LMFDB - Embedded newform 504.2.be.a.139.20

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			139.20
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12708 + 0.854224i) q^{2} +(1.71594 - 0.235665i) q^{3} +(0.540602 - 1.92555i) q^{4} +(-0.892228 + 1.54538i) q^{5} +(-1.73269 + 1.73141i) q^{6} +(1.41708 - 2.23425i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 - 0.808775i) q^{9} +O(q^{10})$	\(q+(-1.12708 + 0.854224i) q^{2} +(1.71594 - 0.235665i) q^{3} +(0.540602 - 1.92555i) q^{4} +(-0.892228 + 1.54538i) q^{5} +(-1.73269 + 1.73141i) q^{6} +(1.41708 - 2.23425i) 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} +(0.473857 - 3.43154i) q^{12} +(3.26020 - 5.64683i) q^{13} +(0.311400 + 3.72868i) q^{14} +(-1.16682 + 2.86206i) q^{15} +(-3.41550 - 2.08191i) q^{16} +2.13328i q^{17} +(-2.56516 + 3.37934i) q^{18} +3.59936i q^{19} +(2.49338 + 2.55347i) q^{20} +(1.90509 - 4.16781i) q^{21} +(7.47042 + 3.14658i) q^{22} +(-3.94496 - 2.27763i) q^{23} +(2.39723 + 4.27239i) 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} +(-1.12975 - 4.22249i) q^{30} +(-2.00268 + 3.46875i) q^{31} +(5.62795 - 0.571128i) q^{32} +(-6.08759 - 7.84242i) q^{33} +(-1.82230 - 2.40437i) q^{34} +(2.18843 + 4.18339i) q^{35} +(0.00441969 - 6.00000i) q^{36} -0.505819i q^{37} +(-3.07466 - 4.05675i) q^{38} +(4.26356 - 10.4580i) q^{39} +(-4.99146 - 0.748050i) q^{40} +(5.60580 + 3.23651i) q^{41} +(1.41306 + 6.32481i) 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} +(-6.35144 - 2.76753i) q^{48} +(-2.98378 - 6.33222i) q^{49} +(-2.36645 - 0.996763i) q^{50} +(0.502738 + 3.66058i) q^{51} +(-9.11079 - 9.33037i) q^{52} -0.827775i q^{53} +(-3.60528 + 6.40328i) q^{54} +10.2282 q^{55} +(7.34810 + 1.41611i) q^{56} +(0.848242 + 6.17629i) q^{57} +(-3.45578 + 8.20451i) q^{58} +(0.346079 + 0.199809i) q^{59} +(4.88026 + 3.79401i) q^{60} +(3.66024 + 6.33971i) q^{61} +(-0.705912 - 5.62028i) q^{62} +(2.28682 - 7.60069i) q^{63} +(-5.85526 + 5.45124i) q^{64} +(5.81768 + 10.0765i) q^{65} +(13.5604 + 3.63884i) q^{66} +(3.40363 - 5.89527i) q^{67} +(4.10774 + 1.15325i) q^{68} +(-7.30609 - 2.97859i) q^{69} +(-6.04008 - 2.84560i) q^{70} +1.96610i q^{71} +(5.12036 + 6.76623i) q^{72} +14.3518i q^{73} +(0.432083 + 0.570096i) q^{74} +(1.92840 + 2.48429i) q^{75} +(6.93075 + 1.94582i) q^{76} +(-15.1519 - 0.631065i) q^{77} +(4.12808 + 15.4289i) 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} +(-6.99544 - 5.92147i) q^{84} +(-3.29674 - 1.90337i) q^{85} +(4.21704 + 1.77624i) q^{86} +(8.61307 - 6.68579i) q^{87} +(10.0974 - 12.6836i) q^{88} -7.91828i q^{89} +(-2.93367 - 6.97931i) q^{90} +(-7.99650 - 15.2861i) q^{91} +(-6.51834 + 6.36494i) q^{92} +(-2.61903 + 6.42413i) q^{93} +(-6.09715 - 2.56815i) q^{94} +(-5.56239 - 3.21145i) q^{95} +(9.52265 - 2.30633i) 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.12708	+	0.854224i	−0.796963	+	0.604028i
$2$	−1.12708	+	0.854224i	−0.796963	+	0.604028i
$3$	1.71594	−	0.235665i	0.990700	−	0.136061i
$3$	1.71594	−	0.235665i	0.990700	−	0.136061i
$4$	0.540602	−	1.92555i	0.270301	−	0.962776i
$5$	−0.892228	+	1.54538i	−0.399017	+	0.691117i	−0.993605	−	0.112913i	$-0.963982\pi$
$5$	−0.892228	+	1.54538i	−0.399017	+	0.691117i	0.594588	+	0.804030i	$0.297315\pi$
$6$	−1.73269	+	1.73141i	−0.707367	+	0.706846i
$7$	1.41708	−	2.23425i	0.535605	−	0.844469i
$7$	1.41708	−	2.23425i	0.535605	−	0.844469i
$8$	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	−0.867929	−	0.496688i	$-0.834549\pi$
$11$	−2.86592	−	4.96393i	−0.864109	−	1.49668i	0.00382055	−	0.999993i	$-0.498784\pi$
$12$	0.473857	−	3.43154i	0.136791	−	0.990600i
$13$	3.26020	−	5.64683i	0.904216	−	1.56615i	0.0822504	−	0.996612i	$-0.473789\pi$
$13$	3.26020	−	5.64683i	0.904216	−	1.56615i	0.821966	−	0.569537i	$-0.192877\pi$
$14$	0.311400	+	3.72868i	0.0832251	+	0.996531i
$15$	−1.16682	+	2.86206i	−0.301272	+	0.738981i
$16$	−3.41550	−	2.08191i	−0.853875	−	0.520478i
$17$			2.13328i			0.517396i	0.965958	+	0.258698i	$0.0832934\pi$
$17$			2.13328i			0.517396i	−0.965958	+	0.258698i	$0.916707\pi$
$18$	−2.56516	+	3.37934i	−0.604615	+	0.796518i
$19$			3.59936i			0.825749i	0.910788	+	0.412875i	$0.135475\pi$
$19$			3.59936i			0.825749i	−0.910788	+	0.412875i	$0.864525\pi$
$20$	2.49338	+	2.55347i	0.557536	+	0.570973i
$21$	1.90509	−	4.16781i	0.415725	−	0.909491i
$22$	7.47042	+	3.14658i	1.59270	+	0.670854i
$23$	−3.94496	−	2.27763i	−0.822582	−	0.474918i	0.0287242	−	0.999587i	$-0.490856\pi$
$23$	−3.94496	−	2.27763i	−0.822582	−	0.474918i	−0.851306	+	0.524670i	$0.824189\pi$
$24$	2.39723	+	4.27239i	0.489333	+	0.872097i
$25$	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	$-0.467963\pi$
$29$	5.45171	−	3.14755i	1.01236	−	0.584485i	0.911881	+	0.410454i	$0.134630\pi$
$30$	−1.12975	−	4.22249i	−0.206262	−	0.770917i
$31$	−2.00268	+	3.46875i	−0.359692	+	0.623005i	−0.987909	−	0.155033i	$-0.950452\pi$
$31$	−2.00268	+	3.46875i	−0.359692	+	0.623005i	0.628217	+	0.778038i	$0.283785\pi$
$32$	5.62795	−	0.571128i	0.994890	−	0.100962i
$33$	−6.08759	−	7.84242i	−1.05971	−	1.36519i
$34$	−1.82230	−	2.40437i	−0.312522	−	0.412346i
$35$	2.18843	+	4.18339i	0.369911	+	0.707123i
$36$	0.00441969	−	6.00000i	0.000736615	−	1.00000i
$37$		−	0.505819i		−	0.0831561i	−0.999135	−	0.0415780i	$-0.986761\pi$
$37$		−	0.505819i		−	0.0831561i	0.999135	−	0.0415780i	$-0.0132385\pi$
$38$	−3.07466	−	4.05675i	−0.498776	−	0.658092i
$39$	4.26356	−	10.4580i	0.682716	−	1.67461i
$40$	−4.99146	−	0.748050i	−0.789220	−	0.118277i
$41$	5.60580	+	3.23651i	0.875479	+	0.505458i	0.869165	−	0.494522i	$-0.164657\pi$
$41$	5.60580	+	3.23651i	0.875479	+	0.505458i	0.00631369	+	0.999980i	$0.497990\pi$
$42$	1.41306	+	6.32481i	0.218040	+	0.975940i
$43$	−1.61781	−	2.80212i	−0.246713	−	0.427320i	0.715899	−	0.698204i	$-0.246017\pi$
$43$	−1.61781	−	2.80212i	−0.246713	−	0.427320i	−0.962612	+	0.270884i	$0.912684\pi$
$44$	−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	0.984654	−	0.174517i	$-0.0558365\pi$
$47$	2.33909	+	4.05142i	0.341191	+	0.590960i	−0.643463	+	0.765477i	$0.722503\pi$
$48$	−6.35144	−	2.76753i	−0.916751	−	0.399459i
$49$	−2.98378	−	6.33222i	−0.426255	−	0.904603i
$50$	−2.36645	−	0.996763i	−0.334667	−	0.140964i
$51$	0.502738	+	3.66058i	0.0703975	+	0.512584i
$52$	−9.11079	−	9.33037i	−1.26344	−	1.29389i
$53$		−	0.827775i		−	0.113704i	−0.998383	−	0.0568518i	$-0.981894\pi$
$53$		−	0.827775i		−	0.113704i	0.998383	−	0.0568518i	$-0.0181063\pi$
$54$	−3.60528	+	6.40328i	−0.490617	+	0.871375i
$55$	10.2282			1.37918
$56$	7.34810	+	1.41611i	0.981932	+	0.189236i
$57$	0.848242	+	6.17629i	0.112352	+	0.818070i
$58$	−3.45578	+	8.20451i	−0.453767	+	1.07731i
$59$	0.346079	+	0.199809i	0.0450556	+	0.0260129i	0.522359	−	0.852726i	$-0.325052\pi$
$59$	0.346079	+	0.199809i	0.0450556	+	0.0260129i	−0.477303	+	0.878739i	$0.658386\pi$
$60$	4.88026	+	3.79401i	0.630039	+	0.489804i
$61$	3.66024	+	6.33971i	0.468645	+	0.811717i	0.999358	−	0.0358346i	$-0.0114089\pi$
$61$	3.66024	+	6.33971i	0.468645	+	0.811717i	−0.530713	+	0.847552i	$0.678076\pi$
$62$	−0.705912	−	5.62028i	−0.0896510	−	0.713776i
$63$	2.28682	−	7.60069i	0.288112	−	0.957597i
$64$	−5.85526	+	5.45124i	−0.731907	+	0.681404i
$65$	5.81768	+	10.0765i	0.721595	+	1.24984i
$66$	13.5604	+	3.63884i	1.66917	+	0.447910i
$67$	3.40363	−	5.89527i	0.415820	−	0.720221i	−0.579694	−	0.814834i	$-0.696828\pi$
$67$	3.40363	−	5.89527i	0.415820	−	0.720221i	0.995514	+	0.0946128i	$0.0301613\pi$
$68$	4.10774	+	1.15325i	0.498136	+	0.139853i
$69$	−7.30609	−	2.97859i	−0.879550	−	0.358580i
$70$	−6.04008	−	2.84560i	−0.721928	−	0.340114i
$71$			1.96610i			0.233333i	0.993171	+	0.116667i	$0.0372209\pi$
$71$			1.96610i			0.233333i	−0.993171	+	0.116667i	$0.962779\pi$
$72$	5.12036	+	6.76623i	0.603441	+	0.797408i
$73$			14.3518i			1.67976i	0.542775	+	0.839878i	$0.317374\pi$
$73$			14.3518i			1.67976i	−0.542775	+	0.839878i	$0.682626\pi$
$74$	0.432083	+	0.570096i	0.0502286	+	0.0662723i
$75$	1.92840	+	2.48429i	0.222673	+	0.286861i
$76$	6.93075	+	1.94582i	0.795012	+	0.223201i
$77$	−15.1519	−	0.631065i	−1.72672	−	0.0719165i
$78$	4.12808	+	15.4289i	0.467413	+	1.74698i
$79$	−2.17052	+	1.25315i	−0.244203	+	0.140990i	−0.617107	−	0.786879i	$-0.711695\pi$
$79$	−2.17052	+	1.25315i	−0.244203	+	0.140990i	0.372904	+	0.927870i	$0.378362\pi$
$80$	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	$-0.655900\pi$
$83$	0.533641	−	0.308098i	0.0585747	−	0.0338181i	0.529001	+	0.848621i	$0.322567\pi$
$84$	−6.99544	−	5.92147i	−0.763265	−	0.646086i
$85$	−3.29674	−	1.90337i	−0.357581	−	0.206450i
$86$	4.21704	+	1.77624i	0.454735	+	0.191537i
$87$	8.61307	−	6.68579i	0.923418	−	0.716792i
$88$	10.0974	−	12.6836i	1.07639	−	1.35208i
$89$		−	7.91828i		−	0.839336i	−0.907678	−	0.419668i	$-0.862147\pi$
$89$		−	7.91828i		−	0.839336i	0.907678	−	0.419668i	$-0.137853\pi$
$90$	−2.93367	−	6.97931i	−0.309236	−	0.735684i
$91$	−7.99650	−	15.2861i	−0.838261	−	1.60242i
$92$	−6.51834	+	6.36494i	−0.679584	+	0.663591i
$93$	−2.61903	+	6.42413i	−0.271580	+	0.666152i
$94$	−6.09715	−	2.56815i	−0.628873	−	0.264884i
$95$	−5.56239	−	3.21145i	−0.570689	−	0.329488i
$96$	9.52265	−	2.30633i	0.971901	−	0.235389i
$97$	−14.0224	+	8.09583i	−1.42376	+	0.822007i	−0.996618	−	0.0821777i	$-0.973812\pi$
$97$	−14.0224	+	8.09583i	−1.42376	+	0.822007i	−0.427141	+	0.904185i	$0.640479\pi$
$98$	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	0.999948	+	0.0102441i	$0.00326086\pi$
$101$	5.11383	+	8.85742i	0.508845	+	0.881346i	−0.491102	+	0.871102i	$0.663406\pi$
$102$	−3.69358	−	3.69631i	−0.365719	−	0.365989i
$103$	1.35296	−	2.34340i	0.133311	−	0.230902i	−0.791640	−	0.610988i	$-0.790772\pi$
$103$	1.35296	−	2.34340i	0.133311	−	0.230902i	0.924951	+	0.380086i	$0.124106\pi$
$104$	18.2388	+	2.73337i	1.78846	+	0.268029i
$105$	4.74109	+	6.66273i	0.462683	+	0.650216i
$106$	0.707106	+	0.932966i	0.0686802	+	0.0906176i
$107$	−12.8015			−1.23756			−0.618782	−	0.785562i	$-0.712374\pi$
$107$	−12.8015			−1.23756			−0.618782	+	0.785562i	$0.712374\pi$
$108$	−1.40640	−	10.2967i	−0.135331	−	0.990800i
$109$			3.59420i			0.344262i	0.985074	+	0.172131i	$0.0550652\pi$
$109$			3.59420i			0.344262i	−0.985074	+	0.172131i	$0.944935\pi$
$110$	−11.5280	+	8.73721i	−1.09915	+	0.833060i
$111$	−0.119204	−	0.867956i	−0.0113143	−	0.0823828i
$112$	−9.49155	+	4.68086i	−0.896867	+	0.442300i
$113$	−1.14317	+	1.98003i	−0.107541	+	0.186266i	−0.914773	−	0.403967i	$-0.867631\pi$
$113$	−1.14317	+	1.98003i	−0.107541	+	0.186266i	0.807233	+	0.590233i	$0.200964\pi$
$114$	−6.23197	−	6.23657i	−0.583678	−	0.584108i
$115$	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
$119$	4.76629	+	3.02302i	0.436925	+	0.277120i
$120$	−8.74136	−	0.107300i	−0.797973	−	0.00979515i
$121$	−10.9270	+	18.9262i	−0.993368	+	1.72056i
$122$	−9.54090	−	4.01868i	−0.863793	−	0.363834i
$123$	10.3820	+	4.23258i	0.936110	+	0.381639i
$124$	5.59660	+	5.73148i	0.502589	+	0.514702i
$125$	−12.1623			−1.08783
$126$	3.91527	+	10.5200i	0.348800	+	0.937197i
$127$			7.43645i			0.659878i	0.944002	+	0.329939i	$0.107028\pi$
$127$			7.43645i			0.659878i	−0.944002	+	0.329939i	$0.892972\pi$
$128$	1.94274	−	11.1457i	0.171716	−	0.985147i
$129$	−3.43643	−	4.42703i	−0.302561	−	0.389778i
$130$	−15.1646	−	6.38740i	−1.33002	−	0.560212i
$131$	−8.58229	−	4.95499i	−0.749838	−	0.432919i	0.0757972	−	0.997123i	$-0.475850\pi$
$131$	−8.58229	−	4.95499i	−0.749838	−	0.432919i	−0.825635	+	0.564204i	$0.809183\pi$
$132$	−18.3919	+	7.48234i	−1.60081	+	0.651254i
$133$	8.04188	+	5.10057i	0.697319	+	0.442275i
$134$	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	0.981531	+	0.191303i	$0.0612712\pi$
$137$	7.68342	+	13.3081i	0.656438	+	1.13698i	−0.325093	+	0.945682i	$0.605395\pi$
$138$	10.7789	−	2.88394i	0.917561	−	0.245498i
$139$	−13.0426	−	7.53017i	−1.10626	−	0.638701i	−0.168403	−	0.985718i	$-0.553861\pi$
$139$	−13.0426	−	7.53017i	−1.10626	−	0.638701i	−0.937859	+	0.347018i	$0.887194\pi$
$140$	9.23841	−	1.95238i	0.780788	−	0.165006i
$141$	4.96852	+	6.40076i	0.418424	+	0.539041i
$142$	−1.67949	−	2.21595i	−0.140940	−	0.185958i
$143$	−37.3739			−3.12536
$144$	−11.5509	−	3.25212i	−0.962577	−	0.271010i
$145$			11.2333i			0.932877i
$146$	−12.2597	−	16.1756i	−1.01462	−	1.33870i
$147$	−6.61229	−	10.1626i	−0.545372	−	0.838194i
$148$	−0.973980	−	0.273446i	−0.0800607	−	0.0224772i
$149$	−9.61138	−	5.54913i	−0.787395	−	0.454603i	0.0516496	−	0.998665i	$-0.483552\pi$
$149$	−9.61138	−	5.54913i	−0.787395	−	0.454603i	−0.839045	+	0.544062i	$0.816885\pi$
$150$	−4.29560	−	1.15270i	−0.350734	−	0.0941175i
$151$	−7.73466	+	4.46561i	−0.629438	+	0.363406i	−0.780534	−	0.625113i	$-0.785053\pi$
$151$	−7.73466	+	4.46561i	−0.629438	+	0.363406i	0.151097	+	0.988519i	$0.451720\pi$
$152$	−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
$156$	−17.8324	−	13.8633i	−1.42774	−	1.10995i
$157$	7.85645	−	13.6078i	0.627013	−	1.08602i	−0.361135	−	0.932513i	$-0.617611\pi$
$157$	7.85645	−	13.6078i	0.627013	−	1.08602i	0.988148	−	0.153504i	$-0.0490559\pi$
$158$	1.37587	−	3.26651i	0.109458	−	0.259869i
$159$	−0.195077	−	1.42042i	−0.0154706	−	0.112646i
$160$	−4.13880	+	9.20692i	−0.327201	+	0.727871i
$161$	−10.6791	+	5.58648i	−0.841632	+	0.440276i
$162$	−4.67744	+	11.8373i	−0.367494	+	0.930026i
$163$	19.0694			1.49363			0.746815	−	0.665031i	$-0.231582\pi$
$163$	19.0694			1.49363			0.746815	+	0.665031i	$0.231582\pi$
$164$	9.26257	−	9.04459i	0.723285	−	0.706264i
$165$	17.5511	−	2.41043i	1.36635	−	0.187652i
$166$	−0.338269	+	0.803098i	−0.0262548	+	0.0623325i
$167$	0.457013	−	0.791570i	0.0353647	−	0.0612535i	−0.847801	−	0.530314i	$-0.822074\pi$
$167$	0.457013	−	0.791570i	0.0353647	−	0.0612535i	0.883166	+	0.469060i	$0.155407\pi$
$168$	12.9427	+	0.698280i	0.998548	+	0.0538735i
$169$	−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	−1.00000		8.48213e-5i	$-0.999973\pi$
$173$	−6.57744	−	11.3925i	−0.500073	−	0.866153i	0.499927	−	0.866068i	$-0.333360\pi$
$174$	−3.99642	+	14.8929i	−0.302968	+	1.12903i
$175$	4.79977	+	0.199906i	0.362828	+	0.0151115i
$176$	−0.545901	+	22.9209i	−0.0411488	+	1.72773i
$177$	0.640940	+	0.261302i	0.0481760	+	0.0196407i
$178$	6.76399	+	8.92450i	0.506982	+	0.668920i
$179$	8.85532			0.661878			0.330939	−	0.943652i	$-0.392635\pi$
$179$	8.85532			0.661878			0.330939	+	0.943652i	$0.392635\pi$
$180$	9.26836	+	5.36020i	0.690823	+	0.399526i
$181$	−3.11488			−0.231527			−0.115764	−	0.993277i	$-0.536932\pi$
$181$	−3.11488			−0.231527			−0.115764	+	0.993277i	$0.536932\pi$
$182$	22.0704	+	10.3978i	1.63597	+	0.770736i
$183$	7.77481	+	10.0160i	0.574730	+	0.740404i
$184$	1.90958	−	12.7419i	0.140776	−	0.939345i
$185$	0.781684	+	0.451306i	0.0574706	+	0.0331807i
$186$	−2.53581	−	9.47773i	−0.185934	−	0.694941i
$187$	10.5894	−	6.11381i	0.774376	−	0.447086i
$188$	9.06572	−	2.31383i	0.661186	−	0.168753i
$189$	2.13284	−	13.5813i	0.155141	−	0.987892i
$190$	9.01254	−	1.13198i	0.653838	−	0.0821227i
$191$	13.1945	−	7.61786i	0.954722	−	0.551209i	0.0601777	−	0.998188i	$-0.480833\pi$
$191$	13.1945	−	7.61786i	0.954722	−	0.551209i	0.894545	+	0.446978i	$0.147500\pi$
$192$	−8.76263	+	10.7339i	−0.632388	+	0.774652i
$193$	−1.44348	+	2.50019i	−0.103904	+	0.179967i	−0.913290	−	0.407310i	$-0.866467\pi$
$193$	−1.44348	+	2.50019i	−0.103904	+	0.179967i	0.809386	+	0.587277i	$0.199800\pi$
$194$	8.88865	−	21.1029i	0.638168	−	1.51510i
$195$	12.3575	+	15.9197i	0.884939	+	1.14003i
$196$	−13.8061	+	2.32222i	−0.986147	+	0.165873i
$197$			24.7236i			1.76148i	0.473599	+	0.880741i	$0.342955\pi$
$197$			24.7236i			1.76148i	−0.473599	+	0.880741i	$0.657045\pi$
$198$	24.1264	+	3.04835i	1.71459	+	0.216637i
$199$	15.7553			1.11686			0.558432	−	0.829550i	$-0.311403\pi$
$199$	15.7553			1.11686			0.558432	+	0.829550i	$0.311403\pi$
$200$	−3.19863	+	4.01788i	−0.226177	+	0.284107i
$201$	4.45114	−	10.9181i	0.313959	−	0.770101i
$202$	−13.3299	−	5.61463i	−0.937889	−	0.395044i
$203$	0.693077	−	16.6408i	0.0486445	−	1.16796i
$204$	7.32043	+	1.01087i	0.512532	+	0.0707750i
$205$	−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
$210$	−11.0350	−	3.45945i	−0.761490	−	0.238725i
$211$	−2.97597	+	5.15454i	−0.204875	+	0.354853i	−0.950093	−	0.311968i	$-0.899012\pi$
$211$	−2.97597	+	5.15454i	−0.204875	+	0.354853i	0.745218	+	0.666821i	$0.232345\pi$
$212$	−1.59392	−	0.447497i	−0.109471	−	0.0307342i
$213$	0.463341	+	3.37372i	0.0317476	+	0.231163i
$214$	14.4282	−	10.9353i	0.986294	−	0.747524i
$215$	5.77381			0.393771
$216$	10.3808	+	10.4038i	0.706325	+	0.707888i
$217$	4.91211	+	9.38998i	0.333455	+	0.637433i
$218$	−3.07025	−	4.05094i	−0.207944	−	0.274364i
$219$	3.38222	+	24.6270i	0.228550	+	1.66414i
$220$	5.52940	−	19.6950i	0.372792	−	1.32784i
$221$	12.0463	+	6.95491i	0.810319	+	0.467838i
$222$	0.875781	+	0.876426i	0.0587786	+	0.0588219i
$223$	10.9984	+	19.0498i	0.736507	+	1.27567i	0.954059	+	0.299619i	$0.0968595\pi$
$223$	10.9984	+	19.0498i	0.736507	+	1.27567i	−0.217552	+	0.976049i	$0.569807\pi$
$224$	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	$-0.935249\pi$
$227$	−19.4978	+	11.2571i	−1.29412	+	0.747158i	−0.314735	+	0.949180i	$0.601916\pi$
$228$	12.3513	+	1.70558i	0.817987	+	0.112955i
$229$	−14.8397	+	25.7031i	−0.980636	+	1.69851i	−0.320716	+	0.947175i	$0.603923\pi$
$229$	−14.8397	+	25.7031i	−0.980636	+	1.69851i	−0.659920	+	0.751336i	$0.729410\pi$
$230$	−4.46234	+	10.5942i	−0.294238	+	0.698562i
$231$	−26.1485	+	2.48790i	−1.72045	+	0.163692i
$232$	13.9300	+	11.0897i	0.914550	+	0.728072i
$233$	19.4293			1.27286			0.636428	−	0.771336i	$-0.280411\pi$
$233$	19.4293			1.27286			0.636428	+	0.771336i	$0.280411\pi$
$234$	10.7196	+	25.5024i	0.700763	+	1.66714i
$235$	−8.34800			−0.544563
$236$	0.571833	−	0.558376i	0.0372232	−	0.0363472i
$237$	−3.42917	+	2.66185i	−0.222748	+	0.172906i
$238$	−7.95430	+	0.664303i	−0.515601	+	0.0430603i
$239$	−2.79777	−	1.61529i	−0.180972	−	0.104484i	0.406777	−	0.913527i	$-0.366653\pi$
$239$	−2.79777	−	1.61529i	−0.180972	−	0.104484i	−0.587749	+	0.809043i	$0.699986\pi$
$240$	9.94384	−	7.34614i	0.641872	−	0.474192i
$241$	16.1168	−	9.30502i	1.03817	−	0.599389i	0.118858	−	0.992911i	$-0.462077\pi$
$241$	16.1168	−	9.30502i	1.03817	−	0.599389i	0.919315	+	0.393522i	$0.128743\pi$
$242$	−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
$245$	12.4479	+	1.03869i	0.795269	+	0.0663598i
$246$	−15.3168	+	4.09809i	−0.976566	+	0.261285i
$247$	20.3250	+	11.7346i	1.29325	+	0.746656i
$248$	−11.2038	−	1.67906i	−0.711439	−	0.106621i
$249$	0.843089	−	0.654438i	0.0534286	−	0.0414733i
$250$	13.7079	−	10.3894i	0.866963	−	0.657082i
$251$		−	20.9851i		−	1.32457i	−0.749252	−	0.662285i	$-0.769587\pi$
$251$		−	20.9851i		−	1.32457i	0.749252	−	0.662285i	$-0.230413\pi$
$252$	−13.3993	−	8.51234i	−0.844074	−	0.536227i
$253$			26.1100i			1.64152i
$254$	−6.35239	−	8.38144i	−0.398585	−	0.525898i
$255$	−6.10557	−	2.48915i	−0.382346	−	0.155877i
$256$	7.33128	+	14.2215i	0.458205	+	0.888847i
$257$	4.15846	+	2.40089i	0.259398	+	0.149763i	0.624060	−	0.781377i	$-0.285482\pi$
$257$	4.15846	+	2.40089i	0.259398	+	0.149763i	−0.364662	+	0.931140i	$0.618815\pi$
$258$	7.65479	+	2.05412i	0.476566	+	0.127884i
$259$	−1.13013	−	0.716784i	−0.0702227	−	0.0445388i
$260$	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	$-0.670850\pi$
$263$	−0.369176	+	0.213144i	−0.0227644	+	0.0131430i	0.488575	+	0.872522i	$0.337517\pi$
$264$	14.3375	−	24.1440i	0.882414	−	1.48596i
$265$	1.27923	+	0.738564i	0.0785825	+	0.0453696i
$266$	−13.4208	+	1.12084i	−0.822885	+	0.0687231i
$267$	−1.86606	−	13.5873i	−0.114201	−	0.831530i
$268$	−9.51163	−	9.74086i	−0.581015	−	0.595018i
$269$	−8.61268			−0.525124			−0.262562	−	0.964915i	$-0.584567\pi$
$269$	−8.61268			−0.525124			−0.262562	+	0.964915i	$0.584567\pi$
$270$	−6.67879	−	11.2847i	−0.406458	−	0.686767i
$271$	−8.40451			−0.510538			−0.255269	−	0.966870i	$-0.582164\pi$
$271$	−8.40451			−0.510538			−0.255269	+	0.966870i	$0.582164\pi$
$272$	4.44130	−	7.28621i	0.269293	−	0.441791i
$273$	−17.3239	−	24.3456i	−1.04849	−	1.47346i
$274$	−20.0279	−	8.43584i	−1.20993	−	0.509628i
$275$	5.20370	−	9.01307i	0.313795	−	0.543509i
$276$	−9.68511	+	12.4580i	−0.582975	+	0.749885i
$277$	4.27391	−	2.46754i	0.256794	−	0.148260i	−0.366077	−	0.930585i	$-0.619299\pi$
$277$	4.27391	−	2.46754i	0.256794	−	0.148260i	0.622871	+	0.782324i	$0.285966\pi$
$278$	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	−0.959112	−	0.283027i	$-0.908661\pi$
$281$	−12.1476	−	21.0402i	−0.724665	−	1.25516i	0.234447	−	0.972129i	$-0.424672\pi$
$282$	−11.0676	−	2.96992i	−0.659065	−	0.176856i
$283$	20.3161	+	11.7295i	1.20766	+	0.697245i	0.962248	−	0.272173i	$-0.0877422\pi$
$283$	20.3161	+	11.7295i	1.20766	+	0.697245i	0.245416	+	0.969418i	$0.421076\pi$
$284$	3.78583	+	1.06288i	0.224648	+	0.0630702i
$285$	−10.3016	−	4.19981i	−0.610213	−	0.248775i
$286$	42.1233	−	31.9257i	2.49080	−	1.88781i
$287$	15.1750	−	7.93839i	0.895754	−	0.468589i
$288$	15.7968	−	6.20169i	0.930836	−	0.365438i
$289$	12.4491			0.732301
$290$	−9.59578	−	12.6608i	−0.563484	−	0.743469i
$291$	−22.1537	+	17.1966i	−1.29867	+	1.00808i
$292$	27.6352	+	7.75863i	1.61723	+	0.454040i
$293$	−3.83631	+	6.64468i	−0.224119	+	0.388186i	−0.956055	−	0.293188i	$-0.905284\pi$
$293$	−3.83631	+	6.64468i	−0.224119	+	0.388186i	0.731936	+	0.681374i	$0.238617\pi$
$294$	16.1337	+	5.80561i	0.940934	+	0.338590i
$295$	−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
$300$	5.82613	−	2.37023i	0.336372	−	0.136845i
$301$	−8.55322	−	0.356235i	−0.492999	−	0.0205330i
$302$	4.90292	−	11.6402i	0.282131	−	0.669819i
$303$	10.8624	+	13.9937i	0.624030	+	0.803916i
$304$	7.49355	−	12.2936i	0.429785	−	0.705087i
$305$	−13.0631			−0.747989
$306$	−7.20907	−	5.47221i	−0.412115	−	0.312825i
$307$		−	4.42681i		−	0.252651i	−0.991989	−	0.126326i	$-0.959682\pi$
$307$		−	4.42681i		−	0.252651i	0.991989	−	0.126326i	$-0.0403184\pi$
$308$	−9.40630	+	28.8346i	−0.535974	+	1.64301i
$309$	1.76935	−	4.33998i	0.100655	−	0.246893i
$310$	9.31533	+	3.92367i	0.529075	+	0.222849i
$311$	4.85257	−	8.40489i	0.275164	−	0.476598i	−0.695013	−	0.718998i	$-0.744601\pi$
$311$	4.85257	−	8.40489i	0.275164	−	0.476598i	0.970176	+	0.242400i	$0.0779345\pi$
$312$	31.9409	+	0.392075i	1.80830	+	0.0221969i
$313$	−12.7693	+	7.37236i	−0.721764	+	0.416710i	−0.815401	−	0.578896i	$-0.803484\pi$
$313$	−12.7693	+	7.37236i	−0.721764	+	0.416710i	0.0936379	+	0.995606i	$0.470150\pi$
$314$	2.76927	+	22.0482i	0.156279	+	1.24425i
$315$	9.70562	+	10.3156i	0.546850	+	0.581216i
$316$	1.23962	+	4.85691i	0.0697340	+	0.273222i
$317$	−21.0016	+	12.1253i	−1.17956	+	0.681022i	−0.955914	−	0.293647i	$-0.905131\pi$
$317$	−21.0016	+	12.1253i	−1.17956	+	0.681022i	−0.223651	+	0.974669i	$0.571798\pi$
$318$	1.43322	+	1.43428i	0.0803710	+	0.0804302i
$319$	−31.2484	−	18.0413i	−1.74957	−	1.01012i
$320$	−3.20003	−	13.9124i	−0.178887	−	0.777725i
$321$	−21.9666	+	3.01686i	−1.22606	+	0.168384i
$322$	7.26407	−	15.4187i	0.404811	−	0.859253i
$323$	−7.67843			−0.427239
$324$	−4.83988	−	17.3371i	−0.268882	−	0.963173i
$325$	11.8392			0.656719
$326$	−21.4927	+	16.2895i	−1.19037	+	0.902195i
$327$	0.847026	+	6.16744i	0.0468407	+	0.341060i
$328$	−2.71351	+	18.1063i	−0.149829	+	0.999751i
$329$	12.3666	+	0.515057i	0.681790	+	0.0283960i
$330$	−17.7224	+	17.7093i	−0.975583	+	0.974865i
$331$	10.8579	+	18.8065i	0.596806	+	1.03370i	0.993289	+	0.115656i	$0.0368970\pi$
$331$	10.8579	+	18.8065i	0.596806	+	1.03370i	−0.396484	+	0.918042i	$0.629770\pi$
$332$	−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
$336$	−15.1839	+	10.2689i	−0.828347	+	0.560215i
$337$	−10.2990	+	17.8383i	−0.561020	+	0.971715i	0.436388	+	0.899759i	$0.356258\pi$
$337$	−10.2990	+	17.8383i	−0.561020	+	0.971715i	−0.997408	+	0.0719563i	$0.977076\pi$
$338$	38.4682	+	16.2030i	2.09239	+	0.881327i
$339$	−1.49500	+	3.66703i	−0.0811971	+	0.199166i
$340$	−5.44726	+	5.31907i	−0.295419	+	0.288467i
$341$	22.9581			1.24325
$342$	−12.1635	−	9.23294i	−0.657724	−	0.499260i
$343$	−18.3760	−	2.30672i	−0.992213	−	0.124551i
$344$	5.69997	−	7.15988i	0.307322	−	0.386035i
$345$	11.1218	−	8.63314i	0.598776	−	0.464793i
$346$	17.1450	+	7.22156i	0.921720	+	0.388234i
$347$	4.25303	−	7.36647i	0.228315	−	0.395453i	−0.728994	−	0.684520i	$-0.760012\pi$
$347$	4.25303	−	7.36647i	0.228315	−	0.395453i	0.957309	+	0.289067i	$0.0933452\pi$
$348$	−8.21760	−	20.1993i	−0.440510	−	1.08279i
$349$	−12.8783	−	22.3058i	−0.689359	−	1.19400i	−0.972046	−	0.234792i	$-0.924559\pi$
$349$	−12.8783	−	22.3058i	−0.689359	−	1.19400i	0.282687	−	0.959212i	$-0.408774\pi$
$350$	−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	$-0.529770\pi$
$353$	13.5681	−	7.83357i	0.722159	−	0.416939i	0.815547	+	0.578691i	$0.196436\pi$
$354$	−0.945599	+	0.252999i	−0.0502580	+	0.0134468i
$355$	−3.03838	−	1.75421i	−0.161261	−	0.0931039i
$356$	−15.2471	−	4.28063i	−0.808092	−	0.226873i
$357$	8.89110	+	4.06409i	0.470567	+	0.215094i
$358$	−9.98062	+	7.56443i	−0.527492	+	0.399793i
$359$			32.3708i			1.70847i	0.519890	+	0.854233i	$0.325973\pi$
$359$			32.3708i			1.70847i	−0.519890	+	0.854233i	$0.674027\pi$
$360$	−15.0250	+	1.87591i	−0.791885	+	0.0988691i
$361$	6.04462			0.318138
$362$	3.51071	−	2.66081i	0.184519	−	0.139849i
$363$	−14.2900	+	35.0514i	−0.750028	+	1.83972i
$364$	−33.7571	+	7.13398i	−1.76935	+	0.373922i
$365$	−22.1791	−	12.8051i	−1.16091	−	0.670251i
$366$	−17.3187	−	4.64737i	−0.905264	−	0.242922i
$367$	−3.24428	−	5.61925i	−0.169350	−	0.293323i	0.768842	−	0.639439i	$-0.220833\pi$
$367$	−3.24428	−	5.61925i	−0.169350	−	0.293323i	−0.938191	+	0.346117i	$0.887500\pi$
$368$	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
$371$	−1.84946	−	1.17302i	−0.0960192	−	0.0609002i
$372$	10.9542	+	8.51597i	0.567946	+	0.441532i
$373$	−0.507153	−	0.292805i	−0.0262594	−	0.0151609i	0.486813	−	0.873506i	$-0.338159\pi$
$373$	−0.507153	−	0.292805i	−0.0262594	−	0.0151609i	−0.513072	+	0.858345i	$0.671493\pi$
$374$	−6.71253	+	15.9365i	−0.347097	+	0.824056i
$375$	−20.8699	+	2.86624i	−1.07772	+	0.148012i
$376$	−8.24123	+	10.3520i	−0.425009	+	0.533865i
$377$		−	41.0465i		−	2.11400i
$378$	9.19758	+	17.1291i	0.473072	+	0.881024i
$379$	16.9407			0.870186			0.435093	−	0.900386i	$-0.356716\pi$
$379$	16.9407			0.870186			0.435093	+	0.900386i	$0.356716\pi$
$380$	−9.19085	+	8.97456i	−0.471481	+	0.460385i
$381$	1.75251	+	12.7605i	0.0897837	+	0.653741i
$382$	−8.36387	+	19.8570i	−0.427933	+	1.01597i
$383$	−3.02865	+	5.24577i	−0.154757	+	0.268046i	−0.932970	−	0.359953i	$-0.882793\pi$
$383$	−3.02865	+	5.24577i	−0.154757	+	0.268046i	0.778214	+	0.628000i	$0.216126\pi$
$384$	0.706997	−	19.5832i	0.0360788	−	0.999349i
$385$	14.4942	−	22.8525i	0.738693	−	1.16467i
$386$	−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	$-0.496887\pi$
$389$	17.3692	−	10.0281i	0.880654	−	0.508446i	0.870874	+	0.491506i	$0.163553\pi$
$390$	−27.5268	−	7.38666i	−1.39388	−	0.374038i
$391$	4.85881	−	8.41570i	0.245721	−	0.425600i
$392$	13.5768	−	14.4108i	0.685731	−	0.727855i
$393$	−15.8944	−	6.47994i	−0.801769	−	0.326870i
$394$	−21.1195	−	27.8653i	−1.06398	−	1.40384i
$395$		−	4.47239i		−	0.225030i
$396$	−29.7962	+	17.1736i	−1.49732	+	0.863006i
$397$	1.83014			0.0918522			0.0459261	−	0.998945i	$-0.485376\pi$
$397$	1.83014			0.0918522			0.0459261	+	0.998945i	$0.485376\pi$
$398$	−17.7574	+	13.4586i	−0.890099	+	0.674617i
$399$	15.0014	+	6.85710i	0.751011	+	0.343284i
$400$	0.172928	−	7.26080i	0.00864642	−	0.363040i
$401$	−2.12035	+	3.67256i	−0.105885	+	0.183399i	−0.914100	−	0.405490i	$-0.867101\pi$
$401$	−2.12035	+	3.67256i	−0.105885	+	0.183399i	0.808214	+	0.588889i	$0.200434\pi$
$402$	4.30970	+	16.1078i	0.214948	+	0.803382i
$403$	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
$408$	−9.11419	+	5.11396i	−0.451220	+	0.253179i
$409$	4.20386	+	2.42710i	0.207868	+	0.120012i	0.600320	−	0.799760i	$-0.295040\pi$
$409$	4.20386	+	2.42710i	0.207868	+	0.120012i	−0.392452	+	0.919772i	$0.628373\pi$
$410$	6.34099	−	15.0544i	0.313159	−	0.743484i
$411$	16.3205	+	21.0252i	0.805033	+	1.03710i
$412$	−3.78092	−	3.87204i	−0.186272	−	0.190762i
$413$	0.936844	−	0.490084i	0.0460991	−	0.0241155i
$414$	17.8163	−	7.48889i	0.875626	−	0.368059i
$415$			1.09957i			0.0539759i
$416$	15.1232	−	33.6421i	0.741474	−	1.64944i
$417$	−24.1550	−	9.84765i	−1.18288	−	0.482242i
$418$	−11.3257	+	26.8887i	−0.553957	+	1.31517i
$419$	−1.99126	−	1.14965i	−0.0972795	−	0.0561643i	0.450571	−	0.892741i	$-0.351220\pi$
$419$	−1.99126	−	1.14965i	−0.0972795	−	0.0561643i	−0.547850	+	0.836576i	$0.684554\pi$
$420$	15.3925	−	5.52734i	0.751076	−	0.269706i
$421$	33.3629	−	19.2621i	1.62601	−	0.938776i	0.640739	−	0.767758i	$-0.278628\pi$
$421$	33.3629	−	19.2621i	1.62601	−	0.938776i	0.985268	−	0.171017i	$-0.0547055\pi$
$422$	−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
$426$	−3.40413	−	3.40664i	−0.164931	−	0.165052i
$427$	19.3514	+	0.805969i	0.936479	+	0.0390036i
$428$	−6.92050	+	24.6499i	−0.334515	+	1.19150i
$429$	−64.1315	+	8.80772i	−3.09630	+	0.425241i
$430$	−6.50753	+	4.93213i	−0.313821	+	0.237849i
$431$			1.15387i			0.0555802i	0.999614	+	0.0277901i	$0.00884700\pi$
$431$			1.15387i			0.0555802i	−0.999614	+	0.0277901i	$0.991153\pi$
$432$	−20.5871	−	2.85831i	−0.990499	−	0.137520i
$433$			7.47255i			0.359108i	0.983748	+	0.179554i	$0.0574654\pi$
$433$			7.47255i			0.359108i	−0.983748	+	0.179554i	$0.942535\pi$
$434$	−13.5575	−	6.38718i	−0.650779	−	0.306595i
$435$	2.64730	+	19.2758i	0.126928	+	0.924202i
$436$	6.92082	+	1.94303i	0.331447	+	0.0930543i
$437$	8.19799	−	14.1993i	0.392163	−	0.679246i
$438$	−24.8490	−	24.8673i	−1.18733	−	1.18820i
$439$	−14.7953	−	25.6262i	−0.706141	−	1.22307i	−0.966278	−	0.257501i	$-0.917101\pi$
$439$	−14.7953	−	25.6262i	−0.706141	−	1.22307i	0.260137	−	0.965572i	$-0.416232\pi$
$440$	10.5919	+	26.9211i	0.504949	+	1.28341i
$441$	−13.7413	−	15.8801i	−0.654346	−	0.756195i
$442$	−19.5181	+	2.45149i	−0.928381	+	0.116606i
$443$	18.6850	+	32.3634i	0.887751	+	1.53763i	0.842528	+	0.538653i	$0.181067\pi$
$443$	18.6850	+	32.3634i	0.887751	+	1.53763i	0.0452234	+	0.998977i	$0.485600\pi$
$444$	−1.73574	−	0.239686i	−0.0823744	−	0.0113750i
$445$	12.2368	+	7.06491i	0.580079	+	0.334909i
$446$	−28.6688	−	12.0755i	−1.35751	−	0.571790i
$447$	−17.8003	−	7.25694i	−0.841926	−	0.343241i
$448$	3.88209	+	20.8070i	0.183412	+	0.983036i
$449$	20.3300			0.959430			0.479715	−	0.877424i	$-0.340740\pi$
$449$	20.3300			0.959430			0.479715	+	0.877424i	$0.340740\pi$
$450$	−7.64266	−	0.965644i	−0.360278	−	0.0455209i
$451$		−	37.1024i		−	1.74708i
$452$	3.19466	+	3.27165i	0.150264	+	0.153885i
$453$	−12.2199	+	9.48552i	−0.574139	+	0.445669i
$454$	12.3595	−	29.3431i	0.580058	−	1.37714i
$455$	30.7576	+	1.28103i	1.44194	+	0.0600556i
$456$	−15.3778	+	8.62849i	−0.720134	+	0.404066i
$457$	−15.1229	−	26.1936i	−0.707420	−	1.22529i	−0.965811	−	0.259247i	$-0.916526\pi$
$457$	−15.1229	−	26.1936i	−0.707420	−	1.22529i	0.258391	−	0.966040i	$-0.416808\pi$
$458$	−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	0.994243	−	0.107145i	$-0.0341710\pi$
$461$	8.68136	+	15.0366i	0.404331	+	0.700322i	−0.589912	+	0.807467i	$0.700838\pi$
$462$	27.3462	−	25.1408i	1.27226	−	1.16965i
$463$	−10.6731	−	6.16211i	−0.496021	−	0.286378i	0.231048	−	0.972942i	$-0.425785\pi$
$463$	−10.6731	−	6.16211i	−0.496021	−	0.286378i	−0.727069	+	0.686565i	$0.759118\pi$
$464$	−25.1732	−	0.599544i	−1.16864	−	0.0278331i
$465$	−7.59099	−	9.77920i	−0.352024	−	0.453500i
$466$	−21.8983	+	16.5970i	−1.01442	+	0.768840i
$467$			17.5154i			0.810515i	0.914203	+	0.405258i	$0.132818\pi$
$467$			17.5154i			0.810515i	−0.914203	+	0.405258i	$0.867182\pi$
$468$	−33.8666	−	19.5861i	−1.56548	−	0.905370i
$469$	−8.34831	−	15.9586i	−0.385489	−	0.736901i
$470$	9.40883	−	7.13106i	0.433997	−	0.328931i
$471$	10.2743	−	25.2016i	0.473417	−	1.16123i
$472$	−0.167521	+	1.11781i	−0.00771078	+	0.0514512i
$473$	−9.27303	+	16.0614i	−0.426374	+	0.738502i
$474$	1.59112	−	5.92939i	0.0730823	−	0.272346i
$475$	−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	−0.982616	−	0.185649i	$-0.940561\pi$
$479$	−14.2716	−	24.7191i	−0.652085	−	1.12944i	0.330531	−	0.943795i	$-0.392772\pi$
$480$	−4.93221	+	16.7739i	−0.225123	+	0.765622i
$481$	−2.85627	−	1.64907i	−0.130235	−	0.0751911i
$482$	−10.2163	+	24.2548i	−0.465338	+	1.10478i
$483$	−17.0082	+	12.1028i	−0.773901	+	0.550695i
$484$	30.5362	+	31.2721i	1.38801	+	1.42146i
$485$		−	28.8933i		−	1.31198i
$486$	−5.23658	+	21.4144i	−0.237536	+	0.971379i
$487$		−	6.55560i		−	0.297063i	−0.988908	−	0.148531i	$-0.952545\pi$
$487$		−	6.55560i		−	0.297063i	0.988908	−	0.148531i	$-0.0474546\pi$
$488$	−12.8960	+	16.1990i	−0.583775	+	0.733294i
$489$	32.7220	−	4.49399i	1.47974	−	0.203225i
$490$	−14.9171	+	9.46264i	−0.673884	+	0.427479i
$491$	−11.3501	+	19.6589i	−0.512222	+	0.887194i	0.487678	+	0.873024i	$0.337844\pi$
$491$	−11.3501	+	19.6589i	−0.512222	+	0.887194i	−0.999900	+	0.0141705i	$0.995489\pi$
$492$	13.7626	−	17.7029i	0.620464	−	0.798107i
$493$	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
$497$	4.39277	+	2.78612i	0.197043	+	0.124974i
$498$	−0.391189	+	1.45779i	−0.0175296	+	0.0653251i
$499$	−4.33054	+	7.50072i	−0.193862	+	0.335778i	−0.946527	−	0.322625i	$-0.895435\pi$
$499$	−4.33054	+	7.50072i	−0.193862	+	0.335778i	0.752665	+	0.658404i	$0.228768\pi$
$500$	−6.57499	+	23.4192i	−0.294042	+	1.04734i
$501$	0.597664	−	1.46599i	0.0267016	−	0.0654957i
$502$	17.9260	+	23.6519i	0.800077	+	1.05563i
$503$	24.8692			1.10886			0.554432	−	0.832229i	$-0.312935\pi$
$503$	24.8692			1.10886			0.554432	+	0.832229i	$0.312935\pi$
$504$	22.3734	−	1.85192i	0.996592	−	0.0824910i
$505$	−18.2508			−0.812151
$506$	−22.3038	−	29.4280i	−0.991525	−	1.30823i
$507$	−31.3474	−	40.3837i	−1.39219	−	1.79350i
$508$	14.3193	+	4.02015i	0.635314	+	0.178366i
$509$	15.9985	−	27.7102i	0.709120	−	1.22823i	−0.256064	−	0.966660i	$-0.582426\pi$
$509$	15.9985	−	27.7102i	0.709120	−	1.22823i	0.965184	−	0.261571i	$-0.0842407\pi$
$510$	9.00774	−	2.41006i	0.398869	−	0.106719i
$511$	32.0657	+	20.3377i	1.41850	+	0.899686i
$512$	−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
$516$	−10.3822	+	4.22376i	−0.457051	+	0.185941i
$517$	13.4073	−	23.2221i	0.589652	−	1.02131i
$518$	1.88603	−	0.157512i	0.0828676	−	0.00692067i
$519$	−13.9713	−	17.9987i	−0.613273	−	0.790057i
$520$	−20.4973	+	25.7471i	−0.898865	+	1.12909i
$521$			23.2939i			1.02052i	0.860019	+	0.510262i	$0.170452\pi$
$521$			23.2939i			1.02052i	−0.860019	+	0.510262i	$0.829548\pi$
$522$	−3.34790	+	26.4972i	−0.146533	+	1.15975i
$523$		−	27.2889i		−	1.19326i	−0.802516	−	0.596631i	$-0.796506\pi$
$523$		−	27.2889i		−	1.19326i	0.802516	−	0.596631i	$-0.203494\pi$
$524$	−14.1807	+	13.8470i	−0.619486	+	0.604908i
$525$	8.28324	−	0.788108i	0.361510	−	0.0343958i
$526$	0.234017	−	0.555589i	0.0102036	−	0.0242248i
$527$	−7.39980	−	4.27228i	−0.322340	−	0.186103i
$528$	4.46491	+	39.4596i	0.194310	+	1.71726i
$529$	−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
$534$	13.7098	+	13.7199i	0.593281	+	0.593719i
$535$	11.4218	−	19.7832i	0.493809	−	0.855302i
$536$	19.0412	+	2.85363i	0.822455	+	0.123258i
$537$	15.1952	−	2.08689i	0.655723	−	0.0900558i
$538$	9.70714	−	7.35716i	0.418505	−	0.317190i
$539$	−22.8814	+	32.9590i	−0.985571	+	1.41964i
$540$	17.1672	+	7.01357i	0.738759	+	0.301816i
$541$		−	39.6550i		−	1.70490i	−0.522806	−	0.852452i	$-0.675115\pi$
$541$		−	39.6550i		−	1.70490i	0.522806	−	0.852452i	$-0.324885\pi$
$542$	9.47252	−	7.17934i	0.406880	−	0.308379i
$543$	−5.34496	+	0.734068i	−0.229374	+	0.0315019i
$544$	1.21837	+	12.0060i	0.0522374	+	0.514752i
$545$	−5.55442	−	3.20685i	−0.237925	−	0.137366i
$546$	40.3220	+	12.6408i	1.72562	+	0.540977i
$547$	14.5062	+	25.1255i	0.620242	+	1.07429i	0.989440	+	0.144940i	$0.0462989\pi$
$547$	14.5062	+	25.1255i	0.620242	+	1.07429i	−0.369199	+	0.929351i	$0.620368\pi$
$548$	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
$552$	0.273910	−	22.3144i	0.0116584	−	0.949764i
$553$	−0.275939	+	6.62531i	−0.0117341	+	0.281737i
$554$	−2.70919	+	6.43199i	−0.115102	+	0.273269i
$555$	1.44768	+	0.590200i	0.0614507	+	0.0250526i
$556$	−21.5506	+	21.0434i	−0.913949	+	0.892441i
$557$			34.2229i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$557$			34.2229i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$558$	−6.58487	−	15.6656i	−0.278760	−	0.663179i
$559$	−21.0975			−0.892329
$560$	1.23490	−	18.8445i	0.0521839	−	0.796325i
$561$	16.7301	−	12.9865i	0.706344	−	0.548291i
$562$	31.6644	+	13.3372i	1.33568	+	0.562596i
$563$	−10.9590	−	6.32720i	−0.461868	−	0.266660i	0.250961	−	0.967997i	$-0.419253\pi$
$563$	−10.9590	−	6.32720i	−0.461868	−	0.266660i	−0.712830	+	0.701337i	$0.752587\pi$
$564$	15.0110	−	6.10687i	0.632076	−	0.257146i
$565$	−2.03994	−	3.53328i	−0.0858210	−	0.148646i
$566$	−32.9173	+	4.13445i	−1.38362	+	0.173784i
$567$	0.459209	−	23.8073i	0.0192849	−	0.999814i
$568$	−5.17486	+	2.03600i	−0.217132	+	0.0854288i
$569$	−2.51898	−	4.36301i	−0.105601	−	0.182907i	0.808382	−	0.588658i	$-0.200343\pi$
$569$	−2.51898	−	4.36301i	−0.105601	−	0.182907i	−0.913984	+	0.405751i	$0.867010\pi$
$570$	15.1982	−	4.06636i	0.636584	−	0.170321i
$571$	8.56623	−	14.8371i	0.358486	−	0.620915i	−0.629222	−	0.777225i	$-0.716627\pi$
$571$	8.56623	−	14.8371i	0.358486	−	0.620915i	0.987708	+	0.156310i	$0.0499599\pi$
$572$	−20.2044	+	71.9654i	−0.844789	+	3.00903i
$573$	20.8458	−	16.1813i	0.870846	−	0.675984i
$574$	−10.3223	+	21.9101i	−0.430842	+	0.914508i
$575$		−	8.27103i		−	0.344926i
$576$	−12.5066	+	20.4838i	−0.521107	+	0.853491i
$577$			17.0368i			0.709252i	0.935008	+	0.354626i	$0.115392\pi$
$577$			17.0368i			0.709252i	−0.935008	+	0.354626i	$0.884608\pi$
$578$	−14.0311	+	10.6343i	−0.583617	+	0.442330i
$579$	−1.88773	+	4.63036i	−0.0784514	+	0.192431i
$580$	21.6304	+	6.07276i	0.898152	+	0.252157i
$581$	0.0678418	−	1.62889i	0.00281455	−	0.0675776i
$582$	10.2792	−	38.3061i	0.426087	−	1.58784i
$583$	−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	$-0.627079\pi$
$587$	5.20552	−	3.00541i	0.214855	−	0.124046i	0.603566	+	0.797313i	$0.293746\pi$
$588$	−23.1432	+	7.23840i	−0.954408	+	0.298507i
$589$	−12.4853	−	7.20837i	−0.514446	−	0.297016i
$590$	0.391467	−	0.929396i	0.0161164	−	0.0382626i
$591$	5.82647	+	42.4242i	0.239669	+	1.74510i
$592$	−1.05307	+	1.72762i	−0.0432809	+	0.0710049i
$593$			22.4175i			0.920575i	0.887770	+	0.460287i	$0.152254\pi$
$593$			22.4175i			0.920575i	−0.887770	+	0.460287i	$0.847746\pi$
$594$	42.1179	−	0.454941i	1.72812	−	0.0186664i
$595$	−8.92434	+	4.66852i	−0.365862	+	0.191391i
$596$	−15.8811	+	15.5073i	−0.650514	+	0.635206i
$597$	27.0352	−	3.71297i	1.10648	−	0.151962i
$598$	16.3054	−	38.7112i	0.666776	−	1.58302i
$599$	−37.3706	−	21.5759i	−1.52692	−	0.881569i	−0.999489	−	0.0319734i	$-0.989821\pi$
$599$	−37.3706	−	21.5759i	−1.52692	−	0.881569i	−0.527434	−	0.849596i	$-0.676846\pi$
$600$	−4.54179	+	7.64825i	−0.185418	+	0.312239i
$601$	−19.6346	+	11.3361i	−0.800914	+	0.462408i	−0.843791	−	0.536673i	$-0.819681\pi$
$601$	−19.6346	+	11.3361i	−0.800914	+	0.462408i	0.0428769	+	0.999080i	$0.486348\pi$
$602$	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
$606$	−24.1965	−	6.49299i	−0.982917	−	0.263760i
$607$	−9.69474	+	16.7918i	−0.393498	+	0.681558i	−0.992908	−	0.118884i	$-0.962068\pi$
$607$	−9.69474	+	16.7918i	−0.393498	+	0.681558i	0.599411	+	0.800442i	$0.295402\pi$
$608$	2.05569	+	20.2570i	0.0833694	+	0.821530i
$609$	−2.73238	−	28.7181i	−0.110721	−	1.16371i
$610$	14.7231	−	11.1588i	0.596120	−	0.451806i
$611$	30.5035			1.23404
$612$	12.7997	+	0.00942843i	0.517396	+	0.000381122i
$613$			11.2484i			0.454317i	0.973858	+	0.227159i	$0.0729436\pi$
$613$			11.2484i			0.454317i	−0.973858	+	0.227159i	$0.927056\pi$
$614$	3.78149	+	4.98935i	0.152608	+	0.201354i
$615$	−15.8040	+	12.2677i	−0.637281	+	0.494682i
$616$	−14.0296	−	40.5339i	−0.565270	−	1.63316i
$617$	4.16806	−	7.21930i	0.167800	−	0.290638i	−0.769846	−	0.638230i	$-0.779667\pi$
$617$	4.16806	−	7.21930i	0.167800	−	0.290638i	0.937646	+	0.347592i	$0.113000\pi$
$618$	1.71313	+	6.40291i	0.0689121	+	0.257563i
$619$	−10.1564	+	5.86379i	−0.408220	+	0.235686i	−0.690025	−	0.723786i	$-0.742400\pi$
$619$	−10.1564	+	5.86379i	−0.408220	+	0.235686i	0.281805	+	0.959472i	$0.409067\pi$
$620$	−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
$623$	−17.6914	−	11.2208i	−0.708793	−	0.449552i
$624$	−36.3347	+	26.8428i	−1.45455	+	1.07457i
$625$	6.31231	−	10.9332i	0.252492	−	0.437329i
$626$	8.09433	−	19.2171i	0.323514	−	0.768068i
$627$	28.2277	−	21.9114i	1.12730	−	0.875057i
$628$	−21.9552	−	22.4844i	−0.876110	−	0.897224i
$629$	1.07905			0.0430246
$630$	−19.7508	−	3.33565i	−0.786890	−	0.132896i
$631$		−	17.6401i		−	0.702240i	−0.936330	−	0.351120i	$-0.885801\pi$
$631$		−	17.6401i		−	0.702240i	0.936330	−	0.351120i	$-0.114199\pi$
$632$	−5.54603	−	4.41519i	−0.220609	−	0.175627i
$633$	−3.89186	+	9.54623i	−0.154688	+	0.379429i
$634$	13.3127	−	31.6061i	0.528713	−	1.25524i
$635$	−11.4922	−	6.63501i	−0.456053	−	0.263302i
$636$	−2.84054	−	0.392247i	−0.112635	−	0.0155536i
$637$	−45.4847	−	3.79539i	−1.80217	−	0.150379i
$638$	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	0.756615	−	0.653860i	$-0.226852\pi$
$641$	−4.75856	−	8.24207i	−0.187952	−	0.325542i	−0.944567	+	0.328318i	$0.893518\pi$
$642$	22.1810	−	22.1646i	0.875413	−	0.874768i
$643$	−23.8893	−	13.7925i	−0.942101	−	0.543922i	−0.0514829	−	0.998674i	$-0.516395\pi$
$643$	−23.8893	−	13.7925i	−0.942101	−	0.543922i	−0.890618	+	0.454751i	$0.849728\pi$
$644$	4.98391	+	23.5832i	0.196394	+	0.929310i
$645$	9.90754	−	1.36068i	0.390109	−	0.0535769i
$646$	8.65418	−	6.55910i	0.340494	−	0.258064i
$647$	26.8727			1.05647			0.528237	−	0.849097i	$-0.322853\pi$
$647$	26.8727			1.05647			0.528237	+	0.849097i	$0.322853\pi$
$648$	20.2647	+	15.4059i	0.796073	+	0.605201i
$649$		−	2.29055i		−	0.0899119i
$650$	−13.3437	+	10.1133i	−0.523381	+	0.396677i
$651$	10.6418	+	14.9551i	0.417084	+	0.586135i
$652$	10.3090	−	36.7191i	0.403730	−	1.43803i
$653$	24.8287	+	14.3349i	0.971624	+	0.560967i	0.899731	−	0.436445i	$-0.143763\pi$
$653$	24.8287	+	14.3349i	0.971624	+	0.560967i	0.0718927	+	0.997412i	$0.477096\pi$
$654$	−6.22304	−	6.22763i	−0.243340	−	0.243520i
$655$	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	−0.954412	−	0.298491i	$-0.903517\pi$
$659$	−18.8863	−	32.7121i	−0.735707	−	1.27428i	0.218706	−	0.975791i	$-0.429817\pi$
$660$	4.84673	−	35.0986i	0.188659	−	1.36621i
$661$	−4.81546	+	8.34062i	−0.187300	+	0.324412i	−0.944349	−	0.328945i	$-0.893307\pi$
$661$	−4.81546	+	8.34062i	−0.187300	+	0.324412i	0.757049	+	0.653358i	$0.226640\pi$
$662$	−28.3027	−	11.9212i	−1.10001	−	0.463332i
$663$	22.3097	+	9.09535i	0.866438	+	0.353234i
$664$	1.36354	+	1.08551i	0.0529155	+	0.0421260i
$665$	−15.0575	+	7.87693i	−0.583906	+	0.305454i
$666$	1.70933	+	1.29751i	0.0662353	+	0.0502774i
$667$	−28.6758			−1.11033
$668$	−1.27715	−	1.30793i	−0.0494143	−	0.0506052i
$669$	23.3620	+	30.0964i	0.903227	+	1.16359i
$670$	−15.8318	−	6.66842i	−0.611634	−	0.257624i
$671$	20.9799	−	36.3383i	0.809921	−	1.40282i
$672$	8.34140	−	24.5443i	0.321776	−	0.946816i
$673$	−1.48211	−	2.56709i	−0.0571311	−	0.0989540i	0.836045	−	0.548660i	$-0.184862\pi$
$673$	−1.48211	−	2.56709i	−0.0571311	−	0.0989540i	−0.893176	+	0.449706i	$0.851529\pi$
$674$	−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	0.938137	+	0.346263i	$0.112550\pi$
$677$	20.0073	+	34.6536i	0.768942	+	1.33185i	−0.169196	+	0.985582i	$0.554117\pi$
$678$	−1.44749	−	5.41009i	−0.0555906	−	0.207773i
$679$	−1.78267	+	42.8020i	−0.0684126	+	1.64259i
$680$	1.59580	−	10.6482i	0.0611961	−	0.408339i
$681$	−30.8043	+	23.9114i	−1.18042	+	0.916289i
$682$	−25.8756	+	19.6114i	−0.990827	+	0.750959i
$683$	7.37335			0.282133			0.141067	−	0.990000i	$-0.454947\pi$
$683$	7.37335			0.282133			0.141067	+	0.990000i	$0.454947\pi$
$684$	21.5961	+	0.0159080i	0.825749	+	0.000608259i
$685$	−27.4214			−1.04772
$686$	22.6817	−	13.0974i	0.865990	−	0.500062i
$687$	−19.4068	+	47.6023i	−0.740415	+	1.81614i
$688$	−0.308160	+	12.9388i	−0.0117485	+	0.493287i
$689$	−4.67430	−	2.69871i	−0.178077	−	0.102813i
$690$	−5.16044	+	19.2307i	−0.196455	+	0.732100i
$691$	−28.3406	+	16.3625i	−1.07813	+	0.622457i	−0.930391	−	0.366569i	$-0.880532\pi$
$691$	−28.3406	+	16.3625i	−1.07813	+	0.622457i	−0.147737	+	0.989027i	$0.547199\pi$
$692$	−25.4925	+	6.50642i	−0.969081	+	0.247337i
$693$	−44.2831	+	10.4314i	−1.68218	+	0.396256i
$694$	1.49912	+	11.9356i	0.0569060	+	0.453070i
$695$	23.2740	−	13.4373i	0.882834	−	0.509704i
$696$	26.5166	+	15.7464i	1.00511	+	0.596867i
$697$	−6.90437	+	11.9587i	−0.261522	+	0.452969i
$698$	33.5690	+	14.1394i	1.27061	+	0.535186i
$699$	33.3396	−	4.57880i	1.26102	−	0.173186i
$700$	2.97969	−	9.13413i	0.112622	−	0.345238i
$701$		−	5.14751i		−	0.194419i	−0.995264	−	0.0972094i	$-0.969008\pi$
$701$		−	5.14751i		−	0.194419i	0.995264	−	0.0972094i	$-0.0309917\pi$
$702$	24.4043	+	41.2344i	0.921079	+	1.55629i
$703$	1.82062			0.0686661
$704$	43.8403	+	13.4422i	1.65229	+	0.506623i
$705$	−14.3247	+	1.96733i	−0.539499	+	0.0740939i
$706$	−8.60071	+	20.4193i	−0.323692	+	0.768489i
$707$	27.0364	+	1.12605i	1.01681	+	0.0423493i
$708$	0.849644	−	1.09290i	0.0319316	−	0.0410738i
$709$	−18.9392	+	10.9345i	−0.711276	+	0.410655i	−0.811533	−	0.584306i	$-0.801367\pi$
$709$	−18.9392	+	10.9345i	−0.711276	+	0.410655i	0.100257	+	0.994962i	$0.468033\pi$
$710$	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
$714$	−13.4926	+	3.01445i	−0.504947	+	0.112813i
$715$	33.3461	−	57.7571i	1.24707	−	2.15999i
$716$	4.78720	−	17.0514i	0.178906	−	0.637240i
$717$	−5.18148	−	2.11241i	−0.193506	−	0.0788895i
$718$	−27.6519	−	36.4844i	−1.03196	−	1.36159i
$719$	−44.0176			−1.64158			−0.820790	−	0.571230i	$-0.806466\pi$
$719$	−44.0176			−1.64158			−0.820790	+	0.571230i	$0.806466\pi$
$720$	15.3318	−	14.9490i	0.571384	−	0.557116i
$721$	−3.31849	−	6.34363i	−0.123587	−	0.236249i
$722$	−6.81275	+	5.16347i	−0.253544	+	0.192164i
$723$	25.4626	−	19.7651i	0.946965	−	0.735070i
$724$	−1.68391	+	5.99786i	−0.0625820	+	0.222909i
$725$	9.89875	+	5.71505i	0.367631	+	0.212252i
$726$	−13.8359	−	51.7124i	−0.513498	−	1.91923i
$727$	−14.7080	−	25.4750i	−0.545489	−	0.944815i	−0.998576	−	0.0533487i	$-0.983011\pi$
$727$	−14.7080	−	25.4750i	−0.545489	−	0.944815i	0.453087	−	0.891466i	$-0.350323\pi$
$728$	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
$732$	23.4894	−	9.55612i	0.868193	−	0.353204i
$733$	−17.7078	+	30.6708i	−0.654052	+	1.13285i	0.328079	+	0.944650i	$0.393599\pi$
$733$	−17.7078	+	30.6708i	−0.654052	+	1.13285i	−0.982131	+	0.188201i	$0.939734\pi$
$734$	8.45665	+	3.56198i	0.312141	+	0.131475i
$735$	21.6047	−	1.15120i	0.796903	−	0.0424626i
$736$	−23.5029	−	10.5653i	−0.866327	−	0.389442i
$737$	−39.0182			−1.43725
$738$	−25.3171	+	10.6417i	−0.931934	+	0.391727i
$739$	−34.7390			−1.27789			−0.638947	−	0.769251i	$-0.720630\pi$
$739$	−34.7390			−1.27789			−0.638947	+	0.769251i	$0.720630\pi$
$740$	1.29159	−	1.26120i	0.0474799	−	0.0463625i
$741$	37.6419	+	15.3461i	1.38281	+	0.563752i
$742$	3.08651	−	0.257769i	0.113309	−	0.00946300i
$743$	−5.76237	−	3.32691i	−0.211401	−	0.122052i	0.390561	−	0.920577i	$-0.372281\pi$
$743$	−5.76237	−	3.32691i	−0.211401	−	0.122052i	−0.601962	+	0.798525i	$0.705614\pi$
$744$	−19.6207	−	0.240845i	−0.719330	−	0.00882980i
$745$	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
$749$	−18.1407	+	28.6017i	−0.662846	+	1.04508i
$750$	21.0736	−	21.0580i	0.769498	−	0.768931i
$751$	14.8725	+	8.58662i	0.542704	+	0.313330i	0.746174	−	0.665751i	$-0.231889\pi$
$751$	14.8725	+	8.58662i	0.542704	+	0.313330i	−0.203470	+	0.979081i	$0.565222\pi$
$752$	0.445549	−	18.7074i	0.0162475	−	0.682188i
$753$	−4.94546	−	36.0093i	−0.180222	−	1.31225i
$754$	35.0629	+	46.2626i	1.27692	+	1.68478i
$755$		−	15.9374i		−	0.580020i
$756$	−24.9984	−	11.4490i	−0.909184	−	0.416395i
$757$		−	38.6795i		−	1.40583i	−0.711274	−	0.702915i	$-0.751882\pi$
$757$		−	38.6795i		−	1.40583i	0.711274	−	0.702915i	$-0.248118\pi$
$758$	−19.0935	+	14.4712i	−0.693506	+	0.525616i
$759$	6.15321	+	44.8033i	0.223347	+	1.62626i
$760$	2.69250	−	17.9661i	0.0976673	−	0.651698i
$761$	30.3784	+	17.5390i	1.10122	+	0.635787i	0.936540	−	0.350560i	$-0.114009\pi$
$761$	30.3784	+	17.5390i	1.10122	+	0.635787i	0.164676	+	0.986348i	$0.447342\pi$
$762$	−12.8756	−	12.8850i	−0.466432	−	0.466776i
$763$	8.03036	+	5.09326i	0.290718	+	0.184388i
$764$	−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
$768$	15.9316	+	22.6756i	0.574881	+	0.818237i
$769$	−30.3192	−	17.5048i	−1.09334	−	0.631239i	−0.158875	−	0.987299i	$-0.550787\pi$
$769$	−30.3192	−	17.5048i	−1.09334	−	0.631239i	−0.934463	+	0.356060i	$0.884120\pi$
$770$	3.18507	+	38.1378i	0.114782	+	1.37439i
$771$	7.70149	+	3.13979i	0.277362	+	0.113077i
$772$	4.03389	+	4.13111i	0.145183	+	0.148682i
$773$	−48.1597			−1.73218			−0.866091	−	0.499886i	$-0.833375\pi$
$773$	−48.1597			−1.73218			−0.866091	+	0.499886i	$0.833375\pi$
$774$	13.6193	+	1.72078i	0.489535	+	0.0618523i
$775$	−7.27259			−0.261239
$776$	−35.8295	−	28.5238i	−1.28620	−	1.02395i
$777$	−2.10816	−	0.963630i	−0.0756297	−	0.0345700i
$778$	−11.0102	+	26.1397i	−0.394734	+	0.937152i
$779$	−11.6494	+	20.1773i	−0.417381	+	0.722926i
$780$	37.3347	−	15.1888i	1.33680	−	0.543845i
$781$	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
$786$	23.4496	−	6.27404i	0.836418	−	0.223788i
$787$	28.3882	+	16.3900i	1.01193	+	0.584239i	0.911756	−	0.410731i	$-0.134727\pi$
$787$	28.3882	+	16.3900i	1.01193	+	0.584239i	0.100175	+	0.994970i	$0.468060\pi$
$788$	47.6065	+	13.3656i	1.69591	+	0.476130i
$789$	−0.583255	+	0.452745i	−0.0207644	+	0.0161182i
$790$	3.82042	+	5.04072i	0.135924	+	0.179341i
$791$	2.80393	+	5.36000i	0.0996964	+	0.190580i
$792$	18.9125	−	44.8086i	0.672027	−	1.59220i
$793$	47.7324			1.69503
$794$	−2.06271	+	1.56335i	−0.0732029	+	0.0554813i
$795$	2.36914	+	0.965865i	0.0840248	+	0.0342557i
$796$	8.51734	−	30.3376i	0.301889	−	1.07529i
$797$	−3.40500	+	5.89764i	−0.120611	+	0.208905i	−0.920009	−	0.391897i	$-0.871819\pi$
$797$	−3.40500	+	5.89764i	−0.120611	+	0.208905i	0.799398	+	0.600802i	$0.205152\pi$
$798$	−22.7653	+	5.08612i	−0.805882	+	0.180047i
$799$	−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
$804$	−18.6170	−	14.4732i	−0.656571	−	0.510431i
$805$	0.894948	−	21.4878i	0.0315428	−	0.757344i
$806$	−34.0382	−	14.3371i	−1.19894	−	0.505001i
$807$	−14.7789	+	2.02970i	−0.520241	+	0.0714490i
$808$	−18.0174	+	22.6321i	−0.633851	+	0.796196i
$809$	7.74558			0.272320			0.136160	−	0.990687i	$-0.456524\pi$
$809$	7.74558			0.272320			0.136160	+	0.990687i	$0.456524\pi$
$810$	−14.1198	−	17.7900i	−0.496121	−	0.625077i
$811$			36.9006i			1.29576i	0.761744	+	0.647878i	$0.224344\pi$
$811$			36.9006i			1.29576i	−0.761744	+	0.647878i	$0.775656\pi$
$812$	−31.6681	−	10.3306i	−1.11133	−	0.362534i
$813$	−14.4217	+	1.98065i	−0.505790	+	0.0694643i
$814$	1.59160	−	3.77868i	0.0557855	−	0.132443i
$815$	−17.0143	+	29.4696i	−0.595984	+	1.03227i
$816$	5.90392	−	13.5494i	0.206678	−	0.474323i
$817$	10.0858	−	5.82307i	0.352859	−	0.203723i
$818$	−6.81136	+	0.855513i	−0.238154	+	0.0299123i
$819$	−35.4643	−	37.6930i	−1.23922	−	1.31710i
$820$	5.71305	+	22.3841i	0.199508	+	0.781686i
$821$	−1.27921	+	0.738551i	−0.0446447	+	0.0257756i	−0.522156	−	0.852850i	$-0.674872\pi$
$821$	−1.27921	+	0.738551i	−0.0446447	+	0.0257756i	0.477512	+	0.878625i	$0.341539\pi$
$822$	−36.3547	−	9.75557i	−1.26802	−	0.340265i
$823$	6.36180	+	3.67299i	0.221758	+	0.128032i	0.606764	−	0.794882i	$-0.292467\pi$
$823$	6.36180	+	3.67299i	0.221758	+	0.128032i	−0.385006	+	0.922914i	$0.625801\pi$
$824$	7.56897	+	1.13433i	0.263678	+	0.0395163i
$825$	6.80519	−	16.6923i	0.236926	−	0.581150i
$826$	−0.637253	+	1.35264i	−0.0221729	+	0.0470643i
$827$	12.3241			0.428552			0.214276	−	0.976773i	$-0.431261\pi$
$827$	12.3241			0.428552			0.214276	+	0.976773i	$0.431261\pi$
$828$	−13.6832	+	23.6597i	−0.475524	+	0.822232i
$829$	−0.588826			−0.0204508			−0.0102254	−	0.999948i	$-0.503255\pi$
$829$	−0.588826			−0.0204508			−0.0102254	+	0.999948i	$0.503255\pi$
$830$	−0.939282	−	1.23930i	−0.0326030	−	0.0430168i
$831$	6.75228	−	5.24137i	0.234234	−	0.181821i
$832$	11.6929	+	50.8357i	0.405378	+	1.76241i
$833$	13.5084	−	6.36524i	0.468038	−	0.220542i
$834$	35.6367	−	9.53475i	1.23400	−	0.330161i
$835$	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	−0.999599	−	0.0283235i	$-0.990983\pi$
$839$	−15.1874	−	26.3054i	−0.524328	−	0.908163i	0.475271	−	0.879840i	$-0.342350\pi$
$840$	−12.6269	+	19.3784i	−0.435670	+	0.668617i
$841$	5.31412	−	9.20433i	0.183246	−	0.317391i
$842$	−21.1484	+	50.2092i	−0.728821	+	1.73032i
$843$	−25.8030	−	33.2411i	−0.888703	−	1.14488i
$844$	8.31651	+	8.51694i	0.286266	+	0.293165i
$845$	52.6692			1.81188
$846$	−19.6912	−	2.48797i	−0.676999	−	0.0855383i
$847$	26.8015	+	51.2337i	0.920910	+	1.76041i
$848$	−1.72336	+	2.82727i	−0.0591803	+	0.0970887i
$849$	37.6254	+	15.3393i	1.29130	+	0.526445i
$850$	2.12637	−	5.04830i	0.0729339	−	0.173155i
$851$	−1.15207	+	1.99544i	−0.0394923	+	0.0684027i
$852$	6.74675	+	0.931652i	0.231140	+	0.0319179i
$853$	−0.381441	−	0.660676i	−0.0130603	−	0.0226211i	0.859421	−	0.511268i	$-0.170824\pi$
$853$	−0.381441	−	0.660676i	−0.0130603	−	0.0226211i	−0.872482	+	0.488647i	$0.837491\pi$
$854$	−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	$-0.745870\pi$
$857$	−12.4869	+	7.20931i	−0.426544	+	0.246266i	0.271329	+	0.962487i	$0.412537\pi$
$858$	64.7574	−	64.7097i	2.21078	−	2.20915i
$859$	−8.64422	−	4.99075i	−0.294937	−	0.170282i	0.345229	−	0.938518i	$-0.387801\pi$
$859$	−8.64422	−	4.99075i	−0.294937	−	0.170282i	−0.640166	+	0.768236i	$0.721135\pi$
$860$	3.12133	−	11.1178i	0.106437	−	0.379113i
$861$	24.1687	−	17.1981i	0.823667	−	0.586108i
$862$	−0.985667	−	1.30050i	−0.0335720	−	0.0442953i
$863$			20.5530i			0.699633i	0.936818	+	0.349816i	$0.113756\pi$
$863$			20.5530i			0.699633i	−0.936818	+	0.349816i	$0.886244\pi$
$864$	25.6449	−	14.3645i	0.872457	−	0.488690i
$865$	23.4743			0.798151
$866$	−6.38324	−	8.42214i	−0.216911	−	0.286196i
$867$	21.3620	−	2.93382i	0.725491	−	0.0996377i
$868$	20.7364	−	4.38227i	0.703839	−	0.148744i
$869$	12.4411	+	7.18287i	0.422035	+	0.243662i
$870$	−19.4495	−	19.4639i	−0.659401	−	0.659887i
$871$	−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
$875$	−17.2350	+	27.1738i	−0.582649	+	0.918641i
$876$	49.2489	+	6.80073i	1.66397	+	0.229775i
$877$	−15.3343	−	8.85327i	−0.517803	−	0.298954i	0.218232	−	0.975897i	$-0.429971\pi$
$877$	−15.3343	−	8.85327i	−0.517803	−	0.298954i	−0.736035	+	0.676943i	$0.763304\pi$
$878$	38.5660	+	16.2442i	1.30154	+	0.548215i
$879$	−5.01697	+	12.3060i	−0.169218	+	0.415070i
$880$	−34.9345	−	21.2943i	−1.17764	−	0.717831i
$881$			2.58804i			0.0871932i	0.999049	+	0.0435966i	$0.0138816\pi$
$881$			2.58804i			0.0871932i	−0.999049	+	0.0435966i	$0.986118\pi$
$882$	29.0526	+	6.15996i	0.978253	+	0.207417i
$883$	−41.4416			−1.39462			−0.697310	−	0.716769i	$-0.745620\pi$
$883$	−41.4416			−1.39462			−0.697310	+	0.716769i	$0.745620\pi$
$884$	19.9043	−	19.4359i	0.669453	−	0.653698i
$885$	−0.975677	+	0.757358i	−0.0327970	+	0.0254583i
$886$	−48.7050	−	20.5148i	−1.63628	−	0.689208i
$887$	−10.7798	+	18.6711i	−0.361949	+	0.626914i	−0.988282	−	0.152642i	$-0.951222\pi$
$887$	−10.7798	+	18.6711i	−0.361949	+	0.626914i	0.626333	+	0.779556i	$0.284555\pi$
$888$	2.16105	−	1.21256i	0.0725202	−	0.0406910i
$889$	16.6149	+	10.5380i	0.557246	+	0.353434i
$890$	−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
$894$	26.2614	−	7.02635i	0.878312	−	0.234996i
$895$	−7.90097	+	13.6849i	−0.264100	+	0.457435i
$896$	−22.1492	−	20.1348i	−0.739954	−	0.672658i
$897$	−40.6389	+	31.5455i	−1.35689	+	1.05327i
$898$	−22.9134	+	17.3663i	−0.764631	+	0.579522i
$899$			25.2141i			0.840939i
$900$	9.43874	−	5.44019i	0.314625	−	0.181340i
$901$	1.76587			0.0588298
$902$	31.6937	+	41.8172i	1.05529	+	1.39236i
$903$	−14.7608	+	1.40441i	−0.491208	+	0.0467359i
$904$	−6.39534	−	0.958444i	−0.212706	−	0.0318774i
$905$	2.77919	−	4.81369i	0.0923832	−	0.160012i
$906$	5.66995	−	21.1294i	0.188371	−	0.701977i
$907$	−8.95976	−	15.5188i	−0.297504	−	0.515292i	0.678060	−	0.735006i	$-0.262821\pi$
$907$	−8.95976	−	15.5188i	−0.297504	−	0.515292i	−0.975564	+	0.219714i	$0.929487\pi$
$908$	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	$-0.535723\pi$
$911$	20.9042	−	12.0691i	0.692589	−	0.399866i	0.804581	+	0.593843i	$0.202390\pi$
$912$	9.96134	−	22.8611i	0.329853	−	0.757007i
$913$	−3.05875	−	1.76597i	−0.101230	−	0.0584450i
$914$	39.4199	+	16.6039i	1.30389	+	0.549207i
$915$	−22.4155	+	3.07850i	−0.741033	+	0.101772i
$916$	41.4704	+	42.4698i	1.37022	+	1.40324i
$917$	−23.2325	+	12.1534i	−0.767204	+	0.401341i
$918$	−13.6600	−	7.69107i	−0.450846	−	0.253843i
$919$		−	48.2663i		−	1.59216i	−0.605193	−	0.796079i	$-0.706904\pi$
$919$		−	48.2663i		−	1.59216i	0.605193	−	0.796079i	$-0.293096\pi$
$920$	17.9874	+	14.3197i	0.593026	+	0.472107i
$921$	−1.04324	−	7.59615i	−0.0343760	−	0.250302i
$922$	−22.6291	−	9.53152i	−0.745251	−	0.313904i
$923$	11.1022	+	6.40988i	0.365435	+	0.210984i
$924$	−9.34537	+	51.6953i	−0.307440	+	1.70065i
$925$	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	$-0.692812\pi$
$929$	−4.33140	+	2.50073i	−0.142108	+	0.0820464i	0.427260	+	0.904129i	$0.359479\pi$
$930$	16.9093	+	4.53750i	0.554476	+	0.148790i
$931$	22.7919	−	10.7397i	0.746975	−	0.351980i
$932$	10.5035	−	37.4121i	0.344054	−	1.22547i
$933$	6.34600	−	15.5659i	0.207759	−	0.509605i
$934$	−14.9621	−	19.7412i	−0.489574	−	0.645951i
$935$			21.8197i			0.713580i
$936$	54.9011	−	6.85456i	1.79450	−	0.224048i
$937$		−	34.4040i		−	1.12393i	−0.827161	−	0.561965i	$-0.810046\pi$
$937$		−	34.4040i		−	1.12393i	0.827161	−	0.561965i	$-0.189954\pi$
$938$	23.0414	+	10.8553i	0.752329	+	0.354437i
$939$	−20.1740	+	15.6598i	−0.658353	+	0.511039i
$940$	−4.51294	+	16.0745i	−0.147196	+	0.524292i
$941$	−1.17611	+	2.03707i	−0.0383400	+	0.0664067i	−0.884559	−	0.466429i	$-0.845540\pi$
$941$	−1.17611	+	2.03707i	−0.0383400	+	0.0664067i	0.846219	+	0.532836i	$0.178874\pi$
$942$	9.94788	+	37.1808i	0.324120	+	1.21142i
$943$	−14.7431	−	25.5358i	−0.480102	−	0.831561i
$944$	−0.766048	−	1.40295i	−0.0249327	−	0.0456622i
$945$	19.0853	+	15.4137i	0.620845	+	0.501406i
$946$	−3.26859	−	26.0236i	−0.106271	−	0.846101i
$947$	−14.7188	−	25.4936i	−0.478295	−	0.828432i	0.521395	−	0.853315i	$-0.325412\pi$
$947$	−14.7188	−	25.4936i	−0.478295	−	0.828432i	−0.999690	+	0.0248838i	$0.992078\pi$
$948$	3.27172	+	8.04204i	0.106260	+	0.261193i
$949$	81.0424	+	46.7899i	2.63075	+	1.51886i
$950$	3.58771	−	8.51771i	0.116401	−	0.276351i
$951$	−33.1800	+	25.7556i	−1.07593	+	0.835182i
$952$	−3.02096	+	15.6755i	−0.0979099	+	0.508047i
$953$	12.9601			0.419819			0.209909	−	0.977721i	$-0.432683\pi$
$953$	12.9601			0.419819			0.209909	+	0.977721i	$0.432683\pi$
$954$	2.79733	+	2.12338i	0.0905670	+	0.0687469i
$955$			27.1875i			0.879767i
$956$	−4.62280	+	4.51401i	−0.149512	+	0.145994i
$957$	−57.8722	−	23.5937i	−1.87074	−	0.762675i
$958$	37.2008	+	15.6692i	1.20190	+	0.506248i
$959$	40.6216	+	1.69186i	1.31174	+	0.0546329i
$960$	−8.76973	−	23.1187i	−0.283042	−	0.746153i
$961$	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
$966$	8.83108	−	28.1696i	0.284135	−	0.906341i
$967$	8.60670	+	4.96908i	0.276773	+	0.159795i	0.631961	−	0.775000i	$-0.282250\pi$
$967$	8.60670	+	4.96908i	0.276773	+	0.159795i	−0.355189	+	0.934795i	$0.615583\pi$
$968$	−61.1300	−	9.16131i	−1.96479	−	0.294456i
$969$	−13.1758	+	1.80954i	−0.423266	+	0.0581306i
$970$	24.6814	+	32.5650i	0.792472	+	1.04560i
$971$		−	41.2521i		−	1.32384i	−0.749573	−	0.661922i	$-0.769741\pi$
$971$		−	41.2521i		−	1.32384i	0.749573	−	0.661922i	$-0.230259\pi$
$972$	−12.3907	−	28.6089i	−0.397432	−	0.917632i
$973$	−35.3067	+	18.4697i	−1.13188	+	0.592112i
$974$	5.59995	+	7.38866i	0.179434	+	0.236748i
$975$	20.3154	−	2.79008i	0.650612	−	0.0893539i
$976$	0.697201	−	29.2736i	0.0223169	−	0.937025i
$977$	−1.36989	+	2.37272i	−0.0438268	+	0.0759102i	−0.887107	−	0.461564i	$-0.847288\pi$
$977$	−1.36989	+	2.37272i	−0.0438268	+	0.0759102i	0.843280	+	0.537475i	$0.180622\pi$
$978$	−33.0413	+	33.0170i	−1.05655	+	1.05577i
$979$	−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	0.975859	+	0.218402i	$0.0700844\pi$
$983$	21.2281	+	36.7681i	0.677071	+	1.17272i	−0.298788	+	0.954320i	$0.596582\pi$
$984$	−0.389227	+	31.7088i	−0.0124081	+	1.01084i
$985$	−38.2074	−	22.0591i	−1.21739	−	0.702860i
$986$	−17.5025	−	7.37215i	−0.557393	−	0.234777i
$987$	21.3417	−	2.03055i	0.679314	−	0.0646332i
$988$	33.5833	−	32.7930i	1.06843	−	1.04328i
$989$			14.7390i			0.468674i
$990$	−26.2371	+	34.5647i	−0.833870	+	1.09854i
$991$			14.3136i			0.454685i	0.973815	+	0.227343i	$0.0730037\pi$
$991$			14.3136i			0.454685i	−0.973815	+	0.227343i	$0.926996\pi$
$992$	−9.28989	+	20.6657i	−0.294954	+	0.656137i
$993$	23.0636	+	29.7120i	0.731902	+	0.942883i
$994$	−7.33096	+	0.612244i	−0.232524	+	0.0194192i
$995$	−14.0573	+	24.3480i	−0.445647	+	0.771884i
$996$	−0.804379	−	1.97720i	−0.0254877	−	0.0626501i
$997$	8.01970	+	13.8905i	0.253986	+	0.439917i	0.964620	−	0.263645i	$-0.0849248\pi$
$997$	8.01970	+	13.8905i	0.253986	+	0.439917i	−0.710633	+	0.703563i	$0.751591\pi$
$998$	−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.139.20	yes	184
7.6	odd	2	inner	504.2.be.a.139.19	✓	184
8.3	odd	2	inner	504.2.be.a.139.82	yes	184
9.7	even	3	inner	504.2.be.a.475.81	yes	184
56.27	even	2	inner	504.2.be.a.139.81	yes	184
63.34	odd	6	inner	504.2.be.a.475.82	yes	184
72.43	odd	6	inner	504.2.be.a.475.19	yes	184
504.475	even	6	inner	504.2.be.a.475.20	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.19	✓	184	7.6	odd	2	inner
504.2.be.a.139.20	yes	184	1.1	even	1	trivial
504.2.be.a.139.81	yes	184	56.27	even	2	inner
504.2.be.a.139.82	yes	184	8.3	odd	2	inner
504.2.be.a.475.19	yes	184	72.43	odd	6	inner
504.2.be.a.475.20	yes	184	504.475	even	6	inner
504.2.be.a.475.81	yes	184	9.7	even	3	inner
504.2.be.a.475.82	yes	184	63.34	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-1.12708 + 0.854224i) q^{2} +(1.71594 - 0.235665i) q^{3} +(0.540602 - 1.92555i) q^{4} +(-0.892228 + 1.54538i) q^{5} +(-1.73269 + 1.73141i) q^{6} +(1.41708 - 2.23425i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 - 0.808775i) q^{9} +O(q^{10})\)	\(q+(-1.12708 + 0.854224i) q^{2} +(1.71594 - 0.235665i) q^{3} +(0.540602 - 1.92555i) q^{4} +(-0.892228 + 1.54538i) q^{5} +(-1.73269 + 1.73141i) q^{6} +(1.41708 - 2.23425i) 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} +(0.473857 - 3.43154i) q^{12} +(3.26020 - 5.64683i) q^{13} +(0.311400 + 3.72868i) q^{14} +(-1.16682 + 2.86206i) q^{15} +(-3.41550 - 2.08191i) q^{16} +2.13328i q^{17} +(-2.56516 + 3.37934i) q^{18} +3.59936i q^{19} +(2.49338 + 2.55347i) q^{20} +(1.90509 - 4.16781i) q^{21} +(7.47042 + 3.14658i) q^{22} +(-3.94496 - 2.27763i) q^{23} +(2.39723 + 4.27239i) 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} +(-1.12975 - 4.22249i) q^{30} +(-2.00268 + 3.46875i) q^{31} +(5.62795 - 0.571128i) q^{32} +(-6.08759 - 7.84242i) q^{33} +(-1.82230 - 2.40437i) q^{34} +(2.18843 + 4.18339i) q^{35} +(0.00441969 - 6.00000i) q^{36} -0.505819i q^{37} +(-3.07466 - 4.05675i) q^{38} +(4.26356 - 10.4580i) q^{39} +(-4.99146 - 0.748050i) q^{40} +(5.60580 + 3.23651i) q^{41} +(1.41306 + 6.32481i) 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} +(-6.35144 - 2.76753i) q^{48} +(-2.98378 - 6.33222i) q^{49} +(-2.36645 - 0.996763i) q^{50} +(0.502738 + 3.66058i) q^{51} +(-9.11079 - 9.33037i) q^{52} -0.827775i q^{53} +(-3.60528 + 6.40328i) q^{54} +10.2282 q^{55} +(7.34810 + 1.41611i) q^{56} +(0.848242 + 6.17629i) q^{57} +(-3.45578 + 8.20451i) q^{58} +(0.346079 + 0.199809i) q^{59} +(4.88026 + 3.79401i) q^{60} +(3.66024 + 6.33971i) q^{61} +(-0.705912 - 5.62028i) q^{62} +(2.28682 - 7.60069i) q^{63} +(-5.85526 + 5.45124i) q^{64} +(5.81768 + 10.0765i) q^{65} +(13.5604 + 3.63884i) q^{66} +(3.40363 - 5.89527i) q^{67} +(4.10774 + 1.15325i) q^{68} +(-7.30609 - 2.97859i) q^{69} +(-6.04008 - 2.84560i) q^{70} +1.96610i q^{71} +(5.12036 + 6.76623i) q^{72} +14.3518i q^{73} +(0.432083 + 0.570096i) q^{74} +(1.92840 + 2.48429i) q^{75} +(6.93075 + 1.94582i) q^{76} +(-15.1519 - 0.631065i) q^{77} +(4.12808 + 15.4289i) 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} +(-6.99544 - 5.92147i) q^{84} +(-3.29674 - 1.90337i) q^{85} +(4.21704 + 1.77624i) q^{86} +(8.61307 - 6.68579i) q^{87} +(10.0974 - 12.6836i) q^{88} -7.91828i q^{89} +(-2.93367 - 6.97931i) q^{90} +(-7.99650 - 15.2861i) q^{91} +(-6.51834 + 6.36494i) q^{92} +(-2.61903 + 6.42413i) q^{93} +(-6.09715 - 2.56815i) q^{94} +(-5.56239 - 3.21145i) q^{95} +(9.52265 - 2.30633i) 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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