LMFDB - Embedded newform 384.2.v.a.229.26

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			229.26
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17584 + 0.785745i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.765208 + 1.84782i) q^{4} +(1.34312 + 1.63660i) q^{5} +(1.40740 + 0.138678i) q^{6} +(2.27625 - 1.52094i) q^{7} +(-0.552156 + 2.77401i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(1.17584 + 0.785745i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.765208 + 1.84782i) q^{4} +(1.34312 + 1.63660i) q^{5} +(1.40740 + 0.138678i) q^{6} +(2.27625 - 1.52094i) q^{7} +(-0.552156 + 2.77401i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.293349 + 2.97974i) q^{10} +(-5.37629 + 1.63088i) q^{11} +(1.54591 + 1.26892i) q^{12} +(-4.48489 - 3.68066i) q^{13} +(3.87158 + 0.000166343i) q^{14} +(1.95602 + 0.810209i) q^{15} +(-2.82891 + 2.82794i) q^{16} +(6.89563 - 2.85626i) q^{17} +(1.30659 - 0.541140i) q^{18} +(-0.104845 - 1.06451i) q^{19} +(-1.99638 + 3.73420i) q^{20} +(1.29050 - 2.41436i) q^{21} +(-7.60313 - 2.30674i) q^{22} +(-4.94980 + 0.984576i) q^{23} +(0.820700 + 2.70674i) q^{24} +(0.100970 - 0.507609i) q^{25} +(-2.38147 - 7.85185i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(4.55223 + 3.04227i) q^{28} +(-0.600058 + 1.97813i) q^{29} +(1.66335 + 2.48961i) q^{30} +(3.77236 + 3.77236i) q^{31} +(-5.54840 + 1.10241i) q^{32} +(-3.97267 + 3.97267i) q^{33} +(10.3525 + 2.05970i) q^{34} +(5.54645 + 1.68250i) q^{35} +(1.96154 + 0.390349i) q^{36} +(6.33038 + 0.623488i) q^{37} +(0.713152 - 1.33408i) q^{38} +(-5.69037 - 1.13189i) q^{39} +(-5.28156 + 2.82218i) q^{40} +(0.767908 + 3.86054i) q^{41} +(3.41451 - 1.82490i) q^{42} +(-9.63017 - 5.14743i) q^{43} +(-7.12756 - 8.68648i) q^{44} +(2.10698 - 0.207520i) q^{45} +(-6.59380 - 2.73158i) q^{46} +(-1.45424 - 3.51085i) q^{47} +(-1.16180 + 3.82756i) q^{48} +(0.189259 - 0.456911i) q^{49} +(0.517576 - 0.517532i) q^{50} +(4.73497 - 5.76958i) q^{51} +(3.36933 - 11.1038i) q^{52} +(-0.0652695 - 0.215165i) q^{53} +(0.897215 - 1.09316i) q^{54} +(-9.89013 - 6.60837i) q^{55} +(2.96226 + 7.15412i) q^{56} +(-0.594271 - 0.889389i) q^{57} +(-2.25988 + 1.85447i) q^{58} +(9.97201 - 8.18381i) q^{59} +(-0.000363861 + 4.23436i) q^{60} +(1.46620 + 2.74306i) q^{61} +(1.47158 + 7.39981i) q^{62} -2.73762i q^{63} +(-7.39025 - 3.06337i) q^{64} -12.2836i q^{65} +(-7.79275 + 1.54973i) q^{66} +(-6.20500 - 11.6087i) q^{67} +(10.5545 + 10.5563i) q^{68} +(-3.90121 + 3.20164i) q^{69} +(5.19974 + 6.33645i) q^{70} +(6.26088 + 9.37007i) q^{71} +(1.99974 + 2.00026i) q^{72} +(-7.56594 - 5.05540i) q^{73} +(6.95362 + 5.70719i) q^{74} +(-0.150238 - 0.495268i) q^{75} +(1.88680 - 1.00831i) q^{76} +(-9.75730 + 11.8893i) q^{77} +(-5.80160 - 5.80210i) q^{78} +(-1.24699 + 3.01049i) q^{79} +(-8.42779 - 0.831528i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-2.13046 + 5.14276i) q^{82} +(-5.37290 + 0.529185i) q^{83} +(5.44883 + 0.537135i) q^{84} +(13.9362 + 7.44908i) q^{85} +(-7.27898 - 13.6194i) q^{86} +(0.403278 + 2.02742i) q^{87} +(-1.55552 - 15.8144i) q^{88} +(1.61165 + 0.320578i) q^{89} +(2.64054 + 1.41154i) q^{90} +(-15.8068 - 1.55683i) q^{91} +(-5.60695 - 8.39295i) q^{92} +(5.10520 + 1.54865i) q^{93} +(1.04868 - 5.27087i) q^{94} +(1.60136 - 1.60136i) q^{95} +(-4.37358 + 3.58773i) q^{96} +(-2.77097 - 2.77097i) q^{97} +(0.581554 - 0.388546i) q^{98} +(-1.63088 + 5.37629i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	1.17584	+	0.785745i	0.831446	+	0.555606i
$2$	1.17584	+	0.785745i	0.831446	+	0.555606i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	0.765208	+	1.84782i	0.382604	+	0.923912i
$5$	1.34312	+	1.63660i	0.600663	+	0.731910i	0.981230	−	0.192843i	$-0.0617709\pi$
$5$	1.34312	+	1.63660i	0.600663	+	0.731910i	−0.380566	+	0.924754i	$0.624271\pi$
$6$	1.40740	+	0.138678i	0.574568	+	0.0566149i
$7$	2.27625	−	1.52094i	0.860340	−	0.574861i	−0.0452685	−	0.998975i	$-0.514414\pi$
$7$	2.27625	−	1.52094i	0.860340	−	0.574861i	0.905609	+	0.424114i	$0.139414\pi$
$8$	−0.552156	+	2.77401i	−0.195217	+	0.980760i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	0.293349	+	2.97974i	0.0927652	+	0.942276i
$11$	−5.37629	+	1.63088i	−1.62101	+	0.491729i	−0.964830	−	0.262873i	$-0.915330\pi$
$11$	−5.37629	+	1.63088i	−1.62101	+	0.491729i	−0.656183	+	0.754602i	$0.727830\pi$
$12$	1.54591	+	1.26892i	0.446266	+	0.366305i
$13$	−4.48489	−	3.68066i	−1.24389	−	1.02083i	−0.998680	−	0.0513591i	$-0.983645\pi$
$13$	−4.48489	−	3.68066i	−1.24389	−	1.02083i	−0.245205	−	0.969471i	$-0.578855\pi$
$14$	3.87158		0.000166343i	1.03472		4.44572e-5i
$15$	1.95602	+	0.810209i	0.505042	+	0.209195i
$16$	−2.82891	+	2.82794i	−0.707228	+	0.706985i
$17$	6.89563	−	2.85626i	1.67244	−	0.692746i	0.673514	−	0.739174i	$-0.264784\pi$
$17$	6.89563	−	2.85626i	1.67244	−	0.692746i	0.998922	+	0.0464287i	$0.0147840\pi$
$18$	1.30659	−	0.541140i	0.307965	−	0.127548i
$19$	−0.104845	−	1.06451i	−0.0240531	−	0.244215i	−0.999692	−	0.0248310i	$-0.992095\pi$
$19$	−0.104845	−	1.06451i	−0.0240531	−	0.244215i	0.975639	−	0.219384i	$-0.0704048\pi$
$20$	−1.99638	+	3.73420i	−0.446405	+	0.834992i
$21$	1.29050	−	2.41436i	0.281611	−	0.526857i
$22$	−7.60313	−	2.30674i	−1.62099	−	0.491799i
$23$	−4.94980	+	0.984576i	−1.03210	+	0.205298i	−0.681954	−	0.731395i	$-0.738869\pi$
$23$	−4.94980	+	0.984576i	−1.03210	+	0.205298i	−0.350150	+	0.936694i	$0.613869\pi$
$24$	0.820700	+	2.70674i	0.167525	+	0.552511i
$25$	0.100970	−	0.507609i	0.0201940	−	0.101522i
$26$	−2.38147	−	7.85185i	−0.467044	−	1.53988i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	4.55223	+	3.04227i	0.860291	+	0.574935i
$29$	−0.600058	+	1.97813i	−0.111428	+	0.367329i	−0.994864	−	0.101224i	$-0.967724\pi$
$29$	−0.600058	+	1.97813i	−0.111428	+	0.367329i	0.883436	+	0.468552i	$0.155224\pi$
$30$	1.66335	+	2.48961i	0.303685	+	0.454539i
$31$	3.77236	+	3.77236i	0.677536	+	0.677536i	0.959442	−	0.281906i	$-0.0909667\pi$
$31$	3.77236	+	3.77236i	0.677536	+	0.677536i	−0.281906	+	0.959442i	$0.590967\pi$
$32$	−5.54840	+	1.10241i	−0.980827	+	0.194880i
$33$	−3.97267	+	3.97267i	−0.691554	+	0.691554i
$34$	10.3525	+	2.05970i	1.77543	+	0.353235i
$35$	5.54645	+	1.68250i	0.937522	+	0.284394i
$36$	1.96154	+	0.390349i	0.326923	+	0.0650582i
$37$	6.33038	+	0.623488i	1.04071	+	0.102501i	0.603905	−	0.797056i	$-0.293611\pi$
$37$	6.33038	+	0.623488i	1.04071	+	0.102501i	0.436803	+	0.899557i	$0.356111\pi$
$38$	0.713152	−	1.33408i	0.115689	−	0.216416i
$39$	−5.69037	−	1.13189i	−0.911189	−	0.181247i
$40$	−5.28156	+	2.82218i	−0.835088	+	0.446225i
$41$	0.767908	+	3.86054i	0.119927	+	0.602914i	0.993271	+	0.115811i	$0.0369466\pi$
$41$	0.767908	+	3.86054i	0.119927	+	0.602914i	−0.873344	+	0.487104i	$0.838053\pi$
$42$	3.41451	−	1.82490i	0.526870	−	0.281589i
$43$	−9.63017	−	5.14743i	−1.46859	−	0.784976i	−0.473203	−	0.880953i	$-0.656902\pi$
$43$	−9.63017	−	5.14743i	−1.46859	−	0.784976i	−0.995384	+	0.0959773i	$0.969402\pi$
$44$	−7.12756	−	8.68648i	−1.07452	−	1.30954i
$45$	2.10698	−	0.207520i	0.314091	−	0.0309352i
$46$	−6.59380	−	2.73158i	−0.972203	−	0.402749i
$47$	−1.45424	−	3.51085i	−0.212123	−	0.512110i	0.781626	−	0.623747i	$-0.214391\pi$
$47$	−1.45424	−	3.51085i	−0.212123	−	0.512110i	−0.993749	+	0.111637i	$0.964391\pi$
$48$	−1.16180	+	3.82756i	−0.167691	+	0.552461i
$49$	0.189259	−	0.456911i	0.0270369	−	0.0652729i
$50$	0.517576	−	0.517532i	0.0731963	−	0.0731900i
$51$	4.73497	−	5.76958i	0.663028	−	0.807902i
$52$	3.36933	−	11.1038i	0.467242	−	1.53981i
$53$	−0.0652695	−	0.215165i	−0.00896545	−	0.0295551i	0.952343	−	0.305028i	$-0.0986657\pi$
$53$	−0.0652695	−	0.215165i	−0.00896545	−	0.0295551i	−0.961309	+	0.275472i	$0.911166\pi$
$54$	0.897215	−	1.09316i	0.122095	−	0.148761i
$55$	−9.89013	−	6.60837i	−1.33358	−	0.891073i
$56$	2.96226	+	7.15412i	0.395848	+	0.956010i
$57$	−0.594271	−	0.889389i	−0.0787131	−	0.117802i
$58$	−2.25988	+	1.85447i	−0.296736	+	0.243504i
$59$	9.97201	−	8.18381i	1.29824	−	1.06544i	0.304647	−	0.952465i	$-0.401462\pi$
$59$	9.97201	−	8.18381i	1.29824	−	1.06544i	0.993598	−	0.112977i	$-0.0360385\pi$
$60$	−0.000363861		4.23436i	−4.69742e−5		0.546653i
$61$	1.46620	+	2.74306i	0.187727	+	0.351213i	0.958125	−	0.286351i	$-0.0924423\pi$
$61$	1.46620	+	2.74306i	0.187727	+	0.351213i	−0.770398	+	0.637564i	$0.779942\pi$
$62$	1.47158	+	7.39981i	0.186891	+	0.939777i
$63$		−	2.73762i		−	0.344908i
$64$	−7.39025	−	3.06337i	−0.923781	−	0.382922i
$65$		−	12.2836i		−	1.52359i
$66$	−7.79275	+	1.54973i	−0.959221	+	0.190758i
$67$	−6.20500	−	11.6087i	−0.758062	−	1.41823i	−0.903377	−	0.428848i	$-0.858920\pi$
$67$	−6.20500	−	11.6087i	−0.758062	−	1.41823i	0.145315	−	0.989385i	$-0.453580\pi$
$68$	10.5545	+	10.5563i	1.27992	+	1.28014i
$69$	−3.90121	+	3.20164i	−0.469650	+	0.385432i
$70$	5.19974	+	6.33645i	0.621487	+	0.757351i
$71$	6.26088	+	9.37007i	0.743030	+	1.11202i	0.989733	+	0.142932i	$0.0456529\pi$
$71$	6.26088	+	9.37007i	0.743030	+	1.11202i	−0.246703	+	0.969091i	$0.579347\pi$
$72$	1.99974	+	2.00026i	0.235672	+	0.235733i
$73$	−7.56594	−	5.05540i	−0.885526	−	0.591690i	0.0274860	−	0.999622i	$-0.491250\pi$
$73$	−7.56594	−	5.05540i	−0.885526	−	0.591690i	−0.913012	+	0.407933i	$0.866250\pi$
$74$	6.95362	+	5.70719i	0.808342	+	0.663448i
$75$	−0.150238	−	0.495268i	−0.0173480	−	0.0571887i
$76$	1.88680	−	1.00831i	0.216431	−	0.115661i
$77$	−9.75730	+	11.8893i	−1.11195	+	1.35491i
$78$	−5.80160	−	5.80210i	−0.656902	−	0.656959i
$79$	−1.24699	+	3.01049i	−0.140297	+	0.338706i	−0.978374	−	0.206846i	$-0.933680\pi$
$79$	−1.24699	+	3.01049i	−0.140297	+	0.338706i	0.838077	+	0.545552i	$0.183680\pi$
$80$	−8.42779	−	0.831528i	−0.942256	−	0.0929676i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−2.13046	+	5.14276i	−0.235270	+	0.567923i
$83$	−5.37290	+	0.529185i	−0.589753	+	0.0580856i	−0.388492	−	0.921452i	$-0.627004\pi$
$83$	−5.37290	+	0.529185i	−0.589753	+	0.0580856i	−0.201261	+	0.979538i	$0.564504\pi$
$84$	5.44883	+	0.537135i	0.594516	+	0.0586063i
$85$	13.9362	+	7.44908i	1.51160	+	0.807966i
$86$	−7.27898	−	13.6194i	−0.784913	−	1.46862i
$87$	0.403278	+	2.02742i	0.0432360	+	0.217362i
$88$	−1.55552	−	15.8144i	−0.165819	−	1.68582i
$89$	1.61165	+	0.320578i	0.170835	+	0.0339812i	0.279767	−	0.960068i	$-0.409743\pi$
$89$	1.61165	+	0.320578i	0.170835	+	0.0339812i	−0.108932	+	0.994049i	$0.534743\pi$
$90$	2.64054	+	1.41154i	0.278337	+	0.148790i
$91$	−15.8068	−	1.55683i	−1.65700	−	0.163200i
$92$	−5.60695	−	8.39295i	−0.584565	−	0.875026i
$93$	5.10520	+	1.54865i	0.529385	+	0.160587i
$94$	1.04868	−	5.27087i	0.108163	−	0.543649i
$95$	1.60136	−	1.60136i	0.164296	−	0.164296i
$96$	−4.37358	+	3.58773i	−0.446376	+	0.366171i
$97$	−2.77097	−	2.77097i	−0.281350	−	0.281350i	0.552298	−	0.833647i	$-0.313751\pi$
$97$	−2.77097	−	2.77097i	−0.281350	−	0.281350i	−0.833647	+	0.552298i	$0.813751\pi$
$98$	0.581554	−	0.388546i	0.0587458	−	0.0392490i
$99$	−1.63088	+	5.37629i	−0.163910	+	0.540338i
$100$	1.01524	−	0.201852i	0.101524	−	0.0201852i
$101$	−1.22819	+	12.4701i	−0.122210	+	1.24082i	0.717024	+	0.697048i	$0.245504\pi$
$101$	−1.22819	+	12.4701i	−0.122210	+	1.24082i	−0.839234	+	0.543770i	$0.816996\pi$
$102$	10.1010	−	3.06363i	1.00015	−	0.303344i
$103$	−0.892635	+	4.48758i	−0.0879540	+	0.442174i	0.911565	+	0.411156i	$0.134875\pi$
$103$	−0.892635	+	4.48758i	−0.0879540	+	0.442174i	−0.999519	+	0.0310181i	$0.990125\pi$
$104$	12.6865	−	10.4088i	1.24402	−	1.02067i
$105$	5.68466	−	1.13075i	0.554766	−	0.110350i
$106$	0.0923181	−	0.304285i	0.00896672	−	0.0295548i
$107$	−5.78487	+	10.8227i	−0.559245	+	1.04627i	0.430387	+	0.902645i	$0.358377\pi$
$107$	−5.78487	+	10.8227i	−0.559245	+	1.04627i	−0.989632	+	0.143629i	$0.954123\pi$
$108$	1.91393	−	0.580405i	0.184168	−	0.0558495i
$109$	0.378001	+	3.83791i	0.0362059	+	0.367605i	0.996167	+	0.0874716i	$0.0278787\pi$
$109$	0.378001	+	3.83791i	0.0362059	+	0.367605i	−0.959961	+	0.280133i	$0.909621\pi$
$110$	−6.43673	−	15.5415i	−0.613718	−	1.48183i
$111$	5.87681	−	2.43425i	0.557802	−	0.231049i
$112$	−2.13818	+	10.7397i	−0.202039	+	1.01481i
$113$	10.3107	+	4.27084i	0.969952	+	0.401767i	0.810694	−	0.585470i	$-0.199090\pi$
$113$	10.3107	+	4.27084i	0.969952	+	0.401767i	0.159258	+	0.987237i	$0.449090\pi$
$114$	6.49948e−5	−	1.51273i	6.08732e−6	−	0.141680i
$115$	−8.25955	−	6.77844i	−0.770207	−	0.632093i
$116$	−4.11440	+	0.404876i	−0.382012	+	0.0375918i
$117$	−5.55203	+	1.68419i	−0.513285	+	0.155703i
$118$	18.1559	−	1.78741i	1.67139	−	0.164545i
$119$	11.3520	−	16.9894i	1.04063	−	1.55742i
$120$	−3.32756	+	4.97865i	−0.303763	+	0.454486i
$121$	17.0986	−	11.4249i	1.55442	−	1.03863i
$122$	−0.431332	+	4.37746i	−0.0390510	+	0.396317i
$123$	2.49708	+	3.04270i	0.225154	+	0.274351i
$124$	−4.08402	+	9.85730i	−0.366756	+	0.885211i
$125$	10.3023	−	5.50669i	0.921465	−	0.492533i
$126$	2.15107	−	3.21901i	0.191633	−	0.286772i
$127$	−7.70853			−0.684022			−0.342011	−	0.939696i	$-0.611108\pi$
$127$	−7.70853			−0.684022			−0.342011	+	0.939696i	$0.611108\pi$
$128$	−6.28273	−	9.40889i	−0.555320	−	0.831637i
$129$	−10.9195			−0.961411
$130$	9.65175	−	14.4435i	0.846515	−	1.26678i
$131$	−12.0857	+	6.45992i	−1.05593	+	0.564406i	−0.905558	−	0.424223i	$-0.860547\pi$
$131$	−12.0857	+	6.45992i	−1.05593	+	0.564406i	−0.150372	+	0.988629i	$0.548047\pi$
$132$	−10.3807	−	4.30088i	−0.903527	−	0.374344i
$133$	−1.85771	−	2.26362i	−0.161084	−	0.196281i
$134$	1.82542	−	18.5256i	0.157692	−	1.60037i
$135$	1.76037	−	1.17624i	0.151509	−	0.101235i
$136$	4.11583	+	20.7056i	0.352930	+	1.77549i
$137$	8.67652	−	12.9853i	0.741285	−	1.10941i	−0.248747	−	0.968569i	$-0.580019\pi$
$137$	8.67652	−	12.9853i	0.741285	−	1.10941i	0.990032	−	0.140843i	$-0.0449813\pi$
$138$	−7.10287	+	0.699264i	−0.604637	+	0.0595253i
$139$	5.02978	−	1.52577i	0.426621	−	0.129414i	−0.0696706	−	0.997570i	$-0.522195\pi$
$139$	5.02978	−	1.52577i	0.426621	−	0.129414i	0.496291	+	0.868156i	$0.334695\pi$
$140$	1.13523	+	11.5363i	0.0959444	+	0.974998i
$141$	−2.93753	−	2.41077i	−0.247385	−	0.203023i
$142$	−0.000684746		15.9372i	−5.74626e−5		1.33742i
$143$	30.1148	+	12.4740i	2.51833	+	1.04312i
$144$	0.779687	+	3.92328i	0.0649739	+	0.326940i
$145$	−4.04336	+	1.67481i	−0.335782	+	0.139086i
$146$	−4.92409	−	11.8893i	−0.407521	−	0.983961i
$147$	−0.0484750	−	0.492175i	−0.00399815	−	0.0405939i
$148$	3.69196	+	12.1745i	0.303477	+	1.00074i
$149$	−9.25319	+	17.3115i	−0.758051	+	1.41821i	0.145334	+	0.989383i	$0.453574\pi$
$149$	−9.25319	+	17.3115i	−0.758051	+	1.41821i	−0.903385	+	0.428831i	$0.858926\pi$
$150$	0.212499	−	0.700406i	0.0173504	−	0.0571879i
$151$	−0.890895	+	0.177210i	−0.0725000	+	0.0144211i	−0.231207	−	0.972905i	$-0.574267\pi$
$151$	−0.890895	+	0.177210i	−0.0725000	+	0.0144211i	0.158707	+	0.987326i	$0.449267\pi$
$152$	3.01085	+	0.296934i	0.244212	+	0.0240846i
$153$	1.45611	−	7.32036i	0.117720	−	0.591816i
$154$	−20.8150	+	6.31319i	−1.67732	+	0.508731i
$155$	−1.10710	+	11.2406i	−0.0889246	+	0.902866i
$156$	−2.26279	−	11.3809i	−0.181168	−	0.911204i
$157$	4.73060	−	15.5947i	0.377543	−	1.24459i	−0.538197	−	0.842819i	$-0.680894\pi$
$157$	4.73060	−	15.5947i	0.377543	−	1.24459i	0.915740	−	0.401772i	$-0.131606\pi$
$158$	−3.83173	+	2.56005i	−0.304836	+	0.203666i
$159$	−0.158990	−	0.158990i	−0.0126088	−	0.0126088i
$160$	−9.25638	−	7.59985i	−0.731781	−	0.600821i
$161$	−9.76948	+	9.76948i	−0.769943	+	0.769943i
$162$	0.275959	−	1.38703i	0.0216814	−	0.108975i
$163$	5.15336	+	1.56326i	0.403643	+	0.122444i	0.485577	−	0.874194i	$-0.338610\pi$
$163$	5.15336	+	1.56326i	0.403643	+	0.122444i	−0.0819340	+	0.996638i	$0.526110\pi$
$164$	−6.54598	+	4.37307i	−0.511156	+	0.341480i
$165$	−11.8375	−	1.16589i	−0.921546	−	0.0907644i
$166$	−6.73349	−	3.59950i	−0.522620	−	0.279375i
$167$	−4.89490	−	0.973657i	−0.378779	−	0.0753438i	0.00202906	−	0.999998i	$-0.499354\pi$
$167$	−4.89490	−	0.973657i	−0.378779	−	0.0753438i	−0.380808	+	0.924654i	$0.624354\pi$
$168$	5.98491	+	4.91298i	0.461746	+	0.379044i
$169$	4.03086	+	20.2645i	0.310066	+	1.55881i
$170$	10.5337	+	19.7093i	0.807901	+	1.51163i
$171$	−0.943355	−	0.504234i	−0.0721402	−	0.0385597i
$172$	2.14247	−	21.7337i	0.163362	−	1.65718i
$173$	13.1491	−	1.29508i	0.999710	−	0.0984628i	0.415099	−	0.909776i	$-0.363747\pi$
$173$	13.1491	−	1.29508i	0.999710	−	0.0984628i	0.584611	+	0.811314i	$0.301247\pi$
$174$	−1.11884	+	2.70080i	−0.0848192	+	0.204747i
$175$	−0.542211	−	1.30901i	−0.0409873	−	0.0989521i
$176$	10.5970	−	19.8175i	0.798781	−	1.49380i
$177$	4.93670	−	11.9183i	0.371065	−	0.895831i
$178$	1.64316	+	1.64330i	0.123160	+	0.123170i
$179$	5.46216	−	6.65566i	0.408261	−	0.497467i	−0.527769	−	0.849388i	$-0.676971\pi$
$179$	5.46216	−	6.65566i	0.408261	−	0.497467i	0.936030	+	0.351921i	$0.114471\pi$
$180$	1.99574	+	3.73454i	0.148754	+	0.278356i
$181$	6.22064	+	20.5067i	0.462376	+	1.52425i	0.809893	+	0.586577i	$0.199525\pi$
$181$	6.22064	+	20.5067i	0.462376	+	1.52425i	−0.347517	+	0.937674i	$0.612975\pi$
$182$	−17.3630	−	14.2507i	−1.28703	−	1.05633i
$183$	2.58614	+	1.72800i	0.191173	+	0.127738i
$184$	0.00183991	−	14.2744i	0.000135640	−	1.05232i
$185$	7.48209	+	11.1977i	0.550094	+	0.823274i
$186$	4.78607	+	5.83235i	0.350932	+	0.427649i
$187$	−32.4147	+	26.6021i	−2.37040	+	1.94533i
$188$	5.37464	−	5.37372i	0.391986	−	0.391919i
$189$	−1.29050	−	2.41436i	−0.0938704	−	0.175619i
$190$	3.14120	−	0.624683i	0.227887	−	0.0453193i
$191$			9.14211i			0.661500i	0.943718	+	0.330750i	$0.107302\pi$
$191$			9.14211i			0.661500i	−0.943718	+	0.330750i	$0.892698\pi$
$192$	−7.96168	+	0.782085i	−0.574585	+	0.0564421i
$193$			16.6694i			1.19989i	0.800041	+	0.599945i	$0.204811\pi$
$193$			16.6694i			1.19989i	−0.800041	+	0.599945i	$0.795189\pi$
$194$	−1.08095	−	5.43550i	−0.0776074	−	0.390246i
$195$	−5.79043	−	10.8331i	−0.414661	−	0.775777i
$196$	0.989113		8.49951e-5i	0.0706509		6.07108e-6i
$197$	−5.59383	+	4.59074i	−0.398544	+	0.327076i	−0.812224	−	0.583346i	$-0.801743\pi$
$197$	−5.59383	+	4.59074i	−0.398544	+	0.327076i	0.413680	+	0.910422i	$0.364243\pi$
$198$	−6.14205	+	5.04021i	−0.436497	+	0.358192i
$199$	8.65607	+	12.9547i	0.613613	+	0.918336i	0.999992	−	0.00400374i	$-0.00127443\pi$
$199$	8.65607	+	12.9547i	0.613613	+	0.918336i	−0.386379	+	0.922340i	$0.626274\pi$
$200$	1.35236	+	0.560371i	0.0956264	+	0.0396242i
$201$	−10.9446	−	7.31298i	−0.771976	−	0.515818i
$202$	−11.2425	+	13.6978i	−0.791017	+	0.963772i
$203$	1.64273	+	5.41535i	0.115297	+	0.380083i
$204$	14.2844	+	4.33447i	1.00011	+	0.303473i
$205$	−5.28676	+	6.44194i	−0.369243	+	0.449924i
$206$	−4.57569	+	4.57530i	−0.318804	+	0.318776i
$207$	−1.93132	+	4.66261i	−0.134236	+	0.324074i
$208$	23.0961	−	2.27075i	1.60142	−	0.157449i
$209$	2.29976	+	5.55212i	0.159078	+	0.384048i
$210$	7.57274	+	3.13711i	0.522569	+	0.216481i
$211$	23.2617	−	2.29108i	1.60140	−	0.157725i	0.742495	−	0.669852i	$-0.233642\pi$
$211$	23.2617	−	2.29108i	1.60140	−	0.157725i	0.858910	+	0.512127i	$0.171142\pi$
$212$	0.347642	−	0.285252i	0.0238761	−	0.0195912i
$213$	9.93863	+	5.31231i	0.680983	+	0.363993i
$214$	−15.3060	+	8.18039i	−1.04630	+	0.559200i
$215$	−4.51022	−	22.6744i	−0.307594	−	1.54638i
$216$	2.70653	+	0.821398i	0.184156	+	0.0558890i
$217$	14.3243	+	2.84929i	0.972400	+	0.193422i
$218$	−2.57115	+	4.80979i	−0.174140	+	0.325760i
$219$	−9.05566	−	0.891905i	−0.611925	−	0.0602693i
$220$	4.64311	−	23.3320i	0.313038	−	1.57304i
$221$	−41.4391	−	12.5704i	−2.78749	−	0.845577i
$222$	8.82290	+	1.75538i	0.592154	+	0.117813i
$223$	2.28155	−	2.28155i	0.152784	−	0.152784i	−0.626576	−	0.779360i	$-0.715544\pi$
$223$	2.28155	−	2.28155i	0.152784	−	0.152784i	0.779360	+	0.626576i	$0.215544\pi$
$224$	−10.9528	+	10.9481i	−0.731817	+	0.731502i
$225$	−0.365966	−	0.365966i	−0.0243977	−	0.0243977i
$226$	8.76799	+	13.1234i	0.583238	+	0.872958i
$227$	−1.51695	+	5.00071i	−0.100683	+	0.331909i	−0.992782	−	0.119932i	$-0.961732\pi$
$227$	−1.51695	+	5.00071i	−0.100683	+	0.331909i	0.892099	+	0.451841i	$0.149232\pi$
$228$	1.18869	−	1.77868i	0.0787232	−	0.117796i
$229$	0.368083	−	3.73721i	0.0243236	−	0.246962i	−0.975333	−	0.220741i	$-0.929153\pi$
$229$	0.368083	−	3.73721i	0.0243236	−	0.246962i	0.999656	−	0.0262213i	$-0.00834746\pi$
$230$	−4.38580	−	14.4603i	−0.289191	−	0.953482i
$231$	−3.00059	+	15.0850i	−0.197424	+	0.992519i
$232$	−5.15601	−	2.75680i	−0.338509	−	0.180993i
$233$	−4.37289	+	0.869822i	−0.286478	+	0.0569839i	−0.336237	−	0.941777i	$-0.609154\pi$
$233$	−4.37289	+	0.869822i	−0.286478	+	0.0569839i	0.0497598	+	0.998761i	$0.484154\pi$
$234$	−7.85165	−	2.38214i	−0.513278	−	0.155725i
$235$	3.79264	−	7.09553i	0.247404	−	0.462861i
$236$	22.7529	+	12.1642i	1.48109	+	0.791822i
$237$	0.319392	+	3.24284i	0.0207467	+	0.210645i
$238$	26.6974	−	11.0571i	1.73054	−	0.716725i
$239$	−4.50361	+	1.86546i	−0.291314	+	0.120666i	−0.523555	−	0.851992i	$-0.675394\pi$
$239$	−4.50361	+	1.86546i	−0.291314	+	0.120666i	0.232240	+	0.972658i	$0.425394\pi$
$240$	−7.82463	+	3.23949i	−0.505078	+	0.209108i
$241$	−5.53586	−	2.29303i	−0.356596	−	0.147707i	0.197191	−	0.980365i	$-0.436818\pi$
$241$	−5.53586	−	2.29303i	−0.356596	−	0.147707i	−0.553787	+	0.832658i	$0.686818\pi$
$242$	29.0823	+	0.00124953i	1.86948	+	8.03228e-5i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	−3.94675	+	4.80828i	−0.252665	+	0.307819i
$245$	1.00198	−	0.303947i	0.0640140	−	0.0194184i
$246$	0.545382	+	5.53980i	0.0347723	+	0.353205i
$247$	−3.44787	+	5.16011i	−0.219383	+	0.328330i
$248$	−12.5475	+	8.38162i	−0.796766	+	0.532234i
$249$	−4.48902	+	2.99947i	−0.284480	+	0.190084i
$250$	16.4407	+	1.61998i	1.03980	+	0.102457i
$251$	−2.62647	−	3.20036i	−0.165781	−	0.202005i	0.683493	−	0.729957i	$-0.260460\pi$
$251$	−2.62647	−	3.20036i	−0.165781	−	0.202005i	−0.849274	+	0.527952i	$0.822960\pi$
$252$	5.05864	−	2.09485i	0.318664	−	0.131963i
$253$	25.0058	−	13.3659i	1.57210	−	0.840307i
$254$	−9.06402	−	6.05694i	−0.568727	−	0.380047i
$255$	15.8021			0.989569
$256$	0.00549956	−	16.0000i	0.000343722	−	1.00000i
$257$	−7.45209			−0.464849			−0.232424	−	0.972614i	$-0.574666\pi$
$257$	−7.45209			−0.464849			−0.232424	+	0.972614i	$0.574666\pi$
$258$	−12.8396	−	8.57997i	−0.799361	−	0.534166i
$259$	15.3578	−	8.20891i	0.954287	−	0.510077i
$260$	22.6979	−	9.39948i	1.40766	−	0.582931i
$261$	1.31138	+	1.59792i	0.0811722	+	0.0989086i
$262$	−19.2867	−	1.90041i	−1.19154	−	0.117408i
$263$	−9.32660	+	6.23184i	−0.575103	+	0.384271i	−0.808840	−	0.588028i	$-0.799904\pi$
$263$	−9.32660	+	6.23184i	−0.575103	+	0.384271i	0.233737	+	0.972300i	$0.424904\pi$
$264$	−8.82670	−	13.2138i	−0.543246	−	0.813251i
$265$	0.264474	−	0.395813i	0.0162465	−	0.0243146i
$266$	−0.405738	−	4.12135i	−0.0248774	−	0.252696i
$267$	1.57247	−	0.477004i	0.0962337	−	0.0291922i
$268$	16.7028	−	20.3489i	1.02029	−	1.24300i
$269$	−4.57253	−	3.75258i	−0.278792	−	0.228799i	0.484597	−	0.874737i	$-0.338966\pi$
$269$	−4.57253	−	3.75258i	−0.278792	−	0.228799i	−0.763389	+	0.645939i	$0.776466\pi$
$270$	2.99414		0.000128644i	0.182218		7.82904e-6i
$271$	4.48966	+	1.85968i	0.272727	+	0.112967i	0.514856	−	0.857277i	$-0.327845\pi$
$271$	4.48966	+	1.85968i	0.272727	+	0.112967i	−0.242128	+	0.970244i	$0.577845\pi$
$272$	−11.4298	+	27.5806i	−0.693033	+	1.67232i
$273$	−14.6742	+	6.07826i	−0.888124	+	0.367873i
$274$	20.4054	−	8.45116i	1.23273	−	0.510553i
$275$	0.285007	+	2.89373i	0.0171866	+	0.174498i
$276$	−8.90130	−	4.75883i	−0.535795	−	0.286448i
$277$	3.59905	−	6.73334i	0.216246	−	0.404567i	−0.750286	−	0.661113i	$-0.770084\pi$
$277$	3.59905	−	6.73334i	0.216246	−	0.404567i	0.966532	+	0.256546i	$0.0825844\pi$
$278$	7.11309	+	2.15807i	0.426615	+	0.129432i
$279$	5.23241	−	1.04079i	0.313256	−	0.0623106i
$280$	−7.72977	+	14.4569i	−0.461942	+	0.863965i
$281$	3.16192	−	15.8961i	0.188625	−	0.948280i	−0.764251	−	0.644919i	$-0.776891\pi$
$281$	3.16192	−	15.8961i	0.188625	−	0.948280i	0.952876	−	0.303361i	$-0.0981088\pi$
$282$	−1.55982	−	5.14284i	−0.0928860	−	0.306251i
$283$	0.0376902	−	0.382675i	0.00224045	−	0.0227477i	−0.994000	−	0.109385i	$-0.965112\pi$
$283$	0.0376902	−	0.382675i	0.00224045	−	0.0227477i	0.996240	+	0.0866369i	$0.0276120\pi$
$284$	−12.5234	+	18.7391i	−0.743126	+	1.11196i
$285$	0.657396	−	2.16714i	0.0389408	−	0.128371i
$286$	25.6089	+	38.3300i	1.51429	+	2.26650i
$287$	7.61959	+	7.61959i	0.449770	+	0.449770i
$288$	−2.16591	+	5.22579i	−0.127627	+	0.307932i
$289$	27.3707	−	27.3707i	1.61004	−	1.61004i
$290$	−6.07032	−	1.20773i	−0.356462	−	0.0709205i
$291$	−3.75001	−	1.13755i	−0.219829	−	0.0666845i
$292$	3.55197	−	17.8490i	0.207864	−	1.04453i
$293$	−15.9733	−	1.57323i	−0.933171	−	0.0919094i	−0.380009	−	0.924983i	$-0.624079\pi$
$293$	−15.9733	−	1.57323i	−0.933171	−	0.0919094i	−0.553162	+	0.833073i	$0.686579\pi$
$294$	0.329725	−	0.616809i	0.0192300	−	0.0359730i
$295$	26.7873	+	5.32832i	1.55962	+	0.310227i
$296$	−5.22492	+	17.2163i	−0.303692	+	1.00068i
$297$	1.09606	+	5.51026i	0.0635998	+	0.319738i
$298$	−24.4827	+	13.0849i	−1.41825	+	0.757990i
$299$	25.8232	+	13.8028i	1.49339	+	0.798236i
$300$	0.800206	−	0.656597i	0.0461999	−	0.0379086i
$301$	−29.7496	+	2.93008i	−1.71474	+	0.168887i
$302$	−1.18679	−	0.491646i	−0.0682923	−	0.0282910i
$303$	4.79518	+	11.5766i	0.275476	+	0.665057i
$304$	3.30697	+	2.71491i	0.189667	+	0.155711i
$305$	−2.52001	+	6.08385i	−0.144295	+	0.348360i
$306$	7.46410	−	7.46346i	0.426694	−	0.426657i
$307$	0.681842	−	0.830827i	0.0389148	−	0.0474178i	−0.753189	−	0.657804i	$-0.771486\pi$
$307$	0.681842	−	0.830827i	0.0389148	−	0.0474178i	0.792104	+	0.610386i	$0.208986\pi$
$308$	−29.4357	−	8.93199i	−1.67726	−	0.508947i
$309$	1.32820	+	4.37848i	0.0755585	+	0.249083i
$310$	−10.1340	+	12.3473i	−0.575574	+	0.701277i
$311$	−5.55147	−	3.70937i	−0.314795	−	0.210339i	0.388128	−	0.921606i	$-0.373122\pi$
$311$	−5.55147	−	3.70937i	−0.314795	−	0.210339i	−0.702923	+	0.711266i	$0.748122\pi$
$312$	6.28183	−	15.1602i	0.355639	−	0.858275i
$313$	−6.23934	−	9.33784i	−0.352668	−	0.527806i	0.612143	−	0.790747i	$-0.290308\pi$
$313$	−6.23934	−	9.33784i	−0.352668	−	0.527806i	−0.964812	+	0.262941i	$0.915308\pi$
$314$	17.8159	−	14.6198i	1.00541	−	0.825045i
$315$	4.48039	−	3.67696i	0.252441	−	0.207173i
$316$	−6.51706		0.000560015i	−0.366613		3.15033e-5i
$317$	−3.60418	−	6.74294i	−0.202431	−	0.378721i	0.760137	−	0.649763i	$-0.225132\pi$
$317$	−3.60418	−	6.74294i	−0.202431	−	0.378721i	−0.962568	+	0.271042i	$0.912632\pi$
$318$	−0.0620216	−	0.311874i	−0.00347800	−	0.0174890i
$319$		−	11.6136i		−	0.650237i
$320$	−4.91250	−	16.2094i	−0.274617	−	0.906132i
$321$			12.2718i			0.684944i
$322$	−19.1637	+	3.81104i	−1.06795	+	0.212381i
$323$	−3.76349	−	7.04099i	−0.209406	−	0.391771i
$324$	1.41434	−	1.41409i	0.0785742	−	0.0785607i
$325$	−2.32117	+	1.90494i	−0.128756	+	0.105667i
$326$	4.83122	+	5.88737i	0.267577	+	0.326072i
$327$	2.14254	+	3.20654i	0.118483	+	0.177322i
$328$	−11.1332	−	0.00143502i	−0.614726	−	7.92357e-5i
$329$	−8.65001	−	5.77975i	−0.476890	−	0.318648i
$330$	−13.0029	−	10.6721i	−0.715787	−	0.587482i
$331$	5.53559	+	18.2484i	0.304264	+	1.00302i	0.967129	+	0.254285i	$0.0818400\pi$
$331$	5.53559	+	18.2484i	0.304264	+	1.00302i	−0.662866	+	0.748738i	$0.730660\pi$
$332$	−5.08923	−	9.52324i	−0.279308	−	0.522656i
$333$	4.03538	−	4.91713i	0.221138	−	0.269457i
$334$	−4.99059	−	4.99101i	−0.273073	−	0.273096i
$335$	10.6648	−	25.7471i	0.582680	−	1.40671i
$336$	3.17695	+	10.4795i	0.173317	+	0.571703i
$337$	−9.84763	−	23.7743i	−0.536435	−	1.29507i	−0.927196	−	0.374576i	$-0.877788\pi$
$337$	−9.84763	−	23.7743i	−0.536435	−	1.29507i	0.390762	−	0.920492i	$-0.372212\pi$
$338$	−11.1831	+	26.9951i	−0.608279	+	1.46834i
$339$	11.1065	−	1.09390i	0.603223	−	0.0594123i
$340$	−3.10047	+	31.4518i	−0.168146	+	1.70572i
$341$	−26.4336	−	14.1290i	−1.43146	−	0.765130i
$342$	−0.713037	−	1.33414i	−0.0385566	−	0.0721418i
$343$	3.47445	+	17.4672i	0.187602	+	0.943141i
$344$	19.5964	−	23.8720i	1.05657	−	1.28709i
$345$	−10.4796	−	2.08452i	−0.564203	−	0.112227i
$346$	16.4789	+	8.80907i	0.885911	+	0.473578i
$347$	22.0977	+	2.17644i	1.18627	+	0.116837i	0.671840	−	0.740696i	$-0.265504\pi$
$347$	22.0977	+	2.17644i	1.18627	+	0.116837i	0.514429	+	0.857533i	$0.328004\pi$
$348$	−3.43772	+	2.29658i	−0.184281	+	0.123110i
$349$	−24.6475	−	7.47674i	−1.31935	−	0.400221i	−0.449387	−	0.893337i	$-0.648358\pi$
$349$	−24.6475	−	7.47674i	−1.31935	−	0.400221i	−0.869963	+	0.493116i	$0.835858\pi$
$350$	0.390997	−	1.96523i	0.0208997	−	0.105046i
$351$	−4.10253	+	4.10253i	−0.218977	+	0.218977i
$352$	28.0319	−	14.9756i	1.49411	−	0.798203i
$353$	−14.6284	−	14.6284i	−0.778591	−	0.778591i	0.201000	−	0.979591i	$-0.435581\pi$
$353$	−14.6284	−	14.6284i	−0.778591	−	0.778591i	−0.979591	+	0.201000i	$0.935581\pi$
$354$	15.1695	−	10.1350i	0.806249	−	0.538669i
$355$	−6.92593	+	22.8317i	−0.367590	+	1.21178i
$356$	0.640879	+	3.22336i	0.0339665	+	0.170838i
$357$	2.00278	−	20.3346i	0.105998	−	1.07622i
$358$	11.6523	−	3.53414i	0.615842	−	0.186785i
$359$	5.95949	−	29.9604i	0.314530	−	1.58125i	−0.423126	−	0.906071i	$-0.639067\pi$
$359$	5.95949	−	29.9604i	0.314530	−	1.58125i	0.737655	−	0.675177i	$-0.235933\pi$
$360$	−0.587723	+	5.95937i	−0.0309757	+	0.314087i
$361$	17.5127	−	3.48350i	0.921723	−	0.183342i
$362$	−8.79856	+	29.0005i	−0.462442	+	1.52423i
$363$	9.69394	−	18.1361i	0.508800	−	0.951897i
$364$	−9.21872	−	30.3995i	−0.483192	−	1.59336i
$365$	−1.88832	−	19.1725i	−0.0988393	−	1.00353i
$366$	1.68312	+	4.06390i	0.0879781	+	0.212424i
$367$	4.52747	−	1.87534i	0.236332	−	0.0978919i	−0.261374	−	0.965237i	$-0.584176\pi$
$367$	4.52747	−	1.87534i	0.236332	−	0.0978919i	0.497706	+	0.867346i	$0.334176\pi$
$368$	11.2182	−	16.7830i	0.584790	−	0.874875i
$369$	3.63655	+	1.50631i	0.189311	+	0.0784152i
$370$	−0.000818307		19.0458i	−4.25418e−5		0.990143i
$371$	−0.475822	−	0.390497i	−0.0247034	−	0.0202736i
$372$	1.04491	+	10.6186i	0.0541763	+	0.550546i
$373$	18.7265	−	5.68063i	0.969623	−	0.294132i	0.234538	−	0.972107i	$-0.424642\pi$
$373$	18.7265	−	5.68063i	0.969623	−	0.294132i	0.735085	+	0.677975i	$0.237142\pi$
$374$	−59.0170	+	5.81011i	−3.05170	+	0.300433i
$375$	6.48998	−	9.71294i	0.335141	−	0.501574i
$376$	10.5421	−	2.09554i	0.543667	−	0.108069i
$377$	9.97200	−	6.66307i	0.513584	−	0.343166i
$378$	0.379647	−	3.85292i	0.0195269	−	0.198173i
$379$	−10.9752	−	13.3734i	−0.563760	−	0.686944i	0.410631	−	0.911802i	$-0.365308\pi$
$379$	−10.9752	−	13.3734i	−0.563760	−	0.686944i	−0.974392	+	0.224857i	$0.927808\pi$
$380$	4.18440	+	1.73366i	0.214655	+	0.0889347i
$381$	−6.79832	+	3.63378i	−0.348288	+	0.186164i
$382$	−7.18337	+	10.7497i	−0.367533	+	0.550001i
$383$	−6.52367			−0.333344			−0.166672	−	0.986012i	$-0.553302\pi$
$383$	−6.52367			−0.333344			−0.166672	+	0.986012i	$0.553302\pi$
$384$	−9.97620	−	5.33625i	−0.509096	−	0.272314i
$385$	−32.5633			−1.65958
$386$	−13.0979	+	19.6006i	−0.666666	+	0.997643i
$387$	−9.63017	+	5.14743i	−0.489529	+	0.261659i
$388$	2.99990	−	7.24064i	0.152297	−	0.367588i
$389$	11.6768	+	14.2282i	0.592037	+	0.721399i	0.979715	−	0.200396i	$-0.0642228\pi$
$389$	11.6768	+	14.2282i	0.592037	+	0.721399i	−0.387678	+	0.921795i	$0.626723\pi$
$390$	1.70345	−	17.2879i	0.0862578	−	0.875404i
$391$	−31.3198	+	20.9272i	−1.58391	+	1.05833i
$392$	1.16297	+	0.777291i	0.0587390	+	0.0392591i
$393$	−7.61342	+	11.3943i	−0.384046	+	0.574766i
$394$	−10.1846	+	1.00265i	−0.513093	+	0.0505130i
$395$	−6.60182	+	2.00264i	−0.332174	+	0.100764i
$396$	−11.1824	+	1.10040i	−0.561937	+	0.0552972i
$397$	24.7465	+	20.3089i	1.24199	+	1.01927i	0.998784	+	0.0493000i	$0.0156990\pi$
$397$	24.7465	+	20.3089i	1.24199	+	1.01927i	0.243206	+	0.969975i	$0.421801\pi$
$398$	−0.000946705		22.0342i	−4.74540e−5		1.10447i
$399$	−2.70541	−	1.12062i	−0.135440	−	0.0561011i
$400$	1.14985	+	1.72152i	0.0574927	+	0.0860760i
$401$	−22.9974	+	9.52583i	−1.14844	+	0.475697i	−0.874009	−	0.485911i	$-0.838488\pi$
$401$	−22.9974	+	9.52583i	−1.14844	+	0.475697i	−0.274427	+	0.961608i	$0.588488\pi$
$402$	−7.12303	−	17.1986i	−0.355265	−	0.857789i
$403$	−3.03387	−	30.8034i	−0.151128	−	1.53443i
$404$	−23.9823	+	7.27271i	−1.19317	+	0.361831i
$405$	0.998031	−	1.86718i	0.0495926	−	0.0927812i
$406$	−2.32350	+	7.65837i	−0.115313	+	0.380078i
$407$	−35.0508	+	6.97204i	−1.73740	+	0.345591i
$408$	13.3904	+	16.3206i	0.662924	+	0.807988i
$409$	0.106639	−	0.536111i	0.00527296	−	0.0265090i	−0.978059	−	0.208327i	$-0.933198\pi$
$409$	0.106639	−	0.536111i	0.00527296	−	0.0265090i	0.983332	+	0.181818i	$0.0581982\pi$
$410$	−11.2781	+	3.42065i	−0.556987	+	0.168934i
$411$	1.53077	−	15.5421i	0.0755071	−	0.766636i
$412$	−8.97531	+	1.78450i	−0.442182	+	0.0879160i
$413$	10.2517	−	33.7952i	0.504451	−	1.66295i
$414$	−5.93454	+	3.96497i	−0.291667	+	0.194867i
$415$	−8.08254	−	8.08254i	−0.396756	−	0.396756i
$416$	28.9415	+	15.4776i	1.41898	+	0.758850i
$417$	3.71663	−	3.71663i	0.182004	−	0.182004i
$418$	−1.65840	+	8.33544i	−0.0811148	+	0.407700i
$419$	11.5186	+	3.49412i	0.562719	+	0.170699i	0.558814	−	0.829293i	$-0.311257\pi$
$419$	11.5186	+	3.49412i	0.562719	+	0.170699i	0.00390584	+	0.999992i	$0.498757\pi$
$420$	6.43937	+	9.63900i	0.314209	+	0.470335i
$421$	13.9877	+	1.37767i	0.681721	+	0.0671436i	0.432949	−	0.901418i	$-0.357473\pi$
$421$	13.9877	+	1.37767i	0.681721	+	0.0671436i	0.248772	+	0.968562i	$0.419973\pi$
$422$	29.1523	+	15.5839i	1.41911	+	0.758610i
$423$	−3.72710	−	0.741366i	−0.181218	−	0.0360465i
$424$	0.632908	−	0.0622536i	0.0307367	−	0.00302330i
$425$	−0.753616	−	3.78868i	−0.0365557	−	0.183778i
$426$	7.51213	+	14.0557i	0.363964	+	0.680999i
$427$	7.50945	+	4.01389i	0.363408	+	0.194246i
$428$	−24.4252	−	2.40779i	−1.18063	−	0.116385i
$429$	32.4391	−	3.19497i	1.56617	−	0.154255i
$430$	12.5130	−	30.2054i	0.603430	−	1.45663i
$431$	−6.36275	−	15.3610i	−0.306483	−	0.739915i	−0.999814	−	0.0192958i	$-0.993858\pi$
$431$	−6.36275	−	15.3610i	−0.306483	−	0.739915i	0.693331	−	0.720619i	$-0.256142\pi$
$432$	2.53704	+	3.09248i	0.122063	+	0.148787i
$433$	−12.1584	+	29.3529i	−0.584294	+	1.41061i	0.304593	+	0.952483i	$0.401480\pi$
$433$	−12.1584	+	29.3529i	−0.584294	+	1.41061i	−0.888887	+	0.458127i	$0.848520\pi$
$434$	14.6044	+	14.6056i	0.701031	+	0.701092i
$435$	−2.77642	+	3.38308i	−0.133119	+	0.162206i
$436$	−6.80253	+	3.63528i	−0.325782	+	0.174098i
$437$	1.56705	+	5.16587i	0.0749622	+	0.247117i
$438$	−9.94721	−	8.16418i	−0.475296	−	0.390100i
$439$	0.734291	+	0.490638i	0.0350458	+	0.0234169i	0.572970	−	0.819577i	$-0.305791\pi$
$439$	0.734291	+	0.490638i	0.0350458	+	0.0234169i	−0.537924	+	0.842993i	$0.680791\pi$
$440$	23.7926	−	23.7864i	1.13427	−	1.13397i
$441$	−0.274761	−	0.411209i	−0.0130839	−	0.0195814i
$442$	−38.8487	−	47.3414i	−1.84784	−	2.25180i
$443$	−10.5542	+	8.66157i	−0.501443	+	0.411524i	−0.850819	−	0.525459i	$-0.823894\pi$
$443$	−10.5542	+	8.66157i	−0.501443	+	0.411524i	0.349376	+	0.936983i	$0.386394\pi$
$444$	8.99506	+	8.99660i	0.426886	+	0.426960i
$445$	1.63999	+	3.06821i	0.0777432	+	0.145447i
$446$	4.47546	−	0.890024i	0.211919	−	0.0421438i
$447$			19.6293i			0.928434i
$448$	−21.4812	+	4.26713i	−1.01489	+	0.201603i
$449$		−	18.6739i		−	0.881274i	−0.897685	−	0.440637i	$-0.854753\pi$
$449$		−	18.6739i		−	0.881274i	0.897685	−	0.440637i	$-0.145247\pi$
$450$	−0.142762	−	0.717874i	−0.00672986	−	0.0338409i
$451$	−10.4246	−	19.5030i	−0.490874	−	0.918360i
$452$	−0.00191801	+	22.3205i	−9.02158e−5	+	1.04987i
$453$	−0.702163	+	0.576250i	−0.0329905	+	0.0270746i
$454$	−5.71298	+	4.68811i	−0.268123	+	0.220024i
$455$	−18.6825	−	27.9604i	−0.875851	−	1.31080i
$456$	2.79530	−	1.15743i	0.130902	−	0.0542017i
$457$	7.35822	+	4.91661i	0.344203	+	0.229989i	0.715640	−	0.698469i	$-0.246135\pi$
$457$	7.35822	+	4.91661i	0.344203	+	0.229989i	−0.371437	+	0.928458i	$0.621135\pi$
$458$	3.36931	−	4.10515i	0.157437	−	0.191821i
$459$	−2.16662	−	7.14239i	−0.101129	−	0.333378i
$460$	6.20509	−	20.4491i	0.289314	−	0.953445i
$461$	−2.97166	+	3.62098i	−0.138404	+	0.168646i	−0.837600	−	0.546285i	$-0.816042\pi$
$461$	−2.97166	+	3.62098i	−0.138404	+	0.168646i	0.699196	+	0.714930i	$0.253542\pi$
$462$	−15.3812	+	15.3799i	−0.715597	+	0.715536i
$463$	5.78683	−	13.9706i	0.268937	−	0.649271i	−0.730497	−	0.682916i	$-0.760712\pi$
$463$	5.78683	−	13.9706i	0.268937	−	0.649271i	0.999434	+	0.0336449i	$0.0107115\pi$
$464$	−3.89651	−	7.29287i	−0.180891	−	0.338563i
$465$	4.32240	+	10.4352i	0.200447	+	0.483921i
$466$	−5.82528	−	2.41321i	−0.269851	−	0.111790i
$467$	16.2060	−	1.59616i	0.749927	−	0.0738613i	0.284170	−	0.958774i	$-0.408282\pi$
$467$	16.2060	−	1.59616i	0.749927	−	0.0738613i	0.465757	+	0.884913i	$0.345782\pi$
$468$	−7.36054	−	8.97042i	−0.340241	−	0.414658i
$469$	−31.7803	−	16.9869i	−1.46748	−	0.784383i
$470$	10.0348	−	5.36317i	0.462872	−	0.247384i
$471$	−3.17927	−	15.9833i	−0.146493	−	0.736470i
$472$	17.1959	+	32.1812i	0.791504	+	1.48126i
$473$	60.1694	+	11.9684i	2.76659	+	0.550310i
$474$	−2.17249	+	4.06403i	−0.0997858	+	0.186667i
$475$	−0.550941	−	0.0542629i	−0.0252789	−	0.00248975i
$476$	40.0800	+	7.97599i	1.83707	+	0.365579i
$477$	−0.215165	−	0.0652695i	−0.00985171	−	0.00298848i
$478$	−6.76131	−	1.34521i	−0.309255	−	0.0615284i
$479$	−18.2040	+	18.2040i	−0.831764	+	0.831764i	−0.987758	−	0.155994i	$-0.950142\pi$
$479$	−18.2040	+	18.2040i	−0.831764	+	0.831764i	0.155994	+	0.987758i	$0.450142\pi$
$480$	−11.7459	−	2.33904i	−0.536126	−	0.106762i
$481$	−26.0962	−	26.0962i	−1.18989	−	1.18989i
$482$	−4.70756	−	7.04602i	−0.214424	−	0.320937i
$483$	−4.01061	+	13.2212i	−0.182489	+	0.601586i
$484$	34.1952	+	22.8527i	1.55433	+	1.03876i
$485$	0.813217	−	8.25674i	0.0369263	−	0.374919i
$486$	−0.410466	−	1.35334i	−0.0186191	−	0.0613886i
$487$	5.08888	−	25.5835i	0.230599	−	1.15930i	−0.675867	−	0.737023i	$-0.736231\pi$
$487$	5.08888	−	25.5835i	0.230599	−	1.15930i	0.906467	−	0.422277i	$-0.138769\pi$
$488$	−8.41884	+	2.55264i	−0.381103	+	0.115553i
$489$	5.28178	−	1.05061i	0.238850	−	0.0475102i
$490$	1.41699	+	0.429907i	0.0640132	+	0.0194212i
$491$	3.18175	−	5.95264i	0.143591	−	0.268639i	−0.799837	−	0.600217i	$-0.795081\pi$
$491$	3.18175	−	5.95264i	0.143591	−	0.268639i	0.943428	+	0.331578i	$0.107581\pi$
$492$	−3.71159	+	6.94246i	−0.167331	+	0.312990i
$493$	1.51227	+	15.3543i	0.0681093	+	0.691525i
$494$	−8.10868	+	3.35832i	−0.364827	+	0.151098i
$495$	−10.9893	+	4.55193i	−0.493933	+	0.204594i
$496$	−21.3397	−	0.00366746i	−0.958180	−	0.000164674i
$497$	28.5026	+	11.8062i	1.27852	+	0.529579i
$498$	−7.63520		0.000328048i	−0.342141		1.47002e-5i
$499$	−0.949036	−	0.778854i	−0.0424847	−	0.0348663i	0.612911	−	0.790152i	$-0.289998\pi$
$499$	−0.949036	−	0.778854i	−0.0424847	−	0.0348663i	−0.655396	+	0.755285i	$0.727498\pi$
$500$	18.0588	+	14.8231i	0.807614	+	0.662908i
$501$	−4.77590	+	1.44875i	−0.213371	+	0.0647255i
$502$	−0.573642	−	5.82685i	−0.0256029	−	0.260065i
$503$	4.13115	−	6.18271i	0.184199	−	0.275673i	−0.727866	−	0.685720i	$-0.759488\pi$
$503$	4.13115	−	6.18271i	0.184199	−	0.275673i	0.912065	+	0.410047i	$0.134488\pi$
$504$	7.59418	+	1.51159i	0.338272	+	0.0673317i
$505$	−22.0581	+	14.7388i	−0.981575	+	0.655867i
$506$	39.9051	+	3.93204i	1.77400	+	0.174800i
$507$	13.1075	+	15.9715i	0.582125	+	0.709321i
$508$	−5.89863	−	14.2440i	−0.261709	−	0.631976i
$509$	−8.19501	+	4.38032i	−0.363237	+	0.194154i	−0.642911	−	0.765941i	$-0.722274\pi$
$509$	−8.19501	+	4.38032i	−0.363237	+	0.194154i	0.279674	+	0.960095i	$0.409774\pi$
$510$	18.5808	+	12.4165i	0.822773	+	0.549810i
$511$	−24.9109			−1.10199
$512$	12.5784	−	18.8091i	0.555892	−	0.831255i
$513$	−1.06966			−0.0472266
$514$	−8.76248	−	5.85545i	−0.386496	−	0.258273i
$515$	−8.54330	+	4.56649i	−0.376463	+	0.201224i
$516$	−8.35571	−	20.1774i	−0.367840	−	0.888260i
$517$	13.5442	+	16.5037i	0.595674	+	0.725831i
$518$	24.5085	+	2.41494i	1.07684	+	0.106106i
$519$	10.9860	−	7.34061i	0.482232	−	0.322217i
$520$	34.0747	+	6.78244i	1.49427	+	0.297430i
$521$	8.98062	−	13.4405i	0.393448	−	0.588837i	−0.580874	−	0.813993i	$-0.697289\pi$
$521$	8.98062	−	13.4405i	0.393448	−	0.588837i	0.974323	+	0.225156i	$0.0722893\pi$
$522$	0.286416	+	2.90931i	0.0125361	+	0.127337i
$523$	18.6368	−	5.65340i	0.814929	−	0.247206i	0.144810	−	0.989460i	$-0.453743\pi$
$523$	18.6368	−	5.65340i	0.814929	−	0.247206i	0.670119	+	0.742254i	$0.266243\pi$
$524$	−21.1849	−	17.3890i	−0.925465	−	0.759642i
$525$	−1.09525	−	0.898850i	−0.0478007	−	0.0392290i
$526$	−15.8632		0.000681569i	−0.691670		2.97178e-5i
$527$	36.7876	+	15.2379i	1.60249	+	0.663775i
$528$	0.00386221	−	22.4728i	0.000168081	−	0.978005i
$529$	2.28187	−	0.945182i	0.0992118	−	0.0410949i
$530$	0.621988	−	0.257604i	0.0270174	−	0.0111896i
$531$	−1.26444	−	12.8381i	−0.0548721	−	0.557126i
$532$	2.76124	−	5.16486i	0.119715	−	0.223925i
$533$	10.7653	−	20.1405i	0.466298	−	0.872382i
$534$	2.22378	+	0.674681i	0.0962325	+	0.0291963i
$535$	−25.4823	+	5.06875i	−1.10170	+	0.219141i
$536$	35.6289	−	10.8029i	1.53893	−	0.466614i
$537$	1.67974	−	8.44461i	0.0724860	−	0.364412i
$538$	−2.42800	−	8.00528i	−0.104678	−	0.345132i
$539$	−0.272343	+	2.76514i	−0.0117306	+	0.119103i
$540$	3.52054	+	2.35279i	0.151500	+	0.101248i
$541$	1.20521	−	3.97306i	0.0518162	−	0.170815i	−0.927213	−	0.374534i	$-0.877803\pi$
$541$	1.20521	−	3.97306i	0.0518162	−	0.170815i	0.979029	+	0.203719i	$0.0653028\pi$
$542$	3.81790	+	5.71442i	0.163993	+	0.245455i
$543$	15.1529	+	15.1529i	0.650273	+	0.650273i
$544$	−35.1109	+	23.4495i	−1.50537	+	1.00539i
$545$	−5.77342	+	5.77342i	−0.247306	+	0.247306i
$546$	−22.0305	−	4.38313i	−0.942819	−	0.187581i
$547$	−10.0990	−	3.06349i	−0.431800	−	0.130985i	0.0669000	−	0.997760i	$-0.478689\pi$
$547$	−10.0990	−	3.06349i	−0.431800	−	0.130985i	−0.498700	+	0.866774i	$0.666189\pi$
$548$	30.6340	+	6.09621i	1.30862	+	0.260417i
$549$	3.09535	+	0.304865i	0.132106	+	0.0130113i
$550$	−1.93861	+	3.62651i	−0.0826626	+	0.154635i
$551$	2.16865	+	0.431370i	0.0923874	+	0.0183770i
$552$	−6.72729	−	12.5898i	−0.286333	−	0.535857i
$553$	1.74032	+	8.74920i	0.0740061	+	0.372054i
$554$	9.52260	−	5.08941i	0.404577	−	0.216228i
$555$	11.8772	+	6.34849i	0.504158	+	0.269478i
$556$	6.66818	+	8.12663i	0.282794	+	0.344646i
$557$	−36.6169	+	3.60645i	−1.55151	+	0.152810i	−0.837152	−	0.546971i	$-0.815781\pi$
$557$	−36.6169	+	3.60645i	−1.55151	+	0.152810i	−0.714357	+	0.699781i	$0.753281\pi$
$558$	6.97029	+	2.88754i	0.295076	+	0.122239i
$559$	24.2443	+	58.5310i	1.02543	+	2.47560i
$560$	−20.4484	+	10.9254i	−0.864104	+	0.461682i
$561$	−16.0471	+	38.7411i	−0.677509	+	1.63565i
$562$	16.2082	−	16.2068i	0.683701	−	0.683642i
$563$	3.73345	−	4.54923i	0.157346	−	0.191727i	−0.688370	−	0.725360i	$-0.741673\pi$
$563$	3.73345	−	4.54923i	0.157346	−	0.191727i	0.845716	+	0.533633i	$0.179173\pi$
$564$	2.20686	−	7.27278i	0.0929255	−	0.306239i
$565$	6.85892	+	22.6108i	0.288557	+	0.951244i
$566$	0.345003	−	0.420350i	0.0145015	−	0.0176686i
$567$	−2.27625	−	1.52094i	−0.0955934	−	0.0638735i
$568$	−29.4496	+	12.1940i	−1.23568	+	0.511649i
$569$	−7.05855	−	10.5639i	−0.295910	−	0.442861i	0.653488	−	0.756937i	$-0.273305\pi$
$569$	−7.05855	−	10.5639i	−0.295910	−	0.442861i	−0.949398	+	0.314077i	$0.898305\pi$
$570$	2.47582	−	2.03167i	0.103701	−	0.0850974i
$571$	19.9391	−	16.3636i	0.834426	−	0.684795i	−0.116846	−	0.993150i	$-0.537278\pi$
$571$	19.9391	−	16.3636i	0.834426	−	0.684795i	0.951271	+	0.308355i	$0.0997783\pi$
$572$	−0.00560199	+	65.1921i	−0.000234231	+	2.72582i
$573$	4.30956	+	8.06262i	0.180035	+	0.336821i
$574$	2.97237	+	14.9465i	0.124065	+	0.623855i
$575$			2.61198i			0.108927i
$576$	−6.65290	+	4.44285i	−0.277204	+	0.185119i
$577$		−	16.6897i		−	0.694800i	−0.937717	−	0.347400i	$-0.887065\pi$
$577$		−	16.6897i		−	0.694800i	0.937717	−	0.347400i	$-0.112935\pi$
$578$	53.6899	−	10.6772i	2.23321	−	0.444113i
$579$	7.85790	+	14.7011i	0.326563	+	0.610957i
$580$	−6.18877	−	6.18983i	−0.256975	−	0.257019i
$581$	−11.4252	+	9.37641i	−0.473997	+	0.388999i
$582$	−3.51559	−	4.28413i	−0.145726	−	0.177583i
$583$	0.701816	+	1.05034i	0.0290662	+	0.0435007i
$584$	18.2013	−	18.1966i	0.753175	−	0.752981i
$585$	−10.2134	−	6.82438i	−0.422272	−	0.282153i
$586$	−17.5459	−	14.4008i	−0.724816	−	0.594893i
$587$	9.18017	+	30.2630i	0.378906	+	1.24909i	0.914491	+	0.404605i	$0.132591\pi$
$587$	9.18017	+	30.2630i	0.378906	+	1.24909i	−0.535585	+	0.844481i	$0.679909\pi$
$588$	0.872360	−	0.466190i	0.0359755	−	0.0192253i
$589$	3.62020	−	4.41122i	0.149168	−	0.181761i
$590$	27.3109	+	27.3132i	1.12437	+	1.12447i
$591$	−2.76926	+	6.68558i	−0.113912	+	0.275008i
$592$	−19.6713	+	16.1382i	−0.808485	+	0.663274i
$593$	8.59716	+	20.7554i	0.353043	+	0.852321i	0.996241	+	0.0866213i	$0.0276070\pi$
$593$	8.59716	+	20.7554i	0.353043	+	0.852321i	−0.643198	+	0.765700i	$0.722393\pi$
$594$	−3.04087	+	7.34041i	−0.124768	+	0.301181i
$595$	43.0519	−	4.24025i	1.76496	−	0.173833i
$596$	−39.0692	−	3.85137i	−1.60034	−	0.157758i
$597$	13.7408	+	7.34461i	0.562373	+	0.300595i
$598$	19.5185	+	36.5203i	0.798171	+	1.49343i
$599$	1.68714	+	8.48182i	0.0689346	+	0.346558i	0.999824	−	0.0187426i	$-0.00596629\pi$
$599$	1.68714	+	8.48182i	0.0689346	+	0.346558i	−0.930890	+	0.365300i	$0.880966\pi$
$600$	1.45683	−	0.143296i	0.0594750	−	0.00585003i
$601$	−7.94302	−	1.57996i	−0.324002	−	0.0644481i	0.0304094	−	0.999538i	$-0.490319\pi$
$601$	−7.94302	−	1.57996i	−0.324002	−	0.0644481i	−0.354412	+	0.935089i	$0.615319\pi$
$602$	−37.2831	−	19.9303i	−1.51955	−	0.812298i
$603$	−13.0996	−	1.29020i	−0.533458	−	0.0525410i
$604$	−1.00917	−	1.51061i	−0.0410627	−	0.0614661i
$605$	41.6635	+	12.6385i	1.69386	+	0.513828i
$606$	−3.45788	+	17.3800i	−0.140467	+	0.706015i
$607$	−2.59463	+	2.59463i	−0.105313	+	0.105313i	−0.757800	−	0.652487i	$-0.773726\pi$
$607$	−2.59463	+	2.59463i	−0.105313	+	0.105313i	0.652487	+	0.757800i	$0.273726\pi$
$608$	1.75524	+	5.79073i	0.0711845	+	0.234845i
$609$	4.00154	+	4.00154i	0.162151	+	0.162151i
$610$	−7.74349	+	5.17355i	−0.313525	+	0.209471i
$611$	−6.40012	+	21.0984i	−0.258921	+	0.853548i
$612$	14.6410	−	2.91096i	0.591826	−	0.117669i
$613$	−1.45390	+	14.7617i	−0.0587224	+	0.596218i	0.920125	+	0.391625i	$0.128087\pi$
$613$	−1.45390	+	14.7617i	−0.0587224	+	0.596218i	−0.978847	+	0.204593i	$0.934413\pi$
$614$	1.45456	−	0.441167i	0.0587011	−	0.0178040i
$615$	−1.62580	+	8.17344i	−0.0655586	+	0.329585i
$616$	−27.5935	−	33.6316i	−1.11177	−	1.35505i
$617$	−5.95193	+	1.18391i	−0.239616	+	0.0476625i	−0.313437	−	0.949609i	$-0.601481\pi$
$617$	−5.95193	+	1.18391i	−0.239616	+	0.0476625i	0.0738214	+	0.997271i	$0.476481\pi$
$618$	−1.87862	+	6.19202i	−0.0755692	+	0.249080i
$619$	−18.6054	+	34.8082i	−0.747813	+	1.39906i	0.163162	+	0.986599i	$0.447831\pi$
$619$	−18.6054	+	34.8082i	−0.747813	+	1.39906i	−0.910975	+	0.412461i	$0.864669\pi$
$620$	−21.6178	+	6.55566i	−0.868192	+	0.263282i
$621$	0.494670	+	5.02247i	0.0198504	+	0.201545i
$622$	−3.61303	−	8.72368i	−0.144869	−	0.349788i
$623$	4.15610	−	1.72151i	0.166511	−	0.0689710i
$624$	19.2985	−	12.8900i	0.772557	−	0.516014i
$625$	20.4587	+	8.47428i	0.818349	+	0.338971i
$626$	0.000682390	−	15.8824i	2.72738e−5	−	0.634787i
$627$	4.64546	+	3.81243i	0.185522	+	0.152254i
$628$	32.4361	−	3.19187i	1.29434	−	0.127369i
$629$	45.4328	−	13.7819i	1.81152	−	0.549520i
$630$	8.15739	−	0.803079i	0.324998	−	0.0319954i
$631$	19.5510	−	29.2601i	0.778313	−	1.16483i	−0.204254	−	0.978918i	$-0.565477\pi$
$631$	19.5510	−	29.2601i	0.778313	−	1.16483i	0.982567	−	0.185909i	$-0.0595231\pi$
$632$	−7.66259	−	5.12141i	−0.304801	−	0.203719i
$633$	19.4350	−	12.9861i	0.772472	−	0.516150i
$634$	1.06029	−	10.7606i	0.0421096	−	0.427358i
$635$	−10.3535	−	12.6158i	−0.410867	−	0.500643i
$636$	0.172126	−	0.415447i	0.00682523	−	0.0164736i
$637$	−2.53054	+	1.35260i	−0.100263	+	0.0535919i
$638$	9.12534	−	13.6558i	0.361276	−	0.540637i
$639$	11.2693			0.445806
$640$	6.96012	−	22.9196i	0.275123	−	0.905978i
$641$	−32.8527			−1.29760			−0.648801	−	0.760958i	$-0.724729\pi$
$641$	−32.8527			−1.29760			−0.648801	+	0.760958i	$0.724729\pi$
$642$	−9.64249	+	14.4297i	−0.380559	+	0.569493i
$643$	13.7627	−	7.35631i	0.542747	−	0.290104i	−0.177151	−	0.984184i	$-0.556688\pi$
$643$	13.7627	−	7.35631i	0.542747	−	0.290104i	0.719899	+	0.694079i	$0.244188\pi$
$644$	−25.5280	−	10.5766i	−1.00594	−	0.416777i
$645$	−14.6663	−	17.8709i	−0.577484	−	0.703667i
$646$	1.10716	−	11.2362i	0.0435606	−	0.442084i
$647$	−7.72516	+	5.16179i	−0.303707	+	0.202931i	−0.698080	−	0.716020i	$-0.745962\pi$
$647$	−7.72516	+	5.16179i	−0.303707	+	0.202931i	0.394372	+	0.918951i	$0.370962\pi$
$648$	2.77415	−	0.551441i	0.108979	−	0.0216627i
$649$	−40.2656	+	60.2617i	−1.58056	+	2.36548i
$650$	−4.22613	+	0.416054i	−0.165762	+	0.0163190i
$651$	13.9761	−	4.23960i	0.547766	−	0.166163i
$652$	1.05477	+	10.7187i	0.0413081	+	0.419778i
$653$	15.5230	+	12.7394i	0.607462	+	0.498531i	0.887102	−	0.461574i	$-0.152715\pi$
$653$	15.5230	+	12.7394i	0.607462	+	0.498531i	−0.279640	+	0.960105i	$0.590215\pi$
$654$	−0.000234328		5.45388i	−9.16294e−6		0.213264i
$655$	−26.8049	−	11.1029i	−1.04735	−	0.433828i
$656$	−13.0897	−	8.74952i	−0.511067	−	0.341611i
$657$	−8.40682	+	3.48222i	−0.327981	+	0.135854i
$658$	−5.62963	−	13.5928i	−0.219466	−	0.529902i
$659$	−2.17828	−	22.1165i	−0.0848539	−	0.861536i	−0.939551	−	0.342409i	$-0.888757\pi$
$659$	−2.17828	−	22.1165i	−0.0848539	−	0.861536i	0.854697	−	0.519127i	$-0.173743\pi$
$660$	−6.90377	−	22.7657i	−0.268729	−	0.886155i
$661$	22.8367	−	42.7244i	0.888244	−	1.66179i	0.148486	−	0.988914i	$-0.452560\pi$
$661$	22.8367	−	42.7244i	0.888244	−	1.66179i	0.739758	−	0.672873i	$-0.234940\pi$
$662$	−7.82962	+	25.8068i	−0.304307	+	1.00301i
$663$	−42.4717	+	8.44814i	−1.64946	+	0.328098i
$664$	1.49872	−	15.1967i	0.0581616	−	0.589745i
$665$	1.20952	−	6.08065i	0.0469030	−	0.235797i
$666$	8.60858	−	2.61098i	0.333576	−	0.101173i
$667$	1.02255	−	10.3821i	0.0395933	−	0.401997i
$668$	−1.94647	−	9.78997i	−0.0753113	−	0.378785i
$669$	0.936631	−	3.08766i	0.0362123	−	0.119376i
$670$	32.7708	−	21.8947i	1.26605	−	0.845866i
$671$	−12.3563	−	12.3563i	−0.477010	−	0.477010i
$672$	−4.49862	+	14.8185i	−0.173538	+	0.571636i
$673$	11.8368	−	11.8368i	0.456274	−	0.456274i	−0.441156	−	0.897430i	$-0.645432\pi$
$673$	11.8368	−	11.8368i	0.456274	−	0.456274i	0.897430	+	0.441156i	$0.145432\pi$
$674$	7.10128	−	35.6925i	0.273531	−	1.37482i
$675$	−0.495268	−	0.150238i	−0.0190629	−	0.00578266i
$676$	−34.3608	+	22.9549i	−1.32157	+	0.882879i
$677$	−38.4415	−	3.78616i	−1.47743	−	0.145514i	−0.673035	−	0.739611i	$-0.735010\pi$
$677$	−38.4415	−	3.78616i	−1.47743	−	0.145514i	−0.804394	+	0.594097i	$0.797510\pi$
$678$	13.9190	+	7.44064i	0.534557	+	0.285756i
$679$	−10.5219	−	2.09294i	−0.403793	−	0.0803195i
$680$	−28.3588	+	34.5462i	−1.08751	+	1.32479i
$681$	1.01949	+	5.12532i	0.0390669	+	0.196403i
$682$	−19.9799	−	37.3836i	−0.765069	−	1.43149i
$683$	−28.1767	−	15.0608i	−1.07815	−	0.576284i	−0.165995	−	0.986127i	$-0.553084\pi$
$683$	−28.1767	−	15.0608i	−1.07815	−	0.576284i	−0.912156	+	0.409843i	$0.865584\pi$
$684$	0.209873	−	2.12900i	0.00802469	−	0.0814043i
$685$	32.9054	−	3.24090i	1.25725	−	0.123829i
$686$	−9.63939	+	23.2687i	−0.368034	+	0.888404i
$687$	−1.43709	−	3.46944i	−0.0548284	−	0.132367i
$688$	41.7995	−	12.6719i	1.59359	−	0.483112i
$689$	−0.499221	+	1.20523i	−0.0190188	+	0.0459154i
$690$	−10.6845	−	10.6854i	−0.406750	−	0.406785i
$691$	−2.34890	+	2.86214i	−0.0893562	+	0.108881i	−0.815769	−	0.578378i	$-0.803686\pi$
$691$	−2.34890	+	2.86214i	−0.0893562	+	0.108881i	0.726413	+	0.687258i	$0.241186\pi$
$692$	12.4549	+	23.3063i	0.473464	+	0.885972i
$693$	4.46473	+	14.7182i	0.169601	+	0.559100i
$694$	24.2733	+	19.9223i	0.921403	+	0.756242i
$695$	9.25270	+	6.18245i	0.350975	+	0.234514i
$696$	−5.84674		0.000753621i	−0.221620		2.85659e-5i
$697$	16.3219	+	24.4275i	0.618237	+	0.925257i
$698$	−23.1068	−	28.1581i	−0.874603	−	1.06580i
$699$	−3.44651	+	2.82848i	−0.130359	+	0.106983i
$700$	2.00392	−	2.00358i	0.0757412	−	0.0757281i
$701$	16.9286	+	31.6712i	0.639384	+	1.19620i	0.967812	+	0.251675i	$0.0809813\pi$
$701$	16.9286	+	31.6712i	0.639384	+	1.19620i	−0.328428	+	0.944529i	$0.606519\pi$
$702$	−8.04747	+	1.60038i	−0.303732	+	0.0604025i
$703$		−	6.80412i		−	0.256622i
$704$	44.7281	+	4.41698i	1.68575	+	0.166471i
$705$		−	8.04553i		−	0.303012i
$706$	−5.70649	−	28.6949i	−0.214766	−	1.07995i
$707$	16.1705	+	30.2530i	0.608156	+	1.13778i
$708$	25.8004	+	0.00221705i	0.969640	+	8.33217e-5i
$709$	−2.43911	+	2.00173i	−0.0916028	+	0.0751765i	−0.679080	−	0.734064i	$-0.737621\pi$
$709$	−2.43911	+	2.00173i	−0.0916028	+	0.0751765i	0.587477	+	0.809241i	$0.300121\pi$
$710$	−26.0837	+	21.4045i	−0.978905	+	0.803296i
$711$	1.81034	+	2.70937i	0.0678931	+	0.101609i
$712$	−1.77917	+	4.29373i	−0.0666773	+	0.160915i
$713$	−22.3866	−	14.9582i	−0.838384	−	0.560190i
$714$	18.3328	−	22.3366i	0.686086	−	0.835925i
$715$	20.0330	+	66.0400i	0.749192	+	2.46976i
$716$	16.4782	+	5.00015i	0.615818	+	0.186864i
$717$	−3.09246	+	3.76817i	−0.115490	+	0.140725i
$718$	30.5487	−	30.5460i	1.14007	−	1.13997i
$719$	14.3280	−	34.5909i	0.534345	−	1.29002i	−0.394275	−	0.918992i	$-0.629004\pi$
$719$	14.3280	−	34.5909i	0.534345	−	1.29002i	0.928621	−	0.371031i	$-0.120996\pi$
$720$	−5.37362	+	6.54548i	−0.200263	+	0.243936i
$721$	4.79348	+	11.5725i	0.178519	+	0.430982i
$722$	23.3293	+	9.66451i	0.868228	+	0.359676i
$723$	−5.96312	+	0.587316i	−0.221771	+	0.0218425i
$724$	−33.1327	+	27.1865i	−1.23137	+	1.01038i
$725$	0.943527	+	0.504326i	0.0350417	+	0.0187302i
$726$	25.6489	−	13.7082i	0.951919	−	0.508759i
$727$	−3.76097	−	18.9077i	−0.139487	−	0.701247i	−0.985714	−	0.168425i	$-0.946132\pi$
$727$	−3.76097	−	18.9077i	−0.139487	−	0.701247i	0.846228	−	0.532821i	$-0.178868\pi$
$728$	13.0465	−	42.9885i	0.483535	−	1.59326i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	12.8443	−	24.0275i	0.475389	−	0.889298i
$731$	−81.1085	−	7.98849i	−2.99991	−	0.295465i
$732$	−1.21411	+	6.10101i	−0.0448749	+	0.225500i
$733$	−38.3658	−	11.6381i	−1.41707	−	0.429865i	−0.513423	−	0.858135i	$-0.671623\pi$
$733$	−38.3658	−	11.6381i	−1.41707	−	0.429865i	−0.903650	+	0.428271i	$0.859123\pi$
$734$	6.79712	+	1.35234i	0.250886	+	0.0499156i
$735$	0.740386	−	0.740386i	0.0273096	−	0.0273096i
$736$	26.3780	−	10.9195i	0.972307	−	0.402498i
$737$	52.2924	+	52.2924i	1.92621	+	1.92621i
$738$	3.09243	+	4.62858i	0.113834	+	0.170380i
$739$	−4.90157	+	16.1583i	−0.180307	+	0.594393i	0.819467	+	0.573127i	$0.194270\pi$
$739$	−4.90157	+	16.1583i	−0.180307	+	0.594393i	−0.999774	+	0.0212663i	$0.993230\pi$
$740$	−14.9661	+	22.3942i	−0.550165	+	0.823226i
$741$	−0.608295	+	6.17612i	−0.0223463	+	0.226886i
$742$	−0.252660	−	0.833038i	−0.00927545	−	0.0305818i
$743$	5.42418	−	27.2692i	0.198994	−	1.00041i	−0.744147	−	0.668016i	$-0.767144\pi$
$743$	5.42418	−	27.2692i	0.198994	−	1.00041i	0.943141	−	0.332393i	$-0.107856\pi$
$744$	−7.11483	+	13.3068i	−0.260842	+	0.487850i
$745$	−40.7602	+	8.10771i	−1.49334	+	0.297044i
$746$	26.4830	+	8.03476i	0.969610	+	0.294173i
$747$	−2.54502	+	4.76140i	−0.0931175	+	0.174211i
$748$	−73.9599	−	39.5406i	−2.70424	−	1.44575i
$749$	3.29293	+	33.4337i	0.120321	+	1.22164i
$750$	15.2631	−	6.32141i	0.557329	−	0.230825i
$751$	−34.9214	+	14.4649i	−1.27430	+	0.527832i	−0.914269	−	0.405109i	$-0.867234\pi$
$751$	−34.9214	+	14.4649i	−1.27430	+	0.527832i	−0.360031	+	0.932941i	$0.617234\pi$
$752$	14.0424	+	5.81938i	0.512074	+	0.212211i
$753$	−3.82498	−	1.58436i	−0.139390	−	0.0577372i
$754$	16.9610		0.000728733i	0.617682		2.65389e-5i
$755$	−1.48660	−	1.22002i	−0.0541031	−	0.0444012i
$756$	3.47382	−	4.23212i	0.126342	−	0.153921i
$757$	49.3734	−	14.9773i	1.79451	−	0.544358i	0.796339	−	0.604850i	$-0.206767\pi$
$757$	49.3734	−	14.9773i	1.79451	−	0.544358i	0.998169	+	0.0604924i	$0.0192671\pi$
$758$	−2.39708	−	24.3487i	−0.0870660	−	0.884385i
$759$	15.7525	−	23.5753i	0.571781	−	0.855730i
$760$	3.55798	+	5.32638i	0.129061	+	0.193208i
$761$	−31.1357	+	20.8042i	−1.12867	+	0.754151i	−0.972344	−	0.233555i	$-0.924964\pi$
$761$	−31.1357	+	20.8042i	−1.12867	+	0.754151i	−0.156324	+	0.987706i	$0.549964\pi$
$762$	−10.8490	−	1.06900i	−0.393017	−	0.0387258i
$763$	6.69765	+	8.16111i	0.242471	+	0.295452i
$764$	−16.8930	+	6.99562i	−0.611168	+	0.253093i
$765$	13.9362	−	7.44908i	0.503866	−	0.269322i
$766$	−7.67080	−	5.12594i	−0.277157	−	0.185208i
$767$	−74.8452			−2.70250
$768$	−7.53750	−	14.1133i	−0.271986	−	0.509271i

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)

\(f(q)\)	\(=\)	\(q+(1.17584 + 0.785745i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.765208 + 1.84782i) q^{4} +(1.34312 + 1.63660i) q^{5} +(1.40740 + 0.138678i) q^{6} +(2.27625 - 1.52094i) q^{7} +(-0.552156 + 2.77401i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.17584 + 0.785745i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.765208 + 1.84782i) q^{4} +(1.34312 + 1.63660i) q^{5} +(1.40740 + 0.138678i) q^{6} +(2.27625 - 1.52094i) q^{7} +(-0.552156 + 2.77401i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.293349 + 2.97974i) q^{10} +(-5.37629 + 1.63088i) q^{11} +(1.54591 + 1.26892i) q^{12} +(-4.48489 - 3.68066i) q^{13} +(3.87158 + 0.000166343i) q^{14} +(1.95602 + 0.810209i) q^{15} +(-2.82891 + 2.82794i) q^{16} +(6.89563 - 2.85626i) q^{17} +(1.30659 - 0.541140i) q^{18} +(-0.104845 - 1.06451i) q^{19} +(-1.99638 + 3.73420i) q^{20} +(1.29050 - 2.41436i) q^{21} +(-7.60313 - 2.30674i) q^{22} +(-4.94980 + 0.984576i) q^{23} +(0.820700 + 2.70674i) q^{24} +(0.100970 - 0.507609i) q^{25} +(-2.38147 - 7.85185i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(4.55223 + 3.04227i) q^{28} +(-0.600058 + 1.97813i) q^{29} +(1.66335 + 2.48961i) q^{30} +(3.77236 + 3.77236i) q^{31} +(-5.54840 + 1.10241i) q^{32} +(-3.97267 + 3.97267i) q^{33} +(10.3525 + 2.05970i) q^{34} +(5.54645 + 1.68250i) q^{35} +(1.96154 + 0.390349i) q^{36} +(6.33038 + 0.623488i) q^{37} +(0.713152 - 1.33408i) q^{38} +(-5.69037 - 1.13189i) q^{39} +(-5.28156 + 2.82218i) q^{40} +(0.767908 + 3.86054i) q^{41} +(3.41451 - 1.82490i) q^{42} +(-9.63017 - 5.14743i) q^{43} +(-7.12756 - 8.68648i) q^{44} +(2.10698 - 0.207520i) q^{45} +(-6.59380 - 2.73158i) q^{46} +(-1.45424 - 3.51085i) q^{47} +(-1.16180 + 3.82756i) q^{48} +(0.189259 - 0.456911i) q^{49} +(0.517576 - 0.517532i) q^{50} +(4.73497 - 5.76958i) q^{51} +(3.36933 - 11.1038i) q^{52} +(-0.0652695 - 0.215165i) q^{53} +(0.897215 - 1.09316i) q^{54} +(-9.89013 - 6.60837i) q^{55} +(2.96226 + 7.15412i) q^{56} +(-0.594271 - 0.889389i) q^{57} +(-2.25988 + 1.85447i) q^{58} +(9.97201 - 8.18381i) q^{59} +(-0.000363861 + 4.23436i) q^{60} +(1.46620 + 2.74306i) q^{61} +(1.47158 + 7.39981i) q^{62} -2.73762i q^{63} +(-7.39025 - 3.06337i) q^{64} -12.2836i q^{65} +(-7.79275 + 1.54973i) q^{66} +(-6.20500 - 11.6087i) q^{67} +(10.5545 + 10.5563i) q^{68} +(-3.90121 + 3.20164i) q^{69} +(5.19974 + 6.33645i) q^{70} +(6.26088 + 9.37007i) q^{71} +(1.99974 + 2.00026i) q^{72} +(-7.56594 - 5.05540i) q^{73} +(6.95362 + 5.70719i) q^{74} +(-0.150238 - 0.495268i) q^{75} +(1.88680 - 1.00831i) q^{76} +(-9.75730 + 11.8893i) q^{77} +(-5.80160 - 5.80210i) q^{78} +(-1.24699 + 3.01049i) q^{79} +(-8.42779 - 0.831528i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-2.13046 + 5.14276i) q^{82} +(-5.37290 + 0.529185i) q^{83} +(5.44883 + 0.537135i) q^{84} +(13.9362 + 7.44908i) q^{85} +(-7.27898 - 13.6194i) q^{86} +(0.403278 + 2.02742i) q^{87} +(-1.55552 - 15.8144i) q^{88} +(1.61165 + 0.320578i) q^{89} +(2.64054 + 1.41154i) q^{90} +(-15.8068 - 1.55683i) q^{91} +(-5.60695 - 8.39295i) q^{92} +(5.10520 + 1.54865i) q^{93} +(1.04868 - 5.27087i) q^{94} +(1.60136 - 1.60136i) q^{95} +(-4.37358 + 3.58773i) q^{96} +(-2.77097 - 2.77097i) q^{97} +(0.581554 - 0.388546i) q^{98} +(-1.63088 + 5.37629i) 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

Related objects

Downloads

Learn more