LMFDB - Embedded newform 384.2.v.a.253.4

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			253.4
Character	$\chi$	$=$	384.253
Dual form			384.2.v.a.85.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34358 - 0.441342i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(1.61043 + 1.18596i) q^{4} +(2.46859 + 0.748840i) q^{5} +(0.511199 + 1.31859i) q^{6} +(2.57470 - 0.512139i) q^{7} +(-1.64034 - 2.30419i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})$	\(q+(-1.34358 - 0.441342i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(1.61043 + 1.18596i) q^{4} +(2.46859 + 0.748840i) q^{5} +(0.511199 + 1.31859i) q^{6} +(2.57470 - 0.512139i) q^{7} +(-1.64034 - 2.30419i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(-2.98627 - 2.09562i) q^{10} +(-0.342322 + 0.0337158i) q^{11} +(-0.104890 - 1.99725i) q^{12} +(1.04484 + 3.44439i) q^{13} +(-3.68535 - 0.448220i) q^{14} +(-0.987199 - 2.38331i) q^{15} +(1.18700 + 3.81982i) q^{16} +(-2.21506 + 5.34764i) q^{17} +(0.694982 - 1.23167i) q^{18} +(3.09113 + 1.65224i) q^{19} +(3.08742 + 4.13361i) q^{20} +(-2.02926 - 1.66537i) q^{21} +(0.474819 + 0.105781i) q^{22} +(-1.10734 - 1.65725i) q^{23} +(-0.740540 + 2.72976i) q^{24} +(1.37585 + 0.919314i) q^{25} +(0.116317 - 5.08896i) q^{26} +(0.881921 - 0.471397i) q^{27} +(4.75376 + 2.22872i) q^{28} +(0.640924 - 6.50741i) q^{29} +(0.274531 + 3.63787i) q^{30} +(6.17902 - 6.17902i) q^{31} +(0.0910097 - 5.65612i) q^{32} +(0.243230 + 0.243230i) q^{33} +(5.33626 - 6.20740i) q^{34} +(6.73940 + 0.663773i) q^{35} +(-1.47735 + 1.34812i) q^{36} +(3.27459 + 6.12633i) q^{37} +(-3.42399 - 3.58417i) q^{38} +(1.99971 - 2.99277i) q^{39} +(-2.32387 - 6.91646i) q^{40} +(3.68846 - 2.46455i) q^{41} +(1.99148 + 3.13316i) q^{42} +(0.676727 - 0.824594i) q^{43} +(-0.591274 - 0.351683i) q^{44} +(-1.21605 + 2.27507i) q^{45} +(0.756391 + 2.71538i) q^{46} +(-7.18356 - 2.97553i) q^{47} +(2.19974 - 3.34083i) q^{48} +(-0.100373 + 0.0415760i) q^{49} +(-1.44284 - 1.84240i) q^{50} +(5.53900 - 1.68024i) q^{51} +(-2.40225 + 6.78611i) q^{52} +(0.897741 + 9.11492i) q^{53} +(-1.39298 + 0.244132i) q^{54} +(-0.870303 - 0.173114i) q^{55} +(-5.40345 - 5.09250i) q^{56} +(-0.683791 - 3.43765i) q^{57} +(-3.73312 + 8.46038i) q^{58} +(1.35904 - 4.48016i) q^{59} +(1.23669 - 5.00894i) q^{60} +(8.45098 - 6.93554i) q^{61} +(-11.0291 + 5.57497i) q^{62} +2.62514i q^{63} +(-2.61856 + 7.55931i) q^{64} +9.28522i q^{65} +(-0.219452 - 0.434147i) q^{66} +(-0.239134 + 0.196252i) q^{67} +(-9.90930 + 5.98505i) q^{68} +(-0.578584 + 1.90734i) q^{69} +(-8.76199 - 3.86621i) q^{70} +(1.57021 + 7.89399i) q^{71} +(2.57993 - 1.15930i) q^{72} +(-11.8459 - 2.35630i) q^{73} +(-1.69588 - 9.67645i) q^{74} +(-0.162191 - 1.64675i) q^{75} +(3.01857 + 6.32679i) q^{76} +(-0.864110 + 0.262125i) q^{77} +(-4.00761 + 3.13849i) q^{78} +(-7.38272 + 3.05802i) q^{79} +(0.0697918 + 10.3185i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(-6.04346 + 1.68346i) q^{82} +(4.94666 - 9.25455i) q^{83} +(-1.29293 - 5.08859i) q^{84} +(-9.47262 + 11.5424i) q^{85} +(-1.27317 + 0.809244i) q^{86} +(-5.43689 + 3.63281i) q^{87} +(0.639213 + 0.733470i) q^{88} +(3.47272 - 5.19729i) q^{89} +(2.63795 - 2.52005i) q^{90} +(4.45416 + 8.33316i) q^{91} +(0.182134 - 3.98216i) q^{92} +(-8.69638 - 0.856518i) q^{93} +(8.33849 + 7.16828i) q^{94} +(6.39348 + 6.39348i) q^{95} +(-4.42998 + 3.51785i) q^{96} +(9.98433 - 9.98433i) q^{97} +(0.153209 - 0.0115619i) q^{98} +(0.0337158 - 0.342322i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{32}\right)$	$1$

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 $

$2$	−1.34358	−	0.441342i	−0.950057	−	0.312076i
$2$	−1.34358	−	0.441342i	−0.950057	−	0.312076i
$3$	−0.634393	−	0.773010i	−0.366267	−	0.446298i
$3$	−0.634393	−	0.773010i	−0.366267	−	0.446298i
$4$	1.61043	+	1.18596i	0.805217	+	0.592980i
$5$	2.46859	+	0.748840i	1.10399	+	0.334891i	0.789117	−	0.614243i	$-0.210538\pi$
$5$	2.46859	+	0.748840i	1.10399	+	0.334891i	0.314872	+	0.949134i	$0.398038\pi$
$6$	0.511199	+	1.31859i	0.208696	+	0.538312i
$7$	2.57470	−	0.512139i	0.973144	−	0.193570i	0.317183	−	0.948365i	$-0.397263\pi$
$7$	2.57470	−	0.512139i	0.973144	−	0.193570i	0.655962	+	0.754794i	$0.272263\pi$
$8$	−1.64034	−	2.30419i	−0.579948	−	0.814653i
$9$	−0.195090	+	0.980785i	−0.0650301	+	0.326928i
$10$	−2.98627	−	2.09562i	−0.944341	−	0.662694i
$11$	−0.342322	+	0.0337158i	−0.103214	+	0.0101657i	−0.149492	−	0.988763i	$-0.547764\pi$
$11$	−0.342322	+	0.0337158i	−0.103214	+	0.0101657i	0.0462782	+	0.998929i	$0.485264\pi$
$12$	−0.104890	−	1.99725i	−0.0302792	−	0.576556i
$13$	1.04484	+	3.44439i	0.289788	+	0.955302i	0.974101	+	0.226114i	$0.0726020\pi$
$13$	1.04484	+	3.44439i	0.289788	+	0.955302i	−0.684313	+	0.729188i	$0.739898\pi$
$14$	−3.68535	−	0.448220i	−0.984951	−	0.119792i
$15$	−0.987199	−	2.38331i	−0.254894	−	0.615368i
$16$	1.18700	+	3.81982i	0.296750	+	0.954955i
$17$	−2.21506	+	5.34764i	−0.537232	+	1.29699i	0.389416	+	0.921062i	$0.372677\pi$
$17$	−2.21506	+	5.34764i	−0.537232	+	1.29699i	−0.926648	+	0.375931i	$0.877323\pi$
$18$	0.694982	−	1.23167i	0.163809	−	0.290306i
$19$	3.09113	+	1.65224i	0.709154	+	0.379051i	0.786196	−	0.617977i	$-0.212048\pi$
$19$	3.09113	+	1.65224i	0.709154	+	0.379051i	−0.0770421	+	0.997028i	$0.524548\pi$
$20$	3.08742	+	4.13361i	0.690368	+	0.924303i
$21$	−2.02926	−	1.66537i	−0.442821	−	0.363414i
$22$	0.474819	+	0.105781i	0.101232	+	0.0225526i
$23$	−1.10734	−	1.65725i	−0.230897	−	0.345561i	0.697871	−	0.716223i	$-0.254131\pi$
$23$	−1.10734	−	1.65725i	−0.230897	−	0.345561i	−0.928768	+	0.370662i	$0.879131\pi$
$24$	−0.740540	+	2.72976i	−0.151162	+	0.557210i
$25$	1.37585	+	0.919314i	0.275170	+	0.183863i
$26$	0.116317	−	5.08896i	0.0228117	−	0.998027i
$27$	0.881921	−	0.471397i	0.169726	−	0.0907203i
$28$	4.75376	+	2.22872i	0.898376	+	0.421188i
$29$	0.640924	−	6.50741i	0.119017	−	1.20840i	−0.731275	−	0.682083i	$-0.761074\pi$
$29$	0.640924	−	6.50741i	0.119017	−	1.20840i	0.850291	−	0.526312i	$-0.176426\pi$
$30$	0.274531	+	3.63787i	0.0501222	+	0.664181i
$31$	6.17902	−	6.17902i	1.10979	−	1.10979i	0.116607	−	0.993178i	$-0.462798\pi$
$31$	6.17902	−	6.17902i	1.10979	−	1.10979i	0.993178	−	0.116607i	$-0.0372017\pi$
$32$	0.0910097	−	5.65612i	0.0160884	−	0.999871i
$33$	0.243230	+	0.243230i	0.0423409	+	0.0423409i
$34$	5.33626	−	6.20740i	0.915161	−	1.06456i
$35$	6.73940	+	0.663773i	1.13917	+	0.112198i
$36$	−1.47735	+	1.34812i	−0.246225	+	0.224687i
$37$	3.27459	+	6.12633i	0.538339	+	1.00716i	0.993180	+	0.116589i	$0.0371961\pi$
$37$	3.27459	+	6.12633i	0.538339	+	1.00716i	−0.454841	+	0.890573i	$0.650304\pi$
$38$	−3.42399	−	3.58417i	−0.555444	−	0.581430i
$39$	1.99971	−	2.99277i	0.320209	−	0.479227i
$40$	−2.32387	−	6.91646i	−0.367436	−	1.09359i
$41$	3.68846	−	2.46455i	0.576040	−	0.384898i	−0.233153	−	0.972440i	$-0.574904\pi$
$41$	3.68846	−	2.46455i	0.576040	−	0.384898i	0.809194	+	0.587542i	$0.199904\pi$
$42$	1.99148	+	3.13316i	0.307293	+	0.483457i
$43$	0.676727	−	0.824594i	0.103200	−	0.125749i	−0.718849	−	0.695166i	$-0.755331\pi$
$43$	0.676727	−	0.824594i	0.103200	−	0.125749i	0.822049	+	0.569417i	$0.192831\pi$
$44$	−0.591274	−	0.351683i	−0.0891379	−	0.0530183i
$45$	−1.21605	+	2.27507i	−0.181278	+	0.339147i
$46$	0.756391	+	2.71538i	0.111524	+	0.400360i
$47$	−7.18356	−	2.97553i	−1.04783	−	0.434025i	−0.208713	−	0.977977i	$-0.566928\pi$
$47$	−7.18356	−	2.97553i	−1.04783	−	0.434025i	−0.839117	+	0.543951i	$0.816928\pi$
$48$	2.19974	−	3.34083i	0.317504	−	0.482208i
$49$	−0.100373	+	0.0415760i	−0.0143391	+	0.00593943i
$50$	−1.44284	−	1.84240i	−0.204048	−	0.260554i
$51$	5.53900	−	1.68024i	0.775616	−	0.235280i
$52$	−2.40225	+	6.78611i	−0.333132	+	0.941064i
$53$	0.897741	+	9.11492i	0.123314	+	1.25203i	0.835283	+	0.549820i	$0.185304\pi$
$53$	0.897741	+	9.11492i	0.123314	+	1.25203i	−0.711969	+	0.702211i	$0.752196\pi$
$54$	−1.39298	+	0.244132i	−0.189561	+	0.0332222i
$55$	−0.870303	−	0.173114i	−0.117352	−	0.0233427i
$56$	−5.40345	−	5.09250i	−0.722066	−	0.680515i
$57$	−0.683791	−	3.43765i	−0.0905703	−	0.455328i
$58$	−3.73312	+	8.46038i	−0.490183	+	1.11090i
$59$	1.35904	−	4.48016i	0.176932	−	0.583267i	−0.822953	−	0.568110i	$-0.807675\pi$
$59$	1.35904	−	4.48016i	0.176932	−	0.583267i	0.999885	−	0.0151577i	$-0.00482504\pi$
$60$	1.23669	−	5.00894i	0.159656	−	0.646652i
$61$	8.45098	−	6.93554i	1.08204	−	0.888005i	0.0878993	−	0.996129i	$-0.471985\pi$
$61$	8.45098	−	6.93554i	1.08204	−	0.888005i	0.994137	+	0.108125i	$0.0344846\pi$
$62$	−11.0291	+	5.57497i	−1.40070	+	0.708022i
$63$			2.62514i			0.330736i
$64$	−2.61856	+	7.55931i	−0.327320	+	0.944913i
$65$			9.28522i			1.15169i
$66$	−0.219452	−	0.434147i	−0.0270127	−	0.0534398i
$67$	−0.239134	+	0.196252i	−0.0292149	+	0.0239760i	−0.648887	−	0.760884i	$-0.724765\pi$
$67$	−0.239134	+	0.196252i	−0.0292149	+	0.0239760i	0.619673	+	0.784860i	$0.287265\pi$
$68$	−9.90930	+	5.98505i	−1.20168	+	0.725794i
$69$	−0.578584	+	1.90734i	−0.0696534	+	0.229616i
$70$	−8.76199	−	3.86621i	−1.04726	−	0.462101i
$71$	1.57021	+	7.89399i	0.186350	+	0.936844i	0.954871	+	0.297020i	$0.0959929\pi$
$71$	1.57021	+	7.89399i	0.186350	+	0.936844i	−0.768521	+	0.639824i	$0.779007\pi$
$72$	2.57993	−	1.15930i	0.304047	−	0.136625i
$73$	−11.8459	−	2.35630i	−1.38646	−	0.275784i	−0.555222	−	0.831702i	$-0.687367\pi$
$73$	−11.8459	−	2.35630i	−1.38646	−	0.275784i	−0.831237	+	0.555919i	$0.812367\pi$
$74$	−1.69588	−	9.67645i	−0.197142	−	1.12486i
$75$	−0.162191	−	1.64675i	−0.0187282	−	0.190151i
$76$	3.01857	+	6.32679i	0.346254	+	0.725732i
$77$	−0.864110	+	0.262125i	−0.0984745	+	0.0298719i
$78$	−4.00761	+	3.13849i	−0.453772	+	0.355364i
$79$	−7.38272	+	3.05802i	−0.830621	+	0.344054i	−0.757148	−	0.653243i	$-0.773408\pi$
$79$	−7.38272	+	3.05802i	−0.830621	+	0.344054i	−0.0734722	+	0.997297i	$0.523408\pi$
$80$	0.0697918	+	10.3185i	0.00780296	+	1.15364i
$81$	−0.923880	−	0.382683i	−0.102653	−	0.0425204i
$82$	−6.04346	+	1.68346i	−0.667389	+	0.185907i
$83$	4.94666	−	9.25455i	0.542967	−	1.01582i	−0.449497	−	0.893282i	$-0.648397\pi$
$83$	4.94666	−	9.25455i	0.542967	−	1.01582i	0.992464	−	0.122537i	$-0.0391031\pi$
$84$	−1.29293	−	5.08859i	−0.141070	−	0.555211i
$85$	−9.47262	+	11.5424i	−1.02745	+	1.25195i
$86$	−1.27317	+	0.809244i	−0.137289	+	0.0872630i
$87$	−5.43689	+	3.63281i	−0.582896	+	0.389479i
$88$	0.639213	+	0.733470i	0.0681404	+	0.0781881i
$89$	3.47272	−	5.19729i	0.368107	−	0.550911i	−0.600463	−	0.799653i	$-0.705017\pi$
$89$	3.47272	−	5.19729i	0.368107	−	0.550911i	0.968570	+	0.248741i	$0.0800169\pi$
$90$	2.63795	−	2.52005i	0.278064	−	0.265637i
$91$	4.45416	+	8.33316i	0.466923	+	0.873552i
$92$	0.182134	−	3.98216i	0.0189887	−	0.415169i
$93$	−8.69638	−	0.856518i	−0.901772	−	0.0888168i
$94$	8.33849	+	7.16828i	0.860050	+	0.739351i
$95$	6.39348	+	6.39348i	0.655957	+	0.655957i
$96$	−4.42998	+	3.51785i	−0.452133	+	0.359040i
$97$	9.98433	−	9.98433i	1.01376	−	1.01376i	0.0138515	−	0.999904i	$-0.495591\pi$
$97$	9.98433	−	9.98433i	1.01376	−	1.01376i	0.999904	−	0.0138515i	$-0.00440921\pi$
$98$	0.153209	−	0.0115619i	0.0154765	−	0.00116793i
$99$	0.0337158	−	0.342322i	0.00338857	−	0.0344047i
$100$	1.12545	+	3.11220i	0.112545	+	0.311220i
$101$	−12.4645	+	6.66243i	−1.24027	+	0.662936i	−0.955311	−	0.295604i	$-0.904479\pi$
$101$	−12.4645	+	6.66243i	−1.24027	+	0.662936i	−0.284956	+	0.958540i	$0.591979\pi$
$102$	−8.18367	−	0.187052i	−0.810305	−	0.0185209i
$103$	−16.2171	−	10.8359i	−1.59792	−	1.06769i	−0.952795	−	0.303616i	$-0.901806\pi$
$103$	−16.2171	−	10.8359i	−1.59792	−	1.06769i	−0.645123	−	0.764079i	$-0.723194\pi$
$104$	6.22262	−	8.05749i	0.610178	−	0.790102i
$105$	−3.76232	−	5.63072i	−0.367165	−	0.549502i
$106$	2.81660	−	12.6429i	0.273573	−	1.22798i
$107$	2.62682	+	2.15577i	0.253944	+	0.208406i	0.752749	−	0.658308i	$-0.228728\pi$
$107$	2.62682	+	2.15577i	0.253944	+	0.208406i	−0.498805	+	0.866714i	$0.666228\pi$
$108$	1.97933	+	0.286769i	0.190462	+	0.0275943i
$109$	1.26797	+	0.677746i	0.121450	+	0.0649163i	0.531003	−	0.847370i	$-0.321815\pi$
$109$	1.26797	+	0.677746i	0.121450	+	0.0649163i	−0.409553	+	0.912286i	$0.634315\pi$
$110$	1.09292	+	0.616694i	0.104206	+	0.0587995i
$111$	2.65834	−	6.41779i	0.252318	−	0.609150i
$112$	5.01245	+	9.22697i	0.473632	+	0.871867i
$113$	−1.48248	−	3.57902i	−0.139460	−	0.336686i	0.838683	−	0.544620i	$-0.183326\pi$
$113$	−1.48248	−	3.57902i	−0.139460	−	0.336686i	−0.978143	+	0.207934i	$0.933326\pi$
$114$	−0.598447	+	4.92055i	−0.0560497	+	0.460852i
$115$	−1.49256	−	4.92031i	−0.139182	−	0.458821i
$116$	8.74969	−	9.71965i	0.812388	−	0.902447i
$117$	−3.58204	+	0.352801i	−0.331160	+	0.0326164i
$118$	−3.80327	+	5.41967i	−0.350119	+	0.498921i
$119$	−2.96439	+	14.9030i	−0.271745	+	1.36615i
$120$	−3.87225	+	6.18413i	−0.353486	+	0.564531i
$121$	−10.6726	+	2.12291i	−0.970235	+	0.192992i
$122$	−14.4155	+	5.58871i	−1.30512	+	0.505978i
$123$	−4.24506	−	1.28772i	−0.382764	−	0.116110i
$124$	17.2790	−	2.62285i	1.55170	−	0.235538i
$125$	−5.47464	−	6.67087i	−0.489667	−	0.596661i
$126$	1.15858	−	3.52709i	0.103215	−	0.314219i
$127$	−12.9488			−1.14902			−0.574510	−	0.818497i	$-0.694807\pi$
$127$	−12.9488			−1.14902			−0.574510	+	0.818497i	$0.694807\pi$
$128$	6.85450	−	9.00088i	0.605858	−	0.795573i
$129$	−1.06673			−0.0939204
$130$	4.09796	−	12.4755i	0.359414	−	1.09417i
$131$	6.80375	+	8.29039i	0.594446	+	0.724335i	0.980143	−	0.198291i	$-0.0635390\pi$
$131$	6.80375	+	8.29039i	0.594446	+	0.724335i	−0.385697	+	0.922626i	$0.626039\pi$
$132$	0.103245	+	0.680166i	0.00898634	+	0.0592009i
$133$	8.80491	+	2.67094i	0.763482	+	0.231600i
$134$	0.407911	−	0.158141i	0.0352381	−	0.0136613i
$135$	2.53011	−	0.503270i	0.217757	−	0.0433145i
$136$	15.9554	−	3.66803i	1.36817	−	0.314531i
$137$	−1.44544	+	7.26672i	−0.123492	+	0.620838i	0.868619	+	0.495480i	$0.165008\pi$
$137$	−1.44544	+	7.26672i	−0.123492	+	0.620838i	−0.992112	+	0.125358i	$0.959992\pi$
$138$	1.61916	−	2.30731i	0.137832	−	0.196412i
$139$	−19.1434	+	1.88546i	−1.62372	+	0.159923i	−0.868549	−	0.495603i	$-0.834947\pi$
$139$	−19.1434	+	1.88546i	−1.62372	+	0.159923i	−0.755173	+	0.655526i	$0.772447\pi$
$140$	10.0662	+	9.06161i	0.850745	+	0.765846i
$141$	2.25709	+	7.44062i	0.190081	+	0.626613i
$142$	1.37424	−	11.2992i	0.115323	−	0.948211i
$143$	−0.473804	−	1.14386i	−0.0396215	−	0.0956547i
$144$	−3.97800	+	0.418984i	−0.331500	+	0.0349153i
$145$	6.45519	−	15.5842i	0.536074	−	1.29420i
$146$	14.8760	+	8.39397i	1.23115	+	0.694690i
$147$	0.0958150	+	0.0512142i	0.00790268	+	0.00422407i
$148$	−1.99206	+	13.7496i	−0.163746	+	1.13021i
$149$	8.72671	+	7.16182i	0.714920	+	0.586719i	0.919950	−	0.392036i	$-0.128229\pi$
$149$	8.72671	+	7.16182i	0.714920	+	0.586719i	−0.205030	+	0.978756i	$0.565729\pi$
$150$	−0.508864	+	2.28413i	−0.0415486	+	0.186499i
$151$	−9.67694	−	14.4826i	−0.787498	−	1.17857i	−0.980335	−	0.197343i	$-0.936769\pi$
$151$	−9.67694	−	14.4826i	−0.787498	−	1.17857i	0.192837	−	0.981231i	$-0.438231\pi$
$152$	−1.26343	−	9.83279i	−0.102478	−	0.797544i
$153$	−4.81275	−	3.21578i	−0.389088	−	0.259980i
$154$	1.27669	+	0.0291810i	0.102879	+	0.00235147i
$155$	19.8806	−	10.6264i	1.59685	−	0.853533i
$156$	6.76970	−	2.44809i	0.542010	−	0.196004i
$157$	−0.432763	+	4.39391i	−0.0345382	+	0.350672i	0.962348	+	0.271820i	$0.0876255\pi$
$157$	−0.432763	+	4.39391i	−0.0345382	+	0.350672i	−0.996886	+	0.0788523i	$0.974874\pi$
$158$	11.2689	−	0.850407i	0.896508	−	0.0676548i
$159$	6.47641	−	6.47641i	0.513613	−	0.513613i
$160$	4.46020	−	13.8945i	0.352610	−	1.09846i
$161$	−3.69981	−	3.69981i	−0.291586	−	0.291586i
$162$	1.07242	+	0.921914i	0.0842569	+	0.0724324i
$163$	2.49592	+	0.245827i	0.195495	+	0.0192546i	0.195291	−	0.980745i	$-0.437435\pi$
$163$	2.49592	+	0.245827i	0.195495	+	0.0192546i	0.000204542		1.00000i	$0.499935\pi$
$164$	8.86288	+	0.405365i	0.692074	+	0.0316537i
$165$	0.418296	+	0.782576i	0.0325643	+	0.0609235i
$166$	−10.7307	+	10.2511i	−0.832862	+	0.795640i
$167$	−6.20377	+	9.28459i	−0.480062	+	0.718463i	−0.989894	−	0.141811i	$-0.954708\pi$
$167$	−6.20377	+	9.28459i	−0.480062	+	0.718463i	0.509832	+	0.860274i	$0.329708\pi$
$168$	−0.508648	+	7.40757i	−0.0392430	+	0.571507i
$169$	0.0369905	−	0.0247163i	0.00284543	−	0.00190125i
$170$	17.8214	−	11.3276i	1.36684	−	0.868784i
$171$	−2.22355	+	2.70940i	−0.170039	+	0.207193i
$172$	2.06776	−	0.525385i	0.157665	−	0.0400602i
$173$	−9.26587	+	17.3352i	−0.704471	+	1.31797i	0.233872	+	0.972267i	$0.424860\pi$
$173$	−9.26587	+	17.3352i	−0.704471	+	1.31797i	−0.938343	+	0.345705i	$0.887640\pi$
$174$	8.90823	−	2.48146i	0.675331	−	0.188119i
$175$	4.01322	+	1.66233i	0.303371	+	0.125660i
$176$	−0.535126	−	1.26759i	−0.0403366	−	0.0955482i
$177$	−4.32538	+	1.79163i	−0.325115	+	0.134667i
$178$	−6.95967	+	5.45034i	−0.521649	+	0.408520i
$179$	16.0719	−	4.87536i	1.20127	−	0.364401i	0.374652	−	0.927165i	$-0.377762\pi$
$179$	16.0719	−	4.87536i	1.20127	−	0.364401i	0.826617	+	0.562764i	$0.190262\pi$
$180$	−4.65651	+	2.22167i	−0.347076	+	0.165593i
$181$	0.586988	+	5.95979i	0.0436305	+	0.442988i	0.992038	+	0.125935i	$0.0401931\pi$
$181$	0.586988	+	5.95979i	0.0436305	+	0.442988i	−0.948408	+	0.317052i	$0.897307\pi$
$182$	−2.30677	−	13.1621i	−0.170989	−	0.975640i
$183$	−10.7225	−	2.13283i	−0.792629	−	0.157664i
$184$	−2.00221	+	5.26998i	−0.147605	+	0.388508i
$185$	3.49600	+	17.5756i	0.257031	+	1.29218i
$186$	11.3063	+	4.98888i	0.829018	+	0.365802i
$187$	0.577966	−	1.90530i	0.0422651	−	0.139329i
$188$	−8.03980	−	13.3113i	−0.586363	−	0.970827i
$189$	2.02926	−	1.66537i	0.147607	−	0.121138i
$190$	−5.76847	−	11.4119i	−0.418489	−	0.827906i
$191$		−	16.2911i		−	1.17878i	−0.807848	−	0.589391i	$-0.799368\pi$
$191$		−	16.2911i		−	1.17878i	0.807848	−	0.589391i	$-0.200632\pi$
$192$	7.50462	−	2.77140i	0.541599	−	0.200008i
$193$		−	12.6761i		−	0.912448i	−0.889865	−	0.456224i	$-0.849202\pi$
$193$		−	12.6761i		−	0.912448i	0.889865	−	0.456224i	$-0.150798\pi$
$194$	−17.8213	+	9.00829i	−1.27949	+	0.646757i
$195$	7.17757	−	5.89048i	0.513997	−	0.421826i
$196$	−0.210952	−	0.0520833i	−0.0150680	−	0.00372024i
$197$	−2.16075	+	7.12305i	−0.153947	+	0.507496i	−0.999658	−	0.0261451i	$-0.991677\pi$
$197$	−2.16075	+	7.12305i	−0.153947	+	0.507496i	0.845711	+	0.533641i	$0.179177\pi$
$198$	−0.196381	+	0.445059i	−0.0139562	+	0.0316289i
$199$	2.55848	+	12.8623i	0.181366	+	0.911788i	0.959073	+	0.283160i	$0.0913829\pi$
$199$	2.55848	+	12.8623i	0.181366	+	0.911788i	−0.777707	+	0.628627i	$0.783617\pi$
$200$	−0.138592	−	4.67821i	−0.00979996	−	0.330799i
$201$	0.303410	+	0.0603520i	0.0214009	+	0.00425690i
$202$	19.6875	−	3.45042i	1.38521	−	0.242770i
$203$	−1.68251	−	17.0829i	−0.118089	−	1.19898i
$204$	10.9129	+	3.86312i	0.764056	+	0.270472i
$205$	10.9509	−	3.32191i	0.764841	−	0.232012i
$206$	17.0067	+	21.7162i	1.18491	+	1.51304i
$207$	1.84144	−	0.762750i	0.127989	−	0.0530148i
$208$	−11.9167	+	8.07961i	−0.826275	+	0.560220i
$209$	−1.11387	−	0.461380i	−0.0770480	−	0.0319143i
$210$	2.56993	+	9.22581i	0.177342	+	0.636641i
$211$	−3.20002	+	5.98682i	−0.220299	+	0.412150i	−0.967656	−	0.252272i	$-0.918822\pi$
$211$	−3.20002	+	5.98682i	−0.220299	+	0.412150i	0.747358	+	0.664422i	$0.231322\pi$
$212$	−9.36417	+	15.7437i	−0.643134	+	1.08128i
$213$	5.10601	−	6.22169i	0.349858	−	0.426303i
$214$	−2.57792	−	4.05579i	−0.176223	−	0.277248i
$215$	2.28805	−	1.52883i	0.156044	−	0.104265i
$216$	−2.53284	−	1.25886i	−0.172338	−	0.0856546i
$217$	12.7446	−	19.0736i	0.865159	−	1.29480i
$218$	−1.40451	−	1.47022i	−0.0951255	−	0.0995758i
$219$	5.69352	+	10.6518i	0.384732	+	0.719784i
$220$	−1.19626	−	1.31093i	−0.0806519	−	0.0883831i
$221$	−20.7337	−	2.04210i	−1.39470	−	0.137366i
$222$	−6.40414	+	7.44961i	−0.429818	+	0.499985i
$223$	1.18297	+	1.18297i	0.0792177	+	0.0792177i	0.745605	−	0.666388i	$-0.232160\pi$
$223$	1.18297	+	1.18297i	0.0792177	+	0.0792177i	−0.666388	+	0.745605i	$0.732160\pi$
$224$	−2.66240	−	14.6094i	−0.177889	−	0.976133i
$225$	−1.17007	+	1.17007i	−0.0780043	+	0.0780043i
$226$	0.412263	+	5.46299i	0.0274233	+	0.363393i
$227$	−1.26102	+	12.8034i	−0.0836969	+	0.849789i	0.858072	+	0.513529i	$0.171662\pi$
$227$	−1.26102	+	12.8034i	−0.0836969	+	0.849789i	−0.941769	+	0.336260i	$0.890838\pi$
$228$	2.97571	−	6.34706i	0.197071	−	0.420344i
$229$	21.3287	−	11.4004i	1.40944	−	0.753361i	0.421300	−	0.906921i	$-0.361574\pi$
$229$	21.3287	−	11.4004i	1.40944	−	0.753361i	0.988139	+	0.153560i	$0.0490738\pi$
$230$	−0.166159	+	7.26958i	−0.0109562	+	0.479342i
$231$	0.750811	+	0.501676i	0.0493997	+	0.0330078i
$232$	−16.0456	+	9.19756i	−1.05345	+	0.603849i
$233$	−15.0479	−	22.5207i	−0.985819	−	1.47538i	−0.876515	−	0.481374i	$-0.840138\pi$
$233$	−15.0479	−	22.5207i	−0.985819	−	1.47538i	−0.109303	−	0.994008i	$-0.534862\pi$
$234$	4.96848	+	1.10689i	0.324800	+	0.0723596i
$235$	−15.5051	−	12.7247i	−1.01144	−	0.830069i
$236$	7.50194	−	5.60324i	0.488335	−	0.364740i
$237$	7.04743	+	3.76693i	0.457780	+	0.244688i
$238$	10.5602	−	18.7151i	0.684517	−	1.21312i
$239$	−1.34058	+	3.23644i	−0.0867148	+	0.209348i	−0.961288	−	0.275545i	$-0.911142\pi$
$239$	−1.34058	+	3.23644i	−0.0867148	+	0.209348i	0.874573	+	0.484893i	$0.161142\pi$
$240$	7.93200	−	6.59991i	0.512009	−	0.426023i
$241$	−1.32866	−	3.20767i	−0.0855865	−	0.206624i	0.875292	−	0.483595i	$-0.160669\pi$
$241$	−1.32866	−	3.20767i	−0.0855865	−	0.206624i	−0.960878	+	0.276971i	$0.910669\pi$
$242$	15.2764	+	1.85795i	0.982007	+	0.119434i
$243$	0.290285	+	0.956940i	0.0186218	+	0.0613878i
$244$	21.8350	−	1.14672i	1.39784	−	0.0734111i
$245$	−0.278915	+	0.0274707i	−0.0178192	+	0.00175504i
$246$	5.13526	+	3.60368i	0.327412	+	0.229763i
$247$	−2.46122	+	12.3734i	−0.156604	+	0.787300i
$248$	−24.3733	−	4.10192i	−1.54771	−	0.260472i
$249$	−10.2920	+	2.04720i	−0.652229	+	0.129736i
$250$	4.41151	+	11.3791i	0.279008	+	0.719675i
$251$	−4.12967	−	1.25272i	−0.260663	−	0.0790711i	0.157249	−	0.987559i	$-0.449738\pi$
$251$	−4.12967	−	1.25272i	−0.260663	−	0.0790711i	−0.417911	+	0.908488i	$0.637238\pi$
$252$	−3.11331	+	4.22762i	−0.196120	+	0.266315i
$253$	0.434944	+	0.529980i	0.0273447	+	0.0333196i
$254$	17.3978	+	5.71485i	1.09164	+	0.358581i
$255$	14.9318			0.935065
$256$	−13.1821	+	9.06827i	−0.823878	+	0.566767i
$257$	29.4479			1.83691			0.918456	−	0.395524i	$-0.129437\pi$
$257$	29.4479			1.83691			0.918456	+	0.395524i	$0.129437\pi$
$258$	1.43324	+	0.470793i	0.0892298	+	0.0293103i
$259$	11.5686	+	14.0964i	0.718839	+	0.875907i
$260$	−11.0119	+	14.9532i	−0.682929	+	0.927361i
$261$	6.25733	+	1.89814i	0.387319	+	0.117492i
$262$	−5.48251	−	14.1416i	−0.338711	−	0.873672i
$263$	−14.6323	+	2.91056i	−0.902269	+	0.179473i	−0.624362	−	0.781135i	$-0.714641\pi$
$263$	−14.6323	+	2.91056i	−0.902269	+	0.179473i	−0.277908	+	0.960608i	$0.589641\pi$
$264$	0.161467	−	0.959427i	0.00993762	−	0.0590486i
$265$	−4.60946	+	23.1733i	−0.283157	+	1.42353i
$266$	−10.6513	−	7.47460i	−0.653075	−	0.458297i
$267$	−6.22063	+	0.612678i	−0.380696	+	0.0374953i
$268$	−0.617857	+	0.0324482i	−0.0377416	+	0.00198209i
$269$	−2.38146	−	7.85063i	−0.145200	−	0.478661i	0.853929	−	0.520390i	$-0.174213\pi$
$269$	−2.38146	−	7.85063i	−0.145200	−	0.478661i	−0.999129	+	0.0417289i	$0.986713\pi$
$270$	−3.62152	−	0.440457i	−0.220399	−	0.0268054i
$271$	4.70866	+	11.3677i	0.286031	+	0.690539i	0.999953	−	0.00968592i	$-0.00308317\pi$
$271$	4.70866	+	11.3677i	0.286031	+	0.690539i	−0.713923	+	0.700225i	$0.753083\pi$
$272$	−23.0563	−	2.11349i	−1.39799	−	0.128149i
$273$	3.61592	−	8.72961i	0.218846	−	0.528340i
$274$	5.14918	−	9.12552i	0.311073	−	0.551293i
$275$	−0.501980	−	0.268314i	−0.0302705	−	0.0161799i
$276$	−3.19380	+	2.38546i	−0.192244	+	0.143588i
$277$	−3.63056	−	2.97953i	−0.218139	−	0.179022i	0.518977	−	0.854788i	$-0.326313\pi$
$277$	−3.63056	−	2.97953i	−0.218139	−	0.179022i	−0.737116	+	0.675766i	$0.763813\pi$
$278$	26.5529	+	5.91551i	1.59254	+	0.354789i
$279$	4.85483	+	7.26576i	0.290651	+	0.434990i
$280$	−9.52545	−	16.6176i	−0.569255	−	0.993094i
$281$	9.48457	+	6.33739i	0.565802	+	0.378057i	0.805325	−	0.592834i	$-0.201991\pi$
$281$	9.48457	+	6.33739i	0.565802	+	0.378057i	−0.239523	+	0.970891i	$0.576991\pi$
$282$	0.251270	−	10.9932i	0.0149629	−	0.654638i
$283$	−21.3847	+	11.4304i	−1.27119	+	0.679466i	−0.962393	−	0.271662i	$-0.912427\pi$
$283$	−21.3847	+	11.4304i	−1.27119	+	0.679466i	−0.308798	+	0.951128i	$0.599927\pi$
$284$	−6.83323	+	14.5750i	−0.405477	+	0.864865i
$285$	0.886246	−	8.99821i	0.0524967	−	0.533008i
$286$	0.131760	+	1.74599i	0.00779116	+	0.103242i
$287$	8.23447	−	8.23447i	0.486066	−	0.486066i
$288$	5.52969	+	1.19272i	0.325840	+	0.0702814i
$289$	−11.6699	−	11.6699i	−0.686466	−	0.686466i
$290$	−15.5510	+	18.0897i	−0.913189	+	1.06227i
$291$	−14.0520	−	1.38400i	−0.823742	−	0.0811315i
$292$	−16.2826	−	17.8434i	−0.952866	−	1.04421i
$293$	−10.1175	−	18.9286i	−0.591073	−	1.10582i	−0.982614	−	0.185659i	$-0.940558\pi$
$293$	−10.1175	−	18.9286i	−0.591073	−	1.10582i	0.391541	−	0.920161i	$-0.371942\pi$
$294$	−0.106132	−	0.111098i	−0.00618977	−	0.00647935i
$295$	6.70985	−	10.0420i	0.390662	−	0.584668i
$296$	8.74476	−	17.5945i	0.508279	−	1.02266i
$297$	−0.286008	+	0.191104i	−0.0165959	+	0.0110890i
$298$	−8.56425	−	13.4740i	−0.496114	−	0.780526i
$299$	4.55123	−	5.54569i	0.263204	−	0.320715i
$300$	1.69178	−	2.84434i	0.0976752	−	0.164218i
$301$	1.32006	−	2.46966i	0.0760870	−	0.142349i
$302$	6.61002	+	23.7294i	0.380364	+	1.36547i
$303$	13.0575	+	5.40861i	0.750136	+	0.310717i
$304$	−2.64210	+	13.7688i	−0.151535	+	0.789694i
$305$	26.0556	−	10.7926i	1.49194	−	0.617983i
$306$	5.04707	+	6.44473i	0.288522	+	0.368421i
$307$	−15.0233	+	4.55727i	−0.857425	+	0.260097i	−0.688236	−	0.725487i	$-0.741615\pi$
$307$	−15.0233	+	4.55727i	−0.857425	+	0.260097i	−0.169189	+	0.985584i	$0.554115\pi$
$308$	−1.70246	−	0.602664i	−0.0970068	−	0.0343400i
$309$	1.91174	+	19.4102i	0.108755	+	1.10421i
$310$	−31.4011	+	5.50332i	−1.78346	+	0.312568i
$311$	−26.9961	−	5.36985i	−1.53081	−	0.304496i	−0.643416	−	0.765516i	$-0.722484\pi$
$311$	−26.9961	−	5.36985i	−1.53081	−	0.304496i	−0.887390	+	0.461020i	$0.847484\pi$
$312$	−10.1761	+	0.301468i	−0.576109	+	0.0170673i
$313$	−0.279084	−	1.40305i	−0.0157747	−	0.0793050i	0.972096	−	0.234583i	$-0.0753726\pi$
$313$	−0.279084	−	1.40305i	−0.0157747	−	0.0793050i	−0.987871	+	0.155278i	$0.950373\pi$
$314$	2.52067	−	5.71259i	0.142250	−	0.322380i
$315$	−1.96581	+	6.48041i	−0.110761	+	0.365129i
$316$	−15.5161	−	3.83086i	−0.872847	−	0.215502i
$317$	26.7603	−	21.9616i	1.50301	−	1.23349i	0.602898	−	0.797818i	$-0.294013\pi$
$317$	26.7603	−	21.9616i	1.50301	−	1.23349i	0.900108	−	0.435667i	$-0.143487\pi$
$318$	−11.5599	+	5.84329i	−0.648247	+	0.327675i
$319$			2.24924i			0.125933i
$320$	−12.1249	+	16.7000i	−0.677801	+	0.933557i
$321$		−	3.39817i		−	0.189667i
$322$	3.33813	+	6.60389i	0.186027	+	0.368021i
$323$	−15.6827	+	12.8704i	−0.872606	+	0.716130i
$324$	−1.03400	−	1.71197i	−0.0574445	−	0.0951095i
$325$	−1.72893	+	5.69951i	−0.0959036	+	0.316152i
$326$	−3.24498	−	1.43184i	−0.179723	−	0.0793024i
$327$	−0.280489	−	1.41011i	−0.0155111	−	0.0779795i
$328$	−11.7291	−	4.45620i	−0.647632	−	0.246052i
$329$	−20.0194	−	3.98210i	−1.10370	−	0.219540i
$330$	−0.216632	−	1.23607i	−0.0119252	−	0.0680433i
$331$	−3.22075	−	32.7008i	−0.177028	−	1.79740i	−0.515985	−	0.856598i	$-0.672574\pi$
$331$	−3.22075	−	32.7008i	−0.177028	−	1.79740i	0.338956	−	0.940802i	$-0.389926\pi$
$332$	18.9418	−	9.03732i	1.03957	−	0.495987i
$333$	−6.64745	+	2.01648i	−0.364278	+	0.110503i
$334$	12.4330	−	9.73665i	0.680301	−	0.532766i
$335$	−0.737286	+	0.305394i	−0.0402823	+	0.0166855i
$336$	3.95268	−	9.72821i	0.215636	−	0.530717i
$337$	29.5250	+	12.2296i	1.60833	+	0.666191i	0.992562	−	0.121740i	$-0.0388473\pi$
$337$	29.5250	+	12.2296i	1.60833	+	0.666191i	0.615764	+	0.787930i	$0.288847\pi$
$338$	−0.0606082	+	0.0168829i	−0.00329665	+	0.000918311i
$339$	−1.82614	+	3.41647i	−0.0991825	+	0.185557i
$340$	−28.9439	+	7.35418i	−1.56970	+	0.398836i
$341$	−1.90689	+	2.32355i	−0.103264	+	0.125827i
$342$	4.18329	−	2.65896i	0.226206	−	0.143780i
$343$	−15.5162	+	10.3676i	−0.837796	+	0.559798i
$344$	−3.01008	−	0.206690i	−0.162293	−	0.0111440i
$345$	−2.85658	+	4.27518i	−0.153793	+	0.230168i
$346$	20.1002	−	19.2019i	1.08059	−	1.03230i
$347$	13.7802	+	25.7810i	0.739762	+	1.38400i	0.916619	+	0.399761i	$0.130907\pi$
$347$	13.7802	+	25.7810i	0.739762	+	1.38400i	−0.176857	+	0.984236i	$0.556593\pi$
$348$	−13.0641	−	0.597519i	−0.700311	−	0.0320304i
$349$	−4.76163	−	0.468980i	−0.254884	−	0.0251039i	−0.0302321	−	0.999543i	$-0.509625\pi$
$349$	−4.76163	−	0.468980i	−0.254884	−	0.0251039i	−0.224652	+	0.974439i	$0.572125\pi$
$350$	−4.65844	−	4.00468i	−0.249004	−	0.214059i
$351$	2.54514	+	2.54514i	0.135850	+	0.135850i
$352$	0.159546	+	1.93929i	0.00850384	+	0.103364i
$353$	−26.2312	+	26.2312i	−1.39615	+	1.39615i	−0.585405	+	0.810741i	$0.699065\pi$
$353$	−26.2312	+	26.2312i	−1.39615	+	1.39615i	−0.810741	+	0.585405i	$0.800935\pi$
$354$	6.60223	−	0.498236i	0.350905	−	0.0264809i
$355$	−2.03512	+	20.6629i	−0.108013	+	1.09667i
$356$	11.7564	−	4.25139i	0.623086	−	0.225323i
$357$	13.4007	−	7.16285i	0.709243	−	0.379098i
$358$	−23.7456	−	0.542748i	−1.25500	−	0.0286851i
$359$	16.6301	+	11.1119i	0.877702	+	0.586462i	0.910734	−	0.412993i	$-0.135516\pi$
$359$	16.6301	+	11.1119i	0.877702	+	0.586462i	−0.0330324	+	0.999454i	$0.510516\pi$
$360$	7.23693	−	0.929883i	0.381419	−	0.0490091i
$361$	−3.73066	−	5.58332i	−0.196350	−	0.293859i
$362$	1.84164	−	8.26654i	0.0967942	−	0.434480i
$363$	8.41165	+	6.90326i	0.441497	+	0.362327i
$364$	−2.70964	+	18.7025i	−0.142024	+	0.980275i
$365$	−27.4782	−	14.6874i	−1.43828	−	0.768775i
$366$	13.4652	+	7.59792i	0.703840	+	0.397150i
$367$	−5.55188	+	13.4034i	−0.289806	+	0.699653i	−0.999990	−	0.00436221i	$-0.998611\pi$
$367$	−5.55188	+	13.4034i	−0.289806	+	0.699653i	0.710185	+	0.704016i	$0.248611\pi$
$368$	5.01599	−	6.19701i	0.261477	−	0.323041i
$369$	1.69761	+	4.09840i	0.0883741	+	0.213354i
$370$	3.05966	−	25.1572i	0.159064	−	1.30786i
$371$	6.97952	+	23.0084i	0.362359	+	1.19454i
$372$	−12.9892	−	11.6929i	−0.673456	−	0.606249i
$373$	−28.5933	+	2.81619i	−1.48050	+	0.145817i	−0.805764	−	0.592237i	$-0.798245\pi$
$373$	−28.5933	+	2.81619i	−1.48050	+	0.145817i	−0.674741	+	0.738054i	$0.735745\pi$
$374$	−1.61743	+	2.30485i	−0.0836356	+	0.119181i
$375$	−1.68358	+	8.46391i	−0.0869395	+	0.437075i
$376$	4.92731	+	21.4332i	0.254107	+	1.10533i
$377$	23.0837	−	4.59163i	1.18887	−	0.236481i
$378$	−3.46148	+	1.34197i	−0.178039	+	0.0690234i
$379$	−11.0658	−	3.35679i	−0.568414	−	0.172427i	−0.00702035	−	0.999975i	$-0.502235\pi$
$379$	−11.0658	−	3.35679i	−0.568414	−	0.172427i	−0.561394	+	0.827549i	$0.689735\pi$
$380$	2.71388	+	17.8787i	0.139219	+	0.917158i
$381$	8.21463	+	10.0096i	0.420848	+	0.512805i
$382$	−7.18994	+	21.8885i	−0.367869	+	1.11991i
$383$	−9.32760			−0.476618			−0.238309	−	0.971189i	$-0.576593\pi$
$383$	−9.32760			−0.476618			−0.238309	+	0.971189i	$0.576593\pi$
$384$	−11.3062	+	0.411503i	−0.576968	+	0.0209994i
$385$	−2.32943			−0.118719
$386$	−5.59451	+	17.0314i	−0.284753	+	0.866878i
$387$	0.676727	+	0.824594i	0.0344000	+	0.0419165i
$388$	27.9201	−	4.23811i	1.41743	−	0.215157i
$389$	3.76297	+	1.14148i	0.190790	+	0.0578755i	0.384234	−	0.923236i	$-0.374466\pi$
$389$	3.76297	+	1.14148i	0.190790	+	0.0578755i	−0.193444	+	0.981111i	$0.561966\pi$
$390$	−12.2434	+	4.74659i	−0.619968	+	0.240353i
$391$	11.3152	−	2.25074i	0.572236	−	0.113825i
$392$	0.260446	+	0.163080i	0.0131545	+	0.00823680i
$393$	2.09231	−	10.5187i	0.105543	−	0.530600i
$394$	6.04685	−	8.61679i	0.304636	−	0.434107i
$395$	−20.5149	+	2.02054i	−1.03222	+	0.101664i
$396$	0.460278	−	0.511303i	0.0231298	−	0.0256939i
$397$	−5.94614	−	19.6018i	−0.298428	−	0.983786i	−0.970053	−	0.242894i	$-0.921903\pi$
$397$	−5.94614	−	19.6018i	−0.298428	−	0.983786i	0.671625	−	0.740892i	$-0.265597\pi$
$398$	2.23916	−	18.4108i	0.112239	−	0.922850i
$399$	−3.52111	−	8.50071i	−0.176276	−	0.425568i
$400$	−1.87848	+	6.34673i	−0.0939239	+	0.317337i
$401$	2.89621	−	6.99208i	0.144630	−	0.349168i	−0.834919	−	0.550373i	$-0.814486\pi$
$401$	2.89621	−	6.99208i	0.144630	−	0.349168i	0.979549	+	0.201205i	$0.0644857\pi$
$402$	−0.381021	−	0.214995i	−0.0190036	−	0.0107230i
$403$	27.7391	+	14.8268i	1.38178	+	0.738577i
$404$	−27.9747	−	4.05301i	−1.39179	−	0.201645i
$405$	−1.99412	−	1.63653i	−0.0990884	−	0.0813197i
$406$	−5.27878	+	23.6948i	−0.261981	+	1.17595i
$407$	−1.32752	−	1.98677i	−0.0658027	−	0.0984807i
$408$	−12.9574	−	10.0067i	−0.641489	−	0.495407i
$409$	26.5807	+	17.7607i	1.31433	+	0.878209i	0.997527	−	0.0702813i	$-0.0223897\pi$
$409$	26.5807	+	17.7607i	1.31433	+	0.878209i	0.316806	+	0.948490i	$0.397390\pi$
$410$	−16.1795	−	0.369811i	−0.799048	−	0.0182637i
$411$	6.53423	−	3.49262i	0.322310	−	0.172278i
$412$	−13.2656	−	36.6833i	−0.653550	−	1.80726i
$413$	1.20466	−	12.2311i	0.0592773	−	0.601852i
$414$	−2.81076	+	0.212114i	−0.138142	+	0.0104248i
$415$	19.1415	−	19.1415i	0.939618	−	0.939618i
$416$	19.5770	−	5.59629i	0.959840	−	0.274381i
$417$	13.6019	+	13.6019i	0.666089	+	0.666089i
$418$	1.29295	+	1.11150i	0.0632403	+	0.0543653i
$419$	−2.07764	−	0.204630i	−0.101499	−	0.00999681i	0.0471399	−	0.998888i	$-0.484989\pi$
$419$	−2.07764	−	0.204630i	−0.101499	−	0.00999681i	−0.148639	+	0.988891i	$0.547489\pi$
$420$	0.618821	−	13.5299i	0.0301954	−	0.660190i
$421$	−1.96636	−	3.67881i	−0.0958347	−	0.179294i	0.829436	−	0.558602i	$-0.188662\pi$
$421$	−1.96636	−	3.67881i	−0.0958347	−	0.179294i	−0.925270	+	0.379308i	$0.876162\pi$
$422$	6.94173	−	6.63149i	0.337918	−	0.322816i
$423$	4.31980	−	6.46503i	0.210036	−	0.314341i
$424$	19.5299	−	17.0201i	0.948455	−	0.826571i
$425$	−7.96376	+	5.32121i	−0.386299	+	0.258117i
$426$	−9.60624	+	6.10586i	−0.465424	+	0.295830i
$427$	18.2068	−	22.1850i	0.881086	−	1.07361i
$428$	1.67366	+	6.58703i	0.0808994	+	0.318396i
$429$	−0.583641	+	1.09191i	−0.0281784	+	0.0527182i
$430$	−3.74893	+	1.04430i	−0.180789	+	0.0503604i
$431$	−0.247516	−	0.102525i	−0.0119224	−	0.00493843i	0.376714	−	0.926330i	$-0.377054\pi$
$431$	−0.247516	−	0.102525i	−0.0119224	−	0.00493843i	−0.388637	+	0.921391i	$0.627054\pi$
$432$	2.84749	+	2.80923i	0.137000	+	0.135159i
$433$	25.2602	−	10.4631i	1.21393	−	0.502825i	0.318453	−	0.947939i	$-0.396837\pi$
$433$	25.2602	−	10.4631i	1.21393	−	0.502825i	0.895474	+	0.445114i	$0.146837\pi$
$434$	−25.5414	+	20.0023i	−1.22603	+	0.960141i
$435$	−16.1419	+	4.89659i	−0.773944	+	0.234773i
$436$	1.23821	+	2.59523i	0.0592995	+	0.124289i
$437$	−0.684750	−	6.95238i	−0.0327560	−	0.332578i
$438$	−2.94863	−	16.8244i	−0.140891	−	0.803901i
$439$	14.5369	+	2.89157i	0.693809	+	0.138007i	0.529384	−	0.848382i	$-0.322423\pi$
$439$	14.5369	+	2.89157i	0.693809	+	0.138007i	0.164425	+	0.986390i	$0.447423\pi$
$440$	1.02871	+	2.28931i	0.0490417	+	0.109138i
$441$	−0.0211953	−	0.106556i	−0.00100930	−	0.00507409i
$442$	26.9563	+	11.8944i	1.28218	+	0.565759i
$443$	9.66448	−	31.8595i	0.459173	−	1.51369i	−0.356006	−	0.934484i	$-0.615862\pi$
$443$	9.66448	−	31.8595i	0.459173	−	1.51369i	0.815180	−	0.579208i	$-0.196638\pi$
$444$	11.8923	−	7.18276i	0.564384	−	0.340879i
$445$	12.4647	−	10.2295i	0.590882	−	0.484924i
$446$	−1.06733	−	2.11152i	−0.0505395	−	0.0999833i
$447$		−	11.2892i		−	0.533963i
$448$	−2.87059	+	20.8040i	−0.135623	+	0.982897i
$449$		−	6.89233i		−	0.325269i	−0.986686	−	0.162635i	$-0.948001\pi$
$449$		−	6.89233i		−	0.325269i	0.986686	−	0.162635i	$-0.0519992\pi$
$450$	2.08848	−	1.05568i	0.0984518	−	0.0497653i
$451$	−1.17955	+	0.968030i	−0.0555427	+	0.0455827i
$452$	1.85713	−	7.52193i	0.0873522	−	0.353802i
$453$	−5.05619	+	16.6680i	−0.237560	+	0.783131i
$454$	7.34494	−	16.6458i	0.344715	−	0.781228i
$455$	4.75533	+	23.9066i	0.222933	+	1.12076i
$456$	−6.79934	+	7.21450i	−0.318408	+	0.337850i
$457$	0.242410	+	0.0482184i	0.0113395	+	0.00225556i	0.200757	−	0.979641i	$-0.435660\pi$
$457$	0.242410	+	0.0482184i	0.0113395	+	0.00225556i	−0.189417	+	0.981897i	$0.560660\pi$
$458$	−33.6884	+	5.90418i	−1.57415	+	0.275884i
$459$	0.567347	+	5.76037i	0.0264815	+	0.268871i
$460$	3.43162	−	9.69395i	0.160000	−	0.451983i
$461$	4.66482	−	1.41506i	0.217262	−	0.0659057i	−0.179777	−	0.983707i	$-0.557538\pi$
$461$	4.66482	−	1.41506i	0.217262	−	0.0659057i	0.397039	+	0.917802i	$0.370038\pi$
$462$	−0.787367	−	1.00541i	−0.0366316	−	0.0467758i
$463$	0.407658	−	0.168857i	0.0189455	−	0.00784747i	−0.373191	−	0.927755i	$-0.621736\pi$
$463$	0.407658	−	0.168857i	0.0189455	−	0.00784747i	0.392136	+	0.919907i	$0.371736\pi$
$464$	25.6179	−	5.27609i	1.18928	−	0.244936i
$465$	−20.8264	−	8.62659i	−0.965803	−	0.400049i
$466$	10.2787	+	36.8997i	0.476153	+	1.70935i
$467$	15.0596	−	28.1745i	0.696876	−	1.30376i	−0.245562	−	0.969381i	$-0.578973\pi$
$467$	15.0596	−	28.1745i	0.696876	−	1.30376i	0.942438	−	0.334382i	$-0.108527\pi$
$468$	−6.18706	−	3.68000i	−0.285997	−	0.170108i
$469$	−0.515189	+	0.627760i	−0.0237892	+	0.0289873i
$470$	15.2165	+	23.9398i	0.701883	+	1.10426i
$471$	3.67108	−	2.45294i	0.169154	−	0.113025i
$472$	−12.5524	+	4.21751i	−0.577772	+	0.194126i
$473$	−0.203857	+	0.305094i	−0.00937336	+	0.0140282i
$474$	−7.80631	−	8.17151i	−0.358556	−	0.375330i
$475$	2.73400	+	5.11496i	0.125445	+	0.234691i
$476$	−22.4483	+	20.4846i	−1.02892	+	0.938912i
$477$	−9.11492	−	0.897741i	−0.417344	−	0.0411048i
$478$	3.22956	−	3.75678i	0.147716	−	0.171831i
$479$	−25.3109	−	25.3109i	−1.15648	−	1.15648i	−0.985226	−	0.171257i	$-0.945217\pi$
$479$	−25.3109	−	25.3109i	−1.15648	−	1.15648i	−0.171257	−	0.985226i	$-0.554783\pi$
$480$	−13.5701	+	5.36681i	−0.619389	+	0.244960i
$481$	−17.6800	+	17.6800i	−0.806139	+	0.806139i
$482$	0.369488	+	4.89616i	0.0168297	+	0.223014i
$483$	−0.512858	+	5.20713i	−0.0233358	+	0.236933i
$484$	−19.7052	−	9.23845i	−0.895691	−	0.419929i
$485$	32.1239	−	17.1706i	1.45867	−	0.779677i
$486$	0.0323159	−	1.41384i	0.00146588	−	0.0641333i
$487$	27.7843	+	18.5649i	1.25903	+	0.841255i	0.992461	−	0.122562i	$-0.0391110\pi$
$487$	27.7843	+	18.5649i	1.25903	+	0.841255i	0.266566	+	0.963817i	$0.414111\pi$
$488$	−29.8433	−	8.09599i	−1.35094	−	0.366488i
$489$	−1.39337	−	2.08532i	−0.0630103	−	0.0943015i
$490$	0.386870	+	0.0861876i	0.0174770	+	0.00389356i
$491$	1.43686	+	1.17920i	0.0648445	+	0.0532165i	0.666257	−	0.745722i	$-0.267895\pi$
$491$	1.43686	+	1.17920i	0.0648445	+	0.0532165i	−0.601413	+	0.798938i	$0.705395\pi$
$492$	−5.30920	−	7.10826i	−0.239357	−	0.320465i
$493$	33.3796	+	17.8418i	1.50334	+	0.803552i
$494$	8.76775	−	15.5384i	0.394480	−	0.699108i
$495$	0.339575	−	0.819808i	0.0152628	−	0.0368476i
$496$	30.9373	+	16.2682i	1.38912	+	0.730466i
$497$	8.08565	+	19.5205i	0.362691	+	0.875613i
$498$	14.7317	+	1.79169i	0.660142	+	0.0802878i
$499$	−2.35748	−	7.77157i	−0.105535	−	0.347903i	0.888230	−	0.459400i	$-0.151936\pi$
$499$	−2.35748	−	7.77157i	−0.105535	−	0.347903i	−0.993765	+	0.111497i	$0.964436\pi$
$500$	−0.905175	−	17.2357i	−0.0404807	−	0.770804i
$501$	11.1127	−	1.09451i	0.496479	−	0.0488990i
$502$	4.99568	+	3.50573i	0.222968	+	0.156469i
$503$	−1.29704	+	6.52067i	−0.0578322	+	0.290742i	−0.998868	−	0.0475644i	$-0.984854\pi$
$503$	−1.29704	+	6.52067i	−0.0578322	+	0.290742i	0.941036	+	0.338307i	$0.109854\pi$
$504$	6.04881	−	4.30612i	0.269436	−	0.191810i
$505$	−35.7590	+	7.11290i	−1.59125	+	0.316520i
$506$	−0.350481	−	0.904032i	−0.0155808	−	0.0401891i
$507$	−0.0425725	−	0.0129142i	−0.00189071	−	0.000573541i
$508$	−20.8532	−	15.3567i	−0.925211	−	0.681346i
$509$	−5.97921	−	7.28569i	−0.265024	−	0.322932i	0.623447	−	0.781866i	$-0.285732\pi$
$509$	−5.97921	−	7.28569i	−0.265024	−	0.322932i	−0.888471	+	0.458933i	$0.848232\pi$
$510$	−20.0621	−	6.59002i	−0.888365	−	0.291811i
$511$	−31.7064			−1.40261
$512$	21.7134	−	6.36619i	0.959606	−	0.281348i
$513$	3.50500			0.154749
$514$	−39.5658	−	12.9966i	−1.74517	−	0.573255i
$515$	−31.9191	−	38.8935i	−1.40652	−	1.71385i
$516$	−1.71790	−	1.26510i	−0.0756264	−	0.0556929i
$517$	2.55942	+	0.776391i	0.112563	+	0.0341456i
$518$	−9.32207	−	24.0454i	−0.409588	−	1.05649i
$519$	19.2785	−	3.83473i	0.846233	−	0.168326i
$520$	21.3949	−	15.2309i	0.938228	−	0.667920i
$521$	−2.67369	+	13.4416i	−0.117137	+	0.588886i	0.876976	+	0.480534i	$0.159557\pi$
$521$	−2.67369	+	13.4416i	−0.117137	+	0.588886i	−0.994113	+	0.108352i	$0.965443\pi$
$522$	−7.56952	−	5.31193i	−0.331309	−	0.232497i
$523$	−5.58449	+	0.550024i	−0.244193	+	0.0240509i	−0.219373	−	0.975641i	$-0.570401\pi$
$523$	−5.58449	+	0.550024i	−0.244193	+	0.0240509i	−0.0248197	+	0.999692i	$0.507901\pi$
$524$	1.12493	+	21.4201i	0.0491427	+	0.935742i
$525$	−1.26096	−	4.15683i	−0.0550328	−	0.181419i
$526$	20.9443	+	2.54729i	0.913217	+	0.111067i
$527$	19.3562	+	46.7301i	0.843171	+	2.03560i
$528$	−0.640380	+	1.21781i	−0.0278690	+	0.0529983i
$529$	7.28143	−	17.5789i	0.316584	−	0.764302i
$530$	16.4205	−	29.1009i	0.713263	−	1.26406i
$531$	4.12894	+	2.20696i	0.179181	+	0.0957741i
$532$	11.0121	+	14.7436i	0.477435	+	0.639218i
$533$	12.3427	+	10.1294i	0.534623	+	0.438754i
$534$	8.62833	+	1.92224i	0.373384	+	0.0831833i
$535$	4.87022	+	7.28880i	0.210558	+	0.315122i
$536$	0.844463	+	0.229089i	0.0364752	+	0.00989514i
$537$	−13.9646	−	9.33085i	−0.602617	−	0.402656i
$538$	−0.265116	+	11.5990i	−0.0114300	+	0.500069i
$539$	0.0329583	−	0.0176166i	0.00141962	−	0.000758800i
$540$	4.67143	+	2.19012i	0.201026	+	0.0942478i
$541$	0.121607	−	1.23470i	0.00522831	−	0.0530840i	−0.992217	−	0.124524i	$-0.960260\pi$
$541$	0.121607	−	1.23470i	0.00522831	−	0.0530840i	0.997445	+	0.0714403i	$0.0227595\pi$
$542$	−1.30943	−	17.3516i	−0.0562450	−	0.745314i
$543$	4.23460	−	4.23460i	0.181724	−	0.181724i
$544$	30.0453	+	13.0154i	1.28818	+	0.558029i
$545$	2.62259	+	2.62259i	0.112339	+	0.112339i
$546$	−8.71104	+	10.1331i	−0.372798	+	0.433657i
$547$	39.9881	+	3.93848i	1.70977	+	0.168397i	0.905062	−	0.425279i	$-0.139824\pi$
$547$	39.9881	+	3.93848i	1.70977	+	0.168397i	0.804704	+	0.593677i	$0.202324\pi$
$548$	−10.9458	+	9.98835i	−0.467583	+	0.426681i
$549$	5.15357	+	9.64165i	0.219949	+	0.411496i
$550$	0.556034	+	0.582047i	0.0237094	+	0.0248186i
$551$	12.7330	−	19.0563i	0.542444	−	0.811825i
$552$	5.34394	−	1.79552i	0.227453	−	0.0764223i
$553$	−17.4421	+	11.6545i	−0.741715	+	0.495598i
$554$	3.56298	+	5.60556i	0.151376	+	0.238157i
$555$	11.3683	−	13.8523i	0.482556	−	0.587996i
$556$	−33.0653	−	19.6669i	−1.40228	−	0.834061i
$557$	3.00176	−	5.61591i	0.127189	−	0.237954i	−0.810265	−	0.586064i	$-0.800677\pi$
$557$	3.00176	−	5.61591i	0.127189	−	0.237954i	0.937453	+	0.348111i	$0.113177\pi$
$558$	−3.31618	−	11.9048i	−0.140385	−	0.503970i
$559$	3.54730	+	1.46934i	0.150035	+	0.0621464i
$560$	5.46418	+	26.5312i	0.230904	+	1.12115i
$561$	−1.83947	+	0.761935i	−0.0776627	+	0.0321689i
$562$	−9.94636	−	12.7007i	−0.419562	−	0.535749i
$563$	17.8459	−	5.41350i	0.752116	−	0.228152i	0.109128	−	0.994028i	$-0.465194\pi$
$563$	17.8459	−	5.41350i	0.752116	−	0.228152i	0.642989	+	0.765876i	$0.277694\pi$
$564$	−5.18938	+	14.6595i	−0.218512	+	0.617274i
$565$	−0.979524	−	9.94528i	−0.0412089	−	0.418401i
$566$	33.7769	−	5.91970i	1.41975	−	0.248824i
$567$	−2.57470	−	0.512139i	−0.108127	−	0.0215078i
$568$	15.6136	−	16.5669i	0.655130	−	0.695132i
$569$	−0.111898	−	0.562550i	−0.00469101	−	0.0235833i	0.978369	−	0.206868i	$-0.0663270\pi$
$569$	−0.111898	−	0.562550i	−0.00469101	−	0.0235833i	−0.983060	+	0.183285i	$0.941327\pi$
$570$	−5.16203	+	11.6987i	−0.216214	+	0.490005i
$571$	−8.20064	+	27.0339i	−0.343186	+	1.13133i	0.600259	+	0.799805i	$0.295064\pi$
$571$	−8.20064	+	27.0339i	−0.343186	+	1.13133i	−0.943446	+	0.331528i	$0.892436\pi$
$572$	0.593545	−	2.40403i	0.0248174	−	0.100518i
$573$	−12.5932	+	10.3350i	−0.526088	+	0.431749i
$574$	−14.6979	+	7.42949i	−0.613479	+	0.310101i
$575$		−	3.29813i		−	0.137541i
$576$	−6.90320	−	4.04299i	−0.287633	−	0.168458i
$577$			37.4395i			1.55863i	0.626635	+	0.779313i	$0.284432\pi$
$577$			37.4395i			1.55863i	−0.626635	+	0.779313i	$0.715568\pi$
$578$	10.5291	+	20.8299i	0.437953	+	0.866411i
$579$	−9.79878	+	8.04165i	−0.407223	+	0.334200i
$580$	28.8779	−	17.4418i	1.19909	−	0.724229i
$581$	7.99654	−	26.3611i	0.331752	−	1.09364i
$582$	18.2692	+	8.06125i	0.757283	+	0.334150i
$583$	−0.614634	−	3.08997i	−0.0254555	−	0.127974i
$584$	14.0020	+	31.1603i	0.579406	+	1.28942i
$585$	−9.10681	−	1.81146i	−0.376520	−	0.0748945i
$586$	5.23979	+	29.8974i	0.216454	+	1.23505i
$587$	4.12885	+	41.9209i	0.170416	+	1.73026i	0.577085	+	0.816684i	$0.304190\pi$
$587$	4.12885	+	41.9209i	0.170416	+	1.73026i	−0.406669	+	0.913575i	$0.633310\pi$
$588$	0.0935659	+	0.196110i	0.00385859	+	0.00808743i
$589$	29.3094	−	8.89091i	1.20767	−	0.366344i
$590$	−13.4472	+	10.5309i	−0.553612	+	0.433552i
$591$	6.87696	−	2.84853i	0.282880	−	0.117173i
$592$	−19.5145	+	19.7803i	−0.802042	+	0.812965i
$593$	20.9283	+	8.66880i	0.859424	+	0.355985i	0.768482	−	0.639871i	$-0.221012\pi$
$593$	20.9283	+	8.66880i	0.859424	+	0.355985i	0.0909415	+	0.995856i	$0.471012\pi$
$594$	0.468618	−	0.130538i	0.0192276	−	0.00535602i
$595$	−18.4778	+	34.5696i	−0.757517	+	1.41721i
$596$	5.56016	+	21.8832i	0.227753	+	0.896369i
$597$	8.31965	−	10.1375i	0.340500	−	0.414901i
$598$	−8.56250	+	5.44245i	−0.350147	+	0.222558i
$599$	0.196905	−	0.131568i	0.00804532	−	0.00537571i	−0.551541	−	0.834148i	$-0.685960\pi$
$599$	0.196905	−	0.131568i	0.00804532	−	0.00537571i	0.559586	+	0.828772i	$0.310960\pi$
$600$	−3.52838	+	3.07496i	−0.144046	+	0.125535i
$601$	6.19674	−	9.27408i	0.252770	−	0.378298i	−0.683284	−	0.730153i	$-0.739449\pi$
$601$	6.19674	−	9.27408i	0.252770	−	0.378298i	0.936055	+	0.351855i	$0.114449\pi$
$602$	−2.86358	+	2.73560i	−0.116711	+	0.111495i
$603$	−0.145829	−	0.272826i	−0.00593860	−	0.0111103i
$604$	1.59165	−	34.7997i	0.0647632	−	1.41598i
$605$	−27.9360	−	2.75146i	−1.13576	−	0.111863i
$606$	−15.1569	−	13.0298i	−0.615705	−	0.529298i
$607$	−29.4853	−	29.4853i	−1.19677	−	1.19677i	−0.975128	−	0.221644i	$-0.928858\pi$
$607$	−29.4853	−	29.4853i	−1.19677	−	1.19677i	−0.221644	−	0.975128i	$-0.571142\pi$
$608$	9.62661	−	17.3334i	0.390411	−	0.702964i
$609$	−12.1378	+	12.1378i	−0.491850	+	0.491850i
$610$	−39.7712	+	3.00132i	−1.61029	+	0.121520i
$611$	2.74318	−	27.8519i	0.110977	−	1.12677i
$612$	−3.93684	−	10.8865i	−0.159137	−	0.440062i
$613$	−10.3878	+	5.55241i	−0.419561	+	0.224260i	−0.667647	−	0.744478i	$-0.732698\pi$
$613$	−10.3878	+	5.55241i	−0.419561	+	0.224260i	0.248086	+	0.968738i	$0.420198\pi$
$614$	22.1964	+	0.507337i	0.895773	+	0.0204745i
$615$	−9.51502	−	6.35774i	−0.383683	−	0.256369i
$616$	2.02142	+	1.56110i	0.0814453	+	0.0628984i
$617$	−18.4114	−	27.5546i	−0.741216	−	1.10931i	−0.990044	−	0.140760i	$-0.955045\pi$
$617$	−18.4114	−	27.5546i	−0.741216	−	1.10931i	0.248828	−	0.968548i	$-0.419955\pi$
$618$	5.99796	−	26.9230i	0.241273	−	1.08300i
$619$	−18.8257	−	15.4499i	−0.756670	−	0.620983i	0.174883	−	0.984589i	$-0.444045\pi$
$619$	−18.8257	−	15.4499i	−0.756670	−	0.620983i	−0.931553	+	0.363606i	$0.881545\pi$
$620$	44.6189	+	6.46445i	1.79194	+	0.259619i
$621$	−1.75781	−	0.939570i	−0.0705386	−	0.0377036i
$622$	33.9015	+	19.1293i	1.35933	+	0.767016i
$623$	6.27946	−	15.1600i	0.251581	−	0.607371i
$624$	13.8055	+	4.08609i	0.552663	+	0.163575i
$625$	−11.6854	−	28.2111i	−0.467417	−	1.12845i
$626$	−0.244251	+	2.00828i	−0.00976225	+	0.0802672i
$627$	0.349980	+	1.15373i	0.0139769	+	0.0460755i
$628$	−5.90794	+	6.56287i	−0.235752	+	0.261887i
$629$	−40.0148	+	3.94111i	−1.59549	+	0.157143i
$630$	5.50130	−	7.83937i	0.219177	−	0.312328i
$631$	0.140770	−	0.707700i	0.00560398	−	0.0281731i	−0.977882	−	0.209157i	$-0.932928\pi$
$631$	0.140770	−	0.707700i	0.00560398	−	0.0281731i	0.983486	+	0.180984i	$0.0579281\pi$
$632$	19.1564	+	11.9950i	0.762002	+	0.477134i
$633$	6.65794	−	1.32435i	0.264630	−	0.0526381i
$634$	−45.6472	+	17.6968i	−1.81288	+	0.702830i
$635$	−31.9653	−	9.69658i	−1.26851	−	0.384797i
$636$	18.1106	−	2.74908i	0.718132	−	0.109008i
$637$	−0.248079	−	0.302285i	−0.00982923	−	0.0119770i
$638$	0.992684	−	3.02204i	0.0393007	−	0.119644i
$639$	−8.04864			−0.318399
$640$	23.6612	−	17.0866i	0.935291	−	0.675408i
$641$	6.07689			0.240023			0.120011	−	0.992773i	$-0.461707\pi$
$641$	6.07689			0.240023			0.120011	+	0.992773i	$0.461707\pi$
$642$	−1.49975	+	4.56572i	−0.0591905	+	0.180195i
$643$	−4.16057	−	5.06967i	−0.164077	−	0.199928i	0.684481	−	0.729031i	$-0.260029\pi$
$643$	−4.16057	−	5.06967i	−0.164077	−	0.199928i	−0.848558	+	0.529102i	$0.822529\pi$
$644$	−1.57048	−	10.3461i	−0.0618857	−	0.407695i
$645$	−2.63333	−	0.798811i	−0.103687	−	0.0314532i
$646$	26.7512	−	10.3711i	1.05251	−	0.408045i
$647$	−10.8820	+	2.16457i	−0.427817	+	0.0850980i	−0.404302	−	0.914625i	$-0.632486\pi$
$647$	−10.8820	+	2.16457i	−0.427817	+	0.0850980i	−0.0235145	+	0.999723i	$0.507486\pi$
$648$	0.633703	+	2.75652i	0.0248942	+	0.108286i
$649$	−0.314178	+	1.57948i	−0.0123326	+	0.0620001i
$650$	4.83839	−	6.89472i	0.189777	−	0.270433i
$651$	−22.8292	+	2.24848i	−0.894747	+	0.0881249i
$652$	3.72798	+	3.35595i	0.145999	+	0.131429i
$653$	−0.769872	−	2.53793i	−0.0301274	−	0.0993168i	0.940587	−	0.339552i	$-0.110275\pi$
$653$	−0.769872	−	2.53793i	−0.0301274	−	0.0993168i	−0.970715	+	0.240235i	$0.922775\pi$
$654$	−0.245482	+	2.01840i	−0.00959909	+	0.0789256i
$655$	10.5875	+	25.5605i	0.413689	+	0.998733i
$656$	13.7923	+	11.1638i	0.538500	+	0.435874i
$657$	4.62204	−	11.1586i	0.180323	−	0.435338i
$658$	25.1403	+	14.1857i	0.980069	+	0.553015i
$659$	−3.57036	−	1.90840i	−0.139081	−	0.0743406i	0.400388	−	0.916346i	$-0.368875\pi$
$659$	−3.57036	−	1.90840i	−0.139081	−	0.0743406i	−0.539470	+	0.842005i	$0.681375\pi$
$660$	−0.254465	+	1.75637i	−0.00990505	+	0.0683666i
$661$	−10.8360	−	8.89286i	−0.421471	−	0.345892i	0.399629	−	0.916677i	$-0.369139\pi$
$661$	−10.8360	−	8.89286i	−0.421471	−	0.345892i	−0.821100	+	0.570785i	$0.806639\pi$
$662$	−10.1049	+	45.3578i	−0.392738	+	1.76288i
$663$	11.5748	+	17.3229i	0.449527	+	0.672765i
$664$	−29.4384	+	3.78259i	−1.14243	+	0.146793i
$665$	19.7356	+	13.1869i	0.765315	+	0.511367i
$666$	9.82137	+	0.224485i	0.380570	+	0.00869860i
$667$	−11.4941	+	6.14375i	−0.445055	+	0.237887i
$668$	−21.0019	+	7.59482i	−0.812588	+	0.293852i
$669$	0.163980	−	1.66492i	0.00633985	−	0.0643696i
$670$	1.12539	−	0.0849272i	0.0434776	−	0.00328102i
$671$	−2.65912	+	2.65912i	−0.102654	+	0.102654i
$672$	−9.60422	+	11.3262i	−0.370491	+	0.436917i
$673$	17.6319	+	17.6319i	0.679659	+	0.679659i	0.959923	−	0.280264i	$-0.0904220\pi$
$673$	17.6319	+	17.6319i	0.679659	+	0.679659i	−0.280264	+	0.959923i	$0.590422\pi$
$674$	−34.2718	−	29.4621i	−1.32010	−	1.13484i
$675$	1.64675	+	0.162191i	0.0633836	+	0.00624274i
$676$	0.0888833	+	0.00406529i	0.00341859	+	0.000156357i
$677$	−2.15182	−	4.02577i	−0.0827012	−	0.154723i	0.837171	−	0.546941i	$-0.184208\pi$
$677$	−2.15182	−	4.02577i	−0.0827012	−	0.154723i	−0.919872	+	0.392218i	$0.871708\pi$
$678$	3.96141	−	3.78437i	0.152137	−	0.145338i
$679$	20.5933	−	30.8200i	0.790297	−	1.18276i
$680$	42.1343	+	2.89319i	1.61577	+	0.110949i
$681$	10.6971	−	7.14758i	0.409914	−	0.273896i
$682$	3.58754	−	2.28029i	0.137374	−	0.0873170i
$683$	−1.53192	+	1.86665i	−0.0586173	+	0.0714254i	−0.801494	−	0.598003i	$-0.795961\pi$
$683$	−1.53192	+	1.86665i	−0.0586173	+	0.0714254i	0.742876	+	0.669429i	$0.233461\pi$
$684$	−6.79411	+	1.72628i	−0.259779	+	0.0660058i
$685$	−9.00982	+	16.8562i	−0.344248	+	0.644042i
$686$	25.4230	−	7.08179i	0.970654	−	0.270384i
$687$	−22.3434	−	9.25495i	−0.852455	−	0.353098i
$688$	3.95308	+	1.60618i	0.150710	+	0.0612351i
$689$	−30.4573	+	12.6158i	−1.16033	+	0.480625i
$690$	5.72487	−	4.48333i	0.217942	−	0.170677i
$691$	42.5086	−	12.8948i	1.61710	−	0.490543i	0.653287	−	0.757111i	$-0.273390\pi$
$691$	42.5086	−	12.8948i	1.61710	−	0.490543i	0.963816	+	0.266568i	$0.0858896\pi$
$692$	−35.4809	+	16.9283i	−1.34878	+	0.643517i
$693$	−0.0885087	−	0.898644i	−0.00336217	−	0.0341367i
$694$	−7.13667	−	40.7207i	−0.270904	−	1.54574i
$695$	−48.6692	−	9.68091i	−1.84613	−	0.367218i
$696$	17.2890	+	6.56856i	0.655340	+	0.248981i
$697$	5.00935	+	25.1837i	0.189742	+	0.953900i
$698$	6.19067	+	2.73162i	0.234320	+	0.103393i
$699$	−7.86249	+	25.9192i	−0.297387	+	0.980353i
$700$	4.49157	+	7.43659i	0.169765	+	0.281076i
$701$	5.13187	−	4.21162i	0.193828	−	0.159071i	−0.532474	−	0.846447i	$-0.678737\pi$
$701$	5.13187	−	4.21162i	0.193828	−	0.159071i	0.726302	+	0.687376i	$0.241237\pi$
$702$	−2.29634	−	4.54289i	−0.0866696	−	0.171460i
$703$			24.3477i			0.918291i
$704$	0.641524	−	2.67601i	0.0241784	−	0.100856i
$705$			20.0581i			0.755431i
$706$	46.8207	−	23.6669i	1.76212	−	0.890715i
$707$	−28.6803	+	23.5373i	−1.07863	+	0.885212i
$708$	−9.09054	−	2.24442i	−0.341643	−	0.0843504i
$709$	−9.16345	+	30.2079i	−0.344141	+	1.13448i	0.598627	+	0.801028i	$0.295713\pi$
$709$	−9.16345	+	30.2079i	−0.344141	+	1.13448i	−0.942767	+	0.333452i	$0.891787\pi$
$710$	11.8538	−	26.8642i	0.444863	−	1.00819i
$711$	−1.55897	−	7.83745i	−0.0584658	−	0.293927i
$712$	−17.6720	+	0.523534i	−0.662285	+	0.0196203i
$713$	−17.0825	−	3.39792i	−0.639744	−	0.127253i
$714$	−21.1663	+	3.70958i	−0.792128	+	0.138827i
$715$	−0.313059	−	3.17854i	−0.0117077	−	0.118871i
$716$	31.6647	+	11.2092i	1.18337	+	0.418906i
$717$	3.35226	−	1.01690i	0.125192	−	0.0379767i
$718$	−17.4398	−	22.2693i	−0.650847	−	0.831082i
$719$	28.5626	−	11.8310i	1.06520	−	0.441222i	0.219908	−	0.975521i	$-0.429424\pi$
$719$	28.5626	−	11.8310i	1.06520	−	0.441222i	0.845296	+	0.534299i	$0.179424\pi$
$720$	−10.1338	−	1.94458i	−0.377665	−	0.0724703i
$721$	−47.3036	−	19.5938i	−1.76168	−	0.729711i
$722$	2.54830	+	9.14815i	0.0948378	+	0.340459i
$723$	−1.63667	+	3.06199i	−0.0608683	+	0.113877i
$724$	−6.12276	+	10.2940i	−0.227551	+	0.382573i
$725$	6.86417	−	8.36401i	0.254929	−	0.310632i
$726$	−8.25506	−	12.9875i	−0.306374	−	0.482012i
$727$	39.9487	−	26.6929i	1.48162	−	0.989985i	0.488537	−	0.872543i	$-0.337531\pi$
$727$	39.9487	−	26.6929i	1.48162	−	0.989985i	0.993080	−	0.117442i	$-0.0374694\pi$
$728$	11.8948	−	23.9324i	0.440851	−	0.886996i
$729$	0.555570	−	0.831470i	0.0205767	−	0.0307952i
$730$	30.4372	+	31.8611i	1.12653	+	1.17923i
$731$	2.91064	+	5.44542i	0.107654	+	0.201406i
$732$	−14.7384	−	16.1512i	−0.544747	−	0.596966i
$733$	26.7390	+	2.63356i	0.987627	+	0.0972728i	0.578913	−	0.815390i	$-0.303477\pi$
$733$	26.7390	+	2.63356i	0.987627	+	0.0972728i	0.408714	+	0.912662i	$0.365977\pi$
$734$	13.3749	−	15.5584i	0.493677	−	0.574269i
$735$	0.198177	+	0.198177i	0.00730987	+	0.00730987i
$736$	−9.47441	+	6.11243i	−0.349231	+	0.225307i
$737$	0.0752441	−	0.0752441i	0.00277165	−	0.00277165i
$738$	−0.472090	−	6.25576i	−0.0173779	−	0.230278i
$739$	−2.19455	+	22.2817i	−0.0807279	+	0.819645i	0.866520	+	0.499143i	$0.166352\pi$
$739$	−2.19455	+	22.2817i	−0.0807279	+	0.819645i	−0.947248	+	0.320502i	$0.896148\pi$
$740$	−15.2138	+	32.4504i	−0.559271	+	1.19290i
$741$	11.1261	−	5.94705i	0.408729	−	0.218470i
$742$	0.776994	−	33.9941i	0.0285244	−	1.24796i
$743$	−7.81164	−	5.21957i	−0.286581	−	0.191488i	0.403967	−	0.914773i	$-0.367631\pi$
$743$	−7.81164	−	5.21957i	−0.286581	−	0.191488i	−0.690549	+	0.723286i	$0.742631\pi$
$744$	12.2914	+	21.4431i	0.450626	+	0.786141i
$745$	16.1796	+	24.2145i	0.592776	+	0.887152i
$746$	39.6604	+	8.83562i	1.45207	+	0.323495i
$747$	8.11168	+	6.65709i	0.296791	+	0.243570i
$748$	3.19039	−	2.38292i	0.116652	−	0.0871281i
$749$	7.86732	+	4.20517i	0.287466	+	0.153654i
$750$	5.99750	−	10.6289i	0.218998	−	0.388114i
$751$	14.3533	−	34.6520i	0.523761	−	1.26447i	−0.411790	−	0.911279i	$-0.635096\pi$
$751$	14.3533	−	34.6520i	0.523761	−	1.26447i	0.935551	−	0.353192i	$-0.114904\pi$
$752$	2.83908	−	30.9719i	0.103531	−	1.12943i
$753$	1.65147	+	3.98700i	0.0601829	+	0.145294i
$754$	−33.0414	−	4.01856i	−1.20330	−	0.146347i
$755$	−13.0433	−	42.9980i	−0.474695	−	1.56486i
$756$	5.24305	−	0.275352i	0.190688	−	0.0100144i
$757$	−17.4238	+	1.71610i	−0.633280	+	0.0623727i	−0.409564	−	0.912282i	$-0.634319\pi$
$757$	−17.4238	+	1.71610i	−0.633280	+	0.0623727i	−0.223717	+	0.974654i	$0.571819\pi$
$758$	13.3864	+	9.39394i	0.486216	+	0.341203i
$759$	0.133755	−	0.672432i	0.00485500	−	0.0244077i
$760$	4.24429	−	25.2193i	0.153957	−	0.914799i
$761$	3.10452	−	0.617528i	0.112539	−	0.0223854i	−0.138500	−	0.990363i	$-0.544228\pi$
$761$	3.10452	−	0.617528i	0.112539	−	0.0223854i	0.251038	+	0.967977i	$0.419228\pi$
$762$	−6.61941	−	17.0741i	−0.239796	−	0.618531i
$763$	3.61175	+	1.09561i	0.130754	+	0.0396638i
$764$	19.3206	−	26.2357i	0.698994	−	0.949176i
$765$	−9.47262	−	11.5424i	−0.342483	−	0.417317i
$766$	12.5324	+	4.11666i	0.452814	+	0.148741i
$767$	16.8514			0.608469
$768$	15.3725	+	4.43702i	0.554706	+	0.160107i
$769$	−13.2897			−0.479239			−0.239619	−	0.970867i	$-0.577023\pi$
$769$	−13.2897			−0.479239			−0.239619	+	0.970867i	$0.577023\pi$
$770$	3.12978	+	1.02807i	0.112789	+	0.0370492i
$771$	−18.6816	−	22.7636i	−0.672800	−	0.819810i
$772$	15.0334	−	20.4141i	0.541063	−	0.734719i
$773$	−41.6982	−	12.6490i	−1.49978	−	0.454954i	−0.569559	−	0.821950i	$-0.692886\pi$
$773$	−41.6982	−	12.6490i	−1.49978	−	0.454954i	−0.930222	+	0.366996i	$0.880386\pi$
$774$	−0.545312	−	1.40658i	−0.0196008	−	0.0505585i
$775$	14.1819	−	2.82095i	0.509428	−	0.101332i
$776$	−39.3835	−	6.62807i	−1.41379	−	0.237934i
$777$	3.55761	−	17.8853i	0.127629	−	0.641632i
$778$	−4.55208	−	3.19443i	−0.163200	−	0.114526i
$779$	15.4735	−	1.52401i	0.554397	−	0.0546034i
$780$	18.5449	−	0.973930i	0.664013	−	0.0348723i
$781$	−0.803671	−	2.64935i	−0.0287576	−	0.0948012i
$782$	−16.1963	−	1.96983i	−0.579179	−	0.0704408i
$783$	−2.50233	−	6.04115i	−0.0894258	−	0.215893i
$784$	−0.277956	−	0.334058i	−0.00992702	−	0.0119306i
$785$	−4.35865	+	10.5227i	−0.155567	+	0.375572i
$786$	−7.45355	+	13.2094i	−0.265859	+	0.471163i
$787$	−15.5204	−	8.29583i	−0.553243	−	0.295714i	0.170987	−	0.985273i	$-0.445304\pi$
$787$	−15.5204	−	8.29583i	−0.553243	−	0.295714i	−0.724230	+	0.689559i	$0.757804\pi$
$788$	−11.9274	+	8.90864i	−0.424896	+	0.317357i
$789$	11.5326	+	9.46452i	0.410570	+	0.336946i
$790$	28.4552	+	6.33932i	1.01239	+	0.225543i
$791$	−5.64989	−	8.45565i	−0.200887	−	0.300648i
$792$	−0.844081	+	0.483838i	−0.0299931	+	0.0171924i
$793$	32.7186	+	21.8619i	1.16187	+	0.776339i
$794$	−0.661953	+	28.9609i	−0.0234918	+	1.02779i
$795$	20.8374	−	11.1378i	0.739027	−	0.395018i
$796$	−11.1340	+	23.7482i	−0.394633	+	0.841734i
$797$	−1.19221	+	12.1047i	−0.0422304	+	0.428772i	0.950703	+	0.310102i	$0.100363\pi$
$797$	−1.19221	+	12.1047i	−0.0422304	+	0.428772i	−0.992934	+	0.118670i	$0.962137\pi$
$798$	0.979188	+	12.9754i	0.0346629	+	0.459325i
$799$	31.8241	−	31.8241i	1.12586	−	1.12586i
$800$	5.32497	−	7.69831i	0.188266	−	0.272177i
$801$	4.41993	+	4.41993i	0.156171	+	0.156171i
$802$	−6.97720	+	8.11623i	−0.246374	+	0.286594i
$803$	4.13456	+	0.407219i	0.145906	+	0.0143704i
$804$	0.417047	+	0.457025i	0.0147081	+	0.0161180i
$805$	−6.36277	−	11.9039i	−0.224258	−	0.419558i
$806$	−30.7261	−	32.1635i	−1.08228	−	1.13291i
$807$	−4.55783	+	6.82128i	−0.160443	+	0.240120i
$808$	35.7976	+	17.7920i	1.25935	+	0.625919i
$809$	−10.7148	+	7.15938i	−0.376711	+	0.251710i	−0.729483	−	0.683999i	$-0.760239\pi$
$809$	−10.7148	+	7.15938i	−0.376711	+	0.251710i	0.352772	+	0.935709i	$0.385239\pi$
$810$	1.95699	+	3.07890i	0.0687617	+	0.108181i
$811$	−4.45735	+	5.43130i	−0.156519	+	0.190719i	−0.845365	−	0.534188i	$-0.820617\pi$
$811$	−4.45735	+	5.43130i	−0.156519	+	0.190719i	0.688847	+	0.724907i	$0.258117\pi$
$812$	17.5500	−	29.5062i	0.615884	−	1.03547i
$813$	5.80021	−	10.8514i	0.203422	−	0.380576i
$814$	0.906788	+	3.25529i	0.0317829	+	0.114098i
$815$	5.97733	+	2.47589i	0.209377	+	0.0867267i
$816$	12.9930	+	19.1636i	0.454846	+	0.670858i
$817$	3.45428	−	1.43081i	0.120850	−	0.0500577i
$818$	−27.8749	−	35.5942i	−0.974624	−	1.24452i
$819$	−9.04200	+	2.74286i	−0.315953	+	0.0958433i
$820$	21.5753	+	7.63756i	0.753442	+	0.266715i
$821$	−1.17474	−	11.9274i	−0.0409988	−	0.416268i	−0.993676	−	0.112284i	$-0.964183\pi$
$821$	−1.17474	−	11.9274i	−0.0409988	−	0.416268i	0.952677	−	0.303983i	$-0.0983167\pi$
$822$	−10.3207	+	1.80880i	−0.359977	+	0.0630891i
$823$	−0.0239695	−	0.00476782i	−0.000835523	−	0.000166196i	0.194673	−	0.980868i	$-0.437636\pi$
$823$	−0.0239695	−	0.00476782i	−0.000835523	−	0.000166196i	−0.195508	+	0.980702i	$0.562636\pi$
$824$	1.63358	+	55.1418i	0.0569085	+	1.92096i
$825$	0.111043	+	0.558252i	0.00386603	+	0.0194359i
$826$	−7.01664	+	15.9018i	−0.244140	+	0.553295i
$827$	9.17757	−	30.2544i	0.319135	−	1.05205i	−0.639828	−	0.768518i	$-0.720994\pi$
$827$	9.17757	−	30.2544i	0.319135	−	1.05205i	0.958963	−	0.283530i	$-0.0915056\pi$
$828$	3.87011	+	0.955515i	0.134496	+	0.0332064i
$829$	−26.9191	+	22.0919i	−0.934939	+	0.767285i	−0.972715	−	0.232002i	$-0.925473\pi$
$829$	−26.9191	+	22.0919i	−0.934939	+	0.767285i	0.0377763	+	0.999286i	$0.487973\pi$
$830$	−34.1661	+	17.2703i	−1.18592	+	0.599459i
$831$			4.69665i			0.162925i
$832$	−28.7732	−	1.12105i	−0.997531	−	0.0388654i
$833$		−	0.628855i		−	0.0217885i
$834$	−12.2722	−	24.2784i	−0.424953	−	0.840693i
$835$	−22.2673	+	18.2743i	−0.770590	+	0.632407i
$836$	−1.24664	−	2.06403i	−0.0431159	−	0.0713859i
$837$	2.53664	−	8.36218i	0.0876791	−	0.289039i
$838$	2.70117	+	1.19189i	0.0933104	+	0.0411730i
$839$	3.13744	+	15.7730i	0.108316	+	0.544543i	0.996394	+	0.0848492i	$0.0270408\pi$
$839$	3.13744	+	15.7730i	0.108316	+	0.544543i	−0.888077	+	0.459694i	$0.847959\pi$
$840$	−6.80273	+	17.9054i	−0.234717	+	0.617795i
$841$	−13.4928	−	2.68388i	−0.465269	−	0.0925477i
$842$	1.01836	+	5.81062i	0.0350951	+	0.200247i
$843$	−1.11808	−	11.3521i	−0.0385088	−	0.390986i
$844$	−12.2535	+	5.84629i	−0.421784	+	0.201237i
$845$	0.109823	−	0.0333145i	0.00377803	−	0.00114605i
$846$	−8.65730	+	6.77981i	−0.297644	+	0.233095i
$847$	−26.3915	+	10.9317i	−0.906822	+	0.375618i
$848$	−33.7517	+	14.2486i	−1.15904	+	0.489300i
$849$	22.4021	+	9.27927i	0.768840	+	0.318464i
$850$	13.0485	−	3.63476i	0.447558	−	0.124671i
$851$	6.52679	−	12.2108i	0.223735	−	0.418579i
$852$	15.6016	−	3.96411i	0.534500	−	0.135808i
$853$	−26.5745	+	32.3811i	−0.909894	+	1.10871i	0.0837884	+	0.996484i	$0.473298\pi$
$853$	−26.5745	+	32.3811i	−0.909894	+	1.10871i	−0.993683	+	0.112226i	$0.964202\pi$
$854$	−34.2535	+	21.7720i	−1.17213	+	0.745022i
$855$	−7.51794	+	5.02333i	−0.257108	+	0.171794i
$856$	0.658430	−	9.58888i	0.0225047	−	0.327741i
$857$	−28.7663	+	43.0518i	−0.982637	+	1.47062i	−0.103168	+	0.994664i	$0.532898\pi$
$857$	−28.7663	+	43.0518i	−0.982637	+	1.47062i	−0.879469	+	0.475956i	$0.842102\pi$
$858$	1.26608	−	1.20949i	0.0432232	−	0.0412915i
$859$	−4.59798	−	8.60221i	−0.156881	−	0.293504i	0.791185	−	0.611576i	$-0.209464\pi$
$859$	−4.59798	−	8.60221i	−0.156881	−	0.293504i	−0.948066	+	0.318073i	$0.896964\pi$
$860$	5.49789	+	0.251459i	0.187477	+	0.00857469i
$861$	−11.5892	−	1.14144i	−0.394960	−	0.0389002i
$862$	0.287310	+	0.246989i	0.00978583	+	0.00841249i
$863$	−5.34576	−	5.34576i	−0.181972	−	0.181972i	0.610243	−	0.792215i	$-0.291072\pi$
$863$	−5.34576	−	5.34576i	−0.181972	−	0.181972i	−0.792215	+	0.610243i	$0.791072\pi$
$864$	−2.58601	−	5.03116i	−0.0879780	−	0.171163i
$865$	−35.8550	+	35.8550i	−1.21911	+	1.21911i
$866$	−38.5570	+	2.90969i	−1.31022	+	0.0988754i
$867$	−1.61765	+	16.4243i	−0.0549383	+	0.557798i
$868$	43.1449	−	15.6023i	1.46443	−	0.529576i
$869$	2.42417	−	1.29574i	0.0822342	−	0.0439551i
$870$	23.8490	+	0.545112i	0.808558	+	0.0184810i
$871$	−0.925826	−	0.618617i	−0.0313704	−	0.0209610i
$872$	−0.518255	−	4.03339i	−0.0175503	−	0.136588i
$873$	7.84464	+	11.7403i	0.265501	+	0.397350i
$874$	−2.14836	+	9.64332i	−0.0726693	+	0.326190i
$875$	−17.5120	−	14.3717i	−0.592013	−	0.485852i
$876$	−3.46359	+	23.9064i	−0.117024	+	0.807721i
$877$	46.4964	+	24.8528i	1.57007	+	0.839221i	0.999843	+	0.0177353i	$0.00564561\pi$
$877$	46.4964	+	24.8528i	1.57007	+	0.839221i	0.570229	+	0.821486i	$0.306854\pi$
$878$	−18.2554	−	10.3008i	−0.616089	−	0.347636i
$879$	−8.21349	+	19.8291i	−0.277034	+	0.668820i
$880$	−0.371787	−	3.52989i	−0.0125329	−	0.118993i
$881$	18.8015	+	45.3909i	0.633439	+	1.52926i	0.835272	+	0.549837i	$0.185310\pi$
$881$	18.8015	+	45.3909i	0.633439	+	1.52926i	−0.201833	+	0.979420i	$0.564690\pi$
$882$	−0.0185499	+	0.152521i	−0.000624608	+	0.00513565i
$883$	−16.4335	−	54.1740i	−0.553032	−	1.82310i	−0.567739	−	0.823209i	$-0.692182\pi$
$883$	−16.4335	−	54.1740i	−0.553032	−	1.82310i	0.0147070	−	0.999892i	$-0.495318\pi$
$884$	−30.9685	−	27.8780i	−1.04158	−	0.937640i
$885$	−12.0193	+	1.18379i	−0.404023	+	0.0397928i
$886$	−27.0460	+	38.5406i	−0.908627	+	1.29480i
$887$	−2.59575	+	13.0497i	−0.0871569	+	0.438167i	0.912425	+	0.409245i	$0.134208\pi$
$887$	−2.59575	+	13.0497i	−0.0871569	+	0.438167i	−0.999582	+	0.0289228i	$0.990792\pi$
$888$	−19.1484	+	4.40206i	−0.642577	+	0.147724i
$889$	−33.3393	+	6.63159i	−1.11816	+	0.222416i
$890$	−21.2620	+	8.24300i	−0.712705	+	0.276306i
$891$	0.329167	+	0.0998518i	0.0110275	+	0.00334516i
$892$	0.502143	+	3.30806i	0.0168130	+	0.110762i
$893$	−17.2890	−	21.0667i	−0.578555	−	0.704972i
$894$	−4.98242	+	15.1680i	−0.166637	+	0.507295i
$895$	43.3259			1.44822
$896$	13.0385	−	26.6850i	0.435587	−	0.891484i
$897$	−7.17414			−0.239538
$898$	−3.04187	+	9.26042i	−0.101509	+	0.309024i
$899$	−36.2491	−	44.1697i	−1.20898	−	1.47314i
$900$	−3.27196	+	0.496664i	−0.109065	+	0.0165555i
$901$	−50.7319	−	15.3893i	−1.69012	−	0.512693i
$902$	2.01205	−	0.780046i	0.0669941	−	0.0259727i
$903$	−2.74651	+	0.546315i	−0.0913982	+	0.0181802i
$904$	−5.81496	+	9.28671i	−0.193403	+	0.308871i
$905$	−3.01389	+	15.1519i	−0.100185	+	0.503665i
$906$	14.1497	−	20.1634i	0.470092	−	0.669883i
$907$	−37.8577	+	3.72866i	−1.25705	+	0.123808i	−0.704518	−	0.709687i	$-0.748837\pi$
$907$	−37.8577	+	3.72866i	−1.25705	+	0.123808i	−0.552528	+	0.833495i	$0.686337\pi$
$908$	−17.2150	+	19.1235i	−0.571301	+	0.634634i
$909$	−4.10270	−	13.5248i	−0.136078	−	0.448589i
$910$	4.16182	−	34.2193i	0.137963	−	1.13436i
$911$	6.99284	+	16.8822i	0.231683	+	0.559332i	0.996376	−	0.0850630i	$-0.0271092\pi$
$911$	6.99284	+	16.8822i	0.231683	+	0.559332i	−0.764693	+	0.644395i	$0.777109\pi$
$912$	12.3195	−	6.69245i	0.407941	−	0.221609i
$913$	−1.38133	+	3.33482i	−0.0457153	+	0.110366i
$914$	−0.304418	−	0.171771i	−0.0100692	−	0.00568169i
$915$	−24.8723	−	13.2945i	−0.822254	−	0.439504i
$916$	47.8689	+	6.93532i	1.58163	+	0.229149i
$917$	21.7634	+	17.8608i	0.718692	+	0.589815i
$918$	1.78001	−	7.98994i	0.0587492	−	0.263707i
$919$	−1.56353	−	2.33998i	−0.0515760	−	0.0771890i	0.804785	−	0.593566i	$-0.202280\pi$
$919$	−1.56353	−	2.33998i	−0.0515760	−	0.0771890i	−0.856361	+	0.516377i	$0.827280\pi$
$920$	−8.88901	+	11.5101i	−0.293062	+	0.379478i
$921$	13.0535	+	8.72207i	0.430127	+	0.287402i
$922$	−6.89209	−	0.157531i	−0.226979	−	0.00518800i
$923$	−25.5493	+	13.6564i	−0.840967	+	0.449506i
$924$	0.614165	+	1.69835i	0.0202045	+	0.0558715i
$925$	−1.12667	+	11.4393i	−0.0370447	+	0.376121i
$926$	−0.622247	+	0.0469577i	−0.0204483	+	0.00154313i
$927$	13.7915	−	13.7915i	0.452972	−	0.452972i
$928$	−36.7484	−	4.21738i	−1.20632	−	0.138442i
$929$	29.2771	+	29.2771i	0.960549	+	0.960549i	0.999251	−	0.0387017i	$-0.0123222\pi$
$929$	29.2771	+	29.2771i	0.960549	+	0.960549i	−0.0387017	+	0.999251i	$0.512322\pi$
$930$	24.1748	+	20.7821i	0.792723	+	0.681473i
$931$	−0.378961	−	0.0373244i	−0.0124200	−	0.00122326i
$932$	2.47505	−	54.1143i	0.0810729	−	1.77257i
$933$	12.9752	+	24.2748i	0.424788	+	0.794722i
$934$	−32.6685	+	31.2084i	−1.06894	+	1.02117i
$935$	2.85353	−	4.27061i	0.0933204	−	0.139664i
$936$	6.68869	+	7.67499i	0.218627	+	0.250865i
$937$	28.7661	−	19.2209i	0.939749	−	0.627920i	0.0115217	−	0.999934i	$-0.496332\pi$
$937$	28.7661	−	19.2209i	0.939749	−	0.627920i	0.928227	+	0.372013i	$0.121332\pi$
$938$	0.969257	−	0.616074i	0.0316473	−	0.0201155i
$939$	−0.907522	+	1.10582i	−0.0296159	+	0.0360870i
$940$	−9.87898	−	38.8807i	−0.322217	−	1.26815i
$941$	−26.7156	+	49.9814i	−0.870904	+	1.62935i	−0.0976759	+	0.995218i	$0.531141\pi$
$941$	−26.7156	+	49.9814i	−0.870904	+	1.62935i	−0.773228	+	0.634128i	$0.781359\pi$
$942$	−6.01499	+	1.67553i	−0.195979	+	0.0545916i
$943$	−8.16877	−	3.38361i	−0.266012	−	0.110186i
$944$	18.7266	−	0.126663i	0.609499	−	0.00412252i
$945$	6.25652	−	2.59153i	0.203525	−	0.0843026i
$946$	0.408550	−	0.319948i	0.0132831	−	0.0104024i
$947$	32.8577	−	9.96729i	1.06773	−	0.323893i	0.292955	−	0.956126i	$-0.405361\pi$
$947$	32.8577	−	9.96729i	1.06773	−	0.323893i	0.774778	+	0.632233i	$0.217861\pi$
$948$	6.88200	+	14.4244i	0.223517	+	0.468481i
$949$	−4.26112	−	43.2639i	−0.138322	−	1.40440i
$950$	−1.41592	−	8.07901i	−0.0459384	−	0.262118i
$951$	−33.9531	−	6.75368i	−1.10100	−	0.219003i
$952$	39.2019	−	17.6155i	1.27054	−	0.570921i
$953$	−4.39827	−	22.1116i	−0.142474	−	0.716265i	−0.984298	−	0.176514i	$-0.943518\pi$
$953$	−4.39827	−	22.1116i	−0.142474	−	0.716265i	0.841824	−	0.539752i	$-0.181482\pi$
$954$	11.8505	+	5.22899i	0.383673	+	0.169295i
$955$	12.1994	−	40.2161i	0.394764	−	1.30136i
$956$	−5.99720	+	3.62221i	−0.193963	+	0.117151i
$957$	1.73869	−	1.42690i	0.0562038	−	0.0461252i
$958$	22.8365	+	45.1780i	0.737815	+	1.45964i
$959$			19.4499i			0.628070i
$960$	20.6012	−	1.22170i	0.664901	−	0.0394301i
$961$		−	45.3606i		−	1.46325i
$962$	31.5575	−	15.9517i	1.01745	−	0.514302i
$963$	−2.62682	+	2.15577i	−0.0846480	+	0.0694688i
$964$	1.66444	−	6.74148i	0.0536081	−	0.217128i
$965$	9.49239	−	31.2922i	0.305571	−	1.00733i
$966$	2.98719	−	6.76987i	0.0961113	−	0.217817i
$967$	1.32769	+	6.67474i	0.0426956	+	0.214645i	0.996243	−	0.0865963i	$-0.0275990\pi$
$967$	1.32769	+	6.67474i	0.0426956	+	0.214645i	−0.953548	+	0.301241i	$0.902599\pi$
$968$	22.3983	+	21.1094i	0.719908	+	0.678480i
$969$	19.8979	+	3.95795i	0.639214	+	0.127148i
$970$	−50.7393	+	8.89251i	−1.62914	+	0.285521i
$971$	3.07578	+	31.2289i	0.0987064	+	1.00218i	0.909179	+	0.416406i	$0.136711\pi$
$971$	3.07578	+	31.2289i	0.0987064	+	1.00218i	−0.810472	+	0.585777i	$0.800789\pi$
$972$	−0.667408	+	1.88536i	−0.0214071	+	0.0604728i
$973$	−48.3229	+	14.6586i	−1.54916	+	0.469932i
$974$	−29.1371	−	37.2058i	−0.933612	−	1.19215i
$975$	5.50260	−	2.27925i	0.176224	−	0.0729944i
$976$	36.5238	+	24.0487i	1.16910	+	0.769781i
$977$	−25.8704	−	10.7159i	−0.827667	−	0.342831i	−0.0716881	−	0.997427i	$-0.522839\pi$
$977$	−25.8704	−	10.7159i	−0.827667	−	0.342831i	−0.755979	+	0.654596i	$0.772839\pi$
$978$	0.951767	+	3.41676i	0.0304341	+	0.109256i
$979$	−1.01356	+	1.89623i	−0.0323935	+	0.0606039i
$980$	−0.481754	−	0.286542i	−0.0153891	−	0.00915325i
$981$	−0.912093	+	1.11139i	−0.0291209	+	0.0354839i
$982$	−1.41011	−	2.21850i	−0.0449984	−	0.0707951i
$983$	44.9117	−	30.0090i	1.43246	−	0.957140i	0.434044	−	0.900892i	$-0.357086\pi$
$983$	44.9117	−	30.0090i	1.43246	−	0.957140i	0.998417	−	0.0562479i	$-0.0179137\pi$
$984$	3.99618	+	11.8937i	0.127394	+	0.379158i
$985$	−10.6681	+	15.9659i	−0.339912	+	0.508715i
$986$	−36.9740	−	38.7037i	−1.17749	−	1.23258i
$987$	9.62196	+	18.0014i	0.306270	+	0.572991i
$988$	−18.6380	+	17.0076i	−0.592953	+	0.541085i
$989$	−2.11593	−	0.208401i	−0.0672827	−	0.00662676i
$990$	−0.818063	+	0.951612i	−0.0259998	+	0.0302442i
$991$	23.4835	+	23.4835i	0.745977	+	0.745977i	0.973721	−	0.227744i	$-0.0731350\pi$
$991$	23.4835	+	23.4835i	0.745977	+	0.745977i	−0.227744	+	0.973721i	$0.573135\pi$
$992$	−34.3869	−	35.5117i	−1.09179	−	1.12750i
$993$	−23.2349	+	23.2349i	−0.737336	+	0.737336i
$994$	−2.24854	−	29.7959i	−0.0713194	−	0.945069i
$995$	−3.31599	+	33.6678i	−0.105124	+	1.06734i
$996$	−19.0025	−	8.90899i	−0.602117	−	0.282292i
$997$	51.3364	−	27.4399i	1.62584	−	0.869030i	0.630132	−	0.776488i	$-0.283001\pi$
$997$	51.3364	−	27.4399i	1.62584	−	0.869030i	0.995709	−	0.0925421i	$-0.0294993\pi$
$998$	−0.262446	+	11.4822i	−0.00830758	+	0.363463i
$999$	5.77586	+	3.85931i	0.182740	+	0.122103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.253.4	yes	512
128.85	even	32	inner	384.2.v.a.85.4	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.85.4	✓	512	128.85	even	32	inner
384.2.v.a.253.4	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34358 - 0.441342i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(1.61043 + 1.18596i) q^{4} +(2.46859 + 0.748840i) q^{5} +(0.511199 + 1.31859i) q^{6} +(2.57470 - 0.512139i) q^{7} +(-1.64034 - 2.30419i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})\)	\(q+(-1.34358 - 0.441342i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(1.61043 + 1.18596i) q^{4} +(2.46859 + 0.748840i) q^{5} +(0.511199 + 1.31859i) q^{6} +(2.57470 - 0.512139i) q^{7} +(-1.64034 - 2.30419i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(-2.98627 - 2.09562i) q^{10} +(-0.342322 + 0.0337158i) q^{11} +(-0.104890 - 1.99725i) q^{12} +(1.04484 + 3.44439i) q^{13} +(-3.68535 - 0.448220i) q^{14} +(-0.987199 - 2.38331i) q^{15} +(1.18700 + 3.81982i) q^{16} +(-2.21506 + 5.34764i) q^{17} +(0.694982 - 1.23167i) q^{18} +(3.09113 + 1.65224i) q^{19} +(3.08742 + 4.13361i) q^{20} +(-2.02926 - 1.66537i) q^{21} +(0.474819 + 0.105781i) q^{22} +(-1.10734 - 1.65725i) q^{23} +(-0.740540 + 2.72976i) q^{24} +(1.37585 + 0.919314i) q^{25} +(0.116317 - 5.08896i) q^{26} +(0.881921 - 0.471397i) q^{27} +(4.75376 + 2.22872i) q^{28} +(0.640924 - 6.50741i) q^{29} +(0.274531 + 3.63787i) q^{30} +(6.17902 - 6.17902i) q^{31} +(0.0910097 - 5.65612i) q^{32} +(0.243230 + 0.243230i) q^{33} +(5.33626 - 6.20740i) q^{34} +(6.73940 + 0.663773i) q^{35} +(-1.47735 + 1.34812i) q^{36} +(3.27459 + 6.12633i) q^{37} +(-3.42399 - 3.58417i) q^{38} +(1.99971 - 2.99277i) q^{39} +(-2.32387 - 6.91646i) q^{40} +(3.68846 - 2.46455i) q^{41} +(1.99148 + 3.13316i) q^{42} +(0.676727 - 0.824594i) q^{43} +(-0.591274 - 0.351683i) q^{44} +(-1.21605 + 2.27507i) q^{45} +(0.756391 + 2.71538i) q^{46} +(-7.18356 - 2.97553i) q^{47} +(2.19974 - 3.34083i) q^{48} +(-0.100373 + 0.0415760i) q^{49} +(-1.44284 - 1.84240i) q^{50} +(5.53900 - 1.68024i) q^{51} +(-2.40225 + 6.78611i) q^{52} +(0.897741 + 9.11492i) q^{53} +(-1.39298 + 0.244132i) q^{54} +(-0.870303 - 0.173114i) q^{55} +(-5.40345 - 5.09250i) q^{56} +(-0.683791 - 3.43765i) q^{57} +(-3.73312 + 8.46038i) q^{58} +(1.35904 - 4.48016i) q^{59} +(1.23669 - 5.00894i) q^{60} +(8.45098 - 6.93554i) q^{61} +(-11.0291 + 5.57497i) q^{62} +2.62514i q^{63} +(-2.61856 + 7.55931i) q^{64} +9.28522i q^{65} +(-0.219452 - 0.434147i) q^{66} +(-0.239134 + 0.196252i) q^{67} +(-9.90930 + 5.98505i) q^{68} +(-0.578584 + 1.90734i) q^{69} +(-8.76199 - 3.86621i) q^{70} +(1.57021 + 7.89399i) q^{71} +(2.57993 - 1.15930i) q^{72} +(-11.8459 - 2.35630i) q^{73} +(-1.69588 - 9.67645i) q^{74} +(-0.162191 - 1.64675i) q^{75} +(3.01857 + 6.32679i) q^{76} +(-0.864110 + 0.262125i) q^{77} +(-4.00761 + 3.13849i) q^{78} +(-7.38272 + 3.05802i) q^{79} +(0.0697918 + 10.3185i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(-6.04346 + 1.68346i) q^{82} +(4.94666 - 9.25455i) q^{83} +(-1.29293 - 5.08859i) q^{84} +(-9.47262 + 11.5424i) q^{85} +(-1.27317 + 0.809244i) q^{86} +(-5.43689 + 3.63281i) q^{87} +(0.639213 + 0.733470i) q^{88} +(3.47272 - 5.19729i) q^{89} +(2.63795 - 2.52005i) q^{90} +(4.45416 + 8.33316i) q^{91} +(0.182134 - 3.98216i) q^{92} +(-8.69638 - 0.856518i) q^{93} +(8.33849 + 7.16828i) q^{94} +(6.39348 + 6.39348i) q^{95} +(-4.42998 + 3.51785i) q^{96} +(9.98433 - 9.98433i) q^{97} +(0.153209 - 0.0115619i) q^{98} +(0.0337158 - 0.342322i) 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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