LMFDB - Embedded newform 768.2.z.a.421.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			421.7
Character	$\chi$	$=$	768.421
Dual form			768.2.z.a.301.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29983 - 0.557180i) q^{2} +(-0.857729 - 0.514103i) q^{3} +(1.37910 + 1.44848i) q^{4} +(2.06438 - 0.738647i) q^{5} +(0.828451 + 1.14615i) q^{6} +(-3.17676 + 0.963660i) q^{7} +(-0.985532 - 2.65117i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(-1.29983 - 0.557180i) q^{2} +(-0.857729 - 0.514103i) q^{3} +(1.37910 + 1.44848i) q^{4} +(2.06438 - 0.738647i) q^{5} +(0.828451 + 1.14615i) q^{6} +(-3.17676 + 0.963660i) q^{7} +(-0.985532 - 2.65117i) q^{8} +(0.471397 + 0.881921i) q^{9} +(-3.09489 - 0.190118i) q^{10} +(-1.45483 + 1.96162i) q^{11} +(-0.438229 - 1.95140i) q^{12} +(0.910294 - 0.430537i) q^{13} +(4.66617 + 0.517436i) q^{14} +(-2.15042 - 0.427745i) q^{15} +(-0.196161 + 3.99519i) q^{16} +(5.26006 - 1.04629i) q^{17} +(-0.121345 - 1.40900i) q^{18} +(0.0686178 + 1.39675i) q^{19} +(3.91690 + 1.97153i) q^{20} +(3.22022 + 0.806623i) q^{21} +(2.98401 - 1.73916i) q^{22} +(0.185662 + 1.88506i) q^{23} +(-0.517658 + 2.78065i) q^{24} +(-0.148990 + 0.122273i) q^{25} +(-1.42311 + 0.0524261i) q^{26} +(0.0490677 - 0.998795i) q^{27} +(-5.77691 - 3.27247i) q^{28} +(-1.17661 + 7.93205i) q^{29} +(2.55684 + 1.75416i) q^{30} +(-0.947486 - 0.392461i) q^{31} +(2.48101 - 5.08376i) q^{32} +(2.25633 - 0.934601i) q^{33} +(-7.42014 - 1.57080i) q^{34} +(-5.84623 + 4.33586i) q^{35} +(-0.627337 + 1.89906i) q^{36} +(-2.75145 - 3.03576i) q^{37} +(0.689049 - 1.85376i) q^{38} +(-1.00213 - 0.0987008i) q^{39} +(-3.99279 - 4.74507i) q^{40} +(2.94796 + 2.41933i) q^{41} +(-3.73629 - 2.84271i) q^{42} +(1.70718 + 2.84825i) q^{43} +(-4.84772 + 0.597977i) q^{44} +(1.62457 + 1.47242i) q^{45} +(0.808989 - 2.55370i) q^{46} +(9.02304 + 6.02900i) q^{47} +(2.22219 - 3.32594i) q^{48} +(3.34288 - 2.23364i) q^{49} +(0.261790 - 0.0759196i) q^{50} +(-5.04960 - 1.80678i) q^{51} +(1.87901 + 0.724784i) q^{52} +(0.133250 + 0.898298i) q^{53} +(-0.620288 + 1.27092i) q^{54} +(-1.55439 + 5.12413i) q^{55} +(5.68563 + 7.47243i) q^{56} +(0.659216 - 1.23331i) q^{57} +(5.94897 - 9.65471i) q^{58} +(7.89483 + 3.73398i) q^{59} +(-2.34607 - 3.70473i) q^{60} +(1.84798 - 0.462896i) q^{61} +(1.01290 + 1.03805i) q^{62} +(-2.34739 - 2.34739i) q^{63} +(-6.05745 + 5.22563i) q^{64} +(1.56118 - 1.56118i) q^{65} +(-3.45357 - 0.0423601i) q^{66} +(-0.0115877 - 0.0462605i) q^{67} +(8.76968 + 6.17612i) q^{68} +(0.809867 - 1.71232i) q^{69} +(10.0149 - 2.37847i) q^{70} +(7.32888 + 3.91737i) q^{71} +(1.87355 - 2.11892i) q^{72} +(9.20082 + 2.79104i) q^{73} +(1.88495 + 5.47902i) q^{74} +(0.190654 - 0.0282809i) q^{75} +(-1.92852 + 2.02565i) q^{76} +(2.73133 - 7.63355i) q^{77} +(1.24760 + 0.686658i) q^{78} +(-1.90119 - 2.84533i) q^{79} +(2.54608 + 8.39247i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(-2.48384 - 4.78726i) q^{82} +(4.39398 - 4.84801i) q^{83} +(3.27263 + 5.77682i) q^{84} +(10.0859 - 6.04527i) q^{85} +(-0.632045 - 4.65344i) q^{86} +(5.08710 - 6.19865i) q^{87} +(6.63438 + 1.92378i) q^{88} +(-1.13112 + 11.4845i) q^{89} +(-1.29125 - 2.81907i) q^{90} +(-2.47690 + 2.24493i) q^{91} +(-2.47442 + 2.86861i) q^{92} +(0.610920 + 0.823730i) q^{93} +(-8.36915 - 12.8641i) q^{94} +(1.17336 + 2.83273i) q^{95} +(-4.74161 + 3.08499i) q^{96} +(-1.53305 + 3.70111i) q^{97} +(-5.58970 + 1.04076i) q^{98} +(-2.41580 - 0.358350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{57}{64}\right)$

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 $

$2$	−1.29983	−	0.557180i	−0.919117	−	0.393986i
$2$	−1.29983	−	0.557180i	−0.919117	−	0.393986i
$3$	−0.857729	−	0.514103i	−0.495210	−	0.296817i
$3$	−0.857729	−	0.514103i	−0.495210	−	0.296817i
$4$	1.37910	+	1.44848i	0.689551	+	0.724238i
$5$	2.06438	−	0.738647i	0.923218	−	0.330333i	0.167986	−	0.985789i	$-0.446274\pi$
$5$	2.06438	−	0.738647i	0.923218	−	0.330333i	0.755233	+	0.655457i	$0.227524\pi$
$6$	0.828451	+	1.14615i	0.338214	+	0.467915i
$7$	−3.17676	+	0.963660i	−1.20070	+	0.364229i	−0.826403	−	0.563079i	$-0.809617\pi$
$7$	−3.17676	+	0.963660i	−1.20070	+	0.364229i	−0.374299	+	0.927308i	$0.622117\pi$
$8$	−0.985532	−	2.65117i	−0.348438	−	0.937332i
$9$	0.471397	+	0.881921i	0.157132	+	0.293974i
$10$	−3.09489	−	0.190118i	−0.978692	−	0.0601205i
$11$	−1.45483	+	1.96162i	−0.438649	+	0.591450i	−0.966110	−	0.258129i	$-0.916894\pi$
$11$	−1.45483	+	1.96162i	−0.438649	+	0.591450i	0.527461	+	0.849579i	$0.323144\pi$
$12$	−0.438229	−	1.95140i	−0.126506	−	0.563320i
$13$	0.910294	−	0.430537i	0.252470	−	0.119410i	−0.297131	−	0.954837i	$-0.596030\pi$
$13$	0.910294	−	0.430537i	0.252470	−	0.119410i	0.549601	+	0.835427i	$0.314780\pi$
$14$	4.66617	+	0.517436i	1.24709	+	0.138291i
$15$	−2.15042	−	0.427745i	−0.555235	−	0.110443i
$16$	−0.196161	+	3.99519i	−0.0490402	+	0.998797i
$17$	5.26006	−	1.04629i	1.27575	−	0.253763i	0.489682	−	0.871901i	$-0.337113\pi$
$17$	5.26006	−	1.04629i	1.27575	−	0.253763i	0.786069	+	0.618138i	$0.212113\pi$
$18$	−0.121345	−	1.40900i	−0.0286014	−	0.332104i
$19$	0.0686178	+	1.39675i	0.0157420	+	0.320436i	0.993732	+	0.111786i	$0.0356570\pi$
$19$	0.0686178	+	1.39675i	0.0157420	+	0.320436i	−0.977990	+	0.208650i	$0.933093\pi$
$20$	3.91690	+	1.97153i	0.875845	+	0.440848i
$21$	3.22022	+	0.806623i	0.702709	+	0.176020i
$22$	2.98401	−	1.73916i	0.636192	−	0.370790i
$23$	0.185662	+	1.88506i	0.0387132	+	0.393062i	0.994943	+	0.100444i	$0.0320264\pi$
$23$	0.185662	+	1.88506i	0.0387132	+	0.393062i	−0.956229	+	0.292618i	$0.905474\pi$
$24$	−0.517658	+	2.78065i	−0.105666	+	0.567598i
$25$	−0.148990	+	0.122273i	−0.0297981	+	0.0244547i
$26$	−1.42311	+	0.0524261i	−0.279095	+	0.0102816i
$27$	0.0490677	−	0.998795i	0.00944308	−	0.192218i
$28$	−5.77691	−	3.27247i	−1.09173	−	0.618440i
$29$	−1.17661	+	7.93205i	−0.218491	+	1.47294i	0.551117	+	0.834428i	$0.314202\pi$
$29$	−1.17661	+	7.93205i	−0.218491	+	1.47294i	−0.769608	+	0.638517i	$0.779548\pi$
$30$	2.55684	+	1.75416i	0.466813	+	0.320265i
$31$	−0.947486	−	0.392461i	−0.170173	−	0.0704881i	0.295970	−	0.955197i	$-0.404357\pi$
$31$	−0.947486	−	0.392461i	−0.170173	−	0.0704881i	−0.466144	+	0.884709i	$0.654357\pi$
$32$	2.48101	−	5.08376i	0.438585	−	0.898690i
$33$	2.25633	−	0.934601i	0.392776	−	0.162693i
$34$	−7.42014	−	1.57080i	−1.27254	−	0.269390i
$35$	−5.84623	+	4.33586i	−0.988194	+	0.732894i
$36$	−0.627337	+	1.89906i	−0.104556	+	0.316511i
$37$	−2.75145	−	3.03576i	−0.452336	−	0.499076i	0.471499	−	0.881867i	$-0.343713\pi$
$37$	−2.75145	−	3.03576i	−0.452336	−	0.499076i	−0.923835	+	0.382791i	$0.874963\pi$
$38$	0.689049	−	1.85376i	0.111778	−	0.300720i
$39$	−1.00213	−	0.0987008i	−0.160469	−	0.0158048i
$40$	−3.99279	−	4.74507i	−0.631316	−	0.750261i
$41$	2.94796	+	2.41933i	0.460395	+	0.377836i	0.835808	−	0.549021i	$-0.184999\pi$
$41$	2.94796	+	2.41933i	0.460395	+	0.377836i	−0.375414	+	0.926857i	$0.622499\pi$
$42$	−3.73629	−	2.84271i	−0.576523	−	0.438640i
$43$	1.70718	+	2.84825i	0.260342	+	0.434354i	0.959950	−	0.280173i	$-0.0903918\pi$
$43$	1.70718	+	2.84825i	0.260342	+	0.434354i	−0.699608	+	0.714527i	$0.746642\pi$
$44$	−4.84772	+	0.597977i	−0.730821	+	0.0901484i
$45$	1.62457	+	1.47242i	0.242177	+	0.219496i
$46$	0.808989	−	2.55370i	0.119279	−	0.376522i
$47$	9.02304	+	6.02900i	1.31615	+	0.879420i	0.997651	−	0.0685048i	$-0.0218228\pi$
$47$	9.02304	+	6.02900i	1.31615	+	0.879420i	0.318494	+	0.947925i	$0.396823\pi$
$48$	2.22219	−	3.32594i	0.320745	−	0.480058i
$49$	3.34288	−	2.23364i	0.477554	−	0.319091i
$50$	0.261790	−	0.0759196i	0.0370227	−	0.0107367i
$51$	−5.04960	−	1.80678i	−0.707086	−	0.252999i
$52$	1.87901	+	0.724784i	0.260572	+	0.100510i
$53$	0.133250	+	0.898298i	0.0183033	+	0.123391i	0.996402	−	0.0847495i	$-0.0270090\pi$
$53$	0.133250	+	0.898298i	0.0183033	+	0.123391i	−0.978099	+	0.208140i	$0.933259\pi$
$54$	−0.620288	+	1.27092i	−0.0844105	+	0.172951i
$55$	−1.55439	+	5.12413i	−0.209594	+	0.690938i
$56$	5.68563	+	7.47243i	0.759774	+	0.998545i
$57$	0.659216	−	1.23331i	0.0873154	−	0.163356i
$58$	5.94897	−	9.65471i	0.781138	−	1.26773i
$59$	7.89483	+	3.73398i	1.02782	+	0.486123i	0.865655	−	0.500641i	$-0.166902\pi$
$59$	7.89483	+	3.73398i	1.02782	+	0.486123i	0.162165	+	0.986764i	$0.448152\pi$
$60$	−2.34607	−	3.70473i	−0.302876	−	0.478278i
$61$	1.84798	−	0.462896i	0.236610	−	0.0592677i	−0.122861	−	0.992424i	$-0.539207\pi$
$61$	1.84798	−	0.462896i	0.236610	−	0.0592677i	0.359471	+	0.933156i	$0.382957\pi$
$62$	1.01290	+	1.03805i	0.128638	+	0.131833i
$63$	−2.34739	−	2.34739i	−0.295743	−	0.295743i
$64$	−6.05745	+	5.22563i	−0.757182	+	0.653204i
$65$	1.56118	−	1.56118i	0.193640	−	0.193640i
$66$	−3.45357	−	0.0423601i	−0.425106	−	0.00521417i
$67$	−0.0115877	−	0.0462605i	−0.00141566	−	0.00565162i	0.969319	−	0.245805i	$-0.0790523\pi$
$67$	−0.0115877	−	0.0462605i	−0.00141566	−	0.00565162i	−0.970735	+	0.240153i	$0.922802\pi$
$68$	8.76968	+	6.17612i	1.06348	+	0.748965i
$69$	0.809867	−	1.71232i	0.0974965	−	0.206139i
$70$	10.0149	−	2.37847i	1.19702	−	0.284281i
$71$	7.32888	+	3.91737i	0.869778	+	0.464906i	0.844987	−	0.534786i	$-0.179608\pi$
$71$	7.32888	+	3.91737i	0.869778	+	0.464906i	0.0247911	+	0.999693i	$0.492108\pi$
$72$	1.87355	−	2.11892i	0.220800	−	0.249717i
$73$	9.20082	+	2.79104i	1.07687	+	0.326666i	0.778411	−	0.627755i	$-0.216026\pi$
$73$	9.20082	+	2.79104i	1.07687	+	0.326666i	0.298463	+	0.954421i	$0.403526\pi$
$74$	1.88495	+	5.47902i	0.219121	+	0.636923i
$75$	0.190654	−	0.0282809i	0.0220149	−	0.00326560i
$76$	−1.92852	+	2.02565i	−0.221217	+	0.232358i
$77$	2.73133	−	7.63355i	0.311264	−	0.869924i
$78$	1.24760	+	0.686658i	0.141262	+	0.0777487i
$79$	−1.90119	−	2.84533i	−0.213901	−	0.320125i	0.708967	−	0.705241i	$-0.249161\pi$
$79$	−1.90119	−	2.84533i	−0.213901	−	0.320125i	−0.922868	+	0.385116i	$0.874161\pi$
$80$	2.54608	+	8.39247i	0.284661	+	0.938307i
$81$	−0.555570	+	0.831470i	−0.0617300	+	0.0923855i
$82$	−2.48384	−	4.78726i	−0.274294	−	0.528664i
$83$	4.39398	−	4.84801i	0.482302	−	0.532138i	−0.450381	−	0.892837i	$-0.648712\pi$
$83$	4.39398	−	4.84801i	0.482302	−	0.532138i	0.932682	+	0.360698i	$0.117462\pi$
$84$	3.27263	+	5.77682i	0.357074	+	0.630303i
$85$	10.0859	−	6.04527i	1.09397	−	0.655701i
$86$	−0.632045	−	4.65344i	−0.0681552	−	0.501793i
$87$	5.08710	−	6.19865i	0.545394	−	0.664565i
$88$	6.63438	+	1.92378i	0.707227	+	0.205076i
$89$	−1.13112	+	11.4845i	−0.119899	+	1.21735i	0.727392	+	0.686222i	$0.240732\pi$
$89$	−1.13112	+	11.4845i	−0.119899	+	1.21735i	−0.847291	+	0.531129i	$0.821768\pi$
$90$	−1.29125	−	2.81907i	−0.136110	−	0.297157i
$91$	−2.47690	+	2.24493i	−0.259649	+	0.235332i
$92$	−2.47442	+	2.86861i	−0.257976	+	0.299074i
$93$	0.610920	+	0.823730i	0.0633495	+	0.0854169i
$94$	−8.36915	−	12.8641i	−0.863212	−	1.32683i
$95$	1.17336	+	2.83273i	0.120384	+	0.290632i
$96$	−4.74161	+	3.08499i	−0.483938	+	0.314860i
$97$	−1.53305	+	3.70111i	−0.155658	+	0.375791i	−0.982400	−	0.186790i	$-0.940192\pi$
$97$	−1.53305	+	3.70111i	−0.155658	+	0.375791i	0.826742	+	0.562581i	$0.190192\pi$
$98$	−5.58970	+	1.04076i	−0.564645	+	0.105133i
$99$	−2.41580	−	0.358350i	−0.242797	−	0.0360155i
$100$	−0.382583	−	0.0471817i	−0.0382583	−	0.00471817i
$101$	3.72400	+	0.182949i	0.370552	+	0.0182041i	0.233492	−	0.972359i	$-0.424985\pi$
$101$	3.72400	+	0.182949i	0.370552	+	0.0182041i	0.137060	+	0.990563i	$0.456235\pi$
$102$	5.55691	+	5.16204i	0.550216	+	0.511118i
$103$	5.19532	+	6.33052i	0.511910	+	0.623765i	0.963256	−	0.268585i	$-0.0865559\pi$
$103$	5.19532	+	6.33052i	0.511910	+	0.623765i	−0.451346	+	0.892349i	$0.649056\pi$
$104$	−2.03855	−	1.98904i	−0.199897	−	0.195042i
$105$	7.24356	−	0.713428i	0.706899	−	0.0696235i
$106$	0.327312	−	1.24188i	0.0317913	−	0.120622i
$107$	1.29868	−	5.18462i	0.125548	−	0.501216i	−0.874326	−	0.485339i	$-0.838696\pi$
$107$	1.29868	−	5.18462i	0.125548	−	0.501216i	0.999874	−	0.0158766i	$-0.00505388\pi$
$108$	1.51440	−	1.30637i	0.145723	−	0.125705i
$109$	−1.29250	+	0.0634964i	−0.123799	+	0.00608186i	−0.110873	−	0.993835i	$-0.535365\pi$
$109$	−1.29250	+	0.0634964i	−0.123799	+	0.00608186i	−0.0129261	+	0.999916i	$0.504115\pi$
$110$	4.87550	−	5.79441i	0.464861	−	0.552475i
$111$	0.799307	+	4.01839i	0.0758669	+	0.381409i
$112$	−3.22685	−	12.8808i	−0.304908	−	1.21712i
$113$	2.77525	−	13.9521i	0.261074	−	1.31251i	−0.598348	−	0.801237i	$-0.704176\pi$
$113$	2.77525	−	13.9521i	0.261074	−	1.31251i	0.859421	−	0.511269i	$-0.170824\pi$
$114$	−1.54404	+	1.23578i	−0.144613	+	0.115742i
$115$	1.77567	+	3.75434i	0.165582	+	0.350094i
$116$	−13.1120	+	9.23481i	−1.21742	+	0.857431i
$117$	0.808810	+	0.599854i	0.0747745	+	0.0554565i
$118$	−8.18142	−	9.25237i	−0.753161	−	0.851750i
$119$	−15.7017	+	8.39272i	−1.43937	+	0.769360i
$120$	0.985278	+	6.12269i	0.0899432	+	0.558922i
$121$	1.46173	+	4.81869i	0.132885	+	0.438062i
$122$	−2.65998	−	0.427975i	−0.240823	−	0.0387470i
$123$	−1.28477	−	3.59069i	−0.115844	−	0.323761i
$124$	−0.738208	−	1.91365i	−0.0662930	−	0.171851i
$125$	−5.85323	+	9.76552i	−0.523528	+	0.873455i
$126$	1.74328	+	4.35911i	0.155304	+	0.388341i
$127$		−	11.5737i		−	1.02700i	−0.858089	−	0.513501i	$-0.828348\pi$
$127$		−	11.5737i		−	1.02700i	0.858089	−	0.513501i	$-0.171652\pi$
$128$	10.7853	−	3.41733i	0.953291	−	0.302052i
$129$		−	3.32069i		−	0.292371i
$130$	−2.89912	+	1.15940i	−0.254269	+	0.101686i
$131$	−1.76025	+	2.93681i	−0.153794	+	0.256590i	−0.924977	−	0.380024i	$-0.875916\pi$
$131$	−1.76025	+	2.93681i	−0.153794	+	0.256590i	0.771182	+	0.636614i	$0.219666\pi$
$132$	4.46545	+	1.97932i	0.388667	+	0.172278i
$133$	−1.56397	−	4.37101i	−0.135614	−	0.379015i
$134$	−0.0107135	+	0.0665871i	−0.000925504	+	0.00575225i
$135$	−0.636463	−	2.09814i	−0.0547780	−	0.180579i
$136$	−7.95785	−	12.9142i	−0.682380	−	1.10738i
$137$	−16.5095	+	8.82451i	−1.41050	+	0.753929i	−0.988293	−	0.152569i	$-0.951245\pi$
$137$	−16.5095	+	8.82451i	−1.41050	+	0.753929i	−0.422209	+	0.906498i	$0.638745\pi$
$138$	−2.00676	+	1.77448i	−0.170826	+	0.151054i
$139$	−4.72308	−	3.50287i	−0.400606	−	0.297110i	0.376576	−	0.926386i	$-0.377101\pi$
$139$	−4.72308	−	3.50287i	−0.400606	−	0.297110i	−0.777182	+	0.629276i	$0.783351\pi$
$140$	−14.3429	−	2.48853i	−1.21220	−	0.210319i
$141$	−4.63979	−	9.81001i	−0.390741	−	0.826152i
$142$	−7.34360	−	9.17541i	−0.616261	−	0.769983i
$143$	−0.479778	+	2.41201i	−0.0401211	+	0.201702i
$144$	−3.61591	+	1.71032i	−0.301326	+	0.142527i
$145$	3.43002	+	17.2439i	0.284847	+	1.43202i
$146$	−10.4044	−	8.75438i	−0.861071	−	0.724517i
$147$	−4.01560	+	0.197274i	−0.331201	+	0.0162709i
$148$	0.602692	−	8.17203i	0.0495410	−	0.671737i
$149$	3.72017	−	14.8517i	0.304768	−	1.21670i	−0.603176	−	0.797608i	$-0.706098\pi$
$149$	3.72017	−	14.8517i	0.304768	−	1.21670i	0.907943	−	0.419093i	$-0.137652\pi$
$150$	−0.263575	−	0.0694685i	−0.0215208	−	0.00567208i
$151$	−18.1900	+	1.79156i	−1.48028	+	0.145795i	−0.805666	−	0.592371i	$-0.798192\pi$
$151$	−18.1900	+	1.79156i	−1.48028	+	0.145795i	−0.674619	+	0.738166i	$0.735692\pi$
$152$	3.63540	−	1.55846i	0.294870	−	0.126408i
$153$	3.40232	+	4.14574i	0.275061	+	0.335163i
$154$	−7.80352	+	8.40046i	−0.628825	+	0.676928i
$155$	−2.24586	−	0.110332i	−0.180392	−	0.00886208i
$156$	−1.23907	−	1.58767i	−0.0992048	−	0.127116i
$157$	−15.2218	−	2.25794i	−1.21483	−	0.180203i	−0.491606	−	0.870818i	$-0.663590\pi$
$157$	−15.2218	−	2.25794i	−1.21483	−	0.180203i	−0.723223	+	0.690615i	$0.757340\pi$
$158$	0.885856	+	4.75774i	0.0704749	+	0.378506i
$159$	0.347525	−	0.839000i	0.0275605	−	0.0665370i
$160$	1.36665	−	12.3274i	0.108043	−	0.974566i
$161$	−2.40636	−	5.80947i	−0.189648	−	0.457850i
$162$	1.18542	−	0.771214i	0.0931357	−	0.0605923i
$163$	14.3900	+	19.4026i	1.12711	+	1.51973i	0.823835	+	0.566829i	$0.191830\pi$
$163$	14.3900	+	19.4026i	1.12711	+	1.51973i	0.303275	+	0.952903i	$0.401920\pi$
$164$	0.561199	+	7.60656i	0.0438223	+	0.593972i
$165$	3.96757	−	3.59600i	0.308875	−	0.279948i
$166$	−8.41263	+	3.85334i	−0.652947	+	0.299077i
$167$	−0.332203	+	3.37292i	−0.0257067	+	0.261004i	0.973738	+	0.227673i	$0.0731117\pi$
$167$	−0.332203	+	3.37292i	−0.0257067	+	0.261004i	−0.999444	+	0.0333313i	$0.989388\pi$
$168$	−1.03513	−	9.33231i	−0.0798619	−	0.720004i
$169$	−7.60384	+	9.26530i	−0.584911	+	0.712716i
$170$	−16.4782	+	2.23813i	−1.26382	+	0.171657i
$171$	−1.19948	+	0.718938i	−0.0917262	+	0.0549786i
$172$	−1.77125	+	6.40083i	−0.135057	+	0.488059i
$173$	4.06330	−	4.48316i	0.308927	−	0.340849i	−0.566622	−	0.823978i	$-0.691750\pi$
$173$	4.06330	−	4.48316i	0.308927	−	0.340849i	0.875549	+	0.483129i	$0.160500\pi$
$174$	−10.0661	+	5.22274i	−0.763110	+	0.395935i
$175$	0.355477	−	0.532009i	0.0268715	−	0.0402161i
$176$	−7.55165	−	6.19713i	−0.569227	−	0.467126i
$177$	−4.85198	−	7.26149i	−0.364697	−	0.545807i
$178$	7.86918	−	14.2976i	0.589820	−	1.07165i
$179$	7.52395	−	21.0280i	0.562366	−	1.57171i	−0.237410	−	0.971410i	$-0.576298\pi$
$179$	7.52395	−	21.0280i	0.562366	−	1.57171i	0.799776	−	0.600299i	$-0.204952\pi$
$180$	0.107676	+	4.38377i	0.00802569	+	0.326747i
$181$	−8.22068	+	1.21942i	−0.611039	+	0.0906390i	−0.445076	−	0.895493i	$-0.646823\pi$
$181$	−8.22068	+	1.21942i	−0.611039	+	0.0906390i	−0.165963	+	0.986132i	$0.553073\pi$
$182$	4.47036	−	1.53794i	0.331365	−	0.114000i
$183$	−1.82304	−	0.553015i	−0.134763	−	0.0408800i
$184$	4.81465	−	2.35001i	0.354940	−	0.173245i
$185$	−7.92240	−	4.23461i	−0.582466	−	0.311335i
$186$	−0.335124	−	1.41110i	−0.0245725	−	0.103467i
$187$	−5.60009	+	11.8404i	−0.409519	+	0.865856i
$188$	3.71082	+	21.3842i	0.270639	+	1.55961i
$189$	0.806623	+	3.22022i	0.0586732	+	0.234236i
$190$	0.0531815	−	4.33583i	0.00385819	−	0.314554i
$191$	−4.99173	+	4.99173i	−0.361189	+	0.361189i	−0.864250	−	0.503062i	$-0.832207\pi$
$191$	−4.99173	+	4.99173i	−0.361189	+	0.361189i	0.503062	+	0.864250i	$0.332207\pi$
$192$	7.88216	−	1.36802i	0.568846	−	0.0987284i
$193$	18.0333	+	18.0333i	1.29807	+	1.29807i	0.929668	+	0.368399i	$0.120094\pi$
$193$	18.0333	+	18.0333i	1.29807	+	1.29807i	0.368399	+	0.929668i	$0.379906\pi$
$194$	4.05489	−	3.95662i	0.291124	−	0.284069i
$195$	−2.14167	+	0.536461i	−0.153368	+	0.0384168i
$196$	7.84554	+	1.76166i	0.560396	+	0.125833i
$197$	−11.5027	−	5.44039i	−0.819536	−	0.387612i	−0.0286608	−	0.999589i	$-0.509124\pi$
$197$	−11.5027	−	5.44039i	−0.819536	−	0.387612i	−0.790875	+	0.611978i	$0.790374\pi$
$198$	2.94045	+	1.81183i	0.208969	+	0.128761i
$199$	−6.69001	+	12.5161i	−0.474243	+	0.887245i	0.525102	+	0.851039i	$0.324027\pi$
$199$	−6.69001	+	12.5161i	−0.474243	+	0.887245i	−0.999344	+	0.0362060i	$0.988473\pi$
$200$	0.471003	+	0.274495i	0.0333049	+	0.0194098i
$201$	−0.0138436	+	0.0456362i	−0.000976452	+	0.00321893i
$202$	−4.73863	−	2.31274i	−0.333409	−	0.162724i
$203$	−3.90599	−	26.3321i	−0.274147	−	1.84815i
$204$	−4.34684	−	9.80595i	−0.304340	−	0.686554i
$205$	7.87275	+	2.81691i	0.549857	+	0.196742i
$206$	−3.22578	−	11.1233i	−0.224751	−	0.774998i
$207$	−1.57495	+	1.05235i	−0.109467	+	0.0731434i
$208$	1.54151	+	3.72125i	0.106885	+	0.258022i
$209$	−2.83971	−	1.89744i	−0.196427	−	0.131248i
$210$	−9.81288	−	3.10863i	−0.677153	−	0.214516i
$211$	−19.1848	−	17.3881i	−1.32074	−	1.19705i	−0.964937	−	0.262483i	$-0.915459\pi$
$211$	−19.1848	−	17.3881i	−1.32074	−	1.19705i	−0.355799	−	0.934562i	$-0.615791\pi$
$212$	−1.11740	+	1.43185i	−0.0767431	+	0.0983400i
$213$	−4.27226	−	7.12784i	−0.292731	−	0.488391i
$214$	−4.57682	+	6.01551i	−0.312865	+	0.411212i
$215$	5.62811	+	4.61887i	0.383834	+	0.315004i
$216$	−2.69634	+	0.854258i	−0.183463	+	0.0581249i
$217$	3.38813	+	0.333702i	0.230002	+	0.0226532i
$218$	1.71540	+	0.637620i	0.116182	+	0.0431851i
$219$	−6.45692	−	7.12412i	−0.436319	−	0.481403i
$220$	−9.56583	+	4.81520i	−0.644928	+	0.324641i
$221$	4.33773	−	3.21708i	0.291788	−	0.216404i
$222$	1.20000	−	5.66857i	0.0805390	−	0.380449i
$223$	−16.2614	+	6.73568i	−1.08894	+	0.451055i	−0.853638	−	0.520867i	$-0.825609\pi$
$223$	−16.2614	+	6.73568i	−1.08894	+	0.451055i	−0.235304	+	0.971922i	$0.575609\pi$
$224$	−2.98257	+	18.5407i	−0.199282	+	1.23880i
$225$	−0.178069	−	0.0737586i	−0.0118713	−	0.00491724i
$226$	−11.3812	+	16.5890i	−0.757065	+	1.10349i
$227$	2.47400	−	16.6783i	0.164205	−	1.10698i	−0.737726	−	0.675100i	$-0.764100\pi$
$227$	2.47400	−	16.6783i	0.164205	−	1.10698i	0.901931	−	0.431880i	$-0.142150\pi$
$228$	2.69554	−	0.745997i	0.178517	−	0.0494048i
$229$	−0.124450	+	2.53323i	−0.00822388	+	0.167401i	0.991170	+	0.132595i	$0.0423311\pi$
$229$	−0.124450	+	2.53323i	−0.00822388	+	0.167401i	−0.999394	+	0.0348053i	$0.988919\pi$
$230$	−0.216222	−	5.86936i	−0.0142572	−	0.387014i
$231$	−6.26717	+	5.14333i	−0.412349	+	0.338406i
$232$	22.1888	−	4.69789i	1.45677	−	0.308432i
$233$	−0.396296	−	4.02366i	−0.0259622	−	0.263599i	−0.999400	−	0.0346458i	$-0.988970\pi$
$233$	−0.396296	−	4.02366i	−0.0259622	−	0.263599i	0.973437	−	0.228953i	$-0.0735303\pi$
$234$	−0.717086	−	1.23036i	−0.0468774	−	0.0804311i
$235$	23.0803	+	5.78131i	1.50559	+	0.377131i
$236$	5.47920	+	16.5850i	0.356665	+	1.07959i
$237$	0.167912	+	3.41793i	0.0109071	+	0.222018i
$238$	25.0857	−	2.16043i	1.62607	−	0.140040i
$239$	7.42672	−	1.47727i	0.480395	−	0.0955565i	0.0510481	−	0.998696i	$-0.483744\pi$
$239$	7.42672	−	1.47727i	0.480395	−	0.0955565i	0.429347	+	0.903140i	$0.358744\pi$
$240$	2.13075	−	8.50741i	0.137539	−	0.549151i
$241$	16.5716	+	3.29631i	1.06747	+	0.212334i	0.697410	−	0.716673i	$-0.254336\pi$
$241$	16.5716	+	3.29631i	1.06747	+	0.212334i	0.370064	+	0.929006i	$0.379336\pi$
$242$	0.784876	−	7.07791i	0.0504537	−	0.454985i
$243$	0.903989	−	0.427555i	0.0579909	−	0.0274277i
$244$	3.21905	+	2.03838i	0.206079	+	0.130494i
$245$	5.25110	−	7.08029i	0.335480	−	0.452343i
$246$	−0.330682	+	5.38312i	−0.0210835	+	0.343215i
$247$	0.663814	+	1.24191i	0.0422375	+	0.0790208i
$248$	−0.106707	+	2.89873i	−0.00677588	+	0.184070i
$249$	−6.26122	+	1.89932i	−0.396789	+	0.120364i
$250$	13.0493	−	9.43219i	0.825312	−	0.596544i
$251$	2.45084	−	0.876925i	0.154696	−	0.0553510i	−0.258403	−	0.966037i	$-0.583196\pi$
$251$	2.45084	−	0.876925i	0.154696	−	0.0553510i	0.413099	+	0.910686i	$0.364446\pi$
$252$	0.162848	−	6.63741i	0.0102585	−	0.418118i
$253$	−3.96787	−	2.37825i	−0.249458	−	0.149519i
$254$	−6.44864	+	15.0438i	−0.404624	+	0.943934i
$255$	−11.7589			−0.736369
$256$	−15.9230	−	1.56740i	−0.995190	−	0.0979623i
$257$	21.2505			1.32557			0.662783	−	0.748811i	$-0.269375\pi$
$257$	21.2505			1.32557			0.662783	+	0.748811i	$0.269375\pi$
$258$	−1.85022	+	4.31632i	−0.115190	+	0.268723i
$259$	11.6661	+	6.99242i	0.724899	+	0.434488i
$260$	4.41435	+	0.108305i	0.273766	+	0.00671681i
$261$	−7.55009	+	2.70147i	−0.467339	+	0.167217i
$262$	3.92436	−	2.83656i	0.242448	−	0.175243i
$263$	−26.4958	+	8.03742i	−1.63380	+	0.495608i	−0.968090	−	0.250601i	$-0.919372\pi$
$263$	−26.4958	+	8.03742i	−1.63380	+	0.495608i	−0.665711	+	0.746209i	$0.731872\pi$
$264$	−4.70147	−	5.06084i	−0.289356	−	0.311473i
$265$	0.938603	+	1.75600i	0.0576579	+	0.107870i
$266$	−0.402545	+	6.55297i	−0.0246816	+	0.401788i
$267$	6.87439	−	9.26904i	0.420706	−	0.567256i
$268$	0.0510267	−	0.0805824i	0.00311695	−	0.00492235i
$269$	28.2044	−	13.3397i	1.71965	−	0.813334i	0.727820	−	0.685768i	$-0.240534\pi$
$269$	28.2044	−	13.3397i	1.71965	−	0.813334i	0.991830	−	0.127566i	$-0.0407164\pi$
$270$	−0.341748	+	3.08184i	−0.0207981	+	0.187555i
$271$	−26.4965	−	5.27048i	−1.60955	−	0.320159i	−0.693263	−	0.720685i	$-0.743828\pi$
$271$	−26.4965	−	5.27048i	−1.60955	−	0.320159i	−0.916286	+	0.400525i	$0.868828\pi$
$272$	3.14831	+	21.2202i	0.190894	+	1.28666i
$273$	3.27863	−	0.652159i	0.198432	−	0.0394705i
$274$	26.3763	−	2.27158i	1.59345	−	0.137231i
$275$	−0.0230970	−	0.470150i	−0.00139280	−	0.0283511i
$276$	3.59714	−	1.18839i	0.216522	−	0.0715326i
$277$	5.14793	+	1.28949i	0.309309	+	0.0774779i	0.394527	−	0.918884i	$-0.370909\pi$
$277$	5.14793	+	1.28949i	0.309309	+	0.0774779i	−0.0852177	+	0.996362i	$0.527159\pi$
$278$	4.18745	+	7.18473i	0.251147	+	0.430912i
$279$	−0.100522	−	1.02061i	−0.00601807	−	0.0611025i
$280$	17.2568	+	11.2263i	1.03129	+	0.670897i
$281$	−18.8032	+	15.4314i	−1.12170	+	0.920558i	−0.997427	−	0.0716899i	$-0.977161\pi$
$281$	−18.8032	+	15.4314i	−1.12170	+	0.920558i	−0.124276	+	0.992248i	$0.539661\pi$
$282$	0.564983	+	15.3365i	0.0336443	+	0.913276i
$283$	0.391341	−	7.96593i	0.0232628	−	0.473526i	−0.958696	−	0.284432i	$-0.908195\pi$
$283$	0.391341	−	7.96593i	0.0232628	−	0.473526i	0.981959	−	0.189094i	$-0.0605550\pi$
$284$	4.43306	+	16.0182i	0.263054	+	0.950503i
$285$	0.449894	−	3.03294i	0.0266494	−	0.179656i
$286$	1.96755	−	2.86787i	0.116344	−	0.169581i
$287$	−11.6964	−	4.84480i	−0.690416	−	0.285980i
$288$	5.65301	−	0.208408i	0.333107	−	0.0122805i
$289$	10.8675	−	4.50148i	0.639267	−	0.264793i
$290$	5.14950	−	24.3252i	0.302389	−	1.42842i
$291$	3.21770	−	2.38641i	0.188625	−	0.139894i
$292$	8.64611	+	17.1763i	0.505975	+	1.00517i
$293$	−9.09704	−	10.0370i	−0.531454	−	0.586370i	0.414751	−	0.909935i	$-0.363869\pi$
$293$	−9.09704	−	10.0370i	−0.531454	−	0.586370i	−0.946206	+	0.323565i	$0.895119\pi$
$294$	5.32951	+	1.98099i	0.310823	+	0.115534i
$295$	19.0560	+	1.87685i	1.10948	+	0.109275i
$296$	−5.33669	+	10.2864i	−0.310189	+	0.597886i
$297$	1.88787	+	1.54933i	0.109545	+	0.0899015i
$298$	−13.1107	+	17.2319i	−0.759480	+	0.998216i
$299$	0.980595	+	1.63602i	0.0567093	+	0.0946137i
$300$	0.303896	+	0.237156i	0.0175454	+	0.0136922i
$301$	−8.16804	−	7.40308i	−0.470798	−	0.426706i
$302$	24.6421	+	7.80641i	1.41800	+	0.449208i
$303$	−3.10013	−	2.07144i	−0.178098	−	0.119001i
$304$	−5.59373		0.000154032i	−0.320822		8.83435e-6i
$305$	3.47302	−	2.32060i	0.198865	−	0.132877i
$306$	−2.11251	−	7.28445i	−0.120764	−	0.416424i
$307$	−24.0408	−	8.60193i	−1.37208	−	0.490938i	−0.455303	−	0.890337i	$-0.650469\pi$
$307$	−24.0408	−	8.60193i	−1.37208	−	0.490938i	−0.916778	+	0.399398i	$0.869219\pi$
$308$	14.8238	−	6.57118i	0.844664	−	0.374428i
$309$	−1.20164	−	8.10080i	−0.0683589	−	0.460838i
$310$	2.85775	+	1.39476i	0.162310	+	0.0792171i
$311$	−1.10926	+	3.65674i	−0.0629003	+	0.207355i	−0.982758	−	0.184899i	$-0.940804\pi$
$311$	−1.10926	+	3.65674i	−0.0629003	+	0.207355i	0.919857	+	0.392253i	$0.128304\pi$
$312$	0.725954	+	2.75408i	0.0410990	+	0.155919i
$313$	11.5067	−	21.5275i	0.650395	−	1.21680i	−0.313263	−	0.949666i	$-0.601422\pi$
$313$	11.5067	−	21.5275i	0.650395	−	1.21680i	0.963658	−	0.267138i	$-0.0860778\pi$
$314$	18.5276	+	11.4162i	1.04557	+	0.644253i
$315$	−6.57978	−	3.11201i	−0.370729	−	0.175342i
$316$	1.49946	−	6.67783i	0.0843512	−	0.375657i
$317$	−32.8945	+	8.23964i	−1.84754	+	0.462784i	−0.997911	−	0.0646002i	$-0.979423\pi$
$317$	−32.8945	+	8.23964i	−1.84754	+	0.462784i	−0.849627	+	0.527384i	$0.823173\pi$
$318$	−0.919196	+	0.896921i	−0.0515460	+	0.0502968i
$319$	−13.8479	−	13.8479i	−0.775332	−	0.775332i
$320$	−8.64499	+	15.2620i	−0.483269	+	0.853172i
$321$	−3.77934	+	3.77934i	−0.210942	+	0.210942i
$322$	−0.109066	+	8.89208i	−0.00607804	+	0.495536i
$323$	1.82234	+	7.27518i	0.101398	+	0.404802i
$324$	−1.97055	+	0.341951i	−0.109475	+	0.0189973i
$325$	−0.0829819	+	0.175451i	−0.00460301	+	0.00973225i
$326$	−7.89372	−	33.2379i	−0.437193	−	1.84088i
$327$	1.14126	+	0.610015i	0.0631117	+	0.0337339i
$328$	3.50876	−	10.1999i	0.193739	−	0.563195i
$329$	−34.4739	−	10.4576i	−1.90061	−	0.576543i
$330$	−7.16078	+	2.46352i	−0.394188	+	0.135613i
$331$	12.1802	−	1.80676i	0.669485	−	0.0993087i	0.196669	−	0.980470i	$-0.436988\pi$
$331$	12.1802	−	1.80676i	0.669485	−	0.0993087i	0.472816	+	0.881161i	$0.343238\pi$
$332$	13.0820	−	0.321324i	0.717966	−	0.0176350i
$333$	1.38028	−	3.85761i	0.0756386	−	0.211396i
$334$	2.31113	−	4.19911i	0.126459	−	0.229765i
$335$	−0.0580915	−	0.0869400i	−0.00317388	−	0.00475004i
$336$	−3.85429	+	12.7071i	−0.210269	+	0.693232i
$337$	−4.77914	+	7.15248i	−0.260336	+	0.389621i	−0.938494	−	0.345296i	$-0.887779\pi$
$337$	−4.77914	+	7.15248i	−0.260336	+	0.389621i	0.678158	+	0.734916i	$0.262779\pi$
$338$	15.0461	−	7.80659i	0.818401	−	0.424622i
$339$	−9.55324	+	10.5404i	−0.518861	+	0.572474i
$340$	22.6659	+	6.27217i	1.22923	+	0.340156i
$341$	2.14829	−	1.28764i	0.116337	−	0.0697295i
$342$	1.95969	−	0.266171i	0.105968	−	0.0143929i
$343$	6.27494	−	7.64603i	0.338815	−	0.412847i
$344$	5.86874	−	7.33307i	0.316421	−	0.395372i
$345$	0.407073	−	4.13308i	0.0219161	−	0.222518i
$346$	−7.77952	+	3.56335i	−0.418230	+	0.191567i
$347$	17.0294	−	15.4345i	0.914185	−	0.828569i	−0.0714525	−	0.997444i	$-0.522763\pi$
$347$	17.0294	−	15.4345i	0.914185	−	0.828569i	0.985637	+	0.168875i	$0.0540134\pi$
$348$	15.9942	−	1.18003i	0.857380	−	0.0632560i
$349$	−5.32090	−	7.17440i	−0.284821	−	0.384037i	0.637507	−	0.770445i	$-0.279966\pi$
$349$	−5.32090	−	7.17440i	−0.284821	−	0.384037i	−0.922328	+	0.386408i	$0.873716\pi$
$350$	−0.758483	+	0.493455i	−0.0405426	+	0.0263763i
$351$	−0.385352	−	0.930323i	−0.0205686	−	0.0496570i
$352$	6.36292	+	12.2628i	0.339145	+	0.653611i
$353$	1.48886	−	3.59443i	0.0792441	−	0.191312i	−0.879292	−	0.476283i	$-0.841984\pi$
$353$	1.48886	−	3.59443i	0.0792441	−	0.191312i	0.958536	+	0.284971i	$0.0919838\pi$
$354$	2.26077	+	12.1421i	0.120159	+	0.645346i
$355$	18.0231	+	2.67348i	0.956569	+	0.141894i
$356$	−18.1949	+	14.1998i	−0.964328	+	0.752590i
$357$	17.7825	+	0.873598i	0.941150	+	0.0462357i
$358$	−21.4962	+	23.1406i	−1.13611	+	1.22302i
$359$	12.7639	+	15.5528i	0.673651	+	0.820846i	0.991881	−	0.127167i	$-0.0405884\pi$
$359$	12.7639	+	15.5528i	0.673651	+	0.820846i	−0.318230	+	0.948014i	$0.603088\pi$
$360$	2.30259	−	5.75814i	0.121357	−	0.303481i
$361$	16.9623	−	1.67064i	0.892753	−	0.0879285i
$362$	11.3649	+	2.99536i	0.597326	+	0.157433i
$363$	1.22353	−	4.88461i	0.0642187	−	0.256375i
$364$	−6.66761	−	0.491740i	−0.349478	−	0.0257742i
$365$	21.0556	−	1.03439i	1.10210	−	0.0541426i
$366$	2.06151	+	1.73459i	0.107757	+	0.0906683i
$367$	−3.30639	−	16.6224i	−0.172592	−	0.867680i	−0.965911	−	0.258874i	$-0.916649\pi$
$367$	−3.30639	−	16.6224i	−0.172592	−	0.867680i	0.793319	−	0.608806i	$-0.208351\pi$
$368$	−7.56759	+	0.371981i	−0.394488	+	0.0193908i
$369$	−0.743999	+	3.74034i	−0.0387311	+	0.194714i
$370$	7.93831	+	9.91846i	0.412693	+	0.515636i
$371$	−1.28896	−	2.72527i	−0.0669193	−	0.141489i
$372$	−0.350632	+	2.02091i	−0.0181794	+	0.104779i
$373$	−29.9811	−	22.2355i	−1.55236	−	1.15131i	−0.929407	−	0.369056i	$-0.879681\pi$
$373$	−29.9811	−	22.2355i	−1.55236	−	1.15131i	−0.622957	−	0.782256i	$-0.714069\pi$
$374$	13.8764	−	12.2702i	0.717531	−	0.634478i
$375$	10.0410	−	5.36700i	0.518513	−	0.277151i
$376$	7.09145	−	29.8634i	0.365713	−	1.54009i
$377$	2.34398	+	7.72707i	0.120721	+	0.397965i
$378$	0.745771	−	4.63516i	0.0383583	−	0.238407i
$379$	3.89340	+	10.8813i	0.199990	+	0.558936i	0.999108	−	0.0422397i	$-0.0134493\pi$
$379$	3.89340	+	10.8813i	0.199990	+	0.558936i	−0.799117	+	0.601175i	$0.794699\pi$
$380$	−2.48497	+	5.60620i	−0.127476	+	0.287592i
$381$	−5.95008	+	9.92711i	−0.304832	+	0.508581i
$382$	9.26967	−	3.70709i	0.474278	−	0.189671i
$383$		−	37.8820i		−	1.93568i	−0.251567	−	0.967840i	$-0.580946\pi$
$383$		−	37.8820i		−	1.93568i	0.251567	−	0.967840i	$-0.419054\pi$
$384$	−11.0077	−	2.61359i	−0.561734	−	0.133374i
$385$		−	17.7760i		−	0.905951i
$386$	−13.3924	−	33.4880i	−0.681655	−	1.70449i
$387$	−1.70718	+	2.84825i	−0.0867807	+	0.144785i
$388$	−7.47521	+	2.88362i	−0.379496	+	0.146394i
$389$	−1.98355	−	5.54364i	−0.100570	−	0.281074i	0.880712	−	0.473653i	$-0.157065\pi$
$389$	−1.98355	−	5.54364i	−0.100570	−	0.281074i	−0.981281	+	0.192579i	$0.938315\pi$
$390$	3.08271	+	0.495990i	0.156099	+	0.0251154i
$391$	2.94891	+	9.72127i	0.149133	+	0.491626i
$392$	−9.21628	−	6.66123i	−0.465493	−	0.336443i
$393$	3.01964	−	1.61403i	0.152321	−	0.0814171i
$394$	11.9203	+	13.4807i	0.600536	+	0.679146i
$395$	−6.02647	−	4.46954i	−0.303225	−	0.224887i
$396$	−2.81257	−	3.99342i	−0.141337	−	0.200677i
$397$	11.6611	+	24.6553i	0.585254	+	1.23741i	0.951715	+	0.306982i	$0.0993190\pi$
$397$	11.6611	+	24.6553i	0.585254	+	1.23741i	−0.366462	+	0.930433i	$0.619431\pi$
$398$	15.6696	−	12.5413i	0.785446	−	0.628637i
$399$	−0.905684	+	4.55318i	−0.0453409	+	0.227944i
$400$	−0.459279	−	0.619230i	−0.0229639	−	0.0309615i
$401$	4.32995	+	21.7681i	0.216227	+	1.08705i	0.924521	+	0.381130i	$0.124465\pi$
$401$	4.32995	+	21.7681i	0.216227	+	1.08705i	−0.708294	+	0.705918i	$0.750535\pi$
$402$	0.0434219	−	0.0516058i	0.00216569	−	0.00257386i
$403$	−1.03146	+	0.0506724i	−0.0513807	+	0.00252417i
$404$	4.87078	+	5.64643i	0.242330	+	0.280920i
$405$	−0.532745	+	2.12684i	−0.0264723	+	0.105683i
$406$	−9.59459	+	36.4035i	−0.476171	+	1.80667i
$407$	9.95791	−	0.980768i	0.493595	−	0.0486149i
$408$	0.186462	+	15.1680i	0.00923126	+	0.750929i
$409$	8.77671	+	10.6945i	0.433980	+	0.528807i	0.943376	−	0.331726i	$-0.107631\pi$
$409$	8.77671	+	10.6945i	0.433980	+	0.528807i	−0.509395	+	0.860533i	$0.670131\pi$
$410$	−8.66368	−	8.04804i	−0.427869	−	0.397464i
$411$	18.6974	+	0.918543i	0.922274	+	0.0453084i
$412$	−2.00473	+	16.2557i	−0.0987657	+	0.800862i
$413$	−28.6783	−	4.25402i	−1.41117	−	0.209327i
$414$	2.63352	−	0.490341i	0.129430	−	0.0240989i
$415$	5.48987	−	13.2537i	0.269487	−	0.650600i
$416$	0.0697064	−	5.69588i	0.00341764	−	0.279264i
$417$	2.25028	+	5.43266i	0.110197	+	0.266039i
$418$	2.63392	+	4.04857i	0.128829	+	0.198022i
$419$	12.2189	+	16.4752i	0.596930	+	0.804867i	0.993583	−	0.113101i	$-0.0360785\pi$
$419$	12.2189	+	16.4752i	0.596930	+	0.804867i	−0.396653	+	0.917968i	$0.629829\pi$
$420$	11.0230	+	9.50823i	0.537867	+	0.463954i
$421$	−10.9531	+	9.92728i	−0.533820	+	0.483826i	−0.893384	−	0.449294i	$-0.851675\pi$
$421$	−10.9531	+	9.92728i	−0.533820	+	0.483826i	0.359564	+	0.933120i	$0.382925\pi$
$422$	15.2486	+	33.2909i	0.742291	+	1.62058i
$423$	−1.06367	+	10.7997i	−0.0517176	+	0.525097i
$424$	2.25022	−	1.23857i	0.109280	−	0.0601502i
$425$	−0.655765	+	0.799052i	−0.0318093	+	0.0387597i
$426$	1.58171	+	11.6454i	0.0766343	+	0.564220i
$427$	−5.42453	+	3.25134i	−0.262511	+	0.157343i
$428$	9.30080	−	5.26901i	0.449571	−	0.254687i
$429$	1.65154	−	1.82219i	0.0797371	−	0.0879764i
$430$	−4.74203	−	9.13960i	−0.228681	−	0.440751i
$431$	−16.2699	+	24.3496i	−0.783694	+	1.17288i	0.197585	+	0.980286i	$0.436690\pi$
$431$	−16.2699	+	24.3496i	−0.783694	+	1.17288i	−0.981278	+	0.192594i	$0.938310\pi$
$432$	3.98075	+	0.391959i	0.191524	+	0.0188581i
$433$	12.2894	+	18.3924i	0.590592	+	0.883884i	0.999589	−	0.0286517i	$-0.00912138\pi$
$433$	12.2894	+	18.3924i	0.590592	+	0.883884i	−0.408997	+	0.912536i	$0.634121\pi$
$434$	−4.21806	−	2.32156i	−0.202473	−	0.111438i
$435$	5.92309	−	16.5539i	0.283990	−	0.793700i
$436$	−1.87446	−	1.78459i	−0.0897704	−	0.0854661i
$437$	−2.62021	+	0.388672i	−0.125342	+	0.0185927i
$438$	4.42347	+	12.8578i	0.211362	+	0.614369i
$439$	23.9671	+	7.27033i	1.14389	+	0.346994i	0.804675	−	0.593716i	$-0.202340\pi$
$439$	23.9671	+	7.27033i	1.14389	+	0.346994i	0.339211	+	0.940710i	$0.389840\pi$
$440$	15.1169	−	0.929038i	0.720668	−	0.0442902i
$441$	3.54572	+	1.89523i	0.168844	+	0.0902488i
$442$	−7.43080	+	1.76475i	−0.353447	+	0.0839408i
$443$	0.801862	−	1.69540i	0.0380976	−	0.0805507i	−0.884043	−	0.467406i	$-0.845189\pi$
$443$	0.801862	−	1.69540i	0.0380976	−	0.0805507i	0.922140	+	0.386855i	$0.126439\pi$
$444$	−4.71821	+	6.69954i	−0.223916	+	0.317946i
$445$	6.14790	+	24.5438i	0.291438	+	1.16349i
$446$	24.8900	+	0.305290i	1.17857	+	0.0144559i
$447$	−10.8262	+	10.8262i	−0.512062	+	0.512062i
$448$	14.2074	−	22.4379i	0.671234	−	1.06009i
$449$	26.2675	+	26.2675i	1.23964	+	1.23964i	0.960148	+	0.279492i	$0.0901662\pi$
$449$	26.2675	+	26.2675i	1.23964	+	1.23964i	0.279492	+	0.960148i	$0.409834\pi$
$450$	0.190362	+	0.195090i	0.00897375	+	0.00919662i
$451$	−9.03460	+	2.26305i	−0.425423	+	0.106563i
$452$	24.0367	−	15.2215i	1.13059	−	0.715959i
$453$	16.5232	+	7.81488i	0.776326	+	0.367175i
$454$	−12.5086	+	20.3005i	−0.587058	+	0.952750i
$455$	−3.45504	+	6.46393i	−0.161975	+	0.303034i
$456$	−3.91939	−	0.532235i	−0.183542	−	0.0249242i
$457$	8.48637	−	27.9758i	0.396976	−	1.30865i	−0.499790	−	0.866147i	$-0.666589\pi$
$457$	8.48637	−	27.9758i	0.396976	−	1.30865i	0.896765	−	0.442506i	$-0.145911\pi$
$458$	1.57323	−	3.22343i	0.0735122	−	0.150621i
$459$	−0.786932	−	5.30506i	−0.0367308	−	0.247619i
$460$	−2.98924	+	7.74963i	−0.139374	+	0.361328i
$461$	−19.4794	−	6.96985i	−0.907248	−	0.324618i	−0.158411	−	0.987373i	$-0.550637\pi$
$461$	−19.4794	−	6.96985i	−0.907248	−	0.324618i	−0.748836	+	0.662755i	$0.769387\pi$
$462$	11.0120	−	3.19350i	0.512325	−	0.148575i
$463$	−19.2188	+	12.8416i	−0.893172	+	0.596798i	−0.915218	−	0.402959i	$-0.867982\pi$
$463$	−19.2188	+	12.8416i	−0.893172	+	0.596798i	0.0220466	+	0.999757i	$0.492982\pi$
$464$	−31.4592	−	6.25673i	−1.46046	−	0.290461i
$465$	1.86962	+	1.24924i	0.0867014	+	0.0579320i
$466$	−1.72679	+	5.45088i	−0.0799919	+	0.252507i
$467$	22.6510	+	20.5296i	1.04816	+	0.949998i	0.998809	−	0.0487837i	$-0.0155345\pi$
$467$	22.6510	+	20.5296i	1.04816	+	0.949998i	0.0493517	+	0.998781i	$0.484284\pi$
$468$	0.246556	+	1.99880i	0.0113971	+	0.0923946i
$469$	0.0813906	+	0.135792i	0.00375827	+	0.00627029i
$470$	−26.7791	−	20.3746i	−1.23523	−	0.939808i
$471$	11.8953	+	9.76224i	0.548108	+	0.449820i
$472$	2.11882	−	24.6105i	0.0975266	−	1.13279i
$473$	−8.07084	−	0.794908i	−0.371098	−	0.0365499i
$474$	1.68614	−	4.53627i	0.0774472	−	0.208358i
$475$	−0.181008	−	0.199712i	−0.00830523	−	0.00916341i
$476$	−33.8108	−	11.1691i	−1.54972	−	0.511934i
$477$	−0.729414	+	0.540970i	−0.0333976	+	0.0247693i
$478$	−10.4766	−	2.21783i	−0.479187	−	0.101441i
$479$	26.4963	−	10.9751i	1.21065	−	0.501467i	0.316223	−	0.948685i	$-0.397585\pi$
$479$	26.4963	−	10.9751i	1.21065	−	0.501467i	0.894425	+	0.447218i	$0.147585\pi$
$480$	−7.50976	+	9.87096i	−0.342772	+	0.450545i
$481$	−3.81164	−	1.57883i	−0.173796	−	0.0719886i
$482$	−19.7036	−	13.5180i	−0.897476	−	0.615729i
$483$	−0.922659	+	6.22006i	−0.0419824	+	0.283023i
$484$	−4.96387	+	8.76274i	−0.225630	+	0.398306i
$485$	−0.430984	+	8.77289i	−0.0195700	+	0.398356i
$486$	−1.41325	+	0.0520630i	−0.0641065	+	0.00236163i
$487$	19.0124	−	15.6030i	0.861533	−	0.707042i	−0.0959954	−	0.995382i	$-0.530603\pi$
$487$	19.0124	−	15.6030i	0.861533	−	0.707042i	0.957528	+	0.288340i	$0.0931034\pi$
$488$	−3.04846	−	4.44313i	−0.137997	−	0.201131i
$489$	−2.36775	−	24.0401i	−0.107073	−	1.08713i
$490$	−10.7705	+	6.27734i	−0.486562	+	0.283581i
$491$	39.2488	+	9.83131i	1.77127	+	0.443681i	0.984764	−	0.173899i	$-0.0556365\pi$
$491$	39.2488	+	9.83131i	1.77127	+	0.443681i	0.786509	+	0.617579i	$0.211886\pi$
$492$	3.42920	−	6.81288i	0.154600	−	0.307148i
$493$	2.11020	+	42.9541i	0.0950387	+	1.93456i
$494$	−0.170877	−	1.98413i	−0.00768812	−	0.0892703i
$495$	−5.25181	+	1.04465i	−0.236051	+	0.0469535i
$496$	1.75382	−	3.70840i	0.0787487	−	0.166512i
$497$	−27.0571	−	5.38199i	−1.21368	−	0.241415i
$498$	9.19676	+	1.01984i	0.412117	+	0.0457000i
$499$	−22.7429	+	10.7566i	−1.01811	+	0.481532i	−0.862377	−	0.506266i	$-0.831025\pi$
$499$	−22.7429	+	10.7566i	−1.01811	+	0.481532i	−0.155737	+	0.987799i	$0.549775\pi$
$500$	−22.2173	+	4.98938i	−0.993588	+	0.223132i
$501$	2.01897	−	2.72226i	0.0902008	−	0.121622i
$502$	−3.67428	−	0.225709i	−0.163991	−	0.0100739i
$503$	1.22638	+	2.29440i	0.0546817	+	0.102302i	0.907777	−	0.419452i	$-0.137778\pi$
$503$	1.22638	+	2.29440i	0.0546817	+	0.102302i	−0.853096	+	0.521754i	$0.825278\pi$
$504$	−3.90991	+	8.53675i	−0.174161	+	0.380257i
$505$	7.82289	−	2.37305i	0.348114	−	0.105599i
$506$	3.83244	+	5.30214i	0.170373	+	0.235709i
$507$	11.2853	−	4.03796i	0.501200	−	0.179332i
$508$	16.7642	−	15.9613i	0.743793	−	0.708169i
$509$	−21.8068	−	13.0705i	−0.966569	−	0.579339i	−0.0585576	−	0.998284i	$-0.518650\pi$
$509$	−21.8068	−	13.0705i	−0.966569	−	0.579339i	−0.908012	+	0.418945i	$0.862400\pi$
$510$	15.2845	+	6.55180i	0.676809	+	0.290119i
$511$	−31.9184			−1.41199
$512$	19.8239	+	10.9093i	0.876100	+	0.482129i
$513$	1.39843			0.0617423
$514$	−27.6219	−	11.8403i	−1.21835	−	0.522254i
$515$	15.4011	+	9.23108i	0.678655	+	0.406770i
$516$	4.80994	−	4.57957i	0.211746	−	0.201604i
$517$	−24.9536	+	8.92855i	−1.09746	+	0.392677i
$518$	−11.2679	−	15.5891i	−0.495085	−	0.684945i
$519$	−5.79002	+	1.75638i	−0.254154	+	0.0770967i
$520$	−5.67754	−	2.60036i	−0.248977	−	0.114034i
$521$	−17.2331	−	32.2409i	−0.754997	−	1.41250i	−0.905699	−	0.423922i	$-0.860653\pi$
$521$	−17.2331	−	32.2409i	−0.754997	−	1.41250i	0.150701	−	0.988579i	$-0.451847\pi$
$522$	11.3190	+	0.695321i	0.495420	+	0.0304334i
$523$	−0.631552	+	0.851549i	−0.0276158	+	0.0372357i	−0.816800	−	0.576921i	$-0.804254\pi$
$523$	−0.631552	+	0.851549i	−0.0276158	+	0.0372357i	0.789184	+	0.614157i	$0.210504\pi$
$524$	−6.68146	+	1.50047i	−0.291881	+	0.0655483i
$525$	−0.578410	+	0.273568i	−0.0252439	+	0.0119395i
$526$	38.9183	+	4.31568i	1.69692	+	0.188173i
$527$	−5.39446	−	1.07302i	−0.234986	−	0.0467417i
$528$	3.29130	+	9.19778i	0.143236	+	0.400282i
$529$	19.0391	−	3.78711i	0.827786	−	0.164657i
$530$	−0.241612	−	2.80547i	−0.0104950	−	0.121862i
$531$	0.428524	+	8.72281i	0.0185964	+	0.378538i
$532$	4.17442	−	8.29344i	0.180984	−	0.359566i
$533$	3.72513	+	0.933096i	0.161353	+	0.0404169i
$534$	−14.1000	+	8.21788i	−0.610169	+	0.355622i
$535$	−1.14863	−	11.6623i	−0.0496598	−	0.504204i
$536$	−0.111225	+	0.0763121i	−0.00480418	+	0.00329618i
$537$	−17.2641	+	14.1683i	−0.745000	+	0.611405i
$538$	−44.0934	+	1.62436i	−1.90100	+	0.0700311i
$539$	−0.481788	+	9.80703i	−0.0207521	+	0.422418i
$540$	2.16135	−	3.81544i	0.0930098	−	0.164190i
$541$	1.62052	−	10.9247i	0.0696717	−	0.469688i	−0.926059	−	0.377379i	$-0.876825\pi$
$541$	1.62052	−	10.9247i	0.0696717	−	0.469688i	0.995730	−	0.0923088i	$-0.0294247\pi$
$542$	31.5043	+	21.6140i	1.35322	+	0.928403i
$543$	7.67803	+	3.18034i	0.329496	+	0.136482i
$544$	7.73119	−	29.3367i	0.331472	−	1.25780i
$545$	−2.62131	+	1.08578i	−0.112284	+	0.0465098i
$546$	−4.62502	−	0.979091i	−0.197933	−	0.0419012i
$547$	31.6979	−	23.5087i	1.35530	−	1.00516i	0.357854	−	0.933778i	$-0.383509\pi$
$547$	31.6979	−	23.5087i	1.35530	−	1.00516i	0.997449	−	0.0713836i	$-0.0227415\pi$
$548$	−35.5504	−	11.7437i	−1.51864	−	0.501666i
$549$	1.27937	+	1.41157i	0.0546022	+	0.0602443i
$550$	−0.231936	+	0.623982i	−0.00988978	+	0.0266067i
$551$	−11.1598	−	1.09915i	−0.475424	−	0.0468252i
$552$	−5.33781	−	0.459553i	−0.227192	−	0.0195599i
$553$	8.78156	+	7.20684i	0.373430	+	0.306466i
$554$	−5.97294	−	4.54443i	−0.253766	−	0.193075i
$555$	4.61824	+	7.70507i	0.196033	+	0.327062i
$556$	−1.43978	−	11.6721i	−0.0610601	−	0.495006i
$557$	−31.8099	−	28.8308i	−1.34783	−	1.22160i	−0.953045	−	0.302829i	$-0.902069\pi$
$557$	−31.8099	−	28.8308i	−1.34783	−	1.22160i	−0.394785	−	0.918773i	$-0.629181\pi$
$558$	−0.438004	+	1.38263i	−0.0185422	+	0.0585313i
$559$	2.78031	+	1.85774i	0.117595	+	0.0785742i
$560$	−16.1758	−	24.2073i	−0.683551	−	1.02295i
$561$	10.8905	−	7.27683i	0.459799	−	0.307228i
$562$	33.0389	−	9.58135i	1.39366	−	0.404165i
$563$	9.62818	+	3.44502i	0.405779	+	0.145190i	0.531865	−	0.846829i	$-0.321491\pi$
$563$	9.62818	+	3.44502i	0.405779	+	0.145190i	−0.126086	+	0.992019i	$0.540241\pi$
$564$	7.81082	−	20.2496i	0.328895	−	0.852663i
$565$	−4.57652	−	30.8524i	−0.192536	−	1.29797i
$566$	−4.94714	+	10.1363i	−0.207944	+	0.426060i
$567$	0.963660	−	3.17676i	0.0404699	−	0.133411i
$568$	3.16279	−	23.2908i	0.132708	−	0.977262i
$569$	7.37589	−	13.7993i	0.309214	−	0.578498i	−0.678532	−	0.734571i	$-0.737384\pi$
$569$	7.37589	−	13.7993i	0.309214	−	0.578498i	0.987746	+	0.156073i	$0.0498835\pi$
$570$	−2.27468	+	3.69163i	−0.0952758	+	0.154625i
$571$	−0.655844	−	0.310191i	−0.0274462	−	0.0129811i	0.413783	−	0.910376i	$-0.364207\pi$
$571$	−0.655844	−	0.310191i	−0.0274462	−	0.0129811i	−0.441229	+	0.897395i	$0.645457\pi$
$572$	−4.15540	+	2.63146i	−0.173746	+	0.110027i
$573$	6.84781	−	1.71529i	0.286071	−	0.0716571i
$574$	12.5039	+	12.8144i	0.521901	+	0.534863i
$575$	−0.258154	−	0.258154i	−0.0107658	−	0.0107658i
$576$	−7.46406	−	2.87885i	−0.311003	−	0.119952i
$577$	−0.673708	+	0.673708i	−0.0280468	+	0.0280468i	−0.720991	−	0.692944i	$-0.756313\pi$
$577$	−0.673708	+	0.673708i	−0.0280468	+	0.0280468i	0.692944	+	0.720991i	$0.256313\pi$
$578$	−16.6341	−	0.204026i	−0.691886	−	0.00848638i
$579$	−6.19672	−	24.7387i	−0.257527	−	1.02810i
$580$	−20.2470	+	28.7493i	−0.840709	+	1.19375i
$581$	−9.28679	+	19.6353i	−0.385281	+	0.814608i
$582$	−5.51210	+	1.30908i	−0.228484	+	0.0542631i
$583$	−1.95597	−	1.04549i	−0.0810081	−	0.0432997i
$584$	−1.66817	−	27.1436i	−0.0690293	−	1.12321i
$585$	2.11277	+	0.640902i	0.0873523	+	0.0264980i
$586$	6.23214	+	18.1151i	0.257447	+	0.748328i
$587$	−11.7436	+	1.74200i	−0.484709	+	0.0718998i	−0.384613	−	0.923078i	$-0.625665\pi$
$587$	−11.7436	+	1.74200i	−0.484709	+	0.0718998i	−0.100096	+	0.994978i	$0.531915\pi$
$588$	−5.82367	−	5.54444i	−0.240164	−	0.228649i
$589$	0.483155	−	1.35033i	0.0199081	−	0.0556393i
$590$	−23.7238	−	13.0572i	−0.976693	−	0.537557i
$591$	7.06931	+	10.5800i	0.290792	+	0.435202i
$592$	12.6682	−	10.3971i	0.520658	−	0.427317i
$593$	3.35078	−	5.01480i	0.137600	−	0.205933i	−0.756269	−	0.654260i	$-0.772980\pi$
$593$	3.35078	−	5.01480i	0.137600	−	0.205933i	0.893870	+	0.448327i	$0.147980\pi$
$594$	−1.59065	−	3.06575i	−0.0652650	−	0.125789i
$595$	−26.2150	+	28.9237i	−1.07471	+	1.18576i
$596$	26.6428	−	15.0935i	1.09133	−	0.618253i
$597$	12.1728	−	7.29609i	0.498199	−	0.298609i
$598$	−0.363044	−	2.67292i	−0.0148460	−	0.109304i
$599$	22.9459	−	27.9597i	0.937545	−	1.14240i	−0.0520676	−	0.998644i	$-0.516581\pi$
$599$	22.9459	−	27.9597i	0.937545	−	1.14240i	0.989613	−	0.143759i	$-0.0459189\pi$
$600$	−0.262873	−	0.477586i	−0.0107318	−	0.0194974i
$601$	1.98095	−	20.1129i	0.0808045	−	0.820422i	−0.866306	−	0.499514i	$-0.833512\pi$
$601$	1.98095	−	20.1129i	0.0808045	−	0.820422i	0.947110	−	0.320908i	$-0.103988\pi$
$602$	6.49219	+	14.1738i	0.264602	+	0.577680i
$603$	0.0353357	−	0.0320265i	0.00143898	−	0.00130422i
$604$	−27.6809	−	23.8771i	−1.12632	−	0.971545i
$605$	6.57688	+	8.86789i	0.267388	+	0.360531i
$606$	2.87547	+	4.41984i	0.116808	+	0.179544i
$607$	0.406289	+	0.980868i	0.0164908	+	0.0398122i	0.931910	−	0.362688i	$-0.118141\pi$
$607$	0.406289	+	0.980868i	0.0164908	+	0.0398122i	−0.915420	+	0.402501i	$0.868141\pi$
$608$	7.27097	+	3.11651i	0.294877	+	0.126391i
$609$	−10.1871	+	24.5939i	−0.412802	+	0.996593i
$610$	−5.80732	+	1.08128i	−0.235132	+	0.0437797i
$611$	10.8093	+	1.60341i	0.437299	+	0.0648671i
$612$	−1.31286	+	10.6456i	−0.0530691	+	0.430322i
$613$	13.3558	+	0.656126i	0.539434	+	0.0265007i	0.316962	−	0.948438i	$-0.397337\pi$
$613$	13.3558	+	0.656126i	0.539434	+	0.0265007i	0.222472	+	0.974939i	$0.428587\pi$
$614$	26.4561	+	24.5761i	1.06768	+	0.991810i
$615$	−5.30450	−	6.46355i	−0.213898	−	0.260635i
$616$	−22.9297	+	0.281877i	−0.923864	+	0.0113572i
$617$	−39.6125	+	3.90149i	−1.59474	+	0.157068i	−0.856019	−	0.516945i	$-0.827069\pi$
$617$	−39.6125	+	3.90149i	−1.59474	+	0.157068i	−0.738719	+	0.674013i	$0.764569\pi$
$618$	−2.95168	+	11.1992i	−0.118734	+	0.450497i
$619$	2.75654	−	11.0047i	0.110795	−	0.442318i	−0.889086	−	0.457740i	$-0.848659\pi$
$619$	2.75654	−	11.0047i	0.110795	−	0.442318i	0.999881	+	0.0154221i	$0.00490919\pi$
$620$	−2.93745	−	3.40523i	−0.117971	−	0.136757i
$621$	1.89190	−	0.0929430i	0.0759193	−	0.00372968i
$622$	3.47931	−	4.13507i	0.139507	−	0.165801i
$623$	−7.47382	−	37.5734i	−0.299432	−	1.50535i
$624$	0.590906	−	3.98432i	0.0236552	−	0.159500i
$625$	−4.68200	+	23.5380i	−0.187280	+	0.941520i
$626$	−26.9513	+	21.5707i	−1.07719	+	0.862138i
$627$	1.46023	+	3.08739i	0.0583158	+	0.123298i
$628$	−17.7218	−	25.1623i	−0.707176	−	1.00408i
$629$	−17.6491	−	13.0895i	−0.703715	−	0.521911i
$630$	6.81863	+	7.71119i	0.271661	+	0.307221i
$631$	21.0625	−	11.2581i	0.838485	−	0.448180i	0.00451524	−	0.999990i	$-0.498563\pi$
$631$	21.0625	−	11.2581i	0.838485	−	0.448180i	0.833970	+	0.551810i	$0.186063\pi$
$632$	−5.66979	+	7.84455i	−0.225532	+	0.312039i
$633$	7.51609	+	24.7772i	0.298738	+	0.984806i
$634$	47.3481	+	7.61804i	1.88043	+	0.302551i
$635$	−8.54889	−	23.8925i	−0.339252	−	0.948146i
$636$	1.69454	−	0.653684i	0.0671930	−	0.0259203i
$637$	2.08134	−	3.47250i	0.0824656	−	0.137586i
$638$	10.2841	+	25.7156i	0.407151	+	1.01809i
$639$			8.31013i			0.328744i
$640$	19.7407	−	15.0212i	0.780319	−	0.593763i
$641$		−	21.2408i		−	0.838960i	−0.907765	−	0.419480i	$-0.862212\pi$
$641$		−	21.2408i		−	0.838960i	0.907765	−	0.419480i	$-0.137788\pi$
$642$	7.01826	−	2.80672i	0.276989	−	0.110772i
$643$	−12.7997	+	21.3550i	−0.504770	+	0.842157i	−0.999641	−	0.0268091i	$-0.991465\pi$
$643$	−12.7997	+	21.3550i	−0.504770	+	0.842157i	0.494871	+	0.868967i	$0.335215\pi$
$644$	5.09626	−	11.4974i	0.200821	−	0.453061i
$645$	−2.45282	−	6.85517i	−0.0965796	−	0.269922i
$646$	1.68486	−	10.4718i	0.0662900	−	0.412009i
$647$	10.2377	+	33.7492i	0.402486	+	1.32682i	0.890898	+	0.454204i	$0.150076\pi$
$647$	10.2377	+	33.7492i	0.402486	+	1.32682i	−0.488412	+	0.872613i	$0.662424\pi$
$648$	2.75190	+	0.653474i	0.108105	+	0.0256709i
$649$	−18.8103	+	10.0543i	−0.738369	+	0.394667i
$650$	0.205620	−	0.181820i	0.00806507	−	0.00713155i
$651$	−2.73454	−	2.02807i	−0.107175	−	0.0794865i
$652$	−8.25901	+	47.6017i	−0.323448	+	1.86423i
$653$	5.47443	+	11.5747i	0.214231	+	0.452954i	0.982275	−	0.187443i	$-0.0600200\pi$
$653$	5.47443	+	11.5747i	0.214231	+	0.452954i	−0.768044	+	0.640397i	$0.778770\pi$
$654$	−1.14355	−	1.42880i	−0.0447163	−	0.0558705i
$655$	−1.46457	+	7.36289i	−0.0572255	+	0.287692i
$656$	−10.2440	+	11.3031i	−0.399959	+	0.441312i
$657$	1.87576	+	9.43008i	0.0731804	+	0.367903i
$658$	38.9834	+	32.8012i	1.51973	+	1.27872i
$659$	−7.95558	+	0.390832i	−0.309905	+	0.0152247i	−0.203426	−	0.979090i	$-0.565208\pi$
$659$	−7.95558	+	0.390832i	−0.309905	+	0.0152247i	−0.106479	+	0.994315i	$0.533958\pi$
$660$	10.6804	+	0.787686i	0.415734	+	0.0306606i
$661$	4.70191	−	18.7711i	0.182883	−	0.730111i	−0.807277	−	0.590173i	$-0.799060\pi$
$661$	4.70191	−	18.7711i	0.182883	−	0.730111i	0.990160	−	0.139938i	$-0.0446904\pi$
$662$	−16.8389	−	4.43809i	−0.654461	−	0.172491i
$663$	−5.37451	+	0.529343i	−0.208729	+	0.0205580i
$664$	−17.1833	−	6.87134i	−0.666842	−	0.266660i
$665$	−6.45726	−	7.86820i	−0.250402	−	0.305116i
$666$	−3.94350	+	4.24517i	−0.152808	+	0.164497i
$667$	−15.1708	−	0.745296i	−0.587417	−	0.0288580i
$668$	−5.34373	+	4.17041i	−0.206755	+	0.161358i
$669$	17.4107	+	2.58263i	0.673136	+	0.0998502i
$670$	0.0270676	+	0.145374i	0.00104571	+	0.00561630i
$671$	−1.78049	+	4.29847i	−0.0687349	+	0.165941i
$672$	12.0901	−	14.3696i	0.466385	−	0.554318i
$673$	−9.98720	−	24.1112i	−0.384978	−	0.929419i	−0.990987	−	0.133961i	$-0.957230\pi$
$673$	−9.98720	−	24.1112i	−0.384978	−	0.929419i	0.606008	−	0.795458i	$-0.292770\pi$
$674$	10.1973	−	6.63415i	0.392784	−	0.255538i
$675$	0.114815	+	0.154811i	0.00441925	+	0.00595866i
$676$	−23.9070	+	1.76382i	−0.919501	+	0.0678392i
$677$	10.3453	−	9.37646i	0.397604	−	0.360367i	−0.448134	−	0.893967i	$-0.647911\pi$
$677$	10.3453	−	9.37646i	0.397604	−	0.360367i	0.845737	+	0.533600i	$0.179161\pi$
$678$	18.2904	−	8.37779i	0.702440	−	0.321747i
$679$	1.30352	−	13.2349i	0.0500246	−	0.507909i
$680$	−25.9670	−	20.7817i	−0.995791	−	0.796943i
$681$	−10.6964	+	13.0336i	−0.409887	+	0.499449i
$682$	−3.50986	+	0.476720i	−0.134399	+	0.0182546i
$683$	20.5536	−	12.3193i	0.786461	−	0.471386i	−0.0636617	−	0.997972i	$-0.520278\pi$
$683$	20.5536	−	12.3193i	0.786461	−	0.471386i	0.850122	+	0.526585i	$0.176528\pi$
$684$	−2.69556	−	0.745922i	−0.103067	−	0.0285211i
$685$	−27.5637	+	30.4118i	−1.05315	+	1.16198i
$686$	−12.4166	+	6.44225i	−0.474066	+	0.245966i
$687$	1.40909	−	2.10885i	0.0537600	−	0.0804575i
$688$	−11.7142	+	6.26177i	−0.446599	+	0.238728i
$689$	0.508047	+	0.760346i	0.0193551	+	0.0289669i
$690$	−2.83199	+	5.14548i	−0.107812	+	0.195885i
$691$	2.18578	−	6.10885i	0.0831511	−	0.232392i	−0.892771	−	0.450510i	$-0.851242\pi$
$691$	2.18578	−	6.10885i	0.0831511	−	0.232392i	0.975922	+	0.218119i	$0.0699920\pi$
$692$	12.0975	−	0.297143i	0.459876	−	0.0112957i
$693$	8.01973	−	1.18961i	0.304644	−	0.0451897i
$694$	−30.7351	+	10.5738i	−1.16669	+	0.401376i
$695$	−12.3376	−	3.74257i	−0.467992	−	0.141964i
$696$	−21.4472	−	7.37783i	−0.812954	−	0.279656i
$697$	18.0378	+	9.64140i	0.683230	+	0.365194i
$698$	2.91882	+	12.2902i	0.110479	+	0.465190i
$699$	−1.72866	+	3.65495i	−0.0653840	+	0.138243i
$700$	1.26084	−	0.218794i	0.0476553	−	0.00826965i
$701$	6.66164	+	26.5948i	0.251607	+	1.00447i	0.955695	+	0.294358i	$0.0951059\pi$
$701$	6.66164	+	26.5948i	0.251607	+	1.00447i	−0.704088	+	0.710112i	$0.748644\pi$
$702$	−0.0174658	+	1.42397i	−0.000659205	+	0.0537443i
$703$	4.05139	−	4.05139i	0.152801	−	0.152801i
$704$	−1.43810	−	19.4848i	−0.0542003	−	0.734363i
$705$	−16.8244	−	16.8244i	−0.633644	−	0.633644i
$706$	−3.93801	+	3.84257i	−0.148209	+	0.144617i
$707$	−12.0066	+	3.00749i	−0.451553	+	0.113108i
$708$	3.82673	−	17.0423i	0.143817	−	0.640489i
$709$	13.7377	+	6.49744i	0.515930	+	0.244017i	0.667742	−	0.744393i	$-0.267261\pi$
$709$	13.7377	+	6.49744i	0.515930	+	0.244017i	−0.151812	+	0.988409i	$0.548511\pi$
$710$	−21.9374	−	13.5172i	−0.823295	−	0.507291i
$711$	1.61314	−	3.01798i	0.0604976	−	0.113183i
$712$	31.5621	−	8.31951i	1.18284	−	0.311787i
$713$	0.563901	−	1.85893i	0.0211183	−	0.0696176i
$714$	−22.6274	−	11.0436i	−0.846810	−	0.413296i
$715$	0.791178	+	5.33369i	0.0295884	+	0.199469i
$716$	40.8349	−	18.1015i	1.52607	−	0.676485i
$717$	−7.12958	−	2.55101i	−0.266259	−	0.0952690i
$718$	−7.92510	−	27.3277i	−0.295762	−	1.01986i
$719$	21.1275	−	14.1170i	0.787924	−	0.526474i	−0.0952868	−	0.995450i	$-0.530377\pi$
$719$	21.1275	−	14.1170i	0.787924	−	0.526474i	0.883211	+	0.468976i	$0.155377\pi$
$720$	−6.20129	+	6.20163i	−0.231108	+	0.231121i
$721$	−22.6048	−	15.1040i	−0.841845	−	0.562503i
$722$	−22.9789	−	7.27951i	−0.855187	−	0.270915i
$723$	−12.5193	−	11.3469i	−0.465599	−	0.421994i
$724$	−13.1035	−	10.2258i	−0.486986	−	0.380037i
$725$	−0.794574	−	1.32567i	−0.0295097	−	0.0492340i
$726$	−4.31198	+	5.66742i	−0.160033	+	0.210338i
$727$	−16.1699	−	13.2703i	−0.599709	−	0.492168i	0.284866	−	0.958567i	$-0.408051\pi$
$727$	−16.1699	−	13.2703i	−0.599709	−	0.492168i	−0.884574	+	0.466399i	$0.845551\pi$
$728$	8.39275	+	4.35424i	0.311056	+	0.161379i
$729$	−0.995185	−	0.0980171i	−0.0368587	−	0.00363026i
$730$	−27.9449	−	10.3872i	−1.03429	−	0.384448i
$731$	11.9599	+	13.1958i	0.442355	+	0.488063i
$732$	−1.71313	−	3.40330i	−0.0633193	−	0.125790i
$733$	−33.3023	+	24.6987i	−1.23005	+	0.912266i	−0.998170	−	0.0604783i	$-0.980737\pi$
$733$	−33.3023	+	24.6987i	−1.23005	+	0.912266i	−0.231879	+	0.972745i	$0.574487\pi$
$734$	−4.96390	+	23.4484i	−0.183221	+	0.865498i
$735$	−8.14401	+	3.37336i	−0.300396	+	0.124428i
$736$	10.0438	+	3.73300i	0.370220	+	0.137600i
$737$	0.107604	+	0.0445708i	0.00396363	+	0.00164179i
$738$	3.05111	−	4.44725i	0.112313	−	0.163706i
$739$	4.13071	−	27.8470i	0.151951	−	1.02437i	−0.770273	−	0.637714i	$-0.779880\pi$
$739$	4.13071	−	27.8470i	0.151951	−	1.02437i	0.922224	−	0.386655i	$-0.126370\pi$
$740$	−4.79206	−	17.3153i	−0.176160	−	0.636525i
$741$	0.0690964	−	1.40649i	0.00253832	−	0.0516687i
$742$	0.156955	+	4.26056i	0.00576200	+	0.156410i
$743$	22.4044	−	18.3868i	0.821936	−	0.674546i	−0.126342	−	0.991987i	$-0.540324\pi$
$743$	22.4044	−	18.3868i	0.821936	−	0.674546i	0.948278	+	0.317441i	$0.102824\pi$
$744$	1.58177	−	2.43147i	0.0579906	−	0.0891419i
$745$	−3.29035	−	33.4075i	−0.120549	−	1.22396i
$746$	26.5811	+	45.6072i	0.973203	+	1.66980i
$747$	6.34687	+	1.58981i	0.232220	+	0.0581680i
$748$	−24.8736	+	8.21752i	−0.909470	+	0.300462i
$749$	0.870615	+	17.7218i	0.0318116	+	0.647539i
$750$	−16.0419	+	1.38156i	−0.585767	+	0.0504473i
$751$	7.60785	−	1.51329i	0.277614	−	0.0552209i	−0.0543195	−	0.998524i	$-0.517299\pi$
$751$	7.60785	−	1.51329i	0.277614	−	0.0552209i	0.331934	+	0.943303i	$0.392299\pi$
$752$	−25.8569	+	34.8661i	−0.942906	+	1.27143i
$753$	−2.55299	−	0.507821i	−0.0930360	−	0.0185060i
$754$	1.25860	−	11.3499i	0.0458355	−	0.413338i
$755$	−36.2278	+	17.1345i	−1.31847	+	0.623588i
$756$	−3.55199	+	5.60938i	−0.129185	+	0.204011i
$757$	−18.4954	+	24.9382i	−0.672227	+	0.906393i	−0.999254	−	0.0386219i	$-0.987703\pi$
$757$	−18.4954	+	24.9382i	−0.672227	+	0.906393i	0.327027	+	0.945015i	$0.393953\pi$
$758$	1.00211	−	16.3131i	0.0363982	−	0.592520i
$759$	2.18069	+	4.07979i	0.0791541	+	0.148087i
$760$	6.35369	−	5.90252i	0.230473	−	0.214107i
$761$	8.16749	−	2.47758i	0.296071	−	0.0898122i	−0.138755	−	0.990327i	$-0.544310\pi$
$761$	8.16749	−	2.47758i	0.296071	−	0.0898122i	0.434826	+	0.900515i	$0.356810\pi$
$762$	13.2653	−	9.58826i	0.480550	−	0.347346i
$763$	4.04477	−	1.44724i	0.146431	−	0.0523937i
$764$	−14.1145	−	0.346297i	−0.510644	−	0.0125286i
$765$	10.0859	+	6.04527i	0.364657	+	0.218567i
$766$	−21.1071	+	49.2401i	−0.762630	+	1.77912i
$767$	8.79424			0.317541
$768$	12.8518	+	9.53048i	0.463751	+	0.343902i
$769$	−18.2613			−0.658519			−0.329260	−	0.944239i	$-0.606799\pi$
$769$	−18.2613			−0.658519			−0.329260	+	0.944239i	$0.606799\pi$
$770$	−9.90445	+	23.1058i	−0.356932	+	0.832674i
$771$	−18.2271	−	10.9249i	−0.656434	−	0.393451i
$772$	−1.25105	+	50.9906i	−0.0450261	+	1.83519i
$773$	−5.62918	+	2.01415i	−0.202467	+	0.0724440i	−0.436171	−	0.899864i	$-0.643666\pi$
$773$	−5.62918	+	2.01415i	−0.202467	+	0.0724440i	0.233703	+	0.972308i	$0.424916\pi$
$774$	3.80602	−	2.75103i	0.136805	−	0.0988837i
$775$	0.189154	−	0.0573792i	0.00679460	−	0.00206112i
$776$	11.3232	+	0.416823i	0.406478	+	0.0149631i
$777$	−6.41157	−	11.9952i	−0.230014	−	0.430325i
$778$	−0.510538	+	8.31097i	−0.0183037	+	0.297963i
$779$	−3.17691	+	4.28357i	−0.113825	+	0.153475i
$780$	−3.73063	−	2.36233i	−0.133578	−	0.0845848i
$781$	−18.3467	+	8.67734i	−0.656496	+	0.310500i
$782$	1.58342	−	14.2790i	0.0566229	−	0.510618i
$783$	7.86476	+	1.56440i	0.281064	+	0.0559070i
$784$	8.26807	+	13.7936i	0.295288	+	0.492628i
$785$	−33.0913	+	6.58227i	−1.18108	+	0.234931i
$786$	−4.82432	+	0.415479i	−0.172078	+	0.0148196i
$787$	1.99251	+	40.5585i	0.0710254	+	1.44575i	0.724745	+	0.689017i	$0.241958\pi$
$787$	1.99251	+	40.5585i	0.0710254	+	1.44575i	−0.653719	+	0.756737i	$0.726792\pi$
$788$	−7.98317	−	24.1643i	−0.284389	−	0.860817i
$789$	26.8583	+	6.72765i	0.956180	+	0.239511i
$790$	5.34303	+	9.16745i	0.190097	+	0.326163i
$791$	4.62879	+	46.9969i	0.164581	+	1.67102i
$792$	1.43080	+	6.75786i	0.0508411	+	0.240130i
$793$	1.48292	−	1.21700i	0.0526599	−	0.0432168i
$794$	−1.41996	−	38.5450i	−0.0503925	−	1.36791i
$795$	0.0976991	−	1.98871i	0.00346503	−	0.0705323i
$796$	−27.3555	+	7.57070i	−0.969591	+	0.268336i
$797$	6.89980	−	46.5146i	0.244403	−	1.64763i	−0.425335	−	0.905036i	$-0.639844\pi$
$797$	6.89980	−	46.5146i	0.244403	−	1.64763i	0.669738	−	0.742597i	$-0.266406\pi$
$798$	3.71417	−	5.41372i	0.131480	−	0.191644i
$799$	53.7698	+	22.2722i	1.90224	+	0.787933i
$800$	0.251960	+	1.06079i	0.00890814	+	0.0375047i
$801$	−10.6616	+	4.41618i	−0.376709	+	0.156038i
$802$	6.50058	−	30.7074i	0.229543	−	1.08431i
$803$	−18.8606	+	13.9880i	−0.665577	+	0.493625i
$804$	−0.0851946	+	0.0428848i	−0.00300458	+	0.00151243i
$805$	−9.25878	−	10.2155i	−0.326329	−	0.360049i
$806$	1.36895	+	0.508843i	0.0482193	+	0.0179232i
$807$	−31.0496	−	3.05812i	−1.09300	−	0.107651i
$808$	−3.18509	−	10.0533i	−0.112051	−	0.353673i
$809$	26.6785	+	21.8945i	0.937966	+	0.769769i	0.973283	−	0.229607i	$-0.0737442\pi$
$809$	26.6785	+	21.8945i	0.937966	+	0.769769i	−0.0353172	+	0.999376i	$0.511244\pi$
$810$	1.87751	−	2.46769i	0.0659689	−	0.0867057i
$811$	−13.2152	−	22.0483i	−0.464050	−	0.774221i	0.533379	−	0.845876i	$-0.320922\pi$
$811$	−13.2152	−	22.0483i	−0.464050	−	0.774221i	−0.997429	+	0.0716553i	$0.977172\pi$
$812$	32.7546	−	41.9723i	1.14946	−	1.47294i
$813$	20.0172	+	18.1426i	0.702036	+	0.636288i
$814$	−13.4900	−	4.27352i	−0.472825	−	0.149787i
$815$	44.0381	+	29.4253i	1.54259	+	1.03072i
$816$	8.20895	−	19.8197i	0.287371	−	0.693828i
$817$	−3.86115	+	2.57994i	−0.135084	+	0.0902605i
$818$	−5.44947	−	18.7911i	−0.190536	−	0.657017i
$819$	−3.14745	−	1.12618i	−0.109981	−	0.0393518i
$820$	6.77708	+	15.2883i	0.236666	+	0.533890i
$821$	6.44281	+	43.4339i	0.224856	+	1.51585i	0.748051	+	0.663641i	$0.230990\pi$
$821$	6.44281	+	43.4339i	0.224856	+	1.51585i	−0.523195	+	0.852213i	$0.675260\pi$
$822$	−23.7916	−	11.6118i	−0.829826	−	0.405006i
$823$	2.02595	−	6.67865i	0.0706201	−	0.232803i	−0.914524	−	0.404531i	$-0.867435\pi$
$823$	2.02595	−	6.67865i	0.0706201	−	0.232803i	0.985144	+	0.171728i	$0.0549349\pi$
$824$	11.6632	−	20.0126i	0.406305	−	0.697173i
$825$	−0.221894	+	0.415135i	−0.00772537	+	0.0144531i
$826$	34.9065	+	21.5085i	1.21455	+	0.748375i
$827$	−23.6683	−	11.1943i	−0.823028	−	0.389263i	−0.0308278	−	0.999525i	$-0.509814\pi$
$827$	−23.6683	−	11.1943i	−0.823028	−	0.389263i	−0.792200	+	0.610262i	$0.791064\pi$
$828$	−3.69632	−	0.829984i	−0.128456	−	0.0288439i
$829$	35.8404	−	8.97755i	1.24479	−	0.311803i	0.436023	−	0.899935i	$-0.356387\pi$
$829$	35.8404	−	8.97755i	1.24479	−	0.311803i	0.808765	+	0.588132i	$0.200137\pi$
$830$	−14.5206	+	14.1687i	−0.504017	+	0.491803i
$831$	−3.75259	−	3.75259i	−0.130176	−	0.130176i
$832$	−3.26424	+	7.36482i	−0.113167	+	0.255329i
$833$	15.2467	−	15.2467i	0.528267	−	0.528267i
$834$	0.101992	−	8.31533i	0.00353171	−	0.287936i
$835$	1.80560	+	7.20836i	0.0624854	+	0.249456i
$836$	−1.16786	−	6.73001i	−0.0403914	−	0.232762i
$837$	−0.438480	+	0.927087i	−0.0151561	+	0.0320448i
$838$	−6.70274	−	28.2230i	−0.231542	−	0.974948i
$839$	10.3443	+	5.52916i	0.357126	+	0.190888i	0.640196	−	0.768211i	$-0.278853\pi$
$839$	10.3443	+	5.52916i	0.357126	+	0.190888i	−0.283070	+	0.959099i	$0.591353\pi$
$840$	−9.03018	−	18.5008i	−0.311571	−	0.638340i
$841$	−33.7817	−	10.2476i	−1.16489	−	0.353365i
$842$	19.7684	−	6.80092i	0.681263	−	0.234375i
$843$	24.0613	−	3.56916i	0.828716	−	0.122928i
$844$	−1.27156	−	51.7686i	−0.0437690	−	1.78195i
$845$	−8.85342	+	24.7437i	−0.304567	+	0.851207i
$846$	7.39994	−	13.4450i	0.254415	−	0.462250i
$847$	−9.28715	−	13.8992i	−0.319110	−	0.477582i
$848$	−3.61501	+	0.356147i	−0.124140	+	0.0122302i
$849$	−4.43097	+	6.63142i	−0.152071	+	0.227590i
$850$	1.29760	−	0.673250i	0.0445072	−	0.0230923i
$851$	5.21175	−	5.75028i	0.178656	−	0.197117i
$852$	4.43262	−	16.0183i	0.151859	−	0.548777i
$853$	24.7027	−	14.8062i	0.845804	−	0.506956i	−0.0243681	−	0.999703i	$-0.507757\pi$
$853$	24.7027	−	14.8062i	0.845804	−	0.506956i	0.870172	+	0.492747i	$0.164007\pi$
$854$	8.86253	−	1.20374i	0.303269	−	0.0411911i
$855$	−1.94513	+	2.37015i	−0.0665221	+	0.0810574i
$856$	−15.0252	+	1.66658i	−0.513551	+	0.0569625i
$857$	−3.14141	+	31.8952i	−0.107308	+	1.08952i	0.779190	+	0.626788i	$0.215631\pi$
$857$	−3.14141	+	31.8952i	−0.107308	+	1.08952i	−0.886498	+	0.462732i	$0.846869\pi$
$858$	−3.16201	+	1.44833i	−0.107949	+	0.0494452i
$859$	22.2724	−	20.1865i	0.759923	−	0.688755i	−0.196576	−	0.980489i	$-0.562982\pi$
$859$	22.2724	−	20.1865i	0.759923	−	0.688755i	0.956499	+	0.291734i	$0.0942322\pi$
$860$	1.07141	+	14.5221i	0.0365349	+	0.495198i
$861$	7.54160	+	10.1687i	0.257017	+	0.346547i
$862$	34.7152	−	22.5850i	1.18240	−	0.769250i
$863$	10.7774	+	26.0190i	0.366867	+	0.885696i	0.994260	+	0.106993i	$0.0341223\pi$
$863$	10.7774	+	26.0190i	0.366867	+	0.885696i	−0.627392	+	0.778703i	$0.715878\pi$
$864$	−4.95589	−	2.72747i	−0.168603	−	0.0927905i
$865$	5.07672	−	12.2563i	0.172614	−	0.416727i
$866$	−5.72624	−	30.7544i	−0.194586	−	1.04508i
$867$	−11.6356	−	1.72598i	−0.395167	−	0.0586174i
$868$	4.18922	+	5.36784i	0.142191	+	0.182196i
$869$	8.34737	+	0.410080i	0.283165	+	0.0139110i
$870$	−16.9225	+	18.2170i	−0.573727	+	0.617615i
$871$	−0.0304650	−	0.0371218i	−0.00103227	−	0.00125782i
$872$	1.44214	+	3.36406i	0.0488370	+	0.113922i
$873$	−3.98677	+	0.392662i	−0.134932	+	0.0132896i
$874$	3.62238	+	0.954724i	0.122529	+	0.0322940i
$875$	9.18366	−	36.6632i	0.310464	−	1.23944i
$876$	1.41436	−	19.1776i	0.0477867	−	0.647950i
$877$	24.5154	−	1.20436i	0.827825	−	0.0406684i	0.369256	−	0.929328i	$-0.379612\pi$
$877$	24.5154	−	1.20436i	0.827825	−	0.0406684i	0.458568	+	0.888659i	$0.348362\pi$
$878$	−27.1022	−	22.8041i	−0.914654	−	0.769603i
$879$	2.64272	+	13.2859i	0.0891368	+	0.448121i
$880$	−20.1669	−	7.21522i	−0.679828	−	0.243225i
$881$	−4.56506	+	22.9501i	−0.153801	+	0.773209i	0.824475	+	0.565899i	$0.191471\pi$
$881$	−4.56506	+	22.9501i	−0.153801	+	0.773209i	−0.978275	+	0.207310i	$0.933529\pi$
$882$	−3.55284	−	4.43907i	−0.119630	−	0.149471i
$883$	1.93385	+	4.08879i	0.0650794	+	0.137599i	0.933907	−	0.357516i	$-0.116376\pi$
$883$	1.93385	+	4.08879i	0.0650794	+	0.137599i	−0.868828	+	0.495114i	$0.835126\pi$
$884$	10.6420	+	1.84642i	0.357931	+	0.0621018i
$885$	−15.3800	−	11.4066i	−0.516993	−	0.383428i
$886$	−1.98692	+	1.75694i	−0.0667520	+	0.0590255i
$887$	21.9183	−	11.7156i	0.735946	−	0.393371i	−0.0604305	−	0.998172i	$-0.519247\pi$
$887$	21.9183	−	11.7156i	0.735946	−	0.393371i	0.796377	+	0.604801i	$0.206747\pi$
$888$	9.86571	−	6.07935i	0.331071	−	0.204010i
$889$	11.1531	+	36.7669i	0.374064	+	1.23312i
$890$	5.68410	−	35.3282i	0.190532	−	1.18420i
$891$	−0.822762	−	2.29947i	−0.0275636	−	0.0770350i
$892$	−32.1825	−	14.2650i	−1.07755	−	0.477628i
$893$	−7.80185	+	13.0166i	−0.261079	+	0.435584i
$894$	20.1043	−	8.04005i	0.672390	−	0.268900i
$895$		−	48.9673i		−	1.63680i
$896$	−30.9691	+	21.2494i	−1.03460	+	0.709891i
$897$		−	1.90739i		−	0.0636860i
$898$	−19.5075	−	48.7789i	−0.650973	−	1.62777i
$899$	4.22784	−	7.05373i	0.141006	−	0.235255i
$900$	−0.138738	−	0.359649i	−0.00462459	−	0.0119883i
$901$	1.64078	+	4.58568i	0.0546624	+	0.152771i
$902$	13.0043	+	2.09233i	0.432997	+	0.0696668i
$903$	3.20002	+	10.5490i	0.106490	+	0.351050i
$904$	−39.7246	+	6.39259i	−1.32122	+	0.212614i
$905$	−16.0699	+	8.58953i	−0.534181	+	0.285526i
$906$	−17.1230	−	19.3644i	−0.568873	−	0.643338i
$907$	2.41099	+	1.78811i	0.0800555	+	0.0593732i	0.634987	−	0.772523i	$-0.281005\pi$
$907$	2.41099	+	1.78811i	0.0800555	+	0.0593732i	−0.554931	+	0.831896i	$0.687255\pi$
$908$	27.5701	−	19.4176i	0.914945	−	0.644396i
$909$	1.59414	+	3.37052i	0.0528742	+	0.111793i
$910$	8.09253	−	6.47691i	0.268265	−	0.214708i
$911$	−6.80013	+	34.1866i	−0.225298	+	1.13265i	0.688110	+	0.725607i	$0.258441\pi$
$911$	−6.80013	+	34.1866i	−0.225298	+	1.13265i	−0.913408	+	0.407045i	$0.866559\pi$
$912$	4.79798	+	2.87562i	0.158877	+	0.0952213i
$913$	3.11743	+	15.6724i	0.103172	+	0.518679i
$914$	−26.6184	+	31.6353i	−0.880458	+	1.04640i
$915$	−4.17194	+	0.204954i	−0.137920	+	0.00677557i
$916$	−3.84096	+	3.31332i	−0.126909	+	0.109475i
$917$	2.76182	−	11.0258i	0.0912035	−	0.364105i
$918$	−1.93300	+	7.33413i	−0.0637985	+	0.242062i
$919$	25.8347	−	2.54450i	0.852210	−	0.0839353i	0.337527	−	0.941316i	$-0.390410\pi$
$919$	25.8347	−	2.54450i	0.852210	−	0.0839353i	0.514683	+	0.857381i	$0.327910\pi$
$920$	8.20343	−	8.40763i	0.270459	−	0.277191i
$921$	16.1982	+	19.7376i	0.533749	+	0.650375i
$922$	21.4364	+	19.9132i	0.705971	+	0.655805i
$923$	8.35801	+	0.410603i	0.275107	+	0.0135152i
$924$	−16.0931	−	1.98466i	−0.529423	−	0.0652906i
$925$	0.781132	+	0.115870i	0.0256835	+	0.00380978i
$926$	32.1361	−	5.98351i	1.05606	−	0.196630i
$927$	−3.13396	+	7.56605i	−0.102933	+	0.248502i
$928$	37.4054	+	25.6611i	1.22789	+	0.842367i
$929$	9.58232	+	23.1338i	0.314386	+	0.758995i	0.999532	+	0.0305890i	$0.00973830\pi$
$929$	9.58232	+	23.1338i	0.314386	+	0.758995i	−0.685146	+	0.728406i	$0.740262\pi$
$930$	−1.73413	−	2.66551i	−0.0568643	−	0.0874054i
$931$	3.34921	+	4.51589i	0.109766	+	0.148002i
$932$	5.28165	−	6.12307i	0.173006	−	0.200568i
$933$	2.83138	−	2.56621i	0.0926953	−	0.0840141i
$934$	−18.0036	−	39.3056i	−0.589097	−	1.28612i
$935$	−2.81484	+	28.5796i	−0.0920552	+	0.934652i
$936$	0.793211	−	2.73547i	0.0259269	−	0.0894117i
$937$	−9.40573	+	11.4609i	−0.307272	+	0.374412i	−0.903635	−	0.428303i	$-0.859112\pi$
$937$	−9.40573	+	11.4609i	−0.307272	+	0.374412i	0.596364	+	0.802714i	$0.296612\pi$
$938$	−0.0301331	−	0.221855i	−0.000983881	−	0.00724383i
$939$	−20.9369	+	12.5491i	−0.683251	+	0.409525i
$940$	23.4559	+	41.4042i	0.765048	+	1.35046i
$941$	32.6433	−	36.0163i	1.06414	−	1.17410i	0.0799829	−	0.996796i	$-0.474513\pi$
$941$	32.6433	−	36.0163i	1.06414	−	1.17410i	0.984157	−	0.177301i	$-0.0567366\pi$
$942$	−10.0225	−	19.3171i	−0.326552	−	0.629384i
$943$	−4.01326	+	6.00627i	−0.130690	+	0.195591i
$944$	−16.4666	+	30.8089i	−0.535942	+	1.00274i
$945$	4.04378	+	6.05194i	0.131544	+	0.196870i
$946$	10.0478	+	5.53015i	0.326682	+	0.179801i
$947$	2.39787	−	6.70161i	0.0779204	−	0.217773i	−0.896266	−	0.443516i	$-0.853731\pi$
$947$	2.39787	−	6.70161i	0.0779204	−	0.217773i	0.974187	+	0.225743i	$0.0724810\pi$
$948$	−4.71922	+	4.95689i	−0.153273	+	0.160992i
$949$	9.57710	−	1.42063i	0.310886	−	0.0461155i
$950$	0.124004	+	0.360445i	0.00402322	+	0.0116944i
$951$	32.4506	+	9.84377i	1.05228	+	0.319206i
$952$	37.7251	+	33.3566i	1.22268	+	1.08109i
$953$	−17.9938	−	9.61790i	−0.582877	−	0.311554i	0.153475	−	0.988152i	$-0.450953\pi$
$953$	−17.9938	−	9.61790i	−0.582877	−	0.311554i	−0.736352	+	0.676598i	$0.763453\pi$
$954$	1.24953	−	0.296753i	0.0404550	−	0.00960774i
$955$	−6.61769	+	13.9919i	−0.214144	+	0.452768i
$956$	12.3820	+	8.72013i	0.400462	+	0.282029i
$957$	4.75849	+	18.9970i	0.153820	+	0.614084i
$958$	−40.5558	−	0.497440i	−1.31030	−	0.0160715i
$959$	43.9429	−	43.9429i	1.41899	−	1.41899i
$960$	15.2613	−	8.64625i	0.492556	−	0.279056i
$961$	−21.1766	−	21.1766i	−0.683116	−	0.683116i
$962$	4.07478	+	4.17598i	0.131376	+	0.134639i
$963$	5.18462	−	1.29868i	0.167072	−	0.0418493i
$964$	18.0794	+	28.5496i	0.582297	+	0.919519i
$965$	50.5479	+	23.9074i	1.62719	+	0.769605i
$966$	4.66499	−	7.57092i	0.150094	−	0.243590i
$967$	−4.48942	+	8.39912i	−0.144370	+	0.270097i	−0.943705	−	0.330788i	$-0.892685\pi$
$967$	−4.48942	+	8.39912i	−0.144370	+	0.270097i	0.799335	+	0.600886i	$0.205185\pi$
$968$	11.3346	−	8.62428i	0.364308	−	0.277195i
$969$	2.17712	−	7.17700i	0.0699392	−	0.230558i
$970$	5.44828	−	11.1631i	0.174934	−	0.358426i
$971$	−6.22720	−	41.9803i	−0.199840	−	1.34721i	−0.824299	−	0.566155i	$-0.808430\pi$
$971$	−6.22720	−	41.9803i	−0.199840	−	1.34721i	0.624458	−	0.781058i	$-0.285320\pi$
$972$	1.86600	+	0.719764i	0.0598518	+	0.0230865i
$973$	18.3797	+	6.57635i	0.589225	+	0.210828i
$974$	−33.4065	+	9.68795i	−1.07041	+	0.310422i
$975$	0.161376	−	0.107828i	0.00516815	−	0.00345325i
$976$	1.48685	+	7.47384i	0.0475930	+	0.239232i
$977$	36.5116	+	24.3963i	1.16811	+	0.780505i	0.979480	−	0.201543i	$-0.0645956\pi$
$977$	36.5116	+	24.3963i	1.16811	+	0.780505i	0.188629	+	0.982048i	$0.439596\pi$
$978$	−10.3170	+	32.5673i	−0.329902	+	1.04139i
$979$	−20.8825	−	18.9268i	−0.667409	−	0.604904i
$980$	17.4974	−	2.15834i	0.558934	−	0.0689458i
$981$	−0.665279	−	1.10995i	−0.0212407	−	0.0354380i
$982$	−45.5388	−	34.6476i	−1.45320	−	1.10565i
$983$	25.1352	+	20.6279i	0.801689	+	0.657929i	0.943281	−	0.331996i	$-0.107722\pi$
$983$	25.1352	+	20.6279i	0.801689	+	0.657929i	−0.141592	+	0.989925i	$0.545222\pi$
$984$	−8.25336	+	6.94488i	−0.263107	+	0.221395i
$985$	−27.7645	−	2.73457i	−0.884651	−	0.0871306i
$986$	21.1903	−	57.0087i	0.674836	−	1.81553i
$987$	24.1930	+	26.6929i	0.770072	+	0.849644i
$988$	−0.883408	+	2.67424i	−0.0281049	+	0.0850788i
$989$	−5.05217	+	3.74694i	−0.160650	+	0.119146i
$990$	7.40851	+	1.56834i	0.235458	+	0.0498451i
$991$	8.41620	−	3.48611i	0.267350	−	0.110740i	−0.244982	−	0.969528i	$-0.578782\pi$
$991$	8.41620	−	3.48611i	0.267350	−	0.110740i	0.512331	+	0.858788i	$0.328782\pi$
$992$	−4.34590	+	3.84308i	−0.137983	+	0.122018i
$993$	−11.3762	−	4.71217i	−0.361012	−	0.149536i
$994$	32.1708	+	22.0713i	1.02040	+	0.700061i
$995$	−4.56572	+	30.7796i	−0.144743	+	0.975779i
$996$	−11.3860	−	6.44986i	−0.360778	−	0.204372i
$997$	1.04037	−	21.1772i	0.0329489	−	0.670690i	−0.924342	−	0.381564i	$-0.875385\pi$
$997$	1.04037	−	21.1772i	0.0329489	−	0.670690i	0.957291	−	0.289126i	$-0.0933645\pi$
$998$	35.5553	−	1.30982i	1.12548	−	0.0414617i
$999$	−3.16711	+	2.59918i	−0.100203	+	0.0822344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.421.7	yes	2048
256.45	even	64	inner	768.2.z.a.301.7	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.301.7	✓	2048	256.45	even	64	inner
768.2.z.a.421.7	yes	2048	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29983 - 0.557180i) q^{2} +(-0.857729 - 0.514103i) q^{3} +(1.37910 + 1.44848i) q^{4} +(2.06438 - 0.738647i) q^{5} +(0.828451 + 1.14615i) q^{6} +(-3.17676 + 0.963660i) q^{7} +(-0.985532 - 2.65117i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(-1.29983 - 0.557180i) q^{2} +(-0.857729 - 0.514103i) q^{3} +(1.37910 + 1.44848i) q^{4} +(2.06438 - 0.738647i) q^{5} +(0.828451 + 1.14615i) q^{6} +(-3.17676 + 0.963660i) q^{7} +(-0.985532 - 2.65117i) q^{8} +(0.471397 + 0.881921i) q^{9} +(-3.09489 - 0.190118i) q^{10} +(-1.45483 + 1.96162i) q^{11} +(-0.438229 - 1.95140i) q^{12} +(0.910294 - 0.430537i) q^{13} +(4.66617 + 0.517436i) q^{14} +(-2.15042 - 0.427745i) q^{15} +(-0.196161 + 3.99519i) q^{16} +(5.26006 - 1.04629i) q^{17} +(-0.121345 - 1.40900i) q^{18} +(0.0686178 + 1.39675i) q^{19} +(3.91690 + 1.97153i) q^{20} +(3.22022 + 0.806623i) q^{21} +(2.98401 - 1.73916i) q^{22} +(0.185662 + 1.88506i) q^{23} +(-0.517658 + 2.78065i) q^{24} +(-0.148990 + 0.122273i) q^{25} +(-1.42311 + 0.0524261i) q^{26} +(0.0490677 - 0.998795i) q^{27} +(-5.77691 - 3.27247i) q^{28} +(-1.17661 + 7.93205i) q^{29} +(2.55684 + 1.75416i) q^{30} +(-0.947486 - 0.392461i) q^{31} +(2.48101 - 5.08376i) q^{32} +(2.25633 - 0.934601i) q^{33} +(-7.42014 - 1.57080i) q^{34} +(-5.84623 + 4.33586i) q^{35} +(-0.627337 + 1.89906i) q^{36} +(-2.75145 - 3.03576i) q^{37} +(0.689049 - 1.85376i) q^{38} +(-1.00213 - 0.0987008i) q^{39} +(-3.99279 - 4.74507i) q^{40} +(2.94796 + 2.41933i) q^{41} +(-3.73629 - 2.84271i) q^{42} +(1.70718 + 2.84825i) q^{43} +(-4.84772 + 0.597977i) q^{44} +(1.62457 + 1.47242i) q^{45} +(0.808989 - 2.55370i) q^{46} +(9.02304 + 6.02900i) q^{47} +(2.22219 - 3.32594i) q^{48} +(3.34288 - 2.23364i) q^{49} +(0.261790 - 0.0759196i) q^{50} +(-5.04960 - 1.80678i) q^{51} +(1.87901 + 0.724784i) q^{52} +(0.133250 + 0.898298i) q^{53} +(-0.620288 + 1.27092i) q^{54} +(-1.55439 + 5.12413i) q^{55} +(5.68563 + 7.47243i) q^{56} +(0.659216 - 1.23331i) q^{57} +(5.94897 - 9.65471i) q^{58} +(7.89483 + 3.73398i) q^{59} +(-2.34607 - 3.70473i) q^{60} +(1.84798 - 0.462896i) q^{61} +(1.01290 + 1.03805i) q^{62} +(-2.34739 - 2.34739i) q^{63} +(-6.05745 + 5.22563i) q^{64} +(1.56118 - 1.56118i) q^{65} +(-3.45357 - 0.0423601i) q^{66} +(-0.0115877 - 0.0462605i) q^{67} +(8.76968 + 6.17612i) q^{68} +(0.809867 - 1.71232i) q^{69} +(10.0149 - 2.37847i) q^{70} +(7.32888 + 3.91737i) q^{71} +(1.87355 - 2.11892i) q^{72} +(9.20082 + 2.79104i) q^{73} +(1.88495 + 5.47902i) q^{74} +(0.190654 - 0.0282809i) q^{75} +(-1.92852 + 2.02565i) q^{76} +(2.73133 - 7.63355i) q^{77} +(1.24760 + 0.686658i) q^{78} +(-1.90119 - 2.84533i) q^{79} +(2.54608 + 8.39247i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(-2.48384 - 4.78726i) q^{82} +(4.39398 - 4.84801i) q^{83} +(3.27263 + 5.77682i) q^{84} +(10.0859 - 6.04527i) q^{85} +(-0.632045 - 4.65344i) q^{86} +(5.08710 - 6.19865i) q^{87} +(6.63438 + 1.92378i) q^{88} +(-1.13112 + 11.4845i) q^{89} +(-1.29125 - 2.81907i) q^{90} +(-2.47690 + 2.24493i) q^{91} +(-2.47442 + 2.86861i) q^{92} +(0.610920 + 0.823730i) q^{93} +(-8.36915 - 12.8641i) q^{94} +(1.17336 + 2.83273i) q^{95} +(-4.74161 + 3.08499i) q^{96} +(-1.53305 + 3.70111i) q^{97} +(-5.58970 + 1.04076i) q^{98} +(-2.41580 - 0.358350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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