LMFDB - Embedded newform 570.2.k.b.77.10

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			77.10
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.66046 - 0.492817i) q^{3} -1.00000i q^{4} +(1.86278 - 1.23695i) q^{5} +(-1.52260 + 0.825649i) q^{6} +(-3.33681 - 3.33681i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.51426 + 1.63661i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.66046 - 0.492817i) 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} +(-0.492817 + 1.66046i) q^{12} +(1.14909 - 1.14909i) q^{13} -4.71896 q^{14} +(-3.70266 + 1.13590i) q^{15} -1.00000 q^{16} +(-4.95340 + 4.95340i) q^{17} +(2.93511 - 0.620596i) 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} +(-3.36829 - 3.95659i) q^{27} +(-3.33681 + 3.33681i) q^{28} +1.91798 q^{29} +(-1.81497 + 3.42138i) q^{30} -3.49143 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.00162589 - 0.00547816i) 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} +(7.83564 + 2.32558i) q^{42} +(1.52133 - 1.52133i) q^{43} +0.00329918 q^{44} +(6.70792 - 0.0613876i) q^{45} -1.82298 q^{46} +(-2.07305 + 2.07305i) q^{47} +(1.66046 + 0.492817i) 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} +(-0.492817 + 1.66046i) q^{57} +(1.35622 - 1.35622i) q^{58} +11.8886 q^{59} +(1.13590 + 3.70266i) q^{60} -1.95331 q^{61} +(-2.46881 + 2.46881i) q^{62} +(-2.92857 - 13.8506i) 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} +(-0.620596 - 2.93511i) q^{72} +(10.3760 - 10.3760i) q^{73} -9.49246 q^{74} +(-5.49219 + 6.69596i) q^{75} -1.00000 q^{76} +(0.0110087 - 0.0110087i) q^{77} +(-0.800855 + 2.69834i) 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} +(-3.18473 - 0.945213i) q^{87} +(0.00233287 - 0.00233287i) q^{88} -6.59825 q^{89} +(4.69981 - 4.78663i) q^{90} -7.66856 q^{91} +(-1.28904 + 1.28904i) q^{92} +(5.79738 + 1.72063i) 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
$3$	−1.66046	−	0.492817i	−0.958668	−	0.284528i
$3$	−1.66046	−	0.492817i	−0.958668	−	0.284528i
$4$		−	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	$0.000158318\pi$
$11$			0.00329918i			0.000994740i	−1.00000		0.000497370i	$0.999842\pi$
$12$	−0.492817	+	1.66046i	−0.142264	+	0.479334i
$13$	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
$15$	−3.70266	+	1.13590i	−0.956024	+	0.293289i
$16$	−1.00000			−0.250000
$17$	−4.95340	+	4.95340i	−1.20138	+	1.20138i	−0.227627	+	0.973748i	$0.573097\pi$
$17$	−4.95340	+	4.95340i	−1.20138	+	1.20138i	−0.973748	+	0.227627i	$0.926903\pi$
$18$	2.93511	−	0.620596i	0.691812	−	0.146276i
$19$		−	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	0.559826	−	0.828610i	$-0.310868\pi$
$23$	−1.28904	−	1.28904i	−0.268783	−	0.268783i	−0.828610	+	0.559826i	$0.810868\pi$
$24$	0.825649	+	1.52260i	0.168535	+	0.310799i
$25$	1.93989	−	4.60834i	0.387979	−	0.921668i
$26$		−	1.62506i		−	0.318700i
$27$	−3.36829	−	3.95659i	−0.648227	−	0.761447i
$28$	−3.33681	+	3.33681i	−0.630597	+	0.630597i
$29$	1.91798			0.356160			0.178080	−	0.984016i	$-0.443011\pi$
$29$	1.91798			0.356160			0.178080	+	0.984016i	$0.443011\pi$
$30$	−1.81497	+	3.42138i	−0.331367	+	0.624656i
$31$	−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
$33$	0.00162589	−	0.00547816i	0.000283031	−	0.000953625i
$34$			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	$-0.908318\pi$
$41$		−	3.63777i		−	0.568125i	0.958806	−	0.284062i	$-0.0916823\pi$
$42$	7.83564	+	2.32558i	1.20907	+	0.358845i
$43$	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
$45$	6.70792	−	0.0613876i	0.999958	−	0.00915113i
$46$	−1.82298			−0.268783
$47$	−2.07305	+	2.07305i	−0.302386	+	0.302386i	−0.841947	−	0.539561i	$-0.818590\pi$
$47$	−2.07305	+	2.07305i	−0.302386	+	0.302386i	0.539561	+	0.841947i	$0.318590\pi$
$48$	1.66046	+	0.492817i	0.239667	+	0.0711320i
$49$			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	0.986252	−	0.165245i	$-0.0528416\pi$
$53$	5.97702	+	5.97702i	0.821007	+	0.821007i	−0.165245	+	0.986252i	$0.552842\pi$
$54$	−5.17947	−	0.415995i	−0.704837	−	0.0566098i
$55$	0.00408093	+	0.00614564i	0.000550272	+	0.000828678i
$56$			4.71896i			0.630597i
$57$	−0.492817	+	1.66046i	−0.0652752	+	0.219933i
$58$	1.35622	−	1.35622i	0.178080	−	0.178080i
$59$	11.8886			1.54776			0.773882	−	0.633330i	$-0.218312\pi$
$59$	11.8886			1.54776			0.773882	+	0.633330i	$0.218312\pi$
$60$	1.13590	+	3.70266i	0.146645	+	0.478012i
$61$	−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
$63$	−2.92857	−	13.8506i	−0.368965	−	1.74502i
$64$			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	$-0.938613\pi$
$71$		−	3.22989i		−	0.383318i	0.981462	−	0.191659i	$-0.0613867\pi$
$72$	−0.620596	−	2.93511i	−0.0731380	−	0.345906i
$73$	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
$75$	−5.49219	+	6.69596i	−0.634183	+	0.773183i
$76$	−1.00000			−0.114708
$77$	0.0110087	−	0.0110087i	0.00125456	−	0.00125456i
$78$	−0.800855	+	2.69834i	−0.0906790	+	0.305527i
$79$		−	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	$0.00667960\pi$
$83$	9.29959	+	9.29959i	1.02076	+	1.02076i	0.0209831	+	0.999780i	$0.493320\pi$
$84$	7.18507	−	3.89620i	0.783955	−	0.425110i
$85$	−3.09997	+	15.3542i	−0.336238	+	1.66540i
$86$		−	2.15149i		−	0.232001i
$87$	−3.18473	−	0.945213i	−0.341439	−	0.101338i
$88$	0.00233287	−	0.00233287i	0.000248685	−	0.000248685i
$89$	−6.59825			−0.699413			−0.349706	−	0.936859i	$-0.613719\pi$
$89$	−6.59825			−0.699413			−0.349706	+	0.936859i	$0.613719\pi$
$90$	4.69981	−	4.78663i	0.495403	−	0.504555i
$91$	−7.66856			−0.803884
$92$	−1.28904	+	1.28904i	−0.134392	+	0.134392i
$93$	5.79738	+	1.72063i	0.601160	+	0.178421i
$94$			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	$-0.701988\pi$
$101$		−	16.1869i		−	1.61066i	0.592826	−	0.805330i	$-0.298012\pi$
$102$	3.45226	−	11.6318i	0.341825	−	1.15172i
$103$	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
$105$	16.1454	+	8.56478i	1.57563	+	0.835837i
$106$	8.45278			0.821007
$107$	13.2302	−	13.2302i	1.27901	−	1.27901i	0.337791	−	0.941221i	$-0.390320\pi$
$107$	13.2302	−	13.2302i	1.27901	−	1.27901i	0.941221	−	0.337791i	$-0.109680\pi$
$108$	−3.95659	+	3.36829i	−0.380723	+	0.324114i
$109$		−	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	0.738113	−	0.674678i	$-0.235717\pi$
$113$	0.674324	+	0.674324i	0.0634351	+	0.0634351i	−0.674678	+	0.738113i	$0.735717\pi$
$114$	0.825649	+	1.52260i	0.0773291	+	0.142604i
$115$	−3.99568	−	0.806715i	−0.372599	−	0.0752265i
$116$		−	1.91798i		−	0.178080i
$117$	4.76971	−	1.00850i	0.440960	−	0.0932362i
$118$	8.40651	−	8.40651i	0.773882	−	0.773882i
$119$	33.0570			3.03033
$120$	3.42138	+	1.81497i	0.312328	+	0.165684i
$121$	11.0000			0.999999
$122$	−1.38120	+	1.38120i	−0.125048	+	0.125048i
$123$	−1.79276	+	6.04038i	−0.161647	+	0.544643i
$124$			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	$0.246240\pi$
$131$			15.9941i			1.39741i	−0.715409	+	0.698706i	$0.753760\pi$
$132$	−0.00547816	−	0.00162589i	−0.000476812	−	0.000141516i
$133$	−3.33681	+	3.33681i	−0.289338	+	0.289338i
$134$	−7.87184			−0.680024
$135$	−11.1685	−	3.20385i	−0.961231	−	0.275743i
$136$	7.00516			0.600688
$137$	4.73854	−	4.73854i	0.404841	−	0.404841i	−0.475094	−	0.879935i	$-0.657586\pi$
$137$	4.73854	−	4.73854i	0.404841	−	0.404841i	0.879935	+	0.475094i	$0.157586\pi$
$138$	3.02698	+	0.898394i	0.257674	+	0.0764764i
$139$			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
$147$	7.52460	−	25.3528i	0.620618	−	2.09107i
$148$	−6.71219	+	6.71219i	−0.551738	+	0.551738i
$149$	9.46498			0.775402			0.387701	−	0.921785i	$-0.373269\pi$
$149$	9.46498			0.775402			0.387701	+	0.921785i	$0.373269\pi$
$150$	0.851196	+	8.61832i	0.0694999	+	0.703683i
$151$	−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
$153$	−20.5609	+	4.34738i	−1.66225	+	0.351465i
$154$		−	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
$162$	8.39531	+	3.24328i	0.659597	+	0.254816i
$163$	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
$165$	−0.00374755	−	0.0122158i	−0.000291746	−	0.000950995i
$166$	13.1516			1.02076
$167$	10.1823	−	10.1823i	0.787928	−	0.787928i	−0.193226	−	0.981154i	$-0.561895\pi$
$167$	10.1823	−	10.1823i	0.787928	−	0.787928i	0.981154	+	0.193226i	$0.0618952\pi$
$168$	2.32558	−	7.83564i	0.179423	−	0.604533i
$169$			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	0.532746	−	0.846275i	$-0.321160\pi$
$173$	−4.12383	−	4.12383i	−0.313529	−	0.313529i	−0.846275	+	0.532746i	$0.821160\pi$
$174$	−2.92031	+	1.58358i	−0.221388	+	0.120051i
$175$	−21.8502	+	8.90409i	−1.65172	+	0.673086i
$176$		−	0.00329918i		−	0.000248685i
$177$	−19.7406	−	5.85890i	−1.48379	−	0.440382i
$178$	−4.66567	+	4.66567i	−0.349706	+	0.349706i
$179$	−1.74920			−0.130741			−0.0653706	−	0.997861i	$-0.520823\pi$
$179$	−1.74920			−0.130741			−0.0653706	+	0.997861i	$0.520823\pi$
$180$	−0.0613876	−	6.70792i	−0.00457556	−	0.499979i
$181$	−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
$183$	3.24339	+	0.962624i	0.239759	+	0.0711592i
$184$			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	$-0.970100\pi$
$191$		−	2.59256i		−	0.187591i	0.995591	−	0.0937954i	$-0.0299000\pi$
$192$	0.492817	−	1.66046i	0.0355660	−	0.119833i
$193$	−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
$195$	−2.94943	+	5.55994i	−0.211213	+	0.398155i
$196$	15.2685			1.09061
$197$	−7.67888	+	7.67888i	−0.547097	+	0.547097i	−0.925600	−	0.378503i	$-0.876439\pi$
$197$	−7.67888	+	7.67888i	−0.547097	+	0.547097i	0.378503	+	0.925600i	$0.376439\pi$
$198$	0.00204746	+	0.00968345i	0.000145506	+	0.000688173i
$199$		−	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
$207$	−1.13133	−	5.35064i	−0.0786331	−	0.371895i
$208$	−1.14909	+	1.14909i	−0.0796749	+	0.0796749i
$209$	0.00329918			0.000228209
$210$	17.4727	−	5.36028i	1.20573	−	0.369894i
$211$	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
$213$	−1.59175	+	5.36311i	−0.109065	+	0.367474i
$214$		−	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
$222$	15.7619	+	4.67805i	1.05787	+	0.313970i
$223$	−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
$225$	12.4194	−	8.41174i	0.827963	−	0.560783i
$226$	0.953638			0.0634351
$227$	−8.94878	+	8.94878i	−0.593952	+	0.593952i	−0.938696	−	0.344745i	$-0.887965\pi$
$227$	−8.94878	+	8.94878i	−0.593952	+	0.593952i	0.344745	+	0.938696i	$0.387965\pi$
$228$	1.66046	+	0.492817i	0.109967	+	0.0326376i
$229$		−	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	0.219012	−	0.975722i	$-0.429717\pi$
$233$	−11.5507	−	11.5507i	−0.756711	−	0.756711i	−0.975722	+	0.219012i	$0.929717\pi$
$234$	2.65958	−	4.08582i	0.173862	−	0.267098i
$235$	−1.29737	+	6.42592i	−0.0846312	+	0.419181i
$236$		−	11.8886i		−	0.773882i
$237$	−6.16363	+	20.7673i	−0.400371	+	1.34898i
$238$	23.3749	−	23.3749i	1.51517	−	1.51517i
$239$	−10.3774			−0.671261			−0.335631	−	0.941994i	$-0.608949\pi$
$239$	−10.3774			−0.671261			−0.335631	+	0.941994i	$0.608949\pi$
$240$	3.70266	−	1.13590i	0.239006	−	0.0733223i
$241$	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
$243$	−1.99337	−	15.4605i	−0.127875	−	0.991790i
$244$			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	$0.226728\pi$
$251$			20.7089i			1.30713i	−0.756869	+	0.653567i	$0.773272\pi$
$252$	−13.8506	+	2.92857i	−0.872509	+	0.184482i
$253$	0.00425277	−	0.00425277i	0.000267370	−	0.000267370i
$254$	0.458306			0.0287567
$255$	12.7142	−	23.9674i	0.796193	−	1.50089i
$256$	1.00000			0.0625000
$257$	7.24360	−	7.24360i	0.451843	−	0.451843i	−0.444123	−	0.895966i	$-0.646485\pi$
$257$	7.24360	−	7.24360i	0.451843	−	0.451843i	0.895966	+	0.444123i	$0.146485\pi$
$258$	−1.06029	+	3.57247i	−0.0660109	+	0.222412i
$259$			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	0.763290	−	0.646056i	$-0.223583\pi$
$263$	1.90123	+	1.90123i	0.117235	+	0.117235i	−0.646056	+	0.763290i	$0.723583\pi$
$264$	−0.00502332	+	0.00272396i	−0.000309164	+	0.000167648i
$265$	18.5272	+	3.74058i	1.13811	+	0.229782i
$266$			4.71896i			0.289338i
$267$	10.9561	+	3.25173i	0.670505	+	0.199003i
$268$	−5.56623	+	5.56623i	−0.340012	+	0.340012i
$269$	−21.4029			−1.30496			−0.652480	−	0.757806i	$-0.726271\pi$
$269$	−21.4029			−1.30496			−0.652480	+	0.757806i	$0.726271\pi$
$270$	−10.1628	+	5.63186i	−0.618487	+	0.342744i
$271$	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
$273$	12.7334	+	3.77920i	0.770657	+	0.228727i
$274$		−	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	$-0.923860\pi$
$281$		−	7.94326i		−	0.473855i	0.971527	−	0.236928i	$-0.0761404\pi$
$282$	1.44481	−	4.86804i	0.0860373	−	0.289888i
$283$	−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
$285$	1.13590	+	3.70266i	0.0672851	+	0.219327i
$286$	0.00536135			0.000317023
$287$	−12.1385	+	12.1385i	−0.716515	+	0.716515i
$288$	−2.93511	+	0.620596i	−0.172953	+	0.0365690i
$289$		−	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	0.991697	−	0.128593i	$-0.0410462\pi$
$293$	14.7740	+	14.7740i	0.863104	+	0.863104i	−0.128593	+	0.991697i	$0.541046\pi$
$294$	−12.6065	−	23.2478i	−0.735223	−	1.35584i
$295$	22.1458	−	14.7056i	1.28938	−	0.856196i
$296$			9.49246i			0.551738i
$297$	0.0130535	−	0.0111126i	0.000757441	−	0.000644817i
$298$	6.69275	−	6.69275i	0.387701	−	0.387701i
$299$	−2.96244			−0.171322
$300$	6.69596	+	5.49219i	0.386591	+	0.317092i
$301$	−10.1528			−0.585197
$302$	−8.16146	+	8.16146i	−0.469639	+	0.469639i
$303$	−7.97720	+	26.8778i	−0.458278	+	1.54409i
$304$			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	$0.0570921\pi$
$311$			6.29224i			0.356800i	−0.983958	+	0.178400i	$0.942908\pi$
$312$	2.69834	+	0.800855i	0.152763	+	0.0453395i
$313$	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
$315$	−22.5879	−	22.1782i	−1.27268	−	1.24960i
$316$	−12.5069			−0.703570
$317$	−12.9036	+	12.9036i	−0.724736	+	0.724736i	−0.969566	−	0.244830i	$-0.921268\pi$
$317$	−12.9036	+	12.9036i	−0.724736	+	0.724736i	0.244830	+	0.969566i	$0.421268\pi$
$318$	−14.0355	−	4.16568i	−0.787073	−	0.233600i
$319$			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
$327$	−7.66110	+	25.8127i	−0.423660	+	1.42745i
$328$	−2.57229	+	2.57229i	−0.142031	+	0.142031i
$329$	13.8348			0.762735
$330$	−0.0112878	−	0.00598792i	−0.000621371	−	0.000329624i
$331$	−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
$333$	−5.89099	−	27.8614i	−0.322824	−	1.52680i
$334$		−	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
$342$	−0.620596	−	2.93511i	−0.0335580	−	0.158712i
$343$	27.5905	−	27.5905i	1.48975	−	1.48975i
$344$	−2.15149			−0.116001
$345$	6.23711	+	3.30866i	0.335795	+	0.178132i
$346$	−5.83198			−0.313529
$347$	−2.64462	+	2.64462i	−0.141971	+	0.141971i	−0.774520	−	0.632549i	$-0.782009\pi$
$347$	−2.64462	+	2.64462i	−0.141971	+	0.141971i	0.632549	+	0.774520i	$0.282009\pi$
$348$	−0.945213	+	3.18473i	−0.0506688	+	0.170720i
$349$			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	0.797238	−	0.603665i	$-0.206293\pi$
$353$	3.63692	+	3.63692i	0.193574	+	0.193574i	−0.603665	+	0.797238i	$0.706293\pi$
$354$	−18.1016	+	9.81581i	−0.962087	+	0.521705i
$355$	−3.99523	−	6.01658i	−0.212045	−	0.319327i
$356$			6.59825i			0.349706i
$357$	−54.8899	−	16.2911i	−2.90508	−	0.862215i
$358$	−1.23687	+	1.23687i	−0.0653706	+	0.0653706i
$359$	19.0031			1.00295			0.501473	−	0.865173i	$-0.332792\pi$
$359$	19.0031			1.00295			0.501473	+	0.865173i	$0.332792\pi$
$360$	−4.78663	−	4.69981i	−0.252277	−	0.247702i
$361$	−1.00000			−0.0526316
$362$	−11.9197	+	11.9197i	−0.626485	+	0.626485i
$363$	−18.2651	−	5.42098i	−0.958667	−	0.284528i
$364$			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
$372$	1.72063	−	5.79738i	0.0892107	−	0.300580i
$373$	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
$375$	−1.94814	+	19.2667i	−0.100602	+	0.994927i
$376$	2.93174			0.151193
$377$	2.20393	−	2.20393i	0.113508	−	0.113508i
$378$	15.8948	+	18.6710i	0.817540	+	0.960332i
$379$			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	0.972117	−	0.234498i	$-0.0753446\pi$
$383$	14.4355	+	14.4355i	0.737619	+	0.737619i	−0.234498	+	0.972117i	$0.575345\pi$
$384$	−0.825649	−	1.52260i	−0.0421337	−	0.0776997i
$385$	0.00688954	−	0.0341241i	0.000351124	−	0.00173912i
$386$			1.67302i			0.0851547i
$387$	6.31486	−	1.33521i	0.321002	−	0.0678724i
$388$	7.72270	−	7.72270i	0.392061	−	0.392061i
$389$	−0.566176			−0.0287063			−0.0143531	−	0.999897i	$-0.504569\pi$
$389$	−0.566176			−0.0287063			−0.0143531	+	0.999897i	$0.504569\pi$
$390$	1.84591	+	6.01703i	0.0934711	+	0.304684i
$391$	12.7703			0.645819
$392$	10.7965	−	10.7965i	0.545305	−	0.545305i
$393$	7.88217	−	26.5576i	0.397603	−	1.33965i
$394$			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	$-0.690474\pi$
$401$		−	33.0910i		−	1.65249i	0.563313	−	0.826243i	$-0.309526\pi$
$402$	13.0709	+	3.87938i	0.651917	+	0.193486i
$403$	−4.01195	+	4.01195i	−0.199850	+	0.199850i
$404$	−16.1869			−0.805330
$405$	16.9659	+	10.8239i	0.843045	+	0.537843i
$406$	−9.05086			−0.449187
$407$	0.0221447	−	0.0221447i	0.00109767	−	0.00109767i
$408$	−11.6318	−	3.45226i	−0.575860	−	0.170912i
$409$		−	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
$417$	10.3689	−	34.9361i	0.507765	−	1.71083i
$418$	0.00233287	−	0.00233287i	0.000114104	−	0.000114104i
$419$	16.7418			0.817888			0.408944	−	0.912559i	$-0.365897\pi$
$419$	16.7418			0.817888			0.408944	+	0.912559i	$0.365897\pi$
$420$	8.56478	−	16.1454i	0.417919	−	0.787813i
$421$	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
$423$	−8.60498	+	1.81943i	−0.418389	+	0.0884636i
$424$		−	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	$-0.635316\pi$
$431$		−	37.8255i		−	1.82199i	0.412418	−	0.910995i	$-0.364684\pi$
$432$	3.36829	+	3.95659i	0.162057	+	0.190362i
$433$	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
$435$	−7.10164	+	2.17864i	−0.340497	+	0.104458i
$436$	−15.5455			−0.744495
$437$	−1.28904	+	1.28904i	−0.0616631	+	0.0616631i
$438$	−7.23157	+	24.3655i	−0.345538	+	1.16423i
$439$			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	0.506954	−	0.861973i	$-0.330772\pi$
$443$	−7.47230	−	7.47230i	−0.355020	−	0.355020i	−0.861973	+	0.506954i	$0.830772\pi$
$444$	14.4532	−	7.83744i	0.685919	−	0.371949i
$445$	−12.2911	+	8.16172i	−0.582653	+	0.386903i
$446$			6.45532i			0.305668i
$447$	−15.7162	−	4.66451i	−0.743353	−	0.220624i
$448$	3.33681	−	3.33681i	0.157649	−	0.157649i
$449$	−21.7175			−1.02491			−0.512456	−	0.858714i	$-0.671264\pi$
$449$	−21.7175			−1.02491			−0.512456	+	0.858714i	$0.671264\pi$
$450$	2.83388	−	14.7299i	0.133590	−	0.694373i
$451$	0.0120017			0.000565136
$452$	0.674324	−	0.674324i	0.0317175	−	0.0317175i
$453$	19.1651	+	5.68812i	0.900456	+	0.267251i
$454$			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	$0.353860\pi$
$461$			38.4951i			1.79289i	−0.443151	+	0.896447i	$0.646140\pi$
$462$	−0.00767251	+	0.0258512i	−0.000356957	+	0.00120271i
$463$	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
$465$	12.9276	−	3.96592i	0.599502	−	0.183915i
$466$	−16.3351			−0.756711
$467$	−15.9962	+	15.9962i	−0.740216	+	0.740216i	−0.972619	−	0.232404i	$-0.925341\pi$
$467$	−15.9962	+	15.9962i	−0.740216	+	0.740216i	0.232404	+	0.972619i	$0.425341\pi$
$468$	−1.00850	−	4.76971i	−0.0466181	−	0.220480i
$469$			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
$477$	5.24577	+	24.8098i	0.240187	+	1.13596i
$478$	−7.33796	+	7.33796i	−0.335631	+	0.335631i
$479$	14.7942			0.675966			0.337983	−	0.941152i	$-0.390255\pi$
$479$	14.7942			0.675966			0.337983	+	0.941152i	$0.390255\pi$
$480$	1.81497	−	3.42138i	0.0828419	−	0.156164i
$481$	−15.4258			−0.703355
$482$	10.1868	−	10.1868i	0.463994	−	0.463994i
$483$	4.23948	−	14.2842i	0.192903	−	0.649954i
$484$		−	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	$-0.866302\pi$
$491$		−	18.0717i		−	0.815564i	0.913079	−	0.407782i	$-0.133698\pi$
$492$	6.04038	+	1.79276i	0.272321	+	0.0808237i
$493$	−9.50052	+	9.50052i	−0.427882	+	0.427882i
$494$	−1.62506			−0.0731147
$495$	0.000202529		0.0221306i	9.10299e−6		0.000994698i
$496$	3.49143			0.156770
$497$	−10.7775	+	10.7775i	−0.483438	+	0.483438i
$498$	−21.8377	−	6.48134i	−0.978572	−	0.290436i
$499$			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	0.933850	−	0.357664i	$-0.116427\pi$
$503$	12.9225	+	12.9225i	0.576187	+	0.576187i	−0.357664	+	0.933850i	$0.616427\pi$
$504$	−7.72308	+	11.8647i	−0.344013	+	0.528495i
$505$	−20.0225	−	30.1527i	−0.890989	−	1.34178i
$506$		−	0.00601433i		−	0.000267370i
$507$	5.10519	−	17.2010i	0.226729	−	0.763925i
$508$	0.324072	−	0.324072i	0.0143783	−	0.0143783i
$509$	19.0740			0.845441			0.422721	−	0.906260i	$-0.361075\pi$
$509$	19.0740			0.845441			0.422721	+	0.906260i	$0.361075\pi$
$510$	−7.95719	−	25.9378i	−0.352350	−	1.14854i
$511$	−69.2457			−3.06325
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.95659	+	3.36829i	−0.174688	+	0.148714i
$514$		−	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	$0.144708\pi$
$521$			20.0460i			0.878229i	−0.898431	+	0.439115i	$0.855292\pi$
$522$	5.62948	−	1.19029i	0.246396	−	0.0520976i
$523$	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
$525$	40.6695	−	4.01676i	1.77496	−	0.175306i
$526$	2.68875			0.117235
$527$	17.2944	−	17.2944i	0.753357	−	0.753357i
$528$	−0.00162589	+	0.00547816i	−7.07578e−5	+	0.000238406i
$529$		−	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
$537$	2.90448	+	0.862035i	0.125337	+	0.0371996i
$538$	−15.1342	+	15.1342i	−0.652480	+	0.652480i
$539$	−0.0503736			−0.00216975
$540$	−3.20385	+	11.1685i	−0.137872	+	0.480616i
$541$	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
$543$	27.9904	+	8.30740i	1.20118	+	0.356505i
$544$		−	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
$552$	0.898394	−	3.02698i	0.0382382	−	0.128837i
$553$	−41.7332	+	41.7332i	−1.77468	+	1.77468i
$554$	23.5144			0.999031
$555$	32.4774	+	17.2286i	1.37859	+	0.731312i
$556$	21.0400			0.892294
$557$	−0.190340	+	0.190340i	−0.00806496	+	0.00806496i	−0.711128	−	0.703063i	$-0.751815\pi$
$557$	−0.190340	+	0.190340i	−0.00806496	+	0.00806496i	0.703063	+	0.711128i	$0.251815\pi$
$558$	−10.2477	+	2.16677i	−0.433820	+	0.0917265i
$559$		−	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	$0.0462081\pi$
$563$	26.9104	+	26.9104i	1.13414	+	1.13414i	0.144658	+	0.989482i	$0.453792\pi$
$564$	−2.42059	−	4.46386i	−0.101925	−	0.187963i
$565$	2.09022	+	0.422010i	0.0879364	+	0.0177541i
$566$			12.6056i			0.529853i
$567$	15.3049	−	39.6171i	0.642744	−	1.66376i
$568$	−2.28388	+	2.28388i	−0.0958294	+	0.0958294i
$569$	8.17866			0.342867			0.171434	−	0.985196i	$-0.445160\pi$
$569$	8.17866			0.342867			0.171434	+	0.985196i	$0.445160\pi$
$570$	3.42138	+	1.81497i	0.143306	+	0.0760209i
$571$	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
$573$	−1.27766	+	4.30484i	−0.0533749	+	0.179837i
$574$			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
$582$	−18.1348	−	5.38232i	−0.751712	−	0.223104i
$583$	−0.0197193	+	0.0197193i	−0.000816688	+	0.000816688i
$584$	−14.6739			−0.607212
$585$	7.63745	−	7.77853i	0.315770	−	0.321603i
$586$	20.8935			0.863104
$587$	−26.0323	+	26.0323i	−1.07447	+	1.07447i	−0.0774740	+	0.996994i	$0.524685\pi$
$587$	−26.0323	+	26.0323i	−1.07447	+	1.07447i	−0.996994	+	0.0774740i	$0.975315\pi$
$588$	−25.3528	−	7.52460i	−1.04553	−	0.310309i
$589$			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	0.904490	−	0.426494i	$-0.140251\pi$
$593$	11.6400	+	11.6400i	0.477997	+	0.477997i	−0.426494	+	0.904490i	$0.640251\pi$
$594$	0.00137244	−	0.0170880i	5.63120e−5	−	0.000701129i
$595$	61.5780	−	40.8900i	2.52445	−	1.67633i
$596$		−	9.46498i		−	0.387701i
$597$	−4.05272	+	13.6549i	−0.165867	+	0.558860i
$598$	−2.09476	+	2.09476i	−0.0856611	+	0.0856611i
$599$	−11.6334			−0.475328			−0.237664	−	0.971347i	$-0.576382\pi$
$599$	−11.6334			−0.475328			−0.237664	+	0.971347i	$0.576382\pi$
$600$	8.61832	−	0.851196i	0.351842	−	0.0347499i
$601$	−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
$603$	−4.88524	−	23.1047i	−0.198942	−	0.940897i
$604$			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
$612$	4.34738	+	20.5609i	0.175732	+	0.831126i
$613$	−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
$615$	4.13216	+	13.4695i	0.166625	+	0.543141i
$616$	−0.0155687			−0.000627280
$617$	24.2856	−	24.2856i	0.977701	−	0.977701i	−0.0220560	−	0.999757i	$-0.507021\pi$
$617$	24.2856	−	24.2856i	0.977701	−	0.977701i	0.999757	+	0.0220560i	$0.00702122\pi$
$618$	−0.162820	+	0.548593i	−0.00654957	+	0.0220676i
$619$		−	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
$627$	−0.00547816	−	0.00162589i	−0.000218777	−	6.49318e-5i
$628$	−8.81673	+	8.81673i	−0.351826	+	0.351826i
$629$	66.4962			2.65138
$630$	−31.6544	+	0.289686i	−1.26114	+	0.0115413i
$631$	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
$633$	−24.6946	−	7.32924i	−0.981522	−	0.291311i
$634$			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	$-0.927093\pi$
$641$		−	11.4967i		−	0.454092i	0.973884	−	0.227046i	$-0.0729067\pi$
$642$	−9.22077	+	31.0678i	−0.363915	+	1.22615i
$643$	−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
$645$	−3.90490	+	7.36108i	−0.153755	+	0.289842i
$646$	7.00516			0.275614
$647$	−10.4682	+	10.4682i	−0.411548	+	0.411548i	−0.882278	−	0.470729i	$-0.843991\pi$
$647$	−10.4682	+	10.4682i	−0.411548	+	0.411548i	0.470729	+	0.882278i	$0.343991\pi$
$648$	3.24328	−	8.39531i	0.127408	−	0.329799i
$649$			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	0.565860	−	0.824501i	$-0.308544\pi$
$653$	−6.60928	−	6.60928i	−0.258641	−	0.258641i	−0.824501	+	0.565860i	$0.808544\pi$
$654$	12.8351	+	23.6696i	0.501894	+	0.925554i
$655$	19.7840	+	29.7935i	0.773023	+	1.16413i
$656$			3.63777i			0.142031i
$657$	43.0696	−	9.10660i	1.68031	−	0.355282i
$658$	9.78265	−	9.78265i	0.381368	−	0.381368i
$659$	−17.5688			−0.684382			−0.342191	−	0.939630i	$-0.611169\pi$
$659$	−17.5688			−0.684382			−0.342191	+	0.939630i	$0.611169\pi$
$660$	−0.0122158	+	0.00374755i	−0.000475497	+	0.000145873i
$661$	−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
$663$	5.61012	−	18.9023i	0.217879	−	0.734105i
$664$		−	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
$672$	−7.83564	−	2.32558i	−0.302266	−	0.0897113i
$673$	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
$675$	−24.7675	+	7.84685i	−0.953300	+	0.302025i
$676$	10.3592			0.398431
$677$	−30.2637	+	30.2637i	−1.16313	+	1.16313i	−0.179342	+	0.983787i	$0.557397\pi$
$677$	−30.2637	+	30.2637i	−1.16313	+	1.16313i	−0.983787	+	0.179342i	$0.942603\pi$
$678$	−1.58348	−	0.469969i	−0.0608132	−	0.0180491i
$679$		−	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	0.993504	−	0.113800i	$-0.0363024\pi$
$683$	22.9904	+	22.9904i	0.879703	+	0.879703i	−0.113800	+	0.993504i	$0.536302\pi$
$684$	−2.51426	−	1.63661i	−0.0961352	−	0.0625772i
$685$	2.96550	−	14.6882i	0.113306	−	0.561207i
$686$		−	39.0189i		−	1.48975i
$687$	−7.70671	+	25.9664i	−0.294029	+	0.990680i
$688$	−1.52133	+	1.52133i	−0.0580003	+	0.0580003i
$689$	13.7362			0.523309
$690$	6.74987	−	2.07073i	0.256963	−	0.0788312i
$691$	−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
$693$	0.0456957	−	0.00966186i	0.00173584	−	0.000367024i
$694$			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	$-0.837711\pi$
$701$		−	25.8432i		−	0.976085i	0.872820	−	0.488043i	$-0.162289\pi$
$702$	−6.42968	+	5.47365i	−0.242673	+	0.206590i
$703$	−6.71219	+	6.71219i	−0.253155	+	0.253155i
$704$	−0.00329918			−0.000124342
$705$	5.32104	−	10.0306i	0.200402	−	0.377775i
$706$	5.14338			0.193574
$707$	−54.0127	+	54.0127i	−2.03136	+	2.03136i
$708$	−5.85890	+	19.7406i	−0.220191	+	0.741896i
$709$		−	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
$717$	17.2314	+	5.11418i	0.643517	+	0.190993i
$718$	13.4372	−	13.4372i	0.501473	−	0.501473i
$719$	−46.4403			−1.73193			−0.865965	−	0.500105i	$-0.833295\pi$
$719$	−46.4403			−1.73193			−0.865965	+	0.500105i	$0.833295\pi$
$720$	−6.70792	+	0.0613876i	−0.249990	+	0.00228778i
$721$	−1.55908			−0.0580630
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	−23.9210	−	7.09964i	−0.889632	−	0.264039i
$724$			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
$732$	0.962624	−	3.24339i	0.0355796	−	0.119879i
$733$	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
$735$	−17.3436	−	56.5343i	−0.639728	−	2.08530i
$736$	1.82298			0.0671958
$737$	0.0183640	−	0.0183640i	0.000676447	−	0.000676447i
$738$	−2.25759	−	10.6773i	−0.0831030	−	0.393035i
$739$		−	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	0.892901	−	0.450253i	$-0.148666\pi$
$743$	12.0657	+	12.0657i	0.442649	+	0.442649i	−0.450253	+	0.892901i	$0.648666\pi$
$744$	−2.88269	−	5.31604i	−0.105685	−	0.194895i
$745$	17.6312	−	11.7077i	0.645956	−	0.428938i
$746$		−	6.61149i		−	0.242064i
$747$	8.16184	+	38.6014i	0.298626	+	1.41235i
$748$	−0.0163421	+	0.0163421i	−0.000597528	+	0.000597528i
$749$	−88.2932			−3.22616
$750$	12.2461	+	15.0011i	0.447163	+	0.547764i
$751$	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
$753$	10.2057	−	34.3863i	0.371916	−	1.25311i
$754$		−	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	$0.311922\pi$
$761$			45.8185i			1.66092i	−0.557078	+	0.830460i	$0.688078\pi$
$762$	−0.761000	−	0.225861i	−0.0275681	−	0.00818209i
$763$	−51.8724	+	51.8724i	−1.87791	+	1.87791i
$764$	−2.59256			−0.0937954
$765$	−32.9229	+	33.5311i	−1.19033	+	1.21232i
$766$	20.4149			0.737619
$767$	13.6610	−	13.6610i	0.493272	−	0.493272i
$768$	−1.66046	−	0.492817i	−0.0599167	−	0.0177830i
$769$		−	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	0.560890	−	0.827890i	$-0.310459\pi$
$773$	−7.42336	−	7.42336i	−0.267000	−	0.267000i	−0.827890	+	0.560890i	$0.810459\pi$
$774$	3.52115	−	5.40941i	0.126565	−	0.194437i
$775$	−6.77299	+	16.0897i	−0.243293	+	0.577958i
$776$		−	10.9215i		−	0.392061i
$777$	22.0755	−	74.3795i	0.791954	−	2.66835i
$778$	−0.400347	+	0.400347i	−0.0143531	+	0.0143531i
$779$	−3.63777			−0.130337
$780$	5.55994	+	2.94943i	0.199078	+	0.105607i
$781$	0.0106560			0.000381301
$782$	9.02993	−	9.02993i	0.322910	−	0.322910i
$783$	−6.46031	−	7.58867i	−0.230873	−	0.271197i
$784$		−	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
$792$	0.00968345	−	0.00204746i	0.000344086	−	7.27532e-5i
$793$	−2.24452	+	2.24452i	−0.0797054	+	0.0797054i
$794$	15.5947			0.553436
$795$	−28.9202	−	15.3416i	−1.02569	−	0.544110i
$796$	−8.22358			−0.291477
$797$	0.0667197	−	0.0667197i	0.00236333	−	0.00236333i	−0.705924	−	0.708287i	$-0.749468\pi$
$797$	0.0667197	−	0.0667197i	0.00236333	−	0.00236333i	0.708287	+	0.705924i	$0.249468\pi$
$798$	2.32558	−	7.83564i	0.0823247	−	0.277379i
$799$		−	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
$807$	35.5387	+	10.5477i	1.25102	+	0.371298i
$808$	−11.4459	+	11.4459i	−0.402665	+	0.402665i
$809$	2.41703			0.0849783			0.0424892	−	0.999097i	$-0.486471\pi$
$809$	2.41703			0.0849783			0.0424892	+	0.999097i	$0.486471\pi$
$810$	19.6504	−	4.34309i	0.690444	−	0.152601i
$811$	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
$813$	−8.11312	−	2.40794i	−0.284540	−	0.0844500i
$814$		−	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	$0.0291802\pi$
$821$			5.24603i			0.183088i	−0.995801	+	0.0915438i	$0.970820\pi$
$822$	−3.30252	+	11.1273i	−0.115189	+	0.388108i
$823$	−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
$825$	−0.0220912	−	0.0181197i	−0.000769116	−	0.000630847i
$826$	−56.1018			−1.95203
$827$	24.7201	−	24.7201i	0.859602	−	0.859602i	−0.131689	−	0.991291i	$-0.542040\pi$
$827$	24.7201	−	24.7201i	0.859602	−	0.859602i	0.991291	+	0.131689i	$0.0420400\pi$
$828$	−5.35064	+	1.13133i	−0.185947	+	0.0393165i
$829$			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
$837$	11.7601	+	13.8142i	0.406489	+	0.477487i
$838$	11.8382	−	11.8382i	0.408944	−	0.408944i
$839$	21.2177			0.732517			0.366258	−	0.930513i	$-0.380639\pi$
$839$	21.2177			0.732517			0.366258	+	0.930513i	$0.380639\pi$
$840$	−5.36028	−	17.4727i	−0.184947	−	0.602866i
$841$	−25.3214			−0.873150
$842$	14.3887	−	14.3887i	0.495867	−	0.495867i
$843$	−3.91457	+	13.1895i	−0.134825	+	0.454270i
$844$		−	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
$852$	5.36311	+	1.59175i	0.183737	+	0.0545323i
$853$	−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
$855$	−0.0613876	−	6.70792i	−0.00209941	−	0.229406i
$856$	−18.7103			−0.639506
$857$	−22.6298	+	22.6298i	−0.773020	+	0.773020i	−0.978633	−	0.205613i	$-0.934081\pi$
$857$	−22.6298	+	22.6298i	−0.773020	+	0.773020i	0.205613	+	0.978633i	$0.434081\pi$
$858$	−0.00890231	−	0.00264216i	−0.000303920	−	9.02020e-5i
$859$			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	$0.114490\pi$
$863$	37.8370	+	37.8370i	1.28799	+	1.28799i	0.351976	+	0.936009i	$0.385510\pi$
$864$	5.17947	+	0.415995i	0.176209	+	0.0141524i
$865$	−12.7828	−	2.58080i	−0.434628	−	0.0877499i
$866$		−	5.28008i		−	0.179424i
$867$	−15.8058	+	53.2548i	−0.536792	+	1.80863i
$868$	11.6502	−	11.6502i	0.395434	−	0.395434i
$869$	0.0412626			0.00139974
$870$	−3.48108	+	6.56215i	−0.118020	+	0.222478i
$871$	−12.7922			−0.433446
$872$	−10.9923	+	10.9923i	−0.372248	+	0.372248i
$873$	6.77787	+	32.0559i	0.229396	+	1.08493i
$874$			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	$0.0304233\pi$
$881$			5.66516i			0.190864i	−0.995436	+	0.0954321i	$0.969577\pi$
$882$	9.47560	+	44.8148i	0.319060	+	1.50899i
$883$	−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
$885$	−44.0195	+	13.5043i	−1.47970	+	0.453942i
$886$	−10.5674			−0.355020
$887$	9.96724	−	9.96724i	0.334667	−	0.334667i	−0.519689	−	0.854356i	$-0.673952\pi$
$887$	9.96724	−	9.96724i	0.334667	−	0.334667i	0.854356	+	0.519689i	$0.173952\pi$
$888$	4.67805	−	15.7619i	0.156985	−	0.528934i
$889$		−	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
$897$	4.91902	+	1.45994i	0.164241	+	0.0487460i
$898$	−15.3566	+	15.3566i	−0.512456	+	0.512456i
$899$	−6.69649			−0.223340
$900$	−8.41174	−	12.4194i	−0.280391	−	0.413982i
$901$	−59.2131			−1.97268
$902$	0.00848646	−	0.00848646i	0.000282568	−	0.000282568i
$903$	16.8583	+	5.00347i	0.561010	+	0.166505i
$904$		−	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	$-0.866062\pi$
$911$		−	24.6576i		−	0.816944i	0.912771	−	0.408472i	$-0.133938\pi$
$912$	0.492817	−	1.66046i	0.0163188	−	0.0549834i
$913$	−0.0306810	+	0.0306810i	−0.00101539	+	0.00101539i
$914$	22.5032			0.744341
$915$	7.23245	−	2.21877i	0.239097	−	0.0733503i
$916$	−15.6381			−0.516696
$917$	53.3692	−	53.3692i	1.76241	−	1.76241i
$918$	27.7166	−	23.5954i	0.914784	−	0.778764i
$919$		−	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
$927$	0.969718	−	0.205036i	0.0318497	−	0.00673427i
$928$	−1.35622	+	1.35622i	−0.0445200	+	0.0445200i
$929$	13.8105			0.453109			0.226555	−	0.973998i	$-0.427254\pi$
$929$	13.8105			0.453109			0.226555	+	0.973998i	$0.427254\pi$
$930$	6.33685	−	11.9455i	0.207793	−	0.391709i
$931$	15.2685			0.500406
$932$	−11.5507	+	11.5507i	−0.378355	+	0.378355i
$933$	3.10092	−	10.4480i	0.101520	−	0.342053i
$934$			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	$-0.954480\pi$
$941$		−	8.74362i		−	0.285034i	0.989792	−	0.142517i	$-0.0455196\pi$
$942$	20.7039	+	6.14480i	0.674568	+	0.200209i
$943$	−4.68923	+	4.68923i	−0.152702	+	0.152702i
$944$	−11.8886			−0.386941
$945$	26.5765	+	47.9577i	0.864533	+	1.56006i
$946$	0.00709815			0.000230781
$947$	−28.7624	+	28.7624i	−0.934651	+	0.934651i	−0.997992	−	0.0633409i	$-0.979824\pi$
$947$	−28.7624	+	28.7624i	−0.934651	+	0.934651i	0.0633409	+	0.997992i	$0.479824\pi$
$948$	20.7673	+	6.16363i	0.674490	+	0.200186i
$949$		−	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	0.854160	−	0.520010i	$-0.174072\pi$
$953$	10.3155	+	10.3155i	0.334151	+	0.334151i	−0.520010	+	0.854160i	$0.674072\pi$
$954$	21.2525	+	13.8339i	0.688076	+	0.447889i
$955$	−3.20687	−	4.82936i	−0.103772	−	0.156275i
$956$			10.3774i			0.335631i
$957$	0.00311843	−	0.0105070i	0.000100804	−	0.000339643i
$958$	10.4611	−	10.4611i	0.337983	−	0.337983i
$959$	−31.6232			−1.02117
$960$	−1.13590	−	3.70266i	−0.0366611	−	0.119503i
$961$	−18.8099			−0.606772
$962$	−10.9077	+	10.9077i	−0.351677	+	0.351677i
$963$	54.9169	−	11.6116i	1.76967	−	0.374177i
$964$		−	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	$0.0149093\pi$
$971$			2.91801i			0.0936433i	−0.998903	+	0.0468217i	$0.985091\pi$
$972$	−15.4605	+	1.99337i	−0.495895	+	0.0639374i
$973$	70.2063	−	70.2063i	2.25071	−	2.25071i
$974$	15.0609			0.482584
$975$	1.38324	+	14.0052i	0.0442992	+	0.448527i
$976$	1.95331			0.0625239
$977$	9.00845	−	9.00845i	0.288206	−	0.288206i	−0.548165	−	0.836370i	$-0.684673\pi$
$977$	9.00845	−	9.00845i	0.288206	−	0.288206i	0.836370	+	0.548165i	$0.184673\pi$
$978$	−1.26116	+	4.24926i	−0.0403275	+	0.135876i
$979$		−	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	0.590608	−	0.806958i	$-0.298888\pi$
$983$	−6.78318	−	6.78318i	−0.216350	−	0.216350i	−0.806958	+	0.590608i	$0.798888\pi$
$984$	5.53886	−	3.00352i	0.176573	−	0.0957488i
$985$	−4.80564	+	23.8025i	−0.153120	+	0.758410i
$986$			13.4358i			0.427882i
$987$	−22.9721	−	6.81801i	−0.731210	−	0.217020i
$988$	−1.14909	+	1.14909i	−0.0365573	+	0.0365573i
$989$	−3.92212			−0.124716
$990$	0.0157919	+	0.0155055i	0.000501901	+	0.000492798i
$991$	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
$993$	36.9991	+	10.9811i	1.17413	+	0.348476i
$994$			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.77.10	yes	36
3.2	odd	2	inner	570.2.k.b.77.5	✓	36
5.3	odd	4	inner	570.2.k.b.533.5	yes	36
15.8	even	4	inner	570.2.k.b.533.10	yes	36

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.66046 - 0.492817i) q^{3} -1.00000i q^{4} +(1.86278 - 1.23695i) q^{5} +(-1.52260 + 0.825649i) q^{6} +(-3.33681 - 3.33681i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.51426 + 1.63661i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.66046 - 0.492817i) 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} +(-0.492817 + 1.66046i) q^{12} +(1.14909 - 1.14909i) q^{13} -4.71896 q^{14} +(-3.70266 + 1.13590i) q^{15} -1.00000 q^{16} +(-4.95340 + 4.95340i) q^{17} +(2.93511 - 0.620596i) 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} +(-3.36829 - 3.95659i) q^{27} +(-3.33681 + 3.33681i) q^{28} +1.91798 q^{29} +(-1.81497 + 3.42138i) q^{30} -3.49143 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.00162589 - 0.00547816i) 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} +(7.83564 + 2.32558i) q^{42} +(1.52133 - 1.52133i) q^{43} +0.00329918 q^{44} +(6.70792 - 0.0613876i) q^{45} -1.82298 q^{46} +(-2.07305 + 2.07305i) q^{47} +(1.66046 + 0.492817i) 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} +(-0.492817 + 1.66046i) q^{57} +(1.35622 - 1.35622i) q^{58} +11.8886 q^{59} +(1.13590 + 3.70266i) q^{60} -1.95331 q^{61} +(-2.46881 + 2.46881i) q^{62} +(-2.92857 - 13.8506i) 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} +(-0.620596 - 2.93511i) q^{72} +(10.3760 - 10.3760i) q^{73} -9.49246 q^{74} +(-5.49219 + 6.69596i) q^{75} -1.00000 q^{76} +(0.0110087 - 0.0110087i) q^{77} +(-0.800855 + 2.69834i) 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} +(-3.18473 - 0.945213i) q^{87} +(0.00233287 - 0.00233287i) q^{88} -6.59825 q^{89} +(4.69981 - 4.78663i) q^{90} -7.66856 q^{91} +(-1.28904 + 1.28904i) q^{92} +(5.79738 + 1.72063i) 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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