LMFDB - Embedded newform 570.2.m.b.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

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([0, 1, 2]))

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

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

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.10
Root			$0.850665 - 0.850665i$ of defining polynomial
Character	$\chi$	$=$	570.37
Dual form			570.2.m.b.493.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.23583 - 0.0328054i) q^{5} -1.00000 q^{6} +(-3.17648 - 3.17648i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.23583 - 0.0328054i) q^{5} -1.00000 q^{6} +(-3.17648 - 3.17648i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.55777 - 1.60417i) q^{10} +1.49820 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-2.38967 - 2.38967i) q^{13} -4.49222 q^{14} +(-1.60417 - 1.55777i) q^{15} -1.00000 q^{16} +(0.853306 + 0.853306i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.34485 + 0.349716i) q^{19} +(-0.0328054 - 2.23583i) q^{20} +4.49222i q^{21} +(1.05939 - 1.05939i) q^{22} +(4.67468 - 4.67468i) q^{23} +1.00000i q^{24} +(4.99785 - 0.146694i) q^{25} -3.37950 q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.17648 + 3.17648i) q^{28} -5.40423 q^{29} +(-2.23583 + 0.0328054i) q^{30} +0.364245i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.05939 - 1.05939i) q^{33} +1.20676 q^{34} +(-7.20626 - 6.99785i) q^{35} +1.00000 q^{36} +(4.29845 - 4.29845i) q^{37} +(-2.82498 + 3.31956i) q^{38} +3.37950i q^{39} +(-1.60417 - 1.55777i) q^{40} +1.79412i q^{41} +(3.17648 + 3.17648i) q^{42} +(0.623738 - 0.623738i) q^{43} -1.49820i q^{44} +(0.0328054 + 2.23583i) q^{45} -6.61099i q^{46} +(-5.24209 - 5.24209i) q^{47} +(0.707107 + 0.707107i) q^{48} +13.1800i q^{49} +(3.43028 - 3.63774i) q^{50} -1.20676i q^{51} +(-2.38967 + 2.38967i) q^{52} +(5.27391 + 5.27391i) q^{53} -1.00000i q^{54} +(3.34972 - 0.0491491i) q^{55} +4.49222i q^{56} +(3.31956 + 2.82498i) q^{57} +(-3.82137 + 3.82137i) q^{58} -1.49134 q^{59} +(-1.55777 + 1.60417i) q^{60} +15.2432 q^{61} +(0.257560 + 0.257560i) q^{62} +(3.17648 - 3.17648i) q^{63} +1.00000i q^{64} +(-5.42128 - 5.26449i) q^{65} -1.49820 q^{66} +(0.989147 - 0.989147i) q^{67} +(0.853306 - 0.853306i) q^{68} -6.61099 q^{69} +(-10.0438 + 0.147369i) q^{70} -8.98443i q^{71} +(0.707107 - 0.707107i) q^{72} +(-11.2572 + 11.2572i) q^{73} -6.07893i q^{74} +(-3.63774 - 3.43028i) q^{75} +(0.349716 + 4.34485i) q^{76} +(-4.75900 - 4.75900i) q^{77} +(2.38967 + 2.38967i) q^{78} +7.95317 q^{79} +(-2.23583 + 0.0328054i) q^{80} -1.00000 q^{81} +(1.26863 + 1.26863i) q^{82} +(3.94546 - 3.94546i) q^{83} +4.49222 q^{84} +(1.93584 + 1.87985i) q^{85} -0.882099i q^{86} +(3.82137 + 3.82137i) q^{87} +(-1.05939 - 1.05939i) q^{88} +9.30909 q^{89} +(1.60417 + 1.55777i) q^{90} +15.1814i q^{91} +(-4.67468 - 4.67468i) q^{92} +(0.257560 - 0.257560i) q^{93} -7.41343 q^{94} +(-9.70286 + 0.924440i) q^{95} +1.00000 q^{96} +(8.79952 - 8.79952i) q^{97} +(9.31967 + 9.31967i) q^{98} +1.49820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	2.23583	−	0.0328054i	0.999892	−	0.0146710i
$5$	2.23583	−	0.0328054i	0.999892	−	0.0146710i
$6$	−1.00000			−0.408248
$7$	−3.17648	−	3.17648i	−1.20060	−	1.20060i	−0.973986	−	0.226610i	$-0.927236\pi$
$7$	−3.17648	−	3.17648i	−1.20060	−	1.20060i	−0.226610	−	0.973986i	$-0.572764\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	1.55777	−	1.60417i	0.492611	−	0.507282i
$11$	1.49820			0.451724			0.225862	−	0.974159i	$-0.427480\pi$
$11$	1.49820			0.451724			0.225862	+	0.974159i	$0.427480\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−2.38967	−	2.38967i	−0.662774	−	0.662774i	0.293259	−	0.956033i	$-0.405260\pi$
$13$	−2.38967	−	2.38967i	−0.662774	−	0.662774i	−0.956033	+	0.293259i	$0.905260\pi$
$14$	−4.49222			−1.20060
$15$	−1.60417	−	1.55777i	−0.414194	−	0.402215i
$16$	−1.00000			−0.250000
$17$	0.853306	+	0.853306i	0.206957	+	0.206957i	0.802973	−	0.596016i	$-0.203250\pi$
$17$	0.853306	+	0.853306i	0.206957	+	0.206957i	−0.596016	+	0.802973i	$0.703250\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−4.34485	+	0.349716i	−0.996776	+	0.0802304i
$19$	−4.34485	+	0.349716i	−0.996776	+	0.0802304i
$20$	−0.0328054	−	2.23583i	−0.00733551	−	0.499946i
$21$			4.49222i			0.980282i
$22$	1.05939	−	1.05939i	0.225862	−	0.225862i
$23$	4.67468	−	4.67468i	0.974737	−	0.974737i	−0.0249512	−	0.999689i	$-0.507943\pi$
$23$	4.67468	−	4.67468i	0.974737	−	0.974737i	0.999689	+	0.0249512i	$0.00794305\pi$
$24$			1.00000i			0.204124i
$25$	4.99785	−	0.146694i	0.999570	−	0.0293389i
$26$	−3.37950			−0.662774
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−3.17648	+	3.17648i	−0.600298	+	0.600298i
$29$	−5.40423			−1.00354			−0.501771	−	0.865001i	$-0.667318\pi$
$29$	−5.40423			−1.00354			−0.501771	+	0.865001i	$0.667318\pi$
$30$	−2.23583	+	0.0328054i	−0.408204	+	0.00598942i
$31$			0.364245i			0.0654204i	0.999465	+	0.0327102i	$0.0104138\pi$
$31$			0.364245i			0.0654204i	−0.999465	+	0.0327102i	$0.989586\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.05939	−	1.05939i	−0.184416	−	0.184416i
$34$	1.20676			0.206957
$35$	−7.20626	−	6.99785i	−1.21808	−	1.18285i
$36$	1.00000			0.166667
$37$	4.29845	−	4.29845i	0.706661	−	0.706661i	−0.259170	−	0.965832i	$-0.583449\pi$
$37$	4.29845	−	4.29845i	0.706661	−	0.706661i	0.965832	+	0.259170i	$0.0834491\pi$
$38$	−2.82498	+	3.31956i	−0.458273	+	0.538503i
$39$			3.37950i			0.541153i
$40$	−1.60417	−	1.55777i	−0.253641	−	0.246305i
$41$			1.79412i			0.280194i	0.990138	+	0.140097i	$0.0447415\pi$
$41$			1.79412i			0.280194i	−0.990138	+	0.140097i	$0.955259\pi$
$42$	3.17648	+	3.17648i	0.490141	+	0.490141i
$43$	0.623738	−	0.623738i	0.0951192	−	0.0951192i	−0.657946	−	0.753065i	$-0.728574\pi$
$43$	0.623738	−	0.623738i	0.0951192	−	0.0951192i	0.753065	+	0.657946i	$0.228574\pi$
$44$		−	1.49820i		−	0.225862i
$45$	0.0328054	+	2.23583i	0.00489034	+	0.333297i
$46$		−	6.61099i		−	0.974737i
$47$	−5.24209	−	5.24209i	−0.764637	−	0.764637i	0.212520	−	0.977157i	$-0.431833\pi$
$47$	−5.24209	−	5.24209i	−0.764637	−	0.764637i	−0.977157	+	0.212520i	$0.931833\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			13.1800i			1.88286i
$50$	3.43028	−	3.63774i	0.485115	−	0.514454i
$51$		−	1.20676i		−	0.168980i
$52$	−2.38967	+	2.38967i	−0.331387	+	0.331387i
$53$	5.27391	+	5.27391i	0.724427	+	0.724427i	0.969504	−	0.245077i	$-0.0788132\pi$
$53$	5.27391	+	5.27391i	0.724427	+	0.724427i	−0.245077	+	0.969504i	$0.578813\pi$
$54$		−	1.00000i		−	0.136083i
$55$	3.34972	−	0.0491491i	0.451676	−	0.00662726i
$56$			4.49222i			0.600298i
$57$	3.31956	+	2.82498i	0.439686	+	0.374178i
$58$	−3.82137	+	3.82137i	−0.501771	+	0.501771i
$59$	−1.49134			−0.194156			−0.0970781	−	0.995277i	$-0.530950\pi$
$59$	−1.49134			−0.194156			−0.0970781	+	0.995277i	$0.530950\pi$
$60$	−1.55777	+	1.60417i	−0.201107	+	0.207097i
$61$	15.2432			1.95169			0.975844	−	0.218468i	$-0.0701060\pi$
$61$	15.2432			1.95169			0.975844	+	0.218468i	$0.0701060\pi$
$62$	0.257560	+	0.257560i	0.0327102	+	0.0327102i
$63$	3.17648	−	3.17648i	0.400198	−	0.400198i
$64$			1.00000i			0.125000i
$65$	−5.42128	−	5.26449i	−0.672426	−	0.652979i
$66$	−1.49820			−0.184416
$67$	0.989147	−	0.989147i	0.120844	−	0.120844i	−0.644099	−	0.764942i	$-0.722767\pi$
$67$	0.989147	−	0.989147i	0.120844	−	0.120844i	0.764942	+	0.644099i	$0.222767\pi$
$68$	0.853306	−	0.853306i	0.103478	−	0.103478i
$69$	−6.61099			−0.795870
$70$	−10.0438	+	0.147369i	−1.20047	+	0.0176140i
$71$		−	8.98443i		−	1.06626i	−0.846035	−	0.533128i	$-0.821016\pi$
$71$		−	8.98443i		−	1.06626i	0.846035	−	0.533128i	$-0.178984\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−11.2572	+	11.2572i	−1.31756	+	1.31756i	−0.401850	+	0.915706i	$0.631633\pi$
$73$	−11.2572	+	11.2572i	−1.31756	+	1.31756i	−0.915706	+	0.401850i	$0.868367\pi$
$74$		−	6.07893i		−	0.706661i
$75$	−3.63774	−	3.43028i	−0.420050	−	0.396095i
$76$	0.349716	+	4.34485i	0.0401152	+	0.498388i
$77$	−4.75900	−	4.75900i	−0.542338	−	0.542338i
$78$	2.38967	+	2.38967i	0.270576	+	0.270576i
$79$	7.95317			0.894801			0.447401	−	0.894334i	$-0.352350\pi$
$79$	7.95317			0.894801			0.447401	+	0.894334i	$0.352350\pi$
$80$	−2.23583	+	0.0328054i	−0.249973	+	0.00366776i
$81$	−1.00000			−0.111111
$82$	1.26863	+	1.26863i	0.140097	+	0.140097i
$83$	3.94546	−	3.94546i	0.433071	−	0.433071i	−0.456601	−	0.889672i	$-0.650933\pi$
$83$	3.94546	−	3.94546i	0.433071	−	0.433071i	0.889672	+	0.456601i	$0.150933\pi$
$84$	4.49222			0.490141
$85$	1.93584	+	1.87985i	0.209971	+	0.203898i
$86$		−	0.882099i		−	0.0951192i
$87$	3.82137	+	3.82137i	0.409694	+	0.409694i
$88$	−1.05939	−	1.05939i	−0.112931	−	0.112931i
$89$	9.30909			0.986762			0.493381	−	0.869813i	$-0.335761\pi$
$89$	9.30909			0.986762			0.493381	+	0.869813i	$0.335761\pi$
$90$	1.60417	+	1.55777i	0.169094	+	0.164204i
$91$			15.1814i			1.59145i
$92$	−4.67468	−	4.67468i	−0.487369	−	0.487369i
$93$	0.257560	−	0.257560i	0.0267078	−	0.0267078i
$94$	−7.41343			−0.764637
$95$	−9.70286	+	0.924440i	−0.995492	+	0.0948455i
$96$	1.00000			0.102062
$97$	8.79952	−	8.79952i	0.893456	−	0.893456i	−0.101391	−	0.994847i	$-0.532329\pi$
$97$	8.79952	−	8.79952i	0.893456	−	0.893456i	0.994847	+	0.101391i	$0.0323292\pi$
$98$	9.31967	+	9.31967i	0.941429	+	0.941429i
$99$			1.49820i			0.150575i
$100$	−0.146694	−	4.99785i	−0.0146694	−	0.499785i
$101$	2.17827			0.216746			0.108373	−	0.994110i	$-0.465436\pi$
$101$	2.17827			0.216746			0.108373	+	0.994110i	$0.465436\pi$
$102$	−0.853306	−	0.853306i	−0.0844898	−	0.0844898i
$103$	9.44827	+	9.44827i	0.930966	+	0.930966i	0.997766	−	0.0668005i	$-0.0212791\pi$
$103$	9.44827	+	9.44827i	0.930966	+	0.930966i	−0.0668005	+	0.997766i	$0.521279\pi$
$104$			3.37950i			0.331387i
$105$	0.147369	+	10.0438i	0.0143817	+	0.980176i
$106$	7.45843			0.724427
$107$	0.300245	−	0.300245i	0.0290258	−	0.0290258i	−0.692445	−	0.721471i	$-0.743466\pi$
$107$	0.300245	−	0.300245i	0.0290258	−	0.0290258i	0.721471	+	0.692445i	$0.243466\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	7.83545			0.750500			0.375250	−	0.926924i	$-0.377557\pi$
$109$	7.83545			0.750500			0.375250	+	0.926924i	$0.377557\pi$
$110$	2.33385	−	2.40336i	0.222524	−	0.229151i
$111$	−6.07893			−0.576987
$112$	3.17648	+	3.17648i	0.300149	+	0.300149i
$113$	12.3606	+	12.3606i	1.16279	+	1.16279i	0.983862	+	0.178928i	$0.0572631\pi$
$113$	12.3606	+	12.3606i	1.16279	+	1.16279i	0.178928	+	0.983862i	$0.442737\pi$
$114$	4.34485	−	0.349716i	0.406932	−	0.0327539i
$115$	10.2984	−	10.6051i	0.960332	−	0.988933i
$116$			5.40423i			0.501771i
$117$	2.38967	−	2.38967i	0.220925	−	0.220925i
$118$	−1.05454	+	1.05454i	−0.0970781	+	0.0970781i
$119$		−	5.42101i		−	0.496943i
$120$	0.0328054	+	2.23583i	0.00299471	+	0.204102i
$121$	−8.75540			−0.795945
$122$	10.7786	−	10.7786i	0.975844	−	0.975844i
$123$	1.26863	−	1.26863i	0.114389	−	0.114389i
$124$	0.364245			0.0327102
$125$	11.1695	−	0.491940i	0.999032	−	0.0440004i
$126$		−	4.49222i		−	0.400198i
$127$	8.31864	−	8.31864i	0.738160	−	0.738160i	−0.234062	−	0.972222i	$-0.575202\pi$
$127$	8.31864	−	8.31864i	0.738160	−	0.738160i	0.972222	+	0.234062i	$0.0752017\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.882099			−0.0776645
$130$	−7.55598	+	0.110866i	−0.662703	+	0.00972358i
$131$	8.07719			0.705707			0.352854	−	0.935679i	$-0.385211\pi$
$131$	8.07719			0.705707			0.352854	+	0.935679i	$0.385211\pi$
$132$	−1.05939	+	1.05939i	−0.0922078	+	0.0922078i
$133$	14.9122	+	12.6904i	1.29305	+	1.10040i
$134$		−	1.39887i		−	0.120844i
$135$	1.55777	−	1.60417i	0.134072	−	0.138065i
$136$		−	1.20676i		−	0.103478i
$137$	6.99785	+	6.99785i	0.597866	+	0.597866i	0.939744	−	0.341878i	$-0.111063\pi$
$137$	6.99785	+	6.99785i	0.597866	+	0.597866i	−0.341878	+	0.939744i	$0.611063\pi$
$138$	−4.67468	+	4.67468i	−0.397935	+	0.397935i
$139$			10.8866i			0.923393i	0.887038	+	0.461696i	$0.152759\pi$
$139$			10.8866i			0.923393i	−0.887038	+	0.461696i	$0.847241\pi$
$140$	−6.99785	+	7.20626i	−0.591426	+	0.609040i
$141$			7.41343i			0.624324i
$142$	−6.35295	−	6.35295i	−0.533128	−	0.533128i
$143$	−3.58020	−	3.58020i	−0.299391	−	0.299391i
$144$		−	1.00000i		−	0.0833333i
$145$	−12.0829	+	0.177288i	−1.00343	+	0.0147230i
$146$			15.9201i			1.31756i
$147$	9.31967	−	9.31967i	0.768674	−	0.768674i
$148$	−4.29845	−	4.29845i	−0.353331	−	0.353331i
$149$		−	12.6624i		−	1.03735i	−0.854972	−	0.518674i	$-0.826426\pi$
$149$		−	12.6624i		−	1.03735i	0.854972	−	0.518674i	$-0.173574\pi$
$150$	−4.99785	+	0.146694i	−0.408073	+	0.0119776i
$151$			15.4280i			1.25551i	0.778411	+	0.627755i	$0.216026\pi$
$151$			15.4280i			1.25551i	−0.778411	+	0.627755i	$0.783974\pi$
$152$	3.31956	+	2.82498i	0.269252	+	0.229136i
$153$	−0.853306	+	0.853306i	−0.0689857	+	0.0689857i
$154$	−6.73024			−0.542338
$155$	0.0119492	+	0.814389i	0.000959784	+	0.0654133i
$156$	3.37950			0.270576
$157$	−13.2948	−	13.2948i	−1.06104	−	1.06104i	−0.998012	−	0.0630301i	$-0.979924\pi$
$157$	−13.2948	−	13.2948i	−1.06104	−	1.06104i	−0.0630301	−	0.998012i	$-0.520076\pi$
$158$	5.62374	−	5.62374i	0.447401	−	0.447401i
$159$		−	7.45843i		−	0.591492i
$160$	−1.55777	+	1.60417i	−0.123153	+	0.126820i
$161$	−29.6980			−2.34053
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	0.0438073	−	0.0438073i	0.00343125	−	0.00343125i	−0.705389	−	0.708820i	$-0.749228\pi$
$163$	0.0438073	−	0.0438073i	0.00343125	−	0.00343125i	0.708820	+	0.705389i	$0.249228\pi$
$164$	1.79412			0.140097
$165$	−2.40336	−	2.33385i	−0.187101	−	0.181690i
$166$		−	5.57973i		−	0.433071i
$167$	−6.61861	+	6.61861i	−0.512164	+	0.512164i	−0.915189	−	0.403025i	$-0.867959\pi$
$167$	−6.61861	+	6.61861i	−0.512164	+	0.512164i	0.403025	+	0.915189i	$0.367959\pi$
$168$	3.17648	−	3.17648i	0.245070	−	0.245070i
$169$		−	1.57899i		−	0.121461i
$170$	2.69810	−	0.0395881i	0.206935	−	0.00303627i
$171$	−0.349716	−	4.34485i	−0.0267435	−	0.332259i
$172$	−0.623738	−	0.623738i	−0.0475596	−	0.0475596i
$173$	−17.7594	−	17.7594i	−1.35022	−	1.35022i	−0.885412	−	0.464807i	$-0.846124\pi$
$173$	−17.7594	−	17.7594i	−1.35022	−	1.35022i	−0.464807	−	0.885412i	$-0.653876\pi$
$174$	5.40423			0.409694
$175$	−16.3415	−	15.4096i	−1.23530	−	1.16485i
$176$	−1.49820			−0.112931
$177$	1.05454	+	1.05454i	0.0792640	+	0.0792640i
$178$	6.58252	−	6.58252i	0.493381	−	0.493381i
$179$	−9.00631			−0.673164			−0.336582	−	0.941654i	$-0.609271\pi$
$179$	−9.00631			−0.673164			−0.336582	+	0.941654i	$0.609271\pi$
$180$	2.23583	−	0.0328054i	0.166649	−	0.00244517i
$181$			18.7616i			1.39454i	0.716808	+	0.697271i	$0.245602\pi$
$181$			18.7616i			1.39454i	−0.716808	+	0.697271i	$0.754398\pi$
$182$	10.7349	+	10.7349i	0.795724	+	0.795724i
$183$	−10.7786	−	10.7786i	−0.796773	−	0.796773i
$184$	−6.61099			−0.487369
$185$	9.46959	−	9.75161i	0.696218	−	0.716953i
$186$		−	0.364245i		−	0.0267078i
$187$	1.27842	+	1.27842i	0.0934875	+	0.0934875i
$188$	−5.24209	+	5.24209i	−0.382319	+	0.382319i
$189$	−4.49222			−0.326761
$190$	−6.20728	+	7.51463i	−0.450323	+	0.545169i
$191$	−6.38310			−0.461865			−0.230932	−	0.972970i	$-0.574178\pi$
$191$	−6.38310			−0.461865			−0.230932	+	0.972970i	$0.574178\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−15.6976	−	15.6976i	−1.12994	−	1.12994i	−0.990186	−	0.139754i	$-0.955369\pi$
$193$	−15.6976	−	15.6976i	−1.12994	−	1.12994i	−0.139754	−	0.990186i	$-0.544631\pi$
$194$		−	12.4444i		−	0.893456i
$195$	0.110866	+	7.55598i	0.00793927	+	0.541095i
$196$	13.1800			0.941429
$197$	2.62159	+	2.62159i	0.186780	+	0.186780i	0.794303	−	0.607522i	$-0.207836\pi$
$197$	2.62159	+	2.62159i	0.186780	+	0.186780i	−0.607522	+	0.794303i	$0.707836\pi$
$198$	1.05939	+	1.05939i	0.0752874	+	0.0752874i
$199$			6.73685i			0.477563i	0.971073	+	0.238781i	$0.0767479\pi$
$199$			6.73685i			0.477563i	−0.971073	+	0.238781i	$0.923252\pi$
$200$	−3.63774	−	3.43028i	−0.257227	−	0.242558i
$201$	−1.39887			−0.0986684
$202$	1.54027	−	1.54027i	0.108373	−	0.108373i
$203$	17.1664	+	17.1664i	1.20485	+	1.20485i
$204$	−1.20676			−0.0844898
$205$	0.0588568	+	4.01134i	0.00411073	+	0.280164i
$206$	13.3619			0.930966
$207$	4.67468	+	4.67468i	0.324912	+	0.324912i
$208$	2.38967	+	2.38967i	0.165694	+	0.165694i
$209$	−6.50945	+	0.523945i	−0.450268	+	0.0362420i
$210$	7.20626	+	6.99785i	0.497279	+	0.482897i
$211$			15.1654i			1.04403i	0.852937	+	0.522013i	$0.174819\pi$
$211$			15.1654i			1.04403i	−0.852937	+	0.522013i	$0.825181\pi$
$212$	5.27391	−	5.27391i	0.362213	−	0.362213i
$213$	−6.35295	+	6.35295i	−0.435297	+	0.435297i
$214$		−	0.424610i		−	0.0290258i
$215$	1.37411	−	1.41503i	0.0937135	−	0.0965045i
$216$	−1.00000			−0.0680414
$217$	1.15702	−	1.15702i	0.0785434	−	0.0785434i
$218$	5.54050	−	5.54050i	0.375250	−	0.375250i
$219$	15.9201			1.07578
$220$	−0.0491491	−	3.34972i	−0.00331363	−	0.225838i
$221$		−	4.07823i		−	0.274332i
$222$	−4.29845	+	4.29845i	−0.288493	+	0.288493i
$223$	−1.90756	−	1.90756i	−0.127739	−	0.127739i	0.640347	−	0.768086i	$-0.278791\pi$
$223$	−1.90756	−	1.90756i	−0.127739	−	0.127739i	−0.768086	+	0.640347i	$0.778791\pi$
$224$	4.49222			0.300149
$225$	0.146694	+	4.99785i	0.00977963	+	0.333190i
$226$	17.4806			1.16279
$227$	19.8625	−	19.8625i	1.31832	−	1.31832i	0.403212	−	0.915106i	$-0.367894\pi$
$227$	19.8625	−	19.8625i	1.31832	−	1.31832i	0.915106	−	0.403212i	$-0.132106\pi$
$228$	2.82498	−	3.31956i	0.187089	−	0.219843i
$229$			19.0279i			1.25740i	0.777648	+	0.628700i	$0.216413\pi$
$229$			19.0279i			1.25740i	−0.777648	+	0.628700i	$0.783587\pi$
$230$	−0.216876	−	14.7810i	−0.0143004	−	0.974633i
$231$			6.73024i			0.442817i
$232$	3.82137	+	3.82137i	0.250885	+	0.250885i
$233$	−8.22028	+	8.22028i	−0.538529	+	0.538529i	−0.923097	−	0.384568i	$-0.874350\pi$
$233$	−8.22028	+	8.22028i	−0.538529	+	0.538529i	0.384568	+	0.923097i	$0.374350\pi$
$234$		−	3.37950i		−	0.220925i
$235$	−11.8924	−	11.5484i	−0.775773	−	0.753337i
$236$			1.49134i			0.0970781i
$237$	−5.62374	−	5.62374i	−0.365301	−	0.365301i
$238$	−3.83323	−	3.83323i	−0.248472	−	0.248472i
$239$			5.40164i			0.349403i	0.984621	+	0.174702i	$0.0558961\pi$
$239$			5.40164i			0.349403i	−0.984621	+	0.174702i	$0.944104\pi$
$240$	1.60417	+	1.55777i	0.103548	+	0.100554i
$241$		−	24.3252i		−	1.56692i	−0.621440	−	0.783462i	$-0.713452\pi$
$241$		−	24.3252i		−	1.56692i	0.621440	−	0.783462i	$-0.286548\pi$
$242$	−6.19100	+	6.19100i	−0.397973	+	0.397973i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		−	15.2432i		−	0.975844i
$245$	0.432375	+	29.4682i	0.0276235	+	1.88266i
$246$		−	1.79412i		−	0.114389i
$247$	11.2184	+	9.54703i	0.713812	+	0.607463i
$248$	0.257560	−	0.257560i	0.0163551	−	0.0163551i
$249$	−5.57973			−0.353601
$250$	7.55018	−	8.24589i	0.477516	−	0.521516i
$251$	−28.4372			−1.79494			−0.897470	−	0.441075i	$-0.854597\pi$
$251$	−28.4372			−1.79494			−0.897470	+	0.441075i	$0.854597\pi$
$252$	−3.17648	−	3.17648i	−0.200099	−	0.200099i
$253$	7.00360	−	7.00360i	0.440313	−	0.440313i
$254$		−	11.7643i		−	0.738160i
$255$	−0.0395881	−	2.69810i	−0.00247910	−	0.168961i
$256$	1.00000			0.0625000
$257$	−14.1711	+	14.1711i	−0.883966	+	0.883966i	−0.993935	−	0.109969i	$-0.964925\pi$
$257$	−14.1711	+	14.1711i	−0.883966	+	0.883966i	0.109969	+	0.993935i	$0.464925\pi$
$258$	−0.623738	+	0.623738i	−0.0388323	+	0.0388323i
$259$	−27.3079			−1.69683
$260$	−5.26449	+	5.42128i	−0.326490	+	0.336213i
$261$		−	5.40423i		−	0.334514i
$262$	5.71144	−	5.71144i	0.352854	−	0.352854i
$263$	−3.16396	+	3.16396i	−0.195098	+	0.195098i	−0.797895	−	0.602797i	$-0.794053\pi$
$263$	−3.16396	+	3.16396i	−0.195098	+	0.195098i	0.602797	+	0.797895i	$0.294053\pi$
$264$			1.49820i			0.0922078i
$265$	11.9646	+	11.6185i	0.734977	+	0.713721i
$266$	19.5180	−	1.57100i	1.19673	−	0.0963243i
$267$	−6.58252	−	6.58252i	−0.402844	−	0.402844i
$268$	−0.989147	−	0.989147i	−0.0604218	−	0.0604218i
$269$	5.14967			0.313981			0.156990	−	0.987600i	$-0.449821\pi$
$269$	5.14967			0.313981			0.156990	+	0.987600i	$0.449821\pi$
$270$	−0.0328054	−	2.23583i	−0.00199647	−	0.136068i
$271$	−9.33799			−0.567242			−0.283621	−	0.958936i	$-0.591536\pi$
$271$	−9.33799			−0.567242			−0.283621	+	0.958936i	$0.591536\pi$
$272$	−0.853306	−	0.853306i	−0.0517392	−	0.0517392i
$273$	10.7349	−	10.7349i	0.649706	−	0.649706i
$274$	9.89645			0.597866
$275$	7.48777	−	0.219778i	0.451530	−	0.0132531i
$276$			6.61099i			0.397935i
$277$	6.94186	+	6.94186i	0.417096	+	0.417096i	0.884202	−	0.467106i	$-0.154703\pi$
$277$	6.94186	+	6.94186i	0.417096	+	0.417096i	−0.467106	+	0.884202i	$0.654703\pi$
$278$	7.69802	+	7.69802i	0.461696	+	0.461696i
$279$	−0.364245			−0.0218068
$280$	0.147369	+	10.0438i	0.00880698	+	0.600233i
$281$		−	13.9366i		−	0.831390i	−0.909504	−	0.415695i	$-0.863538\pi$
$281$		−	13.9366i		−	0.831390i	0.909504	−	0.415695i	$-0.136462\pi$
$282$	5.24209	+	5.24209i	0.312162	+	0.312162i
$283$	−13.0086	+	13.0086i	−0.773280	+	0.773280i	−0.978678	−	0.205399i	$-0.934151\pi$
$283$	−13.0086	+	13.0086i	−0.773280	+	0.773280i	0.205399	+	0.978678i	$0.434151\pi$
$284$	−8.98443			−0.533128
$285$	7.51463	+	6.20728i	0.445128	+	0.367687i
$286$	−5.06316			−0.299391
$287$	5.69897	−	5.69897i	0.336400	−	0.336400i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	15.5437i		−	0.914338i
$290$	−8.41856	+	8.66929i	−0.494355	+	0.509078i
$291$	−12.4444			−0.729504
$292$	11.2572	+	11.2572i	0.658778	+	0.658778i
$293$	−11.5186	−	11.5186i	−0.672924	−	0.672924i	0.285465	−	0.958389i	$-0.407852\pi$
$293$	−11.5186	−	11.5186i	−0.672924	−	0.672924i	−0.958389	+	0.285465i	$0.907852\pi$
$294$		−	13.1800i		−	0.768674i
$295$	−3.33438	+	0.0489241i	−0.194135	+	0.00284847i
$296$	−6.07893			−0.353331
$297$	1.05939	−	1.05939i	0.0614719	−	0.0614719i
$298$	−8.95370	−	8.95370i	−0.518674	−	0.518674i
$299$	−22.3418			−1.29206
$300$	−3.43028	+	3.63774i	−0.198047	+	0.210025i
$301$	−3.96258			−0.228399
$302$	10.9092	+	10.9092i	0.627755	+	0.627755i
$303$	−1.54027	−	1.54027i	−0.0884860	−	0.0884860i
$304$	4.34485	−	0.349716i	0.249194	−	0.0200576i
$305$	34.0811	−	0.500058i	1.95148	−	0.0286333i
$306$			1.20676i			0.0689857i
$307$	−19.8832	+	19.8832i	−1.13480	+	1.13480i	−0.145427	+	0.989369i	$0.546455\pi$
$307$	−19.8832	+	19.8832i	−1.13480	+	1.13480i	−0.989369	+	0.145427i	$0.953545\pi$
$308$	−4.75900	+	4.75900i	−0.271169	+	0.271169i
$309$		−	13.3619i		−	0.760130i
$310$	0.584310	+	0.567411i	0.0331866	+	0.0322268i
$311$	25.6191			1.45272			0.726362	−	0.687312i	$-0.241210\pi$
$311$	25.6191			1.45272			0.726362	+	0.687312i	$0.241210\pi$
$312$	2.38967	−	2.38967i	0.135288	−	0.135288i
$313$	−1.42367	+	1.42367i	−0.0804705	+	0.0804705i	−0.746196	−	0.665726i	$-0.768122\pi$
$313$	−1.42367	+	1.42367i	−0.0804705	+	0.0804705i	0.665726	+	0.746196i	$0.268122\pi$
$314$	−18.8017			−1.06104
$315$	6.99785	−	7.20626i	0.394284	−	0.406027i
$316$		−	7.95317i		−	0.447401i
$317$	−22.0096	+	22.0096i	−1.23618	+	1.23618i	−0.274630	+	0.961550i	$0.588555\pi$
$317$	−22.0096	+	22.0096i	−1.23618	+	1.23618i	−0.961550	+	0.274630i	$0.911445\pi$
$318$	−5.27391	−	5.27391i	−0.295746	−	0.295746i
$319$	−8.09662			−0.453324
$320$	0.0328054	+	2.23583i	0.00183388	+	0.124987i
$321$	−0.424610			−0.0236994
$322$	−20.9997	+	20.9997i	−1.17027	+	1.17027i
$323$	−4.00590	−	3.40907i	−0.222894	−	0.189686i
$324$			1.00000i			0.0555556i
$325$	−12.2937	−	11.5926i	−0.681934	−	0.643044i
$326$		−	0.0619528i		−	0.00343125i
$327$	−5.54050	−	5.54050i	−0.306390	−	0.306390i
$328$	1.26863	−	1.26863i	0.0700485	−	0.0700485i
$329$			33.3027i			1.83604i
$330$	−3.34972	+	0.0491491i	−0.184396	+	0.00270557i
$331$		−	19.0483i		−	1.04699i	−0.852028	−	0.523496i	$-0.824628\pi$
$331$		−	19.0483i		−	1.04699i	0.852028	−	0.523496i	$-0.175372\pi$
$332$	−3.94546	−	3.94546i	−0.216535	−	0.216535i
$333$	4.29845	+	4.29845i	0.235554	+	0.235554i
$334$			9.36013i			0.512164i
$335$	2.17911	−	2.24401i	0.119058	−	0.122603i
$336$		−	4.49222i		−	0.245070i
$337$	10.2649	−	10.2649i	0.559164	−	0.559164i	−0.369905	−	0.929069i	$-0.620610\pi$
$337$	10.2649	−	10.2649i	0.559164	−	0.559164i	0.929069	+	0.369905i	$0.120610\pi$
$338$	−1.11651	−	1.11651i	−0.0607304	−	0.0607304i
$339$		−	17.4806i		−	0.949414i
$340$	1.87985	−	1.93584i	0.101949	−	0.104985i
$341$			0.545712i			0.0295520i
$342$	−3.31956	−	2.82498i	−0.179501	−	0.152758i
$343$	19.6306	−	19.6306i	1.05996	−	1.05996i
$344$	−0.882099			−0.0475596
$345$	−14.7810	+	0.216876i	−0.795784	+	0.0116762i
$346$	−25.1155			−1.35022
$347$	−21.2020	−	21.2020i	−1.13818	−	1.13818i	−0.988776	−	0.149404i	$-0.952264\pi$
$347$	−21.2020	−	21.2020i	−1.13818	−	1.13818i	−0.149404	−	0.988776i	$-0.547736\pi$
$348$	3.82137	−	3.82137i	0.204847	−	0.204847i
$349$			19.7333i			1.05630i	0.849152	+	0.528148i	$0.177114\pi$
$349$			19.7333i			1.05630i	−0.849152	+	0.528148i	$0.822886\pi$
$350$	−22.4514	+	0.658983i	−1.20008	+	0.0352241i
$351$	−3.37950			−0.180384
$352$	−1.05939	+	1.05939i	−0.0564655	+	0.0564655i
$353$	18.4563	−	18.4563i	0.982329	−	0.982329i	−0.0175180	−	0.999847i	$-0.505576\pi$
$353$	18.4563	−	18.4563i	0.982329	−	0.982329i	0.999847	+	0.0175180i	$0.00557644\pi$
$354$	1.49134			0.0792640
$355$	−0.294738	−	20.0876i	−0.0156431	−	1.06614i
$356$		−	9.30909i		−	0.493381i
$357$	−3.83323	+	3.83323i	−0.202876	+	0.202876i
$358$	−6.36843	+	6.36843i	−0.336582	+	0.336582i
$359$			1.52209i			0.0803327i	0.999193	+	0.0401663i	$0.0127888\pi$
$359$			1.52209i			0.0803327i	−0.999193	+	0.0401663i	$0.987211\pi$
$360$	1.55777	−	1.60417i	0.0821018	−	0.0845469i
$361$	18.7554	−	3.03893i	0.987126	−	0.159944i
$362$	13.2665	+	13.2665i	0.697271	+	0.697271i
$363$	6.19100	+	6.19100i	0.324943	+	0.324943i
$364$	15.1814			0.795724
$365$	−24.7999	+	25.5384i	−1.29808	+	1.33674i
$366$	−15.2432			−0.796773
$367$	−15.6342	−	15.6342i	−0.816099	−	0.816099i	0.169442	−	0.985540i	$-0.445804\pi$
$367$	−15.6342	−	15.6342i	−0.816099	−	0.816099i	−0.985540	+	0.169442i	$0.945804\pi$
$368$	−4.67468	+	4.67468i	−0.243684	+	0.243684i
$369$	−1.79412			−0.0933980
$370$	−0.199422	−	13.5914i	−0.0103674	−	0.706585i
$371$		−	33.5049i		−	1.73949i
$372$	−0.257560	−	0.257560i	−0.0133539	−	0.0133539i
$373$	10.2074	+	10.2074i	0.528520	+	0.528520i	0.920131	−	0.391611i	$-0.128082\pi$
$373$	10.2074	+	10.2074i	0.528520	+	0.528520i	−0.391611	+	0.920131i	$0.628082\pi$
$374$	1.80796			0.0934875
$375$	−8.24589	−	7.55018i	−0.425816	−	0.389890i
$376$			7.41343i			0.382319i
$377$	12.9143	+	12.9143i	0.665121	+	0.665121i
$378$	−3.17648	+	3.17648i	−0.163380	+	0.163380i
$379$	17.3997			0.893762			0.446881	−	0.894593i	$-0.352535\pi$
$379$	17.3997			0.893762			0.446881	+	0.894593i	$0.352535\pi$
$380$	0.924440	+	9.70286i	0.0474228	+	0.497746i
$381$	−11.7643			−0.602705
$382$	−4.51353	+	4.51353i	−0.230932	+	0.230932i
$383$	14.2959	+	14.2959i	0.730485	+	0.730485i	0.970716	−	0.240231i	$-0.0772230\pi$
$383$	14.2959	+	14.2959i	0.730485	+	0.730485i	−0.240231	+	0.970716i	$0.577223\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−10.7964	−	10.4842i	−0.550236	−	0.534323i
$386$	−22.1998			−1.12994
$387$	0.623738	+	0.623738i	0.0317064	+	0.0317064i
$388$	−8.79952	−	8.79952i	−0.446728	−	0.446728i
$389$		−	11.0275i		−	0.559116i	−0.960129	−	0.279558i	$-0.909812\pi$
$389$		−	11.0275i		−	0.559116i	0.960129	−	0.279558i	$-0.0901879\pi$
$390$	5.42128	+	5.26449i	0.274517	+	0.266578i
$391$	7.97786			0.403457
$392$	9.31967	−	9.31967i	0.470715	−	0.470715i
$393$	−5.71144	−	5.71144i	−0.288104	−	0.288104i
$394$	3.70748			0.186780
$395$	17.7819	−	0.260907i	0.894705	−	0.0131276i
$396$	1.49820			0.0752874
$397$	−1.09266	−	1.09266i	−0.0548392	−	0.0548392i	0.679155	−	0.733995i	$-0.262346\pi$
$397$	−1.09266	−	1.09266i	−0.0548392	−	0.0548392i	−0.733995	+	0.679155i	$0.762346\pi$
$398$	4.76367	+	4.76367i	0.238781	+	0.238781i
$399$	−1.57100	−	19.5180i	−0.0786484	−	0.977122i
$400$	−4.99785	+	0.146694i	−0.249892	+	0.00733472i
$401$			13.6821i			0.683249i	0.939836	+	0.341625i	$0.110977\pi$
$401$			13.6821i			0.683249i	−0.939836	+	0.341625i	$0.889023\pi$
$402$	−0.989147	+	0.989147i	−0.0493342	+	0.0493342i
$403$	0.870424	−	0.870424i	0.0433589	−	0.0433589i
$404$		−	2.17827i		−	0.108373i
$405$	−2.23583	+	0.0328054i	−0.111099	+	0.00163011i
$406$	24.2770			1.20485
$407$	6.43994	−	6.43994i	0.319216	−	0.319216i
$408$	−0.853306	+	0.853306i	−0.0422449	+	0.0422449i
$409$	13.9275			0.688673			0.344336	−	0.938846i	$-0.388104\pi$
$409$	13.9275			0.688673			0.344336	+	0.938846i	$0.388104\pi$
$410$	2.87806	+	2.79483i	0.142137	+	0.138027i
$411$		−	9.89645i		−	0.488156i
$412$	9.44827	−	9.44827i	0.465483	−	0.465483i
$413$	4.73721	+	4.73721i	0.233103	+	0.233103i
$414$	6.61099			0.324912
$415$	8.69194	−	8.95080i	0.426670	−	0.439378i
$416$	3.37950			0.165694
$417$	7.69802	−	7.69802i	0.376974	−	0.376974i
$418$	−4.23239	+	4.97336i	−0.207013	+	0.243255i
$419$			31.7859i			1.55284i	0.630215	+	0.776421i	$0.282967\pi$
$419$			31.7859i			1.55284i	−0.630215	+	0.776421i	$0.717033\pi$
$420$	10.0438	−	0.147369i	0.490088	−	0.00719087i
$421$		−	29.9617i		−	1.46025i	−0.683316	−	0.730123i	$-0.739463\pi$
$421$		−	29.9617i		−	1.46025i	0.683316	−	0.730123i	$-0.260537\pi$
$422$	10.7235	+	10.7235i	0.522013	+	0.522013i
$423$	5.24209	−	5.24209i	0.254879	−	0.254879i
$424$		−	7.45843i		−	0.362213i
$425$	4.38987	+	4.13952i	0.212940	+	0.200796i
$426$			8.98443i			0.435297i
$427$	−48.4196	−	48.4196i	−2.34319	−	2.34319i
$428$	−0.300245	−	0.300245i	−0.0145129	−	0.0145129i
$429$			5.06316i			0.244452i
$430$	−0.0289376	−	1.97222i	−0.00139550	−	0.0951090i
$431$			19.4154i			0.935207i	0.883938	+	0.467603i	$0.154882\pi$
$431$			19.4154i			0.935207i	−0.883938	+	0.467603i	$0.845118\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	5.53848	+	5.53848i	0.266162	+	0.266162i	0.827552	−	0.561390i	$-0.189733\pi$
$433$	5.53848	+	5.53848i	0.266162	+	0.266162i	−0.561390	+	0.827552i	$0.689733\pi$
$434$		−	1.63627i		−	0.0785434i
$435$	8.66929	+	8.41856i	0.415661	+	0.403639i
$436$		−	7.83545i		−	0.375250i
$437$	−18.6759	+	21.9456i	−0.893392	+	1.04980i
$438$	11.2572	−	11.2572i	0.537890	−	0.537890i
$439$	19.2533			0.918908			0.459454	−	0.888202i	$-0.348045\pi$
$439$	19.2533			0.918908			0.459454	+	0.888202i	$0.348045\pi$
$440$	−2.40336	−	2.33385i	−0.114576	−	0.111262i
$441$	−13.1800			−0.627619
$442$	−2.88374	−	2.88374i	−0.137166	−	0.137166i
$443$	−0.822360	+	0.822360i	−0.0390715	+	0.0390715i	−0.726373	−	0.687301i	$-0.758795\pi$
$443$	−0.822360	+	0.822360i	−0.0390715	+	0.0390715i	0.687301	+	0.726373i	$0.258795\pi$
$444$			6.07893i			0.288493i
$445$	20.8135	−	0.305388i	0.986655	−	0.0144768i
$446$	−2.69769			−0.127739
$447$	−8.95370	+	8.95370i	−0.423495	+	0.423495i
$448$	3.17648	−	3.17648i	0.150074	−	0.150074i
$449$	34.0243			1.60570			0.802852	−	0.596178i	$-0.203315\pi$
$449$	34.0243			1.60570			0.802852	+	0.596178i	$0.203315\pi$
$450$	3.63774	+	3.43028i	0.171485	+	0.161705i
$451$			2.68795i			0.126570i
$452$	12.3606	−	12.3606i	0.581395	−	0.581395i
$453$	10.9092	−	10.9092i	0.512560	−	0.512560i
$454$		−	28.0898i		−	1.31832i
$455$	0.498033	+	33.9431i	0.0233482	+	1.59128i
$456$	−0.349716	−	4.34485i	−0.0163770	−	0.203466i
$457$	26.2360	+	26.2360i	1.22727	+	1.22727i	0.964994	+	0.262273i	$0.0844722\pi$
$457$	26.2360	+	26.2360i	1.22727	+	1.22727i	0.262273	+	0.964994i	$0.415528\pi$
$458$	13.4548	+	13.4548i	0.628700	+	0.628700i
$459$	1.20676			0.0563266
$460$	−10.6051	−	10.2984i	−0.494466	−	0.480166i
$461$	−26.7535			−1.24604			−0.623018	−	0.782207i	$-0.714094\pi$
$461$	−26.7535			−1.24604			−0.623018	+	0.782207i	$0.714094\pi$
$462$	4.75900	+	4.75900i	0.221409	+	0.221409i
$463$	−16.5215	+	16.5215i	−0.767820	+	0.767820i	−0.977722	−	0.209902i	$-0.932685\pi$
$463$	−16.5215	+	16.5215i	−0.767820	+	0.767820i	0.209902	+	0.977722i	$0.432685\pi$
$464$	5.40423			0.250885
$465$	0.567411	−	0.584310i	0.0263130	−	0.0270967i
$466$			11.6252i			0.538529i
$467$	6.89955	+	6.89955i	0.319273	+	0.319273i	0.848488	−	0.529215i	$-0.177513\pi$
$467$	6.89955	+	6.89955i	0.319273	+	0.319273i	−0.529215	+	0.848488i	$0.677513\pi$
$468$	−2.38967	−	2.38967i	−0.110462	−	0.110462i
$469$	−6.28401			−0.290168
$470$	−16.5752	+	0.243201i	−0.764555	+	0.0112180i
$471$			18.8017i			0.866337i
$472$	1.05454	+	1.05454i	0.0485391	+	0.0485391i
$473$	0.934485	−	0.934485i	0.0429677	−	0.0429677i
$474$	−7.95317			−0.365301
$475$	−21.6636	+	2.38519i	−0.993993	+	0.109440i
$476$	−5.42101			−0.248472
$477$	−5.27391	+	5.27391i	−0.241476	+	0.241476i
$478$	3.81954	+	3.81954i	0.174702	+	0.174702i
$479$		−	10.1104i		−	0.461958i	−0.972959	−	0.230979i	$-0.925807\pi$
$479$		−	10.1104i		−	0.461958i	0.972959	−	0.230979i	$-0.0741929\pi$
$480$	2.23583	−	0.0328054i	0.102051	−	0.00149735i
$481$	−20.5437			−0.936714
$482$	−17.2005	−	17.2005i	−0.783462	−	0.783462i
$483$	20.9997	+	20.9997i	0.955518	+	0.955518i
$484$			8.75540i			0.397973i
$485$	19.3855	−	19.9629i	0.880252	−	0.906468i
$486$	1.00000			0.0453609
$487$	19.5066	−	19.5066i	0.883928	−	0.883928i	−0.110003	−	0.993931i	$-0.535086\pi$
$487$	19.5066	−	19.5066i	0.883928	−	0.883928i	0.993931	+	0.110003i	$0.0350860\pi$
$488$	−10.7786	−	10.7786i	−0.487922	−	0.487922i
$489$	−0.0619528			−0.00280160
$490$	21.1429	+	20.5314i	0.955140	+	0.927516i
$491$	−14.0700			−0.634970			−0.317485	−	0.948263i	$-0.602838\pi$
$491$	−14.0700			−0.634970			−0.317485	+	0.948263i	$0.602838\pi$
$492$	−1.26863	−	1.26863i	−0.0571944	−	0.0571944i
$493$	−4.61146	−	4.61146i	−0.207690	−	0.207690i
$494$	14.6834	−	1.18187i	0.660638	−	0.0531747i
$495$	0.0491491	+	3.34972i	0.00220909	+	0.150559i
$496$		−	0.364245i		−	0.0163551i
$497$	−28.5388	+	28.5388i	−1.28014	+	1.28014i
$498$	−3.94546	+	3.94546i	−0.176800	+	0.176800i
$499$		−	4.43607i		−	0.198586i	−0.995058	−	0.0992929i	$-0.968342\pi$
$499$		−	4.43607i		−	0.198586i	0.995058	−	0.0992929i	$-0.0316581\pi$
$500$	−0.491940	−	11.1695i	−0.0220002	−	0.499516i
$501$	9.36013			0.418180
$502$	−20.1081	+	20.1081i	−0.897470	+	0.897470i
$503$	−3.35985	+	3.35985i	−0.149808	+	0.149808i	−0.778032	−	0.628224i	$-0.783782\pi$
$503$	−3.35985	+	3.35985i	−0.149808	+	0.149808i	0.628224	+	0.778032i	$0.283782\pi$
$504$	−4.49222			−0.200099
$505$	4.87023	−	0.0714589i	0.216722	−	0.00317988i
$506$		−	9.90459i		−	0.440313i
$507$	−1.11651	+	1.11651i	−0.0495861	+	0.0495861i
$508$	−8.31864	−	8.31864i	−0.369080	−	0.369080i
$509$	−37.6552			−1.66904			−0.834519	−	0.550979i	$-0.814254\pi$
$509$	−37.6552			−1.66904			−0.834519	+	0.550979i	$0.814254\pi$
$510$	−1.93584	−	1.87985i	−0.0857203	−	0.0832412i
$511$	71.5164			3.16370
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.82498	+	3.31956i	−0.124726	+	0.146562i
$514$			20.0409i			0.883966i
$515$	21.4347	+	20.8147i	0.944524	+	0.917207i
$516$			0.882099i			0.0388323i
$517$	−7.85370	−	7.85370i	−0.345405	−	0.345405i
$518$	−19.3096	+	19.3096i	−0.848414	+	0.848414i
$519$			25.1155i			1.10245i
$520$	0.110866	+	7.55598i	0.00486179	+	0.331351i
$521$		−	27.2139i		−	1.19226i	−0.802887	−	0.596131i	$-0.796704\pi$
$521$		−	27.2139i		−	1.19226i	0.802887	−	0.596131i	$-0.203296\pi$
$522$	−3.82137	−	3.82137i	−0.167257	−	0.167257i
$523$	11.9984	+	11.9984i	0.524655	+	0.524655i	0.918974	−	0.394319i	$-0.129019\pi$
$523$	11.9984	+	11.9984i	0.524655	+	0.524655i	−0.394319	+	0.918974i	$0.629019\pi$
$524$		−	8.07719i		−	0.352854i
$525$	0.658983	+	22.4514i	0.0287604	+	0.979860i
$526$			4.47451i			0.195098i
$527$	−0.310812	+	0.310812i	−0.0135392	+	0.0135392i
$528$	1.05939	+	1.05939i	0.0461039	+	0.0461039i
$529$		−	20.7052i		−	0.900226i
$530$	16.6758	−	0.244677i	0.724349	−	0.0106281i
$531$		−	1.49134i		−	0.0647187i
$532$	12.6904	−	14.9122i	0.550200	−	0.646525i
$533$	4.28734	−	4.28734i	0.185705	−	0.185705i
$534$	−9.30909			−0.402844
$535$	0.661446	−	0.681146i	0.0285968	−	0.0294485i
$536$	−1.39887			−0.0604218
$537$	6.36843	+	6.36843i	0.274818	+	0.274818i
$538$	3.64136	−	3.64136i	0.156990	−	0.156990i
$539$			19.7463i			0.850533i
$540$	−1.60417	−	1.55777i	−0.0690323	−	0.0670358i
$541$	−2.33439			−0.100363			−0.0501816	−	0.998740i	$-0.515980\pi$
$541$	−2.33439			−0.100363			−0.0501816	+	0.998740i	$0.515980\pi$
$542$	−6.60295	+	6.60295i	−0.283621	+	0.283621i
$543$	13.2665	−	13.2665i	0.569319	−	0.569319i
$544$	−1.20676			−0.0517392
$545$	17.5187	−	0.257045i	0.750420	−	0.0110106i
$546$		−	15.1814i		−	0.649706i
$547$	−8.46036	+	8.46036i	−0.361739	+	0.361739i	−0.864453	−	0.502714i	$-0.832335\pi$
$547$	−8.46036	+	8.46036i	−0.361739	+	0.361739i	0.502714	+	0.864453i	$0.332335\pi$
$548$	6.99785	−	6.99785i	0.298933	−	0.298933i
$549$			15.2432i			0.650563i
$550$	5.13925	−	5.45006i	0.219138	−	0.232391i
$551$	23.4806	−	1.88995i	1.00031	−	0.0805145i
$552$	4.67468	+	4.67468i	0.198967	+	0.198967i
$553$	−25.2630	−	25.2630i	−1.07429	−	1.07429i
$554$	9.81727			0.417096
$555$	−13.5914	+	0.199422i	−0.576925	+	0.00846498i
$556$	10.8866			0.461696
$557$	14.2030	+	14.2030i	0.601801	+	0.601801i	0.940790	−	0.338989i	$-0.110085\pi$
$557$	14.2030	+	14.2030i	0.601801	+	0.601801i	−0.338989	+	0.940790i	$0.610085\pi$
$558$	−0.257560	+	0.257560i	−0.0109034	+	0.0109034i
$559$	−2.98105			−0.126085
$560$	7.20626	+	6.99785i	0.304520	+	0.295713i
$561$		−	1.80796i		−	0.0763322i
$562$	−9.85468	−	9.85468i	−0.415695	−	0.415695i
$563$	−30.8429	−	30.8429i	−1.29987	−	1.29987i	−0.928472	−	0.371401i	$-0.878877\pi$
$563$	−30.8429	−	30.8429i	−1.29987	−	1.29987i	−0.371401	−	0.928472i	$-0.621123\pi$
$564$	7.41343			0.312162
$565$	28.0417	+	27.2307i	1.17972	+	1.14561i
$566$			18.3969i			0.773280i
$567$	3.17648	+	3.17648i	0.133399	+	0.133399i
$568$	−6.35295	+	6.35295i	−0.266564	+	0.266564i
$569$	13.5457			0.567864			0.283932	−	0.958844i	$-0.408361\pi$
$569$	13.5457			0.567864			0.283932	+	0.958844i	$0.408361\pi$
$570$	9.70286	−	0.924440i	0.406408	−	0.0387205i
$571$	10.5825			0.442863			0.221431	−	0.975176i	$-0.428927\pi$
$571$	10.5825			0.442863			0.221431	+	0.975176i	$0.428927\pi$
$572$	−3.58020	+	3.58020i	−0.149696	+	0.149696i
$573$	4.51353	+	4.51353i	0.188556	+	0.188556i
$574$		−	8.05956i		−	0.336400i
$575$	22.6776	−	24.0491i	0.945720	−	1.00292i
$576$	−1.00000			−0.0416667
$577$	−4.85640	−	4.85640i	−0.202175	−	0.202175i	0.598757	−	0.800931i	$-0.295662\pi$
$577$	−4.85640	−	4.85640i	−0.202175	−	0.202175i	−0.800931	+	0.598757i	$0.795662\pi$
$578$	−10.9911	−	10.9911i	−0.457169	−	0.457169i
$579$			22.1998i			0.922592i
$580$	0.177288	+	12.0829i	0.00736149	+	0.501717i
$581$	−25.0653			−1.03989
$582$	−8.79952	+	8.79952i	−0.364752	+	0.364752i
$583$	7.90137	+	7.90137i	0.327241	+	0.327241i
$584$	15.9201			0.658778
$585$	5.26449	−	5.42128i	0.217660	−	0.224142i
$586$	−16.2898			−0.672924
$587$	7.59468	+	7.59468i	0.313466	+	0.313466i	0.846251	−	0.532785i	$-0.178854\pi$
$587$	7.59468	+	7.59468i	0.313466	+	0.313466i	−0.532785	+	0.846251i	$0.678854\pi$
$588$	−9.31967	−	9.31967i	−0.384337	−	0.384337i
$589$	−0.127383	−	1.58259i	−0.00524870	−	0.0652095i
$590$	−2.32317	+	2.39236i	−0.0956434	+	0.0984919i
$591$		−	3.70748i		−	0.152505i
$592$	−4.29845	+	4.29845i	−0.176665	+	0.176665i
$593$	16.8852	−	16.8852i	0.693392	−	0.693392i	−0.269585	−	0.962977i	$-0.586886\pi$
$593$	16.8852	−	16.8852i	0.693392	−	0.693392i	0.962977	+	0.269585i	$0.0868865\pi$
$594$		−	1.49820i		−	0.0614719i
$595$	−0.177838	−	12.1204i	−0.00729066	−	0.496890i
$596$	−12.6624			−0.518674
$597$	4.76367	−	4.76367i	0.194964	−	0.194964i
$598$	−15.7981	+	15.7981i	−0.646031	+	0.646031i
$599$	40.3029			1.64673			0.823365	−	0.567512i	$-0.192094\pi$
$599$	40.3029			1.64673			0.823365	+	0.567512i	$0.192094\pi$
$600$	0.146694	+	4.99785i	0.00598878	+	0.204036i
$601$			37.1125i			1.51385i	0.653503	+	0.756924i	$0.273299\pi$
$601$			37.1125i			1.51385i	−0.653503	+	0.756924i	$0.726701\pi$
$602$	−2.80197	+	2.80197i	−0.114200	+	0.114200i
$603$	0.989147	+	0.989147i	0.0402812	+	0.0402812i
$604$	15.4280			0.627755
$605$	−19.5756	+	0.287224i	−0.795860	+	0.0116773i
$606$	−2.17827			−0.0884860
$607$	−21.9049	+	21.9049i	−0.889091	+	0.889091i	−0.994436	−	0.105345i	$-0.966405\pi$
$607$	−21.9049	+	21.9049i	−0.889091	+	0.889091i	0.105345	+	0.994436i	$0.466405\pi$
$608$	2.82498	−	3.31956i	0.114568	−	0.134626i
$609$		−	24.2770i		−	0.983753i
$610$	23.7454	−	24.4526i	0.961422	−	0.990056i
$611$			25.0537i			1.01356i
$612$	0.853306	+	0.853306i	0.0344928	+	0.0344928i
$613$	3.66633	−	3.66633i	0.148082	−	0.148082i	−0.629179	−	0.777261i	$-0.716609\pi$
$613$	3.66633	−	3.66633i	0.148082	−	0.148082i	0.777261	+	0.629179i	$0.216609\pi$
$614$			28.1191i			1.13480i
$615$	2.79483	−	2.87806i	0.112698	−	0.116055i
$616$			6.73024i			0.271169i
$617$	−21.5484	−	21.5484i	−0.867507	−	0.867507i	0.124689	−	0.992196i	$-0.460207\pi$
$617$	−21.5484	−	21.5484i	−0.867507	−	0.867507i	−0.992196	+	0.124689i	$0.960207\pi$
$618$	−9.44827	−	9.44827i	−0.380065	−	0.380065i
$619$			23.0888i			0.928017i	0.885831	+	0.464008i	$0.153589\pi$
$619$			23.0888i			0.928017i	−0.885831	+	0.464008i	$0.846411\pi$
$620$	0.814389	−	0.0119492i	0.0327067	−	0.000479892i
$621$		−	6.61099i		−	0.265290i
$622$	18.1154	−	18.1154i	0.726362	−	0.726362i
$623$	−29.5701	−	29.5701i	−1.18470	−	1.18470i
$624$		−	3.37950i		−	0.135288i
$625$	24.9570	−	1.46631i	0.998278	−	0.0586525i
$626$			2.01337i			0.0804705i
$627$	4.97336	+	4.23239i	0.198617	+	0.169025i
$628$	−13.2948	+	13.2948i	−0.530521	+	0.530521i
$629$	7.33579			0.292497
$630$	−0.147369	−	10.0438i	−0.00587132	−	0.400155i
$631$	37.3658			1.48751			0.743754	−	0.668453i	$-0.233043\pi$
$631$	37.3658			1.48751			0.743754	+	0.668453i	$0.233043\pi$
$632$	−5.62374	−	5.62374i	−0.223700	−	0.223700i
$633$	10.7235	−	10.7235i	0.426222	−	0.426222i
$634$			31.1262i			1.23618i
$635$	18.3262	−	18.8719i	0.727251	−	0.748910i
$636$	−7.45843			−0.295746
$637$	31.4958	−	31.4958i	1.24791	−	1.24791i
$638$	−5.72518	+	5.72518i	−0.226662	+	0.226662i
$639$	8.98443			0.355419
$640$	1.60417	+	1.55777i	0.0634102	+	0.0615763i
$641$			35.6140i			1.40667i	0.710859	+	0.703335i	$0.248307\pi$
$641$			35.6140i			1.40667i	−0.710859	+	0.703335i	$0.751693\pi$
$642$	−0.300245	+	0.300245i	−0.0118497	+	0.0118497i
$643$	−35.3543	+	35.3543i	−1.39424	+	1.39424i	−0.578694	+	0.815545i	$0.696437\pi$
$643$	−35.3543	+	35.3543i	−1.39424	+	1.39424i	−0.815545	+	0.578694i	$0.803563\pi$
$644$			29.6980i			1.17027i
$645$	−1.97222	+	0.0289376i	−0.0776561	+	0.00113942i
$646$	−5.24317	+	0.422022i	−0.206290	+	0.0166042i
$647$	20.9716	+	20.9716i	0.824480	+	0.824480i	0.986747	−	0.162267i	$-0.0518804\pi$
$647$	20.9716	+	20.9716i	0.824480	+	0.824480i	−0.162267	+	0.986747i	$0.551880\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−2.23433			−0.0877051
$650$	−16.8902	+	0.495754i	−0.662489	+	0.0194451i
$651$	−1.63627			−0.0641304
$652$	−0.0438073	−	0.0438073i	−0.00171563	−	0.00171563i
$653$	31.2511	−	31.2511i	1.22295	−	1.22295i	0.256372	−	0.966578i	$-0.417473\pi$
$653$	31.2511	−	31.2511i	1.22295	−	1.22295i	0.966578	−	0.256372i	$-0.0825272\pi$
$654$	−7.83545			−0.306390
$655$	18.0592	−	0.264975i	0.705631	−	0.0103534i
$656$		−	1.79412i		−	0.0700485i
$657$	−11.2572	−	11.2572i	−0.439185	−	0.439185i
$658$	23.5486	+	23.5486i	0.918020	+	0.918020i
$659$	32.1135			1.25097			0.625483	−	0.780238i	$-0.284902\pi$
$659$	32.1135			1.25097			0.625483	+	0.780238i	$0.284902\pi$
$660$	−2.33385	+	2.40336i	−0.0908451	+	0.0935507i
$661$		−	1.31818i		−	0.0512712i	−0.999671	−	0.0256356i	$-0.991839\pi$
$661$		−	1.31818i		−	0.0512712i	0.999671	−	0.0256356i	$-0.00816097\pi$
$662$	−13.4692	−	13.4692i	−0.523496	−	0.523496i
$663$	−2.88374	+	2.88374i	−0.111995	+	0.111995i
$664$	−5.57973			−0.216535
$665$	33.7574	+	27.8844i	1.30905	+	1.08131i
$666$	6.07893			0.235554
$667$	−25.2630	+	25.2630i	−0.978189	+	0.978189i
$668$	6.61861	+	6.61861i	0.256082	+	0.256082i
$669$			2.69769i			0.104299i
$670$	−0.0458903	−	3.12762i	−0.00177290	−	0.120831i
$671$	22.8373			0.881625
$672$	−3.17648	−	3.17648i	−0.122535	−	0.122535i
$673$	2.51419	+	2.51419i	0.0969147	+	0.0969147i	0.753902	−	0.656987i	$-0.228169\pi$
$673$	2.51419	+	2.51419i	0.0969147	+	0.0969147i	−0.656987	+	0.753902i	$0.728169\pi$
$674$		−	14.5167i		−	0.559164i
$675$	3.43028	−	3.63774i	0.132032	−	0.140017i
$676$	−1.57899			−0.0607304
$677$	−18.7510	+	18.7510i	−0.720658	+	0.720658i	−0.968739	−	0.248081i	$-0.920200\pi$
$677$	−18.7510	+	18.7510i	−0.720658	+	0.720658i	0.248081	+	0.968739i	$0.420200\pi$
$678$	−12.3606	−	12.3606i	−0.474707	−	0.474707i
$679$	−55.9030			−2.14536
$680$	−0.0395881	−	2.69810i	−0.00151814	−	0.103467i
$681$	−28.0898			−1.07640
$682$	0.385877	+	0.385877i	0.0147760	+	0.0147760i
$683$	−17.3262	−	17.3262i	−0.662968	−	0.662968i	0.293110	−	0.956079i	$-0.405310\pi$
$683$	−17.3262	−	17.3262i	−0.662968	−	0.662968i	−0.956079	+	0.293110i	$0.905310\pi$
$684$	−4.34485	+	0.349716i	−0.166129	+	0.0133717i
$685$	15.8755	+	15.4164i	0.606573	+	0.589031i
$686$		−	27.7619i		−	1.05996i
$687$	13.4548	−	13.4548i	0.513331	−	0.513331i
$688$	−0.623738	+	0.623738i	−0.0237798	+	0.0237798i
$689$		−	25.2058i		−	0.960263i
$690$	−10.2984	+	10.6051i	−0.392054	+	0.403730i
$691$	−10.3859			−0.395097			−0.197549	−	0.980293i	$-0.563298\pi$
$691$	−10.3859			−0.395097			−0.197549	+	0.980293i	$0.563298\pi$
$692$	−17.7594	+	17.7594i	−0.675110	+	0.675110i
$693$	4.75900	−	4.75900i	0.180779	−	0.180779i
$694$	−29.9841			−1.13818
$695$	0.357141	+	24.3406i	0.0135471	+	0.923293i
$696$		−	5.40423i		−	0.204847i
$697$	−1.53093	+	1.53093i	−0.0579881	+	0.0579881i
$698$	13.9535	+	13.9535i	0.528148	+	0.528148i
$699$	11.6252			0.439707
$700$	−15.4096	+	16.3415i	−0.582427	+	0.617651i
$701$	31.8741			1.20387			0.601934	−	0.798546i	$-0.294397\pi$
$701$	31.8741			1.20387			0.601934	+	0.798546i	$0.294397\pi$
$702$	−2.38967	+	2.38967i	−0.0901921	+	0.0901921i
$703$	−17.1729	+	20.1794i	−0.647688	+	0.761079i
$704$			1.49820i			0.0564655i
$705$	0.243201	+	16.5752i	0.00915946	+	0.624256i
$706$		−	26.1011i		−	0.982329i
$707$	−6.91921	−	6.91921i	−0.260224	−	0.260224i
$708$	1.05454	−	1.05454i	0.0396320	−	0.0396320i
$709$			13.1134i			0.492483i	0.969209	+	0.246241i	$0.0791956\pi$
$709$			13.1134i			0.492483i	−0.969209	+	0.246241i	$0.920804\pi$
$710$	−14.4125	−	13.9957i	−0.540892	−	0.525249i
$711$			7.95317i			0.298267i
$712$	−6.58252	−	6.58252i	−0.246690	−	0.246690i
$713$	1.70273	+	1.70273i	0.0637677	+	0.0637677i
$714$			5.42101i			0.202876i
$715$	−8.12215	−	7.88725i	−0.303751	−	0.294967i
$716$			9.00631i			0.336582i
$717$	3.81954	−	3.81954i	0.142643	−	0.142643i
$718$	1.07628	+	1.07628i	0.0401663	+	0.0401663i
$719$		−	16.8894i		−	0.629869i	−0.949113	−	0.314935i	$-0.898017\pi$
$719$		−	16.8894i		−	0.629869i	0.949113	−	0.314935i	$-0.101983\pi$
$720$	−0.0328054	−	2.23583i	−0.00122259	−	0.0833244i
$721$		−	60.0244i		−	2.23543i
$722$	11.1132	−	15.4109i	0.413591	−	0.573535i
$723$	−17.2005	+	17.2005i	−0.639694	+	0.639694i
$724$	18.7616			0.697271
$725$	−27.0095	+	0.792771i	−1.00311	+	0.0294428i
$726$	8.75540			0.324943
$727$	10.7209	+	10.7209i	0.397617	+	0.397617i	0.877392	−	0.479775i	$-0.159282\pi$
$727$	10.7209	+	10.7209i	0.397617	+	0.397617i	−0.479775	+	0.877392i	$0.659282\pi$
$728$	10.7349	−	10.7349i	0.397862	−	0.397862i
$729$		−	1.00000i		−	0.0370370i
$730$	0.522265	+	35.5946i	0.0193299	+	1.31741i
$731$	1.06448			0.0393712
$732$	−10.7786	+	10.7786i	−0.398387	+	0.398387i
$733$	−24.7783	+	24.7783i	−0.915207	+	0.915207i	−0.996676	−	0.0814690i	$-0.974039\pi$
$733$	−24.7783	+	24.7783i	−0.915207	+	0.915207i	0.0814690	+	0.996676i	$0.474039\pi$
$734$	−22.1101			−0.816099
$735$	20.5314	−	21.1429i	0.757314	−	0.779868i
$736$			6.61099i			0.243684i
$737$	1.48194	−	1.48194i	0.0545880	−	0.0545880i
$738$	−1.26863	+	1.26863i	−0.0466990	+	0.0466990i
$739$		−	0.497280i		−	0.0182928i	−0.999958	−	0.00914638i	$-0.997089\pi$
$739$		−	0.497280i		−	0.0182928i	0.999958	−	0.00914638i	$-0.00291142\pi$
$740$	−9.75161	−	9.46959i	−0.358476	−	0.348109i
$741$	−1.18187	−	14.6834i	−0.0434169	−	0.539408i
$742$	−23.6915	−	23.6915i	−0.869743	−	0.869743i
$743$	−15.6060	−	15.6060i	−0.572529	−	0.572529i	0.360305	−	0.932835i	$-0.382673\pi$
$743$	−15.6060	−	15.6060i	−0.572529	−	0.572529i	−0.932835	+	0.360305i	$0.882673\pi$
$744$	−0.364245			−0.0133539
$745$	−0.415396	−	28.3110i	−0.0152189	−	1.03724i
$746$	14.4355			0.528520
$747$	3.94546	+	3.94546i	0.144357	+	0.144357i
$748$	1.27842	−	1.27842i	0.0467438	−	0.0467438i
$749$	−1.90744			−0.0696964
$750$	−11.1695	+	0.491940i	−0.407853	+	0.0179631i
$751$			5.39804i			0.196977i	0.995138	+	0.0984887i	$0.0314008\pi$
$751$			5.39804i			0.196977i	−0.995138	+	0.0984887i	$0.968599\pi$
$752$	5.24209	+	5.24209i	0.191159	+	0.191159i
$753$	20.1081	+	20.1081i	0.732781	+	0.732781i
$754$	18.2636			0.665121
$755$	0.506121	+	34.4943i	0.0184196	+	1.25538i
$756$			4.49222i			0.163380i
$757$	−3.00432	−	3.00432i	−0.109194	−	0.109194i	0.650399	−	0.759593i	$-0.274602\pi$
$757$	−3.00432	−	3.00432i	−0.109194	−	0.109194i	−0.759593	+	0.650399i	$0.774602\pi$
$758$	12.3034	−	12.3034i	0.446881	−	0.446881i
$759$	−9.90459			−0.359514
$760$	7.51463	+	6.20728i	0.272584	+	0.225162i
$761$	−9.42821			−0.341772			−0.170886	−	0.985291i	$-0.554663\pi$
$761$	−9.42821			−0.341772			−0.170886	+	0.985291i	$0.554663\pi$
$762$	−8.31864	+	8.31864i	−0.301353	+	0.301353i
$763$	−24.8891	−	24.8891i	−0.901047	−	0.901047i
$764$			6.38310i			0.230932i
$765$	−1.87985	+	1.93584i	−0.0679662	+	0.0699903i
$766$	20.2174			0.730485
$767$	3.56381	+	3.56381i	0.128682	+	0.128682i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$		−	25.1986i		−	0.908683i	−0.890828	−	0.454342i	$-0.849875\pi$
$769$		−	25.1986i		−	0.908683i	0.890828	−	0.454342i	$-0.150125\pi$
$770$	−15.0477	+	0.220788i	−0.542280	+	0.00795665i
$771$	20.0409			0.721755
$772$	−15.6976	+	15.6976i	−0.564970	+	0.564970i
$773$	−8.32250	−	8.32250i	−0.299340	−	0.299340i	0.541416	−	0.840755i	$-0.317889\pi$
$773$	−8.32250	−	8.32250i	−0.299340	−	0.299340i	−0.840755	+	0.541416i	$0.817889\pi$
$774$	0.882099			0.0317064
$775$	0.0534327	+	1.82044i	0.00191936	+	0.0653922i
$776$	−12.4444			−0.446728
$777$	19.3096	+	19.3096i	0.692727	+	0.692727i
$778$	−7.79761	−	7.79761i	−0.279558	−	0.279558i
$779$	−0.627432	−	7.79517i	−0.0224801	−	0.279291i
$780$	7.55598	−	0.110866i	0.270547	−	0.00396963i
$781$		−	13.4605i		−	0.481654i
$782$	5.64120	−	5.64120i	0.201729	−	0.201729i
$783$	−3.82137	+	3.82137i	−0.136565	+	0.136565i
$784$		−	13.1800i		−	0.470715i
$785$	−30.1611	−	29.2888i	−1.07649	−	1.04536i
$786$	−8.07719			−0.288104
$787$	−33.1356	+	33.1356i	−1.18116	+	1.18116i	−0.201710	+	0.979445i	$0.564650\pi$
$787$	−33.1356	+	33.1356i	−1.18116	+	1.18116i	−0.979445	+	0.201710i	$0.935350\pi$
$788$	2.62159	−	2.62159i	0.0933901	−	0.0933901i
$789$	4.47451			0.159297
$790$	12.3892	−	12.7582i	0.440789	−	0.453916i
$791$		−	78.5265i		−	2.79208i
$792$	1.05939	−	1.05939i	0.0376437	−	0.0376437i
$793$	−36.4261	−	36.4261i	−1.29353	−	1.29353i
$794$	−1.54526			−0.0548392
$795$	−0.244677	−	16.6758i	−0.00867779	−	0.591428i
$796$	6.73685			0.238781
$797$	10.3195	−	10.3195i	0.365534	−	0.365534i	−0.500311	−	0.865846i	$-0.666781\pi$
$797$	10.3195	−	10.3195i	0.365534	−	0.365534i	0.865846	+	0.500311i	$0.166781\pi$
$798$	−14.9122	−	12.6904i	−0.527885	−	0.449237i
$799$		−	8.94620i		−	0.316494i
$800$	−3.43028	+	3.63774i	−0.121279	+	0.128614i
$801$			9.30909i			0.328921i
$802$	9.67468	+	9.67468i	0.341625	+	0.341625i
$803$	−16.8655	+	16.8655i	−0.595172	+	0.595172i
$804$			1.39887i			0.0493342i
$805$	−66.3996	+	0.974255i	−2.34028	+	0.0343380i
$806$		−	1.23097i		−	0.0433589i
$807$	−3.64136	−	3.64136i	−0.128182	−	0.128182i
$808$	−1.54027	−	1.54027i	−0.0541864	−	0.0541864i
$809$		−	27.5401i		−	0.968260i	−0.874996	−	0.484130i	$-0.839136\pi$
$809$		−	27.5401i		−	0.968260i	0.874996	−	0.484130i	$-0.160864\pi$
$810$	−1.55777	+	1.60417i	−0.0547345	+	0.0563646i
$811$			39.9597i			1.40318i	0.712583	+	0.701588i	$0.247525\pi$
$811$			39.9597i			1.40318i	−0.712583	+	0.701588i	$0.752475\pi$
$812$	17.1664	−	17.1664i	0.602423	−	0.602423i
$813$	6.60295	+	6.60295i	0.231576	+	0.231576i
$814$		−	9.10745i		−	0.319216i
$815$	0.0965084	−	0.0993826i	0.00338054	−	0.00348122i
$816$			1.20676i			0.0422449i
$817$	−2.49192	+	2.92818i	−0.0871811	+	0.102444i
$818$	9.84826	−	9.84826i	0.344336	−	0.344336i
$819$	−15.1814			−0.530482
$820$	4.01134	−	0.0588568i	0.140082	−	0.00205537i
$821$	23.0062			0.802922			0.401461	−	0.915876i	$-0.368502\pi$
$821$	23.0062			0.802922			0.401461	+	0.915876i	$0.368502\pi$
$822$	−6.99785	−	6.99785i	−0.244078	−	0.244078i
$823$	15.1426	−	15.1426i	0.527839	−	0.527839i	−0.392088	−	0.919928i	$-0.628247\pi$
$823$	15.1426	−	15.1426i	0.527839	−	0.527839i	0.919928	+	0.392088i	$0.128247\pi$
$824$		−	13.3619i		−	0.465483i
$825$	−5.45006	−	5.13925i	−0.189747	−	0.178926i
$826$	6.69943			0.233103
$827$	30.6119	−	30.6119i	1.06448	−	1.06448i	0.0667089	−	0.997772i	$-0.478750\pi$
$827$	30.6119	−	30.6119i	1.06448	−	1.06448i	0.997772	−	0.0667089i	$-0.0212499\pi$
$828$	4.67468	−	4.67468i	0.162456	−	0.162456i
$829$	20.6550			0.717377			0.358688	−	0.933457i	$-0.383224\pi$
$829$	20.6550			0.717377			0.358688	+	0.933457i	$0.383224\pi$
$830$	−0.183045	−	12.4753i	−0.00635359	−	0.433024i
$831$		−	9.81727i		−	0.340557i
$832$	2.38967	−	2.38967i	0.0828468	−	0.0828468i
$833$	−11.2466	+	11.2466i	−0.389671	+	0.389671i
$834$		−	10.8866i		−	0.376974i
$835$	−14.5809	+	15.0152i	−0.504595	+	0.519622i
$836$	0.523945	+	6.50945i	0.0181210	+	0.225134i
$837$	0.257560	+	0.257560i	0.00890258	+	0.00890258i
$838$	22.4760	+	22.4760i	0.776421	+	0.776421i
$839$	14.8706			0.513391			0.256696	−	0.966492i	$-0.417366\pi$
$839$	14.8706			0.513391			0.256696	+	0.966492i	$0.417366\pi$
$840$	6.99785	−	7.20626i	0.241449	−	0.248640i
$841$	0.205753			0.00709491
$842$	−21.1861	−	21.1861i	−0.730123	−	0.730123i
$843$	−9.85468	+	9.85468i	−0.339413	+	0.339413i
$844$	15.1654			0.522013
$845$	−0.0517994	−	3.53035i	−0.00178195	−	0.121448i
$846$		−	7.41343i		−	0.254879i
$847$	27.8113	+	27.8113i	0.955608	+	0.955608i
$848$	−5.27391	−	5.27391i	−0.181107	−	0.181107i
$849$	18.3969			0.631380
$850$	6.03118	−	0.177024i	0.206868	−	0.00607189i
$851$		−	40.1878i		−	1.37762i
$852$	6.35295	+	6.35295i	0.217649	+	0.217649i
$853$	18.8845	−	18.8845i	0.646592	−	0.646592i	−0.305576	−	0.952168i	$-0.598849\pi$
$853$	18.8845	−	18.8845i	0.646592	−	0.646592i	0.952168	+	0.305576i	$0.0988490\pi$
$854$	−68.4756			−2.34319
$855$	−0.924440	−	9.70286i	−0.0316152	−	0.331831i
$856$	−0.424610			−0.0145129
$857$	−3.38649	+	3.38649i	−0.115680	+	0.115680i	−0.762577	−	0.646897i	$-0.776066\pi$
$857$	−3.38649	+	3.38649i	−0.115680	+	0.115680i	0.646897	+	0.762577i	$0.276066\pi$
$858$	3.58020	+	3.58020i	0.122226	+	0.122226i
$859$			20.3135i			0.693089i	0.938034	+	0.346544i	$0.112645\pi$
$859$			20.3135i			0.693089i	−0.938034	+	0.346544i	$0.887355\pi$
$860$	−1.41503	−	1.37411i	−0.0482522	−	0.0468567i
$861$	−8.05956			−0.274669
$862$	13.7288	+	13.7288i	0.467603	+	0.467603i
$863$	−20.2596	−	20.2596i	−0.689645	−	0.689645i	0.272508	−	0.962153i	$-0.412147\pi$
$863$	−20.2596	−	20.2596i	−0.689645	−	0.689645i	−0.962153	+	0.272508i	$0.912147\pi$
$864$			1.00000i			0.0340207i
$865$	−40.2895	−	39.1243i	−1.36988	−	1.33026i
$866$	7.83259			0.266162
$867$	−10.9911	+	10.9911i	−0.373277	+	0.373277i
$868$	−1.15702	−	1.15702i	−0.0392717	−	0.0392717i
$869$	11.9154			0.404203
$870$	12.0829	−	0.177288i	0.409650	−	0.00601063i
$871$	−4.72746			−0.160184
$872$	−5.54050	−	5.54050i	−0.187625	−	0.187625i
$873$	8.79952	+	8.79952i	0.297819	+	0.297819i
$874$	2.31197	+	28.7237i	0.0782036	+	0.971595i
$875$	−37.0423	−	33.9171i	−1.25226	−	1.14661i
$876$		−	15.9201i		−	0.537890i
$877$	−22.8421	+	22.8421i	−0.771322	+	0.771322i	−0.978338	−	0.207016i	$-0.933625\pi$
$877$	−22.8421	+	22.8421i	−0.771322	+	0.771322i	0.207016	+	0.978338i	$0.433625\pi$
$878$	13.6141	−	13.6141i	0.459454	−	0.459454i
$879$			16.2898i			0.549440i
$880$	−3.34972	+	0.0491491i	−0.112919	+	0.00165681i
$881$	−43.2232			−1.45623			−0.728113	−	0.685457i	$-0.759603\pi$
$881$	−43.2232			−1.45623			−0.728113	+	0.685457i	$0.759603\pi$
$882$	−9.31967	+	9.31967i	−0.313810	+	0.313810i
$883$	−33.6956	+	33.6956i	−1.13395	+	1.13395i	−0.144431	+	0.989515i	$0.546135\pi$
$883$	−33.6956	+	33.6956i	−1.13395	+	1.13395i	−0.989515	+	0.144431i	$0.953865\pi$
$884$	−4.07823			−0.137166
$885$	2.39236	+	2.32317i	0.0804183	+	0.0780925i
$886$			1.16299i			0.0390715i
$887$	−22.5354	+	22.5354i	−0.756666	+	0.756666i	−0.975714	−	0.219048i	$-0.929705\pi$
$887$	−22.5354	+	22.5354i	−0.756666	+	0.756666i	0.219048	+	0.975714i	$0.429705\pi$
$888$	4.29845	+	4.29845i	0.144247	+	0.144247i
$889$	−52.8480			−1.77246
$890$	14.5014	−	14.9333i	0.486089	−	0.500566i
$891$	−1.49820			−0.0501916
$892$	−1.90756	+	1.90756i	−0.0638697	+	0.0638697i
$893$	24.6093	+	20.9428i	0.823519	+	0.700825i
$894$			12.6624i			0.423495i
$895$	−20.1366	+	0.295456i	−0.673091	+	0.00987600i
$896$		−	4.49222i		−	0.150074i
$897$	15.7981	+	15.7981i	0.527482	+	0.527482i
$898$	24.0588	−	24.0588i	0.802852	−	0.802852i
$899$		−	1.96847i		−	0.0656520i
$900$	4.99785	−	0.146694i	0.166595	−	0.00488981i
$901$			9.00051i			0.299850i
$902$	1.90067	+	1.90067i	0.0632852	+	0.0632852i
$903$	2.80197	+	2.80197i	0.0932436	+	0.0932436i
$904$		−	17.4806i		−	0.581395i
$905$	0.615483	+	41.9478i	0.0204593	+	1.39439i
$906$		−	15.4280i		−	0.512560i
$907$	−16.4318	+	16.4318i	−0.545611	+	0.545611i	−0.925168	−	0.379558i	$-0.876076\pi$
$907$	−16.4318	+	16.4318i	−0.545611	+	0.545611i	0.379558	+	0.925168i	$0.376076\pi$
$908$	−19.8625	−	19.8625i	−0.659159	−	0.659159i
$909$			2.17827i			0.0722485i
$910$	24.3535	+	23.6492i	0.807312	+	0.783964i
$911$		−	12.8284i		−	0.425024i	−0.977158	−	0.212512i	$-0.931836\pi$
$911$		−	12.8284i		−	0.425024i	0.977158	−	0.212512i	$-0.0681644\pi$
$912$	−3.31956	−	2.82498i	−0.109922	−	0.0935446i
$913$	5.91109	−	5.91109i	0.195629	−	0.195629i
$914$	37.1033			1.22727
$915$	−24.4526	−	23.7454i	−0.808377	−	0.784998i
$916$	19.0279			0.628700
$917$	−25.6570	−	25.6570i	−0.847269	−	0.847269i
$918$	0.853306	−	0.853306i	0.0281633	−	0.0281633i
$919$			15.1134i			0.498544i	0.968434	+	0.249272i	$0.0801913\pi$
$919$			15.1134i			0.498544i	−0.968434	+	0.249272i	$0.919809\pi$
$920$	−14.7810	+	0.216876i	−0.487316	+	0.00715020i
$921$	28.1191			0.926557
$922$	−18.9176	+	18.9176i	−0.623018	+	0.623018i
$923$	−21.4698	+	21.4698i	−0.706687	+	0.706687i
$924$	6.73024			0.221409
$925$	20.8525	−	22.1136i	0.685625	−	0.727090i
$926$			23.3650i			0.767820i
$927$	−9.44827	+	9.44827i	−0.310322	+	0.310322i
$928$	3.82137	−	3.82137i	0.125443	−	0.125443i
$929$		−	54.6979i		−	1.79458i	−0.441442	−	0.897290i	$-0.645533\pi$
$929$		−	54.6979i		−	1.79458i	0.441442	−	0.897290i	$-0.354467\pi$
$930$	−0.0119492	−	0.814389i	−0.000391830	−	0.0267049i
$931$	−4.60926	−	57.2651i	−0.151063	−	1.87679i
$932$	8.22028	+	8.22028i	0.269264	+	0.269264i
$933$	−18.1154	−	18.1154i	−0.593072	−	0.593072i
$934$	9.75744			0.319273
$935$	2.90027	+	2.81639i	0.0948490	+	0.0921059i
$936$	−3.37950			−0.110462
$937$	19.3024	+	19.3024i	0.630582	+	0.630582i	0.948214	−	0.317632i	$-0.102888\pi$
$937$	19.3024	+	19.3024i	0.630582	+	0.630582i	−0.317632	+	0.948214i	$0.602888\pi$
$938$	−4.44346	+	4.44346i	−0.145084	+	0.145084i
$939$	2.01337			0.0657039
$940$	−11.5484	+	11.8924i	−0.376668	+	0.387886i
$941$		−	3.83170i		−	0.124910i	−0.998048	−	0.0624549i	$-0.980107\pi$
$941$		−	3.83170i		−	0.124910i	0.998048	−	0.0624549i	$-0.0198930\pi$
$942$	13.2948	+	13.2948i	0.433168	+	0.433168i
$943$	8.38692	+	8.38692i	0.273116	+	0.273116i
$944$	1.49134			0.0485391
$945$	−10.0438	+	0.147369i	−0.326725	+	0.00479391i
$946$		−	1.32156i		−	0.0429677i
$947$	−22.3934	−	22.3934i	−0.727689	−	0.727689i	0.242470	−	0.970159i	$-0.422042\pi$
$947$	−22.3934	−	22.3934i	−0.727689	−	0.727689i	−0.970159	+	0.242470i	$0.922042\pi$
$948$	−5.62374	+	5.62374i	−0.182651	+	0.182651i
$949$	53.8019			1.74648
$950$	−13.6319	+	17.0051i	−0.442277	+	0.551717i
$951$	31.1262			1.00934
$952$	−3.83323	+	3.83323i	−0.124236	+	0.124236i
$953$	−0.832761	−	0.832761i	−0.0269758	−	0.0269758i	0.693490	−	0.720466i	$-0.256072\pi$
$953$	−0.832761	−	0.832761i	−0.0269758	−	0.0269758i	−0.720466	+	0.693490i	$0.756072\pi$
$954$			7.45843i			0.241476i
$955$	−14.2715	+	0.209400i	−0.461815	+	0.00677603i
$956$	5.40164			0.174702
$957$	5.72518	+	5.72518i	0.185069	+	0.185069i
$958$	−7.14916	−	7.14916i	−0.230979	−	0.230979i
$959$		−	44.4570i		−	1.43559i
$960$	1.55777	−	1.60417i	0.0502769	−	0.0517742i
$961$	30.8673			0.995720
$962$	−14.5266	+	14.5266i	−0.468357	+	0.468357i
$963$	0.300245	+	0.300245i	0.00967526	+	0.00967526i
$964$	−24.3252			−0.783462
$965$	−35.6122	−	34.5822i	−1.14640	−	1.11324i
$966$	29.6980			0.955518
$967$	−8.69878	−	8.69878i	−0.279734	−	0.279734i	0.553269	−	0.833003i	$-0.313380\pi$
$967$	−8.69878	−	8.69878i	−0.279734	−	0.279734i	−0.833003	+	0.553269i	$0.813380\pi$
$968$	6.19100	+	6.19100i	0.198986	+	0.198986i
$969$	0.422022	+	5.24317i	0.0135573	+	0.168435i
$970$	−0.408244	−	27.8235i	−0.0131079	−	0.893360i
$971$			27.6771i			0.888202i	0.895977	+	0.444101i	$0.146477\pi$
$971$			27.6771i			0.888202i	−0.895977	+	0.444101i	$0.853523\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	34.5812	−	34.5812i	1.10862	−	1.10862i
$974$		−	27.5865i		−	0.883928i
$975$	0.495754	+	16.8902i	0.0158768	+	0.540920i
$976$	−15.2432			−0.487922
$977$	14.3182	−	14.3182i	0.458079	−	0.458079i	−0.439946	−	0.898024i	$-0.645002\pi$
$977$	14.3182	−	14.3182i	0.458079	−	0.458079i	0.898024	+	0.439946i	$0.145002\pi$
$978$	−0.0438073	+	0.0438073i	−0.00140080	+	0.00140080i
$979$	13.9469			0.445744
$980$	29.4682	−	0.432375i	0.941328	−	0.0138117i
$981$			7.83545i			0.250167i
$982$	−9.94898	+	9.94898i	−0.317485	+	0.317485i
$983$	32.4108	+	32.4108i	1.03374	+	1.03374i	0.999410	+	0.0343335i	$0.0109308\pi$
$983$	32.4108	+	32.4108i	1.03374	+	1.03374i	0.0343335	+	0.999410i	$0.489069\pi$
$984$	−1.79412			−0.0571944
$985$	5.94742	+	5.77541i	0.189500	+	0.184020i
$986$	−6.52159			−0.207690
$987$	23.5486	−	23.5486i	0.749560	−	0.749560i
$988$	9.54703	−	11.2184i	0.303731	−	0.356906i
$989$		−	5.83155i		−	0.185433i
$990$	2.40336	+	2.33385i	0.0763838	+	0.0741747i
$991$			26.7718i			0.850435i	0.905091	+	0.425218i	$0.139802\pi$
$991$			26.7718i			0.850435i	−0.905091	+	0.425218i	$0.860198\pi$
$992$	−0.257560	−	0.257560i	−0.00817755	−	0.00817755i
$993$	−13.4692	+	13.4692i	−0.427432	+	0.427432i
$994$			40.3600i			1.28014i
$995$	0.221005	+	15.0624i	0.00700633	+	0.477511i
$996$			5.57973i			0.176800i
$997$	−3.08169	−	3.08169i	−0.0975982	−	0.0975982i	0.656622	−	0.754220i	$-0.271985\pi$
$997$	−3.08169	−	3.08169i	−0.0975982	−	0.0975982i	−0.754220	+	0.656622i	$0.771985\pi$
$998$	−3.13678	−	3.13678i	−0.0992929	−	0.0992929i
$999$		−	6.07893i		−	0.192329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.b.37.10	yes	20
3.2	odd	2		1710.2.p.c.37.1		20
5.3	odd	4	inner	570.2.m.b.493.5	yes	20
15.8	even	4		1710.2.p.c.1063.6		20
19.18	odd	2	inner	570.2.m.b.37.5	✓	20
57.56	even	2		1710.2.p.c.37.6		20
95.18	even	4	inner	570.2.m.b.493.10	yes	20
285.113	odd	4		1710.2.p.c.1063.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.5	✓	20	19.18	odd	2	inner
570.2.m.b.37.10	yes	20	1.1	even	1	trivial
570.2.m.b.493.5	yes	20	5.3	odd	4	inner
570.2.m.b.493.10	yes	20	95.18	even	4	inner
1710.2.p.c.37.1		20	3.2	odd	2
1710.2.p.c.37.6		20	57.56	even	2
1710.2.p.c.1063.1		20	285.113	odd	4
1710.2.p.c.1063.6		20	15.8	even	4

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.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.23583 - 0.0328054i) q^{5} -1.00000 q^{6} +(-3.17648 - 3.17648i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.23583 - 0.0328054i) q^{5} -1.00000 q^{6} +(-3.17648 - 3.17648i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.55777 - 1.60417i) q^{10} +1.49820 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-2.38967 - 2.38967i) q^{13} -4.49222 q^{14} +(-1.60417 - 1.55777i) q^{15} -1.00000 q^{16} +(0.853306 + 0.853306i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.34485 + 0.349716i) q^{19} +(-0.0328054 - 2.23583i) q^{20} +4.49222i q^{21} +(1.05939 - 1.05939i) q^{22} +(4.67468 - 4.67468i) q^{23} +1.00000i q^{24} +(4.99785 - 0.146694i) q^{25} -3.37950 q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.17648 + 3.17648i) q^{28} -5.40423 q^{29} +(-2.23583 + 0.0328054i) q^{30} +0.364245i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.05939 - 1.05939i) q^{33} +1.20676 q^{34} +(-7.20626 - 6.99785i) q^{35} +1.00000 q^{36} +(4.29845 - 4.29845i) q^{37} +(-2.82498 + 3.31956i) q^{38} +3.37950i q^{39} +(-1.60417 - 1.55777i) q^{40} +1.79412i q^{41} +(3.17648 + 3.17648i) q^{42} +(0.623738 - 0.623738i) q^{43} -1.49820i q^{44} +(0.0328054 + 2.23583i) q^{45} -6.61099i q^{46} +(-5.24209 - 5.24209i) q^{47} +(0.707107 + 0.707107i) q^{48} +13.1800i q^{49} +(3.43028 - 3.63774i) q^{50} -1.20676i q^{51} +(-2.38967 + 2.38967i) q^{52} +(5.27391 + 5.27391i) q^{53} -1.00000i q^{54} +(3.34972 - 0.0491491i) q^{55} +4.49222i q^{56} +(3.31956 + 2.82498i) q^{57} +(-3.82137 + 3.82137i) q^{58} -1.49134 q^{59} +(-1.55777 + 1.60417i) q^{60} +15.2432 q^{61} +(0.257560 + 0.257560i) q^{62} +(3.17648 - 3.17648i) q^{63} +1.00000i q^{64} +(-5.42128 - 5.26449i) q^{65} -1.49820 q^{66} +(0.989147 - 0.989147i) q^{67} +(0.853306 - 0.853306i) q^{68} -6.61099 q^{69} +(-10.0438 + 0.147369i) q^{70} -8.98443i q^{71} +(0.707107 - 0.707107i) q^{72} +(-11.2572 + 11.2572i) q^{73} -6.07893i q^{74} +(-3.63774 - 3.43028i) q^{75} +(0.349716 + 4.34485i) q^{76} +(-4.75900 - 4.75900i) q^{77} +(2.38967 + 2.38967i) q^{78} +7.95317 q^{79} +(-2.23583 + 0.0328054i) q^{80} -1.00000 q^{81} +(1.26863 + 1.26863i) q^{82} +(3.94546 - 3.94546i) q^{83} +4.49222 q^{84} +(1.93584 + 1.87985i) q^{85} -0.882099i q^{86} +(3.82137 + 3.82137i) q^{87} +(-1.05939 - 1.05939i) q^{88} +9.30909 q^{89} +(1.60417 + 1.55777i) q^{90} +15.1814i q^{91} +(-4.67468 - 4.67468i) q^{92} +(0.257560 - 0.257560i) q^{93} -7.41343 q^{94} +(-9.70286 + 0.924440i) q^{95} +1.00000 q^{96} +(8.79952 - 8.79952i) q^{97} +(9.31967 + 9.31967i) q^{98} +1.49820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Introduction

L-functions

Modular forms

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