LMFDB - Embedded newform 315.2.t.b.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	315.101
Dual form			315.2.t.b.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.692853i q^{2} +(-1.66836 + 0.465377i) q^{3} +1.51995 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.322438 - 1.15593i) q^{6} +(-0.669425 - 2.55966i) q^{7} +2.43881i q^{8} +(2.56685 - 1.55283i) q^{9} +O(q^{10})$	\(q+0.692853i q^{2} +(-1.66836 + 0.465377i) q^{3} +1.51995 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.322438 - 1.15593i) q^{6} +(-0.669425 - 2.55966i) q^{7} +2.43881i q^{8} +(2.56685 - 1.55283i) q^{9} +(0.600029 + 0.346427i) q^{10} +(1.74818 - 1.00931i) q^{11} +(-2.53583 + 0.707351i) q^{12} +(3.66483 - 2.11589i) q^{13} +(1.77347 - 0.463814i) q^{14} +(-0.431152 + 1.67753i) q^{15} +1.35017 q^{16} +(-1.55343 + 2.69061i) q^{17} +(1.07588 + 1.77845i) q^{18} +(-0.112967 + 0.0652213i) q^{19} +(0.759977 - 1.31632i) q^{20} +(2.30805 + 3.95890i) q^{21} +(0.699304 + 1.21123i) q^{22} +(0.326784 + 0.188669i) q^{23} +(-1.13497 - 4.06882i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.46600 + 2.53919i) q^{26} +(-3.55978 + 3.78523i) q^{27} +(-1.01750 - 3.89057i) q^{28} +(7.55077 + 4.35944i) q^{29} +(-1.16228 - 0.298725i) q^{30} -3.61134i q^{31} +5.81309i q^{32} +(-2.44688 + 2.49745i) q^{33} +(-1.86420 - 1.07630i) q^{34} +(-2.55145 - 0.700092i) q^{35} +(3.90149 - 2.36023i) q^{36} +(2.94155 + 5.09492i) q^{37} +(-0.0451888 - 0.0782693i) q^{38} +(-5.12957 + 5.23560i) q^{39} +(2.11207 + 1.21941i) q^{40} +(-1.02221 - 1.77052i) q^{41} +(-2.74294 + 1.59914i) q^{42} +(4.79579 - 8.30655i) q^{43} +(2.65715 - 1.53411i) q^{44} +(-0.0613670 - 2.99937i) q^{45} +(-0.130720 + 0.226414i) q^{46} -4.62554 q^{47} +(-2.25257 + 0.628337i) q^{48} +(-6.10374 + 3.42701i) q^{49} +(0.600029 - 0.346427i) q^{50} +(1.33952 - 5.21184i) q^{51} +(5.57038 - 3.21606i) q^{52} +(-8.28624 - 4.78406i) q^{53} +(-2.62261 - 2.46640i) q^{54} -2.01862i q^{55} +(6.24254 - 1.63260i) q^{56} +(0.158117 - 0.161385i) q^{57} +(-3.02045 + 5.23157i) q^{58} -11.3677 q^{59} +(-0.655331 + 2.54977i) q^{60} -5.36204i q^{61} +2.50213 q^{62} +(-5.69304 - 5.53076i) q^{63} -1.32729 q^{64} -4.23178i q^{65} +(-1.73037 - 1.69533i) q^{66} -13.5243 q^{67} +(-2.36114 + 4.08961i) q^{68} +(-0.632996 - 0.162690i) q^{69} +(0.485061 - 1.76778i) q^{70} +7.48885i q^{71} +(3.78706 + 6.26006i) q^{72} +(-1.34658 - 0.777450i) q^{73} +(-3.53003 + 2.03806i) q^{74} +(1.23721 + 1.21215i) q^{75} +(-0.171704 + 0.0991334i) q^{76} +(-3.75377 - 3.79908i) q^{77} +(-3.62750 - 3.55404i) q^{78} -2.71622 q^{79} +(0.675084 - 1.16928i) q^{80} +(4.17743 - 7.97177i) q^{81} +(1.22671 - 0.708240i) q^{82} +(-0.308490 + 0.534320i) q^{83} +(3.50813 + 6.01735i) q^{84} +(1.55343 + 2.69061i) q^{85} +(5.75522 + 3.32278i) q^{86} +(-14.6262 - 3.75916i) q^{87} +(2.46152 + 4.26347i) q^{88} +(0.725466 + 1.25654i) q^{89} +(2.07813 - 0.0425183i) q^{90} +(-7.86930 - 7.96430i) q^{91} +(0.496697 + 0.286768i) q^{92} +(1.68063 + 6.02502i) q^{93} -3.20482i q^{94} +0.130443i q^{95} +(-2.70528 - 9.69833i) q^{96} +(11.3504 + 6.55314i) q^{97} +(-2.37441 - 4.22900i) q^{98} +(2.92002 - 5.30537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			0.692853i			0.489921i	0.969533	+	0.244961i	$0.0787751\pi$
$2$			0.692853i			0.489921i	−0.969533	+	0.244961i	$0.921225\pi$
$3$	−1.66836	+	0.465377i	−0.963228	+	0.268685i
$3$	−1.66836	+	0.465377i	−0.963228	+	0.268685i
$4$	1.51995			0.759977
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.322438	−	1.15593i	−0.131635	−	0.471906i
$7$	−0.669425	−	2.55966i	−0.253019	−	0.967461i
$7$	−0.669425	−	2.55966i	−0.253019	−	0.967461i
$8$			2.43881i			0.862250i
$9$	2.56685	−	1.55283i	0.855616	−	0.517611i
$10$	0.600029	+	0.346427i	0.189746	+	0.109550i
$11$	1.74818	−	1.00931i	0.527095	−	0.304318i	−0.212738	−	0.977109i	$-0.568238\pi$
$11$	1.74818	−	1.00931i	0.527095	−	0.304318i	0.739833	+	0.672791i	$0.234905\pi$
$12$	−2.53583	+	0.707351i	−0.732031	+	0.204195i
$13$	3.66483	−	2.11589i	1.01644	−	0.586843i	0.103370	−	0.994643i	$-0.467037\pi$
$13$	3.66483	−	2.11589i	1.01644	−	0.586843i	0.913071	+	0.407800i	$0.133704\pi$
$14$	1.77347	−	0.463814i	0.473980	−	0.123959i
$15$	−0.431152	+	1.67753i	−0.111323	+	0.433136i
$16$	1.35017			0.337542
$17$	−1.55343	+	2.69061i	−0.376761	+	0.652569i	−0.990589	−	0.136871i	$-0.956296\pi$
$17$	−1.55343	+	2.69061i	−0.376761	+	0.652569i	0.613828	+	0.789440i	$0.289629\pi$
$18$	1.07588	+	1.77845i	0.253588	+	0.419185i
$19$	−0.112967	+	0.0652213i	−0.0259163	+	0.0149628i	−0.512902	−	0.858447i	$-0.671430\pi$
$19$	−0.112967	+	0.0652213i	−0.0259163	+	0.0149628i	0.486986	+	0.873410i	$0.338096\pi$
$20$	0.759977	−	1.31632i	0.169936	−	0.294338i
$21$	2.30805	+	3.95890i	0.503658	+	0.863903i
$22$	0.699304	+	1.21123i	0.149092	+	0.258235i
$23$	0.326784	+	0.188669i	0.0681392	+	0.0393402i	0.533683	−	0.845685i	$-0.320808\pi$
$23$	0.326784	+	0.188669i	0.0681392	+	0.0393402i	−0.465543	+	0.885025i	$0.654141\pi$
$24$	−1.13497	−	4.06882i	−0.231674	−	0.830544i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.46600	+	2.53919i	0.287507	+	0.497976i
$27$	−3.55978	+	3.78523i	−0.685079	+	0.728469i
$28$	−1.01750	−	3.89057i	−0.192289	−	0.735248i
$29$	7.55077	+	4.35944i	1.40214	+	0.809527i	0.994612	−	0.103665i	$-0.0330569\pi$
$29$	7.55077	+	4.35944i	1.40214	+	0.809527i	0.407530	+	0.913192i	$0.366390\pi$
$30$	−1.16228	−	0.298725i	−0.212203	−	0.0545395i
$31$		−	3.61134i		−	0.648616i	−0.945951	−	0.324308i	$-0.894869\pi$
$31$		−	3.61134i		−	0.648616i	0.945951	−	0.324308i	$-0.105131\pi$
$32$			5.81309i			1.02762i
$33$	−2.44688	+	2.49745i	−0.425947	+	0.434751i
$34$	−1.86420	−	1.07630i	−0.319708	−	0.184583i
$35$	−2.55145	−	0.700092i	−0.431273	−	0.118337i
$36$	3.90149	−	2.36023i	0.650249	−	0.393372i
$37$	2.94155	+	5.09492i	0.483588	+	0.837599i	0.999822	−	0.0188484i	$-0.00599998\pi$
$37$	2.94155	+	5.09492i	0.483588	+	0.837599i	−0.516234	+	0.856447i	$0.672667\pi$
$38$	−0.0451888	−	0.0782693i	−0.00733059	−	0.0126970i
$39$	−5.12957	+	5.23560i	−0.821389	+	0.838366i
$40$	2.11207	+	1.21941i	0.333948	+	0.192805i
$41$	−1.02221	−	1.77052i	−0.159642	−	0.276508i	0.775098	−	0.631842i	$-0.217701\pi$
$41$	−1.02221	−	1.77052i	−0.159642	−	0.276508i	−0.934740	+	0.355333i	$0.884367\pi$
$42$	−2.74294	+	1.59914i	−0.423245	+	0.246753i
$43$	4.79579	−	8.30655i	0.731351	−	1.26674i	−0.224954	−	0.974369i	$-0.572223\pi$
$43$	4.79579	−	8.30655i	0.731351	−	1.26674i	0.956306	−	0.292368i	$-0.0944433\pi$
$44$	2.65715	−	1.53411i	0.400580	−	0.231275i
$45$	−0.0613670	−	2.99937i	−0.00914805	−	0.447120i
$46$	−0.130720	+	0.226414i	−0.0192736	+	0.0333829i
$47$	−4.62554			−0.674704			−0.337352	−	0.941379i	$-0.609531\pi$
$47$	−4.62554			−0.674704			−0.337352	+	0.941379i	$0.609531\pi$
$48$	−2.25257	+	0.628337i	−0.325130	+	0.0906926i
$49$	−6.10374	+	3.42701i	−0.871963	+	0.489572i
$50$	0.600029	−	0.346427i	0.0848569	−	0.0489921i
$51$	1.33952	−	5.21184i	0.187571	−	0.729803i
$52$	5.57038	−	3.21606i	0.772472	−	0.445987i
$53$	−8.28624	−	4.78406i	−1.13820	−	0.657142i	−0.192218	−	0.981352i	$-0.561568\pi$
$53$	−8.28624	−	4.78406i	−1.13820	−	0.657142i	−0.945985	+	0.324210i	$0.894901\pi$
$54$	−2.62261	−	2.46640i	−0.356892	−	0.335635i
$55$		−	2.01862i		−	0.272191i
$56$	6.24254	−	1.63260i	0.834194	−	0.218166i
$57$	0.158117	−	0.161385i	0.0209430	−	0.0213759i
$58$	−3.02045	+	5.23157i	−0.396605	+	0.686939i
$59$	−11.3677			−1.47995			−0.739974	−	0.672635i	$-0.765162\pi$
$59$	−11.3677			−1.47995			−0.739974	+	0.672635i	$0.765162\pi$
$60$	−0.655331	+	2.54977i	−0.0846029	+	0.329174i
$61$		−	5.36204i		−	0.686539i	−0.939237	−	0.343269i	$-0.888466\pi$
$61$		−	5.36204i		−	0.686539i	0.939237	−	0.343269i	$-0.111534\pi$
$62$	2.50213			0.317771
$63$	−5.69304	−	5.53076i	−0.717255	−	0.696810i
$64$	−1.32729			−0.165911
$65$		−	4.23178i		−	0.524888i
$66$	−1.73037	−	1.69533i	−0.212994	−	0.208680i
$67$	−13.5243			−1.65226			−0.826129	−	0.563482i	$-0.809462\pi$
$67$	−13.5243			−1.65226			−0.826129	+	0.563482i	$0.809462\pi$
$68$	−2.36114	+	4.08961i	−0.286330	+	0.495938i
$69$	−0.632996	−	0.162690i	−0.0762037	−	0.0195856i
$70$	0.485061	−	1.76778i	0.0579759	−	0.211290i
$71$			7.48885i			0.888763i	0.895838	+	0.444381i	$0.146576\pi$
$71$			7.48885i			0.888763i	−0.895838	+	0.444381i	$0.853424\pi$
$72$	3.78706	+	6.26006i	0.446310	+	0.737756i
$73$	−1.34658	−	0.777450i	−0.157606	−	0.0909936i	0.419123	−	0.907929i	$-0.362338\pi$
$73$	−1.34658	−	0.777450i	−0.157606	−	0.0909936i	−0.576729	+	0.816936i	$0.695671\pi$
$74$	−3.53003	+	2.03806i	−0.410358	+	0.236920i
$75$	1.23721	+	1.21215i	0.142860	+	0.139967i
$76$	−0.171704	+	0.0991334i	−0.0196958	+	0.0113714i
$77$	−3.75377	−	3.79908i	−0.427781	−	0.432946i
$78$	−3.62750	−	3.55404i	−0.410734	−	0.402416i
$79$	−2.71622			−0.305599			−0.152799	−	0.988257i	$-0.548829\pi$
$79$	−2.71622			−0.305599			−0.152799	+	0.988257i	$0.548829\pi$
$80$	0.675084	−	1.16928i	0.0754767	−	0.130729i
$81$	4.17743	−	7.97177i	0.464159	−	0.885752i
$82$	1.22671	−	0.708240i	0.135467	−	0.0782121i
$83$	−0.308490	+	0.534320i	−0.0338612	+	0.0586493i	−0.882459	−	0.470389i	$-0.844114\pi$
$83$	−0.308490	+	0.534320i	−0.0338612	+	0.0586493i	0.848598	+	0.529038i	$0.177447\pi$
$84$	3.50813	+	6.01735i	0.382768	+	0.656547i
$85$	1.55343	+	2.69061i	0.168493	+	0.291838i
$86$	5.75522	+	3.32278i	0.620602	+	0.358305i
$87$	−14.6262	−	3.75916i	−1.56809	−	0.403024i
$88$	2.46152	+	4.26347i	0.262399	+	0.454488i
$89$	0.725466	+	1.25654i	0.0768992	+	0.133193i	0.901911	−	0.431923i	$-0.142165\pi$
$89$	0.725466	+	1.25654i	0.0768992	+	0.133193i	−0.825011	+	0.565116i	$0.808831\pi$
$90$	2.07813	−	0.0425183i	0.219054	−	0.00448182i
$91$	−7.86930	−	7.96430i	−0.824927	−	0.834885i
$92$	0.496697	+	0.286768i	0.0517842	+	0.0298976i
$93$	1.68063	+	6.02502i	0.174274	+	0.624765i
$94$		−	3.20482i		−	0.330552i
$95$			0.130443i			0.0133831i
$96$	−2.70528	−	9.69833i	−0.276106	−	0.989832i
$97$	11.3504	+	6.55314i	1.15246	+	0.665371i	0.949485	−	0.313814i	$-0.101607\pi$
$97$	11.3504	+	6.55314i	1.15246	+	0.665371i	0.202972	+	0.979185i	$0.434940\pi$
$98$	−2.37441	−	4.22900i	−0.239852	−	0.427193i
$99$	2.92002	−	5.30537i	0.293473	−	0.533210i
$100$	−0.759977	−	1.31632i	−0.0759977	−	0.131632i
$101$	1.75267	+	3.03572i	0.174398	+	0.302065i	0.939953	−	0.341305i	$-0.110869\pi$
$101$	1.75267	+	3.03572i	0.174398	+	0.302065i	−0.765555	+	0.643370i	$0.777536\pi$
$102$	3.61104	+	0.928094i	0.357546	+	0.0918950i
$103$	16.3988	+	9.46785i	1.61582	+	0.932895i	0.987985	+	0.154550i	$0.0493929\pi$
$103$	16.3988	+	9.46785i	1.61582	+	0.932895i	0.627837	+	0.778345i	$0.283940\pi$
$104$	5.16026	+	8.93784i	0.506005	+	0.876427i
$105$	4.58253	−	0.0193783i	0.447210	−	0.00189113i
$106$	3.31466	−	5.74115i	0.321948	−	0.557630i
$107$	5.65103	−	3.26262i	0.546306	−	0.315410i	−0.201325	−	0.979525i	$-0.564525\pi$
$107$	5.65103	−	3.26262i	0.546306	−	0.315410i	0.747631	+	0.664115i	$0.231191\pi$
$108$	−5.41070	+	5.75338i	−0.520645	+	0.553619i
$109$	−8.24885	+	14.2874i	−0.790096	+	1.36849i	0.135810	+	0.990735i	$0.456636\pi$
$109$	−8.24885	+	14.2874i	−0.790096	+	1.36849i	−0.925907	+	0.377752i	$0.876697\pi$
$110$	1.39861			0.133352
$111$	−7.27862	−	7.13122i	−0.690856	−	0.676866i
$112$	−0.903837	−	3.45597i	−0.0854046	−	0.326559i
$113$	14.5020	−	8.37272i	1.36423	−	0.787639i	0.374047	−	0.927410i	$-0.377970\pi$
$113$	14.5020	−	8.37272i	1.36423	−	0.787639i	0.990184	+	0.139771i	$0.0446366\pi$
$114$	0.111816	+	0.109552i	0.0104725	+	0.0102604i
$115$	0.326784	−	0.188669i	0.0304728	−	0.0175935i
$116$	11.4768	+	6.62614i	1.06560	+	0.615222i
$117$	6.12145	−	11.1220i	0.565928	−	1.02823i
$118$		−	7.87615i		−	0.725058i
$119$	7.92696	+	2.17508i	0.726663	+	0.199389i
$120$	−4.09118	−	1.05150i	−0.373472	−	0.0959883i
$121$	−3.46259	+	5.99737i	−0.314781	+	0.545216i
$122$	3.71511			0.336350
$123$	2.52937	+	2.47815i	0.228065	+	0.223447i
$124$		−	5.48908i		−	0.492934i
$125$	−1.00000			−0.0894427
$126$	3.83201	−	3.94444i	0.341382	−	0.351399i
$127$	−20.6934			−1.83624			−0.918121	−	0.396300i	$-0.870294\pi$
$127$	−20.6934			−1.83624			−0.918121	+	0.396300i	$0.870294\pi$
$128$			10.7066i			0.946336i
$129$	−4.13543	+	16.0902i	−0.364104	+	1.41666i
$130$	2.93201			0.257154
$131$	−3.17382	+	5.49722i	−0.277298	+	0.480294i	−0.970712	−	0.240245i	$-0.922772\pi$
$131$	−3.17382	+	5.49722i	−0.277298	+	0.480294i	0.693414	+	0.720539i	$0.256106\pi$
$132$	−3.71914	+	3.79601i	−0.323710	+	0.330401i
$133$	0.242567	+	0.245496i	0.0210333	+	0.0212872i
$134$		−	9.37036i		−	0.809476i
$135$	1.49822	+	4.97547i	0.128946	+	0.428221i
$136$	−6.56190	−	3.78851i	−0.562678	−	0.324862i
$137$	−1.27365	+	0.735340i	−0.108815	+	0.0628243i	−0.553420	−	0.832902i	$-0.686677\pi$
$137$	−1.27365	+	0.735340i	−0.108815	+	0.0628243i	0.444605	+	0.895727i	$0.353344\pi$
$138$	0.112720	−	0.438573i	0.00959539	−	0.0373338i
$139$	−8.43461	+	4.86972i	−0.715414	+	0.413045i	−0.813063	−	0.582176i	$-0.802201\pi$
$139$	−8.43461	+	4.86972i	−0.715414	+	0.413045i	0.0976482	+	0.995221i	$0.468868\pi$
$140$	−3.87808	−	1.06411i	−0.327758	−	0.0899335i
$141$	7.71706	−	2.15262i	0.649894	−	0.181283i
$142$	−5.18868			−0.435424
$143$	4.27118	−	7.39790i	0.357174	−	0.618644i
$144$	3.46568	−	2.09658i	0.288807	−	0.174715i
$145$	7.55077	−	4.35944i	0.627057	−	0.362032i
$146$	0.538659	−	0.932984i	0.0445797	−	0.0772143i
$147$	8.58838	−	8.55802i	0.708358	−	0.705853i
$148$	4.47102	+	7.74404i	0.367516	+	0.636556i
$149$	−20.8597	−	12.0433i	−1.70889	−	0.986628i	−0.935939	−	0.352163i	$-0.885446\pi$
$149$	−20.8597	−	12.0433i	−1.70889	−	0.986628i	−0.772951	−	0.634465i	$-0.781220\pi$
$150$	−0.839845	+	0.857204i	−0.0685730	+	0.0699904i
$151$	5.51919	+	9.55953i	0.449146	+	0.777943i	0.998331	−	0.0577577i	$-0.0183951\pi$
$151$	5.51919	+	9.55953i	0.449146	+	0.777943i	−0.549185	+	0.835701i	$0.685062\pi$
$152$	−0.159063	−	0.275504i	−0.0129017	−	0.0223464i
$153$	0.190658	+	9.31860i	0.0154138	+	0.753364i
$154$	2.63221	−	2.60081i	0.212109	−	0.209579i
$155$	−3.12751	−	1.80567i	−0.251208	−	0.145035i
$156$	−7.79671	+	7.95787i	−0.624237	+	0.637139i
$157$			7.77660i			0.620640i	0.950632	+	0.310320i	$0.100436\pi$
$157$			7.77660i			0.620640i	−0.950632	+	0.310320i	$0.899564\pi$
$158$		−	1.88194i		−	0.149719i
$159$	16.0508	+	4.12532i	1.27291	+	0.327159i
$160$	5.03429	+	2.90655i	0.397995	+	0.229783i
$161$	0.264171	−	0.962757i	0.0208196	−	0.0758759i
$162$	5.52327	+	2.89435i	0.433949	+	0.227401i
$163$	1.67343	+	2.89847i	0.131073	+	0.227025i	0.924091	−	0.382174i	$-0.124824\pi$
$163$	1.67343	+	2.89847i	0.131073	+	0.227025i	−0.793017	+	0.609199i	$0.791491\pi$
$164$	−1.55371	−	2.69110i	−0.121324	−	0.210140i
$165$	0.939419	+	3.36779i	0.0731337	+	0.262182i
$166$	−0.370206	−	0.213738i	−0.0287335	−	0.0165893i
$167$	6.83216	+	11.8336i	0.528688	+	0.915715i	0.999440	+	0.0334496i	$0.0106493\pi$
$167$	6.83216	+	11.8336i	0.528688	+	0.915715i	−0.470752	+	0.882266i	$0.656017\pi$
$168$	−9.65502	+	5.62890i	−0.744901	+	0.434279i
$169$	2.45400	−	4.25044i	0.188769	−	0.326957i
$170$	−1.86420	+	1.07630i	−0.142978	+	0.0825481i
$171$	−0.188691	+	0.342831i	−0.0144295	+	0.0262170i
$172$	7.28938	−	12.6256i	0.555810	−	0.962691i
$173$	−22.9044			−1.74139			−0.870695	−	0.491824i	$-0.836330\pi$
$173$	−22.9044			−1.74139			−0.870695	+	0.491824i	$0.836330\pi$
$174$	2.60455	−	10.1338i	0.197450	−	0.768241i
$175$	−1.88202	+	1.85957i	−0.142267	+	0.140570i
$176$	2.36033	−	1.36274i	0.177917	−	0.102720i
$177$	18.9654	−	5.29026i	1.42553	−	0.397640i
$178$	−0.870601	+	0.502642i	−0.0652543	+	0.0376746i
$179$	−12.0215	−	6.94064i	−0.898533	−	0.518768i	−0.0218088	−	0.999762i	$-0.506942\pi$
$179$	−12.0215	−	6.94064i	−0.898533	−	0.518768i	−0.876724	+	0.480994i	$0.840276\pi$
$180$	−0.0932750	−	4.55891i	−0.00695231	−	0.339801i
$181$			7.90831i			0.587820i	0.955833	+	0.293910i	$0.0949567\pi$
$181$			7.90831i			0.587820i	−0.955833	+	0.293910i	$0.905043\pi$
$182$	5.51809	−	5.45227i	0.409028	−	0.404149i
$183$	2.49537	+	8.94581i	0.184463	+	0.661293i
$184$	−0.460128	+	0.796965i	−0.0339211	+	0.0587531i
$185$	5.88310			0.432534
$186$	−4.17446	+	1.16443i	−0.306086	+	0.0853804i
$187$			6.27155i			0.458621i
$188$	−7.03060			−0.512759
$189$	12.0719	+	6.57789i	0.878103	+	0.478471i
$190$	−0.0903776			−0.00655668
$191$		−	24.1704i		−	1.74891i	−0.485109	−	0.874454i	$-0.661220\pi$
$191$		−	24.1704i		−	1.74891i	0.485109	−	0.874454i	$-0.338780\pi$
$192$	2.21439	−	0.617688i	0.159810	−	0.0445778i
$193$	19.0297			1.36979			0.684894	−	0.728643i	$-0.259849\pi$
$193$	19.0297			1.36979			0.684894	+	0.728643i	$0.259849\pi$
$194$	−4.54037	+	7.86415i	−0.325979	+	0.564613i
$195$	1.96937	+	7.06014i	0.141030	+	0.505587i
$196$	−9.27740	+	5.20889i	−0.662672	+	0.372064i
$197$			11.4882i			0.818502i	0.912422	+	0.409251i	$0.134210\pi$
$197$			11.4882i			0.818502i	−0.912422	+	0.409251i	$0.865790\pi$
$198$	3.67584	+	2.02314i	0.261231	+	0.143779i
$199$	−8.95697	−	5.17131i	−0.634943	−	0.366584i	0.147721	−	0.989029i	$-0.452806\pi$
$199$	−8.95697	−	5.17131i	−0.634943	−	0.366584i	−0.782664	+	0.622445i	$0.786140\pi$
$200$	2.11207	−	1.21941i	0.149346	−	0.0862250i
$201$	22.5634	−	6.29390i	1.59150	−	0.443937i
$202$	−2.10331	+	1.21435i	−0.147988	+	0.0854411i
$203$	6.10401	−	22.2457i	0.428418	−	1.56134i
$204$	2.03602	−	7.92175i	0.142550	−	0.554634i
$205$	−2.04442			−0.142788
$206$	−6.55983	+	11.3620i	−0.457045	+	0.791626i
$207$	1.13178	−	0.0231561i	0.0786639	−	0.00160946i
$208$	4.94814	−	2.85681i	0.343092	−	0.198084i
$209$	−0.131657	+	0.228037i	−0.00910691	+	0.0157736i
$210$	0.0134263	+	3.17503i	0.000926504	+	0.219098i
$211$	−1.58523	−	2.74569i	−0.109131	−	0.189021i	0.806287	−	0.591524i	$-0.201474\pi$
$211$	−1.58523	−	2.74569i	−0.109131	−	0.189021i	−0.915419	+	0.402503i	$0.868140\pi$
$212$	−12.5947	−	7.27156i	−0.865008	−	0.499413i
$213$	−3.48514	−	12.4941i	−0.238798	−	0.856081i
$214$	2.26052	+	3.91534i	0.154526	+	0.267647i
$215$	−4.79579	−	8.30655i	−0.327070	−	0.566502i
$216$	−9.23147	−	8.68163i	−0.628122	−	0.590710i
$217$	−9.24382	+	2.41752i	−0.627511	+	0.164112i
$218$	−9.89909	−	5.71524i	−0.670451	−	0.387085i
$219$	2.60839	+	0.670398i	0.176259	+	0.0453013i
$220$		−	3.06821i		−	0.206859i
$221$			13.1475i			0.884398i
$222$	4.94089	−	5.04302i	0.331611	−	0.338465i
$223$	12.6066	+	7.27841i	0.844198	+	0.487398i	0.858689	−	0.512497i	$-0.171279\pi$
$223$	12.6066	+	7.27841i	0.844198	+	0.487398i	−0.0144907	+	0.999895i	$0.504613\pi$
$224$	14.8796	−	3.89143i	0.994182	−	0.260007i
$225$	−2.62822	−	1.44654i	−0.175214	−	0.0964361i
$226$	5.80107	+	10.0477i	0.385881	+	0.668366i
$227$	4.92687	+	8.53359i	0.327008	+	0.566394i	0.981917	−	0.189314i	$-0.0606263\pi$
$227$	4.92687	+	8.53359i	0.327008	+	0.566394i	−0.654909	+	0.755708i	$0.727293\pi$
$228$	0.240330	−	0.245297i	0.0159162	−	0.0162452i
$229$	23.4791	+	13.5557i	1.55155	+	0.895785i	0.998016	+	0.0629548i	$0.0200524\pi$
$229$	23.4791	+	13.5557i	1.55155	+	0.895785i	0.553529	+	0.832830i	$0.313281\pi$
$230$	0.130720	+	0.226414i	0.00861942	+	0.0149293i
$231$	8.03064	+	4.59132i	0.528377	+	0.302087i
$232$	−10.6318	+	18.4149i	−0.698015	+	1.20900i
$233$	4.89683	−	2.82719i	0.320802	−	0.185215i	−0.330948	−	0.943649i	$-0.607368\pi$
$233$	4.89683	−	2.82719i	0.320802	−	0.185215i	0.651750	+	0.758434i	$0.274035\pi$
$234$	7.70595	+	4.24127i	0.503753	+	0.277260i
$235$	−2.31277	+	4.00583i	−0.150868	+	0.261312i
$236$	−17.2784			−1.12473
$237$	4.53163	−	1.26407i	0.294361	−	0.0821099i
$238$	−1.50701	+	5.49222i	−0.0976851	+	0.356008i
$239$	6.69751	−	3.86681i	0.433226	−	0.250123i	−0.267494	−	0.963560i	$-0.586196\pi$
$239$	6.69751	−	3.86681i	0.433226	−	0.250123i	0.700720	+	0.713436i	$0.252862\pi$
$240$	−0.582128	+	2.26495i	−0.0375762	+	0.146202i
$241$	−3.53829	+	2.04283i	−0.227921	+	0.131590i	−0.609613	−	0.792699i	$-0.708675\pi$
$241$	−3.53829	+	2.04283i	−0.227921	+	0.131590i	0.381691	+	0.924290i	$0.375342\pi$
$242$	−4.15530	−	2.39906i	−0.267113	−	0.154218i
$243$	−3.25958	+	15.2439i	−0.209102	+	0.977894i
$244$		−	8.15005i		−	0.521754i
$245$	−0.0839957	+	6.99950i	−0.00536629	+	0.447181i
$246$	−1.71699	+	1.75248i	−0.109471	+	0.111734i
$247$	−0.276003	+	0.478050i	−0.0175616	+	0.0304176i
$248$	8.80739			0.559270
$249$	0.266012	−	1.03500i	0.0168578	−	0.0655906i
$250$		−	0.692853i		−	0.0438199i
$251$	−0.300087			−0.0189413			−0.00947065	−	0.999955i	$-0.503015\pi$
$251$	−0.300087			−0.0189413			−0.00947065	+	0.999955i	$0.503015\pi$
$252$	−8.65316	−	8.40650i	−0.545098	−	0.529560i
$253$	0.761702			0.0478878
$254$		−	14.3375i		−	0.899614i
$255$	−3.84382	−	3.76598i	−0.240709	−	0.235835i
$256$	−10.0727			−0.629541
$257$	7.50640	−	13.0015i	0.468236	−	0.811009i	−0.531105	−	0.847306i	$-0.678223\pi$
$257$	7.50640	−	13.0015i	0.468236	−	0.811009i	0.999341	+	0.0362973i	$0.0115563\pi$
$258$	−11.1481	−	2.86525i	−0.694052	−	0.178382i
$259$	11.0721	−	10.9400i	0.687988	−	0.679781i
$260$		−	6.43212i		−	0.398903i
$261$	26.1511	−	0.535051i	1.61872	−	0.0331188i
$262$	−3.80877	−	2.19899i	−0.235306	−	0.135854i
$263$	−9.71568	+	5.60935i	−0.599094	+	0.345887i	−0.768685	−	0.639627i	$-0.779089\pi$
$263$	−9.71568	+	5.60935i	−0.599094	+	0.345887i	0.169591	+	0.985515i	$0.445755\pi$
$264$	−6.09082	−	5.96748i	−0.374864	−	0.367273i
$265$	−8.28624	+	4.78406i	−0.509020	+	0.293883i
$266$	−0.170092	+	0.168064i	−0.0104290	+	0.0103046i
$267$	−1.79510	−	1.75875i	−0.109859	−	0.107634i
$268$	−20.5563			−1.25568
$269$	9.56875	−	16.5736i	0.583417	−	1.01051i	−0.411654	−	0.911340i	$-0.635049\pi$
$269$	9.56875	−	16.5736i	0.583417	−	1.01051i	0.995071	−	0.0991673i	$-0.0316179\pi$
$270$	−3.44727	+	1.03805i	−0.209794	+	0.0631735i
$271$	−25.9294	+	14.9704i	−1.57510	+	0.909385i	−0.579572	+	0.814921i	$0.696780\pi$
$271$	−25.9294	+	14.9704i	−1.57510	+	0.909385i	−0.995528	+	0.0944638i	$0.969886\pi$
$272$	−2.09739	+	3.63278i	−0.127173	+	0.220270i
$273$	16.8352	+	9.62513i	1.01891	+	0.582539i
$274$	−0.509483	−	0.882450i	−0.0307790	−	0.0533108i
$275$	−1.74818	−	1.00931i	−0.105419	−	0.0608637i
$276$	−0.962124	−	0.247281i	−0.0579131	−	0.0148846i
$277$	−11.5525	−	20.0096i	−0.694125	−	1.20226i	−0.970475	−	0.241202i	$-0.922458\pi$
$277$	−11.5525	−	20.0096i	−0.694125	−	1.20226i	0.276350	−	0.961057i	$-0.410875\pi$
$278$	−3.37401	−	5.84395i	−0.202359	−	0.350497i
$279$	−5.60781	−	9.26977i	−0.335731	−	0.554967i
$280$	1.70739	−	6.22250i	0.102036	−	0.371865i
$281$	−6.99836	−	4.04051i	−0.417487	−	0.241036i	0.276514	−	0.961010i	$-0.410821\pi$
$281$	−6.99836	−	4.04051i	−0.417487	−	0.241036i	−0.694002	+	0.719973i	$0.744154\pi$
$282$	1.49145	+	5.34679i	0.0888144	+	0.318397i
$283$		−	15.1775i		−	0.902206i	−0.892472	−	0.451103i	$-0.851031\pi$
$283$		−	15.1775i		−	0.902206i	0.892472	−	0.451103i	$-0.148969\pi$
$284$			11.3827i			0.675439i
$285$	−0.0607050	−	0.217625i	−0.00359585	−	0.0128910i
$286$	5.12566	+	2.95930i	0.303087	+	0.174987i
$287$	−3.84763	+	3.80173i	−0.227118	+	0.224409i
$288$	9.02676	+	14.9213i	0.531907	+	0.879248i
$289$	3.67374	+	6.36310i	0.216102	+	0.374300i
$290$	3.02045	+	5.23157i	0.177367	+	0.307209i
$291$	−21.9862	−	5.65080i	−1.28885	−	0.331256i
$292$	−2.04674	−	1.18169i	−0.119777	−	0.0691530i
$293$	−11.2769	−	19.5322i	−0.658804	−	1.14108i	−0.980926	−	0.194384i	$-0.937729\pi$
$293$	−11.2769	−	19.5322i	−0.658804	−	1.14108i	0.322121	−	0.946698i	$-0.395604\pi$
$294$	5.92945	+	5.95049i	0.345813	+	0.347040i
$295$	−5.68385	+	9.84472i	−0.330927	+	0.573182i
$296$	−12.4255	+	7.17389i	−0.722220	+	0.416974i
$297$	−2.40264	+	10.2102i	−0.139415	+	0.592454i
$298$	8.34426	−	14.4527i	0.483370	−	0.837222i
$299$	1.59681			0.0923460
$300$	1.88050	+	1.84242i	0.108571	+	0.106372i
$301$	−24.4724	−	6.71499i	−1.41057	−	0.387045i
$302$	−6.62335	+	3.82399i	−0.381131	+	0.220046i
$303$	−4.33684	−	4.24902i	−0.249145	−	0.244100i
$304$	−0.152524	+	0.0880598i	−0.00874785	+	0.00505057i
$305$	−4.64366	−	2.68102i	−0.265895	−	0.153515i
$306$	−6.45643	+	0.132098i	−0.369089	+	0.00755154i
$307$		−	9.43781i		−	0.538644i	−0.963050	−	0.269322i	$-0.913200\pi$
$307$		−	9.43781i		−	0.538644i	0.963050	−	0.269322i	$-0.0867996\pi$
$308$	−5.70555	−	5.77443i	−0.325104	−	0.329029i
$309$	−31.7652	−	8.16417i	−1.80706	−	0.464443i
$310$	1.25107	−	2.16691i	0.0710558	−	0.123072i
$311$	24.4959			1.38903			0.694517	−	0.719476i	$-0.255618\pi$
$311$	24.4959			1.38903			0.694517	+	0.719476i	$0.255618\pi$
$312$	−12.7686	−	12.5101i	−0.722882	−	0.708243i
$313$			2.01438i			0.113859i	0.998378	+	0.0569297i	$0.0181311\pi$
$313$			2.01438i			0.113859i	−0.998378	+	0.0569297i	$0.981869\pi$
$314$	−5.38804			−0.304065
$315$	−7.63630	+	2.16493i	−0.430257	+	0.121980i
$316$	−4.12853			−0.232248
$317$			0.753803i			0.0423378i	0.999776	+	0.0211689i	$0.00673878\pi$
$317$			0.753803i			0.0423378i	−0.999776	+	0.0211689i	$0.993261\pi$
$318$	−2.85824	+	11.1209i	−0.160282	+	0.623627i
$319$	17.6001			0.985416
$320$	−0.663643	+	1.14946i	−0.0370988	+	0.0642569i
$321$	−7.90960	+	8.07309i	−0.441471	+	0.450596i
$322$	0.667049	+	0.183032i	0.0371732	+	0.0102000i
$323$		−	0.405266i		−	0.0225496i
$324$	6.34950	−	12.1167i	0.352750	−	0.673151i
$325$	−3.66483	−	2.11589i	−0.203288	−	0.117369i
$326$	−2.00821	+	1.15944i	−0.111225	+	0.0642155i
$327$	7.11301	−	27.6754i	0.393351	−	1.53045i
$328$	4.31796	−	2.49297i	0.238419	−	0.137651i
$329$	3.09645	+	11.8398i	0.170713	+	0.652750i
$330$	−2.33338	+	0.650880i	−0.128448	+	0.0358297i
$331$	−6.21181			−0.341432			−0.170716	−	0.985320i	$-0.554608\pi$
$331$	−6.21181			−0.341432			−0.170716	+	0.985320i	$0.554608\pi$
$332$	−0.468891	+	0.812142i	−0.0257337	+	0.0445721i
$333$	15.4621	+	8.51015i	0.847316	+	0.466353i
$334$	−8.19898	+	4.73369i	−0.448628	+	0.259016i
$335$	−6.76215	+	11.7124i	−0.369456	+	0.639917i
$336$	3.11626	+	5.34518i	0.170006	+	0.291604i
$337$	0.271095	+	0.469551i	0.0147675	+	0.0255780i	0.873315	−	0.487156i	$-0.161966\pi$
$337$	0.271095	+	0.469551i	0.0147675	+	0.0255780i	−0.858547	+	0.512735i	$0.828633\pi$
$338$	2.94494	+	1.70026i	0.160183	+	0.0924819i
$339$	−20.2980	+	20.7176i	−1.10244	+	1.12522i
$340$	2.36114	+	4.08961i	0.128051	+	0.221790i
$341$	−3.64497	−	6.31326i	−0.197386	−	0.341882i
$342$	−0.237532	−	0.130735i	−0.0128443	−	0.00706934i
$343$	12.8580	+	13.3294i	0.694265	+	0.719719i
$344$	20.2581	+	11.6960i	1.09225	+	0.630608i
$345$	−0.457391	+	0.466845i	−0.0246251	+	0.0251341i
$346$		−	15.8694i		−	0.853144i
$347$			8.46147i			0.454235i	0.973867	+	0.227118i	$0.0729302\pi$
$347$			8.46147i			0.454235i	−0.973867	+	0.227118i	$0.927070\pi$
$348$	−22.2311	−	5.71375i	−1.19171	−	0.306289i
$349$	−7.21930	−	4.16806i	−0.386440	−	0.223111i	0.294176	−	0.955751i	$-0.404955\pi$
$349$	−7.21930	−	4.16806i	−0.386440	−	0.223111i	−0.680617	+	0.732640i	$0.738288\pi$
$350$	−1.28841	−	1.30396i	−0.0688684	−	0.0696998i
$351$	−5.03684	+	21.4043i	−0.268847	+	1.14248i
$352$	5.86721	+	10.1623i	0.312724	+	0.541653i
$353$	−4.65500	−	8.06270i	−0.247761	−	0.429134i	0.715143	−	0.698978i	$-0.246361\pi$
$353$	−4.65500	−	8.06270i	−0.247761	−	0.429134i	−0.962904	+	0.269843i	$0.913028\pi$
$354$	3.66538	+	13.1403i	0.194813	+	0.698397i
$355$	6.48553	+	3.74442i	0.344216	+	0.198733i
$356$	1.10267	+	1.90989i	0.0584417	+	0.101224i
$357$	−14.2373	+	0.0602055i	−0.753515	+	0.00318641i
$358$	4.80885	−	8.32917i	0.254156	−	0.440210i
$359$	−10.9957	+	6.34836i	−0.580329	+	0.335053i	−0.761264	−	0.648442i	$-0.775421\pi$
$359$	−10.9957	+	6.34836i	−0.580329	+	0.335053i	0.180935	+	0.983495i	$0.442088\pi$
$360$	7.31491	−	0.149663i	0.385529	−	0.00788791i
$361$	−9.49149	+	16.4397i	−0.499552	+	0.865250i
$362$	−5.47930			−0.287986
$363$	2.98580	−	11.6172i	0.156714	−	0.609744i
$364$	−11.9610	−	12.1054i	−0.626925	−	0.634494i
$365$	−1.34658	+	0.777450i	−0.0704833	+	0.0406936i
$366$	−6.19814	+	1.72892i	−0.323982	+	0.0903723i
$367$	25.5849	−	14.7714i	1.33552	−	0.771063i	0.349380	−	0.936981i	$-0.386392\pi$
$367$	25.5849	−	14.7714i	1.33552	−	0.771063i	0.986140	+	0.165918i	$0.0530588\pi$
$368$	0.441214	+	0.254735i	0.0229998	+	0.0132790i
$369$	−5.37317	−	2.95733i	−0.279716	−	0.153952i
$370$			4.07613i			0.211908i
$371$	−6.69857	+	24.4126i	−0.347772	+	1.26744i
$372$	2.55449	+	9.15775i	0.132444	+	0.474807i
$373$	2.94478	−	5.10051i	0.152475	−	0.264094i	−0.779662	−	0.626201i	$-0.784609\pi$
$373$	2.94478	−	5.10051i	0.152475	−	0.264094i	0.932137	+	0.362106i	$0.117942\pi$
$374$	−4.34527			−0.224688
$375$	1.66836	−	0.465377i	0.0861537	−	0.0240319i
$376$		−	11.2808i		−	0.581764i
$377$	36.8964			1.90026
$378$	−4.55752	+	8.36407i	−0.234413	+	0.430202i
$379$	5.42114			0.278465			0.139233	−	0.990260i	$-0.455536\pi$
$379$	5.42114			0.278465			0.139233	+	0.990260i	$0.455536\pi$
$380$			0.198267i			0.0101709i
$381$	34.5240	−	9.63022i	1.76872	−	0.493371i
$382$	16.7465			0.856827
$383$	−7.07774	+	12.2590i	−0.361655	+	0.626406i	−0.988233	−	0.152953i	$-0.951122\pi$
$383$	−7.07774	+	12.2590i	−0.361655	+	0.626406i	0.626578	+	0.779359i	$0.284455\pi$
$384$	−4.98259	−	17.8624i	−0.254267	−	0.911538i
$385$	−5.16699	+	1.35132i	−0.263334	+	0.0688694i
$386$			13.1848i			0.671088i
$387$	−0.588606	−	28.7687i	−0.0299205	−	1.46240i
$388$	17.2520	+	9.96048i	0.875840	+	0.505667i
$389$	5.86183	−	3.38433i	0.297206	−	0.171592i	−0.343981	−	0.938977i	$-0.611776\pi$
$389$	5.86183	−	3.38433i	0.297206	−	0.171592i	0.641187	+	0.767384i	$0.278442\pi$
$390$	−4.89164	+	1.36449i	−0.247698	+	0.0690935i
$391$	−1.01527	+	0.586166i	−0.0513444	+	0.0296437i
$392$	−8.35782	−	14.8859i	−0.422134	−	0.751850i
$393$	2.73680	−	10.6484i	0.138053	−	0.537139i
$394$	−7.95966			−0.401002
$395$	−1.35811	+	2.35232i	−0.0683339	+	0.118358i
$396$	4.43829	−	8.06392i	0.223033	−	0.405227i
$397$	11.5661	−	6.67770i	0.580487	−	0.335144i	−0.180840	−	0.983513i	$-0.557882\pi$
$397$	11.5661	−	6.67770i	0.580487	−	0.335144i	0.761327	+	0.648368i	$0.224548\pi$
$398$	3.58296	−	6.20587i	0.179598	−	0.311072i
$399$	−0.518937	−	0.296690i	−0.0259794	−	0.0148531i
$400$	−0.675084	−	1.16928i	−0.0337542	−	0.0584640i
$401$	−5.65816	−	3.26674i	−0.282555	−	0.163133i	0.352025	−	0.935991i	$-0.385493\pi$
$401$	−5.65816	−	3.26674i	−0.282555	−	0.163133i	−0.634580	+	0.772858i	$0.718827\pi$
$402$	4.36075	+	15.6331i	0.217494	+	0.779710i
$403$	−7.64121	−	13.2350i	−0.380636	−	0.659281i
$404$	2.66398	+	4.61415i	0.132538	+	0.229563i
$405$	−4.81504	−	7.60364i	−0.239261	−	0.377828i
$406$	15.4130	+	4.22918i	0.764936	+	0.209891i
$407$	10.2847	+	5.93787i	0.509794	+	0.294330i
$408$	12.7107	+	3.26685i	0.629273	+	0.161733i
$409$		−	1.99112i		−	0.0984547i	−0.998788	−	0.0492274i	$-0.984324\pi$
$409$		−	1.99112i		−	0.0984547i	0.998788	−	0.0492274i	$-0.0156759\pi$
$410$		−	1.41648i		−	0.0699550i
$411$	1.78269	−	1.81954i	0.0879336	−	0.0897512i
$412$	24.9254	+	14.3907i	1.22799	+	0.708979i
$413$	7.60983	+	29.0975i	0.374455	+	1.43179i
$414$	0.0160438	+	0.784155i	0.000788508	+	0.0385391i
$415$	0.308490	+	0.534320i	0.0151432	+	0.0262288i
$416$	12.2999	+	21.3040i	0.603051	+	1.04452i
$417$	11.8057	−	12.0497i	0.578128	−	0.590077i
$418$	−0.157996	−	0.0912191i	−0.00772784	−	0.00446167i
$419$	−6.83997	−	11.8472i	−0.334154	−	0.578772i	0.649168	−	0.760645i	$-0.275117\pi$
$419$	−6.83997	−	11.8472i	−0.334154	−	0.578772i	−0.983322	+	0.181873i	$0.941784\pi$
$420$	6.96524	−	0.0294541i	0.339869	−	0.00143721i
$421$	17.7189	−	30.6900i	0.863567	−	1.49574i	−0.00489699	−	0.999988i	$-0.501559\pi$
$421$	17.7189	−	30.6900i	0.863567	−	1.49574i	0.868464	−	0.495753i	$-0.165108\pi$
$422$	1.90236	−	1.09833i	0.0926056	−	0.0534658i
$423$	−11.8731	+	7.18268i	−0.577288	+	0.349234i
$424$	11.6674	−	20.2086i	0.566621	−	0.981416i
$425$	3.10685			0.150704
$426$	8.65658	−	2.41469i	0.419413	−	0.116992i
$427$	−13.7250	+	3.58949i	−0.664200	+	0.173707i
$428$	8.58930	−	4.95904i	0.415180	−	0.239704i
$429$	−3.68306	+	14.3301i	−0.177820	+	0.691863i
$430$	5.75522	−	3.32278i	0.277542	−	0.160239i
$431$	27.7347	+	16.0127i	1.33594	+	0.771303i	0.986202	−	0.165546i	$-0.0529387\pi$
$431$	27.7347	+	16.0127i	1.33594	+	0.771303i	0.349734	+	0.936849i	$0.386272\pi$
$432$	−4.80630	+	5.11070i	−0.231243	+	0.245889i
$433$		−	16.7950i		−	0.807116i	−0.914954	−	0.403558i	$-0.867773\pi$
$433$		−	16.7950i		−	0.807116i	0.914954	−	0.403558i	$-0.132227\pi$
$434$	−1.67499	−	6.40461i	−0.0804021	−	0.307431i
$435$	−10.5686	+	10.7871i	−0.506726	+	0.517200i
$436$	−12.5379	+	21.7162i	−0.600455	+	1.04002i
$437$	−0.0492209			−0.00235456
$438$	−0.464487	+	1.80723i	−0.0221941	+	0.0863529i
$439$			27.1583i			1.29620i	0.761557	+	0.648098i	$0.224435\pi$
$439$			27.1583i			1.29620i	−0.761557	+	0.648098i	$0.775565\pi$
$440$	4.92304			0.234697
$441$	−10.3458	+	18.2747i	−0.492658	+	0.870223i
$442$	−9.10930			−0.433285
$443$		−	29.1824i		−	1.38650i	−0.720698	−	0.693249i	$-0.756179\pi$
$443$		−	29.1824i		−	1.38650i	0.720698	−	0.693249i	$-0.243821\pi$
$444$	−11.0632	−	10.8391i	−0.525035	−	0.514402i
$445$	1.45093			0.0687808
$446$	−5.04287	+	8.73451i	−0.238787	+	0.413591i
$447$	40.4061	+	10.3850i	1.91114	+	0.491194i
$448$	0.888519	+	3.39740i	0.0419786	+	0.160512i
$449$		−	5.85431i		−	0.276282i	−0.990413	−	0.138141i	$-0.955887\pi$
$449$		−	5.85431i		−	0.276282i	0.990413	−	0.138141i	$-0.0441127\pi$
$450$	1.00224	−	1.82097i	0.0472461	−	0.0858413i
$451$	−3.57400	−	2.06345i	−0.168293	−	0.0971640i
$452$	22.0423	−	12.7261i	1.03678	−	0.598587i
$453$	−13.6568	−	13.3802i	−0.641652	−	0.628658i
$454$	−5.91253	+	3.41360i	−0.277489	+	0.160208i
$455$	−10.8319	+	2.83286i	−0.507809	+	0.132807i
$456$	0.393587	+	0.385617i	0.0184314	+	0.0180582i
$457$	−36.1660			−1.69177			−0.845887	−	0.533362i	$-0.820928\pi$
$457$	−36.1660			−1.69177			−0.845887	+	0.533362i	$0.820928\pi$
$458$	−9.39210	+	16.2676i	−0.438864	+	0.760135i
$459$	−4.65475	−	15.4581i	−0.217265	−	0.721520i
$460$	0.496697	−	0.286768i	0.0231586	−	0.0133706i
$461$	6.43557	−	11.1467i	0.299734	−	0.519155i	−0.676341	−	0.736589i	$-0.736435\pi$
$461$	6.43557	−	11.1467i	0.299734	−	0.519155i	0.976075	+	0.217434i	$0.0697687\pi$
$462$	−3.18111	+	5.56406i	−0.147999	+	0.258863i
$463$	−4.82883	−	8.36377i	−0.224415	−	0.388697i	0.731729	−	0.681596i	$-0.238714\pi$
$463$	−4.82883	−	8.36377i	−0.224415	−	0.388697i	−0.956144	+	0.292898i	$0.905380\pi$
$464$	10.1948	+	5.88597i	0.473282	+	0.273249i
$465$	6.05814	+	1.55704i	0.280939	+	0.0722059i
$466$	1.95883	+	3.39279i	0.0907409	+	0.157168i
$467$	10.1218	+	17.5314i	0.468380	+	0.811258i	0.999347	−	0.0361343i	$-0.0115044\pi$
$467$	10.1218	+	17.5314i	0.468380	+	0.811258i	−0.530967	+	0.847393i	$0.678171\pi$
$468$	9.30432	−	16.9050i	0.430092	−	0.781434i
$469$	9.05352	+	34.6177i	0.418053	+	1.59850i
$470$	−2.77545	−	1.60241i	−0.128022	−	0.0739136i
$471$	−3.61905	−	12.9742i	−0.166757	−	0.597818i
$472$		−	27.7237i		−	1.27609i
$473$		−	19.3618i		−	0.890255i
$474$	0.875812	+	3.13976i	0.0402274	+	0.144214i
$475$	0.112967	+	0.0652213i	0.00518327	+	0.00299256i
$476$	12.0486	+	3.30602i	0.552247	+	0.151531i
$477$	−28.6984	+	0.587167i	−1.31401	+	0.0268845i
$478$	2.67913	+	4.64040i	0.122541	+	0.212247i
$479$	20.0999	+	34.8140i	0.918386	+	1.59069i	0.801867	+	0.597502i	$0.203840\pi$
$479$	20.0999	+	34.8140i	0.918386	+	1.59069i	0.116519	+	0.993189i	$0.462827\pi$
$480$	−9.75164	−	2.50633i	−0.445099	−	0.114398i
$481$	21.5606	+	12.4480i	0.983078	+	0.567580i
$482$	−1.41538	−	2.45152i	−0.0644690	−	0.111664i
$483$	0.00731217	+	1.72916i	0.000332715	+	0.0786797i
$484$	−5.26297	+	9.11573i	−0.239226	+	0.414352i
$485$	11.3504	−	6.55314i	0.515394	−	0.297563i
$486$	−10.5618	−	2.25841i	−0.479091	−	0.102444i
$487$	13.4870	−	23.3601i	0.611153	−	1.05855i	−0.379893	−	0.925030i	$-0.624039\pi$
$487$	13.4870	−	23.3601i	0.611153	−	1.05855i	0.991046	−	0.133518i	$-0.0426273\pi$
$488$	13.0770			0.591968
$489$	−4.14076	−	4.05691i	−0.187252	−	0.183460i
$490$	−4.84963	−	0.0581967i	−0.219084	−	0.00262906i
$491$	−14.3734	+	8.29847i	−0.648662	+	0.374505i	−0.787943	−	0.615748i	$-0.788854\pi$
$491$	−14.3734	+	8.29847i	−0.648662	+	0.374505i	0.139282	+	0.990253i	$0.455521\pi$
$492$	3.84452	+	3.76667i	0.173324	+	0.169815i
$493$	−23.4591	+	13.5441i	−1.05654	+	0.609996i
$494$	−0.331219	−	0.191229i	−0.0149022	−	0.00860381i
$495$	−3.13458	−	5.18149i	−0.140889	−	0.232891i
$496$		−	4.87592i		−	0.218935i
$497$	19.1689	−	5.01323i	0.859844	−	0.224874i
$498$	0.717105	+	0.184307i	0.0321343	+	0.00825901i
$499$	16.2291	−	28.1096i	0.726514	−	1.25836i	−0.231834	−	0.972755i	$-0.574473\pi$
$499$	16.2291	−	28.1096i	0.726514	−	1.25836i	0.958348	−	0.285603i	$-0.0921940\pi$
$500$	−1.51995			−0.0679744
$501$	−16.9056	−	16.5633i	−0.755287	−	0.739992i
$502$		−	0.207916i		−	0.00927975i
$503$	−27.0679			−1.20690			−0.603449	−	0.797402i	$-0.706207\pi$
$503$	−27.0679			−1.20690			−0.603449	+	0.797402i	$0.706207\pi$
$504$	13.4885	−	13.8843i	0.600825	−	0.618454i
$505$	3.50535			0.155986
$506$			0.527748i			0.0234612i
$507$	−2.11609	+	8.23330i	−0.0939788	+	0.365654i
$508$	−31.4530			−1.39550
$509$	−9.97119	+	17.2706i	−0.441965	+	0.765506i	−0.997835	−	0.0657630i	$-0.979052\pi$
$509$	−9.97119	+	17.2706i	−0.441965	+	0.765506i	0.555870	+	0.831269i	$0.312385\pi$
$510$	2.60927	−	2.66320i	0.115541	−	0.117929i
$511$	−1.08857	+	3.96724i	−0.0481556	+	0.175500i
$512$			14.4343i			0.637911i
$513$	0.155258	−	0.659778i	0.00685481	−	0.0291299i
$514$	9.00811	+	5.20083i	0.397331	+	0.229399i
$515$	16.3988	−	9.46785i	0.722618	−	0.417203i
$516$	−6.28566	+	24.4563i	−0.276711	+	1.07663i
$517$	−8.08625	+	4.66860i	−0.355633	+	0.205325i
$518$	7.57985	+	7.67135i	0.333039	+	0.337060i
$519$	38.2128	−	10.6592i	1.67735	−	0.467886i
$520$	10.3205			0.452585
$521$	3.24484	−	5.62023i	0.142159	−	0.246227i	−0.786150	−	0.618035i	$-0.787929\pi$
$521$	3.24484	−	5.62023i	0.142159	−	0.246227i	0.928309	+	0.371809i	$0.121262\pi$
$522$	0.370712	+	18.1189i	0.0162256	+	0.793043i
$523$	14.7364	−	8.50804i	0.644376	−	0.372031i	−0.141922	−	0.989878i	$-0.545328\pi$
$523$	14.7364	−	8.50804i	0.644376	−	0.372031i	0.786298	+	0.617847i	$0.211995\pi$
$524$	−4.82406	+	8.35552i	−0.210740	+	0.365012i
$525$	2.27449	−	3.97828i	0.0992667	−	0.173626i
$526$	−3.88646	−	6.73154i	−0.169458	−	0.293509i
$527$	9.71672	+	5.60995i	0.423267	+	0.244373i
$528$	−3.30370	+	3.37198i	−0.143775	+	0.146747i
$529$	−11.4288	−	19.7953i	−0.496905	−	0.860664i
$530$	−3.31466	−	5.74115i	−0.143979	−	0.249380i
$531$	−29.1792	+	17.6521i	−1.26627	+	0.766037i
$532$	0.368691	+	0.373142i	0.0159848	+	0.0161778i
$533$	−7.49244	−	4.32576i	−0.324534	−	0.187370i
$534$	1.21856	−	1.24374i	0.0527322	−	0.0538221i
$535$		−	6.52525i		−	0.282111i
$536$		−	32.9833i		−	1.42466i
$537$	23.2863	+	5.98494i	1.00488	+	0.258269i
$538$	11.4830	+	6.62974i	0.495069	+	0.285828i
$539$	−7.21150	+	12.1516i	−0.310621	+	0.523405i
$540$	2.27723	+	7.56249i	0.0979962	+	0.325438i
$541$	9.31312	+	16.1308i	0.400402	+	0.693517i	0.993774	−	0.111411i	$-0.0355371\pi$
$541$	9.31312	+	16.1308i	0.400402	+	0.693517i	−0.593372	+	0.804928i	$0.702204\pi$
$542$	−10.3723	−	17.9653i	−0.445527	−	0.771675i
$543$	−3.68034	−	13.1939i	−0.157939	−	0.566205i
$544$	−15.6408	−	9.03021i	−0.670593	−	0.387167i
$545$	8.24885	+	14.2874i	0.353342	+	0.612006i
$546$	−6.66880	+	11.6643i	−0.285398	+	0.499188i
$547$	7.71255	−	13.3585i	0.329765	−	0.571170i	−0.652700	−	0.757616i	$-0.726364\pi$
$547$	7.71255	−	13.3585i	0.329765	−	0.571170i	0.982465	+	0.186447i	$0.0596972\pi$
$548$	−1.93588	+	1.11768i	−0.0826969	+	0.0477451i
$549$	−8.32634	−	13.7635i	−0.355360	−	0.587414i
$550$	0.699304	−	1.21123i	0.0298184	−	0.0516470i
$551$	−1.13731			−0.0484512
$552$	0.396770	−	1.54376i	0.0168877	−	0.0657067i
$553$	1.81831	+	6.95260i	0.0773223	+	0.295655i
$554$	13.8637	−	8.00422i	0.589013	−	0.340067i
$555$	−9.81513	+	2.73786i	−0.416629	+	0.116216i
$556$	−12.8202	+	7.40176i	−0.543698	+	0.313904i
$557$	−29.6043	−	17.0920i	−1.25437	−	0.724213i	−0.282399	−	0.959297i	$-0.591130\pi$
$557$	−29.6043	−	17.0920i	−1.25437	−	0.724213i	−0.971975	+	0.235084i	$0.924464\pi$
$558$	6.42259	−	3.88539i	0.271890	−	0.164482i
$559$		−	40.5895i		−	1.71675i
$560$	−3.44488	−	0.945242i	−0.145573	−	0.0399437i
$561$	−2.91863	−	10.4632i	−0.123225	−	0.441757i
$562$	2.79948	−	4.84884i	0.118089	−	0.204536i
$563$	33.2663			1.40201			0.701005	−	0.713157i	$-0.252735\pi$
$563$	33.2663			1.40201			0.701005	+	0.713157i	$0.252735\pi$
$564$	11.7296	−	3.27188i	0.493904	−	0.137771i
$565$		−	16.7454i		−	0.704486i
$566$	10.5158			0.442010
$567$	−23.2015	−	5.35630i	−0.974372	−	0.224944i
$568$	−18.2639			−0.766336
$569$			4.37601i			0.183452i	0.995784	+	0.0917259i	$0.0292384\pi$
$569$			4.37601i			0.183452i	−0.995784	+	0.0917259i	$0.970762\pi$
$570$	0.150782	−	0.0420596i	0.00631558	−	0.00176168i
$571$	12.9963			0.543878			0.271939	−	0.962315i	$-0.412335\pi$
$571$	12.9963			0.543878			0.271939	+	0.962315i	$0.412335\pi$
$572$	6.49200	−	11.2445i	0.271444	−	0.470155i
$573$	11.2483	+	40.3249i	0.469906	+	1.68460i
$574$	−2.63405	−	2.66584i	−0.109943	−	0.111270i
$575$		−	0.377338i		−	0.0157361i
$576$	−3.40694	+	2.06105i	−0.141956	+	0.0858771i
$577$	39.0948	+	22.5714i	1.62754	+	0.939659i	0.984825	+	0.173551i	$0.0555243\pi$
$577$	39.0948	+	22.5714i	1.62754	+	0.939659i	0.642712	+	0.766108i	$0.277809\pi$
$578$	−4.40870	+	2.54536i	−0.183378	+	0.105873i
$579$	−31.7484	+	8.85598i	−1.31942	+	0.368042i
$580$	11.4768	−	6.62614i	0.476549	−	0.275136i
$581$	1.57419	+	0.431943i	0.0653084	+	0.0179200i
$582$	3.91518	−	15.2332i	0.162289	−	0.631437i
$583$	−19.3144			−0.799921
$584$	1.89605	−	3.28406i	0.0784593	−	0.135895i
$585$	−6.57125	−	10.8623i	−0.271688	−	0.449103i
$586$	13.5329	−	7.81325i	0.559041	−	0.322762i
$587$	−18.3176	+	31.7270i	−0.756048	+	1.30951i	0.188804	+	0.982015i	$0.439539\pi$
$587$	−18.3176	+	31.7270i	−0.756048	+	1.30951i	−0.944852	+	0.327498i	$0.893795\pi$
$588$	13.0540	−	13.0078i	0.538336	−	0.536432i
$589$	0.235537	+	0.407961i	0.00970512	+	0.0168098i
$590$	−6.82095	−	3.93808i	−0.280814	−	0.162128i
$591$	−5.34635	−	19.1665i	−0.219919	−	0.788404i
$592$	3.97159	+	6.87899i	0.163231	+	0.282725i
$593$	17.5445	+	30.3879i	0.720465	+	1.24788i	0.960814	+	0.277195i	$0.0894047\pi$
$593$	17.5445	+	30.3879i	0.720465	+	1.24788i	−0.240349	+	0.970687i	$0.577262\pi$
$594$	−7.07416	−	1.66468i	−0.290256	−	0.0683026i
$595$	5.84715	−	5.77741i	0.239710	−	0.236851i
$596$	−31.7057	−	18.3053i	−1.29872	−	0.749815i
$597$	17.3501	+	4.45924i	0.710091	+	0.182505i
$598$			1.10636i			0.0452423i
$599$			23.2954i			0.951824i	0.879493	+	0.475912i	$0.157882\pi$
$599$			23.2954i			0.951824i	−0.879493	+	0.475912i	$0.842118\pi$
$600$	−2.95622	+	3.01732i	−0.120687	+	0.123181i
$601$	−16.6006	−	9.58436i	−0.677152	−	0.390954i	0.121629	−	0.992576i	$-0.461188\pi$
$601$	−16.6006	−	9.58436i	−0.677152	−	0.390954i	−0.798781	+	0.601622i	$0.794522\pi$
$602$	4.65250	−	16.9558i	0.189622	−	0.691066i
$603$	−34.7149	+	21.0010i	−1.41370	+	0.855226i
$604$	8.38892	+	14.5300i	0.341340	+	0.591219i
$605$	3.46259	+	5.99737i	0.140774	+	0.243828i
$606$	2.94395	−	3.00480i	0.119590	−	0.122062i
$607$	−10.0518	−	5.80338i	−0.407988	−	0.235552i	0.281937	−	0.959433i	$-0.409023\pi$
$607$	−10.0518	−	5.80338i	−0.407988	−	0.235552i	−0.689925	+	0.723881i	$0.742356\pi$
$608$	−0.379138	−	0.656686i	−0.0153761	−	0.0266321i
$609$	0.168957	+	39.9545i	0.00684648	+	1.61904i
$610$	1.85755	−	3.21738i	0.0752102	−	0.130268i
$611$	−16.9518	+	9.78713i	−0.685797	+	0.395945i
$612$	0.289791	+	14.1638i	0.0117141	+	0.572540i
$613$	−20.6458	+	35.7596i	−0.833877	+	1.44432i	0.0610640	+	0.998134i	$0.480551\pi$
$613$	−20.6458	+	35.7596i	−0.833877	+	1.44432i	−0.894941	+	0.446184i	$0.852783\pi$
$614$	6.53902			0.263893
$615$	3.41082	−	0.951423i	0.137538	−	0.0383651i
$616$	9.26525	−	9.15473i	0.373308	−	0.368855i
$617$	−25.5921	+	14.7756i	−1.03030	+	0.594842i	−0.917070	−	0.398727i	$-0.869452\pi$
$617$	−25.5921	+	14.7756i	−1.03030	+	0.594842i	−0.113228	+	0.993569i	$0.536119\pi$
$618$	5.65657	−	22.0086i	0.227541	−	0.885317i
$619$	23.4035	−	13.5120i	0.940667	−	0.543095i	0.0504980	−	0.998724i	$-0.483919\pi$
$619$	23.4035	−	13.5120i	0.940667	−	0.543095i	0.890169	+	0.455630i	$0.150586\pi$
$620$	−4.75368	−	2.74454i	−0.190912	−	0.110223i
$621$	−1.87743	+	0.565335i	−0.0753388	+	0.0226861i
$622$			16.9721i			0.680518i
$623$	2.73068	−	2.69811i	0.109402	−	0.108098i
$624$	−6.92579	+	7.06894i	−0.277253	+	0.282984i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.39567			−0.0557822
$627$	0.113528	−	0.441718i	0.00453389	−	0.0176405i
$628$			11.8201i			0.471672i
$629$	−18.2779			−0.728788
$630$	−1.49998	−	5.29084i	−0.0597607	−	0.210792i
$631$	18.4242			0.733455			0.366728	−	0.930328i	$-0.380478\pi$
$631$	18.4242			0.733455			0.366728	+	0.930328i	$0.380478\pi$
$632$		−	6.62435i		−	0.263503i
$633$	3.92251	+	3.84308i	0.155906	+	0.152749i
$634$	−0.522275			−0.0207422
$635$	−10.3467	+	17.9210i	−0.410596	+	0.711173i
$636$	24.3965	+	6.27029i	0.967385	+	0.248633i
$637$	−15.1180	+	25.4743i	−0.598997	+	1.00933i
$638$			12.1943i			0.482776i
$639$	11.6289	+	19.2227i	0.460033	+	0.760440i
$640$	9.27216	+	5.35329i	0.366514	+	0.211607i
$641$	26.5487	−	15.3279i	1.04861	−	0.605416i	0.126351	−	0.991986i	$-0.459674\pi$
$641$	26.5487	−	15.3279i	1.04861	−	0.605416i	0.922260	+	0.386570i	$0.126340\pi$
$642$	−5.59347	−	5.48019i	−0.220757	−	0.216286i
$643$	−14.1405	+	8.16403i	−0.557647	+	0.321958i	−0.752201	−	0.658934i	$-0.771008\pi$
$643$	−14.1405	+	8.16403i	−0.557647	+	0.321958i	0.194553	+	0.980892i	$0.437674\pi$
$644$	0.401528	−	1.46335i	0.0158224	−	0.0576639i
$645$	11.8668	+	11.6265i	0.467254	+	0.457792i
$646$	0.280790			0.0110475
$647$	20.6290	−	35.7305i	0.811010	−	1.40471i	−0.101148	−	0.994871i	$-0.532251\pi$
$647$	20.6290	−	35.7305i	0.811010	−	1.40471i	0.912158	−	0.409839i	$-0.134415\pi$
$648$	19.4416	+	10.1880i	0.763740	+	0.400221i
$649$	−19.8727	+	11.4735i	−0.780074	+	0.450376i
$650$	1.46600	−	2.53919i	0.0575014	−	0.0995953i
$651$	14.2970	−	8.33516i	0.560342	−	0.326681i
$652$	2.54354	+	4.40553i	0.0996126	+	0.172534i
$653$	11.6994	+	6.75464i	0.457832	+	0.264330i	0.711132	−	0.703058i	$-0.248183\pi$
$653$	11.6994	+	6.75464i	0.457832	+	0.264330i	−0.253300	+	0.967388i	$0.581516\pi$
$654$	19.1750	+	4.92828i	0.749801	+	0.192711i
$655$	3.17382	+	5.49722i	0.124011	+	0.214794i
$656$	−1.38015	−	2.39049i	−0.0538859	−	0.0933331i
$657$	−4.66372	+	0.0954195i	−0.181949	+	0.00372267i
$658$	−8.20325	+	2.14539i	−0.319796	+	0.0836359i
$659$	12.7045	+	7.33495i	0.494897	+	0.285729i	0.726604	−	0.687057i	$-0.241098\pi$
$659$	12.7045	+	7.33495i	0.494897	+	0.285729i	−0.231707	+	0.972786i	$0.574431\pi$
$660$	1.42787	+	5.11888i	0.0555799	+	0.199252i
$661$		−	3.07886i		−	0.119754i	−0.998206	−	0.0598769i	$-0.980929\pi$
$661$		−	3.07886i		−	0.119754i	0.998206	−	0.0598769i	$-0.0190708\pi$
$662$		−	4.30387i		−	0.167275i
$663$	−6.11855	−	21.9348i	−0.237625	−	0.851877i
$664$	−1.30311	−	0.752349i	−0.0505704	−	0.0291968i
$665$	0.333889	−	0.0873216i	0.0129477	−	0.00338619i
$666$	−5.89629	+	10.7129i	−0.228476	+	0.415118i
$667$	1.64498	+	2.84919i	0.0636939	+	0.110321i
$668$	10.3846	+	17.9866i	0.401791	+	0.695922i
$669$	−24.4195	−	6.27620i	−0.944112	−	0.242652i
$670$	−8.11497	−	4.68518i	−0.313509	−	0.181004i
$671$	−5.41196	−	9.37379i	−0.208926	−	0.361871i
$672$	−23.0135	+	13.4169i	−0.887764	+	0.517568i
$673$	7.33909	−	12.7117i	0.282901	−	0.489999i	−0.689197	−	0.724574i	$-0.742036\pi$
$673$	7.33909	−	12.7117i	0.282901	−	0.489999i	0.972098	+	0.234575i	$0.0753698\pi$
$674$	−0.325330	+	0.187829i	−0.0125312	+	0.00723491i
$675$	5.05800	+	1.19024i	0.194682	+	0.0458124i
$676$	3.72996	−	6.46048i	0.143460	−	0.248480i
$677$	−16.8234			−0.646578			−0.323289	−	0.946300i	$-0.604789\pi$
$677$	−16.8234			−0.646578			−0.323289	+	0.946300i	$0.604789\pi$
$678$	−14.3542	−	14.0636i	−0.551272	−	0.540108i
$679$	9.17560	−	33.4400i	0.352127	−	1.28331i
$680$	−6.56190	+	3.78851i	−0.251637	+	0.145283i
$681$	−12.1911	−	11.9442i	−0.467165	−	0.457704i
$682$	4.37417	−	2.52543i	0.167496	−	0.0967036i
$683$	8.69305	+	5.01894i	0.332630	+	0.192044i	0.657008	−	0.753883i	$-0.271822\pi$
$683$	8.69305	+	5.01894i	0.332630	+	0.192044i	−0.324378	+	0.945928i	$0.605155\pi$
$684$	−0.286801	+	0.521088i	−0.0109661	+	0.0199243i
$685$			1.47068i			0.0561918i
$686$	−9.23531	+	8.90869i	−0.352606	+	0.340135i
$687$	−45.4801	−	11.6891i	−1.73518	−	0.445968i
$688$	6.47513	−	11.2152i	0.246862	−	0.427577i
$689$	−40.4902			−1.54256
$690$	−0.323455	−	0.316905i	−0.0123137	−	0.0120644i
$691$			26.8933i			1.02307i	0.859262	+	0.511536i	$0.170923\pi$
$691$			26.8933i			1.02307i	−0.859262	+	0.511536i	$0.829077\pi$
$692$	−34.8136			−1.32342
$693$	−15.5347	−	3.92271i	−0.590114	−	0.149011i
$694$	−5.86256			−0.222540
$695$			9.73945i			0.369438i
$696$	9.16788	−	35.6705i	0.347508	−	1.35209i
$697$	6.35169			0.240588
$698$	2.88786	−	5.00192i	0.109307	−	0.189325i
$699$	−6.85397	+	6.99564i	−0.259241	+	0.264599i
$700$	−2.86058	+	2.82646i	−0.108120	+	0.106830i
$701$		−	34.6386i		−	1.30828i	−0.756372	−	0.654142i	$-0.773030\pi$
$701$		−	34.6386i		−	1.30828i	0.756372	−	0.654142i	$-0.226970\pi$
$702$	−14.8301	−	3.48979i	−0.559725	−	0.131714i
$703$	−0.664594	−	0.383704i	−0.0250656	−	0.0144717i
$704$	−2.32033	+	1.33964i	−0.0874507	+	0.0504897i
$705$	1.99431	−	7.75948i	0.0751100	−	0.292239i
$706$	5.58627	−	3.22524i	0.210242	−	0.121383i
$707$	6.59713	−	6.51844i	0.248111	−	0.245151i
$708$	28.8266	−	8.04096i	1.08337	−	0.302198i
$709$	−21.5574			−0.809607			−0.404803	−	0.914404i	$-0.632660\pi$
$709$	−21.5574			−0.809607			−0.404803	+	0.914404i	$0.632660\pi$
$710$	−2.59434	+	4.49352i	−0.0973638	+	0.168639i
$711$	−6.97213	+	4.21783i	−0.261475	+	0.158181i
$712$	−3.06448	+	1.76928i	−0.114846	+	0.0663064i
$713$	0.681348	−	1.18013i	0.0255167	−	0.0441962i
$714$	−0.0417136	−	9.86433i	−0.00156109	−	0.369163i
$715$	−4.27118	−	7.39790i	−0.159733	−	0.276666i
$716$	−18.2722	−	10.5495i	−0.682864	−	0.394252i
$717$	−9.37434	+	9.56810i	−0.350091	+	0.357327i
$718$	−4.39848	−	7.61839i	−0.164150	−	0.284316i
$719$	−17.6098	−	30.5011i	−0.656736	−	1.13750i	−0.981456	−	0.191690i	$-0.938603\pi$
$719$	−17.6098	−	30.5011i	−0.656736	−	1.13750i	0.324719	−	0.945810i	$-0.394730\pi$
$720$	−0.0828557	−	4.04966i	−0.00308785	−	0.150922i
$721$	13.2567	−	48.3134i	0.493706	−	1.79929i
$722$	−11.3903	−	6.57621i	−0.423904	−	0.244741i
$723$	4.95245	−	5.05482i	0.184184	−	0.187991i
$724$			12.0203i			0.446730i
$725$		−	8.71887i		−	0.323811i
$726$	8.04901	+	2.06872i	0.298727	+	0.0767775i
$727$	−12.3448	−	7.12725i	−0.457842	−	0.264335i	0.253295	−	0.967389i	$-0.418486\pi$
$727$	−12.3448	−	7.12725i	−0.457842	−	0.264335i	−0.711136	+	0.703054i	$0.751819\pi$
$728$	19.4234	−	19.1917i	0.719880	−	0.711293i
$729$	−1.65598	−	26.9492i	−0.0613327	−	0.998117i
$730$	−0.538659	−	0.932984i	−0.0199367	−	0.0345313i
$731$	14.8998	+	25.8072i	0.551089	+	0.954515i
$732$	3.79284	+	13.5972i	0.140188	+	0.502568i
$733$	−15.6356	−	9.02720i	−0.577513	−	0.333427i	0.182631	−	0.983181i	$-0.441538\pi$
$733$	−15.6356	−	9.02720i	−0.577513	−	0.333427i	−0.760144	+	0.649754i	$0.774872\pi$
$734$	10.2344	+	17.7266i	0.377760	+	0.654300i
$735$	−3.11727	−	11.7168i	−0.114982	−	0.432179i
$736$	−1.09675	+	1.89963i	−0.0404267	+	0.0700212i
$737$	−23.6429	+	13.6502i	−0.870897	+	0.502812i
$738$	2.04900	−	3.72282i	0.0754246	−	0.137039i
$739$	3.53742	−	6.12699i	0.130126	−	0.225385i	−0.793599	−	0.608441i	$-0.791795\pi$
$739$	3.53742	−	6.12699i	0.130126	−	0.225385i	0.923725	+	0.383056i	$0.125128\pi$
$740$	8.94204			0.328716
$741$	0.237998	−	0.926005i	0.00874308	−	0.0340177i
$742$	−16.9143	−	4.64113i	−0.620944	−	0.170381i
$743$	−9.07790	+	5.24113i	−0.333036	+	0.192278i	−0.657188	−	0.753727i	$-0.728254\pi$
$743$	−9.07790	+	5.24113i	−0.333036	+	0.192278i	0.324152	+	0.946005i	$0.394921\pi$
$744$	−14.6939	+	4.09875i	−0.538704	+	0.150268i
$745$	−20.8597	+	12.0433i	−0.764239	+	0.441234i
$746$	3.53391	+	2.04030i	0.129386	+	0.0747008i
$747$	0.0378622	+	1.85055i	0.00138531	+	0.0677082i
$748$			9.53247i			0.348542i
$749$	−12.1342	−	12.2806i	−0.443372	−	0.448725i
$750$	0.322438	+	1.15593i	0.0117738	+	0.0422086i
$751$	12.8608	−	22.2756i	0.469297	−	0.812847i	−0.530087	−	0.847944i	$-0.677841\pi$
$751$	12.8608	−	22.2756i	0.469297	−	0.812847i	0.999384	+	0.0350966i	$0.0111739\pi$
$752$	−6.24525			−0.227741
$753$	0.500653	−	0.139653i	0.0182448	−	0.00508925i
$754$			25.5638i			0.930978i
$755$	11.0384			0.401728
$756$	18.3488	+	9.99810i	0.667338	+	0.363627i
$757$	−28.6184			−1.04015			−0.520077	−	0.854120i	$-0.674097\pi$
$757$	−28.6184			−1.04015			−0.520077	+	0.854120i	$0.674097\pi$
$758$			3.75606i			0.136426i
$759$	−1.27079	+	0.354478i	−0.0461269	+	0.0128667i
$760$	−0.318125			−0.0115396
$761$	22.8686	−	39.6096i	0.828986	−	1.43585i	−0.0698485	−	0.997558i	$-0.522252\pi$
$761$	22.8686	−	39.6096i	0.828986	−	1.43585i	0.898834	−	0.438288i	$-0.144415\pi$
$762$	6.67233	+	23.9201i	0.241713	+	0.866534i
$763$	42.0930	+	11.5499i	1.52387	+	0.418134i
$764$		−	36.7379i		−	1.32913i
$765$	8.16547	+	4.49419i	0.295223	+	0.162488i
$766$	−8.49369	−	4.90383i	−0.306890	−	0.177183i
$767$	−41.6607	+	24.0528i	−1.50428	+	0.868497i
$768$	16.8048	−	4.68758i	0.606392	−	0.169148i
$769$	8.20326	−	4.73616i	0.295817	−	0.170790i	−0.344745	−	0.938696i	$-0.612035\pi$
$769$	8.20326	−	4.73616i	0.295817	−	0.170790i	0.640562	+	0.767906i	$0.278701\pi$
$770$	−0.936264	−	3.57996i	−0.0337406	−	0.129013i
$771$	−6.47279	+	25.1844i	−0.233112	+	0.906995i
$772$	28.9243			1.04101
$773$	−11.8211	+	20.4748i	−0.425176	+	0.736426i	−0.996437	−	0.0843421i	$-0.973121\pi$
$773$	−11.8211	+	20.4748i	−0.425176	+	0.736426i	0.571261	+	0.820769i	$0.306454\pi$
$774$	19.9325	−	0.407818i	0.716459	−	0.0146587i
$775$	−3.12751	+	1.80567i	−0.112344	+	0.0648616i
$776$	−15.9819	+	27.6814i	−0.573716	+	0.993706i
$777$	−13.3810	+	23.4046i	−0.480042	+	0.839636i
$778$	2.34484	+	4.06139i	0.0840667	+	0.145608i
$779$	0.230951	+	0.133339i	0.00827467	+	0.00477738i
$780$	2.99336	+	10.7311i	0.107179	+	0.384234i
$781$	7.55857	+	13.0918i	0.270467	+	0.468462i
$782$	−0.406127	−	0.703433i	−0.0145231	−	0.0251547i
$783$	−43.3805	+	13.0628i	−1.55029	+	0.466826i
$784$	−8.24108	+	4.62703i	−0.294324	+	0.165251i
$785$	6.73473	+	3.88830i	0.240373	+	0.138779i
$786$	7.37775	+	1.89620i	0.263156	+	0.0676352i
$787$			16.6352i			0.592981i	0.955036	+	0.296490i	$0.0958163\pi$
$787$			16.6352i			0.592981i	−0.955036	+	0.296490i	$0.904184\pi$
$788$			17.4616i			0.622043i
$789$	13.5988	−	13.8799i	0.484130	−	0.494136i
$790$	−1.62981	−	0.940971i	−0.0579860	−	0.0334783i
$791$	−31.1393	−	31.5152i	−1.10719	−	1.12055i
$792$	12.9388	+	7.12137i	0.459760	+	0.253047i
$793$	−11.3455	−	19.6510i	−0.402890	−	0.697826i
$794$	4.62667	+	8.01363i	0.164194	+	0.284393i
$795$	11.5980	−	11.8378i	0.411340	−	0.419842i
$796$	−13.6142	−	7.86015i	−0.482542	−	0.278596i
$797$	16.1736	+	28.0134i	0.572897	+	0.992287i	0.996267	+	0.0863298i	$0.0275139\pi$
$797$	16.1736	+	28.0134i	0.572897	+	0.992287i	−0.423370	+	0.905957i	$0.639153\pi$
$798$	0.205563	−	0.359548i	0.00727684	−	0.0127278i
$799$	7.18542	−	12.4455i	0.254202	−	0.440291i
$800$	5.03429	−	2.90655i	0.177989	−	0.102762i
$801$	3.81336	+	2.09883i	0.134739	+	0.0741586i
$802$	2.26337	−	3.92028i	0.0799225	−	0.138430i
$803$	−3.13875			−0.110764
$804$	34.2954	−	9.56644i	1.20950	−	0.337382i
$805$	−0.701686	−	0.710157i	−0.0247312	−	0.0250298i
$806$	9.16989	−	5.29424i	0.322996	−	0.186482i
$807$	−8.25117	+	32.1037i	−0.290455	+	1.13010i
$808$	−7.40355	+	4.27444i	−0.260456	+	0.150374i
$809$	10.6494	+	6.14843i	0.374413	+	0.216167i	0.675384	−	0.737466i	$-0.263978\pi$
$809$	10.6494	+	6.14843i	0.374413	+	0.216167i	−0.300972	+	0.953633i	$0.597311\pi$
$810$	5.26821	−	3.33612i	0.185106	−	0.117219i
$811$		−	41.9744i		−	1.47392i	−0.675936	−	0.736961i	$-0.736260\pi$
$811$		−	41.9744i		−	1.47392i	0.675936	−	0.736961i	$-0.263740\pi$
$812$	9.27781	−	33.8125i	0.325587	−	1.18659i
$813$	36.2928	−	37.0429i	1.27284	−	1.29915i
$814$	−4.11408	+	7.12579i	−0.144198	+	0.249759i
$815$	3.34686			0.117235
$816$	1.80858	−	7.03686i	0.0633131	−	0.246339i
$817$			1.25115i			0.0437722i
$818$	1.37956			0.0482351
$819$	−32.5665	−	8.22346i	−1.13797	−	0.287351i
$820$	−3.10742			−0.108516
$821$		−	48.9264i		−	1.70754i	−0.520648	−	0.853771i	$-0.674310\pi$
$821$		−	48.9264i		−	1.70754i	0.520648	−	0.853771i	$-0.325690\pi$
$822$	1.26067	+	1.23514i	0.0439710	+	0.0430806i
$823$	4.18043			0.145721			0.0728603	−	0.997342i	$-0.476787\pi$
$823$	4.18043			0.145721			0.0728603	+	0.997342i	$0.476787\pi$
$824$	−23.0903	+	39.9936i	−0.804389	+	1.39324i
$825$	3.38630	+	0.870332i	0.117896	+	0.0303011i
$826$	−20.1603	+	5.27250i	−0.701466	+	0.183454i
$827$			24.5548i			0.853855i	0.904286	+	0.426928i	$0.140404\pi$
$827$			24.5548i			0.853855i	−0.904286	+	0.426928i	$0.859596\pi$
$828$	1.72025	−	0.0351962i	0.0597828	−	0.00122315i
$829$	−1.05268	−	0.607767i	−0.0365612	−	0.0211086i	0.481608	−	0.876387i	$-0.340053\pi$
$829$	−1.05268	−	0.607767i	−0.0365612	−	0.0211086i	−0.518169	+	0.855278i	$0.673386\pi$
$830$	−0.370206	+	0.213738i	−0.0128500	+	0.00741897i
$831$	28.5858	+	28.0069i	0.991630	+	0.971549i
$832$	−4.86428	+	2.80839i	−0.168639	+	0.0973635i
$833$	0.260962	−	21.7464i	0.00904180	−	0.753468i
$834$	8.34869	+	8.17963i	0.289092	+	0.283237i
$835$	13.6643			0.472873
$836$	−0.200113	+	0.346605i	−0.00692104	+	0.0119876i
$837$	13.6698	+	12.8556i	0.472497	+	0.444354i
$838$	8.20835	−	4.73909i	0.283553	−	0.163709i
$839$	21.0332	−	36.4306i	0.726147	−	1.25772i	−0.232352	−	0.972632i	$-0.574642\pi$
$839$	21.0332	−	36.4306i	0.726147	−	1.25772i	0.958500	−	0.285093i	$-0.0920244\pi$
$840$	0.0472600	+	11.1759i	0.00163063	+	0.385607i
$841$	23.5094	+	40.7194i	0.810668	+	1.40412i
$842$	21.2637	+	12.2766i	0.732796	+	0.423080i
$843$	13.5561	+	3.48414i	0.466899	+	0.120000i
$844$	−2.40947	−	4.17333i	−0.0829374	−	0.143652i
$845$	−2.45400	−	4.25044i	−0.0844200	−	0.146220i
$846$	−4.97654	−	8.22629i	−0.171097	−	0.282826i
$847$	17.6692	+	4.84825i	0.607121	+	0.166588i
$848$	−11.1878	−	6.45929i	−0.384191	−	0.221813i
$849$	7.06323	+	25.3215i	0.242410	+	0.869030i
$850$			2.15259i			0.0738333i
$851$			2.21992i			0.0760978i
$852$	−5.29725	−	18.9904i	−0.181481	−	0.650602i
$853$	−27.8513	−	16.0799i	−0.953609	−	0.550567i	−0.0594092	−	0.998234i	$-0.518922\pi$
$853$	−27.8513	−	16.0799i	−0.953609	−	0.550567i	−0.894200	+	0.447667i	$0.852255\pi$
$854$	−2.48699	−	9.50942i	−0.0851030	−	0.325406i
$855$	0.202555	+	0.334827i	0.00692725	+	0.0114508i
$856$	7.95693	+	13.7818i	0.271962	+	0.471052i
$857$	−24.2266	−	41.9617i	−0.827565	−	1.43338i	−0.899943	−	0.436007i	$-0.856392\pi$
$857$	−24.2266	−	41.9617i	−0.827565	−	1.43338i	0.0723789	−	0.997377i	$-0.476941\pi$
$858$	−9.92864	−	2.55182i	−0.338958	−	0.0871176i
$859$	−2.40240	−	1.38702i	−0.0819687	−	0.0473246i	0.458455	−	0.888717i	$-0.348403\pi$
$859$	−2.40240	−	1.38702i	−0.0819687	−	0.0473246i	−0.540424	+	0.841393i	$0.681736\pi$
$860$	−7.28938	−	12.6256i	−0.248566	−	0.430529i
$861$	4.64999	−	8.13326i	0.158471	−	0.277181i
$862$	−11.0944	+	19.2161i	−0.377878	+	0.654504i
$863$	40.2110	−	23.2158i	1.36880	−	0.790275i	0.378022	−	0.925797i	$-0.376604\pi$
$863$	40.2110	−	23.2158i	1.36880	−	0.790275i	0.990774	+	0.135521i	$0.0432709\pi$
$864$	−22.0039	−	20.6933i	−0.748588	−	0.704001i
$865$	−11.4522	+	19.8358i	−0.389386	+	0.674437i
$866$	11.6365			0.395423
$867$	−9.09036	−	8.90627i	−0.308725	−	0.302473i
$868$	−14.0502	+	3.67453i	−0.476894	+	0.124722i
$869$	−4.74843	+	2.74151i	−0.161080	+	0.0929993i
$870$	−7.47385	−	7.32250i	−0.253387	−	0.248256i
$871$	−49.5643	+	28.6160i	−1.67942	+	0.969615i
$872$	−34.8444	−	20.1174i	−1.17998	−	0.681261i
$873$	39.3106	−	0.804293i	1.33046	−	0.0272212i
$874$		−	0.0341029i		−	0.00115355i
$875$	0.669425	+	2.55966i	0.0226307	+	0.0865324i
$876$	3.96463	+	1.01897i	0.133953	+	0.0344279i
$877$	−3.16107	+	5.47513i	−0.106742	+	0.184882i	−0.914448	−	0.404702i	$-0.867375\pi$
$877$	−3.16107	+	5.47513i	−0.106742	+	0.184882i	0.807707	+	0.589584i	$0.200708\pi$
$878$	−18.8167			−0.635034
$879$	27.9038	+	27.3387i	0.941171	+	0.922112i
$880$		−	2.72548i		−	0.0918758i
$881$	10.4850			0.353247			0.176624	−	0.984278i	$-0.443482\pi$
$881$	10.4850			0.353247			0.176624	+	0.984278i	$0.443482\pi$
$882$	−12.6617	−	7.16813i	−0.426341	−	0.241364i
$883$	−24.3398			−0.819100			−0.409550	−	0.912288i	$-0.634314\pi$
$883$	−24.3398			−0.819100			−0.409550	+	0.912288i	$0.634314\pi$
$884$			19.9836i			0.672122i
$885$	4.90121	−	19.0697i	0.164752	−	0.641020i
$886$	20.2191			0.679275
$887$	21.9605	−	38.0367i	0.737362	−	1.27715i	−0.216317	−	0.976323i	$-0.569405\pi$
$887$	21.9605	−	38.0367i	0.737362	−	1.27715i	0.953679	−	0.300825i	$-0.0972622\pi$
$888$	17.3917	−	17.7512i	0.583628	−	0.595691i
$889$	13.8527	+	52.9681i	0.464604	+	1.77649i
$890$			1.00528i			0.0336972i
$891$	−0.743104	−	18.1524i	−0.0248949	−	0.608128i
$892$	19.1614	+	11.0628i	0.641571	+	0.370411i
$893$	0.522531	−	0.301684i	0.0174858	−	0.0100955i
$894$	−7.19529	+	27.9955i	−0.240647	+	0.936310i
$895$	−12.0215	+	6.94064i	−0.401836	+	0.232000i
$896$	27.4052	−	7.16725i	0.915544	−	0.239441i
$897$	−2.66406	+	0.743119i	−0.0889503	+	0.0248120i
$898$	4.05618			0.135357
$899$	15.7434	−	27.2684i	0.525072	−	0.909452i
$900$	−3.99477	−	2.19868i	−0.133159	−	0.0732892i
$901$	25.7441	−	14.8634i	0.857661	−	0.495171i
$902$	1.42967	−	2.47626i	0.0476027	−	0.0824504i
$903$	43.9538	−	0.185869i	1.46269	−	0.00618532i
$904$	20.4195	+	35.3676i	0.679142	+	1.17631i
$905$	6.84880	+	3.95416i	0.227662	+	0.131441i
$906$	9.27053	−	9.46215i	0.307993	−	0.314359i
$907$	−5.41633	−	9.38135i	−0.179846	−	0.311503i	0.761982	−	0.647599i	$-0.224227\pi$
$907$	−5.41633	−	9.38135i	−0.179846	−	0.311503i	−0.941828	+	0.336096i	$0.890893\pi$
$908$	7.48861	+	12.9707i	0.248518	+	0.430446i
$909$	9.21281	+	5.07063i	0.305570	+	0.168182i
$910$	−1.96276	−	7.50494i	−0.0650648	−	0.248786i
$911$	−6.64047	−	3.83388i	−0.220009	−	0.127022i	0.385946	−	0.922522i	$-0.373875\pi$
$911$	−6.64047	−	3.83388i	−0.220009	−	0.127022i	−0.605954	+	0.795500i	$0.707209\pi$
$912$	0.213484	−	0.217896i	0.00706916	−	0.00721527i
$913$			1.24545i			0.0412183i
$914$		−	25.0577i		−	0.828836i
$915$	8.99498	+	2.31185i	0.297365	+	0.0764275i
$916$	35.6872	+	20.6040i	1.17914	+	0.680776i
$917$	16.1957	+	4.44393i	0.534828	+	0.146751i
$918$	10.7102	−	3.22506i	0.353488	−	0.106443i
$919$	7.09655	+	12.2916i	0.234094	+	0.405462i	0.959009	−	0.283376i	$-0.0914544\pi$
$919$	7.09655	+	12.2916i	0.234094	+	0.405462i	−0.724915	+	0.688838i	$0.758121\pi$
$920$	0.460128	+	0.796965i	0.0151700	+	0.0262752i
$921$	4.39213	+	15.7457i	0.144726	+	0.518837i
$922$	7.72305	+	4.45890i	0.254345	+	0.146846i
$923$	15.8456	+	27.4454i	0.521564	+	0.903375i
$924$	12.2062	+	6.97860i	0.401555	+	0.229579i
$925$	2.94155	−	5.09492i	0.0967176	−	0.167520i
$926$	5.79487	−	3.34567i	0.190431	−	0.109946i
$927$	56.7952	−	1.16203i	1.86540	−	0.0381660i
$928$	−25.3418	+	43.8933i	−0.831886	+	1.44087i
$929$	10.3538			0.339697			0.169849	−	0.985470i	$-0.445672\pi$
$929$	10.3538			0.339697			0.169849	+	0.985470i	$0.445672\pi$
$930$	−1.07880	+	4.19740i	−0.0353752	+	0.137638i
$931$	0.466005	−	0.785231i	0.0152727	−	0.0257349i
$932$	7.44296	−	4.29720i	0.243802	−	0.140759i
$933$	−40.8680	+	11.3998i	−1.33796	+	0.373213i
$934$	−12.1467	+	7.01291i	−0.397453	+	0.229470i
$935$	5.43132	+	3.13578i	0.177623	+	0.102551i
$936$	27.1246	+	14.9291i	0.886594	+	0.487972i
$937$		−	27.0680i		−	0.884273i	−0.896948	−	0.442136i	$-0.854221\pi$
$937$		−	27.0680i		−	0.884273i	0.896948	−	0.442136i	$-0.145779\pi$
$938$	−23.9850	+	6.27276i	−0.783137	+	0.204813i
$939$	−0.937445	−	3.36071i	−0.0305924	−	0.109673i
$940$	−3.51530	+	6.08868i	−0.114656	+	0.198591i
$941$	−42.7122			−1.39238			−0.696189	−	0.717858i	$-0.745123\pi$
$941$	−42.7122			−1.39238			−0.696189	+	0.717858i	$0.745123\pi$
$942$	8.98920	−	2.50747i	0.292884	−	0.0816978i
$943$		−	0.771435i		−	0.0251214i
$944$	−15.3483			−0.499545
$945$	11.7326	−	7.16565i	0.381661	−	0.233098i
$946$	13.4149			0.436155
$947$			35.0457i			1.13883i	0.822049	+	0.569417i	$0.192831\pi$
$947$			35.0457i			1.13883i	−0.822049	+	0.569417i	$0.807169\pi$
$948$	6.88787	−	1.92132i	0.223708	−	0.0624016i
$949$	−6.58000			−0.213596
$950$	−0.0451888	+	0.0782693i	−0.00146612	+	0.00253939i
$951$	−0.350802	−	1.25762i	−0.0113755	−	0.0407810i
$952$	−5.30461	+	19.3324i	−0.171923	+	0.626566i
$953$			22.6751i			0.734518i	0.930119	+	0.367259i	$0.119704\pi$
$953$			22.6751i			0.734518i	−0.930119	+	0.367259i	$0.880296\pi$
$954$	−0.406821	−	19.8838i	−0.0131713	−	0.643761i
$955$	−20.9322	−	12.0852i	−0.677349	−	0.391068i
$956$	10.1799	−	5.87738i	0.329242	−	0.190088i
$957$	−29.3633	+	8.19067i	−0.949180	+	0.264767i
$958$	−24.1210	+	13.9263i	−0.779313	+	0.449937i
$959$	2.73483	+	2.76785i	0.0883124	+	0.0893785i
$960$	0.572262	−	2.22656i	0.0184697	−	0.0718620i
$961$	17.9582			0.579297
$962$	−8.62464	+	14.9383i	−0.278070	+	0.481631i
$963$	9.43904	−	17.1498i	0.304169	−	0.552643i
$964$	−5.37804	+	3.10501i	−0.173215	+	0.100006i
$965$	9.51485	−	16.4802i	0.306294	−	0.530517i
$966$	−1.19806	+	0.00506626i	−0.0385469	+	0.000163004i
$967$	14.4168	+	24.9707i	0.463614	+	0.803004i	0.999138	−	0.0415167i	$-0.0132190\pi$
$967$	14.4168	+	24.9707i	0.463614	+	0.803004i	−0.535523	+	0.844520i	$0.679886\pi$
$968$	−14.6265	−	8.44460i	−0.470113	−	0.271420i
$969$	0.188601	+	0.676129i	0.00605875	+	0.0217204i
$970$	4.54037	+	7.86415i	0.145782	+	0.252503i
$971$	6.27559	+	10.8696i	0.201393	+	0.348824i	0.948978	−	0.315343i	$-0.102120\pi$
$971$	6.27559	+	10.8696i	0.201393	+	0.348824i	−0.747584	+	0.664167i	$0.768786\pi$
$972$	−4.95441	+	23.1700i	−0.158913	+	0.743177i
$973$	18.1112	+	18.3298i	0.580618	+	0.587627i
$974$	16.1851	+	9.34450i	0.518605	+	0.299417i
$975$	7.09895	+	1.82454i	0.227348	+	0.0584321i
$976$		−	7.23966i		−	0.231736i
$977$			55.4474i			1.77392i	0.461847	+	0.886960i	$0.347187\pi$
$977$			55.4474i			1.77392i	−0.461847	+	0.886960i	$0.652813\pi$
$978$	2.81084	−	2.86894i	0.0898809	−	0.0917386i
$979$	2.53649	+	1.46444i	0.0810664	+	0.0468037i
$980$	−0.127670	+	10.6389i	−0.00407826	+	0.339848i
$981$	1.01241	+	49.4827i	0.0323239	+	1.57986i
$982$	−5.74963	−	9.95865i	−0.183478	−	0.317793i
$983$	−27.7617	−	48.0847i	−0.885461	−	1.53366i	−0.845184	−	0.534475i	$-0.820509\pi$
$983$	−27.7617	−	48.0847i	−0.885461	−	1.53366i	−0.0402769	−	0.999189i	$-0.512824\pi$
$984$	−6.04373	+	6.16865i	−0.192667	+	0.196649i
$985$	9.94909	+	5.74411i	0.317004	+	0.183023i
$986$	−9.38409	−	16.2537i	−0.298850	−	0.517624i
$987$	−10.6760	−	18.3120i	−0.339820	−	0.582879i
$988$	−0.419511	+	0.726615i	−0.0133464	+	0.0231167i
$989$	3.13438	−	1.80963i	0.0996674	−	0.0575430i
$990$	3.59002	−	2.17180i	0.114098	−	0.0690244i
$991$	−21.4737	+	37.1936i	−0.682136	+	1.18149i	0.292192	+	0.956360i	$0.405615\pi$
$991$	−21.4737	+	37.1936i	−0.682136	+	1.18149i	−0.974328	+	0.225134i	$0.927718\pi$
$992$	20.9931			0.666531
$993$	10.3635	−	2.89083i	0.328877	−	0.0917377i
$994$	3.47343	+	13.2813i	0.110171	+	0.421256i
$995$	−8.95697	+	5.17131i	−0.283955	+	0.163942i
$996$	0.404326	−	1.57316i	0.0128116	−	0.0498474i
$997$	−17.8833	+	10.3249i	−0.566371	+	0.326994i	−0.755699	−	0.654920i	$-0.772702\pi$
$997$	−17.8833	+	10.3249i	−0.566371	+	0.326994i	0.189328	+	0.981914i	$0.439369\pi$
$998$	19.4758	+	11.2444i	0.616497	+	0.355935i
$999$	−29.7567	−	7.00230i	−0.941461	−	0.221543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.101.9	✓	30
3.2	odd	2		945.2.t.b.521.7		30
7.5	odd	6		315.2.be.b.236.9	yes	30
9.4	even	3		945.2.be.b.206.7		30
9.5	odd	6		315.2.be.b.311.9	yes	30
21.5	even	6		945.2.be.b.656.7		30
63.5	even	6	inner	315.2.t.b.131.7	yes	30
63.40	odd	6		945.2.t.b.341.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.9	✓	30	1.1	even	1	trivial
315.2.t.b.131.7	yes	30	63.5	even	6	inner
315.2.be.b.236.9	yes	30	7.5	odd	6
315.2.be.b.311.9	yes	30	9.5	odd	6
945.2.t.b.341.9		30	63.40	odd	6
945.2.t.b.521.7		30	3.2	odd	2
945.2.be.b.206.7		30	9.4	even	3
945.2.be.b.656.7		30	21.5	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.692853i q^{2} +(-1.66836 + 0.465377i) q^{3} +1.51995 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.322438 - 1.15593i) q^{6} +(-0.669425 - 2.55966i) q^{7} +2.43881i q^{8} +(2.56685 - 1.55283i) q^{9} +O(q^{10})\)	\(q+0.692853i q^{2} +(-1.66836 + 0.465377i) q^{3} +1.51995 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.322438 - 1.15593i) q^{6} +(-0.669425 - 2.55966i) q^{7} +2.43881i q^{8} +(2.56685 - 1.55283i) q^{9} +(0.600029 + 0.346427i) q^{10} +(1.74818 - 1.00931i) q^{11} +(-2.53583 + 0.707351i) q^{12} +(3.66483 - 2.11589i) q^{13} +(1.77347 - 0.463814i) q^{14} +(-0.431152 + 1.67753i) q^{15} +1.35017 q^{16} +(-1.55343 + 2.69061i) q^{17} +(1.07588 + 1.77845i) q^{18} +(-0.112967 + 0.0652213i) q^{19} +(0.759977 - 1.31632i) q^{20} +(2.30805 + 3.95890i) q^{21} +(0.699304 + 1.21123i) q^{22} +(0.326784 + 0.188669i) q^{23} +(-1.13497 - 4.06882i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.46600 + 2.53919i) q^{26} +(-3.55978 + 3.78523i) q^{27} +(-1.01750 - 3.89057i) q^{28} +(7.55077 + 4.35944i) q^{29} +(-1.16228 - 0.298725i) q^{30} -3.61134i q^{31} +5.81309i q^{32} +(-2.44688 + 2.49745i) q^{33} +(-1.86420 - 1.07630i) q^{34} +(-2.55145 - 0.700092i) q^{35} +(3.90149 - 2.36023i) q^{36} +(2.94155 + 5.09492i) q^{37} +(-0.0451888 - 0.0782693i) q^{38} +(-5.12957 + 5.23560i) q^{39} +(2.11207 + 1.21941i) q^{40} +(-1.02221 - 1.77052i) q^{41} +(-2.74294 + 1.59914i) q^{42} +(4.79579 - 8.30655i) q^{43} +(2.65715 - 1.53411i) q^{44} +(-0.0613670 - 2.99937i) q^{45} +(-0.130720 + 0.226414i) q^{46} -4.62554 q^{47} +(-2.25257 + 0.628337i) q^{48} +(-6.10374 + 3.42701i) q^{49} +(0.600029 - 0.346427i) q^{50} +(1.33952 - 5.21184i) q^{51} +(5.57038 - 3.21606i) q^{52} +(-8.28624 - 4.78406i) q^{53} +(-2.62261 - 2.46640i) q^{54} -2.01862i q^{55} +(6.24254 - 1.63260i) q^{56} +(0.158117 - 0.161385i) q^{57} +(-3.02045 + 5.23157i) q^{58} -11.3677 q^{59} +(-0.655331 + 2.54977i) q^{60} -5.36204i q^{61} +2.50213 q^{62} +(-5.69304 - 5.53076i) q^{63} -1.32729 q^{64} -4.23178i q^{65} +(-1.73037 - 1.69533i) q^{66} -13.5243 q^{67} +(-2.36114 + 4.08961i) q^{68} +(-0.632996 - 0.162690i) q^{69} +(0.485061 - 1.76778i) q^{70} +7.48885i q^{71} +(3.78706 + 6.26006i) q^{72} +(-1.34658 - 0.777450i) q^{73} +(-3.53003 + 2.03806i) q^{74} +(1.23721 + 1.21215i) q^{75} +(-0.171704 + 0.0991334i) q^{76} +(-3.75377 - 3.79908i) q^{77} +(-3.62750 - 3.55404i) q^{78} -2.71622 q^{79} +(0.675084 - 1.16928i) q^{80} +(4.17743 - 7.97177i) q^{81} +(1.22671 - 0.708240i) q^{82} +(-0.308490 + 0.534320i) q^{83} +(3.50813 + 6.01735i) q^{84} +(1.55343 + 2.69061i) q^{85} +(5.75522 + 3.32278i) q^{86} +(-14.6262 - 3.75916i) q^{87} +(2.46152 + 4.26347i) q^{88} +(0.725466 + 1.25654i) q^{89} +(2.07813 - 0.0425183i) q^{90} +(-7.86930 - 7.96430i) q^{91} +(0.496697 + 0.286768i) q^{92} +(1.68063 + 6.02502i) q^{93} -3.20482i q^{94} +0.130443i q^{95} +(-2.70528 - 9.69833i) q^{96} +(11.3504 + 6.55314i) q^{97} +(-2.37441 - 4.22900i) q^{98} +(2.92002 - 5.30537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

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