LMFDB - Embedded newform 384.2.v.a.85.4

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			85.4
Character	$\chi$	$=$	384.85
Dual form			384.2.v.a.253.4

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

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	0.314872	−	0.949134i	$-0.398038\pi$
$5$	2.46859	−	0.748840i	1.10399	−	0.334891i	0.789117	+	0.614243i	$0.210538\pi$
$6$	0.511199	−	1.31859i	0.208696	−	0.538312i
$7$	2.57470	+	0.512139i	0.973144	+	0.193570i	0.655962	−	0.754794i	$-0.272263\pi$
$7$	2.57470	+	0.512139i	0.973144	+	0.193570i	0.317183	+	0.948365i	$0.397263\pi$
$8$	−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	0.0462782	−	0.998929i	$-0.485264\pi$
$11$	−0.342322	−	0.0337158i	−0.103214	−	0.0101657i	−0.149492	+	0.988763i	$0.547764\pi$
$12$	−0.104890	+	1.99725i	−0.0302792	+	0.576556i
$13$	1.04484	−	3.44439i	0.289788	−	0.955302i	−0.684313	−	0.729188i	$-0.739898\pi$
$13$	1.04484	−	3.44439i	0.289788	−	0.955302i	0.974101	−	0.226114i	$-0.0726020\pi$
$14$	−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	−0.926648	−	0.375931i	$-0.877323\pi$
$17$	−2.21506	−	5.34764i	−0.537232	−	1.29699i	0.389416	−	0.921062i	$-0.372677\pi$
$18$	0.694982	+	1.23167i	0.163809	+	0.290306i
$19$	3.09113	−	1.65224i	0.709154	−	0.379051i	−0.0770421	−	0.997028i	$-0.524548\pi$
$19$	3.09113	−	1.65224i	0.709154	−	0.379051i	0.786196	+	0.617977i	$0.212048\pi$
$20$	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	−0.928768	−	0.370662i	$-0.879131\pi$
$23$	−1.10734	+	1.65725i	−0.230897	+	0.345561i	0.697871	+	0.716223i	$0.254131\pi$
$24$	−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	0.850291	+	0.526312i	$0.176426\pi$
$29$	0.640924	+	6.50741i	0.119017	+	1.20840i	−0.731275	+	0.682083i	$0.761074\pi$
$30$	0.274531	−	3.63787i	0.0501222	−	0.664181i
$31$	6.17902	+	6.17902i	1.10979	+	1.10979i	0.993178	+	0.116607i	$0.0372017\pi$
$31$	6.17902	+	6.17902i	1.10979	+	1.10979i	0.116607	+	0.993178i	$0.462798\pi$
$32$	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	−0.454841	−	0.890573i	$-0.650304\pi$
$37$	3.27459	−	6.12633i	0.538339	−	1.00716i	0.993180	−	0.116589i	$-0.0371961\pi$
$38$	−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	0.809194	−	0.587542i	$-0.199904\pi$
$41$	3.68846	+	2.46455i	0.576040	+	0.384898i	−0.233153	+	0.972440i	$0.574904\pi$
$42$	1.99148	−	3.13316i	0.307293	−	0.483457i
$43$	0.676727	+	0.824594i	0.103200	+	0.125749i	0.822049	−	0.569417i	$-0.192831\pi$
$43$	0.676727	+	0.824594i	0.103200	+	0.125749i	−0.718849	+	0.695166i	$0.755331\pi$
$44$	−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	−0.839117	−	0.543951i	$-0.816928\pi$
$47$	−7.18356	+	2.97553i	−1.04783	+	0.434025i	−0.208713	+	0.977977i	$0.566928\pi$
$48$	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	−0.711969	−	0.702211i	$-0.752196\pi$
$53$	0.897741	−	9.11492i	0.123314	−	1.25203i	0.835283	−	0.549820i	$-0.185304\pi$
$54$	−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	0.999885	+	0.0151577i	$0.00482504\pi$
$59$	1.35904	+	4.48016i	0.176932	+	0.583267i	−0.822953	+	0.568110i	$0.807675\pi$
$60$	1.23669	+	5.00894i	0.159656	+	0.646652i
$61$	8.45098	+	6.93554i	1.08204	+	0.888005i	0.994137	−	0.108125i	$-0.0344846\pi$
$61$	8.45098	+	6.93554i	1.08204	+	0.888005i	0.0878993	+	0.996129i	$0.471985\pi$
$62$	−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	0.619673	−	0.784860i	$-0.287265\pi$
$67$	−0.239134	−	0.196252i	−0.0292149	−	0.0239760i	−0.648887	+	0.760884i	$0.724765\pi$
$68$	−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	−0.768521	−	0.639824i	$-0.779007\pi$
$71$	1.57021	−	7.89399i	0.186350	−	0.936844i	0.954871	−	0.297020i	$-0.0959929\pi$
$72$	2.57993	+	1.15930i	0.304047	+	0.136625i
$73$	−11.8459	+	2.35630i	−1.38646	+	0.275784i	−0.831237	−	0.555919i	$-0.812367\pi$
$73$	−11.8459	+	2.35630i	−1.38646	+	0.275784i	−0.555222	+	0.831702i	$0.687367\pi$
$74$	−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	−0.0734722	−	0.997297i	$-0.523408\pi$
$79$	−7.38272	−	3.05802i	−0.830621	−	0.344054i	−0.757148	+	0.653243i	$0.773408\pi$
$80$	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	0.992464	+	0.122537i	$0.0391031\pi$
$83$	4.94666	+	9.25455i	0.542967	+	1.01582i	−0.449497	+	0.893282i	$0.648397\pi$
$84$	−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	0.968570	−	0.248741i	$-0.0800169\pi$
$89$	3.47272	+	5.19729i	0.368107	+	0.550911i	−0.600463	+	0.799653i	$0.705017\pi$
$90$	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	0.999904	+	0.0138515i	$0.00440921\pi$
$97$	9.98433	+	9.98433i	1.01376	+	1.01376i	0.0138515	+	0.999904i	$0.495591\pi$
$98$	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	−0.284956	−	0.958540i	$-0.591979\pi$
$101$	−12.4645	−	6.66243i	−1.24027	−	0.662936i	−0.955311	+	0.295604i	$0.904479\pi$
$102$	−8.18367	+	0.187052i	−0.810305	+	0.0185209i
$103$	−16.2171	+	10.8359i	−1.59792	+	1.06769i	−0.645123	+	0.764079i	$0.723194\pi$
$103$	−16.2171	+	10.8359i	−1.59792	+	1.06769i	−0.952795	+	0.303616i	$0.901806\pi$
$104$	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	−0.498805	−	0.866714i	$-0.666228\pi$
$107$	2.62682	−	2.15577i	0.253944	−	0.208406i	0.752749	+	0.658308i	$0.228728\pi$
$108$	1.97933	−	0.286769i	0.190462	−	0.0275943i
$109$	1.26797	−	0.677746i	0.121450	−	0.0649163i	−0.409553	−	0.912286i	$-0.634315\pi$
$109$	1.26797	−	0.677746i	0.121450	−	0.0649163i	0.531003	+	0.847370i	$0.321815\pi$
$110$	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	−0.978143	−	0.207934i	$-0.933326\pi$
$113$	−1.48248	+	3.57902i	−0.139460	+	0.336686i	0.838683	+	0.544620i	$0.183326\pi$
$114$	−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	−0.385697	−	0.922626i	$-0.626039\pi$
$131$	6.80375	−	8.29039i	0.594446	−	0.724335i	0.980143	+	0.198291i	$0.0635390\pi$
$132$	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	−0.992112	−	0.125358i	$-0.959992\pi$
$137$	−1.44544	−	7.26672i	−0.123492	−	0.620838i	0.868619	−	0.495480i	$-0.165008\pi$
$138$	1.61916	+	2.30731i	0.137832	+	0.196412i
$139$	−19.1434	−	1.88546i	−1.62372	−	0.159923i	−0.755173	−	0.655526i	$-0.772447\pi$
$139$	−19.1434	−	1.88546i	−1.62372	−	0.159923i	−0.868549	+	0.495603i	$0.834947\pi$
$140$	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	−0.205030	−	0.978756i	$-0.565729\pi$
$149$	8.72671	−	7.16182i	0.714920	−	0.586719i	0.919950	+	0.392036i	$0.128229\pi$
$150$	−0.508864	−	2.28413i	−0.0415486	−	0.186499i
$151$	−9.67694	+	14.4826i	−0.787498	+	1.17857i	0.192837	+	0.981231i	$0.438231\pi$
$151$	−9.67694	+	14.4826i	−0.787498	+	1.17857i	−0.980335	+	0.197343i	$0.936769\pi$
$152$	−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	−0.996886	−	0.0788523i	$-0.974874\pi$
$157$	−0.432763	−	4.39391i	−0.0345382	−	0.350672i	0.962348	−	0.271820i	$-0.0876255\pi$
$158$	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	0.000204542	−	1.00000i	$-0.499935\pi$
$163$	2.49592	−	0.245827i	0.195495	−	0.0192546i	0.195291	+	0.980745i	$0.437435\pi$
$164$	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	0.509832	−	0.860274i	$-0.329708\pi$
$167$	−6.20377	−	9.28459i	−0.480062	−	0.718463i	−0.989894	+	0.141811i	$0.954708\pi$
$168$	−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	−0.938343	−	0.345705i	$-0.887640\pi$
$173$	−9.26587	−	17.3352i	−0.704471	−	1.31797i	0.233872	−	0.972267i	$-0.424860\pi$
$174$	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	0.826617	−	0.562764i	$-0.190262\pi$
$179$	16.0719	+	4.87536i	1.20127	+	0.364401i	0.374652	+	0.927165i	$0.377762\pi$
$180$	−4.65651	−	2.22167i	−0.347076	−	0.165593i
$181$	0.586988	−	5.95979i	0.0436305	−	0.442988i	−0.948408	−	0.317052i	$-0.897307\pi$
$181$	0.586988	−	5.95979i	0.0436305	−	0.442988i	0.992038	−	0.125935i	$-0.0401931\pi$
$182$	−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	$0.200632\pi$
$191$			16.2911i			1.17878i	−0.807848	+	0.589391i	$0.799368\pi$
$192$	7.50462	+	2.77140i	0.541599	+	0.200008i
$193$			12.6761i			0.912448i	0.889865	+	0.456224i	$0.150798\pi$
$193$			12.6761i			0.912448i	−0.889865	+	0.456224i	$0.849202\pi$
$194$	−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	0.845711	−	0.533641i	$-0.179177\pi$
$197$	−2.16075	−	7.12305i	−0.153947	−	0.507496i	−0.999658	+	0.0261451i	$0.991677\pi$
$198$	−0.196381	−	0.445059i	−0.0139562	−	0.0316289i
$199$	2.55848	−	12.8623i	0.181366	−	0.911788i	−0.777707	−	0.628627i	$-0.783617\pi$
$199$	2.55848	−	12.8623i	0.181366	−	0.911788i	0.959073	−	0.283160i	$-0.0913829\pi$
$200$	−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	0.747358	−	0.664422i	$-0.231322\pi$
$211$	−3.20002	−	5.98682i	−0.220299	−	0.412150i	−0.967656	+	0.252272i	$0.918822\pi$
$212$	−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	−0.666388	−	0.745605i	$-0.732160\pi$
$223$	1.18297	−	1.18297i	0.0792177	−	0.0792177i	0.745605	+	0.666388i	$0.232160\pi$
$224$	−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	−0.941769	−	0.336260i	$-0.890838\pi$
$227$	−1.26102	−	12.8034i	−0.0836969	−	0.849789i	0.858072	−	0.513529i	$-0.171662\pi$
$228$	2.97571	+	6.34706i	0.197071	+	0.420344i
$229$	21.3287	+	11.4004i	1.40944	+	0.753361i	0.988139	−	0.153560i	$-0.0490738\pi$
$229$	21.3287	+	11.4004i	1.40944	+	0.753361i	0.421300	+	0.906921i	$0.361574\pi$
$230$	−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	−0.109303	+	0.994008i	$0.534862\pi$
$233$	−15.0479	+	22.5207i	−0.985819	+	1.47538i	−0.876515	+	0.481374i	$0.840138\pi$
$234$	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	0.874573	−	0.484893i	$-0.161142\pi$
$239$	−1.34058	−	3.23644i	−0.0867148	−	0.209348i	−0.961288	+	0.275545i	$0.911142\pi$
$240$	7.93200	+	6.59991i	0.512009	+	0.426023i
$241$	−1.32866	+	3.20767i	−0.0855865	+	0.206624i	−0.960878	−	0.276971i	$-0.910669\pi$
$241$	−1.32866	+	3.20767i	−0.0855865	+	0.206624i	0.875292	+	0.483595i	$0.160669\pi$
$242$	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	−0.417911	−	0.908488i	$-0.637238\pi$
$251$	−4.12967	+	1.25272i	−0.260663	+	0.0790711i	0.157249	+	0.987559i	$0.449738\pi$
$252$	−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	−0.277908	−	0.960608i	$-0.589641\pi$
$263$	−14.6323	−	2.91056i	−0.902269	−	0.179473i	−0.624362	+	0.781135i	$0.714641\pi$
$264$	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	−0.999129	−	0.0417289i	$-0.986713\pi$
$269$	−2.38146	+	7.85063i	−0.145200	+	0.478661i	0.853929	+	0.520390i	$0.174213\pi$
$270$	−3.62152	+	0.440457i	−0.220399	+	0.0268054i
$271$	4.70866	−	11.3677i	0.286031	−	0.690539i	−0.713923	−	0.700225i	$-0.753083\pi$
$271$	4.70866	−	11.3677i	0.286031	−	0.690539i	0.999953	+	0.00968592i	$0.00308317\pi$
$272$	−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	−0.737116	−	0.675766i	$-0.763813\pi$
$277$	−3.63056	+	2.97953i	−0.218139	+	0.179022i	0.518977	+	0.854788i	$0.326313\pi$
$278$	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	−0.239523	−	0.970891i	$-0.576991\pi$
$281$	9.48457	−	6.33739i	0.565802	−	0.378057i	0.805325	+	0.592834i	$0.201991\pi$
$282$	0.251270	+	10.9932i	0.0149629	+	0.654638i
$283$	−21.3847	−	11.4304i	−1.27119	−	0.679466i	−0.308798	−	0.951128i	$-0.599927\pi$
$283$	−21.3847	−	11.4304i	−1.27119	−	0.679466i	−0.962393	+	0.271662i	$0.912427\pi$
$284$	−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	0.391541	+	0.920161i	$0.371942\pi$
$293$	−10.1175	+	18.9286i	−0.591073	+	1.10582i	−0.982614	+	0.185659i	$0.940558\pi$
$294$	−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	−0.169189	−	0.985584i	$-0.554115\pi$
$307$	−15.0233	−	4.55727i	−0.857425	−	0.260097i	−0.688236	+	0.725487i	$0.741615\pi$
$308$	−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	−0.887390	−	0.461020i	$-0.847484\pi$
$311$	−26.9961	+	5.36985i	−1.53081	+	0.304496i	−0.643416	+	0.765516i	$0.722484\pi$
$312$	−10.1761	−	0.301468i	−0.576109	−	0.0170673i
$313$	−0.279084	+	1.40305i	−0.0157747	+	0.0793050i	−0.987871	−	0.155278i	$-0.950373\pi$
$313$	−0.279084	+	1.40305i	−0.0157747	+	0.0793050i	0.972096	+	0.234583i	$0.0753726\pi$
$314$	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	0.900108	+	0.435667i	$0.143487\pi$
$317$	26.7603	+	21.9616i	1.50301	+	1.23349i	0.602898	+	0.797818i	$0.294013\pi$
$318$	−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	0.338956	+	0.940802i	$0.389926\pi$
$331$	−3.22075	+	32.7008i	−0.177028	+	1.79740i	−0.515985	+	0.856598i	$0.672574\pi$
$332$	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	0.615764	−	0.787930i	$-0.288847\pi$
$337$	29.5250	−	12.2296i	1.60833	−	0.666191i	0.992562	+	0.121740i	$0.0388473\pi$
$338$	−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	−0.176857	−	0.984236i	$-0.556593\pi$
$347$	13.7802	−	25.7810i	0.739762	−	1.38400i	0.916619	−	0.399761i	$-0.130907\pi$
$348$	−13.0641	+	0.597519i	−0.700311	+	0.0320304i
$349$	−4.76163	+	0.468980i	−0.254884	+	0.0251039i	−0.224652	−	0.974439i	$-0.572125\pi$
$349$	−4.76163	+	0.468980i	−0.254884	+	0.0251039i	−0.0302321	+	0.999543i	$0.509625\pi$
$350$	−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	−0.810741	−	0.585405i	$-0.800935\pi$
$353$	−26.2312	−	26.2312i	−1.39615	−	1.39615i	−0.585405	−	0.810741i	$-0.699065\pi$
$354$	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	−0.0330324	−	0.999454i	$-0.510516\pi$
$359$	16.6301	−	11.1119i	0.877702	−	0.586462i	0.910734	+	0.412993i	$0.135516\pi$
$360$	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	0.710185	−	0.704016i	$-0.248611\pi$
$367$	−5.55188	−	13.4034i	−0.289806	−	0.699653i	−0.999990	+	0.00436221i	$0.998611\pi$
$368$	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	−0.674741	−	0.738054i	$-0.735745\pi$
$373$	−28.5933	−	2.81619i	−1.48050	−	0.145817i	−0.805764	+	0.592237i	$0.798245\pi$
$374$	−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	−0.561394	−	0.827549i	$-0.689735\pi$
$379$	−11.0658	+	3.35679i	−0.568414	+	0.172427i	−0.00702035	+	0.999975i	$0.502235\pi$
$380$	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	−0.193444	−	0.981111i	$-0.561966\pi$
$389$	3.76297	−	1.14148i	0.190790	−	0.0578755i	0.384234	+	0.923236i	$0.374466\pi$
$390$	−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	0.671625	+	0.740892i	$0.265597\pi$
$397$	−5.94614	+	19.6018i	−0.298428	+	0.983786i	−0.970053	+	0.242894i	$0.921903\pi$
$398$	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	0.979549	−	0.201205i	$-0.0644857\pi$
$401$	2.89621	+	6.99208i	0.144630	+	0.349168i	−0.834919	+	0.550373i	$0.814486\pi$
$402$	−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	0.316806	−	0.948490i	$-0.397390\pi$
$409$	26.5807	−	17.7607i	1.31433	−	0.878209i	0.997527	+	0.0702813i	$0.0223897\pi$
$410$	−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	−0.148639	−	0.988891i	$-0.547489\pi$
$419$	−2.07764	+	0.204630i	−0.101499	+	0.00999681i	0.0471399	+	0.998888i	$0.484989\pi$
$420$	0.618821	+	13.5299i	0.0301954	+	0.660190i
$421$	−1.96636	+	3.67881i	−0.0958347	+	0.179294i	−0.925270	−	0.379308i	$-0.876162\pi$
$421$	−1.96636	+	3.67881i	−0.0958347	+	0.179294i	0.829436	+	0.558602i	$0.188662\pi$
$422$	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	−0.388637	−	0.921391i	$-0.627054\pi$
$431$	−0.247516	+	0.102525i	−0.0119224	+	0.00493843i	0.376714	+	0.926330i	$0.377054\pi$
$432$	2.84749	−	2.80923i	0.137000	−	0.135159i
$433$	25.2602	+	10.4631i	1.21393	+	0.502825i	0.895474	−	0.445114i	$-0.146837\pi$
$433$	25.2602	+	10.4631i	1.21393	+	0.502825i	0.318453	+	0.947939i	$0.396837\pi$
$434$	−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	0.164425	−	0.986390i	$-0.447423\pi$
$439$	14.5369	−	2.89157i	0.693809	−	0.138007i	0.529384	+	0.848382i	$0.322423\pi$
$440$	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	0.815180	+	0.579208i	$0.196638\pi$
$443$	9.66448	+	31.8595i	0.459173	+	1.51369i	−0.356006	+	0.934484i	$0.615862\pi$
$444$	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	$0.0519992\pi$
$449$			6.89233i			0.325269i	−0.986686	+	0.162635i	$0.948001\pi$
$450$	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	−0.189417	−	0.981897i	$-0.560660\pi$
$457$	0.242410	−	0.0482184i	0.0113395	−	0.00225556i	0.200757	+	0.979641i	$0.435660\pi$
$458$	−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	0.397039	−	0.917802i	$-0.370038\pi$
$461$	4.66482	+	1.41506i	0.217262	+	0.0659057i	−0.179777	+	0.983707i	$0.557538\pi$
$462$	−0.787367	+	1.00541i	−0.0366316	+	0.0467758i
$463$	0.407658	+	0.168857i	0.0189455	+	0.00784747i	0.392136	−	0.919907i	$-0.371736\pi$
$463$	0.407658	+	0.168857i	0.0189455	+	0.00784747i	−0.373191	+	0.927755i	$0.621736\pi$
$464$	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	0.942438	+	0.334382i	$0.108527\pi$
$467$	15.0596	+	28.1745i	0.696876	+	1.30376i	−0.245562	+	0.969381i	$0.578973\pi$
$468$	−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	−0.171257	+	0.985226i	$0.554783\pi$
$479$	−25.3109	+	25.3109i	−1.15648	+	1.15648i	−0.985226	+	0.171257i	$0.945217\pi$
$480$	−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	0.266566	−	0.963817i	$-0.414111\pi$
$487$	27.7843	−	18.5649i	1.25903	−	0.841255i	0.992461	+	0.122562i	$0.0391110\pi$
$488$	−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	−0.601413	−	0.798938i	$-0.705395\pi$
$491$	1.43686	−	1.17920i	0.0648445	−	0.0532165i	0.666257	+	0.745722i	$0.267895\pi$
$492$	−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	−0.993765	−	0.111497i	$-0.964436\pi$
$499$	−2.35748	+	7.77157i	−0.105535	+	0.347903i	0.888230	+	0.459400i	$0.151936\pi$
$500$	−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	0.941036	−	0.338307i	$-0.109854\pi$
$503$	−1.29704	−	6.52067i	−0.0578322	−	0.290742i	−0.998868	+	0.0475644i	$0.984854\pi$
$504$	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	−0.888471	−	0.458933i	$-0.848232\pi$
$509$	−5.97921	+	7.28569i	−0.265024	+	0.322932i	0.623447	+	0.781866i	$0.285732\pi$
$510$	−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	−0.994113	−	0.108352i	$-0.965443\pi$
$521$	−2.67369	−	13.4416i	−0.117137	−	0.588886i	0.876976	−	0.480534i	$-0.159557\pi$
$522$	−7.56952	+	5.31193i	−0.331309	+	0.232497i
$523$	−5.58449	−	0.550024i	−0.244193	−	0.0240509i	−0.0248197	−	0.999692i	$-0.507901\pi$
$523$	−5.58449	−	0.550024i	−0.244193	−	0.0240509i	−0.219373	+	0.975641i	$0.570401\pi$
$524$	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	0.997445	−	0.0714403i	$-0.0227595\pi$
$541$	0.121607	+	1.23470i	0.00522831	+	0.0530840i	−0.992217	+	0.124524i	$0.960260\pi$
$542$	−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	0.804704	−	0.593677i	$-0.202324\pi$
$547$	39.9881	−	3.93848i	1.70977	−	0.168397i	0.905062	+	0.425279i	$0.139824\pi$
$548$	−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	0.937453	−	0.348111i	$-0.113177\pi$
$557$	3.00176	+	5.61591i	0.127189	+	0.237954i	−0.810265	+	0.586064i	$0.800677\pi$
$558$	−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	0.642989	−	0.765876i	$-0.277694\pi$
$563$	17.8459	+	5.41350i	0.752116	+	0.228152i	0.109128	+	0.994028i	$0.465194\pi$
$564$	−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	−0.983060	−	0.183285i	$-0.941327\pi$
$569$	−0.111898	+	0.562550i	−0.00469101	+	0.0235833i	0.978369	+	0.206868i	$0.0663270\pi$
$570$	−5.16203	−	11.6987i	−0.216214	−	0.490005i
$571$	−8.20064	−	27.0339i	−0.343186	−	1.13133i	−0.943446	−	0.331528i	$-0.892436\pi$
$571$	−8.20064	−	27.0339i	−0.343186	−	1.13133i	0.600259	−	0.799805i	$-0.295064\pi$
$572$	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	$-0.715568\pi$
$577$		−	37.4395i		−	1.55863i	0.626635	−	0.779313i	$-0.284432\pi$
$578$	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	−0.406669	−	0.913575i	$-0.633310\pi$
$587$	4.12885	−	41.9209i	0.170416	−	1.73026i	0.577085	−	0.816684i	$-0.304190\pi$
$588$	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	0.0909415	−	0.995856i	$-0.471012\pi$
$593$	20.9283	−	8.66880i	0.859424	−	0.355985i	0.768482	+	0.639871i	$0.221012\pi$
$594$	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	0.559586	−	0.828772i	$-0.310960\pi$
$599$	0.196905	+	0.131568i	0.00804532	+	0.00537571i	−0.551541	+	0.834148i	$0.685960\pi$
$600$	−3.52838	−	3.07496i	−0.144046	−	0.125535i
$601$	6.19674	+	9.27408i	0.252770	+	0.378298i	0.936055	−	0.351855i	$-0.114449\pi$
$601$	6.19674	+	9.27408i	0.252770	+	0.378298i	−0.683284	+	0.730153i	$0.739449\pi$
$602$	−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	−0.221644	+	0.975128i	$0.571142\pi$
$607$	−29.4853	+	29.4853i	−1.19677	+	1.19677i	−0.975128	+	0.221644i	$0.928858\pi$
$608$	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	0.248086	−	0.968738i	$-0.420198\pi$
$613$	−10.3878	−	5.55241i	−0.419561	−	0.224260i	−0.667647	+	0.744478i	$0.732698\pi$
$614$	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	0.248828	+	0.968548i	$0.419955\pi$
$617$	−18.4114	+	27.5546i	−0.741216	+	1.10931i	−0.990044	+	0.140760i	$0.955045\pi$
$618$	5.99796	+	26.9230i	0.241273	+	1.08300i
$619$	−18.8257	+	15.4499i	−0.756670	+	0.620983i	−0.931553	−	0.363606i	$-0.881545\pi$
$619$	−18.8257	+	15.4499i	−0.756670	+	0.620983i	0.174883	+	0.984589i	$0.444045\pi$
$620$	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	0.983486	−	0.180984i	$-0.0579281\pi$
$631$	0.140770	+	0.707700i	0.00560398	+	0.0281731i	−0.977882	+	0.209157i	$0.932928\pi$
$632$	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	−0.848558	−	0.529102i	$-0.822529\pi$
$643$	−4.16057	+	5.06967i	−0.164077	+	0.199928i	0.684481	+	0.729031i	$0.260029\pi$
$644$	−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	−0.0235145	−	0.999723i	$-0.507486\pi$
$647$	−10.8820	−	2.16457i	−0.427817	−	0.0850980i	−0.404302	+	0.914625i	$0.632486\pi$
$648$	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	−0.970715	−	0.240235i	$-0.922775\pi$
$653$	−0.769872	+	2.53793i	−0.0301274	+	0.0993168i	0.940587	+	0.339552i	$0.110275\pi$
$654$	−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	−0.539470	−	0.842005i	$-0.681375\pi$
$659$	−3.57036	+	1.90840i	−0.139081	+	0.0743406i	0.400388	+	0.916346i	$0.368875\pi$
$660$	−0.254465	−	1.75637i	−0.00990505	−	0.0683666i
$661$	−10.8360	+	8.89286i	−0.421471	+	0.345892i	−0.821100	−	0.570785i	$-0.806639\pi$
$661$	−10.8360	+	8.89286i	−0.421471	+	0.345892i	0.399629	+	0.916677i	$0.369139\pi$
$662$	−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	−0.280264	−	0.959923i	$-0.590422\pi$
$673$	17.6319	−	17.6319i	0.679659	−	0.679659i	0.959923	+	0.280264i	$0.0904220\pi$
$674$	−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	−0.919872	−	0.392218i	$-0.871708\pi$
$677$	−2.15182	+	4.02577i	−0.0827012	+	0.154723i	0.837171	+	0.546941i	$0.184208\pi$
$678$	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	0.742876	−	0.669429i	$-0.233461\pi$
$683$	−1.53192	−	1.86665i	−0.0586173	−	0.0714254i	−0.801494	+	0.598003i	$0.795961\pi$
$684$	−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	0.963816	−	0.266568i	$-0.0858896\pi$
$691$	42.5086	+	12.8948i	1.61710	+	0.490543i	0.653287	+	0.757111i	$0.273390\pi$
$692$	−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	0.726302	−	0.687376i	$-0.241237\pi$
$701$	5.13187	+	4.21162i	0.193828	+	0.159071i	−0.532474	+	0.846447i	$0.678737\pi$
$702$	−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	−0.942767	−	0.333452i	$-0.891787\pi$
$709$	−9.16345	−	30.2079i	−0.344141	−	1.13448i	0.598627	−	0.801028i	$-0.295713\pi$
$710$	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	0.845296	−	0.534299i	$-0.179424\pi$
$719$	28.5626	+	11.8310i	1.06520	+	0.441222i	0.219908	+	0.975521i	$0.429424\pi$
$720$	−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	0.993080	+	0.117442i	$0.0374694\pi$
$727$	39.9487	+	26.6929i	1.48162	+	0.989985i	0.488537	+	0.872543i	$0.337531\pi$
$728$	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	0.408714	−	0.912662i	$-0.365977\pi$
$733$	26.7390	−	2.63356i	0.987627	−	0.0972728i	0.578913	+	0.815390i	$0.303477\pi$
$734$	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	−0.947248	−	0.320502i	$-0.896148\pi$
$739$	−2.19455	−	22.2817i	−0.0807279	−	0.819645i	0.866520	−	0.499143i	$-0.166352\pi$
$740$	−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	−0.690549	−	0.723286i	$-0.742631\pi$
$743$	−7.81164	+	5.21957i	−0.286581	+	0.191488i	0.403967	+	0.914773i	$0.367631\pi$
$744$	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	0.935551	+	0.353192i	$0.114904\pi$
$751$	14.3533	+	34.6520i	0.523761	+	1.26447i	−0.411790	+	0.911279i	$0.635096\pi$
$752$	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	−0.223717	−	0.974654i	$-0.571819\pi$
$757$	−17.4238	−	1.71610i	−0.633280	−	0.0623727i	−0.409564	+	0.912282i	$0.634319\pi$
$758$	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	0.251038	−	0.967977i	$-0.419228\pi$
$761$	3.10452	+	0.617528i	0.112539	+	0.0223854i	−0.138500	+	0.990363i	$0.544228\pi$
$762$	−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	−0.930222	−	0.366996i	$-0.880386\pi$
$773$	−41.6982	+	12.6490i	−1.49978	+	0.454954i	−0.569559	+	0.821950i	$0.692886\pi$
$774$	−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	−0.724230	−	0.689559i	$-0.757804\pi$
$787$	−15.5204	+	8.29583i	−0.553243	+	0.295714i	0.170987	+	0.985273i	$0.445304\pi$
$788$	−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	−0.992934	−	0.118670i	$-0.962137\pi$
$797$	−1.19221	−	12.1047i	−0.0422304	−	0.428772i	0.950703	−	0.310102i	$-0.100363\pi$
$798$	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	0.352772	−	0.935709i	$-0.385239\pi$
$809$	−10.7148	−	7.15938i	−0.376711	−	0.251710i	−0.729483	+	0.683999i	$0.760239\pi$
$810$	1.95699	−	3.07890i	0.0687617	−	0.108181i
$811$	−4.45735	−	5.43130i	−0.156519	−	0.190719i	0.688847	−	0.724907i	$-0.258117\pi$
$811$	−4.45735	−	5.43130i	−0.156519	−	0.190719i	−0.845365	+	0.534188i	$0.820617\pi$
$812$	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	0.952677	+	0.303983i	$0.0983167\pi$
$821$	−1.17474	+	11.9274i	−0.0409988	+	0.416268i	−0.993676	+	0.112284i	$0.964183\pi$
$822$	−10.3207	−	1.80880i	−0.359977	−	0.0630891i
$823$	−0.0239695	+	0.00476782i	−0.000835523	+	0.000166196i	−0.195508	−	0.980702i	$-0.562636\pi$
$823$	−0.0239695	+	0.00476782i	−0.000835523	+	0.000166196i	0.194673	+	0.980868i	$0.437636\pi$
$824$	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	0.958963	+	0.283530i	$0.0915056\pi$
$827$	9.17757	+	30.2544i	0.319135	+	1.05205i	−0.639828	+	0.768518i	$0.720994\pi$
$828$	3.87011	−	0.955515i	0.134496	−	0.0332064i
$829$	−26.9191	−	22.0919i	−0.934939	−	0.767285i	0.0377763	−	0.999286i	$-0.487973\pi$
$829$	−26.9191	−	22.0919i	−0.934939	−	0.767285i	−0.972715	+	0.232002i	$0.925473\pi$
$830$	−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	−0.888077	−	0.459694i	$-0.847959\pi$
$839$	3.13744	−	15.7730i	0.108316	−	0.544543i	0.996394	−	0.0848492i	$-0.0270408\pi$
$840$	−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	−0.993683	−	0.112226i	$-0.964202\pi$
$853$	−26.5745	−	32.3811i	−0.909894	−	1.10871i	0.0837884	−	0.996484i	$-0.473298\pi$
$854$	−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	−0.879469	−	0.475956i	$-0.842102\pi$
$857$	−28.7663	−	43.0518i	−0.982637	−	1.47062i	−0.103168	−	0.994664i	$-0.532898\pi$
$858$	1.26608	+	1.20949i	0.0432232	+	0.0412915i
$859$	−4.59798	+	8.60221i	−0.156881	+	0.293504i	−0.948066	−	0.318073i	$-0.896964\pi$
$859$	−4.59798	+	8.60221i	−0.156881	+	0.293504i	0.791185	+	0.611576i	$0.209464\pi$
$860$	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	−0.792215	−	0.610243i	$-0.791072\pi$
$863$	−5.34576	+	5.34576i	−0.181972	+	0.181972i	0.610243	+	0.792215i	$0.291072\pi$
$864$	−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	0.570229	−	0.821486i	$-0.306854\pi$
$877$	46.4964	−	24.8528i	1.57007	−	0.839221i	0.999843	−	0.0177353i	$-0.00564561\pi$
$878$	−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	−0.201833	−	0.979420i	$-0.564690\pi$
$881$	18.8015	−	45.3909i	0.633439	−	1.52926i	0.835272	−	0.549837i	$-0.185310\pi$
$882$	−0.0185499	−	0.152521i	−0.000624608	−	0.00513565i
$883$	−16.4335	+	54.1740i	−0.553032	+	1.82310i	0.0147070	+	0.999892i	$0.495318\pi$
$883$	−16.4335	+	54.1740i	−0.553032	+	1.82310i	−0.567739	+	0.823209i	$0.692182\pi$
$884$	−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	−0.999582	−	0.0289228i	$-0.990792\pi$
$887$	−2.59575	−	13.0497i	−0.0871569	−	0.438167i	0.912425	−	0.409245i	$-0.134208\pi$
$888$	−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	−0.552528	−	0.833495i	$-0.686337\pi$
$907$	−37.8577	−	3.72866i	−1.25705	−	0.123808i	−0.704518	+	0.709687i	$0.748837\pi$
$908$	−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	−0.764693	−	0.644395i	$-0.777109\pi$
$911$	6.99284	−	16.8822i	0.231683	−	0.559332i	0.996376	+	0.0850630i	$0.0271092\pi$
$912$	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	−0.856361	−	0.516377i	$-0.827280\pi$
$919$	−1.56353	+	2.33998i	−0.0515760	+	0.0771890i	0.804785	+	0.593566i	$0.202280\pi$
$920$	−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	−0.0387017	−	0.999251i	$-0.512322\pi$
$929$	29.2771	−	29.2771i	0.960549	−	0.960549i	0.999251	+	0.0387017i	$0.0123222\pi$
$930$	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	0.928227	−	0.372013i	$-0.121332\pi$
$937$	28.7661	+	19.2209i	0.939749	+	0.627920i	0.0115217	+	0.999934i	$0.496332\pi$
$938$	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	−0.773228	−	0.634128i	$-0.781359\pi$
$941$	−26.7156	−	49.9814i	−0.870904	−	1.62935i	−0.0976759	−	0.995218i	$-0.531141\pi$
$942$	−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	0.774778	−	0.632233i	$-0.217861\pi$
$947$	32.8577	+	9.96729i	1.06773	+	0.323893i	0.292955	+	0.956126i	$0.405361\pi$
$948$	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	0.841824	+	0.539752i	$0.181482\pi$
$953$	−4.39827	+	22.1116i	−0.142474	+	0.716265i	−0.984298	+	0.176514i	$0.943518\pi$
$954$	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	−0.953548	−	0.301241i	$-0.902599\pi$
$967$	1.32769	−	6.67474i	0.0426956	−	0.214645i	0.996243	+	0.0865963i	$0.0275990\pi$
$968$	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	−0.810472	−	0.585777i	$-0.800789\pi$
$971$	3.07578	−	31.2289i	0.0987064	−	1.00218i	0.909179	−	0.416406i	$-0.136711\pi$
$972$	−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	−0.755979	−	0.654596i	$-0.772839\pi$
$977$	−25.8704	+	10.7159i	−0.827667	+	0.342831i	−0.0716881	+	0.997427i	$0.522839\pi$
$978$	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	0.998417	+	0.0562479i	$0.0179137\pi$
$983$	44.9117	+	30.0090i	1.43246	+	0.957140i	0.434044	+	0.900892i	$0.357086\pi$
$984$	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	−0.227744	−	0.973721i	$-0.573135\pi$
$991$	23.4835	−	23.4835i	0.745977	−	0.745977i	0.973721	+	0.227744i	$0.0731350\pi$
$992$	−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	0.995709	+	0.0925421i	$0.0294993\pi$
$997$	51.3364	+	27.4399i	1.62584	+	0.869030i	0.630132	+	0.776488i	$0.283001\pi$
$998$	−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.85.4	✓	512
128.125	even	32	inner	384.2.v.a.253.4	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.85.4	✓	512	1.1	even	1	trivial
384.2.v.a.253.4	yes	512	128.125	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.34358 + 0.441342i) q^{2} +(-0.634393 + 0.773010i) q^{3} +(1.61043 - 1.18596i) q^{4} +(2.46859 - 0.748840i) q^{5} +(0.511199 - 1.31859i) q^{6} +(2.57470 + 0.512139i) q^{7} +(-1.64034 + 2.30419i) q^{8} +(-0.195090 - 0.980785i) q^{9} +O(q^{10})\)	\(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

Related objects

Downloads

Learn more