0761404\pi$
$281$			7.94326i			0.473855i	−0.971527	+	0.236928i	$0.923860\pi$
$282$	−4.86804	+	1.44481i	−0.289888	+	0.0860373i
$283$	−8.91351	+	8.91351i	−0.529853	+	0.529853i	−0.920529	−	0.390675i	$-0.872242\pi$
$283$	−8.91351	+	8.91351i	−0.529853	+	0.529853i	0.390675	+	0.920529i	$0.372242\pi$
$284$	3.22989			0.191659
$285$	−2.48348	+	2.97192i	−0.147109	+	0.176041i
$286$	0.00536135			0.000317023
$287$	12.1385	−	12.1385i	0.716515	−	0.716515i
$288$	−0.620596	+	2.93511i	−0.0365690	+	0.172953i
$289$		−	32.0723i		−	1.88661i
$290$	−0.848756	+	4.20391i	−0.0498407	+	0.246862i
$291$	−9.01736	+	16.6291i	−0.528607	+	0.974816i
$292$	−10.3760	−	10.3760i	−0.607212	−	0.607212i
$293$	−14.7740	−	14.7740i	−0.863104	−	0.863104i	0.128593	−	0.991697i	$-0.458954\pi$
$293$	−14.7740	−	14.7740i	−0.863104	−	0.863104i	−0.991697	+	0.128593i	$0.958954\pi$
$294$	12.6065	−	23.2478i	0.735223	−	1.35584i
$295$	22.1458	−	14.7056i	1.28938	−	0.856196i
$296$		−	9.49246i		−	0.551738i
$297$	−0.0111126	+	0.0130535i	−0.000644817	+	0.000757441i
$298$	6.69275	−	6.69275i	0.387701	−	0.387701i
$299$	2.96244			0.171322
$300$	0.950048	−	8.60799i	0.0548511	−	0.496982i
$301$	−10.1528			−0.585197
$302$	8.16146	−	8.16146i	0.469639	−	0.469639i
$303$	−26.8778	+	7.97720i	−1.54409	+	0.458278i
$304$			1.00000i			0.0573539i
$305$	3.63858	−	2.41615i	0.208345	−	0.138348i
$306$	−11.4647	−	17.6128i	−0.655393	−	1.00686i
$307$	−20.3918	−	20.3918i	−1.16382	−	1.16382i	−0.983632	−	0.180188i	$-0.942329\pi$
$307$	−20.3918	−	20.3918i	−1.16382	−	1.16382i	−0.180188	−	0.983632i	$-0.557671\pi$
$308$	0.0110087	+	0.0110087i	0.000627280	+	0.000627280i
$309$	0.503045	+	0.272783i	0.0286172	+	0.0155181i
$310$	−1.54505	+	7.65265i	−0.0877527	+	0.434642i
$311$		−	6.29224i		−	0.356800i	−0.983958	−	0.178400i	$-0.942908\pi$
$311$		−	6.29224i		−	0.356800i	0.983958	−	0.178400i	$-0.0570921\pi$
$312$	0.800855	+	2.69834i	0.0453395	+	0.152763i
$313$	5.94003	−	5.94003i	0.335750	−	0.335750i	−0.519015	−	0.854765i	$-0.673701\pi$
$313$	5.94003	−	5.94003i	0.335750	−	0.335750i	0.854765	+	0.519015i	$0.173701\pi$
$314$	12.4687			0.703651
$315$	−29.4232	+	11.6773i	−1.65781	+	0.657943i
$316$	−12.5069			−0.703570
$317$	12.9036	−	12.9036i	0.724736	−	0.724736i	−0.244830	−	0.969566i	$-0.578732\pi$
$317$	12.9036	−	12.9036i	0.724736	−	0.724736i	0.969566	+	0.244830i	$0.0787321\pi$
$318$	4.16568	+	14.0355i	0.233600	+	0.787073i
$319$			0.00632776i			0.000354287i
$320$	−1.23695	−	1.86278i	−0.0691478	−	0.104133i
$321$	−28.4883	−	15.4482i	−1.59006	−	0.862233i
$322$	6.08292	+	6.08292i	0.338988	+	0.338988i
$323$	−4.95340	−	4.95340i	−0.275614	−	0.275614i
$324$	−8.22972	−	3.64303i	−0.457207	−	0.202391i
$325$	−3.06628	−	7.52450i	−0.170087	−	0.417384i
$326$			2.55908i			0.141735i
$327$	25.8127	−	7.66110i	1.42745	−	0.423660i
$328$	−2.57229	+	2.57229i	−0.142031	+	0.142031i
$329$	−13.8348			−0.762735
$330$	−0.00113947	−	0.0127268i	−6.27258e−5	−	0.000700585i
$331$	−22.2824			−1.22475			−0.612376	−	0.790567i	$-0.709786\pi$
$331$	−22.2824			−1.22475			−0.612376	+	0.790567i	$0.709786\pi$
$332$	−9.29959	+	9.29959i	−0.510381	+	0.510381i
$333$	27.8614	+	5.89099i	1.52680	+	0.322824i
$334$		−	14.3999i		−	0.787928i
$335$	17.2538	+	3.48349i	0.942678	+	0.190324i
$336$	−3.89620	+	7.18507i	−0.212555	+	0.391978i
$337$	19.0330	+	19.0330i	1.03679	+	1.03679i	0.999297	+	0.0374972i	$0.0119385\pi$
$337$	19.0330	+	19.0330i	1.03679	+	1.03679i	0.0374972	+	0.999297i	$0.488061\pi$
$338$	−7.32506	−	7.32506i	−0.398431	−	0.398431i
$339$	0.787371	−	1.45201i	0.0427641	−	0.0788622i
$340$	15.3542	+	3.09997i	0.832699	+	0.168119i
$341$			0.0115188i			0.000623780i
$342$	−2.93511	−	0.620596i	−0.158712	−	0.0335580i
$343$	27.5905	−	27.5905i	1.48975	−	1.48975i
$344$	2.15149			0.116001
$345$	−0.629620	−	7.03223i	−0.0338976	−	0.378603i
$346$	−5.83198			−0.313529
$347$	2.64462	−	2.64462i	0.141971	−	0.141971i	−0.632549	−	0.774520i	$-0.717991\pi$
$347$	2.64462	−	2.64462i	0.141971	−	0.141971i	0.774520	+	0.632549i	$0.217991\pi$
$348$	−3.18473	+	0.945213i	−0.170720	+	0.0506688i
$349$			27.9124i			1.49412i	0.664758	+	0.747059i	$0.268535\pi$
$349$			27.9124i			1.49412i	−0.664758	+	0.747059i	$0.731465\pi$
$350$	9.15427	−	21.7466i	0.489316	−	1.16240i
$351$	−8.41693	+	0.676015i	−0.449263	+	0.0360830i
$352$	−0.00233287	−	0.00233287i	−0.000124342	−	0.000124342i
$353$	−3.63692	−	3.63692i	−0.193574	−	0.193574i	0.603665	−	0.797238i	$-0.293707\pi$
$353$	−3.63692	−	3.63692i	−0.193574	−	0.193574i	−0.797238	+	0.603665i	$0.793707\pi$
$354$	18.1016	+	9.81581i	0.962087	+	0.521705i
$355$	−3.99523	−	6.01658i	−0.212045	−	0.319327i
$356$		−	6.59825i		−	0.349706i
$357$	−16.2911	−	54.8899i	−0.862215	−	2.90508i
$358$	−1.23687	+	1.23687i	−0.0653706	+	0.0653706i
$359$	−19.0031			−1.00295			−0.501473	−	0.865173i	$-0.667208\pi$
$359$	−19.0031			−1.00295			−0.501473	+	0.865173i	$0.667208\pi$
$360$	6.23511	−	2.47456i	0.328619	−	0.130421i
$361$	−1.00000			−0.0526316
$362$	11.9197	−	11.9197i	0.626485	−	0.626485i
$363$	5.42098	+	18.2651i	0.284528	+	0.958667i
$364$			7.66856i			0.401942i
$365$	−6.49360	+	32.1630i	−0.339891	+	1.68349i
$366$	2.97410	+	1.61275i	0.155459	+	0.0842997i
$367$	3.36608	+	3.36608i	0.175708	+	0.175708i	0.789482	−	0.613774i	$-0.210349\pi$
$367$	3.36608	+	3.36608i	0.175708	+	0.175708i	−0.613774	+	0.789482i	$0.710349\pi$
$368$	−1.28904	−	1.28904i	−0.0671958	−	0.0671958i
$369$	−5.95360	−	9.14632i	−0.309932	−	0.476138i
$370$	−17.6824	+	11.7417i	−0.919262	+	0.610424i
$371$			39.8883i			2.07090i
$372$	−5.79738	+	1.72063i	−0.300580	+	0.0892107i
$373$	4.67503	−	4.67503i	0.242064	−	0.242064i	−0.575640	−	0.817704i	$-0.695247\pi$
$373$	4.67503	−	4.67503i	0.242064	−	0.242064i	0.817704	+	0.575640i	$0.195247\pi$
$374$	0.0231113			0.00119506
$375$	−17.2099	+	8.87794i	−0.888718	+	0.458455i
$376$	2.93174			0.151193
$377$	−2.20393	+	2.20393i	−0.113508	+	0.113508i
$378$	−18.6710	−	15.8948i	−0.960332	−	0.817540i
$379$			6.60335i			0.339191i	0.985514	+	0.169596i	$0.0542461\pi$
$379$			6.60335i			0.339191i	−0.985514	+	0.169596i	$0.945754\pi$
$380$	1.86278	−	1.23695i	0.0955586	−	0.0634544i
$381$	−0.378400	+	0.697816i	−0.0193860	+	0.0357502i
$382$	−1.83322	−	1.83322i	−0.0937954	−	0.0937954i
$383$	−14.4355	−	14.4355i	−0.737619	−	0.737619i	0.234498	−	0.972117i	$-0.424655\pi$
$383$	−14.4355	−	14.4355i	−0.737619	−	0.737619i	−0.972117	+	0.234498i	$0.924655\pi$
$384$	0.825649	−	1.52260i	0.0421337	−	0.0776997i
$385$	0.00688954	−	0.0341241i	0.000351124	−	0.00173912i
$386$		−	1.67302i		−	0.0851547i
$387$	−1.33521	+	6.31486i	−0.0678724	+	0.321002i
$388$	7.72270	−	7.72270i	0.392061	−	0.392061i
$389$	0.566176			0.0287063			0.0143531	−	0.999897i	$-0.495431\pi$
$389$	0.566176			0.0287063			0.0143531	+	0.999897i	$0.495431\pi$
$390$	4.03579	−	4.82954i	0.204360	−	0.244553i
$391$	12.7703			0.645819
$392$	−10.7965	+	10.7965i	−0.545305	+	0.545305i
$393$	26.5576	−	7.88217i	1.33965	−	0.397603i
$394$			10.8596i			0.547097i
$395$	15.4705	+	23.2977i	0.778405	+	1.17223i
$396$	0.00829500	−	0.00539946i	0.000416840	−	0.000271333i
$397$	11.0271	+	11.0271i	0.553436	+	0.553436i	0.927431	−	0.373995i	$-0.122012\pi$
$397$	11.0271	+	11.0271i	0.553436	+	0.553436i	−0.373995	+	0.927431i	$0.622012\pi$
$398$	5.81495	+	5.81495i	0.291477	+	0.291477i
$399$	−7.18507	−	3.89620i	−0.359703	−	0.195054i
$400$	−1.93989	+	4.60834i	−0.0969947	+	0.230417i
$401$			33.0910i			1.65249i	0.563313	+	0.826243i	$0.309526\pi$
$401$			33.0910i			1.65249i	−0.563313	+	0.826243i	$0.690474\pi$
$402$	3.87938	+	13.0709i	0.193486	+	0.651917i
$403$	−4.01195	+	4.01195i	−0.199850	+	0.199850i
$404$	16.1869			0.805330
$405$	3.39361	+	19.8364i	0.168630	+	0.985679i
$406$	−9.05086			−0.449187
$407$	−0.0221447	+	0.0221447i	−0.00109767	+	0.00109767i
$408$	3.45226	+	11.6318i	0.170912	+	0.575860i
$409$		−	26.2274i		−	1.29686i	−0.761274	−	0.648430i	$-0.775426\pi$
$409$		−	26.2274i		−	1.29686i	0.761274	−	0.648430i	$-0.224574\pi$
$410$	7.97342	+	1.60981i	0.393779	+	0.0795028i
$411$	−10.2034	−	5.53293i	−0.503296	−	0.272919i
$412$	−0.233618	−	0.233618i	−0.0115095	−	0.0115095i
$413$	39.6699	+	39.6699i	1.95203	+	1.95203i
$414$	4.58344	−	2.98350i	0.225264	−	0.146631i
$415$	28.8262	+	5.81993i	1.41502	+	0.285689i
$416$		−	1.62506i		−	0.0796749i
$417$	−34.9361	+	10.3689i	−1.71083	+	0.507765i
$418$	0.00233287	−	0.00233287i	0.000114104	−	0.000114104i
$419$	−16.7418			−0.817888			−0.408944	−	0.912559i	$-0.634103\pi$
$419$	−16.7418			−0.817888			−0.408944	+	0.912559i	$0.634103\pi$
$420$	18.2036	−	1.62983i	0.888246	−	0.0795277i
$421$	20.3487			0.991734			0.495867	−	0.868399i	$-0.334850\pi$
$421$	20.3487			0.991734			0.495867	+	0.868399i	$0.334850\pi$
$422$	−10.5162	+	10.5162i	−0.511920	+	0.511920i
$423$	−1.81943	+	8.60498i	−0.0884636	+	0.418389i
$424$		−	8.45278i		−	0.410503i
$425$	−13.2179	−	32.4360i	−0.641162	−	1.57338i
$426$	2.66676	−	4.91783i	0.129205	−	0.238269i
$427$	6.51781	+	6.51781i	0.315419	+	0.315419i
$428$	13.2302	+	13.2302i	0.639506	+	0.639506i
$429$	0.00442659	−	0.00816317i	0.000213718	−	0.000394122i
$430$	−2.66129	−	4.00775i	−0.128339	−	0.193271i
$431$			37.8255i			1.82199i	0.412418	+	0.910995i	$0.364684\pi$
$431$			37.8255i			1.82199i	−0.412418	+	0.910995i	$0.635316\pi$
$432$	3.95659	+	3.36829i	0.190362	+	0.162057i
$433$	3.73358	−	3.73358i	0.179424	−	0.179424i	−0.611681	−	0.791105i	$-0.709506\pi$
$433$	3.73358	−	3.73358i	0.179424	−	0.179424i	0.791105	+	0.611681i	$0.209506\pi$
$434$	−16.4759			−0.790868
$435$	5.70009	+	4.76327i	0.273298	+	0.228381i
$436$	−15.5455			−0.744495
$437$	1.28904	−	1.28904i	0.0616631	−	0.0616631i
$438$	−24.3655	+	7.23157i	−1.16423	+	0.345538i
$439$			9.80030i			0.467743i	0.972268	+	0.233871i	$0.0751395\pi$
$439$			9.80030i			0.467743i	−0.972268	+	0.233871i	$0.924861\pi$
$440$	−0.00145997	+	0.00723128i	−6.96014e−5	+	0.000344738i
$441$	−24.9886	−	38.3891i	−1.18993	−	1.82805i
$442$	8.04954	+	8.04954i	0.382878	+	0.382878i
$443$	7.47230	+	7.47230i	0.355020	+	0.355020i	0.861973	−	0.506954i	$-0.169228\pi$
$443$	7.47230	+	7.47230i	0.355020	+	0.355020i	−0.506954	+	0.861973i	$0.669228\pi$
$444$	−14.4532	−	7.83744i	−0.685919	−	0.371949i
$445$	−12.2911	+	8.16172i	−0.582653	+	0.386903i
$446$		−	6.45532i		−	0.305668i
$447$	−4.66451	−	15.7162i	−0.220624	−	0.743353i
$448$	3.33681	−	3.33681i	0.157649	−	0.157649i
$449$	21.7175			1.02491			0.512456	−	0.858714i	$-0.328736\pi$
$449$	21.7175			1.02491			0.512456	+	0.858714i	$0.328736\pi$
$450$	−12.3221	−	8.55372i	−0.580869	−	0.403226i
$451$	0.0120017			0.000565136
$452$	−0.674324	+	0.674324i	−0.0317175	+	0.0317175i
$453$	−5.68812	−	19.1651i	−0.267251	−	0.900456i
$454$			12.6555i			0.593952i
$455$	14.2848	−	9.48565i	0.669684	−	0.444694i
$456$	1.52260	+	0.825649i	0.0713022	+	0.0386646i
$457$	15.9122	+	15.9122i	0.744341	+	0.744341i	0.973410	−	0.229069i	$-0.0735683\pi$
$457$	15.9122	+	15.9122i	0.744341	+	0.744341i	−0.229069	+	0.973410i	$0.573568\pi$
$458$	11.0578	+	11.0578i	0.516696	+	0.516696i
$459$	−36.2831	+	2.91411i	−1.69355	+	0.136019i
$460$	−0.806715	+	3.99568i	−0.0376133	+	0.186299i
$461$		−	38.4951i		−	1.79289i	−0.443151	−	0.896447i	$-0.646140\pi$
$461$		−	38.4951i		−	1.79289i	0.443151	−	0.896447i	$-0.353860\pi$
$462$	0.0258512	−	0.00767251i	0.00120271	−	0.000356957i
$463$	10.3976	−	10.3976i	0.483219	−	0.483219i	−0.422939	−	0.906158i	$-0.639002\pi$
$463$	10.3976	−	10.3976i	0.483219	−	0.483219i	0.906158	+	0.422939i	$0.139002\pi$
$464$	1.91798			0.0890400
$465$	10.3762	+	8.67089i	0.481187	+	0.402103i
$466$	−16.3351			−0.756711
$467$	15.9962	−	15.9962i	0.740216	−	0.740216i	−0.232404	−	0.972619i	$-0.574659\pi$
$467$	15.9962	−	15.9962i	0.740216	−	0.740216i	0.972619	+	0.232404i	$0.0746591\pi$
$468$	4.76971	+	1.00850i	0.220480	+	0.0466181i
$469$			37.1469i			1.71528i
$470$	−3.62643	−	5.46119i	−0.167275	−	0.251906i
$471$	10.2948	−	18.9849i	0.474359	−	0.874776i
$472$	−8.40651	−	8.40651i	−0.386941	−	0.386941i
$473$	−0.00501915	−	0.00501915i	−0.000230781	−	0.000230781i
$474$	−10.3263	+	19.0430i	−0.474305	+	0.874676i
$475$	−4.60834	−	1.93989i	−0.211445	−	0.0890084i
$476$			33.0570i			1.51517i
$477$	24.8098	+	5.24577i	1.13596	+	0.240187i
$478$	−7.33796	+	7.33796i	−0.335631	+	0.335631i
$479$	−14.7942			−0.675966			−0.337983	−	0.941152i	$-0.609745\pi$
$479$	−14.7942			−0.675966			−0.337983	+	0.941152i	$0.609745\pi$
$480$	−3.85755	+	0.345380i	−0.176072	+	0.0157644i
$481$	−15.4258			−0.703355
$482$	−10.1868	+	10.1868i	−0.463994	+	0.463994i
$483$	14.2842	−	4.23948i	0.649954	−	0.192903i
$484$		−	11.0000i		−	0.500000i
$485$	−23.9383	−	4.83307i	−1.08698	−	0.219458i
$486$	−12.3417	+	9.52268i	−0.559833	+	0.431958i
$487$	10.6497	+	10.6497i	0.482584	+	0.482584i	0.905956	−	0.423372i	$-0.139154\pi$
$487$	10.6497	+	10.6497i	0.482584	+	0.482584i	−0.423372	+	0.905956i	$0.639154\pi$
$488$	−1.38120	−	1.38120i	−0.0625239	−	0.0625239i
$489$	3.89646	+	2.11291i	0.176204	+	0.0955489i
$490$	33.4662	+	6.75672i	1.51185	+	0.305238i
$491$			18.0717i			0.815564i	0.913079	+	0.407782i	$0.133698\pi$
$491$			18.0717i			0.815564i	−0.913079	+	0.407782i	$0.866302\pi$
$492$	1.79276	+	6.04038i	0.0808237	+	0.272321i
$493$	−9.50052	+	9.50052i	−0.427882	+	0.427882i
$494$	1.62506			0.0731147
$495$	−0.0203185	−	0.00877288i	−0.000913250	−	0.000394312i
$496$	3.49143			0.156770
$497$	10.7775	−	10.7775i	0.483438	−	0.483438i
$498$	6.48134	+	21.8377i	0.290436	+	0.978572i
$499$			19.9749i			0.894200i	0.894484	+	0.447100i	$0.147543\pi$
$499$			19.9749i			0.894200i	−0.894484	+	0.447100i	$0.852457\pi$
$500$	10.9839	−	2.08671i	0.491214	−	0.0933205i
$501$	−21.9253	−	11.8893i	−0.979548	−	0.531173i
$502$	14.6434	+	14.6434i	0.653567	+	0.653567i
$503$	−12.9225	−	12.9225i	−0.576187	−	0.576187i	0.357664	−	0.933850i	$-0.383573\pi$
$503$	−12.9225	−	12.9225i	−0.576187	−	0.576187i	−0.933850	+	0.357664i	$0.883573\pi$
$504$	7.72308	+	11.8647i	0.344013	+	0.528495i
$505$	−20.0225	−	30.1527i	−0.890989	−	1.34178i
$506$			0.00601433i			0.000267370i
$507$	−17.2010	+	5.10519i	−0.763925	+	0.226729i
$508$	0.324072	−	0.324072i	0.0143783	−	0.0143783i
$509$	−19.0740			−0.845441			−0.422721	−	0.906260i	$-0.638925\pi$
$509$	−19.0740			−0.845441			−0.422721	+	0.906260i	$0.638925\pi$
$510$	17.3972	−	20.8188i	0.770360	−	0.921872i
$511$	−69.2457			−3.06325
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.36829	+	3.95659i	−0.148714	+	0.174688i
$514$		−	10.2440i		−	0.451843i
$515$	−0.146204	+	0.724153i	−0.00644253	+	0.0319100i
$516$	1.77638	−	3.27586i	0.0782006	−	0.144212i
$517$	−0.00683938	−	0.00683938i	−0.000300796	−	0.000300796i
$518$	−31.6745	−	31.6745i	−1.39170	−	1.39170i
$519$	−4.81517	+	8.87976i	−0.211363	+	0.389778i
$520$	−3.02712	+	2.01012i	−0.132748	+	0.0881495i
$521$		−	20.0460i		−	0.878229i	−0.898431	−	0.439115i	$-0.855292\pi$
$521$		−	20.0460i		−	0.878229i	0.898431	−	0.439115i	$-0.144708\pi$
$522$	−1.19029	+	5.62948i	−0.0520976	+	0.246396i
$523$	7.71687	−	7.71687i	0.337435	−	0.337435i	−0.517966	−	0.855401i	$-0.673311\pi$
$523$	7.71687	−	7.71687i	0.337435	−	0.337435i	0.855401	+	0.517966i	$0.173311\pi$
$524$	−15.9941			−0.698706
$525$	−25.5530	−	31.8933i	−1.11523	−	1.39194i
$526$	2.68875			0.117235
$527$	−17.2944	+	17.2944i	−0.753357	+	0.753357i
$528$	−0.00547816	+	0.00162589i	−0.000238406	+	7.07578e-5i
$529$		−	19.6768i		−	0.855511i
$530$	−15.7457	+	10.4557i	−0.683948	+	0.454167i
$531$	29.8911	−	19.4570i	1.29716	−	0.844360i
$532$	3.33681	+	3.33681i	0.144669	+	0.144669i
$533$	4.18012	+	4.18012i	0.181061	+	0.181061i
$534$	−10.0465	−	5.44784i	−0.434754	−	0.235751i
$535$	8.27981	−	41.0101i	0.357967	−	1.77302i
$536$		−	7.87184i		−	0.340012i
$537$	0.862035	+	2.90448i	0.0371996	+	0.125337i
$538$	−15.1342	+	15.1342i	−0.652480	+	0.652480i
$539$	0.0503736			0.00216975
$540$	1.38026	−	11.5367i	0.0593967	−	0.496459i
$541$	13.4099			0.576536			0.288268	−	0.957550i	$-0.406921\pi$
$541$	13.4099			0.576536			0.288268	+	0.957550i	$0.406921\pi$
$542$	−3.45497	+	3.45497i	−0.148404	+	0.148404i
$543$	−8.30740	−	27.9904i	−0.356505	−	1.20118i
$544$		−	7.00516i		−	0.300344i
$545$	19.2291	+	28.9579i	0.823683	+	1.24042i
$546$	11.6761	+	6.33154i	0.499692	+	0.270965i
$547$	−6.28103	−	6.28103i	−0.268557	−	0.268557i	0.559961	−	0.828519i	$-0.310816\pi$
$547$	−6.28103	−	6.28103i	−0.268557	−	0.268557i	−0.828519	+	0.559961i	$0.810816\pi$
$548$	4.73854	+	4.73854i	0.202420	+	0.202420i
$549$	4.91113	−	3.19680i	0.209602	−	0.136436i
$550$	0.0152762	−	0.00622515i	0.000651379	−	0.000265441i
$551$			1.91798i			0.0817087i
$552$	−3.02698	+	0.898394i	−0.128837	+	0.0382382i
$553$	−41.7332	+	41.7332i	−1.77468	+	1.77468i
$554$	−23.5144			−0.999031
$555$	3.27851	+	36.6177i	0.139165	+	1.55433i
$556$	21.0400			0.892294
$557$	0.190340	−	0.190340i	0.00806496	−	0.00806496i	−0.703063	−	0.711128i	$-0.748185\pi$
$557$	0.190340	−	0.190340i	0.00806496	−	0.00806496i	0.711128	+	0.703063i	$0.248185\pi$
$558$	−2.16677	+	10.2477i	−0.0917265	+	0.433820i
$559$		−	3.49629i		−	0.147877i
$560$	−10.3432	−	2.08826i	−0.437080	−	0.0882451i
$561$	0.0190818	−	0.0351892i	0.000805635	−	0.00148569i
$562$	−5.61673	−	5.61673i	−0.236928	−	0.236928i
$563$	−26.9104	−	26.9104i	−1.13414	−	1.13414i	−0.989482	−	0.144658i	$-0.953792\pi$
$563$	−26.9104	−	26.9104i	−1.13414	−	1.13414i	−0.144658	−	0.989482i	$-0.546208\pi$
$564$	2.42059	−	4.46386i	0.101925	−	0.187963i
$565$	2.09022	+	0.422010i	0.0879364	+	0.0177541i
$566$		−	12.6056i		−	0.529853i
$567$	−39.6171	+	15.3049i	−1.66376	+	0.642744i
$568$	−2.28388	+	2.28388i	−0.0958294	+	0.0958294i
$569$	−8.17866			−0.342867			−0.171434	−	0.985196i	$-0.554840\pi$
$569$	−8.17866			−0.342867			−0.171434	+	0.985196i	$0.554840\pi$
$570$	−0.345380	−	3.85755i	−0.0144664	−	0.161575i
$571$	45.6052			1.90852			0.954259	−	0.298982i	$-0.0966469\pi$
$571$	45.6052			1.90852			0.954259	+	0.298982i	$0.0966469\pi$
$572$	−0.00379104	+	0.00379104i	−0.000158512	+	0.000158512i
$573$	−4.30484	+	1.27766i	−0.179837	+	0.0533749i
$574$			17.1665i			0.716515i
$575$	8.44094	−	3.43974i	0.352011	−	0.143447i
$576$	−1.63661	−	2.51426i	−0.0681920	−	0.104761i
$577$	−1.91976	−	1.91976i	−0.0799205	−	0.0799205i	0.666016	−	0.745937i	$-0.267998\pi$
$577$	−1.91976	−	1.91976i	−0.0799205	−	0.0799205i	−0.745937	+	0.666016i	$0.767998\pi$
$578$	22.6785	+	22.6785i	0.943303	+	0.943303i
$579$	−2.54734	−	1.38133i	−0.105864	−	0.0574062i
$580$	−2.37245	−	3.57277i	−0.0985107	−	0.148351i
$581$			62.0619i			2.57476i
$582$	−5.38232	−	18.1348i	−0.223104	−	0.751712i
$583$	−0.0197193	+	0.0197193i	−0.000816688	+	0.000816688i
$584$	14.6739			0.607212
$585$	−4.02129	−	10.1324i	−0.166260	−	0.418923i
$586$	20.8935			0.863104
$587$	26.0323	−	26.0323i	1.07447	−	1.07447i	0.0774740	−	0.996994i	$-0.475315\pi$
$587$	26.0323	−	26.0323i	1.07447	−	1.07447i	0.996994	−	0.0774740i	$-0.0246855\pi$
$588$	7.52460	+	25.3528i	0.310309	+	1.04553i
$589$			3.49143i			0.143862i
$590$	−5.26101	+	26.0579i	−0.216592	+	1.07279i
$591$	16.5348	+	8.96620i	0.680149	+	0.368820i
$592$	6.71219	+	6.71219i	0.275869	+	0.275869i
$593$	−11.6400	−	11.6400i	−0.477997	−	0.477997i	0.426494	−	0.904490i	$-0.359749\pi$
$593$	−11.6400	−	11.6400i	−0.477997	−	0.477997i	−0.904490	+	0.426494i	$0.859749\pi$
$594$	−0.00137244	−	0.0170880i	−5.63120e−5	−	0.000701129i
$595$	61.5780	−	40.8900i	2.52445	−	1.67633i
$596$			9.46498i			0.387701i
$597$	13.6549	−	4.05272i	0.558860	−	0.165867i
$598$	−2.09476	+	2.09476i	−0.0856611	+	0.0856611i
$599$	11.6334			0.475328			0.237664	−	0.971347i	$-0.423618\pi$
$599$	11.6334			0.475328			0.237664	+	0.971347i	$0.423618\pi$
$600$	5.41498	+	6.75855i	0.221066	+	0.275917i
$601$	−9.12827			−0.372350			−0.186175	−	0.982517i	$-0.559609\pi$
$601$	−9.12827			−0.372350			−0.186175	+	0.982517i	$0.559609\pi$
$602$	7.17911	−	7.17911i	0.292599	−	0.292599i
$603$	23.1047	+	4.88524i	0.940897	+	0.198942i
$604$			11.5421i			0.469639i
$605$	−20.4906	+	13.6065i	−0.833059	+	0.553182i
$606$	13.3647	−	24.6462i	0.542905	−	1.00118i
$607$	−26.6678	−	26.6678i	−1.08241	−	1.08241i	−0.996284	−	0.0861303i	$-0.972550\pi$
$607$	−26.6678	−	26.6678i	−1.08241	−	1.08241i	−0.0861303	−	0.996284i	$-0.527450\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$	−7.47284	+	13.7808i	−0.302815	+	0.558427i
$610$	−0.864390	+	4.28135i	−0.0349981	+	0.173347i
$611$		−	4.76424i		−	0.192741i
$612$	20.5609	+	4.34738i	0.831126	+	0.175732i
$613$	−11.8727	+	11.8727i	−0.479532	+	0.479532i	−0.904982	−	0.425450i	$-0.860116\pi$
$613$	−11.8727	+	11.8727i	−0.479532	+	0.479532i	0.425450	+	0.904982i	$0.360116\pi$
$614$	28.8383			1.16382
$615$	9.03434	−	10.8112i	0.364300	−	0.435949i
$616$	−0.0155687			−0.000627280
$617$	−24.2856	+	24.2856i	−0.977701	+	0.977701i	−0.999757	−	0.0220560i	$-0.992979\pi$
$617$	−24.2856	+	24.2856i	−0.977701	+	0.977701i	0.0220560	+	0.999757i	$0.492979\pi$
$618$	−0.548593	+	0.162820i	−0.0220676	+	0.00654957i
$619$		−	13.1124i		−	0.527030i	−0.964655	−	0.263515i	$-0.915118\pi$
$619$		−	13.1124i		−	0.527030i	0.964655	−	0.263515i	$-0.0848819\pi$
$620$	−4.31873	−	6.50376i	−0.173444	−	0.261197i
$621$	−0.758350	−	9.44206i	−0.0304315	−	0.378897i
$622$	4.44929	+	4.44929i	0.178400	+	0.178400i
$623$	−22.0171	−	22.0171i	−0.882095	−	0.882095i
$624$	−2.47431	−	1.34173i	−0.0990515	−	0.0537120i
$625$	−17.4736	−	17.8794i	−0.698945	−	0.715175i
$626$			8.40047i			0.335750i
$627$	−0.00162589	−	0.00547816i	−6.49318e−5	−	0.000218777i
$628$	−8.81673	+	8.81673i	−0.351826	+	0.351826i
$629$	−66.4962			−2.65138
$630$	12.5482	−	29.0625i	0.499933	−	1.15788i
$631$	38.4496			1.53066			0.765328	−	0.643641i	$-0.222577\pi$
$631$	38.4496			1.53066			0.765328	+	0.643641i	$0.222577\pi$
$632$	8.84374	−	8.84374i	0.351785	−	0.351785i
$633$	7.32924	+	24.6946i	0.291311	+	0.981522i
$634$			18.2484i			0.724736i
$635$	−1.00454	−	0.202812i	−0.0398638	−	0.00804836i
$636$	−12.8702	−	6.97903i	−0.510336	−	0.276737i
$637$	17.5449	+	17.5449i	0.695154	+	0.695154i
$638$	−0.00447440	−	0.00447440i	−0.000177143	−	0.000177143i
$639$	−5.28606	−	8.12080i	−0.209113	−	0.321254i
$640$	2.19184	+	0.442526i	0.0866402	+	0.0174924i
$641$			11.4967i			0.454092i	0.973884	+	0.227046i	$0.0729067\pi$
$641$			11.4967i			0.454092i	−0.973884	+	0.227046i	$0.927093\pi$
$642$	31.0678	−	9.22077i	1.22615	−	0.363915i
$643$	−35.5378	+	35.5378i	−1.40147	+	1.40147i	−0.606035	+	0.795438i	$0.707241\pi$
$643$	−35.5378	+	35.5378i	−1.40147	+	1.40147i	−0.795438	+	0.606035i	$0.792759\pi$
$644$	−8.60255			−0.338988
$645$	−8.29949	+	0.743082i	−0.326792	+	0.0292588i
$646$	7.00516			0.275614
$647$	10.4682	−	10.4682i	0.411548	−	0.411548i	−0.470729	−	0.882278i	$-0.656009\pi$
$647$	10.4682	−	10.4682i	0.411548	−	0.411548i	0.882278	+	0.470729i	$0.156009\pi$
$648$	8.39531	−	3.24328i	0.329799	−	0.127408i
$649$			0.0392226i			0.00153962i
$650$	7.48881	+	3.15243i	0.293735	+	0.123649i
$651$	−13.6033	+	25.0861i	−0.533155	+	0.983203i
$652$	−1.80955	−	1.80955i	−0.0708673	−	0.0708673i
$653$	6.60928	+	6.60928i	0.258641	+	0.258641i	0.824501	−	0.565860i	$-0.191456\pi$
$653$	6.60928	+	6.60928i	0.258641	+	0.258641i	−0.565860	+	0.824501i	$0.691456\pi$
$654$	−12.8351	+	23.6696i	−0.501894	+	0.925554i
$655$	19.7840	+	29.7935i	0.773023	+	1.16413i
$656$		−	3.63777i		−	0.142031i
$657$	−9.10660	+	43.0696i	−0.355282	+	1.68031i
$658$	9.78265	−	9.78265i	0.381368	−	0.381368i
$659$	17.5688			0.684382			0.342191	−	0.939630i	$-0.388831\pi$
$659$	17.5688			0.684382			0.342191	+	0.939630i	$0.388831\pi$
$660$	0.00980490	+	0.00819345i	0.000381655	+	0.000318930i
$661$	−49.5755			−1.92826			−0.964132	−	0.265422i	$-0.914489\pi$
$661$	−49.5755			−1.92826			−0.964132	+	0.265422i	$0.914489\pi$
$662$	15.7560	−	15.7560i	0.612376	−	0.612376i
$663$	18.9023	−	5.61012i	0.734105	−	0.217879i
$664$		−	13.1516i		−	0.510381i
$665$	2.08826	−	10.3432i	0.0809792	−	0.401092i
$666$	−23.8665	+	15.5354i	−0.924810	+	0.601986i
$667$	−2.47235	−	2.47235i	−0.0957299	−	0.0957299i
$668$	10.1823	+	10.1823i	0.393964	+	0.393964i
$669$	−9.82886	−	5.32983i	−0.380006	−	0.206063i
$670$	−14.6635	+	9.73710i	−0.566501	+	0.376177i
$671$			0.00644432i			0.000248780i
$672$	−2.32558	−	7.83564i	−0.0897113	−	0.302266i
$673$	1.10810	−	1.10810i	0.0427143	−	0.0427143i	−0.685427	−	0.728141i	$-0.740384\pi$
$673$	1.10810	−	1.10810i	0.0427143	−	0.0427143i	0.728141	+	0.685427i	$0.240384\pi$
$674$	−26.9167			−1.03679
$675$	−23.1976	+	11.6992i	−0.892876	+	0.450303i
$676$	10.3592			0.398431
$677$	30.2637	−	30.2637i	1.16313	−	1.16313i	0.179342	−	0.983787i	$-0.442603\pi$
$677$	30.2637	−	30.2637i	1.16313	−	1.16313i	0.983787	−	0.179342i	$-0.0573969\pi$
$678$	0.469969	+	1.58348i	0.0180491	+	0.0608132i
$679$		−	51.5383i		−	1.97786i
$680$	−13.0491	+	8.66506i	−0.500409	+	0.332290i
$681$	19.2692	+	10.4490i	0.738398	+	0.400406i
$682$	−0.00814505	−	0.00814505i	−0.000311890	−	0.000311890i
$683$	−22.9904	−	22.9904i	−0.879703	−	0.879703i	0.113800	−	0.993504i	$-0.463698\pi$
$683$	−22.9904	−	22.9904i	−0.879703	−	0.879703i	−0.993504	+	0.113800i	$0.963698\pi$
$684$	2.51426	−	1.63661i	0.0961352	−	0.0625772i
$685$	2.96550	−	14.6882i	0.113306	−	0.561207i
$686$			39.0189i			1.48975i
$687$	25.9664	−	7.70671i	0.990680	−	0.294029i
$688$	−1.52133	+	1.52133i	−0.0580003	+	0.0580003i
$689$	−13.7362			−0.523309
$690$	5.41775	+	4.52733i	0.206250	+	0.172353i
$691$	−5.79714			−0.220534			−0.110267	−	0.993902i	$-0.535171\pi$
$691$	−5.79714			−0.220534			−0.110267	+	0.993902i	$0.535171\pi$
$692$	4.12383	−	4.12383i	0.156765	−	0.156765i
$693$	0.00966186	−	0.0456957i	0.000367024	−	0.00173584i
$694$			3.74006i			0.141971i
$695$	−26.0255	−	39.1929i	−0.987203	−	1.48667i
$696$	1.58358	−	2.92031i	0.0600254	−	0.110694i
$697$	18.0193	+	18.0193i	0.682531	+	0.682531i
$698$	−19.7371	−	19.7371i	−0.747059	−	0.747059i
$699$	−13.4871	+	24.8718i	−0.510129	+	0.940739i
$700$	8.90409	+	21.8502i	0.336543	+	0.825859i
$701$			25.8432i			0.976085i	0.872820	+	0.488043i	$0.162289\pi$
$701$			25.8432i			0.976085i	−0.872820	+	0.488043i	$0.837711\pi$
$702$	5.47365	−	6.42968i	0.206590	−	0.242673i
$703$	−6.71219	+	6.71219i	−0.253155	+	0.253155i
$704$	0.00329918			0.000124342
$705$	−11.3094	+	1.01257i	−0.425935	+	0.0381354i
$706$	5.14338			0.193574
$707$	54.0127	−	54.0127i	2.03136	−	2.03136i
$708$	−19.7406	+	5.85890i	−0.741896	+	0.220191i
$709$		−	32.2841i		−	1.21246i	−0.795291	−	0.606228i	$-0.792682\pi$
$709$		−	32.2841i		−	1.21246i	0.795291	−	0.606228i	$-0.207318\pi$
$710$	7.07941	+	1.42931i	0.265686	+	0.0536411i
$711$	20.4690	+	31.4457i	0.767646	+	1.17931i
$712$	4.66567	+	4.66567i	0.174853	+	0.174853i
$713$	−4.50059	−	4.50059i	−0.168548	−	0.168548i
$714$	50.3326	+	27.2935i	1.88365	+	1.02143i
$715$	0.0117512	+	0.00237253i	0.000439471	+	8.87278e-5i
$716$		−	1.74920i		−	0.0653706i
$717$	5.11418	+	17.2314i	0.190993	+	0.643517i
$718$	13.4372	−	13.4372i	0.501473	−	0.501473i
$719$	46.4403			1.73193			0.865965	−	0.500105i	$-0.166705\pi$
$719$	46.4403			1.73193			0.865965	+	0.500105i	$0.166705\pi$
$720$	−2.65911	+	6.15866i	−0.0990992	+	0.229520i
$721$	−1.55908			−0.0580630
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	7.09964	+	23.9210i	0.264039	+	0.889632i
$724$			16.8570i			0.626485i
$725$	−3.72068	+	8.83871i	−0.138182	+	0.328261i
$726$	−16.7486	−	9.08213i	−0.621597	−	0.337070i
$727$	24.1873	+	24.1873i	0.897056	+	0.897056i	0.995175	−	0.0981183i	$-0.0312824\pi$
$727$	24.1873	+	24.1873i	0.897056	+	0.897056i	−0.0981183	+	0.995175i	$0.531282\pi$
$728$	−5.42249	−	5.42249i	−0.200971	−	0.200971i
$729$	4.30927	+	26.6539i	0.159603	+	0.987181i
$730$	−18.1510	−	27.3343i	−0.671798	−	1.01169i
$731$		−	15.0715i		−	0.557441i
$732$	−3.24339	+	0.962624i	−0.119879	+	0.0355796i
$733$	22.2566	−	22.2566i	0.822065	−	0.822065i	−0.164339	−	0.986404i	$-0.552549\pi$
$733$	22.2566	−	22.2566i	0.822065	−	0.822065i	0.986404	+	0.164339i	$0.0525491\pi$
$734$	−4.76035			−0.175708
$735$	37.9191	−	45.3769i	1.39867	−	1.67375i
$736$	1.82298			0.0671958
$737$	−0.0183640	+	0.0183640i	−0.000676447	+	0.000676447i
$738$	10.6773	+	2.25759i	0.393035	+	0.0831030i
$739$		−	32.3498i		−	1.19001i	−0.803724	−	0.595003i	$-0.797151\pi$
$739$		−	32.3498i		−	1.19001i	0.803724	−	0.595003i	$-0.202849\pi$
$740$	4.20066	−	20.8060i	0.154419	−	0.764843i
$741$	1.34173	−	2.47431i	0.0492895	−	0.0908959i
$742$	−28.2053	−	28.2053i	−1.03545	−	1.03545i
$743$	−12.0657	−	12.0657i	−0.442649	−	0.442649i	0.450253	−	0.892901i	$-0.351334\pi$
$743$	−12.0657	−	12.0657i	−0.442649	−	0.442649i	−0.892901	+	0.450253i	$0.851334\pi$
$744$	2.88269	−	5.31604i	0.105685	−	0.194895i
$745$	17.6312	−	11.7077i	0.645956	−	0.428938i
$746$			6.61149i			0.242064i
$747$	38.6014	+	8.16184i	1.41235	+	0.298626i
$748$	−0.0163421	+	0.0163421i	−0.000597528	+	0.000597528i
$749$	88.2932			3.22616
$750$	5.89161	−	18.4469i	0.215131	−	0.673586i
$751$	0.958420			0.0349732			0.0174866	−	0.999847i	$-0.494434\pi$
$751$	0.958420			0.0349732			0.0174866	+	0.999847i	$0.494434\pi$
$752$	−2.07305	+	2.07305i	−0.0755965	+	0.0755965i
$753$	34.3863	−	10.2057i	1.25311	−	0.371916i
$754$		−	3.11682i		−	0.113508i
$755$	21.5003	−	14.2770i	0.782476	−	0.519592i
$756$	24.4417	−	1.96306i	0.888936	−	0.0713959i
$757$	−11.0571	−	11.0571i	−0.401877	−	0.401877i	0.477017	−	0.878894i	$-0.341718\pi$
$757$	−11.0571	−	11.0571i	−0.401877	−	0.401877i	−0.878894	+	0.477017i	$0.841718\pi$
$758$	−4.66927	−	4.66927i	−0.169596	−	0.169596i
$759$	0.00915740	+	0.00496572i	0.000332393	+	0.000180244i
$760$	−0.442526	+	2.19184i	−0.0160521	+	0.0795065i
$761$		−	45.8185i		−	1.66092i	−0.557078	−	0.830460i	$-0.688078\pi$
$761$		−	45.8185i		−	1.66092i	0.557078	−	0.830460i	$-0.311922\pi$
$762$	−0.225861	−	0.761000i	−0.00818209	−	0.0275681i
$763$	−51.8724	+	51.8724i	−1.87791	+	1.87791i
$764$	2.59256			0.0937954
$765$	−17.3347	−	43.6779i	−0.626737	−	1.57918i
$766$	20.4149			0.737619
$767$	−13.6610	+	13.6610i	−0.493272	+	0.493272i
$768$	0.492817	+	1.66046i	0.0177830	+	0.0599167i
$769$		−	26.0419i		−	0.939095i	−0.882907	−	0.469548i	$-0.844417\pi$
$769$		−	26.0419i		−	0.939095i	0.882907	−	0.469548i	$-0.155583\pi$
$770$	0.0192577	+	0.0290010i	0.000694000	+	0.00104512i
$771$	−15.5975	−	8.45794i	−0.561729	−	0.304605i
$772$	1.18301	+	1.18301i	0.0425774	+	0.0425774i
$773$	7.42336	+	7.42336i	0.267000	+	0.267000i	0.827890	−	0.560890i	$-0.189541\pi$
$773$	7.42336	+	7.42336i	0.267000	+	0.267000i	−0.560890	+	0.827890i	$0.689541\pi$
$774$	−3.52115	−	5.40941i	−0.126565	−	0.194437i
$775$	−6.77299	+	16.0897i	−0.243293	+	0.577958i
$776$			10.9215i			0.392061i
$777$	−74.3795	+	22.0755i	−2.66835	+	0.791954i
$778$	−0.400347	+	0.400347i	−0.0143531	+	0.0143531i
$779$	3.63777			0.130337
$780$	0.561262	+	6.26874i	0.0200964	+	0.224457i
$781$	0.0106560			0.000381301
$782$	−9.02993	+	9.02993i	−0.322910	+	0.322910i
$783$	7.58867	+	6.46031i	0.271197	+	0.230873i
$784$		−	15.2685i		−	0.545305i
$785$	27.3295	+	5.51774i	0.975432	+	0.196937i
$786$	−13.2055	+	24.3526i	−0.471025	+	0.868628i
$787$	16.1249	+	16.1249i	0.574791	+	0.574791i	0.933464	−	0.358672i	$-0.116770\pi$
$787$	16.1249	+	16.1249i	0.574791	+	0.574791i	−0.358672	+	0.933464i	$0.616770\pi$
$788$	−7.67888	−	7.67888i	−0.273549	−	0.273549i
$789$	2.21996	−	4.09388i	0.0790327	−	0.145746i
$790$	−27.4132	−	5.53465i	−0.975319	−	0.196914i
$791$			4.50018i			0.160008i
$792$	−0.00204746	+	0.00968345i	−7.27532e−5	+	0.000344086i
$793$	−2.24452	+	2.24452i	−0.0797054	+	0.0797054i
$794$	−15.5947			−0.553436
$795$	2.91942	+	32.6071i	0.103541	+	1.15645i
$796$	−8.22358			−0.291477
$797$	−0.0667197	+	0.0667197i	−0.00236333	+	0.00236333i	−0.708287	−	0.705924i	$-0.750532\pi$
$797$	−0.0667197	+	0.0667197i	−0.00236333	+	0.00236333i	0.705924	+	0.708287i	$0.250532\pi$
$798$	7.83564	−	2.32558i	0.277379	−	0.0823247i
$799$		−	20.5373i		−	0.726559i
$800$	−1.88688	−	4.63030i	−0.0667112	−	0.163706i
$801$	−16.5897	+	10.7987i	−0.586169	+	0.381555i
$802$	−23.3989	−	23.3989i	−0.826243	−	0.826243i
$803$	−0.0342324	−	0.0342324i	−0.00120804	−	0.00120804i
$804$	−11.9857	−	6.49938i	−0.422701	−	0.229215i
$805$	10.6410	+	16.0247i	0.375044	+	0.564795i
$806$		−	5.67376i		−	0.199850i
$807$	10.5477	+	35.5387i	0.371298	+	1.25102i
$808$	−11.4459	+	11.4459i	−0.402665	+	0.402665i
$809$	−2.41703			−0.0849783			−0.0424892	−	0.999097i	$-0.513529\pi$
$809$	−2.41703			−0.0849783			−0.0424892	+	0.999097i	$0.513529\pi$
$810$	−16.4261	−	11.6268i	−0.577155	−	0.408525i
$811$	5.82179			0.204431			0.102215	−	0.994762i	$-0.467407\pi$
$811$	5.82179			0.204431			0.102215	+	0.994762i	$0.467407\pi$
$812$	6.39993	−	6.39993i	0.224593	−	0.224593i
$813$	2.40794	+	8.11312i	0.0844500	+	0.284540i
$814$		−	0.0313173i		−	0.00109767i
$815$	−1.13246	+	5.60911i	−0.0396684	+	0.196479i
$816$	−10.6660	−	5.78381i	−0.373386	−	0.202474i
$817$	−1.52133	−	1.52133i	−0.0532247	−	0.0532247i
$818$	18.5455	+	18.5455i	0.648430	+	0.648430i
$819$	19.2808	−	12.5504i	0.673725	−	0.438547i
$820$	−6.77637	+	4.49975i	−0.236641	+	0.157138i
$821$		−	5.24603i		−	0.183088i	−0.995801	−	0.0915438i	$-0.970820\pi$
$821$		−	5.24603i		−	0.183088i	0.995801	−	0.0915438i	$-0.0291802\pi$
$822$	11.1273	−	3.30252i	0.388108	−	0.115189i
$823$	−1.84676	+	1.84676i	−0.0643738	+	0.0643738i	−0.738561	−	0.674187i	$-0.764494\pi$
$823$	−1.84676	+	1.84676i	−0.0643738	+	0.0643738i	0.674187	+	0.738561i	$0.264494\pi$
$824$	0.330386			0.0115095
$825$	0.00313438	−	0.0283993i	0.000109125	−	0.000988736i
$826$	−56.1018			−1.95203
$827$	−24.7201	+	24.7201i	−0.859602	+	0.859602i	−0.991291	−	0.131689i	$-0.957960\pi$
$827$	−24.7201	+	24.7201i	−0.859602	+	0.859602i	0.131689	+	0.991291i	$0.457960\pi$
$828$	−1.13133	+	5.35064i	−0.0393165	+	0.185947i
$829$			4.44183i			0.154271i	0.997021	+	0.0771356i	$0.0245774\pi$
$829$			4.44183i			0.154271i	−0.997021	+	0.0771356i	$0.975423\pi$
$830$	−24.4985	+	16.2679i	−0.850357	+	0.564668i
$831$	−19.4146	+	35.8029i	−0.673486	+	1.24199i
$832$	1.14909	+	1.14909i	0.0398374	+	0.0398374i
$833$	75.6311	+	75.6311i	2.62046	+	2.62046i
$834$	17.3716	−	32.0354i	0.601531	−	1.10930i
$835$	6.37233	−	31.5623i	0.220524	−	1.09226i
$836$			0.00329918i			0.000114104i
$837$	13.8142	+	11.7601i	0.477487	+	0.406489i
$838$	11.8382	−	11.8382i	0.408944	−	0.408944i
$839$	−21.2177			−0.732517			−0.366258	−	0.930513i	$-0.619361\pi$
$839$	−21.2177			−0.732517			−0.366258	+	0.930513i	$0.619361\pi$
$840$	−11.7194	+	14.0244i	−0.404359	+	0.483887i
$841$	−25.3214			−0.873150
$842$	−14.3887	+	14.3887i	−0.495867	+	0.495867i
$843$	−13.1895	+	3.91457i	−0.454270	+	0.134825i
$844$		−	14.8721i		−	0.511920i
$845$	−12.8138	−	19.2969i	−0.440810	−	0.663833i
$846$	−4.79811	−	7.37117i	−0.164962	−	0.253426i
$847$	−36.7048	−	36.7048i	−1.26119	−	1.26119i
$848$	5.97702	+	5.97702i	0.205252	+	0.205252i
$849$	−19.1933	−	10.4078i	−0.658711	−	0.357195i
$850$	32.2822	+	13.5893i	1.10727	+	0.466108i
$851$		−	17.3045i		−	0.593192i
$852$	1.59175	+	5.36311i	0.0545323	+	0.183737i
$853$	−2.75570	+	2.75570i	−0.0943535	+	0.0943535i	−0.752708	−	0.658354i	$-0.771253\pi$
$853$	−2.75570	+	2.75570i	−0.0943535	+	0.0943535i	0.658354	+	0.752708i	$0.271253\pi$
$854$	−9.21758			−0.315419
$855$	−6.15866	−	2.65911i	−0.210622	−	0.0909396i
$856$	−18.7103			−0.639506
$857$	22.6298	−	22.6298i	0.773020	−	0.773020i	−0.205613	−	0.978633i	$-0.565919\pi$
$857$	22.6298	−	22.6298i	0.773020	−	0.773020i	0.978633	+	0.205613i	$0.0659188\pi$
$858$	0.00264216	+	0.00890231i	9.02020e−5	+	0.000303920i
$859$			14.0009i			0.477705i	0.971056	+	0.238853i	$0.0767713\pi$
$859$			14.0009i			0.477705i	−0.971056	+	0.238853i	$0.923229\pi$
$860$	4.71573	+	0.952091i	0.160805	+	0.0324660i
$861$	26.1377	+	14.1735i	0.890769	+	0.483031i
$862$	−26.7467	−	26.7467i	−0.910995	−	0.910995i
$863$	−37.8370	−	37.8370i	−1.28799	−	1.28799i	−0.936009	−	0.351976i	$-0.885510\pi$
$863$	−37.8370	−	37.8370i	−1.28799	−	1.28799i	−0.351976	−	0.936009i	$-0.614490\pi$
$864$	−5.17947	+	0.415995i	−0.176209	+	0.0141524i
$865$	−12.7828	−	2.58080i	−0.434628	−	0.0877499i
$866$			5.28008i			0.179424i
$867$	53.2548	−	15.8058i	1.80863	−	0.536792i
$868$	11.6502	−	11.6502i	0.395434	−	0.395434i
$869$	−0.0412626			−0.00139974
$870$	−7.39871	+	0.662432i	−0.250840	+	0.0224585i
$871$	−12.7922			−0.433446
$872$	10.9923	−	10.9923i	0.372248	−	0.372248i
$873$	−32.0559	−	6.77787i	−1.08493	−	0.229396i
$874$			1.82298i			0.0616631i
$875$	29.6881	−	43.6140i	1.00364	−	1.47442i
$876$	12.1155	−	22.3425i	0.409346	−	0.754884i
$877$	27.3198	+	27.3198i	0.922525	+	0.922525i	0.997207	−	0.0746821i	$-0.0237942\pi$
$877$	27.3198	+	27.3198i	0.922525	+	0.922525i	−0.0746821	+	0.997207i	$0.523794\pi$
$878$	−6.92986	−	6.92986i	−0.233871	−	0.233871i
$879$	17.2507	−	31.8125i	0.581853	−	1.07301i
$880$	−0.00408093	−	0.00614564i	−0.000137568	−	0.000207170i
$881$		−	5.66516i		−	0.190864i	−0.995436	−	0.0954321i	$-0.969577\pi$
$881$		−	5.66516i		−	0.190864i	0.995436	−	0.0954321i	$-0.0304233\pi$
$882$	44.8148	+	9.47560i	1.50899	+	0.319060i
$883$	−27.0837	+	27.0837i	−0.911439	+	0.911439i	−0.996385	−	0.0849469i	$-0.972928\pi$
$883$	−27.0837	+	27.0837i	−0.911439	+	0.911439i	0.0849469	+	0.996385i	$0.472928\pi$
$884$	−11.3838			−0.382878
$885$	35.3320	+	29.5251i	1.18767	+	0.992476i
$886$	−10.5674			−0.355020
$887$	−9.96724	+	9.96724i	−0.334667	+	0.334667i	−0.854356	−	0.519689i	$-0.826048\pi$
$887$	−9.96724	+	9.96724i	−0.334667	+	0.334667i	0.519689	+	0.854356i	$0.326048\pi$
$888$	15.7619	−	4.67805i	0.528934	−	0.156985i
$889$		−	2.16273i		−	0.0725355i
$890$	2.91990	−	14.4623i	0.0978751	−	0.484778i
$891$	−0.0271513	−	0.0120190i	−0.000909603	−	0.000402652i
$892$	4.56460	+	4.56460i	0.152834	+	0.152834i
$893$	−2.07305	−	2.07305i	−0.0693721	−	0.0693721i
$894$	14.4114	+	7.81476i	0.481988	+	0.261365i
$895$	−3.25837	+	2.16368i	−0.108915	+	0.0723238i
$896$			4.71896i			0.157649i
$897$	1.45994	+	4.91902i	0.0487460	+	0.164241i
$898$	−15.3566	+	15.3566i	−0.512456	+	0.512456i
$899$	6.69649			0.223340
$900$	14.7614	−	2.66464i	0.492048	−	0.0888214i
$901$	−59.2131			−1.97268
$902$	−0.00848646	+	0.00848646i	−0.000282568	+	0.000282568i
$903$	−5.00347	−	16.8583i	−0.166505	−	0.561010i
$904$		−	0.953638i		−	0.0317175i
$905$	31.4008	−	20.8513i	1.04380	−	0.693120i
$906$	17.5739	+	9.52968i	0.583854	+	0.316603i
$907$	−24.3414	−	24.3414i	−0.808242	−	0.808242i	0.176126	−	0.984368i	$-0.443643\pi$
$907$	−24.3414	−	24.3414i	−0.808242	−	0.808242i	−0.984368	+	0.176126i	$0.943643\pi$
$908$	−8.94878	−	8.94878i	−0.296976	−	0.296976i
$909$	−26.4917	−	40.6982i	−0.878673	−	1.34987i
$910$	−3.39354	+	16.8083i	−0.112495	+	0.557189i
$911$			24.6576i			0.816944i	0.912771	+	0.408472i	$0.133938\pi$
$911$			24.6576i			0.816944i	−0.912771	+	0.408472i	$0.866062\pi$
$912$	−1.66046	+	0.492817i	−0.0549834	+	0.0163188i
$913$	−0.0306810	+	0.0306810i	−0.00101539	+	0.00101539i
$914$	−22.5032			−0.744341
$915$	5.80508	+	4.85101i	0.191910	+	0.160369i
$916$	−15.6381			−0.516696
$917$	−53.3692	+	53.3692i	−1.76241	+	1.76241i
$918$	23.5954	−	27.7166i	0.778764	−	0.914784i
$919$		−	39.8544i		−	1.31468i	−0.753596	−	0.657338i	$-0.771682\pi$
$919$		−	39.8544i		−	1.31468i	0.753596	−	0.657338i	$-0.228318\pi$
$920$	−2.25494	−	3.39580i	−0.0743431	−	0.111956i
$921$	23.8103	−	43.9092i	0.784577	−	1.44686i
$922$	27.2201	+	27.2201i	0.896447	+	0.896447i
$923$	3.71143	+	3.71143i	0.122163	+	0.122163i
$924$	−0.0128543	+	0.0237048i	−0.000422874	+	0.000779832i
$925$	−43.9530	+	17.9111i	−1.44516	+	0.588914i
$926$			14.7045i			0.483219i
$927$	−0.205036	+	0.969718i	−0.00673427	+	0.0318497i
$928$	−1.35622	+	1.35622i	−0.0445200	+	0.0445200i
$929$	−13.8105			−0.453109			−0.226555	−	0.973998i	$-0.572746\pi$
$929$	−13.8105			−0.453109			−0.226555	+	0.973998i	$0.572746\pi$
$930$	−13.4684	+	1.20587i	−0.441645	+	0.0395420i
$931$	15.2685			0.500406
$932$	11.5507	−	11.5507i	0.378355	−	0.378355i
$933$	10.4480	−	3.10092i	0.342053	−	0.101520i
$934$			22.6220i			0.740216i
$935$	0.0506563	+	0.0102273i	0.00165664	+	0.000334470i
$936$	−4.08582	+	2.65958i	−0.133549	+	0.0869310i
$937$	−33.2655	−	33.2655i	−1.08674	−	1.08674i	−0.995863	−	0.0908728i	$-0.971034\pi$
$937$	−33.2655	−	33.2655i	−1.08674	−	1.08674i	−0.0908728	−	0.995863i	$-0.528966\pi$
$938$	−26.2668	−	26.2668i	−0.857642	−	0.857642i
$939$	12.7905	+	6.93584i	0.417403	+	0.226343i
$940$	6.42592	+	1.29737i	0.209590	+	0.0423156i
$941$			8.74362i			0.285034i	0.989792	+	0.142517i	$0.0455196\pi$
$941$			8.74362i			0.285034i	−0.989792	+	0.142517i	$0.954480\pi$
$942$	6.14480	+	20.7039i	0.200209	+	0.674568i
$943$	−4.68923	+	4.68923i	−0.152702	+	0.152702i
$944$	11.8886			0.386941
$945$	−33.8900	−	43.1013i	−1.10244	−	1.40208i
$946$	0.00709815			0.000230781
$947$	28.7624	−	28.7624i	0.934651	−	0.934651i	−0.0633409	−	0.997992i	$-0.520176\pi$
$947$	28.7624	−	28.7624i	0.934651	−	0.934651i	0.997992	+	0.0633409i	$0.0201755\pi$
$948$	−6.16363	−	20.7673i	−0.200186	−	0.674490i
$949$		−	23.8460i		−	0.774073i
$950$	4.63030	−	1.88688i	0.150227	−	0.0612184i
$951$	27.7850	+	15.0668i	0.900989	+	0.488574i
$952$	−23.3749	−	23.3749i	−0.757584	−	0.757584i
$953$	−10.3155	−	10.3155i	−0.334151	−	0.334151i	0.520010	−	0.854160i	$-0.325928\pi$
$953$	−10.3155	−	10.3155i	−0.334151	−	0.334151i	−0.854160	+	0.520010i	$0.825928\pi$
$954$	−21.2525	+	13.8339i	−0.688076	+	0.447889i
$955$	−3.20687	−	4.82936i	−0.103772	−	0.156275i
$956$		−	10.3774i		−	0.335631i
$957$	−0.0105070	+	0.00311843i	−0.000339643	+	0.000100804i
$958$	10.4611	−	10.4611i	0.337983	−	0.337983i
$959$	31.6232			1.02117
$960$	2.48348	−	2.97192i	0.0801540	−	0.0959184i
$961$	−18.8099			−0.606772
$962$	10.9077	−	10.9077i	0.351677	−	0.351677i
$963$	11.6116	−	54.9169i	0.374177	−	1.76967i
$964$		−	14.4062i		−	0.463994i
$965$	0.740357	−	3.66701i	0.0238329	−	0.118045i
$966$	−7.10269	+	13.0982i	−0.228525	+	0.421428i
$967$	23.9335	+	23.9335i	0.769650	+	0.769650i	0.978045	−	0.208394i	$-0.0668238\pi$
$967$	23.9335	+	23.9335i	0.769650	+	0.769650i	−0.208394	+	0.978045i	$0.566824\pi$
$968$	7.77817	+	7.77817i	0.250000	+	0.250000i
$969$	5.78381	−	10.6660i	0.185803	−	0.342643i
$970$	20.3444	−	13.5094i	0.653220	−	0.433762i
$971$		−	2.91801i		−	0.0936433i	−0.998903	−	0.0468217i	$-0.985091\pi$
$971$		−	2.91801i		−	0.0936433i	0.998903	−	0.0468217i	$-0.0149093\pi$
$972$	1.99337	−	15.4605i	0.0639374	−	0.495895i
$973$	70.2063	−	70.2063i	2.25071	−	2.25071i
$974$	−15.0609			−0.482584
$975$	10.9830	−	8.79964i	0.351738	−	0.281814i
$976$	1.95331			0.0625239
$977$	−9.00845	+	9.00845i	−0.288206	+	0.288206i	−0.836370	−	0.548165i	$-0.815327\pi$
$977$	−9.00845	+	9.00845i	−0.288206	+	0.288206i	0.548165	+	0.836370i	$0.315327\pi$
$978$	−4.24926	+	1.26116i	−0.135876	+	0.0403275i
$979$		−	0.0217688i		−	0.000695734i
$980$	−28.4419	+	18.8865i	−0.908544	+	0.603306i
$981$	25.4419	+	39.0855i	0.812298	+	1.24790i
$982$	−12.7786	−	12.7786i	−0.407782	−	0.407782i
$983$	6.78318	+	6.78318i	0.216350	+	0.216350i	0.806958	−	0.590608i	$-0.201112\pi$
$983$	6.78318	+	6.78318i	0.216350	+	0.216350i	−0.590608	+	0.806958i	$0.701112\pi$
$984$	−5.53886	−	3.00352i	−0.176573	−	0.0957488i
$985$	−4.80564	+	23.8025i	−0.153120	+	0.758410i
$986$		−	13.4358i		−	0.427882i
$987$	−6.81801	−	22.9721i	−0.217020	−	0.731210i
$988$	−1.14909	+	1.14909i	−0.0365573	+	0.0365573i
$989$	3.92212			0.124716
$990$	0.0205707	−	0.00816401i	0.000653781	−	0.000259469i
$991$	25.2666			0.802619			0.401309	−	0.915943i	$-0.368555\pi$
$991$	25.2666			0.802619			0.401309	+	0.915943i	$0.368555\pi$
$992$	−2.46881	+	2.46881i	−0.0783848	+	0.0783848i
$993$	−10.9811	−	36.9991i	−0.348476	−	1.17413i
$994$			15.2417i			0.483438i
$995$	10.1722	+	15.3187i	0.322480	+	0.485636i
$996$	−20.0246	−	10.8586i	−0.634504	−	0.344068i
$997$	−31.5798	−	31.5798i	−1.00014	−	1.00014i	−1.00000		0.000142894i	$-0.999955\pi$
$997$	−31.5798	−	31.5798i	−1.00014	−	1.00014i	−0.000142894	−	1.00000i	$-0.500045\pi$
$998$	−14.1244	−	14.1244i	−0.447100	−	0.447100i
$999$	3.94882	+	49.1660i	0.124935	+	1.55554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.5	✓	36
3.2	odd	2	inner	570.2.k.b.77.10	yes	36
5.3	odd	4	inner	570.2.k.b.533.10	yes	36
15.8	even	4	inner	570.2.k.b.533.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.5	✓	36	1.1	even	1	trivial
570.2.k.b.77.10	yes	36	3.2	odd	2	inner
570.2.k.b.533.5	yes	36	15.8	even	4	inner
570.2.k.b.533.10	yes	36	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.492817 + 1.66046i) q^{3} -1.00000i q^{4} +(-1.86278 + 1.23695i) q^{5} +(-1.52260 - 0.825649i) q^{6} +(-3.33681 - 3.33681i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.51426 + 1.63661i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.492817 + 1.66046i) q^{3} -1.00000i q^{4} +(-1.86278 + 1.23695i) q^{5} +(-1.52260 - 0.825649i) q^{6} +(-3.33681 - 3.33681i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.51426 + 1.63661i) q^{9} +(0.442526 - 2.19184i) q^{10} -0.00329918i q^{11} +(1.66046 - 0.492817i) q^{12} +(1.14909 - 1.14909i) q^{13} +4.71896 q^{14} +(-2.97192 - 2.48348i) q^{15} -1.00000 q^{16} +(4.95340 - 4.95340i) q^{17} +(0.620596 - 2.93511i) q^{18} -1.00000i q^{19} +(1.23695 + 1.86278i) q^{20} +(3.89620 - 7.18507i) q^{21} +(0.00233287 + 0.00233287i) q^{22} +(1.28904 + 1.28904i) q^{23} +(-0.825649 + 1.52260i) q^{24} +(1.93989 - 4.60834i) q^{25} +1.62506i q^{26} +(-3.95659 - 3.36829i) q^{27} +(-3.33681 + 3.33681i) q^{28} -1.91798 q^{29} +(3.85755 - 0.345380i) q^{30} -3.49143 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.00547816 - 0.00162589i) q^{33} +7.00516i q^{34} +(10.3432 + 2.08826i) q^{35} +(1.63661 + 2.51426i) q^{36} +(-6.71219 - 6.71219i) q^{37} +(0.707107 + 0.707107i) q^{38} +(2.47431 + 1.34173i) q^{39} +(-2.19184 - 0.442526i) q^{40} +3.63777i q^{41} +(2.32558 + 7.83564i) q^{42} +(1.52133 - 1.52133i) q^{43} -0.00329918 q^{44} +(2.65911 - 6.15866i) q^{45} -1.82298 q^{46} +(2.07305 - 2.07305i) q^{47} +(-0.492817 - 1.66046i) q^{48} +15.2685i q^{49} +(1.88688 + 4.63030i) q^{50} +(10.6660 + 5.78381i) q^{51} +(-1.14909 - 1.14909i) q^{52} +(-5.97702 - 5.97702i) q^{53} +(5.17947 - 0.415995i) q^{54} +(0.00408093 + 0.00614564i) q^{55} -4.71896i q^{56} +(1.66046 - 0.492817i) q^{57} +(1.35622 - 1.35622i) q^{58} -11.8886 q^{59} +(-2.48348 + 2.97192i) q^{60} -1.95331 q^{61} +(2.46881 - 2.46881i) q^{62} +(13.8506 + 2.92857i) q^{63} +1.00000i q^{64} +(-0.719129 + 3.56186i) q^{65} +(-0.00272396 + 0.00502332i) q^{66} +(-5.56623 - 5.56623i) q^{67} +(-4.95340 - 4.95340i) q^{68} +(-1.50514 + 2.77566i) q^{69} +(-8.79037 + 5.83713i) q^{70} +3.22989i q^{71} +(-2.93511 - 0.620596i) q^{72} +(10.3760 - 10.3760i) q^{73} +9.49246 q^{74} +(8.60799 + 0.950048i) q^{75} -1.00000 q^{76} +(-0.0110087 + 0.0110087i) q^{77} +(-2.69834 + 0.800855i) q^{78} -12.5069i q^{79} +(1.86278 - 1.23695i) q^{80} +(3.64303 - 8.22972i) q^{81} +(-2.57229 - 2.57229i) q^{82} +(-9.29959 - 9.29959i) q^{83} +(-7.18507 - 3.89620i) q^{84} +(-3.09997 + 15.3542i) q^{85} +2.15149i q^{86} +(-0.945213 - 3.18473i) q^{87} +(0.00233287 - 0.00233287i) q^{88} +6.59825 q^{89} +(2.47456 + 6.23511i) q^{90} -7.66856 q^{91} +(1.28904 - 1.28904i) q^{92} +(-1.72063 - 5.79738i) q^{93} +2.93174i q^{94} +(1.23695 + 1.86278i) q^{95} +(1.52260 + 0.825649i) q^{96} +(7.72270 + 7.72270i) q^{97} +(-10.7965 - 10.7965i) q^{98} +(0.00539946 + 0.00829500i) 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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