LMFDB - Embedded newform 630.2.r.b.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3, 1]))

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

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

chi := DirichletCharacter("630.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	630.59
Dual form			630.2.r.b.299.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.60626 + 0.648019i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 + 1.71507i) q^{6} +(-1.47445 + 2.19682i) q^{7} -1.00000 q^{8} +(2.16014 - 2.08177i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.60626 + 0.648019i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 + 1.71507i) q^{6} +(-1.47445 + 2.19682i) q^{7} -1.00000 q^{8} +(2.16014 - 2.08177i) q^{9} +(-0.381768 + 2.20324i) q^{10} -3.61095i q^{11} +(1.36433 + 1.06705i) q^{12} +(1.68621 - 2.92060i) q^{13} +(1.16527 + 2.37532i) q^{14} +(2.87183 - 2.59858i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.40634 + 3.69870i) q^{17} +(-0.722799 - 2.91163i) q^{18} +(-4.15471 + 2.39873i) q^{19} +(1.71718 + 1.43224i) q^{20} +(0.944768 - 4.48413i) q^{21} +(-3.12718 - 1.80548i) q^{22} +7.98909 q^{23} +(1.60626 - 0.648019i) q^{24} +(3.81112 - 3.23656i) q^{25} +(-1.68621 - 2.92060i) q^{26} +(-2.12072 + 4.74368i) q^{27} +(2.63972 + 0.178501i) q^{28} +(7.66188 - 4.42359i) q^{29} +(-0.814522 - 3.78636i) q^{30} +(5.58511 - 3.22456i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.33997 + 5.80013i) q^{33} +(6.40634 - 3.69870i) q^{34} +(1.40104 - 5.74779i) q^{35} +(-2.88294 - 0.829851i) q^{36} +(-5.56251 + 3.21152i) q^{37} +4.79745i q^{38} +(-0.815885 + 5.78394i) q^{39} +(2.09894 - 0.770998i) q^{40} +(1.31158 - 2.27173i) q^{41} +(-3.41099 - 3.06026i) q^{42} +(0.660123 - 0.381122i) q^{43} +(-3.12718 + 1.80548i) q^{44} +(-2.92897 + 6.03499i) q^{45} +(3.99454 - 6.91875i) q^{46} +(-7.12570 - 4.11402i) q^{47} +(0.241929 - 1.71507i) q^{48} +(-2.65201 - 6.47818i) q^{49} +(-0.897383 - 4.91881i) q^{50} +(-12.6871 - 1.78965i) q^{51} -3.37242 q^{52} +(-1.47706 + 2.55834i) q^{53} +(3.04779 + 4.20844i) q^{54} +(2.78404 + 7.57918i) q^{55} +(1.47445 - 2.19682i) q^{56} +(5.11913 - 6.54531i) q^{57} -8.84718i q^{58} +(0.562645 + 0.974530i) q^{59} +(-3.68635 - 1.18779i) q^{60} +(1.45633 + 0.840811i) q^{61} -6.44913i q^{62} +(1.38826 + 7.81490i) q^{63} +1.00000 q^{64} +(-1.28748 + 7.43024i) q^{65} +(6.19304 + 0.873594i) q^{66} +(-4.11272 + 2.37448i) q^{67} -7.39740i q^{68} +(-12.8325 + 5.17708i) q^{69} +(-4.27721 - 4.08723i) q^{70} -1.40979i q^{71} +(-2.16014 + 2.08177i) q^{72} +(2.78262 - 4.81964i) q^{73} +6.42303i q^{74} +(-4.02430 + 7.66844i) q^{75} +(4.15471 + 2.39873i) q^{76} +(7.93260 + 5.32416i) q^{77} +(4.60109 + 3.59855i) q^{78} +(-0.0862526 + 0.149394i) q^{79} +(0.381768 - 2.20324i) q^{80} +(0.332429 - 8.99386i) q^{81} +(-1.31158 - 2.27173i) q^{82} +(11.5262 - 6.65467i) q^{83} +(-4.35575 + 1.42387i) q^{84} +(-16.2982 - 2.82409i) q^{85} -0.762245i q^{86} +(-9.44040 + 12.0705i) q^{87} +3.61095i q^{88} +(7.08044 + 12.2637i) q^{89} +(3.76197 + 5.55406i) q^{90} +(3.92979 + 8.01056i) q^{91} +(-3.99454 - 6.91875i) q^{92} +(-6.88156 + 8.79875i) q^{93} +(-7.12570 + 4.11402i) q^{94} +(6.87110 - 8.23806i) q^{95} +(-1.36433 - 1.06705i) q^{96} +(4.18720 + 7.25244i) q^{97} +(-6.93627 - 0.942388i) q^{98} +(-7.51719 - 7.80017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.60626	+	0.648019i	−0.927375	+	0.374134i
$3$	−1.60626	+	0.648019i	−0.927375	+	0.374134i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.09894	+	0.770998i	−0.938676	+	0.344801i
$5$	−2.09894	+	0.770998i	−0.938676	+	0.344801i
$6$	−0.241929	+	1.71507i	−0.0987671	+	0.700175i
$7$	−1.47445	+	2.19682i	−0.557289	+	0.830319i
$7$	−1.47445	+	2.19682i	−0.557289	+	0.830319i
$8$	−1.00000			−0.353553
$9$	2.16014	−	2.08177i	0.720047	−	0.693925i
$10$	−0.381768	+	2.20324i	−0.120726	+	0.696725i
$11$		−	3.61095i		−	1.08874i	−0.838844	−	0.544372i	$-0.816768\pi$
$11$		−	3.61095i		−	1.08874i	0.838844	−	0.544372i	$-0.183232\pi$
$12$	1.36433	+	1.06705i	0.393848	+	0.308031i
$13$	1.68621	−	2.92060i	0.467670	−	0.810028i	−0.531647	−	0.846966i	$-0.678427\pi$
$13$	1.68621	−	2.92060i	0.467670	−	0.810028i	0.999318	+	0.0369373i	$0.0117602\pi$
$14$	1.16527	+	2.37532i	0.311433	+	0.634830i
$15$	2.87183	−	2.59858i	0.741502	−	0.670950i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.40634	+	3.69870i	1.55377	+	0.897067i	0.997830	+	0.0658408i	$0.0209729\pi$
$17$	6.40634	+	3.69870i	1.55377	+	0.897067i	0.555935	+	0.831226i	$0.312360\pi$
$18$	−0.722799	−	2.91163i	−0.170365	−	0.686277i
$19$	−4.15471	+	2.39873i	−0.953157	+	0.550305i	−0.894060	−	0.447947i	$-0.852155\pi$
$19$	−4.15471	+	2.39873i	−0.953157	+	0.550305i	−0.0590966	+	0.998252i	$0.518822\pi$
$20$	1.71718	+	1.43224i	0.383972	+	0.320258i
$21$	0.944768	−	4.48413i	0.206165	−	0.978517i
$22$	−3.12718	−	1.80548i	−0.666716	−	0.384929i
$23$	7.98909			1.66584			0.832920	−	0.553394i	$-0.186667\pi$
$23$	7.98909			1.66584			0.832920	+	0.553394i	$0.186667\pi$
$24$	1.60626	−	0.648019i	0.327876	−	0.132276i
$25$	3.81112	−	3.23656i	0.762225	−	0.647312i
$26$	−1.68621	−	2.92060i	−0.330693	−	0.572777i
$27$	−2.12072	+	4.74368i	−0.408133	+	0.912923i
$28$	2.63972	+	0.178501i	0.498861	+	0.0337336i
$29$	7.66188	−	4.42359i	1.42278	−	0.821440i	0.426240	−	0.904610i	$-0.359838\pi$
$29$	7.66188	−	4.42359i	1.42278	−	0.821440i	0.996535	+	0.0831703i	$0.0265045\pi$
$30$	−0.814522	−	3.78636i	−0.148711	−	0.691292i
$31$	5.58511	−	3.22456i	1.00312	−	0.579149i	0.0939467	−	0.995577i	$-0.470052\pi$
$31$	5.58511	−	3.22456i	1.00312	−	0.579149i	0.909169	+	0.416428i	$0.136718\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.33997	+	5.80013i	0.407336	+	1.00967i
$34$	6.40634	−	3.69870i	1.09868	−	0.634322i
$35$	1.40104	−	5.74779i	0.236819	−	0.971554i
$36$	−2.88294	−	0.829851i	−0.480490	−	0.138308i
$37$	−5.56251	+	3.21152i	−0.914471	+	0.527970i	−0.881867	−	0.471498i	$-0.843713\pi$
$37$	−5.56251	+	3.21152i	−0.914471	+	0.527970i	−0.0326040	+	0.999468i	$0.510380\pi$
$38$			4.79745i			0.778249i
$39$	−0.815885	+	5.78394i	−0.130646	+	0.926171i
$40$	2.09894	−	0.770998i	0.331872	−	0.121905i
$41$	1.31158	−	2.27173i	0.204835	−	0.354785i	−0.745245	−	0.666791i	$-0.767668\pi$
$41$	1.31158	−	2.27173i	0.204835	−	0.354785i	0.950080	+	0.312006i	$0.101001\pi$
$42$	−3.41099	−	3.06026i	−0.526327	−	0.472208i
$43$	0.660123	−	0.381122i	0.100668	−	0.0581206i	−0.448821	−	0.893622i	$-0.648156\pi$
$43$	0.660123	−	0.381122i	0.100668	−	0.0581206i	0.549489	+	0.835501i	$0.314823\pi$
$44$	−3.12718	+	1.80548i	−0.471440	+	0.272186i
$45$	−2.92897	+	6.03499i	−0.436625	+	0.899643i
$46$	3.99454	−	6.91875i	0.588963	−	1.02011i
$47$	−7.12570	−	4.11402i	−1.03939	−	0.600092i	−0.119730	−	0.992807i	$-0.538203\pi$
$47$	−7.12570	−	4.11402i	−1.03939	−	0.600092i	−0.919660	+	0.392714i	$0.871536\pi$
$48$	0.241929	−	1.71507i	0.0349194	−	0.247549i
$49$	−2.65201	−	6.47818i	−0.378858	−	0.925455i
$50$	−0.897383	−	4.91881i	−0.126909	−	0.695625i
$51$	−12.6871	−	1.78965i	−1.77655	−	0.250600i
$52$	−3.37242			−0.467670
$53$	−1.47706	+	2.55834i	−0.202889	+	0.351415i	−0.949458	−	0.313893i	$-0.898367\pi$
$53$	−1.47706	+	2.55834i	−0.202889	+	0.351415i	0.746569	+	0.665308i	$0.231700\pi$
$54$	3.04779	+	4.20844i	0.414752	+	0.572696i
$55$	2.78404	+	7.57918i	0.375399	+	1.02198i
$56$	1.47445	−	2.19682i	0.197031	−	0.293562i
$57$	5.11913	−	6.54531i	0.678045	−	0.866948i
$58$		−	8.84718i		−	1.16169i
$59$	0.562645	+	0.974530i	0.0732502	+	0.126873i	0.900324	−	0.435220i	$-0.143330\pi$
$59$	0.562645	+	0.974530i	0.0732502	+	0.126873i	−0.827074	+	0.562093i	$0.809996\pi$
$60$	−3.68635	−	1.18779i	−0.475906	−	0.153342i
$61$	1.45633	+	0.840811i	0.186464	+	0.107655i	0.590326	−	0.807165i	$-0.298999\pi$
$61$	1.45633	+	0.840811i	0.186464	+	0.107655i	−0.403862	+	0.914820i	$0.632333\pi$
$62$		−	6.44913i		−	0.819040i
$63$	1.38826	+	7.81490i	0.174904	+	0.984585i
$64$	1.00000			0.125000
$65$	−1.28748	+	7.43024i	−0.159692	+	0.921607i
$66$	6.19304	+	0.873594i	0.762311	+	0.107532i
$67$	−4.11272	+	2.37448i	−0.502448	+	0.290089i	−0.729724	−	0.683742i	$-0.760351\pi$
$67$	−4.11272	+	2.37448i	−0.502448	+	0.290089i	0.227276	+	0.973830i	$0.427018\pi$
$68$		−	7.39740i		−	0.897067i
$69$	−12.8325	+	5.17708i	−1.54486	+	0.623247i
$70$	−4.27721	−	4.08723i	−0.511224	−	0.488518i
$71$		−	1.40979i		−	0.167311i	−0.996495	−	0.0836554i	$-0.973341\pi$
$71$		−	1.40979i		−	0.167311i	0.996495	−	0.0836554i	$-0.0266595\pi$
$72$	−2.16014	+	2.08177i	−0.254575	+	0.245339i
$73$	2.78262	−	4.81964i	0.325681	−	0.564096i	−0.655969	−	0.754788i	$-0.727740\pi$
$73$	2.78262	−	4.81964i	0.325681	−	0.564096i	0.981650	+	0.190692i	$0.0610731\pi$
$74$			6.42303i			0.746662i
$75$	−4.02430	+	7.66844i	−0.464686	+	0.885475i
$76$	4.15471	+	2.39873i	0.476578	+	0.275153i
$77$	7.93260	+	5.32416i	0.904004	+	0.606745i
$78$	4.60109	+	3.59855i	0.520971	+	0.407455i
$79$	−0.0862526	+	0.149394i	−0.00970417	+	0.0168081i	−0.870837	−	0.491572i	$-0.836422\pi$
$79$	−0.0862526	+	0.149394i	−0.00970417	+	0.0168081i	0.861133	+	0.508381i	$0.169756\pi$
$80$	0.381768	−	2.20324i	0.0426829	−	0.246329i
$81$	0.332429	−	8.99386i	0.0369366	−	0.999318i
$82$	−1.31158	−	2.27173i	−0.144840	−	0.250871i
$83$	11.5262	−	6.65467i	1.26517	−	0.730445i	0.291098	−	0.956693i	$-0.405980\pi$
$83$	11.5262	−	6.65467i	1.26517	−	0.730445i	0.974070	+	0.226249i	$0.0726462\pi$
$84$	−4.35575	+	1.42387i	−0.475252	+	0.155357i
$85$	−16.2982	−	2.82409i	−1.76779	−	0.306315i
$86$		−	0.762245i		−	0.0821950i
$87$	−9.44040	+	12.0705i	−1.01212	+	1.29409i
$88$			3.61095i			0.384929i
$89$	7.08044	+	12.2637i	0.750525	+	1.29995i	0.947568	+	0.319553i	$0.103533\pi$
$89$	7.08044	+	12.2637i	0.750525	+	1.29995i	−0.197043	+	0.980395i	$0.563134\pi$
$90$	3.76197	+	5.55406i	0.396547	+	0.585449i
$91$	3.92979	+	8.01056i	0.411954	+	0.839735i
$92$	−3.99454	−	6.91875i	−0.416460	−	0.721330i
$93$	−6.88156	+	8.79875i	−0.713584	+	0.912388i
$94$	−7.12570	+	4.11402i	−0.734960	+	0.424329i
$95$	6.87110	−	8.23806i	0.704960	−	0.845208i
$96$	−1.36433	−	1.06705i	−0.139246	−	0.108906i
$97$	4.18720	+	7.25244i	0.425145	+	0.736373i	0.996434	−	0.0843759i	$-0.0268896\pi$
$97$	4.18720	+	7.25244i	0.425145	+	0.736373i	−0.571289	+	0.820749i	$0.693556\pi$
$98$	−6.93627	−	0.942388i	−0.700670	−	0.0951955i
$99$	−7.51719	−	7.80017i	−0.755506	−	0.783947i
$100$	−4.70851	−	1.68225i	−0.470851	−	0.168225i
$101$	15.7774			1.56991			0.784954	−	0.619554i	$-0.212686\pi$
$101$	15.7774			1.56991			0.784954	+	0.619554i	$0.212686\pi$
$102$	−7.89341	+	10.0925i	−0.781564	+	0.999307i
$103$	−4.00416			−0.394542			−0.197271	−	0.980349i	$-0.563208\pi$
$103$	−4.00416			−0.394542			−0.197271	+	0.980349i	$0.563208\pi$
$104$	−1.68621	+	2.92060i	−0.165346	+	0.286388i
$105$	1.47424	+	10.1403i	0.143871	+	0.989596i
$106$	1.47706	+	2.55834i	0.143465	+	0.248488i
$107$	1.60810	+	2.78531i	0.155461	+	0.269266i	0.933227	−	0.359288i	$-0.116980\pi$
$107$	1.60810	+	2.78531i	0.155461	+	0.269266i	−0.777766	+	0.628554i	$0.783647\pi$
$108$	5.16851	−	0.535245i	0.497340	−	0.0515040i
$109$	3.65311	−	6.32737i	0.349904	−	0.606052i	−0.636328	−	0.771419i	$-0.719547\pi$
$109$	3.65311	−	6.32737i	0.349904	−	0.606052i	0.986232	+	0.165367i	$0.0528808\pi$
$110$	7.95578	+	1.37854i	0.758554	+	0.131439i
$111$	6.85371	−	8.76314i	0.650526	−	0.831761i
$112$	−1.16527	−	2.37532i	−0.110108	−	0.224446i
$113$	6.81995	−	11.8125i	0.641567	−	1.11123i	−0.343517	−	0.939147i	$-0.611618\pi$
$113$	6.81995	−	11.8125i	0.641567	−	1.11123i	0.985083	−	0.172079i	$-0.0550485\pi$
$114$	−3.10884	−	7.70595i	−0.291170	−	0.721729i
$115$	−16.7686	+	6.15957i	−1.56368	+	0.574383i
$116$	−7.66188	−	4.42359i	−0.711388	−	0.410720i
$117$	−2.43758	−	9.81922i	−0.225354	−	0.907787i
$118$	1.12529			0.103591
$119$	−17.5712	+	8.62001i	−1.61075	+	0.790195i
$120$	−2.87183	+	2.59858i	−0.262161	+	0.237217i
$121$	−2.03898			−0.185361
$122$	1.45633	−	0.840811i	0.131850	−	0.0761235i
$123$	−0.634620	+	4.49892i	−0.0572218	+	0.405654i
$124$	−5.58511	−	3.22456i	−0.501558	−	0.289574i
$125$	−5.50395	+	9.73173i	−0.492288	+	0.870432i
$126$	7.46204	+	2.70518i	0.664771	+	0.240997i
$127$			8.41042i			0.746304i	0.927770	+	0.373152i	$0.121723\pi$
$127$			8.41042i			0.746304i	−0.927770	+	0.373152i	$0.878277\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.813355	+	1.03995i	−0.0716119	+	0.0915629i
$130$	5.79103	+	4.83011i	0.507907	+	0.423628i
$131$	−5.79423			−0.506244			−0.253122	−	0.967434i	$-0.581457\pi$
$131$	−5.79423			−0.506244			−0.253122	+	0.967434i	$0.581457\pi$
$132$	3.85308	−	4.92653i	0.335367	−	0.428800i
$133$	0.856351	−	12.6639i	0.0742551	−	1.09810i
$134$			4.74896i			0.410247i
$135$	0.793899	−	11.5918i	0.0683280	−	0.997663i
$136$	−6.40634	−	3.69870i	−0.549339	−	0.317161i
$137$	7.45676			0.637074			0.318537	−	0.947910i	$-0.396808\pi$
$137$	7.45676			0.637074			0.318537	+	0.947910i	$0.396808\pi$
$138$	−1.93279	+	13.7019i	−0.164530	+	1.16638i
$139$	7.19444	+	4.15371i	0.610225	+	0.352313i	0.773053	−	0.634341i	$-0.218728\pi$
$139$	7.19444	+	4.15371i	0.610225	+	0.352313i	−0.162829	+	0.986654i	$0.552062\pi$
$140$	−5.67825	+	1.66056i	−0.479900	+	0.140343i
$141$	14.1117	+	1.99060i	1.18842	+	0.167639i
$142$	−1.22091	−	0.704893i	−0.102456	−	0.0591533i
$143$	−10.5461	−	6.08882i	−0.881913	−	0.509173i
$144$	0.722799	+	2.91163i	0.0602332	+	0.242635i
$145$	−12.6713	+	15.1922i	−1.05229	+	1.26164i
$146$	−2.78262	−	4.81964i	−0.230291	−	0.398876i
$147$	8.45780	+	8.68710i	0.697587	+	0.716500i
$148$	5.56251	+	3.21152i	0.457236	+	0.263985i
$149$		−	11.6902i		−	0.957700i	−0.877897	−	0.478850i	$-0.841054\pi$
$149$		−	11.6902i		−	0.957700i	0.877897	−	0.478850i	$-0.158946\pi$
$150$	4.62891	+	7.31937i	0.377949	+	0.597624i
$151$	−9.06398			−0.737617			−0.368808	−	0.929505i	$-0.620234\pi$
$151$	−9.06398			−0.737617			−0.368808	+	0.929505i	$0.620234\pi$
$152$	4.15471	−	2.39873i	0.336992	−	0.194562i
$153$	21.5385	−	5.34683i	1.74128	−	0.432266i
$154$	8.57716	−	4.20775i	0.691167	−	0.339070i
$155$	−9.23669	+	11.0743i	−0.741909	+	0.889508i
$156$	5.41698	−	2.18539i	0.433705	−	0.174971i
$157$	−9.89018	−	17.1303i	−0.789322	−	1.36715i	−0.926383	−	0.376584i	$-0.877099\pi$
$157$	−9.89018	−	17.1303i	−0.789322	−	1.36715i	0.137060	−	0.990563i	$-0.456235\pi$
$158$	0.0862526	+	0.149394i	0.00686189	+	0.0118851i
$159$	0.714686	−	5.06652i	0.0566783	−	0.401801i
$160$	−1.71718	−	1.43224i	−0.135755	−	0.113228i
$161$	−11.7795	+	17.5506i	−0.928354	+	1.38318i
$162$	−7.62270	−	4.78482i	−0.598896	−	0.375931i
$163$	−11.4067	+	6.58566i	−0.893442	+	0.515829i	−0.875067	−	0.484002i	$-0.839183\pi$
$163$	−11.4067	+	6.58566i	−0.893442	+	0.515829i	−0.0183750	+	0.999831i	$0.505849\pi$
$164$	−2.62317			−0.204835
$165$	−9.38334	−	10.3700i	−0.730492	−	0.807306i
$166$		−	13.3093i		−	1.03300i
$167$	1.88823	+	1.09017i	0.146116	+	0.0843601i	0.571276	−	0.820758i	$-0.306449\pi$
$167$	1.88823	+	1.09017i	0.146116	+	0.0843601i	−0.425160	+	0.905118i	$0.639782\pi$
$168$	−0.944768	+	4.48413i	−0.0728904	+	0.345958i
$169$	0.813400	+	1.40885i	0.0625692	+	0.108373i
$170$	−10.5948	+	12.7026i	−0.812588	+	0.974248i
$171$	−3.98117	+	13.8308i	−0.304448	+	1.05767i
$172$	−0.660123	−	0.381122i	−0.0503339	−	0.0290603i
$173$	−22.4575	−	12.9658i	−1.70741	−	0.985773i	−0.937745	−	0.347326i	$-0.887090\pi$
$173$	−22.4575	−	12.9658i	−1.70741	−	0.985773i	−0.769665	−	0.638448i	$-0.779577\pi$
$174$	5.73314	+	14.2109i	0.434628	+	1.07732i
$175$	1.49083	+	13.1445i	0.112696	+	0.993630i
$176$	3.12718	+	1.80548i	0.235720	+	0.136093i
$177$	−1.53527	−	1.20074i	−0.115398	−	0.0902535i
$178$	14.1609			1.06140
$179$	12.3911	+	7.15401i	0.926155	+	0.534716i	0.885593	−	0.464461i	$-0.153752\pi$
$179$	12.3911	+	7.15401i	0.926155	+	0.534716i	0.0405613	+	0.999177i	$0.487085\pi$
$180$	6.69094	−	0.480932i	0.498713	−	0.0358466i
$181$		−	4.19706i		−	0.311965i	−0.987760	−	0.155982i	$-0.950146\pi$
$181$		−	4.19706i		−	0.311965i	0.987760	−	0.155982i	$-0.0498543\pi$
$182$	8.90225	+	0.601981i	0.659879	+	0.0446218i
$183$	−2.88410	−	0.406833i	−0.213199	−	0.0300740i
$184$	−7.98909			−0.588963
$185$	9.19932	−	11.0295i	0.676347	−	0.810903i
$186$	4.17916	+	10.3590i	0.306431	+	0.759557i
$187$	13.3558	−	23.1330i	0.976675	−	1.69165i
$188$			8.22805i			0.600092i
$189$	−7.29411	−	11.6532i	−0.530569	−	0.847642i
$190$	−3.69883	−	10.0696i	−0.268341	−	0.730524i
$191$	16.2887	+	9.40430i	1.17861	+	0.680471i	0.955693	−	0.294366i	$-0.0951084\pi$
$191$	16.2887	+	9.40430i	1.17861	+	0.680471i	0.222918	+	0.974837i	$0.428442\pi$
$192$	−1.60626	+	0.648019i	−0.115922	+	0.0467668i
$193$	4.76835	−	2.75301i	0.343233	−	0.198166i	−0.318468	−	0.947934i	$-0.603168\pi$
$193$	4.76835	−	2.75301i	0.343233	−	0.198166i	0.661701	+	0.749768i	$0.269835\pi$
$194$	8.37439			0.601246
$195$	−2.74691	−	12.7692i	−0.196710	−	0.914421i
$196$	−4.28427	+	5.53580i	−0.306019	+	0.395414i
$197$	13.1218			0.934888			0.467444	−	0.884023i	$-0.345175\pi$
$197$	13.1218			0.934888			0.467444	+	0.884023i	$0.345175\pi$
$198$	−10.5137	+	2.60999i	−0.747179	+	0.185484i
$199$	−9.55302	−	5.51544i	−0.677195	−	0.390979i	0.121602	−	0.992579i	$-0.461197\pi$
$199$	−9.55302	−	5.51544i	−0.677195	−	0.390979i	−0.798797	+	0.601600i	$0.794530\pi$
$200$	−3.81112	+	3.23656i	−0.269487	+	0.228859i
$201$	5.06738	−	6.47915i	0.357426	−	0.457004i
$202$	7.88869	−	13.6636i	0.555047	−	0.961369i
$203$	−1.57923	+	23.3541i	−0.110840	+	1.63914i
$204$	4.79366	+	11.8821i	0.335623	+	0.831917i
$205$	−1.00144	+	5.77946i	−0.0699437	+	0.403655i
$206$	−2.00208	+	3.46771i	−0.139492	+	0.241607i
$207$	17.2576	−	16.6315i	1.19948	−	1.15597i
$208$	1.68621	+	2.92060i	0.116918	+	0.202507i
$209$	8.66168	+	15.0025i	0.599141	+	1.03774i
$210$	9.51892	+	3.79344i	0.656868	+	0.261772i
$211$	7.09074	−	12.2815i	0.488147	−	0.845495i	−0.511761	−	0.859128i	$-0.671006\pi$
$211$	7.09074	−	12.2815i	0.488147	−	0.845495i	0.999907	+	0.0136335i	$0.00433983\pi$
$212$	2.95411			0.202889
$213$	0.913568	+	2.26448i	0.0625966	+	0.155160i
$214$	3.21620			0.219855
$215$	−1.09172	+	1.30891i	−0.0744545	+	0.0892668i
$216$	2.12072	−	4.74368i	0.144297	−	0.322767i
$217$	−1.15118	+	17.0239i	−0.0781470	+	1.15566i
$218$	−3.65311	−	6.32737i	−0.247420	−	0.428543i
$219$	−1.34639	+	9.54478i	−0.0909807	+	0.644977i
$220$	5.17175	−	6.20064i	0.348679	−	0.418047i
$221$	21.6048	−	12.4736i	1.45330	−	0.839063i
$222$	−4.16225	−	10.3171i	−0.279352	−	0.692436i
$223$	1.85603	+	3.21474i	0.124289	+	0.215275i	0.921455	−	0.388485i	$-0.127002\pi$
$223$	1.85603	+	3.21474i	0.124289	+	0.215275i	−0.797166	+	0.603761i	$0.793668\pi$
$224$	−2.63972	−	0.178501i	−0.176374	−	0.0119266i
$225$	1.49478	−	14.9253i	0.0996518	−	0.995022i
$226$	−6.81995	−	11.8125i	−0.453656	−	0.785755i
$227$			16.1336i			1.07083i	0.844591	+	0.535413i	$0.179844\pi$
$227$			16.1336i			1.07083i	−0.844591	+	0.535413i	$0.820156\pi$
$228$	−8.22797	−	1.16064i	−0.544911	−	0.0768654i
$229$			7.74473i			0.511786i	0.966705	+	0.255893i	$0.0823695\pi$
$229$			7.74473i			0.511786i	−0.966705	+	0.255893i	$0.917631\pi$
$230$	−3.04997	+	17.6019i	−0.201109	+	1.16063i
$231$	−16.1920	−	3.41151i	−1.06535	−	0.224461i
$232$	−7.66188	+	4.42359i	−0.503027	+	0.290423i
$233$	−8.53036	−	14.7750i	−0.558842	−	0.967944i	−0.997593	−	0.0693349i	$-0.977912\pi$
$233$	−8.53036	−	14.7750i	−0.558842	−	0.967944i	0.438751	−	0.898609i	$-0.355421\pi$
$234$	−9.72248	−	2.79860i	−0.635578	−	0.182950i
$235$	18.1283	+	3.14120i	1.18256	+	0.204909i
$236$	0.562645	−	0.974530i	0.0366251	−	0.0634365i
$237$	0.0417340	−	0.295859i	0.00271091	−	0.0192181i
$238$	−1.32045	+	19.5271i	−0.0855918	+	1.26575i
$239$	−11.0069	−	6.35481i	−0.711975	−	0.411059i	0.0998171	−	0.995006i	$-0.468174\pi$
$239$	−11.0069	−	6.35481i	−0.711975	−	0.411059i	−0.811792	+	0.583947i	$0.801508\pi$
$240$	0.814522	+	3.78636i	0.0525772	+	0.244409i
$241$		−	6.34032i		−	0.408416i	−0.978928	−	0.204208i	$-0.934538\pi$
$241$		−	6.34032i		−	0.408416i	0.978928	−	0.204208i	$-0.0654618\pi$
$242$	−1.01949	+	1.76581i	−0.0655352	+	0.113510i
$243$	5.29423	+	14.6619i	0.339625	+	0.940561i
$244$		−	1.68162i		−	0.107655i
$245$	10.5611	+	11.5526i	0.674722	+	0.738072i
$246$	3.57887	+	2.79906i	0.228180	+	0.178461i
$247$			16.1790i			1.02945i
$248$	−5.58511	+	3.22456i	−0.354655	+	0.204760i
$249$	−14.2018	+	18.1583i	−0.900000	+	1.15074i
$250$	5.67595	+	9.63242i	0.358979	+	0.609208i
$251$	−16.1974			−1.02237			−0.511186	−	0.859470i	$-0.670794\pi$
$251$	−16.1974			−1.02237			−0.511186	+	0.859470i	$0.670794\pi$
$252$	6.07378	−	5.10972i	0.382612	−	0.321882i
$253$		−	28.8482i		−	1.81367i
$254$	7.28364	+	4.20521i	0.457016	+	0.263858i
$255$	28.0093	−	6.02534i	1.75401	−	0.377322i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	0.955954i		−	0.0596308i	−0.999555	−	0.0298154i	$-0.990508\pi$
$257$		−	0.955954i		−	0.0596308i	0.999555	−	0.0298154i	$-0.00949194\pi$
$258$	0.493949	+	1.22436i	0.0307519	+	0.0762255i
$259$	1.14652	−	16.9550i	0.0712413	−	1.05353i
$260$	7.07851	−	2.60013i	0.438991	−	0.161253i
$261$	7.34184	−	25.5059i	0.454448	−	1.57877i
$262$	−2.89711	+	5.01795i	−0.178984	+	0.310010i
$263$	−16.4734			−1.01579			−0.507896	−	0.861419i	$-0.669577\pi$
$263$	−16.4734			−1.01579			−0.507896	+	0.861419i	$0.669577\pi$
$264$	−2.33997	−	5.80013i	−0.144015	−	0.356973i
$265$	1.12779	−	6.50862i	0.0692793	−	0.399821i
$266$	−10.5391	−	7.07359i	−0.646195	−	0.433710i
$267$	−19.3201	−	15.1104i	−1.18237	−	0.924742i
$268$	4.11272	+	2.37448i	0.251224	+	0.145044i
$269$	8.79451	−	15.2325i	0.536210	−	0.928744i	−0.462893	−	0.886414i	$-0.653189\pi$
$269$	8.79451	−	15.2325i	0.536210	−	0.928744i	0.999104	−	0.0423298i	$-0.0134780\pi$
$270$	−9.64184	−	6.48343i	−0.586784	−	0.394569i
$271$	−5.44818	+	3.14551i	−0.330953	+	0.191076i	−0.656264	−	0.754531i	$-0.727864\pi$
$271$	−5.44818	+	3.14551i	−0.330953	+	0.191076i	0.325311	+	0.945607i	$0.394531\pi$
$272$	−6.40634	+	3.69870i	−0.388441	+	0.224267i
$273$	−11.5033	−	10.3205i	−0.696209	−	0.624623i
$274$	3.72838	−	6.45775i	0.225240	−	0.390127i
$275$	−11.6871	−	13.7618i	−0.704757	−	0.829867i
$276$	10.8998	+	8.52477i	0.656088	+	0.513131i
$277$			2.76733i			0.166273i	0.996538	+	0.0831365i	$0.0264938\pi$
$277$			2.76733i			0.166273i	−0.996538	+	0.0831365i	$0.973506\pi$
$278$	7.19444	−	4.15371i	0.431494	−	0.249123i
$279$	5.35181	−	18.5925i	0.320405	−	1.11310i
$280$	−1.40104	+	5.74779i	−0.0837282	+	0.343496i
$281$	3.01229	−	1.73915i	0.179698	−	0.103749i	−0.407453	−	0.913226i	$-0.633583\pi$
$281$	3.01229	−	1.73915i	0.179698	−	0.103749i	0.587151	+	0.809477i	$0.300249\pi$
$282$	8.77976	−	11.2258i	0.522827	−	0.668486i
$283$	6.11408	+	10.5899i	0.363444	+	0.629504i	0.988525	−	0.151056i	$-0.0482673\pi$
$283$	6.11408	+	10.5899i	0.363444	+	0.629504i	−0.625081	+	0.780560i	$0.714934\pi$
$284$	−1.22091	+	0.704893i	−0.0724477	+	0.0418277i
$285$	−5.69834	+	17.6851i	−0.337541	+	1.04757i
$286$	−10.5461	+	6.08882i	−0.623607	+	0.360039i
$287$	3.05671	+	6.23086i	0.180432	+	0.367796i
$288$	2.88294	+	0.829851i	0.169879	+	0.0488994i
$289$	18.8608	+	32.6678i	1.10946	+	1.92164i
$290$	6.82116	+	18.5697i	0.400552	+	1.09045i
$291$	−11.4254	−	8.93591i	−0.669771	−	0.523833i
$292$	−5.56524			−0.325681
$293$	−10.8450	−	6.26137i	−0.633572	−	0.365793i	0.148562	−	0.988903i	$-0.452536\pi$
$293$	−10.8450	−	6.26137i	−0.633572	−	0.365793i	−0.782134	+	0.623110i	$0.785869\pi$
$294$	11.7521	−	2.98112i	0.685399	−	0.173862i
$295$	−1.93232	−	1.61169i	−0.112504	−	0.0938359i
$296$	5.56251	−	3.21152i	0.323314	−	0.186666i
$297$	17.1292	+	7.65782i	0.993938	+	0.444352i
$298$	−10.1240	−	5.84511i	−0.586469	−	0.338598i
$299$	13.4713	−	23.3329i	0.779064	−	1.34938i
$300$	8.65322	−	0.349073i	0.499594	−	0.0201538i
$301$	−0.136062	+	2.01211i	−0.00784246	+	0.115976i
$302$	−4.53199	+	7.84964i	−0.260787	+	0.451696i
$303$	−25.3426	+	10.2240i	−1.45589	+	0.587356i
$304$		−	4.79745i		−	0.275153i
$305$	−3.70501	−	0.641989i	−0.212148	−	0.0367602i
$306$	6.13874	−	21.3263i	0.350928	−	1.21914i
$307$	7.45350			0.425394			0.212697	−	0.977118i	$-0.431775\pi$
$307$	7.45350			0.425394			0.212697	+	0.977118i	$0.431775\pi$
$308$	0.644560	−	9.53191i	0.0367272	−	0.543131i
$309$	6.43173	−	2.59478i	0.365888	−	0.147612i
$310$	4.97227	+	13.5364i	0.282406	+	0.768813i
$311$	−11.2612	−	19.5049i	−0.638563	−	1.10602i	−0.985748	−	0.168227i	$-0.946196\pi$
$311$	−11.2612	−	19.5049i	−0.638563	−	1.10602i	0.347186	−	0.937796i	$-0.387137\pi$
$312$	0.815885	−	5.78394i	0.0461904	−	0.327451i
$313$	10.2965	−	17.8341i	0.581995	−	1.00804i	−0.413248	−	0.910618i	$-0.635606\pi$
$313$	10.2965	−	17.8341i	0.581995	−	1.00804i	0.995243	−	0.0974258i	$-0.0310609\pi$
$314$	−19.7804			−1.11627
$315$	−8.93915	−	15.3327i	−0.503664	−	0.863900i
$316$	0.172505			0.00970417
$317$	−4.35758	+	7.54755i	−0.244746	+	0.423912i	−0.962060	−	0.272837i	$-0.912038\pi$
$317$	−4.35758	+	7.54755i	−0.244746	+	0.423912i	0.717314	+	0.696750i	$0.245371\pi$
$318$	−4.03039	−	3.15220i	−0.226013	−	0.176766i
$319$	−15.9734	−	27.6667i	−0.894337	−	1.54904i
$320$	−2.09894	+	0.770998i	−0.117334	+	0.0431001i
$321$	−4.38796	−	3.43185i	−0.244912	−	0.191547i
$322$	9.30948	+	18.9766i	0.518797	+	1.05753i
$323$	−35.4887			−1.97464
$324$	−7.95512	+	4.20904i	−0.441951	+	0.233835i
$325$	−3.02635	−	16.5883i	−0.167872	−	0.920153i
$326$			13.1713i			0.729492i
$327$	−1.76758	+	12.5307i	−0.0977477	+	0.692948i
$328$	−1.31158	+	2.27173i	−0.0724201	+	0.125435i
$329$	19.5442	−	9.58794i	1.07751	−	0.528600i
$330$	−13.6724	+	2.94120i	−0.752640	+	0.161908i
$331$	7.18237	−	12.4402i	0.394779	−	0.683777i	−0.598294	−	0.801276i	$-0.704155\pi$
$331$	7.18237	−	12.4402i	0.394779	−	0.683777i	0.993073	+	0.117500i	$0.0374879\pi$
$332$	−11.5262	−	6.65467i	−0.632584	−	0.365222i
$333$	−5.33016	+	18.5172i	−0.292091	+	1.01474i
$334$	1.88823	−	1.09017i	0.103320	−	0.0596516i
$335$	6.80164	−	8.15479i	0.371613	−	0.445544i
$336$	3.41099	+	3.06026i	0.186085	+	0.166951i
$337$	9.09613	+	5.25165i	0.495498	+	0.286076i	0.726852	−	0.686794i	$-0.240982\pi$
$337$	9.09613	+	5.25165i	0.495498	+	0.286076i	−0.231355	+	0.972870i	$0.574316\pi$
$338$	1.62680			0.0884863
$339$	−3.29988	+	23.3934i	−0.179225	+	1.27055i
$340$	5.70338	+	15.5267i	0.309309	+	0.842055i
$341$	−11.6437	−	20.1676i	−0.630544	−	1.09213i
$342$	9.98721	+	10.3632i	0.540046	+	0.560376i
$343$	18.1416	+	3.72578i	0.979556	+	0.201173i
$344$	−0.660123	+	0.381122i	−0.0355915	+	0.0205487i
$345$	22.9433	−	20.7603i	1.23522	−	1.11770i
$346$	−22.4575	+	12.9658i	−1.20732	+	0.697047i
$347$	−6.83069	−	11.8311i	−0.366691	−	0.635127i	0.622355	−	0.782735i	$-0.286176\pi$
$347$	−6.83069	−	11.8311i	−0.366691	−	0.635127i	−0.989046	+	0.147608i	$0.952843\pi$
$348$	15.1735	+	2.14039i	0.813387	+	0.114737i
$349$	−30.2742	+	17.4788i	−1.62054	+	0.935620i	−0.633766	+	0.773525i	$0.718492\pi$
$349$	−30.2742	+	17.4788i	−1.62054	+	0.935620i	−0.986775	+	0.162095i	$0.948175\pi$
$350$	12.1289	+	5.28115i	0.648315	+	0.282289i
$351$	10.2784	+	14.1926i	0.548622	+	0.757546i
$352$	3.12718	−	1.80548i	0.166679	−	0.0962322i
$353$			10.0636i			0.535633i	0.963470	+	0.267816i	$0.0863021\pi$
$353$			10.0636i			0.535633i	−0.963470	+	0.267816i	$0.913698\pi$
$354$	−1.80751	+	0.729210i	−0.0960681	+	0.0387571i
$355$	1.08694	+	2.95906i	0.0576889	+	0.157051i
$356$	7.08044	−	12.2637i	0.375263	−	0.649974i
$357$	22.6380	−	25.2324i	1.19813	−	1.33544i
$358$	12.3911	−	7.15401i	0.654890	−	0.378101i
$359$	3.51811	−	2.03118i	0.185679	−	0.107202i	−0.404279	−	0.914636i	$-0.632478\pi$
$359$	3.51811	−	2.03118i	0.185679	−	0.107202i	0.589958	+	0.807434i	$0.299144\pi$
$360$	2.92897	−	6.03499i	0.154370	−	0.318072i
$361$	2.00777	−	3.47755i	0.105672	−	0.183029i
$362$	−3.63476	−	2.09853i	−0.191039	−	0.110296i
$363$	3.27513	−	1.32130i	0.171900	−	0.0693500i
$364$	4.97245	−	7.40858i	0.260627	−	0.388315i
$365$	−2.12463	+	12.2615i	−0.111208	+	0.641798i
$366$	−1.79438	+	2.29429i	−0.0937937	+	0.119924i
$367$	−15.4047			−0.804120			−0.402060	−	0.915613i	$-0.631706\pi$
$367$	−15.4047			−0.804120			−0.402060	+	0.915613i	$0.631706\pi$
$368$	−3.99454	+	6.91875i	−0.208230	+	0.360665i
$369$	−1.89602	−	7.63768i	−0.0987030	−	0.397602i
$370$	−4.95215	−	13.4816i	−0.257450	−	0.700874i
$371$	−3.44236	−	7.01696i	−0.178718	−	0.364303i
$372$	11.0607	+	1.56023i	0.573471	+	0.0808942i
$373$			29.2392i			1.51395i	0.653444	+	0.756974i	$0.273323\pi$
$373$			29.2392i			1.51395i	−0.653444	+	0.756974i	$0.726677\pi$
$374$	−13.3558	−	23.1330i	−0.690614	−	1.19618i
$375$	2.53443	−	19.1984i	0.130877	−	0.991399i
$376$	7.12570	+	4.11402i	0.367480	+	0.212165i
$377$		−	29.8364i		−	1.53665i
$378$	−13.7390	+	0.490312i	−0.706657	+	0.0252189i
$379$	32.1478			1.65132			0.825662	−	0.564166i	$-0.190802\pi$
$379$	32.1478			1.65132			0.825662	+	0.564166i	$0.190802\pi$
$380$	−10.5699	−	1.83151i	−0.542225	−	0.0939545i
$381$	−5.45012	−	13.5093i	−0.279218	−	0.692104i
$382$	16.2887	−	9.40430i	0.833404	−	0.481166i
$383$			6.34301i			0.324112i	0.986782	+	0.162056i	$0.0518126\pi$
$383$			6.34301i			0.324112i	−0.986782	+	0.162056i	$0.948187\pi$
$384$	−0.241929	+	1.71507i	−0.0123459	+	0.0875219i
$385$	−20.7550	−	5.05909i	−1.05777	−	0.257835i
$386$		−	5.50601i		−	0.280249i
$387$	0.632549	−	2.19751i	0.0321543	−	0.111706i
$388$	4.18720	−	7.25244i	0.212573	−	0.368187i
$389$			24.2709i			1.23058i	0.788299	+	0.615292i	$0.210962\pi$
$389$			24.2709i			1.23058i	−0.788299	+	0.615292i	$0.789038\pi$
$390$	−12.4319	−	4.00571i	−0.629514	−	0.202837i
$391$	51.1808	+	29.5492i	2.58832	+	1.49437i
$392$	2.65201	+	6.47818i	0.133947	+	0.327198i
$393$	9.30703	−	3.75477i	0.469478	−	0.189403i
$394$	6.56089	−	11.3638i	0.330533	−	0.572500i
$395$	0.0658569	−	0.380070i	0.00331362	−	0.0191234i
$396$	−2.99655	+	10.4102i	−0.150582	+	0.523130i
$397$	−3.23274	−	5.59927i	−0.162246	−	0.281019i	0.773428	−	0.633885i	$-0.218541\pi$
$397$	−3.23274	−	5.59927i	−0.162246	−	0.281019i	−0.935674	+	0.352866i	$0.885207\pi$
$398$	−9.55302	+	5.51544i	−0.478849	+	0.276464i
$399$	6.83095	+	20.8965i	0.341975	+	1.04613i
$400$	0.897383	+	4.91881i	0.0448692	+	0.245941i
$401$			36.0669i			1.80109i	0.434759	+	0.900547i	$0.356833\pi$
$401$			36.0669i			1.80109i	−0.434759	+	0.900547i	$0.643167\pi$
$402$	−3.07741	−	7.62806i	−0.153488	−	0.380453i
$403$		−	21.7492i		−	1.08340i
$404$	−7.88869	−	13.6636i	−0.392477	−	0.679790i
$405$	6.23650	+	19.1339i	0.309894	+	0.950771i
$406$	19.4356	+	13.0447i	0.964574	+	0.647398i
$407$	11.5966	+	20.0860i	0.574824	+	0.995624i
$408$	12.6871	+	1.78965i	0.628104	+	0.0886006i
$409$	−30.8153	+	17.7912i	−1.52372	+	0.879718i	−0.524110	+	0.851651i	$0.675602\pi$
$409$	−30.8153	+	17.7912i	−1.52372	+	0.879718i	−0.999606	+	0.0280674i	$0.991065\pi$
$410$	4.50444	+	3.75700i	0.222458	+	0.185545i
$411$	−11.9775	+	4.83212i	−0.590806	+	0.238351i
$412$	2.00208	+	3.46771i	0.0986355	+	0.170842i
$413$	−2.97046	−	0.200866i	−0.146167	−	0.00988396i
$414$	−5.77450	−	23.2612i	−0.283801	−	1.14323i
$415$	−19.0621	+	22.8545i	−0.935724	+	1.12188i
$416$	3.37242			0.165346
$417$	−14.2478	−	2.00981i	−0.697719	−	0.0984206i
$418$	17.3234			0.847313
$419$	9.77575	−	16.9321i	0.477576	−	0.827187i	−0.522093	−	0.852888i	$-0.674849\pi$
$419$	9.77575	−	16.9321i	0.477576	−	0.827187i	0.999670	+	0.0257018i	$0.00818203\pi$
$420$	8.04468	−	6.34690i	0.392540	−	0.309697i
$421$	6.82851	+	11.8273i	0.332801	+	0.576428i	0.983060	−	0.183284i	$-0.0586729\pi$
$421$	6.82851	+	11.8273i	0.332801	+	0.576428i	−0.650259	+	0.759713i	$0.725340\pi$
$422$	−7.09074	−	12.2815i	−0.345172	−	0.597855i
$423$	−23.9570	+	5.94722i	−1.16483	+	0.289164i
$424$	1.47706	−	2.55834i	0.0717323	−	0.124244i
$425$	36.3864	−	6.63830i	1.76500	−	0.322005i
$426$	2.41788	+	0.341068i	0.117147	+	0.0165248i
$427$	−3.99439	+	1.95955i	−0.193302	+	0.0948294i
$428$	1.60810	−	2.78531i	0.0777304	−	0.134633i
$429$	20.8855	+	2.94612i	1.00836	+	0.142240i
$430$	0.587689	+	1.59991i	0.0283409	+	0.0771544i
$431$	6.33629	+	3.65826i	0.305208	+	0.176212i	0.644780	−	0.764368i	$-0.276949\pi$
$431$	6.33629	+	3.65826i	0.305208	+	0.176212i	−0.339572	+	0.940580i	$0.610282\pi$
$432$	−3.04779	−	4.20844i	−0.146637	−	0.202479i
$433$	7.45007			0.358027			0.179014	−	0.983847i	$-0.442709\pi$
$433$	7.45007			0.358027			0.179014	+	0.983847i	$0.442709\pi$
$434$	14.1676	+	9.50891i	0.680064	+	0.456442i
$435$	10.5085	−	32.6138i	0.503846	−	1.56371i
$436$	−7.30622			−0.349904
$437$	−33.1924	+	19.1636i	−1.58781	+	0.916720i
$438$	7.59283	+	5.93840i	0.362799	+	0.283748i
$439$	13.2005	+	7.62131i	0.630025	+	0.363745i	0.780762	−	0.624829i	$-0.214831\pi$
$439$	13.2005	+	7.62131i	0.630025	+	0.363745i	−0.150737	+	0.988574i	$0.548165\pi$
$440$	−2.78404	−	7.57918i	−0.132724	−	0.361323i
$441$	−19.2148	−	8.47292i	−0.914992	−	0.403472i
$442$		−	24.9471i		−	1.18661i
$443$	1.09863	−	1.90288i	0.0521974	−	0.0904086i	−0.838746	−	0.544523i	$-0.816711\pi$
$443$	1.09863	−	1.90288i	0.0521974	−	0.0904086i	0.890944	+	0.454114i	$0.150044\pi$
$444$	−11.0160	−	1.55392i	−0.522794	−	0.0737457i
$445$	−24.3167	−	20.2818i	−1.15272	−	0.961448i
$446$	3.71206			0.175771
$447$	7.57549	+	18.7775i	0.358308	+	0.888147i
$448$	−1.47445	+	2.19682i	−0.0696611	+	0.103790i
$449$			11.6919i			0.551773i	0.961190	+	0.275886i	$0.0889713\pi$
$449$			11.6919i			0.551773i	−0.961190	+	0.275886i	$0.911029\pi$
$450$	−12.1783	−	8.75718i	−0.574092	−	0.412818i
$451$	−8.20311	−	4.73607i	−0.386269	−	0.223013i
$452$	−13.6399			−0.641567
$453$	14.5591	−	5.87364i	0.684047	−	0.275967i
$454$	13.9721	+	8.06681i	0.655744	+	0.378594i
$455$	−14.4245	−	13.7839i	−0.676233	−	0.646197i
$456$	−5.11913	+	6.54531i	−0.239725	+	0.306512i
$457$	18.8329	+	10.8732i	0.880964	+	0.508625i	0.870976	−	0.491325i	$-0.163487\pi$
$457$	18.8329	+	10.8732i	0.880964	+	0.508625i	0.00998773	+	0.999950i	$0.496821\pi$
$458$	6.70713	+	3.87236i	0.313404	+	0.180944i
$459$	−31.1315	+	22.5457i	−1.45309	+	1.05234i
$460$	13.7187	+	11.4423i	0.639636	+	0.533499i
$461$	−7.88022	−	13.6489i	−0.367019	−	0.635695i	0.622079	−	0.782954i	$-0.286288\pi$
$461$	−7.88022	−	13.6489i	−0.367019	−	0.635695i	−0.989098	+	0.147259i	$0.952955\pi$
$462$	−11.0504	+	12.3169i	−0.514113	+	0.573034i
$463$	6.80572	+	3.92928i	0.316288	+	0.182609i	0.649737	−	0.760159i	$-0.274879\pi$
$463$	6.80572	+	3.92928i	0.316288	+	0.182609i	−0.333449	+	0.942768i	$0.608212\pi$
$464$			8.84718i			0.410720i
$465$	7.66018	−	23.7737i	0.355232	−	1.10248i
$466$	−17.0607			−0.790323
$467$	22.1423	−	12.7839i	1.02462	−	0.591567i	0.109184	−	0.994022i	$-0.465176\pi$
$467$	22.1423	−	12.7839i	1.02462	−	0.591567i	0.915440	+	0.402455i	$0.131843\pi$
$468$	−7.28490	+	7.02061i	−0.336745	+	0.324528i
$469$	0.847695	−	12.5359i	0.0391429	−	0.578855i
$470$	11.7845	−	14.1290i	0.543580	−	0.651722i
$471$	26.9870	+	21.1067i	1.24349	+	0.972544i
$472$	−0.562645	−	0.974530i	−0.0258979	−	0.0448564i
$473$	−1.37621	−	2.38367i	−0.0632784	−	0.109601i
$474$	−0.235354	−	0.184072i	−0.0108102	−	0.00845471i
$475$	−8.07051	+	22.5888i	−0.370300	+	1.03645i
$476$	16.2507	+	10.9071i	0.744851	+	0.499925i
$477$	2.13523	+	8.60128i	0.0977655	+	0.393825i
$478$	−11.0069	+	6.35481i	−0.503442	+	0.290662i
$479$	−7.96636			−0.363992			−0.181996	−	0.983299i	$-0.558256\pi$
$479$	−7.96636			−0.363992			−0.181996	+	0.983299i	$0.558256\pi$
$480$	3.68635	+	1.18779i	0.168258	+	0.0542147i
$481$			21.6612i			0.987663i
$482$	−5.49087	−	3.17016i	−0.250102	−	0.144397i
$483$	7.54783	−	35.8241i	0.343438	−	1.63005i
$484$	1.01949	+	1.76581i	0.0463404	+	0.0802639i
$485$	−14.3803	−	11.9941i	−0.652976	−	0.544625i
$486$	15.3447	+	2.74601i	0.696049	+	0.124562i
$487$	−1.35301	−	0.781161i	−0.0613108	−	0.0353978i	0.469031	−	0.883182i	$-0.344603\pi$
$487$	−1.35301	−	0.781161i	−0.0613108	−	0.0353978i	−0.530342	+	0.847784i	$0.677936\pi$
$488$	−1.45633	−	0.840811i	−0.0659248	−	0.0380617i
$489$	14.0545	−	17.9700i	0.635566	−	0.812633i
$490$	15.2854	−	3.36984i	0.690525	−	0.152234i
$491$	−3.63710	−	2.09988i	−0.164140	−	0.0947663i	0.415680	−	0.909511i	$-0.363544\pi$
$491$	−3.63710	−	2.09988i	−0.164140	−	0.0947663i	−0.579820	+	0.814745i	$0.696877\pi$
$492$	4.21349	−	1.69986i	0.189959	−	0.0766358i
$493$	65.4461			2.94754
$494$	14.0114	+	8.08950i	0.630404	+	0.363964i
$495$	21.7921	+	10.5764i	0.979481	+	0.475373i
$496$			6.44913i			0.289574i
$497$	3.09704	+	2.07866i	0.138921	+	0.0932404i
$498$	8.62470	+	21.3782i	0.386482	+	0.957982i
$499$	−11.1563			−0.499427			−0.249713	−	0.968320i	$-0.580336\pi$
$499$	−11.1563			−0.499427			−0.249713	+	0.968320i	$0.580336\pi$
$500$	11.1799	−	0.0993046i	0.499980	−	0.00444104i
$501$	−3.73945	−	0.527488i	−0.167066	−	0.0235664i
$502$	−8.09871	+	14.0274i	−0.361463	+	0.626072i
$503$		−	15.9146i		−	0.709598i	−0.934943	−	0.354799i	$-0.884549\pi$
$503$		−	15.9146i		−	0.709598i	0.934943	−	0.354799i	$-0.115451\pi$
$504$	−1.38826	−	7.81490i	−0.0618380	−	0.348104i
$505$	−33.1158	+	12.1643i	−1.47364	+	0.541306i
$506$	−24.9833	−	14.4241i	−1.11064	−	0.641230i
$507$	−2.21949	−	1.73588i	−0.0985712	−	0.0770932i
$508$	7.28364	−	4.20521i	0.323159	−	0.186576i
$509$	−14.0765			−0.623930			−0.311965	−	0.950094i	$-0.600987\pi$
$509$	−14.0765			−0.623930			−0.311965	+	0.950094i	$0.600987\pi$
$510$	8.78653	−	27.2694i	0.389074	−	1.20751i
$511$	6.48503	+	13.2192i	0.286881	+	0.584783i
$512$	−1.00000			−0.0441942
$513$	−2.56781	−	24.7957i	−0.113372	−	1.09476i
$514$	−0.827880	−	0.477977i	−0.0365162	−	0.0210827i
$515$	8.40451	−	3.08720i	0.370347	−	0.136038i
$516$	1.30730	+	0.184409i	0.0575509	+	0.00811815i
$517$	−14.8555	+	25.7306i	−0.653346	+	1.13163i
$518$	−14.1102	−	9.47043i	−0.619968	−	0.416107i
$519$	44.4746	+	6.27362i	1.95222	+	0.275381i
$520$	1.28748	−	7.43024i	0.0564597	−	0.325837i
$521$	15.9369	−	27.6036i	0.698209	−	1.20933i	−0.270877	−	0.962614i	$-0.587314\pi$
$521$	15.9369	−	27.6036i	0.698209	−	1.20933i	0.969087	−	0.246720i	$-0.0793529\pi$
$522$	−18.4178	−	19.1112i	−0.806126	−	0.836473i
$523$	5.99562	+	10.3847i	0.262170	+	0.454092i	0.966818	−	0.255465i	$-0.0822285\pi$
$523$	5.99562	+	10.3847i	0.262170	+	0.454092i	−0.704648	+	0.709557i	$0.748895\pi$
$524$	2.89711	+	5.01795i	0.126561	+	0.219210i
$525$	−10.9125	−	20.1474i	−0.476262	−	0.879303i
$526$	−8.23669	+	14.2664i	−0.359137	+	0.622043i
$527$	47.7068			2.07814
$528$	−6.19304	−	0.873594i	−0.269518	−	0.0380183i
$529$	40.8255			1.77502
$530$	−5.07273	−	4.23100i	−0.220345	−	0.183783i
$531$	3.24415	+	0.933823i	0.140784	+	0.0405245i
$532$	−11.3955	+	5.59035i	−0.494056	+	0.242372i
$533$	−4.42321	−	7.66122i	−0.191590	−	0.331844i
$534$	−22.7461	+	9.17653i	−0.984318	+	0.397107i
$535$	−5.52278	−	4.60636i	−0.238770	−	0.199150i
$536$	4.11272	−	2.37448i	0.177642	−	0.102562i
$537$	−24.5393	−	3.46152i	−1.05895	−	0.149376i
$538$	−8.79451	−	15.2325i	−0.379158	−	0.656721i
$539$	−23.3924	+	9.57627i	−1.00758	+	0.412479i
$540$	−10.4357	+	5.10836i	−0.449083	+	0.219829i
$541$	−8.92677	−	15.4616i	−0.383792	−	0.664747i	0.607809	−	0.794083i	$-0.292049\pi$
$541$	−8.92677	−	15.4616i	−0.383792	−	0.664747i	−0.991601	+	0.129336i	$0.958715\pi$
$542$			6.29101i			0.270222i
$543$	2.71977	+	6.74157i	0.116717	+	0.289308i
$544$			7.39740i			0.317161i
$545$	−2.78928	+	16.0973i	−0.119479	+	0.689534i
$546$	−14.6894	+	4.80189i	−0.628649	+	0.205502i
$547$	−16.3179	+	9.42113i	−0.697702	+	0.402818i	−0.806491	−	0.591247i	$-0.798636\pi$
$547$	−16.3179	+	9.42113i	−0.697702	+	0.402818i	0.108789	+	0.994065i	$0.465303\pi$
$548$	−3.72838	−	6.45775i	−0.159269	−	0.275861i
$549$	4.89625	−	1.21547i	0.208967	−	0.0518752i
$550$	−17.7616	+	3.24041i	−0.757357	+	0.138171i
$551$	−21.2219	+	36.7575i	−0.904085	+	1.56592i
$552$	12.8325	−	5.17708i	0.546190	−	0.220351i
$553$	−0.201016	−	0.409754i	−0.00854806	−	0.0174245i
$554$	2.39658	+	1.38367i	0.101821	+	0.0587864i
$555$	−7.62919	+	23.6775i	−0.323841	+	1.00506i
$556$		−	8.30743i		−	0.352313i
$557$	−16.8982	+	29.2685i	−0.716000	+	1.24015i	0.246573	+	0.969124i	$0.420696\pi$
$557$	−16.8982	+	29.2685i	−0.716000	+	1.24015i	−0.962573	+	0.271024i	$0.912638\pi$
$558$	−13.4256	−	13.9310i	−0.568352	−	0.589748i
$559$		−	2.57061i		−	0.108725i
$560$	4.27721	+	4.08723i	0.180745	+	0.172717i
$561$	−6.46232	+	45.8124i	−0.272840	+	1.93420i
$562$		−	3.47830i		−	0.146723i
$563$	19.5776	−	11.3032i	0.825100	−	0.476371i	−0.0270723	−	0.999633i	$-0.508618\pi$
$563$	19.5776	−	11.3032i	0.825100	−	0.476371i	0.852172	+	0.523262i	$0.175285\pi$
$564$	−5.33193	−	13.2164i	−0.224515	−	0.556510i
$565$	−5.20727	+	30.0519i	−0.219071	+	1.26429i
$566$	12.2282			0.513988
$567$	19.2677	+	13.9913i	0.809168	+	0.587578i
$568$			1.40979i			0.0591533i
$569$	−11.3581	−	6.55760i	−0.476156	−	0.274909i	0.242657	−	0.970112i	$-0.421981\pi$
$569$	−11.3581	−	6.55760i	−0.476156	−	0.274909i	−0.718813	+	0.695203i	$0.755314\pi$
$570$	12.4666	+	13.7774i	0.522166	+	0.577074i
$571$	−18.7178	−	32.4202i	−0.783317	−	1.35674i	−0.930000	−	0.367561i	$-0.880193\pi$
$571$	−18.7178	−	32.4202i	−0.783317	−	1.35674i	0.146683	−	0.989184i	$-0.453140\pi$
$572$			12.1776i			0.509173i
$573$	−32.2581	−	4.55035i	−1.34760	−	0.190093i
$574$	6.92444	+	0.468239i	0.289020	+	0.0195439i
$575$	30.4474	−	25.8572i	1.26974	−	1.07832i
$576$	2.16014	−	2.08177i	0.0900059	−	0.0867406i
$577$	−9.64764	+	16.7102i	−0.401636	+	0.695655i	−0.993924	−	0.110072i	$-0.964892\pi$
$577$	−9.64764	+	16.7102i	−0.401636	+	0.695655i	0.592287	+	0.805727i	$0.298225\pi$
$578$	37.7215			1.56901
$579$	−5.87520	+	7.51202i	−0.244165	+	0.312189i
$580$	19.4924	+	3.37757i	0.809379	+	0.140246i
$581$	−2.37573	+	35.1330i	−0.0985620	+	1.45756i
$582$	−13.4515	+	5.42677i	−0.557581	+	0.224947i
$583$	9.23804	+	5.33358i	0.382600	+	0.220894i
$584$	−2.78262	+	4.81964i	−0.115146	+	0.199438i
$585$	12.6869	+	18.7306i	0.524540	+	0.774415i
$586$	−10.8450	+	6.26137i	−0.448003	+	0.258655i
$587$	−20.0370	+	11.5683i	−0.827014	+	0.477477i	−0.852829	−	0.522190i	$-0.825115\pi$
$587$	−20.0370	+	11.5683i	−0.827014	+	0.477477i	0.0258152	+	0.999667i	$0.491782\pi$
$588$	3.29435	−	11.6682i	0.135857	−	0.481189i
$589$	−15.4697	+	26.7943i	−0.637417	+	1.10404i
$590$	−2.36192	+	0.867597i	−0.0972388	+	0.0357184i
$591$	−21.0770	+	8.50317i	−0.866992	+	0.349774i
$592$		−	6.42303i		−	0.263985i
$593$	−12.4103	+	7.16507i	−0.509629	+	0.294234i	−0.732681	−	0.680572i	$-0.761731\pi$
$593$	−12.4103	+	7.16507i	−0.509629	+	0.294234i	0.223052	+	0.974806i	$0.428398\pi$
$594$	15.1965	−	11.0054i	0.623519	−	0.451558i
$595$	30.2349	−	31.6402i	1.23951	−	1.29712i
$596$	−10.1240	+	5.84511i	−0.414696	+	0.239425i
$597$	18.9187	+	2.66869i	0.774292	+	0.109222i
$598$	−13.4713	−	23.3329i	−0.550881	−	0.954154i
$599$	−4.89074	+	2.82367i	−0.199830	+	0.115372i	−0.596576	−	0.802556i	$-0.703473\pi$
$599$	−4.89074	+	2.82367i	−0.199830	+	0.115372i	0.396746	+	0.917928i	$0.370139\pi$
$600$	4.02430	−	7.66844i	0.164291	−	0.313063i
$601$	11.9185	−	6.88116i	0.486167	−	0.280688i	−0.236816	−	0.971554i	$-0.576104\pi$
$601$	11.9185	−	6.88116i	0.486167	−	0.280688i	0.722983	+	0.690866i	$0.242771\pi$
$602$	1.67451	+	1.12389i	0.0682480	+	0.0458063i
$603$	−3.94093	+	13.6910i	−0.160487	+	0.557539i
$604$	4.53199	+	7.84964i	0.184404	+	0.319397i
$605$	4.27969	−	1.57205i	0.173994	−	0.0639128i
$606$	−3.81701	+	27.0593i	−0.155055	+	1.09921i
$607$	−5.66533			−0.229949			−0.114974	−	0.993368i	$-0.536679\pi$
$607$	−5.66533			−0.229949			−0.114974	+	0.993368i	$0.536679\pi$
$608$	−4.15471	−	2.39873i	−0.168496	−	0.0972812i
$609$	−12.5972	−	38.5361i	−0.510466	−	1.56156i
$610$	−2.40848	+	2.88764i	−0.0975167	+	0.116917i
$611$	−24.0308	+	13.8742i	−0.972183	+	0.561290i
$612$	−15.3997	−	15.9794i	−0.622497	−	0.645931i
$613$	−4.30137	−	2.48340i	−0.173731	−	0.100304i	0.410613	−	0.911810i	$-0.365315\pi$
$613$	−4.30137	−	2.48340i	−0.173731	−	0.100304i	−0.584344	+	0.811506i	$0.698648\pi$
$614$	3.72675	−	6.45492i	0.150399	−	0.260499i
$615$	−2.13663	−	9.93227i	−0.0861571	−	0.400508i
$616$	−7.93260	−	5.32416i	−0.319614	−	0.214517i
$617$	−12.3417	+	21.3765i	−0.496858	+	0.860584i	−0.999993	−	0.00362388i	$-0.998846\pi$
$617$	−12.3417	+	21.3765i	−0.496858	+	0.860584i	0.503135	+	0.864208i	$0.332180\pi$
$618$	0.968723	−	6.86743i	0.0389678	−	0.276249i
$619$		−	31.9421i		−	1.28386i	−0.766763	−	0.641930i	$-0.778134\pi$
$619$		−	31.9421i		−	1.28386i	0.766763	−	0.641930i	$-0.221866\pi$
$620$	14.2090	+	2.46207i	0.570646	+	0.0988791i
$621$	−16.9426	+	37.8977i	−0.679884	+	1.52078i
$622$	−22.5224			−0.903064
$623$	−37.3808	−	2.52774i	−1.49763	−	0.101272i
$624$	−4.60109	−	3.59855i	−0.184191	−	0.144057i
$625$	4.04933	−	24.6699i	0.161973	−	0.986795i
$626$	−10.2965	−	17.8341i	−0.411532	−	0.712795i
$627$	−23.6348	−	18.4849i	−0.943883	−	0.738217i
$628$	−9.89018	+	17.1303i	−0.394661	+	0.683573i
$629$	−47.5138			−1.89450
$630$	−17.7481	+	0.0751862i	−0.707100	+	0.00299549i
$631$	−29.5217			−1.17524			−0.587620	−	0.809137i	$-0.699935\pi$
$631$	−29.5217			−1.17524			−0.587620	+	0.809137i	$0.699935\pi$
$632$	0.0862526	−	0.149394i	0.00343094	−	0.00594257i
$633$	−3.43091	+	24.3222i	−0.136366	+	0.966722i
$634$	4.35758	+	7.54755i	0.173062	+	0.299751i
$635$	−6.48442	−	17.6530i	−0.257326	−	0.700538i
$636$	−4.74508	+	1.91432i	−0.188155	+	0.0759079i
$637$	−23.3920	−	3.17813i	−0.926825	−	0.125922i
$638$	−31.9467			−1.26478
$639$	−2.93485	−	3.04534i	−0.116101	−	0.120472i
$640$	−0.381768	+	2.20324i	−0.0150907	+	0.0870906i
$641$			30.6755i			1.21161i	0.795614	+	0.605804i	$0.207149\pi$
$641$			30.6755i			1.21161i	−0.795614	+	0.605804i	$0.792851\pi$
$642$	−5.16605	+	2.08416i	−0.203888	+	0.0822551i
$643$	−9.01650	+	15.6170i	−0.355576	+	0.615876i	−0.987216	−	0.159386i	$-0.949049\pi$
$643$	−9.01650	+	15.6170i	−0.355576	+	0.615876i	0.631640	+	0.775262i	$0.282382\pi$
$644$	21.0890	+	1.42606i	0.831022	+	0.0561947i
$645$	0.905383	−	2.80990i	0.0356494	−	0.110640i
$646$	−17.7443	+	30.7341i	−0.698141	+	1.20922i
$647$	0.566867	+	0.327281i	0.0222858	+	0.0128667i	0.511102	−	0.859520i	$-0.329238\pi$
$647$	0.566867	+	0.327281i	0.0222858	+	0.0128667i	−0.488816	+	0.872387i	$0.662571\pi$
$648$	−0.332429	+	8.99386i	−0.0130591	+	0.353312i
$649$	3.51898	−	2.03169i	0.138132	−	0.0797506i
$650$	−15.8791	−	5.67325i	−0.622828	−	0.222523i
$651$	−9.18273	−	28.0908i	−0.359900	−	1.10097i
$652$	11.4067	+	6.58566i	0.446721	+	0.257914i
$653$	−8.32983			−0.325971			−0.162986	−	0.986628i	$-0.552112\pi$
$653$	−8.32983			−0.325971			−0.162986	+	0.986628i	$0.552112\pi$
$654$	9.96810	+	7.79612i	0.389783	+	0.304852i
$655$	12.1617	−	4.46734i	0.475199	−	0.174553i
$656$	1.31158	+	2.27173i	0.0512088	+	0.0886962i
$657$	−4.02255	−	16.2039i	−0.156934	−	0.632174i
$658$	1.46872	−	21.7198i	0.0572566	−	0.846725i
$659$	32.1220	−	18.5456i	1.25129	−	0.722435i	0.279928	−	0.960021i	$-0.409689\pi$
$659$	32.1220	−	18.5456i	1.25129	−	0.722435i	0.971367	+	0.237586i	$0.0763561\pi$
$660$	−4.28904	+	13.3112i	−0.166951	+	0.518139i
$661$	−11.4479	+	6.60942i	−0.445270	+	0.257077i	−0.705831	−	0.708381i	$-0.749426\pi$
$661$	−11.4479	+	6.60942i	−0.445270	+	0.257077i	0.260560	+	0.965458i	$0.416093\pi$
$662$	−7.18237	−	12.4402i	−0.279151	−	0.483503i
$663$	−26.6199	+	34.0361i	−1.03383	+	1.32185i
$664$	−11.5262	+	6.65467i	−0.447304	+	0.258251i
$665$	7.96644	+	27.2411i	0.308925	+	1.05637i
$666$	13.3713	+	13.8747i	0.518128	+	0.537632i
$667$	61.2114	−	35.3404i	2.37012	−	1.36839i
$668$		−	2.18034i		−	0.0843601i
$669$	−5.06448	−	3.96097i	−0.195804	−	0.153140i
$670$	−3.66144	−	9.96779i	−0.141454	−	0.385089i
$671$	3.03613	−	5.25873i	0.117208	−	0.203011i
$672$	4.35575	−	1.42387i	0.168027	−	0.0549270i
$673$	−25.9475	+	14.9808i	−1.00020	+	0.577466i	−0.908308	−	0.418302i	$-0.862625\pi$
$673$	−25.9475	+	14.9808i	−1.00020	+	0.577466i	−0.0918934	+	0.995769i	$0.529292\pi$
$674$	9.09613	−	5.25165i	0.350370	−	0.202286i
$675$	7.27090	+	24.9426i	0.279857	+	0.960042i
$676$	0.813400	−	1.40885i	0.0312846	−	0.0541865i
$677$	−36.3274	−	20.9737i	−1.39618	−	0.806083i	−0.402187	−	0.915557i	$-0.631750\pi$
$677$	−36.3274	−	20.9737i	−1.39618	−	0.806083i	−0.993990	+	0.109474i	$0.965083\pi$
$678$	18.6093	+	14.5545i	0.714687	+	0.558961i
$679$	−22.1061	−	1.49484i	−0.848353	−	0.0573667i
$680$	16.2982	+	2.82409i	0.625009	+	0.108299i
$681$	−10.4549	−	25.9148i	−0.400632	−	0.993057i
$682$	−23.2875			−0.891724
$683$	−17.3451	+	30.0426i	−0.663691	+	1.14955i	0.315947	+	0.948777i	$0.397678\pi$
$683$	−17.3451	+	30.0426i	−0.663691	+	1.14955i	−0.979638	+	0.200770i	$0.935656\pi$
$684$	13.9684	−	3.46759i	0.534094	−	0.132587i
$685$	−15.6513	+	5.74915i	−0.598006	+	0.219664i
$686$	12.2974	−	13.8482i	0.469518	−	0.528728i
$687$	−5.01873	−	12.4400i	−0.191477	−	0.474617i
$688$			0.762245i			0.0290603i
$689$	4.98125	+	8.62779i	0.189771	+	0.328692i
$690$	−6.50729	−	30.2496i	−0.247728	−	1.15158i
$691$	10.2119	+	5.89584i	0.388479	+	0.224288i	0.681501	−	0.731817i	$-0.261328\pi$
$691$	10.2119	+	5.89584i	0.388479	+	0.224288i	−0.293022	+	0.956106i	$0.594661\pi$
$692$			25.9317i			0.985773i
$693$	28.2192	−	5.01294i	1.07196	−	0.190426i
$694$	−13.6614			−0.518579
$695$	−18.3032	−	3.17151i	−0.694281	−	0.120302i
$696$	9.44040	−	12.0705i	0.357837	−	0.457530i
$697$	16.8049	−	9.70231i	0.636531	−	0.367501i
$698$			34.9576i			1.32317i
$699$	23.2765	+	18.2047i	0.880397	+	0.688564i
$700$	10.6380	−	7.86334i	0.402080	−	0.297206i
$701$			32.3472i			1.22174i	0.791732	+	0.610869i	$0.209180\pi$
$701$			32.3472i			1.22174i	−0.791732	+	0.610869i	$0.790820\pi$
$702$	17.4304	−	1.80507i	0.657867	−	0.0681279i
$703$	15.4071	−	26.6859i	0.581089	−	1.00648i
$704$		−	3.61095i		−	0.136093i
$705$	−31.1544	+	6.70193i	−1.17334	+	0.252409i
$706$	8.71536	+	5.03181i	0.328007	+	0.189375i
$707$	−23.2629	+	34.6600i	−0.874893	+	1.30352i
$708$	−0.272240	+	1.92995i	−0.0102314	+	0.0725321i
$709$	11.9774	−	20.7454i	0.449820	−	0.779111i	−0.548554	−	0.836115i	$-0.684822\pi$
$709$	11.9774	−	20.7454i	0.449820	−	0.779111i	0.998374	+	0.0570043i	$0.0181549\pi$
$710$	3.10609	+	0.538210i	0.116570	+	0.0201987i
$711$	0.124686	+	0.502270i	0.00467611	+	0.0188366i
$712$	−7.08044	−	12.2637i	−0.265351	−	0.459601i
$713$	44.6199	−	25.7613i	1.67103	−	0.964769i
$714$	−10.5329	−	32.2213i	−0.394186	−	1.20585i
$715$	26.8302	+	4.64903i	1.00339	+	0.173864i
$716$		−	14.3080i		−	0.534716i
$717$	21.7979	+	3.07483i	0.814058	+	0.114832i
$718$		−	4.06236i		−	0.151606i
$719$	10.7973	+	18.7015i	0.402672	+	0.697448i	0.994047	−	0.108948i	$-0.0347482\pi$
$719$	10.7973	+	18.7015i	0.402672	+	0.697448i	−0.591376	+	0.806396i	$0.701415\pi$
$720$	−3.76197	−	5.55406i	−0.140200	−	0.206988i
$721$	5.90393	−	8.79642i	0.219874	−	0.327596i
$722$	−2.00777	−	3.47755i	−0.0747213	−	0.129421i
$723$	4.10865	+	10.1842i	0.152802	+	0.378754i
$724$	−3.63476	+	2.09853i	−0.135085	+	0.0779912i
$725$	14.8832	−	41.6570i	0.552747	−	1.54710i
$726$	0.493287	−	3.49699i	0.0183076	−	0.129785i
$727$	−16.1191	−	27.9190i	−0.597823	−	1.03546i	−0.993142	−	0.116916i	$-0.962699\pi$
$727$	−16.1191	−	27.9190i	−0.597823	−	1.03546i	0.395319	−	0.918544i	$-0.370634\pi$
$728$	−3.92979	−	8.01056i	−0.145648	−	0.296891i
$729$	−18.0051	−	20.1201i	−0.666855	−	0.745187i
$730$	9.55649	+	7.97075i	0.353702	+	0.295011i
$731$	5.63863			0.208552
$732$	1.08972	+	2.70112i	0.0402773	+	0.0998363i
$733$	19.6399			0.725416			0.362708	−	0.931903i	$-0.381852\pi$
$733$	19.6399			0.725416			0.362708	+	0.931903i	$0.381852\pi$
$734$	−7.70236	+	13.3409i	−0.284299	+	0.492421i
$735$	−24.4502	−	11.7128i	−0.901858	−	0.432032i
$736$	3.99454	+	6.91875i	0.147241	+	0.255029i
$737$	8.57413	+	14.8508i	0.315832	+	0.547037i
$738$	−7.56244	−	2.17684i	−0.278377	−	0.0801305i
$739$	−18.6678	+	32.3336i	−0.686706	+	1.18941i	0.286191	+	0.958172i	$0.407611\pi$
$739$	−18.6678	+	32.3336i	−0.686706	+	1.18941i	−0.972897	+	0.231237i	$0.925723\pi$
$740$	−14.1515	−	2.45211i	−0.520218	−	0.0901412i
$741$	−10.4843	−	25.9877i	−0.385151	−	0.954682i
$742$	−7.79805	−	0.527313i	−0.286275	−	0.0193583i
$743$	6.11862	−	10.5978i	0.224470	−	0.388794i	−0.731690	−	0.681637i	$-0.761268\pi$
$743$	6.11862	−	10.5978i	0.224470	−	0.388794i	0.956160	+	0.292843i	$0.0946015\pi$
$744$	6.88156	−	8.79875i	0.252290	−	0.322578i
$745$	9.01314	+	24.5371i	0.330216	+	0.898970i
$746$	25.3219	+	14.6196i	0.927101	+	0.535262i
$747$	11.0448	−	38.3700i	0.404107	−	1.40389i
$748$	−26.7117			−0.976675
$749$	−8.48987	−	0.574095i	−0.310213	−	0.0209770i
$750$	−15.3590	−	11.7941i	−0.560833	−	0.430658i
$751$	16.0433			0.585427			0.292713	−	0.956200i	$-0.405442\pi$
$751$	16.0433			0.585427			0.292713	+	0.956200i	$0.405442\pi$
$752$	7.12570	−	4.11402i	0.259848	−	0.150023i
$753$	26.0173	−	10.4962i	0.948121	−	0.382504i
$754$	−25.8391	−	14.9182i	−0.941003	−	0.543288i
$755$	19.0248	−	6.98831i	0.692383	−	0.254331i
$756$	−6.44487	+	12.1435i	−0.234398	+	0.441653i
$757$			5.92914i			0.215498i	0.994178	+	0.107749i	$0.0343643\pi$
$757$			5.92914i			0.215498i	−0.994178	+	0.107749i	$0.965636\pi$
$758$	16.0739	−	27.8408i	0.583831	−	1.01122i
$759$	18.6942	+	46.3377i	0.678556	+	1.68195i
$760$	−6.87110	+	8.23806i	−0.249241	+	0.298826i
$761$	−14.5872			−0.528786			−0.264393	−	0.964415i	$-0.585172\pi$
$761$	−14.5872			−0.528786			−0.264393	+	0.964415i	$0.585172\pi$
$762$	−14.4245	−	2.03472i	−0.522544	−	0.0737103i
$763$	8.51375	+	17.3546i	0.308218	+	0.628278i
$764$		−	18.8086i		−	0.680471i
$765$	−41.0856	+	27.8288i	−1.48545	+	1.00615i
$766$	5.49320	+	3.17150i	0.198478	+	0.114591i
$767$	3.79495			0.137028
$768$	1.36433	+	1.06705i	0.0492311	+	0.0385039i
$769$	−28.3116	−	16.3457i	−1.02094	−	0.589441i	−0.106565	−	0.994306i	$-0.533985\pi$
$769$	−28.3116	−	16.3457i	−1.02094	−	0.589441i	−0.914377	+	0.404865i	$0.867319\pi$
$770$	−14.7588	+	15.4448i	−0.531870	+	0.556592i
$771$	0.619476	+	1.53551i	0.0223099	+	0.0553000i
$772$	−4.76835	−	2.75301i	−0.171617	−	0.0990828i
$773$	14.5424	+	8.39605i	0.523053	+	0.301985i	0.738183	−	0.674601i	$-0.235684\pi$
$773$	14.5424	+	8.39605i	0.523053	+	0.301985i	−0.215130	+	0.976585i	$0.569017\pi$
$774$	−1.58682	−	1.64656i	−0.0570371	−	0.0591843i
$775$	10.8490	−	30.3658i	0.389709	−	1.09077i
$776$	−4.18720	−	7.25244i	−0.150312	−	0.260347i
$777$	9.14558	+	27.9772i	0.328096	+	1.00367i
$778$	21.0192	+	12.1355i	0.753576	+	0.435077i
$779$			12.5845i			0.450887i
$780$	−9.68500	+	8.76349i	−0.346779	+	0.313783i
$781$	−5.09067			−0.182158
$782$	51.1808	−	29.5492i	1.83022	−	1.05668i
$783$	4.73541	+	45.7267i	0.169230	+	1.63414i
$784$	6.93627	+	0.942388i	0.247724	+	0.0336567i
$785$	33.9663	+	28.3302i	1.21231	+	1.01115i
$786$	1.40179	−	9.93751i	0.0500002	−	0.354459i
$787$	10.9653	+	18.9925i	0.390872	+	0.677010i	0.992565	−	0.121717i	$-0.0388402\pi$
$787$	10.9653	+	18.9925i	0.390872	+	0.677010i	−0.601693	+	0.798728i	$0.705507\pi$
$788$	−6.56089	−	11.3638i	−0.233722	−	0.404818i
$789$	26.4605	−	10.6751i	0.942019	−	0.380042i
$790$	−0.296222	−	0.247069i	−0.0105391	−	0.00879031i
$791$	15.8942	+	32.3991i	0.565133	+	1.15198i
$792$	7.51719	+	7.80017i	0.267112	+	0.277167i
$793$	4.91134	−	2.83557i	0.174407	−	0.100694i
$794$	−6.46548			−0.229451
$795$	2.40619	+	11.1854i	0.0853388	+	0.396704i
$796$			11.0309i			0.390979i
$797$	−19.5566	−	11.2910i	−0.692730	−	0.399948i	0.111904	−	0.993719i	$-0.464305\pi$
$797$	−19.5566	−	11.2910i	−0.692730	−	0.399948i	−0.804634	+	0.593771i	$0.797638\pi$
$798$	21.5124	+	4.53248i	0.761530	+	0.160448i
$799$	−30.4331	−	52.7117i	−1.07665	−	1.86480i
$800$	4.70851	+	1.68225i	0.166471	+	0.0594765i
$801$	40.8250	+	11.7514i	1.44248	+	0.415216i
$802$	31.2348	+	18.0334i	1.10294	+	0.636783i
$803$	−17.4035	−	10.0479i	−0.614155	−	0.354583i
$804$	−8.14480	−	1.14891i	−0.287245	−	0.0405189i
$805$	11.1930	−	45.9196i	0.394503	−	1.61845i
$806$	−18.8353	−	10.8746i	−0.663446	−	0.383041i
$807$	−4.25529	+	30.1664i	−0.149793	+	1.06191i
$808$	−15.7774			−0.555047
$809$	−13.7016	−	7.91060i	−0.481721	−	0.278122i	0.239412	−	0.970918i	$-0.423045\pi$
$809$	−13.7016	−	7.91060i	−0.481721	−	0.278122i	−0.721133	+	0.692796i	$0.756379\pi$
$810$	19.6887	+	4.16598i	0.691790	+	0.146378i
$811$			20.5447i			0.721421i	0.932678	+	0.360710i	$0.117466\pi$
$811$			20.5447i			0.721421i	−0.932678	+	0.360710i	$0.882534\pi$
$812$	21.0149	−	10.3094i	0.737477	−	0.361789i
$813$	6.71284	−	8.58302i	0.235430	−	0.301020i
$814$	23.1933			0.812924
$815$	18.8645	−	22.6175i	0.660794	−	0.792255i
$816$	7.89341	−	10.0925i	0.276325	−	0.353308i
$817$	−1.82842	+	3.16691i	−0.0639682	+	0.110796i
$818$			35.5824i			1.24411i
$819$	25.1651	+	9.12301i	0.879340	+	0.318784i
$820$	5.50588	−	2.02246i	0.192274	−	0.0706273i
$821$	11.7506	+	6.78423i	0.410100	+	0.236771i	0.690833	−	0.723015i	$-0.257244\pi$
$821$	11.7506	+	6.78423i	0.410100	+	0.236771i	−0.280733	+	0.959786i	$0.590578\pi$
$822$	−1.80401	+	12.7889i	−0.0629219	+	0.446063i
$823$	16.4510	−	9.49800i	0.573446	−	0.331079i	−0.185078	−	0.982724i	$-0.559254\pi$
$823$	16.4510	−	9.49800i	0.573446	−	0.331079i	0.758525	+	0.651644i	$0.225921\pi$
$824$	4.00416			0.139492
$825$	27.6904	+	14.5316i	0.964055	+	0.505924i
$826$	−1.65918	+	2.47206i	−0.0577304	+	0.0860139i
$827$	45.9391			1.59746			0.798730	−	0.601689i	$-0.205505\pi$
$827$	45.9391			1.59746			0.798730	+	0.601689i	$0.205505\pi$
$828$	−23.0321	−	6.62975i	−0.800420	−	0.230400i
$829$	23.0544	+	13.3105i	0.800714	+	0.462292i	0.843721	−	0.536782i	$-0.180360\pi$
$829$	23.0544	+	13.3105i	0.800714	+	0.462292i	−0.0430068	+	0.999075i	$0.513694\pi$
$830$	10.2615	+	27.9355i	0.356181	+	0.969656i
$831$	−1.79329	−	4.44506i	−0.0622084	−	0.154197i
$832$	1.68621	−	2.92060i	0.0584588	−	0.101254i
$833$	6.97122	−	51.3104i	0.241538	−	1.77780i
$834$	−8.86446	+	11.3341i	−0.306951	+	0.392467i
$835$	−4.80382	−	0.832385i	−0.166243	−	0.0288059i
$836$	8.66168	−	15.0025i	0.299571	−	0.518871i
$837$	3.45186	+	33.3324i	0.119314	+	1.15214i
$838$	−9.77575	−	16.9321i	−0.337698	−	0.584909i
$839$	−11.2983	−	19.5693i	−0.390062	−	0.675607i	0.602396	−	0.798198i	$-0.294213\pi$
$839$	−11.2983	−	19.5693i	−0.390062	−	0.675607i	−0.992457	+	0.122591i	$0.960880\pi$
$840$	−1.47424	−	10.1403i	−0.0508662	−	0.349875i
$841$	24.6363	−	42.6713i	0.849527	−	1.47142i
$842$	13.6570			0.470652
$843$	−3.71153	+	4.74555i	−0.127832	+	0.163445i
$844$	−14.1815			−0.488147
$845$	−2.79350	−	2.32997i	−0.0960994	−	0.0801533i
$846$	−6.82805	+	23.7210i	−0.234753	+	0.815544i
$847$	3.00636	−	4.47926i	0.103300	−	0.153909i
$848$	−1.47706	−	2.55834i	−0.0507224	−	0.0878537i
$849$	−16.6833	−	13.0481i	−0.572568	−	0.447809i
$850$	12.4443	−	34.8307i	0.426835	−	1.19468i
$851$	−44.4394	+	25.6571i	−1.52336	+	0.879514i
$852$	1.50431	−	1.92341i	0.0515370	−	0.0658951i
$853$	−5.34386	−	9.25584i	−0.182970	−	0.316914i	0.759920	−	0.650016i	$-0.225238\pi$
$853$	−5.34386	−	9.25584i	−0.182970	−	0.316914i	−0.942891	+	0.333102i	$0.891905\pi$
$854$	−0.300172	+	4.43902i	−0.0102717	+	0.151900i
$855$	−2.30725	−	32.0995i	−0.0789062	−	1.09778i
$856$	−1.60810	−	2.78531i	−0.0549637	−	0.0951999i
$857$		−	27.2333i		−	0.930273i	−0.885239	−	0.465137i	$-0.846005\pi$
$857$		−	27.2333i		−	0.930273i	0.885239	−	0.465137i	$-0.153995\pi$
$858$	12.9942	−	16.6143i	0.443614	−	0.567204i
$859$			26.1550i			0.892397i	0.894934	+	0.446198i	$0.147222\pi$
$859$			26.1550i			0.892397i	−0.894934	+	0.446198i	$0.852778\pi$
$860$	1.67941	+	0.291000i	0.0572673	+	0.00992303i
$861$	−8.94759	−	8.02757i	−0.304933	−	0.273579i
$862$	6.33629	−	3.65826i	0.215815	−	0.124601i
$863$	−25.1857	−	43.6229i	−0.857331	−	1.48494i	−0.874466	−	0.485087i	$-0.838788\pi$
$863$	−25.1857	−	43.6229i	−0.857331	−	1.48494i	0.0171355	−	0.999853i	$-0.494545\pi$
$864$	−5.16851	+	0.535245i	−0.175836	+	0.0182094i
$865$	57.1336	+	9.89986i	1.94260	+	0.336605i
$866$	3.72503	−	6.45195i	0.126582	−	0.219246i
$867$	−51.4647	−	40.2509i	−1.74783	−	1.36699i
$868$	15.3187	−	7.51501i	0.519952	−	0.255076i
$869$	0.539454	+	0.311454i	0.0182997	+	0.0105653i
$870$	−22.9901	−	25.4076i	−0.779437	−	0.861397i
$871$			16.0155i			0.542663i
$872$	−3.65311	+	6.32737i	−0.123710	+	0.214272i
$873$	24.1429	+	6.94950i	0.817113	+	0.235205i
$874$			38.3272i			1.29644i
$875$	−13.2635	−	26.4401i	−0.448389	−	0.893838i
$876$	8.93922	−	3.60638i	0.302028	−	0.121848i
$877$		−	34.2640i		−	1.15701i	−0.815677	−	0.578507i	$-0.803636\pi$
$877$		−	34.2640i		−	1.15701i	0.815677	−	0.578507i	$-0.196364\pi$
$878$	13.2005	−	7.62131i	0.445495	−	0.257207i
$879$	21.4774	+	3.02961i	0.724415	+	0.102186i
$880$	−7.95578	−	1.37854i	−0.268189	−	0.0464707i
$881$	−8.34204			−0.281050			−0.140525	−	0.990077i	$-0.544879\pi$
$881$	−8.34204			−0.281050			−0.140525	+	0.990077i	$0.544879\pi$
$882$	−16.9452	+	12.4041i	−0.570574	+	0.417667i
$883$			32.5885i			1.09669i	0.836252	+	0.548345i	$0.184742\pi$
$883$			32.5885i			1.09669i	−0.836252	+	0.548345i	$0.815258\pi$
$884$	−21.6048	−	12.4736i	−0.726650	−	0.419531i
$885$	4.14821	+	1.33660i	0.139441	+	0.0449295i
$886$	−1.09863	−	1.90288i	−0.0369091	−	0.0639285i
$887$		−	22.6116i		−	0.759222i	−0.925146	−	0.379611i	$-0.876058\pi$
$887$		−	22.6116i		−	0.759222i	0.925146	−	0.379611i	$-0.123942\pi$
$888$	−6.85371	+	8.76314i	−0.229996	+	0.294072i
$889$	−18.4762	−	12.4007i	−0.619670	−	0.415907i
$890$	−29.7229	+	10.9180i	−0.996314	+	0.365973i
$891$	−32.4764	−	1.20039i	−1.08800	−	0.0402144i
$892$	1.85603	−	3.21474i	0.0621446	−	0.107638i
$893$	39.4737			1.32094
$894$	20.0496	+	2.82820i	0.670558	+	0.0945892i
$895$	−31.5239	−	5.46234i	−1.05373	−	0.182586i
$896$	1.16527	+	2.37532i	0.0389291	+	0.0793538i
$897$	−6.51818	+	46.2084i	−0.217636	+	1.54285i
$898$	10.1254	+	5.84593i	0.337890	+	0.195081i
$899$	28.5283	−	49.4125i	0.951472	−	1.64800i
$900$	−13.6731	+	6.16815i	−0.455770	+	0.205605i
$901$	−18.9251	+	10.9264i	−0.630485	+	0.364011i
$902$	−8.20311	+	4.73607i	−0.273134	+	0.157694i
$903$	−1.08534	−	3.32015i	−0.0361178	−	0.110488i
$904$	−6.81995	+	11.8125i	−0.226828	+	0.392878i
$905$	3.23592	+	8.80939i	0.107566	+	0.292834i
$906$	2.19284	−	15.5454i	0.0728522	−	0.516461i
$907$			4.76791i			0.158316i	0.996862	+	0.0791578i	$0.0252231\pi$
$907$			4.76791i			0.158316i	−0.996862	+	0.0791578i	$0.974777\pi$
$908$	13.9721	−	8.06681i	0.463681	−	0.267706i
$909$	34.0814	−	32.8450i	1.13041	−	1.08940i
$910$	−19.1494	+	5.60009i	−0.634798	+	0.185641i
$911$	−45.4053	+	26.2148i	−1.50434	+	0.868534i	−0.504357	+	0.863495i	$0.668271\pi$
$911$	−45.4053	+	26.2148i	−1.50434	+	0.868534i	−0.999987	+	0.00503892i	$0.998396\pi$
$912$	3.10884	+	7.70595i	0.102944	+	0.255170i
$913$	−24.0297	−	41.6206i	−0.795266	−	1.37744i
$914$	18.8329	−	10.8732i	0.622935	−	0.359652i
$915$	6.36723	−	1.36972i	0.210494	−	0.0452815i
$916$	6.70713	−	3.87236i	0.221610	−	0.127946i
$917$	8.54328	−	12.7289i	0.282124	−	0.420344i
$918$	3.95942	+	38.2336i	0.130680	+	1.26190i
$919$	11.9138	+	20.6354i	0.393001	+	0.680698i	0.992844	−	0.119420i	$-0.0381034\pi$
$919$	11.9138	+	20.6354i	0.393001	+	0.680698i	−0.599842	+	0.800118i	$0.704770\pi$
$920$	16.7686	−	6.15957i	0.552846	−	0.203075i
$921$	−11.9723	+	4.83001i	−0.394499	+	0.159154i
$922$	−15.7604			−0.519043
$923$	−4.11742	−	2.37719i	−0.135526	−	0.0782462i
$924$	5.14153	+	15.7284i	0.169144	+	0.517427i
$925$	−10.8051	+	30.2429i	−0.355271	+	0.994380i
$926$	6.80572	−	3.92928i	0.223650	−	0.129124i
$927$	−8.64957	+	8.33577i	−0.284089	+	0.273783i
$928$	7.66188	+	4.42359i	0.251514	+	0.145211i
$929$	5.24880	−	9.09118i	0.172207	−	0.298272i	−0.766984	−	0.641666i	$-0.778243\pi$
$929$	5.24880	−	9.09118i	0.172207	−	0.298272i	0.939191	+	0.343394i	$0.111577\pi$
$930$	−16.7586	−	18.5208i	−0.549535	−	0.607320i
$931$	26.5577	+	20.5536i	0.870394	+	0.673616i
$932$	−8.53036	+	14.7750i	−0.279421	+	0.483972i
$933$	30.7279	+	24.0325i	1.00599	+	0.786790i
$934$		−	25.5677i		−	0.836602i
$935$	−10.1976	+	58.8521i	−0.333499	+	1.92467i
$936$	2.43758	+	9.81922i	0.0796747	+	0.320951i
$937$	−21.2575			−0.694452			−0.347226	−	0.937781i	$-0.612876\pi$
$937$	−21.2575			−0.694452			−0.347226	+	0.937781i	$0.612876\pi$
$938$	−10.4326	−	7.00209i	−0.340636	−	0.228626i
$939$	−4.98206	+	35.3186i	−0.162583	+	1.15258i
$940$	−6.34381	−	17.2702i	−0.206912	−	0.563292i
$941$	30.0733	+	52.0884i	0.980361	+	1.69803i	0.660972	+	0.750411i	$0.270144\pi$
$941$	30.0733	+	52.0884i	0.980361	+	1.69803i	0.319389	+	0.947624i	$0.396522\pi$
$942$	31.7724	−	12.8181i	1.03520	−	0.417635i
$943$	10.4784	−	18.1490i	0.341222	−	0.591014i
$944$	−1.12529			−0.0366251
$945$	24.2945	+	18.8356i	0.790300	+	0.612721i
$946$	−2.75243			−0.0894892
$947$	25.7890	−	44.6679i	0.838030	−	1.45151i	−0.0535089	−	0.998567i	$-0.517041\pi$
$947$	25.7890	−	44.6679i	0.838030	−	1.45151i	0.891539	−	0.452944i	$-0.149626\pi$
$948$	−0.277088	+	0.111787i	−0.00899940	+	0.00363066i
$949$	−9.38415	−	16.2538i	−0.304622	−	0.527622i
$950$	15.5272	+	18.2837i	0.503770	+	0.593201i
$951$	2.10845	−	14.9471i	0.0683711	−	0.484693i
$952$	17.5712	−	8.62001i	0.569485	−	0.279376i
$953$	21.6816			0.702337			0.351169	−	0.936312i	$-0.385784\pi$
$953$	21.6816			0.702337			0.351169	+	0.936312i	$0.385784\pi$
$954$	8.51654	+	2.45147i	0.275733	+	0.0793694i
$955$	−41.4398	−	7.18052i	−1.34096	−	0.232356i
$956$			12.7096i			0.411059i
$957$	43.5859	+	34.0888i	1.40893	+	1.10194i
$958$	−3.98318	+	6.89907i	−0.128691	+	0.222899i
$959$	−10.9946	+	16.3811i	−0.355034	+	0.528975i
$960$	2.87183	−	2.59858i	0.0926878	−	0.0838688i
$961$	5.29563	−	9.17230i	0.170827	−	0.295881i
$962$	18.7591	+	10.8306i	0.604818	+	0.349192i
$963$	9.27211	+	2.66896i	0.298789	+	0.0860062i
$964$	−5.49087	+	3.17016i	−0.176849	+	0.102104i
$965$	−7.88592	+	9.45479i	−0.253857	+	0.304360i
$966$	−27.2507	−	24.4487i	−0.876776	−	0.786623i
$967$	−24.9910	−	14.4286i	−0.803657	−	0.463992i	0.0410912	−	0.999155i	$-0.486917\pi$
$967$	−24.9910	−	14.4286i	−0.803657	−	0.463992i	−0.844748	+	0.535164i	$0.820250\pi$
$968$	2.03898			0.0655352
$969$	57.0040	−	22.9973i	1.83123	−	0.738781i
$970$	−17.5774	+	6.45664i	−0.564375	+	0.207310i
$971$	−14.9307	−	25.8608i	−0.479150	−	0.829911i	0.520565	−	0.853822i	$-0.325722\pi$
$971$	−14.9307	−	25.8608i	−0.479150	−	0.829911i	−0.999714	+	0.0239109i	$0.992388\pi$
$972$	10.0505	−	11.9159i	0.322369	−	0.382202i
$973$	−19.7328	+	9.68043i	−0.632604	+	0.310340i
$974$	−1.35301	+	0.781161i	−0.0433533	+	0.0250300i
$975$	15.6106	+	24.6840i	0.499940	+	0.790520i
$976$	−1.45633	+	0.840811i	−0.0466159	+	0.0269137i
$977$	0.215010	+	0.372408i	0.00687877	+	0.0119144i	0.869444	−	0.494031i	$-0.164477\pi$
$977$	0.215010	+	0.372408i	0.00687877	+	0.0119144i	−0.862566	+	0.505945i	$0.831144\pi$
$978$	−8.53527	−	21.1566i	−0.272928	−	0.676512i
$979$	44.2836	−	25.5671i	1.41531	−	0.817129i
$980$	4.72435	−	14.9225i	0.150914	−	0.476681i
$981$	−5.28092	−	21.2730i	−0.168607	−	0.679193i
$982$	−3.63710	+	2.09988i	−0.116065	+	0.0670099i
$983$		−	7.98937i		−	0.254821i	−0.991850	−	0.127411i	$-0.959333\pi$
$983$		−	7.98937i		−	0.254821i	0.991850	−	0.127411i	$-0.0406666\pi$
$984$	0.634620	−	4.49892i	0.0202310	−	0.143420i
$985$	−27.5419	+	10.1169i	−0.877557	+	0.322350i
$986$	32.7231	−	56.6780i	1.04211	−	1.80500i
$987$	−25.1799	+	28.0658i	−0.801487	+	0.893343i
$988$	14.0114	−	8.08950i	0.445763	−	0.257361i
$989$	5.27378	−	3.04482i	0.167697	−	0.0968196i
$990$	20.0554	−	13.5843i	0.637404	−	0.431737i
$991$	28.7067	−	49.7215i	0.911900	−	1.57946i	0.100522	−	0.994935i	$-0.467949\pi$
$991$	28.7067	−	49.7215i	0.911900	−	1.57946i	0.811378	−	0.584522i	$-0.198718\pi$
$992$	5.58511	+	3.22456i	0.177327	+	0.102380i
$993$	−3.47524	+	24.6366i	−0.110284	+	0.781817i
$994$	3.34869	−	1.64279i	0.106214	−	0.0521060i
$995$	24.3036	+	4.21123i	0.770477	+	0.133505i
$996$	22.8265	+	3.21991i	0.723284	+	0.102027i
$997$	−25.2757			−0.800490			−0.400245	−	0.916408i	$-0.631075\pi$
$997$	−25.2757			−0.800490			−0.400245	+	0.916408i	$0.631075\pi$
$998$	−5.57817	+	9.66168i	−0.176574	+	0.305835i
$999$	−3.43790	−	33.1975i	−0.108770	−	1.05032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.59.3	yes	48
3.2	odd	2		1890.2.r.a.1529.23		48
5.4	even	2		630.2.r.a.59.22	✓	48
7.5	odd	6		630.2.bi.a.509.12	yes	48
9.2	odd	6		630.2.bi.b.479.13	yes	48
9.7	even	3		1890.2.bi.a.899.15		48
15.14	odd	2		1890.2.r.b.1529.23		48
21.5	even	6		1890.2.bi.b.719.18		48
35.19	odd	6		630.2.bi.b.509.13	yes	48
45.29	odd	6		630.2.bi.a.479.12	yes	48
45.34	even	6		1890.2.bi.b.899.18		48
63.47	even	6		630.2.r.a.299.22	yes	48
63.61	odd	6		1890.2.r.b.89.23		48
105.89	even	6		1890.2.bi.a.719.15		48
315.124	odd	6		1890.2.r.a.89.23		48
315.299	even	6	inner	630.2.r.b.299.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.22	✓	48	5.4	even	2
630.2.r.a.299.22	yes	48	63.47	even	6
630.2.r.b.59.3	yes	48	1.1	even	1	trivial
630.2.r.b.299.3	yes	48	315.299	even	6	inner
630.2.bi.a.479.12	yes	48	45.29	odd	6
630.2.bi.a.509.12	yes	48	7.5	odd	6
630.2.bi.b.479.13	yes	48	9.2	odd	6
630.2.bi.b.509.13	yes	48	35.19	odd	6
1890.2.r.a.89.23		48	315.124	odd	6
1890.2.r.a.1529.23		48	3.2	odd	2
1890.2.r.b.89.23		48	63.61	odd	6
1890.2.r.b.1529.23		48	15.14	odd	2
1890.2.bi.a.719.15		48	105.89	even	6
1890.2.bi.a.899.15		48	9.7	even	3
1890.2.bi.b.719.18		48	21.5	even	6
1890.2.bi.b.899.18		48	45.34	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.60626 + 0.648019i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 + 1.71507i) q^{6} +(-1.47445 + 2.19682i) q^{7} -1.00000 q^{8} +(2.16014 - 2.08177i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.60626 + 0.648019i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.09894 + 0.770998i) q^{5} +(-0.241929 + 1.71507i) q^{6} +(-1.47445 + 2.19682i) q^{7} -1.00000 q^{8} +(2.16014 - 2.08177i) q^{9} +(-0.381768 + 2.20324i) q^{10} -3.61095i q^{11} +(1.36433 + 1.06705i) q^{12} +(1.68621 - 2.92060i) q^{13} +(1.16527 + 2.37532i) q^{14} +(2.87183 - 2.59858i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.40634 + 3.69870i) q^{17} +(-0.722799 - 2.91163i) q^{18} +(-4.15471 + 2.39873i) q^{19} +(1.71718 + 1.43224i) q^{20} +(0.944768 - 4.48413i) q^{21} +(-3.12718 - 1.80548i) q^{22} +7.98909 q^{23} +(1.60626 - 0.648019i) q^{24} +(3.81112 - 3.23656i) q^{25} +(-1.68621 - 2.92060i) q^{26} +(-2.12072 + 4.74368i) q^{27} +(2.63972 + 0.178501i) q^{28} +(7.66188 - 4.42359i) q^{29} +(-0.814522 - 3.78636i) q^{30} +(5.58511 - 3.22456i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.33997 + 5.80013i) q^{33} +(6.40634 - 3.69870i) q^{34} +(1.40104 - 5.74779i) q^{35} +(-2.88294 - 0.829851i) q^{36} +(-5.56251 + 3.21152i) q^{37} +4.79745i q^{38} +(-0.815885 + 5.78394i) q^{39} +(2.09894 - 0.770998i) q^{40} +(1.31158 - 2.27173i) q^{41} +(-3.41099 - 3.06026i) q^{42} +(0.660123 - 0.381122i) q^{43} +(-3.12718 + 1.80548i) q^{44} +(-2.92897 + 6.03499i) q^{45} +(3.99454 - 6.91875i) q^{46} +(-7.12570 - 4.11402i) q^{47} +(0.241929 - 1.71507i) q^{48} +(-2.65201 - 6.47818i) q^{49} +(-0.897383 - 4.91881i) q^{50} +(-12.6871 - 1.78965i) q^{51} -3.37242 q^{52} +(-1.47706 + 2.55834i) q^{53} +(3.04779 + 4.20844i) q^{54} +(2.78404 + 7.57918i) q^{55} +(1.47445 - 2.19682i) q^{56} +(5.11913 - 6.54531i) q^{57} -8.84718i q^{58} +(0.562645 + 0.974530i) q^{59} +(-3.68635 - 1.18779i) q^{60} +(1.45633 + 0.840811i) q^{61} -6.44913i q^{62} +(1.38826 + 7.81490i) q^{63} +1.00000 q^{64} +(-1.28748 + 7.43024i) q^{65} +(6.19304 + 0.873594i) q^{66} +(-4.11272 + 2.37448i) q^{67} -7.39740i q^{68} +(-12.8325 + 5.17708i) q^{69} +(-4.27721 - 4.08723i) q^{70} -1.40979i q^{71} +(-2.16014 + 2.08177i) q^{72} +(2.78262 - 4.81964i) q^{73} +6.42303i q^{74} +(-4.02430 + 7.66844i) q^{75} +(4.15471 + 2.39873i) q^{76} +(7.93260 + 5.32416i) q^{77} +(4.60109 + 3.59855i) q^{78} +(-0.0862526 + 0.149394i) q^{79} +(0.381768 - 2.20324i) q^{80} +(0.332429 - 8.99386i) q^{81} +(-1.31158 - 2.27173i) q^{82} +(11.5262 - 6.65467i) q^{83} +(-4.35575 + 1.42387i) q^{84} +(-16.2982 - 2.82409i) q^{85} -0.762245i q^{86} +(-9.44040 + 12.0705i) q^{87} +3.61095i q^{88} +(7.08044 + 12.2637i) q^{89} +(3.76197 + 5.55406i) q^{90} +(3.92979 + 8.01056i) q^{91} +(-3.99454 - 6.91875i) q^{92} +(-6.88156 + 8.79875i) q^{93} +(-7.12570 + 4.11402i) q^{94} +(6.87110 - 8.23806i) q^{95} +(-1.36433 - 1.06705i) q^{96} +(4.18720 + 7.25244i) q^{97} +(-6.93627 - 0.942388i) q^{98} +(-7.51719 - 7.80017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

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