LMFDB - Embedded newform 384.2.v.a.37.5

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			37.5
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26619 + 0.629900i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.20645 - 1.59514i) q^{4} +(2.98357 - 2.44855i) q^{5} +(-1.15240 - 0.819743i) q^{6} +(-2.04572 + 1.36691i) q^{7} +(-0.522814 + 2.77969i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(-1.26619 + 0.629900i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.20645 - 1.59514i) q^{4} +(2.98357 - 2.44855i) q^{5} +(-1.15240 - 0.819743i) q^{6} +(-2.04572 + 1.36691i) q^{7} +(-0.522814 + 2.77969i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-2.23541 + 4.97967i) q^{10} +(0.959618 + 3.16344i) q^{11} +(1.97551 + 0.312052i) q^{12} +(4.43568 - 5.40489i) q^{13} +(1.72925 - 3.01936i) q^{14} +(3.56587 + 1.47703i) q^{15} +(-1.08895 - 3.84892i) q^{16} +(-3.65108 + 1.51233i) q^{17} +(0.179713 - 1.40275i) q^{18} +(5.95936 - 0.586946i) q^{19} +(-0.306249 - 7.71326i) q^{20} +(-2.16985 - 1.15981i) q^{21} +(-3.20770 - 3.40104i) q^{22} +(1.08122 - 0.215068i) q^{23} +(-2.69792 + 0.849255i) q^{24} +(1.93082 - 9.70689i) q^{25} +(-2.21185 + 9.63763i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-0.287657 + 4.91233i) q^{28} +(5.57069 + 1.68985i) q^{29} +(-5.44544 + 0.375945i) q^{30} +(-1.83643 - 1.83643i) q^{31} +(3.80324 + 4.18752i) q^{32} +(-2.33754 + 2.33754i) q^{33} +(3.67033 - 4.21470i) q^{34} +(-2.75661 + 9.08732i) q^{35} +(0.656042 + 1.88934i) q^{36} +(-0.175248 + 1.77933i) q^{37} +(-7.17594 + 4.49699i) q^{38} +(6.85765 + 1.36407i) q^{39} +(5.24635 + 9.57352i) q^{40} +(2.09598 + 10.5372i) q^{41} +(3.47800 + 0.101746i) q^{42} +(1.80711 - 3.38086i) q^{43} +(6.20386 + 2.28581i) q^{44} +(0.378314 + 3.84109i) q^{45} +(-1.23355 + 0.953376i) q^{46} +(-1.08886 - 2.62875i) q^{47} +(2.88112 - 2.77473i) q^{48} +(-0.362239 + 0.874522i) q^{49} +(3.66959 + 13.5070i) q^{50} +(-3.05486 - 2.50706i) q^{51} +(-3.27012 - 13.5963i) q^{52} +(-5.92059 + 1.79599i) q^{53} +(1.32183 - 0.502759i) q^{54} +(10.6089 + 7.08865i) q^{55} +(-2.73005 - 6.40111i) q^{56} +(3.32687 + 4.97901i) q^{57} +(-8.11796 + 1.36931i) q^{58} +(-9.26227 - 11.2861i) q^{59} +(6.65813 - 3.90610i) q^{60} +(-0.421211 + 0.225142i) q^{61} +(3.48202 + 1.16849i) q^{62} -2.46037i q^{63} +(-7.45333 - 2.90652i) q^{64} -26.9868i q^{65} +(1.48734 - 4.43218i) q^{66} +(-3.99868 + 2.13734i) q^{67} +(-1.99248 + 7.64853i) q^{68} +(0.699356 + 0.852168i) q^{69} +(-2.23372 - 13.2426i) q^{70} +(1.75803 + 2.63108i) q^{71} +(-2.02077 - 1.97902i) q^{72} +(-4.01832 - 2.68495i) q^{73} +(-0.898901 - 2.36335i) q^{74} +(9.47090 - 2.87297i) q^{75} +(6.25343 - 10.2141i) q^{76} +(-6.28724 - 5.15981i) q^{77} +(-9.54229 + 2.59247i) q^{78} +(-3.57266 + 8.62517i) q^{79} +(-12.6732 - 8.81718i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-9.29128 - 12.0218i) q^{82} +(0.707625 + 7.18464i) q^{83} +(-4.46789 + 2.06196i) q^{84} +(-7.19022 + 13.4520i) q^{85} +(-0.158530 + 5.41909i) q^{86} +(1.13569 + 5.70950i) q^{87} +(-9.29507 + 1.01355i) q^{88} +(9.88754 + 1.96675i) q^{89} +(-2.89851 - 4.62523i) q^{90} +(-1.68618 + 17.1201i) q^{91} +(0.961376 - 1.98417i) q^{92} +(0.753898 - 2.48527i) q^{93} +(3.03455 + 2.64261i) q^{94} +(16.3430 - 16.3430i) q^{95} +(-1.90023 + 5.32814i) q^{96} +(-8.11239 - 8.11239i) q^{97} +(-0.0921996 - 1.33548i) q^{98} +(-3.16344 - 0.959618i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

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 $

$2$	−1.26619	+	0.629900i	−0.895328	+	0.445406i
$2$	−1.26619	+	0.629900i	−0.895328	+	0.445406i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$4$	1.20645	−	1.59514i	0.603226	−	0.797570i
$5$	2.98357	−	2.44855i	1.33429	−	1.09502i	0.346700	−	0.937976i	$-0.387302\pi$
$5$	2.98357	−	2.44855i	1.33429	−	1.09502i	0.987591	−	0.157049i	$-0.0501980\pi$
$6$	−1.15240	−	0.819743i	−0.470464	−	0.334659i
$7$	−2.04572	+	1.36691i	−0.773211	+	0.516643i	−0.878467	−	0.477802i	$-0.841434\pi$
$7$	−2.04572	+	1.36691i	−0.773211	+	0.516643i	0.105257	+	0.994445i	$0.466434\pi$
$8$	−0.522814	+	2.77969i	−0.184843	+	0.982768i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	−2.23541	+	4.97967i	−0.706898	+	1.57471i
$11$	0.959618	+	3.16344i	0.289336	+	0.953812i	0.974304	+	0.225239i	$0.0723163\pi$
$11$	0.959618	+	3.16344i	0.289336	+	0.953812i	−0.684968	+	0.728573i	$0.740184\pi$
$12$	1.97551	+	0.312052i	0.570279	+	0.0900817i
$13$	4.43568	−	5.40489i	1.23024	−	1.49905i	0.426017	−	0.904715i	$-0.359916\pi$
$13$	4.43568	−	5.40489i	1.23024	−	1.49905i	0.804220	−	0.594332i	$-0.202584\pi$
$14$	1.72925	−	3.01936i	0.462162	−	0.806958i
$15$	3.56587	+	1.47703i	0.920704	+	0.381368i
$16$	−1.08895	−	3.84892i	−0.272236	−	0.962230i
$17$	−3.65108	+	1.51233i	−0.885516	+	0.366793i	−0.778634	−	0.627479i	$-0.784087\pi$
$17$	−3.65108	+	1.51233i	−0.885516	+	0.366793i	−0.106882	+	0.994272i	$0.534087\pi$
$18$	0.179713	−	1.40275i	0.0423586	−	0.330631i
$19$	5.95936	−	0.586946i	1.36717	−	0.134655i	0.612351	−	0.790586i	$-0.290224\pi$
$19$	5.95936	−	0.586946i	1.36717	−	0.134655i	0.754821	+	0.655931i	$0.227724\pi$
$20$	−0.306249	−	7.71326i	−0.0684795	−	1.72474i
$21$	−2.16985	−	1.15981i	−0.473501	−	0.253091i
$22$	−3.20770	−	3.40104i	−0.683885	−	0.725103i
$23$	1.08122	−	0.215068i	0.225450	−	0.0448448i	−0.0810726	−	0.996708i	$-0.525835\pi$
$23$	1.08122	−	0.215068i	0.225450	−	0.0448448i	0.306522	+	0.951863i	$0.400835\pi$
$24$	−2.69792	+	0.849255i	−0.550710	+	0.173353i
$25$	1.93082	−	9.70689i	0.386164	−	1.94138i
$26$	−2.21185	+	9.63763i	−0.433780	+	1.89010i
$27$	−0.995185	−	0.0980171i	−0.191523	−	0.0188634i
$28$	−0.287657	+	4.91233i	−0.0543620	+	0.928342i
$29$	5.57069	+	1.68985i	1.03445	+	0.313797i	0.761455	−	0.648218i	$-0.224485\pi$
$29$	5.57069	+	1.68985i	1.03445	+	0.313797i	0.272996	+	0.962015i	$0.411985\pi$
$30$	−5.44544	+	0.375945i	−0.994196	+	0.0686378i
$31$	−1.83643	−	1.83643i	−0.329832	−	0.329832i	0.522690	−	0.852523i	$-0.324928\pi$
$31$	−1.83643	−	1.83643i	−0.329832	−	0.329832i	−0.852523	+	0.522690i	$0.824928\pi$
$32$	3.80324	+	4.18752i	0.672325	+	0.740256i
$33$	−2.33754	+	2.33754i	−0.406914	+	0.406914i
$34$	3.67033	−	4.21470i	0.629456	−	0.722814i
$35$	−2.75661	+	9.08732i	−0.465952	+	1.53604i
$36$	0.656042	+	1.88934i	0.109340	+	0.314890i
$37$	−0.175248	+	1.77933i	−0.0288107	+	0.292519i	0.969973	+	0.243213i	$0.0782013\pi$
$37$	−0.175248	+	1.77933i	−0.0288107	+	0.292519i	−0.998784	+	0.0493069i	$0.984299\pi$
$38$	−7.17594	+	4.49699i	−1.16409	+	0.729507i
$39$	6.85765	+	1.36407i	1.09810	+	0.218426i
$40$	5.24635	+	9.57352i	0.829521	+	1.51371i
$41$	2.09598	+	10.5372i	0.327337	+	1.64563i	0.697440	+	0.716644i	$0.254323\pi$
$41$	2.09598	+	10.5372i	0.327337	+	1.64563i	−0.370103	+	0.928991i	$0.620677\pi$
$42$	3.47800	+	0.101746i	0.536667	+	0.0156997i
$43$	1.80711	−	3.38086i	0.275581	−	0.515576i	−0.705613	−	0.708597i	$-0.749328\pi$
$43$	1.80711	−	3.38086i	0.275581	−	0.515576i	0.981195	+	0.193021i	$0.0618285\pi$
$44$	6.20386	+	2.28581i	0.935267	+	0.344599i
$45$	0.378314	+	3.84109i	0.0563957	+	0.572595i
$46$	−1.23355	+	0.953376i	−0.181878	+	0.140568i
$47$	−1.08886	−	2.62875i	−0.158827	−	0.383443i	0.824354	−	0.566074i	$-0.191538\pi$
$47$	−1.08886	−	2.62875i	−0.158827	−	0.383443i	−0.983181	+	0.182631i	$0.941538\pi$
$48$	2.88112	−	2.77473i	0.415854	−	0.400498i
$49$	−0.362239	+	0.874522i	−0.0517484	+	0.124932i
$50$	3.66959	+	13.5070i	0.518959	+	1.91017i
$51$	−3.05486	−	2.50706i	−0.427766	−	0.351058i
$52$	−3.27012	−	13.5963i	−0.453485	−	1.88546i
$53$	−5.92059	+	1.79599i	−0.813255	+	0.246698i	−0.669402	−	0.742901i	$-0.733449\pi$
$53$	−5.92059	+	1.79599i	−0.813255	+	0.246698i	−0.143854	+	0.989599i	$0.545949\pi$
$54$	1.32183	−	0.502759i	0.179878	−	0.0684168i
$55$	10.6089	+	7.08865i	1.43051	+	0.955834i
$56$	−2.73005	−	6.40111i	−0.364818	−	0.855385i
$57$	3.32687	+	4.97901i	0.440654	+	0.659485i
$58$	−8.11796	+	1.36931i	−1.06594	+	0.179799i
$59$	−9.26227	−	11.2861i	−1.20585	−	1.46933i	−0.843370	−	0.537333i	$-0.819432\pi$
$59$	−9.26227	−	11.2861i	−1.20585	−	1.46933i	−0.362475	−	0.931993i	$-0.618068\pi$
$60$	6.65813	−	3.90610i	0.859561	−	0.504275i
$61$	−0.421211	+	0.225142i	−0.0539305	+	0.0288265i	−0.498142	−	0.867096i	$-0.665984\pi$
$61$	−0.421211	+	0.225142i	−0.0539305	+	0.0288265i	0.444211	+	0.895922i	$0.353484\pi$
$62$	3.48202	+	1.16849i	0.442217	+	0.148399i
$63$		−	2.46037i		−	0.309978i
$64$	−7.45333	−	2.90652i	−0.931666	−	0.363315i
$65$		−	26.9868i		−	3.34731i
$66$	1.48734	−	4.43218i	0.183080	−	0.545564i
$67$	−3.99868	+	2.13734i	−0.488517	+	0.261118i	−0.697215	−	0.716863i	$-0.745578\pi$
$67$	−3.99868	+	2.13734i	−0.488517	+	0.261118i	0.208698	+	0.977980i	$0.433078\pi$
$68$	−1.99248	+	7.64853i	−0.241623	+	0.927520i
$69$	0.699356	+	0.852168i	0.0841926	+	0.102589i
$70$	−2.23372	−	13.2426i	−0.266981	−	1.58280i
$71$	1.75803	+	2.63108i	0.208640	+	0.312252i	0.921000	−	0.389562i	$-0.127374\pi$
$71$	1.75803	+	2.63108i	0.208640	+	0.312252i	−0.712360	+	0.701814i	$0.752374\pi$
$72$	−2.02077	−	1.97902i	−0.238150	−	0.233229i
$73$	−4.01832	−	2.68495i	−0.470308	−	0.314250i	0.297734	−	0.954649i	$-0.403769\pi$
$73$	−4.01832	−	2.68495i	−0.470308	−	0.314250i	−0.768043	+	0.640399i	$0.778769\pi$
$74$	−0.898901	−	2.36335i	−0.104495	−	0.274733i
$75$	9.47090	−	2.87297i	1.09360	−	0.331741i
$76$	6.25343	−	10.2141i	0.717317	−	1.17164i
$77$	−6.28724	−	5.15981i	−0.716498	−	0.588015i
$78$	−9.54229	+	2.59247i	−1.08045	+	0.293539i
$79$	−3.57266	+	8.62517i	−0.401956	+	0.970407i	0.585235	+	0.810864i	$0.301002\pi$
$79$	−3.57266	+	8.62517i	−0.401956	+	0.970407i	−0.987191	+	0.159544i	$0.948998\pi$
$80$	−12.6732	−	8.81718i	−1.41691	−	0.985790i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−9.29128	−	12.0218i	−1.02605	−	1.32759i
$83$	0.707625	+	7.18464i	0.0776719	+	0.788616i	0.952572	+	0.304313i	$0.0984269\pi$
$83$	0.707625	+	7.18464i	0.0776719	+	0.788616i	−0.874900	+	0.484303i	$0.839073\pi$
$84$	−4.46789	+	2.06196i	−0.487486	+	0.224979i
$85$	−7.19022	+	13.4520i	−0.779889	+	1.45907i
$86$	−0.158530	+	5.41909i	−0.0170948	+	0.584356i
$87$	1.13569	+	5.70950i	0.121759	+	0.612122i
$88$	−9.29507	+	1.01355i	−0.990858	+	0.108045i
$89$	9.88754	+	1.96675i	1.04808	+	0.208475i	0.688947	−	0.724812i	$-0.258073\pi$
$89$	9.88754	+	1.96675i	1.04808	+	0.208475i	0.359130	+	0.933287i	$0.383073\pi$
$90$	−2.89851	−	4.62523i	−0.305530	−	0.487542i
$91$	−1.68618	+	17.1201i	−0.176760	+	1.79467i
$92$	0.961376	−	1.98417i	0.100230	−	0.206864i
$93$	0.753898	−	2.48527i	0.0781756	−	0.257711i
$94$	3.03455	+	2.64261i	0.312990	+	0.272565i
$95$	16.3430	−	16.3430i	1.67676	−	1.67676i
$96$	−1.90023	+	5.32814i	−0.193941	+	0.543801i
$97$	−8.11239	−	8.11239i	−0.823688	−	0.823688i	0.162947	−	0.986635i	$-0.447900\pi$
$97$	−8.11239	−	8.11239i	−0.823688	−	0.823688i	−0.986635	+	0.162947i	$0.947900\pi$
$98$	−0.0921996	−	1.33548i	−0.00931357	−	0.134904i
$99$	−3.16344	−	0.959618i	−0.317937	−	0.0964453i
$100$	−13.1544	−	14.7908i	−1.31544	−	1.47908i
$101$	2.05405	+	0.202307i	0.204386	+	0.0201303i	0.199692	−	0.979859i	$-0.436006\pi$
$101$	2.05405	+	0.202307i	0.204386	+	0.0201303i	0.00469404	+	0.999989i	$0.498506\pi$
$102$	5.44721	+	1.25014i	0.539354	+	0.123783i
$103$	1.44636	−	7.27132i	0.142514	−	0.716464i	−0.841765	−	0.539844i	$-0.818483\pi$
$103$	1.44636	−	7.27132i	0.142514	−	0.716464i	0.984279	−	0.176621i	$-0.0565166\pi$
$104$	12.7049	+	15.1556i	1.24582	+	1.48613i
$105$	−9.31375	+	1.85262i	−0.908929	+	0.180797i
$106$	6.36527	−	6.00343i	0.618249	−	0.583105i
$107$	−11.7341	−	6.27198i	−1.13437	−	0.606336i	−0.206210	−	0.978508i	$-0.566113\pi$
$107$	−11.7341	−	6.27198i	−1.13437	−	0.606336i	−0.928164	+	0.372172i	$0.878613\pi$
$108$	−1.35699	+	1.46921i	−0.130577	+	0.141374i
$109$	4.17695	−	0.411394i	0.400079	−	0.0394044i	0.104023	−	0.994575i	$-0.466828\pi$
$109$	4.17695	−	0.411394i	0.400079	−	0.0394044i	0.296056	+	0.955171i	$0.404328\pi$
$110$	−17.8980	−	2.29299i	−1.70651	−	0.218628i
$111$	−1.65184	+	0.684213i	−0.156785	+	0.0649427i
$112$	7.48881	+	6.38534i	0.707626	+	0.603358i
$113$	−15.8685	−	6.57293i	−1.49278	−	0.618329i	−0.520859	−	0.853643i	$-0.674388\pi$
$113$	−15.8685	−	6.57293i	−1.49278	−	0.618329i	−0.971919	+	0.235314i	$0.924388\pi$
$114$	−7.34870	−	4.20875i	−0.688269	−	0.394186i
$115$	2.69929	−	3.28909i	0.251710	−	0.306709i
$116$	9.41632	−	6.84731i	0.874283	−	0.635756i
$117$	2.02967	+	6.69093i	0.187643	+	0.618577i
$118$	18.8369	+	8.45601i	1.73408	+	0.778439i
$119$	5.40188	−	8.08449i	0.495190	−	0.741104i
$120$	−5.96998	+	9.13980i	−0.544982	+	0.834345i
$121$	0.0596949	−	0.0398869i	0.00542681	−	0.00362608i
$122$	0.391514	−	0.550392i	0.0354461	−	0.0498302i
$123$	−8.30494	+	6.81569i	−0.748832	+	0.614550i
$124$	−5.14492	+	0.713797i	−0.462028	+	0.0641009i
$125$	−8.90989	−	16.6692i	−0.796925	−	1.49094i
$126$	1.54979	+	3.11529i	0.138066	+	0.277532i
$127$	−11.1669			−0.990904			−0.495452	−	0.868635i	$-0.664998\pi$
$127$	−11.1669			−0.990904			−0.495452	+	0.868635i	$0.664998\pi$
$128$	11.2681	−	1.01466i	0.995970	−	0.0896839i
$129$	3.83352			0.337522
$130$	16.9990	+	34.1703i	1.49091	+	2.99694i
$131$	0.976252	+	1.82644i	0.0852955	+	0.159577i	0.920952	−	0.389675i	$-0.127413\pi$
$131$	0.976252	+	1.82644i	0.0852955	+	0.159577i	−0.835657	+	0.549252i	$0.814913\pi$
$132$	0.908574	+	6.54884i	0.0790812	+	0.570003i
$133$	−11.3889	+	9.34664i	−0.987544	+	0.810456i
$134$	3.71676	−	5.22504i	0.321080	−	0.451375i
$135$	−3.20920	+	2.14432i	−0.276204	+	0.184554i
$136$	−2.29496	−	10.9395i	−0.196791	−	0.938056i
$137$	−6.41394	+	9.59913i	−0.547980	+	0.820109i	−0.997313	−	0.0732546i	$-0.976661\pi$
$137$	−6.41394	+	9.59913i	−0.547980	+	0.820109i	0.449334	+	0.893364i	$0.351661\pi$
$138$	−1.42230	−	0.638479i	−0.121074	−	0.0543509i
$139$	−0.690060	−	2.27482i	−0.0585301	−	0.192948i	0.922800	−	0.385280i	$-0.125895\pi$
$139$	−0.690060	−	2.27482i	−0.0585301	−	0.192948i	−0.981330	+	0.192332i	$0.938395\pi$
$140$	11.1698	+	15.3606i	0.944023	+	1.29821i
$141$	1.80506	−	2.19948i	0.152014	−	0.185229i
$142$	−3.88332	−	2.22405i	−0.325881	−	0.186639i
$143$	21.3546	+	8.84537i	1.78576	+	0.739687i
$144$	3.80525	+	1.23292i	0.317104	+	0.102743i
$145$	20.7582	−	8.59833i	1.72387	−	0.714052i
$146$	6.77919	+	0.868513i	0.561050	+	0.0718786i
$147$	−0.942018	+	0.0927807i	−0.0776963	+	0.00765242i
$148$	2.62685	+	2.42622i	0.215925	+	0.199434i
$149$	−14.2336	−	7.60800i	−1.16606	−	0.623272i	−0.229338	−	0.973347i	$-0.573656\pi$
$149$	−14.2336	−	7.60800i	−1.16606	−	0.623272i	−0.936722	+	0.350075i	$0.886156\pi$
$150$	−10.1822	+	9.60342i	−0.831376	+	0.784116i
$151$	−6.22354	+	1.23794i	−0.506465	+	0.100742i	−0.441708	−	0.897159i	$-0.645627\pi$
$151$	−6.22354	+	1.23794i	−0.506465	+	0.100742i	−0.0647569	+	0.997901i	$0.520627\pi$
$152$	−1.48411	+	16.8720i	−0.120377	+	1.36850i
$153$	0.770977	−	3.87596i	0.0623298	−	0.313353i
$154$	11.2110	+	2.57294i	0.903407	+	0.207333i
$155$	−9.97569	−	0.982519i	−0.801266	−	0.0789178i
$156$	10.4493	−	9.29323i	0.836615	−	0.744054i
$157$	−2.75689	−	0.836292i	−0.220023	−	0.0667434i	0.178348	−	0.983967i	$-0.442925\pi$
$157$	−2.75689	−	0.836292i	−0.220023	−	0.0667434i	−0.398372	+	0.917224i	$0.630425\pi$
$158$	−0.909339	−	13.1715i	−0.0723431	−	1.04787i
$159$	−4.37487	−	4.37487i	−0.346950	−	0.346950i
$160$	21.6006	+	3.18133i	1.70768	+	0.251506i
$161$	−1.91790	+	1.91790i	−0.151152	+	0.151152i
$162$	1.06650	+	0.928751i	0.0837921	+	0.0729696i
$163$	−6.88047	+	22.6819i	−0.538920	+	1.77658i	0.0864537	+	0.996256i	$0.472447\pi$
$163$	−6.88047	+	22.6819i	−0.538920	+	1.77658i	−0.625374	+	0.780325i	$0.715053\pi$
$164$	19.3370	+	9.36925i	1.50997	+	0.731616i
$165$	−1.25062	+	12.6978i	−0.0973609	+	0.988522i
$166$	−5.42159	−	8.65135i	−0.420797	−	0.671475i
$167$	2.73125	+	0.543280i	0.211351	+	0.0420403i	0.299630	−	0.954055i	$-0.403137\pi$
$167$	2.73125	+	0.543280i	0.211351	+	0.0420403i	−0.0882792	+	0.996096i	$0.528137\pi$
$168$	4.35834	−	5.42515i	0.336253	−	0.418559i
$169$	−7.00143	−	35.1985i	−0.538571	−	2.70758i
$170$	0.630769	−	21.5618i	0.0483778	−	1.65371i
$171$	−2.82282	+	5.28112i	−0.215866	+	0.403857i
$172$	−3.21276	−	6.96144i	−0.244970	−	0.530804i
$173$	0.531236	+	5.39373i	0.0403891	+	0.410078i	0.994028	+	0.109125i	$0.0348048\pi$
$173$	0.531236	+	5.39373i	0.0403891	+	0.410078i	−0.953639	+	0.300953i	$0.902695\pi$
$174$	−5.03441	−	6.51391i	−0.381657	−	0.493819i
$175$	9.31851	+	22.4969i	0.704413	+	1.70060i
$176$	11.1309	−	7.13831i	0.839020	−	0.538070i
$177$	5.58726	−	13.4888i	0.419964	−	1.01388i
$178$	−13.7583	+	3.73788i	−1.03123	+	0.280166i
$179$	−14.2679	−	11.7094i	−1.06643	−	0.875199i	−0.0739106	−	0.997265i	$-0.523548\pi$
$179$	−14.2679	−	11.7094i	−1.06643	−	0.875199i	−0.992522	+	0.122066i	$0.961048\pi$
$180$	6.58349	+	4.03062i	0.490704	+	0.300425i
$181$	11.6163	−	3.52377i	0.863433	−	0.261920i	0.172652	−	0.984983i	$-0.444767\pi$
$181$	11.6163	−	3.52377i	0.863433	−	0.261920i	0.690782	+	0.723063i	$0.257267\pi$
$182$	−8.64892	−	22.7393i	−0.641101	−	1.68555i
$183$	−0.397115	−	0.265344i	−0.0293556	−	0.0196148i
$184$	0.0325449	+	3.11789i	0.00239924	+	0.229854i
$185$	3.83390	+	5.73784i	0.281874	+	0.421855i
$186$	0.610896	+	3.62169i	0.0447931	+	0.265556i
$187$	−8.28779	−	10.0987i	−0.606063	−	0.738490i
$188$	−5.50689	−	1.43457i	−0.401631	−	0.104627i
$189$	2.16985	−	1.15981i	0.157834	−	0.0843638i
$190$	−10.3988	+	30.9877i	−0.754409	+	2.24808i
$191$			11.4088i			0.825512i	0.910842	+	0.412756i	$0.135434\pi$
$191$			11.4088i			0.825512i	−0.910842	+	0.412756i	$0.864566\pi$
$192$	−0.950154	−	7.94338i	−0.0685714	−	0.573264i
$193$		−	9.92348i		−	0.714308i	−0.934046	−	0.357154i	$-0.883747\pi$
$193$		−	9.92348i		−	0.714308i	0.934046	−	0.357154i	$-0.116253\pi$
$194$	15.3818	+	5.16180i	1.10435	+	0.370595i
$195$	23.8003	−	12.7215i	1.70437	−	0.911006i
$196$	0.957961	+	1.63289i	0.0684258	+	0.116635i
$197$	2.07042	+	2.52281i	0.147511	+	0.179743i	0.841524	−	0.540220i	$-0.181659\pi$
$197$	2.07042	+	2.52281i	0.147511	+	0.179743i	−0.694013	+	0.719963i	$0.744159\pi$
$198$	4.60996	−	0.777594i	0.327616	−	0.0552612i
$199$	6.03645	+	9.03418i	0.427912	+	0.640416i	0.981295	−	0.192511i	$-0.0616632\pi$
$199$	6.03645	+	9.03418i	0.427912	+	0.640416i	−0.553382	+	0.832927i	$0.686663\pi$
$200$	25.9727	+	10.4420i	1.83655	+	0.738359i
$201$	−3.76993	−	2.51899i	−0.265910	−	0.177676i
$202$	−2.72825	+	1.03769i	−0.191959	+	0.0730117i
$203$	−13.7060	+	4.15766i	−0.961970	+	0.291810i
$204$	−7.68465	+	1.84828i	−0.538033	+	0.129406i
$205$	32.0544	+	26.3063i	2.23877	+	1.83731i
$206$	2.74885	+	10.1179i	0.191521	+	0.704947i
$207$	−0.421871	+	1.01849i	−0.0293221	+	0.0707897i
$208$	−25.6332	−	11.1870i	−1.77734	−	0.775676i
$209$	7.57548	+	18.2888i	0.524007	+	1.26506i
$210$	10.6260	−	8.21249i	0.733262	−	0.566716i
$211$	−0.106935	−	1.08573i	−0.00736172	−	0.0747448i	0.990802	−	0.135320i	$-0.0432064\pi$
$211$	−0.106935	−	1.08573i	−0.00736172	−	0.0747448i	−0.998164	+	0.0605756i	$0.980706\pi$
$212$	−4.27805	+	11.6109i	−0.293818	+	0.797443i
$213$	−1.49168	+	2.79073i	−0.102208	+	0.191218i
$214$	18.8082	+	0.550216i	1.28570	+	0.0376120i
$215$	−2.88658	−	14.5118i	−0.196863	−	0.989697i
$216$	0.792754	−	2.71506i	0.0539401	−	0.184736i
$217$	6.26705	+	1.24659i	0.425435	+	0.0846243i
$218$	−5.02966	+	3.15196i	−0.340651	+	0.213478i
$219$	0.473696	−	4.80952i	0.0320094	−	0.324997i
$220$	24.1066	−	8.37059i	1.62526	−	0.564345i
$221$	−8.02105	+	26.4419i	−0.539554	+	1.77867i
$222$	1.66055	−	1.90683i	0.111449	−	0.127978i
$223$	−16.9852	+	16.9852i	−1.13741	+	1.13741i	−0.148502	+	0.988912i	$0.547445\pi$
$223$	−16.9852	+	16.9852i	−1.13741	+	1.13741i	−0.988912	+	0.148502i	$0.952555\pi$
$224$	−13.5043	−	3.36783i	−0.902297	−	0.225023i
$225$	6.99828	+	6.99828i	0.466552	+	0.466552i
$226$	24.2327	−	1.67299i	1.61193	−	0.111286i
$227$	8.78060	+	2.66357i	0.582789	+	0.176787i	0.567894	−	0.823102i	$-0.307759\pi$
$227$	8.78060	+	2.66357i	0.582789	+	0.176787i	0.0148953	+	0.999889i	$0.495259\pi$
$228$	11.9559	+	0.700116i	0.791800	+	0.0463663i
$229$	13.3368	+	1.31356i	0.881320	+	0.0868025i	0.528545	−	0.848906i	$-0.322738\pi$
$229$	13.3368	+	1.31356i	0.881320	+	0.0868025i	0.352776	+	0.935708i	$0.385238\pi$
$230$	−1.34600	+	5.86488i	−0.0887526	+	0.386719i
$231$	1.58676	−	7.97717i	0.104401	−	0.524859i
$232$	−7.60969	+	14.6013i	−0.499601	+	0.958622i
$233$	−11.5813	+	2.30366i	−0.758716	+	0.150918i	−0.559264	−	0.828989i	$-0.688916\pi$
$233$	−11.5813	+	2.30366i	−0.758716	+	0.150918i	−0.199452	+	0.979908i	$0.563916\pi$
$234$	−6.78456	−	7.19347i	−0.443520	−	0.470252i
$235$	−9.68533	−	5.17692i	−0.631801	−	0.337705i
$236$	−29.1774	+	1.15847i	−1.89929	+	0.0754098i
$237$	−9.29086	+	0.915070i	−0.603506	+	0.0594402i
$238$	−1.74737	+	13.6391i	−0.113265	+	0.884092i
$239$	−2.48517	+	1.02939i	−0.160752	+	0.0665859i	−0.461609	−	0.887084i	$-0.652728\pi$
$239$	−2.48517	+	1.02939i	−0.160752	+	0.0665859i	0.300856	+	0.953670i	$0.402728\pi$
$240$	1.80194	−	15.3332i	0.116315	−	0.989752i
$241$	−0.203878	−	0.0844492i	−0.0131330	−	0.00543985i	0.376107	−	0.926576i	$-0.377262\pi$
$241$	−0.203878	−	0.0844492i	−0.0131330	−	0.00543985i	−0.389240	+	0.921136i	$0.627262\pi$
$242$	−0.0504601	+	0.0881060i	−0.00324370	+	0.00566367i
$243$	0.634393	−	0.773010i	0.0406963	−	0.0495886i
$244$	−0.149038	+	0.943514i	−0.00954118	+	0.0604023i
$245$	1.06055	+	3.49615i	0.0677559	+	0.223361i
$246$	6.22240	−	13.8612i	0.396726	−	0.883759i
$247$	23.2615	−	34.8132i	1.48009	−	2.21511i
$248$	6.06481	−	4.14459i	0.385116	−	0.263181i
$249$	−6.00271	+	4.01088i	−0.380406	+	0.254179i
$250$	21.7815	+	15.4940i	1.37758	+	0.979927i
$251$	10.3345	−	8.48127i	0.652305	−	0.535333i	−0.249008	−	0.968501i	$-0.580105\pi$
$251$	10.3345	−	8.48127i	0.652305	−	0.535333i	0.901313	+	0.433169i	$0.142605\pi$
$252$	−3.92464	−	2.96832i	−0.247229	−	0.186987i
$253$	1.71791	+	3.21399i	0.108004	+	0.202062i
$254$	14.1394	−	7.03404i	0.887185	−	0.441355i
$255$	−15.2530			−0.955181
$256$	−13.6284	+	8.38253i	−0.851775	+	0.523908i
$257$	13.6022			0.848482			0.424241	−	0.905549i	$-0.360541\pi$
$257$	13.6022			0.848482			0.424241	+	0.905549i	$0.360541\pi$
$258$	−4.85394	+	2.41473i	−0.302193	+	0.150335i
$259$	−2.07367	−	3.87956i	−0.128851	−	0.241064i
$260$	−43.0478	−	32.5583i	−2.66971	−	2.01918i
$261$	−4.49997	+	3.69303i	−0.278541	+	0.228593i
$262$	−2.38659	−	1.69767i	−0.147444	−	0.104882i
$263$	17.4449	−	11.6563i	1.07570	−	0.718760i	0.114171	−	0.993461i	$-0.463579\pi$
$263$	17.4449	−	11.6563i	1.07570	−	0.718760i	0.961530	+	0.274701i	$0.0885788\pi$
$264$	−5.27554	−	7.71974i	−0.324687	−	0.475117i
$265$	−13.2669	+	19.8553i	−0.814979	+	1.21970i
$266$	8.53303	−	19.0084i	0.523194	−	1.16548i
$267$	2.92643	+	9.64715i	0.179095	+	0.590396i
$268$	−1.41486	+	8.95706i	−0.0864265	+	0.547139i
$269$	−10.7267	+	13.0706i	−0.654021	+	0.796927i	−0.989409	−	0.145153i	$-0.953632\pi$
$269$	−10.7267	+	13.0706i	−0.654021	+	0.796927i	0.335388	+	0.942080i	$0.391132\pi$
$270$	2.71274	−	4.73658i	0.165092	−	0.288259i
$271$	−6.30946	−	2.61346i	−0.383272	−	0.158757i	0.182724	−	0.983164i	$-0.441508\pi$
$271$	−6.30946	−	2.61346i	−0.383272	−	0.158757i	−0.565997	+	0.824408i	$0.691508\pi$
$272$	9.79664	+	12.4059i	0.594009	+	0.752216i
$273$	−15.8934	+	6.58327i	−0.961914	+	0.398438i
$274$	2.07474	−	16.1944i	0.125340	−	0.978341i
$275$	32.5600	−	3.20688i	1.96344	−	0.193382i
$276$	2.20307	−	0.0874712i	0.132609	−	0.00526515i
$277$	7.73714	+	4.13559i	0.464880	+	0.248483i	0.687169	−	0.726497i	$-0.258853\pi$
$277$	7.73714	+	4.13559i	0.464880	+	0.248483i	−0.222290	+	0.974981i	$0.571353\pi$
$278$	2.30665	+	2.44568i	0.138344	+	0.146682i
$279$	2.54720	−	0.506669i	0.152497	−	0.0303335i
$280$	−23.8187	−	12.4135i	−1.42344	−	0.741848i
$281$	−2.02756	+	10.1932i	−0.120954	+	0.608077i	0.871993	+	0.489518i	$0.162827\pi$
$281$	−2.02756	+	10.1932i	−0.120954	+	0.608077i	−0.992947	+	0.118559i	$0.962173\pi$
$282$	−0.900096	+	3.92196i	−0.0536000	+	0.233549i
$283$	−9.76745	−	0.962010i	−0.580615	−	0.0571856i	−0.196553	−	0.980493i	$-0.562975\pi$
$283$	−9.76745	−	0.962010i	−0.580615	−	0.0571856i	−0.384061	+	0.923308i	$0.625475\pi$
$284$	6.31793	+	0.369966i	0.374900	+	0.0219535i
$285$	22.1173	+	6.70920i	1.31011	+	0.397419i
$286$	−32.6106	+	2.25138i	−1.92830	+	0.133127i
$287$	−18.6912	−	18.6912i	−1.10331	−	1.10331i
$288$	−5.59477	+	0.835817i	−0.329675	+	0.0492510i
$289$	−0.977589	+	0.977589i	−0.0575052	+	0.0575052i
$290$	−20.8676	+	23.9627i	−1.22539	+	1.40714i
$291$	3.33033	−	10.9786i	0.195228	−	0.643579i
$292$	−9.13079	+	3.17051i	−0.534339	+	0.185540i
$293$	1.35019	−	13.7087i	0.0788790	−	0.800872i	−0.871628	−	0.490168i	$-0.836935\pi$
$293$	1.35019	−	13.7087i	0.0788790	−	0.800872i	0.950507	−	0.310704i	$-0.100565\pi$
$294$	1.13433	−	0.710854i	0.0661553	−	0.0414579i
$295$	−55.2692	−	10.9937i	−3.21790	−	0.640080i
$296$	−4.85435	−	1.41739i	−0.282153	−	0.0823843i
$297$	−0.644926	−	3.24226i	−0.0374224	−	0.188135i
$298$	22.8146	+	0.667419i	1.32162	+	0.0386626i
$299$	3.63353	−	6.79785i	0.210132	−	0.393130i
$300$	6.84340	−	18.5735i	0.395104	−	1.07234i
$301$	0.924485	+	9.38645i	0.0532864	+	0.541026i
$302$	7.10038	−	5.48767i	0.408581	−	0.315780i
$303$	0.789856	+	1.90688i	0.0453760	+	0.109547i
$304$	−8.74853	−	22.2980i	−0.501763	−	1.27888i
$305$	−0.705440	+	1.70308i	−0.0403934	+	0.0975182i
$306$	1.46527	+	5.39332i	0.0837638	+	0.308316i
$307$	16.7181	+	13.7202i	0.954155	+	0.783055i	0.976238	−	0.216701i	$-0.0695298\pi$
$307$	16.7181	+	13.7202i	0.954155	+	0.783055i	−0.0220829	+	0.999756i	$0.507030\pi$
$308$	−15.8159	+	3.80397i	−0.901193	+	0.216752i
$309$	7.09454	−	2.15210i	0.403594	−	0.122429i
$310$	13.2500	−	5.03963i	0.752547	−	0.286232i
$311$	−20.1315	−	13.4515i	−1.14155	−	0.762762i	−0.166789	−	0.985993i	$-0.553340\pi$
$311$	−20.1315	−	13.4515i	−1.14155	−	0.762762i	−0.974766	+	0.223230i	$0.928340\pi$
$312$	−7.37697	+	18.3490i	−0.417639	+	1.03881i
$313$	5.99527	+	8.97255i	0.338872	+	0.507159i	0.961294	−	0.275523i	$-0.0888512\pi$
$313$	5.99527	+	8.97255i	0.338872	+	0.507159i	−0.622422	+	0.782682i	$0.713851\pi$
$314$	4.01751	−	0.677661i	0.226721	−	0.0382426i
$315$	−6.02434	−	7.34068i	−0.339433	−	0.413600i
$316$	9.44811	+	16.1048i	0.531498	+	0.905963i
$317$	11.2516	−	6.01408i	0.631950	−	0.337785i	−0.124127	−	0.992266i	$-0.539613\pi$
$317$	11.2516	−	6.01408i	0.631950	−	0.337785i	0.756078	+	0.654482i	$0.227113\pi$
$318$	8.29512	+	2.78367i	0.465167	+	0.156100i
$319$			19.2441i			1.07746i
$320$	−29.3543	+	9.57805i	−1.64095	+	0.535429i
$321$		−	13.3051i		−	0.742619i
$322$	1.22033	−	3.63650i	0.0680064	−	0.202654i
$323$	−20.8704	+	11.1555i	−1.16126	+	0.620708i
$324$	−1.93541	−	0.504183i	−0.107523	−	0.0280102i
$325$	−43.9002	−	53.4925i	−2.43514	−	2.96723i
$326$	−5.57535	−	33.0535i	−0.308790	−	1.83066i
$327$	2.33182	+	3.48981i	0.128950	+	0.192987i
$328$	−30.3859	+	0.317172i	−1.67778	+	0.0175129i
$329$	5.82078	+	3.88932i	0.320910	+	0.214425i
$330$	−6.41482	−	16.8655i	−0.353124	−	0.928417i
$331$	−13.5473	+	4.10953i	−0.744628	+	0.225880i	−0.639727	−	0.768602i	$-0.720953\pi$
$331$	−13.5473	+	4.10953i	−0.744628	+	0.225880i	−0.104901	+	0.994483i	$0.533453\pi$
$332$	12.3142	+	7.53916i	0.675831	+	0.413765i
$333$	−1.38209	−	1.13425i	−0.0757382	−	0.0621568i
$334$	−3.80049	+	1.03252i	−0.207953	+	0.0564971i
$335$	−6.69695	+	16.1679i	−0.365893	+	0.883345i
$336$	−2.10117	+	9.61457i	−0.114628	+	0.524518i
$337$	8.72310	+	21.0594i	0.475177	+	1.14718i	0.961846	+	0.273593i	$0.0882120\pi$
$337$	8.72310	+	21.0594i	0.475177	+	1.14718i	−0.486668	+	0.873587i	$0.661788\pi$
$338$	31.0367	+	40.1577i	1.68817	+	2.18429i
$339$	−1.68353	−	17.0932i	−0.0914369	−	0.928374i
$340$	12.7831	+	27.6986i	0.693261	+	1.50217i
$341$	4.04715	−	7.57169i	0.219166	−	0.410030i
$342$	0.247634	−	8.46497i	0.0133905	−	0.457733i
$343$	−3.81431	−	19.1758i	−0.205954	−	1.03540i
$344$	8.45295	+	6.79075i	0.455753	+	0.366133i
$345$	4.17315	+	0.830092i	0.224675	+	0.0446906i
$346$	−4.07015	−	6.49484i	−0.218813	−	0.349165i
$347$	−0.661997	+	6.72137i	−0.0355379	+	0.360822i	0.960926	+	0.276804i	$0.0892753\pi$
$347$	−0.661997	+	6.72137i	−0.0355379	+	0.360822i	−0.996464	+	0.0840179i	$0.973225\pi$
$348$	10.4776	+	5.07665i	0.561659	+	0.272137i
$349$	6.33637	−	20.8882i	0.339178	−	1.11812i	−0.607062	−	0.794655i	$-0.707652\pi$
$349$	6.33637	−	20.8882i	0.339178	−	1.11812i	0.946240	−	0.323466i	$-0.104848\pi$
$350$	−25.9697	−	22.6155i	−1.38814	−	1.20885i
$351$	−4.94409	+	4.94409i	−0.263896	+	0.263896i
$352$	−9.59731	+	16.0497i	−0.511538	+	0.855454i
$353$	−6.52212	−	6.52212i	−0.347138	−	0.347138i	0.511905	−	0.859042i	$-0.328940\pi$
$353$	−6.52212	−	6.52212i	−0.347138	−	0.347138i	−0.859042	+	0.511905i	$0.828940\pi$
$354$	1.42211	+	20.5988i	0.0755842	+	1.09481i
$355$	11.6875	+	3.54538i	0.620310	+	0.188169i
$356$	15.0661	−	13.3992i	0.798501	−	0.710157i
$357$	9.67631	+	0.953033i	0.512125	+	0.0504399i
$358$	25.4415	+	5.83888i	1.34463	+	0.308594i
$359$	5.49887	−	27.6447i	0.290219	−	1.45903i	−0.510441	−	0.859913i	$-0.670518\pi$
$359$	5.49887	−	27.6447i	0.290219	−	1.45903i	0.800660	−	0.599119i	$-0.204482\pi$
$360$	−10.8748	−	0.956579i	−0.573153	−	0.0504161i
$361$	16.5346	−	3.28894i	0.870242	−	0.173102i
$362$	−12.4888	+	11.7789i	−0.656396	+	0.619083i
$363$	0.0633171	+	0.0338437i	0.00332329	+	0.00177633i
$364$	25.2746	+	23.3443i	1.32475	+	1.22357i
$365$	−18.5632	+	1.82831i	−0.971640	+	0.0956982i
$366$	0.669961	+	0.0858318i	0.0350194	+	0.00448650i
$367$	26.2430	−	10.8702i	1.36988	−	0.567421i	0.428121	−	0.903721i	$-0.359176\pi$
$367$	26.2430	−	10.8702i	1.36988	−	0.567421i	0.941755	+	0.336300i	$0.109176\pi$
$368$	−2.00517	−	3.92733i	−0.104527	−	0.204726i
$369$	−9.92583	−	4.11141i	−0.516718	−	0.214032i
$370$	−8.46870	−	4.85020i	−0.440267	−	0.252150i
$371$	9.65693	−	11.7670i	0.501363	−	0.610912i
$372$	−3.05481	−	4.20093i	−0.158385	−	0.217808i
$373$	7.82879	+	25.8081i	0.405360	+	1.33629i	0.887746	+	0.460333i	$0.152270\pi$
$373$	7.82879	+	25.8081i	0.405360	+	1.33629i	−0.482387	+	0.875958i	$0.660230\pi$
$374$	16.8550	+	7.56635i	0.871553	+	0.391247i
$375$	10.5009	−	15.7156i	0.542262	−	0.811552i
$376$	7.87638	−	1.65236i	0.406193	−	0.0852137i
$377$	33.8433	−	22.6133i	1.74302	−	1.16465i
$378$	−2.01687	+	2.83533i	−0.103737	+	0.145833i
$379$	24.5562	−	20.1528i	1.26137	−	1.03518i	0.263864	−	0.964560i	$-0.415003\pi$
$379$	24.5562	−	20.1528i	1.26137	−	1.03518i	0.997503	−	0.0706177i	$-0.0224970\pi$
$380$	−6.35232	−	45.7864i	−0.325867	−	2.34879i
$381$	−5.26405	−	9.84835i	−0.269685	−	0.504546i
$382$	−7.18640	−	14.4457i	−0.367688	−	0.739104i
$383$	1.16704			0.0596330			0.0298165	−	0.999555i	$-0.490508\pi$
$383$	1.16704			0.0596330			0.0298165	+	0.999555i	$0.490508\pi$
$384$	6.20660	+	9.45929i	0.316729	+	0.482717i
$385$	−31.3925			−1.59991
$386$	6.25080	+	12.5650i	0.318157	+	0.639540i
$387$	1.80711	+	3.38086i	0.0918604	+	0.171859i
$388$	−22.7276	+	3.15319i	−1.15382	+	0.160079i
$389$	−14.8032	+	12.1486i	−0.750550	+	0.615961i	−0.929895	−	0.367826i	$-0.880102\pi$
$389$	−14.8032	+	12.1486i	−0.750550	+	0.615961i	0.179345	+	0.983786i	$0.442602\pi$
$390$	−22.1223	+	31.0996i	−1.12021	+	1.57479i
$391$	−3.62236	+	2.42038i	−0.183191	+	0.122404i
$392$	−2.24151	−	1.46412i	−0.113214	−	0.0739494i
$393$	−1.15057	+	1.72195i	−0.0580388	+	0.0868611i
$394$	−4.21065	−	1.89019i	−0.212130	−	0.0952265i
$395$	10.4599	+	34.4816i	0.526294	+	1.73496i
$396$	−5.34726	+	3.88839i	−0.268710	+	0.195399i
$397$	20.5557	−	25.0472i	1.03166	−	1.25709i	0.0658546	−	0.997829i	$-0.479023\pi$
$397$	20.5557	−	25.0472i	1.03166	−	1.25709i	0.965809	−	0.259256i	$-0.0834774\pi$
$398$	−13.3339	−	7.63659i	−0.668368	−	0.382788i
$399$	−13.6117	−	5.63815i	−0.681437	−	0.282260i
$400$	−39.4636	+	3.13870i	−1.97318	+	0.156935i
$401$	29.4276	−	12.1893i	1.46954	−	0.608705i	0.502788	−	0.864410i	$-0.332308\pi$
$401$	29.4276	−	12.1893i	1.46954	−	0.608705i	0.966755	+	0.255705i	$0.0823076\pi$
$402$	6.36014	+	0.814827i	0.317215	+	0.0406399i
$403$	−18.0715	+	1.77989i	−0.900205	+	0.0886625i
$404$	2.80083	−	3.03243i	0.139346	−	0.150869i
$405$	−3.40393	−	1.81944i	−0.169142	−	0.0904085i
$406$	14.7354	−	13.8977i	0.731305	−	0.689734i
$407$	−5.79696	+	1.15309i	−0.287345	+	0.0571564i
$408$	8.56596	−	7.18082i	0.424078	−	0.355504i
$409$	−6.96876	+	35.0343i	−0.344583	+	1.73234i	0.287809	+	0.957688i	$0.407073\pi$
$409$	−6.96876	+	35.0343i	−0.344583	+	1.73234i	−0.632392	+	0.774649i	$0.717927\pi$
$410$	−57.1571	−	13.1177i	−2.82279	−	0.647835i
$411$	−11.4892	−	1.13159i	−0.566720	−	0.0558170i
$412$	−9.85382	−	11.0796i	−0.485463	−	0.545855i
$413$	34.3751	+	10.4276i	1.69149	+	0.513108i
$414$	−0.107378	−	1.55533i	−0.00527732	−	0.0764403i
$415$	19.7032	+	19.7032i	0.967191	+	0.967191i
$416$	39.5031	−	1.98160i	1.93680	−	0.0971559i
$417$	1.68092	−	1.68092i	0.0823151	−	0.0823151i
$418$	−21.1121	−	18.3853i	−1.03263	−	0.899253i
$419$	−5.03762	+	16.6068i	−0.246104	+	0.811295i	0.743657	+	0.668561i	$0.233089\pi$
$419$	−5.03762	+	16.6068i	−0.246104	+	0.811295i	−0.989761	+	0.142734i	$0.954411\pi$
$420$	−8.28141	+	17.0918i	−0.404091	+	0.833997i
$421$	0.466805	−	4.73955i	0.0227507	−	0.230992i	−0.977085	−	0.212851i	$-0.931725\pi$
$421$	0.466805	−	4.73955i	0.0227507	−	0.230992i	0.999835	−	0.0181410i	$-0.00577476\pi$
$422$	0.819302	+	1.30738i	0.0398830	+	0.0636422i
$423$	2.79067	+	0.555098i	0.135687	+	0.0269898i
$424$	−1.89693	−	17.3964i	−0.0921229	−	0.844842i
$425$	7.63040	+	38.3606i	0.370129	+	1.86076i
$426$	0.130859	−	4.47319i	0.00634013	−	0.216727i
$427$	0.553933	−	1.03634i	0.0268067	−	0.0501518i
$428$	−24.1613	+	11.1506i	−1.16788	+	0.538985i
$429$	2.26557	+	23.0028i	0.109383	+	1.11058i
$430$	12.7959	+	16.5564i	0.617075	+	0.798420i
$431$	−7.58467	−	18.3110i	−0.365341	−	0.882011i	−0.994500	−	0.104734i	$-0.966601\pi$
$431$	−7.58467	−	18.3110i	−0.365341	−	0.882011i	0.629159	−	0.777276i	$-0.283399\pi$
$432$	0.706441	+	3.93712i	0.0339887	+	0.189425i
$433$	−1.54887	+	3.73930i	−0.0744339	+	0.179699i	−0.956717	−	0.291020i	$-0.906005\pi$
$433$	−1.54887	+	3.73930i	−0.0744339	+	0.179699i	0.882283	+	0.470719i	$0.156005\pi$
$434$	−8.72048	+	2.36920i	−0.418596	+	0.113725i
$435$	17.3684	+	14.2539i	0.832751	+	0.683421i
$436$	4.38306	−	7.15915i	0.209911	−	0.342861i
$437$	6.31715	−	1.91629i	0.302190	−	0.0916684i
$438$	2.42973	+	6.38812i	0.116097	+	0.305236i
$439$	33.3724	+	22.2987i	1.59278	+	1.06426i	0.956064	+	0.293159i	$0.0947066\pi$
$439$	33.3724	+	22.2987i	1.59278	+	1.06426i	0.636714	+	0.771100i	$0.280293\pi$
$440$	−25.2507	+	25.7834i	−1.20378	+	1.22918i
$441$	−0.525889	−	0.787049i	−0.0250424	−	0.0374785i
$442$	−6.49958	−	38.5328i	−0.309154	−	1.83282i
$443$	−1.80619	−	2.20085i	−0.0858149	−	0.104566i	0.728333	−	0.685223i	$-0.240295\pi$
$443$	−1.80619	−	2.20085i	−0.0858149	−	0.104566i	−0.814148	+	0.580658i	$0.802795\pi$
$444$	−0.901447	+	3.46038i	−0.0427808	+	0.164223i
$445$	34.3158	−	18.3422i	1.62673	−	0.869503i
$446$	10.8075	−	32.2054i	0.511748	−	1.52497i
$447$		−	16.1393i		−	0.763362i
$448$	19.2204	−	4.24209i	0.908079	−	0.200420i
$449$			27.7113i			1.30778i	0.756590	+	0.653889i	$0.226864\pi$
$449$			27.7113i			1.30778i	−0.756590	+	0.653889i	$0.773136\pi$
$450$	−13.2693	−	4.45291i	−0.625522	−	0.209912i
$451$	−31.3224	+	16.7422i	−1.47492	+	0.788359i
$452$	−29.6293	+	17.3825i	−1.39364	+	0.817603i
$453$	−4.02552	−	4.90511i	−0.189136	−	0.230462i
$454$	−12.7956	+	2.15833i	−0.600530	+	0.101295i
$455$	36.8885	+	55.2076i	1.72936	+	2.58817i
$456$	−15.5794	+	6.64455i	−0.729573	+	0.311160i
$457$	12.1272	+	8.10312i	0.567285	+	0.379048i	0.805887	−	0.592070i	$-0.201689\pi$
$457$	12.1272	+	8.10312i	0.567285	+	0.379048i	−0.238601	+	0.971118i	$0.576689\pi$
$458$	−17.7143	+	6.73763i	−0.827733	+	0.314829i
$459$	3.78173	−	1.14717i	0.176516	−	0.0535455i
$460$	−1.99000	−	8.27387i	−0.0927842	−	0.385771i
$461$	0.415165	+	0.340717i	0.0193362	+	0.0158688i	0.644012	−	0.765016i	$-0.277269\pi$
$461$	0.415165	+	0.340717i	0.0193362	+	0.0158688i	−0.624676	+	0.780884i	$0.714769\pi$
$462$	3.01569	+	11.1001i	0.140303	+	0.516422i
$463$	6.18436	−	14.9304i	0.287412	−	0.693873i	−0.712558	−	0.701613i	$-0.752464\pi$
$463$	6.18436	−	14.9304i	0.287412	−	0.693873i	0.999970	+	0.00773975i	$0.00246366\pi$
$464$	0.437925	−	23.2813i	0.0203302	−	1.08081i
$465$	−3.83600	−	9.26093i	−0.177890	−	0.429465i
$466$	13.2130	−	10.2119i	0.612081	−	0.473058i
$467$	0.340199	+	3.45410i	0.0157425	+	0.159836i	0.999842	−	0.0177823i	$-0.00566059\pi$
$467$	0.340199	+	3.45410i	0.0157425	+	0.159836i	−0.984099	+	0.177619i	$0.943161\pi$
$468$	13.1217	+	4.83468i	0.606550	+	0.223483i
$469$	5.25865	−	9.83824i	0.242822	−	0.454288i
$470$	15.5244	+	0.454150i	0.716085	+	0.0209484i
$471$	−0.562043	−	2.82558i	−0.0258976	−	0.130196i
$472$	36.2143	−	19.8457i	1.66690	−	0.913472i
$473$	12.4293	+	2.47234i	0.571499	+	0.113678i
$474$	11.1876	−	7.01096i	0.513861	−	0.322024i
$475$	5.80904	−	58.9802i	0.266537	−	2.70620i
$476$	−6.37878	−	18.3703i	−0.292371	−	0.842002i
$477$	1.79599	−	5.92059i	0.0822327	−	0.271085i
$478$	2.49828	−	2.86881i	0.114269	−	0.131216i
$479$	−2.28697	+	2.28697i	−0.104494	+	0.104494i	−0.757421	−	0.652927i	$-0.773541\pi$
$479$	−2.28697	+	2.28697i	−0.104494	+	0.104494i	0.652927	+	0.757421i	$0.273541\pi$
$480$	7.37676	+	20.5497i	0.336702	+	0.937960i
$481$	8.83972	+	8.83972i	0.403057	+	0.403057i
$482$	0.311342	−	0.0214946i	0.0141813	−	0.000979052i
$483$	−2.59553	−	0.787344i	−0.118101	−	0.0358254i
$484$	0.00839393	−	0.143343i	0.000381542	−	0.00651561i
$485$	−44.0674	−	4.34026i	−2.00100	−	0.197081i
$486$	−0.316341	+	1.37838i	−0.0143495	+	0.0625245i
$487$	−2.73762	+	13.7629i	−0.124053	+	0.623658i	0.867867	+	0.496796i	$0.165490\pi$
$487$	−2.73762	+	13.7629i	−0.124053	+	0.623658i	−0.991920	+	0.126862i	$0.959510\pi$
$488$	−0.405609	−	1.28854i	−0.0183611	−	0.0583296i
$489$	−23.2471	+	4.62413i	−1.05127	+	0.209110i
$490$	−3.54508	−	3.75874i	−0.160150	−	0.169803i
$491$	−15.7806	−	8.43492i	−0.712170	−	0.380663i	0.0751792	−	0.997170i	$-0.476047\pi$
$491$	−15.7806	−	8.43492i	−0.712170	−	0.380663i	−0.787349	+	0.616507i	$0.788547\pi$
$492$	0.852465	+	21.4704i	0.0384321	+	0.967959i
$493$	−22.8946	+	2.25492i	−1.03112	+	0.101557i
$494$	−7.52447	+	58.7324i	−0.338542	+	2.64250i
$495$	−11.7880	+	4.88275i	−0.529831	+	0.219463i
$496$	−5.06850	+	9.06803i	−0.227582	+	0.407167i
$497$	−7.19290	−	2.97940i	−0.322646	−	0.133644i
$498$	5.07409	−	8.85963i	0.227376	−	0.397010i
$499$	8.97029	−	10.9303i	0.401565	−	0.489309i	−0.532490	−	0.846436i	$-0.678744\pi$
$499$	8.97029	−	10.9303i	0.401565	−	0.489309i	0.934056	+	0.357127i	$0.116244\pi$
$500$	−37.3391	−	5.89811i	−1.66986	−	0.263772i
$501$	0.808374	+	2.66485i	0.0361155	+	0.119057i
$502$	−7.74299	+	17.2485i	−0.345586	+	0.769839i
$503$	−8.13683	+	12.1776i	−0.362803	+	0.542974i	−0.967300	−	0.253634i	$-0.918374\pi$
$503$	−8.13683	+	12.1776i	−0.362803	+	0.542974i	0.604497	+	0.796607i	$0.293374\pi$
$504$	6.83906	+	1.28632i	0.304636	+	0.0572971i
$505$	6.62377	−	4.42586i	0.294754	−	0.196948i
$506$	−4.19969	−	2.98739i	−0.186699	−	0.132806i
$507$	27.7419	−	22.7672i	1.23206	−	1.01113i
$508$	−13.4724	+	17.8128i	−0.597739	+	0.790315i
$509$	−14.8006	−	27.6900i	−0.656027	−	1.22734i	−0.961412	−	0.275111i	$-0.911285\pi$
$509$	−14.8006	−	27.6900i	−0.656027	−	1.22734i	0.305386	−	0.952229i	$-0.401215\pi$
$510$	19.3132	−	9.60787i	0.855201	−	0.425444i
$511$	11.8905			0.526003
$512$	11.9759	−	19.1984i	0.529266	−	0.848456i
$513$	−5.98820			−0.264385
$514$	−17.2229	+	8.56803i	−0.759670	+	0.377919i
$515$	−13.4889	−	25.2359i	−0.594391	−	1.11203i
$516$	4.62495	−	6.11500i	0.203602	−	0.269198i
$517$	7.27100	−	5.96715i	0.319778	−	0.262435i
$518$	5.06938	+	3.60604i	0.222736	+	0.158440i
$519$	−4.50642	+	3.01110i	−0.197810	+	0.132172i
$520$	75.0150	+	14.1091i	3.28962	+	0.618725i
$521$	−11.0340	+	16.5136i	−0.483409	+	0.723472i	−0.990362	−	0.138501i	$-0.955772\pi$
$521$	−11.0340	+	16.5136i	−0.483409	+	0.723472i	0.506953	+	0.861973i	$0.330772\pi$
$522$	3.37156	−	7.51059i	0.147569	−	0.328729i
$523$	3.85021	+	12.6924i	0.168358	+	0.555002i	1.00000		0.000310263i	$-9.87599e-5\pi$
$523$	3.85021	+	12.6924i	0.168358	+	0.555002i	−0.831642	+	0.555312i	$0.812599\pi$
$524$	4.09123	+	0.646253i	0.178726	+	0.0282317i
$525$	−15.4478	+	18.8231i	−0.674195	+	0.821509i
$526$	−14.7462	+	25.7476i	−0.642965	+	1.12265i
$527$	9.48221	+	3.92766i	0.413052	+	0.171092i
$528$	11.5425	+	6.45156i	0.502322	+	0.280768i
$529$	−20.1264	+	8.33665i	−0.875063	+	0.362463i
$530$	4.29149	−	33.4973i	0.186411	−	1.45503i
$531$	14.5299	−	1.43107i	0.630544	−	0.0621032i
$532$	1.16902	+	29.4432i	0.0506834	+	1.27652i
$533$	66.2495	+	35.4111i	2.86959	+	1.53383i
$534$	−9.78215	−	10.3717i	−0.423315	−	0.448829i
$535$	−50.3666	+	10.0185i	−2.17754	+	0.433139i
$536$	−3.85057	−	12.2325i	−0.166319	−	0.528364i
$537$	3.60089	−	18.1029i	0.155390	−	0.781198i
$538$	5.34889	−	23.3065i	0.230607	−	1.00482i
$539$	−3.11411	−	0.306713i	−0.134134	−	0.0132111i
$540$	−0.451257	+	7.70614i	−0.0194190	+	0.331620i
$541$	13.3912	+	4.06219i	0.575734	+	0.174647i	0.564706	−	0.825292i	$-0.308990\pi$
$541$	13.3912	+	4.06219i	0.575734	+	0.174647i	0.0110282	+	0.999939i	$0.496490\pi$
$542$	9.63517	−	0.665197i	0.413866	−	0.0285727i
$543$	8.58358	+	8.58358i	0.368356	+	0.368356i
$544$	−20.2188	−	9.53723i	−0.866875	−	0.408905i
$545$	11.4549	−	11.4549i	0.490673	−	0.490673i
$546$	15.9772	−	18.3469i	0.683762	−	0.785175i
$547$	−3.71293	+	12.2399i	−0.158754	+	0.523340i	−0.999846	−	0.0175511i	$-0.994413\pi$
$547$	−3.71293	+	12.2399i	−0.158754	+	0.523340i	0.841092	+	0.540891i	$0.181913\pi$
$548$	7.57386	+	21.8120i	0.323539	+	0.931764i
$549$	0.0468136	−	0.475306i	0.00199796	−	0.0202856i
$550$	−39.2070	+	24.5700i	−1.67179	+	1.04767i
$551$	34.1896	+	6.80074i	1.45653	+	0.289721i
$552$	−2.73440	+	1.49847i	−0.116384	+	0.0637790i
$553$	−4.48114	−	22.5282i	−0.190557	−	0.957997i
$554$	−12.4017	−	0.362798i	−0.526896	−	0.0154138i
$555$	−3.25304	+	6.08600i	−0.138084	+	0.258336i
$556$	−4.46119	−	1.64372i	−0.189196	−	0.0697094i
$557$	−2.95877	−	30.0409i	−0.125367	−	1.27287i	−0.827760	−	0.561083i	$-0.810385\pi$
$557$	−2.95877	−	30.0409i	−0.125367	−	1.27287i	0.702393	−	0.711789i	$-0.252115\pi$
$558$	−2.90607	+	2.24602i	−0.123024	+	0.0950815i
$559$	−10.2574	−	24.7636i	−0.433843	−	1.04739i
$560$	37.9782	+	0.714375i	1.60487	+	0.0301879i
$561$	4.99942	−	12.0697i	0.211076	−	0.509582i
$562$	−3.85345	−	14.1837i	−0.162548	−	0.598302i
$563$	34.8402	+	28.5926i	1.46834	+	1.20503i	0.932734	+	0.360566i	$0.117416\pi$
$563$	34.8402	+	28.5926i	1.46834	+	1.20503i	0.535605	+	0.844469i	$0.320084\pi$
$564$	−1.33075	−	5.53290i	−0.0560347	−	0.232977i
$565$	−63.4387	+	19.2439i	−2.66889	+	0.809598i
$566$	12.9734	−	4.93443i	0.545312	−	0.207410i
$567$	2.04572	+	1.36691i	0.0859123	+	0.0574048i
$568$	−8.23271	+	3.51122i	−0.345437	+	0.147327i
$569$	−13.9186	−	20.8306i	−0.583498	−	0.873266i	0.415848	−	0.909434i	$-0.363485\pi$
$569$	−13.9186	−	20.8306i	−0.583498	−	0.873266i	−0.999346	+	0.0361679i	$0.988485\pi$
$570$	−32.2307	+	5.43657i	−1.34999	+	0.227713i
$571$	24.5933	+	29.9670i	1.02920	+	1.25408i	0.966666	+	0.256039i	$0.0824176\pi$
$571$	24.5933	+	29.9670i	1.02920	+	1.25408i	0.0625320	+	0.998043i	$0.480082\pi$
$572$	39.8729	−	23.3921i	1.66717	−	0.978072i
$573$	−10.0617	+	5.37807i	−0.420332	+	0.224672i
$574$	35.4401	+	11.8929i	1.47924	+	0.496402i
$575$		−	10.9105i		−	0.455001i
$576$	6.55753	−	4.58244i	0.273230	−	0.190935i
$577$		−	10.9632i		−	0.456405i	−0.973614	−	0.228202i	$-0.926715\pi$
$577$		−	10.9632i		−	0.456405i	0.973614	−	0.228202i	$-0.0732848\pi$
$578$	0.622026	−	1.85359i	0.0258729	−	0.0770993i
$579$	8.75173	−	4.67790i	0.363709	−	0.194407i
$580$	11.3282	−	43.4857i	0.470380	−	1.80565i
$581$	−11.2683	−	13.7305i	−0.467490	−	0.569638i
$582$	2.69862	+	15.9988i	0.111861	+	0.663170i
$583$	−11.3630	−	17.0059i	−0.470608	−	0.704314i
$584$	9.56417	−	9.76594i	0.395768	−	0.404117i
$585$	22.4387	+	14.9931i	0.927727	+	0.619888i
$586$	6.92553	+	18.2083i	0.286091	+	0.752177i
$587$	−14.5873	+	4.42502i	−0.602084	+	0.182640i	−0.576588	−	0.817035i	$-0.695616\pi$
$587$	−14.5873	+	4.42502i	−0.602084	+	0.182640i	−0.0254955	+	0.999675i	$0.508116\pi$
$588$	−0.988502	+	1.61459i	−0.0407651	+	0.0665844i
$589$	−12.0218	−	9.86606i	−0.495351	−	0.406524i
$590$	76.9060	−	20.8940i	3.16617	−	0.860191i
$591$	−1.24893	+	3.01519i	−0.0513743	+	0.124028i
$592$	7.03932	−	1.26307i	0.289314	−	0.0519119i
$593$	4.95416	+	11.9604i	0.203443	+	0.491155i	0.992365	−	0.123339i	$-0.0393603\pi$
$593$	4.95416	+	11.9604i	0.203443	+	0.491155i	−0.788922	+	0.614494i	$0.789360\pi$
$594$	2.85890	+	3.69907i	0.117302	+	0.151775i
$595$	−3.67839	−	37.3474i	−0.150799	−	1.53109i
$596$	−29.3080	+	13.5259i	−1.20050	+	0.554040i
$597$	−5.12187	+	9.58235i	−0.209624	+	0.392180i
$598$	−0.318755	+	10.8961i	−0.0130348	+	0.445574i
$599$	0.615640	+	3.09503i	0.0251544	+	0.126460i	0.991322	−	0.131455i	$-0.0419648\pi$
$599$	0.615640	+	3.09503i	0.0251544	+	0.126460i	−0.966168	+	0.257914i	$0.916965\pi$
$600$	3.03443	+	27.8282i	0.123880	+	1.13608i
$601$	20.5609	+	4.08982i	0.838697	+	0.166827i	0.595707	−	0.803202i	$-0.296872\pi$
$601$	20.5609	+	4.08982i	0.838697	+	0.166827i	0.242990	+	0.970029i	$0.421872\pi$
$602$	−7.08310	−	11.3027i	−0.288685	−	0.460662i
$603$	0.444415	−	4.51223i	0.0180980	−	0.183752i
$604$	−5.53372	+	11.4209i	−0.225164	+	0.464711i
$605$	0.0804388	−	0.265171i	0.00327030	−	0.0107807i
$606$	−2.20125	−	1.91694i	−0.0894196	−	0.0778702i
$607$	−19.7502	+	19.7502i	−0.801636	+	0.801636i	−0.983351	−	0.181715i	$-0.941835\pi$
$607$	−19.7502	+	19.7502i	−0.801636	+	0.801636i	0.181715	+	0.983351i	$0.441835\pi$
$608$	25.1228	+	22.7227i	1.01886	+	0.921526i
$609$	−10.1277	−	10.1277i	−0.410394	−	0.410394i
$610$	−0.179553	−	2.60077i	−0.00726991	−	0.105302i
$611$	−19.0380	−	5.77511i	−0.770194	−	0.233636i
$612$	−5.25256	−	5.90598i	−0.212322	−	0.238735i
$613$	−24.3473	−	2.39800i	−0.983377	−	0.0968541i	−0.406470	−	0.913664i	$-0.633240\pi$
$613$	−24.3473	−	2.39800i	−0.983377	−	0.0968541i	−0.576907	+	0.816810i	$0.695740\pi$
$614$	−29.8106	−	6.84160i	−1.20306	−	0.276104i
$615$	−8.08979	+	40.6701i	−0.326212	+	1.63998i
$616$	17.6297	−	14.7790i	0.710322	−	0.595461i
$617$	32.0204	−	6.36925i	1.28909	−	0.256417i	0.497499	−	0.867464i	$-0.334252\pi$
$617$	32.0204	−	6.36925i	1.28909	−	0.256417i	0.791594	+	0.611048i	$0.209252\pi$
$618$	−7.62739	+	7.19381i	−0.306819	+	0.289378i
$619$	2.50042	+	1.33650i	0.100500	+	0.0537185i	0.520881	−	0.853629i	$-0.325603\pi$
$619$	2.50042	+	1.33650i	0.100500	+	0.0537185i	−0.420381	+	0.907348i	$0.638103\pi$
$620$	−13.6024	+	14.7273i	−0.546287	+	0.591461i
$621$	−1.09709	+	0.108054i	−0.0440248	+	0.00433607i
$622$	33.9633	+	4.35120i	1.36181	+	0.174467i
$623$	−22.9155	+	9.49193i	−0.918092	+	0.380286i
$624$	−2.21740	−	27.8800i	−0.0887672	−	1.11609i
$625$	−21.6802	−	8.98024i	−0.867209	−	0.359210i
$626$	−13.2429	−	7.58450i	−0.529294	−	0.303137i
$627$	−12.5583	+	15.3023i	−0.501528	+	0.611114i
$628$	−4.66006	+	3.38867i	−0.185956	+	0.135223i
$629$	−2.05108	−	6.76149i	−0.0817817	−	0.269598i
$630$	12.2518	+	5.49993i	0.488124	+	0.219123i
$631$	14.7194	−	22.0292i	0.585972	−	0.876969i	−0.413465	−	0.910520i	$-0.635682\pi$
$631$	14.7194	−	22.0292i	0.585972	−	0.876969i	0.999437	+	0.0335513i	$0.0106817\pi$
$632$	−22.1074	−	14.4402i	−0.879387	−	0.574402i
$633$	0.907121	−	0.606119i	0.0360548	−	0.0240911i
$634$	−10.4583	+	14.7023i	−0.415352	+	0.583903i
$635$	−33.3172	+	27.3428i	−1.32215	+	1.08506i
$636$	−12.2566	+	1.70046i	−0.486006	+	0.0674275i
$637$	3.11992	+	5.83696i	0.123616	+	0.231269i
$638$	−12.1219	−	24.3667i	−0.479910	−	0.964685i
$639$	−3.16438			−0.125181
$640$	31.1347	−	30.6178i	1.23071	−	1.21028i
$641$	5.16639			0.204060			0.102030	−	0.994781i	$-0.467466\pi$
$641$	5.16639			0.204060			0.102030	+	0.994781i	$0.467466\pi$
$642$	8.38089	+	16.8467i	0.330767	+	0.664888i
$643$	−22.5356	−	42.1612i	−0.888718	−	1.66267i	−0.738746	−	0.673984i	$-0.764582\pi$
$643$	−22.5356	−	42.1612i	−0.888718	−	1.66267i	−0.149972	−	0.988690i	$-0.547918\pi$
$644$	0.745464	+	5.37317i	0.0293754	+	0.211733i
$645$	11.4375	−	9.38655i	0.450353	−	0.369595i
$646$	19.3990	−	27.2712i	0.763244	−	1.07297i
$647$	1.87949	−	1.25584i	0.0738905	−	0.0493720i	−0.518076	−	0.855334i	$-0.673352\pi$
$647$	1.87949	−	1.25584i	0.0738905	−	0.0493720i	0.591967	+	0.805962i	$0.298352\pi$
$648$	2.76817	−	0.580723i	0.108744	−	0.0228130i
$649$	26.8147	−	40.1310i	1.05257	−	1.57528i
$650$	89.2808	+	40.0788i	3.50188	+	1.57202i
$651$	1.85487	+	6.11469i	0.0726981	+	0.239653i
$652$	27.8798	+	38.3399i	1.09186	+	1.50151i
$653$	10.7906	−	13.1484i	0.422269	−	0.514536i	−0.517809	−	0.855496i	$-0.673252\pi$
$653$	10.7906	−	13.1484i	0.422269	−	0.514536i	0.940078	+	0.340960i	$0.110752\pi$
$654$	−5.15075	−	2.94994i	−0.201410	−	0.115352i
$655$	7.38484	+	3.05890i	0.288550	+	0.119521i
$656$	38.2745	−	19.5417i	1.49437	−	0.762975i
$657$	4.46491	−	1.84943i	0.174193	−	0.0721531i
$658$	−9.82007	−	1.25809i	−0.382826	−	0.0490456i
$659$	18.7899	−	1.85065i	0.731952	−	0.0720910i	0.274827	−	0.961494i	$-0.411379\pi$
$659$	18.7899	−	1.85065i	0.731952	−	0.0720910i	0.457125	+	0.889403i	$0.348879\pi$
$660$	18.7460	+	17.3142i	0.729685	+	0.673955i
$661$	−18.2178	−	9.73761i	−0.708590	−	0.378749i	0.0773905	−	0.997001i	$-0.475341\pi$
$661$	−18.2178	−	9.73761i	−0.708590	−	0.378749i	−0.785980	+	0.618252i	$0.787841\pi$
$662$	14.5648	−	13.7369i	0.566078	−	0.533899i
$663$	−27.1007	+	5.39067i	−1.05251	+	0.209356i
$664$	−20.3410	−	1.78925i	−0.789384	−	0.0694365i
$665$	−11.0939	+	55.7726i	−0.430202	+	2.16277i
$666$	2.46445	+	0.565597i	0.0954956	+	0.0219164i
$667$	6.38657	+	0.629022i	0.247289	+	0.0243558i
$668$	4.16174	−	3.70129i	0.161022	−	0.143207i
$669$	−22.9864	−	6.97285i	−0.888706	−	0.269586i
$670$	−1.70455	−	24.6899i	−0.0658527	−	0.953855i
$671$	−1.11642	−	1.11642i	−0.0430991	−	0.0430991i
$672$	−3.39574	−	13.4974i	−0.130994	−	0.520672i
$673$	−20.7520	+	20.7520i	−0.799932	+	0.799932i	−0.983084	−	0.183153i	$-0.941370\pi$
$673$	−20.7520	+	20.7520i	−0.799932	+	0.799932i	0.183153	+	0.983084i	$0.441370\pi$
$674$	−24.3104	−	21.1705i	−0.936401	−	0.815455i
$675$	−2.87297	+	9.47090i	−0.110580	+	0.364535i
$676$	−64.5935	−	31.2971i	−2.48437	−	1.20373i
$677$	−0.679573	+	6.89982i	−0.0261181	+	0.265182i	0.973253	+	0.229734i	$0.0737857\pi$
$677$	−0.679573	+	6.89982i	−0.0261181	+	0.265182i	−0.999372	+	0.0354476i	$0.988714\pi$
$678$	12.8987	+	20.5827i	0.495370	+	0.790473i
$679$	27.6846	+	5.50681i	1.06244	+	0.211332i
$680$	−33.6331	−	27.0195i	−1.28977	−	1.03615i
$681$	1.79009	+	8.99939i	0.0685964	+	0.344858i
$682$	−0.355041	+	12.1365i	−0.0135952	+	0.464730i
$683$	13.4658	−	25.1928i	0.515256	−	0.963976i	−0.480933	−	0.876757i	$-0.659702\pi$
$683$	13.4658	−	25.1928i	0.515256	−	0.963976i	0.996189	−	0.0872189i	$-0.0277980\pi$
$684$	5.01853	+	10.8742i	0.191888	+	0.415786i
$685$	4.36755	+	44.3445i	0.166876	+	1.69432i
$686$	16.9085	+	21.8775i	0.645569	+	0.835289i
$687$	5.12847	+	12.3812i	0.195663	+	0.472373i
$688$	−14.9805	−	3.27384i	−0.571126	−	0.124814i
$689$	−16.5547	+	39.9666i	−0.630684	+	1.52261i
$690$	−5.80686	+	1.57762i	−0.221063	+	0.0600589i
$691$	14.0454	+	11.5268i	0.534312	+	0.438499i	0.862458	−	0.506128i	$-0.168924\pi$
$691$	14.0454	+	11.5268i	0.534312	+	0.438499i	−0.328146	+	0.944627i	$0.606424\pi$
$692$	9.24467	+	5.65988i	0.351430	+	0.215156i
$693$	7.78323	−	2.36102i	0.295660	−	0.0896876i
$694$	−3.39558	−	8.92749i	−0.128894	−	0.338883i
$695$	−7.62885	−	5.09744i	−0.289379	−	0.193357i
$696$	−16.4644	+	0.171857i	−0.624081	+	0.00651423i
$697$	−23.5883	−	35.3023i	−0.893469	−	1.33717i
$698$	5.13446	+	30.4396i	0.194342	+	1.15216i
$699$	−7.49104	−	9.12786i	−0.283337	−	0.345247i
$700$	47.1280	+	12.2771i	1.78127	+	0.464030i
$701$	1.59344	−	0.851710i	0.0601833	−	0.0321686i	−0.441031	−	0.897492i	$-0.645387\pi$
$701$	1.59344	−	0.851710i	0.0601833	−	0.0321686i	0.501214	+	0.865323i	$0.332887\pi$
$702$	3.14586	−	9.37442i	0.118733	−	0.353815i
$703$			10.7065i			0.403804i
$704$	2.04224	−	26.3673i	0.0769699	−	0.993755i
$705$		−	10.9821i		−	0.413609i
$706$	12.3665	+	4.14993i	0.465419	+	0.156185i
$707$	−4.47856	+	2.39384i	−0.168434	+	0.0900297i
$708$	−14.7758	−	25.1861i	−0.555309	−	0.946551i
$709$	−4.30893	−	5.25044i	−0.161825	−	0.197184i	0.685785	−	0.727804i	$-0.259459\pi$
$709$	−4.30893	−	5.25044i	−0.161825	−	0.197184i	−0.847610	+	0.530620i	$0.821959\pi$
$710$	−17.0318	+	2.87288i	−0.639193	+	0.107817i
$711$	−5.18670	−	7.76245i	−0.194516	−	0.291114i
$712$	−10.6363	+	26.4560i	−0.398612	+	0.991481i
$713$	−2.38054	−	1.59062i	−0.0891519	−	0.0595694i
$714$	−12.8523	+	4.88839i	−0.480986	+	0.182943i
$715$	85.3712	−	25.8971i	3.19270	−	0.968495i
$716$	−35.8916	+	8.63251i	−1.34133	+	0.322612i
$717$	−2.07935	−	1.70647i	−0.0776546	−	0.0637295i
$718$	10.4508	+	38.4671i	0.390020	+	1.43558i
$719$	16.4978	−	39.8292i	0.615264	−	1.48538i	−0.241882	−	0.970306i	$-0.577765\pi$
$719$	16.4978	−	39.8292i	0.615264	−	1.48538i	0.857146	−	0.515073i	$-0.172235\pi$
$720$	14.3721	−	5.63883i	0.535616	−	0.210147i
$721$	6.98039	+	16.8521i	0.259963	+	0.627607i
$722$	−18.8642	+	14.5795i	−0.702052	+	0.542594i
$723$	−0.0216301	−	0.219614i	−0.000804431	−	0.00816752i
$724$	8.39362	−	22.7809i	0.311946	−	0.846645i
$725$	27.1592	−	50.8113i	1.00867	−	1.88708i
$726$	−0.101489	−	0.00296897i	−0.00376662	−	0.000110189i
$727$	−3.63264	−	18.2625i	−0.134727	−	0.677318i	−0.987825	−	0.155568i	$-0.950279\pi$
$727$	−3.63264	−	18.2625i	−0.134727	−	0.677318i	0.853098	−	0.521750i	$-0.174721\pi$
$728$	−46.7069	−	13.6377i	−1.73107	−	0.505446i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	22.3527	−	14.0079i	0.827312	−	0.518456i
$731$	−1.48493	+	15.0767i	−0.0549220	+	0.557632i
$732$	−0.902361	+	0.313330i	−0.0333522	+	0.0115810i
$733$	13.0686	−	43.0814i	0.482700	−	1.59125i	−0.290362	−	0.956917i	$-0.593776\pi$
$733$	13.0686	−	43.0814i	0.482700	−	1.59125i	0.773062	−	0.634331i	$-0.218724\pi$
$734$	−26.3814	+	30.2942i	−0.973756	+	1.11818i
$735$	−2.58339	+	2.58339i	−0.0952899	+	0.0952899i
$736$	5.01274	+	3.70968i	0.184772	+	0.136740i
$737$	−10.5986	−	10.5986i	−0.390403	−	0.390403i
$738$	15.1577	−	1.04647i	0.557963	−	0.0385209i
$739$	0.529674	+	0.160675i	0.0194844	+	0.00591052i	0.300012	−	0.953935i	$-0.403009\pi$
$739$	0.529674	+	0.160675i	0.0194844	+	0.00591052i	−0.280527	+	0.959846i	$0.590509\pi$
$740$	13.7781	+	0.806819i	0.506493	+	0.0296593i
$741$	41.6679	+	4.10393i	1.53071	+	0.150762i
$742$	−4.81543	+	20.9821i	−0.176780	+	0.770277i
$743$	−3.74382	+	18.8214i	−0.137347	+	0.690492i	0.849338	+	0.527850i	$0.177002\pi$
$743$	−3.74382	+	18.8214i	−0.137347	+	0.690492i	−0.986685	+	0.162642i	$0.947998\pi$
$744$	6.51413	+	3.39494i	0.238819	+	0.124464i
$745$	−61.0954	+	12.1526i	−2.23836	+	0.445238i
$746$	−26.1692	−	27.7465i	−0.958123	−	1.01587i
$747$	−6.36694	−	3.40320i	−0.232954	−	0.124517i
$748$	−26.1077	+	1.03659i	−0.954590	+	0.0379013i
$749$	32.5779	−	3.20864i	1.19037	−	0.117241i
$750$	−3.39675	+	26.5134i	−0.124032	+	0.968133i
$751$	2.90097	−	1.20162i	0.105858	−	0.0438478i	−0.329126	−	0.944286i	$-0.606754\pi$
$751$	2.90097	−	1.20162i	0.105858	−	0.0438478i	0.434984	+	0.900438i	$0.356754\pi$
$752$	−8.93214	+	7.05352i	−0.325722	+	0.257215i
$753$	12.3514	+	5.11613i	0.450111	+	0.186442i
$754$	−28.6077	+	49.9505i	−1.04183	+	1.81909i
$755$	−15.5372	+	18.9321i	−0.565456	+	0.689011i
$756$	0.767764	−	4.86048i	0.0279233	−	0.176774i
$757$	6.27384	+	20.6821i	0.228027	+	0.751703i	0.994053	+	0.108894i	$0.0347310\pi$
$757$	6.27384	+	20.6821i	0.228027	+	0.751703i	−0.766027	+	0.642809i	$0.777769\pi$
$758$	−18.3985	+	40.9851i	−0.668264	+	1.48865i
$759$	−2.02467	+	3.03013i	−0.0734907	+	0.109987i
$760$	36.8841	+	53.9728i	1.33793	+	1.95780i
$761$	−30.2127	+	20.1875i	−1.09521	+	0.731795i	−0.965668	−	0.259779i	$-0.916350\pi$
$761$	−30.2127	+	20.1875i	−1.09521	+	0.731795i	−0.129540	+	0.991574i	$0.541350\pi$
$762$	12.8687	+	9.15401i	0.466185	+	0.331615i
$763$	−7.98255	+	6.55111i	−0.288988	+	0.237166i
$764$	18.1986	+	13.7642i	0.658404	+	0.497970i
$765$	−7.19022	−	13.4520i	−0.259963	−	0.486357i
$766$	−1.47769	+	0.735119i	−0.0533911	+	0.0265609i
$767$	−102.085			−3.68606
$768$	−13.8171	−	8.06768i	−0.498582	−	0.291117i
$769$	10.2358			0.369111			0.184555	−	0.982822i	$-0.440916\pi$
$769$	10.2358			0.369111			0.184555	+	0.982822i	$0.440916\pi$
$770$	39.7487	−	19.7741i	1.43244	−	0.712609i
$771$	6.41204	+	11.9961i	0.230924	+	0.432028i
$772$	−15.8293	−	11.9722i	−0.569710	−	0.430889i
$773$	−20.0823	+	16.4811i	−0.722311	+	0.592785i	−0.922053	−	0.387063i	$-0.873489\pi$
$773$	−20.0823	+	16.4811i	−0.722311	+	0.592785i	0.199742	+	0.979848i	$0.435989\pi$
$774$	−4.41774	−	3.14250i	−0.158792	−	0.112955i
$775$	−21.3718	+	14.2802i	−0.767698	+	0.512960i
$776$	26.7912	−	18.3086i	0.961747	−	0.657242i
$777$	2.44395	−	3.65762i	0.0876761	−	0.131216i
$778$	11.0911	−	24.7070i	0.397636	−	0.885787i
$779$	18.6755	+	61.5648i	0.669118	+	2.20579i
$780$	8.42130	−	53.3127i	0.301531	−	1.90890i
$781$	−6.63623	+	8.08626i	−0.237463	+	0.289349i
$782$	3.06198	−	5.34638i	0.109496	−	0.191186i
$783$	−5.37823	−	2.22774i	−0.192202	−	0.0796128i
$784$	3.76043	+	0.441923i	0.134301	+	0.0157829i
$785$	−10.2731	+	4.25524i	−0.366661	+	0.151876i
$786$	0.372181	−	2.90506i	0.0132752	−	0.103620i
$787$	10.2945	−	1.01392i	0.366959	−	0.0361423i	0.0871426	−	0.996196i	$-0.472226\pi$
$787$	10.2945	−	1.01392i	0.366959	−	0.0361423i	0.279816	+	0.960054i	$0.409726\pi$
$788$	6.52210	−	0.258955i	0.232340	−	0.00922490i
$789$	18.5035	+	9.89030i	0.658740	+	0.352104i
$790$	−34.9641	−	37.0714i	−1.24397	−	1.31894i
$791$	41.4471	−	8.24433i	1.47369	−	0.293135i
$792$	4.32133	−	8.29167i	0.153552	−	0.294632i
$793$	−0.651489	+	3.27526i	−0.0231351	+	0.116308i
$794$	−10.2501	+	44.6625i	−0.363764	+	1.58501i
$795$	−23.7648	−	2.34063i	−0.842850	−	0.0830135i
$796$	21.6935	+	1.27033i	0.768905	+	0.0450256i
$797$	1.02587	+	0.311194i	0.0363382	+	0.0110231i	0.308401	−	0.951256i	$-0.400206\pi$
$797$	1.02587	+	0.311194i	0.0363382	+	0.0110231i	−0.272063	+	0.962279i	$0.587706\pi$
$798$	20.7864	−	1.43506i	0.735830	−	0.0508006i
$799$	7.95105	+	7.95105i	0.281288	+	0.281288i
$800$	47.9912	−	28.8323i	1.69675	−	1.01938i
$801$	−7.12852	+	7.12852i	−0.251874	+	0.251874i
$802$	−29.5827	+	33.9703i	−1.04460	+	1.19953i
$803$	4.63763	−	15.2882i	0.163659	−	0.539510i
$804$	−8.56638	+	2.97453i	−0.302113	+	0.104904i
$805$	−1.02611	+	10.4182i	−0.0361655	+	0.367195i
$806$	21.7607	−	13.6369i	0.766489	−	0.480339i
$807$	−16.5838	−	3.29871i	−0.583776	−	0.116120i
$808$	−1.63624	+	5.60386i	−0.0575627	+	0.197143i
$809$	2.22966	+	11.2093i	0.0783906	+	0.394096i	0.999982	+	0.00593574i	$0.00188942\pi$
$809$	2.22966	+	11.2093i	0.0783906	+	0.394096i	−0.921592	+	0.388161i	$0.873111\pi$
$810$	5.45607	+	0.159612i	0.191707	+	0.00560819i
$811$	−0.326243	+	0.610357i	−0.0114559	+	0.0214325i	−0.887584	−	0.460646i	$-0.847618\pi$
$811$	−0.326243	+	0.610357i	−0.0114559	+	0.0214325i	0.876128	+	0.482078i	$0.160118\pi$
$812$	−9.90354	+	26.8789i	−0.347546	+	0.943266i
$813$	−0.669390	−	6.79643i	−0.0234765	−	0.238361i
$814$	6.61370	−	5.11153i	0.231810	−	0.179159i
$815$	35.0093	+	84.5200i	1.22632	+	2.96061i
$816$	−6.32289	+	14.4880i	−0.221345	+	0.507180i
$817$	8.78483	−	21.2084i	0.307342	−	0.741990i
$818$	−13.2444	−	48.7496i	−0.463079	−	1.70449i
$819$	−13.2980	−	10.9134i	−0.464671	−	0.381346i
$820$	80.6343	−	19.3939i	2.81587	−	0.677263i
$821$	10.8369	−	3.28733i	0.378209	−	0.114729i	−0.0954555	−	0.995434i	$-0.530431\pi$
$821$	10.8369	−	3.28733i	0.378209	−	0.114729i	0.473665	+	0.880705i	$0.342931\pi$
$822$	15.2602	−	5.80424i	0.532262	−	0.202446i
$823$	−42.3139	−	28.2732i	−1.47497	−	0.985543i	−0.994067	−	0.108768i	$-0.965309\pi$
$823$	−42.3139	−	28.2732i	−1.47497	−	0.985543i	−0.480902	−	0.876774i	$-0.659691\pi$
$824$	19.4558	+	7.82196i	0.677776	+	0.272491i
$825$	18.1769	+	27.2036i	0.632838	+	0.947109i
$826$	−50.0936	+	8.44963i	−1.74298	+	0.294000i
$827$	−2.13121	−	2.59689i	−0.0741096	−	0.0903028i	0.734636	−	0.678462i	$-0.237353\pi$
$827$	−2.13121	−	2.59689i	−0.0741096	−	0.0903028i	−0.808745	+	0.588159i	$0.799853\pi$
$828$	1.11566	+	1.90170i	0.0387719	+	0.0660886i
$829$	−27.6079	+	14.7567i	−0.958862	+	0.512522i	−0.875089	−	0.483963i	$-0.839197\pi$
$829$	−27.6079	+	14.7567i	−0.958862	+	0.512522i	−0.0837729	+	0.996485i	$0.526697\pi$
$830$	−37.3589	−	12.5369i	−1.29675	−	0.435161i
$831$			8.77305i			0.304334i
$832$	−48.7700	+	27.3921i	−1.69080	+	0.949649i
$833$		−	3.74077i		−	0.129610i
$834$	−1.06955	+	3.18717i	−0.0370354	+	0.110363i
$835$	9.47913	−	5.06670i	0.328039	−	0.175340i
$836$	38.3127	+	9.98065i	1.32507	+	0.345188i
$837$	1.64758	+	2.00759i	0.0569488	+	0.0693923i
$838$	−4.08206	−	24.2005i	−0.141012	−	0.835992i
$839$	−8.87562	−	13.2833i	−0.306420	−	0.458591i	0.646018	−	0.763322i	$-0.276433\pi$
$839$	−8.87562	−	13.2833i	−0.306420	−	0.458591i	−0.952438	+	0.304732i	$0.901433\pi$
$840$	−0.280346	−	26.8579i	−0.00967285	−	0.926686i
$841$	4.06436	+	2.71572i	0.140150	+	0.0936454i
$842$	2.39438	+	6.29519i	0.0825158	+	0.216947i
$843$	−9.94541	+	3.01691i	−0.342538	+	0.103908i
$844$	−1.86091	−	1.13931i	−0.0640550	−	0.0392166i
$845$	−107.075	−	87.8738i	−3.68348	−	3.02295i
$846$	−3.88316	+	1.05498i	−0.133506	+	0.0362711i
$847$	−0.0675976	+	0.163195i	−0.00232268	+	0.00560745i
$848$	13.3598	+	20.8321i	0.458778	+	0.715379i
$849$	−3.75593	−	9.06761i	−0.128903	−	0.311200i
$850$	−33.8249	−	43.7653i	−1.16018	−	1.50114i
$851$	0.193194	+	1.96153i	0.00662261	+	0.0672405i
$852$	2.65197	+	5.74632i	0.0908550	+	0.196866i
$853$	9.73030	−	18.2041i	0.333159	−	0.623297i	−0.658442	−	0.752632i	$-0.728784\pi$
$853$	9.73030	−	18.2041i	0.333159	−	0.623297i	0.991601	+	0.129335i	$0.0412841\pi$
$854$	−0.0485943	+	1.66112i	−0.00166286	+	0.0568422i
$855$	4.50902	+	22.6684i	0.154205	+	0.775242i
$856$	23.5689	−	29.3379i	0.805568	−	1.00275i
$857$	−38.0243	−	7.56351i	−1.29889	−	0.258364i	−0.503251	−	0.864140i	$-0.667863\pi$
$857$	−38.0243	−	7.56351i	−1.29889	−	0.258364i	−0.795635	+	0.605776i	$0.792863\pi$
$858$	−17.3581	−	27.6987i	−0.592595	−	0.945617i
$859$	5.06953	−	51.4718i	0.172970	−	1.75620i	−0.381849	−	0.924225i	$-0.624713\pi$
$859$	5.06953	−	51.4718i	0.172970	−	1.75620i	0.554820	−	0.831971i	$-0.312787\pi$
$860$	−26.6309	−	12.9033i	−0.908106	−	0.439999i
$861$	7.67319	−	25.2951i	0.261502	−	0.862055i
$862$	21.1377	+	18.4076i	0.719953	+	0.626964i
$863$	28.7375	−	28.7375i	0.978236	−	0.978236i	−0.0215319	−	0.999768i	$-0.506854\pi$
$863$	28.7375	−	28.7375i	0.978236	−	0.978236i	0.999768	+	0.0215319i	$0.00685434\pi$
$864$	−3.37448	−	4.54014i	−0.114802	−	0.154459i
$865$	14.7918	+	14.7918i	0.502936	+	0.502936i
$866$	−0.394229	−	5.71029i	−0.0133965	−	0.194043i
$867$	−1.32299	−	0.401324i	−0.0449311	−	0.0136297i
$868$	9.54939	−	8.49287i	0.324127	−	0.288267i
$869$	−30.7136	−	3.02502i	−1.04189	−	0.102617i
$870$	−30.9701	−	7.10770i	−1.04999	−	0.240974i
$871$	−6.18478	+	31.0930i	−0.209563	+	1.05355i
$872$	−1.04022	+	11.8257i	−0.0352264	+	0.400469i
$873$	11.2522	−	2.23820i	0.380829	−	0.0757517i
$874$	−6.79161	+	6.40554i	−0.229730	+	0.216671i
$875$	41.0125	+	21.9216i	1.38648	+	0.741086i
$876$	−7.10036	−	6.55807i	−0.239899	−	0.221577i
$877$	23.4015	−	2.30485i	0.790212	−	0.0778291i	0.305145	−	0.952306i	$-0.401295\pi$
$877$	23.4015	−	2.30485i	0.790212	−	0.0778291i	0.485067	+	0.874477i	$0.338795\pi$
$878$	−56.3016	−	7.21305i	−1.90009	−	0.243429i
$879$	12.7265	−	5.27149i	0.429254	−	0.177803i
$880$	15.7311	−	48.5521i	0.530297	−	1.63669i
$881$	−11.6029	−	4.80610i	−0.390913	−	0.161922i	0.178565	−	0.983928i	$-0.442855\pi$
$881$	−11.6029	−	4.80610i	−0.390913	−	0.161922i	−0.569478	+	0.822007i	$0.692855\pi$
$882$	1.16164	+	0.665293i	0.0391143	+	0.0224016i
$883$	−32.3215	+	39.3838i	−1.08770	+	1.32537i	−0.145866	+	0.989304i	$0.546597\pi$
$883$	−32.3215	+	39.3838i	−1.08770	+	1.32537i	−0.941838	+	0.336067i	$0.890903\pi$
$884$	32.5015	+	44.6955i	1.09314	+	1.50327i
$885$	−16.3581	−	53.9255i	−0.549872	−	1.81269i
$886$	3.67329	+	1.64897i	0.123407	+	0.0553982i
$887$	11.3620	−	17.0044i	0.381497	−	0.570951i	−0.590177	−	0.807274i	$-0.700942\pi$
$887$	11.3620	−	17.0044i	0.381497	−	0.570951i	0.971675	+	0.236323i	$0.0759422\pi$
$888$	−1.03830	−	4.94931i	−0.0348429	−	0.166088i
$889$	22.8444	−	15.2642i	0.766178	−	0.511944i
$890$	−31.8965	+	44.8401i	−1.06917	+	1.50305i
$891$	2.55541	−	2.09717i	0.0856093	−	0.0702577i
$892$	6.60195	+	47.5857i	0.221050	+	1.59329i
$893$	−8.03188	−	15.0266i	−0.268776	−	0.502845i
$894$	10.1661	+	20.4353i	0.340006	+	0.683459i
$895$	−71.2402			−2.38130
$896$	−21.6645	+	17.4782i	−0.723760	+	0.583906i
$897$	7.70800			0.257363
$898$	−17.4554	−	35.0877i	−0.582493	−	1.17089i
$899$	−7.12688	−	13.3335i	−0.237695	−	0.444696i
$900$	19.6063	−	2.72015i	0.653544	−	0.0906716i
$901$	18.9004	−	15.5111i	0.629663	−	0.516751i
$902$	29.1141	−	40.9287i	0.969394	−	1.36278i
$903$	−7.84231	+	5.24007i	−0.260976	+	0.174379i
$904$	26.5669	−	40.6729i	0.883603	−	1.35276i
$905$	26.0299	−	38.9565i	0.865263	−	1.29496i
$906$	8.18679	+	3.67511i	0.271988	+	0.122097i
$907$	−2.66744	−	8.79338i	−0.0885709	−	0.291979i	0.901453	−	0.432876i	$-0.142501\pi$
$907$	−2.66744	−	8.79338i	−0.0885709	−	0.291979i	−0.990024	+	0.140897i	$0.955001\pi$
$908$	14.8421	−	10.7928i	0.492554	−	0.358172i
$909$	−1.30938	+	1.59549i	−0.0434295	+	0.0529190i
$910$	−81.4830	−	46.6670i	−2.70114	−	1.54700i
$911$	7.61469	+	3.15411i	0.252286	+	0.104500i	0.505243	−	0.862977i	$-0.331403\pi$
$911$	7.61469	+	3.15411i	0.252286	+	0.104500i	−0.252957	+	0.967478i	$0.581403\pi$
$912$	15.5410	−	18.2267i	0.514615	−	0.603547i
$913$	−22.0491	+	9.13304i	−0.729719	+	0.302259i
$914$	−20.4594	−	2.62115i	−0.676737	−	0.0866999i
$915$	−1.83453	+	0.180685i	−0.0606476	+	0.00597326i
$916$	18.1855	−	19.6893i	0.600866	−	0.650553i
$917$	−4.49372	−	2.40194i	−0.148396	−	0.0793191i
$918$	−4.06577	+	3.83465i	−0.134190	+	0.126562i
$919$	12.1771	−	2.42217i	0.401685	−	0.0799001i	0.00988643	−	0.999951i	$-0.496853\pi$
$919$	12.1771	−	2.42217i	0.401685	−	0.0799001i	0.391799	+	0.920051i	$0.371853\pi$
$920$	7.73142	+	9.22275i	0.254897	+	0.304065i
$921$	−4.21928	+	21.2118i	−0.139030	+	0.698951i
$922$	−0.740293	−	0.169899i	−0.0243803	−	0.00559531i
$923$	22.0188	+	2.16866i	0.724757	+	0.0713824i
$924$	−10.8104	−	12.1552i	−0.355635	−	0.399876i
$925$	16.9334	+	5.13668i	0.556765	+	0.168893i
$926$	1.57409	+	22.8001i	0.0517277	+	0.749259i
$927$	5.24233	+	5.24233i	0.172181	+	0.172181i
$928$	14.1104	+	29.7543i	0.463196	+	0.976733i
$929$	15.6586	−	15.6586i	0.513741	−	0.513741i	−0.401930	−	0.915671i	$-0.631660\pi$
$929$	15.6586	−	15.6586i	0.513741	−	0.513741i	0.915671	+	0.401930i	$0.131660\pi$
$930$	10.6905	+	9.30976i	0.350557	+	0.305279i
$931$	−1.64542	+	5.42421i	−0.0539263	+	0.177771i
$932$	−10.2976	+	21.2531i	−0.337310	+	0.696167i
$933$	2.37319	−	24.0954i	0.0776947	−	0.788848i
$934$	−2.60649	−	4.15923i	−0.0852869	−	0.136094i
$935$	−49.4543	−	9.83707i	−1.61733	−	0.321707i
$936$	−19.6598	+	2.14374i	−0.642602	+	0.0700704i
$937$	−1.46447	−	7.36240i	−0.0478422	−	0.240519i	0.949463	−	0.313878i	$-0.101628\pi$
$937$	−1.46447	−	7.36240i	−0.0478422	−	0.240519i	−0.997306	+	0.0733587i	$0.976628\pi$
$938$	−0.461320	+	15.7695i	−0.0150626	+	0.514891i
$939$	−5.08693	+	9.51698i	−0.166006	+	0.310575i
$940$	−19.9428	+	9.20375i	−0.650462	+	0.300193i
$941$	3.23200	+	32.8151i	0.105360	+	1.06974i	0.891910	+	0.452213i	$0.149365\pi$
$941$	3.23200	+	32.8151i	0.105360	+	1.06974i	−0.786550	+	0.617527i	$0.788135\pi$
$942$	2.49148	+	3.22368i	0.0811770	+	0.105033i
$943$	4.53243	+	10.9423i	0.147596	+	0.356329i
$944$	−33.3533	+	47.9397i	−1.08556	+	1.56030i
$945$	3.63405	−	8.77336i	0.118216	−	0.285398i
$946$	−17.2951	+	4.69876i	−0.562312	+	0.152770i
$947$	−29.1082	−	23.8885i	−0.945889	−	0.776271i	0.0288582	−	0.999584i	$-0.490813\pi$
$947$	−29.1082	−	23.8885i	−0.945889	−	0.776271i	−0.974747	+	0.223313i	$0.928313\pi$
$948$	−9.74932	+	15.9242i	−0.316643	+	0.517194i
$949$	−32.3359	+	9.80897i	−1.04967	+	0.318413i
$950$	29.7963	+	78.3390i	0.966719	+	2.54165i
$951$	10.6079	+	7.08797i	0.343985	+	0.229843i
$952$	19.6482	+	19.2422i	0.636801	+	0.623644i
$953$	−24.1655	−	36.1662i	−0.782797	−	1.17154i	−0.981497	−	0.191478i	$-0.938672\pi$
$953$	−24.1655	−	36.1662i	−0.782797	−	1.17154i	0.198700	−	0.980060i	$-0.436328\pi$
$954$	1.45532	+	8.62786i	0.0471177	+	0.279337i
$955$	27.9350	+	34.0389i	0.903956	+	1.10147i
$956$	−1.35622	+	5.20611i	−0.0438632	+	0.168378i
$957$	−16.9718	+	9.07162i	−0.548621	+	0.293244i
$958$	1.45516	−	4.33629i	0.0470142	−	0.140099i
$959$		−	28.4044i		−	0.917227i
$960$	−22.2846	−	21.3731i	−0.719232	−	0.689813i
$961$		−	24.2551i		−	0.782422i
$962$	−16.7609	−	5.62459i	−0.540392	−	0.181344i
$963$	11.7341	−	6.27198i	0.378125	−	0.202112i
$964$	−0.380678	+	0.223331i	−0.0122608	+	0.00719300i
$965$	−24.2981	−	29.6074i	−0.782184	−	0.953094i
$966$	3.78237	−	0.637997i	0.121696	−	0.0205272i
$967$	−8.59168	−	12.8584i	−0.276290	−	0.413497i	0.667210	−	0.744869i	$-0.267488\pi$
$967$	−8.59168	−	12.8584i	−0.276290	−	0.413497i	−0.943500	+	0.331373i	$0.892488\pi$
$968$	0.0796637	+	0.186787i	0.00256049	+	0.00600355i
$969$	−19.6765	−	13.1474i	−0.632101	−	0.422356i
$970$	58.5315	−	22.2625i	1.87933	−	0.714805i
$971$	−36.0408	+	10.9328i	−1.15660	+	0.350852i	−0.809583	−	0.587006i	$-0.800307\pi$
$971$	−36.0408	+	10.9328i	−1.15660	+	0.350852i	−0.347020	+	0.937858i	$0.612807\pi$
$972$	−0.467695	−	1.94455i	−0.0150013	−	0.0623714i
$973$	4.52115	+	3.71041i	0.144941	+	0.118950i
$974$	−5.20294	−	19.1509i	−0.166713	−	0.613633i
$975$	26.4818	−	63.9327i	0.848097	−	2.04749i
$976$	1.32523	+	1.37604i	0.0424196	+	0.0440460i
$977$	15.1634	+	36.6078i	0.485121	+	1.17119i	0.957147	+	0.289602i	$0.0935229\pi$
$977$	15.1634	+	36.6078i	0.485121	+	1.17119i	−0.472026	+	0.881585i	$0.656477\pi$
$978$	26.5224	−	20.4983i	0.848091	−	0.655464i
$979$	3.26656	+	33.1659i	0.104400	+	1.05999i
$980$	6.85636	+	2.52622i	0.219018	+	0.0806972i
$981$	−1.97853	+	3.70156i	−0.0631695	+	0.118182i
$982$	25.2944	+	0.739962i	0.807176	+	0.0236131i
$983$	2.08996	+	10.5069i	0.0666593	+	0.335119i	0.999696	−	0.0246626i	$-0.00785115\pi$
$983$	2.08996	+	10.5069i	0.0666593	+	0.335119i	−0.933036	+	0.359782i	$0.882851\pi$
$984$	−14.6036	−	26.6485i	−0.465544	−	0.849523i
$985$	12.3545	+	2.45746i	0.393646	+	0.0783010i
$986$	27.5684	−	17.2765i	0.877958	−	0.550195i
$987$	−0.686178	+	6.96688i	−0.0218413	+	0.221758i
$988$	−27.4681	−	79.1058i	−0.873878	−	2.51669i
$989$	1.22677	−	4.04410i	0.0390089	−	0.128595i
$990$	11.8502	−	13.6077i	0.376623	−	0.432482i
$991$	30.0178	−	30.0178i	0.953547	−	0.953547i	−0.0454205	−	0.998968i	$-0.514463\pi$
$991$	30.0178	−	30.0178i	0.953547	−	0.953547i	0.998968	+	0.0454205i	$0.0144628\pi$
$992$	0.705704	−	14.6745i	0.0224061	−	0.465915i
$993$	−10.0104	−	10.0104i	−0.317672	−	0.317672i
$994$	10.9843	−	0.758337i	0.348400	−	0.0240530i
$995$	40.1308	+	12.1735i	1.27223	+	0.385927i
$996$	−0.844064	+	14.4141i	−0.0267452	+	0.456728i
$997$	−22.4162	−	2.20781i	−0.709929	−	0.0699219i	−0.263394	−	0.964688i	$-0.584842\pi$
$997$	−22.4162	−	2.20781i	−0.709929	−	0.0699219i	−0.446535	+	0.894766i	$0.647342\pi$
$998$	−4.47304	+	19.4902i	−0.141592	+	0.616952i
$999$	0.348809	−	1.75358i	0.0110358	−	0.0554809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.5	✓	512
128.45	even	32	inner	384.2.v.a.301.5	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.5	✓	512	1.1	even	1	trivial
384.2.v.a.301.5	yes	512	128.45	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)

\(f(q)\)	\(=\)	\(q+(-1.26619 + 0.629900i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.20645 - 1.59514i) q^{4} +(2.98357 - 2.44855i) q^{5} +(-1.15240 - 0.819743i) q^{6} +(-2.04572 + 1.36691i) q^{7} +(-0.522814 + 2.77969i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(-1.26619 + 0.629900i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.20645 - 1.59514i) q^{4} +(2.98357 - 2.44855i) q^{5} +(-1.15240 - 0.819743i) q^{6} +(-2.04572 + 1.36691i) q^{7} +(-0.522814 + 2.77969i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-2.23541 + 4.97967i) q^{10} +(0.959618 + 3.16344i) q^{11} +(1.97551 + 0.312052i) q^{12} +(4.43568 - 5.40489i) q^{13} +(1.72925 - 3.01936i) q^{14} +(3.56587 + 1.47703i) q^{15} +(-1.08895 - 3.84892i) q^{16} +(-3.65108 + 1.51233i) q^{17} +(0.179713 - 1.40275i) q^{18} +(5.95936 - 0.586946i) q^{19} +(-0.306249 - 7.71326i) q^{20} +(-2.16985 - 1.15981i) q^{21} +(-3.20770 - 3.40104i) q^{22} +(1.08122 - 0.215068i) q^{23} +(-2.69792 + 0.849255i) q^{24} +(1.93082 - 9.70689i) q^{25} +(-2.21185 + 9.63763i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-0.287657 + 4.91233i) q^{28} +(5.57069 + 1.68985i) q^{29} +(-5.44544 + 0.375945i) q^{30} +(-1.83643 - 1.83643i) q^{31} +(3.80324 + 4.18752i) q^{32} +(-2.33754 + 2.33754i) q^{33} +(3.67033 - 4.21470i) q^{34} +(-2.75661 + 9.08732i) q^{35} +(0.656042 + 1.88934i) q^{36} +(-0.175248 + 1.77933i) q^{37} +(-7.17594 + 4.49699i) q^{38} +(6.85765 + 1.36407i) q^{39} +(5.24635 + 9.57352i) q^{40} +(2.09598 + 10.5372i) q^{41} +(3.47800 + 0.101746i) q^{42} +(1.80711 - 3.38086i) q^{43} +(6.20386 + 2.28581i) q^{44} +(0.378314 + 3.84109i) q^{45} +(-1.23355 + 0.953376i) q^{46} +(-1.08886 - 2.62875i) q^{47} +(2.88112 - 2.77473i) q^{48} +(-0.362239 + 0.874522i) q^{49} +(3.66959 + 13.5070i) q^{50} +(-3.05486 - 2.50706i) q^{51} +(-3.27012 - 13.5963i) q^{52} +(-5.92059 + 1.79599i) q^{53} +(1.32183 - 0.502759i) q^{54} +(10.6089 + 7.08865i) q^{55} +(-2.73005 - 6.40111i) q^{56} +(3.32687 + 4.97901i) q^{57} +(-8.11796 + 1.36931i) q^{58} +(-9.26227 - 11.2861i) q^{59} +(6.65813 - 3.90610i) q^{60} +(-0.421211 + 0.225142i) q^{61} +(3.48202 + 1.16849i) q^{62} -2.46037i q^{63} +(-7.45333 - 2.90652i) q^{64} -26.9868i q^{65} +(1.48734 - 4.43218i) q^{66} +(-3.99868 + 2.13734i) q^{67} +(-1.99248 + 7.64853i) q^{68} +(0.699356 + 0.852168i) q^{69} +(-2.23372 - 13.2426i) q^{70} +(1.75803 + 2.63108i) q^{71} +(-2.02077 - 1.97902i) q^{72} +(-4.01832 - 2.68495i) q^{73} +(-0.898901 - 2.36335i) q^{74} +(9.47090 - 2.87297i) q^{75} +(6.25343 - 10.2141i) q^{76} +(-6.28724 - 5.15981i) q^{77} +(-9.54229 + 2.59247i) q^{78} +(-3.57266 + 8.62517i) q^{79} +(-12.6732 - 8.81718i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-9.29128 - 12.0218i) q^{82} +(0.707625 + 7.18464i) q^{83} +(-4.46789 + 2.06196i) q^{84} +(-7.19022 + 13.4520i) q^{85} +(-0.158530 + 5.41909i) q^{86} +(1.13569 + 5.70950i) q^{87} +(-9.29507 + 1.01355i) q^{88} +(9.88754 + 1.96675i) q^{89} +(-2.89851 - 4.62523i) q^{90} +(-1.68618 + 17.1201i) q^{91} +(0.961376 - 1.98417i) q^{92} +(0.753898 - 2.48527i) q^{93} +(3.03455 + 2.64261i) q^{94} +(16.3430 - 16.3430i) q^{95} +(-1.90023 + 5.32814i) q^{96} +(-8.11239 - 8.11239i) q^{97} +(-0.0921996 - 1.33548i) q^{98} +(-3.16344 - 0.959618i) 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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