LMFDB - Embedded newform 504.2.cs.b.85.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.12
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.808719 - 1.16016i) q^{2} +(-0.339544 - 1.69844i) q^{3} +(-0.691947 + 1.87649i) q^{4} +(0.642635 + 0.371025i) q^{5} +(-1.69587 + 1.76749i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.73662 - 0.714781i) q^{8} +(-2.76942 + 1.15339i) q^{9} +O(q^{10})$	\(q+(-0.808719 - 1.16016i) q^{2} +(-0.339544 - 1.69844i) q^{3} +(-0.691947 + 1.87649i) q^{4} +(0.642635 + 0.371025i) q^{5} +(-1.69587 + 1.76749i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.73662 - 0.714781i) q^{8} +(-2.76942 + 1.15339i) q^{9} +(-0.0892617 - 1.04561i) q^{10} +(1.90044 - 1.09722i) q^{11} +(3.42206 + 0.538083i) q^{12} +(-4.66604 - 2.69394i) q^{13} +(-0.600369 + 1.28045i) q^{14} +(0.411963 - 1.21746i) q^{15} +(-3.04242 - 2.59686i) q^{16} -6.22894 q^{17} +(3.57780 + 2.28020i) q^{18} -2.61201i q^{19} +(-1.14089 + 0.949166i) q^{20} +(-1.30112 + 1.14328i) q^{21} +(-2.80987 - 1.31747i) q^{22} +(-2.99969 + 5.19562i) q^{23} +(-2.14322 - 4.40529i) q^{24} +(-2.22468 - 3.85326i) q^{25} +(0.648111 + 7.59200i) q^{26} +(2.89931 + 4.31207i) q^{27} +(1.97106 - 0.339000i) q^{28} +(1.96761 - 1.13600i) q^{29} +(-1.74561 + 0.506638i) q^{30} +(-3.47145 + 6.01273i) q^{31} +(-0.552318 + 5.62983i) q^{32} +(-2.50884 - 2.85523i) q^{33} +(5.03746 + 7.22658i) q^{34} -0.742050i q^{35} +(-0.248036 - 5.99487i) q^{36} -7.96166i q^{37} +(-3.03035 + 2.11238i) q^{38} +(-2.99118 + 8.83972i) q^{39} +(2.02385 + 0.556012i) q^{40} +(0.812301 - 1.40695i) q^{41} +(2.37863 + 0.584924i) q^{42} +(8.36404 - 4.82898i) q^{43} +(0.743914 + 4.32536i) q^{44} +(-2.20766 - 0.286314i) q^{45} +(8.45366 - 0.721669i) q^{46} +(-0.367428 - 0.636404i) q^{47} +(-3.37759 + 6.04912i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.67126 + 5.69719i) q^{50} +(2.11500 + 10.5795i) q^{51} +(8.28380 - 6.89171i) q^{52} +10.9969i q^{53} +(2.65797 - 6.85093i) q^{54} +1.62838 q^{55} +(-1.98733 - 2.01259i) q^{56} +(-4.43635 + 0.886892i) q^{57} +(-2.90919 - 1.36404i) q^{58} +(-1.87466 - 1.08233i) q^{59} +(1.99949 + 1.61546i) q^{60} +(-8.89678 + 5.13656i) q^{61} +(9.78316 - 0.835165i) q^{62} +(2.38358 + 1.82169i) q^{63} +(6.97818 - 3.91217i) q^{64} +(-1.99904 - 3.46244i) q^{65} +(-1.28358 + 5.21974i) q^{66} +(-13.9388 - 8.04760i) q^{67} +(4.31010 - 11.6885i) q^{68} +(9.84299 + 3.33066i) q^{69} +(-0.860898 + 0.600110i) q^{70} +8.07997 q^{71} +(-6.75442 + 5.13593i) q^{72} +2.61232 q^{73} +(-9.23681 + 6.43875i) q^{74} +(-5.78917 + 5.08685i) q^{75} +(4.90141 + 1.80737i) q^{76} +(-1.90044 - 1.09722i) q^{77} +(12.6745 - 3.67860i) q^{78} +(1.09247 + 1.89221i) q^{79} +(-0.991661 - 2.79765i) q^{80} +(6.33937 - 6.38846i) q^{81} +(-2.28921 + 0.195424i) q^{82} +(1.14554 - 0.661378i) q^{83} +(-1.24503 - 3.23263i) q^{84} +(-4.00293 - 2.31110i) q^{85} +(-12.3666 - 5.79835i) q^{86} +(-2.59753 - 2.95616i) q^{87} +(4.41650 - 4.36106i) q^{88} -3.81859 q^{89} +(1.45321 + 2.79279i) q^{90} +5.38788i q^{91} +(-7.67389 - 9.22398i) q^{92} +(11.3910 + 3.85447i) q^{93} +(-0.441185 + 0.940947i) q^{94} +(0.969121 - 1.67857i) q^{95} +(9.74948 - 0.973494i) q^{96} +(-8.79181 - 15.2279i) q^{97} +(1.40909 - 0.120291i) q^{98} +(-3.99758 + 5.23060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.808719	−	1.16016i	−0.571851	−	0.820358i
$2$	−0.808719	−	1.16016i	−0.571851	−	0.820358i
$3$	−0.339544	−	1.69844i	−0.196036	−	0.980597i
$3$	−0.339544	−	1.69844i	−0.196036	−	0.980597i
$4$	−0.691947	+	1.87649i	−0.345974	+	0.938244i
$5$	0.642635	+	0.371025i	0.287395	+	0.165928i	0.636766	−	0.771057i	$-0.280272\pi$
$5$	0.642635	+	0.371025i	0.287395	+	0.165928i	−0.349372	+	0.936984i	$0.613605\pi$
$6$	−1.69587	+	1.76749i	−0.692337	+	0.721574i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	2.73662	−	0.714781i	0.967541	−	0.252713i
$9$	−2.76942	+	1.15339i	−0.923140	+	0.384464i
$10$	−0.0892617	−	1.04561i	−0.0282270	−	0.330652i
$11$	1.90044	−	1.09722i	0.573003	−	0.330823i	−0.185345	−	0.982674i	$-0.559340\pi$
$11$	1.90044	−	1.09722i	0.573003	−	0.330823i	0.758348	+	0.651850i	$0.226007\pi$
$12$	3.42206	+	0.538083i	0.987862	+	0.155331i
$13$	−4.66604	−	2.69394i	−1.29413	−	0.747165i	−0.314744	−	0.949177i	$-0.601919\pi$
$13$	−4.66604	−	2.69394i	−1.29413	−	0.747165i	−0.979383	+	0.202012i	$0.935252\pi$
$14$	−0.600369	+	1.28045i	−0.160455	+	0.342215i
$15$	0.411963	−	1.21746i	0.106368	−	0.314346i
$16$	−3.04242	−	2.59686i	−0.760604	−	0.649216i
$17$	−6.22894			−1.51074			−0.755370	−	0.655298i	$-0.772543\pi$
$17$	−6.22894			−1.51074			−0.755370	+	0.655298i	$0.772543\pi$
$18$	3.57780	+	2.28020i	0.843296	+	0.537449i
$19$		−	2.61201i		−	0.599236i	−0.954059	−	0.299618i	$-0.903141\pi$
$19$		−	2.61201i		−	0.599236i	0.954059	−	0.299618i	$-0.0968592\pi$
$20$	−1.14089	+	0.949166i	−0.255112	+	0.212240i
$21$	−1.30112	+	1.14328i	−0.283928	+	0.249483i
$22$	−2.80987	−	1.31747i	−0.599066	−	0.280886i
$23$	−2.99969	+	5.19562i	−0.625479	+	1.08336i	0.362969	+	0.931801i	$0.381763\pi$
$23$	−2.99969	+	5.19562i	−0.625479	+	1.08336i	−0.988448	+	0.151560i	$0.951570\pi$
$24$	−2.14322	−	4.40529i	−0.437483	−	0.899227i
$25$	−2.22468	−	3.85326i	−0.444936	−	0.770652i
$26$	0.648111	+	7.59200i	0.127105	+	1.48891i
$27$	2.89931	+	4.31207i	0.557973	+	0.829859i
$28$	1.97106	−	0.339000i	0.372495	−	0.0640650i
$29$	1.96761	−	1.13600i	0.365377	−	0.210950i	−0.306060	−	0.952012i	$-0.599011\pi$
$29$	1.96761	−	1.13600i	0.365377	−	0.210950i	0.671437	+	0.741062i	$0.265678\pi$
$30$	−1.74561	+	0.506638i	−0.318703	+	0.0924991i
$31$	−3.47145	+	6.01273i	−0.623491	+	1.07992i	0.365340	+	0.930874i	$0.380953\pi$
$31$	−3.47145	+	6.01273i	−0.623491	+	1.07992i	−0.988831	+	0.149043i	$0.952381\pi$
$32$	−0.552318	+	5.62983i	−0.0976370	+	0.995222i
$33$	−2.50884	−	2.85523i	−0.436733	−	0.497032i
$34$	5.03746	+	7.22658i	0.863918	+	1.23935i
$35$		−	0.742050i		−	0.125429i
$36$	−0.248036	−	5.99487i	−0.0413393	−	0.999145i
$37$		−	7.96166i		−	1.30889i	−0.756110	−	0.654445i	$-0.772903\pi$
$37$		−	7.96166i		−	1.30889i	0.756110	−	0.654445i	$-0.227097\pi$
$38$	−3.03035	+	2.11238i	−0.491588	+	0.342674i
$39$	−2.99118	+	8.83972i	−0.478972	+	1.41549i
$40$	2.02385	+	0.556012i	0.319999	+	0.0879132i
$41$	0.812301	−	1.40695i	0.126860	−	0.219728i	−0.795598	−	0.605824i	$-0.792843\pi$
$41$	0.812301	−	1.40695i	0.126860	−	0.219728i	0.922458	+	0.386096i	$0.126177\pi$
$42$	2.37863	+	0.584924i	0.367030	+	0.0902557i
$43$	8.36404	−	4.82898i	1.27550	−	0.736413i	0.299486	−	0.954101i	$-0.403185\pi$
$43$	8.36404	−	4.82898i	1.27550	−	0.736413i	0.976018	+	0.217688i	$0.0698516\pi$
$44$	0.743914	+	4.32536i	0.112149	+	0.652073i
$45$	−2.20766	−	0.286314i	−0.329099	−	0.0426812i
$46$	8.45366	−	0.721669i	1.24642	−	0.106404i
$47$	−0.367428	−	0.636404i	−0.0535948	−	0.0928290i	0.837983	−	0.545696i	$-0.183735\pi$
$47$	−0.367428	−	0.636404i	−0.0535948	−	0.0928290i	−0.891578	+	0.452867i	$0.850401\pi$
$48$	−3.37759	+	6.04912i	−0.487513	+	0.873116i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.67126	+	5.69719i	−0.377773	+	0.805705i
$51$	2.11500	+	10.5795i	0.296159	+	1.48143i
$52$	8.28380	−	6.89171i	1.14876	−	0.955708i
$53$			10.9969i			1.51054i	0.655414	+	0.755269i	$0.272494\pi$
$53$			10.9969i			1.51054i	−0.655414	+	0.755269i	$0.727506\pi$
$54$	2.65797	−	6.85093i	0.361704	−	0.932293i
$55$	1.62838			0.219571
$56$	−1.98733	−	2.01259i	−0.265568	−	0.268944i
$57$	−4.43635	+	0.886892i	−0.587609	+	0.117472i
$58$	−2.90919	−	1.36404i	−0.381996	−	0.179108i
$59$	−1.87466	−	1.08233i	−0.244060	−	0.140908i	0.372982	−	0.927839i	$-0.378335\pi$
$59$	−1.87466	−	1.08233i	−0.244060	−	0.140908i	−0.617041	+	0.786931i	$0.711669\pi$
$60$	1.99949	+	1.61546i	0.258133	+	0.208555i
$61$	−8.89678	+	5.13656i	−1.13912	+	0.657669i	−0.946212	−	0.323549i	$-0.895124\pi$
$61$	−8.89678	+	5.13656i	−1.13912	+	0.657669i	−0.192904	+	0.981218i	$0.561791\pi$
$62$	9.78316	−	0.835165i	1.24246	−	0.106066i
$63$	2.38358	+	1.82169i	0.300303	+	0.229512i
$64$	6.97818	−	3.91217i	0.872272	−	0.489021i
$65$	−1.99904	−	3.46244i	−0.247950	−	0.429463i
$66$	−1.28358	+	5.21974i	−0.157997	+	0.642506i
$67$	−13.9388	−	8.04760i	−1.70290	−	0.983170i	−0.942796	−	0.333370i	$-0.891814\pi$
$67$	−13.9388	−	8.04760i	−1.70290	−	0.983170i	−0.760105	−	0.649800i	$-0.774853\pi$
$68$	4.31010	−	11.6885i	0.522677	−	1.41744i
$69$	9.84299	+	3.33066i	1.18496	+	0.400965i
$70$	−0.860898	+	0.600110i	−0.102897	+	0.0717269i
$71$	8.07997			0.958915			0.479458	−	0.877565i	$-0.340833\pi$
$71$	8.07997			0.958915			0.479458	+	0.877565i	$0.340833\pi$
$72$	−6.75442	+	5.13593i	−0.796017	+	0.605275i
$73$	2.61232			0.305749			0.152874	−	0.988246i	$-0.451147\pi$
$73$	2.61232			0.305749			0.152874	+	0.988246i	$0.451147\pi$
$74$	−9.23681	+	6.43875i	−1.07376	+	0.748489i
$75$	−5.78917	+	5.08685i	−0.668475	+	0.587378i
$76$	4.90141	+	1.80737i	0.562230	+	0.207320i
$77$	−1.90044	−	1.09722i	−0.216575	−	0.125039i
$78$	12.6745	−	3.67860i	1.43511	−	0.416519i
$79$	1.09247	+	1.89221i	0.122912	+	0.212890i	0.920915	−	0.389764i	$-0.127443\pi$
$79$	1.09247	+	1.89221i	0.122912	+	0.212890i	−0.798003	+	0.602654i	$0.794110\pi$
$80$	−0.991661	−	2.79765i	−0.110871	−	0.312786i
$81$	6.33937	−	6.38846i	0.704374	−	0.709829i
$82$	−2.28921	+	0.195424i	−0.252801	+	0.0215810i
$83$	1.14554	−	0.661378i	0.125739	−	0.0725957i	−0.435811	−	0.900038i	$-0.643538\pi$
$83$	1.14554	−	0.661378i	0.125739	−	0.0725957i	0.561550	+	0.827443i	$0.310205\pi$
$84$	−1.24503	−	3.23263i	−0.135844	−	0.352709i
$85$	−4.00293	−	2.31110i	−0.434179	−	0.250673i
$86$	−12.3666	−	5.79835i	−1.33352	−	0.625252i
$87$	−2.59753	−	2.95616i	−0.278484	−	0.316933i
$88$	4.41650	−	4.36106i	0.470800	−	0.464891i
$89$	−3.81859			−0.404770			−0.202385	−	0.979306i	$-0.564869\pi$
$89$	−3.81859			−0.404770			−0.202385	+	0.979306i	$0.564869\pi$
$90$	1.45321	+	2.79279i	0.153182	+	0.294386i
$91$			5.38788i			0.564803i
$92$	−7.67389	−	9.22398i	−0.800058	−	0.961666i
$93$	11.3910	+	3.85447i	1.18119	+	0.399690i
$94$	−0.441185	+	0.940947i	−0.0455047	+	0.0970513i
$95$	0.969121	−	1.67857i	0.0994298	−	0.172217i
$96$	9.74948	−	0.973494i	0.995052	−	0.0993568i
$97$	−8.79181	−	15.2279i	−0.892673	−	1.54615i	−0.836658	−	0.547725i	$-0.815494\pi$
$97$	−8.79181	−	15.2279i	−0.892673	−	1.54615i	−0.0560146	−	0.998430i	$-0.517839\pi$
$98$	1.40909	−	0.120291i	0.142339	−	0.0121512i
$99$	−3.99758	+	5.23060i	−0.401772	+	0.525695i
$100$	8.76996	−	1.50833i	0.876996	−	0.150833i
$101$	1.62046	−	0.935571i	0.161241	−	0.0930928i	−0.417208	−	0.908811i	$-0.636991\pi$
$101$	1.62046	−	0.935571i	0.161241	−	0.0930928i	0.578449	+	0.815718i	$0.303658\pi$
$102$	10.5635	−	11.0096i	1.04594	−	1.09011i
$103$	5.00608	−	8.67078i	0.493264	−	0.854358i	−0.506706	−	0.862119i	$-0.669137\pi$
$103$	5.00608	−	8.67078i	0.493264	−	0.854358i	0.999970	+	0.00776118i	$0.00247048\pi$
$104$	−14.6948	−	4.03709i	−1.44094	−	0.395869i
$105$	−1.26033	+	0.251959i	−0.122996	+	0.0245887i
$106$	12.7582	−	8.89339i	1.23918	−	0.863803i
$107$		−	17.6603i		−	1.70729i	−0.520858	−	0.853643i	$-0.674388\pi$
$107$		−	17.6603i		−	1.70729i	0.520858	−	0.853643i	$-0.325612\pi$
$108$	−10.0977	+	2.45680i	−0.971654	+	0.236406i
$109$		−	7.28980i		−	0.698236i	−0.937079	−	0.349118i	$-0.886481\pi$
$109$		−	7.28980i		−	0.698236i	0.937079	−	0.349118i	$-0.113519\pi$
$110$	−1.31690	−	1.88918i	−0.125562	−	0.180127i
$111$	−13.5224	+	2.70334i	−1.28349	+	0.256589i
$112$	−0.727740	+	3.93324i	−0.0687650	+	0.371656i
$113$	3.02662	−	5.24227i	0.284721	−	0.493151i	−0.687821	−	0.725881i	$-0.741432\pi$
$113$	3.02662	−	5.24227i	0.284721	−	0.493151i	0.972541	+	0.232730i	$0.0747658\pi$
$114$	4.61670	+	4.42963i	0.432393	+	0.414873i
$115$	−3.85541	+	2.22592i	−0.359519	+	0.207568i
$116$	0.770210	+	4.47826i	0.0715122	+	0.415796i
$117$	16.0294	+	2.07887i	1.48192	+	0.192192i
$118$	0.260389	+	3.05021i	0.0239708	+	0.280794i
$119$	3.11447	+	5.39442i	0.285503	+	0.494506i
$120$	0.257169	−	3.62618i	0.0234762	−	0.331024i
$121$	−3.09223	+	5.35590i	−0.281112	+	0.486900i
$122$	13.1542	+	6.16767i	1.19093	+	0.558394i
$123$	−2.66543	−	0.901926i	−0.240334	−	0.0813240i
$124$	−8.88075	−	10.6746i	−0.797515	−	0.958609i
$125$		−	7.01190i		−	0.627164i
$126$	0.185811	−	4.23857i	0.0165534	−	0.377602i
$127$	13.6995			1.21564			0.607819	−	0.794076i	$-0.292045\pi$
$127$	13.6995			1.21564			0.607819	+	0.794076i	$0.292045\pi$
$128$	−10.1821	−	4.93196i	−0.899982	−	0.435928i
$129$	−11.0417	−	12.5662i	−0.972168	−	1.10639i
$130$	−2.40032	+	5.11935i	−0.210522	+	0.448996i
$131$	0.965470	+	0.557414i	0.0843535	+	0.0487015i	0.541583	−	0.840647i	$-0.317825\pi$
$131$	0.965470	+	0.557414i	0.0843535	+	0.0487015i	−0.457230	+	0.889349i	$0.651158\pi$
$132$	7.09379	−	2.73215i	0.617435	−	0.237803i
$133$	−2.26207	+	1.30600i	−0.196146	+	0.113245i
$134$	1.93610	+	22.6796i	0.167254	+	1.95921i
$135$	0.263310	+	3.84681i	0.0226621	+	0.331080i
$136$	−17.0462	+	4.45233i	−1.46170	+	0.381784i
$137$	0.186902	+	0.323724i	0.0159682	+	0.0276576i	0.873899	−	0.486107i	$-0.161584\pi$
$137$	0.186902	+	0.323724i	0.0159682	+	0.0276576i	−0.857931	+	0.513765i	$0.828250\pi$
$138$	−4.09611	−	14.1130i	−0.348684	−	1.20138i
$139$	16.0865	+	9.28754i	1.36444	+	0.787759i	0.990211	−	0.139578i	$-0.0445747\pi$
$139$	16.0865	+	9.28754i	1.36444	+	0.787759i	0.374227	+	0.927337i	$0.377908\pi$
$140$	1.39245	+	0.513460i	0.117683	+	0.0433953i
$141$	−0.956137	+	0.840142i	−0.0805213	+	0.0707527i
$142$	−6.53442	−	9.37406i	−0.548356	−	0.786654i
$143$	−11.8233			−0.988718
$144$	11.4209	+	3.68270i	0.951744	+	0.306892i
$145$	1.68594			0.140010
$146$	−2.11263	−	3.03071i	−0.174843	−	0.250823i
$147$	1.64067	+	0.555168i	0.135320	+	0.0457895i
$148$	14.9400	+	5.50905i	1.22806	+	0.452841i
$149$	5.16393	+	2.98140i	0.423046	+	0.244246i	0.696380	−	0.717674i	$-0.254793\pi$
$149$	5.16393	+	2.98140i	0.423046	+	0.244246i	−0.273334	+	0.961919i	$0.588126\pi$
$150$	10.5834	+	2.60254i	0.864128	+	0.212496i
$151$	1.85945	+	3.22066i	0.151320	+	0.262093i	0.931713	−	0.363196i	$-0.118314\pi$
$151$	1.85945	+	3.22066i	0.151320	+	0.262093i	−0.780393	+	0.625289i	$0.784981\pi$
$152$	−1.86702	−	7.14808i	−0.151435	−	0.579786i
$153$	17.2506	−	7.18442i	1.39462	−	0.580826i
$154$	0.263970	+	3.09215i	0.0212713	+	0.249173i
$155$	−4.46175	+	2.57599i	−0.358376	+	0.206909i
$156$	−14.5179	−	11.7295i	−1.16236	−	0.939114i
$157$	−11.4251	−	6.59627i	−0.911820	−	0.526439i	−0.0308036	−	0.999525i	$-0.509807\pi$
$157$	−11.4251	−	6.59627i	−0.911820	−	0.526439i	−0.881016	+	0.473086i	$0.843140\pi$
$158$	1.31177	−	2.79770i	0.104359	−	0.222573i
$159$	18.6776	−	3.73393i	1.48123	−	0.296120i
$160$	−2.44375	+	3.41300i	−0.193195	+	0.269821i
$161$	5.99938			0.472818
$162$	−12.5384	−	2.18822i	−0.985110	−	0.171923i
$163$		−	1.23030i		−	0.0963646i	−0.998839	−	0.0481823i	$-0.984657\pi$
$163$		−	1.23030i		−	0.0963646i	0.998839	−	0.0481823i	$-0.0153428\pi$
$164$	2.07805	+	2.49781i	0.162268	+	0.195046i
$165$	−0.552907	−	2.76571i	−0.0430438	−	0.215310i
$166$	−1.69373	−	0.794143i	−0.131459	−	0.0616374i
$167$	10.1184	−	17.5256i	0.782988	−	1.35618i	−0.147205	−	0.989106i	$-0.547028\pi$
$167$	10.1184	−	17.5256i	0.782988	−	1.35618i	0.930194	−	0.367069i	$-0.119639\pi$
$168$	−2.74349	+	4.05873i	−0.211665	+	0.313138i
$169$	8.01462	+	13.8817i	0.616510	+	1.06783i
$170$	0.556006	+	6.51307i	0.0426437	+	0.499530i
$171$	3.01267	+	7.23375i	0.230385	+	0.553179i
$172$	3.27405	+	19.0364i	0.249644	+	1.45151i
$173$	5.37718	−	3.10452i	0.408820	−	0.236032i	−0.281463	−	0.959572i	$-0.590820\pi$
$173$	5.37718	−	3.10452i	0.408820	−	0.236032i	0.690282	+	0.723540i	$0.257486\pi$
$174$	−1.32895	+	5.40425i	−0.100747	+	0.409695i
$175$	−2.22468	+	3.85326i	−0.168170	+	0.291279i
$176$	−8.63124	−	1.59698i	−0.650604	−	0.120377i
$177$	−1.20175	+	3.55150i	−0.0903293	+	0.266947i
$178$	3.08817	+	4.43018i	0.231468	+	0.332056i
$179$		−	6.89973i		−	0.515710i	−0.966184	−	0.257855i	$-0.916984\pi$
$179$		−	6.89973i		−	0.515710i	0.966184	−	0.257855i	$-0.0830157\pi$
$180$	2.06485	−	3.94454i	0.153905	−	0.294009i
$181$		−	2.13939i		−	0.159020i	−0.996834	−	0.0795099i	$-0.974664\pi$
$181$		−	2.13939i		−	0.159020i	0.996834	−	0.0795099i	$-0.0253355\pi$
$182$	6.25081	−	4.35728i	0.463341	−	0.322983i
$183$	11.7450	+	13.3666i	0.868216	+	0.988087i
$184$	−4.49528	+	16.3626i	−0.331397	+	1.20626i
$185$	2.95398	−	5.11644i	0.217181	−	0.376168i
$186$	−4.74029	−	16.3326i	−0.347575	−	1.19756i
$187$	−11.8377	+	6.83450i	−0.865659	+	0.499788i
$188$	1.44844	−	0.249116i	0.105639	−	0.0181687i
$189$	2.28471	−	4.66692i	0.166188	−	0.339468i
$190$	−2.73116	+	0.233152i	−0.198139	+	0.0169147i
$191$	10.0972	+	17.4888i	0.730605	+	1.26544i	0.956625	+	0.291322i	$0.0940950\pi$
$191$	10.0972	+	17.4888i	0.730605	+	1.26544i	−0.226021	+	0.974123i	$0.572572\pi$
$192$	−9.01400	−	10.5237i	−0.650529	−	0.759481i
$193$	4.75859	−	8.24212i	0.342531	−	0.593281i	−0.642371	−	0.766394i	$-0.722049\pi$
$193$	4.75859	−	8.24212i	0.342531	−	0.593281i	0.984902	+	0.173113i	$0.0553825\pi$
$194$	−10.5567	+	22.5150i	−0.757925	+	1.61648i
$195$	−5.20199	+	4.57091i	−0.372522	+	0.327329i
$196$	−1.27911	−	1.53749i	−0.0913652	−	0.109821i
$197$			6.65722i			0.474307i	0.971472	+	0.237154i	$0.0762145\pi$
$197$			6.65722i			0.474307i	−0.971472	+	0.237154i	$0.923786\pi$
$198$	9.30126	+	0.407750i	0.661012	+	0.0289775i
$199$	−12.1788			−0.863329			−0.431664	−	0.902034i	$-0.642074\pi$
$199$	−12.1788			−0.863329			−0.431664	+	0.902034i	$0.642074\pi$
$200$	−8.84234	−	8.95475i	−0.625248	−	0.633196i
$201$	−8.93553	+	26.4069i	−0.630264	+	1.86260i
$202$	−2.39591	−	1.12338i	−0.168575	−	0.0790405i
$203$	−1.96761	−	1.13600i	−0.138099	−	0.0797317i
$204$	−21.3158	−	3.35169i	−1.49240	−	0.234665i
$205$	1.04402	−	0.602768i	0.0729179	−	0.0420991i
$206$	−14.1080	+	1.20437i	−0.982952	+	0.0839123i
$207$	2.31481	−	17.8487i	0.160891	−	1.24057i
$208$	7.20025	+	20.3132i	0.499248	+	1.40846i
$209$	−2.86594	−	4.96396i	−0.198241	−	0.343364i
$210$	1.31157	+	1.25842i	0.0905067	+	0.0868394i
$211$	5.41445	+	3.12604i	0.372746	+	0.215205i	0.674658	−	0.738131i	$-0.264291\pi$
$211$	5.41445	+	3.12604i	0.372746	+	0.215205i	−0.301911	+	0.953336i	$0.597625\pi$
$212$	−20.6355	−	7.60927i	−1.41725	−	0.522607i
$213$	−2.74350	−	13.7234i	−0.187982	−	0.940309i
$214$	−20.4888	+	14.2822i	−1.40059	+	0.976313i
$215$	7.16669			0.488765
$216$	11.0165	+	9.72813i	0.749578	+	0.661916i
$217$	6.94290			0.471315
$218$	−8.45735	+	5.89540i	−0.572804	+	0.399287i
$219$	−0.886997	−	4.43687i	−0.0599377	−	0.299816i
$220$	−1.12675	+	3.05564i	−0.0759657	+	0.206011i
$221$	29.0645	+	16.7804i	1.95509	+	1.12877i
$222$	14.0721	+	13.5020i	0.944461	+	0.906192i
$223$	1.96173	+	3.39782i	0.131367	+	0.227535i	0.924204	−	0.381899i	$-0.124730\pi$
$223$	1.96173	+	3.39782i	0.131367	+	0.227535i	−0.792837	+	0.609434i	$0.791397\pi$
$224$	5.15173	−	2.33659i	0.344215	−	0.156120i
$225$	10.6054	+	8.10536i	0.707026	+	0.540357i
$226$	−8.52956	+	0.728149i	−0.567378	+	0.0484357i
$227$	6.86785	−	3.96515i	0.455835	−	0.263176i	−0.254456	−	0.967084i	$-0.581897\pi$
$227$	6.86785	−	3.96515i	0.455835	−	0.263176i	0.710291	+	0.703908i	$0.248563\pi$
$228$	1.40548	−	8.93844i	0.0930800	−	0.591963i
$229$	−17.0356	−	9.83550i	−1.12574	−	0.649948i	−0.182882	−	0.983135i	$-0.558543\pi$
$229$	−17.0356	−	9.83550i	−1.12574	−	0.649948i	−0.942861	+	0.333187i	$0.891876\pi$
$230$	5.70037	+	2.67275i	0.375871	+	0.176236i
$231$	−1.21828	+	3.60034i	−0.0801569	+	0.236885i
$232$	4.57262	−	4.51522i	0.300207	−	0.296439i
$233$	12.8572			0.842306			0.421153	−	0.906990i	$-0.361626\pi$
$233$	12.8572			0.842306			0.421153	+	0.906990i	$0.361626\pi$
$234$	−10.5515	−	20.2779i	−0.689770	−	1.32561i
$235$		−	0.545300i		−	0.0355714i
$236$	3.32815	−	2.76885i	0.216644	−	0.180237i
$237$	2.84287	−	2.49798i	0.184664	−	0.162261i
$238$	3.73967	−	7.97586i	0.242407	−	0.516998i
$239$	−8.16249	+	14.1378i	−0.527988	+	0.914501i	0.471480	+	0.881877i	$0.343720\pi$
$239$	−8.16249	+	14.1378i	−0.527988	+	0.914501i	−0.999468	+	0.0326247i	$0.989613\pi$
$240$	−4.41493	+	2.63421i	−0.284983	+	0.170037i
$241$	−13.1974	−	22.8586i	−0.850119	−	1.47245i	−0.881100	−	0.472930i	$-0.843196\pi$
$241$	−13.1974	−	22.8586i	−0.850119	−	1.47245i	0.0309811	−	0.999520i	$-0.490137\pi$
$242$	8.71445	−	0.743932i	0.560186	−	0.0478218i
$243$	−13.0029	−	8.59790i	−0.834138	−	0.551555i
$244$	−3.48259	−	20.2489i	−0.222950	−	1.29631i
$245$	−0.642635	+	0.371025i	−0.0410564	+	0.0237039i
$246$	1.10920	+	3.82173i	0.0707202	+	0.243665i
$247$	−7.03660	+	12.1877i	−0.447728	+	0.775487i
$248$	−5.20225	+	18.9359i	−0.330343	+	1.20243i
$249$	−1.51228	−	1.72107i	−0.0958365	−	0.109068i
$250$	−8.13494	+	5.67066i	−0.514499	+	0.358644i
$251$		−	30.3945i		−	1.91848i	−0.282587	−	0.959242i	$-0.591193\pi$
$251$		−	30.3945i		−	1.91848i	0.282587	−	0.959242i	$-0.408807\pi$
$252$	−5.06769	+	3.21224i	−0.319235	+	0.202352i
$253$			13.1652i			0.827692i
$254$	−11.0791	−	15.8937i	−0.695163	−	0.997257i
$255$	−2.56609	+	7.58348i	−0.160695	+	0.474896i
$256$	2.51261	+	15.8015i	0.157038	+	0.987593i
$257$	−8.65110	+	14.9841i	−0.539640	+	0.934685i	0.459283	+	0.888290i	$0.348106\pi$
$257$	−8.65110	+	14.9841i	−0.539640	+	0.934685i	−0.998923	+	0.0463946i	$0.985227\pi$
$258$	−5.64917	+	22.9727i	−0.351702	+	1.43022i
$259$	−6.89500	+	3.98083i	−0.428435	+	0.247357i
$260$	7.88045	−	1.35535i	0.488725	−	0.0840552i
$261$	−4.13889	+	5.41550i	−0.256191	+	0.335211i
$262$	−0.134103	−	1.57089i	−0.00828494	−	0.0970500i
$263$	4.29809	+	7.44451i	0.265032	+	0.459048i	0.967572	−	0.252596i	$-0.0812843\pi$
$263$	4.29809	+	7.44451i	0.265032	+	0.459048i	−0.702540	+	0.711644i	$0.747951\pi$
$264$	−8.90661	−	6.02040i	−0.548164	−	0.370530i
$265$	−4.08012	+	7.06698i	−0.250640	+	0.434121i
$266$	3.34455	+	1.56817i	0.205068	+	0.0961507i
$267$	1.29658	+	6.48566i	0.0793494	+	0.396916i
$268$	24.7462	−	20.5876i	1.51161	−	1.25759i
$269$			4.41443i			0.269152i	0.990903	+	0.134576i	$0.0429673\pi$
$269$			4.41443i			0.269152i	−0.990903	+	0.134576i	$0.957033\pi$
$270$	4.24997	−	3.41647i	0.258645	−	0.207920i
$271$	−6.50617			−0.395222			−0.197611	−	0.980281i	$-0.563318\pi$
$271$	−6.50617			−0.395222			−0.197611	+	0.980281i	$0.563318\pi$
$272$	18.9510	+	16.1757i	1.14908	+	0.980796i
$273$	9.15101	−	1.82942i	0.553844	−	0.110722i
$274$	0.224421	−	0.478639i	0.0135578	−	0.0289156i
$275$	−8.45573	−	4.88192i	−0.509899	−	0.294391i
$276$	−13.0608	+	16.1656i	−0.786167	+	0.973055i
$277$	−10.4564	+	6.03700i	−0.628263	+	0.362728i	−0.780079	−	0.625681i	$-0.784821\pi$
$277$	−10.4564	+	6.03700i	−0.628263	+	0.362728i	0.151816	+	0.988409i	$0.451488\pi$
$278$	−2.23441	−	26.1739i	−0.134011	−	1.56981i
$279$	2.67886	−	20.6557i	0.160379	−	1.23662i
$280$	−0.530404	−	2.03071i	−0.0316977	−	0.121358i
$281$	7.77630	+	13.4689i	0.463895	+	0.803490i	0.999151	−	0.0412001i	$-0.0131181\pi$
$281$	7.77630	+	13.4689i	0.463895	+	0.803490i	−0.535256	+	0.844690i	$0.679785\pi$
$282$	1.74795	+	0.429834i	0.104089	+	0.0255963i
$283$	18.2344	+	10.5276i	1.08392	+	0.625804i	0.931952	−	0.362581i	$-0.118104\pi$
$283$	18.2344	+	10.5276i	1.08392	+	0.625804i	0.151971	+	0.988385i	$0.451438\pi$
$284$	−5.59091	+	15.1620i	−0.331760	+	0.899697i
$285$	−3.18001	−	1.07605i	−0.188368	−	0.0637397i
$286$	9.56177	+	13.7170i	0.565399	+	0.811102i
$287$	−1.62460			−0.0958972
$288$	−4.96380	−	16.2284i	−0.292495	−	0.956267i
$289$	21.7997			1.28234
$290$	−1.36345	−	1.95596i	−0.0800647	−	0.114858i
$291$	−22.8785	+	20.1029i	−1.34116	+	1.17845i
$292$	−1.80759	+	4.90198i	−0.105781	+	0.286867i
$293$	−22.5227	−	13.0035i	−1.31579	−	0.759673i	−0.332743	−	0.943018i	$-0.607974\pi$
$293$	−22.5227	−	13.0035i	−1.31579	−	0.759673i	−0.983049	+	0.183345i	$0.941308\pi$
$294$	−0.682754	−	2.35241i	−0.0398191	−	0.137196i
$295$	−0.803146	−	1.39109i	−0.0467610	−	0.0809924i
$296$	−5.69085	−	21.7880i	−0.330774	−	1.26640i
$297$	10.2412	+	5.01364i	0.594257	+	0.290921i
$298$	−0.717269	−	8.40211i	−0.0415503	−	0.486721i
$299$	27.9934	−	16.1620i	1.61890	−	0.934671i
$300$	−5.53961	−	14.3831i	−0.319829	−	0.830411i
$301$	−8.36404	−	4.82898i	−0.482095	−	0.278338i
$302$	2.23271	−	4.76187i	0.128478	−	0.274015i
$303$	−2.13923	−	2.43459i	−0.122896	−	0.139863i
$304$	−6.78303	+	7.94682i	−0.389033	+	0.455782i
$305$	−7.62317			−0.436502
$306$	−22.2859	−	14.2032i	−1.27400	−	0.811946i
$307$			15.8370i			0.903864i	0.892052	+	0.451932i	$0.149265\pi$
$307$			15.8370i			0.903864i	−0.892052	+	0.451932i	$0.850735\pi$
$308$	3.37392	−	2.80693i	0.192247	−	0.159940i
$309$	−16.4266	−	5.55843i	−0.934478	−	0.316208i
$310$	6.59686	+	3.09309i	0.374677	+	0.175676i
$311$	6.73422	−	11.6640i	0.381862	−	0.661405i	−0.609466	−	0.792812i	$-0.708616\pi$
$311$	6.73422	−	11.6640i	0.381862	−	0.661405i	0.991328	+	0.131407i	$0.0419495\pi$
$312$	−1.86725	+	26.3290i	−0.105712	+	1.49059i
$313$	4.36807	+	7.56572i	0.246898	+	0.427640i	0.962664	−	0.270701i	$-0.0872554\pi$
$313$	4.36807	+	7.56572i	0.246898	+	0.427640i	−0.715766	+	0.698341i	$0.753922\pi$
$314$	1.58694	+	18.5894i	0.0895561	+	1.04906i
$315$	0.855876	+	2.05505i	0.0482231	+	0.115789i
$316$	−4.30663	+	0.740693i	−0.242267	+	0.0416672i
$317$	−20.9949	+	12.1214i	−1.17919	+	0.680808i	−0.955828	−	0.293927i	$-0.905038\pi$
$317$	−20.9949	+	12.1214i	−1.17919	+	0.680808i	−0.223366	+	0.974735i	$0.571704\pi$
$318$	−19.4369	−	18.6493i	−1.08997	−	1.04580i
$319$	2.49288	−	4.31780i	0.139575	−	0.241750i
$320$	5.93593	+	0.0749840i	0.331829	+	0.00419173i
$321$	−29.9950	+	5.99645i	−1.67416	+	0.334689i
$322$	−4.85181	−	6.96025i	−0.270381	−	0.387880i
$323$			16.2701i			0.905290i
$324$	7.60136	+	16.3162i	0.422298	+	0.906457i
$325$			23.9726i			1.32976i
$326$	−1.42735	+	0.994967i	−0.0790534	+	0.0551061i
$327$	−12.3813	+	2.47521i	−0.684688	+	0.136879i
$328$	1.21730	−	4.43089i	0.0672141	−	0.244655i
$329$	−0.367428	+	0.636404i	−0.0202569	+	0.0350861i
$330$	−2.76153	+	2.87815i	−0.152017	+	0.158437i
$331$	20.4780	−	11.8230i	1.12557	−	0.649849i	0.182754	−	0.983159i	$-0.441499\pi$
$331$	20.4780	−	11.8230i	1.12557	−	0.649849i	0.942817	+	0.333310i	$0.108165\pi$
$332$	0.448415	+	2.60723i	0.0246100	+	0.143090i
$333$	9.18292	+	22.0492i	0.503221	+	1.20829i
$334$	−28.5155	+	2.43431i	−1.56030	+	0.133199i
$335$	−5.97172	−	10.3433i	−0.326270	−	0.565116i
$336$	6.92749	−	0.0994840i	0.377926	−	0.00542730i
$337$	−9.52224	+	16.4930i	−0.518709	+	0.898431i	0.481054	+	0.876691i	$0.340254\pi$
$337$	−9.52224	+	16.4930i	−0.518709	+	0.898431i	−0.999764	+	0.0217400i	$0.993079\pi$
$338$	9.62347	−	20.5247i	0.523448	−	1.11640i
$339$	−9.93137	−	3.36057i	−0.539398	−	0.182521i
$340$	7.10656	−	5.91230i	0.385408	−	0.320640i
$341$			15.2357i			0.825061i
$342$	5.95591	−	9.34526i	0.322059	−	0.505334i
$343$	1.00000			0.0539949
$344$	19.4375	−	19.1935i	1.04800	−	1.03485i
$345$	5.08968	+	5.79240i	0.274019	+	0.311852i
$346$	−7.95037	−	3.72772i	−0.427415	−	0.200403i
$347$	12.5489	+	7.24511i	0.673661	+	0.388938i	0.797462	−	0.603369i	$-0.206175\pi$
$347$	12.5489	+	7.24511i	0.673661	+	0.388938i	−0.123802	+	0.992307i	$0.539509\pi$
$348$	7.34455	−	2.82872i	0.393709	−	0.151636i
$349$	0.156116	−	0.0901335i	0.00835669	−	0.00482474i	−0.495816	−	0.868428i	$-0.665131\pi$
$349$	0.156116	−	0.0901335i	0.00835669	−	0.00482474i	0.504173	+	0.863603i	$0.331798\pi$
$350$	6.26954	−	0.535216i	0.335121	−	0.0286085i
$351$	−1.91184	−	27.9309i	−0.102047	−	1.49084i
$352$	5.12750	+	11.3051i	0.273297	+	0.602566i
$353$	12.0312	+	20.8387i	0.640357	+	1.10913i	0.985353	+	0.170527i	$0.0545471\pi$
$353$	12.0312	+	20.8387i	0.640357	+	1.10913i	−0.344996	+	0.938604i	$0.612120\pi$
$354$	5.09219	−	1.47794i	0.270647	−	0.0785514i
$355$	5.19246	+	2.99787i	0.275587	+	0.159110i
$356$	2.64226	−	7.16554i	0.140040	−	0.379773i
$357$	8.10462	−	7.12140i	0.428942	−	0.376904i
$358$	−8.00480	+	5.57994i	−0.423067	+	0.294909i
$359$	−26.5922			−1.40348			−0.701742	−	0.712431i	$-0.747594\pi$
$359$	−26.5922			−1.40348			−0.701742	+	0.712431i	$0.747594\pi$
$360$	−6.24619	+	0.794462i	−0.329203	+	0.0418718i
$361$	12.1774			0.640916
$362$	−2.48204	+	1.73017i	−0.130453	+	0.0909356i
$363$	10.1466	+	3.43341i	0.532560	+	0.180207i
$364$	−10.1103	−	3.72813i	−0.529923	−	0.195407i
$365$	1.67877	+	0.969236i	0.0878706	+	0.0507321i
$366$	6.00899	−	24.4359i	0.314095	−	1.27729i
$367$	−1.16549	−	2.01868i	−0.0608379	−	0.105374i	0.834002	−	0.551761i	$-0.186044\pi$
$367$	−1.16549	−	2.01868i	−0.0608379	−	0.105374i	−0.894840	+	0.446387i	$0.852711\pi$
$368$	22.6186	−	8.01745i	1.17908	−	0.417939i
$369$	−0.626840	+	4.83333i	−0.0326320	+	0.251613i
$370$	−8.32483	+	0.710671i	−0.432787	+	0.0369460i
$371$	9.52359	−	5.49844i	0.494440	−	0.285465i
$372$	−15.1148	+	18.7080i	−0.783668	+	0.969962i
$373$	−2.68565	−	1.55056i	−0.139058	−	0.0802850i	0.428857	−	0.903372i	$-0.358916\pi$
$373$	−2.68565	−	1.55056i	−0.139058	−	0.0802850i	−0.567915	+	0.823087i	$0.692250\pi$
$374$	17.5025	+	8.20645i	0.905033	+	0.424346i
$375$	−11.9093	+	2.38085i	−0.614995	+	0.122947i
$376$	−1.46040	−	1.47896i	−0.0753143	−	0.0762717i
$377$	−12.2413			−0.630458
$378$	−7.26206	+	1.12359i	−0.373520	+	0.0577913i
$379$		−	11.9190i		−	0.612238i	−0.951993	−	0.306119i	$-0.900969\pi$
$379$		−	11.9190i		−	0.612238i	0.951993	−	0.306119i	$-0.0990305\pi$
$380$	2.47923	+	2.98003i	0.127182	+	0.152872i
$381$	−4.65160	−	23.2679i	−0.238309	−	1.19205i
$382$	12.1240	−	25.8578i	0.620320	−	1.32300i
$383$	9.34948	−	16.1938i	0.477736	−	0.827463i	−0.521938	−	0.852983i	$-0.674791\pi$
$383$	9.34948	−	16.1938i	0.477736	−	0.827463i	0.999674	+	0.0255203i	$0.00812426\pi$
$384$	−4.91938	+	18.9684i	−0.251041	+	0.967976i
$385$	−0.814190	−	1.41022i	−0.0414950	−	0.0718714i
$386$	−13.4106	+	1.14483i	−0.682579	+	0.0582702i
$387$	−17.5938	+	23.0205i	−0.894344	+	1.17020i
$388$	34.6584	−	5.96085i	1.75951	−	0.302616i
$389$	28.3575	−	16.3722i	1.43778	−	0.830104i	0.440088	−	0.897955i	$-0.354947\pi$
$389$	28.3575	−	16.3722i	1.43778	−	0.830104i	0.997696	+	0.0678504i	$0.0216141\pi$
$390$	9.50994	+	2.33857i	0.481554	+	0.118418i
$391$	18.6849	−	32.3632i	0.944936	−	1.63668i
$392$	−0.749291	+	2.72737i	−0.0378449	+	0.137753i
$393$	0.618917	−	1.82906i	0.0312202	−	0.0922640i
$394$	7.72345	−	5.38382i	0.389102	−	0.271233i
$395$			1.62133i			0.0815780i
$396$	−7.04905	−	11.1207i	−0.354228	−	0.558837i
$397$		−	15.8342i		−	0.794696i	−0.917668	−	0.397348i	$-0.869931\pi$
$397$		−	15.8342i		−	0.794696i	0.917668	−	0.397348i	$-0.130069\pi$
$398$	9.84919	+	14.1293i	0.493695	+	0.708239i
$399$	2.98625	+	3.39855i	0.149499	+	0.170140i
$400$	−3.23798	+	17.5004i	−0.161899	+	0.875021i
$401$	12.5323	−	21.7066i	0.625835	−	1.08398i	−0.362544	−	0.931967i	$-0.618092\pi$
$401$	12.5323	−	21.7066i	0.625835	−	1.08398i	0.988379	−	0.152011i	$-0.0485749\pi$
$402$	37.8625	−	10.9891i	1.88841	−	0.548085i
$403$	32.3958	−	18.7037i	1.61375	−	0.931700i
$404$	0.634317	+	3.68813i	0.0315585	+	0.183491i
$405$	6.44418	−	1.75338i	0.320214	−	0.0871260i
$406$	0.273301	+	3.20146i	0.0135637	+	0.158886i
$407$	−8.73567	−	15.1306i	−0.433011	−	0.749997i
$408$	13.3500	+	27.4403i	0.660923	+	1.35850i
$409$	−1.79953	+	3.11688i	−0.0889810	+	0.154120i	−0.907081	−	0.420957i	$-0.861694\pi$
$409$	−1.79953	+	3.11688i	−0.0889810	+	0.154120i	0.818100	+	0.575076i	$0.195028\pi$
$410$	−1.54363	−	0.723767i	−0.0762345	−	0.0357443i
$411$	0.486366	−	0.427362i	0.0239907	−	0.0210802i
$412$	12.8067	+	15.3936i	0.630940	+	0.758387i
$413$			2.16467i			0.106516i
$414$	−22.5794	+	11.7490i	−1.10972	+	0.577432i
$415$	0.981552			0.0481825
$416$	17.7436	−	24.7811i	0.869949	−	1.21499i
$417$	10.3123	−	30.4755i	0.504995	−	1.49239i
$418$	−3.44125	+	7.33940i	−0.168317	+	0.358982i
$419$	−3.44283	−	1.98772i	−0.168193	−	0.0971063i	0.413540	−	0.910486i	$-0.364292\pi$
$419$	−3.44283	−	1.98772i	−0.168193	−	0.0971063i	−0.581734	+	0.813379i	$0.697625\pi$
$420$	0.399285	−	2.53934i	0.0194831	−	0.123907i
$421$	10.1242	−	5.84520i	0.493422	−	0.284878i	−0.232571	−	0.972579i	$-0.574714\pi$
$421$	10.1242	−	5.84520i	0.493422	−	0.284878i	0.725993	+	0.687702i	$0.241380\pi$
$422$	−0.752066	−	8.80972i	−0.0366100	−	0.428851i
$423$	1.75158	+	1.33868i	0.0851650	+	0.0650888i
$424$	7.86037	+	30.0943i	0.381733	+	1.46151i
$425$	13.8574	+	24.0017i	0.672183	+	1.16426i
$426$	−13.7026	+	14.2813i	−0.663893	+	0.691929i
$427$	8.89678	+	5.13656i	0.430545	+	0.248575i
$428$	33.1394	+	12.2200i	1.60185	+	0.590676i
$429$	4.01455	+	20.0813i	0.193824	+	0.969534i
$430$	−5.79584	−	8.31452i	−0.279500	−	0.400962i
$431$	−19.2325			−0.926398			−0.463199	−	0.886254i	$-0.653298\pi$
$431$	−19.2325			−0.926398			−0.463199	+	0.886254i	$0.653298\pi$
$432$	2.37694	−	20.6482i	0.114361	−	0.993439i
$433$	−8.80799			−0.423285			−0.211642	−	0.977347i	$-0.567881\pi$
$433$	−8.80799			−0.423285			−0.211642	+	0.977347i	$0.567881\pi$
$434$	−5.61485	−	8.05488i	−0.269522	−	0.386647i
$435$	−0.572452	−	2.86348i	−0.0274470	−	0.137293i
$436$	13.6792	+	5.04416i	0.655116	+	0.241571i
$437$	13.5710	+	7.83522i	0.649189	+	0.374809i
$438$	−4.43016	+	4.61724i	−0.211681	+	0.220620i
$439$	1.57478	+	2.72760i	0.0751601	+	0.130181i	0.901156	−	0.433495i	$-0.142720\pi$
$439$	1.57478	+	2.72760i	0.0751601	+	0.130181i	−0.825996	+	0.563676i	$0.809387\pi$
$440$	4.45626	−	1.16394i	0.212444	−	0.0554885i
$441$	0.385842	−	2.97508i	0.0183734	−	0.141671i
$442$	−4.03705	−	47.2901i	−0.192023	−	2.24936i
$443$	−15.7528	+	9.09486i	−0.748437	+	0.432110i	−0.825129	−	0.564945i	$-0.808897\pi$
$443$	−15.7528	+	9.09486i	−0.748437	+	0.432110i	0.0766921	+	0.997055i	$0.475564\pi$
$444$	4.28403	−	27.2452i	0.203311	−	1.29300i
$445$	−2.45396	−	1.41679i	−0.116329	−	0.0671625i
$446$	2.35553	−	5.02381i	0.111538	−	0.237884i
$447$	3.31035	−	9.78297i	0.156574	−	0.462718i
$448$	−6.87713	−	4.08719i	−0.324914	−	0.193102i
$449$	−26.5079			−1.25099			−0.625493	−	0.780230i	$-0.715102\pi$
$449$	−26.5079			−1.25099			−0.625493	+	0.780230i	$0.715102\pi$
$450$	0.826741	−	18.8589i	0.0389729	−	0.889018i
$451$		−	3.56508i		−	0.167873i
$452$	7.74279	+	9.30680i	0.364190	+	0.437755i
$453$	4.83874	−	4.25172i	0.227344	−	0.199763i
$454$	−10.1544	−	4.76111i	−0.476568	−	0.223450i
$455$	−1.99904	+	3.46244i	−0.0937164	+	0.162322i
$456$	−11.5067	+	5.59811i	−0.538849	+	0.262155i
$457$	−12.0961	−	20.9511i	−0.565833	−	0.980052i	−0.996972	−	0.0777663i	$-0.975221\pi$
$457$	−12.0961	−	20.9511i	−0.565833	−	0.980052i	0.431138	−	0.902286i	$-0.358112\pi$
$458$	2.36624	+	27.7182i	0.110567	+	1.29518i
$459$	−18.0597	−	26.8597i	−0.842952	−	1.25370i
$460$	−1.50918	−	8.77485i	−0.0703657	−	0.409130i
$461$	−23.0445	+	13.3048i	−1.07329	+	0.619665i	−0.929079	−	0.369882i	$-0.879398\pi$
$461$	−23.0445	+	13.3048i	−1.07329	+	0.619665i	−0.144212	+	0.989547i	$0.546065\pi$
$462$	5.16222	−	1.49826i	0.240168	−	0.0697054i
$463$	−0.0784983	+	0.135963i	−0.00364812	+	0.00631873i	−0.867844	−	0.496837i	$-0.834495\pi$
$463$	−0.0784983	+	0.135963i	−0.00364812	+	0.00631873i	0.864196	+	0.503156i	$0.167828\pi$
$464$	−8.93634	−	1.65343i	−0.414859	−	0.0767585i
$465$	5.89013	+	6.70336i	0.273148	+	0.310861i
$466$	−10.3979	−	14.9165i	−0.481673	−	0.690992i
$467$		−	19.1638i		−	0.886795i	−0.896325	−	0.443398i	$-0.853773\pi$
$467$		−	19.1638i		−	0.886795i	0.896325	−	0.443398i	$-0.146227\pi$
$468$	−14.9925	+	28.6405i	−0.693027	+	1.32391i
$469$			16.0952i			0.743207i
$470$	−0.632636	+	0.440994i	−0.0291813	+	0.0203416i
$471$	−7.32407	+	21.6446i	−0.337475	+	0.997329i
$472$	−5.90385	−	1.62197i	−0.271747	−	0.0746570i
$473$	10.5969	−	18.3543i	0.487245	−	0.843933i
$474$	−5.19714	−	1.27802i	−0.238713	−	0.0587014i
$475$	−10.0648	+	5.81089i	−0.461802	+	0.266622i
$476$	−12.2776	+	2.11161i	−0.562744	+	0.0967856i
$477$	−12.6837	−	30.4550i	−0.580748	−	1.39444i
$478$	23.0033	−	1.96374i	1.05215	−	0.0898195i
$479$	6.25194	+	10.8287i	0.285658	+	0.494775i	0.972769	−	0.231778i	$-0.0744544\pi$
$479$	6.25194	+	10.8287i	0.285658	+	0.494775i	−0.687110	+	0.726553i	$0.741121\pi$
$480$	6.62654	+	2.99170i	0.302459	+	0.136552i
$481$	−21.4482	+	37.1494i	−0.977955	+	1.69387i
$482$	−15.8466	+	33.7973i	−0.721794	+	1.53942i
$483$	−2.03705	−	10.1896i	−0.0926892	−	0.463643i
$484$	−7.91062	−	9.50853i	−0.359574	−	0.432206i
$485$		−	13.0479i		−	0.592476i
$486$	0.540771	+	22.0388i	0.0245299	+	0.999699i
$487$	−21.4313			−0.971145			−0.485573	−	0.874196i	$-0.661389\pi$
$487$	−21.4313			−0.971145			−0.485573	+	0.874196i	$0.661389\pi$
$488$	−20.6756	+	20.4161i	−0.935940	+	0.924192i
$489$	−2.08960	+	0.417741i	−0.0944948	+	0.0188909i
$490$	0.950160	+	0.445504i	0.0429238	+	0.0201258i
$491$	−32.3378	−	18.6703i	−1.45939	−	0.842577i	−0.460405	−	0.887709i	$-0.652296\pi$
$491$	−32.3378	−	18.6703i	−1.45939	−	0.842577i	−0.998981	+	0.0451316i	$0.985629\pi$
$492$	3.53679	−	4.37756i	0.159451	−	0.197356i
$493$	−12.2562	+	7.07609i	−0.551989	+	0.318691i
$494$	19.8304	−	1.69287i	0.892211	−	0.0761660i
$495$	−4.50967	+	1.87816i	−0.202695	+	0.0844172i
$496$	26.1758	−	9.27835i	1.17533	−	0.416610i
$497$	−4.03998	−	6.99746i	−0.181218	−	0.313879i
$498$	−0.773712	+	3.14634i	−0.0346708	+	0.140991i
$499$	1.63605	+	0.944573i	0.0732396	+	0.0422849i	0.536173	−	0.844108i	$-0.319870\pi$
$499$	1.63605	+	0.944573i	0.0732396	+	0.0422849i	−0.462933	+	0.886393i	$0.653203\pi$
$500$	13.1578	+	4.85187i	0.588433	+	0.216982i
$501$	−33.2020	−	11.2349i	−1.48335	−	0.501937i
$502$	−35.2625	+	24.5806i	−1.57384	+	1.09709i
$503$	−7.28361			−0.324760			−0.162380	−	0.986728i	$-0.551917\pi$
$503$	−7.28361			−0.324760			−0.162380	+	0.986728i	$0.551917\pi$
$504$	7.82506	+	3.28154i	0.348556	+	0.146171i
$505$	1.38848			0.0617866
$506$	15.2738	−	10.6470i	0.679004	−	0.473316i
$507$	20.8560	−	18.3258i	0.926249	−	0.813879i
$508$	−9.47936	+	25.7070i	−0.420578	+	1.14056i
$509$	33.8209	+	19.5265i	1.49908	+	0.865497i	0.999999	−	0.00105662i	$-0.000336334\pi$
$509$	33.8209	+	19.5265i	1.49908	+	0.865497i	0.499085	+	0.866553i	$0.333670\pi$
$510$	10.8733	−	3.15582i	0.481478	−	0.139742i
$511$	−1.30616	−	2.26233i	−0.0577811	−	0.100080i
$512$	16.3003	−	15.6940i	0.720377	−	0.693583i
$513$	11.2632	−	7.57303i	0.497281	−	0.334358i
$514$	24.3803	−	2.08129i	1.07537	−	0.0918018i
$515$	6.43416	−	3.71476i	0.283523	−	0.163692i
$516$	31.2206	−	12.0245i	1.37441	−	0.529349i
$517$	−1.39655	−	0.806296i	−0.0614200	−	0.0354609i
$518$	10.1945	+	4.77994i	0.447922	+	0.210018i
$519$	−7.09864	−	8.07872i	−0.311596	−	0.354616i
$520$	−7.94550	−	8.04650i	−0.348433	−	0.352862i
$521$	−12.4343			−0.544756			−0.272378	−	0.962190i	$-0.587810\pi$
$521$	−12.4343			−0.544756			−0.272378	+	0.962190i	$0.587810\pi$
$522$	9.63005	+	0.422164i	0.421496	+	0.0184776i
$523$			32.5367i			1.42273i	0.702822	+	0.711366i	$0.251923\pi$
$523$			32.5367i			1.42273i	−0.702822	+	0.711366i	$0.748077\pi$
$524$	−1.71404	+	1.42599i	−0.0748780	+	0.0622947i
$525$	7.29992	+	2.47014i	0.318595	+	0.107806i
$526$	5.16088	−	11.0070i	0.225025	−	0.479928i
$527$	21.6235	−	37.4529i	0.941933	−	1.63148i
$528$	0.218311	+	15.2019i	0.00950077	+	0.661579i
$529$	−6.49629	−	11.2519i	−0.282447	−	0.489213i
$530$	11.4985	−	0.981601i	0.499463	−	0.0426380i
$531$	6.44007	+	0.835220i	0.279475	+	0.0362455i
$532$	−0.885472	−	5.14843i	−0.0383901	−	0.223213i
$533$	−7.58046	+	4.37658i	−0.328346	+	0.189571i
$534$	6.47584	−	6.74932i	0.280237	−	0.292072i
$535$	6.55242	−	11.3491i	0.283286	−	0.490665i
$536$	−43.8976	−	12.0600i	−1.89609	−	0.520912i
$537$	−11.7188	+	2.34276i	−0.505704	+	0.101098i
$538$	5.12145	−	3.57003i	0.220801	−	0.153915i
$539$			2.19443i			0.0945210i
$540$	−7.40068	−	2.16769i	−0.318475	−	0.0932825i
$541$		−	25.0150i		−	1.07548i	−0.843111	−	0.537740i	$-0.819278\pi$
$541$		−	25.0150i		−	1.07548i	0.843111	−	0.537740i	$-0.180722\pi$
$542$	5.26166	+	7.54821i	0.226008	+	0.324223i
$543$	−3.63364	+	0.726419i	−0.155934	+	0.0311736i
$544$	3.44036	−	35.0679i	0.147504	−	1.50352i
$545$	2.70470	−	4.68468i	0.115857	−	0.200670i
$546$	−9.52302	−	9.13715i	−0.407548	−	0.391034i
$547$	5.26826	−	3.04163i	0.225254	−	0.130051i	−0.383126	−	0.923696i	$-0.625153\pi$
$547$	5.26826	−	3.04163i	0.225254	−	0.130051i	0.608381	+	0.793645i	$0.291819\pi$
$548$	−0.736792	+	0.126720i	−0.0314742	+	0.00541321i
$549$	18.7144	−	24.4868i	0.798713	−	1.04507i
$550$	1.17450	+	13.7581i	0.0500807	+	0.586647i
$551$	−2.96725	−	5.13942i	−0.126409	−	0.218947i
$552$	29.3172	+	2.07918i	1.24782	+	0.0884956i
$553$	1.09247	−	1.89221i	0.0464564	−	0.0804648i
$554$	15.4602	+	7.24886i	0.656840	+	0.307975i
$555$	−9.69299	−	3.27991i	−0.411444	−	0.139224i
$556$	−28.5590	+	23.7596i	−1.21117	+	1.00763i
$557$			5.30217i			0.224660i	0.993671	+	0.112330i	$0.0358314\pi$
$557$			5.30217i			0.224660i	−0.993671	+	0.112330i	$0.964169\pi$
$558$	−26.1304	+	13.5967i	−1.10619	+	0.575596i
$559$	−52.0359			−2.20089
$560$	−1.92700	+	2.25763i	−0.0814307	+	0.0954022i
$561$	15.6274	+	17.7851i	0.659791	+	0.750886i
$562$	9.33731	−	19.9144i	0.393870	−	0.840036i
$563$	5.92183	+	3.41897i	0.249575	+	0.144092i	0.619570	−	0.784942i	$-0.287307\pi$
$563$	5.92183	+	3.41897i	0.249575	+	0.144092i	−0.369994	+	0.929034i	$0.620640\pi$
$564$	−0.914921	−	2.37552i	−0.0385251	−	0.100027i
$565$	3.89003	−	2.24591i	0.163655	−	0.0944861i
$566$	−2.53275	−	29.6688i	−0.106460	−	1.24707i
$567$	−8.70225	−	2.29583i	−0.365460	−	0.0964156i
$568$	22.1118	−	5.77541i	0.927790	−	0.242331i
$569$	18.0034	+	31.1827i	0.754740	+	1.30725i	0.945503	+	0.325612i	$0.105570\pi$
$569$	18.0034	+	31.1827i	0.754740	+	1.30725i	−0.190763	+	0.981636i	$0.561096\pi$
$570$	1.32334	+	4.55955i	0.0554288	+	0.190978i
$571$	−1.59916	−	0.923273i	−0.0669226	−	0.0386378i	0.466165	−	0.884698i	$-0.345635\pi$
$571$	−1.59916	−	0.923273i	−0.0669226	−	0.0386378i	−0.533088	+	0.846060i	$0.678969\pi$
$572$	8.18113	−	22.1864i	0.342070	−	0.927659i
$573$	26.2753	−	23.0877i	1.09767	−	0.964501i
$574$	1.31385	+	1.88480i	0.0548389	+	0.0786700i
$575$	26.6934			1.11319
$576$	−14.8132	+	18.8830i	−0.617218	+	0.786792i
$577$	24.6845			1.02763			0.513815	−	0.857901i	$-0.328232\pi$
$577$	24.6845			1.02763			0.513815	+	0.857901i	$0.328232\pi$
$578$	−17.6299	−	25.2912i	−0.733305	−	1.05198i
$579$	−15.6145	−	5.28364i	−0.648918	−	0.219580i
$580$	−1.16658	+	3.16365i	−0.0484397	+	0.131363i
$581$	−1.14554	−	0.661378i	−0.0475250	−	0.0274386i
$582$	41.8249	+	10.2851i	1.73370	+	0.426330i
$583$	12.0660	+	20.8989i	0.499722	+	0.865543i
$584$	7.14892	−	1.86724i	0.295824	−	0.0772668i
$585$	9.52973	+	7.28327i	0.394006	+	0.301126i
$586$	3.12840	+	36.6462i	0.129233	+	1.51384i
$587$	−22.5953	+	13.0454i	−0.932608	+	0.538442i	−0.887635	−	0.460547i	$-0.847653\pi$
$587$	−22.5953	+	13.0454i	−0.932608	+	0.538442i	−0.0449726	+	0.998988i	$0.514320\pi$
$588$	−2.17702	+	2.69455i	−0.0897788	+	0.111121i
$589$	15.7053	+	9.06746i	0.647125	+	0.373618i
$590$	−0.964369	+	2.05678i	−0.0397024	+	0.0846763i
$591$	11.3069	−	2.26042i	0.465104	−	0.0929813i
$592$	−20.6753	+	24.2227i	−0.849751	+	0.995547i
$593$	−9.49980			−0.390110			−0.195055	−	0.980792i	$-0.562489\pi$
$593$	−9.49980			−0.390110			−0.195055	+	0.980792i	$0.562489\pi$
$594$	−2.46565	−	15.9361i	−0.101167	−	0.653867i
$595$			4.62219i			0.189491i
$596$	−9.16773	+	7.62709i	−0.375525	+	0.312418i
$597$	4.13522	+	20.6849i	0.169243	+	0.846578i
$598$	−41.3893	−	19.4063i	−1.69253	−	0.793583i
$599$	−10.2407	+	17.7375i	−0.418425	+	0.724734i	−0.995781	−	0.0917587i	$-0.970751\pi$
$599$	−10.2407	+	17.7375i	−0.418425	+	0.724734i	0.577356	+	0.816493i	$0.304084\pi$
$600$	−12.2068	+	18.0587i	−0.498339	+	0.737245i
$601$	23.5054	+	40.7125i	0.958804	+	1.66070i	0.725412	+	0.688315i	$0.241649\pi$
$601$	23.5054	+	40.7125i	0.958804	+	1.66070i	0.233392	+	0.972383i	$0.425017\pi$
$602$	1.16176	+	13.6089i	0.0473499	+	0.554658i
$603$	47.8846	+	6.21020i	1.95001	+	0.252899i
$604$	−7.33017	+	1.26071i	−0.298260	+	0.0512974i
$605$	−3.97435	+	2.29459i	−0.161580	+	0.0932884i
$606$	−1.09447	+	4.45075i	−0.0444600	+	0.180799i
$607$	17.0225	−	29.4838i	0.690920	−	1.19671i	−0.280617	−	0.959820i	$-0.590539\pi$
$607$	17.0225	−	29.4838i	0.690920	−	1.19671i	0.971537	−	0.236889i	$-0.0761277\pi$
$608$	14.7052	+	1.44266i	0.596373	+	0.0585076i
$609$	−1.26134	+	3.72760i	−0.0511122	+	0.151050i
$610$	6.16500	+	8.84411i	0.249614	+	0.358087i
$611$			3.95931i			0.160177i
$612$	1.54500	+	37.3417i	0.0624530	+	1.50945i
$613$		−	21.3980i		−	0.864256i	−0.901812	−	0.432128i	$-0.857763\pi$
$613$		−	21.3980i		−	0.864256i	0.901812	−	0.432128i	$-0.142237\pi$
$614$	18.3734	−	12.8077i	0.741492	−	0.516875i
$615$	−1.37826	−	1.56855i	−0.0555768	−	0.0632501i
$616$	−5.98504	−	1.64427i	−0.241144	−	0.0662495i
$617$	−16.5991	+	28.7506i	−0.668256	+	1.15745i	0.310135	+	0.950693i	$0.399626\pi$
$617$	−16.5991	+	28.7506i	−0.668256	+	1.15745i	−0.978391	+	0.206762i	$0.933708\pi$
$618$	6.83584	+	23.5527i	0.274978	+	0.947430i
$619$	−11.7407	+	6.77852i	−0.471900	+	0.272452i	−0.717035	−	0.697037i	$-0.754501\pi$
$619$	−11.7407	+	6.77852i	−0.471900	+	0.272452i	0.245134	+	0.969489i	$0.421168\pi$
$620$	−1.74652	−	10.1549i	−0.0701420	−	0.407829i
$621$	−31.1009	+	2.12883i	−1.24804	+	0.0854269i
$622$	−18.9782	+	1.62013i	−0.760957	+	0.0649611i
$623$	1.90930	+	3.30700i	0.0764943	+	0.132492i
$624$	32.0559	−	19.1264i	1.28326	−	0.765670i
$625$	−8.52181	+	14.7602i	−0.340872	+	0.590408i
$626$	5.24491	−	11.1862i	0.209629	−	0.447091i
$627$	−7.45788	+	6.55312i	−0.297839	+	0.261706i
$628$	20.2834	−	16.8747i	0.809394	−	0.673375i
$629$			49.5927i			1.97739i
$630$	1.69203	−	2.65491i	0.0674119	−	0.105774i
$631$	−11.3421			−0.451522			−0.225761	−	0.974183i	$-0.572487\pi$
$631$	−11.3421			−0.451522			−0.225761	+	0.974183i	$0.572487\pi$
$632$	4.34218	+	4.39738i	0.172723	+	0.174918i
$633$	3.47095	−	10.2576i	0.137958	−	0.407702i
$634$	31.0418	+	14.5547i	1.23283	+	0.578040i
$635$	8.80379	+	5.08287i	0.349368	+	0.201708i
$636$	−5.91724	+	37.6320i	−0.234634	+	1.49220i
$637$	4.66604	−	2.69394i	0.184875	−	0.106738i
$638$	−7.02538	+	0.599741i	−0.278138	+	0.0237440i
$639$	−22.3768	+	9.31937i	−0.885213	+	0.368669i
$640$	−4.71351	−	6.94728i	−0.186318	−	0.274615i
$641$	−3.24257	−	5.61629i	−0.128074	−	0.221830i	0.794857	−	0.606797i	$-0.207546\pi$
$641$	−3.24257	−	5.61629i	−0.128074	−	0.221830i	−0.922930	+	0.384967i	$0.874213\pi$
$642$	31.2144	+	29.9496i	1.23193	+	1.18202i
$643$	17.4165	+	10.0554i	0.686839	+	0.396547i	0.802427	−	0.596751i	$-0.203542\pi$
$643$	17.4165	+	10.0554i	0.686839	+	0.396547i	−0.115588	+	0.993297i	$0.536875\pi$
$644$	−4.15126	+	11.2578i	−0.163582	+	0.443618i
$645$	−2.43341	−	12.1722i	−0.0958154	−	0.479281i
$646$	18.8759	−	13.1579i	0.742662	−	0.517691i
$647$	−34.7980			−1.36805			−0.684024	−	0.729459i	$-0.739772\pi$
$647$	−34.7980			−1.36805			−0.684024	+	0.729459i	$0.739772\pi$
$648$	12.7821	−	22.0140i	0.502128	−	0.864793i
$649$	−4.75022			−0.186462
$650$	27.8121	−	19.3871i	1.09088	−	0.760425i
$651$	−2.35742	−	11.7921i	−0.0923946	−	0.462170i
$652$	2.30864	+	0.851303i	0.0904135	+	0.0333396i
$653$	−32.2279	−	18.6068i	−1.26118	−	0.728141i	−0.287874	−	0.957668i	$-0.592949\pi$
$653$	−32.2279	−	18.6068i	−1.26118	−	0.728141i	−0.973302	+	0.229528i	$0.926282\pi$
$654$	12.8846	+	12.3626i	0.503830	+	0.483415i
$655$	0.413630	+	0.716427i	0.0161618	+	0.0279931i
$656$	−6.12500	+	2.17108i	−0.239141	+	0.0847666i
$657$	−7.23460	+	3.01303i	−0.282249	+	0.117549i
$658$	1.03548	−	0.0883962i	0.0403671	−	0.00344604i
$659$	−35.0162	+	20.2166i	−1.36404	+	0.787527i	−0.990158	−	0.139951i	$-0.955305\pi$
$659$	−35.0162	+	20.2166i	−1.36404	+	0.787527i	−0.373878	+	0.927478i	$0.621972\pi$
$660$	5.57241	+	0.876204i	0.216906	+	0.0341062i
$661$	29.1641	+	16.8379i	1.13435	+	0.654919i	0.945026	−	0.326995i	$-0.106036\pi$
$661$	29.1641	+	16.8379i	1.13435	+	0.654919i	0.189327	+	0.981914i	$0.439369\pi$
$662$	−30.2775	−	14.1963i	−1.17677	−	0.551755i
$663$	18.6319	−	55.0621i	0.723602	−	2.13843i
$664$	2.66217	−	2.62875i	0.103312	−	0.102015i
$665$	−1.93824			−0.0751618
$666$	18.1542	−	28.4853i	0.703461	−	1.10378i
$667$			13.6306i			0.527780i
$668$	25.8852	+	31.1140i	1.00153	+	1.20384i
$669$	5.10491	−	4.48560i	0.197367	−	0.173423i
$670$	−7.17048	+	15.2930i	−0.277020	+	0.590820i
$671$	−11.2718	+	19.5234i	−0.435145	+	0.753692i
$672$	−5.71781	−	7.95655i	−0.220569	−	0.306931i
$673$	−12.0471	−	20.8662i	−0.464383	−	0.804334i	0.534791	−	0.844984i	$-0.320390\pi$
$673$	−12.0471	−	20.8662i	−0.464383	−	0.804334i	−0.999173	+	0.0406503i	$0.987057\pi$
$674$	26.8353	−	2.29087i	1.03366	−	0.0882411i
$675$	10.1655	−	20.7648i	0.391270	−	0.799237i
$676$	−31.5946	+	5.43392i	−1.21518	+	0.208997i
$677$	−36.5803	+	21.1196i	−1.40590	+	0.811694i	−0.994989	−	0.0999835i	$-0.968121\pi$
$677$	−36.5803	+	21.1196i	−1.40590	+	0.811694i	−0.410906	+	0.911678i	$0.634788\pi$
$678$	4.13288	+	14.2397i	0.158722	+	0.546874i
$679$	−8.79181	+	15.2279i	−0.337399	+	0.584392i
$680$	−12.6064	−	3.46337i	−0.483435	−	0.132814i
$681$	−9.06652	−	10.3183i	−0.347430	−	0.395398i
$682$	17.6759	−	12.3214i	0.676845	−	0.471812i
$683$			32.8025i			1.25515i	0.778555	+	0.627577i	$0.215953\pi$
$683$			32.8025i			1.25515i	−0.778555	+	0.627577i	$0.784047\pi$
$684$	−15.6587	+	0.647872i	−0.598724	+	0.0247720i
$685$			0.277382i			0.0105982i
$686$	−0.808719	−	1.16016i	−0.0308770	−	0.0442952i
$687$	−10.9207	+	32.2736i	−0.416651	+	1.23131i
$688$	−37.9871	−	7.02849i	−1.44824	−	0.267958i
$689$	29.6250	−	51.3119i	1.12862	−	1.95483i
$690$	2.60399	−	10.5893i	0.0991322	−	0.403127i
$691$	16.6684	−	9.62349i	0.634095	−	0.366095i	−0.148241	−	0.988951i	$-0.547361\pi$
$691$	16.6684	−	9.62349i	0.634095	−	0.366095i	0.782336	+	0.622856i	$0.214028\pi$
$692$	2.10486	+	12.2384i	0.0800150	+	0.465234i
$693$	6.52863	+	0.846705i	0.248002	+	0.0321637i
$694$	−1.74304	−	20.4180i	−0.0661648	−	0.775057i
$695$	6.89182	+	11.9370i	0.261422	+	0.452796i
$696$	−9.22145	−	6.23321i	−0.349538	−	0.236269i
$697$	−5.05977	+	8.76379i	−0.191653	+	0.331952i
$698$	−0.230823	−	0.108227i	−0.00873679	−	0.00409644i
$699$	−4.36560	−	21.8373i	−0.165122	−	0.825962i
$700$	−5.69124	−	6.84084i	−0.215108	−	0.258559i
$701$		−	47.5011i		−	1.79409i	−0.441938	−	0.897046i	$-0.645709\pi$
$701$		−	47.5011i		−	1.79409i	0.441938	−	0.897046i	$-0.354291\pi$
$702$	−30.8582	+	24.8063i	−1.16467	+	0.936253i
$703$	−20.7959			−0.784333
$704$	8.96908	−	15.0914i	0.338035	−	0.568779i
$705$	−0.926161	+	0.185153i	−0.0348812	+	0.00697328i
$706$	14.4464	−	30.8108i	0.543696	−	1.15958i
$707$	−1.62046	−	0.935571i	−0.0609435	−	0.0351858i
$708$	−5.83280	−	4.71253i	−0.219210	−	0.177108i
$709$	19.2613	−	11.1205i	0.723373	−	0.417640i	−0.0926199	−	0.995702i	$-0.529524\pi$
$709$	19.2613	−	11.1205i	0.723373	−	0.417640i	0.815993	+	0.578062i	$0.196191\pi$
$710$	−0.721231	−	8.44853i	−0.0270673	−	0.317068i
$711$	−5.20796	−	3.98027i	−0.195314	−	0.149272i
$712$	−10.4500	+	2.72946i	−0.391632	+	0.102291i
$713$	−20.8265	−	36.0726i	−0.779960	−	1.35093i
$714$	−14.8163	−	3.64346i	−0.554487	−	0.136353i
$715$	−7.59809	−	4.38676i	−0.284153	−	0.164056i
$716$	12.9473	+	4.77425i	0.483862	+	0.178422i
$717$	26.7839	+	9.06311i	1.00026	+	0.338468i
$718$	21.5056	+	30.8513i	0.802583	+	1.15136i
$719$	9.25229			0.345052			0.172526	−	0.985005i	$-0.444807\pi$
$719$	9.25229			0.345052			0.172526	+	0.985005i	$0.444807\pi$
$720$	5.97311	+	6.60408i	0.222605	+	0.246120i
$721$	−10.0122			−0.372872
$722$	−9.84810	−	14.1278i	−0.366508	−	0.525781i
$723$	−34.3429	+	30.1765i	−1.27723	+	1.12228i
$724$	4.01455	+	1.48035i	0.149199	+	0.0550167i
$725$	−8.75462	−	5.05448i	−0.325139	−	0.187719i
$726$	−4.22247	−	14.5484i	−0.156710	−	0.539942i
$727$	−4.38796	−	7.60016i	−0.162740	−	0.281875i	0.773110	−	0.634272i	$-0.218700\pi$
$727$	−4.38796	−	7.60016i	−0.162740	−	0.281875i	−0.935851	+	0.352397i	$0.885367\pi$
$728$	3.85116	+	14.7446i	0.142733	+	0.546470i
$729$	−10.1880	+	25.0041i	−0.377332	+	0.926078i
$730$	−0.233180	−	2.73148i	−0.00863038	−	0.101097i
$731$	−52.0991	+	30.0794i	−1.92696	+	1.11253i
$732$	−33.2092	+	12.7904i	−1.22745	+	0.472746i
$733$	21.6336	+	12.4901i	0.799054	+	0.461334i	0.843140	−	0.537694i	$-0.180704\pi$
$733$	21.6336	+	12.4901i	0.799054	+	0.461334i	−0.0440863	+	0.999028i	$0.514038\pi$
$734$	−1.39944	+	2.98470i	−0.0516544	+	0.110167i
$735$	0.848368	+	0.965499i	0.0312925	+	0.0356130i
$736$	−27.5936	−	19.7574i	−1.01712	−	0.728266i
$737$	−35.3198			−1.30102
$738$	6.11437	−	3.18157i	0.225073	−	0.117115i
$739$		−	41.1794i		−	1.51481i	−0.652945	−	0.757405i	$-0.726467\pi$
$739$		−	41.1794i		−	1.51481i	0.652945	−	0.757405i	$-0.273533\pi$
$740$	7.55694	+	9.08341i	0.277799	+	0.333913i
$741$	23.0894	+	7.81298i	0.848211	+	0.287017i
$742$	−14.0810	−	6.60220i	−0.516929	−	0.242374i
$743$	13.4767	−	23.3424i	0.494413	−	0.856349i	−0.505566	−	0.862788i	$-0.668716\pi$
$743$	13.4767	−	23.3424i	0.494413	−	0.856349i	0.999979	+	0.00643928i	$0.00204970\pi$
$744$	33.9279	+	2.40617i	1.24386	+	0.0882143i
$745$	2.21235	+	3.83190i	0.0810542	+	0.140390i
$746$	0.373036	+	4.36975i	0.0136578	+	0.159988i
$747$	−2.40965	+	3.15289i	−0.0881646	+	0.115358i
$748$	−4.63380	−	26.9424i	−0.169428	−	0.985113i
$749$	−15.2943	+	8.83015i	−0.558841	+	0.322647i
$750$	12.3935	+	11.8913i	0.452545	+	0.434209i
$751$	−7.23406	+	12.5298i	−0.263975	+	0.457218i	−0.967295	−	0.253656i	$-0.918367\pi$
$751$	−7.23406	+	12.5298i	−0.263975	+	0.457218i	0.703320	+	0.710874i	$0.251700\pi$
$752$	−0.534784	+	2.89036i	−0.0195016	+	0.105401i
$753$	−51.6233	+	10.3203i	−1.88126	+	0.376092i
$754$	9.89976	+	14.2019i	0.360528	+	0.517201i
$755$			2.75961i			0.100432i
$756$	7.17651	+	7.51649i	0.261007	+	0.273372i
$757$			40.6897i			1.47889i	0.673215	+	0.739447i	$0.264913\pi$
$757$			40.6897i			1.47889i	−0.673215	+	0.739447i	$0.735087\pi$
$758$	−13.8280	+	9.63912i	−0.502254	+	0.350109i
$759$	22.3604	−	4.47018i	0.811632	−	0.162257i
$760$	1.45231	−	5.28631i	0.0526808	−	0.191755i
$761$	−21.9728	+	38.0580i	−0.796513	+	1.37960i	0.125361	+	0.992111i	$0.459991\pi$
$761$	−21.9728	+	38.0580i	−0.796513	+	1.37960i	−0.921874	+	0.387489i	$0.873342\pi$
$762$	−23.2327	+	24.2138i	−0.841630	+	0.877173i
$763$	−6.31315	+	3.64490i	−0.228552	+	0.131954i
$764$	−39.8042	+	6.84588i	−1.44007	+	0.247675i
$765$	13.7514	+	1.78344i	0.497183	+	0.0644803i
$766$	−26.3485	+	2.24931i	−0.952009	+	0.0812708i
$767$	5.83148	+	10.1004i	0.210563	+	0.364705i
$768$	25.9848	−	9.63283i	0.937645	−	0.347595i
$769$	23.4008	−	40.5314i	0.843854	−	1.46160i	−0.0427582	−	0.999085i	$-0.513615\pi$
$769$	23.4008	−	40.5314i	0.843854	−	1.46160i	0.886612	−	0.462513i	$-0.153052\pi$
$770$	−0.977630	+	2.08506i	−0.0352313	+	0.0751405i
$771$	28.3871	+	9.60562i	1.02234	+	0.345938i
$772$	12.1736	+	14.6326i	0.438136	+	0.526637i
$773$		−	23.3305i		−	0.839139i	−0.907723	−	0.419570i	$-0.862181\pi$
$773$		−	23.3305i		−	0.839139i	0.907723	−	0.419570i	$-0.137819\pi$
$774$	40.9359	+	1.79456i	1.47141	+	0.0645040i
$775$	30.8915			1.10965
$776$	−34.9444	−	35.3886i	−1.25443	−	1.27038i
$777$	9.10237	+	10.3591i	0.326546	+	0.371631i
$778$	−41.9277	−	19.6588i	−1.50318	−	0.704801i
$779$	−3.67496	−	2.12174i	−0.131669	−	0.0760191i
$780$	−4.97775	−	12.9243i	−0.178232	−	0.462764i
$781$	15.3555	−	8.86548i	0.549461	−	0.317232i
$782$	−52.6574	+	4.49524i	−1.88302	+	0.160749i
$783$	10.6033	+	5.19087i	0.378929	+	0.185507i
$784$	3.77016	−	1.33638i	0.134648	−	0.0477278i
$785$	−4.89476	−	8.47798i	−0.174702	−	0.302592i
$786$	−2.62254	+	0.761154i	−0.0935428	+	0.0271495i
$787$	−16.8349	−	9.71965i	−0.600100	−	0.346468i	0.168981	−	0.985619i	$-0.445952\pi$
$787$	−16.8349	−	9.71965i	−0.600100	−	0.346468i	−0.769081	+	0.639151i	$0.779286\pi$
$788$	−12.4922	−	4.60645i	−0.445016	−	0.164098i
$789$	11.1847	−	9.82780i	0.398185	−	0.349879i
$790$	1.88100	−	1.31120i	0.0669231	−	0.0466504i
$791$	−6.05325			−0.215229
$792$	−7.20112	+	17.1716i	−0.255881	+	0.610165i
$793$	55.3503			1.96555
$794$	−18.3702	+	12.8054i	−0.651935	+	0.454447i
$795$	13.3882	+	4.53031i	0.474832	+	0.160673i
$796$	8.42706	−	22.8533i	0.298689	−	0.810013i
$797$	−28.7000	−	16.5699i	−1.01661	−	0.586937i	−0.103486	−	0.994631i	$-0.533000\pi$
$797$	−28.7000	−	16.5699i	−1.01661	−	0.586937i	−0.913119	+	0.407694i	$0.866333\pi$
$798$	1.52783	−	6.21299i	0.0540845	−	0.219938i
$799$	2.28869	+	3.96412i	0.0809679	+	0.140241i
$800$	22.9219	−	10.3963i	0.810412	−	0.367566i
$801$	10.5753	−	4.40434i	0.373659	−	0.155620i
$802$	−35.3183	+	3.01504i	−1.24713	+	0.106465i
$803$	4.96454	−	2.86628i	0.175195	−	0.101149i
$804$	−43.3692	−	35.0396i	−1.52952	−	1.23575i
$805$	3.85541	+	2.22592i	0.135885	+	0.0784534i
$806$	−47.8985	−	22.4583i	−1.68715	−	0.791061i
$807$	7.49766	−	1.49889i	0.263930	−	0.0527635i
$808$	3.76584	−	3.71857i	0.132482	−	0.130819i
$809$	10.8447			0.381281			0.190640	−	0.981660i	$-0.438944\pi$
$809$	10.8447			0.381281			0.190640	+	0.981660i	$0.438944\pi$
$810$	−7.24573	−	6.05829i	−0.254589	−	0.212867i
$811$		−	2.77391i		−	0.0974051i	−0.998813	−	0.0487026i	$-0.984491\pi$
$811$		−	2.77391i		−	0.0974051i	0.998813	−	0.0487026i	$-0.0155086\pi$
$812$	3.49318	−	2.90615i	0.122587	−	0.101986i
$813$	2.20913	+	11.0504i	0.0774776	+	0.387553i
$814$	−10.4893	+	22.3712i	−0.367648	+	0.784110i
$815$	0.456472	−	0.790634i	0.0159895	−	0.0276947i
$816$	21.0388	−	37.6796i	0.736506	−	1.31905i
$817$	−12.6133	−	21.8469i	−0.441285	−	0.764328i
$818$	5.07139	−	0.432933i	0.177317	−	0.0151371i
$819$	−6.21434	−	14.9213i	−0.217147	−	0.521392i
$820$	0.408677	+	2.37618i	0.0142716	+	0.0829800i
$821$	−11.5137	+	6.64743i	−0.401830	+	0.231997i	−0.687273	−	0.726399i	$-0.741193\pi$
$821$	−11.5137	+	6.64743i	−0.401830	+	0.231997i	0.285443	+	0.958396i	$0.407859\pi$
$822$	−0.889142	−	0.218647i	−0.0310124	−	0.00762620i
$823$	−5.66710	+	9.81571i	−0.197543	+	0.342154i	−0.947731	−	0.319070i	$-0.896629\pi$
$823$	−5.66710	+	9.81571i	−0.197543	+	0.342154i	0.750188	+	0.661224i	$0.229963\pi$
$824$	7.50202	−	27.3069i	0.261345	−	0.951280i
$825$	−5.42056	+	16.0192i	−0.188720	+	0.557717i
$826$	2.51136	−	1.75061i	0.0873815	−	0.0609114i
$827$			1.64353i			0.0571512i	0.999592	+	0.0285756i	$0.00909714\pi$
$827$			1.64353i			0.0571512i	−0.999592	+	0.0285756i	$0.990903\pi$
$828$	31.8911	+	16.6941i	1.10829	+	0.580159i
$829$			38.1735i			1.32582i	0.748698	+	0.662911i	$0.230679\pi$
$829$			38.1735i			1.32582i	−0.748698	+	0.662911i	$0.769321\pi$
$830$	−0.793800	−	1.13876i	−0.0275532	−	0.0395269i
$831$	13.8039	+	15.7098i	0.478852	+	0.544965i
$832$	−43.0996	−	0.544444i	−1.49421	−	0.0188752i
$833$	3.11447	−	5.39442i	0.107910	−	0.186906i
$834$	−43.6963	+	12.6822i	−1.51308	+	0.439149i
$835$	13.0049	−	7.50839i	0.450054	−	0.259839i
$836$	11.2979	−	1.94311i	0.390746	−	0.0672038i
$837$	−35.9921	+	2.46363i	−1.24407	+	0.0851554i
$838$	0.478207	+	5.60174i	0.0165194	+	0.193509i
$839$	1.91381	+	3.31482i	0.0660721	+	0.114440i	0.897169	−	0.441687i	$-0.145620\pi$
$839$	1.91381	+	3.31482i	0.0660721	+	0.114440i	−0.831097	+	0.556128i	$0.812287\pi$
$840$	−3.26895	+	1.59038i	−0.112790	+	0.0548732i
$841$	−11.9190	+	20.6443i	−0.411000	+	0.711873i
$842$	−14.9690	−	7.01856i	−0.515865	−	0.241875i
$843$	20.2358	−	17.7809i	0.696959	−	0.612407i
$844$	−9.61249	+	7.99711i	−0.330875	+	0.275272i
$845$			11.8945i			0.409184i
$846$	0.136544	−	3.11474i	0.00469449	−	0.107087i
$847$	6.18446			0.212501
$848$	28.5574	−	33.4571i	0.980665	−	1.14892i
$849$	11.6892	−	34.5447i	0.401173	−	1.18557i
$850$	16.6391	−	35.4875i	0.570717	−	1.21721i
$851$	41.3657	+	23.8825i	1.41800	+	0.818682i
$852$	27.6501	+	4.34769i	0.947277	+	0.148949i
$853$	15.0826	−	8.70792i	0.516417	−	0.298153i	−0.219051	−	0.975714i	$-0.570296\pi$
$853$	15.0826	−	8.70792i	0.516417	−	0.298153i	0.735467	+	0.677560i	$0.236963\pi$
$854$	−1.23576	−	14.4757i	−0.0422868	−	0.495349i
$855$	−0.747856	+	5.76644i	−0.0255761	+	0.197208i
$856$	−12.6233	−	48.3296i	−0.431454	−	1.65187i
$857$	7.29559	+	12.6363i	0.249213	+	0.431649i	0.963308	−	0.268400i	$-0.0864949\pi$
$857$	7.29559	+	12.6363i	0.249213	+	0.431649i	−0.714095	+	0.700049i	$0.753162\pi$
$858$	20.0509	−	20.8976i	0.684526	−	0.713434i
$859$	−7.16806	−	4.13848i	−0.244571	−	0.141203i	0.372705	−	0.927950i	$-0.378430\pi$
$859$	−7.16806	−	4.13848i	−0.244571	−	0.141203i	−0.617276	+	0.786747i	$0.711764\pi$
$860$	−4.95898	+	13.4482i	−0.169100	+	0.458580i
$861$	0.551624	+	2.75929i	0.0187993	+	0.0940365i
$862$	15.5537	+	22.3128i	0.529761	+	0.759978i
$863$	4.50001			0.153182			0.0765911	−	0.997063i	$-0.475596\pi$
$863$	4.50001			0.153182			0.0765911	+	0.997063i	$0.475596\pi$
$864$	−25.8776	+	13.9410i	−0.880373	+	0.474282i
$865$	4.60742			0.156657
$866$	7.12319	+	10.2187i	0.242056	+	0.347245i
$867$	−7.40197	−	37.0256i	−0.251384	−	1.25746i
$868$	−4.80412	+	13.0283i	−0.163062	+	0.442208i
$869$	4.15232	+	2.39735i	0.140858	+	0.0813244i
$870$	−2.85914	+	2.97988i	−0.0969340	+	0.101028i
$871$	43.3595	+	75.1008i	1.46918	+	2.54469i
$872$	−5.21061	−	19.9494i	−0.176454	−	0.675573i
$873$	41.9119	+	32.0319i	1.41850	+	1.08412i
$874$	−1.88501	−	22.0810i	−0.0637613	−	0.746902i
$875$	−6.07249	+	3.50595i	−0.205287	+	0.118523i
$876$	8.93950	+	1.40564i	0.302038	+	0.0474923i
$877$	0.995012	+	0.574470i	0.0335992	+	0.0193985i	0.516705	−	0.856163i	$-0.327158\pi$
$877$	0.995012	+	0.574470i	0.0335992	+	0.0193985i	−0.483106	+	0.875562i	$0.660492\pi$
$878$	1.89090	−	4.03286i	0.0638147	−	0.136102i
$879$	−14.4383	+	42.6688i	−0.486990	+	1.43918i
$880$	−4.95422	−	4.22868i	−0.167007	−	0.142549i
$881$	32.7534			1.10349			0.551744	−	0.834013i	$-0.313962\pi$
$881$	32.7534			1.10349			0.551744	+	0.834013i	$0.313962\pi$
$882$	−3.76361	+	1.95837i	−0.126727	+	0.0659417i
$883$		−	25.1351i		−	0.845864i	−0.906161	−	0.422932i	$-0.861001\pi$
$883$		−	25.1351i		−	0.845864i	0.906161	−	0.422932i	$-0.138999\pi$
$884$	−51.5993	+	42.9281i	−1.73547	+	1.44383i
$885$	−2.08998	+	1.83643i	−0.0702540	+	0.0617311i
$886$	23.2911	+	10.9206i	0.782479	+	0.366883i
$887$	10.8987	−	18.8771i	0.365942	−	0.633830i	−0.622985	−	0.782234i	$-0.714080\pi$
$887$	10.8987	−	18.8771i	0.365942	−	0.633830i	0.988927	+	0.148404i	$0.0474136\pi$
$888$	−35.0735	+	17.0636i	−1.17699	+	0.572616i
$889$	−6.84977	−	11.8641i	−0.229734	−	0.397911i
$890$	0.340854	+	3.99278i	0.0114255	+	0.133838i
$891$	5.03804	−	19.0965i	0.168781	−	0.639757i
$892$	−7.73339	+	1.33006i	−0.258933	+	0.0445336i
$893$	−1.66229	+	0.959725i	−0.0556265	+	0.0321160i
$894$	−14.0270	+	4.07113i	−0.469132	+	0.136159i
$895$	2.55997	−	4.43401i	0.0855705	−	0.148212i
$896$	0.819860	+	11.2840i	0.0273896	+	0.376971i
$897$	−36.9552	−	42.0574i	−1.23390	−	1.40426i
$898$	21.4374	+	30.7534i	0.715377	+	1.02626i
$899$			15.7743i			0.526102i
$900$	−22.5480	+	14.2924i	−0.751600	+	0.476414i
$901$		−	68.4990i		−	2.28203i
$902$	−4.13607	+	2.88315i	−0.137716	+	0.0959983i
$903$	−5.36179	+	15.8455i	−0.178429	+	0.527305i
$904$	4.53565	−	16.5095i	0.150853	−	0.549097i
$905$	0.793769	−	1.37485i	0.0263858	−	0.0457015i
$906$	−8.84586	−	2.17527i	−0.293884	−	0.0722685i
$907$	−25.5221	+	14.7352i	−0.847449	+	0.489275i	−0.859789	−	0.510649i	$-0.829405\pi$
$907$	−25.5221	+	14.7352i	−0.847449	+	0.489275i	0.0123405	+	0.999924i	$0.496072\pi$
$908$	2.68838	+	15.6311i	0.0892169	+	0.518737i
$909$	−3.40864	+	4.46001i	−0.113058	+	0.147929i
$910$	5.63365	−	0.480931i	0.186754	−	0.0159427i
$911$	−11.9420	−	20.6841i	−0.395654	−	0.685294i	0.597530	−	0.801847i	$-0.296149\pi$
$911$	−11.9420	−	20.6841i	−0.395654	−	0.685294i	−0.993184	+	0.116553i	$0.962816\pi$
$912$	15.8004	+	8.82229i	0.523202	+	0.292135i
$913$	1.45135	−	2.51381i	0.0480327	−	0.0831951i
$914$	−14.5243	+	30.9770i	−0.480421	+	1.02463i
$915$	2.58840	+	12.9475i	0.0855700	+	0.428032i
$916$	30.2439	−	25.1614i	0.999287	−	0.831357i
$917$		−	1.11483i		−	0.0368149i
$918$	−16.5564	+	42.6740i	−0.546441	+	1.40845i
$919$	−1.05674			−0.0348586			−0.0174293	−	0.999848i	$-0.505548\pi$
$919$	−1.05674			−0.0348586			−0.0174293	+	0.999848i	$0.505548\pi$
$920$	−8.95974	+	8.84728i	−0.295394	+	0.291686i
$921$	26.8982	−	5.37735i	0.886326	−	0.177190i
$922$	34.0722	+	15.9755i	1.12211	+	0.526127i
$923$	−37.7014	−	21.7669i	−1.24096	−	0.716468i
$924$	−5.91300	−	4.77733i	−0.194524	−	0.157163i
$925$	−30.6783	+	17.7122i	−1.00870	+	0.582372i
$926$	0.221222	−	0.0188852i	0.00726980	−	0.000620606i
$927$	−3.86311	+	29.7870i	−0.126881	+	0.978334i
$928$	5.30875	+	11.7048i	0.174268	+	0.384227i
$929$	−21.4926	−	37.2263i	−0.705150	−	1.22136i	−0.966637	−	0.256149i	$-0.917546\pi$
$929$	−21.4926	−	37.2263i	−0.705150	−	1.22136i	0.261487	−	0.965207i	$-0.415787\pi$
$930$	3.01352	−	12.2546i	0.0988171	−	0.401845i
$931$	2.26207	+	1.30600i	0.0741362	+	0.0428026i
$932$	−8.89653	+	24.1265i	−0.291416	+	0.790289i
$933$	−22.0972	−	7.47724i	−0.723430	−	0.244794i
$934$	−22.2331	+	15.4981i	−0.727489	+	0.507114i
$935$	−10.1431			−0.331715
$936$	45.3523	−	5.76843i	1.48239	−	0.188547i
$937$	−41.0728			−1.34179			−0.670894	−	0.741553i	$-0.734090\pi$
$937$	−41.0728			−1.34179			−0.670894	+	0.741553i	$0.734090\pi$
$938$	18.6730	−	13.0165i	0.609696	−	0.425003i
$939$	11.3668	−	9.98782i	0.370941	−	0.325940i
$940$	1.02325	+	0.377319i	0.0333747	+	0.0123068i
$941$	−9.04544	−	5.22239i	−0.294873	−	0.170245i	0.345264	−	0.938505i	$-0.387789\pi$
$941$	−9.04544	−	5.22239i	−0.294873	−	0.170245i	−0.640137	+	0.768260i	$0.721123\pi$
$942$	31.0343	−	9.00726i	1.01115	−	0.293472i
$943$	4.87330	+	8.44081i	0.158697	+	0.274870i
$944$	2.89282	+	8.16114i	0.0941532	+	0.265622i
$945$	3.19978	−	2.15144i	0.104089	−	0.0699862i
$946$	−29.8639	+	2.54941i	−0.970959	+	0.0828885i
$947$	34.7928	−	20.0876i	1.13061	−	0.652759i	0.186524	−	0.982450i	$-0.440278\pi$
$947$	34.7928	−	20.0876i	1.13061	−	0.652759i	0.944089	+	0.329691i	$0.106945\pi$
$948$	2.72032	+	7.06308i	0.0883518	+	0.229398i
$949$	−12.1892	−	7.03743i	−0.395678	−	0.228445i
$950$	14.8811	+	6.97736i	0.482807	+	0.226375i
$951$	27.7163	+	31.5430i	0.898762	+	1.02285i
$952$	12.3790	+	12.5363i	0.401204	+	0.406304i
$953$	57.5735			1.86499			0.932494	−	0.361185i	$-0.117628\pi$
$953$	57.5735			1.86499			0.932494	+	0.361185i	$0.117628\pi$
$954$	−25.0751	+	39.3447i	−0.811837	+	1.27383i
$955$			14.9852i			0.484910i
$956$	−20.8815	−	25.0995i	−0.675356	−	0.811775i
$957$	−8.17998	−	2.76794i	−0.264421	−	0.0894747i
$958$	7.50695	−	16.0106i	0.242538	−	0.517279i
$959$	0.186902	−	0.323724i	0.00603539	−	0.0104536i
$960$	−1.88815	−	10.1073i	−0.0609399	−	0.326212i
$961$	−8.60191	−	14.8989i	−0.277481	−	0.480611i
$962$	60.4449	−	5.16004i	1.94882	−	0.166366i
$963$	20.3693	+	48.9088i	0.656391	+	1.57606i
$964$	52.0257	−	8.94784i	1.67564	−	0.288191i
$965$	6.11607	−	3.53112i	0.196883	−	0.113671i
$966$	−10.1742	+	10.6038i	−0.327349	+	0.341173i
$967$	21.4406	−	37.1362i	0.689483	−	1.19422i	−0.282522	−	0.959261i	$-0.591171\pi$
$967$	21.4406	−	37.1362i	0.689483	−	1.19422i	0.972005	−	0.234959i	$-0.0754956\pi$
$968$	−4.63396	+	16.8673i	−0.148941	+	0.542136i
$969$	27.6338	−	5.52440i	0.887725	−	0.177469i
$970$	−15.1377	+	10.5521i	−0.486042	+	0.338808i
$971$			46.1913i			1.48235i	0.671313	+	0.741174i	$0.265731\pi$
$971$			46.1913i			1.48235i	−0.671313	+	0.741174i	$0.734269\pi$
$972$	25.1312	−	18.4506i	0.806083	−	0.591802i
$973$		−	18.5751i		−	0.595490i
$974$	17.3319	+	24.8638i	0.555350	+	0.796686i
$975$	40.7161	−	8.13976i	1.30396	−	0.260681i
$976$	40.4067	+	7.47616i	1.29339	+	0.239306i
$977$	8.43665	−	14.6127i	0.269912	−	0.467502i	−0.698926	−	0.715194i	$-0.746339\pi$
$977$	8.43665	−	14.6127i	0.269912	−	0.467502i	0.968839	+	0.247691i	$0.0796719\pi$
$978$	2.17454	+	2.08643i	0.0695342	+	0.0667167i
$979$	−7.25699	+	4.18982i	−0.231934	+	0.133907i
$980$	−0.251555	−	1.46263i	−0.00803564	−	0.0467219i
$981$	8.40801	+	20.1885i	0.268447	+	0.644570i
$982$	4.49171	+	52.6161i	0.143336	+	1.67905i
$983$	17.6117	+	30.5043i	0.561725	+	0.972936i	0.997346	+	0.0728057i	$0.0231953\pi$
$983$	17.6117	+	30.5043i	0.561725	+	0.972936i	−0.435622	+	0.900130i	$0.643471\pi$
$984$	−7.93895	−	0.563030i	−0.253084	−	0.0179487i
$985$	−2.47000	+	4.27816i	−0.0787006	+	0.136314i
$986$	18.1212	+	8.49654i	0.577096	+	0.270585i
$987$	1.20565	+	0.407968i	0.0383764	+	0.0129858i
$988$	−18.0012	−	21.6374i	−0.572695	−	0.688376i
$989$			57.9418i			1.84244i
$990$	5.82603	+	3.71304i	0.185163	+	0.118008i
$991$	2.89177			0.0918600			0.0459300	−	0.998945i	$-0.485375\pi$
$991$	2.89177			0.0918600			0.0459300	+	0.998945i	$0.485375\pi$
$992$	−31.9333	−	22.8646i	−1.01388	−	0.725951i
$993$	−27.0338	−	30.7663i	−0.857892	−	0.976338i
$994$	−4.85096	+	10.3460i	−0.153863	+	0.328155i
$995$	−7.82649	−	4.51862i	−0.248116	−	0.143250i
$996$	4.27598	−	1.64688i	0.135490	−	0.0521833i
$997$	−8.88165	+	5.12782i	−0.281285	+	0.162400i	−0.634005	−	0.773329i	$-0.718590\pi$
$997$	−8.88165	+	5.12782i	−0.281285	+	0.162400i	0.352720	+	0.935729i	$0.385257\pi$
$998$	−0.227246	−	2.66197i	−0.00719336	−	0.0842633i
$999$	34.3313	−	23.0833i	1.08619	−	0.730325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.12	✓	72
8.5	even	2	inner	504.2.cs.b.85.13	yes	72
9.7	even	3	inner	504.2.cs.b.421.13	yes	72
72.61	even	6	inner	504.2.cs.b.421.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.12	✓	72	1.1	even	1	trivial
504.2.cs.b.85.13	yes	72	8.5	even	2	inner
504.2.cs.b.421.12	yes	72	72.61	even	6	inner
504.2.cs.b.421.13	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.808719 - 1.16016i) q^{2} +(-0.339544 - 1.69844i) q^{3} +(-0.691947 + 1.87649i) q^{4} +(0.642635 + 0.371025i) q^{5} +(-1.69587 + 1.76749i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.73662 - 0.714781i) q^{8} +(-2.76942 + 1.15339i) q^{9} +O(q^{10})\)	\(q+(-0.808719 - 1.16016i) q^{2} +(-0.339544 - 1.69844i) q^{3} +(-0.691947 + 1.87649i) q^{4} +(0.642635 + 0.371025i) q^{5} +(-1.69587 + 1.76749i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.73662 - 0.714781i) q^{8} +(-2.76942 + 1.15339i) q^{9} +(-0.0892617 - 1.04561i) q^{10} +(1.90044 - 1.09722i) q^{11} +(3.42206 + 0.538083i) q^{12} +(-4.66604 - 2.69394i) q^{13} +(-0.600369 + 1.28045i) q^{14} +(0.411963 - 1.21746i) q^{15} +(-3.04242 - 2.59686i) q^{16} -6.22894 q^{17} +(3.57780 + 2.28020i) q^{18} -2.61201i q^{19} +(-1.14089 + 0.949166i) q^{20} +(-1.30112 + 1.14328i) q^{21} +(-2.80987 - 1.31747i) q^{22} +(-2.99969 + 5.19562i) q^{23} +(-2.14322 - 4.40529i) q^{24} +(-2.22468 - 3.85326i) q^{25} +(0.648111 + 7.59200i) q^{26} +(2.89931 + 4.31207i) q^{27} +(1.97106 - 0.339000i) q^{28} +(1.96761 - 1.13600i) q^{29} +(-1.74561 + 0.506638i) q^{30} +(-3.47145 + 6.01273i) q^{31} +(-0.552318 + 5.62983i) q^{32} +(-2.50884 - 2.85523i) q^{33} +(5.03746 + 7.22658i) q^{34} -0.742050i q^{35} +(-0.248036 - 5.99487i) q^{36} -7.96166i q^{37} +(-3.03035 + 2.11238i) q^{38} +(-2.99118 + 8.83972i) q^{39} +(2.02385 + 0.556012i) q^{40} +(0.812301 - 1.40695i) q^{41} +(2.37863 + 0.584924i) q^{42} +(8.36404 - 4.82898i) q^{43} +(0.743914 + 4.32536i) q^{44} +(-2.20766 - 0.286314i) q^{45} +(8.45366 - 0.721669i) q^{46} +(-0.367428 - 0.636404i) q^{47} +(-3.37759 + 6.04912i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.67126 + 5.69719i) q^{50} +(2.11500 + 10.5795i) q^{51} +(8.28380 - 6.89171i) q^{52} +10.9969i q^{53} +(2.65797 - 6.85093i) q^{54} +1.62838 q^{55} +(-1.98733 - 2.01259i) q^{56} +(-4.43635 + 0.886892i) q^{57} +(-2.90919 - 1.36404i) q^{58} +(-1.87466 - 1.08233i) q^{59} +(1.99949 + 1.61546i) q^{60} +(-8.89678 + 5.13656i) q^{61} +(9.78316 - 0.835165i) q^{62} +(2.38358 + 1.82169i) q^{63} +(6.97818 - 3.91217i) q^{64} +(-1.99904 - 3.46244i) q^{65} +(-1.28358 + 5.21974i) q^{66} +(-13.9388 - 8.04760i) q^{67} +(4.31010 - 11.6885i) q^{68} +(9.84299 + 3.33066i) q^{69} +(-0.860898 + 0.600110i) q^{70} +8.07997 q^{71} +(-6.75442 + 5.13593i) q^{72} +2.61232 q^{73} +(-9.23681 + 6.43875i) q^{74} +(-5.78917 + 5.08685i) q^{75} +(4.90141 + 1.80737i) q^{76} +(-1.90044 - 1.09722i) q^{77} +(12.6745 - 3.67860i) q^{78} +(1.09247 + 1.89221i) q^{79} +(-0.991661 - 2.79765i) q^{80} +(6.33937 - 6.38846i) q^{81} +(-2.28921 + 0.195424i) q^{82} +(1.14554 - 0.661378i) q^{83} +(-1.24503 - 3.23263i) q^{84} +(-4.00293 - 2.31110i) q^{85} +(-12.3666 - 5.79835i) q^{86} +(-2.59753 - 2.95616i) q^{87} +(4.41650 - 4.36106i) q^{88} -3.81859 q^{89} +(1.45321 + 2.79279i) q^{90} +5.38788i q^{91} +(-7.67389 - 9.22398i) q^{92} +(11.3910 + 3.85447i) q^{93} +(-0.441185 + 0.940947i) q^{94} +(0.969121 - 1.67857i) q^{95} +(9.74948 - 0.973494i) q^{96} +(-8.79181 - 15.2279i) q^{97} +(1.40909 - 0.120291i) q^{98} +(-3.99758 + 5.23060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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