LMFDB - Embedded newform 504.2.be.a.475.81

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(139,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("504.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			475.81
Character	$\chi$	$=$	504.475
Dual form			504.2.be.a.139.81

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30332 + 0.548965i) q^{2} +(-1.71594 - 0.235665i) q^{3} +(1.39728 + 1.43095i) q^{4} +(-0.892228 - 1.54538i) q^{5} +(-2.10705 - 1.24914i) q^{6} +(-2.64346 - 0.110098i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 + 0.808775i) q^{9} +O(q^{10})$	\(q+(1.30332 + 0.548965i) q^{2} +(-1.71594 - 0.235665i) q^{3} +(1.39728 + 1.43095i) q^{4} +(-0.892228 - 1.54538i) q^{5} +(-2.10705 - 1.24914i) q^{6} +(-2.64346 - 0.110098i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 + 0.808775i) q^{9} +(-0.314496 - 2.50393i) q^{10} +(-2.86592 + 4.96393i) q^{11} +(-2.06042 - 2.78472i) q^{12} +(3.26020 + 5.64683i) q^{13} +(-3.38483 - 1.59466i) q^{14} +(1.16682 + 2.86206i) q^{15} +(-0.0952399 + 3.99887i) q^{16} +2.13328i q^{17} +(3.32120 + 2.64001i) q^{18} +3.59936i q^{19} +(0.964680 - 3.43606i) q^{20} +(4.51008 + 0.811892i) q^{21} +(-6.46023 + 4.89629i) q^{22} +(3.94496 - 2.27763i) q^{23} +(-1.15667 - 4.76047i) q^{24} +(0.907857 - 1.57245i) q^{25} +(1.14917 + 9.14935i) q^{26} +(-4.76663 - 2.06863i) q^{27} +(-3.53610 - 3.93650i) q^{28} +(-5.45171 - 3.14755i) q^{29} +(-0.0504307 + 4.37072i) q^{30} +(-2.00268 - 3.46875i) q^{31} +(-2.31936 + 5.15951i) q^{32} +(6.08759 - 7.84242i) q^{33} +(-1.17109 + 2.78034i) q^{34} +(2.18843 + 4.18339i) q^{35} +(2.87931 + 5.26399i) q^{36} -0.505819i q^{37} +(-1.97592 + 4.69111i) q^{38} +(-4.26356 - 10.4580i) q^{39} +(3.14356 - 3.94871i) q^{40} +(-5.60580 + 3.23651i) q^{41} +(5.43237 + 3.53403i) q^{42} +(-1.61781 + 2.80212i) q^{43} +(-11.1076 + 2.83498i) q^{44} +(-1.32771 - 5.18611i) q^{45} +(6.39188 - 0.802826i) q^{46} +(2.33909 - 4.05142i) q^{47} +(1.10582 - 6.83938i) q^{48} +(6.97576 + 0.582079i) q^{49} +(2.04645 - 1.55103i) q^{50} +(0.502738 - 3.66058i) q^{51} +(-3.52494 + 12.5554i) q^{52} -0.827775i q^{53} +(-5.07683 - 5.31279i) q^{54} +10.2282 q^{55} +(-2.44766 - 7.07170i) q^{56} +(0.848242 - 6.17629i) q^{57} +(-5.37742 - 7.09505i) q^{58} +(-0.346079 + 0.199809i) q^{59} +(-2.46510 + 5.66875i) q^{60} +(3.66024 - 6.33971i) q^{61} +(-0.705912 - 5.62028i) q^{62} +(-7.54771 - 2.45603i) q^{63} +(-5.85526 + 5.45124i) q^{64} +(5.81768 - 10.0765i) q^{65} +(12.2393 - 6.87930i) q^{66} +(3.40363 + 5.89527i) q^{67} +(-3.05262 + 2.98078i) q^{68} +(-7.30609 + 2.97859i) q^{69} +(0.555680 + 6.65366i) q^{70} +1.96610i q^{71} +(0.862910 + 8.44129i) q^{72} +14.3518i q^{73} +(0.277676 - 0.659243i) q^{74} +(-1.92840 + 2.48429i) q^{75} +(-5.15050 + 5.02930i) q^{76} +(8.12247 - 12.8064i) q^{77} +(0.184274 - 15.9706i) q^{78} +(2.17052 + 1.25315i) q^{79} +(6.26476 - 3.42072i) q^{80} +(7.69177 + 4.67298i) q^{81} +(-9.08287 + 1.14082i) q^{82} +(-0.533641 - 0.308098i) q^{83} +(5.14005 + 7.58814i) q^{84} +(3.29674 - 1.90337i) q^{85} +(-3.64678 + 2.76394i) q^{86} +(8.61307 + 6.68579i) q^{87} +(-16.0331 - 2.40281i) q^{88} -7.91828i q^{89} +(1.11656 - 7.48802i) q^{90} +(-7.99650 - 15.2861i) q^{91} +(8.77137 + 2.46258i) q^{92} +(2.61903 + 6.42413i) q^{93} +(5.27266 - 3.99621i) q^{94} +(5.56239 - 3.21145i) q^{95} +(5.19581 - 8.30684i) q^{96} +(14.0224 + 8.09583i) q^{97} +(8.77209 + 4.58808i) q^{98} +(-12.2941 + 12.0225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.30332	+	0.548965i	0.921585	+	0.388177i
$2$	1.30332	+	0.548965i	0.921585	+	0.388177i
$3$	−1.71594	−	0.235665i	−0.990700	−	0.136061i
$3$	−1.71594	−	0.235665i	−0.990700	−	0.136061i
$4$	1.39728	+	1.43095i	0.698638	+	0.715475i
$5$	−0.892228	−	1.54538i	−0.399017	−	0.691117i	0.594588	−	0.804030i	$-0.297315\pi$
$5$	−0.892228	−	1.54538i	−0.399017	−	0.691117i	−0.993605	+	0.112913i	$0.963982\pi$
$6$	−2.10705	−	1.24914i	−0.860199	−	0.509959i
$7$	−2.64346	−	0.110098i	−0.999134	−	0.0416131i
$7$	−2.64346	−	0.110098i	−0.999134	−	0.0416131i
$8$	1.03555	+	2.63204i	0.366124	+	0.930566i
$9$	2.88892	+	0.808775i	0.962975	+	0.269592i
$10$	−0.314496	−	2.50393i	−0.0994523	−	0.791812i
$11$	−2.86592	+	4.96393i	−0.864109	+	1.49668i	0.00382055	+	0.999993i	$0.498784\pi$
$11$	−2.86592	+	4.96393i	−0.864109	+	1.49668i	−0.867929	+	0.496688i	$0.834549\pi$
$12$	−2.06042	−	2.78472i	−0.594793	−	0.803879i
$13$	3.26020	+	5.64683i	0.904216	+	1.56615i	0.821966	+	0.569537i	$0.192877\pi$
$13$	3.26020	+	5.64683i	0.904216	+	1.56615i	0.0822504	+	0.996612i	$0.473789\pi$
$14$	−3.38483	−	1.59466i	−0.904634	−	0.426190i
$15$	1.16682	+	2.86206i	0.301272	+	0.738981i
$16$	−0.0952399	+	3.99887i	−0.0238100	+	0.999717i
$17$			2.13328i			0.517396i	0.965958	+	0.258698i	$0.0832934\pi$
$17$			2.13328i			0.517396i	−0.965958	+	0.258698i	$0.916707\pi$
$18$	3.32120	+	2.64001i	0.782814	+	0.622256i
$19$			3.59936i			0.825749i	0.910788	+	0.412875i	$0.135475\pi$
$19$			3.59936i			0.825749i	−0.910788	+	0.412875i	$0.864525\pi$
$20$	0.964680	−	3.43606i	0.215709	−	0.768327i
$21$	4.51008	+	0.811892i	0.984180	+	0.177169i
$22$	−6.46023	+	4.89629i	−1.37733	+	1.04389i
$23$	3.94496	−	2.27763i	0.822582	−	0.474918i	−0.0287242	−	0.999587i	$-0.509144\pi$
$23$	3.94496	−	2.27763i	0.822582	−	0.474918i	0.851306	+	0.524670i	$0.175811\pi$
$24$	−1.15667	−	4.76047i	−0.236105	−	0.971728i
$25$	0.907857	−	1.57245i	0.181571	−	0.314491i
$26$	1.14917	+	9.14935i	0.225370	+	1.79433i
$27$	−4.76663	−	2.06863i	−0.917339	−	0.398108i
$28$	−3.53610	−	3.93650i	−0.668260	−	0.743928i
$29$	−5.45171	−	3.14755i	−1.01236	−	0.584485i	−0.100477	−	0.994939i	$-0.532037\pi$
$29$	−5.45171	−	3.14755i	−1.01236	−	0.584485i	−0.911881	+	0.410454i	$0.865370\pi$
$30$	−0.0504307	+	4.37072i	−0.00920735	+	0.797980i
$31$	−2.00268	−	3.46875i	−0.359692	−	0.623005i	0.628217	−	0.778038i	$-0.283785\pi$
$31$	−2.00268	−	3.46875i	−0.359692	−	0.623005i	−0.987909	+	0.155033i	$0.950452\pi$
$32$	−2.31936	+	5.15951i	−0.410009	+	0.912081i
$33$	6.08759	−	7.84242i	1.05971	−	1.36519i
$34$	−1.17109	+	2.78034i	−0.200841	+	0.476824i
$35$	2.18843	+	4.18339i	0.369911	+	0.707123i
$36$	2.87931	+	5.26399i	0.479885	+	0.877332i
$37$		−	0.505819i		−	0.0831561i	−0.999135	−	0.0415780i	$-0.986761\pi$
$37$		−	0.505819i		−	0.0831561i	0.999135	−	0.0415780i	$-0.0132385\pi$
$38$	−1.97592	+	4.69111i	−0.320536	+	0.760998i
$39$	−4.26356	−	10.4580i	−0.682716	−	1.67461i
$40$	3.14356	−	3.94871i	0.497041	−	0.624346i
$41$	−5.60580	+	3.23651i	−0.875479	+	0.505458i	−0.869165	−	0.494522i	$-0.835343\pi$
$41$	−5.60580	+	3.23651i	−0.875479	+	0.505458i	−0.00631369	+	0.999980i	$0.502010\pi$
$42$	5.43237	+	3.53403i	0.838233	+	0.545312i
$43$	−1.61781	+	2.80212i	−0.246713	+	0.427320i	−0.962612	−	0.270884i	$-0.912684\pi$
$43$	−1.61781	+	2.80212i	−0.246713	+	0.427320i	0.715899	+	0.698204i	$0.246017\pi$
$44$	−11.1076	+	2.83498i	−1.67454	+	0.427389i
$45$	−1.32771	−	5.18611i	−0.197924	−	0.773100i
$46$	6.39188	−	0.802826i	0.942431	−	0.118370i
$47$	2.33909	−	4.05142i	0.341191	−	0.590960i	−0.643463	−	0.765477i	$-0.722503\pi$
$47$	2.33909	−	4.05142i	0.341191	−	0.590960i	0.984654	+	0.174517i	$0.0558365\pi$
$48$	1.10582	−	6.83938i	0.159611	−	0.987180i
$49$	6.97576	+	0.582079i	0.996537	+	0.0831541i
$50$	2.04645	−	1.55103i	0.289411	−	0.219348i
$51$	0.502738	−	3.66058i	0.0703975	−	0.512584i
$52$	−3.52494	+	12.5554i	−0.488821	+	1.74112i
$53$		−	0.827775i		−	0.113704i	−0.998383	−	0.0568518i	$-0.981894\pi$
$53$		−	0.827775i		−	0.113704i	0.998383	−	0.0568518i	$-0.0181063\pi$
$54$	−5.07683	−	5.31279i	−0.690869	−	0.722980i
$55$	10.2282			1.37918
$56$	−2.44766	−	7.07170i	−0.327083	−	0.944996i
$57$	0.848242	−	6.17629i	0.112352	−	0.818070i
$58$	−5.37742	−	7.09505i	−0.706090	−	0.931626i
$59$	−0.346079	+	0.199809i	−0.0450556	+	0.0260129i	−0.522359	−	0.852726i	$-0.674948\pi$
$59$	−0.346079	+	0.199809i	−0.0450556	+	0.0260129i	0.477303	+	0.878739i	$0.341614\pi$
$60$	−2.46510	+	5.66875i	−0.318243	+	0.731833i
$61$	3.66024	−	6.33971i	0.468645	−	0.811717i	−0.530713	−	0.847552i	$-0.678076\pi$
$61$	3.66024	−	6.33971i	0.468645	−	0.811717i	0.999358	+	0.0358346i	$0.0114089\pi$
$62$	−0.705912	−	5.62028i	−0.0896510	−	0.713776i
$63$	−7.54771	−	2.45603i	−0.950922	−	0.309430i
$64$	−5.85526	+	5.45124i	−0.731907	+	0.681404i
$65$	5.81768	−	10.0765i	0.721595	−	1.24984i
$66$	12.2393	−	6.87930i	1.50655	−	0.846783i
$67$	3.40363	+	5.89527i	0.415820	+	0.720221i	0.995514	−	0.0946128i	$-0.0301613\pi$
$67$	3.40363	+	5.89527i	0.415820	+	0.720221i	−0.579694	+	0.814834i	$0.696828\pi$
$68$	−3.05262	+	2.98078i	−0.370184	+	0.361472i
$69$	−7.30609	+	2.97859i	−0.879550	+	0.358580i
$70$	0.555680	+	6.65366i	0.0664164	+	0.795265i
$71$			1.96610i			0.233333i	0.993171	+	0.116667i	$0.0372209\pi$
$71$			1.96610i			0.233333i	−0.993171	+	0.116667i	$0.962779\pi$
$72$	0.862910	+	8.44129i	0.101695	+	0.994816i
$73$			14.3518i			1.67976i	0.542775	+	0.839878i	$0.317374\pi$
$73$			14.3518i			1.67976i	−0.542775	+	0.839878i	$0.682626\pi$
$74$	0.277676	−	0.659243i	0.0322792	−	0.0766354i
$75$	−1.92840	+	2.48429i	−0.222673	+	0.286861i
$76$	−5.15050	+	5.02930i	−0.590803	+	0.576900i
$77$	8.12247	−	12.8064i	0.925642	−	1.45943i
$78$	0.184274	−	15.9706i	0.0208649	−	1.80831i
$79$	2.17052	+	1.25315i	0.244203	+	0.140990i	0.617107	−	0.786879i	$-0.288305\pi$
$79$	2.17052	+	1.25315i	0.244203	+	0.140990i	−0.372904	+	0.927870i	$0.621638\pi$
$80$	6.26476	−	3.42072i	0.700422	−	0.382448i
$81$	7.69177	+	4.67298i	0.854641	+	0.519220i
$82$	−9.08287	+	1.14082i	−1.00303	+	0.125982i
$83$	−0.533641	−	0.308098i	−0.0585747	−	0.0338181i	0.470427	−	0.882439i	$-0.344100\pi$
$83$	−0.533641	−	0.308098i	−0.0585747	−	0.0338181i	−0.529001	+	0.848621i	$0.677433\pi$
$84$	5.14005	+	7.58814i	0.560825	+	0.827934i
$85$	3.29674	−	1.90337i	0.357581	−	0.206450i
$86$	−3.64678	+	2.76394i	−0.393243	+	0.298043i
$87$	8.61307	+	6.68579i	0.923418	+	0.716792i
$88$	−16.0331	−	2.40281i	−1.70913	−	0.256141i
$89$		−	7.91828i		−	0.839336i	−0.907678	−	0.419668i	$-0.862147\pi$
$89$		−	7.91828i		−	0.839336i	0.907678	−	0.419668i	$-0.137853\pi$
$90$	1.11656	−	7.48802i	0.117696	−	0.789307i
$91$	−7.99650	−	15.2861i	−0.838261	−	1.60242i
$92$	8.77137	+	2.46258i	0.914479	+	0.256741i
$93$	2.61903	+	6.42413i	0.271580	+	0.666152i
$94$	5.27266	−	3.99621i	0.543833	−	0.412177i
$95$	5.56239	−	3.21145i	0.570689	−	0.329488i
$96$	5.19581	−	8.30684i	0.530295	−	0.847813i
$97$	14.0224	+	8.09583i	1.42376	+	0.822007i	0.996618	−	0.0821777i	$-0.0261875\pi$
$97$	14.0224	+	8.09583i	1.42376	+	0.822007i	0.427141	+	0.904185i	$0.359521\pi$
$98$	8.77209	+	4.58808i	0.886115	+	0.463466i
$99$	−12.2941	+	12.0225i	−1.23561	+	1.20831i
$100$	3.51863	−	0.898054i	0.351863	−	0.0898054i
$101$	5.11383	−	8.85742i	0.508845	−	0.881346i	−0.491102	−	0.871102i	$-0.663406\pi$
$101$	5.11383	−	8.85742i	0.508845	−	0.881346i	0.999948	−	0.0102441i	$-0.00326086\pi$
$102$	2.66476	−	4.49492i	0.263850	−	0.445063i
$103$	1.35296	+	2.34340i	0.133311	+	0.230902i	0.924951	−	0.380086i	$-0.124106\pi$
$103$	1.35296	+	2.34340i	0.133311	+	0.230902i	−0.791640	+	0.610988i	$0.790772\pi$
$104$	−11.4866	+	14.4286i	−1.12635	+	1.41484i
$105$	−2.76934	−	7.69420i	−0.270260	−	0.750877i
$106$	0.454419	−	1.07885i	0.0441371	−	0.104788i
$107$	−12.8015			−1.23756			−0.618782	−	0.785562i	$-0.712374\pi$
$107$	−12.8015			−1.23756			−0.618782	+	0.785562i	$0.712374\pi$
$108$	−3.70019	−	9.71126i	−0.356051	−	0.934466i
$109$			3.59420i			0.344262i	0.985074	+	0.172131i	$0.0550652\pi$
$109$			3.59420i			0.344262i	−0.985074	+	0.172131i	$0.944935\pi$
$110$	13.3306	+	5.61494i	1.27103	+	0.535363i
$111$	−0.119204	+	0.867956i	−0.0113143	+	0.0823828i
$112$	0.692030	−	10.5604i	0.0653907	−	0.997860i
$113$	−1.14317	−	1.98003i	−0.107541	−	0.186266i	0.807233	−	0.590233i	$-0.200964\pi$
$113$	−1.14317	−	1.98003i	−0.107541	−	0.186266i	−0.914773	+	0.403967i	$0.867631\pi$
$114$	4.49610	−	7.58402i	0.421098	−	0.710309i
$115$	−7.03962	−	4.06432i	−0.656448	−	0.379000i
$116$	−3.11356	−	12.1991i	−0.289087	−	1.13266i
$117$	4.85145	+	18.9500i	0.448517	+	1.75193i
$118$	−0.560739	+	0.0704293i	−0.0516202	+	0.00648355i
$119$	0.234870	−	5.63923i	0.0215305	−	0.516948i
$120$	−6.32475	+	6.03493i	−0.577368	+	0.550912i
$121$	−10.9270	−	18.9262i	−0.993368	−	1.72056i
$122$	8.25073	−	6.25333i	0.746986	−	0.566149i
$123$	10.3820	−	4.23258i	0.936110	−	0.381639i
$124$	2.16531	−	7.71253i	0.194450	−	0.692606i
$125$	−12.1623			−1.08783
$126$	−8.48879	−	7.34441i	−0.756242	−	0.654292i
$127$			7.43645i			0.659878i	0.944002	+	0.329939i	$0.107028\pi$
$127$			7.43645i			0.659878i	−0.944002	+	0.329939i	$0.892972\pi$
$128$	−10.6238	+	3.89037i	−0.939020	+	0.343863i
$129$	3.43643	−	4.42703i	0.302561	−	0.389778i
$130$	13.1139	−	9.93921i	1.15017	−	0.871726i
$131$	8.58229	−	4.95499i	0.749838	−	0.432919i	−0.0757972	−	0.997123i	$-0.524150\pi$
$131$	8.58229	−	4.95499i	0.749838	−	0.432919i	0.825635	+	0.564204i	$0.190817\pi$
$132$	19.7282	−	2.24699i	1.71712	−	0.195575i
$133$	0.396282	−	9.51476i	0.0343620	−	0.825034i
$134$	1.19973	+	9.55188i	0.103640	+	0.825157i
$135$	1.05610	+	9.21197i	0.0908942	+	0.792840i
$136$	−5.61487	+	2.20912i	−0.481471	+	0.189431i
$137$	7.68342	−	13.3081i	0.656438	−	1.13698i	−0.325093	−	0.945682i	$-0.605395\pi$
$137$	7.68342	−	13.3081i	0.656438	−	1.13698i	0.981531	−	0.191303i	$-0.0612712\pi$
$138$	−11.1573	−	0.128736i	−0.949772	−	0.0109588i
$139$	13.0426	−	7.53017i	1.10626	−	0.638701i	0.168403	−	0.985718i	$-0.446139\pi$
$139$	13.0426	−	7.53017i	1.10626	−	0.638701i	0.937859	+	0.347018i	$0.112806\pi$
$140$	−2.92840	+	8.97689i	−0.247495	+	0.758685i
$141$	−4.96852	+	6.40076i	−0.418424	+	0.539041i
$142$	−1.07932	+	2.56246i	−0.0905745	+	0.215036i
$143$	−37.3739			−3.12536
$144$	−3.50932	+	11.4754i	−0.292444	+	0.956283i
$145$			11.2333i			0.932877i
$146$	−7.87866	+	18.7050i	−0.652042	+	1.54804i
$147$	−11.8328	−	2.64275i	−0.975955	−	0.217971i
$148$	0.723801	−	0.706768i	0.0594961	−	0.0580960i
$149$	9.61138	−	5.54913i	0.787395	−	0.454603i	−0.0516496	−	0.998665i	$-0.516448\pi$
$149$	9.61138	−	5.54913i	0.787395	−	0.454603i	0.839045	+	0.544062i	$0.183115\pi$
$150$	−3.87711	+	2.17920i	−0.316565	+	0.177931i
$151$	7.73466	+	4.46561i	0.629438	+	0.363406i	0.780534	−	0.625113i	$-0.214947\pi$
$151$	7.73466	+	4.46561i	0.629438	+	0.363406i	−0.151097	+	0.988519i	$0.548280\pi$
$152$	−9.47365	+	3.72733i	−0.768414	+	0.302326i
$153$	−1.72534	+	6.16288i	−0.139486	+	0.498239i
$154$	17.6164	−	12.2319i	1.41957	−	0.985672i
$155$	−3.57370	+	6.18983i	−0.287046	+	0.497179i
$156$	9.00745	−	20.7136i	0.721173	−	1.65841i
$157$	7.85645	+	13.6078i	0.627013	+	1.08602i	0.988148	+	0.153504i	$0.0490559\pi$
$157$	7.85645	+	13.6078i	0.627013	+	1.08602i	−0.361135	+	0.932513i	$0.617611\pi$
$158$	2.14094	+	2.82479i	0.170324	+	0.224728i
$159$	−0.195077	+	1.42042i	−0.0154706	+	0.112646i
$160$	10.0428	−	1.01915i	0.793956	−	0.0805711i
$161$	−10.6791	+	5.58648i	−0.841632	+	0.440276i
$162$	7.45952	+	10.3129i	0.586075	+	0.810257i
$163$	19.0694			1.49363			0.746815	−	0.665031i	$-0.231582\pi$
$163$	19.0694			1.49363			0.746815	+	0.665031i	$0.231582\pi$
$164$	−12.4641	−	3.49932i	−0.973285	−	0.273251i
$165$	−17.5511	−	2.41043i	−1.36635	−	0.187652i
$166$	−0.526369	−	0.694499i	−0.0408541	−	0.0539036i
$167$	0.457013	+	0.791570i	0.0353647	+	0.0612535i	0.883166	−	0.469060i	$-0.155407\pi$
$167$	0.457013	+	0.791570i	0.0353647	+	0.0612535i	−0.847801	+	0.530314i	$0.822074\pi$
$168$	2.53350	+	12.7115i	0.195464	+	0.980711i
$169$	−14.7578	+	25.5612i	−1.13521	+	1.96625i
$170$	5.34158	−	0.670907i	0.409680	−	0.0514562i
$171$	−2.91107	+	10.3983i	−0.222615	+	0.795176i
$172$	−6.27023	+	1.60034i	−0.478100	+	0.122025i
$173$	−6.57744	+	11.3925i	−0.500073	+	0.866153i	0.499927	+	0.866068i	$0.333360\pi$
$173$	−6.57744	+	11.3925i	−0.500073	+	0.866153i	−1.00000		8.48213e-5i	$0.999973\pi$
$174$	7.55530	+	13.4420i	0.572766	+	1.01903i
$175$	−2.57301	+	4.05677i	−0.194501	+	0.306663i
$176$	−19.5771	−	11.9332i	−1.47568	−	0.899500i
$177$	0.640940	−	0.261302i	0.0481760	−	0.0196407i
$178$	4.34685	−	10.3200i	0.325810	−	0.773519i
$179$	8.85532			0.661878			0.330939	−	0.943652i	$-0.392635\pi$
$179$	8.85532			0.661878			0.330939	+	0.943652i	$0.392635\pi$
$180$	5.56589	−	9.14632i	0.414857	−	0.681726i
$181$	−3.11488			−0.231527			−0.115764	−	0.993277i	$-0.536932\pi$
$181$	−3.11488			−0.231527			−0.115764	+	0.993277i	$0.536932\pi$
$182$	−2.03045	−	24.3124i	−0.150507	−	1.80216i
$183$	−7.77481	+	10.0160i	−0.574730	+	0.740404i
$184$	10.0800	+	8.02469i	0.743109	+	0.591588i
$185$	−0.781684	+	0.451306i	−0.0574706	+	0.0331807i
$186$	−0.113196	+	9.81044i	−0.00829993	+	0.719337i
$187$	−10.5894	−	6.11381i	−0.774376	−	0.447086i
$188$	9.06572	−	2.31383i	0.661186	−	0.168753i
$189$	12.3726	+	5.99313i	0.899977	+	0.435936i
$190$	9.01254	−	1.13198i	0.653838	−	0.0821227i
$191$	−13.1945	−	7.61786i	−0.954722	−	0.551209i	−0.0601777	−	0.998188i	$-0.519167\pi$
$191$	−13.1945	−	7.61786i	−0.954722	−	0.551209i	−0.894545	+	0.446978i	$0.852500\pi$
$192$	11.3320	−	7.97414i	0.817813	−	0.575484i
$193$	−1.44348	−	2.50019i	−0.103904	−	0.179967i	0.809386	−	0.587277i	$-0.199800\pi$
$193$	−1.44348	−	2.50019i	−0.103904	−	0.179967i	−0.913290	+	0.407310i	$0.866467\pi$
$194$	13.8313	+	18.2492i	0.993031	+	1.31022i
$195$	−12.3575	+	15.9197i	−0.884939	+	1.14003i
$196$	8.91413	+	10.7953i	0.636724	+	0.771092i
$197$			24.7236i			1.76148i	0.473599	+	0.880741i	$0.342955\pi$
$197$			24.7236i			1.76148i	−0.473599	+	0.880741i	$0.657045\pi$
$198$	−22.6231	+	8.92012i	−1.60775	+	0.633926i
$199$	15.7553			1.11686			0.558432	−	0.829550i	$-0.311403\pi$
$199$	15.7553			1.11686			0.558432	+	0.829550i	$0.311403\pi$
$200$	5.07890	+	0.761154i	0.359132	+	0.0538217i
$201$	−4.45114	−	10.9181i	−0.313959	−	0.770101i
$202$	11.5274	−	8.73672i	0.811062	−	0.614714i
$203$	14.0648	+	8.92064i	0.987159	+	0.626106i
$204$	5.94058	−	4.39545i	0.415924	−	0.307743i
$205$	10.0033	+	5.77541i	0.698661	+	0.403372i
$206$	0.476896	+	3.79692i	0.0332270	+	0.264544i
$207$	13.2388	−	3.38930i	0.920159	−	0.235573i
$208$	−22.8914	+	12.4993i	−1.58723	+	0.866670i
$209$	−17.8669	−	10.3155i	−1.23588	−	0.713537i
$210$	0.614519	−	11.5483i	0.0424058	−	0.796906i
$211$	−2.97597	−	5.15454i	−0.204875	−	0.354853i	0.745218	−	0.666821i	$-0.232345\pi$
$211$	−2.97597	−	5.15454i	−0.204875	−	0.354853i	−0.950093	+	0.311968i	$0.899012\pi$
$212$	1.18451	−	1.15663i	0.0813522	−	0.0794377i
$213$	0.463341	−	3.37372i	0.0317476	−	0.231163i
$214$	−16.6844	−	7.02755i	−1.14052	−	0.480394i
$215$	5.77381			0.393771
$216$	0.508610	−	14.6881i	0.0346065	−	0.999401i
$217$	4.91211	+	9.38998i	0.333455	+	0.637433i
$218$	−1.97309	+	4.68439i	−0.133634	+	0.317267i
$219$	3.38222	−	24.6270i	0.228550	−	1.66414i
$220$	14.2917	+	14.6361i	0.963544	+	0.986766i
$221$	−12.0463	+	6.95491i	−0.810319	+	0.467838i
$222$	−0.631837	+	1.06578i	−0.0424061	+	0.0715308i
$223$	10.9984	−	19.0498i	0.736507	−	1.27567i	−0.217552	−	0.976049i	$-0.569807\pi$
$223$	10.9984	−	19.0498i	0.736507	−	1.27567i	0.954059	−	0.299619i	$-0.0968595\pi$
$224$	6.69919	−	13.3836i	0.447609	−	0.894229i
$225$	3.89449	−	3.80845i	0.259633	−	0.253897i
$226$	−0.402950	−	3.20818i	−0.0268038	−	0.213405i
$227$	19.4978	+	11.2571i	1.29412	+	0.747158i	0.979381	−	0.202022i	$-0.0647511\pi$
$227$	19.4978	+	11.2571i	1.29412	+	0.747158i	0.314735	+	0.949180i	$0.398084\pi$
$228$	10.0232	−	7.41620i	0.663803	−	0.491150i
$229$	−14.8397	−	25.7031i	−0.980636	−	1.69851i	−0.659920	−	0.751336i	$-0.729410\pi$
$229$	−14.8397	−	25.7031i	−0.980636	−	1.69851i	−0.320716	−	0.947175i	$-0.603923\pi$
$230$	−6.94369	−	9.16161i	−0.457853	−	0.604099i
$231$	−16.9557	+	20.0609i	−1.11560	+	1.31991i
$232$	2.63893	−	17.6086i	0.173254	−	1.15606i
$233$	19.4293			1.27286			0.636428	−	0.771336i	$-0.280411\pi$
$233$	19.4293			1.27286			0.636428	+	0.771336i	$0.280411\pi$
$234$	−4.07991	+	27.3612i	−0.266712	+	1.78866i
$235$	−8.34800			−0.544563
$236$	−0.769484	−	0.216034i	−0.0500892	−	0.0140626i
$237$	−3.42917	−	2.66185i	−0.222748	−	0.172906i
$238$	3.40185	−	7.22078i	0.220509	−	0.468054i
$239$	2.79777	−	1.61529i	0.180972	−	0.104484i	−0.406777	−	0.913527i	$-0.633347\pi$
$239$	2.79777	−	1.61529i	0.180972	−	0.104484i	0.587749	+	0.809043i	$0.300014\pi$
$240$	−11.5561	+	4.39338i	−0.745944	+	0.283591i
$241$	−16.1168	−	9.30502i	−1.03817	−	0.599389i	−0.118858	−	0.992911i	$-0.537923\pi$
$241$	−16.1168	−	9.30502i	−1.03817	−	0.599389i	−0.919315	+	0.393522i	$0.871257\pi$
$242$	−3.85161	−	30.6654i	−0.247591	−	1.97125i
$243$	−12.0974	−	9.83124i	−0.776047	−	0.630675i
$244$	14.1862	−	3.62071i	0.908177	−	0.231792i
$245$	−5.32443	−	11.2996i	−0.340165	−	0.721903i
$246$	15.8545	+	0.182935i	1.01085	+	0.0116635i
$247$	−20.3250	+	11.7346i	−1.29325	+	0.746656i
$248$	7.05599	−	8.86321i	0.448056	−	0.562814i
$249$	0.843089	+	0.654438i	0.0534286	+	0.0414733i
$250$	−15.8514	−	6.67670i	−1.00253	−	0.422271i
$251$		−	20.9851i		−	1.32457i	−0.749252	−	0.662285i	$-0.769587\pi$
$251$		−	20.9851i		−	1.32457i	0.749252	−	0.662285i	$-0.230413\pi$
$252$	−7.03178	−	14.2321i	−0.442960	−	0.896541i
$253$			26.1100i			1.64152i
$254$	−4.08234	+	9.69205i	−0.256149	+	0.608134i
$255$	−6.10557	+	2.48915i	−0.382346	+	0.155877i
$256$	−15.9819	−	0.761703i	−0.998866	−	0.0476064i
$257$	−4.15846	+	2.40089i	−0.259398	+	0.149763i	−0.624060	−	0.781377i	$-0.714518\pi$
$257$	−4.15846	+	2.40089i	−0.259398	+	0.149763i	0.364662	+	0.931140i	$0.381185\pi$
$258$	6.90904	−	3.88335i	0.430138	−	0.241767i
$259$	−0.0556896	+	1.33711i	−0.00346038	+	0.0830840i
$260$	22.5479	−	5.75486i	1.39836	−	0.356902i
$261$	−13.2039	−	13.5022i	−0.817303	−	0.835768i
$262$	13.9056	−	1.74655i	0.859089	−	0.107902i
$263$	0.369176	+	0.213144i	0.0227644	+	0.0131430i	0.511339	−	0.859379i	$-0.329150\pi$
$263$	0.369176	+	0.213144i	0.0227644	+	0.0131430i	−0.488575	+	0.872522i	$0.662483\pi$
$264$	26.9456	+	7.90152i	1.65839	+	0.486305i
$265$	−1.27923	+	0.738564i	−0.0785825	+	0.0453696i
$266$	5.73974	−	12.1832i	0.351926	−	0.747000i
$267$	−1.86606	+	13.5873i	−0.114201	+	0.831530i
$268$	−3.68002	+	13.1077i	−0.224793	+	0.800683i
$269$	−8.61268			−0.525124			−0.262562	−	0.964915i	$-0.584567\pi$
$269$	−8.61268			−0.525124			−0.262562	+	0.964915i	$0.584567\pi$
$270$	−3.68062	+	12.5859i	−0.223995	+	0.765953i
$271$	−8.40451			−0.510538			−0.255269	−	0.966870i	$-0.582164\pi$
$271$	−8.40451			−0.510538			−0.255269	+	0.966870i	$0.582164\pi$
$272$	−8.53069	−	0.203173i	−0.517249	−	0.0123192i
$273$	10.1191	+	28.1146i	0.612438	+	1.70157i
$274$	17.3196	−	13.1267i	1.04631	−	0.793014i
$275$	5.20370	+	9.01307i	0.313795	+	0.543509i
$276$	−14.4708	−	6.29275i	−0.871042	−	0.378779i
$277$	−4.27391	−	2.46754i	−0.256794	−	0.148260i	0.366077	−	0.930585i	$-0.380701\pi$
$277$	−4.27391	−	2.46754i	−0.256794	−	0.148260i	−0.622871	+	0.782324i	$0.714034\pi$
$278$	21.1325	−	2.65426i	1.26744	−	0.159192i
$279$	−2.98016	−	11.6407i	−0.178418	−	0.696908i
$280$	−8.74462	+	10.0922i	−0.522591	+	0.603121i
$281$	−12.1476	+	21.0402i	−0.724665	+	1.25516i	0.234447	+	0.972129i	$0.424672\pi$
$281$	−12.1476	+	21.0402i	−0.724665	+	1.25516i	−0.959112	+	0.283027i	$0.908661\pi$
$282$	−9.98935	+	5.61469i	−0.594857	+	0.334350i
$283$	−20.3161	+	11.7295i	−1.20766	+	0.697245i	−0.962248	−	0.272173i	$-0.912258\pi$
$283$	−20.3161	+	11.7295i	−1.20766	+	0.697245i	−0.245416	+	0.969418i	$0.578924\pi$
$284$	−2.81339	+	2.74719i	−0.166944	+	0.163016i
$285$	−10.3016	+	4.19981i	−0.610213	+	0.248775i
$286$	−48.7101	−	20.5170i	−2.88029	−	1.21319i
$287$	15.1750	−	7.93839i	0.895754	−	0.468589i
$288$	−10.8733	+	13.0296i	−0.640718	+	0.767776i
$289$	12.4491			0.732301
$290$	−6.16670	+	14.6406i	−0.362121	+	0.859726i
$291$	−22.1537	−	17.1966i	−1.29867	−	1.00808i
$292$	−20.5368	+	20.0535i	−1.20182	+	1.17354i
$293$	−3.83631	−	6.64468i	−0.224119	−	0.388186i	0.731936	−	0.681374i	$-0.238617\pi$
$293$	−3.83631	−	6.64468i	−0.224119	−	0.388186i	−0.956055	+	0.293188i	$0.905284\pi$
$294$	−13.9712	−	9.94015i	−0.814815	−	0.579721i
$295$	0.617563	+	0.356550i	0.0359559	+	0.0207592i
$296$	1.33133	−	0.523802i	0.0773822	−	0.0304454i
$297$	23.9293	−	17.7327i	1.38852	−	1.02895i
$298$	15.5730	−	1.95598i	0.902118	−	0.113307i
$299$	25.7227	+	14.8510i	1.48758	+	0.858857i
$300$	−6.24941	+	0.711793i	−0.360810	+	0.0410954i
$301$	4.58512	−	7.22919i	0.264282	−	0.416683i
$302$	7.62926	+	10.0662i	0.439015	+	0.579243i
$303$	−10.8624	+	13.9937i	−0.624030	+	0.803916i
$304$	−14.3933	−	0.342802i	−0.825515	−	0.0196611i
$305$	−13.0631			−0.747989
$306$	−5.63187	+	7.08504i	−0.321953	+	0.405025i
$307$		−	4.42681i		−	0.252651i	−0.991989	−	0.126326i	$-0.959682\pi$
$307$		−	4.42681i		−	0.252651i	0.991989	−	0.126326i	$-0.0403184\pi$
$308$	29.6747	−	6.27123i	1.69087	−	0.357336i
$309$	−1.76935	−	4.33998i	−0.100655	−	0.246893i
$310$	−8.05566	+	6.10548i	−0.457531	+	0.346768i
$311$	4.85257	+	8.40489i	0.275164	+	0.476598i	0.970176	−	0.242400i	$-0.0779345\pi$
$311$	4.85257	+	8.40489i	0.275164	+	0.476598i	−0.695013	+	0.718998i	$0.744601\pi$
$312$	23.1106	−	22.0516i	1.30838	−	1.24843i
$313$	12.7693	+	7.37236i	0.721764	+	0.416710i	0.815401	−	0.578896i	$-0.196516\pi$
$313$	12.7693	+	7.37236i	0.721764	+	0.416710i	−0.0936379	+	0.995606i	$0.529850\pi$
$314$	2.76927	+	22.0482i	0.156279	+	1.24425i
$315$	2.93877	+	13.8555i	0.165581	+	0.780666i
$316$	1.23962	+	4.85691i	0.0697340	+	0.273222i
$317$	21.0016	+	12.1253i	1.17956	+	0.681022i	0.955914	−	0.293647i	$-0.0948691\pi$
$317$	21.0016	+	12.1253i	1.17956	+	0.681022i	0.223651	+	0.974669i	$0.428202\pi$
$318$	−1.03401	+	1.74416i	−0.0579841	+	0.0978078i
$319$	31.2484	−	18.0413i	1.74957	−	1.01012i
$320$	13.6485	+	4.18488i	0.762973	+	0.233942i
$321$	21.9666	+	3.01686i	1.22606	+	0.168384i
$322$	−16.9851	+	1.41851i	−0.946540	+	0.0790502i
$323$	−7.67843			−0.427239
$324$	4.06072	+	17.5360i	0.225596	+	0.974221i
$325$	11.8392			0.656719
$326$	24.8535	+	10.4684i	1.37651	+	0.579792i
$327$	0.847026	−	6.16744i	0.0468407	−	0.341060i
$328$	−14.3237	−	11.4031i	−0.790895	−	0.629631i
$329$	−6.62933	+	10.4522i	−0.365487	+	0.576250i
$330$	−21.5514	−	12.7765i	−1.18637	−	0.703322i
$331$	10.8579	−	18.8065i	0.596806	−	1.03370i	−0.396484	−	0.918042i	$-0.629770\pi$
$331$	10.8579	−	18.8065i	0.596806	−	1.03370i	0.993289	−	0.115656i	$-0.0368970\pi$
$332$	−0.304771	−	1.19411i	−0.0167265	−	0.0655353i
$333$	0.409093	−	1.46127i	0.0224182	−	0.0800772i
$334$	0.161090	+	1.28255i	0.00881443	+	0.0701781i
$335$	6.07364	−	10.5198i	0.331838	−	0.574761i
$336$	−3.67619	+	17.9579i	−0.200552	+	0.979683i
$337$	−10.2990	−	17.8383i	−0.561020	−	0.971715i	−0.997408	−	0.0719563i	$-0.977076\pi$
$337$	−10.2990	−	17.8383i	−0.561020	−	0.971715i	0.436388	−	0.899759i	$-0.356258\pi$
$338$	−33.2663	+	25.2129i	−1.80945	+	1.37140i
$339$	1.49500	+	3.66703i	0.0811971	+	0.199166i
$340$	7.33008	+	2.05793i	0.397529	+	0.111607i
$341$	22.9581			1.24325
$342$	−9.50233	+	11.9542i	−0.513827	+	0.646408i
$343$	−18.3760	−	2.30672i	−0.992213	−	0.124551i
$344$	−9.05063	−	1.35638i	−0.487977	−	0.0731312i
$345$	11.1218	+	8.63314i	0.598776	+	0.464793i
$346$	−14.8266	+	11.2372i	−0.797080	+	0.604117i
$347$	4.25303	+	7.36647i	0.228315	+	0.395453i	0.957309	−	0.289067i	$-0.0933452\pi$
$347$	4.25303	+	7.36647i	0.228315	+	0.395453i	−0.728994	+	0.684520i	$0.760012\pi$
$348$	2.46779	+	21.6668i	0.132288	+	1.16146i
$349$	−12.8783	+	22.3058i	−0.689359	+	1.19400i	0.282687	+	0.959212i	$0.408774\pi$
$349$	−12.8783	+	22.3058i	−0.689359	+	1.19400i	−0.972046	+	0.234792i	$0.924559\pi$
$350$	−5.58047	+	3.87477i	−0.298289	+	0.207115i
$351$	−3.85897	−	33.6605i	−0.205976	−	1.79666i
$352$	−18.9643	−	26.2999i	−1.01080	−	1.40179i
$353$	−13.5681	−	7.83357i	−0.722159	−	0.416939i	0.0933875	−	0.995630i	$-0.470230\pi$
$353$	−13.5681	−	7.83357i	−0.722159	−	0.416939i	−0.815547	+	0.578691i	$0.803564\pi$
$354$	0.978794	+	0.0112936i	0.0520223	+	0.000600250i
$355$	3.03838	−	1.75421i	0.161261	−	0.0931039i
$356$	11.3307	−	11.0640i	0.600524	−	0.586392i
$357$	−1.73199	+	9.62126i	−0.0916667	+	0.509211i
$358$	11.5413	+	4.86126i	0.609977	+	0.256925i
$359$			32.3708i			1.70847i	0.519890	+	0.854233i	$0.325973\pi$
$359$			32.3708i			1.70847i	−0.519890	+	0.854233i	$0.674027\pi$
$360$	12.2751	−	8.86509i	0.646956	−	0.467231i
$361$	6.04462			0.318138
$362$	−4.05968	−	1.70996i	−0.213372	−	0.0898735i
$363$	14.2900	+	35.0514i	0.750028	+	1.83972i
$364$	10.7003	−	32.8015i	0.560851	−	1.71927i
$365$	22.1791	−	12.8051i	1.16091	−	0.670251i
$366$	−15.6315	+	8.78595i	−0.817070	+	0.459249i
$367$	−3.24428	+	5.61925i	−0.169350	+	0.293323i	−0.938191	−	0.346117i	$-0.887500\pi$
$367$	−3.24428	+	5.61925i	−0.169350	+	0.293323i	0.768842	+	0.639439i	$0.220833\pi$
$368$	8.73220	+	15.9923i	0.455198	+	0.833656i
$369$	−18.8123	+	4.81620i	−0.979331	+	0.250721i
$370$	−1.26653	+	0.159078i	−0.0658440	+	0.00827007i
$371$	−0.0911363	+	2.18819i	−0.00473156	+	0.113605i
$372$	−5.53312	+	12.7240i	−0.286879	+	0.659708i
$373$	0.507153	−	0.292805i	0.0262594	−	0.0151609i	−0.486813	−	0.873506i	$-0.661841\pi$
$373$	0.507153	−	0.292805i	0.0262594	−	0.0151609i	0.513072	+	0.858345i	$0.328507\pi$
$374$	−10.4451	−	13.7815i	−0.540105	−	0.712623i
$375$	20.8699	+	2.86624i	1.07772	+	0.148012i
$376$	13.0857	+	1.96111i	0.674845	+	0.101136i
$377$		−	41.0465i		−	2.11400i
$378$	12.8355	+	14.6031i	0.660186	+	0.751103i
$379$	16.9407			0.870186			0.435093	−	0.900386i	$-0.356716\pi$
$379$	16.9407			0.870186			0.435093	+	0.900386i	$0.356716\pi$
$380$	12.3676	+	3.47223i	0.634446	+	0.178122i
$381$	1.75251	−	12.7605i	0.0897837	−	0.653741i
$382$	−13.0147	−	17.1718i	−0.665891	−	0.878587i
$383$	−3.02865	−	5.24577i	−0.154757	−	0.268046i	0.778214	−	0.628000i	$-0.216126\pi$
$383$	−3.02865	−	5.24577i	−0.154757	−	0.268046i	−0.932970	+	0.359953i	$0.882793\pi$
$384$	19.1467	−	4.17199i	0.977074	−	0.212901i
$385$	−27.0379	−	1.12611i	−1.37798	−	0.0573918i
$386$	−0.508804	−	4.05096i	−0.0258975	−	0.206188i
$387$	−6.94001	+	6.78668i	−0.352781	+	0.344987i
$388$	8.00842	+	31.3775i	0.406566	+	1.59295i
$389$	−17.3692	−	10.0281i	−0.880654	−	0.508446i	−0.00978018	−	0.999952i	$-0.503113\pi$
$389$	−17.3692	−	10.0281i	−0.880654	−	0.508446i	−0.870874	+	0.491506i	$0.836447\pi$
$390$	−24.8451	+	13.9646i	−1.25808	+	0.707127i
$391$	4.85881	+	8.41570i	0.245721	+	0.425600i
$392$	5.69172	+	18.9632i	0.287475	+	0.957788i
$393$	−15.8944	+	6.47994i	−0.801769	+	0.326870i
$394$	−13.5724	+	32.2227i	−0.683766	+	1.62335i
$395$		−	4.47239i		−	0.225030i
$396$	−34.3819	−	0.793525i	−1.72776	−	0.0398761i
$397$	1.83014			0.0918522			0.0459261	−	0.998945i	$-0.485376\pi$
$397$	1.83014			0.0918522			0.0459261	+	0.998945i	$0.485376\pi$
$398$	20.5342	+	8.64910i	1.02928	+	0.433540i
$399$	−2.92229	+	16.2334i	−0.146297	+	0.812686i
$400$	6.20157	+	3.78016i	0.310079	+	0.189008i
$401$	−2.12035	−	3.67256i	−0.105885	−	0.183399i	0.808214	−	0.588889i	$-0.200434\pi$
$401$	−2.12035	−	3.67256i	−0.105885	−	0.183399i	−0.914100	+	0.405490i	$0.867101\pi$
$402$	0.192381	−	16.6732i	0.00959508	−	0.831585i
$403$	13.0583	−	22.6176i	0.650479	−	1.12666i
$404$	19.8200	−	5.05862i	0.986080	−	0.251676i
$405$	0.358737	−	16.0561i	0.0178258	−	0.797834i
$406$	13.4339	+	19.3475i	0.666711	+	0.960202i
$407$	2.51085	+	1.44964i	0.124458	+	0.0718559i
$408$	10.1554	−	2.46751i	0.502768	−	0.122160i
$409$	−4.20386	+	2.42710i	−0.207868	+	0.120012i	−0.600320	−	0.799760i	$-0.704960\pi$
$409$	−4.20386	+	2.42710i	−0.207868	+	0.120012i	0.392452	+	0.919772i	$0.371627\pi$
$410$	9.86699	+	13.0187i	0.487296	+	0.642946i
$411$	−16.3205	+	21.0252i	−0.805033	+	1.03710i
$412$	−1.46283	+	5.21039i	−0.0720682	+	0.256698i
$413$	0.936844	−	0.490084i	0.0460991	−	0.0241155i
$414$	19.1150	+	2.85029i	0.939449	+	0.140084i
$415$			1.09957i			0.0539759i
$416$	−36.6965	+	3.72398i	−1.79919	+	0.182583i
$417$	−24.1550	+	9.84765i	−1.18288	+	0.482242i
$418$	−17.6235	−	23.2527i	−0.861993	−	1.13733i
$419$	1.99126	−	1.14965i	0.0972795	−	0.0561643i	−0.450571	−	0.892741i	$-0.648780\pi$
$419$	1.99126	−	1.14965i	0.0972795	−	0.0561643i	0.547850	+	0.836576i	$0.315446\pi$
$420$	7.14050	−	14.7137i	0.348421	−	0.717956i
$421$	−33.3629	−	19.2621i	−1.62601	−	0.938776i	−0.985268	−	0.171017i	$-0.945295\pi$
$421$	−33.3629	−	19.2621i	−1.62601	−	0.938776i	−0.640739	−	0.767758i	$-0.721372\pi$
$422$	−1.04898	−	8.35171i	−0.0510637	−	0.406555i
$423$	10.0341	−	9.81244i	0.487876	−	0.477097i
$424$	2.17874	−	0.857206i	0.105809	−	0.0416296i
$425$	3.35448	+	1.93671i	0.162716	+	0.0939443i
$426$	2.45593	−	4.14267i	0.118990	−	0.200713i
$427$	−10.3737	+	16.3558i	−0.502017	+	0.791512i
$428$	−17.8872	−	18.3183i	−0.864610	−	0.885447i
$429$	64.1315	+	8.80772i	3.09630	+	0.425241i
$430$	7.52512	+	3.16962i	0.362893	+	0.152853i
$431$			1.15387i			0.0555802i	0.999614	+	0.0277901i	$0.00884700\pi$
$431$			1.15387i			0.0555802i	−0.999614	+	0.0277901i	$0.991153\pi$
$432$	8.72614	−	18.8641i	0.419837	−	0.907600i
$433$			7.47255i			0.359108i	0.983748	+	0.179554i	$0.0574654\pi$
$433$			7.47255i			0.359108i	−0.983748	+	0.179554i	$0.942535\pi$
$434$	1.24727	+	14.9347i	0.0598709	+	0.716889i
$435$	2.64730	−	19.2758i	0.126928	−	0.924202i
$436$	−5.14312	+	5.02209i	−0.246311	+	0.240514i
$437$	8.19799	+	14.1993i	0.392163	+	0.679246i
$438$	17.9274	−	30.2400i	0.856606	−	1.44493i
$439$	−14.7953	+	25.6262i	−0.706141	+	1.22307i	0.260137	+	0.965572i	$0.416232\pi$
$439$	−14.7953	+	25.6262i	−0.706141	+	1.22307i	−0.966278	+	0.257501i	$0.917101\pi$
$440$	10.5919	+	26.9211i	0.504949	+	1.28341i
$441$	19.6817	+	7.32340i	0.937222	+	0.348733i
$442$	−19.5181	+	2.45149i	−0.928381	+	0.116606i
$443$	18.6850	−	32.3634i	0.887751	−	1.53763i	0.0452234	−	0.998977i	$-0.485600\pi$
$443$	18.6850	−	32.3634i	0.887751	−	1.53763i	0.842528	−	0.538653i	$-0.181067\pi$
$444$	−1.40856	+	1.04220i	−0.0668474	+	0.0494606i
$445$	−12.2368	+	7.06491i	−0.580079	+	0.334909i
$446$	24.7921	−	18.7902i	1.17394	−	0.889742i
$447$	−17.8003	+	7.25694i	−0.841926	+	0.343241i
$448$	16.0783	−	13.7655i	0.759628	−	0.650357i
$449$	20.3300			0.959430			0.479715	−	0.877424i	$-0.340740\pi$
$449$	20.3300			0.959430			0.479715	+	0.877424i	$0.340740\pi$
$450$	7.16647	−	2.82568i	0.337830	−	0.133204i
$451$		−	37.1024i		−	1.74708i
$452$	1.23600	−	4.40248i	0.0581367	−	0.207075i
$453$	−12.2199	−	9.48552i	−0.574139	−	0.445669i
$454$	19.2321	+	25.3752i	0.902608	+	1.19092i
$455$	−16.4882	+	25.9964i	−0.772979	+	1.21873i
$456$	17.1346	−	4.16328i	0.802403	−	0.194963i
$457$	−15.1229	+	26.1936i	−0.707420	+	1.22529i	0.258391	+	0.966040i	$0.416808\pi$
$457$	−15.1229	+	26.1936i	−0.707420	+	1.22529i	−0.965811	+	0.259247i	$0.916526\pi$
$458$	−5.23076	−	41.6458i	−0.244417	−	1.94598i
$459$	4.41296	−	10.1685i	0.205979	−	0.474627i
$460$	−4.02044	−	15.7523i	−0.187454	−	0.734456i
$461$	8.68136	−	15.0366i	0.404331	−	0.700322i	−0.589912	−	0.807467i	$-0.700838\pi$
$461$	8.68136	−	15.0366i	0.404331	−	0.700322i	0.994243	+	0.107145i	$0.0341710\pi$
$462$	−33.1114	+	16.8376i	−1.54048	+	0.783358i
$463$	10.6731	−	6.16211i	0.496021	−	0.286378i	−0.231048	−	0.972942i	$-0.574215\pi$
$463$	10.6731	−	6.16211i	0.496021	−	0.286378i	0.727069	+	0.686565i	$0.240882\pi$
$464$	13.1058	−	21.5009i	0.608424	−	0.998154i
$465$	7.59099	−	9.77920i	0.352024	−	0.453500i
$466$	25.3226	+	10.6660i	1.17304	+	0.494093i
$467$			17.5154i			0.810515i	0.914203	+	0.405258i	$0.132818\pi$
$467$			17.5154i			0.810515i	−0.914203	+	0.405258i	$0.867182\pi$
$468$	−20.3377	+	33.4206i	−0.940112	+	1.54487i
$469$	−8.34831	−	15.9586i	−0.385489	−	0.736901i
$470$	−10.8801	−	4.58275i	−0.501861	−	0.211387i
$471$	−10.2743	−	25.2016i	−0.473417	−	1.16123i
$472$	−0.884288	−	0.703981i	−0.0407026	−	0.0324033i
$473$	−9.27303	−	16.0614i	−0.426374	−	0.738502i
$474$	−3.00803	−	5.35173i	−0.138164	−	0.245813i
$475$	5.65983	+	3.26770i	0.259691	+	0.149932i
$476$	8.39764	−	7.54348i	0.384905	−	0.345755i
$477$	0.669483	−	2.39138i	0.0306535	−	0.109494i
$478$	4.53312	−	0.569364i	0.207340	−	0.0260421i
$479$	−14.2716	+	24.7191i	−0.652085	+	1.12944i	0.330531	+	0.943795i	$0.392772\pi$
$479$	−14.2716	+	24.7191i	−0.652085	+	1.12944i	−0.982616	+	0.185649i	$0.940561\pi$
$480$	−17.4731	−	0.617932i	−0.797535	−	0.0282046i
$481$	2.85627	−	1.64907i	0.130235	−	0.0751911i
$482$	−15.8972	−	20.9749i	−0.724096	−	0.955383i
$483$	19.6413	−	7.06939i	0.893710	−	0.321668i
$484$	11.8144	−	42.0812i	0.537016	−	1.91278i
$485$		−	28.8933i		−	1.31198i
$486$	−10.3697	−	19.4543i	−0.470381	−	0.882464i
$487$		−	6.55560i		−	0.297063i	−0.988908	−	0.148531i	$-0.952545\pi$
$487$		−	6.55560i		−	0.297063i	0.988908	−	0.148531i	$-0.0474546\pi$
$488$	20.4767	+	3.06877i	0.926939	+	0.138917i
$489$	−32.7220	−	4.49399i	−1.47974	−	0.203225i
$490$	−0.736362	−	17.6499i	−0.0332655	−	0.797340i
$491$	−11.3501	−	19.6589i	−0.512222	−	0.887194i	−0.999900	−	0.0141705i	$-0.995489\pi$
$491$	−11.3501	−	19.6589i	−0.512222	−	0.887194i	0.487678	−	0.873024i	$-0.337844\pi$
$492$	20.5631	+	8.94200i	0.927055	+	0.403137i
$493$	6.71460	−	11.6300i	0.302410	−	0.523790i
$494$	−32.9318	+	4.13626i	−1.48167	+	0.186099i
$495$	29.5486	+	8.27234i	1.32811	+	0.371814i
$496$	14.0618	−	7.67809i	0.631393	−	0.344757i
$497$	0.216464	−	5.19731i	0.00970973	−	0.233131i
$498$	0.739550	+	1.31577i	0.0331400	+	0.0589609i
$499$	−4.33054	−	7.50072i	−0.193862	−	0.335778i	0.752665	−	0.658404i	$-0.228768\pi$
$499$	−4.33054	−	7.50072i	−0.193862	−	0.335778i	−0.946527	+	0.322625i	$0.895435\pi$
$500$	−16.9942	−	17.4037i	−0.760002	−	0.778318i
$501$	−0.597664	−	1.46599i	−0.0267016	−	0.0654957i
$502$	11.5201	−	27.3503i	0.514167	−	1.22070i
$503$	24.8692			1.10886			0.554432	−	0.832229i	$-0.312935\pi$
$503$	24.8692			1.10886			0.554432	+	0.832229i	$0.312935\pi$
$504$	−1.35170	−	22.4092i	−0.0602095	−	0.998186i
$505$	−18.2508			−0.812151
$506$	−14.3335	+	34.0297i	−0.637201	+	1.51280i
$507$	31.3474	−	40.3837i	1.39219	−	1.79350i
$508$	−10.6412	+	10.3908i	−0.472126	+	0.461016i
$509$	15.9985	+	27.7102i	0.709120	+	1.22823i	0.965184	+	0.261571i	$0.0842407\pi$
$509$	15.9985	+	27.7102i	0.709120	+	1.22823i	−0.256064	+	0.966660i	$0.582426\pi$
$510$	−9.32396	−	0.107583i	−0.412872	−	0.00476384i
$511$	1.58011	−	37.9385i	0.0698999	−	1.67830i
$512$	−20.4113	−	9.76621i	−0.902060	−	0.431610i
$513$	7.44574	−	17.1568i	0.328737	−	0.757492i
$514$	−6.73780	+	0.846274i	−0.297192	+	0.0373275i
$515$	2.41430	−	4.18169i	0.106387	−	0.184267i
$516$	11.1365	−	1.26842i	0.490257	−	0.0558391i
$517$	13.4073	+	23.2221i	0.589652	+	1.02131i
$518$	−0.806608	+	1.71211i	−0.0354403	+	0.0752258i
$519$	13.9713	−	17.9987i	0.613273	−	0.790057i
$520$	32.5463	+	4.87759i	1.42725	+	0.213896i
$521$			23.2939i			1.02052i	0.860019	+	0.510262i	$0.170452\pi$
$521$			23.2939i			1.02052i	−0.860019	+	0.510262i	$0.829548\pi$
$522$	−9.79667	−	24.8462i	−0.428789	−	1.08749i
$523$		−	27.2889i		−	1.19326i	−0.802516	−	0.596631i	$-0.796506\pi$
$523$		−	27.2889i		−	1.19326i	0.802516	−	0.596631i	$-0.203494\pi$
$524$	19.0822	+	5.35735i	0.833609	+	0.234037i
$525$	5.37117	−	6.35482i	0.234417	−	0.277347i
$526$	0.364146	+	0.480459i	0.0158775	+	0.0209490i
$527$	7.39980	−	4.27228i	0.322340	−	0.186103i
$528$	30.7810	+	25.0904i	1.33957	+	1.09192i
$529$	−1.12484	+	1.94828i	−0.0489061	+	0.0847079i
$530$	−2.07269	+	0.260332i	−0.0900319	+	0.0113081i
$531$	−1.16140	+	0.297333i	−0.0504003	+	0.0129031i
$532$	14.1689	−	12.7277i	0.614298	−	0.551815i
$533$	−36.5520	−	21.1033i	−1.58324	−	0.914086i
$534$	−9.89102	+	16.6842i	−0.428026	+	0.721996i
$535$	11.4218	+	19.7832i	0.493809	+	0.855302i
$536$	−11.9919	+	15.0634i	−0.517972	+	0.650638i
$537$	−15.1952	−	2.08689i	−0.655723	−	0.0900558i
$538$	−11.2251	−	4.72805i	−0.483947	−	0.203841i
$539$	−22.8814	+	32.9590i	−0.985571	+	1.41964i
$540$	−11.7062	+	14.3829i	−0.503755	+	0.618941i
$541$		−	39.6550i		−	1.70490i	−0.522806	−	0.852452i	$-0.675115\pi$
$541$		−	39.6550i		−	1.70490i	0.522806	−	0.852452i	$-0.324885\pi$
$542$	−10.9537	−	4.61378i	−0.470504	−	0.198179i
$543$	5.34496	+	0.734068i	0.229374	+	0.0315019i
$544$	−11.0067	−	4.94785i	−0.471907	−	0.212137i
$545$	5.55442	−	3.20685i	0.237925	−	0.137366i
$546$	−2.24545	+	42.1973i	−0.0960963	+	1.80588i
$547$	14.5062	−	25.1255i	0.620242	−	1.07429i	−0.369199	−	0.929351i	$-0.620368\pi$
$547$	14.5062	−	25.1255i	0.620242	−	1.07429i	0.989440	−	0.144940i	$-0.0462989\pi$
$548$	29.7790	−	7.60045i	1.27210	−	0.324675i
$549$	15.7015	−	15.3546i	0.670126	−	0.655320i
$550$	1.83422	+	14.6035i	0.0782114	+	0.622697i
$551$	11.3292	−	19.6227i	0.482638	−	0.835954i
$552$	−15.4056	−	16.1454i	−0.655706	−	0.687195i
$553$	−5.59971	−	3.55162i	−0.238124	−	0.151030i
$554$	−4.21567	−	5.56222i	−0.179107	−	0.236316i
$555$	1.44768	−	0.590200i	0.0614507	−	0.0250526i
$556$	28.9995	+	8.14164i	1.22985	+	0.345283i
$557$			34.2229i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$557$			34.2229i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$558$	2.50621	−	16.8075i	0.106096	−	0.711518i
$559$	−21.0975			−0.892329
$560$	−16.9373	+	8.35280i	−0.715730	+	0.352970i
$561$	16.7301	+	12.9865i	0.706344	+	0.548291i
$562$	−27.3825	+	20.7535i	−1.15506	+	0.875435i
$563$	10.9590	−	6.32720i	0.461868	−	0.266660i	−0.250961	−	0.967997i	$-0.580747\pi$
$563$	10.9590	−	6.32720i	0.461868	−	0.266660i	0.712830	+	0.701337i	$0.247413\pi$
$564$	−16.1016	+	1.83393i	−0.677998	+	0.0772223i
$565$	−2.03994	+	3.53328i	−0.0858210	+	0.148646i
$566$	−32.9173	+	4.13445i	−1.38362	+	0.173784i
$567$	−19.8184	−	13.1997i	−0.832294	−	0.554334i
$568$	−5.17486	+	2.03600i	−0.217132	+	0.0854288i
$569$	−2.51898	+	4.36301i	−0.105601	+	0.182907i	−0.913984	−	0.405751i	$-0.867010\pi$
$569$	−2.51898	+	4.36301i	−0.105601	+	0.182907i	0.808382	+	0.588658i	$0.200343\pi$
$570$	−15.7318	−	0.181518i	−0.658932	−	0.00760296i
$571$	8.56623	+	14.8371i	0.358486	+	0.620915i	0.987708	−	0.156310i	$-0.0499599\pi$
$571$	8.56623	+	14.8371i	0.358486	+	0.620915i	−0.629222	+	0.777225i	$0.716627\pi$
$572$	−52.2217	−	53.4802i	−2.18350	−	2.23612i
$573$	20.8458	+	16.1813i	0.870846	+	0.675984i
$574$	24.1358	−	2.01570i	1.00741	−	0.0841336i
$575$		−	8.27103i		−	0.344926i
$576$	−21.3242	+	11.0126i	−0.888509	+	0.458859i
$577$			17.0368i			0.709252i	0.935008	+	0.354626i	$0.115392\pi$
$577$			17.0368i			0.709252i	−0.935008	+	0.354626i	$0.884608\pi$
$578$	16.2252	+	6.83413i	0.674878	+	0.284262i
$579$	1.88773	+	4.63036i	0.0784514	+	0.192431i
$580$	−16.0743	+	15.6961i	−0.667451	+	0.651743i
$581$	1.37674	+	0.873196i	0.0571166	+	0.0362263i
$582$	−19.4331	−	34.5742i	−0.805526	−	1.43315i
$583$	4.10901	+	2.37234i	0.170178	+	0.0982523i
$584$	−37.7746	+	14.8621i	−1.56313	+	0.614999i
$585$	24.9565	−	24.4051i	1.03182	−	1.00903i
$586$	−1.35223	−	10.7661i	−0.0558603	−	0.444744i
$587$	−5.20552	−	3.00541i	−0.214855	−	0.124046i	0.388711	−	0.921360i	$-0.372921\pi$
$587$	−5.20552	−	3.00541i	−0.214855	−	0.124046i	−0.603566	+	0.797313i	$0.706254\pi$
$588$	−12.7521	−	20.6249i	−0.525887	−	0.850555i
$589$	12.4853	−	7.20837i	0.514446	−	0.297016i
$590$	0.609148	+	0.803718i	0.0250782	+	0.0330886i
$591$	5.82647	−	42.4242i	0.239669	−	1.74510i
$592$	2.02270	+	0.0481741i	0.0831325	+	0.00197994i
$593$			22.4175i			0.920575i	0.887770	+	0.460287i	$0.152254\pi$
$593$			22.4175i			0.920575i	−0.887770	+	0.460287i	$0.847746\pi$
$594$	40.9221	−	9.97496i	1.67906	−	0.409278i
$595$	−8.92434	+	4.66852i	−0.365862	+	0.191391i
$596$	21.3703	+	5.99974i	0.875361	+	0.245759i
$597$	−27.0352	−	3.71297i	−1.10648	−	0.151962i
$598$	25.3722	+	33.4765i	1.03755	+	1.36895i
$599$	37.3706	−	21.5759i	1.52692	−	0.881569i	0.527434	−	0.849596i	$-0.323154\pi$
$599$	37.3706	−	21.5759i	1.52692	−	0.881569i	0.999489	−	0.0319734i	$-0.0101792\pi$
$600$	−8.53572	−	2.50301i	−0.348469	−	0.102185i
$601$	19.6346	+	11.3361i	0.800914	+	0.462408i	0.843791	−	0.536673i	$-0.180319\pi$
$601$	19.6346	+	11.3361i	0.800914	+	0.462408i	−0.0428769	+	0.999080i	$0.513652\pi$
$602$	9.94443	−	6.90486i	0.405305	−	0.281421i
$603$	5.06490	+	19.7837i	0.206259	+	0.805657i
$604$	4.41739	+	17.3076i	0.179741	+	0.704237i
$605$	−19.4988	+	33.7730i	−0.792741	+	1.37307i
$606$	−21.8392	+	12.2751i	−0.887158	+	0.498643i
$607$	−9.69474	−	16.7918i	−0.393498	−	0.681558i	0.599411	−	0.800442i	$-0.295402\pi$
$607$	−9.69474	−	16.7918i	−0.393498	−	0.681558i	−0.992908	+	0.118884i	$0.962068\pi$
$608$	−18.5709	−	8.34822i	−0.753150	−	0.338565i
$609$	−22.0322	−	18.6219i	−0.892790	−	0.754598i
$610$	−17.0253	−	7.17116i	−0.689335	−	0.290352i
$611$	30.5035			1.23404
$612$	−11.2296	+	6.14236i	−0.453928	+	0.248290i
$613$			11.2484i			0.454317i	0.973858	+	0.227159i	$0.0729436\pi$
$613$			11.2484i			0.454317i	−0.973858	+	0.227159i	$0.927056\pi$
$614$	2.43016	−	5.76954i	0.0980733	−	0.232840i
$615$	−15.8040	−	12.2677i	−0.637281	−	0.494682i
$616$	42.1182	+	8.11694i	1.69699	+	0.327041i
$617$	4.16806	+	7.21930i	0.167800	+	0.290638i	0.937646	−	0.347592i	$-0.113000\pi$
$617$	4.16806	+	7.21930i	0.167800	+	0.290638i	−0.769846	+	0.638230i	$0.779667\pi$
$618$	0.0764723	−	6.62769i	0.00307617	−	0.266605i
$619$	10.1564	+	5.86379i	0.408220	+	0.235686i	0.690025	−	0.723786i	$-0.257600\pi$
$619$	10.1564	+	5.86379i	0.408220	+	0.235686i	−0.281805	+	0.959472i	$0.590933\pi$
$620$	−13.8508	+	3.53511i	−0.556261	+	0.141973i
$621$	−23.5158	+	2.69593i	−0.943655	+	0.108184i
$622$	1.71045	+	13.6181i	0.0685828	+	0.546038i
$623$	−0.871786	+	20.9316i	−0.0349274	+	0.838609i
$624$	42.2260	−	16.0534i	1.69039	−	0.642650i
$625$	6.31231	+	10.9332i	0.252492	+	0.437329i
$626$	12.5953	+	16.6184i	0.503409	+	0.664206i
$627$	28.2277	+	21.9114i	1.12730	+	0.875057i
$628$	−8.49442	+	30.2560i	−0.338964	+	1.20735i
$629$	1.07905			0.0430246
$630$	−3.77600	+	19.6713i	−0.150439	+	0.783725i
$631$		−	17.6401i		−	0.702240i	−0.936330	−	0.351120i	$-0.885801\pi$
$631$		−	17.6401i		−	0.702240i	0.936330	−	0.351120i	$-0.114199\pi$
$632$	−1.05065	+	7.01060i	−0.0417926	+	0.278867i
$633$	3.89186	+	9.54623i	0.154688	+	0.379429i
$634$	20.7154	+	27.3322i	0.822712	+	1.08550i
$635$	11.4922	−	6.63501i	0.456053	−	0.263302i
$636$	−2.30512	+	1.70557i	−0.0914040	+	0.0676301i
$637$	19.4554	+	41.2886i	0.770853	+	1.63591i
$638$	50.6306	−	6.35925i	2.00449	−	0.251765i
$639$	−1.59013	+	5.67992i	−0.0629047	+	0.224694i
$640$	15.4910	+	12.9468i	0.612334	+	0.511766i
$641$	−4.75856	+	8.24207i	−0.187952	+	0.325542i	−0.944567	−	0.328318i	$-0.893518\pi$
$641$	−4.75856	+	8.24207i	−0.187952	+	0.325542i	0.756615	+	0.653860i	$0.226852\pi$
$642$	26.9733	+	15.9908i	1.06455	+	0.631107i
$643$	23.8893	−	13.7925i	0.942101	−	0.543922i	0.0514829	−	0.998674i	$-0.483605\pi$
$643$	23.8893	−	13.7925i	0.942101	−	0.543922i	0.890618	+	0.454751i	$0.150272\pi$
$644$	−22.9156	−	7.47543i	−0.903003	−	0.294573i
$645$	−9.90754	−	1.36068i	−0.390109	−	0.0535769i
$646$	−10.0074	−	4.21519i	−0.393737	−	0.165844i
$647$	26.8727			1.05647			0.528237	−	0.849097i	$-0.322853\pi$
$647$	26.8727			1.05647			0.528237	+	0.849097i	$0.322853\pi$
$648$	−4.33422	+	25.0841i	−0.170264	+	0.985398i
$649$		−	2.29055i		−	0.0899119i
$650$	15.4302	+	6.49929i	0.605223	+	0.254923i
$651$	−6.21601	−	17.2703i	−0.243625	−	0.676876i
$652$	26.6452	+	27.2874i	1.04351	+	1.06866i
$653$	−24.8287	+	14.3349i	−0.971624	+	0.560967i	−0.899731	−	0.436445i	$-0.856237\pi$
$653$	−24.8287	+	14.3349i	−0.971624	+	0.560967i	−0.0718927	+	0.997412i	$0.522904\pi$
$654$	4.48965	−	7.57315i	0.175559	−	0.296134i
$655$	−15.3147	−	8.84196i	−0.598396	−	0.345484i
$656$	−12.4085	−	22.7251i	−0.484469	−	0.887265i
$657$	−11.6074	+	41.4614i	−0.452848	+	1.61756i
$658$	−14.3780	+	9.98331i	−0.560514	+	0.389190i
$659$	−18.8863	+	32.7121i	−0.735707	+	1.27428i	0.218706	+	0.975791i	$0.429817\pi$
$659$	−18.8863	+	32.7121i	−0.735707	+	1.27428i	−0.954412	+	0.298491i	$0.903517\pi$
$660$	−21.0745	−	28.4828i	−0.820323	−	1.10869i
$661$	−4.81546	−	8.34062i	−0.187300	−	0.324412i	0.757049	−	0.653358i	$-0.226640\pi$
$661$	−4.81546	−	8.34062i	−0.187300	−	0.324412i	−0.944349	+	0.328945i	$0.893307\pi$
$662$	24.4754	−	18.5502i	0.951265	−	0.720975i
$663$	22.3097	−	9.09535i	0.866438	−	0.353234i
$664$	0.258311	−	1.72361i	0.0100244	−	0.0668892i
$665$	−15.0575	+	7.87693i	−0.583906	+	0.305454i
$666$	1.33536	−	1.67992i	0.0517443	−	0.0650957i
$667$	−28.6758			−1.11033
$668$	−0.494124	+	1.76001i	−0.0191182	+	0.0680966i
$669$	−23.3620	+	30.0964i	−0.903227	+	1.16359i
$670$	13.6909	−	10.3765i	0.528926	−	0.400879i
$671$	20.9799	+	36.3383i	0.809921	+	1.40282i
$672$	−14.6495	+	21.3867i	−0.565116	+	0.825011i
$673$	−1.48211	+	2.56709i	−0.0571311	+	0.0989540i	−0.893176	−	0.449706i	$-0.851529\pi$
$673$	−1.48211	+	2.56709i	−0.0571311	+	0.0989540i	0.836045	+	0.548660i	$0.184862\pi$
$674$	−3.63021	−	28.9028i	−0.139831	−	1.11329i
$675$	−7.58025	+	5.61729i	−0.291764	+	0.216210i
$676$	−57.1975	+	14.5984i	−2.19991	+	0.561478i
$677$	20.0073	−	34.6536i	0.768942	−	1.33185i	−0.169196	−	0.985582i	$-0.554117\pi$
$677$	20.0073	−	34.6536i	0.768942	−	1.33185i	0.938137	−	0.346263i	$-0.112550\pi$
$678$	−0.0646147	+	5.60001i	−0.00248151	+	0.215067i
$679$	−36.1763	−	22.9448i	−1.38832	−	0.880542i
$680$	8.42369	+	6.70609i	0.323034	+	0.257167i
$681$	−30.8043	−	23.9114i	−1.18042	−	0.916289i
$682$	29.9218	+	12.6032i	1.14576	+	0.482602i
$683$	7.37335			0.282133			0.141067	−	0.990000i	$-0.454947\pi$
$683$	7.37335			0.282133			0.141067	+	0.990000i	$0.454947\pi$
$684$	−18.9470	+	10.3637i	−0.724456	+	0.396264i
$685$	−27.4214			−1.04772
$686$	−22.6835	−	13.0942i	−0.866061	−	0.499938i
$687$	19.4068	+	47.6023i	0.740415	+	1.81614i
$688$	−11.0512	−	6.73627i	−0.421325	−	0.256818i
$689$	4.67430	−	2.69871i	0.178077	−	0.102813i
$690$	9.75591	+	17.3572i	0.371401	+	0.660777i
$691$	28.3406	+	16.3625i	1.07813	+	0.622457i	0.930391	−	0.366569i	$-0.119468\pi$
$691$	28.3406	+	16.3625i	1.07813	+	0.622457i	0.147737	+	0.989027i	$0.452801\pi$
$692$	−25.4925	+	6.50642i	−0.969081	+	0.247337i
$693$	33.8227	−	30.4275i	1.28482	−	1.15584i
$694$	1.49912	+	11.9356i	0.0569060	+	0.453070i
$695$	−23.2740	−	13.4373i	−0.882834	−	0.509704i
$696$	−8.67797	+	29.5934i	−0.328938	+	1.12174i
$697$	−6.90437	−	11.9587i	−0.261522	−	0.452969i
$698$	−29.0296	+	22.0019i	−1.09879	+	0.832783i
$699$	−33.3396	−	4.57880i	−1.26102	−	0.173186i
$700$	−9.40024	+	1.98658i	−0.355295	+	0.0750855i
$701$		−	5.14751i		−	0.194419i	−0.995264	−	0.0972094i	$-0.969008\pi$
$701$		−	5.14751i		−	0.194419i	0.995264	−	0.0972094i	$-0.0309917\pi$
$702$	13.4490	−	45.9888i	0.507598	−	1.73573i
$703$	1.82062			0.0686661
$704$	−10.2788	−	44.6879i	−0.387397	−	1.68424i
$705$	14.3247	+	1.96733i	0.539499	+	0.0740939i
$706$	−13.3833	−	17.6581i	−0.503685	−	0.664570i
$707$	−14.4934	+	22.8512i	−0.545080	+	0.859408i
$708$	1.26948	+	0.552042i	0.0477100	+	0.0207470i
$709$	18.9392	+	10.9345i	0.711276	+	0.410655i	0.811533	−	0.584306i	$-0.198633\pi$
$709$	18.9392	+	10.9345i	0.711276	+	0.410655i	−0.100257	+	0.994962i	$0.531967\pi$
$710$	4.92298	−	0.618331i	0.184756	−	0.0232055i
$711$	5.25695	+	5.37572i	0.197151	+	0.201605i
$712$	20.8412	−	8.19980i	0.781058	−	0.307301i
$713$	−15.8010	−	9.12272i	−0.591753	−	0.341648i
$714$	−7.53906	+	11.5888i	−0.282142	+	0.433698i
$715$	33.3461	+	57.7571i	1.24707	+	2.15999i
$716$	12.3733	+	12.6715i	0.462413	+	0.473557i
$717$	−5.18148	+	2.11241i	−0.193506	+	0.0788895i
$718$	−17.7704	+	42.1895i	−0.663187	+	1.57450i
$719$	−44.0176			−1.64158			−0.820790	−	0.571230i	$-0.806466\pi$
$719$	−44.0176			−1.64158			−0.820790	+	0.571230i	$0.806466\pi$
$720$	20.8650	−	4.81542i	0.777593	−	0.179460i
$721$	−3.31849	−	6.34363i	−0.123587	−	0.236249i
$722$	7.87807	+	3.31828i	0.293191	+	0.123494i
$723$	25.4626	+	19.7651i	0.946965	+	0.735070i
$724$	−4.35235	−	4.45724i	−0.161754	−	0.165652i
$725$	−9.89875	+	5.71505i	−0.367631	+	0.212252i
$726$	−0.617621	+	53.5278i	−0.0229221	+	1.98660i
$727$	−14.7080	+	25.4750i	−0.545489	+	0.944815i	0.453087	+	0.891466i	$0.350323\pi$
$727$	−14.7080	+	25.4750i	−0.545489	+	0.944815i	−0.998576	+	0.0533487i	$0.983011\pi$
$728$	31.9528	−	36.8767i	1.18425	−	1.36674i
$729$	18.4415	+	19.7208i	0.683020	+	0.730399i
$730$	35.9360	−	4.51360i	1.33005	−	0.167056i
$731$	−5.97771	−	3.45123i	−0.221094	−	0.127648i
$732$	−25.1960	+	2.86976i	−0.931269	+	0.106069i
$733$	−17.7078	−	30.6708i	−0.654052	−	1.13285i	−0.982131	−	0.188201i	$-0.939734\pi$
$733$	−17.7078	−	30.6708i	−0.654052	−	1.13285i	0.328079	−	0.944650i	$-0.393599\pi$
$734$	−7.31309	+	5.54268i	−0.269931	+	0.204584i
$735$	6.47351	+	20.6442i	0.238779	+	0.761473i
$736$	2.60163	+	25.6367i	0.0958974	+	0.944982i
$737$	−39.0182			−1.43725
$738$	−27.1624	−	4.05026i	−0.999861	−	0.149092i
$739$	−34.7390			−1.27789			−0.638947	−	0.769251i	$-0.720630\pi$
$739$	−34.7390			−1.27789			−0.638947	+	0.769251i	$0.720630\pi$
$740$	−1.73803	−	0.487953i	−0.0638911	−	0.0179375i
$741$	37.6419	−	15.3461i	1.38281	−	0.563752i
$742$	−1.32002	+	2.80188i	−0.0484594	+	0.102860i
$743$	5.76237	−	3.32691i	0.211401	−	0.122052i	−0.390561	−	0.920577i	$-0.627719\pi$
$743$	5.76237	−	3.32691i	0.211401	−	0.122052i	0.601962	+	0.798525i	$0.294386\pi$
$744$	−14.1964	+	13.5459i	−0.520466	+	0.496617i
$745$	−17.1511	−	9.90219i	−0.628368	−	0.362788i
$746$	0.821721	−	0.103209i	0.0300854	−	0.00377875i
$747$	−1.29247	−	1.32167i	−0.0472888	−	0.0483572i
$748$	−6.04780	−	23.6956i	−0.221129	−	0.866399i
$749$	33.8402	+	1.40942i	1.23649	+	0.0514989i
$750$	25.6267	+	15.1925i	0.935753	+	0.554750i
$751$	−14.8725	+	8.58662i	−0.542704	+	0.313330i	−0.746174	−	0.665751i	$-0.768111\pi$
$751$	−14.8725	+	8.58662i	−0.542704	+	0.313330i	0.203470	+	0.979081i	$0.434778\pi$
$752$	15.9783	+	9.73955i	0.582668	+	0.355165i
$753$	−4.94546	+	36.0093i	−0.180222	+	1.31225i
$754$	22.5331	−	53.4967i	0.820607	−	1.94823i
$755$		−	15.9374i		−	0.580020i
$756$	8.71212	+	26.0787i	0.316857	+	0.948473i
$757$		−	38.6795i		−	1.40583i	−0.711274	−	0.702915i	$-0.751882\pi$
$757$		−	38.6795i		−	1.40583i	0.711274	−	0.702915i	$-0.248118\pi$
$758$	22.0791	+	9.29985i	0.801950	+	0.337786i
$759$	6.15321	−	44.8033i	0.223347	−	1.62626i
$760$	14.2128	+	11.3148i	0.515553	+	0.410431i
$761$	−30.3784	+	17.5390i	−1.10122	+	0.635787i	−0.936540	−	0.350560i	$-0.885991\pi$
$761$	−30.3784	+	17.5390i	−1.10122	+	0.635787i	−0.164676	+	0.986348i	$0.552658\pi$
$762$	9.28915	−	15.6690i	0.336510	−	0.567626i
$763$	0.395714	−	9.50112i	0.0143258	−	0.343964i
$764$	−7.53561	−	29.5250i	−0.272629	−	1.06818i
$765$	11.0634	−	2.83238i	0.399999	−	0.102405i
$766$	−1.06755	−	8.49953i	−0.0385721	−	0.307100i
$767$	−2.25657	−	1.30283i	−0.0814801	−	0.0470426i
$768$	27.2445	+	5.07340i	0.983100	+	0.183071i
$769$	30.3192	−	17.5048i	1.09334	−	0.631239i	0.158875	−	0.987299i	$-0.449213\pi$
$769$	30.3192	−	17.5048i	1.09334	−	0.631239i	0.934463	+	0.356060i	$0.115880\pi$
$770$	−34.6208	−	16.3105i	−1.24765	−	0.587791i
$771$	7.70149	−	3.13979i	0.277362	−	0.113077i
$772$	1.56070	−	5.55900i	0.0561708	−	0.200073i
$773$	−48.1597			−1.73218			−0.866091	−	0.499886i	$-0.833375\pi$
$773$	−48.1597			−1.73218			−0.866091	+	0.499886i	$0.833375\pi$
$774$	−12.7707	+	5.03539i	−0.459033	+	0.180993i
$775$	−7.27259			−0.261239
$776$	−6.78760	+	45.2912i	−0.243661	+	1.62586i
$777$	0.410670	−	2.28128i	0.0147327	−	0.0818406i
$778$	−17.1325	−	22.6049i	−0.614231	−	0.810426i
$779$	−11.6494	−	20.1773i	−0.417381	−	0.722926i
$780$	−40.0472	+	4.56127i	−1.43392	+	0.163320i
$781$	−9.75958	−	5.63470i	−0.349225	−	0.201625i
$782$	1.71265	+	13.6357i	0.0612443	+	0.487610i
$783$	19.4752	+	26.2808i	0.695987	+	0.939198i
$784$	−2.99203	+	27.8397i	−0.106858	+	0.994274i
$785$	14.0195	−	24.2825i	0.500377	−	0.866678i
$786$	−24.2728	−	0.280067i	−0.865781	−	0.00998965i
$787$	−28.3882	+	16.3900i	−1.01193	+	0.584239i	−0.911756	−	0.410731i	$-0.865273\pi$
$787$	−28.3882	+	16.3900i	−1.01193	+	0.584239i	−0.100175	+	0.994970i	$0.531940\pi$
$788$	−35.3782	+	34.5456i	−1.26030	+	1.23064i
$789$	−0.583255	−	0.452745i	−0.0207644	−	0.0161182i
$790$	2.45518	−	5.82894i	0.0873514	−	0.207384i
$791$	2.80393	+	5.36000i	0.0996964	+	0.190580i
$792$	−44.3750	−	19.9087i	−1.57680	−	0.707424i
$793$	47.7324			1.69503
$794$	2.38526	+	1.00468i	0.0846496	+	0.0356549i
$795$	2.36914	−	0.965865i	0.0840248	−	0.0342557i
$796$	22.0145	+	22.5451i	0.780283	+	0.799088i
$797$	−3.40500	−	5.89764i	−0.120611	−	0.208905i	0.799398	−	0.600802i	$-0.205152\pi$
$797$	−3.40500	−	5.89764i	−0.120611	−	0.208905i	−0.920009	+	0.391897i	$0.871819\pi$
$798$	−12.7202	+	19.5530i	−0.450291	+	0.692170i
$799$	8.64280	+	4.98992i	0.305760	+	0.176531i
$800$	6.00745	+	8.33119i	0.212395	+	0.294552i
$801$	6.40410	−	22.8753i	0.226278	−	0.808259i
$802$	−0.747389	−	5.95051i	−0.0263912	−	0.210120i
$803$	−71.2415	−	41.1313i	−2.51406	−	1.45149i
$804$	9.40374	−	21.6249i	0.331644	−	0.762651i
$805$	18.1615	+	11.5189i	0.640108	+	0.405989i
$806$	29.4353	−	22.3094i	1.03682	−	0.785815i
$807$	14.7789	+	2.02970i	0.520241	+	0.0714490i
$808$	28.6087	+	4.28747i	1.00645	+	0.150833i
$809$	7.74558			0.272320			0.136160	−	0.990687i	$-0.456524\pi$
$809$	7.74558			0.272320			0.136160	+	0.990687i	$0.456524\pi$
$810$	9.28178	−	20.7293i	0.326128	−	0.728353i
$811$			36.9006i			1.29576i	0.761744	+	0.647878i	$0.224344\pi$
$811$			36.9006i			1.29576i	−0.761744	+	0.647878i	$0.775656\pi$
$812$	6.88748	+	32.5907i	0.241703	+	1.14371i
$813$	14.4217	+	1.98065i	0.505790	+	0.0694643i
$814$	2.47663	+	3.26771i	0.0868059	+	0.114533i
$815$	−17.0143	−	29.4696i	−0.595984	−	1.03227i
$816$	14.5903	+	2.35902i	0.510763	+	0.0825821i
$817$	−10.0858	−	5.82307i	−0.352859	−	0.203723i
$818$	−6.81136	+	0.855513i	−0.238154	+	0.0299123i
$819$	−10.7383	−	50.6278i	−0.375225	−	1.76908i
$820$	5.71305	+	22.3841i	0.199508	+	0.781686i
$821$	1.27921	+	0.738551i	0.0446447	+	0.0257756i	0.522156	−	0.852850i	$-0.325128\pi$
$821$	1.27921	+	0.738551i	0.0446447	+	0.0257756i	−0.477512	+	0.878625i	$0.658461\pi$
$822$	−32.8129	+	18.4431i	−1.14448	+	0.643277i
$823$	−6.36180	+	3.67299i	−0.221758	+	0.128032i	−0.606764	−	0.794882i	$-0.707533\pi$
$823$	−6.36180	+	3.67299i	−0.221758	+	0.128032i	0.385006	+	0.922914i	$0.374199\pi$
$824$	−4.76685	+	5.98776i	−0.166061	+	0.208593i
$825$	−6.80519	−	16.6923i	−0.236926	−	0.581150i
$826$	1.49004	−	0.124441i	0.0518453	−	0.00432985i
$827$	12.3241			0.428552			0.214276	−	0.976773i	$-0.431261\pi$
$827$	12.3241			0.428552			0.214276	+	0.976773i	$0.431261\pi$
$828$	23.3482	+	14.2083i	0.811405	+	0.493771i
$829$	−0.588826			−0.0204508			−0.0102254	−	0.999948i	$-0.503255\pi$
$829$	−0.588826			−0.0204508			−0.0102254	+	0.999948i	$0.503255\pi$
$830$	−0.603627	+	1.43309i	−0.0209522	+	0.0497434i
$831$	6.75228	+	5.24137i	0.234234	+	0.181821i
$832$	−49.8715	−	15.2915i	−1.72898	−	0.530138i
$833$	−1.24174	+	14.8812i	−0.0430236	+	0.515604i
$834$	−36.8877	−	0.425622i	−1.27732	−	0.0147381i
$835$	0.815520	−	1.41252i	0.0282222	−	0.0488824i
$836$	−10.2041	−	39.9803i	−0.352916	−	1.38275i
$837$	2.37049	+	20.6770i	0.0819363	+	0.714703i
$838$	3.22637	−	0.405235i	0.111453	−	0.0139986i
$839$	−15.1874	+	26.3054i	−0.524328	+	0.908163i	0.475271	+	0.879840i	$0.342350\pi$
$839$	−15.1874	+	26.3054i	−0.524328	+	0.908163i	−0.999599	+	0.0283235i	$0.990983\pi$
$840$	17.3836	−	15.2568i	0.599793	−	0.526408i
$841$	5.31412	+	9.20433i	0.183246	+	0.317391i
$842$	−32.9083	−	43.4196i	−1.13409	−	1.49634i
$843$	25.8030	−	33.2411i	0.888703	−	1.14488i
$844$	3.21763	−	11.4608i	0.110756	−	0.394496i
$845$	52.6692			1.81188
$846$	18.4643	−	7.28035i	0.634817	−	0.250304i
$847$	26.8015	+	51.2337i	0.920910	+	1.76041i
$848$	3.31016	+	0.0788372i	0.113671	+	0.00270728i
$849$	37.6254	−	15.3393i	1.29130	−	0.526445i
$850$	3.30877	+	4.36564i	0.113490	+	0.149740i
$851$	−1.15207	−	1.99544i	−0.0394923	−	0.0684027i
$852$	5.47504	−	4.05100i	0.187572	−	0.138785i
$853$	−0.381441	+	0.660676i	−0.0130603	+	0.0226211i	−0.872482	−	0.488647i	$-0.837491\pi$
$853$	−0.381441	+	0.660676i	−0.0130603	+	0.0226211i	0.859421	+	0.511268i	$0.170824\pi$
$854$	−22.4989	+	15.6220i	−0.769898	+	0.534575i
$855$	18.6667	−	4.77891i	0.638387	−	0.163435i
$856$	−13.2566	−	33.6940i	−0.453102	−	1.15164i
$857$	12.4869	+	7.20931i	0.426544	+	0.246266i	0.697873	−	0.716221i	$-0.254130\pi$
$857$	12.4869	+	7.20931i	0.426544	+	0.246266i	−0.271329	+	0.962487i	$0.587463\pi$
$858$	78.7487	+	46.6852i	2.68844	+	1.59381i
$859$	8.64422	−	4.99075i	0.294937	−	0.170282i	−0.345229	−	0.938518i	$-0.612199\pi$
$859$	8.64422	−	4.99075i	0.294937	−	0.170282i	0.640166	+	0.768236i	$0.278865\pi$
$860$	8.06761	+	8.26204i	0.275103	+	0.281733i
$861$	−27.9103	+	10.0456i	−0.951181	+	0.342354i
$862$	−0.633436	+	1.50386i	−0.0215749	+	0.0512218i
$863$			20.5530i			0.699633i	0.936818	+	0.349816i	$0.113756\pi$
$863$			20.5530i			0.699633i	−0.936818	+	0.349816i	$0.886244\pi$
$864$	21.7287	−	19.7956i	0.739224	−	0.673459i
$865$	23.4743			0.798151
$866$	−4.10217	+	9.73911i	−0.139397	+	0.330948i
$867$	−21.3620	−	2.93382i	−0.725491	−	0.0996377i
$868$	−6.57303	+	20.1494i	−0.223103	+	0.683914i
$869$	−12.4411	+	7.18287i	−0.422035	+	0.243662i
$870$	14.0320	−	23.6692i	0.475729	−	0.802460i
$871$	−22.1930	+	38.4395i	−0.751982	+	1.30247i
$872$	−9.46007	+	3.72199i	−0.320359	+	0.126042i
$873$	33.9619	+	34.7292i	1.14944	+	1.17541i
$874$	2.88966	+	23.0067i	0.0977441	+	0.778212i
$875$	32.1507	+	1.33905i	1.08689	+	0.0452681i
$876$	39.9659	−	29.5709i	1.35032	−	0.999107i
$877$	15.3343	−	8.85327i	0.517803	−	0.298954i	−0.218232	−	0.975897i	$-0.570029\pi$
$877$	15.3343	−	8.85327i	0.517803	−	0.298954i	0.736035	+	0.676943i	$0.236696\pi$
$878$	−33.3509	+	25.2770i	−1.12554	+	0.853058i
$879$	5.01697	+	12.3060i	0.169218	+	0.415070i
$880$	−0.974136	+	40.9014i	−0.0328381	+	1.37878i
$881$			2.58804i			0.0871932i	0.999049	+	0.0435966i	$0.0138816\pi$
$881$			2.58804i			0.0871932i	−0.999049	+	0.0435966i	$0.986118\pi$
$882$	21.6312	+	20.3493i	0.728360	+	0.685195i
$883$	−41.4416			−1.39462			−0.697310	−	0.716769i	$-0.745620\pi$
$883$	−41.4416			−1.39462			−0.697310	+	0.716769i	$0.745620\pi$
$884$	−26.7841	−	7.51967i	−0.900846	−	0.252914i
$885$	−0.975677	−	0.757358i	−0.0327970	−	0.0254583i
$886$	42.1188	−	31.9224i	1.41501	−	1.07245i
$887$	−10.7798	−	18.6711i	−0.361949	−	0.626914i	0.626333	−	0.779556i	$-0.284555\pi$
$887$	−10.7798	−	18.6711i	−0.361949	−	0.626914i	−0.988282	+	0.152642i	$0.951222\pi$
$888$	−2.40794	+	0.585067i	−0.0808050	+	0.0196336i
$889$	0.818737	−	19.6579i	0.0274596	−	0.659306i
$890$	−19.8268	+	2.49027i	−0.664596	+	0.0834739i
$891$	−45.2403	+	24.7890i	−1.51561	+	0.830462i
$892$	42.6271	−	10.8796i	1.42726	−	0.364277i
$893$	14.5825	+	8.41921i	0.487985	+	0.281738i
$894$	−27.1833	−	0.313649i	−0.909145	−	0.0104900i
$895$	−7.90097	−	13.6849i	−0.264100	−	0.457435i
$896$	28.5119	−	9.11437i	0.952516	−	0.304490i
$897$	−40.6389	−	31.5455i	−1.35689	−	1.05327i
$898$	26.4964	+	11.1604i	0.884196	+	0.372428i
$899$			25.2141i			0.840939i
$900$	10.8914	+	0.251370i	0.363046	+	0.00837900i
$901$	1.76587			0.0588298
$902$	20.3679	−	48.3562i	0.678176	−	1.61008i
$903$	−9.57146	+	11.3243i	−0.318518	+	0.376850i
$904$	4.02771	−	5.05931i	0.133960	−	0.168270i
$905$	2.77919	+	4.81369i	0.0923832	+	0.160012i
$906$	−10.7191	−	19.0709i	−0.356120	−	0.633589i
$907$	−8.95976	+	15.5188i	−0.297504	+	0.515292i	−0.975564	−	0.219714i	$-0.929487\pi$
$907$	−8.95976	+	15.5188i	−0.297504	+	0.515292i	0.678060	+	0.735006i	$0.262821\pi$
$908$	11.1355	+	43.6297i	0.369545	+	1.44790i
$909$	21.9371	−	21.4525i	0.727609	−	0.711534i
$910$	−35.7605	+	24.8301i	−1.18545	+	0.823109i
$911$	−20.9042	−	12.0691i	−0.692589	−	0.399866i	0.111992	−	0.993709i	$-0.464277\pi$
$911$	−20.9042	−	12.0691i	−0.692589	−	0.399866i	−0.804581	+	0.593843i	$0.797610\pi$
$912$	24.6174	+	3.98023i	0.815163	+	0.131799i
$913$	3.05875	−	1.76597i	0.101230	−	0.0584450i
$914$	−34.0893	+	25.8367i	−1.12758	+	0.854602i
$915$	22.4155	+	3.07850i	0.741033	+	0.101772i
$916$	16.0447	−	57.1493i	0.530133	−	1.88827i
$917$	−23.2325	+	12.1534i	−0.767204	+	0.401341i
$918$	11.3337	−	10.8303i	0.374067	−	0.357453i
$919$		−	48.2663i		−	1.59216i	−0.605193	−	0.796079i	$-0.706904\pi$
$919$		−	48.2663i		−	1.59216i	0.605193	−	0.796079i	$-0.293096\pi$
$920$	3.40756	−	22.7374i	0.112344	−	0.749629i
$921$	−1.04324	+	7.59615i	−0.0343760	+	0.250302i
$922$	19.5691	−	14.8317i	0.644474	−	0.488455i
$923$	−11.1022	+	6.40988i	−0.365435	+	0.210984i
$924$	−52.3980	+	3.76779i	−1.72377	+	0.123951i
$925$	−0.795377	−	0.459211i	−0.0261518	−	0.0150988i
$926$	17.2932	−	2.17204i	0.568290	−	0.0713778i
$927$	2.01332	+	7.86414i	0.0661261	+	0.258292i
$928$	28.8843	−	20.8279i	0.948174	−	0.683708i
$929$	4.33140	+	2.50073i	0.142108	+	0.0820464i	0.569368	−	0.822082i	$-0.307188\pi$
$929$	4.33140	+	2.50073i	0.142108	+	0.0820464i	−0.427260	+	0.904129i	$0.640521\pi$
$930$	15.2619	−	8.57822i	0.500458	−	0.281291i
$931$	−2.09511	+	25.1082i	−0.0686645	+	0.822889i
$932$	27.1481	+	27.8024i	0.889265	+	0.910697i
$933$	−6.34600	−	15.5659i	−0.207759	−	0.509605i
$934$	−9.61532	+	22.8281i	−0.314623	+	0.746959i
$935$			21.8197i			0.713580i
$936$	−44.8533	+	32.3930i	−1.46607	+	1.05880i
$937$		−	34.4040i		−	1.12393i	−0.827161	−	0.561965i	$-0.810046\pi$
$937$		−	34.4040i		−	1.12393i	0.827161	−	0.561965i	$-0.189954\pi$
$938$	−2.11978	−	25.3821i	−0.0692133	−	0.828755i
$939$	−20.1740	−	15.6598i	−0.658353	−	0.511039i
$940$	−11.6645	−	11.9456i	−0.380453	−	0.389622i
$941$	−1.17611	−	2.03707i	−0.0383400	−	0.0664067i	0.846219	−	0.532836i	$-0.178874\pi$
$941$	−1.17611	−	2.03707i	−0.0383400	−	0.0664067i	−0.884559	+	0.466429i	$0.845540\pi$
$942$	0.444064	−	38.4860i	0.0144684	−	1.25394i
$943$	−14.7431	+	25.5358i	−0.480102	+	0.831561i
$944$	−0.766048	−	1.40295i	−0.0249327	−	0.0456622i
$945$	−1.77753	−	24.4677i	−0.0578229	−	0.795936i
$946$	−3.26859	−	26.0236i	−0.106271	−	0.846101i
$947$	−14.7188	+	25.4936i	−0.478295	+	0.828432i	−0.999690	−	0.0248838i	$-0.992078\pi$
$947$	−14.7188	+	25.4936i	−0.478295	+	0.828432i	0.521395	+	0.853315i	$0.325412\pi$
$948$	−0.982516	−	8.62631i	−0.0319106	−	0.280170i
$949$	−81.0424	+	46.7899i	−2.63075	+	1.51886i
$950$	5.58270	+	7.36590i	0.181127	+	0.238981i
$951$	−33.1800	−	25.7556i	−1.07593	−	0.835182i
$952$	15.0859	−	5.22154i	0.488937	−	0.169231i
$953$	12.9601			0.419819			0.209909	−	0.977721i	$-0.432683\pi$
$953$	12.9601			0.419819			0.209909	+	0.977721i	$0.432683\pi$
$954$	2.18533	−	2.74921i	0.0707527	−	0.0890088i
$955$			27.1875i			0.879767i
$956$	6.22065	+	1.74646i	0.201190	+	0.0564845i
$957$	−57.8722	+	23.5937i	−1.87074	+	0.762675i
$958$	−32.1703	+	24.3823i	−1.03938	+	0.787755i
$959$	−21.7760	+	34.3334i	−0.703183	+	1.10868i
$960$	−22.4338	−	10.3975i	−0.724048	−	0.335577i
$961$	7.47853	−	12.9532i	0.241243	−	0.417845i
$962$	4.62791	−	0.581270i	0.149210	−	0.0187409i
$963$	−36.9825	−	10.3535i	−1.19174	−	0.333637i
$964$	−9.20455	−	36.0640i	−0.296459	−	1.16154i
$965$	−2.57583	+	4.46147i	−0.0829190	+	0.143620i
$966$	29.4797	+	1.56871i	0.948494	+	0.0504723i
$967$	−8.60670	+	4.96908i	−0.276773	+	0.159795i	−0.631961	−	0.775000i	$-0.717750\pi$
$967$	−8.60670	+	4.96908i	−0.276773	+	0.159795i	0.355189	+	0.934795i	$0.384417\pi$
$968$	38.4990	−	48.3595i	1.23740	−	1.55433i
$969$	13.1758	+	1.80954i	0.423266	+	0.0581306i
$970$	15.8614	−	37.6572i	0.509279	−	1.20910i
$971$		−	41.2521i		−	1.32384i	−0.749573	−	0.661922i	$-0.769741\pi$
$971$		−	41.2521i		−	1.32384i	0.749573	−	0.661922i	$-0.230259\pi$
$972$	−2.83535	−	31.0477i	−0.0909440	−	0.995856i
$973$	−35.3067	+	18.4697i	−1.13188	+	0.592112i
$974$	3.59879	−	8.54403i	0.115313	−	0.273768i
$975$	−20.3154	−	2.79008i	−0.650612	−	0.0893539i
$976$	25.0031	+	15.2406i	0.800329	+	0.487839i
$977$	−1.36989	−	2.37272i	−0.0438268	−	0.0759102i	0.843280	−	0.537475i	$-0.180622\pi$
$977$	−1.36989	−	2.37272i	−0.0438268	−	0.0759102i	−0.887107	+	0.461564i	$0.847288\pi$
$978$	−40.1802	−	23.8203i	−1.28482	−	0.761690i
$979$	39.3058	+	22.6932i	1.25622	+	0.725278i
$980$	8.72944	−	23.4076i	0.278852	−	0.747729i
$981$	−2.90690	+	10.3834i	−0.0928101	+	0.331516i
$982$	−4.00072	−	31.8526i	−0.127668	−	1.01646i
$983$	21.2281	−	36.7681i	0.677071	−	1.17272i	−0.298788	−	0.954320i	$-0.596582\pi$
$983$	21.2281	−	36.7681i	0.677071	−	1.17272i	0.975859	−	0.218402i	$-0.0700844\pi$
$984$	21.8914	+	22.9427i	0.697872	+	0.731386i
$985$	38.2074	−	22.0591i	1.21739	−	0.702860i
$986$	15.1357	−	11.4715i	0.482020	−	0.365328i
$987$	13.8388	−	16.3731i	0.440493	−	0.521162i
$988$	−45.1912	−	12.6875i	−1.43772	−	0.403643i
$989$			14.7390i			0.468674i
$990$	33.9700	+	27.0026i	1.07964	+	0.858200i
$991$			14.3136i			0.454685i	0.973815	+	0.227343i	$0.0730037\pi$
$991$			14.3136i			0.454685i	−0.973815	+	0.227343i	$0.926996\pi$
$992$	22.5420	−	2.28757i	0.715709	−	0.0726306i
$993$	−23.0636	+	29.7120i	−0.731902	+	0.942883i
$994$	3.13526	−	6.65492i	0.0994444	−	0.211081i
$995$	−14.0573	−	24.3480i	−0.445647	−	0.771884i
$996$	0.241560	+	2.12085i	0.00765411	+	0.0672017i
$997$	8.01970	−	13.8905i	0.253986	−	0.439917i	−0.710633	−	0.703563i	$-0.751591\pi$
$997$	8.01970	−	13.8905i	0.253986	−	0.439917i	0.964620	+	0.263645i	$0.0849248\pi$
$998$	−1.52644	−	12.1531i	−0.0483188	−	0.384701i
$999$	−1.04635	+	2.41105i	−0.0331051	+	0.0762823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.be.a.475.81	yes	184
7.6	odd	2	inner	504.2.be.a.475.82	yes	184
8.3	odd	2	inner	504.2.be.a.475.19	yes	184
9.4	even	3	inner	504.2.be.a.139.20	yes	184
56.27	even	2	inner	504.2.be.a.475.20	yes	184
63.13	odd	6	inner	504.2.be.a.139.19	✓	184
72.67	odd	6	inner	504.2.be.a.139.82	yes	184
504.139	even	6	inner	504.2.be.a.139.81	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.19	✓	184	63.13	odd	6	inner
504.2.be.a.139.20	yes	184	9.4	even	3	inner
504.2.be.a.139.81	yes	184	504.139	even	6	inner
504.2.be.a.139.82	yes	184	72.67	odd	6	inner
504.2.be.a.475.19	yes	184	8.3	odd	2	inner
504.2.be.a.475.20	yes	184	56.27	even	2	inner
504.2.be.a.475.81	yes	184	1.1	even	1	trivial
504.2.be.a.475.82	yes	184	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.30332 + 0.548965i) q^{2} +(-1.71594 - 0.235665i) q^{3} +(1.39728 + 1.43095i) q^{4} +(-0.892228 - 1.54538i) q^{5} +(-2.10705 - 1.24914i) q^{6} +(-2.64346 - 0.110098i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 + 0.808775i) q^{9} +O(q^{10})\)	\(q+(1.30332 + 0.548965i) q^{2} +(-1.71594 - 0.235665i) q^{3} +(1.39728 + 1.43095i) q^{4} +(-0.892228 - 1.54538i) q^{5} +(-2.10705 - 1.24914i) q^{6} +(-2.64346 - 0.110098i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 + 0.808775i) q^{9} +(-0.314496 - 2.50393i) q^{10} +(-2.86592 + 4.96393i) q^{11} +(-2.06042 - 2.78472i) q^{12} +(3.26020 + 5.64683i) q^{13} +(-3.38483 - 1.59466i) q^{14} +(1.16682 + 2.86206i) q^{15} +(-0.0952399 + 3.99887i) q^{16} +2.13328i q^{17} +(3.32120 + 2.64001i) q^{18} +3.59936i q^{19} +(0.964680 - 3.43606i) q^{20} +(4.51008 + 0.811892i) q^{21} +(-6.46023 + 4.89629i) q^{22} +(3.94496 - 2.27763i) q^{23} +(-1.15667 - 4.76047i) q^{24} +(0.907857 - 1.57245i) q^{25} +(1.14917 + 9.14935i) q^{26} +(-4.76663 - 2.06863i) q^{27} +(-3.53610 - 3.93650i) q^{28} +(-5.45171 - 3.14755i) q^{29} +(-0.0504307 + 4.37072i) q^{30} +(-2.00268 - 3.46875i) q^{31} +(-2.31936 + 5.15951i) q^{32} +(6.08759 - 7.84242i) q^{33} +(-1.17109 + 2.78034i) q^{34} +(2.18843 + 4.18339i) q^{35} +(2.87931 + 5.26399i) q^{36} -0.505819i q^{37} +(-1.97592 + 4.69111i) q^{38} +(-4.26356 - 10.4580i) q^{39} +(3.14356 - 3.94871i) q^{40} +(-5.60580 + 3.23651i) q^{41} +(5.43237 + 3.53403i) q^{42} +(-1.61781 + 2.80212i) q^{43} +(-11.1076 + 2.83498i) q^{44} +(-1.32771 - 5.18611i) q^{45} +(6.39188 - 0.802826i) q^{46} +(2.33909 - 4.05142i) q^{47} +(1.10582 - 6.83938i) q^{48} +(6.97576 + 0.582079i) q^{49} +(2.04645 - 1.55103i) q^{50} +(0.502738 - 3.66058i) q^{51} +(-3.52494 + 12.5554i) q^{52} -0.827775i q^{53} +(-5.07683 - 5.31279i) q^{54} +10.2282 q^{55} +(-2.44766 - 7.07170i) q^{56} +(0.848242 - 6.17629i) q^{57} +(-5.37742 - 7.09505i) q^{58} +(-0.346079 + 0.199809i) q^{59} +(-2.46510 + 5.66875i) q^{60} +(3.66024 - 6.33971i) q^{61} +(-0.705912 - 5.62028i) q^{62} +(-7.54771 - 2.45603i) q^{63} +(-5.85526 + 5.45124i) q^{64} +(5.81768 - 10.0765i) q^{65} +(12.2393 - 6.87930i) q^{66} +(3.40363 + 5.89527i) q^{67} +(-3.05262 + 2.98078i) q^{68} +(-7.30609 + 2.97859i) q^{69} +(0.555680 + 6.65366i) q^{70} +1.96610i q^{71} +(0.862910 + 8.44129i) q^{72} +14.3518i q^{73} +(0.277676 - 0.659243i) q^{74} +(-1.92840 + 2.48429i) q^{75} +(-5.15050 + 5.02930i) q^{76} +(8.12247 - 12.8064i) q^{77} +(0.184274 - 15.9706i) q^{78} +(2.17052 + 1.25315i) q^{79} +(6.26476 - 3.42072i) q^{80} +(7.69177 + 4.67298i) q^{81} +(-9.08287 + 1.14082i) q^{82} +(-0.533641 - 0.308098i) q^{83} +(5.14005 + 7.58814i) q^{84} +(3.29674 - 1.90337i) q^{85} +(-3.64678 + 2.76394i) q^{86} +(8.61307 + 6.68579i) q^{87} +(-16.0331 - 2.40281i) q^{88} -7.91828i q^{89} +(1.11656 - 7.48802i) q^{90} +(-7.99650 - 15.2861i) q^{91} +(8.77137 + 2.46258i) q^{92} +(2.61903 + 6.42413i) q^{93} +(5.27266 - 3.99621i) q^{94} +(5.56239 - 3.21145i) q^{95} +(5.19581 - 8.30684i) q^{96} +(14.0224 + 8.09583i) q^{97} +(8.77209 + 4.58808i) q^{98} +(-12.2941 + 12.0225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

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