LMFDB - Embedded newform 315.2.be.b.236.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (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			236.9
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.600029 - 0.346427i) q^{2} +(-0.431152 + 1.67753i) q^{3} +(-0.759977 + 1.31632i) q^{4} +1.00000 q^{5} +(0.322438 + 1.15593i) q^{6} +(2.55145 - 0.700092i) q^{7} +2.43881i q^{8} +(-2.62822 - 1.44654i) q^{9} +O(q^{10})$	\(q+(0.600029 - 0.346427i) q^{2} +(-0.431152 + 1.67753i) q^{3} +(-0.759977 + 1.31632i) q^{4} +1.00000 q^{5} +(0.322438 + 1.15593i) q^{6} +(2.55145 - 0.700092i) q^{7} +2.43881i q^{8} +(-2.62822 - 1.44654i) q^{9} +(0.600029 - 0.346427i) q^{10} +2.01862i q^{11} +(-1.88050 - 1.84242i) q^{12} +(-3.66483 + 2.11589i) q^{13} +(1.28841 - 1.30396i) q^{14} +(-0.431152 + 1.67753i) q^{15} +(-0.675084 - 1.16928i) q^{16} +(1.55343 + 2.69061i) q^{17} +(-2.07813 + 0.0425183i) q^{18} +(-0.112967 - 0.0652213i) q^{19} +(-0.759977 + 1.31632i) q^{20} +(0.0743645 + 4.58197i) q^{21} +(0.699304 + 1.21123i) q^{22} -0.377338i q^{23} +(-4.09118 - 1.05150i) q^{24} +1.00000 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} +(0.322438 + 1.15593i) q^{30} +(-3.12751 - 1.80567i) q^{31} +(-5.03429 - 2.90655i) q^{32} +(-3.38630 - 0.870332i) 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} -0.0903776 q^{38} +(-1.96937 - 7.06014i) q^{39} +2.43881i q^{40} +(1.02221 + 1.77052i) q^{41} +(1.63194 + 2.72355i) q^{42} +(4.79579 - 8.30655i) q^{43} +(-2.65715 - 1.53411i) q^{44} +(-2.62822 - 1.44654i) q^{45} +(-0.130720 - 0.226414i) q^{46} +(-2.31277 - 4.00583i) q^{47} +(2.25257 - 0.628337i) q^{48} +(6.01974 - 3.57249i) q^{49} +(0.600029 - 0.346427i) q^{50} +(-5.18334 + 1.44586i) q^{51} -6.43212i q^{52} +(8.28624 - 4.78406i) q^{53} +(0.824662 - 3.50445i) q^{54} +2.01862i q^{55} +(1.70739 + 6.22250i) q^{56} +(0.158117 - 0.161385i) q^{57} +6.04090 q^{58} +(-5.68385 + 9.84472i) q^{59} +(-1.88050 - 1.84242i) q^{60} +(4.64366 - 2.68102i) q^{61} -2.50213 q^{62} +(-7.71846 - 1.85078i) q^{63} -1.32729 q^{64} +(-3.66483 + 2.11589i) q^{65} +(-2.33338 + 0.650880i) q^{66} +(6.76215 - 11.7124i) q^{67} -4.72227 q^{68} +(0.632996 + 0.162690i) q^{69} +(1.28841 - 1.30396i) q^{70} +7.48885i q^{71} +(3.52784 - 6.40973i) q^{72} +(-1.34658 + 0.777450i) q^{73} -4.07613i q^{74} +(-0.431152 + 1.67753i) q^{75} +(0.171704 - 0.0991334i) q^{76} +(1.41322 + 5.15040i) q^{77} +(-3.62750 - 3.55404i) q^{78} +(1.35811 + 2.35232i) q^{79} +(-0.675084 - 1.16928i) q^{80} +(4.81504 + 7.60364i) q^{81} +(1.22671 + 0.708240i) q^{82} +(0.308490 - 0.534320i) q^{83} +(-6.08785 - 3.38431i) q^{84} +(1.55343 + 2.69061i) q^{85} -6.64556i q^{86} +(-10.5686 + 10.7871i) q^{87} -4.92304 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} +(4.37750 - 4.46798i) q^{93} +(-2.77545 - 1.60241i) q^{94} +(-0.112967 - 0.0652213i) q^{95} +(7.04636 - 7.19201i) 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 + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.600029	−	0.346427i	0.424284	−	0.244961i	−0.272624	−	0.962121i	$-0.587892\pi$
$2$	0.600029	−	0.346427i	0.424284	−	0.244961i	0.696909	+	0.717160i	$0.254558\pi$
$3$	−0.431152	+	1.67753i	−0.248926	+	0.968523i
$3$	−0.431152	+	1.67753i	−0.248926	+	0.968523i
$4$	−0.759977	+	1.31632i	−0.379989	+	0.658159i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.322438	+	1.15593i	0.131635	+	0.471906i
$7$	2.55145	−	0.700092i	0.964356	−	0.264610i
$7$	2.55145	−	0.700092i	0.964356	−	0.264610i
$8$			2.43881i			0.862250i
$9$	−2.62822	−	1.44654i	−0.876072	−	0.482180i
$10$	0.600029	−	0.346427i	0.189746	−	0.109550i
$11$			2.01862i			0.608637i	0.952570	+	0.304318i	$0.0984287\pi$
$11$			2.01862i			0.608637i	−0.952570	+	0.304318i	$0.901571\pi$
$12$	−1.88050	−	1.84242i	−0.542853	−	0.531860i
$13$	−3.66483	+	2.11589i	−1.01644	+	0.586843i	−0.913071	−	0.407800i	$-0.866296\pi$
$13$	−3.66483	+	2.11589i	−1.01644	+	0.586843i	−0.103370	+	0.994643i	$0.532963\pi$
$14$	1.28841	−	1.30396i	0.344342	−	0.348499i
$15$	−0.431152	+	1.67753i	−0.111323	+	0.433136i
$16$	−0.675084	−	1.16928i	−0.168771	−	0.292320i
$17$	1.55343	+	2.69061i	0.376761	+	0.652569i	0.990589	−	0.136871i	$-0.0437045\pi$
$17$	1.55343	+	2.69061i	0.376761	+	0.652569i	−0.613828	+	0.789440i	$0.710371\pi$
$18$	−2.07813	+	0.0425183i	−0.489819	+	0.0100217i
$19$	−0.112967	−	0.0652213i	−0.0259163	−	0.0149628i	0.486986	−	0.873410i	$-0.338096\pi$
$19$	−0.112967	−	0.0652213i	−0.0259163	−	0.0149628i	−0.512902	+	0.858447i	$0.671430\pi$
$20$	−0.759977	+	1.31632i	−0.169936	+	0.294338i
$21$	0.0743645	+	4.58197i	0.0162277	+	0.999868i
$22$	0.699304	+	1.21123i	0.149092	+	0.258235i
$23$		−	0.377338i		−	0.0786804i	−0.999226	−	0.0393402i	$-0.987474\pi$
$23$		−	0.377338i		−	0.0786804i	0.999226	−	0.0393402i	$-0.0125256\pi$
$24$	−4.09118	−	1.05150i	−0.835109	−	0.214636i
$25$	1.00000			0.200000
$26$	−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	$0.366390\pi$
$30$	0.322438	+	1.15593i	0.0588688	+	0.211043i
$31$	−3.12751	−	1.80567i	−0.561718	−	0.324308i	0.192117	−	0.981372i	$-0.438465\pi$
$31$	−3.12751	−	1.80567i	−0.561718	−	0.324308i	−0.753835	+	0.657064i	$0.771798\pi$
$32$	−5.03429	−	2.90655i	−0.889945	−	0.513810i
$33$	−3.38630	−	0.870332i	−0.589479	−	0.151505i
$34$	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	−0.516234	−	0.856447i	$-0.672667\pi$
$37$	2.94155	−	5.09492i	0.483588	−	0.837599i	0.999822	+	0.0188484i	$0.00599998\pi$
$38$	−0.0903776			−0.0146612
$39$	−1.96937	−	7.06014i	−0.315352	−	1.13053i
$40$			2.43881i			0.385610i
$41$	1.02221	+	1.77052i	0.159642	+	0.276508i	0.934740	−	0.355333i	$-0.115633\pi$
$41$	1.02221	+	1.77052i	0.159642	+	0.276508i	−0.775098	+	0.631842i	$0.782299\pi$
$42$	1.63194	+	2.72355i	0.251814	+	0.420253i
$43$	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
$45$	−2.62822	−	1.44654i	−0.391791	−	0.215638i
$46$	−0.130720	−	0.226414i	−0.0192736	−	0.0333829i
$47$	−2.31277	−	4.00583i	−0.337352	−	0.584311i	0.646582	−	0.762845i	$-0.276198\pi$
$47$	−2.31277	−	4.00583i	−0.337352	−	0.584311i	−0.983934	+	0.178534i	$0.942865\pi$
$48$	2.25257	−	0.628337i	0.325130	−	0.0906926i
$49$	6.01974	−	3.57249i	0.859963	−	0.510356i
$50$	0.600029	−	0.346427i	0.0848569	−	0.0489921i
$51$	−5.18334	+	1.44586i	−0.725813	+	0.202460i
$52$		−	6.43212i		−	0.891974i
$53$	8.28624	−	4.78406i	1.13820	−	0.657142i	0.192218	−	0.981352i	$-0.438432\pi$
$53$	8.28624	−	4.78406i	1.13820	−	0.657142i	0.945985	+	0.324210i	$0.105099\pi$
$54$	0.824662	−	3.50445i	0.112222	−	0.476895i
$55$			2.01862i			0.272191i
$56$	1.70739	+	6.22250i	0.228160	+	0.831516i
$57$	0.158117	−	0.161385i	0.0209430	−	0.0213759i
$58$	6.04090			0.793209
$59$	−5.68385	+	9.84472i	−0.739974	+	1.28167i	0.212532	+	0.977154i	$0.431829\pi$
$59$	−5.68385	+	9.84472i	−0.739974	+	1.28167i	−0.952506	+	0.304519i	$0.901504\pi$
$60$	−1.88050	−	1.84242i	−0.242771	−	0.237855i
$61$	4.64366	−	2.68102i	0.594560	−	0.343269i	−0.172338	−	0.985038i	$-0.555132\pi$
$61$	4.64366	−	2.68102i	0.594560	−	0.343269i	0.766898	+	0.641768i	$0.221799\pi$
$62$	−2.50213			−0.317771
$63$	−7.71846	−	1.85078i	−0.972435	−	0.233176i
$64$	−1.32729			−0.165911
$65$	−3.66483	+	2.11589i	−0.454566	+	0.262444i
$66$	−2.33338	+	0.650880i	−0.287219	+	0.0801177i
$67$	6.76215	−	11.7124i	0.826129	−	1.43090i	−0.0749250	−	0.997189i	$-0.523872\pi$
$67$	6.76215	−	11.7124i	0.826129	−	1.43090i	0.901054	−	0.433708i	$-0.142795\pi$
$68$	−4.72227			−0.572659
$69$	0.632996	+	0.162690i	0.0762037	+	0.0195856i
$70$	1.28841	−	1.30396i	0.153994	−	0.155853i
$71$			7.48885i			0.888763i	0.895838	+	0.444381i	$0.146576\pi$
$71$			7.48885i			0.888763i	−0.895838	+	0.444381i	$0.853424\pi$
$72$	3.52784	−	6.40973i	0.415760	−	0.755393i
$73$	−1.34658	+	0.777450i	−0.157606	+	0.0909936i	−0.576729	−	0.816936i	$-0.695671\pi$
$73$	−1.34658	+	0.777450i	−0.157606	+	0.0909936i	0.419123	+	0.907929i	$0.362338\pi$
$74$		−	4.07613i		−	0.473840i
$75$	−0.431152	+	1.67753i	−0.0497851	+	0.193705i
$76$	0.171704	−	0.0991334i	0.0196958	−	0.0113714i
$77$	1.41322	+	5.15040i	0.161051	+	0.586942i
$78$	−3.62750	−	3.55404i	−0.410734	−	0.402416i
$79$	1.35811	+	2.35232i	0.152799	+	0.264656i	0.932256	−	0.361801i	$-0.117838\pi$
$79$	1.35811	+	2.35232i	0.152799	+	0.264656i	−0.779456	+	0.626457i	$0.784505\pi$
$80$	−0.675084	−	1.16928i	−0.0754767	−	0.130729i
$81$	4.81504	+	7.60364i	0.535004	+	0.844849i
$82$	1.22671	+	0.708240i	0.135467	+	0.0782121i
$83$	0.308490	−	0.534320i	0.0338612	−	0.0586493i	−0.848598	−	0.529038i	$-0.822553\pi$
$83$	0.308490	−	0.534320i	0.0338612	−	0.0586493i	0.882459	+	0.470389i	$0.155886\pi$
$84$	−6.08785	−	3.38431i	−0.664239	−	0.369258i
$85$	1.55343	+	2.69061i	0.168493	+	0.291838i
$86$		−	6.64556i		−	0.716609i
$87$	−10.5686	+	10.7871i	−1.13307	+	1.15649i
$88$	−4.92304			−0.524797
$89$	−0.725466	+	1.25654i	−0.0768992	+	0.133193i	−0.901911	−	0.431923i	$-0.857835\pi$
$89$	−0.725466	+	1.25654i	−0.0768992	+	0.133193i	0.825011	+	0.565116i	$0.191169\pi$
$90$	−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
$93$	4.37750	−	4.46798i	0.453926	−	0.463308i
$94$	−2.77545	−	1.60241i	−0.286266	−	0.165276i
$95$	−0.112967	−	0.0652213i	−0.0115901	−	0.00669157i
$96$	7.04636	−	7.19201i	0.719166	−	0.734031i
$97$	−11.3504	−	6.55314i	−1.15246	−	0.665371i	−0.202972	−	0.979185i	$-0.565060\pi$
$97$	−11.3504	−	6.55314i	−1.15246	−	0.665371i	−0.949485	+	0.313814i	$0.898393\pi$
$98$	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
$101$	3.50535			0.348795			0.174398	−	0.984675i	$-0.444202\pi$
$101$	3.50535			0.348795			0.174398	+	0.984675i	$0.444202\pi$
$102$	−2.60927	+	2.66320i	−0.258356	+	0.263697i
$103$			18.9357i			1.86579i	0.360148	+	0.932895i	$0.382726\pi$
$103$			18.9357i			1.86579i	−0.360148	+	0.932895i	$0.617274\pi$
$104$	−5.16026	−	8.93784i	−0.506005	−	0.876427i
$105$	0.0743645	+	4.58197i	0.00725723	+	0.447155i
$106$	3.31466	−	5.74115i	0.321948	−	0.557630i
$107$	−5.65103	−	3.26262i	−0.546306	−	0.315410i	0.201325	−	0.979525i	$-0.435475\pi$
$107$	−5.65103	−	3.26262i	−0.546306	−	0.315410i	−0.747631	+	0.664115i	$0.768809\pi$
$108$	2.27723	+	7.56249i	0.219126	+	0.727701i
$109$	−8.24885	−	14.2874i	−0.790096	−	1.36849i	−0.925907	−	0.377752i	$-0.876697\pi$
$109$	−8.24885	−	14.2874i	−0.790096	−	1.36849i	0.135810	−	0.990735i	$-0.456636\pi$
$110$	0.699304	+	1.21123i	0.0666760	+	0.115486i
$111$	7.27862	+	7.13122i	0.690856	+	0.676866i
$112$	−2.54104	−	2.51073i	−0.240106	−	0.237242i
$113$	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	$0.0446366\pi$
$114$	0.0389665	−	0.151611i	0.00364955	−	0.0141997i
$115$		−	0.377338i		−	0.0351869i
$116$	−11.4768	+	6.62614i	−1.06560	+	0.615222i
$117$	12.6927	−	0.259692i	1.17344	−	0.0240085i
$118$			7.87615i			0.725058i
$119$	5.84715	+	5.77741i	0.536008	+	0.529614i
$120$	−4.09118	−	1.05150i	−0.373472	−	0.0959883i
$121$	6.92517			0.629561
$122$	1.85755	−	3.21738i	0.168175	−	0.291288i
$123$	−3.41082	+	0.951423i	−0.307543	+	0.0857870i
$124$	4.75368	−	2.74454i	0.426893	−	0.246467i
$125$	1.00000			0.0894427
$126$	−5.27246	+	1.56336i	−0.469708	+	0.139275i
$127$	−20.6934			−1.83624			−0.918121	−	0.396300i	$-0.870294\pi$
$127$	−20.6934			−1.83624			−0.918121	+	0.396300i	$0.870294\pi$
$128$	9.27216	−	5.35329i	0.819551	−	0.473168i
$129$	11.8668	+	11.6265i	1.04481	+	1.02365i
$130$	−1.46600	+	2.53919i	−0.128577	+	0.222702i
$131$	−6.34764			−0.554596			−0.277298	−	0.960784i	$-0.589439\pi$
$131$	−6.34764			−0.554596			−0.277298	+	0.960784i	$0.589439\pi$
$132$	3.71914	−	3.79601i	0.323710	−	0.330401i
$133$	−0.333889	−	0.0873216i	−0.0289519	−	0.00757174i
$134$		−	9.37036i		−	0.809476i
$135$	3.55978	−	3.78523i	0.306377	−	0.325781i
$136$	−6.56190	+	3.78851i	−0.562678	+	0.324862i
$137$		−	1.47068i		−	0.125649i	−0.998025	−	0.0628243i	$-0.979989\pi$
$137$		−	1.47068i		−	0.125649i	0.998025	−	0.0628243i	$-0.0200108\pi$
$138$	0.436176	−	0.121668i	0.0371297	−	0.0103571i
$139$	8.43461	−	4.86972i	0.715414	−	0.413045i	−0.0976482	−	0.995221i	$-0.531132\pi$
$139$	8.43461	−	4.86972i	0.715414	−	0.413045i	0.813063	+	0.582176i	$0.197799\pi$
$140$	−1.01750	+	3.89057i	−0.0859941	+	0.328813i
$141$	7.71706	−	2.15262i	0.649894	−	0.181283i
$142$	2.59434	+	4.49352i	0.217712	+	0.377088i
$143$	−4.27118	−	7.39790i	−0.357174	−	0.618644i
$144$	0.0828557	+	4.04966i	0.00690465	+	0.337471i
$145$	7.55077	+	4.35944i	0.627057	+	0.362032i
$146$	−0.538659	+	0.932984i	−0.0445797	+	0.0772143i
$147$	3.39754	+	11.6386i	0.280224	+	0.959935i
$148$	4.47102	+	7.74404i	0.367516	+	0.636556i
$149$			24.0867i			1.97326i	0.162987	+	0.986628i	$0.447887\pi$
$149$			24.0867i			1.97326i	−0.162987	+	0.986628i	$0.552113\pi$
$150$	0.322438	+	1.15593i	0.0263269	+	0.0943812i
$151$	−11.0384			−0.898291			−0.449146	−	0.893459i	$-0.648272\pi$
$151$	−11.0384			−0.898291			−0.449146	+	0.893459i	$0.648272\pi$
$152$	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
$156$	10.7901	+	2.77322i	0.863897	+	0.222035i
$157$	6.73473	+	3.88830i	0.537490	+	0.310320i	0.744061	−	0.668112i	$-0.232897\pi$
$157$	6.73473	+	3.88830i	0.537490	+	0.310320i	−0.206571	+	0.978432i	$0.566230\pi$
$158$	1.62981	+	0.940971i	0.129661	+	0.0748596i
$159$	4.45278	+	15.9631i	0.353129	+	1.26595i
$160$	−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	−0.793017	−	0.609199i	$-0.791491\pi$
$163$	1.67343	−	2.89847i	0.131073	−	0.227025i	0.924091	+	0.382174i	$0.124824\pi$
$164$	−3.10742			−0.242649
$165$	−3.38630	−	0.870332i	−0.263623	−	0.0677553i
$166$		−	0.427477i		−	0.0331786i
$167$	−6.83216	−	11.8336i	−0.528688	−	0.915715i	−0.999440	−	0.0334496i	$-0.989351\pi$
$167$	−6.83216	−	11.8336i	−0.528688	−	0.915715i	0.470752	−	0.882266i	$-0.343983\pi$
$168$	−11.1746	+	0.181361i	−0.862137	+	0.0139923i
$169$	2.45400	−	4.25044i	0.188769	−	0.326957i
$170$	1.86420	+	1.07630i	0.142978	+	0.0825481i
$171$	0.202555	+	0.334827i	0.0154898	+	0.0256048i
$172$	7.28938	+	12.6256i	0.555810	+	0.962691i
$173$	−11.4522	−	19.8358i	−0.870695	−	1.50809i	−0.861279	−	0.508132i	$-0.830336\pi$
$173$	−11.4522	−	19.8358i	−0.870695	−	1.50809i	−0.00941519	−	0.999956i	$-0.502997\pi$
$174$	−2.60455	+	10.1338i	−0.197450	+	0.768241i
$175$	2.55145	−	0.700092i	0.192871	−	0.0529219i
$176$	2.36033	−	1.36274i	0.177917	−	0.102720i
$177$	−14.0642	−	13.7794i	−1.05713	−	1.03572i
$178$			1.00528i			0.0753492i
$179$	12.0215	−	6.94064i	0.898533	−	0.518768i	0.0218088	−	0.999762i	$-0.493058\pi$
$179$	12.0215	−	6.94064i	0.898533	−	0.518768i	0.876724	+	0.480994i	$0.159724\pi$
$180$	3.90149	−	2.36023i	0.290800	−	0.175921i
$181$		−	7.90831i		−	0.587820i	−0.955833	−	0.293910i	$-0.905043\pi$
$181$		−	7.90831i		−	0.587820i	0.955833	−	0.293910i	$-0.0949567\pi$
$182$	−1.96276	+	7.50494i	−0.145489	+	0.556303i
$183$	2.49537	+	8.94581i	0.184463	+	0.661293i
$184$	0.920256			0.0678422
$185$	2.94155	−	5.09492i	0.216267	−	0.374586i
$186$	1.07880	−	4.19740i	0.0791014	−	0.307768i
$187$	−5.43132	+	3.13578i	−0.397178	+	0.229311i
$188$	7.03060			0.512759
$189$	6.43256	−	12.1500i	0.467900	−	0.883781i
$190$	−0.0903776			−0.00655668
$191$	−20.9322	+	12.0852i	−1.51460	+	0.874454i	−0.514745	+	0.857343i	$0.672113\pi$
$191$	−20.9322	+	12.0852i	−1.51460	+	0.874454i	−0.999854	+	0.0171103i	$0.994553\pi$
$192$	0.572262	−	2.22656i	0.0412994	−	0.160688i
$193$	−9.51485	+	16.4802i	−0.684894	+	1.18627i	0.288576	+	0.957457i	$0.406818\pi$
$193$	−9.51485	+	16.4802i	−0.684894	+	1.18627i	−0.973470	+	0.228814i	$0.926515\pi$
$194$	−9.08074			−0.651959
$195$	−1.96937	−	7.06014i	−0.141030	−	0.505587i
$196$	0.127670	+	10.6389i	0.00911926	+	0.759922i
$197$			11.4882i			0.818502i	0.912422	+	0.409251i	$0.134210\pi$
$197$			11.4882i			0.818502i	−0.912422	+	0.409251i	$0.865790\pi$
$198$	−0.0858283	−	4.19495i	−0.00609956	−	0.298122i
$199$	−8.95697	+	5.17131i	−0.634943	+	0.366584i	−0.782664	−	0.622445i	$-0.786140\pi$
$199$	−8.95697	+	5.17131i	−0.634943	+	0.366584i	0.147721	+	0.989029i	$0.452806\pi$
$200$			2.43881i			0.172450i
$201$	16.7324	+	16.3935i	1.18021	+	1.15631i
$202$	2.10331	−	1.21435i	0.147988	−	0.0854411i
$203$	22.3174	+	5.83664i	1.56637	+	0.409652i
$204$	2.03602	−	7.92175i	0.142550	−	0.554634i
$205$	1.02221	+	1.77052i	0.0713941	+	0.123658i
$206$	6.55983	+	11.3620i	0.457045	+	0.791626i
$207$	−0.545835	+	0.991725i	−0.0379381	+	0.0689297i
$208$	4.94814	+	2.85681i	0.343092	+	0.198084i
$209$	0.131657	−	0.228037i	0.00910691	−	0.0157736i
$210$	1.63194	+	2.72355i	0.112614	+	0.187943i
$211$	−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	$0.868140\pi$
$212$			14.5431i			0.998825i
$213$	−12.5628	−	3.22883i	−0.860787	−	0.221236i
$214$	−4.52104			−0.309052
$215$	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
$219$	−0.723614	−	2.59413i	−0.0488973	−	0.175295i
$220$	−2.65715	−	1.53411i	−0.179145	−	0.103429i
$221$	−11.3861	−	6.57376i	−0.765911	−	0.442199i
$222$	6.83783	+	1.75743i	0.458925	+	0.117951i
$223$	−12.6066	−	7.27841i	−0.844198	−	0.487398i	0.0144907	−	0.999895i	$-0.495387\pi$
$223$	−12.6066	−	7.27841i	−0.844198	−	0.487398i	−0.858689	+	0.512497i	$0.828721\pi$
$224$	−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
$227$	9.85374			0.654015			0.327008	−	0.945022i	$-0.393960\pi$
$227$	9.85374			0.654015			0.327008	+	0.945022i	$0.393960\pi$
$228$	0.0922688	+	0.330780i	0.00611065	+	0.0219065i
$229$			27.1114i			1.79157i	0.444488	+	0.895785i	$0.353386\pi$
$229$			27.1114i			1.79157i	−0.444488	+	0.895785i	$0.646614\pi$
$230$	−0.130720	−	0.226414i	−0.00861942	−	0.0149293i
$231$	−9.24926	+	0.150114i	−0.608557	+	0.00987676i
$232$	−10.6318	+	18.4149i	−0.698015	+	1.20900i
$233$	−4.89683	−	2.82719i	−0.320802	−	0.185215i	0.330948	−	0.943649i	$-0.392632\pi$
$233$	−4.89683	−	2.82719i	−0.320802	−	0.185215i	−0.651750	+	0.758434i	$0.725965\pi$
$234$	7.52602	−	4.55291i	0.491991	−	0.297633i
$235$	−2.31277	−	4.00583i	−0.150868	−	0.261312i
$236$	−8.63919	−	14.9635i	−0.562363	−	0.974042i
$237$	−4.53163	+	1.26407i	−0.294361	+	0.0821099i
$238$	5.50991	+	1.44100i	0.357154	+	0.0934062i
$239$	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	$0.252862\pi$
$240$	2.25257	−	0.628337i	0.145403	−	0.0405590i
$241$			4.08567i			0.263181i	0.991304	+	0.131590i	$0.0420084\pi$
$241$			4.08567i			0.263181i	−0.991304	+	0.131590i	$0.957992\pi$
$242$	4.15530	−	2.39906i	0.267113	−	0.154218i
$243$	−14.8314	+	4.79905i	−0.951432	+	0.307859i
$244$			8.15005i			0.521754i
$245$	6.01974	−	3.57249i	0.384587	−	0.228238i
$246$	−1.71699	+	1.75248i	−0.109471	+	0.111734i
$247$	0.552005			0.0351232
$248$	4.40369	−	7.62742i	0.279635	−	0.484342i
$249$	0.763333	+	0.747875i	0.0483742	+	0.0473946i
$250$	0.600029	−	0.346427i	0.0379491	−	0.0219100i
$251$	0.300087			0.0189413			0.00947065	−	0.999955i	$-0.496985\pi$
$251$	0.300087			0.0189413			0.00947065	+	0.999955i	$0.496985\pi$
$252$	8.30207	−	8.75341i	0.522981	−	0.551413i
$253$	0.761702			0.0478878
$254$	−12.4166	+	7.16875i	−0.779089	+	0.449807i
$255$	−5.18334	+	1.44586i	−0.324594	+	0.0905430i
$256$	5.03633	−	8.72318i	0.314771	−	0.545199i
$257$	15.0128			0.936472			0.468236	−	0.883603i	$-0.344890\pi$
$257$	15.0128			0.936472			0.468236	+	0.883603i	$0.344890\pi$
$258$	11.1481	+	2.86525i	0.694052	+	0.178382i
$259$	3.93830	−	15.0588i	0.244714	−	0.935705i
$260$		−	6.43212i		−	0.398903i
$261$	−13.5389	−	22.3800i	−0.838039	−	1.38529i
$262$	−3.80877	+	2.19899i	−0.235306	+	0.135854i
$263$		−	11.2187i		−	0.691775i	−0.938276	−	0.345887i	$-0.887578\pi$
$263$		−	11.2187i		−	0.691775i	0.938276	−	0.345887i	$-0.112422\pi$
$264$	2.12258	−	8.25854i	0.130636	−	0.508278i
$265$	8.28624	−	4.78406i	0.509020	−	0.293883i
$266$	−0.230594	+	0.0632726i	−0.0141386	+	0.00387949i
$267$	−1.79510	−	1.75875i	−0.109859	−	0.107634i
$268$	10.2782	+	17.8023i	0.627839	+	1.08745i
$269$	−9.56875	−	16.5736i	−0.583417	−	1.01051i	−0.995071	−	0.0991673i	$-0.968382\pi$
$269$	−9.56875	−	16.5736i	−0.583417	−	1.01051i	0.411654	−	0.911340i	$-0.364951\pi$
$270$	0.824662	−	3.50445i	0.0501873	−	0.213274i
$271$	−25.9294	−	14.9704i	−1.57510	−	0.909385i	−0.995528	−	0.0944638i	$-0.969886\pi$
$271$	−25.9294	−	14.9704i	−1.57510	−	0.909385i	−0.579572	−	0.814921i	$-0.696780\pi$
$272$	2.09739	−	3.63278i	0.127173	−	0.220270i
$273$	−9.96749	−	16.6348i	−0.603260	−	1.00678i
$274$	−0.509483	−	0.882450i	−0.0307790	−	0.0533108i
$275$			2.01862i			0.121727i
$276$	−0.695214	+	0.709583i	−0.0418470	+	0.0427119i
$277$	23.1051			1.38825			0.694125	−	0.719855i	$-0.255792\pi$
$277$	23.1051			1.38825			0.694125	+	0.719855i	$0.255792\pi$
$278$	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	$0.744154\pi$
$282$	3.88473	−	3.96503i	0.231332	−	0.236114i
$283$	−13.1441	−	7.58873i	−0.781334	−	0.451103i	0.0555692	−	0.998455i	$-0.482303\pi$
$283$	−13.1441	−	7.58873i	−0.781334	−	0.451103i	−0.836903	+	0.547352i	$0.815636\pi$
$284$	−9.85771	−	5.69135i	−0.584948	−	0.337720i
$285$	0.158117	−	0.161385i	0.00936602	−	0.00955960i
$286$	−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
$290$	6.04090			0.354734
$291$	15.8868	−	16.2152i	0.931303	−	0.950552i
$292$		−	2.36338i		−	0.138306i
$293$	11.2769	+	19.5322i	0.658804	+	1.14108i	0.980926	+	0.194384i	$0.0622708\pi$
$293$	11.2769	+	19.5322i	0.658804	+	1.14108i	−0.322121	+	0.946698i	$0.604396\pi$
$294$	6.07054	+	5.80649i	0.354041	+	0.338641i
$295$	−5.68385	+	9.84472i	−0.330927	+	0.573182i
$296$	12.4255	+	7.17389i	0.722220	+	0.416974i
$297$	7.64095	+	7.18584i	0.443373	+	0.416965i
$298$	8.34426	+	14.4527i	0.483370	+	0.837222i
$299$	0.798406	+	1.38288i	0.0461730	+	0.0799740i
$300$	−1.88050	−	1.84242i	−0.108571	−	0.106372i
$301$	6.42085	−	24.5512i	0.370092	−	1.41511i
$302$	−6.62335	+	3.82399i	−0.381131	+	0.220046i
$303$	−1.51134	+	5.88033i	−0.0868240	+	0.337816i
$304$			0.176120i			0.0101011i
$305$	4.64366	−	2.68102i	0.265895	−	0.153515i
$306$	−3.34261	−	5.52538i	−0.191084	−	0.315865i
$307$			9.43781i			0.538644i	0.963050	+	0.269322i	$0.0867996\pi$
$307$			9.43781i			0.538644i	−0.963050	+	0.269322i	$0.913200\pi$
$308$	−7.85358	−	2.05394i	−0.447499	−	0.117034i
$309$	−31.7652	−	8.16417i	−1.80706	−	0.464443i
$310$	−2.50213			−0.142112
$311$	12.2479	−	21.2141i	0.694517	−	1.20294i	−0.275826	−	0.961208i	$-0.588951\pi$
$311$	12.2479	−	21.2141i	0.694517	−	1.20294i	0.970343	−	0.241731i	$-0.0777153\pi$
$312$	17.2184	−	4.80293i	0.974797	−	0.271912i
$313$	−1.74450	+	1.00719i	−0.0986051	+	0.0569297i	−0.548492	−	0.836156i	$-0.684798\pi$
$313$	−1.74450	+	1.00719i	−0.0986051	+	0.0569297i	0.449887	+	0.893086i	$0.351464\pi$
$314$	5.38804			0.304065
$315$	−7.71846	−	1.85078i	−0.434886	−	0.104279i
$316$	−4.12853			−0.232248
$317$	0.652813	−	0.376902i	0.0366656	−	0.0211689i	−0.481555	−	0.876416i	$-0.659928\pi$
$317$	0.652813	−	0.376902i	0.0366656	−	0.0211689i	0.518221	+	0.855247i	$0.326595\pi$
$318$	8.20184	+	8.03574i	0.459936	+	0.450622i
$319$	−8.80005	+	15.2421i	−0.492708	+	0.853395i
$320$	−1.32729			−0.0741975
$321$	7.90960	−	8.07309i	0.441471	−	0.450596i
$322$	−0.492035	−	0.486166i	−0.0274200	−	0.0270930i
$323$		−	0.405266i		−	0.0225496i
$324$	−13.6681	+	0.559533i	−0.759341	+	0.0310852i
$325$	−3.66483	+	2.11589i	−0.203288	+	0.117369i
$326$		−	2.31888i		−	0.128431i
$327$	27.5241	−	7.67764i	1.52209	−	0.424575i
$328$	−4.31796	+	2.49297i	−0.238419	+	0.137651i
$329$	−8.70535	−	8.60151i	−0.479941	−	0.474217i
$330$	−2.33338	+	0.650880i	−0.128448	+	0.0358297i
$331$	3.10590	+	5.37958i	0.170716	+	0.295689i	0.938670	−	0.344816i	$-0.112059\pi$
$331$	3.10590	+	5.37958i	0.170716	+	0.295689i	−0.767954	+	0.640504i	$0.778725\pi$
$332$	0.468891	+	0.812142i	0.0257337	+	0.0445721i
$333$	−15.1010	+	9.13547i	−0.827532	+	0.500620i
$334$	−8.19898	−	4.73369i	−0.448628	−	0.259016i
$335$	6.76215	−	11.7124i	0.369456	−	0.639917i
$336$	5.30741	−	3.18017i	0.289543	−	0.173492i
$337$	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	$0.828633\pi$
$338$		−	3.40052i		−	0.184964i
$339$	7.79293	+	27.9374i	0.423254	+	1.51735i
$340$	−4.72227			−0.256101
$341$	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
$345$	0.632996	+	0.162690i	0.0340793	+	0.00875893i
$346$	−13.7433	−	7.93470i	−0.738844	−	0.426572i
$347$	−7.32785	−	4.23073i	−0.393379	−	0.227118i	0.290244	−	0.956953i	$-0.406264\pi$
$347$	−7.32785	−	4.23073i	−0.393379	−	0.227118i	−0.683623	+	0.729835i	$0.739597\pi$
$348$	−6.16731	−	22.1096i	−0.330602	−	1.18520i
$349$	7.21930	+	4.16806i	0.386440	+	0.223111i	0.680617	−	0.732640i	$-0.261712\pi$
$349$	7.21930	+	4.16806i	0.386440	+	0.223111i	−0.294176	+	0.955751i	$0.595045\pi$
$350$	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
$353$	−9.31001			−0.495522			−0.247761	−	0.968821i	$-0.579695\pi$
$353$	−9.31001			−0.495522			−0.247761	+	0.968821i	$0.579695\pi$
$354$	−13.2125	−	3.39582i	−0.702235	−	0.180486i
$355$			7.48885i			0.397467i
$356$	−1.10267	−	1.90989i	−0.0584417	−	0.101224i
$357$	−12.2128	+	7.31784i	−0.646369	+	0.387301i
$358$	4.80885	−	8.32917i	0.254156	−	0.440210i
$359$	10.9957	+	6.34836i	0.580329	+	0.335053i	0.761264	−	0.648442i	$-0.224579\pi$
$359$	10.9957	+	6.34836i	0.580329	+	0.335053i	−0.180935	+	0.983495i	$0.557912\pi$
$360$	3.52784	−	6.40973i	0.185934	−	0.337822i
$361$	−9.49149	−	16.4397i	−0.499552	−	0.865250i
$362$	−2.73965	−	4.74522i	−0.143993	−	0.249403i
$363$	−2.98580	+	11.6172i	−0.156714	+	0.609744i
$364$	−4.50307	−	16.4112i	−0.236025	−	0.860180i
$365$	−1.34658	+	0.777450i	−0.0704833	+	0.0406936i
$366$	4.59636	+	4.50328i	0.240256	+	0.235390i
$367$		−	29.5429i		−	1.54213i	−0.636759	−	0.771063i	$-0.719725\pi$
$367$		−	29.5429i		−	1.54213i	0.636759	−	0.771063i	$-0.280275\pi$
$368$	−0.441214	+	0.254735i	−0.0229998	+	0.0132790i
$369$	−0.125460	−	6.13196i	−0.00653117	−	0.319217i
$370$		−	4.07613i		−	0.211908i
$371$	17.7926	−	18.0074i	0.923746	−	0.934898i
$372$	2.55449	+	9.15775i	0.132444	+	0.474807i
$373$	−5.88956			−0.304950			−0.152475	−	0.988307i	$-0.548724\pi$
$373$	−5.88956			−0.304950			−0.152475	+	0.988307i	$0.548724\pi$
$374$	−2.17263	+	3.76311i	−0.112344	+	0.194586i
$375$	−0.431152	+	1.67753i	−0.0222646	+	0.0866273i
$376$	9.76947	−	5.64041i	0.503822	−	0.290882i
$377$	−36.8964			−1.90026
$378$	−0.349357	−	9.51875i	−0.0179690	−	0.489592i
$379$	5.42114			0.278465			0.139233	−	0.990260i	$-0.455536\pi$
$379$	5.42114			0.278465			0.139233	+	0.990260i	$0.455536\pi$
$380$	0.171704	−	0.0991334i	0.00880823	−	0.00508544i
$381$	8.92200	−	34.7138i	0.457088	−	1.77844i
$382$	−8.37327	+	14.5029i	−0.428414	+	0.742034i
$383$	−14.1555			−0.723311			−0.361655	−	0.932312i	$-0.617788\pi$
$383$	−14.1555			−0.723311			−0.361655	+	0.932312i	$0.617788\pi$
$384$	4.98259	+	17.8624i	0.254267	+	0.911538i
$385$	1.41322	+	5.15040i	0.0720243	+	0.262489i
$386$			13.1848i			0.671088i
$387$	−24.6201	+	14.8941i	−1.25151	+	0.757110i
$388$	17.2520	−	9.96048i	0.875840	−	0.505667i
$389$			6.76865i			0.343184i	0.985168	+	0.171592i	$0.0548911\pi$
$389$			6.76865i			0.343184i	−0.985168	+	0.171592i	$0.945109\pi$
$390$	−3.62750	−	3.55404i	−0.183686	−	0.179966i
$391$	1.01527	−	0.586166i	0.0513444	−	0.0296437i
$392$	8.71263	+	14.6810i	0.440054	+	0.741504i
$393$	2.73680	−	10.6484i	0.138053	−	0.537139i
$394$	3.97983	+	6.89326i	0.200501	+	0.347278i
$395$	1.35811	+	2.35232i	0.0683339	+	0.118358i
$396$	4.76441	+	7.87563i	0.239421	+	0.395765i
$397$	11.5661	+	6.67770i	0.580487	+	0.335144i	0.761327	−	0.648368i	$-0.224548\pi$
$397$	11.5661	+	6.67770i	0.580487	+	0.335144i	−0.180840	+	0.983513i	$0.557882\pi$
$398$	−3.58296	+	6.20587i	−0.179598	+	0.311072i
$399$	0.290442	−	0.522460i	0.0145403	−	0.0261557i
$400$	−0.675084	−	1.16928i	−0.0337542	−	0.0584640i
$401$			6.53348i			0.326266i	0.986604	+	0.163133i	$0.0521600\pi$
$401$			6.53348i			0.326266i	−0.986604	+	0.163133i	$0.947840\pi$
$402$	15.7191	+	4.04005i	0.783996	+	0.201499i
$403$	15.2824			0.761272
$404$	−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
$408$	−3.52617	−	12.6412i	−0.174571	−	0.625833i
$409$	−1.72436	−	0.995562i	−0.0852643	−	0.0492274i	0.456762	−	0.889589i	$-0.349009\pi$
$409$	−1.72436	−	0.995562i	−0.0852643	−	0.0492274i	−0.542026	+	0.840362i	$0.682343\pi$
$410$	1.22671	+	0.708240i	0.0605828	+	0.0349775i
$411$	2.46711	+	0.634087i	0.121694	+	0.0312772i
$412$	−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
$416$	24.5998			1.20610
$417$	4.53251	+	16.2489i	0.221958	+	0.795712i
$418$		−	0.182438i		−	0.00892334i
$419$	6.83997	+	11.8472i	0.334154	+	0.578772i	0.983322	−	0.181873i	$-0.0582160\pi$
$419$	6.83997	+	11.8472i	0.334154	+	0.578772i	−0.649168	+	0.760645i	$0.724883\pi$
$420$	−6.08785	−	3.38431i	−0.297057	−	0.165137i
$421$	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
$423$	0.283855	+	13.8737i	0.0138015	+	0.674563i
$424$	11.6674	+	20.2086i	0.566621	+	0.981416i
$425$	1.55343	+	2.69061i	0.0753522	+	0.130514i
$426$	−8.65658	+	2.41469i	−0.419413	+	0.116992i
$427$	9.97109	−	10.0915i	0.482535	−	0.488360i
$428$	8.58930	−	4.95904i	0.415180	−	0.239704i
$429$	14.2517	−	3.97542i	0.688080	−	0.191935i
$430$		−	6.64556i		−	0.320477i
$431$	−27.7347	+	16.0127i	−1.33594	+	0.771303i	−0.986202	−	0.165546i	$-0.947061\pi$
$431$	−27.7347	+	16.0127i	−1.33594	+	0.771303i	−0.349734	+	0.936849i	$0.613728\pi$
$432$	−6.82915	−	1.60702i	−0.328567	−	0.0773180i
$433$			16.7950i			0.807116i	0.914954	+	0.403558i	$0.132227\pi$
$433$			16.7950i			0.807116i	−0.914954	+	0.403558i	$0.867773\pi$
$434$	−6.38405	+	1.75172i	−0.306444	+	0.0840853i
$435$	−10.5686	+	10.7871i	−0.506726	+	0.517200i
$436$	25.0757			1.20091
$437$	−0.0246105	+	0.0426266i	−0.00117728	+	0.00203911i
$438$	−1.33287	−	1.30587i	−0.0636868	−	0.0623971i
$439$	−23.5198	+	13.5792i	−1.12254	+	0.648098i	−0.942048	−	0.335479i	$-0.891102\pi$
$439$	−23.5198	+	13.5792i	−1.12254	+	0.648098i	−0.180491	+	0.983577i	$0.557769\pi$
$440$	−4.92304			−0.234697
$441$	−20.9889	+	0.681472i	−0.999473	+	0.0324511i
$442$	−9.10930			−0.433285
$443$	−25.2727	+	14.5912i	−1.20074	+	0.693249i	−0.960720	−	0.277519i	$-0.910488\pi$
$443$	−25.2727	+	14.5912i	−1.20074	+	0.693249i	−0.240022	+	0.970767i	$0.577155\pi$
$444$	−14.9185	+	4.16142i	−0.708003	+	0.197492i
$445$	−0.725466	+	1.25654i	−0.0343904	+	0.0595659i
$446$	−10.0857			−0.477574
$447$	−40.4061	−	10.3850i	−1.91114	−	0.491194i
$448$	−3.38650	+	0.929221i	−0.159997	+	0.0439016i
$449$		−	5.85431i		−	0.276282i	−0.990413	−	0.138141i	$-0.955887\pi$
$449$		−	5.85431i		−	0.276282i	0.990413	−	0.138141i	$-0.0441127\pi$
$450$	−2.07813	+	0.0425183i	−0.0979638	+	0.00200433i
$451$	−3.57400	+	2.06345i	−0.168293	+	0.0971640i
$452$			25.4523i			1.19717i
$453$	4.75922	−	18.5172i	0.223608	−	0.870015i
$454$	5.91253	−	3.41360i	0.277489	−	0.160208i
$455$	−7.86930	+	7.96430i	−0.368918	+	0.373372i
$456$	0.393587	+	0.385617i	0.0184314	+	0.0180582i
$457$	18.0830	+	31.3207i	0.845887	+	1.46512i	0.884849	+	0.465879i	$0.154262\pi$
$457$	18.0830	+	31.3207i	0.845887	+	1.46512i	−0.0389616	+	0.999241i	$0.512405\pi$
$458$	9.39210	+	16.2676i	0.438864	+	0.760135i
$459$	15.7144	+	3.69790i	0.733487	+	0.172603i
$460$	0.496697	+	0.286768i	0.0231586	+	0.0133706i
$461$	−6.43557	+	11.1467i	−0.299734	+	0.519155i	−0.976075	−	0.217434i	$-0.930231\pi$
$461$	−6.43557	+	11.1467i	−0.299734	+	0.519155i	0.676341	+	0.736589i	$0.263565\pi$
$462$	−5.49782	+	3.29426i	−0.255782	+	0.153263i
$463$	−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	$0.905380\pi$
$464$		−	11.7719i		−	0.546499i
$465$	4.37750	−	4.46798i	0.203002	−	0.207198i
$466$	−3.91765			−0.181482
$467$	−10.1218	+	17.5314i	−0.468380	+	0.811258i	−0.999347	−	0.0361343i	$-0.988496\pi$
$467$	−10.1218	+	17.5314i	−0.468380	+	0.811258i	0.530967	+	0.847393i	$0.321829\pi$
$468$	−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
$471$	−9.42643	+	9.62127i	−0.434347	+	0.443325i
$472$	−24.0094	−	13.8618i	−1.10512	−	0.638043i
$473$	16.7678	+	9.68088i	0.770983	+	0.445127i
$474$	−2.28120	+	2.32835i	−0.104779	+	0.106945i
$475$	−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
$479$	40.1997			1.83677			0.918386	−	0.395686i	$-0.129493\pi$
$479$	40.1997			1.83677			0.918386	+	0.395686i	$0.129493\pi$
$480$	7.04636	−	7.19201i	0.321621	−	0.328269i
$481$			24.8960i			1.13516i
$482$	1.41538	+	2.45152i	0.0644690	+	0.111664i
$483$	1.72895	−	0.0280605i	0.0786700	−	0.00127680i
$484$	−5.26297	+	9.11573i	−0.239226	+	0.414352i
$485$	−11.3504	−	6.55314i	−0.515394	−	0.297563i
$486$	−7.23672	+	8.01755i	−0.328264	+	0.363683i
$487$	13.4870	+	23.3601i	0.611153	+	1.05855i	0.991046	+	0.133518i	$0.0426273\pi$
$487$	13.4870	+	23.3601i	0.611153	+	1.05855i	−0.379893	+	0.925030i	$0.624039\pi$
$488$	6.53850	+	11.3250i	0.295984	+	0.512660i
$489$	4.14076	+	4.05691i	0.187252	+	0.183460i
$490$	2.37441	−	4.22900i	0.107265	−	0.191047i
$491$	−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	$0.455521\pi$
$492$	1.33977	−	5.21279i	0.0604015	−	0.235011i
$493$			27.0882i			1.21999i
$494$	0.331219	−	0.191229i	0.0149022	−	0.00860381i
$495$	2.92002	−	5.30537i	0.131245	−	0.238459i
$496$			4.87592i			0.218935i
$497$	5.24288	+	19.1074i	0.235175	+	0.857083i
$498$	0.717105	+	0.184307i	0.0321343	+	0.00825901i
$499$	−32.4582			−1.45303			−0.726514	−	0.687152i	$-0.758861\pi$
$499$	−32.4582			−1.45303			−0.726514	+	0.687152i	$0.758861\pi$
$500$	−0.759977	+	1.31632i	−0.0339872	+	0.0588676i
$501$	22.7970	−	6.35906i	1.01849	−	0.284102i
$502$	0.180061	−	0.103958i	0.00803650	−	0.00463987i
$503$	27.0679			1.20690			0.603449	−	0.797402i	$-0.293793\pi$
$503$	27.0679			1.20690			0.603449	+	0.797402i	$0.293793\pi$
$504$	4.51370	−	18.8239i	0.201056	−	0.838482i
$505$	3.50535			0.155986
$506$	0.457043	−	0.263874i	0.0203180	−	0.0117306i
$507$	6.07221	+	5.94924i	0.269676	+	0.264215i
$508$	15.7265	−	27.2391i	0.697751	−	1.20854i
$509$	−19.9424			−0.883931			−0.441965	−	0.897032i	$-0.645719\pi$
$509$	−19.9424			−0.883931			−0.441965	+	0.897032i	$0.645719\pi$
$510$	−2.60927	+	2.66320i	−0.115541	+	0.117929i
$511$	−2.89144	+	2.92635i	−0.127910	+	0.129454i
$512$			14.4343i			0.637911i
$513$	−0.649014	+	0.195432i	−0.0286547	+	0.00862852i
$514$	9.00811	−	5.20083i	0.397331	−	0.229399i
$515$			18.9357i			0.834407i
$516$	−24.3226	+	6.78462i	−1.07074	+	0.298676i
$517$	8.08625	−	4.66860i	0.355633	−	0.205325i
$518$	−2.85366	−	10.4000i	−0.125383	−	0.456950i
$519$	38.2128	−	10.6592i	1.67735	−	0.467886i
$520$	−5.16026	−	8.93784i	−0.226293	−	0.391950i
$521$	−3.24484	−	5.62023i	−0.142159	−	0.246227i	0.786150	−	0.618035i	$-0.212071\pi$
$521$	−3.24484	−	5.62023i	−0.142159	−	0.246227i	−0.928309	+	0.371809i	$0.878738\pi$
$522$	−15.8768	−	8.73841i	−0.694908	−	0.382470i
$523$	14.7364	+	8.50804i	0.644376	+	0.372031i	0.786298	−	0.617847i	$-0.211995\pi$
$523$	14.7364	+	8.50804i	0.644376	+	0.372031i	−0.141922	+	0.989878i	$0.545328\pi$
$524$	4.82406	−	8.35552i	0.210740	−	0.365012i
$525$	0.0743645	+	4.58197i	0.00324553	+	0.199974i
$526$	−3.88646	−	6.73154i	−0.169458	−	0.293509i
$527$		−	11.2199i		−	0.488747i
$528$	1.26837	+	4.54708i	0.0551989	+	0.197886i
$529$	22.8576			0.993809
$530$	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
$534$	−1.68639	−	0.433430i	−0.0729774	−	0.0187563i
$535$	−5.65103	−	3.26262i	−0.244315	−	0.141056i
$536$	28.5643	+	16.4916i	1.23379	+	0.712330i
$537$	6.46003	+	23.1590i	0.278771	+	0.999384i
$538$	−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	−0.593372	−	0.804928i	$-0.702204\pi$
$541$	9.31312	−	16.1308i	0.400402	−	0.693517i	0.993774	+	0.111411i	$0.0355371\pi$
$542$	−20.7445			−0.891054
$543$	13.2664	+	3.40968i	0.569317	+	0.146324i
$544$		−	18.0604i		−	0.774334i
$545$	−8.24885	−	14.2874i	−0.353342	−	0.612006i
$546$	−11.7435	−	6.52836i	−0.502576	−	0.279388i
$547$	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
$549$	−16.0828	+	0.329052i	−0.686395	+	0.0140436i
$550$	0.699304	+	1.21123i	0.0298184	+	0.0516470i
$551$	−0.568656	−	0.984942i	−0.0242256	−	0.0419599i
$552$	−0.396770	+	1.54376i	−0.0168877	+	0.0657067i
$553$	5.11198	+	5.05100i	0.217383	+	0.214790i
$554$	13.8637	−	8.00422i	0.589013	−	0.340067i
$555$	7.27862	+	7.13122i	0.308960	+	0.302704i
$556$			14.8035i			0.627809i
$557$	29.6043	−	17.0920i	1.25437	−	0.724213i	0.282399	−	0.959297i	$-0.408870\pi$
$557$	29.6043	−	17.0920i	1.25437	−	0.724213i	0.971975	+	0.235084i	$0.0755365\pi$
$558$	6.57614	+	3.61944i	0.278390	+	0.153223i
$559$			40.5895i			1.71675i
$560$	−2.54104	−	2.51073i	−0.107379	−	0.106098i
$561$	−2.91863	−	10.4632i	−0.123225	−	0.441757i
$562$	−5.59896			−0.236178
$563$	16.6332	−	28.8095i	0.701005	−	1.21418i	−0.267109	−	0.963666i	$-0.586069\pi$
$563$	16.6332	−	28.8095i	0.701005	−	1.21418i	0.968114	−	0.250510i	$-0.0805982\pi$
$564$	−3.03126	+	11.7940i	−0.127639	+	0.496619i
$565$	14.5020	−	8.37272i	0.610102	−	0.352243i
$566$	−10.5158			−0.442010
$567$	17.6086	+	16.0293i	0.739490	+	0.673168i
$568$	−18.2639			−0.766336
$569$	3.78974	−	2.18801i	0.158874	−	0.0917259i	−0.418455	−	0.908237i	$-0.637428\pi$
$569$	3.78974	−	2.18801i	0.158874	−	0.0917259i	0.577329	+	0.816512i	$0.304095\pi$
$570$	0.0389665	−	0.151611i	0.00163213	−	0.00635030i
$571$	−6.49815	+	11.2551i	−0.271939	+	0.471012i	−0.969358	−	0.245651i	$-0.920998\pi$
$571$	−6.49815	+	11.2551i	−0.271939	+	0.471012i	0.697419	+	0.716663i	$0.254332\pi$
$572$	12.9840			0.542888
$573$	−11.2483	−	40.3249i	−0.469906	−	1.68460i
$574$	3.62571	+	0.948228i	0.151334	+	0.0395783i
$575$		−	0.377338i		−	0.0157361i
$576$	3.48839	+	1.91997i	0.145350	+	0.0799989i
$577$	39.0948	−	22.5714i	1.62754	−	0.939659i	0.642712	−	0.766108i	$-0.277809\pi$
$577$	39.0948	−	22.5714i	1.62754	−	0.939659i	0.984825	−	0.173551i	$-0.0555243\pi$
$578$		−	5.09073i		−	0.211746i
$579$	−23.5437	−	23.0669i	−0.978443	−	0.958629i
$580$	−11.4768	+	6.62614i	−0.476549	+	0.275136i
$581$	0.413022	−	1.57926i	0.0171350	−	0.0655188i
$582$	3.91518	−	15.2332i	0.162289	−	0.631437i
$583$	9.65721	+	16.7268i	0.399961	+	0.692752i
$584$	−1.89605	−	3.28406i	−0.0784593	−	0.135895i
$585$	12.6927	−	0.259692i	0.524778	−	0.0107369i
$586$	13.5329	+	7.81325i	0.559041	+	0.322762i
$587$	18.3176	−	31.7270i	0.756048	−	1.30951i	−0.188804	−	0.982015i	$-0.560461\pi$
$587$	18.3176	−	31.7270i	0.756048	−	1.30951i	0.944852	−	0.327498i	$-0.106205\pi$
$588$	−17.9021	−	4.37282i	−0.738272	−	0.180332i
$589$	0.235537	+	0.407961i	0.00970512	+	0.0168098i
$590$			7.87615i			0.324256i
$591$	−19.2718	−	4.95317i	−0.792738	−	0.203746i
$592$	−7.94318			−0.326463
$593$	−17.5445	+	30.3879i	−0.720465	+	1.24788i	0.240349	+	0.970687i	$0.422738\pi$
$593$	−17.5445	+	30.3879i	−0.720465	+	1.24788i	−0.960814	+	0.277195i	$0.910595\pi$
$594$	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
$597$	−4.81321	−	17.2552i	−0.196992	−	0.706209i
$598$	0.958133	+	0.553178i	0.0391810	+	0.0226211i
$599$	−20.1744	−	11.6477i	−0.824304	−	0.475912i	0.0275947	−	0.999619i	$-0.491215\pi$
$599$	−20.1744	−	11.6477i	−0.824304	−	0.475912i	−0.851898	+	0.523707i	$0.824549\pi$
$600$	−4.09118	−	1.05150i	−0.167022	−	0.0429273i
$601$	16.6006	+	9.58436i	0.677152	+	0.390954i	0.798781	−	0.601622i	$-0.205478\pi$
$601$	16.6006	+	9.58436i	0.677152	+	0.390954i	−0.121629	+	0.992576i	$0.538812\pi$
$602$	−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
$605$	6.92517			0.281548
$606$	1.13026	+	4.05193i	0.0459135	+	0.164598i
$607$		−	11.6068i		−	0.471104i	−0.971862	−	0.235552i	$-0.924310\pi$
$607$		−	11.6068i		−	0.471104i	0.971862	−	0.235552i	$-0.0756898\pi$
$608$	0.379138	+	0.656686i	0.0153761	+	0.0266321i
$609$	−19.4133	+	34.9216i	−0.786667	+	1.41509i
$610$	1.85755	−	3.21738i	0.0752102	−	0.130268i
$611$	16.9518	+	9.78713i	0.685797	+	0.395945i
$612$	12.4111	+	6.83096i	0.501691	+	0.276125i
$613$	−20.6458	−	35.7596i	−0.833877	−	1.44432i	−0.894941	−	0.446184i	$-0.852783\pi$
$613$	−20.6458	−	35.7596i	−0.833877	−	1.44432i	0.0610640	−	0.998134i	$-0.480551\pi$
$614$	3.26951	+	5.66295i	0.131947	+	0.228538i
$615$	−3.41082	+	0.951423i	−0.137538	+	0.0383651i
$616$	−12.5609	+	3.44658i	−0.506091	+	0.138867i
$617$	−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	$0.536119\pi$
$618$	−21.8883	+	6.10559i	−0.880478	+	0.245603i
$619$		−	27.0241i		−	1.08619i	−0.839672	−	0.543095i	$-0.817252\pi$
$619$		−	27.0241i		−	1.08619i	0.839672	−	0.543095i	$-0.182748\pi$
$620$	4.75368	−	2.74454i	0.190912	−	0.110223i
$621$	−1.42831	−	1.34324i	−0.0573162	−	0.0539023i
$622$		−	16.9721i		−	0.680518i
$623$	−0.971291	+	3.71390i	−0.0389139	+	0.148794i
$624$	−6.92579	+	7.06894i	−0.277253	+	0.282984i
$625$	1.00000			0.0400000
$626$	−0.697835	+	1.20868i	−0.0278911	+	0.0483088i
$627$	0.325774	+	0.319177i	0.0130102	+	0.0127467i
$628$	−10.2365	+	5.91004i	−0.408480	+	0.235836i
$629$	18.2779			0.728788
$630$	−5.27246	+	1.56336i	−0.210060	+	0.0622858i
$631$	18.4242			0.733455			0.366728	−	0.930328i	$-0.380478\pi$
$631$	18.4242			0.733455			0.366728	+	0.930328i	$0.380478\pi$
$632$	−5.73686	+	3.31218i	−0.228200	+	0.131751i
$633$	5.28946	−	1.47545i	0.210237	−	0.0586441i
$634$	0.261138	−	0.452304i	0.0103711	−	0.0179633i
$635$	−20.6934			−0.821192
$636$	−24.3965	−	6.27029i	−0.967385	−	0.248633i
$637$	−14.5023	+	25.8297i	−0.574604	+	1.02341i
$638$			12.1943i			0.482776i
$639$	10.8329	−	19.6823i	0.428544	−	0.778620i
$640$	9.27216	−	5.35329i	0.366514	−	0.211607i
$641$			30.6558i			1.21083i	0.795909	+	0.605416i	$0.206993\pi$
$641$			30.6558i			1.21083i	−0.795909	+	0.605416i	$0.793007\pi$
$642$	1.94925	−	7.58418i	0.0769310	−	0.299324i
$643$	14.1405	−	8.16403i	0.557647	−	0.321958i	−0.194553	−	0.980892i	$-0.562326\pi$
$643$	14.1405	−	8.16403i	0.557647	−	0.321958i	0.752201	+	0.658934i	$0.228992\pi$
$644$	1.46806	+	0.383940i	0.0578496	+	0.0151293i
$645$	11.8668	+	11.6265i	0.467254	+	0.457792i
$646$	−0.140395	−	0.243171i	−0.00552376	−	0.00956744i
$647$	−20.6290	−	35.7305i	−0.811010	−	1.40471i	−0.912158	−	0.409839i	$-0.865585\pi$
$647$	−20.6290	−	35.7305i	−0.811010	−	1.40471i	0.101148	−	0.994871i	$-0.467749\pi$
$648$	−18.5439	+	11.7430i	−0.728472	+	0.461308i
$649$	−19.8727	−	11.4735i	−0.780074	−	0.450376i
$650$	−1.46600	+	2.53919i	−0.0575014	+	0.0995953i
$651$	8.04096	−	14.4645i	0.315150	−	0.566907i
$652$	2.54354	+	4.40553i	0.0996126	+	0.172534i
$653$		−	13.5093i		−	0.528659i	−0.964432	−	0.264330i	$-0.914849\pi$
$653$		−	13.5093i		−	0.528659i	0.964432	−	0.264330i	$-0.0851507\pi$
$654$	13.8555	−	14.1419i	0.541793	−	0.552992i
$655$	−6.34764			−0.248023
$656$	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	$0.574431\pi$
$660$	3.71914	−	3.79601i	0.144767	−	0.147760i
$661$	−2.66637	−	1.53943i	−0.103710	−	0.0598769i	0.447248	−	0.894410i	$-0.352404\pi$
$661$	−2.66637	−	1.53943i	−0.103710	−	0.0598769i	−0.550958	+	0.834533i	$0.685737\pi$
$662$	3.72726	+	2.15194i	0.144864	+	0.0836374i
$663$	15.9368	−	16.2662i	0.618935	−	0.631727i
$664$	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
$668$	20.7691			0.803582
$669$	17.6451	−	18.0098i	0.682199	−	0.696299i
$670$		−	9.37036i		−	0.362009i
$671$	5.41196	+	9.37379i	0.208926	+	0.361871i
$672$	12.9433	−	23.2831i	0.499300	−	0.898165i
$673$	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
$675$	3.55978	−	3.78523i	0.137016	−	0.145694i
$676$	3.72996	+	6.46048i	0.143460	+	0.248480i
$677$	−8.41172	−	14.5695i	−0.323289	−	0.559953i	0.657876	−	0.753127i	$-0.271455\pi$
$677$	−8.41172	−	14.5695i	−0.323289	−	0.559953i	−0.981165	+	0.193174i	$0.938122\pi$
$678$	14.3542	+	14.0636i	0.551272	+	0.540108i
$679$	−33.5477	−	8.77368i	−1.28744	−	0.336703i
$680$	−6.56190	+	3.78851i	−0.251637	+	0.145283i
$681$	−4.24846	+	16.5299i	−0.162801	+	0.633429i
$682$		−	5.05085i		−	0.193407i
$683$	−8.69305	+	5.01894i	−0.332630	+	0.192044i	−0.657008	−	0.753883i	$-0.728178\pi$
$683$	−8.69305	+	5.01894i	−0.332630	+	0.192044i	0.324378	+	0.945928i	$0.394845\pi$
$684$	−0.594676	+	0.0121670i	−0.0227380	+	0.000465218i
$685$		−	1.47068i		−	0.0561918i
$686$	3.09750	−	12.4524i	0.118263	−	0.475433i
$687$	−45.4801	−	11.6891i	−1.73518	−	0.445968i
$688$	−12.9503			−0.493724
$689$	−20.2451	+	35.0656i	−0.771278	+	1.33589i
$690$	0.436176	−	0.121668i	0.0166049	−	0.00463182i
$691$	−23.2903	+	13.4467i	−0.886006	+	0.511536i	−0.872634	−	0.488375i	$-0.837590\pi$
$691$	−23.2903	+	13.4467i	−0.886006	+	0.511536i	−0.0133718	+	0.999911i	$0.504256\pi$
$692$	34.8136			1.32342
$693$	3.73602	−	15.5806i	0.141920	−	0.591860i
$694$	−5.86256			−0.222540
$695$	8.43461	−	4.86972i	0.319943	−	0.184719i
$696$	−26.3076	−	25.7749i	−0.997188	−	0.976994i
$697$	−3.17585	+	5.50073i	−0.120294	+	0.208355i
$698$	5.77571			0.218614
$699$	6.85397	−	6.99564i	0.259241	−	0.264599i
$700$	−1.01750	+	3.89057i	−0.0384577	+	0.147050i
$701$		−	34.6386i		−	1.30828i	−0.756372	−	0.654142i	$-0.773030\pi$
$701$		−	34.6386i		−	1.30828i	0.756372	−	0.654142i	$-0.226970\pi$
$702$	4.39279	+	14.5881i	0.165795	+	0.550593i
$703$	−0.664594	+	0.383704i	−0.0250656	+	0.0144717i
$704$		−	2.67929i		−	0.100979i
$705$	7.71706	−	2.15262i	0.290641	−	0.0810722i
$706$	−5.58627	+	3.22524i	−0.210242	+	0.121383i
$707$	8.94370	−	2.45406i	0.336362	−	0.0922946i
$708$	28.8266	−	8.04096i	1.08337	−	0.302198i
$709$	10.7787	+	18.6693i	0.404803	+	0.701140i	0.994299	−	0.106632i	$-0.0340066\pi$
$709$	10.7787	+	18.6693i	0.404803	+	0.701140i	−0.589495	+	0.807772i	$0.700673\pi$
$710$	2.59434	+	4.49352i	0.0973638	+	0.168639i
$711$	−0.166686	−	8.14695i	−0.00625122	−	0.305535i
$712$	−3.06448	−	1.76928i	−0.114846	−	0.0663064i
$713$	−0.681348	+	1.18013i	−0.0255167	+	0.0441962i
$714$	−4.79293	+	8.62175i	−0.179371	+	0.322661i
$715$	−4.27118	−	7.39790i	−0.159733	−	0.276666i
$716$			21.0989i			0.788504i
$717$	3.59905	+	12.9025i	0.134409	+	0.481851i
$718$	8.79696			0.328300
$719$	17.6098	−	30.5011i	0.656736	−	1.13750i	−0.324719	−	0.945810i	$-0.605270\pi$
$719$	17.6098	−	30.5011i	0.656736	−	1.13750i	0.981456	−	0.191690i	$-0.0613968\pi$
$720$	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
$723$	−6.85383	−	1.76154i	−0.254897	−	0.0655125i
$724$	10.4099	+	6.01014i	0.386879	+	0.223365i
$725$	7.55077	+	4.35944i	0.280428	+	0.161905i
$726$	2.23294	+	8.00501i	0.0828721	+	0.297094i
$727$	12.3448	+	7.12725i	0.457842	+	0.264335i	0.711136	−	0.703054i	$-0.248181\pi$
$727$	12.3448	+	7.12725i	0.457842	+	0.264335i	−0.253295	+	0.967389i	$0.581514\pi$
$728$	−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
$731$	29.7996			1.10218
$732$	−13.6720	−	3.51391i	−0.505330	−	0.129878i
$733$		−	18.0544i		−	0.666855i	−0.942776	−	0.333427i	$-0.891795\pi$
$733$		−	18.0544i		−	0.666855i	0.942776	−	0.333427i	$-0.108205\pi$
$734$	−10.2344	−	17.7266i	−0.377760	−	0.654300i
$735$	3.39754	+	11.6386i	0.125320	+	0.429296i
$736$	−1.09675	+	1.89963i	−0.0404267	+	0.0700212i
$737$	23.6429	+	13.6502i	0.870897	+	0.502812i
$738$	−2.19956	−	3.63589i	−0.0809668	−	0.133839i
$739$	3.53742	+	6.12699i	0.130126	+	0.225385i	0.923725	−	0.383056i	$-0.125128\pi$
$739$	3.53742	+	6.12699i	0.130126	+	0.225385i	−0.793599	+	0.608441i	$0.791795\pi$
$740$	4.47102	+	7.74404i	0.164358	+	0.284676i
$741$	−0.237998	+	0.926005i	−0.00874308	+	0.0340177i
$742$	4.43783	−	16.9688i	0.162918	−	0.622944i
$743$	−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	$0.394921\pi$
$744$	10.8966	+	10.6759i	0.399488	+	0.391398i
$745$			24.0867i			0.882467i
$746$	−3.53391	+	2.04030i	−0.129386	+	0.0747008i
$747$	−1.58369	+	0.958066i	−0.0579444	+	0.0350538i
$748$		−	9.53247i		−	0.348542i
$749$	−16.7024	−	4.36817i	−0.610293	−	0.159609i
$750$	0.322438	+	1.15593i	0.0117738	+	0.0422086i
$751$	−25.7216			−0.938595			−0.469297	−	0.883040i	$-0.655493\pi$
$751$	−25.7216			−0.938595			−0.469297	+	0.883040i	$0.655493\pi$
$752$	−3.12263	+	5.40855i	−0.113870	+	0.197229i
$753$	−0.129383	+	0.503404i	−0.00471498	+	0.0183451i
$754$	−22.1389	+	12.7819i	−0.806251	+	0.465489i
$755$	−11.0384			−0.401728
$756$	11.1047	+	17.7010i	0.403872	+	0.643780i
$757$	−28.6184			−1.04015			−0.520077	−	0.854120i	$-0.674097\pi$
$757$	−28.6184			−1.04015			−0.520077	+	0.854120i	$0.674097\pi$
$758$	3.25284	−	1.87803i	0.118148	−	0.0682131i
$759$	−0.328409	+	1.27778i	−0.0119205	+	0.0463804i
$760$	0.159063	−	0.275504i	0.00576981	−	0.00999360i
$761$	45.7372			1.65797			0.828986	−	0.559269i	$-0.188918\pi$
$761$	45.7372			1.65797			0.828986	+	0.559269i	$0.188918\pi$
$762$	−6.67233	−	23.9201i	−0.241713	−	0.866534i
$763$	−31.0490	−	30.6786i	−1.12405	−	1.11064i
$764$		−	36.7379i		−	1.32913i
$765$	−0.190658	−	9.31860i	−0.00689326	−	0.336915i
$766$	−8.49369	+	4.90383i	−0.306890	+	0.177183i
$767$		−	48.1056i		−	1.73699i
$768$	12.4620	+	12.2096i	0.449683	+	0.440576i
$769$	−8.20326	+	4.73616i	−0.295817	+	0.170790i	−0.640562	−	0.767906i	$-0.721299\pi$
$769$	−8.20326	+	4.73616i	−0.295817	+	0.170790i	0.344745	+	0.938696i	$0.387965\pi$
$770$	2.63221	+	2.60081i	0.0948582	+	0.0937267i
$771$	−6.47279	+	25.1844i	−0.233112	+	0.906995i
$772$	−14.4621	−	25.0492i	−0.520504	−	0.901539i
$773$	11.8211	+	20.4748i	0.425176	+	0.736426i	0.996437	−	0.0843421i	$-0.0268789\pi$
$773$	11.8211	+	20.4748i	0.425176	+	0.736426i	−0.571261	+	0.820769i	$0.693546\pi$
$774$	−9.61308	+	17.4660i	−0.345535	+	0.627801i
$775$	−3.12751	−	1.80567i	−0.112344	−	0.0648616i
$776$	15.9819	−	27.6814i	0.573716	−	0.993706i
$777$	23.5635	+	13.0992i	0.845336	+	0.469932i
$778$	2.34484	+	4.06139i	0.0840667	+	0.145608i
$779$		−	0.266679i		−	0.00955477i
$780$	10.7901	+	2.77322i	0.386346	+	0.0992972i
$781$	−15.1171			−0.540934
$782$	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
$786$	−2.04672	−	7.33742i	−0.0730041	−	0.261717i
$787$	14.4065	+	8.31760i	0.513536	+	0.296490i	0.734286	−	0.678840i	$-0.237517\pi$
$787$	14.4065	+	8.31760i	0.513536	+	0.296490i	−0.220750	+	0.975330i	$0.570850\pi$
$788$	−15.1222	−	8.73079i	−0.538705	−	0.311021i
$789$	18.8197	+	4.83696i	0.669999	+	0.172200i
$790$	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
$794$	9.25334			0.328389
$795$	4.45278	+	15.9631i	0.157924	+	0.566152i
$796$		−	15.7203i		−	0.557191i
$797$	−16.1736	−	28.0134i	−0.572897	−	0.992287i	−0.996267	−	0.0863298i	$-0.972486\pi$
$797$	−16.1736	−	28.0134i	−0.572897	−	0.992287i	0.423370	−	0.905957i	$-0.360847\pi$
$798$	−0.00672089	−	0.414108i	−0.000237917	−	0.0146593i
$799$	7.18542	−	12.4455i	0.254202	−	0.440291i
$800$	−5.03429	−	2.90655i	−0.177989	−	0.102762i
$801$	3.72432	−	2.25305i	0.131593	−	0.0796077i
$802$	2.26337	+	3.92028i	0.0799225	+	0.138430i
$803$	−1.56938	−	2.71824i	−0.0553821	−	0.0959246i
$804$	−34.2954	+	9.56644i	−1.20950	+	0.337382i
$805$	−0.264171	−	0.962757i	−0.00931081	−	0.0339327i
$806$	9.16989	−	5.29424i	0.322996	−	0.186482i
$807$	31.9282	−	8.90614i	1.12393	−	0.313511i
$808$			8.54888i			0.300749i
$809$	−10.6494	+	6.14843i	−0.374413	+	0.216167i	−0.675384	−	0.737466i	$-0.736022\pi$
$809$	−10.6494	+	6.14843i	−0.374413	+	0.216167i	0.300972	+	0.953633i	$0.402689\pi$
$810$	5.52327	+	2.89435i	0.194068	+	0.101697i
$811$			41.9744i			1.47392i	0.675936	+	0.736961i	$0.263740\pi$
$811$			41.9744i			1.47392i	−0.675936	+	0.736961i	$0.736260\pi$
$812$	−24.6436	+	24.9411i	−0.864819	+	0.875260i
$813$	36.2928	−	37.0429i	1.27284	−	1.29915i
$814$	8.22815			0.288397
$815$	1.67343	−	2.89847i	0.0586177	−	0.101529i
$816$	5.18980	+	5.08471i	0.181679	+	0.178000i
$817$	−1.08353	+	0.625576i	−0.0379079	+	0.0218861i
$818$	−1.37956			−0.0482351
$819$	32.2029	−	9.54864i	1.12526	−	0.333656i
$820$	−3.10742			−0.108516
$821$	−42.3715	+	24.4632i	−1.47878	+	0.853771i	−0.999712	−	0.0240091i	$-0.992357\pi$
$821$	−42.3715	+	24.4632i	−1.47878	+	0.853771i	−0.479063	+	0.877780i	$0.659024\pi$
$822$	1.70000	−	0.474203i	0.0592944	−	0.0165397i
$823$	−2.09021	+	3.62036i	−0.0728603	+	0.126198i	−0.900154	−	0.435572i	$-0.856546\pi$
$823$	−2.09021	+	3.62036i	−0.0728603	+	0.126198i	0.827294	+	0.561770i	$0.189879\pi$
$824$	−46.1806			−1.60878
$825$	−3.38630	−	0.870332i	−0.117896	−	0.0303011i
$826$	5.51403	+	20.0956i	0.191858	+	0.699214i
$827$			24.5548i			0.853855i	0.904286	+	0.426928i	$0.140404\pi$
$827$			24.5548i			0.853855i	−0.904286	+	0.426928i	$0.859596\pi$
$828$	−0.890605	−	1.47218i	−0.0309507	−	0.0511618i
$829$	−1.05268	+	0.607767i	−0.0365612	+	0.0211086i	−0.518169	−	0.855278i	$-0.673386\pi$
$829$	−1.05268	+	0.607767i	−0.0365612	+	0.0211086i	0.481608	+	0.876387i	$0.340053\pi$
$830$		−	0.427477i		−	0.0148379i
$831$	−9.96180	+	38.7595i	−0.345571	+	1.34455i
$832$	4.86428	−	2.80839i	0.168639	−	0.0973635i
$833$	18.9634	+	10.6472i	0.657043	+	0.368903i
$834$	8.34869	+	8.17963i	0.289092	+	0.283237i
$835$	−6.83216	−	11.8336i	−0.236437	−	0.409520i
$836$	0.200113	+	0.346605i	0.00692104	+	0.0119876i
$837$	−17.9681	+	5.41059i	−0.621070	+	0.187017i
$838$	8.20835	+	4.73909i	0.283553	+	0.163709i
$839$	−21.0332	+	36.4306i	−0.726147	+	1.25772i	0.232352	+	0.972632i	$0.425358\pi$
$839$	−21.0332	+	36.4306i	−0.726147	+	1.25772i	−0.958500	+	0.285093i	$0.907976\pi$
$840$	−11.1746	+	0.181361i	−0.385559	+	0.00625755i
$841$	23.5094	+	40.7194i	0.810668	+	1.40412i
$842$		−	24.5532i		−	0.846159i
$843$	9.79543	−	9.99790i	0.337373	−	0.344346i
$844$	4.81894			0.165875
$845$	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
$849$	18.3974	−	18.7777i	0.631398	−	0.644448i
$850$	1.86420	+	1.07630i	0.0639415	+	0.0369167i
$851$	−1.92250	−	1.10996i	−0.0659026	−	0.0380489i
$852$	13.7976	−	14.0828i	0.472698	−	0.482468i
$853$	27.8513	+	16.0799i	0.953609	+	0.550567i	0.894200	−	0.447667i	$-0.147745\pi$
$853$	27.8513	+	16.0799i	0.953609	+	0.550567i	0.0594092	+	0.998234i	$0.481078\pi$
$854$	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
$857$	−48.4532			−1.65513			−0.827565	−	0.561371i	$-0.810274\pi$
$857$	−48.4532			−1.65513			−0.827565	+	0.561371i	$0.810274\pi$
$858$	7.17426	−	7.32255i	0.244925	−	0.249988i
$859$		−	2.77405i		−	0.0946493i	−0.998880	−	0.0473246i	$-0.984930\pi$
$859$		−	2.77405i		−	0.0946493i	0.998880	−	0.0473246i	$-0.0150695\pi$
$860$	7.28938	+	12.6256i	0.248566	+	0.430529i
$861$	−8.03644	+	4.81539i	−0.273881	+	0.164108i
$862$	−11.0944	+	19.2161i	−0.377878	+	0.654504i
$863$	−40.2110	−	23.2158i	−1.36880	−	0.790275i	−0.378022	−	0.925797i	$-0.623396\pi$
$863$	−40.2110	−	23.2158i	−1.36880	−	0.790275i	−0.990774	+	0.135521i	$0.956729\pi$
$864$	−28.9229	+	8.70929i	−0.983977	+	0.296296i
$865$	−11.4522	−	19.8358i	−0.389386	−	0.674437i
$866$	5.81824	+	10.0775i	0.197712	+	0.342447i
$867$	9.09036	+	8.90627i	0.308725	+	0.302473i
$868$	10.2073	−	10.3305i	0.346459	−	0.350642i
$869$	−4.74843	+	2.74151i	−0.161080	+	0.0929993i
$870$	−2.60455	+	10.1338i	−0.0883024	+	0.343568i
$871$			57.2319i			1.93923i
$872$	34.8444	−	20.1174i	1.17998	−	0.681261i
$873$	20.3519	+	33.6419i	0.688806	+	1.13860i
$874$			0.0341029i			0.00115355i
$875$	2.55145	−	0.700092i	0.0862546	−	0.0236674i
$876$	3.96463	+	1.01897i	0.133953	+	0.0344279i
$877$	6.32213			0.213483			0.106742	−	0.994287i	$-0.465958\pi$
$877$	6.32213			0.213483			0.106742	+	0.994287i	$0.465958\pi$
$878$	−9.40837	+	16.2958i	−0.317517	+	0.549956i
$879$	−37.6279	+	10.4960i	−1.26916	+	0.354022i
$880$	2.36033	−	1.36274i	0.0795668	−	0.0459379i
$881$	−10.4850			−0.353247			−0.176624	−	0.984278i	$-0.556518\pi$
$881$	−10.4850			−0.353247			−0.176624	+	0.984278i	$0.556518\pi$
$882$	−12.3579	+	7.68003i	−0.416112	+	0.258600i
$883$	−24.3398			−0.819100			−0.409550	−	0.912288i	$-0.634314\pi$
$883$	−24.3398			−0.819100			−0.409550	+	0.912288i	$0.634314\pi$
$884$	17.3063	−	9.99181i	0.582075	−	0.336061i
$885$	−14.0642	−	13.7794i	−0.472763	−	0.463189i
$886$	−10.1096	+	17.5103i	−0.339637	+	0.588269i
$887$	43.9210			1.47472			0.737362	−	0.675498i	$-0.236071\pi$
$887$	43.9210			1.47472			0.737362	+	0.675498i	$0.236071\pi$
$888$	−17.3917	+	17.7512i	−0.583628	+	0.595691i
$889$	−52.7981	+	14.4873i	−1.77079	+	0.485888i
$890$			1.00528i			0.0336972i
$891$	−15.3489	+	9.71974i	−0.514206	+	0.325623i
$892$	19.1614	−	11.0628i	0.641571	−	0.370411i
$893$			0.603367i			0.0201909i
$894$	−27.8425	+	7.76645i	−0.931192	+	0.259749i
$895$	12.0215	−	6.94064i	0.401836	−	0.232000i
$896$	19.9096	−	20.1500i	0.665134	−	0.673164i
$897$	−2.66406	+	0.743119i	−0.0889503	+	0.0248120i
$898$	−2.02809	−	3.51276i	−0.0676783	−	0.117222i
$899$	−15.7434	−	27.2684i	−0.525072	−	0.909452i
$900$	3.90149	−	2.36023i	0.130050	−	0.0786744i
$901$	25.7441	+	14.8634i	0.857661	+	0.495171i
$902$	−1.42967	+	2.47626i	−0.0476027	+	0.0824504i
$903$	38.4170	+	21.3565i	1.27844	+	0.710699i
$904$	20.4195	+	35.3676i	0.679142	+	1.17631i
$905$		−	7.90831i		−	0.262881i
$906$	−3.55919	−	12.7596i	−0.118246	−	0.423909i
$907$	10.8327			0.359692			0.179846	−	0.983695i	$-0.442440\pi$
$907$	10.8327			0.359692			0.179846	+	0.983695i	$0.442440\pi$
$908$	−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	$0.707209\pi$
$912$	−0.295446	−	0.0759343i	−0.00978319	−	0.00251443i
$913$	1.07859	+	0.622724i	0.0356961	+	0.0206092i
$914$	21.7006	+	12.5289i	0.717793	+	0.414418i
$915$	2.49537	+	8.94581i	0.0824943	+	0.295739i
$916$	−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	−0.724915	−	0.688838i	$-0.758121\pi$
$919$	7.09655	−	12.2916i	0.234094	−	0.405462i	0.959009	+	0.283376i	$0.0914544\pi$
$920$	0.920256			0.0303399
$921$	−15.8322	−	4.06913i	−0.521689	−	0.134082i
$922$			8.91781i			0.293692i
$923$	−15.8456	−	27.4454i	−0.521564	−	0.903375i
$924$	6.83163	−	12.2891i	0.224744	−	0.404280i
$925$	2.94155	−	5.09492i	0.0967176	−	0.167520i
$926$	−5.79487	−	3.34567i	−0.190431	−	0.109946i
$927$	27.3913	−	49.7671i	0.899647	−	1.63457i
$928$	−25.3418	−	43.8933i	−0.831886	−	1.44087i
$929$	5.17690	+	8.96666i	0.169849	+	0.294187i	0.938367	−	0.345642i	$-0.112339\pi$
$929$	5.17690	+	8.96666i	0.169849	+	0.294187i	−0.768518	+	0.639828i	$0.779005\pi$
$930$	1.07880	−	4.19740i	0.0353752	−	0.137638i
$931$	−0.913033	+	0.0109566i	−0.0299234	+	0.000359089i
$932$	7.44296	−	4.29720i	0.243802	−	0.140759i
$933$	30.3065	+	29.6928i	0.992190	+	0.972098i
$934$			14.0258i			0.458939i
$935$	−5.43132	+	3.13578i	−0.177623	+	0.102551i
$936$	0.633339	+	30.9551i	0.0207013	+	1.01180i
$937$			27.0680i			0.884273i	0.896948	+	0.442136i	$0.145779\pi$
$937$			27.0680i			0.884273i	−0.896948	+	0.442136i	$0.854221\pi$
$938$	−6.56011	−	23.9080i	−0.214195	−	0.780623i
$939$	−0.937445	−	3.36071i	−0.0305924	−	0.109673i
$940$	7.03060			0.229313
$941$	−21.3561	+	36.9899i	−0.696189	+	1.20583i	0.273589	+	0.961847i	$0.411789\pi$
$941$	−21.3561	+	36.9899i	−0.696189	+	1.20583i	−0.969778	+	0.243988i	$0.921544\pi$
$942$	−2.32307	+	9.03861i	−0.0756896	+	0.294494i
$943$	0.668083	−	0.385718i	0.0217558	−	0.0125607i
$944$	15.3483			0.499545
$945$	6.43256	−	12.1500i	0.209251	−	0.395239i
$946$	13.4149			0.436155
$947$	30.3505	−	17.5229i	0.986259	−	0.569417i	0.0821048	−	0.996624i	$-0.473836\pi$
$947$	30.3505	−	17.5229i	0.986259	−	0.569417i	0.904154	+	0.427207i	$0.140502\pi$
$948$	1.78002	−	6.92573i	0.0578125	−	0.224937i
$949$	3.29000	−	5.69844i	0.106798	−	0.184979i
$950$	−0.0903776			−0.00293224
$951$	0.350802	+	1.25762i	0.0113755	+	0.0407810i
$952$	−14.0900	+	14.2601i	−0.456660	+	0.462173i
$953$			22.6751i			0.734518i	0.930119	+	0.367259i	$0.119704\pi$
$953$			22.6751i			0.734518i	−0.930119	+	0.367259i	$0.880296\pi$
$954$	−17.0164	+	10.2942i	−0.550928	+	0.333287i
$955$	−20.9322	+	12.0852i	−0.677349	+	0.391068i
$956$			11.7548i			0.380176i
$957$	−21.7750	−	21.3340i	−0.703885	−	0.689631i
$958$	24.1210	−	13.9263i	0.779313	−	0.449937i
$959$	−1.02961	−	3.75236i	−0.0332479	−	0.121170i
$960$	0.572262	−	2.22656i	0.0184697	−	0.0718620i
$961$	−8.97910	−	15.5523i	−0.289648	−	0.501686i
$962$	8.62464	+	14.9383i	0.278070	+	0.481631i
$963$	10.1326	+	16.7493i	0.326519	+	0.539739i
$964$	−5.37804	−	3.10501i	−0.173215	−	0.100006i
$965$	−9.51485	+	16.4802i	−0.306294	+	0.530517i
$966$	1.02770	−	0.615792i	0.0330657	−	0.0198128i
$967$	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	$0.679886\pi$
$968$			16.8892i			0.542839i
$969$	0.679846	+	0.174731i	0.0218398	+	0.00561317i
$970$	−9.08074			−0.291565
$971$	−6.27559	+	10.8696i	−0.201393	+	0.348824i	−0.948978	−	0.315343i	$-0.897880\pi$
$971$	−6.27559	+	10.8696i	−0.201393	+	0.348824i	0.747584	+	0.664167i	$0.231214\pi$
$972$	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
$975$	−1.96937	−	7.06014i	−0.0630704	−	0.226105i
$976$	−6.26973	−	3.61983i	−0.200689	−	0.115868i
$977$	−48.0189	−	27.7237i	−1.53626	−	0.886960i	−0.999053	−	0.0435090i	$-0.986146\pi$
$977$	−48.0189	−	27.7237i	−1.53626	−	0.886960i	−0.537206	−	0.843451i	$-0.680520\pi$
$978$	3.89000	+	0.999791i	0.124388	+	0.0319698i
$979$	−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
$983$	−55.5234			−1.77092			−0.885461	−	0.464713i	$-0.846157\pi$
$983$	−55.5234			−1.77092			−0.885461	+	0.464713i	$0.846157\pi$
$984$	−2.32034	−	8.31835i	−0.0739698	−	0.265179i
$985$			11.4882i			0.366045i
$986$	9.38409	+	16.2537i	0.298850	+	0.517624i
$987$	18.1826	−	10.8949i	0.578759	−	0.346789i
$988$	−0.419511	+	0.726615i	−0.0133464	+	0.0231167i
$989$	−3.13438	−	1.80963i	−0.0996674	−	0.0575430i
$990$	−0.0858283	−	4.19495i	−0.00272780	−	0.133324i
$991$	−21.4737	−	37.1936i	−0.682136	−	1.18149i	−0.974328	−	0.225134i	$-0.927718\pi$
$991$	−21.4737	−	37.1936i	−0.682136	−	1.18149i	0.292192	−	0.956360i	$-0.405615\pi$
$992$	10.4965	+	18.1805i	0.333265	+	0.577233i
$993$	−10.3635	+	2.89083i	−0.328877	+	0.0917377i
$994$	9.76519	+	9.64871i	0.309733	+	0.306038i
$995$	−8.95697	+	5.17131i	−0.283955	+	0.163942i
$996$	−1.56456	+	0.436422i	−0.0495749	+	0.0138285i
$997$			20.6499i			0.653989i	0.945026	+	0.326994i	$0.106036\pi$
$997$			20.6499i			0.653989i	−0.945026	+	0.326994i	$0.893964\pi$
$998$	−19.4758	+	11.2444i	−0.616497	+	0.355935i
$999$	−8.81418	−	29.2712i	−0.278868	−	0.926100i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.9	✓	30	7.3	odd	6
315.2.t.b.131.7	yes	30	9.5	odd	6
315.2.be.b.236.9	yes	30	1.1	even	1	trivial
315.2.be.b.311.9	yes	30	63.59	even	6	inner
945.2.t.b.341.9		30	9.4	even	3
945.2.t.b.521.7		30	21.17	even	6
945.2.be.b.206.7		30	63.31	odd	6
945.2.be.b.656.7		30	3.2	odd	2

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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.600029 - 0.346427i) q^{2} +(-0.431152 + 1.67753i) q^{3} +(-0.759977 + 1.31632i) q^{4} +1.00000 q^{5} +(0.322438 + 1.15593i) q^{6} +(2.55145 - 0.700092i) q^{7} +2.43881i q^{8} +(-2.62822 - 1.44654i) q^{9} +O(q^{10})\)	\(q+(0.600029 - 0.346427i) q^{2} +(-0.431152 + 1.67753i) q^{3} +(-0.759977 + 1.31632i) q^{4} +1.00000 q^{5} +(0.322438 + 1.15593i) q^{6} +(2.55145 - 0.700092i) q^{7} +2.43881i q^{8} +(-2.62822 - 1.44654i) q^{9} +(0.600029 - 0.346427i) q^{10} +2.01862i q^{11} +(-1.88050 - 1.84242i) q^{12} +(-3.66483 + 2.11589i) q^{13} +(1.28841 - 1.30396i) q^{14} +(-0.431152 + 1.67753i) q^{15} +(-0.675084 - 1.16928i) q^{16} +(1.55343 + 2.69061i) q^{17} +(-2.07813 + 0.0425183i) q^{18} +(-0.112967 - 0.0652213i) q^{19} +(-0.759977 + 1.31632i) q^{20} +(0.0743645 + 4.58197i) q^{21} +(0.699304 + 1.21123i) q^{22} -0.377338i q^{23} +(-4.09118 - 1.05150i) q^{24} +1.00000 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} +(0.322438 + 1.15593i) q^{30} +(-3.12751 - 1.80567i) q^{31} +(-5.03429 - 2.90655i) q^{32} +(-3.38630 - 0.870332i) 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} -0.0903776 q^{38} +(-1.96937 - 7.06014i) q^{39} +2.43881i q^{40} +(1.02221 + 1.77052i) q^{41} +(1.63194 + 2.72355i) q^{42} +(4.79579 - 8.30655i) q^{43} +(-2.65715 - 1.53411i) q^{44} +(-2.62822 - 1.44654i) q^{45} +(-0.130720 - 0.226414i) q^{46} +(-2.31277 - 4.00583i) q^{47} +(2.25257 - 0.628337i) q^{48} +(6.01974 - 3.57249i) q^{49} +(0.600029 - 0.346427i) q^{50} +(-5.18334 + 1.44586i) q^{51} -6.43212i q^{52} +(8.28624 - 4.78406i) q^{53} +(0.824662 - 3.50445i) q^{54} +2.01862i q^{55} +(1.70739 + 6.22250i) q^{56} +(0.158117 - 0.161385i) q^{57} +6.04090 q^{58} +(-5.68385 + 9.84472i) q^{59} +(-1.88050 - 1.84242i) q^{60} +(4.64366 - 2.68102i) q^{61} -2.50213 q^{62} +(-7.71846 - 1.85078i) q^{63} -1.32729 q^{64} +(-3.66483 + 2.11589i) q^{65} +(-2.33338 + 0.650880i) q^{66} +(6.76215 - 11.7124i) q^{67} -4.72227 q^{68} +(0.632996 + 0.162690i) q^{69} +(1.28841 - 1.30396i) q^{70} +7.48885i q^{71} +(3.52784 - 6.40973i) q^{72} +(-1.34658 + 0.777450i) q^{73} -4.07613i q^{74} +(-0.431152 + 1.67753i) q^{75} +(0.171704 - 0.0991334i) q^{76} +(1.41322 + 5.15040i) q^{77} +(-3.62750 - 3.55404i) q^{78} +(1.35811 + 2.35232i) q^{79} +(-0.675084 - 1.16928i) q^{80} +(4.81504 + 7.60364i) q^{81} +(1.22671 + 0.708240i) q^{82} +(0.308490 - 0.534320i) q^{83} +(-6.08785 - 3.38431i) q^{84} +(1.55343 + 2.69061i) q^{85} -6.64556i q^{86} +(-10.5686 + 10.7871i) q^{87} -4.92304 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} +(4.37750 - 4.46798i) q^{93} +(-2.77545 - 1.60241i) q^{94} +(-0.112967 - 0.0652213i) q^{95} +(7.04636 - 7.19201i) q^{96} +(-11.3504 - 6.55314i) q^{97} +(2.37441 - 4.22900i) q^{98} +(2.92002 - 5.30537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

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