LMFDB - Embedded newform 504.2.be.a.475.82

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			475.82
Character	$\chi$	$=$	504.475
Dual form			504.2.be.a.139.82

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30332 + 0.548965i) q^{2} +(1.71594 + 0.235665i) q^{3} +(1.39728 + 1.43095i) q^{4} +(0.892228 + 1.54538i) q^{5} +(2.10705 + 1.24914i) q^{6} +(-1.41708 - 2.23425i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 + 0.808775i) q^{9} +O(q^{10})$	\(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} +(-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} +(2.06042 + 2.78472i) q^{12} +(-3.26020 - 5.64683i) q^{13} +(-0.620376 - 3.68987i) 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} +(-1.90509 - 4.16781i) 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} +(1.21706 - 5.14964i) 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} +(-0.194959 - 6.47781i) 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} +(-2.98378 + 6.33222i) 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} +(4.41318 - 6.04349i) 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} +(-2.28682 - 7.60069i) 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} +(5.14875 - 4.25093i) 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} +(15.1519 - 0.631065i) 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} +(3.30199 - 8.54967i) 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} +(-7.36498 + 6.61491i) 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	0.993605	−	0.112913i	$-0.0360182\pi$
$5$	0.892228	+	1.54538i	0.399017	+	0.691117i	−0.594588	+	0.804030i	$0.702685\pi$
$6$	2.10705	+	1.24914i	0.860199	+	0.509959i
$7$	−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	0.00382055	+	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	$-0.807123\pi$
$13$	−3.26020	−	5.64683i	−0.904216	−	1.56615i	−0.0822504	−	0.996612i	$-0.526211\pi$
$14$	−0.620376	−	3.68987i	−0.165803	−	0.986159i
$15$	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	$-0.916707\pi$
$17$		−	2.13328i		−	0.517396i	0.965958	−	0.258698i	$-0.0832934\pi$
$18$	3.32120	+	2.64001i	0.782814	+	0.622256i
$19$		−	3.59936i		−	0.825749i	−0.910788	−	0.412875i	$-0.864525\pi$
$19$		−	3.59936i		−	0.825749i	0.910788	−	0.412875i	$-0.135475\pi$
$20$	−0.964680	+	3.43606i	−0.215709	+	0.768327i
$21$	−1.90509	−	4.16781i	−0.415725	−	0.909491i
$22$	−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
$28$	1.21706	−	5.14964i	0.230003	−	0.973190i
$29$	−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	0.987909	−	0.155033i	$-0.0495484\pi$
$31$	2.00268	+	3.46875i	0.359692	+	0.623005i	−0.628217	+	0.778038i	$0.716215\pi$
$32$	−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	0.00631369	−	0.999980i	$-0.497990\pi$
$41$	5.60580	−	3.23651i	0.875479	−	0.505458i	0.869165	+	0.494522i	$0.164657\pi$
$42$	−0.194959	−	6.47781i	−0.0300828	−	0.999547i
$43$	−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	−0.984654	−	0.174517i	$-0.944164\pi$
$47$	−2.33909	+	4.05142i	−0.341191	+	0.590960i	0.643463	+	0.765477i	$0.277497\pi$
$48$	−1.10582	+	6.83938i	−0.159611	+	0.987180i
$49$	−2.98378	+	6.33222i	−0.426255	+	0.904603i
$50$	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
$56$	4.41318	−	6.04349i	0.589736	−	0.807596i
$57$	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	−0.477303	−	0.878739i	$-0.658386\pi$
$59$	0.346079	−	0.199809i	0.0450556	−	0.0260129i	0.522359	+	0.852726i	$0.325052\pi$
$60$	−2.46510	+	5.66875i	−0.318243	+	0.731833i
$61$	−3.66024	+	6.33971i	−0.468645	+	0.811717i	−0.999358	−	0.0358346i	$-0.988591\pi$
$61$	−3.66024	+	6.33971i	−0.468645	+	0.811717i	0.530713	+	0.847552i	$0.321924\pi$
$62$	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
$66$	−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
$70$	5.14875	−	4.25093i	0.615393	−	0.508083i
$71$			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	$-0.682626\pi$
$73$		−	14.3518i		−	1.67976i	0.542775	−	0.839878i	$-0.317374\pi$
$74$	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
$77$	15.1519	−	0.631065i	1.72672	−	0.0719165i
$78$	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	0.529001	−	0.848621i	$-0.322567\pi$
$83$	0.533641	+	0.308098i	0.0585747	+	0.0338181i	−0.470427	+	0.882439i	$0.655900\pi$
$84$	3.30199	−	8.54967i	0.360277	−	0.932845i
$85$	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	$0.137853\pi$
$89$			7.91828i			0.839336i	−0.907678	+	0.419668i	$0.862147\pi$
$90$	−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	−0.427141	−	0.904185i	$-0.640479\pi$
$97$	−14.0224	−	8.09583i	−1.42376	−	0.822007i	−0.996618	+	0.0821777i	$0.973812\pi$
$98$	−7.36498	+	6.61491i	−0.743976	+	0.668207i
$99$	−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	$0.336594\pi$
$101$	−5.11383	+	8.85742i	−0.508845	+	0.881346i	−0.999948	+	0.0102441i	$0.996739\pi$
$102$	2.66476	−	4.49492i	0.263850	−	0.445063i
$103$	−1.35296	−	2.34340i	−0.133311	−	0.230902i	0.791640	−	0.610988i	$-0.209228\pi$
$103$	−1.35296	−	2.34340i	−0.133311	−	0.230902i	−0.924951	+	0.380086i	$0.875894\pi$
$104$	11.4866	−	14.4286i	1.12635	−	1.41484i
$105$	4.74109	−	6.66273i	0.462683	−	0.650216i
$106$	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
$112$	9.06945	−	5.45391i	0.856982	−	0.515346i
$113$	−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
$119$	−4.76629	+	3.02302i	−0.436925	+	0.277120i
$120$	−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
$126$	1.19205	−	11.1615i	0.106196	−	0.994345i
$127$			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	−0.825635	−	0.564204i	$-0.809183\pi$
$131$	−8.58229	+	4.95499i	−0.749838	+	0.432919i	0.0757972	+	0.997123i	$0.475850\pi$
$132$	−19.7282	+	2.24699i	−1.71712	+	0.195575i
$133$	−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	−0.325093	−	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	−0.937859	−	0.347018i	$-0.887194\pi$
$139$	−13.0426	+	7.53017i	−1.10626	+	0.638701i	−0.168403	+	0.985718i	$0.553861\pi$
$140$	9.04407	−	2.71383i	0.764363	−	0.229360i
$141$	−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
$147$	−6.61229	+	10.1626i	−0.545372	+	0.838194i
$148$	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
$154$	20.0942	+	7.49538i	1.61924	+	0.603995i
$155$	−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	$-0.950944\pi$
$157$	−7.85645	−	13.6078i	−0.627013	−	1.08602i	0.361135	−	0.932513i	$-0.382389\pi$
$158$	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	0.847801	−	0.530314i	$-0.177926\pi$
$167$	−0.457013	−	0.791570i	−0.0353647	−	0.0612535i	−0.883166	+	0.469060i	$0.844593\pi$
$168$	8.99701	−	9.33026i	0.694135	−	0.719845i
$169$	−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	$-0.666640\pi$
$173$	6.57744	−	11.3925i	0.500073	−	0.866153i	1.00000		8.48213e-5i	$-2.69995e-5\pi$
$174$	−7.55530	−	13.4420i	−0.572766	−	1.01903i
$175$	−4.79977	+	0.199906i	−0.362828	+	0.0151115i
$176$	−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	$-0.463068\pi$
$181$	3.11488			0.231527			0.115764	+	0.993277i	$0.463068\pi$
$182$	−18.8135	+	15.5329i	−1.39455	+	1.15137i
$183$	−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
$189$	−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	$-0.519167\pi$
$191$	−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
$196$	−13.2303	+	4.57821i	−0.945019	+	0.327015i
$197$			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	$-0.688597\pi$
$199$	−15.7553			−1.11686			−0.558432	+	0.829550i	$0.688597\pi$
$200$	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
$203$	0.693077	+	16.6408i	0.0486445	+	1.16796i
$204$	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
$210$	9.83676	−	6.08097i	0.678801	−	0.419627i
$211$	−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	$0.430193\pi$
$223$	−10.9984	+	19.0498i	−0.736507	+	1.27567i	−0.954059	+	0.299619i	$0.903140\pi$
$224$	14.8144	−	2.12938i	0.989827	−	0.142275i
$225$	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	−0.314735	−	0.949180i	$-0.601916\pi$
$227$	−19.4978	−	11.2571i	−1.29412	−	0.747158i	−0.979381	+	0.202022i	$0.935249\pi$
$228$	10.0232	−	7.41620i	0.663803	−	0.491150i
$229$	14.8397	+	25.7031i	0.980636	+	1.69851i	0.659920	+	0.751336i	$0.270590\pi$
$229$	14.8397	+	25.7031i	0.980636	+	1.69851i	0.320716	+	0.947175i	$0.396077\pi$
$230$	6.94369	+	9.16161i	0.457853	+	0.604099i
$231$	26.1485	+	2.48790i	1.72045	+	0.163692i
$232$	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
$238$	−7.87152	+	1.32344i	−0.510235	+	0.0857856i
$239$	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	0.919315	−	0.393522i	$-0.128743\pi$
$241$	16.1168	+	9.30502i	1.03817	+	0.599389i	0.118858	+	0.992911i	$0.462077\pi$
$242$	−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
$246$	15.8545	+	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	$0.230413\pi$
$251$			20.9851i			1.32457i	−0.749252	+	0.662285i	$0.769587\pi$
$252$	7.68089	−	13.8926i	0.483851	−	0.875151i
$253$			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	−0.364662	−	0.931140i	$-0.618815\pi$
$257$	4.15846	−	2.40089i	0.259398	−	0.149763i	0.624060	+	0.781377i	$0.285482\pi$
$258$	−6.90904	+	3.88335i	−0.430138	+	0.241767i
$259$	−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	$-0.329150\pi$
$263$	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
$266$	−13.2812	+	2.23296i	−0.814320	+	0.136911i
$267$	−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	$-0.415433\pi$
$269$	8.61268			0.525124			0.262562	+	0.964915i	$0.415433\pi$
$270$	−3.68062	+	12.5859i	−0.223995	+	0.765953i
$271$	8.40451			0.510538			0.255269	−	0.966870i	$-0.417836\pi$
$271$	8.40451			0.510538			0.255269	+	0.966870i	$0.417836\pi$
$272$	8.53069	+	0.203173i	0.517249	+	0.0123192i
$273$	−17.3239	+	24.3456i	−1.04849	+	1.47346i
$274$	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
$280$	13.2771	+	1.42789i	0.793458	+	0.0853328i
$281$	−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	0.245416	−	0.969418i	$-0.421076\pi$
$283$	20.3161	−	11.7295i	1.20766	−	0.697245i	0.962248	+	0.272173i	$0.0877422\pi$
$284$	−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	0.956055	−	0.293188i	$-0.0947161\pi$
$293$	3.83631	+	6.64468i	0.224119	+	0.388186i	−0.731936	+	0.681374i	$0.761383\pi$
$294$	−14.1968	+	9.61514i	−0.827974	+	0.560766i
$295$	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
$301$	8.55322	−	0.356235i	0.492999	−	0.0205330i
$302$	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	$0.0403184\pi$
$307$			4.42681i			0.252651i	−0.991989	+	0.126326i	$0.959682\pi$
$308$	22.0744	+	20.7999i	1.25781	+	1.18518i
$309$	−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	0.695013	−	0.718998i	$-0.255399\pi$
$311$	−4.85257	−	8.40489i	−0.275164	−	0.476598i	−0.970176	+	0.242400i	$0.922065\pi$
$312$	23.1106	−	22.0516i	1.30838	−	1.24843i
$313$	−12.7693	−	7.37236i	−0.721764	−	0.416710i	0.0936379	−	0.995606i	$-0.470150\pi$
$313$	−12.7693	−	7.37236i	−0.721764	−	0.416710i	−0.815401	+	0.578896i	$0.803484\pi$
$314$	−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	$-0.0948691\pi$
$317$	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
$322$	−10.8515	−	13.1434i	−0.604731	−	0.732454i
$323$	−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
$329$	12.3666	−	0.515057i	0.681790	−	0.0283960i
$330$	−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
$336$	16.8480	−	7.22126i	0.919131	−	0.393952i
$337$	−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	$-0.591226\pi$
$349$	12.8783	−	22.3058i	0.689359	−	1.19400i	0.972046	−	0.234792i	$-0.0754409\pi$
$350$	−6.36536	−	2.37436i	−0.340243	−	0.126915i
$351$	−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	0.815547	−	0.578691i	$-0.196436\pi$
$353$	13.5681	+	7.83357i	0.722159	+	0.416939i	−0.0933875	+	0.995630i	$0.529770\pi$
$354$	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
$357$	−8.89110	+	4.06409i	−0.470567	+	0.215094i
$358$	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
$364$	−33.0470	+	9.91631i	−1.73213	+	0.519756i
$365$	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	−0.768842	−	0.639439i	$-0.779167\pi$
$367$	3.24428	−	5.61925i	0.169350	−	0.293323i	0.938191	+	0.346117i	$0.112500\pi$
$368$	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
$372$	−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
$378$	4.67587	−	18.8716i	0.240501	−	0.970649i
$379$	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	0.932970	−	0.359953i	$-0.117207\pi$
$383$	3.02865	+	5.24577i	0.154757	+	0.268046i	−0.778214	+	0.628000i	$0.783874\pi$
$384$	−19.1467	+	4.17199i	−0.977074	+	0.212901i
$385$	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	$-0.503113\pi$
$389$	−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
$392$	−19.7565	−	1.29608i	−0.997855	−	0.0654618i
$393$	−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	$-0.514624\pi$
$397$	−1.83014			−0.0918522			−0.0459261	+	0.998945i	$0.514624\pi$
$398$	−20.5342	−	8.64910i	−1.02928	−	0.433540i
$399$	−15.0014	+	6.85710i	−0.751011	+	0.343284i
$400$	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
$406$	−8.23193	+	22.0688i	−0.408544	+	1.09525i
$407$	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	−0.392452	−	0.919772i	$-0.628373\pi$
$409$	4.20386	−	2.42710i	0.207868	−	0.120012i	0.600320	+	0.799760i	$0.295040\pi$
$410$	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	−0.547850	−	0.836576i	$-0.684554\pi$
$419$	−1.99126	+	1.14965i	−0.0972795	+	0.0561643i	0.450571	+	0.892741i	$0.351220\pi$
$420$	16.1587	−	2.52541i	0.788462	−	0.123227i
$421$	−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
$427$	19.3514	−	0.805969i	0.936479	−	0.0390036i
$428$	−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	$-0.942535\pi$
$433$		−	7.47255i		−	0.359108i	0.983748	−	0.179554i	$-0.0574654\pi$
$434$	11.5568	−	9.54156i	0.554744	−	0.458010i
$435$	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	$-0.583768\pi$
$439$	14.7953	−	25.6262i	0.706141	−	1.22307i	0.966278	−	0.257501i	$-0.0828989\pi$
$440$	−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	0.0452234	−	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
$448$	20.4768	+	5.35731i	0.967438	+	0.253109i
$449$	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
$455$	−30.7576	+	1.28103i	−1.44194	+	0.0600556i
$456$	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	−0.994243	−	0.107145i	$-0.965829\pi$
$461$	−8.68136	+	15.0366i	−0.404331	+	0.700322i	0.589912	+	0.807467i	$0.299162\pi$
$462$	32.7141	+	17.5971i	1.52200	+	0.818693i
$463$	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	$-0.867182\pi$
$467$		−	17.5154i		−	0.810515i	0.914203	−	0.405258i	$-0.132818\pi$
$468$	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
$476$	−10.9856	−	2.59633i	−0.503525	−	0.119002i
$477$	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	$-0.607228\pi$
$479$	14.2716	−	24.7191i	0.652085	−	1.12944i	0.982616	−	0.185649i	$-0.0594389\pi$
$480$	−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
$483$	−17.0082	−	12.1028i	−0.773901	−	0.550695i
$484$	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
$490$	−16.7938	−	5.47973i	−0.758668	−	0.247549i
$491$	−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
$497$	4.39277	−	2.78612i	0.197043	−	0.124974i
$498$	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	$-0.687065\pi$
$503$	−24.8692			−1.10886			−0.554432	+	0.832229i	$0.687065\pi$
$504$	17.6372	−	13.8899i	0.785622	−	0.618706i
$505$	−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	$-0.915759\pi$
$509$	−15.9985	−	27.7102i	−0.709120	−	1.22823i	0.256064	−	0.966660i	$-0.417574\pi$
$510$	9.32396	+	0.107583i	0.412872	+	0.00476384i
$511$	−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
$516$	−11.1365	+	1.26842i	−0.490257	+	0.0558391i
$517$	−13.4073	−	23.2221i	−0.589652	−	1.02131i
$518$	−1.86640	+	0.313798i	−0.0820051	+	0.0137875i
$519$	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	$-0.829548\pi$
$521$		−	23.2939i		−	1.02052i	0.860019	−	0.510262i	$-0.170452\pi$
$522$	−9.79667	−	24.8462i	−0.428789	−	1.08749i
$523$			27.2889i			1.19326i	0.802516	+	0.596631i	$0.203494\pi$
$523$			27.2889i			1.19326i	−0.802516	+	0.596631i	$0.796506\pi$
$524$	−19.0822	−	5.35735i	−0.833609	−	0.234037i
$525$	−8.28324	−	0.788108i	−0.361510	−	0.0343958i
$526$	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
$532$	−18.5354	−	4.38063i	−0.803611	−	0.189924i
$533$	−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
$546$	−35.9435	+	22.2198i	−1.53824	+	0.950921i
$547$	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
$553$	−0.275939	−	6.62531i	−0.0117341	−	0.281737i
$554$	−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
$560$	16.5204	+	9.14965i	0.698115	+	0.386643i
$561$	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	−0.712830	−	0.701337i	$-0.752587\pi$
$563$	−10.9590	+	6.32720i	−0.461868	+	0.266660i	0.250961	+	0.967997i	$0.419253\pi$
$564$	−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
$567$	−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	−0.913984	−	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
$574$	−15.4200	−	18.6768i	−0.643618	−	0.779555i
$575$		−	8.27103i		−	0.344926i
$576$	−21.3242	+	11.0126i	−0.888509	+	0.458859i
$577$		−	17.0368i		−	0.709252i	−0.935008	−	0.354626i	$-0.884608\pi$
$577$		−	17.0368i		−	0.709252i	0.935008	−	0.354626i	$-0.115392\pi$
$578$	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
$581$	−0.0678418	−	1.62889i	−0.00281455	−	0.0675776i
$582$	−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	0.603566	−	0.797313i	$-0.293746\pi$
$587$	5.20552	+	3.00541i	0.214855	+	0.124046i	−0.388711	+	0.921360i	$0.627079\pi$
$588$	−23.7813	+	4.73805i	−0.980725	+	0.195394i
$589$	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	$-0.847746\pi$
$593$		−	22.4175i		−	0.920575i	0.887770	−	0.460287i	$-0.152254\pi$
$594$	−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	0.0428769	−	0.999080i	$-0.486348\pi$
$601$	−19.6346	−	11.3361i	−0.800914	−	0.462408i	−0.843791	+	0.536673i	$0.819681\pi$
$602$	11.3431	+	4.23113i	0.462311	+	0.172448i
$603$	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	0.992908	−	0.118884i	$-0.0379317\pi$
$607$	9.69474	+	16.7918i	0.393498	+	0.681558i	−0.599411	+	0.800442i	$0.704598\pi$
$608$	18.5709	+	8.34822i	0.753150	+	0.338565i
$609$	−2.73238	+	28.7181i	−0.110721	+	1.16371i
$610$	−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
$616$	17.3516	+	39.2269i	0.699116	+	1.58050i
$617$	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	0.281805	−	0.959472i	$-0.409067\pi$
$619$	−10.1564	−	5.86379i	−0.408220	−	0.235686i	−0.690025	+	0.723786i	$0.742400\pi$
$620$	−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
$624$	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
$630$	18.3124	−	8.11642i	0.729583	−	0.323366i
$631$		−	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
$637$	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	−0.944567	−	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	−0.890618	−	0.454751i	$-0.849728\pi$
$643$	−23.8893	+	13.7925i	−0.942101	+	0.543922i	−0.0514829	+	0.998674i	$0.516395\pi$
$644$	−6.92769	−	23.0871i	−0.272989	−	0.909761i
$645$	−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	$-0.677147\pi$
$647$	−26.8727			−1.05647			−0.528237	+	0.849097i	$0.677147\pi$
$648$	−4.33422	+	25.0841i	−0.170264	+	0.985398i
$649$			2.29055i			0.0899119i
$650$	−15.4302	−	6.49929i	−0.605223	−	0.254923i
$651$	10.6418	−	14.9551i	0.417084	−	0.586135i
$652$	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
$658$	16.4003	+	6.11752i	0.639351	+	0.238486i
$659$	−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	0.944349	−	0.328945i	$-0.106693\pi$
$661$	4.81546	+	8.34062i	0.187300	+	0.324412i	−0.757049	+	0.653358i	$0.773360\pi$
$662$	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
$672$	25.9225	−	0.162668i	0.999980	−	0.00627507i
$673$	−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	$0.445883\pi$
$677$	−20.0073	+	34.6536i	−0.768942	+	1.33185i	−0.938137	+	0.346263i	$0.887450\pi$
$678$	0.0646147	−	5.60001i	0.00248151	−	0.215067i
$679$	1.78267	+	42.8020i	0.0684126	+	1.64259i
$680$	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
$686$	25.2161	+	7.08141i	0.962757	+	0.270369i
$687$	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	−0.147737	−	0.989027i	$-0.547199\pi$
$691$	−28.3406	−	16.3625i	−1.07813	−	0.622457i	−0.930391	+	0.366569i	$0.880532\pi$
$692$	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
$696$	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
$700$	−6.99266	−	6.58891i	−0.264298	−	0.249037i
$701$		−	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
$707$	27.0364	−	1.12605i	1.01681	−	0.0423493i
$708$	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
$714$	−13.8190	+	0.415901i	−0.517162	+	0.0155647i
$715$	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	$-0.193534\pi$
$719$	44.0176			1.64158			0.820790	+	0.571230i	$0.193534\pi$
$720$	−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	$-0.649677\pi$
$727$	14.7080	−	25.4750i	0.545489	−	0.944815i	0.998576	−	0.0533487i	$-0.0169895\pi$
$728$	−48.5144	−	5.21751i	−1.79806	−	0.193374i
$729$	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	$0.0602656\pi$
$733$	17.7078	+	30.6708i	0.654052	+	1.13285i	−0.328079	+	0.944650i	$0.606401\pi$
$734$	7.31309	−	5.54268i	0.269931	−	0.204584i
$735$	−21.6047	−	1.15120i	−0.796903	−	0.0424626i
$736$	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
$742$	−3.05438	+	0.513532i	−0.112130	+	0.0188524i
$743$	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
$749$	18.1407	+	28.6017i	0.662846	+	1.04508i
$750$	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
$756$	16.4540	−	22.0288i	0.598425	−	0.801179i
$757$		−	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	0.164676	−	0.986348i	$-0.447342\pi$
$761$	30.3784	−	17.5390i	1.10122	−	0.635787i	0.936540	+	0.350560i	$0.114009\pi$
$762$	−9.28915	+	15.6690i	−0.336510	+	0.567626i
$763$	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
$768$	−27.2445	−	5.07340i	−0.983100	−	0.183071i
$769$	−30.3192	+	17.5048i	−1.09334	+	0.631239i	−0.934463	−	0.356060i	$-0.884120\pi$
$769$	−30.3192	+	17.5048i	−1.09334	+	0.631239i	−0.158875	+	0.987299i	$0.550787\pi$
$770$	6.34536	+	37.7409i	0.228671	+	1.36009i
$771$	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	$-0.166625\pi$
$773$	48.1597			1.73218			0.866091	+	0.499886i	$0.166625\pi$
$774$	−12.7707	+	5.03539i	−0.459033	+	0.180993i
$775$	7.27259			0.261239
$776$	6.78760	−	45.2912i	0.243661	−	1.62586i
$777$	−2.10816	+	0.963630i	−0.0756297	+	0.0345700i
$778$	−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
$784$	−25.0375	−	12.5348i	−0.894198	−	0.447672i
$785$	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	0.100175	−	0.994970i	$-0.468060\pi$
$787$	28.3882	−	16.3900i	1.01193	−	0.584239i	0.911756	+	0.410731i	$0.134727\pi$
$788$	−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	0.920009	−	0.391897i	$-0.128181\pi$
$797$	3.40500	+	5.89764i	0.120611	+	0.208905i	−0.799398	+	0.600802i	$0.794848\pi$
$798$	−23.3159	+	0.701726i	−0.825376	+	0.0248408i
$799$	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
$805$	−0.894948	−	21.4878i	−0.0315428	−	0.757344i
$806$	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	$-0.775656\pi$
$811$		−	36.9006i		−	1.29576i	0.761744	−	0.647878i	$-0.224344\pi$
$812$	−22.8438	+	24.2436i	−0.801660	+	0.850783i
$813$	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
$819$	−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	$-0.325128\pi$
$821$	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
$826$	−0.951967	−	1.15303i	−0.0331232	−	0.0401190i
$827$	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	$-0.496745\pi$
$829$	0.588826			0.0204508			0.0102254	+	0.999948i	$0.496745\pi$
$830$	−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
$833$	13.5084	+	6.36524i	0.468038	+	0.220542i
$834$	−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	$-0.657650\pi$
$839$	15.1874	−	26.3054i	0.524328	−	0.908163i	0.999599	−	0.0283235i	$-0.00901687\pi$
$840$	22.4462	+	5.57912i	0.774469	+	0.192498i
$841$	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	−0.859421	−	0.511268i	$-0.829176\pi$
$853$	0.381441	−	0.660676i	0.0130603	−	0.0226211i	0.872482	+	0.488647i	$0.162509\pi$
$854$	25.6634	+	9.57278i	0.878185	+	0.327574i
$855$	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	0.271329	−	0.962487i	$-0.412537\pi$
$857$	−12.4869	−	7.20931i	−0.426544	−	0.246266i	−0.697873	+	0.716221i	$0.745870\pi$
$858$	78.7487	+	46.6852i	2.68844	+	1.59381i
$859$	−8.64422	+	4.99075i	−0.294937	+	0.170282i	−0.640166	−	0.768236i	$-0.721135\pi$
$859$	−8.64422	+	4.99075i	−0.294937	+	0.170282i	0.345229	+	0.938518i	$0.387801\pi$
$860$	−8.06761	−	8.26204i	−0.275103	−	0.281733i
$861$	−24.1687	−	17.1981i	−0.823667	−	0.586108i
$862$	−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
$868$	20.3002	−	6.09141i	0.689033	−	0.206756i
$869$	−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
$875$	−17.2350	−	27.1738i	−0.582649	−	0.918641i
$876$	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	$-0.986118\pi$
$881$		−	2.58804i		−	0.0871932i	0.999049	−	0.0435966i	$-0.0138816\pi$
$882$	−26.6269	+	13.1534i	−0.896573	+	0.442897i
$883$	−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	0.988282	−	0.152642i	$-0.0487782\pi$
$887$	10.7798	+	18.6711i	0.361949	+	0.626914i	−0.626333	+	0.779556i	$0.715445\pi$
$888$	2.40794	−	0.585067i	0.0808050	−	0.0196336i
$889$	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
$894$	27.1833	+	0.313649i	0.909145	+	0.0104900i
$895$	7.90097	+	13.6849i	0.264100	+	0.457435i
$896$	23.7468	+	18.2233i	0.793325	+	0.608798i
$897$	−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
$903$	14.7608	+	1.40441i	0.491208	+	0.0467359i
$904$	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
$910$	−40.7902	−	15.2152i	−1.35218	−	0.504381i
$911$	−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
$924$	32.9767	+	40.8936i	1.08485	+	1.34530i
$925$	−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	0.427260	−	0.904129i	$-0.359479\pi$
$929$	−4.33140	−	2.50073i	−0.142108	−	0.0820464i	−0.569368	+	0.822082i	$0.692812\pi$
$930$	−15.2619	+	8.57822i	−0.500458	+	0.281291i
$931$	22.7919	+	10.7397i	0.746975	+	0.351980i
$932$	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	$0.189954\pi$
$937$			34.4040i			1.12393i	−0.827161	+	0.561965i	$0.810046\pi$
$938$	19.6412	−	16.2162i	0.641309	−	0.529479i
$939$	−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	0.884559	−	0.466429i	$-0.154460\pi$
$941$	1.17611	+	2.03707i	0.0383400	+	0.0664067i	−0.846219	+	0.532836i	$0.821126\pi$
$942$	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
$945$	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	−0.999690	−	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
$952$	−12.8925	−	9.41455i	−0.417847	−	0.305127i
$953$	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
$959$	−40.6216	+	1.69186i	−1.31174	+	0.0546329i
$960$	−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
$966$	−15.5231	−	25.1107i	−0.499448	−	0.807923i
$967$	−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	$0.230259\pi$
$971$			41.2521i			1.32384i	−0.749573	+	0.661922i	$0.769741\pi$
$972$	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
$980$	−18.8795	−	16.3610i	−0.603084	−	0.522634i
$981$	−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	$0.403418\pi$
$983$	−21.2281	+	36.7681i	−0.677071	+	1.17272i	−0.975859	+	0.218402i	$0.929916\pi$
$984$	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
$987$	21.3417	+	2.03055i	0.679314	+	0.0646332i
$988$	−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
$994$	7.25466	−	1.21972i	0.230104	−	0.0386873i
$995$	−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	−0.964620	−	0.263645i	$-0.915075\pi$
$997$	−8.01970	+	13.8905i	−0.253986	+	0.439917i	0.710633	+	0.703563i	$0.248409\pi$
$998$	−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.475.82	yes	184
7.6	odd	2	inner	504.2.be.a.475.81	yes	184
8.3	odd	2	inner	504.2.be.a.475.20	yes	184
9.4	even	3	inner	504.2.be.a.139.19	✓	184
56.27	even	2	inner	504.2.be.a.475.19	yes	184
63.13	odd	6	inner	504.2.be.a.139.20	yes	184
72.67	odd	6	inner	504.2.be.a.139.81	yes	184
504.139	even	6	inner	504.2.be.a.139.82	yes	184

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.30332 + 0.548965i) q^{2} +(1.71594 + 0.235665i) q^{3} +(1.39728 + 1.43095i) q^{4} +(0.892228 + 1.54538i) q^{5} +(2.10705 + 1.24914i) q^{6} +(-1.41708 - 2.23425i) q^{7} +(1.03555 + 2.63204i) q^{8} +(2.88892 + 0.808775i) q^{9} +O(q^{10})\)	\(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} +(-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} +(2.06042 + 2.78472i) q^{12} +(-3.26020 - 5.64683i) q^{13} +(-0.620376 - 3.68987i) 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} +(-1.90509 - 4.16781i) 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} +(1.21706 - 5.14964i) 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} +(-0.194959 - 6.47781i) 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} +(-2.98378 + 6.33222i) 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} +(4.41318 - 6.04349i) 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} +(-2.28682 - 7.60069i) 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} +(5.14875 - 4.25093i) 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} +(15.1519 - 0.631065i) 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} +(3.30199 - 8.54967i) 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} +(-7.36498 + 6.61491i) 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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