LMFDB - Embedded newform 384.2.v.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34449 + 0.438569i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.61531 - 1.17931i) q^{4} +(0.414961 + 4.21317i) q^{5} +(0.809970 + 1.15929i) q^{6} +(-0.841223 + 1.25898i) q^{7} +(-1.65457 + 2.29399i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.34449 + 0.438569i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.61531 - 1.17931i) q^{4} +(0.414961 + 4.21317i) q^{5} +(0.809970 + 1.15929i) q^{6} +(-0.841223 + 1.25898i) q^{7} +(-1.65457 + 2.29399i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-2.40568 - 5.48258i) q^{10} +(0.784308 - 0.419221i) q^{11} +(-1.59743 - 1.20342i) q^{12} +(-5.50473 - 0.542168i) q^{13} +(0.578867 - 2.06162i) q^{14} +(3.91129 - 1.62011i) q^{15} +(1.21848 - 3.80990i) q^{16} +(-5.12904 - 2.12452i) q^{17} +(0.874248 - 1.11162i) q^{18} +(3.70651 - 3.04185i) q^{19} +(5.63890 + 6.31622i) q^{20} +(1.44896 + 0.439538i) q^{21} +(-0.870637 + 0.907612i) q^{22} +(-1.31379 + 6.60489i) q^{23} +(2.67551 + 0.917413i) q^{24} +(-12.6747 + 2.52114i) q^{25} +(7.63883 - 1.68526i) q^{26} +(0.773010 + 0.634393i) q^{27} +(0.125881 + 3.02571i) q^{28} +(-0.0996101 + 0.186357i) q^{29} +(-4.54817 + 3.89360i) q^{30} +(-3.51113 + 3.51113i) q^{31} +(0.0326686 + 5.65676i) q^{32} +(-0.628842 - 0.628842i) q^{33} +(7.82770 + 0.606957i) q^{34} +(-5.65336 - 3.02179i) q^{35} +(-0.687898 + 1.87798i) q^{36} +(-1.41029 + 1.71844i) q^{37} +(-3.64931 + 5.71531i) q^{38} +(1.07911 + 5.42508i) q^{39} +(-10.3516 - 6.01906i) q^{40} +(5.17331 + 1.02903i) q^{41} +(-2.14088 + 0.0445153i) q^{42} +(0.959206 - 3.16208i) q^{43} +(0.772514 - 1.60211i) q^{44} +(-2.68574 - 3.27258i) q^{45} +(-1.13032 - 9.45641i) q^{46} +(0.429316 - 1.03646i) q^{47} +(-3.99955 - 0.0600573i) q^{48} +(1.80141 + 4.34899i) q^{49} +(15.9353 - 8.94837i) q^{50} +(-0.544155 + 5.52490i) q^{51} +(-9.53124 + 5.61598i) q^{52} +(2.70031 + 5.05193i) q^{53} +(-1.31753 - 0.513918i) q^{54} +(2.09171 + 3.13046i) q^{55} +(-1.49623 - 4.01283i) q^{56} +(-3.98681 - 2.66390i) q^{57} +(0.0521943 - 0.294242i) q^{58} +(-11.8882 + 1.17088i) q^{59} +(4.40736 - 7.22959i) q^{60} +(-6.06677 + 1.84033i) q^{61} +(3.18081 - 6.26055i) q^{62} -1.51416i q^{63} +(-2.52480 - 7.59114i) q^{64} -23.4173i q^{65} +(1.12126 + 0.569682i) q^{66} +(12.7691 - 3.87346i) q^{67} +(-10.7905 + 2.61694i) q^{68} +(6.70186 - 0.660076i) q^{69} +(8.92616 + 1.58337i) q^{70} +(0.0488394 + 0.0326335i) q^{71} +(0.101250 - 2.82661i) q^{72} +(6.80173 + 10.1795i) q^{73} +(1.14246 - 2.92894i) q^{74} +(6.09184 + 11.3970i) q^{75} +(2.39990 - 9.28465i) q^{76} +(-0.131987 + 1.34009i) q^{77} +(-3.83013 - 6.82070i) q^{78} +(1.95805 + 4.72715i) q^{79} +(16.5573 + 3.55270i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-7.40677 + 0.885325i) q^{82} +(-0.148807 - 0.181321i) q^{83} +(2.85888 - 0.998777i) q^{84} +(6.82260 - 22.4911i) q^{85} +(0.0971461 + 4.67207i) q^{86} +(0.207248 + 0.0412242i) q^{87} +(-0.336001 + 2.49283i) q^{88} +(2.00111 + 10.0603i) q^{89} +(5.04620 + 3.22207i) q^{90} +(5.31328 - 6.47425i) q^{91} +(5.66699 + 12.2183i) q^{92} +(4.37917 + 2.34071i) q^{93} +(-0.122652 + 1.58180i) q^{94} +(14.3539 + 14.3539i) q^{95} +(5.40370 - 1.67333i) q^{96} +(3.64779 - 3.64779i) q^{97} +(-4.32932 - 5.05714i) q^{98} +(-0.419221 + 0.784308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−1.34449	+	0.438569i	−0.950699	+	0.310115i
$2$	−1.34449	+	0.438569i	−0.950699	+	0.310115i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	1.61531	−	1.17931i	0.807657	−	0.589653i
$5$	0.414961	+	4.21317i	0.185576	+	1.88419i	0.413497	+	0.910506i	$0.364307\pi$
$5$	0.414961	+	4.21317i	0.185576	+	1.88419i	−0.227921	+	0.973680i	$0.573193\pi$
$6$	0.809970	+	1.15929i	0.330669	+	0.473277i
$7$	−0.841223	+	1.25898i	−0.317952	+	0.475849i	−0.955678	−	0.294414i	$-0.904875\pi$
$7$	−0.841223	+	1.25898i	−0.317952	+	0.475849i	0.637725	+	0.770264i	$0.279875\pi$
$8$	−1.65457	+	2.29399i	−0.584978	+	0.811049i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−2.40568	−	5.48258i	−0.760742	−	1.73374i
$11$	0.784308	−	0.419221i	0.236478	−	0.126400i	−0.348902	−	0.937159i	$-0.613445\pi$
$11$	0.784308	−	0.419221i	0.236478	−	0.126400i	0.585380	+	0.810759i	$0.300945\pi$
$12$	−1.59743	−	1.20342i	−0.461137	−	0.347399i
$13$	−5.50473	−	0.542168i	−1.52674	−	0.150370i	−0.700483	−	0.713669i	$-0.747032\pi$
$13$	−5.50473	−	0.542168i	−1.52674	−	0.150370i	−0.826253	+	0.563299i	$0.809532\pi$
$14$	0.578867	−	2.06162i	0.154709	−	0.550991i
$15$	3.91129	−	1.62011i	1.00989	−	0.418311i
$16$	1.21848	−	3.80990i	0.304620	−	0.952474i
$17$	−5.12904	−	2.12452i	−1.24398	−	0.515271i	−0.339020	−	0.940779i	$-0.610096\pi$
$17$	−5.12904	−	2.12452i	−1.24398	−	0.515271i	−0.904955	+	0.425508i	$0.860096\pi$
$18$	0.874248	−	1.11162i	0.206062	−	0.262010i
$19$	3.70651	−	3.04185i	0.850331	−	0.697849i	−0.104652	−	0.994509i	$-0.533373\pi$
$19$	3.70651	−	3.04185i	0.850331	−	0.697849i	0.954983	+	0.296660i	$0.0958728\pi$
$20$	5.63890	+	6.31622i	1.26090	+	1.41235i
$21$	1.44896	+	0.439538i	0.316189	+	0.0959150i
$22$	−0.870637	+	0.907612i	−0.185621	+	0.193504i
$23$	−1.31379	+	6.60489i	−0.273945	+	1.37721i	0.561425	+	0.827527i	$0.310253\pi$
$23$	−1.31379	+	6.60489i	−0.273945	+	1.37721i	−0.835370	+	0.549687i	$0.814747\pi$
$24$	2.67551	+	0.917413i	0.546136	+	0.187266i
$25$	−12.6747	+	2.52114i	−2.53493	+	0.504229i
$26$	7.63883	−	1.68526i	1.49810	−	0.330507i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	0.125881	+	3.02571i	0.0237893	+	0.571805i
$29$	−0.0996101	+	0.186357i	−0.0184971	+	0.0346057i	−0.891000	−	0.454003i	$-0.849995\pi$
$29$	−0.0996101	+	0.186357i	−0.0184971	+	0.0346057i	0.872503	+	0.488609i	$0.162495\pi$
$30$	−4.54817	+	3.89360i	−0.830378	+	0.710870i
$31$	−3.51113	+	3.51113i	−0.630617	+	0.630617i	−0.948223	−	0.317606i	$-0.897121\pi$
$31$	−3.51113	+	3.51113i	−0.630617	+	0.630617i	0.317606	+	0.948223i	$0.397121\pi$
$32$	0.0326686	+	5.65676i	0.00577504	+	0.999983i
$33$	−0.628842	−	0.628842i	−0.109467	−	0.109467i
$34$	7.82770	+	0.606957i	1.34244	+	0.104092i
$35$	−5.65336	−	3.02179i	−0.955593	−	0.510775i
$36$	−0.687898	+	1.87798i	−0.114650	+	0.312996i
$37$	−1.41029	+	1.71844i	−0.231850	+	0.282510i	−0.875920	−	0.482457i	$-0.839745\pi$
$37$	−1.41029	+	1.71844i	−0.231850	+	0.282510i	0.644070	+	0.764967i	$0.277245\pi$
$38$	−3.64931	+	5.71531i	−0.591996	+	0.927145i
$39$	1.07911	+	5.42508i	0.172797	+	0.868707i
$40$	−10.3516	−	6.01906i	−1.63672	−	0.951697i
$41$	5.17331	+	1.02903i	0.807935	+	0.160708i	0.581741	−	0.813374i	$-0.302372\pi$
$41$	5.17331	+	1.02903i	0.807935	+	0.160708i	0.226194	+	0.974082i	$0.427372\pi$
$42$	−2.14088	+	0.0445153i	−0.330346	+	0.00686887i
$43$	0.959206	−	3.16208i	0.146278	−	0.482212i	−0.852930	−	0.522026i	$-0.825176\pi$
$43$	0.959206	−	3.16208i	0.146278	−	0.482212i	0.999207	+	0.0398135i	$0.0126764\pi$
$44$	0.772514	−	1.60211i	0.116461	−	0.241527i
$45$	−2.68574	−	3.27258i	−0.400366	−	0.487847i
$46$	−1.13032	−	9.45641i	−0.166656	−	1.39427i
$47$	0.429316	−	1.03646i	0.0626222	−	0.151183i	−0.889471	−	0.456992i	$-0.848927\pi$
$47$	0.429316	−	1.03646i	0.0626222	−	0.151183i	0.952093	+	0.305809i	$0.0989268\pi$
$48$	−3.99955	−	0.0600573i	−0.577285	−	0.00866853i
$49$	1.80141	+	4.34899i	0.257345	+	0.621285i
$50$	15.9353	−	8.94837i	2.25359	−	1.26549i
$51$	−0.544155	+	5.52490i	−0.0761970	+	0.773641i
$52$	−9.53124	+	5.61598i	−1.32175	+	0.778796i
$53$	2.70031	+	5.05193i	0.370917	+	0.693936i	0.996259	−	0.0864141i	$-0.0275408\pi$
$53$	2.70031	+	5.05193i	0.370917	+	0.693936i	−0.625343	+	0.780350i	$0.715041\pi$
$54$	−1.31753	−	0.513918i	−0.179293	−	0.0699353i
$55$	2.09171	+	3.13046i	0.282045	+	0.422111i
$56$	−1.49623	−	4.01283i	−0.199942	−	0.536237i
$57$	−3.98681	−	2.66390i	−0.528067	−	0.352843i
$58$	0.0521943	−	0.294242i	0.00685345	−	0.0386358i
$59$	−11.8882	+	1.17088i	−1.54771	+	0.152436i	−0.835484	−	0.549515i	$-0.814813\pi$
$59$	−11.8882	+	1.17088i	−1.54771	+	0.152436i	−0.712226	+	0.701951i	$0.752313\pi$
$60$	4.40736	−	7.22959i	0.568988	−	0.933336i
$61$	−6.06677	+	1.84033i	−0.776770	+	0.235631i	−0.653686	−	0.756766i	$-0.726778\pi$
$61$	−6.06677	+	1.84033i	−0.776770	+	0.235631i	−0.123084	+	0.992396i	$0.539278\pi$
$62$	3.18081	−	6.26055i	0.403963	−	0.795091i
$63$		−	1.51416i		−	0.190766i
$64$	−2.52480	−	7.59114i	−0.315600	−	0.948892i
$65$		−	23.4173i		−	2.90456i
$66$	1.12126	+	0.569682i	0.138018	+	0.0701230i
$67$	12.7691	−	3.87346i	1.55999	−	0.473219i	0.611827	−	0.790992i	$-0.290435\pi$
$67$	12.7691	−	3.87346i	1.55999	−	0.473219i	0.948167	+	0.317773i	$0.102935\pi$
$68$	−10.7905	+	2.61694i	−1.30854	+	0.317351i
$69$	6.70186	−	0.660076i	0.806809	−	0.0794638i
$70$	8.92616	+	1.58337i	1.06688	+	0.189249i
$71$	0.0488394	+	0.0326335i	0.00579617	+	0.00387288i	0.558465	−	0.829528i	$-0.311391\pi$
$71$	0.0488394	+	0.0326335i	0.00579617	+	0.00387288i	−0.552669	+	0.833401i	$0.686391\pi$
$72$	0.101250	−	2.82661i	0.0119324	−	0.333120i
$73$	6.80173	+	10.1795i	0.796083	+	1.19142i	0.978102	+	0.208127i	$0.0667368\pi$
$73$	6.80173	+	10.1795i	0.796083	+	1.19142i	−0.182019	+	0.983295i	$0.558263\pi$
$74$	1.14246	−	2.92894i	0.132809	−	0.340482i
$75$	6.09184	+	11.3970i	0.703425	+	1.31602i
$76$	2.39990	−	9.28465i	0.275288	−	1.06502i
$77$	−0.131987	+	1.34009i	−0.0150413	+	0.152717i
$78$	−3.83013	−	6.82070i	−0.433677	−	0.772292i
$79$	1.95805	+	4.72715i	0.220298	+	0.531846i	0.994930	−	0.100565i	$-0.0320651\pi$
$79$	1.95805	+	4.72715i	0.220298	+	0.531846i	−0.774632	+	0.632412i	$0.782065\pi$
$80$	16.5573	+	3.55270i	1.85117	+	0.397204i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−7.40677	+	0.885325i	−0.817941	+	0.0977678i
$83$	−0.148807	−	0.181321i	−0.0163336	−	0.0199026i	0.764780	−	0.644292i	$-0.222848\pi$
$83$	−0.148807	−	0.181321i	−0.0163336	−	0.0199026i	−0.781113	+	0.624389i	$0.785348\pi$
$84$	2.85888	−	0.998777i	0.311929	−	0.108975i
$85$	6.82260	−	22.4911i	0.740015	−	2.43950i
$86$	0.0971461	+	4.67207i	0.0104755	+	0.503802i
$87$	0.207248	+	0.0412242i	0.0222193	+	0.00441970i
$88$	−0.336001	+	2.49283i	−0.0358178	+	0.265736i
$89$	2.00111	+	10.0603i	0.212117	+	1.06639i	0.929251	+	0.369450i	$0.120454\pi$
$89$	2.00111	+	10.0603i	0.212117	+	1.06639i	−0.717133	+	0.696936i	$0.754546\pi$
$90$	5.04620	+	3.22207i	0.531916	+	0.339636i
$91$	5.31328	−	6.47425i	0.556983	−	0.678686i
$92$	5.66699	+	12.2183i	0.590825	+	1.27385i
$93$	4.37917	+	2.34071i	0.454098	+	0.242721i
$94$	−0.122652	+	1.58180i	−0.0126506	+	0.163150i
$95$	14.3539	+	14.3539i	1.47268	+	1.47268i
$96$	5.40370	−	1.67333i	0.551513	−	0.170784i
$97$	3.64779	−	3.64779i	0.370376	−	0.370376i	−0.497238	−	0.867614i	$-0.665652\pi$
$97$	3.64779	−	3.64779i	0.370376	−	0.370376i	0.867614	+	0.497238i	$0.165652\pi$
$98$	−4.32932	−	5.05714i	−0.437327	−	0.510848i
$99$	−0.419221	+	0.784308i	−0.0421333	+	0.0788259i
$100$	−17.5003	+	19.0197i	−1.75003	+	1.90197i
$101$	−6.70428	−	5.50206i	−0.667100	−	0.547475i	0.238746	−	0.971082i	$-0.423264\pi$
$101$	−6.70428	−	5.50206i	−0.667100	−	0.547475i	−0.905846	+	0.423607i	$0.860764\pi$
$102$	−1.69144	−	7.66683i	−0.167477	−	0.759130i
$103$	10.1045	−	2.00992i	0.995630	−	0.198043i	0.329723	−	0.944078i	$-0.393045\pi$
$103$	10.1045	−	2.00992i	0.995630	−	0.198043i	0.665907	+	0.746035i	$0.268045\pi$
$104$	10.3517	−	11.7307i	1.01507	−	1.15029i
$105$	−1.25058	+	6.28711i	−0.122044	+	0.613559i
$106$	−5.84617	−	5.60800i	−0.567830	−	0.544697i
$107$	5.32451	+	1.61517i	0.514740	+	0.156145i	0.536959	−	0.843609i	$-0.319573\pi$
$107$	5.32451	+	1.61517i	0.514740	+	0.156145i	−0.0222190	+	0.999753i	$0.507073\pi$
$108$	1.99680	+	0.113129i	0.192142	+	0.0108859i
$109$	9.72895	−	7.98434i	0.931864	−	0.764761i	−0.0402695	−	0.999189i	$-0.512822\pi$
$109$	9.72895	−	7.98434i	0.931864	−	0.764761i	0.972134	+	0.234428i	$0.0753216\pi$
$110$	−4.18520	−	3.29152i	−0.399043	−	0.313834i
$111$	2.05383	+	0.850724i	0.194941	+	0.0807471i
$112$	3.77157	+	4.73901i	0.356380	+	0.447795i
$113$	−12.6805	+	5.25243i	−1.19288	+	0.494107i	−0.888692	−	0.458506i	$-0.848385\pi$
$113$	−12.6805	+	5.25243i	−1.19288	+	0.494107i	−0.304187	+	0.952612i	$0.598385\pi$
$114$	6.52854	+	1.83310i	0.611454	+	0.171686i
$115$	−28.3727	−	2.79446i	−2.64577	−	0.260585i
$116$	0.0588706	+	0.418496i	0.00546600	+	0.0388564i
$117$	4.87822	−	2.60747i	0.450992	−	0.241060i
$118$	15.4700	−	6.78803i	1.42413	−	0.624889i
$119$	6.98939	−	4.67016i	0.640716	−	0.428113i
$120$	−2.75498	+	11.6531i	−0.251494	+	1.06377i
$121$	−5.67188	+	8.48857i	−0.515625	+	0.771688i
$122$	7.34960	−	5.13501i	0.665402	−	0.464902i
$123$	−0.517007	−	5.24926i	−0.0466170	−	0.473310i
$124$	−1.53088	+	9.81226i	−0.137477	+	0.881167i
$125$	−9.73681	−	32.0980i	−0.870887	−	2.87093i
$126$	0.664065	+	2.03578i	0.0591596	+	0.181361i
$127$	4.42958			0.393062			0.196531	−	0.980498i	$-0.437032\pi$
$127$	4.42958			0.393062			0.196531	+	0.980498i	$0.437032\pi$
$128$	6.72382	+	9.09892i	0.594307	+	0.804238i
$129$	−3.30436			−0.290933
$130$	10.2701	+	31.4844i	0.900748	+	2.76136i
$131$	0.154353	+	0.508834i	0.0134859	+	0.0444570i	0.963425	−	0.267978i	$-0.0863554\pi$
$131$	0.154353	+	0.508834i	0.0134859	+	0.0444570i	−0.949939	+	0.312435i	$0.898855\pi$
$132$	−1.75737	−	0.274181i	−0.152960	−	0.0238644i
$133$	0.711629	+	7.22529i	0.0617061	+	0.626512i
$134$	−15.4692	+	10.8080i	−1.33633	+	0.933667i
$135$	−2.35204	+	3.52007i	−0.202431	+	0.302959i
$136$	13.3600	−	8.25082i	1.14561	−	0.707502i
$137$	−12.1783	+	8.13726i	−1.04046	+	0.695213i	−0.953621	−	0.301009i	$-0.902677\pi$
$137$	−12.1783	+	8.13726i	−1.04046	+	0.695213i	−0.0868391	+	0.996222i	$0.527677\pi$
$138$	−8.72110	+	3.82670i	−0.742390	+	0.325750i
$139$	18.4153	−	9.84317i	1.56196	−	0.834887i	0.561993	−	0.827142i	$-0.310035\pi$
$139$	18.4153	−	9.84317i	1.56196	−	0.834887i	0.999970	−	0.00774512i	$-0.00246537\pi$
$140$	−12.6956	+	1.78591i	−1.07297	+	0.150937i
$141$	−1.11646	−	0.109961i	−0.0940226	−	0.00926041i
$142$	−0.0799762	−	0.0224559i	−0.00671145	−	0.00188446i
$143$	−4.54469	+	1.88247i	−0.380046	+	0.157420i
$144$	1.10354	+	3.84476i	0.0919614	+	0.320397i
$145$	−0.826489	−	0.342343i	−0.0686362	−	0.0284300i
$146$	−13.6093	−	10.7032i	−1.12631	−	0.885806i
$147$	3.63880	−	2.98629i	0.300124	−	0.246305i
$148$	−0.251492	+	4.43898i	−0.0206725	+	0.364882i
$149$	11.1564	+	3.38425i	0.913966	+	0.277249i	0.712029	−	0.702150i	$-0.247776\pi$
$149$	11.1564	+	3.38425i	0.913966	+	0.277249i	0.201937	+	0.979399i	$0.435276\pi$
$150$	−13.1888	−	12.6515i	−1.07686	−	1.03299i
$151$	1.00061	−	5.03042i	0.0814287	−	0.409370i	−0.918475	−	0.395480i	$-0.870578\pi$
$151$	1.00061	−	5.03042i	0.0814287	−	0.409370i	0.999904	−	0.0138904i	$-0.00442159\pi$
$152$	0.845314	+	13.5357i	0.0685640	+	1.09789i
$153$	5.44496	−	1.08307i	0.440199	−	0.0875610i
$154$	−0.410265	−	1.85962i	−0.0330601	−	0.149852i
$155$	−16.2499	−	13.3360i	−1.30523	−	1.07117i
$156$	8.14093	+	7.49060i	0.651796	+	0.599728i
$157$	−1.65863	+	3.10309i	−0.132373	+	0.247653i	−0.939372	−	0.342900i	$-0.888591\pi$
$157$	−1.65863	+	3.10309i	−0.132373	+	0.247653i	0.806998	+	0.590554i	$0.201091\pi$
$158$	−4.70577	−	5.49688i	−0.374371	−	0.437308i
$159$	4.05054	−	4.05054i	0.321228	−	0.321228i
$160$	−23.8193	+	2.48497i	−1.88308	+	0.196454i
$161$	−7.21022	−	7.21022i	−0.568245	−	0.568245i
$162$	−0.109329	+	1.40998i	−0.00858973	+	0.110779i
$163$	−14.2323	−	7.60732i	−1.11476	−	0.595851i	−0.192064	−	0.981382i	$-0.561518\pi$
$163$	−14.2323	−	7.60732i	−1.11476	−	0.595851i	−0.922695	+	0.385531i	$0.874018\pi$
$164$	9.57006	−	4.43869i	0.747296	−	0.346604i
$165$	2.38847	−	2.91036i	0.185942	−	0.226571i
$166$	0.279591	+	0.178523i	0.0217005	+	0.0138561i
$167$	−3.95147	−	19.8654i	−0.305774	−	1.53723i	−0.762126	−	0.647429i	$-0.775844\pi$
$167$	−3.95147	−	19.8654i	−0.305774	−	1.53723i	0.456353	−	0.889799i	$-0.349156\pi$
$168$	−3.40570	+	2.59666i	−0.262756	+	0.200337i
$169$	17.2578	+	3.43280i	1.32753	+	0.264061i
$170$	0.690977	+	33.2313i	0.0529955	+	2.54872i
$171$	−1.39189	+	4.58843i	−0.106440	+	0.350886i
$172$	−2.17964	−	6.23895i	−0.166196	−	0.475715i
$173$	−4.57879	−	5.57927i	−0.348119	−	0.424184i	0.569286	−	0.822140i	$-0.307220\pi$
$173$	−4.57879	−	5.57927i	−0.348119	−	0.424184i	−0.917405	+	0.397956i	$0.869720\pi$
$174$	−0.296723	+	0.0354671i	−0.0224945	+	0.00268875i
$175$	7.48814	−	18.0780i	0.566050	−	1.36657i
$176$	−0.641527	−	3.49894i	−0.0483569	−	0.263743i
$177$	4.57142	+	11.0364i	0.343609	+	0.829546i
$178$	−7.10260	−	12.6483i	−0.532362	−	0.948031i
$179$	−1.37679	+	13.9788i	−0.102906	+	1.04483i	0.795587	+	0.605839i	$0.207162\pi$
$179$	−1.37679	+	13.9788i	−0.102906	+	1.04483i	−0.898494	+	0.438986i	$0.855338\pi$
$180$	−8.19768	−	2.11894i	−0.611019	−	0.157937i
$181$	−2.60754	−	4.87837i	−0.193817	−	0.362606i	0.766176	−	0.642631i	$-0.222157\pi$
$181$	−2.60754	−	4.87837i	−0.193817	−	0.362606i	−0.959993	+	0.280025i	$0.909657\pi$
$182$	−4.30425	+	11.0348i	−0.319052	+	0.817955i
$183$	3.52218	+	5.27131i	0.260367	+	0.389667i
$184$	−12.9778	−	13.9421i	−0.956737	−	1.02782i
$185$	−7.82529	−	5.22869i	−0.575327	−	0.384421i
$186$	−6.91432	−	1.22650i	−0.506982	−	0.0899314i
$187$	−4.91339	+	0.483927i	−0.359303	+	0.0353882i
$188$	−0.528824	−	2.18051i	−0.0385684	−	0.159030i
$189$	−1.44896	+	0.439538i	−0.105396	+	0.0319717i
$190$	−25.5939	−	13.0035i	−1.85677	−	0.943373i
$191$			2.83320i			0.205003i	0.994733	+	0.102501i	$0.0326846\pi$
$191$			2.83320i			0.205003i	−0.994733	+	0.102501i	$0.967315\pi$
$192$	−6.53135	+	4.61968i	−0.471360	+	0.333396i
$193$			24.2641i			1.74657i	0.487208	+	0.873286i	$0.338015\pi$
$193$			24.2641i			1.74657i	−0.487208	+	0.873286i	$0.661985\pi$
$194$	−3.30461	+	6.50422i	−0.237257	+	0.466976i
$195$	−22.4090	+	6.79768i	−1.60474	+	0.486792i
$196$	8.03863	+	4.90058i	0.574188	+	0.350041i
$197$	−13.3652	+	1.31636i	−0.952230	+	0.0937865i	−0.562187	−	0.827010i	$-0.690040\pi$
$197$	−13.3652	+	1.31636i	−0.952230	+	0.0937865i	−0.390043	+	0.920797i	$0.627540\pi$
$198$	0.219666	−	1.23835i	0.0156110	−	0.0880059i
$199$	−11.8440	−	7.91391i	−0.839600	−	0.561002i	0.0597597	−	0.998213i	$-0.480967\pi$
$199$	−11.8440	−	7.91391i	−0.839600	−	0.561002i	−0.899359	+	0.437210i	$0.855967\pi$
$200$	15.1876	−	33.2470i	1.07393	−	2.35092i
$201$	−7.41335	−	11.0949i	−0.522897	−	0.782571i
$202$	11.4269	+	4.45718i	0.803992	+	0.313606i
$203$	−0.150826	−	0.282175i	−0.0105859	−	0.0198048i
$204$	5.63656	+	9.56618i	0.394638	+	0.669766i
$205$	−2.18878	+	22.2230i	−0.152871	+	1.55212i
$206$	−12.7040	+	7.13386i	−0.885128	+	0.497039i
$207$	−2.57710	−	6.22167i	−0.179121	−	0.432436i
$208$	−8.77300	+	20.3118i	−0.608298	+	1.40837i
$209$	1.63183	−	3.93960i	0.112876	−	0.272508i
$210$	−1.07593	−	9.00143i	−0.0742465	−	0.621158i
$211$	14.0040	+	17.0639i	0.964075	+	1.17473i	0.984579	+	0.174940i	$0.0559730\pi$
$211$	14.0040	+	17.0639i	0.964075	+	1.17473i	−0.0205037	+	0.999790i	$0.506527\pi$
$212$	10.3196	+	4.97596i	0.708755	+	0.341750i
$213$	0.0170509	−	0.0562094i	0.00116831	−	0.00385140i
$214$	−7.86712	+	0.163581i	−0.537785	+	0.0111821i
$215$	13.7204	+	2.72916i	0.935723	+	0.186127i
$216$	−2.73429	+	0.723633i	−0.186045	+	0.0492370i
$217$	−1.46680	−	7.37408i	−0.0995725	−	0.500585i
$218$	−9.57880	+	15.0017i	−0.648758	+	1.01604i
$219$	7.76675	−	9.46381i	0.524828	−	0.639505i
$220$	7.07053	+	2.58991i	0.476695	+	0.174612i
$221$	27.0821	+	14.4757i	1.82174	+	0.973740i
$222$	−3.13446	−	0.243045i	−0.210371	−	0.0163121i
$223$	18.8562	+	18.8562i	1.26271	+	1.26271i	0.949777	+	0.312929i	$0.101310\pi$
$223$	18.8562	+	18.8562i	1.26271	+	1.26271i	0.312929	+	0.949777i	$0.398690\pi$
$224$	−7.14922	−	4.71747i	−0.477678	−	0.315199i
$225$	9.13791	−	9.13791i	0.609194	−	0.609194i
$226$	14.7452	−	12.6231i	0.980839	−	0.839677i
$227$	9.68282	−	18.1153i	0.642672	−	1.20235i	−0.323933	−	0.946080i	$-0.605005\pi$
$227$	9.68282	−	18.1153i	0.642672	−	1.20235i	0.966604	−	0.256274i	$-0.0824949\pi$
$228$	−9.58151	+	0.398629i	−0.634551	+	0.0263998i
$229$	14.5716	+	11.9586i	0.962921	+	0.790249i	0.977778	−	0.209641i	$-0.0672295\pi$
$229$	14.5716	+	11.9586i	0.962921	+	0.790249i	−0.0148577	+	0.999890i	$0.504730\pi$
$230$	39.3724	−	8.68625i	2.59614	−	0.572754i
$231$	1.32070	−	0.262703i	0.0868954	−	0.0172846i
$232$	−0.262691	−	0.536846i	−0.0172465	−	0.0352457i
$233$	0.578460	−	2.90812i	0.0378962	−	0.190517i	−0.957200	−	0.289426i	$-0.906535\pi$
$233$	0.578460	−	2.90812i	0.0378962	−	0.190517i	0.995096	+	0.0989095i	$0.0315354\pi$
$234$	−5.41518	+	5.64515i	−0.354001	+	0.369035i
$235$	4.54493	+	1.37869i	0.296479	+	0.0899359i
$236$	−17.8223	+	15.9111i	−1.16013	+	1.03573i
$237$	3.95521	−	3.24596i	0.256919	−	0.210848i
$238$	−7.34899	+	9.34432i	−0.476364	+	0.605703i
$239$	20.8587	+	8.63997i	1.34924	+	0.558873i	0.936081	−	0.351785i	$-0.114425\pi$
$239$	20.8587	+	8.63997i	1.34924	+	0.558873i	0.413159	+	0.910659i	$0.364425\pi$
$240$	−1.40662	−	16.8757i	−0.0907972	−	1.08932i
$241$	−10.6084	+	4.39414i	−0.683347	+	0.283052i	−0.697225	−	0.716852i	$-0.745582\pi$
$241$	−10.6084	+	4.39414i	−0.683347	+	0.283052i	0.0138783	+	0.999904i	$0.495582\pi$
$242$	3.90297	−	13.9003i	0.250892	−	0.893546i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−7.62942	+	10.1273i	−0.488423	+	0.648333i
$245$	−17.5755	+	9.39431i	−1.12286	+	0.600180i
$246$	2.99728	+	6.83084i	0.191099	+	0.435519i
$247$	−22.0525	+	14.7350i	−1.40317	+	0.937567i
$248$	−2.24510	−	13.8639i	−0.142564	−	0.880359i
$249$	−0.130317	+	0.195034i	−0.00825853	+	0.0123598i
$250$	27.1682	+	38.8852i	1.71827	+	2.45931i
$251$	0.600093	+	6.09285i	0.0378776	+	0.384577i	0.995370	+	0.0961186i	$0.0306428\pi$
$251$	0.600093	+	6.09285i	0.0378776	+	0.384577i	−0.957492	+	0.288459i	$0.906857\pi$
$252$	−1.78566	−	2.44585i	−0.112486	−	0.154074i
$253$	1.73849	+	5.73104i	0.109298	+	0.360307i
$254$	−5.95553	+	1.94268i	−0.373683	+	0.121894i
$255$	−23.5031			−1.47182
$256$	−13.0306	−	9.28456i	−0.814414	−	0.580285i
$257$	24.7962			1.54675			0.773373	−	0.633951i	$-0.218568\pi$
$257$	24.7962			1.54675			0.773373	+	0.633951i	$0.218568\pi$
$258$	4.44269	−	1.44919i	0.276590	−	0.0902228i
$259$	−0.977114	−	3.22111i	−0.0607149	−	0.200150i
$260$	−27.6161	−	37.8263i	−1.71268	−	2.34589i
$261$	−0.0207118	−	0.210291i	−0.00128203	−	0.0130167i
$262$	−0.430685	−	0.616428i	−0.0266078	−	0.0380831i
$263$	−9.46032	+	14.1584i	−0.583348	+	0.873043i	−0.999340	−	0.0363259i	$-0.988435\pi$
$263$	−9.46032	+	14.1584i	−0.583348	+	0.873043i	0.415992	+	0.909368i	$0.363435\pi$
$264$	2.48302	−	0.402097i	0.152819	−	0.0247473i
$265$	−20.1641	+	13.4732i	−1.23867	+	0.827653i
$266$	−4.12557	−	9.40225i	−0.252955	−	0.576489i
$267$	9.04618	−	4.83529i	0.553617	−	0.295915i
$268$	16.0581	−	21.3155i	0.980905	−	1.30205i
$269$	13.5644	+	1.33598i	0.827037	+	0.0814560i	0.502673	−	0.864476i	$-0.332350\pi$
$269$	13.5644	+	1.33598i	0.827037	+	0.0814560i	0.324364	+	0.945932i	$0.394850\pi$
$270$	1.61850	−	5.76423i	0.0984986	−	0.350800i
$271$	−22.8564	+	9.46743i	−1.38843	+	0.575106i	−0.946721	−	0.322054i	$-0.895627\pi$
$271$	−22.8564	+	9.46743i	−1.38843	+	0.575106i	−0.441707	+	0.897160i	$0.645627\pi$
$272$	−14.3438	+	16.9524i	−0.869722	+	1.02789i
$273$	−7.73783	−	3.20512i	−0.468315	−	0.193982i
$274$	12.8048	−	16.2815i	0.773568	−	0.983601i
$275$	−8.88391	+	7.29083i	−0.535720	+	0.439654i
$276$	10.0472	−	8.96977i	0.604769	−	0.539917i
$277$	5.02338	+	1.52383i	0.301826	+	0.0915578i	0.437565	−	0.899187i	$-0.355841\pi$
$277$	5.02338	+	1.52383i	0.301826	+	0.0915578i	−0.135739	+	0.990745i	$0.543341\pi$
$278$	−20.4423	+	21.3104i	−1.22605	+	1.27811i
$279$	0.968718	−	4.87007i	0.0579956	−	0.291564i
$280$	16.2858	−	7.96902i	0.973265	−	0.476240i
$281$	16.7802	−	3.33779i	1.00102	−	0.199116i	0.332736	−	0.943020i	$-0.392028\pi$
$281$	16.7802	−	3.33779i	1.00102	−	0.199116i	0.668286	+	0.743905i	$0.267028\pi$
$282$	1.54929	−	0.341801i	0.0922589	−	0.0203540i
$283$	3.79580	+	3.11513i	0.225637	+	0.185175i	0.740419	−	0.672146i	$-0.234627\pi$
$283$	3.79580	+	3.11513i	0.225637	+	0.185175i	−0.514782	+	0.857321i	$0.672127\pi$
$284$	0.117376	−	0.00488329i	0.00696497	−	0.000289770i
$285$	9.56910	−	17.9025i	0.566825	−	1.06045i
$286$	5.28470	−	4.52413i	0.312491	−	0.267517i
$287$	−5.64744	+	5.64744i	−0.333358	+	0.333358i
$288$	−3.16989	−	4.68527i	−0.186788	−	0.276082i
$289$	9.77267	+	9.77267i	0.574863	+	0.574863i
$290$	1.26135	+	0.0978045i	0.0740689	+	0.00574328i
$291$	−4.54961	−	2.43182i	−0.266703	−	0.142556i
$292$	22.9917	+	8.42179i	1.34549	+	0.492848i
$293$	6.51831	−	7.94258i	0.380803	−	0.464010i	−0.546971	−	0.837151i	$-0.684219\pi$
$293$	6.51831	−	7.94258i	0.380803	−	0.464010i	0.927775	+	0.373141i	$0.121719\pi$
$294$	−3.58265	+	5.61091i	−0.208944	+	0.327235i
$295$	−9.86626	−	49.6010i	−0.574436	−	2.88788i
$296$	−1.60867	−	6.07847i	−0.0935021	−	0.353304i
$297$	0.872229	+	0.173497i	0.0506119	+	0.0100673i
$298$	−16.4839	+	0.342749i	−0.954886	+	0.0198549i
$299$	10.8130	−	35.6458i	0.625334	−	2.06145i
$300$	23.2808	+	11.2257i	1.34412	+	0.648113i
$301$	3.17408	+	3.86763i	0.182951	+	0.222927i
$302$	0.860873	+	7.20220i	0.0495376	+	0.414440i
$303$	−3.31899	+	8.01276i	−0.190671	+	0.460321i
$304$	−7.07284	−	17.8278i	−0.405655	−	1.02250i
$305$	−10.2711	−	24.7966i	−0.588121	−	1.41985i
$306$	−6.84570	+	3.84417i	−0.391343	+	0.219757i
$307$	−1.55026	+	15.7400i	−0.0884779	+	0.898332i	0.843817	+	0.536632i	$0.180304\pi$
$307$	−1.55026	+	15.7400i	−0.0884779	+	0.898332i	−0.932295	+	0.361700i	$0.882196\pi$
$308$	1.36717	+	2.32031i	0.0779017	+	0.132212i
$309$	−4.85656	−	9.08599i	−0.276280	−	0.516884i
$310$	27.6967	+	10.8034i	1.57306	+	0.613591i
$311$	−9.20947	−	13.7829i	−0.522221	−	0.781559i	0.472806	−	0.881167i	$-0.343241\pi$
$311$	−9.20947	−	13.7829i	−0.522221	−	0.781559i	−0.995027	+	0.0996076i	$0.968241\pi$
$312$	−14.2306	−	6.50068i	−0.805647	−	0.368029i
$313$	−18.5649	−	12.4047i	−1.04935	−	0.701155i	−0.0936850	−	0.995602i	$-0.529865\pi$
$313$	−18.5649	−	12.4047i	−1.04935	−	0.701155i	−0.955668	+	0.294447i	$0.904865\pi$
$314$	0.869101	−	4.89950i	0.0490462	−	0.276495i
$315$	6.37941	−	0.628317i	0.359439	−	0.0354017i
$316$	8.73763	+	5.32670i	0.491530	+	0.299650i
$317$	−2.09059	+	0.634174i	−0.117419	+	0.0356188i	−0.348448	−	0.937328i	$-0.613291\pi$
$317$	−2.09059	+	0.634174i	−0.117419	+	0.0356188i	0.231028	+	0.972947i	$0.425791\pi$
$318$	−3.66947	+	7.22235i	−0.205774	+	0.405009i
$319$			0.187920i			0.0105215i
$320$	30.9350	−	13.7874i	1.72932	−	0.770741i
$321$		−	5.56410i		−	0.310558i
$322$	12.8563	+	6.53190i	0.716452	+	0.364009i
$323$	−25.4733	+	7.72724i	−1.41737	+	0.429955i
$324$	−0.471382	−	1.94366i	−0.0261879	−	0.107981i
$325$	71.1374	−	7.00642i	3.94599	−	0.388646i
$326$	22.4715	+	3.98613i	1.24458	+	0.220771i
$327$	−10.4647	−	6.99229i	−0.578699	−	0.386674i
$328$	−10.9202	+	10.1649i	−0.602967	+	0.561264i
$329$	0.943733	+	1.41240i	0.0520297	+	0.0778679i
$330$	−1.93488	+	4.96047i	−0.106512	+	0.273065i
$331$	−4.54087	−	8.49537i	−0.249589	−	0.466948i	0.725661	−	0.688052i	$-0.241534\pi$
$331$	−4.54087	−	8.49537i	−0.249589	−	0.466948i	−0.975250	+	0.221104i	$0.929034\pi$
$332$	−0.454202	−	0.117403i	−0.0249276	−	0.00644330i
$333$	0.217897	−	2.21234i	0.0119407	−	0.121236i
$334$	14.0250	+	24.9758i	0.767416	+	1.36662i
$335$	21.6182	+	52.1910i	1.18113	+	2.85150i
$336$	3.44012	−	4.98483i	0.187674	−	0.271945i
$337$	0.967110	−	2.33481i	0.0526818	−	0.127185i	−0.895347	−	0.445368i	$-0.853073\pi$
$337$	0.967110	−	2.33481i	0.0526818	−	0.127185i	0.948029	+	0.318183i	$0.103073\pi$
$338$	−24.7085	+	2.95339i	−1.34397	+	0.160643i
$339$	8.70721	+	10.6098i	0.472910	+	0.576243i
$340$	−15.5032	−	44.3761i	−0.840780	−	2.40663i
$341$	−1.28187	+	4.22574i	−0.0694169	+	0.228837i
$342$	−0.140967	−	6.77955i	−0.00762262	−	0.366596i
$343$	−17.3861	−	3.45832i	−0.938764	−	0.186732i
$344$	5.66671	+	7.43229i	0.305529	+	0.400722i
$345$	5.56202	+	27.9621i	0.299449	+	1.50543i
$346$	8.60304	+	5.49317i	0.462502	+	0.295315i
$347$	5.96250	−	7.26533i	0.320084	−	0.390023i	−0.587966	−	0.808886i	$-0.700071\pi$
$347$	5.96250	−	7.26533i	0.320084	−	0.390023i	0.908050	+	0.418863i	$0.137571\pi$
$348$	0.383387	−	0.177819i	0.0205517	−	0.00953208i
$349$	−16.0116	−	8.55837i	−0.857080	−	0.458119i	−0.0165371	−	0.999863i	$-0.505264\pi$
$349$	−16.0116	−	8.55837i	−0.857080	−	0.458119i	−0.840543	+	0.541744i	$0.817764\pi$
$350$	−2.13930	+	27.5897i	−0.114350	+	1.47473i
$351$	−3.91126	−	3.91126i	−0.208768	−	0.208768i
$352$	2.39706	+	4.42294i	0.127763	+	0.235744i
$353$	5.78140	−	5.78140i	0.307713	−	0.307713i	−0.536309	−	0.844022i	$-0.680182\pi$
$353$	5.78140	−	5.78140i	0.307713	−	0.307713i	0.844022	+	0.536309i	$0.180182\pi$
$354$	−10.9865	−	12.8334i	−0.583924	−	0.682090i
$355$	−0.117224	+	0.219310i	−0.00622159	+	0.0116398i
$356$	15.0965	+	13.8906i	0.800115	+	0.736199i
$357$	−6.49798	−	5.33275i	−0.343910	−	0.282239i
$358$	−4.27959	−	19.3982i	−0.226183	−	1.02523i
$359$	−3.19028	+	0.634586i	−0.168376	+	0.0334922i	−0.278559	−	0.960419i	$-0.589857\pi$
$359$	−3.19028	+	0.634586i	−0.168376	+	0.0334922i	0.110182	+	0.993911i	$0.464857\pi$
$360$	11.9510	−	0.746351i	0.629874	−	0.0393362i
$361$	0.778621	−	3.91439i	0.0409801	−	0.206021i
$362$	5.64532	+	5.41534i	0.296711	+	0.284624i
$363$	9.76951	+	2.96355i	0.512767	+	0.155546i
$364$	0.947499	−	16.7239i	0.0496625	−	0.876572i
$365$	−40.0655	+	32.8809i	−2.09713	+	1.72107i
$366$	−7.04737	−	5.54252i	−0.368372	−	0.289712i
$367$	19.1036	+	7.91298i	0.997201	+	0.413054i	0.820770	−	0.571259i	$-0.193545\pi$
$367$	19.1036	+	7.91298i	0.997201	+	0.413054i	0.176431	+	0.984313i	$0.443545\pi$
$368$	23.5631	+	13.0533i	1.22831	+	0.680452i
$369$	−4.87315	+	2.01852i	−0.253686	+	0.105080i
$370$	12.8142	+	3.59800i	0.666177	+	0.187051i
$371$	−8.63184	−	0.850162i	−0.448143	−	0.0441382i
$372$	9.83414	−	1.38339i	0.509877	−	0.0717252i
$373$	−8.72403	+	4.66309i	−0.451713	+	0.241446i	−0.681533	−	0.731787i	$-0.738686\pi$
$373$	−8.72403	+	4.66309i	−0.451713	+	0.241446i	0.229820	+	0.973233i	$0.426186\pi$
$374$	6.39377	−	2.80550i	0.330614	−	0.145069i
$375$	−27.8894	+	18.6351i	−1.44020	+	0.962312i
$376$	1.66730	+	2.69975i	0.0859845	+	0.139229i
$377$	0.649363	−	0.971841i	0.0334439	−	0.0500523i
$378$	1.75535	−	1.22642i	0.0902854	−	0.0630805i
$379$	−0.878175	−	8.91626i	−0.0451088	−	0.457998i	−0.991034	−	0.133612i	$-0.957342\pi$
$379$	−0.878175	−	8.91626i	−0.0451088	−	0.457998i	0.945925	−	0.324386i	$-0.105158\pi$
$380$	40.1137	+	6.25842i	2.05779	+	0.321050i
$381$	−1.28584	−	4.23884i	−0.0658755	−	0.217162i
$382$	−1.24255	−	3.80921i	−0.0635745	−	0.194896i
$383$	−22.0283			−1.12559			−0.562797	−	0.826595i	$-0.690275\pi$
$383$	−22.0283			−1.12559			−0.562797	+	0.826595i	$0.690275\pi$
$384$	6.75530	−	9.07557i	0.344730	−	0.463136i
$385$	−5.70077			−0.290538
$386$	−10.6415	−	32.6229i	−0.541639	−	1.66046i
$387$	0.959206	+	3.16208i	0.0487592	+	0.160737i
$388$	1.59047	−	10.1942i	0.0807437	−	0.517531i
$389$	0.666063	+	6.76265i	0.0337707	+	0.342880i	0.997192	+	0.0748881i	$0.0238600\pi$
$389$	0.666063	+	6.76265i	0.0337707	+	0.342880i	−0.963421	+	0.267992i	$0.913640\pi$
$390$	27.1474	−	18.9673i	1.37466	−	0.960447i
$391$	20.7707	−	31.0856i	1.05042	−	1.57207i
$392$	−12.9571	−	3.06328i	−0.654433	−	0.154719i
$393$	0.442117	−	0.295413i	0.0223019	−	0.0149016i
$394$	17.3921	−	7.63139i	0.876199	−	0.384464i
$395$	−19.1038	+	10.2112i	−0.961215	+	0.513780i
$396$	0.247764	+	1.76129i	0.0124506	+	0.0885083i
$397$	7.24270	+	0.713343i	0.363501	+	0.0358017i	0.278119	−	0.960547i	$-0.410289\pi$
$397$	7.24270	+	0.713343i	0.363501	+	0.0358017i	0.0853816	+	0.996348i	$0.472789\pi$
$398$	19.3950	+	5.44577i	0.972182	+	0.272972i
$399$	6.70760	−	2.77838i	0.335800	−	0.139093i
$400$	−5.83850	+	51.3611i	−0.291925	+	2.56805i
$401$	8.05435	+	3.33622i	0.402215	+	0.166603i	0.574614	−	0.818424i	$-0.305152\pi$
$401$	8.05435	+	3.33622i	0.402215	+	0.166603i	−0.172400	+	0.985027i	$0.555152\pi$
$402$	14.8330	+	11.6657i	0.739805	+	0.581831i
$403$	21.2314	−	17.4242i	1.05761	−	0.867960i
$404$	−17.3181	−	0.981164i	−0.861608	−	0.0488147i
$405$	4.05126	+	1.22894i	0.201309	+	0.0610663i
$406$	0.326537	+	0.313234i	0.0162058	+	0.0155456i
$407$	−0.385693	+	1.93901i	−0.0191181	+	0.0961130i
$408$	−11.7737	−	10.3896i	−0.582887	−	0.514363i
$409$	−25.2604	+	5.02460i	−1.24904	+	0.248450i	−0.774949	−	0.632023i	$-0.782225\pi$
$409$	−25.2604	+	5.02460i	−1.24904	+	0.248450i	−0.474095	+	0.880474i	$0.657225\pi$
$410$	−6.80354	−	30.8386i	−0.336003	−	1.52301i
$411$	11.3220	+	9.29176i	0.558475	+	0.458329i
$412$	13.9517	−	15.1630i	0.687351	−	0.747027i
$413$	8.52649	−	15.9519i	0.419561	−	0.784944i
$414$	6.19352	+	7.23475i	0.304395	+	0.355568i
$415$	0.702188	−	0.702188i	0.0344690	−	0.0344690i
$416$	2.88708	−	31.1566i	0.141551	−	1.52758i
$417$	−14.7650	−	14.7650i	−0.723045	−	0.723045i
$418$	−0.466201	+	6.01242i	−0.0228026	+	0.294077i
$419$	−34.0589	−	18.2049i	−1.66389	−	0.889366i	−0.988379	−	0.152013i	$-0.951424\pi$
$419$	−34.0589	−	18.2049i	−1.66389	−	0.889366i	−0.675508	−	0.737353i	$-0.736076\pi$
$420$	5.39433	+	11.6305i	0.263217	+	0.567509i
$421$	−0.708559	+	0.863382i	−0.0345331	+	0.0420787i	−0.789991	−	0.613119i	$-0.789915\pi$
$421$	−0.708559	+	0.863382i	−0.0345331	+	0.0420787i	0.755458	+	0.655198i	$0.227415\pi$
$422$	−26.3120	−	16.8006i	−1.28085	−	0.817839i
$423$	0.218864	+	1.10030i	0.0106415	+	0.0534985i
$424$	−16.0569	−	2.16427i	−0.779794	−	0.105106i
$425$	70.3650	+	13.9965i	3.41321	+	0.678929i
$426$	0.00172688	+	0.0830511i	8.36675e−5	+	0.00402384i
$427$	2.78656	−	9.18606i	0.134851	−	0.444545i
$428$	10.5055	−	3.67021i	0.507804	−	0.177406i
$429$	3.12066	+	3.80254i	0.150667	+	0.183588i
$430$	−19.6439	+	2.34802i	−0.947312	+	0.113231i
$431$	−6.27854	+	15.1577i	−0.302427	+	0.730123i	0.697482	+	0.716603i	$0.254304\pi$
$431$	−6.27854	+	15.1577i	−0.302427	+	0.730123i	−0.999909	+	0.0135205i	$0.995696\pi$
$432$	3.35887	−	2.17209i	0.161604	−	0.104505i
$433$	8.60322	+	20.7700i	0.413445	+	0.998144i	0.984206	+	0.177028i	$0.0566482\pi$
$433$	8.60322	+	20.7700i	0.413445	+	0.998144i	−0.570761	+	0.821116i	$0.693352\pi$
$434$	5.20614	+	9.27109i	0.249903	+	0.445027i
$435$	−0.0876847	+	0.890277i	−0.00420416	+	0.0426855i
$436$	6.29933	−	24.3706i	0.301683	−	1.16714i
$437$	15.2215	+	28.4775i	0.728144	+	1.36226i
$438$	−6.29179	+	16.1303i	−0.300633	+	0.770734i
$439$	−16.5978	−	24.8404i	−0.792171	−	1.18557i	−0.979137	−	0.203202i	$-0.934865\pi$
$439$	−16.5978	−	24.8404i	−0.792171	−	1.18557i	0.186965	−	0.982366i	$-0.440135\pi$
$440$	−10.6421	−	0.381203i	−0.507343	−	0.0181731i
$441$	−3.91399	−	2.61524i	−0.186380	−	0.124535i
$442$	−42.7603	−	7.58506i	−2.03390	−	0.360785i
$443$	4.01584	−	0.395526i	0.190798	−	0.0187920i	−0.00216656	−	0.999998i	$-0.500690\pi$
$443$	4.01584	−	0.395526i	0.190798	−	0.0187920i	0.192965	+	0.981206i	$0.438190\pi$
$444$	4.32084	−	1.04790i	0.205058	−	0.0497314i
$445$	−41.5552	+	12.6056i	−1.96991	+	0.597564i
$446$	−33.6218	−	17.0823i	−1.59204	−	0.808869i
$447$		−	11.6584i		−	0.551423i
$448$	11.6810	+	3.20716i	0.551876	+	0.151524i
$449$		−	1.27190i		−	0.0600248i	−0.999550	−	0.0300124i	$-0.990445\pi$
$449$		−	1.27190i		−	0.0600248i	0.999550	−	0.0300124i	$-0.00955468\pi$
$450$	−8.27824	+	16.2935i	−0.390240	+	0.768081i
$451$	4.48886	−	1.36168i	0.211372	−	0.0641190i
$452$	−14.2887	+	23.4385i	−0.672086	+	1.10245i
$453$	−5.10428	+	0.502727i	−0.239820	+	0.0236202i
$454$	−5.07366	+	28.6024i	−0.238119	+	1.34238i
$455$	29.4819	+	19.6992i	1.38213	+	0.923511i
$456$	12.7074	−	4.73811i	0.595080	−	0.221882i
$457$	−10.8045	−	16.1700i	−0.505411	−	0.756401i	0.487772	−	0.872971i	$-0.337810\pi$
$457$	−10.8045	−	16.1700i	−0.505411	−	0.756401i	−0.993182	+	0.116571i	$0.962810\pi$
$458$	−24.8361	−	9.68761i	−1.16052	−	0.452672i
$459$	−2.61702	−	4.89610i	−0.122152	−	0.228531i
$460$	−49.1263	+	28.9461i	−2.29053	+	1.34962i
$461$	−1.51390	+	15.3709i	−0.0705094	+	0.715894i	0.893328	+	0.449405i	$0.148364\pi$
$461$	−1.51390	+	15.3709i	−0.0705094	+	0.715894i	−0.963838	+	0.266490i	$0.914136\pi$
$462$	−1.66045	+	0.932418i	−0.0772511	+	0.0433800i
$463$	−6.46123	−	15.5988i	−0.300279	−	0.724937i	−0.999945	−	0.0104676i	$-0.996668\pi$
$463$	−6.46123	−	15.5988i	−0.300279	−	0.724937i	0.699666	−	0.714470i	$-0.253332\pi$
$464$	0.588629	+	0.606577i	0.0273264	+	0.0281596i
$465$	−8.04463	+	19.4215i	−0.373061	+	0.900649i
$466$	0.497675	+	4.16363i	0.0230544	+	0.192876i
$467$	−9.62203	−	11.7245i	−0.445254	−	0.542544i	0.501221	−	0.865319i	$-0.332884\pi$
$467$	−9.62203	−	11.7245i	−0.445254	−	0.542544i	−0.946476	+	0.322775i	$0.895384\pi$
$468$	4.80487	−	9.96479i	0.222105	−	0.460623i
$469$	−5.86505	+	19.3345i	−0.270823	+	0.892783i
$470$	−6.71528	+	0.139631i	−0.309753	+	0.00644068i
$471$	3.45095	+	0.686436i	0.159011	+	0.0316293i
$472$	16.9838	−	29.2087i	0.781744	−	1.34444i
$473$	−0.573298	−	2.88216i	−0.0263603	−	0.132522i
$474$	−3.89417	+	6.09880i	−0.178865	+	0.280127i
$475$	−39.3098	+	47.8991i	−1.80366	+	2.19776i
$476$	5.78252	−	15.7864i	0.265041	−	0.723569i
$477$	−5.05193	−	2.70031i	−0.231312	−	0.123639i
$478$	−31.8336	−	2.46837i	−1.45604	−	0.112901i
$479$	−23.7075	−	23.7075i	−1.08322	−	1.08322i	−0.996207	−	0.0870140i	$-0.972268\pi$
$479$	−23.7075	−	23.7075i	−1.08322	−	1.08322i	−0.0870140	−	0.996207i	$-0.527732\pi$
$480$	9.29235	+	22.0723i	0.424136	+	1.00746i
$481$	8.69493	−	8.69493i	0.396455	−	0.396455i
$482$	12.3358	−	10.5604i	0.561879	−	0.481013i
$483$	−4.80674	+	8.99277i	−0.218714	+	0.409185i
$484$	0.848744	+	20.4006i	0.0385793	+	0.927299i
$485$	16.8824	+	13.8550i	0.766591	+	0.629125i
$486$	1.38100	−	0.304674i	0.0626436	−	0.0138203i
$487$	32.3001	−	6.42489i	1.46366	−	0.291140i	0.601946	−	0.798537i	$-0.294392\pi$
$487$	32.3001	−	6.42489i	1.46366	−	0.291140i	0.861712	+	0.507397i	$0.169392\pi$
$488$	5.81617	−	16.9621i	0.263286	−	0.767837i
$489$	−3.14833	+	15.8277i	−0.142373	+	0.715755i
$490$	19.5101	−	20.3386i	0.881375	−	0.918806i
$491$	40.3489	+	12.2397i	1.82092	+	0.552369i	0.999830	−	0.0184320i	$-0.00586742\pi$
$491$	40.3489	+	12.2397i	1.82092	+	0.552369i	0.821088	+	0.570802i	$0.193367\pi$
$492$	−7.02561	−	7.86949i	−0.316739	−	0.354784i
$493$	0.906824	−	0.744211i	0.0408413	−	0.0335176i
$494$	23.1871	−	29.4827i	1.04324	−	1.32649i
$495$	−3.47838	−	1.44079i	−0.156341	−	0.0647588i
$496$	9.09880	+	17.6553i	0.408548	+	0.792745i
$497$	−0.0821697	+	0.0340358i	−0.00368581	+	0.00152671i
$498$	0.0896748	−	0.319374i	0.00401842	−	0.0143115i
$499$	−0.240170	−	0.0236546i	−0.0107515	−	0.00105893i	0.0926400	−	0.995700i	$-0.470469\pi$
$499$	−0.240170	−	0.0236546i	−0.0107515	−	0.00105893i	−0.103391	+	0.994641i	$0.532969\pi$
$500$	−53.5813	−	40.3656i	−2.39623	−	1.80520i
$501$	−17.8629	+	9.54793i	−0.798056	+	0.426570i
$502$	−3.47896	−	7.92860i	−0.155273	−	0.353871i
$503$	−2.85322	+	1.90646i	−0.127219	+	0.0850049i	−0.617551	−	0.786530i	$-0.711875\pi$
$503$	−2.85322	+	1.90646i	−0.127219	+	0.0850049i	0.490333	+	0.871535i	$0.336875\pi$
$504$	3.47347	+	2.50528i	0.154721	+	0.111594i
$505$	20.3991	−	30.5294i	0.907747	−	1.35854i
$506$	−4.85084	−	6.94288i	−0.215646	−	0.308649i
$507$	−1.72470	−	17.5112i	−0.0765968	−	0.777700i
$508$	7.15516	−	5.22382i	0.317459	−	0.231770i
$509$	−3.94376	−	13.0008i	−0.174804	−	0.576252i	−0.999936	−	0.0113121i	$-0.996399\pi$
$509$	−3.94376	−	13.0008i	−0.174804	−	0.576252i	0.825132	−	0.564940i	$-0.191101\pi$
$510$	31.5998	−	10.3078i	1.39926	−	0.456435i
$511$	−18.5376			−0.820054
$512$	21.5915	+	6.76818i	0.954217	+	0.299114i
$513$	4.79490			0.211700
$514$	−33.3383	+	10.8749i	−1.47049	+	0.479670i
$515$	12.6611	+	41.7381i	0.557915	+	1.83920i
$516$	−5.33758	+	3.89685i	−0.234974	+	0.171549i
$517$	−0.0977905	−	0.992883i	−0.00430082	−	0.0436670i
$518$	2.72640	+	3.90223i	0.119791	+	0.171454i
$519$	−4.00988	+	6.00121i	−0.176014	+	0.263424i
$520$	53.7191	+	38.7455i	2.35574	+	1.69910i
$521$	−11.1128	+	7.42534i	−0.486861	+	0.325310i	−0.774657	−	0.632382i	$-0.782077\pi$
$521$	−11.1128	+	7.42534i	−0.486861	+	0.325310i	0.287796	+	0.957692i	$0.407077\pi$
$522$	0.120074	+	0.273651i	0.00525550	+	0.0119774i
$523$	−37.6298	+	20.1136i	−1.64544	+	0.879505i	−0.652917	+	0.757430i	$0.726455\pi$
$523$	−37.6298	+	20.1136i	−1.64544	+	0.879505i	−0.992521	+	0.122075i	$0.961045\pi$
$524$	0.849399	+	0.639897i	0.0371062	+	0.0279540i
$525$	−19.4732	−	1.91795i	−0.849881	−	0.0837060i
$526$	6.50989	−	23.1848i	0.283845	−	1.01091i
$527$	25.4682	−	10.5493i	1.10941	−	0.459533i
$528$	−3.16205	+	1.62959i	−0.137611	+	0.0709189i
$529$	−20.6493	−	8.55322i	−0.897795	−	0.371879i
$530$	21.2015	−	26.9580i	0.920935	−	1.17098i
$531$	9.23415	−	7.57827i	0.400728	−	0.328869i
$532$	9.67033	+	10.8319i	0.419262	+	0.469622i
$533$	−27.9197	−	8.46936i	−1.20934	−	0.366849i
$534$	−10.0419	+	10.4684i	−0.434556	+	0.453011i
$535$	−4.59553	+	23.1033i	−0.198682	+	0.998842i
$536$	−12.2417	+	35.7011i	−0.528759	+	1.54205i
$537$	13.7765	−	2.74033i	0.594502	−	0.118254i
$538$	−18.8232	+	4.15272i	−0.811524	+	0.179037i
$539$	3.23605	+	2.65576i	0.139387	+	0.114392i
$540$	0.351960	+	8.45979i	0.0151460	+	0.364051i
$541$	−6.34068	+	11.8626i	−0.272607	+	0.510012i	−0.980553	−	0.196255i	$-0.937122\pi$
$541$	−6.34068	+	11.8626i	−0.272607	+	0.510012i	0.707946	+	0.706267i	$0.249622\pi$
$542$	26.5781	−	22.7530i	1.14163	−	0.977325i
$543$	−3.91138	+	3.91138i	−0.167853	+	0.167853i
$544$	11.8503	−	29.0832i	0.508079	−	1.24693i
$545$	37.6765	+	37.6765i	1.61388	+	1.61388i
$546$	11.8091	+	0.915675i	0.505383	+	0.0391873i
$547$	19.2233	+	10.2751i	0.821929	+	0.439330i	0.828052	−	0.560651i	$-0.189449\pi$
$547$	19.2233	+	10.2751i	0.821929	+	0.439330i	−0.00612332	+	0.999981i	$0.501949\pi$
$548$	−10.0754	+	27.5061i	−0.430401	+	1.17500i
$549$	4.02190	−	4.90070i	0.171650	−	0.209157i
$550$	8.74680	−	13.6987i	0.372965	−	0.584113i
$551$	0.197666	+	0.993734i	0.00842086	+	0.0423345i
$552$	−9.57448	+	16.4662i	−0.407517	+	0.700846i
$553$	−7.59855	−	1.51144i	−0.323123	−	0.0642732i
$554$	−7.42219	+	0.154329i	−0.315339	+	0.00655683i
$555$	−2.73198	+	9.00614i	−0.115966	+	0.382289i
$556$	18.1384	−	37.6170i	0.769238	−	1.59532i
$557$	7.85384	+	9.56993i	0.332778	+	0.405491i	0.912338	−	0.409439i	$-0.134275\pi$
$557$	7.85384	+	9.56993i	0.332778	+	0.405491i	−0.579560	+	0.814930i	$0.696775\pi$
$558$	0.833432	+	6.97262i	0.0352820	+	0.295175i
$559$	−6.99454	+	16.8863i	−0.295838	+	0.714215i
$560$	−18.4012	+	17.8567i	−0.777592	+	0.754585i
$561$	1.88937	+	4.56134i	0.0797693	+	0.192580i
$562$	−21.0970	+	11.8469i	−0.889921	+	0.499731i
$563$	1.51768	−	15.4093i	0.0639627	−	0.649424i	−0.908739	−	0.417365i	$-0.862954\pi$
$563$	1.51768	−	15.4093i	0.0639627	−	0.649424i	0.972702	−	0.232059i	$-0.0745463\pi$
$564$	−1.93310	+	1.13902i	−0.0813984	+	0.0479614i
$565$	−27.3912	−	51.2454i	−1.15236	−	2.15591i
$566$	−6.46962	−	2.52355i	−0.271938	−	0.106073i
$567$	0.841223	+	1.25898i	0.0353280	+	0.0528722i
$568$	−0.155669	+	0.0580430i	−0.00653173	+	0.00243543i
$569$	22.9772	+	15.3529i	0.963255	+	0.643626i	0.934501	−	0.355960i	$-0.115846\pi$
$569$	22.9772	+	15.3529i	0.963255	+	0.643626i	0.0287536	+	0.999587i	$0.490846\pi$
$570$	−5.01408	+	28.2665i	−0.210017	+	1.18395i
$571$	10.6990	−	1.05376i	0.447738	−	0.0440983i	0.128364	−	0.991727i	$-0.459027\pi$
$571$	10.6990	−	1.05376i	0.447738	−	0.0440983i	0.319374	+	0.947629i	$0.396527\pi$
$572$	−5.12109	+	8.40035i	−0.214123	+	0.351236i
$573$	2.71120	−	0.822434i	0.113262	−	0.0343577i
$574$	5.11614	−	10.0697i	0.213544	−	0.420302i
$575$		−	87.0269i		−	3.62927i
$576$	6.31671	+	4.90909i	0.263196	+	0.204546i
$577$		−	36.9898i		−	1.53990i	−0.638102	−	0.769952i	$-0.720280\pi$
$577$		−	36.9898i		−	1.53990i	0.638102	−	0.769952i	$-0.279720\pi$
$578$	−17.4253	−	8.85328i	−0.724795	−	0.368248i
$579$	23.2193	−	7.04351i	0.964963	−	0.292718i
$580$	−1.73877	+	0.421691i	−0.0721983	+	0.0175098i
$581$	0.353459	−	0.0348127i	0.0146640	−	0.00144427i
$582$	7.18343	+	1.27424i	0.297763	+	0.0528189i
$583$	4.23575	+	2.83024i	0.175427	+	0.117217i
$584$	−34.6057	−	1.23958i	−1.43199	−	0.0512942i
$585$	13.0100	+	19.4708i	0.537895	+	0.805017i
$586$	−5.28044	+	13.5375i	−0.218133	+	0.559227i
$587$	−1.61644	−	3.02414i	−0.0667175	−	0.124820i	0.846351	−	0.532625i	$-0.178794\pi$
$587$	−1.61644	−	3.02414i	−0.0667175	−	0.124820i	−0.913069	+	0.407805i	$0.866294\pi$
$588$	2.35607	−	9.11506i	0.0971625	−	0.375899i
$589$	−2.33369	+	23.6944i	−0.0961581	+	0.976309i
$590$	35.0186	+	62.3611i	1.44169	+	2.56737i
$591$	5.13938	+	12.4076i	0.211406	+	0.510379i
$592$	4.82867	+	7.46693i	0.198457	+	0.306889i
$593$	5.35278	−	12.9228i	0.219812	−	0.530674i	−0.775051	−	0.631898i	$-0.782276\pi$
$593$	5.35278	−	12.9228i	0.219812	−	0.530674i	0.994864	+	0.101224i	$0.0322760\pi$
$594$	−1.24879	+	0.149267i	−0.0512387	+	0.00612452i
$595$	22.5765	+	27.5095i	0.925546	+	1.12778i
$596$	22.0121	−	7.69015i	0.901652	−	0.315001i
$597$	−4.13501	+	13.6313i	−0.169235	+	0.557892i
$598$	1.09512	+	52.6677i	0.0447827	+	2.15374i
$599$	−12.0998	−	2.40680i	−0.494384	−	0.0983391i	−0.0583996	−	0.998293i	$-0.518600\pi$
$599$	−12.0998	−	2.40680i	−0.494384	−	0.0983391i	−0.435984	+	0.899954i	$0.643600\pi$
$600$	−36.2241	−	4.88254i	−1.47884	−	0.199329i
$601$	3.23464	+	16.2617i	0.131944	+	0.663327i	0.988977	+	0.148066i	$0.0473048\pi$
$601$	3.23464	+	16.2617i	0.131944	+	0.663327i	−0.857034	+	0.515261i	$0.827695\pi$
$602$	−5.96375	−	3.80794i	−0.243064	−	0.155200i
$603$	−8.46514	+	10.3148i	−0.344727	+	0.420051i
$604$	−4.31610	−	9.30574i	−0.175620	−	0.378645i
$605$	−38.1174	−	20.3742i	−1.54969	−	0.828327i
$606$	0.948208	−	12.2287i	0.0385183	−	0.496756i
$607$	−3.71708	−	3.71708i	−0.150871	−	0.150871i	0.627636	−	0.778507i	$-0.284023\pi$
$607$	−3.71708	−	3.71708i	−0.150871	−	0.150871i	−0.778507	+	0.627636i	$0.784023\pi$
$608$	17.3281	+	20.8675i	0.702748	+	0.846287i
$609$	−0.226242	+	0.226242i	−0.00916780	+	0.00916780i
$610$	24.6844	+	28.8343i	0.999444	+	1.16747i
$611$	−2.92521	+	5.47267i	−0.118341	+	0.221401i
$612$	7.51805	−	8.17077i	0.303899	−	0.330284i
$613$	0.0822214	+	0.0674773i	0.00332089	+	0.00272538i	0.636052	−	0.771646i	$-0.280566\pi$
$613$	0.0822214	+	0.0674773i	0.00332089	+	0.00272538i	−0.632731	+	0.774371i	$0.718066\pi$
$614$	−4.81879	−	21.8422i	−0.194470	−	0.881481i
$615$	21.9015	−	4.35647i	0.883152	−	0.175670i
$616$	−2.85576	−	2.52004i	−0.115062	−	0.101535i
$617$	4.54346	−	22.8415i	0.182913	−	0.919565i	−0.774880	−	0.632108i	$-0.782190\pi$
$617$	4.54346	−	22.8415i	0.182913	−	0.919565i	0.957793	−	0.287458i	$-0.0928100\pi$
$618$	10.5144	+	10.0861i	0.422953	+	0.405722i
$619$	−18.5427	−	5.62488i	−0.745296	−	0.226083i	−0.105278	−	0.994443i	$-0.533573\pi$
$619$	−18.5427	−	5.62488i	−0.745296	−	0.226083i	−0.640018	+	0.768360i	$0.721073\pi$
$620$	−41.9760	−	2.37816i	−1.68580	−	0.0955093i
$621$	−5.20568	+	4.27219i	−0.208897	+	0.171437i
$622$	18.4268	+	14.4921i	0.738848	+	0.581079i
$623$	−14.3490	−	5.94357i	−0.574882	−	0.238124i
$624$	21.9839	+	2.49903i	0.880059	+	0.100041i
$625$	71.4973	−	29.6152i	2.85989	−	1.18461i
$626$	30.4007	+	8.53600i	1.21506	+	0.341167i
$627$	−4.24365	−	0.417963i	−0.169475	−	0.0166919i
$628$	0.980271	+	6.96850i	0.0391171	+	0.278073i
$629$	10.8843	−	5.81777i	0.433985	−	0.231970i
$630$	−8.30150	+	3.64258i	−0.330740	+	0.145124i
$631$	−11.8785	+	7.93696i	−0.472876	+	0.315965i	−0.769073	−	0.639161i	$-0.779282\pi$
$631$	−11.8785	+	7.93696i	−0.472876	+	0.315965i	0.296197	+	0.955127i	$0.404282\pi$
$632$	−14.0838	−	3.32965i	−0.560223	−	0.132446i
$633$	12.2640	−	18.3544i	0.487451	−	0.729522i
$634$	2.53265	−	1.76951i	0.100585	−	0.0702763i
$635$	1.83810	+	18.6626i	0.0729428	+	0.740601i
$636$	1.76607	−	11.3197i	0.0700293	−	0.448856i
$637$	−7.55839	−	24.9167i	−0.299474	−	0.987235i
$638$	−0.0824160	−	0.252657i	−0.00326288	−	0.0100028i
$639$	−0.0587387			−0.00232367
$640$	−35.5451	+	32.1042i	−1.40504	+	1.26903i
$641$	6.10324			0.241063			0.120532	−	0.992709i	$-0.461540\pi$
$641$	6.10324			0.241063			0.120532	+	0.992709i	$0.461540\pi$
$642$	2.44024	+	7.48088i	0.0963086	+	0.295247i
$643$	−3.61594	−	11.9202i	−0.142599	−	0.470085i	0.856327	−	0.516435i	$-0.172741\pi$
$643$	−3.61594	−	11.9202i	−0.142599	−	0.470085i	−0.998925	+	0.0463498i	$0.985241\pi$
$644$	−20.1498	−	3.14372i	−0.794015	−	0.123880i
$645$	−1.37118	−	13.9218i	−0.0539902	−	0.548172i
$646$	30.8597	−	21.5610i	1.21416	−	0.848307i
$647$	−3.19542	+	4.78228i	−0.125625	+	0.188011i	−0.888951	−	0.458003i	$-0.848565\pi$
$647$	−3.19542	+	4.78228i	−0.125625	+	0.188011i	0.763326	+	0.646014i	$0.223565\pi$
$648$	1.48620	+	2.40650i	0.0583833	+	0.0945361i
$649$	−8.83313	+	5.90211i	−0.346731	+	0.231678i
$650$	−92.5708	+	40.6187i	−3.63092	+	1.59320i
$651$	−6.63076	+	3.54422i	−0.259880	+	0.138909i
$652$	−31.9610	+	4.49601i	−1.25169	+	0.176077i
$653$	3.08450	+	0.303797i	0.120706	+	0.0118885i	0.158190	−	0.987409i	$-0.449434\pi$
$653$	3.08450	+	0.303797i	0.120706	+	0.0118885i	−0.0374838	+	0.999297i	$0.511934\pi$
$654$	17.1363	+	4.81158i	0.670082	+	0.188148i
$655$	−2.07975	+	0.861461i	−0.0812626	+	0.0336601i
$656$	10.2241	−	18.4559i	0.399183	−	0.720582i
$657$	−11.3109	−	4.68512i	−0.441279	−	0.182784i
$658$	−1.88827	−	1.48506i	−0.0736126	−	0.0578937i
$659$	4.56140	−	3.74344i	0.177687	−	0.145824i	−0.541346	−	0.840800i	$-0.682085\pi$
$659$	4.56140	−	3.74344i	0.177687	−	0.145824i	0.719033	+	0.694976i	$0.244585\pi$
$660$	0.425928	−	7.51788i	0.0165792	−	0.292633i
$661$	17.9604	+	5.44822i	0.698578	+	0.211911i	0.619545	−	0.784961i	$-0.287317\pi$
$661$	17.9604	+	5.44822i	0.698578	+	0.211911i	0.0790322	+	0.996872i	$0.474817\pi$
$662$	9.83097	+	9.43046i	0.382091	+	0.366525i
$663$	5.99085	−	30.1180i	0.232665	−	1.16969i
$664$	0.662160	−	0.0413525i	0.0256968	−	0.00160479i
$665$	−30.1461	+	5.99643i	−1.16901	+	0.232531i
$666$	0.677306	+	3.07004i	0.0262451	+	0.118962i
$667$	−1.10000	−	0.902749i	−0.0425923	−	0.0349546i
$668$	−29.8102	−	27.4288i	−1.15339	−	1.06125i
$669$	12.5706	−	23.5179i	0.486008	−	0.909256i
$670$	−51.9549	−	60.6893i	−2.00719	−	2.34463i
$671$	−3.98670	+	3.98670i	−0.153905	+	0.153905i
$672$	−2.43902	+	8.21079i	−0.0940874	+	0.316738i
$673$	11.0380	+	11.0380i	0.425485	+	0.425485i	0.887087	−	0.461602i	$-0.152725\pi$
$673$	11.0380	+	11.0380i	0.425485	+	0.425485i	−0.461602	+	0.887087i	$0.652725\pi$
$674$	−0.276295	+	3.56328i	−0.0106425	+	0.137252i
$675$	−11.3970	−	6.09184i	−0.438672	−	0.234475i
$676$	31.9252	−	14.8072i	1.22789	−	0.569508i
$677$	17.8898	−	21.7987i	0.687560	−	0.837794i	−0.305890	−	0.952067i	$-0.598954\pi$
$677$	17.8898	−	21.7987i	0.687560	−	0.837794i	0.993449	+	0.114273i	$0.0364539\pi$
$678$	−16.3599	−	10.4460i	−0.628297	−	0.401177i
$679$	1.52388	+	7.66109i	0.0584813	+	0.294005i
$680$	40.3059	+	52.8641i	1.54566	+	2.02724i
$681$	−20.1460	−	4.00729i	−0.771997	−	0.153560i
$682$	−0.129824	−	6.24366i	−0.00497123	−	0.239082i
$683$	5.85725	−	19.3088i	0.224122	−	0.738830i	−0.770700	−	0.637198i	$-0.780094\pi$
$683$	5.85725	−	19.3088i	0.224122	−	0.738830i	0.994822	−	0.101632i	$-0.0324065\pi$
$684$	3.16283	+	9.05322i	0.120934	+	0.346159i
$685$	−39.3372	−	47.9325i	−1.50300	−	1.83141i
$686$	24.8922	−	2.97535i	0.950390	−	0.113599i
$687$	7.21377	−	17.4156i	0.275223	−	0.664446i
$688$	−10.8784	−	7.50740i	−0.414736	−	0.286217i
$689$	−12.1255	−	29.2735i	−0.461944	−	1.11523i
$690$	−19.7414	−	35.1555i	−0.751543	−	1.33835i
$691$	−1.56642	+	15.9042i	−0.0595896	+	0.605023i	0.918298	+	0.395891i	$0.129564\pi$
$691$	−1.56642	+	15.9042i	−0.0595896	+	0.605023i	−0.977887	+	0.209133i	$0.932936\pi$
$692$	−13.9758	−	3.61249i	−0.531282	−	0.137326i
$693$	−0.634768	−	1.18757i	−0.0241129	−	0.0451120i
$694$	−4.83018	+	12.3831i	−0.183351	+	0.470058i
$695$	49.1125	+	73.5021i	1.86294	+	2.78809i
$696$	−0.437474	+	0.407217i	−0.0165824	+	0.0154355i
$697$	−24.3479	−	16.2688i	−0.922243	−	0.616223i
$698$	25.2809	+	4.48447i	0.956895	+	0.169740i
$699$	−2.95081	+	0.290630i	−0.111610	+	0.0109926i
$700$	−9.22374	−	38.0324i	−0.348625	−	1.43749i
$701$	−32.2730	+	9.78991i	−1.21894	+	0.369760i	−0.833263	−	0.552876i	$-0.813530\pi$
$701$	−32.2730	+	9.78991i	−1.21894	+	0.369760i	−0.385672	+	0.922636i	$0.626030\pi$
$702$	6.97402	+	3.54330i	0.263217	+	0.133733i
$703$			10.6593i			0.402023i
$704$	−5.16259	−	4.89534i	−0.194572	−	0.184500i
$705$		−	4.74944i		−	0.178874i
$706$	−5.23750	+	10.3086i	−0.197116	+	0.387969i
$707$	12.5668	−	3.81209i	0.472622	−	0.143368i
$708$	20.3996	+	12.4361i	0.766662	+	0.467379i
$709$	−15.8142	+	1.55756i	−0.593915	+	0.0584956i	−0.390509	−	0.920599i	$-0.627701\pi$
$709$	−15.8142	+	1.55756i	−0.593915	+	0.0584956i	−0.203406	+	0.979094i	$0.565201\pi$
$710$	0.0614236	−	0.346271i	0.00230519	−	0.0129953i
$711$	−4.25433	−	2.84265i	−0.159550	−	0.106608i
$712$	−26.3892	−	12.0549i	−0.988975	−	0.451775i
$713$	−18.5777	−	27.8035i	−0.695741	−	1.04125i
$714$	11.0753	+	4.32003i	0.414481	+	0.161673i
$715$	−9.81703	−	18.3664i	−0.367136	−	0.686863i
$716$	14.2613	+	24.2038i	0.532971	+	0.904539i
$717$	2.21297	−	22.4686i	0.0826447	−	0.839106i
$718$	4.01099	−	2.25235i	0.149689	−	0.0840571i
$719$	12.7340	+	30.7426i	0.474898	+	1.14651i	0.961973	+	0.273146i	$0.0880641\pi$
$719$	12.7340	+	30.7426i	0.474898	+	1.14651i	−0.487074	+	0.873361i	$0.661936\pi$
$720$	−15.7407	+	6.24481i	−0.586621	+	0.232730i
$721$	−5.96973	+	14.4122i	−0.222324	+	0.536738i
$722$	0.669883	+	5.60435i	0.0249305	+	0.208572i
$723$	7.28439	+	8.87605i	0.270909	+	0.330104i
$724$	−9.96508	−	4.80501i	−0.370349	−	0.178577i
$725$	0.792689	−	2.61315i	0.0294397	−	0.0970498i
$726$	−14.4347	+	0.300141i	−0.535724	+	0.0111393i
$727$	−10.5992	−	2.10831i	−0.393101	−	0.0781927i	−0.00541803	−	0.999985i	$-0.501725\pi$
$727$	−10.5992	−	2.10831i	−0.393101	−	0.0781927i	−0.387683	+	0.921793i	$0.626725\pi$
$728$	6.06069	+	22.9007i	0.224624	+	0.848757i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	39.4472	−	61.7796i	1.46001	−	2.28657i
$731$	−11.6377	+	14.1806i	−0.430436	+	0.524488i
$732$	11.9059	+	4.36110i	0.440055	+	0.161191i
$733$	14.8510	+	7.93805i	0.548536	+	0.293198i	0.722290	−	0.691591i	$-0.243090\pi$
$733$	14.8510	+	7.93805i	0.548536	+	0.293198i	−0.173754	+	0.984789i	$0.555590\pi$
$734$	−29.1550	−	2.26067i	−1.07613	−	0.0834429i
$735$	14.0917	+	14.0917i	0.519780	+	0.519780i
$736$	−37.4052	−	7.21605i	−1.37877	−	0.265987i
$737$	8.39106	−	8.39106i	0.309089	−	0.309089i
$738$	5.66664	−	4.85110i	0.208592	−	0.178572i
$739$	−7.69375	+	14.3940i	−0.283019	+	0.529491i	−0.982756	−	0.184910i	$-0.940801\pi$
$739$	−7.69375	+	14.3940i	−0.283019	+	0.529491i	0.699736	+	0.714401i	$0.253301\pi$
$740$	−18.8065	+	0.782425i	−0.691341	+	0.0287625i
$741$	20.5020	+	16.8256i	0.753161	+	0.618103i
$742$	11.9783	−	2.64262i	0.439737	−	0.0970138i
$743$	−48.8564	+	9.71814i	−1.79237	+	0.356524i	−0.975448	−	0.220229i	$-0.929320\pi$
$743$	−48.8564	+	9.71814i	−1.79237	+	0.356524i	−0.816919	+	0.576753i	$0.804320\pi$
$744$	−12.6152	+	6.17290i	−0.462496	+	0.226310i
$745$	−9.62895	+	48.4080i	−0.352778	+	1.77353i
$746$	9.68430	−	10.0956i	0.354567	−	0.369625i
$747$	0.224465	+	0.0680907i	0.00821274	+	0.00249131i
$748$	−7.36597	+	6.57608i	−0.269327	+	0.240445i
$749$	−6.51257	+	5.34472i	−0.237964	+	0.195292i
$750$	29.3243	−	37.2861i	1.07077	−	1.36150i
$751$	18.6066	+	7.70711i	0.678965	+	0.281236i	0.695394	−	0.718629i	$-0.255230\pi$
$751$	18.6066	+	7.70711i	0.678965	+	0.281236i	−0.0164292	+	0.999865i	$0.505230\pi$
$752$	−3.42570	−	2.89856i	−0.124922	−	0.105700i
$753$	5.65630	−	2.34291i	0.206127	−	0.0853806i
$754$	−0.446844	+	1.59142i	−0.0162731	+	0.0579562i
$755$	21.6092	+	2.12832i	0.786440	+	0.0774576i
$756$	−1.82218	+	2.41876i	−0.0662720	+	0.0879694i
$757$	−30.2670	+	16.1780i	−1.10007	+	0.588000i	−0.918517	−	0.395381i	$-0.870613\pi$
$757$	−30.2670	+	16.1780i	−1.10007	+	0.588000i	−0.181554	+	0.983381i	$0.558113\pi$
$758$	5.09110	+	11.6027i	0.184917	+	0.421429i
$759$	4.97960	−	3.32726i	0.180748	−	0.120772i
$760$	−56.6772	+	9.17822i	−2.05590	+	0.332929i
$761$	10.9537	−	16.3934i	0.397073	−	0.594262i	−0.578030	−	0.816016i	$-0.696178\pi$
$761$	10.9537	−	16.3934i	0.397073	−	0.594262i	0.975103	+	0.221754i	$0.0711782\pi$
$762$	3.58783	+	5.13516i	0.129973	+	0.186027i
$763$	1.86790	+	18.9651i	0.0676227	+	0.686584i
$764$	3.34120	+	4.57650i	0.120880	+	0.165572i
$765$	6.82260	+	22.4911i	0.246672	+	0.813167i
$766$	29.6169	−	9.66093i	1.07010	−	0.349064i
$767$	66.0760			2.38587
$768$	−5.10218	+	15.1647i	−0.184109	+	0.547209i
$769$	−34.0327			−1.22725			−0.613624	−	0.789598i	$-0.710289\pi$
$769$	−34.0327			−1.22725			−0.613624	+	0.789598i	$0.710289\pi$
$770$	7.66464	−	2.50018i	0.276214	−	0.0901003i
$771$	−7.19797	−	23.7285i	−0.259228	−	0.854562i
$772$	28.6148	+	39.1942i	1.02987	+	1.41063i
$773$	5.30473	+	53.8598i	0.190798	+	1.93720i	0.323880	+	0.946098i	$0.395013\pi$
$773$	5.30473	+	53.8598i	0.190798	+	1.93720i	−0.133082	+	0.991105i	$0.542487\pi$
$774$	−2.67643	−	3.83071i	−0.0962025	−	0.137692i
$775$	35.6503	−	53.3544i	1.28059	−	1.91655i
$776$	2.33248	+	14.4035i	0.0837312	+	0.517056i
$777$	−2.79877	+	1.87008i	−0.100405	+	0.0670887i
$778$	−3.86140	−	8.80021i	−0.138438	−	0.315503i
$779$	22.3051	−	11.9223i	0.799163	−	0.427161i
$780$	−28.1810	+	37.4074i	−1.00904	+	1.33940i
$781$	0.0519858	+	0.00512015i	0.00186020	+	0.000183213i
$782$	−14.2929	+	50.9037i	−0.511112	+	1.82031i
$783$	−0.195223	+	0.0808642i	−0.00697672	+	0.00288985i
$784$	18.7642	−	1.56404i	0.670150	−	0.0558584i
$785$	−13.7621	−	5.70044i	−0.491190	−	0.203458i
$786$	−0.464864	+	0.591080i	−0.0165811	+	0.0210831i
$787$	6.03403	−	4.95200i	0.215090	−	0.176520i	−0.520679	−	0.853753i	$-0.674321\pi$
$787$	6.03403	−	4.95200i	0.215090	−	0.176520i	0.735769	+	0.677233i	$0.236821\pi$
$788$	−20.0366	+	17.8880i	−0.713774	+	0.637232i
$789$	16.2949	+	4.94300i	0.580114	+	0.175976i
$790$	21.2065	−	22.1072i	0.754495	−	0.786538i
$791$	4.05441	−	20.3829i	0.144158	−	0.724733i
$792$	−1.10557	−	2.25938i	−0.0392846	−	0.0802836i
$793$	34.3936	−	6.84132i	1.22135	−	0.242942i
$794$	−10.0506	+	2.21734i	−0.356682	+	0.0786905i
$795$	18.7464	+	15.3848i	0.664866	+	0.545642i
$796$	−28.4647	+	1.18424i	−1.00891	+	0.0419744i
$797$	2.15162	−	4.02539i	0.0762141	−	0.142587i	−0.840928	−	0.541147i	$-0.817990\pi$
$797$	2.15162	−	4.02539i	0.0762141	−	0.142587i	0.917142	+	0.398561i	$0.130490\pi$
$798$	−7.79980	+	6.67725i	−0.276110	+	0.236372i
$799$	−4.40396	+	4.40396i	−0.155801	+	0.155801i
$800$	−14.6756	−	71.6151i	−0.518860	−	2.53198i
$801$	−7.25305	−	7.25305i	−0.256274	−	0.256274i
$802$	−12.2922	−	0.953130i	−0.434051	−	0.0336562i
$803$	9.60212	+	5.13244i	0.338851	+	0.181120i
$804$	−25.0591	−	9.17908i	−0.883767	−	0.323721i
$805$	27.3859	−	33.3698i	0.965227	−	1.17613i
$806$	−20.9037	+	32.7381i	−0.736303	+	1.15315i
$807$	−2.65909	−	13.3682i	−0.0936044	−	0.470581i
$808$	23.7144	−	6.27603i	0.834268	−	0.220790i
$809$	−20.2292	−	4.02383i	−0.711219	−	0.141470i	−0.173794	−	0.984782i	$-0.555603\pi$
$809$	−20.2292	−	4.02383i	−0.711219	−	0.141470i	−0.537425	+	0.843312i	$0.680603\pi$
$810$	−5.98585	+	0.124464i	−0.210321	+	0.00437321i
$811$	0.867555	−	2.85994i	0.0304640	−	0.100426i	−0.940390	−	0.340098i	$-0.889540\pi$
$811$	0.867555	−	2.85994i	0.0304640	−	0.100426i	0.970854	+	0.239672i	$0.0770398\pi$
$812$	−0.576401	−	0.277932i	−0.0202277	−	0.00975350i
$813$	15.6946	+	19.1240i	0.550435	+	0.670707i
$814$	−0.331829	−	2.77613i	−0.0116306	−	0.0973034i
$815$	26.1451	−	63.1197i	0.915821	−	2.21099i
$816$	20.3863	+	8.80515i	0.713662	+	0.308242i
$817$	−6.06327	−	14.6380i	−0.212127	−	0.512120i
$818$	31.7587	−	17.8339i	1.11042	−	0.623549i
$819$	−0.820930	+	8.33504i	−0.0286856	+	0.291250i
$820$	22.6722	+	38.4784i	0.791746	+	1.34372i
$821$	−0.843021	−	1.57718i	−0.0294216	−	0.0550440i	0.866781	−	0.498689i	$-0.166185\pi$
$821$	−0.843021	−	1.57718i	−0.0294216	−	0.0550440i	−0.896203	+	0.443645i	$0.853685\pi$
$822$	−19.2975	−	7.52719i	−0.673077	−	0.262541i
$823$	5.95871	+	8.91785i	0.207708	+	0.310857i	0.920667	−	0.390349i	$-0.127646\pi$
$823$	5.95871	+	8.91785i	0.207708	+	0.310857i	−0.712959	+	0.701205i	$0.752646\pi$
$824$	−12.1079	+	26.5053i	−0.421799	+	0.923355i
$825$	9.55576	+	6.38495i	0.332689	+	0.222296i
$826$	−4.46776	+	25.1867i	−0.155453	+	0.876358i
$827$	20.1044	−	1.98011i	0.699098	−	0.0688551i	0.257777	−	0.966204i	$-0.417010\pi$
$827$	20.1044	−	1.98011i	0.699098	−	0.0688551i	0.441321	+	0.897349i	$0.354510\pi$
$828$	−11.5001	−	7.01076i	−0.399655	−	0.243641i
$829$	38.0858	−	11.5532i	1.32277	−	0.401259i	0.451594	−	0.892223i	$-0.350855\pi$
$829$	38.0858	−	11.5532i	1.32277	−	0.401259i	0.871180	+	0.490964i	$0.163355\pi$
$830$	−0.636128	+	1.25204i	−0.0220803	+	0.0434591i
$831$		−	5.24942i		−	0.182100i
$832$	9.78268	+	43.1560i	0.339153	+	1.49616i
$833$		−	26.1333i		−	0.905465i
$834$	26.3269	+	13.3759i	0.911626	+	0.463171i
$835$	82.0564	−	24.8915i	2.83968	−	0.861407i
$836$	−2.01006	−	8.28811i	−0.0695194	−	0.286650i
$837$	−4.94157	+	0.486703i	−0.170806	+	0.0168229i
$838$	53.7760	+	9.53909i	1.85766	+	0.329523i
$839$	34.3670	+	22.9633i	1.18648	+	0.792781i	0.982512	−	0.186197i	$-0.0596163\pi$
$839$	34.3670	+	22.9633i	1.18648	+	0.792781i	0.203967	+	0.978978i	$0.434616\pi$
$840$	−12.3534	−	13.2713i	−0.426233	−	0.457903i
$841$	16.0867	+	24.0755i	0.554715	+	0.830189i
$842$	0.573999	−	1.47156i	0.0197813	−	0.0507134i
$843$	−8.06509	−	15.0887i	−0.277776	−	0.519683i
$844$	42.7444	+	11.0486i	1.47132	+	0.380309i
$845$	−7.30162	+	74.1346i	−0.251184	+	2.55031i
$846$	−0.776819	−	1.38336i	−0.0267076	−	0.0475609i
$847$	−5.91561	−	14.2816i	−0.203263	−	0.490720i
$848$	22.5376	−	4.13224i	0.773945	−	0.141902i
$849$	1.87913	−	4.53663i	0.0644916	−	0.155697i
$850$	−100.744	+	12.0418i	−3.45548	+	0.413030i
$851$	−9.49728	−	11.5725i	−0.325563	−	0.396699i
$852$	−0.0387454	−	0.110904i	−0.00132740	−	0.00379951i
$853$	−9.09382	+	29.9783i	−0.311367	+	1.02644i	0.651993	+	0.758225i	$0.273933\pi$
$853$	−9.09382	+	29.9783i	−0.311367	+	1.02644i	−0.963360	+	0.268213i	$0.913567\pi$
$854$	0.282216	+	13.5727i	0.00965724	+	0.464448i
$855$	−19.9094	−	3.96023i	−0.680888	−	0.135437i
$856$	−12.5150	+	9.54197i	−0.427752	+	0.326138i
$857$	−5.57990	−	28.0520i	−0.190606	−	0.958239i	−0.951097	−	0.308892i	$-0.900042\pi$
$857$	−5.57990	−	28.0520i	−0.190606	−	0.958239i	0.760492	−	0.649348i	$-0.224958\pi$
$858$	−5.86338	−	3.74386i	−0.200173	−	0.127813i
$859$	9.18107	−	11.1872i	0.313254	−	0.381701i	−0.592453	−	0.805605i	$-0.701840\pi$
$859$	9.18107	−	11.1872i	0.313254	−	0.381701i	0.905707	+	0.423904i	$0.139340\pi$
$860$	25.3813	−	11.7721i	0.865494	−	0.401425i
$861$	7.04363	+	3.76490i	0.240046	+	0.128307i
$862$	1.79373	−	23.1330i	0.0610946	−	0.787914i
$863$	−41.2578	−	41.2578i	−1.40443	−	1.40443i	−0.785240	−	0.619191i	$-0.787461\pi$
$863$	−41.2578	−	41.2578i	−1.40443	−	1.40443i	−0.619191	−	0.785240i	$-0.712539\pi$
$864$	−3.56336	+	4.39346i	−0.121228	+	0.149469i
$865$	21.6064	−	21.6064i	0.734639	−	0.734639i
$866$	−20.6761	−	24.1520i	−0.702601	−	0.820719i
$867$	6.51501	−	12.1887i	0.221261	−	0.413951i
$868$	−11.0656	−	10.1817i	−0.375592	−	0.345588i
$869$	3.51744	+	2.88669i	0.119321	+	0.0979241i
$870$	−0.272557	−	1.23543i	−0.00924055	−	0.0418849i
$871$	−72.3905	+	14.3994i	−2.45286	+	0.487904i
$872$	2.21880	+	35.5288i	0.0751382	+	1.20316i
$873$	−1.00642	+	5.05962i	−0.0340622	+	0.171242i
$874$	−32.9545	−	31.6120i	−1.11470	−	1.06929i
$875$	48.6015	+	14.7431i	1.64303	+	0.498408i
$876$	1.38502	−	24.4464i	0.0467954	−	0.825967i
$877$	1.20697	−	0.990536i	0.0407565	−	0.0334480i	−0.613795	−	0.789466i	$-0.710358\pi$
$877$	1.20697	−	0.990536i	0.0407565	−	0.0334480i	0.654551	+	0.756018i	$0.272858\pi$
$878$	33.2099	+	26.1184i	1.12078	+	0.881454i
$879$	−9.49274	−	3.93202i	−0.320182	−	0.132624i
$880$	14.4754	−	4.15478i	0.487966	−	0.140058i
$881$	4.34037	−	1.79784i	0.146231	−	0.0605708i	−0.308368	−	0.951267i	$-0.599783\pi$
$881$	4.34037	−	1.79784i	0.146231	−	0.0605708i	0.454599	+	0.890696i	$0.349783\pi$
$882$	6.40929	+	1.79962i	0.215812	+	0.0605963i
$883$	40.7416	+	4.01270i	1.37107	+	0.135038i	0.756586	−	0.653895i	$-0.226866\pi$
$883$	40.7416	+	4.01270i	1.37107	+	0.135038i	0.614480	+	0.788933i	$0.289366\pi$
$884$	60.8174	−	8.55529i	2.04551	−	0.287745i
$885$	−44.6012	+	23.8398i	−1.49925	+	0.801367i
$886$	−5.22580	+	2.29301i	−0.175564	+	0.0770350i
$887$	8.08360	−	5.40129i	0.271421	−	0.181358i	−0.412410	−	0.910998i	$-0.635313\pi$
$887$	8.08360	−	5.40129i	0.271421	−	0.181358i	0.683830	+	0.729641i	$0.260313\pi$
$888$	−5.34976	+	3.30389i	−0.179526	+	0.110871i
$889$	−3.72626	+	5.57675i	−0.124975	+	0.187038i
$890$	50.3422	−	35.1730i	1.68747	−	1.17900i
$891$	−0.0871683	−	0.885035i	−0.00292025	−	0.0296498i
$892$	52.6959	+	8.22148i	1.76439	+	0.275275i
$893$	−1.56150	−	5.14757i	−0.0522536	−	0.172257i
$894$	5.11301	+	15.6746i	0.171005	+	0.524237i
$895$	−59.4664			−1.98774
$896$	−17.1116	+	0.810925i	−0.571658	+	0.0270911i
$897$	−37.2498			−1.24373
$898$	0.557817	+	1.71006i	0.0186146	+	0.0570655i
$899$	−0.304581	−	1.00407i	−0.0101583	−	0.0334875i
$900$	3.98421	−	25.5370i	0.132807	−	0.851233i
$901$	−3.11710	−	31.6484i	−0.103846	−	1.05436i
$902$	−5.43804	+	3.79944i	−0.181067	+	0.126508i
$903$	2.77971	−	4.16012i	0.0925028	−	0.138440i
$904$	8.93170	−	37.7794i	0.297064	−	1.25652i
$905$	19.4713	−	13.0103i	0.647250	−	0.432478i
$906$	6.64217	−	2.91449i	0.220671	−	0.0968275i
$907$	−4.33011	+	2.31449i	−0.143779	+	0.0768514i	−0.541717	−	0.840561i	$-0.682226\pi$
$907$	−4.33011	+	2.31449i	−0.143779	+	0.0768514i	0.397939	+	0.917412i	$0.369726\pi$
$908$	−5.72265	−	40.6809i	−0.189913	−	1.35004i
$909$	8.63118	+	0.850097i	0.286278	+	0.0281959i
$910$	−48.2776	−	13.5555i	−1.60039	−	0.449361i
$911$	−19.4982	+	8.07643i	−0.646005	+	0.267584i	−0.681536	−	0.731784i	$-0.738688\pi$
$911$	−19.4982	+	8.07643i	−0.646005	+	0.267584i	0.0355309	+	0.999369i	$0.488688\pi$
$912$	−15.0070	+	11.9434i	−0.496933	+	0.395487i
$913$	−0.192724	−	0.0798288i	−0.00637823	−	0.00264195i
$914$	21.6182	+	17.0019i	0.715065	+	0.562374i
$915$	−20.7474	+	17.0269i	−0.685886	+	0.562892i
$916$	37.6406	+	2.13254i	1.24368	+	0.0704612i
$917$	−0.770456	−	0.233715i	−0.0254427	−	0.00771796i
$918$	5.66584	+	5.43502i	0.187001	+	0.179383i
$919$	5.91185	−	29.7209i	0.195014	−	0.980400i	−0.751989	−	0.659176i	$-0.770905\pi$
$919$	5.91185	−	29.7209i	0.195014	−	0.980400i	0.947003	−	0.321225i	$-0.104095\pi$
$920$	53.3550	−	60.4631i	1.75906	−	1.99341i
$921$	15.5123	−	3.08559i	0.511148	−	0.101674i
$922$	−4.70578	−	21.3300i	−0.154977	−	0.702466i
$923$	−0.251155	−	0.206117i	−0.00826686	−	0.00678444i
$924$	1.82353	−	1.98185i	0.0599898	−	0.0651981i
$925$	13.5425	−	25.3362i	0.445273	−	0.833048i
$926$	15.5282	+	18.1387i	0.510289	+	0.596076i
$927$	−7.28497	+	7.28497i	−0.239270	+	0.239270i
$928$	−1.05743	−	0.557382i	−0.0347119	−	0.0182970i
$929$	21.1880	+	21.1880i	0.695154	+	0.695154i	0.963361	−	0.268207i	$-0.0864311\pi$
$929$	21.1880	+	21.1880i	0.695154	+	0.695154i	−0.268207	+	0.963361i	$0.586431\pi$
$930$	2.29828	−	29.6401i	0.0753637	−	0.971938i
$931$	19.9059	+	10.6399i	0.652391	+	0.348710i
$932$	−2.49516	−	5.37970i	−0.0817317	−	0.176218i
$933$	−10.5161	+	12.8139i	−0.344281	+	0.419508i
$934$	18.0787	+	11.5435i	0.591554	+	0.377716i
$935$	−4.07773	−	20.5001i	−0.133356	−	0.670425i
$936$	−2.08985	+	15.5048i	−0.0683090	+	0.506792i
$937$	−7.48812	−	1.48948i	−0.244626	−	0.0486592i	0.0712541	−	0.997458i	$-0.477300\pi$
$937$	−7.48812	−	1.48948i	−0.244626	−	0.0486592i	−0.315880	+	0.948799i	$0.602300\pi$
$938$	−0.593998	−	28.5673i	−0.0193947	−	0.932754i
$939$	−6.48144	+	21.3664i	−0.211514	+	0.697267i
$940$	8.96739	−	3.13285i	0.292484	−	0.102182i
$941$	2.31868	+	2.82532i	0.0755869	+	0.0921029i	0.809431	−	0.587215i	$-0.199776\pi$
$941$	2.31868	+	2.82532i	0.0755869	+	0.0921029i	−0.733844	+	0.679318i	$0.762276\pi$
$942$	−4.94082	+	0.590572i	−0.160980	+	0.0192419i
$943$	−13.5933	+	32.8172i	−0.442660	+	1.06867i
$944$	−10.0246	+	46.7194i	−0.326272	+	1.52059i
$945$	−2.45311	−	5.92233i	−0.0797996	−	0.192653i
$946$	2.03482	+	3.62361i	0.0661577	+	0.117814i
$947$	−3.58320	+	36.3809i	−0.116438	+	1.18222i	0.742395	+	0.669963i	$0.233690\pi$
$947$	−3.58320	+	36.3809i	−0.116438	+	1.18222i	−0.858833	+	0.512256i	$0.828810\pi$
$948$	2.56093	−	9.90764i	0.0831753	−	0.321785i
$949$	−31.9227	−	59.7231i	−1.03625	−	1.93869i
$950$	31.8446	−	81.6399i	1.03317	−	2.64875i
$951$	1.21373	+	1.81648i	0.0393580	+	0.0589035i
$952$	−0.851113	+	23.7607i	−0.0275847	+	0.770089i
$953$	−38.9574	−	26.0305i	−1.26195	−	0.843211i	−0.269166	−	0.963094i	$-0.586748\pi$
$953$	−38.9574	−	26.0305i	−1.26195	−	0.843211i	−0.992788	+	0.119883i	$0.961748\pi$
$954$	7.97655	+	1.41493i	0.258250	+	0.0458099i
$955$	−11.9367	+	1.17567i	−0.386263	+	0.0380436i
$956$	43.8826	−	10.6425i	1.41926	−	0.344205i
$957$	0.179828	−	0.0545503i	0.00581303	−	0.00176336i
$958$	42.2718	+	21.4771i	1.36574	+	0.693894i
$959$		−	22.1775i		−	0.716147i
$960$	−22.1737	−	25.6007i	−0.715654	−	0.826259i
$961$			6.34396i			0.204644i
$962$	−7.87693	+	15.5036i	−0.253962	+	0.499856i
$963$	−5.32451	+	1.61517i	−0.171580	+	0.0520482i
$964$	−11.9539	+	19.6085i	−0.385008	+	0.631546i
$965$	−102.229	+	10.0687i	−3.29086	+	0.324122i
$966$	2.51866	−	14.1988i	0.0810367	−	0.456839i
$967$	35.1762	+	23.5040i	1.13119	+	0.755837i	0.972825	−	0.231544i	$-0.0743776\pi$
$967$	35.1762	+	23.5040i	1.13119	+	0.755837i	0.158365	+	0.987381i	$0.449378\pi$
$968$	−10.0882	−	27.0562i	−0.324247	−	0.869618i
$969$	14.7890	+	22.1333i	0.475092	+	0.711025i
$970$	−28.7747	−	11.2239i	−0.923898	−	0.360377i
$971$	8.44190	+	15.7937i	0.270913	+	0.506843i	0.980183	−	0.198094i	$-0.0634751\pi$
$971$	8.44190	+	15.7937i	0.270913	+	0.506843i	−0.709270	+	0.704937i	$0.750975\pi$
$972$	−1.72313	+	1.01530i	−0.0552694	+	0.0325657i
$973$	−3.09901	+	31.4647i	−0.0993496	+	1.00871i
$974$	−40.6095	+	22.8040i	−1.30121	+	0.730689i
$975$	−27.3548	−	66.0403i	−0.876055	−	2.11498i
$976$	−0.380749	+	25.3562i	−0.0121875	+	0.811631i
$977$	−21.5068	+	51.9221i	−0.688064	+	1.66113i	0.0605805	+	0.998163i	$0.480705\pi$
$977$	−21.5068	+	51.9221i	−0.688064	+	1.66113i	−0.748645	+	0.662971i	$0.769295\pi$
$978$	−2.70865	−	22.6610i	−0.0866132	−	0.724620i
$979$	5.78696	+	7.05144i	0.184952	+	0.225365i
$980$	−17.3112	+	35.9017i	−0.552987	+	1.14684i
$981$	−3.65346	+	12.0438i	−0.116646	+	0.384530i
$982$	−59.6166	+	1.23961i	−1.90244	+	0.0395574i
$983$	5.05932	+	1.00636i	0.161367	+	0.0320979i	0.275113	−	0.961412i	$-0.411285\pi$
$983$	5.05932	+	1.00636i	0.161367	+	0.0320979i	−0.113745	+	0.993510i	$0.536285\pi$
$984$	12.8972	+	7.49925i	0.411147	+	0.239067i
$985$	−11.0920	−	55.7635i	−0.353422	−	1.77677i
$986$	−0.892829	+	1.39829i	−0.0284335	+	0.0445306i
$987$	1.07763	−	1.31309i	0.0343013	−	0.0417962i
$988$	−18.2446	+	49.8083i	−0.580440	+	1.58461i
$989$	19.6250	+	10.4898i	0.624038	+	0.333555i
$990$	5.30854	+	0.411622i	0.168716	+	0.0130822i
$991$	17.7466	+	17.7466i	0.563738	+	0.563738i	0.930367	−	0.366629i	$-0.119488\pi$
$991$	17.7466	+	17.7466i	0.563738	+	0.563738i	−0.366629	+	0.930367i	$0.619488\pi$
$992$	−19.9763	−	19.7469i	−0.634248	−	0.626965i
$993$	−6.81142	+	6.81142i	−0.216154	+	0.216154i
$994$	0.0955494	−	0.0817979i	0.00303064	−	0.00259447i
$995$	28.4278	−	53.1847i	0.901223	−	1.68607i
$996$	0.0195008	+	0.468725i	0.000617906	+	0.0148521i
$997$	−26.8550	−	22.0393i	−0.850507	−	0.697993i	0.104516	−	0.994523i	$-0.466671\pi$
$997$	−26.8550	−	22.0393i	−0.850507	−	0.697993i	−0.955024	+	0.296530i	$0.904171\pi$
$998$	0.333280	−	0.0735276i	0.0105498	−	0.00232747i
$999$	−2.18033	+	0.433695i	−0.0689827	+	0.0137215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.3	✓	512
128.69	even	32	inner	384.2.v.a.325.3	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.3	✓	512	1.1	even	1	trivial
384.2.v.a.325.3	yes	512	128.69	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34449 + 0.438569i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.61531 - 1.17931i) q^{4} +(0.414961 + 4.21317i) q^{5} +(0.809970 + 1.15929i) q^{6} +(-0.841223 + 1.25898i) q^{7} +(-1.65457 + 2.29399i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.34449 + 0.438569i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.61531 - 1.17931i) q^{4} +(0.414961 + 4.21317i) q^{5} +(0.809970 + 1.15929i) q^{6} +(-0.841223 + 1.25898i) q^{7} +(-1.65457 + 2.29399i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-2.40568 - 5.48258i) q^{10} +(0.784308 - 0.419221i) q^{11} +(-1.59743 - 1.20342i) q^{12} +(-5.50473 - 0.542168i) q^{13} +(0.578867 - 2.06162i) q^{14} +(3.91129 - 1.62011i) q^{15} +(1.21848 - 3.80990i) q^{16} +(-5.12904 - 2.12452i) q^{17} +(0.874248 - 1.11162i) q^{18} +(3.70651 - 3.04185i) q^{19} +(5.63890 + 6.31622i) q^{20} +(1.44896 + 0.439538i) q^{21} +(-0.870637 + 0.907612i) q^{22} +(-1.31379 + 6.60489i) q^{23} +(2.67551 + 0.917413i) q^{24} +(-12.6747 + 2.52114i) q^{25} +(7.63883 - 1.68526i) q^{26} +(0.773010 + 0.634393i) q^{27} +(0.125881 + 3.02571i) q^{28} +(-0.0996101 + 0.186357i) q^{29} +(-4.54817 + 3.89360i) q^{30} +(-3.51113 + 3.51113i) q^{31} +(0.0326686 + 5.65676i) q^{32} +(-0.628842 - 0.628842i) q^{33} +(7.82770 + 0.606957i) q^{34} +(-5.65336 - 3.02179i) q^{35} +(-0.687898 + 1.87798i) q^{36} +(-1.41029 + 1.71844i) q^{37} +(-3.64931 + 5.71531i) q^{38} +(1.07911 + 5.42508i) q^{39} +(-10.3516 - 6.01906i) q^{40} +(5.17331 + 1.02903i) q^{41} +(-2.14088 + 0.0445153i) q^{42} +(0.959206 - 3.16208i) q^{43} +(0.772514 - 1.60211i) q^{44} +(-2.68574 - 3.27258i) q^{45} +(-1.13032 - 9.45641i) q^{46} +(0.429316 - 1.03646i) q^{47} +(-3.99955 - 0.0600573i) q^{48} +(1.80141 + 4.34899i) q^{49} +(15.9353 - 8.94837i) q^{50} +(-0.544155 + 5.52490i) q^{51} +(-9.53124 + 5.61598i) q^{52} +(2.70031 + 5.05193i) q^{53} +(-1.31753 - 0.513918i) q^{54} +(2.09171 + 3.13046i) q^{55} +(-1.49623 - 4.01283i) q^{56} +(-3.98681 - 2.66390i) q^{57} +(0.0521943 - 0.294242i) q^{58} +(-11.8882 + 1.17088i) q^{59} +(4.40736 - 7.22959i) q^{60} +(-6.06677 + 1.84033i) q^{61} +(3.18081 - 6.26055i) q^{62} -1.51416i q^{63} +(-2.52480 - 7.59114i) q^{64} -23.4173i q^{65} +(1.12126 + 0.569682i) q^{66} +(12.7691 - 3.87346i) q^{67} +(-10.7905 + 2.61694i) q^{68} +(6.70186 - 0.660076i) q^{69} +(8.92616 + 1.58337i) q^{70} +(0.0488394 + 0.0326335i) q^{71} +(0.101250 - 2.82661i) q^{72} +(6.80173 + 10.1795i) q^{73} +(1.14246 - 2.92894i) q^{74} +(6.09184 + 11.3970i) q^{75} +(2.39990 - 9.28465i) q^{76} +(-0.131987 + 1.34009i) q^{77} +(-3.83013 - 6.82070i) q^{78} +(1.95805 + 4.72715i) q^{79} +(16.5573 + 3.55270i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-7.40677 + 0.885325i) q^{82} +(-0.148807 - 0.181321i) q^{83} +(2.85888 - 0.998777i) q^{84} +(6.82260 - 22.4911i) q^{85} +(0.0971461 + 4.67207i) q^{86} +(0.207248 + 0.0412242i) q^{87} +(-0.336001 + 2.49283i) q^{88} +(2.00111 + 10.0603i) q^{89} +(5.04620 + 3.22207i) q^{90} +(5.31328 - 6.47425i) q^{91} +(5.66699 + 12.2183i) q^{92} +(4.37917 + 2.34071i) q^{93} +(-0.122652 + 1.58180i) q^{94} +(14.3539 + 14.3539i) q^{95} +(5.40370 - 1.67333i) q^{96} +(3.64779 - 3.64779i) q^{97} +(-4.32932 - 5.05714i) q^{98} +(-0.419221 + 0.784308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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